LMFDB - Embedded newform 25.9.c.c.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, 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:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 124 x^{9} + 1665 x^{8} - 2456 x^{7} + 4192 x^{6} + 50576 x^{5} + \cdots + 1000000 $ x^12 - 4x^11 + 8x^10 + 124x^9 + 1665x^8 - 2456x^7 + 4192x^6 + 50576x^5 + 221184x^4 + 133760x^3 + 3200x^2 - 80000*x + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$0.908990 + 0.908990i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.c.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.1270 - 18.1270i) q^{2} +(95.3921 - 95.3921i) q^{3} +401.173i q^{4} -3458.34 q^{6} +(-1478.49 - 1478.49i) q^{7} +(2631.55 - 2631.55i) q^{8} -11638.3i q^{9} +O(q^{10})$	\(q+(-18.1270 - 18.1270i) q^{2} +(95.3921 - 95.3921i) q^{3} +401.173i q^{4} -3458.34 q^{6} +(-1478.49 - 1478.49i) q^{7} +(2631.55 - 2631.55i) q^{8} -11638.3i q^{9} -16335.7 q^{11} +(38268.7 + 38268.7i) q^{12} +(-11728.1 + 11728.1i) q^{13} +53601.2i q^{14} +7296.48 q^{16} +(-20145.3 - 20145.3i) q^{17} +(-210967. + 210967. i) q^{18} +119950. i q^{19} -282073. q^{21} +(296117. + 296117. i) q^{22} +(361395. - 361395. i) q^{23} -502057. i q^{24} +425189. q^{26} +(-484333. - 484333. i) q^{27} +(593132. - 593132. i) q^{28} -64977.0i q^{29} -906755. q^{31} +(-805939. - 805939. i) q^{32} +(-1.55830e6 + 1.55830e6i) q^{33} +730347. i q^{34} +4.66897e6 q^{36} +(-1.51171e6 - 1.51171e6i) q^{37} +(2.17432e6 - 2.17432e6i) q^{38} +2.23753e6i q^{39} +2.57423e6 q^{41} +(5.11313e6 + 5.11313e6i) q^{42} +(-2.04074e6 + 2.04074e6i) q^{43} -6.55345e6i q^{44} -1.31020e7 q^{46} +(-1.34679e6 - 1.34679e6i) q^{47} +(696026. - 696026. i) q^{48} -1.39291e6i q^{49} -3.84341e6 q^{51} +(-4.70499e6 - 4.70499e6i) q^{52} +(773924. - 773924. i) q^{53} +1.75590e7i q^{54} -7.78145e6 q^{56} +(1.14423e7 + 1.14423e7i) q^{57} +(-1.17784e6 + 1.17784e6i) q^{58} -1.56073e7i q^{59} +8.14063e6 q^{61} +(1.64367e7 + 1.64367e7i) q^{62} +(-1.72071e7 + 1.72071e7i) q^{63} +2.73505e7i q^{64} +5.64944e7 q^{66} +(-2.76850e7 - 2.76850e7i) q^{67} +(8.08176e6 - 8.08176e6i) q^{68} -6.89484e7i q^{69} -1.45478e7 q^{71} +(-3.06267e7 - 3.06267e7i) q^{72} +(1.43422e7 - 1.43422e7i) q^{73} +5.48055e7i q^{74} -4.81206e7 q^{76} +(2.41523e7 + 2.41523e7i) q^{77} +(4.05596e7 - 4.05596e7i) q^{78} +4.59513e7i q^{79} -1.60443e7 q^{81} +(-4.66629e7 - 4.66629e7i) q^{82} +(2.00811e7 - 2.00811e7i) q^{83} -1.13160e8i q^{84} +7.39848e7 q^{86} +(-6.19829e6 - 6.19829e6i) q^{87} +(-4.29882e7 + 4.29882e7i) q^{88} -3.53615e7i q^{89} +3.46798e7 q^{91} +(1.44982e8 + 1.44982e8i) q^{92} +(-8.64972e7 + 8.64972e7i) q^{93} +4.88265e7i q^{94} -1.53760e8 q^{96} +(-5.33242e6 - 5.33242e6i) q^{97} +(-2.52492e7 + 2.52492e7i) q^{98} +1.90120e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6396 q^{6}+O(q^{10}) $ 12 * q - 6396 * q^6	$ 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) $ 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−18.1270	−	18.1270i	−1.13293	−	1.13293i	−0.989687	−	0.143248i	$-0.954245\pi$
$2$	−18.1270	−	18.1270i	−1.13293	−	1.13293i	−0.143248	−	0.989687i	$-0.545755\pi$
$3$	95.3921	−	95.3921i	1.17768	−	1.17768i	0.197346	−	0.980334i	$-0.436768\pi$
$3$	95.3921	−	95.3921i	1.17768	−	1.17768i	0.980334	−	0.197346i	$-0.0632322\pi$
$4$			401.173i			1.56708i
$5$		0			0
$5$		0			0
$6$	−3458.34			−2.66847
$7$	−1478.49	−	1478.49i	−0.615783	−	0.615783i	0.328664	−	0.944447i	$-0.393402\pi$
$7$	−1478.49	−	1478.49i	−0.615783	−	0.615783i	−0.944447	+	0.328664i	$0.893402\pi$
$8$	2631.55	−	2631.55i	0.642467	−	0.642467i
$9$		−	11638.3i		−	1.77386i
$10$		0			0
$11$	−16335.7			−1.11575			−0.557876	−	0.829924i	$-0.688383\pi$
$11$	−16335.7			−1.11575			−0.557876	+	0.829924i	$0.688383\pi$
$12$	38268.7	+	38268.7i	1.84552	+	1.84552i
$13$	−11728.1	+	11728.1i	−0.410633	+	0.410633i	−0.881959	−	0.471326i	$-0.843775\pi$
$13$	−11728.1	+	11728.1i	−0.410633	+	0.410633i	0.471326	+	0.881959i	$0.343775\pi$
$14$			53601.2i			1.39528i
$15$		0			0
$16$	7296.48			0.111335
$17$	−20145.3	−	20145.3i	−0.241201	−	0.241201i	0.576146	−	0.817347i	$-0.304556\pi$
$17$	−20145.3	−	20145.3i	−0.241201	−	0.241201i	−0.817347	+	0.576146i	$0.804556\pi$
$18$	−210967.	+	210967.i	−2.00967	+	2.00967i
$19$			119950.i			0.920418i	0.887811	+	0.460209i	$0.152225\pi$
$19$			119950.i			0.920418i	−0.887811	+	0.460209i	$0.847775\pi$
$20$		0			0
$21$	−282073.			−1.45039
$22$	296117.	+	296117.i	1.26407	+	1.26407i
$23$	361395.	−	361395.i	1.29143	−	1.29143i	0.357527	−	0.933903i	$-0.383620\pi$
$23$	361395.	−	361395.i	1.29143	−	1.29143i	0.933903	−	0.357527i	$-0.116380\pi$
$24$		−	502057.i		−	1.51324i
$25$		0			0
$26$	425189.			0.930440
$27$	−484333.	−	484333.i	−0.911358	−	0.911358i
$28$	593132.	−	593132.i	0.964982	−	0.964982i
$29$		−	64977.0i		−	0.0918688i	−0.998944	−	0.0459344i	$-0.985373\pi$
$29$		−	64977.0i		−	0.0918688i	0.998944	−	0.0459344i	$-0.0146265\pi$
$30$		0			0
$31$	−906755.			−0.981845			−0.490923	−	0.871203i	$-0.663340\pi$
$31$	−906755.			−0.981845			−0.490923	+	0.871203i	$0.663340\pi$
$32$	−805939.	−	805939.i	−0.768603	−	0.768603i
$33$	−1.55830e6	+	1.55830e6i	−1.31400	+	1.31400i
$34$			730347.i			0.546529i
$35$		0			0
$36$	4.66897e6			2.77978
$37$	−1.51171e6	−	1.51171e6i	−0.806607	−	0.806607i	0.177512	−	0.984119i	$-0.443195\pi$
$37$	−1.51171e6	−	1.51171e6i	−0.806607	−	0.806607i	−0.984119	+	0.177512i	$0.943195\pi$
$38$	2.17432e6	−	2.17432e6i	1.04277	−	1.04277i
$39$			2.23753e6i			0.967187i
$40$		0			0
$41$	2.57423e6			0.910986			0.455493	−	0.890239i	$-0.349463\pi$
$41$	2.57423e6			0.910986			0.455493	+	0.890239i	$0.349463\pi$
$42$	5.11313e6	+	5.11313e6i	1.64320	+	1.64320i
$43$	−2.04074e6	+	2.04074e6i	−0.596916	+	0.596916i	−0.939491	−	0.342574i	$-0.888701\pi$
$43$	−2.04074e6	+	2.04074e6i	−0.596916	+	0.596916i	0.342574	+	0.939491i	$0.388701\pi$
$44$		−	6.55345e6i		−	1.74847i
$45$		0			0
$46$	−1.31020e7			−2.92621
$47$	−1.34679e6	−	1.34679e6i	−0.276000	−	0.276000i	0.555510	−	0.831510i	$-0.312523\pi$
$47$	−1.34679e6	−	1.34679e6i	−0.276000	−	0.276000i	−0.831510	+	0.555510i	$0.812523\pi$
$48$	696026.	−	696026.i	0.131117	−	0.131117i
$49$		−	1.39291e6i		−	0.241623i
$50$		0			0
$51$	−3.84341e6			−0.568114
$52$	−4.70499e6	−	4.70499e6i	−0.643495	−	0.643495i
$53$	773924.	−	773924.i	0.0980832	−	0.0980832i	−0.656362	−	0.754446i	$-0.727906\pi$
$53$	773924.	−	773924.i	0.0980832	−	0.0980832i	0.754446	+	0.656362i	$0.227906\pi$
$54$			1.75590e7i			2.06502i
$55$		0			0
$56$	−7.78145e6			−0.791240
$57$	1.14423e7	+	1.14423e7i	1.08396	+	1.08396i
$58$	−1.17784e6	+	1.17784e6i	−0.104081	+	0.104081i
$59$		−	1.56073e7i		−	1.28801i	−0.765021	−	0.644006i	$-0.777271\pi$
$59$		−	1.56073e7i		−	1.28801i	0.765021	−	0.644006i	$-0.222729\pi$
$60$		0			0
$61$	8.14063e6			0.587948			0.293974	−	0.955813i	$-0.405022\pi$
$61$	8.14063e6			0.587948			0.293974	+	0.955813i	$0.405022\pi$
$62$	1.64367e7	+	1.64367e7i	1.11237	+	1.11237i
$63$	−1.72071e7	+	1.72071e7i	−1.09231	+	1.09231i
$64$			2.73505e7i			1.63022i
$65$		0			0
$66$	5.64944e7			2.97735
$67$	−2.76850e7	−	2.76850e7i	−1.37387	−	1.37387i	−0.854626	−	0.519244i	$-0.826214\pi$
$67$	−2.76850e7	−	2.76850e7i	−1.37387	−	1.37387i	−0.519244	−	0.854626i	$-0.673786\pi$
$68$	8.08176e6	−	8.08176e6i	0.377981	−	0.377981i
$69$		−	6.89484e7i		−	3.04178i
$70$		0			0
$71$	−1.45478e7			−0.572484			−0.286242	−	0.958157i	$-0.592406\pi$
$71$	−1.45478e7			−0.572484			−0.286242	+	0.958157i	$0.592406\pi$
$72$	−3.06267e7	−	3.06267e7i	−1.13965	−	1.13965i
$73$	1.43422e7	−	1.43422e7i	0.505040	−	0.505040i	−0.407960	−	0.913000i	$-0.633760\pi$
$73$	1.43422e7	−	1.43422e7i	0.505040	−	0.505040i	0.913000	+	0.407960i	$0.133760\pi$
