LMFDB - Embedded newform 25.34.b.b.24.5

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			24.5
Root			$58.5034 + 58.5034i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.b.24.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5627.97i q^{2} -1.24605e8i q^{3} +8.55826e9 q^{4} -7.01272e11 q^{6} -7.01560e13i q^{7} -9.65096e13i q^{8} -9.96727e15 q^{9} +O(q^{10})$	\(q-5627.97i q^{2} -1.24605e8i q^{3} +8.55826e9 q^{4} -7.01272e11 q^{6} -7.01560e13i q^{7} -9.65096e13i q^{8} -9.96727e15 q^{9} +9.39806e16 q^{11} -1.06640e18i q^{12} +9.95093e17i q^{13} -3.94836e17 q^{14} +7.29717e19 q^{16} +2.59085e20i q^{17} +5.60955e19i q^{18} +1.31117e21 q^{19} -8.74176e21 q^{21} -5.28920e20i q^{22} +5.44854e22i q^{23} -1.20255e22 q^{24} +5.60036e21 q^{26} +5.49284e23i q^{27} -6.00413e23i q^{28} +9.77301e23 q^{29} +6.82815e24 q^{31} -1.23969e24i q^{32} -1.17104e25i q^{33} +1.45812e24 q^{34} -8.53025e25 q^{36} +7.50351e25i q^{37} -7.37925e24i q^{38} +1.23993e26 q^{39} -2.94248e25 q^{41} +4.91984e25i q^{42} -1.00868e27i q^{43} +8.04311e26 q^{44} +3.06642e26 q^{46} -1.91365e27i q^{47} -9.09262e27i q^{48} +2.80913e27 q^{49} +3.22832e28 q^{51} +8.51627e27i q^{52} +4.33344e28i q^{53} +3.09135e27 q^{54} -6.77072e27 q^{56} -1.63379e29i q^{57} -5.50022e27i q^{58} +1.21137e29 q^{59} +4.03792e29 q^{61} -3.84287e28i q^{62} +6.99264e29i q^{63} +6.19846e29 q^{64} -6.59060e28 q^{66} +1.33311e30i q^{67} +2.21732e30i q^{68} +6.78914e30 q^{69} -4.10877e30 q^{71} +9.61937e29i q^{72} +8.64070e30i q^{73} +4.22295e29 q^{74} +1.12214e31 q^{76} -6.59330e30i q^{77} -6.97831e29i q^{78} +1.76553e31 q^{79} +1.30347e31 q^{81} +1.65602e29i q^{82} -6.43615e30i q^{83} -7.48143e31 q^{84} -5.67680e30 q^{86} -1.21776e32i q^{87} -9.07003e30i q^{88} -1.32441e32 q^{89} +6.98117e31 q^{91} +4.66300e32i q^{92} -8.50820e32i q^{93} -1.07700e31 q^{94} -1.54472e32 q^{96} -2.90988e32i q^{97} -1.58097e31i q^{98} -9.36730e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 5627.97i	− 0.0607235i	−0.999539	−	0.0303618i	$-0.990334\pi$
$2$	− 5627.97i	− 0.0607235i	0.999539	−	0.0303618i	$-0.00966594\pi$
$3$	− 1.24605e8i	− 1.67122i	−0.549323	−	0.835610i	$-0.685114\pi$
$3$	− 1.24605e8i	− 1.67122i	0.549323	−	0.835610i	$-0.314886\pi$
$4$	8.55826e9	0.996313
$5$	0	0
$5$	0	0
$6$	−7.01272e11	−0.101482
$7$	− 7.01560e13i	− 0.797897i	−0.916973	−	0.398949i	$-0.869375\pi$
$7$	− 7.01560e13i	− 0.797897i	0.916973	−	0.398949i	$-0.130625\pi$
$8$	− 9.65096e13i	− 0.121223i
$9$	−9.96727e15	−1.79298
$10$	0	0
$11$	9.39806e16	0.616679	0.308339	−	0.951276i	$-0.400227\pi$
$11$	9.39806e16	0.616679	0.308339	+	0.951276i	$0.400227\pi$
$12$	− 1.06640e18i	− 1.66506i
$13$	9.95093e17i	0.414761i	0.978260	+	0.207381i	$0.0664939\pi$
$13$	9.95093e17i	0.414761i	−0.978260	+	0.207381i	$0.933506\pi$
$14$	−3.94836e17	−0.0484511
$15$	0	0
$16$	7.29717e19	0.988952
$17$	2.59085e20i	1.29132i	0.763624	+	0.645662i	$0.223418\pi$
$17$	2.59085e20i	1.29132i	−0.763624	+	0.645662i	$0.776582\pi$
$18$	5.60955e19i	0.108876i
$19$	1.31117e21	1.04286	0.521430	−	0.853294i	$-0.325399\pi$
$19$	1.31117e21	1.04286	0.521430	+	0.853294i	$0.325399\pi$
$20$	0	0
$21$	−8.74176e21	−1.33346
$22$	− 5.28920e20i	− 0.0374469i
$23$	5.44854e22i	1.85255i	0.376843	+	0.926277i	$0.377010\pi$
$23$	5.44854e22i	1.85255i	−0.376843	+	0.926277i	$0.622990\pi$
$24$	−1.20255e22	−0.202591
$25$	0	0
$26$	5.60036e21	0.0251858
$27$	5.49284e23i	1.32524i
$28$	− 6.00413e23i	− 0.794955i
$29$	9.77301e23	0.725206	0.362603	−	0.931944i	$-0.381888\pi$
$29$	9.77301e23	0.725206	0.362603	+	0.931944i	$0.381888\pi$
$30$	0	0
$31$	6.82815e24	1.68591	0.842957	−	0.537981i	$-0.180813\pi$
$31$	6.82815e24	1.68591	0.842957	+	0.537981i	$0.180813\pi$
$32$	− 1.23969e24i	− 0.181276i
$33$	− 1.17104e25i	− 1.03061i
$34$	1.45812e24	0.0784137
$35$	0	0
$36$	−8.53025e25	−1.78637
$37$	7.50351e25i	0.999852i	0.866068	+	0.499926i	$0.166640\pi$
$37$	7.50351e25i	0.999852i	−0.866068	+	0.499926i	$0.833360\pi$
$38$	− 7.37925e24i	− 0.0633262i
$39$	1.23993e26	0.693158
$40$	0	0
$41$	−2.94248e25	−0.0720741	−0.0360371	−	0.999350i	$-0.511473\pi$
$41$	−2.94248e25	−0.0720741	−0.0360371	+	0.999350i	$0.511473\pi$
$42$	4.91984e25i	0.0809725i
$43$	− 1.00868e27i	− 1.12596i	−0.826471	−	0.562979i	$-0.809655\pi$
$43$	− 1.00868e27i	− 1.12596i	0.826471	−	0.562979i	$-0.190345\pi$
$44$	8.04311e26	0.614405
$45$	0	0
$46$	3.06642e26	0.112494
$47$	− 1.91365e27i	− 0.492321i	−0.969229	−	0.246160i	$-0.920831\pi$
$47$	− 1.91365e27i	− 0.492321i	0.969229	−	0.246160i	$-0.0791690\pi$
$48$	− 9.09262e27i	− 1.65276i
$49$	2.80913e27	0.363360
$50$	0	0
$51$	3.22832e28	2.15809
$52$	8.51627e27i	0.413232i
$53$	4.33344e28i	1.53561i	0.640684	+	0.767804i	$0.278651\pi$
$53$	4.33344e28i	1.53561i	−0.640684	+	0.767804i	$0.721349\pi$
$54$	3.09135e27	0.0804733
$55$	0	0
$56$	−6.77072e27	−0.0967236
$57$	− 1.63379e29i	− 1.74285i
$58$	− 5.50022e27i	− 0.0440371i
$59$	1.21137e29	0.731507	0.365754	−	0.930712i	$-0.380811\pi$
$59$	1.21137e29	0.731507	0.365754	+	0.930712i	$0.380811\pi$
$60$	0	0
$61$	4.03792e29	1.40674	0.703372	−	0.710822i	$-0.251677\pi$
$61$	4.03792e29	1.40674	0.703372	+	0.710822i	$0.251677\pi$
$62$	− 3.84287e28i	− 0.102375i
$63$	6.99264e29i	1.43061i
$64$	6.19846e29	0.977944
$65$	0	0
$66$	−6.59060e28	−0.0625821
$67$	1.33311e30i	0.987713i	0.869543	+	0.493856i	$0.164413\pi$
$67$	1.33311e30i	0.987713i	−0.869543	+	0.493856i	$0.835587\pi$
$68$	2.21732e30i	1.28656i
$69$	6.78914e30	3.09603
$70$	0	0
$71$	−4.10877e30	−1.16936	−0.584681	−	0.811263i	$-0.698780\pi$
$71$	−4.10877e30	−1.16936	−0.584681	+	0.811263i	$0.698780\pi$
$72$	9.61937e29i	0.217350i
$73$	8.64070e30i	1.55497i	0.628902	+	0.777484i	$0.283505\pi$
$73$	8.64070e30i	1.55497i	−0.628902	+	0.777484i	$0.716495\pi$
$74$	4.22295e29	0.0607146
$75$	0	0
$76$	1.12214e31	1.03901
$77$	− 6.59330e30i	− 0.492046i
