LMFDB - Embedded newform 25.34.b.b.24.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.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:	$172.457072203$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 2 x^{8} + 325405868686 x^{7} + \cdots + 34\!\cdots\!68 $ x^10 - 2x^9 + 2x^8 + 325405868686x^7 + 327807761582101561x^6 + 230788916575056333044x^5 + 52482256238971860814088x^4 - 28868477926481009935781561728x^3 + 5099072964771111558047480848223296x^2 - 596428985476749456366946929757065984*x + 34881588984360865981321269538813997568
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{10}\cdot 5^{24}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.7
Root			$7776.84 + 7776.84i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.b.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+56118.7i q^{2} +5.48591e7i q^{3} +5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13i q^{7} +7.87377e14i q^{8} +2.54954e15 q^{9} +O(q^{10})$	\(q+56118.7i q^{2} +5.48591e7i q^{3} +5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13i q^{7} +7.87377e14i q^{8} +2.54954e15 q^{9} +3.54535e16 q^{11} +2.98468e17i q^{12} -1.27272e18i q^{13} +4.14468e18 q^{14} +2.54805e18 q^{16} -1.95420e20i q^{17} +1.43077e20i q^{18} -9.67568e20 q^{19} +4.05165e21 q^{21} +1.98961e21i q^{22} -3.06053e22i q^{23} -4.31948e22 q^{24} +7.14231e22 q^{26} +4.44830e23i q^{27} -4.01821e23i q^{28} +1.16201e23 q^{29} -3.89265e23 q^{31} +6.90651e24i q^{32} +1.94495e24i q^{33} +1.09667e25 q^{34} +1.38711e25 q^{36} +2.73400e25i q^{37} -5.42987e25i q^{38} +6.98200e25 q^{39} -7.27564e26 q^{41} +2.27373e26i q^{42} -1.74161e27i q^{43} +1.92889e26 q^{44} +1.71753e27 q^{46} -2.14063e26i q^{47} +1.39784e26i q^{48} +2.27634e27 q^{49} +1.07206e28 q^{51} -6.92437e27i q^{52} -1.96400e28i q^{53} -2.49633e28 q^{54} +5.81522e28 q^{56} -5.30799e28i q^{57} +6.52106e27i q^{58} -2.54315e29 q^{59} -2.81524e29 q^{61} -2.18451e28i q^{62} -1.88298e29i q^{63} -3.65697e29 q^{64} -1.09148e29 q^{66} +8.18392e29i q^{67} -1.06321e30i q^{68} +1.67898e30 q^{69} -3.59524e30 q^{71} +2.00745e30i q^{72} -2.19852e30i q^{73} -1.53429e30 q^{74} -5.26418e30 q^{76} -2.61844e30i q^{77} +3.91821e30i q^{78} -3.90404e31 q^{79} -1.02299e31 q^{81} -4.08299e31i q^{82} +4.98882e30i q^{83} +2.20435e31 q^{84} +9.77368e31 q^{86} +6.37469e30i q^{87} +2.79153e31i q^{88} +1.23819e32 q^{89} -9.39972e31 q^{91} -1.66512e32i q^{92} -2.13547e31i q^{93} +1.20129e31 q^{94} -3.78885e32 q^{96} -1.97176e32i q^{97} +1.27745e32i q^{98} +9.03903e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	56118.7i	0.605498i	0.953070	+	0.302749i	$0.0979044\pi$
$2$	56118.7i	0.605498i	−0.953070	+	0.302749i	$0.902096\pi$
$3$	5.48591e7i	0.735780i	0.929869	+	0.367890i	$0.119920\pi$
$3$	5.48591e7i	0.735780i	−0.929869	+	0.367890i	$0.880080\pi$
$4$	5.44063e9	0.633372
$5$	0	0
$5$	0	0
$6$	−3.07862e12	−0.445513
$7$	− 7.38557e13i	− 0.839975i	−0.907530	−	0.419987i	$-0.862035\pi$
$7$	− 7.38557e13i	− 0.839975i	0.907530	−	0.419987i	$-0.137965\pi$
$8$	7.87377e14i	0.989004i
$9$	2.54954e15	0.458628
$10$	0	0
$11$	3.54535e16	0.232638	0.116319	−	0.993212i	$-0.462891\pi$
$11$	3.54535e16	0.232638	0.116319	+	0.993212i	$0.462891\pi$
$12$	2.98468e17i	0.466022i
$13$	− 1.27272e18i	− 0.530476i	−0.964183	−	0.265238i	$-0.914549\pi$
$13$	− 1.27272e18i	− 0.530476i	0.964183	−	0.265238i	$-0.0854506\pi$
$14$	4.14468e18	0.508603
$15$	0	0
$16$	2.54805e18	0.0345325
$17$	− 1.95420e20i	− 0.974006i	−0.873400	−	0.487003i	$-0.838090\pi$
$17$	− 1.95420e20i	− 0.974006i	0.873400	−	0.487003i	$-0.161910\pi$
$18$	1.43077e20i	0.277699i
$19$	−9.67568e20	−0.769568	−0.384784	−	0.923007i	$-0.625724\pi$
$19$	−9.67568e20	−0.769568	−0.384784	+	0.923007i	$0.625724\pi$
$20$	0	0
$21$	4.05165e21	0.618036
$22$	1.98961e21i	0.140862i
$23$	− 3.06053e22i	− 1.04061i	−0.853981	−	0.520305i	$-0.825818\pi$
$23$	− 3.06053e22i	− 1.04061i	0.853981	−	0.520305i	$-0.174182\pi$
$24$	−4.31948e22	−0.727689
$25$	0	0
$26$	7.14231e22	0.321202
$27$	4.44830e23i	1.07323i
$28$	− 4.01821e23i	− 0.532017i
$29$	1.16201e23	0.0862271	0.0431135	−	0.999070i	$-0.486272\pi$
$29$	1.16201e23	0.0862271	0.0431135	+	0.999070i	$0.486272\pi$
$30$	0	0
$31$	−3.89265e23	−0.0961121	−0.0480560	−	0.998845i	$-0.515303\pi$
$31$	−3.89265e23	−0.0961121	−0.0480560	+	0.998845i	$0.515303\pi$
$32$	6.90651e24i	1.00991i
$33$	1.94495e24i	0.171170i
$34$	1.09667e25	0.589759
$35$	0	0
$36$	1.38711e25	0.290482
$37$	2.73400e25i	0.364310i	0.983270	+	0.182155i	$0.0583072\pi$
$37$	2.73400e25i	0.364310i	−0.983270	+	0.182155i	$0.941693\pi$
$38$	− 5.42987e25i	− 0.465972i
$39$	6.98200e25	0.390314
$40$	0	0
$41$	−7.27564e26	−1.78212	−0.891061	−	0.453883i	$-0.850038\pi$
$41$	−7.27564e26	−1.78212	−0.891061	+	0.453883i	$0.850038\pi$
$42$	2.27373e26i	0.374220i
$43$	− 1.74161e27i	− 1.94411i	−0.234754	−	0.972055i	$-0.575428\pi$
$43$	− 1.74161e27i	− 1.94411i	0.234754	−	0.972055i	$-0.424572\pi$
$44$	1.92889e26	0.147346
$45$	0	0
$46$	1.71753e27	0.630087
$47$	− 2.14063e26i	− 0.0550714i	−0.999621	−	0.0275357i	$-0.991234\pi$
$47$	− 2.14063e26i	− 0.0550714i	0.999621	−	0.0275357i	$-0.00876599\pi$
$48$	1.39784e26i	0.0254083i
$49$	2.27634e27	0.294443
$50$	0	0
$51$	1.07206e28	0.716654
$52$	− 6.92437e27i	− 0.335989i
$53$	− 1.96400e28i	− 0.695970i	−0.937500	−	0.347985i	$-0.886866\pi$
$53$	− 1.96400e28i	− 0.695970i	0.937500	−	0.347985i	$-0.113134\pi$
$54$	−2.49633e28	−0.649838
$55$	0	0
$56$	5.81522e28	0.830738
$57$	− 5.30799e28i	− 0.566233i
$58$	6.52106e27i	0.0522103i
$59$	−2.54315e29	−1.53573	−0.767864	−	0.640612i	$-0.778681\pi$
$59$	−2.54315e29	−1.53573	−0.767864	+	0.640612i	$0.778681\pi$
$60$	0	0
$61$	−2.81524e29	−0.980785	−0.490392	−	0.871502i	$-0.663147\pi$
$61$	−2.81524e29	−0.980785	−0.490392	+	0.871502i	$0.663147\pi$
$62$	− 2.18451e28i	− 0.0581957i
$63$	− 1.88298e29i	− 0.385236i
$64$	−3.65697e29	−0.576968
$65$	0	0
