LMFDB - Embedded newform 75.22.b.d.49.3

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			49.3
Root			$13.2377i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.22.b.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1271.96i q^{2} +59049.0i q^{3} +479282. q^{4} -7.51077e7 q^{6} -6.32076e8i q^{7} +3.27711e9i q^{8} -3.48678e9 q^{9} +O(q^{10})$	\(q+1271.96i q^{2} +59049.0i q^{3} +479282. q^{4} -7.51077e7 q^{6} -6.32076e8i q^{7} +3.27711e9i q^{8} -3.48678e9 q^{9} +5.97585e10 q^{11} +2.83011e10i q^{12} +7.38499e11i q^{13} +8.03972e11 q^{14} -3.16321e12 q^{16} +8.35876e12i q^{17} -4.43503e12i q^{18} -4.19061e13 q^{19} +3.73234e13 q^{21} +7.60101e13i q^{22} +4.48926e13i q^{23} -1.93510e14 q^{24} -9.39338e14 q^{26} -2.05891e14i q^{27} -3.02943e14i q^{28} +2.76669e15 q^{29} +8.36452e15 q^{31} +2.84914e15i q^{32} +3.52868e15i q^{33} -1.06320e16 q^{34} -1.67115e15 q^{36} +1.77675e16i q^{37} -5.33027e16i q^{38} -4.36077e16 q^{39} +1.45253e17 q^{41} +4.74737e16i q^{42} +1.24744e17i q^{43} +2.86412e16 q^{44} -5.71014e16 q^{46} -4.28566e17i q^{47} -1.86784e17i q^{48} +1.59026e17 q^{49} -4.93577e17 q^{51} +3.53950e17i q^{52} -4.77017e17i q^{53} +2.61884e17 q^{54} +2.07138e18 q^{56} -2.47452e18i q^{57} +3.51911e18i q^{58} -1.61959e18 q^{59} -3.76882e18 q^{61} +1.06393e19i q^{62} +2.20391e18i q^{63} -1.02577e19 q^{64} -4.48832e18 q^{66} +2.81797e18i q^{67} +4.00621e18i q^{68} -2.65086e18 q^{69} +1.00228e19 q^{71} -1.14266e19i q^{72} -1.72739e19i q^{73} -2.25995e19 q^{74} -2.00849e19 q^{76} -3.77719e19i q^{77} -5.54670e19i q^{78} +3.28276e19 q^{79} +1.21577e19 q^{81} +1.84755e20i q^{82} +3.05240e17i q^{83} +1.78885e19 q^{84} -1.58669e20 q^{86} +1.63370e20i q^{87} +1.95835e20i q^{88} -2.34593e20 q^{89} +4.66787e20 q^{91} +2.15162e19i q^{92} +4.93917e20i q^{93} +5.45116e20 q^{94} -1.68239e20 q^{96} +5.92086e20i q^{97} +2.02274e20i q^{98} -2.08365e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1271.96i	0.878328i	0.898407	+	0.439164i	$0.144725\pi$
$2$	1271.96i	0.878328i	−0.898407	+	0.439164i	$0.855275\pi$
$3$	59049.0i	0.577350i
$3$	59049.0i	0.577350i
$4$	479282.	0.228540
$5$	0	0
$5$	0	0
$6$	−7.51077e7	−0.507103
$7$	− 6.32076e8i	− 0.845745i	−0.906189	−	0.422873i	$-0.861022\pi$
$7$	− 6.32076e8i	− 0.845745i	0.906189	−	0.422873i	$-0.138978\pi$
$8$	3.27711e9i	1.07906i
$9$	−3.48678e9	−0.333333
$10$	0	0
$11$	5.97585e10	0.694666	0.347333	−	0.937742i	$-0.387087\pi$
$11$	5.97585e10	0.694666	0.347333	+	0.937742i	$0.387087\pi$
$12$	2.83011e10i	0.131947i
$13$	7.38499e11i	1.48575i	0.669432	+	0.742874i	$0.266538\pi$
$13$	7.38499e11i	1.48575i	−0.669432	+	0.742874i	$0.733462\pi$
$14$	8.03972e11	0.742842
$15$	0	0
$16$	−3.16321e12	−0.719230
$17$	8.35876e12i	1.00561i	0.864401	+	0.502804i	$0.167698\pi$
$17$	8.35876e12i	1.00561i	−0.864401	+	0.502804i	$0.832302\pi$
$18$	− 4.43503e12i	− 0.292776i
$19$	−4.19061e13	−1.56807	−0.784034	−	0.620718i	$-0.786841\pi$
$19$	−4.19061e13	−1.56807	−0.784034	+	0.620718i	$0.786841\pi$
$20$	0	0
$21$	3.73234e13	0.488291
$22$	7.60101e13i	0.610145i
$23$	4.48926e13i	0.225961i	0.993597	+	0.112980i	$0.0360397\pi$
$23$	4.48926e13i	0.225961i	−0.993597	+	0.112980i	$0.963960\pi$
$24$	−1.93510e14	−0.622996
$25$	0	0
$26$	−9.39338e14	−1.30497
$27$	− 2.05891e14i	− 0.192450i
$28$	− 3.02943e14i	− 0.193286i
$29$	2.76669e15	1.22119	0.610593	−	0.791945i	$-0.290931\pi$
$29$	2.76669e15	1.22119	0.610593	+	0.791945i	$0.290931\pi$
$30$	0	0
$31$	8.36452e15	1.83292	0.916459	−	0.400128i	$-0.131034\pi$
$31$	8.36452e15	1.83292	0.916459	+	0.400128i	$0.131034\pi$
$32$	2.84914e15i	0.447341i
$33$	3.52868e15i	0.401066i
$34$	−1.06320e16	−0.883253
$35$	0	0
$36$	−1.67115e15	−0.0761798
$37$	1.77675e16i	0.607447i	0.952760	+	0.303724i	$0.0982299\pi$
$37$	1.77675e16i	0.607447i	−0.952760	+	0.303724i	$0.901770\pi$
$38$	− 5.33027e16i	− 1.37728i
$39$	−4.36077e16	−0.857797
$40$	0	0
$41$	1.45253e17	1.69003	0.845013	−	0.534745i	$-0.179592\pi$
$41$	1.45253e17	1.69003	0.845013	+	0.534745i	$0.179592\pi$
$42$	4.74737e16i	0.428880i
$43$	1.24744e17i	0.880239i	0.897939	+	0.440119i	$0.145064\pi$
$43$	1.24744e17i	0.880239i	−0.897939	+	0.440119i	$0.854936\pi$
$44$	2.86412e16	0.158759
$45$	0	0
$46$	−5.71014e16	−0.198468
$47$	− 4.28566e17i	− 1.18847i	−0.804290	−	0.594237i	$-0.797454\pi$
$47$	− 4.28566e17i	− 1.18847i	0.804290	−	0.594237i	$-0.202546\pi$
$48$	− 1.86784e17i	− 0.415248i
$49$	1.59026e17	0.284715
$50$	0	0
$51$	−4.93577e17	−0.580588
$52$	3.53950e17i	0.339552i
$53$	− 4.77017e17i	− 0.374660i	−0.982297	−	0.187330i	$-0.940017\pi$
$53$	− 4.77017e17i	− 0.374660i	0.982297	−	0.187330i	$-0.0599834\pi$
$54$	2.61884e17	0.169034
$55$	0	0
$56$	2.07138e18	0.912611
$57$	− 2.47452e18i	− 0.905324i
$58$	3.51911e18i	1.07260i
$59$	−1.61959e18	−0.412533	−0.206267	−	0.978496i	$-0.566131\pi$
$59$	−1.61959e18	−0.412533	−0.206267	+	0.978496i	$0.566131\pi$
$60$	0	0
$61$	−3.76882e18	−0.676461	−0.338230	−	0.941063i	$-0.609828\pi$
$61$	−3.76882e18	−0.676461	−0.338230	+	0.941063i	$0.609828\pi$
$62$	1.06393e19i	1.60990i
$63$	2.20391e18i	0.281915i
$64$	−1.02577e19	−1.11214
$65$	0	0
$66$	−4.48832e18	−0.352267
$67$	2.81797e18i	0.188865i	0.995531	+	0.0944324i	$0.0301036\pi$
$67$	2.81797e18i	0.188865i	−0.995531	+	0.0944324i	$0.969896\pi$
$68$	4.00621e18i	0.229821i
$69$	−2.65086e18	−0.130458
$70$	0	0
$71$	1.00228e19	0.365407	0.182704	−	0.983168i	$-0.441515\pi$
$71$	1.00228e19	0.365407	0.182704	+	0.983168i	$0.441515\pi$
$72$	− 1.14266e19i	− 0.359687i
$73$	− 1.72739e19i	− 0.470435i	−0.971943	−	0.235218i	$-0.924420\pi$
$73$	− 1.72739e19i	− 0.470435i	0.971943	−	0.235218i	$-0.0755803\pi$
$74$	−2.25995e19	−0.533538
$75$	0	0
$76$	−2.00849e19	−0.358365
$77$	− 3.77719e19i	− 0.587511i
$78$	− 5.54670e19i	− 0.753427i
$79$	3.28276e19	0.390080	0.195040	−	0.980795i	$-0.437516\pi$