$78$	− 6.97831e29i	− 0.0420910i
$79$	1.76553e31	0.863033	0.431516	−	0.902105i	$-0.357979\pi$
$79$	1.76553e31	0.863033	0.431516	+	0.902105i	$0.357979\pi$
$80$	0	0
$81$	1.30347e31	0.421790
$82$	1.65602e29i	0.00437659i
$83$	− 6.43615e30i	− 0.139264i	−0.997573	−	0.0696318i	$-0.977818\pi$
$83$	− 6.43615e30i	− 0.139264i	0.997573	−	0.0696318i	$-0.0221824\pi$
$84$	−7.48143e31	−1.32855
$85$	0	0
$86$	−5.67680e30	−0.0683722
$87$	− 1.21776e32i	− 1.21198i
$88$	− 9.07003e30i	− 0.0747558i
$89$	−1.32441e32	−0.905911	−0.452956	−	0.891533i	$-0.649630\pi$
$89$	−1.32441e32	−0.905911	−0.452956	+	0.891533i	$0.649630\pi$
$90$	0	0
$91$	6.98117e31	0.330937
$92$	4.66300e32i	1.84572i
$93$	− 8.50820e32i	− 2.81753i
$94$	−1.07700e31	−0.0298955
$95$	0	0
$96$	−1.54472e32	−0.302952
$97$	− 2.90988e32i	− 0.480996i	−0.970650	−	0.240498i	$-0.922689\pi$
$97$	− 2.90988e32i	− 0.480996i	0.970650	−	0.240498i	$-0.0773107\pi$
$98$	− 1.58097e31i	− 0.0220645i
$99$	−9.36730e32	−1.10569
$100$	0	0
$101$	−2.11490e33	−1.79468	−0.897341	−	0.441338i	$-0.854504\pi$
$101$	−2.11490e33	−1.79468	−0.897341	+	0.441338i	$0.854504\pi$
$102$	− 1.81689e32i	− 0.131047i
$103$	9.19643e32i	0.564684i	0.959314	+	0.282342i	$0.0911112\pi$
$103$	9.19643e32i	0.564684i	−0.959314	+	0.282342i	$0.908889\pi$
$104$	9.60360e31	0.0502787
$105$	0	0
$106$	2.43885e32	0.0932476
$107$	3.10653e33i	1.01729i	0.860977	+	0.508644i	$0.169853\pi$
$107$	3.10653e33i	1.01729i	−0.860977	+	0.508644i	$0.830147\pi$
$108$	4.70091e33i	1.32035i
$109$	4.33103e33	1.04485	0.522425	−	0.852685i	$-0.325028\pi$
$109$	4.33103e33	1.04485	0.522425	+	0.852685i	$0.325028\pi$
$110$	0	0
$111$	9.34972e33	1.67097
$112$	− 5.11940e33i	− 0.789082i
$113$	1.60843e33i	0.214096i	0.994254	+	0.107048i	$0.0341398\pi$
$113$	1.60843e33i	0.214096i	−0.994254	+	0.107048i	$0.965860\pi$
$114$	−9.19490e32	−0.105832
$115$	0	0
$116$	8.36400e33	0.722532
$117$	− 9.91836e33i	− 0.743658i
$118$	− 6.81756e32i	− 0.0444197i
$119$	1.81764e34	1.03034
$120$	0	0
$121$	−1.43928e34	−0.619707
$122$	− 2.27253e33i	− 0.0854225i
$123$	3.66646e33i	0.120452i
$124$	5.84371e34	1.67970
$125$	0	0
$126$	3.93544e33	0.0868718
$127$	6.65683e34i	1.28975i	0.764287	+	0.644876i	$0.223091\pi$
$127$	6.65683e34i	1.28975i	−0.764287	+	0.644876i	$0.776909\pi$
$128$	− 1.41374e34i	− 0.240660i
$129$	−1.25686e35	−1.88173
$130$	0	0
$131$	−3.69750e34	−0.429469	−0.214734	−	0.976672i	$-0.568889\pi$
$131$	−3.69750e34	−0.429469	−0.214734	+	0.976672i	$0.568889\pi$
$132$	− 1.00221e35i	− 1.02681i
$133$	− 9.19867e34i	− 0.832095i
$134$	7.50269e33	0.0599774
$135$	0	0
$136$	2.50042e34	0.156538
$137$	1.76237e34i	0.0977705i	0.998804	+	0.0488853i	$0.0155669\pi$
$137$	1.76237e34i	0.0977705i	−0.998804	+	0.0488853i	$0.984433\pi$
$138$	− 3.82091e34i	− 0.188002i
$139$	−1.00540e35	−0.439130	−0.219565	−	0.975598i	$-0.570464\pi$
$139$	−1.00540e35	−0.439130	−0.219565	+	0.975598i	$0.570464\pi$
$140$	0	0
$141$	−2.38450e35	−0.822776
$142$	2.31240e34i	0.0710078i
$143$	9.35195e34i	0.255775i
$144$	−7.27329e35	−1.77317
$145$	0	0
$146$	4.86296e34	0.0944232
$147$	− 3.50031e35i	− 0.607254i
$148$	6.42170e35i	0.996165i
$149$	1.14557e36	1.59019	0.795093	−	0.606487i	$-0.207422\pi$
$149$	1.14557e36	1.59019	0.795093	+	0.606487i	$0.207422\pi$
$150$	0	0
$151$	−6.40257e35	−0.713239	−0.356619	−	0.934250i	$-0.616071\pi$
$151$	−6.40257e35	−0.713239	−0.356619	+	0.934250i	$0.616071\pi$
$152$	− 1.26541e35i	− 0.126419i
$153$	− 2.58237e36i	− 2.31531i
$154$	−3.71069e34	−0.0298788
$155$	0	0
$156$	1.06117e36	0.690602
$157$	− 1.01110e36i	− 0.592172i	−0.955161	−	0.296086i	$-0.904319\pi$
$157$	− 1.01110e36i	− 0.592172i	0.955161	−	0.296086i	$-0.0956815\pi$
$158$	− 9.93633e34i	− 0.0524064i
$159$	5.39967e36	2.56634
$160$	0	0
$161$	3.82248e36	1.47815
$162$	− 7.33587e34i	− 0.0256126i
$163$	4.84374e36i	1.52786i	0.645296	+	0.763932i	$0.276734\pi$
$163$	4.84374e36i	1.52786i	−0.645296	+	0.763932i	$0.723266\pi$
$164$	−2.51825e35	−0.0718083
$165$	0	0
$166$	−3.62225e34	−0.00845658
$167$	− 1.75726e36i	− 0.371548i	−0.982593	−	0.185774i	$-0.940521\pi$
$167$	− 1.75726e36i	− 0.371548i	0.982593	−	0.185774i	$-0.0594792\pi$
$168$	8.43664e35i	0.161647i
$169$	4.76592e36	0.827973
$170$	0	0
$171$	−1.30688e37	−1.86982
$172$	− 8.63252e36i	− 1.12181i
$173$	1.04480e36i	0.123388i	0.998095	+	0.0616942i	$0.0196503\pi$
$173$	1.04480e36i	0.123388i	−0.998095	+	0.0616942i	$0.980350\pi$
$174$	−6.85354e35	−0.0735957
$175$	0	0
$176$	6.85793e36	0.609866
$177$	− 1.50942e37i	− 1.22251i
$178$	7.45372e35i	0.0550101i
$179$	−6.89417e36	−0.463881	−0.231941	−	0.972730i	$-0.574508\pi$
$179$	−6.89417e36	−0.463881	−0.231941	+	0.972730i	$0.574508\pi$
$180$	0	0
$181$	2.73403e36	0.153146	0.0765732	−	0.997064i	$-0.475602\pi$
$181$	2.73403e36	0.153146	0.0765732	+	0.997064i	$0.475602\pi$
$182$	− 3.92898e35i	− 0.0200957i
$183$	− 5.03143e37i	− 2.35098i
$184$	5.25836e36	0.224572
$185$	0	0
$186$	−4.78839e36	−0.171091
$187$	2.43490e37i	0.796332i
$188$	− 1.63775e37i	− 0.490505i
$189$	3.85355e37	1.05741
$190$	0	0
$191$	−7.33764e37	−1.69241	−0.846206	−	0.532856i	$-0.821119\pi$
$191$	−7.33764e37	−1.69241	−0.846206	+	0.532856i	$0.821119\pi$
$192$	− 7.72357e37i	− 1.63436i
$193$	− 3.39286e37i	− 0.658978i	−0.944159	−	0.329489i	$-0.893124\pi$
$193$	− 3.39286e37i	− 0.658978i	0.944159	−	0.329489i	$-0.106876\pi$
$194$	−1.63767e36	−0.0292078
$195$	0	0
$196$	2.40413e37	0.362020
$197$	− 1.22669e38i	− 1.69841i	−0.528063	−	0.849205i	$-0.677081\pi$
$197$	− 1.22669e38i	− 1.69841i	0.528063	−	0.849205i	$-0.322919\pi$
$198$	5.27189e36i	0.0671415i
$199$	4.90395e37	0.574738	0.287369	−	0.957820i	$-0.407219\pi$
$199$	4.90395e37	0.574738	0.287369	+	0.957820i	$0.407219\pi$
$200$	0	0
$201$	1.66111e38	1.65069
$202$	1.19026e37i	0.108979i
$203$	− 6.85635e37i	− 0.578640i
$204$	2.76288e38	2.15013
$205$	0	0
