LMFDB - Embedded newform 75.9.f.c.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.151613669376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{4} + 256 $ x^8 - 7*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$-0.662382 + 1.88713i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.c.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.7465 - 17.7465i) q^{2} +(33.0681 + 33.0681i) q^{3} -373.880i q^{4} +1173.69 q^{6} +(-3270.12 + 3270.12i) q^{7} +(-2091.96 - 2091.96i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(17.7465 - 17.7465i) q^{2} +(33.0681 + 33.0681i) q^{3} -373.880i q^{4} +1173.69 q^{6} +(-3270.12 + 3270.12i) q^{7} +(-2091.96 - 2091.96i) q^{8} +2187.00i q^{9} +17840.5 q^{11} +(12363.5 - 12363.5i) q^{12} +(21029.0 + 21029.0i) q^{13} +116067. i q^{14} +21463.0 q^{16} +(11098.4 - 11098.4i) q^{17} +(38811.7 + 38811.7i) q^{18} -4190.99i q^{19} -216273. q^{21} +(316608. - 316608. i) q^{22} +(194032. + 194032. i) q^{23} -138354. i q^{24} +746383. q^{26} +(-72320.0 + 72320.0i) q^{27} +(1.22263e6 + 1.22263e6i) q^{28} +728886. i q^{29} -1.11923e6 q^{31} +(916437. - 916437. i) q^{32} +(589952. + 589952. i) q^{33} -393916. i q^{34} +817675. q^{36} +(-2.27395e6 + 2.27395e6i) q^{37} +(-74375.6 - 74375.6i) q^{38} +1.39078e6i q^{39} +5.27540e6 q^{41} +(-3.83810e6 + 3.83810e6i) q^{42} +(-1.31140e6 - 1.31140e6i) q^{43} -6.67021e6i q^{44} +6.88681e6 q^{46} +(-496649. + 496649. i) q^{47} +(709743. + 709743. i) q^{48} -1.56225e7i q^{49} +734006. q^{51} +(7.86231e6 - 7.86231e6i) q^{52} +(-1.05225e6 - 1.05225e6i) q^{53} +2.56686e6i q^{54} +1.36819e7 q^{56} +(138588. - 138588. i) q^{57} +(1.29352e7 + 1.29352e7i) q^{58} -2.25128e6i q^{59} -1.64768e7 q^{61} +(-1.98625e7 + 1.98625e7i) q^{62} +(-7.15175e6 - 7.15175e6i) q^{63} -2.70327e7i q^{64} +2.09392e7 q^{66} +(1.76413e7 - 1.76413e7i) q^{67} +(-4.14947e6 - 4.14947e6i) q^{68} +1.28326e7i q^{69} -7.32508e6 q^{71} +(4.57512e6 - 4.57512e6i) q^{72} +(1.61147e7 + 1.61147e7i) q^{73} +8.07097e7i q^{74} -1.56693e6 q^{76} +(-5.83406e7 + 5.83406e7i) q^{77} +(2.46815e7 + 2.46815e7i) q^{78} +1.60705e7i q^{79} -4.78297e6 q^{81} +(9.36201e7 - 9.36201e7i) q^{82} +(6.51143e7 + 6.51143e7i) q^{83} +8.08602e7i q^{84} -4.65455e7 q^{86} +(-2.41029e7 + 2.41029e7i) q^{87} +(-3.73217e7 - 3.73217e7i) q^{88} -1.05991e8i q^{89} -1.37534e8 q^{91} +(7.25448e7 - 7.25448e7i) q^{92} +(-3.70109e7 - 3.70109e7i) q^{93} +1.76276e7i q^{94} +6.06097e7 q^{96} +(-2.43982e7 + 2.43982e7i) q^{97} +(-2.77246e8 - 