LMFDB - Embedded newform 32.8.g.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,8,Mod(5,32)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.99632081549$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.18285 + 6.60873i) q^{2} +(-32.0943 + 77.4825i) q^{3} +(40.6495 - 121.374i) q^{4} +(-324.954 + 134.601i) q^{5} +(-217.343 - 923.612i) q^{6} +(-942.234 + 942.234i) q^{7} +(428.849 + 1383.20i) q^{8} +(-3427.05 - 3427.05i) q^{9} +O(q^{10})$	\(q+(-9.18285 + 6.60873i) q^{2} +(-32.0943 + 77.4825i) q^{3} +(40.6495 - 121.374i) q^{4} +(-324.954 + 134.601i) q^{5} +(-217.343 - 923.612i) q^{6} +(-942.234 + 942.234i) q^{7} +(428.849 + 1383.20i) q^{8} +(-3427.05 - 3427.05i) q^{9} +(2094.47 - 3383.55i) q^{10} +(2181.63 + 5266.92i) q^{11} +(8099.73 + 7045.03i) q^{12} +(6218.92 + 2575.96i) q^{13} +(2425.43 - 14879.4i) q^{14} -29498.2i q^{15} +(-13079.2 - 9867.57i) q^{16} +1379.38i q^{17} +(54118.5 + 8821.65i) q^{18} +(13029.4 + 5396.95i) q^{19} +(3127.76 + 44912.4i) q^{20} +(-42766.3 - 103247. i) q^{21} +(-54841.2 - 33947.5i) q^{22} +(54647.0 + 54647.0i) q^{23} +(-120937. - 11164.5i) q^{24} +(32235.4 - 32235.4i) q^{25} +(-74131.3 + 17444.5i) q^{26} +(206071. - 85357.2i) q^{27} +(76061.3 + 152664. i) q^{28} +(-20553.5 + 49620.7i) q^{29} +(194945. + 270877. i) q^{30} -164013. q^{31} +(185317. + 4175.30i) q^{32} -478112. q^{33} +(-9115.91 - 12666.6i) q^{34} +(179358. - 433008. i) q^{35} +(-555262. + 276646. i) q^{36} +(-204108. + 84544.3i) q^{37} +(-155314. + 36548.3i) q^{38} +(-399184. + 399184. i) q^{39} +(-325536. - 391754. i) q^{40} +(1228.49 + 1228.49i) q^{41} +(1.07505e6 + 665470. i) q^{42} +(-234010. - 564951. i) q^{43} +(727949. - 50695.3i) q^{44} +(1.57492e6 + 652352. i) q^{45} +(-862963. - 140668. i) q^{46} -3069.50i q^{47} +(1.18433e6 - 696719. i) q^{48} -952066. i q^{49} +(-82977.9 + 509048. i) q^{50} +(-106877. - 44270.1i) q^{51} +(565451. - 650104. i) q^{52} +(287200. + 693362. i) q^{53} +(-1.32821e6 + 2.14569e6i) q^{54} +(-1.41786e6 - 1.41786e6i) q^{55} +(-1.70737e6 - 899222. i) q^{56} +(-836338. + 836338. i) q^{57} +(-139189. - 591492. i) q^{58} +(1.90605e6 - 789513. i) q^{59} +(-3.58031e6 - 1.19909e6i) q^{60} +(6522.34 - 15746.3i) q^{61} +(1.50611e6 - 1.08392e6i) q^{62} +6.45816e6 q^{63} +(-1.72933e6 + 1.18637e6i) q^{64} -2.36759e6 q^{65} +(4.39043e6 - 3.15971e6i) q^{66} +(608801. - 1.46978e6i) q^{67} +(167420. + 56070.9i) q^{68} +(-5.98805e6 + 2.48033e6i) q^{69} +(1.21462e6 + 5.16158e6i) q^{70} +(-2.43203e6 + 2.43203e6i) q^{71} +(3.27061e6 - 6.20998e6i) q^{72} +(3.49340e6 + 3.49340e6i) q^{73} +(1.31556e6 - 2.12525e6i) q^{74} +(1.46311e6 + 3.53225e6i) q^{75} +(1.18469e6 - 1.36204e6i) q^{76} +(-7.01827e6 - 2.90706e6i) q^{77} +(1.02755e6 - 6.30374e6i) q^{78} +2.62603e6i q^{79} +(5.57834e6 + 1.44604e6i) q^{80} +8.10688e6i q^{81} +(-19399.9 - 3162.30i) q^{82} +(6.59811e6 + 2.73303e6i) q^{83} +(-1.42699e7 + 993776. i) q^{84} +(-185665. - 448234. i) q^{85} +(5.88249e6 + 3.64135e6i) q^{86} +(-3.18508e6 - 3.18508e6i) q^{87} +(-6.34961e6 + 5.27634e6i) q^{88} +(1.31226e6 - 1.31226e6i) q^{89} +(-1.87734e7 + 4.41774e6i) q^{90} +(-8.28684e6 + 3.43252e6i) q^{91} +(8.85410e6 - 4.41135e6i) q^{92} +(5.26389e6 - 1.27081e7i) q^{93} +(20285.5 + 28186.7i) q^{94} -4.96039e6 q^{95} +(-6.27112e6 + 1.42248e7i) q^{96} -8.71371e6 q^{97} +(6.29194e6 + 8.74268e6i) q^{98} +(1.05734e7 - 2.55265e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−9.18285	+	6.60873i	−0.811657	+	0.584134i
$2$	−9.18285	+	6.60873i	−0.811657	+	0.584134i
$3$	−32.0943	+	77.4825i	−0.686283	+	1.65683i	0.0658552	+	0.997829i	$0.479022\pi$
$3$	−32.0943	+	77.4825i	−0.686283	+	1.65683i	−0.752138	+	0.659005i	$0.770978\pi$
$4$	40.6495	−	121.374i	0.317574	−	0.948233i
$5$	−324.954	+	134.601i	−1.16259	+	0.481562i	−0.878737	−	0.477306i	$-0.841613\pi$
$5$	−324.954	+	134.601i	−1.16259	+	0.481562i	−0.283855	+	0.958867i	$0.591613\pi$
$6$	−217.343	−	923.612i	−0.410787	−	1.74566i
$7$	−942.234	+	942.234i	−1.03828	+	1.03828i	−0.0390451	+	0.999237i	$0.512432\pi$
$7$	−942.234	+	942.234i	−1.03828	+	1.03828i	−0.999237	+	0.0390451i	$0.987568\pi$
$8$	428.849	+	1383.20i	0.296135	+	0.955146i
$9$	−3427.05	−	3427.05i	−1.56701	−	1.56701i
$10$	2094.47	−	3383.55i	0.662330	−	1.06997i
$11$	2181.63	+	5266.92i	0.494204	+	1.19311i	0.952561	+	0.304347i	$0.0984381\pi$
$11$	2181.63	+	5266.92i	0.494204	+	1.19311i	−0.458357	+	0.888768i	$0.651562\pi$
$12$	8099.73	+	7045.03i	1.35312	+	1.17692i
$13$	6218.92	+	2575.96i	0.785079	+	0.325191i	0.738963	−	0.673746i	$-0.235316\pi$
$13$	6218.92	+	2575.96i	0.785079	+	0.325191i	0.0461160	+	0.998936i	$0.485316\pi$
$14$	2425.43	−	14879.4i	0.236233	−	1.44923i
$15$		−	29498.2i		−	2.25671i
$16$	−13079.2	−	9867.57i	−0.798293	−	0.602269i
$17$			1379.38i			0.0680944i	0.999420	+	0.0340472i	$0.0108397\pi$
$17$			1379.38i			0.0680944i	−0.999420	+	0.0340472i	$0.989160\pi$
$18$	54118.5	+	8821.65i	2.18722	+	0.356530i
$19$	13029.4	+	5396.95i	0.435799	+	0.180514i	0.589787	−	0.807559i	$-0.299212\pi$
$19$	13029.4	+	5396.95i	0.435799	+	0.180514i	−0.153988	+	0.988073i	$0.549212\pi$
$20$	3127.76	+	44912.4i	0.0874236	+	1.25534i
$21$	−42766.3	−	103247.i	−1.00771	−	2.43282i
$22$	−54841.2	−	33947.5i	−1.09806	−	0.679718i
$23$	54647.0	+	54647.0i	0.936525	+	0.936525i	0.998102	−	0.0615777i	$-0.0196132\pi$
$23$	54647.0	+	54647.0i	0.936525	+	0.936525i	−0.0615777	+	0.998102i	$0.519613\pi$
$24$	−120937.	−	11164.5i	−1.78575	−	0.164855i
$25$	32235.4	−	32235.4i	0.412613	−	0.412613i
$26$	−74131.3	+	17444.5i	−0.827170	+	0.194649i
$27$	206071.	−	85357.2i	2.01485	−	0.834579i
$28$	76061.3	+	152664.i	0.654803	+	1.31427i
$29$	−20553.5	+	49620.7i	−0.156493	+	0.377807i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$	−20553.5	+	49620.7i	−0.156493	+	0.377807i	0.826115	+	0.563502i	$0.190546\pi$
$30$	194945.	+	270877.i	1.31822	+	1.83168i
$31$	−164013.			−0.988810			−0.494405	−	0.869232i	$-0.664614\pi$
$31$	−164013.			−0.988810			−0.494405	+	0.869232i	$0.664614\pi$
$32$	185317.	+	4175.30i	0.999746	+	0.0225249i
$33$	−478112.			−2.31596
$34$	−9115.91	−	12666.6i	−0.0397763	−	0.0552693i
$35$	179358.	−	433008.i	0.707103	−	1.70710i
$36$	−555262.	+	276646.i	−1.98353	+	0.988249i
$37$	−204108.	+	84544.3i	−0.662452	+	0.274396i	−0.688470	−	0.725265i	$-0.741717\pi$
$37$	−204108.	+	84544.3i	−0.662452	+	0.274396i	0.0260181	+	0.999661i	$0.491717\pi$
$38$	−155314.	+	36548.3i	−0.459164	+	0.108050i
$39$	−399184.	+	399184.i	−1.07757	+	1.07757i
$40$	−325536.	−	391754.i	−0.804246	−	0.967839i
$41$	1228.49	+	1228.49i	0.00278375	+	0.00278375i	0.708497	−	0.705714i	$-0.249373\pi$
$41$	1228.49	+	1228.49i	0.00278375	+	0.00278375i	−0.705714	+	0.708497i	$0.749373\pi$
$42$	1.07505e6	+	665470.i	2.23900	+	1.38598i
$43$	−234010.	−	564951.i	−0.448844	−	1.08361i	−0.972756	−	0.231833i	$-0.925528\pi$
$43$	−234010.	−	564951.i	−0.448844	−	1.08361i	0.523912	−	0.851773i	$-0.324472\pi$
$44$	727949.	−	50695.3i	1.28830	−	0.0897188i
$45$	1.57492e6	+	652352.i	2.57640	+	1.06718i
$46$	−862963.	−	140668.i	−1.30719	−	0.213080i
$47$		−	3069.50i		−	0.00431245i	−0.999998	−	0.00215623i	$-0.999314\pi$
$47$		−	3069.50i		−	0.00431245i	0.999998	−	0.00215623i	$-0.000686349\pi$
$48$	1.18433e6	−	696719.i	1.54571	−	0.909313i
$49$		−	952066.i		−	1.15606i
$50$	−82977.9	+	509048.i	−0.0938788	+	0.575922i
$51$	−106877.	−	44270.1i	−0.112821	−	0.0467320i
$52$	565451.	−	650104.i	0.557677	−	0.641167i
$53$	287200.	+	693362.i	0.264984	+	0.639727i	0.999233	−	0.0391526i	$-0.0124659\pi$
$53$	287200.	+	693362.i	0.264984	+	0.639727i	−0.734250	+	0.678880i	$0.762466\pi$
$54$	−1.32821e6	+	2.14569e6i	−1.14786	+	1.85434i
$55$	−1.41786e6	−	1.41786e6i	−1.14912	−	1.14912i
$56$	−1.70737e6	−	899222.i	−1.29918	−	0.684240i
$57$	−836338.	+	836338.i	−0.598163	+	0.598163i
$58$	−139189.	−	591492.i	−0.0936715	−	0.398062i
$59$	1.90605e6	−	789513.i	1.20824	−	0.500469i	0.314587	−	0.949229i	$-0.398134\pi$
$59$	1.90605e6	−	789513.i	1.20824	−	0.500469i	0.893652	+	0.448760i	$0.148134\pi$
$60$	−3.58031e6	−	1.19909e6i	−2.13989	−	0.716673i
$61$	6522.34	−	15746.3i	0.00367916	−	0.00888229i	−0.922029	−	0.387120i	$-0.873470\pi$
$61$	6522.34	−	15746.3i	0.00367916	−	0.00888229i	0.925708	+	0.378238i	$0.123470\pi$
$62$	1.50611e6	−	1.08392e6i	0.802574	−	0.577598i
$63$	6.45816e6			3.25400
$64$	−1.72933e6	+	1.18637e6i	−0.824609	+	0.565704i
$65$	−2.36759e6			−1.06933
$66$	4.39043e6	−	3.15971e6i	1.87976	−	1.35283i
$67$	608801.	−	1.46978e6i	0.247294	−	0.597021i	−0.750678	−	0.660668i	$-0.770273\pi$
$67$	608801.	−	1.46978e6i	0.247294	−	0.597021i	0.997972	+	0.0636471i	$0.0202732\pi$
$68$	167420.	+	56070.9i	0.0645694	+	0.0216250i
$69$	−5.98805e6	+	2.48033e6i	−2.19439	+	0.908945i
$70$	1.21462e6	+	5.16158e6i	0.423249	+	1.79862i
$71$	−2.43203e6	+	2.43203e6i	−0.806428	+	0.806428i	−0.984091	−	0.177663i	$-0.943146\pi$
$71$	−2.43203e6	+	2.43203e6i	−0.806428	+	0.806428i	0.177663	+	0.984091i	$0.443146\pi$
$72$	3.27061e6	−	6.20998e6i	1.03268	−	1.96077i
$73$	3.49340e6	+	3.49340e6i	1.05104	+	1.05104i	0.998626	+	0.0524113i	$0.0166907\pi$
$73$	3.49340e6	+	3.49340e6i	1.05104	+	1.05104i	0.0524113	+	0.998626i	$0.483309\pi$
$74$	1.31556e6	−	2.12525e6i	0.377399	−	0.609677i
$75$	1.46311e6	+	3.53225e6i	0.400462	+	0.966801i
$76$	1.18469e6	−	1.36204e6i	0.309568	−	0.355913i
$77$	−7.01827e6	−	2.90706e6i	−1.75191	−	0.725667i
$78$	1.02755e6	−	6.30374e6i	0.245172	−	1.50407i
$79$			2.62603e6i			0.599245i	0.954058	+	0.299622i	$0.0968606\pi$
$79$			2.62603e6i			0.599245i	−0.954058	+	0.299622i	$0.903139\pi$
