LMFDB - Embedded newform 25.26.b.c.24.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,26,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, 26, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 26 $
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:	$98.9991949881$
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} + 63646685 x^{8} + \cdots + 17\!\cdots\!56 $ x^10 + 63646685x^8 + 1324242494492980x^6 + 9922658441827346683840x^4 + 24511582941077447838208793600x^2 + 1714054736104734086036246452781056
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{29}\cdot 3^{6}\cdot 5^{24} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.10
Root			$5041.97i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.26.b.c.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11003.9i q^{2} -418448. i q^{3} -8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10i q^{7} -5.93966e11i q^{8} +6.72190e11 q^{9} +O(q^{10})$	\(q+11003.9i q^{2} -418448. i q^{3} -8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10i q^{7} -5.93966e11i q^{8} +6.72190e11 q^{9} -2.19858e12 q^{11} +3.66276e13i q^{12} +6.43659e13i q^{13} +7.77176e14 q^{14} +3.59887e15 q^{16} -5.70025e14i q^{17} +7.39673e15i q^{18} +8.57675e14 q^{19} -2.95538e16 q^{21} -2.41930e16i q^{22} -9.97218e15i q^{23} -2.48544e17 q^{24} -7.08278e17 q^{26} -6.35823e17i q^{27} +6.18214e18i q^{28} +1.82269e18 q^{29} -4.09356e18 q^{31} +1.96715e19i q^{32} +9.19990e17i q^{33} +6.27252e18 q^{34} -5.88382e19 q^{36} -4.56115e19i q^{37} +9.43780e18i q^{38} +2.69338e19 q^{39} +2.18308e20 q^{41} -3.25207e20i q^{42} -6.85002e19i q^{43} +1.92446e20 q^{44} +1.09733e20 q^{46} -1.23525e19i q^{47} -1.50594e21i q^{48} -3.64712e21 q^{49} -2.38526e20 q^{51} -5.63408e21i q^{52} +4.53955e21i q^{53} +6.99655e21 q^{54} -4.19501e22 q^{56} -3.58892e20i q^{57} +2.00568e22i q^{58} -8.45133e21 q^{59} -1.08894e22 q^{61} -4.50452e22i q^{62} -4.74748e22i q^{63} -9.57062e22 q^{64} -1.01235e22 q^{66} -3.89372e22i q^{67} +4.98955e22i q^{68} -4.17284e21 q^{69} -3.71162e22 q^{71} -3.99258e23i q^{72} -2.76367e23i q^{73} +5.01906e23 q^{74} -7.50741e22 q^{76} +1.55279e23i q^{77} +2.96378e23i q^{78} -8.72667e23 q^{79} +3.03480e23 q^{81} +2.40225e24i q^{82} +4.43419e23i q^{83} +2.58690e24 q^{84} +7.53772e23 q^{86} -7.62702e23i q^{87} +1.30588e24i q^{88} +5.97991e23 q^{89} +4.54598e24 q^{91} +8.72886e23i q^{92} +1.71294e24i q^{93} +1.35926e23 q^{94} +8.23151e24 q^{96} -9.83402e24i q^{97} -4.01327e25i q^{98} -1.47786e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 182100520 q^{4} + 11393149520 q^{6} - 555993692930 q^{9}+O(q^{10}) $ 10 * q - 182100520 * q^4 + 11393149520 * q^6 - 555993692930 * q^9	$ 10 q - 182100520 q^{4} + 11393149520 q^{6} - 555993692930 q^{9} - 8289916903080 q^{11} + 891133307021760 q^{14} + 60\!\cdots\!60 q^{16}+ \cdots + 45\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 182100520 * q^4 + 11393149520 * q^6 - 555993692930 * q^9 - 8289916903080 * q^11 + 891133307021760 * q^14 + 6089976035260960 * q^16 - 26946376100390600 * q^19 + 153536191152121920 * q^21 - 1476466505472763200 * q^24 + 663464770878308520 * q^26 - 3021036492115464300 * q^29 - 15601581800953125280 * q^31 + 61934328372191765160 * q^34 - 255633494420041954040 * q^36 + 57026310922020243440 * q^39 + 536365426849982693220 * q^41 - 2053686541960406319840 * q^44 + 3612523521723723462720 * q^46 - 5857016804172155813370 * q^49 - 3359895558029927268880 * q^51 + 32268854676621495090400 * q^54 - 78830910223583237404800 * q^56 + 33094407067760080842600 * q^59 + 23174537108178497679020 * q^61 - 167963646340179319304320 * q^64 + 215372491198081115515840 * q^66 - 410207702498006419143360 * q^69 + 359270258356833457889520 * q^71 + 1777344398251660471679160 * q^74 - 2383599721540520876485600 * q^76 - 720565698511703983868000 * q^79 + 207169016893179802937210 * q^81 + 7675763190633230335330560 * q^84 - 1131684772842662195488080 * q^86 - 8184257338291963026048900 * q^89 + 23945146562217442521934720 * q^91 + 34225484666245805864609760 * q^94 - 20752772325535553602906880 * q^96 + 45729238049768666352546440 * 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 $

$2$	11003.9i	1.89965i	0.312787	+	0.949823i	$0.398738\pi$
$2$	11003.9i	1.89965i	−0.312787	+	0.949823i	$0.601262\pi$
$3$	− 418448.i	− 0.454596i	−0.973825	−	0.227298i	$-0.927011\pi$
$3$	− 418448.i	− 0.454596i	0.973825	−	0.227298i	$-0.0729891\pi$
$4$	−8.75320e7	−2.60866
$5$	0	0
$5$	0	0
$6$	4.60457e9	0.863572
$7$	− 7.06271e10i	− 1.92862i	−0.264782	−	0.964308i	$-0.585300\pi$
$7$	− 7.06271e10i	− 1.92862i	0.264782	−	0.964308i	$-0.414700\pi$
$8$	− 5.93966e11i	− 3.05588i
$9$	6.72190e11	0.793342
$10$	0	0
$11$	−2.19858e12	−0.211219	−0.105610	−	0.994408i	$-0.533679\pi$
$11$	−2.19858e12	−0.211219	−0.105610	+	0.994408i	$0.533679\pi$
$12$	3.66276e13i	1.18589i
$13$	6.43659e13i	0.766239i	0.923699	+	0.383119i	$0.125150\pi$
$13$	6.43659e13i	0.766239i	−0.923699	+	0.383119i	$0.874850\pi$
$14$	7.77176e14	3.66369
$15$	0	0
$16$	3.59887e15	3.19644
$17$	− 5.70025e14i	− 0.237292i	−0.992937	−	0.118646i	$-0.962145\pi$
$17$	− 5.70025e14i	− 0.237292i	0.992937	−	0.118646i	$-0.0378553\pi$
$18$	7.39673e15i	1.50707i
$19$	8.57675e14	0.0889002	0.0444501	−	0.999012i	$-0.485846\pi$
$19$	8.57675e14	0.0889002	0.0444501	+	0.999012i	$0.485846\pi$
$20$	0	0
$21$	−2.95538e16	−0.876741
$22$	− 2.41930e16i	− 0.401242i
$23$	− 9.97218e15i	− 0.0948838i	−0.998874	−	0.0474419i	$-0.984893\pi$
$23$	− 9.97218e15i	− 0.0948838i	0.998874	−	0.0474419i	$-0.0151069\pi$
$24$	−2.48544e17	−1.38919
$25$	0	0
$26$	−7.08278e17	−1.45558
$27$	− 6.35823e17i	− 0.815246i
$28$	6.18214e18i	5.03110i
$29$	1.82269e18	0.956618	0.478309	−	0.878192i	$-0.341250\pi$
$29$	1.82269e18	0.956618	0.478309	+	0.878192i	$0.341250\pi$
$30$	0	0
$31$	−4.09356e18	−0.933425	−0.466713	−	0.884409i	$-0.654562\pi$
$31$	−4.09356e18	−0.933425	−0.466713	+	0.884409i	$0.654562\pi$
$32$	1.96715e19i	3.01622i
$33$	9.19990e17i	0.0960194i
$34$	6.27252e18	0.450770
$35$	0	0
$36$	−5.88382e19	−2.06956
$37$	− 4.56115e19i	− 1.13908i	−0.821965	−	0.569538i	$-0.807122\pi$
$37$	− 4.56115e19i	− 1.13908i	0.821965	−	0.569538i	$-0.192878\pi$
$38$	9.43780e18i	0.168879i
$39$	2.69338e19	0.348329
$40$	0	0
