LMFDB - Embedded newform 17.10.c.a.13.6

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			13.6
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.42963i q^{2} +(150.879 + 150.879i) q^{3} +456.801 q^{4} +(210.983 + 210.983i) q^{5} +(1120.97 - 1120.97i) q^{6} +(-5461.47 + 5461.47i) q^{7} -7197.83i q^{8} +25845.7i q^{9} +O(q^{10})$	\(q-7.42963i q^{2} +(150.879 + 150.879i) q^{3} +456.801 q^{4} +(210.983 + 210.983i) q^{5} +(1120.97 - 1120.97i) q^{6} +(-5461.47 + 5461.47i) q^{7} -7197.83i q^{8} +25845.7i q^{9} +(1567.53 - 1567.53i) q^{10} +(6566.81 - 6566.81i) q^{11} +(68921.4 + 68921.4i) q^{12} +122491. q^{13} +(40576.7 + 40576.7i) q^{14} +63665.7i q^{15} +180405. q^{16} +(-343740. - 20755.1i) q^{17} +192024. q^{18} +464145. i q^{19} +(96377.3 + 96377.3i) q^{20} -1.64804e6 q^{21} +(-48789.0 - 48789.0i) q^{22} +(829781. - 829781. i) q^{23} +(1.08600e6 - 1.08600e6i) q^{24} -1.86410e6i q^{25} -910061. i q^{26} +(-929817. + 929817. i) q^{27} +(-2.49480e6 + 2.49480e6i) q^{28} +(929897. + 929897. i) q^{29} +473013. q^{30} +(-5.27129e6 - 5.27129e6i) q^{31} -5.02563e6i q^{32} +1.98158e6 q^{33} +(-154203. + 2.55386e6i) q^{34} -2.30456e6 q^{35} +1.18063e7i q^{36} +(1.11498e6 + 1.11498e6i) q^{37} +3.44843e6 q^{38} +(1.84812e7 + 1.84812e7i) q^{39} +(1.51862e6 - 1.51862e6i) q^{40} +(1.72411e7 - 1.72411e7i) q^{41} +1.22443e7i q^{42} +7.29437e6i q^{43} +(2.99972e6 - 2.99972e6i) q^{44} +(-5.45301e6 + 5.45301e6i) q^{45} +(-6.16497e6 - 6.16497e6i) q^{46} -5.46941e7 q^{47} +(2.72192e7 + 2.72192e7i) q^{48} -1.93017e7i q^{49} -1.38496e7 q^{50} +(-4.87315e7 - 5.49945e7i) q^{51} +5.59538e7 q^{52} -6.10696e7i q^{53} +(6.90820e6 + 6.90820e6i) q^{54} +2.77097e6 q^{55} +(3.93108e7 + 3.93108e7i) q^{56} +(-7.00296e7 + 7.00296e7i) q^{57} +(6.90879e6 - 6.90879e6i) q^{58} -8.90678e7i q^{59} +2.90825e7i q^{60} +(1.86288e7 - 1.86288e7i) q^{61} +(-3.91637e7 + 3.91637e7i) q^{62} +(-1.41155e8 - 1.41155e8i) q^{63} +5.50286e7 q^{64} +(2.58435e7 + 2.58435e7i) q^{65} -1.47224e7i q^{66} -2.68240e8 q^{67} +(-1.57021e8 - 9.48095e6i) q^{68} +2.50392e8 q^{69} +1.71220e7i q^{70} +(2.78042e8 + 2.78042e8i) q^{71} +1.86033e8 q^{72} +(1.98106e8 + 1.98106e8i) q^{73} +(8.28392e6 - 8.28392e6i) q^{74} +(2.81252e8 - 2.81252e8i) q^{75} +2.12022e8i q^{76} +7.17289e7i q^{77} +(1.37309e8 - 1.37309e8i) q^{78} +(-4.29542e8 + 4.29542e8i) q^{79} +(3.80624e7 + 3.80624e7i) q^{80} +2.28142e8 q^{81} +(-1.28095e8 - 1.28095e8i) q^{82} -5.22381e8i q^{83} -7.52825e8 q^{84} +(-6.81444e7 - 7.69024e7i) q^{85} +5.41945e7 q^{86} +2.80603e8i q^{87} +(-4.72668e7 - 4.72668e7i) q^{88} -2.71477e8 q^{89} +(4.05138e7 + 4.05138e7i) q^{90} +(-6.68980e8 + 6.68980e8i) q^{91} +(3.79045e8 - 3.79045e8i) q^{92} -1.59065e9i q^{93} +4.06357e8i q^{94} +(-9.79269e7 + 9.79269e7i) q^{95} +(7.58260e8 - 7.58260e8i) q^{96} +(6.26088e8 + 6.26088e8i) q^{97} -1.43405e8 q^{98} +(1.69724e8 + 1.69724e8i) 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 $

$2$		−	7.42963i		−	0.328346i	−0.986432	−	0.164173i	$-0.947504\pi$
$2$		−	7.42963i		−	0.328346i	0.986432	−	0.164173i	$-0.0524956\pi$
$3$	150.879	+	150.879i	1.07543	+	1.07543i	0.996913	+	0.0785166i	$0.0250184\pi$
$3$	150.879	+	150.879i	1.07543	+	1.07543i	0.0785166	+	0.996913i	$0.474982\pi$
$4$	456.801			0.892189
$5$	210.983	+	210.983i	0.150967	+	0.150967i	0.778550	−	0.627583i	$-0.215956\pi$
$5$	210.983	+	210.983i	0.150967	+	0.150967i	−0.627583	+	0.778550i	$0.715956\pi$
$6$	1120.97	−	1120.97i	0.353113	−	0.353113i
$7$	−5461.47	+	5461.47i	−0.859743	+	0.859743i	−0.991308	−	0.131565i	$-0.958000\pi$
$7$	−5461.47	+	5461.47i	−0.859743	+	0.859743i	0.131565	+	0.991308i	$0.458000\pi$
$8$		−	7197.83i		−	0.621293i
$9$			25845.7i			1.31310i
$10$	1567.53	−	1567.53i	0.0495696	−	0.0495696i
$11$	6566.81	−	6566.81i	0.135234	−	0.135234i	−0.636249	−	0.771484i	$-0.719515\pi$
$11$	6566.81	−	6566.81i	0.135234	−	0.135234i	0.771484	+	0.636249i	$0.219515\pi$
$12$	68921.4	+	68921.4i	0.959486	+	0.959486i
$13$	122491.			1.18948			0.594741	−	0.803917i	$-0.297254\pi$
$13$	122491.			1.18948			0.594741	+	0.803917i	$0.297254\pi$
$14$	40576.7	+	40576.7i	0.282293	+	0.282293i
$15$			63665.7i			0.324710i
$16$	180405.			0.688189
$17$	−343740.	−	20755.1i	−0.998182	−	0.0602705i
$17$	−343740.	−	20755.1i	−0.998182	−	0.0602705i
$18$	192024.			0.431151
$19$			464145.i			0.817077i	0.912741	+	0.408538i	$0.133961\pi$
$19$			464145.i			0.817077i	−0.912741	+	0.408538i	$0.866039\pi$
$20$	96377.3	+	96377.3i	0.134691	+	0.134691i
$21$	−1.64804e6			−1.84919
$22$	−48789.0	−	48789.0i	−0.0444037	−	0.0444037i
$23$	829781.	−	829781.i	0.618285	−	0.618285i	−0.326807	−	0.945091i	$-0.605973\pi$
$23$	829781.	−	829781.i	0.618285	−	0.618285i	0.945091	+	0.326807i	$0.105973\pi$
$24$	1.08600e6	−	1.08600e6i	0.668157	−	0.668157i
$25$		−	1.86410e6i		−	0.954418i
$26$		−	910061.i		−	0.390562i
$27$	−929817.	+	929817.i	−0.336714	+	0.336714i
$28$	−2.49480e6	+	2.49480e6i	−0.767053	+	0.767053i
$29$	929897.	+	929897.i	0.244143	+	0.244143i	0.818562	−	0.574419i	$-0.194772\pi$
$29$	929897.	+	929897.i	0.244143	+	0.244143i	−0.574419	+	0.818562i	$0.694772\pi$
$30$	473013.			0.106617
$31$	−5.27129e6	−	5.27129e6i	−1.02515	−	1.02515i	−0.999675	−	0.0254783i	$-0.991889\pi$
$31$	−5.27129e6	−	5.27129e6i	−1.02515	−	1.02515i	−0.0254783	−	0.999675i	$-0.508111\pi$
$32$		−	5.02563e6i		−	0.847258i
$33$	1.98158e6			0.290870
$34$	−154203.	+	2.55386e6i	−0.0197896	+	0.327749i
$35$	−2.30456e6			−0.259586
$36$			1.18063e7i			1.17153i
$37$	1.11498e6	+	1.11498e6i	0.0978050	+	0.0978050i	0.754316	−	0.656511i	$-0.227969\pi$
$37$	1.11498e6	+	1.11498e6i	0.0978050	+	0.0978050i	−0.656511	+	0.754316i	$0.727969\pi$
$38$	3.44843e6			0.268284
$39$	1.84812e7	+	1.84812e7i	1.27920	+	1.27920i
$40$	1.51862e6	−	1.51862e6i	0.0937950	−	0.0937950i
$41$	1.72411e7	−	1.72411e7i	0.952880	−	0.952880i	−0.0460589	−	0.998939i	$-0.514666\pi$
$41$	1.72411e7	−	1.72411e7i	0.952880	−	0.952880i	0.998939	+	0.0460589i	$0.0146662\pi$
$42$			1.22443e7i			0.607173i
$43$			7.29437e6i			0.325372i	0.986678	+	0.162686i	$0.0520157\pi$
$43$			7.29437e6i			0.325372i	−0.986678	+	0.162686i	$0.947984\pi$
$44$	2.99972e6	−	2.99972e6i	0.120655	−	0.120655i
$45$	−5.45301e6	+	5.45301e6i	−0.198235	+	0.198235i
$46$	−6.16497e6	−	6.16497e6i	−0.203012	−	0.203012i
$47$	−5.46941e7			−1.63493			−0.817466	−	0.575977i	$-0.804622\pi$
$47$	−5.46941e7			−1.63493			−0.817466	+	0.575977i	$0.804622\pi$
$48$	2.72192e7	+	2.72192e7i	0.740099	+	0.740099i
$49$		−	1.93017e7i		−	0.478315i
$50$	−1.38496e7			−0.313380
$51$	−4.87315e7	−	5.49945e7i	−1.00866	−	1.13829i
$52$	5.59538e7			1.06124
$53$		−	6.10696e7i		−	1.06312i	−0.847020	−	0.531561i	$-0.821606\pi$
$53$		−	6.10696e7i		−	1.06312i	0.847020	−	0.531561i	$-0.178394\pi$
$54$	6.90820e6	+	6.90820e6i	0.110559	+	0.110559i
$55$	2.77097e6			0.0408320
$56$	3.93108e7	+	3.93108e7i	0.534152	+	0.534152i
$57$	−7.00296e7	+	7.00296e7i	−0.878708	+	0.878708i
$58$	6.90879e6	−	6.90879e6i	0.0801634	−	0.0801634i
$59$		−	8.90678e7i		−	0.956944i	−0.878103	−	0.478472i	$-0.841191\pi$
$59$		−	8.90678e7i		−	0.956944i	0.878103	−	0.478472i	$-0.158809\pi$
$60$			2.90825e7i			0.289702i
$61$	1.86288e7	−	1.86288e7i	0.172266	−	0.172266i	−0.615708	−	0.787974i	$-0.711130\pi$
$61$	1.86288e7	−	1.86288e7i	0.172266	−	0.172266i	0.787974	+	0.615708i	$0.211130\pi$
$62$	−3.91637e7	+	3.91637e7i	−0.336606	+	0.336606i
$63$	−1.41155e8	−	1.41155e8i	−1.12893	−	1.12893i
$64$	5.50286e7			0.409995
$65$	2.58435e7	+	2.58435e7i	0.179573	+	0.179573i
$66$		−	1.47224e7i		−	0.0955062i
$67$	−2.68240e8			−1.62625			−0.813124	−	0.582091i	$-0.802235\pi$
$67$	−2.68240e8			−1.62625			−0.813124	+	0.582091i	$0.802235\pi$
$68$	−1.57021e8	−	9.48095e6i	−0.890567	−	0.0537727i
$69$	2.50392e8			1.32984
$70$			1.71220e7i			0.0852342i
$71$	2.78042e8	+	2.78042e8i	1.29852	+	1.29852i	0.929371	+	0.369146i	$0.120350\pi$
$71$	2.78042e8	+	2.78042e8i	1.29852	+	1.29852i	0.369146	+	0.929371i	$0.379650\pi$
$72$	1.86033e8			0.815818
$73$	1.98106e8	+	1.98106e8i	0.816481	+	0.816481i	0.985596	−	0.169116i	$-0.0540912\pi$
$73$	1.98106e8	+	1.98106e8i	0.816481	+	0.816481i	−0.169116	+	0.985596i	$0.554091\pi$
$74$	8.28392e6	−	8.28392e6i	0.0321139	−	0.0321139i
$75$	2.81252e8	−	2.81252e8i	1.02641	−	1.02641i
$76$			2.12022e8i			0.728986i
$77$			7.17289e7i			0.232534i
$78$	1.37309e8	−	1.37309e8i	0.420022	−	0.420022i
$79$	−4.29542e8	+	4.29542e8i	−1.24075	+	1.24075i	−0.281058	+	0.959691i	$0.590685\pi$
$79$	−4.29542e8	+	4.29542e8i	−1.24075	+	1.24075i	−0.959691	+	0.281058i	$0.909315\pi$
$80$	3.80624e7	+	3.80624e7i	0.103894	+	0.103894i
$81$	2.28142e8			0.588874