$79$	3.28276e19	0.390080	0.195040	+	0.980795i	$0.437516\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	1.84755e20i	1.48440i
$83$	3.05240e17i	0.00215934i	0.999999	+	0.00107967i	$0.000343670\pi$
$83$	3.05240e17i	0.00215934i	−0.999999	+	0.00107967i	$0.999656\pi$
$84$	1.78885e19	0.111594
$85$	0	0
$86$	−1.58669e20	−0.773139
$87$	1.63370e20i	0.705052i
$88$	1.95835e20i	0.749587i
$89$	−2.34593e20	−0.797480	−0.398740	−	0.917064i	$-0.630552\pi$
$89$	−2.34593e20	−0.797480	−0.398740	+	0.917064i	$0.630552\pi$
$90$	0	0
$91$	4.66787e20	1.25656
$92$	2.15162e19i	0.0516409i
$93$	4.93917e20i	1.05824i
$94$	5.45116e20	1.04387
$95$	0	0
$96$	−1.68239e20	−0.258272
$97$	5.92086e20i	0.815233i	0.913153	+	0.407616i	$0.133640\pi$
$97$	5.92086e20i	0.815233i	−0.913153	+	0.407616i	$0.866360\pi$
$98$	2.02274e20i	0.250073i
$99$	−2.08365e20	−0.231555
$100$	0	0
$101$	−1.66229e21	−1.49739	−0.748693	−	0.662917i	$-0.769318\pi$
$101$	−1.66229e21	−1.49739	−0.748693	+	0.662917i	$0.769318\pi$
$102$	− 6.27807e20i	− 0.509946i
$103$	1.17919e21i	0.864552i	0.901741	+	0.432276i	$0.142289\pi$
$103$	1.17919e21i	0.864552i	−0.901741	+	0.432276i	$0.857711\pi$
$104$	−2.42014e21	−1.60321
$105$	0	0
$106$	6.06745e20	0.329075
$107$	8.69160e20i	0.427140i	0.976928	+	0.213570i	$0.0685091\pi$
$107$	8.69160e20i	0.427140i	−0.976928	+	0.213570i	$0.931491\pi$
$108$	− 9.86799e19i	− 0.0439825i
$109$	−4.12021e20	−0.166702	−0.0833510	−	0.996520i	$-0.526562\pi$
$109$	−4.12021e20	−0.166702	−0.0833510	+	0.996520i	$0.526562\pi$
$110$	0	0
$111$	−1.04915e21	−0.350710
$112$	1.99939e21i	0.608286i
$113$	2.45943e21i	0.681569i	0.940141	+	0.340785i	$0.110693\pi$
$113$	2.45943e21i	0.681569i	−0.940141	+	0.340785i	$0.889307\pi$
$114$	3.14747e21	0.795172
$115$	0	0
$116$	1.32602e21	0.279089
$117$	− 2.57499e21i	− 0.495249i
$118$	− 2.06005e21i	− 0.362340i
$119$	5.28337e21	0.850487
$120$	0	0
$121$	−3.82917e21	−0.517439
$122$	− 4.79378e21i	− 0.594155i
$123$	8.57702e21i	0.975737i
$124$	4.00896e21	0.418894
$125$	0	0
$126$	−2.80328e21	−0.247614
$127$	− 5.53783e21i	− 0.450195i	−0.974336	−	0.225097i	$-0.927730\pi$
$127$	− 5.53783e21i	− 0.450195i	0.974336	−	0.225097i	$-0.0722700\pi$
$128$	− 7.07226e21i	− 0.529485i
$129$	−7.36600e21	−0.508206
$130$	0	0
$131$	−2.54630e22	−1.49472	−0.747362	−	0.664417i	$-0.768680\pi$
$131$	−2.54630e22	−1.49472	−0.747362	+	0.664417i	$0.768680\pi$
$132$	1.69123e21i	0.0916594i
$133$	2.64878e22i	1.32619i
$134$	−3.58433e21	−0.165885
$135$	0	0
$136$	−2.73926e22	−1.08511
$137$	4.82088e22i	1.76832i	0.467188	+	0.884158i	$0.345267\pi$
$137$	4.82088e22i	1.76832i	−0.467188	+	0.884158i	$0.654733\pi$
$138$	− 3.37178e21i	− 0.114585i
$139$	2.18194e22	0.687363	0.343682	−	0.939086i	$-0.388326\pi$
$139$	2.18194e22	0.687363	0.343682	+	0.939086i	$0.388326\pi$
$140$	0	0
$141$	2.53064e22	0.686166
$142$	1.27486e22i	0.320948i
$143$	4.41316e22i	1.03210i
$144$	1.10294e22	0.239743
$145$	0	0
$146$	2.19716e22	0.413197
$147$	9.39035e21i	0.164380i
$148$	8.51565e21i	0.138826i
$149$	−4.84140e22	−0.735386	−0.367693	−	0.929947i	$-0.619852\pi$
$149$	−4.84140e22	−0.735386	−0.367693	+	0.929947i	$0.619852\pi$
$150$	0	0
$151$	−1.22948e23	−1.62354	−0.811770	−	0.583977i	$-0.801496\pi$
$151$	−1.22948e23	−1.62354	−0.811770	+	0.583977i	$0.801496\pi$
$152$	− 1.37331e23i	− 1.69204i
$153$	− 2.91452e22i	− 0.335202i
$154$	4.80441e22	0.516027
$155$	0	0
$156$	−2.09004e22	−0.196040
$157$	− 5.89828e22i	− 0.517344i	−0.965965	−	0.258672i	$-0.916715\pi$
$157$	− 5.89828e22i	− 0.517344i	0.965965	−	0.258672i	$-0.0832848\pi$
$158$	4.17552e22i	0.342619i
$159$	2.81674e22	0.216310
$160$	0	0
$161$	2.83755e22	0.191105
$162$	1.54640e22i	0.0975920i
$163$	− 3.18244e22i	− 0.188274i	−0.995559	−	0.0941369i	$-0.969991\pi$
$163$	− 3.18244e22i	− 0.188274i	0.995559	−	0.0941369i	$-0.0300091\pi$
$164$	6.96170e22	0.386238
$165$	0	0
$166$	−3.88252e20	−0.00189661
$167$	3.62822e22i	0.166407i	0.996533	+	0.0832033i	$0.0265151\pi$
$167$	3.62822e22i	0.166407i	−0.996533	+	0.0832033i	$0.973485\pi$
$168$	1.22313e23i	0.526896i
$169$	−2.98317e23	−1.20744
$170$	0	0
$171$	1.46118e23	0.522689
$172$	5.97875e22i	0.201169i
$173$	3.21510e23i	1.01791i	0.860792	+	0.508956i	$0.169969\pi$
$173$	3.21510e23i	1.01791i	−0.860792	+	0.508956i	$0.830031\pi$
$174$	−2.07800e23	−0.619267
$175$	0	0
$176$	−1.89028e23	−0.499625
$177$	− 9.56351e22i	− 0.238176i
$178$	− 2.98392e23i	− 0.700449i
$179$	1.80418e23	0.399321	0.199661	−	0.979865i	$-0.436016\pi$
$179$	1.80418e23	0.399321	0.199661	+	0.979865i	$0.436016\pi$
$180$	0	0
$181$	−6.36646e21	−0.0125393	−0.00626965	−	0.999980i	$-0.501996\pi$
$181$	−6.36646e21	−0.0125393	−0.00626965	+	0.999980i	$0.501996\pi$
$182$	5.93733e23i	1.10368i
$183$	− 2.22545e23i	− 0.390555i
$184$	−1.47118e23	−0.243825
$185$	0	0
$186$	−6.28240e23	−0.929479
$187$	4.99507e23i	0.698561i
$188$	− 2.05404e23i	− 0.271613i
$189$	−1.30139e23	−0.162764
$190$	0	0
$191$	8.17882e23	0.915883	0.457942	−	0.888982i	$-0.348587\pi$
$191$	8.17882e23	0.915883	0.457942	+	0.888982i	$0.348587\pi$
$192$	− 6.05707e23i	− 0.642096i
$193$	− 1.80064e23i	− 0.180748i	−0.995908	−	0.0903742i	$-0.971194\pi$
$193$	− 1.80064e23i	− 0.180748i	0.995908	−	0.0903742i	$-0.0288063\pi$
$194$	−7.53107e23	−0.716042
$195$	0	0
$196$	7.62185e22	0.0650686
$197$	− 1.65216e24i	− 1.33708i	−0.743675	−	0.668541i	$-0.766919\pi$
$197$	− 1.65216e24i	− 1.33708i	0.743675	−	0.668541i	$-0.233081\pi$
$198$	− 2.65031e23i	− 0.203382i
$199$	1.52537e24	1.11024	0.555120	−	0.831770i	$-0.312672\pi$
$199$	1.52537e24	1.11024	0.555120	+	0.831770i	$0.312672\pi$
$200$	0	0
$201$	−1.66398e23	−0.109041
$202$	− 2.11436e24i	− 1.31520i
$203$	− 1.74876e24i	− 1.03281i
$204$	−2.36562e23	−0.132687
$205$	0	0
$206$	−1.49987e24	−0.759361
$207$	− 1.56531e23i	− 0.0753202i
$208$	− 2.33603e24i	− 1.06859i
$209$	−2.50425e24	−1.08928
$210$	0	0