$41$	2.18308e20	1.51102	0.755512	−	0.655134i	$-0.227388\pi$
$41$	2.18308e20	1.51102	0.755512	+	0.655134i	$0.227388\pi$
$42$	− 3.25207e20i	− 1.66550i
$43$	− 6.85002e19i	− 0.261419i	−0.991421	−	0.130709i	$-0.958275\pi$
$43$	− 6.85002e19i	− 0.261419i	0.991421	−	0.130709i	$-0.0417254\pi$
$44$	1.92446e20	0.550999
$45$	0	0
$46$	1.09733e20	0.180246
$47$	− 1.23525e19i	− 0.0155071i	−0.999970	−	0.00775356i	$-0.997532\pi$
$47$	− 1.23525e19i	− 0.0155071i	0.999970	−	0.00775356i	$-0.00246806\pi$
$48$	− 1.50594e21i	− 1.45309i
$49$	−3.64712e21	−2.71956
$50$	0	0
$51$	−2.38526e20	−0.107872
$52$	− 5.63408e21i	− 1.99886i
$53$	4.53955e21i	1.26930i	0.772800	+	0.634650i	$0.218856\pi$
$53$	4.53955e21i	1.26930i	−0.772800	+	0.634650i	$0.781144\pi$
$54$	6.99655e21	1.54868
$55$	0	0
$56$	−4.19501e22	−5.89363
$57$	− 3.58892e20i	− 0.0404137i
$58$	2.00568e22i	1.81724i
$59$	−8.45133e21	−0.618407	−0.309204	−	0.950996i	$-0.600062\pi$
$59$	−8.45133e21	−0.618407	−0.309204	+	0.950996i	$0.600062\pi$
$60$	0	0
$61$	−1.08894e22	−0.525266	−0.262633	−	0.964896i	$-0.584591\pi$
$61$	−1.08894e22	−0.525266	−0.262633	+	0.964896i	$0.584591\pi$
$62$	− 4.50452e22i	− 1.77318i
$63$	− 4.74748e22i	− 1.53005i
$64$	−9.57062e22	−2.53332
$65$	0	0
$66$	−1.01235e22	−0.182403
$67$	− 3.89372e22i	− 0.581339i	−0.956824	−	0.290669i	$-0.906122\pi$
$67$	− 3.89372e22i	− 0.581339i	0.956824	−	0.290669i	$-0.0938780\pi$
$68$	4.98955e22i	0.619013i
$69$	−4.17284e21	−0.0431338
$70$	0	0
$71$	−3.71162e22	−0.268432	−0.134216	−	0.990952i	$-0.542852\pi$
$71$	−3.71162e22	−0.268432	−0.134216	+	0.990952i	$0.542852\pi$
$72$	− 3.99258e23i	− 2.42436i
$73$	− 2.76367e23i	− 1.41238i	−0.708024	−	0.706188i	$-0.750413\pi$
$73$	− 2.76367e23i	− 1.41238i	0.708024	−	0.706188i	$-0.249587\pi$
$74$	5.01906e23	2.16384
$75$	0	0
$76$	−7.50741e22	−0.231910
$77$	1.55279e23i	0.407361i
$78$	2.96378e23i	0.661702i
$79$	−8.72667e23	−1.66154	−0.830768	−	0.556619i	$-0.812098\pi$
$79$	−8.72667e23	−1.66154	−0.830768	+	0.556619i	$0.812098\pi$
$80$	0	0
$81$	3.03480e23	0.422735
$82$	2.40225e24i	2.87041i
$83$	4.43419e23i	0.455342i	0.973738	+	0.227671i	$0.0731111\pi$
$83$	4.43419e23i	0.455342i	−0.973738	+	0.227671i	$0.926889\pi$
$84$	2.58690e24	2.28712
$85$	0	0
$86$	7.53772e23	0.496603
$87$	− 7.62702e23i	− 0.434875i
$88$	1.30588e24i	0.645461i
$89$	5.97991e23	0.256637	0.128319	−	0.991733i	$-0.459042\pi$
$89$	5.97991e23	0.256637	0.128319	+	0.991733i	$0.459042\pi$
$90$	0	0
$91$	4.54598e24	1.47778
$92$	8.72886e23i	0.247520i
$93$	1.71294e24i	0.424331i
$94$	1.35926e23	0.0294581
$95$	0	0
$96$	8.23151e24	1.37116
$97$	− 9.83402e24i	− 1.43908i	−0.694452	−	0.719539i	$-0.744353\pi$
$97$	− 9.83402e24i	− 1.43908i	0.694452	−	0.719539i	$-0.255647\pi$
$98$	− 4.01327e25i	− 5.16621i
$99$	−1.47786e24	−0.167569
$100$	0	0
$101$	6.56554e24	0.579766	0.289883	−	0.957062i	$-0.406384\pi$
$101$	6.56554e24	0.579766	0.289883	+	0.957062i	$0.406384\pi$
$102$	− 2.62472e24i	− 0.204918i
$103$	1.60371e25i	1.10831i	0.832413	+	0.554156i	$0.186959\pi$
$103$	1.60371e25i	1.10831i	−0.832413	+	0.554156i	$0.813041\pi$
$104$	3.82312e25	2.34154
$105$	0	0
$106$	−4.99528e25	−2.41122
$107$	3.10689e25i	1.33361i	0.745233	+	0.666804i	$0.232338\pi$
$107$	3.10689e25i	1.33361i	−0.745233	+	0.666804i	$0.767662\pi$
$108$	5.56548e25i	2.12670i
$109$	−5.99855e24	−0.204275	−0.102138	−	0.994770i	$-0.532568\pi$
$109$	−5.99855e24	−0.204275	−0.102138	+	0.994770i	$0.532568\pi$
$110$	0	0
$111$	−1.90860e25	−0.517820
$112$	− 2.54178e26i	− 6.16471i
$113$	3.19736e25i	0.693923i	0.937879	+	0.346962i	$0.112787\pi$
$113$	3.19736e25i	0.693923i	−0.937879	+	0.346962i	$0.887213\pi$
$114$	3.94923e24	0.0767718
$115$	0	0
$116$	−1.59544e26	−2.49549
$117$	4.32661e25i	0.607890i
$118$	− 9.29978e25i	− 1.17476i
$119$	−4.02592e25	−0.457645
$120$	0	0
$121$	−1.03513e26	−0.955386
$122$	− 1.19826e26i	− 0.997820i
$123$	− 9.13505e25i	− 0.686906i
$124$	3.58317e26	2.43499
$125$	0	0
$126$	5.22410e26	2.90656
$127$	− 3.11422e26i	− 1.56965i	−0.619718	−	0.784825i	$-0.712753\pi$
$127$	− 3.11422e26i	− 1.56965i	0.619718	−	0.784825i	$-0.287247\pi$
$128$	− 3.93077e26i	− 1.79619i
$129$	−2.86638e25	−0.118840
$130$	0	0
$131$	7.42883e25	0.254114	0.127057	−	0.991895i	$-0.459447\pi$
$131$	7.42883e25	0.254114	0.127057	+	0.991895i	$0.459447\pi$
$132$	− 8.05286e25i	− 0.250482i
$133$	− 6.05751e25i	− 0.171454i
$134$	4.28462e26	1.10434
$135$	0	0
$136$	−3.38576e26	−0.725136
$137$	5.97553e26i	1.16780i	0.811825	+	0.583901i	$0.198474\pi$
$137$	5.97553e26i	1.16780i	−0.811825	+	0.583901i	$0.801526\pi$
$138$	− 4.59176e25i	− 0.0819390i
$139$	−6.66965e26	−1.08747	−0.543736	−	0.839256i	$-0.682991\pi$
$139$	−6.66965e26	−1.08747	−0.543736	+	0.839256i	$0.682991\pi$
$140$	0	0
$141$	−5.16887e24	−0.00704948
$142$	− 4.08424e26i	− 0.509926i
$143$	− 1.41514e26i	− 0.161844i
$144$	2.41913e27	2.53587
$145$	0	0
$146$	3.04112e27	2.68302
$147$	1.52613e27i	1.23630i
$148$	3.99247e27i	2.97146i
$149$	6.79823e26	0.465123	0.232561	−	0.972582i	$-0.425289\pi$
$149$	6.79823e26	0.465123	0.232561	+	0.972582i	$0.425289\pi$
$150$	0	0
$151$	−1.38341e27	−0.801195	−0.400597	−	0.916254i	$-0.631197\pi$
$151$	−1.38341e27	−0.801195	−0.400597	+	0.916254i	$0.631197\pi$
$152$	− 5.09430e26i	− 0.271669i
$153$	− 3.83165e26i	− 0.188254i
$154$	−1.70868e27	−0.773842
$155$	0	0
$156$	−2.35757e27	−0.908672
$157$	− 2.26682e27i	− 0.806625i	−0.915062	−	0.403312i	$-0.867859\pi$
$157$	− 2.26682e27i	− 0.806625i	0.915062	−	0.403312i	$-0.132141\pi$
$158$	− 9.60276e27i	− 3.15633i
$159$	1.89956e27	0.577018
$160$	0	0
$161$	−7.04306e26	−0.182995
$162$	3.33948e27i	0.803047i
$163$	− 4.82353e27i	− 1.07404i	−0.843570	−	0.537019i	$-0.819550\pi$
$163$	− 4.82353e27i	− 1.07404i	0.843570	−	0.537019i	$-0.180450\pi$
$164$	−1.91090e28	−3.94175
$165$	0	0
$166$	−4.87935e27	−0.864989
$167$	− 1.02034e28i	− 1.67798i	−0.544144	−	0.838992i	$-0.683145\pi$
$167$	− 1.02034e28i	− 1.67798i	0.544144	−	0.838992i	$-0.316855\pi$
$168$	1.75539e28i	2.67922i
$169$	2.91344e27	0.412878
$170$	0	0
$171$	5.76521e26	0.0705283
$172$	5.99597e27i	0.681952i
$173$	9.52715e27i	1.00783i	0.863754	+	0.503914i	$0.168107\pi$
$173$	9.52715e27i	1.00783i	−0.863754	+	0.503914i	$0.831893\pi$
$174$	8.39272e27	0.826108
$175$	0	0
$176$	−7.91240e27	−0.675149
$177$	3.53644e27i	0.281126i
$178$	6.58026e27i	0.487520i
