LMFDB - Embedded newform 17.10.c.a.13.12

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			13.12
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.1

$q$-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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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	$0.319473\pi$
$2$			38.1697i			1.68688i	−0.537224	+	0.843440i	$0.680527\pi$
$3$	−95.6730	−	95.6730i	−0.681936	−	0.681936i	0.278500	−	0.960436i	$-0.410163\pi$
$3$	−95.6730	−	95.6730i	−0.681936	−	0.681936i	−0.960436	+	0.278500i	$0.910163\pi$
$4$	−944.927			−1.84556
$5$	−23.8207	−	23.8207i	−0.0170447	−	0.0170447i	0.698533	−	0.715578i	$-0.253836\pi$
$5$	−23.8207	−	23.8207i	−0.0170447	−	0.0170447i	−0.715578	+	0.698533i	$0.753836\pi$
$6$	3651.81	−	3651.81i	1.15034	−	1.15034i
$7$	3405.47	−	3405.47i	0.536087	−	0.536087i	−0.386290	−	0.922377i	$-0.626244\pi$
$7$	3405.47	−	3405.47i	0.536087	−	0.536087i	0.922377	+	0.386290i	$0.126244\pi$
$8$		−	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	−0.745664	−	0.666322i	$-0.767867\pi$
$11$	−3852.71	+	3852.71i	−0.0793414	+	0.0793414i	0.666322	+	0.745664i	$0.267867\pi$
$12$	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	$-0.777209\pi$
$19$		−	731833.i		−	1.28831i	0.764894	−	0.644156i	$-0.222791\pi$
$20$	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	−0.311352	−	0.950295i	$-0.600782\pi$
$23$	857507.	−	857507.i	0.638943	−	0.638943i	0.950295	+	0.311352i	$0.100782\pi$
$24$	−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	0.990734	−	0.135819i	$-0.0433666\pi$
$29$	3.25622e6	+	3.25622e6i	0.854915	+	0.854915i	−0.135819	+	0.990734i	$0.543367\pi$
$30$	−173977.			−0.0392145
$31$	−5.70757e6	−	5.70757e6i	−1.11000	−	1.11000i	−0.993149	−	0.116853i	$-0.962719\pi$
$31$	−5.70757e6	−	5.70757e6i	−1.11000	−	1.11000i	−0.116853	−	0.993149i	$-0.537281\pi$
$32$		−	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	0.365702	−	0.930732i	$-0.380829\pi$
$37$	−6.44138e6	−	6.44138e6i	−0.565030	−	0.565030i	−0.930732	+	0.365702i	$0.880829\pi$
$38$	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	−0.999373	−	0.0354036i	$-0.988728\pi$
$41$	−1.74418e7	+	1.74418e7i	−0.963970	+	0.963970i	0.0354036	+	0.999373i	$0.488728\pi$
$42$		−	2.48722e7i		−	1.23337i
$43$			1.54236e7i			0.687984i	0.938973	+	0.343992i	$0.111779\pi$
$43$			1.54236e7i			0.687984i	−0.938973	+	0.343992i	$0.888221\pi$
$44$	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	$-0.999406\pi$
$53$		−	214544.i		−	0.00373487i	0.999998	−	0.00186744i	$-0.000594424\pi$
$54$	−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	$-0.748861\pi$
$59$		−	1.32098e8i		−	1.41926i	0.704573	−	0.709632i	$-0.251139\pi$
$60$		−	4.30697e6i		−	0.0429034i
$61$	−4.51277e7	+	4.51277e7i	−0.417310	+	0.417310i	−0.884276	−	0.466965i	$-0.845347\pi$
$61$	−4.51277e7	+	4.51277e7i	−0.417310	+	0.417310i	0.466965	+	0.884276i	$0.345347\pi$
$62$	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	0.888778	−	0.458338i	$-0.151555\pi$
$71$	9.21670e7	+	9.21670e7i	0.430440	+	0.430440i	−0.458338	+	0.888778i	$0.651555\pi$
$72$	−2.27437e7			−0.0997388
$73$	−8.35127e7	−	8.35127e7i	−0.344191	−	0.344191i	0.513749	−	0.857940i	$-0.328256\pi$
$73$	−8.35127e7	−	8.35127e7i	−0.344191	−	0.344191i	−0.857940	+	0.513749i	$0.828256\pi$
$74$	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	−0.360973	−	0.932576i	$-0.617555\pi$