$211$	1.35748e24	0.534277	0.267138	−	0.963658i	$-0.413922\pi$
$211$	1.35748e24	0.534277	0.267138	+	0.963658i	$0.413922\pi$
$212$	− 2.28626e23i	− 0.0856247i
$213$	5.91838e23i	0.210968i
$214$	−1.10553e24	−0.375169
$215$	0	0
$216$	6.74728e23	0.207665
$217$	− 5.28701e24i	− 1.55018i
$218$	− 5.24072e23i	− 0.146419i
$219$	1.02001e24	0.271606
$220$	0	0
$221$	−6.17294e24	−1.49408
$222$	− 1.33448e24i	− 0.308038i
$223$	4.73192e24i	1.04192i	0.853580	+	0.520962i	$0.174427\pi$
$223$	4.73192e24i	1.04192i	−0.853580	+	0.520962i	$0.825573\pi$
$224$	1.80087e24	0.378336
$225$	0	0
$226$	−3.12828e24	−0.598642
$227$	− 8.00226e24i	− 1.46198i	−0.682389	−	0.730989i	$-0.739059\pi$
$227$	− 8.00226e24i	− 1.46198i	0.682389	−	0.730989i	$-0.260941\pi$
$228$	− 1.18599e24i	− 0.206902i
$229$	−2.72111e24	−0.453391	−0.226696	−	0.973966i	$-0.572792\pi$
$229$	−2.72111e24	−0.453391	−0.226696	+	0.973966i	$0.572792\pi$
$230$	0	0
$231$	2.23039e24	0.339200
$232$	9.06674e24i	1.31773i
$233$	− 6.60115e24i	− 0.917028i	−0.888687	−	0.458514i	$-0.848382\pi$
$233$	− 6.60115e24i	− 0.917028i	0.888687	−	0.458514i	$-0.151618\pi$
$234$	3.27527e24	0.434991
$235$	0	0
$236$	−7.76240e23	−0.0942801
$237$	1.93843e24i	0.225213i
$238$	6.72021e24i	0.747007i
$239$	−9.92224e24	−1.05544	−0.527718	−	0.849420i	$-0.676952\pi$
$239$	−9.92224e24	−1.05544	−0.527718	+	0.849420i	$0.676952\pi$
$240$	0	0
$241$	−1.54177e25	−1.50259	−0.751295	−	0.659966i	$-0.770571\pi$
$241$	−1.54177e25	−1.50259	−0.751295	+	0.659966i	$0.770571\pi$
$242$	− 4.87054e24i	− 0.454481i
$243$	7.17898e23i	0.0641500i
$244$	−1.80633e24	−0.154598
$245$	0	0
$246$	−1.09096e25	−0.857018
$247$	− 3.09477e25i	− 2.32975i
$248$	2.74114e25i	1.97783i
$249$	−1.80241e22	−0.00124670
$250$	0	0
$251$	−1.00009e25	−0.636014	−0.318007	−	0.948088i	$-0.603014\pi$
$251$	−1.00009e25	−0.636014	−0.318007	+	0.948088i	$0.603014\pi$
$252$	1.05630e24i	0.0644287i
$253$	2.68271e24i	0.156967i
$254$	7.04387e24	0.395419
$255$	0	0
$256$	−1.25164e25	−0.647080
$257$	3.06596e25i	1.52149i	0.649052	+	0.760744i	$0.275166\pi$
$257$	3.06596e25i	1.52149i	−0.649052	+	0.760744i	$0.724834\pi$
$258$	− 9.36923e24i	− 0.446372i
$259$	1.12304e25	0.513746
$260$	0	0
$261$	−9.64685e24	−0.407062
$262$	− 3.23878e25i	− 1.31286i
$263$	− 2.33455e25i	− 0.909216i	−0.890692	−	0.454608i	$-0.849779\pi$
$263$	− 2.33455e25i	− 0.909216i	0.890692	−	0.454608i	$-0.150221\pi$
$264$	−1.15639e25	−0.432775
$265$	0	0
$266$	−3.36914e25	−1.16483
$267$	− 1.38525e25i	− 0.460425i
$268$	1.35060e24i	0.0431631i
$269$	−2.29737e25	−0.706043	−0.353022	−	0.935615i	$-0.614846\pi$
$269$	−2.29737e25	−0.706043	−0.353022	+	0.935615i	$0.614846\pi$
$270$	0	0
$271$	−4.02085e25	−1.14325	−0.571624	−	0.820516i	$-0.693686\pi$
$271$	−4.02085e25	−1.14325	−0.571624	+	0.820516i	$0.693686\pi$
$272$	− 2.64405e25i	− 0.723263i
$273$	2.75633e25i	0.725477i
$274$	−6.13194e25	−1.55316
$275$	0	0
$276$	−1.27051e24	−0.0298149
$277$	4.48722e25i	1.01377i	0.862013	+	0.506886i	$0.169203\pi$
$277$	4.48722e25i	1.01377i	−0.862013	+	0.506886i	$0.830797\pi$
$278$	2.77532e25i	0.603731i
$279$	−2.91653e25	−0.610973
$280$	0	0
$281$	−6.06489e25	−1.17871	−0.589355	−	0.807874i	$-0.700618\pi$
$281$	−6.06489e25	−1.17871	−0.589355	+	0.807874i	$0.700618\pi$
$282$	3.21886e25i	0.602679i
$283$	1.04229e26i	1.88032i	0.340739	+	0.940158i	$0.389323\pi$
$283$	1.04229e26i	1.88032i	−0.340739	+	0.940158i	$0.610677\pi$
$284$	4.80376e24	0.0835100
$285$	0	0
$286$	−5.61334e25	−0.906521
$287$	− 9.18107e25i	− 1.42933i
$288$	− 9.93433e24i	− 0.149114i
$289$	−7.76980e23	−0.0112456
$290$	0	0
$291$	−3.49621e25	−0.470675
$292$	− 8.27907e24i	− 0.107513i
$293$	6.24634e25i	0.782556i	0.920273	+	0.391278i	$0.127967\pi$
$293$	6.24634e25i	0.782556i	−0.920273	+	0.391278i	$0.872033\pi$
$294$	−1.19441e25	−0.144380
$295$	0	0
$296$	−5.82261e25	−0.655472
$297$	− 1.23037e25i	− 0.133689i
$298$	− 6.15805e25i	− 0.645911i
$299$	−3.31532e25	−0.335720
$300$	0	0
$301$	7.88476e25	0.744458
$302$	− 1.56384e26i	− 1.42600i
$303$	− 9.81568e25i	− 0.864516i
$304$	1.32558e26	1.12780
$305$	0	0
$306$	3.70714e25	0.294418
$307$	− 7.14411e25i	− 0.548271i	−0.961691	−	0.274135i	$-0.911608\pi$
$307$	− 7.14411e25i	− 0.548271i	0.961691	−	0.274135i	$-0.0883917\pi$
$308$	− 1.81034e25i	− 0.134269i
$309$	−6.96297e25	−0.499150
$310$	0	0
$311$	−6.01915e25	−0.403228	−0.201614	−	0.979465i	$-0.564619\pi$
$311$	−6.01915e25	−0.403228	−0.201614	+	0.979465i	$0.564619\pi$
$312$	− 1.42907e26i	− 0.925615i
$313$	− 1.69049e26i	− 1.05876i	−0.848385	−	0.529379i	$-0.822425\pi$
$313$	− 1.69049e26i	− 1.05876i	0.848385	−	0.529379i	$-0.177575\pi$
$314$	7.50235e25	0.454398
$315$	0	0
$316$	1.57337e25	0.0891488
$317$	5.71691e25i	0.313357i	0.987650	+	0.156678i	$0.0500786\pi$
$317$	5.71691e25i	0.313357i	−0.987650	+	0.156678i	$0.949921\pi$
$318$	3.58277e25i	0.189991i
$319$	1.65333e26	0.848316
$320$	0	0
$321$	−5.13230e25	−0.246609
$322$	3.60924e25i	0.167853i
$323$	− 3.50283e26i	− 1.57686i
$324$	5.82695e24	0.0253933
$325$	0	0
$326$	4.04792e25	0.165366
$327$	− 2.43294e25i	− 0.0962454i
$328$	4.76009e26i	1.82364i
$329$	−2.70886e26	−1.00515
$330$	0	0
$331$	6.67957e25	0.232571	0.116285	−	0.993216i	$-0.462901\pi$
$331$	6.67957e25	0.232571	0.116285	+	0.993216i	$0.462901\pi$
$332$	1.46296e23i	0 0.000493495i
$333$	− 6.19515e25i	− 0.202482i
$334$	−4.61493e25	−0.146160
$335$	0	0
$336$	−1.18062e26	−0.351194
$337$	− 3.55365e26i	− 1.02461i	−0.858802	−	0.512307i	$-0.828791\pi$
$337$	− 3.55365e26i	− 1.02461i	0.858802	−	0.512307i	$-0.171209\pi$
$338$	− 3.79446e26i	− 1.06053i
$339$	−1.45227e26	−0.393504
$340$	0	0
$341$	4.99851e26	1.27327
$342$	1.85855e26i	0.459093i
$343$	− 4.53560e26i	− 1.08654i
$344$	−4.08799e26	−0.949832
$345$	0	0
$346$	−4.08947e26	−0.894062
$347$	3.94238e25i	0.0836179i	0.999126	+	0.0418090i	$0.0133121\pi$