$179$	−2.29857e28	−1.58779	−0.793897	−	0.608052i	$-0.791951\pi$
$179$	−2.29857e28	−1.58779	−0.793897	+	0.608052i	$0.791951\pi$
$180$	0	0
$181$	−2.20864e27	−0.132783	−0.0663916	−	0.997794i	$-0.521149\pi$
$181$	−2.20864e27	−0.132783	−0.0663916	+	0.997794i	$0.521149\pi$
$182$	5.00237e28i	2.80726i
$183$	4.55663e27i	0.238784i
$184$	−5.92314e27	−0.289954
$185$	0	0
$186$	−1.88491e28	−0.806080
$187$	1.25325e27i	0.0501206i
$188$	1.08124e27i	0.0404528i
$189$	−4.49063e28	−1.57230
$190$	0	0
$191$	−1.67599e28	−0.514464	−0.257232	−	0.966350i	$-0.582810\pi$
$191$	−1.67599e28	−0.514464	−0.257232	+	0.966350i	$0.582810\pi$
$192$	4.00480e28i	1.15164i
$193$	− 2.90398e28i	− 0.782578i	−0.920268	−	0.391289i	$-0.872029\pi$
$193$	− 2.90398e28i	− 0.782578i	0.920268	−	0.391289i	$-0.127971\pi$
$194$	1.08213e29	2.73374
$195$	0	0
$196$	3.19240e29	7.09441
$197$	− 8.94384e27i	− 0.186507i	−0.995642	−	0.0932537i	$-0.970273\pi$
$197$	− 8.94384e27i	− 0.186507i	0.995642	−	0.0932537i	$-0.0297268\pi$
$198$	− 1.62623e28i	− 0.318322i
$199$	1.94449e27	0.0357390	0.0178695	−	0.999840i	$-0.494312\pi$
$199$	1.94449e27	0.0357390	0.0178695	+	0.999840i	$0.494312\pi$
$200$	0	0
$201$	−1.62932e28	−0.264274
$202$	7.22467e28i	1.10135i
$203$	− 1.28732e29i	− 1.84495i
$204$	2.08786e28	0.281401
$205$	0	0
$206$	−1.76472e29	−2.10540
$207$	− 6.70320e27i	− 0.0752754i
$208$	2.31645e29i	2.44924i
$209$	−1.88567e27	−0.0187774
$210$	0	0
$211$	−6.30554e28	−0.557431	−0.278716	−	0.960374i	$-0.589909\pi$
$211$	−6.30554e28	−0.557431	−0.278716	+	0.960374i	$0.589909\pi$
$212$	− 3.97356e29i	− 3.31117i
$213$	1.55312e28i	0.122028i
$214$	−3.41880e29	−2.53338
$215$	0	0
$216$	−3.77657e29	−2.49130
$217$	2.89116e29i	1.80022i
$218$	− 6.60077e28i	− 0.388050i
$219$	−1.15645e29	−0.642061
$220$	0	0
$221$	3.66902e28	0.181822
$222$	− 2.10021e29i	− 0.983675i
$223$	3.91233e28i	0.173231i	0.996242	+	0.0866154i	$0.0276051\pi$
$223$	3.91233e28i	0.173231i	−0.996242	+	0.0866154i	$0.972395\pi$
$224$	1.38934e30	5.81714
$225$	0	0
$226$	−3.51836e29	−1.31821
$227$	− 3.10822e29i	− 1.10202i	−0.834500	−	0.551008i	$-0.814243\pi$
$227$	− 3.10822e29i	− 1.10202i	0.834500	−	0.551008i	$-0.185757\pi$
$228$	3.14146e28i	0.105426i
$229$	−3.39409e29	−1.07840	−0.539200	−	0.842178i	$-0.681273\pi$
$229$	−3.39409e29	−1.07840	−0.539200	+	0.842178i	$0.681273\pi$
$230$	0	0
$231$	6.49763e28	0.185185
$232$	− 1.08262e30i	− 2.92331i
$233$	− 6.18615e29i	− 1.58296i	−0.611192	−	0.791482i	$-0.709310\pi$
$233$	− 6.18615e29i	− 1.58296i	0.611192	−	0.791482i	$-0.290690\pi$
$234$	−4.76098e29	−1.15478
$235$	0	0
$236$	7.39762e29	1.61321
$237$	3.65165e29i	0.755328i
$238$	− 4.43010e29i	− 0.869363i
$239$	−6.21272e29	−1.15693	−0.578467	−	0.815706i	$-0.696349\pi$
$239$	−6.21272e29	−1.15693	−0.578467	+	0.815706i	$0.696349\pi$
$240$	0	0
$241$	−2.86821e29	−0.481280	−0.240640	−	0.970614i	$-0.577357\pi$
$241$	−2.86821e29	−0.481280	−0.240640	+	0.970614i	$0.577357\pi$
$242$	− 1.13905e30i	− 1.81490i
$243$	− 6.65716e29i	− 1.00742i
$244$	9.53168e29	1.37024
$245$	0	0
$246$	1.00521e30	1.30488
$247$	5.52051e28i	0.0681188i
$248$	2.43143e30i	2.85244i
$249$	1.85548e29	0.206997
$250$	0	0
$251$	−9.43362e29	−0.952263	−0.476132	−	0.879374i	$-0.657961\pi$
$251$	−9.43362e29	−0.952263	−0.476132	+	0.879374i	$0.657961\pi$
$252$	4.15557e30i	3.99139i
$253$	2.19246e28i	0.0200413i
$254$	3.42687e30	2.98178
$255$	0	0
$256$	1.11402e30	0.878808
$257$	9.76952e29i	0.734022i	0.930217	+	0.367011i	$0.119619\pi$
$257$	9.76952e29i	0.734022i	−0.930217	+	0.367011i	$0.880381\pi$
$258$	− 3.15414e29i	− 0.225754i
$259$	−3.22141e30	−2.19684
$260$	0	0
$261$	1.22520e30	0.758926
$262$	8.17464e29i	0.482728i
$263$	− 1.56365e30i	− 0.880423i	−0.897894	−	0.440212i	$-0.854903\pi$
$263$	− 1.56365e30i	− 0.880423i	0.897894	−	0.440212i	$-0.145097\pi$
$264$	5.46443e29	0.293424
$265$	0	0
$266$	6.66565e29	0.325703
$267$	− 2.50228e29i	− 0.116666i
$268$	3.40825e30i	1.51651i
$269$	−1.22545e30	−0.520465	−0.260233	−	0.965546i	$-0.583799\pi$
$269$	−1.22545e30	−0.520465	−0.260233	+	0.965546i	$0.583799\pi$
$270$	0	0
$271$	−4.30067e30	−1.66502	−0.832511	−	0.554008i	$-0.813098\pi$
$271$	−4.30067e30	−1.66502	−0.832511	+	0.554008i	$0.813098\pi$
$272$	− 2.05145e30i	− 0.758489i
$273$	− 1.90226e30i	− 0.671793i
$274$	−6.57543e30	−2.21841
$275$	0	0
$276$	3.65257e29	0.112521
$277$	2.53485e30i	0.746372i	0.927757	+	0.373186i	$0.121735\pi$
$277$	2.53485e30i	0.746372i	−0.927757	+	0.373186i	$0.878265\pi$
$278$	− 7.33924e30i	− 2.06581i
$279$	−2.75165e30	−0.740526
$280$	0	0
$281$	6.20850e30	1.52812	0.764060	−	0.645145i	$-0.223203\pi$
$281$	6.20850e30	1.52812	0.764060	+	0.645145i	$0.223203\pi$
$282$	− 5.68779e28i	− 0.0133915i
$283$	5.38721e30i	1.21348i	0.794900	+	0.606741i	$0.207523\pi$
$283$	5.38721e30i	1.21348i	−0.794900	+	0.606741i	$0.792477\pi$
$284$	3.24886e30	0.700247
$285$	0	0
$286$	1.55721e30	0.307447
$287$	− 1.54185e31i	− 2.91419i
$288$	1.32230e31i	2.39290i
$289$	5.44570e30	0.943693
$290$	0	0
$291$	−4.11502e30	−0.654199
$292$	2.41910e31i	3.68441i
$293$	− 5.63029e30i	− 0.821647i	−0.911715	−	0.410823i	$-0.865241\pi$
$293$	− 5.63029e30i	− 0.821647i	0.911715	−	0.410823i	$-0.134759\pi$
$294$	−1.67934e31	−2.34854
$295$	0	0
$296$	−2.70917e31	−3.48089
$297$	1.39791e30i	0.172196i
$298$	7.48073e30i	0.883569i
$299$	6.41869e29	0.0727037
$300$	0	0
$301$	−4.83797e30	−0.504176
$302$	− 1.52229e31i	− 1.52199i
$303$	− 2.74733e30i	− 0.263559i
$304$	3.08666e30	0.284164
$305$	0	0
$306$	4.21632e30	0.357615
$307$	1.10992e31i	0.903782i	0.892073	+	0.451891i	$0.149250\pi$
$307$	1.10992e31i	0.903782i	−0.892073	+	0.451891i	$0.850750\pi$
$308$	− 1.35919e31i	− 1.06267i
$309$	6.71071e30	0.503834
$310$	0	0
$311$	−8.27207e30	−0.572940	−0.286470	−	0.958089i	$-0.592482\pi$
$311$	−8.27207e30	−0.572940	−0.286470	+	0.958089i	$0.592482\pi$
$312$	− 1.59978e31i	− 1.06445i
$313$	7.97044e30i	0.509540i	0.967002	+	0.254770i	$0.0819998\pi$
$313$	7.97044e30i	0.509540i	−0.967002	+	0.254770i	$0.918000\pi$
$314$	2.49439e31	1.53230
$315$	0	0
$316$	7.63863e31	4.33438
$317$	2.64724e31i	1.44395i	0.691919	+	0.721975i	$0.256766\pi$
$317$	2.64724e31i	1.44395i	−0.691919	+	0.721975i	$0.743234\pi$
$318$	2.09027e31i	1.09613i
$319$	−4.00733e30	−0.202056
$320$	0	0
$321$	1.30007e31	0.606253
$322$	− 7.75014e30i	− 0.347625i
