LMFDB - Embedded newform 32.8.g.a.21.17

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			21.17
Character	$\chi$	$=$	32.21
Dual form			32.8.g.a.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.97890 + 10.5910i) q^{2} +(-50.6460 + 20.9783i) q^{3} +(-96.3368 + 84.2807i) q^{4} +(188.596 - 455.311i) q^{5} +(-423.695 - 452.919i) q^{6} +(-120.832 - 120.832i) q^{7} +(-1275.93 - 684.955i) q^{8} +(578.487 - 578.487i) q^{9} +O(q^{10})$	\(q+(3.97890 + 10.5910i) q^{2} +(-50.6460 + 20.9783i) q^{3} +(-96.3368 + 84.2807i) q^{4} +(188.596 - 455.311i) q^{5} +(-423.695 - 452.919i) q^{6} +(-120.832 - 120.832i) q^{7} +(-1275.93 - 684.955i) q^{8} +(578.487 - 578.487i) q^{9} +(5572.58 + 185.777i) q^{10} +(6471.42 + 2680.55i) q^{11} +(3111.01 - 6289.45i) q^{12} +(-1764.30 - 4259.39i) q^{13} +(798.946 - 1760.50i) q^{14} +27016.1i q^{15} +(2177.54 - 16238.7i) q^{16} -23326.1i q^{17} +(8428.47 + 3824.99i) q^{18} +(-7829.65 - 18902.5i) q^{19} +(20205.2 + 59758.2i) q^{20} +(8654.47 + 3584.80i) q^{21} +(-2640.48 + 79204.2i) q^{22} +(44339.3 - 44339.3i) q^{23} +(78989.7 + 7923.48i) q^{24} +(-116497. - 116497. i) q^{25} +(38091.1 - 35633.3i) q^{26} +(28717.1 - 69329.1i) q^{27} +(21824.3 + 1456.76i) q^{28} +(52563.8 - 21772.6i) q^{29} +(-286126. + 107494. i) q^{30} -119232. q^{31} +(180647. - 41549.6i) q^{32} -383985. q^{33} +(247046. - 92812.1i) q^{34} +(-77804.3 + 32227.6i) q^{35} +(-6974.30 + 104485. i) q^{36} +(-189422. + 457305. i) q^{37} +(169042. - 158134. i) q^{38} +(178709. + 178709. i) q^{39} +(-552502. + 451764. i) q^{40} +(375630. - 375630. i) q^{41} +(-3531.21 + 105923. i) q^{42} +(-551251. - 228336. i) q^{43} +(-849355. + 287180. i) q^{44} +(-154291. - 372492. i) q^{45} +(646018. + 293174. i) q^{46} +123835. i q^{47} +(230375. + 868104. i) q^{48} -794342. i q^{49} +(770285. - 1.69734e6i) q^{50} +(489341. + 1.18137e6i) q^{51} +(528951. + 261640. i) q^{52} +(-794562. - 329118. i) q^{53} +(848524. + 28287.8i) q^{54} +(2.44097e6 - 2.44097e6i) q^{55} +(71408.1 + 236936. i) q^{56} +(793081. + 793081. i) q^{57} +(439739. + 470070. i) q^{58} +(-600550. + 1.44986e6i) q^{59} +(-2.27693e6 - 2.60264e6i) q^{60} +(-99162.1 + 41074.3i) q^{61} +(-474410. - 1.26278e6i) q^{62} -139799. q^{63} +(1.15883e6 + 1.74790e6i) q^{64} -2.27209e6 q^{65} +(-1.52784e6 - 4.06677e6i) q^{66} +(1.13958e6 - 472031. i) q^{67} +(1.96594e6 + 2.24716e6i) q^{68} +(-1.31545e6 + 3.17577e6i) q^{69} +(-650897. - 695792. i) q^{70} +(1.48313e6 + 1.48313e6i) q^{71} +(-1.13434e6 + 341870. i) q^{72} +(3.00335e6 - 3.00335e6i) q^{73} +(-5.59699e6 - 186590. i) q^{74} +(8.34401e6 + 3.45620e6i) q^{75} +(2.34740e6 + 1.16111e6i) q^{76} +(-458057. - 1.10585e6i) q^{77} +(-1.18164e6 + 2.60377e6i) q^{78} +6.45617e6i q^{79} +(-6.98296e6 - 4.05400e6i) q^{80} +5.90287e6i q^{81} +(5.47287e6 + 2.48369e6i) q^{82} +(356701. + 861153. i) q^{83} +(-1.13587e6 + 384057. i) q^{84} +(-1.06206e7 - 4.39921e6i) q^{85} +(224922. - 6.74680e6i) q^{86} +(-2.20539e6 + 2.20539e6i) q^{87} +(-6.42101e6 - 7.85282e6i) q^{88} +(-8.55919e6 - 8.55919e6i) q^{89} +(3.33114e6 - 3.11620e6i) q^{90} +(-301486. + 727852. i) q^{91} +(-534560. + 8.00846e6i) q^{92} +(6.03861e6 - 2.50127e6i) q^{93} +(-1.31153e6 + 492728. i) q^{94} -1.00831e7 q^{95} +(-8.27741e6 + 5.89398e6i) q^{96} +6.51806e6 q^{97} +(8.41285e6 - 3.16061e6i) q^{98} +(5.29430e6 - 2.19297e6i) 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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.97890	+	10.5910i	0.351688	+	0.936117i
$2$	3.97890	+	10.5910i	0.351688	+	0.936117i
$3$	−50.6460	+	20.9783i	−1.08298	+	0.448585i	−0.851554	−	0.524267i	$-0.824339\pi$
$3$	−50.6460	+	20.9783i	−1.08298	+	0.448585i	−0.231427	+	0.972852i	$0.574339\pi$
$4$	−96.3368	+	84.2807i	−0.752631	+	0.658443i
$5$	188.596	−	455.311i	0.674742	−	1.62897i	−0.0987111	−	0.995116i	$-0.531472\pi$
$5$	188.596	−	455.311i	0.674742	−	1.62897i	0.773453	−	0.633854i	$-0.218528\pi$
$6$	−423.695	−	452.919i	−0.800800	−	0.856035i
$7$	−120.832	−	120.832i	−0.133149	−	0.133149i	0.637391	−	0.770540i	$-0.280013\pi$
$7$	−120.832	−	120.832i	−0.133149	−	0.133149i	−0.770540	+	0.637391i	$0.780013\pi$
$8$	−1275.93	−	684.955i	−0.881071	−	0.472984i
$9$	578.487	−	578.487i	0.264512	−	0.264512i
$10$	5572.58	+	185.777i	1.76221	+	0.0587478i
$11$	6471.42	+	2680.55i	1.46597	+	0.607225i	0.965936	−	0.258780i	$-0.0833205\pi$
$11$	6471.42	+	2680.55i	1.46597	+	0.607225i	0.500035	+	0.866005i	$0.333321\pi$
$12$	3111.01	−	6289.45i	0.519717	−	1.05070i
$13$	−1764.30	−	4259.39i	−0.222726	−	0.537707i	0.772533	−	0.634975i	$-0.218990\pi$
$13$	−1764.30	−	4259.39i	−0.222726	−	0.537707i	−0.995258	+	0.0972678i	$0.968990\pi$
$14$	798.946	−	1760.50i	0.0778161	−	0.171470i
$15$			27016.1i			2.06682i
$16$	2177.54	−	16238.7i	0.132907	−	0.991129i
$17$		−	23326.1i		−	1.15152i	−0.817619	−	0.575759i	$-0.804707\pi$
$17$		−	23326.1i		−	1.15152i	0.817619	−	0.575759i	$-0.195293\pi$
$18$	8428.47	+	3824.99i	0.340639	+	0.154588i
$19$	−7829.65	−	18902.5i	−0.261882	−	0.632238i	0.737173	−	0.675704i	$-0.236160\pi$
$19$	−7829.65	−	18902.5i	−0.261882	−	0.632238i	−0.999055	+	0.0434656i	$0.986160\pi$
$20$	20205.2	+	59758.2i	0.564752	+	1.67029i
$21$	8654.47	+	3584.80i	0.203926	+	0.0844690i
$22$	−2640.48	+	79204.2i	−0.0528693	+	1.58587i
$23$	44339.3	−	44339.3i	0.759874	−	0.759874i	−0.216425	−	0.976299i	$-0.569440\pi$
$23$	44339.3	−	44339.3i	0.759874	−	0.759874i	0.976299	+	0.216425i	$0.0694396\pi$
$24$	78989.7	+	7923.48i	1.16636	+	0.116998i
$25$	−116497.	−	116497.i	−1.49116	−	1.49116i
$26$	38091.1	−	35633.3i	0.425027	−	0.397603i
$27$	28717.1	−	69329.1i	0.280780	−	0.677864i
$28$	21824.3	+	1456.76i	0.187883	+	0.0125411i
$29$	52563.8	−	21772.6i	0.400216	−	0.165775i	−0.173491	−	0.984835i	$-0.555505\pi$
$29$	52563.8	−	21772.6i	0.400216	−	0.165775i	0.573707	+	0.819061i	$0.305505\pi$
$30$	−286126.	+	107494.i	−1.93479	+	0.726877i
$31$	−119232.			−0.718829			−0.359415	−	0.933178i	$-0.617024\pi$
$31$	−119232.			−0.718829			−0.359415	+	0.933178i	$0.617024\pi$
$32$	180647.	−	41549.6i	0.974554	−	0.224152i
$33$	−383985.			−1.86001
$34$	247046.	−	92812.1i	1.07796	−	0.404975i
$35$	−77804.3	+	32227.6i	−0.306737	+	0.127054i
$36$	−6974.30	+	104485.i	−0.0249139	+	0.373245i
$37$	−189422.	+	457305.i	−0.614786	+	1.48423i	0.242899	+	0.970052i	$0.421902\pi$
$37$	−189422.	+	457305.i	−0.614786	+	1.48423i	−0.857686	+	0.514174i	$0.828098\pi$
$38$	169042.	−	158134.i	0.499748	−	0.467503i
$39$	178709.	+	178709.i	0.482415	+	0.482415i
$40$	−552502.	+	451764.i	−1.36497	+	1.11610i
$41$	375630.	−	375630.i	0.851170	−	0.851170i	−0.139107	−	0.990277i	$-0.544423\pi$
$41$	375630.	−	375630.i	0.851170	−	0.851170i	0.990277	+	0.139107i	$0.0444232\pi$
$42$	−3531.21	+	105923.i	−0.00735447	+	0.220606i
$43$	−551251.	−	228336.i	−1.05733	−	0.437960i	−0.214826	−	0.976652i	$-0.568918\pi$
$43$	−551251.	−	228336.i	−1.05733	−	0.437960i	−0.842502	+	0.538693i	$0.818918\pi$
$44$	−849355.	+	287180.i	−1.50316	+	0.508241i
$45$	−154291.	−	372492.i	−0.252405	−	0.609359i
$46$	646018.	+	293174.i	0.978570	+	0.444093i
$47$			123835.i			0.173981i	0.996209	+	0.0869905i	$0.0277250\pi$
$47$			123835.i			0.173981i	−0.996209	+	0.0869905i	$0.972275\pi$
$48$	230375.	+	868104.i	0.300670	+	1.13299i
$49$		−	794342.i		−	0.964543i
$50$	770285.	−	1.69734e6i	0.871478	−	1.92032i
$51$	489341.	+	1.18137e6i	0.516554	+	1.24707i
$52$	528951.	+	261640.i	0.521680	+	0.258043i
$53$	−794562.	−	329118.i	−0.733098	−	0.303659i	−0.0152739	−	0.999883i	$-0.504862\pi$
$53$	−794562.	−	329118.i	−0.733098	−	0.303659i	−0.717825	+	0.696224i	$0.754862\pi$
$54$	848524.	+	28287.8i	0.733307	+	0.0244467i
$55$	2.44097e6	−	2.44097e6i	1.97830	−	1.97830i
$56$	71408.1	+	236936.i	0.0543362	+	0.180291i
$57$	793081.	+	793081.i	0.567225	+	0.567225i
$58$	439739.	+	470070.i	0.295936	+	0.316348i
$59$	−600550.	+	1.44986e6i	−0.380686	+	0.919057i	0.611147	+	0.791517i	$0.290708\pi$
$59$	−600550.	+	1.44986e6i	−0.380686	+	0.919057i	−0.991833	+	0.127540i	$0.959292\pi$
$60$	−2.27693e6	−	2.60264e6i	−1.36088	−	1.55555i
$61$	−99162.1	+	41074.3i	−0.0559360	+	0.0231694i	−0.410476	−	0.911871i	$-0.634637\pi$
$61$	−99162.1	+	41074.3i	−0.0559360	+	0.0231694i	0.354540	+	0.935041i	$0.384637\pi$
$62$	−474410.	−	1.26278e6i	−0.252804	−	0.672908i
$63$	−139799.			−0.0704388
$64$	1.15883e6	+	1.74790e6i	0.552572	+	0.833465i
$65$	−2.27209e6			−1.02619
$66$	−1.52784e6	−	4.06677e6i	−0.654144	−	1.74119i
$67$	1.13958e6	−	472031.i	0.462897	−	0.191738i	−0.139032	−	0.990288i	$-0.544399\pi$
$67$	1.13958e6	−	472031.i	0.462897	−	0.191738i	0.601929	+	0.798550i	$0.294399\pi$
$68$	1.96594e6	+	2.24716e6i	0.758209	+	0.866668i
$69$	−1.31545e6	+	3.17577e6i	−0.482061	+	1.16380i
$70$	−650897.	−	695792.i	−0.226813	−	0.242458i
$71$	1.48313e6	+	1.48313e6i	0.491784	+	0.491784i	0.908868	−	0.417084i	$-0.136948\pi$
$71$	1.48313e6	+	1.48313e6i	0.491784	+	0.491784i	−0.417084	+	0.908868i	$0.636948\pi$
$72$	−1.13434e6	+	341870.i	−0.358163	+	0.107944i
$73$	3.00335e6	−	3.00335e6i	0.903600	−	0.903600i	−0.0921459	−	0.995746i	$-0.529373\pi$
$73$	3.00335e6	−	3.00335e6i	0.903600	−	0.903600i	0.995746	+	0.0921459i	$0.0293726\pi$
$74$	−5.59699e6	−	186590.i	−1.60562	−	0.0535276i
$75$	8.34401e6	+	3.45620e6i	2.28381	+	0.945986i
$76$	2.34740e6	+	1.16111e6i	0.613393	+	0.303408i
$77$	−458057.	−	1.10585e6i	−0.114341	−	0.276044i
$78$	−1.18164e6	+	2.60377e6i	−0.281938	+	0.621257i
$79$			6.45617e6i			1.47326i	0.676295	+	0.736631i	$0.263585\pi$
$79$			6.45617e6i			1.47326i	−0.676295	+	0.736631i	$0.736415\pi$
