LMFDB - Embedded newform 17.10.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, 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("17.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	17.4
Dual form			17.10.c.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.1697i q^{2} +(-95.6730 + 95.6730i) q^{3} -944.927 q^{4} +(-23.8207 + 23.8207i) q^{5} +(3651.81 + 3651.81i) q^{6} +(3405.47 + 3405.47i) q^{7} +16524.7i q^{8} +1376.34i q^{9} +O(q^{10})$	\(q-38.1697i q^{2} +(-95.6730 + 95.6730i) q^{3} -944.927 q^{4} +(-23.8207 + 23.8207i) q^{5} +(3651.81 + 3651.81i) q^{6} +(3405.47 + 3405.47i) q^{7} +16524.7i q^{8} +1376.34i q^{9} +(909.229 + 909.229i) q^{10} +(-3852.71 - 3852.71i) q^{11} +(90404.1 - 90404.1i) q^{12} +84561.3 q^{13} +(129986. - 129986. i) q^{14} -4558.00i q^{15} +146941. q^{16} +(-150851. + 309567. i) q^{17} +52534.6 q^{18} +731833. i q^{19} +(22508.8 - 22508.8i) q^{20} -651622. q^{21} +(-147057. + 147057. i) q^{22} +(857507. + 857507. i) q^{23} +(-1.58097e6 - 1.58097e6i) q^{24} +1.95199e6i q^{25} -3.22768e6i q^{26} +(-2.01481e6 - 2.01481e6i) q^{27} +(-3.21792e6 - 3.21792e6i) q^{28} +(3.25622e6 - 3.25622e6i) q^{29} -173977. q^{30} +(-5.70757e6 + 5.70757e6i) q^{31} +2.85196e6i q^{32} +737202. q^{33} +(1.18161e7 + 5.75796e6i) q^{34} -162241. q^{35} -1.30054e6i q^{36} +(-6.44138e6 + 6.44138e6i) q^{37} +2.79339e7 q^{38} +(-8.09024e6 + 8.09024e6i) q^{39} +(-393630. - 393630. i) q^{40} +(-1.74418e7 - 1.74418e7i) q^{41} +2.48722e7i q^{42} -1.54236e7i q^{43} +(3.64053e6 + 3.64053e6i) q^{44} +(-32785.4 - 32785.4i) q^{45} +(3.27308e7 - 3.27308e7i) q^{46} +3.04241e7 q^{47} +(-1.40583e7 + 1.40583e7i) q^{48} -1.71592e7i q^{49} +7.45069e7 q^{50} +(-1.51848e7 - 4.40496e7i) q^{51} -7.99043e7 q^{52} +214544. i q^{53} +(-7.69048e7 + 7.69048e7i) q^{54} +183549. q^{55} +(-5.62743e7 + 5.62743e7i) q^{56} +(-7.00167e7 - 7.00167e7i) q^{57} +(-1.24289e8 - 1.24289e8i) q^{58} +1.32098e8i q^{59} +4.30697e6i q^{60} +(-4.51277e7 - 4.51277e7i) q^{61} +(2.17856e8 + 2.17856e8i) q^{62} +(-4.68709e6 + 4.68709e6i) q^{63} +1.84092e8 q^{64} +(-2.01431e6 + 2.01431e6i) q^{65} -2.81388e7i q^{66} -4.10480e6 q^{67} +(1.42544e8 - 2.92518e8i) q^{68} -1.64080e8 q^{69} +6.19270e6i q^{70} +(9.21670e7 - 9.21670e7i) q^{71} -2.27437e7 q^{72} +(-8.35127e7 + 8.35127e7i) q^{73} +(2.45866e8 + 2.45866e8i) q^{74} +(-1.86753e8 - 1.86753e8i) q^{75} -6.91529e8i q^{76} -2.62406e7i q^{77} +(3.08802e8 + 3.08802e8i) q^{78} +(1.97887e8 + 1.97887e8i) q^{79} +(-3.50023e6 + 3.50023e6i) q^{80} +3.58436e8 q^{81} +(-6.65748e8 + 6.65748e8i) q^{82} +4.27934e8i q^{83} +6.15736e8 q^{84} +(-3.78071e6 - 1.09675e7i) q^{85} -5.88715e8 q^{86} +6.23065e8i q^{87} +(6.36650e7 - 6.36650e7i) q^{88} -5.00841e8 q^{89} +(-1.25141e6 + 1.25141e6i) q^{90} +(2.87971e8 + 2.87971e8i) q^{91} +(-8.10281e8 - 8.10281e8i) q^{92} -1.09212e9i q^{93} -1.16128e9i q^{94} +(-1.74328e7 - 1.74328e7i) q^{95} +(-2.72856e8 - 2.72856e8i) q^{96} +(-7.92961e8 + 7.92961e8i) q^{97} -6.54962e8 q^{98} +(5.30265e6 - 5.30265e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) $ 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	38.1697i		−	1.68688i	−0.537224	−	0.843440i	$-0.680527\pi$
$2$		−	38.1697i		−	1.68688i	0.537224	−	0.843440i	$-0.319473\pi$
$3$	−95.6730	+	95.6730i	−0.681936	+	0.681936i	−0.960436	−	0.278500i	$-0.910163\pi$
$3$	−95.6730	+	95.6730i	−0.681936	+	0.681936i	0.278500	+	0.960436i	$0.410163\pi$
$4$	−944.927			−1.84556
$5$	−23.8207	+	23.8207i	−0.0170447	+	0.0170447i	−0.715578	−	0.698533i	$-0.753836\pi$
$5$	−23.8207	+	23.8207i	−0.0170447	+	0.0170447i	0.698533	+	0.715578i	$0.253836\pi$
$6$	3651.81	+	3651.81i	1.15034	+	1.15034i
$7$	3405.47	+	3405.47i	0.536087	+	0.536087i	0.922377	−	0.386290i	$-0.126244\pi$
$7$	3405.47	+	3405.47i	0.536087	+	0.536087i	−0.386290	+	0.922377i	$0.626244\pi$
$8$			16524.7i			1.42636i
$9$			1376.34i			0.0699254i
$10$	909.229	+	909.229i	0.0287523	+	0.0287523i
$11$	−3852.71	−	3852.71i	−0.0793414	−	0.0793414i	0.666322	−	0.745664i	$-0.267867\pi$
$11$	−3852.71	−	3852.71i	−0.0793414	−	0.0793414i	−0.745664	+	0.666322i	$0.767867\pi$
$12$	90404.1	−	90404.1i	1.25856	−	1.25856i
$13$	84561.3			0.821158			0.410579	−	0.911825i	$-0.365327\pi$
$13$	84561.3			0.821158			0.410579	+	0.911825i	$0.365327\pi$
$14$	129986.	−	129986.i	0.904314	−	0.904314i
$15$		−	4558.00i		−	0.0232468i
$16$	146941.			0.560535
$17$	−150851.	+	309567.i	−0.438056	+	0.898948i
$17$	−150851.	+	309567.i	−0.438056	+	0.898948i
$18$	52534.6			0.117956
$19$			731833.i			1.28831i	0.764894	+	0.644156i	$0.222791\pi$
$19$			731833.i			1.28831i	−0.764894	+	0.644156i	$0.777209\pi$
$20$	22508.8	−	22508.8i	0.0314570	−	0.0314570i
$21$	−651622.			−0.731155
$22$	−147057.	+	147057.i	−0.133839	+	0.133839i
$23$	857507.	+	857507.i	0.638943	+	0.638943i	0.950295	−	0.311352i	$-0.100782\pi$
$23$	857507.	+	857507.i	0.638943	+	0.638943i	−0.311352	+	0.950295i	$0.600782\pi$
$24$	−1.58097e6	−	1.58097e6i	−0.972686	−	0.972686i
$25$			1.95199e6i			0.999419i
$26$		−	3.22768e6i		−	1.38519i
$27$	−2.01481e6	−	2.01481e6i	−0.729621	−	0.729621i
$28$	−3.21792e6	−	3.21792e6i	−0.989381	−	0.989381i
$29$	3.25622e6	−	3.25622e6i	0.854915	−	0.854915i	−0.135819	−	0.990734i	$-0.543367\pi$
$29$	3.25622e6	−	3.25622e6i	0.854915	−	0.854915i	0.990734	+	0.135819i	$0.0433666\pi$
$30$	−173977.			−0.0392145
$31$	−5.70757e6	+	5.70757e6i	−1.11000	+	1.11000i	−0.116853	+	0.993149i	$0.537281\pi$
$31$	−5.70757e6	+	5.70757e6i	−1.11000	+	1.11000i	−0.993149	+	0.116853i	$0.962719\pi$
$32$			2.85196e6i			0.480805i
$33$	737202.			0.108212
$34$	1.18161e7	+	5.75796e6i	1.51642	+	0.738947i
$35$	−162241.			−0.0182749
$36$		−	1.30054e6i		−	0.129052i
$37$	−6.44138e6	+	6.44138e6i	−0.565030	+	0.565030i	−0.930732	−	0.365702i	$-0.880829\pi$
$37$	−6.44138e6	+	6.44138e6i	−0.565030	+	0.565030i	0.365702	+	0.930732i	$0.380829\pi$
$38$	2.79339e7			2.17323
$39$	−8.09024e6	+	8.09024e6i	−0.559977	+	0.559977i
$40$	−393630.	−	393630.i	−0.0243119	−	0.0243119i
$41$	−1.74418e7	−	1.74418e7i	−0.963970	−	0.963970i	0.0354036	−	0.999373i	$-0.488728\pi$
$41$	−1.74418e7	−	1.74418e7i	−0.963970	−	0.963970i	−0.999373	+	0.0354036i	$0.988728\pi$
$42$			2.48722e7i			1.23337i
$43$		−	1.54236e7i		−	0.687984i	−0.938973	−	0.343992i	$-0.888221\pi$
$43$		−	1.54236e7i		−	0.687984i	0.938973	−	0.343992i	$-0.111779\pi$
$44$	3.64053e6	+	3.64053e6i	0.146429	+	0.146429i
$45$	−32785.4	−	32785.4i	−0.00119186	−	0.00119186i
$46$	3.27308e7	−	3.27308e7i	1.07782	−	1.07782i
$47$	3.04241e7			0.909447			0.454724	−	0.890633i	$-0.349738\pi$
$47$	3.04241e7			0.909447			0.454724	+	0.890633i	$0.349738\pi$
$48$	−1.40583e7	+	1.40583e7i	−0.382249	+	0.382249i
$49$		−	1.71592e7i		−	0.425221i
$50$	7.45069e7			1.68590
$51$	−1.51848e7	−	4.40496e7i	−0.314299	−	0.911751i
$52$	−7.99043e7			−1.51550
$53$			214544.i			0.00373487i	0.999998	+	0.00186744i	$0.000594424\pi$
$53$			214544.i			0.00373487i	−0.999998	+	0.00186744i	$0.999406\pi$
$54$	−7.69048e7	+	7.69048e7i	−1.23078	+	1.23078i
$55$	183549.			0.00270470
$56$	−5.62743e7	+	5.62743e7i	−0.764653	+	0.764653i
$57$	−7.00167e7	−	7.00167e7i	−0.878547	−	0.878547i
$58$	−1.24289e8	−	1.24289e8i	−1.44214	−	1.44214i
$59$			1.32098e8i			1.41926i	0.704573	+	0.709632i	$0.251139\pi$
$59$			1.32098e8i			1.41926i	−0.704573	+	0.709632i	$0.748861\pi$
$60$			4.30697e6i			0.0429034i
$61$	−4.51277e7	−	4.51277e7i	−0.417310	−	0.417310i	0.466965	−	0.884276i	$-0.345347\pi$
$61$	−4.51277e7	−	4.51277e7i	−0.417310	−	0.417310i	−0.884276	+	0.466965i	$0.845347\pi$
$62$	2.17856e8	+	2.17856e8i	1.87244	+	1.87244i
$63$	−4.68709e6	+	4.68709e6i	−0.0374861	+	0.0374861i
$64$	1.84092e8			1.37159
$65$	−2.01431e6	+	2.01431e6i	−0.0139964	+	0.0139964i
$66$		−	2.81388e7i		−	0.182540i
$67$	−4.10480e6			−0.0248860			−0.0124430	−	0.999923i	$-0.503961\pi$
$67$	−4.10480e6			−0.0248860			−0.0124430	+	0.999923i	$0.503961\pi$
$68$	1.42544e8	−	2.92518e8i	0.808459	−	1.65906i
$69$	−1.64080e8			−0.871437
$70$			6.19270e6i			0.0308275i
$71$	9.21670e7	−	9.21670e7i	0.430440	−	0.430440i	−0.458338	−	0.888778i	$-0.651555\pi$
$71$	9.21670e7	−	9.21670e7i	0.430440	−	0.430440i	0.888778	+	0.458338i	$0.151555\pi$
$72$	−2.27437e7			−0.0997388
$73$	−8.35127e7	+	8.35127e7i	−0.344191	+	0.344191i	−0.857940	−	0.513749i	$-0.828256\pi$
$73$	−8.35127e7	+	8.35127e7i	−0.344191	+	0.344191i	0.513749	+	0.857940i	$0.328256\pi$
$74$	2.45866e8	+	2.45866e8i	0.953137	+	0.953137i
$75$	−1.86753e8	−	1.86753e8i	−0.681540	−	0.681540i
$76$		−	6.91529e8i		−	2.37766i
$77$		−	2.62406e7i		−	0.0850677i
$78$	3.08802e8	+	3.08802e8i	0.944614	+	0.944614i
$79$	1.97887e8	+	1.97887e8i	0.571604	+	0.571604i	0.932576	−	0.360973i	$-0.117555\pi$
