LMFDB - Embedded newform 17.10.c.a.13.9

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			13.9
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17.1503i q^{2} +(97.3786 + 97.3786i) q^{3} +217.866 q^{4} +(882.390 + 882.390i) q^{5} +(-1670.08 + 1670.08i) q^{6} +(7460.78 - 7460.78i) q^{7} +12517.4i q^{8} -717.820i q^{9} +O(q^{10})$	\(q+17.1503i q^{2} +(97.3786 + 97.3786i) q^{3} +217.866 q^{4} +(882.390 + 882.390i) q^{5} +(-1670.08 + 1670.08i) q^{6} +(7460.78 - 7460.78i) q^{7} +12517.4i q^{8} -717.820i q^{9} +(-15133.3 + 15133.3i) q^{10} +(-34934.5 + 34934.5i) q^{11} +(21215.5 + 21215.5i) q^{12} -54354.1 q^{13} +(127955. + 127955. i) q^{14} +171852. i q^{15} -103131. q^{16} +(-252581. + 234074. i) q^{17} +12310.9 q^{18} -716600. i q^{19} +(192242. + 192242. i) q^{20} +1.45304e6 q^{21} +(-599138. - 599138. i) q^{22} +(143564. - 143564. i) q^{23} +(-1.21893e6 + 1.21893e6i) q^{24} -395901. i q^{25} -932191. i q^{26} +(1.98660e6 - 1.98660e6i) q^{27} +(1.62545e6 - 1.62545e6i) q^{28} +(-4.58858e6 - 4.58858e6i) q^{29} -2.94732e6 q^{30} +(2.48975e6 + 2.48975e6i) q^{31} +4.64020e6i q^{32} -6.80374e6 q^{33} +(-4.01445e6 - 4.33185e6i) q^{34} +1.31666e7 q^{35} -156388. i q^{36} +(1.31820e7 + 1.31820e7i) q^{37} +1.22899e7 q^{38} +(-5.29292e6 - 5.29292e6i) q^{39} +(-1.10453e7 + 1.10453e7i) q^{40} +(-1.35933e7 + 1.35933e7i) q^{41} +2.49202e7i q^{42} -1.47802e7i q^{43} +(-7.61102e6 + 7.61102e6i) q^{44} +(633397. - 633397. i) q^{45} +(2.46216e6 + 2.46216e6i) q^{46} +7.91732e6 q^{47} +(-1.00428e7 - 1.00428e7i) q^{48} -7.09730e7i q^{49} +6.78985e6 q^{50} +(-4.73898e7 - 1.80218e6i) q^{51} -1.18419e7 q^{52} -1.83584e7i q^{53} +(3.40709e7 + 3.40709e7i) q^{54} -6.16517e7 q^{55} +(9.33900e7 + 9.33900e7i) q^{56} +(6.97815e7 - 6.97815e7i) q^{57} +(7.86958e7 - 7.86958e7i) q^{58} -8.19772e7i q^{59} +3.74406e7i q^{60} +(1.90537e7 - 1.90537e7i) q^{61} +(-4.27000e7 + 4.27000e7i) q^{62} +(-5.35550e6 - 5.35550e6i) q^{63} -1.32384e8 q^{64} +(-4.79615e7 - 4.79615e7i) q^{65} -1.16686e8i q^{66} -5.75938e7 q^{67} +(-5.50287e7 + 5.09967e7i) q^{68} +2.79600e7 q^{69} +2.25812e8i q^{70} +(-2.02628e7 - 2.02628e7i) q^{71} +8.98528e6 q^{72} +(2.61332e8 + 2.61332e8i) q^{73} +(-2.26076e8 + 2.26076e8i) q^{74} +(3.85523e7 - 3.85523e7i) q^{75} -1.56123e8i q^{76} +5.21277e8i q^{77} +(9.07754e7 - 9.07754e7i) q^{78} +(-3.71346e7 + 3.71346e7i) q^{79} +(-9.10020e7 - 9.10020e7i) q^{80} +3.72776e8 q^{81} +(-2.33130e8 - 2.33130e8i) q^{82} +1.13599e8i q^{83} +3.16568e8 q^{84} +(-4.29420e8 - 1.63304e7i) q^{85} +2.53486e8 q^{86} -8.93659e8i q^{87} +(-4.37291e8 - 4.37291e8i) q^{88} +6.81819e8 q^{89} +(1.08630e7 + 1.08630e7i) q^{90} +(-4.05524e8 + 4.05524e8i) q^{91} +(3.12776e7 - 3.12776e7i) q^{92} +4.84896e8i q^{93} +1.35785e8i q^{94} +(6.32320e8 - 6.32320e8i) q^{95} +(-4.51856e8 + 4.51856e8i) q^{96} +(-1.14542e9 - 1.14542e9i) q^{97} +1.21721e9 q^{98} +(2.50767e7 + 2.50767e7i) 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 $

$2$			17.1503i			0.757945i	0.925408	+	0.378973i	$0.123723\pi$
$2$			17.1503i			0.757945i	−0.925408	+	0.378973i	$0.876277\pi$
$3$	97.3786	+	97.3786i	0.694093	+	0.694093i	0.963130	−	0.269037i	$-0.0867053\pi$
$3$	97.3786	+	97.3786i	0.694093	+	0.694093i	−0.269037	+	0.963130i	$0.586705\pi$
$4$	217.866			0.425519
$5$	882.390	+	882.390i	0.631387	+	0.631387i	0.948416	−	0.317029i	$-0.102685\pi$
$5$	882.390	+	882.390i	0.631387	+	0.631387i	−0.317029	+	0.948416i	$0.602685\pi$
$6$	−1670.08	+	1670.08i	−0.526085	+	0.526085i
$7$	7460.78	−	7460.78i	1.17447	−	1.17447i	0.193342	−	0.981131i	$-0.438067\pi$
$7$	7460.78	−	7460.78i	1.17447	−	1.17447i	0.981131	−	0.193342i	$-0.0619327\pi$
$8$			12517.4i			1.08047i
$9$		−	717.820i		−	0.0364690i
$10$	−15133.3	+	15133.3i	−0.478557	+	0.478557i
$11$	−34934.5	+	34934.5i	−0.719428	+	0.719428i	−0.968488	−	0.249060i	$-0.919878\pi$
$11$	−34934.5	+	34934.5i	−0.719428	+	0.719428i	0.249060	+	0.968488i	$0.419878\pi$
$12$	21215.5	+	21215.5i	0.295350	+	0.295350i
$13$	−54354.1			−0.527821			−0.263911	−	0.964547i	$-0.585012\pi$
$13$	−54354.1			−0.527821			−0.263911	+	0.964547i	$0.585012\pi$
$14$	127955.	+	127955.i	0.890187	+	0.890187i
$15$			171852.i			0.876483i
$16$	−103131.			−0.393415
$17$	−252581.	+	234074.i	−0.733467	+	0.679725i
$17$	−252581.	+	234074.i	−0.733467	+	0.679725i
$18$	12310.9			0.0276415
$19$		−	716600.i		−	1.26149i	−0.775988	−	0.630747i	$-0.782748\pi$
$19$		−	716600.i		−	1.26149i	0.775988	−	0.630747i	$-0.217252\pi$
$20$	192242.	+	192242.i	0.268667	+	0.268667i
$21$	1.45304e6			1.63039
$22$	−599138.	−	599138.i	−0.545287	−	0.545287i
$23$	143564.	−	143564.i	0.106972	−	0.106972i	−0.651595	−	0.758567i	$-0.725900\pi$
$23$	143564.	−	143564.i	0.106972	−	0.106972i	0.758567	+	0.651595i	$0.225900\pi$
$24$	−1.21893e6	+	1.21893e6i	−0.749944	+	0.749944i
$25$		−	395901.i		−	0.202702i
$26$		−	932191.i		−	0.400060i
$27$	1.98660e6	−	1.98660e6i	0.719406	−	0.719406i
$28$	1.62545e6	−	1.62545e6i	0.499761	−	0.499761i
$29$	−4.58858e6	−	4.58858e6i	−1.20472	−	1.20472i	−0.972713	−	0.232011i	$-0.925469\pi$
$29$	−4.58858e6	−	4.58858e6i	−1.20472	−	1.20472i	−0.232011	−	0.972713i	$-0.574531\pi$
$30$	−2.94732e6			−0.664326
$31$	2.48975e6	+	2.48975e6i	0.484203	+	0.484203i	0.906471	−	0.422268i	$-0.138766\pi$
$31$	2.48975e6	+	2.48975e6i	0.484203	+	0.484203i	−0.422268	+	0.906471i	$0.638766\pi$
$32$			4.64020e6i			0.782279i
$33$	−6.80374e6			−0.998700
$34$	−4.01445e6	−	4.33185e6i	−0.515194	−	0.555928i
$35$	1.31666e7			1.48309
$36$		−	156388.i		−	0.0155183i
$37$	1.31820e7	+	1.31820e7i	1.15631	+	1.15631i	0.985263	+	0.171045i	$0.0547145\pi$
$37$	1.31820e7	+	1.31820e7i	1.15631	+	1.15631i	0.171045	+	0.985263i	$0.445286\pi$
$38$	1.22899e7			0.956144
$39$	−5.29292e6	−	5.29292e6i	−0.366357	−	0.366357i
$40$	−1.10453e7	+	1.10453e7i	−0.682192	+	0.682192i
$41$	−1.35933e7	+	1.35933e7i	−0.751275	+	0.751275i	−0.974717	−	0.223442i	$-0.928271\pi$
$41$	−1.35933e7	+	1.35933e7i	−0.751275	+	0.751275i	0.223442	+	0.974717i	$0.428271\pi$
$42$			2.49202e7i			1.23575i
$43$		−	1.47802e7i		−	0.659285i	−0.944106	−	0.329642i	$-0.893072\pi$
$43$		−	1.47802e7i		−	0.659285i	0.944106	−	0.329642i	$-0.106928\pi$
$44$	−7.61102e6	+	7.61102e6i	−0.306130	+	0.306130i
$45$	633397.	−	633397.i	0.0230261	−	0.0230261i
$46$	2.46216e6	+	2.46216e6i	0.0810787	+	0.0810787i
$47$	7.91732e6			0.236667			0.118334	−	0.992974i	$-0.462245\pi$
$47$	7.91732e6			0.236667			0.118334	+	0.992974i	$0.462245\pi$
$48$	−1.00428e7	−	1.00428e7i	−0.273067	−	0.273067i
$49$		−	7.09730e7i		−	1.75878i
$50$	6.78985e6			0.153637
$51$	−4.73898e7	−	1.80218e6i	−0.980887	−	0.0373021i
$52$	−1.18419e7			−0.224598
$53$		−	1.83584e7i		−	0.319590i	−0.987150	−	0.159795i	$-0.948917\pi$
$53$		−	1.83584e7i		−	0.319590i	0.987150	−	0.159795i	$-0.0510832\pi$
$54$	3.40709e7	+	3.40709e7i	0.545271	+	0.545271i
$55$	−6.16517e7			−0.908474
$56$	9.33900e7	+	9.33900e7i	1.26898	+	1.26898i
$57$	6.97815e7	−	6.97815e7i	0.875595	−	0.875595i
$58$	7.86958e7	−	7.86958e7i	0.913115	−	0.913115i
$59$		−	8.19772e7i		−	0.880763i	−0.897811	−	0.440382i	$-0.854843\pi$
$59$		−	8.19772e7i		−	0.880763i	0.897811	−	0.440382i	$-0.145157\pi$
$60$			3.74406e7i			0.372960i
$61$	1.90537e7	−	1.90537e7i	0.176195	−	0.176195i	−0.613500	−	0.789695i	$-0.710239\pi$
$61$	1.90537e7	−	1.90537e7i	0.176195	−	0.176195i	0.789695	+	0.613500i	$0.210239\pi$
$62$	−4.27000e7	+	4.27000e7i	−0.366999	+	0.366999i
$63$	−5.35550e6	−	5.35550e6i	−0.0428319	−	0.0428319i
$64$	−1.32384e8			−0.986339
$65$	−4.79615e7	−	4.79615e7i	−0.333259	−	0.333259i
$66$		−	1.16686e8i		−	0.756960i
$67$	−5.75938e7			−0.349172			−0.174586	−	0.984642i	$-0.555859\pi$
$67$	−5.75938e7			−0.349172			−0.174586	+	0.984642i	$0.555859\pi$
$68$	−5.50287e7	+	5.09967e7i	−0.312104	+	0.289236i
$69$	2.79600e7			0.148497
$70$			2.25812e8i			1.12410i
$71$	−2.02628e7	−	2.02628e7i	−0.0946319	−	0.0946319i	0.658206	−	0.752838i	$-0.271316\pi$
$71$	−2.02628e7	−	2.02628e7i	−0.0946319	−	0.0946319i	−0.752838	+	0.658206i	$0.771316\pi$
$72$	8.98528e6			0.0394035
$73$	2.61332e8	+	2.61332e8i	1.07706	+	1.07706i	0.996772	+	0.0802880i	$0.0255840\pi$
$73$	2.61332e8	+	2.61332e8i	1.07706	+	1.07706i	0.0802880	+	0.996772i	$0.474416\pi$
$74$	−2.26076e8	+	2.26076e8i	−0.876419	+	0.876419i
$75$	3.85523e7	−	3.85523e7i	0.140694	−	0.140694i
$76$		−	1.56123e8i		−	0.536790i
$77$			5.21277e8i			1.68990i
$78$	9.07754e7	−	9.07754e7i	0.277679	−	0.277679i
$79$	−3.71346e7	+	3.71346e7i	−0.107265	+	0.107265i	−0.758702	−	0.651438i	$-0.774166\pi$
$79$	−3.71346e7	+	3.71346e7i	−0.107265	+	0.107265i	0.651438	+	0.758702i	$0.274166\pi$