$80$	−6.98296e6	−	4.05400e6i	−1.52484	−	0.885257i
$81$			5.90287e6i			1.23414i
$82$	5.47287e6	+	2.48369e6i	1.09614	+	0.497449i
$83$	356701.	+	861153.i	0.0684749	+	0.165313i	0.954412	−	0.298492i	$-0.0964837\pi$
$83$	356701.	+	861153.i	0.0684749	+	0.165313i	−0.885937	+	0.463805i	$0.846484\pi$
$84$	−1.13587e6	+	384057.i	−0.209099	+	0.0706997i
$85$	−1.06206e7	−	4.39921e6i	−1.87579	−	0.776977i
$86$	224922.	−	6.74680e6i	0.0381318	−	1.14381i
$87$	−2.20539e6	+	2.20539e6i	−0.359062	+	0.359062i
$88$	−6.42101e6	−	7.85282e6i	−1.00442	−	1.22839i
$89$	−8.55919e6	−	8.55919e6i	−1.28697	−	1.28697i	−0.936619	−	0.350349i	$-0.886063\pi$
$89$	−8.55919e6	−	8.55919e6i	−1.28697	−	1.28697i	−0.350349	−	0.936619i	$-0.613937\pi$
$90$	3.33114e6	−	3.11620e6i	0.481663	−	0.450584i
$91$	−301486.	+	727852.i	−0.0419394	+	0.101251i
$92$	−534560.	+	8.00846e6i	−0.0715713	+	1.07224i
$93$	6.03861e6	−	2.50127e6i	0.778478	−	0.322456i
$94$	−1.31153e6	+	492728.i	−0.162867	+	0.0611871i
$95$	−1.00831e7			−1.20660
$96$	−8.27741e6	+	5.89398e6i	−0.954872	+	0.679923i
$97$	6.51806e6			0.725133			0.362566	−	0.931958i	$-0.381901\pi$
$97$	6.51806e6			0.725133			0.362566	+	0.931958i	$0.381901\pi$
$98$	8.41285e6	−	3.16061e6i	0.902925	−	0.339218i
$99$	5.29430e6	−	2.19297e6i	0.548385	−	0.227148i
$100$	2.10414e7	+	1.40450e6i	2.10414	+	0.140450i
$101$	482769.	−	1.16551e6i	0.0466245	−	0.112562i	−0.898851	−	0.438253i	$-0.855597\pi$
$101$	482769.	−	1.16551e6i	0.0466245	−	0.112562i	0.945476	+	0.325692i	$0.105597\pi$
$102$	−1.05648e7	+	9.88315e6i	−0.985740	+	0.922136i
$103$	−1.15645e7	−	1.15645e7i	−1.04279	−	1.04279i	−0.999043	−	0.0437456i	$-0.986071\pi$
$103$	−1.15645e7	−	1.15645e7i	−1.04279	−	1.04279i	−0.0437456	−	0.999043i	$-0.513929\pi$
$104$	−666375.	+	6.64314e6i	−0.0580901	+	0.579104i
$105$	3.26440e6	−	3.26440e6i	0.275195	−	0.275195i
$106$	324198.	−	9.72470e6i	0.0264387	−	0.793059i
$107$	1.82297e7	+	7.55099e6i	1.43859	+	0.595882i	0.959455	−	0.281861i	$-0.0909517\pi$
$107$	1.82297e7	+	7.55099e6i	1.43859	+	0.595882i	0.479132	+	0.877743i	$0.340952\pi$
$108$	3.07659e6	+	9.09923e6i	0.235010	+	0.695059i
$109$	6.36743e6	+	1.53723e7i	0.470946	+	1.13696i	0.963746	+	0.266822i	$0.0859735\pi$
$109$	6.36743e6	+	1.53723e7i	0.470946	+	1.13696i	−0.492800	+	0.870143i	$0.664027\pi$
$110$	3.55646e7	+	1.61398e7i	2.54767	+	1.15618i
$111$		−	2.71344e7i		−	1.88317i
$112$	−2.22526e6	+	1.69903e6i	−0.149664	+	0.114271i
$113$		−	4.86340e6i		−	0.317078i	−0.987353	−	0.158539i	$-0.949322\pi$
$113$		−	4.86340e6i		−	0.317078i	0.987353	−	0.158539i	$-0.0506783\pi$
$114$	−5.24390e6	+	1.15551e7i	−0.331503	+	0.730476i
$115$	−1.18260e7	−	2.85504e7i	−0.725094	−	1.75053i
$116$	−3.22882e6	+	6.52762e6i	−0.192061	+	0.388286i
$117$	−3.48463e6	−	1.44338e6i	−0.201143	−	0.0833163i
$118$	−1.77449e7	−	591572.i	−0.994228	−	0.0331452i
$119$	−2.81853e6	+	2.81853e6i	−0.153323	+	0.153323i
$120$	1.85048e7	−	3.44706e7i	0.977575	−	1.82102i
$121$	2.09145e7	+	2.09145e7i	1.07324	+	1.07324i
$122$	−829572.	−	886791.i	−0.0413613	−	0.0442142i
$123$	−1.11441e7	+	2.69042e7i	−0.539979	+	1.30362i
$124$	1.14864e7	−	1.00489e7i	0.541013	−	0.473308i
$125$	−3.94420e7	+	1.63374e7i	−1.80623	+	0.748167i
$126$	−556246.	−	1.48061e6i	−0.0247725	−	0.0659390i
$127$	32857.8			0.00142340			0.000711698	−	1.00000i	$-0.499773\pi$
$127$	32857.8			0.00142340			0.000711698		1.00000i	$0.499773\pi$
$128$	−1.39011e7	+	1.92278e7i	−0.585889	+	0.810392i
$129$	3.27087e7			1.34153
$130$	−9.04040e6	−	2.40636e7i	−0.360899	−	0.960636i
$131$	−1.99292e7	+	8.25495e6i	−0.774534	+	0.320822i	−0.734707	−	0.678384i	$-0.762681\pi$
$131$	−1.99292e7	+	8.25495e6i	−0.774534	+	0.320822i	−0.0398265	+	0.999207i	$0.512681\pi$
$132$	3.69919e7	−	3.23625e7i	1.39990	−	1.22471i
$133$	−1.33794e6	+	3.23008e6i	−0.0493125	+	0.119051i
$134$	9.53354e6	+	1.01911e7i	0.342285	+	0.365894i
$135$	−2.61504e7	−	2.61504e7i	−0.914766	−	0.914766i
$136$	−1.59773e7	+	2.97624e7i	−0.544650	+	1.01457i
$137$	2.30010e7	−	2.30010e7i	0.764230	−	0.764230i	−0.212854	−	0.977084i	$-0.568276\pi$
$137$	2.30010e7	−	2.30010e7i	0.764230	−	0.764230i	0.977084	+	0.212854i	$0.0682760\pi$
$138$	−3.88685e7	−	1.29578e6i	−1.25899	−	0.0419716i
$139$	987201.	+	408912.i	0.0311784	+	0.0129145i	0.398218	−	0.917291i	$-0.369629\pi$
$139$	987201.	+	408912.i	0.0311784	+	0.0129145i	−0.367040	+	0.930205i	$0.619629\pi$
$140$	4.77925e6	−	9.66210e6i	0.147201	−	0.297594i
$141$	−2.59785e6	−	6.27176e6i	−0.0780454	−	0.188418i
$142$	−9.80653e6	+	2.16089e7i	−0.287413	+	0.633322i
$143$		−	3.22936e7i		−	0.923508i
$144$	−8.13417e6	−	1.06535e7i	−0.227010	−	0.297320i
$145$		−	2.80391e7i		−	0.763794i
$146$	4.37584e7	+	1.98583e7i	1.16366	+	0.528090i
$147$	1.66639e7	+	4.02303e7i	0.432680	+	1.04458i
$148$	−2.02937e7	−	6.00199e7i	−0.514570	−	1.52188i
$149$	−1.13738e7	−	4.71117e6i	−0.281678	−	0.116675i	0.237372	−	0.971419i	$-0.423714\pi$
$149$	−1.13738e7	−	4.71117e6i	−0.281678	−	0.116675i	−0.519050	+	0.854744i	$0.673714\pi$
$150$	−3.40453e6	+	1.02123e8i	−0.0823642	+	2.47061i
$151$	−1.42237e7	+	1.42237e7i	−0.336196	+	0.336196i	−0.854934	−	0.518737i	$-0.826402\pi$
$151$	−1.42237e7	+	1.42237e7i	−0.336196	+	0.336196i	0.518737	+	0.854934i	$0.326402\pi$
$152$	−2.95726e6	+	2.94811e7i	−0.0683025	+	0.680912i
$153$	−1.34938e7	−	1.34938e7i	−0.304590	−	0.304590i
$154$	9.88943e6	−	9.25132e6i	0.218197	−	0.204118i
$155$	−2.24866e7	+	5.42875e7i	−0.485024	+	1.17095i
$156$	−3.22780e7	−	2.15454e6i	−0.680723	−	0.0454379i
$157$	6.40742e7	−	2.65404e7i	1.32140	−	0.547342i	0.393211	−	0.919448i	$-0.371364\pi$
$157$	6.40742e7	−	2.65404e7i	1.32140	−	0.547342i	0.928190	+	0.372106i	$0.121364\pi$
$158$	−6.83770e7	+	2.56884e7i	−1.37915	+	0.518129i
$159$	4.71457e7			0.930149
$160$	1.51513e7	−	9.00867e7i	0.292436	−	1.73876i
$161$	−1.07152e7			−0.202353
$162$	−6.25170e7	+	2.34869e7i	−1.15530	+	0.434033i
$163$	4.57775e6	−	1.89617e6i	0.0827934	−	0.0342941i	−0.340902	−	0.940099i	$-0.610733\pi$
$163$	4.57775e6	−	1.89617e6i	0.0827934	−	0.0342941i	0.423696	+	0.905805i	$0.360733\pi$
$164$	−4.52863e6	+	6.78453e7i	−0.0801703	+	1.20106i
$165$	−7.24180e7	+	1.74833e8i	−1.25503	+	3.02990i
$166$	−7.70116e6	+	7.20425e6i	−0.130671	+	0.122239i
$167$	−1.71321e7	−	1.71321e7i	−0.284645	−	0.284645i	0.550313	−	0.834958i	$-0.314508\pi$
$167$	−1.71321e7	−	1.71321e7i	−0.284645	−	0.284645i	−0.834958	+	0.550313i	$0.814508\pi$
$168$	−8.58705e6	−	1.05019e7i	−0.139721	−	0.170877i
$169$	2.93402e7	−	2.93402e7i	0.467584	−	0.467584i
$170$	4.33344e6	−	1.29987e8i	0.0676491	−	2.02921i
$171$	−1.54642e7	−	6.40547e6i	−0.236505	−	0.0979636i
$172$	7.23500e7	−	2.44627e7i	1.08415	−	0.366568i
$173$	9.46915e6	+	2.28605e7i	0.139043	+	0.335680i	0.978028	−	0.208476i	$-0.0668502\pi$
$173$	9.46915e6	+	2.28605e7i	0.139043	+	0.335680i	−0.838984	+	0.544155i	$0.816850\pi$
$174$	−3.21323e7	−	1.45822e7i	−0.462401	−	0.209846i
$175$			2.81530e7i			0.397093i
$176$	5.76203e7	−	9.92502e7i	0.796676	−	1.37226i
$177$		−	8.60278e7i		−	1.16609i
$178$	5.65939e7	−	1.24706e8i	0.752142	−	1.65736i
$179$	1.39823e7	+	3.37562e7i	0.182218	+	0.439914i	0.988423	−	0.151723i	$-0.0484821\pi$
$179$	1.39823e7	+	3.37562e7i	0.182218	+	0.439914i	−0.806205	+	0.591636i	$0.798482\pi$
$180$	4.62578e7	+	2.28809e7i	0.591195	+	0.292428i
$181$	1.43784e8	+	5.95574e7i	1.80234	+	0.746553i	0.985498	+	0.169690i	$0.0542765\pi$
$181$	1.43784e8	+	5.95574e7i	1.80234	+	0.746553i	0.816841	+	0.576863i	$0.195724\pi$
$182$	−8.90824e6	−	296979.i	−0.109532	−	0.00365154i
$183$	4.16050e6	−	4.16050e6i	0.0501841	−	0.0501841i
$184$	−8.69442e7	+	2.62033e7i	−1.02891	+	0.310094i
$185$	1.72492e8	+	1.72492e8i	2.00294	+	2.00294i
$186$	5.05179e7	+	5.40023e7i	0.575638	+	0.615343i
$187$	6.25268e7	−	1.50953e8i	0.699231	−	1.68809i
$188$	−1.04369e7	−	1.19299e7i	−0.114557	−	0.130944i
$189$	−1.18471e7	+	4.90722e6i	−0.127642	+	0.0528712i
$190$	−4.01198e7	−	1.06790e8i	−0.424347	−	1.12952i
$191$	−3.32953e7			−0.345753			−0.172876	−	0.984944i	$-0.555306\pi$
$191$	−3.32953e7			−0.345753			−0.172876	+	0.984944i	$0.555306\pi$
$192$	−9.53579e7	−	6.42142e7i	−0.972305	−	0.654752i
$193$	−1.58418e8			−1.58618			−0.793092	−	0.609102i	$-0.791530\pi$
$193$	−1.58418e8			−1.58618			−0.793092	+	0.609102i	$0.791530\pi$
$194$	2.59347e7	+	6.90325e7i	0.255021	+	0.678809i
$195$	1.15072e8	−	4.76645e7i	1.11135	−	0.460334i
$196$	6.69477e7	+	7.65244e7i	0.635096	+	0.725945i
$197$	2.21347e7	−	5.34378e7i	0.206272	−	0.497986i	−0.786558	−	0.617516i	$-0.788139\pi$
$197$	2.21347e7	−	5.34378e7i	0.206272	−	0.497986i	0.992831	+	0.119531i	$0.0381390\pi$
$198$	4.42911e7	+	4.73461e7i	0.405498	+	0.433467i
$199$	−3.94697e7	−	3.94697e7i	−0.355041	−	0.355041i	0.506940	−	0.861981i	$-0.330776\pi$
$199$	−3.94697e7	−	3.94697e7i	−0.355041	−	0.355041i	−0.861981	+	0.506940i	$0.830776\pi$
$200$	6.88465e7	+	2.28437e8i	0.608523	+	2.01911i
$201$	−4.78129e7	+	4.78129e7i	−0.415298	+	0.415298i
$202$	1.42647e7	+	475552.i	0.121768	+	0.00405946i
$203$	−8.98220e6	−	3.72055e6i	−0.0753610	−	0.0312155i
$204$	−1.46708e8	−	7.25677e7i	−1.20990	−	0.598464i
$205$	−1.00186e8	−	2.41871e8i	−0.812211	−	1.96085i
$206$	7.64651e7	−	1.68493e8i	0.609436	−	1.34291i
$207$		−	5.12995e7i		−	0.401991i
$208$	−7.30086e7	+	1.93748e7i	−0.562539	+	0.149285i
$209$		−	1.43314e8i		−	1.08586i
$210$	4.75618e7	+	2.15844e7i	0.354398	+	0.160832i
$211$	−2.09246e6	−	5.05164e6i	−0.0153344	−	0.0370206i	0.916027	−	0.401117i	$-0.131378\pi$
$211$	−2.09246e6	−	5.05164e6i	−0.0153344	−	0.0370206i	−0.931361	+	0.364096i	$0.881378\pi$
$212$	1.04284e8	−	3.52600e7i	0.751695	−	0.254160i
$213$	−1.06228e8	−	4.40010e7i	−0.753199	−	0.311985i