$79$	1.97887e8	+	1.97887e8i	0.571604	+	0.571604i	−0.360973	+	0.932576i	$0.617555\pi$
$80$	−3.50023e6	+	3.50023e6i	−0.00955414	+	0.00955414i
$81$	3.58436e8			0.925185
$82$	−6.65748e8	+	6.65748e8i	−1.62610	+	1.62610i
$83$			4.27934e8i			0.989751i	0.868964	+	0.494875i	$0.164786\pi$
$83$			4.27934e8i			0.989751i	−0.868964	+	0.494875i	$0.835214\pi$
$84$	6.15736e8			1.34939
$85$	−3.78071e6	−	1.09675e7i	−0.00785577	−	0.0227888i
$86$	−5.88715e8			−1.16055
$87$			6.23065e8i			1.16599i
$88$	6.36650e7	−	6.36650e7i	0.113169	−	0.113169i
$89$	−5.00841e8			−0.846145			−0.423072	−	0.906096i	$-0.639048\pi$
$89$	−5.00841e8			−0.846145			−0.423072	+	0.906096i	$0.639048\pi$
$90$	−1.25141e6	+	1.25141e6i	−0.00201052	+	0.00201052i
$91$	2.87971e8	+	2.87971e8i	0.440212	+	0.440212i
$92$	−8.10281e8	−	8.10281e8i	−1.17921	−	1.17921i
$93$		−	1.09212e9i		−	1.51390i
$94$		−	1.16128e9i		−	1.53413i
$95$	−1.74328e7	−	1.74328e7i	−0.0219589	−	0.0219589i
$96$	−2.72856e8	−	2.72856e8i	−0.327879	−	0.327879i
$97$	−7.92961e8	+	7.92961e8i	−0.909450	+	0.909450i	−0.996228	−	0.0867772i	$-0.972343\pi$
$97$	−7.92961e8	+	7.92961e8i	−0.909450	+	0.909450i	0.0867772	+	0.996228i	$0.472343\pi$
$98$	−6.54962e8			−0.717297
$99$	5.30265e6	−	5.30265e6i	0.00554798	−	0.00554798i
$100$		−	1.84449e9i		−	1.84449i
$101$	1.87960e9			1.79729			0.898647	−	0.438672i	$-0.144551\pi$
$101$	1.87960e9			1.79729			0.898647	+	0.438672i	$0.144551\pi$
$102$	−1.68136e9	+	5.79599e8i	−1.53801	+	0.530185i
$103$	8.90797e8			0.779850			0.389925	−	0.920847i	$-0.372501\pi$
$103$	8.90797e8			0.779850			0.389925	+	0.920847i	$0.372501\pi$
$104$			1.39735e9i			1.17127i
$105$	1.55221e7	−	1.55221e7i	0.0124623	−	0.0124623i
$106$	8.18910e6			0.00630028
$107$	1.02025e9	−	1.02025e9i	0.752454	−	0.752454i	−0.222482	−	0.974937i	$-0.571416\pi$
$107$	1.02025e9	−	1.02025e9i	0.752454	−	0.752454i	0.974937	+	0.222482i	$0.0714160\pi$
$108$	1.90385e9	+	1.90385e9i	1.34656	+	1.34656i
$109$	3.02723e8	+	3.02723e8i	0.205412	+	0.205412i	0.802314	−	0.596902i	$-0.203602\pi$
$109$	3.02723e8	+	3.02723e8i	0.205412	+	0.205412i	−0.596902	+	0.802314i	$0.703602\pi$
$110$		−	7.00600e6i		−	0.00456250i
$111$		−	1.23253e9i		−	0.770629i
$112$	5.00402e8	+	5.00402e8i	0.300495	+	0.300495i
$113$	−4.04503e7	−	4.04503e7i	−0.0233383	−	0.0233383i	0.695341	−	0.718680i	$-0.255253\pi$
$113$	−4.04503e7	−	4.04503e7i	−0.0233383	−	0.0233383i	−0.718680	+	0.695341i	$0.755253\pi$
$114$	−2.67252e9	+	2.67252e9i	−1.48200	+	1.48200i
$115$	−4.08528e7			−0.0217812
$116$	−3.07689e9	+	3.07689e9i	−1.57780	+	1.57780i
$117$			1.16385e8i			0.0574198i
$118$	5.04215e9			2.39413
$119$	−1.56794e9	+	5.40500e8i	−0.716750	+	0.247078i
$120$	7.53196e7			0.0331583
$121$		−	2.32826e9i		−	0.987410i
$122$	−1.72251e9	+	1.72251e9i	−0.703952	+	0.703952i
$123$	3.33741e9			1.31473
$124$	5.39324e9	−	5.39324e9i	2.04858	−	2.04858i
$125$	−9.30225e7	−	9.30225e7i	−0.0340795	−	0.0340795i
$126$	1.78905e8	+	1.78905e8i	0.0632345	+	0.0632345i
$127$		−	3.89197e9i		−	1.32756i	−0.747929	−	0.663778i	$-0.768952\pi$
$127$		−	3.89197e9i		−	1.32756i	0.747929	−	0.663778i	$-0.231048\pi$
$128$		−	5.56655e9i		−	1.83291i
$129$	1.47562e9	+	1.47562e9i	0.469161	+	0.469161i
$130$	7.68856e7	+	7.68856e7i	0.0236102	+	0.0236102i
$131$	−3.01607e9	+	3.01607e9i	−0.894790	+	0.894790i	−0.994969	−	0.100180i	$-0.968058\pi$
$131$	−3.01607e9	+	3.01607e9i	−0.894790	+	0.894790i	0.100180	+	0.994969i	$0.468058\pi$
$132$	−6.96602e8			−0.199711
$133$	−2.49223e9	+	2.49223e9i	−0.690647	+	0.690647i
$134$			1.56679e8i			0.0419797i
$135$	9.59884e7			0.0248723
$136$	−5.11550e9	−	2.49278e9i	−1.28222	−	0.624825i
$137$	−5.82746e9			−1.41331			−0.706654	−	0.707560i	$-0.749796\pi$
$137$	−5.82746e9			−1.41331			−0.706654	+	0.707560i	$0.749796\pi$
$138$			6.26291e9i			1.47001i
$139$	3.02588e9	−	3.02588e9i	0.687520	−	0.687520i	−0.274163	−	0.961683i	$-0.588401\pi$
$139$	3.02588e9	−	3.02588e9i	0.687520	−	0.687520i	0.961683	+	0.274163i	$0.0884007\pi$
$140$	1.53306e8			0.0337274
$141$	−2.91077e9	+	2.91077e9i	−0.620185	+	0.620185i
$142$	−3.51799e9	−	3.51799e9i	−0.726101	−	0.726101i
$143$	−3.25790e8	−	3.25790e8i	−0.0651518	−	0.0651518i
$144$			2.02241e8i			0.0391956i
$145$			1.55131e8i			0.0291435i
$146$	3.18766e9	+	3.18766e9i	0.580609	+	0.580609i
$147$	1.64167e9	+	1.64167e9i	0.289974	+	0.289974i
$148$	6.08664e9	−	6.08664e9i	1.04280	−	1.04280i
$149$	9.06968e9			1.50749			0.753744	−	0.657168i	$-0.228246\pi$
$149$	9.06968e9			1.50749			0.753744	+	0.657168i	$0.228246\pi$
$150$	−7.12830e9	+	7.12830e9i	−1.14968	+	1.14968i
$151$			9.99616e9i			1.56472i	0.622826	+	0.782360i	$0.285984\pi$
$151$			9.99616e9i			1.56472i	−0.622826	+	0.782360i	$0.714016\pi$
$152$	−1.20933e10			−1.83760
$153$	−4.26070e8	−	2.07623e8i	−0.0628593	−	0.0306312i
$154$	−1.00159e9			−0.143499
$155$		−	2.71917e8i		−	0.0378393i
$156$	7.64469e9	−	7.64469e9i	1.03347	−	1.03347i
$157$	−1.14843e10			−1.50854			−0.754268	−	0.656567i	$-0.772008\pi$
$157$	−1.14843e10			−1.50854			−0.754268	+	0.656567i	$0.772008\pi$
$158$	7.55328e9	−	7.55328e9i	0.964226	−	0.964226i
$159$	−2.05261e7	−	2.05261e7i	−0.00254695	−	0.00254695i
$160$	−6.79358e7	−	6.79358e7i	−0.00819518	−	0.00819518i
$161$			5.84042e9i			0.685058i
$162$		−	1.36814e10i		−	1.56068i
$163$	−7.80015e9	−	7.80015e9i	−0.865483	−	0.865483i	0.126485	−	0.991968i	$-0.459630\pi$
$163$	−7.80015e9	−	7.80015e9i	−0.865483	−	0.865483i	−0.991968	+	0.126485i	$0.959630\pi$
$164$	1.64812e10	+	1.64812e10i	1.77906	+	1.77906i
$165$	−1.75607e7	+	1.75607e7i	−0.00184443	+	0.00184443i
$166$	1.63341e10			1.66959
$167$	6.69462e9	−	6.69462e9i	0.666042	−	0.666042i	−0.290755	−	0.956798i	$-0.593906\pi$
$167$	6.69462e9	−	6.69462e9i	0.666042	−	0.666042i	0.956798	+	0.290755i	$0.0939065\pi$
$168$		−	1.07679e10i		−	1.04289i
$169$	−3.45388e9			−0.325700
$170$	−4.18626e8	+	1.44309e8i	−0.0384420	+	0.0132517i
$171$	−1.00725e9			−0.0900858
$172$			1.45742e10i			1.26972i
$173$	1.53670e9	−	1.53670e9i	0.130431	−	0.130431i	−0.638877	−	0.769309i	$-0.720601\pi$
$173$	1.53670e9	−	1.53670e9i	0.130431	−	0.130431i	0.769309	+	0.638877i	$0.220601\pi$
$174$	2.37822e10			1.96689
$175$	−6.64744e9	+	6.64744e9i	−0.535776	+	0.535776i
$176$	−5.66121e8	−	5.66121e8i	−0.0444736	−	0.0444736i
$177$	−1.26382e10	−	1.26382e10i	−0.967848	−	0.967848i
$178$			1.91169e10i			1.42734i
$179$			3.30556e9i			0.240662i	0.992734	+	0.120331i	$0.0383955\pi$
$179$			3.30556e9i			0.240662i	−0.992734	+	0.120331i	$0.961604\pi$
$180$	3.09798e7	+	3.09798e7i	0.00219965	+	0.00219965i
$181$	1.40868e9	+	1.40868e9i	0.0975570	+	0.0975570i	0.754201	−	0.656644i	$-0.228025\pi$
$181$	1.40868e9	+	1.40868e9i	0.0975570	+	0.0975570i	−0.656644	+	0.754201i	$0.728025\pi$
$182$	1.09918e10	−	1.09918e10i	0.742584	−	0.742584i
$183$	8.63501e9			0.569158
$184$	−1.41700e10	+	1.41700e10i	−0.911362	+	0.911362i
$185$		−	3.06876e8i		−	0.0192615i
$186$	−4.16860e10			−2.55377
$187$	1.77386e9	−	6.11485e8i	0.106080	−	0.0365678i
$188$	−2.87486e10			−1.67844
$189$		−	1.37227e10i		−	0.782281i
$190$	−6.65404e8	+	6.65404e8i	−0.0370420	+	0.0370420i
$191$	2.46723e10			1.34141			0.670703	−	0.741726i	$-0.265993\pi$
$191$	2.46723e10			1.34141			0.670703	+	0.741726i	$0.265993\pi$
$192$	−1.76127e10	+	1.76127e10i	−0.935340	+	0.935340i
$193$	−1.91130e10	−	1.91130e10i	−0.991566	−	0.991566i	0.00839843	−	0.999965i	$-0.497327\pi$
$193$	−1.91130e10	−	1.91130e10i	−0.991566	−	0.991566i	−0.999965	+	0.00839843i	$0.997327\pi$
$194$	3.02671e10	+	3.02671e10i	1.53413	+	1.53413i
$195$		−	3.85430e8i		−	0.0190893i
$196$			1.62142e10i			0.784772i
$197$	−1.37704e10	−	1.37704e10i	−0.651402	−	0.651402i	0.301928	−	0.953331i	$-0.402370\pi$
$197$	−1.37704e10	−	1.37704e10i	−0.651402	−	0.651402i	−0.953331	+	0.301928i	$0.902370\pi$
$198$	−2.02401e8	−	2.02401e8i	−0.00935877	−	0.00935877i
$199$	9.20906e9	−	9.20906e9i	0.416271	−	0.416271i	−0.467645	−	0.883916i	$-0.654897\pi$
$199$	9.20906e9	−	9.20906e9i	0.416271	−	0.416271i	0.883916	+	0.467645i	$0.154897\pi$
$200$	−3.22561e10			−1.42553
$201$	3.92719e8	−	3.92719e8i	0.0169707	−	0.0169707i
$202$		−	7.17438e10i		−	3.03182i
$203$	2.21779e10			0.916617
$204$	1.43485e10	+	4.16237e10i	0.580058	+	1.68269i
$205$	8.30950e8			0.0328611
$206$		−	3.40015e10i		−	1.31551i
$207$	−1.18022e9	+	1.18022e9i	−0.0446784	+	0.0446784i
$208$	1.24255e10			0.460287
$209$	2.81954e9	−	2.81954e9i	0.102216	−	0.102216i
$210$	−5.92474e8	−	5.92474e8i	−0.0210224	−	0.0210224i
$211$	3.54499e10	+	3.54499e10i	1.23124	+	1.23124i	0.963486	+	0.267758i	$0.0862829\pi$
$211$	3.54499e10	+	3.54499e10i	1.23124	+	1.23124i	0.267758	+	0.963486i	$0.413717\pi$