$66$	−1.09148e29	−0.103643
$67$	8.18392e29i	0.606355i	0.952934	+	0.303178i	$0.0980476\pi$
$67$	8.18392e29i	0.606355i	−0.952934	+	0.303178i	$0.901952\pi$
$68$	− 1.06321e30i	− 0.616908i
$69$	1.67898e30	0.765660
$70$	0	0
$71$	−3.59524e30	−1.02321	−0.511606	−	0.859220i	$-0.670949\pi$
$71$	−3.59524e30	−1.02321	−0.511606	+	0.859220i	$0.670949\pi$
$72$	2.00745e30i	0.453585i
$73$	− 2.19852e30i	− 0.395642i	−0.980238	−	0.197821i	$-0.936613\pi$
$73$	− 2.19852e30i	− 0.395642i	0.980238	−	0.197821i	$-0.0633865\pi$
$74$	−1.53429e30	−0.220589
$75$	0	0
$76$	−5.26418e30	−0.487423
$77$	− 2.61844e30i	− 0.195410i
$78$	3.91821e30i	0.236334i
$79$	−3.90404e31	−1.90839	−0.954194	−	0.299188i	$-0.903284\pi$
$79$	−3.90404e31	−1.90839	−0.954194	+	0.299188i	$0.903284\pi$
$80$	0	0
$81$	−1.02299e31	−0.331032
$82$	− 4.08299e31i	− 1.07907i
$83$	4.98882e30i	0.107947i	0.998542	+	0.0539734i	$0.0171886\pi$
$83$	4.98882e30i	0.107947i	−0.998542	+	0.0539734i	$0.982811\pi$
$84$	2.20435e31	0.391447
$85$	0	0
$86$	9.77368e31	1.17715
$87$	6.37469e30i	0.0634441i
$88$	2.79153e31i	0.230080i
$89$	1.23819e32	0.846937	0.423469	−	0.905911i	$-0.360812\pi$
$89$	1.23819e32	0.846937	0.423469	+	0.905911i	$0.360812\pi$
$90$	0	0
$91$	−9.39972e31	−0.445587
$92$	− 1.66512e32i	− 0.659093i
$93$	− 2.13547e31i	− 0.0707173i
$94$	1.20129e31	0.0333456
$95$	0	0
$96$	−3.78885e32	−0.743073
$97$	− 1.97176e32i	− 0.325926i	−0.986632	−	0.162963i	$-0.947895\pi$
$97$	− 1.97176e32i	− 0.325926i	0.986632	−	0.162963i	$-0.0521052\pi$
$98$	1.27745e32i	0.178285i
$99$	9.03903e31	0.106694
$100$	0	0
$101$	−1.97472e33	−1.67573	−0.837865	−	0.545878i	$-0.816196\pi$
$101$	−1.97472e33	−1.67573	−0.837865	+	0.545878i	$0.816196\pi$
$102$	6.01624e32i	0.433932i
$103$	5.57056e32i	0.342046i	0.985267	+	0.171023i	$0.0547072\pi$
$103$	5.57056e32i	0.342046i	−0.985267	+	0.171023i	$0.945293\pi$
$104$	1.00211e33	0.524643
$105$	0	0
$106$	1.10217e33	0.421409
$107$	− 3.76704e33i	− 1.23358i	−0.787127	−	0.616791i	$-0.788432\pi$
$107$	− 3.76704e33i	− 1.23358i	0.787127	−	0.616791i	$-0.211568\pi$
$108$	2.42016e33i	0.679753i
$109$	−7.25238e33	−1.74962	−0.874810	−	0.484467i	$-0.839014\pi$
$109$	−7.25238e33	−1.74962	−0.874810	+	0.484467i	$0.839014\pi$
$110$	0	0
$111$	−1.49985e33	−0.268051
$112$	− 1.88188e32i	− 0.0290064i
$113$	− 3.76366e32i	− 0.0500976i	−0.999686	−	0.0250488i	$-0.992026\pi$
$113$	− 3.76366e32i	− 0.0500976i	0.999686	−	0.0250488i	$-0.00797411\pi$
$114$	2.97878e33	0.342853
$115$	0	0
$116$	6.32207e32	0.0546138
$117$	− 3.24484e33i	− 0.243291i
$118$	− 1.42719e34i	− 0.929881i
$119$	−1.44329e34	−0.818140
$120$	0	0
$121$	−2.19682e34	−0.945880
$122$	− 1.57988e34i	− 0.593863i
$123$	− 3.99135e34i	− 1.31125i
$124$	−2.11785e33	−0.0608747
$125$	0	0
$126$	1.05671e34	0.233260
$127$	4.97180e34i	0.963279i	0.876369	+	0.481640i	$0.159959\pi$
$127$	4.97180e34i	0.963279i	−0.876369	+	0.481640i	$0.840041\pi$
$128$	3.88040e34i	0.660560i
$129$	9.55430e34	1.43044
$130$	0	0
$131$	3.26112e34	0.378782	0.189391	−	0.981902i	$-0.439349\pi$
$131$	3.26112e34	0.378782	0.189391	+	0.981902i	$0.439349\pi$
$132$	1.05817e34i	0.108414i
$133$	7.14604e34i	0.646418i
$134$	−4.59271e34	−0.367147
$135$	0	0
$136$	1.53869e35	0.963296
$137$	4.83496e34i	0.268228i	0.990966	+	0.134114i	$0.0428188\pi$
$137$	4.83496e34i	0.268228i	−0.990966	+	0.134114i	$0.957181\pi$
$138$	9.42222e34i	0.463605i
$139$	1.61945e35	0.707334	0.353667	−	0.935371i	$-0.384935\pi$
$139$	1.61945e35	0.707334	0.353667	+	0.935371i	$0.384935\pi$
$140$	0	0
$141$	1.17433e34	0.0405204
$142$	− 2.01760e35i	− 0.619552i
$143$	− 4.51223e34i	− 0.123409i
$144$	6.49637e33	0.0158376
$145$	0	0
$146$	1.23378e35	0.239561
$147$	1.24878e35i	0.216645i
$148$	1.48747e35i	0.230744i
$149$	4.97369e35	0.690407	0.345204	−	0.938528i	$-0.387810\pi$
$149$	4.97369e35	0.690407	0.345204	+	0.938528i	$0.387810\pi$
$150$	0	0
$151$	1.20125e35	0.133818	0.0669090	−	0.997759i	$-0.478686\pi$
$151$	1.20125e35	0.133818	0.0669090	+	0.997759i	$0.478686\pi$
$152$	− 7.61841e35i	− 0.761106i
$153$	− 4.98232e35i	− 0.446707i
$154$	1.46944e35	0.118320
$155$	0	0
$156$	3.79864e35	0.247214
$157$	1.58453e36i	0.928018i	0.885830	+	0.464009i	$0.153590\pi$
$157$	1.58453e36i	0.928018i	−0.885830	+	0.464009i	$0.846410\pi$
$158$	− 2.19089e36i	− 1.15553i
$159$	1.07743e36	0.512081
$160$	0	0
$161$	−2.26038e36	−0.874086
$162$	− 5.74090e35i	− 0.200439i
$163$	− 3.31440e36i	− 1.04546i	−0.852497	−	0.522732i	$-0.824913\pi$
$163$	− 3.31440e36i	− 1.04546i	0.852497	−	0.522732i	$-0.175087\pi$
$164$	−3.95840e36	−1.12875
$165$	0	0
$166$	−2.79966e35	−0.0653615
$167$	− 7.73877e36i	− 1.63625i	−0.575039	−	0.818126i	$-0.695013\pi$
$167$	− 7.73877e36i	− 1.63625i	0.575039	−	0.818126i	$-0.304987\pi$
$168$	3.19018e36i	0.611240i
$169$	4.13633e36	0.718595
$170$	0	0
$171$	−2.46686e36	−0.352946
$172$	− 9.47543e36i	− 1.23135i
$173$	4.62098e36i	0.545725i	0.962053	+	0.272862i	$0.0879703\pi$
$173$	4.62098e36i	0.545725i	−0.962053	+	0.272862i	$0.912030\pi$
$174$	−3.57739e35	−0.0384153
$175$	0	0
$176$	9.03374e34	0.00803357
$177$	− 1.39515e37i	− 1.12996i
$178$	6.94855e36i	0.512819i
$179$	1.73851e37	1.16977	0.584886	−	0.811115i	$-0.301139\pi$
$179$	1.73851e37	1.16977	0.584886	+	0.811115i	$0.301139\pi$
$180$	0	0
$181$	−2.20579e37	−1.23557	−0.617785	−	0.786347i	$-0.711970\pi$
$181$	−2.20579e37	−1.23557	−0.617785	+	0.786347i	$0.711970\pi$
$182$	− 5.27500e36i	− 0.269802i
$183$	− 1.54442e37i	− 0.721641i
$184$	2.40979e37	1.02917
$185$	0	0
$186$	1.19840e36	0.0428192
$187$	− 6.92833e36i	− 0.226591i
$188$	− 1.16463e36i	− 0.0348807i
$189$	3.28532e37	0.901485
$190$	0	0
$191$	3.27319e37	0.754954	0.377477	−	0.926019i	$-0.376792\pi$
$191$	3.27319e37	0.754954	0.377477	+	0.926019i	$0.376792\pi$
$192$	− 2.00618e37i	− 0.424521i
$193$	− 8.15189e37i	− 1.58330i	−0.610976	−	0.791649i	$-0.709223\pi$
$193$	− 8.15189e37i	− 1.58330i	0.610976	−	0.791649i	$-0.290777\pi$