$79$	1.97887e8	−	1.97887e8i	0.571604	−	0.571604i	0.932576	+	0.360973i	$0.117555\pi$
$80$	−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	$-0.835214\pi$
$83$		−	4.27934e8i		−	0.989751i	0.868964	−	0.494875i	$-0.164786\pi$
$84$	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	0.0867772	−	0.996228i	$-0.472343\pi$
$97$	−7.92961e8	−	7.92961e8i	−0.909450	−	0.909450i	−0.996228	+	0.0867772i	$0.972343\pi$
$98$	−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	0.974937	−	0.222482i	$-0.0714160\pi$
$107$	1.02025e9	+	1.02025e9i	0.752454	+	0.752454i	−0.222482	+	0.974937i	$0.571416\pi$
$108$	1.90385e9	−	1.90385e9i	1.34656	−	1.34656i
$109$	3.02723e8	−	3.02723e8i	0.205412	−	0.205412i	−0.596902	−	0.802314i	$-0.703602\pi$
$109$	3.02723e8	−	3.02723e8i	0.205412	−	0.205412i	0.802314	+	0.596902i	$0.203602\pi$
$110$			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	−0.718680	−	0.695341i	$-0.755253\pi$
$113$	−4.04503e7	+	4.04503e7i	−0.0233383	+	0.0233383i	0.695341	+	0.718680i	$0.255253\pi$
$114$	−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	$0.231048\pi$
$127$			3.89197e9i			1.32756i	−0.747929	+	0.663778i	$0.768952\pi$
$128$			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	0.100180	−	0.994969i	$-0.468058\pi$
$131$	−3.01607e9	−	3.01607e9i	−0.894790	−	0.894790i	−0.994969	+	0.100180i	$0.968058\pi$
$132$	−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	0.961683	−	0.274163i	$-0.0884007\pi$
$139$	3.02588e9	+	3.02588e9i	0.687520	+	0.687520i	−0.274163	+	0.961683i	$0.588401\pi$
$140$	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	$-0.714016\pi$
$151$		−	9.99616e9i		−	1.56472i	0.622826	−	0.782360i	$-0.285984\pi$
$152$	−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	−0.991968	−	0.126485i	$-0.959630\pi$
$163$	−7.80015e9	+	7.80015e9i	−0.865483	+	0.865483i	0.126485	+	0.991968i	$0.459630\pi$
$164$	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	0.956798	−	0.290755i	$-0.0939065\pi$
$167$	6.69462e9	+	6.69462e9i	0.666042	+	0.666042i	−0.290755	+	0.956798i	$0.593906\pi$
$168$			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	0.769309	−	0.638877i	$-0.220601\pi$
$173$	1.53670e9	+	1.53670e9i	0.130431	+	0.130431i	−0.638877	+	0.769309i	$0.720601\pi$
$174$	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	$-0.961604\pi$
$179$		−	3.30556e9i		−	0.240662i	0.992734	−	0.120331i	$-0.0383955\pi$
$180$	3.09798e7	−	3.09798e7i	0.00219965	−	0.00219965i
$181$	1.40868e9	−	1.40868e9i	0.0975570	−	0.0975570i	−0.656644	−	0.754201i	$-0.728025\pi$
$181$	1.40868e9	−	1.40868e9i	0.0975570	−	0.0975570i	0.754201	+	0.656644i	$0.228025\pi$
$182$	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	−0.999965	−	0.00839843i	$-0.997327\pi$
$193$	−1.91130e10	+	1.91130e10i	−0.991566	+	0.991566i	0.00839843	+	0.999965i	$0.497327\pi$
$194$	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	−0.953331	−	0.301928i	$-0.902370\pi$
$197$	−1.37704e10	+	1.37704e10i	−0.651402	+	0.651402i	0.301928	+	0.953331i	$0.402370\pi$
$198$	−2.02401e8	+	2.02401e8i	−0.00935877	+	0.00935877i
$199$	9.20906e9	+	9.20906e9i	0.416271	+	0.416271i	0.883916	−	0.467645i	$-0.154897\pi$
$199$	9.20906e9	+	9.20906e9i	0.416271	+	0.416271i	−0.467645	+	0.883916i	$0.654897\pi$
$200$	−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	0.267758	−	0.963486i	$-0.413717\pi$
$211$	3.54499e10	−	3.54499e10i	1.23124	−	1.23124i	0.963486	−	0.267758i	$-0.0862829\pi$