$323$	− 4.88897e29i	− 0.0210953i
$324$	−2.65643e31	−1.10277
$325$	0	0
$326$	5.30778e31	2.04029
$327$	2.51008e30i	0.0928626i
$328$	− 1.29668e32i	− 4.61751i
$329$	−8.72421e29	−0.0299073
$330$	0	0
$331$	−1.55467e31	−0.494071	−0.247035	−	0.969006i	$-0.579456\pi$
$331$	−1.55467e31	−0.494071	−0.247035	+	0.969006i	$0.579456\pi$
$332$	− 3.88133e31i	− 1.18783i
$333$	− 3.06596e31i	− 0.903678i
$334$	1.12277e32	3.18758
$335$	0	0
$336$	−1.06360e32	−2.80245
$337$	− 5.02293e30i	− 0.127522i	−0.997965	−	0.0637608i	$-0.979691\pi$
$337$	− 5.02293e30i	− 0.127522i	0.997965	−	0.0637608i	$-0.0203095\pi$
$338$	3.20592e31i	0.784322i
$339$	1.33793e31	0.315455
$340$	0	0
$341$	9.00000e30	0.197157
$342$	6.34400e30i	0.133979i
$343$	1.62870e32i	3.31638i
$344$	−4.06868e31	−0.798864
$345$	0	0
$346$	−1.04836e32	−1.91452
$347$	− 1.03151e32i	− 1.81701i	−0.417879	−	0.908503i	$-0.637226\pi$
$347$	− 1.03151e32i	− 1.81701i	0.417879	−	0.908503i	$-0.362774\pi$
$348$	6.67609e31i	1.13444i
$349$	8.10691e31	1.32904	0.664519	−	0.747271i	$-0.268636\pi$
$349$	8.10691e31	1.32904	0.664519	+	0.747271i	$0.268636\pi$
$350$	0	0
$351$	4.09253e31	0.624673
$352$	− 4.32494e31i	− 0.637084i
$353$	5.76769e31i	0.820008i	0.912084	+	0.410004i	$0.134473\pi$
$353$	5.76769e31i	0.820008i	−0.912084	+	0.410004i	$0.865527\pi$
$354$	−3.89147e31	−0.534039
$355$	0	0
$356$	−5.23434e31	−0.669479
$357$	1.68464e31i	0.208043i
$358$	− 2.52933e32i	− 3.01625i
$359$	−1.44570e31	−0.166493	−0.0832467	−	0.996529i	$-0.526529\pi$
$359$	−1.44570e31	−0.166493	−0.0832467	+	0.996529i	$0.526529\pi$
$360$	0	0
$361$	−9.23409e31	−0.992097
$362$	− 2.43037e31i	− 0.252241i
$363$	4.33149e31i	0.434315i
$364$	−3.97919e32	−3.85503
$365$	0	0
$366$	−5.01408e31	−0.453605
$367$	9.78544e31i	0.855568i	0.903881	+	0.427784i	$0.140706\pi$
$367$	9.78544e31i	0.855568i	−0.903881	+	0.427784i	$0.859294\pi$
$368$	− 3.58886e31i	− 0.303290i
$369$	1.46745e32	1.19876
$370$	0	0
$371$	3.20615e32	2.44799
$372$	− 1.49937e32i	− 1.10694i
$373$	5.60597e31i	0.400212i	0.979774	+	0.200106i	$0.0641287\pi$
$373$	5.60597e31i	0.400212i	−0.979774	+	0.200106i	$0.935871\pi$
$374$	−1.37906e31	−0.0952114
$375$	0	0
$376$	−7.33696e30	−0.0473880
$377$	1.17319e32i	0.732998i
$378$	− 4.94146e32i	− 2.98681i
$379$	2.05156e32	1.19976	0.599879	−	0.800091i	$-0.295215\pi$
$379$	2.05156e32	1.19976	0.599879	+	0.800091i	$0.295215\pi$
$380$	0	0
$381$	−1.30314e32	−0.713557
$382$	− 1.84425e32i	− 0.977299i
$383$	1.17765e32i	0.603993i	0.953309	+	0.301997i	$0.0976531\pi$
$383$	1.17765e32i	0.603993i	−0.953309	+	0.301997i	$0.902347\pi$
$384$	−1.64482e32	−0.816541
$385$	0	0
$386$	3.19552e32	1.48662
$387$	− 4.60452e31i	− 0.207394i
$388$	8.60792e32i	3.75406i
$389$	1.81043e31	0.0764560	0.0382280	−	0.999269i	$-0.487829\pi$
$389$	1.81043e31	0.0764560	0.0382280	+	0.999269i	$0.487829\pi$
$390$	0	0
$391$	−5.68439e30	−0.0225151
$392$	2.16626e33i	8.31066i
$393$	− 3.10858e31i	− 0.115519i
$394$	9.84174e31	0.354298
$395$	0	0
$396$	1.29360e32	0.437131
$397$	− 2.64215e32i	− 0.865118i	−0.901606	−	0.432559i	$-0.857611\pi$
$397$	− 2.64215e32i	− 0.865118i	0.901606	−	0.432559i	$-0.142389\pi$
$398$	2.13970e31i	0.0678914i
$399$	−2.53475e31	−0.0779425
$400$	0	0
$401$	−5.85566e32	−1.69150	−0.845749	−	0.533581i	$-0.820846\pi$
$401$	−5.85566e32	−1.69150	−0.845749	+	0.533581i	$0.820846\pi$
$402$	− 1.79289e32i	− 0.502028i
$403$	− 2.63486e32i	− 0.715227i
$404$	−5.74695e32	−1.51241
$405$	0	0
$406$	1.41655e33	3.50475
$407$	1.00281e32i	0.240595i
$408$	1.41676e32i	0.329644i
$409$	1.45035e32	0.327288	0.163644	−	0.986519i	$-0.447675\pi$
$409$	1.45035e32	0.327288	0.163644	+	0.986519i	$0.447675\pi$
$410$	0	0
$411$	2.50045e32	0.530878
$412$	− 1.40376e33i	− 2.89121i
$413$	5.96893e32i	1.19267i
$414$	7.37616e31	0.142997
$415$	0	0
$416$	−1.26618e33	−2.31115
$417$	2.79090e32i	0.494361i
$418$	− 2.07497e31i	− 0.0356705i
$419$	−9.57851e32	−1.59817	−0.799085	−	0.601219i	$-0.794682\pi$
$419$	−9.57851e32	−1.59817	−0.799085	+	0.601219i	$0.794682\pi$
$420$	0	0
$421$	−6.05056e32	−0.951194	−0.475597	−	0.879663i	$-0.657768\pi$
$421$	−6.05056e32	−0.951194	−0.475597	+	0.879663i	$0.657768\pi$
$422$	− 6.93857e32i	− 1.05892i
$423$	− 8.30322e30i	− 0.0123025i
$424$	2.69634e33	3.87883
$425$	0	0
$426$	−1.70904e32	−0.231810
$427$	7.69084e32i	1.01304i
$428$	− 2.71952e33i	− 3.47893i
$429$	−5.92160e31	−0.0735738
$430$	0	0
$431$	1.39054e32	0.163011	0.0815057	−	0.996673i	$-0.474027\pi$
$431$	1.39054e32	0.163011	0.0815057	+	0.996673i	$0.474027\pi$
$432$	− 2.28824e33i	− 2.60589i
$433$	− 8.29892e32i	− 0.918169i	−0.888392	−	0.459085i	$-0.848177\pi$
$433$	− 8.29892e32i	− 0.918169i	0.888392	−	0.459085i	$-0.151823\pi$
$434$	−3.18141e33	−3.41978
$435$	0	0
$436$	5.25066e32	0.532884
$437$	− 8.55290e30i	− 0.00843520i
$438$	− 1.27255e33i	− 1.21969i
$439$	−2.32179e32	−0.216280	−0.108140	−	0.994136i	$-0.534489\pi$
$439$	−2.32179e32	−0.216280	−0.108140	+	0.994136i	$0.534489\pi$
$440$	0	0
$441$	−2.45156e33	−2.15754
$442$	4.03736e32i	0.345398i
$443$	1.86142e33i	1.54810i	0.633127	+	0.774048i	$0.281771\pi$
$443$	1.86142e33i	1.54810i	−0.633127	+	0.774048i	$0.718229\pi$
$444$	1.67064e33	1.35081
$445$	0	0
$446$	−4.30510e32	−0.329077
$447$	− 2.84471e32i	− 0.211443i
$448$	6.75945e33i	4.88580i
$449$	−1.07392e32	−0.0754902	−0.0377451	−	0.999287i	$-0.512017\pi$
$449$	−1.07392e32	−0.0754902	−0.0377451	+	0.999287i	$0.512017\pi$
$450$	0	0
$451$	−4.79967e32	−0.319157
$452$	− 2.79872e33i	− 1.81021i
$453$	5.78884e32i	0.364220i
$454$	3.42026e33	2.09344
$455$	0	0
$456$	−2.13170e32	−0.123500
$457$	− 3.21506e31i	− 0.0181233i	−0.999959	−	0.00906163i	$-0.997116\pi$
$457$	− 3.21506e31i	− 0.0181233i	0.999959	−	0.00906163i	$-0.00288445\pi$
$458$	− 3.73483e33i	− 2.04858i
$459$	−3.62435e32	−0.193451
$460$	0	0
$461$	−2.80044e31	−0.0141568	−0.00707840	−	0.999975i	$-0.502253\pi$
$461$	−2.80044e31	−0.0141568	−0.00707840	+	0.999975i	$0.502253\pi$
$462$	7.14994e32i	0.351785i
$463$	− 5.73654e32i	− 0.274718i	−0.990521	−	0.137359i	$-0.956139\pi$
$463$	− 5.73654e32i	− 0.274718i	0.990521	−	0.137359i	$-0.0438615\pi$
$464$	6.55964e33	3.05777
$465$	0	0
$466$	6.80719e33	3.00707
$467$	− 3.10395e32i	− 0.133492i	−0.997770	−	0.0667458i	$-0.978738\pi$
$467$	− 3.10395e32i	− 0.133492i	0.997770	−	0.0667458i	$-0.0212617\pi$
$468$	− 3.78717e33i	− 1.58578i
