LMFDB - Embedded newform 25.34.b.c.24.4

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20265063301 x^{10} + \cdots + 39\!\cdots\!96 $ x^12 + 20265063301x^10 + 151877130254993985540x^8 + 529361026408998369955851761920x^6 + 862054500541443268723145801151954288640x^4 + 544606882049987247786598582768552479276511789056*x^2 + 39700341273686227371481766034965422500156905479886340096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{47}\cdot 3^{10}\cdot 5^{36}\cdot 7^{2}\cdot 11^{4} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.4
Root			$-48092.0i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.c.24.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-96184.0i q^{2} -1.07272e8i q^{3} -6.61431e8 q^{4} -1.03179e13 q^{6} -8.61302e13i q^{7} -7.62595e14i q^{8} -5.94832e15 q^{9} +O(q^{10})$	\(q-96184.0i q^{2} -1.07272e8i q^{3} -6.61431e8 q^{4} -1.03179e13 q^{6} -8.61302e13i q^{7} -7.62595e14i q^{8} -5.94832e15 q^{9} +9.57101e16 q^{11} +7.09533e16i q^{12} -2.44486e18i q^{13} -8.28435e18 q^{14} -7.90311e19 q^{16} -6.06607e19i q^{17} +5.72133e20i q^{18} +1.50149e21 q^{19} -9.23940e21 q^{21} -9.20578e21i q^{22} -1.88217e22i q^{23} -8.18055e22 q^{24} -2.35157e23 q^{26} +4.17567e22i q^{27} +5.69692e22i q^{28} -2.67431e24 q^{29} +2.64569e24 q^{31} +1.05089e24i q^{32} -1.02671e25i q^{33} -5.83459e24 q^{34} +3.93440e24 q^{36} -1.12777e26i q^{37} -1.44419e26i q^{38} -2.62266e26 q^{39} +7.31837e26 q^{41} +8.88682e26i q^{42} -3.88890e26i q^{43} -6.33056e25 q^{44} -1.81034e27 q^{46} +3.28337e27i q^{47} +8.47786e27i q^{48} +3.12582e26 q^{49} -6.50723e27 q^{51} +1.61711e27i q^{52} -3.35567e28i q^{53} +4.01633e27 q^{54} -6.56825e28 q^{56} -1.61068e29i q^{57} +2.57226e29i q^{58} -2.93443e29 q^{59} +7.07686e28 q^{61} -2.54473e29i q^{62} +5.12330e29i q^{63} -5.77794e29 q^{64} -9.87527e29 q^{66} +1.99482e30i q^{67} +4.01229e28i q^{68} -2.01905e30 q^{69} -1.15434e30 q^{71} +4.53616e30i q^{72} +2.83903e30i q^{73} -1.08474e31 q^{74} -9.93131e29 q^{76} -8.24353e30i q^{77} +2.52258e31i q^{78} -6.93520e30 q^{79} -2.85877e31 q^{81} -7.03910e31i q^{82} -4.09391e31i q^{83} +6.11122e30 q^{84} -3.74050e31 q^{86} +2.86880e32i q^{87} -7.29881e31i q^{88} +1.49837e32 q^{89} -2.10577e32 q^{91} +1.24492e31i q^{92} -2.83809e32i q^{93} +3.15807e32 q^{94} +1.12731e32 q^{96} +1.00351e33i q^{97} -3.00654e31i q^{98} -5.69314e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) $ 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9	$ 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+ \cdots - 33\!\cdots\!32 q^{99}+O(q^{100}) $ 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9 + 301521793111780384 * q^11 + 14172220017979782912 * q^14 + 129023040011717337632 * q^16 - 3423168725199973224400 * q^19 - 21120795321652308296256 * q^21 - 423790032309447397723200 * q^24 - 723658493334872996337176 * q^26 - 2610446812821454716031400 * q^29 + 21650642793601151809506704 * q^31 - 17744819333309063470980248 * q^34 + 337428823503549785822326792 * q^36 - 1159928172465211851270376912 * q^39 + 896017159299045986791643864 * q^41 - 14343610684444535018100501728 * q^44 + 6987518581952661848987190144 * q^46 + 14346854147129333747058470516 * q^49 - 109840725610127342641737389776 * q^51 + 365294374336526194478458799200 * q^54 - 785146678781996293241501500800 * q^56 + 356630312442075454139067599600 * q^59 - 564635378121172028506416574616 * q^61 - 3875937069585082792868959215744 * q^64 + 10122417492310860521089546318528 * q^66 - 632254481633966368511307646272 * q^69 + 16902436063987485405313234340144 * q^71 - 40989454834346150858579084952968 * q^74 + 58820079845469675507259388916000 * q^76 + 44105010702804710887789495271200 * q^79 - 266327929778353521323811147439348 * q^81 + 471983223984448297035157677303552 * q^84 - 257647761243091711315108096211216 * q^86 + 672982716682338963896412426721800 * q^89 + 389267538804687732313205728966864 * q^91 - 2972282194336784425374584270690528 * q^94 + 6303457980346245345128406163058944 * q^96 - 3321764604884454158829134325248032 * 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 $

$2$	− 96184.0i	− 1.03779i	−0.854839	−	0.518893i	$-0.826344\pi$
$2$	− 96184.0i	− 1.03779i	0.854839	−	0.518893i	$-0.173656\pi$
$3$	− 1.07272e8i	− 1.43876i	−0.694618	−	0.719379i	$-0.744427\pi$
$3$	− 1.07272e8i	− 1.43876i	0.694618	−	0.719379i	$-0.255573\pi$
$4$	−6.61431e8	−0.0770007
$5$	0	0
$5$	0	0
$6$	−1.03179e13	−1.49312
$7$	− 8.61302e13i	− 0.979575i	−0.871842	−	0.489788i	$-0.837074\pi$
$7$	− 8.61302e13i	− 0.979575i	0.871842	−	0.489788i	$-0.162926\pi$
$8$	− 7.62595e14i	− 0.957876i
$9$	−5.94832e15	−1.07002
$10$	0	0
$11$	9.57101e16	0.628027	0.314014	−	0.949418i	$-0.398326\pi$
$11$	9.57101e16	0.628027	0.314014	+	0.949418i	$0.398326\pi$
$12$	7.09533e16i	0.110785i
$13$	− 2.44486e18i	− 1.01904i	−0.860460	−	0.509518i	$-0.829824\pi$
$13$	− 2.44486e18i	− 1.01904i	0.860460	−	0.509518i	$-0.170176\pi$
$14$	−8.28435e18	−1.01659
$15$	0	0
$16$	−7.90311e19	−1.07107
$17$	− 6.06607e19i	− 0.302343i	−0.988508	−	0.151172i	$-0.951695\pi$
$17$	− 6.06607e19i	− 0.302343i	0.988508	−	0.151172i	$-0.0483046\pi$
$18$	5.72133e20i	1.11045i
$19$	1.50149e21	1.19423	0.597115	−	0.802156i	$-0.296314\pi$
$19$	1.50149e21	1.19423	0.597115	+	0.802156i	$0.296314\pi$
$20$	0	0
$21$	−9.23940e21	−1.40937
$22$	− 9.20578e21i	− 0.651758i
$23$	− 1.88217e22i	− 0.639955i	−0.947425	−	0.319977i	$-0.896325\pi$
$23$	− 1.88217e22i	− 0.639955i	0.947425	−	0.319977i	$-0.103675\pi$
$24$	−8.18055e22	−1.37815
$25$	0	0
$26$	−2.35157e23	−1.05754
$27$	4.17567e22i	0.100745i
$28$	5.69692e22i	0.0754280i
$29$	−2.67431e24	−1.98447	−0.992235	−	0.124376i	$-0.960307\pi$
$29$	−2.67431e24	−1.98447	−0.992235	+	0.124376i	$0.960307\pi$
$30$	0	0
$31$	2.64569e24	0.653236	0.326618	−	0.945156i	$-0.394091\pi$
$31$	2.64569e24	0.653236	0.326618	+	0.945156i	$0.394091\pi$
$32$	1.05089e24i	0.153667i
$33$	− 1.02671e25i	− 0.903579i
$34$	−5.83459e24	−0.313768
$35$	0	0
$36$	3.93440e24	0.0823925
$37$	− 1.12777e26i	− 1.50277i	−0.659862	−	0.751387i	$-0.729385\pi$
$37$	− 1.12777e26i	− 1.50277i	0.659862	−	0.751387i	$-0.270615\pi$
$38$	− 1.44419e26i	− 1.23935i
$39$	−2.62266e26	−1.46614
$40$	0	0
$41$	7.31837e26	1.79259	0.896294	−	0.443460i	$-0.146249\pi$
