LMFDB - Embedded newform 75.22.b.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,Mod(49,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("75.49");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	75.b (of order $2$, degree $1$, not 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:	$209.608008215$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{649})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 325x^{2} + 26244 $ x^4 + 325*x^2 + 26244
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-12.2377i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.22.b.d.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1937.96i q^{2} +59049.0i q^{3} -1.65852e6 q^{4} +1.14434e8 q^{6} -4.78205e7i q^{7} -8.50053e8i q^{8} -3.48678e9 q^{9} +O(q^{10})$	\(q-1937.96i q^{2} +59049.0i q^{3} -1.65852e6 q^{4} +1.14434e8 q^{6} -4.78205e7i q^{7} -8.50053e8i q^{8} -3.48678e9 q^{9} +1.60111e11 q^{11} -9.79338e10i q^{12} -7.86968e11i q^{13} -9.26741e10 q^{14} -5.12553e12 q^{16} +2.97477e12i q^{17} +6.75723e12i q^{18} +2.99456e13 q^{19} +2.82376e12 q^{21} -3.10287e14i q^{22} -1.91401e14i q^{23} +5.01948e13 q^{24} -1.52511e15 q^{26} -2.05891e14i q^{27} +7.93112e13i q^{28} -9.68170e14 q^{29} +2.80459e15 q^{31} +8.15035e15i q^{32} +9.45437e15i q^{33} +5.76496e15 q^{34} +5.78290e15 q^{36} -3.05038e16i q^{37} -5.80331e16i q^{38} +4.64697e16 q^{39} -2.22806e16 q^{41} -5.47231e15i q^{42} +1.63711e17i q^{43} -2.65546e17 q^{44} -3.70927e17 q^{46} -4.08678e17i q^{47} -3.02657e17i q^{48} +5.56259e17 q^{49} -1.75657e17 q^{51} +1.30520e18i q^{52} +4.34009e17i q^{53} -3.99008e17 q^{54} -4.06500e16 q^{56} +1.76826e18i q^{57} +1.87627e18i q^{58} +5.14341e18 q^{59} +1.98980e18 q^{61} -5.43517e18i q^{62} +1.66740e17i q^{63} +5.04601e18 q^{64} +1.83222e19 q^{66} +1.36361e19i q^{67} -4.93370e18i q^{68} +1.13020e19 q^{69} +7.35641e18 q^{71} +2.96395e18i q^{72} +6.81650e19i q^{73} -5.91149e19 q^{74} -4.96652e19 q^{76} -7.65658e18i q^{77} -9.00562e19i q^{78} +2.12282e19 q^{79} +1.21577e19 q^{81} +4.31789e19i q^{82} +1.10803e20i q^{83} -4.68325e18 q^{84} +3.17266e20 q^{86} -5.71695e19i q^{87} -1.36102e20i q^{88} +7.67205e18 q^{89} -3.76333e19 q^{91} +3.17442e20i q^{92} +1.65608e20i q^{93} -7.92000e20 q^{94} -4.81270e20 q^{96} -4.63755e20i q^{97} -1.07801e21i q^{98} -5.58271e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2358472 q^{4} + 78653268 q^{6} - 13947137604 q^{9}+O(q^{10}) $ 4 * q - 2358472 * q^4 + 78653268 * q^6 - 13947137604 * q^9	$ 4 q - 2358472 q^{4} + 78653268 q^{6} - 13947137604 q^{9} + 439738245936 q^{11} + 1422595413792 q^{14} - 16577472881120 q^{16} - 23921170023248 q^{19} + 80294371034976 q^{21} - 286630441537104 q^{24} - 49\!\cdots\!32 q^{26}+ \cdots - 15\!\cdots\!36 q^{99}+O(q^{100}) $ 4 * q - 2358472 * q^4 + 78653268 * q^6 - 13947137604 * q^9 + 439738245936 * q^11 + 1422595413792 * q^14 - 16577472881120 * q^16 - 23921170023248 * q^19 + 80294371034976 * q^21 - 286630441537104 * q^24 - 4928894727939432 * q^26 + 3597040087348104 * q^29 + 22338215053889984 * q^31 - 9734014974827304 * q^34 + 8223483379795272 * q^36 + 5724081327983688 * q^39 + 245944041232936104 * q^41 - 473810478271184736 * q^44 - 856055962790322336 * q^46 + 1430570793882941340 * q^49 - 1338467112735508728 * q^51 - 274246987950072468 * q^54 + 4061460640101137280 * q^56 + 7047646661807714448 * q^59 - 3558046256902027720 * q^61 - 10423384026926965888 * q^64 + 27667662691008290544 * q^66 + 17302347849719695392 * q^69 + 34758454262300841888 * q^71 - 163428852787350574968 * q^74 - 139500225872185580128 * q^76 + 108111571188381182080 * q^79 + 48630661836227715204 * q^81 + 26410407726770964288 * q^84 + 317193734530493170416 * q^86 - 453841535930896131048 * q^89 + 858308349370370000704 * q^91 - 493766231937670239552 * q^94 - 1299017949048779200704 * q^96 - 1533272456452746444336 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1937.96i	− 1.33822i	−0.743162	−	0.669112i	$-0.766675\pi$
$2$	− 1937.96i	− 1.33822i	0.743162	−	0.669112i	$-0.233325\pi$
$3$	59049.0i	0.577350i
$3$	59049.0i	0.577350i
$4$	−1.65852e6	−0.790843
$5$	0	0
$5$	0	0
$6$	1.14434e8	0.772624
$7$	− 4.78205e7i	− 0.0639860i	−0.999488	−	0.0319930i	$-0.989815\pi$
$7$	− 4.78205e7i	− 0.0639860i	0.999488	−	0.0319930i	$-0.0101854\pi$
$8$	− 8.50053e8i	− 0.279899i
$9$	−3.48678e9	−0.333333
$10$	0	0
$11$	1.60111e11	1.86122	0.930609	−	0.366016i	$-0.119278\pi$
$11$	1.60111e11	1.86122	0.930609	+	0.366016i	$0.119278\pi$
$12$	− 9.79338e10i	− 0.456593i
$13$	− 7.86968e11i	− 1.58326i	−0.611001	−	0.791630i	$-0.709233\pi$
$13$	− 7.86968e11i	− 1.58326i	0.611001	−	0.791630i	$-0.290767\pi$
$14$	−9.26741e10	−0.0856276
$15$	0	0
$16$	−5.12553e12	−1.16541
$17$	2.97477e12i	0.357881i	0.983860	+	0.178941i	$0.0572670\pi$
$17$	2.97477e12i	0.357881i	−0.983860	+	0.178941i	$0.942733\pi$
$18$	6.75723e12i	0.446075i
$19$	2.99456e13	1.12052	0.560260	−	0.828317i	$-0.310701\pi$
$19$	2.99456e13	1.12052	0.560260	+	0.828317i	$0.310701\pi$
$20$	0	0
$21$	2.82376e12	0.0369423
$22$	− 3.10287e14i	− 2.49073i
$23$	− 1.91401e14i	− 0.963390i	−0.876339	−	0.481695i	$-0.840021\pi$
$23$	− 1.91401e14i	− 0.963390i	0.876339	−	0.481695i	$-0.159979\pi$
$24$	5.01948e13	0.161600
$25$	0	0
$26$	−1.52511e15	−2.11876
$27$	− 2.05891e14i	− 0.192450i
$28$	7.93112e13i	0.0506029i
$29$	−9.68170e14	−0.427339	−0.213670	−	0.976906i	$-0.568542\pi$
$29$	−9.68170e14	−0.427339	−0.213670	+	0.976906i	$0.568542\pi$
$30$	0	0
$31$	2.80459e15	0.614570	0.307285	−	0.951618i	$-0.400580\pi$
$31$	2.80459e15	0.614570	0.307285	+	0.951618i	$0.400580\pi$
$32$	8.15035e15i	1.27968i
$33$	9.45437e15i	1.07457i
$34$	5.76496e15	0.478925
$35$	0	0
$36$	5.78290e15	0.263614
$37$	− 3.05038e16i	− 1.04288i	−0.853287	−	0.521441i	$-0.825395\pi$
$37$	− 3.05038e16i	− 1.04288i	0.853287	−	0.521441i	$-0.174605\pi$
$38$	− 5.80331e16i	− 1.49951i
$39$	4.64697e16	0.914095
$40$	0	0
$41$	−2.22806e16	−0.259237	−0.129618	−	0.991564i	$-0.541375\pi$
$41$	−2.22806e16	−0.259237	−0.129618	+	0.991564i	$0.541375\pi$
$42$	− 5.47231e15i	− 0.0494371i
$43$	1.63711e17i	1.15521i	0.816317	+	0.577604i	$0.196012\pi$
$43$	1.63711e17i	1.15521i	−0.816317	+	0.577604i	$0.803988\pi$
$44$	−2.65546e17	−1.47193
$45$	0	0
$46$	−3.70927e17	−1.28923