$206$	5.17573e36	0.0342896
$207$	− 5.43071e38i	− 3.32159i
$208$	7.26137e37i	0.410179i
$209$	1.23225e38	0.643110
$210$	0	0
$211$	−2.26597e38	−1.01063	−0.505316	−	0.862934i	$-0.668624\pi$
$211$	−2.26597e38	−1.01063	−0.505316	+	0.862934i	$0.668624\pi$
$212$	3.70867e38i	1.52995i
$213$	5.11972e38i	1.95426i
$214$	1.74835e37	0.0617733
$215$	0	0
$216$	5.30111e37	0.160650
$217$	− 4.79036e38i	− 1.34519i
$218$	− 2.43749e37i	− 0.0634469i
$219$	1.07667e39	2.59870
$220$	0	0
$221$	−2.57814e38	−0.535591
$222$	− 5.26200e37i	− 0.101467i
$223$	− 7.70736e38i	− 1.37999i	−0.723815	−	0.689994i	$-0.757613\pi$
$223$	− 7.70736e38i	− 1.37999i	0.723815	−	0.689994i	$-0.242387\pi$
$224$	−8.69719e37	−0.144639
$225$	0	0
$226$	9.05221e36	0.0130007
$227$	− 3.75970e38i	− 0.502026i	−0.967984	−	0.251013i	$-0.919236\pi$
$227$	− 3.75970e38i	− 0.502026i	0.967984	−	0.251013i	$-0.0807637\pi$
$228$	− 1.39824e39i	− 1.73642i
$229$	−8.87055e38	−1.02486	−0.512431	−	0.858729i	$-0.671255\pi$
$229$	−8.87055e38	−1.02486	−0.512431	+	0.858729i	$0.671255\pi$
$230$	0	0
$231$	−8.21557e38	−0.822318
$232$	− 9.43189e37i	− 0.0879118i
$233$	− 9.06227e38i	− 0.786800i	−0.919367	−	0.393400i	$-0.871299\pi$
$233$	− 9.06227e38i	− 0.786800i	0.919367	−	0.393400i	$-0.128701\pi$
$234$	−5.58203e37	−0.0451575
$235$	0	0
$236$	1.03672e39	0.728810
$237$	− 2.19993e39i	− 1.44232i
$238$	− 1.02296e38i	− 0.0625661i
$239$	−2.67931e39	−1.52918	−0.764589	−	0.644518i	$-0.777058\pi$
$239$	−2.67931e39	−1.52918	−0.764589	+	0.644518i	$0.777058\pi$
$240$	0	0
$241$	4.69772e38	0.233672	0.116836	−	0.993151i	$-0.462725\pi$
$241$	4.69772e38	0.233672	0.116836	+	0.993151i	$0.462725\pi$
$242$	8.10022e37i	0.0376308i
$243$	1.42932e39i	0.620335i
$244$	3.45575e39	1.40156
$245$	0	0
$246$	2.06348e37	0.00731425
$247$	1.30474e39i	0.432538i
$248$	− 6.58982e38i	− 0.204372i
$249$	−8.01974e38	−0.232740
$250$	0	0
$251$	−1.31521e38	−0.0334486	−0.0167243	−	0.999860i	$-0.505324\pi$
$251$	−1.31521e38	−0.0334486	−0.0167243	+	0.999860i	$0.505324\pi$
$252$	5.98448e39i	1.42534i
$253$	5.12057e39i	1.14243i
$254$	3.74645e38	0.0783183
$255$	0	0
$256$	5.24487e39	0.963330
$257$	− 4.96495e39i	− 0.855104i	−0.903991	−	0.427552i	$-0.859376\pi$
$257$	− 4.96495e39i	− 0.855104i	0.903991	−	0.427552i	$-0.140624\pi$
$258$	7.07356e38i	0.114265i
$259$	5.26416e39	0.797779
$260$	0	0
$261$	−9.74103e39	−1.30028
$262$	2.08094e38i	0.0260789i
$263$	6.41705e39i	0.755206i	0.925968	+	0.377603i	$0.123252\pi$
$263$	6.41705e39i	0.755206i	−0.925968	+	0.377603i	$0.876748\pi$
$264$	−1.13017e39	−0.124933
$265$	0	0
$266$	−5.17699e38	−0.0505278
$267$	1.65027e40i	1.51398i
$268$	1.14091e40i	0.984071i
$269$	1.97544e39	0.160233	0.0801164	−	0.996786i	$-0.474471\pi$
$269$	1.97544e39	0.160233	0.0801164	+	0.996786i	$0.474471\pi$
$270$	0	0
$271$	−1.48531e40	−1.06616	−0.533082	−	0.846063i	$-0.678966\pi$
$271$	−1.48531e40	−1.06616	−0.533082	+	0.846063i	$0.678966\pi$
$272$	1.89059e40i	1.27706i
$273$	− 8.69887e39i	− 0.553069i
$274$	9.91858e37	0.00593697
$275$	0	0
$276$	5.81032e40	3.08461
$277$	− 6.46494e39i	− 0.323332i	−0.986846	−	0.161666i	$-0.948313\pi$
$277$	− 6.46494e39i	− 0.323332i	0.986846	−	0.161666i	$-0.0516866\pi$
$278$	5.65835e38i	0.0266655i
$279$	−6.80581e40	−3.02281
$280$	0	0
$281$	−1.46554e40	−0.578554	−0.289277	−	0.957245i	$-0.593415\pi$
$281$	−1.46554e40	−0.578554	−0.289277	+	0.957245i	$0.593415\pi$
$282$	1.34199e39i	0.0499619i
$283$	− 2.68962e40i	− 0.944529i	−0.881457	−	0.472265i	$-0.843437\pi$
$283$	− 2.68962e40i	− 0.944529i	0.881457	−	0.472265i	$-0.156563\pi$
$284$	−3.51639e40	−1.16505
$285$	0	0
$286$	5.26325e38	0.0155315
$287$	2.06432e39i	0.0575077i
$288$	1.23564e40i	0.325023i
$289$	−2.68705e40	−0.667516
$290$	0	0
$291$	−3.62584e40	−0.803850
$292$	7.39493e40i	1.54923i
$293$	− 4.27715e40i	− 0.846912i	−0.905917	−	0.423456i	$-0.860817\pi$
$293$	− 4.27715e40i	− 0.846912i	0.905917	−	0.423456i	$-0.139183\pi$
$294$	−1.96997e39	−0.0368746
$295$	0	0
$296$	7.24160e39	0.121205
$297$	5.16220e40i	0.817248i
$298$	− 6.44723e39i	− 0.0965617i
$299$	−5.42181e40	−0.768368
$300$	0	0
$301$	−7.07647e40	−0.898399
$302$	3.60335e39i	0.0433104i
$303$	2.63527e41i	2.99931i
$304$	9.56787e40	1.03134
$305$	0	0
$306$	−1.45335e40	−0.140594
$307$	5.26223e40i	0.482377i	0.970478	+	0.241189i	$0.0775372\pi$
$307$	5.26223e40i	0.482377i	−0.970478	+	0.241189i	$0.922463\pi$
$308$	− 5.64272e40i	− 0.490232i
$309$	1.14592e41	0.943711
$310$	0	0
$311$	3.83170e40	0.283691	0.141845	−	0.989889i	$-0.454696\pi$
$311$	3.83170e40	0.283691	0.141845	+	0.989889i	$0.454696\pi$
$312$	− 1.19665e40i	− 0.0840268i
$313$	− 8.13055e40i	− 0.541550i	−0.962643	−	0.270775i	$-0.912720\pi$
$313$	− 8.13055e40i	− 0.541550i	0.962643	−	0.270775i	$-0.0872799\pi$
$314$	−5.69042e39	−0.0359588
$315$	0	0
$316$	1.51098e41	0.859850
$317$	− 7.49503e40i	− 0.404852i	−0.979298	−	0.202426i	$-0.935118\pi$
$317$	− 7.49503e40i	− 0.404852i	0.979298	−	0.202426i	$-0.0648825\pi$
$318$	− 3.03892e40i	− 0.155837i
$319$	9.18474e40	0.447219
$320$	0	0
$321$	3.87089e41	1.70011
$322$	− 2.15128e40i	− 0.0897584i
$323$	3.39706e41i	1.34667i
$324$	1.11554e41	0.420235
$325$	0	0
$326$	2.72604e40	0.0927774
$327$	− 5.39666e41i	− 1.74617i
$328$	2.83977e39i	0.00873705i
$329$	−1.34254e41	−0.392821
$330$	0	0
$331$	−5.91449e41	−1.56587	−0.782935	−	0.622103i	$-0.786278\pi$
$331$	−5.91449e41	−1.56587	−0.782935	+	0.622103i	$0.786278\pi$
$332$	− 5.50822e40i	− 0.138750i
$333$	− 7.47895e41i	− 1.79271i
$334$	−9.88982e39	−0.0225617
$335$	0	0
$336$	−6.37902e41	−1.31873
$337$	− 1.33169e41i	− 0.262126i	−0.991374	−	0.131063i	$-0.958161\pi$
$337$	− 1.33169e41i	− 0.262126i	0.991374	−	0.131063i	$-0.0418391\pi$
$338$	− 2.68225e40i	− 0.0502774i
$339$	2.00418e41	0.357801
$340$	0	0
$341$	6.41714e41	1.03967
$342$	7.35510e40i	0.113542i
$343$	− 7.39453e41i	− 1.08782i
$344$	−9.73469e40	−0.136492