2.77246e8i) q^{98} +3.90172e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 1296 q^{6}+O(q^{10}) $ 8 * q + 1296 * q^6	$ 8 q + 1296 q^{6} + 107952 q^{11} + 401920 q^{16} - 953208 q^{21} + 4257936 q^{26} - 2908312 q^{31} + 3919104 q^{36} + 33914208 q^{41} + 50759328 q^{46} + 854064 q^{51} + 60954240 q^{56} + 29647000 q^{61} + 52666848 q^{66} - 28246944 q^{71} - 59323136 q^{76} - 38263752 q^{81} - 432922128 q^{86} - 517149432 q^{91} + 132129792 q^{96}+O(q^{100}) $ 8 * q + 1296 * q^6 + 107952 * q^11 + 401920 * q^16 - 953208 * q^21 + 4257936 * q^26 - 2908312 * q^31 + 3919104 * q^36 + 33914208 * q^41 + 50759328 * q^46 + 854064 * q^51 + 60954240 * q^56 + 29647000 * q^61 + 52666848 * q^66 - 28246944 * q^71 - 59323136 * q^76 - 38263752 * q^81 - 432922128 * q^86 - 517149432 * q^91 + 132129792 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	17.7465	−	17.7465i	1.10916	−	1.10916i	0.115898	−	0.993261i	$-0.463025\pi$
$2$	17.7465	−	17.7465i	1.10916	−	1.10916i	0.993261	−	0.115898i	$-0.0369746\pi$
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$		−	373.880i		−	1.46047i
$5$		0			0
$5$		0			0
$6$	1173.69			0.905625
$7$	−3270.12	+	3270.12i	−1.36198	+	1.36198i	−0.490592	+	0.871389i	$0.663219\pi$
$7$	−3270.12	+	3270.12i	−1.36198	+	1.36198i	−0.871389	+	0.490592i	$0.836781\pi$
$8$	−2091.96	−	2091.96i	−0.510733	−	0.510733i
$9$			2187.00i			0.333333i
$10$		0			0
$11$	17840.5			1.21853			0.609266	−	0.792966i	$-0.291464\pi$
$11$	17840.5			1.21853			0.609266	+	0.792966i	$0.291464\pi$
$12$	12363.5	−	12363.5i	0.596234	−	0.596234i
$13$	21029.0	+	21029.0i	0.736282	+	0.736282i	0.971856	−	0.235574i	$-0.0756970\pi$
$13$	21029.0	+	21029.0i	0.736282	+	0.736282i	−0.235574	+	0.971856i	$0.575697\pi$
$14$			116067.i			3.02131i
$15$		0			0
$16$	21463.0			0.327500
$17$	11098.4	−	11098.4i	0.132881	−	0.132881i	−0.637538	−	0.770419i	$-0.720047\pi$
$17$	11098.4	−	11098.4i	0.132881	−	0.132881i	0.770419	+	0.637538i	$0.220047\pi$
$18$	38811.7	+	38811.7i	0.369720	+	0.369720i
$19$		−	4190.99i		−	0.0321590i	−0.999871	−	0.0160795i	$-0.994882\pi$
$19$		−	4190.99i		−	0.0321590i	0.999871	−	0.0160795i	$-0.00511848\pi$
$20$		0			0
$21$	−216273.			−1.11205
$22$	316608.	−	316608.i	1.35155	−	1.35155i
$23$	194032.	+	194032.i	0.693366	+	0.693366i	0.962971	−	0.269605i	$-0.0868931\pi$
$23$	194032.	+	194032.i	0.693366	+	0.693366i	−0.269605	+	0.962971i	$0.586893\pi$
$24$		−	138354.i		−	0.417012i
$25$		0			0
$26$	746383.			1.63331
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	1.22263e6	+	1.22263e6i	1.98913	+	1.98913i