$347$	3.94238e25i	0.0836179i	−0.999126	+	0.0418090i	$0.986688\pi$
$348$	7.83004e25i	0.161132i
$349$	5.84299e26	1.16672	0.583362	−	0.812212i	$-0.301737\pi$
$349$	5.84299e26	1.16672	0.583362	+	0.812212i	$0.301737\pi$
$350$	0	0
$351$	1.52050e26	0.285932
$352$	1.70260e26i	0.310753i
$353$	4.96062e26i	0.878823i	0.898286	+	0.439412i	$0.144813\pi$
$353$	4.96062e26i	0.878823i	−0.898286	+	0.439412i	$0.855187\pi$
$354$	1.21644e26	0.209197
$355$	0	0
$356$	−1.12436e26	−0.182256
$357$	3.11978e26i	0.491029i
$358$	2.29483e26i	0.350735i
$359$	3.35136e26	0.497426	0.248713	−	0.968577i	$-0.419992\pi$
$359$	3.35136e26	0.497426	0.248713	+	0.968577i	$0.419992\pi$
$360$	0	0
$361$	1.04192e27	1.45884
$362$	− 8.09785e24i	− 0.0110136i
$363$	− 2.26109e26i	− 0.298743i
$364$	2.23723e26	0.287174
$365$	0	0
$366$	2.83068e26	0.343035
$367$	− 9.70198e25i	− 0.114253i	−0.998367	−	0.0571264i	$-0.981806\pi$
$367$	− 9.70198e25i	− 0.114253i	0.998367	−	0.0571264i	$-0.0181938\pi$
$368$	− 1.42005e26i	− 0.162518i
$369$	−5.06465e26	−0.563342
$370$	0	0
$371$	−3.01511e26	−0.316867
$372$	2.36725e26i	0.241849i
$373$	1.03252e27i	1.02554i	0.858525	+	0.512771i	$0.171381\pi$
$373$	1.03252e27i	1.02554i	−0.858525	+	0.512771i	$0.828619\pi$
$374$	−6.35350e26	−0.613566
$375$	0	0
$376$	1.40446e27	1.28244
$377$	2.04320e27i	1.81437i
$378$	− 1.65531e26i	− 0.142960i
$379$	−2.20881e26	−0.185544	−0.0927721	−	0.995687i	$-0.529573\pi$
$379$	−2.20881e26	−0.185544	−0.0927721	+	0.995687i	$0.529573\pi$
$380$	0	0
$381$	3.27003e26	0.259920
$382$	1.04031e27i	0.804446i
$383$	− 1.59547e27i	− 1.20033i	−0.799876	−	0.600165i	$-0.795101\pi$
$383$	− 1.59547e27i	− 1.20033i	0.799876	−	0.600165i	$-0.204899\pi$
$384$	4.17610e26	0.305698
$385$	0	0
$386$	2.29033e26	0.158756
$387$	− 4.34955e26i	− 0.293413i
$388$	2.83776e26i	0.186313i
$389$	3.60474e26	0.230358	0.115179	−	0.993345i	$-0.463256\pi$
$389$	3.60474e26	0.230358	0.115179	+	0.993345i	$0.463256\pi$
$390$	0	0
$391$	−3.75247e26	−0.227228
$392$	5.21147e26i	0.307225i
$393$	− 1.50357e27i	− 0.862980i
$394$	2.10148e27	1.17440
$395$	0	0
$396$	−9.98656e25	−0.0529196
$397$	1.47191e27i	0.759595i	0.925070	+	0.379798i	$0.124006\pi$
$397$	1.47191e27i	0.759595i	−0.925070	+	0.379798i	$0.875994\pi$
$398$	1.94020e27i	0.975156i
$399$	−1.56408e27	−0.765674
$400$	0	0
$401$	1.00401e27	0.466360	0.233180	−	0.972434i	$-0.425087\pi$
$401$	1.00401e27	0.466360	0.233180	+	0.972434i	$0.425087\pi$
$402$	− 2.11651e26i	− 0.0957740i
$403$	6.17719e27i	2.72325i
$404$	−7.96708e26	−0.342212
$405$	0	0
$406$	2.22434e27	0.907148
$407$	1.06176e27i	0.421973i
$408$	− 1.61750e27i	− 0.626489i
$409$	4.41838e27	1.66789	0.833947	−	0.551845i	$-0.186076\pi$
$409$	4.41838e27	1.66789	0.833947	+	0.551845i	$0.186076\pi$
$410$	0	0
$411$	−2.84668e27	−1.02094
$412$	5.65163e26i	0.197584i
$413$	1.02370e27i	0.348898i
$414$	1.99100e26	0.0661559
$415$	0	0
$416$	−2.10409e27	−0.664635
$417$	1.28841e27i	0.396849i
$418$	− 3.18529e27i	− 0.956749i
$419$	2.36639e27	0.693169	0.346584	−	0.938019i	$-0.387341\pi$
$419$	2.36639e27	0.693169	0.346584	+	0.938019i	$0.387341\pi$
$420$	0	0
$421$	2.72067e27	0.758078	0.379039	−	0.925381i	$-0.376255\pi$
$421$	2.72067e27	0.758078	0.379039	+	0.925381i	$0.376255\pi$
$422$	1.72665e27i	0.469271i
$423$	1.49432e27i	0.396158i
$424$	1.56324e27	0.404281
$425$	0	0
$426$	−7.52791e26	−0.185299
$427$	2.38218e27i	0.572114i
$428$	4.16573e26i	0.0976183i
$429$	−2.60593e27	−0.595883
$430$	0	0
$431$	8.87397e27	1.93244	0.966222	−	0.257713i	$-0.0829688\pi$
$431$	8.87397e27	1.93244	0.966222	+	0.257713i	$0.0829688\pi$
$432$	6.51276e26i	0.138416i
$433$	− 3.39994e27i	− 0.705258i	−0.935763	−	0.352629i	$-0.885288\pi$
$433$	− 3.39994e27i	− 0.705258i	0.935763	−	0.352629i	$-0.114712\pi$
$434$	6.72484e27	1.36157
$435$	0	0
$436$	−1.97474e26	−0.0380980
$437$	− 1.88128e27i	− 0.354322i
$438$	1.29740e27i	0.238559i
$439$	−2.29516e27	−0.412037	−0.206018	−	0.978548i	$-0.566051\pi$
$439$	−2.29516e27	−0.412037	−0.206018	+	0.978548i	$0.566051\pi$
$440$	0	0
$441$	−5.54491e26	−0.0949050
$442$	− 7.85170e27i	− 1.31229i
$443$	− 5.65265e27i	− 0.922599i	−0.887245	−	0.461299i	$-0.847383\pi$
$443$	− 5.65265e27i	− 0.922599i	0.887245	−	0.461299i	$-0.152617\pi$
$444$	−5.02841e26	−0.0801510
$445$	0	0
$446$	−6.01879e27	−0.915152
$447$	− 2.85880e27i	− 0.424576i
$448$	6.48364e27i	0.940589i
$449$	−1.23324e28	−1.74768	−0.873839	−	0.486216i	$-0.838377\pi$
$449$	−1.23324e28	−1.74768	−0.873839	+	0.486216i	$0.838377\pi$
$450$	0	0
$451$	8.68008e27	1.17400
$452$	1.17876e27i	0.155766i
$453$	− 7.25995e27i	− 0.937351i
$454$	1.01785e28	1.28410
$455$	0	0
$456$	8.10926e27	0.976900
$457$	7.62646e27i	0.897848i	0.893570	+	0.448924i	$0.148193\pi$
$457$	7.62646e27i	0.897848i	−0.893570	+	0.448924i	$0.851807\pi$
$458$	− 3.46113e27i	− 0.398226i
$459$	1.72100e27	0.193529
$460$	0	0
$461$	−9.04851e26	−0.0972114	−0.0486057	−	0.998818i	$-0.515478\pi$
$461$	−9.04851e26	−0.0972114	−0.0486057	+	0.998818i	$0.515478\pi$
$462$	2.83696e27i	0.297929i
$463$	− 1.19705e27i	− 0.122889i	−0.998111	−	0.0614443i	$-0.980429\pi$
$463$	− 1.19705e27i	− 0.122889i	0.998111	−	0.0614443i	$-0.0195707\pi$
$464$	−8.75161e27	−0.878313
$465$	0	0
$466$	8.39637e27	0.805452
$467$	1.16951e28i	1.09693i	0.836174	+	0.548464i	$0.184787\pi$
$467$	1.16951e28i	1.09693i	−0.836174	+	0.548464i	$0.815213\pi$
$468$	− 1.23415e27i	− 0.113184i
$469$	1.78117e27	0.159732
$470$	0	0
$471$	3.48288e27	0.298689
$472$	− 5.30757e27i	− 0.445148i
$473$	7.45451e27i	0.611472i
$474$	−2.46560e27	−0.197811
$475$	0	0
$476$	2.53222e27	0.194370
$477$	1.66326e27i	0.124887i
$478$	− 1.26206e28i	− 0.927019i
$479$	−2.04856e28	−1.47206	−0.736029	−	0.676950i	$-0.763301\pi$
$479$	−2.04856e28	−1.47206	−0.736029	+	0.676950i	$0.763301\pi$
$480$	0	0
$481$	−1.31213e28	−0.902513
$482$	− 1.96106e28i	− 1.31977i
$483$	1.67555e27i	0.110335i