$41$	7.31837e26	1.79259	0.896294	+	0.443460i	$0.146249\pi$
$42$	8.88682e26i	1.46263i
$43$	− 3.88890e26i	− 0.434107i	−0.976160	−	0.217054i	$-0.930355\pi$
$43$	− 3.88890e26i	− 0.434107i	0.976160	−	0.217054i	$-0.0696446\pi$
$44$	−6.33056e25	−0.0483585
$45$	0	0
$46$	−1.81034e27	−0.664136
$47$	3.28337e27i	0.844704i	0.906432	+	0.422352i	$0.138795\pi$
$47$	3.28337e27i	0.844704i	−0.906432	+	0.422352i	$0.861205\pi$
$48$	8.47786e27i	1.54101i
$49$	3.12582e26	0.0404323
$50$	0	0
$51$	−6.50723e27	−0.434999
$52$	1.61711e27i	0.0784664i
$53$	− 3.35567e28i	− 1.18912i	−0.804050	−	0.594562i	$-0.797325\pi$
$53$	− 3.35567e28i	− 1.18912i	0.804050	−	0.594562i	$-0.202675\pi$
$54$	4.01633e27	0.104552
$55$	0	0
$56$	−6.56825e28	−0.938312
$57$	− 1.61068e29i	− 1.71821i
$58$	2.57226e29i	2.05946i
$59$	−2.93443e29	−1.77201	−0.886005	−	0.463676i	$-0.846530\pi$
$59$	−2.93443e29	−1.77201	−0.886005	+	0.463676i	$0.846530\pi$
$60$	0	0
$61$	7.07686e28	0.246546	0.123273	−	0.992373i	$-0.460661\pi$
$61$	7.07686e28	0.246546	0.123273	+	0.992373i	$0.460661\pi$
$62$	− 2.54473e29i	− 0.677920i
$63$	5.12330e29i	1.04817i
$64$	−5.77794e29	−0.911598
$65$	0	0
$66$	−9.87527e29	−0.937722
$67$	1.99482e30i	1.47798i	0.673715	+	0.738991i	$0.264698\pi$
$67$	1.99482e30i	1.47798i	−0.673715	+	0.738991i	$0.735302\pi$
$68$	4.01229e28i	0.0232807i
$69$	−2.01905e30	−0.920739
$70$	0	0
$71$	−1.15434e30	−0.328527	−0.164263	−	0.986417i	$-0.552525\pi$
$71$	−1.15434e30	−0.328527	−0.164263	+	0.986417i	$0.552525\pi$
$72$	4.53616e30i	1.02495i
$73$	2.83903e30i	0.510908i	0.966821	+	0.255454i	$0.0822250\pi$
$73$	2.83903e30i	0.510908i	−0.966821	+	0.255454i	$0.917775\pi$
$74$	−1.08474e31	−1.55956
$75$	0	0
$76$	−9.93131e29	−0.0919565
$77$	− 8.24353e30i	− 0.615200i
$78$	2.52258e31i	1.52154i
$79$	−6.93520e30	−0.339010	−0.169505	−	0.985529i	$-0.554217\pi$
$79$	−6.93520e30	−0.339010	−0.169505	+	0.985529i	$0.554217\pi$
$80$	0	0
$81$	−2.85877e31	−0.925075
$82$	− 7.03910e31i	− 1.86032i
$83$	− 4.09391e31i	− 0.885828i	−0.896564	−	0.442914i	$-0.853945\pi$
$83$	− 4.09391e31i	− 0.885828i	0.896564	−	0.442914i	$-0.146055\pi$
$84$	6.11122e30	0.108523
$85$	0	0
$86$	−3.74050e31	−0.450510
$87$	2.86880e32i	2.85517i
$88$	− 7.29881e31i	− 0.601572i
$89$	1.49837e32	1.02491	0.512454	−	0.858715i	$-0.328736\pi$
$89$	1.49837e32	1.02491	0.512454	+	0.858715i	$0.328736\pi$
$90$	0	0
$91$	−2.10577e32	−0.998222
$92$	1.24492e31i	0.0492769i
$93$	− 2.83809e32i	− 0.939849i
$94$	3.15807e32	0.876623
$95$	0	0
$96$	1.12731e32	0.221090
$97$	1.00351e33i	1.65878i	0.558673	+	0.829388i	$0.311311\pi$
$97$	1.00351e33i	1.65878i	−0.558673	+	0.829388i	$0.688689\pi$
$98$	− 3.00654e31i	− 0.0419601i
$99$	−5.69314e32	−0.672003
$100$	0	0
$101$	−8.22627e31	−0.0698072	−0.0349036	−	0.999391i	$-0.511112\pi$
$101$	−8.22627e31	−0.0698072	−0.0349036	+	0.999391i	$0.511112\pi$
$102$	6.25891e32i	0.451436i
$103$	− 1.80950e33i	− 1.11108i	−0.831491	−	0.555539i	$-0.812512\pi$
$103$	− 1.80950e33i	− 1.11108i	0.831491	−	0.555539i	$-0.187488\pi$
$104$	−1.86444e33	−0.976110
$105$	0	0
$106$	−3.22762e33	−1.23406
$107$	− 2.36850e33i	− 0.775605i	−0.921743	−	0.387802i	$-0.873234\pi$
$107$	− 2.36850e33i	− 0.775605i	0.921743	−	0.387802i	$-0.126766\pi$
$108$	− 2.76192e31i	− 0.00775744i
$109$	3.69273e33	0.890862	0.445431	−	0.895316i	$-0.353051\pi$
$109$	3.69273e33	0.890862	0.445431	+	0.895316i	$0.353051\pi$
$110$	0	0
$111$	−1.20979e34	−2.16213
$112$	6.80697e33i	1.04920i
$113$	1.24016e34i	1.65076i	0.564575	+	0.825382i	$0.309040\pi$
$113$	1.24016e34i	1.65076i	−0.564575	+	0.825382i	$0.690960\pi$
$114$	−1.54922e34	−1.78313
$115$	0	0
$116$	1.76887e33	0.152806
$117$	1.45428e34i	1.09039i
$118$	2.82246e34i	1.83897i
$119$	−5.22472e33	−0.296168
$120$	0	0
$121$	−1.40647e34	−0.605582
$122$	− 6.80681e33i	− 0.255862i
$123$	− 7.85059e34i	− 2.57910i
$124$	−1.74994e33	−0.0502997
$125$	0	0
$126$	4.92780e34	1.08777
$127$	− 3.85830e34i	− 0.747541i	−0.927521	−	0.373771i	$-0.878065\pi$
$127$	− 3.85830e34i	− 0.747541i	0.927521	−	0.373771i	$-0.121935\pi$
$128$	6.46016e34i	1.09971i
$129$	−4.17171e34	−0.624575
$130$	0	0
$131$	7.28441e34	0.846093	0.423046	−	0.906108i	$-0.360961\pi$
$131$	7.28441e34	0.846093	0.423046	+	0.906108i	$0.360961\pi$
$132$	6.79095e33i	0.0695762i
$133$	− 1.29324e35i	− 1.16984i
$134$	1.91870e35	1.53383
$135$	0	0
$136$	−4.62596e34	−0.289608
$137$	− 1.31044e35i	− 0.726990i	−0.931596	−	0.363495i	$-0.881583\pi$
$137$	− 1.31044e35i	− 0.726990i	0.931596	−	0.363495i	$-0.118417\pi$
$138$	1.94200e35i	0.955531i
$139$	2.86050e35	1.24939	0.624694	−	0.780870i	$-0.285224\pi$
$139$	2.86050e35	1.24939	0.624694	+	0.780870i	$0.285224\pi$
$140$	0	0
$141$	3.52215e35	1.21532
$142$	1.11029e35i	0.340941i
$143$	− 2.33998e35i	− 0.639982i
$144$	4.70102e35	1.14607
$145$	0	0
$146$	2.73069e35	0.530214
$147$	− 3.35314e34i	− 0.0581723i
$148$	7.45944e34i	0.115715i
$149$	4.76533e35	0.661485	0.330742	−	0.943721i	$-0.392701\pi$
$149$	4.76533e35	0.661485	0.330742	+	0.943721i	$0.392701\pi$
$150$	0	0
$151$	2.97234e35	0.331115	0.165557	−	0.986200i	$-0.447058\pi$
$151$	2.97234e35	0.331115	0.165557	+	0.986200i	$0.447058\pi$
$152$	− 1.14503e36i	− 1.14392i
$153$	3.60829e35i	0.323514i
$154$	−7.92896e35	−0.638446
$155$	0	0
$156$	1.73471e35	0.112894
$157$	2.26342e36i	1.32562i	0.748786	+	0.662812i	$0.230637\pi$
$157$	2.26342e36i	1.32562i	−0.748786	+	0.662812i	$0.769363\pi$
$158$	6.67056e35i	0.351820i
$159$	−3.59971e36	−1.71086
$160$	0	0
$161$	−1.62112e36	−0.626884
$162$	2.74968e36i	0.960030i
$163$	− 1.48676e35i	− 0.0468970i	−0.999725	−	0.0234485i	$-0.992535\pi$
$163$	− 1.48676e35i	− 0.0468970i	0.999725	−	0.0234485i	$-0.00746458\pi$
$164$	−4.84059e35	−0.138031
$165$	0	0
$166$	−3.93768e36	−0.919300
$167$	1.71469e36i	0.362546i	0.983433	+	0.181273i	$0.0580217\pi$
$167$	1.71469e36i	0.362546i	−0.983433	+	0.181273i	$0.941978\pi$
$168$	7.04592e36i	1.35000i
$169$	−2.21226e35	−0.0384331
$170$	0	0
$171$	−8.93133e36	−1.27785
$172$	2.57224e35i	0.0334265i
$173$	6.70788e36i	0.792181i	0.918211	+	0.396090i	$0.129633\pi$
$173$	6.70788e36i	0.792181i	−0.918211	+	0.396090i	$0.870367\pi$
$174$	2.75932e37	2.96306
$175$	0	0
$176$	−7.56408e36	−0.672662
$177$	3.14784e37i	2.54949i
$178$	− 1.44120e37i	− 1.06364i
$179$	7.92192e36	0.533035	0.266517	−	0.963830i	$-0.414127\pi$