$345$	0	0
$346$	5.88013e39	0.00749257
$347$	− 1.89271e41i	− 0.229957i	−0.993368	−	0.114979i	$-0.963320\pi$
$347$	− 1.89271e41i	− 0.229957i	0.993368	−	0.114979i	$-0.0366800\pi$
$348$	− 1.04219e42i	− 1.20751i
$349$	5.82757e41	0.643974	0.321987	−	0.946744i	$-0.395649\pi$
$349$	5.82757e41	0.643974	0.321987	+	0.946744i	$0.395649\pi$
$350$	0	0
$351$	−5.46588e41	−0.549658
$352$	− 1.16507e41i	− 0.111789i
$353$	5.33261e41i	0.488267i	0.969742	+	0.244134i	$0.0785035\pi$
$353$	5.33261e41i	0.488267i	−0.969742	+	0.244134i	$0.921496\pi$
$354$	−8.49500e40	−0.0742351
$355$	0	0
$356$	−1.13346e42	−0.902571
$357$	− 2.26486e42i	− 1.72193i
$358$	3.88002e40i	0.0281685i
$359$	1.28621e42	0.891772	0.445886	−	0.895090i	$-0.352889\pi$
$359$	1.28621e42	0.891772	0.445886	+	0.895090i	$0.352889\pi$
$360$	0	0
$361$	1.38408e41	0.0875575
$362$	− 1.53871e40i	− 0.00929959i
$363$	1.79341e42i	1.03567i
$364$	5.97467e41	0.329717
$365$	0	0
$366$	−2.83168e41	−0.142760
$367$	1.99600e42i	0.961988i	0.876724	+	0.480994i	$0.159724\pi$
$367$	1.99600e42i	0.961988i	−0.876724	+	0.480994i	$0.840276\pi$
$368$	3.97589e42i	1.83209i
$369$	2.93284e41	0.129227
$370$	0	0
$371$	3.04017e42	1.22526
$372$	− 7.28154e42i	− 2.80714i
$373$	− 4.88676e42i	− 1.80229i	−0.433516	−	0.901146i	$-0.642727\pi$
$373$	− 4.88676e42i	− 1.80229i	0.433516	−	0.901146i	$-0.357273\pi$
$374$	1.37035e41	0.0483561
$375$	0	0
$376$	−1.84686e41	−0.0596807
$377$	9.72506e41i	0.300788i
$378$	− 2.16877e41i	− 0.0642094i
$379$	6.55646e42	1.85833	0.929164	−	0.369667i	$-0.120528\pi$
$379$	6.55646e42	1.85833	0.929164	+	0.369667i	$0.120528\pi$
$380$	0	0
$381$	8.29473e42	2.15546
$382$	4.12961e41i	0.102769i
$383$	− 8.72699e41i	− 0.208010i	−0.994577	−	0.104005i	$-0.966834\pi$
$383$	− 8.72699e41i	− 0.208010i	0.994577	−	0.104005i	$-0.0331658\pi$
$384$	−1.76158e42	−0.402196
$385$	0	0
$386$	−1.90949e41	−0.0400155
$387$	1.00538e43i	2.01882i
$388$	− 2.49035e42i	− 0.479222i
$389$	−1.58040e42	−0.291474	−0.145737	−	0.989323i	$-0.546555\pi$
$389$	−1.58040e42	−0.291474	−0.145737	+	0.989323i	$0.546555\pi$
$390$	0	0
$391$	−1.41164e43	−2.39225
$392$	− 2.71108e41i	− 0.0440476i
$393$	4.60726e42i	0.717737i
$394$	−6.90379e41	−0.103133
$395$	0	0
$396$	−8.01678e42	−1.10161
$397$	5.01270e42i	0.660736i	0.943852	+	0.330368i	$0.107173\pi$
$397$	5.01270e42i	0.660736i	−0.943852	+	0.330368i	$0.892827\pi$
$398$	− 2.75993e41i	− 0.0349001i
$399$	−1.14620e43	−1.39061
$400$	0	0
$401$	8.66109e42	0.967588	0.483794	−	0.875182i	$-0.339258\pi$
$401$	8.66109e42	0.967588	0.483794	+	0.875182i	$0.339258\pi$
$402$	− 9.34870e41i	− 0.100235i
$403$	6.79465e42i	0.699252i
$404$	−1.80999e43	−1.78806
$405$	0	0
$406$	−3.85874e41	−0.0351371
$407$	7.05184e42i	0.616588i
$408$	− 3.11564e42i	− 0.261610i
$409$	−6.15808e42	−0.496605	−0.248302	−	0.968683i	$-0.579873\pi$
$409$	−6.15808e42	−0.496605	−0.248302	+	0.968683i	$0.579873\pi$
$410$	0	0
$411$	2.19600e42	0.163396
$412$	7.87055e42i	0.562601i
$413$	− 8.49849e42i	− 0.583668i
$414$	−3.05639e42	−0.201699
$415$	0	0
$416$	1.23361e42	0.0751862
$417$	1.25277e43i	0.733883i
$418$	− 6.93507e41i	− 0.0390519i
$419$	−1.55362e43	−0.841031	−0.420516	−	0.907285i	$-0.638151\pi$
$419$	−1.55362e43	−0.841031	−0.420516	+	0.907285i	$0.638151\pi$
$420$	0	0
$421$	1.08104e43	0.540987	0.270494	−	0.962722i	$-0.412813\pi$
$421$	1.08104e43	0.540987	0.270494	+	0.962722i	$0.412813\pi$
$422$	1.27528e42i	0.0613691i
$423$	1.90739e43i	0.882720i
$424$	4.18218e42	0.186151
$425$	0	0
$426$	2.88136e42	0.118670
$427$	− 2.83284e43i	− 1.12244i
$428$	2.65865e43i	1.01354i
$429$	1.16530e43	0.427456
$430$	0	0
$431$	−4.98547e42	−0.169368	−0.0846840	−	0.996408i	$-0.526988\pi$
$431$	−4.98547e42	−0.169368	−0.0846840	+	0.996408i	$0.526988\pi$
$432$	4.00822e43i	1.31060i
$433$	− 1.01098e43i	− 0.318194i	−0.987263	−	0.159097i	$-0.949142\pi$
$433$	− 1.01098e43i	− 0.318194i	0.987263	−	0.159097i	$-0.0508583\pi$
$434$	−2.69600e42	−0.0816845
$435$	0	0
$436$	3.70661e43	1.04100
$437$	7.14399e43i	1.93195i
$438$	− 6.05948e42i	− 0.157802i
$439$	4.36398e43	1.09451	0.547253	−	0.836967i	$-0.315674\pi$
$439$	4.36398e43	1.09451	0.547253	+	0.836967i	$0.315674\pi$
$440$	0	0
$441$	−2.79994e43	−0.651496
$442$	1.45097e42i	0.0325230i
$443$	1.22624e43i	0.264798i	0.991196	+	0.132399i	$0.0422681\pi$
$443$	1.22624e43i	0.264798i	−0.991196	+	0.132399i	$0.957732\pi$
$444$	8.00174e43	1.66481
$445$	0	0
$446$	−4.33768e42	−0.0837978
$447$	− 1.42743e44i	− 2.65755i
$448$	− 4.34859e43i	− 0.780299i
$449$	−8.39293e43	−1.45161	−0.725803	−	0.687903i	$-0.758532\pi$
$449$	−8.39293e43	−1.45161	−0.725803	+	0.687903i	$0.758532\pi$
$450$	0	0
$451$	−2.76536e42	−0.0444466
$452$	1.37654e43i	0.213306i
$453$	7.97791e43i	1.19198i
$454$	−2.11595e42	−0.0304848
$455$	0	0
$456$	−1.57676e43	−0.211274
$457$	− 9.02636e42i	− 0.116653i	−0.998298	−	0.0583264i	$-0.981424\pi$
$457$	− 9.02636e42i	− 0.116653i	0.998298	−	0.0583264i	$-0.0185764\pi$
$458$	4.99232e42i	0.0622332i
$459$	−1.42311e44	−1.71131
$460$	0	0
$461$	−3.52096e42	−0.0394091	−0.0197045	−	0.999806i	$-0.506273\pi$
$461$	−3.52096e42	−0.0394091	−0.0197045	+	0.999806i	$0.506273\pi$
$462$	4.62370e42i	0.0499341i
$463$	2.80824e42i	0.0292650i	0.999893	+	0.0146325i	$0.00465783\pi$
$463$	2.80824e42i	0.0292650i	−0.999893	+	0.0146325i	$0.995342\pi$
$464$	7.13154e43	0.717194
$465$	0	0
$466$	−5.10022e42	−0.0477773
$467$	1.17834e44i	1.06547i	0.846282	+	0.532736i	$0.178836\pi$
$467$	1.17834e44i	1.06547i	−0.846282	+	0.532736i	$0.821164\pi$
$468$	− 8.48839e43i	− 0.740916i
$469$	9.35254e43	0.788094
$470$	0	0
$471$	−1.25987e44	−0.989650
$472$	− 1.16909e43i	− 0.0886756i
$473$	− 9.47961e43i	− 0.694355i
$474$	−1.23811e43	−0.0875826
$475$	0	0
$476$	1.55558e44	1.02654
$477$	− 4.31925e44i	− 2.75331i
$478$	1.50791e43i	0.0928571i
$479$	−2.89874e43	−0.172454	−0.0862271	−	0.996276i	$-0.527481\pi$