$82$	−1.28095e8	−	1.28095e8i	−0.312875	−	0.312875i
$83$		−	5.22381e8i		−	1.20819i	−0.796912	−	0.604096i	$-0.793534\pi$
$83$		−	5.22381e8i		−	1.20819i	0.796912	−	0.604096i	$-0.206466\pi$
$84$	−7.52825e8			−1.64982
$85$	−6.81444e7	−	7.69024e7i	−0.141594	−	0.159792i
$86$	5.41945e7			0.106835
$87$			2.80603e8i			0.525117i
$88$	−4.72668e7	−	4.72668e7i	−0.0840203	−	0.0840203i
$89$	−2.71477e8			−0.458647			−0.229324	−	0.973350i	$-0.573651\pi$
$89$	−2.71477e8			−0.458647			−0.229324	+	0.973350i	$0.573651\pi$
$90$	4.05138e7	+	4.05138e7i	0.0650897	+	0.0650897i
$91$	−6.68980e8	+	6.68980e8i	−1.02265	+	1.02265i
$92$	3.79045e8	−	3.79045e8i	0.551626	−	0.551626i
$93$		−	1.59065e9i		−	2.20496i
$94$			4.06357e8i			0.536824i
$95$	−9.79269e7	+	9.79269e7i	−0.123352	+	0.123352i
$96$	7.58260e8	−	7.58260e8i	0.911166	−	0.911166i
$97$	6.26088e8	+	6.26088e8i	0.718063	+	0.718063i	0.968208	−	0.250145i	$-0.0804783\pi$
$97$	6.26088e8	+	6.26088e8i	0.718063	+	0.718063i	−0.250145	+	0.968208i	$0.580478\pi$
$98$	−1.43405e8			−0.157053
$99$	1.69724e8	+	1.69724e8i	0.177576	+	0.177576i
$100$		−	8.51521e8i		−	0.851521i
$101$	1.26751e8			0.121201			0.0606004	−	0.998162i	$-0.480698\pi$
$101$	1.26751e8			0.121201			0.0606004	+	0.998162i	$0.480698\pi$
$102$	−4.08589e8	+	3.62057e8i	−0.373754	+	0.331189i
$103$	−1.02919e9			−0.901007			−0.450504	−	0.892775i	$-0.648756\pi$
$103$	−1.02919e9			−0.901007			−0.450504	+	0.892775i	$0.648756\pi$
$104$		−	8.81667e8i		−	0.739018i
$105$	−3.47709e8	−	3.47709e8i	−0.279167	−	0.279167i
$106$	−4.53724e8			−0.349072
$107$	1.29224e9	+	1.29224e9i	0.953051	+	0.953051i	0.998946	−	0.0458957i	$-0.0146142\pi$
$107$	1.29224e9	+	1.29224e9i	0.953051	+	0.953051i	−0.0458957	+	0.998946i	$0.514614\pi$
$108$	−4.24741e8	+	4.24741e8i	−0.300412	+	0.300412i
$109$	−1.72603e7	+	1.72603e7i	−0.0117119	+	0.0117119i	−0.712939	−	0.701227i	$-0.752636\pi$
$109$	−1.72603e7	+	1.72603e7i	−0.0117119	+	0.0117119i	0.701227	+	0.712939i	$0.252636\pi$
$110$		−	2.05873e7i		−	0.0134070i
$111$			3.36454e8i			0.210365i
$112$	−9.85275e8	+	9.85275e8i	−0.591666	+	0.591666i
$113$	4.90898e8	−	4.90898e8i	0.283229	−	0.283229i	−0.551166	−	0.834396i	$-0.685817\pi$
$113$	4.90898e8	−	4.90898e8i	0.283229	−	0.283229i	0.834396	+	0.551166i	$0.185817\pi$
$114$	5.20294e8	+	5.20294e8i	0.288521	+	0.288521i
$115$	3.50140e8			0.186682
$116$	4.24778e8	+	4.24778e8i	0.217821	+	0.217821i
$117$			3.16586e9i			1.56191i
$118$	−6.61741e8			−0.314209
$119$	1.99068e9	−	1.76397e9i	0.909997	−	0.806363i
$120$	4.58255e8			0.201740
$121$			2.27170e9i			0.963423i
$122$	−1.38405e8	−	1.38405e8i	−0.0565629	−	0.0565629i
$123$	5.20263e9			2.04951
$124$	−2.40793e9	−	2.40793e9i	−0.914630	−	0.914630i
$125$	8.05370e8	−	8.05370e8i	0.295053	−	0.295053i
$126$	−1.04873e9	+	1.04873e9i	−0.370679	+	0.370679i
$127$		−	5.69057e8i		−	0.194106i	−0.995279	−	0.0970530i	$-0.969058\pi$
$127$		−	5.69057e8i		−	0.194106i	0.995279	−	0.0970530i	$-0.0309416\pi$
$128$		−	2.98196e9i		−	0.981878i
$129$	−1.10056e9	+	1.10056e9i	−0.349914	+	0.349914i
$130$	1.92008e8	−	1.92008e8i	0.0589622	−	0.0589622i
$131$	8.87374e8	+	8.87374e8i	0.263260	+	0.263260i	0.826377	−	0.563117i	$-0.190398\pi$
$131$	8.87374e8	+	8.87374e8i	0.263260	+	0.263260i	−0.563117	+	0.826377i	$0.690398\pi$
$132$	9.05188e8			0.259511
$133$	−2.53492e9	−	2.53492e9i	−0.702476	−	0.702476i
$134$			1.99292e9i			0.533973i
$135$	−3.92352e8			−0.101666
$136$	−1.49392e8	+	2.47418e9i	−0.0374457	+	0.620164i
$137$	−5.43864e9			−1.31901			−0.659505	−	0.751700i	$-0.729234\pi$
$137$	−5.43864e9			−1.31901			−0.659505	+	0.751700i	$0.729234\pi$
$138$		−	1.86032e9i		−	0.436649i
$139$	2.33384e8	+	2.33384e8i	0.0530278	+	0.0530278i	0.733123	−	0.680096i	$-0.238062\pi$
$139$	2.33384e8	+	2.33384e8i	0.0530278	+	0.0530278i	−0.680096	+	0.733123i	$0.738062\pi$
$140$	−1.05272e9			−0.231600
$141$	−8.25216e9	−	8.25216e9i	−1.75825	−	1.75825i
$142$	2.06575e9	−	2.06575e9i	0.426364	−	0.426364i
$143$	8.04373e8	−	8.04373e8i	0.160859	−	0.160859i
$144$			4.66268e9i			0.903659i
$145$			3.92386e8i			0.0737152i
$146$	1.47186e9	−	1.47186e9i	0.268088	−	0.268088i
$147$	2.91222e9	−	2.91222e9i	0.514394	−	0.514394i
$148$	5.09325e8	+	5.09325e8i	0.0872605	+	0.0872605i
$149$	−1.26223e9			−0.209797			−0.104898	−	0.994483i	$-0.533452\pi$
$149$	−1.26223e9			−0.209797			−0.104898	+	0.994483i	$0.533452\pi$
$150$	−2.08960e9	−	2.08960e9i	−0.337018	−	0.337018i
$151$			1.24303e10i			1.94574i	0.231345	+	0.972872i	$0.425687\pi$
$151$			1.24303e10i			1.94574i	−0.231345	+	0.972872i	$0.574313\pi$
$152$	3.34084e9			0.507644
$153$	5.36430e8	−	8.88419e9i	0.0791410	−	1.31071i
$154$	5.32919e8			0.0763516
$155$		−	2.22431e9i		−	0.309530i
$156$	8.44223e9	+	8.44223e9i	1.14129	+	1.14129i
$157$	−9.77853e9			−1.28447			−0.642237	−	0.766506i	$-0.721994\pi$
$157$	−9.77853e9			−1.28447			−0.642237	+	0.766506i	$0.721994\pi$
$158$	3.19134e9	+	3.19134e9i	0.407395	+	0.407395i
$159$	9.21409e9	−	9.21409e9i	1.14331	−	1.14331i
$160$	1.06032e9	−	1.06032e9i	0.127908	−	0.127908i
$161$			9.06366e9i			1.06313i
$162$		−	1.69501e9i		−	0.193354i
$163$	−9.35010e9	+	9.35010e9i	−1.03746	+	1.03746i	−0.0381909	+	0.999270i	$0.512159\pi$
$163$	−9.35010e9	+	9.35010e9i	−1.03746	+	1.03746i	−0.999270	+	0.0381909i	$0.987841\pi$
$164$	7.87575e9	−	7.87575e9i	0.850149	−	0.850149i
$165$	4.18081e8	+	4.18081e8i	0.0439119	+	0.0439119i
$166$	−3.88110e9			−0.396705
$167$	2.21589e9	+	2.21589e9i	0.220457	+	0.220457i	0.808691	−	0.588234i	$-0.200177\pi$
$167$	2.21589e9	+	2.21589e9i	0.220457	+	0.220457i	−0.588234	+	0.808691i	$0.700177\pi$
$168$			1.18623e10i			1.14889i
$169$	4.39948e9			0.414869
$170$	−5.71356e8	+	5.06288e8i	−0.0524671	+	0.0464919i
$171$	−1.19962e10			−1.07290
$172$			3.33207e9i			0.290293i
$173$	−9.01583e9	−	9.01583e9i	−0.765241	−	0.765241i	0.212023	−	0.977265i	$-0.431995\pi$
$173$	−9.01583e9	−	9.01583e9i	−0.765241	−	0.765241i	−0.977265	+	0.212023i	$0.931995\pi$
$174$	2.08478e9			0.172420
$175$	1.01807e10	+	1.01807e10i	0.820554	+	0.820554i
$176$	1.18468e9	−	1.18468e9i	0.0930669	−	0.0930669i
$177$	1.34384e10	−	1.34384e10i	1.02913	−	1.02913i
$178$			2.01698e9i			0.150595i
$179$			5.42019e9i			0.394617i	0.980341	+	0.197308i	$0.0632201\pi$
$179$			5.42019e9i			0.394617i	−0.980341	+	0.197308i	$0.936780\pi$
$180$	−2.49094e9	+	2.49094e9i	−0.176863	+	0.176863i
$181$	1.10991e10	−	1.10991e10i	0.768661	−	0.768661i	−0.209210	−	0.977871i	$-0.567089\pi$
$181$	1.10991e10	−	1.10991e10i	0.768661	−	0.768661i	0.977871	+	0.209210i	$0.0670893\pi$
$182$	4.97027e9	+	4.97027e9i	0.335783	+	0.335783i
$183$	5.62136e9			0.370520
$184$	−5.97263e9	−	5.97263e9i	−0.384136	−	0.384136i
$185$			4.70486e8i			0.0295307i
$186$	−1.18179e10			−0.723991
$187$	−2.39357e9	+	2.12098e9i	−0.143139	+	0.126838i
$188$	−2.49843e10			−1.45867
$189$		−	1.01563e10i		−	0.578974i
$190$	7.27561e8	+	7.27561e8i	0.0405022	+	0.0405022i
$191$	1.15717e10			0.629139			0.314570	−	0.949234i	$-0.398140\pi$
$191$	1.15717e10			0.629139			0.314570	+	0.949234i	$0.398140\pi$
$192$	8.30264e9	+	8.30264e9i	0.440921	+	0.440921i
$193$	−9.85963e9	+	9.85963e9i	−0.511508	+	0.511508i	−0.914988	−	0.403480i	$-0.867800\pi$
$193$	−9.85963e9	+	9.85963e9i	−0.511508	+	0.511508i	0.403480	+	0.914988i	$0.367800\pi$
$194$	4.65160e9	−	4.65160e9i	0.235773	−	0.235773i
$195$			7.79846e9i			0.386236i
$196$		−	8.81705e9i		−	0.426747i
$197$	−8.10661e8	+	8.10661e8i	−0.0383479	+	0.0383479i	−0.726021	−	0.687673i	$-0.758632\pi$
$197$	−8.10661e8	+	8.10661e8i	−0.0383479	+	0.0383479i	0.687673	+	0.726021i	$0.258632\pi$
$198$	1.26098e9	−	1.26098e9i	0.0583064	−	0.0583064i
$199$	−1.53839e10	−	1.53839e10i	−0.695388	−	0.695388i	0.268024	−	0.963412i	$-0.413629\pi$
$199$	−1.53839e10	−	1.53839e10i	−0.695388	−	0.695388i	−0.963412	+	0.268024i	$0.913629\pi$
$200$	−1.34175e10			−0.592973
$201$	−4.04716e10	−	4.04716e10i	−1.74891	−	1.74891i
$202$		−	9.41713e8i		−	0.0397958i
$203$	−1.01572e10			−0.419800
$204$	−2.22606e10	−	2.51215e10i	−0.899913	−	1.01557i
$205$	7.27518e9			0.287708
$206$			7.64651e9i			0.295843i
$207$	2.14463e10	+	2.14463e10i	0.811868	+	0.811868i
$208$	2.20979e10			0.818589
$209$	3.04795e9	+	3.04795e9i	0.110497	+	0.110497i
$210$	−2.58335e9	+	2.58335e9i	−0.0916634	+	0.0916634i
$211$	3.17554e10	−	3.17554e10i	1.10293	−	1.10293i	0.108870	−	0.994056i	$-0.465277\pi$
$211$	3.17554e10	−	3.17554e10i	1.10293	−	1.10293i	0.994056	−	0.108870i	$-0.0347232\pi$
$212$		−	2.78966e10i		−	0.948506i
$213$			8.39012e10i			2.79293i
$214$	9.60086e9	−	9.60086e9i	0.312931	−	0.312931i
$215$	−1.53899e9	+	1.53899e9i	−0.0491205	+	0.0491205i