$74$			5.48055e7i			1.82767i
$75$		0			0
$76$	−4.81206e7			−1.44237
$77$	2.41523e7	+	2.41523e7i	0.687061	+	0.687061i
$78$	4.05596e7	−	4.05596e7i	1.09576	−	1.09576i
$79$			4.59513e7i			1.17975i	0.807495	+	0.589874i	$0.200823\pi$
$79$			4.59513e7i			1.17975i	−0.807495	+	0.589874i	$0.799177\pi$
$80$		0			0
$81$	−1.60443e7			−0.372717
$82$	−4.66629e7	−	4.66629e7i	−1.03209	−	1.03209i
$83$	2.00811e7	−	2.00811e7i	0.423130	−	0.423130i	−0.463150	−	0.886280i	$-0.653281\pi$
$83$	2.00811e7	−	2.00811e7i	0.423130	−	0.423130i	0.886280	+	0.463150i	$0.153281\pi$
$84$		−	1.13160e8i		−	2.27288i
$85$		0			0
$86$	7.39848e7			1.35253
$87$	−6.19829e6	−	6.19829e6i	−0.108192	−	0.108192i
$88$	−4.29882e7	+	4.29882e7i	−0.716834	+	0.716834i
$89$		−	3.53615e7i		−	0.563600i	−0.959473	−	0.281800i	$-0.909069\pi$
$89$		−	3.53615e7i		−	0.563600i	0.959473	−	0.281800i	$-0.0909314\pi$
$90$		0			0
$91$	3.46798e7			0.505721
$92$	1.44982e8	+	1.44982e8i	2.02378	+	2.02378i
$93$	−8.64972e7	+	8.64972e7i	−1.15630	+	1.15630i
$94$			4.88265e7i			0.625380i
$95$		0			0
$96$	−1.53760e8			−1.81034
$97$	−5.33242e6	−	5.33242e6i	−0.0602334	−	0.0602334i	0.676348	−	0.736582i	$-0.263561\pi$
$97$	−5.33242e6	−	5.33242e6i	−0.0602334	−	0.0602334i	−0.736582	+	0.676348i	$0.763561\pi$
$98$	−2.52492e7	+	2.52492e7i	−0.273743	+	0.273743i
$99$			1.90120e8i			1.97919i
$100$		0			0
$101$	9.38217e7			0.901608			0.450804	−	0.892623i	$-0.351137\pi$
$101$	9.38217e7			0.901608			0.450804	+	0.892623i	$0.351137\pi$
$102$	6.96693e7	+	6.96693e7i	0.643637	+	0.643637i
$103$	−8.14568e7	+	8.14568e7i	−0.723734	+	0.723734i	−0.969364	−	0.245630i	$-0.921005\pi$
$103$	−8.14568e7	+	8.14568e7i	−0.723734	+	0.723734i	0.245630	+	0.969364i	$0.421005\pi$
$104$			6.17259e7i			0.527636i
$105$		0			0
$106$	−2.80578e7			−0.222244
$107$	−1.65592e8	−	1.65592e8i	−1.26329	−	1.26329i	−0.949486	−	0.313808i	$-0.898395\pi$
$107$	−1.65592e8	−	1.65592e8i	−1.26329	−	1.26329i	−0.313808	−	0.949486i	$-0.601605\pi$
$108$	1.94301e8	−	1.94301e8i	1.42817	−	1.42817i
$109$		−	2.72814e7i		−	0.193268i	−0.995320	−	0.0966342i	$-0.969192\pi$
$109$		−	2.72814e7i		−	0.193268i	0.995320	−	0.0966342i	$-0.0308077\pi$
$110$		0			0
$111$	−2.88411e8			−1.89985
$112$	−1.07878e7	−	1.07878e7i	−0.0685584	−	0.0685584i
$113$	1.13277e8	−	1.13277e8i	0.694751	−	0.694751i	−0.268522	−	0.963273i	$-0.586535\pi$
$113$	1.13277e8	−	1.13277e8i	0.694751	−	0.694751i	0.963273	+	0.268522i	$0.0865353\pi$
$114$		−	4.14827e8i		−	2.45611i
$115$		0			0
$116$	2.60670e7			0.143966
$117$	1.36495e8	+	1.36495e8i	0.728404	+	0.728404i
$118$	−2.82913e8	+	2.82913e8i	−1.45923	+	1.45923i
$119$			5.95695e7i			0.297054i
$120$		0			0
$121$	5.24968e7			0.244901
$122$	−1.47565e8	−	1.47565e8i	−0.666106	−	0.666106i
$123$	2.45561e8	−	2.45561e8i	1.07285	−	1.07285i
$124$		−	3.63766e8i		−	1.53863i
$125$		0			0
$126$	6.23826e8			2.47504
$127$	1.14891e8	+	1.14891e8i	0.441642	+	0.441642i	0.892564	−	0.450922i	$-0.148905\pi$
$127$	1.14891e8	+	1.14891e8i	0.441642	+	0.441642i	−0.450922	+	0.892564i	$0.648905\pi$
$128$	2.89462e8	−	2.89462e8i	1.07833	−	1.07833i
$129$			3.89341e8i			1.40595i
$130$		0			0
$131$	2.96659e8			1.00733			0.503666	−	0.863898i	$-0.331984\pi$
$131$	2.96659e8			1.00733			0.503666	+	0.863898i	$0.331984\pi$
$132$	−6.25147e8	−	6.25147e8i	−2.05914	−	2.05914i
$133$	1.77345e8	−	1.77345e8i	0.566777	−	0.566777i
$134$			1.00369e9i			3.11301i
$135$		0			0
$136$	−1.06027e8			−0.309927
$137$	2.10070e8	+	2.10070e8i	0.596322	+	0.596322i	0.939332	−	0.343010i	$-0.111446\pi$
$137$	2.10070e8	+	2.10070e8i	0.596322	+	0.596322i	−0.343010	+	0.939332i	$0.611446\pi$
$138$	−1.24983e9	+	1.24983e9i	−3.44614	+	3.44614i
$139$		−	6.11697e8i		−	1.63862i	−0.573353	−	0.819308i	$-0.694358\pi$
$139$		−	6.11697e8i		−	1.63862i	0.573353	−	0.819308i	$-0.305642\pi$
$140$		0			0
$141$	−2.56947e8			−0.650079
$142$	2.63707e8	+	2.63707e8i	0.648587	+	0.648587i
$143$	1.91587e8	−	1.91587e8i	0.458164	−	0.458164i
$144$		−	8.49185e7i		−	0.197493i
$145$		0			0
$146$	−5.19962e8			−1.14435
$147$	−1.32873e8	−	1.32873e8i	−0.284555	−	0.284555i
$148$	6.06458e8	−	6.06458e8i	1.26402	−	1.26402i
$149$		−	9.02377e7i		−	0.183081i	−0.995801	−	0.0915404i	$-0.970821\pi$
$149$		−	9.02377e7i		−	0.183081i	0.995801	−	0.0915404i	$-0.0291791\pi$
$150$		0			0
$151$	6.80057e8			1.30809			0.654045	−	0.756456i	$-0.273071\pi$
$151$	6.80057e8			1.30809			0.654045	+	0.756456i	$0.273071\pi$
$152$	3.15653e8	+	3.15653e8i	0.591338	+	0.591338i
$153$	−2.34457e8	+	2.34457e8i	−0.427856	+	0.427856i
$154$		−	8.75614e8i		−	1.55679i
$155$		0			0
$156$	−8.97637e8			−1.51566
$157$	3.18328e8	+	3.18328e8i	0.523934	+	0.523934i	0.918757	−	0.394823i	$-0.129194\pi$
$157$	3.18328e8	+	3.18328e8i	0.523934	+	0.523934i	−0.394823	+	0.918757i	$0.629194\pi$
$158$	8.32957e8	−	8.32957e8i	1.33658	−	1.33658i
$159$		−	1.47652e8i		−	0.231021i
$160$		0			0
$161$	−1.06864e9			−1.59048
$162$	2.90833e8	+	2.90833e8i	0.422264	+	0.422264i
$163$	−1.91857e8	+	1.91857e8i	−0.271786	+	0.271786i	−0.829819	−	0.558033i	$-0.811556\pi$
$163$	−1.91857e8	+	1.91857e8i	−0.271786	+	0.271786i	0.558033	+	0.829819i	$0.311556\pi$
$164$			1.03271e9i			1.42759i
$165$		0			0
$166$	−7.28017e8			−0.958758
$167$	8.01564e8	+	8.01564e8i	1.03056	+	1.03056i	0.999518	+	0.0310401i	$0.00988195\pi$
$167$	8.01564e8	+	8.01564e8i	1.03056	+	1.03056i	0.0310401	+	0.999518i	$0.490118\pi$
$168$	−7.42289e8	+	7.42289e8i	−0.931828	+	0.931828i
$169$			5.40635e8i			0.662762i
$170$		0			0
$171$	1.39601e9			1.63269
$172$	−8.18689e8	−	8.18689e8i	−0.935417	−	0.935417i
$173$	−5.45363e8	+	5.45363e8i	−0.608837	+	0.608837i	−0.942642	−	0.333805i	$-0.891667\pi$
$173$	−5.45363e8	+	5.45363e8i	−0.608837	+	0.608837i	0.333805	+	0.942642i	$0.391667\pi$
$174$			2.24712e8i			0.245149i
$175$		0			0
$176$	−1.19193e8			−0.124223
$177$	−1.48881e9	−	1.48881e9i	−1.51687	−	1.51687i
$178$	−6.40997e8	+	6.40997e8i	−0.638522	+	0.638522i
$179$			3.27871e8i			0.319368i	0.987168	+	0.159684i	$0.0510474\pi$
$179$			3.27871e8i			0.319368i	−0.987168	+	0.159684i	$0.948953\pi$
$180$		0			0
$181$	7.47914e8			0.696847			0.348423	−	0.937337i	$-0.386717\pi$
$181$	7.47914e8			0.696847			0.348423	+	0.937337i	$0.386717\pi$
$182$	−6.28639e8	−	6.28639e8i	−0.572949	−	0.572949i
$183$	7.76551e8	−	7.76551e8i	0.692414	−	0.692414i
$184$		−	1.90206e9i		−	1.65940i
$185$		0			0
$186$	3.13586e9			2.62002
$187$	3.29088e8	+	3.29088e8i	0.269120	+	0.269120i
$188$	5.40297e8	−	5.40297e8i	0.432515	−	0.432515i
$189$			1.43217e9i			1.12240i
$190$		0			0
$191$	1.88619e8			0.141727			0.0708634	−	0.997486i	$-0.477425\pi$
$191$	1.88619e8			0.141727			0.0708634	+	0.997486i	$0.477425\pi$
$192$	2.60902e9	+	2.60902e9i	1.91988	+	1.91988i
$193$	−8.27230e8	+	8.27230e8i	−0.596207	+	0.596207i	−0.939301	−	0.343094i	$-0.888525\pi$
$193$	−8.27230e8	+	8.27230e8i	−0.596207	+	0.596207i	0.343094	+	0.939301i	$0.388525\pi$
$194$			1.93321e8i			0.136481i
$195$		0			0
$196$	5.58798e8			0.378644
$197$	−5.97958e7	−	5.97958e7i	−0.0397014	−	0.0397014i	0.686977	−	0.726679i	$-0.258937\pi$
$197$	−5.97958e7	−	5.97958e7i	−0.0397014	−	0.0397014i	−0.726679	+	0.686977i	$0.758937\pi$
$198$	3.44629e9	−	3.44629e9i	2.24229	−	2.24229i
$199$		−	1.79499e9i		−	1.14459i	−0.820049	−	0.572294i	$-0.806054\pi$
$199$		−	1.79499e9i		−	1.14459i	0.820049	−	0.572294i	$-0.193946\pi$
$200$		0			0
$201$	−5.28186e9			−3.23596
$202$	−1.70070e9	−	1.70070e9i	−1.02146	−	1.02146i
$203$	−9.60682e7	+	9.60682e7i	−0.0565712	+	0.0565712i
$204$		−	1.54187e9i		−	0.890282i
$205$		0			0
$206$	2.95313e9			1.63989
$207$	−4.20602e9	−	4.20602e9i	−2.29082	−	2.29082i
$208$	−8.55736e7	+	8.55736e7i	−0.0457179	+	0.0457179i
$209$		−	1.95947e9i		−	1.02696i
