LMFDB - Embedded newform 37.9.d.a.6.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, 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:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.10
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.40563 + 6.40563i) q^{2} +7.09124i q^{3} +173.936i q^{4} +(773.631 + 773.631i) q^{5} +(-45.4238 - 45.4238i) q^{6} +1906.19 q^{7} +(-2754.01 - 2754.01i) q^{8} +6510.71 q^{9} +O(q^{10})$	\(q+(-6.40563 + 6.40563i) q^{2} +7.09124i q^{3} +173.936i q^{4} +(773.631 + 773.631i) q^{5} +(-45.4238 - 45.4238i) q^{6} +1906.19 q^{7} +(-2754.01 - 2754.01i) q^{8} +6510.71 q^{9} -9911.18 q^{10} -9267.22i q^{11} -1233.42 q^{12} +(19159.8 + 19159.8i) q^{13} +(-12210.3 + 12210.3i) q^{14} +(-5486.00 + 5486.00i) q^{15} -9245.30 q^{16} +(98862.2 + 98862.2i) q^{17} +(-41705.2 + 41705.2i) q^{18} +(-58069.6 - 58069.6i) q^{19} +(-134562. + 134562. i) q^{20} +13517.2i q^{21} +(59362.4 + 59362.4i) q^{22} +(-275166. - 275166. i) q^{23} +(19529.3 - 19529.3i) q^{24} +806384. i q^{25} -245461. q^{26} +92694.6i q^{27} +331554. i q^{28} +(-659283. + 659283. i) q^{29} -70282.5i q^{30} +(71709.1 - 71709.1i) q^{31} +(764248. - 764248. i) q^{32} +65716.1 q^{33} -1.26655e6 q^{34} +(1.47468e6 + 1.47468e6i) q^{35} +1.13245e6i q^{36} +(518429. - 1.80103e6i) q^{37} +743944. q^{38} +(-135866. + 135866. i) q^{39} -4.26117e6i q^{40} -1.43295e6i q^{41} +(-86586.2 - 86586.2i) q^{42} +(-3.21260e6 - 3.21260e6i) q^{43} +1.61190e6 q^{44} +(5.03689e6 + 5.03689e6i) q^{45} +3.52522e6 q^{46} -240217. q^{47} -65560.6i q^{48} -2.13126e6 q^{49} +(-5.16540e6 - 5.16540e6i) q^{50} +(-701055. + 701055. i) q^{51} +(-3.33257e6 + 3.33257e6i) q^{52} +5.79072e6 q^{53} +(-593767. - 593767. i) q^{54} +(7.16941e6 - 7.16941e6i) q^{55} +(-5.24965e6 - 5.24965e6i) q^{56} +(411785. - 411785. i) q^{57} -8.44624e6i q^{58} +(-7.35808e6 - 7.35808e6i) q^{59} +(-954212. - 954212. i) q^{60} +(3.89899e6 - 3.89899e6i) q^{61} +918684. i q^{62} +1.24106e7 q^{63} +7.42418e6i q^{64} +2.96452e7i q^{65} +(-420952. + 420952. i) q^{66} +2.46646e7i q^{67} +(-1.71957e7 + 1.71957e7i) q^{68} +(1.95126e6 - 1.95126e6i) q^{69} -1.88925e7 q^{70} +3.02794e7 q^{71} +(-1.79306e7 - 1.79306e7i) q^{72} -4.79088e6i q^{73} +(8.21587e6 + 1.48576e7i) q^{74} -5.71826e6 q^{75} +(1.01004e7 - 1.01004e7i) q^{76} -1.76650e7i q^{77} -1.74062e6i q^{78} +(-1.51125e7 - 1.51125e7i) q^{79} +(-7.15245e6 - 7.15245e6i) q^{80} +4.20595e7 q^{81} +(9.17897e6 + 9.17897e6i) q^{82} -7.94336e7 q^{83} -2.35113e6 q^{84} +1.52966e8i q^{85} +4.11574e7 q^{86} +(-4.67513e6 - 4.67513e6i) q^{87} +(-2.55220e7 + 2.55220e7i) q^{88} +(-2.32392e6 + 2.32392e6i) q^{89} -6.45289e7 q^{90} +(3.65221e7 + 3.65221e7i) q^{91} +(4.78612e7 - 4.78612e7i) q^{92} +(508506. + 508506. i) q^{93} +(1.53874e6 - 1.53874e6i) q^{94} -8.98489e7i q^{95} +(5.41946e6 + 5.41946e6i) q^{96} +(3.39885e7 + 3.39885e7i) q^{97} +(1.36520e7 - 1.36520e7i) q^{98} -6.03362e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−6.40563	+	6.40563i	−0.400352	+	0.400352i	−0.878357	−	0.478005i	$-0.841360\pi$
$2$	−6.40563	+	6.40563i	−0.400352	+	0.400352i	0.478005	+	0.878357i	$0.341360\pi$
$3$			7.09124i			0.0875461i	0.999042	+	0.0437731i	$0.0139379\pi$
$3$			7.09124i			0.0875461i	−0.999042	+	0.0437731i	$0.986062\pi$
$4$			173.936i			0.679437i
$5$	773.631	+	773.631i	1.23781	+	1.23781i	0.960894	+	0.276915i	$0.0893120\pi$
$5$	773.631	+	773.631i	1.23781	+	1.23781i	0.276915	+	0.960894i	$0.410688\pi$
$6$	−45.4238	−	45.4238i	−0.0350492	−	0.0350492i
$7$	1906.19			0.793913			0.396957	−	0.917837i	$-0.370066\pi$
$7$	1906.19			0.793913			0.396957	+	0.917837i	$0.370066\pi$
$8$	−2754.01	−	2754.01i	−0.672365	−	0.672365i
$9$	6510.71			0.992336
$10$	−9911.18			−0.991118
$11$		−	9267.22i		−	0.632964i	−0.948599	−	0.316482i	$-0.897498\pi$
$11$		−	9267.22i		−	0.632964i	0.948599	−	0.316482i	$-0.102502\pi$
$12$	−1233.42			−0.0594821
$13$	19159.8	+	19159.8i	0.670837	+	0.670837i	0.957909	−	0.287072i	$-0.0926820\pi$
$13$	19159.8	+	19159.8i	0.670837	+	0.670837i	−0.287072	+	0.957909i	$0.592682\pi$
$14$	−12210.3	+	12210.3i	−0.317844	+	0.317844i
$15$	−5486.00	+	5486.00i	−0.108365	+	0.108365i
$16$	−9245.30			−0.141072
$17$	98862.2	+	98862.2i	1.18368	+	1.18368i	0.978784	+	0.204897i	$0.0656860\pi$
$17$	98862.2	+	98862.2i	1.18368	+	1.18368i	0.204897	+	0.978784i	$0.434314\pi$
$18$	−41705.2	+	41705.2i	−0.397283	+	0.397283i
$19$	−58069.6	−	58069.6i	−0.445589	−	0.445589i	0.448296	−	0.893885i	$-0.352031\pi$
$19$	−58069.6	−	58069.6i	−0.445589	−	0.445589i	−0.893885	+	0.448296i	$0.852031\pi$
$20$	−134562.	+	134562.i	−0.841014	+	0.841014i
$21$			13517.2i			0.0695040i
$22$	59362.4	+	59362.4i	0.253408	+	0.253408i
$23$	−275166.	−	275166.i	−0.983293	−	0.983293i	0.0165698	−	0.999863i	$-0.494725\pi$
$23$	−275166.	−	275166.i	−0.983293	−	0.983293i	−0.999863	+	0.0165698i	$0.994725\pi$
$24$	19529.3	−	19529.3i	0.0588630	−	0.0588630i
$25$			806384.i			2.06434i
$26$	−245461.			−0.537141
$27$			92694.6i			0.174421i
$28$			331554.i			0.539414i
$29$	−659283.	+	659283.i	−0.932137	+	0.932137i	−0.997839	−	0.0657023i	$-0.979071\pi$
$29$	−659283.	+	659283.i	−0.932137	+	0.932137i	0.0657023	+	0.997839i	$0.479071\pi$
$30$		−	70282.5i		−	0.0867685i
$31$	71709.1	−	71709.1i	0.0776476	−	0.0776476i	−0.667216	−	0.744864i	$-0.732514\pi$
$31$	71709.1	−	71709.1i	0.0776476	−	0.0776476i	0.744864	+	0.667216i	$0.232514\pi$
$32$	764248.	−	764248.i	0.728844	−	0.728844i
$33$	65716.1			0.0554135
$34$	−1.26655e6			−0.947777
$35$	1.47468e6	+	1.47468e6i	0.982713	+	0.982713i
$36$			1.13245e6i			0.674230i
$37$	518429.	−	1.80103e6i	0.276619	−	0.960980i
$37$	518429.	−	1.80103e6i	0.276619	−	0.960980i
$38$	743944.			0.356784
$39$	−135866.	+	135866.i	−0.0587291	+	0.0587291i
$40$		−	4.26117e6i		−	1.66452i
$41$		−	1.43295e6i		−	0.507104i	−0.967322	−	0.253552i	$-0.918401\pi$
$41$		−	1.43295e6i		−	0.507104i	0.967322	−	0.253552i	$-0.0815989\pi$
$42$	−86586.2	−	86586.2i	−0.0278260	−	0.0278260i
$43$	−3.21260e6	−	3.21260e6i	−0.939686	−	0.939686i	0.0585956	−	0.998282i	$-0.481338\pi$
$43$	−3.21260e6	−	3.21260e6i	−0.939686	−	0.939686i	−0.998282	+	0.0585956i	$0.981338\pi$
$44$	1.61190e6			0.430059
$45$	5.03689e6	+	5.03689e6i	1.22832	+	1.22832i
$46$	3.52522e6			0.787326
$47$	−240217.			−0.0492281			−0.0246141	−	0.999697i	$-0.507836\pi$
$47$	−240217.			−0.0492281			−0.0246141	+	0.999697i	$0.507836\pi$
$48$		−	65560.6i		−	0.0123503i
$49$	−2.13126e6			−0.369702
$50$	−5.16540e6	−	5.16540e6i	−0.826463	−	0.826463i
$51$	−701055.	+	701055.i	−0.103627	+	0.103627i
$52$	−3.33257e6	+	3.33257e6i	−0.455791	+	0.455791i
$53$	5.79072e6			0.733886			0.366943	−	0.930243i	$-0.380404\pi$
$53$	5.79072e6			0.733886			0.366943	+	0.930243i	$0.380404\pi$
$54$	−593767.	−	593767.i	−0.0698298	−	0.0698298i
$55$	7.16941e6	−	7.16941e6i	0.783489	−	0.783489i
$56$	−5.24965e6	−	5.24965e6i	−0.533800	−	0.533800i
$57$	411785.	−	411785.i	0.0390096	−	0.0390096i
$58$		−	8.44624e6i		−	0.746365i
$59$	−7.35808e6	−	7.35808e6i	−0.607234	−	0.607234i	0.334988	−	0.942222i	$-0.391268\pi$
$59$	−7.35808e6	−	7.35808e6i	−0.607234	−	0.607234i	−0.942222	+	0.334988i	$0.891268\pi$
$60$	−954212.	−	954212.i	−0.0736275	−	0.0736275i
$61$	3.89899e6	−	3.89899e6i	0.281600	−	0.281600i	−0.552147	−	0.833747i	$-0.686191\pi$
$61$	3.89899e6	−	3.89899e6i	0.281600	−	0.281600i	0.833747	+	0.552147i	$0.186191\pi$
$62$			918684.i			0.0621726i
$63$	1.24106e7			0.787828
$64$			7.42418e6i			0.442515i
$65$			2.96452e7i			1.66074i
$66$	−420952.	+	420952.i	−0.0221849	+	0.0221849i
$67$			2.46646e7i			1.22398i	0.790865	+	0.611990i	$0.209631\pi$
$67$			2.46646e7i			1.22398i	−0.790865	+	0.611990i	$0.790369\pi$
$68$	−1.71957e7	+	1.71957e7i	−0.804237	+	0.804237i
$69$	1.95126e6	−	1.95126e6i	0.0860835	−	0.0860835i
$70$	−1.88925e7			−0.786862
$71$	3.02794e7			1.19155			0.595777	−	0.803150i	$-0.296844\pi$
$71$	3.02794e7			1.19155			0.595777	+	0.803150i	$0.296844\pi$
$72$	−1.79306e7	−	1.79306e7i	−0.667212	−	0.667212i
$73$		−	4.79088e6i		−	0.168703i	−0.996436	−	0.0843517i	$-0.973118\pi$
$73$		−	4.79088e6i		−	0.168703i	0.996436	−	0.0843517i	$-0.0268819\pi$
$74$	8.21587e6	+	1.48576e7i	0.273985	+	0.495475i
$75$	−5.71826e6			−0.180725
$76$	1.01004e7	−	1.01004e7i	0.302750	−	0.302750i
$77$		−	1.76650e7i		−	0.502518i
$78$		−	1.74062e6i		−	0.0470246i
$79$	−1.51125e7	−	1.51125e7i	−0.387997	−	0.387997i	0.485975	−	0.873973i	$-0.338465\pi$
$79$	−1.51125e7	−	1.51125e7i	−0.387997	−	0.387997i	−0.873973	+	0.485975i	$0.838465\pi$