$212$		−	2.02729e8i		−	0.00689294i
$213$			1.76358e10i			0.587066i
$214$	−3.89427e10	−	3.89427e10i	−1.26930	−	1.26930i
$215$	3.67401e8	+	3.67401e8i	0.0117265	+	0.0117265i
$216$	3.32942e10	−	3.32942e10i	1.04070	−	1.04070i
$217$	−3.88739e10			−1.19012
$218$	1.15549e10	−	1.15549e10i	0.346506	−	0.346506i
$219$		−	1.59798e10i		−	0.469433i
$220$	−1.73440e8			−0.00499169
$221$	−1.27562e10	+	2.61774e10i	−0.359713	+	0.738178i
$222$	−4.70455e10			−1.29996
$223$			8.60424e9i			0.232992i	0.993191	+	0.116496i	$0.0371662\pi$
$223$			8.60424e9i			0.232992i	−0.993191	+	0.116496i	$0.962834\pi$
$224$	−9.71227e9	+	9.71227e9i	−0.257753	+	0.257753i
$225$	−2.68661e9			−0.0698848
$226$	−1.54398e9	+	1.54398e9i	−0.0393688	+	0.0393688i
$227$	5.49392e10	+	5.49392e10i	1.37330	+	1.37330i	0.855503	+	0.517798i	$0.173248\pi$
$227$	5.49392e10	+	5.49392e10i	1.37330	+	1.37330i	0.517798	+	0.855503i	$0.326752\pi$
$228$	6.61607e10	+	6.61607e10i	1.62141	+	1.62141i
$229$			4.32400e10i			1.03902i	0.854463	+	0.519512i	$0.173886\pi$
$229$			4.32400e10i			1.03902i	−0.854463	+	0.519512i	$0.826114\pi$
$230$			1.55934e9i			0.0367422i
$231$	2.51051e9	+	2.51051e9i	0.0580108	+	0.0580108i
$232$	5.38081e10	+	5.38081e10i	1.21942	+	1.21942i
$233$	−3.74790e9	+	3.74790e9i	−0.0833079	+	0.0833079i	−0.747533	−	0.664225i	$-0.768762\pi$
$233$	−3.74790e9	+	3.74790e9i	−0.0833079	+	0.0833079i	0.664225	+	0.747533i	$0.268762\pi$
$234$	4.44239e9			0.0968603
$235$	−7.24723e8	+	7.24723e8i	−0.0155013	+	0.0155013i
$236$		−	1.24823e11i		−	2.61934i
$237$	−3.78649e10			−0.779595
$238$	2.06307e10	+	5.98478e10i	0.416791	+	1.20907i
$239$	6.63919e10			1.31621			0.658104	−	0.752927i	$-0.271359\pi$
$239$	6.63919e10			1.31621			0.658104	+	0.752927i	$0.271359\pi$
$240$		−	6.69755e8i		−	0.0130306i
$241$	5.61502e10	−	5.61502e10i	1.07220	−	1.07220i	0.0750155	−	0.997182i	$-0.476099\pi$
$241$	5.61502e10	−	5.61502e10i	1.07220	−	1.07220i	0.997182	−	0.0750155i	$-0.0239006\pi$
$242$	−8.88691e10			−1.66564
$243$	5.36490e9	−	5.36490e9i	0.0987038	−	0.0987038i
$244$	4.26424e10	+	4.26424e10i	0.770172	+	0.770172i
$245$	4.08744e8	+	4.08744e8i	0.00724777	+	0.00724777i
$246$		−	1.27388e11i		−	2.21779i
$247$			6.18848e10i			1.05791i
$248$	−9.43160e10	−	9.43160e10i	−1.58326	−	1.58326i
$249$	−4.09418e10	−	4.09418e10i	−0.674947	−	0.674947i
$250$	−3.55064e9	+	3.55064e9i	−0.0574880	+	0.0574880i
$251$	−2.43313e10			−0.386932			−0.193466	−	0.981107i	$-0.561973\pi$
$251$	−2.43313e10			−0.386932			−0.193466	+	0.981107i	$0.561973\pi$
$252$	4.42896e9	−	4.42896e9i	0.0691829	−	0.0691829i
$253$		−	6.60745e9i		−	0.101389i
$254$	−1.48555e11			−2.23943
$255$	1.41100e9	+	6.87580e8i	0.0208977	+	0.0101834i
$256$	−1.18218e11			−1.72030
$257$		−	6.20805e10i		−	0.887679i	−0.896106	−	0.443839i	$-0.853616\pi$
$257$		−	6.20805e10i		−	0.887679i	0.896106	−	0.443839i	$-0.146384\pi$
$258$	5.63241e10	−	5.63241e10i	0.791418	−	0.791418i
$259$	−4.38718e10			−0.605810
$260$	1.90338e9	−	1.90338e9i	0.0258312	−	0.0258312i
$261$	4.48167e9	+	4.48167e9i	0.0597803	+	0.0597803i
$262$	1.15123e11	+	1.15123e11i	1.50940	+	1.50940i
$263$		−	3.11356e10i		−	0.401288i	−0.979664	−	0.200644i	$-0.935697\pi$
$263$		−	3.11356e10i		−	0.401288i	0.979664	−	0.200644i	$-0.0643034\pi$
$264$			1.21820e10i			0.154349i
$265$	−5.11060e6	−	5.11060e6i	−6.36598e−5	−	6.36598e-5i
$266$	9.51278e10	+	9.51278e10i	1.16504	+	1.16504i
$267$	4.79169e10	−	4.79169e10i	0.577017	−	0.577017i
$268$	3.87874e9			0.0459287
$269$	−2.47797e10	+	2.47797e10i	−0.288543	+	0.288543i	−0.836504	−	0.547961i	$-0.815404\pi$
$269$	−2.47797e10	+	2.47797e10i	−0.288543	+	0.288543i	0.547961	+	0.836504i	$0.315404\pi$
$270$		−	3.66385e9i		−	0.0419566i
$271$	−1.41065e10			−0.158876			−0.0794378	−	0.996840i	$-0.525313\pi$
$271$	−1.41065e10			−0.158876			−0.0794378	+	0.996840i	$0.525313\pi$
$272$	−2.21662e10	+	4.54880e10i	−0.245545	+	0.503891i
$273$	−5.51020e10			−0.600393
$274$			2.22432e11i			2.38408i
$275$	7.52046e9	−	7.52046e9i	0.0792953	−	0.0792953i
$276$	1.55044e11			1.60829
$277$	−7.78310e10	+	7.78310e10i	−0.794317	+	0.794317i	−0.982193	−	0.187876i	$-0.939840\pi$
$277$	−7.78310e10	+	7.78310e10i	−0.794317	+	0.794317i	0.187876	+	0.982193i	$0.439840\pi$
$278$	−1.15497e11	−	1.15497e11i	−1.15976	−	1.15976i
$279$	−7.85557e9	−	7.85557e9i	−0.0776174	−	0.0776174i
$280$		−	2.68099e9i		−	0.0260666i
$281$			3.69253e10i			0.353302i	0.984274	+	0.176651i	$0.0565263\pi$
$281$			3.69253e10i			0.353302i	−0.984274	+	0.176651i	$0.943474\pi$
$282$	1.11103e11	+	1.11103e11i	1.04618	+	1.04618i
$283$	−2.63672e10	−	2.63672e10i	−0.244357	−	0.244357i	0.574293	−	0.818650i	$-0.305277\pi$
$283$	−2.63672e10	−	2.63672e10i	−0.244357	−	0.244357i	−0.818650	+	0.574293i	$0.805277\pi$
$284$	−8.70911e10	+	8.70911e10i	−0.794404	+	0.794404i
$285$	3.33569e9			0.0299491
$286$	−1.24353e10	+	1.24353e10i	−0.109903	+	0.109903i
$287$		−	1.18795e11i		−	1.03354i
$288$	−3.92528e9			−0.0336205
$289$	−7.30756e10	−	9.33973e10i	−0.616214	−	0.787578i
$290$	5.92130e9			0.0491616
$291$		−	1.51730e11i		−	1.24037i
$292$	7.89134e10	−	7.89134e10i	0.635226	−	0.635226i
$293$	2.03656e11			1.61433			0.807166	−	0.590325i	$-0.201000\pi$
$293$	2.03656e11			1.61433			0.807166	+	0.590325i	$0.201000\pi$
$294$	6.26622e10	−	6.26622e10i	0.489151	−	0.489151i
$295$	−3.14667e9	−	3.14667e9i	−0.0241909	−	0.0241909i
$296$	−1.06442e11	−	1.06442e11i	−0.805936	−	0.805936i
$297$			1.55250e10i			0.115778i
$298$		−	3.46187e11i		−	2.54295i
$299$	7.25119e10	+	7.25119e10i	0.524673	+	0.524673i
$300$	1.76468e11	+	1.76468e11i	1.25782	+	1.25782i
$301$	5.25246e10	−	5.25246e10i	0.368819	−	0.368819i
$302$	3.81550e11			2.63949
$303$	−1.79827e11	+	1.79827e11i	−1.22564	+	1.22564i
$304$			1.07536e11i			0.722143i
$305$	2.14995e9			0.0142259
$306$	−7.92492e9	+	1.62630e10i	−0.0516712	+	0.106036i
$307$	1.07324e11			0.689563			0.344781	−	0.938683i	$-0.387953\pi$
$307$	1.07324e11			0.689563			0.344781	+	0.938683i	$0.387953\pi$
$308$			2.47954e10i			0.156998i
$309$	−8.52252e10	+	8.52252e10i	−0.531808	+	0.531808i
$310$	−1.03790e10			−0.0638303
$311$	3.66504e10	−	3.66504e10i	0.222156	−	0.222156i	−0.587250	−	0.809406i	$-0.699789\pi$
$311$	3.66504e10	−	3.66504e10i	0.222156	−	0.222156i	0.809406	+	0.587250i	$0.199789\pi$
$312$	−1.33689e11	−	1.33689e11i	−0.798729	−	0.798729i
$313$	−2.07139e11	−	2.07139e11i	−1.21986	−	1.21986i	−0.967679	−	0.252186i	$-0.918851\pi$
$313$	−2.07139e11	−	2.07139e11i	−1.21986	−	1.21986i	−0.252186	−	0.967679i	$-0.581149\pi$
$314$			4.38352e11i			2.54472i
$315$		−	2.23299e8i		−	0.00127788i
$316$	−1.86989e11	−	1.86989e11i	−1.05493	−	1.05493i
$317$	6.79753e10	+	6.79753e10i	0.378081	+	0.378081i	0.870409	−	0.492329i	$-0.163854\pi$
$317$	6.79753e10	+	6.79753e10i	0.378081	+	0.378081i	−0.492329	+	0.870409i	$0.663854\pi$
$318$	−7.83476e8	+	7.83476e8i	−0.00429639	+	0.00429639i
$319$	−2.50906e10			−0.135660
$320$	−4.38521e9	+	4.38521e9i	−0.0233784	+	0.0233784i
$321$			1.95221e11i			1.02625i
$322$	2.22927e11			1.15561
$323$	−2.26551e11	−	1.10398e11i	−1.15813	−	0.564352i
$324$	−3.38696e11			−1.70749
$325$			1.65063e11i			0.820681i
$326$	−2.97729e11	+	2.97729e11i	−1.45997	+	1.45997i
$327$	−5.79249e10			−0.280156
$328$	2.88220e11	−	2.88220e11i	1.37497	−	1.37497i
$329$	1.03608e11	+	1.03608e11i	0.487543	+	0.487543i
$330$	6.70285e8	+	6.70285e8i	0.00311134	+	0.00311134i
$331$			3.04918e11i			1.39623i	0.715985	+	0.698116i	$0.245978\pi$
$331$			3.04918e11i			1.39623i	−0.715985	+	0.698116i	$0.754022\pi$
$332$		−	4.04367e11i		−	1.82665i
$333$	−8.86555e9	−	8.86555e9i	−0.0395100	−	0.0395100i
$334$	−2.55532e11	−	2.55532e11i	−1.12353	−	1.12353i
$335$	9.77792e7	−	9.77792e7i	0.000424175	−	0.000424175i
$336$	−9.57499e10			−0.409837
$337$	−1.20194e11	+	1.20194e11i	−0.507630	+	0.507630i	−0.913798	−	0.406168i	$-0.866865\pi$
$337$	−1.20194e11	+	1.20194e11i	−0.507630	+	0.507630i	0.406168	+	0.913798i	$0.366865\pi$
$338$			1.31834e11i			0.549416i
$339$	7.74000e9			0.0318304
$340$	3.57250e9	+	1.03635e10i	0.0144983	+	0.0420582i
$341$	4.39793e10			0.176138
$342$			3.84466e10i			0.151964i
$343$	1.95858e11	−	1.95858e11i	0.764043	−	0.764043i
$344$	2.54871e11			0.981312
$345$	3.90851e9	−	3.90851e9i	0.0148534	−	0.0148534i
$346$	−5.86555e10	−	5.86555e10i	−0.220022	−	0.220022i
$347$	−1.41887e11	−	1.41887e11i	−0.525363	−	0.525363i	0.393823	−	0.919186i	$-0.371152\pi$
$347$	−1.41887e11	−	1.41887e11i	−0.525363	−	0.525363i	−0.919186	+	0.393823i	$0.871152\pi$
$348$		−	5.88751e11i		−	2.15191i
$349$		−	3.31661e10i		−	0.119669i	−0.998208	−	0.0598343i	$-0.980943\pi$
$349$		−	3.31661e10i		−	0.119669i	0.998208	−	0.0598343i	$-0.0190572\pi$