$210$		0			0
$211$	−1.17722e9			−0.593920			−0.296960	−	0.954890i	$-0.595973\pi$
$211$	−1.17722e9			−0.593920			−0.296960	+	0.954890i	$0.595973\pi$
$212$	3.10477e8	+	3.10477e8i	0.153705	+	0.153705i
$213$	−1.38774e9	+	1.38774e9i	−0.674203	+	0.674203i
$214$			6.00336e9i			2.86246i
$215$		0			0
$216$	−2.54909e9			−1.17104
$217$	1.34063e9	+	1.34063e9i	0.604603	+	0.604603i
$218$	−4.94529e8	+	4.94529e8i	−0.218961	+	0.218961i
$219$		−	2.73627e9i		−	1.18955i
$220$		0			0
$221$	4.72532e8			0.198090
$222$	5.22801e9	+	5.22801e9i	2.15241	+	2.15241i
$223$	−4.44024e8	+	4.44024e8i	−0.179550	+	0.179550i	−0.791160	−	0.611609i	$-0.790522\pi$
$223$	−4.44024e8	+	4.44024e8i	−0.179550	+	0.179550i	0.611609	+	0.791160i	$0.290522\pi$
$224$			2.38315e9i			0.946585i
$225$		0			0
$226$	−4.10675e9			−1.57422
$227$	2.77306e7	+	2.77306e7i	0.0104437	+	0.0104437i	0.712309	−	0.701866i	$-0.247649\pi$
$227$	2.77306e7	+	2.77306e7i	0.0104437	+	0.0104437i	−0.701866	+	0.712309i	$0.747649\pi$
$228$	−4.59032e9	+	4.59032e9i	−1.69865	+	1.69865i
$229$			4.86094e9i			1.76758i	0.467888	+	0.883788i	$0.345015\pi$
$229$			4.86094e9i			1.76758i	−0.467888	+	0.883788i	$0.654985\pi$
$230$		0			0
$231$	4.60787e9			1.61827
$232$	−1.70990e8	−	1.70990e8i	−0.0590227	−	0.0590227i
$233$	1.83552e9	−	1.83552e9i	0.622780	−	0.622780i	−0.323461	−	0.946241i	$-0.604846\pi$
$233$	1.83552e9	−	1.83552e9i	0.622780	−	0.622780i	0.946241	+	0.323461i	$0.104846\pi$
$234$		−	4.94847e9i		−	1.65047i
$235$		0			0
$236$	6.26123e9			2.01842
$237$	4.38339e9	+	4.38339e9i	1.38937	+	1.38937i
$238$	1.07981e9	−	1.07981e9i	0.336543	−	0.336543i
$239$		−	1.66860e9i		−	0.511400i	−0.966756	−	0.255700i	$-0.917694\pi$
$239$		−	1.66860e9i		−	0.511400i	0.966756	−	0.255700i	$-0.0823059\pi$
$240$		0			0
$241$	2.10688e9			0.624557			0.312278	−	0.949991i	$-0.398908\pi$
$241$	2.10688e9			0.624557			0.312278	+	0.949991i	$0.398908\pi$
$242$	−9.51607e8	−	9.51607e8i	−0.277457	−	0.277457i
$243$	1.64722e9	−	1.64722e9i	0.472417	−	0.472417i
$244$			3.26580e9i			0.921362i
$245$		0			0
$246$	−8.90255e9			−2.43094
$247$	−1.40678e9	−	1.40678e9i	−0.377953	−	0.377953i
$248$	−2.38617e9	+	2.38617e9i	−0.630803	+	0.630803i
$249$		−	3.83115e9i		−	0.996624i
$250$		0			0
$251$	−1.49763e9			−0.377319			−0.188660	−	0.982043i	$-0.560414\pi$
$251$	−1.49763e9			−0.377319			−0.188660	+	0.982043i	$0.560414\pi$
$252$	−6.90304e9	−	6.90304e9i	−1.71174	−	1.71174i
$253$	−5.90365e9	+	5.90365e9i	−1.44092	+	1.44092i
$254$		−	4.16524e9i		−	1.00070i
$255$		0			0
$256$	−3.49238e9			−0.813133
$257$	4.04859e9	+	4.04859e9i	0.928050	+	0.928050i	0.997580	−	0.0695294i	$-0.0221498\pi$
$257$	4.04859e9	+	4.04859e9i	0.928050	+	0.928050i	−0.0695294	+	0.997580i	$0.522150\pi$
$258$	7.05756e9	−	7.05756e9i	1.59285	−	1.59285i
$259$			4.47011e9i			0.993390i
$260$		0			0
$261$	−7.56222e8			−0.162962
$262$	−5.37753e9	−	5.37753e9i	−1.14124	−	1.14124i
$263$	2.53404e9	−	2.53404e9i	0.529651	−	0.529651i	−0.390817	−	0.920468i	$-0.627808\pi$
$263$	2.53404e9	−	2.53404e9i	0.529651	−	0.529651i	0.920468	+	0.390817i	$0.127808\pi$
$264$			8.20146e9i			1.68840i
$265$		0			0
$266$	−6.42945e9			−1.28424
$267$	−3.37321e9	−	3.37321e9i	−0.663740	−	0.663740i
$268$	1.11065e10	−	1.11065e10i	2.15297	−	2.15297i
$269$		−	8.18803e9i		−	1.56376i	−0.623428	−	0.781881i	$-0.714261\pi$
$269$		−	8.18803e9i		−	1.56376i	0.623428	−	0.781881i	$-0.285739\pi$
$270$		0			0
$271$	9.31816e9			1.72764			0.863820	−	0.503801i	$-0.168066\pi$
$271$	9.31816e9			1.72764			0.863820	+	0.503801i	$0.168066\pi$
$272$	−1.46990e8	−	1.46990e8i	−0.0268542	−	0.0268542i
$273$	3.30818e9	−	3.30818e9i	0.595577	−	0.595577i
$274$		−	7.61584e9i		−	1.35119i
$275$		0			0
$276$	2.76603e10			4.76672
$277$	2.03174e9	+	2.03174e9i	0.345103	+	0.345103i	0.858282	−	0.513179i	$-0.171532\pi$
$277$	2.03174e9	+	2.03174e9i	0.345103	+	0.345103i	−0.513179	+	0.858282i	$0.671532\pi$
$278$	−1.10882e10	+	1.10882e10i	−1.85645	+	1.85645i
$279$			1.05531e10i			1.74165i
$280$		0			0
$281$	−4.93431e9			−0.791409			−0.395704	−	0.918378i	$-0.629500\pi$
$281$	−4.93431e9			−0.791409			−0.395704	+	0.918378i	$0.629500\pi$
$282$	4.65766e9	+	4.65766e9i	0.736498	+	0.736498i
$283$	−1.27718e9	+	1.27718e9i	−0.199116	+	0.199116i	−0.799621	−	0.600505i	$-0.794966\pi$
$283$	−1.27718e9	+	1.27718e9i	−0.199116	+	0.199116i	0.600505	+	0.799621i	$0.294966\pi$
$284$		−	5.83618e9i		−	0.897130i
$285$		0			0
$286$	−6.94576e9			−1.03814
$287$	−3.80598e9	−	3.80598e9i	−0.560970	−	0.560970i
$288$	−9.37975e9	+	9.37975e9i	−1.36339	+	1.36339i
$289$		−	6.16409e9i		−	0.883644i
$290$		0			0
$291$	−1.01734e9			−0.141871
$292$	5.75372e9	+	5.75372e9i	0.791439	+	0.791439i
$293$	−1.55516e9	+	1.55516e9i	−0.211010	+	0.211010i	−0.804697	−	0.593686i	$-0.797672\pi$
$293$	−1.55516e9	+	1.55516e9i	−0.211010	+	0.211010i	0.593686	+	0.804697i	$0.297672\pi$
$294$			4.81715e9i			0.644764i
$295$		0			0
$296$	−7.95628e9			−1.03644
$297$	7.91193e9	+	7.91193e9i	1.01685	+	1.01685i
$298$	−1.63573e9	+	1.63573e9i	−0.207419	+	0.207419i
$299$			8.47694e9i			1.06061i
$300$		0			0
$301$	6.03444e9			0.735142
$302$	−1.23274e10	−	1.23274e10i	−1.48198	−	1.48198i
$303$	8.94985e9	−	8.94985e9i	1.06181	−	1.06181i
$304$			8.75211e8i			0.102475i
$305$		0			0
$306$	8.49999e9			0.969466
$307$	−5.17193e9	−	5.17193e9i	−0.582236	−	0.582236i	0.353281	−	0.935517i	$-0.385066\pi$
$307$	−5.17193e9	−	5.17193e9i	−0.582236	−	0.582236i	−0.935517	+	0.353281i	$0.885066\pi$
$308$	−9.68924e9	+	9.68924e9i	−1.07668	+	1.07668i
$309$			1.55407e10i			1.70465i
$310$		0			0
$311$	−1.55035e10			−1.65725			−0.828624	−	0.559806i	$-0.810876\pi$
$311$	−1.55035e10			−1.65725			−0.828624	+	0.559806i	$0.810876\pi$
$312$	5.88816e9	+	5.88816e9i	0.621386	+	0.621386i
$313$	1.34334e10	−	1.34334e10i	1.39961	−	1.39961i	0.598462	−	0.801151i	$-0.295779\pi$
$313$	1.34334e10	−	1.34334e10i	1.39961	−	1.39961i	0.801151	−	0.598462i	$-0.204221\pi$
$314$		−	1.15406e10i		−	1.18717i
$315$		0			0
$316$	−1.84344e10			−1.84876
$317$	5.23230e8	+	5.23230e8i	0.0518150	+	0.0518150i	0.732539	−	0.680725i	$-0.238335\pi$
$317$	5.23230e8	+	5.23230e8i	0.0518150	+	0.0518150i	−0.680725	+	0.732539i	$0.738335\pi$
$318$	−2.67649e9	+	2.67649e9i	−0.261732	+	0.261732i
$319$			1.06145e9i			0.102503i
$320$		0			0
$321$	−3.15924e10			−2.97551
$322$	1.93712e10	+	1.93712e10i	1.80191	+	1.80191i
$323$	2.41643e9	−	2.41643e9i	0.222005	−	0.222005i
$324$		−	6.43652e9i		−	0.584079i
$325$		0			0
$326$	6.95557e9			0.615832
$327$	−2.60243e9	−	2.60243e9i	−0.227608	−	0.227608i
$328$	6.77420e9	−	6.77420e9i	0.585279	−	0.585279i
$329$			3.98245e9i			0.339912i
$330$		0			0
$331$	2.31172e10			1.92585			0.962925	−	0.269770i	$-0.0869477\pi$
$331$	2.31172e10			1.92585			0.962925	+	0.269770i	$0.0869477\pi$
$332$	8.05598e9	+	8.05598e9i	0.663080	+	0.663080i
$333$	−1.75937e10	+	1.75937e10i	−1.43081	+	1.43081i
$334$		−	2.90598e10i		−	2.33511i
$335$		0			0
$336$	−2.05814e9			−0.161480
$337$	−8.96413e7	−	8.96413e7i	−0.00695006	−	0.00695006i	0.703623	−	0.710573i	$-0.251564\pi$
$337$	−8.96413e7	−	8.96413e7i	−0.00695006	−	0.00695006i	−0.710573	+	0.703623i	$0.751564\pi$
$338$	9.80007e9	−	9.80007e9i	0.750866	−	0.750866i
$339$		−	2.16115e10i		−	1.63639i
$340$		0			0
$341$	1.48125e10			1.09550
$342$	−2.53054e10	−	2.53054e10i	−1.84973	−	1.84973i
$343$	−1.05826e10	+	1.05826e10i	−0.764570	+	0.764570i
$344$			1.07406e10i			0.766999i
$345$		0			0
$346$	1.97715e10			1.37954
$347$	−1.55738e10	−	1.55738e10i	−1.07418	−	1.07418i	−0.997018	−	0.0771634i	$-0.975414\pi$
$347$	−1.55738e10	−	1.55738e10i	−1.07418	−	1.07418i	−0.0771634	−	0.997018i	$-0.524586\pi$
$348$	2.48659e9	−	2.48659e9i	0.169546	−	0.169546i
