LMFDB - Embedded newform 25.34.b.c.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:	$12$
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			24.7
Root			$9129.22i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.c.24.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18258.4i q^{2} -3.67420e7i q^{3} +8.25656e9 q^{4} +6.70852e11 q^{6} +1.51681e13i q^{7} +3.07591e14i q^{8} +4.20908e15 q^{9} +O(q^{10})$	\(q+18258.4i q^{2} -3.67420e7i q^{3} +8.25656e9 q^{4} +6.70852e11 q^{6} +1.51681e13i q^{7} +3.07591e14i q^{8} +4.20908e15 q^{9} -2.61480e17 q^{11} -3.03363e17i q^{12} -3.70714e17i q^{13} -2.76946e17 q^{14} +6.53072e19 q^{16} +3.71730e20i q^{17} +7.68513e19i q^{18} -1.42255e21 q^{19} +5.57308e20 q^{21} -4.77422e21i q^{22} -3.26990e22i q^{23} +1.13015e22 q^{24} +6.76865e21 q^{26} -3.58901e23i q^{27} +1.25237e23i q^{28} -6.41343e23 q^{29} -1.44554e23 q^{31} +3.83459e24i q^{32} +9.60732e24i q^{33} -6.78720e24 q^{34} +3.47526e25 q^{36} -1.34909e26i q^{37} -2.59736e25i q^{38} -1.36208e25 q^{39} +6.37865e26 q^{41} +1.01756e25i q^{42} +3.37044e26i q^{43} -2.15893e27 q^{44} +5.97033e26 q^{46} -3.12828e27i q^{47} -2.39952e27i q^{48} +7.50092e27 q^{49} +1.36581e28 q^{51} -3.06082e27i q^{52} -4.06250e28i q^{53} +6.55298e27 q^{54} -4.66557e27 q^{56} +5.22675e28i q^{57} -1.17099e28i q^{58} +8.77955e28 q^{59} -1.84902e28 q^{61} -2.63933e27i q^{62} +6.38439e28i q^{63} +4.90971e29 q^{64} -1.75415e29 q^{66} -7.69531e29i q^{67} +3.06921e30i q^{68} -1.20143e30 q^{69} +2.72988e30 q^{71} +1.29468e30i q^{72} +4.44452e30i q^{73} +2.46323e30 q^{74} -1.17454e31 q^{76} -3.96617e30i q^{77} -2.48694e29i q^{78} +1.16758e31 q^{79} +1.02118e31 q^{81} +1.16464e31i q^{82} -4.84088e31i q^{83} +4.60145e30 q^{84} -6.15390e30 q^{86} +2.35643e31i q^{87} -8.04290e31i q^{88} -1.18101e32 q^{89} +5.62303e30 q^{91} -2.69981e32i q^{92} +5.31122e30i q^{93} +5.71176e31 q^{94} +1.40891e32 q^{96} +2.71846e31i q^{97} +1.36955e32i q^{98} -1.10059e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18258.4i	0.197001i	0.995137	+	0.0985006i	$0.0314046\pi$
$2$	18258.4i	0.197001i	−0.995137	+	0.0985006i	$0.968595\pi$
$3$	− 3.67420e7i	− 0.492791i	−0.969169	−	0.246395i	$-0.920754\pi$
$3$	− 3.67420e7i	− 0.492791i	0.969169	−	0.246395i	$-0.0792462\pi$
$4$	8.25656e9	0.961191
$5$	0	0
$5$	0	0
$6$	6.70852e11	0.0970803
$7$	1.51681e13i	0.172510i	0.996273	+	0.0862550i	$0.0274900\pi$
$7$	1.51681e13i	0.172510i	−0.996273	+	0.0862550i	$0.972510\pi$
$8$	3.07591e14i	0.386357i
$9$	4.20908e15	0.757157
$10$	0	0
$11$	−2.61480e17	−1.71577	−0.857887	−	0.513839i	$-0.828223\pi$
$11$	−2.61480e17	−1.71577	−0.857887	+	0.513839i	$0.828223\pi$
$12$	− 3.03363e17i	− 0.473666i
$13$	− 3.70714e17i	− 0.154516i	−0.997011	−	0.0772580i	$-0.975383\pi$
$13$	− 3.70714e17i	− 0.154516i	0.997011	−	0.0772580i	$-0.0246165\pi$
$14$	−2.76946e17	−0.0339847
$15$	0	0
$16$	6.53072e19	0.885078
$17$	3.71730e20i	1.85276i	0.376585	+	0.926382i	$0.377098\pi$
$17$	3.71730e20i	1.85276i	−0.376585	+	0.926382i	$0.622902\pi$
$18$	7.68513e19i	0.149161i
$19$	−1.42255e21	−1.13145	−0.565723	−	0.824595i	$-0.691403\pi$
$19$	−1.42255e21	−1.13145	−0.565723	+	0.824595i	$0.691403\pi$
$20$	0	0
$21$	5.57308e20	0.0850113
$22$	− 4.77422e21i	− 0.338009i
$23$	− 3.26990e22i	− 1.11180i	−0.831250	−	0.555898i	$-0.812374\pi$
$23$	− 3.26990e22i	− 1.11180i	0.831250	−	0.555898i	$-0.187626\pi$
$24$	1.13015e22	0.190393
$25$	0	0
$26$	6.76865e21	0.0304398
$27$	− 3.58901e23i	− 0.865911i
$28$	1.25237e23i	0.165815i
$29$	−6.41343e23	−0.475909	−0.237954	−	0.971276i	$-0.576477\pi$
$29$	−6.41343e23	−0.475909	−0.237954	+	0.971276i	$0.576477\pi$
$30$	0	0
$31$	−1.44554e23	−0.0356914	−0.0178457	−	0.999841i	$-0.505681\pi$
$31$	−1.44554e23	−0.0356914	−0.0178457	+	0.999841i	$0.505681\pi$
$32$	3.83459e24i	0.560718i
$33$	9.60732e24i	0.845517i
$34$	−6.78720e24	−0.364997
$35$	0	0
$36$	3.47526e25	0.727772
$37$	− 1.34909e26i	− 1.79768i	−0.438273	−	0.898842i	$-0.644410\pi$
$37$	− 1.34909e26i	− 1.79768i	0.438273	−	0.898842i	$-0.355590\pi$
$38$	− 2.59736e25i	− 0.222896i
$39$	−1.36208e25	−0.0761440
$40$	0	0
$41$	6.37865e26	1.56241	0.781205	−	0.624275i	$-0.214605\pi$
$41$	6.37865e26	1.56241	0.781205	+	0.624275i	$0.214605\pi$
$42$	1.01756e25i	0.0167473i
$43$	3.37044e26i	0.376233i	0.982147	+	0.188117i	$0.0602383\pi$
$43$	3.37044e26i	0.376233i	−0.982147	+	0.188117i	$0.939762\pi$
$44$	−2.15893e27	−1.64919
$45$	0	0
$46$	5.97033e26	0.219025
$47$	− 3.12828e27i	− 0.804807i	−0.915462	−	0.402403i	$-0.868175\pi$
$47$	− 3.12828e27i	− 0.804807i	0.915462	−	0.402403i	$-0.131825\pi$
$48$	− 2.39952e27i	− 0.436158i
$49$	7.50092e27	0.970240
$50$	0	0
$51$	1.36581e28	0.913025
$52$	− 3.06082e27i	− 0.148519i
$53$	− 4.06250e28i	− 1.43960i	−0.694182	−	0.719799i	$-0.744234\pi$
$53$	− 4.06250e28i	− 1.43960i	0.694182	−	0.719799i	$-0.255766\pi$
$54$	6.55298e27	0.170585
$55$	0	0
$56$	−4.66557e27	−0.0666504
$57$	5.22675e28i	0.557566i
$58$	− 1.17099e28i	− 0.0937545i
$59$	8.77955e28	0.530169	0.265084	−	0.964225i	$-0.414600\pi$
$59$	8.77955e28	0.530169	0.265084	+	0.964225i	$0.414600\pi$
$60$	0	0
$61$	−1.84902e28	−0.0644168	−0.0322084	−	0.999481i	$-0.510254\pi$
$61$	−1.84902e28	−0.0644168	−0.0322084	+	0.999481i	$0.510254\pi$
$62$	− 2.63933e27i	− 0.00703124i
$63$	6.38439e28i	0.130617i
$64$	4.90971e29	0.774616
$65$	0	0
$66$	−1.75415e29	−0.166568
$67$	− 7.69531e29i	− 0.570154i	−0.958505	−	0.285077i	$-0.907981\pi$
$67$	− 7.69531e29i	− 0.570154i	0.958505	−	0.285077i	$-0.0920192\pi$
$68$	3.06921e30i	1.78086i
$69$	−1.20143e30	−0.547883
$70$	0	0
$71$	2.72988e30	0.776929	0.388464	−	0.921464i	$-0.373006\pi$
$71$	2.72988e30	0.776929	0.388464	+	0.921464i	$0.373006\pi$
$72$	1.29468e30i	0.292533i
$73$	4.44452e30i	0.799831i	0.916552	+	0.399915i	$0.130960\pi$
$73$	4.44452e30i	0.799831i	−0.916552	+	0.399915i	$0.869040\pi$
$74$	2.46323e30	0.354146