$80$	−9.10020e7	−	9.10020e7i	−0.248397	−	0.248397i
$81$	3.72776e8			0.962201
$82$	−2.33130e8	−	2.33130e8i	−0.569425	−	0.569425i
$83$			1.13599e8i			0.262739i	0.991333	+	0.131369i	$0.0419374\pi$
$83$			1.13599e8i			0.262739i	−0.991333	+	0.131369i	$0.958063\pi$
$84$	3.16568e8			0.693761
$85$	−4.29420e8	−	1.63304e7i	−0.892271	−	0.0339321i
$86$	2.53486e8			0.499702
$87$		−	8.93659e8i		−	1.67238i
$88$	−4.37291e8	−	4.37291e8i	−0.777317	−	0.777317i
$89$	6.81819e8			1.15190			0.575949	−	0.817485i	$-0.304633\pi$
$89$	6.81819e8			1.15190			0.575949	+	0.817485i	$0.304633\pi$
$90$	1.08630e7	+	1.08630e7i	0.0174525	+	0.0174525i
$91$	−4.05524e8	+	4.05524e8i	−0.619912	+	0.619912i
$92$	3.12776e7	−	3.12776e7i	0.0455185	−	0.0455185i
$93$			4.84896e8i			0.672164i
$94$			1.35785e8i			0.179381i
$95$	6.32320e8	−	6.32320e8i	0.796491	−	0.796491i
$96$	−4.51856e8	+	4.51856e8i	−0.542974	+	0.542974i
$97$	−1.14542e9	−	1.14542e9i	−1.31369	−	1.31369i	−0.918676	−	0.395013i	$-0.870740\pi$
$97$	−1.14542e9	−	1.14542e9i	−1.31369	−	1.31369i	−0.395013	−	0.918676i	$-0.629260\pi$
$98$	1.21721e9			1.33306
$99$	2.50767e7	+	2.50767e7i	0.0262368	+	0.0262368i
$100$		−	8.62533e7i		−	0.0862533i
$101$	−1.17936e9			−1.12772			−0.563858	−	0.825872i	$-0.690683\pi$
$101$	−1.17936e9			−1.12772			−0.563858	+	0.825872i	$0.690683\pi$
$102$	3.09080e7	−	8.12751e8i	0.0282729	−	0.743459i
$103$	−2.87825e8			−0.251977			−0.125988	−	0.992032i	$-0.540210\pi$
$103$	−2.87825e8			−0.251977			−0.125988	+	0.992032i	$0.540210\pi$
$104$		−	6.80374e8i		−	0.570293i
$105$	1.28215e9	+	1.28215e9i	1.02941	+	1.02941i
$106$	3.14852e8			0.242231
$107$	−4.85698e7	−	4.85698e7i	−0.0358211	−	0.0358211i	0.688969	−	0.724790i	$-0.258063\pi$
$107$	−4.85698e7	−	4.85698e7i	−0.0358211	−	0.0358211i	−0.724790	+	0.688969i	$0.758063\pi$
$108$	4.32813e8	−	4.32813e8i	0.306121	−	0.306121i
$109$	−1.69842e9	+	1.69842e9i	−1.15246	+	1.15246i	−0.166402	+	0.986058i	$0.553215\pi$
$109$	−1.69842e9	+	1.69842e9i	−1.15246	+	1.15246i	−0.986058	+	0.166402i	$0.946785\pi$
$110$		−	1.05735e9i		−	0.688574i
$111$			2.56729e9i			1.60517i
$112$	−7.69440e8	+	7.69440e8i	−0.462055	+	0.462055i
$113$	1.97485e9	−	1.97485e9i	1.13941	−	1.13941i	0.150854	−	0.988556i	$-0.451798\pi$
$113$	1.97485e9	−	1.97485e9i	1.13941	−	1.13941i	0.988556	−	0.150854i	$-0.0482024\pi$
$114$	1.19678e9	+	1.19678e9i	0.663653	+	0.663653i
$115$	2.53358e8			0.135081
$116$	−9.99695e8	−	9.99695e8i	−0.512633	−	0.512633i
$117$			3.90164e7i			0.0192491i
$118$	1.40594e9			0.667570
$119$	−1.38076e8	+	3.63083e9i	−0.0631187	+	1.65976i
$120$	−2.15115e9			−0.947009
$121$		−	8.28881e7i		−	0.0351526i
$122$	3.26777e8	+	3.26777e8i	0.133546	+	0.133546i
$123$	−2.64740e9			−1.04291
$124$	5.42430e8	+	5.42430e8i	0.206037	+	0.206037i
$125$	2.07276e9	−	2.07276e9i	0.759370	−	0.759370i
$126$	9.18487e7	−	9.18487e7i	0.0324643	−	0.0324643i
$127$			4.35945e9i			1.48701i	0.668728	+	0.743507i	$0.266839\pi$
$127$			4.35945e9i			1.48701i	−0.668728	+	0.743507i	$0.733161\pi$
$128$			1.05346e8i			0.0346875i
$129$	1.43928e9	−	1.43928e9i	0.457605	−	0.457605i
$130$	8.22556e8	−	8.22556e8i	0.252592	−	0.252592i
$131$	4.19802e8	+	4.19802e8i	0.124544	+	0.124544i	0.766631	−	0.642087i	$-0.221931\pi$
$131$	4.19802e8	+	4.19802e8i	0.124544	+	0.124544i	−0.642087	+	0.766631i	$0.721931\pi$
$132$	−1.48230e9			−0.424966
$133$	−5.34640e9	−	5.34640e9i	−1.48159	−	1.48159i
$134$		−	9.87753e8i		−	0.264653i
$135$	3.50592e9			0.908447
$136$	−2.93001e9	−	3.16167e9i	−0.734419	−	0.792486i
$137$	−2.51782e9			−0.610636			−0.305318	−	0.952250i	$-0.598763\pi$
$137$	−2.51782e9			−0.610636			−0.305318	+	0.952250i	$0.598763\pi$
$138$			4.79524e8i			0.112552i
$139$	−8.99323e8	−	8.99323e8i	−0.204338	−	0.204338i	0.597518	−	0.801856i	$-0.296154\pi$
$139$	−8.99323e8	−	8.99323e8i	−0.204338	−	0.204338i	−0.801856	+	0.597518i	$0.796154\pi$
$140$	2.86856e9			0.631085
$141$	7.70978e8	+	7.70978e8i	0.164269	+	0.164269i
$142$	3.47515e8	−	3.47515e8i	0.0717258	−	0.0717258i
$143$	1.89883e9	−	1.89883e9i	0.379729	−	0.379729i
$144$			7.40297e7i			0.0143475i
$145$		−	8.09784e9i		−	1.52129i
$146$	−4.48193e9	+	4.48193e9i	−0.816352	+	0.816352i
$147$	6.91125e9	−	6.91125e9i	1.22075	−	1.22075i
$148$	2.87191e9	+	2.87191e9i	0.492031	+	0.492031i
$149$	1.57163e9			0.261223			0.130612	−	0.991434i	$-0.458306\pi$
$149$	1.57163e9			0.261223			0.130612	+	0.991434i	$0.458306\pi$
$150$	6.61186e8	+	6.61186e8i	0.106638	+	0.106638i
$151$			8.34738e9i			1.30663i	0.757084	+	0.653317i	$0.226623\pi$
$151$			8.34738e9i			1.30663i	−0.757084	+	0.653317i	$0.773377\pi$
$152$	8.97000e9			1.36300
$153$	1.68023e8	+	1.81308e8i	0.0247889	+	0.0267488i
$154$	−8.94008e9			−1.28085
$155$			4.39385e9i			0.611439i
$156$	−1.15315e9	−	1.15315e9i	−0.155892	−	0.155892i
$157$	1.34348e9			0.176474			0.0882372	−	0.996099i	$-0.471877\pi$
$157$	1.34348e9			0.176474			0.0882372	+	0.996099i	$0.471877\pi$
$158$	−6.36871e8	−	6.36871e8i	−0.0813008	−	0.0813008i
$159$	1.78771e9	−	1.78771e9i	0.221825	−	0.221825i
$160$	−4.09446e9	+	4.09446e9i	−0.493920	+	0.493920i
$161$		−	2.14219e9i		−	0.251271i
$162$			6.39324e9i			0.729296i
$163$	−3.43970e9	+	3.43970e9i	−0.381660	+	0.381660i	−0.871700	−	0.490040i	$-0.836982\pi$
$163$	−3.43970e9	+	3.43970e9i	−0.381660	+	0.381660i	0.490040	+	0.871700i	$0.336982\pi$
$164$	−2.96152e9	+	2.96152e9i	−0.319682	+	0.319682i
$165$	−6.00355e9	−	6.00355e9i	−0.630566	−	0.630566i
$166$	−1.94827e9			−0.199142
$167$	−5.75440e9	−	5.75440e9i	−0.572501	−	0.572501i	0.360326	−	0.932827i	$-0.382666\pi$
$167$	−5.75440e9	−	5.75440e9i	−0.572501	−	0.572501i	−0.932827	+	0.360326i	$0.882666\pi$
$168$			1.81884e10i			1.76158i
$169$	−7.65013e9			−0.721405
$170$	2.80071e8	−	7.36469e9i	0.0257187	−	0.676292i
$171$	−5.14390e8			−0.0460055
$172$		−	3.22010e9i		−	0.280538i
$173$	4.37354e9	+	4.37354e9i	0.371215	+	0.371215i	0.867920	−	0.496705i	$-0.165457\pi$
$173$	4.37354e9	+	4.37354e9i	0.371215	+	0.371215i	−0.496705	+	0.867920i	$0.665457\pi$
$174$	1.53266e10			1.26757
$175$	−2.95373e9	−	2.95373e9i	−0.238068	−	0.238068i
$176$	3.60284e9	−	3.60284e9i	0.283033	−	0.283033i
$177$	7.98283e9	−	7.98283e9i	0.611332	−	0.611332i
$178$			1.16934e10i			0.873076i
$179$			2.59694e10i			1.89071i	0.326049	+	0.945353i	$0.394282\pi$
$179$			2.59694e10i			1.89071i	−0.326049	+	0.945353i	$0.605718\pi$
$180$	1.37996e8	−	1.37996e8i	0.00979803	−	0.00979803i
$181$	8.07374e9	−	8.07374e9i	0.559141	−	0.559141i	−0.369922	−	0.929063i	$-0.620616\pi$
$181$	8.07374e9	−	8.07374e9i	0.559141	−	0.559141i	0.929063	+	0.369922i	$0.120616\pi$
$182$	−6.95487e9	−	6.95487e9i	−0.469860	−	0.469860i
$183$	3.71084e9			0.244592
$184$	1.79705e9	+	1.79705e9i	0.115579	+	0.115579i
$185$			2.32633e10i			1.46016i
$186$	−8.31613e9			−0.509463
$187$	6.46531e8	−	1.70010e10i	0.0386636	−	1.01669i
$188$	1.72491e9			0.100706
$189$		−	2.96432e10i		−	1.68985i
$190$	1.08445e10	+	1.08445e10i	0.603697	+	0.603697i
$191$	−8.71201e9			−0.473661			−0.236831	−	0.971551i	$-0.576109\pi$
$191$	−8.71201e9			−0.473661			−0.236831	+	0.971551i	$0.576109\pi$
$192$	−1.28914e10	−	1.28914e10i	−0.684611	−	0.684611i
$193$	6.23208e9	−	6.23208e9i	0.323314	−	0.323314i	−0.526723	−	0.850037i	$-0.676579\pi$
$193$	6.23208e9	−	6.23208e9i	0.323314	−	0.323314i	0.850037	+	0.526723i	$0.176579\pi$
$194$	1.96444e10	−	1.96444e10i	0.995704	−	0.995704i
$195$		−	9.34084e9i		−	0.462626i
$196$		−	1.54626e10i		−	0.748392i
$197$	−4.02050e9	+	4.02050e9i	−0.190188	+	0.190188i	−0.795777	−	0.605590i	$-0.792937\pi$
$197$	−4.02050e9	+	4.02050e9i	−0.190188	+	0.190188i	0.605590	+	0.795777i	$0.292937\pi$
$198$	−4.30074e8	+	4.30074e8i	−0.0198861	+	0.0198861i
$199$	2.76038e10	+	2.76038e10i	1.24776	+	1.24776i	0.956707	+	0.291052i	$0.0940051\pi$
$199$	2.76038e10	+	2.76038e10i	1.24776	+	1.24776i	0.291052	+	0.956707i	$0.405995\pi$
$200$	4.95568e9			0.219012
$201$	−5.60840e9	−	5.60840e9i	−0.242358	−	0.242358i
$202$		−	2.02264e10i		−	0.854746i
$203$	−6.84688e10			−2.82983
$204$	−1.03246e10	−	3.92634e8i	−0.417386	−	0.0158727i
$205$	−2.39892e10			−0.948690
$206$		−	4.93629e9i		−	0.190985i
$207$	−1.03053e8	−	1.03053e8i	−0.00390115	−	0.00390115i
$208$	5.60561e9			0.207653
$209$	2.50340e10	+	2.50340e10i	0.907555	+	0.907555i
$210$	−2.19893e10	+	2.19893e10i	−0.780233	+	0.780233i
$211$	2.70345e10	−	2.70345e10i	0.938960	−	0.938960i	−0.0592813	−	0.998241i	$-0.518881\pi$
$211$	2.70345e10	−	2.70345e10i	0.938960	−	0.938960i	0.998241	+	0.0592813i	$0.0188809\pi$
$212$		−	3.99966e9i		−	0.135991i
$213$		−	3.94633e9i		−	0.131367i
$214$	8.32989e8	−	8.32989e8i	0.0271505	−	0.0271505i
$215$	1.30419e10	−	1.30419e10i	0.416264	−	0.416264i
