LMFDB - Embedded newform 25.10.b.b.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,10,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, 10, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$12.8758959041$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{1009})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 505x^{2} + 63504 $ x^4 + 505*x^2 + 63504
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-16.3824i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.10.b.b.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-36.7648i q^{2} -193.530i q^{3} -839.648 q^{4} -7115.07 q^{6} +7647.66i q^{7} +12045.9i q^{8} -17770.7 q^{9} +O(q^{10})$	\(q-36.7648i q^{2} -193.530i q^{3} -839.648 q^{4} -7115.07 q^{6} +7647.66i q^{7} +12045.9i q^{8} -17770.7 q^{9} -48361.0 q^{11} +162497. i q^{12} -100456. i q^{13} +281164. q^{14} +12964.5 q^{16} -201958. i q^{17} +653335. i q^{18} +58048.1 q^{19} +1.48005e6 q^{21} +1.77798e6i q^{22} +1.14078e6i q^{23} +2.33123e6 q^{24} -3.69324e6 q^{26} -370091. i q^{27} -6.42134e6i q^{28} -1.56407e6 q^{29} -4.10744e6 q^{31} +5.69086e6i q^{32} +9.35929e6i q^{33} -7.42493e6 q^{34} +1.49211e7 q^{36} -1.70821e7i q^{37} -2.13412e6i q^{38} -1.94412e7 q^{39} -8.52969e6 q^{41} -5.44136e7i q^{42} -2.56254e7i q^{43} +4.06062e7 q^{44} +4.19406e7 q^{46} +4.58297e7i q^{47} -2.50902e6i q^{48} -1.81331e7 q^{49} -3.90848e7 q^{51} +8.43476e7i q^{52} +5.56483e7i q^{53} -1.36063e7 q^{54} -9.21228e7 q^{56} -1.12340e7i q^{57} +5.75026e7i q^{58} -2.15699e7 q^{59} -1.15309e8 q^{61} +1.51009e8i q^{62} -1.35904e8i q^{63} +2.15861e8 q^{64} +3.44092e8 q^{66} -7.69254e7i q^{67} +1.69573e8i q^{68} +2.20775e8 q^{69} +1.95870e8 q^{71} -2.14064e8i q^{72} -3.40942e8i q^{73} -6.28021e8 q^{74} -4.87399e7 q^{76} -3.69849e8i q^{77} +7.14751e8i q^{78} +5.92965e8 q^{79} -4.21404e8 q^{81} +3.13592e8i q^{82} -7.88477e8i q^{83} -1.24272e9 q^{84} -9.42111e8 q^{86} +3.02693e8i q^{87} -5.82552e8i q^{88} -8.40110e8 q^{89} +7.68253e8 q^{91} -9.57856e8i q^{92} +7.94910e8i q^{93} +1.68492e9 q^{94} +1.10135e9 q^{96} +2.35903e8i q^{97} +6.66658e8i q^{98} +8.59408e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2088 q^{4} - 10672 q^{6} - 5012 q^{9}+O(q^{10}) $ 4 * q - 2088 * q^4 - 10672 * q^6 - 5012 * q^9	$ 4 q - 2088 q^{4} - 10672 q^{6} - 5012 q^{9} + 47968 q^{11} + 880704 q^{14} - 624096 q^{16} + 593040 q^{19} + 2169408 q^{21} + 5757120 q^{24} - 6606872 q^{26} + 7333960 q^{29} + 3226288 q^{31} - 47758616 q^{34} + 23603464 q^{36} - 40818544 q^{39} - 53914552 q^{41} + 51644704 q^{44} + 88782528 q^{46} - 26308228 q^{49} + 3559568 q^{51} + 97135840 q^{54} - 86298240 q^{56} + 109991120 q^{59} - 549159432 q^{61} + 338882432 q^{64} + 945597376 q^{66} + 429377856 q^{69} - 14261872 q^{71} - 1039794056 q^{74} - 194944480 q^{76} - 13755040 q^{79} - 550718716 q^{81} - 2323858176 q^{84} - 424776272 q^{86} - 1660177320 q^{89} + 1363261808 q^{91} + 2696297824 q^{94} + 1606720768 q^{96} + 3927464096 q^{99}+O(q^{100}) $ 4 * q - 2088 * q^4 - 10672 * q^6 - 5012 * q^9 + 47968 * q^11 + 880704 * q^14 - 624096 * q^16 + 593040 * q^19 + 2169408 * q^21 + 5757120 * q^24 - 6606872 * q^26 + 7333960 * q^29 + 3226288 * q^31 - 47758616 * q^34 + 23603464 * q^36 - 40818544 * q^39 - 53914552 * q^41 + 51644704 * q^44 + 88782528 * q^46 - 26308228 * q^49 + 3559568 * q^51 + 97135840 * q^54 - 86298240 * q^56 + 109991120 * q^59 - 549159432 * q^61 + 338882432 * q^64 + 945597376 * q^66 + 429377856 * q^69 - 14261872 * q^71 - 1039794056 * q^74 - 194944480 * q^76 - 13755040 * q^79 - 550718716 * q^81 - 2323858176 * q^84 - 424776272 * q^86 - 1660177320 * q^89 + 1363261808 * q^91 + 2696297824 * q^94 + 1606720768 * q^96 + 3927464096 * 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 $

$2$	− 36.7648i	− 1.62479i	−0.583109	−	0.812394i	$-0.698164\pi$
$2$	− 36.7648i	− 1.62479i	0.583109	−	0.812394i	$-0.301836\pi$
$3$	− 193.530i	− 1.37944i	−0.724078	−	0.689718i	$-0.757734\pi$
$3$	− 193.530i	− 1.37944i	0.724078	−	0.689718i	$-0.242266\pi$
$4$	−839.648	−1.63994
$5$	0	0
$5$	0	0
$6$	−7115.07	−2.24129
$7$	7647.66i	1.20389i	0.798537	+	0.601946i	$0.205608\pi$
$7$	7647.66i	1.20389i	−0.798537	+	0.601946i	$0.794392\pi$
$8$	12045.9i	1.03976i
$9$	−17770.7	−0.902844
$10$	0	0
$11$	−48361.0	−0.995929	−0.497965	−	0.867197i	$-0.665919\pi$
$11$	−48361.0	−0.995929	−0.497965	+	0.867197i	$0.665919\pi$
$12$	162497.i	2.26219i
$13$	− 100456.i	− 0.975507i	−0.872981	−	0.487754i	$-0.837816\pi$
$13$	− 100456.i	− 0.975507i	0.872981	−	0.487754i	$-0.162184\pi$
$14$	281164.	1.95607
$15$	0	0
$16$	12964.5	0.0494557
$17$	− 201958.i	− 0.586463i	−0.956042	−	0.293231i	$-0.905269\pi$
$17$	− 201958.i	− 0.586463i	0.956042	−	0.293231i	$-0.0947306\pi$
$18$	653335.i	1.46693i
$19$	58048.1	0.102187	0.0510936	−	0.998694i	$-0.483729\pi$
$19$	58048.1	0.102187	0.0510936	+	0.998694i	$0.483729\pi$
$20$	0	0
$21$	1.48005e6	1.66069
$22$	1.77798e6i	1.61817i
$23$	1.14078e6i	0.850017i	0.905189	+	0.425009i	$0.139729\pi$
$23$	1.14078e6i	0.850017i	−0.905189	+	0.425009i	$0.860271\pi$
$24$	2.33123e6	1.43428
$25$	0	0
$26$	−3.69324e6	−1.58499
$27$	− 370091.i	− 0.134021i
$28$	− 6.42134e6i	− 1.97431i
$29$	−1.56407e6	−0.410643	−0.205322	−	0.978695i	$-0.565824\pi$
$29$	−1.56407e6	−0.410643	−0.205322	+	0.978695i	$0.565824\pi$
$30$	0	0
$31$	−4.10744e6	−0.798810	−0.399405	−	0.916775i	$-0.630783\pi$
$31$	−4.10744e6	−0.798810	−0.399405	+	0.916775i	$0.630783\pi$
$32$	5.69086e6i	0.959407i
$33$	9.35929e6i	1.37382i
$34$	−7.42493e6	−0.952878
$35$	0	0
$36$	1.49211e7	1.48061
$37$	− 1.70821e7i	− 1.49842i	−0.662330	−	0.749212i	$-0.730432\pi$
$37$	− 1.70821e7i	− 1.49842i	0.662330	−	0.749212i	$-0.269568\pi$
$38$	− 2.13412e6i	− 0.166033i
$39$	−1.94412e7	−1.34565
$40$	0	0
$41$	−8.52969e6	−0.471418	−0.235709	−	0.971824i	$-0.575741\pi$
$41$	−8.52969e6	−0.471418	−0.235709	+	0.971824i	$0.575741\pi$
$42$	− 5.44136e7i	− 2.69827i
$43$	− 2.56254e7i	− 1.14304i	−0.820587	−	0.571521i	$-0.806354\pi$
$43$	− 2.56254e7i	− 1.14304i	0.820587	−	0.571521i	$-0.193646\pi$
$44$	4.06062e7	1.63326
$45$	0	0
$46$	4.19406e7	1.38110
$47$	4.58297e7i	1.36996i	0.728564	+	0.684978i	$0.240188\pi$
$47$	4.58297e7i	1.36996i	−0.728564	+	0.684978i	$0.759812\pi$