$194$	1.10652e37	0.197348
$195$	0	0
$196$	1.23847e37	0.186492
$197$	− 1.16510e38i	− 1.61313i	−0.591145	−	0.806565i	$-0.701324\pi$
$197$	− 1.16510e38i	− 1.61313i	0.591145	−	0.806565i	$-0.298676\pi$
$198$	5.07259e36i	0.0646032i
$199$	1.05328e38	1.23443	0.617216	−	0.786794i	$-0.288261\pi$
$199$	1.05328e38	1.23443	0.617216	+	0.786794i	$0.288261\pi$
$200$	0	0
$201$	−4.48962e37	−0.446144
$202$	− 1.10819e38i	− 1.01465i
$203$	− 8.58211e36i	− 0.0724285i
$204$	5.83265e37	0.453909
$205$	0	0
$206$	−3.12613e37	−0.207108
$207$	− 7.80296e37i	− 0.477253i
$208$	− 3.24294e36i	− 0.0183187i
$209$	−3.43037e37	−0.179031
$210$	0	0
$211$	3.80288e38	1.69610	0.848051	−	0.529915i	$-0.177776\pi$
$211$	3.80288e38	1.69610	0.848051	+	0.529915i	$0.177776\pi$
$212$	− 1.06854e38i	− 0.440808i
$213$	− 1.97232e38i	− 0.752858i
$214$	2.11401e38	0.746931
$215$	0	0
$216$	−3.50249e38	−1.06143
$217$	2.87495e37i	0.0807317i
$218$	− 4.06994e38i	− 1.05939i
$219$	1.20609e38	0.291106
$220$	0	0
$221$	−2.48714e38	−0.516687
$222$	− 8.41696e37i	− 0.162305i
$223$	4.60089e38i	0.823780i	0.911234	+	0.411890i	$0.135131\pi$
$223$	4.60089e38i	0.823780i	−0.911234	+	0.411890i	$0.864869\pi$
$224$	5.10085e38	0.848301
$225$	0	0
$226$	2.11212e37	0.0303340
$227$	− 1.13977e39i	− 1.52192i	−0.648801	−	0.760958i	$-0.724729\pi$
$227$	− 1.13977e39i	− 1.52192i	0.648801	−	0.760958i	$-0.275271\pi$
$228$	− 2.88788e38i	− 0.358636i
$229$	1.46028e39	1.68713	0.843566	−	0.537025i	$-0.180452\pi$
$229$	1.46028e39	1.68713	0.843566	+	0.537025i	$0.180452\pi$
$230$	0	0
$231$	1.43645e38	0.143779
$232$	9.14941e37i	0.0852789i
$233$	− 2.05161e37i	− 0.0178124i	−0.999960	−	0.00890620i	$-0.997165\pi$
$233$	− 2.05161e37i	− 0.0178124i	0.999960	−	0.00890620i	$-0.00283497\pi$
$234$	1.82096e38	0.147313
$235$	0	0
$236$	−1.38364e39	−0.972688
$237$	− 2.14172e39i	− 1.40415i
$238$	− 8.09954e38i	− 0.495382i
$239$	−9.20750e38	−0.525505	−0.262752	−	0.964863i	$-0.584630\pi$
$239$	−9.20750e38	−0.525505	−0.262752	+	0.964863i	$0.584630\pi$
$240$	0	0
$241$	1.79093e39	0.890834	0.445417	−	0.895323i	$-0.353056\pi$
$241$	1.79093e39	0.890834	0.445417	+	0.895323i	$0.353056\pi$
$242$	− 1.23283e39i	− 0.572728i
$243$	1.91164e39i	0.829663i
$244$	−1.53167e39	−0.621202
$245$	0	0
$246$	2.23989e39	0.793959
$247$	1.23144e39i	0.408238i
$248$	− 3.06499e38i	− 0.0950552i
$249$	−2.73682e38	−0.0794250
$250$	0	0
$251$	−4.16615e39	−1.05954	−0.529772	−	0.848140i	$-0.677723\pi$
$251$	−4.16615e39	−1.05954	−0.529772	+	0.848140i	$0.677723\pi$
$252$	− 1.02446e39i	− 0.243998i
$253$	− 1.08507e39i	− 0.242085i
$254$	−2.79011e39	−0.583264
$255$	0	0
$256$	−5.31894e39	−0.976936
$257$	1.03274e40i	1.77867i	0.457254	+	0.889336i	$0.348833\pi$
$257$	1.03274e40i	1.77867i	−0.457254	+	0.889336i	$0.651167\pi$
$258$	5.36175e39i	0.866126i
$259$	2.01922e39	0.306011
$260$	0	0
$261$	2.96260e38	0.0395462
$262$	1.83010e39i	0.229352i
$263$	− 7.85107e39i	− 0.923972i	−0.886887	−	0.461986i	$-0.847137\pi$
$263$	− 7.85107e39i	− 0.923972i	0.886887	−	0.461986i	$-0.152863\pi$
$264$	−1.53141e39	−0.169288
$265$	0	0
$266$	−4.01027e39	−0.391405
$267$	6.79258e39i	0.623159i
$268$	4.45257e39i	0.384049i
$269$	−1.76099e40	−1.42838	−0.714189	−	0.699953i	$-0.753204\pi$
$269$	−1.76099e40	−1.42838	−0.714189	+	0.699953i	$0.753204\pi$
$270$	0	0
$271$	1.63883e40	1.17636	0.588179	−	0.808730i	$-0.299845\pi$
$271$	1.63883e40	1.17636	0.588179	+	0.808730i	$0.299845\pi$
$272$	− 4.97940e38i	− 0.0336349i
$273$	− 5.15660e39i	− 0.327853i
$274$	−2.71332e39	−0.162411
$275$	0	0
$276$	9.13470e39	0.484947
$277$	3.39112e40i	1.69601i	0.529991	+	0.848003i	$0.322195\pi$
$277$	3.39112e40i	1.69601i	−0.529991	+	0.848003i	$0.677805\pi$
$278$	9.08817e39i	0.428289i
$279$	−9.92449e38	−0.0440797
$280$	0	0
$281$	3.38855e40	1.33770	0.668851	−	0.743396i	$-0.266786\pi$
$281$	3.38855e40	1.33770	0.668851	+	0.743396i	$0.266786\pi$
$282$	6.59017e38i	0.0245350i
$283$	2.32437e40i	0.816263i	0.912923	+	0.408131i	$0.133819\pi$
$283$	2.32437e40i	0.816263i	−0.912923	+	0.408131i	$0.866181\pi$
$284$	−1.95604e40	−0.648074
$285$	0	0
$286$	2.53220e39	0.0747238
$287$	5.37347e40i	1.49694i
$288$	1.76084e40i	0.463175i
$289$	2.06553e39	0.0513118
$290$	0	0
$291$	1.08169e40	0.239810
$292$	− 1.19613e40i	− 0.250589i
$293$	3.19376e40i	0.632393i	0.948694	+	0.316197i	$0.102406\pi$
$293$	3.19376e40i	0.632393i	−0.948694	+	0.316197i	$0.897594\pi$
$294$	−7.00797e39	−0.131178
$295$	0	0
$296$	−2.15269e40	−0.360303
$297$	1.57708e40i	0.249674i
$298$	2.79117e40i	0.418040i
$299$	−3.89519e40	−0.552019
$300$	0	0
$301$	−1.28628e41	−1.63300
$302$	6.74127e39i	0.0810265i
$303$	− 1.08332e41i	− 1.23297i
$304$	−2.46541e39	−0.0265751
$305$	0	0
$306$	2.79601e40	0.270480
$307$	9.23782e40i	0.846810i	0.905940	+	0.423405i	$0.139165\pi$
$307$	9.23782e40i	0.846810i	−0.905940	+	0.423405i	$0.860835\pi$
$308$	− 1.42460e40i	− 0.123767i
$309$	−3.05596e40	−0.251670
$310$	0	0
$311$	2.21387e40	0.163910	0.0819550	−	0.996636i	$-0.473884\pi$
$311$	2.21387e40	0.163910	0.0819550	+	0.996636i	$0.473884\pi$
$312$	5.49746e40i	0.386022i
$313$	2.73315e40i	0.182046i	0.995849	+	0.0910231i	$0.0290137\pi$
$313$	2.73315e40i	0.182046i	−0.995849	+	0.0910231i	$0.970986\pi$
$314$	−8.89219e40	−0.561913
$315$	0	0
$316$	−2.12404e41	−1.20872
$317$	− 2.26706e41i	− 1.22457i	−0.790636	−	0.612286i	$-0.790250\pi$
$317$	− 2.26706e41i	− 1.22457i	0.790636	−	0.612286i	$-0.209750\pi$
$318$	6.04642e40i	0.310064i
$319$	4.11974e39	0.0200597
$320$	0	0
$321$	2.06656e41	0.907644
$322$	− 1.26849e41i	− 0.529257i
$323$	1.89082e41i	0.749565i
$324$	−5.56572e40	−0.209666
$325$	0	0
$326$	1.86000e41	0.633027
$327$	− 3.97859e41i	− 1.28733i
$328$	− 5.72867e41i	− 1.76253i
$329$	−1.58097e40	−0.0462586
$330$	0	0
$331$	−2.06805e41	−0.547520	−0.273760	−	0.961798i	$-0.588267\pi$
$331$	−2.06805e41	−0.547520	−0.273760	+	0.961798i	$0.588267\pi$
$332$	2.71423e40i	0.0683705i
$333$	6.97046e40i	0.167083i