$80$	−7.15245e6	−	7.15245e6i	−0.174620	−	0.174620i
$81$	4.20595e7			0.977066
$82$	9.17897e6	+	9.17897e6i	0.203020	+	0.203020i
$83$	−7.94336e7			−1.67376			−0.836878	−	0.547390i	$-0.815622\pi$
$83$	−7.94336e7			−1.67376			−0.836878	+	0.547390i	$0.815622\pi$
$84$	−2.35113e6			−0.0472236
$85$			1.52966e8i			2.93034i
$86$	4.11574e7			0.752410
$87$	−4.67513e6	−	4.67513e6i	−0.0816050	−	0.0816050i
$88$	−2.55220e7	+	2.55220e7i	−0.425583	+	0.425583i
$89$	−2.32392e6	+	2.32392e6i	−0.0370391	+	0.0370391i	−0.725384	−	0.688345i	$-0.758338\pi$
$89$	−2.32392e6	+	2.32392e6i	−0.0370391	+	0.0370391i	0.688345	+	0.725384i	$0.258338\pi$
$90$	−6.45289e7			−0.983522
$91$	3.65221e7	+	3.65221e7i	0.532586	+	0.532586i
$92$	4.78612e7	−	4.78612e7i	0.668086	−	0.668086i
$93$	508506.	+	508506.i	0.00679774	+	0.00679774i
$94$	1.53874e6	−	1.53874e6i	0.0197085	−	0.0197085i
$95$		−	8.98489e7i		−	1.10311i
$96$	5.41946e6	+	5.41946e6i	0.0638074	+	0.0638074i
$97$	3.39885e7	+	3.39885e7i	0.383924	+	0.383924i	0.872514	−	0.488590i	$-0.162488\pi$
$97$	3.39885e7	+	3.39885e7i	0.383924	+	0.383924i	−0.488590	+	0.872514i	$0.662488\pi$
$98$	1.36520e7	−	1.36520e7i	0.148011	−	0.148011i
$99$		−	6.03362e7i		−	0.628113i
$100$	−1.40259e8			−1.40259
$101$		−	1.35306e8i		−	1.30026i	−0.759821	−	0.650132i	$-0.774714\pi$
$101$		−	1.35306e8i		−	1.30026i	0.759821	−	0.650132i	$-0.225286\pi$
$102$		−	8.98139e6i		−	0.0829742i
$103$	−5.29713e7	+	5.29713e7i	−0.470643	+	0.470643i	−0.902123	−	0.431480i	$-0.857992\pi$
$103$	−5.29713e7	+	5.29713e7i	−0.470643	+	0.470643i	0.431480	+	0.902123i	$0.357992\pi$
$104$		−	1.05532e8i		−	0.902095i
$105$	−1.04573e7	+	1.04573e7i	−0.0860327	+	0.0860327i
$106$	−3.70932e7	+	3.70932e7i	−0.293813	+	0.293813i
$107$	2.45405e8			1.87219			0.936093	−	0.351753i	$-0.114414\pi$
$107$	2.45405e8			1.87219			0.936093	+	0.351753i	$0.114414\pi$
$108$	−1.61229e7			−0.118508
$109$	−1.30021e7	−	1.30021e7i	−0.0921103	−	0.0921103i	0.659550	−	0.751661i	$-0.270747\pi$
$109$	−1.30021e7	−	1.30021e7i	−0.0921103	−	0.0921103i	−0.751661	+	0.659550i	$0.770747\pi$
$110$			9.18491e7i			0.627342i
$111$	1.27715e7	+	3.67630e6i	0.0841300	+	0.0242169i
$112$	−1.76233e7			−0.111999
$113$	1.76371e8	−	1.76371e8i	1.08172	−	1.08172i	0.0853700	−	0.996349i	$-0.472793\pi$
$113$	1.76371e8	−	1.76371e8i	1.08172	−	1.08172i	0.996349	−	0.0853700i	$-0.0272072\pi$
$114$			5.27548e6i			0.0312351i
$115$		−	4.25753e8i		−	2.43426i
$116$	−1.14673e8	−	1.14673e8i	−0.633329	−	0.633329i
$117$	1.24744e8	+	1.24744e8i	0.665695	+	0.665695i
$118$	9.42662e7			0.486214
$119$	1.88450e8	+	1.88450e8i	0.939740	+	0.939740i
$120$	3.02170e7			0.145722
$121$	1.28477e8			0.599357
$122$			4.99510e7i			0.225478i
$123$	1.01614e7			0.0443950
$124$	1.24728e7	+	1.24728e7i	0.0527566	+	0.0527566i
$125$	−3.21644e8	+	3.21644e8i	−1.31746	+	1.31746i
$126$	−7.94978e7	+	7.94978e7i	−0.315408	+	0.315408i
$127$	−8.84498e7			−0.340002			−0.170001	−	0.985444i	$-0.554377\pi$
$127$	−8.84498e7			−0.340002			−0.170001	+	0.985444i	$0.554377\pi$
$128$	1.48091e8	+	1.48091e8i	0.551682	+	0.551682i
$129$	2.27813e7	−	2.27813e7i	0.0822659	−	0.0822659i
$130$	−1.89896e8	−	1.89896e8i	−0.664878	−	0.664878i
$131$	−258711.	+	258711.i	−0.000878477	+	0.000878477i	−0.707546	−	0.706667i	$-0.750198\pi$
$131$	−258711.	+	258711.i	−0.000878477	+	0.000878477i	0.706667	+	0.707546i	$0.250198\pi$
$132$			1.14304e7i			0.0376500i
$133$	−1.10691e8	−	1.10691e8i	−0.353759	−	0.353759i
$134$	−1.57992e8	−	1.57992e8i	−0.490023	−	0.490023i
$135$	−7.17114e7	+	7.17114e7i	−0.215900	+	0.215900i
$136$		−	5.44535e8i		−	1.59173i
$137$	1.46205e8			0.415031			0.207516	−	0.978232i	$-0.433462\pi$
$137$	1.46205e8			0.415031			0.207516	+	0.978232i	$0.433462\pi$
$138$			2.49981e7i			0.0689273i
$139$			6.36066e8i			1.70390i	0.523627	+	0.851948i	$0.324579\pi$
$139$			6.36066e8i			1.70390i	−0.523627	+	0.851948i	$0.675421\pi$
$140$	−2.56501e8	+	2.56501e8i	−0.667692	+	0.667692i
$141$		−	1.70344e6i		−	0.00430973i
$142$	−1.93959e8	+	1.93959e8i	−0.477041	+	0.477041i
$143$	1.77558e8	−	1.77558e8i	0.424615	−	0.424615i
$144$	−6.01935e7			−0.139991
$145$	−1.02008e9			−2.30762
$146$	3.06886e7	+	3.06886e7i	0.0675406	+	0.0675406i
$147$		−	1.51132e7i		−	0.0323660i
$148$	3.13264e8	+	9.01734e7i	0.652925	+	0.187945i
$149$	4.23396e8			0.859016			0.429508	−	0.903063i	$-0.358687\pi$
$149$	4.23396e8			0.859016			0.429508	+	0.903063i	$0.358687\pi$
$150$	3.66290e7	−	3.66290e7i	0.0723537	−	0.0723537i
$151$			7.42029e8i			1.42729i	0.700506	+	0.713646i	$0.252958\pi$
$151$			7.42029e8i			1.42729i	−0.700506	+	0.713646i	$0.747042\pi$
$152$			3.19848e8i			0.599197i
$153$	6.43663e8	+	6.43663e8i	1.17461	+	1.17461i
$154$	1.13156e8	+	1.13156e8i	0.201184	+	0.201184i
$155$	1.10953e8			0.192226
$156$	−2.36321e7	−	2.36321e7i	−0.0399028	−	0.0399028i
$157$	−1.04987e9			−1.72797			−0.863984	−	0.503520i	$-0.832038\pi$
$157$	−1.04987e9			−1.72797			−0.863984	+	0.503520i	$0.832038\pi$
$158$	1.93610e8			0.310671
$159$			4.10633e7i			0.0642489i
$160$	1.18249e9			1.80434
$161$	−5.24517e8	−	5.24517e8i	−0.780649	−	0.780649i
$162$	−2.69417e8	+	2.69417e8i	−0.391170	+	0.391170i
$163$	−1.93658e8	+	1.93658e8i	−0.274338	+	0.274338i	−0.830844	−	0.556506i	$-0.812142\pi$
$163$	−1.93658e8	+	1.93658e8i	−0.274338	+	0.274338i	0.556506	+	0.830844i	$0.312142\pi$
$164$	2.49242e8			0.344545
$165$	5.08400e7	+	5.08400e7i	0.0685914	+	0.0685914i
$166$	5.08822e8	−	5.08822e8i	0.670091	−	0.670091i
$167$	−3.33667e8	−	3.33667e8i	−0.428991	−	0.428991i	0.459294	−	0.888284i	$-0.348103\pi$
$167$	−3.33667e8	−	3.33667e8i	−0.428991	−	0.428991i	−0.888284	+	0.459294i	$0.848103\pi$
$168$	3.72265e7	−	3.72265e7i	0.0467321	−	0.0467321i
$169$		−	8.15375e7i		−	0.0999563i
$170$	−9.79841e8	−	9.79841e8i	−1.17317	−	1.17317i
$171$	−3.78075e8	−	3.78075e8i	−0.442174	−	0.442174i
$172$	5.58787e8	−	5.58787e8i	0.638458	−	0.638458i
$173$		−	1.70698e9i		−	1.90565i	−0.303517	−	0.952826i	$-0.598161\pi$
$173$		−	1.70698e9i		−	1.90565i	0.303517	−	0.952826i	$-0.401839\pi$
$174$	5.98943e7			0.0653414
$175$			1.53712e9i			1.63891i
$176$			8.56783e7i			0.0892936i
$177$	5.21779e7	−	5.21779e7i	0.0531610	−	0.0531610i
$178$		−	2.97723e7i		−	0.0296574i
$179$	1.28472e9	−	1.28472e9i	1.25140	−	1.25140i	0.296314	−	0.955091i	$-0.404242\pi$
$179$	1.28472e9	−	1.28472e9i	1.25140	−	1.25140i	0.955091	−	0.296314i	$-0.0957575\pi$
$180$	−8.76096e8	+	8.76096e8i	−0.834568	+	0.834568i
$181$	3.20228e8			0.298363			0.149182	−	0.988810i	$-0.452336\pi$
$181$	3.20228e8			0.298363			0.149182	+	0.988810i	$0.452336\pi$
$182$	−4.67893e8			−0.426443
$183$	2.76487e7	+	2.76487e7i	0.0246530	+	0.0246530i
$184$			1.51562e9i			1.32226i
$185$	1.79441e9	−	9.92260e8i	1.53191	−	0.847108i
$186$	−6.51460e6			−0.00544297
$187$	9.16178e8	−	9.16178e8i	0.749227	−	0.749227i
$188$		−	4.17824e7i		−	0.0334474i
$189$			1.76693e8i			0.138475i
$190$	5.75538e8	+	5.75538e8i	0.441631	+	0.441631i
$191$	3.89039e8	+	3.89039e8i	0.292321	+	0.292321i	0.837996	−	0.545676i	$-0.183727\pi$
$191$	3.89039e8	+	3.89039e8i	0.292321	+	0.292321i	−0.545676	+	0.837996i	$0.683727\pi$
$192$	−5.26466e7			−0.0387405
$193$	−8.06039e8	−	8.06039e8i	−0.580934	−	0.580934i	0.354226	−	0.935160i	$-0.384744\pi$
$193$	−8.06039e8	−	8.06039e8i	−0.580934	−	0.580934i	−0.935160	+	0.354226i	$0.884744\pi$
$194$	−4.35435e8			−0.307409
$195$	−2.10221e8			−0.145391
$196$		−	3.70702e8i		−	0.251189i
$197$	−2.02620e9			−1.34530			−0.672648	−	0.739963i	$-0.734843\pi$
$197$	−2.02620e9			−1.34530			−0.672648	+	0.739963i	$0.734843\pi$
$198$	3.86491e8	+	3.86491e8i	0.251466	+	0.251466i
$199$	−1.18490e9	+	1.18490e9i	−0.755561	+	0.755561i	−0.975511	−	0.219950i	$-0.929410\pi$
$199$	−1.18490e9	+	1.18490e9i	−0.755561	+	0.755561i	0.219950	+	0.975511i	$0.429410\pi$
$200$	2.22079e9	−	2.22079e9i	1.38799	−	1.38799i
$201$	−1.74902e8			−0.107155
$202$	8.66720e8	+	8.66720e8i	0.520563	+	0.520563i
$203$	−1.25672e9	+	1.25672e9i	−0.740036	+	0.740036i
$204$	−1.21939e8	−	1.21939e8i	−0.0704078	−	0.0704078i
$205$	1.10858e9	−	1.10858e9i	0.627698	−	0.627698i
$206$		−	6.78629e8i		−	0.376845i
$207$	−1.79153e9	−	1.79153e9i	−0.975757	−	0.975757i
$208$	−1.77138e8	−	1.77138e8i	−0.0946364	−	0.0946364i
$209$	−5.38144e8	+	5.38144e8i	−0.282042	+	0.282042i
$210$		−	1.33971e8i		−	0.0688867i
$211$	6.25164e8			0.315402			0.157701	−	0.987487i	$-0.449592\pi$
$211$	6.25164e8			0.315402			0.157701	+	0.987487i	$0.449592\pi$
$212$			1.00721e9i			0.498630i
$213$			2.14718e8i			0.104316i
$214$	−1.57198e9	+	1.57198e9i	−0.749533	+	0.749533i