$75$	0	0
$76$	−1.17454e31	−1.08754
$77$	− 3.96617e30i	− 0.295988i
$78$	− 2.48694e29i	− 0.0150005i
$79$	1.16758e31	0.570743	0.285371	−	0.958417i	$-0.407883\pi$
$79$	1.16758e31	0.570743	0.285371	+	0.958417i	$0.407883\pi$
$80$	0	0
$81$	1.02118e31	0.330445
$82$	1.16464e31i	0.307796i
$83$	− 4.84088e31i	− 1.04746i	−0.851886	−	0.523728i	$-0.824541\pi$
$83$	− 4.84088e31i	− 1.04746i	0.851886	−	0.523728i	$-0.175459\pi$
$84$	4.60145e30	0.0817121
$85$	0	0
$86$	−6.15390e30	−0.0741184
$87$	2.35643e31i	0.234523i
$88$	− 8.04290e31i	− 0.662901i
$89$	−1.18101e32	−0.807831	−0.403915	−	0.914796i	$-0.632351\pi$
$89$	−1.18101e32	−0.807831	−0.403915	+	0.914796i	$0.632351\pi$
$90$	0	0
$91$	5.62303e30	0.0266555
$92$	− 2.69981e32i	− 1.06865i
$93$	5.31122e30i	0.0175884i
$94$	5.71176e31	0.158548
$95$	0	0
$96$	1.40891e32	0.276317
$97$	2.71846e31i	0.0449355i	0.999748	+	0.0224678i	$0.00715231\pi$
$97$	2.71846e31i	0.0449355i	−0.999748	+	0.0224678i	$0.992848\pi$
$98$	1.36955e32i	0.191138i
$99$	−1.10059e33	−1.29911
$100$	0	0
$101$	−1.30031e33	−1.10343	−0.551714	−	0.834033i	$-0.686026\pi$
$101$	−1.30031e33	−1.10343	−0.551714	+	0.834033i	$0.686026\pi$
$102$	2.49376e32i	0.179867i
$103$	1.73233e33i	1.06369i	0.846841	+	0.531846i	$0.178502\pi$
$103$	1.73233e33i	1.06369i	−0.846841	+	0.531846i	$0.821498\pi$
$104$	1.14028e32	0.0596983
$105$	0	0
$106$	7.41749e32	0.283603
$107$	− 3.72062e32i	− 0.121838i	−0.998143	−	0.0609191i	$-0.980597\pi$
$107$	− 3.72062e32i	− 0.121838i	0.998143	−	0.0609191i	$-0.0194032\pi$
$108$	− 2.96329e33i	− 0.832305i
$109$	5.92448e33	1.42927	0.714633	−	0.699500i	$-0.246594\pi$
$109$	5.92448e33	1.42927	0.714633	+	0.699500i	$0.246594\pi$
$110$	0	0
$111$	−4.95684e33	−0.885882
$112$	9.90588e32i	0.152685i
$113$	2.74196e33i	0.364978i	0.983208	+	0.182489i	$0.0584154\pi$
$113$	2.74196e33i	0.364978i	−0.983208	+	0.182489i	$0.941585\pi$
$114$	−9.54322e32	−0.109841
$115$	0	0
$116$	−5.29529e33	−0.457439
$117$	− 1.56036e33i	− 0.116993i
$118$	1.60301e33i	0.104444i
$119$	−5.63844e33	−0.319620
$120$	0	0
$121$	4.51469e34	1.94388
$122$	− 3.37602e32i	− 0.0126902i
$123$	− 2.34364e34i	− 0.769941i
$124$	−1.19352e33	−0.0343062
$125$	0	0
$126$	−1.16569e33	−0.0257317
$127$	− 7.72774e34i	− 1.49724i	−0.663000	−	0.748619i	$-0.730717\pi$
$127$	− 7.72774e34i	− 1.49724i	0.663000	−	0.748619i	$-0.269283\pi$
$128$	4.19033e34i	0.713318i
$129$	1.23837e34	0.185404
$130$	0	0
$131$	−1.77088e34	−0.205690	−0.102845	−	0.994697i	$-0.532795\pi$
$131$	−1.77088e34	−0.205690	−0.102845	+	0.994697i	$0.532795\pi$
$132$	7.93235e34i	0.812703i
$133$	− 2.15774e34i	− 0.195186i
$134$	1.40504e34	0.112321
$135$	0	0
$136$	−1.14341e35	−0.715828
$137$	1.26744e35i	0.703133i	0.936163	+	0.351567i	$0.114351\pi$
$137$	1.26744e35i	0.703133i	−0.936163	+	0.351567i	$0.885649\pi$
$138$	− 2.19362e34i	− 0.107934i
$139$	−1.04160e35	−0.454941	−0.227471	−	0.973785i	$-0.573046\pi$
$139$	−1.04160e35	−0.454941	−0.227471	+	0.973785i	$0.573046\pi$
$140$	0	0
$141$	−1.14940e35	−0.396601
$142$	4.98434e34i	0.153056i
$143$	9.69344e34i	0.265114i
$144$	2.74884e35	0.670143
$145$	0	0
$146$	−8.11501e34	−0.157568
$147$	− 2.75599e35i	− 0.478125i
$148$	− 1.11389e36i	− 1.72792i
$149$	3.09463e35	0.429572	0.214786	−	0.976661i	$-0.431095\pi$
$149$	3.09463e35	0.429572	0.214786	+	0.976661i	$0.431095\pi$
$150$	0	0
$151$	1.12720e36	1.25569	0.627844	−	0.778340i	$-0.283938\pi$
$151$	1.12720e36	1.25569	0.627844	+	0.778340i	$0.283938\pi$
$152$	− 4.37564e35i	− 0.437142i
$153$	1.56464e36i	1.40283i
$154$	7.24160e34	0.0583100
$155$	0	0
$156$	−1.12461e35	−0.0731889
$157$	− 1.58631e36i	− 0.929061i	−0.885557	−	0.464530i	$-0.846223\pi$
$157$	− 1.58631e36i	− 0.929061i	0.885557	−	0.464530i	$-0.153777\pi$
$158$	2.13182e35i	0.112437i
$159$	−1.49264e36	−0.709421
$160$	0	0
$161$	4.95982e35	0.191796
$162$	1.86451e35i	0.0650979i
$163$	− 3.56599e36i	− 1.12483i	−0.826857	−	0.562413i	$-0.809873\pi$
$163$	− 3.56599e36i	− 1.12483i	0.826857	−	0.562413i	$-0.190127\pi$
$164$	5.26657e36	1.50177
$165$	0	0
$166$	8.83869e35	0.206350
$167$	− 6.77798e36i	− 1.43311i	−0.697532	−	0.716553i	$-0.745719\pi$
$167$	− 6.77798e36i	− 1.43311i	0.697532	−	0.716553i	$-0.254281\pi$
$168$	1.71423e35i	0.0328447i
$169$	5.61870e36	0.976125
$170$	0	0
$171$	−5.98764e36	−0.856683
$172$	2.78283e36i	0.361632i
$173$	1.72200e36i	0.203364i	0.994817	+	0.101682i	$0.0324224\pi$
$173$	1.72200e36i	0.203364i	−0.994817	+	0.101682i	$0.967578\pi$
$174$	−4.30247e35	−0.0462014
$175$	0	0
$176$	−1.70766e37	−1.51859
$177$	− 3.22578e36i	− 0.261262i
$178$	− 2.15635e36i	− 0.159144i
$179$	6.69163e36	0.450253	0.225127	−	0.974330i	$-0.427720\pi$
$179$	6.69163e36	0.450253	0.225127	+	0.974330i	$0.427720\pi$
$180$	0	0
$181$	1.34636e37	0.754163	0.377082	−	0.926180i	$-0.376928\pi$
$181$	1.34636e37	0.754163	0.377082	+	0.926180i	$0.376928\pi$
$182$	1.02668e35i	0.00525117i
$183$	6.79367e35i	0.0317440i
$184$	1.00579e37	0.429550
$185$	0	0
$186$	−9.69745e34	−0.00346493
$187$	− 9.72001e37i	− 3.17892i
$188$	− 2.58289e37i	− 0.773573i
$189$	5.44386e36	0.149378
$190$	0	0
$191$	−6.65942e36	−0.153598	−0.0767990	−	0.997047i	$-0.524470\pi$
$191$	−6.65942e36	−0.153598	−0.0767990	+	0.997047i	$0.524470\pi$
$192$	− 1.80393e37i	− 0.381723i
$193$	− 5.05982e37i	− 0.982742i	−0.870950	−	0.491371i	$-0.836496\pi$
$193$	− 5.05982e37i	− 0.982742i	0.870950	−	0.491371i	$-0.163504\pi$
$194$	−4.96349e35	−0.00885235
$195$	0	0
$196$	6.19318e37	0.932586
$197$	− 2.33016e37i	− 0.322621i	−0.986904	−	0.161311i	$-0.948428\pi$
$197$	− 2.33016e37i	− 0.322621i	0.986904	−	0.161311i	$-0.0515721\pi$
$198$	− 2.00951e37i	− 0.255926i
$199$	1.24079e38	1.45420	0.727100	−	0.686531i	$-0.240868\pi$
$199$	1.24079e38	1.45420	0.727100	+	0.686531i	$0.240868\pi$
$200$	0	0
$201$	−2.82742e37	−0.280967
$202$	− 2.37416e37i	− 0.217377i
$203$	− 9.72798e36i	− 0.0820990i
$204$	1.12769e38	0.877591
