LMFDB - Embedded newform 25.34.b.b.24.2

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			24.2
Root			$16897.1 - 16897.1i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.b.24.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-129081. i q^{2} +6.82881e7i q^{3} -8.07187e9 q^{4} +8.81467e12 q^{6} -1.39338e14i q^{7} -6.68716e13i q^{8} +8.95800e14 q^{9} +O(q^{10})$	\(q-129081. i q^{2} +6.82881e7i q^{3} -8.07187e9 q^{4} +8.81467e12 q^{6} -1.39338e14i q^{7} -6.68716e13i q^{8} +8.95800e14 q^{9} -1.11807e17 q^{11} -5.51213e17i q^{12} -3.82676e18i q^{13} -1.79859e19 q^{14} -7.79687e19 q^{16} +1.35670e20i q^{17} -1.15630e20i q^{18} -1.50898e21 q^{19} +9.51513e21 q^{21} +1.44321e22i q^{22} -2.26444e22i q^{23} +4.56653e21 q^{24} -4.93961e23 q^{26} +4.40790e23i q^{27} +1.12472e24i q^{28} +6.82827e23 q^{29} -5.41504e24 q^{31} +9.48983e24i q^{32} -7.63507e24i q^{33} +1.75124e25 q^{34} -7.23078e24 q^{36} -7.55931e24i q^{37} +1.94780e26i q^{38} +2.61322e26 q^{39} -1.95728e26 q^{41} -1.22822e27i q^{42} -5.44732e26i q^{43} +9.02490e26 q^{44} -2.92295e27 q^{46} -3.58134e27i q^{47} -5.32433e27i q^{48} -1.16841e28 q^{49} -9.26465e27 q^{51} +3.08891e28i q^{52} -4.28944e28i q^{53} +5.68974e28 q^{54} -9.31777e27 q^{56} -1.03045e29i q^{57} -8.81397e28i q^{58} +2.15590e28 q^{59} +5.24247e29 q^{61} +6.98976e29i q^{62} -1.24819e29i q^{63} +5.55207e29 q^{64} -9.85539e29 q^{66} -1.47500e30i q^{67} -1.09511e30i q^{68} +1.54634e30 q^{69} -1.24706e30 q^{71} -5.99036e28i q^{72} +9.14380e30i q^{73} -9.75760e29 q^{74} +1.21803e31 q^{76} +1.55789e31i q^{77} -3.37316e31i q^{78} +2.52252e31 q^{79} -2.51209e31 q^{81} +2.52647e31i q^{82} +1.28605e31i q^{83} -7.68050e31 q^{84} -7.03143e31 q^{86} +4.66289e31i q^{87} +7.47670e30i q^{88} -1.22503e32 q^{89} -5.33214e32 q^{91} +1.82783e32i q^{92} -3.69782e32i q^{93} -4.62282e32 q^{94} -6.48042e32 q^{96} +2.05513e31i q^{97} +1.50819e33i q^{98} -1.00156e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 129081.i	− 1.39273i	−0.717689	−	0.696364i	$-0.754800\pi$
$2$	− 129081.i	− 1.39273i	0.717689	−	0.696364i	$-0.245200\pi$
$3$	6.82881e7i	0.915892i	0.888980	+	0.457946i	$0.151415\pi$
$3$	6.82881e7i	0.915892i	−0.888980	+	0.457946i	$0.848585\pi$
$4$	−8.07187e9	−0.939690
$5$	0	0
$5$	0	0
$6$	8.81467e12	1.27559
$7$	− 1.39338e14i	− 1.58472i	−0.610054	−	0.792360i	$-0.708852\pi$
$7$	− 1.39338e14i	− 1.58472i	0.610054	−	0.792360i	$-0.291148\pi$
$8$	− 6.68716e13i	− 0.0839957i
$9$	8.95800e14	0.161142
$10$	0	0
$11$	−1.11807e17	−0.733650	−0.366825	−	0.930290i	$-0.619555\pi$
$11$	−1.11807e17	−0.733650	−0.366825	+	0.930290i	$0.619555\pi$
$12$	− 5.51213e17i	− 0.860654i
$13$	− 3.82676e18i	− 1.59502i	−0.603306	−	0.797510i	$-0.706150\pi$
$13$	− 3.82676e18i	− 1.59502i	0.603306	−	0.797510i	$-0.293850\pi$
$14$	−1.79859e19	−2.20708
$15$	0	0
$16$	−7.79687e19	−1.05667
$17$	1.35670e20i	0.676203i	0.941110	+	0.338101i	$0.109785\pi$
$17$	1.35670e20i	0.676203i	−0.941110	+	0.338101i	$0.890215\pi$
$18$	− 1.15630e20i	− 0.224427i
$19$	−1.50898e21	−1.20019	−0.600093	−	0.799930i	$-0.704870\pi$
$19$	−1.50898e21	−1.20019	−0.600093	+	0.799930i	$0.704870\pi$
$20$	0	0
$21$	9.51513e21	1.45143
$22$	1.44321e22i	1.02177i
$23$	− 2.26444e22i	− 0.769931i	−0.922931	−	0.384965i	$-0.874213\pi$
$23$	− 2.26444e22i	− 0.769931i	0.922931	−	0.384965i	$-0.125787\pi$
$24$	4.56653e21	0.0769310
$25$	0	0
$26$	−4.93961e23	−2.22143
$27$	4.40790e23i	1.06348i
$28$	1.12472e24i	1.48914i
$29$	6.82827e23	0.506691	0.253346	−	0.967376i	$-0.418469\pi$
$29$	6.82827e23	0.506691	0.253346	+	0.967376i	$0.418469\pi$
$30$	0	0
$31$	−5.41504e24	−1.33701	−0.668503	−	0.743709i	$-0.733065\pi$
$31$	−5.41504e24	−1.33701	−0.668503	+	0.743709i	$0.733065\pi$
$32$	9.48983e24i	1.38766i
$33$	− 7.63507e24i	− 0.671944i
$34$	1.75124e25	0.941766
$35$	0	0
$36$	−7.23078e24	−0.151424
$37$	− 7.55931e24i	− 0.100729i	−0.998731	−	0.0503644i	$-0.983962\pi$
$37$	− 7.55931e24i	− 0.100729i	0.998731	−	0.0503644i	$-0.0160383\pi$
$38$	1.94780e26i	1.67153i
$39$	2.61322e26	1.46087
$40$	0	0
$41$	−1.95728e26	−0.479423	−0.239711	−	0.970844i	$-0.577053\pi$
$41$	−1.95728e26	−0.479423	−0.239711	+	0.970844i	$0.577053\pi$
$42$	− 1.22822e27i	− 2.02145i
$43$	− 5.44732e26i	− 0.608069i	−0.952661	−	0.304035i	$-0.901666\pi$
$43$	− 5.44732e26i	− 0.608069i	0.952661	−	0.304035i	$-0.0983339\pi$
$44$	9.02490e26	0.689403
$45$	0	0
$46$	−2.92295e27	−1.07230
$47$	− 3.58134e27i	− 0.921363i	−0.887565	−	0.460682i	$-0.847605\pi$
$47$	− 3.58134e27i	− 0.921363i	0.887565	−	0.460682i	$-0.152395\pi$
$48$	− 5.32433e27i	− 0.967798i
$49$	−1.16841e28	−1.51134
$50$	0	0
$51$	−9.26465e27	−0.619329
$52$	3.08891e28i	1.49882i
$53$	− 4.28944e28i	− 1.52002i	−0.649912	−	0.760010i	$-0.725194\pi$
$53$	− 4.28944e28i	− 1.52002i	0.649912	−	0.760010i	$-0.274806\pi$
$54$	5.68974e28	1.48114
$55$	0	0
$56$	−9.31777e27	−0.133110
$57$	− 1.03045e29i	− 1.09924i
$58$	− 8.81397e28i	− 0.705683i
$59$	2.15590e28	0.130188	0.0650940	−	0.997879i	$-0.479265\pi$
$59$	2.15590e28	0.130188	0.0650940	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	5.24247e29	1.82639	0.913196	−	0.407521i	$-0.133607\pi$
$61$	5.24247e29	1.82639	0.913196	+	0.407521i	$0.133607\pi$
$62$	6.98976e29i	1.86209i
$63$	− 1.24819e29i	− 0.255365i
$64$	5.55207e29	0.875962
$65$	0	0
$66$	−9.85539e29	−0.935834
$67$	− 1.47500e30i	− 1.09284i	−0.837510	−	0.546422i	$-0.815989\pi$
$67$	− 1.47500e30i	− 1.09284i	0.837510	−	0.546422i	$-0.184011\pi$
$68$	− 1.09511e30i	− 0.635421i
$69$	1.54634e30	0.705173
$70$	0	0
$71$	−1.24706e30	−0.354914	−0.177457	−	0.984129i	$-0.556787\pi$
$71$	−1.24706e30	−0.354914	−0.177457	+	0.984129i	$0.556787\pi$
$72$	− 5.99036e28i	− 0.0135353i
$73$	9.14380e30i	1.64551i	0.568398	+	0.822753i	$0.307563\pi$
$73$	9.14380e30i	1.64551i	−0.568398	+	0.822753i	$0.692437\pi$