$216$	6.69267e9	+	6.69267e9i	0.209198	+	0.209198i
$217$	5.75780e10			1.76274
$218$	1.28238e8	+	1.28238e8i	0.00384557	+	0.00384557i
$219$			5.97800e10i			1.75613i
$220$	1.26578e9			0.0364298
$221$	−4.21049e10	−	2.54231e9i	−1.18732	−	0.0716907i
$222$	2.49973e9			0.0690725
$223$		−	2.69095e10i		−	0.728675i	−0.931267	−	0.364337i	$-0.881295\pi$
$223$		−	2.69095e10i		−	0.728675i	0.931267	−	0.364337i	$-0.118705\pi$
$224$	2.74473e10	+	2.74473e10i	0.728424	+	0.728424i
$225$	4.81789e10			1.25324
$226$	−3.64719e9	−	3.64719e9i	−0.0929973	−	0.0929973i
$227$	−2.62108e10	+	2.62108e10i	−0.655186	+	0.655186i	−0.954237	−	0.299051i	$-0.903330\pi$
$227$	−2.62108e10	+	2.62108e10i	−0.655186	+	0.655186i	0.299051	+	0.954237i	$0.403330\pi$
$228$	−3.19896e10	+	3.19896e10i	−0.783973	+	0.783973i
$229$		−	5.83786e10i		−	1.40280i	−0.712770	−	0.701398i	$-0.752560\pi$
$229$		−	5.83786e10i		−	1.40280i	0.712770	−	0.701398i	$-0.247440\pi$
$230$		−	2.60141e9i		−	0.0612962i
$231$	−1.08224e10	+	1.08224e10i	−0.250074	+	0.250074i
$232$	6.69324e9	−	6.69324e9i	0.151684	−	0.151684i
$233$	3.56054e10	+	3.56054e10i	0.791433	+	0.791433i	0.981727	−	0.190295i	$-0.0609443\pi$
$233$	3.56054e10	+	3.56054e10i	0.791433	+	0.791433i	−0.190295	+	0.981727i	$0.560944\pi$
$234$	2.35211e10			0.512846
$235$	−1.15395e10	−	1.15395e10i	−0.246821	−	0.246821i
$236$		−	4.06862e10i		−	0.853774i
$237$	−1.29617e11			−2.66868
$238$	−1.31057e10	−	1.47900e10i	−0.264766	−	0.298794i
$239$	−3.61330e10			−0.716331			−0.358165	−	0.933658i	$-0.616598\pi$
$239$	−3.61330e10			−0.716331			−0.358165	+	0.933658i	$0.616598\pi$
$240$			1.14856e10i			0.223462i
$241$	2.30963e10	+	2.30963e10i	0.441027	+	0.441027i	0.892357	−	0.451330i	$-0.149050\pi$
$241$	2.30963e10	+	2.30963e10i	0.441027	+	0.441027i	−0.451330	+	0.892357i	$0.649050\pi$
$242$	1.68779e10			0.316337
$243$	5.27233e10	+	5.27233e10i	0.970005	+	0.970005i
$244$	8.50963e9	−	8.50963e9i	0.153694	−	0.153694i
$245$	4.07235e9	−	4.07235e9i	0.0722100	−	0.0722100i
$246$		−	3.86536e10i		−	0.672949i
$247$			5.68535e10i			0.971898i
$248$	−3.79418e10	+	3.79418e10i	−0.636921	+	0.636921i
$249$	7.88161e10	−	7.88161e10i	1.29932	−	1.29932i
$250$	−5.98360e9	−	5.98360e9i	−0.0968797	−	0.0968797i
$251$	8.70058e10			1.38362			0.691809	−	0.722080i	$-0.256814\pi$
$251$	8.70058e10			1.38362			0.691809	+	0.722080i	$0.256814\pi$
$252$	−6.44799e10	−	6.44799e10i	−1.00721	−	1.00721i
$253$		−	1.08980e10i		−	0.167227i
$254$	−4.22788e9			−0.0637340
$255$	1.32139e9	−	2.18845e10i	0.0195704	−	0.324119i
$256$	6.01976e9			0.0875990
$257$		−	1.29137e11i		−	1.84651i	−0.384189	−	0.923255i	$-0.625519\pi$
$257$		−	1.29137e11i		−	1.84651i	0.384189	−	0.923255i	$-0.374481\pi$
$258$	8.17678e9	+	8.17678e9i	0.114893	+	0.114893i
$259$	−1.21789e10			−0.168174
$260$	1.18053e10	+	1.18053e10i	0.160213	+	0.160213i
$261$	−2.40338e10	+	2.40338e10i	−0.320583	+	0.320583i
$262$	6.59286e9	−	6.59286e9i	0.0864406	−	0.0864406i
$263$			1.10536e11i			1.42464i	0.701855	+	0.712319i	$0.252355\pi$
$263$			1.10536e11i			1.42464i	−0.701855	+	0.712319i	$0.747645\pi$
$264$		−	1.42631e10i		−	0.180716i
$265$	1.28847e10	−	1.28847e10i	0.160497	−	0.160497i
$266$	−1.88335e10	+	1.88335e10i	−0.230655	+	0.230655i
$267$	−4.09601e10	−	4.09601e10i	−0.493242	−	0.493242i
$268$	−1.22532e11			−1.45092
$269$	−3.37672e10	−	3.37672e10i	−0.393196	−	0.393196i	0.482629	−	0.875825i	$-0.339682\pi$
$269$	−3.37672e10	−	3.37672e10i	−0.393196	−	0.393196i	−0.875825	+	0.482629i	$0.839682\pi$
$270$			2.91503e9i			0.0333815i
$271$	−1.59153e10			−0.179248			−0.0896238	−	0.995976i	$-0.528566\pi$
$271$	−1.59153e10			−0.179248			−0.0896238	+	0.995976i	$0.528566\pi$
$272$	−6.20123e10	−	3.74432e9i	−0.686938	−	0.0414775i
$273$	−2.01869e11			−2.19957
$274$			4.04071e10i			0.433092i
$275$	−1.22412e10	−	1.22412e10i	−0.129070	−	0.129070i
$276$	1.14379e11			1.18647
$277$	1.91353e10	+	1.91353e10i	0.195289	+	0.195289i	0.797977	−	0.602688i	$-0.205904\pi$
$277$	1.91353e10	+	1.91353e10i	0.195289	+	0.195289i	−0.602688	+	0.797977i	$0.705904\pi$
$278$	1.73395e9	−	1.73395e9i	0.0174115	−	0.0174115i
$279$	1.36240e11	−	1.36240e11i	1.34613	−	1.34613i
$280$			1.65878e10i			0.161279i
$281$		−	2.22999e10i		−	0.213366i	−0.994293	−	0.106683i	$-0.965977\pi$
$281$		−	2.22999e10i		−	0.213366i	0.994293	−	0.106683i	$-0.0340230\pi$
$282$	−6.13105e10	+	6.13105e10i	−0.577316	+	0.577316i
$283$	1.08599e11	−	1.08599e11i	1.00643	−	1.00643i	0.00645397	−	0.999979i	$-0.497946\pi$
$283$	1.08599e11	−	1.08599e11i	1.00643	−	1.00643i	0.999979	−	0.00645397i	$-0.00205438\pi$
$284$	1.27010e11	+	1.27010e11i	1.15852	+	1.15852i
$285$	−2.95502e10			−0.265313
$286$	−5.97620e9	−	5.97620e9i	−0.0528175	−	0.0528175i
$287$			1.88324e11i			1.63846i
$288$	1.29891e11			1.11253
$289$	1.17726e11	+	1.42687e10i	0.992735	+	0.120322i
$290$	2.91528e9			0.0242041
$291$			1.88927e11i			1.54445i
$292$	9.04952e10	+	9.04952e10i	0.728455	+	0.728455i
$293$	−1.78080e11			−1.41159			−0.705797	−	0.708414i	$-0.749411\pi$
$293$	−1.78080e11			−1.41159			−0.705797	+	0.708414i	$0.749411\pi$
$294$	−2.16367e10	−	2.16367e10i	−0.168900	−	0.168900i
$295$	1.87918e10	−	1.87918e10i	0.144467	−	0.144467i
$296$	8.02547e9	−	8.02547e9i	0.0607656	−	0.0607656i
$297$			1.22119e10i			0.0910705i
$298$			9.37787e9i			0.0688860i
$299$	1.01641e11	−	1.01641e11i	0.735439	−	0.735439i
$300$	1.28476e11	−	1.28476e11i	0.915750	−	0.915750i
$301$	−3.98380e10	−	3.98380e10i	−0.279736	−	0.279736i
$302$	9.23526e10			0.638878
$303$	1.91240e10	+	1.91240e10i	0.130343	+	0.130343i
$304$			8.37340e10i			0.562303i
$305$	7.86071e9			0.0520131
$306$	−6.60063e10	−	3.98548e9i	−0.430367	−	0.0259857i
$307$	−3.09874e10			−0.199096			−0.0995480	−	0.995033i	$-0.531740\pi$
$307$	−3.09874e10			−0.199096			−0.0995480	+	0.995033i	$0.531740\pi$
$308$			3.27658e10i			0.207464i
$309$	−1.55283e11	−	1.55283e11i	−0.968970	−	0.968970i
$310$	−1.65258e10			−0.101633
$311$	−1.48346e11	−	1.48346e11i	−0.899196	−	0.899196i	0.0961692	−	0.995365i	$-0.469341\pi$
$311$	−1.48346e11	−	1.48346e11i	−0.899196	−	0.899196i	−0.995365	+	0.0961692i	$0.969341\pi$
$312$	1.33025e11	−	1.33025e11i	0.794761	−	0.794761i
$313$	−4.27382e10	+	4.27382e10i	−0.251690	+	0.251690i	−0.821663	−	0.569973i	$-0.806954\pi$
$313$	−4.27382e10	+	4.27382e10i	−0.251690	+	0.251690i	0.569973	+	0.821663i	$0.306954\pi$
$314$			7.26509e10i			0.421752i
$315$		−	5.95629e10i		−	0.340862i
$316$	−1.96215e11	+	1.96215e11i	−1.10698	+	1.10698i
$317$	−2.26497e11	+	2.26497e11i	−1.25978	+	1.25978i	−0.308587	+	0.951196i	$0.599856\pi$
$317$	−2.26497e11	+	2.26497e11i	−1.25978	+	1.25978i	−0.951196	+	0.308587i	$0.900144\pi$
$318$	−6.84573e10	−	6.84573e10i	−0.375403	−	0.375403i
$319$	1.22129e10			0.0660330
$320$	1.16101e10	+	1.16101e10i	0.0618959	+	0.0618959i
$321$			3.89942e11i			2.04988i
$322$	6.73396e10			0.349075
$323$	9.63339e9	−	1.59545e11i	0.0492456	−	0.815591i
$324$	1.04215e11			0.525386
$325$		−	2.28335e11i		−	1.13526i
$326$	6.94678e10	+	6.94678e10i	0.340647	+	0.340647i
$327$	−5.20842e9			−0.0251907
$328$	−1.24099e11	−	1.24099e11i	−0.592018	−	0.592018i
$329$	2.98710e11	−	2.98710e11i	1.40562	−	1.40562i
$330$	3.10619e9	−	3.10619e9i	0.0144183	−	0.0144183i
$331$			4.42168e10i			0.202470i	0.994863	+	0.101235i	$0.0322794\pi$
$331$			4.42168e10i			0.202470i	−0.994863	+	0.101235i	$0.967721\pi$
$332$		−	2.38624e11i		−	1.07793i
$333$	−2.88175e10	+	2.88175e10i	−0.128427	+	0.128427i
$334$	1.64632e10	−	1.64632e10i	0.0723861	−	0.0723861i
$335$	−5.65941e10	−	5.65941e10i	−0.245510	−	0.245510i
$336$	−2.97314e11			−1.27259
$337$	2.43966e10	+	2.43966e10i	0.103037	+	0.103037i	0.756746	−	0.653709i	$-0.226788\pi$
$337$	2.43966e10	+	2.43966e10i	0.103037	+	0.103037i	−0.653709	+	0.756746i	$0.726788\pi$
$338$		−	3.26865e10i		−	0.136221i
$339$	1.48132e11			0.609186
$340$	−3.11284e10	−	3.51291e10i	−0.126329	−	0.142564i
$341$	−6.92311e10			−0.277272
$342$			8.91270e10i			0.352283i
$343$	−1.14974e11	−	1.14974e11i	−0.448515	−	0.448515i
$344$	5.25036e10			0.202151
$345$	5.28286e10	+	5.28286e10i	0.200763	+	0.200763i
$346$	−6.69843e10	+	6.69843e10i	−0.251264	+	0.251264i
$347$	4.36707e10	−	4.36707e10i	0.161699	−	0.161699i	−0.621620	−	0.783319i	$-0.713525\pi$
$347$	4.36707e10	−	4.36707e10i	0.161699	−	0.161699i	0.783319	+	0.621620i	$0.213525\pi$
$348$			1.28180e11i			0.468503i
$349$			7.62659e10i			0.275179i	0.990489	+	0.137590i	$0.0439355\pi$
$349$			7.62659e10i			0.275179i	−0.990489	+	0.137590i	$0.956064\pi$
$350$	7.56389e10	−	7.56389e10i	0.269426	−	0.269426i
$351$	−1.13894e11	+	1.13894e11i	−0.400515	+	0.400515i
$352$	−3.30023e10	−	3.30023e10i	−0.114578	−	0.114578i