$214$	−7.43811e6	+	2.23114e8i	−0.0518817	+	1.55625i
$215$	−2.07927e8	+	2.07927e8i	−1.42685	+	1.42685i
$216$	−8.41281e7	+	6.87890e7i	−0.568006	+	0.464441i
$217$	1.44070e7	+	1.44070e7i	0.0957113	+	0.0957113i
$218$	−1.37472e8	+	1.28602e8i	−0.898706	+	0.840718i
$219$	−8.91026e7	+	2.15113e8i	−0.573239	+	1.38392i
$220$	−2.94286e7	+	4.40882e8i	−0.186333	+	2.79153i
$221$	−9.93550e7	+	4.11542e7i	−0.619180	+	0.256473i
$222$	2.87379e8	−	1.07965e8i	1.76287	−	0.662289i
$223$	2.37424e8			1.43370			0.716850	−	0.697227i	$-0.245583\pi$
$223$	2.37424e8			1.43370			0.716850	+	0.697227i	$0.245583\pi$
$224$	−2.68484e7	−	1.68074e7i	−0.159606	−	0.0999152i
$225$	−1.34784e8			−0.788859
$226$	5.15081e7	−	1.93510e7i	0.296822	−	0.111512i
$227$	−7.75932e6	+	3.21402e6i	−0.0440285	+	0.0182372i	−0.404589	−	0.914499i	$-0.632585\pi$
$227$	−7.75932e6	+	3.21402e6i	−0.0440285	+	0.0182372i	0.360561	+	0.932736i	$0.382585\pi$
$228$	−1.43244e8	−	9.56148e6i	−0.800397	−	0.0534260i
$229$	−1.41855e7	+	3.42468e7i	−0.0780586	+	0.188450i	−0.958091	−	0.286463i	$-0.907520\pi$
$229$	−1.41855e7	+	3.42468e7i	−0.0780586	+	0.188450i	0.880033	+	0.474913i	$0.157520\pi$
$230$	2.55322e8	−	2.38847e8i	1.38370	−	1.29441i
$231$	4.63975e7	+	4.63975e7i	0.247658	+	0.247658i
$232$	−8.19809e7	−	8.22352e6i	−0.431027	−	0.0432364i
$233$	−8.69803e6	+	8.69803e6i	−0.0450480	+	0.0450480i	−0.729272	−	0.684224i	$-0.760141\pi$
$233$	−8.69803e6	+	8.69803e6i	−0.0450480	+	0.0450480i	0.684224	+	0.729272i	$0.260141\pi$
$234$	1.42180e6	−	4.26486e7i	0.00725411	−	0.217595i
$235$	5.63836e7	+	2.33548e7i	0.283410	+	0.117392i
$236$	−6.43397e7	−	1.90289e8i	−0.318630	−	0.942371i
$237$	−1.35439e8	−	3.26979e8i	−0.660884	−	1.59551i
$238$	−4.10656e7	−	1.86363e7i	−0.197451	−	0.0896066i
$239$		−	1.96743e8i		−	0.932196i	−0.884733	−	0.466098i	$-0.845659\pi$
$239$		−	1.96743e8i		−	0.932196i	0.884733	−	0.466098i	$-0.154341\pi$
$240$	4.38705e8	+	5.88287e7i	2.04849	+	0.274695i
$241$			1.35929e8i			0.625537i	0.949829	+	0.312768i	$0.101256\pi$
$241$			1.35929e8i			0.625537i	−0.949829	+	0.312768i	$0.898744\pi$
$242$	−1.38288e8	+	3.04721e8i	−0.627234	+	1.38213i
$243$	−6.10277e7	−	1.47334e8i	−0.272838	−	0.658690i
$244$	6.09119e6	−	1.23144e7i	0.0268434	−	0.0542687i
$245$	−3.61673e8	−	1.49810e8i	−1.57121	−	0.650817i
$246$	−3.29282e8	−	1.09775e7i	−1.41025	−	0.0470143i
$247$	−6.66992e7	+	6.66992e7i	−0.281631	+	0.281631i
$248$	1.52131e8	+	8.16683e7i	0.633339	+	0.339995i
$249$	−3.61310e7	−	3.61310e7i	−0.148314	−	0.148314i
$250$	−3.29965e8	−	3.52724e8i	−1.33560	−	1.42773i
$251$	−5.65659e7	+	1.36562e8i	−0.225786	+	0.545096i	−0.995656	−	0.0931047i	$-0.970321\pi$
$251$	−5.65659e7	+	1.36562e8i	−0.225786	+	0.545096i	0.769870	+	0.638200i	$0.220321\pi$
$252$	1.34678e7	−	1.17824e7i	0.0530145	−	0.0463799i
$253$	4.05793e8	−	1.68085e8i	1.57537	−	0.652539i
$254$	130738.	+	347996.i	0.000500591	+	0.00133246i
$255$	6.30180e8			2.37998
$256$	−2.58952e8	−	7.07207e7i	−0.964672	−	0.263455i
$257$	−1.15082e8			−0.422902			−0.211451	−	0.977389i	$-0.567819\pi$
$257$	−1.15082e8			−0.422902			−0.211451	+	0.977389i	$0.567819\pi$
$258$	1.30145e8	+	3.46417e8i	0.471799	+	1.25583i
$259$	7.81451e7	−	3.23687e7i	0.279481	−	0.115765i
$260$	2.18886e8	−	1.91493e8i	0.772344	−	0.675688i
$261$	1.78123e7	−	4.30027e7i	0.0620123	−	0.149711i
$262$	−1.66724e8	−	1.78224e8i	−0.572722	−	0.612225i
$263$	−1.34558e8	−	1.34558e8i	−0.456104	−	0.456104i	0.441270	−	0.897374i	$-0.354528\pi$
$263$	−1.34558e8	−	1.34558e8i	−0.456104	−	0.456104i	−0.897374	+	0.441270i	$0.854528\pi$
$264$	4.89937e8	+	2.63012e8i	1.63880	+	0.879756i
$265$	−2.99702e8	+	2.99702e8i	−0.989304	+	0.989304i
$266$	−3.95332e7	−	1.31794e6i	−0.128788	−	0.00429350i
$267$	6.13046e8	+	2.53932e8i	1.97108	+	0.816447i
$268$	−7.00007e7	+	1.41519e8i	−0.222142	+	0.449099i
$269$	1.90583e8	+	4.60107e8i	0.596967	+	1.44121i	0.876657	+	0.481116i	$0.159768\pi$
$269$	1.90583e8	+	4.60107e8i	0.596967	+	1.44121i	−0.279690	+	0.960090i	$0.590232\pi$
$270$	1.72908e8	−	3.81007e8i	0.534616	−	1.17804i
$271$			5.76054e8i			1.75821i	0.476629	+	0.879105i	$0.341859\pi$
$271$			5.76054e8i			1.75821i	−0.476629	+	0.879105i	$0.658141\pi$
$272$	−3.78784e8	−	5.07936e7i	−1.14130	−	0.153044i
$273$		−	4.31875e7i		−	0.128466i
$274$	3.35121e8	+	1.52084e8i	0.984179	+	0.446638i
$275$	−4.41625e8	−	1.06618e9i	−1.28053	−	3.09147i
$276$	−1.40930e8	−	4.16810e8i	−0.403480	−	1.19332i
$277$	1.89907e8	+	7.86622e7i	0.536862	+	0.222375i	0.634606	−	0.772836i	$-0.281163\pi$
$277$	1.89907e8	+	7.86622e7i	0.536862	+	0.222375i	−0.0977438	+	0.995212i	$0.531163\pi$
$278$	−402799.	+	1.20824e7i	−0.00112443	+	0.0337285i
$279$	−6.89739e7	+	6.89739e7i	−0.190139	+	0.190139i
$280$	1.21347e8	+	1.21724e7i	0.330351	+	0.0331376i
$281$	4.45593e7	+	4.45593e7i	0.119802	+	0.119802i	0.764466	−	0.644664i	$-0.223003\pi$
$281$	4.45593e7	+	4.45593e7i	0.119802	+	0.119802i	−0.644664	+	0.764466i	$0.723003\pi$
$282$	5.60874e7	−	5.24684e7i	0.148934	−	0.139324i
$283$	−1.10369e8	+	2.66454e8i	−0.289464	+	0.698828i	−0.999988	−	0.00484485i	$-0.998458\pi$
$283$	−1.10369e8	+	2.66454e8i	−0.289464	+	0.698828i	0.710524	+	0.703673i	$0.248458\pi$
$284$	−2.67879e8	−	1.78807e7i	−0.693943	−	0.0463203i
$285$	5.10671e8	−	2.11527e8i	1.30672	−	0.541263i
$286$	3.42020e8	−	1.28493e8i	0.864512	−	0.324787i
$287$	−9.07759e7			−0.226665
$288$	8.04660e7	−	1.28538e8i	0.198490	−	0.317072i
$289$	−1.33768e8			−0.325994
$290$	2.96961e8	−	1.11565e8i	0.715001	−	0.268617i
$291$	−3.30114e8	+	1.36738e8i	−0.785305	+	0.325284i
$292$	−3.62087e7	+	5.42457e8i	−0.0851086	+	1.27505i
$293$	−7.51609e7	+	1.81455e8i	−0.174564	+	0.421436i	−0.986811	−	0.161879i	$-0.948245\pi$
$293$	−7.51609e7	+	1.81455e8i	−0.174564	+	0.421436i	0.812246	+	0.583315i	$0.198245\pi$
$294$	−3.59773e8	+	3.36559e8i	−0.825682	+	0.772406i
$295$	5.46874e8	+	5.46874e8i	1.24025	+	1.24025i
$296$	5.54922e8	−	4.53742e8i	1.24369	−	1.01692i
$297$	3.71680e8	−	3.71680e8i	0.823232	−	0.823232i
$298$	4.64074e6	−	1.39204e8i	0.0101585	−	0.304716i
$299$	−2.67087e8	−	1.10631e8i	−0.577834	−	0.239347i
$300$	−1.09513e9	+	3.70279e8i	−2.34174	+	0.791781i
$301$	3.90184e7	+	9.41987e7i	0.0824682	+	0.199096i
$302$	−2.07237e8	−	9.40479e7i	−0.432955	−	0.196483i
$303$			6.91559e7i			0.142817i
$304$	−3.24000e8	+	8.59821e7i	−0.661435	+	0.175530i
$305$			5.28961e7i			0.106751i
$306$	8.92221e7	−	1.96603e8i	0.178011	−	0.392253i
$307$	−2.97980e8	−	7.19387e8i	−0.587763	−	1.41899i	−0.885636	−	0.464380i	$-0.846277\pi$
$307$	−2.97980e8	−	7.19387e8i	−0.587763	−	1.41899i	0.297873	−	0.954606i	$-0.403723\pi$
$308$	1.37329e8	+	6.79284e7i	0.267816	+	0.132472i
$309$	8.28298e8	+	3.43092e8i	1.59710	+	0.661540i
$310$	−6.64428e8	−	2.21505e7i	−1.26672	−	0.0422296i
$311$	−1.47975e8	+	1.47975e8i	−0.278950	+	0.278950i	−0.832690	−	0.553739i	$-0.813200\pi$
$311$	−1.47975e8	+	1.47975e8i	−0.278950	+	0.278950i	0.553739	+	0.832690i	$0.313200\pi$
$312$	−1.05612e8	−	3.50428e8i	−0.196867	−	0.653217i
$313$	−7.31414e7	−	7.31414e7i	−0.134821	−	0.134821i	0.636476	−	0.771297i	$-0.280392\pi$
$313$	−7.31414e7	−	7.31414e7i	−0.134821	−	0.134821i	−0.771297	+	0.636476i	$0.780392\pi$
$314$	5.36033e8	+	5.73006e8i	0.977097	+	1.04449i
$315$	−2.63655e7	+	6.36520e7i	−0.0475280	+	0.114743i
$316$	−5.44130e8	−	6.21966e8i	−0.970059	−	1.10882i
$317$	6.68410e8	−	2.76865e8i	1.17852	−	0.488158i	0.294518	−	0.955646i	$-0.404841\pi$
$317$	6.68410e8	−	2.76865e8i	1.17852	−	0.488158i	0.883999	+	0.467488i	$0.154841\pi$
$318$	1.87588e8	+	4.99318e8i	0.327122	+	0.870728i
$319$	3.98525e8			0.687367
$320$	1.01439e9	−	1.97979e8i	1.73053	−	0.337749i
$321$	−1.08167e9			−1.82527
$322$	−4.26346e7	−	1.13484e8i	−0.0711651	−	0.189426i
$323$	−4.40921e8	+	1.82635e8i	−0.728034	+	0.301561i
$324$	−4.97498e8	−	5.68663e8i	−0.812612	−	0.928854i
$325$	−2.90671e8	+	7.01742e8i	−0.469688	+	1.13393i
$326$	3.82966e7	+	4.09381e7i	0.0612208	+	0.0654435i
$327$	−6.44969e8	−	6.44969e8i	−1.02005	−	1.02005i
$328$	−7.36565e8	+	2.21987e8i	−1.15253	+	0.347351i
$329$	1.49632e7	−	1.49632e7i	0.0231654	−	0.0231654i
$330$	−2.13979e9	−	7.13355e7i	−3.27772	−	0.109271i
$331$	−2.75546e8	−	1.14135e8i	−0.417635	−	0.172990i	0.163963	−	0.986466i	$-0.447572\pi$
$331$	−2.75546e8	−	1.14135e8i	−0.417635	−	0.172990i	−0.581598	+	0.813477i	$0.697572\pi$
$332$	−1.06942e8	−	5.28977e7i	−0.160385	−	0.0793329i
$333$	1.54967e8	+	3.74123e8i	0.229977	+	0.555213i
$334$	1.13279e8	−	2.49613e8i	0.166355	−	0.366568i
$335$		−	6.07888e8i		−	0.883419i
$336$	7.70578e7	−	1.32731e8i	0.110823	−	0.190891i
$337$			7.15152e8i			1.01787i	0.860804	+	0.508937i	$0.169961\pi$
$337$			7.15152e8i			1.01787i	−0.860804	+	0.508937i	$0.830039\pi$
$338$	4.27483e8	+	1.93999e8i	0.602158	+	0.273270i
$339$	1.02026e8	+	2.46312e8i	0.142236	+	0.343389i
$340$	1.39392e9	−	4.71308e8i	1.92337	−	0.650322i
$341$	−7.71598e8	−	3.19607e8i	−1.05378	−	0.436491i
$342$	6.30972e6	−	1.89267e8i	0.00852940	−	0.255849i
$343$	−1.95492e8	+	1.95492e8i	−0.261577	+	0.261577i
$344$	5.46956e8	+	6.68921e8i	0.724433	+	0.885973i
$345$	1.19788e9	+	1.19788e9i	1.57053	+	1.57053i
$346$	−2.04438e8	+	1.91247e8i	−0.265336	+	0.248215i
$347$	−2.81842e8	+	6.80426e8i	−0.362120	+	0.874234i	0.632870	+	0.774258i	$0.281877\pi$
$347$	−2.81842e8	+	6.80426e8i	−0.362120	+	0.874234i	−0.994990	+	0.0999761i	$0.968123\pi$
$348$	2.65885e7	−	3.98333e8i	0.0338194	−	0.506662i
$349$	4.13759e8	−	1.71385e8i	0.521025	−	0.215816i	−0.106642	−	0.994297i	$-0.534010\pi$
$349$	4.13759e8	−	1.71385e8i	0.521025	−	0.215816i	0.627667	+	0.778482i	$0.284010\pi$
$350$	−2.98168e8	+	1.12018e8i	−0.371725	+	0.139653i
