LMFDB - Embedded newform 37.9.d.a.6.11

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			6.11
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.51546 + 5.51546i) q^{2} -143.656i q^{3} +195.159i q^{4} +(357.883 + 357.883i) q^{5} +(792.331 + 792.331i) q^{6} -623.716 q^{7} +(-2488.35 - 2488.35i) q^{8} -14076.1 q^{9} +O(q^{10})$	\(q+(-5.51546 + 5.51546i) q^{2} -143.656i q^{3} +195.159i q^{4} +(357.883 + 357.883i) q^{5} +(792.331 + 792.331i) q^{6} -623.716 q^{7} +(-2488.35 - 2488.35i) q^{8} -14076.1 q^{9} -3947.78 q^{10} +11450.3i q^{11} +28035.9 q^{12} +(14875.2 + 14875.2i) q^{13} +(3440.08 - 3440.08i) q^{14} +(51412.1 - 51412.1i) q^{15} -22512.0 q^{16} +(9389.60 + 9389.60i) q^{17} +(77636.3 - 77636.3i) q^{18} +(151804. + 151804. i) q^{19} +(-69844.2 + 69844.2i) q^{20} +89600.7i q^{21} +(-63153.8 - 63153.8i) q^{22} +(289500. + 289500. i) q^{23} +(-357467. + 357467. i) q^{24} -134465. i q^{25} -164087. q^{26} +1.07959e6i q^{27} -121724. i q^{28} +(38945.2 - 38945.2i) q^{29} +567123. i q^{30} +(-559835. + 559835. i) q^{31} +(761182. - 761182. i) q^{32} +1.64491e6 q^{33} -103576. q^{34} +(-223217. - 223217. i) q^{35} -2.74709e6i q^{36} +(1.79795e6 - 529010. i) q^{37} -1.67453e6 q^{38} +(2.13691e6 - 2.13691e6i) q^{39} -1.78108e6i q^{40} +4.22428e6i q^{41} +(-494189. - 494189. i) q^{42} +(864201. + 864201. i) q^{43} -2.23464e6 q^{44} +(-5.03760e6 - 5.03760e6i) q^{45} -3.19345e6 q^{46} +506194. q^{47} +3.23399e6i q^{48} -5.37578e6 q^{49} +(741634. + 741634. i) q^{50} +(1.34887e6 - 1.34887e6i) q^{51} +(-2.90303e6 + 2.90303e6i) q^{52} -6.50047e6 q^{53} +(-5.95446e6 - 5.95446e6i) q^{54} +(-4.09787e6 + 4.09787e6i) q^{55} +(1.55203e6 + 1.55203e6i) q^{56} +(2.18075e7 - 2.18075e7i) q^{57} +429601. i q^{58} +(400903. + 400903. i) q^{59} +(1.00336e7 + 1.00336e7i) q^{60} +(-4.01240e6 + 4.01240e6i) q^{61} -6.17549e6i q^{62} +8.77950e6 q^{63} +2.63348e6i q^{64} +1.06471e7i q^{65} +(-9.07243e6 + 9.07243e6i) q^{66} -2.61978e7i q^{67} +(-1.83247e6 + 1.83247e6i) q^{68} +(4.15884e7 - 4.15884e7i) q^{69} +2.46229e6 q^{70} -4.54274e7 q^{71} +(3.50263e7 + 3.50263e7i) q^{72} +4.65495e7i q^{73} +(-6.99879e6 + 1.28343e7i) q^{74} -1.93167e7 q^{75} +(-2.96259e7 + 2.96259e7i) q^{76} -7.14175e6i q^{77} +2.35721e7i q^{78} +(2.23071e7 + 2.23071e7i) q^{79} +(-8.05665e6 - 8.05665e6i) q^{80} +6.27369e7 q^{81} +(-2.32988e7 - 2.32988e7i) q^{82} -2.48914e7 q^{83} -1.74864e7 q^{84} +6.72075e6i q^{85} -9.53293e6 q^{86} +(-5.59472e6 - 5.59472e6i) q^{87} +(2.84924e7 - 2.84924e7i) q^{88} +(6.18244e7 - 6.18244e7i) q^{89} +5.55694e7 q^{90} +(-9.27788e6 - 9.27788e6i) q^{91} +(-5.64986e7 + 5.64986e7i) q^{92} +(8.04237e7 + 8.04237e7i) q^{93} +(-2.79189e6 + 2.79189e6i) q^{94} +1.08656e8i q^{95} +(-1.09349e8 - 1.09349e8i) q^{96} +(8.56145e7 + 8.56145e7i) q^{97} +(2.96499e7 - 2.96499e7i) q^{98} -1.61176e8i 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 $

$2$	−5.51546	+	5.51546i	−0.344716	+	0.344716i	−0.858137	−	0.513421i	$-0.828378\pi$
$2$	−5.51546	+	5.51546i	−0.344716	+	0.344716i	0.513421	+	0.858137i	$0.328378\pi$
$3$		−	143.656i		−	1.77353i	−0.462217	−	0.886767i	$-0.652946\pi$
$3$		−	143.656i		−	1.77353i	0.462217	−	0.886767i	$-0.347054\pi$
$4$			195.159i			0.762341i
$5$	357.883	+	357.883i	0.572613	+	0.572613i	0.932858	−	0.360245i	$-0.117307\pi$
$5$	357.883	+	357.883i	0.572613	+	0.572613i	−0.360245	+	0.932858i	$0.617307\pi$
$6$	792.331	+	792.331i	0.611366	+	0.611366i
$7$	−623.716			−0.259773			−0.129887	−	0.991529i	$-0.541461\pi$
$7$	−623.716			−0.259773			−0.129887	+	0.991529i	$0.541461\pi$
$8$	−2488.35	−	2488.35i	−0.607508	−	0.607508i
$9$	−14076.1			−2.14542
$10$	−3947.78			−0.394778
$11$			11450.3i			0.782072i	0.920375	+	0.391036i	$0.127883\pi$
$11$			11450.3i			0.782072i	−0.920375	+	0.391036i	$0.872117\pi$
$12$	28035.9			1.35204
$13$	14875.2	+	14875.2i	0.520821	+	0.520821i	0.917819	−	0.396999i	$-0.129948\pi$
$13$	14875.2	+	14875.2i	0.520821	+	0.520821i	−0.396999	+	0.917819i	$0.629948\pi$
$14$	3440.08	−	3440.08i	0.0895482	−	0.0895482i
$15$	51412.1	−	51412.1i	1.01555	−	1.01555i
$16$	−22512.0			−0.343505
$17$	9389.60	+	9389.60i	0.112422	+	0.112422i	0.761080	−	0.648658i	$-0.224669\pi$
$17$	9389.60	+	9389.60i	0.112422	+	0.112422i	−0.648658	+	0.761080i	$0.724669\pi$
$18$	77636.3	−	77636.3i	0.739562	−	0.739562i
$19$	151804.	+	151804.i	1.16484	+	1.16484i	0.983402	+	0.181441i	$0.0580762\pi$
$19$	151804.	+	151804.i	1.16484	+	1.16484i	0.181441	+	0.983402i	$0.441924\pi$
$20$	−69844.2	+	69844.2i	−0.436526	+	0.436526i
$21$			89600.7i			0.460717i
$22$	−63153.8	−	63153.8i	−0.269593	−	0.269593i
$23$	289500.	+	289500.i	1.03451	+	1.03451i	0.999383	+	0.0351322i	$0.0111852\pi$
$23$	289500.	+	289500.i	1.03451	+	1.03451i	0.0351322	+	0.999383i	$0.488815\pi$
$24$	−357467.	+	357467.i	−1.07744	+	1.07744i
$25$		−	134465.i		−	0.344229i
$26$	−164087.			−0.359071
$27$			1.07959e6i			2.03145i
$28$		−	121724.i		−	0.198036i
$29$	38945.2	−	38945.2i	0.0550632	−	0.0550632i	−0.679039	−	0.734102i	$-0.737603\pi$
$29$	38945.2	−	38945.2i	0.0550632	−	0.0550632i	0.734102	+	0.679039i	$0.237603\pi$
$30$			567123.i			0.700152i
$31$	−559835.	+	559835.i	−0.606196	+	0.606196i	−0.941950	−	0.335754i	$-0.891009\pi$
$31$	−559835.	+	559835.i	−0.606196	+	0.606196i	0.335754	+	0.941950i	$0.391009\pi$
$32$	761182.	−	761182.i	0.725920	−	0.725920i
$33$	1.64491e6			1.38703
$34$	−103576.			−0.0775074
$35$	−223217.	−	223217.i	−0.148750	−	0.148750i
$36$		−	2.74709e6i		−	1.63554i
$37$	1.79795e6	−	529010.i	0.959336	−	0.282265i
$37$	1.79795e6	−	529010.i	0.959336	−	0.282265i
$38$	−1.67453e6			−0.803081
$39$	2.13691e6	−	2.13691e6i	0.923693	−	0.923693i
$40$		−	1.78108e6i		−	0.695733i
$41$			4.22428e6i			1.49492i	0.664309	+	0.747458i	$0.268726\pi$
$41$			4.22428e6i			1.49492i	−0.664309	+	0.747458i	$0.731274\pi$
$42$	−494189.	−	494189.i	−0.158817	−	0.158817i
$43$	864201.	+	864201.i	0.252779	+	0.252779i	0.822109	−	0.569330i	$-0.192797\pi$
$43$	864201.	+	864201.i	0.252779	+	0.252779i	−0.569330	+	0.822109i	$0.692797\pi$
$44$	−2.23464e6			−0.596206
$45$	−5.03760e6	−	5.03760e6i	−1.22850	−	1.22850i
$46$	−3.19345e6			−0.713228
$47$	506194.			0.103735			0.0518675	−	0.998654i	$-0.483483\pi$
$47$	506194.			0.103735			0.0518675	+	0.998654i	$0.483483\pi$
$48$			3.23399e6i			0.609218i
$49$	−5.37578e6			−0.932518
$50$	741634.	+	741634.i	0.118662	+	0.118662i
$51$	1.34887e6	−	1.34887e6i	0.199384	−	0.199384i
$52$	−2.90303e6	+	2.90303e6i	−0.397043	+	0.397043i
$53$	−6.50047e6			−0.823836			−0.411918	−	0.911221i	$-0.635141\pi$
$53$	−6.50047e6			−0.823836			−0.411918	+	0.911221i	$0.635141\pi$
$54$	−5.95446e6	−	5.95446e6i	−0.700272	−	0.700272i
$55$	−4.09787e6	+	4.09787e6i	−0.447824	+	0.447824i
$56$	1.55203e6	+	1.55203e6i	0.157814	+	0.157814i
$57$	2.18075e7	−	2.18075e7i	2.06589	−	2.06589i
$58$			429601.i			0.0379624i
$59$	400903.	+	400903.i	0.0330850	+	0.0330850i	0.723456	−	0.690371i	$-0.242553\pi$
$59$	400903.	+	400903.i	0.0330850	+	0.0330850i	−0.690371	+	0.723456i	$0.742553\pi$
$60$	1.00336e7	+	1.00336e7i	0.774194	+	0.774194i
$61$	−4.01240e6	+	4.01240e6i	−0.289791	+	0.289791i	−0.836998	−	0.547207i	$-0.815691\pi$
$61$	−4.01240e6	+	4.01240e6i	−0.289791	+	0.289791i	0.547207	+	0.836998i	$0.315691\pi$
$62$		−	6.17549e6i		−	0.417931i
$63$	8.77950e6			0.557324
$64$			2.63348e6i			0.156967i
$65$			1.06471e7i			0.596457i
$66$	−9.07243e6	+	9.07243e6i	−0.478132	+	0.478132i
$67$		−	2.61978e7i		−	1.30007i	−0.759905	−	0.650034i	$-0.774754\pi$
$67$		−	2.61978e7i		−	1.30007i	0.759905	−	0.650034i	$-0.225246\pi$
$68$	−1.83247e6	+	1.83247e6i	−0.0857039	+	0.0857039i
$69$	4.15884e7	−	4.15884e7i	1.83475	−	1.83475i
$70$	2.46229e6			0.102553
$71$	−4.54274e7			−1.78766			−0.893829	−	0.448408i	$-0.851991\pi$
$71$	−4.54274e7			−1.78766			−0.893829	+	0.448408i	$0.851991\pi$
$72$	3.50263e7	+	3.50263e7i	1.30336	+	1.30336i
$73$			4.65495e7i			1.63917i	0.572960	+	0.819584i	$0.305795\pi$
$73$			4.65495e7i			1.63917i	−0.572960	+	0.819584i	$0.694205\pi$
$74$	−6.99879e6	+	1.28343e7i	−0.233398	+	0.428000i
$75$	−1.93167e7			−0.610503
$76$	−2.96259e7	+	2.96259e7i	−0.888008	+	0.888008i
$77$		−	7.14175e6i		−	0.203162i
$78$			2.35721e7i			0.636824i
$79$	2.23071e7	+	2.23071e7i	0.572711	+	0.572711i	0.932885	−	0.360174i	$-0.117283\pi$
$79$	2.23071e7	+	2.23071e7i	0.572711	+	0.572711i	−0.360174	+	0.932885i	$0.617283\pi$
$80$	−8.05665e6	−	8.05665e6i	−0.196696	−	0.196696i
$81$	6.27369e7			1.45741