$48$	− 2.50902e6i	− 0.0682210i
$49$	−1.81331e7	−0.449355
$50$	0	0
$51$	−3.90848e7	−0.808988
$52$	8.43476e7i	1.59977i
$53$	5.56483e7i	0.968748i	0.874861	+	0.484374i	$0.160953\pi$
$53$	5.56483e7i	0.968748i	−0.874861	+	0.484374i	$0.839047\pi$
$54$	−1.36063e7	−0.217755
$55$	0	0
$56$	−9.21228e7	−1.25176
$57$	− 1.12340e7i	− 0.140961i
$58$	5.75026e7i	0.667209i
$59$	−2.15699e7	−0.231747	−0.115873	−	0.993264i	$-0.536967\pi$
$59$	−2.15699e7	−0.231747	−0.115873	+	0.993264i	$0.536967\pi$
$60$	0	0
$61$	−1.15309e8	−1.06630	−0.533148	−	0.846022i	$-0.678991\pi$
$61$	−1.15309e8	−1.06630	−0.533148	+	0.846022i	$0.678991\pi$
$62$	1.51009e8i	1.29790i
$63$	− 1.35904e8i	− 1.08693i
$64$	2.15861e8	1.60829
$65$	0	0
$66$	3.44092e8	2.23217
$67$	− 7.69254e7i	− 0.466373i	−0.972432	−	0.233186i	$-0.925085\pi$
$67$	− 7.69254e7i	− 0.466373i	0.972432	−	0.233186i	$-0.0749152\pi$
$68$	1.69573e8i	0.961762i
$69$	2.20775e8	1.17254
$70$	0	0
$71$	1.95870e8	0.914754	0.457377	−	0.889273i	$-0.348789\pi$
$71$	1.95870e8	0.914754	0.457377	+	0.889273i	$0.348789\pi$
$72$	− 2.14064e8i	− 0.938742i
$73$	− 3.40942e8i	− 1.40517i	−0.711601	−	0.702583i	$-0.752030\pi$
$73$	− 3.40942e8i	− 1.40517i	0.711601	−	0.702583i	$-0.247970\pi$
$74$	−6.28021e8	−2.43462
$75$	0	0
$76$	−4.87399e7	−0.167581
$77$	− 3.69849e8i	− 1.19899i
$78$	7.14751e8i	2.18640i
$79$	5.92965e8	1.71280	0.856401	−	0.516311i	$-0.172695\pi$
$79$	5.92965e8	1.71280	0.856401	+	0.516311i	$0.172695\pi$
$80$	0	0
$81$	−4.21404e8	−1.08772
$82$	3.13592e8i	0.765954i
$83$	− 7.88477e8i	− 1.82363i	−0.410598	−	0.911817i	$-0.634680\pi$
$83$	− 7.88477e8i	− 1.82363i	0.410598	−	0.911817i	$-0.365320\pi$
$84$	−1.24272e9	−2.72343
$85$	0	0
$86$	−9.42111e8	−1.85720
$87$	3.02693e8i	0.566456i
$88$	− 5.82552e8i	− 1.03553i
$89$	−8.40110e8	−1.41932	−0.709661	−	0.704543i	$-0.751152\pi$
$89$	−8.40110e8	−1.41932	−0.709661	+	0.704543i	$0.751152\pi$
$90$	0	0
$91$	7.68253e8	1.17441
$92$	− 9.57856e8i	− 1.39397i
$93$	7.94910e8i	1.10191i
$94$	1.68492e9	2.22589
$95$	0	0
$96$	1.10135e9	1.32344
$97$	2.35903e8i	0.270558i	0.990808	+	0.135279i	$0.0431931\pi$
$97$	2.35903e8i	0.270558i	−0.990808	+	0.135279i	$0.956807\pi$
$98$	6.66658e8i	0.730106i
$99$	8.59408e8	0.899169
$100$	0	0
$101$	−6.52957e8	−0.624365	−0.312182	−	0.950022i	$-0.601060\pi$
$101$	−6.52957e8	−0.624365	−0.312182	+	0.950022i	$0.601060\pi$
$102$	1.43694e9i	1.31443i
$103$	− 9.53214e8i	− 0.834493i	−0.908793	−	0.417247i	$-0.862995\pi$
$103$	− 9.53214e8i	− 0.834493i	0.908793	−	0.417247i	$-0.137005\pi$
$104$	1.21008e9	1.01430
$105$	0	0
$106$	2.04590e9	1.57401
$107$	− 1.33363e9i	− 0.983573i	−0.870716	−	0.491787i	$-0.836344\pi$
$107$	− 1.33363e9i	− 0.983573i	0.870716	−	0.491787i	$-0.163656\pi$
$108$	3.10746e8i	0.219785i
$109$	−1.93368e9	−1.31210	−0.656049	−	0.754718i	$-0.727774\pi$
$109$	−1.93368e9	−1.31210	−0.656049	+	0.754718i	$0.727774\pi$
$110$	0	0
$111$	−3.30590e9	−2.06698
$112$	9.91483e7i	0.0595393i
$113$	9.74289e8i	0.562128i	0.959689	+	0.281064i	$0.0906873\pi$
$113$	9.74289e8i	0.562128i	−0.959689	+	0.281064i	$0.909313\pi$
$114$	−4.13016e8	−0.229031
$115$	0	0
$116$	1.31327e9	0.673429
$117$	1.78517e9i	0.880731i
$118$	7.93011e8i	0.376539i
$119$	1.54450e9	0.706037
$120$	0	0
$121$	−1.91571e7	−0.00812446
$122$	4.23929e9i	1.73250i
$123$	1.65075e9i	0.650290i
$124$	3.44880e9	1.31000
$125$	0	0
$126$	−4.99648e9	−1.76602
$127$	1.25137e9i	0.426845i	0.976960	+	0.213422i	$0.0684611\pi$
$127$	1.25137e9i	0.426845i	−0.976960	+	0.213422i	$0.931539\pi$
$128$	− 5.02235e9i	− 1.65372i
$129$	−4.95927e9	−1.57675
$130$	0	0
$131$	2.23060e9	0.661760	0.330880	−	0.943673i	$-0.392655\pi$
$131$	2.23060e9	0.661760	0.330880	+	0.943673i	$0.392655\pi$
$132$	− 7.85851e9i	− 2.25298i
$133$	4.43932e8i	0.123022i
$134$	−2.82814e9	−0.757757
$135$	0	0
$136$	2.43276e9	0.609781
$137$	− 3.91202e9i	− 0.948764i	−0.880319	−	0.474382i	$-0.842672\pi$
$137$	− 3.91202e9i	− 0.948764i	0.880319	−	0.474382i	$-0.157328\pi$
$138$	− 8.11675e9i	− 1.90514i
$139$	−1.64295e9	−0.373299	−0.186649	−	0.982427i	$-0.559763\pi$
$139$	−1.64295e9	−0.373299	−0.186649	+	0.982427i	$0.559763\pi$
$140$	0	0
$141$	8.86939e9	1.88977
$142$	− 7.20110e9i	− 1.48628i
$143$	4.85815e9i	0.971537i
$144$	−2.30388e8	−0.0446508
$145$	0	0
$146$	−1.25347e10	−2.28310
$147$	3.50929e9i	0.619856i
$148$	1.43430e10i	2.45732i
$149$	6.33624e9	1.05316	0.526579	−	0.850126i	$-0.323475\pi$
$149$	6.33624e9	1.05316	0.526579	+	0.850126i	$0.323475\pi$
$150$	0	0
$151$	5.67989e9	0.889086	0.444543	−	0.895757i	$-0.353366\pi$
$151$	5.67989e9	0.889086	0.444543	+	0.895757i	$0.353366\pi$
$152$	6.99241e8i	0.106250i
$153$	3.58893e9i	0.529484i
$154$	−1.35974e10	−1.94811
$155$	0	0
$156$	1.63238e10	2.20678
$157$	− 4.23621e9i	− 0.556454i	−0.960515	−	0.278227i	$-0.910253\pi$
$157$	− 4.23621e9i	− 0.556454i	0.960515	−	0.278227i	$-0.0897468\pi$
$158$	− 2.18002e10i	− 2.78294i
$159$	1.07696e10	1.33633
$160$	0	0
$161$	−8.72432e9	−1.02333
$162$	1.54928e10i	1.76731i
$163$	− 8.56450e9i	− 0.950293i	−0.879907	−	0.475147i	$-0.842395\pi$
$163$	− 8.56450e9i	− 0.950293i	0.879907	−	0.475147i	$-0.157605\pi$
$164$	7.16193e9	0.773095
$165$	0	0
$166$	−2.89882e10	−2.96302
$167$	5.87750e9i	0.584748i	0.956304	+	0.292374i	$0.0944452\pi$
$167$	5.87750e9i	0.584748i	−0.956304	+	0.292374i	$0.905555\pi$
$168$	1.78285e10i	1.72672i
$169$	5.13100e8	0.0483851
$170$	0	0
$171$	−1.03155e9	−0.0922591
$172$	2.15163e10i	1.87452i
$173$	− 1.48147e10i	− 1.25743i	−0.777635	−	0.628715i	$-0.783581\pi$
$173$	− 1.48147e10i	− 1.25743i	0.777635	−	0.628715i	$-0.216419\pi$
$174$	1.11285e10	0.920372
$175$	0	0
$176$	−6.26978e8	−0.0492544
$177$	4.17441e9i	0.319680i
$178$	3.08864e10i	2.30610i
$179$	−5.95512e9	−0.433563	−0.216781	−	0.976220i	$-0.569556\pi$
$179$	−5.95512e9	−0.433563	−0.216781	+	0.976220i	$0.569556\pi$
$180$	0	0
$181$	1.02707e10	0.711290	0.355645	−	0.934621i	$-0.384261\pi$
$181$	1.02707e10	0.711290	0.355645	+	0.934621i	$0.384261\pi$
$182$	− 2.82446e10i	− 1.90816i
$183$	2.23156e10i	1.47089i
$184$	−1.37417e10	−0.883815
$185$	0	0
$186$	2.92247e10	1.79036
$187$	9.76689e9i	0.584075i
$188$	− 3.84808e10i	− 2.24664i
$189$	2.83033e9	0.161346
$190$	0	0
$191$	2.09899e9	0.114120	0.0570599	−	0.998371i	$-0.481827\pi$
$191$	2.09899e9	0.114120	0.0570599	+	0.998371i	$0.481827\pi$