$216$	2.48672e10	+	2.48672e10i	0.777293	+	0.777293i
$217$	3.71509e10			1.13737
$218$	−2.91285e10	−	2.91285e10i	−0.873502	−	0.873502i
$219$			5.08963e10i			1.49516i
$220$	−1.34318e10			−0.386573
$221$	1.37288e10	−	1.27229e10i	0.387140	−	0.358773i
$222$	−4.40299e10			−1.21663
$223$			6.60414e10i			1.78832i	0.447752	+	0.894158i	$0.352225\pi$
$223$			6.60414e10i			1.78832i	−0.447752	+	0.894158i	$0.647775\pi$
$224$	3.46195e10	+	3.46195e10i	0.918765	+	0.918765i
$225$	−2.84186e8			−0.00739233
$226$	3.38693e10	+	3.38693e10i	0.863611	+	0.863611i
$227$	−2.67072e10	+	2.67072e10i	−0.667593	+	0.667593i	−0.957158	−	0.289565i	$-0.906489\pi$
$227$	−2.67072e10	+	2.67072e10i	−0.667593	+	0.667593i	0.289565	+	0.957158i	$0.406489\pi$
$228$	1.52030e10	−	1.52030e10i	0.372582	−	0.372582i
$229$		−	2.64797e10i		−	0.636288i	−0.948042	−	0.318144i	$-0.896940\pi$
$229$		−	2.64797e10i		−	0.636288i	0.948042	−	0.318144i	$-0.103060\pi$
$230$			4.34518e9i			0.102384i
$231$	−5.07612e10	+	5.07612e10i	−1.17295	+	1.17295i
$232$	5.74373e10	−	5.74373e10i	1.30166	−	1.30166i
$233$	−3.21859e10	−	3.21859e10i	−0.715425	−	0.715425i	0.252239	−	0.967665i	$-0.418833\pi$
$233$	−3.21859e10	−	3.21859e10i	−0.715425	−	0.715425i	−0.967665	+	0.252239i	$0.918833\pi$
$234$	−6.69146e8			−0.0145898
$235$	6.98617e9	+	6.98617e9i	0.149429	+	0.149429i
$236$		−	1.78600e10i		−	0.374781i
$237$	−7.23223e9			−0.148903
$238$	−6.22700e10	−	2.36806e9i	−1.25800	−	0.0478405i
$239$	3.15730e10			0.625929			0.312964	−	0.949765i	$-0.398678\pi$
$239$	3.15730e10			0.625929			0.312964	+	0.949765i	$0.398678\pi$
$240$		−	1.77233e10i		−	0.344821i
$241$	5.02071e9	+	5.02071e9i	0.0958713	+	0.0958713i	0.753416	−	0.657544i	$-0.228405\pi$
$241$	5.02071e9	+	5.02071e9i	0.0958713	+	0.0958713i	−0.657544	+	0.753416i	$0.728405\pi$
$242$	1.42156e9			0.0266438
$243$	−2.80187e9	−	2.80187e9i	−0.0515490	−	0.0515490i
$244$	4.15114e9	−	4.15114e9i	0.0749744	−	0.0749744i
$245$	6.26258e10	−	6.26258e10i	1.11047	−	1.11047i
$246$		−	4.54038e10i		−	0.790468i
$247$			3.89501e10i			0.665844i
$248$	−3.11653e10	+	3.11653e10i	−0.523164	+	0.523164i
$249$	−1.10621e10	+	1.10621e10i	−0.182365	+	0.182365i
$250$	3.55485e10	+	3.55485e10i	0.575561	+	0.575561i
$251$	−5.74029e10			−0.912855			−0.456428	−	0.889761i	$-0.650871\pi$
$251$	−5.74029e10			−0.912855			−0.456428	+	0.889761i	$0.650871\pi$
$252$	−1.16678e9	−	1.16678e9i	−0.0182258	−	0.0182258i
$253$			1.00306e10i			0.153917i
$254$	−7.47661e10			−1.12708
$255$	−4.02260e10	−	4.34065e10i	−0.595767	−	0.642871i
$256$	−6.95874e10			−1.01263
$257$			3.44724e10i			0.492915i	0.969154	+	0.246457i	$0.0792665\pi$
$257$			3.44724e10i			0.492915i	−0.969154	+	0.246457i	$0.920733\pi$
$258$	2.46841e10	+	2.46841e10i	0.346840	+	0.346840i
$259$	1.96696e11			2.71611
$260$	−1.04492e10	−	1.04492e10i	−0.141808	−	0.141808i
$261$	−3.29378e9	+	3.29378e9i	−0.0439351	+	0.0439351i
$262$	−7.19974e9	+	7.19974e9i	−0.0943976	+	0.0943976i
$263$		−	1.19112e11i		−	1.53516i	−0.640952	−	0.767581i	$-0.721460\pi$
$263$		−	1.19112e11i		−	1.53516i	0.640952	−	0.767581i	$-0.278540\pi$
$264$		−	8.51655e10i		−	1.07906i
$265$	1.61992e10	−	1.61992e10i	0.201785	−	0.201785i
$266$	9.16925e10	−	9.16925e10i	1.12297	−	1.12297i
$267$	6.63946e10	+	6.63946e10i	0.799525	+	0.799525i
$268$	−1.25477e10			−0.148579
$269$	−8.38974e10	−	8.38974e10i	−0.976929	−	0.976929i	0.0228106	−	0.999740i	$-0.492739\pi$
$269$	−8.38974e10	−	8.38974e10i	−0.976929	−	0.976929i	−0.999740	+	0.0228106i	$0.992739\pi$
$270$			6.01277e10i			0.688553i
$271$	4.58480e9			0.0516367			0.0258184	−	0.999667i	$-0.491781\pi$
$271$	4.58480e9			0.0516367			0.0258184	+	0.999667i	$0.491781\pi$
$272$	2.60490e10	−	2.41404e10i	0.288557	−	0.267414i
$273$	−7.89787e10			−0.860554
$274$		−	4.31815e10i		−	0.462829i
$275$	1.38306e10	+	1.38306e10i	0.145829	+	0.145829i
$276$	6.09153e9			0.0631881
$277$	−9.69688e10	−	9.69688e10i	−0.989631	−	0.989631i	0.0103160	−	0.999947i	$-0.496716\pi$
$277$	−9.69688e10	−	9.69688e10i	−0.989631	−	0.989631i	−0.999947	+	0.0103160i	$0.996716\pi$
$278$	1.54237e10	−	1.54237e10i	0.154877	−	0.154877i
$279$	1.78719e9	−	1.78719e9i	0.0176584	−	0.0176584i
$280$			1.64813e11i			1.60243i
$281$			1.43100e11i			1.36918i	0.728928	+	0.684590i	$0.240019\pi$
$281$			1.43100e11i			1.36918i	−0.728928	+	0.684590i	$0.759981\pi$
$282$	−1.32225e10	+	1.32225e10i	−0.124507	+	0.124507i
$283$	−1.18261e11	+	1.18261e11i	−1.09598	+	1.09598i	−0.101108	+	0.994875i	$0.532239\pi$
$283$	−1.18261e11	+	1.18261e11i	−1.09598	+	1.09598i	−0.994875	+	0.101108i	$0.967761\pi$
$284$	−4.41458e9	−	4.41458e9i	−0.0402677	−	0.0402677i
$285$	1.23149e11			1.10568
$286$	3.25656e10	+	3.25656e10i	0.287814	+	0.287814i
$287$			2.02834e11i			1.76470i
$288$	3.33083e9			0.0285289
$289$	9.00651e9	−	1.18245e11i	0.0759480	−	0.997112i
$290$	1.38881e11			1.15306
$291$		−	2.23079e11i		−	1.82364i
$292$	5.69353e10	+	5.69353e10i	0.458309	+	0.458309i
$293$	−6.00192e10			−0.475758			−0.237879	−	0.971295i	$-0.576452\pi$
$293$	−6.00192e10			−0.475758			−0.237879	+	0.971295i	$0.576452\pi$
$294$	1.18530e11	+	1.18530e11i	0.925265	+	0.925265i
$295$	7.23359e10	−	7.23359e10i	0.556102	−	0.556102i
$296$	−1.65005e11	+	1.65005e11i	−1.24935	+	1.24935i
$297$			1.38802e11i			1.03512i
$298$			2.69540e10i			0.197993i
$299$	−7.80326e9	+	7.80326e9i	−0.0564619	+	0.0564619i
$300$	8.39923e9	−	8.39923e9i	0.0598679	−	0.0598679i
$301$	−1.10272e11	−	1.10272e11i	−0.774312	−	0.774312i
$302$	−1.43161e11			−0.990358
$303$	−1.14844e11	−	1.14844e11i	−0.782740	−	0.782740i
$304$			7.39039e10i			0.496291i
$305$	3.36255e10			0.222495
$306$	−3.10949e9	+	2.88165e9i	−0.0202742	+	0.0187886i
$307$	−2.28024e11			−1.46507			−0.732535	−	0.680729i	$-0.761663\pi$
$307$	−2.28024e11			−1.46507			−0.732535	+	0.680729i	$0.761663\pi$
$308$			1.13568e11i			0.719083i
$309$	−2.80280e10	−	2.80280e10i	−0.174895	−	0.174895i
$310$	−7.53561e10			−0.463437
$311$	2.49859e10	+	2.49859e10i	0.151452	+	0.151452i	0.778766	−	0.627315i	$-0.215846\pi$
$311$	2.49859e10	+	2.49859e10i	0.151452	+	0.151452i	−0.627315	+	0.778766i	$0.715846\pi$
$312$	6.62539e10	−	6.62539e10i	0.395836	−	0.395836i
$313$	1.42939e11	−	1.42939e11i	0.841786	−	0.841786i	−0.147305	−	0.989091i	$-0.547060\pi$
$313$	1.42939e11	−	1.42939e11i	0.841786	−	0.841786i	0.989091	+	0.147305i	$0.0470600\pi$
$314$			2.30411e10i			0.133758i
$315$		−	9.45128e9i		−	0.0540870i
$316$	−8.09036e9	+	8.09036e9i	−0.0456432	+	0.0456432i
$317$	2.17665e11	−	2.17665e11i	1.21066	−	1.21066i	0.239848	−	0.970811i	$-0.422903\pi$
$317$	2.17665e11	−	2.17665e11i	1.21066	−	1.21066i	0.970811	−	0.239848i	$-0.0770975\pi$
$318$	3.06599e10	+	3.06599e10i	0.168131	+	0.168131i
$319$	3.20600e11			1.73342
$320$	−1.16814e11	−	1.16814e11i	−0.622761	−	0.622761i
$321$		−	9.45932e9i		−	0.0497264i
$322$	3.67393e10			0.190450
$323$	1.67737e11	+	1.81000e11i	0.857470	+	0.925265i
$324$	8.12152e10			0.409435
$325$			2.15189e10i			0.106990i
$326$	−5.89921e10	−	5.89921e10i	−0.289278	−	0.289278i
$327$	−3.30780e11			−1.59983
$328$	−1.70154e11	−	1.70154e11i	−0.811726	−	0.811726i
$329$	5.90694e10	−	5.90694e10i	0.277959	−	0.277959i
$330$	1.02963e11	−	1.02963e11i	0.477934	−	0.477934i
$331$			1.74695e11i			0.799934i	0.916530	+	0.399967i	$0.130978\pi$
$331$			1.74695e11i			0.799934i	−0.916530	+	0.399967i	$0.869022\pi$
$332$			2.47494e10i			0.111800i
$333$	9.46231e9	−	9.46231e9i	0.0421695	−	0.0421695i
$334$	9.86900e10	−	9.86900e10i	0.433924	−	0.433924i
$335$	−5.08202e10	−	5.08202e10i	−0.220462	−	0.220462i
$336$	−1.49854e11			−0.641419
$337$	1.41678e11	+	1.41678e11i	0.598369	+	0.598369i	0.939878	−	0.341509i	$-0.110938\pi$
$337$	1.41678e11	+	1.41678e11i	0.598369	+	0.598369i	−0.341509	+	0.939878i	$0.610938\pi$
$338$		−	1.31202e11i		−	0.546785i
$339$	3.84615e11			1.58171
$340$	−9.35558e10	−	3.55782e9i	−0.379678	−	0.0144387i
$341$	−1.73956e11			−0.696698
$342$		−	8.82196e9i		−	0.0348697i
$343$	−2.28444e11	−	2.28444e11i	−0.891162	−	0.891162i
$344$	1.85011e11			0.712334
$345$	2.46716e10	+	2.46716e10i	0.0937588	+	0.0937588i
$346$	−7.50077e10	+	7.50077e10i	−0.281361	+	0.281361i
$347$	−4.35481e10	+	4.35481e10i	−0.161245	+	0.161245i	−0.783118	−	0.621873i	$-0.786372\pi$
$347$	−4.35481e10	+	4.35481e10i	−0.161245	+	0.161245i	0.621873	+	0.783118i	$0.286372\pi$
$348$		−	1.94698e11i		−	0.711630i
$349$			4.21517e10i			0.152090i	0.997104	+	0.0760450i	$0.0242293\pi$
$349$			4.21517e10i			0.152090i	−0.997104	+	0.0760450i	$0.975771\pi$
$350$	5.06576e10	−	5.06576e10i	0.180442	−	0.180442i
$351$	−1.07980e11	+	1.07980e11i	−0.379718	+	0.379718i
$352$	−1.62103e11	−	1.62103e11i	−0.562793	−	0.562793i