$469$	−2.75002e33	−1.12118
$470$	0	0
$471$	−9.48546e32	−0.366688
$472$	5.01980e33i	1.88978i
$473$	1.50603e32i	0.0552166i
$474$	−4.01826e33	−1.43486
$475$	0	0
$476$	3.52397e33	1.19384
$477$	3.05144e33i	1.00699i
$478$	− 6.83644e33i	− 2.19776i
$479$	−4.51990e33	−1.41558	−0.707790	−	0.706423i	$-0.750308\pi$
$479$	−4.51990e33	−1.41558	−0.707790	+	0.706423i	$0.750308\pi$
$480$	0	0
$481$	2.93583e33	0.872805
$482$	− 3.15616e33i	− 0.914262i
$483$	2.94715e32i	0.0831886i
$484$	9.06073e33	2.49228
$485$	0	0
$486$	7.32549e33	1.91374
$487$	− 9.92789e32i	− 0.252781i	−0.991981	−	0.126391i	$-0.959661\pi$
$487$	− 9.92789e32i	− 0.252781i	0.991981	−	0.126391i	$-0.0403393\pi$
$488$	6.46791e33i	1.60515i
$489$	−2.01839e33	−0.488254
$490$	0	0
$491$	−2.94756e33	−0.677554	−0.338777	−	0.940867i	$-0.610013\pi$
$491$	−2.94756e33	−0.677554	−0.338777	+	0.940867i	$0.610013\pi$
$492$	7.99610e33i	1.79190i
$493$	− 1.03898e33i	− 0.226998i
$494$	−6.07473e32	−0.129402
$495$	0	0
$496$	−1.47322e34	−2.98364
$497$	2.62141e33i	0.517702i
$498$	2.04175e33i	0.393221i
$499$	2.99602e33	0.562714	0.281357	−	0.959603i	$-0.409215\pi$
$499$	2.99602e33	0.562714	0.281357	+	0.959603i	$0.409215\pi$
$500$	0	0
$501$	−4.26958e33	−0.762805
$502$	− 1.03807e34i	− 1.80896i
$503$	3.33386e33i	0.566693i	0.959018	+	0.283347i	$0.0914447\pi$
$503$	3.33386e33i	0.566693i	−0.959018	+	0.283347i	$0.908555\pi$
$504$	−2.81984e34	−4.67566
$505$	0	0
$506$	−2.41257e32	−0.0380714
$507$	− 1.21912e33i	− 0.187693i
$508$	2.72594e34i	4.09468i
$509$	9.93252e33	1.45575	0.727876	−	0.685709i	$-0.240508\pi$
$509$	9.93252e33	1.45575	0.727876	+	0.685709i	$0.240508\pi$
$510$	0	0
$511$	−1.95190e34	−2.72393
$512$	− 9.30849e32i	− 0.126767i
$513$	− 5.45329e32i	− 0.0724756i
$514$	−1.07503e34	−1.39438
$515$	0	0
$516$	2.50900e33	0.310012
$517$	2.71579e31i	0.00327540i
$518$	− 3.54482e34i	− 4.17323i
$519$	3.98661e33	0.458155
$520$	0	0
$521$	9.94456e33	1.08922	0.544608	−	0.838691i	$-0.316678\pi$
$521$	9.94456e33	1.08922	0.544608	+	0.838691i	$0.316678\pi$
$522$	1.34820e34i	1.44169i
$523$	7.17197e33i	0.748803i	0.927267	+	0.374401i	$0.122152\pi$
$523$	7.17197e33i	0.748803i	−0.927267	+	0.374401i	$0.877848\pi$
$524$	−6.50261e33	−0.662898
$525$	0	0
$526$	1.72062e34	1.67249
$527$	2.33343e33i	0.221494i
$528$	3.31093e33i	0.306920i
$529$	1.09463e34	0.990997
$530$	0	0
$531$	−5.68090e33	−0.490609
$532$	5.30227e33i	0.447266i
$533$	1.40516e34i	1.15781i
$534$	2.75349e33	0.221625
$535$	0	0
$536$	−2.31273e34	−1.77650
$537$	9.61830e33i	0.721805i
$538$	− 1.34848e34i	− 0.988700i
$539$	8.01848e33	0.574424
$540$	0	0
$541$	1.93584e34	1.32405	0.662023	−	0.749483i	$-0.269698\pi$
$541$	1.93584e34	1.32405	0.662023	+	0.749483i	$0.269698\pi$
$542$	− 4.73243e34i	− 3.16295i
$543$	9.24201e32i	0.0603627i
$544$	1.12133e34	0.715725
$545$	0	0
$546$	2.09323e34	1.27617
$547$	1.61834e34i	0.964337i	0.876078	+	0.482169i	$0.160151\pi$
$547$	1.61834e34i	0.964337i	−0.876078	+	0.482169i	$0.839849\pi$
$548$	− 5.23050e34i	− 3.04640i
$549$	−7.31972e33	−0.416716
$550$	0	0
$551$	1.56328e33	0.0850436
$552$	2.47852e33i	0.131812i
$553$	6.16339e34i	3.20447i
$554$	−2.78933e34	−1.41784
$555$	0	0
$556$	5.83808e34	2.83684
$557$	− 1.09645e34i	− 0.520953i	−0.965480	−	0.260476i	$-0.916120\pi$
$557$	− 1.09645e34i	− 0.520953i	0.965480	−	0.260476i	$-0.0838797\pi$
$558$	− 3.02789e34i	− 1.40674i
$559$	4.40908e33	0.200309
$560$	0	0
$561$	5.24418e32	0.0227846
$562$	6.83179e34i	2.90289i
$563$	− 1.82665e33i	− 0.0759102i	−0.999279	−	0.0379551i	$-0.987916\pi$
$563$	− 1.82665e33i	− 0.0759102i	0.999279	−	0.0379551i	$-0.0120844\pi$
$564$	4.52442e32	0.0183897
$565$	0	0
$566$	−5.92804e34	−2.30519
$567$	− 2.14339e34i	− 0.815293i
$568$	2.20458e34i	0.820296i
$569$	3.22829e34	1.17508	0.587542	−	0.809193i	$-0.300096\pi$
$569$	3.22829e34	1.17508	0.587542	+	0.809193i	$0.300096\pi$
$570$	0	0
$571$	−9.23601e33	−0.321761	−0.160880	−	0.986974i	$-0.551433\pi$
$571$	−9.23601e33	−0.321761	−0.160880	+	0.986974i	$0.551433\pi$
$572$	1.23870e34i	0.422197i
$573$	7.01315e33i	0.233873i
$574$	1.69664e35	5.53593
$575$	0	0
$576$	−6.43327e34	−2.00979
$577$	− 3.72256e34i	− 1.13801i	−0.822335	−	0.569003i	$-0.807329\pi$
$577$	− 3.72256e34i	− 1.13801i	0.822335	−	0.569003i	$-0.192671\pi$
$578$	5.99241e34i	1.79268i
$579$	−1.21517e34	−0.355757
$580$	0	0
$581$	3.13174e34	0.878181
$582$	− 4.52814e34i	− 1.24275i
$583$	− 9.98055e33i	− 0.268100i
$584$	−1.64153e35	−4.31606
$585$	0	0
$586$	6.19553e34	1.56084
$587$	3.62671e34i	0.894411i	0.894431	+	0.447205i	$0.147581\pi$
$587$	3.62671e34i	0.894411i	−0.894431	+	0.447205i	$0.852419\pi$
$588$	− 1.33585e35i	− 3.22509i
$589$	−3.51094e33	−0.0829817
$590$	0	0
$591$	−3.74253e33	−0.0847855
$592$	− 1.64150e35i	− 3.64099i
$593$	− 4.50782e34i	− 0.979000i	−0.872003	−	0.489500i	$-0.837179\pi$
$593$	− 4.50782e34i	− 0.979000i	0.872003	−	0.489500i	$-0.162821\pi$
$594$	−1.53825e34	−0.327111
$595$	0	0
$596$	−5.95063e34	−1.21335
$597$	− 8.13667e32i	− 0.0162468i
$598$	7.06308e33i	0.138111i
$599$	2.41289e33	0.0462064	0.0231032	−	0.999733i	$-0.492645\pi$
$599$	2.41289e33	0.0462064	0.0231032	+	0.999733i	$0.492645\pi$
$600$	0	0
$601$	−9.16411e34	−1.68329	−0.841646	−	0.540030i	$-0.818413\pi$
$601$	−9.16411e34	−1.68329	−0.841646	+	0.540030i	$0.818413\pi$
$602$	− 5.32367e34i	− 0.957757i
$603$	− 2.61732e34i	− 0.461201i
$604$	1.21092e35	2.09004
$605$	0	0
$606$	3.02315e34	0.500670
$607$	1.55450e33i	0.0252192i	0.999920	+	0.0126096i	$0.00401387\pi$
$607$	1.55450e33i	0.0252192i	−0.999920	+	0.0126096i	$0.995986\pi$
$608$	1.68718e34i	0.268143i
$609$	−5.38674e34	−0.838707
$610$	0	0
$611$	7.95080e32	0.0118822
$612$	3.35392e34i	0.491089i
$613$	1.25803e35i	1.80482i	0.430875	+	0.902412i	$0.358205\pi$
$613$	1.25803e35i	1.80482i	−0.430875	+	0.902412i	$0.641795\pi$
$614$	−1.22135e35	−1.71687
$615$	0	0
$616$	9.22306e34	1.24485
$617$	1.01184e35i	1.33828i	0.743136	+	0.669141i	$0.233338\pi$
$617$	1.01184e35i	1.33828i	−0.743136	+	0.669141i	$0.766662\pi$
$618$	7.38442e34i	0.957107i
$619$	7.24722e34	0.920531	0.460265	−	0.887781i	$-0.347754\pi$
$619$	7.24722e34	0.920531	0.460265	+	0.887781i	$0.347754\pi$
$620$	0	0
$621$	−6.34054e33	−0.0773537
$622$	− 9.10252e34i	− 1.08838i
$623$	− 4.22344e34i	− 0.494955i
$624$	9.69312e34	1.11341
$625$	0	0