$82$	−2.32988e7	−	2.32988e7i	−0.515322	−	0.515322i
$83$	−2.48914e7			−0.524489			−0.262244	−	0.965001i	$-0.584463\pi$
$83$	−2.48914e7			−0.524489			−0.262244	+	0.965001i	$0.584463\pi$
$84$	−1.74864e7			−0.351224
$85$			6.72075e6i			0.128748i
$86$	−9.53293e6			−0.174274
$87$	−5.59472e6	−	5.59472e6i	−0.0976565	−	0.0976565i
$88$	2.84924e7	−	2.84924e7i	0.475115	−	0.475115i
$89$	6.18244e7	−	6.18244e7i	0.985372	−	0.985372i	−0.0145229	−	0.999895i	$-0.504623\pi$
$89$	6.18244e7	−	6.18244e7i	0.985372	−	0.985372i	0.999895	+	0.0145229i	$0.00462295\pi$
$90$	5.55694e7			0.846965
$91$	−9.27788e6	−	9.27788e6i	−0.135295	−	0.135295i
$92$	−5.64986e7	+	5.64986e7i	−0.788653	+	0.788653i
$93$	8.04237e7	+	8.04237e7i	1.07511	+	1.07511i
$94$	−2.79189e6	+	2.79189e6i	−0.0357592	+	0.0357592i
$95$			1.08656e8i			1.33401i
$96$	−1.09349e8	−	1.09349e8i	−1.28744	−	1.28744i
$97$	8.56145e7	+	8.56145e7i	0.967076	+	0.967076i	0.999475	−	0.0323995i	$-0.0103149\pi$
$97$	8.56145e7	+	8.56145e7i	0.967076	+	0.967076i	−0.0323995	+	0.999475i	$0.510315\pi$
$98$	2.96499e7	−	2.96499e7i	0.321454	−	0.321454i
$99$		−	1.61176e8i		−	1.67787i
$100$	2.62420e7			0.262420
$101$		−	1.39908e8i		−	1.34448i	−0.740331	−	0.672242i	$-0.765331\pi$
$101$		−	1.39908e8i		−	1.34448i	0.740331	−	0.672242i	$-0.234669\pi$
$102$			1.48793e7i			0.137462i
$103$	−1.15152e8	+	1.15152e8i	−1.02311	+	1.02311i	−0.0233816	+	0.999727i	$0.507443\pi$
$103$	−1.15152e8	+	1.15152e8i	−1.02311	+	1.02311i	−0.999727	+	0.0233816i	$0.992557\pi$
$104$		−	7.40293e7i		−	0.632805i
$105$	−3.20666e7	+	3.20666e7i	−0.263812	+	0.263812i
$106$	3.58531e7	−	3.58531e7i	0.283990	−	0.283990i
$107$	−1.25632e8			−0.958439			−0.479220	−	0.877695i	$-0.659080\pi$
$107$	−1.25632e8			−0.958439			−0.479220	+	0.877695i	$0.659080\pi$
$108$	−2.10693e8			−1.54865
$109$	1.44935e7	+	1.44935e7i	0.102675	+	0.102675i	0.756578	−	0.653903i	$-0.226870\pi$
$109$	1.44935e7	+	1.44935e7i	0.102675	+	0.102675i	−0.653903	+	0.756578i	$0.726870\pi$
$110$		−	4.52033e7i		−	0.308745i
$111$	−7.59956e7	−	2.58287e8i	−0.500607	−	1.70142i
$112$	1.40411e7			0.0892336
$113$	9.34053e7	−	9.34053e7i	0.572872	−	0.572872i	−0.360058	−	0.932930i	$-0.617243\pi$
$113$	9.34053e7	−	9.34053e7i	0.572872	−	0.572872i	0.932930	+	0.360058i	$0.117243\pi$
$114$			2.40557e8i			1.42429i
$115$			2.07214e8i			1.18475i
$116$	7.60052e6	+	7.60052e6i	0.0419770	+	0.0419770i
$117$	−2.09384e8	−	2.09384e8i	−1.11738	−	1.11738i
$118$	−4.42233e6			−0.0228099
$119$	−5.85644e6	−	5.85644e6i	−0.0292042	−	0.0292042i
$120$	−2.55863e8			−1.23391
$121$	8.32492e7			0.388364
$122$		−	4.42605e7i		−	0.199791i
$123$	6.06844e8			2.65129
$124$	−1.09257e8	−	1.09257e8i	−0.462128	−	0.462128i
$125$	1.87921e8	−	1.87921e8i	0.769723	−	0.769723i
$126$	−4.84230e7	+	4.84230e7i	−0.192119	+	0.192119i
$127$	−2.41137e8			−0.926933			−0.463466	−	0.886115i	$-0.653395\pi$
$127$	−2.41137e8			−0.926933			−0.463466	+	0.886115i	$0.653395\pi$
$128$	1.80338e8	+	1.80338e8i	0.671811	+	0.671811i
$129$	1.24148e8	−	1.24148e8i	0.448312	−	0.448312i
$130$	−5.87238e7	−	5.87238e7i	−0.205609	−	0.205609i
$131$	3.31258e8	−	3.31258e8i	1.12482	−	1.12482i	0.133809	−	0.991007i	$-0.457279\pi$
$131$	3.31258e8	−	3.31258e8i	1.12482	−	1.12482i	0.991007	−	0.133809i	$-0.0427208\pi$
$132$			3.21019e8i			1.05739i
$133$	−9.46823e7	−	9.46823e7i	−0.302595	−	0.302595i
$134$	1.44493e8	+	1.44493e8i	0.448155	+	0.448155i
$135$	−3.86368e8	+	3.86368e8i	−1.16323	+	1.16323i
$136$		−	4.67292e7i		−	0.136594i
$137$	8.88669e7			0.252265			0.126133	−	0.992013i	$-0.459743\pi$
$137$	8.88669e7			0.252265			0.126133	+	0.992013i	$0.459743\pi$
$138$			4.58759e8i			1.26493i
$139$			1.11347e8i			0.298278i	0.988816	+	0.149139i	$0.0476501\pi$
$139$			1.11347e8i			0.298278i	−0.988816	+	0.149139i	$0.952350\pi$
$140$	4.35630e7	−	4.35630e7i	0.113398	−	0.113398i
$141$		−	7.27179e7i		−	0.183978i
$142$	2.50553e8	−	2.50553e8i	0.616235	−	0.616235i
$143$	−1.70325e8	+	1.70325e8i	−0.407319	+	0.407319i
$144$	3.16881e8			0.736964
$145$	2.78756e7			0.0630598
$146$	−2.56742e8	−	2.56742e8i	−0.565048	−	0.565048i
$147$			7.72264e8i			1.65385i
$148$	1.03241e8	+	3.50887e8i	0.215182	+	0.731342i
$149$	−2.63681e8			−0.534975			−0.267488	−	0.963561i	$-0.586193\pi$
$149$	−2.63681e8			−0.534975			−0.267488	+	0.963561i	$0.586193\pi$
$150$	1.06540e8	−	1.06540e8i	0.210450	−	0.210450i
$151$			6.16313e8i			1.18548i	0.805394	+	0.592739i	$0.201954\pi$
$151$			6.16313e8i			1.18548i	−0.805394	+	0.592739i	$0.798046\pi$
$152$		−	7.55481e8i		−	1.41530i
$153$	−1.32169e8	−	1.32169e8i	−0.241193	−	0.241193i
$154$	3.93900e7	+	3.93900e7i	0.0700331	+	0.0700331i
$155$	−4.00710e8			−0.694231
$156$	4.17038e8	+	4.17038e8i	0.704169	+	0.704169i
$157$	6.21331e8			1.02264			0.511322	−	0.859389i	$-0.329156\pi$
$157$	6.21331e8			1.02264			0.511322	+	0.859389i	$0.329156\pi$
$158$	−2.46068e8			−0.394846
$159$			9.33832e8i			1.46110i
$160$	5.44828e8			0.831342
$161$	−1.80566e8	−	1.80566e8i	−0.268740	−	0.268740i
$162$	−3.46023e8	+	3.46023e8i	−0.502395	+	0.502395i
$163$	5.11346e8	−	5.11346e8i	0.724377	−	0.724377i	−0.245116	−	0.969494i	$-0.578826\pi$
$163$	5.11346e8	−	5.11346e8i	0.724377	−	0.724377i	0.969494	+	0.245116i	$0.0788262\pi$
$164$	−8.24407e8			−1.13964
$165$	5.88685e8	+	5.88685e8i	0.794232	+	0.794232i
$166$	1.37287e8	−	1.37287e8i	0.180800	−	0.180800i
$167$	−1.94411e8	−	1.94411e8i	−0.249951	−	0.249951i	0.570999	−	0.820951i	$-0.306556\pi$
$167$	−1.94411e8	−	1.94411e8i	−0.249951	−	0.249951i	−0.820951	+	0.570999i	$0.806556\pi$
$168$	2.22958e8	−	2.22958e8i	0.279889	−	0.279889i
$169$		−	3.73190e8i		−	0.457492i
$170$	−3.70680e7	−	3.70680e7i	−0.0443817	−	0.0443817i
$171$	−2.13680e9	−	2.13680e9i	−2.49908	−	2.49908i
$172$	−1.68657e8	+	1.68657e8i	−0.192704	+	0.192704i
$173$		−	3.89147e8i		−	0.434439i	−0.976123	−	0.217220i	$-0.930301\pi$
$173$		−	3.89147e8i		−	0.434439i	0.976123	−	0.217220i	$-0.0696987\pi$
$174$	6.17149e7			0.0673276
$175$			8.38678e7i			0.0894217i
$176$		−	2.57769e8i		−	0.268646i
$177$	5.75922e7	−	5.75922e7i	0.0586774	−	0.0586774i
$178$			6.81981e8i			0.679347i
$179$	3.60925e8	−	3.60925e8i	0.351565	−	0.351565i	−0.509127	−	0.860691i	$-0.670032\pi$
$179$	3.60925e8	−	3.60925e8i	0.351565	−	0.351565i	0.860691	+	0.509127i	$0.170032\pi$
$180$	9.83135e8	−	9.83135e8i	0.936533	−	0.936533i
$181$	2.61228e8			0.243392			0.121696	−	0.992567i	$-0.461167\pi$
$181$	2.61228e8			0.243392			0.121696	+	0.992567i	$0.461167\pi$
$182$	1.02344e8			0.0932771
$183$	5.76406e8	+	5.76406e8i	0.513954	+	0.513954i
$184$		−	1.44075e9i		−	1.25695i
$185$	8.32780e8	+	4.54132e8i	0.710957	+	0.387700i
$186$	−8.87148e8			−0.741215
$187$	−1.07514e8	+	1.07514e8i	−0.0879221	+	0.0879221i
$188$			9.87884e7i			0.0790815i
$189$		−	6.73360e8i		−	0.527716i
$190$	−5.99287e8	−	5.99287e8i	−0.459854	−	0.459854i
$191$	−8.10191e8	−	8.10191e8i	−0.608771	−	0.608771i	0.333854	−	0.942625i	$-0.391651\pi$
$191$	−8.10191e8	−	8.10191e8i	−0.608771	−	0.608771i	−0.942625	+	0.333854i	$0.891651\pi$
$192$	3.78315e8			0.278387
$193$	1.63036e9	+	1.63036e9i	1.17504	+	1.17504i	0.980991	+	0.194053i	$0.0621633\pi$
$193$	1.63036e9	+	1.63036e9i	1.17504	+	1.17504i	0.194053	+	0.980991i	$0.437837\pi$
$194$	−9.44407e8			−0.666734
$195$	1.52953e9			1.05784
$196$		−	1.04913e9i		−	0.710897i
$197$	−4.23479e8			−0.281169			−0.140584	−	0.990069i	$-0.544898\pi$
$197$	−4.23479e8			−0.281169			−0.140584	+	0.990069i	$0.544898\pi$
$198$	8.88960e8	+	8.88960e8i	0.578391	+	0.578391i
$199$	−1.74304e9	+	1.74304e9i	−1.11146	+	1.11146i	−0.118507	+	0.992953i	$0.537811\pi$
$199$	−1.74304e9	+	1.74304e9i	−1.11146	+	1.11146i	−0.992953	+	0.118507i	$0.962189\pi$
$200$	−3.34595e8	+	3.34595e8i	−0.209122	+	0.209122i
$201$	−3.76348e9			−2.30572
$202$	7.71655e8	+	7.71655e8i	0.463466	+	0.463466i
$203$	−2.42907e7	+	2.42907e7i	−0.0143040	+	0.0143040i
$204$	2.63245e8	+	2.63245e8i	0.151999	+	0.151999i
$205$	−1.51180e9	+	1.51180e9i	−0.856008	+	0.856008i
$206$		−	1.27023e9i		−	0.705364i
$207$	−4.07503e9	−	4.07503e9i	−2.21947	−	2.21947i
$208$	−3.34869e8	−	3.34869e8i	−0.178905	−	0.178905i
$209$	−1.73820e9	+	1.73820e9i	−0.910991	+	0.910991i
$210$		−	3.53724e8i		−	0.181881i
$211$	1.01474e9			0.511949			0.255974	−	0.966684i	$-0.417604\pi$
$211$	1.01474e9			0.511949			0.255974	+	0.966684i	$0.417604\pi$
$212$		−	1.26863e9i		−	0.628044i
$213$			6.52593e9i			3.17047i
$214$	6.92918e8	−	6.92918e8i	0.330390	−	0.330390i
$215$			6.18565e8i			0.289489i
$216$	2.68641e9	−	2.68641e9i	1.23412	−	1.23412i