$353$	8.21034e10			0.281433			0.140717	−	0.990050i	$-0.455059\pi$
$353$	8.21034e10			0.281433			0.140717	+	0.990050i	$0.455059\pi$
$354$	−9.98425e10	−	9.98425e10i	−0.337910	−	0.337910i
$355$			1.17324e11i			0.392068i
$356$	−1.24011e11			−0.409200
$357$	5.66496e11	+	3.42052e10i	1.84582	+	0.111451i
$358$	4.02700e10			0.129571
$359$		−	3.07800e11i		−	0.978011i	−0.872281	−	0.489006i	$-0.837360\pi$
$359$		−	3.07800e11i		−	0.978011i	0.872281	−	0.489006i	$-0.162640\pi$
$360$	3.92498e10	+	3.92498e10i	0.123162	+	0.123162i
$361$	1.07257e11			0.332386
$362$	−8.24623e10	−	8.24623e10i	−0.252387	−	0.252387i
$363$	−3.42751e11	+	3.42751e11i	−1.03609	+	1.03609i
$364$	−3.05590e11	+	3.05590e11i	−0.912396	+	0.912396i
$365$			8.35943e10i			0.246524i
$366$		−	4.17646e10i		−	0.121659i
$367$	−1.18051e11	+	1.18051e11i	−0.339681	+	0.339681i	−0.856247	−	0.516566i	$-0.827210\pi$
$367$	−1.18051e11	+	1.18051e11i	−0.339681	+	0.339681i	0.516566	+	0.856247i	$0.327210\pi$
$368$	1.49696e11	−	1.49696e11i	0.425497	−	0.425497i
$369$	4.45609e11	+	4.45609e11i	1.25122	+	1.25122i
$370$	3.49554e9			0.00969631
$371$	3.33530e11	+	3.33530e11i	0.914012	+	0.914012i
$372$		−	7.26609e11i		−	1.96724i
$373$	−2.08619e11			−0.558038			−0.279019	−	0.960286i	$-0.590009\pi$
$373$	−2.08619e11			−0.558038			−0.279019	+	0.960286i	$0.590009\pi$
$374$	1.57581e10	+	1.77833e10i	0.0416468	+	0.0469993i
$375$	2.43026e11			0.634618
$376$			3.93679e11i			1.01577i
$377$	1.13904e11	+	1.13904e11i	0.290404	+	0.290404i
$378$	−7.54579e10			−0.190104
$379$	3.66060e10	+	3.66060e10i	0.0911329	+	0.0911329i	0.751204	−	0.660071i	$-0.229474\pi$
$379$	3.66060e10	+	3.66060e10i	0.0911329	+	0.0911329i	−0.660071	+	0.751204i	$0.729474\pi$
$380$	−4.47331e10	+	4.47331e10i	−0.110053	+	0.110053i
$381$	8.58585e10	−	8.58585e10i	0.208747	−	0.208747i
$382$		−	8.59734e10i		−	0.206576i
$383$			2.51526e11i			0.597295i	0.954364	+	0.298647i	$0.0965355\pi$
$383$			2.51526e11i			0.597295i	−0.954364	+	0.298647i	$0.903465\pi$
$384$	4.49915e11	−	4.49915e11i	1.05594	−	1.05594i
$385$	−1.51336e10	+	1.51336e10i	−0.0351050	+	0.0351050i
$386$	7.32534e10	+	7.32534e10i	0.167952	+	0.167952i
$387$	−1.88528e11			−0.427244
$388$	2.85997e11	+	2.85997e11i	0.640648	+	0.640648i
$389$		−	7.12928e11i		−	1.57860i	−0.614007	−	0.789301i	$-0.710443\pi$
$389$		−	7.12928e11i		−	1.57860i	0.614007	−	0.789301i	$-0.289557\pi$
$390$	5.79397e10			0.126819
$391$	−3.02451e11	+	2.68007e11i	−0.654425	+	0.579896i
$392$	−1.38931e11			−0.297174
$393$			2.67771e11i			0.566236i
$394$	6.02291e9	+	6.02291e9i	0.0125914	+	0.0125914i
$395$	−1.81252e11			−0.374625
$396$	7.75299e10	+	7.75299e10i	0.158431	+	0.158431i
$397$	−3.32501e11	+	3.32501e11i	−0.671794	+	0.671794i	−0.958129	−	0.286336i	$-0.907563\pi$
$397$	−3.32501e11	+	3.32501e11i	−0.671794	+	0.671794i	0.286336	+	0.958129i	$0.407563\pi$
$398$	−1.14297e11	+	1.14297e11i	−0.228328	+	0.228328i
$399$		−	7.64929e11i		−	1.51093i
$400$		−	3.36292e11i		−	0.656820i
$401$	5.15951e10	−	5.15951e10i	0.0996457	−	0.0996457i	−0.655526	−	0.755172i	$-0.727553\pi$
$401$	5.15951e10	−	5.15951e10i	0.0996457	−	0.0996457i	0.755172	+	0.655526i	$0.227553\pi$
$402$	−3.00689e11	+	3.00689e11i	−0.574250	+	0.574250i
$403$	−6.45684e11	−	6.45684e11i	−1.21940	−	1.21940i
$404$	5.78999e10			0.108134
$405$	4.81341e10	+	4.81341e10i	0.0889007	+	0.0889007i
$406$			7.54643e10i			0.137840i
$407$	1.46438e10			0.0264532
$408$	−3.95841e11	+	3.50761e11i	−0.707213	+	0.626672i
$409$	5.81498e11			1.02753			0.513764	−	0.857932i	$-0.328251\pi$
$409$	5.81498e11			1.02753			0.513764	+	0.857932i	$0.328251\pi$
$410$		−	5.40519e10i		−	0.0944678i
$411$	−8.20575e11	−	8.20575e11i	−1.41850	−	1.41850i
$412$	−4.70135e11			−0.803869
$413$	4.86441e11	+	4.86441e11i	0.822726	+	0.822726i
$414$	1.59338e11	−	1.59338e11i	0.266574	−	0.266574i
$415$	1.10214e11	−	1.10214e11i	0.182398	−	0.182398i
$416$		−	6.15593e11i		−	1.00780i
$417$			7.04252e10i			0.114055i
$418$	2.26452e10	−	2.26452e10i	0.0362813	−	0.0362813i
$419$	−2.37853e11	+	2.37853e11i	−0.377004	+	0.377004i	−0.870020	−	0.493016i	$-0.835894\pi$
$419$	−2.37853e11	+	2.37853e11i	−0.377004	+	0.377004i	0.493016	+	0.870020i	$0.335894\pi$
$420$	−1.58834e11	−	1.58834e11i	−0.249069	−	0.249069i
$421$	5.95939e11			0.924555			0.462277	−	0.886735i	$-0.347032\pi$
$421$	5.95939e11			0.924555			0.462277	+	0.886735i	$0.347032\pi$
$422$	−2.35931e11	−	2.35931e11i	−0.362142	−	0.362142i
$423$		−	1.41361e12i		−	2.14682i
$424$	−4.39568e11			−0.660511
$425$	−3.86895e10	+	6.40764e11i	−0.0575233	+	0.952683i
$426$	6.23355e11			0.917048
$427$			2.03481e11i			0.296209i
$428$	5.90296e11	+	5.90296e11i	0.850301	+	0.850301i
$429$	2.42725e11			0.345985
$430$	1.14341e10	+	1.14341e10i	0.0161285	+	0.0161285i
$431$	−5.55197e11	+	5.55197e11i	−0.774996	+	0.774996i	−0.978975	−	0.203979i	$-0.934612\pi$
$431$	−5.55197e11	+	5.55197e11i	−0.774996	+	0.774996i	0.203979	+	0.978975i	$0.434612\pi$
$432$	−1.67743e11	+	1.67743e11i	−0.231723	+	0.231723i
$433$		−	1.00079e11i		−	0.136819i	−0.997657	−	0.0684094i	$-0.978208\pi$
$433$		−	1.00079e11i		−	0.136819i	0.997657	−	0.0684094i	$-0.0217924\pi$
$434$		−	4.27783e11i		−	0.578788i
$435$	−5.92026e10	+	5.92026e10i	−0.0792755	+	0.0792755i
$436$	−7.88451e9	+	7.88451e9i	−0.0104493	+	0.0104493i
$437$	3.85139e11	+	3.85139e11i	0.505186	+	0.505186i
$438$	4.44144e11			0.576620
$439$	4.57283e11	+	4.57283e11i	0.587618	+	0.587618i	0.936986	−	0.349368i	$-0.113604\pi$
$439$	4.57283e11	+	4.57283e11i	0.587618	+	0.587618i	−0.349368	+	0.936986i	$0.613604\pi$
$440$		−	1.99450e10i		−	0.0253686i
$441$	4.98867e11			0.628074
$442$	−1.88884e10	+	3.12824e11i	−0.0235394	+	0.389852i
$443$	5.21586e11			0.643442			0.321721	−	0.946835i	$-0.395739\pi$
$443$	5.21586e11			0.643442			0.321721	+	0.946835i	$0.395739\pi$
$444$			1.53693e11i			0.187685i
$445$	−5.72772e10	−	5.72772e10i	−0.0692408	−	0.0692408i
$446$	−1.99928e11			−0.239258
$447$	−1.90443e11	−	1.90443e11i	−0.225622	−	0.225622i
$448$	−3.00537e11	+	3.00537e11i	−0.352490	+	0.352490i
$449$	−5.46803e11	+	5.46803e11i	−0.634925	+	0.634925i	−0.949299	−	0.314374i	$-0.898205\pi$
$449$	−5.46803e11	+	5.46803e11i	−0.634925	+	0.634925i	0.314374	+	0.949299i	$0.398205\pi$
$450$		−	3.57951e11i		−	0.411498i
$451$		−	2.26438e11i		−	0.257724i
$452$	2.24242e11	−	2.24242e11i	0.252694	−	0.252694i
$453$	−1.87547e12	+	1.87547e12i	−2.09251	+	2.09251i
$454$	1.94737e11	+	1.94737e11i	0.215128	+	0.215128i
$455$	−2.82287e11			−0.308773
$456$	5.04061e11	+	5.04061e11i	0.545936	+	0.545936i
$457$		−	1.10713e12i		−	1.18734i	−0.804710	−	0.593669i	$-0.797679\pi$
$457$		−	1.10713e12i		−	1.18734i	0.804710	−	0.593669i	$-0.202321\pi$
$458$	−4.33732e11			−0.460603
$459$	3.38914e11	−	3.00317e11i	0.356395	−	0.315808i
$460$	1.59944e11			0.166555
$461$		−	7.20595e11i		−	0.743083i	−0.928416	−	0.371541i	$-0.878829\pi$
$461$		−	7.20595e11i		−	0.743083i	0.928416	−	0.371541i	$-0.121171\pi$
$462$	8.04061e10	+	8.04061e10i	0.0821107	+	0.0821107i
$463$	7.75230e11			0.784000			0.392000	−	0.919965i	$-0.371783\pi$
$463$	7.75230e11			0.784000			0.392000	+	0.919965i	$0.371783\pi$
$464$	1.67758e11	+	1.67758e11i	0.168016	+	0.168016i
$465$	3.35600e11	−	3.35600e11i	0.332877	−	0.332877i
$466$	2.64535e11	−	2.64535e11i	0.259864	−	0.259864i
$467$			1.33811e12i			1.30187i	0.759134	+	0.650934i	$0.225623\pi$
$467$			1.33811e12i			1.30187i	−0.759134	+	0.650934i	$0.774377\pi$
$468$			1.44617e12i			1.39351i
$469$	1.46498e12	−	1.46498e12i	1.39815	−	1.39815i
$470$	−8.57345e10	+	8.57345e10i	−0.0810429	+	0.0810429i
$471$	−1.47537e12	−	1.47537e12i	−1.38136	−	1.38136i
$472$	−6.41095e11			−0.594543
$473$	4.79007e10	+	4.79007e10i	0.0440014	+	0.0440014i
$474$			9.63009e11i			0.876250i
$475$	8.65212e11			0.779832
$476$	9.09343e11	−	8.05784e11i	0.811889	−	0.719428i
$477$	1.57838e12			1.39598
$478$			2.68455e11i			0.235205i
$479$	−4.78799e11	−	4.78799e11i	−0.415569	−	0.415569i	0.468104	−	0.883673i	$-0.344937\pi$
$479$	−4.78799e11	−	4.78799e11i	−0.415569	−	0.415569i	−0.883673	+	0.468104i	$0.844937\pi$
$480$	3.19960e11			0.275113
$481$	1.36575e11	+	1.36575e11i	0.116337	+	0.116337i
$482$	1.71597e11	−	1.71597e11i	0.144810	−	0.144810i
$483$	−1.36751e12	+	1.36751e12i	−1.14332	+	1.14332i
$484$			1.03771e12i			0.859555i
$485$			2.64188e11i			0.216808i
$486$	3.91714e11	−	3.91714e11i	0.318498	−	0.318498i
$487$	6.45783e11	−	6.45783e11i	0.520243	−	0.520243i	−0.397402	−	0.917645i	$-0.630088\pi$
$487$	6.45783e11	−	6.45783e11i	0.520243	−	0.520243i	0.917645	+	0.397402i	$0.130088\pi$
$488$	−1.34087e11	−	1.34087e11i	−0.107028	−	0.107028i