$353$	1.90620e11			0.653405			0.326702	−	0.945127i	$-0.394063\pi$
$353$	1.90620e11			0.653405			0.326702	+	0.945127i	$0.394063\pi$
$354$	1.36908e11	+	1.36908e11i	0.463356	+	0.463356i
$355$		−	3.57594e10i		−	0.119499i
$356$	1.48545e11			0.490155
$357$	−3.67011e11	+	3.40119e11i	−1.19584	+	1.10822i
$358$	−4.45385e11			−1.43305
$359$			3.44172e10i			0.109358i	0.998504	+	0.0546790i	$0.0174136\pi$
$359$			3.44172e10i			0.109358i	−0.998504	+	0.0546790i	$0.982586\pi$
$360$	7.92852e9	+	7.92852e9i	0.0248789	+	0.0248789i
$361$	−1.90828e11			−0.591370
$362$	1.38467e11	+	1.38467e11i	0.423798	+	0.423798i
$363$	8.07152e9	−	8.07152e9i	0.0243992	−	0.0243992i
$364$	−8.83497e10	+	8.83497e10i	−0.263784	+	0.263784i
$365$			4.61193e11i			1.36008i
$366$			6.36421e10i			0.185387i
$367$	2.82143e11	−	2.82143e11i	0.811844	−	0.811844i	−0.173067	−	0.984910i	$-0.555368\pi$
$367$	2.82143e11	−	2.82143e11i	0.811844	−	0.811844i	0.984910	+	0.173067i	$0.0553676\pi$
$368$	−1.48059e10	+	1.48059e10i	−0.0420842	+	0.0420842i
$369$	9.75757e9	+	9.75757e9i	0.0273983	+	0.0273983i
$370$	−3.98974e11			−1.10672
$371$	−1.36968e11	−	1.36968e11i	−0.375349	−	0.375349i
$372$			1.05642e11i			0.286018i
$373$	1.16645e11			0.312016			0.156008	−	0.987756i	$-0.450137\pi$
$373$	1.16645e11			0.312016			0.156008	+	0.987756i	$0.450137\pi$
$374$	2.91574e11	+	1.10882e10i	0.770595	+	0.0293049i
$375$	4.03684e11			1.05415
$376$			9.91047e10i			0.255711i
$377$	2.49408e11	+	2.49408e11i	0.635879	+	0.635879i
$378$	5.08392e11			1.28081
$379$	2.02796e11	+	2.02796e11i	0.504875	+	0.504875i	0.912949	−	0.408074i	$-0.133799\pi$
$379$	2.02796e11	+	2.02796e11i	0.504875	+	0.504875i	−0.408074	+	0.912949i	$0.633799\pi$
$380$	1.37761e11	−	1.37761e11i	0.338922	−	0.338922i
$381$	−4.24517e11	+	4.24517e11i	−1.03213	+	1.03213i
$382$		−	1.49414e11i		−	0.359010i
$383$		−	2.62825e11i		−	0.624125i	−0.950062	−	0.312063i	$-0.898980\pi$
$383$		−	2.62825e11i		−	0.624125i	0.950062	−	0.312063i	$-0.101020\pi$
$384$	−1.02584e10	+	1.02584e10i	−0.0240763	+	0.0240763i
$385$	−4.59970e11	+	4.59970e11i	−1.06698	+	1.06698i
$386$	1.06882e11	+	1.06882e11i	0.245055	+	0.245055i
$387$	−1.06095e10			−0.0240435
$388$	−2.49548e11	−	2.49548e11i	−0.558999	−	0.558999i
$389$		−	4.43883e11i		−	0.982867i	−0.870915	−	0.491434i	$-0.836473\pi$
$389$		−	4.43883e11i		−	0.982867i	0.870915	−	0.491434i	$-0.163527\pi$
$390$	1.60199e11			0.350645
$391$	−2.65692e9	+	6.98659e10i	−0.00574889	+	0.151172i
$392$	8.88400e11			1.90030
$393$			8.17594e10i			0.172890i
$394$	−6.89530e10	−	6.89530e10i	−0.144152	−	0.144152i
$395$	−6.55344e10			−0.135451
$396$	5.46335e9	+	5.46335e9i	0.0111643	+	0.0111643i
$397$	−5.06690e11	+	5.06690e11i	−1.02373	+	1.02373i	−0.0240181	+	0.999712i	$0.507646\pi$
$397$	−5.06690e11	+	5.06690e11i	−1.02373	+	1.02373i	−0.999712	+	0.0240181i	$0.992354\pi$
$398$	−4.73415e11	+	4.73415e11i	−0.945733	+	0.945733i
$399$		−	1.04125e12i		−	2.05673i
$400$			4.08298e10i			0.0797458i
$401$	4.20270e9	−	4.20270e9i	0.00811668	−	0.00811668i	−0.703037	−	0.711153i	$-0.748173\pi$
$401$	4.20270e9	−	4.20270e9i	0.00811668	−	0.00811668i	0.711153	+	0.703037i	$0.248173\pi$
$402$	9.61860e10	−	9.61860e10i	0.183694	−	0.183694i
$403$	−1.35328e11	−	1.35328e11i	−0.255573	−	0.255573i
$404$	−2.56942e11			−0.479864
$405$	3.28934e11	+	3.28934e11i	0.607521	+	0.607521i
$406$		−	1.17426e12i		−	2.14486i
$407$	−9.21013e11			−1.66376
$408$	2.25587e10	−	5.93199e11i	0.0403036	−	1.05981i
$409$	8.83784e11			1.56168			0.780839	−	0.624732i	$-0.214792\pi$
$409$	8.83784e11			1.56168			0.780839	+	0.624732i	$0.214792\pi$
$410$		−	4.11424e11i		−	0.719055i
$411$	−2.45182e11	−	2.45182e11i	−0.423838	−	0.423838i
$412$	−6.27071e10			−0.107221
$413$	−6.11614e11	−	6.11614e11i	−1.03443	−	1.03443i
$414$	1.76739e9	−	1.76739e9i	0.00295686	−	0.00295686i
$415$	−1.00239e11	+	1.00239e11i	−0.165890	+	0.165890i
$416$		−	2.52214e11i		−	0.412903i
$417$		−	1.75150e11i		−	0.283659i
$418$	−4.29342e11	+	4.29342e11i	−0.687877	+	0.687877i
$419$	−5.34321e11	+	5.34321e11i	−0.846913	+	0.846913i	−0.989747	−	0.142833i	$-0.954379\pi$
$419$	−5.34321e11	+	5.34321e11i	−0.846913	+	0.846913i	0.142833	+	0.989747i	$0.454379\pi$
$420$	2.79336e11	+	2.79336e11i	0.438032	+	0.438032i
$421$	8.69830e11			1.34948			0.674738	−	0.738057i	$-0.264257\pi$
$421$	8.69830e11			1.34948			0.674738	+	0.738057i	$0.264257\pi$
$422$	4.63651e11	+	4.63651e11i	0.711680	+	0.711680i
$423$		−	5.68322e9i		−	0.00863103i
$424$	2.29800e11			0.345305
$425$	9.26703e10	+	9.99972e10i	0.137781	+	0.148675i
$426$	6.76810e10			0.0995688
$427$		−	2.84310e11i		−	0.413873i
$428$	−1.05817e10	−	1.05817e10i	−0.0152426	−	0.0152426i
$429$	3.69811e11			0.527135
$430$	2.23673e11	+	2.23673e11i	0.315505	+	0.315505i
$431$	5.93600e11	−	5.93600e11i	0.828603	−	0.828603i	−0.158721	−	0.987324i	$-0.550737\pi$
$431$	5.93600e11	−	5.93600e11i	0.828603	−	0.828603i	0.987324	+	0.158721i	$0.0507370\pi$
$432$	−2.04881e11	+	2.04881e11i	−0.283025	+	0.283025i
$433$			7.65233e11i			1.04616i	0.852283	+	0.523080i	$0.175217\pi$
$433$			7.65233e11i			1.04616i	−0.852283	+	0.523080i	$0.824783\pi$
$434$			6.37151e11i			0.862062i
$435$	7.88556e11	−	7.88556e11i	1.05592	−	1.05592i
$436$	−3.70027e11	+	3.70027e11i	−0.490394	+	0.490394i
$437$	−1.02878e11	−	1.02878e11i	−0.134944	−	0.134944i
$438$	−8.72889e11			−1.13325
$439$	3.71648e11	+	3.71648e11i	0.477575	+	0.477575i	0.904355	−	0.426781i	$-0.140352\pi$
$439$	3.71648e11	+	3.71648e11i	0.477575	+	0.477575i	−0.426781	+	0.904355i	$0.640352\pi$
$440$		−	7.71721e11i		−	0.981575i
$441$	−5.09458e10			−0.0641409
$442$	2.18202e11	+	2.35454e11i	0.271931	+	0.293431i
$443$	3.31208e10			0.0408587			0.0204294	−	0.999791i	$-0.493497\pi$
$443$	3.31208e10			0.0408587			0.0204294	+	0.999791i	$0.493497\pi$
$444$			5.59324e11i			0.683031i
$445$	6.01631e11	+	6.01631e11i	0.727294	+	0.727294i
$446$	−1.13263e12			−1.35545
$447$	1.53043e11	+	1.53043e11i	0.181313	+	0.181313i
$448$	−9.87690e11	+	9.87690e11i	−1.15843	+	1.15843i
$449$	7.25101e11	−	7.25101e11i	0.841957	−	0.841957i	−0.147156	−	0.989113i	$-0.547012\pi$
$449$	7.25101e11	−	7.25101e11i	0.841957	−	0.841957i	0.989113	+	0.147156i	$0.0470119\pi$
$450$		−	4.87389e9i		−	0.00560298i
$451$		−	9.49752e11i		−	1.08098i
$452$	4.30251e11	−	4.30251e11i	0.484841	−	0.484841i
$453$	−8.12857e11	+	8.12857e11i	−0.906926	+	0.906926i
$454$	−4.58037e11	−	4.58037e11i	−0.505999	−	0.505999i
$455$	−7.15660e11			−0.782809
$456$	8.73486e11	+	8.73486e11i	0.946050	+	0.946050i
$457$		−	7.69863e11i		−	0.825640i	−0.910813	−	0.412820i	$-0.864544\pi$
$457$		−	7.69863e11i		−	0.825640i	0.910813	−	0.412820i	$-0.135456\pi$
$458$	4.54136e11			0.482272
$459$	−3.67660e10	+	9.66791e11i	−0.0386624	+	1.01666i
$460$	5.51980e10			0.0574795
$461$			1.11125e12i			1.14593i	0.819581	+	0.572963i	$0.194206\pi$
$461$			1.11125e12i			1.14593i	−0.819581	+	0.572963i	$0.805794\pi$
$462$	−8.70573e11	−	8.70573e11i	−0.889029	−	0.889029i
$463$	−4.08973e11			−0.413600			−0.206800	−	0.978383i	$-0.566305\pi$
$463$	−4.08973e11			−0.413600			−0.206800	+	0.978383i	$0.566305\pi$
$464$	4.73227e11	+	4.73227e11i	0.473956	+	0.473956i
$465$	−4.27867e11	+	4.27867e11i	−0.424395	+	0.424395i
$466$	5.52000e11	−	5.52000e11i	0.542253	−	0.542253i
$467$		−	6.23914e11i		−	0.607014i	−0.952829	−	0.303507i	$-0.901842\pi$
$467$		−	6.23914e11i		−	0.607014i	0.952829	−	0.303507i	$-0.0981576\pi$
$468$			8.50035e9i			0.00819087i
$469$	−4.29695e11	+	4.29695e11i	−0.410093	+	0.410093i
$470$	−1.19815e11	+	1.19815e11i	−0.113259	+	0.113259i
$471$	1.30826e11	+	1.30826e11i	0.122490	+	0.122490i
$472$	1.02615e12			0.951634
$473$	5.16339e11	+	5.16339e11i	0.474308	+	0.474308i
$474$		−	1.24035e11i		−	0.112861i
$475$	−2.83703e11			−0.255707
$476$	−3.00821e10	+	7.91033e11i	−0.0268582	+	0.706258i
$477$	−1.31780e10			−0.0116551
$478$			5.41487e11i			0.474420i
$479$	−6.67820e11	−	6.67820e11i	−0.579628	−	0.579628i	0.355172	−	0.934801i	$-0.384422\pi$
$479$	−6.67820e11	−	6.67820e11i	−0.579628	−	0.579628i	−0.934801	+	0.355172i	$0.884422\pi$
$480$	−7.97426e11			−0.685654
$481$	−7.16496e11	−	7.16496e11i	−0.610324	−	0.610324i
$482$	−8.61070e10	+	8.61070e10i	−0.0726652	+	0.0726652i
$483$	2.08604e11	−	2.08604e11i	0.174405	−	0.174405i
$484$		−	1.80585e10i		−	0.0149581i
$485$		−	2.02142e12i		−	1.65889i
$486$	4.80531e10	−	4.80531e10i	0.0390713	−	0.0390713i
$487$	8.15409e11	−	8.15409e11i	0.656894	−	0.656894i	−0.297750	−	0.954644i	$-0.596236\pi$
$487$	8.15409e11	−	8.15409e11i	0.656894	−	0.656894i	0.954644	+	0.297750i	$0.0962363\pi$
$488$	2.38503e11	+	2.38503e11i	0.190373	+	0.190373i
$489$	−6.69907e11			−0.529816