$74$	−9.75760e29	−0.140288
$75$	0	0
$76$	1.21803e31	1.12780
$77$	1.55789e31i	1.16263i
$78$	− 3.37316e31i	− 2.03459i
$79$	2.52252e31	1.23307	0.616536	−	0.787327i	$-0.288536\pi$
$79$	2.52252e31	1.23307	0.616536	+	0.787327i	$0.288536\pi$
$80$	0	0
$81$	−2.51209e31	−0.812891
$82$	2.52647e31i	0.667706i
$83$	1.28605e31i	0.278273i	0.990273	+	0.139136i	$0.0444327\pi$
$83$	1.28605e31i	0.278273i	−0.990273	+	0.139136i	$0.955567\pi$
$84$	−7.68050e31	−1.36390
$85$	0	0
$86$	−7.03143e31	−0.846875
$87$	4.66289e31i	0.464074i
$88$	7.47670e30i	0.0616234i
$89$	−1.22503e32	−0.837935	−0.418967	−	0.908001i	$-0.637608\pi$
$89$	−1.22503e32	−0.837935	−0.418967	+	0.908001i	$0.637608\pi$
$90$	0	0
$91$	−5.33214e32	−2.52766
$92$	1.82783e32i	0.723496i
$93$	− 3.69782e32i	− 1.22455i
$94$	−4.62282e32	−1.28321
$95$	0	0
$96$	−6.48042e32	−1.27095
$97$	2.05513e31i	0.0339707i	0.999856	+	0.0169854i	$0.00540687\pi$
$97$	2.05513e31i	0.0339707i	−0.999856	+	0.0169854i	$0.994593\pi$
$98$	1.50819e33i	2.10488i
$99$	−1.00156e32	−0.118222
$100$	0	0
$101$	4.29097e32	0.364127	0.182064	−	0.983287i	$-0.441722\pi$
$101$	4.29097e32	0.364127	0.182064	+	0.983287i	$0.441722\pi$
$102$	1.19589e33i	0.862556i
$103$	1.12430e33i	0.690346i	0.938539	+	0.345173i	$0.112180\pi$
$103$	1.12430e33i	0.690346i	−0.938539	+	0.345173i	$0.887820\pi$
$104$	−2.55902e32	−0.133975
$105$	0	0
$106$	−5.53684e33	−2.11697
$107$	6.03479e33i	1.97619i	0.153831	+	0.988097i	$0.450839\pi$
$107$	6.03479e33i	1.97619i	−0.153831	+	0.988097i	$0.549161\pi$
$108$	− 3.55800e33i	− 0.999342i
$109$	1.99935e32	0.0482337	0.0241169	−	0.999709i	$-0.492323\pi$
$109$	1.99935e32	0.0482337	0.0241169	+	0.999709i	$0.492323\pi$
$110$	0	0
$111$	5.16211e32	0.0922567
$112$	1.08640e34i	1.67453i
$113$	− 9.03195e33i	− 1.20223i	−0.799163	−	0.601114i	$-0.794724\pi$
$113$	− 9.03195e33i	− 1.20223i	0.799163	−	0.601114i	$-0.205276\pi$
$114$	−1.33011e34	−1.53094
$115$	0	0
$116$	−5.51169e33	−0.476133
$117$	− 3.42801e33i	− 0.257025i
$118$	− 2.78285e33i	− 0.181316i
$119$	1.89040e34	1.07159
$120$	0	0
$121$	−1.07244e34	−0.461758
$122$	− 6.76702e34i	− 2.54367i
$123$	− 1.33659e34i	− 0.439100i
$124$	4.37095e34	1.25637
$125$	0	0
$126$	−1.61117e34	−0.355654
$127$	7.84484e34i	1.51993i	0.649966	+	0.759963i	$0.274783\pi$
$127$	7.84484e34i	1.51993i	−0.649966	+	0.759963i	$0.725217\pi$
$128$	9.85056e33i	0.167686i
$129$	3.71987e34	0.556926
$130$	0	0
$131$	1.29629e35	1.50566	0.752829	−	0.658216i	$-0.228689\pi$
$131$	1.29629e35	1.50566	0.752829	+	0.658216i	$0.228689\pi$
$132$	6.16293e34i	0.631419i
$133$	2.10258e35i	1.90196i
$134$	−1.90394e35	−1.52203
$135$	0	0
$136$	9.07248e33	0.0567981
$137$	− 3.35566e35i	− 1.86161i	−0.365518	−	0.930804i	$-0.619108\pi$
$137$	− 3.35566e35i	− 1.86161i	0.365518	−	0.930804i	$-0.380892\pi$
$138$	− 1.99603e35i	− 0.982114i
$139$	1.22685e35	0.535855	0.267927	−	0.963439i	$-0.413661\pi$
$139$	1.22685e35	0.535855	0.267927	+	0.963439i	$0.413661\pi$
$140$	0	0
$141$	2.44563e35	0.843869
$142$	1.60971e35i	0.494299i
$143$	4.27858e35i	1.17019i
$144$	−6.98443e34	−0.170275
$145$	0	0
$146$	1.18029e36	2.29174
$147$	− 7.97887e35i	− 1.38422i
$148$	6.10178e34i	0.0946538i
$149$	−6.68791e34	−0.0928361	−0.0464181	−	0.998922i	$-0.514781\pi$
$149$	−6.68791e34	−0.0928361	−0.0464181	+	0.998922i	$0.514781\pi$
$150$	0	0
$151$	−6.76462e34	−0.0753570	−0.0376785	−	0.999290i	$-0.511996\pi$
$151$	−6.76462e34	−0.0753570	−0.0376785	+	0.999290i	$0.511996\pi$
$152$	1.00908e35i	0.100810i
$153$	1.21533e35i	0.108965i
$154$	2.01094e36	1.61923
$155$	0	0
$156$	−2.10936e36	−1.37276
$157$	7.84957e35i	0.459729i	0.973223	+	0.229864i	$0.0738282\pi$
$157$	7.84957e35i	0.459729i	−0.973223	+	0.229864i	$0.926172\pi$
$158$	− 3.25609e36i	− 1.71733i
$159$	2.92918e36	1.39217
$160$	0	0
$161$	−3.15523e36	−1.22012
$162$	3.24262e36i	1.13214i
$163$	4.51268e36i	1.42344i	0.702464	+	0.711720i	$0.252083\pi$
$163$	4.51268e36i	1.42344i	−0.702464	+	0.711720i	$0.747917\pi$
$164$	1.57989e36	0.450509
$165$	0	0
$166$	1.66005e36	0.387558
$167$	7.01398e36i	1.48300i	0.670950	+	0.741502i	$0.265886\pi$
$167$	7.01398e36i	1.48300i	−0.670950	+	0.741502i	$0.734114\pi$
$168$	− 6.36293e35i	− 0.121914i
$169$	−8.88797e36	−1.54409
$170$	0	0
$171$	−1.35174e36	−0.193401
$172$	4.39701e36i	0.571397i
$173$	− 1.06789e37i	− 1.26115i	−0.776129	−	0.630574i	$-0.782819\pi$
$173$	− 1.06789e37i	− 1.26115i	0.776129	−	0.630574i	$-0.217181\pi$
$174$	6.01889e36	0.646329
$175$	0	0
$176$	8.71743e36	0.775228
$177$	1.47222e36i	0.119238i
$178$	1.58127e37i	1.16702i
$179$	−1.01966e36	−0.0686086	−0.0343043	−	0.999411i	$-0.510922\pi$
$179$	−1.01966e36	−0.0686086	−0.0343043	+	0.999411i	$0.510922\pi$
$180$	0	0
$181$	−3.22152e37	−1.80453	−0.902266	−	0.431180i	$-0.858097\pi$
$181$	−3.22152e37	−1.80453	−0.902266	+	0.431180i	$0.858097\pi$
$182$	6.88276e37i	3.52034i
$183$	3.57998e37i	1.67278i
$184$	−1.51427e36	−0.0646709
$185$	0	0
$186$	−4.77318e37	−1.70547
$187$	− 1.51688e37i	− 0.496096i
$188$	2.89081e37i	0.865796i
$189$	6.14189e37	1.68532
$190$	0	0
$191$	−2.89210e37	−0.667057	−0.333529	−	0.942740i	$-0.608239\pi$
$191$	−2.89210e37	−0.667057	−0.333529	+	0.942740i	$0.608239\pi$
$192$	3.79140e37i	0.802286i
$193$	− 4.75455e37i	− 0.923451i	−0.887023	−	0.461726i	$-0.847230\pi$
$193$	− 4.75455e37i	− 0.923451i	0.887023	−	0.461726i	$-0.152770\pi$
$194$	2.65277e36	0.0473120
$195$	0	0
$196$	9.43128e37	1.42019
$197$	2.87965e37i	0.398701i	0.979928	+	0.199350i	$0.0638832\pi$
$197$	2.87965e37i	0.398701i	−0.979928	+	0.199350i	$0.936117\pi$
$198$	1.29283e37i	0.164651i
$199$	1.09912e38	1.28815	0.644076	−	0.764961i	$-0.277242\pi$
$199$	1.09912e38	1.28815	0.644076	+	0.764961i	$0.277242\pi$
$200$	0	0
$201$	1.00725e38	1.00093
$202$	− 5.53881e37i	− 0.507130i
$203$	− 9.51438e37i	− 0.802964i
$204$	7.47831e37	0.581977