$334$	4.34290e41	0.990747
$335$	0	0
$336$	1.03238e40	0.0213423
$337$	− 5.63835e40i	− 0.110984i	−0.998459	−	0.0554918i	$-0.982327\pi$
$337$	− 5.63835e40i	− 0.110984i	0.998459	−	0.0554918i	$-0.0176727\pi$
$338$	2.32125e41i	0.435108i
$339$	2.06471e40	0.0368608
$340$	0	0
$341$	−1.38008e40	−0.0223593
$342$	− 1.38437e41i	− 0.213708i
$343$	− 7.39098e41i	− 1.08730i
$344$	1.37130e42	1.92273
$345$	0	0
$346$	−2.59323e41	−0.330435
$347$	− 2.54567e41i	− 0.309289i	−0.987970	−	0.154645i	$-0.950577\pi$
$347$	− 2.54567e41i	− 0.309289i	0.987970	−	0.154645i	$-0.0494233\pi$
$348$	3.46823e40i	0.0401837i
$349$	1.42434e42	1.57397	0.786983	−	0.616974i	$-0.211642\pi$
$349$	1.42434e42	1.57397	0.786983	+	0.616974i	$0.211642\pi$
$350$	0	0
$351$	5.66143e41	0.569323
$352$	2.44860e41i	0.234944i
$353$	4.58433e41i	0.419752i	0.977728	+	0.209876i	$0.0673061\pi$
$353$	4.58433e41i	0.419752i	−0.977728	+	0.209876i	$0.932694\pi$
$354$	7.82941e41	0.684187
$355$	0	0
$356$	6.73651e41	0.536427
$357$	− 7.91774e41i	− 0.601971i
$358$	9.75628e41i	0.708295i
$359$	−1.13078e42	−0.784004	−0.392002	−	0.919964i	$-0.628217\pi$
$359$	−1.13078e42	−0.784004	−0.392002	+	0.919964i	$0.628217\pi$
$360$	0	0
$361$	−6.44582e41	−0.407764
$362$	− 1.23786e42i	− 0.748135i
$363$	− 1.20516e42i	− 0.695959i
$364$	−5.11404e41	−0.282222
$365$	0	0
$366$	8.66707e41	0.436952
$367$	− 1.40753e42i	− 0.678369i	−0.940720	−	0.339185i	$-0.889849\pi$
$367$	− 1.40753e42i	− 0.678369i	0.940720	−	0.339185i	$-0.110151\pi$
$368$	− 7.79840e40i	− 0.0359349i
$369$	−1.85496e42	−0.817332
$370$	0	0
$371$	−1.45053e42	−0.584597
$372$	− 1.16183e41i	− 0.0447904i
$373$	− 4.43848e42i	− 1.63696i	−0.574535	−	0.818480i	$-0.694817\pi$
$373$	− 4.43848e42i	− 1.63696i	0.574535	−	0.818480i	$-0.305183\pi$
$374$	3.88809e41	0.137200
$375$	0	0
$376$	1.68548e41	0.0544658
$377$	− 1.47891e41i	− 0.0457414i
$378$	1.84368e42i	0.545847i
$379$	1.41996e42	0.402466	0.201233	−	0.979543i	$-0.435505\pi$
$379$	1.41996e42	0.402466	0.201233	+	0.979543i	$0.435505\pi$
$380$	0	0
$381$	−2.72748e42	−0.708761
$382$	1.83687e42i	0.457123i
$383$	1.04448e40i	0.00248955i	0.999999	+	0.00124478i	$0.000396224\pi$
$383$	1.04448e40i	0.00248955i	−0.999999	+	0.00124478i	$0.999604\pi$
$384$	−2.12875e42	−0.486027
$385$	0	0
$386$	4.57473e42	0.958684
$387$	− 4.44030e42i	− 0.891624i
$388$	− 1.07276e42i	− 0.206433i
$389$	−3.78074e41	−0.0697282	−0.0348641	−	0.999392i	$-0.511100\pi$
$389$	−3.78074e41	−0.0697282	−0.0348641	+	0.999392i	$0.511100\pi$
$390$	0	0
$391$	−5.98090e42	−1.01356
$392$	1.79233e42i	0.291205i
$393$	1.78902e42i	0.278700i
$394$	6.53838e42	0.976747
$395$	0	0
$396$	4.91780e41	0.0675772
$397$	1.40626e43i	1.85363i	0.375519	+	0.926815i	$0.377464\pi$
$397$	1.40626e43i	1.85363i	−0.375519	+	0.926815i	$0.622536\pi$
$398$	5.91086e42i	0.747446i
$399$	−3.92025e42	−0.475621
$400$	0	0
$401$	−3.90184e42	−0.435900	−0.217950	−	0.975960i	$-0.569937\pi$
$401$	−3.90184e42	−0.435900	−0.217950	+	0.975960i	$0.569937\pi$
$402$	− 2.51952e42i	− 0.270139i
$403$	4.95424e41i	0.0509852i
$404$	−1.07437e43	−1.06136
$405$	0	0
$406$	4.81617e41	0.0438553
$407$	9.69301e41i	0.0847522i
$408$	8.44112e42i	0.708773i
$409$	−1.05489e43	−0.850694	−0.425347	−	0.905030i	$-0.639848\pi$
$409$	−1.05489e43	−0.850694	−0.425347	+	0.905030i	$0.639848\pi$
$410$	0	0
$411$	−2.65242e42	−0.197357
$412$	3.03073e42i	0.216642i
$413$	1.87826e43i	1.28997i
$414$	4.37892e42	0.288976
$415$	0	0
$416$	8.79002e42	0.535735
$417$	8.88418e42i	0.520442i
$418$	− 1.92508e42i	− 0.108403i
$419$	−2.64714e43	−1.43300	−0.716498	−	0.697589i	$-0.754256\pi$
$419$	−2.64714e43	−1.43300	−0.716498	+	0.697589i	$0.754256\pi$
$420$	0	0
$421$	2.92799e43	1.46526	0.732630	−	0.680627i	$-0.238293\pi$
$421$	2.92799e43	1.46526	0.732630	+	0.680627i	$0.238293\pi$
$422$	2.13413e43i	1.02699i
$423$	− 5.45762e41i	− 0.0252573i
$424$	1.54641e43	0.688317
$425$	0	0
$426$	1.10684e43	0.455854
$427$	2.07922e43i	0.823834i
$428$	− 2.04951e43i	− 0.781316i
$429$	2.47537e42	0.0908017
$430$	0	0
$431$	7.41005e42	0.251736	0.125868	−	0.992047i	$-0.459828\pi$
$431$	7.41005e42	0.251736	0.125868	+	0.992047i	$0.459828\pi$
$432$	1.13345e42i	0.0370613i
$433$	− 2.63001e43i	− 0.827766i	−0.910330	−	0.413883i	$-0.864172\pi$
$433$	− 2.63001e43i	− 0.827766i	0.910330	−	0.413883i	$-0.135828\pi$
$434$	−1.61338e42	−0.0488829
$435$	0	0
$436$	−3.94575e43	−1.10816
$437$	2.96128e43i	0.800821i
$438$	6.76840e42i	0.176264i
$439$	−1.79135e43	−0.449278	−0.224639	−	0.974442i	$-0.572120\pi$
$439$	−1.79135e43	−0.449278	−0.224639	+	0.974442i	$0.572120\pi$
$440$	0	0
$441$	5.80362e42	0.135040
$442$	− 1.39575e43i	− 0.312853i
$443$	− 3.40634e43i	− 0.735575i	−0.929910	−	0.367788i	$-0.880115\pi$
$443$	− 3.40634e43i	− 0.735575i	0.929910	−	0.367788i	$-0.119885\pi$
$444$	−8.16011e42	−0.169776
$445$	0	0
$446$	−2.58196e43	−0.498797
$447$	2.72852e43i	0.507988i
$448$	2.70088e43i	0.484638i
$449$	−8.25218e43	−1.42726	−0.713632	−	0.700521i	$-0.752951\pi$
$449$	−8.25218e43	−1.42726	−0.713632	+	0.700521i	$0.752951\pi$
$450$	0	0
$451$	−2.57947e43	−0.414589
$452$	− 2.04767e42i	− 0.0317304i
$453$	6.58996e42i	0.0984605i
$454$	6.39625e43	0.921517
$455$	0	0
$456$	4.17939e43	0.560006
$457$	− 1.09927e44i	− 1.42065i	−0.703876	−	0.710323i	$-0.748549\pi$
$457$	− 1.09927e44i	− 1.42065i	0.703876	−	0.710323i	$-0.251451\pi$
$458$	8.19488e43i	1.02156i
$459$	8.69288e43	1.04533
$460$	0	0
$461$	5.08918e43	0.569616	0.284808	−	0.958585i	$-0.408070\pi$
$461$	5.08918e43	0.569616	0.284808	+	0.958585i	$0.408070\pi$
$462$	8.06120e42i	0.0870576i
$463$	5.67339e43i	0.591229i	0.955307	+	0.295615i	$0.0955245\pi$
$463$	5.67339e43i	0.591229i	−0.955307	+	0.295615i	$0.904476\pi$
$464$	2.96086e41	0.00297764
$465$	0	0
$466$	1.15134e42	0.0107854
$467$	− 8.56548e43i	− 0.774503i	−0.921974	−	0.387251i	$-0.873425\pi$
$467$	− 8.56548e43i	− 0.774503i	0.921974	−	0.387251i	$-0.126575\pi$