$490$	1.07405e12	+	1.07405e12i	0.841674	+	0.841674i
$491$			9.77635e11i			0.759119i	0.925167	+	0.379560i	$0.123924\pi$
$491$			9.77635e11i			0.759119i	−0.925167	+	0.379560i	$0.876076\pi$
$492$	−5.76778e11			−0.443778
$493$	2.23306e12	+	8.49207e10i	1.70251	+	0.0647444i
$494$	−6.68008e11			−0.504673
$495$			4.42548e10i			0.0331312i
$496$	−2.56771e11	−	2.56771e11i	−0.190493	−	0.190493i
$497$	−3.02353e11			−0.222285
$498$	−1.89719e11	−	1.89719e11i	−0.138223	−	0.138223i
$499$	6.69481e11	−	6.69481e11i	0.483376	−	0.483376i	−0.422832	−	0.906208i	$-0.638964\pi$
$499$	6.69481e11	−	6.69481e11i	0.483376	−	0.483376i	0.906208	+	0.422832i	$0.138964\pi$
$500$	4.51583e11	−	4.51583e11i	0.323126	−	0.323126i
$501$		−	1.12071e12i		−	0.794738i
$502$		−	9.84479e11i		−	0.691894i
$503$	5.21867e11	−	5.21867e11i	0.363500	−	0.363500i	−0.501600	−	0.865100i	$-0.667255\pi$
$503$	5.21867e11	−	5.21867e11i	0.363500	−	0.363500i	0.865100	+	0.501600i	$0.167255\pi$
$504$	6.70372e10	−	6.70372e10i	0.0462784	−	0.0462784i
$505$	−1.04065e12	−	1.04065e12i	−0.712024	−	0.712024i
$506$	−1.72029e11			−0.116661
$507$	−7.44959e11	−	7.44959e11i	−0.500722	−	0.500722i
$508$			9.49775e11i			0.632753i
$509$	−2.67500e11			−0.176642			−0.0883209	−	0.996092i	$-0.528150\pi$
$509$	−2.67500e11			−0.176642			−0.0883209	+	0.996092i	$0.528150\pi$
$510$	7.44436e11	−	6.89891e11i	0.487261	−	0.451559i
$511$	3.89948e12			2.52996
$512$		−	1.13951e12i		−	0.732831i
$513$	−1.42360e12	−	1.42360e12i	−0.907527	−	0.907527i
$514$	−5.91213e11			−0.373602
$515$	−2.53974e11	−	2.53974e11i	−0.159095	−	0.159095i
$516$	3.13569e11	−	3.13569e11i	0.194720	−	0.194720i
$517$	−2.76588e11	+	2.76588e11i	−0.170265	+	0.170265i
$518$			3.37341e12i			2.05866i
$519$			8.51778e11i			0.515316i
$520$	6.00355e11	−	6.00355e11i	0.360075	−	0.360075i
$521$	−1.79523e12	+	1.79523e12i	−1.06746	+	1.06746i	−0.0699049	+	0.997554i	$0.522270\pi$
$521$	−1.79523e12	+	1.79523e12i	−1.06746	+	1.06746i	−0.997554	+	0.0699049i	$0.977730\pi$
$522$	−5.64894e10	−	5.64894e10i	−0.0333004	−	0.0333004i
$523$	−2.26847e12			−1.32579			−0.662895	−	0.748712i	$-0.730672\pi$
$523$	−2.26847e12			−1.32579			−0.662895	+	0.748712i	$0.730672\pi$
$524$	9.14603e10	+	9.14603e10i	0.0529959	+	0.0529959i
$525$		−	5.75261e11i		−	0.330482i
$526$	2.04281e12			1.16357
$527$	−1.21165e12	−	4.60776e10i	−0.684272	−	0.0260221i
$528$	7.01679e11			0.392903
$529$			1.75993e12i			0.977114i
$530$	2.77822e11	+	2.77822e11i	0.152942	+	0.152942i
$531$	−5.88449e10			−0.0321206
$532$	−1.16480e12	−	1.16480e12i	−0.630446	−	0.630446i
$533$	7.38853e11	−	7.38853e11i	0.396539	−	0.396539i
$534$	−1.13869e12	+	1.13869e12i	−0.605996	+	0.605996i
$535$		−	8.57150e10i		−	0.0452340i
$536$		−	7.20927e11i		−	0.377268i
$537$	−2.52887e12	+	2.52887e12i	−1.31233	+	1.31233i
$538$	1.43887e12	−	1.43887e12i	0.740459	−	0.740459i
$539$	2.47940e12	+	2.47940e12i	1.26531	+	1.26531i
$540$	7.63819e11			0.386561
$541$	5.97882e11	+	5.97882e11i	0.300074	+	0.300074i	0.841043	−	0.540969i	$-0.181942\pi$
$541$	5.97882e11	+	5.97882e11i	0.300074	+	0.300074i	−0.540969	+	0.841043i	$0.681942\pi$
$542$			7.86310e10i			0.0391378i
$543$	1.57242e12			0.776191
$544$	−1.08615e12	−	1.17203e12i	−0.531734	−	0.573776i
$545$	−2.99734e12			−1.45530
$546$		−	1.35451e12i		−	0.652253i
$547$	2.28757e12	+	2.28757e12i	1.09252	+	1.09252i	0.995258	+	0.0972654i	$0.0310096\pi$
$547$	2.28757e12	+	2.28757e12i	1.09252	+	1.09252i	0.0972654	+	0.995258i	$0.468990\pi$
$548$	−5.48547e11			−0.259837
$549$	−1.36771e10	−	1.36771e10i	−0.00642567	−	0.00642567i
$550$	−2.37200e11	+	2.37200e11i	−0.110531	+	0.110531i
$551$	−3.28818e12	+	3.28818e12i	−1.51975	+	1.51975i
$552$			3.49988e11i			0.160445i
$553$			5.54107e11i			0.251959i
$554$	1.66305e12	−	1.66305e12i	0.750086	−	0.750086i
$555$	−2.26535e12	+	2.26535e12i	−1.01348	+	1.01348i
$556$	−1.95932e11	−	1.95932e11i	−0.0869497	−	0.0869497i
$557$	2.60766e12			1.14790			0.573948	−	0.818892i	$-0.305411\pi$
$557$	2.60766e12			1.14790			0.573948	+	0.818892i	$0.305411\pi$
$558$	3.06509e10	+	3.06509e10i	0.0133841	+	0.0133841i
$559$			8.03365e11i			0.347985i
$560$	−1.35789e12			−0.583471
$561$	1.71850e12	−	1.59258e12i	0.732514	−	0.678841i
$562$	−2.45421e12			−1.03776
$563$		−	1.28685e12i		−	0.539809i	−0.962887	−	0.269905i	$-0.913008\pi$
$563$		−	1.28685e12i		−	0.539809i	0.962887	−	0.269905i	$-0.0869922\pi$
$564$	1.67970e11	+	1.67970e11i	0.0698996	+	0.0698996i
$565$	3.48517e12			1.43882
$566$	−2.02822e12	−	2.02822e12i	−0.830695	−	0.830695i
$567$	2.78120e12	−	2.78120e12i	1.13008	−	1.13008i
$568$	2.53639e11	−	2.53639e11i	0.102247	−	0.102247i
$569$		−	1.78057e12i		−	0.712120i	−0.934463	−	0.356060i	$-0.884120\pi$
$569$		−	1.78057e12i		−	0.712120i	0.934463	−	0.356060i	$-0.115880\pi$
$570$			2.11205e12i			0.838044i
$571$	−2.33995e12	+	2.33995e12i	−0.921178	+	0.921178i	−0.997113	−	0.0759350i	$-0.975806\pi$
$571$	−2.33995e12	+	2.33995e12i	−0.921178	+	0.921178i	0.0759350	+	0.997113i	$0.475806\pi$
$572$	4.13690e11	−	4.13690e11i	0.161582	−	0.161582i
$573$	−8.48363e11	−	8.48363e11i	−0.328765	−	0.328765i
$574$	−3.47867e12			−1.33755
$575$	−5.68370e10	−	5.68370e10i	−0.0216833	−	0.0216833i
$576$			9.50280e10i			0.0359708i
$577$	2.72309e12			1.02275			0.511377	−	0.859357i	$-0.329136\pi$
$577$	2.72309e12			1.02275			0.511377	+	0.859357i	$0.329136\pi$
$578$	2.02795e12	+	1.54465e11i	0.755756	+	0.0575644i
$579$	1.21374e12			0.448821
$580$		−	1.76424e12i		−	0.647339i
$581$	8.47540e11	+	8.47540e11i	0.308580	+	0.308580i
$582$	3.82588e12			1.38222
$583$	6.41340e11	+	6.41340e11i	0.229922	+	0.229922i
$584$	−3.27121e12	+	3.27121e12i	−1.16373	+	1.16373i
$585$	−3.44277e10	+	3.44277e10i	−0.0121537	+	0.0121537i
$586$		−	1.02935e12i		−	0.360599i
$587$		−	2.10387e12i		−	0.731388i	−0.930735	−	0.365694i	$-0.880832\pi$
$587$		−	2.10387e12i		−	0.731388i	0.930735	−	0.365694i	$-0.119168\pi$
$588$	1.50572e12	−	1.50572e12i	0.519454	−	0.519454i
$589$	1.78415e12	−	1.78415e12i	0.610819	−	0.610819i
$590$	1.24059e12	+	1.24059e12i	0.421495	+	0.421495i
$591$	−7.83021e11			−0.264016
$592$	−1.35948e12	−	1.35948e12i	−0.454909	−	0.454909i
$593$		−	2.56437e12i		−	0.851599i	−0.904818	−	0.425799i	$-0.859993\pi$
$593$		−	2.56437e12i		−	0.851599i	0.904818	−	0.425799i	$-0.140007\pi$
$594$	−2.38050e12			−0.784566
$595$	−3.32564e12	+	3.08197e12i	−1.08780	+	1.00810i
$596$	3.42404e11			0.111155
$597$			5.37605e12i			1.73212i
$598$	−1.33829e11	−	1.33829e11i	−0.0427951	−	0.0427951i
$599$	−1.25542e12			−0.398446			−0.199223	−	0.979954i	$-0.563842\pi$
$599$	−1.25542e12			−0.398446			−0.199223	+	0.979954i	$0.563842\pi$
$600$	4.82577e11	+	4.82577e11i	0.152015	+	0.152015i
$601$	2.16588e12	−	2.16588e12i	0.677172	−	0.677172i	−0.282187	−	0.959359i	$-0.591060\pi$
$601$	2.16588e12	−	2.16588e12i	0.677172	−	0.677172i	0.959359	+	0.282187i	$0.0910599\pi$
$602$	1.89120e12	−	1.89120e12i	0.586886	−	0.586886i
$603$			4.13420e10i			0.0127340i
$604$			1.81861e12i			0.555998i
$605$	7.31396e10	−	7.31396e10i	0.0221949	−	0.0221949i
$606$	1.96962e12	−	1.96962e12i	0.593274	−	0.593274i
$607$	−3.05652e12	−	3.05652e12i	−0.913856	−	0.913856i	0.0827175	−	0.996573i	$-0.473640\pi$
$607$	−3.05652e12	−	3.05652e12i	−0.913856	−	0.913856i	−0.996573	+	0.0827175i	$0.973640\pi$
$608$	3.32516e12			0.986840
$609$	−6.66740e12	−	6.66740e12i	−1.96417	−	1.96417i
$610$			5.76689e11i			0.168639i
$611$	−4.30339e11			−0.124918
$612$	3.66065e10	+	3.95007e10i	0.0105482	+	0.0113821i
$613$	−2.94392e12			−0.842082			−0.421041	−	0.907042i	$-0.638335\pi$
$613$	−2.94392e12			−0.842082			−0.421041	+	0.907042i	$0.638335\pi$
$614$		−	3.91070e12i		−	1.11044i
$615$	−2.33604e12	−	2.33604e12i	−0.658479	−	0.658479i
$616$	−6.52506e12			−1.82588
$617$	3.33143e12	+	3.33143e12i	0.925438	+	0.925438i	0.997407	−	0.0719691i	$-0.0229283\pi$
$617$	3.33143e12	+	3.33143e12i	0.925438	+	0.925438i	−0.0719691	+	0.997407i	$0.522928\pi$
$618$	4.80689e11	−	4.80689e11i	0.132561	−	0.132561i
$619$	1.09062e12	−	1.09062e12i	0.298584	−	0.298584i	−0.541875	−	0.840459i	$-0.682285\pi$
$619$	1.09062e12	−	1.09062e12i	0.298584	−	0.298584i	0.840459	+	0.541875i	$0.182285\pi$
$620$			9.57270e11i			0.260179i
$621$		−	5.70407e11i		−	0.153912i
$622$	−4.28517e11	+	4.28517e11i	−0.114792	+	0.114792i
$623$	5.08691e12	−	5.08691e12i	1.35287	−	1.35287i
$624$	5.45866e11	+	5.45866e11i	0.144130	+	0.144130i
$625$	2.88471e12			0.756211
$626$	2.45145e12	+	2.45145e12i	0.638027	+	0.638027i
$627$			4.87556e12i			1.25985i
$628$	2.92697e11			0.0750932
$629$	−6.41509e12	−	2.43959e11i	−1.63409	−	0.0621425i
$630$	1.62093e11			0.0409950