$47$	− 4.08678e17i	− 1.13332i	−0.823951	−	0.566662i	$-0.808235\pi$
$47$	− 4.08678e17i	− 1.13332i	0.823951	−	0.566662i	$-0.191765\pi$
$48$	− 3.02657e17i	− 0.672850i
$49$	5.56259e17	0.995906
$50$	0	0
$51$	−1.75657e17	−0.206623
$52$	1.30520e18i	1.25211i
$53$	4.34009e17i	0.340881i	0.985368	+	0.170440i	$0.0545190\pi$
$53$	4.34009e17i	0.340881i	−0.985368	+	0.170440i	$0.945481\pi$
$54$	−3.99008e17	−0.257541
$55$	0	0
$56$	−4.06500e16	−0.0179096
$57$	1.76826e18i	0.646932i
$58$	1.87627e18i	0.571875i
$59$	5.14341e18	1.31010	0.655051	−	0.755584i	$-0.272647\pi$
$59$	5.14341e18	1.31010	0.655051	+	0.755584i	$0.272647\pi$
$60$	0	0
$61$	1.98980e18	0.357147	0.178573	−	0.983927i	$-0.442852\pi$
$61$	1.98980e18	0.357147	0.178573	+	0.983927i	$0.442852\pi$
$62$	− 5.43517e18i	− 0.822432i
$63$	1.66740e17i	0.0213287i
$64$	5.04601e18	0.547089
$65$	0	0
$66$	1.83222e19	1.43802
$67$	1.36361e19i	0.913913i	0.889489	+	0.456956i	$0.151060\pi$
$67$	1.36361e19i	0.913913i	−0.889489	+	0.456956i	$0.848940\pi$
$68$	− 4.93370e18i	− 0.283028i
$69$	1.13020e19	0.556213
$70$	0	0
$71$	7.35641e18	0.268196	0.134098	−	0.990968i	$-0.457186\pi$
$71$	7.35641e18	0.268196	0.134098	+	0.990968i	$0.457186\pi$
$72$	2.96395e18i	0.0932996i
$73$	6.81650e19i	1.85640i	0.372081	+	0.928200i	$0.378644\pi$
$73$	6.81650e19i	1.85640i	−0.372081	+	0.928200i	$0.621356\pi$
$74$	−5.91149e19	−1.39561
$75$	0	0
$76$	−4.96652e19	−0.886155
$77$	− 7.65658e18i	− 0.119092i
$78$	− 9.00562e19i	− 1.22326i
$79$	2.12282e19	0.252249	0.126124	−	0.992014i	$-0.459746\pi$
$79$	2.12282e19	0.252249	0.126124	+	0.992014i	$0.459746\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	4.31789e19i	0.346917i
$83$	1.10803e20i	0.783849i	0.919997	+	0.391924i	$0.128191\pi$
$83$	1.10803e20i	0.783849i	−0.919997	+	0.391924i	$0.871809\pi$
$84$	−4.68325e18	−0.0292156
$85$	0	0
$86$	3.17266e20	1.54593
$87$	− 5.71695e19i	− 0.246724i
$88$	− 1.36102e20i	− 0.520952i
$89$	7.67205e18	0.0260805	0.0130403	−	0.999915i	$-0.495849\pi$
$89$	7.67205e18	0.0260805	0.0130403	+	0.999915i	$0.495849\pi$
$90$	0	0
$91$	−3.76333e19	−0.101306
$92$	3.17442e20i	0.761890i
$93$	1.65608e20i	0.354822i
$94$	−7.92000e20	−1.51664
$95$	0	0
$96$	−4.81270e20	−0.738824
$97$	− 4.63755e20i	− 0.638535i	−0.947665	−	0.319268i	$-0.896563\pi$
$97$	− 4.63755e20i	− 0.638535i	0.947665	−	0.319268i	$-0.103437\pi$
$98$	− 1.07801e21i	− 1.33274i
$99$	−5.58271e20	−0.620406
$100$	0	0
$101$	1.75642e20	0.158217	0.0791086	−	0.996866i	$-0.474793\pi$
$101$	1.75642e20	0.158217	0.0791086	+	0.996866i	$0.474793\pi$
$102$	3.40415e20i	0.276508i
$103$	− 1.29018e21i	− 0.945933i	−0.881080	−	0.472967i	$-0.843183\pi$
$103$	− 1.29018e21i	− 0.945933i	0.881080	−	0.472967i	$-0.156817\pi$
$104$	−6.68965e20	−0.443152
$105$	0	0
$106$	8.41091e20	0.456175
$107$	− 5.76913e19i	− 0.0283518i	−0.999900	−	0.0141759i	$-0.995488\pi$
$107$	− 5.76913e19i	− 0.0283518i	0.999900	−	0.0141759i	$-0.00451248\pi$
$108$	3.41474e20i	0.152198i
$109$	5.74941e20	0.232619	0.116309	−	0.993213i	$-0.462894\pi$
$109$	5.74941e20	0.232619	0.116309	+	0.993213i	$0.462894\pi$
$110$	0	0
$111$	1.80122e21	0.602109
$112$	2.45106e20i	0.0745700i
$113$	− 4.56755e21i	− 1.26578i	−0.774240	−	0.632892i	$-0.781868\pi$
$113$	− 4.56755e21i	− 1.26578i	0.774240	−	0.632892i	$-0.218132\pi$
$114$	3.42680e21	0.865740
$115$	0	0
$116$	1.60573e21	0.337958
$117$	2.74399e21i	0.527753i
$118$	− 9.96770e21i	− 1.75321i
$119$	1.42255e20	0.0228994
$120$	0	0
$121$	1.82352e22	2.46413
$122$	− 3.85615e21i	− 0.477942i
$123$	− 1.31565e21i	− 0.149671i
$124$	−4.65146e21	−0.486028
$125$	0	0
$126$	3.23134e20	0.0285425
$127$	− 1.84938e22i	− 1.50344i	−0.659480	−	0.751722i	$-0.729224\pi$
$127$	− 1.84938e22i	− 1.50344i	0.659480	−	0.751722i	$-0.270776\pi$
$128$	7.31359e21i	0.547553i
$129$	−9.66700e21	−0.666960
$130$	0	0
$131$	−1.25296e22	−0.735509	−0.367754	−	0.929923i	$-0.619873\pi$
$131$	−1.25296e22	−0.735509	−0.367754	+	0.929923i	$0.619873\pi$
$132$	− 1.56802e22i	− 0.849820i
$133$	− 1.43201e21i	− 0.0716976i
$134$	2.64261e22	1.22302
$135$	0	0
$136$	2.52871e21	0.100171
$137$	− 3.84075e22i	− 1.40880i	−0.709801	−	0.704402i	$-0.751215\pi$
$137$	− 3.84075e22i	− 1.40880i	0.709801	−	0.704402i	$-0.248785\pi$
$138$	− 2.19028e22i	− 0.744338i
$139$	9.58856e21	0.302063	0.151032	−	0.988529i	$-0.451740\pi$
$139$	9.58856e21	0.302063	0.151032	+	0.988529i	$0.451740\pi$
$140$	0	0
$141$	2.41320e22	0.654324
$142$	− 1.42564e22i	− 0.358907i
$143$	− 1.26002e23i	− 2.94679i
$144$	1.78716e22	0.388470
$145$	0	0
$146$	1.32101e23	2.48428
$147$	3.28465e22i	0.574986i
$148$	5.05911e22i	0.824757i
$149$	−3.44428e22	−0.523170	−0.261585	−	0.965180i	$-0.584245\pi$
$149$	−3.44428e22	−0.523170	−0.261585	+	0.965180i	$0.584245\pi$
$150$	0	0
$151$	−3.63152e22	−0.479546	−0.239773	−	0.970829i	$-0.577073\pi$
$151$	−3.63152e22	−0.479546	−0.239773	+	0.970829i	$0.577073\pi$
$152$	− 2.54553e22i	− 0.313632i
$153$	− 1.03724e22i	− 0.119294i
$154$	−1.48381e22	−0.159372
$155$	0	0
$156$	−7.70708e22	−0.722906
$157$	9.41986e22i	0.826225i	0.910680	+	0.413112i	$0.135558\pi$
$157$	9.41986e22i	0.826225i	−0.910680	+	0.413112i	$0.864442\pi$
$158$	− 4.11393e22i	− 0.337565i
$159$	−2.56278e22	−0.196808
$160$	0	0
$161$	−9.15290e21	−0.0616435
$162$	− 2.35610e22i	− 0.148692i
$163$	− 1.80771e23i	− 1.06945i	−0.845027	−	0.534723i	$-0.820416\pi$
$163$	− 1.80771e23i	− 1.06945i	0.845027	−	0.534723i	$-0.179584\pi$
$164$	3.69528e22	0.205016
$165$	0	0
$166$	2.14732e23	1.04897
$167$	− 3.71934e22i	− 0.170586i	−0.996356	−	0.0852929i	$-0.972817\pi$
$167$	− 3.71934e22i	− 0.170586i	0.996356	−	0.0852929i	$-0.0271826\pi$
$168$	− 2.40034e21i	− 0.0103401i
$169$	−3.72255e23	−1.50671
$170$	0	0
$171$	−1.04414e23	−0.373507
$172$	− 2.71518e23i	− 0.913589i
$173$	2.58398e23i	0.818096i	0.912513	+	0.409048i	$0.134139\pi$
$173$	2.58398e23i	0.818096i	−0.912513	+	0.409048i	$0.865861\pi$
$174$	−1.10792e23	−0.330172
$175$	0	0
$176$	−8.20652e23	−2.16908
$177$	3.03713e23i	0.756388i
$178$	− 1.48681e22i	− 0.0349016i
$179$	3.35184e23	0.741868	0.370934	−	0.928659i	$-0.379038\pi$
$179$	3.35184e23	0.741868	0.370934	+	0.928659i	$0.379038\pi$
$180$	0	0
$181$	−1.92267e23	−0.378687	−0.189343	−	0.981911i	$-0.560636\pi$
$181$	−1.92267e23	−0.378687	−0.189343	+	0.981911i	$0.560636\pi$