$29$			728886.i			1.03055i	0.857026	+	0.515273i	$0.172309\pi$
$29$			728886.i			1.03055i	−0.857026	+	0.515273i	$0.827691\pi$
$30$		0			0
$31$	−1.11923e6			−1.21192			−0.605960	−	0.795495i	$-0.707211\pi$
$31$	−1.11923e6			−1.21192			−0.605960	+	0.795495i	$0.707211\pi$
$32$	916437.	−	916437.i	0.873983	−	0.873983i
$33$	589952.	+	589952.i	0.497463	+	0.497463i
$34$		−	393916.i		−	0.294773i
$35$		0			0
$36$	817675.			0.486823
$37$	−2.27395e6	+	2.27395e6i	−1.21332	+	1.21332i	−0.243390	+	0.969929i	$0.578259\pi$
$37$	−2.27395e6	+	2.27395e6i	−1.21332	+	1.21332i	−0.969929	+	0.243390i	$0.921741\pi$
$38$	−74375.6	−	74375.6i	−0.0356694	−	0.0356694i
$39$			1.39078e6i			0.601172i
$40$		0			0
$41$	5.27540e6			1.86689			0.933447	−	0.358715i	$-0.116785\pi$
$41$	5.27540e6			1.86689			0.933447	+	0.358715i	$0.116785\pi$
$42$	−3.83810e6	+	3.83810e6i	−1.23344	+	1.23344i
$43$	−1.31140e6	−	1.31140e6i	−0.383584	−	0.383584i	0.488808	−	0.872392i	$-0.337432\pi$
$43$	−1.31140e6	−	1.31140e6i	−0.383584	−	0.383584i	−0.872392	+	0.488808i	$0.837432\pi$
$44$		−	6.67021e6i		−	1.77963i
$45$		0			0
$46$	6.88681e6			1.53811
$47$	−496649.	+	496649.i	−0.101779	+	0.101779i	−0.756163	−	0.654384i	$-0.772928\pi$
$47$	−496649.	+	496649.i	−0.101779	+	0.101779i	0.654384	+	0.756163i	$0.272928\pi$
$48$	709743.	+	709743.i	0.133701	+	0.133701i
$49$		−	1.56225e7i		−	2.70999i
$50$		0			0
$51$	734006.			0.108497
$52$	7.86231e6	−	7.86231e6i	1.07532	−	1.07532i
$53$	−1.05225e6	−	1.05225e6i	−0.133357	−	0.133357i	0.637277	−	0.770635i	$-0.280061\pi$
$53$	−1.05225e6	−	1.05225e6i	−0.133357	−	0.133357i	−0.770635	+	0.637277i	$0.780061\pi$
$54$			2.56686e6i			0.301875i
$55$		0			0
$56$	1.36819e7			1.39122
$57$	138588.	−	138588.i	0.0131288	−	0.0131288i
$58$	1.29352e7	+	1.29352e7i	1.14304	+	1.14304i
$59$		−	2.25128e6i		−	0.185790i	−0.995676	−	0.0928949i	$-0.970388\pi$
$59$		−	2.25128e6i		−	0.185790i	0.995676	−	0.0928949i	$-0.0296120\pi$
$60$		0			0
$61$	−1.64768e7			−1.19002			−0.595009	−	0.803719i	$-0.702852\pi$
$61$	−1.64768e7			−1.19002			−0.595009	+	0.803719i	$0.702852\pi$
$62$	−1.98625e7	+	1.98625e7i	−1.34421	+	1.34421i
$63$	−7.15175e6	−	7.15175e6i	−0.453994	−	0.453994i
$64$		−	2.70327e7i		−	1.61127i
$65$		0			0
$66$	2.09392e7			1.10353
$67$	1.76413e7	−	1.76413e7i	0.875449	−	0.875449i	−0.117611	−	0.993060i	$-0.537524\pi$
$67$	1.76413e7	−	1.76413e7i	0.875449	−	0.875449i	0.993060	+	0.117611i	$0.0375236\pi$
$68$	−4.14947e6	−	4.14947e6i	−0.194069	−	0.194069i