$212$			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	$-0.962834\pi$
$223$		−	8.60424e9i		−	0.232992i	0.993191	−	0.116496i	$-0.0371662\pi$
$224$	−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	0.517798	−	0.855503i	$-0.326752\pi$
$227$	5.49392e10	−	5.49392e10i	1.37330	−	1.37330i	0.855503	−	0.517798i	$-0.173248\pi$
$228$	6.61607e10	−	6.61607e10i	1.62141	−	1.62141i
$229$		−	4.32400e10i		−	1.03902i	−0.854463	−	0.519512i	$-0.826114\pi$
$229$		−	4.32400e10i		−	1.03902i	0.854463	−	0.519512i	$-0.173886\pi$
$230$		−	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	0.664225	−	0.747533i	$-0.268762\pi$
$233$	−3.74790e9	−	3.74790e9i	−0.0833079	−	0.0833079i	−0.747533	+	0.664225i	$0.768762\pi$
$234$	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	0.997182	+	0.0750155i	$0.0239006\pi$
$241$	5.61502e10	+	5.61502e10i	1.07220	+	1.07220i	0.0750155	+	0.997182i	$0.476099\pi$
$242$	−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	$0.146384\pi$
$257$			6.20805e10i			0.887679i	−0.896106	+	0.443839i	$0.853616\pi$
$258$	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	$0.0643034\pi$
$263$			3.11356e10i			0.401288i	−0.979664	+	0.200644i	$0.935697\pi$
$264$		−	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	0.547961	−	0.836504i	$-0.315404\pi$
$269$	−2.47797e10	−	2.47797e10i	−0.288543	−	0.288543i	−0.836504	+	0.547961i	$0.815404\pi$
$270$			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	0.187876	−	0.982193i	$-0.439840\pi$
$277$	−7.78310e10	−	7.78310e10i	−0.794317	−	0.794317i	−0.982193	+	0.187876i	$0.939840\pi$
$278$	−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	$-0.943474\pi$
$281$		−	3.69253e10i		−	0.353302i	0.984274	−	0.176651i	$-0.0565263\pi$
$282$	1.11103e11	−	1.11103e11i	1.04618	−	1.04618i
$283$	−2.63672e10	+	2.63672e10i	−0.244357	+	0.244357i	−0.818650	−	0.574293i	$-0.805277\pi$
$283$	−2.63672e10	+	2.63672e10i	−0.244357	+	0.244357i	0.574293	+	0.818650i	$0.305277\pi$
$284$	−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	0.809406	−	0.587250i	$-0.199789\pi$
$311$	3.66504e10	+	3.66504e10i	0.222156	+	0.222156i	−0.587250	+	0.809406i	$0.699789\pi$
$312$	−1.33689e11	+	1.33689e11i	−0.798729	+	0.798729i
$313$	−2.07139e11	+	2.07139e11i	−1.21986	+	1.21986i	−0.252186	+	0.967679i	$0.581149\pi$
$313$	−2.07139e11	+	2.07139e11i	−1.21986	+	1.21986i	−0.967679	+	0.252186i	$0.918851\pi$
$314$		−	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	−0.492329	−	0.870409i	$-0.663854\pi$
$317$	6.79753e10	−	6.79753e10i	0.378081	−	0.378081i	0.870409	+	0.492329i	$0.163854\pi$
$318$	−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	$-0.754022\pi$
$331$		−	3.04918e11i		−	1.39623i	0.715985	−	0.698116i	$-0.245978\pi$
$332$			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	0.406168	−	0.913798i	$-0.366865\pi$
$337$	−1.20194e11	−	1.20194e11i	−0.507630	−	0.507630i	−0.913798	+	0.406168i	$0.866865\pi$
$338$		−	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	−0.919186	−	0.393823i	$-0.871152\pi$
$347$	−1.41887e11	+	1.41887e11i	−0.525363	+	0.525363i	0.393823	+	0.919186i	$0.371152\pi$
$348$			5.88751e11i			2.15191i
$349$			3.31661e10i			0.119669i	0.998208	+	0.0598343i	$0.0190572\pi$
$349$			3.31661e10i			0.119669i	−0.998208	+	0.0598343i	$0.980943\pi$
$350$	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	$0.0143151\pi$
$359$			2.82979e10i			0.0899142i	−0.998989	+	0.0449571i	$0.985685\pi$