$489$	−2.82146e12			−2.23143
$490$	−3.02560e10	−	3.02560e10i	−0.0237099	−	0.0237099i
$491$		−	1.46909e12i		−	1.14073i	−0.821391	−	0.570365i	$-0.806802\pi$
$491$		−	1.46909e12i		−	1.14073i	0.821391	−	0.570365i	$-0.193198\pi$
$492$	2.37656e12			1.82855
$493$	−3.00343e11	−	3.38943e11i	−0.228984	−	0.258414i
$494$	4.22400e11			0.319119
$495$			7.16177e10i			0.0536164i
$496$	−9.50965e11	−	9.50965e11i	−0.705500	−	0.705500i
$497$	−3.03704e12			−2.23278
$498$	−5.85574e11	−	5.85574e11i	−0.426629	−	0.426629i
$499$	1.24018e12	−	1.24018e12i	0.895432	−	0.895432i	−0.0995964	−	0.995028i	$-0.531755\pi$
$499$	1.24018e12	−	1.24018e12i	0.895432	−	0.895432i	0.995028	+	0.0995964i	$0.0317552\pi$
$500$	3.67894e11	−	3.67894e11i	0.263243	−	0.263243i
$501$			6.68659e11i			0.474171i
$502$		−	6.46421e11i		−	0.454306i
$503$	−1.46385e12	+	1.46385e12i	−1.01962	+	1.01962i	−0.0198191	+	0.999804i	$0.506309\pi$
$503$	−1.46385e12	+	1.46385e12i	−1.01962	+	1.01962i	−0.999804	+	0.0198191i	$0.993691\pi$
$504$	−1.01601e12	+	1.01601e12i	−0.701394	+	0.701394i
$505$	2.67424e10	+	2.67424e10i	0.0182974	+	0.0182974i
$506$	−8.09684e10			−0.0549083
$507$	6.63787e11	+	6.63787e11i	0.446162	+	0.446162i
$508$		−	2.59946e11i		−	0.173179i
$509$	−8.76512e11			−0.578799			−0.289400	−	0.957208i	$-0.593456\pi$
$509$	−8.76512e11			−0.578799			−0.289400	+	0.957208i	$0.593456\pi$
$510$	−1.62593e11	−	9.81744e9i	−0.106423	−	0.00642588i
$511$	−2.16391e12			−1.40393
$512$		−	1.57149e12i		−	1.01064i
$513$	−4.31570e11	−	4.31570e11i	−0.275121	−	0.275121i
$514$	−9.59440e11			−0.606295
$515$	−2.17142e11	−	2.17142e11i	−0.136023	−	0.136023i
$516$	−5.02738e11	+	5.02738e11i	−0.312189	+	0.312189i
$517$	−3.59165e11	+	3.59165e11i	−0.221099	+	0.221099i
$518$			9.04848e10i			0.0552194i
$519$		−	2.72059e12i		−	1.64593i
$520$	1.86017e11	−	1.86017e11i	0.111568	−	0.111568i
$521$	1.51761e12	−	1.51761e12i	0.902380	−	0.902380i	−0.0932620	−	0.995642i	$-0.529729\pi$
$521$	1.51761e12	−	1.51761e12i	0.902380	−	0.902380i	0.995642	+	0.0932620i	$0.0297294\pi$
$522$	1.78562e11	+	1.78562e11i	0.105262	+	0.105262i
$523$	2.72230e12			1.59103			0.795514	−	0.605935i	$-0.207201\pi$
$523$	2.72230e12			1.59103			0.795514	+	0.605935i	$0.207201\pi$
$524$	4.05353e11	+	4.05353e11i	0.234878	+	0.234878i
$525$			3.07210e12i			1.76490i
$526$	8.21245e11			0.467775
$527$	1.70255e12	+	1.92136e12i	0.961503	+	1.08508i
$528$	3.57487e11			0.200174
$529$			4.24078e11i			0.235448i
$530$	−9.57283e10	−	9.57283e10i	−0.0526986	−	0.0526986i
$531$	2.30202e12			1.25656
$532$	−1.15795e12	−	1.15795e12i	−0.626741	−	0.626741i
$533$	2.11188e12	−	2.11188e12i	1.13343	−	1.13343i
$534$	−3.04319e11	+	3.04319e11i	−0.161954	+	0.161954i
$535$			5.45282e11i			0.287759i
$536$			1.93075e12i			1.01038i
$537$	−8.17790e11	+	8.17790e11i	−0.424383	+	0.424383i
$538$	−2.50878e11	+	2.50878e11i	−0.129105	+	0.129105i
$539$	−1.26751e11	−	1.26751e11i	−0.0646847	−	0.0646847i
$540$	−1.79227e11			−0.0907048
$541$	5.12550e11	+	5.12550e11i	0.257246	+	0.257246i	0.823933	−	0.566687i	$-0.191775\pi$
$541$	5.12550e11	+	5.12550e11i	0.257246	+	0.257246i	−0.566687	+	0.823933i	$0.691775\pi$
$542$			1.18245e11i			0.0588553i
$543$	3.34924e12			1.65328
$544$	−1.04308e11	+	1.72751e12i	−0.0510647	+	0.845718i
$545$	−7.28327e9			−0.00353624
$546$			1.49981e12i			0.722222i
$547$	1.98642e12	+	1.98642e12i	0.948697	+	0.948697i	0.998747	−	0.0500500i	$-0.0159381\pi$
$547$	1.98642e12	+	1.98642e12i	0.948697	+	0.948697i	−0.0500500	+	0.998747i	$0.515938\pi$
$548$	−2.48438e12			−1.17681
$549$	4.81473e11	+	4.81473e11i	0.226202	+	0.226202i
$550$	−9.09474e10	+	9.09474e10i	−0.0423797	+	0.0423797i
$551$	−4.31607e11	+	4.31607e11i	−0.199483	+	0.199483i
$552$		−	1.80228e12i		−	0.826222i
$553$		−	4.69186e12i		−	2.13345i
$554$	1.42168e11	−	1.42168e11i	0.0641223	−	0.0641223i
$555$	−7.09863e10	+	7.09863e10i	−0.0317582	+	0.0317582i
$556$	1.06610e11	+	1.06610e11i	0.0473108	+	0.0473108i
$557$	−1.37990e12			−0.607434			−0.303717	−	0.952762i	$-0.598228\pi$
$557$	−1.37990e12			−0.607434			−0.303717	+	0.952762i	$0.598228\pi$
$558$	−1.01221e12	−	1.01221e12i	−0.441996	−	0.441996i
$559$			8.93492e11i			0.387024i
$560$	−4.15753e11			−0.178644
$561$	−6.81149e11	−	4.11280e10i	−0.290341	−	0.0175309i
$562$	−1.65680e11			−0.0700579
$563$			4.17543e12i			1.75151i	0.482753	+	0.875757i	$0.339637\pi$
$563$			4.17543e12i			1.75151i	−0.482753	+	0.875757i	$0.660363\pi$
$564$	−3.76959e12	−	3.76959e12i	−1.56869	−	1.56869i
$565$	2.07143e11			0.0855168
$566$	−8.06847e11	−	8.06847e11i	−0.330459	−	0.330459i
$567$	−1.24599e12	+	1.24599e12i	−0.506280	+	0.506280i
$568$	2.00130e12	−	2.00130e12i	0.806760	−	0.806760i
$569$			3.40895e12i			1.36338i	0.731643	+	0.681688i	$0.238754\pi$
$569$			3.40895e12i			1.36338i	−0.731643	+	0.681688i	$0.761246\pi$
$570$			2.19547e11i			0.0871144i
$571$	2.38105e11	−	2.38105e11i	0.0937360	−	0.0937360i	−0.658684	−	0.752420i	$-0.728887\pi$
$571$	2.38105e11	−	2.38105e11i	0.0937360	−	0.0937360i	0.752420	+	0.658684i	$0.228887\pi$
$572$	3.67438e11	−	3.67438e11i	0.143517	−	0.143517i
$573$	1.74592e12	+	1.74592e12i	0.676595	+	0.676595i
$574$	1.39918e12			0.537983
$575$	−1.54679e12	−	1.54679e12i	−0.590102	−	0.590102i
$576$			1.42225e12i			0.538363i
$577$	−1.06334e12			−0.399374			−0.199687	−	0.979860i	$-0.563993\pi$
$577$	−1.06334e12			−0.399374			−0.199687	+	0.979860i	$0.563993\pi$
$578$	1.06011e11	−	8.74663e11i	0.0395073	−	0.325961i
$579$	−2.97521e12			−1.10018
$580$			1.79242e11i			0.0657679i
$581$	2.85297e12	+	2.85297e12i	1.03873	+	1.03873i
$582$	1.40365e12			0.507115
$583$	−4.01032e11	−	4.01032e11i	−0.143771	−	0.143771i
$584$	1.42594e12	−	1.42594e12i	0.507274	−	0.507274i
$585$	−6.67943e11	+	6.67943e11i	−0.235797	+	0.235797i
$586$			1.32307e12i			0.463492i
$587$			2.58249e11i			0.0897773i	0.998992	+	0.0448886i	$0.0142933\pi$
$587$			2.58249e11i			0.0897773i	−0.998992	+	0.0448886i	$0.985707\pi$
$588$	1.33030e12	−	1.33030e12i	0.458937	−	0.458937i
$589$	2.44664e12	−	2.44664e12i	0.837629	−	0.837629i
$590$	−1.39616e11	−	1.39616e11i	−0.0474353	−	0.0474353i
$591$	−2.44623e11			−0.0824809
$592$	2.01148e11	+	2.01148e11i	0.0673083	+	0.0673083i
$593$		−	3.46885e12i		−	1.15197i	−0.817461	−	0.575983i	$-0.804619\pi$
$593$		−	3.46885e12i		−	1.15197i	0.817461	−	0.575983i	$-0.195381\pi$
$594$	9.07296e10			0.0299027
$595$	7.92169e11	+	4.78314e10i	0.259114	+	0.0156454i
$596$	−5.76585e11			−0.187178
$597$		−	4.64220e12i		−	1.49568i
$598$	−7.55152e11	−	7.55152e11i	−0.241479	−	0.241479i
$599$	9.92138e10			0.0314885			0.0157442	−	0.999876i	$-0.494988\pi$
$599$	9.92138e10			0.0314885			0.0157442	+	0.999876i	$0.494988\pi$
$600$	−2.02441e12	−	2.02441e12i	−0.637701	−	0.637701i
$601$	−2.58480e12	+	2.58480e12i	−0.808148	+	0.808148i	−0.984353	−	0.176205i	$-0.943618\pi$
$601$	−2.58480e12	+	2.58480e12i	−0.808148	+	0.808148i	0.176205	+	0.984353i	$0.443618\pi$
$602$	−2.95981e11	+	2.95981e11i	−0.0918502	+	0.0918502i
$603$		−	6.93284e12i		−	2.13542i
$604$			5.67817e12i			1.73597i
$605$	−4.79291e11	+	4.79291e11i	−0.145446	+	0.145446i
$606$	1.42084e11	−	1.42084e11i	0.0427976	−	0.0427976i
$607$	2.84124e11	+	2.84124e11i	0.0849491	+	0.0849491i	0.748305	−	0.663355i	$-0.230868\pi$
$607$	2.84124e11	+	2.84124e11i	0.0849491	+	0.0849491i	−0.663355	+	0.748305i	$0.730868\pi$
$608$	2.33262e12			0.692274
$609$	−1.53251e12	−	1.53251e12i	−0.451465	−	0.451465i
$610$		−	5.84022e10i		−	0.0170783i
$611$	−6.69951e12			−1.94472
$612$	2.45042e11	−	4.05830e12i	0.0706087	−	1.16940i
$613$	−8.10830e11			−0.231930			−0.115965	−	0.993253i	$-0.536996\pi$
$613$	−8.10830e11			−0.231930			−0.115965	+	0.993253i	$0.536996\pi$
$614$			2.30225e11i			0.0653725i
$615$	1.09767e12	+	1.09767e12i	0.309409	+	0.309409i
$616$	5.16292e11			0.144472
$617$	1.78188e11	+	1.78188e11i	0.0494989	+	0.0494989i	0.731423	−	0.681924i	$-0.238857\pi$
$617$	1.78188e11	+	1.78188e11i	0.0494989	+	0.0494989i	−0.681924	+	0.731423i	$0.738857\pi$
$618$	−1.15369e12	+	1.15369e12i	−0.318158	+	0.318158i
$619$	−3.12312e12	+	3.12312e12i	−0.855029	+	0.855029i	−0.990747	−	0.135719i	$-0.956666\pi$
$619$	−3.12312e12	+	3.12312e12i	−0.855029	+	0.855029i	0.135719	+	0.990747i	$0.456666\pi$
$620$		−	1.01606e12i		−	0.276159i
$621$			1.54309e12i			0.416370i
$622$	−1.10216e12	+	1.10216e12i	−0.295248	+	0.295248i
$623$	1.48267e12	−	1.48267e12i	0.394318	−	0.394318i
$624$	3.33410e12	+	3.33410e12i	0.880335	+	0.880335i
$625$	−3.30098e12			−0.865331
$626$	3.17529e11	+	3.17529e11i	0.0826416	+	0.0826416i
$627$			9.19742e11i			0.237663i
$628$	−4.46684e12			−1.14599
$629$	−3.60123e11	−	4.06406e11i	−0.0917324	−	0.103522i