$205$	0	0
$206$	−3.16296e37	−0.209549
$207$	− 1.37633e38i	− 0.841805i
$208$	− 2.42103e37i	− 0.136759i
$209$	3.71970e38	1.94130
$210$	0	0
$211$	−2.15498e38	−0.961133	−0.480567	−	0.876958i	$-0.659569\pi$
$211$	−2.15498e38	−0.961133	−0.480567	+	0.876958i	$0.659569\pi$
$212$	− 3.35423e38i	− 1.38373i
$213$	− 1.00301e38i	− 0.382863i
$214$	6.79328e36	0.0240023
$215$	0	0
$216$	1.10395e38	0.334550
$217$	− 2.19262e36i	− 0.00615711i
$218$	1.08172e38i	0.281567i
$219$	1.63301e38	0.394149
$220$	0	0
$221$	1.37805e38	0.286282
$222$	− 9.05042e37i	− 0.174520i
$223$	− 1.94520e37i	− 0.0348285i	−0.999848	−	0.0174142i	$-0.994457\pi$
$223$	− 1.94520e37i	− 0.0348285i	0.999848	−	0.0174142i	$-0.00554340\pi$
$224$	−5.81636e37	−0.0967294
$225$	0	0
$226$	−5.00639e37	−0.0719011
$227$	− 1.37345e39i	− 1.83395i	−0.398947	−	0.916974i	$-0.630624\pi$
$227$	− 1.37345e39i	− 1.83395i	0.398947	−	0.916974i	$-0.369376\pi$
$228$	4.31550e38i	0.535927i
$229$	3.69693e38	0.427126	0.213563	−	0.976929i	$-0.431493\pi$
$229$	3.69693e38	0.427126	0.213563	+	0.976929i	$0.431493\pi$
$230$	0	0
$231$	−1.45725e38	−0.145860
$232$	− 1.97271e38i	− 0.183871i
$233$	− 2.02428e39i	− 1.75751i	−0.477275	−	0.878754i	$-0.658375\pi$
$233$	− 2.02428e39i	− 1.75751i	0.477275	−	0.878754i	$-0.341625\pi$
$234$	2.84898e37	0.0230477
$235$	0	0
$236$	7.24889e38	0.509593
$237$	− 4.28994e38i	− 0.281257i
$238$	− 1.02949e38i	− 0.0629655i
$239$	6.31944e38	0.360673	0.180336	−	0.983605i	$-0.442281\pi$
$239$	6.31944e38	0.360673	0.180336	+	0.983605i	$0.442281\pi$
$240$	0	0
$241$	−1.82829e39	−0.909420	−0.454710	−	0.890640i	$-0.650257\pi$
$241$	−1.82829e39	−0.909420	−0.454710	+	0.890640i	$0.650257\pi$
$242$	8.24311e38i	0.382946i
$243$	− 2.37036e39i	− 1.02875i
$244$	−1.52665e38	−0.0619168
$245$	0	0
$246$	4.27913e38	0.151679
$247$	5.27360e38i	0.174826i
$248$	− 4.44636e37i	− 0.0137896i
$249$	−1.77864e39	−0.516177
$250$	0	0
$251$	−2.17903e39	−0.554174	−0.277087	−	0.960845i	$-0.589369\pi$
$251$	−2.17903e39	−0.554174	−0.277087	+	0.960845i	$0.589369\pi$
$252$	5.27131e38i	0.125548i
$253$	8.55015e39i	1.90759i
$254$	1.41096e39	0.294958
$255$	0	0
$256$	3.45232e39	0.634091
$257$	1.48926e39i	0.256492i	0.991742	+	0.128246i	$0.0409348\pi$
$257$	1.48926e39i	0.256492i	−0.991742	+	0.128246i	$0.959065\pi$
$258$	2.26107e38i	0.0365249i
$259$	2.04632e39	0.310118
$260$	0	0
$261$	−2.69947e39	−0.360338
$262$	− 3.23335e38i	− 0.0405211i
$263$	1.17319e40i	1.38069i	0.723479	+	0.690346i	$0.242542\pi$
$263$	1.17319e40i	1.38069i	−0.723479	+	0.690346i	$0.757458\pi$
$264$	−2.95512e39	−0.326671
$265$	0	0
$266$	3.93970e38	0.0384518
$267$	4.33929e39i	0.398091i
$268$	− 6.35369e39i	− 0.548027i
$269$	−2.30936e40	−1.87318	−0.936590	−	0.350428i	$-0.886036\pi$
$269$	−2.30936e40	−1.87318	−0.936590	+	0.350428i	$0.886036\pi$
$270$	0	0
$271$	2.16176e40	1.55172	0.775861	−	0.630903i	$-0.217316\pi$
$271$	2.16176e40	1.55172	0.775861	+	0.630903i	$0.217316\pi$
$272$	2.42766e40i	1.63984i
$273$	− 2.06602e38i	− 0.0131356i
$274$	−2.31414e39	−0.138518
$275$	0	0
$276$	−9.91967e39	−0.526620
$277$	1.86721e40i	0.933847i	0.884298	+	0.466924i	$0.154638\pi$
$277$	1.86721e40i	0.933847i	−0.884298	+	0.466924i	$0.845362\pi$
$278$	− 1.90179e39i	− 0.0896239i
$279$	−6.08441e38	−0.0270240
$280$	0	0
$281$	−6.80173e39	−0.268513	−0.134256	−	0.990947i	$-0.542865\pi$
$281$	−6.80173e39	−0.268513	−0.134256	+	0.990947i	$0.542865\pi$
$282$	− 2.09862e39i	− 0.0781309i
$283$	− 3.60211e40i	− 1.26497i	−0.774573	−	0.632485i	$-0.782035\pi$
$283$	− 3.60211e40i	− 1.26497i	0.774573	−	0.632485i	$-0.217965\pi$
$284$	2.25395e40	0.746777
$285$	0	0
$286$	−1.76987e39	−0.0522278
$287$	9.67521e39i	0.269531i
$288$	1.61401e40i	0.424552i
$289$	−9.79285e40	−2.43274
$290$	0	0
$291$	9.98819e38	0.0221438
$292$	3.66965e40i	0.768790i
$293$	6.02024e40i	1.19206i	0.802962	+	0.596030i	$0.203256\pi$
$293$	6.02024e40i	1.19206i	−0.802962	+	0.596030i	$0.796744\pi$
$294$	5.03201e39	0.0941912
$295$	0	0
$296$	4.14968e40	0.694547
$297$	9.38457e40i	1.48571i
$298$	5.65032e39i	0.0846261i
$299$	−1.21220e40	−0.171790
$300$	0	0
$301$	−5.11233e39	−0.0649040
$302$	2.05809e40i	0.247372i
$303$	4.77760e40i	0.543759i
$304$	−9.29029e40	−1.00142
$305$	0	0
$306$	−2.85679e40	−0.276360
$307$	− 2.05983e41i	− 1.88820i	−0.329664	−	0.944098i	$-0.606936\pi$
$307$	− 2.05983e41i	− 1.88820i	0.329664	−	0.944098i	$-0.393064\pi$
$308$	− 3.27469e40i	− 0.284501i
$309$	6.36493e40	0.524178
$310$	0	0
$311$	−1.19843e41	−0.887294	−0.443647	−	0.896202i	$-0.646316\pi$
$311$	−1.19843e41	−0.887294	−0.443647	+	0.896202i	$0.646316\pi$
$312$	− 4.18962e39i	− 0.0294188i
$313$	2.13282e41i	1.42060i	0.703897	+	0.710302i	$0.251442\pi$
$313$	2.13282e41i	1.42060i	−0.703897	+	0.710302i	$0.748558\pi$
$314$	2.89636e40	0.183026
$315$	0	0
$316$	9.64022e40	0.548593
$317$	2.31538e41i	1.25068i	0.780354	+	0.625338i	$0.215039\pi$
$317$	2.31538e41i	1.25068i	−0.780354	+	0.625338i	$0.784961\pi$
$318$	− 2.72534e40i	− 0.139757i
$319$	1.67699e41	0.816552
$320$	0	0
$321$	−1.36703e40	−0.0600407
$322$	9.05586e39i	0.0377840i
$323$	− 5.28805e41i	− 2.09630i
$324$	8.43142e40	0.317620
$325$	0	0
$326$	6.51094e40	0.221592
$327$	− 2.17677e41i	− 0.704329i
$328$	1.96201e41i	0.603647i
$329$	4.74502e40	0.138837
$330$	0	0
$331$	−3.27790e40	−0.0867830	−0.0433915	−	0.999058i	$-0.513816\pi$
$331$	−3.27790e40	−0.0867830	−0.0433915	+	0.999058i	$0.513816\pi$
$332$	− 3.99690e41i	− 1.00680i
$333$	− 5.67844e41i	− 1.36113i
$334$	1.23755e41	0.282324
$335$	0	0
$336$	3.63962e40	0.0752416
$337$	− 5.05149e41i	− 0.994321i	−0.867659	−	0.497160i	$-0.834376\pi$
$337$	− 5.05149e41i	− 0.994321i	0.867659	−	0.497160i	$-0.165624\pi$
$338$	1.02589e41i	0.192298i
$339$	1.00745e41	0.179858
$340$	0	0
$341$	3.77981e40	0.0612383
$342$	− 1.09325e41i	− 0.168767i
$343$	2.31040e41i	0.339886i
$344$	−1.03672e41	−0.145360
$345$	0	0
