LMFDB - Embedded newform 41.10.c.a.9.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,10,Mod(9,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("41.9");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	41.c (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:	$21.1164692827$
Analytic rank:	$0$
Dimension:	$62$
Relative dimension:	$31$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			9.20
Character	$\chi$	$=$	41.9
Dual form			41.10.c.a.32.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.9877i q^{2} +(64.9677 + 64.9677i) q^{3} +316.344 q^{4} +2181.64i q^{5} +(-908.750 + 908.750i) q^{6} +(4287.58 + 4287.58i) q^{7} +11586.6i q^{8} -11241.4i q^{9} +O(q^{10})$	\(q+13.9877i q^{2} +(64.9677 + 64.9677i) q^{3} +316.344 q^{4} +2181.64i q^{5} +(-908.750 + 908.750i) q^{6} +(4287.58 + 4287.58i) q^{7} +11586.6i q^{8} -11241.4i q^{9} -30516.2 q^{10} +(-7004.36 - 7004.36i) q^{11} +(20552.1 + 20552.1i) q^{12} +(69649.1 + 69649.1i) q^{13} +(-59973.5 + 59973.5i) q^{14} +(-141736. + 141736. i) q^{15} -102.737 q^{16} +(369194. - 369194. i) q^{17} +157242. q^{18} +(16364.4 - 16364.4i) q^{19} +690149. i q^{20} +557108. i q^{21} +(97975.0 - 97975.0i) q^{22} -1.18099e6 q^{23} +(-752757. + 752757. i) q^{24} -2.80644e6 q^{25} +(-974233. + 974233. i) q^{26} +(2.00909e6 - 2.00909e6i) q^{27} +(1.35635e6 + 1.35635e6i) q^{28} +(-1.87104e6 - 1.87104e6i) q^{29} +(-1.98257e6 - 1.98257e6i) q^{30} -9.63425e6 q^{31} +5.93092e6i q^{32} -910114. i q^{33} +(5.16418e6 + 5.16418e6i) q^{34} +(-9.35397e6 + 9.35397e6i) q^{35} -3.55615e6i q^{36} +1.85238e7 q^{37} +(228900. + 228900. i) q^{38} +9.04988e6i q^{39} -2.52779e7 q^{40} +(-1.49537e7 + 1.01867e7i) q^{41} -7.79268e6 q^{42} -2.26672e7i q^{43} +(-2.21578e6 - 2.21578e6i) q^{44} +2.45247e7 q^{45} -1.65193e7i q^{46} +(-2.28012e7 + 2.28012e7i) q^{47} +(-6674.60 - 6674.60i) q^{48} -3.58688e6i q^{49} -3.92557e7i q^{50} +4.79713e7 q^{51} +(2.20331e7 + 2.20331e7i) q^{52} +(2.66763e7 + 2.66763e7i) q^{53} +(2.81025e7 + 2.81025e7i) q^{54} +(1.52810e7 - 1.52810e7i) q^{55} +(-4.96787e7 + 4.96787e7i) q^{56} +2.12631e6 q^{57} +(2.61716e7 - 2.61716e7i) q^{58} +1.39693e8 q^{59} +(-4.48373e7 + 4.48373e7i) q^{60} -8.06617e7i q^{61} -1.34761e8i q^{62} +(4.81985e7 - 4.81985e7i) q^{63} -8.30127e7 q^{64} +(-1.51949e8 + 1.51949e8i) q^{65} +1.27304e7 q^{66} +(1.95925e8 - 1.95925e8i) q^{67} +(1.16792e8 - 1.16792e8i) q^{68} +(-7.67260e7 - 7.67260e7i) q^{69} +(-1.30841e8 - 1.30841e8i) q^{70} +(1.12212e8 + 1.12212e8i) q^{71} +1.30250e8 q^{72} -1.71187e8i q^{73} +2.59106e8i q^{74} +(-1.82328e8 - 1.82328e8i) q^{75} +(5.17676e6 - 5.17676e6i) q^{76} -6.00635e7i q^{77} -1.26587e8 q^{78} +(2.52965e8 + 2.52965e8i) q^{79} -224136. i q^{80} +3.97867e7 q^{81} +(-1.42488e8 - 2.09168e8i) q^{82} -5.34872e8 q^{83} +1.76238e8i q^{84} +(8.05448e8 + 8.05448e8i) q^{85} +3.17063e8 q^{86} -2.43114e8i q^{87} +(8.11570e7 - 8.11570e7i) q^{88} +(2.89750e7 + 2.89750e7i) q^{89} +3.43045e8i q^{90} +5.97253e8i q^{91} -3.73598e8 q^{92} +(-6.25915e8 - 6.25915e8i) q^{93} +(-3.18937e8 - 3.18937e8i) q^{94} +(3.57012e7 + 3.57012e7i) q^{95} +(-3.85318e8 + 3.85318e8i) q^{96} +(-5.24970e8 + 5.24970e8i) q^{97} +5.01723e7 q^{98} +(-7.87388e7 + 7.87388e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 148 q^{3} - 15876 q^{4} - 4372 q^{6} - 2 q^{7}+O(q^{10}) $ 62 * q - 148 * q^3 - 15876 * q^4 - 4372 * q^6 - 2 * q^7	\( 62 q - 148 q^{3} - 15876 q^{4} - 4372 q^{6} - 2 q^{7} + 64940 q^{10} - 101136 q^{11} + 88610 q^{12} - 212164 q^{13} - 486724 q^{14} - 280448 q^{15} + 4065276 q^{16} + 989130 q^{17} + 631900 q^{18} - 557304 q^{19} + 878738 q^{22} - 2585064 q^{23} + 8160792 q^{24} - 13556490 q^{25} - 4638930 q^{26} - 4560520 q^{27} - 15062678 q^{28} - 645332 q^{29} + 24289990 q^{30} - 10831104 q^{31} + 3975452 q^{34} + 29170524 q^{35} - 3116208 q^{37} + 29714800 q^{38} - 35676784 q^{40} + 38183180 q^{41} - 88501252 q^{42} + 88194656 q^{44} - 44608688 q^{45} - 37901682 q^{47} - 65214646 q^{48} + 22786536 q^{51} + 67233198 q^{52} + 98223480 q^{53} - 222847538 q^{54} + 341535988 q^{55} + 37845552 q^{56} + 543416000 q^{57} - 39712038 q^{58} + 476227372 q^{59} - 73813254 q^{60} - 329401706 q^{63} - 1473830612 q^{64} - 283361396 q^{65} + 1055141156 q^{66} + 137841616 q^{67} - 1702495104 q^{68} - 643435264 q^{69} - 1945980994 q^{70} + 43024650 q^{71} + 298006608 q^{72} + 511623892 q^{75} + 2630680074 q^{76} + 2932953920 q^{78} - 559013342 q^{79} - 3103395126 q^{81} - 1636160042 q^{82} + 4760276320 q^{83} + 234551440 q^{85} + 4427686276 q^{86} - 1446984286 q^{88} - 373768662 q^{89} - 546085324 q^{92} + 246761008 q^{93} - 931400058 q^{94} - 2067661068 q^{95} - 7929456644 q^{96} - 949806418 q^{97} + 5988587276 q^{98} + 1756047684 q^{99}+O(q^{100}) \) 62 * q - 148 * q^3 - 15876 * q^4 - 4372 * q^6 - 2 * q^7 + 64940 * q^10 - 101136 * q^11 + 88610 * q^12 - 212164 * q^13 - 486724 * q^14 - 280448 * q^15 + 4065276 * q^16 + 989130 * q^17 + 631900 * q^18 - 557304 * q^19 + 878738 * q^22 - 2585064 * q^23 + 8160792 * q^24 - 13556490 * q^25 - 4638930 * q^26 - 4560520 * q^27 - 15062678 * q^28 - 645332 * q^29 + 24289990 * q^30 - 10831104 * q^31 + 3975452 * q^34 + 29170524 * q^35 - 3116208 * q^37 + 29714800 * q^38 - 35676784 * q^40 + 38183180 * q^41 - 88501252 * q^42 + 88194656 * q^44 - 44608688 * q^45 - 37901682 * q^47 - 65214646 * q^48 + 22786536 * q^51 + 67233198 * q^52 + 98223480 * q^53 - 222847538 * q^54 + 341535988 * q^55 + 37845552 * q^56 + 543416000 * q^57 - 39712038 * q^58 + 476227372 * q^59 - 73813254 * q^60 - 329401706 * q^63 - 1473830612 * q^64 - 283361396 * q^65 + 1055141156 * q^66 + 137841616 * q^67 - 1702495104 * q^68 - 643435264 * q^69 - 1945980994 * q^70 + 43024650 * q^71 + 298006608 * q^72 + 511623892 * q^75 + 2630680074 * q^76 + 2932953920 * q^78 - 559013342 * q^79 - 3103395126 * q^81 - 1636160042 * q^82 + 4760276320 * q^83 + 234551440 * q^85 + 4427686276 * q^86 - 1446984286 * q^88 - 373768662 * q^89 - 546085324 * q^92 + 246761008 * q^93 - 931400058 * q^94 - 2067661068 * q^95 - 7929456644 * q^96 - 949806418 * q^97 + 5988587276 * q^98 + 1756047684 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			13.9877i			0.618176i	0.951033	+	0.309088i	$0.100024\pi$
$2$			13.9877i			0.618176i	−0.951033	+	0.309088i	$0.899976\pi$
$3$	64.9677	+	64.9677i	0.463075	+	0.463075i	0.899662	−	0.436587i	$-0.143813\pi$
$3$	64.9677	+	64.9677i	0.463075	+	0.463075i	−0.436587	+	0.899662i	$0.643813\pi$
$4$	316.344			0.617859
$5$			2181.64i			1.56106i	0.625121	+	0.780528i	$0.285050\pi$
$5$			2181.64i			1.56106i	−0.625121	+	0.780528i	$0.714950\pi$
$6$	−908.750	+	908.750i	−0.286262	+	0.286262i
$7$	4287.58	+	4287.58i	0.674949	+	0.674949i	0.958853	−	0.283903i	$-0.0916295\pi$
$7$	4287.58	+	4287.58i	0.674949	+	0.674949i	−0.283903	+	0.958853i	$0.591630\pi$
$8$			11586.6i			1.00012i
$9$		−	11241.4i		−	0.571123i
$10$	−30516.2			−0.965007
$11$	−7004.36	−	7004.36i	−0.144245	−	0.144245i	0.631296	−	0.775542i	$-0.282523\pi$
$11$	−7004.36	−	7004.36i	−0.144245	−	0.144245i	−0.775542	+	0.631296i	$0.782523\pi$
$12$	20552.1	+	20552.1i	0.286115	+	0.286115i
$13$	69649.1	+	69649.1i	0.676349	+	0.676349i	0.959172	−	0.282823i	$-0.0912710\pi$
$13$	69649.1	+	69649.1i	0.676349	+	0.676349i	−0.282823	+	0.959172i	$0.591271\pi$
$14$	−59973.5	+	59973.5i	−0.417237	+	0.417237i
$15$	−141736.	+	141736.i	−0.722886	+	0.722886i
$16$	−102.737			−0.000391912
$17$	369194.	−	369194.i	1.07210	−	1.07210i	0.0749063	−	0.997191i	$-0.476134\pi$
$17$	369194.	−	369194.i	1.07210	−	1.07210i	0.997191	−	0.0749063i	$-0.0238658\pi$
$18$	157242.			0.353054
$19$	16364.4	−	16364.4i	0.0288077	−	0.0288077i	−0.692556	−	0.721364i	$-0.743516\pi$
$19$	16364.4	−	16364.4i	0.0288077	−	0.0288077i	0.721364	+	0.692556i	$0.243516\pi$
$20$			690149.i			0.964512i
$21$			557108.i			0.625105i
$22$	97975.0	−	97975.0i	0.0891689	−	0.0891689i
$23$	−1.18099e6			−0.879974			−0.439987	−	0.898004i	$-0.645017\pi$
$23$	−1.18099e6			−0.879974			−0.439987	+	0.898004i	$0.645017\pi$
$24$	−752757.	+	752757.i	−0.463131	+	0.463131i
$25$	−2.80644e6			−1.43690
$26$	−974233.	+	974233.i	−0.418102	+	0.418102i
$27$	2.00909e6	−	2.00909e6i	0.727548	−	0.727548i
$28$	1.35635e6	+	1.35635e6i	0.417023	+	0.417023i
$29$	−1.87104e6	−	1.87104e6i	−0.491238	−	0.491238i	0.417458	−	0.908696i	$-0.362921\pi$
$29$	−1.87104e6	−	1.87104e6i	−0.491238	−	0.491238i	−0.908696	+	0.417458i	$0.862921\pi$
$30$	−1.98257e6	−	1.98257e6i	−0.446871	−	0.446871i
$31$	−9.63425e6			−1.87366			−0.936829	−	0.349788i	$-0.886254\pi$
$31$	−9.63425e6			−1.87366			−0.936829	+	0.349788i	$0.886254\pi$
$32$			5.93092e6i			0.999879i
$33$		−	910114.i		−	0.133593i
$34$	5.16418e6	+	5.16418e6i	0.662744	+	0.662744i
$35$	−9.35397e6	+	9.35397e6i	−1.05363	+	1.05363i
$36$		−	3.55615e6i		−	0.352873i
$37$	1.85238e7			1.62488			0.812442	−	0.583042i	$-0.198138\pi$
$37$	1.85238e7			1.62488			0.812442	+	0.583042i	$0.198138\pi$
$38$	228900.	+	228900.i	0.0178082	+	0.0178082i
$39$			9.04988e6i			0.626401i
$40$	−2.52779e7			−1.56124
$41$	−1.49537e7	+	1.01867e7i	−0.826460	+	0.562996i
$41$	−1.49537e7	+	1.01867e7i	−0.826460	+	0.562996i
$42$	−7.79268e6			−0.386425
$43$		−	2.26672e7i		−	1.01109i	−0.862800	−	0.505545i	$-0.831291\pi$
$43$		−	2.26672e7i		−	1.01109i	0.862800	−	0.505545i	$-0.168709\pi$