$484$	−1.83525e27	−0.118255
$485$	0	0
$486$	−9.13134e26	−0.0563448
$487$	3.75693e27i	0.226871i	0.993545	+	0.113436i	$0.0361856\pi$
$487$	3.75693e27i	0.226871i	−0.993545	+	0.113436i	$0.963814\pi$
$488$	− 1.23508e28i	− 0.729942i
$489$	1.87920e27	0.108700
$490$	0	0
$491$	−1.53173e28	−0.848841	−0.424420	−	0.905465i	$-0.639522\pi$
$491$	−1.53173e28	−0.848841	−0.424420	+	0.905465i	$0.639522\pi$
$492$	4.11081e27i	0.222995i
$493$	2.31261e28i	1.22803i
$494$	3.93640e28	2.04629
$495$	0	0
$496$	−2.64587e28	−1.31829
$497$	− 6.33518e27i	− 0.309042i
$498$	− 2.29259e25i	− 0.00109501i
$499$	−3.84836e27	−0.179978	−0.0899890	−	0.995943i	$-0.528683\pi$
$499$	−3.84836e27	−0.179978	−0.0899890	+	0.995943i	$0.528683\pi$
$500$	0	0
$501$	−2.14243e27	−0.0960749
$502$	− 1.27208e28i	− 0.558629i
$503$	− 2.25177e28i	− 0.968411i	−0.874954	−	0.484205i	$-0.839109\pi$
$503$	− 2.25177e28i	− 0.968411i	0.874954	−	0.484205i	$-0.160891\pi$
$504$	−7.22246e27	−0.304204
$505$	0	0
$506$	−3.41229e27	−0.137869
$507$	− 1.76153e28i	− 0.697119i
$508$	− 2.65418e27i	− 0.102887i
$509$	−2.09122e27	−0.0794078	−0.0397039	−	0.999211i	$-0.512641\pi$
$509$	−2.09122e27	−0.0794078	−0.0397039	+	0.999211i	$0.512641\pi$
$510$	0	0
$511$	−1.09184e28	−0.397869
$512$	− 3.07519e28i	− 1.09783i
$513$	8.62810e27i	0.301775i
$514$	−3.89976e28	−1.33637
$515$	0	0
$516$	−3.53039e27	−0.116145
$517$	− 2.56104e28i	− 0.825594i
$518$	1.42846e28i	0.451237i
$519$	−1.89849e28	−0.587692
$520$	0	0
$521$	−3.76486e27	−0.111932	−0.0559659	−	0.998433i	$-0.517824\pi$
$521$	−3.76486e27	−0.111932	−0.0559659	+	0.998433i	$0.517824\pi$
$522$	− 1.22704e28i	− 0.357534i
$523$	− 1.74944e28i	− 0.499611i	−0.968296	−	0.249806i	$-0.919633\pi$
$523$	− 1.74944e28i	− 0.499611i	0.968296	−	0.249806i	$-0.0803667\pi$
$524$	−1.22040e28	−0.341604
$525$	0	0
$526$	2.96944e28	0.798590
$527$	6.99170e28i	1.84320i
$528$	− 1.11619e28i	− 0.288459i
$529$	3.74562e28	0.948942
$530$	0	0
$531$	5.64716e27	0.137511
$532$	1.26952e28i	0.303086i
$533$	1.07269e29i	2.51095i
$534$	1.76197e28	0.404404
$535$	0	0
$536$	−9.23480e27	−0.203797
$537$	1.06535e28i	0.230548i
$538$	− 2.92215e28i	− 0.620138i
$539$	9.50317e27	0.197782
$540$	0	0
$541$	−6.99960e28	−1.40121	−0.700603	−	0.713552i	$-0.747085\pi$
$541$	−6.99960e28	−1.40121	−0.700603	+	0.713552i	$0.747085\pi$
$542$	− 5.11434e28i	− 1.00415i
$543$	− 3.75933e26i	− 0.00723956i
$544$	−2.38153e28	−0.449849
$545$	0	0
$546$	−3.50593e28	−0.637207
$547$	− 3.00896e28i	− 0.536476i	−0.963353	−	0.268238i	$-0.913559\pi$
$547$	− 3.00896e28i	− 0.536476i	0.963353	−	0.268238i	$-0.0864413\pi$
$548$	2.31056e28i	0.404130i
$549$	1.31411e28	0.225487
$550$	0	0
$551$	−1.15941e29	−1.91490
$552$	− 8.68717e27i	− 0.140773i
$553$	− 2.07495e28i	− 0.329909i
$554$	−5.70754e28	−0.890424
$555$	0	0
$556$	1.04576e28	0.157090
$557$	− 1.17263e29i	− 1.72855i	−0.503017	−	0.864277i	$-0.667777\pi$
$557$	− 1.17263e29i	− 1.72855i	0.503017	−	0.864277i	$-0.332223\pi$
$558$	− 3.70969e28i	− 0.536635i
$559$	−9.21233e28	−1.30781
$560$	0	0
$561$	−2.94954e28	−0.403315
$562$	− 7.71427e28i	− 1.03529i
$563$	6.46986e28i	0.852230i	0.904669	+	0.426115i	$0.140118\pi$
$563$	6.46986e28i	0.852230i	−0.904669	+	0.426115i	$0.859882\pi$
$564$	1.21289e28	0.156816
$565$	0	0
$566$	−1.32575e29	−1.65153
$567$	− 7.68456e27i	− 0.0939717i
$568$	3.28459e28i	0.394297i
$569$	1.35009e29	1.59105	0.795527	−	0.605918i	$-0.207194\pi$
$569$	1.35009e29	1.59105	0.795527	+	0.605918i	$0.207194\pi$
$570$	0	0
$571$	2.55750e28	0.290494	0.145247	−	0.989395i	$-0.453602\pi$
$571$	2.55750e28	0.290494	0.145247	+	0.989395i	$0.453602\pi$
$572$	2.11515e28i	0.235875i
$573$	4.82951e28i	0.528786i
$574$	1.16779e29	1.25542
$575$	0	0
$576$	3.57664e28	0.370714
$577$	1.52580e29i	1.55293i	0.630160	+	0.776465i	$0.282989\pi$
$577$	1.52580e29i	1.55293i	−0.630160	+	0.776465i	$0.717011\pi$
$578$	− 9.88284e26i	− 0.00987733i
$579$	1.06326e28	0.104355
$580$	0	0
$581$	1.92935e26	0.00182625
$582$	− 4.44702e28i	− 0.413407i
$583$	− 2.85058e28i	− 0.260264i
$584$	5.66084e28	0.507629
$585$	0	0
$586$	−7.94506e28	−0.687341
$587$	1.08485e29i	0.921868i	0.887434	+	0.460934i	$0.152486\pi$
$587$	1.08485e29i	0.921868i	−0.887434	+	0.460934i	$0.847514\pi$
$588$	4.50063e27i	0.0375674i
$589$	−3.50525e29	−2.87414
$590$	0	0
$591$	9.75587e28	0.771965
$592$	− 5.62023e28i	− 0.436894i
$593$	8.82363e28i	0.673865i	0.941529	+	0.336933i	$0.109389\pi$
$593$	8.82363e28i	0.673865i	−0.941529	+	0.336933i	$0.890611\pi$
$594$	1.56498e28	0.117422
$595$	0	0
$596$	−2.32040e28	−0.168065
$597$	9.00714e28i	0.640998i
$598$	− 4.21694e28i	− 0.294873i
$599$	−9.23342e28	−0.634426	−0.317213	−	0.948354i	$-0.602747\pi$
$599$	−9.23342e28	−0.634426	−0.317213	+	0.948354i	$0.602747\pi$
$600$	0	0
$601$	−7.30699e28	−0.484793	−0.242397	−	0.970177i	$-0.577934\pi$
$601$	−7.30699e28	−0.484793	−0.242397	+	0.970177i	$0.577934\pi$
$602$	1.00291e29i	0.653878i
$603$	− 9.82566e27i	− 0.0629550i
$604$	−5.89267e28	−0.371043
$605$	0	0
$606$	1.24851e29	0.759329
$607$	− 8.07544e28i	− 0.482709i	−0.970437	−	0.241354i	$-0.922408\pi$
$607$	− 8.07544e28i	− 0.482709i	0.970437	−	0.241354i	$-0.0775916\pi$
$608$	− 1.19396e29i	− 0.701461i
$609$	1.03262e29	0.596294
$610$	0	0
$611$	3.16496e29	1.76577
$612$	− 1.39688e28i	− 0.0766070i
$613$	− 2.21326e29i	− 1.19316i	−0.802555	−	0.596578i	$-0.796527\pi$
$613$	− 2.21326e29i	− 1.19316i	0.802555	−	0.596578i	$-0.203473\pi$
$614$	9.08699e28	0.481562
$615$	0	0
$616$	1.23783e29	0.633960
$617$	2.16026e29i	1.08771i	0.839180	+	0.543854i	$0.183035\pi$
$617$	2.16026e29i	1.08771i	−0.839180	+	0.543854i	$0.816965\pi$
$618$	− 8.85659e28i	− 0.438417i
$619$	2.09908e29	1.02159	0.510795	−	0.859702i	$-0.329351\pi$
$619$	2.09908e29	1.02159	0.510795	+	0.859702i	$0.329351\pi$
$620$	0	0
$621$	9.24299e27	0.0434861
$622$	− 7.65609e28i	− 0.354167i