$179$	7.92192e36	0.533035	0.266517	+	0.963830i	$0.414127\pi$
$180$	0	0
$181$	2.84989e37	1.59637	0.798183	−	0.602416i	$-0.205795\pi$
$181$	2.84989e37	1.59637	0.798183	+	0.602416i	$0.205795\pi$
$182$	2.02541e37i	1.03594i
$183$	− 7.59152e36i	− 0.354720i
$184$	−1.43533e37	−0.612997
$185$	0	0
$186$	−2.72979e37	−0.975362
$187$	− 5.80585e36i	− 0.189880i
$188$	− 2.17172e36i	− 0.0650428i
$189$	3.59651e36	0.0986874
$190$	0	0
$191$	−1.67422e37	−0.386155	−0.193077	−	0.981184i	$-0.561847\pi$
$191$	−1.67422e37	−0.386155	−0.193077	+	0.981184i	$0.561847\pi$
$192$	6.19813e37i	1.31157i
$193$	− 2.80272e37i	− 0.544357i	−0.962247	−	0.272179i	$-0.912256\pi$
$193$	− 2.80272e37i	− 0.544357i	0.962247	−	0.272179i	$-0.0877441\pi$
$194$	9.65216e37	1.72146
$195$	0	0
$196$	−2.06751e35	−0.00311332
$197$	5.75950e37i	0.797428i	0.917075	+	0.398714i	$0.130543\pi$
$197$	5.75950e37i	0.797428i	−0.917075	+	0.398714i	$0.869457\pi$
$198$	5.47589e37i	0.697396i
$199$	1.44611e38	1.69483	0.847415	−	0.530931i	$-0.178158\pi$
$199$	1.44611e38	1.69483	0.847415	+	0.530931i	$0.178158\pi$
$200$	0	0
$201$	2.13989e38	2.12646
$202$	7.91236e36i	0.0724450i
$203$	2.30339e38i	1.94394i
$204$	4.30408e36	0.0334952
$205$	0	0
$206$	−1.74045e38	−1.15306
$207$	1.11957e38i	0.684766i
$208$	1.93220e38i	1.09146i
$209$	1.43708e38	0.750008
$210$	0	0
$211$	−4.42459e37	−0.197339	−0.0986695	−	0.995120i	$-0.531459\pi$
$211$	−4.42459e37	−0.197339	−0.0986695	+	0.995120i	$0.531459\pi$
$212$	2.21954e37i	0.0915634i
$213$	1.23829e38i	0.472670i
$214$	−2.27812e38	−0.804912
$215$	0	0
$216$	3.18435e37	0.0965014
$217$	− 2.27873e38i	− 0.639894i
$218$	− 3.55182e38i	− 0.924524i
$219$	3.04550e38	0.735073
$220$	0	0
$221$	−1.48307e38	−0.308099
$222$	1.16363e39i	2.24383i
$223$	4.20819e38i	0.753469i	0.926321	+	0.376734i	$0.122953\pi$
$223$	4.20819e38i	0.753469i	−0.926321	+	0.376734i	$0.877047\pi$
$224$	9.05132e37	0.150529
$225$	0	0
$226$	1.19284e39	1.71314
$227$	− 2.29758e38i	− 0.306793i	−0.988165	−	0.153396i	$-0.950979\pi$
$227$	− 2.29758e38i	− 0.306793i	0.988165	−	0.153396i	$-0.0490211\pi$
$228$	1.06536e38i	0.132303i
$229$	1.22734e39	1.41801	0.709007	−	0.705202i	$-0.249144\pi$
$229$	1.22734e39	1.41801	0.709007	+	0.705202i	$0.249144\pi$
$230$	0	0
$231$	−8.84304e38	−0.885123
$232$	2.03942e39i	1.90088i
$233$	− 2.11378e39i	− 1.83522i	−0.397486	−	0.917608i	$-0.630117\pi$
$233$	− 2.11378e39i	− 1.83522i	0.397486	−	0.917608i	$-0.369883\pi$
$234$	1.39879e39	1.13159
$235$	0	0
$236$	1.94093e38	0.136446
$237$	7.43956e38i	0.487753i
$238$	5.02535e38i	0.307359i
$239$	9.09248e38	0.518940	0.259470	−	0.965751i	$-0.416452\pi$
$239$	9.09248e38	0.518940	0.259470	+	0.965751i	$0.416452\pi$
$240$	0	0
$241$	−1.71576e39	−0.853443	−0.426722	−	0.904383i	$-0.640332\pi$
$241$	−1.71576e39	−0.853443	−0.426722	+	0.904383i	$0.640332\pi$
$242$	1.35280e39i	0.628465i
$243$	3.29880e39i	1.43170i
$244$	−4.68085e37	−0.0189842
$245$	0	0
$246$	−7.55101e39	−2.67655
$247$	− 3.67093e39i	− 1.21696i
$248$	− 2.01759e39i	− 0.625720i
$249$	−4.39163e39	−1.27449
$250$	0	0
$251$	3.71395e39	0.944537	0.472269	−	0.881455i	$-0.343435\pi$
$251$	3.71395e39	0.944537	0.472269	+	0.881455i	$0.343435\pi$
$252$	− 3.38871e38i	− 0.0807096i
$253$	− 1.80143e39i	− 0.401909i
$254$	−3.71107e39	−0.775788
$255$	0	0
$256$	1.25043e39	0.229668
$257$	3.64681e39i	0.628082i	0.949409	+	0.314041i	$0.101683\pi$
$257$	3.64681e39i	0.628082i	−0.949409	+	0.314041i	$0.898317\pi$
$258$	4.01252e39i	0.648175i
$259$	−9.71354e39	−1.47208
$260$	0	0
$261$	1.59076e40	2.12343
$262$	− 7.00644e39i	− 0.878064i
$263$	− 3.70275e39i	− 0.435767i	−0.975975	−	0.217884i	$-0.930085\pi$
$263$	− 3.70275e39i	− 0.435767i	0.975975	−	0.217884i	$-0.0699153\pi$
$264$	−7.82961e39	−0.865517
$265$	0	0
$266$	−1.24389e40	−1.21404
$267$	− 1.60734e40i	− 1.47459i
$268$	− 1.31944e39i	− 0.113806i
$269$	1.93097e40	1.56626	0.783129	−	0.621859i	$-0.213622\pi$
$269$	1.93097e40	1.56626	0.783129	+	0.621859i	$0.213622\pi$
$270$	0	0
$271$	−5.56561e37	−0.00399502	−0.00199751	−	0.999998i	$-0.500636\pi$
$271$	−5.56561e37	−0.00399502	−0.00199751	+	0.999998i	$0.500636\pi$
$272$	4.79409e39i	0.323831i
$273$	2.25891e40i	1.43620i
$274$	−1.26044e40	−0.754460
$275$	0	0
$276$	1.33546e39	0.0708976
$277$	− 2.59199e40i	− 1.29634i	−0.761497	−	0.648168i	$-0.775535\pi$
$277$	− 2.59199e40i	− 1.29634i	0.761497	−	0.648168i	$-0.224465\pi$
$278$	− 2.75134e40i	− 1.29660i
$279$	−1.57374e40	−0.698977
$280$	0	0
$281$	4.04959e40	1.59866	0.799331	−	0.600891i	$-0.205187\pi$
$281$	4.04959e40	1.59866	0.799331	+	0.600891i	$0.205187\pi$
$282$	− 3.38774e40i	− 1.26125i
$283$	− 4.05121e40i	− 1.42269i	−0.702846	−	0.711343i	$-0.748087\pi$
$283$	− 4.05121e40i	− 1.42269i	0.702846	−	0.711343i	$-0.251913\pi$
$284$	7.63516e38	0.0252968
$285$	0	0
$286$	−2.25069e40	−0.664165
$287$	− 6.30332e40i	− 1.75597i
$288$	− 6.25102e39i	− 0.164428i
$289$	3.65748e40	0.908588
$290$	0	0
$291$	1.07649e41	2.38658
$292$	− 1.87782e39i	− 0.0393403i
$293$	− 7.90241e38i	− 0.0156475i	−0.999969	−	0.00782373i	$-0.997510\pi$
$293$	− 7.90241e38i	− 0.0156475i	0.999969	−	0.00782373i	$-0.00249040\pi$
$294$	−3.22519e39	−0.0603704
$295$	0	0
$296$	−8.60035e40	−1.43947
$297$	3.99654e39i	0.0632707i
$298$	− 4.58349e40i	− 0.686480i
$299$	−4.60164e40	−0.652136
$300$	0	0
$301$	−3.34951e40	−0.425241
$302$	− 2.85891e40i	− 0.343627i
$303$	8.82452e39i	0.100436i
$304$	−1.18664e41	−1.27910
$305$	0	0
$306$	3.47060e40	0.335739
$307$	1.53513e41i	1.40722i	0.710585	+	0.703612i	$0.248431\pi$
$307$	1.53513e41i	1.40722i	−0.710585	+	0.703612i	$0.751569\pi$
$308$	5.45253e39i	0.0473708i
$309$	−1.94110e41	−1.59857
$310$	0	0
$311$	−2.01085e41	−1.48879	−0.744395	−	0.667739i	$-0.767262\pi$
$311$	−2.01085e41	−1.48879	−0.744395	+	0.667739i	$0.767262\pi$
$312$	2.00003e41i	1.40438i
$313$	6.89540e40i	0.459280i	0.973276	+	0.229640i	$0.0737549\pi$
$313$	6.89540e40i	0.459280i	−0.973276	+	0.229640i	$0.926245\pi$
$314$	2.17705e41	1.37571
$315$	0	0
$316$	4.58716e39	0.0261040
$317$	− 2.25823e41i	− 1.21981i	−0.792476	−	0.609903i	$-0.791208\pi$
$317$	− 2.25823e41i	− 1.21981i	0.792476	−	0.609903i	$-0.208792\pi$
$318$	3.46234e41i	1.77551i
$319$	−2.55958e41	−1.24630
$320$	0	0
$321$	−2.54075e41	−1.11591
$322$	1.55925e41i	0.650571i