$80$	5.57834e6	+	1.44604e6i	1.21812	+	0.315766i
$81$			8.10688e6i			1.69495i
$82$	−19399.9	−	3162.30i	−0.00388553	−	0.000633365i
$83$	6.59811e6	+	2.73303e6i	1.26662	+	0.524651i	0.911935	−	0.410335i	$-0.134588\pi$
$83$	6.59811e6	+	2.73303e6i	1.26662	+	0.524651i	0.354685	+	0.934986i	$0.384588\pi$
$84$	−1.42699e7	+	993776.i	−2.62690	+	0.182941i
$85$	−185665.	−	448234.i	−0.0327916	−	0.0791660i
$86$	5.88249e6	+	3.64135e6i	0.997278	+	0.617331i
$87$	−3.18508e6	−	3.18508e6i	−0.518565	−	0.518565i
$88$	−6.34961e6	+	5.27634e6i	−0.993248	+	0.825360i
$89$	1.31226e6	−	1.31226e6i	0.197313	−	0.197313i	−0.601534	−	0.798847i	$-0.705444\pi$
$89$	1.31226e6	−	1.31226e6i	0.197313	−	0.197313i	0.798847	+	0.601534i	$0.205444\pi$
$90$	−1.87734e7	+	4.41774e6i	−2.71453	+	0.638781i
$91$	−8.28684e6	+	3.43252e6i	−1.15277	+	0.477495i
$92$	8.85410e6	−	4.41135e6i	1.18546	−	0.590628i
$93$	5.26389e6	−	1.27081e7i	0.678604	−	1.63829i
$94$	20285.5	+	28186.7i	0.00251905	+	0.00350023i
$95$	−4.96039e6			−0.593585
$96$	−6.27112e6	+	1.42248e7i	−0.723429	+	1.64096i
$97$	−8.71371e6			−0.969398			−0.484699	−	0.874681i	$-0.661071\pi$
$97$	−8.71371e6			−0.969398			−0.484699	+	0.874681i	$0.661071\pi$
$98$	6.29194e6	+	8.74268e6i	0.675295	+	0.938325i
$99$	1.05734e7	−	2.55265e7i	1.09520	−	2.64404i
$100$	−2.60218e6	−	5.22289e6i	−0.260218	−	0.522289i
$101$	255602.	−	105874.i	0.0246853	−	0.0102250i	−0.370307	−	0.928910i	$-0.620747\pi$
$101$	255602.	−	105874.i	0.0246853	−	0.0102250i	0.394992	+	0.918685i	$0.370747\pi$
$102$	1.27401e6	−	299798.i	0.118870	−	0.0279723i
$103$	3.21409e6	−	3.21409e6i	0.289820	−	0.289820i	−0.547189	−	0.837009i	$-0.684302\pi$
$103$	3.21409e6	−	3.21409e6i	0.289820	−	0.289820i	0.837009	+	0.547189i	$0.184302\pi$
$104$	−896093.	+	9.70671e6i	−0.0781153	+	0.846166i
$105$	2.77942e7	+	2.77942e7i	2.34310	+	2.34310i
$106$	−7.21956e6	−	4.46901e6i	−0.588762	−	0.364453i
$107$	9.47034e6	+	2.28634e7i	0.747347	+	1.80426i	0.572970	+	0.819576i	$0.305791\pi$
$107$	9.47034e6	+	2.28634e7i	0.747347	+	1.80426i	0.174377	+	0.984679i	$0.444209\pi$
$108$	−1.98348e6	−	2.84813e7i	−0.151511	−	2.17559i
$109$	−489670.	−	202828.i	−0.0362168	−	0.0150015i	0.364501	−	0.931203i	$-0.381239\pi$
$109$	−489670.	−	202828.i	−0.0362168	−	0.0150015i	−0.400718	+	0.916201i	$0.631239\pi$
$110$	2.23903e7	+	3.64975e6i	1.60393	+	0.261450i
$111$		−	1.85282e7i		−	1.28589i
$112$	2.16213e7	−	3.02614e6i	1.45418	−	0.203529i
$113$		−	2.31329e7i		−	1.50819i	−0.656766	−	0.754094i	$-0.728076\pi$
$113$		−	2.31329e7i		−	1.50819i	0.656766	−	0.754094i	$-0.271924\pi$
$114$	2.15284e6	−	1.32071e7i	0.136096	−	0.834911i
$115$	−2.51133e7	−	1.04023e7i	−1.53979	−	0.637802i
$116$	5.18716e6	+	4.51172e6i	0.308551	+	0.268373i
$117$	−1.24846e7	−	3.01405e7i	−0.720650	−	1.73980i
$118$	−1.22853e7	+	1.98466e7i	−0.688335	+	1.11198i
$119$	−1.29969e6	−	1.29969e6i	−0.0707012	−	0.0707012i
$120$	4.08019e7	−	1.26503e7i	2.15549	−	0.668290i
$121$	−9.20142e6	+	9.20142e6i	−0.472178	+	0.472178i
$122$	44169.5	+	187700.i	0.00220223	+	0.00935849i
$123$	−134614.	+	55759.1i	−0.00652264	+	0.00270177i
$124$	−6.66705e6	+	1.99069e7i	−0.314020	+	0.937623i
$125$	4.37953e6	−	1.05731e7i	0.200559	−	0.484193i
$126$	−5.93043e7	+	4.26802e7i	−2.64113	+	1.90077i
$127$	−1.97294e7			−0.854676			−0.427338	−	0.904092i	$-0.640549\pi$
$127$	−1.97294e7			−0.854676			−0.427338	+	0.904092i	$0.640549\pi$
$128$	8.03980e6	−	2.23229e7i	0.338852	−	0.940840i
$129$	5.12842e7			2.10339
$130$	2.17413e7	−	1.56468e7i	0.867926	−	0.624631i
$131$	5.04552e6	−	1.21810e7i	0.196090	−	0.473404i	−0.794998	−	0.606612i	$-0.792528\pi$
$131$	5.04552e6	−	1.21810e7i	0.196090	−	0.473404i	0.991088	+	0.133208i	$0.0425280\pi$
$132$	−1.94350e7	+	5.80303e7i	−0.735488	+	2.19607i
$133$	−1.73619e7	+	7.19154e6i	−0.639907	+	0.265058i
$134$	4.12282e6	+	1.75201e7i	0.148022	+	0.629029i
$135$	−5.54744e7	+	5.54744e7i	−1.94055	+	1.94055i
$136$	−1.90795e6	+	591543.i	−0.0650401	+	0.0201651i
$137$	−9.30101e6	−	9.30101e6i	−0.309035	−	0.309035i	0.535500	−	0.844535i	$-0.320123\pi$
$137$	−9.30101e6	−	9.30101e6i	−0.309035	−	0.309035i	−0.844535	+	0.535500i	$0.820123\pi$
$138$	3.85955e7	−	6.23498e7i	1.25014	−	2.01957i
$139$	−1.26412e7	−	3.05185e7i	−0.399242	−	0.963855i	−0.987846	−	0.155434i	$-0.950322\pi$
$139$	−1.26412e7	−	3.05185e7i	−0.399242	−	0.963855i	0.588604	−	0.808421i	$-0.299678\pi$
$140$	−4.52651e7	−	3.93709e7i	−1.39417	−	1.21263i
$141$	237832.	+	98513.3i	0.00714502	+	0.00295957i
$142$	6.26036e6	−	3.84057e7i	0.183481	−	1.12560i
$143$			3.83744e7i			1.09740i
$144$	1.10065e7	+	7.86398e7i	0.307173	+	2.19469i
$145$		−	1.88910e7i		−	0.514596i
$146$	−5.51662e7	−	8.99244e6i	−1.46703	−	0.239135i
$147$	7.37684e7	+	3.05559e7i	1.91540	+	0.793385i
$148$	1.96459e6	+	2.82101e7i	0.0498145	+	0.715300i
$149$	1.33006e7	+	3.21104e7i	0.329396	+	0.795232i	0.998637	+	0.0521870i	$0.0166192\pi$
$149$	1.33006e7	+	3.21104e7i	0.329396	+	0.795232i	−0.669241	+	0.743045i	$0.733381\pi$
$150$	−3.67792e7	−	2.27669e7i	−0.889779	−	0.550787i
$151$	3.58874e7	+	3.58874e7i	0.848248	+	0.848248i	0.989914	−	0.141667i	$-0.0452461\pi$
$151$	3.58874e7	+	3.58874e7i	0.848248	+	0.848248i	−0.141667	+	0.989914i	$0.545246\pi$
$152$	−1.87742e6	+	2.03367e7i	−0.0433620	+	0.469708i
$153$	4.72719e6	−	4.72719e6i	0.106704	−	0.106704i
$154$	8.36598e7	−	1.96867e7i	1.84584	−	0.434361i
$155$	5.32968e7	−	2.20763e7i	1.14958	−	0.476173i
$156$	3.22239e7	+	6.46771e7i	0.679582	+	1.36400i
$157$	2.22877e6	−	5.38073e6i	0.0459639	−	0.110967i	−0.899230	−	0.437476i	$-0.855872\pi$
$157$	2.22877e6	−	5.38073e6i	0.0459639	−	0.110967i	0.945194	+	0.326509i	$0.105872\pi$
$158$	−1.73547e7	−	2.41144e7i	−0.350039	−	0.486381i
$159$	−6.29409e7			−1.24178
$160$	−6.07815e7	+	2.35870e7i	−1.17314	+	0.455252i
$161$	−1.02981e8			−1.94475
$162$	−5.35761e7	−	7.44442e7i	−0.990077	−	1.37572i
$163$	−3.08525e7	+	7.44844e7i	−0.557999	+	1.34713i	0.353350	+	0.935491i	$0.385043\pi$
$163$	−3.08525e7	+	7.44844e7i	−0.557999	+	1.34713i	−0.911348	+	0.411636i	$0.864957\pi$
$164$	199045.	−	99169.5i	0.00352369	−	0.00175560i
$165$	1.55365e8	−	6.43541e7i	2.69252	−	1.11528i
$166$	−7.86513e7	+	1.85081e7i	−1.33453	+	0.314040i
$167$	−9.48573e6	+	9.48573e6i	−0.157603	+	0.157603i	−0.781503	−	0.623901i	$-0.785547\pi$
$167$	−9.48573e6	+	9.48573e6i	−0.157603	+	0.157603i	0.623901	+	0.781503i	$0.285547\pi$
$168$	1.24471e8	−	1.03432e8i	2.02528	−	1.68295i
$169$	−1.23305e7	−	1.23305e7i	−0.196506	−	0.196506i
$170$	4.66719e6	+	2.88906e6i	0.0728592	+	0.0451009i
$171$	−2.61567e7	−	6.31479e7i	−0.400034	−	0.965768i
$172$	−7.80827e7	+	5.43778e6i	−1.17005	+	0.0814840i
$173$	−3.28191e7	−	1.35941e7i	−0.481909	−	0.199613i	0.128485	−	0.991712i	$-0.458989\pi$
$173$	−3.28191e7	−	1.35941e7i	−0.481909	−	0.199613i	−0.610394	+	0.792098i	$0.708989\pi$
$174$	5.02974e7	+	8.19879e6i	0.723808	+	0.117985i
$175$			6.07466e7i			0.856818i
$176$	2.34376e7	−	9.04147e7i	0.324056	−	1.25010i
$177$			1.73025e8i			2.34532i
$178$	−3.37792e6	+	2.07227e7i	−0.0448931	+	0.275407i
$179$	3.95431e7	+	1.63793e7i	0.515329	+	0.213456i	0.625164	−	0.780493i	$-0.285032\pi$
$179$	3.95431e7	+	1.63793e7i	0.515329	+	0.213456i	−0.109835	+	0.993950i	$0.535032\pi$
$180$	1.43198e8	−	1.64636e8i	1.83014	−	2.10412i
$181$	−5.79073e7	−	1.39801e8i	−0.725869	−	1.75240i	−0.655894	−	0.754853i	$-0.727708\pi$
$181$	−5.79073e7	−	1.39801e8i	−0.725869	−	1.75240i	−0.0699752	−	0.997549i	$-0.522292\pi$
$182$	5.34122e7	−	8.62858e7i	0.656736	−	1.06094i
$183$	1.01073e6	+	1.01073e6i	0.0121915	+	0.0121915i
$184$	−5.21524e7	+	9.90231e7i	−0.617181	+	1.17186i
$185$	5.49461e7	−	5.49461e7i	0.638023	−	0.638023i
$186$	3.56472e7	+	1.51485e8i	0.406191	+	1.72613i
$187$	−7.26506e6	+	3.00929e6i	−0.0812444	+	0.0336525i
$188$	−372557.	−	124773.i	−0.00408921	−	0.00136952i
$189$	−1.13740e8	+	2.74593e8i	−1.22546	+	2.95851i
$190$	4.55505e7	−	3.27819e7i	0.481788	−	0.346734i
$191$	−1.71221e8			−1.77803			−0.889016	−	0.457877i	$-0.848610\pi$
$191$	−1.71221e8			−1.77803			−0.889016	+	0.457877i	$0.848610\pi$
$192$	−3.64210e7	−	1.72068e8i	−0.371362	−	1.75447i
$193$	1.08765e8			1.08902			0.544511	−	0.838753i	$-0.316715\pi$
$193$	1.08765e8			1.08902			0.544511	+	0.838753i	$0.316715\pi$
$194$	8.00167e7	−	5.75865e7i	0.786819	−	0.566259i
$195$	7.59862e7	−	1.83447e8i	0.733861	−	1.77170i
$196$	−1.15556e8	−	3.87010e7i	−1.09622	−	0.367135i
$197$	4.23623e7	−	1.75470e7i	0.394773	−	0.163520i	−0.176461	−	0.984308i	$-0.556465\pi$
$197$	4.23623e7	−	1.75470e7i	0.394773	−	0.163520i	0.571234	+	0.820787i	$0.306465\pi$
$198$	7.16036e7	+	3.04283e8i	0.655551	+	2.78580i
$199$	−2.61226e7	+	2.61226e7i	−0.234980	+	0.234980i	−0.814768	−	0.579788i	$-0.803135\pi$
$199$	−2.61226e7	+	2.61226e7i	−0.234980	+	0.234980i	0.579788	+	0.814768i	$0.303135\pi$
$200$	5.84121e7	+	3.07639e7i	0.516295	+	0.271917i
$201$	9.43429e7	+	9.43429e7i	0.819451	+	0.819451i
$202$	−1.64746e6	+	2.66142e6i	−0.0140632	+	0.0227187i
$203$	−2.73880e7	−	6.61205e7i	−0.229786	−	0.554754i
$204$	−9.71774e6	+	1.11726e7i	−0.0801419	+	0.0921399i
$205$	−564561.	−	233849.i	−0.00457691	−	0.00189582i
$206$	−8.27347e6	+	5.07556e7i	−0.0659405	+	0.404528i
$207$		−	3.74556e8i		−	2.93508i
$208$	−5.59203e7	−	9.50573e7i	−0.430872	−	0.732426i
$209$			8.03989e7i			0.609169i
$210$	−4.38914e8	−	7.15457e7i	−3.27048	−	0.533109i
$211$	1.88894e8	+	7.82426e7i	1.38430	+	0.573396i	0.945628	−	0.325251i	$-0.105449\pi$
$211$	1.88894e8	+	7.82426e7i	1.38430	+	0.573396i	0.438673	+	0.898647i	$0.355449\pi$
$212$	9.58306e7	−	6.67377e6i	0.690762	−	0.0481056i
$213$	−1.10386e8	−	2.66494e8i	−0.782679	−	1.88956i