$215$		−	4.97073e9i		−	2.32630i
$216$	2.55282e8	−	2.55282e8i	0.117275	−	0.117275i
$217$	1.36691e8	−	1.36691e8i	0.0616454	−	0.0616454i
$218$	1.66573e8			0.0737530
$219$	3.39732e7			0.0147693
$220$	1.24702e9	+	1.24702e9i	0.532331	+	0.532331i
$221$			3.78835e9i			1.58811i
$222$	−1.05359e8	+	5.82606e7i	−0.0433769	+	0.0239863i
$223$	−2.15209e9			−0.870246			−0.435123	−	0.900371i	$-0.643295\pi$
$223$	−2.15209e9			−0.870246			−0.435123	+	0.900371i	$0.643295\pi$
$224$	1.45680e9	−	1.45680e9i	0.578639	−	0.578639i
$225$			5.25014e9i			2.04852i
$226$			2.25954e9i			0.866136i
$227$	−2.28454e9	−	2.28454e9i	−0.860389	−	0.860389i	0.130994	−	0.991383i	$-0.458183\pi$
$227$	−2.28454e9	−	2.28454e9i	−0.860389	−	0.860389i	−0.991383	+	0.130994i	$0.958183\pi$
$228$	7.16242e7	+	7.16242e7i	0.0265046	+	0.0265046i
$229$	−9.84705e8			−0.358067			−0.179034	−	0.983843i	$-0.557297\pi$
$229$	−9.84705e8			−0.358067			−0.179034	+	0.983843i	$0.557297\pi$
$230$	2.72722e9	+	2.72722e9i	0.974559	+	0.974559i
$231$	1.25267e8			0.0439935
$232$	3.63134e9			1.25347
$233$			3.16752e9i			1.07472i	0.843352	+	0.537361i	$0.180579\pi$
$233$			3.16752e9i			1.07472i	−0.843352	+	0.537361i	$0.819421\pi$
$234$	−1.59812e9			−0.533024
$235$	−1.85840e8	−	1.85840e8i	−0.0609350	−	0.0609350i
$236$	1.27983e9	−	1.27983e9i	0.412578	−	0.412578i
$237$	1.07167e8	−	1.07167e8i	0.0339677	−	0.0339677i
$238$	−2.41428e9			−0.752452
$239$	1.76393e9	+	1.76393e9i	0.540617	+	0.540617i	0.923710	−	0.383093i	$-0.125141\pi$
$239$	1.76393e9	+	1.76393e9i	0.540617	+	0.540617i	−0.383093	+	0.923710i	$0.625141\pi$
$240$	5.07197e7	−	5.07197e7i	0.0152873	−	0.0152873i
$241$	−3.61881e8	−	3.61881e8i	−0.107275	−	0.107275i	0.651432	−	0.758707i	$-0.274169\pi$
$241$	−3.61881e8	−	3.61881e8i	−0.107275	−	0.107275i	−0.758707	+	0.651432i	$0.774169\pi$
$242$	−8.22978e8	+	8.22978e8i	−0.239953	+	0.239953i
$243$			9.06423e8i			0.259960i
$244$	6.78175e8	+	6.78175e8i	0.191330	+	0.191330i
$245$	−1.64881e9	−	1.64881e9i	−0.457620	−	0.457620i
$246$	−6.50902e7	+	6.50902e7i	−0.0177736	+	0.0177736i
$247$		−	2.22520e9i		−	0.597835i
$248$	−3.94975e8			−0.104415
$249$		−	5.63283e8i		−	0.146531i
$250$		−	4.12067e9i		−	1.05489i
$251$	4.46492e9	−	4.46492e9i	1.12491	−	1.12491i	0.133922	−	0.990992i	$-0.457243\pi$
$251$	4.46492e9	−	4.46492e9i	1.12491	−	1.12491i	0.990992	−	0.133922i	$-0.0427571\pi$
$252$			2.15865e9i			0.535280i
$253$	−2.55002e9	+	2.55002e9i	−0.622389	+	0.622389i
$254$	5.66576e8	−	5.66576e8i	0.136120	−	0.136120i
$255$	−1.08472e9			−0.256540
$256$	−3.79782e9			−0.884249
$257$	−1.07276e8	−	1.07276e8i	−0.0245906	−	0.0245906i	0.694705	−	0.719295i	$-0.255535\pi$
$257$	−1.07276e8	−	1.07276e8i	−0.0245906	−	0.0245906i	−0.719295	+	0.694705i	$0.755535\pi$
$258$			2.91857e8i			0.0658706i
$259$	9.88221e8	−	3.43310e9i	0.219612	−	0.762934i
$260$	−5.15636e9			−1.12837
$261$	−4.29240e9	+	4.29240e9i	−0.924993	+	0.924993i
$262$		−	3.31442e6i		−	0.000703399i
$263$			7.61959e8i			0.159261i	0.996824	+	0.0796303i	$0.0253740\pi$
$263$			7.61959e8i			0.159261i	−0.996824	+	0.0796303i	$0.974626\pi$
$264$	−1.80983e8	−	1.80983e8i	−0.0372581	−	0.0372581i
$265$	4.47988e9	+	4.47988e9i	0.908411	+	0.908411i
$266$	1.41810e9			0.283256
$267$	−1.64795e7	−	1.64795e7i	−0.00324263	−	0.00324263i
$268$	−4.29006e9			−0.831618
$269$	4.73158e9			0.903643			0.451822	−	0.892108i	$-0.350774\pi$
$269$	4.73158e9			0.903643			0.451822	+	0.892108i	$0.350774\pi$
$270$		−	9.18713e8i		−	0.172872i
$271$	3.00182e9			0.556553			0.278277	−	0.960501i	$-0.410237\pi$
$271$	3.00182e9			0.556553			0.278277	+	0.960501i	$0.410237\pi$
$272$	−9.14011e8	−	9.14011e8i	−0.166984	−	0.166984i
$273$	−2.58987e8	+	2.58987e8i	−0.0466258	+	0.0466258i
$274$	−9.36536e8	+	9.36536e8i	−0.166158	+	0.166158i
$275$	7.47294e9			1.30666
$276$	3.39395e8	+	3.39395e8i	0.0584883	+	0.0584883i
$277$	1.15932e9	−	1.15932e9i	0.196917	−	0.196917i	−0.601760	−	0.798677i	$-0.705534\pi$
$277$	1.15932e9	−	1.15932e9i	0.196917	−	0.196917i	0.798677	+	0.601760i	$0.205534\pi$
$278$	−4.07440e9	−	4.07440e9i	−0.682157	−	0.682157i
$279$	4.66878e8	−	4.66878e8i	0.0770524	−	0.0770524i
$280$		−	8.12258e9i		−	1.32148i
$281$	−4.38094e9	−	4.38094e9i	−0.702655	−	0.702655i	0.262325	−	0.964980i	$-0.415511\pi$
$281$	−4.38094e9	−	4.38094e9i	−0.702655	−	0.702655i	−0.964980	+	0.262325i	$0.915511\pi$
$282$	1.09116e7	+	1.09116e7i	0.00172541	+	0.00172541i
$283$	2.01797e9	−	2.01797e9i	0.314607	−	0.314607i	−0.532084	−	0.846691i	$-0.678591\pi$
$283$	2.01797e9	−	2.01797e9i	0.314607	−	0.314607i	0.846691	+	0.532084i	$0.178591\pi$
$284$			5.26668e9i			0.809587i
$285$	6.37139e8			0.0965729
$286$			2.27474e9i			0.339991i
$287$		−	2.73148e9i		−	0.402597i
$288$	4.97580e9	−	4.97580e9i	0.723258	−	0.723258i
$289$			1.25717e10i			1.80220i
$290$	6.53427e9	−	6.53427e9i	0.923858	−	0.923858i
$291$	−2.41021e8	+	2.41021e8i	−0.0336111	+	0.0336111i
$292$	8.33306e8			0.114623
$293$	1.10981e10			1.50584			0.752920	−	0.658112i	$-0.228645\pi$
$293$	1.10981e10			1.50584			0.752920	+	0.658112i	$0.228645\pi$
$294$	9.68098e7	+	9.68098e7i	0.0129578	+	0.0129578i
$295$		−	1.13849e10i		−	1.50328i
$296$	−6.38781e9	+	3.53230e9i	−0.832119	+	0.460140i
$297$	8.59022e8			0.110402
$298$	−2.71211e9	+	2.71211e9i	−0.343908	+	0.343908i
$299$		−	1.05442e10i		−	1.31926i
$300$		−	9.94611e8i		−	0.122791i
$301$	−6.12381e9	−	6.12381e9i	−0.746029	−	0.746029i
$302$	−4.75316e9	−	4.75316e9i	−0.571419	−	0.571419i
$303$	9.59487e8			0.113833
$304$	5.36871e8	+	5.36871e8i	0.0628602	+	0.0628602i
$305$	6.03276e9			0.697135
$306$	−8.24613e9			−0.940513
$307$		−	1.54831e9i		−	0.174303i	−0.996195	−	0.0871516i	$-0.972224\pi$
$307$		−	1.54831e9i		−	0.174303i	0.996195	−	0.0871516i	$-0.0277764\pi$
$308$	3.07259e9			0.341430
$309$	−3.75632e8	−	3.75632e8i	−0.0412030	−	0.0412030i
$310$	−7.10722e8	+	7.10722e8i	−0.0769579	+	0.0769579i
$311$	−1.29184e10	+	1.29184e10i	−1.38092	+	1.38092i	−0.537918	+	0.842997i	$0.680789\pi$
$311$	−1.29184e10	+	1.29184e10i	−1.38092	+	1.38092i	−0.842997	+	0.537918i	$0.819211\pi$
$312$	7.48354e8			0.0789749
$313$	3.84846e9	+	3.84846e9i	0.400968	+	0.400968i	0.878574	−	0.477606i	$-0.158495\pi$
$313$	3.84846e9	+	3.84846e9i	0.400968	+	0.400968i	−0.477606	+	0.878574i	$0.658495\pi$
$314$	6.72505e9	−	6.72505e9i	0.691794	−	0.691794i
$315$	9.60125e9	+	9.60125e9i	0.975181	+	0.975181i
$316$	2.62861e9	−	2.62861e9i	0.263620	−	0.263620i
$317$			9.84944e9i			0.975381i	0.873016	+	0.487691i	$0.162161\pi$
$317$			9.84944e9i			0.975381i	−0.873016	+	0.487691i	$0.837839\pi$
$318$	−2.63036e8	−	2.63036e8i	−0.0257221	−	0.0257221i
$319$	6.10972e9	+	6.10972e9i	0.590009	+	0.590009i
$320$	−5.74357e9	+	5.74357e9i	−0.547750	+	0.547750i
$321$			1.74023e9i			0.163903i
$322$	6.71972e9			0.625068
$323$		−	1.14818e10i		−	1.05487i
$324$			7.31565e9i			0.663855i
$325$	−1.54501e10	+	1.54501e10i	−1.38484	+	1.38484i
$326$		−	2.48101e9i		−	0.219663i
$327$	9.22011e7	−	9.22011e7i	0.00806390	−	0.00806390i
$328$	−3.94637e9	+	3.94637e9i	−0.340959	+	0.340959i
$329$	−4.57899e8			−0.0390828
$330$	−6.51324e8			−0.0549213
$331$	8.61899e9	+	8.61899e9i	0.718033	+	0.718033i	0.968202	−	0.250169i	$-0.0804862\pi$
$331$	8.61899e9	+	8.61899e9i	0.718033	+	0.718033i	−0.250169	+	0.968202i	$0.580486\pi$
$332$		−	1.38164e10i		−	1.13721i
$333$	3.37534e9	−	1.17260e10i	0.274499	−	0.953614i
$334$	4.27470e9			0.343494
$335$	−1.90813e10	+	1.90813e10i	−1.51505	+	1.51505i
$336$		−	1.24971e8i		−	0.00980508i
$337$		−	1.16839e10i		−	0.905873i	−0.891543	−	0.452936i	$-0.850376\pi$
$337$		−	1.16839e10i		−	0.905873i	0.891543	−	0.452936i	$-0.149624\pi$
$338$	5.22298e8	+	5.22298e8i	0.0400177	+	0.0400177i
$339$	1.25069e9	+	1.25069e9i	0.0947003	+	0.0947003i
$340$	−2.66062e10			−1.99098
$341$	−6.64545e8	−	6.64545e8i	−0.0491481	−	0.0491481i
$342$	4.84361e9			0.354050
$343$	−1.50514e10			−1.08742
$344$			1.76951e10i			1.26362i
$345$	3.01912e9			0.213110
$346$	1.09343e10	+	1.09343e10i	0.762931	+	0.762931i
$347$	1.16780e10	−	1.16780e10i	0.805475	−	0.805475i	−0.178470	−	0.983945i	$-0.557115\pi$
$347$	1.16780e10	−	1.16780e10i	0.805475	−	0.805475i	0.983945	+	0.178470i	$0.0571148\pi$
$348$	8.13173e8	−	8.13173e8i	0.0554455	−	0.0554455i
$349$	−6.85241e9			−0.461893			−0.230946	−	0.972966i	$-0.574182\pi$
$349$	−6.85241e9			−0.461893			−0.230946	+	0.972966i	$0.574182\pi$
$350$	−9.84620e9	−	9.84620e9i	−0.656140	−	0.656140i
$351$	−1.77601e9	+	1.77601e9i	−0.117008	+	0.117008i
$352$	−7.08246e9	−	7.08246e9i	−0.461332	−	0.461332i