$346$	−3.14411e40	−0.0400629
$347$	− 5.54748e40i	− 0.0673999i	−0.999432	−	0.0337000i	$-0.989271\pi$
$347$	− 5.54748e40i	− 0.0673999i	0.999432	−	0.0337000i	$-0.0107291\pi$
$348$	1.94560e41i	0.225422i
$349$	4.36140e41	0.481955	0.240978	−	0.970531i	$-0.422532\pi$
$349$	4.36140e41	0.481955	0.240978	+	0.970531i	$0.422532\pi$
$350$	0	0
$351$	−1.33050e41	−0.133797
$352$	− 1.00267e42i	− 0.962065i
$353$	2.19124e41i	0.200635i	0.994955	+	0.100318i	$0.0319859\pi$
$353$	2.19124e41i	0.200635i	−0.994955	+	0.100318i	$0.968014\pi$
$354$	5.88978e40	0.0514689
$355$	0	0
$356$	−9.75113e41	−0.776479
$357$	2.07168e41i	0.157506i
$358$	1.22179e41i	0.0887004i
$359$	1.83249e42	1.27053	0.635264	−	0.772295i	$-0.280891\pi$
$359$	1.83249e42	1.27053	0.635264	+	0.772295i	$0.280891\pi$
$360$	0	0
$361$	4.42885e41	0.280170
$362$	2.45825e41i	0.148571i
$363$	− 1.65879e42i	− 0.957925i
$364$	4.64269e40	0.0256211
$365$	0	0
$366$	−1.24042e40	−0.00625360
$367$	− 2.46022e42i	− 1.18572i	−0.805304	−	0.592862i	$-0.797998\pi$
$367$	− 2.46022e42i	− 1.18572i	0.805304	−	0.592862i	$-0.202002\pi$
$368$	− 2.13548e42i	− 0.984026i
$369$	2.68483e42	1.18299
$370$	0	0
$371$	6.16205e41	0.248345
$372$	4.38524e40i	0.0169058i
$373$	9.17264e41i	0.338297i	0.985591	+	0.169149i	$0.0541018\pi$
$373$	9.17264e41i	0.338297i	−0.985591	+	0.169149i	$0.945898\pi$
$374$	1.77472e42	0.626251
$375$	0	0
$376$	9.62231e41	0.310942
$377$	2.37755e41i	0.0735355i
$378$	9.93964e40i	0.0294277i
$379$	−5.49346e42	−1.55704	−0.778518	−	0.627622i	$-0.784028\pi$
$379$	−5.49346e42	−1.55704	−0.778518	+	0.627622i	$0.784028\pi$
$380$	0	0
$381$	−2.83933e42	−0.737825
$382$	− 1.21591e41i	− 0.0302590i
$383$	2.70725e42i	0.645281i	0.946522	+	0.322640i	$0.104570\pi$
$383$	2.70725e42i	0.645281i	−0.946522	+	0.322640i	$0.895430\pi$
$384$	1.53961e42	0.351517
$385$	0	0
$386$	9.23844e41	0.193601
$387$	1.41865e42i	0.284868i
$388$	2.24452e41i	0.0431916i
$389$	−5.33079e42	−0.983157	−0.491579	−	0.870833i	$-0.663580\pi$
$389$	−5.33079e42	−0.983157	−0.491579	+	0.870833i	$0.663580\pi$
$390$	0	0
$391$	1.21552e43	2.05990
$392$	2.30721e42i	0.374859i
$393$	6.50657e41i	0.101362i
$394$	4.25451e41	0.0635568
$395$	0	0
$396$	−9.08712e42	−1.24869
$397$	− 8.08784e42i	− 1.06608i	−0.846091	−	0.533039i	$-0.821050\pi$
$397$	− 8.08784e42i	− 1.06608i	0.846091	−	0.533039i	$-0.178950\pi$
$398$	2.26550e42i	0.286479i
$399$	−7.92799e41	−0.0961857
$400$	0	0
$401$	−1.16113e43	−1.29717	−0.648587	−	0.761140i	$-0.724640\pi$
$401$	−1.16113e43	−1.29717	−0.648587	+	0.761140i	$0.724640\pi$
$402$	− 5.16242e41i	− 0.0553507i
$403$	5.35882e40i	0.00551488i
$404$	−1.07361e43	−1.06061
$405$	0	0
$406$	1.77618e41	0.0161736
$407$	3.52761e43i	3.08442i
$408$	4.20111e42i	0.352753i
$409$	−4.40488e42	−0.355222	−0.177611	−	0.984101i	$-0.556837\pi$
$409$	−4.40488e42	−0.355222	−0.177611	+	0.984101i	$0.556837\pi$
$410$	0	0
$411$	4.65683e42	0.346498
$412$	1.43031e43i	1.02241i
$413$	1.33169e42i	0.0914594i
$414$	2.51296e42	0.165836
$415$	0	0
$416$	1.42154e42	0.0866399
$417$	3.82704e42i	0.224191i
$418$	6.79158e42i	0.382439i
$419$	−2.34926e43	−1.27174	−0.635871	−	0.771796i	$-0.719359\pi$
$419$	−2.34926e43	−1.27174	−0.635871	+	0.771796i	$0.719359\pi$
$420$	0	0
$421$	−4.10149e42	−0.205252	−0.102626	−	0.994720i	$-0.532724\pi$
$421$	−4.10149e42	−0.205252	−0.102626	+	0.994720i	$0.532724\pi$
$422$	− 3.93466e42i	− 0.189344i
$423$	− 1.31672e43i	− 0.609365i
$424$	1.24959e43	0.556199
$425$	0	0
$426$	1.83135e42	0.0754245
$427$	− 2.80461e41i	− 0.0111125i
$428$	− 3.07196e42i	− 0.117110i
$429$	3.56157e42	0.130646
$430$	0	0
$431$	1.92923e43	0.655404	0.327702	−	0.944781i	$-0.393726\pi$
$431$	1.92923e43	0.655404	0.327702	+	0.944781i	$0.393726\pi$
$432$	− 2.34389e43i	− 0.766398i
$433$	1.20050e43i	0.377843i	0.981992	+	0.188922i	$0.0604992\pi$
$433$	1.20050e43i	0.377843i	−0.981992	+	0.188922i	$0.939501\pi$
$434$	4.00338e40	0.00121296
$435$	0	0
$436$	4.89159e43	1.37380
$437$	4.65160e43i	1.25794i
$438$	2.98162e42i	0.0776478i
$439$	−3.55254e43	−0.890993	−0.445496	−	0.895284i	$-0.646973\pi$
$439$	−3.55254e43	−0.890993	−0.445496	+	0.895284i	$0.646973\pi$
$440$	0	0
$441$	3.15720e43	0.734625
$442$	2.51611e42i	0.0563978i
$443$	4.50074e43i	0.971901i	0.873986	+	0.485951i	$0.161526\pi$
$443$	4.50074e43i	0.971901i	−0.873986	+	0.485951i	$0.838474\pi$
$444$	−4.09265e43	−0.851501
$445$	0	0
$446$	3.55163e41	0.00686124
$447$	− 1.13703e43i	− 0.211689i
$448$	7.44711e42i	0.133629i
$449$	4.48522e43	0.775745	0.387872	−	0.921713i	$-0.373210\pi$
$449$	4.48522e43	0.775745	0.387872	+	0.921713i	$0.373210\pi$
$450$	0	0
$451$	−1.66789e44	−2.68074
$452$	2.26392e43i	0.350814i
$453$	− 4.14156e43i	− 0.618791i
$454$	2.50771e43	0.361290
$455$	0	0
$456$	−1.60770e43	−0.215419
$457$	− 5.99465e43i	− 0.774723i	−0.921928	−	0.387362i	$-0.873386\pi$
$457$	− 5.99465e43i	− 0.774723i	0.921928	−	0.387362i	$-0.126614\pi$
$458$	6.75002e42i	0.0841442i
$459$	1.33414e44	1.60433
$460$	0	0
$461$	3.64117e43	0.407546	0.203773	−	0.979018i	$-0.434680\pi$
$461$	3.64117e43	0.407546	0.203773	+	0.979018i	$0.434680\pi$
$462$	− 2.66071e42i	− 0.0287346i
$463$	− 4.93497e43i	− 0.514278i	−0.966374	−	0.257139i	$-0.917220\pi$
$463$	− 4.93497e43i	− 0.514278i	0.966374	−	0.257139i	$-0.0827798\pi$
$464$	−4.18844e43	−0.421216
$465$	0	0
$466$	3.69601e43	0.346231
$467$	− 6.19636e43i	− 0.560284i	−0.959959	−	0.280142i	$-0.909619\pi$
$467$	− 6.19636e43i	− 0.560284i	0.959959	−	0.280142i	$-0.0903815\pi$
$468$	− 1.28833e43i	− 0.112452i
$469$	1.16723e43	0.0983572
$470$	0	0
$471$	−5.82843e43	−0.457832
$472$	2.70051e43i	0.204834i
$473$	− 8.81305e43i	− 0.645531i
$474$	7.83275e42	0.0554079
$475$	0	0
$476$	−4.65542e43	−0.307216
$477$	− 1.70994e44i	− 1.09000i
$478$	1.15383e43i	0.0710530i
$479$	−1.65648e44	−0.985483	−0.492741	−	0.870176i	$-0.664005\pi$
$479$	−1.65648e44	−0.985483	−0.492741	+	0.870176i	$0.664005\pi$