$44$	−2.21578e6	−	2.21578e6i	−0.0891231	−	0.0891231i
$45$	2.45247e7			0.891554
$46$		−	1.65193e7i		−	0.543979i
$47$	−2.28012e7	+	2.28012e7i	−0.681582	+	0.681582i	−0.960357	−	0.278775i	$-0.910072\pi$
$47$	−2.28012e7	+	2.28012e7i	−0.681582	+	0.681582i	0.278775	+	0.960357i	$0.410072\pi$
$48$	−6674.60	−	6674.60i	−0.000181485	−	0.000181485i
$49$		−	3.58688e6i		−	0.0888863i
$50$		−	3.92557e7i		−	0.888254i
$51$	4.79713e7			0.992923
$52$	2.20331e7	+	2.20331e7i	0.417888	+	0.417888i
$53$	2.66763e7	+	2.66763e7i	0.464391	+	0.464391i	0.900092	−	0.435701i	$-0.143499\pi$
$53$	2.66763e7	+	2.66763e7i	0.464391	+	0.464391i	−0.435701	+	0.900092i	$0.643499\pi$
$54$	2.81025e7	+	2.81025e7i	0.449753	+	0.449753i
$55$	1.52810e7	−	1.52810e7i	0.225175	−	0.225175i
$56$	−4.96787e7	+	4.96787e7i	−0.675031	+	0.675031i
$57$	2.12631e6			0.0266802
$58$	2.61716e7	−	2.61716e7i	0.303671	−	0.303671i
$59$	1.39693e8			1.50087			0.750433	−	0.660947i	$-0.229845\pi$
$59$	1.39693e8			1.50087			0.750433	+	0.660947i	$0.229845\pi$
$60$	−4.48373e7	+	4.48373e7i	−0.446642	+	0.446642i
$61$		−	8.06617e7i		−	0.745904i	−0.927851	−	0.372952i	$-0.878346\pi$
$61$		−	8.06617e7i		−	0.745904i	0.927851	−	0.372952i	$-0.121654\pi$
$62$		−	1.34761e8i		−	1.15825i
$63$	4.81985e7	−	4.81985e7i	0.385479	−	0.385479i
$64$	−8.30127e7			−0.618493
$65$	−1.51949e8	+	1.51949e8i	−1.05582	+	1.05582i
$66$	1.27304e7			0.0825838
$67$	1.95925e8	−	1.95925e8i	1.18783	−	1.18783i	0.210162	−	0.977667i	$-0.432601\pi$
$67$	1.95925e8	−	1.95925e8i	1.18783	−	1.18783i	0.977667	−	0.210162i	$-0.0673991\pi$
$68$	1.16792e8	−	1.16792e8i	0.662404	−	0.662404i
$69$	−7.67260e7	−	7.67260e7i	−0.407494	−	0.407494i
$70$	−1.30841e8	−	1.30841e8i	−0.651331	−	0.651331i
$71$	1.12212e8	+	1.12212e8i	0.524056	+	0.524056i	0.918794	−	0.394737i	$-0.129164\pi$
$71$	1.12212e8	+	1.12212e8i	0.524056	+	0.524056i	−0.394737	+	0.918794i	$0.629164\pi$
$72$	1.30250e8			0.571192
$73$		−	1.71187e8i		−	0.705534i	−0.935711	−	0.352767i	$-0.885241\pi$
$73$		−	1.71187e8i		−	0.705534i	0.935711	−	0.352767i	$-0.114759\pi$
$74$			2.59106e8i			1.00446i
$75$	−1.82328e8	−	1.82328e8i	−0.665391	−	0.665391i
$76$	5.17676e6	−	5.17676e6i	0.0177991	−	0.0177991i
$77$		−	6.00635e7i		−	0.194716i
$78$	−1.26587e8			−0.387226
$79$	2.52965e8	+	2.52965e8i	0.730699	+	0.730699i	0.970758	−	0.240059i	$-0.0771668\pi$
$79$	2.52965e8	+	2.52965e8i	0.730699	+	0.730699i	−0.240059	+	0.970758i	$0.577167\pi$
$80$		−	224136.i		−	0.000611796i
$81$	3.97867e7			0.102696
$82$	−1.42488e8	−	2.09168e8i	−0.348030	−	0.510897i
$83$	−5.34872e8			−1.23708			−0.618541	−	0.785753i	$-0.712276\pi$
$83$	−5.34872e8			−1.23708			−0.618541	+	0.785753i	$0.712276\pi$
$84$			1.76238e8i			0.386226i
$85$	8.05448e8	+	8.05448e8i	1.67360	+	1.67360i
$86$	3.17063e8			0.625032
$87$		−	2.43114e8i		−	0.454960i
$88$	8.11570e7	−	8.11570e7i	0.144263	−	0.144263i
$89$	2.89750e7	+	2.89750e7i	0.0489518	+	0.0489518i	0.731159	−	0.682207i	$-0.238980\pi$
$89$	2.89750e7	+	2.89750e7i	0.0489518	+	0.0489518i	−0.682207	+	0.731159i	$0.738980\pi$
$90$			3.43045e8i			0.551137i
$91$			5.97253e8i			0.913002i
$92$	−3.73598e8			−0.543700
$93$	−6.25915e8	−	6.25915e8i	−0.867645	−	0.867645i
$94$	−3.18937e8	−	3.18937e8i	−0.421337	−	0.421337i
$95$	3.57012e7	+	3.57012e7i	0.0449704	+	0.0449704i
$96$	−3.85318e8	+	3.85318e8i	−0.463019	+	0.463019i
$97$	−5.24970e8	+	5.24970e8i	−0.602090	+	0.602090i	−0.940867	−	0.338776i	$-0.889987\pi$
$97$	−5.24970e8	+	5.24970e8i	−0.602090	+	0.602090i	0.338776	+	0.940867i	$0.389987\pi$
$98$	5.01723e7			0.0549474
$99$	−7.87388e7	+	7.87388e7i	−0.0823817	+	0.0823817i
$100$	−8.87798e8			−0.887798
$101$	−4.89734e7	+	4.89734e7i	−0.0468289	+	0.0468289i	−0.730133	−	0.683305i	$-0.760542\pi$
$101$	−4.89734e7	+	4.89734e7i	−0.0468289	+	0.0468289i	0.683305	+	0.730133i	$0.260542\pi$
$102$			6.71009e8i			0.613801i
$103$			2.72222e8i			0.238317i	0.992875	+	0.119158i	$0.0380197\pi$
$103$			2.72222e8i			0.238317i	−0.992875	+	0.119158i	$0.961980\pi$
$104$	−8.07000e8	+	8.07000e8i	−0.676431	+	0.676431i
$105$	−1.21541e9			−0.975824
$106$	−3.73140e8	+	3.73140e8i	−0.287075	+	0.287075i
$107$	1.12472e9			0.829500			0.414750	−	0.909935i	$-0.363869\pi$
$107$	1.12472e9			0.829500			0.414750	+	0.909935i	$0.363869\pi$
$108$	6.35562e8	−	6.35562e8i	0.449522	−	0.449522i
$109$	1.53668e9	−	1.53668e9i	1.04271	−	1.04271i	0.0436643	−	0.999046i	$-0.486097\pi$
$109$	1.53668e9	−	1.53668e9i	1.04271	−	1.04271i	0.999046	−	0.0436643i	$-0.0139032\pi$
$110$	2.13746e8	+	2.13746e8i	0.139198	+	0.139198i
$111$	1.20345e9	+	1.20345e9i	0.752444	+	0.752444i
$112$	−440495.	−	440495.i	−0.000264521	−	0.000264521i
$113$	−1.87030e9			−1.07909			−0.539546	−	0.841956i	$-0.681404\pi$
$113$	−1.87030e9			−1.07909			−0.539546	+	0.841956i	$0.681404\pi$
$114$			2.97422e7i			0.0164931i
$115$		−	2.57649e9i		−	1.37369i
$116$	−5.91892e8	−	5.91892e8i	−0.303516	−	0.303516i
$117$	7.82954e8	−	7.82954e8i	0.386278	−	0.386278i
$118$			1.95399e9i			0.927799i
$119$	3.16590e9			1.44722
$120$	−1.64225e9	−	1.64225e9i	−0.722974	−	0.722974i
$121$		−	2.25983e9i		−	0.958387i
$122$	1.12827e9			0.461100
$123$	−1.63331e9	−	3.09703e8i	−0.643423	−	0.122004i
$124$	−3.04773e9			−1.15766
$125$		−	1.86162e9i		−	0.682018i
$126$	6.74186e8	+	6.74186e8i	0.238294	+	0.238294i
$127$	8.62150e8			0.294080			0.147040	−	0.989131i	$-0.453025\pi$
$127$	8.62150e8			0.294080			0.147040	+	0.989131i	$0.453025\pi$
$128$			1.87547e9i			0.617542i
$129$	1.47264e9	−	1.47264e9i	0.468211	−	0.468211i
$130$	−2.12543e9	−	2.12543e9i	−0.652681	−	0.652681i
$131$			7.76960e8i			0.230504i	0.993336	+	0.115252i	$0.0367675\pi$
$131$			7.76960e8i			0.230504i	−0.993336	+	0.115252i	$0.963233\pi$
$132$		−	2.87909e8i		−	0.0825414i
$133$	1.40327e8			0.0388874
$134$	2.74055e9	+	2.74055e9i	0.734287	+	0.734287i
$135$	4.38311e9	+	4.38311e9i	1.13574	+	1.13574i
$136$	4.27771e9	+	4.27771e9i	1.07223	+	1.07223i
$137$	3.80044e9	−	3.80044e9i	0.921702	−	0.921702i	−0.0754473	−	0.997150i	$-0.524038\pi$
$137$	3.80044e9	−	3.80044e9i	0.921702	−	0.921702i	0.997150	+	0.0754473i	$0.0240385\pi$
$138$	1.07322e9	−	1.07322e9i	0.251903	−	0.251903i
$139$	−1.58535e9			−0.360213			−0.180106	−	0.983647i	$-0.557644\pi$
$139$	−1.58535e9			−0.360213			−0.180106	+	0.983647i	$0.557644\pi$
$140$	−2.95907e9	+	2.95907e9i	−0.650997	+	0.650997i
$141$	−2.96269e9			−0.631247
$142$	−1.56960e9	+	1.56960e9i	−0.323959	+	0.323959i
$143$		−	9.75695e8i		−	0.195120i
$144$			1.15491e6i			0.000223830i
$145$	4.08194e9	−	4.08194e9i	0.766850	−	0.766850i
$146$	2.39452e9			0.436144
$147$	2.33032e8	−	2.33032e8i	0.0411611	−	0.0411611i
$148$	5.85989e9			1.00395
$149$	−3.39121e9	+	3.39121e9i	−0.563659	+	0.563659i	−0.930345	−	0.366686i	$-0.880492\pi$
$149$	−3.39121e9	+	3.39121e9i	−0.563659	+	0.563659i	0.366686	+	0.930345i	$0.380492\pi$
$150$	2.55035e9	−	2.55035e9i	0.411328	−	0.411328i
$151$	8.52765e8	+	8.52765e8i	0.133485	+	0.133485i	0.770692	−	0.637207i	$-0.219910\pi$
$151$	8.52765e8	+	8.52765e8i	0.133485	+	0.133485i	−0.637207	+	0.770692i	$0.719910\pi$
$152$	1.89608e8	+	1.89608e8i	0.0288112	+	0.0288112i
$153$	−4.15026e9	−	4.15026e9i	−0.612299	−	0.612299i
$154$	8.40152e8			0.120369
$155$		−	2.10185e10i		−	2.92488i
$156$			2.86287e9i			0.387027i
$157$	6.81414e9	+	6.81414e9i	0.895081	+	0.895081i	0.994996	−	0.0999148i	$-0.0318570\pi$
$157$	6.81414e9	+	6.81414e9i	0.895081	+	0.895081i	−0.0999148	+	0.994996i	$0.531857\pi$
$158$	−3.53840e9	+	3.53840e9i	−0.451700	+	0.451700i
$159$			3.46619e9i			0.430096i
$160$	−1.29391e10			−1.56087
$161$	−5.06358e9	−	5.06358e9i	−0.593938	−	0.593938i
$162$			5.56525e8i			0.0634845i
$163$	9.37255e9			1.03995			0.519976	−	0.854181i	$-0.325941\pi$
$163$	9.37255e9			1.03995			0.519976	+	0.854181i	$0.325941\pi$
$164$	−4.73051e9	+	3.22249e9i	−0.510635	+	0.347852i
$165$	1.98554e9			0.208546
$166$		−	7.48164e9i		−	0.764734i
$167$	−2.29791e9	−	2.29791e9i	−0.228617	−	0.228617i	0.583498	−	0.812115i	$-0.301684\pi$
$167$	−2.29791e9	−	2.29791e9i	−0.228617	−	0.228617i	−0.812115	+	0.583498i	$0.801684\pi$
$168$	−6.45501e9			−0.625181
$169$		−	9.02494e8i		−	0.0851048i
$170$	−1.12664e10	+	1.12664e10i	−1.03458	+	1.03458i
$171$	−1.83959e8	−	1.83959e8i	−0.0164527	−	0.0164527i
$172$		−	7.17063e9i		−	0.624711i
$173$			1.65200e10i			1.40217i	0.713076	+	0.701086i	$0.247301\pi$
$173$			1.65200e10i			1.40217i	−0.713076	+	0.701086i	$0.752699\pi$
$174$	3.40061e9			0.281245
$175$	−1.20328e10	−	1.20328e10i	−0.969832	−	0.969832i
$176$	719609.	+	719609.i	5.65314e−5	+	5.65314e-5i
$177$	9.07555e9	+	9.07555e9i	0.695014	+	0.695014i
$178$	−4.05294e8	+	4.05294e8i	−0.0302608	+	0.0302608i
$179$	−1.51393e10	+	1.51393e10i	−1.10222	+	1.10222i	−0.108077	+	0.994142i	$0.534469\pi$
$179$	−1.51393e10	+	1.51393e10i	−1.10222	+	1.10222i	−0.994142	+	0.108077i	$0.965531\pi$
$180$	7.75824e9			0.550855
$181$	−7.31004e9	+	7.31004e9i	−0.506251	+	0.506251i	−0.913374	−	0.407122i	$-0.866532\pi$
$181$	−7.31004e9	+	7.31004e9i	−0.506251	+	0.506251i	0.407122	+	0.913374i	$0.366532\pi$
$182$	−8.35421e9			−0.564396
$183$	5.24040e9	−	5.24040e9i	0.345410	−	0.345410i
$184$		−	1.36837e10i		−	0.880081i
$185$			4.04123e10i			2.53653i
$186$	8.75512e9	−	8.75512e9i	0.536357	−	0.536357i
$187$	−5.17193e9			−0.309290
$188$	−7.21303e9	+	7.21303e9i	−0.421121	+	0.421121i
$189$	1.72282e10			0.982116