$353$	−1.12776e10	+	1.12776e10i	−0.726301	+	0.726301i	−0.969881	−	0.243580i	$-0.921678\pi$
$353$	−1.12776e10	+	1.12776e10i	−0.726301	+	0.726301i	0.243580	+	0.969881i	$0.421678\pi$
$354$			6.68464e8i			0.0425662i
$355$	2.34251e10	+	2.34251e10i	1.47492	+	1.47492i
$356$	−4.04213e8	−	4.04213e8i	−0.0251658	−	0.0251658i
$357$	−1.33634e9	+	1.33634e9i	−0.0822706	+	0.0822706i
$358$			1.64589e10i			1.00200i
$359$	3.56654e9			0.214719			0.107359	−	0.994220i	$-0.465760\pi$
$359$	3.56654e9			0.214719			0.107359	+	0.994220i	$0.465760\pi$
$360$		−	2.77433e10i		−	1.65176i
$361$		−	1.02394e10i		−	0.602901i
$362$	−2.05126e9	+	2.05126e9i	−0.119450	+	0.119450i
$363$			9.11064e8i			0.0524714i
$364$	−6.35250e9	+	6.35250e9i	−0.361859	+	0.361859i
$365$	3.70637e9	−	3.70637e9i	0.208823	−	0.208823i
$366$	−3.54214e8			−0.0197397
$367$	1.17947e10			0.650164			0.325082	−	0.945686i	$-0.394608\pi$
$367$	1.17947e10			0.650164			0.325082	+	0.945686i	$0.394608\pi$
$368$	2.54399e9	+	2.54399e9i	0.138715	+	0.138715i
$369$		−	9.32956e9i		−	0.503217i
$370$	−5.13824e9	+	1.78503e10i	−0.274162	+	0.952444i
$371$	1.10382e10			0.582642
$372$	−8.84475e7	+	8.84475e7i	−0.00461864	+	0.00461864i
$373$		−	1.87538e10i		−	0.968846i	−0.874834	−	0.484423i	$-0.839030\pi$
$373$		−	1.87538e10i		−	0.968846i	0.874834	−	0.484423i	$-0.160970\pi$
$374$			1.17374e10i			0.599908i
$375$	−2.28086e9	−	2.28086e9i	−0.115338	−	0.115338i
$376$	6.61561e8	+	6.61561e8i	0.0330993	+	0.0330993i
$377$	−2.52634e10			−1.25062
$378$	−1.13183e9	−	1.13183e9i	−0.0554388	−	0.0554388i
$379$	2.63352e10			1.27638			0.638190	−	0.769879i	$-0.279683\pi$
$379$	2.63352e10			1.27638			0.638190	+	0.769879i	$0.279683\pi$
$380$	1.56279e10			0.749493
$381$		−	6.27218e8i		−	0.0297659i
$382$	−4.98407e9			−0.234062
$383$	1.31001e9	+	1.31001e9i	0.0608807	+	0.0608807i	0.736892	−	0.676011i	$-0.236293\pi$
$383$	1.31001e9	+	1.31001e9i	0.0608807	+	0.0608807i	−0.676011	+	0.736892i	$0.736293\pi$
$384$	−1.05015e9	+	1.05015e9i	−0.0482976	+	0.0482976i
$385$	1.36662e10	−	1.36662e10i	0.622022	−	0.622022i
$386$	1.03264e10			0.465156
$387$	−2.09163e10	−	2.09163e10i	−0.932484	−	0.932484i
$388$	−5.91182e9	+	5.91182e9i	−0.260852	+	0.260852i
$389$	9.49689e9	+	9.49689e9i	0.414747	+	0.414747i	0.883388	−	0.468642i	$-0.155256\pi$
$389$	9.49689e9	+	9.49689e9i	0.414747	+	0.414747i	−0.468642	+	0.883388i	$0.655256\pi$
$390$	1.34660e9	−	1.34660e9i	0.0582075	−	0.0582075i
$391$		−	5.44070e10i		−	2.32781i
$392$	5.86950e9	+	5.86950e9i	0.248575	+	0.248575i
$393$	−1.83458e6	−	1.83458e6i	−7.69072e−5	−	7.69072e-5i
$394$	1.29791e10	−	1.29791e10i	0.538591	−	0.538591i
$395$		−	2.33830e10i		−	0.960534i
$396$	1.04946e10			0.426763
$397$			6.23097e9i			0.250838i	0.992104	+	0.125419i	$0.0400275\pi$
$397$			6.23097e9i			0.250838i	−0.992104	+	0.125419i	$0.959972\pi$
$398$		−	1.51801e10i		−	0.604980i
$399$	7.84939e8	−	7.84939e8i	0.0309702	−	0.0309702i
$400$		−	7.45527e9i		−	0.291221i
$401$	−2.70231e10	+	2.70231e10i	−1.04510	+	1.04510i	−0.0461670	+	0.998934i	$0.514701\pi$
$401$	−2.70231e10	+	2.70231e10i	−1.04510	+	1.04510i	−0.998934	+	0.0461670i	$0.985299\pi$
$402$	1.12036e9	−	1.12036e9i	0.0428996	−	0.0428996i
$403$	2.74786e9			0.104178
$404$	2.35346e10			0.883448
$405$	3.25385e10	+	3.25385e10i	1.20942	+	1.20942i
$406$		−	1.61001e10i		−	0.592549i
$407$	−1.66906e10	−	4.80439e9i	−0.608265	−	0.175090i
$408$	3.86142e9			0.139350
$409$	7.32216e8	−	7.32216e8i	0.0261665	−	0.0261665i	−0.693902	−	0.720069i	$-0.744110\pi$
$409$	7.32216e8	−	7.32216e8i	0.0261665	−	0.0261665i	0.720069	+	0.693902i	$0.244110\pi$
$410$			1.42023e10i			0.502600i
$411$			1.03678e9i			0.0363344i
$412$	−9.21361e9	−	9.21361e9i	−0.319772	−	0.319772i
$413$	−1.40259e10	−	1.40259e10i	−0.482091	−	0.482091i
$414$	2.29517e10			0.781291
$415$	−6.14523e10	−	6.14523e10i	−2.07179	−	2.07179i
$416$	2.92856e10			0.977870
$417$	−4.51049e9			−0.149169
$418$		−	6.89430e9i		−	0.225832i
$419$	5.78552e10			1.87710			0.938548	−	0.345149i	$-0.112172\pi$
$419$	5.78552e10			1.87710			0.938548	+	0.345149i	$0.112172\pi$
$420$	−1.81891e9	−	1.81891e9i	−0.0584538	−	0.0584538i
$421$	−1.34022e10	+	1.34022e10i	−0.426628	+	0.426628i	−0.887478	−	0.460850i	$-0.847545\pi$
$421$	−1.34022e10	+	1.34022e10i	−0.426628	+	0.426628i	0.460850	+	0.887478i	$0.347545\pi$
$422$	−4.00457e9	+	4.00457e9i	−0.126272	+	0.126272i
$423$	−1.56399e9			−0.0488508
$424$	−1.59477e10	−	1.59477e10i	−0.493440	−	0.493440i
$425$	−7.97209e10	+	7.97209e10i	−2.44352	+	2.44352i
$426$	−1.37541e9	−	1.37541e9i	−0.0417631	−	0.0417631i
$427$	7.43220e9	−	7.43220e9i	0.223566	−	0.223566i
$428$			4.26848e10i			1.27203i
$429$	1.25910e9	+	1.25910e9i	0.0371734	+	0.0371734i
$430$	3.18407e10	+	3.18407e10i	0.931340	+	0.931340i
$431$	4.88687e9	−	4.88687e9i	0.141619	−	0.141619i	−0.632743	−	0.774362i	$-0.718071\pi$
$431$	4.88687e9	−	4.88687e9i	0.141619	−	0.141619i	0.774362	+	0.632743i	$0.218071\pi$
$432$		−	8.56990e8i		−	0.0246060i
$433$	9.32011e9			0.265137			0.132568	−	0.991174i	$-0.457678\pi$
$433$	9.32011e9			0.265137			0.132568	+	0.991174i	$0.457678\pi$
$434$			1.75118e9i			0.0493597i
$435$		−	7.23365e9i		−	0.202023i
$436$	2.26154e9	−	2.26154e9i	0.0625832	−	0.0625832i
$437$			3.19575e10i			0.876289i
$438$	−2.17620e8	+	2.17620e8i	−0.00591292	+	0.00591292i
$439$	−4.96657e9	+	4.96657e9i	−0.133721	+	0.133721i	−0.770799	−	0.637078i	$-0.780143\pi$
$439$	−4.96657e9	+	4.96657e9i	−0.133721	+	0.133721i	0.637078	+	0.770799i	$0.280143\pi$
$440$	−3.94892e10			−1.05358
$441$	−1.38760e10			−0.366868
$442$	−2.42668e10	−	2.42668e10i	−0.635803	−	0.635803i
$443$		−	5.00265e10i		−	1.29893i	−0.760392	−	0.649464i	$-0.774993\pi$
$443$		−	5.00265e10i		−	1.29893i	0.760392	−	0.649464i	$-0.225007\pi$
$444$	−6.39441e8	+	2.22143e9i	−0.0164539	+	0.0571611i
$445$	−3.59571e9			−0.0916948
$446$	1.37855e10	−	1.37855e10i	0.348404	−	0.348404i
$447$			3.00240e9i			0.0752035i
$448$			1.41519e10i			0.351319i
$449$	8.93081e9	+	8.93081e9i	0.219738	+	0.219738i	0.808388	−	0.588650i	$-0.200340\pi$
$449$	8.93081e9	+	8.93081e9i	0.219738	+	0.219738i	−0.588650	+	0.808388i	$0.700340\pi$
$450$	−3.36304e10	−	3.36304e10i	−0.820129	−	0.820129i
$451$	−1.32795e10			−0.320978
$452$	3.06773e10	+	3.06773e10i	0.734960	+	0.734960i
$453$	−5.26190e9			−0.124954
$454$	2.92678e10			0.688916
$455$			5.65092e10i			1.31848i
$456$	−2.26812e9			−0.0524574
$457$	−8.66967e9	−	8.66967e9i	−0.198764	−	0.198764i	0.600706	−	0.799470i	$-0.294886\pi$
$457$	−8.66967e9	−	8.66967e9i	−0.198764	−	0.198764i	−0.799470	+	0.600706i	$0.794886\pi$
$458$	6.30765e9	−	6.30765e9i	0.143353	−	0.143353i
$459$	−9.16399e9	+	9.16399e9i	−0.206459	+	0.206459i
$460$	7.40538e10			1.65393
$461$	2.37521e10	+	2.37521e10i	0.525895	+	0.525895i	0.919346	−	0.393451i	$-0.128719\pi$
$461$	2.37521e10	+	2.37521e10i	0.525895	+	0.525895i	−0.393451	+	0.919346i	$0.628719\pi$
$462$	−8.02414e8	+	8.02414e8i	−0.0176129	+	0.0176129i
$463$	−1.20208e10	−	1.20208e10i	−0.261584	−	0.261584i	0.564114	−	0.825697i	$-0.309218\pi$
$463$	−1.20208e10	−	1.20208e10i	−0.261584	−	0.261584i	−0.825697	+	0.564114i	$0.809218\pi$
$464$	6.09527e9	−	6.09527e9i	0.131499	−	0.131499i
$465$			7.86793e8i			0.0168286i
$466$	−2.02900e10	−	2.02900e10i	−0.430267	−	0.430267i
$467$	−4.56248e10	−	4.56248e10i	−0.959253	−	0.959253i	0.0399491	−	0.999202i	$-0.487280\pi$
$467$	−4.56248e10	−	4.56248e10i	−0.959253	−	0.959253i	−0.999202	+	0.0399491i	$0.987280\pi$
$468$	−2.16974e10	+	2.16974e10i	−0.452298	+	0.452298i
$469$			4.70153e10i			0.971734i
$470$	2.38084e9			0.0487909
$471$		−	7.44485e9i		−	0.151277i
$472$			4.05284e10i			0.816567i
$473$	−2.97719e10	+	2.97719e10i	−0.594787	+	0.594787i
$474$			1.37294e9i			0.0271980i
$475$	4.68264e10	−	4.68264e10i	0.919849	−	0.919849i
$476$	−3.27782e10	+	3.27782e10i	−0.638494	+	0.638494i
$477$	3.77017e10			0.728261
$478$	−2.25982e10			−0.432874
$479$	2.30447e10	+	2.30447e10i	0.437753	+	0.437753i	0.891255	−	0.453502i	$-0.149826\pi$
$479$	2.30447e10	+	2.30447e10i	0.437753	+	0.437753i	−0.453502	+	0.891255i	$0.649826\pi$
$480$			8.38533e9i			0.157963i
$481$	4.44403e10	−	2.45744e10i	0.830227	−	0.459094i
$482$	4.63615e9			0.0858953
$483$	3.71947e9	−	3.71947e9i	0.0683428	−	0.0683428i
$484$			2.23468e10i			0.407225i
$485$			5.25891e10i			0.950449i
$486$	−5.80621e9	−	5.80621e9i	−0.104075	−	0.104075i
$487$	6.79720e10	+	6.79720e10i	1.20841	+	1.20841i	0.971542	+	0.236868i	$0.0761209\pi$
$487$	6.79720e10	+	6.79720e10i	1.20841	+	1.20841i	0.236868	+	0.971542i	$0.423879\pi$
$488$	−2.14757e10			−0.378677