$360$	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	−0.478693	−	0.877982i	$-0.658889\pi$
$367$	1.38767e11	−	1.38767e11i	0.399289	−	0.399289i	0.877982	+	0.478693i	$0.158889\pi$
$368$	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	0.656962	−	0.753924i	$-0.271841\pi$
$379$	−3.89471e10	−	3.89471e10i	−0.0969615	−	0.0969615i	−0.753924	+	0.656962i	$0.771841\pi$
$380$	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	$-0.830441\pi$
$383$		−	4.27720e11i		−	1.01570i	0.861446	−	0.507849i	$-0.169559\pi$
$384$	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	$0.251323\pi$
$389$			6.41336e11i			1.42008i	−0.704162	+	0.710039i	$0.748677\pi$
$390$	−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	−0.218451	−	0.975848i	$-0.570100\pi$
$397$	3.74870e11	−	3.74870e11i	0.757397	−	0.757397i	0.975848	+	0.218451i	$0.0701004\pi$
$398$	−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	−0.949520	−	0.313707i	$-0.898429\pi$
$401$	−3.29215e11	+	3.29215e11i	−0.635813	+	0.635813i	0.313707	+	0.949520i	$0.398429\pi$
$402$	−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	−0.858950	−	0.512060i	$-0.828883\pi$
$419$	−2.18854e11	+	2.18854e11i	−0.346890	+	0.346890i	0.512060	+	0.858950i	$0.328883\pi$
$420$	−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	−0.959614	−	0.281319i	$-0.909228\pi$
$431$	−4.85922e11	+	4.85922e11i	−0.678295	+	0.678295i	0.281319	+	0.959614i	$0.409228\pi$
$432$	−2.96058e11	+	2.96058e11i	−0.408978	+	0.408978i
$433$			1.31231e11i			0.179407i	0.995969	+	0.0897036i	$0.0285920\pi$
$433$			1.31231e11i			0.179407i	−0.995969	+	0.0897036i	$0.971408\pi$
$434$		−	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	0.371560	−	0.928409i	$-0.378823\pi$
$439$	−4.33339e11	−	4.33339e11i	−0.556848	−	0.556848i	−0.928409	+	0.371560i	$0.878823\pi$
$440$		−	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	−0.144178	−	0.989552i	$-0.546054\pi$
$449$	7.28043e11	−	7.28043e11i	0.845374	−	0.845374i	0.989552	+	0.144178i	$0.0460538\pi$
$450$		−	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	$-0.675761\pi$
$457$		−	1.58775e12i		−	1.70278i	0.524535	−	0.851389i	$-0.324239\pi$
$458$	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	$0.348355\pi$
$461$			1.72351e12i			1.77730i	−0.458588	+	0.888649i	$0.651645\pi$
$462$	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	$-0.781739\pi$
$467$		−	1.30167e12i		−	1.26641i	0.773984	−	0.633206i	$-0.218261\pi$
$468$			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	0.0536687	−	0.998559i	$-0.482909\pi$
$479$	−1.08866e12	−	1.08866e12i	−0.944890	−	0.944890i	−0.998559	+	0.0536687i	$0.982909\pi$
$480$	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	−0.147096	+	0.989122i	$0.546993\pi$
$487$	−1.41040e12	+	1.41040e12i	−1.13622	+	1.13622i	−0.989122	+	0.147096i	$0.953007\pi$
$488$	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	$0.201061\pi$
$491$			1.52090e12i			1.18096i	−0.807053	+	0.590480i	$0.798939\pi$
$492$	−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	−0.0641439	−	0.997941i	$-0.520432\pi$
$499$	1.29332e12	−	1.29332e12i	0.933797	−	0.933797i	0.997941	+	0.0641439i	$0.0204317\pi$
$500$	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	−0.968701	−	0.248230i	$-0.920151\pi$
$503$	−1.03436e12	+	1.03436e12i	−0.720472	+	0.720472i	0.248230	+	0.968701i	$0.420151\pi$
$504$	−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	−0.515810	−	0.856703i	$-0.672509\pi$