$480$	0	0
$481$	−5.00127e43	−0.277771
$482$	− 3.33818e43i	− 0.179157i
$483$	− 1.82234e43i	− 0.0945152i
$484$	3.72758e44	1.86844
$485$	0	0
$486$	4.32790e43	0.202665
$487$	− 3.41088e44i	− 1.54397i	−0.635642	−	0.771984i	$-0.719264\pi$
$487$	− 3.41088e44i	− 1.54397i	0.635642	−	0.771984i	$-0.280736\pi$
$488$	− 5.68741e42i	− 0.0248879i
$489$	−1.31022e44	−0.554303
$490$	0	0
$491$	4.35160e44	1.72109	0.860547	−	0.509371i	$-0.170122\pi$
$491$	4.35160e44	1.72109	0.860547	+	0.509371i	$0.170122\pi$
$492$	− 1.93505e44i	− 0.740060i
$493$	− 2.38406e44i	− 0.881747i
$494$	−9.62876e42	−0.0344410
$495$	0	0
$496$	−9.44044e42	−0.0315896
$497$	4.14072e43i	0.134028i
$498$	− 3.24751e43i	− 0.101687i
$499$	6.19626e44	1.87703	0.938514	−	0.345242i	$-0.112203\pi$
$499$	6.19626e44	1.87703	0.938514	+	0.345242i	$0.112203\pi$
$500$	0	0
$501$	−2.49037e44	−0.706222
$502$	− 3.97856e43i	− 0.109173i
$503$	5.28443e44i	1.40322i	0.712560	+	0.701611i	$0.247536\pi$
$503$	5.28443e44i	1.40322i	−0.712560	+	0.701611i	$0.752464\pi$
$504$	−1.96378e43	−0.0504648
$505$	0	0
$506$	−1.56112e44	−0.375797
$507$	− 2.06443e44i	− 0.481025i
$508$	− 6.38046e44i	− 1.43913i
$509$	4.72823e43	0.103242	0.0516209	−	0.998667i	$-0.483561\pi$
$509$	4.72823e43	0.103242	0.0516209	+	0.998667i	$0.483561\pi$
$510$	0	0
$511$	−6.74151e43	−0.137979
$512$	4.22980e44i	0.838235i
$513$	5.10556e44i	0.979731i
$514$	−2.71916e43	−0.0505293
$515$	0	0
$516$	1.02247e44	0.178209
$517$	8.17985e44i	1.38087i
$518$	3.73626e43i	0.0610937i
$519$	6.32699e43	0.100216
$520$	0	0
$521$	−4.38738e44	−0.652203	−0.326102	−	0.945335i	$-0.605735\pi$
$521$	−4.38738e44	−0.652203	−0.326102	+	0.945335i	$0.605735\pi$
$522$	− 4.92881e43i	− 0.0709869i
$523$	− 1.40016e44i	− 0.195389i	−0.995216	−	0.0976944i	$-0.968853\pi$
$523$	− 1.40016e44i	− 0.195389i	0.995216	−	0.0976944i	$-0.0311468\pi$
$524$	−1.46214e44	−0.197707
$525$	0	0
$526$	−2.14205e44	−0.271998
$527$	− 5.37351e43i	− 0.0661277i
$528$	6.27428e44i	0.748349i
$529$	−2.04220e44	−0.236091
$530$	0	0
$531$	3.69539e44	0.401421
$532$	− 1.78156e44i	− 0.187611i
$533$	− 2.36465e44i	− 0.241417i
$534$	−7.92286e43	−0.0784244
$535$	0	0
$536$	2.36701e44	0.220283
$537$	− 2.45864e44i	− 0.221881i
$538$	− 4.21653e44i	− 0.369018i
$539$	−1.96134e45	−1.66471
$540$	0	0
$541$	1.56960e45	1.25324	0.626622	−	0.779324i	$-0.284437\pi$
$541$	1.56960e45	1.25324	0.626622	+	0.779324i	$0.284437\pi$
$542$	3.94704e44i	0.305691i
$543$	− 4.94681e44i	− 0.371645i
$544$	−1.42543e45	−1.03888
$545$	0	0
$546$	3.77222e42	0.00258773
$547$	2.11683e45i	1.40895i	0.709730	+	0.704474i	$0.248817\pi$
$547$	2.11683e45i	1.40895i	−0.709730	+	0.704474i	$0.751183\pi$
$548$	1.04647e45i	0.675845i
$549$	−7.78267e43	−0.0487736
$550$	0	0
$551$	9.12345e44	0.538465
$552$	− 3.69548e44i	− 0.211678i
$553$	1.77100e44i	0.0984588i
$554$	−3.40922e44	−0.183969
$555$	0	0
$556$	−8.60001e44	−0.437285
$557$	1.56733e45i	0.773661i	0.922151	+	0.386830i	$0.126430\pi$
$557$	1.56733e45i	0.773661i	−0.922151	+	0.386830i	$0.873570\pi$
$558$	− 1.11092e43i	− 0.00532375i
$559$	1.24947e44	0.0581341
$560$	0	0
$561$	−3.57133e45	−1.56654
$562$	− 1.24189e44i	− 0.0528974i
$563$	1.29413e44i	0.0535291i	0.999642	+	0.0267646i	$0.00852044\pi$
$563$	1.29413e44i	0.0535291i	−0.999642	+	0.0267646i	$0.991480\pi$
$564$	−9.49006e44	−0.381209
$565$	0	0
$566$	6.57688e44	0.249200
$567$	1.54894e44i	0.0570050i
$568$	8.39687e44i	0.300172i
$569$	2.93499e45	1.01919	0.509593	−	0.860415i	$-0.329796\pi$
$569$	2.93499e45	1.01919	0.509593	+	0.860415i	$0.329796\pi$
$570$	0	0
$571$	−9.20277e44	−0.301594	−0.150797	−	0.988565i	$-0.548184\pi$
$571$	−9.20277e44	−0.301594	−0.150797	+	0.988565i	$0.548184\pi$
$572$	8.00345e44i	0.254825i
$573$	2.44681e44i	0.0756917i
$574$	−1.76654e44	−0.0530979
$575$	0	0
$576$	2.06654e45	0.586506
$577$	6.78370e45i	1.87097i	0.353371	+	0.935483i	$0.385035\pi$
$577$	6.78370e45i	1.87097i	−0.353371	+	0.935483i	$0.614965\pi$
$578$	− 1.78802e45i	− 0.479251i
$579$	−1.85908e45	−0.484286
$580$	0	0
$581$	7.34270e44	0.180697
$582$	1.82369e43i	0.00436236i
$583$	1.06226e46i	2.47003i
$584$	−1.36709e45	−0.309020
$585$	0	0
$586$	−1.09920e45	−0.234837
$587$	− 1.92291e45i	− 0.399421i	−0.979855	−	0.199710i	$-0.936000\pi$
$587$	− 1.92291e45i	− 0.399421i	0.979855	−	0.199710i	$-0.0640001\pi$
$588$	− 2.27550e45i	− 0.459570i
$589$	2.05636e44	0.0403828
$590$	0	0
$591$	−8.56148e44	−0.158985
$592$	− 8.81055e45i	− 1.59109i
$593$	− 3.84061e45i	− 0.674524i	−0.941411	−	0.337262i	$-0.890499\pi$
$593$	− 3.84061e45i	− 0.674524i	0.941411	−	0.337262i	$-0.109501\pi$
$594$	−1.71348e45	−0.292686
$595$	0	0
$596$	2.55510e45	0.412900
$597$	− 4.55893e45i	− 0.716616i
$598$	− 2.21328e44i	− 0.0338429i
$599$	1.48464e45	0.220840	0.110420	−	0.993885i	$-0.464780\pi$
$599$	1.48464e45	0.220840	0.110420	+	0.993885i	$0.464780\pi$
$600$	0	0
$601$	5.01345e45	0.705843	0.352921	−	0.935653i	$-0.385188\pi$
$601$	5.01345e45	0.705843	0.352921	+	0.935653i	$0.385188\pi$
$602$	− 9.33431e43i	− 0.0127862i
$603$	− 3.23902e45i	− 0.431696i
$604$	9.30680e45	1.20695
$605$	0	0
$606$	−8.72316e44	−0.107121
$607$	− 3.29284e45i	− 0.393511i	−0.980453	−	0.196756i	$-0.936959\pi$
$607$	− 3.29284e45i	− 0.393511i	0.980453	−	0.196756i	$-0.0630406\pi$
$608$	− 5.45491e45i	− 0.634422i
$609$	−3.57426e44	−0.0404576
$610$	0	0
$611$	−1.15970e45	−0.124355
$612$	1.29186e46i	1.34839i
$613$	− 1.00399e46i	− 1.02008i	−0.860152	−	0.510038i	$-0.829631\pi$
$613$	− 1.00399e46i	− 1.02008i	0.860152	−	0.510038i	$-0.170369\pi$
$614$	3.76092e45	0.371977
$615$	0	0
$616$	1.21996e45	0.114357
$617$	− 1.43698e46i	− 1.31144i	−0.755006	−	0.655718i	$-0.772366\pi$
$617$	− 1.43698e46i	− 1.31144i	0.755006	−	0.655718i	$-0.227634\pi$
$618$	1.16214e45i	0.103264i
$619$	−1.61224e46	−1.39487	−0.697435	−	0.716648i	$-0.745675\pi$
$619$	−1.61224e46	−1.39487	−0.697435	+	0.716648i	$0.745675\pi$
$620$	0	0