$350$	2.53731e11	+	2.53731e11i	0.903789	+	0.903789i
$351$	−1.70375e11	−	1.70375e11i	−0.599134	−	0.599134i
$352$	1.09878e10	−	1.09878e10i	0.0381477	−	0.0381477i
$353$	3.10706e11			1.06504			0.532518	−	0.846419i	$-0.321246\pi$
$353$	3.10706e11			1.06504			0.532518	+	0.846419i	$0.321246\pi$
$354$	−4.82398e11	+	4.82398e11i	−1.63264	+	1.63264i
$355$			4.39096e9i			0.0146735i
$356$	4.73258e11			1.56161
$357$	9.82982e10	−	2.01721e11i	0.320286	−	0.657270i
$358$	1.26172e11			0.405967
$359$		−	2.82979e10i		−	0.0899142i	−0.998989	−	0.0449571i	$-0.985685\pi$
$359$		−	2.82979e10i		−	0.0899142i	0.998989	−	0.0449571i	$-0.0143151\pi$
$360$	5.41770e8	−	5.41770e8i	0.00170002	−	0.00170002i
$361$	−2.12892e11			−0.659747
$362$	5.37689e10	−	5.37689e10i	0.164567	−	0.164567i
$363$	2.22752e11	+	2.22752e11i	0.673351	+	0.673351i
$364$	−2.72111e11	−	2.72111e11i	−0.812438	−	0.812438i
$365$		−	3.97866e9i		−	0.0117333i
$366$		−	3.29596e11i		−	0.960101i
$367$	1.38767e11	+	1.38767e11i	0.399289	+	0.399289i	0.877982	−	0.478693i	$-0.158889\pi$
$367$	1.38767e11	+	1.38767e11i	0.399289	+	0.399289i	−0.478693	+	0.877982i	$0.658889\pi$
$368$	1.26003e11	+	1.26003e11i	0.358150	+	0.358150i
$369$	2.40059e10	−	2.40059e10i	0.0674060	−	0.0674060i
$370$	−1.17134e10			−0.0324919
$371$	−7.30624e8	+	7.30624e8i	−0.00200222	+	0.00200222i
$372$			1.03198e12i			2.79400i
$373$	2.86863e11			0.767335			0.383667	−	0.923471i	$-0.374661\pi$
$373$	2.86863e11			0.767335			0.383667	+	0.923471i	$0.374661\pi$
$374$	−2.33402e10	−	6.77077e10i	−0.0616855	−	0.178944i
$375$	1.77995e10			0.0464801
$376$			5.02750e11i			1.29720i
$377$	2.75350e11	−	2.75350e11i	0.702020	−	0.702020i
$378$	−5.23793e11			−1.31961
$379$	−3.89471e10	+	3.89471e10i	−0.0969615	+	0.0969615i	−0.753924	−	0.656962i	$-0.771841\pi$
$379$	−3.89471e10	+	3.89471e10i	−0.0969615	+	0.0969615i	0.656962	+	0.753924i	$0.271841\pi$
$380$	1.64727e10	+	1.64727e10i	0.0405265	+	0.0405265i
$381$	3.72357e11	+	3.72357e11i	0.905309	+	0.905309i
$382$		−	9.41736e11i		−	2.26279i
$383$			4.27720e11i			1.01570i	0.861446	+	0.507849i	$0.169559\pi$
$383$			4.27720e11i			1.01570i	−0.861446	+	0.507849i	$0.830441\pi$
$384$	5.32568e11	+	5.32568e11i	1.24993	+	1.24993i
$385$	6.25068e8	+	6.25068e8i	0.00144995	+	0.00144995i
$386$	−7.29539e11	+	7.29539e11i	−1.67265	+	1.67265i
$387$	2.12282e10			0.0481075
$388$	7.49291e11	−	7.49291e11i	1.67845	−	1.67845i
$389$		−	6.41336e11i		−	1.42008i	−0.704162	−	0.710039i	$-0.748677\pi$
$389$		−	6.41336e11i		−	1.42008i	0.704162	−	0.710039i	$-0.251323\pi$
$390$	−1.47118e10			−0.0322013
$391$	−3.94812e11	+	1.36100e11i	−0.854269	+	0.294484i
$392$	2.83551e11			0.606518
$393$		−	5.77114e11i		−	1.22038i
$394$	−5.25613e11	+	5.25613e11i	−1.09884	+	1.09884i
$395$	−9.42760e9			−0.0194856
$396$	−5.01062e9	+	5.01062e9i	−0.0102391	+	0.0102391i
$397$	3.74870e11	+	3.74870e11i	0.757397	+	0.757397i	0.975848	−	0.218451i	$-0.0701004\pi$
$397$	3.74870e11	+	3.74870e11i	0.757397	+	0.757397i	−0.218451	+	0.975848i	$0.570100\pi$
$398$	−3.51507e11	−	3.51507e11i	−0.702199	−	0.702199i
$399$		−	4.76879e11i		−	0.941955i
$400$			2.86827e11i			0.560209i
$401$	−3.29215e11	−	3.29215e11i	−0.635813	−	0.635813i	0.313707	−	0.949520i	$-0.398429\pi$
$401$	−3.29215e11	−	3.29215e11i	−0.635813	−	0.635813i	−0.949520	+	0.313707i	$0.898429\pi$
$402$	−1.49900e10	−	1.49900e10i	−0.0286275	−	0.0286275i
$403$	−4.82640e11	+	4.82640e11i	−0.911487	+	0.911487i
$404$	−1.77609e12			−3.31702
$405$	−8.53819e9	+	8.53819e9i	−0.0157695	+	0.0157695i
$406$		−	8.46524e11i		−	1.54622i
$407$	4.96336e10			0.0896605
$408$	7.27907e11	−	2.50924e11i	1.30049	−	0.448303i
$409$	7.09692e11			1.25405			0.627025	−	0.778999i	$-0.284272\pi$
$409$	7.09692e11			1.25405			0.627025	+	0.778999i	$0.284272\pi$
$410$		−	3.17171e10i		−	0.0554328i
$411$	5.57531e11	−	5.57531e11i	0.963786	−	0.963786i
$412$	−8.41738e11			−1.43926
$413$	−4.49856e11	+	4.49856e11i	−0.760849	+	0.760849i
$414$	4.50488e10	+	4.50488e10i	0.0753670	+	0.0753670i
$415$	−1.01937e10	−	1.01937e10i	−0.0168700	−	0.0168700i
$416$			2.41166e11i			0.394817i
$417$			5.78991e11i			0.937690i
$418$	−1.07621e11	−	1.07621e11i	−0.172427	−	0.172427i
$419$	−2.18854e11	−	2.18854e11i	−0.346890	−	0.346890i	0.512060	−	0.858950i	$-0.328883\pi$
$419$	−2.18854e11	−	2.18854e11i	−0.346890	−	0.346890i	−0.858950	+	0.512060i	$0.828883\pi$
$420$	−1.46673e10	+	1.46673e10i	−0.0230000	+	0.0230000i
$421$	1.13495e12			1.76080			0.880398	−	0.474235i	$-0.157275\pi$
$421$	1.13495e12			1.76080			0.880398	+	0.474235i	$0.157275\pi$
$422$	1.35311e12	−	1.35311e12i	2.07696	−	2.07696i
$423$			4.18740e10i			0.0635935i
$424$	−3.54529e9			−0.00532727
$425$	−6.04272e11	−	2.94461e11i	−0.898425	−	0.437801i
$426$	6.73153e11			0.990309
$427$		−	3.07362e11i		−	0.447429i
$428$	−9.64063e11	+	9.64063e11i	−1.38870	+	1.38870i
$429$	6.23387e10			0.0888587
$430$	1.40236e10	−	1.40236e10i	0.0197811	−	0.0197811i
$431$	−4.85922e11	−	4.85922e11i	−0.678295	−	0.678295i	0.281319	−	0.959614i	$-0.409228\pi$
$431$	−4.85922e11	−	4.85922e11i	−0.678295	−	0.678295i	−0.959614	+	0.281319i	$0.909228\pi$
$432$	−2.96058e11	−	2.96058e11i	−0.408978	−	0.408978i
$433$		−	1.31231e11i		−	0.179407i	−0.995969	−	0.0897036i	$-0.971408\pi$
$433$		−	1.31231e11i		−	0.179407i	0.995969	−	0.0897036i	$-0.0285920\pi$
$434$			1.48380e12i			2.00758i
$435$	−1.48418e10	−	1.48418e10i	−0.0198740	−	0.0198740i
$436$	−2.86051e11	−	2.86051e11i	−0.379101	−	0.379101i
$437$	−6.27552e11	+	6.27552e11i	−0.823158	+	0.823158i
$438$	−6.09945e11			−0.791876
$439$	−4.33339e11	+	4.33339e11i	−0.556848	+	0.556848i	−0.928409	−	0.371560i	$-0.878823\pi$
$439$	−4.33339e11	+	4.33339e11i	−0.556848	+	0.556848i	0.371560	+	0.928409i	$0.378823\pi$
$440$			3.03309e9i			0.00385787i
$441$	2.36170e10			0.0297338
$442$	9.99183e11	+	4.86900e11i	1.24522	+	0.606792i
$443$	−4.51857e11			−0.557422			−0.278711	−	0.960375i	$-0.589907\pi$
$443$	−4.51857e11			−0.557422			−0.278711	+	0.960375i	$0.589907\pi$
$444$			1.16465e12i			1.42224i
$445$	1.19304e10	−	1.19304e10i	0.0144223	−	0.0144223i
$446$	3.28422e11			0.393029
$447$	−8.67724e11	+	8.67724e11i	−1.02801	+	1.02801i
$448$	6.26920e11	+	6.26920e11i	0.735294	+	0.735294i
$449$	7.28043e11	+	7.28043e11i	0.845374	+	0.845374i	0.989552	−	0.144178i	$-0.0460538\pi$
$449$	7.28043e11	+	7.28043e11i	0.845374	+	0.845374i	−0.144178	+	0.989552i	$0.546054\pi$
$450$			1.02547e11i			0.117887i
$451$			1.34396e11i			0.152965i
$452$	3.82226e10	+	3.82226e10i	0.0430722	+	0.0430722i
$453$	−9.56363e11	−	9.56363e11i	−1.06704	−	1.06704i
$454$	2.09701e12	−	2.09701e12i	2.31659	−	2.31659i
$455$	−1.37193e10			−0.0150066
$456$	1.15701e12	−	1.15701e12i	1.25312	−	1.25312i
$457$			1.58775e12i			1.70278i	0.524535	+	0.851389i	$0.324239\pi$
$457$			1.58775e12i			1.70278i	−0.524535	+	0.851389i	$0.675761\pi$
$458$	1.65046e12			1.75271
$459$	9.27656e11	−	3.19782e11i	0.975506	−	0.336277i
$460$	3.86029e10			0.0401985
$461$		−	1.72351e12i		−	1.77730i	−0.458588	−	0.888649i	$-0.651645\pi$
$461$		−	1.72351e12i		−	1.77730i	0.458588	−	0.888649i	$-0.348355\pi$
$462$	9.58256e10	−	9.58256e10i	0.0978572	−	0.0978572i
$463$	−8.31463e10			−0.0840869			−0.0420435	−	0.999116i	$-0.513387\pi$
$463$	−8.31463e10			−0.0840869			−0.0420435	+	0.999116i	$0.513387\pi$
$464$	4.78472e11	−	4.78472e11i	0.479209	−	0.479209i
$465$	2.60151e10	+	2.60151e10i	0.0258040	+	0.0258040i
$466$	1.43056e11	+	1.43056e11i	0.140530	+	0.140530i
$467$			1.30167e12i			1.26641i	0.773984	+	0.633206i	$0.218261\pi$
$467$			1.30167e12i			1.26641i	−0.773984	+	0.633206i	$0.781739\pi$
$468$		−	1.09976e11i		−	0.105972i
$469$	−1.39788e10	−	1.39788e10i	−0.0133411	−	0.0133411i
$470$	2.76625e10	+	2.76625e10i	0.0261487	+	0.0261487i
$471$	1.09874e12	−	1.09874e12i	1.02873	−	1.02873i
$472$	−2.18289e12			−2.02438
$473$	−5.94228e10	+	5.94228e10i	−0.0545855	+	0.0545855i
$474$			1.44529e12i			1.31508i
$475$	−1.42853e12			−1.28756
$476$	1.48159e12	−	5.10733e11i	1.32281	−	0.455998i
$477$	−2.95287e8			−0.000261163
$478$		−	2.53416e12i		−	2.22028i
$479$	−1.08866e12	+	1.08866e12i	−0.944890	+	0.944890i	−0.998559	−	0.0536687i	$-0.982909\pi$
$479$	−1.08866e12	+	1.08866e12i	−0.944890	+	0.944890i	0.0536687	+	0.998559i	$0.482909\pi$
$480$	1.29992e10			0.0111772
$481$	−5.44692e11	+	5.44692e11i	−0.463979	+	0.463979i
$482$	−2.14324e12	−	2.14324e12i	−1.80867	−	1.80867i
$483$	−5.58770e11	−	5.58770e11i	−0.467166	−	0.467166i
$484$			2.20004e12i			1.82233i
$485$		−	3.77778e10i		−	0.0310026i
$486$	−2.04777e11	−	2.04777e11i	−0.166501	−	0.166501i
$487$	−1.41040e12	−	1.41040e12i	−1.13622	−	1.13622i	−0.989122	−	0.147096i	$-0.953007\pi$