$349$			2.37106e10i			1.59823i	0.601175	+	0.799117i	$0.294699\pi$
$349$			2.37106e10i			1.59823i	−0.601175	+	0.799117i	$0.705301\pi$
$350$		0			0
$351$	1.13606e10			0.748467
$352$	1.31656e10	+	1.31656e10i	0.857570	+	0.857570i
$353$	−1.54184e9	+	1.54184e9i	−0.0992977	+	0.0992977i	−0.755010	−	0.655713i	$-0.772368\pi$
$353$	−1.54184e9	+	1.54184e9i	−0.0992977	+	0.0992977i	0.655713	+	0.755010i	$0.272368\pi$
$354$			5.39753e10i			3.43702i
$355$		0			0
$356$	1.41861e10			0.883207
$357$	5.68246e9	+	5.68246e9i	0.349835	+	0.349835i
$358$	5.94330e9	−	5.94330e9i	0.361823	−	0.361823i
$359$		−	9.69700e9i		−	0.583794i	−0.956450	−	0.291897i	$-0.905714\pi$
$359$		−	9.69700e9i		−	0.583794i	0.956450	−	0.291897i	$-0.0942864\pi$
$360$		0			0
$361$	2.59562e9			0.152831
$362$	−1.35574e10	−	1.35574e10i	−0.789482	−	0.789482i
$363$	5.00778e9	−	5.00778e9i	0.288415	−	0.288415i
$364$			1.39126e10i			0.792506i
$365$		0			0
$366$	−2.81530e10			−1.56892
$367$	1.62256e10	+	1.62256e10i	0.894409	+	0.894409i	0.994935	−	0.100525i	$-0.0320523\pi$
$367$	1.62256e10	+	1.62256e10i	0.894409	+	0.894409i	−0.100525	+	0.994935i	$0.532052\pi$
$368$	2.63691e9	−	2.63691e9i	0.143782	−	0.143782i
$369$		−	2.99596e10i		−	1.61596i
$370$		0			0
$371$	−2.28848e9			−0.120796
$372$	−3.47003e10	−	3.47003e10i	−1.81202	−	1.81202i
$373$	−1.87707e10	+	1.87707e10i	−0.969719	+	0.969719i	−0.999555	−	0.0298363i	$-0.990501\pi$
$373$	−1.87707e10	+	1.87707e10i	−0.969719	+	0.969719i	0.0298363	+	0.999555i	$0.490501\pi$
$374$		−	1.19307e10i		−	0.609791i
$375$		0			0
$376$	−7.08829e9			−0.354642
$377$	7.62056e8	+	7.62056e8i	0.0377243	+	0.0377243i
$378$	2.59608e10	−	2.59608e10i	1.27160	−	1.27160i
$379$		−	1.08734e10i		−	0.526995i	−0.964660	−	0.263498i	$-0.915124\pi$
$379$		−	1.08734e10i		−	0.526995i	0.964660	−	0.263498i	$-0.0848761\pi$
$380$		0			0
$381$	2.19193e10			1.04023
$382$	−3.41909e9	−	3.41909e9i	−0.160567	−	0.160567i
$383$	−3.29552e7	+	3.29552e7i	−0.00153154	+	0.00153154i	−0.707872	−	0.706341i	$-0.750345\pi$
$383$	−3.29552e7	+	3.29552e7i	−0.00153154	+	0.00153154i	0.706341	+	0.707872i	$0.250345\pi$
$384$		−	5.52247e10i		−	2.53985i
$385$		0			0
$386$	2.99903e10			1.35093
$387$	2.37507e10	+	2.37507e10i	1.05885	+	1.05885i
$388$	2.13922e9	−	2.13922e9i	0.0943907	−	0.0943907i
$389$			2.20431e10i			0.962663i	0.876539	+	0.481331i	$0.159847\pi$
$389$			2.20431e10i			0.962663i	−0.876539	+	0.481331i	$0.840153\pi$
$390$		0			0
$391$	−1.45608e10			−0.622988
$392$	−3.66551e9	−	3.66551e9i	−0.155235	−	0.155235i
$393$	2.82989e10	−	2.82989e10i	1.18631	−	1.18631i
$394$			2.16783e9i			0.0899582i
$395$		0			0
$396$	−7.62710e10			−3.10155
$397$	−2.74626e10	−	2.74626e10i	−1.10556	−	1.10556i	−0.993728	−	0.111827i	$-0.964330\pi$
$397$	−2.74626e10	−	2.74626e10i	−1.10556	−	1.10556i	−0.111827	−	0.993728i	$-0.535670\pi$
$398$	−3.25376e10	+	3.25376e10i	−1.29674	+	1.29674i
$399$		−	3.38346e10i		−	1.33496i
$400$		0			0
$401$	−4.74772e10			−1.83615			−0.918073	−	0.396411i	$-0.870255\pi$
$401$	−4.74772e10			−1.83615			−0.918073	+	0.396411i	$0.870255\pi$
$402$	9.57441e10	+	9.57441e10i	3.66613	+	3.66613i
$403$	1.06345e10	−	1.06345e10i	0.403178	−	0.403178i
$404$			3.76388e10i			1.41289i
$405$		0			0
$406$	3.48285e9			0.128183
$407$	2.46949e10	+	2.46949e10i	0.899973	+	0.899973i
$408$	−1.01141e10	+	1.01141e10i	−0.364995	+	0.364995i
$409$		−	1.53681e10i		−	0.549195i	−0.961559	−	0.274597i	$-0.911455\pi$
$409$		−	1.53681e10i		−	0.549195i	0.961559	−	0.274597i	$-0.0885446\pi$
$410$		0			0
$411$	4.00779e10			1.40455
$412$	−3.26783e10	−	3.26783e10i	−1.13415	−	1.13415i
$413$	−2.30753e10	+	2.30753e10i	−0.793135	+	0.793135i
$414$			1.52485e11i			5.19069i
$415$		0			0
$416$	1.89042e10			0.631227
$417$	−5.83511e10	−	5.83511e10i	−1.92977	−	1.92977i
$418$	−3.55191e10	+	3.55191e10i	−1.16348	+	1.16348i
$419$		−	1.15939e10i		−	0.376162i	−0.982154	−	0.188081i	$-0.939773\pi$
$419$		−	1.15939e10i		−	0.376162i	0.982154	−	0.188081i	$-0.0602267\pi$
$420$		0			0
$421$	−8.67547e9			−0.276162			−0.138081	−	0.990421i	$-0.544093\pi$
$421$	−8.67547e9			−0.276162			−0.138081	+	0.990421i	$0.544093\pi$
$422$	2.13394e10	+	2.13394e10i	0.672873	+	0.672873i
$423$	−1.56744e10	+	1.56744e10i	−0.489585	+	0.489585i
$424$		−	4.07323e9i		−	0.126031i
$425$		0			0
$426$	5.03111e10			1.52766
$427$	−1.20359e10	−	1.20359e10i	−0.362048	−	0.362048i
$428$	6.64311e10	−	6.64311e10i	1.97969	−	1.97969i
$429$		−	3.65517e10i		−	1.07914i
$430$		0			0
$431$	−2.62390e10			−0.760394			−0.380197	−	0.924906i	$-0.624144\pi$
$431$	−2.62390e10			−0.760394			−0.380197	+	0.924906i	$0.624144\pi$
$432$	−3.53393e9	−	3.53393e9i	−0.101466	−	0.101466i
$433$	−3.46348e10	+	3.46348e10i	−0.985284	+	0.985284i	−0.999893	−	0.0146092i	$-0.995350\pi$
$433$	−3.46348e10	+	3.46348e10i	−0.985284	+	0.985284i	0.0146092	+	0.999893i	$0.495350\pi$
$434$		−	4.86031e10i		−	1.36995i
$435$		0			0
$436$	1.09446e10			0.302868
$437$	4.33493e10	+	4.33493e10i	1.18866	+	1.18866i
$438$	−4.96003e10	+	4.96003e10i	−1.34768	+	1.34768i
$439$			3.36968e10i			0.907259i	0.891190	+	0.453629i	$0.149871\pi$
$439$			3.36968e10i			0.907259i	−0.891190	+	0.453629i	$0.850129\pi$
$440$		0			0
$441$	−1.62111e10			−0.428606
$442$	−8.56556e9	−	8.56556e9i	−0.224423	−	0.224423i
$443$	−1.69254e10	+	1.69254e10i	−0.439464	+	0.439464i	−0.891832	−	0.452368i	$-0.850579\pi$
$443$	−1.69254e10	+	1.69254e10i	−0.439464	+	0.439464i	0.452368	+	0.891832i	$0.350579\pi$
$444$		−	1.15703e11i		−	2.97722i
$445$		0			0
$446$	1.60976e10			0.406838
$447$	−8.60796e9	−	8.60796e9i	−0.215611	−	0.215611i
$448$	4.04376e10	−	4.04376e10i	1.00386	−	1.00386i
$449$			2.96471e10i			0.729452i	0.931115	+	0.364726i	$0.118837\pi$
$449$			2.96471e10i			0.729452i	−0.931115	+	0.364726i	$0.881163\pi$
$450$		0			0
$451$	−4.20519e10			−1.01643
$452$	4.54438e10	+	4.54438e10i	1.08873	+	1.08873i
$453$	6.48720e10	−	6.48720e10i	1.54051	−	1.54051i
$454$		−	1.00534e9i		−	0.0236642i
$455$		0			0
$456$	6.02216e10			1.39281
$457$	−2.23296e10	−	2.23296e10i	−0.511936	−	0.511936i	0.403183	−	0.915119i	$-0.367904\pi$
$457$	−2.23296e10	−	2.23296e10i	−0.511936	−	0.511936i	−0.915119	+	0.403183i	$0.867904\pi$
$458$	8.81140e10	−	8.81140e10i	2.00255	−	2.00255i
$459$			1.95141e10i			0.439641i
$460$		0			0
$461$	3.35820e10			0.743537			0.371769	−	0.928325i	$-0.378751\pi$
$461$	3.35820e10			0.743537			0.371769	+	0.928325i	$0.378751\pi$
$462$	−8.35266e10	−	8.35266e10i	−1.83340	−	1.83340i
$463$	4.33351e10	−	4.33351e10i	0.943009	−	0.943009i	−0.0554521	−	0.998461i	$-0.517660\pi$
$463$	4.33351e10	−	4.33351e10i	0.943009	−	0.943009i	0.998461	+	0.0554521i	$0.0176600\pi$
$464$		−	4.74103e8i		−	0.0102282i
$465$		0			0
$466$	−6.65447e10			−1.41114
$467$	−3.37084e9	−	3.37084e9i	−0.0708712	−	0.0708712i	0.670783	−	0.741654i	$-0.265958\pi$
$467$	−3.37084e9	−	3.37084e9i	−0.0708712	−	0.0708712i	−0.741654	+	0.670783i	$0.765958\pi$
$468$	−5.47580e10	+	5.47580e10i	−1.14147	+	1.14147i
$469$			8.18643e10i			1.69201i
$470$		0			0
$471$	6.07320e10			1.23405
$472$	−4.10713e10	−	4.10713e10i	−0.827505	−	0.827505i
$473$	3.33369e10	−	3.33369e10i	0.666010	−	0.666010i
$474$		−	1.58915e11i		−	3.14812i
$475$		0			0
$476$	−2.38977e10			−0.465509
$477$	−9.00715e9	−	9.00715e9i	−0.173986	−	0.173986i
$478$	−3.02466e10	+	3.02466e10i	−0.579383	+	0.579383i
$479$			5.57216e10i			1.05848i	0.848473	+	0.529239i	$0.177522\pi$
$479$			5.57216e10i			1.05848i	−0.848473	+	0.529239i	$0.822478\pi$
$480$		0			0
$481$	3.54589e10			0.662438
$482$	−3.81913e10	−	3.81913e10i	−0.707582	−	0.707582i
$483$	−1.01940e11	+	1.01940e11i	−1.87308	+	1.87308i
$484$			2.10603e10i			0.383781i
$485$		0			0
$486$	−5.97180e10			−1.07043