$351$	−3.45965e8			−0.427029
$352$	1.28042e9	+	2.15348e8i	1.56478	+	0.263174i
$353$	4.11765e8			0.498240			0.249120	−	0.968473i	$-0.419859\pi$
$353$	4.11765e8			0.498240			0.249120	+	0.968473i	$0.419859\pi$
$354$	9.11117e8	−	3.42296e8i	1.09160	−	0.410100i
$355$	9.54996e8	−	3.95572e8i	1.13293	−	0.469274i
$356$	1.54594e9	+	1.03191e8i	1.81601	+	0.121217i
$357$	8.36194e7	−	2.01875e8i	0.0972676	−	0.234825i
$358$	−3.01876e8	+	2.82398e8i	−0.347727	+	0.325290i
$359$	2.38544e8	+	2.38544e8i	0.272106	+	0.272106i	0.829947	−	0.557842i	$-0.188370\pi$
$359$	2.38544e8	+	2.38544e8i	0.272106	+	0.272106i	−0.557842	+	0.829947i	$0.688370\pi$
$360$	−5.82757e7	+	5.80955e8i	−0.0658308	+	0.656271i
$361$	3.36063e8	−	3.36063e8i	0.375964	−	0.375964i
$362$	−5.86671e7	+	1.75979e9i	−0.0650002	+	1.94975i
$363$	−1.49798e9	−	6.20484e8i	−1.64374	−	0.680860i
$364$	−3.22997e7	−	9.55284e7i	−0.0351029	−	0.103819i
$365$	−8.01039e8	−	1.93388e9i	−0.862241	−	2.08163i
$366$	6.06178e7	+	2.75095e7i	0.0646274	+	0.0293291i
$367$			6.57930e8i			0.694782i	0.937720	+	0.347391i	$0.112932\pi$
$367$			6.57930e8i			0.694782i	−0.937720	+	0.347391i	$0.887068\pi$
$368$	−6.23460e8	−	8.16562e8i	−0.652141	−	0.854126i
$369$		−	4.34594e8i		−	0.450289i
$370$	−1.14053e9	+	2.51318e9i	−1.17058	+	2.57939i
$371$	5.62403e7	+	1.35776e8i	0.0571793	+	0.138043i
$372$	−3.70931e8	+	7.49902e8i	−0.373588	+	0.755274i
$373$	−1.47142e9	−	6.09481e8i	−1.46810	−	0.608106i	−0.501673	−	0.865057i	$-0.667282\pi$
$373$	−1.47142e9	−	6.09481e8i	−1.46810	−	0.608106i	−0.966424	+	0.256952i	$0.917282\pi$
$374$	1.84752e9	+	6.15921e7i	1.82616	+	0.0608800i
$375$	1.65485e9	−	1.65485e9i	1.62050	−	1.62050i
$376$	8.48216e7	−	1.58005e8i	0.0822903	−	0.153290i
$377$	−1.85477e8	−	1.85477e8i	−0.178277	−	0.178277i
$378$	−9.91104e7	−	1.05947e8i	−0.0943839	−	0.100894i
$379$	6.11320e8	−	1.47586e9i	0.576808	−	1.39254i	−0.318854	−	0.947804i	$-0.603298\pi$
$379$	6.11320e8	−	1.47586e9i	0.576808	−	1.39254i	0.895662	−	0.444734i	$-0.146702\pi$
$380$	9.71377e8	−	8.49814e8i	0.908124	−	0.794476i
$381$	−1.66412e6	+	689299.i	−0.00154151	+	0.000638514i
$382$	−1.32478e8	−	3.52629e8i	−0.121597	−	0.323665i
$383$	−1.11947e9			−1.01816			−0.509081	−	0.860719i	$-0.670015\pi$
$383$	−1.11947e9			−1.01816			−0.509081	+	0.860719i	$0.670015\pi$
$384$	3.00670e8	−	1.26543e9i	0.270976	−	1.14046i
$385$	−5.89892e8			−0.526818
$386$	−6.30328e8	−	1.67780e9i	−0.557842	−	1.48485i
$387$	−4.50981e8	+	1.86802e8i	−0.395521	+	0.163830i
$388$	−6.27929e8	+	5.49347e8i	−0.545757	+	0.477458i
$389$	−2.80022e8	+	6.76032e8i	−0.241195	+	0.582296i	−0.997402	−	0.0720364i	$-0.977050\pi$
$389$	−2.80022e8	+	6.76032e8i	−0.241195	+	0.582296i	0.756207	+	0.654332i	$0.227050\pi$
$390$	9.62672e8	+	1.02907e9i	0.821774	+	0.878456i
$391$	−1.03426e9	−	1.03426e9i	−0.875009	−	0.875009i
$392$	−5.44088e8	+	1.01352e9i	−0.456214	+	0.849830i
$393$	8.36160e8	−	8.36160e8i	0.694889	−	0.694889i
$394$	6.54029e8	+	2.18038e7i	0.538716	+	0.0179595i
$395$	2.93956e9	+	1.21761e9i	2.39990	+	0.994071i
$396$	−3.25211e8	+	6.57470e8i	−0.263167	+	0.532039i
$397$	−4.59659e8	−	1.10972e9i	−0.368697	−	0.890113i	−0.993964	−	0.109702i	$-0.965010\pi$
$397$	−4.59659e8	−	1.10972e9i	−0.368697	−	0.890113i	0.625268	−	0.780410i	$-0.284990\pi$
$398$	2.60976e8	−	5.75068e8i	0.207496	−	0.457224i
$399$		−	1.91659e8i		−	0.151051i
$400$	−2.14543e9	+	1.63808e9i	−1.67612	+	1.27975i
$401$		−	1.46572e9i		−	1.13513i	−0.823328	−	0.567565i	$-0.807885\pi$
$401$		−	1.46572e9i		−	1.13513i	0.823328	−	0.567565i	$-0.192115\pi$
$402$	−6.96628e8	−	3.16142e8i	−0.534822	−	0.242712i
$403$	2.10360e8	+	5.07854e8i	0.160102	+	0.386520i
$404$	5.17213e7	+	1.52969e8i	0.0390243	+	0.115417i
$405$	2.68764e9	+	1.11326e9i	2.01038	+	0.832728i
$406$	3.66493e6	−	1.09934e8i	0.00271784	−	0.0815248i
$407$	−2.45166e9	+	2.45166e9i	−1.80252	+	1.80252i
$408$	1.84824e8	−	1.84252e9i	0.134725	−	1.34308i
$409$	5.60951e8	+	5.60951e8i	0.405409	+	0.405409i	0.880134	−	0.474725i	$-0.157453\pi$
$409$	5.60951e8	+	5.60951e8i	0.405409	+	0.405409i	−0.474725	+	0.880134i	$0.657453\pi$
$410$	2.16301e9	−	2.02345e9i	1.54994	−	1.44993i
$411$	−6.82386e8	+	1.64743e9i	−0.484824	+	1.17047i
$412$	2.08875e9	+	1.39423e8i	1.47145	+	0.0982185i
$413$	2.47754e8	−	1.02623e8i	0.173059	−	0.0716835i
$414$	5.43310e8	−	2.04115e8i	0.376311	−	0.141376i
$415$	4.59365e8			0.315493
$416$	−4.95692e8	−	6.96141e8i	−0.337586	−	0.474101i
$417$	−5.85760e7			−0.0395588
$418$	1.51783e9	−	5.70230e8i	1.01650	−	0.381885i
$419$	−3.06253e8	+	1.26854e8i	−0.203391	+	0.0842471i	−0.482053	−	0.876142i	$-0.660109\pi$
$419$	−3.06253e8	+	1.26854e8i	−0.203391	+	0.0842471i	0.278663	+	0.960389i	$0.410109\pi$
$420$	−3.93559e7	+	5.89607e8i	−0.0259202	+	0.388320i
$421$	−1.90584e8	+	4.60112e8i	−0.124480	+	0.300522i	−0.973818	−	0.227327i	$-0.927001\pi$
$421$	−1.90584e8	+	4.60112e8i	−0.124480	+	0.300522i	0.849338	+	0.527849i	$0.177001\pi$
$422$	4.51760e7	−	4.22611e7i	0.0292627	−	0.0273745i
$423$	7.16371e7	+	7.16371e7i	0.0460200	+	0.0460200i
$424$	7.88372e8	+	9.64170e8i	0.502286	+	0.614289i
$425$	−2.71742e9	+	2.71742e9i	−1.71710	+	1.71710i
$426$	4.33433e7	−	1.30013e9i	0.0271636	−	0.814804i
$427$	1.69450e7	+	7.01885e6i	0.0105328	+	0.00436283i
$428$	−2.39259e9	+	8.08973e8i	−1.47508	+	0.498747i
$429$	6.77464e8	+	1.63554e9i	0.414272	+	1.00014i
$430$	−3.02947e9	−	1.37483e9i	−1.83750	−	0.833890i
$431$			6.32436e7i			0.0380493i	0.999819	+	0.0190246i	$0.00605609\pi$
$431$			6.32436e7i			0.0380493i	−0.999819	+	0.0190246i	$0.993944\pi$
$432$	−1.06328e9	−	6.17293e8i	−0.634532	−	0.368382i
$433$			1.02639e9i			0.607581i	0.952739	+	0.303790i	$0.0982522\pi$
$433$			1.02639e9i			0.607581i	−0.952739	+	0.303790i	$0.901748\pi$
$434$	−9.52596e7	+	2.09907e8i	−0.0559364	+	0.123257i
$435$	5.88212e8	+	1.42007e9i	0.342627	+	0.827174i
$436$	−1.90901e9	−	9.44269e8i	−1.10307	−	0.545624i
$437$	−1.18528e9	−	4.90961e8i	−0.679419	−	0.281424i
$438$	−2.63278e9	−	8.77706e7i	−1.49712	−	0.0499103i
$439$	7.47807e8	−	7.47807e8i	0.421856	−	0.421856i	−0.463987	−	0.885842i	$-0.653581\pi$
$439$	7.47807e8	−	7.47807e8i	0.421856	−	0.421856i	0.885842	+	0.463987i	$0.153581\pi$
$440$	−4.78645e9	+	1.44254e9i	−2.67873	+	0.807319i
$441$	−4.59517e8	−	4.59517e8i	−0.255133	−	0.255133i
$442$	−8.31186e8	−	8.88516e8i	−0.457847	−	0.489427i
$443$	1.26198e9	−	3.04670e9i	0.689669	−	1.66501i	−0.0557774	−	0.998443i	$-0.517764\pi$
$443$	1.26198e9	−	3.04670e9i	0.689669	−	1.66501i	0.745447	−	0.666565i	$-0.232236\pi$
$444$	2.28691e9	+	2.61404e9i	1.23996	+	1.41733i
$445$	−5.51132e9	+	2.28287e9i	−2.96480	+	1.22806i
$446$	9.44687e8	+	2.51455e9i	0.504215	+	1.34211i
$447$	6.74868e8			0.357390
$448$	7.11792e7	−	3.51225e8i	0.0374007	−	0.184549i
$449$	3.14676e9			1.64060			0.820298	−	0.571937i	$-0.193808\pi$
$449$	3.14676e9			1.64060			0.820298	+	0.571937i	$0.193808\pi$
$450$	−5.36291e8	−	1.42749e9i	−0.277432	−	0.738464i
$451$	3.43775e9	−	1.42396e9i	1.76464	−	0.730939i
$452$	4.09891e8	+	4.68524e8i	0.208777	+	0.238642i
$453$	4.21985e8	−	1.01876e9i	0.213281	−	0.514907i
$454$	−6.49131e7	−	6.93904e7i	−0.0325564	−	0.0348020i
$455$	2.74540e8	+	2.74540e8i	0.136636	+	0.136636i
$456$	−4.68689e8	−	1.55514e9i	−0.231477	−	0.768055i
$457$	1.53618e9	−	1.53618e9i	0.752895	−	0.752895i	−0.222124	−	0.975018i	$-0.571299\pi$
$457$	1.53618e9	−	1.53618e9i	0.752895	−	0.752895i	0.975018	+	0.222124i	$0.0712989\pi$
$458$	−4.19149e8	−	1.39734e7i	−0.203864	−	0.00679633i
$459$	−1.61718e9	−	6.69857e8i	−0.780572	−	0.323324i
$460$	3.54552e9	+	1.75375e9i	1.69835	+	0.840072i
$461$	1.42593e9	+	3.44249e9i	0.677867	+	1.63651i	0.767895	+	0.640575i	$0.221304\pi$
$461$	1.42593e9	+	3.44249e9i	0.677867	+	1.63651i	−0.0900287	+	0.995939i	$0.528696\pi$
$462$	−3.06783e8	+	6.76005e8i	−0.144739	+	0.318936i
$463$		−	2.87570e9i		−	1.34651i	−0.739409	−	0.673256i	$-0.764895\pi$
$463$		−	2.87570e9i		−	1.34651i	0.739409	−	0.673256i	$-0.235105\pi$
$464$	−2.39098e8	−	9.00976e8i	−0.111113	−	0.418698i
$465$		−	3.22117e9i		−	1.48569i
$466$	−1.26729e8	−	5.75119e7i	−0.0580130	−	0.0263273i
$467$	8.88675e8	+	2.14545e9i	0.403770	+	0.974786i	0.986742	+	0.162295i	$0.0518895\pi$
$467$	8.88675e8	+	2.14545e9i	0.403770	+	0.974786i	−0.582973	+	0.812492i	$0.698111\pi$
$468$	4.57347e8	−	1.54636e8i	0.206246	−	0.0697349i
$469$	−1.94734e8	−	8.06614e7i	−0.0871639	−	0.0361045i
$470$	−2.30057e7	+	6.90083e8i	−0.0102210	+	0.306590i
$471$	−2.68833e9	+	2.68833e9i	−1.18552	+	1.18552i
$472$	1.75934e9	−	1.43856e9i	0.770111	−	0.629696i
$473$	−2.95531e9	−	2.95531e9i	−1.28407	−	1.28407i
$474$	2.92412e9	−	2.73545e9i	1.26116	−	1.17979i
$475$	−1.28995e9	+	3.11421e9i	−0.552261	+	1.33328i
$476$	3.39805e7	−	5.09076e8i	0.0144413	−	0.216350i
$477$	−6.50034e8	+	2.69253e8i	−0.274234	+	0.113592i
$478$	2.08370e9	−	7.82821e8i	0.872644	−	0.327842i
$479$	3.54468e9			1.47368			0.736838	−	0.676069i	$-0.236318\pi$
$479$	3.54468e9			1.47368			0.736838	+	0.676069i	$0.236318\pi$
$480$	1.12251e9	+	4.88038e9i	0.463282	+	2.01423i
$481$	2.28204e9			0.935008
$482$	−1.43962e9	+	5.40848e8i	−0.585576	+	0.219994i
$483$	5.42681e8	−	2.24786e8i	0.219144	−	0.0907725i
$484$	−3.77751e9	−	2.52147e8i	−1.51442	−	0.101087i
$485$	1.22928e9	−	2.96775e9i	0.489277	−	1.18122i
$486$	1.31758e9	−	1.23257e9i	0.520657	−	0.487062i
$487$	1.61940e9	+	1.61940e9i	0.635335	+	0.635335i	0.949401	−	0.314066i	$-0.101691\pi$
$487$	1.61940e9	+	1.61940e9i	0.635335	+	0.635335i	−0.314066	+	0.949401i	$0.601691\pi$
$488$	1.54658e8	+	1.55138e7i	0.0602424	+	0.00604293i
$489$	−1.92067e8	+	1.92067e8i	−0.0742798	+	0.0742798i