$468$	− 1.76540e43i	− 0.154094i
$469$	6.04429e43	0.509323
$470$	0	0
$471$	−8.69259e43	−0.682817
$472$	− 2.00242e44i	− 1.51884i
$473$	− 6.17462e43i	− 0.452273i
$474$	1.20190e44	0.850212
$475$	0	0
$476$	−7.85239e43	−0.518187
$477$	− 5.00732e43i	− 0.319192i
$478$	− 5.16713e43i	− 0.318192i
$479$	1.29441e44	0.770079	0.385040	−	0.922900i	$-0.374188\pi$
$479$	1.29441e44	0.770079	0.385040	+	0.922900i	$0.374188\pi$
$480$	0	0
$481$	3.47961e43	0.193258
$482$	1.00504e44i	0.539398i
$483$	− 1.24002e44i	− 0.643134i
$484$	−1.19521e44	−0.599094
$485$	0	0
$486$	−1.07279e44	−0.502359
$487$	− 2.61068e44i	− 1.18175i	−0.806762	−	0.590876i	$-0.798782\pi$
$487$	− 2.61068e44i	− 1.18175i	0.806762	−	0.590876i	$-0.201218\pi$
$488$	− 2.21666e44i	− 0.970000i
$489$	1.81825e44	0.769231
$490$	0	0
$491$	−1.66397e44	−0.658114	−0.329057	−	0.944310i	$-0.606731\pi$
$491$	−1.66397e44	−0.658114	−0.329057	+	0.944310i	$0.606731\pi$
$492$	− 2.17154e44i	− 0.830509i
$493$	− 2.27080e43i	− 0.0839857i
$494$	−6.91068e43	−0.247187
$495$	0	0
$496$	−9.91868e41	−0.00331899
$497$	2.65529e44i	0.859472i
$498$	− 1.53587e43i	− 0.0480917i
$499$	−6.52589e43	−0.197688	−0.0988441	−	0.995103i	$-0.531515\pi$
$499$	−6.52589e43	−0.197688	−0.0988441	+	0.995103i	$0.531515\pi$
$500$	0	0
$501$	4.24542e44	1.20392
$502$	− 2.33799e44i	− 0.641552i
$503$	− 1.10537e43i	− 0.0293519i	−0.999892	−	0.0146759i	$-0.995328\pi$
$503$	− 1.10537e43i	− 0.0293519i	0.999892	−	0.0146759i	$-0.00467167\pi$
$504$	1.48262e44	0.381000
$505$	0	0
$506$	6.08926e43	0.146582
$507$	2.26915e44i	0.528727i
$508$	2.70497e44i	0.610114i
$509$	4.80472e44	1.04912	0.524559	−	0.851374i	$-0.324230\pi$
$509$	4.80472e44	1.04912	0.524559	+	0.851374i	$0.324230\pi$
$510$	0	0
$511$	−1.62373e44	−0.332329
$512$	3.48319e43i	0.0690276i
$513$	− 4.30404e44i	− 0.825923i
$514$	−5.79562e44	−1.07698
$515$	0	0
$516$	5.19814e44	0.905999
$517$	− 7.58928e42i	− 0.0128117i
$518$	1.13316e44i	0.185289i
$519$	−2.53503e44	−0.401533
$520$	0	0
$521$	−2.39684e44	−0.356301	−0.178150	−	0.984003i	$-0.557011\pi$
$521$	−2.39684e44	−0.356301	−0.178150	+	0.984003i	$0.557011\pi$
$522$	1.66257e43i	0.0239451i
$523$	7.19573e44i	1.00415i	0.864825	+	0.502073i	$0.167429\pi$
$523$	7.19573e44i	1.00415i	−0.864825	+	0.502073i	$0.832571\pi$
$524$	1.77425e44	0.239910
$525$	0	0
$526$	4.40592e44	0.559463
$527$	7.60702e43i	0.0936138i
$528$	4.95583e42i	0.00591094i
$529$	−7.16821e43	−0.0828690
$530$	0	0
$531$	−6.48388e44	−0.704329
$532$	3.88789e44i	0.409423i
$533$	9.25982e44i	0.945374i
$534$	−3.81191e44	−0.377322
$535$	0	0
$536$	−6.44383e44	−0.599688
$537$	9.53729e44i	0.860695i
$538$	− 9.88243e44i	− 0.864880i
$539$	8.07041e43	0.0684985
$540$	0	0
$541$	8.82482e44	0.704613	0.352307	−	0.935885i	$-0.385397\pi$
$541$	8.82482e44	0.704613	0.352307	+	0.935885i	$0.385397\pi$
$542$	9.19689e44i	0.712283i
$543$	− 1.21007e45i	− 0.909107i
$544$	1.34967e45	0.983662
$545$	0	0
$546$	2.89382e44	0.198515
$547$	5.81429e44i	0.386996i	0.981101	+	0.193498i	$0.0619832\pi$
$547$	5.81429e44i	0.386996i	−0.981101	+	0.193498i	$0.938017\pi$
$548$	2.63052e44i	0.169888i
$549$	−7.17759e44	−0.449816
$550$	0	0
$551$	−1.12433e44	−0.0663576
$552$	1.32199e45i	0.757240i
$553$	2.88335e45i	1.60300i
$554$	−1.90306e45	−1.02693
$555$	0	0
$556$	8.81085e44	0.448006
$557$	− 2.61541e45i	− 1.29101i	−0.763757	−	0.645504i	$-0.776647\pi$
$557$	− 2.61541e45i	− 1.29101i	0.763757	−	0.645504i	$-0.223353\pi$
$558$	− 5.56950e43i	− 0.0266902i
$559$	−2.21657e45	−1.03130
$560$	0	0
$561$	3.80082e44	0.166721
$562$	1.90161e45i	0.809976i
$563$	1.43034e45i	0.591632i	0.955245	+	0.295816i	$0.0955915\pi$
$563$	1.43034e45i	0.591632i	−0.955245	+	0.295816i	$0.904408\pi$
$564$	6.38908e43	0.0256645
$565$	0	0
$566$	−1.30441e45	−0.494245
$567$	7.55537e44i	0.278058i
$568$	− 2.83081e45i	− 1.01196i
$569$	−5.30235e45	−1.84127	−0.920633	−	0.390430i	$-0.872326\pi$
$569$	−5.30235e45	−1.84127	−0.920633	+	0.390430i	$0.872326\pi$
$570$	0	0
$571$	−3.41063e45	−1.11774	−0.558868	−	0.829257i	$-0.688764\pi$
$571$	−3.41063e45	−1.11774	−0.558868	+	0.829257i	$0.688764\pi$
$572$	− 2.45493e44i	− 0.0781637i
$573$	1.79564e45i	0.555480i
$574$	−3.01552e45	−0.906393
$575$	0	0
$576$	−9.32360e44	−0.264614
$577$	− 2.80984e45i	− 0.774962i	−0.921878	−	0.387481i	$-0.873345\pi$
$577$	− 2.80984e45i	− 0.774962i	0.921878	−	0.387481i	$-0.126655\pi$
$578$	1.15915e44i	0.0310692i
$579$	4.47205e45	1.16496
$580$	0	0
$581$	3.68453e44	0.0906725
$582$	6.07028e44i	0.145204i
$583$	− 6.96309e44i	− 0.161909i
$584$	1.73106e45	0.391292
$585$	0	0
$586$	−1.79230e45	−0.382913
$587$	5.96514e45i	1.23906i	0.784973	+	0.619529i	$0.212677\pi$
$587$	5.96514e45i	1.23906i	−0.784973	+	0.619529i	$0.787323\pi$
$588$	6.79412e44i	0.137217i
$589$	3.76641e44	0.0739648
$590$	0	0
$591$	6.39162e45	1.18691
$592$	6.96638e43i	0.0125805i
$593$	− 1.29305e45i	− 0.227099i	−0.993532	−	0.113549i	$-0.963778\pi$
$593$	− 1.29305e45i	− 0.227099i	0.993532	−	0.113549i	$-0.0362220\pi$
$594$	−8.85038e44	−0.151177
$595$	0	0
$596$	2.70600e45	0.437285
$597$	5.77818e45i	0.908270i
$598$	− 2.18593e45i	− 0.334246i
$599$	1.23551e46	1.83782	0.918910	−	0.394467i	$-0.129071\pi$
$599$	1.23551e46	1.83782	0.918910	+	0.394467i	$0.129071\pi$
$600$	0	0
$601$	−4.92073e45	−0.692788	−0.346394	−	0.938089i	$-0.612594\pi$
$601$	−4.92073e45	−0.692788	−0.346394	+	0.938089i	$0.612594\pi$
$602$	− 7.21841e45i	− 0.988780i
$603$	2.08653e45i	0.278092i
$604$	6.53556e44	0.0847566
$605$	0	0
$606$	6.07943e45	0.746559
$607$	− 2.23242e45i	− 0.266786i	−0.991063	−	0.133393i	$-0.957413\pi$
$607$	− 2.23242e45i	− 0.266786i	0.991063	−	0.133393i	$-0.0425872\pi$
$608$	− 6.68252e45i	− 0.777197i
$609$	4.70807e44	0.0532914
$610$	0	0
$611$	−2.72441e44	−0.0292141
$612$	− 2.71069e45i	− 0.282932i
$613$	1.28306e45i	0.130362i	0.997873	+	0.0651808i	$0.0207624\pi$
$613$	1.28306e45i	0.130362i	−0.997873	+	0.0651808i	$0.979238\pi$
$614$	−5.18414e45	−0.512742