$205$	0	0
$206$	1.45125e38	0.961464
$207$	− 2.02848e37i	− 0.124068i
$208$	2.98368e38i	1.68541i
$209$	1.68714e38	0.880516
$210$	0	0
$211$	9.20360e37	0.410485	0.205242	−	0.978711i	$-0.434202\pi$
$211$	9.20360e37	0.410485	0.205242	+	0.978711i	$0.434202\pi$
$212$	3.46238e38i	1.42835i
$213$	− 8.51591e37i	− 0.325063i
$214$	7.78974e38	2.75230
$215$	0	0
$216$	2.94763e37	0.0893278
$217$	7.54521e38i	2.11878i
$218$	− 2.58077e37i	− 0.0671765i
$219$	−6.24413e38	−1.50711
$220$	0	0
$221$	5.19177e38	1.07856
$222$	− 6.66328e37i	− 0.128488i
$223$	8.19419e38i	1.46715i	0.679606	+	0.733577i	$0.262151\pi$
$223$	8.19419e38i	1.46715i	−0.679606	+	0.733577i	$0.737849\pi$
$224$	1.32229e39	2.19905
$225$	0	0
$226$	−1.16585e39	−1.67438
$227$	− 3.68201e38i	− 0.491652i	−0.969314	−	0.245826i	$-0.920941\pi$
$227$	− 3.68201e38i	− 0.491652i	0.969314	−	0.245826i	$-0.0790592\pi$
$228$	8.31768e38i	1.03294i
$229$	−5.37397e38	−0.620883	−0.310442	−	0.950592i	$-0.600477\pi$
$229$	−5.37397e38	−0.620883	−0.310442	+	0.950592i	$0.600477\pi$
$230$	0	0
$231$	−1.06386e39	−1.06484
$232$	− 4.56617e37i	− 0.0425599i
$233$	− 5.60193e38i	− 0.486368i	−0.969980	−	0.243184i	$-0.921808\pi$
$233$	− 5.60193e38i	− 0.486368i	0.969980	−	0.243184i	$-0.0781918\pi$
$234$	−4.42490e38	−0.357966
$235$	0	0
$236$	−1.74022e38	−0.122336
$237$	1.72258e39i	1.12936i
$238$	− 2.44014e39i	− 1.49244i
$239$	−4.65466e38	−0.265658	−0.132829	−	0.991139i	$-0.542406\pi$
$239$	−4.65466e38	−0.265658	−0.132829	+	0.991139i	$0.542406\pi$
$240$	0	0
$241$	−8.56759e38	−0.426165	−0.213082	−	0.977034i	$-0.568350\pi$
$241$	−8.56759e38	−0.426165	−0.213082	+	0.977034i	$0.568350\pi$
$242$	1.38431e39i	0.643103i
$243$	7.34921e38i	0.318961i
$244$	−4.23166e39	−1.71624
$245$	0	0
$246$	−1.72528e39	−0.611546
$247$	5.77450e39i	1.91432i
$248$	3.62112e38i	0.112303i
$249$	−8.78222e38	−0.254868
$250$	0	0
$251$	−5.15351e39	−1.31065	−0.655325	−	0.755347i	$-0.727468\pi$
$251$	−5.15351e39	−1.31065	−0.655325	+	0.755347i	$0.727468\pi$
$252$	1.00752e39i	0.239964i
$253$	2.53180e39i	0.564859i
$254$	1.01262e40	2.11684
$255$	0	0
$256$	6.04071e39	1.10950
$257$	− 5.66916e39i	− 0.976388i	−0.872735	−	0.488194i	$-0.837656\pi$
$257$	− 5.66916e39i	− 0.976388i	0.872735	−	0.488194i	$-0.162344\pi$
$258$	− 4.80163e39i	− 0.775646i
$259$	−1.05330e39	−0.159627
$260$	0	0
$261$	6.11676e38	0.0816494
$262$	− 1.67326e40i	− 2.09697i
$263$	1.47291e39i	0.173343i	0.996237	+	0.0866715i	$0.0276231\pi$
$263$	1.47291e39i	0.173343i	−0.996237	+	0.0866715i	$0.972377\pi$
$264$	−5.10569e38	−0.0564404
$265$	0	0
$266$	2.71403e40	2.64891
$267$	− 8.36547e39i	− 0.767458i
$268$	1.19060e40i	1.02693i
$269$	2.15538e39	0.174828	0.0874139	−	0.996172i	$-0.472140\pi$
$269$	2.15538e39	0.174828	0.0874139	+	0.996172i	$0.472140\pi$
$270$	0	0
$271$	−6.55007e39	−0.470168	−0.235084	−	0.971975i	$-0.575536\pi$
$271$	−6.55007e39	−0.470168	−0.235084	+	0.971975i	$0.575536\pi$
$272$	− 1.05780e40i	− 0.714525i
$273$	− 3.64121e40i	− 2.31506i
$274$	−4.33150e40	−2.59271
$275$	0	0
$276$	−1.24819e40	−0.662644
$277$	− 2.17785e40i	− 1.08921i	−0.838693	−	0.544604i	$-0.816680\pi$
$277$	− 2.17785e40i	− 1.08921i	0.838693	−	0.544604i	$-0.183320\pi$
$278$	− 1.58362e40i	− 0.746299i
$279$	−4.85079e39	−0.215448
$280$	0	0
$281$	4.97063e38	0.0196226	0.00981131	−	0.999952i	$-0.496877\pi$
$281$	4.97063e38	0.0196226	0.00981131	+	0.999952i	$0.496877\pi$
$282$	− 3.15683e40i	− 1.17528i
$283$	2.67595e40i	0.939728i	0.882739	+	0.469864i	$0.155697\pi$
$283$	2.67595e40i	0.939728i	−0.882739	+	0.469864i	$0.844303\pi$
$284$	1.00661e40	0.333509
$285$	0	0
$286$	5.52281e40	1.62975
$287$	2.72724e40i	0.759751i
$288$	8.50098e39i	0.223611i
$289$	2.18481e40	0.542750
$290$	0	0
$291$	−1.40341e39	−0.0311135
$292$	− 7.38076e40i	− 1.54627i
$293$	− 1.28487e40i	− 0.254415i	−0.991876	−	0.127207i	$-0.959399\pi$
$293$	− 1.28487e40i	− 0.254415i	0.991876	−	0.127207i	$-0.0406013\pi$
$294$	−1.02992e41	−1.92784
$295$	0	0
$296$	−5.05503e38	−0.00846079
$297$	− 4.92833e40i	− 0.780222i
$298$	8.63280e39i	0.129295i
$299$	−8.66547e40	−1.22805
$300$	0	0
$301$	−7.59019e40	−0.963619
$302$	8.73181e39i	0.104952i
$303$	2.93022e40i	0.333501i
$304$	1.17653e41	1.26820
$305$	0	0
$306$	1.56876e40	0.151758
$307$	5.95612e40i	0.545984i	0.962016	+	0.272992i	$0.0880133\pi$
$307$	5.95612e40i	0.545984i	−0.962016	+	0.272992i	$0.911987\pi$
$308$	− 1.25751e41i	− 1.09251i
$309$	−7.67761e40	−0.632283
$310$	0	0
$311$	−3.80156e40	−0.281459	−0.140730	−	0.990048i	$-0.544945\pi$
$311$	−3.80156e40	−0.281459	−0.140730	+	0.990048i	$0.544945\pi$
$312$	− 1.74750e40i	− 0.122706i
$313$	2.52982e41i	1.68503i	0.538673	+	0.842515i	$0.318926\pi$
$313$	2.52982e41i	1.68503i	−0.538673	+	0.842515i	$0.681074\pi$
$314$	1.01323e41	0.640277
$315$	0	0
$316$	−2.03615e41	−1.15870
$317$	2.56047e41i	1.38306i	0.722348	+	0.691530i	$0.243063\pi$
$317$	2.56047e41i	1.38306i	−0.722348	+	0.691530i	$0.756937\pi$
$318$	− 3.78100e41i	− 1.93892i
$319$	−7.63446e40	−0.371734
$320$	0	0
$321$	−4.12104e41	−1.80998
$322$	4.07279e41i	1.69930i
$323$	− 2.04723e41i	− 0.811569i
$324$	2.02773e41	0.763865
$325$	0	0
$326$	5.82499e41	1.98246
$327$	1.36532e40i	0.0441769i
$328$	1.30886e40i	0.0402695i
$329$	−4.99017e41	−1.46010
$330$	0	0
$331$	3.97632e41	1.05274	0.526368	−	0.850257i	$-0.323553\pi$
$331$	3.97632e41	1.05274	0.526368	+	0.850257i	$0.323553\pi$
$332$	− 1.03809e41i	− 0.261490i
$333$	− 6.77163e39i	− 0.0162317i
$334$	9.05368e41	2.06542
$335$	0	0
$336$	−7.41883e41	−1.53369
$337$	− 3.16941e41i	− 0.623857i	−0.950106	−	0.311928i	$-0.899025\pi$
$337$	− 3.16941e41i	− 0.623857i	0.950106	−	0.311928i	$-0.100975\pi$
$338$	1.14726e42i	2.15049i
$339$	6.16774e41	1.10111
$340$	0	0
$341$	6.05438e41	0.980894
$342$	1.74484e41i	0.269354i
$343$	5.50823e41i	0.810324i
$344$	−3.64271e40	−0.0510752
$345$	0	0
