LMFDB - Embedded newform 25.34.b.b.24.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			24.10
Root			$-16501.2 + 16501.2i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.b.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+138106. i q^{2} +1.45282e7i q^{3} -1.04832e10 q^{4} -2.00642e12 q^{6} +3.75584e13i q^{7} -2.61472e14i q^{8} +5.34799e15 q^{9} +O(q^{10})$	\(q+138106. i q^{2} +1.45282e7i q^{3} -1.04832e10 q^{4} -2.00642e12 q^{6} +3.75584e13i q^{7} -2.61472e14i q^{8} +5.34799e15 q^{9} -7.18987e16 q^{11} -1.52302e17i q^{12} -1.13201e18i q^{13} -5.18702e18 q^{14} -5.39393e19 q^{16} -1.70846e20i q^{17} +7.38588e20i q^{18} +8.48651e20 q^{19} -5.45655e20 q^{21} -9.92962e21i q^{22} +3.95696e22i q^{23} +3.79872e21 q^{24} +1.56337e23 q^{26} +1.58460e23i q^{27} -3.93732e23i q^{28} -9.30999e23 q^{29} -8.60649e23 q^{31} -9.69535e24i q^{32} -1.04456e24i q^{33} +2.35948e25 q^{34} -5.60641e25 q^{36} -5.07725e25i q^{37} +1.17203e26i q^{38} +1.64461e25 q^{39} -1.78283e26 q^{41} -7.53580e25i q^{42} -8.10579e26i q^{43} +7.53730e26 q^{44} -5.46479e27 q^{46} -5.64217e27i q^{47} -7.83641e26i q^{48} +6.32036e27 q^{49} +2.48208e27 q^{51} +1.18671e28i q^{52} -5.15002e28i q^{53} -2.18842e28 q^{54} +9.82047e27 q^{56} +1.23294e28i q^{57} -1.28576e29i q^{58} -1.40126e29 q^{59} -8.28448e28 q^{61} -1.18860e29i q^{62} +2.00862e29i q^{63} +8.75647e29 q^{64} +1.44259e29 q^{66} +2.02520e29i q^{67} +1.79102e30i q^{68} -5.74875e29 q^{69} +6.89895e30 q^{71} -1.39835e30i q^{72} +3.84757e30i q^{73} +7.01196e30 q^{74} -8.89659e30 q^{76} -2.70040e30i q^{77} +2.27129e30i q^{78} -9.36491e30 q^{79} +2.74277e31 q^{81} -2.46218e31i q^{82} -7.23102e31i q^{83} +5.72021e30 q^{84} +1.11945e32 q^{86} -1.35257e31i q^{87} +1.87995e31i q^{88} -4.37547e31 q^{89} +4.25165e31 q^{91} -4.14817e32i q^{92} -1.25037e31i q^{93} +7.79216e32 q^{94} +1.40856e32 q^{96} -1.02091e33i q^{97} +8.72877e32i q^{98} -3.84514e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	138106.i	1.49010i	0.667007	+	0.745051i	$0.267575\pi$
$2$	138106.i	1.49010i	−0.667007	+	0.745051i	$0.732425\pi$
$3$	1.45282e7i	0.194855i	0.995243	+	0.0974273i	$0.0310613\pi$
$3$	1.45282e7i	0.194855i	−0.995243	+	0.0974273i	$0.968939\pi$
$4$	−1.04832e10	−1.22041
$5$	0	0
$5$	0	0
$6$	−2.00642e12	−0.290353
$7$	3.75584e13i	0.427158i	0.976926	+	0.213579i	$0.0685121\pi$
$7$	3.75584e13i	0.427158i	−0.976926	+	0.213579i	$0.931488\pi$
$8$	− 2.61472e14i	− 0.328428i
$9$	5.34799e15	0.962032
$10$	0	0
$11$	−7.18987e16	−0.471783	−0.235891	−	0.971779i	$-0.575801\pi$
$11$	−7.18987e16	−0.471783	−0.235891	+	0.971779i	$0.575801\pi$
$12$	− 1.52302e17i	− 0.237802i
$13$	− 1.13201e18i	− 0.471830i	−0.971774	−	0.235915i	$-0.924191\pi$
$13$	− 1.13201e18i	− 0.471830i	0.971774	−	0.235915i	$-0.0758087\pi$
$14$	−5.18702e18	−0.636510
$15$	0	0
$16$	−5.39393e19	−0.731014
$17$	− 1.70846e20i	− 0.851526i	−0.904835	−	0.425763i	$-0.860006\pi$
$17$	− 1.70846e20i	− 0.851526i	0.904835	−	0.425763i	$-0.139994\pi$
$18$	7.38588e20i	1.43353i
$19$	8.48651e20	0.674986	0.337493	−	0.941328i	$-0.390421\pi$
$19$	8.48651e20	0.674986	0.337493	+	0.941328i	$0.390421\pi$
$20$	0	0
$21$	−5.45655e20	−0.0832338
$22$	− 9.92962e21i	− 0.703005i
$23$	3.95696e22i	1.34540i	0.739914	+	0.672702i	$0.234866\pi$
$23$	3.95696e22i	1.34540i	−0.739914	+	0.672702i	$0.765134\pi$
$24$	3.79872e21	0.0639958
$25$	0	0
$26$	1.56337e23	0.703075
$27$	1.58460e23i	0.382311i
$28$	− 3.93732e23i	− 0.521307i
$29$	−9.30999e23	−0.690848	−0.345424	−	0.938447i	$-0.612265\pi$
$29$	−9.30999e23	−0.690848	−0.345424	+	0.938447i	$0.612265\pi$
$30$	0	0
$31$	−8.60649e23	−0.212500	−0.106250	−	0.994339i	$-0.533884\pi$
$31$	−8.60649e23	−0.212500	−0.106250	+	0.994339i	$0.533884\pi$
$32$	− 9.69535e24i	− 1.41772i
$33$	− 1.04456e24i	− 0.0919290i
$34$	2.35948e25	1.26886
$35$	0	0
$36$	−5.60641e25	−1.17407
$37$	− 5.07725e25i	− 0.676550i	−0.941047	−	0.338275i	$-0.890157\pi$
$37$	− 5.07725e25i	− 0.676550i	0.941047	−	0.338275i	$-0.109843\pi$
$38$	1.17203e26i	1.00580i
$39$	1.64461e25	0.0919383
$40$	0	0
$41$	−1.78283e26	−0.436692	−0.218346	−	0.975871i	$-0.570066\pi$
$41$	−1.78283e26	−0.436692	−0.218346	+	0.975871i	$0.570066\pi$
$42$	− 7.53580e25i	− 0.124027i
$43$	− 8.10579e26i	− 0.904827i	−0.891808	−	0.452414i	$-0.850563\pi$
$43$	− 8.10579e26i	− 0.904827i	0.891808	−	0.452414i	$-0.149437\pi$
$44$	7.53730e26	0.575767
$45$	0	0
$46$	−5.46479e27	−2.00479
$47$	− 5.64217e27i	− 1.45155i	−0.687933	−	0.725775i	$-0.741482\pi$
$47$	− 5.64217e27i	− 1.45155i	0.687933	−	0.725775i	$-0.258518\pi$
$48$	− 7.83641e26i	− 0.142441i
$49$	6.32036e27	0.817536
$50$	0	0
$51$	2.48208e27	0.165924
$52$	1.18671e28i	0.575825i
$53$	− 5.15002e28i	− 1.82497i	−0.409105	−	0.912487i	$-0.634159\pi$
$53$	− 5.15002e28i	− 1.82497i	0.409105	−	0.912487i	$-0.365841\pi$
$54$	−2.18842e28	−0.569682
$55$	0	0
$56$	9.82047e27	0.140291
$57$	1.23294e28i	0.131524i
$58$	− 1.28576e29i	− 1.02943i
$59$	−1.40126e29	−0.846175	−0.423088	−	0.906089i	$-0.639054\pi$
$59$	−1.40126e29	−0.846175	−0.423088	+	0.906089i	$0.639054\pi$
$60$	0	0
$61$	−8.28448e28	−0.288618	−0.144309	−	0.989533i	$-0.546096\pi$
$61$	−8.28448e28	−0.288618	−0.144309	+	0.989533i	$0.546096\pi$
$62$	− 1.18860e29i	− 0.316646i
$63$	2.00862e29i	0.410940i
$64$	8.75647e29	1.38153
$65$	0	0
$66$	1.44259e29	0.136984
$67$	2.02520e29i	0.150049i	0.997182	+	0.0750246i	$0.0239035\pi$
$67$	2.02520e29i	0.150049i	−0.997182	+	0.0750246i	$0.976096\pi$
$68$	1.79102e30i	1.03921i
$69$	−5.74875e29	−0.262158
$70$	0	0
$71$	6.89895e30	1.96345	0.981726	−	0.190302i	$-0.0609466\pi$
$71$	6.89895e30	1.96345	0.981726	+	0.190302i	$0.0609466\pi$
$72$	− 1.39835e30i	− 0.315959i
$73$	3.84757e30i	0.692404i	0.938160	+	0.346202i	$0.112529\pi$
$73$	3.84757e30i	0.692404i	−0.938160	+	0.346202i	$0.887471\pi$
$74$	7.01196e30	1.00813