$621$	−1.17357e46	−0.962716
$622$	− 2.18815e45i	− 0.174798i
$623$	− 1.79138e45i	− 0.139359i
$624$	−8.89535e44	−0.0673934
$625$	0	0
$626$	−3.89420e45	−0.279861
$627$	− 1.36669e46i	− 0.956657i
$628$	− 1.30975e46i	− 0.893004i
$629$	5.01498e46	3.33068
$630$	0	0
$631$	2.47683e46	1.56103	0.780516	−	0.625136i	$-0.214957\pi$
$631$	2.47683e46	1.56103	0.780516	+	0.625136i	$0.214957\pi$
$632$	3.59138e45i	0.220510i
$633$	7.91785e45i	0.473638i
$634$	−4.22752e45	−0.246384
$635$	0	0
$636$	−1.23241e46	−0.681889
$637$	− 2.78069e45i	− 0.149918i
$638$	3.06192e45i	0.160862i
$639$	1.14903e46	0.588257
$640$	0	0
$641$	−3.57575e46	−1.73864	−0.869321	−	0.494249i	$-0.835443\pi$
$641$	−3.57575e46	−1.73864	−0.869321	+	0.494249i	$0.835443\pi$
$642$	− 2.49599e44i	− 0.0118281i
$643$	1.88292e46i	0.869663i	0.900512	+	0.434831i	$0.143192\pi$
$643$	1.88292e46i	0.869663i	−0.900512	+	0.434831i	$0.856808\pi$
$644$	4.09511e45	0.184352
$645$	0	0
$646$	9.65515e45	0.412974
$647$	− 2.33501e46i	− 0.973573i	−0.873521	−	0.486787i	$-0.838169\pi$
$647$	− 2.33501e46i	− 0.973573i	0.873521	−	0.486787i	$-0.161831\pi$
$648$	3.14105e45i	0.127669i
$649$	−2.29568e46	−0.909649
$650$	0	0
$651$	−8.05612e43	−0.00303417
$652$	− 2.94428e46i	− 1.08117i
$653$	2.35876e46i	0.844531i	0.906472	+	0.422266i	$0.138765\pi$
$653$	2.35876e46i	0.844531i	−0.906472	+	0.422266i	$0.861235\pi$
$654$	3.97445e45	0.138754
$655$	0	0
$656$	4.16572e46	1.38285
$657$	1.87074e46i	0.605598i
$658$	8.66366e44i	0.0273511i
$659$	−2.73242e46	−0.841276	−0.420638	−	0.907228i	$-0.638194\pi$
$659$	−2.73242e46	−0.841276	−0.420638	+	0.907228i	$0.638194\pi$
$660$	0	0
$661$	−2.72690e46	−0.798629	−0.399315	−	0.916814i	$-0.630752\pi$
$661$	−2.72690e46	−0.798629	−0.399315	+	0.916814i	$0.630752\pi$
$662$	− 5.98494e44i	− 0.0170963i
$663$	− 5.06325e45i	− 0.141077i
$664$	1.48901e46	0.404692
$665$	0	0
$666$	1.03679e46	0.268144
$667$	2.09713e46i	0.529114i
$668$	− 5.59628e46i	− 1.37749i
$669$	−7.14706e44	−0.0171631
$670$	0	0
$671$	4.83482e45	0.110525
$672$	2.13705e45i	0.0476674i
$673$	− 1.12643e46i	− 0.245163i	−0.992458	−	0.122581i	$-0.960883\pi$
$673$	− 1.12643e46i	− 0.245163i	0.992458	−	0.122581i	$-0.0391173\pi$
$674$	9.22324e45	0.195882
$675$	0	0
$676$	4.63912e46	0.938242
$677$	4.69606e46i	0.926874i	0.886130	+	0.463437i	$0.153384\pi$
$677$	4.69606e46i	0.926874i	−0.886130	+	0.463437i	$0.846616\pi$
$678$	1.83945e45i	0.0354322i
$679$	−4.12340e44	−0.00775183
$680$	0	0
$681$	−5.04634e46	−0.903753
$682$	6.90134e44i	0.0120640i
$683$	− 1.23577e46i	− 0.210860i	−0.994427	−	0.105430i	$-0.966378\pi$
$683$	− 1.23577e46i	− 0.210860i	0.994427	−	0.105430i	$-0.0336220\pi$
$684$	−4.94373e46	−0.823435
$685$	0	0
$686$	−4.21842e45	−0.0669579
$687$	− 1.35833e46i	− 0.210484i
$688$	2.20114e46i	0.332996i
$689$	−1.50602e46	−0.222441
$690$	0	0
$691$	−3.45406e46	−0.486342	−0.243171	−	0.969983i	$-0.578188\pi$
$691$	−3.45406e46	−0.486342	−0.243171	+	0.969983i	$0.578188\pi$
$692$	1.42178e46i	0.195471i
$693$	− 1.66939e46i	− 0.224109i
$694$	1.01288e45	0.0132779
$695$	0	0
$696$	−7.24815e45	−0.0906097
$697$	2.37113e47i	2.89478i
$698$	7.96324e45i	0.0949457i
$699$	−7.43761e46	−0.866084
$700$	0	0
$701$	4.58600e46	0.509433	0.254716	−	0.967016i	$-0.418018\pi$
$701$	4.58600e46	0.509433	0.254716	+	0.967016i	$0.418018\pi$
$702$	− 2.42928e45i	− 0.0263582i
$703$	1.91915e47i	2.03398i
$704$	−1.28379e47	−1.32907
$705$	0	0
$706$	−4.00086e45	−0.0395254
$707$	− 1.97233e46i	− 0.190352i
$708$	− 2.66339e46i	− 0.251123i
$709$	−1.01825e46	−0.0937978	−0.0468989	−	0.998900i	$-0.514934\pi$
$709$	−1.01825e46	−0.0937978	−0.0468989	+	0.998900i	$0.514934\pi$
$710$	0	0
$711$	4.91445e46	0.432142
$712$	− 3.63269e46i	− 0.312111i
$713$	4.72678e45i	0.0396815i
$714$	−3.78256e45	−0.0310288
$715$	0	0
$716$	5.52498e46	0.432779
$717$	− 2.32189e46i	− 0.177736i
$718$	3.34585e46i	0.250295i
$719$	2.37751e46	0.173818	0.0869092	−	0.996216i	$-0.472301\pi$
$719$	2.37751e46	0.173818	0.0869092	+	0.996216i	$0.472301\pi$
$720$	0	0
$721$	−2.62762e46	−0.183498
$722$	8.08638e45i	0.0551938i
$723$	6.71752e46i	0.448154i
$724$	1.11163e47	0.724895
$725$	0	0
$726$	3.02869e46	0.188712
$727$	7.60235e46i	0.463053i	0.972829	+	0.231526i	$0.0743719\pi$
$727$	7.60235e46i	0.463053i	−0.972829	+	0.231526i	$0.925628\pi$
$728$	1.72959e45i	0.0102985i
$729$	−3.03238e46	−0.176514
$730$	0	0
$731$	−1.25289e47	−0.697072
$732$	5.60924e45i	0.0305120i
$733$	− 9.46431e46i	− 0.503354i	−0.967811	−	0.251677i	$-0.919018\pi$
$733$	− 9.46431e46i	− 0.503354i	0.967811	−	0.251677i	$-0.0809820\pi$
$734$	4.49197e46	0.233589
$735$	0	0
$736$	1.25387e47	0.623404
$737$	2.01217e47i	0.978255i
$738$	4.90207e46i	0.233050i
$739$	−1.36554e46	−0.0634851	−0.0317425	−	0.999496i	$-0.510106\pi$
$739$	−1.36554e46	−0.0634851	−0.0317425	+	0.999496i	$0.510106\pi$
$740$	0	0
$741$	1.93763e46	0.0861529
$742$	1.12509e46i	0.0489243i
$743$	2.14591e47i	0.912632i	0.889818	+	0.456316i	$0.150831\pi$
$743$	2.14591e47i	0.912632i	−0.889818	+	0.456316i	$0.849169\pi$
$744$	−1.63368e45	−0.00679538
$745$	0	0
$746$	−1.67478e46	−0.0666449
$747$	− 2.03757e47i	− 0.793089i
$748$	− 8.02539e47i	− 3.05555i
$749$	5.64349e45	0.0210183
$750$	0	0
$751$	−3.00124e47	−1.06965	−0.534825	−	0.844963i	$-0.679622\pi$
$751$	−3.00124e47	−1.06965	−0.534825	+	0.844963i	$0.679622\pi$
$752$	− 2.04300e47i	− 0.712317i
$753$	8.00619e46i	0.273092i
$754$	−4.34103e45	−0.0144866
$755$	0	0
$756$	4.49476e46	0.143581
$757$	− 3.75997e47i	− 1.17517i	−0.809161	−	0.587587i	$-0.800078\pi$
$757$	− 3.75997e47i	− 1.17517i	0.809161	−	0.587587i	$-0.199922\pi$
$758$	− 1.00302e47i	− 0.306738i
$759$	3.14150e47	0.940043
$760$	0	0
$761$	2.05125e47	0.587723	0.293861	−	0.955848i	$-0.405060\pi$
$761$	2.05125e47	0.587723	0.293861	+	0.955848i	$0.405060\pi$
$762$	− 5.18417e46i	− 0.145352i
$763$	8.98632e46i	0.246563i
$764$	−5.49839e46	−0.147637