$323$	− 9.10814e40i	− 0.361067i
$324$	1.89088e40	0.0712314
$325$	0	0
$326$	−1.43002e40	−0.0486691
$327$	− 3.96128e41i	− 1.28173i
$328$	− 5.58095e41i	− 1.71708i
$329$	2.82797e41	0.827451
$330$	0	0
$331$	−1.74008e41	−0.460688	−0.230344	−	0.973109i	$-0.573985\pi$
$331$	−1.74008e41	−0.460688	−0.230344	+	0.973109i	$0.573985\pi$
$332$	2.70784e40i	0.0682094i
$333$	6.70836e41i	1.60800i
$334$	1.64925e41	0.376245
$335$	0	0
$336$	7.30200e41	1.50954
$337$	8.05374e41i	1.58527i	0.609695	+	0.792636i	$0.291292\pi$
$337$	8.05374e41i	1.58527i	−0.609695	+	0.792636i	$0.708708\pi$
$338$	2.12784e40i	0.0398853i
$339$	1.33035e42	2.37505
$340$	0	0
$341$	2.53219e41	0.410250
$342$	8.59052e41i	1.32614i
$343$	− 6.92795e41i	− 1.01918i
$344$	−2.96565e41	−0.415821
$345$	0	0
$346$	6.45191e41	0.822115
$347$	6.26061e41i	0.760642i	0.924854	+	0.380321i	$0.124187\pi$
$347$	6.26061e41i	0.760642i	−0.924854	+	0.380321i	$0.875813\pi$
$348$	− 1.89751e41i	− 0.219850i
$349$	9.05089e40	0.100017	0.0500083	−	0.998749i	$-0.484075\pi$
$349$	9.05089e40	0.100017	0.0500083	+	0.998749i	$0.484075\pi$
$350$	0	0
$351$	1.02089e41	0.102663
$352$	1.00581e41i	0.0965073i
$353$	1.08093e42i	0.989725i	0.868971	+	0.494862i	$0.164782\pi$
$353$	1.08093e42i	0.989725i	−0.868971	+	0.494862i	$0.835218\pi$
$354$	3.02772e42	2.64583
$355$	0	0
$356$	−9.91071e40	−0.0789186
$357$	5.60469e41i	0.426114i
$358$	− 7.61962e41i	− 0.553176i
$359$	2.08351e41	0.144456	0.0722282	−	0.997388i	$-0.476989\pi$
$359$	2.08351e41	0.144456	0.0722282	+	0.997388i	$0.476989\pi$
$360$	0	0
$361$	6.73698e41	0.426183
$362$	− 2.74114e42i	− 1.65669i
$363$	1.50876e42i	0.871285i
$364$	1.39282e41	0.0768638
$365$	0	0
$366$	−7.30183e41	−0.368124
$367$	− 1.16121e42i	− 0.559654i	−0.960050	−	0.279827i	$-0.909723\pi$
$367$	− 1.16121e42i	− 0.559654i	0.960050	−	0.279827i	$-0.0902771\pi$
$368$	1.48750e42i	0.685437i
$369$	−4.35320e42	−1.91811
$370$	0	0
$371$	−2.89024e42	−1.16484
$372$	1.87720e41i	0.0723690i
$373$	1.34955e42i	0.497728i	0.968538	+	0.248864i	$0.0800572\pi$
$373$	1.34955e42i	0.497728i	−0.968538	+	0.248864i	$0.919943\pi$
$374$	−5.58430e41	−0.197055
$375$	0	0
$376$	2.50388e42	0.809122
$377$	6.53832e42i	2.02225i
$378$	− 3.45927e41i	− 0.102416i
$379$	−3.19198e42	−0.904717	−0.452358	−	0.891836i	$-0.649417\pi$
$379$	−3.19198e42	−0.904717	−0.452358	+	0.891836i	$0.649417\pi$
$380$	0	0
$381$	−4.13890e42	−1.07553
$382$	1.61033e42i	0.400746i
$383$	3.06206e42i	0.729849i	0.931037	+	0.364925i	$0.118905\pi$
$383$	3.06206e42i	0.729849i	−0.931037	+	0.364925i	$0.881095\pi$
$384$	6.92997e42	1.58222
$385$	0	0
$386$	−2.69577e42	−0.564926
$387$	2.31324e42i	0.464504i
$388$	− 6.63752e41i	− 0.127727i
$389$	−5.44019e42	−1.00333	−0.501667	−	0.865061i	$-0.667280\pi$
$389$	−5.44019e42	−1.00333	−0.501667	+	0.865061i	$0.667280\pi$
$390$	0	0
$391$	−1.14174e42	−0.193486
$392$	− 2.38374e41i	− 0.0387292i
$393$	− 7.81416e42i	− 1.21732i
$394$	5.53971e42	0.827560
$395$	0	0
$396$	3.76562e41	0.0517447
$397$	4.34919e42i	0.573277i	0.958039	+	0.286639i	$0.0925379\pi$
$397$	4.34919e42i	0.573277i	−0.958039	+	0.286639i	$0.907462\pi$
$398$	− 1.39093e43i	− 1.75887i
$399$	−1.38729e43	−1.68311
$400$	0	0
$401$	−1.13262e42	−0.126532	−0.0632660	−	0.997997i	$-0.520152\pi$
$401$	−1.13262e42	−0.126532	−0.0632660	+	0.997997i	$0.520152\pi$
$402$	− 2.05823e43i	− 2.20681i
$403$	− 6.46834e42i	− 0.665671i
$404$	5.44111e40	0.00537520
$405$	0	0
$406$	2.21549e43	2.01739
$407$	− 1.07939e43i	− 0.943783i
$408$	4.96238e42i	0.416675i
$409$	−6.57876e42	−0.530530	−0.265265	−	0.964176i	$-0.585459\pi$
$409$	−6.57876e42	−0.530530	−0.265265	+	0.964176i	$0.585459\pi$
$410$	0	0
$411$	−1.40574e43	−1.04596
$412$	1.19686e42i	0.0855538i
$413$	2.52743e43i	1.73582i
$414$	1.07685e43	0.710640
$415$	0	0
$416$	2.56928e42	0.156593
$417$	− 3.06853e43i	− 1.79757i
$418$	− 1.38224e43i	− 0.778349i
$419$	2.13895e43	1.15789	0.578947	−	0.815365i	$-0.303464\pi$
$419$	2.13895e43	1.15789	0.578947	+	0.815365i	$0.303464\pi$
$420$	0	0
$421$	−5.34625e42	−0.267544	−0.133772	−	0.991012i	$-0.542709\pi$
$421$	−5.34625e42	−0.267544	−0.133772	+	0.991012i	$0.542709\pi$
$422$	4.25575e42i	0.204796i
$423$	− 1.95305e43i	− 0.903852i
$424$	−2.55902e43	−1.13903
$425$	0	0
$426$	1.19104e43	0.490531
$427$	− 6.09531e42i	− 0.241511i
$428$	1.56660e42i	0.0597221i
$429$	−2.51016e43	−0.920779
$430$	0	0
$431$	2.33735e43	0.794053	0.397026	−	0.917807i	$-0.370042\pi$
$431$	2.33735e43	0.794053	0.397026	+	0.917807i	$0.370042\pi$
$432$	− 3.30008e42i	− 0.107905i
$433$	1.61313e43i	0.507714i	0.967242	+	0.253857i	$0.0816993\pi$
$433$	1.61313e43i	0.507714i	−0.967242	+	0.253857i	$0.918301\pi$
$434$	−2.19178e43	−0.664074
$435$	0	0
$436$	−2.44249e42	−0.0685970
$437$	− 2.82605e43i	− 0.764252i
$438$	− 2.92928e43i	− 0.762849i
$439$	−4.60088e43	−1.15392	−0.576961	−	0.816772i	$-0.695762\pi$
$439$	−4.60088e43	−1.15392	−0.576961	+	0.816772i	$0.695762\pi$
$440$	0	0
$441$	−1.85934e42	−0.0432635
$442$	1.42648e43i	0.319741i
$443$	5.92450e43i	1.27935i	0.768644	+	0.639676i	$0.220932\pi$
$443$	5.92450e43i	1.27935i	−0.768644	+	0.639676i	$0.779068\pi$
$444$	8.00193e42	0.166485
$445$	0	0
$446$	4.04761e43	0.781940
$447$	− 5.11189e43i	− 0.951716i
$448$	4.97655e43i	0.892978i
$449$	1.64413e43	0.284361	0.142181	−	0.989841i	$-0.454589\pi$
$449$	1.64413e43	0.284361	0.142181	+	0.989841i	$0.454589\pi$
$450$	0	0
$451$	7.00442e43	1.12579
$452$	− 8.20283e42i	− 0.127110i
$453$	− 3.18850e43i	− 0.476394i
$454$	−2.20991e43	−0.318385
$455$	0	0
$456$	−1.22830e44	−1.64583
$457$	2.69494e42i	0.0348283i	0.999848	+	0.0174141i	$0.00554338\pi$
$457$	2.69494e42i	0.0348283i	−0.999848	+	0.0174141i	$0.994457\pi$
$458$	− 1.18051e44i	− 1.47160i
$459$	2.53299e42	0.0304596
$460$	0	0
$461$	−8.91542e43	−0.997876	−0.498938	−	0.866638i	$-0.666276\pi$
$461$	−8.91542e43	−0.997876	−0.498938	+	0.866638i	$0.666276\pi$
$462$	8.50559e43i	0.918569i
$463$	7.81223e43i	0.814121i	0.913401	+	0.407060i	$0.133446\pi$
$463$	7.81223e43i	0.814121i	−0.913401	+	0.407060i	$0.866554\pi$
$464$	2.11354e44	2.12551
$465$	0	0
$466$	−2.03312e44	−1.90456
$467$	1.34336e44i	1.21469i	0.794439	+	0.607344i	$0.207765\pi$
$467$	1.34336e44i	1.21469i	−0.794439	+	0.607344i	$0.792235\pi$
$468$	− 9.61907e42i	− 0.0839608i
$469$	1.71814e44	1.44780
$470$	0	0