$487$	−2.57866e9	−	2.57866e9i	−0.0458435	−	0.0458435i	0.683813	−	0.729657i	$-0.260320\pi$
$487$	−2.57866e9	−	2.57866e9i	−0.0458435	−	0.0458435i	−0.729657	+	0.683813i	$0.760320\pi$
$488$	2.14224e10	−	2.14224e10i	0.377737	−	0.377737i
$489$			3.66033e10i			0.640154i
$490$		0			0
$491$	−9.97413e10			−1.71612			−0.858062	−	0.513545i	$-0.828332\pi$
$491$	−9.97413e10			−1.71612			−0.858062	+	0.513545i	$0.828332\pi$
$492$	9.85125e10	+	9.85125e10i	1.68124	+	1.68124i
$493$	−1.30898e9	+	1.30898e9i	−0.0221588	+	0.0221588i
$494$			5.10013e10i			0.856393i
$495$		0			0
$496$	−6.61611e9			−0.109314
$497$	2.15088e10	+	2.15088e10i	0.352526	+	0.352526i
$498$	−6.94470e10	+	6.94470e10i	−1.12911	+	1.12911i
$499$		−	1.65611e10i		−	0.267108i	−0.991042	−	0.133554i	$-0.957361\pi$
$499$		−	1.65611e10i		−	0.267108i	0.991042	−	0.133554i	$-0.0426389\pi$
$500$		0			0
$501$	1.52926e11			2.42734
$502$	2.71474e10	+	2.71474e10i	0.427478	+	0.427478i
$503$	−2.56750e10	+	2.56750e10i	−0.401088	+	0.401088i	−0.878616	−	0.477529i	$-0.841533\pi$
$503$	−2.56750e10	+	2.56750e10i	−0.401088	+	0.401088i	0.477529	+	0.878616i	$0.341533\pi$
$504$			9.05628e10i			1.40355i
$505$		0			0
$506$	2.14030e11			3.26493
$507$	5.15723e10	+	5.15723e10i	0.780521	+	0.780521i
$508$	−4.60911e10	+	4.60911e10i	−0.692089	+	0.692089i
$509$		−	1.02958e11i		−	1.53388i	−0.641721	−	0.766938i	$-0.721779\pi$
$509$		−	1.02958e11i		−	1.53388i	0.641721	−	0.766938i	$-0.278221\pi$
$510$		0			0
$511$	−4.24098e10			−0.621989
$512$	−1.07960e10	−	1.07960e10i	−0.157102	−	0.157102i
$513$	5.80956e10	−	5.80956e10i	0.838830	−	0.838830i
$514$		−	1.46777e11i		−	2.10284i
$515$		0			0
$516$	−1.56193e11			−2.20324
$517$	2.20008e10	+	2.20008e10i	0.307947	+	0.307947i
$518$	8.10296e10	−	8.10296e10i	1.12545	−	1.12545i
$519$			1.04047e11i			1.43403i
$520$		0			0
$521$	4.03932e10			0.548223			0.274112	−	0.961698i	$-0.411616\pi$
$521$	4.03932e10			0.548223			0.274112	+	0.961698i	$0.411616\pi$
$522$	1.37080e10	+	1.37080e10i	0.184626	+	0.184626i
$523$	5.67473e10	−	5.67473e10i	0.758470	−	0.758470i	−0.217574	−	0.976044i	$-0.569814\pi$
$523$	5.67473e10	−	5.67473e10i	0.758470	−	0.758470i	0.976044	+	0.217574i	$0.0698142\pi$
$524$			1.19012e11i			1.57857i
$525$		0			0
$526$	−9.18687e10			−1.20012
$527$	1.82669e10	+	1.82669e10i	0.236822	+	0.236822i
$528$	−1.13701e10	+	1.13701e10i	−0.146294	+	0.146294i
$529$		−	1.82902e11i		−	2.33558i
$530$		0			0
$531$	−1.81642e11			−2.28475
$532$	7.11461e10	+	7.11461e10i	0.888187	+	0.888187i
$533$	−3.01908e10	+	3.01908e10i	−0.374081	+	0.374081i
$534$			1.22292e11i			1.50395i
$535$		0			0
$536$	−1.45709e11			−1.76533
$537$	3.12763e10	+	3.12763e10i	0.376113	+	0.376113i
$538$	−1.48424e11	+	1.48424e11i	−1.77164	+	1.77164i
$539$			2.27542e10i			0.269592i
$540$		0			0
$541$	4.47297e10			0.522164			0.261082	−	0.965317i	$-0.415921\pi$
$541$	4.47297e10			0.522164			0.261082	+	0.965317i	$0.415921\pi$
$542$	−1.68910e11	−	1.68910e11i	−1.95730	−	1.95730i
$543$	7.13450e10	−	7.13450e10i	0.820662	−	0.820662i
$544$			3.24718e10i			0.370775i
$545$		0			0
$546$	−1.19934e11			−1.34950
$547$	−4.47125e8	−	4.47125e8i	−0.00499436	−	0.00499436i	0.704605	−	0.709600i	$-0.251124\pi$
$547$	−4.47125e8	−	4.47125e8i	−0.00499436	−	0.00499436i	−0.709600	+	0.704605i	$0.751124\pi$
$548$	−8.42743e10	+	8.42743e10i	−0.934486	+	0.934486i
$549$		−	9.47430e10i		−	1.04294i
$550$		0			0
$551$	7.79398e9			0.0845577
$552$	−1.81441e11	−	1.81441e11i	−1.95425	−	1.95425i
$553$	6.79387e10	−	6.79387e10i	0.726469	−	0.726469i
$554$		−	7.36586e10i		−	0.781959i
$555$		0			0
$556$	2.45396e11			2.56785
$557$	−4.27365e10	−	4.27365e10i	−0.443995	−	0.443995i	0.449357	−	0.893352i	$-0.351653\pi$
$557$	−4.27365e10	−	4.27365e10i	−0.443995	−	0.443995i	−0.893352	+	0.449357i	$0.851653\pi$
$558$	1.91295e11	−	1.91295e11i	1.97318	−	1.97318i
$559$		−	4.78679e10i		−	0.490227i
$560$		0			0
$561$	6.27848e10			0.633875
$562$	8.94440e10	+	8.94440e10i	0.896615	+	0.896615i
$563$	2.64620e10	−	2.64620e10i	0.263384	−	0.263384i	−0.563043	−	0.826427i	$-0.690370\pi$
$563$	2.64620e10	−	2.64620e10i	0.263384	−	0.263384i	0.826427	+	0.563043i	$0.190370\pi$
$564$		−	1.03080e11i		−	1.01873i
$565$		0			0
$566$	4.63028e10			0.451171
$567$	2.37213e10	+	2.37213e10i	0.229513	+	0.229513i
$568$	−3.82832e10	+	3.82832e10i	−0.367802	+	0.367802i
$569$			1.60803e11i			1.53407i	0.641607	+	0.767034i	$0.278268\pi$
$569$			1.60803e11i			1.53407i	−0.641607	+	0.767034i	$0.721732\pi$
$570$		0			0
$571$	5.54369e10			0.521500			0.260750	−	0.965406i	$-0.416030\pi$
$571$	5.54369e10			0.521500			0.260750	+	0.965406i	$0.416030\pi$
$572$	7.68594e10	+	7.68594e10i	0.717981	+	0.717981i
$573$	1.79928e10	−	1.79928e10i	0.166909	−	0.166909i
$574$			1.37982e11i			1.27108i
$575$		0			0
$576$	3.18313e11			2.89178
$577$	−1.17837e10	−	1.17837e10i	−0.106311	−	0.106311i	0.651951	−	0.758261i	$-0.273951\pi$
$577$	−1.17837e10	−	1.17837e10i	−0.106311	−	0.106311i	−0.758261	+	0.651951i	$0.773951\pi$
$578$	−1.11736e11	+	1.11736e11i	−1.00111	+	1.00111i
$579$			1.57822e11i			1.40428i
$580$		0			0
$581$	−5.93794e10			−0.521113
$582$	1.84413e10	+	1.84413e10i	0.160731	+	0.160731i
$583$	−1.26426e10	+	1.26426e10i	−0.109437	+	0.109437i
$584$		−	7.54845e10i		−	0.648943i
$585$		0			0
$586$	5.63805e10			0.478122
$587$	1.30845e11	+	1.30845e11i	1.10206	+	1.10206i	0.994162	+	0.107897i	$0.0344118\pi$
$587$	1.30845e11	+	1.30845e11i	1.10206	+	1.10206i	0.107897	+	0.994162i	$0.465588\pi$
$588$	5.33049e10	−	5.33049e10i	0.445921	−	0.445921i
$589$		−	1.08765e11i		−	0.903708i
$590$		0			0
$591$	−1.14081e10			−0.0935111
$592$	−1.10302e10	−	1.10302e10i	−0.0898039	−	0.0898039i
$593$	−1.31029e11	+	1.31029e11i	−1.05962	+	1.05962i	−0.0615124	+	0.998106i	$0.519592\pi$
$593$	−1.31029e11	+	1.31029e11i	−1.05962	+	1.05962i	−0.998106	+	0.0615124i	$0.980408\pi$
$594$		−	2.86838e11i		−	2.30405i
$595$		0			0
$596$	3.62009e10			0.286903
$597$	−1.71227e11	−	1.71227e11i	−1.34796	−	1.34796i
$598$	1.53661e11	−	1.53661e11i	1.20160	−	1.20160i
$599$		−	3.44801e10i		−	0.267831i	−0.990993	−	0.133916i	$-0.957245\pi$
$599$		−	3.44801e10i		−	0.267831i	0.990993	−	0.133916i	$-0.0427552\pi$
$600$		0			0
$601$	1.28545e11			0.985272			0.492636	−	0.870235i	$-0.336033\pi$
$601$	1.28545e11			0.985272			0.492636	+	0.870235i	$0.336033\pi$
$602$	−1.09386e11	−	1.09386e11i	−0.832868	−	0.832868i
$603$	−3.22206e11	+	3.22206e11i	−2.43705	+	2.43705i
$604$			2.72820e11i			2.04988i
$605$		0			0
$606$	−3.24467e11			−2.40591
$607$	−1.02614e11	−	1.02614e11i	−0.755880	−	0.755880i	0.219690	−	0.975570i	$-0.429495\pi$
$607$	−1.02614e11	−	1.02614e11i	−0.755880	−	0.755880i	−0.975570	+	0.219690i	$0.929495\pi$
$608$	9.66721e10	−	9.66721e10i	0.707436	−	0.707436i
$609$			1.83283e10i			0.133246i
$610$		0			0
$611$	3.15906e10			0.226669
$612$	−9.40579e10	−	9.40579e10i	−0.670486	−	0.670486i
$613$	1.40056e11	−	1.40056e11i	0.991882	−	0.991882i	−0.00808504	−	0.999967i	$-0.502574\pi$
$613$	1.40056e11	−	1.40056e11i	0.991882	−	0.991882i	0.999967	+	0.00808504i	$0.00257358\pi$
$614$			1.87503e11i			1.31927i
$615$		0			0
$616$	1.27116e11			0.882828
$617$	1.80671e10	+	1.80671e10i	0.124666	+	0.124666i	0.766687	−	0.642021i	$-0.221904\pi$
$617$	1.80671e10	+	1.80671e10i	0.124666	+	0.124666i	−0.642021	+	0.766687i	$0.721904\pi$
$618$	2.81705e11	−	2.81705e11i	1.93126	−	1.93126i
$619$		−	2.53005e11i		−	1.72332i	−0.507486	−	0.861660i	$-0.669425\pi$
$619$		−	2.53005e11i		−	1.72332i	0.507486	−	0.861660i	$-0.330575\pi$
$620$		0			0
$621$	−3.50071e11			−2.35391
$622$	2.81031e11	+	2.81031e11i	1.87755	+	1.87755i
$623$	−5.22818e10	+	5.22818e10i	−0.347055	+	0.347055i
$624$			1.63261e10i			0.107682i
$625$		0			0
$626$	−4.87013e11			−3.17134