$190$	−4.99378e8	+	4.99378e8i	−0.0277996	+	0.0277996i
$191$	−6.75577e9	+	6.75577e9i	−0.367303	+	0.367303i	−0.866493	−	0.499190i	$-0.833631\pi$
$191$	−6.75577e9	+	6.75577e9i	−0.367303	+	0.367303i	0.499190	+	0.866493i	$0.333631\pi$
$192$	−5.39314e9	−	5.39314e9i	−0.286409	−	0.286409i
$193$	1.41175e10	+	1.41175e10i	0.732402	+	0.732402i	0.971095	−	0.238693i	$-0.0767189\pi$
$193$	1.41175e10	+	1.41175e10i	0.732402	+	0.732402i	−0.238693	+	0.971095i	$0.576719\pi$
$194$	−7.34313e9	−	7.34313e9i	−0.372198	−	0.372198i
$195$	−1.97436e10			−0.977847
$196$		−	1.13469e9i		−	0.0549192i
$197$			7.11998e9i			0.336807i	0.985718	+	0.168403i	$0.0538611\pi$
$197$			7.11998e9i			0.336807i	−0.985718	+	0.168403i	$0.946139\pi$
$198$	−1.10138e9	−	1.10138e9i	−0.0509264	−	0.0509264i
$199$	−2.01841e9	+	2.01841e9i	−0.0912368	+	0.0912368i	−0.751252	−	0.660015i	$-0.770550\pi$
$199$	−2.01841e9	+	2.01841e9i	−0.0912368	+	0.0912368i	0.660015	+	0.751252i	$0.270550\pi$
$200$		−	3.25172e10i		−	1.43707i
$201$	2.54576e10			1.10011
$202$	−6.85026e8	−	6.85026e8i	−0.0289485	−	0.0289485i
$203$		−	1.60445e10i		−	0.663122i
$204$	1.51754e10			0.613486
$205$	−2.22237e10	−	3.26236e10i	−0.878868	−	1.29015i
$206$	−3.80776e9			−0.147322
$207$			1.32760e10i			0.502573i
$208$	−7.15556e6	−	7.15556e6i	−0.000265069	−	0.000265069i
$209$	−2.29244e8			−0.00831073
$210$		−	1.70008e10i		−	0.603231i
$211$	1.49239e10	−	1.49239e10i	0.518336	−	0.518336i	−0.398732	−	0.917068i	$-0.630550\pi$
$211$	1.49239e10	−	1.49239e10i	0.518336	−	0.518336i	0.917068	+	0.398732i	$0.130550\pi$
$212$	8.43887e9	+	8.43887e9i	0.286928	+	0.286928i
$213$			1.45803e10i			0.485355i
$214$			1.57322e10i			0.512777i
$215$	4.94517e10			1.57837
$216$	2.32786e10	+	2.32786e10i	0.727636	+	0.727636i
$217$	−4.13076e10	−	4.13076e10i	−1.26462	−	1.26462i
$218$	2.14946e10	+	2.14946e10i	0.644578	+	0.644578i
$219$	1.11216e10	−	1.11216e10i	0.326715	−	0.326715i
$220$	4.83405e9	−	4.83405e9i	0.139126	−	0.139126i
$221$	5.14280e10			1.45022
$222$	−1.68335e10	+	1.68335e10i	−0.465142	+	0.465142i
$223$	−3.44151e10			−0.931916			−0.465958	−	0.884807i	$-0.654290\pi$
$223$	−3.44151e10			−0.931916			−0.465958	+	0.884807i	$0.654290\pi$
$224$	−2.54293e10	+	2.54293e10i	−0.674868	+	0.674868i
$225$			3.15483e10i			0.820644i
$226$		−	2.61612e10i		−	0.667068i
$227$	2.55139e10	−	2.55139e10i	0.637764	−	0.637764i	−0.312239	−	0.950004i	$-0.601079\pi$
$227$	2.55139e10	−	2.55139e10i	0.637764	−	0.637764i	0.950004	+	0.312239i	$0.101079\pi$
$228$	6.72645e8			0.0164846
$229$	−3.08594e10	+	3.08594e10i	−0.741529	+	0.741529i	−0.972872	−	0.231343i	$-0.925688\pi$
$229$	−3.08594e10	+	3.08594e10i	−0.741529	+	0.741529i	0.231343	+	0.972872i	$0.425688\pi$
$230$	3.60392e10			0.849181
$231$	3.90219e9	−	3.90219e9i	0.0901684	−	0.0901684i
$232$	2.16791e10	−	2.16791e10i	0.491298	−	0.491298i
$233$	−2.51174e10	−	2.51174e10i	−0.558308	−	0.558308i	0.370518	−	0.928825i	$-0.379180\pi$
$233$	−2.51174e10	−	2.51174e10i	−0.558308	−	0.558308i	−0.928825	+	0.370518i	$0.879180\pi$
$234$	1.09517e10	+	1.09517e10i	0.238788	+	0.238788i
$235$	−4.97441e10	−	4.97441e10i	−1.06399	−	1.06399i
$236$	4.41911e10			0.927323
$237$			3.28691e10i			0.676737i
$238$			4.42837e10i			0.894638i
$239$	−3.50175e10	−	3.50175e10i	−0.694216	−	0.694216i	0.268941	−	0.963157i	$-0.413326\pi$
$239$	−3.50175e10	−	3.50175e10i	−0.694216	−	0.694216i	−0.963157	+	0.268941i	$0.913326\pi$
$240$	1.45616e7	−	1.45616e7i	0.000283308	−	0.000283308i
$241$		−	6.97584e10i		−	1.33205i	−0.745930	−	0.666024i	$-0.767995\pi$
$241$		−	6.97584e10i		−	1.33205i	0.745930	−	0.666024i	$-0.232005\pi$
$242$	3.16098e10			0.592451
$243$	−3.69600e10	−	3.69600e10i	−0.679992	−	0.679992i
$244$		−	2.55168e10i		−	0.460863i
$245$	7.82530e9			0.138757
$246$	4.33204e9	−	2.28463e10i	0.0754196	−	0.397748i
$247$	2.27953e9			0.0389681
$248$		−	1.11629e11i		−	1.87388i
$249$	−3.47494e10	−	3.47494e10i	−0.572862	−	0.572862i
$250$	2.60398e10			0.421607
$251$			4.97944e10i			0.791860i	0.918281	+	0.395930i	$0.129578\pi$
$251$			4.97944e10i			0.791860i	−0.918281	+	0.395930i	$0.870422\pi$
$252$	1.52473e10	−	1.52473e10i	0.238171	−	0.238171i
$253$	8.27206e9	+	8.27206e9i	0.126932	+	0.126932i
$254$			1.20595e10i			0.181793i
$255$			1.04656e11i			1.55001i
$256$	−6.87361e10			−1.00024
$257$	5.76144e10	+	5.76144e10i	0.823820	+	0.823820i	0.986653	−	0.162834i	$-0.0520635\pi$
$257$	5.76144e10	+	5.76144e10i	0.823820	+	0.823820i	−0.162834	+	0.986653i	$0.552063\pi$
$258$	2.05988e10	+	2.05988e10i	0.289437	+	0.289437i
$259$	7.94223e10	+	7.94223e10i	1.09671	+	1.09671i
$260$	−4.80683e10	+	4.80683e10i	−0.652346	+	0.652346i
$261$	−2.10331e10	+	2.10331e10i	−0.280557	+	0.280557i
$262$	−1.08679e10			−0.142492
$263$	4.03060e10	−	4.03060e10i	0.519480	−	0.519480i	−0.397934	−	0.917414i	$-0.630273\pi$
$263$	4.03060e10	−	4.03060e10i	0.519480	−	0.519480i	0.917414	+	0.397934i	$0.130273\pi$
$264$	1.05452e10			0.133609
$265$	−5.81981e10	+	5.81981e10i	−0.724940	+	0.724940i
$266$			1.96286e9i			0.0240393i
$267$			3.76488e9i			0.0453367i
$268$	6.19797e10	−	6.19797e10i	0.733910	−	0.733910i
$269$	9.25437e10			1.07761			0.538805	−	0.842431i	$-0.318876\pi$
$269$	9.25437e10			1.07761			0.538805	+	0.842431i	$0.318876\pi$
$270$	−6.13097e10	+	6.13097e10i	−0.702089	+	0.702089i
$271$	−1.08669e11			−1.22390			−0.611948	−	0.790898i	$-0.709614\pi$
$271$	−1.08669e11			−1.22390			−0.611948	+	0.790898i	$0.709614\pi$
$272$	−3.79300e7	+	3.79300e7i	−0.000420167	+	0.000420167i
$273$	−3.88021e10	+	3.88021e10i	−0.422789	+	0.422789i
$274$	5.31594e10	+	5.31594e10i	0.569774	+	0.569774i
$275$	1.96573e10	+	1.96573e10i	0.207265	+	0.207265i
$276$	−2.42718e10	−	2.42718e10i	−0.251774	−	0.251774i
$277$	−1.33279e11			−1.36020			−0.680102	−	0.733118i	$-0.738064\pi$
$277$	−1.33279e11			−1.36020			−0.680102	+	0.733118i	$0.738064\pi$
$278$		−	2.21755e10i		−	0.222675i
$279$			1.08303e11i			1.07009i
$280$	−1.08381e11	−	1.08381e11i	−1.05376	−	1.05376i
$281$	1.01178e11	−	1.01178e11i	0.968073	−	0.968073i	−0.0314331	−	0.999506i	$-0.510007\pi$
$281$	1.01178e11	−	1.01178e11i	0.968073	−	0.968073i	0.999506	+	0.0314331i	$0.0100071\pi$
$282$		−	4.14412e10i		−	0.390222i
$283$	−1.10029e11			−1.01969			−0.509845	−	0.860266i	$-0.670297\pi$
$283$	−1.10029e11			−1.01969			−0.509845	+	0.860266i	$0.670297\pi$
$284$	3.54977e10	+	3.54977e10i	0.323793	+	0.323793i
$285$			4.63885e9i			0.0416493i
$286$	1.36478e10			0.120619
$287$	−1.07791e11	−	2.04390e10i	−0.937812	−	0.177825i
$288$	6.66719e10			0.571053
$289$		−	1.54020e11i		−	1.29878i
$290$	5.70970e10	+	5.70970e10i	0.474048	+	0.474048i
$291$	−6.82122e10			−0.557626
$292$		−	5.41539e10i		−	0.435920i
$293$	−1.30371e11	+	1.30371e11i	−1.03342	+	1.03342i	−0.0339965	+	0.999422i	$0.510824\pi$
$293$	−1.30371e11	+	1.30371e11i	−1.03342	+	1.03342i	−0.999422	+	0.0339965i	$0.989176\pi$
$294$	3.25958e9	+	3.25958e9i	0.0254448	+	0.0254448i
$295$			3.04761e11i			2.34293i
$296$			2.14629e11i			1.62508i
$297$	−2.81447e10			−0.209891
$298$	−4.74353e10	−	4.74353e10i	−0.348440	−	0.348440i
$299$	−8.22547e10	−	8.22547e10i	−0.595169	−	0.595169i
$300$	−5.76782e10	−	5.76782e10i	−0.411118	−	0.411118i
$301$	9.71875e10	−	9.71875e10i	0.682435	−	0.682435i
$302$	−1.19282e10	+	1.19282e10i	−0.0825173	+	0.0825173i
$303$	−6.36337e9			−0.0433706
$304$	−1.68123e6	+	1.68123e6i	−1.12901e−5	+	1.12901e-5i
$305$	1.75975e11			1.16440
$306$	5.80526e10	−	5.80526e10i	0.378508	−	0.378508i
$307$			4.43022e10i			0.284645i	0.989820	+	0.142322i	$0.0454569\pi$
$307$			4.43022e10i			0.284645i	−0.989820	+	0.142322i	$0.954543\pi$
$308$		−	1.90007e10i		−	0.120307i
$309$	−1.76856e10	+	1.76856e10i	−0.110359	+	0.110359i
$310$	2.94001e11			1.80809
$311$	7.36950e9	−	7.36950e9i	0.0446700	−	0.0446700i	−0.684419	−	0.729089i	$-0.739944\pi$
$311$	7.36950e9	−	7.36950e9i	0.0446700	−	0.0446700i	0.729089	+	0.684419i	$0.239944\pi$
$312$	−1.04858e11			−0.626477
$313$	1.46178e11	−	1.46178e11i	0.860860	−	0.860860i	−0.130578	−	0.991438i	$-0.541683\pi$
$313$	1.46178e11	−	1.46178e11i	0.860860	−	0.860860i	0.991438	+	0.130578i	$0.0416833\pi$
$314$	−9.53143e10	+	9.53143e10i	−0.553318	+	0.553318i
$315$	1.05152e11	+	1.05152e11i	0.601754	+	0.601754i
$316$	8.00239e10	+	8.00239e10i	0.451469	+	0.451469i
$317$	−1.94065e11	−	1.94065e11i	−1.07940	−	1.07940i	−0.996564	−	0.0828321i	$-0.973603\pi$
$317$	−1.94065e11	−	1.94065e11i	−1.07940	−	1.07940i	−0.0828321	−	0.996564i	$-0.526397\pi$
$318$	−4.84841e10			−0.265875
$319$			2.62109e10i			0.141717i
$320$		−	1.81104e11i		−	0.965502i
$321$	7.30703e10	+	7.30703e10i	0.384121	+	0.384121i
$322$	7.08279e10	−	7.08279e10i	0.367158	−	0.367158i
$323$		−	1.20832e10i		−	0.0617692i
$324$	1.25863e10			0.0634519
$325$	−1.95466e11	−	1.95466e11i	−0.971843	−	0.971843i
$326$			1.31101e11i			0.642873i
$327$	1.99669e11			0.965707
$328$	−1.18029e11	−	1.73263e11i	−0.563064	−	0.826560i
$329$	−1.95524e11			−0.920067
$330$			2.77732e10i			0.128918i
$331$	−1.74013e11	−	1.74013e11i	−0.796812	−	0.796812i	0.185779	−	0.982592i	$-0.440519\pi$
$331$	−1.74013e11	−	1.74013e11i	−0.796812	−	0.796812i	−0.982592	+	0.185779i	$0.940519\pi$
$332$	−1.69203e11			−0.764341
$333$		−	2.08234e11i		−	0.928008i
$334$	3.21425e10	−	3.21425e10i	0.141325	−	0.141325i
$335$	4.27439e11	+	4.27439e11i	1.85427	+	1.85427i
$336$		−	5.72358e7i		−	0.000244986i