$214$	−2.38063e8	−	1.47364e8i	−1.66052	−	1.02789i
$215$	1.52085e8	+	1.52085e8i	1.04365	+	1.04365i
$216$	2.06439e8	+	2.48431e8i	1.39381	+	1.67733i
$217$	1.54539e8	−	1.54539e8i	1.02666	−	1.02666i
$218$	5.83700e6	−	1.37356e6i	0.0381585	−	0.00897942i
$219$	−3.82795e8	+	1.58559e8i	−2.46270	+	1.02008i
$220$	−2.29727e8	+	1.14456e8i	−1.45456	+	0.724701i
$221$	−3.55322e6	+	8.57823e6i	−0.0221436	+	0.0534595i
$222$	1.22448e8	+	1.70142e8i	0.751130	+	1.04370i
$223$	2.42908e8			1.46682			0.733408	−	0.679789i	$-0.237929\pi$
$223$	2.42908e8			1.46682			0.733408	+	0.679789i	$0.237929\pi$
$224$	−1.78546e8	+	1.70678e8i	−1.06141	+	1.01463i
$225$	−2.20944e8			−1.29314
$226$	1.52879e8	+	2.12426e8i	0.880985	+	1.22413i
$227$	−1.16560e8	+	2.81401e8i	−0.661394	+	1.59675i	0.134226	+	0.990951i	$0.457145\pi$
$227$	−1.16560e8	+	2.81401e8i	−0.661394	+	1.59675i	−0.795620	+	0.605796i	$0.792855\pi$
$228$	6.75129e7	+	1.35506e8i	0.377237	+	0.757159i
$229$	−9.23290e7	+	3.82439e7i	−0.508059	+	0.210445i	−0.621963	−	0.783047i	$-0.713664\pi$
$229$	−9.23290e7	+	3.82439e7i	−0.508059	+	0.210445i	0.113904	+	0.993492i	$0.463664\pi$
$230$	2.99358e8	−	7.04445e7i	1.62234	−	0.381768i
$231$	4.50493e8	−	4.50493e8i	2.40462	−	2.40462i
$232$	−7.74496e7	−	7.14990e6i	−0.407203	−	0.0375917i
$233$	1.73585e7	+	1.73585e7i	0.0899014	+	0.0899014i	0.750627	−	0.660726i	$-0.229751\pi$
$233$	1.73585e7	+	1.73585e7i	0.0899014	+	0.0899014i	−0.660726	+	0.750627i	$0.729751\pi$
$234$	3.13835e8	+	1.94268e8i	1.60120	+	0.991166i
$235$	413156.	+	997446.i	0.00207671	+	0.00501363i
$236$	−1.83462e7	−	2.63438e8i	−0.0908561	−	1.30463i
$237$	−2.03471e8	−	8.42804e7i	−0.992849	−	0.411251i
$238$	2.05242e7	+	3.34557e6i	0.0986841	+	0.0160861i
$239$		−	8.34100e7i		−	0.395208i	−0.980282	−	0.197604i	$-0.936684\pi$
$239$		−	8.34100e7i		−	0.395208i	0.980282	−	0.197604i	$-0.0633160\pi$
$240$	−2.91075e8	+	3.85814e8i	−1.35915	+	1.80152i
$241$		−	3.21036e8i		−	1.47739i	−0.674041	−	0.738694i	$-0.735443\pi$
$241$		−	3.21036e8i		−	1.47739i	0.674041	−	0.738694i	$-0.264557\pi$
$242$	2.36856e7	−	1.45305e8i	0.107431	−	0.659062i
$243$	−1.77464e8	−	7.35082e7i	−0.793395	−	0.328635i
$244$	−1.64606e6	−	1.43172e6i	−0.00725407	−	0.00630949i
$245$	1.28149e8	+	3.09378e8i	0.556715	+	1.34403i
$246$	867647.	−	1.40166e6i	0.00371595	−	0.00600301i
$247$	6.71264e7	+	6.71264e7i	0.283435	+	0.283435i
$248$	−7.03368e7	−	2.26863e8i	−0.292821	−	0.944458i
$249$	−4.23523e8	+	4.23523e8i	−1.73852	+	1.73852i
$250$	2.96583e7	+	1.26035e8i	0.120048	+	0.510152i
$251$	1.16613e8	−	4.83027e7i	0.465467	−	0.192803i	−0.137609	−	0.990487i	$-0.543942\pi$
$251$	1.16613e8	−	4.83027e7i	0.465467	−	0.192803i	0.603076	+	0.797684i	$0.293942\pi$
$252$	2.62521e8	−	7.83852e8i	1.03338	−	3.08555i
$253$	−1.68602e8	+	4.07041e8i	−0.654547	+	1.58022i
$254$	1.81172e8	−	1.30386e8i	0.693704	−	0.499246i
$255$	4.06891e7			0.153669
$256$	7.36976e7	+	2.58121e8i	0.274545	+	0.961574i
$257$	−3.80282e8			−1.39746			−0.698731	−	0.715385i	$-0.746251\pi$
$257$	−3.80282e8			−1.39746			−0.698731	+	0.715385i	$0.746251\pi$
$258$	−4.70935e8	+	3.38923e8i	−1.70723	+	1.22866i
$259$	1.12657e8	−	2.71978e8i	0.402911	−	0.972713i
$260$	−9.62414e7	+	2.87364e8i	−0.339590	+	1.01397i
$261$	2.40490e8	−	9.96144e7i	0.837251	−	0.346801i
$262$	3.41684e7	+	1.45200e8i	0.117373	+	0.498785i
$263$	−3.43037e8	+	3.43037e8i	−1.16278	+	1.16278i	−0.178911	+	0.983865i	$0.557258\pi$
$263$	−3.43037e8	+	3.43037e8i	−1.16278	+	1.16278i	−0.983865	+	0.178911i	$0.942742\pi$
$264$	−2.05038e8	−	6.61324e8i	−0.685835	−	2.21208i
$265$	−1.86654e8	−	1.86654e8i	−0.616136	−	0.616136i
$266$	1.11905e8	−	1.80779e8i	0.364555	−	0.588928i
$267$	5.95611e7	+	1.43793e8i	0.191502	+	0.462327i
$268$	−1.53645e8	−	1.33638e8i	−0.487581	−	0.424091i
$269$	1.36636e8	+	5.65963e7i	0.427987	+	0.177278i	0.586270	−	0.810116i	$-0.300596\pi$
$269$	1.36636e8	+	5.65963e7i	0.427987	+	0.177278i	−0.158283	+	0.987394i	$0.550596\pi$
$270$	1.42798e8	−	8.76029e8i	0.441519	−	2.70860i
$271$		−	4.70579e8i		−	1.43628i	−0.695897	−	0.718141i	$-0.744993\pi$
$271$		−	4.70579e8i		−	1.43628i	0.695897	−	0.718141i	$-0.255007\pi$
$272$	1.36111e7	−	1.80412e7i	0.0410111	−	0.0543593i
$273$		−	7.52249e8i		−	2.23765i
$274$	1.46878e8	+	2.39419e7i	0.431349	+	0.0703125i
$275$	2.40107e8	+	9.94555e7i	0.696210	+	0.288380i
$276$	5.76363e7	+	8.27616e8i	0.165012	+	2.36945i
$277$	8.98204e7	+	2.16846e8i	0.253919	+	0.613016i	0.998514	−	0.0545016i	$-0.0173570\pi$
$277$	8.98204e7	+	2.16846e8i	0.253919	+	0.613016i	−0.744594	+	0.667517i	$0.767357\pi$
$278$	3.17771e8	+	1.96705e8i	0.887069	+	0.549109i
$279$	5.62081e8	+	5.62081e8i	1.54947	+	1.54947i
$280$	6.75854e8	+	6.23927e7i	1.83992	+	0.169856i
$281$	1.76482e8	−	1.76482e8i	0.474492	−	0.474492i	−0.428873	−	0.903365i	$-0.641089\pi$
$281$	1.76482e8	−	1.76482e8i	0.474492	−	0.474492i	0.903365	+	0.428873i	$0.141089\pi$
$282$	−2.83502e6	+	667135.i	−0.00752809	+	0.00177150i
$283$	3.10216e7	−	1.28496e7i	0.0813602	−	0.0337005i	−0.341632	−	0.939834i	$-0.610980\pi$
$283$	3.10216e7	−	1.28496e7i	0.0813602	−	0.0337005i	0.422992	+	0.906133i	$0.360980\pi$
$284$	1.96325e8	+	3.94046e8i	0.508581	+	1.02078i
$285$	1.59200e8	−	3.84343e8i	0.407368	−	0.983473i
$286$	−2.53606e8	−	3.52386e8i	−0.641029	−	0.890713i
$287$	−2.31506e6			−0.00578063
$288$	−6.20780e8	−	6.49398e8i	−1.53131	−	1.60191i
$289$	4.08436e8			0.995363
$290$	1.24845e8	+	1.73473e8i	0.300593	+	0.417675i
$291$	2.79660e8	−	6.75160e8i	0.665282	−	1.60613i
$292$	5.66012e8	−	2.82002e8i	1.33041	−	0.662846i
$293$	−1.39329e7	+	5.77120e6i	−0.0323598	+	0.0134038i	−0.398805	−	0.917036i	$-0.630575\pi$
$293$	−1.39329e7	+	5.77120e6i	−0.0323598	+	0.0134038i	0.366445	+	0.930440i	$0.380575\pi$
$294$	−8.79340e8	+	2.06925e8i	−2.01809	+	0.474895i
$295$	−5.13112e8	+	5.13112e8i	−1.16368	+	1.16368i
$296$	−2.04473e8	−	2.46065e8i	−0.458264	−	0.551480i
$297$	8.99139e8	+	8.99139e8i	1.99150	+	1.99150i
$298$	−3.34346e8	−	2.06965e8i	−0.731879	−	0.453044i
$299$	1.99077e8	+	4.80615e8i	0.430697	+	1.03980i
$300$	4.88197e8	−	3.39987e7i	1.04393	−	0.0727007i
$301$	7.52808e8	+	3.11823e8i	1.59112	+	0.659062i
$302$	−5.66719e8	−	9.23786e7i	−1.18398	−	0.192996i
$303$			2.32026e7i			0.0479168i
$304$	−1.17160e8	−	1.99156e8i	−0.239178	−	0.406571i
$305$			5.99475e6i			0.0120982i
$306$	−1.21684e7	+	7.46497e7i	−0.0242777	+	0.148937i
$307$	−7.96277e8	−	3.29829e8i	−1.57065	−	0.650585i	−0.583753	−	0.811931i	$-0.698417\pi$
$307$	−7.96277e8	−	3.29829e8i	−1.57065	−	0.650585i	−0.986898	+	0.161346i	$0.948417\pi$
$308$	−6.38131e8	+	7.33665e8i	−1.24446	+	1.43077i
$309$	1.45882e8	+	3.52190e8i	0.281285	+	0.679081i
$310$	−3.43521e8	+	5.54947e8i	−0.654918	+	1.05800i
$311$	−7.11472e8	−	7.11472e8i	−1.34121	−	1.34121i	−0.894859	−	0.446349i	$-0.852724\pi$
$311$	−7.11472e8	−	7.11472e8i	−1.34121	−	1.34121i	−0.446349	−	0.894859i	$-0.647276\pi$
$312$	−7.23341e8	−	3.80962e8i	−1.34835	−	0.710134i
$313$	6.35645e7	−	6.35645e7i	0.117168	−	0.117168i	−0.646092	−	0.763260i	$-0.723598\pi$
$313$	6.35645e7	−	6.35645e7i	0.117168	−	0.117168i	0.763260	+	0.646092i	$0.223598\pi$
$314$	1.50933e7	+	6.41398e7i	0.0275125	+	0.116916i
$315$	−2.09861e9	+	8.69272e8i	−3.78307	+	1.56700i
$316$	3.18731e8	+	1.06747e8i	0.568224	+	0.190305i
$317$	−2.81786e8	+	6.80291e8i	−0.496834	+	1.19946i	0.454345	+	0.890826i	$0.349873\pi$
$317$	−2.81786e8	+	6.80291e8i	−0.496834	+	1.19946i	−0.951180	+	0.308638i	$0.900127\pi$
$318$	5.77977e8	−	4.15959e8i	1.00790	−	0.725364i
$319$	−3.06188e8			−0.528106
$320$	4.02268e8	−	6.18284e8i	0.686263	−	1.05478i
$321$	−2.07546e9			−3.50224
$322$	9.45655e8	−	6.80570e8i	1.57847	−	1.13600i
$323$	−7.44442e6	+	1.79724e7i	−0.0122920	+	0.0296755i
$324$	9.83963e8	+	3.29540e8i	1.60721	+	0.538271i
$325$	2.83507e8	−	1.17432e8i	0.458112	−	0.189756i
$326$	−2.08934e8	−	8.87875e8i	−0.334000	−	1.41935i
$327$	3.14312e7	−	3.14312e7i	0.0497100	−	0.0497100i
$328$	−1.17241e6	+	2.22609e6i	−0.00183452	+	0.00348325i
$329$	2.89218e6	+	2.89218e6i	0.00447755	+	0.00447755i
$330$	−1.00139e9	+	1.61772e9i	−1.53393	+	2.47801i
$331$	2.39307e8	+	5.77738e8i	0.362708	+	0.875655i	0.994902	+	0.100845i	$0.0321546\pi$
$331$	2.39307e8	+	5.77738e8i	0.362708	+	0.875655i	−0.632194	+	0.774810i	$0.717845\pi$
$332$	5.99928e8	−	6.89742e8i	0.899738	−	1.03444i
$333$	9.89226e8	+	4.09751e8i	1.46805	+	0.608086i
$334$	2.44174e7	−	1.49795e8i	0.0358581	−	0.219980i
$335$			5.59555e8i			0.813179i
$336$	−4.59446e8	+	1.77239e9i	−0.660765	+	2.54901i
$337$		−	7.93300e8i		−	1.12910i	−0.825399	−	0.564550i	$-0.809050\pi$
$337$		−	7.93300e8i		−	1.12910i	0.825399	−	0.564550i	$-0.190950\pi$
$338$	1.94717e8	+	3.17401e7i	0.274281	+	0.0447096i
$339$	1.79239e9	+	7.42434e8i	2.49882	+	1.03504i
$340$	−6.19511e7	+	4.31436e6i	−0.0854816	+	0.00595306i
$341$	−3.57816e8	−	8.63844e8i	−0.488674	−	1.17976i
$342$	6.57521e8	+	4.07015e8i	0.888829	+	0.550198i
$343$	1.21099e8	+	1.21099e8i	0.162036	+	0.162036i
$344$	6.81085e8	−	5.65961e8i	0.902083	−	0.749605i
$345$	1.61199e9	−	1.61199e9i	2.11347	−	2.11347i
$346$	3.91212e8	−	9.20597e7i	0.507746	−	0.119482i
$347$	−5.29505e8	+	2.19328e8i	−0.680325	+	0.281800i	−0.695963	−	0.718078i	$-0.745022\pi$
$347$	−5.29505e8	+	2.19328e8i	−0.680325	+	0.281800i	0.0156375	+	0.999878i	$0.495022\pi$
$348$	−5.16057e8	+	2.57114e8i	−0.656403	+	0.327038i
$349$	−2.42415e7	+	5.85242e7i	−0.0305260	+	0.0736964i	−0.938407	−	0.345531i	$-0.887699\pi$
$349$	−2.42415e7	+	5.85242e7i	−0.0305260	+	0.0736964i	0.907881	+	0.419227i	$0.137699\pi$
$350$	−4.01457e8	−	5.57827e8i	−0.500497	−	0.695442i
$351$	1.50141e9			1.85321