$631$			8.86330e11i			0.222568i	0.993789	+	0.111284i	$0.0354964\pi$
$631$			8.86330e11i			0.222568i	−0.993789	+	0.111284i	$0.964504\pi$
$632$	−4.64831e11	−	4.64831e11i	−0.115896	−	0.115896i
$633$	5.26516e12			1.30345
$634$	3.73303e12	+	3.73303e12i	0.917613	+	0.917613i
$635$	−3.84674e12	+	3.84674e12i	−0.938881	+	0.938881i
$636$	3.89481e11	−	3.89481e11i	0.0943907	−	0.0943907i
$637$			3.85767e12i			0.928320i
$638$			5.49839e12i			1.31384i
$639$	−1.45451e10	+	1.45451e10i	−0.00345114	+	0.00345114i
$640$	−9.29561e10	+	9.29561e10i	−0.0219012	+	0.0219012i
$641$	4.78331e11	+	4.78331e11i	0.111910	+	0.111910i	0.760844	−	0.648935i	$-0.224785\pi$
$641$	4.78331e11	+	4.78331e11i	0.111910	+	0.111910i	−0.648935	+	0.760844i	$0.724785\pi$
$642$	1.62231e11			0.0376899
$643$	−1.69712e12	−	1.69712e12i	−0.391529	−	0.391529i	0.483703	−	0.875232i	$-0.339292\pi$
$643$	−1.69712e12	−	1.69712e12i	−0.391529	−	0.391529i	−0.875232	+	0.483703i	$0.839292\pi$
$644$		−	4.66710e11i		−	0.106920i
$645$	2.54001e12			0.577851
$646$	−3.10420e12	+	2.87676e12i	−0.701300	+	0.649915i
$647$	−3.20876e12			−0.719893			−0.359947	−	0.932973i	$-0.617205\pi$
$647$	−3.20876e12			−0.719893			−0.359947	+	0.932973i	$0.617205\pi$
$648$			4.66621e12i			1.03962i
$649$	2.86383e12	+	2.86383e12i	0.633646	+	0.633646i
$650$	−3.69056e11			−0.0810927
$651$	3.61770e12	+	3.61770e12i	0.789439	+	0.789439i
$652$	−7.49394e11	+	7.49394e11i	−0.162404	+	0.162404i
$653$	2.30458e12	−	2.30458e12i	0.496001	−	0.496001i	−0.414189	−	0.910191i	$-0.635935\pi$
$653$	2.30458e12	−	2.30458e12i	0.496001	−	0.496001i	0.910191	+	0.414189i	$0.135935\pi$
$654$		−	5.67298e12i		−	1.21258i
$655$			7.40857e11i			0.157271i
$656$	1.40190e12	−	1.40190e12i	0.295563	−	0.295563i
$657$	1.87589e11	−	1.87589e11i	0.0392793	−	0.0392793i
$658$	1.01306e12	+	1.01306e12i	0.210678	+	0.210678i
$659$	7.89910e12			1.63152			0.815762	−	0.578388i	$-0.196318\pi$
$659$	7.89910e12			1.63152			0.815762	+	0.578388i	$0.196318\pi$
$660$	−1.30797e12	−	1.30797e12i	−0.268318	−	0.268318i
$661$		−	2.00399e12i		−	0.408309i	−0.978939	−	0.204154i	$-0.934556\pi$
$661$		−	2.00399e12i		−	0.408309i	0.978939	−	0.204154i	$-0.0654445\pi$
$662$	−2.99608e12			−0.606306
$663$	2.57583e12	+	9.79559e10i	0.517733	+	0.0196888i
$664$	−1.42197e12			−0.283880
$665$		−	9.43521e12i		−	1.87092i
$666$	1.62282e11	+	1.62282e11i	0.0319621	+	0.0319621i
$667$	−1.31751e12			−0.257743
$668$	−1.25369e12	−	1.25369e12i	−0.243610	−	0.243610i
$669$	−6.43101e12	+	6.43101e12i	−1.24126	+	1.24126i
$670$	8.71584e11	−	8.71584e11i	0.167098	−	0.167098i
$671$			1.33126e12i			0.253519i
$672$			6.74240e12i			1.27542i
$673$	3.01372e12	−	3.01372e12i	0.566286	−	0.566286i	−0.364800	−	0.931086i	$-0.618863\pi$
$673$	3.01372e12	−	3.01372e12i	0.566286	−	0.566286i	0.931086	+	0.364800i	$0.118863\pi$
$674$	−2.42983e12	+	2.42983e12i	−0.453531	+	0.453531i
$675$	−7.86499e11	−	7.86499e11i	−0.145825	−	0.145825i
$676$	−1.66670e12			−0.306971
$677$	−2.78451e12	−	2.78451e12i	−0.509449	−	0.509449i	0.404908	−	0.914357i	$-0.367303\pi$
$677$	−2.78451e12	−	2.78451e12i	−0.509449	−	0.509449i	−0.914357	+	0.404908i	$0.867303\pi$
$678$			6.59629e12i			1.19885i
$679$	−1.70915e13			−3.08578
$680$	2.04414e11	−	5.37524e12i	0.0366624	−	0.964068i
$681$	−5.20142e12			−0.926744
$682$		−	2.98340e12i		−	0.528059i
$683$	5.08069e12	+	5.08069e12i	0.893366	+	0.893366i	0.994838	−	0.101472i	$-0.0323552\pi$
$683$	5.08069e12	+	5.08069e12i	0.893366	+	0.893366i	−0.101472	+	0.994838i	$0.532355\pi$
$684$	−1.12068e11			−0.0195762
$685$	−2.22170e12	−	2.22170e12i	−0.385548	−	0.385548i
$686$	3.91790e12	−	3.91790e12i	0.675452	−	0.675452i
$687$	2.57856e12	−	2.57856e12i	0.441643	−	0.441643i
$688$			1.52430e12i			0.259372i
$689$			9.97852e11i			0.168686i
$690$	−4.23127e11	+	4.23127e11i	−0.0710641	+	0.0710641i
$691$	8.25801e11	−	8.25801e11i	0.137792	−	0.137792i	−0.634846	−	0.772638i	$-0.718937\pi$
$691$	8.25801e11	−	8.25801e11i	0.137792	−	0.137792i	0.772638	+	0.634846i	$0.218937\pi$
$692$	9.52844e11	+	9.52844e11i	0.157959	+	0.157959i
$693$	3.74183e11			0.0616290
$694$	−7.46864e11	−	7.46864e11i	−0.122215	−	0.122215i
$695$		−	1.58711e12i		−	0.258033i
$696$	1.11863e13			1.80695
$697$	2.51571e11	−	6.61527e12i	0.0403751	−	1.06170i
$698$	−7.22916e11			−0.115276
$699$		−	6.26844e12i		−	0.993144i
$700$	−6.43517e11	−	6.43517e11i	−0.101302	−	0.101302i
$701$	6.97976e12			1.09172			0.545858	−	0.837878i	$-0.316204\pi$
$701$	6.97976e12			1.09172			0.545858	+	0.837878i	$0.316204\pi$
$702$	−1.85189e12	−	1.85189e12i	−0.287805	−	0.287805i
$703$	9.44622e12	−	9.44622e12i	1.45868	−	1.45868i
$704$	4.62477e12	−	4.62477e12i	0.709600	−	0.709600i
$705$			1.36061e12i			0.207435i
$706$			3.26920e12i			0.495245i
$707$	−8.79893e12	+	8.79893e12i	−1.32447	+	1.32447i
$708$	1.73918e12	−	1.73918e12i	0.260133	−	0.260133i
$709$	−6.58038e12	−	6.58038e12i	−0.978009	−	0.978009i	0.0217544	−	0.999763i	$-0.493075\pi$
$709$	−6.58038e12	−	6.58038e12i	−0.978009	−	0.978009i	−0.999763	+	0.0217544i	$0.993075\pi$
$710$	6.13287e11			0.0905735
$711$	2.66560e10	+	2.66560e10i	0.00391184	+	0.00391184i
$712$			8.53464e12i			1.24459i
$713$	7.14873e11			0.103592
$714$	−5.83316e12	−	6.29436e12i	−0.839967	−	0.906378i
$715$	3.35102e12			0.479512
$716$			5.65785e12i			0.804531i
$717$	3.07453e12	+	3.07453e12i	0.434453	+	0.434453i
$718$	−5.90267e11			−0.0828874
$719$	4.76621e12	+	4.76621e12i	0.665110	+	0.665110i	0.956580	−	0.291470i	$-0.0941444\pi$
$719$	4.76621e12	+	4.76621e12i	0.665110	+	0.665110i	−0.291470	+	0.956580i	$0.594144\pi$
$720$	−6.53231e10	+	6.53231e10i	−0.00905880	+	0.00905880i
$721$	−2.14740e12	+	2.14740e12i	−0.295940	+	0.295940i
$722$		−	3.27276e12i		−	0.448226i
$723$			9.77820e11i			0.133087i
$724$	1.75899e12	−	1.75899e12i	0.237925	−	0.237925i
$725$	−1.81663e12	+	1.81663e12i	−0.244199	+	0.244199i
$726$	1.38429e11	+	1.38429e11i	0.0184933	+	0.0184933i
$727$	−1.09765e12			−0.145733			−0.0728667	−	0.997342i	$-0.523215\pi$
$727$	−1.09765e12			−0.145733			−0.0728667	+	0.997342i	$0.523215\pi$
$728$	−5.07612e12	−	5.07612e12i	−0.669794	−	0.669794i
$729$		−	7.88304e12i		−	1.03376i
$730$	−7.90963e12			−1.03087
$731$	3.45967e12	+	3.73320e12i	0.448132	+	0.483564i
$732$	8.08464e11			0.104078
$733$		−	5.10680e12i		−	0.653403i	−0.945128	−	0.326701i	$-0.894063\pi$
$733$		−	5.10680e12i		−	0.653403i	0.945128	−	0.326701i	$-0.105937\pi$
$734$	4.83885e12	+	4.83885e12i	0.615333	+	0.615333i
$735$	1.21968e13			1.54154
$736$	6.66163e11	+	6.66163e11i	0.0836816	+	0.0836816i
$737$	2.01201e12	−	2.01201e12i	0.251204	−	0.251204i
$738$	−1.67346e11	+	1.67346e11i	−0.0207664	+	0.0207664i
$739$			4.59083e12i			0.566228i	0.959086	+	0.283114i	$0.0913674\pi$
$739$			4.59083e12i			0.566228i	−0.959086	+	0.283114i	$0.908633\pi$
$740$			5.06828e12i			0.621324i
$741$	−3.79291e12	+	3.79291e12i	−0.462158	+	0.462158i
$742$	2.34904e12	−	2.34904e12i	0.284494	−	0.284494i
$743$	1.33213e12	+	1.33213e12i	0.160361	+	0.160361i	0.782727	−	0.622366i	$-0.213828\pi$
$743$	1.33213e12	+	1.33213e12i	0.160361	+	0.160361i	−0.622366	+	0.782727i	$0.713828\pi$
$744$	−6.06966e12			−0.726250
$745$	1.38679e12	+	1.38679e12i	0.164933	+	0.164933i
$746$			2.00051e12i			0.236491i
$747$	8.15439e10			0.00958183
$748$	1.40857e11	−	3.70394e12i	0.0164521	−	0.432621i
$749$	−7.24738e11			−0.0841420
$750$			6.92332e12i			0.798986i
$751$	−2.36140e12	−	2.36140e12i	−0.270888	−	0.270888i	0.558570	−	0.829458i	$-0.311350\pi$
$751$	−2.36140e12	−	2.36140e12i	−0.270888	−	0.270888i	−0.829458	+	0.558570i	$0.811350\pi$
$752$	−8.16524e11			−0.0931084
$753$	−5.58981e12	−	5.58981e12i	−0.633607	−	0.633607i
$754$	−4.27744e12	+	4.27744e12i	−0.481962	+	0.481962i
$755$	−7.36565e12	+	7.36565e12i	−0.824992	+	0.824992i
$756$		−	6.45824e12i		−	0.719062i
$757$		−	9.95427e12i		−	1.10174i	−0.834592	−	0.550869i	$-0.814297\pi$
$757$		−	9.95427e12i		−	1.10174i	0.834592	−	0.550869i	$-0.185703\pi$
$758$	−3.47803e12	+	3.47803e12i	−0.382668	+	0.382668i
$759$	−9.76769e11	+	9.76769e11i	−0.106833	+	0.106833i
$760$	7.91504e12	+	7.91504e12i	0.860581	+	0.860581i
$761$	−9.18933e12			−0.993237			−0.496618	−	0.867969i	$-0.665425\pi$
$761$	−9.18933e12			−0.993237			−0.496618	+	0.867969i	$0.665425\pi$
$762$	−7.28062e12	−	7.28062e12i	−0.782296	−	0.782296i
$763$			2.53431e13i			2.70707i
$764$	−1.89805e12			−0.201552
$765$	−1.17223e10	+	3.08246e11i	−0.00123747	+	0.0325403i
$766$	4.50753e12			0.473053
$767$			4.45580e12i			0.464886i
$768$	−6.77633e12	−	6.77633e12i	−0.702860	−	0.702860i
$769$	−7.03483e11			−0.0725412			−0.0362706	−	0.999342i	$-0.511548\pi$
$769$	−7.03483e11			−0.0725412			−0.0362706	+	0.999342i	$0.511548\pi$