$623$	1.48280e29i	0.674465i
$624$	1.37940e29	0.616953
$625$	0	0
$626$	2.15023e29	0.929938
$627$	− 1.47873e29i	− 0.628899i
$628$	− 2.82694e28i	− 0.118234i
$629$	−1.48514e29	−0.610853
$630$	0	0
$631$	4.81094e28	0.191391	0.0956955	−	0.995411i	$-0.469492\pi$
$631$	4.81094e28	0.191391	0.0956955	+	0.995411i	$0.469492\pi$
$632$	1.07580e29i	0.420921i
$633$	8.01576e28i	0.308465i
$634$	−7.27166e28	−0.275230
$635$	0	0
$636$	1.35001e28	0.0494354
$637$	1.17441e29i	0.423014i
$638$	2.10296e29i	0.745100i
$639$	−3.49474e28	−0.121802
$640$	0	0
$641$	−5.04867e28	−0.170282	−0.0851408	−	0.996369i	$-0.527134\pi$
$641$	−5.04867e28	−0.170282	−0.0851408	+	0.996369i	$0.527134\pi$
$642$	− 6.52806e28i	− 0.216604i
$643$	− 3.93930e29i	− 1.28589i	−0.765912	−	0.642945i	$-0.777712\pi$
$643$	− 3.93930e29i	− 1.28589i	0.765912	−	0.642945i	$-0.222288\pi$
$644$	1.35999e28	0.0436751
$645$	0	0
$646$	4.45545e29	1.38500
$647$	1.38475e29i	0.423523i	0.977321	+	0.211762i	$0.0679201\pi$
$647$	1.38475e29i	0.423523i	−0.977321	+	0.211762i	$0.932080\pi$
$648$	3.98420e28i	0.119896i
$649$	−9.67842e28	−0.286573
$650$	0	0
$651$	3.12193e29	0.894998
$652$	− 1.52528e28i	− 0.0430280i
$653$	1.16655e29i	0.323830i	0.986805	+	0.161915i	$0.0517670\pi$
$653$	1.16655e29i	0.323830i	−0.986805	+	0.161915i	$0.948233\pi$
$654$	3.09459e28	0.0845350
$655$	0	0
$656$	−4.59464e29	−1.21552
$657$	6.02303e28i	0.156812i
$658$	− 3.44555e29i	− 0.882849i
$659$	3.36819e29	0.849377	0.424688	−	0.905340i	$-0.360384\pi$
$659$	3.36819e29	0.849377	0.424688	+	0.905340i	$0.360384\pi$
$660$	0	0
$661$	4.31449e29	1.05394	0.526968	−	0.849885i	$-0.323329\pi$
$661$	4.31449e29	1.05394	0.526968	+	0.849885i	$0.323329\pi$
$662$	8.49612e28i	0.204273i
$663$	− 3.64506e29i	− 0.862606i
$664$	−1.00030e27	−0.00233006
$665$	0	0
$666$	7.87995e28	0.177846
$667$	1.24204e29i	0.275940i
$668$	1.73894e28i	0.0380305i
$669$	−2.79415e29	−0.601555
$670$	0	0
$671$	−2.25219e29	−0.469915
$672$	1.06340e29i	0.218433i
$673$	− 1.19710e29i	− 0.242088i	−0.992647	−	0.121044i	$-0.961376\pi$
$673$	− 1.19710e29i	− 0.242088i	0.992647	−	0.121044i	$-0.0386243\pi$
$674$	4.52008e29	0.899948
$675$	0	0
$676$	−1.42978e29	−0.275949
$677$	− 7.71503e29i	− 1.46608i	−0.680188	−	0.733038i	$-0.738102\pi$
$677$	− 7.71503e29i	− 1.46608i	0.680188	−	0.733038i	$-0.261898\pi$
$678$	− 1.84722e29i	− 0.345626i
$679$	3.74243e29	0.689479
$680$	0	0
$681$	4.72525e29	0.844074
$682$	6.35788e29i	1.11835i
$683$	6.40488e29i	1.10941i	0.832046	+	0.554707i	$0.187170\pi$
$683$	6.40488e29i	1.10941i	−0.832046	+	0.554707i	$0.812830\pi$
$684$	7.00316e28	0.119455
$685$	0	0
$686$	5.76908e29	0.954340
$687$	− 1.60679e29i	− 0.261766i
$688$	− 3.94591e29i	− 0.633094i
$689$	3.52277e29	0.556650
$690$	0	0
$691$	1.07309e30	1.64482	0.822408	−	0.568898i	$-0.192630\pi$
$691$	1.07309e30	1.64482	0.822408	+	0.568898i	$0.192630\pi$
$692$	1.54094e29i	0.232633i
$693$	1.31702e29i	0.195837i
$694$	−5.01454e28	−0.0734440
$695$	0	0
$696$	−5.35382e29	−0.760794
$697$	1.21413e30i	1.69950i
$698$	7.43202e29i	1.02477i
$699$	3.89791e29	0.529446
$700$	0	0
$701$	−7.18115e29	−0.946574	−0.473287	−	0.880908i	$-0.656933\pi$
$701$	−7.18115e29	−0.946574	−0.473287	+	0.880908i	$0.656933\pi$
$702$	1.93401e29i	0.251142i
$703$	− 7.44568e29i	− 0.952518i
$704$	−6.12985e29	−0.772568
$705$	0	0
$706$	−6.30969e29	−0.771895
$707$	1.05070e30i	1.26641i
$708$	− 4.58362e28i	− 0.0544327i
$709$	−4.24360e29	−0.496534	−0.248267	−	0.968692i	$-0.579861\pi$
$709$	−4.24360e29	−0.496534	−0.248267	+	0.968692i	$0.579861\pi$
$710$	0	0
$711$	−1.14463e29	−0.130027
$712$	− 7.68786e29i	− 0.860529i
$713$	3.75505e29i	0.414167i
$714$	−3.96822e29	−0.431285
$715$	0	0
$716$	8.64710e28	0.0912607
$717$	− 5.85898e29i	− 0.609356i
$718$	4.26277e29i	0.436904i
$719$	5.73272e29	0.579038	0.289519	−	0.957172i	$-0.406505\pi$
$719$	5.73272e29	0.579038	0.289519	+	0.957172i	$0.406505\pi$
$720$	0	0
$721$	7.45334e29	0.731191
$722$	1.32527e30i	1.28134i
$723$	− 9.10400e29i	− 0.867521i
$724$	−3.05133e27	−0.00286572
$725$	0	0
$726$	2.87600e29	0.262395
$727$	− 1.42987e30i	− 1.28583i	−0.765937	−	0.642916i	$-0.777725\pi$
$727$	− 1.42987e30i	− 1.28583i	0.765937	−	0.642916i	$-0.222275\pi$
$728$	1.52971e30i	1.35591i
$729$	−4.23912e28	−0.0370370
$730$	0	0
$731$	−1.04270e30	−0.885175
$732$	− 1.06662e29i	− 0.0892572i
$733$	1.99143e30i	1.64276i	0.570381	+	0.821380i	$0.306795\pi$
$733$	1.99143e30i	1.64276i	−0.570381	+	0.821380i	$0.693205\pi$
$734$	1.23405e29	0.100351
$735$	0	0
$736$	−1.27905e29	−0.101081
$737$	1.68398e29i	0.131198i
$738$	− 6.44200e29i	− 0.494799i
$739$	2.11124e30	1.59872	0.799359	−	0.600854i	$-0.205173\pi$
$739$	2.11124e30	1.59872	0.799359	+	0.600854i	$0.205173\pi$
$740$	0	0
$741$	1.82743e30	1.34508
$742$	− 3.83509e29i	− 0.278313i
$743$	1.11538e30i	0.798067i	0.916936	+	0.399033i	$0.130654\pi$
$743$	1.11538e30i	0.798067i	−0.916936	+	0.399033i	$0.869346\pi$
$744$	−1.61862e30	−1.14190
$745$	0	0
$746$	−1.31331e30	−0.900763
$747$	− 1.06431e27i	0 0.000719781i
$748$	2.39405e29i	0.159649i
$749$	5.49375e29	0.361251
$750$	0	0
$751$	−2.28371e30	−1.46023	−0.730116	−	0.683323i	$-0.760534\pi$
$751$	−2.28371e30	−1.46023	−0.730116	+	0.683323i	$0.760534\pi$
$752$	1.35564e30i	0.854787i
$753$	− 5.90546e29i	− 0.367203i
$754$	−2.59886e30	−1.59361
$755$	0	0
$756$	−6.23732e28	−0.0371980
$757$	− 9.73411e29i	− 0.572519i	−0.958152	−	0.286259i	$-0.907588\pi$
$757$	− 9.73411e29i	− 0.572519i	0.958152	−	0.286259i	$-0.0924119\pi$
$758$	− 2.80951e29i	− 0.162969i
$759$	−1.58412e29	−0.0906251
$760$	0	0
$761$	−3.06985e30	−1.70836	−0.854179	−	0.519979i	$-0.825940\pi$
$761$	−3.06985e30	−1.70836	−0.854179	+	0.519979i	$0.825940\pi$
$762$	4.15933e29i	0.228295i
$763$	2.60428e29i	0.140987i
$764$	3.91996e29	0.209316
$765$	0	0
$766$	2.02936e30	1.05428
$767$	− 1.19607e30i	− 0.612920i