$217$	3.49178e8	−	3.49178e8i	0.157474	−	0.157474i
$218$	−1.59876e8			−0.0707878
$219$	6.68712e9			2.90712
$220$	−7.99738e8	−	7.99738e8i	−0.341395	−	0.341395i
$221$			2.79343e8i			0.117103i
$222$	1.84372e9	+	1.00542e9i	0.759073	+	0.413938i
$223$	1.97135e8			0.0797157			0.0398578	−	0.999205i	$-0.487309\pi$
$223$	1.97135e8			0.0797157			0.0398578	+	0.999205i	$0.487309\pi$
$224$	−4.74762e8	+	4.74762e8i	−0.188575	+	0.188575i
$225$			1.89274e9i			0.738517i
$226$			1.03035e9i			0.394957i
$227$	−2.71983e9	−	2.71983e9i	−1.02433	−	1.02433i	−0.999697	−	0.0246309i	$-0.992159\pi$
$227$	−2.71983e9	−	2.71983e9i	−1.02433	−	1.02433i	−0.0246309	−	0.999697i	$-0.507841\pi$
$228$	4.25594e9	+	4.25594e9i	1.57491	+	1.57491i
$229$	4.57885e9			1.66500			0.832501	−	0.554024i	$-0.186908\pi$
$229$	4.57885e9			1.66500			0.832501	+	0.554024i	$0.186908\pi$
$230$	−1.14288e9	−	1.14288e9i	−0.408404	−	0.408404i
$231$	−1.02596e9			−0.360314
$232$	−1.93819e8			−0.0669027
$233$		−	4.93853e9i		−	1.67561i	−0.545967	−	0.837807i	$-0.683837\pi$
$233$		−	4.93853e9i		−	1.67561i	0.545967	−	0.837807i	$-0.316163\pi$
$234$	2.30970e9			0.770359
$235$	1.81158e8	+	1.81158e8i	0.0594000	+	0.0594000i
$236$	−7.82399e7	+	7.82399e7i	−0.0252221	+	0.0252221i
$237$	3.20456e9	−	3.20456e9i	1.01572	−	1.01572i
$238$	6.46020e7			0.0201344
$239$	2.48543e9	+	2.48543e9i	0.761745	+	0.761745i	0.976638	−	0.214892i	$-0.0689401\pi$
$239$	2.48543e9	+	2.48543e9i	0.761745	+	0.761745i	−0.214892	+	0.976638i	$0.568940\pi$
$240$	−1.15739e9	+	1.15739e9i	−0.348846	+	0.348846i
$241$	−3.44921e9	−	3.44921e9i	−1.02247	−	1.02247i	−0.999742	−	0.0227302i	$-0.992764\pi$
$241$	−3.44921e9	−	3.44921e9i	−1.02247	−	1.02247i	−0.0227302	−	0.999742i	$-0.507236\pi$
$242$	−4.59158e8	+	4.59158e8i	−0.133875	+	0.133875i
$243$		−	1.92934e9i		−	0.553329i
$244$	−7.83058e8	−	7.83058e8i	−0.220920	−	0.220920i
$245$	−1.92390e9	−	1.92390e9i	−0.533971	−	0.533971i
$246$	−3.34702e9	+	3.34702e9i	−0.913942	+	0.913942i
$247$			4.51620e9i			1.21335i
$248$	2.78613e9			0.736538
$249$			3.57580e9i			0.930199i
$250$			2.07294e9i			0.530672i
$251$	−2.71009e9	+	2.71009e9i	−0.682793	+	0.682793i	−0.960629	−	0.277835i	$-0.910383\pi$
$251$	−2.71009e9	+	2.71009e9i	−0.682793	+	0.682793i	0.277835	+	0.960629i	$0.410383\pi$
$252$			1.71340e9i			0.424871i
$253$	−3.31486e9	+	3.31486e9i	−0.809065	+	0.809065i
$254$	1.32998e9	−	1.32998e9i	0.319529	−	0.319529i
$255$	9.65478e8			0.228340
$256$	−2.66346e9			−0.620136
$257$	3.25945e9	+	3.25945e9i	0.747156	+	0.747156i	0.973944	−	0.226788i	$-0.0728225\pi$
$257$	3.25945e9	+	3.25945e9i	0.747156	+	0.747156i	−0.226788	+	0.973944i	$0.572823\pi$
$258$			1.36947e9i			0.309081i
$259$	−1.12141e9	+	3.29952e8i	−0.249210	+	0.0733250i
$260$	−2.07789e9			−0.454704
$261$	−5.48197e8	+	5.48197e8i	−0.118134	+	0.118134i
$262$			3.65408e9i			0.775485i
$263$		−	3.91860e9i		−	0.819045i	−0.912300	−	0.409522i	$-0.865695\pi$
$263$		−	3.91860e9i		−	0.819045i	0.912300	−	0.409522i	$-0.134305\pi$
$264$	−4.09311e9	−	4.09311e9i	−0.842632	−	0.842632i
$265$	−2.32641e9	−	2.32641e9i	−0.471739	−	0.471739i
$266$	1.04443e9			0.208619
$267$	−8.88146e9	−	8.88146e9i	−1.74759	−	1.74759i
$268$	5.11275e9			0.991096
$269$	−7.53000e9			−1.43809			−0.719045	−	0.694963i	$-0.755421\pi$
$269$	−7.53000e9			−1.43809			−0.719045	+	0.694963i	$0.755421\pi$
$270$		−	4.26200e9i		−	0.801970i
$271$	8.08111e9			1.49828			0.749142	−	0.662410i	$-0.230466\pi$
$271$	8.08111e9			1.49828			0.749142	+	0.662410i	$0.230466\pi$
$272$	−2.11378e8	−	2.11378e8i	−0.0386176	−	0.0386176i
$273$	−1.33282e9	+	1.33282e9i	−0.239951	+	0.239951i
$274$	−4.90142e8	+	4.90142e8i	−0.0869600	+	0.0869600i
$275$	1.53966e9			0.269212
$276$	8.11637e9	+	8.11637e9i	1.39870	+	1.39870i
$277$	−1.42122e9	+	1.42122e9i	−0.241402	+	0.241402i	−0.817430	−	0.576028i	$-0.804602\pi$
$277$	−1.42122e9	+	1.42122e9i	−0.241402	+	0.241402i	0.576028	+	0.817430i	$0.304602\pi$
$278$	−6.14132e8	−	6.14132e8i	−0.102821	−	0.102821i
$279$	7.88030e9	−	7.88030e9i	1.30055	−	1.30055i
$280$			1.11089e9i			0.180733i
$281$	−2.30594e9	−	2.30594e9i	−0.369848	−	0.369848i	0.497573	−	0.867422i	$-0.334224\pi$
$281$	−2.30594e9	−	2.30594e9i	−0.369848	−	0.369848i	−0.867422	+	0.497573i	$0.834224\pi$
$282$	4.01073e8	+	4.01073e8i	0.0634201	+	0.0634201i
$283$	−1.72231e9	+	1.72231e9i	−0.268514	+	0.268514i	−0.828501	−	0.559987i	$-0.810806\pi$
$283$	−1.72231e9	+	1.72231e9i	−0.268514	+	0.268514i	0.559987	+	0.828501i	$0.310806\pi$
$284$		−	8.86558e9i		−	1.36281i
$285$	1.56091e10			2.36591
$286$		−	1.87884e9i		−	0.280819i
$287$		−	2.63475e9i		−	0.388340i
$288$	−1.07145e10	+	1.07145e10i	−1.55740	+	1.55740i
$289$		−	6.79943e9i		−	0.974723i
$290$	−1.53747e8	+	1.53747e8i	−0.0217378	+	0.0217378i
$291$	1.22991e10	−	1.22991e10i	1.71514	−	1.71514i
$292$	−9.08456e9			−1.24960
$293$	9.18701e9			1.24653			0.623266	−	0.782010i	$-0.285805\pi$
$293$	9.18701e9			1.24653			0.623266	+	0.782010i	$0.285805\pi$
$294$	−4.25939e9	−	4.25939e9i	−0.570110	−	0.570110i
$295$			2.86953e8i			0.0378898i
$296$	−5.79030e9	−	3.15757e9i	−0.754283	−	0.411326i
$297$	−1.23617e10			−1.58874
$298$	1.45432e9	−	1.45432e9i	0.184415	−	0.184415i
$299$			8.61271e9i			1.07759i
$300$		−	3.76983e9i		−	0.465411i
$301$	−5.39016e8	−	5.39016e8i	−0.0656653	−	0.0656653i
$302$	−3.39925e9	−	3.39925e9i	−0.408654	−	0.408654i
$303$	−2.00986e10			−2.38449
$304$	−3.41740e9	−	3.41740e9i	−0.400130	−	0.400130i
$305$	−2.87194e9			−0.331876
$306$	1.45795e9			0.166286
$307$		−	7.76580e9i		−	0.874244i	−0.899402	−	0.437122i	$-0.855998\pi$
$307$		−	7.76580e9i		−	0.874244i	0.899402	−	0.437122i	$-0.144002\pi$
$308$	1.39378e9			0.154878
$309$	1.65423e10	+	1.65423e10i	1.81452	+	1.81452i
$310$	2.21010e9	−	2.21010e9i	0.239313	−	0.239313i
$311$	9.31588e9	−	9.31588e9i	0.995824	−	0.995824i	−0.00416781	−	0.999991i	$-0.501327\pi$
$311$	9.31588e9	−	9.31588e9i	0.995824	−	0.995824i	0.999991	+	0.00416781i	$0.00132666\pi$
$312$	−1.06348e10			−1.12230
$313$	1.18295e10	+	1.18295e10i	1.23251	+	1.23251i	0.962996	+	0.269515i	$0.0868633\pi$
$313$	1.18295e10	+	1.18295e10i	1.23251	+	1.23251i	0.269515	+	0.962996i	$0.413137\pi$
$314$	−3.42693e9	+	3.42693e9i	−0.352522	+	0.352522i
$315$	3.14203e9	+	3.14203e9i	0.319131	+	0.319131i
$316$	−4.35345e9	+	4.35345e9i	−0.436601	+	0.436601i
$317$			1.09934e10i			1.08867i	0.838869	+	0.544334i	$0.183217\pi$
$317$			1.09934e10i			1.08867i	−0.838869	+	0.544334i	$0.816783\pi$
$318$	−5.15052e9	−	5.15052e9i	−0.503666	−	0.503666i
$319$	4.45935e8	+	4.45935e8i	0.0430634	+	0.0430634i
$320$	−9.42477e8	+	9.42477e8i	−0.0898816	+	0.0898816i
$321$			1.80478e10i			1.69982i
$322$	1.99181e9			0.185278
$323$			2.85075e9i			0.261908i
$324$			1.22437e10i			1.11105i
$325$	2.00018e9	−	2.00018e9i	0.179282	−	0.179282i
$326$			5.64062e9i			0.499409i
$327$	2.08208e9	−	2.08208e9i	0.182098	−	0.182098i
$328$	1.05115e10	−	1.05115e10i	0.908174	−	0.908174i
$329$	−3.15721e8			−0.0269476
$330$	−6.49374e9			−0.547569
$331$	6.31408e9	+	6.31408e9i	0.526015	+	0.526015i	0.919382	−	0.393367i	$-0.128690\pi$
$331$	6.31408e9	+	6.31408e9i	0.526015	+	0.526015i	−0.393367	+	0.919382i	$0.628690\pi$
$332$		−	4.85778e9i		−	0.399840i
$333$	−2.53082e10	+	7.44641e9i	−2.05818	+	0.605578i
$334$	2.14453e9			0.172325
$335$	9.37576e9	−	9.37576e9i	0.744436	−	0.744436i
$336$		−	2.01709e9i		−	0.158259i
$337$			5.22724e6i			0.000405278i	1.00000		0.000202639i	$6.45020e-5\pi$
$337$			5.22724e6i			0.000405278i	−1.00000		0.000202639i	$0.999935\pi$
$338$	2.05832e9	+	2.05832e9i	0.157705	+	0.157705i
$339$	−1.34182e10	−	1.34182e10i	−1.01601	−	1.01601i
$340$	−1.31162e9			−0.0981503
$341$	−6.41028e9	−	6.41028e9i	−0.474089	−	0.474089i
$342$	2.35709e10			1.72295
$343$	6.94856e9			0.502017
$344$		−	4.30087e9i		−	0.307130i
$345$	2.97676e10			2.10120
$346$	2.14632e9	+	2.14632e9i	0.149758	+	0.149758i
$347$	−1.07548e10	+	1.07548e10i	−0.741793	+	0.741793i	−0.972923	−	0.231130i	$-0.925758\pi$
$347$	−1.07548e10	+	1.07548e10i	−0.741793	+	0.741793i	0.231130	+	0.972923i	$0.425758\pi$
$348$	1.09186e9	−	1.09186e9i	0.0744476	−	0.0744476i
$349$	2.02607e10			1.36570			0.682848	−	0.730561i	$-0.260741\pi$
$349$	2.02607e10			1.36570			0.682848	+	0.730561i	$0.260741\pi$
$350$	−4.62569e8	−	4.62569e8i	−0.0308251	−	0.0308251i
$351$	−1.60591e10	+	1.60591e10i	−1.05802	+	1.05802i
$352$	8.71577e9	+	8.71577e9i	0.567721	+	0.567721i
$353$	1.31020e10	−	1.31020e10i	0.843795	−	0.843795i	−0.145555	−	0.989350i	$-0.546497\pi$