$471$	2.42802e44	1.90725
$472$	2.23779e44i	1.69737i
$473$	− 3.72207e43i	− 0.272631i
$474$	7.15567e43	0.506183
$475$	0	0
$476$	3.45579e42	0.0228052
$477$	1.99606e44i	1.27239i
$478$	− 8.74551e43i	− 0.538549i
$479$	−6.08543e43	−0.362039	−0.181020	−	0.983479i	$-0.557940\pi$
$479$	−6.08543e43	−0.362039	−0.181020	+	0.983479i	$0.557940\pi$
$480$	0	0
$481$	−2.75725e44	−1.53138
$482$	1.65028e44i	0.885692i
$483$	1.73901e44i	0.901933i
$484$	9.30285e42	0.0466302
$485$	0	0
$486$	3.17292e44	1.48580
$487$	− 2.29550e44i	− 1.03908i	−0.854446	−	0.519541i	$-0.826103\pi$
$487$	− 2.29550e44i	− 1.03908i	0.854446	−	0.519541i	$-0.173897\pi$
$488$	− 5.39678e43i	− 0.236161i
$489$	−1.59488e43	−0.0674734
$490$	0	0
$491$	−5.01787e43	−0.198461	−0.0992305	−	0.995064i	$-0.531638\pi$
$491$	−5.01787e43	−0.198461	−0.0992305	+	0.995064i	$0.531638\pi$
$492$	5.19262e43i	0.198592i
$493$	1.62226e44i	0.599992i
$494$	−3.53085e44	−1.26295
$495$	0	0
$496$	−2.09092e44	−0.699663
$497$	9.94235e43i	0.321817i
$498$	4.22405e44i	1.32265i
$499$	1.28404e44	0.388974	0.194487	−	0.980905i	$-0.437696\pi$
$499$	1.28404e44	0.388974	0.194487	+	0.980905i	$0.437696\pi$
$500$	0	0
$501$	1.83939e44	0.521615
$502$	− 3.57222e44i	− 0.980228i
$503$	− 3.85407e44i	− 1.02341i	−0.859163	−	0.511703i	$-0.829015\pi$
$503$	− 3.85407e44i	− 1.02341i	0.859163	−	0.511703i	$-0.170985\pi$
$504$	3.90700e44	1.00401
$505$	0	0
$506$	−1.73268e44	−0.417096
$507$	2.37314e43i	0.0552959i
$508$	2.55200e43i	0.0575612i
$509$	−5.40769e44	−1.18078	−0.590389	−	0.807119i	$-0.701026\pi$
$509$	−5.40769e44	−1.18078	−0.590389	+	0.807119i	$0.701026\pi$
$510$	0	0
$511$	2.44526e44	0.500473
$512$	4.34652e44i	0.861365i
$513$	6.26972e43i	0.120313i
$514$	3.50765e44	0.651815
$515$	0	0
$516$	2.75930e43	0.0480927
$517$	3.14251e44i	0.530497i
$518$	9.34287e44i	1.52770i
$519$	7.19570e44	1.13976
$520$	0	0
$521$	−9.57656e42	−0.0142360	−0.00711799	−	0.999975i	$-0.502266\pi$
$521$	−9.57656e42	−0.0142360	−0.00711799	+	0.999975i	$0.502266\pi$
$522$	− 1.53006e45i	− 2.20366i
$523$	7.88861e43i	0.110084i	0.998484	+	0.0550418i	$0.0175292\pi$
$523$	7.88861e43i	0.110084i	−0.998484	+	0.0550418i	$0.982471\pi$
$524$	−4.81813e43	−0.0651497
$525$	0	0
$526$	−3.56145e44	−0.452233
$527$	− 1.60489e44i	− 0.197502i
$528$	8.11417e44i	0.967798i
$529$	5.10749e44	0.590458
$530$	0	0
$531$	1.74549e45	1.89609
$532$	8.55386e43i	0.0900783i
$533$	− 1.78924e45i	− 1.82671i
$534$	−1.54601e45	−1.53031
$535$	0	0
$536$	1.52124e45	1.41572
$537$	− 8.49804e44i	− 0.766907i
$538$	− 1.85729e45i	− 1.62544i
$539$	2.99173e43	0.0253926
$540$	0	0
$541$	−1.96609e45	−1.56981	−0.784907	−	0.619613i	$-0.787289\pi$
$541$	−1.96609e45	−1.56981	−0.784907	+	0.619613i	$0.787289\pi$
$542$	5.35323e42i	0.00414598i
$543$	− 3.05715e45i	− 2.29678i
$544$	6.37476e43	0.0464603
$545$	0	0
$546$	2.17271e45	1.49047
$547$	− 4.44935e44i	− 0.296146i	−0.988976	−	0.148073i	$-0.952693\pi$
$547$	− 4.44935e44i	− 0.296146i	0.988976	−	0.148073i	$-0.0473070\pi$
$548$	8.66767e43i	0.0559787i
$549$	−4.20954e44	−0.263810
$550$	0	0
$551$	−4.01544e45	−2.36991
$552$	1.53972e45i	0.881954i
$553$	5.97331e44i	0.332086i
$554$	−2.49308e45	−1.34532
$555$	0	0
$556$	−1.89202e44	−0.0962037
$557$	− 1.02978e45i	− 0.508318i	−0.967162	−	0.254159i	$-0.918201\pi$
$557$	− 1.02978e45i	− 0.508318i	0.967162	−	0.254159i	$-0.0817986\pi$
$558$	1.51368e45i	0.725389i
$559$	−9.50782e44	−0.442370
$560$	0	0
$561$	−6.22807e44	−0.273191
$562$	− 3.89506e45i	− 1.65907i
$563$	3.82628e45i	1.58266i	0.611388	+	0.791331i	$0.290612\pi$
$563$	3.82628e45i	1.58266i	−0.611388	+	0.791331i	$0.709388\pi$
$564$	−2.32966e44	−0.0935808
$565$	0	0
$566$	−3.89662e45	−1.47644
$567$	2.46227e45i	0.906180i
$568$	8.80294e44i	0.314688i
$569$	1.77526e45	0.616468	0.308234	−	0.951311i	$-0.400262\pi$
$569$	1.77526e45	0.616468	0.308234	+	0.951311i	$0.400262\pi$
$570$	0	0
$571$	1.00861e45	0.330544	0.165272	−	0.986248i	$-0.447150\pi$
$571$	1.00861e45	0.330544	0.165272	+	0.986248i	$0.447150\pi$
$572$	1.54774e44i	0.0492791i
$573$	1.79597e45i	0.555583i
$574$	−6.06279e45	−1.82233
$575$	0	0
$576$	3.43690e45	0.975430
$577$	3.07790e45i	0.848895i	0.905452	+	0.424448i	$0.139532\pi$
$577$	3.07790e45i	0.848895i	−0.905452	+	0.424448i	$0.860468\pi$
$578$	− 3.51791e45i	− 0.942921i
$579$	−3.00654e45	−0.783198
$580$	0	0
$581$	−3.52609e45	−0.867735
$582$	− 1.03541e46i	− 2.47676i
$583$	− 3.21171e45i	− 0.746803i
$584$	2.16503e45	0.489387
$585$	0	0
$586$	−7.60085e43	−0.0162387
$587$	3.80587e45i	0.790544i	0.918564	+	0.395272i	$0.129350\pi$
$587$	3.80587e45i	0.790544i	−0.918564	+	0.395272i	$0.870650\pi$
$588$	2.21787e43i	0.00447931i
$589$	3.97247e45	0.780114
$590$	0	0
$591$	6.17835e45	1.14731
$592$	8.91292e45i	1.60958i
$593$	1.41796e45i	0.249036i	0.992217	+	0.124518i	$0.0397384\pi$
$593$	1.41796e45i	0.249036i	−0.992217	+	0.124518i	$0.960262\pi$
$594$	3.84403e44	0.0656615
$595$	0	0
$596$	−3.15194e44	−0.0509348
$597$	− 1.55128e46i	− 2.43845i
$598$	4.42605e45i	0.676778i
$599$	−7.86874e45	−1.17048	−0.585239	−	0.810861i	$-0.698999\pi$
$599$	−7.86874e45	−1.17048	−0.585239	+	0.810861i	$0.698999\pi$
$600$	0	0
$601$	6.55936e45	0.923491	0.461746	−	0.887012i	$-0.347223\pi$
$601$	6.55936e45	0.923491	0.461746	+	0.887012i	$0.347223\pi$
$602$	3.22170e45i	0.441309i
$603$	− 1.18658e46i	− 1.58147i
$604$	−1.96600e44	−0.0254961
$605$	0	0
$606$	8.48778e44	0.104231
$607$	1.16821e46i	1.39607i	0.716062	+	0.698037i	$0.245943\pi$
$607$	1.16821e46i	1.39607i	−0.716062	+	0.698037i	$0.754057\pi$
$608$	1.57790e45i	0.183514i
$609$	2.47090e46	2.79685
$610$	0	0
$611$	8.02738e45	0.860783
$612$	− 2.38664e44i	− 0.0249108i
$613$	2.09504e45i	0.212860i	0.994320	+	0.106430i	$0.0339420\pi$
$613$	2.09504e45i	0.212860i	−0.994320	+	0.106430i	$0.966058\pi$
$614$	1.47655e46	1.46040
$615$	0	0
$616$	−6.28648e45	−0.589285
$617$	1.98589e45i	0.181238i	0.995886	+	0.0906192i	$0.0288846\pi$
$617$	1.98589e45i	0.181238i	−0.995886	+	0.0906192i	$0.971115\pi$
$618$	1.86702e46i	1.65898i
$619$	8.02615e45	0.694403	0.347201	−	0.937791i	$-0.387132\pi$
$619$	8.02615e45	0.694403	0.347201	+	0.937791i	$0.387132\pi$
$620$	0	0
$621$	7.85931e44	0.0644723
$622$	1.93412e46i	1.54505i
$623$	− 1.29055e46i	− 1.00397i
$624$	2.07272e46	1.57035
$625$	0	0
$626$	6.63227e45	0.476635