$182$	7.29316e22i	0.135571i
$183$	1.17496e23i	0.206199i
$184$	−1.62701e23	−0.269652
$185$	0	0
$186$	3.20941e23	0.474831
$187$	4.76292e23i	0.666095i
$188$	6.77800e23i	0.896281i
$189$	−9.84583e21	−0.0123141
$190$	0	0
$191$	−4.60821e23	−0.516038	−0.258019	−	0.966140i	$-0.583070\pi$
$191$	−4.60821e23	−0.516038	−0.258019	+	0.966140i	$0.583070\pi$
$192$	2.97962e23i	0.315862i
$193$	1.29600e24i	1.30093i	0.759536	+	0.650465i	$0.225426\pi$
$193$	1.29600e24i	1.30093i	−0.759536	+	0.650465i	$0.774574\pi$
$194$	−8.98736e23	−0.854503
$195$	0	0
$196$	−9.22566e23	−0.787605
$197$	− 2.05711e24i	− 1.66480i	−0.554172	−	0.832402i	$-0.686965\pi$
$197$	− 2.05711e24i	− 1.66480i	0.554172	−	0.832402i	$-0.313035\pi$
$198$	1.08190e24i	0.830242i
$199$	−5.34557e22	−0.0389078	−0.0194539	−	0.999811i	$-0.506193\pi$
$199$	−5.34557e22	−0.0389078	−0.0194539	+	0.999811i	$0.506193\pi$
$200$	0	0
$201$	−8.05198e23	−0.527648
$202$	− 3.40386e23i	− 0.211730i
$203$	4.62984e22i	0.0273437i
$204$	2.91330e23	0.163406
$205$	0	0
$206$	−2.50032e24	−1.26587
$207$	6.67374e23i	0.321130i
$208$	4.03363e24i	1.84515i
$209$	4.79460e24	2.08553
$210$	0	0
$211$	−3.16142e24	−1.24427	−0.622137	−	0.782908i	$-0.713735\pi$
$211$	−3.16142e24	−1.24427	−0.622137	+	0.782908i	$0.713735\pi$
$212$	− 7.19813e23i	− 0.269583i
$213$	4.34388e23i	0.154843i
$214$	−1.11803e23	−0.0379410
$215$	0	0
$216$	−1.75018e23	−0.0538665
$217$	− 1.34117e23i	− 0.0393239i
$218$	− 1.11421e24i	− 0.311296i
$219$	−4.02508e24	−1.07179
$220$	0	0
$221$	2.34105e24	0.566619
$222$	− 3.49068e24i	− 0.805756i
$223$	− 3.10623e24i	− 0.683963i	−0.939707	−	0.341981i	$-0.888902\pi$
$223$	− 3.10623e24i	− 0.683963i	0.939707	−	0.341981i	$-0.111098\pi$
$224$	3.89754e23	0.0818817
$225$	0	0
$226$	−8.85171e24	−1.69390
$227$	2.04882e24i	0.374310i	0.982330	+	0.187155i	$0.0599267\pi$
$227$	2.04882e24i	0.374310i	−0.982330	+	0.187155i	$0.940073\pi$
$228$	− 2.93268e24i	− 0.511622i
$229$	−4.12622e24	−0.687512	−0.343756	−	0.939059i	$-0.611699\pi$
$229$	−4.12622e24	−0.687512	−0.343756	+	0.939059i	$0.611699\pi$
$230$	0	0
$231$	4.52113e23	0.0687577
$232$	8.22995e23i	0.119612i
$233$	3.43270e24i	0.476869i	0.971159	+	0.238434i	$0.0766342\pi$
$233$	3.43270e24i	0.476869i	−0.971159	+	0.238434i	$0.923366\pi$
$234$	5.31773e24	0.706252
$235$	0	0
$236$	−8.53044e24	−1.03609
$237$	1.25351e24i	0.145636i
$238$	− 2.75684e23i	− 0.0306445i
$239$	−8.29149e24	−0.881972	−0.440986	−	0.897514i	$-0.645371\pi$
$239$	−8.29149e24	−0.881972	−0.440986	+	0.897514i	$0.645371\pi$
$240$	0	0
$241$	−1.30526e25	−1.27209	−0.636045	−	0.771652i	$-0.719431\pi$
$241$	−1.30526e25	−1.27209	−0.636045	+	0.771652i	$0.719431\pi$
$242$	− 3.53389e25i	− 3.29756i
$243$	7.17898e23i	0.0641500i
$244$	−3.30012e24	−0.282447
$245$	0	0
$246$	−2.54967e24	−0.200293
$247$	− 2.35662e25i	− 1.77407i
$248$	− 2.38405e24i	− 0.172017i
$249$	−6.54282e24	−0.452555
$250$	0	0
$251$	−1.77630e25	−1.12965	−0.564823	−	0.825212i	$-0.691056\pi$
$251$	−1.77630e25	−1.12965	−0.564823	+	0.825212i	$0.691056\pi$
$252$	− 2.76541e23i	− 0.0168676i
$253$	− 3.06453e25i	− 1.79308i
$254$	−3.58402e25	−2.01194
$255$	0	0
$256$	2.47557e25	1.27984
$257$	5.70058e24i	0.282893i	0.989946	+	0.141446i	$0.0451752\pi$
$257$	5.70058e24i	0.282893i	−0.989946	+	0.141446i	$0.954825\pi$
$258$	1.87342e25i	0.892542i
$259$	−1.45871e24	−0.0667299
$260$	0	0
$261$	3.37580e24	0.142446
$262$	2.42818e25i	0.984275i
$263$	9.73572e23i	0.0379169i	0.999820	+	0.0189584i	$0.00603502\pi$
$263$	9.73572e23i	0.0379169i	−0.999820	+	0.0189584i	$0.993965\pi$
$264$	8.03672e24	0.300772
$265$	0	0
$266$	−2.77518e24	−0.0959474
$267$	4.53027e23i	0.0150576i
$268$	− 2.26157e25i	− 0.722761i
$269$	5.78587e25	1.77816	0.889078	−	0.457756i	$-0.151347\pi$
$269$	5.78587e25	1.77816	0.889078	+	0.457756i	$0.151347\pi$
$270$	0	0
$271$	4.29033e25	1.21987	0.609934	−	0.792452i	$-0.291196\pi$
$271$	4.29033e25	1.21987	0.609934	+	0.792452i	$0.291196\pi$
$272$	− 1.52473e25i	− 0.417079i
$273$	− 2.22221e24i	− 0.0584893i
$274$	−7.44321e25	−1.88530
$275$	0	0
$276$	−1.87446e25	−0.439877
$277$	− 6.39000e25i	− 1.44366i	−0.692073	−	0.721828i	$-0.743302\pi$
$277$	− 6.39000e25i	− 1.44366i	0.692073	−	0.721828i	$-0.256698\pi$
$278$	− 1.85822e25i	− 0.404228i
$279$	−9.77899e24	−0.204857
$280$	0	0
$281$	3.23104e25	0.627951	0.313976	−	0.949431i	$-0.398339\pi$
$281$	3.23104e25	0.627951	0.313976	+	0.949431i	$0.398339\pi$
$282$	− 4.67668e25i	− 0.875632i
$283$	− 1.00627e25i	− 0.181534i	−0.995872	−	0.0907668i	$-0.971068\pi$
$283$	− 1.00627e25i	− 0.181534i	0.995872	−	0.0907668i	$-0.0289318\pi$
$284$	−1.22007e25	−0.212101
$285$	0	0
$286$	−2.44186e26	−3.94346
$287$	1.06547e24i	0.0165875i
$288$	− 2.84185e25i	− 0.426560i
$289$	6.02427e25	0.871921
$290$	0	0
$291$	2.73842e25	0.368659
$292$	− 1.13053e26i	− 1.46812i
$293$	4.93011e25i	0.617656i	0.951118	+	0.308828i	$0.0999367\pi$
$293$	4.93011e25i	0.617656i	−0.951118	+	0.308828i	$0.900063\pi$
$294$	6.36551e25	0.769461
$295$	0	0
$296$	−2.59298e25	−0.291902
$297$	− 3.29654e25i	− 0.358191i
$298$	6.67487e25i	0.700119i
$299$	−1.50627e26	−1.52530
$300$	0	0
$301$	7.82877e24	0.0739172
$302$	7.03772e25i	0.641740i
$303$	1.03715e25i	0.0913467i
$304$	−1.53487e26	−1.30587
$305$	0	0
$306$	−2.01012e25	−0.159642
$307$	1.49828e25i	0.114985i	0.998346	+	0.0574925i	$0.0183105\pi$
$307$	1.49828e25i	0.114985i	−0.998346	+	0.0574925i	$0.981689\pi$
$308$	1.26986e25i	0.0941830i
$309$	7.61840e25	0.546135
$310$	0	0
$311$	−1.48794e26	−0.996786	−0.498393	−	0.866951i	$-0.666076\pi$
$311$	−1.48794e26	−0.996786	−0.498393	+	0.866951i	$0.666076\pi$
$312$	− 3.95017e25i	− 0.255854i
$313$	− 1.10961e26i	− 0.694951i	−0.937689	−	0.347476i	$-0.887039\pi$
$313$	− 1.10961e26i	− 0.694951i	0.937689	−	0.347476i	$-0.112961\pi$
$314$	1.82553e26	1.10567
$315$	0	0
$316$	−3.52074e25	−0.199489
$317$	− 7.14805e25i	− 0.391801i	−0.980624	−	0.195900i	$-0.937237\pi$
$317$	− 7.14805e25i	− 0.391801i	0.980624	−	0.195900i	$-0.0627629\pi$
$318$	4.96656e25i	0.263373i
$319$	−1.55014e26	−0.795371
$320$	0	0
$321$	3.40661e24	0.0163689
$322$	1.77379e25i	0.0824928i
$323$	8.90810e25i	0.401013i
$324$	−2.01637e25	−0.0878715
$325$	0	0
$326$	−3.50326e26	−1.43116
$327$	3.39497e25i	0.134302i
$328$	1.89397e25i	0.0725601i