$353$	1.31020e10	−	1.31020e10i	0.843795	−	0.843795i	0.989350	+	0.145555i	$0.0464967\pi$
$354$			6.35295e8i			0.0404541i
$355$	−1.62577e10	−	1.62577e10i	−1.02364	−	1.02364i
$356$	1.20656e10	+	1.20656e10i	0.751189	+	0.751189i
$357$	−8.41314e8	+	8.41314e8i	−0.0517947	+	0.0517947i
$358$			3.98134e9i			0.242380i
$359$	2.68292e10			1.61521			0.807607	−	0.589721i	$-0.200762\pi$
$359$	2.68292e10			1.61521			0.807607	+	0.589721i	$0.200762\pi$
$360$			2.50707e10i			1.49264i
$361$			2.91050e10i			1.71372i
$362$	−1.44080e9	+	1.44080e9i	−0.0839012	+	0.0839012i
$363$		−	1.19593e10i		−	0.688776i
$364$	1.81066e9	−	1.81066e9i	0.103141	−	0.103141i
$365$	−1.66593e10	+	1.66593e10i	−0.938608	+	0.938608i
$366$	−6.35830e9			−0.354337
$367$	2.08430e9			0.114894			0.0574469	−	0.998349i	$-0.481704\pi$
$367$	2.08430e9			0.114894			0.0574469	+	0.998349i	$0.481704\pi$
$368$	−6.51721e9	−	6.51721e9i	−0.355361	−	0.355361i
$369$		−	5.94614e10i		−	3.20723i
$370$	−7.09791e9	+	2.08842e9i	−0.378725	+	0.111432i
$371$	4.05445e9			0.214011
$372$	−1.56954e10	+	1.56954e10i	−0.819600	+	0.819600i
$373$		−	9.52542e9i		−	0.492095i	−0.969258	−	0.246048i	$-0.920868\pi$
$373$		−	9.52542e9i		−	0.492095i	0.969258	−	0.246048i	$-0.0791319\pi$
$374$		−	1.18598e9i		−	0.0606163i
$375$	−2.69960e10	−	2.69960e10i	−1.36513	−	1.36513i
$376$	−1.25959e9	−	1.25959e9i	−0.0630198	−	0.0630198i
$377$	1.15863e9			0.0573561
$378$	3.71389e9	+	3.71389e9i	0.181912	+	0.181912i
$379$	−2.74549e10			−1.33065			−0.665323	−	0.746556i	$-0.731706\pi$
$379$	−2.74549e10			−1.33065			−0.665323	+	0.746556i	$0.731706\pi$
$380$	−2.12052e10			−1.01697
$381$			3.46408e10i			1.64395i
$382$	8.93716e9			0.419707
$383$	−3.84881e9	−	3.84881e9i	−0.178867	−	0.178867i	0.611995	−	0.790862i	$-0.290367\pi$
$383$	−3.84881e9	−	3.84881e9i	−0.178867	−	0.178867i	−0.790862	+	0.611995i	$0.790367\pi$
$384$	2.59066e10	−	2.59066e10i	1.19148	−	1.19148i
$385$	2.55591e9	−	2.55591e9i	0.116333	−	0.116333i
$386$	−1.79844e10			−0.810114
$387$	−1.21646e10	−	1.21646e10i	−0.542318	−	0.542318i
$388$	−1.67085e10	+	1.67085e10i	−0.737242	+	0.737242i
$389$	1.40095e10	+	1.40095e10i	0.611820	+	0.611820i	0.943420	−	0.331600i	$-0.107588\pi$
$389$	1.40095e10	+	1.40095e10i	0.611820	+	0.611820i	−0.331600	+	0.943420i	$0.607588\pi$
$390$	−8.43605e9	+	8.43605e9i	−0.364654	+	0.364654i
$391$			5.43657e9i			0.232604i
$392$	1.33768e10	+	1.33768e10i	0.566512	+	0.566512i
$393$	−4.75873e10	−	4.75873e10i	−1.99490	−	1.99490i
$394$	2.33568e9	−	2.33568e9i	0.0969234	−	0.0969234i
$395$			1.59667e10i			0.655883i
$396$	3.14550e10			1.27911
$397$		−	4.69037e10i		−	1.88819i	−0.329680	−	0.944093i	$-0.606941\pi$
$397$		−	4.69037e10i		−	1.88819i	0.329680	−	0.944093i	$-0.393059\pi$
$398$		−	1.92273e10i		−	0.766277i
$399$	−1.36017e10	+	1.36017e10i	−0.536663	+	0.536663i
$400$			3.02706e9i			0.118245i
$401$	1.49572e10	−	1.49572e10i	0.578458	−	0.578458i	−0.356021	−	0.934478i	$-0.615867\pi$
$401$	1.49572e10	−	1.49572e10i	0.578458	−	0.578458i	0.934478	+	0.356021i	$0.115867\pi$
$402$	2.07574e10	−	2.07574e10i	0.794818	−	0.794818i
$403$	−1.66553e10			−0.631439
$404$	2.73043e10			1.02496
$405$	2.24525e10	+	2.24525e10i	0.834534	+	0.834534i
$406$		−	2.67949e8i		−	0.00986163i
$407$	6.05733e9	+	2.05871e10i	0.220752	+	0.750270i
$408$	−6.71295e9			−0.242255
$409$	−8.49869e9	+	8.49869e9i	−0.303710	+	0.303710i	−0.842463	−	0.538754i	$-0.818895\pi$
$409$	−8.49869e9	+	8.49869e9i	−0.303710	+	0.303710i	0.538754	+	0.842463i	$0.318895\pi$
$410$		−	1.66765e10i		−	0.590160i
$411$		−	1.27663e10i		−	0.447401i
$412$	−2.24729e10	−	2.24729e10i	−0.779958	−	0.779958i
$413$	−2.50050e8	−	2.50050e8i	−0.00859460	−	0.00859460i
$414$	4.49514e10			1.53018
$415$	−8.90819e9	−	8.90819e9i	−0.300329	−	0.300329i
$416$	2.26454e10			0.756148
$417$	1.59957e10			0.529006
$418$		−	1.91739e10i		−	0.628067i
$419$	−1.02661e9			−0.0333081			−0.0166540	−	0.999861i	$-0.505301\pi$
$419$	−1.02661e9			−0.0333081			−0.0166540	+	0.999861i	$0.505301\pi$
$420$	−6.25809e9	−	6.25809e9i	−0.201115	−	0.201115i
$421$	−1.28308e10	+	1.28308e10i	−0.408436	+	0.408436i	−0.881193	−	0.472757i	$-0.843259\pi$
$421$	−1.28308e10	+	1.28308e10i	−0.408436	+	0.408436i	0.472757	+	0.881193i	$0.343259\pi$
$422$	−5.59678e9	+	5.59678e9i	−0.176477	+	0.176477i
$423$	−7.12524e9			−0.222555
$424$	1.61754e10	+	1.61754e10i	0.500487	+	0.500487i
$425$	1.26257e9	−	1.26257e9i	0.0386989	−	0.0386989i
$426$	−3.59935e10	−	3.59935e10i	−1.09291	−	1.09291i
$427$	2.50260e9	−	2.50260e9i	0.0752800	−	0.0752800i
$428$		−	2.45182e10i		−	0.730658i
$429$	2.44683e10	+	2.44683e10i	0.722394	+	0.722394i
$430$	−3.41167e9	−	3.41167e9i	−0.0997915	−	0.0997915i
$431$	−3.90311e10	+	3.90311e10i	−1.13110	+	1.13110i	−0.141108	+	0.989994i	$0.545067\pi$
$431$	−3.90311e10	+	3.90311e10i	−1.13110	+	1.13110i	−0.989994	+	0.141108i	$0.954933\pi$
$432$		−	2.43038e10i		−	0.697812i
$433$	−5.20950e10			−1.48199			−0.740993	−	0.671512i	$-0.765645\pi$
$433$	−5.20950e10			−1.48199			−0.740993	+	0.671512i	$0.765645\pi$
$434$			3.85175e9i			0.108567i
$435$		−	4.00451e9i		−	0.111839i
$436$	−2.82854e9	+	2.82854e9i	−0.0782737	+	0.0782737i
$437$			8.78941e10i			2.41009i
$438$	−3.68826e10	+	3.68826e10i	−1.00213	+	1.00213i
$439$	−1.96244e10	+	1.96244e10i	−0.528371	+	0.528371i	−0.920086	−	0.391716i	$-0.871882\pi$
$439$	−1.96244e10	+	1.96244e10i	−0.528371	+	0.528371i	0.391716	+	0.920086i	$0.371882\pi$
$440$	2.03939e10			0.544114
$441$	7.56701e10			2.00064
$442$	−1.54071e9	−	1.54071e9i	−0.0403674	−	0.0403674i
$443$			1.41671e10i			0.367846i	0.982941	+	0.183923i	$0.0588797\pi$
$443$			1.41671e10i			0.367846i	−0.982941	+	0.183923i	$0.941120\pi$
$444$	5.04071e10	−	1.48313e10i	1.29706	−	0.381633i
$445$	4.42518e10			1.12847
$446$	−1.08729e9	+	1.08729e9i	−0.0274793	+	0.0274793i
$447$			3.78794e10i			0.948796i
$448$		−	1.64254e9i		−	0.0407760i
$449$	−3.34861e9	−	3.34861e9i	−0.0823909	−	0.0823909i	0.664710	−	0.747101i	$-0.268555\pi$
$449$	−3.34861e9	−	3.34861e9i	−0.0823909	−	0.0823909i	−0.747101	+	0.664710i	$0.768555\pi$
$450$	−1.04393e10	−	1.04393e10i	−0.254579	−	0.254579i
$451$	−4.83693e10			−1.16913
$452$	1.82289e10	+	1.82289e10i	0.436724	+	0.436724i
$453$	8.85372e10			2.10249
$454$	3.00023e10			0.706205
$455$		−	6.64079e9i		−	0.154944i
$456$	−1.08530e11			−2.51009
$457$	−4.84871e10	−	4.84871e10i	−1.11163	−	1.11163i	−0.992930	−	0.118704i	$-0.962126\pi$
$457$	−4.84871e10	−	4.84871e10i	−1.11163	−	1.11163i	−0.118704	−	0.992930i	$-0.537874\pi$
$458$	−2.52545e10	+	2.52545e10i	−0.573953	+	0.573953i
$459$	−1.01369e10	+	1.01369e10i	−0.228379	+	0.228379i
$460$	−4.04397e10			−0.903186
$461$	1.89413e10	+	1.89413e10i	0.419379	+	0.419379i	0.884990	−	0.465611i	$-0.154165\pi$
$461$	1.89413e10	+	1.89413e10i	0.419379	+	0.419379i	−0.465611	+	0.884990i	$0.654165\pi$
$462$	5.65862e9	−	5.65862e9i	0.124206	−	0.124206i
$463$	−1.66776e10	−	1.66776e10i	−0.362918	−	0.362918i	0.501968	−	0.864886i	$-0.332610\pi$
$463$	−1.66776e10	−	1.66776e10i	−0.362918	−	0.362918i	−0.864886	+	0.501968i	$0.832610\pi$
$464$	−8.76733e8	+	8.76733e8i	−0.0189145	+	0.0189145i
$465$			5.75646e10i			1.23124i
$466$	2.72383e10	+	2.72383e10i	0.577612	+	0.577612i
$467$	5.02019e9	+	5.02019e9i	0.105549	+	0.105549i	0.757909	−	0.652360i	$-0.226221\pi$
$467$	5.02019e9	+	5.02019e9i	0.105549	+	0.105549i	−0.652360	+	0.757909i	$0.726221\pi$
$468$	4.08633e10	−	4.08633e10i	0.851825	−	0.851825i
$469$			1.63400e10i			0.337723i
$470$	−1.99834e9			−0.0409523
$471$		−	8.92581e10i		−	1.81369i
$472$		−	1.99518e9i		−	0.0401988i
$473$	−9.89537e9	+	9.89537e9i	−0.197691	+	0.197691i
$474$			3.53493e10i			0.700273i
$475$	2.04122e10	−	2.04122e10i	0.400973	−	0.400973i
$476$	1.14294e9	−	1.14294e9i	0.0222636	−	0.0222636i
$477$	9.15013e10			1.76748
$478$	−2.74166e10			−0.525172
$479$	2.03718e10	+	2.03718e10i	0.386979	+	0.386979i	0.873608	−	0.486629i	$-0.161774\pi$
$479$	2.03718e10	+	2.03718e10i	0.386979	+	0.386979i	−0.486629	+	0.873608i	$0.661774\pi$
$480$		−	7.82680e10i		−	1.47441i
$481$	3.46139e10	+	1.88757e10i	0.646652	+	0.352633i
$482$	3.80480e10			0.704926
$483$	−2.59394e10	+	2.59394e10i	−0.476619	+	0.476619i
$484$			1.62469e10i			0.296066i
$485$			6.12799e10i			1.10752i
$486$	1.06412e10	+	1.06412e10i	0.190742	+	0.190742i
$487$	2.22147e10	+	2.22147e10i	0.394935	+	0.394935i	0.876442	−	0.481507i	$-0.159911\pi$
$487$	2.22147e10	+	2.22147e10i	0.394935	+	0.394935i	−0.481507	+	0.876442i	$0.659911\pi$
$488$	1.99685e10			0.352101
$489$	−7.34581e10	−	7.34581e10i	−1.28471	−	1.28471i