$346$	−1.37844e42	−1.75644
$347$	3.65901e41i	0.444557i	0.974983	+	0.222279i	$0.0713494\pi$
$347$	3.65901e41i	0.444557i	−0.974983	+	0.222279i	$0.928651\pi$
$348$	− 3.76383e41i	− 0.436086i
$349$	−1.01851e42	−1.12550	−0.562752	−	0.826626i	$-0.690257\pi$
$349$	−1.01851e42	−1.12550	−0.562752	+	0.826626i	$0.690257\pi$
$350$	0	0
$351$	1.68680e42	1.69627
$352$	− 1.06103e42i	− 1.01806i
$353$	1.09904e42i	1.00631i	0.864197	+	0.503153i	$0.167827\pi$
$353$	1.09904e42i	1.00631i	−0.864197	+	0.503153i	$0.832173\pi$
$354$	1.90036e41	0.166066
$355$	0	0
$356$	9.88826e41	0.787399
$357$	1.29092e42i	0.981462i
$358$	1.31618e41i	0.0955531i
$359$	1.88943e42	1.31000	0.655002	−	0.755627i	$-0.272668\pi$
$359$	1.88943e42	1.31000	0.655002	+	0.755627i	$0.272668\pi$
$360$	0	0
$361$	6.96243e41	0.440445
$362$	4.15836e42i	2.51322i
$363$	− 7.32349e41i	− 0.422921i
$364$	4.30403e42	2.37522
$365$	0	0
$366$	4.62106e42	2.32972
$367$	− 3.72944e42i	− 1.79744i	−0.438527	−	0.898718i	$-0.644500\pi$
$367$	− 3.72944e42i	− 1.79744i	0.438527	−	0.898718i	$-0.355500\pi$
$368$	1.76555e42i	0.813565i
$369$	−1.75333e41	−0.0772553
$370$	0	0
$371$	−5.97683e42	−2.40880
$372$	2.98484e42i	1.15070i
$373$	− 2.08286e42i	− 0.768181i	−0.923295	−	0.384091i	$-0.874515\pi$
$373$	− 2.08286e42i	− 0.768181i	0.923295	−	0.384091i	$-0.125485\pi$
$374$	−1.95800e42	−0.690926
$375$	0	0
$376$	−2.39490e41	−0.0773906
$377$	− 2.61301e42i	− 0.808183i
$378$	− 7.92799e42i	− 2.34719i
$379$	−1.44890e42	−0.410668	−0.205334	−	0.978692i	$-0.565828\pi$
$379$	−1.44890e42	−0.410668	−0.205334	+	0.978692i	$0.565828\pi$
$380$	0	0
$381$	−5.35709e42	−1.39209
$382$	3.73314e42i	0.929029i
$383$	3.31373e42i	0.789837i	0.918716	+	0.394919i	$0.129227\pi$
$383$	3.31373e42i	0.789837i	−0.918716	+	0.394919i	$0.870773\pi$
$384$	−6.72676e41	−0.153582
$385$	0	0
$386$	−6.13721e42	−1.28612
$387$	− 4.87970e41i	− 0.0979857i
$388$	− 1.65887e41i	− 0.0319219i
$389$	−3.52845e42	−0.650752	−0.325376	−	0.945585i	$-0.605491\pi$
$389$	−3.52845e42	−0.650752	−0.325376	+	0.945585i	$0.605491\pi$
$390$	0	0
$391$	3.07217e42	0.520629
$392$	7.81337e41i	0.126946i
$393$	8.85213e42i	1.37902i
$394$	3.71707e42	0.555282
$395$	0	0
$396$	8.08450e41	0.111092
$397$	2.11298e42i	0.278517i	0.990256	+	0.139258i	$0.0444719\pi$
$397$	2.11298e42i	0.278517i	−0.990256	+	0.139258i	$0.955528\pi$
$398$	− 1.41874e43i	− 1.79405i
$399$	−1.43581e43	−1.74199
$400$	0	0
$401$	−3.95709e42	−0.442073	−0.221037	−	0.975266i	$-0.570944\pi$
$401$	−3.95709e42	−0.442073	−0.221037	+	0.975266i	$0.570944\pi$
$402$	− 1.30016e43i	− 1.39402i
$403$	2.07221e43i	2.13255i
$404$	−3.46362e42	−0.342167
$405$	0	0
$406$	−1.22812e43	−1.11831
$407$	8.45182e41i	0.0738996i
$408$	6.19542e41i	0.0520209i
$409$	−4.44989e42	−0.358851	−0.179426	−	0.983772i	$-0.557424\pi$
$409$	−4.44989e42	−0.358851	−0.179426	+	0.983772i	$0.557424\pi$
$410$	0	0
$411$	2.29151e43	1.70503
$412$	− 9.07519e42i	− 0.648711i
$413$	− 3.00399e42i	− 0.206311i
$414$	−2.61838e42	−0.172793
$415$	0	0
$416$	3.63153e43	2.21335
$417$	8.37792e42i	0.490785i
$418$	− 2.17777e43i	− 1.22632i
$419$	−2.01206e43	−1.08920	−0.544601	−	0.838695i	$-0.683319\pi$
$419$	−2.01206e43	−1.08920	−0.544601	+	0.838695i	$0.683319\pi$
$420$	0	0
$421$	−1.46744e43	−0.734354	−0.367177	−	0.930151i	$-0.619676\pi$
$421$	−1.46744e43	−0.734354	−0.367177	+	0.930151i	$0.619676\pi$
$422$	− 1.18801e43i	− 0.571694i
$423$	− 3.20816e42i	− 0.148471i
$424$	−2.86842e42	−0.127675
$425$	0	0
$426$	−1.09924e43	−0.452724
$427$	− 7.30476e43i	− 2.89432i
$428$	− 4.87120e43i	− 1.85701i
$429$	−2.92176e43	−1.07176
$430$	0	0
$431$	9.38421e42	0.318803	0.159402	−	0.987214i	$-0.449044\pi$
$431$	9.38421e42	0.318803	0.159402	+	0.987214i	$0.449044\pi$
$432$	− 3.43678e43i	− 1.12375i
$433$	− 3.99047e42i	− 0.125595i	−0.998026	−	0.0627976i	$-0.979998\pi$
$433$	− 3.99047e42i	− 0.125595i	0.998026	−	0.0627976i	$-0.0200023\pi$
$434$	9.73941e43	2.95088
$435$	0	0
$436$	−1.61385e42	−0.0453248
$437$	3.41699e43i	0.924060i
$438$	8.05996e43i	2.09899i
$439$	−9.80249e42	−0.245851	−0.122925	−	0.992416i	$-0.539228\pi$
$439$	−9.80249e42	−0.245851	−0.122925	+	0.992416i	$0.539228\pi$
$440$	0	0
$441$	−1.04666e43	−0.243540
$442$	− 6.70157e43i	− 1.50214i
$443$	2.57496e42i	0.0556044i	0.999613	+	0.0278022i	$0.00885086\pi$
$443$	2.57496e42i	0.0556044i	−0.999613	+	0.0278022i	$0.991149\pi$
$444$	−4.16679e42	−0.0866926
$445$	0	0
$446$	1.05771e44	2.04335
$447$	− 4.56704e42i	− 0.0850278i
$448$	− 7.73615e43i	− 1.38815i
$449$	7.29533e43	1.26177	0.630885	−	0.775876i	$-0.282692\pi$
$449$	7.29533e43	1.26177	0.630885	+	0.775876i	$0.282692\pi$
$450$	0	0
$451$	2.18837e43	0.351728
$452$	7.29048e43i	1.12972i
$453$	− 4.61943e42i	− 0.0690188i
$454$	−4.75276e43	−0.684737
$455$	0	0
$456$	−6.89080e42	−0.0923315
$457$	1.18400e44i	1.53015i	0.643939	+	0.765077i	$0.277299\pi$
$457$	1.18400e44i	1.53015i	−0.643939	+	0.765077i	$0.722701\pi$
$458$	6.93676e43i	0.864721i
$459$	−5.98020e43	−0.719129
$460$	0	0
$461$	−1.64770e44	−1.84423	−0.922113	−	0.386921i	$-0.873539\pi$
$461$	−1.64770e44	−1.84423	−0.922113	+	0.386921i	$0.873539\pi$
$462$	1.37323e44i	1.48303i
$463$	5.84287e43i	0.608892i	0.952530	+	0.304446i	$0.0984713\pi$
$463$	5.84287e43i	0.608892i	−0.952530	+	0.304446i	$0.901529\pi$
$464$	−5.32391e43	−0.535407
$465$	0	0
$466$	−7.23100e43	−0.677378
$467$	9.91255e43i	0.896307i	0.893957	+	0.448154i	$0.147918\pi$
$467$	9.91255e43i	0.896307i	−0.893957	+	0.448154i	$0.852082\pi$
$468$	2.76705e43i	0.241524i
$469$	−2.05524e44	−1.73185
$470$	0	0
$471$	−5.36032e43	−0.421062
$472$	− 1.44169e42i	− 0.0109352i
$473$	6.09047e43i	0.446110i
$474$	2.22352e44	1.57289
$475$	0	0
$476$	−1.52591e44	−1.00696
$477$	− 3.84248e43i	− 0.244939i
$478$	6.00826e43i	0.369989i
$479$	1.45337e44	0.864647	0.432324	−	0.901719i	$-0.357694\pi$