$329$	−1.95432e25	−0.0725168
$330$	0	0
$331$	−5.05668e26	−1.76065	−0.880323	−	0.474375i	$-0.842674\pi$
$331$	−5.05668e26	−1.76065	−0.880323	+	0.474375i	$0.842674\pi$
$332$	− 1.83769e26i	− 0.619901i
$333$	1.06360e26i	0.347628i
$334$	−7.20791e25	−0.228282
$335$	0	0
$336$	−1.44732e25	−0.0430530
$337$	− 3.50546e26i	− 1.01072i	−0.862909	−	0.505360i	$-0.831360\pi$
$337$	− 3.50546e26i	− 1.01072i	0.862909	−	0.505360i	$-0.168640\pi$
$338$	7.21413e26i	2.01632i
$339$	2.69709e26	0.730801
$340$	0	0
$341$	4.49044e26	1.14385
$342$	2.02349e26i	0.499835i
$343$	− 5.33106e25i	− 0.127710i
$344$	1.39163e26	0.323341
$345$	0	0
$346$	5.00763e26	1.09480
$347$	3.51664e26i	0.745879i	0.927856	+	0.372940i	$0.121650\pi$
$347$	3.51664e26i	0.745879i	−0.927856	+	0.372940i	$0.878350\pi$
$348$	9.48166e25i	0.195120i
$349$	−5.74285e26	−1.14673	−0.573364	−	0.819300i	$-0.694362\pi$
$349$	−5.74285e26	−1.14673	−0.573364	+	0.819300i	$0.694362\pi$
$350$	0	0
$351$	−1.62030e26	−0.304698
$352$	1.30496e27i	2.38176i
$353$	1.85373e25i	0.0328406i	0.999865	+	0.0164203i	$0.00522698\pi$
$353$	1.85373e25i	0.0328406i	−0.999865	+	0.0164203i	$0.994773\pi$
$354$	5.88583e26	1.01222
$355$	0	0
$356$	−1.27242e25	−0.0206256
$357$	8.40001e24i	0.0132210i
$358$	− 6.49572e26i	− 0.992785i
$359$	3.41606e26	0.507030	0.253515	−	0.967331i	$-0.418413\pi$
$359$	3.41606e26	0.507030	0.253515	+	0.967331i	$0.418413\pi$
$360$	0	0
$361$	1.82527e26	0.255565
$362$	3.72605e26i	0.506768i
$363$	1.07677e27i	1.42267i
$364$	6.24154e25	0.0801175
$365$	0	0
$366$	2.27702e26	0.275940
$367$	− 5.79162e26i	− 0.682034i	−0.940057	−	0.341017i	$-0.889229\pi$
$367$	− 5.79162e26i	− 0.682034i	0.940057	−	0.341017i	$-0.110771\pi$
$368$	9.81031e26i	1.12274i
$369$	7.76878e25	0.0864123
$370$	0	0
$371$	2.07546e25	0.0218116
$372$	− 2.74664e26i	− 0.280609i
$373$	− 1.74513e27i	− 1.73335i	−0.498877	−	0.866673i	$-0.666254\pi$
$373$	− 1.74513e27i	− 1.73335i	0.498877	−	0.866673i	$-0.333746\pi$
$374$	9.23032e26	0.891384
$375$	0	0
$376$	−3.47398e26	−0.317216
$377$	7.61919e26i	0.676588i
$378$	1.90808e25i	0.0164790i
$379$	−1.08818e27	−0.914093	−0.457046	−	0.889443i	$-0.651093\pi$
$379$	−1.08818e27	−0.914093	−0.457046	+	0.889443i	$0.651093\pi$
$380$	0	0
$381$	1.09204e27	0.868014
$382$	8.93050e26i	0.690575i
$383$	− 2.35974e27i	− 1.77532i	−0.460498	−	0.887661i	$-0.652329\pi$
$383$	− 2.35974e27i	− 1.77532i	0.460498	−	0.887661i	$-0.347671\pi$
$384$	−4.31860e26	−0.316130
$385$	0	0
$386$	2.51159e27	1.74094
$387$	− 5.70827e26i	− 0.385070i
$388$	7.69145e26i	0.504981i
$389$	2.72162e27	1.73923	0.869616	−	0.493729i	$-0.164367\pi$
$389$	2.72162e27	1.73923	0.869616	+	0.493729i	$0.164367\pi$
$390$	0	0
$391$	5.69373e26	0.344779
$392$	− 4.72850e26i	− 0.278753i
$393$	− 7.39859e26i	− 0.424646i
$394$	−3.98660e27	−2.22788
$395$	0	0
$396$	9.25903e26	0.490644
$397$	2.20086e27i	1.13577i	0.823106	+	0.567887i	$0.192239\pi$
$397$	2.20086e27i	1.13577i	−0.823106	+	0.567887i	$0.807761\pi$
$398$	1.03595e26i	0.0520673i
$399$	8.45589e25	0.0413946
$400$	0	0
$401$	2.61699e27	1.21559	0.607793	−	0.794096i	$-0.292055\pi$
$401$	2.61699e27	1.21559	0.607793	+	0.794096i	$0.292055\pi$
$402$	1.56044e27i	0.706111i
$403$	− 2.20712e27i	− 0.973023i
$404$	−2.91305e26	−0.125125
$405$	0	0
$406$	8.97242e25	0.0365920
$407$	− 4.88398e27i	− 1.94103i
$408$	1.49318e26i	0.0578335i
$409$	8.92474e26	0.336900	0.168450	−	0.985710i	$-0.446124\pi$
$409$	8.92474e26	0.336900	0.168450	+	0.985710i	$0.446124\pi$
$410$	0	0
$411$	2.26793e27	0.813373
$412$	2.13979e27i	0.748085i
$413$	− 2.45961e26i	− 0.0838282i
$414$	1.29334e27	0.429744
$415$	0	0
$416$	6.41407e27	2.02607
$417$	5.66195e26i	0.174396i
$418$	− 9.29172e27i	− 2.79091i
$419$	2.48238e27	0.727144	0.363572	−	0.931566i	$-0.381557\pi$
$419$	2.48238e27	0.727144	0.363572	+	0.931566i	$0.381557\pi$
$420$	0	0
$421$	4.09797e27	1.14184	0.570922	−	0.821004i	$-0.306586\pi$
$421$	4.09797e27	1.14184	0.570922	+	0.821004i	$0.306586\pi$
$422$	6.12669e27i	1.66512i
$423$	1.42497e27i	0.377774i
$424$	3.68931e26	0.0954121
$425$	0	0
$426$	8.41825e26	0.207215
$427$	− 9.51534e25i	− 0.0228524i
$428$	9.56820e25i	0.0224218i
$429$	7.44029e27	1.70133
$430$	0	0
$431$	−4.89793e27	−1.06660	−0.533299	−	0.845927i	$-0.679048\pi$
$431$	−4.89793e27	−1.06660	−0.533299	+	0.845927i	$0.679048\pi$
$432$	1.05530e27i	0.224283i
$433$	− 2.06118e27i	− 0.427557i	−0.976882	−	0.213778i	$-0.931423\pi$
$433$	− 2.06118e27i	− 0.427557i	0.976882	−	0.213778i	$-0.0685770\pi$
$434$	−2.59913e26	−0.0526242
$435$	0	0
$436$	−9.53549e26	−0.183965
$437$	− 5.73161e27i	− 1.07950i
$438$	7.80042e27i	1.43430i
$439$	−1.00358e28	−1.80167	−0.900835	−	0.434161i	$-0.857045\pi$
$439$	−1.00358e28	−1.80167	−0.900835	+	0.434161i	$0.857045\pi$
$440$	0	0
$441$	−1.93956e27	−0.331969
$442$	− 4.53684e27i	− 0.758263i
$443$	4.23345e27i	0.690964i	0.938425	+	0.345482i	$0.112285\pi$
$443$	4.23345e27i	0.690964i	−0.938425	+	0.345482i	$0.887715\pi$
$444$	−2.98735e27	−0.476173
$445$	0	0
$446$	−6.01973e27	−0.915295
$447$	− 2.03382e27i	− 0.302053i
$448$	− 2.41303e26i	− 0.0350061i
$449$	6.74432e27	0.955766	0.477883	−	0.878424i	$-0.341404\pi$
$449$	6.74432e27	0.955766	0.477883	+	0.878424i	$0.341404\pi$
$450$	0	0
$451$	−3.56737e27	−0.482496
$452$	7.57537e27i	1.00104i
$453$	− 2.14438e27i	− 0.276866i
$454$	3.97052e27	0.500911
$455$	0	0
$456$	1.50311e27	0.181076
$457$	1.13821e28i	1.34000i	0.742362	+	0.669998i	$0.233705\pi$
$457$	1.13821e28i	1.34000i	−0.742362	+	0.669998i	$0.766295\pi$
$458$	7.99644e27i	0.920045i
$459$	6.12478e26	0.0688743
$460$	0	0
$461$	6.24175e27	0.670574	0.335287	−	0.942116i	$-0.391167\pi$
$461$	6.24175e27	0.670574	0.335287	+	0.942116i	$0.391167\pi$
$462$	− 8.76175e26i	− 0.0920132i
$463$	− 2.31855e27i	− 0.238021i	−0.992893	−	0.119011i	$-0.962028\pi$
$463$	− 2.31855e27i	− 0.238021i	0.992893	−	0.119011i	$-0.0379723\pi$
$464$	4.96238e27	0.498025
$465$	0	0
$466$	6.65242e27	0.638157
$467$	9.47846e26i	0.0889018i	0.999012	+	0.0444509i	$0.0141538\pi$
$467$	9.47846e26i	0.0889018i	−0.999012	+	0.0444509i	$0.985846\pi$
$468$	− 4.55096e27i	− 0.417370i
$469$	6.52086e26	0.0584776
$470$	0	0
$471$	−5.56234e27	−0.477021
$472$	− 4.37217e27i	− 0.366696i
$473$	2.62120e28i	2.15009i
$474$	2.42924e27	0.194893
$475$	0	0
$476$	−2.35932e26	−0.0181098