$627$	− 1.54159e46i	− 1.07908i
$628$	− 1.49709e45i	− 0.102074i
$629$	−6.84116e45	−0.454354
$630$	0	0
$631$	−2.32504e46	−1.46536	−0.732682	−	0.680571i	$-0.761732\pi$
$631$	−2.32504e46	−1.46536	−0.732682	+	0.680571i	$0.761732\pi$
$632$	5.28875e45i	0.324729i
$633$	4.74637e45i	0.283923i
$634$	−2.17206e46	−1.26590
$635$	0	0
$636$	2.38096e45	0.131738
$637$	− 7.64220e44i	− 0.0412020i
$638$	2.46191e46i	1.29339i
$639$	6.86638e45	0.351531
$640$	0	0
$641$	1.10320e46	0.536412	0.268206	−	0.963362i	$-0.413569\pi$
$641$	1.10320e46	0.536412	0.268206	+	0.963362i	$0.413569\pi$
$642$	2.44379e46i	1.15807i
$643$	− 1.90982e46i	− 0.882085i	−0.897486	−	0.441042i	$-0.854609\pi$
$643$	− 1.90982e46i	− 0.882085i	0.897486	−	0.441042i	$-0.145391\pi$
$644$	1.07226e45	0.0482705
$645$	0	0
$646$	−8.76058e45	−0.374711
$647$	2.77860e46i	1.15853i	0.815141	+	0.579263i	$0.196659\pi$
$647$	2.77860e46i	1.15853i	−0.815141	+	0.579263i	$0.803341\pi$
$648$	2.18009e46i	0.886107i
$649$	−2.80855e46	−1.11287
$650$	0	0
$651$	−2.44445e46	−0.920652
$652$	9.83389e43i	0.00361110i
$653$	1.10232e46i	0.394676i	0.980335	+	0.197338i	$0.0632297\pi$
$653$	1.10232e46i	0.394676i	−0.980335	+	0.197338i	$0.936770\pi$
$654$	−3.81012e46	−1.33017
$655$	0	0
$656$	−5.78379e46	−1.91999
$657$	− 1.68875e46i	− 0.546683i
$658$	− 2.72006e46i	− 0.858718i
$659$	−2.82127e46	−0.868632	−0.434316	−	0.900761i	$-0.643010\pi$
$659$	−2.82127e46	−0.868632	−0.434316	+	0.900761i	$0.643010\pi$
$660$	0	0
$661$	3.86133e44	0.0113087	0.00565435	−	0.999984i	$-0.498200\pi$
$661$	3.86133e44	0.0113087	0.00565435	+	0.999984i	$0.498200\pi$
$662$	1.67368e46i	0.478096i
$663$	1.59093e46i	0.443279i
$664$	−3.12199e46	−0.848514
$665$	0	0
$666$	6.45237e46	1.66876
$667$	5.03350e46i	1.26997i
$668$	− 1.13415e45i	− 0.0279163i
$669$	4.51423e46	1.08406
$670$	0	0
$671$	6.77327e45	0.154838
$672$	− 9.70957e45i	− 0.216574i
$673$	3.62752e46i	0.789517i	0.918785	+	0.394759i	$0.129172\pi$
$673$	3.62752e46i	0.789517i	−0.918785	+	0.394759i	$0.870828\pi$
$674$	7.74641e46	1.64517
$675$	0	0
$676$	1.46326e44	0.00295937
$677$	− 6.71996e46i	− 1.32634i	−0.748471	−	0.663168i	$-0.769212\pi$
$677$	− 6.71996e46i	− 1.32634i	0.748471	−	0.663168i	$-0.230788\pi$
$678$	− 1.27959e47i	− 2.46479i
$679$	8.64325e46	1.62490
$680$	0	0
$681$	−2.46468e46	−0.441400
$682$	− 2.43556e46i	− 0.425752i
$683$	− 5.58915e45i	− 0.0953684i	−0.998862	−	0.0476842i	$-0.984816\pi$
$683$	− 5.58915e45i	− 0.0953684i	0.998862	−	0.0476842i	$-0.0151841\pi$
$684$	5.90746e45	0.0983955
$685$	0	0
$686$	−6.66358e46	−1.05769
$687$	− 1.31660e47i	− 2.04018i
$688$	3.07344e46i	0.464960i
$689$	−8.20415e46	−1.21176
$690$	0	0
$691$	5.89510e46	0.830048	0.415024	−	0.909810i	$-0.363773\pi$
$691$	5.89510e46	0.830048	0.415024	+	0.909810i	$0.363773\pi$
$692$	− 4.43680e45i	− 0.0609985i
$693$	4.90352e46i	0.658278i
$694$	6.02171e46	0.789384
$695$	0	0
$696$	2.18773e47	2.73490
$697$	− 4.43938e46i	− 0.541977i
$698$	− 8.70551e45i	− 0.103796i
$699$	−2.26750e47	−2.64043
$700$	0	0
$701$	−9.67830e46	−1.07511	−0.537554	−	0.843229i	$-0.680651\pi$
$701$	−9.67830e46	−1.07511	−0.537554	+	0.843229i	$0.680651\pi$
$702$	− 9.81937e45i	− 0.106542i
$703$	− 1.69334e47i	− 1.79466i
$704$	−5.53007e46	−0.572508
$705$	0	0
$706$	1.03968e47	1.02712
$707$	7.08530e45i	0.0683814i
$708$	− 2.08208e46i	− 0.196313i
$709$	1.89011e46	0.174110	0.0870552	−	0.996203i	$-0.472254\pi$
$709$	1.89011e46	0.174110	0.0870552	+	0.996203i	$0.472254\pi$
$710$	0	0
$711$	4.12528e46	0.362748
$712$	− 1.14265e47i	− 0.981735i
$713$	− 4.97963e46i	− 0.418042i
$714$	5.39081e46	0.442215
$715$	0	0
$716$	−5.23980e45	−0.0410440
$717$	− 9.75372e46i	− 0.746628i
$718$	− 2.00400e46i	− 0.149915i
$719$	−1.61675e47	−1.18199	−0.590997	−	0.806674i	$-0.701265\pi$
$719$	−1.61675e47	−1.18199	−0.590997	+	0.806674i	$0.701265\pi$
$720$	0	0
$721$	−1.55853e47	−1.08838
$722$	− 6.47989e46i	− 0.442287i
$723$	1.84053e47i	1.22790i
$724$	−1.88501e46	−0.122921
$725$	0	0
$726$	1.45118e47	0.904208
$727$	6.77908e44i	0.00412908i	0.999998	+	0.00206454i	$0.000657164\pi$
$727$	6.77908e44i	0.00412908i	−0.999998	+	0.00206454i	$0.999343\pi$
$728$	1.60585e47i	0.956173i
$729$	1.94950e47	1.13480
$730$	0	0
$731$	−2.35903e46	−0.131249
$732$	5.02127e45i	0.0273137i
$733$	− 1.03172e46i	− 0.0548714i	−0.999624	−	0.0274357i	$-0.991266\pi$
$733$	− 1.03172e46i	− 0.0548714i	0.999624	−	0.0274357i	$-0.00873415\pi$
$734$	−1.11690e47	−0.580802
$735$	0	0
$736$	1.97795e46	0.0983401
$737$	1.90924e47i	0.928213i
$738$	4.18708e47i	1.99059i
$739$	−3.22918e46	−0.150127	−0.0750636	−	0.997179i	$-0.523916\pi$
$739$	−3.22918e46	−0.150127	−0.0750636	+	0.997179i	$0.523916\pi$
$740$	0	0
$741$	−3.93790e47	−1.75091
$742$	2.77995e47i	1.20885i
$743$	− 3.20296e47i	− 1.36218i	−0.732198	−	0.681092i	$-0.761506\pi$
$743$	− 3.20296e47i	− 1.36218i	0.732198	−	0.681092i	$-0.238494\pi$
$744$	−2.16432e47	−0.900259
$745$	0	0
$746$	1.29805e47	0.516535
$747$	2.43519e47i	0.947856i
$748$	3.84017e45i	0.0146209i
$749$	−2.03999e47	−0.759763
$750$	0	0
$751$	−5.04227e47	−1.79708	−0.898540	−	0.438891i	$-0.855371\pi$
$751$	−5.04227e47	−1.79708	−0.898540	+	0.438891i	$0.855371\pi$
$752$	− 2.59488e47i	− 0.904739i
$753$	− 3.98404e47i	− 1.35896i
$754$	6.28882e47	2.09866
$755$	0	0
$756$	−2.37884e45	−0.00759900
$757$	− 5.03192e47i	− 1.57272i	−0.617767	−	0.786361i	$-0.711962\pi$
$757$	− 5.03192e47i	− 1.57272i	0.617767	−	0.786361i	$-0.288038\pi$
$758$	3.07017e47i	0.938903i
$759$	−1.93243e47	−0.578249
$760$	0	0
$761$	−3.34360e47	−0.958004	−0.479002	−	0.877814i	$-0.659001\pi$
$761$	−3.34360e47	−0.958004	−0.479002	+	0.877814i	$0.659001\pi$
$762$	3.98096e47i	1.11617i
$763$	− 3.18055e47i	− 0.872666i
$764$	1.10738e46	0.0297342
$765$	0	0
$766$	2.94521e47	0.757428
$767$	7.17429e47i	1.80574i
$768$	− 1.34137e47i	− 0.330436i
$769$	5.27752e47	1.27246	0.636231	−	0.771498i	$-0.280492\pi$
$769$	5.27752e47	1.27246	0.636231	+	0.771498i	$0.280492\pi$
$770$	0	0
$771$	3.91202e47	0.903658
$772$	1.85380e46i	0.0419159i
$773$	− 1.62889e47i	− 0.360520i	−0.983619	−	0.180260i	$-0.942306\pi$
$773$	− 1.62889e47i	− 0.360520i	0.983619	−	0.180260i	$-0.0576939\pi$
$774$	2.22497e47	0.482056
$775$	0	0
$776$	7.65272e47	1.58890
$777$	1.04200e48i	2.11797i
$778$	5.23259e47i	1.04125i
$779$	1.09884e48	2.14076