$626$	−8.77062e34	−0.967946
$627$	7.89053e32i	0.00853615i
$628$	1.98419e35i	2.10421i
$629$	−2.59997e34	−0.270293
$630$	0	0
$631$	3.67312e34	0.367002	0.183501	−	0.983020i	$-0.441257\pi$
$631$	3.67312e34	0.367002	0.183501	+	0.983020i	$0.441257\pi$
$632$	5.18334e35i	5.07746i
$633$	2.63854e34i	0.253406i
$634$	−2.91300e35	−2.74300
$635$	0	0
$636$	−1.66273e35	−1.50524
$637$	− 2.34750e35i	− 2.08383i
$638$	− 4.40964e34i	− 0.383835i
$639$	−2.49491e34	−0.212958
$640$	0	0
$641$	4.16518e34	0.341907	0.170954	−	0.985279i	$-0.445315\pi$
$641$	4.16518e34	0.341907	0.170954	+	0.985279i	$0.445315\pi$
$642$	1.43059e35i	1.15167i
$643$	− 1.03651e35i	− 0.818343i	−0.912458	−	0.409171i	$-0.865818\pi$
$643$	− 1.03651e35i	− 0.818343i	0.912458	−	0.409171i	$-0.134182\pi$
$644$	6.16494e34	0.477370
$645$	0	0
$646$	5.37978e33	0.0400736
$647$	1.50099e35i	1.09667i	0.836260	+	0.548333i	$0.184737\pi$
$647$	1.50099e35i	1.09667i	−0.836260	+	0.548333i	$0.815263\pi$
$648$	− 1.80257e35i	− 1.29183i
$649$	1.85809e34	0.130620
$650$	0	0
$651$	1.20980e35	0.818373
$652$	4.22213e35i	2.80180i
$653$	− 2.54834e35i	− 1.65898i	−0.558519	−	0.829492i	$-0.688630\pi$
$653$	− 2.54834e35i	− 1.65898i	0.558519	−	0.829492i	$-0.311370\pi$
$654$	−2.76208e34	−0.176406
$655$	0	0
$656$	7.85663e35	4.82990
$657$	− 1.85771e35i	− 1.12050i
$658$	− 9.60006e33i	− 0.0568133i
$659$	2.97012e34	0.172467	0.0862337	−	0.996275i	$-0.472517\pi$
$659$	2.97012e34	0.172467	0.0862337	+	0.996275i	$0.472517\pi$
$660$	0	0
$661$	−1.44950e35	−0.810399	−0.405200	−	0.914228i	$-0.632798\pi$
$661$	−1.44950e35	−0.810399	−0.405200	+	0.914228i	$0.632798\pi$
$662$	− 1.71075e35i	− 0.938560i
$663$	− 1.53529e34i	− 0.0826556i
$664$	2.63376e35	1.39147
$665$	0	0
$666$	3.37376e35	1.71667
$667$	− 1.81762e34i	− 0.0907676i
$668$	8.93122e35i	4.37729i
$669$	1.63711e34	0.0787500
$670$	0	0
$671$	2.39411e34	0.110946
$672$	− 5.81368e35i	− 2.64445i
$673$	− 3.33613e35i	− 1.48955i	−0.667317	−	0.744774i	$-0.732557\pi$
$673$	− 3.33613e35i	− 1.48955i	0.667317	−	0.744774i	$-0.267443\pi$
$674$	5.52720e34	0.242246
$675$	0	0
$676$	−2.55019e35	−1.07706
$677$	2.77900e35i	1.15221i	0.817377	+	0.576103i	$0.195427\pi$
$677$	2.77900e35i	1.15221i	−0.817377	+	0.576103i	$0.804573\pi$
$678$	1.47225e35i	0.599253i
$679$	−6.94549e35	−2.77543
$680$	0	0
$681$	−1.30063e35	−0.500972
$682$	9.90354e34i	0.374529i
$683$	− 4.15368e35i	− 1.54232i	−0.636643	−	0.771159i	$-0.719677\pi$
$683$	− 4.15368e35i	− 1.54232i	0.636643	−	0.771159i	$-0.280323\pi$
$684$	−5.04641e34	−0.183984
$685$	0	0
$686$	−1.79221e36	−6.29994
$687$	1.42025e35i	0.490236i
$688$	− 2.46523e35i	− 0.835608i
$689$	−2.92192e35	−0.972586
$690$	0	0
$691$	4.18833e35	1.34451	0.672256	−	0.740318i	$-0.265325\pi$
$691$	4.18833e35	1.34451	0.672256	+	0.740318i	$0.265325\pi$
$692$	− 8.33931e35i	− 2.62908i
$693$	1.04377e35i	0.323177i
$694$	1.13507e36	3.45167
$695$	0	0
$696$	−4.53019e35	−1.32893
$697$	− 1.24441e35i	− 0.358554i
$698$	8.92079e35i	2.52470i
$699$	−2.58858e35	−0.719609
$700$	0	0
$701$	3.15026e35	0.845029	0.422515	−	0.906356i	$-0.361147\pi$
$701$	3.15026e35	0.845029	0.422515	+	0.906356i	$0.361147\pi$
$702$	4.50339e35i	1.18666i
$703$	− 3.91199e34i	− 0.101264i
$704$	2.10417e35	0.535086
$705$	0	0
$706$	−6.34673e35	−1.55773
$707$	− 4.63705e35i	− 1.11815i
$708$	− 3.09552e35i	− 0.733360i
$709$	2.19302e35	0.510464	0.255232	−	0.966880i	$-0.417848\pi$
$709$	2.19302e35	0.510464	0.255232	+	0.966880i	$0.417848\pi$
$710$	0	0
$711$	−5.86598e35	−1.31817
$712$	− 3.55186e35i	− 0.784254i
$713$	4.08217e34i	0.0885670i
$714$	−1.85376e35	−0.395209
$715$	0	0
$716$	2.01198e36	4.14201
$717$	2.59970e35i	0.525937i
$718$	− 1.59084e35i	− 0.316279i
$719$	5.84662e35	1.14234	0.571168	−	0.820833i	$-0.306490\pi$
$719$	5.84662e35	1.14234	0.571168	+	0.820833i	$0.306490\pi$
$720$	0	0
$721$	1.13266e36	2.13751
$722$	− 1.01611e36i	− 1.88463i
$723$	1.20020e35i	0.218788i
$724$	1.93327e35	0.346386
$725$	0	0
$726$	−4.76634e35	−0.825045
$727$	− 6.80932e35i	− 1.15857i	−0.815124	−	0.579287i	$-0.803331\pi$
$727$	− 6.80932e35i	− 1.15857i	0.815124	−	0.579287i	$-0.196669\pi$
$728$	− 2.70016e36i	− 4.51593i
$729$	−2.14318e34	−0.0352343
$730$	0	0
$731$	−3.90469e34	−0.0620324
$732$	− 3.98851e35i	− 0.622906i
$733$	− 7.38126e35i	− 1.13326i	−0.823971	−	0.566632i	$-0.808246\pi$
$733$	− 7.38126e35i	− 1.13326i	0.823971	−	0.566632i	$-0.191754\pi$
$734$	−1.07678e36	−1.62528
$735$	0	0
$736$	1.96168e35	0.286191
$737$	8.56064e34i	0.122790i
$738$	1.61477e36i	2.27722i
$739$	−8.56912e35	−1.18818	−0.594088	−	0.804400i	$-0.702487\pi$
$739$	−8.56912e35	−1.18818	−0.594088	+	0.804400i	$0.702487\pi$
$740$	0	0
$741$	2.31004e34	0.0309665
$742$	3.52802e36i	4.65032i
$743$	5.38846e35i	0.698401i	0.937048	+	0.349201i	$0.113547\pi$
$743$	5.38846e35i	0.698401i	−0.937048	+	0.349201i	$0.886453\pi$
$744$	1.01743e36	1.29671
$745$	0	0
$746$	−6.16877e35	−0.760262
$747$	2.98062e35i	0.361242i
$748$	− 1.09699e35i	− 0.130747i
$749$	2.19430e36	2.57202
$750$	0	0
$751$	1.45167e35	0.164577	0.0822883	−	0.996609i	$-0.473777\pi$
$751$	1.45167e35	0.164577	0.0822883	+	0.996609i	$0.473777\pi$
$752$	− 4.44550e34i	− 0.0495676i
$753$	3.94748e35i	0.432895i
$754$	−1.29097e36	−1.39244
$755$	0	0
$756$	3.93074e36	4.10159
$757$	8.93687e35i	0.917248i	0.888630	+	0.458624i	$0.151658\pi$
$757$	8.93687e35i	0.917248i	−0.888630	+	0.458624i	$0.848342\pi$
$758$	2.25752e36i	2.27912i
$759$	9.17431e33	0.00911069
$760$	0	0
$761$	−1.00712e36	−0.967776	−0.483888	−	0.875130i	$-0.660776\pi$
$761$	−1.00712e36	−0.967776	−0.483888	+	0.875130i	$0.660776\pi$
$762$	− 1.43396e36i	− 1.35551i
$763$	4.23660e35i	0.393968i
$764$	1.46703e36	1.34206
$765$	0	0
$766$	−1.29588e36	−1.14737
$767$	− 5.43978e35i	− 0.473848i
$768$	− 4.66160e35i	− 0.399502i
$769$	1.58710e36	1.33822	0.669108	−	0.743165i	$-0.266676\pi$
$769$	1.58710e36	1.33822	0.669108	+	0.743165i	$0.266676\pi$
$770$	0	0
$771$	4.08803e35	0.333684
$772$	2.54192e36i	2.04148i
$773$	− 2.56502e35i	− 0.202697i	−0.994851	−	0.101349i	$-0.967684\pi$
$773$	− 2.56502e35i	− 0.202697i	0.994851	−	0.101349i	$-0.0323157\pi$
$774$	5.06678e35	0.393976
$775$	0	0
$776$	−5.84107e36	−4.39766
$777$	1.34799e36i	0.998676i
$778$	1.99218e35i	0.145239i
$779$	1.87237e35	0.134330
$780$	0	0
$781$	8.16029e34	0.0566980
$782$	− 6.25507e34i	− 0.0427708i