$352$	3.82302e8	+	9.85157e8i	0.467204	+	1.20394i
$353$	−1.07856e9			−1.30507			−0.652536	−	0.757758i	$-0.726295\pi$
$353$	−1.07856e9			−1.30507			−0.652536	+	0.757758i	$0.726295\pi$
$354$	−1.14347e9	−	1.58886e9i	−1.36998	−	1.90359i
$355$	4.62947e8	−	1.11765e9i	0.549202	−	1.32589i
$356$	−1.05931e8	−	2.12617e8i	−0.124437	−	0.249760i
$357$	1.42416e8	−	5.89908e7i	0.165661	−	0.0686191i
$358$	−4.71364e8	+	1.10921e8i	−0.542958	+	0.127768i
$359$	6.15839e7	−	6.15839e7i	0.0702484	−	0.0702484i	−0.671110	−	0.741358i	$-0.734182\pi$
$359$	6.15839e7	−	6.15839e7i	0.0702484	−	0.0702484i	0.741358	+	0.671110i	$0.234182\pi$
$360$	−2.26932e8	+	2.45818e9i	−0.256352	+	2.77687i
$361$	−4.91425e8	−	4.91425e8i	−0.549771	−	0.549771i
$362$	1.45566e9	+	9.01074e8i	1.61279	+	0.998345i
$363$	−4.17636e8	−	1.00826e9i	−0.458273	−	1.10637i
$364$	7.97628e7	+	1.14534e9i	0.0866853	+	1.24474i
$365$	−1.60541e9	−	6.64982e8i	−1.72807	−	0.715789i
$366$	−1.59611e7	−	2.60176e6i	−0.0170168	−	0.00277385i
$367$		−	8.98361e8i		−	0.948680i	−0.880342	−	0.474340i	$-0.842687\pi$
$367$		−	8.98361e8i		−	0.948680i	0.880342	−	0.474340i	$-0.157313\pi$
$368$	−1.75508e8	−	1.25398e9i	−0.183582	−	1.31166i
$369$		−	8.42022e6i		−	0.00872431i
$370$	−1.41438e8	+	8.67686e8i	−0.145165	+	0.890546i
$371$	−9.23919e8	−	3.82700e8i	−0.939345	−	0.389089i
$372$	−1.32846e9	−	1.15548e9i	−1.33798	−	1.16375i
$373$	4.81828e7	+	1.16324e8i	0.0480741	+	0.116061i	0.946092	−	0.323897i	$-0.104993\pi$
$373$	4.81828e7	+	1.16324e8i	0.0480741	+	0.116061i	−0.898018	+	0.439958i	$0.854993\pi$
$374$	4.68264e7	−	7.56466e7i	0.0462850	−	0.0747720i
$375$	6.78674e8	+	6.78674e8i	0.664587	+	0.664587i
$376$	4.24573e6	−	1.31635e6i	0.00411902	−	0.00127707i
$377$	−2.55642e8	+	2.55642e8i	−0.245718	+	0.245718i
$378$	−7.70252e8	−	3.27323e9i	−0.733519	−	3.11713i
$379$	1.27116e9	−	5.26532e8i	1.19940	−	0.496806i	0.308593	−	0.951194i	$-0.400142\pi$
$379$	1.27116e9	−	5.26532e8i	1.19940	−	0.496806i	0.890804	+	0.454388i	$0.150142\pi$
$380$	−2.01637e8	+	6.02062e8i	−0.188507	+	0.562857i
$381$	6.33202e8	−	1.52868e9i	0.586550	−	1.41606i
$382$	1.57229e9	−	1.13155e9i	1.44315	−	1.03861i
$383$	4.16276e8			0.378605			0.189302	−	0.981919i	$-0.439377\pi$
$383$	4.16276e8			0.378605			0.189302	+	0.981919i	$0.439377\pi$
$384$	1.47160e9	+	1.33938e9i	1.32627	+	1.20710i
$385$	2.67191e9			2.38622
$386$	−9.98769e8	+	7.18795e8i	−0.883913	+	0.636136i
$387$	−1.13415e9	+	2.73808e9i	−0.994676	+	2.40136i
$388$	−3.54208e8	+	1.05762e9i	−0.307856	+	0.919216i
$389$	−7.99948e8	+	3.31349e8i	−0.689030	+	0.285406i	−0.699596	−	0.714539i	$-0.746637\pi$
$389$	−7.99948e8	+	3.31349e8i	−0.689030	+	0.285406i	0.0105660	+	0.999944i	$0.496637\pi$
$390$	5.14581e8	+	2.18674e9i	0.439266	+	1.86668i
$391$	−7.53788e7	+	7.53788e7i	−0.0637721	+	0.0637721i
$392$	1.31690e9	−	4.08292e8i	1.10421	−	0.342350i
$393$	7.81878e8	+	7.81878e8i	0.649778	+	0.649778i
$394$	−2.73043e8	+	4.41093e8i	−0.224903	+	0.363323i
$395$	−3.53464e8	−	8.53339e8i	−0.288573	−	0.696677i
$396$	−2.66845e9	−	2.32098e9i	−2.15936	−	1.87818i
$397$	2.41474e8	+	1.00022e8i	0.193688	+	0.0802284i	0.477419	−	0.878676i	$-0.341572\pi$
$397$	2.41474e8	+	1.00022e8i	0.193688	+	0.0802284i	−0.283731	+	0.958904i	$0.591572\pi$
$398$	6.72428e7	−	4.12517e8i	0.0534632	−	0.327983i
$399$		−	1.57605e9i		−	1.24212i
$400$	−7.39700e8	+	1.03529e8i	−0.577890	+	0.0808824i
$401$			1.50542e9i			1.16588i	0.812515	+	0.582940i	$0.198098\pi$
$401$			1.50542e9i			1.16588i	−0.812515	+	0.582940i	$0.801902\pi$
$402$	−1.48982e9	−	2.42850e8i	−1.14378	−	0.186444i
$403$	−1.01999e9	−	4.22492e8i	−0.776294	−	0.321552i
$404$	−2.46023e6	−	3.53271e7i	−0.00185627	−	0.0266547i
$405$	−1.09119e9	−	2.63437e9i	−0.816221	−	1.97053i
$406$	6.88472e8	+	4.26175e8i	0.510558	+	0.316043i
$407$	−8.90576e8	−	8.90576e8i	−0.654773	−	0.654773i
$408$	1.54001e7	−	1.66818e8i	0.0112257	−	0.121600i
$409$	−1.09703e9	+	1.09703e9i	−0.792846	+	0.792846i	−0.981956	−	0.189110i	$-0.939440\pi$
$409$	−1.09703e9	+	1.09703e9i	−0.792846	+	0.792846i	0.189110	+	0.981956i	$0.439440\pi$
$410$	6.72972e6	−	1.58363e6i	0.00482229	−	0.00113478i
$411$	1.01917e9	−	4.22156e8i	0.724106	−	0.299935i
$412$	−2.59456e8	−	5.20758e8i	−0.182777	−	0.366856i
$413$	−1.05204e9	+	2.53985e9i	−0.734865	+	1.77412i
$414$	2.47534e9	+	3.43949e9i	1.71448	+	2.38228i
$415$	−2.51195e9			−1.72521
$416$	1.14172e9	+	5.03335e8i	0.777555	+	0.342792i
$417$	2.77036e9			1.87094
$418$	−5.31334e8	−	7.38291e8i	−0.355837	−	0.494436i
$419$	−4.72491e8	+	1.14069e9i	−0.313794	+	0.757566i	0.685764	+	0.727824i	$0.259468\pi$
$419$	−4.72491e8	+	1.14069e9i	−0.313794	+	0.757566i	−0.999558	+	0.0297413i	$0.990532\pi$
$420$	4.50331e9	−	2.24367e9i	2.96592	−	1.47770i
$421$	2.65366e9	−	1.09918e9i	1.73323	−	0.717929i	0.733987	−	0.679164i	$-0.237657\pi$
$421$	2.65366e9	−	1.09918e9i	1.73323	−	0.717929i	0.999248	−	0.0387656i	$-0.0123426\pi$
$422$	−2.25167e9	+	5.29861e8i	−1.45852	+	0.343217i
$423$	−1.05193e7	+	1.05193e7i	−0.00675765	+	0.00675765i
$424$	−8.35893e8	+	6.94602e8i	−0.532562	+	0.442543i
$425$	4.44647e7	+	4.44647e7i	0.0280966	+	0.0280966i
$426$	2.77484e9	+	1.71767e9i	1.73902	+	1.07648i
$427$	8.69115e6	+	2.09823e7i	0.00540231	+	0.0130423i
$428$	3.15999e9	−	2.20066e8i	1.94819	−	0.135675i
$429$	−2.97334e9	−	1.23160e9i	−1.81821	−	0.753128i
$430$	−2.40167e9	−	3.91487e8i	−1.45671	−	0.237453i
$431$			2.01631e9i			1.21307i	0.795055	+	0.606537i	$0.207442\pi$
$431$			2.01631e9i			1.21307i	−0.795055	+	0.606537i	$0.792558\pi$
$432$	−3.53752e9	−	9.17008e8i	−2.11108	−	0.547243i
$433$			1.26908e9i			0.751246i	0.926773	+	0.375623i	$0.122571\pi$
$433$			1.26908e9i			0.751246i	−0.926773	+	0.375623i	$0.877429\pi$
$434$	−3.97802e8	+	2.44041e9i	−0.233589	+	1.43301i
$435$	1.46372e9	+	6.06292e8i	0.852600	+	0.353159i
$436$	−4.45228e7	+	5.11883e7i	−0.0257265	+	0.0295779i
$437$	4.17090e8	+	1.00694e9i	0.239081	+	0.577192i
$438$	2.46728e9	−	3.98581e9i	1.40300	−	2.26651i
$439$	1.03573e9	+	1.03573e9i	0.584282	+	0.584282i	0.936077	−	0.351795i	$-0.114429\pi$
$439$	1.03573e9	+	1.03573e9i	0.584282	+	0.584282i	−0.351795	+	0.936077i	$0.614429\pi$
$440$	1.35314e9	−	2.56923e9i	0.757281	−	1.43787i
$441$	−3.26278e9	+	3.26278e9i	−1.81156	+	1.81156i
$442$	−2.40625e7	−	1.02255e8i	−0.0132545	−	0.0563256i
$443$	2.78141e9	−	1.15210e9i	1.52003	−	0.629617i	0.542433	−	0.840099i	$-0.317503\pi$
$443$	2.78141e9	−	1.15210e9i	1.52003	−	0.629617i	0.977598	+	0.210482i	$0.0675032\pi$
$444$	−2.24884e9	−	7.53161e8i	−1.21932	−	0.408364i
$445$	−2.49794e8	+	6.03056e8i	−0.134376	+	0.324412i
$446$	−2.23059e9	+	1.60532e9i	−1.19055	+	0.856818i
$447$	−2.91487e9			−1.54363
$448$	5.11598e8	−	2.74727e9i	0.268816	−	1.44354i
$449$	−7.64866e8			−0.398770			−0.199385	−	0.979921i	$-0.563895\pi$
$449$	−7.64866e8			−0.398770			−0.199385	+	0.979921i	$0.563895\pi$
$450$	2.02890e9	−	1.46016e9i	1.04958	−	0.755365i
$451$	−3.79026e6	+	9.15050e6i	−0.00194559	+	0.00469707i
$452$	−2.80773e9	−	9.40341e8i	−1.43012	−	0.478962i
$453$	−3.93243e9	+	1.62886e9i	−1.98754	+	0.823268i
$454$	−7.89350e8	−	3.35438e9i	−0.395889	−	1.68235i
$455$	2.23083e9	−	2.23083e9i	1.11026	−	1.11026i
$456$	−1.51548e9	−	7.98160e8i	−0.748470	−	0.394196i
$457$	4.76663e8	+	4.76663e8i	0.233617	+	0.233617i	0.814201	−	0.580584i	$-0.197176\pi$
$457$	4.76663e8	+	4.76663e8i	0.233617	+	0.233617i	−0.580584	+	0.814201i	$0.697176\pi$
$458$	5.95100e8	−	9.61365e8i	0.289441	−	0.467584i
$459$	1.17740e8	+	2.84249e8i	0.0568301	+	0.137200i
$460$	−2.28341e9	+	2.62525e9i	−1.09378	+	1.25753i
$461$	1.73599e9	+	7.19072e8i	0.825268	+	0.341837i	0.755028	−	0.655693i	$-0.227623\pi$
$461$	1.73599e9	+	7.19072e8i	0.825268	+	0.341837i	0.0702401	+	0.997530i	$0.477623\pi$
$462$	−1.15963e9	+	7.11400e9i	−0.547105	+	3.35635i
$463$		−	2.16463e9i		−	1.01356i	−0.862075	−	0.506780i	$-0.830836\pi$
$463$		−	2.16463e9i		−	1.01356i	0.862075	−	0.506780i	$-0.169164\pi$
$464$	7.58460e8	−	4.46187e8i	0.352468	−	0.207350i
$465$			4.83809e9i			2.23146i
$466$	−2.74118e8	−	4.46829e7i	−0.125484	−	0.0204546i
$467$	2.61962e9	+	1.08508e9i	1.19023	+	0.493008i	0.887829	−	0.460173i	$-0.152213\pi$
$467$	2.61962e9	+	1.08508e9i	1.19023	+	0.493008i	0.302398	+	0.953182i	$0.402213\pi$
$468$	−4.16576e9	+	2.90109e8i	−1.87860	+	0.130828i
$469$	8.11240e8	+	1.95851e9i	0.363115	+	0.876637i
$470$	−1.03858e7	−	6.42897e6i	−0.00461421	−	0.00285627i
$471$	3.45381e8	+	3.45381e8i	0.152309	+	0.152309i
$472$	1.90946e9	+	2.29787e9i	0.835823	+	1.00584i
$473$	2.46503e9	−	2.46503e9i	1.07104	−	1.07104i
$474$	2.42543e9	−	5.70749e8i	1.04608	−	0.246162i
$475$	5.93980e8	−	2.46035e8i	0.254299	−	0.105334i
$476$	−2.10581e8	+	1.04917e8i	−0.0894941	+	0.0445884i
$477$	1.39194e9	−	3.36043e9i	0.587226	−	1.41769i
$478$	5.51234e8	+	7.65941e8i	0.230854	+	0.320773i
$479$	8.33412e7			0.0346486			0.0173243	−	0.999850i	$-0.494485\pi$
$479$	8.33412e7			0.0346486			0.0173243	+	0.999850i	$0.494485\pi$
$480$	1.23164e8	−	5.46651e9i	0.0508322	−	2.25614i
$481$	−1.48712e9			−0.609308
$482$	2.12164e9	+	2.94803e9i	0.862993	+	1.19913i
$483$	3.30509e9	−	7.97919e9i	1.33465	−	3.22214i
$484$	7.42779e8	+	1.49085e9i	0.297784	+	0.597687i
$485$	2.83156e9	−	1.17287e9i	1.12701	−	0.466825i
$486$	2.11542e9	−	4.97799e8i	0.835931	−	0.196710i
$487$	−2.56343e9	+	2.56343e9i	−1.00570	+	1.00570i	−0.00572134	+	0.999984i	$0.501821\pi$
$487$	−2.56343e9	+	2.56343e9i	−1.00570	+	1.00570i	−0.999984	+	0.00572134i	$0.998179\pi$
$488$	2.45774e7	+	2.26891e6i	0.00957341	+	0.000883787i
$489$	−4.78105e9	−	4.78105e9i	−1.84902	−	1.84902i
$490$	−3.22137e9	−	1.99407e9i	−1.23695	−	0.765694i