$479$	1.45337e44	0.864647	0.432324	+	0.901719i	$0.357694\pi$
$480$	0	0
$481$	−2.89277e43	−0.160664
$482$	1.10591e44i	0.593531i
$483$	− 2.15465e44i	− 1.11750i
$484$	8.65661e43	0.433910
$485$	0	0
$486$	9.48640e43	0.444225
$487$	3.00271e43i	0.135921i	0.997688	+	0.0679604i	$0.0216492\pi$
$487$	3.00271e43i	0.135921i	−0.997688	+	0.0679604i	$0.978351\pi$
$488$	− 3.50573e43i	− 0.153409i
$489$	−3.08162e44	−1.30372
$490$	0	0
$491$	−2.65183e44	−1.04882	−0.524410	−	0.851466i	$-0.675714\pi$
$491$	−2.65183e44	−1.04882	−0.524410	+	0.851466i	$0.675714\pi$
$492$	1.07888e44i	0.412617i
$493$	9.26391e43i	0.342626i
$494$	7.45376e44	2.66613
$495$	0	0
$496$	4.22203e44	1.41278
$497$	1.73763e44i	0.562439i
$498$	1.13361e44i	0.354961i
$499$	5.34386e44	1.61881	0.809405	−	0.587251i	$-0.199790\pi$
$499$	5.34386e44	1.61881	0.809405	+	0.587251i	$0.199790\pi$
$500$	0	0
$501$	−4.78971e44	−1.35827
$502$	6.65218e44i	1.82538i
$503$	6.08597e44i	1.61606i	0.589140	+	0.808031i	$0.299466\pi$
$503$	6.08597e44i	1.61606i	−0.589140	+	0.808031i	$0.700534\pi$
$504$	−8.34686e42	−0.0214496
$505$	0	0
$506$	3.26806e44	0.786695
$507$	− 6.06942e44i	− 1.41422i
$508$	− 6.33225e44i	− 1.42826i
$509$	−1.32394e44	−0.289084	−0.144542	−	0.989499i	$-0.546171\pi$
$509$	−1.32394e44	−0.289084	−0.144542	+	0.989499i	$0.546171\pi$
$510$	0	0
$511$	1.27408e45	2.60767
$512$	− 6.95122e44i	− 1.37755i
$513$	− 6.65142e44i	− 1.27637i
$514$	−7.31779e44	−1.35984
$515$	0	0
$516$	−3.00263e44	−0.523337
$517$	4.00418e44i	0.675958i
$518$	1.35961e44i	0.222317i
$519$	7.29242e44	1.15508
$520$	0	0
$521$	7.67376e44	1.14074	0.570369	−	0.821389i	$-0.306800\pi$
$521$	7.67376e44	1.14074	0.570369	+	0.821389i	$0.306800\pi$
$522$	− 7.89555e43i	− 0.113715i
$523$	4.46260e44i	0.622745i	0.950288	+	0.311373i	$0.100789\pi$
$523$	4.46260e44i	0.622745i	−0.950288	+	0.311373i	$0.899211\pi$
$524$	−1.04635e45	−1.41485
$525$	0	0
$526$	1.90124e44	0.241420
$527$	− 7.34659e44i	− 0.904087i
$528$	5.95296e44i	0.710025i
$529$	3.52236e44	0.407207
$530$	0	0
$531$	1.93126e43	0.0209788
$532$	− 1.69718e45i	− 1.78725i
$533$	7.49003e44i	0.764689i
$534$	−1.07982e45	−1.06886
$535$	0	0
$536$	−9.86358e43	−0.0917942
$537$	− 6.96303e43i	− 0.0628381i
$538$	− 2.78217e44i	− 0.243487i
$539$	1.30636e45	1.10879
$540$	0	0
$541$	2.76410e44	0.220698	0.110349	−	0.993893i	$-0.464803\pi$
$541$	2.76410e44	0.220698	0.110349	+	0.993893i	$0.464803\pi$
$542$	8.45487e44i	0.654815i
$543$	− 2.19991e45i	− 1.65276i
$544$	−1.28749e45	−0.938341
$545$	0	0
$546$	−4.70010e45	−3.22425
$547$	− 1.10195e45i	− 0.733453i	−0.930329	−	0.366726i	$-0.880479\pi$
$547$	− 1.10195e45i	− 0.733453i	0.930329	−	0.366726i	$-0.119521\pi$
$548$	2.70864e45i	1.74933i
$549$	4.69620e44	0.294309
$550$	0	0
$551$	−1.03037e45	−0.608124
$552$	− 1.03406e44i	− 0.0592315i
$553$	− 3.51484e45i	− 1.95407i
$554$	−2.81118e45	−1.51697
$555$	0	0
$556$	−9.90297e44	−0.503537
$557$	9.98180e44i	0.492718i	0.969179	+	0.246359i	$0.0792342\pi$
$557$	9.98180e44i	0.492718i	−0.969179	+	0.246359i	$0.920766\pi$
$558$	6.26143e44i	0.300061i
$559$	−2.08456e45	−0.969882
$560$	0	0
$561$	1.03585e45	0.454370
$562$	− 6.41612e43i	− 0.0273290i
$563$	− 2.41489e45i	− 0.998870i	−0.866351	−	0.499435i	$-0.833541\pi$
$563$	− 2.41489e45i	− 0.998870i	0.866351	−	0.499435i	$-0.166459\pi$
$564$	−1.97408e45	−0.792975
$565$	0	0
$566$	3.45414e45	1.30878
$567$	3.50030e45i	1.28820i
$568$	8.33927e43i	0.0298113i
$569$	−3.12759e45	−1.08607	−0.543035	−	0.839710i	$-0.682725\pi$
$569$	−3.12759e45	−1.08607	−0.543035	+	0.839710i	$0.682725\pi$
$570$	0	0
$571$	4.44750e44	0.145754	0.0728770	−	0.997341i	$-0.476782\pi$
$571$	4.44750e44	0.145754	0.0728770	+	0.997341i	$0.476782\pi$
$572$	− 3.45361e45i	− 1.09961i
$573$	− 1.97496e45i	− 0.610952i
$574$	3.52033e45	1.05813
$575$	0	0
$576$	4.97354e44	0.141154
$577$	− 2.41991e45i	− 0.667420i	−0.942676	−	0.333710i	$-0.891699\pi$
$577$	− 2.41991e45i	− 0.667420i	0.942676	−	0.333710i	$-0.108301\pi$
$578$	− 2.82017e45i	− 0.755903i
$579$	3.24679e45	0.845781
$580$	0	0
$581$	1.79197e45	0.440985
$582$	1.81153e44i	0.0433326i
$583$	4.79589e45i	1.11516i
$584$	6.11461e44	0.138216
$585$	0	0
$586$	−1.65851e45	−0.354330
$587$	− 5.33169e45i	− 1.10748i	−0.832689	−	0.553741i	$-0.813200\pi$
$587$	− 5.33169e45i	− 1.10748i	0.832689	−	0.553741i	$-0.186800\pi$
$588$	6.44044e45i	1.30074i
$589$	8.17117e45	1.60466
$590$	0	0
$591$	−1.96646e45	−0.365167
$592$	5.89389e44i	0.106437i
$593$	− 4.45568e45i	− 0.782549i	−0.920274	−	0.391274i	$-0.872034\pi$
$593$	− 4.45568e45i	− 0.782549i	0.920274	−	0.391274i	$-0.127966\pi$
$594$	−6.36152e45	−1.08664
$595$	0	0
$596$	5.39840e44	0.0872372
$597$	7.50565e45i	1.17981i
$598$	1.11854e46i	1.71035i
$599$	6.35076e44	0.0944676	0.0472338	−	0.998884i	$-0.484959\pi$
$599$	6.35076e44	0.0944676	0.0472338	+	0.998884i	$0.484959\pi$
$600$	0	0
$601$	5.17167e45	0.728119	0.364059	−	0.931376i	$-0.381390\pi$
$601$	5.17167e45	0.728119	0.364059	+	0.931376i	$0.381390\pi$
$602$	9.79747e45i	1.34206i
$603$	− 1.32131e45i	− 0.176103i
$604$	5.46031e44	0.0708122
$605$	0	0
$606$	3.78235e45	0.464476
$607$	− 8.40877e45i	− 1.00489i	−0.864609	−	0.502446i	$-0.832434\pi$
$607$	− 8.40877e45i	− 1.00489i	0.864609	−	0.502446i	$-0.167566\pi$
$608$	− 1.43199e46i	− 1.66545i
$609$	6.49719e45	0.735428
$610$	0	0
$611$	−1.37049e46	−1.46959
$612$	− 9.81001e44i	− 0.102393i
$613$	− 2.24884e45i	− 0.228486i	−0.993453	−	0.114243i	$-0.963556\pi$
$613$	− 2.24884e45i	− 0.228486i	0.993453	−	0.114243i	$-0.0364443\pi$
$614$	7.68820e45	0.760408
$615$	0	0
$616$	1.04179e45	0.0976558
$617$	− 2.01918e46i	− 1.84277i	−0.388654	−	0.921384i	$-0.627060\pi$
$617$	− 2.01918e46i	− 1.84277i	0.388654	−	0.921384i	$-0.372940\pi$
$618$	9.91031e45i	0.880597i
$619$	6.12733e44	0.0530122	0.0265061	−	0.999649i	$-0.491562\pi$
$619$	6.12733e44	0.0530122	0.0265061	+	0.999649i	$0.491562\pi$