$783$	− 1.15891e36i	− 0.779879i
$784$	−1.31255e37	−8.69292
$785$	0	0
$786$	3.42066e35	0.219446
$787$	− 3.06819e36i	− 1.93731i	−0.248418	−	0.968653i	$-0.579911\pi$
$787$	− 3.06819e36i	− 1.93731i	0.248418	−	0.968653i	$-0.420089\pi$
$788$	7.82872e35i	0.486534i
$789$	−6.54304e35	−0.400237
$790$	0	0
$791$	2.25821e36	1.33831
$792$	8.77800e35i	0.512072i
$793$	− 7.00904e35i	− 0.402479i
$794$	2.90740e36	1.64342
$795$	0	0
$796$	−1.70205e35	−0.0932307
$797$	− 2.63790e36i	− 1.42243i	−0.702976	−	0.711214i	$-0.748146\pi$
$797$	− 2.63790e36i	− 1.42243i	0.702976	−	0.711214i	$-0.251854\pi$
$798$	− 2.78922e35i	− 0.148063i
$799$	−7.04123e33	−0.00367971
$800$	0	0
$801$	4.01964e35	0.203601
$802$	− 6.44353e36i	− 3.21325i
$803$	6.07614e35i	0.298321i
$804$	1.42617e36	0.689401
$805$	0	0
$806$	2.89938e36	1.35868
$807$	5.12786e35i	0.236601i
$808$	− 3.89970e36i	− 1.77170i
$809$	−1.49529e36	−0.668914	−0.334457	−	0.942411i	$-0.608553\pi$
$809$	−1.49529e36	−0.668914	−0.334457	+	0.942411i	$0.608553\pi$
$810$	0	0
$811$	−3.69909e36	−1.60448	−0.802240	−	0.597001i	$-0.796359\pi$
$811$	−3.69909e36	−1.60448	−0.802240	+	0.597001i	$0.796359\pi$
$812$	1.12681e37i	4.81284i
$813$	1.79961e36i	0.756912i
$814$	−1.10348e36	−0.457045
$815$	0	0
$816$	−8.58424e35	−0.344806
$817$	− 5.87510e34i	− 0.0232402i
$818$	1.59595e36i	0.621732i
$819$	3.05576e36	1.17239
$820$	0	0
$821$	4.34580e36	1.61726	0.808630	−	0.588318i	$-0.200210\pi$
$821$	4.34580e36	1.61726	0.808630	+	0.588318i	$0.200210\pi$
$822$	2.75147e36i	1.00848i
$823$	2.75082e36i	0.993034i	0.868027	+	0.496517i	$0.165388\pi$
$823$	2.75082e36i	0.993034i	−0.868027	+	0.496517i	$0.834612\pi$
$824$	9.52552e36	3.38687
$825$	0	0
$826$	−6.56817e36	−2.26565
$827$	2.52838e35i	0.0859062i	0.999077	+	0.0429531i	$0.0136766\pi$
$827$	2.52838e35i	0.0859062i	−0.999077	+	0.0429531i	$0.986323\pi$
$828$	5.86745e35i	0.196368i
$829$	−2.36903e36	−0.780978	−0.390489	−	0.920608i	$-0.627694\pi$
$829$	−2.36903e36	−0.780978	−0.390489	+	0.920608i	$0.627694\pi$
$830$	0	0
$831$	1.06070e36	0.339298
$832$	− 6.16022e36i	− 1.94113i
$833$	2.07895e36i	0.645330i
$834$	−3.07109e36	−0.939111
$835$	0	0
$836$	1.65056e35	0.0489839
$837$	2.60278e36i	0.760972i
$838$	− 1.05401e37i	− 3.03596i
$839$	−3.84035e36	−1.08980	−0.544900	−	0.838501i	$-0.683432\pi$
$839$	−3.84035e36	−1.08980	−0.544900	+	0.838501i	$0.683432\pi$
$840$	0	0
$841$	−3.08152e35	−0.0848818
$842$	− 6.65799e36i	− 1.80693i
$843$	− 2.59793e36i	− 0.694678i
$844$	5.51936e36	1.45415
$845$	0	0
$846$	9.13681e34	0.0233703
$847$	7.31085e36i	1.84257i
$848$	1.63372e37i	4.05724i
$849$	2.25426e36	0.551644
$850$	0	0
$851$	−4.54846e35	−0.108080
$852$	− 1.35948e36i	− 0.318330i
$853$	5.50445e36i	1.27014i	0.772455	+	0.635070i	$0.219029\pi$
$853$	5.50445e36i	1.27014i	−0.772455	+	0.635070i	$0.780971\pi$
$854$	−8.46295e36	−1.92441
$855$	0	0
$856$	1.84538e37	4.07535
$857$	− 1.64592e36i	− 0.358219i	−0.983829	−	0.179109i	$-0.942678\pi$
$857$	− 1.64592e36i	− 0.358219i	0.983829	−	0.179109i	$-0.0573216\pi$
$858$	− 6.51609e35i	− 0.139764i
$859$	9.07912e36	1.91924	0.959619	−	0.281301i	$-0.0907661\pi$
$859$	9.07912e36	1.91924	0.959619	+	0.281301i	$0.0907661\pi$
$860$	0	0
$861$	−6.45182e36	−1.32478
$862$	1.53014e36i	0.309664i
$863$	− 3.86548e36i	− 0.771025i	−0.922703	−	0.385512i	$-0.874025\pi$
$863$	− 3.86548e36i	− 0.771025i	0.922703	−	0.385512i	$-0.125975\pi$
$864$	1.25076e37	2.45897
$865$	0	0
$866$	9.13207e36	1.74420
$867$	− 2.27874e36i	− 0.428999i
$868$	− 2.53069e37i	− 4.69616i
$869$	1.91863e36	0.350948
$870$	0	0
$871$	2.50623e36	0.445444
$872$	3.56294e36i	0.624241i
$873$	− 6.61033e36i	− 1.14168i
$874$	9.41155e34	0.0160239
$875$	0	0
$876$	1.01227e37	1.67492
$877$	− 3.82388e36i	− 0.623748i	−0.950123	−	0.311874i	$-0.899043\pi$
$877$	− 3.82388e36i	− 0.623748i	0.950123	−	0.311874i	$-0.100957\pi$
$878$	− 2.55488e36i	− 0.410855i
$879$	−2.35598e36	−0.373517
$880$	0	0
$881$	−1.18948e37	−1.83298	−0.916488	−	0.400061i	$-0.868989\pi$
$881$	−1.18948e37	−1.83298	−0.916488	+	0.400061i	$0.868989\pi$
$882$	− 2.69768e37i	− 4.09857i
$883$	2.26008e36i	0.338544i	0.985569	+	0.169272i	$0.0541416\pi$
$883$	2.26008e36i	0.338544i	−0.985569	+	0.169272i	$0.945858\pi$
$884$	−3.21157e36	−0.474312
$885$	0	0
$886$	−2.04829e37	−2.94083
$887$	9.18825e36i	1.30073i	0.759622	+	0.650365i	$0.225384\pi$
$887$	9.18825e36i	1.30073i	−0.759622	+	0.650365i	$0.774616\pi$
$888$	1.13365e37i	1.58240i
$889$	−2.19948e37	−3.02725
$890$	0	0
$891$	−6.67226e35	−0.0892897
$892$	− 3.42455e36i	− 0.451900i
$893$	− 1.05944e34i	− 0.00137859i
$894$	3.13029e36	0.401667
$895$	0	0
$896$	−2.77619e37	−3.46416
$897$	− 2.68589e35i	− 0.0330508i
$898$	− 1.18173e36i	− 0.143405i
$899$	−7.46130e36	−0.892932
$900$	0	0
$901$	2.58766e36	0.301194
$902$	− 5.28153e36i	− 0.606286i
$903$	2.02444e36i	0.229196i
$904$	1.89913e37	2.12055
$905$	0	0
$906$	−6.36999e36	−0.691889
$907$	9.71863e36i	1.04115i	0.853815	+	0.520576i	$0.174283\pi$
$907$	9.71863e36i	1.04115i	−0.853815	+	0.520576i	$0.825717\pi$
$908$	2.72069e37i	2.87478i
$909$	4.41329e36	0.459953
$910$	0	0
$911$	−1.55044e37	−1.57208	−0.786042	−	0.618173i	$-0.787873\pi$
$911$	−1.55044e37	−1.57208	−0.786042	+	0.618173i	$0.787873\pi$
$912$	− 1.29161e36i	− 0.129180i
$913$	− 9.74891e35i	− 0.0961770i
$914$	3.53783e35	0.0344278
$915$	0	0
$916$	2.97092e37	2.81318
$917$	− 5.24677e36i	− 0.490089i
$918$	− 3.98821e36i	− 0.367489i
$919$	−1.12812e36	−0.102545	−0.0512724	−	0.998685i	$-0.516328\pi$
$919$	−1.12812e36	−0.102545	−0.0512724	+	0.998685i	$0.516328\pi$
$920$	0	0
$921$	4.64445e36	0.410856
$922$	− 3.08159e35i	− 0.0268929i
$923$	− 2.38902e36i	− 0.205683i
$924$	−5.68750e36	−0.483083
$925$	0	0
$926$	6.31245e36	0.521868
$927$	1.07800e37i	0.879271i
$928$	3.58552e37i	2.88537i
$929$	−2.05674e37	−1.63299	−0.816496	−	0.577351i	$-0.804086\pi$
$929$	−2.05674e37	−1.63299	−0.816496	+	0.577351i	$0.804086\pi$
$930$	0	0
$931$	−3.12805e36	−0.241770
$932$	5.41486e37i	4.12941i
$933$	3.46143e36i	0.260456i
$934$	3.41557e36	0.253587
$935$	0	0
$936$	2.56986e37	1.85764
$937$	− 1.39662e37i	− 0.996173i	−0.867127	−	0.498086i	$-0.834036\pi$
$937$	− 1.39662e37i	− 0.996173i	0.867127	−	0.498086i	$-0.165964\pi$
$938$	− 3.02610e37i	− 2.12985i
$939$	3.33522e36	0.231635
$940$	0	0
$941$	−8.01115e36	−0.541782	−0.270891	−	0.962610i	$-0.587318\pi$