$75$	0	0
$76$	−8.89659e30	−0.823757
$77$	− 2.70040e30i	− 0.201526i
$78$	2.27129e30i	0.136997i
$79$	−9.36491e30	−0.457780	−0.228890	−	0.973452i	$-0.573510\pi$
$79$	−9.36491e30	−0.457780	−0.228890	+	0.973452i	$0.573510\pi$
$80$	0	0
$81$	2.74277e31	0.887537
$82$	− 2.46218e31i	− 0.650716i
$83$	− 7.23102e31i	− 1.56463i	−0.622884	−	0.782314i	$-0.714039\pi$
$83$	− 7.23102e31i	− 1.56463i	0.622884	−	0.782314i	$-0.285961\pi$
$84$	5.72021e30	0.101579
$85$	0	0
$86$	1.11945e32	1.34829
$87$	− 1.35257e31i	− 0.134615i
$88$	1.87995e31i	0.154947i
$89$	−4.37547e31	−0.299288	−0.149644	−	0.988740i	$-0.547813\pi$
$89$	−4.37547e31	−0.299288	−0.149644	+	0.988740i	$0.547813\pi$
$90$	0	0
$91$	4.25165e31	0.201546
$92$	− 4.14817e32i	− 1.64194i
$93$	− 1.25037e31i	− 0.0414065i
$94$	7.79216e32	2.16296
$95$	0	0
$96$	1.40856e32	0.276248
$97$	− 1.02091e33i	− 1.68754i	−0.536703	−	0.843771i	$-0.680331\pi$
$97$	− 1.02091e33i	− 1.68754i	0.536703	−	0.843771i	$-0.319669\pi$
$98$	8.72877e32i	1.21821i
$99$	−3.84514e32	−0.453870
$100$	0	0
$101$	2.20022e33	1.86709	0.933543	−	0.358466i	$-0.116700\pi$
$101$	2.20022e33	1.86709	0.933543	+	0.358466i	$0.116700\pi$
$102$	3.42790e32i	0.247244i
$103$	1.21369e33i	0.745234i	0.927985	+	0.372617i	$0.121539\pi$
$103$	1.21369e33i	0.745234i	−0.927985	+	0.372617i	$0.878461\pi$
$104$	−2.95990e32	−0.154962
$105$	0	0
$106$	7.11246e33	2.71940
$107$	− 3.78167e33i	− 1.23837i	−0.785244	−	0.619187i	$-0.787462\pi$
$107$	− 3.78167e33i	− 1.23837i	0.785244	−	0.619187i	$-0.212538\pi$
$108$	− 1.66117e33i	− 0.466575i
$109$	4.93974e33	1.19170	0.595849	−	0.803096i	$-0.296816\pi$
$109$	4.93974e33	1.19170	0.595849	+	0.803096i	$0.296816\pi$
$110$	0	0
$111$	7.37632e32	0.131829
$112$	− 2.02587e33i	− 0.312259i
$113$	3.63884e33i	0.484360i	0.970231	+	0.242180i	$0.0778625\pi$
$113$	3.63884e33i	0.484360i	−0.970231	+	0.242180i	$0.922138\pi$
$114$	−1.70275e33	−0.195984
$115$	0	0
$116$	9.75986e33	0.843115
$117$	− 6.05399e33i	− 0.453916i
$118$	− 1.93522e34i	− 1.26089i
$119$	6.41670e33	0.363737
$120$	0	0
$121$	−1.80557e34	−0.777421
$122$	− 1.14413e34i	− 0.430070i
$123$	− 2.59012e33i	− 0.0850915i
$124$	9.02236e33	0.259336
$125$	0	0
$126$	−2.77401e34	−0.612343
$127$	3.03012e34i	0.587082i	0.955947	+	0.293541i	$0.0948337\pi$
$127$	3.03012e34i	0.587082i	−0.955947	+	0.293541i	$0.905166\pi$
$128$	3.76492e34i	0.640902i
$129$	1.17762e34	0.176310
$130$	0	0
$131$	−7.83378e34	−0.909903	−0.454951	−	0.890516i	$-0.650343\pi$
$131$	−7.83378e34	−0.909903	−0.454951	+	0.890516i	$0.650343\pi$
$132$	1.09503e34i	0.112191i
$133$	3.18739e34i	0.288326i
$134$	−2.79691e34	−0.223589
$135$	0	0
$136$	−4.46715e34	−0.279665
$137$	1.43675e35i	0.797060i	0.917155	+	0.398530i	$0.130480\pi$
$137$	1.43675e35i	0.797060i	−0.917155	+	0.398530i	$0.869520\pi$
$138$	− 7.93934e34i	− 0.390642i
$139$	−3.03428e35	−1.32529	−0.662647	−	0.748932i	$-0.730567\pi$
$139$	−3.03428e35	−1.32529	−0.662647	+	0.748932i	$0.730567\pi$
$140$	0	0
$141$	8.19705e34	0.282841
$142$	9.52783e35i	2.92574i
$143$	8.13902e34i	0.222601i
$144$	−2.88467e35	−0.703259
$145$	0	0
$146$	−5.31371e35	−1.03175
$147$	9.18234e34i	0.159301i
$148$	5.32259e35i	0.825666i
$149$	8.47533e35	1.17648	0.588238	−	0.808688i	$-0.299822\pi$
$149$	8.47533e35	1.17648	0.588238	+	0.808688i	$0.299822\pi$
$150$	0	0
$151$	−1.42730e36	−1.59000	−0.794999	−	0.606610i	$-0.792529\pi$
$151$	−1.42730e36	−1.59000	−0.794999	+	0.606610i	$0.792529\pi$
$152$	− 2.21899e35i	− 0.221685i
$153$	− 9.13684e35i	− 0.819195i
$154$	3.72940e35	0.300294
$155$	0	0
$156$	−1.72408e35	−0.112202
$157$	− 1.47748e36i	− 0.865320i	−0.901557	−	0.432660i	$-0.857575\pi$
$157$	− 1.47748e36i	− 0.865320i	0.901557	−	0.432660i	$-0.142425\pi$
$158$	− 1.29335e36i	− 0.682139i
$159$	7.48204e35	0.355605
$160$	0	0
$161$	−1.48617e36	−0.574701
$162$	3.78792e36i	1.32252i
$163$	1.91804e36i	0.605011i	0.953148	+	0.302505i	$0.0978230\pi$
$163$	1.91804e36i	0.605011i	−0.953148	+	0.302505i	$0.902177\pi$
$164$	1.86897e36	0.532942
$165$	0	0
$166$	9.98644e36	2.33146
$167$	− 3.91696e36i	− 0.828185i	−0.910235	−	0.414093i	$-0.864099\pi$
$167$	− 3.91696e36i	− 0.828185i	0.910235	−	0.414093i	$-0.135901\pi$
$168$	1.42674e35i	0.0273363i
$169$	4.47468e36	0.777376
$170$	0	0
$171$	4.53858e36	0.649358
$172$	8.49747e36i	1.10426i
$173$	1.42658e37i	1.68475i	0.538892	+	0.842375i	$0.318843\pi$
$173$	1.42658e37i	1.68475i	−0.538892	+	0.842375i	$0.681157\pi$
$174$	1.86798e36	0.200590
$175$	0	0
$176$	3.87817e36	0.344880
$177$	− 2.03577e36i	− 0.164881i
$178$	− 6.04277e36i	− 0.445970i
$179$	1.89294e37	1.27368	0.636842	−	0.770994i	$-0.280240\pi$
$179$	1.89294e37	1.27368	0.636842	+	0.770994i	$0.280240\pi$
$180$	0	0
$181$	2.60338e37	1.45828	0.729140	−	0.684365i	$-0.239920\pi$
$181$	2.60338e37	1.45828	0.729140	+	0.684365i	$0.239920\pi$
$182$	5.87177e36i	0.300325i
$183$	− 1.20358e36i	− 0.0562385i
$184$	1.03464e37	0.441869
$185$	0	0
$186$	1.72683e36	0.0616999
$187$	1.22836e37i	0.401735i
$188$	5.91481e37i	1.77148i
$189$	−5.95148e36	−0.163307
$190$	0	0
$191$	−7.37079e37	−1.70006	−0.850029	−	0.526736i	$-0.823415\pi$
$191$	−7.37079e37	−1.70006	−0.850029	+	0.526736i	$0.823415\pi$
$192$	1.27216e37i	0.269197i
$193$	− 9.51744e36i	− 0.184852i	−0.995720	−	0.0924261i	$-0.970538\pi$
$193$	− 9.51744e36i	− 0.184852i	0.995720	−	0.0924261i	$-0.0294622\pi$
$194$	1.40994e38	2.51461
$195$	0	0
$196$	−6.62577e37	−0.997726
$197$	5.57117e37i	0.771353i	0.922634	+	0.385677i	$0.126032\pi$
$197$	5.57117e37i	0.771353i	−0.922634	+	0.385677i	$0.873968\pi$
$198$	− 5.31035e37i	− 0.676313i
$199$	−1.97421e37	−0.231375	−0.115688	−	0.993286i	$-0.536907\pi$
$199$	−1.97421e37	−0.231375	−0.115688	+	0.993286i	$0.536907\pi$
$200$	0	0
$201$	−2.94225e36	−0.0292378
$202$	3.03863e38i	2.78215i
$203$	− 3.49668e37i	− 0.295101i
$204$	−2.60202e37	−0.202494