$627$	−1.86917e11	−	1.86917e11i	−1.20943	−	1.20943i
$628$	−1.27705e11	+	1.27705e11i	−0.821048	+	0.821048i
$629$			6.09078e10i			0.389108i
$630$		0			0
$631$	−1.51249e11			−0.954061			−0.477031	−	0.878887i	$-0.658287\pi$
$631$	−1.51249e11			−0.954061			−0.477031	+	0.878887i	$0.658287\pi$
$632$	1.20923e11	+	1.20923e11i	0.757950	+	0.757950i
$633$	−1.12297e11	+	1.12297e11i	−0.699448	+	0.699448i
$634$		−	1.89691e10i		−	0.117406i
$635$		0			0
$636$	5.92342e10			0.362029
$637$	1.63362e10	+	1.63362e10i	0.0992184	+	0.0992184i
$638$	1.92408e10	−	1.92408e10i	0.116129	−	0.116129i
$639$			1.69311e11i			1.01551i
$640$		0			0
$641$	2.54503e11			1.50751			0.753755	−	0.657156i	$-0.228241\pi$
$641$	2.54503e11			1.50751			0.753755	+	0.657156i	$0.228241\pi$
$642$	5.72673e11	+	5.72673e11i	3.37106	+	3.37106i
$643$	7.13377e10	−	7.13377e10i	0.417326	−	0.417326i	−0.466955	−	0.884281i	$-0.654649\pi$
$643$	7.13377e10	−	7.13377e10i	0.417326	−	0.417326i	0.884281	+	0.466955i	$0.154649\pi$
$644$		−	4.28710e11i		−	2.49241i
$645$		0			0
$646$	−8.76049e10			−0.503035
$647$	1.57110e11	+	1.57110e11i	0.896574	+	0.896574i	0.995131	−	0.0985575i	$-0.0314228\pi$
$647$	1.57110e11	+	1.57110e11i	0.896574	+	0.896574i	−0.0985575	+	0.995131i	$0.531423\pi$
$648$	−4.22212e10	+	4.22212e10i	−0.239459	+	0.239459i
$649$			2.54956e11i			1.43710i
$650$		0			0
$651$	2.55771e11			1.42406
$652$	−7.69679e10	−	7.69679e10i	−0.425911	−	0.425911i
$653$	−1.43680e10	+	1.43680e10i	−0.0790212	+	0.0790212i	−0.745513	−	0.666491i	$-0.767795\pi$
$653$	−1.43680e10	+	1.43680e10i	−0.0790212	+	0.0790212i	0.666491	+	0.745513i	$0.267795\pi$
$654$			9.43483e10i			0.515731i
$655$		0			0
$656$	1.87828e10			0.101425
$657$	−1.66919e11	−	1.66919e11i	−0.895869	−	0.895869i
$658$	7.21897e10	−	7.21897e10i	0.385098	−	0.385098i
$659$		−	2.62601e11i		−	1.39237i	−0.717862	−	0.696186i	$-0.754879\pi$
$659$		−	2.62601e11i		−	1.39237i	0.717862	−	0.696186i	$-0.245121\pi$
$660$		0			0
$661$	−1.78810e11			−0.936666			−0.468333	−	0.883552i	$-0.655145\pi$
$661$	−1.78810e11			−0.936666			−0.468333	+	0.883552i	$0.655145\pi$
$662$	−4.19044e11	−	4.19044e11i	−2.18186	−	2.18186i
$663$	4.50758e10	−	4.50758e10i	0.233286	−	0.233286i
$664$		−	1.05688e11i		−	0.543695i
$665$		0			0
$666$	6.37842e11			3.24202
$667$	−2.34824e10	−	2.34824e10i	−0.118642	−	0.118642i
$668$	−3.21566e11	+	3.21566e11i	−1.61497	+	1.61497i
$669$			8.47126e10i			0.422906i
$670$		0			0
$671$	−1.32983e11			−0.656003
$672$	2.27334e11	+	2.27334e11i	1.11477	+	1.11477i
$673$	−2.05834e10	+	2.05834e10i	−0.100336	+	0.100336i	−0.755493	−	0.655157i	$-0.772602\pi$
$673$	−2.05834e10	+	2.05834e10i	−0.100336	+	0.100336i	0.655157	+	0.755493i	$0.272602\pi$
$674$			3.24985e9i			0.0157479i
$675$		0			0
$676$	−2.16888e11			−1.03860
$677$	−5.45205e10	−	5.45205e10i	−0.259540	−	0.259540i	0.565327	−	0.824867i	$-0.308750\pi$
$677$	−5.45205e10	−	5.45205e10i	−0.259540	−	0.259540i	−0.824867	+	0.565327i	$0.808750\pi$
$678$	−3.91751e11	+	3.91751e11i	−1.85392	+	1.85392i
$679$			1.57679e10i			0.0741814i
$680$		0			0
$681$	5.29057e9			0.0245988
$682$	−2.68505e11	−	2.68505e11i	−1.24112	−	1.24112i
$683$	−4.26609e10	+	4.26609e10i	−0.196041	+	0.196041i	−0.798300	−	0.602259i	$-0.794267\pi$
$683$	−4.26609e10	+	4.26609e10i	−0.196041	+	0.196041i	0.602259	+	0.798300i	$0.294267\pi$
$684$			5.60042e11i			2.55856i
$685$		0			0
$686$	3.83662e11			1.73242
$687$	4.63695e11	+	4.63695e11i	2.08164	+	2.08164i
$688$	−1.48902e10	+	1.48902e10i	−0.0664579	+	0.0664579i
$689$			1.81533e10i			0.0805523i
$690$		0			0
$691$	−2.25188e11			−0.987720			−0.493860	−	0.869542i	$-0.664414\pi$
$691$	−2.25188e11			−0.987720			−0.493860	+	0.869542i	$0.664414\pi$
$692$	−2.18785e11	−	2.18785e11i	−0.954097	−	0.954097i
$693$	2.81091e11	−	2.81091e11i	1.21875	−	1.21875i
$694$			5.64613e11i			2.43396i
$695$		0			0
$696$	−3.26222e10			−0.139020
$697$	−5.18587e10	−	5.18587e10i	−0.219731	−	0.219731i
$698$	4.29801e11	−	4.29801e11i	1.81070	−	1.81070i
$699$		−	3.50188e11i		−	1.46687i
$700$		0			0
$701$	−2.45386e11			−1.01620			−0.508099	−	0.861299i	$-0.669652\pi$
$701$	−2.45386e11			−1.01620			−0.508099	+	0.861299i	$0.669652\pi$
$702$	−2.05933e11	−	2.05933e11i	−0.847964	−	0.847964i
$703$	1.81329e11	−	1.81329e11i	0.742416	−	0.742416i
$704$		−	4.46791e11i		−	1.81892i
$705$		0			0
$706$	5.58976e10			0.224996
$707$	−1.38715e11	−	1.38715e11i	−0.555195	−	0.555195i
$708$	5.97272e11	−	5.97272e11i	2.37705	−	2.37705i
$709$		−	9.30597e10i		−	0.368279i	−0.982900	−	0.184139i	$-0.941050\pi$
$709$		−	9.30597e10i		−	0.368279i	0.982900	−	0.184139i	$-0.0589498\pi$
$710$		0			0
$711$	5.34794e11			2.09271
$712$	−9.30555e10	−	9.30555e10i	−0.362094	−	0.362094i
$713$	−3.27697e11	+	3.27697e11i	−1.26798	+	1.26798i
$714$		−	2.06011e11i		−	0.792681i
$715$		0			0
$716$	−1.31533e11			−0.500475
$717$	−1.59171e11	−	1.59171e11i	−0.602265	−	0.602265i
$718$	−1.75777e11	+	1.75777e11i	−0.661400	+	0.661400i
$719$		−	3.59479e11i		−	1.34511i	−0.740047	−	0.672555i	$-0.765197\pi$
$719$		−	3.59479e11i		−	1.34511i	0.740047	−	0.672555i	$-0.234803\pi$
$720$		0			0
$721$	2.40867e11			0.891325
$722$	−4.70506e10	−	4.70506e10i	−0.173148	−	0.173148i
$723$	2.00980e11	−	2.00980e11i	0.735528	−	0.735528i
$724$			3.00043e11i			1.09202i
$725$		0			0
$726$	−1.81552e11			−0.653512
$727$	4.37897e9	+	4.37897e9i	0.0156760	+	0.0156760i	0.714901	−	0.699225i	$-0.246472\pi$
$727$	4.37897e9	+	4.37897e9i	0.0156760	+	0.0156760i	−0.699225	+	0.714901i	$0.746472\pi$
$728$	9.12615e10	−	9.12615e10i	0.324909	−	0.324909i
$729$		−	4.19529e11i		−	1.48543i
$730$		0			0
$731$	8.22227e10			0.287953
$732$	3.11531e11	+	3.11531e11i	1.08507	+	1.08507i
$733$	−1.20761e11	+	1.20761e11i	−0.418322	+	0.418322i	−0.884625	−	0.466303i	$-0.845586\pi$
$733$	−1.20761e11	+	1.20761e11i	−0.418322	+	0.418322i	0.466303	+	0.884625i	$0.345586\pi$
$734$		−	5.88241e11i		−	2.02662i
$735$		0			0
$736$	−5.82524e11			−1.98519
$737$	4.52255e11	+	4.52255e11i	1.53290	+	1.53290i
$738$	−5.43077e11	+	5.43077e11i	−1.83078	+	1.83078i
$739$		−	1.10111e11i		−	0.369194i	−0.982814	−	0.184597i	$-0.940902\pi$
$739$		−	1.10111e11i		−	0.369194i	0.982814	−	0.184597i	$-0.0590979\pi$
$740$		0			0
$741$	−2.68391e11			−0.890216
$742$	4.14833e10	+	4.14833e10i	0.136854	+	0.136854i
$743$	3.37139e11	−	3.37139e11i	1.10625	−	1.10625i	0.112611	−	0.993639i	$-0.464079\pi$
$743$	3.37139e11	−	3.37139e11i	1.10625	−	1.10625i	0.993639	−	0.112611i	$-0.0359215\pi$
$744$			4.55243e11i			1.48577i
$745$		0			0
$746$	6.80512e11			2.19726
$747$	−2.33709e11	−	2.33709e11i	−0.750574	−	0.750574i
$748$	−1.32021e11	+	1.32021e11i	−0.421733	+	0.421733i
$749$			4.89654e11i			1.55583i
$750$		0			0
$751$	1.56114e10			0.0490773			0.0245387	−	0.999699i	$-0.492188\pi$
$751$	1.56114e10			0.0490773			0.0245387	+	0.999699i	$0.492188\pi$
$752$	−9.82684e9	−	9.82684e9i	−0.0307286	−	0.0307286i
$753$	−1.42862e11	+	1.42862e11i	−0.444361	+	0.444361i
$754$		−	2.76275e10i		−	0.0854784i
$755$		0			0
$756$	−5.74547e11			−1.75889
$757$	2.34539e11	+	2.34539e11i	0.714218	+	0.714218i	0.967415	−	0.253197i	$-0.0814821\pi$
$757$	2.34539e11	+	2.34539e11i	0.714218	+	0.714218i	−0.253197	+	0.967415i	$0.581482\pi$
$758$	−1.97101e11	+	1.97101e11i	−0.597051	+	0.597051i
$759$			1.12632e12i			3.39387i
$760$		0			0
$761$	−2.40071e10			−0.0715816			−0.0357908	−	0.999359i	$-0.511395\pi$
$761$	−2.40071e10			−0.0715816			−0.0357908	+	0.999359i	$0.511395\pi$
$762$	−3.97331e11	−	3.97331e11i	−1.17851	−	1.17851i
$763$	−4.03354e10	+	4.03354e10i	−0.119011	+	0.119011i
$764$			7.56688e10i			0.222097i
$765$		0			0
$766$	1.19475e9			0.00347027
$767$	1.83044e11	+	1.83044e11i	0.528900	+	0.528900i