$521$	5.73309e11	−	5.73309e11i	0.340893	−	0.340893i	0.856703	+	0.515810i	$0.172509\pi$
$522$	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	0.717444	−	0.696617i	$-0.245312\pi$
$541$	4.14970e10	+	4.14970e10i	0.0208271	+	0.0208271i	−0.696617	+	0.717444i	$0.745312\pi$
$542$		−	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	0.562595	−	0.826733i	$-0.309803\pi$
$547$	−5.53062e11	−	5.53062e11i	−0.264138	−	0.264138i	−0.826733	+	0.562595i	$0.809803\pi$
$548$	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	$0.0474700\pi$
$563$			7.08396e11i			0.297159i	−0.988900	+	0.148579i	$0.952530\pi$
$564$	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	$0.0395515\pi$
$569$			6.19769e11i			0.247870i	−0.992290	+	0.123935i	$0.960449\pi$
$570$			1.27322e11i			0.0505206i
$571$	2.03361e12	−	2.03361e12i	0.800580	−	0.800580i	−0.182607	−	0.983186i	$-0.558453\pi$
$571$	2.03361e12	−	2.03361e12i	0.800580	−	0.800580i	0.983186	+	0.182607i	$0.0584534\pi$
$572$	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	$-0.972872\pi$
$587$		−	4.89722e11i		−	0.170247i	0.996370	−	0.0851233i	$-0.0271284\pi$
$588$	−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	$0.0692623\pi$
$593$			1.30014e12i			0.431762i	−0.976420	+	0.215881i	$0.930738\pi$
$594$	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	0.431427	−	0.902148i	$-0.358010\pi$
$601$	4.26533e12	−	4.26533e12i	1.33357	−	1.33357i	0.902148	−	0.431427i	$-0.141990\pi$
$602$	−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	0.637310	−	0.770607i	$-0.280047\pi$
$607$	−4.45831e11	−	4.45831e11i	−0.133297	−	0.133297i	−0.770607	+	0.637310i	$0.780047\pi$
$608$	−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	0.899545	−	0.436828i	$-0.143898\pi$
$617$	1.66571e12	+	1.66571e12i	0.462717	+	0.462717i	−0.436828	+	0.899545i	$0.643898\pi$
$618$	3.25302e12	−	3.25302e12i	0.897096	−	0.897096i
$619$	1.14158e12	−	1.14158e12i	0.312535	−	0.312535i	−0.533356	−	0.845891i	$-0.679069\pi$
$619$	1.14158e12	−	1.14158e12i	0.312535	−	0.312535i	0.845891	+	0.533356i	$0.179069\pi$
$620$		−	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	$-0.758808\pi$
$631$		−	5.47382e12i		−	1.37454i	0.726400	−	0.687272i	$-0.241192\pi$
$632$	−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	0.610563	−	0.791967i	$-0.290943\pi$
$641$	−7.75369e11	−	7.75369e11i	−0.181404	−	0.181404i	−0.791967	+	0.610563i	$0.790943\pi$
$642$	7.45153e12			1.73116
$643$	−2.59943e12	−	2.59943e12i	−0.599692	−	0.599692i	0.340539	−	0.940231i	$-0.389391\pi$
$643$	−2.59943e12	−	2.59943e12i	−0.599692	−	0.599692i	−0.940231	+	0.340539i	$0.889391\pi$
$644$			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	−0.939538	−	0.342445i	$-0.888745\pi$
$653$	−2.77429e12	+	2.77429e12i	−0.597093	+	0.597093i	0.342445	+	0.939538i	$0.388745\pi$
$654$		−	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	$0.238557\pi$
$661$			6.68704e12i			1.36247i	−0.732064	+	0.681235i	$0.761443\pi$
$662$	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	−0.837447	−	0.546518i	$-0.815953\pi$
$673$	−1.54830e12	+	1.54830e12i	−0.290929	+	0.290929i	0.546518	+	0.837447i	$0.315953\pi$
$674$	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	0.766419	−	0.642341i	$-0.222037\pi$
$677$	6.78181e11	+	6.78181e11i	0.124079	+	0.124079i	−0.642341	+	0.766419i	$0.722037\pi$
$678$			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	0.563644	−	0.826018i	$-0.309399\pi$