$765$	0	0
$766$	−4.94302e46	−0.127121
$767$	− 3.25470e46i	− 0.0819195i
$768$	− 1.26845e47i	− 0.312474i
$769$	3.91739e47	0.944522	0.472261	−	0.881459i	$-0.343438\pi$
$769$	3.91739e47	0.944522	0.472261	+	0.881459i	$0.343438\pi$
$770$	0	0
$771$	5.47185e46	0.126397
$772$	− 4.17767e47i	− 0.944602i
$773$	6.18683e47i	1.36933i	0.728860	+	0.684663i	$0.240051\pi$
$773$	6.18683e47i	1.36933i	−0.728860	+	0.684663i	$0.759949\pi$
$774$	−2.59023e46	−0.0561193
$775$	0	0
$776$	−8.36174e45	−0.0173611
$777$	− 7.51860e46i	− 0.152823i
$778$	− 9.73319e46i	− 0.193683i
$779$	−9.07396e47	−1.76778
$780$	0	0
$781$	−7.13811e47	−1.33303
$782$	2.21935e47i	0.405802i
$783$	2.30179e47i	0.412095i
$784$	4.89864e47	0.858738
$785$	0	0
$786$	−1.18800e46	−0.0199684
$787$	− 2.50651e45i	− 0.00412559i	−0.999998	−	0.00206280i	$-0.999343\pi$
$787$	− 2.50651e45i	− 0.00412559i	0.999998	−	0.00206280i	$-0.000656609\pi$
$788$	− 1.92391e47i	− 0.310101i
$789$	4.31052e47	0.680392
$790$	0	0
$791$	−4.15904e46	−0.0629624
$792$	− 3.38532e47i	− 0.501920i
$793$	6.85457e45i	0.00995342i
$794$	1.47671e47	0.210019
$795$	0	0
$796$	1.02447e48	1.39776
$797$	− 7.37335e47i	− 0.985378i	−0.870206	−	0.492689i	$-0.836014\pi$
$797$	− 7.37335e47i	− 0.985378i	0.870206	−	0.492689i	$-0.163986\pi$
$798$	− 1.44753e46i	− 0.0189487i
$799$	1.16288e48	1.49112
$800$	0	0
$801$	−4.97099e47	−0.611655
$802$	− 2.12004e47i	− 0.255545i
$803$	− 1.16216e48i	− 1.37233i
$804$	−2.33447e47	−0.270062
$805$	0	0
$806$	−9.78438e44	−0.00108644
$807$	8.48506e47i	0.923085i
$808$	− 3.99963e47i	− 0.426317i
$809$	9.92771e47	1.03681	0.518404	−	0.855136i	$-0.326526\pi$
$809$	9.92771e47	1.03681	0.518404	+	0.855136i	$0.326526\pi$
$810$	0	0
$811$	1.07185e47	0.107470	0.0537351	−	0.998555i	$-0.482887\pi$
$811$	1.07185e47	0.107470	0.0537351	+	0.998555i	$0.482887\pi$
$812$	− 8.03197e46i	− 0.0789128i
$813$	− 7.94274e47i	− 0.764674i
$814$	−6.44087e47	−0.607634
$815$	0	0
$816$	8.91973e47	0.808098
$817$	− 4.79463e47i	− 0.425688i
$818$	− 8.04262e46i	− 0.0699791i
$819$	2.36678e46	0.0201824
$820$	0	0
$821$	−1.20939e48	−0.990610	−0.495305	−	0.868719i	$-0.664944\pi$
$821$	−1.20939e48	−0.990610	−0.495305	+	0.868719i	$0.664944\pi$
$822$	8.50264e46i	0.0682604i
$823$	2.45743e48i	1.93367i	0.255396	+	0.966837i	$0.417794\pi$
$823$	2.45743e48i	1.93367i	−0.255396	+	0.966837i	$0.582206\pi$
$824$	−5.32848e47	−0.410965
$825$	0	0
$826$	−2.43146e46	−0.0180176
$827$	1.80057e48i	1.30789i	0.756544	+	0.653943i	$0.226886\pi$
$827$	1.80057e48i	1.30789i	−0.756544	+	0.653943i	$0.773114\pi$
$828$	− 1.13637e48i	− 0.809135i
$829$	−6.57735e47	−0.459094	−0.229547	−	0.973298i	$-0.573724\pi$
$829$	−6.57735e47	−0.459094	−0.229547	+	0.973298i	$0.573724\pi$
$830$	0	0
$831$	6.86049e47	0.460191
$832$	− 1.82010e47i	− 0.119691i
$833$	2.78832e48i	1.79763i
$834$	−6.98757e46	−0.0441658
$835$	0	0
$836$	3.07119e48	1.86596
$837$	5.18807e46i	0.0309055i
$838$	− 4.28937e47i	− 0.250534i
$839$	−6.26140e47	−0.358591	−0.179295	−	0.983795i	$-0.557382\pi$
$839$	−6.26140e47	−0.358591	−0.179295	+	0.983795i	$0.557382\pi$
$840$	0	0
$841$	−1.40475e48	−0.773511
$842$	− 7.48868e46i	− 0.0404348i
$843$	2.49910e47i	0.132321i
$844$	−1.77928e48	−0.923832
$845$	0	0
$846$	2.40413e47	0.120046
$847$	6.84793e47i	0.335338i
$848$	− 2.65311e48i	− 1.27416i
$849$	−1.32349e48	−0.623365
$850$	0	0
$851$	−4.41140e48	−1.99866
$852$	− 8.28145e47i	− 0.368005i
$853$	3.16331e48i	1.37874i	0.724410	+	0.689370i	$0.242112\pi$
$853$	3.16331e48i	1.37874i	−0.724410	+	0.689370i	$0.757888\pi$
$854$	5.12079e45	0.00218918
$855$	0	0
$856$	1.14443e47	0.0470730
$857$	3.13666e48i	1.26556i	0.774330	+	0.632782i	$0.218087\pi$
$857$	3.13666e48i	1.26556i	−0.774330	+	0.632782i	$0.781913\pi$
$858$	6.50286e46i	0.0257374i
$859$	−2.20270e48	−0.855202	−0.427601	−	0.903968i	$-0.640641\pi$
$859$	−2.20270e48	−0.855202	−0.427601	+	0.903968i	$0.640641\pi$
$860$	0	0
$861$	3.55487e47	0.132822
$862$	3.52247e47i	0.129115i
$863$	5.00806e47i	0.180091i	0.995938	+	0.0900453i	$0.0287012\pi$
$863$	5.00806e47i	0.180091i	−0.995938	+	0.0900453i	$0.971299\pi$
$864$	1.37624e48	0.485532
$865$	0	0
$866$	−2.19192e47	−0.0744356
$867$	3.59809e48i	1.19883i
$868$	− 1.81035e46i	− 0.00591816i
$869$	−3.05300e48	−0.979266
$870$	0	0
$871$	−2.85276e47	−0.0880979
$872$	1.82232e48i	0.552207i
$873$	1.14422e47i	0.0340233i
$874$	−8.49310e47	−0.247815
$875$	0	0
$876$	1.34830e48	0.378852
$877$	1.77120e48i	0.488400i	0.969725	+	0.244200i	$0.0785253\pi$
$877$	1.77120e48i	0.488400i	−0.969725	+	0.244200i	$0.921475\pi$
$878$	− 6.48638e47i	− 0.175527i
$879$	2.21196e48	0.587436
$880$	0	0
$881$	1.59935e48	0.409111	0.204555	−	0.978855i	$-0.434425\pi$
$881$	1.59935e48	0.409111	0.204555	+	0.978855i	$0.434425\pi$
$882$	5.76455e47i	0.144722i
$883$	− 2.38704e48i	− 0.588177i	−0.955778	−	0.294089i	$-0.904984\pi$
$883$	− 2.38704e48i	− 0.588177i	0.955778	−	0.294089i	$-0.0950161\pi$
$884$	1.13780e48	0.275171
$885$	0	0
$886$	−8.21764e47	−0.191466
$887$	− 5.13361e48i	− 1.17404i	−0.809572	−	0.587020i	$-0.800301\pi$
$887$	− 5.13361e48i	− 1.17404i	0.809572	−	0.587020i	$-0.199699\pi$
$888$	− 1.52468e48i	− 0.342266i
$889$	1.17215e48	0.258289
$890$	0	0
$891$	−2.67018e48	−0.566968
$892$	− 1.60607e47i	− 0.0334768i
$893$	4.45015e48i	0.910595i
$894$	2.07604e47	0.0417030
$895$	0	0
$896$	−6.35594e47	−0.123054
$897$	4.45386e47i	0.0846566i
$898$	8.18931e47i	0.152823i
$899$	9.27089e46	0.0169858
$900$	0	0
$901$	1.51015e49	2.66724
$902$	− 3.04531e48i	− 0.528109i
$903$	1.87837e47i	0.0319841i
$904$	−8.43402e47	−0.141012
$905$	0	0
$906$	7.56185e47	0.121903
$907$	− 5.18589e48i	− 0.820924i	−0.911878	−	0.410462i	$-0.865368\pi$
$907$	− 5.18589e48i	− 0.820924i	0.911878	−	0.410462i	$-0.134632\pi$
$908$	− 1.13400e49i	− 1.76277i
$909$	−5.47311e48	−0.835469
$910$	0	0
$911$	−6.63747e48	−0.977123	−0.488562	−	0.872529i	$-0.662478\pi$