$479$	−2.89874e43	−0.172454	−0.0862271	+	0.996276i	$0.527481\pi$
$480$	0	0
$481$	−7.46669e43	−0.414700
$482$	− 2.64386e42i	− 0.0141894i
$483$	− 4.76299e44i	− 2.47031i
$484$	−1.23177e44	−0.617422
$485$	0	0
$486$	8.04418e42	0.0376689
$487$	− 2.41311e44i	− 1.09232i	−0.837682	−	0.546158i	$-0.816090\pi$
$487$	− 2.41311e44i	− 1.09232i	0.837682	−	0.546158i	$-0.183910\pi$
$488$	− 3.89698e43i	− 0.170530i
$489$	6.03552e44	2.55340
$490$	0	0
$491$	−2.36480e44	−0.935297	−0.467648	−	0.883915i	$-0.654899\pi$
$491$	−2.36480e44	−0.935297	−0.467648	+	0.883915i	$0.654899\pi$
$492$	3.13785e43i	0.120008i
$493$	2.53204e44i	0.936476i
$494$	7.34305e42	0.0262653
$495$	0	0
$496$	4.98262e44	1.66729
$497$	2.88255e44i	0.933031i
$498$	4.51349e42i	0.0141328i
$499$	4.17695e44	1.26532	0.632659	−	0.774430i	$-0.281963\pi$
$499$	4.17695e44	1.26532	0.632659	+	0.774430i	$0.281963\pi$
$500$	0	0
$501$	−2.18963e44	−0.620938
$502$	7.40196e41i	0.00203112i
$503$	1.63646e44i	0.434543i	0.976111	+	0.217271i	$0.0697157\pi$
$503$	1.63646e44i	0.434543i	−0.976111	+	0.217271i	$0.930284\pi$
$504$	6.74856e43	0.173423
$505$	0	0
$506$	2.88184e43	0.0693724
$507$	− 5.93856e44i	− 1.38373i
$508$	5.69709e44i	1.28500i
$509$	9.46414e43	0.206651	0.103326	−	0.994648i	$-0.467052\pi$
$509$	9.46414e43	0.206651	0.103326	+	0.994648i	$0.467052\pi$
$510$	0	0
$511$	6.06197e44	1.24071
$512$	− 1.50957e44i	− 0.299157i
$513$	7.20207e44i	1.38204i
$514$	−2.79426e43	−0.0519249
$515$	0	0
$516$	−1.07565e45	−1.87479
$517$	− 1.79846e44i	− 0.303604i
$518$	− 2.96265e43i	− 0.0484440i
$519$	1.30187e44	0.206209
$520$	0	0
$521$	7.82192e44	1.16276	0.581381	−	0.813631i	$-0.302512\pi$
$521$	7.82192e44	1.16276	0.581381	+	0.813631i	$0.302512\pi$
$522$	5.48222e43i	0.0789575i
$523$	− 8.02848e44i	− 1.12035i	−0.828373	−	0.560177i	$-0.810733\pi$
$523$	− 8.02848e44i	− 1.12035i	0.828373	−	0.560177i	$-0.189267\pi$
$524$	−3.16442e44	−0.427885
$525$	0	0
$526$	3.61150e43	0.0458588
$527$	1.76907e45i	2.17706i
$528$	− 8.54530e44i	− 1.01922i
$529$	−2.10365e45	−2.43196
$530$	0	0
$531$	−1.20741e45	−1.31158
$532$	− 7.87246e44i	− 0.829027i
$533$	− 2.92804e43i	− 0.0298936i
$534$	9.28768e43	0.0919341
$535$	0	0
$536$	1.28658e44	0.119734
$537$	8.59046e44i	0.775248i
$538$	− 1.11177e43i	− 0.00972990i
$539$	2.64004e44	0.224076
$540$	0	0
$541$	−2.90457e44	−0.231914	−0.115957	−	0.993254i	$-0.536994\pi$
$541$	−2.90457e44	−0.231914	−0.115957	+	0.993254i	$0.536994\pi$
$542$	8.35929e43i	0.0647413i
$543$	− 3.40673e44i	− 0.255941i
$544$	3.21186e44	0.234086
$545$	0	0
$546$	−4.89570e43	−0.0335843
$547$	2.63690e45i	1.75511i	0.479480	+	0.877553i	$0.340825\pi$
$547$	2.63690e45i	1.75511i	−0.479480	+	0.877553i	$0.659175\pi$
$548$	1.50828e44i	0.0974100i
$549$	−4.02470e45	−2.52226
$550$	0	0
$551$	1.28141e45	0.756289
$552$	− 6.55217e44i	− 0.375310i
$553$	− 1.23862e45i	− 0.688611i
$554$	−3.63845e43	−0.0196338
$555$	0	0
$556$	−8.60445e44	−0.437511
$557$	1.37430e45i	0.678378i	0.940718	+	0.339189i	$0.110153\pi$
$557$	1.37430e45i	0.678378i	−0.940718	+	0.339189i	$0.889847\pi$
$558$	3.83029e44i	0.183555i
$559$	1.00373e45	0.467004
$560$	0	0
$561$	3.03400e45	1.33085
$562$	8.24803e43i	0.0351319i
$563$	1.83620e45i	0.759505i	0.925088	+	0.379753i	$0.123991\pi$
$563$	1.83620e45i	0.759505i	−0.925088	+	0.379753i	$0.876009\pi$
$564$	−2.04072e45	−0.819743
$565$	0	0
$566$	−1.51371e44	−0.0573552
$567$	− 9.14459e44i	− 0.336546i
$568$	3.96535e44i	0.141754i
$569$	5.13991e45	1.78485	0.892427	−	0.451192i	$-0.149001\pi$
$569$	5.13991e45	1.78485	0.892427	+	0.451192i	$0.149001\pi$
$570$	0	0
$571$	5.28676e45	1.73258	0.866291	−	0.499540i	$-0.166498\pi$
$571$	5.28676e45	1.73258	0.866291	+	0.499540i	$0.166498\pi$
$572$	8.00364e44i	0.254832i
$573$	9.14305e45i	2.82839i
$574$	1.16180e43	0.00349207
$575$	0	0
$576$	−6.17817e45	−1.75343
$577$	1.37030e45i	0.377934i	0.981983	+	0.188967i	$0.0605139\pi$
$577$	1.37030e45i	0.377934i	−0.981983	+	0.188967i	$0.939486\pi$
$578$	1.51227e44i	0.0405340i
$579$	−4.22767e45	−1.10130
$580$	0	0
$581$	−4.51534e44	−0.111118
$582$	2.04062e44i	0.0488126i
$583$	4.07259e45i	0.946978i
$584$	8.33910e44	0.188498
$585$	0	0
$586$	−2.40717e44	−0.0514275
$587$	− 1.82654e45i	− 0.379402i	−0.981842	−	0.189701i	$-0.939248\pi$
$587$	− 1.82654e45i	− 0.379402i	0.981842	−	0.189701i	$-0.0607518\pi$
$588$	− 2.99566e45i	− 0.605015i
$589$	8.95290e45	1.75817
$590$	0	0
$591$	−1.52852e46	−2.83842
$592$	5.47544e45i	0.988805i
$593$	− 9.10503e45i	− 1.59911i	−0.600592	−	0.799556i	$-0.705068\pi$
$593$	− 9.10503e45i	− 1.59911i	0.600592	−	0.799556i	$-0.294932\pi$
$594$	2.90527e44	0.0496262
$595$	0	0
$596$	9.80408e45	1.58432
$597$	− 6.11055e45i	− 0.960514i
$598$	3.05138e44i	0.0466580i
$599$	−1.51052e45	−0.224690	−0.112345	−	0.993669i	$-0.535836\pi$
$599$	−1.51052e45	−0.224690	−0.112345	+	0.993669i	$0.535836\pi$
$600$	0	0
$601$	1.17313e46	1.65165	0.825825	−	0.563927i	$-0.190710\pi$
$601$	1.17313e46	1.65165	0.825825	+	0.563927i	$0.190710\pi$
$602$	3.98262e44i	0.0545540i
$603$	− 1.32874e46i	− 1.77095i
$604$	−5.47949e45	−0.710609
$605$	0	0
$606$	1.48312e45	0.182129
$607$	9.39432e45i	1.12267i	0.827589	+	0.561335i	$0.189712\pi$
$607$	9.39432e45i	1.12267i	−0.827589	+	0.561335i	$0.810288\pi$
$608$	− 1.62546e45i	− 0.189045i
$609$	−8.54334e45	−0.967035
$610$	0	0
$611$	1.90426e45	0.204196
$612$	− 2.21006e46i	− 2.30678i
$613$	− 9.71928e45i	− 0.987498i	−0.869604	−	0.493749i	$-0.835626\pi$
$613$	− 9.71928e45i	− 0.987498i	0.869604	−	0.493749i	$-0.164374\pi$
$614$	2.96157e44	0.0292916
$615$	0	0
$616$	−6.36317e44	−0.0596474
$617$	− 1.24293e46i	− 1.13433i	−0.823603	−	0.567166i	$-0.808040\pi$
$617$	− 1.24293e46i	− 1.13433i	0.823603	−	0.567166i	$-0.191960\pi$
$618$	− 6.44920e44i	− 0.0573054i
$619$	1.07266e46	0.928043	0.464021	−	0.885824i	$-0.346406\pi$