$491$	−9.35620e8	−	2.25879e9i	−0.356709	−	0.861173i	−0.995758	−	0.0920066i	$-0.970672\pi$
$491$	−9.35620e8	−	2.25879e9i	−0.356709	−	0.861173i	0.639049	−	0.769166i	$-0.279328\pi$
$492$	1.29570e6	+	1.86053e7i	0.000490484	+	0.00704300i
$493$	−6.84455e7	−	2.83511e7i	−0.0257265	−	0.0106563i
$494$	−1.06003e9	−	1.72792e8i	−0.395617	−	0.0644880i
$495$			9.71815e9i			3.60135i
$496$	2.14517e9	+	1.61841e9i	0.789360	+	0.595529i
$497$		−	4.58309e9i		−	1.67460i
$498$	1.09020e9	−	6.68810e9i	0.395553	−	2.42661i
$499$	1.86424e9	+	7.72192e8i	0.671660	+	0.278211i	0.692336	−	0.721576i	$-0.256582\pi$
$499$	1.86424e9	+	7.72192e8i	0.671660	+	0.278211i	−0.0206759	+	0.999786i	$0.506582\pi$
$500$	−1.10528e9	−	9.61353e8i	−0.395436	−	0.343944i
$501$	−4.30540e8	−	1.03942e9i	−0.152961	−	0.369281i
$502$	−7.51620e8	+	1.21422e9i	−0.265177	+	0.428385i
$503$	2.96998e9	+	2.96998e9i	1.04056	+	1.04056i	0.999142	+	0.0414155i	$0.0131867\pi$
$503$	2.96998e9	+	2.96998e9i	1.04056	+	1.04056i	0.0414155	+	0.999142i	$0.486813\pi$
$504$	2.76957e9	+	8.93292e9i	0.963621	+	3.10804i
$505$	−6.88083e7	+	6.88083e7i	−0.0237750	+	0.0237750i
$506$	−1.14178e9	−	4.85204e9i	−0.391791	−	1.66494i
$507$	1.35113e9	−	5.59657e8i	0.460437	−	0.190719i
$508$	−8.01991e8	+	2.39464e9i	−0.271423	+	0.810432i
$509$	−1.32192e9	+	3.19140e9i	−0.444318	+	1.07268i	0.530100	+	0.847935i	$0.322154\pi$
$509$	−1.32192e9	+	3.19140e9i	−0.444318	+	1.07268i	−0.974418	+	0.224743i	$0.927846\pi$
$510$	−3.73642e8	+	2.68903e8i	−0.124727	+	0.0897635i
$511$	−6.58319e9			−2.18255
$512$	−2.38260e9	−	1.88324e9i	−0.784525	−	0.620097i
$513$	3.14564e9			1.02872
$514$	3.49207e9	−	2.51318e9i	1.13426	−	0.816305i
$515$	−6.11815e8	+	1.47705e9i	−0.197376	+	0.476508i
$516$	2.08468e9	−	6.22456e9i	0.667982	−	1.99450i
$517$	1.61668e7	−	6.69650e6i	0.00514525	−	0.00213123i
$518$	7.62916e8	+	3.24205e9i	0.241170	+	1.02486i
$519$	2.10661e9	−	2.10661e9i	0.661452	−	0.661452i
$520$	−1.01534e9	−	3.27485e9i	−0.316665	−	1.02136i
$521$	−1.68712e7	−	1.68712e7i	−0.00522654	−	0.00522654i	0.704489	−	0.709715i	$-0.251176\pi$
$521$	−1.68712e7	−	1.68712e7i	−0.00522654	−	0.00522654i	−0.709715	+	0.704489i	$0.751176\pi$
$522$	−1.55006e9	+	2.50408e9i	−0.476983	+	0.770551i
$523$	−5.34109e6	−	1.28945e7i	−0.00163258	−	0.00394139i	0.923061	−	0.384653i	$-0.125679\pi$
$523$	−5.34109e6	−	1.28945e7i	−0.00163258	−	0.00394139i	−0.924694	+	0.380712i	$0.875679\pi$
$524$	−1.27335e9	−	1.10754e9i	−0.386624	−	0.336280i
$525$	−4.70679e9	−	1.94962e9i	−1.41961	−	0.588020i
$526$	8.83021e8	−	5.41710e9i	0.264558	−	1.62299i
$527$		−	2.26236e8i		−	0.0673324i
$528$	6.25334e9	+	4.71780e9i	1.84881	+	1.39483i
$529$			2.56777e9i			0.754157i
$530$	2.94756e9	+	4.80470e8i	0.859997	+	0.140185i
$531$	−9.23783e9	−	3.82644e9i	−2.67756	−	1.10908i
$532$	1.67112e8	+	2.39962e9i	0.0481192	+	0.690957i
$533$	4.47536e6	+	1.08045e7i	0.00128021	+	0.00309071i
$534$	−1.49723e9	−	9.26809e8i	−0.425495	−	0.263388i
$535$	−6.15486e9	−	6.15486e9i	−1.73772	−	1.73772i
$536$	2.29408e9	+	2.11782e8i	0.643474	+	0.0594035i
$537$	−2.53821e9	+	2.53821e9i	−0.707324	+	0.707324i
$538$	−1.62873e9	+	3.83272e8i	−0.450933	+	0.106113i
$539$	5.01446e9	−	2.07706e9i	1.37931	−	0.571331i
$540$	4.47814e9	+	8.98816e9i	1.22383	+	2.45636i
$541$	1.12606e9	−	2.71856e9i	0.305754	−	0.738156i	−0.694079	−	0.719899i	$-0.744188\pi$
$541$	1.12606e9	−	2.71856e9i	0.305754	−	0.738156i	0.999833	−	0.0182575i	$-0.00581185\pi$
$542$	3.10993e9	+	4.32125e9i	0.838982	+	1.16577i
$543$	1.26906e10			3.40159
$544$	−5.75930e6	+	2.55621e8i	−0.00153382	+	0.0680771i
$545$	1.86421e8			0.0493296
$546$	4.97141e9	+	6.90779e9i	1.30709	+	1.81621i
$547$	−2.16234e9	+	5.22035e9i	−0.564896	+	1.36378i	0.340914	+	0.940095i	$0.389264\pi$
$547$	−2.16234e9	+	5.22035e9i	−0.564896	+	1.36378i	−0.905810	+	0.423685i	$0.860736\pi$
$548$	−1.50698e9	+	7.50818e8i	−0.391179	+	0.194896i
$549$	−7.63158e7	+	3.16110e7i	−0.0196839	+	0.00815334i
$550$	−2.86214e9	+	6.73516e8i	−0.733536	+	0.172615i
$551$	−5.35600e8	+	5.35600e8i	−0.136399	+	0.136399i
$552$	−5.99876e9	−	7.21898e9i	−1.51801	−	1.82679i
$553$	−2.47433e9	−	2.47433e9i	−0.622185	−	0.622185i
$554$	−2.25788e9	−	1.39766e9i	−0.564179	−	0.349235i
$555$	2.49390e9	+	6.02082e9i	0.619234	+	1.49496i
$556$	−4.21801e9	+	2.93748e8i	−1.04075	+	0.0724792i
$557$	4.36275e9	+	1.80711e9i	1.06971	+	0.443089i	0.846889	−	0.531770i	$-0.178473\pi$
$557$	4.36275e9	+	1.80711e9i	1.06971	+	0.443089i	0.222823	+	0.974859i	$0.428473\pi$
$558$	−8.87614e9	−	1.44687e9i	−2.16274	−	0.352540i
$559$		−	4.11619e9i		−	0.996676i
$560$	−6.61861e9	+	3.89359e9i	−1.59261	+	0.936898i
$561$		−	6.59496e8i		−	0.157704i
$562$	−4.54287e8	+	2.78693e9i	−0.107958	+	0.662292i
$563$	−2.89292e8	−	1.19829e8i	−0.0683214	−	0.0282997i	0.348261	−	0.937398i	$-0.386772\pi$
$563$	−2.89292e8	−	1.19829e8i	−0.0683214	−	0.0282997i	−0.416582	+	0.909098i	$0.636772\pi$
$564$	2.16247e7	−	2.48621e7i	0.00507543	−	0.00583527i
$565$	3.11370e9	+	7.51714e9i	0.726286	+	1.75341i
$566$	−1.99948e8	+	3.23009e8i	−0.0463510	+	0.0748786i
$567$	−7.63857e9	−	7.63857e9i	−1.75983	−	1.75983i
$568$	−4.40696e9	−	2.32101e9i	−1.00907	−	0.531445i
$569$	2.75173e9	−	2.75173e9i	0.626201	−	0.626201i	−0.320909	−	0.947110i	$-0.603988\pi$
$569$	2.75173e9	−	2.75173e9i	0.626201	−	0.626201i	0.947110	+	0.320909i	$0.103988\pi$
$570$	1.07811e9	+	4.58148e9i	0.243837	+	1.03620i
$571$	−2.71716e9	+	1.12548e9i	−0.610785	+	0.252996i	−0.666564	−	0.745448i	$-0.732236\pi$
$571$	−2.71716e9	+	1.12548e9i	−0.610785	+	0.252996i	0.0557789	+	0.998443i	$0.482236\pi$
$572$	4.65765e9	+	1.55990e9i	1.04059	+	0.348506i
$573$	5.49521e9	−	1.32666e10i	1.22023	−	2.94590i
$574$	2.12588e7	−	1.52996e7i	0.00469189	−	0.00337666i
$575$	3.52314e9			0.772845
$576$	9.99223e9	+	1.86076e9i	2.17863	+	0.405706i
$577$	4.34556e9			0.941739			0.470869	−	0.882203i	$-0.343940\pi$
$577$	4.34556e9			0.941739			0.470869	+	0.882203i	$0.343940\pi$
$578$	−3.75061e9	+	2.69924e9i	−0.807893	+	0.581426i
$579$	−3.49072e9	+	8.42735e9i	−0.747378	+	1.80433i
$580$	−2.29287e9	−	7.67908e8i	−0.487957	−	0.163422i
$581$	−8.79212e9	+	3.64181e9i	−1.85985	+	0.770373i
$582$	1.89387e9	+	8.04809e9i	0.398216	+	1.69224i
$583$	−3.02532e9	+	3.02532e9i	−0.632312	+	0.632312i
$584$	−3.33393e9	+	6.33020e9i	−0.692646	+	1.31514i
$585$	8.11386e9	+	8.11386e9i	1.67564	+	1.67564i
$586$	8.98035e7	−	1.45075e8i	0.0184354	−	0.0297818i
$587$	−2.31408e9	−	5.58667e9i	−0.472220	−	1.14004i	−0.963180	−	0.268857i	$-0.913354\pi$
$587$	−2.31408e9	−	5.58667e9i	−0.472220	−	1.14004i	0.490960	−	0.871182i	$-0.336646\pi$
$588$	6.70734e9	−	7.71148e9i	1.36060	−	1.56429i
$589$	−2.13699e9	−	8.85170e8i	−0.430922	−	0.178494i
$590$	1.32081e9	−	8.10284e9i	0.264764	−	1.62426i
$591$			3.84550e9i			0.766295i
$592$	3.50383e9	+	9.08275e8i	0.694091	+	0.179925i
$593$		−	2.25871e9i		−	0.444805i	−0.974955	−	0.222402i	$-0.928610\pi$
$593$		−	2.25871e9i		−	0.444805i	0.974955	−	0.222402i	$-0.0713898\pi$
$594$	−1.41988e10	−	2.31450e9i	−2.77971	−	0.453110i
$595$	5.97281e8	+	2.47402e8i	0.116244	+	0.0481497i
$596$	4.43803e9	−	3.09070e8i	0.858673	−	0.0597992i
$597$	−1.18566e9	−	2.86243e9i	−0.228060	−	0.550585i
$598$	−5.00435e9	−	3.09777e9i	−0.956959	−	0.592372i
$599$	−3.88497e9	−	3.88497e9i	−0.738574	−	0.738574i	0.233728	−	0.972302i	$-0.424908\pi$
$599$	−3.88497e9	−	3.88497e9i	−0.738574	−	0.738574i	−0.972302	+	0.233728i	$0.924908\pi$
$600$	−4.25836e9	+	3.53857e9i	−0.804846	+	0.668803i
$601$	6.48422e9	−	6.48422e9i	1.21842	−	1.21842i	0.250235	−	0.968185i	$-0.419492\pi$
$601$	6.48422e9	−	6.48422e9i	1.21842	−	1.21842i	0.968185	−	0.250235i	$-0.0805079\pi$
$602$	−8.97368e9	+	2.11168e9i	−1.67642	+	0.394493i
$603$	−7.12338e9	+	2.95060e9i	−1.32305	+	0.548025i
$604$	5.81460e9	−	2.89699e9i	1.07372	−	0.534955i
$605$	1.75153e9	−	4.22856e9i	0.321568	−	0.776334i
$606$	−1.53340e8	−	2.13066e8i	−0.0279898	−	0.0388920i
$607$	−2.45401e9			−0.445365			−0.222683	−	0.974891i	$-0.571481\pi$
$607$	−2.45401e9			−0.445365			−0.222683	+	0.974891i	$0.571481\pi$
$608$	2.39203e9	+	1.05455e9i	0.431622	+	0.190284i
$609$	6.00218e9			1.07683
$610$	−3.96177e7	−	5.50489e7i	−0.00706699	−	0.00981961i
$611$	7.90691e6	−	1.90890e7i	0.00140237	−	0.00338562i
$612$	−3.81599e8	−	7.65914e8i	−0.0672942	−	0.135067i
$613$	−1.97453e9	+	8.17877e8i	−0.346220	+	0.143409i	−0.549016	−	0.835812i	$-0.684997\pi$
$613$	−1.97453e9	+	8.17877e8i	−0.346220	+	0.143409i	0.202796	+	0.979221i	$0.434997\pi$
$614$	9.49184e9	−	2.23361e9i	1.65486	−	0.389420i
$615$	3.62383e7	−	3.62383e7i	0.00628211	−	0.00628211i
$616$	1.01127e9	−	1.09544e10i	0.174315	−	1.88823i
$617$	−3.30459e9	−	3.30459e9i	−0.566395	−	0.566395i	0.364722	−	0.931117i	$-0.381164\pi$
$617$	−3.30459e9	−	3.30459e9i	−0.566395	−	0.566395i	−0.931117	+	0.364722i	$0.881164\pi$
$618$	−3.66713e9	−	2.27001e9i	−0.624982	−	0.386873i
$619$	−1.41702e8	−	3.42098e8i	−0.0240136	−	0.0579741i	0.911418	−	0.411482i	$-0.134989\pi$
$619$	−1.41702e8	−	3.42098e8i	−0.0240136	−	0.0579741i	−0.935432	+	0.353508i	$0.884989\pi$
$620$	−5.12994e8	−	7.36623e9i	−0.0864453	−	1.24129i
$621$	1.59257e10	+	6.59663e9i	2.66856	+	1.10535i
$622$	1.12353e10	+	1.83142e9i	1.87205	+	0.305155i
$623$			2.47291e9i			0.409733i
$624$	9.16000e9	−	1.28205e9i	1.50921	−	0.211231i
$625$			7.58682e9i			1.24302i
$626$	−1.63623e8	+	1.00378e9i	−0.0266584	+	0.163542i
$627$	−6.22950e9	−	2.58034e9i	−1.00929	−	0.418063i
$628$	−5.62482e8	−	4.89239e8i	−0.0906253	−	0.0788246i
$629$	−1.16618e8	−	2.81542e8i	−0.0186849	−	0.0451092i
$630$	1.35264e10	−	2.18515e10i	2.15522	−	3.48169i