$477$	− 1.51330e27i	− 0.113627i
$478$	1.60685e28i	1.18028i
$479$	1.76996e28	1.27186	0.635932	−	0.771745i	$-0.280616\pi$
$479$	1.76996e28	1.27186	0.635932	+	0.771745i	$0.280616\pi$
$480$	0	0
$481$	−2.40055e28	−1.65115
$482$	2.52954e28i	1.70234i
$483$	− 5.40470e26i	− 0.0355899i
$484$	−3.02434e28	−1.94874
$485$	0	0
$486$	1.39125e27	0.0858471
$487$	− 1.99209e28i	− 1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$487$	− 1.99209e28i	− 1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$488$	− 1.69144e27i	− 0.0999649i
$489$	1.06743e28	0.617445
$490$	0	0
$491$	−5.71237e27	−0.316563	−0.158282	−	0.987394i	$-0.550595\pi$
$491$	−5.71237e27	−0.316563	−0.158282	+	0.987394i	$0.550595\pi$
$492$	2.18203e27i	0.118366i
$493$	− 2.88008e27i	− 0.152937i
$494$	−4.56702e28	−2.37411
$495$	0	0
$496$	−1.43750e28	−0.716226
$497$	− 3.51787e26i	− 0.0171608i
$498$	1.26797e28i	0.605620i
$499$	1.17032e28	0.547332	0.273666	−	0.961825i	$-0.411764\pi$
$499$	1.17032e28	0.547332	0.273666	+	0.961825i	$0.411764\pi$
$500$	0	0
$501$	2.19623e27	0.0984878
$502$	3.44239e28i	1.51172i
$503$	− 3.15184e28i	− 1.35550i	−0.735292	−	0.677750i	$-0.762955\pi$
$503$	− 3.15184e28i	− 1.35550i	0.735292	−	0.677750i	$-0.237045\pi$
$504$	1.41738e26	0.00596987
$505$	0	0
$506$	−5.93893e28	−2.39954
$507$	− 2.19813e28i	− 0.869899i
$508$	3.06723e28i	1.18899i
$509$	−4.58029e28	−1.73923	−0.869613	−	0.493733i	$-0.835632\pi$
$509$	−4.58029e28	−1.73923	−0.869613	+	0.493733i	$0.835632\pi$
$510$	0	0
$511$	3.25969e27	0.118784
$512$	− 3.26377e28i	− 1.16516i
$513$	− 6.16552e27i	− 0.215644i
$514$	1.10475e28	0.378574
$515$	0	0
$516$	1.60329e28	0.527461
$517$	− 6.54337e28i	− 2.10936i
$518$	2.82691e27i	0.0892996i
$519$	−1.52581e28	−0.472328
$520$	0	0
$521$	−5.19044e27	−0.154315	−0.0771575	−	0.997019i	$-0.524584\pi$
$521$	−5.19044e27	−0.154315	−0.0771575	+	0.997019i	$0.524584\pi$
$522$	− 6.54215e27i	− 0.190625i
$523$	− 2.08282e27i	− 0.0594817i	−0.999558	−	0.0297408i	$-0.990532\pi$
$523$	− 2.08282e27i	− 0.0594817i	0.999558	−	0.0297408i	$-0.00946820\pi$
$524$	2.07805e28	0.581672
$525$	0	0
$526$	1.88674e27	0.0507413
$527$	8.34299e27i	0.219943i
$528$	− 4.84587e28i	− 1.25232i
$529$	2.83724e27	0.0718805
$530$	0	0
$531$	−1.79340e28	−0.436701
$532$	2.37502e27i	0.0567016i
$533$	1.75342e28i	0.410439i
$534$	8.77946e26	0.0201504
$535$	0	0
$536$	1.15914e28	0.255803
$537$	1.97923e28i	0.428318i
$538$	− 1.12128e29i	− 2.37957i
$539$	8.90630e28	1.85360
$540$	0	0
$541$	−1.25240e28	−0.250710	−0.125355	−	0.992112i	$-0.540007\pi$
$541$	−1.25240e28	−0.250710	−0.125355	+	0.992112i	$0.540007\pi$
$542$	− 8.31446e28i	− 1.63246i
$543$	− 1.13532e28i	− 0.218635i
$544$	−2.42454e28	−0.457974
$545$	0	0
$546$	−4.30654e27	−0.0782718
$547$	− 5.63104e28i	− 1.00397i	−0.864875	−	0.501987i	$-0.832603\pi$
$547$	− 5.63104e28i	− 1.00397i	0.864875	−	0.501987i	$-0.167397\pi$
$548$	6.36996e28i	1.11414i
$549$	−6.93801e27	−0.119049
$550$	0	0
$551$	−2.89924e28	−0.478842
$552$	− 9.60733e27i	− 0.155683i
$553$	− 1.01514e27i	− 0.0161404i
$554$	−1.23835e29	−1.93193
$555$	0	0
$556$	−1.59028e28	−0.238885
$557$	− 4.80914e28i	− 0.708904i	−0.935074	−	0.354452i	$-0.884667\pi$
$557$	− 4.80914e28i	− 0.708904i	0.935074	−	0.354452i	$-0.115333\pi$
$558$	1.89513e28i	0.274144i
$559$	1.28836e29	1.82899
$560$	0	0
$561$	−2.81246e28	−0.384570
$562$	− 6.26161e28i	− 0.840339i
$563$	− 1.81812e28i	− 0.239488i	−0.992805	−	0.119744i	$-0.961793\pi$
$563$	− 1.81812e28i	− 0.239488i	0.992805	−	0.119744i	$-0.0382074\pi$
$564$	−4.00234e28	−0.517468
$565$	0	0
$566$	−1.95011e28	−0.242933
$567$	− 5.81386e26i	− 0.00710956i
$568$	− 6.25333e27i	− 0.0750679i
$569$	−1.75144e28	−0.206403	−0.103201	−	0.994660i	$-0.532909\pi$
$569$	−1.75144e28	−0.206403	−0.103201	+	0.994660i	$0.532909\pi$
$570$	0	0
$571$	1.67794e29	1.90589	0.952946	−	0.303140i	$-0.0980350\pi$
$571$	1.67794e29	1.90589	0.952946	+	0.303140i	$0.0980350\pi$
$572$	2.08977e29i	2.33045i
$573$	− 2.72110e28i	− 0.297935i
$574$	2.06484e27	0.0221978
$575$	0	0
$576$	−1.75943e28	−0.182363
$577$	− 7.49346e28i	− 0.762669i	−0.924437	−	0.381335i	$-0.875465\pi$
$577$	− 7.49346e28i	− 0.762669i	0.924437	−	0.381335i	$-0.124535\pi$
$578$	− 1.16748e29i	− 1.16683i
$579$	−7.65276e28	−0.751092
$580$	0	0
$581$	5.29867e27	0.0501554
$582$	− 5.30694e28i	− 0.493348i
$583$	6.94895e28i	0.634453i
$584$	5.79439e28	0.519604
$585$	0	0
$586$	9.55433e28	0.826562
$587$	− 1.69908e29i	− 1.44382i	−0.691985	−	0.721912i	$-0.743264\pi$
$587$	− 1.69908e29i	− 1.44382i	0.691985	−	0.721912i	$-0.256736\pi$
$588$	− 5.44766e28i	− 0.454724i
$589$	8.39849e28	0.688638
$590$	0	0
$591$	1.21471e29	0.961175
$592$	1.56348e29i	1.21539i
$593$	− 1.26592e29i	− 0.966787i	−0.875403	−	0.483394i	$-0.839404\pi$
$593$	− 1.26592e29i	− 0.966787i	0.875403	−	0.483394i	$-0.160596\pi$
$594$	−6.38854e28	−0.479340
$595$	0	0
$596$	5.71241e28	0.413746
$597$	− 3.15650e27i	− 0.0224634i
$598$	2.91907e29i	2.04119i
$599$	−1.73983e29	−1.19544	−0.597718	−	0.801706i	$-0.703926\pi$
$599$	−1.73983e29	−1.19544	−0.597718	+	0.801706i	$0.703926\pi$
$600$	0	0
$601$	−2.58691e29	−1.71633	−0.858164	−	0.513376i	$-0.828395\pi$
$601$	−2.58691e29	−1.71633	−0.858164	+	0.513376i	$0.828395\pi$
$602$	− 1.51718e28i	− 0.0989178i
$603$	− 4.75461e28i	− 0.304638i
$604$	6.02294e28	0.379246
$605$	0	0
$606$	2.00994e28	0.122242
$607$	1.61646e29i	0.966238i	0.875555	+	0.483119i	$0.160496\pi$
$607$	1.61646e29i	0.966238i	−0.875555	+	0.483119i	$0.839504\pi$
$608$	2.44067e29i	1.43391i
$609$	−2.73387e27	−0.0157869
$610$	0	0
$611$	−3.21617e29	−1.79434
$612$	1.72028e28i	0.0943427i
$613$	8.86426e28i	0.477868i	0.971036	+	0.238934i	$0.0767979\pi$
$613$	8.86426e28i	0.477868i	−0.971036	+	0.238934i	$0.923202\pi$
$614$	2.90361e28	0.153876
$615$	0	0
$616$	−6.50850e27	−0.0333337
$617$	7.14976e28i	0.359996i	0.983667	+	0.179998i	$0.0576091\pi$
$617$	7.14976e28i	0.359996i	−0.983667	+	0.179998i	$0.942391\pi$
$618$	− 1.47641e29i	− 0.730851i
$619$	3.79378e28	0.184638	0.0923188	−	0.995730i	$-0.470572\pi$
$619$	3.79378e28	0.184638	0.0923188	+	0.995730i	$0.470572\pi$
$620$	0	0
$621$	−3.94078e28	−0.185404
$622$	2.88356e29i	1.33392i
$623$	− 3.66882e26i	− 0.00166879i
$624$	−2.38182e29	−1.06530
$625$	0	0
$626$	−2.15037e29	−0.930000
$627$	2.83116e29i	1.20408i