$205$	0	0
$206$	−1.67617e38	−1.11048
$207$	2.11618e38i	1.29432i
$208$	6.10600e37i	0.344915i
$209$	−6.10169e37	−0.318447
$210$	0	0
$211$	1.86677e37	0.0832589	0.0416294	−	0.999133i	$-0.486745\pi$
$211$	1.86677e37	0.0832589	0.0416294	+	0.999133i	$0.486745\pi$
$212$	5.39887e38i	2.22721i
$213$	1.00229e38i	0.382587i
$214$	5.22270e38	1.84530
$215$	0	0
$216$	4.14328e37	0.125562
$217$	− 3.23246e37i	− 0.0907710i
$218$	6.82205e38i	1.77575i
$219$	−5.58983e37	−0.134918
$220$	0	0
$221$	−1.93400e38	−0.401776
$222$	1.01871e38i	0.196439i
$223$	2.13813e38i	0.382828i	0.981509	+	0.191414i	$0.0613073\pi$
$223$	2.13813e38i	0.382828i	−0.981509	+	0.191414i	$0.938693\pi$
$224$	3.64142e38	0.605589
$225$	0	0
$226$	−5.02544e38	−0.721746
$227$	2.97111e38i	0.396727i	0.980128	+	0.198364i	$0.0635627\pi$
$227$	2.97111e38i	0.396727i	−0.980128	+	0.198364i	$0.936437\pi$
$228$	− 1.29251e38i	− 0.160513i
$229$	6.71382e38	0.775683	0.387841	−	0.921726i	$-0.373221\pi$
$229$	6.71382e38	0.775683	0.387841	+	0.921726i	$0.373221\pi$
$230$	0	0
$231$	3.92319e37	0.0392683
$232$	2.43430e38i	0.226894i
$233$	− 1.66756e39i	− 1.44780i	−0.689906	−	0.723899i	$-0.742348\pi$
$233$	− 1.66756e39i	− 1.44780i	0.689906	−	0.723899i	$-0.257652\pi$
$234$	8.36090e38	0.676381
$235$	0	0
$236$	1.46897e39	1.03268
$237$	− 1.36055e38i	− 0.0892005i
$238$	8.86182e38i	0.542005i
$239$	−6.59391e38	−0.376338	−0.188169	−	0.982137i	$-0.560255\pi$
$239$	−6.59391e38	−0.376338	−0.188169	+	0.982137i	$0.560255\pi$
$240$	0	0
$241$	1.79835e39	0.894524	0.447262	−	0.894403i	$-0.352399\pi$
$241$	1.79835e39	0.894524	0.447262	+	0.894403i	$0.352399\pi$
$242$	− 2.49360e39i	− 1.15844i
$243$	1.27936e39i	0.555251i
$244$	8.68479e38	0.352231
$245$	0	0
$246$	3.57710e38	0.126795
$247$	− 9.60683e38i	− 0.318479i
$248$	2.25036e38i	0.0697909i
$249$	1.05054e39	0.304875
$250$	0	0
$251$	4.62035e39	1.17506	0.587528	−	0.809204i	$-0.300101\pi$
$251$	4.62035e39	1.17506	0.587528	+	0.809204i	$0.300101\pi$
$252$	− 2.10568e39i	− 0.501514i
$253$	− 2.84501e39i	− 0.634738i
$254$	−4.18477e39	−0.874812
$255$	0	0
$256$	2.32218e39	0.426517
$257$	4.29716e39i	0.740090i	0.929014	+	0.370045i	$0.120658\pi$
$257$	4.29716e39i	0.740090i	−0.929014	+	0.370045i	$0.879342\pi$
$258$	1.62636e39i	0.262720i
$259$	1.90693e39	0.288994
$260$	0	0
$261$	−4.97898e39	−0.664618
$262$	− 1.08189e40i	− 1.35585i
$263$	5.41479e39i	0.637253i	0.947880	+	0.318627i	$0.103222\pi$
$263$	5.41479e39i	0.637253i	−0.947880	+	0.318627i	$0.896778\pi$
$264$	−2.73123e38	−0.0301921
$265$	0	0
$266$	−4.40197e39	−0.429635
$267$	− 6.35677e38i	− 0.0583177i
$268$	− 2.12306e39i	− 0.183121i
$269$	−9.46661e39	−0.767860	−0.383930	−	0.923362i	$-0.625430\pi$
$269$	−9.46661e39	−0.767860	−0.383930	+	0.923362i	$0.625430\pi$
$270$	0	0
$271$	−2.02716e40	−1.45511	−0.727555	−	0.686050i	$-0.759343\pi$
$271$	−2.02716e40	−1.45511	−0.727555	+	0.686050i	$0.759343\pi$
$272$	9.21533e39i	0.622478i
$273$	6.17688e38i	0.0392722i
$274$	−1.98423e40	−1.18770
$275$	0	0
$276$	6.02653e39	0.319939
$277$	− 2.14513e40i	− 1.07285i	−0.843949	−	0.536423i	$-0.819775\pi$
$277$	− 2.14513e40i	− 1.07285i	0.843949	−	0.536423i	$-0.180225\pi$
$278$	− 4.19052e40i	− 1.97482i
$279$	−4.60274e39	−0.204431
$280$	0	0
$281$	−2.22768e40	−0.879425	−0.439712	−	0.898139i	$-0.644920\pi$
$281$	−2.22768e40	−0.879425	−0.439712	+	0.898139i	$0.644920\pi$
$282$	1.13206e40i	0.421462i
$283$	− 1.45996e40i	− 0.512702i	−0.966584	−	0.256351i	$-0.917480\pi$
$283$	− 1.45996e40i	− 0.512702i	0.966584	−	0.256351i	$-0.0825204\pi$
$284$	−7.23231e40	−2.39621
$285$	0	0
$286$	−1.12404e40	−0.331699
$287$	− 6.69600e39i	− 0.186537i
$288$	− 5.18507e40i	− 1.36389i
$289$	1.10661e40	0.274903
$290$	0	0
$291$	1.48320e40	0.328825
$292$	− 4.03349e40i	− 0.845015i
$293$	3.33509e40i	0.660377i	0.943915	+	0.330188i	$0.107112\pi$
$293$	3.33509e40i	0.660377i	−0.943915	+	0.330188i	$0.892888\pi$
$294$	−1.26813e40	−0.237374
$295$	0	0
$296$	−1.32756e40	−0.222198
$297$	− 1.13931e40i	− 0.180368i
$298$	1.17049e41i	1.75307i
$299$	4.47933e40	0.634802
$300$	0	0
$301$	3.04440e40	0.386504
$302$	− 1.97119e41i	− 2.36926i
$303$	3.19653e40i	0.363810i
$304$	−4.57757e40	−0.493424
$305$	0	0
$306$	1.26185e41	1.22069
$307$	8.68250e40i	0.795906i	0.917406	+	0.397953i	$0.130279\pi$
$307$	8.68250e40i	0.795906i	−0.917406	+	0.397953i	$0.869721\pi$
$308$	2.83089e40i	0.245944i
$309$	−1.76327e40	−0.145212
$310$	0	0
$311$	1.66474e41	1.23254	0.616270	−	0.787535i	$-0.288643\pi$
$311$	1.66474e41	1.23254	0.616270	+	0.787535i	$0.288643\pi$
$312$	− 4.30019e39i	− 0.0301951i
$313$	− 2.38300e41i	− 1.58724i	−0.608416	−	0.793618i	$-0.708195\pi$
$313$	− 2.38300e41i	− 1.58724i	0.608416	−	0.793618i	$-0.291805\pi$
$314$	2.04048e41	1.28942
$315$	0	0
$316$	9.81743e40	0.558677
$317$	− 1.03851e41i	− 0.560964i	−0.959859	−	0.280482i	$-0.909506\pi$
$317$	− 1.03851e41i	− 0.560964i	0.959859	−	0.280482i	$-0.0904943\pi$
$318$	1.03331e41i	0.529888i
$319$	6.69377e40	0.325930
$320$	0	0
$321$	5.49408e40	0.241303
$322$	− 2.05248e41i	− 0.856363i
$323$	− 1.44989e41i	− 0.574768i
$324$	−2.87530e41	−1.08316
$325$	0	0
$326$	−2.64893e41	−0.901528
$327$	7.17654e40i	0.232208i
$328$	4.66160e40i	0.143422i
$329$	2.11911e41	0.620041
$330$	0	0
$331$	−1.38040e41	−0.365463	−0.182732	−	0.983163i	$-0.558494\pi$
$331$	−1.38040e41	−0.365463	−0.182732	+	0.983163i	$0.558494\pi$
$332$	7.58043e41i	1.90948i
$333$	− 2.71531e41i	− 0.650863i
$334$	5.40954e41	1.23408
$335$	0	0
$336$	2.94323e40	0.0608451
$337$	1.52333e40i	0.0299847i	0.999888	+	0.0149923i	$0.00477239\pi$
$337$	1.52333e40i	0.0299847i	−0.999888	+	0.0149923i	$0.995228\pi$
$338$	6.17978e41i	1.15837i
$339$	−5.28657e40	−0.0943798
$340$	0	0
$341$	6.18796e40	0.100254
$342$	6.26803e41i	0.967610i
$343$	5.27746e41i	0.776376i
$344$	−2.11944e41	−0.297171
$345$	0	0