$615$	0	0
$616$	2.06170e45	0.193261
$617$	− 1.81527e46i	− 1.65667i	−0.560235	−	0.828333i	$-0.689289\pi$
$617$	− 1.81527e46i	− 1.65667i	0.560235	−	0.828333i	$-0.310711\pi$
$618$	− 1.71496e45i	− 0.152386i
$619$	1.88787e46	1.63334	0.816670	−	0.577104i	$-0.195817\pi$
$619$	1.88787e46	1.63334	0.816670	+	0.577104i	$0.195817\pi$
$620$	0	0
$621$	1.36142e46	1.11681
$622$	1.24239e45i	0.0992472i
$623$	− 9.14471e45i	− 0.711406i
$624$	1.77905e44	0.0134785
$625$	0	0
$626$	−1.53381e45	−0.110229
$627$	− 1.88187e45i	− 0.131727i
$628$	8.62084e45i	0.587781i
$629$	5.34279e45	0.354840
$630$	0	0
$631$	−1.84920e46	−1.16547	−0.582733	−	0.812664i	$-0.698017\pi$
$631$	−1.84920e46	−1.16547	−0.582733	+	0.812664i	$0.698017\pi$
$632$	− 3.07395e46i	− 1.88740i
$633$	2.08622e46i	1.24796i
$634$	1.27224e46	0.741476
$635$	0	0
$636$	5.86192e45	0.324338
$637$	− 2.89713e45i	− 0.156195i
$638$	2.31195e44i	0.0121461i
$639$	−9.16623e45	−0.469274
$640$	0	0
$641$	−2.03686e46	−0.990382	−0.495191	−	0.868784i	$-0.664902\pi$
$641$	−2.03686e46	−0.990382	−0.495191	+	0.868784i	$0.664902\pi$
$642$	1.15973e46i	0.549577i
$643$	− 3.33285e46i	− 1.53934i	−0.638440	−	0.769671i	$-0.720420\pi$
$643$	− 3.33285e46i	− 1.53934i	0.638440	−	0.769671i	$-0.279580\pi$
$644$	−1.22979e46	−0.553622
$645$	0	0
$646$	−1.06110e46	−0.453860
$647$	2.86276e46i	1.19361i	0.802385	+	0.596807i	$0.203564\pi$
$647$	2.86276e46i	1.19361i	−0.802385	+	0.596807i	$0.796436\pi$
$648$	− 8.05480e45i	− 0.327391i
$649$	−9.01638e45	−0.357269
$650$	0	0
$651$	−1.57717e45	−0.0594007
$652$	− 1.80324e46i	− 0.662168i
$653$	− 4.94384e43i	− 0.00177010i	−1.00000		0.000885048i	$-0.999718\pi$
$653$	− 4.94384e43i	− 0.00177010i	1.00000		0.000885048i	$-0.000281720\pi$
$654$	2.23273e46	0.779478
$655$	0	0
$656$	−1.85387e45	−0.0615412
$657$	− 5.60522e45i	− 0.181453i
$658$	− 8.87222e44i	− 0.0280095i
$659$	−3.69093e45	−0.113639	−0.0568194	−	0.998384i	$-0.518096\pi$
$659$	−3.69093e45	−0.113639	−0.0568194	+	0.998384i	$0.518096\pi$
$660$	0	0
$661$	−1.92860e46	−0.564830	−0.282415	−	0.959292i	$-0.591136\pi$
$661$	−1.92860e46	−0.564830	−0.282415	+	0.959292i	$0.591136\pi$
$662$	− 1.16056e46i	− 0.331522i
$663$	− 1.36442e46i	− 0.380168i
$664$	−3.92808e45	−0.106760
$665$	0	0
$666$	−3.91173e45	−0.101168
$667$	− 3.55638e45i	− 0.0897287i
$668$	− 4.21037e46i	− 1.03636i
$669$	−2.52400e46	−0.606120
$670$	0	0
$671$	−9.98104e45	−0.228168
$672$	2.79828e46i	0.624163i
$673$	6.71207e46i	1.46086i	0.682989	+	0.730428i	$0.260680\pi$
$673$	6.71207e46i	1.46086i	−0.682989	+	0.730428i	$0.739320\pi$
$674$	3.16417e45	0.0672003
$675$	0	0
$676$	2.25042e46	0.455138
$677$	− 6.40029e46i	− 1.26324i	−0.775278	−	0.631621i	$-0.782390\pi$
$677$	− 6.40029e46i	− 1.26324i	0.775278	−	0.631621i	$-0.217610\pi$
$678$	1.15869e45i	0.0223191i
$679$	−1.45625e46	−0.273770
$680$	0	0
$681$	6.25268e46	1.11980
$682$	− 7.74485e44i	− 0.0135385i
$683$	8.73990e46i	1.49130i	0.666338	+	0.745650i	$0.267861\pi$
$683$	8.73990e46i	1.49130i	−0.666338	+	0.745650i	$0.732139\pi$
$684$	−1.34212e46	−0.223546
$685$	0	0
$686$	4.14772e46	0.658357
$687$	8.01093e46i	1.24136i
$688$	− 4.43770e45i	− 0.0671350i
$689$	−2.49962e46	−0.369196
$690$	0	0
$691$	4.89363e46	0.689039	0.344519	−	0.938779i	$-0.388042\pi$
$691$	4.89363e46	0.689039	0.344519	+	0.938779i	$0.388042\pi$
$692$	2.51410e46i	0.345647i
$693$	− 6.67584e45i	− 0.0896205i
$694$	1.42859e46	0.187274
$695$	0	0
$696$	−5.01928e45	−0.0627464
$697$	1.42181e47i	1.73580i
$698$	7.99324e46i	0.953034i
$699$	1.12550e45	0.0131060
$700$	0	0
$701$	−3.51093e46	−0.390009	−0.195004	−	0.980802i	$-0.562472\pi$
$701$	−3.51093e46	−0.390009	−0.195004	+	0.980802i	$0.562472\pi$
$702$	3.17712e46i	0.344724i
$703$	− 2.64533e46i	− 0.280361i
$704$	−1.29652e46	−0.134225
$705$	0	0
$706$	−2.57267e46	−0.254159
$707$	1.45845e47i	1.40757i
$708$	− 7.59049e46i	− 0.715684i
$709$	−9.47916e46	−0.873187	−0.436593	−	0.899659i	$-0.643815\pi$
$709$	−9.47916e46	−0.873187	−0.436593	+	0.899659i	$0.643815\pi$
$710$	0	0
$711$	−9.95351e46	−0.875241
$712$	9.74920e46i	0.837624i
$713$	1.19136e46i	0.100015i
$714$	4.44333e46	0.364492
$715$	0	0
$716$	9.45857e46	0.740901
$717$	− 5.05115e46i	− 0.386656i
$718$	− 6.34577e46i	− 0.474713i
$719$	1.57057e46	0.114823	0.0574116	−	0.998351i	$-0.481715\pi$
$719$	1.57057e46	0.114823	0.0574116	+	0.998351i	$0.481715\pi$
$720$	0	0
$721$	4.11417e46	0.287310
$722$	− 3.61731e46i	− 0.246900i
$723$	9.82486e46i	0.655457i
$724$	−1.20009e47	−0.782576
$725$	0	0
$726$	6.76317e46	0.421402
$727$	− 5.94494e46i	− 0.362101i	−0.983474	−	0.181051i	$-0.942050\pi$
$727$	− 5.94494e46i	− 0.362101i	0.983474	−	0.181051i	$-0.0579498\pi$
$728$	− 7.40112e46i	− 0.440687i
$729$	−1.61739e47	−0.941480
$730$	0	0
$731$	−3.40345e47	−1.89358
$732$	− 8.40259e46i	− 0.457068i
$733$	2.58199e47i	1.37322i	0.727028	+	0.686608i	$0.240901\pi$
$733$	2.58199e47i	1.37322i	−0.727028	+	0.686608i	$0.759099\pi$
$734$	7.89885e46	0.410751
$735$	0	0
$736$	2.11376e47	1.05093
$737$	2.90149e46i	0.141061i
$738$	− 1.04098e47i	− 0.494893i
$739$	1.03631e47	0.481790	0.240895	−	0.970551i	$-0.422559\pi$
$739$	1.03631e47	0.481790	0.240895	+	0.970551i	$0.422559\pi$
$740$	0	0
$741$	−6.75556e46	−0.300373
$742$	− 8.14018e46i	− 0.353973i
$743$	− 2.33354e47i	− 0.992428i	−0.868200	−	0.496214i	$-0.834723\pi$
$743$	− 2.33354e47i	− 0.992428i	0.868200	−	0.496214i	$-0.165277\pi$
$744$	1.68142e46	0.0699397
$745$	0	0
$746$	2.49081e47	0.991176
$747$	1.27192e46i	0.0495075i
$748$	− 3.76945e46i	− 0.143516i
$749$	−2.78217e47	−1.03618
$750$	0	0
$751$	−1.20809e47	−0.430568	−0.215284	−	0.976552i	$-0.569068\pi$
$751$	−1.20809e47	−0.430568	−0.215284	+	0.976552i	$0.569068\pi$
$752$	− 5.45442e44i	− 0.00190175i
$753$	− 2.28551e47i	− 0.779591i
$754$	8.29945e45	0.0276963
$755$	0	0
$756$	1.78742e47	0.570976
$757$	− 5.96569e47i	− 1.86457i	−0.361724	−	0.932285i	$-0.617812\pi$
$757$	− 5.96569e47i	− 1.86457i	0.361724	−	0.932285i	$-0.382188\pi$