$487$	−1.41040e12	−	1.41040e12i	−1.13622	−	1.13622i	−0.147096	−	0.989122i	$-0.546993\pi$
$488$	7.45723e11	−	7.45723e11i	0.595235	−	0.595235i
$489$	1.49253e12			1.18041
$490$	1.56017e10	−	1.56017e10i	0.0122261	−	0.0122261i
$491$		−	1.52090e12i		−	1.18096i	−0.807053	−	0.590480i	$-0.798939\pi$
$491$		−	1.52090e12i		−	1.18096i	0.807053	−	0.590480i	$-0.201061\pi$
$492$	−3.15361e12			−2.42642
$493$	5.16813e11	+	1.49922e12i	0.394023	+	1.14302i
$494$	2.36212e12			1.78456
$495$			2.52626e8i			0.000189127i
$496$	−8.38675e11	+	8.38675e11i	−0.622195	+	0.622195i
$497$	6.27743e11			0.461507
$498$	−1.56274e12	+	1.56274e12i	−1.13855	+	1.13855i
$499$	1.29332e12	+	1.29332e12i	0.933797	+	0.933797i	0.997941	−	0.0641439i	$-0.0204317\pi$
$499$	1.29332e12	+	1.29332e12i	0.933797	+	0.933797i	−0.0641439	+	0.997941i	$0.520432\pi$
$500$	8.78995e10	+	8.78995e10i	0.0628958	+	0.0628958i
$501$			1.28099e12i			0.908397i
$502$			9.28720e11i			0.652707i
$503$	−1.03436e12	−	1.03436e12i	−0.720472	−	0.720472i	0.248230	−	0.968701i	$-0.420151\pi$
$503$	−1.03436e12	−	1.03436e12i	−0.720472	−	0.720472i	−0.968701	+	0.248230i	$0.920151\pi$
$504$	−7.74527e10	−	7.74527e10i	−0.0534687	−	0.0534687i
$505$	−4.47734e10	+	4.47734e10i	−0.0306344	+	0.0306344i
$506$	−2.52205e11			−0.171031
$507$	3.30444e11	−	3.30444e11i	0.222107	−	0.222107i
$508$			3.67763e12i			2.45009i
$509$	4.28087e11			0.282685			0.141342	−	0.989961i	$-0.454858\pi$
$509$	4.28087e11			0.282685			0.141342	+	0.989961i	$0.454858\pi$
$510$	2.62447e10	−	5.38577e10i	0.0171782	−	0.0352518i
$511$	−5.68799e11			−0.369033
$512$			1.66228e12i			1.06903i
$513$	1.47451e12	−	1.47451e12i	0.939979	−	0.939979i
$514$	−2.36959e12			−1.49741
$515$	−2.12194e10	+	2.12194e10i	−0.0132923	+	0.0132923i
$516$	−1.39436e12	−	1.39436e12i	−0.865865	−	0.865865i
$517$	−1.17215e11	−	1.17215e11i	−0.0721568	−	0.0721568i
$518$			1.67458e12i			1.02193i
$519$			2.94042e11i			0.177892i
$520$	−3.32859e10	−	3.32859e10i	−0.0199639	−	0.0199639i
$521$	5.73309e11	+	5.73309e11i	0.340893	+	0.340893i	0.856703	−	0.515810i	$-0.172509\pi$
$521$	5.73309e11	+	5.73309e11i	0.340893	+	0.340893i	−0.515810	+	0.856703i	$0.672509\pi$
$522$	1.71064e11	−	1.71064e11i	0.100842	−	0.100842i
$523$	2.06333e12			1.20590			0.602949	−	0.797779i	$-0.293992\pi$
$523$	2.06333e12			1.20590			0.602949	+	0.797779i	$0.293992\pi$
$524$	2.84997e12	−	2.84997e12i	1.65139	−	1.65139i
$525$		−	1.27196e12i		−	0.730730i
$526$	−1.18844e12			−0.676924
$527$	−9.05880e11	−	2.62787e12i	−0.511591	−	1.48408i
$528$	1.08325e11			0.0606563
$529$		−	3.30518e11i		−	0.183504i
$530$	−1.95070e8	+	1.95070e8i	−0.000107386	+	0.000107386i
$531$	−1.81812e11			−0.0992426
$532$	2.35498e12	−	2.35498e12i	1.27463	−	1.27463i
$533$	−1.47490e12	−	1.47490e12i	−0.791571	−	0.791571i
$534$	−1.82898e12	−	1.82898e12i	−0.973358	−	0.973358i
$535$			4.86062e10i			0.0256507i
$536$		−	6.78306e10i		−	0.0354964i
$537$	−3.16253e11	−	3.16253e11i	−0.164116	−	0.164116i
$538$	9.45835e11	+	9.45835e11i	0.486738	+	0.486738i
$539$	−6.61095e10	+	6.61095e10i	−0.0337376	+	0.0337376i
$540$	−9.07021e10			−0.0459034
$541$	4.14970e10	−	4.14970e10i	0.0208271	−	0.0208271i	−0.696617	−	0.717444i	$-0.745312\pi$
$541$	4.14970e10	−	4.14970e10i	0.0208271	−	0.0208271i	0.717444	+	0.696617i	$0.245312\pi$
$542$			5.38441e11i			0.268004i
$543$	−2.69545e11			−0.133055
$544$	−8.82874e11	−	4.30223e11i	−0.432219	−	0.210619i
$545$	−1.44221e10			−0.00700238
$546$			2.10323e12i			1.01279i
$547$	−5.53062e11	+	5.53062e11i	−0.264138	+	0.264138i	−0.826733	−	0.562595i	$-0.809803\pi$
$547$	−5.53062e11	+	5.53062e11i	−0.264138	+	0.264138i	0.562595	+	0.826733i	$0.309803\pi$
$548$	5.50652e12			2.60835
$549$	6.21112e10	−	6.21112e10i	0.0291806	−	0.0291806i
$550$	−2.87054e11	−	2.87054e11i	−0.133762	−	0.133762i
$551$	2.38301e12	+	2.38301e12i	1.10140	+	1.10140i
$552$		−	2.71138e12i		−	1.24298i
$553$			1.34779e12i			0.612859i
$554$	2.97079e12	+	2.97079e12i	1.33992	+	1.33992i
$555$	2.93598e10	+	2.93598e10i	0.0131351	+	0.0131351i
$556$	−2.85924e12	+	2.85924e12i	−1.26886	+	1.26886i
$557$	1.21784e12			0.536096			0.268048	−	0.963406i	$-0.413621\pi$
$557$	1.21784e12			0.536096			0.268048	+	0.963406i	$0.413621\pi$
$558$	−2.99845e11	+	2.99845e11i	−0.130931	+	0.130931i
$559$		−	1.30424e12i		−	0.564943i
$560$	−2.38398e10			−0.0102437
$561$	−1.11208e11	+	2.28213e11i	−0.0474027	+	0.0972765i
$562$	1.40943e12			0.595977
$563$		−	7.08396e11i		−	0.297159i	−0.988900	−	0.148579i	$-0.952530\pi$
$563$		−	7.08396e11i		−	0.297159i	0.988900	−	0.148579i	$-0.0474700\pi$
$564$	2.75046e12	−	2.75046e12i	1.14459	−	1.14459i
$565$	1.92711e9			0.000795587
$566$	−1.00643e12	+	1.00643e12i	−0.412200	+	0.412200i
$567$	1.22064e12	+	1.22064e12i	0.495980	+	0.495980i
$568$	1.52303e12	+	1.52303e12i	0.613962	+	0.613962i
$569$		−	6.19769e11i		−	0.247870i	−0.992290	−	0.123935i	$-0.960449\pi$
$569$		−	6.19769e11i		−	0.247870i	0.992290	−	0.123935i	$-0.0395515\pi$
$570$		−	1.27322e11i		−	0.0505206i
$571$	2.03361e12	+	2.03361e12i	0.800580	+	0.800580i	0.983186	−	0.182607i	$-0.0584534\pi$
$571$	2.03361e12	+	2.03361e12i	0.800580	+	0.800580i	−0.182607	+	0.983186i	$0.558453\pi$
$572$	3.07848e11	+	3.07848e11i	0.120242	+	0.120242i
$573$	−2.36048e12	+	2.36048e12i	−0.914754	+	0.914754i
$574$	−4.53436e12			−1.74346
$575$	−1.67384e12	+	1.67384e12i	−0.638572	+	0.638572i
$576$			2.53374e11i			0.0959094i
$577$	−1.62060e11			−0.0608673			−0.0304336	−	0.999537i	$-0.509689\pi$
$577$	−1.62060e11			−0.0608673			−0.0304336	+	0.999537i	$0.509689\pi$
$578$	−3.56495e12	+	2.78927e12i	−1.32855	+	1.03948i
$579$	3.65720e12			1.35237
$580$		−	1.46587e11i		−	0.0537862i
$581$	−1.45732e12	+	1.45732e12i	−0.530592	+	0.530592i
$582$	−5.79149e12			−2.09236
$583$	8.26578e8	−	8.26578e8i	0.000296330	−	0.000296330i
$584$	−1.38002e12	−	1.38002e12i	−0.490940	−	0.490940i
$585$	−2.77238e9	−	2.77238e9i	−0.000978703	−	0.000978703i
$586$		−	7.77349e12i		−	2.72318i
$587$			4.89722e11i			0.170247i	0.996370	+	0.0851233i	$0.0271284\pi$
$587$			4.89722e11i			0.170247i	−0.996370	+	0.0851233i	$0.972872\pi$
$588$	−1.55126e12	−	1.55126e12i	−0.535165	−	0.535165i
$589$	−4.17699e12	−	4.17699e12i	−1.43003	−	1.43003i
$590$	−1.20108e11	+	1.20108e11i	−0.0408072	+	0.0408072i
$591$	2.63492e12			0.888430
$592$	−9.46502e11	+	9.46502e11i	−0.316719	+	0.316719i
$593$		−	1.30014e12i		−	0.431762i	−0.976420	−	0.215881i	$-0.930738\pi$
$593$		−	1.30014e12i		−	0.431762i	0.976420	−	0.215881i	$-0.0692623\pi$
$594$	5.92584e11			0.195304
$595$	2.44743e10	−	5.02245e10i	0.00800542	−	0.0164282i
$596$	−8.57019e12			−2.78216
$597$			1.76212e12i			0.567741i
$598$	2.76776e12	−	2.76776e12i	0.885060	−	0.885060i
$599$	1.04261e12			0.330903			0.165451	−	0.986218i	$-0.447092\pi$
$599$	1.04261e12			0.330903			0.165451	+	0.986218i	$0.447092\pi$
$600$	3.08604e12	−	3.08604e12i	0.972121	−	0.972121i
$601$	4.26533e12	+	4.26533e12i	1.33357	+	1.33357i	0.902148	+	0.431427i	$0.141990\pi$
$601$	4.26533e12	+	4.26533e12i	1.33357	+	1.33357i	0.431427	+	0.902148i	$0.358010\pi$
$602$	−2.00485e12	−	2.00485e12i	−0.622153	−	0.622153i
$603$		−	5.64961e9i		−	0.00174016i
$604$		−	9.44564e12i		−	2.88779i
$605$	5.54608e10	+	5.54608e10i	0.0168301	+	0.0168301i
$606$	6.86395e12	+	6.86395e12i	2.06751	+	2.06751i
$607$	−4.45831e11	+	4.45831e11i	−0.133297	+	0.133297i	−0.770607	−	0.637310i	$-0.780047\pi$
$607$	−4.45831e11	+	4.45831e11i	−0.133297	+	0.133297i	0.637310	+	0.770607i	$0.280047\pi$
$608$	−2.08716e12			−0.619427
$609$	−2.12183e12	+	2.12183e12i	−0.625075	+	0.625075i
$610$		−	8.20629e10i		−	0.0239973i
$611$	2.57270e12			0.746800
$612$	4.02605e11	+	1.96189e11i	0.116011	+	0.0565318i
$613$	5.77576e11			0.165210			0.0826052	−	0.996582i	$-0.473676\pi$
$613$	5.77576e11			0.165210			0.0826052	+	0.996582i	$0.473676\pi$
$614$		−	4.09652e12i		−	1.16321i
$615$	−7.94995e10	+	7.94995e10i	−0.0224092	+	0.0224092i
$616$	4.33618e11			0.121337
$617$	1.66571e12	−	1.66571e12i	0.462717	−	0.462717i	−0.436828	−	0.899545i	$-0.643898\pi$
$617$	1.66571e12	−	1.66571e12i	0.462717	−	0.462717i	0.899545	+	0.436828i	$0.143898\pi$
$618$	3.25302e12	+	3.25302e12i	0.897096	+	0.897096i
$619$	1.14158e12	+	1.14158e12i	0.312535	+	0.312535i	0.845891	−	0.533356i	$-0.179069\pi$
$619$	1.14158e12	+	1.14158e12i	0.312535	+	0.312535i	−0.533356	+	0.845891i	$0.679069\pi$
$620$			2.56941e11i			0.0698347i
$621$		−	3.45543e12i		−	0.932373i
$622$	−1.39894e12	−	1.39894e12i	−0.374750	−	0.374750i
$623$	−1.70560e12	−	1.70560e12i	−0.453607	−	0.453607i
$624$	−1.18879e12	+	1.18879e12i	−0.313887	+	0.313887i
$625$	−3.80805e12			−0.998257
$626$	−7.90642e12	+	7.90642e12i	−2.05776	+	2.05776i
$627$			5.39509e11i			0.139410i