$770$	−7.88864e12	−	7.88864e12i	−0.808712	−	0.808712i
$771$	−3.35687e12	+	3.35687e12i	−0.342129	+	0.342129i
$772$	1.35776e12	−	1.35776e12i	0.137576	−	0.137576i
$773$			7.75675e12i			0.781398i	0.920518	+	0.390699i	$0.127767\pi$
$773$			7.75675e12i			0.781398i	−0.920518	+	0.390699i	$0.872233\pi$
$774$		−	1.81957e11i		−	0.0182236i
$775$	9.85694e11	−	9.85694e11i	0.0981487	−	0.0981487i
$776$	1.43377e13	−	1.43377e13i	1.41939	−	1.41939i
$777$	1.91540e13	+	1.91540e13i	1.88523	+	1.88523i
$778$	7.61274e12			0.744960
$779$	9.74098e12	+	9.74098e12i	0.947729	+	0.947729i
$780$		−	2.03505e12i		−	0.196856i
$781$	1.41574e12			0.136162
$782$	−1.19822e12	−	4.55672e10i	−0.114580	−	0.00435734i
$783$	−1.82314e13			−1.73337
$784$			7.31953e12i			0.691928i
$785$	1.18547e12	+	1.18547e12i	0.111424	+	0.111424i
$786$	−1.40220e12			−0.131042
$787$	8.40833e12	+	8.40833e12i	0.781310	+	0.781310i	0.980052	−	0.198742i	$-0.0636855\pi$
$787$	8.40833e12	+	8.40833e12i	0.781310	+	0.781310i	−0.198742	+	0.980052i	$0.563686\pi$
$788$	−8.75929e11	+	8.75929e11i	−0.0809284	+	0.0809284i
$789$	1.15989e13	−	1.15989e13i	1.06555	−	1.06555i
$790$		−	1.12394e12i		−	0.102664i
$791$		−	2.94678e13i		−	2.67641i
$792$	−3.13896e11	+	3.13896e11i	−0.0283480	+	0.0283480i
$793$	−1.03564e12	+	1.03564e12i	−0.0929996	+	0.0929996i
$794$	−8.68991e12	−	8.68991e12i	−0.775931	−	0.775931i
$795$	3.15492e12			0.280115
$796$	6.01393e12	+	6.01393e12i	0.530945	+	0.530945i
$797$			1.21193e13i			1.06394i	0.846765	+	0.531968i	$0.178547\pi$
$797$			1.21193e13i			1.06394i	−0.846765	+	0.531968i	$0.821453\pi$
$798$	1.78578e13			1.55889
$799$	−1.99977e12	+	1.85324e12i	−0.173588	+	0.160869i
$800$	1.83706e12			0.158569
$801$		−	4.89424e11i		−	0.0420086i
$802$	7.20777e10	+	7.20777e10i	0.00615200	+	0.00615200i
$803$	−1.82590e13			−1.54973
$804$	−1.22188e12	−	1.22188e12i	−0.103128	−	0.103128i
$805$	1.89025e12	−	1.89025e12i	0.158649	−	0.158649i
$806$	2.32092e12	−	2.32092e12i	0.193710	−	0.193710i
$807$		−	1.63396e13i		−	1.35616i
$808$		−	1.47626e13i		−	1.21846i
$809$	−6.45723e12	+	6.45723e12i	−0.530003	+	0.530003i	−0.920573	−	0.390570i	$-0.872278\pi$
$809$	−6.45723e12	+	6.45723e12i	−0.530003	+	0.530003i	0.390570	+	0.920573i	$0.372278\pi$
$810$	−5.64133e12	+	5.64133e12i	−0.460468	+	0.460468i
$811$	−2.88142e12	−	2.88142e12i	−0.233891	−	0.233891i	0.580424	−	0.814315i	$-0.302887\pi$
$811$	−2.88142e12	−	2.88142e12i	−0.233891	−	0.233891i	−0.814315	+	0.580424i	$0.802887\pi$
$812$	−1.49170e13			−1.20415
$813$	4.46462e11	+	4.46462e11i	0.0358407	+	0.0358407i
$814$		−	1.57957e13i		−	1.26104i
$815$	−6.07032e12			−0.481950
$816$	4.88737e12	+	1.85861e11i	0.385895	+	0.0146752i
$817$	−1.05915e13			−0.831684
$818$			1.51572e13i			1.18367i
$819$	2.91093e11	+	2.91093e11i	0.0226076	+	0.0226076i
$820$	−5.22643e12			−0.403685
$821$	−4.45362e12	−	4.45362e12i	−0.342113	−	0.342113i	0.515048	−	0.857161i	$-0.327774\pi$
$821$	−4.45362e12	−	4.45362e12i	−0.342113	−	0.342113i	−0.857161	+	0.515048i	$0.827774\pi$
$822$	4.20496e12	−	4.20496e12i	0.321246	−	0.321246i
$823$	1.16571e13	−	1.16571e13i	0.885709	−	0.885709i	−0.108399	−	0.994108i	$-0.534572\pi$
$823$	1.16571e13	−	1.16571e13i	0.885709	−	0.885709i	0.994108	+	0.108399i	$0.0345723\pi$
$824$		−	3.60283e12i		−	0.272252i
$825$			2.69361e12i			0.202438i
$826$	1.04894e13	−	1.04894e13i	0.784044	−	0.784044i
$827$	1.21629e13	−	1.21629e13i	0.904197	−	0.904197i	−0.0915986	−	0.995796i	$-0.529198\pi$
$827$	1.21629e13	−	1.21629e13i	0.904197	−	0.904197i	0.995796	+	0.0915986i	$0.0291977\pi$
$828$	−2.24517e10	−	2.24517e10i	−0.00166002	−	0.00166002i
$829$	2.13805e11			0.0157225			0.00786126	−	0.999969i	$-0.497498\pi$
$829$	2.13805e11			0.0157225			0.00786126	+	0.999969i	$0.497498\pi$
$830$	−1.71913e12	−	1.71913e12i	−0.125735	−	0.125735i
$831$		−	1.88854e13i		−	1.37379i
$832$	7.19562e12			0.520611
$833$	1.66129e13	+	1.79264e13i	1.19548	+	1.29000i
$834$	3.00388e12			0.214998
$835$		−	1.01553e13i		−	0.722939i
$836$	5.45406e12	+	5.45406e12i	0.386182	+	0.386182i
$837$	9.89227e12			0.696677
$838$	−9.16379e12	−	9.16379e12i	−0.641914	−	0.641914i
$839$	2.66073e12	−	2.66073e12i	0.185384	−	0.185384i	−0.608313	−	0.793697i	$-0.708154\pi$
$839$	2.66073e12	−	2.66073e12i	0.185384	−	0.185384i	0.793697	+	0.608313i	$0.208154\pi$
$840$	−1.60492e13	+	1.60492e13i	−1.11224	+	1.11224i
$841$			2.76030e13i			1.90272i
$842$			1.49179e13i			1.02283i
$843$	−1.39349e13	+	1.39349e13i	−0.950338	+	0.950338i
$844$	5.88989e12	−	5.88989e12i	0.399545	−	0.399545i
$845$	−6.75040e12	−	6.75040e12i	−0.455485	−	0.455485i
$846$	9.74691e10			0.00654185
$847$	−6.18410e11	−	6.18410e11i	−0.0412858	−	0.0412858i
$848$			1.89332e12i			0.125731i
$849$	−2.30322e13			−1.52143
$850$	−1.71499e12	+	1.58933e12i	−0.112687	+	0.104431i
$851$	3.78491e12			0.247385
$852$		−	8.59771e11i		−	0.0558990i
$853$	−1.85927e13	−	1.85927e13i	−1.20246	−	1.20246i	−0.973416	−	0.229045i	$-0.926440\pi$
$853$	−1.85927e13	−	1.85927e13i	−1.20246	−	1.20246i	−0.229045	−	0.973416i	$-0.573560\pi$
$854$	4.87602e12			0.313693
$855$	−4.53892e11	−	4.53892e11i	−0.0290473	−	0.0290473i
$856$	6.07970e11	−	6.07970e11i	0.0387035	−	0.0387035i
$857$	−4.02896e12	+	4.02896e12i	−0.255141	+	0.255141i	−0.823074	−	0.567934i	$-0.807743\pi$
$857$	−4.02896e12	+	4.02896e12i	−0.255141	+	0.255141i	0.567934	+	0.823074i	$0.307743\pi$
$858$			6.34239e12i			0.399540i
$859$			1.45341e13i			0.910794i	0.890288	+	0.455397i	$0.150503\pi$
$859$			1.45341e13i			0.910794i	−0.890288	+	0.455397i	$0.849497\pi$
$860$	2.84139e12	−	2.84139e12i	0.177128	−	0.177128i
$861$	−1.97517e13	+	1.97517e13i	−1.22487	+	1.22487i
$862$	1.01804e13	+	1.01804e13i	0.628036	+	0.628036i
$863$	1.96660e13			1.20689			0.603445	−	0.797404i	$-0.293794\pi$
$863$	1.96660e13			1.20689			0.603445	+	0.797404i	$0.293794\pi$
$864$	9.21823e12	+	9.21823e12i	0.562776	+	0.562776i
$865$			7.71833e12i			0.468760i
$866$	−1.31240e13			−0.792932
$867$	1.23916e13	−	1.06375e13i	0.744804	−	0.639374i
$868$	8.09391e12			0.483971
$869$		−	2.59456e12i		−	0.154338i
$870$	1.35240e13	+	1.35240e13i	0.800329	+	0.800329i
$871$	3.13046e12			0.184300
$872$	−2.12599e13	−	2.12599e13i	−1.24519	−	1.24519i
$873$	−8.22206e11	+	8.22206e11i	−0.0479090	+	0.0479090i
$874$	1.76439e12	−	1.76439e12i	0.102280	−	0.102280i
$875$		−	3.09288e13i		−	1.78372i
$876$			1.10886e13i			0.636219i
$877$	1.30065e13	−	1.30065e13i	0.742441	−	0.742441i	−0.230606	−	0.973047i	$-0.574071\pi$
$877$	1.30065e13	−	1.30065e13i	0.742441	−	0.742441i	0.973047	+	0.230606i	$0.0740710\pi$
$878$	−6.37389e12	+	6.37389e12i	−0.361975	+	0.361975i
$879$	−5.84459e12	−	5.84459e12i	−0.330220	−	0.330220i
$880$	6.35822e12			0.357407
$881$	9.97571e12	+	9.97571e12i	0.557894	+	0.557894i	0.928708	−	0.370813i	$-0.120921\pi$
$881$	9.97571e12	+	9.97571e12i	0.557894	+	0.557894i	−0.370813	+	0.928708i	$0.620921\pi$
$882$		−	8.73738e11i		−	0.0486153i
$883$	6.63294e12			0.367183			0.183592	−	0.983003i	$-0.441228\pi$
$883$	6.63294e12			0.367183			0.183592	+	0.983003i	$0.441228\pi$
$884$	2.99104e12	−	2.77188e12i	0.164735	−	0.152665i
$885$	1.40879e13			0.771974
$886$			5.68034e11i			0.0309687i
$887$	−1.78741e13	−	1.78741e13i	−0.969547	−	0.969547i	0.0300031	−	0.999550i	$-0.490448\pi$
$887$	−1.78741e13	−	1.78741e13i	−0.969547	−	0.969547i	−0.999550	+	0.0300031i	$0.990448\pi$
$888$	−3.21359e13			−1.73433
$889$	3.25249e13	+	3.25249e13i	1.74646	+	1.74646i
$890$	−1.03182e13	+	1.03182e13i	−0.551249	+	0.551249i
$891$	−1.30227e13	+	1.30227e13i	−0.692234	+	0.692234i
$892$			1.43881e13i			0.760962i
$893$		−	5.67355e12i		−	0.298555i
$894$	−2.62474e12	+	2.62474e12i	−0.137426	+	0.137426i
$895$	−2.29152e13	+	2.29152e13i	−1.19377	+	1.19377i
$896$	7.85962e11	+	7.85962e11i	0.0407395	+	0.0407395i
$897$	−1.51974e12			−0.0783797
$898$	1.24357e13	+	1.24357e13i	0.638158	+	0.638158i
$899$		−	2.28488e13i		−	1.16666i
$900$	−6.19144e10			−0.00314558
$901$	4.29722e12	+	4.63698e12i	0.217233	+	0.234408i
$902$	1.62886e13			0.819320
$903$		−	2.14763e13i		−	1.07489i
$904$	2.47200e13	+	2.47200e13i	1.23109	+	1.23109i
$905$	1.42484e13			0.706068
$906$	−1.39408e13	−	1.39408e13i	−0.687401	−	0.687401i
$907$	2.65895e12	−	2.65895e12i	0.130460	−	0.130460i	−0.638862	−	0.769322i	$-0.720594\pi$
$907$	2.65895e12	−	2.65895e12i	0.130460	−	0.130460i	0.769322	+	0.638862i	$0.220594\pi$
$908$	−5.81858e12	+	5.81858e12i	−0.284073	+	0.284073i
$909$			8.46567e11i			0.0411267i
$910$		−	1.22738e13i		−	0.593326i
$911$	4.03264e11	−	4.03264e11i	0.0193980	−	0.0193980i	−0.697341	−	0.716739i	$-0.745634\pi$
$911$	4.03264e11	−	4.03264e11i	0.0193980	−	0.0193980i	0.716739	+	0.697341i	$0.245634\pi$