$490$	2.12224e10			0.368137
$491$	2.59213e10			0.445996			0.222998	−	0.974819i	$-0.428416\pi$
$491$	2.59213e10			0.445996			0.222998	+	0.974819i	$0.428416\pi$
$492$			1.18431e11i			2.02118i
$493$	7.31359e8			0.0123806
$494$	−2.49089e10	−	2.49089e10i	−0.418261	−	0.418261i
$495$	5.76821e10	−	5.76821e10i	0.960772	−	0.960772i
$496$	1.26030e10	−	1.26030e10i	0.208232	−	0.208232i
$497$	2.83338e10			0.464386
$498$	−1.97222e10	−	1.97222e10i	−0.320655	−	0.320655i
$499$	3.93715e10	−	3.93715e10i	0.635009	−	0.635009i	−0.314311	−	0.949320i	$-0.601773\pi$
$499$	3.93715e10	−	3.93715e10i	0.635009	−	0.635009i	0.949320	+	0.314311i	$0.101773\pi$
$500$	3.66745e10	+	3.66745e10i	0.586791	+	0.586791i
$501$	−2.79284e10	+	2.79284e10i	−0.443297	+	0.443297i
$502$		−	2.98948e10i		−	0.470740i
$503$	−5.41175e10	−	5.41175e10i	−0.845407	−	0.845407i	0.144149	−	0.989556i	$-0.453955\pi$
$503$	−5.41175e10	−	5.41175e10i	−0.845407	−	0.845407i	−0.989556	+	0.144149i	$0.953955\pi$
$504$	−2.18465e10	−	2.18465e10i	−0.338579	−	0.338579i
$505$	5.00705e10	−	5.00705e10i	0.769869	−	0.769869i
$506$		−	3.65660e10i		−	0.557796i
$507$	−5.36111e10			−0.811377
$508$		−	4.70601e10i		−	0.706639i
$509$		−	7.72997e10i		−	1.15161i	−0.817586	−	0.575807i	$-0.804688\pi$
$509$		−	7.72997e10i		−	1.15161i	0.817586	−	0.575807i	$-0.195312\pi$
$510$	−5.32506e9	+	5.32506e9i	−0.0787125	+	0.0787125i
$511$		−	2.90337e10i		−	0.425812i
$512$	−3.14762e10	+	3.14762e10i	−0.458040	+	0.458040i
$513$	−1.63886e11	+	1.63886e11i	−2.36631	+	2.36631i
$514$	−3.59547e10			−0.515114
$515$	−8.24217e10			−1.17169
$516$	2.42286e10	+	2.42286e10i	0.341767	+	0.341767i
$517$			5.79608e9i			0.0811282i
$518$	4.36526e9	−	8.00494e9i	0.0606305	−	0.111183i
$519$	−5.59033e10			−0.770492
$520$	2.64938e10	−	2.64938e10i	0.362352	−	0.362352i
$521$		−	4.47969e10i		−	0.607991i	−0.952673	−	0.303996i	$-0.901679\pi$
$521$		−	4.47969e10i		−	0.607991i	0.952673	−	0.303996i	$-0.0983208\pi$
$522$		−	6.04712e9i		−	0.0814454i
$523$	4.35269e10	+	4.35269e10i	0.581769	+	0.581769i	0.935389	−	0.353620i	$-0.115049\pi$
$523$	4.35269e10	+	4.35269e10i	0.581769	+	0.581769i	−0.353620	+	0.935389i	$0.615049\pi$
$524$	6.46481e10	+	6.46481e10i	0.857494	+	0.857494i
$525$	1.20481e10			0.158592
$526$	2.16129e10	+	2.16129e10i	0.282338	+	0.282338i
$527$	−1.05132e10			−0.136299
$528$	−3.70301e10			−0.476453
$529$			8.93091e10i			1.14044i
$530$	2.56624e10			0.325232
$531$	−5.64315e9	−	5.64315e9i	−0.0709813	−	0.0709813i
$532$	1.84781e10	−	1.84781e10i	0.230681	−	0.230681i
$533$	−6.28368e10	+	6.28368e10i	−0.778584	+	0.778584i
$534$	9.79708e10			1.20485
$535$	−4.49615e10	−	4.49615e10i	−0.548815	−	0.548815i
$536$	−6.51895e10	+	6.51895e10i	−0.789802	+	0.789802i
$537$	−5.18492e10	−	5.18492e10i	−0.623512	−	0.623512i
$538$	4.15315e10	−	4.15315e10i	0.495733	−	0.495733i
$539$		−	6.15544e10i		−	0.729296i
$540$	−7.54033e10	−	7.54033e10i	−0.886779	−	0.886779i
$541$	−5.83083e10	−	5.83083e10i	−0.680677	−	0.680677i	0.279476	−	0.960153i	$-0.409839\pi$
$541$	−5.83083e10	−	5.83083e10i	−0.680677	−	0.680677i	−0.960153	+	0.279476i	$0.909839\pi$
$542$	−4.45711e10	+	4.45711e10i	−0.516483	+	0.516483i
$543$		−	3.75271e10i		−	0.431664i
$544$	1.42944e10			0.163219
$545$			1.03739e10i			0.117586i
$546$		−	1.47023e10i		−	0.165430i
$547$	6.29787e10	−	6.29787e10i	0.703468	−	0.703468i	−0.261685	−	0.965153i	$-0.584278\pi$
$547$	6.29787e10	−	6.29787e10i	0.703468	−	0.703468i	0.965153	+	0.261685i	$0.0842781\pi$
$548$			1.73432e10i			0.192312i
$549$	5.64790e10	−	5.64790e10i	0.621724	−	0.621724i
$550$	−8.49195e9	+	8.49195e9i	−0.0928018	+	0.0928018i
$551$	1.18240e10			0.128280
$552$	−2.06973e11			−2.22925
$553$	−1.39133e10	−	1.39133e10i	−0.148775	−	0.148775i
$554$		−	1.56773e10i		−	0.166430i
$555$	6.52389e10	−	1.19634e11i	0.687598	−	1.26091i
$556$	−2.17305e10			−0.227389
$557$	2.78306e10	−	2.78306e10i	0.289136	−	0.289136i	−0.547603	−	0.836738i	$-0.684459\pi$
$557$	2.78306e10	−	2.78306e10i	0.289136	−	0.289136i	0.836738	+	0.547603i	$0.184459\pi$
$558$			8.69270e10i			0.896639i
$559$			2.57103e10i			0.263305i
$560$	5.02506e9	+	5.02506e9i	0.0510963	+	0.0510963i
$561$	1.54450e10	+	1.54450e10i	0.155933	+	0.155933i
$562$	2.54367e10			0.254986
$563$	5.59051e10	+	5.59051e10i	0.556439	+	0.556439i	0.928292	−	0.371853i	$-0.121277\pi$
$563$	5.59051e10	+	5.59051e10i	0.556439	+	0.556439i	−0.371853	+	0.928292i	$0.621277\pi$
$564$	1.41916e10			0.140254
$565$	6.68563e10			0.656068
$566$		−	1.89987e10i		−	0.185122i
$567$	−3.91300e10			−0.378598
$568$	1.13039e11	+	1.13039e11i	1.08602	+	1.08602i
$569$	5.40656e10	−	5.40656e10i	0.515789	−	0.515789i	−0.400505	−	0.916294i	$-0.631165\pi$
$569$	5.40656e10	−	5.40656e10i	0.515789	−	0.515789i	0.916294	+	0.400505i	$0.131165\pi$
$570$	−8.60913e10	+	8.60913e10i	−0.815567	+	0.815567i
$571$	1.56486e11			1.47208			0.736041	−	0.676937i	$-0.236693\pi$
$571$	1.56486e11			1.47208			0.736041	+	0.676937i	$0.236693\pi$
$572$	−3.32406e10	−	3.32406e10i	−0.310516	−	0.310516i
$573$	−1.16389e11	+	1.16389e11i	−1.07968	+	1.07968i
$574$	1.45319e10	+	1.45319e10i	0.133867	+	0.133867i
$575$	3.89275e10	−	3.89275e10i	0.356110	−	0.356110i
$576$		−	3.70691e10i		−	0.336762i
$577$	−2.71818e10	−	2.71818e10i	−0.245231	−	0.245231i	0.573779	−	0.819010i	$-0.305477\pi$
$577$	−2.71818e10	−	2.71818e10i	−0.245231	−	0.245231i	−0.819010	+	0.573779i	$0.805477\pi$
$578$	3.75020e10	+	3.75020e10i	0.336003	+	0.336003i
$579$	2.34211e11	−	2.34211e11i	2.08398	−	2.08398i
$580$			5.44019e9i			0.0480731i
$581$	1.55251e10			0.136248
$582$			1.35670e11i			1.18247i
$583$		−	7.44324e10i		−	0.644299i
$584$	1.15831e11	−	1.15831e11i	0.995807	−	0.995807i
$585$		−	1.49870e11i		−	1.27965i
$586$	−5.06706e10	+	5.06706e10i	−0.429700	+	0.429700i
$587$	−6.52987e10	+	6.52987e10i	−0.549987	+	0.549987i	−0.926437	−	0.376450i	$-0.877145\pi$
$587$	−6.52987e10	+	6.52987e10i	−0.549987	+	0.549987i	0.376450	+	0.926437i	$0.377145\pi$
$588$	−1.50715e11			−1.26080
$589$	−1.69970e11			−1.41225
$590$	−1.58268e9	−	1.58268e9i	−0.0130612	−	0.0130612i
$591$			6.08354e10i			0.498662i
$592$	−4.04754e10	+	1.19091e10i	−0.329537	+	0.0969596i
$593$	1.44349e11			1.16734			0.583669	−	0.811992i	$-0.301617\pi$
$593$	1.44349e11			1.16734			0.583669	+	0.811992i	$0.301617\pi$
$594$	6.81804e10	−	6.81804e10i	0.547663	−	0.547663i
$595$		−	4.19184e9i		−	0.0334454i
$596$		−	5.14598e10i		−	0.407834i
$597$	2.50398e11	+	2.50398e11i	1.97121	+	1.97121i
$598$	−4.75031e10	−	4.75031e10i	−0.371464	−	0.371464i
$599$	−2.02308e11			−1.57147			−0.785733	−	0.618566i	$-0.787714\pi$
$599$	−2.02308e11			−1.57147			−0.785733	+	0.618566i	$0.787714\pi$
$600$	4.80667e10	+	4.80667e10i	0.370885	+	0.370885i
$601$	−2.13947e11			−1.63987			−0.819933	−	0.572459i	$-0.805990\pi$
$601$	−2.13947e11			−1.63987			−0.819933	+	0.572459i	$0.805990\pi$
$602$	5.94585e9			0.0452718
$603$			3.68764e11i			2.78920i
$604$	−1.20279e11			−0.903739
$605$	2.97935e10	+	2.97935e10i	0.222382	+	0.222382i
$606$	1.10853e11	−	1.10853e11i	0.821972	−	0.821972i
$607$	4.58227e10	−	4.58227e10i	0.337540	−	0.337540i	−0.517900	−	0.855441i	$-0.673286\pi$
$607$	4.58227e10	−	4.58227e10i	0.337540	−	0.337540i	0.855441	+	0.517900i	$0.173286\pi$
$608$	2.31100e11			1.69117
$609$	3.48952e9	+	3.48952e9i	0.0253686	+	0.0253686i
$610$	1.58401e10	−	1.58401e10i	0.114403	−	0.114403i
$611$	7.52971e9	+	7.52971e9i	0.0540273	+	0.0540273i
$612$	2.57940e10	−	2.57940e10i	0.183871	−	0.183871i
$613$			5.47046e10i			0.387420i	0.981059	+	0.193710i	$0.0620521\pi$
$613$			5.47046e10i			0.387420i	−0.981059	+	0.193710i	$0.937948\pi$
$614$	4.28320e10	+	4.28320e10i	0.301366	+	0.301366i
$615$	2.17179e11	+	2.17179e11i	1.51816	+	1.51816i
$616$	−1.77712e10	+	1.77712e10i	−0.123422	+	0.123422i
$617$		−	2.31028e11i		−	1.59413i	−0.603894	−	0.797065i	$-0.706385\pi$
$617$		−	2.31028e11i		−	1.59413i	0.603894	−	0.797065i	$-0.293615\pi$
$618$	−1.82476e11			−1.25099
$619$			3.44956e10i			0.234964i	0.993075	+	0.117482i	$0.0374823\pi$
$619$			3.44956e10i			0.234964i	−0.993075	+	0.117482i	$0.962518\pi$
$620$		−	7.82024e10i		−	0.529241i
$621$	−3.12542e11	+	3.12542e11i	−2.10156	+	2.10156i
$622$			1.02763e11i			0.686553i
$623$	−3.85609e10	+	3.85609e10i	−0.255973	+	0.255973i
$624$	−4.81060e10	+	4.81060e10i	−0.317294	+	0.317294i
$625$	8.19819e10			0.537277
$626$	−1.30491e11			−0.849733
$627$	2.49703e11	+	2.49703e11i	1.61567	+	1.61567i
$628$			1.21259e11i			0.779604i
$629$	2.18492e10	+	1.19148e10i	0.139583	+	0.0761177i