$346$	−1.97019e42	−2.51045
$347$	1.11878e42i	1.35928i	0.733547	+	0.679639i	$0.237864\pi$
$347$	1.11878e42i	1.35928i	−0.733547	+	0.679639i	$0.762136\pi$
$348$	1.41793e41i	0.164285i
$349$	6.63572e41	0.733278	0.366639	−	0.930363i	$-0.380508\pi$
$349$	6.63572e41	0.733278	0.366639	+	0.930363i	$0.380508\pi$
$350$	0	0
$351$	1.79378e41	0.180386
$352$	6.97084e41i	0.668853i
$353$	− 4.28180e41i	− 0.392052i	−0.980599	−	0.196026i	$-0.937196\pi$
$353$	− 4.28180e41i	− 0.392052i	0.980599	−	0.196026i	$-0.0628037\pi$
$354$	2.81152e41	0.245690
$355$	0	0
$356$	4.58690e41	0.365253
$357$	9.32230e40i	0.0708757i
$358$	2.61426e42i	1.89792i
$359$	9.04901e41	0.627397	0.313698	−	0.949523i	$-0.398432\pi$
$359$	9.04901e41	0.627397	0.313698	+	0.949523i	$0.398432\pi$
$360$	0	0
$361$	−8.60562e41	−0.544394
$362$	3.59541e42i	2.17299i
$363$	− 2.62317e41i	− 0.151484i
$364$	−4.45710e41	−0.245968
$365$	0	0
$366$	1.66222e41	0.0838011
$367$	− 2.16128e41i	− 0.104165i	−0.998643	−	0.0520823i	$-0.983414\pi$
$367$	− 2.16128e41i	− 0.104165i	0.998643	−	0.0520823i	$-0.0165858\pi$
$368$	− 2.13436e42i	− 0.983510i
$369$	−9.53454e41	−0.420112
$370$	0	0
$371$	1.93426e42	0.779553
$372$	1.31079e41i	0.0505328i
$373$	− 3.17253e42i	− 1.17007i	−0.811009	−	0.585033i	$-0.801081\pi$
$373$	− 3.17253e42i	− 1.17007i	0.811009	−	0.585033i	$-0.198919\pi$
$374$	−1.69644e42	−0.598627
$375$	0	0
$376$	−1.47527e42	−0.476730
$377$	1.05390e42i	0.325963i
$378$	− 8.21933e41i	− 0.243345i
$379$	5.62885e42	1.59541	0.797705	−	0.603048i	$-0.206047\pi$
$379$	5.62885e42	1.59541	0.797705	+	0.603048i	$0.206047\pi$
$380$	0	0
$381$	−4.40221e41	−0.114396
$382$	− 1.01795e43i	− 2.53326i
$383$	− 1.01197e42i	− 0.241205i	−0.992701	−	0.120603i	$-0.961517\pi$
$383$	− 1.01197e42i	− 0.241205i	0.992701	−	0.120603i	$-0.0384827\pi$
$384$	−5.46975e41	−0.124883
$385$	0	0
$386$	1.31441e42	0.275449
$387$	− 4.33497e42i	− 0.870472i
$388$	1.07024e43i	2.05949i
$389$	9.74782e42	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$389$	9.74782e42	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$390$	0	0
$391$	6.76032e42	1.14565
$392$	− 1.65260e42i	− 0.268502i
$393$	− 1.13811e42i	− 0.177299i
$394$	−7.69409e42	−1.14940
$395$	0	0
$396$	4.03094e42	0.553906
$397$	− 5.84553e42i	− 0.770514i	−0.922809	−	0.385257i	$-0.874113\pi$
$397$	− 5.84553e42i	− 0.770514i	0.922809	−	0.385257i	$-0.125887\pi$
$398$	− 2.72649e42i	− 0.344773i
$399$	−4.63070e41	−0.0561816
$400$	0	0
$401$	6.82021e42	0.761931	0.380966	−	0.924589i	$-0.375592\pi$
$401$	6.82021e42	0.761931	0.380966	+	0.924589i	$0.375592\pi$
$402$	− 4.06341e41i	− 0.0435673i
$403$	9.74265e41i	0.100264i
$404$	−2.30654e43	−2.27860
$405$	0	0
$406$	4.82911e42	0.439732
$407$	3.65048e42i	0.319185i
$408$	− 6.48996e41i	− 0.0544941i
$409$	7.09650e42	0.572281	0.286141	−	0.958188i	$-0.407628\pi$
$409$	7.09650e42	0.572281	0.286141	+	0.958188i	$0.407628\pi$
$410$	0	0
$411$	−2.08733e42	−0.155311
$412$	− 1.27233e43i	− 0.909488i
$413$	− 5.26290e42i	− 0.361451i
$414$	−2.92256e43	−1.92867
$415$	0	0
$416$	−1.09753e43	−0.668921
$417$	− 4.40826e42i	− 0.258239i
$418$	− 8.42678e42i	− 0.474518i
$419$	1.41115e43	0.763912	0.381956	−	0.924181i	$-0.375251\pi$
$419$	1.41115e43	0.763912	0.381956	+	0.924181i	$0.375251\pi$
$420$	0	0
$421$	−9.28037e42	−0.464420	−0.232210	−	0.972666i	$-0.574596\pi$
$421$	−9.28037e42	−0.464420	−0.232210	+	0.972666i	$0.574596\pi$
$422$	2.57811e42i	0.124064i
$423$	− 3.01743e43i	− 1.39644i
$424$	−1.34659e43	−0.599374
$425$	0	0
$426$	−1.38422e43	−0.570095
$427$	− 3.11151e42i	− 0.123285i
$428$	3.96441e43i	1.51132i
$429$	−1.18245e42	−0.0433749
$430$	0	0
$431$	−2.40707e43	−0.817738	−0.408869	−	0.912593i	$-0.634077\pi$
$431$	−2.40707e43	−0.817738	−0.408869	+	0.912593i	$0.634077\pi$
$432$	− 8.54721e42i	− 0.279475i
$433$	− 4.96426e43i	− 1.56244i	−0.624253	−	0.781222i	$-0.714597\pi$
$433$	− 4.96426e43i	− 1.56244i	0.624253	−	0.781222i	$-0.285403\pi$
$434$	4.46420e42	0.135258
$435$	0	0
$436$	−5.17843e43	−1.45436
$437$	3.35808e43i	0.908128i
$438$	− 7.71986e42i	− 0.201042i
$439$	−4.80839e43	−1.20597	−0.602984	−	0.797754i	$-0.706022\pi$
$439$	−4.80839e43	−1.20597	−0.602984	+	0.797754i	$0.706022\pi$
$440$	0	0
$441$	3.38013e43	0.786495
$442$	− 2.67096e43i	− 0.598687i
$443$	8.49113e42i	0.183360i	0.995789	+	0.0916799i	$0.0292236\pi$
$443$	8.49113e42i	0.183360i	−0.995789	+	0.0916799i	$0.970776\pi$
$444$	−7.73275e42	−0.160885
$445$	0	0
$446$	−2.95287e43	−0.570453
$447$	1.23131e43i	0.229242i
$448$	3.28879e43i	0.590131i
$449$	8.15651e43	1.41072	0.705359	−	0.708851i	$-0.250786\pi$
$449$	8.15651e43	1.41072	0.705359	+	0.708851i	$0.250786\pi$
$450$	0	0
$451$	1.28183e43	0.206024
$452$	− 3.81467e43i	− 0.591116i
$453$	− 2.07361e43i	− 0.309819i
$454$	−4.10327e43	−0.591165
$455$	0	0
$456$	3.22378e42	0.0431962
$457$	3.82156e43i	0.493882i	0.969030	+	0.246941i	$0.0794254\pi$
$457$	3.82156e43i	0.493882i	−0.969030	+	0.246941i	$0.920575\pi$
$458$	9.27216e43i	1.15585i
$459$	2.70722e43	0.325548
$460$	0	0
$461$	1.42045e44	1.58987	0.794933	−	0.606698i	$-0.207506\pi$
$461$	1.42045e44	1.58987	0.794933	+	0.606698i	$0.207506\pi$
$462$	5.41814e42i	0.0585137i
$463$	− 1.76412e43i	− 0.183841i	−0.995766	−	0.0919203i	$-0.970700\pi$
$463$	− 1.76412e43i	− 0.183841i	0.995766	−	0.0919203i	$-0.0293005\pi$
$464$	5.02175e43	0.505020
$465$	0	0
$466$	2.30299e44	2.15737
$467$	1.44747e44i	1.30882i	0.756140	+	0.654410i	$0.227083\pi$
$467$	1.44747e44i	1.30882i	−0.756140	+	0.654410i	$0.772917\pi$
$468$	6.34653e43i	0.553962i
$469$	−7.60631e42	−0.0640947
$470$	0	0
$471$	2.14651e43	0.168612
$472$	3.66390e43i	0.277908i
$473$	5.82796e43i	0.426882i
$474$	1.87900e43	0.132918
$475$	0	0
$476$	−6.72677e43	−0.443907
$477$	− 2.75423e44i	− 1.75568i
$478$	− 9.10656e43i	− 0.560782i
$479$	2.82253e44	1.67920	0.839602	−	0.543203i	$-0.182788\pi$