$489$	−1.37328e9	−	1.37328e9i	−0.0240172	−	0.0240172i
$490$	2.11233e10			0.366418
$491$	−4.86770e10			−0.837525			−0.418763	−	0.908096i	$-0.637536\pi$
$491$	−4.86770e10			−0.837525			−0.418763	+	0.908096i	$0.637536\pi$
$492$			1.76744e9i			0.0301636i
$493$	−1.30356e11			−2.20670
$494$	1.42538e10	+	1.42538e10i	0.239344	+	0.239344i
$495$	4.66780e10	−	4.66780e10i	0.777484	−	0.777484i
$496$	−6.62973e8	+	6.62973e8i	−0.0109539	+	0.0109539i
$497$	5.77182e10			0.945991
$498$	3.60818e9	+	3.60818e9i	0.0586638	+	0.0586638i
$499$	−2.76883e10	+	2.76883e10i	−0.446575	+	0.446575i	−0.894214	−	0.447639i	$-0.852265\pi$
$499$	−2.76883e10	+	2.76883e10i	−0.446575	+	0.446575i	0.447639	+	0.894214i	$0.352265\pi$
$500$	−5.59455e10	−	5.59455e10i	−0.895128	−	0.895128i
$501$	2.36611e9	−	2.36611e9i	0.0375565	−	0.0375565i
$502$			5.72013e10i			0.900722i
$503$	−7.13085e10	−	7.13085e10i	−1.11396	−	1.11396i	−0.992610	−	0.121350i	$-0.961278\pi$
$503$	−7.13085e10	−	7.13085e10i	−1.11396	−	1.11396i	−0.121350	−	0.992610i	$-0.538722\pi$
$504$	−3.41790e10	−	3.41790e10i	−0.529709	−	0.529709i
$505$	1.04677e11	−	1.04677e11i	1.60948	−	1.60948i
$506$		−	3.26690e10i		−	0.498349i
$507$	5.78201e8			0.00875079
$508$		−	1.53846e10i		−	0.231010i
$509$		−	1.28603e10i		−	0.191593i	−0.995401	−	0.0957965i	$-0.969460\pi$
$509$		−	1.28603e10i		−	0.191593i	0.995401	−	0.0957965i	$-0.0305398\pi$
$510$	6.94828e9	−	6.94828e9i	0.102706	−	0.102706i
$511$		−	9.13230e9i		−	0.133936i
$512$	−1.35839e10	+	1.35839e10i	−0.197672	+	0.197672i
$513$	5.38274e9	−	5.38274e9i	0.0777202	−	0.0777202i
$514$	1.37434e9			0.0196898
$515$	−8.19605e10			−1.16513
$516$	3.96249e9	+	3.96249e9i	0.0558945	+	0.0558945i
$517$			2.22615e9i			0.0311596i
$518$	1.56610e10	+	2.83213e10i	0.217520	+	0.393364i
$519$	1.21046e10			0.166832
$520$	8.16431e10	−	8.16431e10i	1.11662	−	1.11662i
$521$		−	1.88728e10i		−	0.256145i	−0.991765	−	0.128072i	$-0.959121\pi$
$521$		−	1.88728e10i		−	0.256145i	0.991765	−	0.128072i	$-0.0408789\pi$
$522$		−	5.49910e10i		−	0.740645i
$523$	−2.04372e10	−	2.04372e10i	−0.273158	−	0.273158i	0.557212	−	0.830370i	$-0.311871\pi$
$523$	−2.04372e10	−	2.04372e10i	−0.273158	−	0.273158i	−0.830370	+	0.557212i	$0.811871\pi$
$524$	−4.49992e7	−	4.49992e7i	−0.000596870	−	0.000596870i
$525$	−1.09001e10			−0.143480
$526$	−4.88082e9	−	4.88082e9i	−0.0637602	−	0.0637602i
$527$	1.41786e10			0.183820
$528$	−6.07565e8			−0.00781731
$529$			7.31213e10i			0.933730i
$530$	−5.73928e10			−0.727368
$531$	−4.79063e10	−	4.79063e10i	−0.602580	−	0.602580i
$532$	1.92532e10	−	1.92532e10i	0.240357	−	0.240357i
$533$	2.74551e10	−	2.74551e10i	0.340184	−	0.340184i
$534$	2.11122e8			0.00259639
$535$	1.89853e11	+	1.89853e11i	2.31741	+	2.31741i
$536$	6.79265e10	−	6.79265e10i	0.822962	−	0.822962i
$537$	9.11028e9	+	9.11028e9i	0.109556	+	0.109556i
$538$	−3.03087e10	+	3.03087e10i	−0.361775	+	0.361775i
$539$			1.97508e10i			0.234008i
$540$	−1.24732e10	−	1.24732e10i	−0.146691	−	0.146691i
$541$	−7.43345e10	−	7.43345e10i	−0.867763	−	0.867763i	0.124461	−	0.992224i	$-0.460280\pi$
$541$	−7.43345e10	−	7.43345e10i	−0.867763	−	0.867763i	−0.992224	+	0.124461i	$0.960280\pi$
$542$	−1.92285e10	+	1.92285e10i	−0.222817	+	0.222817i
$543$			2.27081e9i			0.0261205i
$544$	1.51110e11			1.72544
$545$		−	2.01177e10i		−	0.228030i
$546$		−	3.31794e9i		−	0.0373335i
$547$	−5.22640e10	+	5.22640e10i	−0.583785	+	0.583785i	−0.935941	−	0.352156i	$-0.885449\pi$
$547$	−5.22640e10	+	5.22640e10i	−0.583785	+	0.583785i	0.352156	+	0.935941i	$0.385449\pi$
$548$			2.54303e10i			0.281988i
$549$	2.53852e10	−	2.53852e10i	0.279442	−	0.279442i
$550$	−4.78689e10	+	4.78689e10i	−0.523121	+	0.523121i
$551$	7.65686e10			0.830700
$552$	−1.07476e10			−0.115759
$553$	−2.88073e10	−	2.88073e10i	−0.308036	−	0.308036i
$554$			1.48523e10i			0.157672i
$555$	7.03635e9	+	1.27246e10i	0.0741610	+	0.134113i
$556$	−1.10635e11			−1.15769
$557$	−4.66964e10	+	4.66964e10i	−0.485135	+	0.485135i	−0.906767	−	0.421632i	$-0.861457\pi$
$557$	−4.66964e10	+	4.66964e10i	−0.485135	+	0.485135i	0.421632	+	0.906767i	$0.361457\pi$
$558$			5.98129e9i			0.0616961i
$559$		−	1.23105e11i		−	1.26075i
$560$	−1.36339e10	−	1.36339e10i	−0.138633	−	0.138633i
$561$	6.49683e9	+	6.49683e9i	0.0655919	+	0.0655919i
$562$	5.61253e10			0.562618
$563$	−6.10858e10	−	6.10858e10i	−0.608005	−	0.608005i	0.334420	−	0.942424i	$-0.391460\pi$
$563$	−6.10858e10	−	6.10858e10i	−0.608005	−	0.608005i	−0.942424	+	0.334420i	$0.891460\pi$
$564$	2.96289e8			0.00292819
$565$	2.72893e11			2.67792
$566$			2.58527e10i			0.251907i
$567$	8.01732e10			0.775705
$568$	−8.33898e10	−	8.33898e10i	−0.801160	−	0.801160i
$569$	−7.65393e10	+	7.65393e10i	−0.730189	+	0.730189i	−0.970657	−	0.240468i	$-0.922699\pi$
$569$	−7.65393e10	+	7.65393e10i	−0.730189	+	0.730189i	0.240468	+	0.970657i	$0.422699\pi$
$570$	−4.08128e9	+	4.08128e9i	−0.0386631	+	0.0386631i
$571$	−1.28878e11			−1.21236			−0.606182	−	0.795326i	$-0.707300\pi$
$571$	−1.28878e11			−1.21236			−0.606182	+	0.795326i	$0.707300\pi$
$572$	3.08837e10	+	3.08837e10i	0.288499	+	0.288499i
$573$	−2.75877e9	+	2.75877e9i	−0.0255915	+	0.0255915i
$574$	1.74968e10	+	1.74968e10i	0.161180	+	0.161180i
$575$	2.21889e11	−	2.21889e11i	2.02985	−	2.02985i
$576$			4.83367e10i			0.439124i
$577$	−1.38027e11	−	1.38027e11i	−1.24526	−	1.24526i	−0.957790	−	0.287468i	$-0.907186\pi$
$577$	−1.38027e11	−	1.38027e11i	−1.24526	−	1.24526i	−0.287468	−	0.957790i	$-0.592814\pi$
$578$	−8.05296e10	−	8.05296e10i	−0.721513	−	0.721513i
$579$	5.71581e9	−	5.71581e9i	0.0508585	−	0.0508585i
$580$		−	1.77429e11i		−	1.56788i
$581$	−1.51415e11			−1.32882
$582$		−	3.08777e9i		−	0.0269125i
$583$		−	5.36638e10i		−	0.464523i
$584$	−1.31941e10	+	1.31941e10i	−0.113430	+	0.113430i
$585$			1.93011e11i			1.64801i
$586$	−7.10904e10	+	7.10904e10i	−0.602865	+	0.602865i
$587$	−1.17069e11	+	1.17069e11i	−0.986032	+	0.986032i	−0.999904	−	0.0138714i	$-0.995584\pi$
$587$	−1.17069e11	+	1.17069e11i	−0.986032	+	0.986032i	0.0138714	+	0.999904i	$0.495584\pi$
$588$	2.62874e9			0.0219906
$589$	−8.32824e9			−0.0691978
$590$	7.29272e10	+	7.29272e10i	0.601841	+	0.601841i
$591$		−	1.43683e10i		−	0.117775i
$592$	−4.79303e9	+	1.66511e10i	−0.0390233	+	0.135567i
$593$	1.57372e11			1.27265			0.636323	−	0.771423i	$-0.280455\pi$
$593$	1.57372e11			1.27265			0.636323	+	0.771423i	$0.280455\pi$
$594$	−5.50257e9	+	5.50257e9i	−0.0441998	+	0.0441998i
$595$			2.91581e11i			2.32644i
$596$			7.36437e10i			0.583647i
$597$	−8.40240e9	−	8.40240e9i	−0.0661464	−	0.0661464i
$598$	6.75423e10	+	6.75423e10i	0.528167	+	0.528167i
$599$	2.45869e11			1.90984			0.954920	−	0.296863i	$-0.0959406\pi$
$599$	2.45869e11			1.90984			0.954920	+	0.296863i	$0.0959406\pi$
$600$	1.57481e10	+	1.57481e10i	0.121513	+	0.121513i
$601$	−1.56288e10			−0.119792			−0.0598959	−	0.998205i	$-0.519077\pi$
$601$	−1.56288e10			−0.119792			−0.0598959	+	0.998205i	$0.519077\pi$
$602$	7.84537e10			0.597348
$603$			1.60584e11i			1.21460i
$604$	−1.29065e11			−0.969755
$605$	9.93941e10	+	9.93941e10i	0.741889	+	0.741889i
$606$	−6.14611e9	+	6.14611e9i	−0.0455733	+	0.0455733i
$607$	−1.46356e11	+	1.46356e11i	−1.07809	+	1.07809i	−0.0814098	+	0.996681i	$0.525942\pi$
$607$	−1.46356e11	+	1.46356e11i	−1.07809	+	1.07809i	−0.996681	+	0.0814098i	$0.974058\pi$
$608$	−8.87592e10			−0.649529
$609$	−8.91166e9	−	8.91166e9i	−0.0647873	−	0.0647873i
$610$	−3.86436e10	+	3.86436e10i	−0.279099	+	0.279099i
$611$	−4.60251e9	−	4.60251e9i	−0.0330240	−	0.0330240i
$612$	−1.11956e11	+	1.11956e11i	−0.798073	+	0.798073i
$613$		−	2.27695e11i		−	1.61255i	−0.591543	−	0.806274i	$-0.701481\pi$
$613$		−	2.27695e11i		−	1.61255i	0.591543	−	0.806274i	$-0.298519\pi$
$614$	9.91791e9	+	9.91791e9i	0.0697825	+	0.0697825i
$615$	7.86119e9	+	7.86119e9i	0.0549525	+	0.0549525i
$616$	−4.86497e10	+	4.86497e10i	−0.337876	+	0.337876i
$617$			7.84955e9i			0.0541632i	0.999633	+	0.0270816i	$0.00862139\pi$
$617$			7.84955e9i			0.0541632i	−0.999633	+	0.0270816i	$0.991379\pi$
$618$	4.81232e9			0.0329914
$619$			9.48514e10i			0.646073i	0.946387	+	0.323036i	$0.104704\pi$
$619$			9.48514e10i			0.646073i	−0.946387	+	0.323036i	$0.895296\pi$
$620$			1.92987e10i			0.130605i
$621$	2.55064e10	−	2.55064e10i	0.171507	−	0.171507i
$622$		−	1.65501e11i		−	1.10570i
$623$	−4.42982e9	+	4.42982e9i	−0.0294059	+	0.0294059i
$624$	1.25613e9	−	1.25613e9i	0.00828505	−	0.00828505i
$625$	−1.82674e11			−1.19717
$626$	−4.93036e10			−0.321056
$627$	−3.81611e9	−	3.81611e9i	−0.0246917	−	0.0246917i
$628$		−	1.82610e11i		−	1.17405i