$631$	4.63798e9	+	4.63798e9i	0.734896	+	0.734896i	0.971585	−	0.236689i	$-0.0760623\pi$
$631$	4.63798e9	+	4.63798e9i	0.734896	+	0.734896i	−0.236689	+	0.971585i	$0.576062\pi$
$632$	−3.63232e9	+	1.12617e9i	−0.572366	+	0.177457i
$633$	−1.21249e10	+	1.21249e10i	−1.90004	+	1.90004i
$634$	−1.90826e9	−	8.10925e9i	−0.297389	−	1.26377i
$635$	6.41117e9	−	2.65559e9i	0.993640	−	0.411579i
$636$	−2.55851e9	+	7.63938e9i	−0.394356	+	1.17749i
$637$	2.45249e9	−	5.92083e9i	0.375940	−	0.907600i
$638$	2.81168e9	−	2.02351e9i	0.428641	−	0.308485i
$639$	1.66694e10			2.52736
$640$	3.92104e8	+	8.33609e9i	0.0591250	+	1.25699i
$641$	−6.57434e9			−0.985936			−0.492968	−	0.870047i	$-0.664088\pi$
$641$	−6.57434e9			−0.985936			−0.492968	+	0.870047i	$0.664088\pi$
$642$	1.90586e10	−	1.37161e10i	2.84262	−	2.04578i
$643$	−1.25084e9	+	3.01980e9i	−0.185552	+	0.447961i	−0.989094	−	0.147286i	$-0.952946\pi$
$643$	−1.25084e9	+	3.01980e9i	−0.185552	+	0.447961i	0.803542	+	0.595248i	$0.202946\pi$
$644$	−4.18611e9	+	1.24992e10i	−0.617603	+	1.84408i
$645$	−1.66650e10	+	6.90288e9i	−2.44538	+	1.01291i
$646$	−5.04138e7	−	2.14236e8i	−0.00735759	−	0.0312665i
$647$	−1.50159e9	+	1.50159e9i	−0.217965	+	0.217965i	−0.807640	−	0.589675i	$-0.799256\pi$
$647$	−1.50159e9	+	1.50159e9i	−0.217965	+	0.217965i	0.589675	+	0.807640i	$0.299256\pi$
$648$	−1.12134e10	+	3.47662e9i	−1.61892	+	0.501932i
$649$	8.31660e9	+	8.31660e9i	1.19423	+	1.19423i
$650$	−1.82732e9	+	2.95198e9i	−0.260987	+	0.421616i
$651$	7.01423e9	+	1.69339e10i	0.996430	+	2.40559i
$652$	7.78633e9	+	6.77243e9i	1.10019	+	0.956926i
$653$	−4.65272e9	−	1.92722e9i	−0.653899	−	0.270854i	0.0309697	−	0.999520i	$-0.490140\pi$
$653$	−4.65272e9	−	1.92722e9i	−0.653899	−	0.270854i	−0.684869	+	0.728666i	$0.740140\pi$
$654$	−8.09078e7	+	4.96348e8i	−0.0113102	+	0.0693848i
$655$			4.63739e9i			0.644806i
$656$	−3.94552e6	−	2.81900e7i	−0.000545683	−	0.00389881i
$657$		−	2.39441e10i		−	3.29397i
$658$	−4.56721e7	−	7.44484e6i	−0.00624972	−	0.00101874i
$659$	−7.26621e9	−	3.00976e9i	−0.989029	−	0.409669i	−0.171267	−	0.985225i	$-0.554786\pi$
$659$	−7.26621e9	−	3.00976e9i	−0.989029	−	0.409669i	−0.817763	+	0.575555i	$0.804786\pi$
$660$	−1.49542e9	−	2.14732e10i	−0.202469	−	2.90732i
$661$	−4.80936e9	−	1.16108e10i	−0.647712	−	1.56371i	−0.816047	−	0.577985i	$-0.803839\pi$
$661$	−4.80936e9	−	1.16108e10i	−0.647712	−	1.56371i	0.168336	−	0.985730i	$-0.446161\pi$
$662$	−6.01563e9	−	3.72377e9i	−0.805895	−	0.498861i
$663$	−5.50625e8	−	5.50625e8i	−0.0733767	−	0.0733767i
$664$	−9.50730e8	+	1.02986e10i	−0.126029	+	1.36517i
$665$	4.67385e9	−	4.67385e9i	0.616309	−	0.616309i
$666$	−1.17918e10	+	2.77484e9i	−1.54676	+	0.363981i
$667$	−3.83481e9	+	1.58843e9i	−0.500384	+	0.207266i
$668$	7.65730e8	+	1.53691e9i	0.0993935	+	0.199494i
$669$	−7.79597e9	+	1.88211e10i	−1.00665	+	2.43027i
$670$	−3.69795e9	−	5.13831e9i	−0.475006	−	0.660023i
$671$	9.71639e7			0.0124158
$672$	−7.49422e9	−	1.93120e10i	−0.952652	−	2.45490i
$673$	−1.12540e10			−1.42316			−0.711580	−	0.702605i	$-0.752020\pi$
$673$	−1.12540e10			−1.42316			−0.711580	+	0.702605i	$0.752020\pi$
$674$	5.24270e9	+	7.28475e9i	0.659546	+	0.916442i
$675$	3.89124e9	−	9.39429e9i	0.486996	−	1.17571i
$676$	−1.99782e9	+	9.95369e8i	−0.248739	+	0.123928i
$677$	1.45115e10	−	6.01085e9i	1.79743	−	0.744518i	0.810001	−	0.586428i	$-0.199466\pi$
$677$	1.45115e10	−	6.01085e9i	1.79743	−	0.744518i	0.987425	−	0.158090i	$-0.0505337\pi$
$678$	−2.13658e10	+	5.02778e9i	−2.63279	+	0.619545i
$679$	8.21035e9	−	8.21035e9i	1.00651	−	1.00651i
$680$	5.40375e8	−	4.49036e8i	0.0659044	−	0.0547646i
$681$	−1.80628e10	−	1.80628e10i	−2.19164	−	2.19164i
$682$	8.99468e9	+	5.56784e9i	1.08578	+	0.672112i
$683$	3.67123e9	+	8.86314e9i	0.440899	+	1.06443i	0.975634	+	0.219405i	$0.0704116\pi$
$683$	3.67123e9	+	8.86314e9i	0.440899	+	1.06443i	−0.534735	+	0.845020i	$0.679588\pi$
$684$	−8.72777e9	+	6.07813e8i	−1.04281	+	0.0726230i
$685$	4.27433e9	+	1.77048e9i	0.508102	+	0.210463i
$686$	−1.91234e9	−	3.11724e8i	−0.226168	−	0.0368668i
$687$		−	8.38129e9i		−	0.986194i
$688$	−2.51402e9	+	9.69824e9i	−0.294312	+	1.13536i
$689$			5.05178e9i			0.588407i
$690$	−4.14946e9	+	2.54558e10i	−0.480861	+	2.94996i
$691$	−6.29502e9	−	2.60748e9i	−0.725812	−	0.300641i	−0.0109822	−	0.999940i	$-0.503496\pi$
$691$	−6.29502e9	−	2.60748e9i	−0.725812	−	0.300641i	−0.714830	+	0.699299i	$0.753496\pi$
$692$	−2.98405e9	+	3.43079e9i	−0.342322	+	0.393570i
$693$	1.40893e10	+	3.40146e10i	1.60814	+	3.88239i
$694$	3.41288e9	−	5.51341e9i	0.387582	−	0.626126i
$695$	8.21562e9	+	8.21562e9i	0.928311	+	0.928311i
$696$	3.03968e9	−	5.77152e9i	0.341740	−	0.648870i
$697$	−1.69455e6	+	1.69455e6i	−0.000189557	+	0.000189557i
$698$	−1.64164e8	−	6.97624e8i	−0.0182719	−	0.0776475i
$699$	−1.90209e9	+	7.87871e8i	−0.210650	+	0.0872539i
$700$	7.37305e9	+	2.46932e9i	0.812463	+	0.272103i
$701$	−3.27667e9	+	7.91057e9i	−0.359268	+	0.867351i	0.636135	+	0.771578i	$0.280532\pi$
$701$	−3.27667e9	+	7.91057e9i	−0.359268	+	0.867351i	−0.995403	+	0.0957728i	$0.969468\pi$
$702$	−1.37873e10	+	9.92244e9i	−1.50417	+	1.08253i
$703$	−3.11568e9			−0.338228
$704$	−1.00213e10	−	6.52003e9i	−1.08247	−	0.704280i
$705$	−9.05446e7			−0.00973196
$706$	9.90429e9	−	7.12793e9i	1.05927	−	0.762337i
$707$	−1.41079e8	+	3.40594e8i	−0.0150139	+	0.0362468i
$708$	2.10007e10	+	7.03336e9i	2.22391	+	0.744811i
$709$	9.81732e9	−	4.06647e9i	1.03450	−	0.428504i	0.200166	−	0.979762i	$-0.435852\pi$
$709$	9.81732e9	−	4.06647e9i	1.03450	−	0.428504i	0.834335	+	0.551258i	$0.185852\pi$
$710$	3.13509e9	+	1.33227e10i	0.328735	+	1.39698i
$711$	8.99951e9	−	8.99951e9i	0.939021	−	0.939021i
$712$	2.37788e9	+	1.25236e9i	0.246894	+	0.130031i
$713$	−8.96283e9	−	8.96283e9i	−0.926045	−	0.926045i
$714$	−9.17934e8	+	1.48289e9i	−0.0943773	+	0.152464i
$715$	−5.16521e9	−	1.24699e10i	−0.528466	−	1.27583i
$716$	3.59542e9	−	4.13369e9i	0.366062	−	0.420864i
$717$	6.46281e9	+	2.67698e9i	0.654794	+	0.271224i
$718$	−1.58525e8	+	9.72507e8i	−0.0159831	+	0.0980522i
$719$		−	7.53894e9i		−	0.756413i	−0.925721	−	0.378207i	$-0.876541\pi$
$719$		−	7.53894e9i		−	0.756413i	0.925721	−	0.378207i	$-0.123459\pi$
$720$	−1.41616e10	−	2.40729e10i	−1.41400	−	2.40361i
$721$			6.05685e9i			0.601829i
$722$	7.76037e9	+	1.26499e9i	0.767366	+	0.125085i
$723$	2.48747e10	+	1.03034e10i	2.44779	+	1.01391i
$724$	−1.93220e10	+	1.34561e9i	−1.89220	+	0.131776i
$725$	9.36990e8	+	2.26209e9i	0.0913170	+	0.220459i
$726$	1.04984e10	+	6.49868e9i	1.01823	+	0.630299i
$727$	6.85089e9	+	6.85089e9i	0.661267	+	0.661267i	0.955679	−	0.294412i	$-0.0951237\pi$
$727$	6.85089e9	+	6.85089e9i	0.661267	+	0.661267i	−0.294412	+	0.955679i	$0.595124\pi$
$728$	−8.30166e9	−	9.99032e9i	−0.797453	−	0.959665i
$729$	−1.14563e9	+	1.14563e9i	−0.109521	+	0.109521i
$730$	1.91369e10	−	4.50327e9i	1.82071	−	0.428448i
$731$	7.79279e8	−	3.22788e8i	0.0737874	−	0.0305638i
$732$	1.63763e8	−	8.15909e7i	0.0154321	−	0.00768870i
$733$	4.08063e9	−	9.85151e9i	0.382704	−	0.923930i	−0.608737	−	0.793372i	$-0.708323\pi$
$733$	4.08063e9	−	9.85151e9i	0.382704	−	0.923930i	0.991441	−	0.130557i	$-0.0416767\pi$
$734$	5.93702e9	+	8.24952e9i	0.554157	+	0.770003i
$735$	−2.80842e10			−2.60890
$736$	9.89884e9	+	1.03552e10i	0.915192	+	0.957382i
$737$	9.06937e9			0.834528
$738$	5.56469e7	+	7.73216e7i	0.00509617	+	0.00708114i
$739$	−4.82296e9	+	1.16437e10i	−0.439601	+	1.06129i	0.536486	+	0.843909i	$0.319751\pi$
$739$	−4.82296e9	+	1.16437e10i	−0.439601	+	1.06129i	−0.976087	+	0.217381i	$0.930249\pi$
$740$	−4.43549e9	−	8.90256e9i	−0.402375	−	0.807614i
$741$	−7.35550e9	+	3.04675e9i	−0.664123	+	0.275089i
$742$	1.10134e10	−	2.59165e9i	0.989706	−	0.232897i
$743$	6.48390e9	−	6.48390e9i	0.579930	−	0.579930i	−0.354954	−	0.934884i	$-0.615503\pi$
$743$	6.48390e9	−	6.48390e9i	0.579930	−	0.579930i	0.934884	+	0.354954i	$0.115503\pi$
$744$	1.98353e10	+	1.83113e9i	1.76577	+	0.163010i
$745$	−8.64416e9	−	8.64416e9i	−0.765906	−	0.765906i
$746$	−1.21121e9	−	7.49755e8i	−0.106815	−	0.0661201i
$747$	−1.32458e10	−	3.19783e10i	−1.16267	−	2.80694i
$748$	6.99279e7	+	1.00411e9i	0.00610935	+	0.0877258i
$749$	−3.04660e10	−	1.26194e10i	−2.64928	−	1.09737i
$750$	−1.07173e10	−	1.74699e9i	−0.927625	−	0.151209i
$751$			1.29550e10i			1.11608i	0.829813	+	0.558041i	$0.188447\pi$
$751$			1.29550e10i			1.11608i	−0.829813	+	0.558041i	$0.811553\pi$
$752$	−3.02885e7	+	4.01467e7i	−0.00259726	+	0.00344260i
$753$			1.05857e10i			0.903519i
$754$	6.58054e8	−	4.03699e9i	0.0559064	−	0.342971i
$755$	−1.64922e10	−	6.83131e9i	−1.39465	−	0.577683i
$756$	2.87050e10	+	2.49672e10i	2.41619	+	2.10157i
$757$	7.82016e9	+	1.88795e10i	0.655209	+	1.58182i	0.805117	+	0.593116i	$0.202102\pi$
$757$	7.82016e9	+	1.88795e10i	0.655209	+	1.58182i	−0.149908	+	0.988700i	$0.547898\pi$
$758$	−8.19317e9	+	1.32358e10i	−0.683297	+	1.10385i
$759$	−2.61274e10	−	2.61274e10i	−2.16895	−	2.16895i
$760$	−2.12726e9	−	6.86121e9i	−0.175781	−	0.566961i
$761$	4.89046e7	−	4.89046e7i	0.00402257	−	0.00402257i	−0.705093	−	0.709115i	$-0.749095\pi$
$761$	4.89046e7	−	4.89046e7i	0.00402257	−	0.00402257i	0.709115	+	0.705093i	$0.249095\pi$
$762$	4.28806e9	+	1.82223e10i	0.351090	+	1.49198i
$763$	6.52495e8	−	2.70272e8i	0.0531791	−	0.0220275i
$764$	−6.96003e9	+	2.07817e10i	−0.564657	+	1.68599i
$765$	−8.99838e8	+	2.17240e9i	−0.0726690	+	0.175439i
$766$	−3.82260e9	+	2.75106e9i	−0.307297	+	0.221156i
$767$	1.38874e10			1.11131
$768$	−2.23651e10	−	2.57393e9i	−1.78158	−	0.205037i
$769$	1.01395e10			0.804031			0.402015	−	0.915633i	$-0.368310\pi$
$769$	1.01395e10			0.804031			0.402015	+	0.915633i	$0.368310\pi$