$479$	2.82253e44	1.67920	0.839602	+	0.543203i	$0.182788\pi$
$480$	0	0
$481$	−5.74751e43	−0.319217
$482$	2.48362e44i	1.33293i
$483$	− 2.15914e43i	− 0.111983i
$484$	1.89282e44	0.948770
$485$	0	0
$486$	−1.76687e44	−0.827382
$487$	− 2.41873e44i	− 1.09486i	−0.836850	−	0.547432i	$-0.815605\pi$
$487$	− 2.41873e44i	− 1.09486i	0.836850	−	0.547432i	$-0.184395\pi$
$488$	2.16616e43i	0.0947902i
$489$	−2.78657e43	−0.117889
$490$	0	0
$491$	−3.36324e44	−1.33019	−0.665095	−	0.746759i	$-0.731609\pi$
$491$	−3.36324e44	−1.33019	−0.665095	+	0.746759i	$0.731609\pi$
$492$	2.71528e43i	0.103846i
$493$	1.59058e44i	0.588275i
$494$	1.32676e44	0.474566
$495$	0	0
$496$	4.64228e43	0.155340
$497$	2.59113e44i	0.838705i
$498$	1.45085e44i	0.454295i
$499$	8.01313e43	0.242741	0.121371	−	0.992607i	$-0.461271\pi$
$499$	8.01313e43	0.242741	0.121371	+	0.992607i	$0.461271\pi$
$500$	0	0
$501$	5.69063e43	0.161376
$502$	6.38096e44i	1.75095i
$503$	− 2.08304e44i	− 0.553129i	−0.960995	−	0.276565i	$-0.910804\pi$
$503$	− 2.08304e44i	− 0.553129i	0.960995	−	0.276565i	$-0.0891960\pi$
$504$	5.25198e43	0.134964
$505$	0	0
$506$	3.92911e44	0.945825
$507$	6.50090e43i	0.151475i
$508$	− 3.17654e44i	− 0.716478i
$509$	−3.65736e44	−0.798591	−0.399296	−	0.916822i	$-0.630745\pi$
$509$	−3.65736e44	−0.798591	−0.399296	+	0.916822i	$0.630745\pi$
$510$	0	0
$511$	−1.44509e44	−0.295766
$512$	6.44110e44i	1.27646i
$513$	1.34477e44i	0.258054i
$514$	−5.93461e44	−1.10281
$515$	0	0
$516$	−1.23453e44	−0.215169
$517$	4.05665e44i	0.684816i
$518$	2.63358e44i	0.430631i
$519$	−2.07256e44	−0.328281
$520$	0	0
$521$	−3.73678e44	−0.555488	−0.277744	−	0.960655i	$-0.589587\pi$
$521$	−3.73678e44	−0.555488	−0.277744	+	0.960655i	$0.589587\pi$
$522$	− 6.87625e44i	− 0.990349i
$523$	2.43582e44i	0.339913i	0.985452	+	0.169957i	$0.0543628\pi$
$523$	2.43582e44i	0.339913i	−0.985452	+	0.169957i	$0.945637\pi$
$524$	8.21232e44	1.11045
$525$	0	0
$526$	−7.47813e44	−0.949573
$527$	1.47039e44i	0.180949i
$528$	5.63428e43i	0.0672014i
$529$	−7.00750e44	−0.810111
$530$	0	0
$531$	−7.49392e44	−0.814047
$532$	− 3.34141e44i	− 0.351875i
$533$	2.01818e44i	0.206045i
$534$	8.77905e43	0.0868994
$535$	0	0
$536$	5.29533e43	0.0492804
$537$	2.75010e44i	0.248183i
$538$	− 1.30739e45i	− 1.14419i
$539$	−4.54426e44	−0.385699
$540$	0	0
$541$	1.83384e45	1.46422	0.732112	−	0.681184i	$-0.238535\pi$
$541$	1.83384e45	1.46422	0.732112	+	0.681184i	$0.238535\pi$
$542$	− 2.79963e45i	− 2.16826i
$543$	3.78224e44i	0.284153i
$544$	−1.65641e45	−1.20722
$545$	0	0
$546$	−8.53061e43	−0.0585196
$547$	− 2.32228e45i	− 1.54570i	−0.634592	−	0.772848i	$-0.718832\pi$
$547$	− 2.32228e45i	− 1.54570i	0.634592	−	0.772848i	$-0.281168\pi$
$548$	− 1.50617e45i	− 0.972738i
$549$	−4.43053e44	−0.277659
$550$	0	0
$551$	−7.90093e44	−0.466312
$552$	1.50314e44i	0.0861002i
$553$	− 3.51731e44i	− 0.195544i
$554$	2.96255e45	1.59865
$555$	0	0
$556$	3.18090e45	1.61740
$557$	− 2.15312e45i	− 1.06281i	−0.847117	−	0.531406i	$-0.821664\pi$
$557$	− 2.15312e45i	− 1.06281i	0.847117	−	0.531406i	$-0.178336\pi$
$558$	− 6.35664e44i	− 0.304624i
$559$	−9.17585e44	−0.426925
$560$	0	0
$561$	−1.78459e44	−0.0782800
$562$	− 3.07655e45i	− 1.31043i
$563$	2.18829e45i	0.905142i	0.891728	+	0.452571i	$0.149493\pi$
$563$	2.18829e45i	0.905142i	−0.891728	+	0.452571i	$0.850507\pi$
$564$	−8.59314e44	−0.345181
$565$	0	0
$566$	2.01629e45	0.763979
$567$	1.03014e45i	0.379119i
$568$	− 1.80388e45i	− 0.644853i
$569$	−3.69991e45	−1.28481	−0.642404	−	0.766366i	$-0.722063\pi$
$569$	−3.69991e45	−1.28481	−0.642404	+	0.766366i	$0.722063\pi$
$570$	0	0
$571$	4.09741e44	0.134281	0.0671403	−	0.997744i	$-0.478612\pi$
$571$	4.09741e44	0.134281	0.0671403	+	0.997744i	$0.478612\pi$
$572$	− 8.53231e44i	− 0.271664i
$573$	− 1.07084e45i	− 0.331264i
$574$	9.24755e44	0.277959
$575$	0	0
$576$	4.68295e45	1.32907
$577$	2.41392e45i	0.665767i	0.942968	+	0.332884i	$0.108022\pi$
$577$	2.41392e45i	0.665767i	−0.942968	+	0.332884i	$0.891978\pi$
$578$	1.52829e45i	0.409634i
$579$	1.38271e44	0.0360193
$580$	0	0
$581$	2.71585e45	0.668344
$582$	2.04838e45i	0.489983i
$583$	3.70280e45i	0.860992i
$584$	1.00603e45	0.227405
$585$	0	0
$586$	−4.60594e45	−0.984029
$587$	− 3.30502e45i	− 0.686507i	−0.939243	−	0.343253i	$-0.888471\pi$
$587$	− 3.30502e45i	− 0.686507i	0.939243	−	0.343253i	$-0.111529\pi$
$588$	− 9.62604e44i	− 0.194411i
$589$	−7.30390e44	−0.143434
$590$	0	0
$591$	−8.09389e44	−0.150302
$592$	2.73863e45i	0.494568i
$593$	− 3.04911e45i	− 0.535514i	−0.963486	−	0.267757i	$-0.913718\pi$
$593$	− 3.04911e45i	− 0.535514i	0.963486	−	0.267757i	$-0.0862824\pi$
$594$	1.57344e45	0.268766
$595$	0	0
$596$	−8.88487e45	−1.43578
$597$	− 2.86816e44i	− 0.0450845i
$598$	6.18620e45i	0.945920i
$599$	−4.77681e45	−0.710551	−0.355276	−	0.934762i	$-0.615613\pi$
$599$	−4.77681e45	−0.710551	−0.355276	+	0.934762i	$0.615613\pi$
$600$	0	0
$601$	−1.11023e46	−1.56310	−0.781549	−	0.623844i	$-0.785570\pi$
$601$	−1.11023e46	−1.56310	−0.781549	+	0.623844i	$0.785570\pi$
$602$	4.20449e45i	0.575931i
$603$	1.08307e45i	0.144352i
$604$	1.49627e46	1.94045
$605$	0	0
$606$	−4.41458e45	−0.542115
$607$	9.37646e44i	0.112054i	0.998429	+	0.0560268i	$0.0178432\pi$
$607$	9.37646e44i	0.112054i	−0.998429	+	0.0560268i	$0.982157\pi$
$608$	− 8.22797e45i	− 0.956937i
$609$	5.08004e44	0.0575019
$610$	0	0
$611$	−6.38701e45	−0.684885
$612$	9.57834e45i	0.999751i
$613$	− 3.40725e45i	− 0.346183i	−0.984906	−	0.173092i	$-0.944624\pi$
$613$	− 3.40725e45i	− 0.346183i	0.984906	−	0.173092i	$-0.0553757\pi$
$614$	−1.19910e46	−1.18598
$615$	0	0
$616$	−7.06079e44	−0.0661869
$617$	1.51984e46i	1.38705i	0.720432	+	0.693525i	$0.243943\pi$
$617$	1.51984e46i	1.38705i	−0.720432	+	0.693525i	$0.756057\pi$
$618$	− 2.43517e45i	− 0.216381i
$619$	3.99242e45	0.345415	0.172707	−	0.984973i	$-0.444749\pi$