$629$	2.29307e11	−	1.26801e11i	1.46492	−	0.810064i
$630$	−1.23004e11			−0.780831
$631$	3.80212e10	−	3.80212e10i	0.239833	−	0.239833i	−0.576948	−	0.816781i	$-0.695757\pi$
$631$	3.80212e10	−	3.80212e10i	0.239833	−	0.239833i	0.816781	+	0.576948i	$0.195757\pi$
$632$			8.32401e10i			0.521752i
$633$			4.43319e9i			0.0276122i
$634$	−6.30918e10	−	6.30918e10i	−0.390495	−	0.390495i
$635$	−6.84275e10	−	6.84275e10i	−0.420858	−	0.420858i
$636$	−7.14239e9			−0.0436531
$637$	−4.08344e10	−	4.08344e10i	−0.248010	−	0.248010i
$638$	−7.82732e10			−0.472422
$639$	1.97141e11			1.18242
$640$			2.29136e11i			1.36575i
$641$	3.15644e10			0.186967			0.0934835	−	0.995621i	$-0.470200\pi$
$641$	3.15644e10			0.186967			0.0934835	+	0.995621i	$0.470200\pi$
$642$	−1.11472e10	−	1.11472e10i	−0.0656187	−	0.0656187i
$643$	−1.30305e11	+	1.30305e11i	−0.762286	+	0.762286i	−0.976735	−	0.214449i	$-0.931204\pi$
$643$	−1.30305e11	+	1.30305e11i	−0.762286	+	0.762286i	0.214449	+	0.976735i	$0.431204\pi$
$644$	9.12323e10	−	9.12323e10i	0.530402	−	0.530402i
$645$	3.52486e10			0.203659
$646$	7.35479e10	+	7.35479e10i	0.422319	+	0.422319i
$647$	1.33762e9	−	1.33762e9i	0.00763334	−	0.00763334i	−0.703280	−	0.710913i	$-0.748282\pi$
$647$	1.33762e9	−	1.33762e9i	0.00763334	−	0.00763334i	0.710913	+	0.703280i	$0.248282\pi$
$648$	−1.15832e11	−	1.15832e11i	−0.656945	−	0.656945i
$649$	−6.81890e10	+	6.81890e10i	−0.384357	+	0.384357i
$650$		−	1.97936e11i		−	1.10884i
$651$	9.69308e8	+	9.69308e8i	0.00539682	+	0.00539682i
$652$	−3.36842e10	−	3.36842e10i	−0.186395	−	0.186395i
$653$	−1.24179e11	+	1.24179e11i	−0.682958	+	0.682958i	−0.960666	−	0.277708i	$-0.910425\pi$
$653$	−1.24179e11	+	1.24179e11i	−0.682958	+	0.682958i	0.277708	+	0.960666i	$0.410425\pi$
$654$			1.18121e9i			0.00645679i
$655$	−4.00294e8			−0.00217477
$656$			1.32481e10i			0.0715383i
$657$		−	3.11920e10i		−	0.167410i
$658$	2.93313e9	−	2.93313e9i	0.0156469	−	0.0156469i
$659$		−	1.80661e11i		−	0.957903i	−0.877841	−	0.478952i	$-0.841017\pi$
$659$		−	1.80661e11i		−	0.957903i	0.877841	−	0.478952i	$-0.158983\pi$
$660$	−8.84290e9	+	8.84290e9i	−0.0466035	+	0.0466035i
$661$	−6.88448e10	+	6.88448e10i	−0.360633	+	0.360633i	−0.864046	−	0.503413i	$-0.832077\pi$
$661$	−6.88448e10	+	6.88448e10i	−0.360633	+	0.360633i	0.503413	+	0.864046i	$0.332077\pi$
$662$	−1.10420e11			−0.574931
$663$	−2.68641e10			−0.139033
$664$	2.18761e11	+	2.18761e11i	1.12538	+	1.12538i
$665$		−	1.71269e11i		−	0.875772i
$666$	5.34912e10	+	9.67335e10i	0.271885	+	0.491677i
$667$	3.62824e11			1.83313
$668$	5.80367e10	−	5.80367e10i	0.291472	−	0.291472i
$669$		−	1.52610e10i		−	0.0761866i
$670$		−	2.44455e11i		−	1.21311i
$671$	−3.61328e10	−	3.61328e10i	−0.178243	−	0.178243i
$672$	1.03305e10	+	1.03305e10i	0.0506576	+	0.0506576i
$673$	6.21067e10			0.302746			0.151373	−	0.988477i	$-0.451631\pi$
$673$	6.21067e10			0.302746			0.151373	+	0.988477i	$0.451631\pi$
$674$	7.48425e10	+	7.48425e10i	0.362668	+	0.362668i
$675$	−7.47475e10			−0.360065
$676$	1.41823e10			0.0679141
$677$		−	2.14203e11i		−	1.01970i	−0.860264	−	0.509848i	$-0.829702\pi$
$677$		−	2.14203e11i		−	1.01970i	0.860264	−	0.509848i	$-0.170298\pi$
$678$	−1.60229e10			−0.0758268
$679$	6.47884e10	+	6.47884e10i	0.304802	+	0.304802i
$680$	4.21269e11	−	4.21269e11i	1.97026	−	1.97026i
$681$	1.62002e10	−	1.62002e10i	0.0753237	−	0.0753237i
$682$	8.51365e9			0.0393530
$683$	−1.10315e11	−	1.10315e11i	−0.506936	−	0.506936i	0.406648	−	0.913585i	$-0.366697\pi$
$683$	−1.10315e11	−	1.10315e11i	−0.506936	−	0.506936i	−0.913585	+	0.406648i	$0.866697\pi$
$684$	6.57607e10	−	6.57607e10i	0.300429	−	0.300429i
$685$	1.13109e11	+	1.13109e11i	0.513729	+	0.513729i
$686$	9.64133e10	−	9.64133e10i	0.435352	−	0.435352i
$687$		−	6.98278e9i		−	0.0313474i
$688$	2.97015e10	+	2.97015e10i	0.132564	+	0.132564i
$689$	1.10949e11	+	1.10949e11i	0.492318	+	0.492318i
$690$	−1.93393e10	+	1.93393e10i	−0.0853189	+	0.0853189i
$691$		−	5.26263e10i		−	0.230829i	−0.993317	−	0.115414i	$-0.963180\pi$
$691$		−	5.26263e10i		−	0.230829i	0.993317	−	0.115414i	$-0.0368196\pi$
$692$	2.96905e11			1.29477
$693$		−	1.15012e11i		−	0.498667i
$694$			1.49610e11i			0.644947i
$695$	−4.92080e11	+	4.92080e11i	−2.10910	+	2.10910i
$696$			2.57507e10i			0.109737i
$697$	1.41665e11	−	1.41665e11i	0.600249	−	0.600249i
$698$	4.38939e10	−	4.38939e10i	0.184920	−	0.184920i
$699$	−2.24617e10			−0.0940878
$700$	−2.67360e11			−1.11354
$701$	2.25560e11	+	2.25560e11i	0.934093	+	0.934093i	0.997959	−	0.0638656i	$-0.0203429\pi$
$701$	2.25560e11	+	2.25560e11i	0.934093	+	0.934093i	−0.0638656	+	0.997959i	$0.520343\pi$
$702$		−	2.27529e10i		−	0.0936888i
$703$	−1.34690e11	+	7.44802e10i	−0.551460	+	0.304943i
$704$	6.88015e10			0.280096
$705$	1.31783e9	−	1.31783e9i	0.00533462	−	0.00533462i
$706$		−	1.44480e11i		−	0.581551i
$707$		−	2.57918e11i		−	1.03230i
$708$	9.07561e9	+	9.07561e9i	0.0361196	+	0.0361196i
$709$	−3.22384e11	−	3.22384e11i	−1.27582	−	1.27582i	−0.942988	−	0.332828i	$-0.891997\pi$
$709$	−3.22384e11	−	3.22384e11i	−1.27582	−	1.27582i	−0.332828	−	0.942988i	$-0.608003\pi$
$710$	−3.00105e11			−1.18097
$711$	−9.83934e10	−	9.83934e10i	−0.385024	−	0.385024i
$712$	1.28002e10			0.0498077
$713$	−3.94638e10			−0.152701
$714$		−	1.71202e10i		−	0.0658743i
$715$	2.74728e11			1.05119
$716$	2.23460e11	+	2.23460e11i	0.850251	+	0.850251i
$717$	−1.25085e10	+	1.25085e10i	−0.0473290	+	0.0473290i
$718$	−2.28459e10	+	2.28459e10i	−0.0859630	+	0.0859630i
$719$	4.57179e10			0.171069			0.0855344	−	0.996335i	$-0.472740\pi$
$719$	4.57179e10			0.171069			0.0855344	+	0.996335i	$0.472740\pi$
$720$	−4.65676e10	−	4.65676e10i	−0.173282	−	0.173282i
$721$	−1.00973e11	+	1.00973e11i	−0.373650	+	0.373650i
$722$	6.55898e10	+	6.55898e10i	0.241372	+	0.241372i
$723$	2.56618e9	−	2.56618e9i	0.00939149	−	0.00939149i
$724$			5.56992e10i			0.202719i
$725$	−5.31635e11	−	5.31635e11i	−1.92425	−	1.92425i
$726$	−5.83593e9	−	5.83593e9i	−0.0210070	−	0.0210070i
$727$	−2.72945e11	+	2.72945e11i	−0.977098	+	0.977098i	−0.999744	−	0.0226459i	$-0.992791\pi$
$727$	−2.72945e11	+	2.72945e11i	−0.977098	+	0.977098i	0.0226459	+	0.999744i	$0.492791\pi$
$728$		−	2.01164e11i		−	0.716185i
$729$	2.69525e11			0.954307
$730$			4.74832e10i			0.167205i
$731$		−	6.35209e11i		−	2.22458i
$732$	−4.80910e9	+	4.80910e9i	−0.0167502	+	0.0167502i
$733$			1.23148e11i			0.426591i	0.976988	+	0.213296i	$0.0684197\pi$
$733$			1.23148e11i			0.426591i	−0.976988	+	0.213296i	$0.931580\pi$
$734$	−7.55524e10	+	7.55524e10i	−0.260294	+	0.260294i
$735$	1.16921e10	−	1.16921e10i	0.0400629	−	0.0400629i
$736$	−4.20590e11			−1.43333
$737$	2.28572e11			0.774735
$738$	5.97617e10	+	5.97617e10i	0.201464	+	0.201464i
$739$			2.49316e11i			0.835935i	0.908462	+	0.417967i	$0.137257\pi$
$739$			2.49316e11i			0.835935i	−0.908462	+	0.417967i	$0.862743\pi$
$740$	1.72590e11	+	3.12112e11i	0.575557	+	1.04084i
$741$	1.57794e10			0.0523381
$742$	−7.07064e10	+	7.07064e10i	−0.233262	+	0.233262i
$743$		−	3.45674e11i		−	1.13426i	−0.823629	−	0.567128i	$-0.808054\pi$
$743$		−	3.45674e11i		−	1.13426i	0.823629	−	0.567128i	$-0.191946\pi$
$744$		−	2.80086e9i		−	0.00914113i
$745$	3.27552e11	+	3.27552e11i	1.06330	+	1.06330i
$746$	1.20130e11	+	1.20130e11i	0.387879	+	0.387879i
$747$	−5.17170e11			−1.66093
$748$	1.59356e11	+	1.59356e11i	0.509053	+	0.509053i
$749$	4.67788e11			1.48635
$750$	2.92206e10			0.0923516
$751$			5.60956e11i			1.76347i	0.471742	+	0.881736i	$0.343625\pi$
$751$			5.60956e11i			1.76347i	−0.471742	+	0.881736i	$0.656375\pi$
$752$	2.22088e9			0.00694472
$753$	3.16618e10	+	3.16618e10i	0.0984818	+	0.0984818i
$754$	1.61828e11	−	1.61828e11i	0.500689	−	0.500689i
$755$	−5.74056e11	+	5.74056e11i	−1.76672	+	1.76672i
$756$	−3.07333e10			−0.0940853
$757$	1.26208e10	+	1.26208e10i	0.0384331	+	0.0384331i	0.726062	−	0.687629i	$-0.241348\pi$
$757$	1.26208e10	+	1.26208e10i	0.0384331	+	0.0384331i	−0.687629	+	0.726062i	$0.741348\pi$
$758$	−1.68694e11	+	1.68694e11i	−0.511001	+	0.511001i
$759$	−1.80828e10	−	1.80828e10i	−0.0544877	−	0.0544877i
$760$	−2.47445e11	+	2.47445e11i	−0.741692	+	0.741692i
$761$		−	2.95266e10i		−	0.0880390i	−0.999031	−	0.0440195i	$-0.985984\pi$
$761$		−	2.95266e10i		−	0.0880390i	0.999031	−	0.0440195i	$-0.0140164\pi$
$762$	4.01773e9	+	4.01773e9i	0.0119168	+	0.0119168i
$763$	−2.47845e10	−	2.47845e10i	−0.0731276	−	0.0731276i
$764$	−6.76678e10	+	6.76678e10i	−0.198613	+	0.198613i
$765$			9.95916e11i			2.90788i
$766$	−1.67829e10			−0.0487474
$767$		−	2.81958e11i		−	0.814710i
$768$		−	2.69312e10i		−	0.0774126i