$768$	−3.33145e11	+	3.33145e11i	−0.957610	+	0.957610i
$769$			5.35286e11i			1.53067i	0.643635	+	0.765333i	$0.277426\pi$
$769$			5.35286e11i			1.53067i	−0.643635	+	0.765333i	$0.722574\pi$
$770$		0			0
$771$	7.72407e11			2.18589
$772$	−3.31862e11	−	3.31862e11i	−0.934306	−	0.934306i
$773$	−1.01340e9	+	1.01340e9i	−0.00283834	+	0.00283834i	−0.708525	−	0.705686i	$-0.750639\pi$
$773$	−1.01340e9	+	1.01340e9i	−0.00283834	+	0.00283834i	0.705686	+	0.708525i	$0.250639\pi$
$774$		−	8.61056e11i		−	2.39921i
$775$		0			0
$776$	−2.80650e10			−0.0773959
$777$	4.26413e11	+	4.26413e11i	1.16989	+	1.16989i
$778$	3.99574e11	−	3.99574e11i	1.09063	−	1.09063i
$779$			3.08778e11i			0.838488i
$780$		0			0
$781$	2.37648e11			0.638750
$782$	2.63944e11	+	2.63944e11i	0.705804	+	0.705804i
$783$	−3.14705e10	+	3.14705e10i	−0.0837254	+	0.0837254i
$784$		−	1.01633e10i		−	0.0269012i
$785$		0			0
$786$	−1.02595e12			−2.68803
$787$	−2.43615e11	−	2.43615e11i	−0.635046	−	0.635046i	0.314283	−	0.949329i	$-0.398236\pi$
$787$	−2.43615e11	−	2.43615e11i	−0.635046	−	0.635046i	−0.949329	+	0.314283i	$0.898236\pi$
$788$	2.39885e10	−	2.39885e10i	0.0622154	−	0.0622154i
$789$		−	4.83454e11i		−	1.24752i
$790$		0			0
$791$	−3.34960e11			−0.855632
$792$	5.00309e11	+	5.00309e11i	1.27156	+	1.27156i
$793$	−9.54739e10	+	9.54739e10i	−0.241430	+	0.241430i
$794$			9.95628e11i			2.50504i
$795$		0			0
$796$	7.20100e11			1.79366
$797$	7.42279e10	+	7.42279e10i	0.183964	+	0.183964i	0.793081	−	0.609116i	$-0.208476\pi$
$797$	7.42279e10	+	7.42279e10i	0.183964	+	0.183964i	−0.609116	+	0.793081i	$0.708476\pi$
$798$	−6.13319e11	+	6.13319e11i	−1.51243	+	1.51243i
$799$			5.42631e10i			0.133143i
$800$		0			0
$801$	−4.11548e11			−0.999747
$802$	8.60616e11	+	8.60616e11i	2.08023	+	2.08023i
$803$	−2.34291e11	+	2.34291e11i	−0.563499	+	0.563499i
$804$		−	2.11894e12i		−	5.07101i
$805$		0			0
$806$	−3.85542e11			−0.913548
$807$	−7.81073e11	−	7.81073e11i	−1.84161	−	1.84161i
$808$	2.46896e11	−	2.46896e11i	0.579254	−	0.579254i
$809$			1.31570e11i			0.307159i	0.988136	+	0.153579i	$0.0490801\pi$
$809$			1.31570e11i			0.307159i	−0.988136	+	0.153579i	$0.950920\pi$
$810$		0			0
$811$	−3.58770e11			−0.829339			−0.414670	−	0.909972i	$-0.636103\pi$
$811$	−3.58770e11			−0.829339			−0.414670	+	0.909972i	$0.636103\pi$
$812$	−3.85400e10	−	3.85400e10i	−0.0886517	−	0.0886517i
$813$	8.88879e11	−	8.88879e11i	2.03461	−	2.03461i
$814$		−	8.95287e11i		−	2.03922i
$815$		0			0
$816$	−2.80433e10			−0.0632512
$817$	−2.44786e11	−	2.44786e11i	−0.549413	−	0.549413i
$818$	−2.78577e11	+	2.78577e11i	−0.622202	+	0.622202i
$819$		−	4.03613e11i		−	0.897078i
$820$		0			0
$821$	−3.83526e11			−0.844155			−0.422078	−	0.906560i	$-0.638699\pi$
$821$	−3.83526e11			−0.844155			−0.422078	+	0.906560i	$0.638699\pi$
$822$	−7.26491e11	−	7.26491e11i	−1.59127	−	1.59127i
$823$	5.55242e10	−	5.55242e10i	0.121027	−	0.121027i	−0.643999	−	0.765026i	$-0.722726\pi$
$823$	5.55242e10	−	5.55242e10i	0.121027	−	0.121027i	0.765026	+	0.643999i	$0.222726\pi$
$824$			4.28715e11i			0.929950i
$825$		0			0
$826$	8.36570e11			1.79714
$827$	−1.22629e11	−	1.22629e11i	−0.262163	−	0.262163i	0.563769	−	0.825932i	$-0.309351\pi$
$827$	−1.22629e11	−	1.22629e11i	−0.262163	−	0.262163i	−0.825932	+	0.563769i	$0.809351\pi$
$828$	1.68734e12	−	1.68734e12i	3.58990	−	3.58990i
$829$		−	1.71409e11i		−	0.362925i	−0.983398	−	0.181462i	$-0.941917\pi$
$829$		−	1.71409e11i		−	0.362925i	0.983398	−	0.181462i	$-0.0580830\pi$
$830$		0			0
$831$	3.87624e11			0.812843
$832$	−3.20769e11	−	3.20769e11i	−0.669421	−	0.669421i
$833$	−2.80606e10	+	2.80606e10i	−0.0582797	+	0.0582797i
$834$			2.11545e12i			4.37260i
$835$		0			0
$836$	7.86085e11			1.60933
$837$	4.39171e11	+	4.39171e11i	0.894813	+	0.894813i
$838$	−2.10163e11	+	2.10163e11i	−0.426167	+	0.426167i
$839$			1.59205e11i			0.321299i	0.987011	+	0.160650i	$0.0513590\pi$
$839$			1.59205e11i			0.321299i	−0.987011	+	0.160650i	$0.948641\pi$
$840$		0			0
$841$	4.96024e11			0.991560
$842$	1.57260e11	+	1.57260e11i	0.312874	+	0.312874i
$843$	−4.70694e11	+	4.70694e11i	−0.932026	+	0.932026i
$844$		−	4.72269e11i		−	0.930721i
$845$		0			0
$846$	5.68257e11			1.10934
$847$	−7.76162e10	−	7.76162e10i	−0.150806	−	0.150806i
$848$	5.64692e9	−	5.64692e9i	0.0109201	−	0.0109201i
$849$			2.43666e11i			0.468990i
$850$		0			0
$851$	−1.09265e12			−2.08335
$852$	−5.56725e11	−	5.56725e11i	−1.05653	−	1.05653i
$853$	−5.56443e11	+	5.56443e11i	−1.05105	+	1.05105i	−0.0524275	+	0.998625i	$0.516696\pi$
$853$	−5.56443e11	+	5.56443e11i	−1.05105	+	1.05105i	−0.998625	+	0.0524275i	$0.983304\pi$
$854$			4.36347e11i			0.820353i
$855$		0			0
$856$	−8.71527e11			−1.62325
$857$	−2.33652e11	−	2.33652e11i	−0.433157	−	0.433157i	0.456544	−	0.889701i	$-0.349087\pi$
$857$	−2.33652e11	−	2.33652e11i	−0.433157	−	0.433157i	−0.889701	+	0.456544i	$0.849087\pi$
$858$	−6.62571e11	+	6.62571e11i	−1.22260	+	1.22260i
$859$			3.98765e10i			0.0732392i	0.999329	+	0.0366196i	$0.0116590\pi$
$859$			3.98765e10i			0.0732392i	−0.999329	+	0.0366196i	$0.988341\pi$
$860$		0			0
$861$	−7.26121e11			−1.32128
$862$	4.75633e11	+	4.75633e11i	0.861476	+	0.861476i
$863$	4.97782e11	−	4.97782e11i	0.897421	−	0.897421i	−0.0977867	−	0.995207i	$-0.531176\pi$
$863$	4.97782e11	−	4.97782e11i	0.897421	−	0.897421i	0.995207	+	0.0977867i	$0.0311763\pi$
$864$			7.80686e11i			1.40095i
$865$		0			0
$866$	1.25565e12			2.23253
$867$	−5.88005e11	−	5.88005e11i	−1.04065	−	1.04065i
$868$	−5.37825e11	+	5.37825e11i	−0.947463	+	0.947463i
$869$		−	7.50647e11i		−	1.31631i
$870$		0			0
$871$	6.49384e11			1.12831
$872$	−7.17923e10	−	7.17923e10i	−0.124169	−	0.124169i
$873$	−6.20602e10	+	6.20602e10i	−0.106846	+	0.106846i
$874$		−	1.57158e12i		−	2.69334i
$875$		0			0
$876$	1.09772e12			1.86412
$877$	6.70686e11	+	6.70686e11i	1.13376	+	1.13376i	0.989547	+	0.144212i	$0.0460648\pi$
$877$	6.70686e11	+	6.70686e11i	1.13376	+	1.13376i	0.144212	+	0.989547i	$0.453935\pi$
$878$	6.10821e11	−	6.10821e11i	1.02786	−	1.02786i
$879$			2.96699e11i			0.497005i
$880$		0			0
$881$	2.46509e11			0.409193			0.204597	−	0.978846i	$-0.434412\pi$
$881$	2.46509e11			0.409193			0.204597	+	0.978846i	$0.434412\pi$
$882$	2.93858e11	+	2.93858e11i	0.485582	+	0.485582i
$883$	−2.04722e11	+	2.04722e11i	−0.336760	+	0.336760i	−0.855147	−	0.518386i	$-0.826533\pi$
$883$	−2.04722e11	+	2.04722e11i	−0.336760	+	0.336760i	0.518386	+	0.855147i	$0.326533\pi$
$884$			1.89567e11i			0.310423i
$885$		0			0
$886$	6.13611e11			0.995768
$887$	−5.57596e11	−	5.57596e11i	−0.900793	−	0.900793i	0.0947119	−	0.995505i	$-0.469807\pi$
$887$	−5.57596e11	−	5.57596e11i	−0.900793	−	0.900793i	−0.995505	+	0.0947119i	$0.969807\pi$
$888$	−7.58966e11	+	7.58966e11i	−1.22059	+	1.22059i
$889$		−	3.39731e11i		−	0.543911i
$890$		0			0
$891$	2.62094e11			0.415860
$892$	−1.78130e11	−	1.78130e11i	−0.281370	−	0.281370i
$893$	1.61547e11	−	1.61547e11i	0.254035	−	0.254035i
$894$			3.12072e11i			0.488545i
$895$		0			0
$896$	−8.55935e11			−1.32803
$897$	8.08633e11	+	8.08633e11i	1.24905	+	1.24905i
$898$	5.37412e11	−	5.37412e11i	0.826422	−	0.826422i
$899$			5.89182e10i			0.0902009i
$900$		0			0
$901$	−3.11819e10			−0.0473155
$902$	7.62273e11	+	7.62273e11i	1.15155	+	1.15155i
$903$	5.75638e11	−	5.75638e11i	0.865761	−	0.865761i
$904$		−	5.96189e11i		−	0.892710i
$905$		0			0
$906$	−2.35186e12			−3.49060
$907$	4.30665e11	+	4.30665e11i	0.636371	+	0.636371i	0.949658	−	0.313287i	$-0.101430\pi$
$907$	4.30665e11	+	4.30665e11i	0.636371	+	0.636371i	−0.313287	+	0.949658i	$0.601430\pi$
$908$	−1.11248e10	+	1.11248e10i	−0.0163662	+	0.0163662i
$909$		−	1.09192e12i		−	1.59933i
$910$		0			0
$911$	8.28614e11			1.20304			0.601518	−	0.798859i	$-0.294563\pi$