$619$	3.99242e45	0.345415	0.172707	+	0.984973i	$0.444749\pi$
$620$	0	0
$621$	−6.27019e45	−0.514362
$622$	2.29910e46i	1.83661i
$623$	− 1.64336e45i	− 0.127844i
$624$	−8.87091e44	−0.0672082
$625$	0	0
$626$	3.29105e46	2.36515
$627$	− 8.86465e44i	− 0.0620508i
$628$	1.54887e46i	1.05604i
$629$	−8.67429e45	−0.576100
$630$	0	0
$631$	−8.68878e45	−0.547614	−0.273807	−	0.961785i	$-0.588283\pi$
$631$	−8.68878e45	−0.547614	−0.273807	+	0.961785i	$0.588283\pi$
$632$	2.44866e45i	0.150348i
$633$	2.71208e44i	0.0162234i
$634$	1.43425e46	0.835894
$635$	0	0
$636$	−7.84358e45	−0.433982
$637$	− 7.15473e45i	− 0.385738i
$638$	9.24447e45i	0.485669i
$639$	3.68955e46	1.88890
$640$	0	0
$641$	1.75762e46	0.854609	0.427305	−	0.904108i	$-0.359463\pi$
$641$	1.75762e46	0.854609	0.427305	+	0.904108i	$0.359463\pi$
$642$	7.58763e45i	0.359566i
$643$	3.90754e46i	1.80477i	0.430928	+	0.902386i	$0.358186\pi$
$643$	3.90754e46i	1.80477i	−0.430928	+	0.902386i	$0.641814\pi$
$644$	1.55798e46	0.701368
$645$	0	0
$646$	2.00238e46	0.856464
$647$	− 3.44345e46i	− 1.43573i	−0.696182	−	0.717865i	$-0.745119\pi$
$647$	− 3.44345e46i	− 1.43573i	0.696182	−	0.717865i	$-0.254881\pi$
$648$	− 7.17158e45i	− 0.291492i
$649$	1.00749e46	0.399211
$650$	0	0
$651$	4.69617e44	0.0176871
$652$	− 2.01073e46i	− 0.738359i
$653$	− 4.09793e46i	− 1.46723i	−0.679567	−	0.733613i	$-0.737832\pi$
$653$	− 4.09793e46i	− 1.46723i	0.679567	−	0.733613i	$-0.262168\pi$
$654$	−9.91120e45	−0.346014
$655$	0	0
$656$	9.61645e45	0.319228
$657$	2.05768e46i	0.666115i
$658$	2.92661e46i	0.923926i
$659$	−7.05687e44	−0.0217271	−0.0108636	−	0.999941i	$-0.503458\pi$
$659$	−7.05687e44	−0.0217271	−0.0108636	+	0.999941i	$0.503458\pi$
$660$	0	0
$661$	5.13888e45	0.150503	0.0752514	−	0.997165i	$-0.476024\pi$
$661$	5.13888e45	0.150503	0.0752514	+	0.997165i	$0.476024\pi$
$662$	− 1.90641e46i	− 0.544578i
$663$	− 2.80975e45i	− 0.0782878i
$664$	−1.89071e46	−0.513868
$665$	0	0
$666$	3.74999e46	0.969852
$667$	− 3.68393e46i	− 0.929469i
$668$	4.10623e46i	1.01072i
$669$	−3.10631e45	−0.0745958
$670$	0	0
$671$	5.95644e45	0.136165
$672$	5.29031e45i	0.118002i
$673$	− 8.48563e46i	− 1.84687i	−0.383758	−	0.923434i	$-0.625370\pi$
$673$	− 8.48563e46i	− 1.84687i	0.383758	−	0.923434i	$-0.374630\pi$
$674$	−2.10380e45	−0.0446803
$675$	0	0
$676$	−4.69090e46	−0.948715
$677$	1.97690e46i	0.390185i	0.980785	+	0.195093i	$0.0625007\pi$
$677$	1.97690e46i	0.390185i	−0.980785	+	0.195093i	$0.937499\pi$
$678$	− 7.30105e45i	− 0.140636i
$679$	3.83438e46	0.720848
$680$	0	0
$681$	−4.31648e45	−0.0773042
$682$	8.54591e45i	0.149388i
$683$	− 1.05640e47i	− 1.80254i	−0.433254	−	0.901272i	$-0.642635\pi$
$683$	− 1.05640e47i	− 1.80254i	0.433254	−	0.901272i	$-0.357365\pi$
$684$	−4.75789e46	−0.792480
$685$	0	0
$686$	−7.28847e46	−1.15688
$687$	9.75396e45i	0.151145i
$688$	4.37221e46i	0.661442i
$689$	−5.82988e46	−0.861078
$690$	0	0
$691$	−2.86100e46	−0.402838	−0.201419	−	0.979505i	$-0.564555\pi$
$691$	−2.86100e46	−0.402838	−0.201419	+	0.979505i	$0.564555\pi$
$692$	− 1.49551e47i	− 2.05608i
$693$	− 1.44417e46i	− 0.193874i
$694$	−1.54510e47	−2.02546
$695$	0	0
$696$	−3.53660e45	−0.0442113
$697$	3.04589e46i	0.371855i
$698$	9.16430e46i	1.09266i
$699$	2.42266e46	0.282110
$700$	0	0
$701$	5.94385e46	0.660269	0.330134	−	0.943934i	$-0.392906\pi$
$701$	5.94385e46	0.660269	0.330134	+	0.943934i	$0.392906\pi$
$702$	2.47731e46i	0.268793i
$703$	− 4.30881e46i	− 0.456662i
$704$	−6.29579e46	−0.651781
$705$	0	0
$706$	5.91340e46	0.584197
$707$	8.26368e46i	0.797541i
$708$	2.13415e46i	0.201222i
$709$	−6.13936e46	−0.565536	−0.282768	−	0.959188i	$-0.591253\pi$
$709$	−6.13936e46	−0.565536	−0.282768	+	0.959188i	$0.591253\pi$
$710$	0	0
$711$	−5.00835e46	−0.440399
$712$	1.14406e46i	0.0982948i
$713$	− 3.40555e46i	− 0.285898i
$714$	−1.28746e46	−0.105612
$715$	0	0
$716$	−1.98441e47	−1.55441
$717$	− 9.57976e45i	− 0.0733311i
$718$	1.24972e47i	0.934886i
$719$	2.54160e47	1.85815	0.929075	−	0.369891i	$-0.120605\pi$
$719$	2.54160e47	1.85815	0.929075	+	0.369891i	$0.120605\pi$
$720$	0	0
$721$	−4.55841e46	−0.318333
$722$	− 1.18848e47i	− 0.811203i
$723$	2.61267e46i	0.174302i
$724$	−2.72918e47	−1.77969
$725$	0	0
$726$	3.62274e46	0.225727
$727$	− 1.41220e47i	− 0.860157i	−0.902791	−	0.430079i	$-0.858486\pi$
$727$	− 1.41220e47i	− 0.860157i	0.902791	−	0.430079i	$-0.141514\pi$
$728$	− 1.11169e46i	− 0.0661935i
$729$	1.33885e47	0.779343
$730$	0	0
$731$	−1.38484e47	−0.770484
$732$	1.26174e46i	0.0686338i
$733$	− 1.82342e47i	− 0.969778i	−0.874576	−	0.484889i	$-0.838860\pi$
$733$	− 1.82342e47i	− 0.969778i	0.874576	−	0.484889i	$-0.161140\pi$
$734$	2.98484e46	0.155216
$735$	0	0
$736$	3.83641e47	1.90740
$737$	− 1.45609e46i	− 0.0707906i
$738$	− 1.31677e47i	− 0.626010i
$739$	−5.23297e46	−0.243285	−0.121642	−	0.992574i	$-0.538816\pi$
$739$	−5.23297e46	−0.243285	−0.121642	+	0.992574i	$0.538816\pi$
$740$	0	0
$741$	1.39570e46	0.0620570
$742$	2.67132e47i	1.16161i
$743$	− 2.92156e47i	− 1.24251i	−0.783609	−	0.621255i	$-0.786623\pi$
$743$	− 2.92156e47i	− 1.24251i	0.783609	−	0.621255i	$-0.213377\pi$
$744$	−3.26936e45	−0.0135991
$745$	0	0
$746$	4.38145e47	1.74352
$747$	− 3.86715e47i	− 1.50522i
$748$	− 1.28772e47i	− 0.490281i
$749$	1.42033e47	0.528982
$750$	0	0
$751$	−3.59878e47	−1.28261	−0.641307	−	0.767284i	$-0.721608\pi$
$751$	−3.59878e47	−1.28261	−0.641307	+	0.767284i	$0.721608\pi$
$752$	3.04335e47i	1.06110i
$753$	6.71252e46i	0.228965i
$754$	−1.45550e47	−0.485718
$755$	0	0
$756$	6.23907e46	0.199301
$757$	− 3.31803e47i	− 1.03705i	−0.855063	−	0.518524i	$-0.826482\pi$
$757$	− 3.31803e47i	− 1.03705i	0.855063	−	0.518524i	$-0.173518\pi$
$758$	7.77375e47i	2.37733i
$759$	4.13328e46	0.123682
$760$	0	0
$761$	4.31914e47	1.23752	0.618758	−	0.785582i	$-0.287636\pi$
$761$	4.31914e47	1.23752	0.618758	+	0.785582i	$0.287636\pi$