$628$	− 1.56230e29i	− 0.653414i
$629$	9.07416e28	0.373228
$630$	0	0
$631$	4.22002e29	1.67883	0.839415	−	0.543491i	$-0.182898\pi$
$631$	4.22002e29	1.67883	0.839415	+	0.543491i	$0.182898\pi$
$632$	− 1.80451e28i	− 0.0706041i
$633$	− 1.86679e29i	− 0.718382i
$634$	−1.38526e29	−0.524317
$635$	0	0
$636$	4.25042e28	0.155644
$637$	− 4.37758e29i	− 1.57678i
$638$	3.00411e29i	1.06438i
$639$	−2.56502e28	−0.0893988
$640$	0	0
$641$	−2.45898e29	−0.829364	−0.414682	−	0.909966i	$-0.636107\pi$
$641$	−2.45898e29	−0.829364	−0.414682	+	0.909966i	$0.636107\pi$
$642$	− 6.60186e27i	− 0.0219053i
$643$	3.81795e29i	1.24628i	0.782111	+	0.623139i	$0.214143\pi$
$643$	3.81795e29i	1.24628i	−0.782111	+	0.623139i	$0.785857\pi$
$644$	1.51803e28	0.0487503
$645$	0	0
$646$	1.72635e29	0.536646
$647$	3.01566e29i	0.922332i	0.887314	+	0.461166i	$0.152569\pi$
$647$	3.01566e29i	0.922332i	−0.887314	+	0.461166i	$0.847431\pi$
$648$	− 1.03347e28i	− 0.0310999i
$649$	8.23515e29	2.43839
$650$	0	0
$651$	7.91947e27	0.0227037
$652$	2.99812e29i	0.845764i
$653$	2.27685e29i	0.632042i	0.948752	+	0.316021i	$0.102347\pi$
$653$	2.27685e29i	0.632042i	−0.948752	+	0.316021i	$0.897653\pi$
$654$	6.57929e28	0.179727
$655$	0	0
$656$	1.14200e29	0.302117
$657$	− 2.37677e29i	− 0.618800i
$658$	3.78738e28i	0.0970437i
$659$	4.45804e29	1.12421	0.562104	−	0.827066i	$-0.309992\pi$
$659$	4.45804e29	1.12421	0.562104	+	0.827066i	$0.309992\pi$
$660$	0	0
$661$	4.54039e29	1.10912	0.554559	−	0.832144i	$-0.312887\pi$
$661$	4.54039e29	1.10912	0.554559	+	0.832144i	$0.312887\pi$
$662$	9.79963e29i	2.35614i
$663$	1.38236e29i	0.327138i
$664$	9.41886e28	0.219398
$665$	0	0
$666$	2.06121e29	0.465204
$667$	1.85309e29i	0.411694i
$668$	6.16859e28i	0.134907i
$669$	1.83420e29	0.394886
$670$	0	0
$671$	3.18588e29	0.664727
$672$	2.30146e28i	0.0472744i
$673$	5.05512e28i	0.102229i	0.998693	+	0.0511144i	$0.0162773\pi$
$673$	5.05512e28i	0.102229i	−0.998693	+	0.0511144i	$0.983723\pi$
$674$	−6.79342e29	−1.35257
$675$	0	0
$676$	6.17391e29	1.19157
$677$	3.44673e29i	0.654977i	0.944855	+	0.327489i	$0.106202\pi$
$677$	3.44673e29i	0.654977i	−0.944855	+	0.327489i	$0.893798\pi$
$678$	− 5.22685e29i	− 0.977975i
$679$	−2.21770e28	−0.0408573
$680$	0	0
$681$	−1.20981e29	−0.216108
$682$	− 8.70228e29i	− 1.53072i
$683$	3.07293e29i	0.532273i	0.963935	+	0.266137i	$0.0857472\pi$
$683$	3.07293e29i	0.532273i	−0.963935	+	0.266137i	$0.914253\pi$
$684$	1.73172e29	0.295385
$685$	0	0
$686$	−1.03314e29	−0.170905
$687$	− 2.43649e29i	− 0.396935i
$688$	− 8.39108e29i	− 1.34629i
$689$	3.41552e29	0.539703
$690$	0	0
$691$	7.85532e28	0.120405	0.0602025	−	0.998186i	$-0.480825\pi$
$691$	7.85532e28	0.120405	0.0602025	+	0.998186i	$0.480825\pi$
$692$	− 4.28557e29i	− 0.646986i
$693$	2.66968e28i	0.0396973i
$694$	6.81509e29	0.998153
$695$	0	0
$696$	−4.85971e28	−0.0690578
$697$	− 6.62797e28i	− 0.0927761i
$698$	1.11294e30i	1.53458i
$699$	−2.02698e29	−0.275320
$700$	0	0
$701$	7.75849e29	1.02268	0.511338	−	0.859380i	$-0.329150\pi$
$701$	7.75849e29	1.02268	0.511338	+	0.859380i	$0.329150\pi$
$702$	3.14006e29i	0.407755i
$703$	− 9.13453e29i	− 1.16857i
$704$	8.07920e29	1.01825
$705$	0	0
$706$	3.59244e28	0.0439481
$707$	− 8.39929e27i	− 0.0101237i
$708$	− 5.03714e29i	− 0.598184i
$709$	−1.53428e30	−1.79523	−0.897613	−	0.440785i	$-0.854700\pi$
$709$	−1.53428e30	−1.79523	−0.897613	+	0.440785i	$0.854700\pi$
$710$	0	0
$711$	−7.40182e28	−0.0840829
$712$	− 6.52165e27i	− 0.00729991i
$713$	− 5.36801e29i	− 0.592070i
$714$	1.62788e28	0.0176926
$715$	0	0
$716$	−5.55909e29	−0.586701
$717$	− 4.89604e29i	− 0.509206i
$718$	− 6.62017e29i	− 0.678520i
$719$	−5.56901e29	−0.562503	−0.281252	−	0.959634i	$-0.590750\pi$
$719$	−5.56901e29	−0.562503	−0.281252	+	0.959634i	$0.590750\pi$
$720$	0	0
$721$	−6.16973e28	−0.0605265
$722$	− 3.53729e29i	− 0.342003i
$723$	− 7.70743e29i	− 0.734442i
$724$	3.18879e29	0.299482
$725$	0	0
$726$	2.08673e30	1.90384
$727$	1.43096e29i	0.128681i	0.997928	+	0.0643407i	$0.0204945\pi$
$727$	1.43096e29i	0.128681i	−0.997928	+	0.0643407i	$0.979506\pi$
$728$	3.19902e28i	0.0283556i
$729$	−4.23912e28	−0.0370370
$730$	0	0
$731$	−4.87003e29	−0.413428
$732$	− 1.94869e29i	− 0.163071i
$733$	− 6.81141e29i	− 0.561882i	−0.959725	−	0.280941i	$-0.909353\pi$
$733$	− 6.81141e29i	− 0.561882i	0.959725	−	0.280941i	$-0.0906465\pi$
$734$	−1.12239e30	−0.912714
$735$	0	0
$736$	1.55999e30	1.23283
$737$	2.18328e30i	1.70099i
$738$	− 1.50555e29i	− 0.115639i
$739$	−2.16993e30	−1.64315	−0.821577	−	0.570097i	$-0.806906\pi$
$739$	−2.16993e30	−1.64315	−0.821577	+	0.570097i	$0.806906\pi$
$740$	0	0
$741$	1.39156e30	1.02426
$742$	− 4.02214e28i	− 0.0291888i
$743$	− 1.40097e29i	− 0.100241i	−0.998743	−	0.0501206i	$-0.984039\pi$
$743$	− 1.40097e29i	− 0.100241i	0.998743	−	0.0501206i	$-0.0159606\pi$
$744$	1.40776e29	0.0993143
$745$	0	0
$746$	−3.38199e30	−2.31960
$747$	− 3.86347e29i	− 0.261283i
$748$	− 7.89939e29i	− 0.526777i
$749$	−2.75883e27	−0.00181412
$750$	0	0
$751$	8.06099e29	0.515429	0.257715	−	0.966221i	$-0.417031\pi$
$751$	8.06099e29	0.515429	0.257715	+	0.966221i	$0.417031\pi$
$752$	2.09469e30i	1.32079i
$753$	− 1.04889e30i	− 0.652202i
$754$	1.47656e30	0.905427
$755$	0	0
$756$	1.63295e28	0.00973853
$757$	1.54959e30i	0.911401i	0.890133	+	0.455700i	$0.150611\pi$
$757$	1.54959e30i	0.911401i	−0.890133	+	0.455700i	$0.849389\pi$
$758$	2.10885e30i	1.22326i
$759$	1.80958e30	1.03523
$760$	0	0
$761$	2.04061e29	0.113559	0.0567793	−	0.998387i	$-0.481917\pi$
$761$	2.04061e29	0.113559	0.0567793	+	0.998387i	$0.481917\pi$
$762$	− 2.11633e30i	− 1.16160i
$763$	− 2.74940e28i	− 0.0148843i
$764$	7.64280e29	0.408105
$765$	0	0
$766$	−4.57307e30	−2.37578
$767$	− 4.04770e30i	− 2.07423i
$768$	1.46180e30i	0.738915i
$769$	−1.27880e30	−0.637641	−0.318821	−	0.947815i	$-0.603287\pi$
$769$	−1.27880e30	−0.637641	−0.318821	+	0.947815i	$0.603287\pi$
$770$	0	0
$771$	−3.36614e29	−0.163328
$772$	− 2.14944e30i	− 1.02883i
$773$	3.43774e30i	1.62326i	0.584172	+	0.811630i	$0.301419\pi$
$773$	3.43774e30i	1.62326i	−0.584172	+	0.811630i	$0.698581\pi$
$774$	−1.10624e30	−0.515309
$775$	0	0
$776$	−3.94216e29	−0.178725
$777$	− 8.61352e28i	− 0.0385265i
$778$	− 5.27439e30i	− 2.32748i
$779$	−6.67206e29	−0.290480
$780$	0	0
$781$	1.17784e30	0.499172