$630$	−4.42531e11			−0.111921
$631$		−	4.26928e12i		−	1.07207i	−0.844197	−	0.536034i	$-0.819922\pi$
$631$		−	4.26928e12i		−	1.07207i	0.844197	−	0.536034i	$-0.180078\pi$
$632$	3.09177e12	+	3.09177e12i	0.770869	+	0.770869i
$633$	9.58242e12			2.37224
$634$	1.68279e12	+	1.68279e12i	0.413645	+	0.413645i
$635$	1.20062e11	−	1.20062e11i	0.0293037	−	0.0293037i
$636$	4.20900e12	−	4.20900e12i	1.02005	−	1.02005i
$637$		−	2.36428e12i		−	0.568948i
$638$		−	9.07374e10i		−	0.0216817i
$639$	−7.18619e12	+	7.18619e12i	−1.70508	+	1.70508i
$640$	6.29145e11	−	6.29145e11i	0.148232	−	0.148232i
$641$	−5.48256e11	−	5.48256e11i	−0.128269	−	0.128269i	0.640058	−	0.768327i	$-0.278910\pi$
$641$	−5.48256e11	−	5.48256e11i	−0.128269	−	0.128269i	−0.768327	+	0.640058i	$0.778910\pi$
$642$	2.89713e12			0.673070
$643$	2.14290e12	+	2.14290e12i	0.494370	+	0.494370i	0.909680	−	0.415310i	$-0.136327\pi$
$643$	2.14290e12	+	2.14290e12i	0.494370	+	0.494370i	−0.415310	+	0.909680i	$0.636327\pi$
$644$			4.14028e12i			0.948514i
$645$	−4.64401e11			−0.105651
$646$	−1.18536e12	−	7.15725e10i	−0.267796	−	0.0161696i
$647$	7.24325e12			1.62504			0.812521	−	0.582932i	$-0.198095\pi$
$647$	7.24325e12			1.62504			0.812521	+	0.582932i	$0.198095\pi$
$648$		−	1.64213e12i		−	0.365863i
$649$	−5.84891e11	−	5.84891e11i	−0.129412	−	0.129412i
$650$	−1.69644e12			−0.372760
$651$	8.68728e12	+	8.68728e12i	1.89570	+	1.89570i
$652$	−4.27113e12	+	4.27113e12i	−0.925611	+	0.925611i
$653$	3.93770e12	−	3.93770e12i	0.847487	−	0.847487i	−0.142332	−	0.989819i	$-0.545460\pi$
$653$	3.93770e12	−	3.93770e12i	0.847487	−	0.847487i	0.989819	+	0.142332i	$0.0454602\pi$
$654$			3.86966e10i			0.00827129i
$655$			3.74442e11i			0.0794875i
$656$	3.11038e12	−	3.11038e12i	0.655762	−	0.655762i
$657$	−5.12020e12	+	5.12020e12i	−1.07212	+	1.07212i
$658$	−2.21931e12	−	2.21931e12i	−0.461531	−	0.461531i
$659$	2.52820e12			0.522187			0.261094	−	0.965313i	$-0.415917\pi$
$659$	2.52820e12			0.522187			0.261094	+	0.965313i	$0.415917\pi$
$660$	1.90980e11	+	1.90980e11i	0.0391777	+	0.0391777i
$661$			1.43661e12i			0.292707i	0.989232	+	0.146354i	$0.0467538\pi$
$661$			1.43661e12i			0.292707i	−0.989232	+	0.146354i	$0.953246\pi$
$662$	3.28514e11			0.0664804
$663$	−5.96915e12	−	6.73631e12i	−1.19978	−	1.35398i
$664$	−3.76001e12			−0.750641
$665$		−	1.06965e12i		−	0.212102i
$666$	2.14104e11	+	2.14104e11i	0.0421687	+	0.0421687i
$667$	1.54322e12			0.301899
$668$	1.01222e12	+	1.01222e12i	0.196689	+	0.196689i
$669$	4.06007e12	−	4.06007e12i	0.783638	−	0.783638i
$670$	−4.20474e11	+	4.20474e11i	−0.0806125	+	0.0806125i
$671$		−	2.44663e11i		−	0.0465926i
$672$			8.28243e12i			1.56674i
$673$	1.59816e12	−	1.59816e12i	0.300298	−	0.300298i	−0.540833	−	0.841130i	$-0.681891\pi$
$673$	1.59816e12	−	1.59816e12i	0.300298	−	0.300298i	0.841130	+	0.540833i	$0.181891\pi$
$674$	1.81258e11	−	1.81258e11i	0.0338319	−	0.0338319i
$675$	1.73327e12	+	1.73327e12i	0.321365	+	0.321365i
$676$	2.00968e12			0.370141
$677$	−5.99089e12	−	5.99089e12i	−1.09608	−	1.09608i	−0.994864	−	0.101216i	$-0.967727\pi$
$677$	−5.99089e12	−	5.99089e12i	−1.09608	−	1.09608i	−0.101216	−	0.994864i	$-0.532273\pi$
$678$		−	1.10057e12i		−	0.200024i
$679$	−6.83873e12			−1.23470
$680$	−5.53530e11	+	4.90492e11i	−0.0992776	+	0.0879715i
$681$	−7.90930e12			−1.40921
$682$			5.14361e11i			0.0910413i
$683$	3.94120e12	+	3.94120e12i	0.693004	+	0.693004i	0.962892	−	0.269888i	$-0.0869866\pi$
$683$	3.94120e12	+	3.94120e12i	0.693004	+	0.693004i	−0.269888	+	0.962892i	$0.586987\pi$
$684$	−5.47985e12			−0.957230
$685$	−1.14746e12	−	1.14746e12i	−0.199128	−	0.199128i
$686$	−8.54215e11	+	8.54215e11i	−0.147268	+	0.147268i
$687$	8.80809e12	−	8.80809e12i	1.50861	−	1.50861i
$688$			1.31594e12i			0.223917i
$689$		−	7.48045e12i		−	1.26457i
$690$	3.92497e11	−	3.92497e11i	0.0659198	−	0.0659198i
$691$	2.07105e12	−	2.07105e12i	0.345573	−	0.345573i	−0.512885	−	0.858457i	$-0.671423\pi$
$691$	2.07105e12	−	2.07105e12i	0.345573	−	0.345573i	0.858457	+	0.512885i	$0.171423\pi$
$692$	−4.11844e12	−	4.11844e12i	−0.682740	−	0.682740i
$693$	−1.85388e12			−0.305339
$694$	−3.24457e11	−	3.24457e11i	−0.0530933	−	0.0530933i
$695$			9.84801e10i			0.0160109i
$696$	2.01973e12			0.326251
$697$	−6.28430e12	+	5.56862e12i	−1.00858	+	0.893717i
$698$	5.66627e11			0.0903541
$699$			1.07442e13i			1.70226i
$700$	4.65056e12	+	4.65056e12i	0.732089	+	0.732089i
$701$	6.05345e12			0.946830			0.473415	−	0.880840i	$-0.343021\pi$
$701$	6.05345e12			0.946830			0.473415	+	0.880840i	$0.343021\pi$
$702$	8.46190e11	+	8.46190e11i	0.131508	+	0.131508i
$703$	−5.17515e11	+	5.17515e11i	−0.0799141	+	0.0799141i
$704$	3.61362e11	−	3.61362e11i	0.0554455	−	0.0554455i
$705$		−	3.48214e12i		−	0.530878i
$706$		−	6.09998e11i		−	0.0924075i
$707$	−6.92247e11	+	6.92247e11i	−0.104201	+	0.104201i
$708$	6.13868e12	−	6.13868e12i	0.918174	−	0.918174i
$709$	−1.43440e11	−	1.43440e11i	−0.0213187	−	0.0213187i	0.696367	−	0.717686i	$-0.254799\pi$
$709$	−1.43440e11	−	1.43440e11i	−0.0213187	−	0.0213187i	−0.717686	+	0.696367i	$0.754799\pi$
$710$	8.71677e11			0.128734
$711$	−1.11018e13	−	1.11018e13i	−1.62922	−	1.62922i
$712$			1.95405e12i			0.284954i
$713$	−8.74803e12			−1.26767
$714$	2.54132e11	−	4.20886e12i	0.0365947	−	0.606070i
$715$	3.39419e11			0.0485689
$716$			2.47595e12i			0.352073i
$717$	−5.45170e12	−	5.45170e12i	−0.770363	−	0.770363i
$718$	−2.28684e12			−0.321126
$719$	−3.39049e12	−	3.39049e12i	−0.473132	−	0.473132i	0.429795	−	0.902927i	$-0.358586\pi$
$719$	−3.39049e12	−	3.39049e12i	−0.473132	−	0.473132i	−0.902927	+	0.429795i	$0.858586\pi$
$720$	−9.83748e11	+	9.83748e11i	−0.136423	+	0.136423i
$721$	5.62090e12	−	5.62090e12i	0.774635	−	0.774635i
$722$		−	7.96879e11i		−	0.109138i
$723$			6.96947e12i			0.948587i
$724$	5.07008e12	−	5.07008e12i	0.685790	−	0.685790i
$725$	1.73342e12	−	1.73342e12i	0.233014	−	0.233014i
$726$	2.54651e12	+	2.54651e12i	0.340198	+	0.340198i
$727$	7.83796e11			0.104063			0.0520317	−	0.998645i	$-0.483430\pi$
$727$	7.83796e11			0.104063			0.0520317	+	0.998645i	$0.483430\pi$
$728$	4.81520e12	+	4.81520e12i	0.635365	+	0.635365i
$729$			1.14191e13i			1.49747i
$730$	6.21075e11			0.0809452
$731$	1.51395e11	−	2.50736e12i	0.0196103	−	0.324780i
$732$	2.56784e12			0.330574
$733$		−	2.84990e12i		−	0.364638i	−0.983239	−	0.182319i	$-0.941640\pi$
$733$		−	2.84990e12i		−	0.364638i	0.983239	−	0.182319i	$-0.0583603\pi$
$734$	8.77073e11	+	8.77073e11i	0.111533	+	0.111533i
$735$	1.22886e12			0.155314
$736$	−4.17017e12	−	4.17017e12i	−0.523846	−	0.523846i
$737$	−1.76148e12	+	1.76148e12i	−0.219925	+	0.219925i
$738$	3.31071e12	−	3.31071e12i	0.410835	−	0.410835i
$739$			1.51791e13i			1.87217i	0.351770	+	0.936087i	$0.385580\pi$
$739$			1.51791e13i			1.87217i	−0.351770	+	0.936087i	$0.614420\pi$
$740$			2.14918e11i			0.0263470i
$741$	−8.57797e12	+	8.57797e12i	−1.04521	+	1.04521i
$742$	2.47800e12	−	2.47800e12i	0.300113	−	0.300113i
$743$	6.23725e11	+	6.23725e11i	0.0750833	+	0.0750833i	0.743651	−	0.668568i	$-0.233092\pi$
$743$	6.23725e11	+	6.23725e11i	0.0750833	+	0.0750833i	−0.668568	+	0.743651i	$0.733092\pi$
$744$	−1.14492e13			−1.36993
$745$	−2.66309e11	−	2.66309e11i	−0.0316725	−	0.0316725i
$746$			1.54996e12i			0.183230i
$747$	1.35013e13			1.58647
$748$	−1.09338e12	+	9.68865e11i	−0.127707	+	0.113163i
$749$	−1.41151e13			−1.63876
$750$		−	1.80560e12i		−	0.208375i
$751$	5.26912e12	+	5.26912e12i	0.604448	+	0.604448i	0.941490	−	0.337042i	$-0.109426\pi$
$751$	5.26912e12	+	5.26912e12i	0.604448	+	0.604448i	−0.337042	+	0.941490i	$0.609426\pi$
$752$	−9.86706e12			−1.12514
$753$	1.31273e13	+	1.31273e13i	1.48798	+	1.48798i
$754$	8.46263e11	−	8.46263e11i	0.0953530	−	0.0953530i
$755$	−2.62259e12	+	2.62259e12i	−0.293744	+	0.293744i
$756$		−	4.63942e12i		−	0.516554i
$757$		−	8.12481e12i		−	0.899253i	−0.893217	−	0.449626i	$-0.851557\pi$
$757$		−	8.12481e12i		−	0.899253i	0.893217	−	0.449626i	$-0.148443\pi$
$758$	2.71969e11	−	2.71969e11i	0.0299232	−	0.0299232i
$759$	1.64428e12	−	1.64428e12i	0.179841	−	0.179841i
$760$	7.04862e11	+	7.04862e11i	0.0766377	+	0.0766377i
$761$	1.14049e13			1.23271			0.616356	−	0.787467i	$-0.288608\pi$
$761$	1.14049e13			1.23271			0.616356	+	0.787467i	$0.288608\pi$
$762$	−6.37897e11	−	6.37897e11i	−0.0685414	−	0.0685414i
$763$		−	1.88533e11i		−	0.0201385i
$764$	5.28596e12			0.561311
$765$	1.98759e12	−	1.76124e12i	0.209822	−	0.185927i
$766$	1.86875e12			0.196120
$767$		−	1.09100e13i		−	1.13827i
$768$	9.08252e11	+	9.08252e11i	0.0942066	+	0.0942066i
$769$	5.75802e12			0.593751			0.296875	−	0.954916i	$-0.404055\pi$