$630$	−3.46595e10			−0.220019
$631$	1.26777e10	−	1.26777e10i	0.0799690	−	0.0799690i	−0.665991	−	0.745960i	$-0.731991\pi$
$631$	1.26777e10	−	1.26777e10i	0.0799690	−	0.0799690i	0.745960	+	0.665991i	$0.231991\pi$
$632$		−	1.11016e11i		−	0.695853i
$633$		−	1.45774e11i		−	0.907958i
$634$	−6.06337e10	−	6.06337e10i	−0.375281	−	0.375281i
$635$	−8.62987e10	−	8.62987e10i	−0.530773	−	0.530773i
$636$	−1.82246e11			−1.11386
$637$	−7.99656e10	−	7.99656e10i	−0.485675	−	0.485675i
$638$	−4.91907e9			−0.0296893
$639$	6.39441e11			3.83528
$640$			1.29080e11i			0.769375i
$641$	−2.12785e11			−1.26040			−0.630200	−	0.776433i	$-0.717027\pi$
$641$	−2.12785e11			−1.26040			−0.630200	+	0.776433i	$0.717027\pi$
$642$	−9.95419e10	−	9.95419e10i	−0.585957	−	0.585957i
$643$	−1.67840e11	+	1.67840e11i	−0.981865	+	0.981865i	−0.999838	−	0.0179739i	$-0.994278\pi$
$643$	−1.67840e11	+	1.67840e11i	−0.981865	+	0.981865i	0.0179739	+	0.999838i	$0.494278\pi$
$644$	3.52391e10	−	3.52391e10i	0.204871	−	0.204871i
$645$	8.88608e10			0.513418
$646$	−1.57232e10	−	1.57232e10i	−0.0902839	−	0.0902839i
$647$	−9.70578e10	+	9.70578e10i	−0.553877	+	0.553877i	−0.927557	−	0.373681i	$-0.878096\pi$
$647$	−9.70578e10	+	9.70578e10i	−0.553877	+	0.553877i	0.373681	+	0.927557i	$0.378096\pi$
$648$	−1.56112e11	−	1.56112e11i	−0.885391	−	0.885391i
$649$	−4.59046e9	+	4.59046e9i	−0.0258748	+	0.0258748i
$650$			2.20639e10i			0.123603i
$651$	−5.01616e10	−	5.01616e10i	−0.279285	−	0.279285i
$652$	9.97940e10	+	9.97940e10i	0.552223	+	0.552223i
$653$	2.21680e10	−	2.21680e10i	0.121920	−	0.121920i	−0.643514	−	0.765434i	$-0.722524\pi$
$653$	2.21680e10	−	2.21680e10i	0.121920	−	0.121920i	0.765434	+	0.643514i	$0.222524\pi$
$654$			2.29672e10i			0.125545i
$655$	2.37103e11			1.28817
$656$		−	9.50968e10i		−	0.513512i
$657$		−	6.55236e11i		−	3.51671i
$658$	1.74135e9	−	1.74135e9i	0.00928928	−	0.00928928i
$659$		−	2.88284e11i		−	1.52855i	−0.644892	−	0.764273i	$-0.723098\pi$
$659$		−	2.88284e11i		−	1.52855i	0.644892	−	0.764273i	$-0.276902\pi$
$660$	−1.14887e11	+	1.14887e11i	−0.605475	+	0.605475i
$661$	1.41561e10	−	1.41561e10i	0.0741544	−	0.0741544i	−0.669057	−	0.743211i	$-0.733302\pi$
$661$	1.41561e10	−	1.41561e10i	0.0741544	−	0.0741544i	0.743211	+	0.669057i	$0.233302\pi$
$662$	−6.96501e10			−0.362652
$663$	4.01294e10			0.207687
$664$	6.19385e10	+	6.19385e10i	0.318631	+	0.318631i
$665$		−	6.77704e10i		−	0.346540i
$666$	9.85158e10	−	1.80657e11i	0.500736	−	0.918242i
$667$	2.25492e10			0.113927
$668$	3.79412e10	−	3.79412e10i	0.190548	−	0.190548i
$669$		−	2.83196e10i		−	0.141378i
$670$			1.03423e11i			0.513238i
$671$	−4.59433e10	−	4.59433e10i	−0.226637	−	0.226637i
$672$	6.82025e10	+	6.82025e10i	0.334444	+	0.334444i
$673$	9.82715e8			0.00479035			0.00239518	−	0.999997i	$-0.499238\pi$
$673$	9.82715e8			0.00479035			0.00239518	+	0.999997i	$0.499238\pi$
$674$	−2.88307e7	−	2.88307e7i	−0.000139706	−	0.000139706i
$675$	1.45167e11			0.699283
$676$	7.28315e10			0.348765
$677$			1.36414e11i			0.649390i	0.945819	+	0.324695i	$0.105262\pi$
$677$			1.36414e11i			0.649390i	−0.945819	+	0.324695i	$0.894738\pi$
$678$	1.48016e11			0.700469
$679$	−5.33991e10	−	5.33991e10i	−0.251221	−	0.251221i
$680$	1.67236e10	−	1.67236e10i	0.0782157	−	0.0782157i
$681$	−3.90721e11	+	3.90721e11i	−1.81668	+	1.81668i
$682$	7.07113e10			0.326852
$683$	−4.72283e10	−	4.72283e10i	−0.217030	−	0.217030i	0.590216	−	0.807245i	$-0.299043\pi$
$683$	−4.72283e10	−	4.72283e10i	−0.217030	−	0.217030i	−0.807245	+	0.590216i	$0.799043\pi$
$684$	4.17017e11	−	4.17017e11i	1.90515	−	1.90515i
$685$	3.18040e10	+	3.18040e10i	0.144450	+	0.144450i
$686$	−3.83245e10	+	3.83245e10i	−0.173053	+	0.173053i
$687$		−	6.57780e11i		−	2.95294i
$688$	−1.94549e10	−	1.94549e10i	−0.0868309	−	0.0868309i
$689$	−9.66955e10	−	9.66955e10i	−0.429071	−	0.429071i
$690$	−1.64182e11	+	1.64182e11i	−0.724318	+	0.724318i
$691$			4.41050e10i			0.193453i	0.995311	+	0.0967266i	$0.0308373\pi$
$691$			4.41050e10i			0.193453i	−0.995311	+	0.0967266i	$0.969163\pi$
$692$	7.59456e10			0.331191
$693$			1.00528e11i			0.435867i
$694$		−	1.18635e11i		−	0.511416i
$695$	−3.98493e10	+	3.98493e10i	−0.170798	+	0.170798i
$696$			2.78433e10i			0.118654i
$697$	−3.96643e10	+	3.96643e10i	−0.168061	+	0.168061i
$698$	−1.11747e11	+	1.11747e11i	−0.470777	+	0.470777i
$699$	−7.09451e11			−2.97176
$700$	−1.63676e10			−0.0681698
$701$	−5.03322e10	−	5.03322e10i	−0.208437	−	0.208437i	0.595166	−	0.803603i	$-0.297086\pi$
$701$	−5.03322e10	−	5.03322e10i	−0.208437	−	0.208437i	−0.803603	+	0.595166i	$0.797086\pi$
$702$		−	1.77147e11i		−	0.729433i
$703$	3.53241e11	+	1.92630e11i	1.44627	+	0.788682i
$704$	−3.01541e10			−0.122760
$705$	2.60245e10	−	2.60245e10i	0.105348	−	0.105348i
$706$			1.44527e11i			0.581740i
$707$			8.72626e10i			0.349261i
$708$	1.12397e10	+	1.12397e10i	0.0447322	+	0.0447322i
$709$	2.21681e11	+	2.21681e11i	0.877293	+	0.877293i	0.993254	−	0.115961i	$-0.0369948\pi$
$709$	2.21681e11	+	2.21681e11i	0.877293	+	0.877293i	−0.115961	+	0.993254i	$0.536995\pi$
$710$	1.79337e11			0.705728
$711$	−3.13998e11	−	3.13998e11i	−1.22871	−	1.22871i
$712$	−3.07682e11			−1.19724
$713$	−3.24144e11			−1.25424
$714$		−	9.28048e9i		−	0.0357090i
$715$	−1.21913e11			−0.466472
$716$	7.04379e10	+	7.04379e10i	0.268012	+	0.268012i
$717$	3.57047e11	−	3.57047e11i	1.35098	−	1.35098i
$718$	−1.47976e11	+	1.47976e11i	−0.556791	+	0.556791i
$719$	−3.75886e11			−1.40650			−0.703251	−	0.710942i	$-0.748269\pi$
$719$	−3.75886e11			−1.40650			−0.703251	+	0.710942i	$0.748269\pi$
$720$	1.13406e11	+	1.13406e11i	0.421995	+	0.421995i
$721$	7.18220e10	−	7.18220e10i	0.265776	−	0.265776i
$722$	−1.60528e11	−	1.60528e11i	−0.590747	−	0.590747i
$723$	−4.95500e11	+	4.95500e11i	−1.81339	+	1.81339i
$724$			5.09812e10i			0.185548i
$725$	−5.23675e9	−	5.23675e9i	−0.0189544	−	0.0189544i
$726$	6.59609e10	+	6.59609e10i	0.237432	+	0.237432i
$727$	−2.01391e11	+	2.01391e11i	−0.720946	+	0.720946i	−0.968798	−	0.247852i	$-0.920275\pi$
$727$	−2.01391e11	+	2.01391e11i	−0.720946	+	0.720946i	0.247852	+	0.968798i	$0.420275\pi$
$728$			4.61733e10i			0.164386i
$729$	1.34455e11			0.476067
$730$		−	1.83767e11i		−	0.647107i
$731$			1.62290e10i			0.0568358i
$732$	−1.12491e11	+	1.12491e11i	−0.391809	+	0.391809i
$733$		−	4.03311e10i		−	0.139709i	−0.997557	−	0.0698544i	$-0.977747\pi$
$733$		−	4.03311e10i		−	0.139709i	0.997557	−	0.0698544i	$-0.0222535\pi$
$734$	−1.14959e10	+	1.14959e10i	−0.0396058	+	0.0396058i
$735$	−2.76380e11	+	2.76380e11i	−0.947017	+	0.947017i
$736$	4.40724e11			1.50195
$737$	2.99974e11			1.01675
$738$	3.27957e11	+	3.27957e11i	1.10558	+	1.10558i
$739$			1.48792e11i			0.498885i	0.968390	+	0.249443i	$0.0802474\pi$
$739$			1.48792e11i			0.498885i	−0.968390	+	0.249443i	$0.919753\pi$
$740$	−8.86281e10	+	1.62525e11i	−0.295559	+	0.541992i
$741$	6.48781e11			2.15191
$742$	−2.23621e10	+	2.23621e10i	−0.0737730	+	0.0737730i
$743$		−	4.42862e11i		−	1.45316i	−0.687083	−	0.726579i	$-0.741109\pi$
$743$		−	4.42862e11i		−	1.45316i	0.687083	−	0.726579i	$-0.258891\pi$
$744$		−	4.00245e11i		−	1.30627i
$745$	−9.43669e10	−	9.43669e10i	−0.306334	−	0.306334i
$746$	5.25371e10	+	5.25371e10i	0.169633	+	0.169633i
$747$	3.50374e11			1.12525
$748$	−2.09823e10	−	2.09823e10i	−0.0670266	−	0.0670266i
$749$	7.83586e10			0.248977
$750$	2.97790e11			0.941165
$751$			9.69368e10i			0.304740i	0.988324	+	0.152370i	$0.0486905\pi$
$751$			9.69368e10i			0.304740i	−0.988324	+	0.152370i	$0.951310\pi$
$752$	−1.13954e10			−0.0356335
$753$	3.89322e11	+	3.89322e11i	1.21096	+	1.21096i
$754$	−6.39039e9	+	6.39039e9i	−0.0197716	+	0.0197716i
$755$	−2.20568e11	+	2.20568e11i	−0.678820	+	0.678820i
$756$	1.31412e11			0.402299
$757$	−8.17467e10	−	8.17467e10i	−0.248935	−	0.248935i	0.571598	−	0.820534i	$-0.306324\pi$
$757$	−8.17467e10	−	8.17467e10i	−0.248935	−	0.248935i	−0.820534	+	0.571598i	$0.806324\pi$
$758$	1.51426e11	−	1.51426e11i	0.458695	−	0.458695i
$759$	4.76201e11	+	4.76201e11i	1.43490	+	1.43490i
$760$	2.70374e11	−	2.70374e11i	0.810420	−	0.810420i
$761$		−	2.76645e11i		−	0.824867i	−0.910988	−	0.412434i	$-0.864679\pi$
$761$		−	2.76645e11i		−	0.824867i	0.910988	−	0.412434i	$-0.135321\pi$
$762$	−1.91060e11	−	1.91060e11i	−0.566695	−	0.566695i
$763$	−9.03981e9	−	9.03981e9i	−0.0266723	−	0.0266723i
$764$	1.58116e11	−	1.58116e11i	0.464091	−	0.464091i
$765$		−	9.46021e10i		−	0.276220i
$766$	4.24559e10			0.123317
$767$			1.19270e10i			0.0344627i