$620$	0	0
$621$	9.98143e45	0.818806
$622$	4.90708e45i	0.391996i
$623$	1.70693e46i	1.32789i
$624$	−2.03749e46	−1.54366
$625$	0	0
$626$	3.26550e46	2.34679
$627$	1.15211e46i	0.806457i
$628$	− 6.33607e45i	− 0.432002i
$629$	1.02557e45	0.0681131
$630$	0	0
$631$	−3.45501e45	−0.217753	−0.108877	−	0.994055i	$-0.534725\pi$
$631$	−3.45501e45	−0.217753	−0.108877	+	0.994055i	$0.534725\pi$
$632$	− 1.68685e45i	− 0.103573i
$633$	6.28496e45i	0.375960i
$634$	3.30507e46	1.92623
$635$	0	0
$636$	−2.36440e46	−1.30821
$637$	4.47124e46i	2.41061i
$638$	9.85461e45i	0.517724i
$639$	−1.11711e45	−0.0571917
$640$	0	0
$641$	−1.11074e44	−0.00540077	−0.00270039	−	0.999996i	$-0.500860\pi$
$641$	−1.11074e44	−0.00540077	−0.00270039	+	0.999996i	$0.500860\pi$
$642$	5.31946e46i	2.52081i
$643$	− 2.41519e46i	− 1.11550i	−0.830009	−	0.557751i	$-0.811665\pi$
$643$	− 2.41519e46i	− 1.11550i	0.830009	−	0.557751i	$-0.188335\pi$
$644$	2.54686e46	1.14654
$645$	0	0
$646$	−2.64258e46	−1.13029
$647$	2.20068e46i	0.917563i	0.888549	+	0.458781i	$0.151714\pi$
$647$	2.20068e46i	0.917563i	−0.888549	+	0.458781i	$0.848286\pi$
$648$	1.67988e45i	0.0682794i
$649$	−2.41044e45	−0.0955123
$650$	0	0
$651$	−5.15248e46	−1.94057
$652$	− 3.64258e46i	− 1.33759i
$653$	− 2.59836e46i	− 0.930319i	−0.885227	−	0.465159i	$-0.845997\pi$
$653$	− 2.59836e46i	− 0.930319i	0.885227	−	0.465159i	$-0.154003\pi$
$654$	1.76236e45	0.0615264
$655$	0	0
$656$	1.52606e46	0.506593
$657$	8.19102e45i	0.265161i
$658$	6.44135e46i	2.03352i
$659$	8.95518e45	0.275718	0.137859	−	0.990452i	$-0.455978\pi$
$659$	8.95518e45	0.275718	0.137859	+	0.990452i	$0.455978\pi$
$660$	0	0
$661$	5.29479e45	0.155069	0.0775345	−	0.996990i	$-0.475295\pi$
$661$	5.29479e45	0.155069	0.0775345	+	0.996990i	$0.475295\pi$
$662$	− 5.13266e46i	− 1.46617i
$663$	3.54536e46i	0.987841i
$664$	8.60006e44	0.0233737
$665$	0	0
$666$	−8.74086e44	−0.0226063
$667$	− 1.54622e46i	− 0.390117i
$668$	− 5.66159e46i	− 1.39356i
$669$	−5.59565e46	−1.34375
$670$	0	0
$671$	−5.86144e46	−1.33993
$672$	9.02970e46i	2.01410i
$673$	− 5.71426e46i	− 1.24369i	−0.783141	−	0.621844i	$-0.786384\pi$
$673$	− 5.71426e46i	− 1.24369i	0.783141	−	0.621844i	$-0.213616\pi$
$674$	−4.09109e46	−0.868862
$675$	0	0
$676$	7.17426e46	1.45096
$677$	− 8.00955e46i	− 1.58087i	−0.612548	−	0.790433i	$-0.709855\pi$
$677$	− 8.00955e46i	− 1.58087i	0.612548	−	0.790433i	$-0.290145\pi$
$678$	− 7.96136e46i	− 1.53355i
$679$	2.86357e45	0.0538341
$680$	0	0
$681$	2.51437e46	0.450300
$682$	− 7.81503e46i	− 1.36612i
$683$	1.21546e45i	0.0207395i	0.999946	+	0.0103697i	$0.00330085\pi$
$683$	1.21546e45i	0.0207395i	−0.999946	+	0.0103697i	$0.996699\pi$
$684$	1.09111e46	0.181737
$685$	0	0
$686$	7.11005e46	1.12856
$687$	− 3.66978e46i	− 0.568662i
$688$	4.24720e46i	0.642530i
$689$	−1.64147e47	−2.42446
$690$	0	0
$691$	−8.60411e46	−1.21149	−0.605743	−	0.795661i	$-0.707124\pi$
$691$	−8.60411e46	−1.21149	−0.605743	+	0.795661i	$0.707124\pi$
$692$	8.61988e46i	1.18509i
$693$	1.39556e46i	0.187349i
$694$	4.72308e46	0.619147
$695$	0	0
$696$	3.11815e45	0.0389803
$697$	− 2.65544e46i	− 0.324187i
$698$	1.31470e47i	1.56752i
$699$	3.82545e46	0.445460
$700$	0	0
$701$	2.40906e46	0.267609	0.133804	−	0.991008i	$-0.457281\pi$
$701$	2.40906e46	0.267609	0.133804	+	0.991008i	$0.457281\pi$
$702$	− 2.17733e47i	− 2.36245i
$703$	1.14068e46i	0.120893i
$704$	−6.20758e46	−0.642649
$705$	0	0
$706$	1.41864e47	1.40151
$707$	− 5.97896e46i	− 0.577039i
$708$	− 1.18836e46i	− 0.112047i
$709$	−1.49721e46	−0.137917	−0.0689586	−	0.997620i	$-0.521968\pi$
$709$	−1.49721e46	−0.137917	−0.0689586	+	0.997620i	$0.521968\pi$
$710$	0	0
$711$	2.25968e46	0.198700
$712$	8.19195e45i	0.0703829i
$713$	1.22620e47i	1.02940i
$714$	1.66633e47	1.36691
$715$	0	0
$716$	8.23053e45	0.0644708
$717$	− 3.17858e46i	− 0.243314i
$718$	− 2.43889e47i	− 1.82448i
$719$	−4.37252e46	−0.319673	−0.159836	−	0.987144i	$-0.551097\pi$
$719$	−4.37252e46	−0.319673	−0.159836	+	0.987144i	$0.551097\pi$
$720$	0	0
$721$	1.56658e47	1.09401
$722$	− 8.98715e46i	− 0.613420i
$723$	− 5.85064e46i	− 0.390321i
$724$	2.60037e47	1.69570
$725$	0	0
$726$	−9.45321e46	−0.589013
$727$	− 1.19298e47i	− 0.726634i	−0.931666	−	0.363317i	$-0.881644\pi$
$727$	− 1.19298e47i	− 0.726634i	0.931666	−	0.363317i	$-0.118356\pi$
$728$	3.56569e46i	0.212313i
$729$	−1.89835e47	−1.10502
$730$	0	0
$731$	7.39038e46	0.411178
$732$	− 2.88972e47i	− 1.57189i
$733$	− 3.02145e47i	− 1.60694i	−0.595343	−	0.803471i	$-0.702984\pi$
$733$	− 3.02145e47i	− 1.60694i	0.595343	−	0.803471i	$-0.297016\pi$
$734$	−4.81398e47	−2.50334
$735$	0	0
$736$	2.14891e47	1.06840
$737$	1.64915e47i	0.801765i
$738$	2.26321e46i	0.107596i
$739$	4.95875e46	0.230536	0.115268	−	0.993334i	$-0.463227\pi$
$739$	4.95875e46	0.230536	0.115268	+	0.993334i	$0.463227\pi$
$740$	0	0
$741$	−3.94329e47	−1.75331
$742$	7.71493e47i	3.35481i
$743$	7.50450e46i	0.319158i	0.987185	+	0.159579i	$0.0510137\pi$
$743$	7.50450e46i	0.319158i	−0.987185	+	0.159579i	$0.948986\pi$
$744$	−2.47280e46	−0.102857
$745$	0	0
$746$	−2.68856e47	−1.06987
$747$	1.15205e46i	0.0448415i
$748$	1.22441e47i	0.466176i
$749$	8.40876e47	3.13171
$750$	0	0
$751$	−2.61189e47	−0.930884	−0.465442	−	0.885078i	$-0.654105\pi$
$751$	−2.61189e47	−0.930884	−0.465442	+	0.885078i	$0.654105\pi$
$752$	2.79232e47i	0.973580i
$753$	− 3.51923e47i	− 1.20041i
$754$	−3.37289e47	−1.12558
$755$	0	0
$756$	−4.95765e47	−1.58368
$757$	− 7.29946e46i	− 0.228144i	−0.993472	−	0.114072i	$-0.963611\pi$
$757$	− 7.29946e46i	− 0.228144i	0.993472	−	0.114072i	$-0.0363894\pi$
$758$	1.87025e47i	0.571948i
$759$	−1.72892e47	−0.517350
$760$	0	0
$761$	−3.25049e47	−0.931327	−0.465663	−	0.884962i	$-0.654184\pi$
$761$	−3.25049e47	−0.931327	−0.465663	+	0.884962i	$0.654184\pi$
$762$	6.91496e47i	1.93880i