$770$	−2.45358e10	+	1.76579e10i	−1.93679	+	1.39387i
$771$	1.22049e10	−	2.94652e10i	0.959054	−	2.31536i
$772$	4.42122e9	−	1.32012e10i	0.345845	−	1.03265i
$773$	1.35459e10	−	5.61090e9i	1.05482	−	0.436923i	0.213213	−	0.977006i	$-0.431607\pi$
$773$	1.35459e10	−	5.61090e9i	1.05482	−	0.436923i	0.841612	+	0.540083i	$0.181607\pi$
$774$	−7.68049e9	−	3.26386e10i	−0.595382	−	2.53011i
$775$	−5.28703e9	+	5.28703e9i	−0.407996	+	0.407996i
$776$	−3.73686e9	−	1.20528e10i	−0.287072	−	0.925917i
$777$	1.74579e10	+	1.74579e10i	1.33511	+	1.33511i
$778$	5.15601e9	−	8.32937e9i	0.392541	−	0.634138i
$779$	9.37640e6	+	2.26366e7i	0.000710649	+	0.00171566i
$780$	−1.91769e10	−	1.66798e10i	−1.44693	−	1.25852i
$781$	−1.81151e10	−	7.50353e9i	−1.36070	−	0.563621i
$782$	1.94034e8	−	1.19035e9i	0.0145096	−	0.0890125i
$783$			1.19798e10i			0.891829i
$784$	−9.39458e9	+	1.24523e10i	−0.696259	+	0.922876i
$785$			2.04849e9i			0.151143i
$786$	−1.23471e10	−	2.01265e9i	−0.906955	−	0.147839i
$787$	4.62228e9	+	1.91461e9i	0.338022	+	0.140013i	0.545236	−	0.838282i	$-0.316440\pi$
$787$	4.62228e9	+	1.91461e9i	0.338022	+	0.140013i	−0.207215	+	0.978295i	$0.566440\pi$
$788$	−4.07747e8	−	5.85496e9i	−0.0296858	−	0.426267i
$789$	−1.55698e10	−	3.75889e10i	−1.12853	−	2.72452i
$790$	8.88529e9	+	5.50013e9i	0.641176	+	0.396897i
$791$	2.17966e10	+	2.17966e10i	1.56593	+	1.56593i
$792$	3.98427e10	+	3.67815e9i	2.84977	+	0.263082i
$793$	8.11239e7	−	8.11239e7i	0.00577687	−	0.00577687i
$794$	−2.87844e9	+	6.77350e8i	−0.204073	+	0.0480222i
$795$	2.04529e10	−	8.47188e9i	1.44368	−	0.597991i
$796$	2.10873e9	+	4.23247e9i	0.148192	+	0.297439i
$797$	−3.58304e9	+	8.65021e9i	−0.250696	+	0.605233i	−0.998261	−	0.0589557i	$-0.981223\pi$
$797$	−3.58304e9	+	8.65021e9i	−0.250696	+	0.605233i	0.747565	+	0.664189i	$0.231223\pi$
$798$	1.04157e10	+	1.44726e10i	0.725568	+	1.00818i
$799$	4.23399e6			0.000293654
$800$	6.10835e9	−	5.83917e9i	0.421802	−	0.403214i
$801$	−8.99436e9			−0.618381
$802$	−9.94894e9	−	1.38241e10i	−0.681030	−	0.946294i
$803$	−1.07781e10	+	2.60207e10i	−0.734581	+	1.77343i
$804$	1.52857e10	−	7.61577e9i	1.03727	−	0.516794i
$805$	3.34640e10	−	1.38612e10i	2.26096	−	0.936519i
$806$	1.21585e10	−	2.86113e9i	0.817914	−	0.192471i
$807$	−8.77044e9	+	8.77044e9i	−0.587441	+	0.587441i
$808$	2.56059e8	+	3.08144e8i	0.0170766	+	0.0205501i
$809$	−1.64357e10	−	1.64357e10i	−1.09136	−	1.09136i	−0.995384	−	0.0959765i	$-0.969403\pi$
$809$	−1.64357e10	−	1.64357e10i	−1.09136	−	1.09136i	−0.0959765	−	0.995384i	$-0.530597\pi$
$810$	2.74300e10	+	1.69796e10i	1.81355	+	1.12261i
$811$	−7.45997e8	−	1.80100e9i	−0.0491094	−	0.118560i	0.897421	−	0.441175i	$-0.145438\pi$
$811$	−7.45997e8	−	1.80100e9i	−0.0491094	−	0.118560i	−0.946530	+	0.322615i	$0.895438\pi$
$812$	−9.13861e9	+	6.36425e8i	−0.599010	+	0.0417159i
$813$	3.64616e10	+	1.51029e10i	2.37968	+	0.985697i
$814$	1.40636e10	+	2.29245e9i	0.913927	+	0.148976i
$815$		−	2.83568e10i		−	1.83487i
$816$	9.61037e8	+	1.63364e9i	0.0619191	+	0.105254i
$817$		−	8.62390e9i		−	0.553257i
$818$	2.82390e9	−	1.73239e10i	0.180390	−	1.10665i
$819$	4.01628e10	+	1.66360e10i	2.55464	+	1.05817i
$820$	−5.13322e7	+	5.90171e7i	−0.00325118	+	0.00373791i
$821$	−5.41521e9	−	1.30735e10i	−0.341518	−	0.824498i	−0.997563	−	0.0697758i	$-0.977772\pi$
$821$	−5.41521e9	−	1.30735e10i	−0.341518	−	0.824498i	0.656044	−	0.754722i	$-0.272228\pi$
$822$	−6.56901e9	+	1.06120e10i	−0.412524	+	0.666419i
$823$	1.59714e9	+	1.59714e9i	0.0998722	+	0.0998722i	0.755277	−	0.655405i	$-0.227502\pi$
$823$	1.59714e9	+	1.59714e9i	0.0998722	+	0.0998722i	−0.655405	+	0.755277i	$0.727502\pi$
$824$	5.82409e9	+	3.06737e9i	0.362646	+	0.190995i
$825$	−1.54121e10	+	1.54121e10i	−0.955594	+	0.955594i
$826$	−7.12445e9	−	3.02757e10i	−0.439867	−	1.86924i
$827$	5.50061e9	−	2.27843e9i	0.338175	−	0.140077i	−0.207132	−	0.978313i	$-0.566413\pi$
$827$	5.50061e9	−	2.27843e9i	0.338175	−	0.140077i	0.545307	+	0.838236i	$0.316413\pi$
$828$	−4.54613e10	−	1.52255e10i	−2.78314	−	0.932106i
$829$	−1.00363e10	+	2.42298e10i	−0.611834	+	1.47710i	0.249149	+	0.968465i	$0.419849\pi$
$829$	−1.00363e10	+	2.42298e10i	−0.611834	+	1.47710i	−0.860983	+	0.508634i	$0.830151\pi$
$830$	2.30669e10	−	1.66008e10i	1.40028	−	1.00776i
$831$	−1.96845e10			−1.18993
$832$	−1.38106e10	+	2.92324e9i	−0.831345	+	0.175967i
$833$	1.31326e9			0.0787213
$834$	−2.54398e10	+	1.83086e10i	−1.51856	+	1.09288i
$835$	1.80565e9	−	4.35922e9i	0.107332	−	0.259123i
$836$	9.75832e9	+	3.26817e9i	0.577635	+	0.193456i
$837$	−3.37983e10	+	1.39997e10i	−1.99230	+	0.825239i
$838$	−3.19972e9	−	1.35974e10i	−0.187827	−	0.798181i
$839$	4.12464e9	−	4.12464e9i	0.241112	−	0.241112i	−0.576198	−	0.817310i	$-0.695464\pi$
$839$	4.12464e9	−	4.12464e9i	0.241112	−	0.241112i	0.817310	+	0.576198i	$0.195464\pi$
$840$	−2.65254e10	+	5.03644e10i	−1.54413	+	2.93188i
$841$	1.01577e10	+	1.01577e10i	0.588859	+	0.588859i
$842$	−1.71040e10	+	2.76309e10i	−0.987425	+	1.59515i
$843$	8.01021e9	+	1.93383e10i	0.460519	+	1.11179i
$844$	1.71751e10	−	1.97463e10i	0.983331	−	1.13054i
$845$	5.66653e9	+	2.34715e9i	0.323086	+	0.133827i
$846$	2.70780e7	−	1.66116e8i	0.00153752	−	0.00943227i
$847$		−	1.73398e10i		−	0.980509i
$848$	3.08544e9	−	1.19026e10i	0.173753	−	0.670281i
$849$			2.81603e9i			0.157929i
$850$	−7.02168e8	−	1.14458e8i	−0.0392170	−	0.00639262i
$851$	−1.57740e10	−	6.53381e9i	−0.877381	−	0.363423i
$852$	−3.68326e10	+	2.56507e9i	−2.04030	+	0.142089i
$853$	−8.85763e9	−	2.13842e10i	−0.488648	−	1.17970i	−0.955401	−	0.295312i	$-0.904576\pi$
$853$	−8.85763e9	−	2.13842e10i	−0.488648	−	1.17970i	0.466753	−	0.884388i	$-0.345424\pi$
$854$	−2.18476e8	−	1.35240e8i	−0.0120033	−	0.00743022i
$855$	1.69995e10	+	1.69995e10i	0.930153	+	0.930153i
$856$	−2.75633e10	+	2.29043e10i	−1.50201	+	1.24813i
$857$	5.55989e9	−	5.55989e9i	0.301740	−	0.301740i	−0.539954	−	0.841694i	$-0.681558\pi$
$857$	5.55989e9	−	5.55989e9i	0.301740	−	0.301740i	0.841694	+	0.539954i	$0.181558\pi$
$858$	3.54430e10	−	8.34042e9i	1.91569	−	0.450798i
$859$	−2.22047e10	+	9.19750e9i	−1.19528	+	0.495101i	−0.889471	−	0.456992i	$-0.848927\pi$
$859$	−2.22047e10	+	9.19750e9i	−1.19528	+	0.495101i	−0.305808	+	0.952093i	$0.598927\pi$
$860$	2.46414e10	−	1.22770e10i	1.32105	−	0.658185i
$861$	7.43001e7	−	1.79376e8i	0.00396715	−	0.00957755i
$862$	−1.33253e10	−	1.85155e10i	−0.708598	−	0.984600i
$863$	7.02476e9			0.372043			0.186022	−	0.982546i	$-0.440441\pi$
$863$	7.02476e9			0.372043			0.186022	+	0.982546i	$0.440441\pi$
$864$	3.85447e10	−	1.49577e10i	2.03314	−	0.788982i
$865$	1.24945e10			0.656390
$866$	−8.38702e9	−	1.16538e10i	−0.438829	−	0.609754i
$867$	−1.31085e10	+	3.16466e10i	−0.683101	+	1.64915i
$868$	−1.24750e10	−	2.50389e10i	−0.647475	−	1.29956i
$869$	−1.38311e10	+	5.72901e9i	−0.714968	+	0.296149i
$870$	−1.74479e10	+	4.10583e9i	−0.898311	+	0.211389i
$871$	7.57218e9	−	7.57218e9i	0.388291	−	0.388291i
$872$	7.05571e7	−	7.64293e8i	0.00360357	−	0.0390348i
$873$	2.98623e10	+	2.98623e10i	1.51905	+	1.51905i
$874$	−1.04847e10	−	6.49019e9i	−0.531209	−	0.328827i
$875$	5.83582e9	+	1.40889e10i	0.294492	+	0.710966i
$876$	3.68449e9	+	5.29067e10i	0.185188	+	2.65917i
$877$	−2.65157e10	−	1.09831e10i	−1.32741	−	0.549829i	−0.397492	−	0.917606i	$-0.630119\pi$
$877$	−2.65157e10	−	1.09831e10i	−1.32741	−	0.549829i	−0.929914	+	0.367776i	$0.880119\pi$
$878$	−1.63559e10	−	2.66611e9i	−0.815535	−	0.132937i
$879$		−	1.26478e9i		−	0.0628136i
$880$	4.55370e9	+	3.25354e10i	0.225255	+	1.60941i
$881$			2.34668e10i			1.15621i	0.815961	+	0.578107i	$0.196208\pi$
$881$			2.34668e10i			1.15621i	−0.815961	+	0.578107i	$0.803792\pi$
$882$	8.39879e9	−	5.15244e10i	0.412170	−	2.52856i
$883$	−3.08297e9	−	1.27701e9i	−0.150698	−	0.0624210i	0.306060	−	0.952012i	$-0.400989\pi$
$883$	−3.08297e9	−	1.27701e9i	−0.150698	−	0.0624210i	−0.456757	+	0.889591i	$0.650989\pi$
$884$	8.96737e8	+	7.79969e8i	0.0436598	+	0.0379747i
$885$	−2.32892e10	−	5.62251e10i	−1.12941	−	2.72665i
$886$	−1.79274e10	+	2.89611e10i	−0.865963	+	1.39894i
$887$	2.44966e10	+	2.44966e10i	1.17862	+	1.17862i	0.980097	+	0.198521i	$0.0636137\pi$
$887$	2.44966e10	+	2.44966e10i	1.17862	+	1.17862i	0.198521	+	0.980097i	$0.436386\pi$
$888$	2.56282e10	−	7.94579e9i	1.22821	−	0.380795i
$889$	1.85897e10	−	1.85897e10i	0.887395	−	0.887395i
$890$	−1.69161e9	−	7.18859e9i	−0.0804332	−	0.341805i
$891$	−4.26983e10	+	1.76862e10i	−2.02227	+	0.837650i
$892$	9.87410e9	−	2.94827e10i	0.465823	−	1.39088i
$893$	1.65659e7	−	3.99936e7i	0.000778458	−	0.00187936i
$894$	2.67668e10	−	1.92636e10i	1.25290	−	0.901685i
$895$	−1.50544e10			−0.701910
$896$	1.34580e10	+	2.86088e10i	0.625033	+	1.32868i
$897$	−4.36284e10			−2.01835
$898$	7.02365e9	−	5.05479e9i	0.323665	−	0.232936i
$899$	3.37105e9	−	8.13844e9i	0.154741	−	0.373579i
$900$	−8.98128e9	+	2.68169e10i	−0.410667	+	1.22620i
$901$	−9.56407e8	+	3.96157e8i	−0.0435618	+	0.0180439i
$902$	−2.56677e7	−	1.09076e8i	−0.00116457	−	0.00494889i
$903$	−4.83217e10	+	4.83217e10i	−2.18391	+	2.18391i
$904$	3.19974e10	−	9.92052e9i	1.44054	−	0.446627i
$905$	3.76345e10	+	3.76345e10i	1.68778	+	1.68778i
$906$	2.53462e10	−	4.09459e10i	1.13231	−	1.82920i
$907$	−5.81259e9	−	1.40328e10i	−0.258669	−	0.624482i	0.740182	−	0.672406i	$-0.234739\pi$
$907$	−5.81259e9	−	1.40328e10i	−0.258669	−	0.624482i	−0.998851	+	0.0479247i	$0.984739\pi$
$908$	2.94167e10	+	2.55862e10i	1.30405	+	1.13424i
$909$	−1.23879e9	−	5.13125e8i	−0.0547048	−	0.0226595i
$910$	−5.74243e9	+	3.52283e10i	−0.252610	+	1.54970i
$911$		−	4.32012e9i		−	0.189313i	−0.995510	−	0.0946567i	$-0.969825\pi$