$769$	5.75802e12			0.593751			0.296875	+	0.954916i	$0.404055\pi$
$770$	1.12437e11	+	1.12437e11i	0.0115266	+	0.0115266i
$771$	1.94840e13	−	1.94840e13i	1.98579	−	1.98579i
$772$	−4.50389e12	+	4.50389e12i	−0.456362	+	0.456362i
$773$			1.32205e13i			1.33181i	0.746037	+	0.665904i	$0.231954\pi$
$773$			1.32205e13i			1.33181i	−0.746037	+	0.665904i	$0.768046\pi$
$774$			1.40069e12i			0.140284i
$775$	−9.82619e12	+	9.82619e12i	−0.978425	+	0.978425i
$776$	4.50648e12	−	4.50648e12i	0.446128	−	0.446128i
$777$	−1.83754e12	−	1.83754e12i	−0.180859	−	0.180859i
$778$	−5.29679e12			−0.518328
$779$	8.00238e12	+	8.00238e12i	0.778576	+	0.778576i
$780$			3.56234e12i			0.344596i
$781$	3.65170e12			0.351209
$782$	1.99119e12	+	2.24710e12i	0.190407	+	0.214878i
$783$	−1.72927e12			−0.164412
$784$		−	3.48213e12i		−	0.329171i
$785$	−2.06311e12	−	2.06311e12i	−0.193914	−	0.193914i
$786$	1.98944e12			0.185922
$787$	−2.92331e12	−	2.92331e12i	−0.271637	−	0.271637i	0.558122	−	0.829759i	$-0.311522\pi$
$787$	−2.92331e12	−	2.92331e12i	−0.271637	−	0.271637i	−0.829759	+	0.558122i	$0.811522\pi$
$788$	−3.70311e11	+	3.70311e11i	−0.0342135	+	0.0342135i
$789$	−1.66776e13	+	1.66776e13i	−1.53210	+	1.53210i
$790$			1.34664e12i			0.123007i
$791$			5.36205e12i			0.487009i
$792$	1.22164e12	−	1.22164e12i	0.110327	−	0.110327i
$793$	2.28185e12	−	2.28185e12i	0.204907	−	0.204907i
$794$	2.47036e12	+	2.47036e12i	0.220581	+	0.220581i
$795$	3.88804e12			0.345206
$796$	−7.02737e12	−	7.02737e12i	−0.620418	−	0.620418i
$797$			7.40085e12i			0.649709i	0.945764	+	0.324854i	$0.105315\pi$
$797$			7.40085e12i			0.649709i	−0.945764	+	0.324854i	$0.894685\pi$
$798$	−5.68314e12			−0.496107
$799$	1.88005e13	+	1.13518e12i	1.63196	+	0.0985382i
$800$	−9.36826e12			−0.808638
$801$		−	7.01652e12i		−	0.602248i
$802$	−3.83332e11	−	3.83332e11i	−0.0327183	−	0.0327183i
$803$	2.60185e12			0.220833
$804$	−1.84875e13	−	1.84875e13i	−1.56036	−	1.56036i
$805$	−1.91228e12	+	1.91228e12i	−0.160498	+	0.160498i
$806$	−4.79719e12	+	4.79719e12i	−0.400386	+	0.400386i
$807$		−	1.01895e13i		−	0.845710i
$808$		−	9.12332e11i		−	0.0753012i
$809$	4.18337e12	−	4.18337e12i	0.343367	−	0.343367i	−0.514265	−	0.857632i	$-0.671935\pi$
$809$	4.18337e12	−	4.18337e12i	0.343367	−	0.343367i	0.857632	+	0.514265i	$0.171935\pi$
$810$	3.57619e11	−	3.57619e11i	0.0291902	−	0.0291902i
$811$	−2.03188e12	−	2.03188e12i	−0.164932	−	0.164932i	0.619816	−	0.784748i	$-0.287207\pi$
$811$	−2.03188e12	−	2.03188e12i	−0.164932	−	0.164932i	−0.784748	+	0.619816i	$0.787207\pi$
$812$	−4.63982e12			−0.374541
$813$	−2.40128e12	−	2.40128e12i	−0.192768	−	0.192768i
$814$		−	1.08798e11i		−	0.00868581i
$815$	−3.94543e12			−0.313246
$816$	−8.79139e12	−	9.92126e12i	−0.694147	−	0.783360i
$817$	−3.38565e12			−0.265853
$818$		−	4.32032e12i		−	0.337385i
$819$	−1.72902e13	−	1.72902e13i	−1.34284	−	1.34284i
$820$	3.32331e12			0.256689
$821$	−1.08300e13	−	1.08300e13i	−0.831929	−	0.831929i	0.155852	−	0.987780i	$-0.450188\pi$
$821$	−1.08300e13	−	1.08300e13i	−0.831929	−	0.831929i	−0.987780	+	0.155852i	$0.950188\pi$
$822$	−6.09657e12	+	6.09657e12i	−0.465760	+	0.465760i
$823$	−9.70772e12	+	9.70772e12i	−0.737595	+	0.737595i	−0.972112	−	0.234517i	$-0.924649\pi$
$823$	−9.70772e12	+	9.70772e12i	−0.737595	+	0.737595i	0.234517	+	0.972112i	$0.424649\pi$
$824$			7.40794e12i			0.559790i
$825$		−	3.69386e12i		−	0.277612i
$826$	3.61408e12	−	3.61408e12i	0.270139	−	0.270139i
$827$	−5.88393e12	+	5.88393e12i	−0.437414	+	0.437414i	−0.891141	−	0.453727i	$-0.850094\pi$
$827$	−5.88393e12	+	5.88393e12i	−0.437414	+	0.437414i	0.453727	+	0.891141i	$0.350094\pi$
$828$	9.79667e12	+	9.79667e12i	0.724339	+	0.724339i
$829$	2.08992e13			1.53686			0.768431	−	0.639932i	$-0.221038\pi$
$829$	2.08992e13			1.53686			0.768431	+	0.639932i	$0.221038\pi$
$830$	−8.18847e11	−	8.18847e11i	−0.0598896	−	0.0598896i
$831$			5.77422e12i			0.420038i
$832$	6.74050e12			0.487682
$833$	−4.00610e11	+	6.63478e12i	−0.0288283	+	0.477446i
$834$	5.23233e11			0.0374497
$835$			9.35030e11i			0.0665635i
$836$	1.39231e12	+	1.39231e12i	0.0985841	+	0.0985841i
$837$	9.80266e12			0.690366
$838$	1.76716e12	+	1.76716e12i	0.123788	+	0.123788i
$839$	3.08297e11	−	3.08297e11i	0.0214803	−	0.0214803i	−0.696285	−	0.717765i	$-0.745165\pi$
$839$	3.08297e11	−	3.08297e11i	0.0214803	−	0.0214803i	0.717765	+	0.696285i	$0.245165\pi$
$840$	−2.50275e12	+	2.50275e12i	−0.173444	+	0.173444i
$841$		−	1.27777e13i		−	0.880789i
$842$		−	4.42761e12i		−	0.303574i
$843$	3.36458e12	−	3.36458e12i	0.229460	−	0.229460i
$844$	1.45059e13	−	1.45059e13i	0.984018	−	0.984018i
$845$	9.28216e11	+	9.28216e11i	0.0626317	+	0.0626317i
$846$	−1.05026e13			−0.704902
$847$	−1.24068e13	−	1.24068e13i	−0.828296	−	0.828296i
$848$		−	1.10172e13i		−	0.731630i
$849$	3.27704e13			2.16470
$850$	4.76064e12	+	2.87449e11i	0.312810	+	0.0188876i
$851$	1.85039e12			0.120943
$852$			3.83261e13i			2.49182i
$853$	5.58429e12	+	5.58429e12i	0.361158	+	0.361158i	0.864239	−	0.503081i	$-0.167800\pi$
$853$	5.58429e12	+	5.58429e12i	0.361158	+	0.361158i	−0.503081	+	0.864239i	$0.667800\pi$
$854$	1.51179e12			0.0972591
$855$	−2.53099e12	−	2.53099e12i	−0.161973	−	0.161973i
$856$	9.30132e12	−	9.30132e12i	0.592124	−	0.592124i
$857$	1.55340e13	−	1.55340e13i	0.983714	−	0.983714i	−0.0161554	−	0.999869i	$-0.505143\pi$
$857$	1.55340e13	−	1.55340e13i	0.983714	−	0.983714i	0.999869	+	0.0161554i	$0.00514265\pi$
$858$		−	1.80336e12i		−	0.113603i
$859$		−	1.07537e12i		−	0.0673891i	−0.999432	−	0.0336946i	$-0.989273\pi$
$859$		−	1.07537e12i		−	0.0673891i	0.999432	−	0.0336946i	$-0.0107273\pi$
$860$	−7.03012e11	+	7.03012e11i	−0.0438247	+	0.0438247i
$861$	−2.84140e13	+	2.84140e13i	−1.76205	+	1.76205i
$862$	4.12491e12	+	4.12491e12i	0.254467	+	0.254467i
$863$	−1.48503e13			−0.911351			−0.455675	−	0.890146i	$-0.650602\pi$
$863$	−1.48503e13			−0.911351			−0.455675	+	0.890146i	$0.650602\pi$
$864$	4.67292e12	+	4.67292e12i	0.285283	+	0.285283i
$865$		−	3.80438e12i		−	0.231053i
$866$	−7.43548e11			−0.0449240
$867$	1.56095e13	+	1.99152e13i	0.938219	+	1.19701i
$868$	2.63016e13			1.57269
$869$			5.64144e12i			0.335584i
$870$	4.39853e11	+	4.39853e11i	0.0260298	+	0.0260298i
$871$	−3.28569e13			−1.93439
$872$	1.24237e11	+	1.24237e11i	0.00727655	+	0.00727655i
$873$	−1.61817e13	+	1.61817e13i	−0.942886	+	0.942886i
$874$	2.86144e12	−	2.86144e12i	0.165876	−	0.165876i
$875$			8.79702e12i			0.507340i
$876$			2.73076e13i			1.56680i
$877$	8.84348e12	−	8.84348e12i	0.504807	−	0.504807i	−0.408121	−	0.912928i	$-0.633816\pi$
$877$	8.84348e12	−	8.84348e12i	0.504807	−	0.504807i	0.912928	+	0.408121i	$0.133816\pi$
$878$	3.39745e12	−	3.39745e12i	0.192942	−	0.192942i
$879$	−2.68684e13	−	2.68684e13i	−1.51807	−	1.51807i
$880$	4.99897e11			0.0281001
$881$	1.93337e13	+	1.93337e13i	1.08124	+	1.08124i	0.996394	+	0.0848505i	$0.0270413\pi$
$881$	1.93337e13	+	1.93337e13i	1.08124	+	1.08124i	0.0848505	+	0.996394i	$0.472959\pi$
$882$		−	3.70640e12i		−	0.206226i
$883$	−2.79185e13			−1.54550			−0.772749	−	0.634711i	$-0.781119\pi$
$883$	−2.79185e13			−1.54550			−0.772749	+	0.634711i	$0.781119\pi$
$884$	−1.92336e13	−	1.16133e12i	−1.05931	−	0.0639617i
$885$	5.67056e12			0.310729
$886$		−	3.87519e12i		−	0.211272i
$887$	−5.79210e12	−	5.79210e12i	−0.314181	−	0.314181i	0.532346	−	0.846527i	$-0.321311\pi$
$887$	−5.79210e12	−	5.79210e12i	−0.314181	−	0.314181i	−0.846527	+	0.532346i	$0.821311\pi$
$888$	2.42174e12			0.130698
$889$	3.10789e12	+	3.10789e12i	0.166881	+	0.166881i
$890$	−4.25548e11	+	4.25548e11i	−0.0227350	+	0.0227350i
$891$	1.49816e12	−	1.49816e12i	0.0796360	−	0.0796360i
$892$		−	1.22923e13i		−	0.650115i
$893$		−	2.53860e13i		−	1.33586i
$894$	−1.41492e12	+	1.41492e12i	−0.0740820	+	0.0740820i
$895$	−1.14357e12	+	1.14357e12i	−0.0595743	+	0.0595743i
$896$	1.62859e13	+	1.62859e13i	0.844163	+	0.844163i
$897$	3.06708e13			1.58182
$898$	4.06255e12	+	4.06255e12i	0.208475	+	0.208475i
$899$		−	9.80351e12i		−	0.500568i
$900$	2.20081e13			1.11813
$901$	−1.26751e12	+	2.09920e13i	−0.0640750	+	1.06119i
$902$	−1.68235e12			−0.0846229
$903$		−	1.20214e13i		−	0.601672i
$904$	−3.53340e12	−	3.53340e12i	−0.175968	−	0.175968i
$905$	4.68346e12			0.232085
$906$	1.39340e13	+	1.39340e13i	0.687068	+	0.687068i
$907$	3.68015e12	−	3.68015e12i	0.180565	−	0.180565i	−0.611037	−	0.791602i	$-0.709247\pi$
$907$	3.68015e12	−	3.68015e12i	0.180565	−	0.180565i	0.791602	+	0.611037i	$0.209247\pi$
$908$	−1.19731e13	+	1.19731e13i	−0.584549	+	0.584549i
$909$			3.27597e12i			0.159148i
$910$			2.09729e12i			0.101385i
$911$	1.85632e12	−	1.85632e12i	0.0892934	−	0.0892934i	−0.661049	−	0.750343i	$-0.729889\pi$