$911$	−6.63747e48	−0.977123	−0.488562	+	0.872529i	$0.662478\pi$
$912$	3.41344e48i	0.493489i
$913$	1.26580e49i	1.79720i
$914$	1.09453e48	0.152621
$915$	0	0
$916$	3.05239e48	0.410549
$917$	− 2.68609e47i	− 0.0354835i
$918$	2.43594e48i	0.316054i
$919$	7.10984e48	0.906054	0.453027	−	0.891497i	$-0.350344\pi$
$919$	7.10984e48	0.906054	0.453027	+	0.891497i	$0.350344\pi$
$920$	0	0
$921$	−7.56822e48	−0.930486
$922$	6.64821e47i	0.0802869i
$923$	− 1.01200e48i	− 0.120048i
$924$	−1.20319e48	−0.140199
$925$	0	0
$926$	9.01048e47	0.101313
$927$	7.29151e48i	0.805382i
$928$	− 2.45929e48i	− 0.266851i
$929$	1.17316e49	1.25054	0.625272	−	0.780407i	$-0.284988\pi$
$929$	1.17316e49	1.25054	0.625272	+	0.780407i	$0.284988\pi$
$930$	0	0
$931$	−1.06705e49	−1.09777
$932$	− 1.67136e49i	− 1.68930i
$933$	4.40329e48i	0.437250i
$934$	1.13136e48	0.110376
$935$	0	0
$936$	4.79954e47	0.0452010
$937$	− 7.60807e48i	− 0.703998i	−0.936000	−	0.351999i	$-0.885502\pi$
$937$	− 7.60807e48i	− 0.703998i	0.936000	−	0.351999i	$-0.114498\pi$
$938$	2.13119e47i	0.0193765i
$939$	7.83643e48	0.700061
$940$	0	0
$941$	−5.90432e48	−0.509262	−0.254631	−	0.967038i	$-0.581954\pi$
$941$	−5.90432e48	−0.509262	−0.254631	+	0.967038i	$0.581954\pi$
$942$	− 1.06418e48i	− 0.0901935i
$943$	− 2.08575e49i	− 1.73708i
$944$	5.73368e48	0.469241
$945$	0	0
$946$	1.60912e48	0.127170
$947$	7.50195e47i	0.0582639i	0.999576	+	0.0291319i	$0.00927430\pi$
$947$	7.50195e47i	0.0582639i	−0.999576	+	0.0291319i	$0.990726\pi$
$948$	− 3.54201e48i	− 0.270341i
$949$	1.64765e48	0.123587
$950$	0	0
$951$	8.50718e48	0.616321
$952$	− 1.73433e48i	− 0.123487i
$953$	− 1.06031e49i	− 0.741993i	−0.928634	−	0.370997i	$-0.879016\pi$
$953$	− 1.06031e49i	− 0.741993i	0.928634	−	0.370997i	$-0.120984\pi$
$954$	3.12208e48	0.214732
$955$	0	0
$956$	5.21769e48	0.346675
$957$	− 6.16159e48i	− 0.402389i
$958$	− 3.02447e48i	− 0.194141i
$959$	−1.92247e48	−0.121297
$960$	0	0
$961$	−1.63826e49	−0.998726
$962$	− 9.13154e47i	− 0.0547212i
$963$	− 1.56604e48i	− 0.0922507i
$964$	−1.50954e49	−0.874126
$965$	0	0
$966$	3.32731e47	0.0186196
$967$	3.31961e48i	0.182621i	0.995822	+	0.0913104i	$0.0291056\pi$
$967$	3.31961e48i	0.182621i	−0.995822	+	0.0913104i	$0.970894\pi$
$968$	1.38868e49i	0.751030i
$969$	−1.94294e49	−1.03304
$970$	0	0
$971$	1.67736e49	0.862003	0.431001	−	0.902351i	$-0.358160\pi$
$971$	1.67736e49	0.862003	0.431001	+	0.902351i	$0.358160\pi$
$972$	− 1.95710e49i	− 0.988826i
$973$	− 1.57991e48i	− 0.0784819i
$974$	6.22773e48	0.304164
$975$	0	0
$976$	−1.20754e48	−0.0570139
$977$	− 2.50785e49i	− 1.16424i	−0.813104	−	0.582118i	$-0.802224\pi$
$977$	− 2.50785e49i	− 1.16424i	0.813104	−	0.582118i	$-0.197776\pi$
$978$	− 2.39225e48i	− 0.109198i
$979$	3.08812e49	1.38605
$980$	0	0
$981$	2.49366e49	1.08218
$982$	7.94535e48i	0.339058i
$983$	1.24304e49i	0.521616i	0.965391	+	0.260808i	$0.0839890\pi$
$983$	1.24304e49i	0.521616i	−0.965391	+	0.260808i	$0.916011\pi$
$984$	7.20883e48	0.297472
$985$	0	0
$986$	4.35293e48	0.173705
$987$	− 1.74342e48i	− 0.0684177i
$988$	4.35418e48i	0.168042i
$989$	1.10210e49	0.418295
$990$	0	0
$991$	−2.48644e49	−0.912774	−0.456387	−	0.889781i	$-0.650857\pi$
$991$	−2.48644e49	−0.912774	−0.456387	+	0.889781i	$0.650857\pi$
$992$	− 5.54307e47i	− 0.0200128i
$993$	1.20437e48i	0.0427658i
$994$	−7.56031e47	−0.0264037
$995$	0	0
$996$	−1.46854e49	−0.496144
$997$	2.01041e49i	0.668058i	0.942563	+	0.334029i	$0.108408\pi$
$997$	2.01041e49i	0.668058i	−0.942563	+	0.334029i	$0.891592\pi$
$998$	1.13134e49i	0.369777i
$999$	−4.84191e49	−1.55663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.c.24.7		12
5.2	odd	4		5.34.a.b.1.3	✓	6
5.3	odd	4		25.34.a.c.1.4		6
5.4	even	2	inner	25.34.b.c.24.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.3	✓	6	5.2	odd	4
25.34.a.c.1.4		6	5.3	odd	4
25.34.b.c.24.6		12	5.4	even	2	inner
25.34.b.c.24.7		12	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)

\(f(q)\)	\(=\)	\(q+18258.4i q^{2} -3.67420e7i q^{3} +8.25656e9 q^{4} +6.70852e11 q^{6} +1.51681e13i q^{7} +3.07591e14i q^{8} +4.20908e15 q^{9} +O(q^{10})\)	\(q+18258.4i q^{2} -3.67420e7i q^{3} +8.25656e9 q^{4} +6.70852e11 q^{6} +1.51681e13i q^{7} +3.07591e14i q^{8} +4.20908e15 q^{9} -2.61480e17 q^{11} -3.03363e17i q^{12} -3.70714e17i q^{13} -2.76946e17 q^{14} +6.53072e19 q^{16} +3.71730e20i q^{17} +7.68513e19i q^{18} -1.42255e21 q^{19} +5.57308e20 q^{21} -4.77422e21i q^{22} -3.26990e22i q^{23} +1.13015e22 q^{24} +6.76865e21 q^{26} -3.58901e23i q^{27} +1.25237e23i q^{28} -6.41343e23 q^{29} -1.44554e23 q^{31} +3.83459e24i q^{32} +9.60732e24i q^{33} -6.78720e24 q^{34} +3.47526e25 q^{36} -1.34909e26i q^{37} -2.59736e25i q^{38} -1.36208e25 q^{39} +6.37865e26 q^{41} +1.01756e25i q^{42} +3.37044e26i q^{43} -2.15893e27 q^{44} +5.97033e26 q^{46} -3.12828e27i q^{47} -2.39952e27i q^{48} +7.50092e27 q^{49} +1.36581e28 q^{51} -3.06082e27i q^{52} -4.06250e28i q^{53} +6.55298e27 q^{54} -4.66557e27 q^{56} +5.22675e28i q^{57} -1.17099e28i q^{58} +8.77955e28 q^{59} -1.84902e28 q^{61} -2.63933e27i q^{62} +6.38439e28i q^{63} +4.90971e29 q^{64} -1.75415e29 q^{66} -7.69531e29i q^{67} +3.06921e30i q^{68} -1.20143e30 q^{69} +2.72988e30 q^{71} +1.29468e30i q^{72} +4.44452e30i q^{73} +2.46323e30 q^{74} -1.17454e31 q^{76} -3.96617e30i q^{77} -2.48694e29i q^{78} +1.16758e31 q^{79} +1.02118e31 q^{81} +1.16464e31i q^{82} -4.84088e31i q^{83} +4.60145e30 q^{84} -6.15390e30 q^{86} +2.35643e31i q^{87} -8.04290e31i q^{88} -1.18101e32 q^{89} +5.62303e30 q^{91} -2.69981e32i q^{92} +5.31122e30i q^{93} +5.71176e31 q^{94} +1.40891e32 q^{96} +2.71846e31i q^{97} +1.36955e32i q^{98} -1.10059e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 59041291304 q^{4} + 13231518498704 q^{6} - 27\!\cdots\!76 q^{9}+O(q^{10}) \) 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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