$192$	− 4.17754e10i	− 2.21853i
$193$	1.95026e10i	1.01178i	0.862599	+	0.505888i	$0.168835\pi$
$193$	1.95026e10i	1.01178i	−0.862599	+	0.505888i	$0.831165\pi$
$194$	8.67293e9	0.439600
$195$	0	0
$196$	1.52254e10	0.736913
$197$	6.38850e9i	0.302204i	0.988518	+	0.151102i	$0.0482823\pi$
$197$	6.38850e9i	0.302204i	−0.988518	+	0.151102i	$0.951718\pi$
$198$	− 3.15959e10i	− 1.46096i
$199$	−1.32140e10	−0.597303	−0.298652	−	0.954362i	$-0.596537\pi$
$199$	−1.32140e10	−0.597303	−0.298652	+	0.954362i	$0.596537\pi$
$200$	0	0
$201$	−1.48873e10	−0.643331
$202$	2.40058e10i	1.01446i
$203$	− 1.19615e10i	− 0.494370i
$204$	3.28174e10	1.32669
$205$	0	0
$206$	−3.50447e10	−1.35588
$207$	− 2.02725e10i	− 0.767433i
$208$	− 1.30236e9i	− 0.0482444i
$209$	−2.80727e9	−0.101771
$210$	0	0
$211$	2.06410e9	0.0716901	0.0358450	−	0.999357i	$-0.488588\pi$
$211$	2.06410e9	0.0716901	0.0358450	+	0.999357i	$0.488588\pi$
$212$	− 4.67250e10i	− 1.58869i
$213$	− 3.79065e10i	− 1.26184i
$214$	−4.90304e10	−1.59810
$215$	0	0
$216$	4.45808e9	0.139350
$217$	− 3.14123e10i	− 0.961680i
$218$	7.10915e10i	2.13188i
$219$	−6.59824e10	−1.93834
$220$	0	0
$221$	−2.02879e10	−0.572099
$222$	1.21541e11i	3.35840i
$223$	1.59589e10i	0.432145i	0.976377	+	0.216073i	$0.0693248\pi$
$223$	1.59589e10i	0.432145i	−0.976377	+	0.216073i	$0.930675\pi$
$224$	−4.35217e10	−1.15502
$225$	0	0
$226$	3.58195e10	0.913338
$227$	4.86308e10i	1.21561i	0.794085	+	0.607807i	$0.207950\pi$
$227$	4.86308e10i	1.21561i	−0.794085	+	0.607807i	$0.792050\pi$
$228$	9.43262e9i	0.231167i
$229$	6.34109e10	1.52372	0.761858	−	0.647744i	$-0.224287\pi$
$229$	6.34109e10	1.52372	0.761858	+	0.647744i	$0.224287\pi$
$230$	0	0
$231$	−7.15767e10	−1.65393
$232$	− 1.88406e10i	− 0.426971i
$233$	− 2.45281e10i	− 0.545209i	−0.962126	−	0.272605i	$-0.912115\pi$
$233$	− 2.45281e10i	− 0.545209i	0.962126	−	0.272605i	$-0.0878850\pi$
$234$	6.56314e10	1.43100
$235$	0	0
$236$	1.81111e10	0.380050
$237$	− 1.14756e11i	− 2.36270i
$238$	− 5.67833e10i	− 1.14716i
$239$	7.82086e10	1.55047	0.775236	−	0.631671i	$-0.217631\pi$
$239$	7.82086e10	1.55047	0.775236	+	0.631671i	$0.217631\pi$
$240$	0	0
$241$	6.59331e10	1.25900	0.629502	−	0.776999i	$-0.283259\pi$
$241$	6.59331e10	1.25900	0.629502	+	0.776999i	$0.283259\pi$
$242$	7.04304e8i	0.0132005i
$243$	7.42696e10i	1.36642i
$244$	9.68186e10	1.74866
$245$	0	0
$246$	6.06893e10	1.05658
$247$	− 5.83128e9i	− 0.0996844i
$248$	− 4.94777e10i	− 0.830571i
$249$	−1.52594e11	−2.51559
$250$	0	0
$251$	1.83321e10	0.291527	0.145764	−	0.989319i	$-0.453436\pi$
$251$	1.83321e10	0.291527	0.145764	+	0.989319i	$0.453436\pi$
$252$	1.14112e11i	1.78249i
$253$	− 5.51694e10i	− 0.846557i
$254$	4.60064e10	0.693533
$255$	0	0
$256$	−7.41248e10	−1.07866
$257$	6.41469e10i	0.917227i	0.888636	+	0.458613i	$0.151654\pi$
$257$	6.41469e10i	0.917227i	−0.888636	+	0.458613i	$0.848346\pi$
$258$	1.82326e11i	2.56189i
$259$	1.30638e11	1.80394
$260$	0	0
$261$	2.77946e10	0.370747
$262$	− 8.20074e10i	− 1.07522i
$263$	− 2.20901e10i	− 0.284706i	−0.989816	−	0.142353i	$-0.954533\pi$
$263$	− 2.20901e10i	− 0.284706i	0.989816	−	0.142353i	$-0.0454668\pi$
$264$	−1.12741e11	−1.42845
$265$	0	0
$266$	1.63211e10	0.199885
$267$	1.62586e11i	1.95787i
$268$	6.45902e10i	0.764822i
$269$	−7.78901e10	−0.906978	−0.453489	−	0.891262i	$-0.649821\pi$
$269$	−7.78901e10	−0.906978	−0.453489	+	0.891262i	$0.649821\pi$
$270$	0	0
$271$	−9.36671e10	−1.05493	−0.527467	−	0.849576i	$-0.676858\pi$
$271$	−9.36671e10	−1.05493	−0.527467	+	0.849576i	$0.676858\pi$
$272$	− 2.61829e9i	− 0.0290039i
$273$	− 1.48680e11i	− 1.62002i
$274$	−1.43824e11	−1.54154
$275$	0	0
$276$	−1.85373e11	−1.92290
$277$	− 7.45925e10i	− 0.761266i	−0.924726	−	0.380633i	$-0.875706\pi$
$277$	− 7.45925e10i	− 0.761266i	0.924726	−	0.380633i	$-0.124294\pi$
$278$	6.04025e10i	0.606532i
$279$	7.29919e10	0.721200
$280$	0	0
$281$	−1.10771e11	−1.05986	−0.529930	−	0.848041i	$-0.677782\pi$
$281$	−1.10771e11	−1.05986	−0.529930	+	0.848041i	$0.677782\pi$
$282$	− 3.26081e11i	− 3.07047i
$283$	− 1.44123e11i	− 1.33566i	−0.744314	−	0.667830i	$-0.767223\pi$
$283$	− 1.44123e11i	− 1.33566i	0.744314	−	0.667830i	$-0.232777\pi$
$284$	−1.64461e11	−1.50014
$285$	0	0
$286$	1.78609e11	1.57854
$287$	− 6.52321e10i	− 0.567536i
$288$	− 1.01130e11i	− 0.866194i
$289$	7.78009e10	0.656061
$290$	0	0
$291$	4.56542e10	0.373218
$292$	2.86271e11i	2.30438i
$293$	1.39037e11i	1.10211i	0.834469	+	0.551056i	$0.185775\pi$
$293$	1.39037e11i	1.10211i	−0.834469	+	0.551056i	$0.814225\pi$
$294$	1.29018e11	1.00713
$295$	0	0
$296$	2.05770e11	1.55800
$297$	1.78980e10i	0.133475i
$298$	− 2.32950e11i	− 1.71116i
$299$	1.14598e11	0.829198
$300$	0	0
$301$	1.95974e11	1.37610
$302$	− 2.08820e11i	− 1.44458i
$303$	1.26366e11i	0.861271i
$304$	7.52566e8	0.00505375
$305$	0	0
$306$	1.31946e11	0.860300
$307$	− 2.71765e10i	− 0.174611i	−0.996182	−	0.0873053i	$-0.972174\pi$
$307$	− 2.71765e10i	− 0.174611i	0.996182	−	0.0873053i	$-0.0278256\pi$
$308$	3.10543e11i	1.96627i
$309$	−1.84475e11	−1.15113
$310$	0	0
$311$	9.82604e10	0.595603	0.297802	−	0.954628i	$-0.403747\pi$
$311$	9.82604e10	0.595603	0.297802	+	0.954628i	$0.403747\pi$
$312$	− 2.34186e11i	− 1.39916i
$313$	1.82397e11i	1.07416i	0.843533	+	0.537078i	$0.180472\pi$
$313$	1.82397e11i	1.07416i	−0.843533	+	0.537078i	$0.819528\pi$
$314$	−1.55743e11	−0.904120
$315$	0	0
$316$	−4.97882e11	−2.80889
$317$	− 1.52524e11i	− 0.848341i	−0.905582	−	0.424170i	$-0.860566\pi$
$317$	− 1.52524e11i	− 0.848341i	0.905582	−	0.424170i	$-0.139434\pi$
$318$	− 3.95942e11i	− 2.17125i
$319$	7.56400e10	0.408972
$320$	0	0
$321$	−2.58096e11	−1.35678
$322$	3.20747e11i	1.66269i
$323$	− 1.17233e10i	− 0.0599290i
$324$	3.53831e11	1.78379
$325$	0	0
$326$	−3.14872e11	−1.54403
$327$	3.74225e11i	1.80996i
$328$	− 1.02748e11i	− 0.490162i
$329$	−3.50490e11	−1.64928
$330$	0	0
$331$	4.08043e11	1.86845	0.934223	−	0.356690i	$-0.116095\pi$
$331$	4.08043e11	1.86845	0.934223	+	0.356690i	$0.116095\pi$
$332$	6.62043e11i	2.99064i
$333$	3.03561e11i	1.35284i
$334$	2.16085e11	0.950092
$335$	0	0
$336$	1.91881e10	0.0821307
$337$	− 2.48513e11i	− 1.04958i	−0.851233	−	0.524789i	$-0.824144\pi$
$337$	− 2.48513e11i	− 1.04958i	0.851233	−	0.524789i	$-0.175856\pi$
$338$	− 1.88640e10i	− 0.0786156i