$628$	1.08518e13			2.78409
$629$	−1.02235e12	−	2.96573e12i	−0.260418	−	0.755447i
$630$	−8.52327e9			−0.00215563
$631$			5.47382e12i			1.37454i	0.726400	+	0.687272i	$0.241192\pi$
$631$			5.47382e12i			1.37454i	−0.726400	+	0.687272i	$0.758808\pi$
$632$	−3.27002e12	+	3.27002e12i	−0.815312	+	0.815312i
$633$	−6.78320e12			−1.67926
$634$	2.59460e12	−	2.59460e12i	0.637777	−	0.637777i
$635$	9.27095e10	+	9.27095e10i	0.0226278	+	0.0226278i
$636$	1.93957e10	+	1.93957e10i	0.00470055	+	0.00470055i
$637$		−	1.45101e12i		−	0.349174i
$638$			9.57700e11i			0.228842i
$639$	1.26853e11	+	1.26853e11i	0.0300987	+	0.0300987i
$640$	1.32599e11	+	1.32599e11i	0.0312414	+	0.0312414i
$641$	−7.75369e11	+	7.75369e11i	−0.181404	+	0.181404i	−0.791967	−	0.610563i	$-0.790943\pi$
$641$	−7.75369e11	+	7.75369e11i	−0.181404	+	0.181404i	0.610563	+	0.791967i	$0.290943\pi$
$642$	7.45153e12			1.73116
$643$	−2.59943e12	+	2.59943e12i	−0.599692	+	0.599692i	−0.940231	−	0.340539i	$-0.889391\pi$
$643$	−2.59943e12	+	2.59943e12i	−0.599692	+	0.599692i	0.340539	+	0.940231i	$0.389391\pi$
$644$		−	5.51877e12i		−	1.26432i
$645$	−7.03008e10			−0.0159934
$646$	−4.21387e12	+	8.64740e12i	−0.951994	+	1.95362i
$647$	−3.35720e11			−0.0753196			−0.0376598	−	0.999291i	$-0.511990\pi$
$647$	−3.35720e11			−0.0753196			−0.0376598	+	0.999291i	$0.511990\pi$
$648$			5.92305e12i			1.31965i
$649$	5.08937e11	−	5.08937e11i	0.112606	−	0.112606i
$650$	6.30040e12			1.38439
$651$	3.71918e12	−	3.71918e12i	0.811583	−	0.811583i
$652$	7.37057e12	+	7.37057e12i	1.59730	+	1.59730i
$653$	−2.77429e12	−	2.77429e12i	−0.597093	−	0.597093i	0.342445	−	0.939538i	$-0.388745\pi$
$653$	−2.77429e12	−	2.77429e12i	−0.597093	−	0.597093i	−0.939538	+	0.342445i	$0.888745\pi$
$654$			2.21098e12i			0.472590i
$655$		−	1.43690e11i		−	0.0305028i
$656$	−2.56291e12	−	2.56291e12i	−0.540338	−	0.540338i
$657$	−1.14942e11	−	1.14942e11i	−0.0240677	−	0.0240677i
$658$	3.95470e12	−	3.95470e12i	0.822426	−	0.822426i
$659$	3.63105e12			0.749977			0.374989	−	0.927029i	$-0.377647\pi$
$659$	3.63105e12			0.749977			0.374989	+	0.927029i	$0.377647\pi$
$660$	1.65935e10	−	1.65935e10i	0.00340401	−	0.00340401i
$661$		−	6.68704e12i		−	1.36247i	−0.732064	−	0.681235i	$-0.761443\pi$
$661$		−	6.68704e12i		−	1.36247i	0.732064	−	0.681235i	$-0.238557\pi$
$662$	1.16386e13			2.35527
$663$	−1.28405e12	−	3.72489e12i	−0.258089	−	0.748692i
$664$	−7.07149e12			−1.41174
$665$		−	1.18733e11i		−	0.0235438i
$666$	−3.38396e11	+	3.38396e11i	−0.0666485	+	0.0666485i
$667$	5.58446e12			1.09248
$668$	−6.32593e12	+	6.32593e12i	−1.22922	+	1.22922i
$669$	−8.23194e11	−	8.23194e11i	−0.158886	−	0.158886i
$670$	−3.73220e9	−	3.73220e9i	−0.000715531	−	0.000715531i
$671$			3.47728e11i			0.0662199i
$672$		−	1.85840e12i		−	0.351543i
$673$	−1.54830e12	−	1.54830e12i	−0.290929	−	0.290929i	0.546518	−	0.837447i	$-0.315953\pi$
$673$	−1.54830e12	−	1.54830e12i	−0.290929	−	0.290929i	−0.837447	+	0.546518i	$0.815953\pi$
$674$	4.58776e12	+	4.58776e12i	0.856310	+	0.856310i
$675$	3.93289e12	−	3.93289e12i	0.729197	−	0.729197i
$676$	3.26367e12			0.601099
$677$	6.78181e11	−	6.78181e11i	0.124079	−	0.124079i	−0.642341	−	0.766419i	$-0.722037\pi$
$677$	6.78181e11	−	6.78181e11i	0.124079	−	0.124079i	0.766419	+	0.642341i	$0.222037\pi$
$678$		−	2.95434e11i		−	0.0536941i
$679$	−5.40080e12			−0.975089
$680$	1.81235e11	−	6.24752e10i	0.0325051	−	0.0112051i
$681$	−1.05124e13			−1.87301
$682$		−	1.67868e12i		−	0.297124i
$683$	−1.49216e12	+	1.49216e12i	−0.262374	+	0.262374i	−0.826018	−	0.563644i	$-0.809399\pi$
$683$	−1.49216e12	+	1.49216e12i	−0.262374	+	0.262374i	0.563644	+	0.826018i	$0.309399\pi$
$684$	9.51781e11			0.166259
$685$	1.38814e11	−	1.38814e11i	0.0240894	−	0.0240894i
$686$	−7.47584e12	−	7.47584e12i	−1.28885	−	1.28885i
$687$	−4.13690e12	−	4.13690e12i	−0.708549	−	0.708549i
$688$		−	2.26636e12i		−	0.385639i
$689$			1.81422e10i			0.00306692i
$690$	−1.49187e11	−	1.49187e11i	−0.0250559	−	0.0250559i
$691$	1.20911e12	+	1.20911e12i	0.201751	+	0.201751i	0.800750	−	0.598999i	$-0.204435\pi$
$691$	1.20911e12	+	1.20911e12i	0.201751	+	0.201751i	−0.598999	+	0.800750i	$0.704435\pi$
$692$	−1.45207e12	+	1.45207e12i	−0.240719	+	0.240719i
$693$	3.61160e10			0.00594840
$694$	−5.41578e12	+	5.41578e12i	−0.886223	+	0.886223i
$695$			1.44157e11i			0.0234372i
$696$	−1.02960e13			−1.66313
$697$	8.03051e12	−	2.76828e12i	1.28883	−	0.444286i
$698$	−1.26594e12			−0.201866
$699$		−	7.17146e11i		−	0.113621i
$700$	6.28134e12	−	6.28134e12i	0.988807	−	0.988807i
$701$	1.01887e13			1.59363			0.796816	−	0.604222i	$-0.206516\pi$
$701$	1.01887e13			1.59363			0.796816	+	0.604222i	$0.206516\pi$
$702$	−6.50317e12	+	6.50317e12i	−1.01067	+	1.01067i
$703$	−4.71402e12	−	4.71402e12i	−0.727935	−	0.727935i
$704$	−7.09255e11	−	7.09255e11i	−0.108824	−	0.108824i
$705$		−	1.38673e11i		−	0.0211417i
$706$		−	1.18596e13i		−	1.79659i
$707$	6.40091e12	+	6.40091e12i	0.963507	+	0.963507i
$708$	1.19422e13	+	1.19422e13i	1.78622	+	1.78622i
$709$	−6.76573e12	+	6.76573e12i	−1.00556	+	1.00556i	−0.00557191	+	0.999984i	$0.501774\pi$
$709$	−6.76573e12	+	6.76573e12i	−1.00556	+	1.00556i	−0.999984	+	0.00557191i	$0.998226\pi$
$710$	1.67602e11			0.0247523
$711$	−2.72360e11	+	2.72360e11i	−0.0399696	+	0.0399696i
$712$		−	8.27625e12i		−	1.20691i
$713$	−9.78856e12			−1.41846
$714$	−7.69963e12	−	3.75201e12i	−1.10873	−	0.540285i
$715$	1.55211e10			0.00222098
$716$		−	3.12352e12i		−	0.444155i
$717$	−6.35191e12	+	6.35191e12i	−0.897570	+	0.897570i
$718$	−1.08012e12			−0.151674
$719$	−1.71077e12	+	1.71077e12i	−0.238733	+	0.238733i	−0.816325	−	0.577592i	$-0.803992\pi$
$719$	−1.71077e12	+	1.71077e12i	−0.238733	+	0.238733i	0.577592	+	0.816325i	$0.303992\pi$
$720$	−4.81752e9	−	4.81752e9i	−0.000668078	−	0.000668078i
$721$	3.03358e12	+	3.03358e12i	0.418068	+	0.418068i
$722$			8.12604e12i			1.11291i
$723$			1.07441e13i			1.46234i
$724$	−1.33110e12	−	1.33110e12i	−0.180047	−	0.180047i
$725$	6.35611e12	+	6.35611e12i	0.854418	+	0.854418i
$726$	8.50237e12	−	8.50237e12i	1.13586	−	1.13586i
$727$	−5.62075e12			−0.746259			−0.373130	−	0.927779i	$-0.621715\pi$
$727$	−5.62075e12			−0.746259			−0.373130	+	0.927779i	$0.621715\pi$
$728$	−4.75863e12	+	4.75863e12i	−0.627901	+	0.627901i
$729$			8.08164e12i			1.05980i
$730$	−1.51864e11			−0.0197926
$731$	4.77464e12	+	2.32667e12i	0.618461	+	0.301375i
$732$	−8.15946e12			−1.05042
$733$			5.95250e11i			0.0761608i	0.999275	+	0.0380804i	$0.0121243\pi$
$733$			5.95250e11i			0.0761608i	−0.999275	+	0.0380804i	$0.987876\pi$
$734$	5.29668e12	−	5.29668e12i	0.673553	−	0.673553i
$735$	−7.82116e10			−0.00988504
$736$	−2.44558e12	+	2.44558e12i	−0.307207	+	0.307207i
$737$	1.58146e10	+	1.58146e10i	0.00197449	+	0.00197449i
$738$	−9.16297e11	−	9.16297e11i	−0.113706	−	0.113706i
$739$		−	6.94825e12i		−	0.856990i	−0.903544	−	0.428495i	$-0.859044\pi$
$739$		−	6.94825e12i		−	0.856990i	0.903544	−	0.428495i	$-0.140956\pi$
$740$			2.89976e11i			0.0355483i
$741$	−5.92070e12	−	5.92070e12i	−0.721425	−	0.721425i
$742$	2.78877e10	+	2.78877e10i	0.00337750	+	0.00337750i
$743$	2.19475e12	−	2.19475e12i	0.264201	−	0.264201i	−0.562557	−	0.826758i	$-0.690182\pi$
$743$	2.19475e12	−	2.19475e12i	0.264201	−	0.264201i	0.826758	+	0.562557i	$0.190182\pi$
$744$	1.80470e13			2.15937
$745$	−2.16046e11	+	2.16046e11i	−0.0256947	+	0.0256947i
$746$		−	1.09495e13i		−	1.29440i
$747$	−5.88984e11			−0.0692087
$748$	−1.67617e12	+	5.77809e11i	−0.195777	+	0.0674881i
$749$	6.94886e12			0.806762
$750$		−	6.79402e11i		−	0.0784063i
$751$	5.29981e12	−	5.29981e12i	0.607968	−	0.607968i	−0.334446	−	0.942415i	$-0.608549\pi$
$751$	5.29981e12	−	5.29981e12i	0.607968	−	0.607968i	0.942415	+	0.334446i	$0.108549\pi$
$752$	4.47054e12			0.509777
$753$	2.32785e12	−	2.32785e12i	0.263863	−	0.263863i
$754$	−1.05100e13	−	1.05100e13i	−1.18422	−	1.18422i
$755$	−2.38115e11	−	2.38115e11i	−0.0266702	−	0.0266702i
$756$			1.29670e13i			1.44375i
$757$			5.04488e12i			0.558366i	0.960238	+	0.279183i	$0.0900637\pi$
$757$			5.04488e12i			0.558366i	−0.960238	+	0.279183i	$0.909936\pi$
$758$	1.48660e12	+	1.48660e12i	0.163562	+	0.163562i
$759$	6.32155e11	+	6.32155e11i	0.0691410	+	0.0691410i
$760$	2.88072e11	−	2.88072e11i	0.0313213	−	0.0313213i
$761$	1.46542e13			1.58391			0.791956	−	0.610578i	$-0.209063\pi$
$761$	1.46542e13			1.58391			0.791956	+	0.610578i	$0.209063\pi$
$762$	1.42128e13	−	1.42128e13i	1.52715	−	1.52715i
$763$			2.06183e12i			0.220238i
$764$	−2.33136e13			−2.47565
$765$	1.50950e10	−	5.20356e9i	0.00159352	−	0.000549318i
$766$	1.63259e13			1.71336
$767$			1.11704e13i			1.16544i
$768$	1.13103e13	−	1.13103e13i	1.17314	−	1.17314i