$337$		−	3.59751e11i		−	1.51938i	−0.650284	−	0.759691i	$-0.725350\pi$
$337$		−	3.59751e11i		−	1.51938i	0.650284	−	0.759691i	$-0.274650\pi$
$338$	1.26238e10			0.0526097
$339$	−1.21509e11	−	1.21509e11i	−0.499701	−	0.499701i
$340$	2.54798e11	+	2.54798e11i	1.03405	+	1.03405i
$341$	6.74817e10	+	6.74817e10i	0.270266	+	0.270266i
$342$	2.57316e9	−	2.57316e9i	0.0101707	−	0.0101707i
$343$	1.88398e11	−	1.88398e11i	0.734943	−	0.734943i
$344$	2.62637e11			1.01121
$345$	1.67389e11	−	1.67389e11i	0.636121	−	0.636121i
$346$	−2.31077e11			−0.866789
$347$	−1.78858e11	+	1.78858e11i	−0.662257	+	0.662257i	−0.955912	−	0.293655i	$-0.905128\pi$
$347$	−1.78858e11	+	1.78858e11i	−0.662257	+	0.662257i	0.293655	+	0.955912i	$0.405128\pi$
$348$		−	7.69076e10i		−	0.281101i
$349$		−	2.37130e10i		−	0.0855602i	−0.999085	−	0.0427801i	$-0.986379\pi$
$349$		−	2.37130e10i		−	0.0855602i	0.999085	−	0.0427801i	$-0.0136215\pi$
$350$	1.68312e11	−	1.68312e11i	0.599527	−	0.599527i
$351$	2.79862e11			0.984152
$352$	4.15423e10	−	4.15423e10i	0.144228	−	0.144228i
$353$	1.05002e11			0.359925			0.179963	−	0.983673i	$-0.442402\pi$
$353$	1.05002e11			0.359925			0.179963	+	0.983673i	$0.442402\pi$
$354$	−1.26946e11	+	1.26946e11i	−0.429641	+	0.429641i
$355$	−2.44807e11	+	2.44807e11i	−0.818081	+	0.818081i
$356$	9.16606e9	+	9.16606e9i	0.0302453	+	0.0302453i
$357$	2.05681e11	+	2.05681e11i	0.670173	+	0.670173i
$358$	−2.11765e11	−	2.11765e11i	−0.681366	−	0.681366i
$359$	1.60633e11			0.510398			0.255199	−	0.966889i	$-0.417859\pi$
$359$	1.60633e11			0.510398			0.255199	+	0.966889i	$0.417859\pi$
$360$			2.84159e11i			0.891662i
$361$			3.22152e11i			0.998340i
$362$	−1.02251e11	−	1.02251e11i	−0.312952	−	0.312952i
$363$	1.46816e11	−	1.46816e11i	0.443805	−	0.443805i
$364$			1.88937e11i			0.564107i
$365$	3.73469e11			1.10138
$366$	7.33012e10	+	7.33012e10i	0.213524	+	0.213524i
$367$			1.39294e10i			0.0400806i	0.999799	+	0.0200403i	$0.00637945\pi$
$367$			1.39294e10i			0.0400806i	−0.999799	+	0.0200403i	$0.993621\pi$
$368$	1.21331e8			0.000344872
$369$	1.14513e11	+	1.68101e11i	0.321540	+	0.472010i
$370$	−5.65276e11			−1.56802
$371$			2.28753e11i			0.626881i
$372$	−1.98004e11	−	1.98004e11i	−0.536082	−	0.536082i
$373$	6.38138e11			1.70697			0.853483	−	0.521120i	$-0.174486\pi$
$373$	6.38138e11			1.70697			0.853483	+	0.521120i	$0.174486\pi$
$374$		−	7.23435e10i		−	0.191195i
$375$	1.20945e11	−	1.20945e11i	0.315826	−	0.315826i
$376$	−2.64190e11	−	2.64190e11i	−0.681664	−	0.681664i
$377$		−	2.60633e11i		−	0.664496i
$378$			2.40984e11i			0.607121i
$379$	−2.73632e11			−0.681226			−0.340613	−	0.940204i	$-0.610635\pi$
$379$	−2.73632e11			−0.681226			−0.340613	+	0.940204i	$0.610635\pi$
$380$	1.12938e10	+	1.12938e10i	0.0277853	+	0.0277853i
$381$	5.60119e10	+	5.60119e10i	0.136181	+	0.136181i
$382$	−9.44978e10	−	9.44978e10i	−0.227058	−	0.227058i
$383$	−1.71991e11	+	1.71991e11i	−0.408424	+	0.408424i	−0.881189	−	0.472765i	$-0.843256\pi$
$383$	−1.71991e11	+	1.71991e11i	−0.408424	+	0.408424i	0.472765	+	0.881189i	$0.343256\pi$
$384$	−1.21845e11	+	1.21845e11i	−0.285968	+	0.285968i
$385$	1.31037e11			0.303963
$386$	−1.97472e11	+	1.97472e11i	−0.452753	+	0.452753i
$387$	−2.54811e11			−0.577457
$388$	−1.66071e11	+	1.66071e11i	−0.372007	+	0.372007i
$389$		−	7.71706e11i		−	1.70875i	−0.519657	−	0.854375i	$-0.673940\pi$
$389$		−	7.71706e11i		−	1.70875i	0.519657	−	0.854375i	$-0.326060\pi$
$390$		−	2.76168e11i		−	0.604481i
$391$	−4.36013e11	+	4.36013e11i	−0.943417	+	0.943417i
$392$	4.15599e10			0.0888971
$393$	−5.04773e10	+	5.04773e10i	−0.106741	+	0.106741i
$394$	−9.95923e10			−0.208206
$395$	−5.51879e11	+	5.51879e11i	−1.14066	+	1.14066i
$396$	−2.49085e10	+	2.49085e10i	−0.0509002	+	0.0509002i
$397$	−1.66721e10	−	1.66721e10i	−0.0336848	−	0.0336848i	0.690064	−	0.723749i	$-0.257582\pi$
$397$	−1.66721e10	−	1.66721e10i	−0.0336848	−	0.0336848i	−0.723749	+	0.690064i	$0.757582\pi$
$398$	−2.82329e10	−	2.82329e10i	−0.0564004	−	0.0564004i
$399$	9.11673e9	+	9.11673e9i	0.0180078	+	0.0180078i
$400$	2.88326e8			0.000563136
$401$		−	5.04491e11i		−	0.974324i	−0.873312	−	0.487162i	$-0.838032\pi$
$401$		−	5.04491e11i		−	0.974324i	0.873312	−	0.487162i	$-0.161968\pi$
$402$			3.56094e11i			0.680060i
$403$	−6.71017e11	−	6.71017e11i	−1.26725	−	1.26725i
$404$	−1.54924e10	+	1.54924e10i	−0.0289336	+	0.0289336i
$405$			8.68004e10i			0.160315i
$406$	2.24426e11			0.409926
$407$	−1.29747e11	−	1.29747e11i	−0.234382	−	0.234382i
$408$			5.55826e11i			0.993043i
$409$	−3.29521e11			−0.582275			−0.291138	−	0.956681i	$-0.594034\pi$
$409$	−3.29521e11			−0.582275			−0.291138	+	0.956681i	$0.594034\pi$
$410$	4.56330e11	−	3.10859e11i	0.797539	−	0.543295i
$411$	4.93811e11			0.853635
$412$			8.61156e10i			0.147246i
$413$	5.98947e11	+	5.98947e11i	1.01301	+	1.01301i
$414$	−1.85700e11			−0.310678
$415$		−	1.16690e12i		−	1.93115i
$416$	−4.13084e11	+	4.13084e11i	−0.676267	+	0.676267i
$417$	−1.02997e11	−	1.02997e11i	−0.166806	−	0.166806i
$418$		−	3.20660e9i		−	0.00513749i
$419$		−	1.16893e12i		−	1.85279i	−0.376559	−	0.926393i	$-0.622893\pi$
$419$		−	1.16893e12i		−	1.85279i	0.376559	−	0.926393i	$-0.377107\pi$
$420$	−3.84488e11			−0.602921
$421$	2.17407e11	+	2.17407e11i	0.337290	+	0.337290i	0.855347	−	0.518056i	$-0.173344\pi$
$421$	2.17407e11	+	2.17407e11i	0.337290	+	0.337290i	−0.518056	+	0.855347i	$0.673344\pi$
$422$	2.08751e11	+	2.08751e11i	0.320423	+	0.320423i
$423$	2.56318e11	+	2.56318e11i	0.389267	+	0.389267i
$424$	−3.09088e11	+	3.09088e11i	−0.464447	+	0.464447i
$425$	−1.03612e12	+	1.03612e12i	−1.54049	+	1.54049i
$426$	−2.03946e11			−0.300035
$427$	3.45843e11	−	3.45843e11i	0.503447	−	0.503447i
$428$	3.55797e11			0.512514
$429$	6.33886e10	−	6.33886e10i	0.0903553	−	0.0903553i
$430$			6.91717e11i			0.975709i
$431$			1.26620e12i			1.76747i	0.467984	+	0.883737i	$0.344980\pi$
$431$			1.26620e12i			1.76747i	−0.467984	+	0.883737i	$0.655020\pi$
$432$	−2.06408e8	+	2.06408e8i	−0.000285135	+	0.000285135i
$433$	4.64460e11			0.634970			0.317485	−	0.948263i	$-0.397162\pi$
$433$	4.64460e11			0.634970			0.317485	+	0.948263i	$0.397162\pi$
$434$	5.77800e11	−	5.77800e11i	0.781760	−	0.781760i
$435$	5.30388e11			0.710219
$436$	4.86119e11	−	4.86119e11i	0.644248	−	0.644248i
$437$	−1.93261e10	+	1.93261e10i	−0.0253500	+	0.0253500i
$438$	1.55566e11	+	1.55566e11i	0.201968	+	0.201968i
$439$	−2.22005e11	−	2.22005e11i	−0.285281	−	0.285281i	0.549930	−	0.835211i	$-0.314654\pi$
$439$	−2.22005e11	−	2.22005e11i	−0.285281	−	0.285281i	−0.835211	+	0.549930i	$0.814654\pi$
$440$	1.77055e11	+	1.77055e11i	0.225202	+	0.225202i
$441$	−4.03216e10			−0.0507650
$442$			7.19361e11i			0.896493i
$443$			5.50971e11i			0.679691i	0.940481	+	0.339846i	$0.110375\pi$
$443$			5.50971e11i			0.679691i	−0.940481	+	0.339846i	$0.889625\pi$
$444$	3.80703e11	+	3.80703e11i	0.464904	+	0.464904i
$445$	−6.32131e10	+	6.32131e10i	−0.0764164	+	0.0764164i
$446$		−	4.81388e11i		−	0.576088i
$447$	−4.40638e11			−0.522033
$448$	−3.55924e11	−	3.55924e11i	−0.417451	−	0.417451i
$449$			4.15790e10i			0.0482799i	0.999709	+	0.0241399i	$0.00768473\pi$
$449$			4.15790e10i			0.0482799i	−0.999709	+	0.0241399i	$0.992315\pi$
$450$	−4.41289e11			−0.507302
$451$	1.76092e11	+	3.33900e10i	0.200422	+	0.0380034i
$452$	−5.91657e11			−0.666726
$453$			1.10804e11i			0.123627i
$454$	3.56881e11	+	3.56881e11i	0.394250	+	0.394250i
$455$	−1.30299e12			−1.42525
$456$			2.46368e10i			0.0266835i
$457$	6.11097e11	−	6.11097e11i	0.655371	−	0.655371i	−0.298910	−	0.954281i	$-0.596623\pi$
$457$	6.11097e11	−	6.11097e11i	0.655371	−	0.655371i	0.954281	+	0.298910i	$0.0966231\pi$
$458$	−4.31653e11	−	4.31653e11i	−0.458395	−	0.458395i
$459$		−	1.48348e12i		−	1.56000i
$460$		−	8.15057e11i		−	0.848746i
$461$	2.77800e11			0.286469			0.143235	−	0.989689i	$-0.454250\pi$
$461$	2.77800e11			0.286469			0.143235	+	0.989689i	$0.454250\pi$
$462$	5.45827e10	+	5.45827e10i	0.0557399	+	0.0557399i
$463$	4.32230e11	+	4.32230e11i	0.437120	+	0.437120i	0.891042	−	0.453922i	$-0.149975\pi$
$463$	4.32230e11	+	4.32230e11i	0.437120	+	0.437120i	−0.453922	+	0.891042i	$0.649975\pi$
$464$	1.92226e8	+	1.92226e8i	0.000192522	+	0.000192522i
$465$	1.36552e12	−	1.36552e12i	1.35444	−	1.35444i
$466$	3.51336e11	−	3.51336e11i	0.345132	−	0.345132i
$467$	−1.21541e12			−1.18249			−0.591243	−	0.806493i	$-0.701363\pi$
$467$	−1.21541e12			−1.18249			−0.591243	+	0.806493i	$0.701363\pi$
$468$	2.47683e11	−	2.47683e11i	0.238665	−	0.238665i
$469$	1.68009e12			1.60345
$470$	6.95807e11	−	6.95807e11i	0.657731	−	0.657731i
$471$			8.85397e11i			0.828980i
$472$			1.61858e12i			1.50105i
$473$	−1.58769e11	+	1.58769e11i	−0.145845	+	0.145845i
$474$	−4.59764e11			−0.418343
$475$	−4.59256e10	+	4.59256e10i	−0.0413936	+	0.0413936i
$476$	1.00151e12			0.894179
$477$	2.99879e11	−	2.99879e11i	0.265224	−	0.265224i
$478$	4.89815e11	−	4.89815e11i	0.429147	−	0.429147i
$479$	−3.75662e11	−	3.75662e11i	−0.326052	−	0.326052i	0.525031	−	0.851083i	$-0.324054\pi$
$479$	−3.75662e11	−	3.75662e11i	−0.326052	−	0.326052i	−0.851083	+	0.525031i	$0.824054\pi$
$480$	−8.40626e11	−	8.40626e11i	−0.722799	−	0.722799i
$481$	1.29017e12	+	1.29017e12i	1.09899	+	1.09899i
$482$	9.75761e11			0.823440
$483$		−	6.57938e11i		−	0.550076i
$484$		−	7.14882e11i		−	0.592148i
$485$	−1.14530e12	−	1.14530e12i	−0.939897	−	0.939897i