$912$	−7.19666e12	+	7.19666e12i	−0.344472	+	0.344472i
$913$	−3.96853e12	−	3.96853e12i	−0.189022	−	0.189022i
$914$	1.32034e13			0.625790
$915$	3.27440e12	+	3.27440e12i	0.154432	+	0.154432i
$916$		−	5.76902e12i		−	0.270753i
$917$	6.26410e12			0.292547
$918$	−1.65808e13	−	6.30549e11i	−0.770572	−	0.0293040i
$919$	2.65353e13			1.22717			0.613585	−	0.789629i	$-0.289727\pi$
$919$	2.65353e13			1.22717			0.613585	+	0.789629i	$0.289727\pi$
$920$			3.17140e12i			0.145950i
$921$	−2.22047e13	−	2.22047e13i	−1.01690	−	1.01690i
$922$	−1.90583e13			−0.868549
$923$	1.10137e12	+	1.10137e12i	0.0499488	+	0.0499488i
$924$	−1.10591e13	+	1.10591e13i	−0.499111	+	0.499111i
$925$	5.21878e12	−	5.21878e12i	0.234386	−	0.234386i
$926$		−	7.01404e12i		−	0.313486i
$927$			2.06606e11i			0.00918935i
$928$	2.12919e13	−	2.12919e13i	0.942430	−	0.942430i
$929$	−1.10082e13	+	1.10082e13i	−0.484893	+	0.484893i	−0.906690	−	0.421797i	$-0.861399\pi$
$929$	−1.10082e13	+	1.10082e13i	−0.484893	+	0.484893i	0.421797	+	0.906690i	$0.361399\pi$
$930$	−7.33807e12	−	7.33807e12i	−0.321668	−	0.321668i
$931$	−5.08592e13			−2.21869
$932$	−7.01221e12	−	7.01221e12i	−0.304427	−	0.304427i
$933$			4.86619e12i			0.210243i
$934$	1.07003e13			0.460083
$935$	1.55720e13	−	1.44311e13i	0.666336	−	0.617513i
$936$	−4.88386e11			−0.0207980
$937$		−	1.83498e13i		−	0.777683i	−0.921305	−	0.388841i	$-0.872875\pi$
$937$		−	1.83498e13i		−	0.777683i	0.921305	−	0.388841i	$-0.127125\pi$
$938$	−7.36941e12	−	7.36941e12i	−0.310828	−	0.310828i
$939$	2.78384e13			1.16856
$940$	1.52205e12	+	1.52205e12i	0.0635847	+	0.0635847i
$941$	−8.25487e12	+	8.25487e12i	−0.343207	+	0.343207i	−0.857572	−	0.514364i	$-0.828028\pi$
$941$	−8.25487e12	+	8.25487e12i	−0.343207	+	0.343207i	0.514364	+	0.857572i	$0.328028\pi$
$942$	−2.24371e12	+	2.24371e12i	−0.0928404	+	0.0928404i
$943$			3.90301e12i			0.160730i
$944$			8.45442e12i			0.346505i
$945$	2.61569e13	−	2.61569e13i	1.06695	−	1.06695i
$946$	−8.85540e12	+	8.85540e12i	−0.359499	+	0.359499i
$947$	−2.49340e13	−	2.49340e13i	−1.00744	−	1.00744i	−0.999972	−	0.00746369i	$-0.997624\pi$
$947$	−2.49340e13	−	2.49340e13i	−1.00744	−	1.00744i	−0.00746369	−	0.999972i	$-0.502376\pi$
$948$	−1.57566e12			−0.0633612
$949$	−1.42045e13	−	1.42045e13i	−0.568495	−	0.568495i
$950$		−	4.86560e12i		−	0.193812i
$951$	4.23918e13			1.68062
$952$	−4.54487e13	−	1.72836e12i	−1.79331	−	0.0681976i
$953$	1.56668e12			0.0615266			0.0307633	−	0.999527i	$-0.490206\pi$
$953$	1.56668e12			0.0615266			0.0307633	+	0.999527i	$0.490206\pi$
$954$		−	2.26007e11i		−	0.00883395i
$955$	−7.68739e12	−	7.68739e12i	−0.299064	−	0.299064i
$956$	6.87867e12			0.266345
$957$	3.12195e13	+	3.12195e13i	1.20316	+	1.20316i
$958$	1.14533e13	−	1.14533e13i	0.439327	−	0.439327i
$959$	−1.87849e13	+	1.87849e13i	−0.717176	+	0.717176i
$960$		−	2.27505e13i		−	0.864509i
$961$		−	1.40420e13i		−	0.531095i
$962$	1.22881e13	−	1.22881e13i	0.462593	−	0.462593i
$963$	−3.48644e10	+	3.48644e10i	−0.00130636	+	0.00130636i
$964$	1.09384e12	+	1.09384e12i	0.0407951	+	0.0407951i
$965$	1.09982e13			0.408273
$966$	3.57762e12	+	3.57762e12i	0.132190	+	0.132190i
$967$		−	5.21004e13i		−	1.91612i	−0.286573	−	0.958058i	$-0.592516\pi$
$967$		−	5.21004e13i		−	1.91612i	0.286573	−	0.958058i	$-0.407484\pi$
$968$	1.03755e12			0.0379812
$969$	−1.29144e12	+	3.39595e13i	−0.0470564	+	1.23738i
$970$	3.46680e13			1.25735
$971$			4.84504e13i			1.74909i	0.484948	+	0.874543i	$0.338838\pi$
$971$			4.84504e13i			1.74909i	−0.484948	+	0.874543i	$0.661162\pi$
$972$	−6.10432e11	−	6.10432e11i	−0.0219351	−	0.0219351i
$973$	−1.34193e13			−0.479979
$974$	1.39845e13	+	1.39845e13i	0.497889	+	0.497889i
$975$	−2.09548e12	+	2.09548e12i	−0.0742612	+	0.0742612i
$976$	−1.96503e12	+	1.96503e12i	−0.0693178	+	0.0693178i
$977$		−	1.73873e12i		−	0.0610530i	−0.999534	−	0.0305265i	$-0.990282\pi$
$977$		−	1.73873e12i		−	0.0610530i	0.999534	−	0.0305265i	$-0.00971840\pi$
$978$		−	1.14891e13i		−	0.401571i
$979$	−2.38190e13	+	2.38190e13i	−0.828708	+	0.828708i
$980$	1.36440e13	−	1.36440e13i	0.472525	−	0.472525i
$981$	1.21916e12	+	1.21916e12i	0.0420291	+	0.0420291i
$982$	−1.67668e13			−0.575371
$983$	5.79977e12	+	5.79977e12i	0.198116	+	0.198116i	0.799192	−	0.601076i	$-0.205261\pi$
$983$	5.79977e12	+	5.79977e12i	0.198116	+	0.198116i	−0.601076	+	0.799192i	$0.705261\pi$
$984$		−	3.31387e13i		−	1.12683i
$985$	−7.09530e12			−0.240164
$986$	−1.45642e12	+	3.82977e13i	−0.0490727	+	1.29041i
$987$	1.15042e13			0.385859
$988$			8.48589e12i			0.283329i
$989$	−2.12190e12	−	2.12190e12i	−0.0705248	−	0.0705248i
$990$	−7.58985e11			−0.0251116
$991$	−1.17162e12	−	1.17162e12i	−0.0385882	−	0.0385882i	0.687549	−	0.726138i	$-0.258686\pi$
$991$	−1.17162e12	−	1.17162e12i	−0.0385882	−	0.0385882i	−0.726138	+	0.687549i	$0.758686\pi$
$992$	−1.15529e13	+	1.15529e13i	−0.378781	+	0.378781i
$993$	−1.70115e13	+	1.70115e13i	−0.555229	+	0.555229i
$994$		−	5.18546e12i		−	0.168480i
$995$			4.87147e13i			1.57564i
$996$	−2.41006e12	+	2.41006e12i	−0.0775998	+	0.0775998i
$997$	−2.65128e13	+	2.65128e13i	−0.849820	+	0.849820i	−0.990110	−	0.140291i	$-0.955196\pi$
$997$	−2.65128e13	+	2.65128e13i	−0.849820	+	0.849820i	0.140291	+	0.990110i	$0.455196\pi$
$998$	1.14818e13	+	1.14818e13i	0.366373	+	0.366373i
$999$	5.23748e13			1.66371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.9	yes	24
17.2	even	8		289.10.a.f.1.8		24
17.4	even	4	inner	17.10.c.a.4.4	✓	24
17.15	even	8		289.10.a.f.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.4	✓	24	17.4	even	4	inner
17.10.c.a.13.9	yes	24	1.1	even	1	trivial
289.10.a.f.1.7		24	17.15	even	8
289.10.a.f.1.8		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)

\(f(q)\)	\(=\)	\(q+17.1503i q^{2} +(97.3786 + 97.3786i) q^{3} +217.866 q^{4} +(882.390 + 882.390i) q^{5} +(-1670.08 + 1670.08i) q^{6} +(7460.78 - 7460.78i) q^{7} +12517.4i q^{8} -717.820i q^{9} +O(q^{10})\)	\(q+17.1503i q^{2} +(97.3786 + 97.3786i) q^{3} +217.866 q^{4} +(882.390 + 882.390i) q^{5} +(-1670.08 + 1670.08i) q^{6} +(7460.78 - 7460.78i) q^{7} +12517.4i q^{8} -717.820i q^{9} +(-15133.3 + 15133.3i) q^{10} +(-34934.5 + 34934.5i) q^{11} +(21215.5 + 21215.5i) q^{12} -54354.1 q^{13} +(127955. + 127955. i) q^{14} +171852. i q^{15} -103131. q^{16} +(-252581. + 234074. i) q^{17} +12310.9 q^{18} -716600. i q^{19} +(192242. + 192242. i) q^{20} +1.45304e6 q^{21} +(-599138. - 599138. i) q^{22} +(143564. - 143564. i) q^{23} +(-1.21893e6 + 1.21893e6i) q^{24} -395901. i q^{25} -932191. i q^{26} +(1.98660e6 - 1.98660e6i) q^{27} +(1.62545e6 - 1.62545e6i) q^{28} +(-4.58858e6 - 4.58858e6i) q^{29} -2.94732e6 q^{30} +(2.48975e6 + 2.48975e6i) q^{31} +4.64020e6i q^{32} -6.80374e6 q^{33} +(-4.01445e6 - 4.33185e6i) q^{34} +1.31666e7 q^{35} -156388. i q^{36} +(1.31820e7 + 1.31820e7i) q^{37} +1.22899e7 q^{38} +(-5.29292e6 - 5.29292e6i) q^{39} +(-1.10453e7 + 1.10453e7i) q^{40} +(-1.35933e7 + 1.35933e7i) q^{41} +2.49202e7i q^{42} -1.47802e7i q^{43} +(-7.61102e6 + 7.61102e6i) q^{44} +(633397. - 633397. i) q^{45} +(2.46216e6 + 2.46216e6i) q^{46} +7.91732e6 q^{47} +(-1.00428e7 - 1.00428e7i) q^{48} -7.09730e7i q^{49} +6.78985e6 q^{50} +(-4.73898e7 - 1.80218e6i) q^{51} -1.18419e7 q^{52} -1.83584e7i q^{53} +(3.40709e7 + 3.40709e7i) q^{54} -6.16517e7 q^{55} +(9.33900e7 + 9.33900e7i) q^{56} +(6.97815e7 - 6.97815e7i) q^{57} +(7.86958e7 - 7.86958e7i) q^{58} -8.19772e7i q^{59} +3.74406e7i q^{60} +(1.90537e7 - 1.90537e7i) q^{61} +(-4.27000e7 + 4.27000e7i) q^{62} +(-5.35550e6 - 5.35550e6i) q^{63} -1.32384e8 q^{64} +(-4.79615e7 - 4.79615e7i) q^{65} -1.16686e8i q^{66} -5.75938e7 q^{67} +(-5.50287e7 + 5.09967e7i) q^{68} +2.79600e7 q^{69} +2.25812e8i q^{70} +(-2.02628e7 - 2.02628e7i) q^{71} +8.98528e6 q^{72} +(2.61332e8 + 2.61332e8i) q^{73} +(-2.26076e8 + 2.26076e8i) q^{74} +(3.85523e7 - 3.85523e7i) q^{75} -1.56123e8i q^{76} +5.21277e8i q^{77} +(9.07754e7 - 9.07754e7i) q^{78} +(-3.71346e7 + 3.71346e7i) q^{79} +(-9.10020e7 - 9.10020e7i) q^{80} +3.72776e8 q^{81} +(-2.33130e8 - 2.33130e8i) q^{82} +1.13599e8i q^{83} +3.16568e8 q^{84} +(-4.29420e8 - 1.63304e7i) q^{85} +2.53486e8 q^{86} -8.93659e8i q^{87} +(-4.37291e8 - 4.37291e8i) q^{88} +6.81819e8 q^{89} +(1.08630e7 + 1.08630e7i) q^{90} +(-4.05524e8 + 4.05524e8i) q^{91} +(3.12776e7 - 3.12776e7i) q^{92} +4.84896e8i q^{93} +1.35785e8i q^{94} +(6.32320e8 - 6.32320e8i) q^{95} +(-4.51856e8 + 4.51856e8i) q^{96} +(-1.14542e9 - 1.14542e9i) q^{97} +1.21721e9 q^{98} +(2.50767e7 + 2.50767e7i) 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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