$758$	7.96864e46i	0.243693i
$759$	5.95258e46	0.178121
$760$	0	0
$761$	−3.41953e47	−0.979760	−0.489880	−	0.871790i	$-0.662959\pi$
$761$	−3.41953e47	−0.979760	−0.489880	+	0.871790i	$0.662959\pi$
$762$	− 1.53063e47i	− 0.429153i
$763$	5.35630e47i	1.46964i
$764$	1.78082e47	0.478167
$765$	0	0
$766$	−5.86149e44	−0.00150742
$767$	3.23671e47i	0.814668i
$768$	− 2.91792e47i	− 0.718809i
$769$	7.47483e47	1.80226	0.901129	−	0.433551i	$-0.142740\pi$
$769$	7.47483e47	1.80226	0.901129	+	0.433551i	$0.142740\pi$
$770$	0	0
$771$	−5.66554e47	−1.30871
$772$	− 4.43514e47i	− 1.00282i
$773$	1.39866e47i	0.309565i	0.987949	+	0.154782i	$0.0494676\pi$
$773$	1.39866e47i	0.309565i	−0.987949	+	0.154782i	$0.950532\pi$
$774$	2.49184e47	0.539877
$775$	0	0
$776$	1.55251e47	0.322342
$777$	1.10772e47i	0.225156i
$778$	− 2.12170e46i	− 0.0422203i
$779$	7.03968e47	1.37147
$780$	0	0
$781$	−1.27464e47	−0.238038
$782$	− 3.35640e47i	− 0.613709i
$783$	5.16898e46i	0.0925414i
$784$	5.80022e45	0.0101679
$785$	0	0
$786$	−1.00397e47	−0.168753
$787$	− 6.12282e47i	− 1.00779i	−0.863766	−	0.503893i	$-0.831901\pi$
$787$	− 6.12282e47i	− 1.00779i	0.863766	−	0.503893i	$-0.168099\pi$
$788$	− 6.33886e47i	− 1.02171i
$789$	4.30702e47	0.679840
$790$	0	0
$791$	−2.77968e46	−0.0420807
$792$	7.11713e46i	0.105521i
$793$	3.58300e47i	0.520283i
$794$	−7.89176e47	−1.12237
$795$	0	0
$796$	5.73049e47	0.781855
$797$	7.29365e47i	0.974726i	0.873199	+	0.487363i	$0.162041\pi$
$797$	7.29365e47i	0.974726i	−0.873199	+	0.487363i	$0.837959\pi$
$798$	− 2.19999e47i	− 0.287988i
$799$	−4.18321e46	−0.0536399
$800$	0	0
$801$	3.15681e47	0.388430
$802$	− 2.18966e47i	− 0.263937i
$803$	− 7.79452e46i	− 0.0920414i
$804$	−2.44264e47	−0.282575
$805$	0	0
$806$	−2.78026e46	−0.0308714
$807$	− 9.66061e47i	− 1.05097i
$808$	− 1.55485e48i	− 1.65730i
$809$	−4.30397e47	−0.449489	−0.224744	−	0.974418i	$-0.572155\pi$
$809$	−4.30397e47	−0.449489	−0.224744	+	0.974418i	$0.572155\pi$
$810$	0	0
$811$	1.20340e48	1.20660	0.603302	−	0.797513i	$-0.293851\pi$
$811$	1.20340e48	1.20660	0.603302	+	0.797513i	$0.293851\pi$
$812$	− 4.66921e46i	− 0.0458742i
$813$	8.99045e47i	0.865541i
$814$	−5.43959e46	−0.0513173
$815$	0	0
$816$	2.73165e46	0.0247479
$817$	1.68512e48i	1.49613i
$818$	− 5.91992e47i	− 0.515094i
$819$	−2.39650e47	−0.204359
$820$	0	0
$821$	1.31428e48	1.07653	0.538264	−	0.842776i	$-0.319080\pi$
$821$	1.31428e48	1.07653	0.538264	+	0.842776i	$0.319080\pi$
$822$	− 1.48850e47i	− 0.119499i
$823$	1.85531e48i	1.45989i	0.683506	+	0.729945i	$0.260454\pi$
$823$	1.85531e48i	1.45989i	−0.683506	+	0.729945i	$0.739546\pi$
$824$	−4.38613e47	−0.338285
$825$	0	0
$826$	−1.05406e48	−0.781076
$827$	− 3.05619e47i	− 0.221993i	−0.993821	−	0.110997i	$-0.964596\pi$
$827$	− 3.05619e47i	− 0.221993i	0.993821	−	0.110997i	$-0.0354043\pi$
$828$	− 4.24530e47i	− 0.302279i
$829$	1.49161e48	1.04113	0.520567	−	0.853821i	$-0.325721\pi$
$829$	1.49161e48	1.04113	0.520567	+	0.853821i	$0.325721\pi$
$830$	0	0
$831$	−1.86034e48	−1.24789
$832$	4.65428e47i	0.306068i
$833$	− 4.44841e47i	− 0.286789i
$834$	−4.98569e47	−0.315127
$835$	0	0
$836$	−1.86634e47	−0.113393
$837$	− 1.73157e47i	− 0.103150i
$838$	− 1.48554e48i	− 0.867676i
$839$	−1.58547e48	−0.907999	−0.454000	−	0.891002i	$-0.650003\pi$
$839$	−1.58547e48	−0.907999	−0.454000	+	0.891002i	$0.650003\pi$
$840$	0	0
$841$	−1.80257e48	−0.992565
$842$	1.64315e48i	0.887212i
$843$	1.85893e48i	0.984254i
$844$	2.06900e48	1.07426
$845$	0	0
$846$	3.06274e46	0.0152933
$847$	1.62248e48i	0.794515i
$848$	− 5.00438e46i	− 0.0240336i
$849$	−1.27513e48	−0.600589
$850$	0	0
$851$	8.36751e47	0.379104
$852$	− 1.07306e48i	− 0.476839i
$853$	1.56569e48i	0.682414i	0.939988	+	0.341207i	$0.110836\pi$
$853$	1.56569e48i	0.682414i	−0.939988	+	0.341207i	$0.889164\pi$
$854$	−1.16683e48	−0.498830
$855$	0	0
$856$	2.96608e48	1.22002
$857$	3.16984e48i	1.27895i	0.768811	+	0.639476i	$0.220849\pi$
$857$	3.16984e48i	1.27895i	−0.768811	+	0.639476i	$0.779151\pi$
$858$	1.38914e47i	0.0549802i
$859$	8.88897e47	0.345115	0.172558	−	0.984999i	$-0.444797\pi$
$859$	8.88897e47	0.345115	0.172558	+	0.984999i	$0.444797\pi$
$860$	0	0
$861$	−2.94784e48	−1.10142
$862$	4.15842e47i	0.152426i
$863$	4.50727e48i	1.62082i	0.585862	+	0.810411i	$0.300756\pi$
$863$	4.50727e48i	1.62082i	−0.585862	+	0.810411i	$0.699244\pi$
$864$	−3.07223e48	−1.08387
$865$	0	0
$866$	1.47593e48	0.501211
$867$	1.13313e47i	0.0377542i
$868$	1.56415e47i	0.0511332i
$869$	−1.38412e48	−0.443963
$870$	0	0
$871$	1.04158e48	0.321657
$872$	− 5.71036e48i	− 1.73038i
$873$	− 5.02708e47i	− 0.149479i
$874$	−1.66183e48	−0.484895
$875$	0	0
$876$	6.56186e47	0.184378
$877$	3.88746e48i	1.07195i	0.844235	+	0.535973i	$0.180055\pi$
$877$	3.88746e48i	1.07195i	−0.844235	+	0.535973i	$0.819945\pi$
$878$	− 1.00528e48i	− 0.272037i
$879$	−1.75207e48	−0.465302
$880$	0	0
$881$	−4.23545e48	−1.08342	−0.541711	−	0.840565i	$-0.682223\pi$
$881$	−4.23545e48	−1.08342	−0.541711	+	0.840565i	$0.682223\pi$
$882$	3.25691e47i	0.0817663i
$883$	2.06647e48i	0.509188i	0.967048	+	0.254594i	$0.0819418\pi$
$883$	2.06647e48i	0.509188i	−0.967048	+	0.254594i	$0.918058\pi$
$884$	−1.35316e48	−0.327255
$885$	0	0
$886$	1.91160e48	0.445389
$887$	1.92447e48i	0.440121i	0.975486	+	0.220060i	$0.0706254\pi$
$887$	1.92447e48i	0.440121i	−0.975486	+	0.220060i	$0.929375\pi$
$888$	− 1.18095e48i	− 0.265104i
$889$	3.67195e48	0.809130
$890$	0	0
$891$	−3.62687e47	−0.0770105
$892$	2.50317e48i	0.521759i
$893$	2.07120e47i	0.0423812i
$894$	−1.53121e48	−0.307585
$895$	0	0
$896$	2.86590e48	0.554854
$897$	− 2.13686e48i	− 0.406164i
$898$	− 4.63102e48i	− 0.864205i
$899$	−4.52331e46	−0.00828746
$900$	0	0
$901$	−3.83806e48	−0.677879
$902$	− 1.44757e48i	− 0.251033i
$903$	− 7.05639e48i	− 1.20153i
$904$	2.96342e47	0.0495467
$905$	0	0
$906$	−3.69820e47	−0.0596177
$907$	2.02864e48i	0.321133i	0.987025	+	0.160567i	$0.0513322\pi$