$490$	1.47570e8	−	4.42654e9i	0.0566647	−	1.69972i
$491$	1.31510e9	+	5.44734e8i	0.501389	+	0.207682i	0.619020	−	0.785375i	$-0.287530\pi$
$491$	1.31510e9	+	5.44734e8i	0.501389	+	0.207682i	−0.117631	+	0.993057i	$0.537530\pi$
$492$	−1.19392e9	−	3.53109e9i	−0.451957	−	1.33669i
$493$	−5.07871e8	−	1.22611e9i	−0.190893	−	0.460855i
$494$	−9.71797e8	−	4.41019e8i	−0.362686	−	0.164594i
$495$		−	2.82414e9i		−	1.04657i
$496$	−2.59632e8	+	1.93616e9i	−0.0955372	+	0.712452i
$497$		−	3.58417e8i		−	0.130961i
$498$	2.38900e8	−	5.26423e8i	0.0866790	−	0.191000i
$499$	1.46788e9	+	3.54378e9i	0.528858	+	1.27678i	0.932272	+	0.361758i	$0.117823\pi$
$499$	1.46788e9	+	3.54378e9i	0.528858	+	1.27678i	−0.403414	+	0.915018i	$0.632177\pi$
$500$	2.42279e9	−	4.89809e9i	0.866803	−	1.75240i
$501$	1.22708e9	+	5.08272e8i	0.435953	+	0.180578i
$502$	−1.67140e9	−	5.57203e7i	−0.589680	−	0.0196585i
$503$	2.20705e9	−	2.20705e9i	0.773256	−	0.773256i	−0.205418	−	0.978674i	$-0.565855\pi$
$503$	2.20705e9	−	2.20705e9i	0.773256	−	0.773256i	0.978674	+	0.205418i	$0.0658554\pi$
$504$	1.78373e8	+	9.57560e7i	0.0620616	+	0.0333165i
$505$	−4.39620e8	−	4.39620e8i	−0.151900	−	0.151900i
$506$	3.39479e9	+	3.62894e9i	1.16489	+	1.24524i
$507$	−8.70458e8	+	2.10147e9i	−0.296633	+	0.716136i
$508$	−3.16541e6	+	2.76928e6i	−0.00107129	+	0.000937224i
$509$	−3.60231e9	+	1.49213e9i	−1.21079	+	0.501526i	−0.894470	−	0.447127i	$-0.852447\pi$
$509$	−3.60231e9	+	1.49213e9i	−1.21079	+	0.501526i	−0.316319	+	0.948653i	$0.602447\pi$
$510$	2.50742e9	+	6.67421e9i	0.837012	+	2.22794i
$511$	−7.25799e8			−0.240627
$512$	−2.81343e8	−	3.02394e9i	−0.0926385	−	0.995700i
$513$	−1.53533e9			−0.502102
$514$	−4.57898e8	−	1.21882e9i	−0.148730	−	0.395886i
$515$	−7.44646e9	+	3.08442e9i	−2.40228	+	0.995058i
$516$	−3.15105e9	+	2.75671e9i	−1.00968	+	0.883319i
$517$	−3.31947e8	+	8.01391e8i	−0.105646	+	0.255051i
$518$	6.53747e8	+	6.98839e8i	0.206660	+	0.220914i
$519$	−9.59149e8	−	9.59149e8i	−0.301162	−	0.301162i
$520$	2.89902e9	+	1.55628e9i	0.904147	+	0.485373i
$521$	8.93588e8	−	8.93588e8i	0.276825	−	0.276825i	−0.555015	−	0.831840i	$-0.687288\pi$
$521$	8.93588e8	−	8.93588e8i	0.276825	−	0.276825i	0.831840	+	0.555015i	$0.187288\pi$
$522$	5.26313e8	+	1.75460e7i	0.161956	+	0.00539923i
$523$	4.86693e9	+	2.01595e9i	1.48764	+	0.616202i	0.970803	−	0.239879i	$-0.0771079\pi$
$523$	4.86693e9	+	2.01595e9i	1.48764	+	0.616202i	0.516841	+	0.856082i	$0.327108\pi$
$524$	1.22418e9	−	2.47490e9i	0.371695	−	0.751447i
$525$	−5.90601e8	−	1.42584e9i	−0.178130	−	0.430044i
$526$	8.89704e8	−	1.96049e9i	0.266560	−	0.587373i
$527$			2.78121e9i			0.827745i
$528$	−8.36144e8	+	6.23540e9i	−0.247208	+	1.84351i
$529$		−	5.27129e8i		−	0.154818i
$530$	−4.36662e9	−	1.98165e9i	−1.27403	−	0.578178i
$531$	4.91312e8	+	1.18613e9i	0.142405	+	0.343797i
$532$	−1.43340e8	−	4.23939e8i	−0.0412741	−	0.122071i
$533$	−2.26268e9	−	9.37232e8i	−0.647258	−	0.268103i
$534$	−2.50136e8	+	7.50311e9i	−0.0710856	+	2.13229i
$535$	6.87609e9	−	6.87609e9i	1.94135	−	1.94135i
$536$	−1.77734e9	−	1.78286e8i	−0.498534	−	0.0500081i
$537$	−1.41629e9	−	1.41629e9i	−0.394678	−	0.394678i
$538$	−4.11467e9	+	3.84917e9i	−1.13919	+	1.06569i
$539$	2.12928e9	−	5.14053e9i	0.585695	−	1.41399i
$540$	4.72321e9	+	3.15272e8i	1.29080	+	0.0861603i
$541$	3.62578e8	−	1.50185e8i	0.0984489	−	0.0407789i	−0.332915	−	0.942957i	$-0.608032\pi$
$541$	3.62578e8	−	1.50185e8i	0.0984489	−	0.0407789i	0.431364	+	0.902178i	$0.358032\pi$
$542$	−6.10096e9	+	2.29206e9i	−1.64589	+	0.618341i
$543$	−8.53151e9			−2.28679
$544$	−9.69191e8	−	4.21379e9i	−0.258115	−	1.12222i
$545$	8.20006e9			2.16985
$546$	4.57397e8	−	1.71838e8i	0.120259	−	0.0451800i
$547$	−1.84279e9	+	7.63308e8i	−0.481415	+	0.199409i	−0.610174	−	0.792267i	$-0.708901\pi$
$547$	−1.84279e9	+	7.63308e8i	−0.481415	+	0.199409i	0.128759	+	0.991676i	$0.458901\pi$
$548$	−2.77302e8	+	4.15437e9i	−0.0719815	+	1.07838i
$549$	−3.36030e7	+	8.11249e7i	−0.00866713	+	0.0209243i
$550$	9.53466e9	−	8.91944e9i	2.44363	−	2.28596i
$551$	−8.23113e8	−	8.23113e8i	−0.209618	−	0.209618i
$552$	3.85368e9	−	3.15103e9i	0.975188	−	0.797381i
$553$	7.80109e8	−	7.80109e8i	0.196163	−	0.196163i
$554$	−7.74863e7	+	2.32429e9i	−0.0193616	+	0.580772i
$555$	−1.23546e10	−	5.11744e9i	−3.06763	−	1.27065i
$556$	−1.29567e8	+	4.38087e7i	−0.0319693	+	0.0108093i
$557$	1.62242e9	+	3.91687e9i	0.397805	+	0.960387i	0.988186	+	0.153262i	$0.0489777\pi$
$557$	1.62242e9	+	3.91687e9i	0.397805	+	0.960387i	−0.590380	+	0.807125i	$0.701022\pi$
$558$	−1.00494e9	−	4.56060e8i	−0.244862	−	0.111123i
$559$			2.75085e9i			0.666078i
$560$	3.53911e8	+	1.33361e9i	0.0851599	+	0.320902i
$561$			8.95687e9i			2.14184i
$562$	−2.94629e8	+	6.49222e8i	−0.0700161	+	0.154282i
$563$	−2.43256e9	−	5.87272e9i	−0.574493	−	1.38695i	−0.897695	−	0.440618i	$-0.854759\pi$
$563$	−2.43256e9	−	5.87272e9i	−0.574493	−	1.38695i	0.323202	−	0.946330i	$-0.395241\pi$
$564$	7.78857e8	+	3.85253e8i	0.182802	+	0.0904209i
$565$	−2.21436e9	−	9.17218e8i	−0.516510	−	0.213945i
$566$	−3.26115e9	−	1.08719e8i	−0.755986	−	0.0252028i
$567$	7.13253e8	−	7.13253e8i	0.164325	−	0.164325i
$568$	−8.76487e8	−	2.90824e9i	−0.200690	−	0.665902i
$569$	1.68534e9	+	1.68534e9i	0.383526	+	0.383526i	0.872371	−	0.488845i	$-0.162582\pi$
$569$	1.68534e9	+	1.68534e9i	0.383526	+	0.383526i	−0.488845	+	0.872371i	$0.662582\pi$
$570$	4.27218e9	+	4.56685e9i	0.966245	+	1.03289i
$571$	2.32599e9	−	5.61545e9i	0.522856	−	1.26229i	−0.413266	−	0.910610i	$-0.635612\pi$
$571$	2.32599e9	−	5.61545e9i	0.522856	−	1.26229i	0.936122	−	0.351676i	$-0.114388\pi$
$572$	2.72173e9	+	3.11106e9i	0.608077	+	0.695061i
$573$	1.68627e9	−	6.98477e8i	0.374444	−	0.155100i
$574$	−3.61188e8	−	9.61404e8i	−0.0797153	−	0.212185i
$575$	−1.03308e10			−2.26619
$576$	1.68151e9	+	3.40773e8i	0.366623	+	0.0742997i
$577$	−6.89229e9			−1.49365			−0.746824	−	0.665021i	$-0.768422\pi$
$577$	−6.89229e9			−1.49365			−0.746824	+	0.665021i	$0.768422\pi$
$578$	−5.32249e8	−	1.41673e9i	−0.114648	−	0.305169i
$579$	8.02323e9	−	3.32333e9i	1.71781	−	0.711538i
$580$	2.36316e9	+	2.70120e9i	0.502915	+	0.574855i
$581$	6.09537e7	−	1.47155e8i	0.0128939	−	0.0311286i
$582$	−2.76167e9	−	2.95216e9i	−0.580686	−	0.620739i
$583$	−4.25973e9	−	4.25973e9i	−0.890312	−	0.890312i
$584$	−5.88921e9	+	1.77490e9i	−1.22352	+	0.368747i
$585$	−1.31437e9	+	1.31437e9i	−0.271440	+	0.271440i
$586$	−2.22084e9	−	7.40374e7i	−0.455905	−	0.0151988i
$587$	1.07638e9	+	4.45851e8i	0.219651	+	0.0909823i	0.489795	−	0.871837i	$-0.337072\pi$
$587$	1.07638e9	+	4.45851e8i	0.219651	+	0.0909823i	−0.270145	+	0.962820i	$0.587072\pi$
$588$	−4.99598e9	−	2.47121e9i	−1.01344	−	0.501289i
$589$	9.33543e8	+	2.25377e9i	0.188248	+	0.454471i
$590$	−3.61596e9	+	7.96787e9i	−0.724840	+	1.59720i
$591$			3.17076e9i			0.631839i
$592$	7.01354e9	+	4.07176e9i	1.38935	+	0.806596i
$593$			2.41665e9i			0.475908i	0.971276	+	0.237954i	$0.0764767\pi$
$593$			2.41665e9i			0.475908i	−0.971276	+	0.237954i	$0.923523\pi$
$594$	5.41533e9	+	2.45757e9i	1.06016	+	0.481121i
$595$	7.51744e8	+	1.81487e9i	0.146306	+	0.353213i
$596$	1.49277e9	−	5.04730e8i	0.288823	−	0.0976556i
$597$	2.82699e9	+	1.17098e9i	0.543769	+	0.225236i
$598$	1.08977e8	−	3.26889e9i	0.0208392	−	0.625095i
$599$	−4.00283e9	+	4.00283e9i	−0.760980	+	0.760980i	−0.976500	−	0.215520i	$-0.930855\pi$
$599$	−4.00283e9	+	4.00283e9i	−0.760980	+	0.760980i	0.215520	+	0.976500i	$0.430855\pi$
$600$	−8.27900e9	−	1.01251e10i	−1.56476	−	1.91369i
$601$	−2.22515e9	−	2.22515e9i	−0.418119	−	0.418119i	0.466436	−	0.884555i	$-0.345538\pi$
$601$	−2.22515e9	−	2.22515e9i	−0.418119	−	0.418119i	−0.884555	+	0.466436i	$0.845538\pi$
$602$	−8.42404e8	+	7.88049e8i	−0.157374	+	0.147220i
$603$	3.86170e8	−	9.32298e8i	0.0717246	−	0.173159i
$604$	1.71482e8	−	2.56905e9i	0.0316658	−	0.474398i
$605$	1.34670e10	−	5.57820e9i	2.47244	−	1.02412i
$606$	−7.32427e8	+	2.75164e8i	−0.133693	+	0.0502271i
$607$	−3.68152e9			−0.668140			−0.334070	−	0.942548i	$-0.608422\pi$
$607$	−3.68152e9			−0.668140			−0.334070	+	0.942548i	$0.608422\pi$
$608$	−2.19979e9	−	3.08935e9i	−0.396935	−	0.557449i
$609$	5.32963e8			0.0956173
$610$	−5.60220e8	+	2.10468e8i	−0.0999319	+	0.0375432i
$611$	5.27463e8	−	2.18482e8i	0.0935509	−	0.0387501i
$612$	2.43722e9	+	1.62683e8i	0.429799	+	0.0286888i
$613$	2.12749e8	−	5.13621e8i	0.0373040	−	0.0900597i	−0.904130	−	0.427258i	$-0.859479\pi$
$613$	2.12749e8	−	5.13621e8i	0.0373040	−	0.0900597i	0.941433	+	0.337199i	$0.109479\pi$
$614$	6.43336e9	−	6.01826e9i	1.12163	−	1.04926i
$615$	1.01480e10	+	1.01480e10i	1.75922	+	1.75922i
$616$	−1.73008e8	+	1.72473e9i	−0.0298218	+	0.297296i
$617$	4.38157e9	−	4.38157e9i	0.750986	−	0.750986i	−0.223677	−	0.974663i	$-0.571806\pi$
$617$	4.38157e9	−	4.38157e9i	0.750986	−	0.750986i	0.974663	+	0.223677i	$0.0718061\pi$
$618$	−3.37963e8	+	1.01376e10i	−0.0575983	+	1.72773i
$619$	−3.55836e9	−	1.47392e9i	−0.603022	−	0.249780i	0.0602198	−	0.998185i	$-0.480820\pi$
$619$	−3.55836e9	−	1.47392e9i	−0.603022	−	0.249780i	−0.663242	+	0.748405i	$0.730820\pi$
$620$	−2.40910e9	−	7.12507e9i	−0.405960	−	1.20065i
$621$	−1.80071e9	−	4.34730e9i	−0.301733	−	0.728449i
$622$	−2.15597e9	−	9.78420e8i	−0.359234	−	0.163027i
$623$			2.06844e9i			0.342717i
$624$	3.29114e9	−	2.51285e9i	0.542252	−	0.414019i
$625$			8.16835e9i			1.33830i
$626$	4.83616e8	−	1.06566e9i	0.0787935	−	0.173624i
$627$	3.00647e9	+	7.25826e9i	0.487103	+	1.17597i
$628$	−3.93586e9	+	7.95704e9i	−0.634134	+	1.28201i
$629$	1.06671e10	+	4.41847e9i	1.70911	+	0.707938i
$630$	−7.79042e8	−	2.59714e7i	−0.124128	−	0.00413812i