$763$	− 2.78585e46i	− 0.0764370i
$764$	2.33447e47	0.626827
$765$	0	0
$766$	4.27739e47	1.10003
$767$	− 8.25012e46i	− 0.207652i
$768$	4.12508e47i	1.01618i
$769$	−4.28447e47	−1.03303	−0.516514	−	0.856279i	$-0.672771\pi$
$769$	−4.28447e47	−1.03303	−0.516514	+	0.856279i	$0.672771\pi$
$770$	0	0
$771$	3.87136e47	0.894266
$772$	3.83781e47i	0.867758i
$773$	8.22105e47i	1.81956i	0.415094	+	0.909779i	$0.363749\pi$
$773$	8.22105e47i	1.81956i	−0.415094	+	0.909779i	$0.636251\pi$
$774$	−6.29875e46	−0.136467
$775$	0	0
$776$	1.37430e45	0.00285340
$777$	− 7.19278e46i	− 0.146201i
$778$	4.55454e47i	0.906320i
$779$	2.95349e47	0.575397
$780$	0	0
$781$	1.39429e47	0.260383
$782$	− 3.96557e47i	− 0.725095i
$783$	3.00983e47i	0.538856i
$784$	9.10996e47	1.59699
$785$	0	0
$786$	1.14264e48	1.92060
$787$	− 9.92861e47i	− 1.63420i	−0.576496	−	0.817100i	$-0.695580\pi$
$787$	− 9.92861e47i	− 1.63420i	0.576496	−	0.817100i	$-0.304420\pi$
$788$	− 2.32442e47i	− 0.374655i
$789$	−1.00582e47	−0.158763
$790$	0	0
$791$	−1.25850e48	−1.90520
$792$	6.69762e45i	0.00993014i
$793$	− 2.00617e48i	− 2.91313i
$794$	2.72744e47	0.387898
$795$	0	0
$796$	−8.87192e47	−1.21046
$797$	1.14954e48i	1.53625i	0.640301	+	0.768124i	$0.278810\pi$
$797$	1.14954e48i	1.53625i	−0.640301	+	0.768124i	$0.721190\pi$
$798$	1.85336e48i	2.42611i
$799$	4.85881e47	0.623028
$800$	0	0
$801$	−1.09738e47	−0.135027
$802$	5.10784e47i	0.615687i
$803$	− 1.02234e48i	− 1.20723i
$804$	−8.13040e47	−0.940561
$805$	0	0
$806$	2.67482e48	2.97006
$807$	1.47187e47i	0.160123i
$808$	− 2.86944e46i	− 0.0305851i
$809$	1.50525e48	1.57202	0.786009	−	0.618215i	$-0.212144\pi$
$809$	1.50525e48	1.57202	0.786009	+	0.618215i	$0.212144\pi$
$810$	0	0
$811$	1.19205e48	1.19522	0.597612	−	0.801786i	$-0.296116\pi$
$811$	1.19205e48	1.19522	0.597612	+	0.801786i	$0.296116\pi$
$812$	7.67989e47i	0.754537i
$813$	− 4.47292e47i	− 0.430623i
$814$	1.09097e47	0.102922
$815$	0	0
$816$	7.22353e47	0.654428
$817$	8.21988e47i	0.729796i
$818$	5.74394e47i	0.499782i
$819$	−4.77653e47	−0.407313
$820$	0	0
$821$	−1.82470e48	−1.49461	−0.747306	−	0.664480i	$-0.768653\pi$
$821$	−1.82470e48	−1.49461	−0.747306	+	0.664480i	$0.768653\pi$
$822$	− 2.95790e48i	− 2.37464i
$823$	− 1.63942e48i	− 1.29001i	−0.764180	−	0.645004i	$-0.776856\pi$
$823$	− 1.63942e48i	− 1.29001i	0.764180	−	0.645004i	$-0.223144\pi$
$824$	7.51836e46	0.0579861
$825$	0	0
$826$	−3.87757e47	−0.287336
$827$	− 1.07814e48i	− 0.783129i	−0.920151	−	0.391565i	$-0.871934\pi$
$827$	− 1.07814e48i	− 0.783129i	0.920151	−	0.391565i	$-0.128066\pi$
$828$	1.63737e47i	0.116586i
$829$	1.12436e48	0.784795	0.392397	−	0.919796i	$-0.371646\pi$
$829$	1.12436e48	0.784795	0.392397	+	0.919796i	$0.371646\pi$
$830$	0	0
$831$	1.48721e48	0.997597
$832$	− 2.12464e48i	− 1.39718i
$833$	− 1.58519e48i	− 1.02197i
$834$	1.08143e48	0.683530
$835$	0	0
$836$	−1.36184e48	−0.827412
$837$	− 2.38689e48i	− 1.42188i
$838$	2.59717e48i	1.51696i
$839$	−2.27412e48	−1.30239	−0.651195	−	0.758911i	$-0.725732\pi$
$839$	−2.27412e48	−1.30239	−0.651195	+	0.758911i	$0.725732\pi$
$840$	0	0
$841$	−1.34982e48	−0.743264
$842$	1.89418e48i	1.02275i
$843$	3.39435e46i	0.0179722i
$844$	−7.42903e47	−0.385729
$845$	0	0
$846$	−4.14112e47	−0.206779
$847$	1.49432e48i	0.731757i
$848$	3.34442e48i	1.60616i
$849$	−1.82736e48	−0.860689
$850$	0	0
$851$	−1.71176e47	−0.0775542
$852$	6.87393e47i	0.305458i
$853$	− 1.39001e48i	− 0.605840i	−0.953016	−	0.302920i	$-0.902038\pi$
$853$	− 1.39001e48i	− 0.605840i	0.953016	−	0.302920i	$-0.0979615\pi$
$854$	−9.42904e48	−4.03100
$855$	0	0
$856$	4.03556e47	0.165992
$857$	7.18028e47i	0.289706i	0.989453	+	0.144853i	$0.0462710\pi$
$857$	7.18028e47i	0.289706i	−0.989453	+	0.144853i	$0.953729\pi$
$858$	3.77142e48i	1.49267i
$859$	4.63630e48	1.80005	0.900025	−	0.435838i	$-0.143548\pi$
$859$	4.63630e48	1.80005	0.900025	+	0.435838i	$0.143548\pi$
$860$	0	0
$861$	−1.86238e48	−0.695850
$862$	− 1.21132e48i	− 0.444006i
$863$	− 4.88949e48i	− 1.75827i	−0.476572	−	0.879135i	$-0.658121\pi$
$863$	− 4.88949e48i	− 1.75827i	0.476572	−	0.879135i	$-0.341879\pi$
$864$	−4.18302e48	−1.47575
$865$	0	0
$866$	−5.15092e47	−0.174920
$867$	1.49197e48i	0.497100i
$868$	− 6.09040e48i	− 1.99100i
$869$	−2.82035e48	−0.904642
$870$	0	0
$871$	−5.64448e48	−1.74311
$872$	− 1.33700e46i	− 0.00405143i
$873$	1.84098e46i	0.00547412i
$874$	4.41067e48	1.28696
$875$	0	0
$876$	5.04018e48	1.41621
$877$	− 7.15117e46i	− 0.0197189i	−0.999951	−	0.00985947i	$-0.996862\pi$
$877$	− 7.15117e46i	− 0.0197189i	0.999951	−	0.00985947i	$-0.00313842\pi$
$878$	1.26531e48i	0.342403i
$879$	8.77410e47	0.233016
$880$	0	0
$881$	−1.25763e48	−0.321698	−0.160849	−	0.986979i	$-0.551423\pi$
$881$	−1.25763e48	−0.321698	−0.160849	+	0.986979i	$0.551423\pi$
$882$	1.35104e48i	0.339185i
$883$	6.34796e47i	0.156417i	0.996937	+	0.0782083i	$0.0249199\pi$
$883$	6.34796e47i	0.156417i	−0.996937	+	0.0782083i	$0.975080\pi$
$884$	−4.19073e48	−1.01351
$885$	0	0
$886$	3.32378e47	0.0774418
$887$	− 5.08980e47i	− 0.116402i	−0.998305	−	0.0582011i	$-0.981464\pi$
$887$	− 5.08980e47i	− 0.116402i	0.998305	−	0.0582011i	$-0.0185365\pi$
$888$	− 3.45198e46i	− 0.00774916i
$889$	1.09309e49	2.40866
$890$	0	0
$891$	2.80869e48	0.596377
$892$	− 6.61425e48i	− 1.37867i
$893$	5.40416e48i	1.10581i
$894$	−5.89517e47	−0.118421
$895$	0	0
$896$	1.37256e48	0.265735
$897$	− 5.91748e48i	− 1.12476i
$898$	− 9.41686e48i	− 1.75730i
$899$	−3.69753e48	−0.677450
$900$	0	0
$901$	5.81949e48	1.02784
$902$	− 2.82476e48i	− 0.489862i
$903$	− 5.18319e48i	− 0.882571i
$904$	−6.03981e47	−0.100982
$905$	0	0
$906$	−5.96278e47	−0.0961244
$907$	4.07509e47i	0.0645085i	0.999480	+	0.0322543i	$0.0102686\pi$
$907$	4.07509e47i	0.0645085i	−0.999480	+	0.0322543i	$0.989731\pi$
$908$	2.97207e48i	0.462001i
$909$	3.84385e47	0.0586763
$910$	0	0