$768$			3.82623e11i			1.09983i
$769$	1.36636e11	−	1.36636e11i	0.390715	−	0.390715i	−0.484228	−	0.874942i	$-0.660899\pi$
$769$	1.36636e11	−	1.36636e11i	0.390715	−	0.390715i	0.874942	+	0.484228i	$0.160899\pi$
$770$			2.81940e10i			0.0802037i
$771$	4.68240e11	−	4.68240e11i	1.32511	−	1.32511i
$772$	−3.18180e11	+	3.18180e11i	−0.895784	+	0.895784i
$773$	−5.03107e11			−1.40910			−0.704551	−	0.709653i	$-0.748852\pi$
$773$	−5.03107e11			−1.40910			−0.704551	+	0.709653i	$0.748852\pi$
$774$	1.34187e11			0.373891
$775$	7.52779e10	+	7.52779e10i	0.208670	+	0.208670i
$776$		−	4.26078e11i		−	1.17501i
$777$	4.73997e10	+	1.61098e11i	0.130044	+	0.441983i
$778$	−1.54538e11			−0.421809
$779$	−6.41260e11	+	6.41260e11i	−1.74134	+	1.74134i
$780$			2.98501e11i			0.806433i
$781$		−	5.20158e11i		−	1.39808i
$782$	−2.99852e10	−	2.99852e10i	−0.0801825	−	0.0801825i
$783$	4.20450e10	+	4.20450e10i	0.111858	+	0.111858i
$784$	1.21019e11			0.320325
$785$	2.22364e11	+	2.22364e11i	0.585579	+	0.585579i
$786$	5.24932e11			1.37535
$787$	5.41984e11			1.41282			0.706411	−	0.707801i	$-0.250313\pi$
$787$	5.41984e11			1.41282			0.706411	+	0.707801i	$0.250313\pi$
$788$		−	8.26458e10i		−	0.214346i
$789$	−5.62931e11			−1.45260
$790$	−8.80637e10	−	8.80637e10i	−0.226094	−	0.226094i
$791$	−5.82584e10	+	5.82584e10i	−0.148817	+	0.148817i
$792$	−4.01063e11	+	4.01063e11i	−1.01932	+	1.01932i
$793$	−1.19370e11			−0.301858
$794$	2.58695e11	+	2.58695e11i	0.650889	+	0.650889i
$795$	−3.34203e11	+	3.34203e11i	−0.836645	+	0.836645i
$796$	−3.40170e11	−	3.40170e11i	−0.847312	−	0.847312i
$797$	−4.69198e10	+	4.69198e10i	−0.116285	+	0.116285i	−0.762855	−	0.646570i	$-0.776203\pi$
$797$	−4.69198e10	+	4.69198e10i	−0.116285	+	0.116285i	0.646570	+	0.762855i	$0.276203\pi$
$798$		−	1.50039e11i		−	0.369993i
$799$	4.75295e9	+	4.75295e9i	0.0116621	+	0.0116621i
$800$	−1.02352e11	−	1.02352e11i	−0.249883	−	0.249883i
$801$	−8.70248e11	+	8.70248e11i	−2.11404	+	2.11404i
$802$			1.64991e11i			0.398808i
$803$	−5.33006e11			−1.28195
$804$		−	7.34479e11i		−	1.75774i
$805$		−	1.29243e11i		−	0.307767i
$806$	9.18614e10	−	9.18614e10i	0.217667	−	0.217667i
$807$			1.08173e12i			2.55050i
$808$	−3.48139e11	+	3.48139e11i	−0.816785	+	0.816785i
$809$	4.78863e11	−	4.78863e11i	1.11794	−	1.11794i	0.125893	−	0.992044i	$-0.459820\pi$
$809$	4.78863e11	−	4.78863e11i	1.11794	−	1.11794i	0.992044	−	0.125893i	$-0.0401797\pi$
$810$	−2.47672e11			−0.575355
$811$	−1.38277e11			−0.319643			−0.159822	−	0.987146i	$-0.551092\pi$
$811$	−1.38277e11			−0.319643			−0.159822	+	0.987146i	$0.551092\pi$
$812$	−4.74057e9	−	4.74057e9i	−0.0109045	−	0.0109045i
$813$		−	1.16090e12i		−	2.65726i
$814$	−1.46956e11	−	8.01384e10i	−0.334727	−	0.182534i
$815$	3.66004e11			0.829575
$816$	−3.03658e10	+	3.03658e10i	−0.0684895	+	0.0684895i
$817$			2.62377e11i			0.588896i
$818$		−	9.37484e10i		−	0.209387i
$819$	1.30596e11	+	1.30596e11i	0.290266	+	0.290266i
$820$	−2.95041e11	−	2.95041e11i	−0.652570	−	0.652570i
$821$	−2.63889e11			−0.580830			−0.290415	−	0.956901i	$-0.593793\pi$
$821$	−2.63889e11			−0.580830			−0.290415	+	0.956901i	$0.593793\pi$
$822$	7.04120e10	+	7.04120e10i	0.154227	+	0.154227i
$823$	1.55536e11			0.339025			0.169513	−	0.985528i	$-0.445781\pi$
$823$	1.55536e11			0.339025			0.169513	+	0.985528i	$0.445781\pi$
$824$	5.73076e11			1.24309
$825$		−	2.21182e11i		−	0.477457i
$826$	2.75828e9			0.00592540
$827$	3.72074e11	+	3.72074e11i	0.795439	+	0.795439i	0.982373	−	0.186934i	$-0.0598550\pi$
$827$	3.72074e11	+	3.72074e11i	0.795439	+	0.795439i	−0.186934	+	0.982373i	$0.559855\pi$
$828$	7.95280e11	−	7.95280e11i	1.69199	−	1.69199i
$829$	4.24349e11	−	4.24349e11i	0.898472	−	0.898472i	−0.0968287	−	0.995301i	$-0.530870\pi$
$829$	4.24349e11	−	4.24349e11i	0.898472	−	0.898472i	0.995301	+	0.0968287i	$0.0308699\pi$
$830$	9.82656e10			0.207057
$831$	2.04166e11	+	2.04166e11i	0.428134	+	0.428134i
$832$	−3.91734e10	+	3.91734e10i	−0.0817519	+	0.0817519i
$833$	−5.04764e10	−	5.04764e10i	−0.104835	−	0.104835i
$834$	−8.82239e10	+	8.82239e10i	−0.182357	+	0.182357i
$835$		−	1.39153e11i		−	0.286250i
$836$	−3.39226e11	−	3.39226e11i	−0.694486	−	0.694486i
$837$	−6.04394e11	−	6.04394e11i	−1.23145	−	1.23145i
$838$	5.66223e9	−	5.66223e9i	0.0114818	−	0.0114818i
$839$			6.63865e11i			1.33978i	0.742462	+	0.669888i	$0.233658\pi$
$839$			6.63865e11i			1.33978i	−0.742462	+	0.669888i	$0.766342\pi$
$840$	1.59586e11			0.320536
$841$			4.97213e11i			0.993936i
$842$		−	1.41535e11i		−	0.281589i
$843$	−3.31263e11	+	3.31263e11i	−0.655939	+	0.655939i
$844$			1.98037e11i			0.390280i
$845$	1.33558e11	−	1.33558e11i	0.261966	−	0.261966i
$846$	3.92990e10	−	3.92990e10i	0.0767185	−	0.0767185i
$847$	−5.19239e10			−0.100887
$848$	1.46338e11			0.282992
$849$	2.47421e11	+	2.47421e11i	0.476218	+	0.476218i
$850$			1.39273e10i			0.0266803i
$851$	6.73655e11	+	3.67358e11i	1.28446	+	0.700440i
$852$	−1.27360e12			−2.41698
$853$	6.12466e11	−	6.12466e11i	1.15687	−	1.15687i	0.171729	−	0.985144i	$-0.445065\pi$
$853$	6.12466e11	−	6.12466e11i	1.15687	−	1.15687i	0.985144	−	0.171729i	$-0.0549352\pi$
$854$			2.76060e10i			0.0519005i
$855$		−	1.52945e12i		−	2.86201i
$856$	3.12616e11	+	3.12616e11i	0.582259	+	0.582259i
$857$	−2.82726e11	−	2.82726e11i	−0.524134	−	0.524134i	0.394683	−	0.918817i	$-0.370854\pi$
$857$	−2.82726e11	−	2.82726e11i	−0.524134	−	0.524134i	−0.918817	+	0.394683i	$0.870854\pi$
$858$	−2.69908e11			−0.498042
$859$	−2.57780e11	−	2.57780e11i	−0.473453	−	0.473453i	0.429577	−	0.903030i	$-0.358663\pi$
$859$	−2.57780e11	−	2.57780e11i	−0.473453	−	0.473453i	−0.903030	+	0.429577i	$0.858663\pi$
$860$	−1.20719e11			−0.220689
$861$	−3.78498e11			−0.688734
$862$		−	4.30549e11i		−	0.779819i
$863$	6.34015e11			1.14303			0.571513	−	0.820593i	$-0.306357\pi$
$863$	6.34015e11			1.14303			0.571513	+	0.820593i	$0.306357\pi$
$864$	8.21767e11	+	8.21767e11i	1.47467	+	1.47467i
$865$	1.39269e11	−	1.39269e11i	0.248765	−	0.248765i
$866$	2.87328e11	−	2.87328e11i	0.510865	−	0.510865i
$867$	−9.76780e11			−1.72870
$868$	6.81453e10	+	6.81453e10i	0.120049	+	0.120049i
$869$	−2.55424e11	+	2.55424e11i	−0.447901	+	0.447901i
$870$	2.20867e10	+	2.20867e10i	0.0385526	+	0.0385526i
$871$	3.89697e11	−	3.89697e11i	0.677103	−	0.677103i
$872$		−	7.21297e10i		−	0.124752i
$873$	−1.20512e12	−	1.20512e12i	−2.07479	−	2.07479i
$874$	−4.84777e11	−	4.84777e11i	−0.830799	−	0.830799i
$875$	−1.17209e11	+	1.17209e11i	−0.199954	+	0.199954i
$876$			1.30505e12i			2.21622i
$877$	5.00783e11			0.846547			0.423274	−	0.906002i	$-0.360881\pi$
$877$	5.00783e11			0.846547			0.423274	+	0.906002i	$0.360881\pi$
$878$		−	2.16476e11i		−	0.364276i
$879$		−	1.31977e12i		−	2.21077i
$880$	9.22512e10	−	9.22512e10i	0.153830	−	0.153830i
$881$			1.00712e11i			0.167177i	0.996500	+	0.0835885i	$0.0266381\pi$
$881$			1.00712e11i			0.167177i	−0.996500	+	0.0835885i	$0.973362\pi$
$882$	−4.17356e11	+	4.17356e11i	−0.689655	+	0.689655i
$883$	−6.58690e10	+	6.58690e10i	−0.108352	+	0.108352i	−0.759204	−	0.650852i	$-0.774412\pi$
$883$	−6.58690e10	+	6.58690e10i	−0.108352	+	0.108352i	0.650852	+	0.759204i	$0.274412\pi$
$884$	−5.45165e10			−0.0892727
$885$	4.12225e10			0.0671988
$886$	−7.81380e10	−	7.81380e10i	−0.126802	−	0.126802i
$887$			5.37698e11i			0.868648i	0.900757	+	0.434324i	$0.143013\pi$
$887$			5.37698e11i			0.868648i	−0.900757	+	0.434324i	$0.856987\pi$
$888$	−4.53605e11	+	8.31813e11i	−0.729501	+	1.33775i
$889$	1.50401e11			0.240793
$890$	−2.44069e11	+	2.44069e11i	−0.389003	+	0.389003i
$891$			7.18357e11i			1.13980i
$892$			3.84727e10i			0.0607706i
$893$	7.68420e10	+	7.68420e10i	0.120835	+	0.120835i
$894$	−2.08922e11	−	2.08922e11i	−0.327066	−	0.327066i
$895$	2.58338e11			0.402621
$896$	−1.12480e11	−	1.12480e11i	−0.174519	−	0.174519i
$897$	1.23727e12			1.91115
$898$	3.69383e10			0.0568030
$899$			4.36057e10i			0.0667582i
$900$	−3.69386e11			−0.563002
$901$	−6.10367e10	−	6.10367e10i	−0.0926173	−	0.0926173i
$902$	2.66779e11	−	2.66779e11i	0.403019	−	0.403019i
$903$	−7.74330e10	+	7.74330e10i	−0.116460	+	0.116460i
$904$	−4.64850e11			−0.696048
$905$	9.34892e10	+	9.34892e10i	0.139369	+	0.139369i
$906$	−4.88324e11	+	4.88324e11i	−0.724761	+	0.724761i
$907$	1.80495e11	+	1.80495e11i	0.266707	+	0.266707i	0.827772	−	0.561065i	$-0.189608\pi$
$907$	1.80495e11	+	1.80495e11i	0.266707	+	0.266707i	−0.561065	+	0.827772i	$0.689608\pi$
$908$	5.30801e11	−	5.30801e11i	0.780887	−	0.780887i
$909$			1.96936e12i			2.88449i
$910$	3.66270e10	+	3.66270e10i	0.0534116	+	0.0534116i
