LMFDB - Embedded newform 32.8.g.a.13.9

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			13.9
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.08567 + 9.53754i) q^{2} +(8.84135 - 21.3449i) q^{3} +(-53.9292 - 116.085i) q^{4} +(-278.144 + 115.211i) q^{5} +(149.772 + 214.223i) q^{6} +(413.550 - 413.550i) q^{7} +(1435.36 + 192.100i) q^{8} +(1169.01 + 1169.01i) q^{9} +O(q^{10})$	\(q+(-6.08567 + 9.53754i) q^{2} +(8.84135 - 21.3449i) q^{3} +(-53.9292 - 116.085i) q^{4} +(-278.144 + 115.211i) q^{5} +(149.772 + 214.223i) q^{6} +(413.550 - 413.550i) q^{7} +(1435.36 + 192.100i) q^{8} +(1169.01 + 1169.01i) q^{9} +(593.864 - 3353.95i) q^{10} +(-1223.09 - 2952.80i) q^{11} +(-2954.62 + 124.770i) q^{12} +(11866.9 + 4915.42i) q^{13} +(1427.52 + 6460.98i) q^{14} +6955.59i q^{15} +(-10567.3 + 12520.7i) q^{16} +22411.2i q^{17} +(-18263.6 + 4035.26i) q^{18} +(43337.4 + 17950.9i) q^{19} +(28374.4 + 26075.0i) q^{20} +(-5170.85 - 12483.5i) q^{21} +(35605.8 + 6304.51i) q^{22} +(-40930.0 - 40930.0i) q^{23} +(16790.9 - 28939.1i) q^{24} +(8847.92 - 8847.92i) q^{25} +(-119099. + 83267.1i) q^{26} +(81969.3 - 33952.8i) q^{27} +(-70309.3 - 25704.4i) q^{28} +(41948.0 - 101272. i) q^{29} +(-66339.2 - 42329.4i) q^{30} +232938. q^{31} +(-55107.8 - 176983. i) q^{32} -73841.1 q^{33} +(-213748. - 136387. i) q^{34} +(-67381.0 + 162672. i) q^{35} +(72660.1 - 198747. i) q^{36} +(183320. - 75933.7i) q^{37} +(-434944. + 304088. i) q^{38} +(209838. - 209838. i) q^{39} +(-421368. + 111937. i) q^{40} +(40383.0 + 40383.0i) q^{41} +(150530. + 26653.5i) q^{42} +(-7947.93 - 19188.0i) q^{43} +(-276815. + 301224. i) q^{44} +(-459835. - 190470. i) q^{45} +(639458. - 141285. i) q^{46} +501183. i q^{47} +(173824. + 336257. i) q^{48} +481496. i q^{49} +(30541.8 + 138233. i) q^{50} +(478365. + 198145. i) q^{51} +(-69366.9 - 1.64265e6i) q^{52} +(-578559. - 1.39676e6i) q^{53} +(-175012. + 988410. i) q^{54} +(680391. + 680391. i) q^{55} +(673035. - 514149. i) q^{56} +(766322. - 766322. i) q^{57} +(710599. + 1.01639e6i) q^{58} +(1.14379e6 - 473773. i) q^{59} +(807436. - 375109. i) q^{60} +(-600170. + 1.44894e6i) q^{61} +(-1.41759e6 + 2.22166e6i) q^{62} +966886. q^{63} +(2.02335e6 + 551465. i) q^{64} -3.86701e6 q^{65} +(449372. - 704262. i) q^{66} +(-857505. + 2.07020e6i) q^{67} +(2.60159e6 - 1.20862e6i) q^{68} +(-1.23552e6 + 511770. i) q^{69} +(-1.14143e6 - 1.63262e6i) q^{70} +(-1.72578e6 + 1.72578e6i) q^{71} +(1.45338e6 + 1.90251e6i) q^{72} +(-1.89131e6 - 1.89131e6i) q^{73} +(-391405. + 2.21053e6i) q^{74} +(-110630. - 267085. i) q^{75} +(-253325. - 5.99888e6i) q^{76} +(-1.72694e6 - 715322. i) q^{77} +(724334. + 3.27835e6i) q^{78} -2.68616e6i q^{79} +(1.49670e6 - 4.70003e6i) q^{80} +1.56579e6i q^{81} +(-630912. + 139397. i) q^{82} +(5.04310e6 + 2.08892e6i) q^{83} +(-1.17029e6 + 1.27348e6i) q^{84} +(-2.58202e6 - 6.23355e6i) q^{85} +(231375. + 40968.2i) q^{86} +(-1.79075e6 - 1.79075e6i) q^{87} +(-1.18834e6 - 4.47328e6i) q^{88} +(-8.46616e6 + 8.46616e6i) q^{89} +(4.61502e6 - 3.22656e6i) q^{90} +(6.94032e6 - 2.87477e6i) q^{91} +(-2.54402e6 + 6.95866e6i) q^{92} +(2.05949e6 - 4.97205e6i) q^{93} +(-4.78005e6 - 3.05003e6i) q^{94} -1.41222e7 q^{95} +(-4.26491e6 - 388495. i) q^{96} +7.64184e6 q^{97} +(-4.59228e6 - 2.93022e6i) q^{98} +(2.02204e6 - 4.88165e6i) 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 $

$2$	−6.08567	+	9.53754i	−0.537902	+	0.843007i
$2$	−6.08567	+	9.53754i	−0.537902	+	0.843007i
$3$	8.84135	−	21.3449i	0.189058	−	0.456425i	−0.800721	−	0.599037i	$-0.795550\pi$
$3$	8.84135	−	21.3449i	0.189058	−	0.456425i	0.989779	+	0.142612i	$0.0455501\pi$
$4$	−53.9292	−	116.085i	−0.421322	−	0.906911i
$5$	−278.144	+	115.211i	−0.995119	+	0.412192i	−0.820005	−	0.572356i	$-0.806029\pi$
$5$	−278.144	+	115.211i	−0.995119	+	0.412192i	−0.175114	+	0.984548i	$0.556029\pi$
$6$	149.772	+	214.223i	0.283075	+	0.404889i
$7$	413.550	−	413.550i	0.455706	−	0.455706i	−0.441537	−	0.897243i	$-0.645567\pi$
$7$	413.550	−	413.550i	0.455706	−	0.455706i	0.897243	+	0.441537i	$0.145567\pi$
$8$	1435.36	+	192.100i	0.991163	+	0.132652i
$9$	1169.01	+	1169.01i	0.534525	+	0.534525i
$10$	593.864	−	3353.95i	0.187796	−	1.06061i
$11$	−1223.09	−	2952.80i	−0.277067	−	0.668898i	0.722685	−	0.691177i	$-0.242908\pi$
$11$	−1223.09	−	2952.80i	−0.277067	−	0.668898i	−0.999752	+	0.0222793i	$0.992908\pi$
$12$	−2954.62	+	124.770i	−0.493591	+	0.0208438i
$13$	11866.9	+	4915.42i	1.49808	+	0.620524i	0.973057	−	0.230564i	$-0.0740573\pi$
$13$	11866.9	+	4915.42i	1.49808	+	0.620524i	0.525022	+	0.851089i	$0.324057\pi$
$14$	1427.52	+	6460.98i	0.139038	+	0.629289i
$15$			6955.59i			0.532126i
$16$	−10567.3	+	12520.7i	−0.644975	+	0.764204i
$17$			22411.2i			1.10635i	0.833064	+	0.553177i	$0.186585\pi$
$17$			22411.2i			1.10635i	−0.833064	+	0.553177i	$0.813415\pi$
$18$	−18263.6	+	4035.26i	−0.738131	+	0.163086i
$19$	43337.4	+	17950.9i	1.44952	+	0.600412i	0.962086	−	0.272747i	$-0.0879321\pi$
$19$	43337.4	+	17950.9i	1.44952	+	0.600412i	0.487436	+	0.873159i	$0.337932\pi$
$20$	28374.4	+	26075.0i	0.793087	+	0.728819i
$21$	−5170.85	−	12483.5i	−0.121841	−	0.294151i
$22$	35605.8	+	6304.51i	0.712921	+	0.126233i
$23$	−40930.0	−	40930.0i	−0.701446	−	0.701446i	0.263275	−	0.964721i	$-0.415197\pi$
$23$	−40930.0	−	40930.0i	−0.701446	−	0.701446i	−0.964721	+	0.263275i	$0.915197\pi$
$24$	16790.9	−	28939.1i	0.247933	−	0.427313i
$25$	8847.92	−	8847.92i	0.113253	−	0.113253i
$26$	−119099.	+	83267.1i	−1.32893	+	0.929109i
$27$	81969.3	−	33952.8i	0.801453	−	0.331973i
$28$	−70309.3	−	25704.4i	−0.605284	−	0.221286i
$29$	41948.0	−	101272.i	0.319388	−	0.771071i	−0.679899	−	0.733306i	$-0.737976\pi$
$29$	41948.0	−	101272.i	0.319388	−	0.771071i	0.999287	−	0.0377648i	$-0.0120238\pi$
$30$	−66339.2	−	42329.4i	−0.448586	−	0.286232i
$31$	232938.			1.40435			0.702175	−	0.712005i	$-0.252213\pi$
$31$	232938.			1.40435			0.702175	+	0.712005i	$0.252213\pi$
$32$	−55107.8	−	176983.i	−0.297295	−	0.954786i
$33$	−73841.1			−0.357684
$34$	−213748.	−	136387.i	−0.932664	−	0.595110i
$35$	−67381.0	+	162672.i	−0.265644	+	0.641321i
$36$	72660.1	−	198747.i	0.259560	−	0.709974i
$37$	183320.	−	75933.7i	0.594982	−	0.246450i	−0.0648102	−	0.997898i	$-0.520644\pi$
$37$	183320.	−	75933.7i	0.594982	−	0.246450i	0.659792	+	0.751448i	$0.270644\pi$
$38$	−434944.	+	304088.i	−1.28585	+	0.898995i
$39$	209838.	−	209838.i	0.566446	−	0.566446i
$40$	−421368.	+	111937.i	−1.04100	+	0.276545i
$41$	40383.0	+	40383.0i	0.0915071	+	0.0915071i	0.751379	−	0.659871i	$-0.229389\pi$
$41$	40383.0	+	40383.0i	0.0915071	+	0.0915071i	−0.659871	+	0.751379i	$0.729389\pi$
$42$	150530.	+	26653.5i	0.313510	+	0.0555113i
$43$	−7947.93	−	19188.0i	−0.0152445	−	0.0368036i	0.916074	−	0.401009i	$-0.131341\pi$
$43$	−7947.93	−	19188.0i	−0.0152445	−	0.0368036i	−0.931319	+	0.364206i	$0.881341\pi$
$44$	−276815.	+	301224.i	−0.489897	+	0.533096i
$45$	−459835.	−	190470.i	−0.752243	−	0.311589i
$46$	639458.	−	141285.i	0.968633	−	0.214015i
$47$			501183.i			0.704131i	0.935975	+	0.352066i	$0.114521\pi$
$47$			501183.i			0.704131i	−0.935975	+	0.352066i	$0.885479\pi$
$48$	173824.	+	336257.i	0.226864	+	0.438862i
$49$			481496.i			0.584664i
$50$	30541.8	+	138233.i	0.0345541	+	0.156393i
$51$	478365.	+	198145.i	0.504968	+	0.209164i
$52$	−69366.9	−	1.64265e6i	−0.0684133	−	1.62006i
$53$	−578559.	−	1.39676e6i	−0.533804	−	1.28872i	−0.928986	−	0.370114i	$-0.879319\pi$
$53$	−578559.	−	1.39676e6i	−0.533804	−	1.28872i	0.395182	−	0.918603i	$-0.370681\pi$
$54$	−175012.	+	988410.i	−0.151248	+	0.854199i
$55$	680391.	+	680391.i	0.551429	+	0.551429i
$56$	673035.	−	514149.i	0.512129	−	0.391229i
$57$	766322.	−	766322.i	0.548086	−	0.548086i
$58$	710599.	+	1.01639e6i	0.478219	+	0.684007i
$59$	1.14379e6	−	473773.i	0.725043	−	0.300323i	0.0105300	−	0.999945i	$-0.496648\pi$
$59$	1.14379e6	−	473773.i	0.725043	−	0.300323i	0.714513	+	0.699622i	$0.246648\pi$
$60$	807436.	−	375109.i	0.482591	−	0.224196i
$61$	−600170.	+	1.44894e6i	−0.338548	+	0.817327i	0.659308	+	0.751873i	$0.270849\pi$
$61$	−600170.	+	1.44894e6i	−0.338548	+	0.817327i	−0.997856	+	0.0654535i	$0.979151\pi$
$62$	−1.41759e6	+	2.22166e6i	−0.755403	+	1.18388i
$63$	966886.			0.487173
$64$	2.02335e6	+	551465.i	0.964807	+	0.262959i
$65$	−3.86701e6			−1.74654
$66$	449372.	−	704262.i	0.192399	−	0.301530i
$67$	−857505.	+	2.07020e6i	−0.348317	+	0.840912i	0.648502	+	0.761213i	$0.275396\pi$
$67$	−857505.	+	2.07020e6i	−0.348317	+	0.840912i	−0.996819	+	0.0796990i	$0.974604\pi$
$68$	2.60159e6	−	1.20862e6i	1.00336	−	0.466131i
$69$	−1.23552e6	+	511770.i	−0.452771	+	0.187544i
$70$	−1.14143e6	−	1.63262e6i	−0.397747	−	0.568907i
$71$	−1.72578e6	+	1.72578e6i	−0.572242	+	0.572242i	−0.932755	−	0.360512i	$-0.882602\pi$
$71$	−1.72578e6	+	1.72578e6i	−0.572242	+	0.572242i	0.360512	+	0.932755i	$0.382602\pi$
$72$	1.45338e6	+	1.90251e6i	0.458896	+	0.600707i
$73$	−1.89131e6	−	1.89131e6i	−0.569026	−	0.569026i	0.362829	−	0.931856i	$-0.381811\pi$
$73$	−1.89131e6	−	1.89131e6i	−0.569026	−	0.569026i	−0.931856	+	0.362829i	$0.881811\pi$
$74$	−391405.	+	2.21053e6i	−0.112283	+	0.634140i
$75$	−110630.	−	267085.i	−0.0302803	−	0.0731031i
$76$	−253325.	−	5.99888e6i	−0.0661959	−	1.56755i
$77$	−1.72694e6	−	715322.i	−0.431082	−	0.178560i
$78$	724334.	+	3.27835e6i	0.172826	+	0.782211i
$79$		−	2.68616e6i		−	0.612966i	−0.951876	−	0.306483i	$-0.900848\pi$
$79$		−	2.68616e6i		−	0.612966i	0.951876	−	0.306483i	$-0.0991523\pi$
$80$	1.49670e6	−	4.70003e6i	0.326829	−	1.02633i
$81$			1.56579e6i			0.327368i
$82$	−630912.	+	139397.i	−0.126363	+	0.0279193i