$339$	1.88554e11	0.775419
$340$	0	0
$341$	1.98640e11	0.795558
$342$	3.79248e10i	0.149902i
$343$	1.69935e11i	0.662917i
$344$	3.08680e11	1.18849
$345$	0	0
$346$	−5.44657e11	−2.04306
$347$	3.44769e11i	1.27657i	0.769799	+	0.638287i	$0.220356\pi$
$347$	3.44769e11i	1.27657i	−0.769799	+	0.638287i	$0.779644\pi$
$348$	− 2.54156e11i	− 0.928953i
$349$	−4.24804e11	−1.53276	−0.766380	−	0.642388i	$-0.777944\pi$
$349$	−4.24804e11	−1.53276	−0.766380	+	0.642388i	$0.777944\pi$
$350$	0	0
$351$	−3.71779e10	−0.130738
$352$	− 2.75216e11i	− 0.955501i
$353$	− 1.53549e11i	− 0.526334i	−0.964750	−	0.263167i	$-0.915233\pi$
$353$	− 1.53549e11i	− 0.526334i	0.964750	−	0.263167i	$-0.0847670\pi$
$354$	1.53471e11	0.519412
$355$	0	0
$356$	7.05397e11	2.32760
$357$	− 2.98907e11i	− 0.973933i
$358$	2.18938e11i	0.704447i
$359$	3.08800e11	0.981189	0.490594	−	0.871388i	$-0.336780\pi$
$359$	3.08800e11	0.981189	0.490594	+	0.871388i	$0.336780\pi$
$360$	0	0
$361$	−3.19318e11	−0.989558
$362$	− 3.77600e11i	− 1.15570i
$363$	3.70745e9i	0.0112072i
$364$	−6.45062e11	−1.92595
$365$	0	0
$366$	8.20429e11	2.38988
$367$	− 1.26543e11i	− 0.364116i	−0.983288	−	0.182058i	$-0.941724\pi$
$367$	− 1.26543e11i	− 0.364116i	0.983288	−	0.182058i	$-0.0582759\pi$
$368$	1.47897e10i	0.0420382i
$369$	1.51578e11	0.425616
$370$	0	0
$371$	−4.25579e11	−1.16627
$372$	− 6.67444e11i	− 1.80706i
$373$	− 2.88008e10i	− 0.0770397i	−0.999258	−	0.0385199i	$-0.987736\pi$
$373$	− 2.88008e10i	− 0.0770397i	0.999258	−	0.0385199i	$-0.0122643\pi$
$374$	3.59077e11	0.948999
$375$	0	0
$376$	−5.52059e11	−1.42443
$377$	1.57120e11i	0.400586i
$378$	− 1.04056e11i	− 0.262154i
$379$	−5.21974e11	−1.29949	−0.649744	−	0.760153i	$-0.725124\pi$
$379$	−5.21974e11	−1.29949	−0.649744	+	0.760153i	$0.725124\pi$
$380$	0	0
$381$	2.42178e11	0.588805
$382$	− 7.71690e10i	− 0.185421i
$383$	1.77381e10i	0.0421223i	0.999778	+	0.0210611i	$0.00670447\pi$
$383$	1.77381e10i	0.0421223i	−0.999778	+	0.0210611i	$0.993296\pi$
$384$	−9.71973e11	−2.28120
$385$	0	0
$386$	7.17007e11	1.64392
$387$	4.55380e11i	1.03199i
$388$	− 1.98076e11i	− 0.443699i
$389$	2.05874e10	0.0455856	0.0227928	−	0.999740i	$-0.492744\pi$
$389$	2.05874e10	0.0455856	0.0227928	+	0.999740i	$0.492744\pi$
$390$	0	0
$391$	2.30390e11	0.498503
$392$	− 2.18429e11i	− 0.467222i
$393$	− 4.31686e11i	− 0.912855i
$394$	2.34872e11	0.491018
$395$	0	0
$396$	−7.21600e11	−1.47458
$397$	− 8.47450e11i	− 1.71221i	−0.516803	−	0.856105i	$-0.672878\pi$
$397$	− 8.47450e11i	− 1.71221i	0.516803	−	0.856105i	$-0.327122\pi$
$398$	4.85809e11i	0.970491i
$399$	8.59139e10	0.169701
$400$	0	0
$401$	−2.81253e11	−0.543185	−0.271592	−	0.962412i	$-0.587550\pi$
$401$	−2.81253e11	−0.543185	−0.271592	+	0.962412i	$0.587550\pi$
$402$	5.47329e11i	1.04528i
$403$	4.12616e11i	0.779245i
$404$	5.48254e11	1.02392
$405$	0	0
$406$	−4.39760e11	−0.803247
$407$	8.26111e11i	1.49232i
$408$	− 4.70811e11i	− 0.841154i
$409$	6.89579e11	1.21851	0.609255	−	0.792975i	$-0.291469\pi$
$409$	6.89579e11	1.21851	0.609255	+	0.792975i	$0.291469\pi$
$410$	0	0
$411$	−7.57091e11	−1.30876
$412$	8.00364e11i	1.36852i
$413$	− 1.64959e11i	− 0.278998i
$414$	−7.45313e11	−1.24692
$415$	0	0
$416$	5.71680e11	0.935908
$417$	3.17958e11i	0.514942i
$418$	1.03208e11i	0.165357i
$419$	4.76873e11	0.755857	0.377928	−	0.925835i	$-0.376637\pi$
$419$	4.76873e11	0.755857	0.377928	+	0.925835i	$0.376637\pi$
$420$	0	0
$421$	1.08180e12	1.67833	0.839165	−	0.543877i	$-0.183044\pi$
$421$	1.08180e12	1.67833	0.839165	+	0.543877i	$0.183044\pi$
$422$	− 7.58860e10i	− 0.116481i
$423$	− 8.14424e11i	− 1.23686i
$424$	−6.70333e11	−1.00727
$425$	0	0
$426$	−1.39363e12	−2.05023
$427$	− 8.81841e11i	− 1.28370i
$428$	1.11978e12i	1.61300i
$429$	9.40196e11	1.34017
$430$	0	0
$431$	−3.36212e11	−0.469316	−0.234658	−	0.972078i	$-0.575397\pi$
$431$	−3.36212e11	−0.469316	−0.234658	+	0.972078i	$0.575397\pi$
$432$	− 4.79806e9i	− 0.00662809i
$433$	− 1.26577e12i	− 1.73045i	−0.501383	−	0.865225i	$-0.667175\pi$
$433$	− 1.26577e12i	− 1.73045i	0.501383	−	0.865225i	$-0.332825\pi$
$434$	−1.15486e12	−1.56253
$435$	0	0
$436$	1.62361e12	2.15176
$437$	6.62203e10i	0.0868609i
$438$	2.42583e12i	3.14939i
$439$	−2.16378e11	−0.278050	−0.139025	−	0.990289i	$-0.544397\pi$
$439$	−2.16378e11	−0.278050	−0.139025	+	0.990289i	$0.544397\pi$
$440$	0	0
$441$	3.22237e11	0.405697
$442$	7.45878e11i	0.929539i
$443$	3.36288e11i	0.414853i	0.978251	+	0.207426i	$0.0665088\pi$
$443$	3.36288e11i	0.414853i	−0.978251	+	0.207426i	$0.933491\pi$
$444$	2.77579e12	3.38972
$445$	0	0
$446$	5.86724e11	0.702145
$447$	− 1.22625e12i	− 1.45276i
$448$	1.65083e12i	1.93620i
$449$	−1.40309e12	−1.62922	−0.814608	−	0.580012i	$-0.803048\pi$
$449$	−1.40309e12	−1.62922	−0.814608	+	0.580012i	$0.803048\pi$
$450$	0	0
$451$	4.12505e11	0.469499
$452$	− 8.18060e11i	− 0.921854i
$453$	− 1.09923e12i	− 1.22644i
$454$	1.78790e12	1.97511
$455$	0	0
$456$	1.35324e11	0.146566
$457$	1.26840e12i	1.36030i	0.733075	+	0.680148i	$0.238084\pi$
$457$	1.26840e12i	1.36030i	−0.733075	+	0.680148i	$0.761916\pi$
$458$	− 2.33129e12i	− 2.47572i
$459$	−7.47428e10	−0.0785981
$460$	0	0
$461$	−3.57771e11	−0.368936	−0.184468	−	0.982839i	$-0.559056\pi$
$461$	−3.57771e11	−0.368936	−0.184468	+	0.982839i	$0.559056\pi$
$462$	2.63150e12i	2.68729i
$463$	3.72773e11i	0.376990i	0.982074	+	0.188495i	$0.0603609\pi$
$463$	3.72773e11i	0.376990i	−0.982074	+	0.188495i	$0.939639\pi$
$464$	−2.02774e10	−0.0203087
$465$	0	0
$466$	−9.01771e11	−0.885849
$467$	− 1.30696e12i	− 1.27155i	−0.771873	−	0.635777i	$-0.780680\pi$
$467$	− 1.30696e12i	− 1.27155i	0.771873	−	0.635777i	$-0.219320\pi$
$468$	− 1.49891e12i	− 1.44434i
$469$	5.88299e11	0.561462
$470$	0	0
$471$	−8.19832e11	−0.767593
$472$	− 2.59828e11i	− 0.240961i
$473$	1.23927e12i	1.13839i
$474$	−4.21898e12	−3.83889
$475$	0	0
$476$	−1.29684e12	−1.15786
$477$	− 9.88908e11i	− 0.874628i
$478$	− 2.87532e12i	− 2.51919i
$479$	−3.77216e10	−0.0327402	−0.0163701	−	0.999866i	$-0.505211\pi$
$479$	−3.77216e10	−0.0327402	−0.0163701	+	0.999866i	$0.505211\pi$
$480$	0	0
$481$	−1.71600e12	−1.46172
$482$	− 2.42401e12i	− 2.04561i
$483$	1.68841e12i	1.41162i
$484$	1.60852e10	0.0133236
$485$	0	0
$486$	2.73050e12	2.22014
$487$	1.89303e12i	1.52503i	0.646973	+	0.762513i	$0.276035\pi$