$941$	−8.01115e36	−0.541782	−0.270891	+	0.962610i	$0.587318\pi$
$942$	− 1.04377e37i	− 0.696578i
$943$	− 2.17701e36i	− 0.143372i
$944$	−3.04152e37	−1.97670
$945$	0	0
$946$	−1.65723e36	−0.104892
$947$	− 1.93560e37i	− 1.20904i	−0.796589	−	0.604522i	$-0.793364\pi$
$947$	− 1.93560e37i	− 1.20904i	0.796589	−	0.604522i	$-0.206636\pi$
$948$	− 3.19637e37i	− 1.97039i
$949$	1.77886e37	1.08222
$950$	0	0
$951$	1.10773e37	0.656414
$952$	2.39126e37i	1.39851i
$953$	− 2.25154e37i	− 1.29963i	−0.760094	−	0.649813i	$-0.774847\pi$
$953$	− 2.25154e37i	− 1.29963i	0.760094	−	0.649813i	$-0.225153\pi$
$954$	−3.35778e37	−1.91292
$955$	0	0
$956$	5.43812e37	3.01804
$957$	1.67686e36i	0.0918539i
$958$	− 4.97366e37i	− 2.68910i
$959$	4.22034e37	2.25224
$960$	0	0
$961$	−2.47559e36	−0.128717
$962$	3.23057e37i	1.65802i
$963$	2.08842e37i	1.05801i
$964$	2.51060e37	1.25549
$965$	0	0
$966$	−3.24303e36	−0.158029
$967$	− 1.09124e37i	− 0.524915i	−0.964944	−	0.262458i	$-0.915467\pi$
$967$	− 1.09124e37i	− 0.524915i	0.964944	−	0.262458i	$-0.0845330\pi$
$968$	6.14834e37i	2.91955i
$969$	−2.04578e35	−0.00958983
$970$	0	0
$971$	−9.90246e36	−0.452379	−0.226190	−	0.974083i	$-0.572627\pi$
$971$	−9.90246e36	−0.452379	−0.226190	+	0.974083i	$0.572627\pi$
$972$	5.82715e37i	2.62801i
$973$	4.71058e37i	2.09732i
$974$	1.09246e37	0.480195
$975$	0	0
$976$	−3.91894e37	−1.67898
$977$	2.53501e37i	1.07225i	0.844137	+	0.536127i	$0.180113\pi$
$977$	2.53501e37i	1.07225i	−0.844137	+	0.536127i	$0.819887\pi$
$978$	− 2.22103e37i	− 0.927509i
$979$	−1.31473e36	−0.0542067
$980$	0	0
$981$	−4.03217e36	−0.162060
$982$	− 3.24347e37i	− 1.28711i
$983$	3.23058e37i	1.26579i	0.774238	+	0.632894i	$0.218133\pi$
$983$	3.23058e37i	1.26579i	−0.774238	+	0.632894i	$0.781867\pi$
$984$	−5.42591e37	−2.09910
$985$	0	0
$986$	1.14329e37	0.431215
$987$	3.65063e35i	0.0135957i
$988$	− 4.83221e36i	− 0.177699i
$989$	−6.83097e35	−0.0248044
$990$	0	0
$991$	1.28289e37	0.454223	0.227111	−	0.973869i	$-0.427072\pi$
$991$	1.28289e37	0.454223	0.227111	+	0.973869i	$0.427072\pi$
$992$	− 8.05266e37i	− 2.81542i
$993$	6.50550e36i	0.224603i
$994$	−2.88458e37	−0.983451
$995$	0	0
$996$	−1.62414e37	−0.539984
$997$	1.23049e37i	0.404006i	0.979385	+	0.202003i	$0.0647451\pi$
$997$	1.23049e37i	0.404006i	−0.979385	+	0.202003i	$0.935255\pi$
$998$	3.29680e37i	1.06896i
$999$	−2.90008e37	−0.928628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.26.b.c.24.10		10
5.2	odd	4		5.26.a.b.1.1	✓	5
5.3	odd	4		25.26.a.c.1.5		5
5.4	even	2	inner	25.26.b.c.24.1		10
15.2	even	4		45.26.a.f.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.b.1.1	✓	5	5.2	odd	4
25.26.a.c.1.5		5	5.3	odd	4
25.26.b.c.24.1		10	5.4	even	2	inner
25.26.b.c.24.10		10	1.1	even	1	trivial
45.26.a.f.1.5		5	15.2	even	4

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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+11003.9i q^{2} -418448. i q^{3} -8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10i q^{7} -5.93966e11i q^{8} +6.72190e11 q^{9} +O(q^{10})\)	\(q+11003.9i q^{2} -418448. i q^{3} -8.75320e7 q^{4} +4.60457e9 q^{6} -7.06271e10i q^{7} -5.93966e11i q^{8} +6.72190e11 q^{9} -2.19858e12 q^{11} +3.66276e13i q^{12} +6.43659e13i q^{13} +7.77176e14 q^{14} +3.59887e15 q^{16} -5.70025e14i q^{17} +7.39673e15i q^{18} +8.57675e14 q^{19} -2.95538e16 q^{21} -2.41930e16i q^{22} -9.97218e15i q^{23} -2.48544e17 q^{24} -7.08278e17 q^{26} -6.35823e17i q^{27} +6.18214e18i q^{28} +1.82269e18 q^{29} -4.09356e18 q^{31} +1.96715e19i q^{32} +9.19990e17i q^{33} +6.27252e18 q^{34} -5.88382e19 q^{36} -4.56115e19i q^{37} +9.43780e18i q^{38} +2.69338e19 q^{39} +2.18308e20 q^{41} -3.25207e20i q^{42} -6.85002e19i q^{43} +1.92446e20 q^{44} +1.09733e20 q^{46} -1.23525e19i q^{47} -1.50594e21i q^{48} -3.64712e21 q^{49} -2.38526e20 q^{51} -5.63408e21i q^{52} +4.53955e21i q^{53} +6.99655e21 q^{54} -4.19501e22 q^{56} -3.58892e20i q^{57} +2.00568e22i q^{58} -8.45133e21 q^{59} -1.08894e22 q^{61} -4.50452e22i q^{62} -4.74748e22i q^{63} -9.57062e22 q^{64} -1.01235e22 q^{66} -3.89372e22i q^{67} +4.98955e22i q^{68} -4.17284e21 q^{69} -3.71162e22 q^{71} -3.99258e23i q^{72} -2.76367e23i q^{73} +5.01906e23 q^{74} -7.50741e22 q^{76} +1.55279e23i q^{77} +2.96378e23i q^{78} -8.72667e23 q^{79} +3.03480e23 q^{81} +2.40225e24i q^{82} +4.43419e23i q^{83} +2.58690e24 q^{84} +7.53772e23 q^{86} -7.62702e23i q^{87} +1.30588e24i q^{88} +5.97991e23 q^{89} +4.54598e24 q^{91} +8.72886e23i q^{92} +1.71294e24i q^{93} +1.35926e23 q^{94} +8.23151e24 q^{96} -9.83402e24i q^{97} -4.01327e25i q^{98} -1.47786e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 182100520 q^{4} + 11393149520 q^{6} - 555993692930 q^{9}+O(q^{10}) \) 10 * q - 182100520 * q^4 + 11393149520 * q^6 - 555993692930 * q^9	\( 10 q - 182100520 q^{4} + 11393149520 q^{6} - 555993692930 q^{9} - 8289916903080 q^{11} + 891133307021760 q^{14} + 60\!\cdots\!60 q^{16}+ \cdots + 45\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 182100520 * q^4 + 11393149520 * q^6 - 555993692930 * q^9 - 8289916903080 * q^11 + 891133307021760 * q^14 + 6089976035260960 * q^16 - 26946376100390600 * q^19 + 153536191152121920 * q^21 - 1476466505472763200 * q^24 + 663464770878308520 * q^26 - 3021036492115464300 * q^29 - 15601581800953125280 * q^31 + 61934328372191765160 * q^34 - 255633494420041954040 * q^36 + 57026310922020243440 * q^39 + 536365426849982693220 * q^41 - 2053686541960406319840 * q^44 + 3612523521723723462720 * q^46 - 5857016804172155813370 * q^49 - 3359895558029927268880 * q^51 + 32268854676621495090400 * q^54 - 78830910223583237404800 * q^56 + 33094407067760080842600 * q^59 + 23174537108178497679020 * q^61 - 167963646340179319304320 * q^64 + 215372491198081115515840 * q^66 - 410207702498006419143360 * q^69 + 359270258356833457889520 * q^71 + 1777344398251660471679160 * q^74 - 2383599721540520876485600 * q^76 - 720565698511703983868000 * q^79 + 207169016893179802937210 * q^81 + 7675763190633230335330560 * q^84 - 1131684772842662195488080 * q^86 - 8184257338291963026048900 * q^89 + 23945146562217442521934720 * q^91 + 34225484666245805864609760 * q^94 - 20752772325535553602906880 * q^96 + 45729238049768666352546440 * q^99

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