$780$	0	0
$781$	−1.10482e47	−0.206324
$782$	1.09817e47i	0.200797i
$783$	− 1.11670e47i	− 0.199926i
$784$	−2.47037e46	−0.0433059
$785$	0	0
$786$	−7.51598e47	−1.26332
$787$	1.50460e46i	0.0247649i	0.999923	+	0.0123825i	$0.00394156\pi$
$787$	1.50460e46i	0.0247649i	−0.999923	+	0.0123825i	$0.996058\pi$
$788$	− 3.80951e46i	− 0.0614025i
$789$	−3.97203e47	−0.626963
$790$	0	0
$791$	1.06816e48	1.61705
$792$	4.34156e47i	0.643696i
$793$	− 1.73020e47i	− 0.251239i
$794$	4.18322e47	0.594939
$795$	0	0
$796$	−9.56503e46	−0.130503
$797$	− 5.86479e47i	− 0.783773i	−0.920014	−	0.391887i	$-0.871823\pi$
$797$	− 5.86479e47i	− 0.783773i	0.920014	−	0.391887i	$-0.128177\pi$
$798$	1.33435e48i	1.74671i
$799$	1.99171e47	0.255391
$800$	0	0
$801$	−8.91280e47	−1.09667
$802$	1.08940e47i	0.131313i
$803$	2.71724e47i	0.320864i
$804$	−1.41539e47	−0.163739
$805$	0	0
$806$	−6.22151e47	−0.690824
$807$	− 2.07140e48i	− 2.25347i
$808$	6.27331e46i	0.0668667i
$809$	−1.28166e48	−1.33852	−0.669258	−	0.743030i	$-0.733388\pi$
$809$	−1.28166e48	−1.33852	−0.669258	+	0.743030i	$0.733388\pi$
$810$	0	0
$811$	−2.05018e47	−0.205564	−0.102782	−	0.994704i	$-0.532774\pi$
$811$	−2.05018e47	−0.205564	−0.102782	+	0.994704i	$0.532774\pi$
$812$	− 1.52353e47i	− 0.149685i
$813$	5.97037e45i	0.00574787i
$814$	−1.03820e48	−0.979445
$815$	0	0
$816$	5.14274e47	0.465915
$817$	− 5.83913e47i	− 0.518423i
$818$	6.32772e47i	0.550576i
$819$	1.25258e48	1.06812
$820$	0	0
$821$	8.74853e47	0.716594	0.358297	−	0.933608i	$-0.383358\pi$
$821$	8.74853e47	0.716594	0.358297	+	0.933608i	$0.383358\pi$
$822$	1.35210e48i	1.08549i
$823$	2.06347e47i	0.162368i	0.996699	+	0.0811841i	$0.0258702\pi$
$823$	2.06347e47i	0.162368i	−0.996699	+	0.0811841i	$0.974130\pi$
$824$	−1.37992e48	−1.06427
$825$	0	0
$826$	2.43099e48	1.80141
$827$	− 2.59525e48i	− 1.88512i	−0.334038	−	0.942559i	$-0.608412\pi$
$827$	− 2.59525e48i	− 1.88512i	0.334038	−	0.942559i	$-0.391588\pi$
$828$	− 7.40521e46i	− 0.0527274i
$829$	2.60174e48	1.81599	0.907996	−	0.418978i	$-0.137612\pi$
$829$	2.60174e48	1.81599	0.907996	+	0.418978i	$0.137612\pi$
$830$	0	0
$831$	−2.78050e48	−1.86511
$832$	1.41263e48i	0.928950i
$833$	− 1.89615e46i	− 0.0122244i
$834$	−2.95143e48	−1.86549
$835$	0	0
$836$	−9.50527e46	−0.0577512
$837$	1.10475e47i	0.0658104i
$838$	− 2.05733e48i	− 1.20165i
$839$	2.01476e48	1.15386	0.576928	−	0.816795i	$-0.304251\pi$
$839$	2.01476e48	1.15386	0.576928	+	0.816795i	$0.304251\pi$
$840$	0	0
$841$	5.33585e48	2.93812
$842$	5.14224e47i	0.277653i
$843$	− 4.34409e48i	− 2.30009i
$844$	2.92656e46	0.0151952
$845$	0	0
$846$	−1.87852e48	−0.938006
$847$	1.21140e48i	0.593213i
$848$	2.65202e48i	1.27364i
$849$	−4.34583e48	−2.04690
$850$	0	0
$851$	−2.12266e48	−0.961707
$852$	− 8.19042e46i	− 0.0363959i
$853$	− 1.85939e48i	− 0.810422i	−0.914223	−	0.405211i	$-0.867198\pi$
$853$	− 1.85939e48i	− 0.810422i	0.914223	−	0.405211i	$-0.132802\pi$
$854$	−5.86272e47	−0.250636
$855$	0	0
$856$	−1.80621e48	−0.742933
$857$	1.28606e48i	0.518891i	0.965758	+	0.259446i	$0.0835398\pi$
$857$	1.28606e48i	0.518891i	−0.965758	+	0.259446i	$0.916460\pi$
$858$	2.41437e48i	0.955572i
$859$	3.42147e48	1.32839	0.664195	−	0.747559i	$-0.268774\pi$
$859$	3.42147e48	1.32839	0.664195	+	0.747559i	$0.268774\pi$
$860$	0	0
$861$	−6.76173e48	−2.52642
$862$	− 2.24816e48i	− 0.824057i
$863$	− 1.37063e48i	− 0.492882i	−0.969158	−	0.246441i	$-0.920739\pi$
$863$	− 1.37063e48i	− 0.492882i	0.969158	−	0.246441i	$-0.0792612\pi$
$864$	−4.38816e46	−0.0154812
$865$	0	0
$866$	1.55157e48	0.526899
$867$	− 3.92347e48i	− 1.30724i
$868$	1.50723e47i	0.0492723i
$869$	−6.63769e47	−0.212907
$870$	0	0
$871$	4.87706e48	1.50612
$872$	− 2.81606e48i	− 0.853335i
$873$	− 5.96919e48i	− 1.77493i
$874$	−2.71821e48	−0.793131
$875$	0	0
$876$	−2.01439e47	−0.0566011
$877$	− 1.64670e48i	− 0.454069i	−0.973887	−	0.227035i	$-0.927097\pi$
$877$	− 1.64670e48i	− 0.454069i	0.973887	−	0.227035i	$-0.0729031\pi$
$878$	4.42531e48i	1.19753i
$879$	−8.47711e46	−0.0225129
$880$	0	0
$881$	−3.42124e48	−0.875148	−0.437574	−	0.899182i	$-0.644162\pi$
$881$	−3.42124e48	−0.875148	−0.437574	+	0.899182i	$0.644162\pi$
$882$	1.78839e47i	0.0448983i
$883$	− 7.49779e48i	− 1.84749i	−0.383012	−	0.923743i	$-0.625113\pi$
$883$	− 7.49779e48i	− 1.84749i	0.383012	−	0.923743i	$-0.374887\pi$
$884$	9.80950e46	0.0237238
$885$	0	0
$886$	5.69842e48	1.32769
$887$	1.29073e48i	0.295186i	0.989048	+	0.147593i	$0.0471526\pi$
$887$	1.29073e48i	0.295186i	−0.989048	+	0.147593i	$0.952847\pi$
$888$	9.22581e48i	2.07105i
$889$	−3.32317e48	−0.732273
$890$	0	0
$891$	−2.73613e48	−0.580972
$892$	− 2.78343e47i	− 0.0580176i
$893$	4.92994e48i	1.00877i
$894$	−4.91682e48	−0.987678
$895$	0	0
$896$	5.56415e48	1.07725
$897$	4.93630e48i	0.938266i
$898$	− 1.58139e48i	− 0.295106i
$899$	−7.07538e48	−1.29633
$900$	0	0
$901$	−2.03557e48	−0.359524
$902$	− 6.73713e48i	− 1.16833i
$903$	3.59311e48i	0.611818i
$904$	9.45743e48	1.58123
$905$	0	0
$906$	−3.06683e48	−0.494395
$907$	− 4.05607e48i	− 0.642074i	−0.947067	−	0.321037i	$-0.895969\pi$
$907$	− 4.05607e48i	− 0.642074i	0.947067	−	0.321037i	$-0.104031\pi$
$908$	1.51969e47i	0.0236232i
$909$	4.89325e47	0.0746953
$910$	0	0
$911$	−7.15538e48	−1.05337	−0.526683	−	0.850062i	$-0.676564\pi$
$911$	−7.15538e48	−1.05337	−0.526683	+	0.850062i	$0.676564\pi$
$912$	1.27294e49i	1.84032i
$913$	− 3.91828e48i	− 0.556324i
$914$	2.59210e47	0.0361443
$915$	0	0
$916$	−8.11802e47	−0.109188
$917$	− 6.27408e48i	− 0.828812i
$918$	− 2.43633e47i	− 0.0316106i
$919$	1.51037e49	1.92476	0.962382	−	0.271700i	$-0.0875859\pi$
$919$	1.51037e49	1.92476	0.962382	+	0.271700i	$0.0875859\pi$
$920$	0	0
$921$	1.64678e49	2.02465
$922$	8.57521e48i	1.03558i
$923$	2.82220e48i	0.334780i
$924$	5.84906e47	0.0681551
$925$	0	0
$926$	7.51412e48	0.844884
$927$	1.07635e49i	1.18888i
$928$	− 2.81040e48i	− 0.304948i
$929$	−1.54374e49	−1.64557	−0.822783	−	0.568356i	$-0.807580\pi$
$929$	−1.54374e49	−1.64557	−0.822783	+	0.568356i	$0.807580\pi$
$930$	0	0
$931$	4.69338e47	0.0482854
$932$	1.39812e48i	0.141313i
$933$	2.15709e49i	2.14201i
$934$	1.29210e49	1.26059
$935$	0	0
$936$	1.10903e49	1.04446
$937$	− 8.72693e48i	− 0.807530i	−0.914863	−	0.403765i	$-0.867701\pi$
$937$	− 8.72693e48i	− 0.807530i	0.914863	−	0.403765i	$-0.132299\pi$