$631$	5.90175e9	−	5.90175e9i	0.935142	−	0.935142i	−0.0628787	−	0.998021i	$-0.520028\pi$
$631$	5.90175e9	−	5.90175e9i	0.935142	−	0.935142i	0.998021	+	0.0628787i	$0.0200281\pi$
$632$	4.42218e9	−	8.23760e9i	0.696830	−	1.29805i
$633$	2.11949e8	+	2.11949e8i	0.0332138	+	0.0332138i
$634$	5.59180e9	+	5.97749e9i	0.871443	+	0.931551i
$635$	6.19685e6	−	1.49605e7i	0.000960424	−	0.00231867i
$636$	−4.54187e9	+	3.97347e9i	−0.700059	+	0.612449i
$637$	−3.38342e9	+	1.40146e9i	−0.518642	+	0.214828i
$638$	1.58569e9	+	4.22077e9i	0.241739	+	0.643456i
$639$	1.71594e9			0.260165
$640$	6.13294e9	+	9.95562e9i	0.924780	+	1.50120i
$641$	5.47883e8			0.0821646			0.0410823	−	0.999156i	$-0.486919\pi$
$641$	5.47883e8			0.0821646			0.0410823	+	0.999156i	$0.486919\pi$
$642$	−4.30384e9	−	1.14559e10i	−0.641924	−	1.70866i
$643$	−5.00484e8	+	2.07307e8i	−0.0742423	+	0.0307522i	−0.419496	−	0.907757i	$-0.637793\pi$
$643$	−5.00484e8	+	2.07307e8i	−0.0742423	+	0.0307522i	0.345253	+	0.938510i	$0.387793\pi$
$644$	1.03227e9	−	9.03083e8i	0.152297	−	0.133238i
$645$	6.16874e9	−	1.48926e10i	0.905185	−	2.18531i
$646$	−3.68866e9	−	3.94308e9i	−0.538338	−	0.575469i
$647$	5.38497e9	+	5.38497e9i	0.781660	+	0.781660i	0.980111	−	0.198451i	$-0.0635910\pi$
$647$	5.38497e9	+	5.38497e9i	0.781660	+	0.781660i	−0.198451	+	0.980111i	$0.563591\pi$
$648$	4.04320e9	−	7.53163e9i	0.583730	−	1.08737i
$649$	−7.77282e9	+	7.77282e9i	−1.11615	+	1.11615i
$650$	−8.58867e9	−	2.86326e8i	−1.22667	−	0.0408944i
$651$	−1.03189e9	−	4.27422e8i	−0.146588	−	0.0607188i
$652$	−2.81196e8	+	5.68487e8i	−0.0397321	+	0.0803255i
$653$	4.95675e9	+	1.19666e10i	0.696628	+	1.68181i	0.730981	+	0.682398i	$0.239063\pi$
$653$	4.95675e9	+	1.19666e10i	0.696628	+	1.68181i	−0.0343532	+	0.999410i	$0.510937\pi$
$654$	4.26458e9	−	9.39711e9i	0.596148	−	1.31363i
$655$			1.06308e10i			1.47816i
$656$	−5.28177e9	−	6.91767e9i	−0.730493	−	0.956746i
$657$		−	3.47480e9i		−	0.478025i
$658$	2.18012e8	+	9.89377e7i	0.0298325	+	0.0135385i
$659$	−2.18667e9	−	5.27908e9i	−0.297635	−	0.718554i	−0.999977	−	0.00671501i	$-0.997863\pi$
$659$	−2.18667e9	−	5.27908e9i	−0.297635	−	0.718554i	0.702343	−	0.711839i	$-0.252137\pi$
$660$	−7.75849e9	−	2.29462e10i	−1.05044	−	3.10676i
$661$	−7.86217e9	−	3.25662e9i	−1.05886	−	0.438593i	−0.215812	−	0.976435i	$-0.569240\pi$
$661$	−7.86217e9	−	3.25662e9i	−1.05886	−	0.438593i	−0.843046	+	0.537842i	$0.819240\pi$
$662$	1.12429e8	−	3.37243e9i	0.0150617	−	0.451793i
$663$	4.16859e9	−	4.16859e9i	0.555510	−	0.555510i
$664$	1.34726e8	−	1.34309e9i	0.0178592	−	0.178040i
$665$	1.21836e9	+	1.21836e9i	0.160657	+	0.160657i
$666$	−3.34572e9	+	3.12984e9i	−0.438864	+	0.410547i
$667$	1.36526e9	−	3.29603e9i	0.178146	−	0.430082i
$668$	3.09436e9	+	2.06547e8i	0.401655	+	0.0268103i
$669$	−1.20246e10	+	4.98075e9i	−1.55267	+	0.643137i
$670$	6.43812e9	−	2.41872e9i	0.826984	−	0.310688i
$671$	−7.51822e8			−0.0960696
$672$	1.71235e9	+	2.87993e8i	0.217671	+	0.0366092i
$673$	3.00559e9			0.380081			0.190041	−	0.981776i	$-0.439138\pi$
$673$	3.00559e9			0.380081			0.190041	+	0.981776i	$0.439138\pi$
$674$	−7.57415e9	+	2.84552e9i	−0.952849	+	0.357974i
$675$	−1.14221e10	+	4.73118e9i	−1.42949	+	0.592115i
$676$	−3.53729e8	+	5.29935e9i	−0.0440410	+	0.659796i
$677$	4.32112e8	−	1.04321e9i	0.0535224	−	0.129215i	−0.894857	−	0.446354i	$-0.852722\pi$
$677$	4.32112e8	−	1.04321e9i	0.0535224	−	0.129215i	0.948379	+	0.317139i	$0.102722\pi$
$678$	−2.20273e9	+	2.06060e9i	−0.271429	+	0.253916i
$679$	−7.87588e8	−	7.87588e8i	−0.0965506	−	0.0965506i
$680$	1.05379e10	+	1.28877e10i	1.28520	+	1.57179i
$681$	3.25554e8	−	3.25554e8i	0.0395010	−	0.0395010i
$682$	3.14829e8	−	9.44365e9i	0.0380040	−	1.13997i
$683$	1.29139e10	+	5.34912e9i	1.55091	+	0.642407i	0.983480	−	0.181017i	$-0.0579389\pi$
$683$	1.29139e10	+	5.34912e9i	1.55091	+	0.642407i	0.567427	+	0.823424i	$0.307939\pi$
$684$	2.02963e9	−	6.86249e8i	0.242504	−	0.0819946i
$685$	−6.13470e9	−	1.48105e10i	−0.729250	−	1.76056i
$686$	−2.84829e9	−	1.29260e9i	−0.336860	−	0.152873i
$687$		−	2.03205e9i		−	0.239104i
$688$	−4.90823e9	+	8.45436e9i	−0.574600	+	0.989740i
$689$			3.96502e9i			0.461825i
$690$	−7.92043e9	+	1.74529e10i	−0.917861	+	2.02253i
$691$	−1.71394e9	−	4.13781e9i	−0.197616	−	0.477086i	0.793745	−	0.608251i	$-0.208128\pi$
$691$	−1.71394e9	−	4.13781e9i	−0.197616	−	0.477086i	−0.991361	+	0.131164i	$0.958128\pi$
$692$	−2.83893e9	−	1.40424e9i	−0.325674	−	0.161091i
$693$	−9.04699e8	−	3.74738e8i	−0.103261	−	0.0427722i
$694$	−8.32778e9	−	2.77628e8i	−0.945739	−	0.0315287i
$695$	3.72364e8	−	3.72364e8i	0.0420747	−	0.0420747i
$696$	4.32452e9	−	1.30333e9i	0.486189	−	0.146528i
$697$	−8.76198e9	−	8.76198e9i	−0.980138	−	0.980138i
$698$	3.46143e9	+	3.70018e9i	0.385267	+	0.411841i
$699$	2.58051e8	−	6.22990e8i	0.0285782	−	0.0689939i
$700$	−2.37276e9	−	2.71217e9i	−0.261463	−	0.298864i
$701$	6.51763e8	−	2.69969e8i	0.0714622	−	0.0296006i	−0.346666	−	0.937989i	$-0.612686\pi$
$701$	6.51763e8	−	2.69969e8i	0.0714622	−	0.0296006i	0.418128	+	0.908388i	$0.362686\pi$
$702$	−1.37656e9	−	3.66410e9i	−0.150181	−	0.399749i
$703$	1.01273e10			1.09939
$704$	2.81391e9	+	1.44177e10i	0.303953	+	1.55737i
$705$	−3.34555e9			−0.359588
$706$	1.63837e9	+	4.36099e9i	0.175225	+	0.466411i
$707$	−1.99164e8	+	8.24963e7i	−0.0211954	+	0.00877944i
$708$	7.25048e9	+	8.28764e9i	0.767804	+	0.877636i
$709$	−1.70027e9	+	4.10481e9i	−0.179166	+	0.432545i	−0.987792	−	0.155778i	$-0.950212\pi$
$709$	−1.70027e9	+	4.10481e9i	−0.179166	+	0.432545i	0.808626	+	0.588323i	$0.200212\pi$
$710$	7.98932e9	+	8.54038e9i	0.837733	+	0.895515i
$711$	3.73481e9	+	3.73481e9i	0.389695	+	0.389695i
$712$	5.05825e9	+	1.67836e10i	0.525194	+	1.74263i
$713$	−5.28665e9	+	5.28665e9i	−0.546220	+	0.546220i
$714$	2.47076e9	+	8.23694e7i	0.254031	+	0.00846880i
$715$	−1.47036e10	−	6.09045e9i	−1.50437	−	0.623129i
$716$	−4.19200e9	−	2.07353e9i	−0.426801	−	0.211112i
$717$	4.12733e9	+	9.96426e9i	0.418169	+	1.00955i
$718$	−1.57727e9	+	3.47555e9i	−0.159026	+	0.350419i
$719$		−	1.64644e10i		−	1.65194i	−0.563713	−	0.825971i	$-0.690628\pi$
$719$		−	1.64644e10i		−	1.65194i	0.563713	−	0.825971i	$-0.309372\pi$
$720$	−6.38474e9	+	1.69436e9i	−0.637499	+	0.169178i
$721$			2.79471e9i			0.277692i
$722$	4.89639e9	+	2.22207e9i	0.484168	+	0.219724i
$723$	−2.85156e9	−	6.88426e9i	−0.280607	−	0.677444i
$724$	−1.88712e10	+	6.38066e9i	−1.84806	+	0.624857i
$725$	−8.65997e9	−	3.58708e9i	−0.843983	−	0.349589i
$726$	6.11209e8	−	1.83339e10i	0.0592805	−	1.77818i
$727$	−2.55497e9	+	2.55497e9i	−0.246612	+	0.246612i	−0.819579	−	0.572966i	$-0.805793\pi$
$727$	−2.55497e9	+	2.55497e9i	−0.246612	+	0.246612i	0.572966	+	0.819579i	$0.305793\pi$
$728$	8.83220e8	−	7.22182e8i	0.0848417	−	0.0693724i
$729$	−2.94683e9	−	2.94683e9i	−0.281714	−	0.281714i
$730$	1.72944e10	−	1.61785e10i	1.64541	−	1.53924i
$731$	−5.32618e9	+	1.28585e10i	−0.504318	+	1.21753i
$732$	−5.01594e7	+	7.51458e8i	−0.00472676	+	0.0708135i
$733$	8.63521e9	−	3.57682e9i	0.809858	−	0.335454i	0.0609608	−	0.998140i	$-0.480584\pi$
$733$	8.63521e9	−	3.57682e9i	0.809858	−	0.335454i	0.748897	+	0.662686i	$0.230584\pi$
$734$	−6.96811e9	+	2.61784e9i	−0.650397	+	0.244347i
$735$	2.14600e10			1.99354
$736$	6.16749e9	−	9.85206e9i	0.570212	−	0.910866i
$737$	8.64003e9			0.795022
$738$	4.60277e9	−	1.72920e9i	0.421523	−	0.158361i
$739$	−4.04546e9	+	1.67568e9i	−0.368733	+	0.152734i	−0.559353	−	0.828930i	$-0.688950\pi$
$739$	−4.04546e9	+	1.67568e9i	−0.368733	+	0.152734i	0.190620	+	0.981664i	$0.438950\pi$
$740$	−3.11550e10	−	2.07958e9i	−2.82629	−	0.188653i
$741$	1.97881e9	−	4.77728e9i	0.178666	−	0.431337i
$742$	−1.21422e9	+	1.13588e9i	−0.109115	+	0.102075i
$743$	−8.66556e9	−	8.66556e9i	−0.775061	−	0.775061i	0.203925	−	0.978986i	$-0.434630\pi$
$743$	−8.66556e9	−	8.66556e9i	−0.775061	−	0.775061i	−0.978986	+	0.203925i	$0.934630\pi$
$744$	−9.41808e9	−	9.44730e8i	−0.838411	−	0.0841012i
$745$	−4.29009e9	+	4.29009e9i	−0.380119	+	0.380119i
$746$	6.00370e8	−	1.80088e10i	0.0529460	−	1.58817i
$747$	7.04513e8	+	2.91819e8i	0.0618396	+	0.0256148i
$748$	6.69879e9	+	1.98121e10i	0.585249	+	1.73091i
$749$	−1.29033e9	−	3.11512e9i	−0.112205	−	0.270887i
$750$	2.41109e10	+	1.09420e10i	2.08689	+	0.947068i
$751$			8.32703e9i			0.717382i	0.933456	+	0.358691i	$0.116777\pi$
$751$			8.32703e9i			0.717382i	−0.933456	+	0.358691i	$0.883223\pi$
$752$	2.01092e9	+	2.69657e8i	0.172438	+	0.0231233i
$753$		−	8.10299e9i		−	0.691612i
$754$	1.22638e9	−	2.70237e9i	0.104190	−	0.229586i
$755$	3.79367e9	+	9.15873e9i	0.320808	+	0.774499i
$756$	7.27725e8	−	1.47122e9i	0.0612549	−	0.123838i
$757$	7.54011e9	+	3.12322e9i	0.631745	+	0.261678i	0.675494	−	0.737365i	$-0.263930\pi$
$757$	7.54011e9	+	3.12322e9i	0.631745	+	0.261678i	−0.0437491	+	0.999043i	$0.513930\pi$
$758$	1.80631e10	+	6.02182e8i	1.50644	+	0.0502210i
$759$	−1.70256e10	+	1.70256e10i	−1.41337	+	1.41337i
$760$	1.28653e10	+	6.90649e9i	1.06310	+	0.570703i
$761$	−1.27990e10	−	1.27990e10i	−1.05276	−	1.05276i	−0.998528	−	0.0542348i	$-0.982728\pi$
$761$	−1.27990e10	−	1.27990e10i	−1.05276	−	1.05276i	−0.0542348	−	0.998528i	$-0.517272\pi$
$762$	−1.39217e7	−	1.48819e7i	−0.00113985	−	0.00121848i
$763$	1.08808e9	−	2.62685e9i	0.0886796	−	0.214091i
$764$	3.20756e9	−	2.80615e9i	0.260224	−	0.227658i
$765$	−8.68878e9	+	3.59901e9i	−0.701687	+	0.290648i
$766$	−4.45426e9	−	1.18563e10i	−0.358076	−	0.953119i
$767$	7.23505e9			0.578972
$768$	1.45985e10	−	1.85064e9i	1.16290	−	0.147421i
$769$	−9.33062e9			−0.739892			−0.369946	−	0.929053i	$-0.620624\pi$
$769$	−9.33062e9			−0.739892			−0.369946	+	0.929053i	$0.620624\pi$