$83$	5.04310e6	+	2.08892e6i	0.968109	+	0.401004i	0.810008	−	0.586419i	$-0.199463\pi$
$83$	5.04310e6	+	2.08892e6i	0.968109	+	0.401004i	0.158101	+	0.987423i	$0.449463\pi$
$84$	−1.17029e6	+	1.27348e6i	−0.215434	+	0.234431i
$85$	−2.58202e6	−	6.23355e6i	−0.456030	−	1.10095i
$86$	231375.	+	40968.2i	0.0392258	+	0.00694547i
$87$	−1.79075e6	−	1.79075e6i	−0.291554	−	0.291554i
$88$	−1.18834e6	−	4.47328e6i	−0.185888	−	0.699740i
$89$	−8.46616e6	+	8.46616e6i	−1.27298	+	1.27298i	−0.328463	+	0.944517i	$0.606531\pi$
$89$	−8.46616e6	+	8.46616e6i	−1.27298	+	1.27298i	−0.944517	+	0.328463i	$0.893469\pi$
$90$	4.61502e6	−	3.22656e6i	0.667306	−	0.466542i
$91$	6.94032e6	−	2.87477e6i	0.965461	−	0.399907i
$92$	−2.54402e6	+	6.95866e6i	−0.340614	+	0.931684i
$93$	2.05949e6	−	4.97205e6i	0.265503	−	0.640981i
$94$	−4.78005e6	−	3.05003e6i	−0.593588	−	0.378754i
$95$	−1.41222e7			−1.68993
$96$	−4.26491e6	−	388495.i	−0.491994	−	0.0448163i
$97$	7.64184e6			0.850153			0.425076	−	0.905158i	$-0.360247\pi$
$97$	7.64184e6			0.850153			0.425076	+	0.905158i	$0.360247\pi$
$98$	−4.59228e6	−	2.93022e6i	−0.492876	−	0.314492i
$99$	2.02204e6	−	4.88165e6i	0.209444	−	0.505642i
$100$	−1.50427e6	−	549946.i	−0.150427	−	0.0549946i
$101$	1.37926e7	−	5.71308e6i	1.33205	−	0.551754i	0.400812	−	0.916160i	$-0.368728\pi$
$101$	1.37926e7	−	5.71308e6i	1.33205	−	0.551754i	0.931240	+	0.364406i	$0.118728\pi$
$102$	−4.80099e6	+	3.35658e6i	−0.447950	+	0.313181i
$103$	1.51012e6	−	1.51012e6i	0.136170	−	0.136170i	−0.635736	−	0.771906i	$-0.719303\pi$
$103$	1.51012e6	−	1.51012e6i	0.136170	−	0.136170i	0.771906	+	0.635736i	$0.219303\pi$
$104$	1.60889e7	+	9.33501e6i	1.40253	+	0.813764i
$105$	2.87648e6	+	2.87648e6i	0.242493	+	0.242493i
$106$	1.68426e7	+	2.98222e6i	1.37353	+	0.243203i
$107$	6.82792e6	+	1.64841e7i	0.538822	+	1.30083i	0.925546	+	0.378636i	$0.123607\pi$
$107$	6.82792e6	+	1.64841e7i	0.538822	+	1.30083i	−0.386724	+	0.922195i	$0.626393\pi$
$108$	−8.36193e6	−	7.68432e6i	−0.638739	−	0.586979i
$109$	−8.80709e6	−	3.64802e6i	−0.651388	−	0.269814i	0.0324214	−	0.999474i	$-0.489678\pi$
$109$	−8.80709e6	−	3.64802e6i	−0.651388	−	0.269814i	−0.683810	+	0.729660i	$0.739678\pi$
$110$	−1.06299e7	+	2.34862e6i	−0.761473	+	0.168244i
$111$		−	4.58431e6i		−	0.318158i
$112$	807844.	+	9.54804e6i	0.0543331	+	0.642172i
$113$			7.64940e6i			0.498715i	0.968411	+	0.249358i	$0.0802195\pi$
$113$			7.64940e6i			0.498715i	−0.968411	+	0.249358i	$0.919781\pi$
$114$	2.64524e6	+	1.19724e7i	0.167224	+	0.756858i
$115$	1.61000e7	+	6.66885e6i	0.987152	+	0.408892i
$116$	−1.40183e7	+	591975.i	−0.833858	+	0.0352128i
$117$	8.12630e6	+	1.96186e7i	0.469075	+	1.13245i
$118$	−2.44210e6	+	1.37922e7i	−0.136828	+	0.772761i
$119$	9.26815e6	+	9.26815e6i	0.504172	+	0.504172i
$120$	−1.33617e6	+	9.98375e6i	−0.0705875	+	0.527423i
$121$	6.55642e6	−	6.55642e6i	0.336448	−	0.336448i
$122$	−1.01669e7	−	1.45419e7i	−0.506907	−	0.725040i
$123$	1.21901e6	−	504931.i	0.0590663	−	0.0244661i
$124$	−1.25622e7	−	2.70406e7i	−0.591683	−	1.27362i
$125$	7.55925e6	−	1.82496e7i	0.346173	−	0.835737i
$126$	−5.88415e6	+	9.22171e6i	−0.262052	+	0.410690i
$127$	−1.82969e7			−0.792618			−0.396309	−	0.918117i	$-0.629709\pi$
$127$	−1.82969e7			−0.792618			−0.396309	+	0.918117i	$0.629709\pi$
$128$	−1.75730e7	+	1.59417e7i	−0.740648	+	0.671893i
$129$	−479836.			−0.0196802
$130$	2.35334e7	−	3.68818e7i	0.939469	−	1.47235i
$131$	3.54750e6	−	8.56442e6i	0.137871	−	0.332850i	−0.839831	−	0.542848i	$-0.817346\pi$
$131$	3.54750e6	−	8.56442e6i	0.137871	−	0.332850i	0.977702	+	0.209998i	$0.0673459\pi$
$132$	3.98219e6	+	8.57181e6i	0.150700	+	0.324387i
$133$	2.53458e7	−	1.04986e7i	0.934168	−	0.386945i
$134$	−1.45261e7	−	2.07770e7i	−0.521534	−	0.745963i
$135$	−1.88875e7	+	1.88875e7i	−0.660704	+	0.660704i
$136$	−4.30520e6	+	3.21681e7i	−0.146760	+	1.09658i
$137$	2.56977e7	+	2.56977e7i	0.853833	+	0.853833i	0.990603	−	0.136770i	$-0.0436722\pi$
$137$	2.56977e7	+	2.56977e7i	0.853833	+	0.853833i	−0.136770	+	0.990603i	$0.543672\pi$
$138$	2.63796e6	−	1.48983e7i	0.0854458	−	0.482570i
$139$	−1.93674e7	−	4.67570e7i	−0.611673	−	1.47671i	−0.861161	−	0.508331i	$-0.830262\pi$
$139$	−1.93674e7	−	4.67570e7i	−0.611673	−	1.47671i	0.249488	−	0.968378i	$-0.419738\pi$
$140$	2.25175e7	−	950888.i	0.693542	−	0.0292874i
$141$	1.06977e7	+	4.43113e6i	0.321383	+	0.133121i
$142$	−5.95715e6	−	2.69621e7i	−0.174594	−	0.790215i
$143$		−	4.10525e7i		−	1.17399i
$144$	−2.69900e7	+	2.28358e6i	−0.753242	+	0.0637306i
$145$			3.30010e7i			0.898957i
$146$	2.95483e7	−	6.52855e6i	0.785774	−	0.173613i
$147$	1.02775e7	+	4.25707e6i	0.266855	+	0.110535i
$148$	−1.87010e7	−	1.71856e7i	−0.474187	−	0.435761i
$149$	−2.26046e7	−	5.45723e7i	−0.559815	−	1.35151i	−0.909912	−	0.414801i	$-0.863851\pi$
$149$	−2.26046e7	−	5.45723e7i	−0.559815	−	1.35151i	0.350097	−	0.936713i	$-0.386149\pi$
$150$	3.22060e6	+	570252.i	0.0779143	+	0.0137958i
$151$	−5.32989e7	−	5.32989e7i	−1.25979	−	1.25979i	−0.951192	−	0.308601i	$-0.900139\pi$
$151$	−5.32989e7	−	5.32989e7i	−1.25979	−	1.25979i	−0.308601	−	0.951192i	$-0.599861\pi$
$152$	5.87562e7	+	3.40911e7i	1.35707	+	0.787388i
$153$	−2.61988e7	+	2.61988e7i	−0.591374	+	0.591374i
$154$	1.73320e7	−	1.21175e7i	0.382407	−	0.267357i
$155$	−6.47905e7	+	2.68371e7i	−1.39749	+	0.578861i
$156$	−3.56754e7	−	1.30426e7i	−0.752373	−	0.275060i
$157$	−1.44500e7	+	3.48855e7i	−0.298003	+	0.719442i	0.701971	+	0.712206i	$0.252304\pi$
$157$	−1.44500e7	+	3.48855e7i	−0.298003	+	0.719442i	−0.999974	+	0.00723688i	$0.997696\pi$
$158$	2.56193e7	+	1.63471e7i	0.516735	+	0.329716i
$159$	−3.49290e7			−0.689123
$160$	3.57183e7	+	4.28777e7i	0.689399	+	0.827583i
$161$	−3.38532e7			−0.639306
$162$	−1.49338e7	−	9.52888e6i	−0.275973	−	0.176092i
$163$	1.22339e7	−	2.95352e7i	0.221263	−	0.534175i	−0.773799	−	0.633431i	$-0.781646\pi$
$163$	1.22339e7	−	2.95352e7i	0.221263	−	0.534175i	0.995062	+	0.0992556i	$0.0316461\pi$
$164$	2.51002e6	−	6.86567e6i	0.0444348	−	0.121543i
$165$	2.05385e7	−	8.50731e6i	0.355938	−	0.147434i
$166$	−5.06138e7	+	3.53863e7i	−0.858797	+	0.600422i
$167$	−2.69638e7	+	2.69638e7i	−0.447996	+	0.447996i	−0.894688	−	0.446692i	$-0.852602\pi$
$167$	−2.69638e7	+	2.69638e7i	−0.447996	+	0.447996i	0.446692	+	0.894688i	$0.352602\pi$
$168$	−5.02392e6	−	1.89116e7i	−0.0817448	−	0.307714i
$169$	7.22914e7	+	7.22914e7i	1.15208	+	1.15208i
$170$	7.51660e7	+	1.33092e7i	1.17341	+	0.207769i
$171$	2.96769e7	+	7.16464e7i	0.453871	+	1.09574i
$172$	−1.79881e6	+	1.95743e6i	−0.0269547	+	0.0293316i
$173$	607194.	+	251508.i	0.00891592	+	0.00369309i	0.387137	−	0.922022i	$-0.373464\pi$
$173$	607194.	+	251508.i	0.00891592	+	0.00369309i	−0.378221	+	0.925715i	$0.623464\pi$
$174$	2.79773e7	−	6.18144e6i	0.402609	−	0.0889544i
$175$		−	7.31811e6i		−	0.103221i
$176$	4.98959e7	+	1.58891e7i	0.689875	+	0.219687i
$177$		−	2.86029e7i		−	0.387707i
$178$	−2.92241e7	−	1.32269e8i	−0.388392	−	1.75787i
$179$	4.57002e7	+	1.89296e7i	0.595569	+	0.246693i	0.660045	−	0.751226i	$-0.270537\pi$
$179$	4.57002e7	+	1.89296e7i	0.595569	+	0.246693i	−0.0644753	+	0.997919i	$0.520537\pi$
$180$	2.68793e6	+	6.36517e7i	0.0343530	+	0.813497i
$181$	−3.10156e7	−	7.48782e7i	−0.388781	−	0.938599i	−0.990199	−	0.139665i	$-0.955397\pi$
$181$	−3.10156e7	−	7.48782e7i	−0.388781	−	0.938599i	0.601418	−	0.798934i	$-0.294603\pi$
$182$	−1.48182e7	+	8.36885e7i	−0.182199	+	1.02900i
$183$	2.56211e7	+	2.56211e7i	0.309044	+	0.309044i
$184$	−5.08865e7	−	6.66118e7i	−0.602199	−	0.788295i
$185$	−4.22410e7	+	4.22410e7i	−0.490494	+	0.490494i
$186$	3.48877e7	+	4.99007e7i	0.397537	+	0.568606i
$187$	6.61758e7	−	2.74109e7i	0.740037	−	0.306534i
$188$	5.81796e7	−	2.70284e7i	0.638584	−	0.296666i
$189$	1.98572e7	−	4.79396e7i	0.213945	−	0.516509i
$190$	8.59430e7	−	1.34691e8i	0.909018	−	1.42463i
$191$	2.34107e7			0.243107			0.121553	−	0.992585i	$-0.461212\pi$
$191$	2.34107e7			0.243107			0.121553	+	0.992585i	$0.461212\pi$
$192$	2.96601e7	−	3.83125e7i	0.302425	−	0.390648i
$193$	−1.34127e8			−1.34297			−0.671486	−	0.741017i	$-0.734344\pi$
$193$	−1.34127e8			−1.34297			−0.671486	+	0.741017i	$0.734344\pi$
$194$	−4.65057e7	+	7.28843e7i	−0.457299	+	0.716685i
$195$	−3.41896e7	+	8.25411e7i	−0.330197	+	0.797166i
$196$	5.58942e7	−	2.59667e7i	0.530238	−	0.246332i
$197$	7.19605e7	−	2.98070e7i	0.670598	−	0.277771i	−0.0212925	−	0.999773i	$-0.506778\pi$
$197$	7.19605e7	−	2.98070e7i	0.670598	−	0.277771i	0.691890	+	0.722003i	$0.256778\pi$
$198$	3.42534e7	+	4.89934e7i	0.313600	+	0.448549i
$199$	−8.29567e7	+	8.29567e7i	−0.746218	+	0.746218i	−0.973767	−	0.227549i	$-0.926929\pi$
$199$	−8.29567e7	+	8.29567e7i	−0.746218	+	0.746218i	0.227549	+	0.973767i	$0.426929\pi$
$200$	1.43996e7	−	1.10002e7i	0.127276	−	0.0972292i
$201$	3.66067e7	+	3.66067e7i	0.317962	+	0.317962i
$202$	−2.94485e7	+	1.66315e8i	−0.251381	+	1.41972i
$203$	−2.45332e7	−	5.92285e7i	−0.205835	−	0.496929i
$204$	−2.79625e6	−	6.62166e7i	−0.0230606	−	0.546086i
$205$	−1.58849e7	−	6.57973e6i	−0.128779	−	0.0533420i
$206$	5.21273e6	+	2.35929e7i	0.0415461	+	0.188038i
$207$		−	9.56949e7i		−	0.749881i
$208$	−1.86945e8	+	9.66391e7i	−1.44043	+	0.744614i
$209$		−	1.49922e8i		−	1.13594i
$210$	−4.49399e7	+	9.92924e6i	−0.334861	+	0.0739858i
$211$	1.35759e8	+	5.62333e7i	0.994904	+	0.412103i	0.819926	−	0.572470i	$-0.194015\pi$
$211$	1.35759e8	+	5.62333e7i	0.994904	+	0.412103i	0.174978	+	0.984572i	$0.444015\pi$
$212$	−1.30942e8	+	1.42488e8i	−0.943848	+	1.02708i
$213$	2.15783e7	+	5.20947e7i	0.152999	+	0.369373i
$214$	−1.98770e8	−	3.51950e7i	−1.38644	−	0.245489i