$769$	2.65238e11	−	2.65238e11i	0.758456	−	0.758456i	−0.217585	−	0.976041i	$-0.569818\pi$
$769$	2.65238e11	−	2.65238e11i	0.758456	−	0.758456i	0.976041	+	0.217585i	$0.0698181\pi$
$770$			1.75081e11i			0.498055i
$771$	7.60718e8	−	7.60718e8i	0.00215281	−	0.00215281i
$772$	1.40199e11	−	1.40199e11i	0.394708	−	0.394708i
$773$	−4.11790e11			−1.15334			−0.576670	−	0.816977i	$-0.695648\pi$
$773$	−4.11790e11			−1.15334			−0.576670	+	0.816977i	$0.695648\pi$
$774$	2.67964e11			0.746643
$775$	5.78251e10	+	5.78251e10i	0.160291	+	0.160291i
$776$		−	1.87209e11i		−	0.516274i
$777$	2.43449e10	+	7.00771e9i	0.0667919	+	0.0192261i
$778$	−1.21667e11			−0.332089
$779$	−8.32111e10	+	8.32111e10i	−0.225960	+	0.225960i
$780$		−	3.65650e10i		−	0.0987840i
$781$		−	2.80606e11i		−	0.754211i
$782$	3.48511e11	+	3.48511e11i	0.931942	+	0.931942i
$783$	−6.11120e10	−	6.11120e10i	−0.162584	−	0.162584i
$784$	1.97041e10			0.0521546
$785$	−8.12209e11	−	8.12209e11i	−2.13889	−	2.13889i
$786$	2.35033e7			6.15799e−5
$787$	4.06229e11			1.05894			0.529471	−	0.848328i	$-0.322391\pi$
$787$	4.06229e11			1.05894			0.529471	+	0.848328i	$0.322391\pi$
$788$		−	3.52429e11i		−	0.914044i
$789$	−5.40323e9			−0.0139426
$790$	1.49783e11	+	1.49783e11i	0.384551	+	0.384551i
$791$	3.36197e11	−	3.36197e11i	0.858791	−	0.858791i
$792$	−1.66167e11	+	1.66167e11i	−0.422321	+	0.422321i
$793$	1.49408e11			0.377816
$794$	−3.99133e10	−	3.99133e10i	−0.100423	−	0.100423i
$795$	−3.17679e10	+	3.17679e10i	−0.0795279	+	0.0795279i
$796$	−2.06097e11	−	2.06097e11i	−0.513356	−	0.513356i
$797$	2.75650e10	−	2.75650e10i	0.0683164	−	0.0683164i	−0.672123	−	0.740439i	$-0.734617\pi$
$797$	2.75650e10	−	2.75650e10i	0.0683164	−	0.0683164i	0.740439	+	0.672123i	$0.234617\pi$
$798$			1.00560e10i			0.0247980i
$799$	−2.37484e10	−	2.37484e10i	−0.0582704	−	0.0582704i
$800$	6.16278e11	+	6.16278e11i	1.50458	+	1.50458i
$801$	−1.51304e10	+	1.51304e10i	−0.0367553	+	0.0367553i
$802$		−	3.46200e11i		−	0.836815i
$803$	−4.43981e10			−0.106783
$804$		−	3.04218e10i		−	0.0728049i
$805$		−	8.11565e11i		−	1.93259i
$806$	−1.76018e10	+	1.76018e10i	−0.0417077	+	0.0417077i
$807$			3.35527e10i			0.0791105i
$808$	−3.72634e11	+	3.72634e11i	−0.874253	+	0.874253i
$809$	−7.06285e10	+	7.06285e10i	−0.164887	+	0.164887i	−0.784728	−	0.619841i	$-0.787197\pi$
$809$	−7.06285e10	+	7.06285e10i	−0.164887	+	0.164887i	0.619841	+	0.784728i	$0.287197\pi$
$810$	−4.16859e11			−0.968387
$811$	−8.55608e10			−0.197784			−0.0988921	−	0.995098i	$-0.531530\pi$
$811$	−8.55608e10			−0.197784			−0.0988921	+	0.995098i	$0.531530\pi$
$812$	−2.18588e11	−	2.18588e11i	−0.502808	−	0.502808i
$813$			2.12866e10i			0.0487241i
$814$	1.37689e11	−	7.61383e10i	0.313617	−	0.173422i
$815$	−2.99640e11			−0.679156
$816$	6.48147e9	−	6.48147e9i	0.0146188	−	0.0146188i
$817$			3.73109e11i			0.837428i
$818$			9.38061e9i			0.0209516i
$819$	2.37785e11	+	2.37785e11i	0.528504	+	0.528504i
$820$	1.92822e11	+	1.92822e11i	0.426481	+	0.426481i
$821$	−3.94886e10			−0.0869158			−0.0434579	−	0.999055i	$-0.513837\pi$
$821$	−3.94886e10			−0.0869158			−0.0434579	+	0.999055i	$0.513837\pi$
$822$	−6.64120e9	−	6.64120e9i	−0.0145465	−	0.0145465i
$823$	5.52596e10			0.120451			0.0602253	−	0.998185i	$-0.480818\pi$
$823$	5.52596e10			0.120451			0.0602253	+	0.998185i	$0.480818\pi$
$824$	2.91767e11			0.632888
$825$			5.29924e10i			0.114393i
$826$	1.79689e11			0.386012
$827$	6.42875e11	+	6.42875e11i	1.37437	+	1.37437i	0.853844	+	0.520529i	$0.174265\pi$
$827$	6.42875e11	+	6.42875e11i	1.37437	+	1.37437i	0.520529	+	0.853844i	$0.325735\pi$
$828$	3.11611e11	−	3.11611e11i	0.662965	−	0.662965i
$829$	−2.63158e11	+	2.63158e11i	−0.557183	+	0.557183i	−0.928505	−	0.371321i	$-0.878905\pi$
$829$	−2.63158e11	+	2.63158e11i	−0.557183	+	0.557183i	0.371321	+	0.928505i	$0.378905\pi$
$830$	7.87281e11			1.65889
$831$	8.22101e9	+	8.22101e9i	0.0172394	+	0.0172394i
$832$	−1.42245e11	+	1.42245e11i	−0.296856	+	0.296856i
$833$	−2.10701e11	−	2.10701e11i	−0.437609	−	0.437609i
$834$	2.88925e10	−	2.88925e10i	0.0597202	−	0.0597202i
$835$		−	5.16271e11i		−	1.06202i
$836$	−9.36026e10	−	9.36026e10i	−0.191630	−	0.191630i
$837$	6.64705e9	+	6.64705e9i	0.0135434	+	0.0135434i
$838$	−3.70599e11	+	3.70599e11i	−0.751498	+	0.751498i
$839$			6.48815e11i			1.30940i	0.755888	+	0.654701i	$0.227206\pi$
$839$			6.48815e11i			1.30940i	−0.755888	+	0.654701i	$0.772794\pi$
$840$	5.75992e10			0.115691
$841$		−	3.69061e11i		−	0.737759i
$842$		−	1.71699e11i		−	0.341602i
$843$	3.10663e10	−	3.10663e10i	0.0615147	−	0.0615147i
$844$			1.08738e11i			0.214296i
$845$	6.30799e10	−	6.30799e10i	0.123727	−	0.123727i
$846$	1.00183e10	−	1.00183e10i	0.0195575	−	0.0195575i
$847$	2.44902e11			0.475837
$848$	−5.35369e10			−0.103531
$849$	1.43099e10	+	1.43099e10i	0.0275426	+	0.0275426i
$850$		−	1.02132e12i		−	1.95654i
$851$	−6.38236e11	+	3.52928e11i	−1.21692	+	0.672927i
$852$	−3.73473e10			−0.0708762
$853$	5.19629e11	−	5.19629e11i	0.981516	−	0.981516i	−0.0183160	−	0.999832i	$-0.505830\pi$
$853$	5.19629e11	−	5.19629e11i	0.981516	−	0.981516i	0.999832	+	0.0183160i	$0.00583048\pi$
$854$			9.52158e10i			0.179010i
$855$		−	5.84980e11i		−	1.09465i
$856$	−6.75849e11	−	6.75849e11i	−1.25879	−	1.25879i
$857$	−3.30937e11	−	3.30937e11i	−0.613511	−	0.613511i	0.330348	−	0.943859i	$-0.392834\pi$
$857$	−3.30937e11	−	3.30937e11i	−0.613511	−	0.613511i	−0.943859	+	0.330348i	$0.892834\pi$
$858$	−1.61307e10			−0.0297649
$859$	−2.42533e11	−	2.42533e11i	−0.445449	−	0.445449i	0.448390	−	0.893838i	$-0.351998\pi$
$859$	−2.42533e11	−	2.42533e11i	−0.445449	−	0.445449i	−0.893838	+	0.448390i	$0.851998\pi$
$860$	8.64589e11			1.58058
$861$	1.93696e10			0.0352458
$862$			6.26069e10i			0.113395i
$863$	−2.92759e11			−0.527797			−0.263898	−	0.964551i	$-0.585008\pi$
$863$	−2.92759e11			−0.527797			−0.263898	+	0.964551i	$0.585008\pi$
$864$	7.08417e10	+	7.08417e10i	0.127126	+	0.127126i
$865$	1.32057e12	−	1.32057e12i	2.35883	−	2.35883i
$866$	−5.97011e10	+	5.97011e10i	−0.106148	+	0.106148i
$867$	−8.91489e10			−0.157776
$868$	2.37755e10	+	2.37755e10i	0.0418842	+	0.0418842i
$869$	−1.40051e11	+	1.40051e11i	−0.245588	+	0.245588i
$870$	4.63360e10	+	4.63360e10i	0.0808801	+	0.0808801i
$871$	−4.72568e11	+	4.72568e11i	−0.821091	+	0.821091i
$872$			7.16159e10i			0.123864i
$873$	2.21289e11	+	2.21289e11i	0.380981	+	0.380981i
$874$	−2.04708e11	−	2.04708e11i	−0.350824	−	0.350824i
$875$	−6.13114e11	+	6.13114e11i	−1.04594	+	1.04594i
$876$			5.90917e9i			0.0100348i
$877$	−6.53368e11			−1.10448			−0.552242	−	0.833684i	$-0.686228\pi$
$877$	−6.53368e11			−1.10448			−0.552242	+	0.833684i	$0.686228\pi$
$878$		−	6.36280e10i		−	0.107071i
$879$			7.86994e10i			0.131830i
$880$	−6.62834e10	+	6.62834e10i	−0.110528	+	0.110528i
$881$			4.59771e11i			0.763199i	0.924328	+	0.381600i	$0.124627\pi$
$881$			4.59771e11i			0.763199i	−0.924328	+	0.381600i	$0.875373\pi$
$882$	8.88845e10	−	8.88845e10i	0.146876	−	0.146876i
$883$	−5.44762e10	+	5.44762e10i	−0.0896115	+	0.0896115i	−0.750492	−	0.660880i	$-0.770183\pi$
$883$	−5.44762e10	+	5.44762e10i	−0.0896115	+	0.0896115i	0.660880	+	0.750492i	$0.270183\pi$
$884$	−6.58931e11			−1.07902
$885$	8.07328e10			0.131606
$886$	3.20451e11	+	3.20451e11i	0.520028	+	0.520028i
$887$		−	2.44416e11i		−	0.394853i	−0.980318	−	0.197427i	$-0.936742\pi$
$887$		−	2.44416e11i		−	0.394853i	0.980318	−	0.197427i	$-0.0632584\pi$
$888$	−2.50483e10	−	4.52975e10i	−0.0402835	−	0.0728487i
$889$	−1.68602e11			−0.269932
$890$	2.30328e10	−	2.30328e10i	0.0367101	−	0.0367101i
$891$		−	3.89775e11i		−	0.618447i
$892$		−	3.74327e11i		−	0.591277i
$893$	1.39493e10	+	1.39493e10i	0.0219355	+	0.0219355i
$894$	−1.92322e10	−	1.92322e10i	−0.0301078	−	0.0301078i
$895$	1.98780e12			3.09800
$896$	2.82289e11	+	2.82289e11i	0.437988	+	0.437988i
$897$	7.47715e10			0.115496
$898$	−1.14415e11			−0.175945
$899$			9.45532e10i			0.144756i
$900$	−9.13188e11			−1.39184
$901$	5.72483e11	+	5.72483e11i	0.868687	+	0.868687i
$902$	8.50636e10	−	8.50636e10i	0.128504	−	0.128504i
$903$	4.34254e10	−	4.34254e10i	0.0653120	−	0.0653120i
$904$	−9.71457e11			−1.45462
$905$	2.47738e11	+	2.47738e11i	0.369317	+	0.369317i
$906$	3.37058e10	−	3.37058e10i	0.0500255	−	0.0500255i
$907$	3.55330e11	+	3.55330e11i	0.525052	+	0.525052i	0.919093	−	0.394041i	$-0.128923\pi$
$907$	3.55330e11	+	3.55330e11i	0.525052	+	0.525052i	−0.394041	+	0.919093i	$0.628923\pi$
$908$	3.97363e11	−	3.97363e11i	0.584580	−	0.584580i
$909$		−	8.80939e11i		−	1.29030i
$910$	−3.61977e11	−	3.61977e11i	−0.527856	−	0.527856i