$770$	−2.34712e9	−	6.24753e9i	−0.185275	−	0.493163i
$771$	5.82842e9	−	2.41421e9i	0.457995	−	0.189708i
$772$	1.52615e10	−	1.33516e10i	1.19381	−	1.04441i
$773$	1.99324e9	−	4.81210e9i	0.155214	−	0.374719i	−0.827075	−	0.562091i	$-0.809997\pi$
$773$	1.99324e9	−	4.81210e9i	0.155214	−	0.374719i	0.982289	+	0.187372i	$0.0599970\pi$
$774$	−3.77282e9	−	4.03305e9i	−0.292464	−	0.312637i
$775$	1.38901e10	+	1.38901e10i	1.07189	+	1.07189i
$776$	−8.31657e9	−	4.46458e9i	−0.638893	−	0.342977i
$777$	−3.27869e9	+	3.27869e9i	−0.250742	+	0.250742i
$778$	−8.27400e9	−	2.75836e8i	−0.629923	−	0.0210001i
$779$	−1.00414e10	−	4.15927e9i	−0.761048	−	0.315237i
$780$	−7.06849e9	+	1.42902e10i	−0.533329	+	1.07822i
$781$	5.62235e9	+	1.35735e10i	0.422317	+	1.01956i
$782$	6.83861e9	−	1.50691e10i	0.511381	−	1.12684i
$783$		−	4.26945e9i		−	0.317838i
$784$	−1.28990e10	−	1.72972e9i	−0.955986	−	0.128194i
$785$		−	3.41791e10i		−	2.52184i
$786$	1.21827e10	+	5.52874e9i	0.894882	+	0.406113i
$787$	−2.95468e9	−	7.13324e9i	−0.216072	−	0.521645i	0.778262	−	0.627939i	$-0.216101\pi$
$787$	−2.95468e9	−	7.13324e9i	−0.216072	−	0.521645i	−0.994335	+	0.106294i	$0.966101\pi$
$788$	2.37139e9	+	7.01355e9i	0.172648	+	0.510618i
$789$	9.63760e9	+	3.99202e9i	0.698553	+	0.289350i
$790$	−1.19941e9	+	3.59775e10i	−0.0865508	+	2.59619i
$791$	−5.87653e8	+	5.87653e8i	−0.0422185	+	0.0422185i
$792$	−8.25722e9	−	8.28284e8i	−0.590603	−	0.0592436i
$793$	3.49903e8	+	3.49903e8i	0.0249168	+	0.0249168i
$794$	9.92402e9	−	9.28368e9i	0.703584	−	0.658186i
$795$	8.89149e9	−	2.14660e10i	0.627610	−	1.51518i
$796$	7.12892e9	+	4.75852e8i	0.500989	+	0.0334407i
$797$	1.43286e8	−	5.93510e7i	0.0100253	−	0.00415263i	−0.377665	−	0.925942i	$-0.623273\pi$
$797$	1.43286e8	−	5.93510e7i	0.0100253	−	0.00415263i	0.387690	+	0.921790i	$0.373273\pi$
$798$	2.02985e9	−	7.62590e8i	0.141401	−	0.0531228i
$799$	2.88859e9			0.200342
$800$	−2.58852e10	−	1.62044e10i	−1.78746	−	1.11897i
$801$	−9.90276e9			−0.680836
$802$	1.55234e10	−	5.83195e9i	1.06262	−	0.399212i
$803$	2.74866e10	−	1.13853e10i	1.87334	−	0.775963i
$804$	5.76438e8	−	8.63585e9i	0.0391162	−	0.586015i
$805$	−2.02084e9	+	4.87874e9i	−0.136536	+	0.329627i
$806$	−4.54166e9	+	4.24862e9i	−0.305522	+	0.285808i
$807$	−1.93045e10	−	1.93045e10i	−1.29301	−	1.29301i
$808$	−1.41430e9	+	1.15643e9i	−0.0943193	+	0.0771220i
$809$	9.85491e9	−	9.85491e9i	0.654384	−	0.654384i	−0.299662	−	0.954046i	$-0.596874\pi$
$809$	9.85491e9	−	9.85491e9i	0.654384	−	0.654384i	0.954046	+	0.299662i	$0.0968737\pi$
$810$	−1.09662e9	+	3.28942e10i	−0.0725031	+	2.17481i
$811$	2.29110e10	+	9.49004e9i	1.50824	+	0.624734i	0.975194	−	0.221352i	$-0.0710471\pi$
$811$	2.29110e10	+	9.49004e9i	1.50824	+	0.624734i	0.533046	+	0.846086i	$0.321047\pi$
$812$	1.17889e9	−	3.98600e8i	0.0772726	−	0.0261271i
$813$	−1.20846e10	−	2.91748e10i	−0.788707	−	1.90411i
$814$	−3.57203e10	−	1.62105e10i	−2.32129	−	1.05344i
$815$		−	2.44191e9i		−	0.158008i
$816$	2.02495e10	−	5.37374e9i	1.30466	−	0.346227i
$817$			1.22078e10i			0.783177i
$818$	−3.70904e9	+	8.17298e9i	−0.236933	+	0.522088i
$819$	2.46647e8	+	5.95459e8i	0.0156885	+	0.0378755i
$820$	3.00366e10	+	1.48573e10i	1.90240	+	0.941003i
$821$	4.46909e9	+	1.85116e9i	0.281850	+	0.116746i	0.519130	−	0.854695i	$-0.326256\pi$
$821$	4.46909e9	+	1.85116e9i	0.281850	+	0.116746i	−0.237280	+	0.971441i	$0.576256\pi$
$822$	−2.01630e10	−	6.72185e8i	−1.26620	−	0.0422122i
$823$	−6.32286e9	+	6.32286e9i	−0.395380	+	0.395380i	−0.876600	−	0.481220i	$-0.840194\pi$
$823$	−6.32286e9	+	6.32286e9i	−0.395380	+	0.395380i	0.481220	+	0.876600i	$0.340194\pi$
$824$	6.83429e9	+	2.26766e10i	0.425548	+	1.41199i
$825$	4.47331e10	+	4.47331e10i	2.77358	+	2.77358i
$826$	2.07266e9	+	2.21562e9i	0.127967	+	0.136794i
$827$	−6.01170e9	+	1.45135e10i	−0.369597	+	0.892285i	0.624220	+	0.781249i	$0.285417\pi$
$827$	−6.01170e9	+	1.45135e10i	−0.369597	+	0.892285i	−0.993816	+	0.111036i	$0.964583\pi$
$828$	4.32355e9	+	4.94202e9i	0.264688	+	0.302551i
$829$	−1.03830e10	+	4.30079e9i	−0.632970	+	0.262185i	−0.676015	−	0.736888i	$-0.736294\pi$
$829$	−1.03830e10	+	4.30079e9i	−0.632970	+	0.262185i	0.0430442	+	0.999073i	$0.486294\pi$
$830$	1.82777e9	+	4.86512e9i	0.110955	+	0.295338i
$831$	−1.12682e10			−0.681165
$832$	5.40049e9	−	8.01972e9i	0.325089	−	0.482756i
$833$	−1.85289e10			−1.11069
$834$	−2.33068e8	−	6.20376e8i	−0.0139124	−	0.0370317i
$835$	−1.10315e10	+	4.56940e9i	−0.655741	+	0.271617i
$836$	1.20786e10	+	1.38064e10i	0.714979	+	0.817255i
$837$	−3.42398e9	+	8.26622e9i	−0.201833	+	0.487268i
$838$	−2.56205e9	−	2.73877e9i	−0.150395	−	0.160769i
$839$	1.62032e9	+	1.62032e9i	0.0947185	+	0.0947185i	0.752878	−	0.658160i	$-0.228665\pi$
$839$	1.62032e9	+	1.62032e9i	0.0947185	+	0.0947185i	−0.658160	+	0.752878i	$0.728665\pi$
$840$	−6.40110e9	+	1.92917e9i	−0.372629	+	0.112303i
$841$	−9.90860e9	+	9.90860e9i	−0.574416	+	0.574416i
$842$	−5.63134e9	−	1.87735e8i	−0.325102	−	0.0108381i
$843$	−3.19152e9	−	1.32197e9i	−0.183485	−	0.0760021i
$844$	6.27336e8	+	3.10305e8i	0.0359171	+	0.0177660i
$845$	−7.82548e9	−	1.88924e10i	−0.446182	−	1.07718i
$846$	−4.73669e8	+	1.04374e9i	−0.0268954	+	0.0592648i
$847$		−	5.05425e9i		−	0.285802i
$848$	−7.07463e9	+	1.21859e10i	−0.398399	+	0.686236i
$849$		−	1.58102e10i		−	0.886666i
$850$	−3.95924e10	−	1.79677e10i	−2.21129	−	1.00352i
$851$	1.18778e10	+	2.86755e10i	0.660665	+	1.59499i
$852$	1.39421e10	−	4.71404e9i	0.772306	−	0.261129i
$853$	1.37983e10	+	5.71545e9i	0.761211	+	0.315304i	0.729306	−	0.684187i	$-0.239843\pi$
$853$	1.37983e10	+	5.71545e9i	0.761211	+	0.315304i	0.0319042	+	0.999491i	$0.489843\pi$
$854$	−6.91392e6	+	2.07391e8i	−0.000379859	+	0.0113943i
$855$	−5.83296e9	+	5.83296e9i	−0.319160	+	0.319160i
$856$	−1.80877e10	−	2.21210e10i	−0.985654	−	1.20544i
$857$	1.30858e10	+	1.30858e10i	0.710181	+	0.710181i	0.966573	−	0.256392i	$-0.0825338\pi$
$857$	1.30858e10	+	1.30858e10i	0.710181	+	0.710181i	−0.256392	+	0.966573i	$0.582534\pi$
$858$	−1.46264e10	+	1.36826e10i	−0.790555	+	0.739545i
$859$	−1.20733e8	+	2.91476e8i	−0.00649906	+	0.0156901i	−0.927096	−	0.374825i	$-0.877703\pi$
$859$	−1.20733e8	+	2.91476e8i	−0.00649906	+	0.0156901i	0.920597	+	0.390515i	$0.127703\pi$
$860$	2.50680e9	−	3.75553e10i	0.134392	−	2.01338i
$861$	4.59744e9	−	1.90432e9i	0.245474	−	0.101678i
$862$	−6.69810e8	+	2.51640e8i	−0.0356186	+	0.0133815i
$863$	−2.49088e10			−1.31922			−0.659608	−	0.751610i	$-0.729278\pi$
$863$	−2.49088e10			−1.31922			−0.659608	+	0.751610i	$0.729278\pi$
$864$	2.30705e9	−	1.37173e10i	0.121691	−	0.723552i
$865$	1.21945e10			0.640631
$866$	−1.08704e10	+	4.08389e9i	−0.568767	+	0.213679i
$867$	6.77481e9	−	2.80622e9i	0.353045	−	0.146236i
$868$	−2.60215e9	−	1.73692e8i	−0.135056	−	0.00901489i
$869$	−1.73061e10	+	4.17806e10i	−0.894602	+	2.15976i
$870$	−1.26995e10	+	1.18800e10i	−0.653834	+	0.611646i
$871$	−4.02113e9	−	4.02113e9i	−0.206198	−	0.206198i
$872$	2.40498e9	−	2.39754e10i	0.122830	−	1.22450i
$873$	3.77062e9	−	3.77062e9i	0.191806	−	0.191806i
$874$	4.83622e8	−	1.45068e10i	0.0245028	−	0.734989i
$875$	6.73992e9	+	2.79177e9i	0.340116	+	0.140881i
$876$	−9.54598e9	−	2.82329e10i	−0.479796	−	1.41903i
$877$	1.20568e9	+	2.91078e9i	0.0603580	+	0.145717i	0.951181	−	0.308633i	$-0.0998715\pi$
$877$	1.20568e9	+	2.91078e9i	0.0603580	+	0.145717i	−0.890823	+	0.454350i	$0.849871\pi$
$878$	1.08954e10	+	4.94455e9i	0.543268	+	0.246545i
$879$		−	1.07667e10i		−	0.534714i
$880$	−3.43227e10	−	4.49534e10i	−1.69782	−	2.22368i
$881$			1.34940e10i			0.664853i	0.943129	+	0.332427i	$0.107867\pi$
$881$			1.34940e10i			0.664853i	−0.943129	+	0.332427i	$0.892133\pi$
$882$	3.03835e9	−	6.69509e9i	0.149107	−	0.328561i
$883$	−1.28493e9	−	3.10210e9i	−0.0628084	−	0.151633i	0.889359	−	0.457209i	$-0.151151\pi$
$883$	−1.28493e9	−	3.10210e9i	−0.0628084	−	0.151633i	−0.952168	+	0.305576i	$0.901151\pi$
$884$	6.10304e9	−	1.23384e10i	0.297141	−	0.600724i
$885$	−3.91694e10	−	1.62245e10i	−1.89953	−	0.786810i
$886$	3.72888e10	+	1.24312e9i	1.80119	+	0.0600475i
$887$	9.72840e9	−	9.72840e9i	0.468068	−	0.468068i	−0.433220	−	0.901288i	$-0.642623\pi$
$887$	9.72840e9	−	9.72840e9i	0.468068	−	0.468068i	0.901288	+	0.433220i	$0.142623\pi$
$888$	−1.85858e10	+	3.46215e10i	−0.890711	+	1.65921i
$889$	−3.97026e6	−	3.97026e6i	−0.000189523	−	0.000189523i
$890$	−4.61067e10	−	4.92869e10i	−2.19230	−	2.34351i
$891$	−1.58229e10	+	3.82000e10i	−0.749403	+	1.80922i
$892$	−2.28727e10	+	2.00103e10i	−1.07905	+	0.944009i
$893$	2.34079e9	−	9.69588e8i	0.109997	−	0.0455624i
$894$	2.68523e9	+	7.14750e9i	0.125690	+	0.334559i
$895$	1.80066e10			0.839556
$896$	4.00302e9	−	6.43632e8i	0.185913	−	0.0298923i
$897$	1.58477e10			0.733150
$898$	1.25206e10	+	3.33272e10i	0.576978	+	1.53579i
$899$	−6.26727e9	+	2.59599e9i	−0.287687	+	0.119164i
$900$	1.29846e10	−	1.13597e10i	0.593720	−	0.519418i
$901$	−7.67705e9	+	1.85340e10i	−0.349669	+	0.844176i
$902$	2.87596e10	+	3.07433e10i	1.30485	+	1.39485i
$903$	−3.95225e9	−	3.95225e9i	−0.178623	−	0.178623i
$904$	−3.33121e9	+	6.20534e9i	−0.149973	+	0.279368i
$905$	5.42343e10	−	5.42343e10i	2.43222	−	2.43222i
$906$	1.24687e10	+	4.15676e8i	0.557022	+	0.0185698i
$907$	1.31097e8	+	5.43022e7i	0.00583401	+	0.00241653i	0.385599	−	0.922667i	$-0.373995\pi$
$907$	1.31097e8	+	5.43022e7i	0.00583401	+	0.00241653i	−0.379765	+	0.925083i	$0.623995\pi$
$908$	4.76629e8	−	9.63589e8i	0.0211290	−	0.0427161i
$909$	−3.94955e8	−	9.53506e8i	−0.0174411	−	0.0421066i
$910$	−1.81528e9	+	4.00001e9i	−0.0798542	+	0.175961i
$911$			2.80998e10i			1.23137i	0.787991	+	0.615686i	$0.211121\pi$