$215$	4.42134e6	+	4.42134e6i	0.0303403	+	0.0303403i
$216$	1.24177e8	−	3.29880e7i	0.838407	−	0.222725i
$217$	9.63317e7	−	9.63317e7i	0.639971	−	0.639971i
$218$	8.83902e7	−	6.17974e7i	0.577838	−	0.403991i
$219$	−5.70915e7	+	2.36481e7i	−0.367297	+	0.152139i
$220$	4.22900e7	−	1.15676e8i	0.267768	−	0.732426i
$221$	−1.10160e8	+	2.65951e8i	−0.686519	+	1.65740i
$222$	4.37230e7	+	2.78986e7i	0.268210	+	0.171138i
$223$	2.93458e8			1.77206			0.886031	−	0.463625i	$-0.153452\pi$
$223$	2.93458e8			1.77206			0.886031	+	0.463625i	$0.153452\pi$
$224$	−9.59811e7	−	5.04014e7i	−0.570581	−	0.299622i
$225$	2.06866e7			0.121074
$226$	−7.29564e7	−	4.65517e7i	−0.420421	−	0.268260i
$227$	8.66350e7	−	2.09155e8i	0.491590	−	1.18680i	−0.462321	−	0.886713i	$-0.652983\pi$
$227$	8.66350e7	−	2.09155e8i	0.491590	−	1.18680i	0.953911	−	0.300090i	$-0.0970167\pi$
$228$	−1.30285e8	−	4.76310e7i	−0.727987	−	0.266145i
$229$	−5.20345e7	+	2.15534e7i	−0.286330	+	0.118602i	−0.521226	−	0.853419i	$-0.674525\pi$
$229$	−5.20345e7	+	2.15534e7i	−0.286330	+	0.118602i	0.234896	+	0.972021i	$0.424525\pi$
$230$	−1.61584e8	+	1.12970e8i	−0.875690	+	0.612233i
$231$	−3.05370e7	+	3.05370e7i	−0.162999	+	0.162999i
$232$	7.96647e7	−	1.37303e8i	0.418849	−	0.721889i
$233$	−7.64563e7	−	7.64563e7i	−0.395975	−	0.395975i	0.480836	−	0.876811i	$-0.340333\pi$
$233$	−7.64563e7	−	7.64563e7i	−0.395975	−	0.395975i	−0.876811	+	0.480836i	$0.840333\pi$
$234$	−2.36567e8	−	4.18876e7i	−1.20698	−	0.213712i
$235$	−5.77418e7	−	1.39401e8i	−0.290237	−	0.700695i
$236$	−1.16681e8	−	1.07226e8i	−0.577843	−	0.531017i
$237$	−5.73358e7	−	2.37493e7i	−0.279773	−	0.115886i
$238$	−1.44798e8	+	3.19924e7i	−0.696216	+	0.153825i
$239$		−	7.23424e7i		−	0.342768i	−0.985204	−	0.171384i	$-0.945176\pi$
$239$		−	7.23424e7i		−	0.342768i	0.985204	−	0.171384i	$-0.0548238\pi$
$240$	−8.70889e7	−	7.35016e7i	−0.406652	−	0.343208i
$241$		−	2.82175e8i		−	1.29855i	−0.760554	−	0.649275i	$-0.775072\pi$
$241$		−	2.82175e8i		−	1.29855i	0.760554	−	0.649275i	$-0.224928\pi$
$242$	2.26319e7	+	1.02432e8i	0.102652	+	0.464604i
$243$	2.12688e8	+	8.80984e7i	0.950872	+	0.393864i
$244$	2.00566e8	−	8.46966e6i	0.883880	−	0.0373252i
$245$	−5.54736e7	−	1.33925e8i	−0.240994	−	0.581810i
$246$	−2.60270e6	+	1.46992e7i	−0.0111468	+	0.0629537i
$247$	4.26043e8	+	4.26043e8i	1.79893	+	1.79893i
$248$	3.34350e8	+	4.47476e7i	1.39194	+	0.186290i
$249$	8.91756e7	−	8.91756e7i	0.366057	−	0.366057i
$250$	1.28054e8	+	1.83158e8i	0.518324	+	0.741371i
$251$	−3.43007e8	+	1.42078e8i	−1.36913	+	0.567112i	−0.941552	−	0.336867i	$-0.890633\pi$
$251$	−3.43007e8	+	1.42078e8i	−1.36913	+	0.567112i	−0.427577	+	0.903979i	$0.640633\pi$
$252$	−5.21434e7	−	1.12241e8i	−0.205257	−	0.441823i
$253$	−7.07970e7	+	1.70919e8i	−0.274848	+	0.663543i
$254$	1.11349e8	−	1.74507e8i	0.426351	−	0.668183i
$255$	−1.55883e8			−0.588719
$256$	−4.51009e7	−	2.64620e8i	−0.168014	−	0.985785i
$257$	−2.33772e8			−0.859067			−0.429534	−	0.903051i	$-0.641322\pi$
$257$	−2.33772e8			−0.859067			−0.429534	+	0.903051i	$0.641322\pi$
$258$	2.92013e6	−	4.57646e6i	0.0105860	−	0.0165905i
$259$	4.44097e7	−	1.07214e8i	0.158828	−	0.383446i
$260$	2.08545e8	+	4.48901e8i	0.735857	+	1.58396i
$261$	1.67425e8	−	6.93496e7i	0.582878	−	0.241436i
$262$	6.00945e7	+	8.59546e7i	0.206434	+	0.295267i
$263$	1.78733e8	−	1.78733e8i	0.605842	−	0.605842i	−0.336014	−	0.941857i	$-0.609079\pi$
$263$	1.78733e8	−	1.78733e8i	0.605842	−	0.605842i	0.941857	+	0.336014i	$0.109079\pi$
$264$	−1.05988e8	−	1.41849e7i	−0.354523	−	0.0474474i
$265$	3.21846e8	+	3.21846e8i	1.06240	+	1.06240i
$266$	−5.41156e7	+	3.05627e8i	−0.176294	+	0.995649i
$267$	1.05857e8	+	2.55562e8i	0.340354	+	0.821687i
$268$	2.86563e8	−	1.21012e7i	0.909386	−	0.0384023i
$269$	−4.22056e8	−	1.74821e8i	−1.32202	−	0.547597i	−0.393649	−	0.919261i	$-0.628787\pi$
$269$	−4.22056e8	−	1.74821e8i	−1.32202	−	0.547597i	−0.928367	+	0.371664i	$0.878787\pi$
$270$	−6.51973e7	−	2.95084e8i	−0.201584	−	0.912373i
$271$		−	2.32888e8i		−	0.710812i	−0.934712	−	0.355406i	$-0.884343\pi$
$271$		−	2.32888e8i		−	0.710812i	0.934712	−	0.355406i	$-0.115657\pi$
$272$	−2.80604e8	−	2.36825e8i	−0.845479	−	0.713570i
$273$		−	1.73557e8i		−	0.516266i
$274$	−4.01481e8	+	8.87052e7i	−1.17907	+	0.260509i
$275$	−3.69480e7	−	1.53043e7i	−0.107134	−	0.0443762i
$276$	1.26039e8	+	1.15826e8i	0.360848	+	0.331607i
$277$	1.77885e8	+	4.29453e8i	0.502876	+	1.21405i	0.947910	+	0.318537i	$0.103192\pi$
$277$	1.77885e8	+	4.29453e8i	0.502876	+	1.21405i	−0.445034	+	0.895514i	$0.646808\pi$
$278$	5.63810e8	+	9.98306e7i	1.57390	+	0.278681i
$279$	2.72307e8	+	2.72307e8i	0.750660	+	0.750660i
$280$	−1.27965e8	+	2.20549e8i	−0.348368	+	0.600415i
$281$	−2.27885e8	+	2.27885e8i	−0.612694	+	0.612694i	−0.943647	−	0.330953i	$-0.892630\pi$
$281$	−2.27885e8	+	2.27885e8i	−0.612694	+	0.612694i	0.330953	+	0.943647i	$0.392630\pi$
$282$	−1.07365e8	+	7.50633e7i	−0.285095	+	0.199322i
$283$	−6.78824e8	+	2.81178e8i	−1.78035	+	0.737444i	−0.787751	+	0.615994i	$0.788754\pi$
$283$	−6.78824e8	+	2.81178e8i	−1.78035	+	0.737444i	−0.992598	+	0.121450i	$0.961246\pi$
$284$	2.93406e8	+	1.07266e8i	0.760071	+	0.277874i
$285$	−1.24859e8	+	3.01437e8i	−0.319495	+	0.771328i
$286$	3.91540e8	+	2.49832e8i	0.989681	+	0.631491i
$287$	3.34008e7			0.0834007
$288$	1.42473e8	−	2.71315e8i	0.351445	−	0.669269i
$289$	−9.19230e7			−0.224017
$290$	−3.14748e8	−	2.00833e8i	−0.757827	−	0.483551i
$291$	6.75642e7	−	1.63114e8i	0.160728	−	0.388031i
$292$	−1.17555e8	+	3.21549e8i	−0.276313	+	0.755800i
$293$	3.81340e8	−	1.57956e8i	0.885678	−	0.366860i	0.106982	−	0.994261i	$-0.465881\pi$
$293$	3.81340e8	−	1.57956e8i	0.885678	−	0.366860i	0.778696	+	0.627401i	$0.215881\pi$
$294$	−1.03147e8	+	7.21147e7i	−0.236724	+	0.165504i
$295$	−2.63555e8	+	2.63555e8i	−0.597714	+	0.597714i
$296$	2.77717e8	−	7.37760e7i	0.622416	−	0.165346i
$297$	−2.00512e8	−	2.00512e8i	−0.444112	−	0.444112i
$298$	6.58050e8	+	1.16517e8i	1.44046	+	0.255054i
$299$	−2.84523e8	−	6.86899e8i	−0.615557	−	1.48609i
$300$	−2.50383e7	+	2.72462e7i	−0.0535403	+	0.0582615i
$301$	−1.12221e7	−	4.64833e6i	−0.0237187	−	0.00982459i
$302$	8.32700e8	−	1.83981e8i	1.73966	−	0.384369i
$303$		−	3.44913e8i		−	0.712296i
$304$	−6.82716e8	+	3.52922e8i	−1.39374	+	0.720479i
$305$		−	4.72160e8i		−	0.952884i
$306$	−9.04349e7	−	4.09310e8i	−0.180431	−	0.816634i
$307$	−2.93107e8	−	1.21409e8i	−0.578152	−	0.239479i	0.0743921	−	0.997229i	$-0.476298\pi$
$307$	−2.93107e8	−	1.21409e8i	−0.578152	−	0.239479i	−0.652544	+	0.757751i	$0.726298\pi$
$308$	1.00947e7	+	2.39048e8i	0.0196864	+	0.466184i
$309$	−1.88818e7	−	4.55848e7i	−0.0364074	−	0.0878953i
$310$	1.38334e8	−	7.81263e8i	0.263731	−	1.48947i
$311$	−2.03546e8	−	2.03546e8i	−0.383708	−	0.383708i	0.488728	−	0.872436i	$-0.337461\pi$
$311$	−2.03546e8	−	2.03546e8i	−0.383708	−	0.383708i	−0.872436	+	0.488728i	$0.837461\pi$
$312$	3.41503e8	−	2.60883e8i	0.636581	−	0.486300i
$313$	2.77851e8	−	2.77851e8i	0.512161	−	0.512161i	−0.403027	−	0.915188i	$-0.632042\pi$
$313$	2.77851e8	−	2.77851e8i	0.512161	−	0.512161i	0.915188	+	0.403027i	$0.132042\pi$
$314$	−2.44783e8	−	3.50119e8i	−0.446199	−	0.638208i
$315$	−2.68934e8	+	1.11396e8i	−0.484795	+	0.200809i
$316$	−3.11822e8	+	1.44862e8i	−0.555906	+	0.258256i
$317$	−2.15333e8	+	5.19859e8i	−0.379666	+	0.916596i	0.612361	+	0.790578i	$0.290220\pi$
$317$	−2.15333e8	+	5.19859e8i	−0.379666	+	0.916596i	−0.992028	+	0.126018i	$0.959780\pi$
$318$	2.12567e8	−	3.33137e8i	0.370681	−	0.580936i
$319$	−3.50341e8			−0.604260
$320$	−6.26317e8	+	7.97252e7i	−1.06849	+	0.136010i
$321$	4.12219e8			0.695601
$322$	2.06019e8	−	3.22876e8i	0.343884	−	0.538940i
$323$	−4.02302e8	+	9.71242e8i	−0.664267	+	1.60368i
$324$	1.81764e8	−	8.44419e7i	0.296893	−	0.137927i
$325$	1.48488e8	−	6.15059e7i	0.239939	−	0.0993859i
$326$	2.07242e8	+	2.96423e8i	0.331296	+	0.473860i
$327$	−1.55733e8	+	1.55733e8i	−0.246300	+	0.246300i
$328$	5.02064e7	+	6.57216e7i	0.0785598	+	0.102837i
$329$	2.07264e8	+	2.07264e8i	0.320877	+	0.320877i
$330$	−4.38515e7	+	2.47659e8i	−0.0671716	+	0.379363i
$331$	−2.68411e8	−	6.48002e8i	−0.406820	−	0.982151i	−0.985969	−	0.166929i	$-0.946615\pi$
$331$	−2.68411e8	−	6.48002e8i	−0.406820	−	0.982151i	0.579149	−	0.815222i	$-0.303385\pi$
$332$	−2.94791e7	−	6.98080e8i	−0.0442110	−	1.04694i
$333$	3.03069e8	+	1.25535e8i	0.449767	+	0.186299i
$334$	−9.30756e7	−	4.21262e8i	−0.136686	−	0.618642i
$335$		−	6.74609e8i		−	0.980381i
$336$	2.10944e8	+	6.71742e7i	0.303376	+	0.0966084i
$337$			3.78886e8i			0.539267i	0.962963	+	0.269634i	$0.0869026\pi$
$337$			3.78886e8i			0.539267i	−0.962963	+	0.269634i	$0.913097\pi$
$338$	−1.12942e9	+	2.49540e8i	−1.59092	+	0.351506i
$339$	1.63276e8	+	6.76310e7i	0.227626	+	0.0942859i
$340$	−5.84372e8	+	6.35903e8i	−0.806331	+	0.877435i
$341$	−2.84905e8	−	6.87821e8i	−0.389098	−	0.939366i
$342$	−8.63935e8	−	1.52972e8i	−1.16786	−	0.206785i
$343$	5.39699e8	+	5.39699e8i	0.722141	+	0.722141i
$344$	−7.72209e6	−	2.90684e7i	−0.0102278	−	0.0385006i
$345$	2.84692e8	−	2.84692e8i	0.373257	−	0.373257i
$346$	−6.09395e6	+	4.26054e6i	−0.00790920	+	0.00552966i
$347$	7.26767e8	−	3.01037e8i	0.933775	−	0.386782i	0.136665	−	0.990617i	$-0.456361\pi$
$347$	7.26767e8	−	3.01037e8i	0.933775	−	0.386782i	0.797109	+	0.603835i	$0.206361\pi$
$348$	−1.11305e8	+	3.04453e8i	−0.141575	+	0.387251i
$349$	−2.36033e8	+	5.69835e8i	−0.297224	+	0.717563i	0.702757	+	0.711430i	$0.251952\pi$
$349$	−2.36033e8	+	5.69835e8i	−0.297224	+	0.717563i	−0.999981	+	0.00613292i	$0.998048\pi$
$350$	6.97968e7	+	4.45356e7i	0.0870156	+	0.0555226i
$351$	1.13961e9			1.40664