$487$	1.89303e12i	1.52503i	−0.646973	+	0.762513i	$0.723965\pi$
$488$	− 1.38899e12i	− 1.10869i
$489$	−1.65748e12	−1.31087
$490$	0	0
$491$	−7.57823e11	−0.588438	−0.294219	−	0.955738i	$-0.595060\pi$
$491$	−7.57823e11	−0.588438	−0.294219	+	0.955738i	$0.595060\pi$
$492$	− 1.38605e12i	− 1.06644i
$493$	3.15876e11i	0.240827i
$494$	−2.14385e11	−0.161966
$495$	0	0
$496$	−5.32510e10	−0.0395057
$497$	1.49794e12i	1.10126i
$498$	5.61006e12i	4.08729i
$499$	−3.90008e11	−0.281593	−0.140796	−	0.990039i	$-0.544966\pi$
$499$	−3.90008e11	−0.281593	−0.140796	+	0.990039i	$0.544966\pi$
$500$	0	0
$501$	1.13747e12	0.806623
$502$	− 6.73973e11i	− 0.473670i
$503$	3.44868e11i	0.240213i	0.992761	+	0.120107i	$0.0383236\pi$
$503$	3.44868e11i	0.240213i	−0.992761	+	0.120107i	$0.961676\pi$
$504$	1.63708e12	1.13014
$505$	0	0
$506$	−2.02829e12	−1.37548
$507$	− 9.93001e10i	− 0.0667442i
$508$	− 1.05071e12i	− 0.699999i
$509$	1.33209e12	0.879636	0.439818	−	0.898087i	$-0.355043\pi$
$509$	1.33209e12	0.879636	0.439818	+	0.898087i	$0.355043\pi$
$510$	0	0
$511$	2.60741e12	1.69167
$512$	1.53738e11i	0.0988703i
$513$	− 2.14831e10i	− 0.0136952i
$514$	2.35835e12	1.49030
$515$	0	0
$516$	4.16404e12	2.58578
$517$	− 2.21637e12i	− 1.36438i
$518$	− 4.80289e12i	− 2.93102i
$519$	−2.86707e12	−1.73455
$520$	0	0
$521$	−1.31345e12	−0.780985	−0.390493	−	0.920606i	$-0.627695\pi$
$521$	−1.31345e12	−0.780985	−0.390493	+	0.920606i	$0.627695\pi$
$522$	− 1.02186e12i	− 0.602385i
$523$	− 1.60667e12i	− 0.939006i	−0.882931	−	0.469503i	$-0.844433\pi$
$523$	− 1.60667e12i	− 0.939006i	0.882931	−	0.469503i	$-0.155567\pi$
$524$	−1.87292e12	−1.08524
$525$	0	0
$526$	−8.12136e11	−0.462587
$527$	8.29529e11i	0.468472i
$528$	1.21339e11i	0.0679433i
$529$	4.99767e11	0.277471
$530$	0	0
$531$	3.83311e11	0.209231
$532$	− 3.72746e11i	− 0.201749i
$533$	8.56858e11i	0.459871i
$534$	5.97744e12	3.18112
$535$	0	0
$536$	9.26634e11	0.484916
$537$	1.15249e12i	0.598072i
$538$	2.86361e12i	1.47365i
$539$	8.76935e11	0.447525
$540$	0	0
$541$	−1.22163e12	−0.613132	−0.306566	−	0.951849i	$-0.599180\pi$
$541$	−1.22163e12	−0.613132	−0.306566	+	0.951849i	$0.599180\pi$
$542$	3.44365e12i	1.71404i
$543$	− 1.98769e12i	− 0.981179i
$544$	1.14931e12	0.562656
$545$	0	0
$546$	−5.46617e12	−2.63218
$547$	1.65203e11i	0.0788996i	0.999222	+	0.0394498i	$0.0125605\pi$
$547$	1.65203e11i	0.0788996i	−0.999222	+	0.0394498i	$0.987439\pi$
$548$	3.28472e12i	1.55591i
$549$	2.04911e12	0.962698
$550$	0	0
$551$	−9.07912e10	−0.0419625
$552$	2.65943e12i	1.21917i
$553$	4.53479e12i	2.06203i
$554$	−2.74238e12	−1.23690
$555$	0	0
$556$	1.37950e12	0.612186
$557$	3.45024e12i	1.51880i	0.650623	+	0.759401i	$0.274508\pi$
$557$	3.45024e12i	1.51880i	−0.650623	+	0.759401i	$0.725492\pi$
$558$	− 2.68353e12i	− 1.17180i
$559$	−2.57422e12	−1.11505
$560$	0	0
$561$	1.89018e12	0.805695
$562$	4.07248e12i	1.72205i
$563$	− 4.38944e11i	− 0.184129i	−0.995753	−	0.0920643i	$-0.970653\pi$
$563$	− 4.38944e11i	− 0.184129i	0.995753	−	0.0920643i	$-0.0293465\pi$
$564$	−7.44717e12	−3.09910
$565$	0	0
$566$	−5.29867e12	−2.17016
$567$	− 3.22275e12i	− 1.30949i
$568$	2.35942e12i	0.951126i
$569$	2.03068e12	0.812150	0.406075	−	0.913840i	$-0.366897\pi$
$569$	2.03068e12	0.812150	0.406075	+	0.913840i	$0.366897\pi$
$570$	0	0
$571$	1.25554e12	0.494276	0.247138	−	0.968980i	$-0.420510\pi$
$571$	1.25554e12	0.494276	0.247138	+	0.968980i	$0.420510\pi$
$572$	− 4.07914e12i	− 1.59326i
$573$	− 4.06217e11i	− 0.157421i
$574$	−2.39824e12	−0.922125
$575$	0	0
$576$	−3.83599e12	−1.45203
$577$	− 1.45596e12i	− 0.546838i	−0.961895	−	0.273419i	$-0.911845\pi$
$577$	− 1.45596e12i	− 0.546838i	0.961895	−	0.273419i	$-0.0881545\pi$
$578$	− 2.86033e12i	− 1.06596i
$579$	3.77432e12	1.39568
$580$	0	0
$581$	6.03000e12	2.19546
$582$	− 1.67847e12i	− 0.606400i
$583$	− 2.69121e12i	− 0.964805i
$584$	4.10695e12	1.46104
$585$	0	0
$586$	5.11165e12	1.79070
$587$	− 7.51503e11i	− 0.261252i	−0.991432	−	0.130626i	$-0.958301\pi$
$587$	− 7.51503e11i	− 0.261252i	0.991432	−	0.130626i	$-0.0416987\pi$
$588$	− 2.94656e12i	− 1.01652i
$589$	−2.38429e11	−0.0816281
$590$	0	0
$591$	1.23636e12	0.416872
$592$	− 2.21462e11i	− 0.0741057i
$593$	1.95284e12i	0.648514i	0.945969	+	0.324257i	$0.105114\pi$
$593$	1.95284e12i	0.648514i	−0.945969	+	0.324257i	$0.894886\pi$
$594$	6.58016e11	0.216869
$595$	0	0
$596$	−5.32021e12	−1.72711
$597$	2.55730e12i	0.823942i
$598$	− 4.21318e12i	− 1.34727i
$599$	4.92766e12	1.56394	0.781969	−	0.623317i	$-0.214215\pi$
$599$	4.92766e12	1.56394	0.781969	+	0.623317i	$0.214215\pi$
$600$	0	0
$601$	−4.36498e12	−1.36473	−0.682366	−	0.731011i	$-0.739049\pi$
$601$	−4.36498e12	−1.36473	−0.682366	+	0.731011i	$0.739049\pi$
$602$	− 7.20494e12i	− 2.23587i
$603$	1.36702e12i	0.421062i
$604$	−4.76911e12	−1.45805
$605$	0	0
$606$	4.64583e12	1.39938
$607$	− 1.49883e12i	− 0.448128i	−0.974574	−	0.224064i	$-0.928068\pi$
$607$	− 1.49883e12i	− 0.448128i	0.974574	−	0.224064i	$-0.0719324\pi$
$608$	3.30343e11i	0.0980391i
$609$	−2.31490e12	−0.681952
$610$	0	0
$611$	4.60386e12	1.33640
$612$	− 3.01343e12i	− 0.868321i
$613$	3.19261e12i	0.913216i	0.889668	+	0.456608i	$0.150936\pi$
$613$	3.19261e12i	0.913216i	−0.889668	+	0.456608i	$0.849064\pi$
$614$	−9.99137e11	−0.283705
$615$	0	0
$616$	4.45516e12	1.24666
$617$	− 1.58167e12i	− 0.439371i	−0.975571	−	0.219685i	$-0.929497\pi$
$617$	− 1.58167e12i	− 0.439371i	0.975571	−	0.219685i	$-0.0705031\pi$
$618$	6.78218e12i	1.87034i
$619$	−2.53778e12	−0.694777	−0.347389	−	0.937721i	$-0.612932\pi$
$619$	−2.53778e12	−0.694777	−0.347389	+	0.937721i	$0.612932\pi$
$620$	0	0
$621$	4.22194e11	0.113920
$622$	− 3.61252e12i	− 0.967729i
$623$	− 6.42488e12i	− 1.70871i
$624$	−2.52046e11	−0.0665501
$625$	0	0
$626$	6.70576e12	1.74527
$627$	5.43289e11i	0.140387i
$628$	3.55693e12i	0.912550i
$629$	−3.44987e12	−0.878770
$630$	0	0
$631$	−6.66150e12	−1.67278	−0.836392	−	0.548131i	$-0.815339\pi$
$631$	−6.66150e12	−1.67278	−0.836392	+	0.548131i	$0.815339\pi$
$632$	7.14279e12i	1.78091i
$633$	− 3.99464e11i	− 0.0988918i
$634$	−5.60749e12	−1.37837
$635$	0	0
$636$	−9.04266e12	−2.19149
$637$	1.82158e12i	0.438349i
$638$	− 2.78089e12i	− 0.664493i
$639$	−3.48073e12	−0.825880
$640$	0	0
$641$	−6.22257e12	−1.45582	−0.727911	−	0.685671i	$-0.759509\pi$