$619$	1.07266e46	0.928043	0.464021	+	0.885824i	$0.346406\pi$
$620$	0	0
$621$	−2.99279e46	−2.45508
$622$	− 2.15647e44i	− 0.0172267i
$623$	9.29149e45i	0.722824i
$624$	9.04801e45	0.685499
$625$	0	0
$626$	−4.57585e44	−0.0328848
$627$	− 1.53544e46i	− 1.07478i
$628$	− 8.65322e45i	− 0.589988i
$629$	−1.94405e46	−1.29113
$630$	0	0
$631$	−1.79249e46	−1.12972	−0.564862	−	0.825186i	$-0.691071\pi$
$631$	−1.79249e46	−1.12972	−0.564862	+	0.825186i	$0.691071\pi$
$632$	− 1.70390e45i	− 0.104620i
$633$	2.82350e46i	1.68899i
$634$	−4.21818e44	−0.0245840
$635$	0	0
$636$	4.62117e46	2.55688
$637$	2.79535e45i	0.150708i
$638$	− 5.16915e44i	− 0.0271567i
$639$	4.09532e46	2.09664
$640$	0	0
$641$	2.31165e46	1.12400	0.561998	−	0.827138i	$-0.310033\pi$
$641$	2.31165e46	1.12400	0.561998	+	0.827138i	$0.310033\pi$
$642$	− 2.17852e45i	− 0.103237i
$643$	− 3.13717e45i	− 0.144896i	−0.997372	−	0.0724480i	$-0.976919\pi$
$643$	− 3.13717e45i	− 0.144896i	0.997372	−	0.0724480i	$-0.0230811\pi$
$644$	3.27138e46	1.47270
$645$	0	0
$646$	1.91185e45	0.0817746
$647$	1.23833e46i	0.516318i	0.966102	+	0.258159i	$0.0831158\pi$
$647$	1.23833e46i	0.516318i	−0.966102	+	0.258159i	$0.916884\pi$
$648$	− 1.25797e45i	− 0.0511308i
$649$	1.13845e46	0.451105
$650$	0	0
$651$	−5.96901e46	−2.24810
$652$	4.14540e46i	1.52223i
$653$	− 9.15492e45i	− 0.327784i	−0.986478	−	0.163892i	$-0.947595\pi$
$653$	− 9.15492e45i	− 0.327784i	0.986478	−	0.163892i	$-0.0524048\pi$
$654$	−3.03723e45	−0.106034
$655$	0	0
$656$	−2.14718e45	−0.0712778
$657$	− 8.61242e46i	− 2.78802i
$658$	7.55578e44i	0.0238535i
$659$	4.32900e46	1.33284	0.666420	−	0.745577i	$-0.267826\pi$
$659$	4.32900e46	1.33284	0.666420	+	0.745577i	$0.267826\pi$
$660$	0	0
$661$	1.40663e46	0.411961	0.205980	−	0.978556i	$-0.433962\pi$
$661$	1.40663e46	0.411961	0.205980	+	0.978556i	$0.433962\pi$
$662$	3.32866e45i	0.0950852i
$663$	3.21248e46i	0.895091i
$664$	−6.21150e44	−0.0168820
$665$	0	0
$666$	−4.20913e45	−0.108860
$667$	5.32487e46i	1.34348i
$668$	− 1.50391e46i	− 0.370178i
$669$	−9.60373e46	−2.30626
$670$	0	0
$671$	3.79486e46	0.867509
$672$	1.08371e46i	0.241724i
$673$	2.27399e46i	0.494926i	0.968897	+	0.247463i	$0.0795969\pi$
$673$	2.27399e46i	0.494926i	−0.968897	+	0.247463i	$0.920403\pi$
$674$	−7.49473e44	−0.0159172
$675$	0	0
$676$	4.07880e46	0.824920
$677$	− 4.02008e46i	− 0.793453i	−0.917937	−	0.396727i	$-0.870146\pi$
$677$	− 4.02008e46i	− 0.793453i	0.917937	−	0.396727i	$-0.129854\pi$
$678$	− 1.12795e45i	− 0.0217270i
$679$	−2.04145e46	−0.383785
$680$	0	0
$681$	−4.68476e46	−0.838996
$682$	− 3.61155e45i	− 0.0631323i
$683$	− 8.62730e46i	− 1.47209i	−0.676935	−	0.736043i	$-0.736692\pi$
$683$	− 8.62730e46i	− 1.47209i	0.676935	−	0.736043i	$-0.263308\pi$
$684$	−1.11846e47	−1.86293
$685$	0	0
$686$	−4.16162e45	−0.0660563
$687$	1.10531e47i	1.71277i
$688$	− 7.36049e46i	− 1.11352i
$689$	−4.31217e46	−0.636911
$690$	0	0
$691$	2.76452e46	0.389252	0.194626	−	0.980877i	$-0.437651\pi$
$691$	2.76452e46	0.389252	0.194626	+	0.980877i	$0.437651\pi$
$692$	8.94170e45i	0.122933i
$693$	6.57172e46i	0.882228i
$694$	−1.06521e45	−0.0139638
$695$	0	0
$696$	−1.17526e46	−0.146920
$697$	− 7.62351e45i	− 0.0930710i
$698$	− 3.27974e45i	− 0.0391043i
$699$	−1.12920e47	−1.31492
$700$	0	0
$701$	5.83426e45	0.0648094	0.0324047	−	0.999475i	$-0.489683\pi$
$701$	5.83426e45	0.0648094	0.0324047	+	0.999475i	$0.489683\pi$
$702$	3.07618e45i	0.0333772i
$703$	9.83841e46i	1.04271i
$704$	5.82535e46	0.603077
$705$	0	0
$706$	3.00118e45	0.0296493
$707$	1.48373e47i	1.43197i
$708$	− 1.29180e47i	− 1.21800i
$709$	3.21473e46	0.296130	0.148065	−	0.988978i	$-0.452696\pi$
$709$	3.21473e46	0.296130	0.148065	+	0.988978i	$0.452696\pi$
$710$	0	0
$711$	−1.75975e47	−1.54740
$712$	1.27818e46i	0.109817i
$713$	3.72035e47i	3.12325i
$714$	−1.27466e46	−0.104562
$715$	0	0
$716$	−5.90021e46	−0.462171
$717$	3.33855e47i	2.55559i
$718$	− 7.23876e45i	− 0.0541515i
$719$	5.61687e46	0.410646	0.205323	−	0.978694i	$-0.434176\pi$
$719$	5.61687e46	0.410646	0.205323	+	0.978694i	$0.434176\pi$
$720$	0	0
$721$	6.45185e46	0.450560
$722$	− 7.78958e44i	− 0.00531680i
$723$	− 5.85358e46i	− 0.390517i
$724$	2.33986e46	0.152582
$725$	0	0
$726$	1.00933e46	0.0628894
$727$	− 2.29582e47i	− 1.39836i	−0.714944	−	0.699181i	$-0.753548\pi$
$727$	− 2.29582e47i	− 1.39836i	0.714944	−	0.699181i	$-0.246452\pi$
$728$	− 6.73750e45i	− 0.0401172i
$729$	2.50561e47	1.45851
$730$	0	0
$731$	2.61333e47	1.45398
$732$	− 4.30603e47i	− 2.34231i
$733$	1.21401e46i	0.0645662i	0.999479	+	0.0322831i	$0.0102778\pi$
$733$	1.21401e46i	0.0645662i	−0.999479	+	0.0322831i	$0.989722\pi$
$734$	1.12334e46	0.0584153
$735$	0	0
$736$	6.75452e46	0.335823
$737$	1.25286e47i	0.609102i
$738$	− 1.65060e45i	− 0.00784713i
$739$	−3.32044e47	−1.54370	−0.771848	−	0.635807i	$-0.780667\pi$
$739$	−3.32044e47	−1.54370	−0.771848	+	0.635807i	$0.780667\pi$
$740$	0	0
$741$	1.62577e47	0.722867
$742$	− 1.71100e46i	− 0.0744020i
$743$	− 1.84054e47i	− 0.782762i	−0.920229	−	0.391381i	$-0.871997\pi$
$743$	− 1.84054e47i	− 0.782762i	0.920229	−	0.391381i	$-0.128003\pi$
$744$	−8.21123e46	−0.341550
$745$	0	0
$746$	−2.75025e46	−0.109442
$747$	6.41508e46i	0.249696i
$748$	2.08385e47i	0.793396i
$749$	2.17942e47	0.811691
$750$	0	0
$751$	−7.67452e45	−0.0273522	−0.0136761	−	0.999906i	$-0.504353\pi$
$751$	−7.67452e45	−0.0273522	−0.0136761	+	0.999906i	$0.504353\pi$
$752$	− 1.39642e47i	− 0.486881i
$753$	1.63881e46i	0.0559000i
$754$	5.47324e45	0.0182649
$755$	0	0
$756$	3.29797e47	1.05351
$757$	1.14623e47i	0.358254i	0.983826	+	0.179127i	$0.0573273\pi$
$757$	1.14623e47i	0.358254i	−0.983826	+	0.179127i	$0.942673\pi$
$758$	− 3.68996e46i	− 0.112844i
$759$	6.38047e47	1.90925
$760$	0	0
$761$	−6.74831e47	−1.93352	−0.966759	−	0.255690i	$-0.917697\pi$
$761$	−6.74831e47	−1.93352	−0.966759	+	0.255690i	$0.917697\pi$
$762$	− 4.66825e46i	− 0.130887i