$352$	−4.55193e8	+	3.79188e8i	−0.556284	+	0.463400i
$353$	−6.14896e8			−0.744029			−0.372015	−	0.928227i	$-0.621333\pi$
$353$	−6.14896e8			−0.744029			−0.372015	+	0.928227i	$0.621333\pi$
$354$	2.72801e8	+	1.74068e8i	0.326839	+	0.208548i
$355$	2.81186e8	−	6.78843e8i	0.333576	−	0.805323i
$356$	1.43936e9	+	5.26217e8i	1.69081	+	0.618145i
$357$	2.79771e8	−	1.15885e8i	0.325435	−	0.134799i
$358$	−4.58658e8	+	3.20668e8i	−0.528322	+	0.369372i
$359$	−5.31550e8	+	5.31550e8i	−0.606336	+	0.606336i	−0.941987	−	0.335651i	$-0.891044\pi$
$359$	−5.31550e8	+	5.31550e8i	−0.606336	+	0.606336i	0.335651	+	0.941987i	$0.391044\pi$
$360$	−6.23438e8	−	3.61727e8i	−0.704263	−	0.408622i
$361$	9.23829e8	+	9.23829e8i	1.03351	+	1.03351i
$362$	9.02904e8	+	1.59872e8i	1.00037	+	0.177130i
$363$	−8.19786e7	−	1.97914e8i	−0.0899554	−	0.217172i
$364$	−7.08003e8	−	6.50630e8i	−0.769450	−	0.707097i
$365$	7.43956e8	+	3.08157e8i	0.800797	+	0.331701i
$366$	−4.00285e8	+	8.84408e7i	−0.426761	+	0.0942907i
$367$			3.10108e8i			0.327478i	0.986504	+	0.163739i	$0.0523555\pi$
$367$			3.10108e8i			0.327478i	−0.986504	+	0.163739i	$0.947645\pi$
$368$	9.44991e8	−	7.99541e7i	0.988462	−	0.0836322i
$369$			9.44160e7i			0.0978257i
$370$	−1.45810e8	−	6.59940e8i	−0.149652	−	0.677327i
$371$	−8.16895e8	−	3.38369e8i	−0.830534	−	0.344019i
$372$	−6.88245e8	+	2.90637e7i	−0.693175	+	0.0292719i
$373$	3.89025e8	+	9.39189e8i	0.388147	+	0.937071i	0.990332	+	0.138714i	$0.0442969\pi$
$373$	3.89025e8	+	9.39189e8i	0.388147	+	0.937071i	−0.602185	+	0.798356i	$0.705703\pi$
$374$	−1.41291e8	+	7.97968e8i	−0.139658	+	0.788742i
$375$	−3.22703e8	−	3.22703e8i	−0.316005	−	0.316005i
$376$	−9.62774e7	+	7.19376e8i	−0.0934043	+	0.697909i
$377$	9.95584e8	−	9.95584e8i	0.956937	−	0.956937i
$378$	3.36381e8	+	4.81133e8i	0.320339	+	0.458189i
$379$	−9.80376e8	+	4.06085e8i	−0.925029	+	0.383160i	−0.793790	−	0.608191i	$-0.791895\pi$
$379$	−9.80376e8	+	4.06085e8i	−0.925029	+	0.383160i	−0.131238	+	0.991351i	$0.541895\pi$
$380$	7.61599e8	+	1.63937e9i	0.712006	+	1.53262i
$381$	−1.61769e8	+	3.90545e8i	−0.149850	+	0.361771i
$382$	−1.42470e8	+	2.23280e8i	−0.130768	+	0.204941i
$383$	−4.09961e7			−0.0372861			−0.0186430	−	0.999826i	$-0.505935\pi$
$383$	−4.09961e7			−0.0372861			−0.0186430	+	0.999826i	$0.505935\pi$
$384$	1.84905e8	+	5.16041e8i	0.166644	+	0.465077i
$385$	5.62752e8			0.502579
$386$	8.16255e8	−	1.27925e9i	0.722388	−	1.13214i
$387$	1.31397e7	−	3.17221e7i	0.0115239	−	0.0278210i
$388$	−4.12119e8	−	8.87100e8i	−0.358188	−	0.771013i
$389$	4.98871e8	−	2.06639e8i	0.429699	−	0.177987i	−0.157342	−	0.987544i	$-0.550293\pi$
$389$	4.98871e8	−	2.06639e8i	0.429699	−	0.177987i	0.587041	+	0.809557i	$0.300293\pi$
$390$	−5.79172e8	−	8.28402e8i	−0.494403	−	0.707156i
$391$	9.17290e8	−	9.17290e8i	0.776047	−	0.776047i
$392$	−9.24955e7	+	6.91118e8i	−0.0775567	+	0.579497i
$393$	−1.51442e8	−	1.51442e8i	−0.125856	−	0.125856i
$394$	−1.53642e8	+	8.67721e8i	−0.126553	+	0.714732i
$395$	3.09475e8	+	7.47139e8i	0.252660	+	0.609975i
$396$	−6.75731e8	+	2.85353e7i	−0.546816	+	0.0230914i
$397$	−2.84129e8	−	1.17690e8i	−0.227902	−	0.0944002i	0.265810	−	0.964025i	$-0.414361\pi$
$397$	−2.84129e8	−	1.17690e8i	−0.227902	−	0.0944002i	−0.493713	+	0.869625i	$0.664361\pi$
$398$	−2.86355e8	−	1.29605e9i	−0.227675	−	1.03046i
$399$		−	6.33825e8i		−	0.499533i
$400$	1.72839e7	+	2.04281e8i	0.0135030	+	0.159594i
$401$		−	1.76463e9i		−	1.36663i	−0.730126	−	0.683313i	$-0.760539\pi$
$401$		−	1.76463e9i		−	1.36663i	0.730126	−	0.683313i	$-0.239461\pi$
$402$	−5.71915e8	+	1.26362e8i	−0.439076	+	0.0970117i
$403$	2.76425e9	+	1.14499e9i	2.10383	+	0.871433i
$404$	−1.40702e9	−	1.29301e9i	−1.06161	−	0.975586i
$405$	−1.80396e8	−	4.35515e8i	−0.134938	−	0.325770i
$406$	7.14195e8	+	1.26458e8i	0.529634	+	0.0937791i
$407$	−4.48434e8	−	4.48434e8i	−0.329699	−	0.329699i
$408$	6.48561e8	+	3.76303e8i	0.472759	+	0.274301i
$409$	−1.92196e9	+	1.92196e9i	−1.38903	+	1.38903i	−0.561668	+	0.827363i	$0.689840\pi$
$409$	−1.92196e9	+	1.92196e9i	−1.38903	+	1.38903i	−0.827363	+	0.561668i	$0.810160\pi$
$410$	1.59424e8	−	1.11460e8i	0.114238	−	0.0798688i
$411$	7.75718e8	−	3.21313e8i	0.551135	−	0.228287i
$412$	−2.56741e8	−	9.38619e7i	−0.180865	−	0.0661225i
$413$	2.77085e8	−	6.68943e8i	0.193548	−	0.467266i
$414$	9.12693e8	+	5.82367e8i	0.632155	+	0.403363i
$415$	−1.64338e9			−1.12867
$416$	2.15987e8	−	2.37111e9i	0.147096	−	1.61482i
$417$	−1.16926e9			−0.789649
$418$	1.42989e9	+	9.12377e8i	0.957603	+	0.611023i
$419$	3.44329e8	−	8.31283e8i	0.228678	−	0.552077i	−0.767339	−	0.641242i	$-0.778420\pi$
$419$	3.44329e8	−	8.31283e8i	0.228678	−	0.552077i	0.996017	+	0.0891644i	$0.0284197\pi$
$420$	1.78789e8	−	4.89042e8i	0.117752	−	0.322087i
$421$	−8.33879e7	+	3.45404e7i	−0.0544648	+	0.0225600i	−0.409750	−	0.912198i	$-0.634384\pi$
$421$	−8.33879e7	+	3.45404e7i	−0.0544648	+	0.0225600i	0.355285	+	0.934758i	$0.384384\pi$
$422$	−1.36251e9	+	9.52592e8i	−0.882566	+	0.617040i
$423$	−5.85886e8	+	5.85886e8i	−0.376376	+	0.376376i
$424$	−5.62119e8	−	2.11600e9i	−0.358136	−	1.34814i
$425$	1.98292e8	+	1.98292e8i	0.125298	+	0.125298i
$426$	−6.28174e8	−	1.11227e8i	−0.393683	−	0.0697070i
$427$	3.51008e8	+	8.47409e8i	0.218183	+	0.526739i
$428$	1.54532e9	−	1.68159e9i	0.952720	−	1.03673i
$429$	−8.76262e8	−	3.62960e8i	−0.535838	−	0.221951i
$430$	−6.90755e7	+	1.52619e7i	−0.0418972	+	0.00925697i
$431$			3.16746e9i			1.90564i	0.303542	+	0.952818i	$0.401831\pi$
$431$			3.16746e9i			1.90564i	−0.303542	+	0.952818i	$0.598169\pi$
$432$	−4.41079e8	+	1.38510e9i	−0.263222	+	0.826587i
$433$			2.25357e9i			1.33403i	0.745047	+	0.667013i	$0.232427\pi$
$433$			2.25357e9i			1.33403i	−0.745047	+	0.667013i	$0.767573\pi$
$434$	3.32524e8	+	1.50501e9i	0.195258	+	0.883742i
$435$	7.04403e8	+	2.91773e8i	0.410307	+	0.169955i
$436$	5.14812e7	+	1.21910e9i	0.0297472	+	0.704430i
$437$	−1.03907e9	−	2.50853e9i	−0.595605	−	1.43792i
$438$	1.21896e8	−	6.88427e8i	0.0693153	−	0.391470i
$439$	−1.28223e9	−	1.28223e9i	−0.723334	−	0.723334i	0.245949	−	0.969283i	$-0.420901\pi$
$439$	−1.28223e9	−	1.28223e9i	−0.723334	−	0.723334i	−0.969283	+	0.245949i	$0.920901\pi$
$440$	8.45901e8	+	1.10731e9i	0.473407	+	0.619704i
$441$	−5.62872e8	+	5.62872e8i	−0.312517	+	0.312517i
$442$	−1.86612e9	−	2.66915e9i	−1.02792	−	1.47026i
$443$	9.33966e8	−	3.86861e8i	0.510409	−	0.211418i	−0.112589	−	0.993642i	$-0.535914\pi$
$443$	9.33966e8	−	3.86861e8i	0.510409	−	0.211418i	0.622998	+	0.782223i	$0.285914\pi$
$444$	−5.32167e8	+	2.47228e8i	−0.288541	+	0.134047i
$445$	1.37942e9	−	3.33021e9i	0.742055	−	1.79148i
$446$	−1.78589e9	+	2.79887e9i	−0.953197	+	1.49386i
$447$	−1.36470e9			−0.722703
$448$	1.06481e9	−	6.08697e8i	0.559501	−	0.319836i
$449$	−2.31644e9			−1.20770			−0.603850	−	0.797098i	$-0.706368\pi$
$449$	−2.31644e9			−1.20770			−0.603850	+	0.797098i	$0.706368\pi$
$450$	−1.25892e8	+	1.97299e8i	−0.0651257	+	0.102066i
$451$	6.98509e7	−	1.68635e8i	0.0358554	−	0.0865625i
$452$	8.87977e8	−	4.12526e8i	0.452290	−	0.210120i
$453$	−1.60889e9	+	6.66426e8i	−0.813175	+	0.336828i
$454$	1.46760e9	+	2.09913e9i	0.736056	+	1.05280i
$455$	−1.59920e9	+	1.59920e9i	−0.795910	+	0.795910i
$456$	1.24716e9	−	9.52734e8i	0.615948	−	0.470538i
$457$	−1.92299e9	−	1.92299e9i	−0.942474	−	0.942474i	0.0559593	−	0.998433i	$-0.482178\pi$
$457$	−1.92299e9	−	1.92299e9i	−0.942474	−	0.942474i	−0.998433	+	0.0559593i	$0.982178\pi$
$458$	1.11098e8	−	6.27448e8i	0.0540355	−	0.305175i
$459$	7.60922e8	+	1.83703e9i	0.367279	+	0.886690i
$460$	−9.41115e7	−	2.22861e9i	−0.0450807	−	1.06753i
$461$	−2.08123e9	−	8.62074e8i	−0.989388	−	0.409818i	−0.171493	−	0.985185i	$-0.554859\pi$
$461$	−2.08123e9	−	8.62074e8i	−0.989388	−	0.409818i	−0.817895	+	0.575367i	$0.804859\pi$
$462$	−1.05410e8	−	4.77086e8i	−0.0497317	−	0.225086i
$463$		−	3.30919e9i		−	1.54949i	−0.632275	−	0.774744i	$-0.717879\pi$
$463$		−	3.30919e9i		−	1.54949i	0.632275	−	0.774744i	$-0.282121\pi$
$464$	8.24715e8	+	1.59538e9i	0.383258	+	0.741399i
$465$			1.62022e9i			0.747290i
$466$	1.19449e9	−	2.63917e8i	0.546805	−	0.120814i
$467$	−4.37630e8	−	1.81272e8i	−0.198837	−	0.0823612i	0.281043	−	0.959695i	$-0.409320\pi$
$467$	−4.37630e8	−	1.81272e8i	−0.198837	−	0.0823612i	−0.479880	+	0.877334i	$0.659320\pi$
$468$	1.83917e9	−	2.00136e9i	0.829397	−	0.902534i
$469$	5.01510e8	+	1.21075e9i	0.224479	+	0.541939i
$470$	1.68094e9	+	2.97634e8i	0.746810	+	0.132233i
$471$	6.16870e8	+	6.16870e8i	0.272032	+	0.272032i
$472$	1.73276e9	−	4.60311e8i	0.758474	−	0.201490i
$473$	−4.69373e7	+	4.69373e7i	−0.0203941	+	0.0203941i
$474$	5.75436e8	−	4.02312e8i	0.248183	−	0.173516i
$475$	5.42274e8	−	2.24617e8i	0.232162	−	0.0961646i
$476$	5.76065e8	−	1.57571e9i	0.244820	−	0.669658i
$477$	9.56488e8	−	2.30917e9i	0.403520	−	0.974184i
$478$	6.89968e8	+	4.40252e8i	0.288956	+	0.184376i
$479$	2.89706e9			1.20443			0.602216	−	0.798333i	$-0.294284\pi$
$479$	2.89706e9			1.20443			0.602216	+	0.798333i	$0.294284\pi$
$480$	1.23102e9	−	3.83307e8i	0.508066	−	0.158199i
$481$	2.54868e9			1.04426
$482$	2.69125e9	+	1.71722e9i	1.09469	+	0.698493i
$483$	−2.99308e8	+	7.22593e8i	−0.120866	+	0.291796i
$484$	−1.11468e9	−	4.07517e8i	−0.446882	−	0.163375i
$485$	−2.12553e9	+	8.80425e8i	−0.846003	+	0.350426i
$486$	−2.13459e9	+	1.49239e9i	−0.843506	+	0.589731i
$487$	2.74145e9	−	2.74145e9i	1.07554	−	1.07554i	0.0786415	−	0.996903i	$-0.474942\pi$
$487$	2.74145e9	−	2.74145e9i	1.07554	−	1.07554i	0.996903	−	0.0786415i	$-0.0250582\pi$
$488$	−1.13980e9	+	1.96445e9i	−0.443976	+	0.765195i
$489$	−5.22263e8	−	5.22263e8i	−0.201980	−	0.201980i