$911$		−	4.32012e9i		−	0.189313i	0.995510	−	0.0946567i	$-0.0301753\pi$
$912$	1.91913e10	−	2.68604e9i	0.837765	−	0.117255i
$913$			4.07142e10i			1.77051i
$914$	−7.52726e9	−	1.22699e9i	−0.326081	−	0.0531532i
$915$	−4.64488e8	−	1.92397e8i	−0.0200448	−	0.00830281i
$916$	8.88688e8	+	1.27609e10i	0.0382046	+	0.548590i
$917$	6.72325e9	+	1.62314e10i	0.287930	+	0.695124i
$918$	−2.95971e9	−	1.83210e9i	−0.126270	−	0.0781629i
$919$	−1.05836e10	−	1.05836e10i	−0.449812	−	0.449812i	0.445480	−	0.895292i	$-0.353033\pi$
$919$	−1.05836e10	−	1.05836e10i	−0.449812	−	0.449812i	−0.895292	+	0.445480i	$0.853033\pi$
$920$	3.61861e9	−	3.91977e10i	0.153209	−	1.65960i
$921$	5.11119e10	−	5.11119e10i	2.15582	−	2.15582i
$922$	−2.06935e10	+	4.86957e9i	−0.869513	+	0.204613i
$923$	−2.13895e10	+	8.85981e9i	−0.895353	+	0.370867i
$924$	−3.63658e10	−	7.29904e10i	−1.51650	−	3.04378i
$925$	−3.85419e9	+	9.30483e9i	−0.160117	+	0.386556i
$926$	1.43054e10	+	1.98774e10i	0.592055	+	0.822663i
$927$	−2.20297e10			−0.908300
$928$	−4.01610e9	+	9.10972e9i	−0.164963	+	0.374186i
$929$	1.65817e10			0.678536			0.339268	−	0.940690i	$-0.389821\pi$
$929$	1.65817e10			0.678536			0.339268	+	0.940690i	$0.389821\pi$
$930$	−3.19736e10	−	4.44275e10i	−1.30347	−	1.81118i
$931$	5.13825e9	−	1.24048e10i	0.208685	−	0.503810i
$932$	2.81248e9	−	1.40126e9i	0.113798	−	0.0566972i
$933$	7.79608e10	−	3.22924e10i	3.14261	−	1.30171i
$934$	−3.12266e10	+	7.34822e9i	−1.25404	+	0.295099i
$935$	1.95576e9	−	1.95576e9i	0.0782484	−	0.0782484i
$936$	3.63363e10	−	3.01944e10i	1.44836	−	1.20354i
$937$	1.60830e10	+	1.60830e10i	0.638674	+	0.638674i	0.950228	−	0.311554i	$-0.100849\pi$
$937$	1.60830e10	+	1.60830e10i	0.638674	+	0.638674i	−0.311554	+	0.950228i	$0.600849\pi$
$938$	−2.03927e10	−	1.26234e10i	−0.806799	−	0.499421i
$939$	2.88508e9	+	6.96519e9i	0.113718	+	0.274538i
$940$	1.37859e8	−	9.60065e6i	0.00541360	−	0.000377010i
$941$	5.14629e9	+	2.13166e9i	0.201340	+	0.0833979i	0.481075	−	0.876679i	$-0.340246\pi$
$941$	5.14629e9	+	2.13166e9i	0.201340	+	0.0833979i	−0.279735	+	0.960077i	$0.590246\pi$
$942$	−5.45412e9	−	8.89055e8i	−0.212592	−	0.0346538i
$943$			1.34267e8i			0.00521409i
$944$	−3.27203e10	−	8.48188e9i	−1.26595	−	0.328163i
$945$		−	1.04540e11i		−	4.02968i
$946$	−6.34529e9	+	3.89267e10i	−0.243687	+	1.49496i
$947$	1.01600e10	+	4.20841e9i	0.388749	+	0.161025i	0.568492	−	0.822689i	$-0.307527\pi$
$947$	1.01600e10	+	4.20841e9i	0.388749	+	0.161025i	−0.179744	+	0.983713i	$0.557527\pi$
$948$	−1.85004e10	+	2.12701e10i	−0.705265	+	0.810850i
$949$	1.27263e10	+	3.07240e10i	0.483360	+	1.16693i
$950$	−3.82846e9	+	6.18475e9i	−0.144874	+	0.234040i
$951$	−4.36669e10	−	4.36669e10i	−1.64634	−	1.64634i
$952$	1.24036e9	−	2.35511e9i	0.0465929	−	0.0884671i
$953$	−1.61580e10	+	1.61580e10i	−0.604730	+	0.604730i	−0.941564	−	0.336834i	$-0.890644\pi$
$953$	−1.61580e10	+	1.61580e10i	−0.604730	+	0.604730i	0.336834	+	0.941564i	$0.390644\pi$
$954$	9.42623e9	+	4.00573e10i	0.351495	+	1.49370i
$955$	5.56389e10	−	2.30464e10i	2.06713	−	0.856232i
$956$	−1.01238e10	−	3.39057e9i	−0.374749	−	0.125508i
$957$	9.82689e9	−	2.37242e10i	0.362430	−	0.874984i
$958$	−7.65309e8	+	5.50779e8i	−0.0281227	+	0.0202394i
$959$	1.75274e10			0.641732
$960$	3.49957e10	+	5.10121e10i	1.27663	+	1.86090i
$961$	−6.12300e8			−0.0222552
$962$	1.36560e10	−	9.82794e9i	0.494549	−	0.355918i
$963$	4.58987e10	−	1.10809e11i	1.65618	−	3.99838i
$964$	−3.89654e10	−	1.30500e10i	−1.40091	−	0.469180i
$965$	−3.53435e10	+	1.46398e10i	−1.26609	+	0.524431i
$966$	2.23821e10	+	9.51141e10i	0.798880	+	3.39489i
$967$	−1.14094e10	+	1.14094e10i	−0.405762	+	0.405762i	−0.880258	−	0.474496i	$-0.842630\pi$
$967$	−1.14094e10	+	1.14094e10i	−0.405762	+	0.405762i	0.474496	+	0.880258i	$0.342630\pi$
$968$	−1.66734e10	−	8.78138e9i	−0.590828	−	0.311171i
$969$	−1.15362e9	−	1.15362e9i	−0.0407316	−	0.0407316i
$970$	−1.82506e10	+	2.94833e10i	−0.642061	+	1.03723i
$971$	−1.40953e10	−	3.40290e10i	−0.494090	−	1.19284i	−0.952621	−	0.304161i	$-0.901624\pi$
$971$	−1.40953e10	−	3.40290e10i	−0.494090	−	1.19284i	0.458530	−	0.888679i	$-0.348376\pi$
$972$	−1.61358e10	+	1.85515e10i	−0.563584	+	0.647958i
$973$	4.06666e10	+	1.68446e10i	1.41528	+	0.586228i
$974$	6.59859e9	−	4.04806e10i	0.228821	−	1.40375i
$975$			2.57357e10i			0.889242i
$976$	−2.40685e8	+	1.41590e8i	−0.00828657	+	0.00487483i
$977$			1.39319e10i			0.477946i	0.971026	+	0.238973i	$0.0768107\pi$
$977$			1.39319e10i			0.477946i	−0.971026	+	0.238973i	$0.923189\pi$
$978$	7.55003e10	+	1.23070e10i	2.58085	+	0.420694i
$979$	9.77443e9	+	4.04870e9i	0.332929	+	0.137904i
$980$	4.27596e10	−	2.97784e9i	1.45125	−	0.101067i
$981$	9.83021e8	+	2.37322e9i	0.0332446	+	0.0802596i
$982$	2.35194e10	+	1.45588e10i	0.792566	+	0.490610i
$983$	−7.46794e9	−	7.46794e9i	−0.250763	−	0.250763i	0.570520	−	0.821283i	$-0.306742\pi$
$983$	−7.46794e9	−	7.46794e9i	−0.250763	−	0.250763i	−0.821283	+	0.570520i	$0.806742\pi$
$984$	−1.34855e8	−	1.62286e8i	−0.00451216	−	0.00542999i
$985$	−1.14040e10	+	1.14040e10i	−0.380215	+	0.380215i
$986$	8.15889e8	−	1.91994e8i	0.0271058	−	0.00637850i
$987$	−3.16916e8	+	1.31271e8i	−0.0104914	+	0.00434569i
$988$	1.08760e10	−	5.41874e9i	0.358775	−	0.178751i
$989$	1.80849e10	−	4.36609e10i	0.594470	−	1.43518i
$990$	−6.42246e10	−	8.92403e10i	−2.10367	−	2.92306i
$991$	−9.19548e9			−0.300135			−0.150067	−	0.988676i	$-0.547949\pi$
$991$	−9.19548e9			−0.300135			−0.150067	+	0.988676i	$0.547949\pi$
$992$	−3.03944e10	−	6.84804e8i	−0.988559	−	0.0222728i
$993$	−5.24450e10			−1.69974
$994$	3.02884e10	+	4.20858e10i	0.978191	+	1.35920i
$995$	4.97254e9	−	1.20048e10i	0.160028	−	0.386343i
$996$	3.41887e10	+	6.86207e10i	1.09641	+	2.20063i
$997$	−6.27893e9	+	2.60082e9i	−0.200656	+	0.0831145i	−0.480748	−	0.876859i	$-0.659635\pi$
$997$	−6.27893e9	+	2.60082e9i	−0.200656	+	0.0831145i	0.280092	+	0.959973i	$0.409635\pi$
$998$	−2.22222e10	+	5.22931e9i	−0.707670	+	0.166528i
$999$	−3.48442e10	+	3.48442e10i	−1.10574	+	1.10574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.6	yes	108
32.5	even	8	inner	32.8.g.a.5.6	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.6	✓	108	32.5	even	8	inner
32.8.g.a.13.6	yes	108	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.18285 + 6.60873i) q^{2} +(-32.0943 + 77.4825i) q^{3} +(40.6495 - 121.374i) q^{4} +(-324.954 + 134.601i) q^{5} +(-217.343 - 923.612i) q^{6} +(-942.234 + 942.234i) q^{7} +(428.849 + 1383.20i) q^{8} +(-3427.05 - 3427.05i) q^{9} +O(q^{10})\)	\(q+(-9.18285 + 6.60873i) q^{2} +(-32.0943 + 77.4825i) q^{3} +(40.6495 - 121.374i) q^{4} +(-324.954 + 134.601i) q^{5} +(-217.343 - 923.612i) q^{6} +(-942.234 + 942.234i) q^{7} +(428.849 + 1383.20i) q^{8} +(-3427.05 - 3427.05i) q^{9} +(2094.47 - 3383.55i) q^{10} +(2181.63 + 5266.92i) q^{11} +(8099.73 + 7045.03i) q^{12} +(6218.92 + 2575.96i) q^{13} +(2425.43 - 14879.4i) q^{14} -29498.2i q^{15} +(-13079.2 - 9867.57i) q^{16} +1379.38i q^{17} +(54118.5 + 8821.65i) q^{18} +(13029.4 + 5396.95i) q^{19} +(3127.76 + 44912.4i) q^{20} +(-42766.3 - 103247. i) q^{21} +(-54841.2 - 33947.5i) q^{22} +(54647.0 + 54647.0i) q^{23} +(-120937. - 11164.5i) q^{24} +(32235.4 - 32235.4i) q^{25} +(-74131.3 + 17444.5i) q^{26} +(206071. - 85357.2i) q^{27} +(76061.3 + 152664. i) q^{28} +(-20553.5 + 49620.7i) q^{29} +(194945. + 270877. i) q^{30} -164013. q^{31} +(185317. + 4175.30i) q^{32} -478112. q^{33} +(-9115.91 - 12666.6i) q^{34} +(179358. - 433008. i) q^{35} +(-555262. + 276646. i) q^{36} +(-204108. + 84544.3i) q^{37} +(-155314. + 36548.3i) q^{38} +(-399184. + 399184. i) q^{39} +(-325536. - 391754. i) q^{40} +(1228.49 + 1228.49i) q^{41} +(1.07505e6 + 665470. i) q^{42} +(-234010. - 564951. i) q^{43} +(727949. - 50695.3i) q^{44} +(1.57492e6 + 652352. i) q^{45} +(-862963. - 140668. i) q^{46} -3069.50i q^{47} +(1.18433e6 - 696719. i) q^{48} -952066. i q^{49} +(-82977.9 + 509048. i) q^{50} +(-106877. - 44270.1i) q^{51} +(565451. - 650104. i) q^{52} +(287200. + 693362. i) q^{53} +(-1.32821e6 + 2.14569e6i) q^{54} +(-1.41786e6 - 1.41786e6i) q^{55} +(-1.70737e6 - 899222. i) q^{56} +(-836338. + 836338. i) q^{57} +(-139189. - 591492. i) q^{58} +(1.90605e6 - 789513. i) q^{59} +(-3.58031e6 - 1.19909e6i) q^{60} +(6522.34 - 15746.3i) q^{61} +(1.50611e6 - 1.08392e6i) q^{62} +6.45816e6 q^{63} +(-1.72933e6 + 1.18637e6i) q^{64} -2.36759e6 q^{65} +(4.39043e6 - 3.15971e6i) q^{66} +(608801. - 1.46978e6i) q^{67} +(167420. + 56070.9i) q^{68} +(-5.98805e6 + 2.48033e6i) q^{69} +(1.21462e6 + 5.16158e6i) q^{70} +(-2.43203e6 + 2.43203e6i) q^{71} +(3.27061e6 - 6.20998e6i) q^{72} +(3.49340e6 + 3.49340e6i) q^{73} +(1.31556e6 - 2.12525e6i) q^{74} +(1.46311e6 + 3.53225e6i) q^{75} +(1.18469e6 - 1.36204e6i) q^{76} +(-7.01827e6 - 2.90706e6i) q^{77} +(1.02755e6 - 6.30374e6i) q^{78} +2.62603e6i q^{79} +(5.57834e6 + 1.44604e6i) q^{80} +8.10688e6i q^{81} +(-19399.9 - 3162.30i) q^{82} +(6.59811e6 + 2.73303e6i) q^{83} +(-1.42699e7 + 993776. i) q^{84} +(-185665. - 448234. i) q^{85} +(5.88249e6 + 3.64135e6i) q^{86} +(-3.18508e6 - 3.18508e6i) q^{87} +(-6.34961e6 + 5.27634e6i) q^{88} +(1.31226e6 - 1.31226e6i) q^{89} +(-1.87734e7 + 4.41774e6i) q^{90} +(-8.28684e6 + 3.43252e6i) q^{91} +(8.85410e6 - 4.41135e6i) q^{92} +(5.26389e6 - 1.27081e7i) q^{93} +(20285.5 + 28186.7i) q^{94} -4.96039e6 q^{95} +(-6.27112e6 + 1.42248e7i) q^{96} -8.71371e6 q^{97} +(6.29194e6 + 8.74268e6i) q^{98} +(1.05734e7 - 2.55265e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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