$769$	−2.31369e12			−0.238581			−0.119291	−	0.992859i	$-0.538062\pi$
$769$	−2.31369e12			−0.238581			−0.119291	+	0.992859i	$0.538062\pi$
$770$	2.38587e10	−	2.38587e10i	0.00244590	−	0.00244590i
$771$	5.93943e12	+	5.93943e12i	0.605340	+	0.605340i
$772$	1.80604e13	+	1.80604e13i	1.83000	+	1.83000i
$773$			3.66057e12i			0.368757i	0.982855	+	0.184379i	$0.0590272\pi$
$773$			3.66057e12i			0.368757i	−0.982855	+	0.184379i	$0.940973\pi$
$774$		−	8.10273e11i		−	0.0811516i
$775$	−1.11411e13	−	1.11411e13i	−1.10936	−	1.10936i
$776$	−1.31035e13	−	1.31035e13i	−1.29720	−	1.29720i
$777$	4.19735e12	−	4.19735e12i	0.413124	−	0.413124i
$778$	−2.44796e13			−2.39550
$779$	1.27645e13	−	1.27645e13i	1.24189	−	1.24189i
$780$			3.64203e11i			0.0352305i
$781$	−7.10186e11			−0.0683034
$782$	5.19488e12	+	1.50699e13i	0.496759	+	1.44105i
$783$	−1.31213e13			−1.24753
$784$		−	2.52139e12i		−	0.238351i
$785$	2.73564e11	−	2.73564e11i	0.0257125	−	0.0257125i
$786$	−2.20283e13			−2.05863
$787$	1.05610e13	−	1.05610e13i	0.981335	−	0.981335i	−0.0184937	−	0.999829i	$-0.505887\pi$
$787$	1.05610e13	−	1.05610e13i	0.981335	−	0.981335i	0.999829	+	0.0184937i	$0.00588706\pi$
$788$	1.30120e13	+	1.30120e13i	1.20220	+	1.20220i
$789$	2.97884e12	+	2.97884e12i	0.273653	+	0.273653i
$790$			3.59849e11i			0.0328699i
$791$		−	2.75504e11i		−	0.0250227i
$792$	8.76248e10	+	8.76248e10i	0.00791341	+	0.00791341i
$793$	−3.81606e12	−	3.81606e12i	−0.342678	−	0.342678i
$794$	1.43087e13	−	1.43087e13i	1.27764	−	1.27764i
$795$	9.77893e8			8.68239e−5
$796$	−8.70189e12	+	8.70189e12i	−0.768254	+	0.768254i
$797$			1.44395e13i			1.26762i	0.773490	+	0.633809i	$0.218510\pi$
$797$			1.44395e13i			1.26762i	−0.773490	+	0.633809i	$0.781490\pi$
$798$	−1.82023e13			−1.58896
$799$	−4.58952e12	+	9.41830e12i	−0.398389	+	0.817546i
$800$	−5.56701e12			−0.480526
$801$		−	6.89328e11i		−	0.0591670i
$802$	−1.25660e13	+	1.25660e13i	−1.07254	+	1.07254i
$803$	6.43501e11			0.0546172
$804$	−3.71090e11	+	3.71090e11i	−0.0313204	+	0.0313204i
$805$	−1.39123e11	−	1.39123e11i	−0.0116766	−	0.0116766i
$806$	1.84222e13	+	1.84222e13i	1.53757	+	1.53757i
$807$		−	4.74150e12i		−	0.393536i
$808$			3.10599e13i			2.56359i
$809$	−1.36356e13	−	1.36356e13i	−1.11919	−	1.11919i	−0.991860	−	0.127334i	$-0.959358\pi$
$809$	−1.36356e13	−	1.36356e13i	−1.11919	−	1.11919i	−0.127334	−	0.991860i	$-0.540642\pi$
$810$	3.25900e11	+	3.25900e11i	0.0266012	+	0.0266012i
$811$	−7.98388e12	+	7.98388e12i	−0.648068	+	0.648068i	−0.952526	−	0.304458i	$-0.901525\pi$
$811$	−7.98388e12	+	7.98388e12i	−0.648068	+	0.648068i	0.304458	+	0.952526i	$0.401525\pi$
$812$	−2.09565e13			−1.69167
$813$	1.34961e12	−	1.34961e12i	0.108343	−	0.108343i
$814$		−	1.89450e12i		−	0.151246i
$815$	3.71610e11			0.0295038
$816$	−2.23127e12	−	6.47269e12i	−0.176176	−	0.511068i
$817$	1.12875e13			0.886337
$818$		−	2.70887e13i		−	2.11543i
$819$	−3.96346e11	+	3.96346e11i	−0.0307820	+	0.0307820i
$820$	−7.85188e11			−0.0606472
$821$	8.84692e12	−	8.84692e12i	0.679591	−	0.679591i	−0.280316	−	0.959908i	$-0.590439\pi$
$821$	8.84692e12	−	8.84692e12i	0.679591	−	0.679591i	0.959908	+	0.280316i	$0.0904393\pi$
$822$	−2.12808e13	−	2.12808e13i	−1.62579	−	1.62579i
$823$	5.08254e12	+	5.08254e12i	0.386173	+	0.386173i	0.873320	−	0.487147i	$-0.161962\pi$
$823$	5.08254e12	+	5.08254e12i	0.386173	+	0.386173i	−0.487147	+	0.873320i	$0.661962\pi$
$824$			1.47202e13i			1.11235i
$825$			1.43901e12i			0.108149i
$826$	1.71709e13	+	1.71709e13i	1.28346	+	1.28346i
$827$	−9.12086e12	−	9.12086e12i	−0.678049	−	0.678049i	0.281510	−	0.959558i	$-0.409165\pi$
$827$	−9.12086e12	−	9.12086e12i	−0.678049	−	0.678049i	−0.959558	+	0.281510i	$0.909165\pi$
$828$	1.11522e12	−	1.11522e12i	0.0824567	−	0.0824567i
$829$	−1.20539e13			−0.886406			−0.443203	−	0.896421i	$-0.646158\pi$
$829$	−1.20539e13			−0.886406			−0.443203	+	0.896421i	$0.646158\pi$
$830$	−3.89090e11	+	3.89090e11i	−0.0284577	+	0.0284577i
$831$		−	1.48927e13i		−	1.08335i
$832$	1.55671e13			1.12630
$833$	5.31193e12	+	2.58849e12i	0.382252	+	0.186271i
$834$	2.20999e13			1.58177
$835$			3.18941e11i			0.0227050i
$836$	−2.66426e12	+	2.66426e12i	−0.188647	+	0.188647i
$837$	2.29994e13			1.61976
$838$	−8.35360e12	+	8.35360e12i	−0.585161	+	0.585161i
$839$	6.43317e11	+	6.43317e11i	0.0448225	+	0.0448225i	0.729163	−	0.684340i	$-0.239910\pi$
$839$	6.43317e11	+	6.43317e11i	0.0448225	+	0.0448225i	−0.684340	+	0.729163i	$0.739910\pi$
$840$	2.56498e11	+	2.56498e11i	0.0177757	+	0.0177757i
$841$		−	6.69879e12i		−	0.461758i
$842$		−	4.33209e13i		−	2.97025i
$843$	−3.53276e12	−	3.53276e12i	−0.240929	−	0.240929i
$844$	−3.34976e13	−	3.34976e13i	−2.27234	−	2.27234i
$845$	8.22739e10	−	8.22739e10i	0.00555146	−	0.00555146i
$846$	1.59832e12			0.107275
$847$	7.92881e12	−	7.92881e12i	0.529338	−	0.529338i
$848$			3.15253e10i			0.00209353i
$849$	5.04525e12			0.333272
$850$	−1.12395e13	+	2.30649e13i	−0.738518	+	1.51554i
$851$	−1.10471e13			−0.722044
$852$		−	1.66645e13i		−	1.08347i
$853$	6.84115e12	−	6.84115e12i	0.442444	−	0.442444i	−0.450389	−	0.892833i	$-0.648715\pi$
$853$	6.84115e12	−	6.84115e12i	0.442444	−	0.442444i	0.892833	+	0.450389i	$0.148715\pi$
$854$	−1.17319e13			−0.754759
$855$	2.39935e10	−	2.39935e10i	0.00153548	−	0.00153548i
$856$	1.68594e13	+	1.68594e13i	1.07327	+	1.07327i
$857$	−7.06858e12	−	7.06858e12i	−0.447629	−	0.447629i	0.446936	−	0.894566i	$-0.352515\pi$
$857$	−7.06858e12	−	7.06858e12i	−0.447629	−	0.447629i	−0.894566	+	0.446936i	$0.852515\pi$
$858$		−	2.37945e12i		−	0.149894i
$859$			1.80838e13i			1.13323i	0.823981	+	0.566617i	$0.191748\pi$
$859$			1.80838e13i			1.13323i	−0.823981	+	0.566617i	$0.808252\pi$
$860$	−3.47167e11	−	3.47167e11i	−0.0216419	−	0.0216419i
$861$	1.13655e13	+	1.13655e13i	0.704811	+	0.704811i
$862$	−1.85475e13	+	1.85475e13i	−1.14420	+	1.14420i
$863$	−2.81134e13			−1.72530			−0.862652	−	0.505799i	$-0.831198\pi$
$863$	−2.81134e13			−1.72530			−0.862652	+	0.505799i	$0.831198\pi$
$864$	5.74617e12	−	5.74617e12i	0.350806	−	0.350806i
$865$			7.32106e10i			0.00444633i
$866$	−5.00904e12			−0.302638
$867$	1.59270e13	+	1.94424e12i	0.957297	+	0.116859i
$868$	3.67330e13			2.19643
$869$		−	1.52480e12i		−	0.0907036i
$870$	−5.66509e11	+	5.66509e11i	−0.0335251	+	0.0335251i
$871$	−3.47107e11			−0.0204353
$872$	−5.00241e12	+	5.00241e12i	−0.292992	+	0.292992i
$873$	−1.09139e12	−	1.09139e12i	−0.0635937	−	0.0635937i
$874$	2.39535e13	+	2.39535e13i	1.38857	+	1.38857i
$875$		−	6.33570e11i		−	0.0365392i
$876$			1.50998e13i			0.866367i
$877$	−2.80977e12	−	2.80977e12i	−0.160388	−	0.160388i	0.622351	−	0.782739i	$-0.286178\pi$
$877$	−2.80977e12	−	2.80977e12i	−0.160388	−	0.160388i	−0.782739	+	0.622351i	$0.786178\pi$
$878$	1.65404e13	+	1.65404e13i	0.939336	+	0.939336i
$879$	−1.94844e13	+	1.94844e13i	−1.10087	+	1.10087i
$880$	2.69708e10			0.00151608
$881$	−8.93195e11	+	8.93195e11i	−0.0499522	+	0.0499522i	−0.731642	−	0.681689i	$-0.761246\pi$
$881$	−8.93195e11	+	8.93195e11i	−0.0499522	+	0.0499522i	0.681689	+	0.731642i	$0.261246\pi$
$882$		−	9.01452e11i		−	0.0501573i
$883$	1.87841e13			1.03984			0.519922	−	0.854214i	$-0.325961\pi$
$883$	1.87841e13			1.03984			0.519922	+	0.854214i	$0.325961\pi$
$884$	1.20537e13	−	2.47357e13i	0.663872	−	1.36235i
$885$	6.02103e11			0.0329933
$886$			1.72472e13i			0.940303i
$887$	−1.36169e13	+	1.36169e13i	−0.738623	+	0.738623i	−0.972312	−	0.233688i	$-0.924920\pi$
$887$	−1.36169e13	+	1.36169e13i	−0.738623	+	0.738623i	0.233688	+	0.972312i	$0.424920\pi$
$888$	2.03673e13			1.09919
$889$	1.32540e13	−	1.32540e13i	0.711686	−	0.711686i
$890$	−4.55379e11	−	4.55379e11i	−0.0243286	−	0.0243286i
$891$	−1.38095e12	−	1.38095e12i	−0.0734054	−	0.0734054i
$892$		−	8.13038e12i		−	0.430001i
$893$			2.22654e13i			1.17165i
$894$	3.31208e13	+	3.31208e13i	1.73413	+	1.73413i
$895$	−7.87408e10	−	7.87408e10i	−0.00410200	−	0.00410200i
$896$	1.89567e13	−	1.89567e13i	0.982599	−	0.982599i
$897$	−1.38749e13			−0.715587
$898$	2.77892e13	−	2.77892e13i	1.42604	−	1.42604i
$899$			3.71702e13i			1.89791i
$900$	2.53865e12			0.128977
$901$	−6.64159e10	−	3.23643e10i	−0.00335746	−	0.00163608i
$902$	5.12987e12			0.258034
$903$			1.00504e13i			0.503022i
$904$	6.68429e11	−	6.68429e11i	0.0332888	−	0.0332888i
$905$	−6.71114e10			−0.00332566
$906$	−3.65041e13	+	3.65041e13i	−1.79997	+	1.79997i
$907$	−1.34042e13	−	1.34042e13i	−0.657670	−	0.657670i	0.297158	−	0.954828i	$-0.403961\pi$
$907$	−1.34042e13	−	1.34042e13i	−0.657670	−	0.657670i	−0.954828	+	0.297158i	$0.903961\pi$
$908$	−5.19135e13	−	5.19135e13i	−2.53451	−	2.53451i
$909$			2.58697e12i			0.125677i
$910$			5.23663e11i			0.0253143i
$911$	−2.57333e13	−	2.57333e13i	−1.23783	−	1.23783i	−0.960885	−	0.276949i	$-0.910677\pi$