$641$	−6.22257e12	−1.45582	−0.727911	+	0.685671i	$0.759509\pi$
$642$	9.48883e12i	2.20447i
$643$	4.55187e11i	0.105012i	0.998621	+	0.0525061i	$0.0167209\pi$
$643$	4.55187e11i	0.105012i	−0.998621	+	0.0525061i	$0.983279\pi$
$644$	7.32535e12	1.67819
$645$	0	0
$646$	−4.31003e11	−0.0973719
$647$	− 2.50192e12i	− 0.561312i	−0.959808	−	0.280656i	$-0.909448\pi$
$647$	− 2.50192e12i	− 0.561312i	0.959808	−	0.280656i	$-0.0905519\pi$
$648$	− 5.07618e12i	− 1.13097i
$649$	1.04314e12	0.230803
$650$	0	0
$651$	−6.07920e12	−1.32658
$652$	7.19116e12i	1.55842i
$653$	− 3.54499e12i	− 0.762966i	−0.924376	−	0.381483i	$-0.875413\pi$
$653$	− 3.54499e12i	− 0.762966i	0.924376	−	0.381483i	$-0.124587\pi$
$654$	1.37583e13	2.94080
$655$	0	0
$656$	−1.10583e11	−0.0233143
$657$	6.05877e12i	1.26865i
$658$	1.28857e13i	2.67973i
$659$	−5.93850e12	−1.22657	−0.613285	−	0.789862i	$-0.710152\pi$
$659$	−5.93850e12	−1.22657	−0.613285	+	0.789862i	$0.710152\pi$
$660$	0	0
$661$	−6.68673e12	−1.36241	−0.681204	−	0.732093i	$-0.738543\pi$
$661$	−6.68673e12	−1.36241	−0.681204	+	0.732093i	$0.738543\pi$
$662$	− 1.50016e13i	− 3.03583i
$663$	3.92630e12i	0.789174i
$664$	9.49790e12	1.89614
$665$	0	0
$666$	1.11604e13	2.19808
$667$	− 1.78426e12i	− 0.349054i
$668$	− 4.93503e12i	− 0.958950i
$669$	3.08851e12	0.596117
$670$	0	0
$671$	5.57645e12	1.06196
$672$	8.42274e12i	1.59328i
$673$	− 8.43444e12i	− 1.58485i	−0.609969	−	0.792425i	$-0.708818\pi$
$673$	− 8.43444e12i	− 1.58485i	0.609969	−	0.792425i	$-0.291182\pi$
$674$	−9.13652e12	−1.70534
$675$	0	0
$676$	−4.30823e11	−0.0793486
$677$	9.48091e12i	1.73461i	0.497781	+	0.867303i	$0.334148\pi$
$677$	9.48091e12i	1.73461i	−0.497781	+	0.867303i	$0.665852\pi$
$678$	− 6.93213e12i	− 1.25989i
$679$	−1.80411e12	−0.325723
$680$	0	0
$681$	9.41150e12	1.67686
$682$	− 7.30295e12i	− 1.29261i
$683$	1.00045e13i	1.75914i	0.475768	+	0.879571i	$0.342170\pi$
$683$	1.00045e13i	1.75914i	−0.475768	+	0.879571i	$0.657830\pi$
$684$	8.66142e11	0.151299
$685$	0	0
$686$	6.24762e12	1.07710
$687$	− 1.22719e13i	− 2.10187i
$688$	− 3.32221e11i	− 0.0565300i
$689$	5.59021e12	0.945021
$690$	0	0
$691$	5.59146e12	0.932983	0.466491	−	0.884526i	$-0.345518\pi$
$691$	5.59146e12	0.932983	0.466491	+	0.884526i	$0.345518\pi$
$692$	1.24391e13i	2.06211i
$693$	6.57246e12i	1.08250i
$694$	1.26754e13	2.07416
$695$	0	0
$696$	−3.64621e12	−0.588980
$697$	1.72264e12i	0.276469i
$698$	1.56178e13i	2.49041i
$699$	−4.74692e12	−0.752081
$700$	0	0
$701$	−6.41878e12	−1.00397	−0.501986	−	0.864876i	$-0.667397\pi$
$701$	−6.41878e12	−1.00397	−0.501986	+	0.864876i	$0.667397\pi$
$702$	1.36684e12i	0.212422i
$703$	− 9.91586e11i	− 0.153120i
$704$	−1.04393e13	−1.60174
$705$	0	0
$706$	−5.64520e12	−0.855181
$707$	− 4.99359e12i	− 0.751667i
$708$	− 3.50503e12i	− 0.524255i
$709$	−1.98300e12	−0.294724	−0.147362	−	0.989083i	$-0.547078\pi$
$709$	−1.98300e12	−0.294724	−0.147362	+	0.989083i	$0.547078\pi$
$710$	0	0
$711$	−1.05374e13	−1.54639
$712$	− 1.01199e13i	− 1.47576i
$713$	− 4.68569e12i	− 0.679002i
$714$	−1.09892e13	−1.58244
$715$	0	0
$716$	5.00020e12	0.711015
$717$	− 1.51357e13i	− 2.13878i
$718$	− 1.13530e13i	− 1.59422i
$719$	9.53823e12	1.33103	0.665515	−	0.746385i	$-0.268212\pi$
$719$	9.53823e12	1.33103	0.665515	+	0.746385i	$0.268212\pi$
$720$	0	0
$721$	7.28986e12	1.00464
$722$	1.17397e13i	1.60782i
$723$	− 1.27600e13i	− 1.73671i
$724$	−8.62377e12	−1.16647
$725$	0	0
$726$	1.36304e11	0.0182093
$727$	− 6.30135e11i	− 0.0836621i	−0.999125	−	0.0418310i	$-0.986681\pi$
$727$	− 6.30135e11i	− 0.0836621i	0.999125	−	0.0418310i	$-0.0133191\pi$
$728$	9.25429e12i	1.22110i
$729$	6.07886e12	0.797165
$730$	0	0
$731$	−5.17524e12	−0.670352
$732$	− 1.87373e13i	− 2.41216i
$733$	− 2.79069e12i	− 0.357061i	−0.983934	−	0.178531i	$-0.942866\pi$
$733$	− 2.79069e12i	− 0.357061i	0.983934	−	0.178531i	$-0.0571344\pi$
$734$	−4.65232e12	−0.591612
$735$	0	0
$736$	−6.49203e12	−0.815512
$737$	3.72019e12i	0.464474i
$738$	− 5.57274e12i	− 0.691537i
$739$	−7.26759e12	−0.896376	−0.448188	−	0.893939i	$-0.647931\pi$
$739$	−7.26759e12	−0.896376	−0.448188	+	0.893939i	$0.647931\pi$
$740$	0	0
$741$	−1.12852e12	−0.137508
$742$	1.56463e13i	1.89494i
$743$	9.19047e12i	1.10634i	0.833069	+	0.553169i	$0.186582\pi$
$743$	9.19047e12i	1.10634i	−0.833069	+	0.553169i	$0.813418\pi$
$744$	−9.57540e12	−1.14572
$745$	0	0
$746$	−1.05885e12	−0.125173
$747$	1.40118e13i	1.64646i
$748$	− 8.20074e12i	− 0.957847i
$749$	1.01991e13	1.18412
$750$	0	0
$751$	−5.21242e11	−0.0597943	−0.0298972	−	0.999553i	$-0.509518\pi$
$751$	−5.21242e11	−0.0597943	−0.0298972	+	0.999553i	$0.509518\pi$
$752$	5.94160e11i	0.0677521i
$753$	− 3.54779e12i	− 0.402143i
$754$	5.77648e12	0.650867
$755$	0	0
$756$	−2.37648e12	−0.264598
$757$	1.15123e13i	1.27417i	0.770792	+	0.637087i	$0.219861\pi$
$757$	1.15123e13i	1.27417i	−0.770792	+	0.637087i	$0.780139\pi$
$758$	1.91903e13i	2.11139i
$759$	−1.06769e13	−1.16777
$760$	0	0
$761$	1.43517e13	1.55121	0.775607	−	0.631217i	$-0.217444\pi$
$761$	1.43517e13	1.55121	0.775607	+	0.631217i	$0.217444\pi$
$762$	− 8.90360e12i	− 0.956684i
$763$	− 1.47882e13i	− 1.57962i
$764$	−1.76242e12	−0.187149
$765$	0	0
$766$	6.52136e11	0.0684398
$767$	2.16682e12i	0.226071i
$768$	1.43453e13i	1.48794i
$769$	7.42318e12	0.765458	0.382729	−	0.923861i	$-0.374984\pi$
$769$	7.42318e12	0.765458	0.382729	+	0.923861i	$0.374984\pi$
$770$	0	0
$771$	1.24143e13	1.26526
$772$	− 1.63753e13i	− 1.65925i
$773$	− 5.82774e12i	− 0.587074i	−0.955948	−	0.293537i	$-0.905168\pi$
$773$	− 5.82774e12i	− 0.587074i	0.955948	−	0.293537i	$-0.0948324\pi$
$774$	1.67419e13	1.67676
$775$	0	0
$776$	−2.84166e12	−0.281316
$777$	− 2.52824e13i	− 2.48842i
$778$	− 7.56890e11i	− 0.0740670i
$779$	−4.95132e11	−0.0481729
$780$	0	0
$781$	−9.47246e12	−0.911031
$782$	− 8.47023e12i	− 0.809962i
$783$	5.78848e11i	0.0550347i
$784$	−2.35087e11	−0.0222232
$785$	0	0
$786$	−1.58708e13	−1.48320
$787$	7.20033e11i	0.0669061i	0.999440	+	0.0334531i	$0.0106504\pi$
$787$	7.20033e11i	0.0669061i	−0.999440	+	0.0334531i	$0.989350\pi$
$788$	− 5.36409e12i	− 0.495596i
$789$	−4.27508e12	−0.392733
$790$	0	0
$791$	−7.45103e12	−0.676741
$792$	1.03523e13i	0.934921i
$793$	1.15834e13i	1.04018i
$794$	−3.11563e13	−2.78198
$795$	0	0
$796$	1.10951e13	0.979539