$768$	− 7.39078e29i	− 0.373592i
$769$	7.51816e29	0.374874	0.187437	−	0.982277i	$-0.439982\pi$
$769$	7.51816e29	0.374874	0.187437	+	0.982277i	$0.439982\pi$
$770$	0	0
$771$	−1.81042e30	−0.878432
$772$	− 8.63013e28i	− 0.0413081i
$773$	1.23771e30i	0.584434i	0.956352	+	0.292217i	$0.0943930\pi$
$773$	1.23771e30i	0.584434i	−0.956352	+	0.292217i	$0.905607\pi$
$774$	5.53243e29	0.257713
$775$	0	0
$776$	−1.94033e30	−0.879686
$777$	6.63144e29i	0.296611i
$778$	4.58507e29i	0.202330i
$779$	−6.08698e30	−2.65008
$780$	0	0
$781$	5.98949e29	0.253836
$782$	− 4.77297e29i	− 0.199580i
$783$	− 5.69637e29i	− 0.235017i
$784$	−5.03033e29	−0.204776
$785$	0	0
$786$	1.91247e30	0.757979
$787$	− 2.14352e30i	− 0.838288i	−0.907920	−	0.419144i	$-0.862330\pi$
$787$	− 2.14352e30i	− 0.838288i	0.907920	−	0.419144i	$-0.137670\pi$
$788$	− 7.91853e29i	− 0.305576i
$789$	1.37853e30	0.524936
$790$	0	0
$791$	1.55454e30	0.576434
$792$	− 6.82834e29i	− 0.249862i
$793$	− 2.78327e30i	− 1.00505i
$794$	−1.87221e30	−0.667174
$795$	0	0
$796$	7.31081e29	0.253734
$797$	− 3.01280e30i	− 1.03195i	−0.856605	−	0.515974i	$-0.827430\pi$
$797$	− 3.01280e30i	− 1.03195i	0.856605	−	0.515974i	$-0.172570\pi$
$798$	− 1.98944e30i	− 0.672513i
$799$	3.58228e30	1.19514
$800$	0	0
$801$	8.17975e29	0.265827
$802$	1.27705e30i	0.409617i
$803$	− 1.03226e30i	− 0.326796i
$804$	−7.97518e28	−0.0249202
$805$	0	0
$806$	−7.85711e30	−2.39191
$807$	− 1.35657e30i	− 0.407634i
$808$	− 5.44752e30i	− 1.61577i
$809$	5.76883e30	1.68900	0.844498	−	0.535559i	$-0.179899\pi$
$809$	5.76883e30	1.68900	0.844498	+	0.535559i	$0.179899\pi$
$810$	0	0
$811$	3.98728e30	1.13752	0.568759	−	0.822504i	$-0.307424\pi$
$811$	3.98728e30	1.13752	0.568759	+	0.822504i	$0.307424\pi$
$812$	− 8.38148e29i	− 0.236038i
$813$	− 2.37427e30i	− 0.660055i
$814$	−1.35051e30	−0.370631
$815$	0	0
$816$	1.56129e30	0.417576
$817$	− 5.22754e30i	− 1.38027i
$818$	5.61998e30i	1.46496i
$819$	−1.62759e30	−0.418855
$820$	0	0
$821$	−4.09615e30	−1.02748	−0.513739	−	0.857946i	$-0.671740\pi$
$821$	−4.09615e30	−1.02748	−0.513739	+	0.857946i	$0.671740\pi$
$822$	− 3.62085e30i	− 0.896719i
$823$	1.43384e30i	0.350592i	0.984516	+	0.175296i	$0.0560882\pi$
$823$	1.43384e30i	0.350592i	−0.984516	+	0.175296i	$0.943912\pi$
$824$	−3.86432e30	−0.932905
$825$	0	0
$826$	−1.30210e30	−0.306447
$827$	3.13142e30i	0.727668i	0.931464	+	0.363834i	$0.118532\pi$
$827$	3.13142e30i	0.727668i	−0.931464	+	0.363834i	$0.881468\pi$
$828$	− 7.50225e28i	− 0.0172136i
$829$	4.44329e30	1.00666	0.503329	−	0.864095i	$-0.332108\pi$
$829$	4.44329e30	1.00666	0.503329	+	0.864095i	$0.332108\pi$
$830$	0	0
$831$	−2.64966e30	−0.585301
$832$	− 7.57531e30i	− 1.65236i
$833$	1.32926e30i	0.286311i
$834$	−1.63880e30	−0.348564
$835$	0	0
$836$	−1.20024e30	−0.248944
$837$	− 1.72218e30i	− 0.352745i
$838$	3.00994e30i	0.608829i
$839$	9.30057e29	0.185784	0.0928922	−	0.995676i	$-0.470389\pi$
$839$	9.30057e29	0.185784	0.0928922	+	0.995676i	$0.470389\pi$
$840$	0	0
$841$	2.52173e30	0.491293
$842$	3.46057e30i	0.665842i
$843$	− 3.58126e30i	− 0.680528i
$844$	6.50614e29	0.122103
$845$	0	0
$846$	−1.90070e30	−0.347957
$847$	2.42033e30i	0.437621i
$848$	1.50891e30i	0.269467i
$849$	−6.15462e30	−1.08560
$850$	0	0
$851$	−7.97630e29	−0.137259
$852$	2.83657e29i	0.0482145i
$853$	− 2.27471e30i	− 0.381911i	−0.981599	−	0.190955i	$-0.938841\pi$
$853$	− 2.27471e30i	− 0.381911i	0.981599	−	0.190955i	$-0.0611586\pi$
$854$	−3.03003e30	−0.502503
$855$	0	0
$856$	−2.84833e30	−0.460910
$857$	− 3.05003e30i	− 0.487534i	−0.969834	−	0.243767i	$-0.921617\pi$
$857$	− 3.05003e30i	− 0.487534i	0.969834	−	0.243767i	$-0.0783832\pi$
$858$	− 3.31462e30i	− 0.523380i
$859$	−1.34073e30	−0.209128	−0.104564	−	0.994518i	$-0.533345\pi$
$859$	−1.34073e30	−0.209128	−0.104564	+	0.994518i	$0.533345\pi$
$860$	0	0
$861$	5.42133e30	0.825225
$862$	1.12873e31i	1.69732i
$863$	1.14916e31i	1.70713i	0.520985	+	0.853566i	$0.325565\pi$
$863$	1.14916e31i	1.70713i	−0.520985	+	0.853566i	$0.674435\pi$
$864$	5.86612e29	0.0860908
$865$	0	0
$866$	4.32457e30	0.619448
$867$	− 4.58799e28i	− 0.00649265i
$868$	− 2.53397e30i	− 0.354278i
$869$	1.96173e30	0.270976
$870$	0	0
$871$	−2.08107e30	−0.280606
$872$	− 1.35024e30i	− 0.179882i
$873$	− 2.06448e30i	− 0.271744i
$874$	2.39290e30	0.311211
$875$	0	0
$876$	4.88871e29	0.0620727
$877$	− 9.06320e30i	− 1.13707i	−0.822660	−	0.568533i	$-0.807511\pi$
$877$	− 9.06320e30i	− 1.13707i	0.822660	−	0.568533i	$-0.192489\pi$
$878$	− 2.91934e30i	− 0.361904i
$879$	−3.68840e30	−0.451809
$880$	0	0
$881$	−6.50767e30	−0.778356	−0.389178	−	0.921163i	$-0.627241\pi$
$881$	−6.50767e30	−0.778356	−0.389178	+	0.921163i	$0.627241\pi$
$882$	− 7.05287e29i	− 0.0833577i
$883$	5.90742e30i	0.689939i	0.938614	+	0.344969i	$0.112111\pi$
$883$	5.90742e30i	0.689939i	−0.938614	+	0.344969i	$0.887889\pi$
$884$	−2.95858e30	−0.341456
$885$	0	0
$886$	7.18992e30	0.810344
$887$	3.42312e30i	0.381263i	0.981662	+	0.190632i	$0.0610536\pi$
$887$	3.42312e30i	0.381263i	−0.981662	+	0.190632i	$0.938946\pi$
$888$	− 3.43819e30i	− 0.378437i
$889$	−3.50032e30	−0.380750
$890$	0	0
$891$	7.26524e29	0.0771852
$892$	2.26792e30i	0.238121i
$893$	1.79595e31i	1.86361i
$894$	3.63627e30	0.372917
$895$	0	0
$896$	−4.47020e30	−0.447810
$897$	− 1.95766e30i	− 0.193828i
$898$	− 1.56863e31i	− 1.53503i
$899$	2.31420e31	2.23833
$900$	0	0
$901$	3.98728e30	0.376761
$902$	1.10407e31i	1.03116i
$903$	4.65587e30i	0.429813i
$904$	−8.05980e30	−0.735455
$905$	0	0
$906$	9.23433e30	0.823302
$907$	1.16251e31i	1.02452i	0.858829	+	0.512262i	$0.171192\pi$
$907$	1.16251e31i	1.02452i	−0.858829	+	0.512262i	$0.828808\pi$
$908$	− 3.83534e30i	− 0.334120i
$909$	5.79606e30	0.499128
$910$	0	0
$911$	−1.34510e31	−1.13191	−0.565957	−	0.824435i	$-0.691493\pi$
$911$	−1.34510e31	−1.13191	−0.565957	+	0.824435i	$0.691493\pi$
$912$	7.82741e30i	0.651137i