$911$	−2.57333e13	−	2.57333e13i	−1.23783	−	1.23783i	−0.276949	−	0.960885i	$-0.589323\pi$
$912$	−1.02883e13	−	1.02883e13i	−0.492456	−	0.492456i
$913$	1.64871e12	−	1.64871e12i	0.0785281	−	0.0785281i
$914$	6.06038e13			2.87238
$915$	−2.05692e11	+	2.05692e11i	−0.00970113	+	0.00970113i
$916$		−	4.08586e13i		−	1.91758i
$917$	−2.05423e13			−0.959370
$918$	−1.22060e13	−	3.54084e13i	−0.567258	−	1.64556i
$919$	−3.39029e13			−1.56790			−0.783949	−	0.620826i	$-0.786797\pi$
$919$	−3.39029e13			−1.56790			−0.783949	+	0.620826i	$0.786797\pi$
$920$		−	6.75081e11i		−	0.0310678i
$921$	−1.02680e13	+	1.02680e13i	−0.470238	+	0.470238i
$922$	−6.57860e13			−2.99809
$923$	7.79376e12	−	7.79376e12i	0.353459	−	0.353459i
$924$	−2.37225e12	−	2.37225e12i	−0.107062	−	0.107062i
$925$	−1.25735e13	−	1.25735e13i	−0.564702	−	0.564702i
$926$			3.17367e12i			0.141844i
$927$			1.22604e12i			0.0545314i
$928$	9.28662e12	+	9.28662e12i	0.411047	+	0.411047i
$929$	3.93559e12	+	3.93559e12i	0.173356	+	0.173356i	0.788452	−	0.615096i	$-0.210883\pi$
$929$	3.93559e12	+	3.93559e12i	0.173356	+	0.173356i	−0.615096	+	0.788452i	$0.710883\pi$
$930$	9.92989e11	−	9.92989e11i	0.0435282	−	0.0435282i
$931$	1.25577e13			0.547818
$932$	3.54149e12	−	3.54149e12i	0.153750	−	0.153750i
$933$			7.01292e12i			0.302992i
$934$	4.96844e13			2.13628
$935$	−2.76886e10	+	5.68206e10i	−0.00118481	+	0.00243138i
$936$	−1.92323e12			−0.0819013
$937$			1.90936e13i			0.809207i	0.914492	+	0.404603i	$0.132590\pi$
$937$			1.90936e13i			0.809207i	−0.914492	+	0.404603i	$0.867410\pi$
$938$	−5.33565e11	+	5.33565e11i	−0.0225048	+	0.0225048i
$939$	3.96352e13			1.66374
$940$	6.84811e11	−	6.84811e11i	0.0286085	−	0.0286085i
$941$	1.64934e12	+	1.64934e12i	0.0685737	+	0.0685737i	0.740562	−	0.671988i	$-0.234559\pi$
$941$	1.64934e12	+	1.64934e12i	0.0685737	+	0.0685737i	−0.671988	+	0.740562i	$0.734559\pi$
$942$	−4.19385e13	−	4.19385e13i	−1.73534	−	1.73534i
$943$		−	2.99129e13i		−	1.23184i
$944$			1.94106e13i			0.795546i
$945$	3.26885e11	+	3.26885e11i	0.0133337	+	0.0133337i
$946$	2.26815e12	+	2.26815e12i	0.0920792	+	0.0920792i
$947$	2.12049e13	−	2.12049e13i	0.856765	−	0.856765i	−0.134191	−	0.990956i	$-0.542843\pi$
$947$	2.12049e13	−	2.12049e13i	0.856765	−	0.856765i	0.990956	+	0.134191i	$0.0428435\pi$
$948$	3.57795e13			1.43879
$949$	−7.06194e12	+	7.06194e12i	−0.282635	+	0.282635i
$950$			5.45266e13i			2.17196i
$951$	−1.30068e13			−0.515654
$952$	−8.93161e12	−	2.59097e13i	−0.352422	−	1.02234i
$953$	6.76956e12			0.265853			0.132927	−	0.991126i	$-0.457563\pi$
$953$	6.76956e12			0.265853			0.132927	+	0.991126i	$0.457563\pi$
$954$			1.12710e10i			0.000440550i
$955$	−5.87712e11	+	5.87712e11i	−0.0228639	+	0.0228639i
$956$	−6.27355e13			−2.42914
$957$	2.40049e12	−	2.40049e12i	0.0925116	−	0.0925116i
$958$	4.15537e13	+	4.15537e13i	1.59392	+	1.59392i
$959$	−1.98452e13	−	1.98452e13i	−0.757656	−	0.757656i
$960$		−	8.39092e11i		−	0.0318852i
$961$		−	3.87131e13i		−	1.46421i
$962$	2.07907e13	+	2.07907e13i	0.782676	+	0.782676i
$963$	1.40422e12	+	1.40422e12i	0.0526157	+	0.0526157i
$964$	−5.30579e13	+	5.30579e13i	−1.97881	+	1.97881i
$965$	9.10571e11			0.0338019
$966$	−2.13281e13	+	2.13281e13i	−0.788053	+	0.788053i
$967$			2.76210e13i			1.01583i	0.861407	+	0.507915i	$0.169584\pi$
$967$			2.76210e13i			1.01583i	−0.861407	+	0.507915i	$0.830416\pi$
$968$	3.84738e13			1.40840
$969$	3.22370e13	−	1.11127e13i	1.17462	−	0.404915i
$970$	−1.44197e12			−0.0522977
$971$			3.68276e13i			1.32950i	0.747068	+	0.664748i	$0.231461\pi$
$971$			3.68276e13i			1.32950i	−0.747068	+	0.664748i	$0.768539\pi$
$972$	−5.06944e12	+	5.06944e12i	−0.182164	+	0.182164i
$973$	2.06091e13			0.737142
$974$	−5.38345e13	+	5.38345e13i	−1.91666	+	1.91666i
$975$	−1.57921e13	−	1.57921e13i	−0.559652	−	0.559652i
$976$	−6.63110e12	−	6.63110e12i	−0.233917	−	0.233917i
$977$			1.06932e13i			0.375477i	0.982219	+	0.187739i	$0.0601158\pi$
$977$			1.06932e13i			0.375477i	−0.982219	+	0.187739i	$0.939884\pi$
$978$		−	5.69694e13i		−	1.99121i
$979$	1.92960e12	+	1.92960e12i	0.0671343	+	0.0671343i
$980$	−3.86234e11	−	3.86234e11i	−0.0133762	−	0.0133762i
$981$	−4.16651e11	+	4.16651e11i	−0.0143635	+	0.0143635i
$982$	−5.80525e13			−1.99214
$983$	−3.03765e13	+	3.03765e13i	−1.03764	+	1.03764i	−0.0383759	+	0.999263i	$0.512218\pi$
$983$	−3.03765e13	+	3.03765e13i	−1.03764	+	1.03764i	−0.999263	+	0.0383759i	$0.987782\pi$
$984$			5.51498e13i			1.87528i
$985$	6.56042e11			0.0222059
$986$	5.72249e13	−	1.97266e13i	1.92814	−	0.664670i
$987$	−1.98250e13			−0.664947
$988$		−	5.84766e13i		−	1.95243i
$989$	1.32258e13	−	1.32258e13i	0.439582	−	0.439582i
$990$	9.64265e9			0.000319035
$991$	3.64086e13	−	3.64086e13i	1.19915	−	1.19915i	0.224727	−	0.974422i	$-0.427851\pi$
$991$	3.64086e13	−	3.64086e13i	1.19915	−	1.19915i	0.974422	−	0.224727i	$-0.0721489\pi$
$992$	−1.62778e13	−	1.62778e13i	−0.533695	−	0.533695i
$993$	−2.91725e13	−	2.91725e13i	−0.952141	−	0.952141i
$994$		−	2.39608e13i		−	0.778506i
$995$			4.38732e11i			0.0141904i
$996$	3.86870e13	+	3.86870e13i	1.24566	+	1.24566i
$997$	3.27196e13	+	3.27196e13i	1.04877	+	1.04877i	0.998748	+	0.0500213i	$0.0159289\pi$
$997$	3.27196e13	+	3.27196e13i	1.04877	+	1.04877i	0.0500213	+	0.998748i	$0.484071\pi$
$998$	4.93655e13	−	4.93655e13i	1.57520	−	1.57520i
$999$	2.59563e13			0.824516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.4.1	✓	24
17.8	even	8		289.10.a.f.1.2		24
17.9	even	8		289.10.a.f.1.1		24
17.13	even	4	inner	17.10.c.a.13.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.1	✓	24	1.1	even	1	trivial
17.10.c.a.13.12	yes	24	17.13	even	4	inner
289.10.a.f.1.1		24	17.9	even	8
289.10.a.f.1.2		24	17.8	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-38.1697i q^{2} +(-95.6730 + 95.6730i) q^{3} -944.927 q^{4} +(-23.8207 + 23.8207i) q^{5} +(3651.81 + 3651.81i) q^{6} +(3405.47 + 3405.47i) q^{7} +16524.7i q^{8} +1376.34i q^{9} +O(q^{10})\)	\(q-38.1697i q^{2} +(-95.6730 + 95.6730i) q^{3} -944.927 q^{4} +(-23.8207 + 23.8207i) q^{5} +(3651.81 + 3651.81i) q^{6} +(3405.47 + 3405.47i) q^{7} +16524.7i q^{8} +1376.34i q^{9} +(909.229 + 909.229i) q^{10} +(-3852.71 - 3852.71i) q^{11} +(90404.1 - 90404.1i) q^{12} +84561.3 q^{13} +(129986. - 129986. i) q^{14} -4558.00i q^{15} +146941. q^{16} +(-150851. + 309567. i) q^{17} +52534.6 q^{18} +731833. i q^{19} +(22508.8 - 22508.8i) q^{20} -651622. q^{21} +(-147057. + 147057. i) q^{22} +(857507. + 857507. i) q^{23} +(-1.58097e6 - 1.58097e6i) q^{24} +1.95199e6i q^{25} -3.22768e6i q^{26} +(-2.01481e6 - 2.01481e6i) q^{27} +(-3.21792e6 - 3.21792e6i) q^{28} +(3.25622e6 - 3.25622e6i) q^{29} -173977. q^{30} +(-5.70757e6 + 5.70757e6i) q^{31} +2.85196e6i q^{32} +737202. q^{33} +(1.18161e7 + 5.75796e6i) q^{34} -162241. q^{35} -1.30054e6i q^{36} +(-6.44138e6 + 6.44138e6i) q^{37} +2.79339e7 q^{38} +(-8.09024e6 + 8.09024e6i) q^{39} +(-393630. - 393630. i) q^{40} +(-1.74418e7 - 1.74418e7i) q^{41} +2.48722e7i q^{42} -1.54236e7i q^{43} +(3.64053e6 + 3.64053e6i) q^{44} +(-32785.4 - 32785.4i) q^{45} +(3.27308e7 - 3.27308e7i) q^{46} +3.04241e7 q^{47} +(-1.40583e7 + 1.40583e7i) q^{48} -1.71592e7i q^{49} +7.45069e7 q^{50} +(-1.51848e7 - 4.40496e7i) q^{51} -7.99043e7 q^{52} +214544. i q^{53} +(-7.69048e7 + 7.69048e7i) q^{54} +183549. q^{55} +(-5.62743e7 + 5.62743e7i) q^{56} +(-7.00167e7 - 7.00167e7i) q^{57} +(-1.24289e8 - 1.24289e8i) q^{58} +1.32098e8i q^{59} +4.30697e6i q^{60} +(-4.51277e7 - 4.51277e7i) q^{61} +(2.17856e8 + 2.17856e8i) q^{62} +(-4.68709e6 + 4.68709e6i) q^{63} +1.84092e8 q^{64} +(-2.01431e6 + 2.01431e6i) q^{65} -2.81388e7i q^{66} -4.10480e6 q^{67} +(1.42544e8 - 2.92518e8i) q^{68} -1.64080e8 q^{69} +6.19270e6i q^{70} +(9.21670e7 - 9.21670e7i) q^{71} -2.27437e7 q^{72} +(-8.35127e7 + 8.35127e7i) q^{73} +(2.45866e8 + 2.45866e8i) q^{74} +(-1.86753e8 - 1.86753e8i) q^{75} -6.91529e8i q^{76} -2.62406e7i q^{77} +(3.08802e8 + 3.08802e8i) q^{78} +(1.97887e8 + 1.97887e8i) q^{79} +(-3.50023e6 + 3.50023e6i) q^{80} +3.58436e8 q^{81} +(-6.65748e8 + 6.65748e8i) q^{82} +4.27934e8i q^{83} +6.15736e8 q^{84} +(-3.78071e6 - 1.09675e7i) q^{85} -5.88715e8 q^{86} +6.23065e8i q^{87} +(6.36650e7 - 6.36650e7i) q^{88} -5.00841e8 q^{89} +(-1.25141e6 + 1.25141e6i) q^{90} +(2.87971e8 + 2.87971e8i) q^{91} +(-8.10281e8 - 8.10281e8i) q^{92} -1.09212e9i q^{93} -1.16128e9i q^{94} +(-1.74328e7 - 1.74328e7i) q^{95} +(-2.72856e8 - 2.72856e8i) q^{96} +(-7.92961e8 + 7.92961e8i) q^{97} -6.54962e8 q^{98} +(5.30265e6 - 5.30265e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

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