$486$	5.16986e11	−	5.16986e11i	0.420354	−	0.420354i
$487$			9.54528e11i			0.768969i	0.923132	+	0.384484i	$0.125621\pi$
$487$			9.54528e11i			0.768969i	−0.923132	+	0.384484i	$0.874379\pi$
$488$	9.34598e11			0.745994
$489$	6.08912e11	+	6.08912e11i	0.481576	+	0.481576i
$490$			1.09458e11i			0.0857759i
$491$	−1.50506e12			−1.16866			−0.584330	−	0.811516i	$-0.698643\pi$
$491$	−1.50506e12			−1.16866			−0.584330	+	0.811516i	$0.698643\pi$
$492$	−5.16688e11	−	9.79726e10i	−0.397544	−	0.0753809i
$493$	−1.38155e12			−1.05331
$494$			3.18854e10i			0.0240891i
$495$	−1.71780e11	−	1.71780e11i	−0.128602	−	0.128602i
$496$	9.89797e8			0.000734308
$497$			9.62239e11i			0.707423i
$498$	4.86064e11	−	4.86064e11i	0.354129	−	0.354129i
$499$	1.79719e11	+	1.79719e11i	0.129761	+	0.129761i	0.769004	−	0.639244i	$-0.220752\pi$
$499$	1.79719e11	+	1.79719e11i	0.129761	+	0.129761i	−0.639244	+	0.769004i	$0.720752\pi$
$500$		−	5.88912e11i		−	0.421391i
$501$		−	2.98579e11i		−	0.211734i
$502$	−6.96510e11			−0.489509
$503$	5.19321e11	+	5.19321e11i	0.361726	+	0.361726i	0.864448	−	0.502722i	$-0.167668\pi$
$503$	5.19321e11	+	5.19321e11i	0.361726	+	0.361726i	−0.502722	+	0.864448i	$0.667668\pi$
$504$	5.58458e11	+	5.58458e11i	0.385526	+	0.385526i
$505$	−1.06842e11	−	1.06842e11i	−0.0731025	−	0.0731025i
$506$	−1.15707e11	+	1.15707e11i	−0.0784663	+	0.0784663i
$507$	5.86329e10	−	5.86329e10i	0.0394099	−	0.0394099i
$508$	2.72736e11			0.181700
$509$	1.66510e12	−	1.66510e12i	1.09954	−	1.09954i	0.105077	−	0.994464i	$-0.466491\pi$
$509$	1.66510e12	−	1.66510e12i	1.09954	−	1.09954i	0.994464	−	0.105077i	$-0.0335089\pi$
$510$	−1.46390e12			−0.958178
$511$	7.33978e11	−	7.33978e11i	0.476200	−	0.476200i
$512$		−	1.21880e9i		−	0.000783823i
$513$		−	6.57549e10i		−	0.0419179i
$514$	−8.05894e11	+	8.05894e11i	−0.509265	+	0.509265i
$515$	−5.93890e11			−0.372026
$516$	4.65859e11	−	4.65859e11i	0.289288	−	0.289288i
$517$	3.19416e11			0.196630
$518$	−1.11094e12	+	1.11094e12i	−0.677962	+	0.677962i
$519$	−1.07326e12	+	1.07326e12i	−0.649312	+	0.649312i
$520$	−1.76058e12	−	1.76058e12i	−1.05595	−	1.05595i
$521$	−8.52019e11	−	8.52019e11i	−0.506617	−	0.506617i	0.406870	−	0.913486i	$-0.366620\pi$
$521$	−8.52019e11	−	8.52019e11i	−0.506617	−	0.506617i	−0.913486	+	0.406870i	$0.866620\pi$
$522$	−2.94205e11	−	2.94205e11i	−0.173434	−	0.173434i
$523$	2.70131e12			1.57876			0.789380	−	0.613905i	$-0.210402\pi$
$523$	2.70131e12			1.57876			0.789380	+	0.613905i	$0.210402\pi$
$524$			2.45786e11i			0.142419i
$525$		−	1.56349e12i		−	0.898210i
$526$	5.63789e11	+	5.63789e11i	0.321130	+	0.321130i
$527$	−3.55690e12	+	3.55690e12i	−2.00874	+	2.00874i
$528$			9.35026e7i			5.23566e-5i
$529$	−4.06422e11			−0.225646
$530$	−8.14058e11	−	8.14058e11i	−0.448140	−	0.448140i
$531$		−	1.57035e12i		−	0.857178i
$532$	4.43916e10			0.0240269
$533$	−1.75101e12	−	3.32020e11i	−0.939757	−	0.178193i
$534$	−5.26620e10			−0.0280261
$535$			2.45373e12i			1.29490i
$536$	2.27012e12	+	2.27012e12i	1.18797	+	1.18797i
$537$	−1.96713e12			−1.02082
$538$			1.29447e12i			0.666152i
$539$	−2.51238e10	+	2.51238e10i	−0.0128214	+	0.0128214i
$540$	1.38657e12	+	1.38657e12i	0.701729	+	0.701729i
$541$			1.98222e12i			0.994864i	0.867503	+	0.497432i	$0.165724\pi$
$541$			1.98222e12i			0.994864i	−0.867503	+	0.497432i	$0.834276\pi$
$542$		−	1.52003e12i		−	0.756583i
$543$	−9.49832e11			−0.468865
$544$	2.18966e12	+	2.18966e12i	1.07197	+	1.07197i
$545$	3.35248e12	+	3.35248e12i	1.62773	+	1.62773i
$546$	−5.42753e11	−	5.42753e11i	−0.261358	−	0.261358i
$547$	−1.88656e12	+	1.88656e12i	−0.901006	+	0.901006i	−0.995523	−	0.0945170i	$-0.969869\pi$
$547$	−1.88656e12	+	1.88656e12i	−0.901006	+	0.901006i	0.0945170	+	0.995523i	$0.469869\pi$
$548$	1.20224e12	−	1.20224e12i	0.569482	−	0.569482i
$549$	−9.06750e11			−0.426003
$550$	−2.74961e11	+	2.74961e11i	−0.128126	+	0.128126i
$551$	−6.12368e10			−0.0283028
$552$	8.88996e11	−	8.88996e11i	0.407544	−	0.407544i
$553$			2.16922e12i			0.986370i
$554$		−	1.86427e12i		−	0.840845i
$555$	−2.62549e12	+	2.62549e12i	−1.17461	+	1.17461i
$556$	−5.01516e11			−0.222561
$557$	1.32936e12	−	1.32936e12i	0.585186	−	0.585186i	−0.351138	−	0.936324i	$-0.614205\pi$
$557$	1.32936e12	−	1.32936e12i	0.585186	−	0.585186i	0.936324	+	0.351138i	$0.114205\pi$
$558$	−1.51491e12			−0.661503
$559$	1.57875e12	−	1.57875e12i	0.683850	−	0.683850i
$560$	9.61001e8	−	9.61001e8i	0.000412931	−	0.000412931i
$561$	−3.36008e11	−	3.36008e11i	−0.143224	−	0.143224i
$562$	1.41525e12	+	1.41525e12i	0.598439	+	0.598439i
$563$	−2.27009e12	−	2.27009e12i	−0.952261	−	0.952261i	0.0466502	−	0.998911i	$-0.485145\pi$
$563$	−2.27009e12	−	2.27009e12i	−0.952261	−	0.952261i	−0.998911	+	0.0466502i	$0.985145\pi$
$564$	−9.37227e11			−0.390022
$565$		−	4.08032e12i		−	1.68452i
$566$		−	1.53906e12i		−	0.630348i
$567$	1.70589e11	+	1.70589e11i	0.0693149	+	0.0693149i
$568$	−1.30016e12	+	1.30016e12i	−0.524120	+	0.524120i
$569$		−	9.26236e11i		−	0.370439i	−0.982697	−	0.185219i	$-0.940700\pi$
$569$		−	9.26236e11i		−	0.370439i	0.982697	−	0.185219i	$-0.0592996\pi$
$570$	−6.48869e10			−0.0257466
$571$	2.36826e12	+	2.36826e12i	0.932324	+	0.932324i	0.997851	−	0.0655264i	$-0.0208726\pi$
$571$	2.36826e12	+	2.36826e12i	0.932324	+	0.932324i	−0.0655264	+	0.997851i	$0.520873\pi$
$572$		−	3.08655e11i		−	0.120557i
$573$	−8.77813e11			−0.340178
$574$	2.85896e11	−	1.50776e12i	0.109927	−	0.579733i
$575$	3.31437e12			1.26443
$576$			9.33179e11i			0.353235i
$577$	−2.68861e12	−	2.68861e12i	−1.00980	−	1.00980i	−0.999951	−	0.00985309i	$-0.996864\pi$
$577$	−2.68861e12	−	2.68861e12i	−1.00980	−	1.00980i	−0.00985309	−	0.999951i	$-0.503136\pi$
$578$	2.15439e12			0.802876
$579$			1.83436e12i			0.678315i
$580$	1.29130e12	−	1.29130e12i	0.473805	−	0.473805i
$581$	−2.29331e12	−	2.29331e12i	−0.834967	−	0.834967i
$582$		−	9.54133e11i		−	0.344711i
$583$		−	3.73700e11i		−	0.133972i
$584$	1.98348e12			0.705619
$585$	1.70813e12	+	1.70813e12i	0.603002	+	0.603002i
$586$	−1.82359e12	−	1.82359e12i	−0.638834	−	0.638834i
$587$	−2.15519e12	−	2.15519e12i	−0.749228	−	0.749228i	0.225106	−	0.974334i	$-0.427727\pi$
$587$	−2.15519e12	−	2.15519e12i	−0.749228	−	0.749228i	−0.974334	+	0.225106i	$0.927727\pi$
$588$	7.37180e10	−	7.37180e10i	0.0254317	−	0.0254317i
$589$	−1.57658e11	+	1.57658e11i	−0.0539757	+	0.0539757i
$590$	−4.26291e12			−1.44835
$591$	−4.62569e11	+	4.62569e11i	−0.155967	+	0.155967i
$592$	−1.90309e9			−0.000636811
$593$	−4.25234e10	+	4.25234e10i	−0.0141215	+	0.0141215i	−0.714132	−	0.700011i	$-0.753179\pi$
$593$	−4.25234e10	+	4.25234e10i	−0.0141215	+	0.0141215i	0.700011	+	0.714132i	$0.253179\pi$
$594$		−	3.93681e11i		−	0.129749i
$595$			6.90685e12i			2.25920i
$596$	−1.07279e12	+	1.07279e12i	−0.348261	+	0.348261i
$597$	−2.62263e11			−0.0844991
$598$	1.15056e12	−	1.15056e12i	0.367919	−	0.367919i
$599$	1.29588e12			0.411286			0.205643	−	0.978627i	$-0.434071\pi$
$599$	1.29588e12			0.411286			0.205643	+	0.978627i	$0.434071\pi$
$600$	2.11256e12	−	2.11256e12i	0.665471	−	0.665471i
$601$	−9.63243e11	+	9.63243e11i	−0.301162	+	0.301162i	−0.841468	−	0.540306i	$-0.818308\pi$
$601$	−9.63243e11	+	9.63243e11i	−0.301162	+	0.301162i	0.540306	+	0.841468i	$0.318308\pi$
$602$	1.35943e12	+	1.35943e12i	0.421865	+	0.421865i
$603$	−2.20247e12	−	2.20247e12i	−0.678396	−	0.678396i
$604$	2.69767e11	+	2.69767e11i	0.0824750	+	0.0824750i
$605$	4.93013e12			1.49610
$606$		−	8.90090e10i		−	0.0268106i
$607$		−	1.64920e12i		−	0.493088i	−0.969132	−	0.246544i	$-0.920705\pi$
$607$		−	1.64920e12i		−	0.493088i	0.969132	−	0.246544i	$-0.0792949\pi$
$608$	9.70558e10	+	9.70558e10i	0.0288042	+	0.0288042i
$609$	1.04237e12	−	1.04237e12i	0.307075	−	0.307075i
$610$			2.46149e12i			0.719802i
$611$	−3.17617e12			−0.921974
$612$	−1.31291e12	−	1.31291e12i	−0.378314	−	0.378314i
$613$			1.51514e12i			0.433391i	0.976239	+	0.216696i	$0.0695279\pi$
$613$			1.51514e12i			0.433391i	−0.976239	+	0.216696i	$0.930472\pi$
$614$	−6.19687e11			−0.175960
$615$	6.75661e11	−	3.56330e12i	0.190454	−	1.00442i
$616$	6.95934e11			0.194740
$617$			3.79761e12i			1.05494i	0.849574	+	0.527469i	$0.176859\pi$
$617$			3.79761e12i			1.05494i	−0.849574	+	0.527469i	$0.823141\pi$
$618$	−2.47381e11	−	2.47381e11i	−0.0682211	−	0.0682211i
$619$	3.95027e12			1.08148			0.540740	−	0.841190i	$-0.318144\pi$
$619$	3.95027e12			1.08148			0.540740	+	0.841190i	$0.318144\pi$
$620$		−	6.64906e12i		−	1.80717i
$621$	−2.37270e12	+	2.37270e12i	−0.640223	+	0.640223i
$622$	1.03082e11	+	1.03082e11i	0.0276139	+	0.0276139i
$623$			2.48465e11i			0.0660799i
$624$		−	9.29761e8i		−	0.000245494i
$625$	−1.41993e12			−0.372227
$626$	2.04470e12	+	2.04470e12i	0.532163	+	0.532163i
$627$	−1.48934e10	−	1.48934e10i	−0.00384849	−	0.00384849i
$628$	2.15561e12	+	2.15561e12i	0.553034	+	0.553034i
$629$	6.83887e12	−	6.83887e12i	1.74203	−	1.74203i
$630$	−1.47083e12	+	1.47083e12i	−0.371990	+	0.371990i
$631$	7.39637e11			0.185732			0.0928659	−	0.995679i	$-0.470397\pi$
$631$	7.39637e11			0.185732			0.0928659	+	0.995679i	$0.470397\pi$
$632$	−2.93101e12	+	2.93101e12i	−0.730788	+	0.730788i
$633$	1.93914e12			0.480057
$634$	2.71453e12	−	2.71453e12i	0.667256	−	0.667256i
$635$			1.88090e12i			0.459076i
$636$			1.09651e12i			0.265738i
$637$	2.49823e11	−	2.49823e11i	0.0601182	−	0.0601182i
$638$	−3.66630e11			−0.0876063