$490$	1.61491e9	+	2.85943e8i	0.620101	+	0.109798i
$491$	9.95103e8	+	2.40239e9i	0.379387	+	0.915922i	0.992081	+	0.125601i	$0.0400859\pi$
$491$	9.95103e8	+	2.40239e9i	0.379387	+	0.915922i	−0.612694	+	0.790320i	$0.709914\pi$
$492$	−1.24355e8	−	1.14278e8i	−0.0470745	−	0.0432598i
$493$	2.26962e9	+	9.40106e8i	0.853077	+	0.353356i
$494$	−6.65615e9	+	1.47064e9i	−2.48416	+	0.548862i
$495$			1.59076e9i			0.589505i
$496$	−2.46152e9	+	2.91655e9i	−0.905770	+	1.07321i
$497$			1.42739e9i			0.521549i
$498$	3.07822e8	+	1.39321e9i	0.111686	+	0.505491i
$499$	−3.23212e9	−	1.33879e9i	−1.16449	−	0.482348i	−0.285123	−	0.958491i	$-0.592035\pi$
$499$	−3.23212e9	−	1.33879e9i	−1.16449	−	0.482348i	−0.879368	+	0.476143i	$0.842035\pi$
$500$	−2.52617e9	+	1.06677e8i	−0.903789	+	0.0381659i
$501$	3.37144e8	+	8.13937e8i	0.119780	+	0.289174i
$502$	7.32351e8	−	4.13608e9i	0.258378	−	1.45924i
$503$	5.69237e8	+	5.69237e8i	0.199437	+	0.199437i	0.799759	−	0.600322i	$-0.204961\pi$
$503$	5.69237e8	+	5.69237e8i	0.199437	+	0.199437i	−0.600322	+	0.799759i	$0.704961\pi$
$504$	1.38783e9	+	1.85739e8i	0.482868	+	0.0646244i
$505$	−3.17812e9	+	3.17812e9i	−1.09812	+	1.09812i
$506$	−1.19930e9	−	1.71539e9i	−0.411530	−	0.588620i
$507$	2.18221e9	−	9.03900e8i	0.743649	−	0.308030i
$508$	9.86737e8	+	2.12399e9i	0.333948	+	0.718834i
$509$	−1.80910e8	+	4.36755e8i	−0.0608065	+	0.146800i	−0.951362	−	0.308074i	$-0.900316\pi$
$509$	−1.80910e8	+	4.36755e8i	−0.0608065	+	0.146800i	0.890556	+	0.454874i	$0.150316\pi$
$510$	9.48652e8	−	1.48674e9i	0.316673	−	0.496294i
$511$	−1.56430e9			−0.518618
$512$	2.79829e9	+	1.18024e9i	0.921399	+	0.388619i
$513$	4.16182e9			1.36104
$514$	1.42266e9	−	2.22961e9i	0.462094	−	0.724200i
$515$	−2.46048e8	+	5.94013e8i	−0.0793771	+	0.191633i
$516$	2.58772e7	+	5.57016e7i	0.00829170	+	0.0178482i
$517$	1.47989e9	−	6.12992e8i	0.470992	−	0.195091i
$518$	7.52299e8	+	1.07603e9i	0.237813	+	0.340150i
$519$	1.07368e7	−	1.07368e7i	0.00337124	−	0.00337124i
$520$	−5.55055e9	−	7.42855e8i	−1.73111	−	0.231682i
$521$	1.56524e9	+	1.56524e9i	0.484897	+	0.484897i	0.906691	−	0.421795i	$-0.138600\pi$
$521$	1.56524e9	+	1.56524e9i	0.484897	+	0.484897i	−0.421795	+	0.906691i	$0.638600\pi$
$522$	−3.57467e8	+	2.01886e9i	−0.109999	+	0.621239i
$523$	−9.96704e8	−	2.40626e9i	−0.304656	−	0.735506i	−0.999861	−	0.0166935i	$-0.994686\pi$
$523$	−9.96704e8	−	2.40626e9i	−0.304656	−	0.735506i	0.695204	−	0.718812i	$-0.255314\pi$
$524$	−1.18551e9	+	5.00626e7i	−0.359953	+	0.0152004i
$525$	−1.56204e8	−	6.47020e7i	−0.0471125	−	0.0195146i
$526$	6.16963e8	+	2.79238e9i	0.184845	+	0.836614i
$527$			5.22043e9i			1.55371i
$528$	7.80299e8	−	9.24542e8i	0.230697	−	0.273343i
$529$		−	5.42995e7i		−	0.0159478i
$530$	−5.02826e9	+	1.11097e9i	−1.46707	+	0.324143i
$531$	1.89094e9	+	7.83254e8i	0.548084	+	0.227024i
$532$	−2.58560e9	−	2.37608e9i	−0.744510	−	0.684179i
$533$	2.80720e8	+	6.77719e8i	0.0803024	+	0.193867i
$534$	−3.08164e9	−	5.45648e8i	−0.875765	−	0.155067i
$535$	−3.79829e9	−	3.79829e9i	−1.07238	−	1.07238i
$536$	−1.62851e9	+	2.80675e9i	−0.456788	+	0.787276i
$537$	8.08102e8	−	8.08102e8i	0.225194	−	0.225194i
$538$	4.23586e9	−	2.96147e9i	1.17274	−	0.819915i
$539$	1.42176e9	−	5.88913e8i	0.391080	−	0.161991i
$540$	3.21114e9	+	1.17396e9i	0.877570	+	0.320831i
$541$	1.16298e9	−	2.80768e9i	0.315778	−	0.762356i	−0.683691	−	0.729772i	$-0.739626\pi$
$541$	1.16298e9	−	2.80768e9i	0.315778	−	0.762356i	0.999469	−	0.0325843i	$-0.0103737\pi$
$542$	2.22118e9	+	1.41728e9i	0.599220	+	0.382347i
$543$	−1.87249e9			−0.501903
$544$	3.96639e9	−	1.23503e9i	1.05633	−	0.328914i
$545$	2.86993e9			0.759424
$546$	1.65531e9	+	1.05621e9i	0.435216	+	0.277701i
$547$	6.68692e8	−	1.61437e9i	0.174691	−	0.421742i	−0.812147	−	0.583453i	$-0.801701\pi$
$547$	6.68692e8	−	1.61437e9i	0.174691	−	0.421742i	0.986838	+	0.161711i	$0.0517013\pi$
$548$	1.59725e9	−	4.36897e9i	0.414612	−	1.13409i
$549$	−2.39542e9	+	9.92217e8i	−0.617844	+	0.255919i
$550$	3.70819e8	−	2.59255e8i	0.0950369	−	0.0664444i
$551$	3.63583e9	−	3.63583e9i	0.925920	−	0.925920i
$552$	−1.87173e9	+	4.97229e8i	−0.473648	+	0.125826i
$553$	−1.11086e9	−	1.11086e9i	−0.279333	−	0.279333i
$554$	−5.17848e9	−	9.16923e8i	−1.29395	−	0.229112i
$555$	5.28163e8	+	1.27510e9i	0.131142	+	0.316605i
$556$	−4.38330e9	+	4.76983e9i	−1.08153	+	1.17690i
$557$	1.26880e9	+	5.25554e8i	0.311100	+	0.128862i	0.532770	−	0.846260i	$-0.321151\pi$
$557$	1.26880e9	+	5.25554e8i	0.311100	+	0.128862i	−0.221670	+	0.975122i	$0.571151\pi$
$558$	−4.25430e9	+	9.39966e8i	−1.03659	+	0.229030i
$559$		−	2.66769e8i		−	0.0645943i
$560$	−1.32474e9	−	2.56266e9i	−0.318766	−	0.616642i
$561$		−	1.65487e9i		−	0.395724i
$562$	−7.86629e8	−	3.56029e9i	−0.186936	−	0.846075i
$563$	−4.46849e9	−	1.85091e9i	−1.05531	−	0.437126i	−0.213528	−	0.976937i	$-0.568496\pi$
$563$	−4.46849e9	−	1.85091e9i	−1.05531	−	0.437126i	−0.841786	+	0.539811i	$0.818496\pi$
$564$	−6.25326e7	−	1.48081e9i	−0.0146767	−	0.347553i
$565$	−8.81296e8	−	2.12764e9i	−0.205566	−	0.496281i
$566$	1.44935e9	−	8.18547e9i	0.335982	−	1.89752i
$567$	6.47533e8	+	6.47533e8i	0.149184	+	0.149184i
$568$	−2.80863e9	+	2.14558e9i	−0.643094	+	0.491276i
$569$	3.75272e9	−	3.75272e9i	0.853992	−	0.853992i	−0.136630	−	0.990622i	$-0.543627\pi$
$569$	3.75272e9	−	3.75272e9i	0.853992	−	0.853992i	0.990622	+	0.136630i	$0.0436273\pi$
$570$	−2.11511e9	−	3.02529e9i	−0.478378	−	0.684235i
$571$	4.88052e9	−	2.02158e9i	1.09708	−	0.454427i	0.240613	−	0.970621i	$-0.422652\pi$
$571$	4.88052e9	−	2.02158e9i	1.09708	−	0.454427i	0.856472	+	0.516194i	$0.172652\pi$
$572$	−4.76557e9	+	2.21393e9i	−1.06470	+	0.494627i
$573$	2.06982e8	−	4.99699e8i	0.0459612	−	0.110960i
$574$	−2.03266e8	+	3.18561e8i	−0.0448614	+	0.0703074i
$575$	−7.24290e8			−0.158882
$576$	1.72064e9	+	3.00997e9i	0.375155	+	0.656272i
$577$	−3.02417e9			−0.655377			−0.327688	−	0.944786i	$-0.606270\pi$
$577$	−3.02417e9			−0.655377			−0.327688	+	0.944786i	$0.606270\pi$
$578$	5.59413e8	−	8.76719e8i	0.120499	−	0.188848i
$579$	−1.18587e9	+	2.86294e9i	−0.253899	+	0.612967i
$580$	3.83091e9	−	1.77972e9i	0.815274	−	0.378750i
$581$	2.94945e9	−	1.22170e9i	0.623913	−	0.258433i
$582$	1.14454e9	+	1.63706e9i	0.240657	+	0.344218i
$583$	−3.41674e9	+	3.41674e9i	−0.714121	+	0.714121i
$584$	−2.35138e9	−	3.07802e9i	−0.488515	−	0.639480i
$585$	−4.52057e9	−	4.52057e9i	−0.933571	−	0.933571i
$586$	−8.14196e8	+	4.59831e9i	−0.167143	+	0.943967i
$587$	−3.18130e8	−	7.68034e8i	−0.0649189	−	0.156728i	0.888091	−	0.459668i	$-0.152032\pi$
$587$	−3.18130e8	−	7.68034e8i	−0.0649189	−	0.156728i	−0.953010	+	0.302940i	$0.902032\pi$
$588$	−6.00762e7	−	1.42264e9i	−0.0121866	−	0.288585i
$589$	1.00949e10	+	4.18146e9i	2.03564	+	0.843188i
$590$	−9.09755e8	−	4.11757e9i	−0.182365	−	0.825389i
$591$		−	1.79952e9i		−	0.358593i
$592$	−9.86450e8	+	3.09771e9i	−0.195411	+	0.613641i
$593$			8.56980e9i			1.68764i	0.536628	+	0.843819i	$0.319698\pi$
$593$			8.56980e9i			1.68764i	−0.536628	+	0.843819i	$0.680302\pi$
$594$	3.13264e9	−	6.92140e8i	0.613278	−	0.135501i
$595$	−3.64568e9	−	1.51009e9i	−0.709527	−	0.293896i
$596$	−5.11596e9	+	5.56709e9i	−0.989840	+	1.07713i
$597$	1.03725e9	+	2.50415e9i	0.199515	+	0.481671i
$598$	8.28284e9	+	1.46659e9i	1.58389	+	0.280450i
$599$	−2.09616e9	−	2.09616e9i	−0.398501	−	0.398501i	0.479203	−	0.877704i	$-0.340926\pi$
$599$	−2.09616e9	−	2.09616e9i	−0.398501	−	0.398501i	−0.877704	+	0.479203i	$0.840926\pi$
$600$	−1.07487e8	−	4.04615e8i	−0.0203154	−	0.0764738i
$601$	4.83078e9	−	4.83078e9i	0.907730	−	0.907730i	−0.0883585	−	0.996089i	$-0.528162\pi$
$601$	4.83078e9	−	4.83078e9i	0.907730	−	0.907730i	0.996089	+	0.0883585i	$0.0281621\pi$
$602$	1.12627e8	−	7.87427e7i	0.0210405	−	0.0147103i
$603$	−3.42251e9	+	1.41765e9i	−0.635673	+	0.263305i
$604$	−3.31281e9	+	9.06155e9i	−0.611741	+	1.67330i
$605$	−1.06826e9	+	2.57900e9i	−0.196125	+	0.473487i
$606$	3.28962e9	+	2.09903e9i	0.600470	+	0.383146i
$607$	3.06582e9			0.556398			0.278199	−	0.960523i	$-0.410263\pi$
$607$	3.06582e9			0.556398			0.278199	+	0.960523i	$0.410263\pi$
$608$	7.88775e8	−	8.65920e9i	0.142328	−	1.56248i
$609$	−1.48113e9			−0.265726
$610$	4.50325e9	+	2.87341e9i	0.803288	+	0.512558i
$611$	−2.46352e9	+	5.94747e9i	−0.436931	+	1.05484i
$612$	4.45417e9	+	1.62840e9i	0.785482	+	0.287165i
$613$	−5.49538e9	+	2.27626e9i	−0.963576	+	0.399126i	−0.808317	−	0.588748i	$-0.799621\pi$
$613$	−5.49538e9	+	2.27626e9i	−0.963576	+	0.399126i	−0.155259	+	0.987874i	$0.549621\pi$
$614$	2.94170e9	−	2.05667e9i	0.512872	−	0.358570i
$615$	−2.80887e8	+	2.80887e8i	−0.0486933	+	0.0486933i
$616$	−2.34136e9	−	1.35849e9i	−0.403586	−	0.234166i
$617$	−1.66490e8	−	1.66490e8i	−0.0285357	−	0.0285357i	0.692695	−	0.721231i	$-0.256423\pi$
$617$	−1.66490e8	−	1.66490e8i	−0.0285357	−	0.0285357i	−0.721231	+	0.692695i	$0.756423\pi$
$618$	5.49675e8	+	9.73278e7i	0.0936800	+	0.0165874i
$619$	−1.58031e9	−	3.81521e9i	−0.267809	−	0.646548i	0.731571	−	0.681766i	$-0.238788\pi$
$619$	−1.58031e9	−	3.81521e9i	−0.267809	−	0.646548i	−0.999380	+	0.0352175i	$0.988788\pi$
$620$	6.60947e9	+	6.07387e9i	1.11377	+	1.02352i
$621$	−4.74469e9	−	1.96531e9i	−0.795036	−	0.329315i
$622$	3.18004e9	−	7.02612e8i	0.529865	−	0.117071i
$623$			7.00236e9i			1.16021i
$624$	4.09906e8	+	4.84474e9i	0.0675365	+	0.798224i
$625$			6.92451e9i			1.13451i
$626$	9.59104e8	+	4.34092e9i	0.156263	+	0.707248i
$627$	−3.20008e9	−	1.32552e9i	−0.518470	−	0.214757i
$628$	4.82895e9	−	2.03920e8i	0.778025	−	0.0328550i
$629$	1.70176e9	+	4.10842e9i	0.272660	+	0.658260i
$630$	5.74199e8	−	3.24289e9i	0.0914893	−	0.516701i