$797$	9.03491e12i	0.793161i	0.918000	+	0.396580i	$0.129803\pi$
$797$	9.03491e12i	0.793161i	−0.918000	+	0.396580i	$0.870197\pi$
$798$	− 3.15861e12i	− 0.275729i
$799$	9.25566e12	0.803428
$800$	0	0
$801$	1.49293e13	1.28143
$802$	1.03402e13i	0.882560i
$803$	1.64883e13i	1.39945i
$804$	1.25001e13	1.05502
$805$	0	0
$806$	1.51697e13	1.26611
$807$	1.50740e13i	1.25112i
$808$	− 7.86544e12i	− 0.649190i
$809$	2.33217e13	1.91422	0.957111	−	0.289721i	$-0.0935624\pi$
$809$	2.33217e13	1.91422	0.957111	+	0.289721i	$0.0935624\pi$
$810$	0	0
$811$	1.16365e13	0.944555	0.472277	−	0.881450i	$-0.343432\pi$
$811$	1.16365e13	0.944555	0.472277	+	0.881450i	$0.343432\pi$
$812$	1.00434e13i	0.810736i
$813$	1.81273e13i	1.45521i
$814$	3.03718e13	2.42471
$815$	0	0
$816$	−5.06716e11	−0.0400091
$817$	− 1.48750e12i	− 0.116804i
$818$	− 2.53522e13i	− 1.97982i
$819$	−1.36524e13	−1.06030
$820$	0	0
$821$	−1.36931e13	−1.05186	−0.525931	−	0.850527i	$-0.676283\pi$
$821$	−1.36931e13	−1.05186	−0.525931	+	0.850527i	$0.676283\pi$
$822$	2.78343e13i	2.12646i
$823$	− 8.13478e12i	− 0.618083i	−0.951049	−	0.309041i	$-0.899992\pi$
$823$	− 8.13478e12i	− 0.618083i	0.951049	−	0.309041i	$-0.100008\pi$
$824$	1.14823e13	0.867674
$825$	0	0
$826$	−6.06468e12	−0.453313
$827$	9.52838e12i	0.708344i	0.935180	+	0.354172i	$0.115237\pi$
$827$	9.52838e12i	0.708344i	−0.935180	+	0.354172i	$0.884763\pi$
$828$	1.70217e13i	1.25854i
$829$	−2.36561e13	−1.73960	−0.869798	−	0.493407i	$-0.835751\pi$
$829$	−2.36561e13	−1.73960	−0.869798	+	0.493407i	$0.835751\pi$
$830$	0	0
$831$	−1.44359e13	−1.05012
$832$	− 2.16845e13i	− 1.56890i
$833$	3.66212e12i	0.263530i
$834$	1.16897e13	0.836671
$835$	0	0
$836$	2.35711e12	0.166898
$837$	1.52013e12i	0.107057i
$838$	− 1.75321e13i	− 1.22811i
$839$	1.43311e12	0.0998509	0.0499255	−	0.998753i	$-0.484102\pi$
$839$	1.43311e12	0.0998509	0.0499255	+	0.998753i	$0.484102\pi$
$840$	0	0
$841$	−1.20608e13	−0.831372
$842$	− 3.97721e13i	− 2.72693i
$843$	2.14375e13i	1.46201i
$844$	−1.73311e12	−0.117567
$845$	0	0
$846$	−2.99421e13	−2.00963
$847$	− 1.46507e11i	− 0.00978097i
$848$	7.21454e11i	0.0479101i
$849$	−2.78921e13	−1.84246
$850$	0	0
$851$	1.94870e13	1.27369
$852$	3.18281e13i	2.06935i
$853$	− 2.03077e13i	− 1.31338i	−0.754161	−	0.656690i	$-0.771956\pi$
$853$	− 2.03077e13i	− 1.31338i	0.754161	−	0.656690i	$-0.228044\pi$
$854$	−3.24207e13	−2.08575
$855$	0	0
$856$	1.60647e13	1.02268
$857$	− 1.23092e12i	− 0.0779498i	−0.999240	−	0.0389749i	$-0.987591\pi$
$857$	− 1.23092e12i	− 0.0779498i	0.999240	−	0.0389749i	$-0.0124092\pi$
$858$	− 3.45661e13i	− 2.17750i
$859$	1.69941e13	1.06495	0.532476	−	0.846445i	$-0.321262\pi$
$859$	1.69941e13	1.06495	0.532476	+	0.846445i	$0.321262\pi$
$860$	0	0
$861$	−1.26243e13	−0.782879
$862$	1.23607e13i	0.762538i
$863$	3.86270e12i	0.237051i	0.992951	+	0.118526i	$0.0378167\pi$
$863$	3.86270e12i	0.237051i	−0.992951	+	0.118526i	$0.962183\pi$
$864$	2.10614e12	0.128580
$865$	0	0
$866$	−4.65357e13	−2.81162
$867$	− 1.50568e13i	− 0.904995i
$868$	2.63752e13i	1.57709i
$869$	−2.86764e13	−1.70583
$870$	0	0
$871$	−7.72761e12	−0.454950
$872$	− 2.32929e13i	− 1.36427i
$873$	− 4.19216e12i	− 0.244272i
$874$	2.43457e12	0.141131
$875$	0	0
$876$	5.54019e13	3.17875
$877$	− 3.44305e12i	− 0.196538i	−0.995160	−	0.0982688i	$-0.968670\pi$
$877$	− 3.44305e12i	− 0.196538i	0.995160	−	0.0982688i	$-0.0313305\pi$
$878$	7.95508e12i	0.451772i
$879$	2.69077e13	1.52029
$880$	0	0
$881$	2.37092e13	1.32594	0.662971	−	0.748645i	$-0.269295\pi$
$881$	2.37092e13	1.32594	0.662971	+	0.748645i	$0.269295\pi$
$882$	− 1.18470e13i	− 0.659172i
$883$	3.07625e13i	1.70294i	0.524407	+	0.851468i	$0.324287\pi$
$883$	3.07625e13i	1.70294i	−0.524407	+	0.851468i	$0.675713\pi$
$884$	1.70347e13	0.938206
$885$	0	0
$886$	1.23635e13	0.674048
$887$	− 1.39503e13i	− 0.756706i	−0.925661	−	0.378353i	$-0.876491\pi$
$887$	− 1.39503e13i	− 0.756706i	0.925661	−	0.378353i	$-0.123509\pi$
$888$	− 3.98225e13i	− 2.14917i
$889$	−9.57008e12	−0.513875
$890$	0	0
$891$	2.03795e13	1.08329
$892$	− 1.33998e13i	− 0.708691i
$893$	2.66032e12i	0.139992i
$894$	−4.50828e13	−2.36043
$895$	0	0
$896$	3.84092e13	1.99090
$897$	− 2.21782e13i	− 1.14383i
$898$	5.15844e13i	2.64713i
$899$	6.42431e12	0.328026
$900$	0	0
$901$	1.12386e13	0.568134
$902$	− 1.51656e13i	− 0.762836i
$903$	− 3.79268e13i	− 1.89824i
$904$	−1.17362e13	−0.584479
$905$	0	0
$906$	−4.04128e13	−1.99270
$907$	9.36080e12i	0.459283i	0.973275	+	0.229641i	$0.0737553\pi$
$907$	9.36080e12i	0.459283i	−0.973275	+	0.229641i	$0.926245\pi$
$908$	− 4.08328e13i	− 1.99353i
$909$	1.16035e13	0.563704
$910$	0	0
$911$	6.17441e12	0.297004	0.148502	−	0.988912i	$-0.452555\pi$
$911$	6.17441e12	0.297004	0.148502	+	0.988912i	$0.452555\pi$
$912$	− 1.45644e11i	− 0.00697132i
$913$	3.81316e13i	1.81621i
$914$	4.66324e13	2.21019
$915$	0	0
$916$	−5.32428e13	−2.49880
$917$	1.70588e13i	0.796687i
$918$	2.74790e12i	0.127705i
$919$	−3.99328e12	−0.184676	−0.0923380	−	0.995728i	$-0.529434\pi$
$919$	−3.99328e12	−0.184676	−0.0923380	+	0.995728i	$0.529434\pi$
$920$	0	0
$921$	−5.25945e12	−0.240864
$922$	1.31534e13i	0.599443i
$923$	− 1.96763e13i	− 0.892350i
$924$	6.00992e13	2.71234
$925$	0	0
$926$	1.37049e13	0.612529
$927$	1.69393e13i	0.753417i
$928$	− 8.90089e12i	− 0.393974i
$929$	−1.84456e13	−0.812496	−0.406248	−	0.913763i	$-0.633163\pi$
$929$	−1.84456e13	−0.812496	−0.406248	+	0.913763i	$0.633163\pi$
$930$	0	0
$931$	−1.05259e12	−0.0459183
$932$	2.05950e13i	0.894108i
$933$	− 1.90163e13i	− 0.821596i
$934$	−4.80499e13	−2.06601
$935$	0	0
$936$	−2.15040e13	−0.915750
$937$	− 8.90163e12i	− 0.377261i	−0.982048	−	0.188630i	$-0.939595\pi$
$937$	− 8.90163e12i	− 0.377261i	0.982048	−	0.188630i	$-0.0604048\pi$
$938$	− 2.16287e13i	− 0.912257i
$939$	3.52991e13	1.48173
$940$	0	0
$941$	−1.64341e13	−0.683270	−0.341635	−	0.939833i	$-0.610981\pi$
$941$	−1.64341e13	−0.683270	−0.341635	+	0.939833i	$0.610981\pi$
$942$	3.01409e13i	1.24718i
$943$	− 9.73052e12i	− 0.400713i
$944$	−2.79643e11	−0.0114612
$945$	0	0
$946$	4.55615e13	1.84964
$947$	4.26042e13i	1.72138i	0.509128	+	0.860691i	$0.329968\pi$
$947$	4.26042e13i	1.72138i	−0.509128	+	0.860691i	$0.670032\pi$
$948$	9.63548e13i	3.87468i
$949$	−3.42497e13	−1.37075
$950$	0	0
$951$	−2.95178e13	−1.17023
$952$	1.86049e13i	0.734111i