$683$	−1.49216e12	−	1.49216e12i	−0.262374	−	0.262374i	−0.826018	+	0.563644i	$0.809399\pi$
$684$	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	−0.598999	−	0.800750i	$-0.704435\pi$
$691$	1.20911e12	−	1.20911e12i	0.201751	−	0.201751i	0.800750	+	0.598999i	$0.204435\pi$
$692$	−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	−0.999984	−	0.00557191i	$-0.998226\pi$
$709$	−6.76573e12	−	6.76573e12i	−1.00556	−	1.00556i	−0.00557191	−	0.999984i	$-0.501774\pi$
$710$	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	0.577592	−	0.816325i	$-0.303992\pi$
$719$	−1.71077e12	−	1.71077e12i	−0.238733	−	0.238733i	−0.816325	+	0.577592i	$0.803992\pi$
$720$	−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	$-0.987876\pi$
$733$		−	5.95250e11i		−	0.0761608i	0.999275	−	0.0380804i	$-0.0121243\pi$
$734$	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	$0.140956\pi$
$739$			6.94825e12i			0.856990i	−0.903544	+	0.428495i	$0.859044\pi$
$740$		−	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	0.826758	−	0.562557i	$-0.190182\pi$
$743$	2.19475e12	+	2.19475e12i	0.264201	+	0.264201i	−0.562557	+	0.826758i	$0.690182\pi$
$744$	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	0.942415	−	0.334446i	$-0.108549\pi$
$751$	5.29981e12	+	5.29981e12i	0.607968	+	0.607968i	−0.334446	+	0.942415i	$0.608549\pi$
$752$	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	$-0.909936\pi$
$757$		−	5.04488e12i		−	0.558366i	0.960238	−	0.279183i	$-0.0900637\pi$
$758$	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	$-0.940973\pi$
$773$		−	3.66057e12i		−	0.368757i	0.982855	−	0.184379i	$-0.0590272\pi$
$774$			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	0.999829	−	0.0184937i	$-0.00588706\pi$
$787$	1.05610e13	+	1.05610e13i	0.981335	+	0.981335i	−0.0184937	+	0.999829i	$0.505887\pi$
$788$	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	$-0.781490\pi$
$797$		−	1.44395e13i		−	1.26762i	0.773490	−	0.633809i	$-0.218510\pi$
$798$	−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	−0.127334	+	0.991860i	$0.540642\pi$
$809$	−1.36356e13	+	1.36356e13i	−1.11919	+	1.11919i	−0.991860	+	0.127334i	$0.959358\pi$
$810$	3.25900e11	−	3.25900e11i	0.0266012	−	0.0266012i
$811$	−7.98388e12	−	7.98388e12i	−0.648068	−	0.648068i	0.304458	−	0.952526i	$-0.401525\pi$
$811$	−7.98388e12	−	7.98388e12i	−0.648068	−	0.648068i	−0.952526	+	0.304458i	$0.901525\pi$
$812$	−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	0.959908	−	0.280316i	$-0.0904393\pi$
$821$	8.84692e12	+	8.84692e12i	0.679591	+	0.679591i	−0.280316	+	0.959908i	$0.590439\pi$
$822$	−2.12808e13	+	2.12808e13i	−1.62579	+	1.62579i
$823$	5.08254e12	−	5.08254e12i	0.386173	−	0.386173i	−0.487147	−	0.873320i	$-0.661962\pi$
$823$	5.08254e12	−	5.08254e12i	0.386173	−	0.386173i	0.873320	+	0.487147i	$0.161962\pi$
$824$		−	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	−0.959558	−	0.281510i	$-0.909165\pi$
$827$	−9.12086e12	+	9.12086e12i	−0.678049	+	0.678049i	0.281510	+	0.959558i	$0.409165\pi$
$828$	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	−0.684340	−	0.729163i	$-0.739910\pi$
$839$	6.43317e11	−	6.43317e11i	0.0448225	−	0.0448225i	0.729163	+	0.684340i	$0.239910\pi$
$840$	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	0.892833	−	0.450389i	$-0.148715\pi$
$853$	6.84115e12	+	6.84115e12i	0.442444	+	0.442444i	−0.450389	+	0.892833i	$0.648715\pi$
$854$	−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	−0.894566	−	0.446936i	$-0.852515\pi$