$911$	8.28614e11			1.20304			0.601518	+	0.798859i	$0.294563\pi$
$912$	8.34881e10	+	8.34881e10i	0.120683	+	0.120683i
$913$	−3.28038e11	+	3.28038e11i	−0.472108	+	0.472108i
$914$			8.09534e11i			1.15998i
$915$		0			0
$916$	−1.95008e12			−2.76994
$917$	−4.38609e11	−	4.38609e11i	−0.620298	−	0.620298i
$918$	3.53731e11	−	3.53731e11i	0.498084	−	0.498084i
$919$			6.26874e11i			0.878856i	0.898278	+	0.439428i	$0.144819\pi$
$919$			6.26874e11i			0.878856i	−0.898278	+	0.439428i	$0.855181\pi$
$920$		0			0
$921$	−9.86722e11			−1.37138
$922$	−6.08739e11	−	6.08739e11i	−0.842379	−	0.842379i
$923$	1.70617e11	−	1.70617e11i	0.235081	−	0.235081i
$924$			1.84855e12i			2.53597i
$925$		0			0
$926$	−1.57107e12			−2.13674
$927$	9.48018e11	+	9.48018e11i	1.28380	+	1.28380i
$928$	−5.23675e10	+	5.23675e10i	−0.0706106	+	0.0706106i
$929$			5.53700e11i			0.743381i	0.928357	+	0.371691i	$0.121222\pi$
$929$			5.53700e11i			0.743381i	−0.928357	+	0.371691i	$0.878778\pi$
$930$		0			0
$931$	1.67079e11			0.222394
$932$	7.36360e11	+	7.36360e11i	0.975948	+	0.975948i
$933$	−1.47891e12	+	1.47891e12i	−1.95171	+	1.95171i
$934$			1.22206e11i			0.160585i
$935$		0			0
$936$	7.18384e11			0.935952
$937$	−5.58660e11	−	5.58660e11i	−0.724751	−	0.724751i	0.244818	−	0.969569i	$-0.421272\pi$
$937$	−5.58660e11	−	5.58660e11i	−0.724751	−	0.724751i	−0.969569	+	0.244818i	$0.921272\pi$
$938$	1.48395e12	−	1.48395e12i	1.91694	−	1.91694i
$939$		−	2.56288e12i		−	3.29659i
$940$		0			0
$941$	1.40164e12			1.78763			0.893814	−	0.448437i	$-0.148019\pi$
$941$	1.40164e12			1.78763			0.893814	+	0.448437i	$0.148019\pi$
$942$	−1.10089e12	−	1.10089e12i	−1.39810	−	1.39810i
$943$	9.30314e11	−	9.30314e11i	1.17647	−	1.17647i
$944$		−	1.13878e11i		−	0.143401i
$945$		0			0
$946$	−1.20859e12			−1.50909
$947$	−5.37414e11	−	5.37414e11i	−0.668205	−	0.668205i	0.289096	−	0.957300i	$-0.406645\pi$
$947$	−5.37414e11	−	5.37414e11i	−0.668205	−	0.668205i	−0.957300	+	0.289096i	$0.906645\pi$
$948$	−1.75850e12	+	1.75850e12i	−2.17725	+	2.17725i
$949$			3.36414e11i			0.414772i
$950$		0			0
$951$	9.98239e10			0.122043
$952$	1.56760e11	+	1.56760e11i	0.190848	+	0.190848i
$953$	−3.14639e11	+	3.14639e11i	−0.381453	+	0.381453i	−0.871625	−	0.490173i	$-0.836934\pi$
$953$	−3.14639e11	+	3.14639e11i	−0.381453	+	0.381453i	0.490173	+	0.871625i	$0.336934\pi$
$954$			3.26544e11i			0.394229i
$955$		0			0
$956$	6.69398e11			0.801406
$957$	1.01254e11	+	1.01254e11i	0.120715	+	0.120715i
$958$	1.01006e12	−	1.01006e12i	1.19919	−	1.19919i
$959$		−	6.21173e11i		−	0.734410i
$960$		0			0
$961$	−3.06872e10			−0.0359802
$962$	−6.42763e11	−	6.42763e11i	−0.750499	−	0.750499i
$963$	−1.92721e12	+	1.92721e12i	−2.24091	+	2.24091i
$964$			8.45224e11i			0.978732i
$965$		0			0
$966$	3.69572e12			4.24415
$967$	−2.13975e11	−	2.13975e11i	−0.244713	−	0.244713i	0.574084	−	0.818796i	$-0.305358\pi$
$967$	−2.13975e11	−	2.13975e11i	−0.244713	−	0.244713i	−0.818796	+	0.574084i	$0.805358\pi$
$968$	1.38148e11	−	1.38148e11i	0.157341	−	0.157341i
$969$		−	4.61016e11i		−	0.522903i
$970$		0			0
$971$	−2.31537e11			−0.260462			−0.130231	−	0.991484i	$-0.541572\pi$
$971$	−2.31537e11			−0.260462			−0.130231	+	0.991484i	$0.541572\pi$
$972$	6.60818e11	+	6.60818e11i	0.740316	+	0.740316i
$973$	−9.04391e11	+	9.04391e11i	−1.00903	+	1.00903i
$974$			9.34864e10i			0.103875i
$975$		0			0
$976$	5.93979e10			0.0654594
$977$	4.86063e11	+	4.86063e11i	0.533476	+	0.533476i	0.921605	−	0.388129i	$-0.126879\pi$
$977$	4.86063e11	+	4.86063e11i	0.533476	+	0.533476i	−0.388129	+	0.921605i	$0.626879\pi$
$978$	6.63506e11	−	6.63506e11i	0.725253	−	0.725253i
$979$			5.77656e11i			0.628837i
$980$		0			0
$981$	−3.17509e11			−0.342831
$982$	1.80801e12	+	1.80801e12i	1.94426	+	1.94426i
$983$	2.87471e11	−	2.87471e11i	0.307879	−	0.307879i	−0.536207	−	0.844086i	$-0.680143\pi$
$983$	2.87471e11	−	2.87471e11i	0.307879	−	0.307879i	0.844086	+	0.536207i	$0.180143\pi$
$984$		−	1.29241e12i		−	1.37854i
$985$		0			0
$986$	4.74558e10			0.0502090
$987$	3.79894e11	+	3.79894e11i	0.400308	+	0.400308i
$988$	5.64362e11	−	5.64362e11i	0.592284	−	0.592284i
$989$			1.47503e12i			1.54175i
$990$		0			0
$991$	2.19541e11			0.227626			0.113813	−	0.993502i	$-0.463694\pi$
$991$	2.19541e11			0.227626			0.113813	+	0.993502i	$0.463694\pi$
$992$	7.30789e11	+	7.30789e11i	0.754649	+	0.754649i
$993$	2.20519e12	−	2.20519e12i	2.26803	−	2.26803i
$994$		−	7.79779e11i		−	0.798777i
$995$		0			0
$996$	1.53695e12			1.56179
$997$	−5.03136e11	−	5.03136e11i	−0.509219	−	0.509219i	0.405067	−	0.914287i	$-0.367248\pi$
$997$	−5.03136e11	−	5.03136e11i	−0.509219	−	0.509219i	−0.914287	+	0.405067i	$0.867248\pi$
$998$	−3.00202e11	+	3.00202e11i	−0.302616	+	0.302616i
$999$			1.46434e12i			1.47022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.c.7.2	✓	12
5.2	odd	4	inner	25.9.c.c.18.5	yes	12
5.3	odd	4	inner	25.9.c.c.18.2	yes	12
5.4	even	2	inner	25.9.c.c.7.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.c.c.7.2	✓	12	1.1	even	1	trivial
25.9.c.c.7.5	yes	12	5.4	even	2	inner
25.9.c.c.18.2	yes	12	5.3	odd	4	inner
25.9.c.c.18.5	yes	12	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.1270 - 18.1270i) q^{2} +(95.3921 - 95.3921i) q^{3} +401.173i q^{4} -3458.34 q^{6} +(-1478.49 - 1478.49i) q^{7} +(2631.55 - 2631.55i) q^{8} -11638.3i q^{9} +O(q^{10})\)	\(q+(-18.1270 - 18.1270i) q^{2} +(95.3921 - 95.3921i) q^{3} +401.173i q^{4} -3458.34 q^{6} +(-1478.49 - 1478.49i) q^{7} +(2631.55 - 2631.55i) q^{8} -11638.3i q^{9} -16335.7 q^{11} +(38268.7 + 38268.7i) q^{12} +(-11728.1 + 11728.1i) q^{13} +53601.2i q^{14} +7296.48 q^{16} +(-20145.3 - 20145.3i) q^{17} +(-210967. + 210967. i) q^{18} +119950. i q^{19} -282073. q^{21} +(296117. + 296117. i) q^{22} +(361395. - 361395. i) q^{23} -502057. i q^{24} +425189. q^{26} +(-484333. - 484333. i) q^{27} +(593132. - 593132. i) q^{28} -64977.0i q^{29} -906755. q^{31} +(-805939. - 805939. i) q^{32} +(-1.55830e6 + 1.55830e6i) q^{33} +730347. i q^{34} +4.66897e6 q^{36} +(-1.51171e6 - 1.51171e6i) q^{37} +(2.17432e6 - 2.17432e6i) q^{38} +2.23753e6i q^{39} +2.57423e6 q^{41} +(5.11313e6 + 5.11313e6i) q^{42} +(-2.04074e6 + 2.04074e6i) q^{43} -6.55345e6i q^{44} -1.31020e7 q^{46} +(-1.34679e6 - 1.34679e6i) q^{47} +(696026. - 696026. i) q^{48} -1.39291e6i q^{49} -3.84341e6 q^{51} +(-4.70499e6 - 4.70499e6i) q^{52} +(773924. - 773924. i) q^{53} +1.75590e7i q^{54} -7.78145e6 q^{56} +(1.14423e7 + 1.14423e7i) q^{57} +(-1.17784e6 + 1.17784e6i) q^{58} -1.56073e7i q^{59} +8.14063e6 q^{61} +(1.64367e7 + 1.64367e7i) q^{62} +(-1.72071e7 + 1.72071e7i) q^{63} +2.73505e7i q^{64} +5.64944e7 q^{66} +(-2.76850e7 - 2.76850e7i) q^{67} +(8.08176e6 - 8.08176e6i) q^{68} -6.89484e7i q^{69} -1.45478e7 q^{71} +(-3.06267e7 - 3.06267e7i) q^{72} +(1.43422e7 - 1.43422e7i) q^{73} +5.48055e7i q^{74} -4.81206e7 q^{76} +(2.41523e7 + 2.41523e7i) q^{77} +(4.05596e7 - 4.05596e7i) q^{78} +4.59513e7i q^{79} -1.60443e7 q^{81} +(-4.66629e7 - 4.66629e7i) q^{82} +(2.00811e7 - 2.00811e7i) q^{83} -1.13160e8i q^{84} +7.39848e7 q^{86} +(-6.19829e6 - 6.19829e6i) q^{87} +(-4.29882e7 + 4.29882e7i) q^{88} -3.53615e7i q^{89} +3.46798e7 q^{91} +(1.44982e8 + 1.44982e8i) q^{92} +(-8.64972e7 + 8.64972e7i) q^{93} +4.88265e7i q^{94} -1.53760e8 q^{96} +(-5.33242e6 - 5.33242e6i) q^{97} +(-2.52492e7 + 2.52492e7i) q^{98} +1.90120e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6396 q^{6}+O(q^{10}) \) 12 * q - 6396 * q^6	\( 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) \) 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Introduction

L-functions

Modular forms

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Database

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