$762$	− 6.07970e46i	− 0.170461i
$763$	1.85528e47i	0.509044i
$764$	7.72696e47	2.07476
$765$	0	0
$766$	1.39758e47	0.359420
$767$	1.58624e47i	0.399251i
$768$	3.37370e46i	0.0831087i
$769$	7.36766e46	0.177642	0.0888209	−	0.996048i	$-0.471690\pi$
$769$	7.36766e46	0.177642	0.0888209	+	0.996048i	$0.471690\pi$
$770$	0	0
$771$	−6.24299e46	−0.144210
$772$	9.97733e46i	0.225595i
$773$	− 3.43337e47i	− 0.759904i	−0.925006	−	0.379952i	$-0.875941\pi$
$773$	− 3.43337e47i	− 0.759904i	0.925006	−	0.379952i	$-0.124059\pi$
$774$	5.98683e47	1.29709
$775$	0	0
$776$	−2.66940e47	−0.554237
$777$	2.77042e46i	0.0563118i
$778$	1.34623e48i	2.67889i
$779$	−1.51300e47	−0.294761
$780$	0	0
$781$	−4.96026e47	−0.926322
$782$	9.33638e47i	1.70713i
$783$	− 1.47526e47i	− 0.264119i
$784$	−3.40916e47	−0.597630
$785$	0	0
$786$	1.57179e47	0.264193
$787$	2.31817e47i	0.381560i	0.981633	+	0.190780i	$0.0611016\pi$
$787$	2.31817e47i	0.381560i	−0.981633	+	0.190780i	$0.938898\pi$
$788$	− 5.84037e47i	− 0.941365i
$789$	−7.86671e46	−0.124172
$790$	0	0
$791$	−1.36669e47	−0.206898
$792$	1.00540e47i	0.149064i
$793$	9.37813e46i	0.136179i
$794$	8.07300e47	1.14815
$795$	0	0
$796$	2.06960e47	0.282372
$797$	9.59340e47i	1.28206i	0.767514	+	0.641032i	$0.221494\pi$
$797$	9.59340e47i	1.28206i	−0.767514	+	0.641032i	$0.778506\pi$
$798$	− 6.39526e46i	− 0.0837164i
$799$	−9.63944e47	−1.23603
$800$	0	0
$801$	−2.34000e47	−0.287925
$802$	9.41909e47i	1.13536i
$803$	− 2.76636e47i	− 0.326664i
$804$	3.08442e46	0.0356819
$805$	0	0
$806$	−1.34551e47	−0.149403
$807$	− 1.37533e47i	− 0.149621i
$808$	− 5.75297e47i	− 0.613204i
$809$	2.85029e47	0.297672	0.148836	−	0.988862i	$-0.452447\pi$
$809$	2.85029e47	0.297672	0.148836	+	0.988862i	$0.452447\pi$
$810$	0	0
$811$	−1.46166e48	−1.46555	−0.732777	−	0.680469i	$-0.761776\pi$
$811$	−1.46166e48	−1.46555	−0.732777	+	0.680469i	$0.761776\pi$
$812$	3.66565e47i	0.360144i
$813$	− 2.94510e47i	− 0.283535i
$814$	−5.04151e47	−0.475618
$815$	0	0
$816$	−1.33882e47	−0.121293
$817$	− 6.87898e47i	− 0.610745i
$818$	9.80066e47i	0.852758i
$819$	2.27378e47	0.193894
$820$	0	0
$821$	−1.92594e48	−1.57754	−0.788771	−	0.614687i	$-0.789282\pi$
$821$	−1.92594e48	−1.57754	−0.788771	+	0.614687i	$0.789282\pi$
$822$	− 2.88272e47i	− 0.231429i
$823$	− 4.92693e47i	− 0.387685i	−0.981033	−	0.193842i	$-0.937905\pi$
$823$	− 4.92693e47i	− 0.387685i	0.981033	−	0.193842i	$-0.0620951\pi$
$824$	3.17345e47	0.244756
$825$	0	0
$826$	7.26836e47	0.538599
$827$	− 4.17990e46i	− 0.0303616i	−0.999885	−	0.0151808i	$-0.995168\pi$
$827$	− 4.17990e46i	− 0.0303616i	0.999885	−	0.0151808i	$-0.00483238\pi$
$828$	− 2.21844e48i	− 1.57960i
$829$	−1.71716e48	−1.19857	−0.599283	−	0.800538i	$-0.704547\pi$
$829$	−1.71716e48	−1.19857	−0.599283	+	0.800538i	$0.704547\pi$
$830$	0	0
$831$	3.11649e47	0.209049
$832$	− 9.91243e47i	− 0.651846i
$833$	− 1.07981e48i	− 0.696153i
$834$	6.08806e47	0.384803
$835$	0	0
$836$	6.39653e47	0.388634
$837$	− 1.36378e47i	− 0.0812409i
$838$	1.94888e48i	1.13831i
$839$	−4.33094e46	−0.0248033	−0.0124016	−	0.999923i	$-0.503948\pi$
$839$	−4.33094e46	−0.0248033	−0.0124016	+	0.999923i	$0.503948\pi$
$840$	0	0
$841$	−9.49316e47	−0.522729
$842$	− 1.28167e48i	− 0.692033i
$843$	− 3.23641e47i	− 0.171360i
$844$	−1.95698e47	−0.101610
$845$	0	0
$846$	4.16724e48	2.08083
$847$	− 6.78143e47i	− 0.332082i
$848$	2.77789e48i	1.33408i
$849$	2.12106e47	0.0999024
$850$	0	0
$851$	2.00905e48	0.910233
$852$	− 1.05072e48i	− 0.466912i
$853$	3.98289e48i	1.73596i	0.496601	+	0.867979i	$0.334581\pi$
$853$	3.98289e48i	1.73596i	−0.496601	+	0.867979i	$0.665419\pi$
$854$	4.29717e47	0.183708
$855$	0	0
$856$	−9.88802e47	−0.406717
$857$	− 3.66149e48i	− 1.47732i	−0.674078	−	0.738660i	$-0.735459\pi$
$857$	− 3.66149e48i	− 1.47732i	0.674078	−	0.738660i	$-0.264541\pi$
$858$	− 1.63303e47i	− 0.0646330i
$859$	−4.14441e48	−1.60907	−0.804536	−	0.593904i	$-0.797586\pi$
$859$	−4.14441e48	−1.60907	−0.804536	+	0.593904i	$0.797586\pi$
$860$	0	0
$861$	9.72808e46	0.0363475
$862$	− 3.32430e48i	− 1.21851i
$863$	− 2.44535e48i	− 0.879353i	−0.898156	−	0.439676i	$-0.855093\pi$
$863$	− 2.44535e48i	− 0.879353i	0.898156	−	0.439676i	$-0.144907\pi$
$864$	1.53632e48	0.542008
$865$	0	0
$866$	6.85593e48	2.32820
$867$	1.60770e47i	0.0535661i
$868$	3.38865e47i	0.110777i
$869$	6.73325e47	0.215973
$870$	0	0
$871$	2.29255e47	0.0707977
$872$	− 1.29160e48i	− 0.391388i
$873$	− 5.45983e48i	− 1.62347i
$874$	−4.63769e48	−1.35320
$875$	0	0
$876$	5.85993e47	0.164655
$877$	− 5.05120e48i	− 1.39284i	−0.717635	−	0.696420i	$-0.754775\pi$
$877$	− 5.05120e48i	− 1.39284i	0.717635	−	0.696420i	$-0.245225\pi$
$878$	− 6.64066e48i	− 1.79702i
$879$	−4.84528e47	−0.128677
$880$	0	0
$881$	−3.16644e48	−0.809971	−0.404985	−	0.914323i	$-0.632723\pi$
$881$	−3.16644e48	−0.809971	−0.404985	+	0.914323i	$0.632723\pi$
$882$	4.66814e48i	1.17196i
$883$	1.69432e48i	0.417489i	0.977970	+	0.208744i	$0.0669376\pi$
$883$	1.69432e48i	0.417489i	−0.977970	+	0.208744i	$0.933062\pi$
$884$	2.02745e48	0.490330
$885$	0	0
$886$	−1.17267e48	−0.273225
$887$	3.16518e48i	0.723868i	0.932204	+	0.361934i	$0.117883\pi$
$887$	3.16518e48i	0.723868i	−0.932204	+	0.361934i	$0.882117\pi$
$888$	− 1.92870e47i	− 0.0432964i
$889$	−1.13806e48	−0.250777
$890$	0	0
$891$	−1.97202e48	−0.418724
$892$	− 2.24145e48i	− 0.467206i
$893$	− 4.78823e48i	− 0.979775i
$894$	−1.70051e48	−0.341594
$895$	0	0
$896$	−1.41404e48	−0.273767
$897$	6.50765e47i	0.123694i
$898$	1.12646e49i	2.10211i
$899$	8.01263e47	0.146805
$900$	0	0
$901$	−8.79861e48	−1.55401
$902$	1.77028e48i	0.306997i
$903$	4.42296e47i	0.0753122i
$904$	9.51455e47	0.159078
$905$	0	0
$906$	2.86378e48	0.461661
$907$	1.08873e48i	0.172346i	0.996280	+	0.0861731i	$0.0274638\pi$
$907$	1.08873e48i	0.172346i	−0.996280	+	0.0861731i	$0.972536\pi$
$908$	− 3.11468e48i	− 0.484169i