$911$	1.85632e12	−	1.85632e12i	0.0892934	−	0.0892934i	0.750343	+	0.661049i	$0.229889\pi$
$912$	−1.26337e13	+	1.26337e13i	−0.604717	+	0.604717i
$913$	−3.43037e12	−	3.43037e12i	−0.163389	−	0.163389i
$914$	−8.22554e12			−0.389858
$915$	1.18601e12	+	1.18601e12i	0.0559364	+	0.0559364i
$916$		−	2.66674e13i		−	1.25156i
$917$	−9.69273e12			−0.452673
$918$	−2.23124e12	−	2.51800e12i	−0.103694	−	0.117021i
$919$	−1.94469e12			−0.0899352			−0.0449676	−	0.998988i	$-0.514318\pi$
$919$	−1.94469e12			−0.0899352			−0.0449676	+	0.998988i	$0.514318\pi$
$920$		−	2.52025e12i		−	0.115984i
$921$	−4.67534e12	−	4.67534e12i	−0.214114	−	0.214114i
$922$	−5.35376e12			−0.243988
$923$	3.40576e13	+	3.40576e13i	1.54456	+	1.54456i
$924$	−4.94366e12	+	4.94366e12i	−0.223113	+	0.223113i
$925$	2.07844e12	−	2.07844e12i	0.0933468	−	0.0933468i
$926$		−	5.75967e12i		−	0.257424i
$927$		−	2.66001e13i		−	1.18311i
$928$	4.67332e12	−	4.67332e12i	0.206852	−	0.206852i
$929$	−3.16461e12	+	3.16461e12i	−0.139396	+	0.139396i	−0.773361	−	0.633966i	$-0.781426\pi$
$929$	−3.16461e12	+	3.16461e12i	−0.139396	+	0.139396i	0.633966	+	0.773361i	$0.281426\pi$
$930$	−2.49339e12	−	2.49339e12i	−0.109299	−	0.109299i
$931$	8.95881e12			0.390820
$932$	1.62646e13	+	1.62646e13i	0.706107	+	0.706107i
$933$		−	4.47645e13i		−	1.93404i
$934$	9.94169e12			0.427464
$935$	−9.52495e11	−	5.75119e10i	−0.0407578	−	0.00246097i
$936$	2.27873e13			0.970402
$937$		−	4.77244e12i		−	0.202261i	−0.994873	−	0.101130i	$-0.967754\pi$
$937$		−	4.77244e12i		−	0.202261i	0.994873	−	0.101130i	$-0.0322460\pi$
$938$	−1.08843e13	−	1.08843e13i	−0.459079	−	0.459079i
$939$	−1.28966e13			−0.541350
$940$	−5.27127e12	−	5.27127e12i	−0.220211	−	0.220211i
$941$	−2.41963e13	+	2.41963e13i	−1.00600	+	1.00600i	−0.00601346	+	0.999982i	$0.501914\pi$
$941$	−2.41963e13	+	2.41963e13i	−1.00600	+	1.00600i	−0.999982	+	0.00601346i	$0.998086\pi$
$942$	−1.09615e13	+	1.09615e13i	−0.453565	+	0.453565i
$943$		−	2.86127e13i		−	1.17830i
$944$		−	1.60682e13i		−	0.658558i
$945$	2.14282e12	−	2.14282e12i	0.0874062	−	0.0874062i
$946$	3.55885e11	−	3.55885e11i	0.0144477	−	0.0144477i
$947$	−3.02765e13	−	3.02765e13i	−1.22330	−	1.22330i	−0.966453	−	0.256842i	$-0.917318\pi$
$947$	−3.02765e13	−	3.02765e13i	−1.22330	−	1.22330i	−0.256842	−	0.966453i	$-0.582682\pi$
$948$	−5.92093e13			−2.38096
$949$	2.42662e13	+	2.42662e13i	0.971189	+	0.971189i
$950$		−	6.42820e12i		−	0.256055i
$951$	−6.83471e13			−2.70962
$952$	−1.26968e13	−	1.43286e13i	−0.500988	−	0.565375i
$953$	3.95158e12			0.155186			0.0775929	−	0.996985i	$-0.475277\pi$
$953$	3.95158e12			0.155186			0.0775929	+	0.996985i	$0.475277\pi$
$954$		−	1.17268e13i		−	0.458366i
$955$	2.44144e12	+	2.44144e12i	0.0949795	+	0.0949795i
$956$	−1.65056e13			−0.639102
$957$	1.84267e12	+	1.84267e12i	0.0710139	+	0.0710139i
$958$	−3.55730e12	+	3.55730e12i	−0.136451	+	0.136451i
$959$	2.97030e13	−	2.97030e13i	1.13401	−	1.13401i
$960$			3.50344e12i			0.133129i
$961$			2.91333e13i			1.10188i
$962$	1.01470e12	−	1.01470e12i	0.0381989	−	0.0381989i
$963$	−3.33988e13	+	3.33988e13i	−1.25145	+	1.25145i
$964$	1.05504e13	+	1.05504e13i	0.393479	+	0.393479i
$965$	−4.16044e12			−0.154442
$966$	1.01601e13	+	1.01601e13i	0.375406	+	0.375406i
$967$		−	7.28844e12i		−	0.268050i	−0.990978	−	0.134025i	$-0.957210\pi$
$967$		−	7.28844e12i		−	0.268050i	0.990978	−	0.134025i	$-0.0427902\pi$
$968$	1.63513e13			0.598568
$969$	2.55254e13	−	2.26185e13i	0.930071	−	0.824151i
$970$	1.96282e12			0.0711882
$971$			5.00497e12i			0.180682i	0.995911	+	0.0903410i	$0.0287957\pi$
$971$			5.00497e12i			0.180682i	−0.995911	+	0.0903410i	$0.971204\pi$
$972$	2.40840e13	+	2.40840e13i	0.865428	+	0.865428i
$973$	−2.54924e12			−0.0911806
$974$	−4.79793e12	−	4.79793e12i	−0.170820	−	0.170820i
$975$	3.44508e13	−	3.44508e13i	1.22090	−	1.22090i
$976$	3.36071e12	−	3.36071e12i	0.118552	−	0.118552i
$977$			3.84384e13i			1.34971i	0.737951	+	0.674854i	$0.235793\pi$
$977$			3.84384e13i			1.34971i	−0.737951	+	0.674854i	$0.764207\pi$
$978$			2.09624e13i			0.732683i
$979$	−1.78274e12	+	1.78274e12i	−0.0620249	+	0.0620249i
$980$	1.86025e12	−	1.86025e12i	0.0644250	−	0.0644250i
$981$	−4.46104e11	−	4.46104e11i	−0.0153789	−	0.0153789i
$982$	−1.09148e13			−0.374555
$983$	−3.43431e12	−	3.43431e12i	−0.117314	−	0.117314i	0.646013	−	0.763326i	$-0.276435\pi$
$983$	−3.43431e12	−	3.43431e12i	−0.117314	−	0.117314i	−0.763326	+	0.646013i	$0.776435\pi$
$984$		−	3.74477e13i		−	1.27335i
$985$	−3.42072e11			−0.0115786
$986$	−2.51822e12	+	2.23143e12i	−0.0848492	+	0.0751862i
$987$	9.01379e13			3.02329
$988$			2.59707e13i			0.867117i
$989$	6.05273e12	+	6.05273e12i	0.201172	+	0.201172i
$990$	5.32093e11			0.0176047
$991$	1.53780e13	+	1.53780e13i	0.506487	+	0.506487i	0.913446	−	0.406960i	$-0.133411\pi$
$991$	1.53780e13	+	1.53780e13i	0.506487	+	0.506487i	−0.406960	+	0.913446i	$0.633411\pi$
$992$	−2.64915e13	+	2.64915e13i	−0.868569	+	0.868569i
$993$	−6.67136e12	+	6.67136e12i	−0.217742	+	0.217742i
$994$			2.25641e13i			0.733126i
$995$		−	6.49149e12i		−	0.209962i
$996$	3.60032e13	−	3.60032e13i	1.15924	−	1.15924i
$997$	−3.64343e13	+	3.64343e13i	−1.16784	+	1.16784i	−0.185120	+	0.982716i	$0.559267\pi$
$997$	−3.64343e13	+	3.64343e13i	−1.16784	+	1.16784i	−0.982716	+	0.185120i	$0.940733\pi$
$998$	−9.21408e12	−	9.21408e12i	−0.294012	−	0.294012i
$999$	−2.07346e12			−0.0658645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.6	yes	24
17.2	even	8		289.10.a.f.1.14		24
17.4	even	4	inner	17.10.c.a.4.7	✓	24
17.15	even	8		289.10.a.f.1.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.7	✓	24	17.4	even	4	inner
17.10.c.a.13.6	yes	24	1.1	even	1	trivial
289.10.a.f.1.13		24	17.15	even	8
289.10.a.f.1.14		24	17.2	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)

\(f(q)\)	\(=\)	\(q-7.42963i q^{2} +(150.879 + 150.879i) q^{3} +456.801 q^{4} +(210.983 + 210.983i) q^{5} +(1120.97 - 1120.97i) q^{6} +(-5461.47 + 5461.47i) q^{7} -7197.83i q^{8} +25845.7i q^{9} +O(q^{10})\)	\(q-7.42963i q^{2} +(150.879 + 150.879i) q^{3} +456.801 q^{4} +(210.983 + 210.983i) q^{5} +(1120.97 - 1120.97i) q^{6} +(-5461.47 + 5461.47i) q^{7} -7197.83i q^{8} +25845.7i q^{9} +(1567.53 - 1567.53i) q^{10} +(6566.81 - 6566.81i) q^{11} +(68921.4 + 68921.4i) q^{12} +122491. q^{13} +(40576.7 + 40576.7i) q^{14} +63665.7i q^{15} +180405. q^{16} +(-343740. - 20755.1i) q^{17} +192024. q^{18} +464145. i q^{19} +(96377.3 + 96377.3i) q^{20} -1.64804e6 q^{21} +(-48789.0 - 48789.0i) q^{22} +(829781. - 829781. i) q^{23} +(1.08600e6 - 1.08600e6i) q^{24} -1.86410e6i q^{25} -910061. i q^{26} +(-929817. + 929817. i) q^{27} +(-2.49480e6 + 2.49480e6i) q^{28} +(929897. + 929897. i) q^{29} +473013. q^{30} +(-5.27129e6 - 5.27129e6i) q^{31} -5.02563e6i q^{32} +1.98158e6 q^{33} +(-154203. + 2.55386e6i) q^{34} -2.30456e6 q^{35} +1.18063e7i q^{36} +(1.11498e6 + 1.11498e6i) q^{37} +3.44843e6 q^{38} +(1.84812e7 + 1.84812e7i) q^{39} +(1.51862e6 - 1.51862e6i) q^{40} +(1.72411e7 - 1.72411e7i) q^{41} +1.22443e7i q^{42} +7.29437e6i q^{43} +(2.99972e6 - 2.99972e6i) q^{44} +(-5.45301e6 + 5.45301e6i) q^{45} +(-6.16497e6 - 6.16497e6i) q^{46} -5.46941e7 q^{47} +(2.72192e7 + 2.72192e7i) q^{48} -1.93017e7i q^{49} -1.38496e7 q^{50} +(-4.87315e7 - 5.49945e7i) q^{51} +5.59538e7 q^{52} -6.10696e7i q^{53} +(6.90820e6 + 6.90820e6i) q^{54} +2.77097e6 q^{55} +(3.93108e7 + 3.93108e7i) q^{56} +(-7.00296e7 + 7.00296e7i) q^{57} +(6.90879e6 - 6.90879e6i) q^{58} -8.90678e7i q^{59} +2.90825e7i q^{60} +(1.86288e7 - 1.86288e7i) q^{61} +(-3.91637e7 + 3.91637e7i) q^{62} +(-1.41155e8 - 1.41155e8i) q^{63} +5.50286e7 q^{64} +(2.58435e7 + 2.58435e7i) q^{65} -1.47224e7i q^{66} -2.68240e8 q^{67} +(-1.57021e8 - 9.48095e6i) q^{68} +2.50392e8 q^{69} +1.71220e7i q^{70} +(2.78042e8 + 2.78042e8i) q^{71} +1.86033e8 q^{72} +(1.98106e8 + 1.98106e8i) q^{73} +(8.28392e6 - 8.28392e6i) q^{74} +(2.81252e8 - 2.81252e8i) q^{75} +2.12022e8i q^{76} +7.17289e7i q^{77} +(1.37309e8 - 1.37309e8i) q^{78} +(-4.29542e8 + 4.29542e8i) q^{79} +(3.80624e7 + 3.80624e7i) q^{80} +2.28142e8 q^{81} +(-1.28095e8 - 1.28095e8i) q^{82} -5.22381e8i q^{83} -7.52825e8 q^{84} +(-6.81444e7 - 7.69024e7i) q^{85} +5.41945e7 q^{86} +2.80603e8i q^{87} +(-4.72668e7 - 4.72668e7i) q^{88} -2.71477e8 q^{89} +(4.05138e7 + 4.05138e7i) q^{90} +(-6.68980e8 + 6.68980e8i) q^{91} +(3.79045e8 - 3.79045e8i) q^{92} -1.59065e9i q^{93} +4.06357e8i q^{94} +(-9.79269e7 + 9.79269e7i) q^{95} +(7.58260e8 - 7.58260e8i) q^{96} +(6.26088e8 + 6.26088e8i) q^{97} -1.43405e8 q^{98} +(1.69724e8 + 1.69724e8i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more