$911$	−9.67356e10	−	9.67356e10i	−0.140447	−	0.140447i	0.633388	−	0.773835i	$-0.281664\pi$
$911$	−9.67356e10	−	9.67356e10i	−0.140447	−	0.140447i	−0.773835	+	0.633388i	$0.781664\pi$
$912$	−3.80708e9	+	3.80708e9i	−0.00550317	+	0.00550317i
$913$			7.36129e11i			1.05943i
$914$	1.11069e11			0.159151
$915$			4.27797e10i			0.0610315i
$916$		−	1.71276e11i		−	0.243284i
$917$	−4.93152e8	+	4.93152e8i	−0.000697434	+	0.000697434i
$918$		−	1.17402e11i		−	0.165312i
$919$	−4.48023e11	+	4.48023e11i	−0.628114	+	0.628114i	−0.947593	−	0.319480i	$-0.896492\pi$
$919$	−4.48023e11	+	4.48023e11i	−0.628114	+	0.628114i	0.319480	+	0.947593i	$0.396492\pi$
$920$	−1.17253e12	+	1.17253e12i	−1.63671	+	1.63671i
$921$	1.09794e10			0.0152596
$922$	−3.04294e11			−0.421085
$923$	5.80146e11	+	5.80146e11i	0.799339	+	0.799339i
$924$			2.17884e10i			0.0298908i
$925$	1.45232e12	+	4.18053e11i	1.98379	+	0.571037i
$926$	1.54002e11			0.209451
$927$	−3.44881e11	+	3.44881e11i	−0.467036	+	0.467036i
$928$			1.00771e12i			1.35876i
$929$		−	1.67053e11i		−	0.224281i	−0.993692	−	0.112140i	$-0.964229\pi$
$929$		−	1.67053e11i		−	0.224281i	0.993692	−	0.112140i	$-0.0357706\pi$
$930$	−5.03990e9	−	5.03990e9i	−0.00673736	−	0.00673736i
$931$	1.23761e11	+	1.23761e11i	0.164735	+	0.164735i
$932$	−5.50946e11			−0.730206
$933$	−9.16074e10	−	9.16074e10i	−0.120894	−	0.120894i
$934$	5.84510e11			0.768077
$935$	1.41757e12			1.85480
$936$		−	6.87091e11i		−	0.895181i
$937$	−1.36147e12			−1.76624			−0.883122	−	0.469143i	$-0.844563\pi$
$937$	−1.36147e12			−1.76624			−0.883122	+	0.469143i	$0.844563\pi$
$938$	−3.01162e11	−	3.01162e11i	−0.389035	−	0.389035i
$939$	−2.72903e10	+	2.72903e10i	−0.0351032	+	0.0351032i
$940$	3.23242e10	−	3.23242e10i	0.0414015	−	0.0414015i
$941$	6.08714e11			0.776345			0.388173	−	0.921587i	$-0.373106\pi$
$941$	6.08714e11			0.776345			0.388173	+	0.921587i	$0.373106\pi$
$942$	4.76889e10	+	4.76889e10i	0.0605639	+	0.0605639i
$943$	−3.94300e11	+	3.94300e11i	−0.498632	+	0.498632i
$944$	6.80277e10	+	6.80277e10i	0.0856639	+	0.0856639i
$945$	−1.36695e11	+	1.36695e11i	−0.171406	+	0.171406i
$946$		−	3.81415e11i		−	0.476248i
$947$	−6.86601e11	−	6.86601e11i	−0.853699	−	0.853699i	0.136888	−	0.990587i	$-0.456290\pi$
$947$	−6.86601e11	−	6.86601e11i	−0.853699	−	0.853699i	−0.990587	+	0.136888i	$0.956290\pi$
$948$	1.86401e10	+	1.86401e10i	0.0230789	+	0.0230789i
$949$	9.17921e10	−	9.17921e10i	0.113172	−	0.113172i
$950$			5.99905e11i			0.736526i
$951$	−6.98447e10			−0.0853909
$952$		−	1.03798e12i		−	1.26370i
$953$		−	1.00418e12i		−	1.21742i	−0.793394	−	0.608709i	$-0.791688\pi$
$953$		−	1.00418e12i		−	1.21742i	0.793394	−	0.608709i	$-0.208312\pi$
$954$	−2.41503e11	+	2.41503e11i	−0.291561	+	0.291561i
$955$			6.01945e11i			0.723674i
$956$	−3.06811e11	+	3.06811e11i	−0.367316	+	0.367316i
$957$	−4.33255e10	+	4.33255e10i	−0.0516530	+	0.0516530i
$958$	−2.95232e11			−0.350510
$959$	2.78694e11			0.329499
$960$	−4.07290e10	−	4.07290e10i	−0.0479534	−	0.0479534i
$961$			8.42607e11i			0.987942i
$962$	−1.27254e11	+	4.42082e11i	−0.148583	+	0.516182i
$963$	1.59776e12			1.85784
$964$	6.29441e10	−	6.29441e10i	0.0728865	−	0.0728865i
$965$		−	1.24715e12i		−	1.43817i
$966$			4.76511e10i			0.0547223i
$967$	7.35723e11	+	7.35723e11i	0.841412	+	0.841412i	0.989043	−	0.147631i	$-0.0471648\pi$
$967$	7.35723e11	+	7.35723e11i	0.841412	+	0.841412i	−0.147631	+	0.989043i	$0.547165\pi$
$968$	−3.53828e11	−	3.53828e11i	−0.402987	−	0.402987i
$969$	8.14200e10			0.0923498
$970$	−3.36866e11	−	3.36866e11i	−0.380514	−	0.380514i
$971$	−8.84040e11			−0.994477			−0.497239	−	0.867614i	$-0.665653\pi$
$971$	−8.84040e11			−0.994477			−0.497239	+	0.867614i	$0.665653\pi$
$972$	−1.57660e11			−0.176626
$973$			1.21246e12i			1.35274i
$974$	−8.70806e11			−0.967578
$975$	−1.09561e11	−	1.09561e11i	−0.121237	−	0.121237i
$976$	−3.60474e10	+	3.60474e10i	−0.0397260	+	0.0397260i
$977$	−9.87707e11	+	9.87707e11i	−1.08405	+	1.08405i	−0.0879239	+	0.996127i	$0.528023\pi$
$977$	−9.87707e11	+	9.87707e11i	−1.08405	+	1.08405i	−0.996127	+	0.0879239i	$0.971977\pi$
$978$	1.75934e10			0.0192307
$979$	2.15363e10	+	2.15363e10i	0.0234444	+	0.0234444i
$980$	2.86787e11	−	2.86787e11i	0.310924	−	0.310924i
$981$	−8.46531e10	−	8.46531e10i	−0.0914044	−	0.0914044i
$982$	3.11807e11	−	3.11807e11i	0.335304	−	0.335304i
$983$			1.76562e12i			1.89096i	0.325681	+	0.945480i	$0.394406\pi$
$983$			1.76562e12i			1.89096i	−0.325681	+	0.945480i	$0.605594\pi$
$984$	−2.79846e10	−	2.79846e10i	−0.0298496	−	0.0298496i
$985$	−1.56753e12	−	1.56753e12i	−1.66522	−	1.66522i
$986$	8.35013e11	−	8.35013e11i	0.883458	−	0.883458i
$987$		−	3.24707e9i		−	0.00342155i
$988$	3.87042e11			0.406191
$989$			1.76799e12i			1.84797i
$990$			5.98003e11i			0.622534i
$991$	−6.49399e11	+	6.49399e11i	−0.673313	+	0.673313i	−0.958478	−	0.285165i	$-0.907952\pi$
$991$	−6.49399e11	+	6.49399e11i	−0.673313	+	0.673313i	0.285165	+	0.958478i	$0.407952\pi$
$992$		−	1.09607e11i		−	0.113186i
$993$	−6.11193e10	+	6.11193e10i	−0.0628610	+	0.0628610i
$994$	−3.69721e11	+	3.69721e11i	−0.378729	+	0.378729i
$995$	−1.83335e12			−1.87048
$996$	9.79751e10			0.0995585
$997$	−4.83114e11	−	4.83114e11i	−0.488955	−	0.488955i	0.419022	−	0.907976i	$-0.362373\pi$
$997$	−4.83114e11	−	4.83114e11i	−0.488955	−	0.488955i	−0.907976	+	0.419022i	$0.862373\pi$
$998$		−	3.54722e11i		−	0.357574i
$999$	1.66946e11	+	4.80555e10i	0.167615	+	0.0482482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.10	✓	50
37.31	odd	4	inner	37.9.d.a.31.10	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.10	✓	50	1.1	even	1	trivial
37.9.d.a.31.10	yes	50	37.31	odd	4	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.40563 + 6.40563i) q^{2} +7.09124i q^{3} +173.936i q^{4} +(773.631 + 773.631i) q^{5} +(-45.4238 - 45.4238i) q^{6} +1906.19 q^{7} +(-2754.01 - 2754.01i) q^{8} +6510.71 q^{9} +O(q^{10})\)	\(q+(-6.40563 + 6.40563i) q^{2} +7.09124i q^{3} +173.936i q^{4} +(773.631 + 773.631i) q^{5} +(-45.4238 - 45.4238i) q^{6} +1906.19 q^{7} +(-2754.01 - 2754.01i) q^{8} +6510.71 q^{9} -9911.18 q^{10} -9267.22i q^{11} -1233.42 q^{12} +(19159.8 + 19159.8i) q^{13} +(-12210.3 + 12210.3i) q^{14} +(-5486.00 + 5486.00i) q^{15} -9245.30 q^{16} +(98862.2 + 98862.2i) q^{17} +(-41705.2 + 41705.2i) q^{18} +(-58069.6 - 58069.6i) q^{19} +(-134562. + 134562. i) q^{20} +13517.2i q^{21} +(59362.4 + 59362.4i) q^{22} +(-275166. - 275166. i) q^{23} +(19529.3 - 19529.3i) q^{24} +806384. i q^{25} -245461. q^{26} +92694.6i q^{27} +331554. i q^{28} +(-659283. + 659283. i) q^{29} -70282.5i q^{30} +(71709.1 - 71709.1i) q^{31} +(764248. - 764248. i) q^{32} +65716.1 q^{33} -1.26655e6 q^{34} +(1.47468e6 + 1.47468e6i) q^{35} +1.13245e6i q^{36} +(518429. - 1.80103e6i) q^{37} +743944. q^{38} +(-135866. + 135866. i) q^{39} -4.26117e6i q^{40} -1.43295e6i q^{41} +(-86586.2 - 86586.2i) q^{42} +(-3.21260e6 - 3.21260e6i) q^{43} +1.61190e6 q^{44} +(5.03689e6 + 5.03689e6i) q^{45} +3.52522e6 q^{46} -240217. q^{47} -65560.6i q^{48} -2.13126e6 q^{49} +(-5.16540e6 - 5.16540e6i) q^{50} +(-701055. + 701055. i) q^{51} +(-3.33257e6 + 3.33257e6i) q^{52} +5.79072e6 q^{53} +(-593767. - 593767. i) q^{54} +(7.16941e6 - 7.16941e6i) q^{55} +(-5.24965e6 - 5.24965e6i) q^{56} +(411785. - 411785. i) q^{57} -8.44624e6i q^{58} +(-7.35808e6 - 7.35808e6i) q^{59} +(-954212. - 954212. i) q^{60} +(3.89899e6 - 3.89899e6i) q^{61} +918684. i q^{62} +1.24106e7 q^{63} +7.42418e6i q^{64} +2.96452e7i q^{65} +(-420952. + 420952. i) q^{66} +2.46646e7i q^{67} +(-1.71957e7 + 1.71957e7i) q^{68} +(1.95126e6 - 1.95126e6i) q^{69} -1.88925e7 q^{70} +3.02794e7 q^{71} +(-1.79306e7 - 1.79306e7i) q^{72} -4.79088e6i q^{73} +(8.21587e6 + 1.48576e7i) q^{74} -5.71826e6 q^{75} +(1.01004e7 - 1.01004e7i) q^{76} -1.76650e7i q^{77} -1.74062e6i q^{78} +(-1.51125e7 - 1.51125e7i) q^{79} +(-7.15245e6 - 7.15245e6i) q^{80} +4.20595e7 q^{81} +(9.17897e6 + 9.17897e6i) q^{82} -7.94336e7 q^{83} -2.35113e6 q^{84} +1.52966e8i q^{85} +4.11574e7 q^{86} +(-4.67513e6 - 4.67513e6i) q^{87} +(-2.55220e7 + 2.55220e7i) q^{88} +(-2.32392e6 + 2.32392e6i) q^{89} -6.45289e7 q^{90} +(3.65221e7 + 3.65221e7i) q^{91} +(4.78612e7 - 4.78612e7i) q^{92} +(508506. + 508506. i) q^{93} +(1.53874e6 - 1.53874e6i) q^{94} -8.98489e7i q^{95} +(5.41946e6 + 5.41946e6i) q^{96} +(3.39885e7 + 3.39885e7i) q^{97} +(1.36520e7 - 1.36520e7i) q^{98} -6.03362e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Introduction

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