$909$	1.17668e49	1.79620
$910$	0	0
$911$	−4.59000e48	−0.675708	−0.337854	−	0.941199i	$-0.609701\pi$
$911$	−4.59000e48	−0.675708	−0.337854	+	0.941199i	$0.609701\pi$
$912$	− 6.65037e47i	− 0.0961460i
$913$	5.19901e48i	0.738165i
$914$	−5.27779e48	−0.735935
$915$	0	0
$916$	−7.03824e48	−0.946648
$917$	− 2.94224e48i	− 0.388673i
$918$	3.73883e48i	0.485100i
$919$	2.32948e48	0.296861	0.148431	−	0.988923i	$-0.452578\pi$
$919$	2.32948e48	0.296861	0.148431	+	0.988923i	$0.452578\pi$
$920$	0	0
$921$	−1.26141e48	−0.155086
$922$	1.96172e49i	2.36906i
$923$	− 7.80969e48i	− 0.926416i
$924$	−4.11276e47	−0.0479232
$925$	0	0
$926$	2.43634e48	0.273941
$927$	6.49079e48i	0.716939i
$928$	9.02637e48i	0.979425i
$929$	3.31257e48	0.353107	0.176553	−	0.984291i	$-0.443505\pi$
$929$	3.31257e48	0.353107	0.176553	+	0.984291i	$0.443505\pi$
$930$	0	0
$931$	5.36378e48	0.551825
$932$	1.74814e49i	1.76690i
$933$	2.41857e48i	0.240166i
$934$	−1.99903e49	−1.95028
$935$	0	0
$936$	−1.58295e48	−0.149079
$937$	8.43738e48i	0.780737i	0.920659	+	0.390368i	$0.127652\pi$
$937$	8.43738e48i	0.780737i	−0.920659	+	0.390368i	$0.872348\pi$
$938$	− 1.05047e48i	− 0.0955078i
$939$	3.46206e48	0.309280
$940$	0	0
$941$	1.19866e49	1.03387	0.516937	−	0.856023i	$-0.327072\pi$
$941$	1.19866e49	1.03387	0.516937	+	0.856023i	$0.327072\pi$
$942$	2.96445e48i	0.251249i
$943$	− 7.05458e48i	− 0.587527i
$944$	7.55830e48	0.618566
$945$	0	0
$946$	−8.04873e48	−0.636098
$947$	− 1.53140e49i	− 1.18936i	−0.803961	−	0.594681i	$-0.797278\pi$
$947$	− 1.53140e49i	− 1.18936i	0.803961	−	0.594681i	$-0.202722\pi$
$948$	1.42629e48i	0.108861i
$949$	4.35550e48	0.326697
$950$	0	0
$951$	1.50877e48	0.109306
$952$	− 1.67779e48i	− 0.119461i
$953$	− 4.05106e48i	− 0.283488i	−0.989903	−	0.141744i	$-0.954729\pi$
$953$	− 4.05106e48i	− 0.283488i	0.989903	−	0.141744i	$-0.0452711\pi$
$954$	3.80374e49	2.61615
$955$	0	0
$956$	6.91254e48	0.459285
$957$	9.72483e47i	0.0635090i
$958$	3.89808e49i	2.50219i
$959$	−5.39619e48	−0.340471
$960$	0	0
$961$	−1.56628e49	−0.954844
$962$	− 7.93763e48i	− 0.475666i
$963$	− 2.02244e49i	− 1.19135i
$964$	−1.88525e49	−1.09168
$965$	0	0
$966$	2.98189e48	0.166866
$967$	1.43741e49i	0.790757i	0.918518	+	0.395378i	$0.129387\pi$
$967$	1.43741e49i	0.790757i	−0.918518	+	0.395378i	$0.870613\pi$
$968$	4.72107e48i	0.255327i
$969$	2.10642e48	0.111996
$970$	0	0
$971$	1.56174e49	0.802585	0.401293	−	0.915950i	$-0.368561\pi$
$971$	1.56174e49	0.802585	0.401293	+	0.915950i	$0.368561\pi$
$972$	− 1.34118e49i	− 0.677632i
$973$	− 1.13963e49i	− 0.566110i
$974$	3.34041e49	1.63146
$975$	0	0
$976$	4.46859e48	0.210984
$977$	− 1.09477e49i	− 0.508235i	−0.967173	−	0.254117i	$-0.918215\pi$
$977$	− 1.09477e49i	− 0.508235i	0.967173	−	0.254117i	$-0.0817849\pi$
$978$	− 3.84841e48i	− 0.175667i
$979$	3.14591e48	0.141199
$980$	0	0
$981$	2.64177e49	1.14645
$982$	− 4.64482e49i	− 1.98212i
$983$	− 1.92109e49i	− 0.806150i	−0.915167	−	0.403075i	$-0.867941\pi$
$983$	− 1.92109e49i	− 0.806150i	0.915167	−	0.403075i	$-0.132059\pi$
$984$	−6.77245e47	−0.0279465
$985$	0	0
$986$	−2.19668e49	−0.876591
$987$	3.07868e48i	0.120818i
$988$	1.00710e49i	0.388673i
$989$	3.20743e49	1.21736
$990$	0	0
$991$	2.18652e49	0.802672	0.401336	−	0.915931i	$-0.368546\pi$
$991$	2.18652e49	0.802672	0.401336	+	0.915931i	$0.368546\pi$
$992$	8.34429e48i	0.301264i
$993$	− 2.00547e48i	− 0.0712122i
$994$	−3.57850e49	−1.24976
$995$	0	0
$996$	−1.10130e49	−0.372071
$997$	1.75251e49i	0.582357i	0.956669	+	0.291179i	$0.0940474\pi$
$997$	1.75251e49i	0.582357i	−0.956669	+	0.291179i	$0.905953\pi$
$998$	1.10666e49i	0.361709i
$999$	8.04539e48	0.258652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.b.24.10		10
5.2	odd	4		25.34.a.b.1.1		5
5.3	odd	4		5.34.a.a.1.5	✓	5
5.4	even	2	inner	25.34.b.b.24.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.5	✓	5	5.3	odd	4
25.34.a.b.1.1		5	5.2	odd	4
25.34.b.b.24.1		10	5.4	even	2	inner
25.34.b.b.24.10		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+138106. i q^{2} +1.45282e7i q^{3} -1.04832e10 q^{4} -2.00642e12 q^{6} +3.75584e13i q^{7} -2.61472e14i q^{8} +5.34799e15 q^{9} +O(q^{10})\)	\(q+138106. i q^{2} +1.45282e7i q^{3} -1.04832e10 q^{4} -2.00642e12 q^{6} +3.75584e13i q^{7} -2.61472e14i q^{8} +5.34799e15 q^{9} -7.18987e16 q^{11} -1.52302e17i q^{12} -1.13201e18i q^{13} -5.18702e18 q^{14} -5.39393e19 q^{16} -1.70846e20i q^{17} +7.38588e20i q^{18} +8.48651e20 q^{19} -5.45655e20 q^{21} -9.92962e21i q^{22} +3.95696e22i q^{23} +3.79872e21 q^{24} +1.56337e23 q^{26} +1.58460e23i q^{27} -3.93732e23i q^{28} -9.30999e23 q^{29} -8.60649e23 q^{31} -9.69535e24i q^{32} -1.04456e24i q^{33} +2.35948e25 q^{34} -5.60641e25 q^{36} -5.07725e25i q^{37} +1.17203e26i q^{38} +1.64461e25 q^{39} -1.78283e26 q^{41} -7.53580e25i q^{42} -8.10579e26i q^{43} +7.53730e26 q^{44} -5.46479e27 q^{46} -5.64217e27i q^{47} -7.83641e26i q^{48} +6.32036e27 q^{49} +2.48208e27 q^{51} +1.18671e28i q^{52} -5.15002e28i q^{53} -2.18842e28 q^{54} +9.82047e27 q^{56} +1.23294e28i q^{57} -1.28576e29i q^{58} -1.40126e29 q^{59} -8.28448e28 q^{61} -1.18860e29i q^{62} +2.00862e29i q^{63} +8.75647e29 q^{64} +1.44259e29 q^{66} +2.02520e29i q^{67} +1.79102e30i q^{68} -5.74875e29 q^{69} +6.89895e30 q^{71} -1.39835e30i q^{72} +3.84757e30i q^{73} +7.01196e30 q^{74} -8.89659e30 q^{76} -2.70040e30i q^{77} +2.27129e30i q^{78} -9.36491e30 q^{79} +2.74277e31 q^{81} -2.46218e31i q^{82} -7.23102e31i q^{83} +5.72021e30 q^{84} +1.11945e32 q^{86} -1.35257e31i q^{87} +1.87995e31i q^{88} -4.37547e31 q^{89} +4.25165e31 q^{91} -4.14817e32i q^{92} -1.25037e31i q^{93} +7.79216e32 q^{94} +1.40856e32 q^{96} -1.02091e33i q^{97} +8.72877e32i q^{98} -3.84514e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * q^99

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