$631$	−6.41310e9	−	6.41310e9i	−1.01617	−	1.01617i	−0.999867	−	0.0162996i	$-0.994811\pi$
$631$	−6.41310e9	−	6.41310e9i	−1.01617	−	1.01617i	−0.0162996	−	0.999867i	$-0.505189\pi$
$632$	5.16012e8	−	3.85559e9i	0.0813111	−	0.607549i
$633$	2.40059e9	−	2.40059e9i	0.376188	−	0.376188i
$634$	−3.64773e9	−	5.21743e9i	−0.568474	−	0.813101i
$635$	5.08917e9	−	2.10800e9i	0.788750	−	0.326711i
$636$	1.88370e9	+	4.05472e9i	0.290343	+	0.624973i
$637$	−2.36675e9	+	5.71385e9i	−0.362798	+	0.875872i
$638$	2.13206e9	−	3.34139e9i	0.325033	−	0.509395i
$639$	−4.03489e9			−0.611756
$640$	3.05118e9	−	6.45871e9i	0.460085	−	0.973903i
$641$	7.98971e9			1.19820			0.599098	−	0.800676i	$-0.295526\pi$
$641$	7.98971e9			1.19820			0.599098	+	0.800676i	$0.295526\pi$
$642$	−2.50863e9	+	3.93155e9i	−0.374165	+	0.586396i
$643$	−1.66639e9	+	4.02303e9i	−0.247195	+	0.596781i	−0.997964	−	0.0637838i	$-0.979683\pi$
$643$	−1.66639e9	+	4.02303e9i	−0.247195	+	0.596781i	0.750769	+	0.660565i	$0.229683\pi$
$644$	1.82568e9	+	3.92983e9i	0.269354	+	0.579794i
$645$	1.33464e8	−	5.52825e7i	0.0195841	−	0.00811201i
$646$	−6.81498e9	−	9.74763e9i	−0.994606	−	1.42261i
$647$	6.67610e9	−	6.67610e9i	0.969077	−	0.969077i	−0.0304594	−	0.999536i	$-0.509697\pi$
$647$	6.67610e9	−	6.67610e9i	0.969077	−	0.969077i	0.999536	+	0.0304594i	$0.00969701\pi$
$648$	−3.00789e8	+	2.24747e9i	−0.0434259	+	0.324475i
$649$	−2.79792e9	−	2.79792e9i	−0.401771	−	0.401771i
$650$	−3.17036e8	+	1.79052e9i	−0.0452806	+	0.255730i
$651$	−1.20449e9	−	2.90789e9i	−0.171108	−	0.413090i
$652$	−4.08835e9	+	1.72646e8i	−0.577672	+	0.0243944i
$653$	9.62036e8	+	3.98488e8i	0.135206	+	0.0560040i	0.449260	−	0.893401i	$-0.351688\pi$
$653$	9.62036e8	+	3.98488e8i	0.135206	+	0.0560040i	−0.314055	+	0.949405i	$0.601688\pi$
$654$	−5.37570e8	−	2.43305e9i	−0.0751473	−	0.340118i
$655$			2.79085e9i			0.388054i
$656$	−9.32362e8	+	7.88856e7i	−0.128950	+	0.0109102i
$657$		−	4.42191e9i		−	0.608318i
$658$	−3.23813e9	+	7.15449e8i	−0.443102	+	0.0979012i
$659$	−4.49010e9	−	1.85986e9i	−0.611163	−	0.253152i	0.0555629	−	0.998455i	$-0.482305\pi$
$659$	−4.49010e9	−	1.85986e9i	−0.611163	−	0.253152i	−0.666725	+	0.745303i	$0.732305\pi$
$660$	−2.09519e9	−	1.92541e9i	−0.283674	−	0.260687i
$661$	4.21011e9	+	1.01641e10i	0.567006	+	1.36887i	0.904067	+	0.427391i	$0.140567\pi$
$661$	4.21011e9	+	1.01641e10i	0.567006	+	1.36887i	−0.337061	+	0.941483i	$0.609433\pi$
$662$	7.81380e9	+	1.38354e9i	1.04679	+	0.185349i
$663$	4.70273e9	+	4.70273e9i	0.626690	+	0.626690i
$664$	6.83737e9	+	3.96713e9i	0.906360	+	0.525881i
$665$	−5.84023e9	+	5.84023e9i	−0.770113	+	0.770113i
$666$	−3.04168e9	+	2.12657e9i	−0.398982	+	0.278946i
$667$	−5.86197e9	+	2.42811e9i	−0.764898	+	0.316831i
$668$	4.58423e9	+	1.67595e9i	0.595043	+	0.217542i
$669$	2.59457e9	−	6.26384e9i	0.335022	−	0.808815i
$670$	6.43411e9	+	4.10545e9i	0.826469	+	0.527349i
$671$	5.01249e9			0.640508
$672$	−1.92441e9	+	1.60309e9i	−0.244628	+	0.203782i
$673$	3.34690e9			0.423243			0.211622	−	0.977352i	$-0.432126\pi$
$673$	3.34690e9			0.423243			0.211622	+	0.977352i	$0.432126\pi$
$674$	−3.61364e9	−	2.30578e9i	−0.454606	−	0.290073i
$675$	4.24846e8	−	1.02567e9i	0.0531702	−	0.128364i
$676$	4.49330e9	−	1.22905e10i	0.559438	−	1.53023i
$677$	−9.01526e9	+	3.73424e9i	−1.11665	+	0.462532i	−0.863224	−	0.504822i	$-0.831558\pi$
$677$	−9.01526e9	+	3.73424e9i	−1.11665	+	0.462532i	−0.253428	+	0.967354i	$0.581558\pi$
$678$	−1.63868e9	+	1.14567e9i	−0.201924	+	0.141174i
$679$	3.16028e9	−	3.16028e9i	0.387420	−	0.387420i
$680$	−2.50865e9	−	9.44337e9i	−0.305956	−	1.15172i
$681$	−3.69843e9	−	3.69843e9i	−0.448748	−	0.448748i
$682$	8.29395e9	+	1.46856e9i	1.00119	+	0.177275i
$683$	−1.36116e9	−	3.28613e9i	−0.163470	−	0.394650i	0.820826	−	0.571178i	$-0.193513\pi$
$683$	−1.36116e9	−	3.28613e9i	−0.163470	−	0.394650i	−0.984296	+	0.176528i	$0.943513\pi$
$684$	6.71659e9	−	7.30887e9i	0.802514	−	0.873281i
$685$	−1.01083e10	−	4.18701e9i	−1.20161	−	0.497722i
$686$	−8.43183e9	+	1.86297e9i	−0.997212	+	0.220329i
$687$			1.30123e9i			0.153111i
$688$	3.24235e8	+	1.03251e8i	0.0379578	+	0.0120875i
$689$		−	1.94191e10i		−	2.26184i
$690$	9.82719e8	+	4.44780e9i	0.113883	+	0.515435i
$691$	−7.42135e9	−	3.07402e9i	−0.855677	−	0.354433i	−0.0886615	−	0.996062i	$-0.528259\pi$
$691$	−7.42135e9	−	3.07402e9i	−0.855677	−	0.354433i	−0.767015	+	0.641629i	$0.778259\pi$
$692$	−3.54931e6	−	8.40495e7i	−0.000407167	−	0.00964193i
$693$	−1.18259e9	−	2.85502e9i	−0.134979	−	0.325869i
$694$	−1.55171e9	+	8.76358e9i	−0.176219	+	0.995230i
$695$	1.07739e10	+	1.07739e10i	1.21738	+	1.21738i
$696$	−2.22637e9	−	2.91438e9i	−0.250302	−	0.327652i
$697$	−9.05031e8	+	9.05031e8i	−0.101239	+	0.101239i
$698$	−3.99840e9	−	5.71900e9i	−0.445033	−	0.636541i
$699$	−2.30793e9	+	9.55975e8i	−0.255595	+	0.105871i
$700$	−8.49520e8	+	3.94660e8i	−0.0936118	+	0.0434891i
$701$	1.21763e9	−	2.93961e9i	0.133506	−	0.322312i	−0.842962	−	0.537973i	$-0.819190\pi$
$701$	1.21763e9	−	2.93961e9i	0.133506	−	0.322312i	0.976468	+	0.215660i	$0.0691904\pi$
$702$	−6.93530e9	+	1.08691e10i	−0.756633	+	1.18580i
$703$	9.30769e9			1.01041
$704$	−8.46369e8	−	6.64903e9i	−0.0914230	−	0.718215i
$705$	−3.48602e9			−0.374686
$706$	3.74205e9	−	5.86459e9i	0.400215	−	0.627222i
$707$	3.34128e9	−	8.06657e9i	0.355587	−	0.858462i
$708$	−3.32035e9	+	1.54253e9i	−0.351615	+	0.163349i
$709$	−8.20428e9	+	3.39833e9i	−0.864527	+	0.358099i	−0.770477	−	0.637468i	$-0.779982\pi$
$709$	−8.20428e9	+	3.39833e9i	−0.864527	+	0.358099i	−0.0940509	+	0.995567i	$0.529982\pi$
$710$	4.76329e9	+	6.81304e9i	0.499462	+	0.714392i
$711$	3.14014e9	−	3.14014e9i	0.327646	−	0.327646i
$712$	−1.37783e10	+	1.05256e10i	−1.43059	+	1.09287i
$713$	−9.53416e9	−	9.53416e9i	−0.985075	−	0.985075i
$714$	−5.97337e8	+	3.37356e9i	−0.0614151	+	0.346853i
$715$	4.72971e9	+	1.14185e10i	0.483909	+	1.16826i
$716$	−2.67137e8	−	6.32595e9i	−0.0271981	−	0.644065i
$717$	−1.54414e9	−	6.39604e8i	−0.156448	−	0.0648029i
$718$	−1.83484e9	−	8.30451e9i	−0.184996	−	0.837295i
$719$			9.65602e9i			0.968829i	0.874839	+	0.484414i	$0.160967\pi$
$719$			9.65602e9i			0.968829i	−0.874839	+	0.484414i	$0.839033\pi$
$720$	7.24402e9	−	3.74472e9i	0.723296	−	0.373900i
$721$		−	1.24902e9i		−	0.124107i
$722$	−1.44332e10	+	3.18893e9i	−1.42719	+	0.315330i
$723$	−6.02300e9	−	2.49481e9i	−0.592691	−	0.245501i
$724$	−7.01956e9	+	7.63855e9i	−0.687424	+	0.748042i
$725$	−5.24889e8	−	1.26719e9i	−0.0511546	−	0.123498i
$726$	2.38651e9	+	4.22564e8i	0.231464	+	0.0409840i
$727$	2.74733e9	+	2.74733e9i	0.265180	+	0.265180i	0.827155	−	0.561974i	$-0.189958\pi$
$727$	2.74733e9	+	2.74733e9i	0.265180	+	0.265180i	−0.561974	+	0.827155i	$0.689958\pi$
$728$	1.05141e10	−	2.79309e9i	1.00998	−	0.268303i
$729$	1.33950e9	−	1.33950e9i	0.128055	−	0.128055i
$730$	−7.46653e9	+	5.22017e9i	−0.710377	+	0.496655i
$731$	4.30026e8	−	1.78123e8i	0.0407178	−	0.0168658i
$732$	1.59249e9	−	4.35595e9i	0.150068	−	0.410482i
$733$	−4.45434e9	+	1.07537e10i	−0.417753	+	1.00855i	0.565244	+	0.824924i	$0.308782\pi$
$733$	−4.45434e9	+	1.07537e10i	−0.417753	+	1.00855i	−0.982997	+	0.183622i	$0.941218\pi$
$734$	−2.95767e9	−	1.88722e9i	−0.276066	−	0.176151i
$735$	−3.34908e9			−0.311115
$736$	−4.98834e9	+	9.49946e9i	−0.461194	+	0.878267i
$737$	7.16170e9			0.658992
$738$	−9.00496e8	−	5.74584e8i	−0.0824678	−	0.0526207i
$739$	3.93066e9	−	9.48944e9i	0.358269	−	0.864938i	−0.637275	−	0.770637i	$-0.719938\pi$
$739$	3.93066e9	−	9.48944e9i	0.358269	−	0.864938i	0.995544	−	0.0943014i	$-0.0300617\pi$
$740$	7.18156e9	+	2.62551e9i	0.651490	+	0.238178i
$741$	1.28606e10	−	5.32705e9i	1.16118	−	0.480976i
$742$	8.19856e9	−	5.73197e9i	0.736757	−	0.515098i
$743$	−4.58652e9	+	4.58652e9i	−0.410225	+	0.410225i	−0.881817	−	0.471592i	$-0.843680\pi$
$743$	−4.58652e9	+	4.58652e9i	−0.410225	+	0.410225i	0.471592	+	0.881817i	$0.343680\pi$
$744$	3.91123e9	−	6.74103e9i	0.348184	−	0.600097i
$745$	1.25747e10	+	1.25747e10i	1.11417	+	1.11417i
$746$	−1.13250e10	−	2.00526e9i	−0.998743	−	0.176841i
$747$	3.45346e9	+	8.33738e9i	0.303132	+	0.731825i
$748$	−6.75080e9	−	6.20374e9i	−0.589793	−	0.541999i
$749$	9.64067e9	+	3.99330e9i	0.838341	+	0.347252i
$750$	5.04166e9	−	1.11393e9i	0.436374	−	0.0964146i
$751$		−	1.68863e10i		−	1.45477i	−0.686231	−	0.727384i	$-0.740736\pi$
$751$		−	1.68863e10i		−	1.45477i	0.686231	−	0.727384i	$-0.259264\pi$
$752$	−6.27517e9	−	5.29614e9i	−0.538100	−	0.454147i
$753$			8.57761e9i			0.732122i
$754$	3.43662e9	+	1.55542e10i	0.291966	+	1.32144i
$755$	2.09654e10	+	8.68416e9i	1.77292	+	0.734367i
$756$	−6.63593e9	+	2.80227e8i	−0.558567	+	0.0235876i
$757$	−2.18501e9	−	5.27508e9i	−0.183070	−	0.441971i	0.805526	−	0.592560i	$-0.201883\pi$
$757$	−2.18501e9	−	5.27508e9i	−0.183070	−	0.441971i	−0.988596	+	0.150590i	$0.951883\pi$
$758$	2.09319e9	−	1.18217e10i	0.174569	−	0.985908i
$759$	3.02231e9	+	3.02231e9i	0.250896	+	0.250896i
$760$	−2.02704e10	−	2.71288e9i	−1.67500	−	0.224173i
$761$	6.01342e9	−	6.01342e9i	0.494624	−	0.494624i	−0.415135	−	0.909760i	$-0.636266\pi$
$761$	6.01342e9	−	6.01342e9i	0.494624	−	0.494624i	0.909760	+	0.415135i	$0.136266\pi$
$762$	−2.74037e9	−	3.91961e9i	−0.224371	−	0.320923i
$763$	−5.15081e9	+	2.13354e9i	−0.419798	+	0.173886i
$764$	−1.26252e9	−	2.71762e9i	−0.102426	−	0.220476i
$765$	4.26866e9	−	1.03055e10i	0.344728	−	0.832247i
$766$	2.49489e8	−	3.91002e8i	0.0200563	−	0.0314324i
$767$	1.59020e10			1.27253
$768$	−6.04703e9	−	1.37692e9i	−0.481702	−	0.109684i
$769$	−1.86985e9			−0.148274			−0.0741369	−	0.997248i	$-0.523620\pi$
$769$	−1.86985e9			−0.148274			−0.0741369	+	0.997248i	$0.523620\pi$