$907$	2.02864e48i	0.321133i	−0.987025	+	0.160567i	$0.948668\pi$
$908$	− 6.20107e48i	− 0.963940i
$909$	−5.03465e48	−0.768537
$910$	0	0
$911$	3.08415e48	0.454028	0.227014	−	0.973891i	$-0.427104\pi$
$911$	3.08415e48	0.454028	0.227014	+	0.973891i	$0.427104\pi$
$912$	− 1.35250e47i	− 0.0195534i
$913$	1.76871e47i	0.0251125i
$914$	6.16894e48	0.860198
$915$	0	0
$916$	7.94481e48	1.06858
$917$	− 2.40852e48i	− 0.318168i
$918$	4.87833e48i	0.632946i
$919$	7.76805e48	0.989933	0.494967	−	0.868912i	$-0.335180\pi$
$919$	7.76805e48	0.989933	0.494967	+	0.868912i	$0.335180\pi$
$920$	0	0
$921$	−5.06778e48	−0.623066
$922$	2.85598e48i	0.344902i
$923$	4.57572e48i	0.542789i
$924$	7.81521e47	0.0910653
$925$	0	0
$926$	−3.18383e48	−0.357988
$927$	1.42024e48i	0.156872i
$928$	8.02544e47i	0.0870818i
$929$	1.29507e49	1.38049	0.690244	−	0.723576i	$-0.257503\pi$
$929$	1.29507e49	1.38049	0.690244	+	0.723576i	$0.257503\pi$
$930$	0	0
$931$	−2.20251e48	−0.226594
$932$	− 1.11621e47i	− 0.0112819i
$933$	1.21451e48i	0.120602i
$934$	4.80683e48	0.468960
$935$	0	0
$936$	2.55491e48	0.240616
$937$	− 1.36587e49i	− 1.26388i	−0.775017	−	0.631940i	$-0.782259\pi$
$937$	− 1.36587e49i	− 1.26388i	0.775017	−	0.631940i	$-0.217741\pi$
$938$	3.39198e48i	0.308394i
$939$	−1.49938e48	−0.133946
$940$	0	0
$941$	−1.17124e45	−0.000101022 0	−5.05109e−5	−	1.00000i	$-0.500016\pi$
$941$	−1.17124e45	−0.000101022 0	−5.05109e−5		1.00000i	$0.500016\pi$
$942$	− 4.87817e48i	− 0.413444i
$943$	2.22673e49i	1.85449i
$944$	−6.48009e47	−0.0530326
$945$	0	0
$946$	3.46511e48	0.273851
$947$	− 1.87235e49i	− 1.45416i	−0.686551	−	0.727081i	$-0.740876\pi$
$947$	− 1.87235e49i	− 1.45416i	0.686551	−	0.727081i	$-0.259124\pi$
$948$	− 1.16523e49i	− 0.889352i
$949$	−2.79809e48	−0.209879
$950$	0	0
$951$	1.24369e49	0.901015
$952$	− 1.13641e49i	− 0.809144i
$953$	− 2.01399e49i	− 1.40937i	−0.709521	−	0.704685i	$-0.751088\pi$
$953$	− 2.01399e49i	− 1.40937i	0.709521	−	0.704685i	$-0.248912\pi$
$954$	2.81004e48	0.193270
$955$	0	0
$956$	−5.00946e48	−0.332840
$957$	2.26005e47i	0.0147595i
$958$	7.26405e48i	0.466282i
$959$	3.57089e48	0.225305
$960$	0	0
$961$	−1.62519e49	−0.990762
$962$	1.95271e48i	0.117017i
$963$	− 9.60423e48i	− 0.565756i
$964$	9.74376e48	0.564229
$965$	0	0
$966$	6.95884e48	0.389417
$967$	− 1.68504e49i	− 0.926985i	−0.886101	−	0.463493i	$-0.846596\pi$
$967$	− 1.68504e49i	− 0.926985i	0.886101	−	0.463493i	$-0.153404\pi$
$968$	− 1.72973e49i	− 0.935478i
$969$	−1.03729e49	−0.551514
$970$	0	0
$971$	−1.57857e49	−0.811234	−0.405617	−	0.914043i	$-0.632943\pi$
$971$	−1.57857e49	−0.811234	−0.405617	+	0.914043i	$0.632943\pi$
$972$	1.04005e49i	0.525485i
$973$	− 1.19606e49i	− 0.594143i
$974$	1.46508e49	0.715549
$975$	0	0
$976$	−7.17338e47	−0.0338690
$977$	1.78305e49i	0.827759i	0.910332	+	0.413880i	$0.135827\pi$
$977$	1.78305e49i	0.827759i	−0.910332	+	0.413880i	$0.864173\pi$
$978$	1.02038e49i	0.465768i
$979$	4.38981e48	0.197030
$980$	0	0
$981$	−1.84903e49	−0.802425
$982$	− 9.33798e48i	− 0.398486i
$983$	1.52674e48i	0.0640667i	0.999487	+	0.0320333i	$0.0101983\pi$
$983$	1.52674e48i	0.0640667i	−0.999487	+	0.0320333i	$0.989802\pi$
$984$	3.14269e49	1.29683
$985$	0	0
$986$	1.27435e48	0.0508532
$987$	− 8.67307e47i	− 0.0340361i
$988$	6.69980e48i	0.258566i
$989$	−5.33025e49	−2.02306
$990$	0	0
$991$	1.40402e49	0.515416	0.257708	−	0.966223i	$-0.417033\pi$
$991$	1.40402e49	0.515416	0.257708	+	0.966223i	$0.417033\pi$
$992$	− 2.68847e48i	− 0.0970648i
$993$	− 1.13451e49i	− 0.402854i
$994$	−1.49011e49	−0.520408
$995$	0	0
$996$	−1.48900e48	−0.0503056
$997$	7.92661e48i	0.263401i	0.991290	+	0.131701i	$0.0420437\pi$
$997$	7.92661e48i	0.263401i	−0.991290	+	0.131701i	$0.957956\pi$
$998$	− 3.66225e48i	− 0.119700i
$999$	−1.21617e49	−0.390988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.b.24.7		10
5.2	odd	4		5.34.a.a.1.2	✓	5
5.3	odd	4		25.34.a.b.1.4		5
5.4	even	2	inner	25.34.b.b.24.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.2	✓	5	5.2	odd	4
25.34.a.b.1.4		5	5.3	odd	4
25.34.b.b.24.4		10	5.4	even	2	inner
25.34.b.b.24.7		10	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+56118.7i q^{2} +5.48591e7i q^{3} +5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13i q^{7} +7.87377e14i q^{8} +2.54954e15 q^{9} +O(q^{10})\)	\(q+56118.7i q^{2} +5.48591e7i q^{3} +5.44063e9 q^{4} -3.07862e12 q^{6} -7.38557e13i q^{7} +7.87377e14i q^{8} +2.54954e15 q^{9} +3.54535e16 q^{11} +2.98468e17i q^{12} -1.27272e18i q^{13} +4.14468e18 q^{14} +2.54805e18 q^{16} -1.95420e20i q^{17} +1.43077e20i q^{18} -9.67568e20 q^{19} +4.05165e21 q^{21} +1.98961e21i q^{22} -3.06053e22i q^{23} -4.31948e22 q^{24} +7.14231e22 q^{26} +4.44830e23i q^{27} -4.01821e23i q^{28} +1.16201e23 q^{29} -3.89265e23 q^{31} +6.90651e24i q^{32} +1.94495e24i q^{33} +1.09667e25 q^{34} +1.38711e25 q^{36} +2.73400e25i q^{37} -5.42987e25i q^{38} +6.98200e25 q^{39} -7.27564e26 q^{41} +2.27373e26i q^{42} -1.74161e27i q^{43} +1.92889e26 q^{44} +1.71753e27 q^{46} -2.14063e26i q^{47} +1.39784e26i q^{48} +2.27634e27 q^{49} +1.07206e28 q^{51} -6.92437e27i q^{52} -1.96400e28i q^{53} -2.49633e28 q^{54} +5.81522e28 q^{56} -5.30799e28i q^{57} +6.52106e27i q^{58} -2.54315e29 q^{59} -2.81524e29 q^{61} -2.18451e28i q^{62} -1.88298e29i q^{63} -3.65697e29 q^{64} -1.09148e29 q^{66} +8.18392e29i q^{67} -1.06321e30i q^{68} +1.67898e30 q^{69} -3.59524e30 q^{71} +2.00745e30i q^{72} -2.19852e30i q^{73} -1.53429e30 q^{74} -5.26418e30 q^{76} -2.61844e30i q^{77} +3.91821e30i q^{78} -3.90404e31 q^{79} -1.02299e31 q^{81} -4.08299e31i q^{82} +4.98882e30i q^{83} +2.20435e31 q^{84} +9.77368e31 q^{86} +6.37469e30i q^{87} +2.79153e31i q^{88} +1.23819e32 q^{89} -9.39972e31 q^{91} -1.66512e32i q^{92} -2.13547e31i q^{93} +1.20129e31 q^{94} -3.78885e32 q^{96} -1.97176e32i q^{97} +1.27745e32i q^{98} +9.03903e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more