$953$	− 3.52200e12i	− 0.138316i	−0.997606	−	0.0691578i	$-0.977969\pi$
$953$	− 3.52200e12i	− 0.138316i	0.997606	−	0.0691578i	$-0.0220312\pi$
$954$	−3.63570e13	−1.42109
$955$	0	0
$956$	−6.56677e13	−2.54268
$957$	− 1.46386e13i	− 0.564151i
$958$	1.38683e12i	0.0531958i
$959$	2.99178e13	1.14221
$960$	0	0
$961$	−9.56859e12	−0.361903
$962$	6.30885e13i	2.37499i
$963$	2.36994e13i	0.888013i
$964$	−5.53606e13	−2.06469
$965$	0	0
$966$	6.20741e13	2.29358
$967$	− 3.34889e13i	− 1.23163i	−0.787890	−	0.615816i	$-0.788826\pi$
$967$	− 3.34889e13i	− 1.23163i	0.787890	−	0.615816i	$-0.211174\pi$
$968$	− 2.30764e11i	− 0.00844750i
$969$	−2.26880e12	−0.0826682
$970$	0	0
$971$	−3.77122e13	−1.36143	−0.680715	−	0.732548i	$-0.738331\pi$
$971$	−3.77122e13	−1.36143	−0.680715	+	0.732548i	$0.738331\pi$
$972$	− 6.23603e13i	− 2.24083i
$973$	− 1.25647e13i	− 0.449411i
$974$	6.95968e13	2.47784
$975$	0	0
$976$	−1.49492e12	−0.0527344
$977$	− 4.00215e13i	− 1.40530i	−0.711537	−	0.702648i	$-0.752001\pi$
$977$	− 4.00215e13i	− 1.40530i	0.711537	−	0.702648i	$-0.247999\pi$
$978$	6.09370e13i	2.12988i
$979$	4.06286e13	1.41355
$980$	0	0
$981$	3.43629e13	1.18462
$982$	2.78612e13i	0.956088i
$983$	− 3.31096e13i	− 1.13100i	−0.824748	−	0.565500i	$-0.808683\pi$
$983$	− 3.31096e13i	− 1.13100i	0.824748	−	0.565500i	$-0.191317\pi$
$984$	−1.98847e13	−0.676147
$985$	0	0
$986$	1.16131e13	0.391293
$987$	6.78301e13i	2.27507i
$988$	4.89622e12i	0.163476i
$989$	2.92330e13	0.971606
$990$	0	0
$991$	1.90619e12	0.0627820	0.0313910	−	0.999507i	$-0.490006\pi$
$991$	1.90619e12	0.0627820	0.0313910	+	0.999507i	$0.490006\pi$
$992$	− 2.33748e13i	− 0.766383i
$993$	− 7.89684e13i	− 2.57740i
$994$	5.50715e13	1.78932
$995$	0	0
$996$	1.28125e14	4.12540
$997$	− 2.13028e13i	− 0.682823i	−0.939914	−	0.341411i	$-0.889095\pi$
$997$	− 2.13028e13i	− 0.682823i	0.939914	−	0.341411i	$-0.110905\pi$
$998$	1.43386e13i	0.457529i
$999$	−6.32195e12	−0.200820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.b.b.24.1		4
3.2	odd	2		225.10.b.h.199.4		4
4.3	odd	2		400.10.c.p.49.4		4
5.2	odd	4		25.10.a.b.1.2		2
5.3	odd	4		5.10.a.b.1.1	✓	2
5.4	even	2	inner	25.10.b.b.24.4		4
15.2	even	4		225.10.a.h.1.1		2
15.8	even	4		45.10.a.f.1.2		2
15.14	odd	2		225.10.b.h.199.1		4
20.3	even	4		80.10.a.f.1.1		2
20.7	even	4		400.10.a.t.1.2		2
20.19	odd	2		400.10.c.p.49.1		4
35.13	even	4		245.10.a.d.1.1		2
40.3	even	4		320.10.a.s.1.2		2
40.13	odd	4		320.10.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.a.b.1.1	✓	2	5.3	odd	4
25.10.a.b.1.2		2	5.2	odd	4
25.10.b.b.24.1		4	1.1	even	1	trivial
25.10.b.b.24.4		4	5.4	even	2	inner
45.10.a.f.1.2		2	15.8	even	4
80.10.a.f.1.1		2	20.3	even	4
225.10.a.h.1.1		2	15.2	even	4
225.10.b.h.199.1		4	15.14	odd	2
225.10.b.h.199.4		4	3.2	odd	2
245.10.a.d.1.1		2	35.13	even	4
320.10.a.k.1.1		2	40.13	odd	4
320.10.a.s.1.2		2	40.3	even	4
400.10.a.t.1.2		2	20.7	even	4
400.10.c.p.49.1		4	20.19	odd	2
400.10.c.p.49.4		4	4.3	odd	2

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-36.7648i q^{2} -193.530i q^{3} -839.648 q^{4} -7115.07 q^{6} +7647.66i q^{7} +12045.9i q^{8} -17770.7 q^{9} +O(q^{10})\)	\(q-36.7648i q^{2} -193.530i q^{3} -839.648 q^{4} -7115.07 q^{6} +7647.66i q^{7} +12045.9i q^{8} -17770.7 q^{9} -48361.0 q^{11} +162497. i q^{12} -100456. i q^{13} +281164. q^{14} +12964.5 q^{16} -201958. i q^{17} +653335. i q^{18} +58048.1 q^{19} +1.48005e6 q^{21} +1.77798e6i q^{22} +1.14078e6i q^{23} +2.33123e6 q^{24} -3.69324e6 q^{26} -370091. i q^{27} -6.42134e6i q^{28} -1.56407e6 q^{29} -4.10744e6 q^{31} +5.69086e6i q^{32} +9.35929e6i q^{33} -7.42493e6 q^{34} +1.49211e7 q^{36} -1.70821e7i q^{37} -2.13412e6i q^{38} -1.94412e7 q^{39} -8.52969e6 q^{41} -5.44136e7i q^{42} -2.56254e7i q^{43} +4.06062e7 q^{44} +4.19406e7 q^{46} +4.58297e7i q^{47} -2.50902e6i q^{48} -1.81331e7 q^{49} -3.90848e7 q^{51} +8.43476e7i q^{52} +5.56483e7i q^{53} -1.36063e7 q^{54} -9.21228e7 q^{56} -1.12340e7i q^{57} +5.75026e7i q^{58} -2.15699e7 q^{59} -1.15309e8 q^{61} +1.51009e8i q^{62} -1.35904e8i q^{63} +2.15861e8 q^{64} +3.44092e8 q^{66} -7.69254e7i q^{67} +1.69573e8i q^{68} +2.20775e8 q^{69} +1.95870e8 q^{71} -2.14064e8i q^{72} -3.40942e8i q^{73} -6.28021e8 q^{74} -4.87399e7 q^{76} -3.69849e8i q^{77} +7.14751e8i q^{78} +5.92965e8 q^{79} -4.21404e8 q^{81} +3.13592e8i q^{82} -7.88477e8i q^{83} -1.24272e9 q^{84} -9.42111e8 q^{86} +3.02693e8i q^{87} -5.82552e8i q^{88} -8.40110e8 q^{89} +7.68253e8 q^{91} -9.57856e8i q^{92} +7.94910e8i q^{93} +1.68492e9 q^{94} +1.10135e9 q^{96} +2.35903e8i q^{97} +6.66658e8i q^{98} +8.59408e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2088 q^{4} - 10672 q^{6} - 5012 q^{9}+O(q^{10}) \) 4 * q - 2088 * q^4 - 10672 * q^6 - 5012 * q^9	\( 4 q - 2088 q^{4} - 10672 q^{6} - 5012 q^{9} + 47968 q^{11} + 880704 q^{14} - 624096 q^{16} + 593040 q^{19} + 2169408 q^{21} + 5757120 q^{24} - 6606872 q^{26} + 7333960 q^{29} + 3226288 q^{31} - 47758616 q^{34} + 23603464 q^{36} - 40818544 q^{39} - 53914552 q^{41} + 51644704 q^{44} + 88782528 q^{46} - 26308228 q^{49} + 3559568 q^{51} + 97135840 q^{54} - 86298240 q^{56} + 109991120 q^{59} - 549159432 q^{61} + 338882432 q^{64} + 945597376 q^{66} + 429377856 q^{69} - 14261872 q^{71} - 1039794056 q^{74} - 194944480 q^{76} - 13755040 q^{79} - 550718716 q^{81} - 2323858176 q^{84} - 424776272 q^{86} - 1660177320 q^{89} + 1363261808 q^{91} + 2696297824 q^{94} + 1606720768 q^{96} + 3927464096 q^{99}+O(q^{100}) \) 4 * q - 2088 * q^4 - 10672 * q^6 - 5012 * q^9 + 47968 * q^11 + 880704 * q^14 - 624096 * q^16 + 593040 * q^19 + 2169408 * q^21 + 5757120 * q^24 - 6606872 * q^26 + 7333960 * q^29 + 3226288 * q^31 - 47758616 * q^34 + 23603464 * q^36 - 40818544 * q^39 - 53914552 * q^41 + 51644704 * q^44 + 88782528 * q^46 - 26308228 * q^49 + 3559568 * q^51 + 97135840 * q^54 - 86298240 * q^56 + 109991120 * q^59 - 549159432 * q^61 + 338882432 * q^64 + 945597376 * q^66 + 429377856 * q^69 - 14261872 * q^71 - 1039794056 * q^74 - 194944480 * q^76 - 13755040 * q^79 - 550718716 * q^81 - 2323858176 * q^84 - 424776272 * q^86 - 1660177320 * q^89 + 1363261808 * q^91 + 2696297824 * q^94 + 1606720768 * q^96 + 3927464096 * q^99

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