$770$	−3.42472e9	+	5.36727e9i	−0.270338	+	0.423678i
$771$	−2.06686e9	+	4.98985e9i	−0.162413	+	0.392100i
$772$	7.23339e9	+	1.55701e10i	0.565824	+	1.21796i
$773$	−1.04454e10	+	4.32662e9i	−0.813384	+	0.336915i	−0.750303	−	0.661094i	$-0.770093\pi$
$773$	−1.04454e10	+	4.32662e9i	−0.813384	+	0.336915i	−0.0630808	+	0.998008i	$0.520093\pi$
$774$	2.22587e8	+	3.18371e8i	0.0172546	+	0.0246797i
$775$	2.06102e9	−	2.06102e9i	0.159047	−	0.159047i
$776$	1.09688e10	+	1.46800e9i	0.842640	+	0.112774i
$777$	−1.89584e9	−	1.89584e9i	−0.144987	−	0.144987i
$778$	−1.06514e9	+	6.01553e9i	−0.0810916	+	0.457979i
$779$	1.02518e9	+	2.47500e9i	0.0776996	+	0.187584i
$780$	1.14256e10	−	4.82488e8i	0.862078	−	0.0364045i
$781$	7.20665e9	+	2.98509e9i	0.541321	+	0.224223i
$782$	3.16636e9	+	1.43310e10i	0.236776	+	1.07165i
$783$		−	9.72540e9i		−	0.724005i
$784$	−6.02867e9	−	5.08810e9i	−0.446802	−	0.377093i
$785$		−	1.13680e10i		−	0.838765i
$786$	2.36601e9	−	5.22758e8i	0.173795	−	0.0383991i
$787$	8.96098e9	+	3.71176e9i	0.655306	+	0.271437i	0.685462	−	0.728109i	$-0.259600\pi$
$787$	8.96098e9	+	3.71176e9i	0.655306	+	0.271437i	−0.0301558	+	0.999545i	$0.509600\pi$
$788$	−7.34091e9	−	6.74603e9i	−0.534451	−	0.491142i
$789$	−2.23480e9	−	5.39528e9i	−0.161983	−	0.391061i
$790$	−9.00923e9	−	1.59521e9i	−0.650119	−	0.115113i
$791$	3.16341e9	+	3.16341e9i	0.227268	+	0.227268i
$792$	3.84012e9	−	6.61847e9i	0.274667	−	0.473390i
$793$	−1.42443e10	+	1.42443e10i	−1.01434	+	1.01434i
$794$	2.85159e9	−	1.99367e9i	0.202169	−	0.141345i
$795$	9.71531e9	−	4.02421e9i	0.685760	−	0.284051i
$796$	1.41038e10	+	5.15620e9i	0.991151	+	0.362355i
$797$	2.30573e8	−	5.56653e8i	0.0161326	−	0.0389475i	−0.915608	−	0.402072i	$-0.868290\pi$
$797$	2.30573e8	−	5.56653e8i	0.0161326	−	0.0389475i	0.931741	+	0.363125i	$0.118290\pi$
$798$	6.04513e9	+	3.85725e9i	0.421110	+	0.268700i
$799$	−1.12321e10			−0.779018
$800$	−2.05352e9	−	1.07834e9i	−0.141802	−	0.0744630i
$801$	−1.97940e10			−1.36088
$802$	1.68303e10	+	1.07390e10i	1.15207	+	0.735111i
$803$	−3.27142e9	+	7.89790e9i	−0.222962	+	0.538279i
$804$	2.27531e9	−	6.22365e9i	0.154399	−	0.422327i
$805$	9.41607e9	−	3.90026e9i	0.636186	−	0.263517i
$806$	−2.77427e10	+	1.93961e10i	−1.86628	+	1.30479i
$807$	−7.46308e9	+	7.46308e9i	−0.499874	+	0.499874i
$808$	2.08948e10	−	5.55075e9i	1.39347	−	0.370179i
$809$	1.10263e10	+	1.10263e10i	0.732165	+	0.732165i	0.971048	−	0.238884i	$-0.0767814\pi$
$809$	1.10263e10	+	1.10263e10i	0.732165	+	0.732165i	−0.238884	+	0.971048i	$0.576781\pi$
$810$	5.25158e9	+	9.29866e8i	0.347210	+	0.0614784i
$811$	−6.93300e9	−	1.67377e10i	−0.456403	−	1.10185i	−0.969843	−	0.243729i	$-0.921629\pi$
$811$	−6.93300e9	−	1.67377e10i	−0.456403	−	1.10185i	0.513441	−	0.858125i	$-0.328371\pi$
$812$	−5.55245e9	+	6.04208e9i	−0.363948	+	0.396041i
$813$	−4.97098e9	−	2.05905e9i	−0.324433	−	0.134384i
$814$	7.00598e9	−	1.54794e9i	0.455285	−	0.100593i
$815$			9.62454e9i			0.622771i
$816$	−7.53593e9	+	3.89561e9i	−0.485536	+	0.250992i
$817$		−	9.74230e8i		−	0.0625006i
$818$	−6.63434e9	−	3.00271e10i	−0.423800	−	1.91813i
$819$	1.14739e10	+	4.75265e9i	0.729824	+	0.302303i
$820$	9.28538e7	+	2.19883e9i	0.00588100	+	0.139265i
$821$	−2.16660e9	−	5.23063e9i	−0.136640	−	0.329878i	0.840717	−	0.541474i	$-0.182134\pi$
$821$	−2.16660e9	−	5.23063e9i	−0.136640	−	0.329878i	−0.977357	+	0.211597i	$0.932134\pi$
$822$	−1.65623e9	+	9.35385e9i	−0.104009	+	0.587407i
$823$	−8.13943e9	−	8.13943e9i	−0.508973	−	0.508973i	0.405238	−	0.914211i	$-0.367189\pi$
$823$	−8.13943e9	−	8.13943e9i	−0.508973	−	0.508973i	−0.914211	+	0.405238i	$0.867189\pi$
$824$	2.45765e9	−	1.87746e9i	0.153030	−	0.116903i
$825$	−6.53340e8	+	6.53340e8i	−0.0405089	+	0.0405089i
$826$	4.69382e9	+	6.71368e9i	0.289799	+	0.414506i
$827$	−2.26273e10	+	9.37252e9i	−1.39111	+	0.576218i	−0.947429	−	0.319965i	$-0.896329\pi$
$827$	−2.26273e10	+	9.37252e9i	−1.39111	+	0.576218i	−0.443685	+	0.896183i	$0.646329\pi$
$828$	−1.11087e10	+	5.16075e9i	−0.680075	+	0.315942i
$829$	−3.59167e9	+	8.67106e9i	−0.218955	+	0.528605i	−0.994745	−	0.102387i	$-0.967352\pi$
$829$	−3.59167e9	+	8.67106e9i	−0.218955	+	0.528605i	0.775789	+	0.630992i	$0.217352\pi$
$830$	1.00010e10	−	1.56738e10i	0.607117	−	0.951481i
$831$	1.07394e10			0.649196
$832$	2.13001e10	+	1.64898e10i	1.28218	+	0.992620i
$833$	−1.07909e10			−0.646844
$834$	7.11572e9	−	1.11518e10i	0.424754	−	0.665680i
$835$	4.39330e9	−	1.06064e10i	0.261149	−	0.630470i
$836$	−1.74037e10	+	8.08519e9i	−1.03019	+	0.478595i
$837$	1.90938e10	−	7.90890e9i	1.12552	−	0.466205i
$838$	5.83292e9	+	8.34296e9i	0.342399	+	0.489741i
$839$	−3.50880e9	+	3.50880e9i	−0.205113	+	0.205113i	−0.802186	−	0.597074i	$-0.796330\pi$
$839$	−3.50880e9	+	3.50880e9i	−0.205113	+	0.205113i	0.597074	+	0.802186i	$0.296330\pi$
$840$	3.57621e9	+	4.68135e9i	0.208183	+	0.272517i
$841$	3.70122e9	+	3.70122e9i	0.214565	+	0.214565i
$842$	1.78041e8	−	1.00552e9i	0.0102784	−	0.0580493i
$843$	2.84937e9	+	6.87899e9i	0.163815	+	0.395483i
$844$	−7.93571e8	−	1.87922e10i	−0.0454346	−	1.07592i
$845$	−2.84362e10	−	1.17787e10i	−1.62134	−	0.671580i
$846$	−2.02240e9	−	9.15342e9i	−0.114834	−	0.519741i
$847$		−	5.42282e9i		−	0.306643i
$848$	2.36023e10	+	7.51602e9i	1.32913	+	0.423256i
$849$			1.69754e10i			0.952016i
$850$	−3.09796e9	+	6.84479e8i	−0.173025	+	0.0382291i
$851$	−1.06112e10	−	4.39532e9i	−0.590219	−	0.244477i
$852$	4.88369e9	−	5.31434e9i	0.270526	−	0.294382i
$853$	−8.33218e8	−	2.01157e9i	−0.0459660	−	0.110972i	0.899229	−	0.437479i	$-0.144128\pi$
$853$	−8.33218e8	−	2.01157e9i	−0.0459660	−	0.110972i	−0.945195	+	0.326507i	$0.894128\pi$
$854$	−1.02183e10	−	1.80930e9i	−0.561406	−	0.0994048i
$855$	−1.65089e10	−	1.65089e10i	−0.903312	−	0.903312i
$856$	6.63391e9	+	2.49722e10i	0.361502	+	1.36081i
$857$	1.34491e10	−	1.34491e10i	0.729893	−	0.729893i	−0.240705	−	0.970598i	$-0.577379\pi$
$857$	1.34491e10	−	1.34491e10i	0.729893	−	0.729893i	0.970598	+	0.240705i	$0.0773788\pi$
$858$	8.79439e9	−	6.14853e9i	0.475335	−	0.332327i
$859$	1.36617e10	−	5.65884e9i	0.735406	−	0.304615i	0.0166348	−	0.999862i	$-0.494705\pi$
$859$	1.36617e10	−	5.65884e9i	0.735406	−	0.304615i	0.718772	+	0.695246i	$0.244705\pi$
$860$	2.74810e8	−	7.51689e8i	0.0147329	−	0.0402990i
$861$	2.95308e8	−	7.12936e8i	0.0157675	−	0.0380662i
$862$	−3.02097e10	−	1.92761e10i	−1.60647	−	1.02505i
$863$	−3.64416e10			−1.93001			−0.965005	−	0.262231i	$-0.915542\pi$
$863$	−3.64416e10			−1.93001			−0.965005	+	0.262231i	$0.915542\pi$
$864$	−1.05262e10	−	1.26361e10i	−0.555231	−	0.666521i
$865$	−1.97864e8			−0.0103947
$866$	−2.14935e10	−	1.37145e10i	−1.12459	−	0.717575i
$867$	−8.12723e8	+	1.96209e9i	−0.0423522	+	0.102247i
$868$	−1.63777e10	−	5.98753e9i	−0.850030	−	0.310763i
$869$	−7.93169e9	+	3.28541e9i	−0.410012	+	0.169833i
$870$	−7.06956e9	+	4.94263e9i	−0.363978	+	0.254473i
$871$	−2.03518e10	+	2.03518e10i	−1.04361	+	1.04361i
$872$	−1.19405e10	−	6.92805e9i	−0.609840	−	0.353837i
$873$	8.93337e9	+	8.93337e9i	0.454428	+	0.454428i
$874$	3.02486e10	+	5.35594e9i	1.53255	+	0.271360i
$875$	−4.42101e9	−	1.06733e10i	−0.223097	−	0.538604i
$876$	5.82408e9	+	5.35212e9i	0.292727	+	0.269006i
$877$	4.82278e9	+	1.99766e9i	0.241434	+	0.100005i	0.500120	−	0.865956i	$-0.333289\pi$
$877$	4.82278e9	+	1.99766e9i	0.241434	+	0.100005i	−0.258686	+	0.965962i	$0.583289\pi$
$878$	2.00325e10	−	4.42608e9i	0.998859	−	0.220693i
$879$		−	9.53621e9i		−	0.473604i
$880$	−1.57089e10	+	1.32910e9i	−0.777062	+	0.0657459i
$881$		−	6.27808e9i		−	0.309322i	−0.987968	−	0.154661i	$-0.950571\pi$
$881$		−	6.27808e9i		−	0.309322i	0.987968	−	0.154661i	$-0.0494286\pi$
$882$	−1.94296e9	−	8.79386e9i	−0.0953506	−	0.431558i
$883$	1.67082e10	+	6.92077e9i	0.816709	+	0.338292i	0.751628	−	0.659588i	$-0.229269\pi$
$883$	1.67082e10	+	6.92077e9i	0.816709	+	0.338292i	0.0650819	+	0.997880i	$0.479269\pi$
$884$	3.68137e10	−	1.55460e9i	1.79236	−	0.0756893i
$885$	3.29537e9	+	7.95572e9i	0.159810	+	0.385814i
$886$	−1.99410e9	+	1.12620e10i	−0.0963230	+	0.544001i
$887$	−1.28831e10	−	1.28831e10i	−0.619851	−	0.619851i	0.325642	−	0.945493i	$-0.394420\pi$
$887$	−1.28831e10	−	1.28831e10i	−0.619851	−	0.619851i	−0.945493	+	0.325642i	$0.894420\pi$
$888$	8.80647e8	−	6.58011e9i	0.0422043	−	0.315347i
$889$	−7.56668e9	+	7.56668e9i	−0.361201	+	0.361201i
$890$	2.33673e10	+	3.34228e10i	1.11108	+	1.58920i
$891$	4.62347e9	−	1.91510e9i	0.218976	−	0.0907027i
$892$	−1.58260e10	−	3.40660e10i	−0.746609	−	1.60710i
$893$	−8.99670e9	+	2.17199e10i	−0.422769	+	1.02065i
$894$	8.30509e9	−	1.30158e10i	0.388743	−	0.609244i
$895$	−1.48921e10			−0.694347
$896$	−6.74637e8	+	1.38600e10i	−0.0313323	+	0.643704i
$897$	−1.71774e10			−0.794663
$898$	1.40971e10	−	2.20932e10i	0.649625	−	1.01810i
$899$	9.77131e9	−	2.35900e10i	0.448532	−	1.08285i
$900$	−1.11561e9	−	2.40139e9i	−0.0510110	−	0.109803i
$901$	3.13032e10	−	1.29662e10i	1.42578	−	0.590576i
$902$	1.18327e9	+	1.69246e9i	0.0536861	+	0.0767885i
$903$	−1.98436e8	+	1.98436e8i	−0.00896839	+	0.00896839i
$904$	−1.46945e9	+	1.09796e10i	−0.0661555	+	0.494308i
$905$	1.72536e10	+	1.72536e10i	0.773766	+	0.773766i
$906$	3.43514e9	−	1.94005e10i	0.153460	−	0.866693i
$907$	−3.04537e9	−	7.35217e9i	−0.135523	−	0.327182i	0.841519	−	0.540228i	$-0.181662\pi$
$907$	−3.04537e9	−	7.35217e9i	−0.135523	−	0.327182i	−0.977042	+	0.213045i	$0.931662\pi$
$908$	−2.89519e10	+	1.22260e9i	−1.28344	+	0.0541982i
$909$	2.28023e10	+	9.44501e9i	1.00694	+	0.417089i
$910$	−5.52024e9	−	2.49847e10i	−0.242836	−	1.09908i
$911$		−	1.96786e10i		−	0.862344i	−0.902270	−	0.431172i	$-0.858100\pi$