$911$	1.82865e11	+	1.82865e11i	0.265496	+	0.265496i	0.827282	−	0.561787i	$-0.189886\pi$
$911$	1.82865e11	+	1.82865e11i	0.265496	+	0.265496i	−0.561787	+	0.827282i	$0.689886\pi$
$912$	−4.90930e11	+	4.90930e11i	−0.709644	+	0.709644i
$913$		−	2.85014e11i		−	0.410188i
$914$	5.34858e11			0.766397
$915$			4.12572e11i			0.588593i
$916$			8.93606e11i			1.26930i
$917$	−2.06611e11	+	2.06611e11i	−0.292197	+	0.292197i
$918$		−	1.11820e11i		−	0.157452i
$919$	−3.97058e10	+	3.97058e10i	−0.0556663	+	0.0556663i	−0.734392	−	0.678726i	$-0.762533\pi$
$919$	−3.97058e10	+	3.97058e10i	−0.0556663	+	0.0556663i	0.678726	+	0.734392i	$0.262533\pi$
$920$	5.15621e11	−	5.15621e11i	0.719747	−	0.719747i
$921$	−1.11561e12			−1.55050
$922$	−2.08940e11			−0.289133
$923$	−6.75740e11	−	6.75740e11i	−0.931049	−	0.931049i
$924$		−	2.00225e11i		−	0.274682i
$925$	−7.11332e10	−	2.41761e11i	−0.0971640	−	0.330232i
$926$	1.83969e11			0.250208
$927$	1.62089e12	−	1.62089e12i	2.19500	−	2.19500i
$928$		−	5.92888e10i		−	0.0799430i
$929$			9.49449e11i			1.27470i	0.770574	+	0.637351i	$0.219970\pi$
$929$			9.49449e11i			1.27470i	−0.770574	+	0.637351i	$0.780030\pi$
$930$	−3.17495e11	−	3.17495e11i	−0.424429	−	0.424429i
$931$	−8.16062e11	−	8.16062e11i	−1.08624	−	1.08624i
$932$	9.63800e11			1.27739
$933$	−1.33828e12	−	1.33828e12i	−1.76613	−	1.76613i
$934$	−5.53773e10			−0.0727686
$935$	−7.69547e10			−0.100691
$936$			1.04204e12i			1.35763i
$937$	1.42958e12			1.85459			0.927297	−	0.374326i	$-0.122126\pi$
$937$	1.42958e12			1.85459			0.927297	+	0.374326i	$0.122126\pi$
$938$	−9.01227e10	−	9.01227e10i	−0.116419	−	0.116419i
$939$	1.69939e12	−	1.69939e12i	2.18590	−	2.18590i
$940$	−3.53547e10	+	3.53547e10i	−0.0452831	+	0.0452831i
$941$	−3.16326e11			−0.403438			−0.201719	−	0.979443i	$-0.564653\pi$
$941$	−3.16326e11			−0.403438			−0.201719	+	0.979443i	$0.564653\pi$
$942$	4.92300e11	+	4.92300e11i	0.625210	+	0.625210i
$943$	−1.22293e12	+	1.22293e12i	−1.54651	+	1.54651i
$944$	−9.02511e9	−	9.02511e9i	−0.0113649	−	0.0113649i
$945$	2.40984e11	−	2.40984e11i	0.302177	−	0.302177i
$946$		−	1.09155e11i		−	0.136295i
$947$	4.34039e11	+	4.34039e11i	0.539671	+	0.539671i	0.923432	−	0.383761i	$-0.125371\pi$
$947$	4.34039e11	+	4.34039e11i	0.539671	+	0.539671i	−0.383761	+	0.923432i	$0.625371\pi$
$948$	6.25400e11	+	6.25400e11i	0.774327	+	0.774327i
$949$	−6.92431e11	+	6.92431e11i	−0.853712	+	0.853712i
$950$			2.25165e11i			0.276444i
$951$	1.57927e12			1.93079
$952$			2.91458e10i			0.0354836i
$953$			3.24784e11i			0.393752i	0.980428	+	0.196876i	$0.0630797\pi$
$953$			3.24784e11i			0.393752i	−0.980428	+	0.196876i	$0.936920\pi$
$954$	−5.04672e11	+	5.04672e11i	−0.609278	+	0.609278i
$955$		−	5.79907e11i		−	0.697180i
$956$	−4.85055e11	+	4.85055e11i	−0.580710	+	0.580710i
$957$	6.40613e10	−	6.40613e10i	0.0763744	−	0.0763744i
$958$	−2.24720e11			−0.266796
$959$	−5.54277e10			−0.0655319
$960$	1.35393e11	+	1.35393e11i	0.159408	+	0.159408i
$961$			2.26061e11i			0.265053i
$962$	−2.95020e11	+	8.68036e10i	−0.344470	+	0.101353i
$963$	1.76841e12			2.05626
$964$	6.73145e11	−	6.73145e11i	0.779472	−	0.779472i
$965$			1.16696e12i			1.34569i
$966$		−	2.86135e11i		−	0.328597i
$967$	−2.57926e11	−	2.57926e11i	−0.294978	−	0.294978i	0.544065	−	0.839043i	$-0.316884\pi$
$967$	−2.57926e11	−	2.57926e11i	−0.294978	−	0.294978i	−0.839043	+	0.544065i	$0.816884\pi$
$968$	−2.07153e11	−	2.07153e11i	−0.235934	−	0.235934i
$969$	4.09528e11			0.464503
$970$	−3.37987e11	−	3.37987e11i	−0.381780	−	0.381780i
$971$	1.26439e12			1.42234			0.711170	−	0.703020i	$-0.248166\pi$
$971$	1.26439e12			1.42234			0.711170	+	0.703020i	$0.248166\pi$
$972$	3.76528e11			0.421825
$973$		−	6.94492e10i		−	0.0774846i
$974$	−2.45049e11			−0.272281
$975$	−2.87339e11	−	2.87339e11i	−0.317962	−	0.317962i
$976$	9.03271e10	−	9.03271e10i	0.0995448	−	0.0995448i
$977$	−1.44857e11	+	1.44857e11i	−0.158987	+	0.158987i	−0.782118	−	0.623131i	$-0.785860\pi$
$977$	−1.44857e11	+	1.44857e11i	−0.158987	+	0.158987i	0.623131	+	0.782118i	$0.285860\pi$
$978$	8.10311e11			0.885719
$979$	7.07909e11	+	7.07909e11i	0.770631	+	0.770631i
$980$	3.75467e11	−	3.75467e11i	0.407068	−	0.407068i
$981$	−2.04012e11	−	2.04012e11i	−0.220282	−	0.220282i
$982$	−1.42968e11	+	1.42968e11i	−0.153742	+	0.153742i
$983$			2.06183e11i			0.220820i	0.993886	+	0.110410i	$0.0352164\pi$
$983$			2.06183e11i			0.220820i	−0.993886	+	0.110410i	$0.964784\pi$
$984$	−1.51004e12	−	1.51004e12i	−1.61068	−	1.61068i
$985$	−1.51556e11	−	1.51556e11i	−0.161001	−	0.161001i
$986$	−4.03378e9	+	4.03378e9i	−0.00426781	+	0.00426781i
$987$			4.53553e10i			0.0477925i
$988$	−8.81379e11			−0.924986
$989$			5.00372e11i			0.523007i
$990$			6.36287e11i			0.662388i
$991$	−4.91216e11	+	4.91216e11i	−0.509305	+	0.509305i	−0.914313	−	0.405008i	$-0.867269\pi$
$991$	−4.91216e11	+	4.91216e11i	−0.509305	+	0.509305i	0.405008	+	0.914313i	$0.367269\pi$
$992$			8.52272e11i			0.880099i
$993$	9.07057e11	−	9.07057e11i	0.932905	−	0.932905i
$994$	−1.56274e11	+	1.56274e11i	−0.160082	+	0.160082i
$995$	−1.24761e12			−1.27287
$996$	−6.97851e11			−0.709129
$997$	9.45516e11	+	9.45516e11i	0.956948	+	0.956948i	0.999111	−	0.0421632i	$-0.0134249\pi$
$997$	9.45516e11	+	9.45516e11i	0.956948	+	0.956948i	−0.0421632	+	0.999111i	$0.513425\pi$
$998$			4.34304e11i			0.437796i
$999$	5.71116e11	+	1.94106e12i	0.573406	+	1.94884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.11	✓	50
37.31	odd	4	inner	37.9.d.a.31.11	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.11	✓	50	1.1	even	1	trivial
37.9.d.a.31.11	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)

\(f(q)\)	\(=\)	\(q+(-5.51546 + 5.51546i) q^{2} -143.656i q^{3} +195.159i q^{4} +(357.883 + 357.883i) q^{5} +(792.331 + 792.331i) q^{6} -623.716 q^{7} +(-2488.35 - 2488.35i) q^{8} -14076.1 q^{9} +O(q^{10})\)	\(q+(-5.51546 + 5.51546i) q^{2} -143.656i q^{3} +195.159i q^{4} +(357.883 + 357.883i) q^{5} +(792.331 + 792.331i) q^{6} -623.716 q^{7} +(-2488.35 - 2488.35i) q^{8} -14076.1 q^{9} -3947.78 q^{10} +11450.3i q^{11} +28035.9 q^{12} +(14875.2 + 14875.2i) q^{13} +(3440.08 - 3440.08i) q^{14} +(51412.1 - 51412.1i) q^{15} -22512.0 q^{16} +(9389.60 + 9389.60i) q^{17} +(77636.3 - 77636.3i) q^{18} +(151804. + 151804. i) q^{19} +(-69844.2 + 69844.2i) q^{20} +89600.7i q^{21} +(-63153.8 - 63153.8i) q^{22} +(289500. + 289500. i) q^{23} +(-357467. + 357467. i) q^{24} -134465. i q^{25} -164087. q^{26} +1.07959e6i q^{27} -121724. i q^{28} +(38945.2 - 38945.2i) q^{29} +567123. i q^{30} +(-559835. + 559835. i) q^{31} +(761182. - 761182. i) q^{32} +1.64491e6 q^{33} -103576. q^{34} +(-223217. - 223217. i) q^{35} -2.74709e6i q^{36} +(1.79795e6 - 529010. i) q^{37} -1.67453e6 q^{38} +(2.13691e6 - 2.13691e6i) q^{39} -1.78108e6i q^{40} +4.22428e6i q^{41} +(-494189. - 494189. i) q^{42} +(864201. + 864201. i) q^{43} -2.23464e6 q^{44} +(-5.03760e6 - 5.03760e6i) q^{45} -3.19345e6 q^{46} +506194. q^{47} +3.23399e6i q^{48} -5.37578e6 q^{49} +(741634. + 741634. i) q^{50} +(1.34887e6 - 1.34887e6i) q^{51} +(-2.90303e6 + 2.90303e6i) q^{52} -6.50047e6 q^{53} +(-5.95446e6 - 5.95446e6i) q^{54} +(-4.09787e6 + 4.09787e6i) q^{55} +(1.55203e6 + 1.55203e6i) q^{56} +(2.18075e7 - 2.18075e7i) q^{57} +429601. i q^{58} +(400903. + 400903. i) q^{59} +(1.00336e7 + 1.00336e7i) q^{60} +(-4.01240e6 + 4.01240e6i) q^{61} -6.17549e6i q^{62} +8.77950e6 q^{63} +2.63348e6i q^{64} +1.06471e7i q^{65} +(-9.07243e6 + 9.07243e6i) q^{66} -2.61978e7i q^{67} +(-1.83247e6 + 1.83247e6i) q^{68} +(4.15884e7 - 4.15884e7i) q^{69} +2.46229e6 q^{70} -4.54274e7 q^{71} +(3.50263e7 + 3.50263e7i) q^{72} +4.65495e7i q^{73} +(-6.99879e6 + 1.28343e7i) q^{74} -1.93167e7 q^{75} +(-2.96259e7 + 2.96259e7i) q^{76} -7.14175e6i q^{77} +2.35721e7i q^{78} +(2.23071e7 + 2.23071e7i) q^{79} +(-8.05665e6 - 8.05665e6i) q^{80} +6.27369e7 q^{81} +(-2.32988e7 - 2.32988e7i) q^{82} -2.48914e7 q^{83} -1.74864e7 q^{84} +6.72075e6i q^{85} -9.53293e6 q^{86} +(-5.59472e6 - 5.59472e6i) q^{87} +(2.84924e7 - 2.84924e7i) q^{88} +(6.18244e7 - 6.18244e7i) q^{89} +5.55694e7 q^{90} +(-9.27788e6 - 9.27788e6i) q^{91} +(-5.64986e7 + 5.64986e7i) q^{92} +(8.04237e7 + 8.04237e7i) q^{93} +(-2.79189e6 + 2.79189e6i) q^{94} +1.08656e8i q^{95} +(-1.09349e8 - 1.09349e8i) q^{96} +(8.56145e7 + 8.56145e7i) q^{97} +(2.96499e7 - 2.96499e7i) q^{98} -1.61176e8i 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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