$911$			2.80998e10i			1.23137i	−0.787991	+	0.615686i	$0.788879\pi$
$912$	1.46055e10	−	1.11516e10i	0.637581	−	0.486805i
$913$			6.52904e9i			0.283924i
$914$	2.23819e10	+	1.01573e10i	0.969582	+	0.440014i
$915$	−1.10967e9	−	2.67897e9i	−0.0478871	−	0.115610i
$916$	−1.51976e9	−	4.49479e9i	−0.0653342	−	0.193230i
$917$	3.40554e9	+	1.41062e9i	0.145845	+	0.0604112i
$918$	6.59843e8	−	1.97927e10i	0.0281508	−	0.844416i
$919$	2.26999e10	−	2.26999e10i	0.964762	−	0.964762i	−0.0346384	−	0.999400i	$-0.511028\pi$
$919$	2.26999e10	−	2.26999e10i	0.964762	−	0.964762i	0.999400	+	0.0346384i	$0.0110279\pi$
$920$	−4.46667e9	+	4.45285e10i	−0.189115	+	1.88530i
$921$	3.01830e10	+	3.01830e10i	1.27307	+	1.27307i
$922$	−3.07857e10	+	2.87993e10i	−1.29357	+	1.21011i
$923$	3.70054e9	−	8.93390e9i	0.154903	−	0.373969i
$924$	−8.38020e9	−	5.59374e8i	−0.349464	−	0.0233265i
$925$	7.53417e10	−	3.12076e10i	3.12996	−	1.29647i
$926$	3.04564e10	−	1.14421e10i	1.26049	−	0.473553i
$927$	−1.33798e10			−0.551659
$928$	8.59086e9	−	6.11717e9i	0.352873	−	0.251266i
$929$	4.17904e9			0.171010			0.0855050	−	0.996338i	$-0.472750\pi$
$929$	4.17904e9			0.171010			0.0855050	+	0.996338i	$0.472750\pi$
$930$	3.41153e10	−	1.28167e10i	1.39078	−	0.522500i
$931$	−1.50150e10	+	6.21943e9i	−0.609821	+	0.252596i
$932$	1.04864e8	−	1.57102e9i	0.00424299	−	0.0635660i
$933$	4.39008e9	−	1.05986e10i	0.176965	−	0.427231i
$934$	−1.91864e10	+	1.79484e10i	−0.770513	+	0.720797i
$935$	−5.69383e10	−	5.69383e10i	−2.27805	−	2.27805i
$936$	3.45748e9	+	4.22846e9i	0.137814	+	0.168545i
$937$	−1.58079e10	+	1.58079e10i	−0.627747	+	0.627747i	−0.947501	−	0.319753i	$-0.896400\pi$
$937$	−1.58079e10	+	1.58079e10i	−0.627747	+	0.627747i	0.319753	+	0.947501i	$0.396400\pi$
$938$	7.94556e7	−	2.38336e9i	0.00314351	−	0.0942932i
$939$	5.23870e9	+	2.16994e9i	0.206488	+	0.0855300i
$940$	−7.40017e9	+	2.50211e9i	−0.290599	+	0.0982562i
$941$	6.08029e9	+	1.46791e10i	0.237881	+	0.574297i	0.997063	−	0.0765820i	$-0.0244007\pi$
$941$	6.08029e9	+	1.46791e10i	0.237881	+	0.574297i	−0.759182	+	0.650879i	$0.774401\pi$
$942$	−3.91686e10	−	1.77754e10i	−1.52672	−	0.692854i
$943$		−	3.33104e10i		−	1.29357i
$944$	2.22360e10	+	1.29092e10i	0.860308	+	0.499458i
$945$			6.31959e9i			0.243600i
$946$	1.95407e10	−	4.30585e10i	0.750449	−	1.65363i
$947$	−6.86741e9	−	1.65794e10i	−0.262765	−	0.634371i	0.736342	−	0.676609i	$-0.236551\pi$
$947$	−6.86741e9	−	1.65794e10i	−0.262765	−	0.634371i	−0.999108	+	0.0422378i	$0.986551\pi$
$948$	4.06058e10	+	2.00852e10i	1.54796	+	0.765680i
$949$	−1.80913e10	−	7.49364e9i	−0.687127	−	0.284617i
$950$	−3.81150e10	−	1.27066e9i	−1.44233	−	0.0480837i
$951$	−2.80442e10	+	2.80442e10i	−1.05733	+	1.05733i
$952$	5.52680e9	−	1.66567e9i	0.207608	−	0.0625692i
$953$	−2.13233e10	−	2.13233e10i	−0.798049	−	0.798049i	0.184739	−	0.982788i	$-0.440856\pi$
$953$	−2.13233e10	−	2.13233e10i	−0.798049	−	0.798049i	−0.982788	+	0.184739i	$0.940856\pi$
$954$	−5.43807e9	−	5.81316e9i	−0.202780	−	0.216767i
$955$	−6.27936e9	+	1.51597e10i	−0.233294	+	0.563221i
$956$	1.65816e10	+	1.89536e10i	0.613797	+	0.701599i
$957$	−2.01837e10	+	8.36037e9i	−0.744405	+	0.308343i
$958$	1.41039e10	+	3.75415e10i	0.518274	+	1.37953i
$959$	−5.55848e9			−0.203513
$960$	−4.72215e10	+	3.13070e10i	−1.72263	+	1.14207i
$961$	−1.32964e10			−0.483285
$962$	9.08000e9	+	2.41690e10i	0.328831	+	0.875277i
$963$	1.49138e10	−	6.17749e9i	0.538141	−	0.222905i
$964$	−1.14562e10	−	1.30950e10i	−0.411880	−	0.470798i
$965$	−2.98770e10	+	7.21294e10i	−1.07026	+	2.58385i
$966$	4.53997e9	+	4.85312e9i	0.162044	+	0.173221i
$967$	4.53291e9	+	4.53291e9i	0.161207	+	0.161207i	0.783101	−	0.621894i	$-0.213637\pi$
$967$	4.53291e9	+	4.53291e9i	0.161207	+	0.161207i	−0.621894	+	0.783101i	$0.713637\pi$
$968$	−1.23599e10	−	4.10108e10i	−0.437976	−	1.45323i
$969$	1.84995e10	−	1.84995e10i	0.653170	−	0.653170i
$970$	3.63225e10	+	1.21090e9i	1.27783	+	0.0425999i
$971$	2.91340e10	+	1.20677e10i	1.02125	+	0.423016i	0.829547	−	0.558436i	$-0.188598\pi$
$971$	2.91340e10	+	1.20677e10i	1.02125	+	0.423016i	0.191705	+	0.981453i	$0.438598\pi$
$972$	1.82966e10	+	9.05022e9i	0.639056	+	0.316102i
$973$	−6.98756e7	−	1.68695e8i	−0.00243181	−	0.00587092i
$974$	−1.07076e10	+	2.35944e10i	−0.371309	+	0.818188i
$975$		−	4.16382e10i		−	1.43872i
$976$	4.51061e8	+	1.69970e9i	0.0155296	+	0.0585191i
$977$			8.00836e9i			0.274734i	0.990520	+	0.137367i	$0.0438640\pi$
$977$			8.00836e9i			0.274734i	−0.990520	+	0.137367i	$0.956136\pi$
$978$	−2.79838e9	−	1.26996e9i	−0.0956579	−	0.0434113i
$979$	−3.24468e10	−	7.83335e10i	−1.10518	−	2.66814i
$980$	4.74685e10	−	1.60498e10i	1.61107	−	0.544727i
$981$	1.25762e10	+	5.20922e9i	0.425311	+	0.176170i
$982$	−5.36591e8	+	1.60956e10i	−0.0180823	+	0.542398i
$983$	−3.37557e9	+	3.37557e9i	−0.113347	+	0.113347i	−0.761506	−	0.648158i	$-0.775539\pi$
$983$	−3.37557e9	+	3.37557e9i	−0.113347	+	0.113347i	0.648158	+	0.761506i	$0.275539\pi$
$984$	3.26472e10	−	2.66946e10i	1.09235	−	0.893183i
$985$	−2.01563e10	−	2.01563e10i	−0.672023	−	0.672023i
$986$	1.09649e10	−	1.02574e10i	0.364280	−	0.340775i
$987$	−4.43925e8	+	1.07173e9i	−0.0146960	+	0.0354793i
$988$	8.04132e8	−	1.20470e10i	0.0265264	−	0.397403i
$989$	−3.45664e10	+	1.43179e10i	−1.13623	+	0.470642i
$990$	2.99103e10	−	1.12370e10i	0.979711	−	0.368066i
$991$	2.37692e10			0.775812			0.387906	−	0.921699i	$-0.373199\pi$
$991$	2.37692e10			0.775812			0.387906	+	0.921699i	$0.373199\pi$
$992$	−2.15388e10	+	4.95403e9i	−0.700538	+	0.161127i
$993$	1.63497e10			0.529891
$994$	3.79598e9	−	1.42611e9i	0.122595	−	0.0460574i
$995$	−2.54148e10	+	1.05272e10i	−0.817912	+	0.338790i
$996$	6.52589e9	+	4.35599e8i	0.209282	+	0.0139695i
$997$	1.83612e10	−	4.43278e10i	0.586769	−	1.41659i	−0.299806	−	0.954000i	$-0.596922\pi$
$997$	1.83612e10	−	4.43278e10i	0.586769	−	1.41659i	0.886575	−	0.462585i	$-0.153078\pi$
$998$	−3.16915e10	+	2.96466e10i	−1.00922	+	0.944100i
$999$	2.62649e10	+	2.62649e10i	0.833483	+	0.833483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.21.17	✓	108
32.29	even	8	inner	32.8.g.a.29.17	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.21.17	✓	108	1.1	even	1	trivial
32.8.g.a.29.17	yes	108	32.29	even	8	inner

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)

\(f(q)\)	\(=\)	\(q+(3.97890 + 10.5910i) q^{2} +(-50.6460 + 20.9783i) q^{3} +(-96.3368 + 84.2807i) q^{4} +(188.596 - 455.311i) q^{5} +(-423.695 - 452.919i) q^{6} +(-120.832 - 120.832i) q^{7} +(-1275.93 - 684.955i) q^{8} +(578.487 - 578.487i) q^{9} +O(q^{10})\)	\(q+(3.97890 + 10.5910i) q^{2} +(-50.6460 + 20.9783i) q^{3} +(-96.3368 + 84.2807i) q^{4} +(188.596 - 455.311i) q^{5} +(-423.695 - 452.919i) q^{6} +(-120.832 - 120.832i) q^{7} +(-1275.93 - 684.955i) q^{8} +(578.487 - 578.487i) q^{9} +(5572.58 + 185.777i) q^{10} +(6471.42 + 2680.55i) q^{11} +(3111.01 - 6289.45i) q^{12} +(-1764.30 - 4259.39i) q^{13} +(798.946 - 1760.50i) q^{14} +27016.1i q^{15} +(2177.54 - 16238.7i) q^{16} -23326.1i q^{17} +(8428.47 + 3824.99i) q^{18} +(-7829.65 - 18902.5i) q^{19} +(20205.2 + 59758.2i) q^{20} +(8654.47 + 3584.80i) q^{21} +(-2640.48 + 79204.2i) q^{22} +(44339.3 - 44339.3i) q^{23} +(78989.7 + 7923.48i) q^{24} +(-116497. - 116497. i) q^{25} +(38091.1 - 35633.3i) q^{26} +(28717.1 - 69329.1i) q^{27} +(21824.3 + 1456.76i) q^{28} +(52563.8 - 21772.6i) q^{29} +(-286126. + 107494. i) q^{30} -119232. q^{31} +(180647. - 41549.6i) q^{32} -383985. q^{33} +(247046. - 92812.1i) q^{34} +(-77804.3 + 32227.6i) q^{35} +(-6974.30 + 104485. i) q^{36} +(-189422. + 457305. i) q^{37} +(169042. - 158134. i) q^{38} +(178709. + 178709. i) q^{39} +(-552502. + 451764. i) q^{40} +(375630. - 375630. i) q^{41} +(-3531.21 + 105923. i) q^{42} +(-551251. - 228336. i) q^{43} +(-849355. + 287180. i) q^{44} +(-154291. - 372492. i) q^{45} +(646018. + 293174. i) q^{46} +123835. i q^{47} +(230375. + 868104. i) q^{48} -794342. i q^{49} +(770285. - 1.69734e6i) q^{50} +(489341. + 1.18137e6i) q^{51} +(528951. + 261640. i) q^{52} +(-794562. - 329118. i) q^{53} +(848524. + 28287.8i) q^{54} +(2.44097e6 - 2.44097e6i) q^{55} +(71408.1 + 236936. i) q^{56} +(793081. + 793081. i) q^{57} +(439739. + 470070. i) q^{58} +(-600550. + 1.44986e6i) q^{59} +(-2.27693e6 - 2.60264e6i) q^{60} +(-99162.1 + 41074.3i) q^{61} +(-474410. - 1.26278e6i) q^{62} -139799. q^{63} +(1.15883e6 + 1.74790e6i) q^{64} -2.27209e6 q^{65} +(-1.52784e6 - 4.06677e6i) q^{66} +(1.13958e6 - 472031. i) q^{67} +(1.96594e6 + 2.24716e6i) q^{68} +(-1.31545e6 + 3.17577e6i) q^{69} +(-650897. - 695792. i) q^{70} +(1.48313e6 + 1.48313e6i) q^{71} +(-1.13434e6 + 341870. i) q^{72} +(3.00335e6 - 3.00335e6i) q^{73} +(-5.59699e6 - 186590. i) q^{74} +(8.34401e6 + 3.45620e6i) q^{75} +(2.34740e6 + 1.16111e6i) q^{76} +(-458057. - 1.10585e6i) q^{77} +(-1.18164e6 + 2.60377e6i) q^{78} +6.45617e6i q^{79} +(-6.98296e6 - 4.05400e6i) q^{80} +5.90287e6i q^{81} +(5.47287e6 + 2.48369e6i) q^{82} +(356701. + 861153. i) q^{83} +(-1.13587e6 + 384057. i) q^{84} +(-1.06206e7 - 4.39921e6i) q^{85} +(224922. - 6.74680e6i) q^{86} +(-2.20539e6 + 2.20539e6i) q^{87} +(-6.42101e6 - 7.85282e6i) q^{88} +(-8.55919e6 - 8.55919e6i) q^{89} +(3.33114e6 - 3.11620e6i) q^{90} +(-301486. + 727852. i) q^{91} +(-534560. + 8.00846e6i) q^{92} +(6.03861e6 - 2.50127e6i) q^{93} +(-1.31153e6 + 492728. i) q^{94} -1.00831e7 q^{95} +(-8.27741e6 + 5.89398e6i) q^{96} +6.51806e6 q^{97} +(8.41285e6 - 3.16061e6i) q^{98} +(5.29430e6 - 2.19297e6i) 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

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