$639$	1.26142e12	−	1.26142e12i	0.299300	−	0.299300i
$640$	−4.09161e12			−0.964017
$641$	5.19777e12	−	5.19777e12i	1.21606	−	1.21606i	0.247063	−	0.968999i	$-0.420534\pi$
$641$	5.19777e12	−	5.19777e12i	1.21606	−	1.21606i	0.968999	−	0.247063i	$-0.0794655\pi$
$642$	−1.02209e12	+	1.02209e12i	−0.237454	+	0.237454i
$643$	2.03825e12	+	2.03825e12i	0.470227	+	0.470227i	0.901988	−	0.431761i	$-0.142108\pi$
$643$	2.03825e12	+	2.03825e12i	0.470227	+	0.470227i	−0.431761	+	0.901988i	$0.642108\pi$
$644$	−1.60183e12	−	1.60183e12i	−0.366970	−	0.366970i
$645$	3.21276e12	+	3.21276e12i	0.730904	+	0.730904i
$646$	1.69017e11			0.0381842
$647$			2.45805e12i			0.551468i	0.961234	+	0.275734i	$0.0889210\pi$
$647$			2.45805e12i			0.551468i	−0.961234	+	0.275734i	$0.911079\pi$
$648$			4.60994e11i			0.102709i
$649$	−9.78462e11	−	9.78462e11i	−0.216493	−	0.216493i
$650$	2.73412e12	−	2.73412e12i	0.600770	−	0.600770i
$651$		−	5.36732e12i		−	1.17123i
$652$	2.96495e12			0.642544
$653$	−2.82280e12	−	2.82280e12i	−0.607534	−	0.607534i	0.334767	−	0.942301i	$-0.391343\pi$
$653$	−2.82280e12	−	2.82280e12i	−0.607534	−	0.607534i	−0.942301	+	0.334767i	$0.891343\pi$
$654$			2.79291e12i			0.596977i
$655$	−1.69505e12			−0.359829
$656$	1.53630e9	−	1.04655e9i	0.000323899	−	0.000220645i
$657$	−1.92438e12			−0.402946
$658$		−	2.73494e12i		−	0.568763i
$659$	−1.87939e12	−	1.87939e12i	−0.388180	−	0.388180i	0.485858	−	0.874038i	$-0.338507\pi$
$659$	−1.87939e12	−	1.87939e12i	−0.388180	−	0.388180i	−0.874038	+	0.485858i	$0.838507\pi$
$660$	6.28114e11			0.128852
$661$		−	2.72467e12i		−	0.555145i	−0.960705	−	0.277573i	$-0.910470\pi$
$661$		−	2.72467e12i		−	0.555145i	0.960705	−	0.277573i	$-0.0895299\pi$
$662$	2.43405e12	−	2.43405e12i	0.492570	−	0.492570i
$663$	3.34116e12	+	3.34116e12i	0.671562	+	0.671562i
$664$		−	6.19737e12i		−	1.23723i
$665$			3.06144e11i			0.0607055i
$666$	2.91271e12			0.573672
$667$	2.20967e12	+	2.20967e12i	0.432277	+	0.432277i
$668$	−7.26928e11	−	7.26928e11i	−0.141253	−	0.141253i
$669$	−2.23587e12	−	2.23587e12i	−0.431547	−	0.431547i
$670$	−5.97889e12	+	5.97889e12i	−1.14626	+	1.14626i
$671$	−5.64983e11	+	5.64983e11i	−0.107593	+	0.107593i
$672$	−3.30417e12			−0.625029
$673$	−2.02724e12	+	2.02724e12i	−0.380923	+	0.380923i	−0.871435	−	0.490512i	$-0.836810\pi$
$673$	−2.02724e12	+	2.02724e12i	−0.380923	+	0.380923i	0.490512	+	0.871435i	$0.336810\pi$
$674$	5.03209e12			0.939245
$675$	−5.63837e12	+	5.63837e12i	−1.04541	+	1.04541i
$676$		−	2.85498e11i		−	0.0525827i
$677$		−	6.73490e12i		−	1.23220i	−0.787667	−	0.616101i	$-0.788711\pi$
$677$		−	6.73490e12i		−	1.23220i	0.787667	−	0.616101i	$-0.211289\pi$
$678$	1.69963e12	−	1.69963e12i	0.308903	−	0.308903i
$679$	−4.50170e12			−0.812761
$680$	−9.33244e12	+	9.33244e12i	−1.67381	+	1.67381i
$681$	3.31515e12			0.590666
$682$	−9.43916e11	+	9.43916e11i	−0.167072	+	0.167072i
$683$	−3.70270e12	+	3.70270e12i	−0.651066	+	0.651066i	−0.953250	−	0.302184i	$-0.902284\pi$
$683$	−3.70270e12	+	3.70270e12i	−0.651066	+	0.651066i	0.302184	+	0.953250i	$0.402284\pi$
$684$	−5.81941e10	−	5.81941e10i	−0.0101654	−	0.0101654i
$685$	8.29119e12	+	8.29119e12i	1.43883	+	1.43883i
$686$	2.63527e12	+	2.63527e12i	0.454324	+	0.454324i
$687$	−4.00973e12			−0.686767
$688$			2.32877e9i			0.000396258i
$689$			3.71596e12i			0.628180i
$690$	2.34138e12	+	2.34138e12i	0.393235	+	0.393235i
$691$	1.58754e12	−	1.58754e12i	0.264895	−	0.264895i	−0.562144	−	0.827039i	$-0.690023\pi$
$691$	1.58754e12	−	1.58754e12i	0.264895	−	0.264895i	0.827039	+	0.562144i	$0.190023\pi$
$692$			5.22599e12i			0.866345i
$693$	−6.75198e11			−0.111207
$694$	−2.50182e12	−	2.50182e12i	−0.409391	−	0.409391i
$695$		−	3.45867e12i		−	0.562312i
$696$	2.81688e12			0.455015
$697$	−1.75996e12	+	9.28167e12i	−0.282459	+	1.48963i
$698$	3.31690e11			0.0528912
$699$		−	3.26364e12i		−	0.517077i
$700$	−3.80651e12	−	3.80651e12i	−0.599219	−	0.599219i
$701$	−7.53968e12			−1.17929			−0.589647	−	0.807661i	$-0.700733\pi$
$701$	−7.53968e12			−1.17929			−0.589647	+	0.807661i	$0.700733\pi$
$702$			3.91464e12i			0.608379i
$703$	3.03130e11	−	3.03130e11i	0.0468091	−	0.0468091i
$704$	5.81451e11	+	5.81451e11i	0.0892146	+	0.0892146i
$705$		−	6.46352e12i		−	0.985413i
$706$			1.46874e12i			0.222497i
$707$	−4.19955e11			−0.0632142
$708$	2.87099e12	+	2.87099e12i	0.429420	+	0.429420i
$709$	−1.86412e12	−	1.86412e12i	−0.277054	−	0.277054i	0.554878	−	0.831932i	$-0.312765\pi$
$709$	−1.86412e12	−	1.86412e12i	−0.277054	−	0.277054i	−0.831932	+	0.554878i	$0.812765\pi$
$710$	−3.42429e12	−	3.42429e12i	−0.505718	−	0.505718i
$711$	2.84368e12	−	2.84368e12i	0.417319	−	0.417319i
$712$	−3.35723e11	+	3.35723e11i	−0.0489577	+	0.0489577i
$713$	1.13779e13			1.64877
$714$	−2.87701e12	+	2.87701e12i	−0.414285	+	0.414285i
$715$	2.12862e12			0.304593
$716$	−4.78923e12	+	4.78923e12i	−0.681016	+	0.681016i
$717$		−	4.55001e12i		−	0.642948i
$718$			2.24689e12i			0.315516i
$719$	−5.83938e12	+	5.83938e12i	−0.814867	+	0.814867i	−0.985359	−	0.170492i	$-0.945464\pi$
$719$	−5.83938e12	+	5.83938e12i	−0.814867	+	0.814867i	0.170492	+	0.985359i	$0.445464\pi$
$720$	−2.51960e9			−0.000349411
$721$	−1.16717e12	+	1.16717e12i	−0.160852	+	0.160852i
$722$	−4.50617e12			−0.617150
$723$	4.53204e12	−	4.53204e12i	0.616839	−	0.616839i
$724$	−2.31248e12	+	2.31248e12i	−0.312792	+	0.312792i
$725$	5.25095e12	+	5.25095e12i	0.705858	+	0.705858i
$726$	2.05362e12	+	2.05362e12i	0.274350	+	0.274350i
$727$	−9.44007e12	−	9.44007e12i	−1.25334	−	1.25334i	−0.954212	−	0.299133i	$-0.903303\pi$
$727$	−9.44007e12	−	9.44007e12i	−1.25334	−	1.25334i	−0.299133	−	0.954212i	$-0.596697\pi$
$728$	−6.92015e12			−0.913113
$729$		−	5.58553e12i		−	0.732471i
$730$			5.22398e12i			0.680845i
$731$	−8.36859e12	−	8.36859e12i	−1.08399	−	1.08399i
$732$	1.65777e12	−	1.65777e12i	0.213414	−	0.213414i
$733$		−	6.30343e12i		−	0.806508i	−0.915088	−	0.403254i	$-0.867879\pi$
$733$		−	6.30343e12i		−	0.806508i	0.915088	−	0.403254i	$-0.132121\pi$
$734$	−1.94840e11			−0.0247768
$735$	5.08391e11	+	5.08391e11i	0.0642547	+	0.0642547i
$736$		−	7.00434e12i		−	0.879867i
$737$	−2.74466e12			−0.342677
$738$	−2.35135e12	+	1.60177e12i	−0.291785	+	0.198768i
$739$	5.12028e12			0.631530			0.315765	−	0.948837i	$-0.397739\pi$
$739$	5.12028e12			0.631530			0.315765	+	0.948837i	$0.397739\pi$
$740$			1.27842e13i			1.56722i
$741$	1.48096e11	+	1.48096e11i	0.0180451	+	0.0180451i
$742$	−3.19974e12			−0.387522
$743$		−	1.18034e13i		−	1.42088i	−0.703758	−	0.710440i	$-0.748496\pi$
$743$		−	1.18034e13i		−	1.42088i	0.703758	−	0.710440i	$-0.251504\pi$
$744$	7.25225e12	−	7.25225e12i	0.867750	−	0.867750i
$745$	−7.39840e12	−	7.39840e12i	−0.879903	−	0.879903i
$746$			8.92610e12i			1.05521i
$747$			6.01271e12i			0.706525i
$748$	−1.63611e12			−0.191097
$749$	4.82232e12	+	4.82232e12i	0.559871	+	0.559871i
$750$	1.69175e12	+	1.69175e12i	0.195236	+	0.195236i
$751$	−1.15442e13	−	1.15442e13i	−1.32430	−	1.32430i	−0.910260	−	0.414037i	$-0.864118\pi$
$751$	−1.15442e13	−	1.15442e13i	−1.32430	−	1.32430i	−0.414037	−	0.910260i	$-0.635882\pi$
$752$	2.34254e9	−	2.34254e9i	0.000267120	−	0.000267120i
$753$	−3.23502e12	+	3.23502e12i	−0.366691	+	0.366691i
$754$	3.64566e12			0.410776
$755$	−1.86043e12	+	1.86043e12i	−0.208378	+	0.208378i
$756$	5.45005e12			0.606809
$757$	−8.77396e12	+	8.77396e12i	−0.971100	+	0.971100i	−0.999594	−	0.0284938i	$-0.990929\pi$
$757$	−8.77396e12	+	8.77396e12i	−0.971100	+	0.971100i	0.0284938	+	0.999594i	$0.490929\pi$
$758$		−	3.82749e12i		−	0.421117i
$759$			1.07483e12i			0.117558i
$760$	−4.13657e11	+	4.13657e11i	−0.0449758	+	0.0449758i
$761$	1.10846e13			1.19809			0.599046	−	0.800714i	$-0.295547\pi$
$761$	1.10846e13			1.19809			0.599046	+	0.800714i	$0.295547\pi$
$762$	−7.83479e11	+	7.83479e11i	−0.0841840	+	0.0841840i
$763$	1.31773e13			1.40755
$764$	−2.13714e12	+	2.13714e12i	−0.226941	+	0.226941i
$765$	9.05437e12	−	9.05437e12i	0.955833	−	0.955833i
$766$	−2.40576e12	−	2.40576e12i	−0.252478	−	0.252478i
$767$	9.72952e12	+	9.72952e12i	1.01511	+	1.01511i
$768$	−4.46562e12	−	4.46562e12i	−0.463187	−	0.463187i
$769$	1.11983e13			1.15473			0.577367	−	0.816485i	$-0.304080\pi$
$769$	1.11983e13			1.15473			0.577367	+	0.816485i	$0.304080\pi$
$770$			1.83291e12i			0.187903i
$771$			7.48615e12i			0.762981i
$772$	4.46598e12	+	4.46598e12i	0.452521	+	0.452521i
$773$	1.12736e13	−	1.12736e13i	1.13568	−	1.13568i	0.146460	−	0.989217i	$-0.453212\pi$
$773$	1.12736e13	−	1.12736e13i	1.13568	−	1.13568i	0.989217	−	0.146460i	$-0.0467879\pi$
$774$		−	3.56423e12i		−	0.356970i
$775$	2.70379e13			2.69225
$776$	−6.08264e12	−	6.08264e12i	−0.602163	−	0.602163i
$777$			1.03198e13i			1.01572i
$778$	1.07944e13			1.05631
$779$	−7.80095e10	+	4.11407e11i	−0.00758977	+	0.0400270i
$780$	−6.24576e12			−0.604171
$781$		−	1.57195e12i		−	0.151185i
$782$	−6.09883e12	−	6.09883e12i	−0.583198	−	0.583198i
$783$	−7.51816e12			−0.714799
$784$			3.68507e8i			3.48356e-5i
$785$	−1.48660e13	+	1.48660e13i	−1.39727	+	1.39727i
$786$	−7.06062e11	−	7.06062e11i	−0.0659844	−	0.0659844i
$787$			1.87918e13i			1.74615i	0.487583	+	0.873077i	$0.337879\pi$
$787$			1.87918e13i			1.74615i	−0.487583	+	0.873077i	$0.662121\pi$
$788$			2.25236e12i			0.208099i
$789$	5.23717e12			0.481116
$790$	−7.71953e12	−	7.71953e12i	−0.705130	−	0.705130i
$791$	−8.01906e12	−	8.01906e12i	−0.728332	−	0.728332i