$782$	− 1.10342e30i	− 0.461392i
$783$	1.99338e29i	0.0822414i
$784$	−2.85112e30	−1.16064
$785$	0	0
$786$	−1.43381e30	−0.568271
$787$	− 1.06317e30i	− 0.415784i	−0.978152	−	0.207892i	$-0.933340\pi$
$787$	− 1.06317e30i	− 0.415784i	0.978152	−	0.207892i	$-0.0666602\pi$
$788$	3.41176e30i	1.31660i
$789$	−5.74885e28	−0.0218913
$790$	0	0
$791$	−2.18423e29	−0.0809925
$792$	4.74560e29i	0.173651i
$793$	− 1.56591e30i	− 0.565456i
$794$	4.26517e30	1.51992
$795$	0	0
$796$	8.86572e28	0.0307699
$797$	2.59470e30i	0.888742i	0.895843	+	0.444371i	$0.146573\pi$
$797$	2.59470e30i	0.888742i	−0.895843	+	0.444371i	$0.853427\pi$
$798$	− 1.63871e29i	− 0.0553953i
$799$	1.21572e30	0.405595
$800$	0	0
$801$	−2.67508e28	−0.00869351
$802$	− 5.07160e30i	− 1.62672i
$803$	1.09139e31i	3.45516i
$804$	1.33544e30	0.417286
$805$	0	0
$806$	−4.27730e30	−1.30212
$807$	3.41650e30i	1.02662i
$808$	− 1.49305e29i	− 0.0442848i
$809$	4.54632e30	1.33107	0.665534	−	0.746367i	$-0.268204\pi$
$809$	4.54632e30	1.33107	0.665534	+	0.746367i	$0.268204\pi$
$810$	0	0
$811$	−5.33885e30	−1.52310	−0.761550	−	0.648106i	$-0.775561\pi$
$811$	−5.33885e30	−1.52310	−0.761550	+	0.648106i	$0.775561\pi$
$812$	− 7.67867e28i	− 0.0216246i
$813$	2.53339e30i	0.704291i
$814$	−9.46493e30	−2.59753
$815$	0	0
$816$	9.00335e29	0.240801
$817$	4.90243e30i	1.29443i
$818$	− 1.72957e30i	− 0.450847i
$819$	1.31219e29	0.0337688
$820$	0	0
$821$	−6.77652e30	−1.69982	−0.849911	−	0.526926i	$-0.823344\pi$
$821$	−6.77652e30	−1.69982	−0.849911	+	0.526926i	$0.823344\pi$
$822$	− 4.39514e30i	− 1.08848i
$823$	2.32096e30i	0.567506i	0.958897	+	0.283753i	$0.0915795\pi$
$823$	2.32096e30i	0.567506i	−0.958897	+	0.283753i	$0.908420\pi$
$824$	−1.09672e30	−0.264766
$825$	0	0
$826$	−4.76661e29	−0.112181
$827$	− 3.93890e30i	− 0.915307i	−0.889131	−	0.457654i	$-0.848690\pi$
$827$	− 3.93890e30i	− 0.915307i	0.889131	−	0.457654i	$-0.151310\pi$
$828$	− 1.10685e30i	− 0.253963i
$829$	−3.15777e30	−0.715415	−0.357708	−	0.933834i	$-0.616442\pi$
$829$	−3.15777e30	−0.715415	−0.357708	+	0.933834i	$0.616442\pi$
$830$	0	0
$831$	3.77323e30	0.833495
$832$	− 3.97105e30i	− 0.866184i
$833$	1.65474e30i	0.356416i
$834$	1.09726e30	0.233381
$835$	0	0
$836$	−7.95194e30	−1.64933
$837$	− 5.77440e29i	− 0.118274i
$838$	− 4.81074e30i	− 0.973082i
$839$	1.71221e28	0.00342024	0.00171012	−	0.999999i	$-0.499456\pi$
$839$	1.71221e28	0.00342024	0.00171012	+	0.999999i	$0.499456\pi$
$840$	0	0
$841$	−4.19549e30	−0.817381
$842$	− 7.94168e30i	− 1.52804i
$843$	1.90790e30i	0.362548i
$844$	5.24327e30	0.984026
$845$	0	0
$846$	2.76153e30	0.505547
$847$	− 8.72016e29i	− 0.157670i
$848$	− 2.22453e30i	− 0.397266i
$849$	5.94193e29	0.104809
$850$	0	0
$851$	−5.83845e30	−1.00470
$852$	− 7.20441e29i	− 0.122457i
$853$	2.27930e30i	0.382680i	0.981524	+	0.191340i	$0.0612833\pi$
$853$	2.27930e30i	0.382680i	−0.981524	+	0.191340i	$0.938717\pi$
$854$	−1.84403e29	−0.0305816
$855$	0	0
$856$	−4.90406e28	−0.00793563
$857$	1.06629e31i	1.70441i	0.523204	+	0.852207i	$0.324737\pi$
$857$	1.06629e31i	1.70441i	−0.523204	+	0.852207i	$0.675263\pi$
$858$	− 1.44190e31i	− 2.27676i
$859$	8.93547e29	0.139376	0.0696882	−	0.997569i	$-0.477800\pi$
$859$	8.93547e29	0.139376	0.0696882	+	0.997569i	$0.477800\pi$
$860$	0	0
$861$	−6.29150e28	−0.00957682
$862$	9.49196e30i	1.42735i
$863$	2.82417e30i	0.419543i	0.977750	+	0.209772i	$0.0672721\pi$
$863$	2.82417e30i	0.419543i	−0.977750	+	0.209772i	$0.932728\pi$
$864$	1.67809e30	0.246275
$865$	0	0
$866$	−3.99448e30	−0.572167
$867$	3.55727e30i	0.503404i
$868$	2.22435e29i	0.0310990i
$869$	3.39886e30	0.469490
$870$	0	0
$871$	1.07312e31	1.44696
$872$	− 4.88730e29i	− 0.0651097i
$873$	1.61701e30i	0.212845i
$874$	−1.11076e31	−1.44461
$875$	0	0
$876$	6.67566e30	0.847620
$877$	− 9.06575e30i	− 1.13739i	−0.822550	−	0.568693i	$-0.807449\pi$
$877$	− 9.06575e30i	− 1.13739i	0.822550	−	0.568693i	$-0.192551\pi$
$878$	1.94490e31i	2.41104i
$879$	−2.91118e30	−0.356604
$880$	0	0
$881$	1.51630e31	1.81359	0.906794	−	0.421574i	$-0.138522\pi$
$881$	1.51630e31	1.81359	0.906794	+	0.421574i	$0.138522\pi$
$882$	3.75877e30i	0.444248i
$883$	− 1.16543e31i	− 1.36113i	−0.732688	−	0.680565i	$-0.761735\pi$
$883$	− 1.16543e31i	− 1.36113i	0.732688	−	0.680565i	$-0.238265\pi$
$884$	−3.88267e30	−0.448107
$885$	0	0
$886$	8.20424e30	0.924664
$887$	7.76908e30i	0.865309i	0.901560	+	0.432655i	$0.142423\pi$
$887$	7.76908e30i	0.865309i	−0.901560	+	0.432655i	$0.857577\pi$
$888$	− 1.53113e30i	− 0.168529i
$889$	−8.84384e29	−0.0961994
$890$	0	0
$891$	1.94657e30	0.206802
$892$	5.15174e30i	0.540907i
$893$	− 1.22381e31i	− 1.26991i
$894$	−3.94144e30	−0.404214
$895$	0	0
$896$	3.49740e29	0.0350357
$897$	− 8.89435e30i	− 0.880630i
$898$	− 1.30702e31i	− 1.27903i
$899$	−2.71532e30	−0.262630
$900$	0	0
$901$	−1.29108e30	−0.121995
$902$	6.91340e30i	0.645688i
$903$	4.62281e29i	0.0426761i
$904$	−3.88266e30	−0.354292
$905$	0	0
$906$	−4.15570e30	−0.370509
$907$	− 5.71533e30i	− 0.503692i	−0.967767	−	0.251846i	$-0.918962\pi$
$907$	− 5.71533e30i	− 0.503692i	0.967767	−	0.251846i	$-0.0810376\pi$
$908$	− 3.39800e30i	− 0.296021i
$909$	−6.12425e29	−0.0527390
$910$	0	0
$911$	2.22259e30	0.187032	0.0935160	−	0.995618i	$-0.470189\pi$
$911$	2.22259e30	0.187032	0.0935160	+	0.995618i	$0.470189\pi$
$912$	− 9.06324e30i	− 0.753942i
$913$	1.77408e31i	1.45891i
$914$	2.20581e31	1.79322
$915$	0	0
$916$	6.84342e30	0.543714
$917$	5.99171e29i	0.0470623i
$918$	− 1.18695e30i	− 0.0921693i
$919$	9.94638e30	0.763576	0.381788	−	0.924250i	$-0.375308\pi$
$919$	9.94638e30	0.763576	0.381788	+	0.924250i	$0.375308\pi$
$920$	0	0
$921$	−8.84722e29	−0.0663866
$922$	− 1.20962e31i	− 0.897378i
$923$	− 5.78926e30i	− 0.424624i
$924$	−7.49838e29	−0.0543766
$925$	0	0
$926$	−4.49324e30	−0.318526
$927$	4.49859e30i	0.315311i
$928$	− 7.89093e30i	− 0.546858i
$929$	−6.57341e30	−0.450429	−0.225214	−	0.974309i	$-0.572308\pi$
$929$	−6.57341e30	−0.450429	−0.225214	+	0.974309i	$0.572308\pi$
$930$	0	0
$931$	1.66575e31	1.11593
$932$	− 5.69320e30i	− 0.377128i
$933$	− 8.78615e30i	− 0.575495i
$934$	1.83688e30	0.118970
$935$	0	0
$936$	2.33254e30	0.147717
$937$	9.88672e30i	0.619137i	0.950877	+	0.309568i	$0.100185\pi$
$937$	9.88672e30i	0.619137i	−0.950877	+	0.309568i	$0.899815\pi$