$763$	− 3.03847e47i	− 0.833682i
$764$	−6.27975e47	−1.68617
$765$	0	0
$766$	−4.91152e45	−0.0126311
$767$	1.20543e47i	0.303401i
$768$	− 6.53535e47i	− 1.60994i
$769$	−1.58437e47	−0.382007	−0.191004	−	0.981589i	$-0.561174\pi$
$769$	−1.58437e47	−0.382007	−0.191004	+	0.981589i	$0.561174\pi$
$770$	0	0
$771$	−6.18657e47	−1.42907
$772$	− 2.90370e47i	− 0.656548i
$773$	− 1.15351e47i	− 0.255305i	−0.991819	−	0.127652i	$-0.959256\pi$
$773$	− 1.15351e47i	− 0.255305i	0.991819	−	0.127652i	$-0.0407442\pi$
$774$	5.65822e46	0.122590
$775$	0	0
$776$	−2.80831e46	−0.0583078
$777$	− 6.55939e47i	− 1.33327i
$778$	8.89447e45i	0.0176993i
$779$	−3.85810e46	−0.0751632
$780$	0	0
$781$	−3.86145e47	−0.721121
$782$	7.94464e46i	0.145266i
$783$	5.36816e47i	0.961072i
$784$	2.04987e47	0.359345
$785$	0	0
$786$	2.59295e46	0.0435835
$787$	− 7.25057e47i	− 1.19341i	−0.802461	−	0.596704i	$-0.796477\pi$
$787$	− 7.25057e47i	− 1.19341i	0.802461	−	0.596704i	$-0.203523\pi$
$788$	− 1.04983e48i	− 1.69215i
$789$	7.99595e47	1.26212
$790$	0	0
$791$	1.12841e47	0.170827
$792$	9.04034e46i	0.134035i
$793$	4.01810e47i	0.583463i
$794$	2.82113e46	0.0401222
$795$	0	0
$796$	4.19693e47	0.572619
$797$	5.72072e47i	0.764519i	0.924055	+	0.382260i	$0.124854\pi$
$797$	5.72072e47i	0.764519i	−0.924055	+	0.382260i	$0.875146\pi$
$798$	6.45077e46i	0.0844430i
$799$	4.95798e47	0.635745
$800$	0	0
$801$	1.32007e48	1.62428
$802$	− 4.87444e46i	− 0.0587553i
$803$	8.12058e47i	0.958916i
$804$	1.42162e48	1.64460
$805$	0	0
$806$	3.82401e46	0.0424611
$807$	− 2.46149e47i	− 0.267784i
$808$	2.04108e47i	0.217557i
$809$	−1.25233e48	−1.30788	−0.653939	−	0.756547i	$-0.726885\pi$
$809$	−1.25233e48	−1.30788	−0.653939	+	0.756547i	$0.726885\pi$
$810$	0	0
$811$	−1.43044e48	−1.43425	−0.717126	−	0.696944i	$-0.754543\pi$
$811$	−1.43044e48	−1.43425	−0.717126	+	0.696944i	$0.754543\pi$
$812$	− 5.86785e47i	− 0.576506i
$813$	1.85077e48i	1.78180i
$814$	3.96876e46	0.0374414
$815$	0	0
$816$	2.35576e48	2.13424
$817$	− 1.32255e48i	− 1.17422i
$818$	3.46575e46i	0.0301556i
$819$	−6.95832e47	−0.593363
$820$	0	0
$821$	−7.52133e47	−0.616074	−0.308037	−	0.951374i	$-0.599672\pi$
$821$	−7.52133e47	−0.616074	−0.308037	+	0.951374i	$0.599672\pi$
$822$	− 1.23590e46i	− 0.00992199i
$823$	− 2.11125e47i	− 0.166128i	−0.996544	−	0.0830638i	$-0.973529\pi$
$823$	− 2.11125e47i	− 0.166128i	0.996544	−	0.0830638i	$-0.0264705\pi$
$824$	8.87544e46	0.0684527
$825$	0	0
$826$	−4.78292e46	−0.0354424
$827$	1.64488e47i	0.119480i	0.998214	+	0.0597399i	$0.0190271\pi$
$827$	1.64488e47i	0.119480i	−0.998214	+	0.0597399i	$0.980973\pi$
$828$	− 4.64774e48i	− 3.30934i
$829$	2.28060e48	1.59184	0.795919	−	0.605404i	$-0.206988\pi$
$829$	2.28060e48	1.59184	0.795919	+	0.605404i	$0.206988\pi$
$830$	0	0
$831$	−8.05561e47	−0.540358
$832$	6.16804e47i	0.405613i
$833$	7.27804e47i	0.469215i
$834$	7.05056e46	0.0445640
$835$	0	0
$836$	1.05459e48	0.640739
$837$	3.75059e48i	2.23424i
$838$	8.74370e46i	0.0510704i
$839$	−1.56509e48	−0.896327	−0.448163	−	0.893952i	$-0.647922\pi$
$839$	−1.56509e48	−0.896327	−0.448163	+	0.893952i	$0.647922\pi$
$840$	0	0
$841$	−8.60958e47	−0.474076
$842$	− 6.08406e46i	− 0.0328506i
$843$	1.82613e48i	0.966892i
$844$	−1.93927e48	−1.00691
$845$	0	0
$846$	1.07347e47	0.0536019
$847$	1.00974e48i	0.494463i
$848$	3.16218e48i	1.51864i
$849$	−3.35140e48	−1.57852
$850$	0	0
$851$	−4.08832e48	−1.85228
$852$	4.38159e48i	1.94706i
$853$	− 1.60296e48i	− 0.698657i	−0.937000	−	0.349329i	$-0.886410\pi$
$853$	− 1.60296e48i	− 0.698657i	0.937000	−	0.349329i	$-0.113590\pi$
$854$	−1.59431e47	−0.0681584
$855$	0	0
$856$	2.99810e47	0.123319
$857$	− 3.00131e48i	− 1.21095i	−0.795864	−	0.605476i	$-0.792983\pi$
$857$	− 3.00131e48i	− 1.21095i	0.795864	−	0.605476i	$-0.207017\pi$
$858$	− 6.55826e46i	− 0.0259566i
$859$	−4.48822e48	−1.74256	−0.871279	−	0.490788i	$-0.836709\pi$
$859$	−4.48822e48	−1.74256	−0.871279	+	0.490788i	$0.836709\pi$
$860$	0	0
$861$	2.57224e47	0.0961081
$862$	2.80581e46i	0.0102846i
$863$	5.23525e47i	0.188260i	0.995560	+	0.0941302i	$0.0300070\pi$
$863$	5.23525e47i	0.188260i	−0.995560	+	0.0941302i	$0.969993\pi$
$864$	6.80943e47	0.240234
$865$	0	0
$866$	−5.68977e46	−0.0193219
$867$	3.34819e48i	1.11557i
$868$	− 4.09971e48i	− 1.34023i
$869$	1.65925e48	0.532214
$870$	0	0
$871$	−1.32657e48	−0.409665
$872$	− 4.17985e47i	− 0.126660i
$873$	2.90035e48i	0.862414i
$874$	4.02062e47	0.117315
$875$	0	0
$876$	9.21444e48	2.58911
$877$	1.66421e48i	0.458898i	0.973321	+	0.229449i	$0.0736924\pi$
$877$	1.66421e48i	0.458898i	−0.973321	+	0.229449i	$0.926308\pi$
$878$	− 2.45603e47i	− 0.0664622i
$879$	−5.32952e48	−1.41538
$880$	0	0
$881$	1.63041e48	0.417055	0.208528	−	0.978016i	$-0.433133\pi$
$881$	1.63041e48	0.417055	0.208528	+	0.978016i	$0.433133\pi$
$882$	1.57580e47i	0.0395611i
$883$	3.57816e48i	0.881674i	0.897587	+	0.440837i	$0.145318\pi$
$883$	3.57816e48i	0.881674i	−0.897587	+	0.440837i	$0.854682\pi$
$884$	−2.20644e48	−0.533616
$885$	0	0
$886$	6.90126e46	0.0160795
$887$	− 3.83241e48i	− 0.876461i	−0.898863	−	0.438230i	$-0.855605\pi$
$887$	− 3.83241e48i	− 0.876461i	0.898863	−	0.438230i	$-0.144395\pi$
$888$	− 9.02338e47i	− 0.202561i
$889$	4.67017e48	1.02909
$890$	0	0
$891$	1.22501e48	0.260109
$892$	− 6.59616e48i	− 1.37490i
$893$	− 2.50913e48i	− 0.513422i
$894$	−8.03356e47	−0.161376
$895$	0	0
$896$	−9.91821e47	−0.192022
$897$	6.75582e48i	1.28411i
$898$	4.72352e47i	0.0881467i
$899$	6.67316e48	1.22264
$900$	0	0
$901$	−1.12273e49	−1.98297
$902$	1.55634e46i	0.00269895i
$903$	8.81761e48i	1.50142i
$904$	1.55229e47	0.0259534
$905$	0	0
$906$	4.48994e47	0.0723812
$907$	9.46008e48i	1.49753i	0.662838	+	0.748763i	$0.269352\pi$
$907$	9.46008e48i	1.49753i	−0.662838	+	0.748763i	$0.730648\pi$
$908$	− 3.21765e48i	− 0.500175i
$909$	2.10798e49	3.21782
$910$	0	0
$911$	7.92211e48	1.16624	0.583120	−	0.812386i	$-0.301832\pi$