$911$		−	1.96786e10i		−	0.862344i	0.902270	−	0.431172i	$-0.141900\pi$
$912$	1.49696e9	+	1.76928e10i	0.0653474	+	0.772352i
$913$		−	1.74462e10i		−	0.758671i
$914$	3.00432e10	−	6.63789e9i	1.30147	−	0.287553i
$915$	−1.00782e10	−	4.17453e9i	−0.434921	−	0.180150i
$916$	5.30820e9	+	4.87805e9i	0.228199	+	0.209706i
$917$	−2.07475e9	−	5.00888e9i	−0.0888531	−	0.214510i
$918$	−2.21515e10	−	3.92223e9i	−0.945046	−	0.167334i
$919$	8.89611e9	+	8.89611e9i	0.378091	+	0.378091i	0.870413	−	0.492322i	$-0.163852\pi$
$919$	8.89611e9	+	8.89611e9i	0.378091	+	0.378091i	−0.492322	+	0.870413i	$0.663852\pi$
$920$	2.18282e10	+	1.26650e10i	0.924188	+	0.536226i
$921$	−5.18293e9	+	5.18293e9i	−0.218608	+	0.218608i
$922$	2.08877e10	−	1.46035e10i	0.877674	−	0.613619i
$923$	−2.89625e10	+	1.19966e10i	−1.21235	+	0.502174i
$924$	5.19171e9	+	1.89804e9i	0.216500	+	0.0791503i
$925$	9.50146e8	−	2.29386e9i	0.0394725	−	0.0952950i
$926$	3.15615e10	+	2.01386e10i	1.30623	+	0.833473i
$927$	3.53068e9			0.145572
$928$	−2.02350e10	−	1.84322e9i	−0.831160	−	0.0757112i
$929$	3.44947e9			0.141155			0.0705777	−	0.997506i	$-0.477516\pi$
$929$	3.44947e9			0.141155			0.0705777	+	0.997506i	$0.477516\pi$
$930$	−1.54529e10	−	9.86014e9i	−0.629971	−	0.401969i
$931$	−8.64329e9	+	2.08667e10i	−0.351039	+	0.847483i
$932$	−4.75217e9	+	1.29986e10i	−0.192281	+	0.525947i
$933$	−6.14428e9	+	2.54504e9i	−0.247677	+	0.102591i
$934$	4.39216e9	−	3.07075e9i	0.176386	−	0.123319i
$935$	−1.52484e10	+	1.52484e10i	−0.610075	+	0.610075i
$936$	7.89539e9	+	2.97208e10i	0.314708	+	1.18466i
$937$	8.44448e9	+	8.44448e9i	0.335339	+	0.335339i	0.854610	−	0.519271i	$-0.173796\pi$
$937$	8.44448e9	+	8.44448e9i	0.335339	+	0.335339i	−0.519271	+	0.854610i	$0.673796\pi$
$938$	−1.45996e10	−	2.58507e9i	−0.577606	−	0.102273i
$939$	−3.47412e9	−	8.38727e9i	−0.136935	−	0.330591i
$940$	−1.30684e10	+	1.42207e10i	−0.513184	+	0.558438i
$941$	1.79228e10	+	7.42385e9i	0.701199	+	0.290446i	0.704657	−	0.709548i	$-0.251101\pi$
$941$	1.79228e10	+	7.42385e9i	0.701199	+	0.290446i	−0.00345804	+	0.999994i	$0.501101\pi$
$942$	−9.63748e9	+	2.12935e9i	−0.375652	+	0.0829983i
$943$		−	3.30575e9i		−	0.128375i
$944$	−6.15476e9	+	1.93275e10i	−0.238127	+	0.747781i
$945$			1.56219e10i			0.602174i
$946$	−1.62021e8	−	7.33312e8i	−0.00622234	−	0.0281624i
$947$	3.41910e10	+	1.41624e10i	1.30824	+	0.541891i	0.924370	−	0.381497i	$-0.124591\pi$
$947$	3.41910e10	+	1.41624e10i	1.30824	+	0.541891i	0.383870	+	0.923387i	$0.374591\pi$
$948$	3.35152e8	+	7.93658e9i	0.0127765	+	0.302555i
$949$	−1.31473e10	−	3.17405e10i	−0.499351	−	1.20554i
$950$	−1.15780e9	+	6.53890e9i	−0.0438130	+	0.247441i
$951$	9.19251e9	+	9.19251e9i	0.346579	+	0.346579i
$952$	1.15227e10	+	1.50835e10i	0.432837	+	0.566596i
$953$	8.09255e9	−	8.09255e9i	0.302873	−	0.302873i	−0.539264	−	0.842137i	$-0.681298\pi$
$953$	8.09255e9	−	8.09255e9i	0.302873	−	0.302873i	0.842137	+	0.539264i	$0.181298\pi$
$954$	1.62029e10	+	2.31754e10i	0.604190	+	0.864186i
$955$	−6.51154e9	+	2.69717e9i	−0.241920	+	0.100207i
$956$	−8.39783e9	+	3.90137e9i	−0.310860	+	0.144416i
$957$	−3.09749e9	+	7.47800e9i	−0.114240	+	0.275799i
$958$	−1.76305e10	+	2.76308e10i	−0.647867	+	1.01535i
$959$	2.12546e10			0.778194
$960$	−3.83576e9	+	1.40736e10i	−0.139927	+	0.513399i
$961$	2.67477e10			0.972196
$962$	−1.55104e10	+	2.43081e10i	−0.561709	+	0.880317i
$963$	−1.12881e10	+	2.72519e10i	−0.407313	+	0.983341i
$964$	−3.27562e10	+	1.52175e10i	−1.17767	+	0.547108i
$965$	3.73068e10	−	1.54530e10i	1.33642	−	0.553562i
$966$	−5.07027e9	−	7.25212e9i	−0.180972	−	0.258848i
$967$	−2.01596e9	+	2.01596e9i	−0.0716952	+	0.0716952i	−0.742045	−	0.670350i	$-0.766144\pi$
$967$	−2.01596e9	+	2.01596e9i	−0.0716952	+	0.0716952i	0.670350	+	0.742045i	$0.266144\pi$
$968$	1.06703e10	−	8.15131e9i	0.378105	−	0.288844i
$969$	1.71742e10	+	1.71742e10i	0.606377	+	0.606377i
$970$	4.53821e9	−	2.56303e10i	0.159655	−	0.901682i
$971$	−4.75603e9	−	1.14821e10i	−0.166716	−	0.402488i	0.818337	−	0.574738i	$-0.194896\pi$
$971$	−4.75603e9	−	1.14821e10i	−0.166716	−	0.402488i	−0.985053	+	0.172250i	$0.944896\pi$
$972$	−1.24325e9	−	2.94409e10i	−0.0434238	−	1.02830i
$973$	−2.73458e10	−	1.13270e10i	−0.951689	−	0.394202i
$974$	9.46311e9	+	4.28302e10i	0.328154	+	1.48523i
$975$		−	3.71326e9i		−	0.128304i
$976$	−1.17996e10	−	2.28259e10i	−0.406249	−	0.785875i
$977$			1.68039e10i			0.576474i	0.957559	+	0.288237i	$0.0930691\pi$
$977$			1.68039e10i			0.576474i	−0.957559	+	0.288237i	$0.906931\pi$
$978$	8.15942e9	−	1.80278e9i	0.278916	−	0.0616250i
$979$	3.53538e10	+	1.46440e10i	1.20419	+	0.498793i
$980$	−1.25550e10	+	1.36621e10i	−0.426114	+	0.463689i
$981$	−6.03100e9	−	1.45601e10i	−0.203961	−	0.492406i
$982$	−2.89688e10	−	5.12932e9i	−0.976202	−	0.172850i
$983$	1.96733e10	+	1.96733e10i	0.660602	+	0.660602i	0.955522	−	0.294920i	$-0.0952931\pi$
$983$	1.96733e10	+	1.96733e10i	0.660602	+	0.660602i	−0.294920	+	0.955522i	$0.595293\pi$
$984$	1.84671e9	−	4.90583e8i	0.0617898	−	0.0164146i
$985$	−1.65813e10	+	1.65813e10i	−0.552830	+	0.552830i
$986$	−2.27784e10	+	1.59254e10i	−0.756754	+	0.529079i
$987$	6.25653e9	−	2.59154e9i	0.207121	−	0.0857922i
$988$	2.64808e10	−	7.24332e10i	0.873539	−	2.38940i
$989$	−4.60056e8	+	1.11067e9i	−0.0151225	+	0.0365089i
$990$	−1.51720e10	−	9.68087e9i	−0.496957	−	0.317096i
$991$	−1.91581e10			−0.625309			−0.312655	−	0.949867i	$-0.601218\pi$
$991$	−1.91581e10			−0.625309			−0.312655	+	0.949867i	$0.601218\pi$
$992$	−1.28367e10	−	4.12261e10i	−0.417507	−	1.34085i
$993$	−1.62047e10			−0.525191
$994$	−1.36138e10	−	8.68662e9i	−0.439669	−	0.280542i
$995$	1.35164e10	−	3.26315e10i	0.434991	−	1.05016i
$996$	−1.51611e10	−	5.54274e9i	−0.486209	−	0.177753i
$997$	3.58971e10	−	1.48691e10i	1.14717	−	0.475172i	0.273584	−	0.961848i	$-0.411791\pi$
$997$	3.58971e10	−	1.48691e10i	1.14717	−	0.475172i	0.873583	+	0.486676i	$0.161791\pi$
$998$	3.24384e10	−	2.26791e10i	1.03301	−	0.722218i
$999$	1.24484e10	−	1.24484e10i	0.395035	−	0.395035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.9	yes	108
32.5	even	8	inner	32.8.g.a.5.9	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.9	✓	108	32.5	even	8	inner
32.8.g.a.13.9	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)

\(f(q)\)	\(=\)	\(q+(-6.08567 + 9.53754i) q^{2} +(8.84135 - 21.3449i) q^{3} +(-53.9292 - 116.085i) q^{4} +(-278.144 + 115.211i) q^{5} +(149.772 + 214.223i) q^{6} +(413.550 - 413.550i) q^{7} +(1435.36 + 192.100i) q^{8} +(1169.01 + 1169.01i) q^{9} +O(q^{10})\)	\(q+(-6.08567 + 9.53754i) q^{2} +(8.84135 - 21.3449i) q^{3} +(-53.9292 - 116.085i) q^{4} +(-278.144 + 115.211i) q^{5} +(149.772 + 214.223i) q^{6} +(413.550 - 413.550i) q^{7} +(1435.36 + 192.100i) q^{8} +(1169.01 + 1169.01i) q^{9} +(593.864 - 3353.95i) q^{10} +(-1223.09 - 2952.80i) q^{11} +(-2954.62 + 124.770i) q^{12} +(11866.9 + 4915.42i) q^{13} +(1427.52 + 6460.98i) q^{14} +6955.59i q^{15} +(-10567.3 + 12520.7i) q^{16} +22411.2i q^{17} +(-18263.6 + 4035.26i) q^{18} +(43337.4 + 17950.9i) q^{19} +(28374.4 + 26075.0i) q^{20} +(-5170.85 - 12483.5i) q^{21} +(35605.8 + 6304.51i) q^{22} +(-40930.0 - 40930.0i) q^{23} +(16790.9 - 28939.1i) q^{24} +(8847.92 - 8847.92i) q^{25} +(-119099. + 83267.1i) q^{26} +(81969.3 - 33952.8i) q^{27} +(-70309.3 - 25704.4i) q^{28} +(41948.0 - 101272. i) q^{29} +(-66339.2 - 42329.4i) q^{30} +232938. q^{31} +(-55107.8 - 176983. i) q^{32} -73841.1 q^{33} +(-213748. - 136387. i) q^{34} +(-67381.0 + 162672. i) q^{35} +(72660.1 - 198747. i) q^{36} +(183320. - 75933.7i) q^{37} +(-434944. + 304088. i) q^{38} +(209838. - 209838. i) q^{39} +(-421368. + 111937. i) q^{40} +(40383.0 + 40383.0i) q^{41} +(150530. + 26653.5i) q^{42} +(-7947.93 - 19188.0i) q^{43} +(-276815. + 301224. i) q^{44} +(-459835. - 190470. i) q^{45} +(639458. - 141285. i) q^{46} +501183. i q^{47} +(173824. + 336257. i) q^{48} +481496. i q^{49} +(30541.8 + 138233. i) q^{50} +(478365. + 198145. i) q^{51} +(-69366.9 - 1.64265e6i) q^{52} +(-578559. - 1.39676e6i) q^{53} +(-175012. + 988410. i) q^{54} +(680391. + 680391. i) q^{55} +(673035. - 514149. i) q^{56} +(766322. - 766322. i) q^{57} +(710599. + 1.01639e6i) q^{58} +(1.14379e6 - 473773. i) q^{59} +(807436. - 375109. i) q^{60} +(-600170. + 1.44894e6i) q^{61} +(-1.41759e6 + 2.22166e6i) q^{62} +966886. q^{63} +(2.02335e6 + 551465. i) q^{64} -3.86701e6 q^{65} +(449372. - 704262. i) q^{66} +(-857505. + 2.07020e6i) q^{67} +(2.60159e6 - 1.20862e6i) q^{68} +(-1.23552e6 + 511770. i) q^{69} +(-1.14143e6 - 1.63262e6i) q^{70} +(-1.72578e6 + 1.72578e6i) q^{71} +(1.45338e6 + 1.90251e6i) q^{72} +(-1.89131e6 - 1.89131e6i) q^{73} +(-391405. + 2.21053e6i) q^{74} +(-110630. - 267085. i) q^{75} +(-253325. - 5.99888e6i) q^{76} +(-1.72694e6 - 715322. i) q^{77} +(724334. + 3.27835e6i) q^{78} -2.68616e6i q^{79} +(1.49670e6 - 4.70003e6i) q^{80} +1.56579e6i q^{81} +(-630912. + 139397. i) q^{82} +(5.04310e6 + 2.08892e6i) q^{83} +(-1.17029e6 + 1.27348e6i) q^{84} +(-2.58202e6 - 6.23355e6i) q^{85} +(231375. + 40968.2i) q^{86} +(-1.79075e6 - 1.79075e6i) q^{87} +(-1.18834e6 - 4.47328e6i) q^{88} +(-8.46616e6 + 8.46616e6i) q^{89} +(4.61502e6 - 3.22656e6i) q^{90} +(6.94032e6 - 2.87477e6i) q^{91} +(-2.54402e6 + 6.95866e6i) q^{92} +(2.05949e6 - 4.97205e6i) q^{93} +(-4.78005e6 - 3.05003e6i) q^{94} -1.41222e7 q^{95} +(-4.26491e6 - 388495. i) q^{96} +7.64184e6 q^{97} +(-4.59228e6 - 2.93022e6i) q^{98} +(2.02204e6 - 4.88165e6i) 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

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