$913$	1.82407e28i	0.00150002i
$914$	−9.70051e30	−0.788605
$915$	0	0
$916$	−1.30418e30	−0.103618
$917$	1.60945e31i	1.26416i
$918$	2.18903e30i	0.169982i
$919$	8.55562e30	0.656808	0.328404	−	0.944537i	$-0.393489\pi$
$919$	8.55562e30	0.656808	0.328404	+	0.944537i	$0.393489\pi$
$920$	0	0
$921$	4.21853e30	0.316544
$922$	− 1.15093e30i	− 0.0853835i
$923$	7.40185e30i	0.542903i
$924$	1.06899e30	0.0775205
$925$	0	0
$926$	1.52259e30	0.107937
$927$	− 4.11157e30i	− 0.288184i
$928$	7.88268e30i	0.546286i
$929$	−9.93712e30	−0.680919	−0.340460	−	0.940259i	$-0.610583\pi$
$929$	−9.93712e30	−0.680919	−0.340460	+	0.940259i	$0.610583\pi$
$930$	0	0
$931$	−6.66418e30	−0.446452
$932$	− 3.16381e30i	− 0.209577i
$933$	− 3.55425e30i	− 0.232804i
$934$	−1.48757e31	−0.963462
$935$	0	0
$936$	8.43852e30	0.534404
$937$	2.14272e30i	0.134183i	0.997747	+	0.0670917i	$0.0213720\pi$
$937$	2.14272e30i	0.134183i	−0.997747	+	0.0670917i	$0.978628\pi$
$938$	2.26557e30i	0.140297i
$939$	9.98217e30	0.611275
$940$	0	0
$941$	1.69148e31	1.01292	0.506459	−	0.862264i	$-0.330954\pi$
$941$	1.69148e31	1.01292	0.506459	+	0.862264i	$0.330954\pi$
$942$	4.43006e30i	0.262347i
$943$	6.52077e30i	0.381879i
$944$	5.12310e30	0.296706
$945$	0	0
$946$	−9.48180e30	−0.537074
$947$	1.96530e31i	1.10092i	0.834862	+	0.550459i	$0.185547\pi$
$947$	1.96530e31i	1.10092i	−0.834862	+	0.550459i	$0.814453\pi$
$948$	9.29057e29i	0.0514701i
$949$	1.27568e31	0.698948
$950$	0	0
$951$	−3.37578e30	−0.180917
$952$	1.73142e31i	0.917728i
$953$	2.39001e31i	1.25292i	0.779452	+	0.626462i	$0.215498\pi$
$953$	2.39001e31i	1.25292i	−0.779452	+	0.626462i	$0.784502\pi$
$954$	−2.11559e30	−0.109692
$955$	0	0
$956$	−4.75555e30	−0.241209
$957$	9.76276e30i	0.489776i
$958$	− 2.60567e31i	− 1.29295i
$959$	3.04716e31	1.49555
$960$	0	0
$961$	4.91397e31	2.35959
$962$	− 1.66897e31i	− 0.792703i
$963$	− 3.03057e30i	− 0.142380i
$964$	−7.38943e30	−0.343401
$965$	0	0
$966$	−2.13122e30	−0.0969100
$967$	− 1.63072e31i	− 0.733504i	−0.930319	−	0.366752i	$-0.880470\pi$
$967$	− 1.63072e31i	− 0.733504i	0.930319	−	0.366752i	$-0.119530\pi$
$968$	− 1.25486e31i	− 0.558348i
$969$	2.06839e31	0.910401
$970$	0	0
$971$	3.09343e31	1.33241	0.666207	−	0.745767i	$-0.267917\pi$
$971$	3.09343e31	1.33241	0.666207	+	0.745767i	$0.267917\pi$
$972$	3.44076e29i	0.0146608i
$973$	− 1.37915e31i	− 0.581334i
$974$	−4.77865e30	−0.199267
$975$	0	0
$976$	1.19216e31	0.486531
$977$	− 1.98044e31i	− 0.799592i	−0.916604	−	0.399796i	$-0.869081\pi$
$977$	− 1.98044e31i	− 0.799592i	0.916604	−	0.399796i	$-0.130919\pi$
$978$	2.39025e30i	0.0954742i
$979$	−1.40189e31	−0.553982
$980$	0	0
$981$	1.43663e30	0.0555673
$982$	− 1.94829e31i	− 0.745561i
$983$	− 4.34284e30i	− 0.164423i	−0.996615	−	0.0822114i	$-0.973802\pi$
$983$	− 4.34284e30i	− 0.164423i	0.996615	−	0.0822114i	$-0.0261983\pi$
$984$	−2.81078e31	−1.05288
$985$	0	0
$986$	−2.94154e31	−1.07862
$987$	− 1.59955e31i	− 0.580322i
$988$	− 1.48327e31i	− 0.532441i
$989$	−5.60008e30	−0.198899
$990$	0	0
$991$	4.70795e30	0.163704	0.0818518	−	0.996645i	$-0.473917\pi$
$991$	4.70795e30	0.163704	0.0818518	+	0.996645i	$0.473917\pi$
$992$	2.38317e31i	0.819939i
$993$	3.94422e30i	0.134275i
$994$	8.05807e30	0.271440
$995$	0	0
$996$	−8.63864e27	−0.000284920 0
$997$	1.58934e31i	0.518700i	0.965783	+	0.259350i	$0.0835084\pi$
$997$	1.58934e31i	0.518700i	−0.965783	+	0.259350i	$0.916492\pi$
$998$	− 4.89494e30i	− 0.158080i
$999$	3.65817e30	0.116903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.b.d.49.3		4
5.2	odd	4		3.22.a.c.1.1	✓	2
5.3	odd	4		75.22.a.d.1.2		2
5.4	even	2	inner	75.22.b.d.49.2		4
15.2	even	4		9.22.a.e.1.2		2
20.7	even	4		48.22.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.1	✓	2	5.2	odd	4
9.22.a.e.1.2		2	15.2	even	4
48.22.a.g.1.1		2	20.7	even	4
75.22.a.d.1.2		2	5.3	odd	4
75.22.b.d.49.2		4	5.4	even	2	inner
75.22.b.d.49.3		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1271.96i q^{2} +59049.0i q^{3} +479282. q^{4} -7.51077e7 q^{6} -6.32076e8i q^{7} +3.27711e9i q^{8} -3.48678e9 q^{9} +O(q^{10})\)	\(q+1271.96i q^{2} +59049.0i q^{3} +479282. q^{4} -7.51077e7 q^{6} -6.32076e8i q^{7} +3.27711e9i q^{8} -3.48678e9 q^{9} +5.97585e10 q^{11} +2.83011e10i q^{12} +7.38499e11i q^{13} +8.03972e11 q^{14} -3.16321e12 q^{16} +8.35876e12i q^{17} -4.43503e12i q^{18} -4.19061e13 q^{19} +3.73234e13 q^{21} +7.60101e13i q^{22} +4.48926e13i q^{23} -1.93510e14 q^{24} -9.39338e14 q^{26} -2.05891e14i q^{27} -3.02943e14i q^{28} +2.76669e15 q^{29} +8.36452e15 q^{31} +2.84914e15i q^{32} +3.52868e15i q^{33} -1.06320e16 q^{34} -1.67115e15 q^{36} +1.77675e16i q^{37} -5.33027e16i q^{38} -4.36077e16 q^{39} +1.45253e17 q^{41} +4.74737e16i q^{42} +1.24744e17i q^{43} +2.86412e16 q^{44} -5.71014e16 q^{46} -4.28566e17i q^{47} -1.86784e17i q^{48} +1.59026e17 q^{49} -4.93577e17 q^{51} +3.53950e17i q^{52} -4.77017e17i q^{53} +2.61884e17 q^{54} +2.07138e18 q^{56} -2.47452e18i q^{57} +3.51911e18i q^{58} -1.61959e18 q^{59} -3.76882e18 q^{61} +1.06393e19i q^{62} +2.20391e18i q^{63} -1.02577e19 q^{64} -4.48832e18 q^{66} +2.81797e18i q^{67} +4.00621e18i q^{68} -2.65086e18 q^{69} +1.00228e19 q^{71} -1.14266e19i q^{72} -1.72739e19i q^{73} -2.25995e19 q^{74} -2.00849e19 q^{76} -3.77719e19i q^{77} -5.54670e19i q^{78} +3.28276e19 q^{79} +1.21577e19 q^{81} +1.84755e20i q^{82} +3.05240e17i q^{83} +1.78885e19 q^{84} -1.58669e20 q^{86} +1.63370e20i q^{87} +1.95835e20i q^{88} -2.34593e20 q^{89} +4.66787e20 q^{91} +2.15162e19i q^{92} +4.93917e20i q^{93} +5.45116e20 q^{94} -1.68239e20 q^{96} +5.92086e20i q^{97} +2.02274e20i q^{98} -2.08365e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2358472 q^{4} + 78653268 q^{6} - 13947137604 q^{9}+O(q^{10}) \) 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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