$938$	− 1.26371e30i	− 0.0782561i
$939$	6.55213e30	0.401230
$940$	0	0
$941$	1.35253e31	0.809947	0.404973	−	0.914328i	$-0.367281\pi$
$941$	1.35253e31	0.809947	0.404973	+	0.914328i	$0.367281\pi$
$942$	1.07796e31i	0.638361i
$943$	4.26454e30i	0.249746i
$944$	−2.63627e31	−1.52681
$945$	0	0
$946$	5.07976e31	2.87731
$947$	2.26830e31i	1.27065i	0.772245	+	0.635325i	$0.219134\pi$
$947$	2.26830e31i	1.27065i	−0.772245	+	0.635325i	$0.780866\pi$
$948$	− 2.07896e30i	− 0.115175i
$949$	5.36437e31	2.93916
$950$	0	0
$951$	4.22085e30	0.226206
$952$	− 1.20924e29i	− 0.00640952i
$953$	3.45875e31i	1.81319i	0.422002	+	0.906595i	$0.361327\pi$
$953$	3.45875e31i	1.81319i	−0.422002	+	0.906595i	$0.638673\pi$
$954$	−2.93270e30	−0.152058
$955$	0	0
$956$	1.37516e31	0.697501
$957$	− 9.15344e30i	− 0.459207i
$958$	− 3.43011e31i	− 1.70204i
$959$	−1.83667e30	−0.0901438
$960$	0	0
$961$	−1.29598e31	−0.622304
$962$	4.65216e31i	2.20961i
$963$	2.01157e29i	0.00945059i
$964$	2.16480e31	1.00602
$965$	0	0
$966$	−1.04741e30	−0.0476272
$967$	1.92820e31i	0.867311i	0.901079	+	0.433655i	$0.142776\pi$
$967$	1.92820e31i	0.867311i	−0.901079	+	0.433655i	$0.857224\pi$
$968$	− 1.55009e31i	− 0.689707i
$969$	−5.26015e30	−0.231525
$970$	0	0
$971$	−2.95793e31	−1.27405	−0.637024	−	0.770844i	$-0.719835\pi$
$971$	−2.95793e31	−1.27405	−0.637024	+	0.770844i	$0.719835\pi$
$972$	− 1.19065e30i	− 0.0507326i
$973$	− 4.58530e29i	− 0.0193278i
$974$	−3.86058e31	−1.60984
$975$	0	0
$976$	−1.01988e31	−0.416222
$977$	− 4.86581e31i	− 1.96455i	−0.187453	−	0.982274i	$-0.560023\pi$
$977$	− 4.86581e31i	− 1.96455i	0.187453	−	0.982274i	$-0.439977\pi$
$978$	− 2.06864e31i	− 0.826280i
$979$	1.22838e30	0.0485415
$980$	0	0
$981$	−2.00469e30	−0.0775396
$982$	1.10703e31i	0.423633i
$983$	4.31738e31i	1.63459i	0.576220	+	0.817294i	$0.304527\pi$
$983$	4.31738e31i	1.63459i	−0.576220	+	0.817294i	$0.695473\pi$
$984$	−1.11837e30	−0.0418926
$985$	0	0
$986$	−5.58146e30	−0.204664
$987$	− 1.15401e30i	− 0.0418676i
$988$	3.90850e31i	1.40301i
$989$	3.13345e31	1.11292
$990$	0	0
$991$	3.44591e31	1.19820	0.599101	−	0.800673i	$-0.295525\pi$
$991$	3.44591e31	1.19820	0.599101	+	0.800673i	$0.295525\pi$
$992$	2.28584e31i	0.786453i
$993$	− 2.98592e31i	− 1.01651i
$994$	−6.81748e29	−0.0229650
$995$	0	0
$996$	1.08514e31	0.357900
$997$	− 3.62353e31i	− 1.18259i	−0.806457	−	0.591293i	$-0.798618\pi$
$997$	− 3.62353e31i	− 1.18259i	0.806457	−	0.591293i	$-0.201382\pi$
$998$	− 2.26804e31i	− 0.732452i
$999$	−6.28046e30	−0.200703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.b.d.49.1		4
5.2	odd	4		3.22.a.c.1.2	✓	2
5.3	odd	4		75.22.a.d.1.1		2
5.4	even	2	inner	75.22.b.d.49.4		4
15.2	even	4		9.22.a.e.1.1		2
20.7	even	4		48.22.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.2	✓	2	5.2	odd	4
9.22.a.e.1.1		2	15.2	even	4
48.22.a.g.1.2		2	20.7	even	4
75.22.a.d.1.1		2	5.3	odd	4
75.22.b.d.49.1		4	1.1	even	1	trivial
75.22.b.d.49.4		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1937.96i q^{2} +59049.0i q^{3} -1.65852e6 q^{4} +1.14434e8 q^{6} -4.78205e7i q^{7} -8.50053e8i q^{8} -3.48678e9 q^{9} +O(q^{10})\)	\(q-1937.96i q^{2} +59049.0i q^{3} -1.65852e6 q^{4} +1.14434e8 q^{6} -4.78205e7i q^{7} -8.50053e8i q^{8} -3.48678e9 q^{9} +1.60111e11 q^{11} -9.79338e10i q^{12} -7.86968e11i q^{13} -9.26741e10 q^{14} -5.12553e12 q^{16} +2.97477e12i q^{17} +6.75723e12i q^{18} +2.99456e13 q^{19} +2.82376e12 q^{21} -3.10287e14i q^{22} -1.91401e14i q^{23} +5.01948e13 q^{24} -1.52511e15 q^{26} -2.05891e14i q^{27} +7.93112e13i q^{28} -9.68170e14 q^{29} +2.80459e15 q^{31} +8.15035e15i q^{32} +9.45437e15i q^{33} +5.76496e15 q^{34} +5.78290e15 q^{36} -3.05038e16i q^{37} -5.80331e16i q^{38} +4.64697e16 q^{39} -2.22806e16 q^{41} -5.47231e15i q^{42} +1.63711e17i q^{43} -2.65546e17 q^{44} -3.70927e17 q^{46} -4.08678e17i q^{47} -3.02657e17i q^{48} +5.56259e17 q^{49} -1.75657e17 q^{51} +1.30520e18i q^{52} +4.34009e17i q^{53} -3.99008e17 q^{54} -4.06500e16 q^{56} +1.76826e18i q^{57} +1.87627e18i q^{58} +5.14341e18 q^{59} +1.98980e18 q^{61} -5.43517e18i q^{62} +1.66740e17i q^{63} +5.04601e18 q^{64} +1.83222e19 q^{66} +1.36361e19i q^{67} -4.93370e18i q^{68} +1.13020e19 q^{69} +7.35641e18 q^{71} +2.96395e18i q^{72} +6.81650e19i q^{73} -5.91149e19 q^{74} -4.96652e19 q^{76} -7.65658e18i q^{77} -9.00562e19i q^{78} +2.12282e19 q^{79} +1.21577e19 q^{81} +4.31789e19i q^{82} +1.10803e20i q^{83} -4.68325e18 q^{84} +3.17266e20 q^{86} -5.71695e19i q^{87} -1.36102e20i q^{88} +7.67205e18 q^{89} -3.76333e19 q^{91} +3.17442e20i q^{92} +1.65608e20i q^{93} -7.92000e20 q^{94} -4.81270e20 q^{96} -4.63755e20i q^{97} -1.07801e21i q^{98} -5.58271e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2358472 q^{4} + 78653268 q^{6} - 13947137604 q^{9}+O(q^{10}) \) 4 * q - 2358472 * q^4 + 78653268 * q^6 - 13947137604 * q^9	\( 4 q - 2358472 q^{4} + 78653268 q^{6} - 13947137604 q^{9} + 439738245936 q^{11} + 1422595413792 q^{14} - 16577472881120 q^{16} - 23921170023248 q^{19} + 80294371034976 q^{21} - 286630441537104 q^{24} - 49\!\cdots\!32 q^{26}+ \cdots - 15\!\cdots\!36 q^{99}+O(q^{100}) \) 4 * q - 2358472 * q^4 + 78653268 * q^6 - 13947137604 * q^9 + 439738245936 * q^11 + 1422595413792 * q^14 - 16577472881120 * q^16 - 23921170023248 * q^19 + 80294371034976 * q^21 - 286630441537104 * q^24 - 4928894727939432 * q^26 + 3597040087348104 * q^29 + 22338215053889984 * q^31 - 9734014974827304 * q^34 + 8223483379795272 * q^36 + 5724081327983688 * q^39 + 245944041232936104 * q^41 - 473810478271184736 * q^44 - 856055962790322336 * q^46 + 1430570793882941340 * q^49 - 1338467112735508728 * q^51 - 274246987950072468 * q^54 + 4061460640101137280 * q^56 + 7047646661807714448 * q^59 - 3558046256902027720 * q^61 - 10423384026926965888 * q^64 + 27667662691008290544 * q^66 + 17302347849719695392 * q^69 + 34758454262300841888 * q^71 - 163428852787350574968 * q^74 - 139500225872185580128 * q^76 + 108111571188381182080 * q^79 + 48630661836227715204 * q^81 + 26410407726770964288 * q^84 + 317193734530493170416 * q^86 - 453841535930896131048 * q^89 + 858308349370370000704 * q^91 - 493766231937670239552 * q^94 - 1299017949048779200704 * q^96 - 1533272456452746444336 * q^99

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