$938$	− 1.65258e49i	− 1.50250i
$939$	7.39687e48	0.660793
$940$	0	0
$941$	−6.99024e48	−0.602925	−0.301463	−	0.953478i	$-0.597475\pi$
$941$	−6.99024e48	−0.602925	−0.301463	+	0.953478i	$0.597475\pi$
$942$	− 2.33537e49i	− 1.97932i
$943$	− 1.37744e49i	− 1.14717i
$944$	2.31912e49	1.89795
$945$	0	0
$946$	−3.58003e48	−0.282933
$947$	2.43383e48i	0.189024i	0.995524	+	0.0945118i	$0.0301290\pi$
$947$	2.43383e48i	0.189024i	−0.995524	+	0.0945118i	$0.969871\pi$
$948$	− 4.92076e47i	− 0.0375573i
$949$	6.94104e48	0.520634
$950$	0	0
$951$	−2.42246e49	−1.75501
$952$	3.98435e48i	0.283692i
$953$	2.16685e48i	0.151633i	0.997122	+	0.0758167i	$0.0241564\pi$
$953$	2.16685e48i	0.151633i	−0.997122	+	0.0758167i	$0.975844\pi$
$954$	1.91989e49	1.32047
$955$	0	0
$956$	−6.01405e47	−0.0399587
$957$	2.74573e49i	1.79313i
$958$	5.85321e48i	0.375719i
$959$	−1.12869e49	−0.712141
$960$	0	0
$961$	−9.40382e48	−0.573282
$962$	2.65204e49i	1.58924i
$963$	1.40886e49i	0.829915i
$964$	1.13485e48	0.0657157
$965$	0	0
$966$	1.67265e49	0.936014
$967$	3.10853e49i	1.71009i	0.518556	+	0.855044i	$0.326470\pi$
$967$	3.10853e49i	1.71009i	−0.518556	+	0.855044i	$0.673530\pi$
$968$	1.07257e49i	0.580072i
$969$	−9.77053e48	−0.519488
$970$	0	0
$971$	−1.05532e49	−0.542334	−0.271167	−	0.962532i	$-0.587410\pi$
$971$	−1.05532e49	−0.542334	−0.271167	+	0.962532i	$0.587410\pi$
$972$	− 2.18193e48i	− 0.110242i
$973$	− 2.46375e49i	− 1.22387i
$974$	−2.20790e49	−1.07834
$975$	0	0
$976$	−5.59292e48	−0.264069
$977$	1.91994e49i	0.891306i	0.895206	+	0.445653i	$0.147029\pi$
$977$	1.91994e49i	0.891306i	−0.895206	+	0.445653i	$0.852971\pi$
$978$	1.53402e48i	0.0700230i
$979$	1.43409e49	0.643670
$980$	0	0
$981$	−2.19655e49	−0.953242
$982$	4.82639e48i	0.205960i
$983$	5.26490e48i	0.220931i	0.993880	+	0.110466i	$0.0352342\pi$
$983$	5.26490e48i	0.220931i	−0.993880	+	0.110466i	$0.964766\pi$
$984$	−5.98682e49	−2.47046
$985$	0	0
$986$	1.56035e49	0.622663
$987$	− 3.03363e49i	− 1.19050i
$988$	2.42807e48i	0.0937069i
$989$	−7.31956e48	−0.277809
$990$	0	0
$991$	−1.70362e48	−0.0625398	−0.0312699	−	0.999511i	$-0.509955\pi$
$991$	−1.70362e48	−0.0625398	−0.0312699	+	0.999511i	$0.509955\pi$
$992$	2.78032e48i	0.100381i
$993$	1.86663e49i	0.662819i
$994$	9.56295e48	0.333977
$995$	0	0
$996$	2.90476e48	0.0981367
$997$	− 3.60379e49i	− 1.19754i	−0.800921	−	0.598770i	$-0.795656\pi$
$997$	− 3.60379e49i	− 1.19754i	0.800921	−	0.598770i	$-0.204344\pi$
$998$	− 1.23504e49i	− 0.403672i
$999$	4.70921e48	0.151397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.c.24.4		12
5.2	odd	4		25.34.a.c.1.5		6
5.3	odd	4		5.34.a.b.1.2	✓	6
5.4	even	2	inner	25.34.b.c.24.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.2	✓	6	5.3	odd	4
25.34.a.c.1.5		6	5.2	odd	4
25.34.b.c.24.4		12	1.1	even	1	trivial
25.34.b.c.24.9		12	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-96184.0i q^{2} -1.07272e8i q^{3} -6.61431e8 q^{4} -1.03179e13 q^{6} -8.61302e13i q^{7} -7.62595e14i q^{8} -5.94832e15 q^{9} +O(q^{10})\)	\(q-96184.0i q^{2} -1.07272e8i q^{3} -6.61431e8 q^{4} -1.03179e13 q^{6} -8.61302e13i q^{7} -7.62595e14i q^{8} -5.94832e15 q^{9} +9.57101e16 q^{11} +7.09533e16i q^{12} -2.44486e18i q^{13} -8.28435e18 q^{14} -7.90311e19 q^{16} -6.06607e19i q^{17} +5.72133e20i q^{18} +1.50149e21 q^{19} -9.23940e21 q^{21} -9.20578e21i q^{22} -1.88217e22i q^{23} -8.18055e22 q^{24} -2.35157e23 q^{26} +4.17567e22i q^{27} +5.69692e22i q^{28} -2.67431e24 q^{29} +2.64569e24 q^{31} +1.05089e24i q^{32} -1.02671e25i q^{33} -5.83459e24 q^{34} +3.93440e24 q^{36} -1.12777e26i q^{37} -1.44419e26i q^{38} -2.62266e26 q^{39} +7.31837e26 q^{41} +8.88682e26i q^{42} -3.88890e26i q^{43} -6.33056e25 q^{44} -1.81034e27 q^{46} +3.28337e27i q^{47} +8.47786e27i q^{48} +3.12582e26 q^{49} -6.50723e27 q^{51} +1.61711e27i q^{52} -3.35567e28i q^{53} +4.01633e27 q^{54} -6.56825e28 q^{56} -1.61068e29i q^{57} +2.57226e29i q^{58} -2.93443e29 q^{59} +7.07686e28 q^{61} -2.54473e29i q^{62} +5.12330e29i q^{63} -5.77794e29 q^{64} -9.87527e29 q^{66} +1.99482e30i q^{67} +4.01229e28i q^{68} -2.01905e30 q^{69} -1.15434e30 q^{71} +4.53616e30i q^{72} +2.83903e30i q^{73} -1.08474e31 q^{74} -9.93131e29 q^{76} -8.24353e30i q^{77} +2.52258e31i q^{78} -6.93520e30 q^{79} -2.85877e31 q^{81} -7.03910e31i q^{82} -4.09391e31i q^{83} +6.11122e30 q^{84} -3.74050e31 q^{86} +2.86880e32i q^{87} -7.29881e31i q^{88} +1.49837e32 q^{89} -2.10577e32 q^{91} +1.24492e31i q^{92} -2.83809e32i q^{93} +3.15807e32 q^{94} +1.12731e32 q^{96} +1.00351e33i q^{97} -3.00654e31i q^{98} -5.69314e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) \) 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+ \cdots - 33\!\cdots\!32 q^{99}+O(q^{100}) \) 12 * q - 59041291304 * q^4 + 13231518498704 * q^6 - 27204205166690876 * q^9 + 301521793111780384 * q^11 + 14172220017979782912 * q^14 + 129023040011717337632 * q^16 - 3423168725199973224400 * q^19 - 21120795321652308296256 * q^21 - 423790032309447397723200 * q^24 - 723658493334872996337176 * q^26 - 2610446812821454716031400 * q^29 + 21650642793601151809506704 * q^31 - 17744819333309063470980248 * q^34 + 337428823503549785822326792 * q^36 - 1159928172465211851270376912 * q^39 + 896017159299045986791643864 * q^41 - 14343610684444535018100501728 * q^44 + 6987518581952661848987190144 * q^46 + 14346854147129333747058470516 * q^49 - 109840725610127342641737389776 * q^51 + 365294374336526194478458799200 * q^54 - 785146678781996293241501500800 * q^56 + 356630312442075454139067599600 * q^59 - 564635378121172028506416574616 * q^61 - 3875937069585082792868959215744 * q^64 + 10122417492310860521089546318528 * q^66 - 632254481633966368511307646272 * q^69 + 16902436063987485405313234340144 * q^71 - 40989454834346150858579084952968 * q^74 + 58820079845469675507259388916000 * q^76 + 44105010702804710887789495271200 * q^79 - 266327929778353521323811147439348 * q^81 + 471983223984448297035157677303552 * q^84 - 257647761243091711315108096211216 * q^86 + 672982716682338963896412426721800 * q^89 + 389267538804687732313205728966864 * q^91 - 2972282194336784425374584270690528 * q^94 + 6303457980346245345128406163058944 * q^96 - 3321764604884454158829134325248032 * q^99

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