$911$	−5.53521e48	−0.814855	−0.407428	−	0.913237i	$-0.633574\pi$
$911$	−5.53521e48	−0.814855	−0.407428	+	0.913237i	$0.633574\pi$
$912$	8.03430e48i	1.16154i
$913$	− 1.43790e48i	− 0.204155i
$914$	1.52832e49	2.13109
$915$	0	0
$916$	4.33780e48	0.583438
$917$	− 1.80623e49i	− 2.38605i
$918$	7.71928e48i	1.00155i
$919$	−5.10117e48	−0.650075	−0.325038	−	0.945701i	$-0.605377\pi$
$919$	−5.10117e48	−0.650075	−0.325038	+	0.945701i	$0.605377\pi$
$920$	0	0
$921$	−4.06732e48	−0.500063
$922$	2.12687e49i	2.56850i
$923$	4.77219e48i	0.566095i
$924$	8.58731e48	1.00062
$925$	0	0
$926$	7.54202e48	0.848021
$927$	1.00715e48i	0.111244i
$928$	6.47990e48i	0.703116i
$929$	−4.04144e48	−0.430801	−0.215401	−	0.976526i	$-0.569106\pi$
$929$	−4.04144e48	−0.430801	−0.215401	+	0.976526i	$0.569106\pi$
$930$	0	0
$931$	1.76311e49	1.81388
$932$	4.52180e48i	0.457035i
$933$	− 2.59601e48i	− 0.257786i
$934$	1.27952e49	1.24831
$935$	0	0
$936$	−2.29237e47	−0.0215890
$937$	4.94756e48i	0.457812i	0.973448	+	0.228906i	$0.0735149\pi$
$937$	4.94756e48i	0.457812i	−0.973448	+	0.228906i	$0.926485\pi$
$938$	2.65292e49i	2.41200i
$939$	−1.72756e49	−1.54331
$940$	0	0
$941$	−1.04427e49	−0.900712	−0.450356	−	0.892849i	$-0.648703\pi$
$941$	−1.04427e49	−0.900712	−0.450356	+	0.892849i	$0.648703\pi$
$942$	6.91913e48i	0.586424i
$943$	4.43214e48i	0.369122i
$944$	−1.68093e48	−0.137566
$945$	0	0
$946$	7.86161e48	0.621309
$947$	1.15016e49i	0.893271i	0.894716	+	0.446636i	$0.147378\pi$
$947$	1.15016e49i	0.893271i	−0.894716	+	0.446636i	$0.852622\pi$
$948$	− 1.39045e49i	− 1.06125i
$949$	3.49912e49	2.62462
$950$	0	0
$951$	−1.74849e49	−1.26673
$952$	− 1.26414e48i	− 0.0900091i
$953$	− 8.00029e48i	− 0.559852i	−0.960022	−	0.279926i	$-0.909690\pi$
$953$	− 8.00029e48i	− 0.559852i	0.960022	−	0.279926i	$-0.0903099\pi$
$954$	−4.95990e48	−0.341134
$955$	0	0
$956$	3.75718e48	0.249636
$957$	− 5.21343e48i	− 0.340468i
$958$	− 1.87601e49i	− 1.20422i
$959$	−4.67571e49	−2.95013
$960$	0	0
$961$	1.29192e49	0.787586
$962$	3.73400e48i	0.223762i
$963$	5.40596e48i	0.318448i
$964$	6.91565e48	0.400463
$965$	0	0
$966$	−2.78123e49	−1.55638
$967$	2.45742e49i	1.35190i	0.736949	+	0.675948i	$0.236266\pi$
$967$	2.45742e49i	1.35190i	−0.736949	+	0.675948i	$0.763734\pi$
$968$	7.17159e47i	0.0387857i
$969$	1.39801e49	0.743309
$970$	0	0
$971$	−3.60689e49	−1.85360	−0.926800	−	0.375556i	$-0.877452\pi$
$971$	−3.60689e49	−1.85360	−0.926800	+	0.375556i	$0.877452\pi$
$972$	− 5.93219e48i	− 0.299724i
$973$	− 1.70947e49i	− 0.849179i
$974$	3.87592e48	0.189301
$975$	0	0
$976$	−4.08749e49	−1.92990
$977$	1.33484e49i	0.619683i	0.950788	+	0.309841i	$0.100276\pi$
$977$	1.33484e49i	0.619683i	−0.950788	+	0.309841i	$0.899724\pi$
$978$	3.97778e49i	1.81572i
$979$	1.36966e49	0.614751
$980$	0	0
$981$	1.79101e47	0.00777250
$982$	3.42300e49i	1.46072i
$983$	1.85345e49i	0.777765i	0.921287	+	0.388882i	$0.127139\pi$
$983$	1.85345e49i	0.777765i	−0.921287	+	0.388882i	$0.872861\pi$
$984$	−8.93798e47	−0.0368825
$985$	0	0
$986$	1.19579e49	0.477185
$987$	− 3.40769e49i	− 1.33730i
$988$	− 4.66110e49i	− 1.79887i
$989$	−1.23351e49	−0.468171
$990$	0	0
$991$	−1.48569e49	−0.545398	−0.272699	−	0.962099i	$-0.587916\pi$
$991$	−1.48569e49	−0.545398	−0.272699	+	0.962099i	$0.587916\pi$
$992$	− 5.13878e49i	− 1.85531i
$993$	2.71535e49i	0.964192i
$994$	2.24294e49	0.783325
$995$	0	0
$996$	7.08890e48	0.239497
$997$	− 2.13570e49i	− 0.709694i	−0.934924	−	0.354847i	$-0.884533\pi$
$997$	− 2.13570e49i	− 0.709694i	0.934924	−	0.354847i	$-0.115467\pi$
$998$	− 6.89789e49i	− 2.25456i
$999$	3.33207e48	0.107123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.b.24.2		10
5.2	odd	4		25.34.a.b.1.5		5
5.3	odd	4		5.34.a.a.1.1	✓	5
5.4	even	2	inner	25.34.b.b.24.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.1	✓	5	5.3	odd	4
25.34.a.b.1.5		5	5.2	odd	4
25.34.b.b.24.2		10	1.1	even	1	trivial
25.34.b.b.24.9		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)

\(f(q)\)	\(=\)	\(q-129081. i q^{2} +6.82881e7i q^{3} -8.07187e9 q^{4} +8.81467e12 q^{6} -1.39338e14i q^{7} -6.68716e13i q^{8} +8.95800e14 q^{9} +O(q^{10})\)	\(q-129081. i q^{2} +6.82881e7i q^{3} -8.07187e9 q^{4} +8.81467e12 q^{6} -1.39338e14i q^{7} -6.68716e13i q^{8} +8.95800e14 q^{9} -1.11807e17 q^{11} -5.51213e17i q^{12} -3.82676e18i q^{13} -1.79859e19 q^{14} -7.79687e19 q^{16} +1.35670e20i q^{17} -1.15630e20i q^{18} -1.50898e21 q^{19} +9.51513e21 q^{21} +1.44321e22i q^{22} -2.26444e22i q^{23} +4.56653e21 q^{24} -4.93961e23 q^{26} +4.40790e23i q^{27} +1.12472e24i q^{28} +6.82827e23 q^{29} -5.41504e24 q^{31} +9.48983e24i q^{32} -7.63507e24i q^{33} +1.75124e25 q^{34} -7.23078e24 q^{36} -7.55931e24i q^{37} +1.94780e26i q^{38} +2.61322e26 q^{39} -1.95728e26 q^{41} -1.22822e27i q^{42} -5.44732e26i q^{43} +9.02490e26 q^{44} -2.92295e27 q^{46} -3.58134e27i q^{47} -5.32433e27i q^{48} -1.16841e28 q^{49} -9.26465e27 q^{51} +3.08891e28i q^{52} -4.28944e28i q^{53} +5.68974e28 q^{54} -9.31777e27 q^{56} -1.03045e29i q^{57} -8.81397e28i q^{58} +2.15590e28 q^{59} +5.24247e29 q^{61} +6.98976e29i q^{62} -1.24819e29i q^{63} +5.55207e29 q^{64} -9.85539e29 q^{66} -1.47500e30i q^{67} -1.09511e30i q^{68} +1.54634e30 q^{69} -1.24706e30 q^{71} -5.99036e28i q^{72} +9.14380e30i q^{73} -9.75760e29 q^{74} +1.21803e31 q^{76} +1.55789e31i q^{77} -3.37316e31i q^{78} +2.52252e31 q^{79} -2.51209e31 q^{81} +2.52647e31i q^{82} +1.28605e31i q^{83} -7.68050e31 q^{84} -7.03143e31 q^{86} +4.66289e31i q^{87} +7.47670e30i q^{88} -1.22503e32 q^{89} -5.33214e32 q^{91} +1.82783e32i q^{92} -3.69782e32i q^{93} -4.62282e32 q^{94} -6.48042e32 q^{96} +2.05513e31i q^{97} +1.50819e33i q^{98} -1.00156e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) \) 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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