$857$	−7.06858e12	+	7.06858e12i	−0.447629	+	0.447629i	0.446936	+	0.894566i	$0.352515\pi$
$858$			2.37945e12i			0.149894i
$859$		−	1.80838e13i		−	1.13323i	−0.823981	−	0.566617i	$-0.808252\pi$
$859$		−	1.80838e13i		−	1.13323i	0.823981	−	0.566617i	$-0.191748\pi$
$860$	−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	−0.782739	−	0.622351i	$-0.786178\pi$
$877$	−2.80977e12	+	2.80977e12i	−0.160388	+	0.160388i	0.622351	+	0.782739i	$0.286178\pi$
$878$	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	0.681689	−	0.731642i	$-0.261246\pi$
$881$	−8.93195e11	−	8.93195e11i	−0.0499522	−	0.0499522i	−0.731642	+	0.681689i	$0.761246\pi$
$882$			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	0.233688	−	0.972312i	$-0.424920\pi$
$887$	−1.36169e13	−	1.36169e13i	−0.738623	−	0.738623i	−0.972312	+	0.233688i	$0.924920\pi$
$888$	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	−0.954828	−	0.297158i	$-0.903961\pi$
$907$	−1.34042e13	+	1.34042e13i	−0.657670	+	0.657670i	0.297158	+	0.954828i	$0.403961\pi$
$908$	−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	−0.276949	+	0.960885i	$0.589323\pi$
$911$	−2.57333e13	+	2.57333e13i	−1.23783	+	1.23783i	−0.960885	+	0.276949i	$0.910677\pi$
$912$	−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	−0.615096	−	0.788452i	$-0.710883\pi$
$929$	3.93559e12	−	3.93559e12i	0.173356	−	0.173356i	0.788452	+	0.615096i	$0.210883\pi$
$930$	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	$-0.867410\pi$
$937$		−	1.90936e13i		−	0.809207i	0.914492	−	0.404603i	$-0.132590\pi$
$938$	−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	−0.671988	−	0.740562i	$-0.734559\pi$
$941$	1.64934e12	−	1.64934e12i	0.0685737	−	0.0685737i	0.740562	+	0.671988i	$0.234559\pi$
$942$	−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	0.990956	−	0.134191i	$-0.0428435\pi$
$947$	2.12049e13	+	2.12049e13i	0.856765	+	0.856765i	−0.134191	+	0.990956i	$0.542843\pi$
$948$	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	$-0.830416\pi$
$967$		−	2.76210e13i		−	1.01583i	0.861407	−	0.507915i	$-0.169584\pi$
$968$	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	$-0.768539\pi$
$971$		−	3.68276e13i		−	1.32950i	0.747068	−	0.664748i	$-0.231461\pi$
$972$	−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	$-0.939884\pi$
$977$		−	1.06932e13i		−	0.375477i	0.982219	−	0.187739i	$-0.0601158\pi$
$978$			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	−0.999263	−	0.0383759i	$-0.987782\pi$
$983$	−3.03765e13	−	3.03765e13i	−1.03764	−	1.03764i	−0.0383759	−	0.999263i	$-0.512218\pi$
$984$		−	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	0.974422	+	0.224727i	$0.0721489\pi$
$991$	3.64086e13	+	3.64086e13i	1.19915	+	1.19915i	0.224727	+	0.974422i	$0.427851\pi$
$992$	−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	0.0500213	−	0.998748i	$-0.484071\pi$
$997$	3.27196e13	−	3.27196e13i	1.04877	−	1.04877i	0.998748	−	0.0500213i	$-0.0159289\pi$
$998$	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.13.12	yes	24
17.2	even	8		289.10.a.f.1.1		24
17.4	even	4	inner	17.10.c.a.4.1	✓	24
17.15	even	8		289.10.a.f.1.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.1	✓	24	17.4	even	4	inner
17.10.c.a.13.12	yes	24	1.1	even	1	trivial
289.10.a.f.1.1		24	17.2	even	8
289.10.a.f.1.2		24	17.15	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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