$792$	−9.12318e11	−	9.12318e11i	−0.0823916	−	0.0823916i
$793$	5.61802e12	−	5.61802e12i	0.504491	−	0.504491i
$794$	2.33205e11	−	2.33205e11i	0.0208231	−	0.0208231i
$795$	−7.56198e12			−0.671404
$796$	−6.38511e11	+	6.38511e11i	−0.0563715	+	0.0563715i
$797$	−5.18374e12			−0.455073			−0.227536	−	0.973770i	$-0.573067\pi$
$797$	−5.18374e12			−0.455073			−0.227536	+	0.973770i	$0.573067\pi$
$798$	−1.27522e11	+	1.27522e11i	−0.0111320	+	0.0111320i
$799$			1.68361e13i			1.46144i
$800$		−	1.66448e13i		−	1.43672i
$801$	3.25720e11	−	3.25720e11i	0.0279575	−	0.0279575i
$802$	7.05667e12			0.602303
$803$	−1.19906e12	+	1.19906e12i	−0.101770	+	0.101770i
$804$	8.05335e12			0.679711
$805$	1.10469e13	−	1.10469e13i	0.927171	−	0.927171i
$806$	9.38600e12	−	9.38600e12i	0.783381	−	0.783381i
$807$	6.01234e12	+	6.01234e12i	0.499014	+	0.499014i
$808$	−5.67437e11	−	5.67437e11i	−0.0468345	−	0.0468345i
$809$	7.37266e11	+	7.37266e11i	0.0605140	+	0.0605140i	0.736716	−	0.676202i	$-0.236375\pi$
$809$	7.37266e11	+	7.37266e11i	0.0605140	+	0.0605140i	−0.676202	+	0.736716i	$0.736375\pi$
$810$	−1.21414e12			−0.0991028
$811$		−	1.63306e13i		−	1.32559i	−0.748802	−	0.662793i	$-0.769371\pi$
$811$		−	1.63306e13i		−	1.32559i	0.748802	−	0.662793i	$-0.230629\pi$
$812$		−	5.07557e12i		−	0.409716i
$813$	−7.05998e12	−	7.05998e12i	−0.566756	−	0.566756i
$814$	1.81487e12	−	1.81487e12i	0.144889	−	0.144889i
$815$			2.04475e13i			1.62342i
$816$	−4.92844e9			−0.000389138
$817$	−3.70935e11	−	3.70935e11i	−0.0291272	−	0.0291272i
$818$		−	4.60925e12i		−	0.359948i
$819$	6.71396e12			0.521436
$820$	−7.03032e12	−	1.03203e13i	−0.543016	−	0.797130i
$821$	1.14529e13			0.879771			0.439886	−	0.898054i	$-0.355019\pi$
$821$	1.14529e13			0.879771			0.439886	+	0.898054i	$0.355019\pi$
$822$			6.90729e12i			0.527697i
$823$	−1.27848e13	−	1.27848e13i	−0.971389	−	0.971389i	0.0282128	−	0.999602i	$-0.491018\pi$
$823$	−1.27848e13	−	1.27848e13i	−0.971389	−	0.971389i	−0.999602	+	0.0282128i	$0.991018\pi$
$824$	−3.15413e12			−0.238346
$825$			2.55418e12i			0.191959i
$826$	−8.37790e12	+	8.37790e12i	−0.626217	+	0.626217i
$827$	1.55643e13	+	1.55643e13i	1.15706	+	1.15706i	0.985105	+	0.171956i	$0.0550086\pi$
$827$	1.55643e13	+	1.55643e13i	1.15706	+	1.15706i	0.171956	+	0.985105i	$0.444991\pi$
$828$			4.19976e12i			0.310519i
$829$			1.60398e12i			0.117951i	0.998259	+	0.0589756i	$0.0187834\pi$
$829$			1.60398e12i			0.117951i	−0.998259	+	0.0589756i	$0.981217\pi$
$830$	1.63222e13			1.19379
$831$	−8.65884e12	−	8.65884e12i	−0.629876	−	0.629876i
$832$	−5.78176e12	−	5.78176e12i	−0.418317	−	0.418317i
$833$	−1.32425e12	−	1.32425e12i	−0.0952948	−	0.0952948i
$834$	1.44069e12	−	1.44069e12i	0.103115	−	0.103115i
$835$	5.01321e12	−	5.01321e12i	0.356884	−	0.356884i
$836$	−7.25198e10			−0.00513486
$837$	−1.93560e13	+	1.93560e13i	−1.36318	+	1.36318i
$838$	1.63507e13			1.14535
$839$	2.18928e12	−	2.18928e12i	0.152536	−	0.152536i	−0.626713	−	0.779250i	$-0.715600\pi$
$839$	2.18928e12	−	2.18928e12i	0.152536	−	0.152536i	0.779250	+	0.626713i	$0.215600\pi$
$840$		−	1.40825e13i		−	0.975942i
$841$		−	7.50557e12i		−	0.517370i
$842$	−3.04103e12	+	3.04103e12i	−0.208505	+	0.208505i
$843$	1.31466e13			0.896581
$844$	4.72108e12	−	4.72108e12i	0.320258	−	0.320258i
$845$	1.96892e12			0.132853
$846$	−3.58530e12	+	3.58530e12i	−0.240635	+	0.240635i
$847$	9.68919e12	−	9.68919e12i	0.646863	−	0.646863i
$848$	−2.74065e9	−	2.74065e9i	−0.000182000	−	0.000182000i
$849$	−7.14833e12	−	7.14833e12i	−0.472194	−	0.472194i
$850$	−1.44929e13	−	1.44929e13i	−0.952294	−	0.952294i
$851$	−2.18764e13			−1.42986
$852$			4.61240e12i			0.299881i
$853$			1.51079e13i			0.977088i	0.872539	+	0.488544i	$0.162472\pi$
$853$			1.51079e13i			0.977088i	−0.872539	+	0.488544i	$0.837528\pi$
$854$	4.83756e12	+	4.83756e12i	0.311219	+	0.311219i
$855$	4.01332e11	−	4.01332e11i	0.0256836	−	0.0256836i
$856$			1.30317e13i			0.829600i
$857$	−1.90482e13			−1.20626			−0.603129	−	0.797644i	$-0.706080\pi$
$857$	−1.90482e13			−1.20626			−0.603129	+	0.797644i	$0.706080\pi$
$858$	8.86662e11	+	8.86662e11i	0.0558554	+	0.0558554i
$859$			2.15441e13i			1.35008i	0.737782	+	0.675040i	$0.235873\pi$
$859$			2.15441e13i			1.35008i	−0.737782	+	0.675040i	$0.764127\pi$
$860$	1.56437e13			0.975209
$861$	−5.67508e12	−	8.33084e12i	−0.351932	−	0.516624i
$862$	−1.77112e13			−1.09261
$863$		−	2.19946e13i		−	1.34980i	−0.737911	−	0.674898i	$-0.764188\pi$
$863$		−	2.19946e13i		−	1.34980i	0.737911	−	0.674898i	$-0.235812\pi$
$864$	1.19157e13	+	1.19157e13i	0.727460	+	0.727460i
$865$	−3.60406e13			−2.18887
$866$			6.49674e12i			0.392523i
$867$	1.00063e13	−	1.00063e13i	0.601434	−	0.601434i
$868$	−1.30674e13	−	1.30674e13i	−0.781359	−	0.781359i
$869$		−	3.54372e12i		−	0.210800i
$870$			7.41892e12i			0.439040i
$871$	2.72920e13			1.60677
$872$	1.78049e13	+	1.78049e13i	1.04284	+	1.04284i
$873$	5.90140e12	+	5.90140e12i	0.343867	+	0.343867i
$874$	−2.70328e11	−	2.70328e11i	−0.0156708	−	0.0156708i
$875$	7.98185e12	−	7.98185e12i	0.460328	−	0.460328i
$876$	3.51825e12	−	3.51825e12i	0.201864	−	0.201864i
$877$	−1.32001e13			−0.753492			−0.376746	−	0.926317i	$-0.622957\pi$
$877$	−1.32001e13			−0.753492			−0.376746	+	0.926317i	$0.622957\pi$
$878$	3.10534e12	−	3.10534e12i	0.176354	−	0.176354i
$879$	−1.69398e13			−0.957101
$880$	−1.56993e9	+	1.56993e9i	−8.82486e−5	+	8.82486e-5i
$881$			6.74919e12i			0.377451i	0.982030	+	0.188725i	$0.0604356\pi$
$881$			6.74919e12i			0.377451i	−0.982030	+	0.188725i	$0.939564\pi$
$882$		−	5.64008e11i		−	0.0313817i
$883$	−1.04804e13	+	1.04804e13i	−0.580170	+	0.580170i	−0.934950	−	0.354780i	$-0.884556\pi$
$883$	−1.04804e13	+	1.04804e13i	−0.580170	+	0.580170i	0.354780	+	0.934950i	$0.384556\pi$
$884$	1.62689e13			0.896033
$885$	−1.97996e13	+	1.97996e13i	−1.08496	+	1.08496i
$886$	−7.70682e12			−0.420169
$887$	−1.37730e13	+	1.37730e13i	−0.747090	+	0.747090i	−0.973932	−	0.226842i	$-0.927160\pi$
$887$	−1.37730e13	+	1.37730e13i	−0.747090	+	0.747090i	0.226842	+	0.973932i	$0.427160\pi$
$888$	−1.39439e13	+	1.39439e13i	−0.752535	+	0.752535i
$889$	3.69654e12	+	3.69654e12i	0.198489	+	0.198489i
$890$	−8.84207e11	−	8.84207e11i	−0.0472388	−	0.0472388i
$891$	−2.78680e11	−	2.78680e11i	−0.0148135	−	0.0148135i
$892$	−1.08870e13			−0.575792
$893$			7.46256e11i			0.0392696i
$894$		−	6.16352e12i		−	0.322708i
$895$	−3.30286e13	−	3.30286e13i	−1.72063	−	1.72063i
$896$	−8.04125e12	+	8.04125e12i	−0.416809	+	0.416809i
$897$		−	1.06878e13i		−	0.551216i
$898$	−5.81596e11			−0.0298454
$899$	1.80261e13	+	1.80261e13i	0.920412	+	0.920412i
$900$			9.98010e12i			0.507042i
$901$	1.96974e13			0.995744
$902$	−4.67050e11	+	2.46313e12i	−0.0234928	+	0.123896i
$903$	1.26281e13			0.632038
$904$		−	2.16705e13i		−	1.07922i
$905$	−1.59479e13	−	1.59479e13i	−0.790286	−	0.790286i
$906$	−1.54990e12			−0.0764234
$907$			1.24135e12i			0.0609063i	0.999536	+	0.0304531i	$0.00969503\pi$
$907$			1.24135e12i			0.0609063i	−0.999536	+	0.0304531i	$0.990305\pi$
$908$	8.07116e12	−	8.07116e12i	0.394048	−	0.394048i
$909$	5.50529e11	+	5.50529e11i	0.0267450	+	0.0267450i
$910$		−	1.82259e13i		−	0.881054i
$911$			1.45991e13i			0.702254i	0.936328	+	0.351127i	$0.114201\pi$
$911$			1.45991e13i			0.702254i	−0.936328	+	0.351127i	$0.885799\pi$
$912$	−2.18451e8			−1.04563e−5
$913$	3.74643e12	+	3.74643e12i	0.178443	+	0.178443i
$914$	8.54786e12	+	8.54786e12i	0.405135	+	0.405135i
$915$	1.14327e13	+	1.14327e13i	0.539204	+	0.539204i
$916$	−9.76218e12	+	9.76218e12i	−0.458160	+	0.458160i
$917$	−3.33128e12	+	3.33128e12i	−0.155578	+	0.155578i
$918$	2.07506e13			0.964357
$919$	−1.48427e13	+	1.48427e13i	−0.686427	+	0.686427i	−0.961440	−	0.275013i	$-0.911318\pi$
$919$	−1.48427e13	+	1.48427e13i	−0.686427	+	0.686427i	0.275013	+	0.961440i	$0.411318\pi$
$920$	2.98529e13			1.37386
$921$	−2.87821e12	+	2.87821e12i	−0.131812	+	0.131812i
$922$			3.88579e12i			0.177088i
$923$			1.56310e13i			0.708890i
$924$	1.23443e12	−	1.23443e12i	0.0557113	−	0.0557113i
$925$	−5.19859e13			−2.33479
$926$	−6.04591e12	+	6.04591e12i	−0.270217	+	0.270217i
$927$	3.06015e12			0.136108
$928$	1.10970e13	−	1.10970e13i	0.491178	−	0.491178i
$929$	9.85977e12	−	9.85977e12i	0.434306	−	0.434306i	−0.455784	−	0.890090i	$-0.650641\pi$
$929$	9.85977e12	−	9.85977e12i	0.434306	−	0.434306i	0.890090	+	0.455784i	$0.150641\pi$
$930$	1.91005e13	+	1.91005e13i	0.837283	+	0.837283i
$931$	−5.86971e10	−	5.86971e10i	−0.00256061	−	0.00256061i
$932$	−7.94574e12	−	7.94574e12i	−0.344955	−	0.344955i
$933$	9.57558e11			0.0413712
$934$		−	1.70008e13i		−	0.730984i
$935$		−	1.12833e13i		−	0.482818i
$936$	9.07181e12	+	9.07181e12i	0.386325	+	0.386325i
$937$	−3.26430e13	+	3.26430e13i	−1.38344	+	1.38344i	−0.545023	+	0.838421i	$0.683479\pi$
$937$	−3.26430e13	+	3.26430e13i	−1.38344	+	1.38344i	−0.838421	+	0.545023i	$0.816521\pi$
$938$			2.35006e13i			0.991213i
$939$	1.89937e13			0.797286
$940$	−1.57362e13	−	1.57362e13i	−0.657394	−	0.657394i
$941$			3.92810e12i			0.163316i	0.996660	+	0.0816580i	$0.0260215\pi$
$941$			3.92810e12i			0.163316i	−0.996660	+	0.0816580i	$0.973978\pi$
$942$	−1.23847e13			−0.512455
$943$	1.76601e13	−	1.20303e13i	0.727263	−	0.495422i
$944$	−1.43517e10			−0.000588207
$945$			3.75859e13i			1.53314i
$946$	−2.22082e12	−	2.22082e12i	−0.0901578	−	0.0901578i
$947$	1.01780e13			0.411232			0.205616	−	0.978633i	$-0.434080\pi$