$911$	7.92211e48	1.16624	0.583120	+	0.812386i	$0.301832\pi$
$912$	− 1.19220e49i	− 1.72359i
$913$	− 6.04873e47i	− 0.0858809i
$914$	−5.08001e46	−0.00708357
$915$	0	0
$916$	−7.59165e48	−1.02108
$917$	2.59402e48i	0.342672i
$918$	8.00923e47i	0.103917i
$919$	−4.92680e48	−0.627854	−0.313927	−	0.949447i	$-0.601645\pi$
$919$	−4.92680e48	−0.627854	−0.313927	+	0.949447i	$0.601645\pi$
$920$	0	0
$921$	6.55699e48	0.806158
$922$	1.98159e46i	0.00239306i
$923$	− 4.08861e48i	− 0.485006i
$924$	−7.03110e48	−0.819286
$925$	0	0
$926$	1.58047e46	0.00177707
$927$	− 9.16633e48i	− 1.01246i
$928$	− 1.21155e48i	− 0.131462i
$929$	−2.38059e48	−0.253761	−0.126881	−	0.991918i	$-0.540497\pi$
$929$	−2.38059e48	−0.253761	−0.126881	+	0.991918i	$0.540497\pi$
$930$	0	0
$931$	3.68326e48	0.378934
$932$	− 7.75573e48i	− 0.783899i
$933$	− 4.77448e48i	− 0.474110i
$934$	6.63166e47	0.0646992
$935$	0	0
$936$	−9.57217e47	−0.0901486
$937$	4.20946e47i	0.0389514i	0.999810	+	0.0194757i	$0.00619970\pi$
$937$	4.20946e47i	0.0389514i	−0.999810	+	0.0194757i	$0.993800\pi$
$938$	− 5.26358e47i	− 0.0478558i
$939$	−1.01310e49	−0.905049
$940$	0	0
$941$	−1.57932e49	−1.36221	−0.681103	−	0.732188i	$-0.738499\pi$
$941$	−1.57932e49	−1.36221	−0.681103	+	0.732188i	$0.738499\pi$
$942$	7.09053e47i	0.0600950i
$943$	− 1.60322e48i	− 0.133521i
$944$	8.83958e48	0.723425
$945$	0	0
$946$	−5.33510e47	−0.0421637
$947$	− 1.67820e49i	− 1.30337i	−0.758490	−	0.651685i	$-0.774062\pi$
$947$	− 1.67820e49i	− 1.30337i	0.758490	−	0.651685i	$-0.225938\pi$
$948$	− 1.88276e49i	− 1.43700i
$949$	−8.59830e48	−0.644941
$950$	0	0
$951$	−9.33916e48	−0.676596
$952$	− 1.75419e48i	− 0.124902i
$953$	2.07777e49i	1.45400i	0.686639	+	0.726999i	$0.259085\pi$
$953$	2.07777e49i	1.45400i	−0.686639	+	0.726999i	$0.740915\pi$
$954$	−2.43086e48	−0.167191
$955$	0	0
$956$	−2.29303e49	−1.52354
$957$	− 1.14446e49i	− 0.747402i
$958$	1.63141e47i	0.0104720i
$959$	1.23641e48	0.0780109
$960$	0	0
$961$	3.02202e49	1.84231
$962$	4.20223e47i	0.0251821i
$963$	− 3.09637e49i	− 1.82397i
$964$	4.02043e48	0.232810
$965$	0	0
$966$	−2.68060e48	−0.150006
$967$	− 1.42054e48i	− 0.0781480i	−0.999236	−	0.0390740i	$-0.987559\pi$
$967$	− 1.42054e48i	− 0.0781480i	0.999236	−	0.0390740i	$-0.0124408\pi$
$968$	1.38904e48i	0.0751229i
$969$	4.23289e49	2.25058
$970$	0	0
$971$	3.67703e49	1.88964	0.944821	−	0.327588i	$-0.106236\pi$
$971$	3.67703e49	1.88964	0.944821	+	0.327588i	$0.106236\pi$
$972$	1.22325e49i	0.618048i
$973$	7.05346e48i	0.350381i
$974$	−1.35809e48	−0.0663293
$975$	0	0
$976$	2.94654e49	1.39120
$977$	5.91833e48i	0.274751i	0.990519	+	0.137375i	$0.0438667\pi$
$977$	5.91833e48i	0.274751i	−0.990519	+	0.137375i	$0.956133\pi$
$978$	− 3.39678e48i	− 0.155051i
$979$	−1.24468e49	−0.558657
$980$	0	0
$981$	−4.31685e49	−1.87339
$982$	1.33090e48i	0.0567945i
$983$	− 4.20754e49i	− 1.76561i	−0.469740	−	0.882805i	$-0.655652\pi$
$983$	− 4.20754e49i	− 1.76561i	0.469740	−	0.882805i	$-0.344348\pi$
$984$	3.53849e47	0.0146015
$985$	0	0
$986$	1.42503e48	0.0568661
$987$	1.67287e49i	0.656491i
$988$	1.11663e49i	0.430943i
$989$	5.49582e49	2.08590
$990$	0	0
$991$	−8.36780e48	−0.307182	−0.153591	−	0.988134i	$-0.549084\pi$
$991$	−8.36780e48	−0.307182	−0.153591	+	0.988134i	$0.549084\pi$
$992$	− 8.46482e48i	− 0.305615i
$993$	7.36974e49i	2.61691i
$994$	1.62229e48	0.0566569
$995$	0	0
$996$	−6.86351e48	−0.231882
$997$	− 4.11174e49i	− 1.36633i	−0.730264	−	0.683166i	$-0.760603\pi$
$997$	− 4.11174e49i	− 1.36633i	0.730264	−	0.683166i	$-0.239397\pi$
$998$	− 2.35077e48i	− 0.0768346i
$999$	−4.12155e49	−1.32504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.b.24.5		10
5.2	odd	4		5.34.a.a.1.3	✓	5
5.3	odd	4		25.34.a.b.1.3		5
5.4	even	2	inner	25.34.b.b.24.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.3	✓	5	5.2	odd	4
25.34.a.b.1.3		5	5.3	odd	4
25.34.b.b.24.5		10	1.1	even	1	trivial
25.34.b.b.24.6		10	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5627.97i q^{2} -1.24605e8i q^{3} +8.55826e9 q^{4} -7.01272e11 q^{6} -7.01560e13i q^{7} -9.65096e13i q^{8} -9.96727e15 q^{9} +O(q^{10})\)	\(q-5627.97i q^{2} -1.24605e8i q^{3} +8.55826e9 q^{4} -7.01272e11 q^{6} -7.01560e13i q^{7} -9.65096e13i q^{8} -9.96727e15 q^{9} +9.39806e16 q^{11} -1.06640e18i q^{12} +9.95093e17i q^{13} -3.94836e17 q^{14} +7.29717e19 q^{16} +2.59085e20i q^{17} +5.60955e19i q^{18} +1.31117e21 q^{19} -8.74176e21 q^{21} -5.28920e20i q^{22} +5.44854e22i q^{23} -1.20255e22 q^{24} +5.60036e21 q^{26} +5.49284e23i q^{27} -6.00413e23i q^{28} +9.77301e23 q^{29} +6.82815e24 q^{31} -1.23969e24i q^{32} -1.17104e25i q^{33} +1.45812e24 q^{34} -8.53025e25 q^{36} +7.50351e25i q^{37} -7.37925e24i q^{38} +1.23993e26 q^{39} -2.94248e25 q^{41} +4.91984e25i q^{42} -1.00868e27i q^{43} +8.04311e26 q^{44} +3.06642e26 q^{46} -1.91365e27i q^{47} -9.09262e27i q^{48} +2.80913e27 q^{49} +3.22832e28 q^{51} +8.51627e27i q^{52} +4.33344e28i q^{53} +3.09135e27 q^{54} -6.77072e27 q^{56} -1.63379e29i q^{57} -5.50022e27i q^{58} +1.21137e29 q^{59} +4.03792e29 q^{61} -3.84287e28i q^{62} +6.99264e29i q^{63} +6.19846e29 q^{64} -6.59060e28 q^{66} +1.33311e30i q^{67} +2.21732e30i q^{68} +6.78914e30 q^{69} -4.10877e30 q^{71} +9.61937e29i q^{72} +8.64070e30i q^{73} +4.22295e29 q^{74} +1.12214e31 q^{76} -6.59330e30i q^{77} -6.97831e29i q^{78} +1.76553e31 q^{79} +1.30347e31 q^{81} +1.65602e29i q^{82} -6.43615e30i q^{83} -7.48143e31 q^{84} -5.67680e30 q^{86} -1.21776e32i q^{87} -9.07003e30i q^{88} -1.32441e32 q^{89} +6.98117e31 q^{91} +4.66300e32i q^{92} -8.50820e32i q^{93} -1.07700e31 q^{94} -1.54472e32 q^{96} -2.90988e32i q^{97} -1.58097e31i q^{98} -9.36730e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) \) 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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