$947$	1.01780e13			0.411232			0.205616	+	0.978633i	$0.434080\pi$
$948$			1.03979e13i			0.418128i
$949$	1.19230e13	−	1.19230e13i	0.477187	−	0.477187i
$950$	−6.42394e11	−	6.42394e11i	−0.0255885	−	0.0255885i
$951$		−	2.52159e13i		−	0.999683i
$952$			3.66821e13i			1.44740i
$953$	2.46501e13			0.968057			0.484029	−	0.875052i	$-0.339173\pi$
$953$	2.46501e13			0.968057			0.484029	+	0.875052i	$0.339173\pi$
$954$	4.19462e12	+	4.19462e12i	0.163955	+	0.163955i
$955$	−1.47387e13	−	1.47387e13i	−0.573380	−	0.573380i
$956$	−1.10776e13	−	1.10776e13i	−0.428927	−	0.428927i
$957$	−1.70286e12	+	1.70286e12i	−0.0656258	+	0.0656258i
$958$	5.25465e12	−	5.25465e12i	0.201558	−	0.201558i
$959$	3.25894e13			1.24421
$960$	1.17659e13	−	1.17659e13i	0.447100	−	0.447100i
$961$	6.63792e13			2.51059
$962$	−1.80465e13	+	1.80465e13i	−0.679368	+	0.679368i
$963$		−	1.26434e13i		−	0.473746i
$964$		−	2.20676e13i		−	0.823018i
$965$	−3.07993e13	+	3.07993e13i	−1.14332	+	1.14332i
$966$	9.20305e12			0.340044
$967$	6.63583e12	−	6.63583e12i	0.244048	−	0.244048i	−0.574474	−	0.818523i	$-0.694793\pi$
$967$	6.63583e12	−	6.63583e12i	0.244048	−	0.244048i	0.818523	+	0.574474i	$0.194793\pi$
$968$	2.61838e13			0.958503
$969$	7.85020e11	−	7.85020e11i	0.0286038	−	0.0286038i
$970$	1.60201e13	−	1.60201e13i	0.581021	−	0.581021i
$971$	−2.75303e13	−	2.75303e13i	−0.993858	−	0.993858i	0.00612348	−	0.999981i	$-0.498051\pi$
$971$	−2.75303e13	−	2.75303e13i	−0.993858	−	0.993858i	−0.999981	+	0.00612348i	$0.998051\pi$
$972$	−1.16921e13	−	1.16921e13i	−0.420139	−	0.420139i
$973$	−6.79733e12	−	6.79733e12i	−0.243125	−	0.243125i
$974$	−1.33517e13			−0.475358
$975$		−	2.53979e13i		−	0.900073i
$976$			8.28696e9i			0.000292328i
$977$	−3.07512e13	−	3.07512e13i	−1.07978	−	1.07978i	−0.996528	−	0.0832533i	$-0.973469\pi$
$977$	−3.07512e13	−	3.07512e13i	−1.07978	−	1.07978i	−0.0832533	−	0.996528i	$-0.526531\pi$
$978$	−8.51730e12	+	8.51730e12i	−0.297699	+	0.297699i
$979$		−	4.05903e11i		−	0.0141221i
$980$	2.47548e12			0.0857319
$981$	−1.72744e13	−	1.72744e13i	−0.595516	−	0.595516i
$982$		−	2.10524e13i		−	0.722438i
$983$	−5.72168e13			−1.95449			−0.977244	−	0.212120i	$-0.931963\pi$
$983$	−5.72168e13			−1.95449			−0.977244	+	0.212120i	$0.931963\pi$
$984$	3.58842e12	−	1.89246e13i	0.122018	−	0.643500i
$985$	−1.55332e13			−0.525774
$986$		−	1.93248e13i		−	0.651130i
$987$	−1.27028e13	−	1.27028e13i	−0.426060	−	0.426060i
$988$	7.21114e11			0.0240768
$989$			2.67697e13i			0.889733i
$990$	2.40281e12	−	2.40281e12i	0.0794989	−	0.0794989i
$991$	2.63560e13	+	2.63560e13i	0.868056	+	0.868056i	0.992257	−	0.124201i	$-0.0396368\pi$
$991$	2.63560e13	+	2.63560e13i	0.868056	+	0.868056i	−0.124201	+	0.992257i	$0.539637\pi$
$992$		−	5.71400e13i		−	1.87343i
$993$		−	2.26104e13i		−	0.737968i
$994$	−1.34595e13			−0.437312
$995$	−4.40345e12	−	4.40345e12i	−0.142426	−	0.142426i
$996$	−1.09927e13	−	1.09927e13i	−0.353948	−	0.353948i
$997$	2.20800e13	+	2.20800e13i	0.707735	+	0.707735i	0.966058	−	0.258324i	$-0.0831701\pi$
$997$	2.20800e13	+	2.20800e13i	0.707735	+	0.707735i	−0.258324	+	0.966058i	$0.583170\pi$
$998$	−2.51387e12	+	2.51387e12i	−0.0802148	+	0.0802148i
$999$	3.72159e13	−	3.72159e13i	1.18218	−	1.18218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.10.c.a.9.20	✓	62
41.32	even	4	inner	41.10.c.a.32.12	yes	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.10.c.a.9.20	✓	62	1.1	even	1	trivial
41.10.c.a.32.12	yes	62	41.32	even	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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	41.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+13.9877i q^{2} +(64.9677 + 64.9677i) q^{3} +316.344 q^{4} +2181.64i q^{5} +(-908.750 + 908.750i) q^{6} +(4287.58 + 4287.58i) q^{7} +11586.6i q^{8} -11241.4i q^{9} +O(q^{10})\)	\(q+13.9877i q^{2} +(64.9677 + 64.9677i) q^{3} +316.344 q^{4} +2181.64i q^{5} +(-908.750 + 908.750i) q^{6} +(4287.58 + 4287.58i) q^{7} +11586.6i q^{8} -11241.4i q^{9} -30516.2 q^{10} +(-7004.36 - 7004.36i) q^{11} +(20552.1 + 20552.1i) q^{12} +(69649.1 + 69649.1i) q^{13} +(-59973.5 + 59973.5i) q^{14} +(-141736. + 141736. i) q^{15} -102.737 q^{16} +(369194. - 369194. i) q^{17} +157242. q^{18} +(16364.4 - 16364.4i) q^{19} +690149. i q^{20} +557108. i q^{21} +(97975.0 - 97975.0i) q^{22} -1.18099e6 q^{23} +(-752757. + 752757. i) q^{24} -2.80644e6 q^{25} +(-974233. + 974233. i) q^{26} +(2.00909e6 - 2.00909e6i) q^{27} +(1.35635e6 + 1.35635e6i) q^{28} +(-1.87104e6 - 1.87104e6i) q^{29} +(-1.98257e6 - 1.98257e6i) q^{30} -9.63425e6 q^{31} +5.93092e6i q^{32} -910114. i q^{33} +(5.16418e6 + 5.16418e6i) q^{34} +(-9.35397e6 + 9.35397e6i) q^{35} -3.55615e6i q^{36} +1.85238e7 q^{37} +(228900. + 228900. i) q^{38} +9.04988e6i q^{39} -2.52779e7 q^{40} +(-1.49537e7 + 1.01867e7i) q^{41} -7.79268e6 q^{42} -2.26672e7i q^{43} +(-2.21578e6 - 2.21578e6i) q^{44} +2.45247e7 q^{45} -1.65193e7i q^{46} +(-2.28012e7 + 2.28012e7i) q^{47} +(-6674.60 - 6674.60i) q^{48} -3.58688e6i q^{49} -3.92557e7i q^{50} +4.79713e7 q^{51} +(2.20331e7 + 2.20331e7i) q^{52} +(2.66763e7 + 2.66763e7i) q^{53} +(2.81025e7 + 2.81025e7i) q^{54} +(1.52810e7 - 1.52810e7i) q^{55} +(-4.96787e7 + 4.96787e7i) q^{56} +2.12631e6 q^{57} +(2.61716e7 - 2.61716e7i) q^{58} +1.39693e8 q^{59} +(-4.48373e7 + 4.48373e7i) q^{60} -8.06617e7i q^{61} -1.34761e8i q^{62} +(4.81985e7 - 4.81985e7i) q^{63} -8.30127e7 q^{64} +(-1.51949e8 + 1.51949e8i) q^{65} +1.27304e7 q^{66} +(1.95925e8 - 1.95925e8i) q^{67} +(1.16792e8 - 1.16792e8i) q^{68} +(-7.67260e7 - 7.67260e7i) q^{69} +(-1.30841e8 - 1.30841e8i) q^{70} +(1.12212e8 + 1.12212e8i) q^{71} +1.30250e8 q^{72} -1.71187e8i q^{73} +2.59106e8i q^{74} +(-1.82328e8 - 1.82328e8i) q^{75} +(5.17676e6 - 5.17676e6i) q^{76} -6.00635e7i q^{77} -1.26587e8 q^{78} +(2.52965e8 + 2.52965e8i) q^{79} -224136. i q^{80} +3.97867e7 q^{81} +(-1.42488e8 - 2.09168e8i) q^{82} -5.34872e8 q^{83} +1.76238e8i q^{84} +(8.05448e8 + 8.05448e8i) q^{85} +3.17063e8 q^{86} -2.43114e8i q^{87} +(8.11570e7 - 8.11570e7i) q^{88} +(2.89750e7 + 2.89750e7i) q^{89} +3.43045e8i q^{90} +5.97253e8i q^{91} -3.73598e8 q^{92} +(-6.25915e8 - 6.25915e8i) q^{93} +(-3.18937e8 - 3.18937e8i) q^{94} +(3.57012e7 + 3.57012e7i) q^{95} +(-3.85318e8 + 3.85318e8i) q^{96} +(-5.24970e8 + 5.24970e8i) q^{97} +5.01723e7 q^{98} +(-7.87388e7 + 7.87388e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 148 q^{3} - 15876 q^{4} - 4372 q^{6} - 2 q^{7}+O(q^{10}) \) 62 * q - 148 * q^3 - 15876 * q^4 - 4372 * q^6 - 2 * q^7	\( 62 q - 148 q^{3} - 15876 q^{4} - 4372 q^{6} - 2 q^{7} + 64940 q^{10} - 101136 q^{11} + 88610 q^{12} - 212164 q^{13} - 486724 q^{14} - 280448 q^{15} + 4065276 q^{16} + 989130 q^{17} + 631900 q^{18} - 557304 q^{19} + 878738 q^{22} - 2585064 q^{23} + 8160792 q^{24} - 13556490 q^{25} - 4638930 q^{26} - 4560520 q^{27} - 15062678 q^{28} - 645332 q^{29} + 24289990 q^{30} - 10831104 q^{31} + 3975452 q^{34} + 29170524 q^{35} - 3116208 q^{37} + 29714800 q^{38} - 35676784 q^{40} + 38183180 q^{41} - 88501252 q^{42} + 88194656 q^{44} - 44608688 q^{45} - 37901682 q^{47} - 65214646 q^{48} + 22786536 q^{51} + 67233198 q^{52} + 98223480 q^{53} - 222847538 q^{54} + 341535988 q^{55} + 37845552 q^{56} + 543416000 q^{57} - 39712038 q^{58} + 476227372 q^{59} - 73813254 q^{60} - 329401706 q^{63} - 1473830612 q^{64} - 283361396 q^{65} + 1055141156 q^{66} + 137841616 q^{67} - 1702495104 q^{68} - 643435264 q^{69} - 1945980994 q^{70} + 43024650 q^{71} + 298006608 q^{72} + 511623892 q^{75} + 2630680074 q^{76} + 2932953920 q^{78} - 559013342 q^{79} - 3103395126 q^{81} - 1636160042 q^{82} + 4760276320 q^{83} + 234551440 q^{85} + 4427686276 q^{86} - 1446984286 q^{88} - 373768662 q^{89} - 546085324 q^{92} + 246761008 q^{93} - 931400058 q^{94} - 2067661068 q^{95} - 7929456644 q^{96} - 949806418 q^{97} + 5988587276 q^{98} + 1756047684 q^{99}+O(q^{100}) \) 62 * q - 148 * q^3 - 15876 * q^4 - 4372 * q^6 - 2 * q^7 + 64940 * q^10 - 101136 * q^11 + 88610 * q^12 - 212164 * q^13 - 486724 * q^14 - 280448 * q^15 + 4065276 * q^16 + 989130 * q^17 + 631900 * q^18 - 557304 * q^19 + 878738 * q^22 - 2585064 * q^23 + 8160792 * q^24 - 13556490 * q^25 - 4638930 * q^26 - 4560520 * q^27 - 15062678 * q^28 - 645332 * q^29 + 24289990 * q^30 - 10831104 * q^31 + 3975452 * q^34 + 29170524 * q^35 - 3116208 * q^37 + 29714800 * q^38 - 35676784 * q^40 + 38183180 * q^41 - 88501252 * q^42 + 88194656 * q^44 - 44608688 * q^45 - 37901682 * q^47 - 65214646 * q^48 + 22786536 * q^51 + 67233198 * q^52 + 98223480 * q^53 - 222847538 * q^54 + 341535988 * q^55 + 37845552 * q^56 + 543416000 * q^57 - 39712038 * q^58 + 476227372 * q^59 - 73813254 * q^60 - 329401706 * q^63 - 1473830612 * q^64 - 283361396 * q^65 + 1055141156 * q^66 + 137841616 * q^67 - 1702495104 * q^68 - 643435264 * q^69 - 1945980994 * q^70 + 43024650 * q^71 + 298006608 * q^72 + 511623892 * q^75 + 2630680074 * q^76 + 2932953920 * q^78 - 559013342 * q^79 - 3103395126 * q^81 - 1636160042 * q^82 + 4760276320 * q^83 + 234551440 * q^85 + 4427686276 * q^86 - 1446984286 * q^88 - 373768662 * q^89 - 546085324 * q^92 + 246761008 * q^93 - 931400058 * q^94 - 2067661068 * q^95 - 7929456644 * q^96 - 949806418 * q^97 + 5988587276 * q^98 + 1756047684 * q^99

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