$69$			1.28326e7i			0.566131i
$70$		0			0
$71$	−7.32508e6			−0.288256			−0.144128	−	0.989559i	$-0.546038\pi$
$71$	−7.32508e6			−0.288256			−0.144128	+	0.989559i	$0.546038\pi$
$72$	4.57512e6	−	4.57512e6i	0.170244	−	0.170244i
$73$	1.61147e7	+	1.61147e7i	0.567454	+	0.567454i	0.931414	−	0.363961i	$-0.118576\pi$
$73$	1.61147e7	+	1.61147e7i	0.567454	+	0.567454i	−0.363961	+	0.931414i	$0.618576\pi$
$74$			8.07097e7i			2.69153i
$75$		0			0
$76$	−1.56693e6			−0.0469672
$77$	−5.83406e7	+	5.83406e7i	−1.65962	+	1.65962i
$78$	2.46815e7	+	2.46815e7i	0.666796	+	0.666796i
$79$			1.60705e7i			0.412591i	0.978490	+	0.206296i	$0.0661409\pi$
$79$			1.60705e7i			0.412591i	−0.978490	+	0.206296i	$0.933859\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	9.36201e7	−	9.36201e7i	2.07068	−	2.07068i
$83$	6.51143e7	+	6.51143e7i	1.37203	+	1.37203i	0.857430	+	0.514600i	$0.172060\pi$
$83$	6.51143e7	+	6.51143e7i	1.37203	+	1.37203i	0.514600	+	0.857430i	$0.327940\pi$
$84$			8.08602e7i			1.62412i
$85$		0			0
$86$	−4.65455e7			−0.850911
$87$	−2.41029e7	+	2.41029e7i	−0.420719	+	0.420719i
$88$	−3.73217e7	−	3.73217e7i	−0.622344	−	0.622344i
$89$		−	1.05991e8i		−	1.68930i	−0.535317	−	0.844651i	$-0.679808\pi$
$89$		−	1.05991e8i		−	1.68930i	0.535317	−	0.844651i	$-0.320192\pi$
$90$		0			0
$91$	−1.37534e8			−2.00561
$92$	7.25448e7	−	7.25448e7i	1.01264	−	1.01264i
$93$	−3.70109e7	−	3.70109e7i	−0.494764	−	0.494764i
$94$			1.76276e7i			0.225778i
$95$		0			0
$96$	6.06097e7			0.713604
$97$	−2.43982e7	+	2.43982e7i	−0.275594	+	0.275594i	−0.831347	−	0.555753i	$-0.812430\pi$
$97$	−2.43982e7	+	2.43982e7i	−0.275594	+	0.275594i	0.555753	+	0.831347i	$0.312430\pi$
$98$	−2.77246e8	−	2.77246e8i	−3.00581	−	3.00581i
$99$			3.90172e7i			0.406177i
$100$		0			0
$101$	−3.33768e7			−0.320745			−0.160372	−	0.987057i	$-0.551269\pi$
$101$	−3.33768e7			−0.320745			−0.160372	+	0.987057i	$0.551269\pi$
$102$	1.30261e7	−	1.30261e7i	0.120341	−	0.120341i
$103$	3.30273e7	+	3.30273e7i	0.293443	+	0.293443i	0.838439	−	0.544996i	$-0.183469\pi$
$103$	3.30273e7	+	3.30273e7i	0.293443	+	0.293443i	−0.544996	+	0.838439i	$0.683469\pi$
$104$		−	8.79836e7i		−	0.752087i
$105$		0			0
$106$	−3.73478e7			−0.295829
$107$	−9.27164e6	+	9.27164e6i	−0.0707329	+	0.0707329i	−0.741588	−	0.670855i	$-0.765927\pi$
$107$	−9.27164e6	+	9.27164e6i	−0.0707329	+	0.0707329i	0.670855	+	0.741588i	$0.265927\pi$
$108$	2.70390e7	+	2.70390e7i	0.198745	+	0.198745i
$109$		−	8.33891e7i		−	0.590749i	−0.955382	−	0.295375i	$-0.904556\pi$
$109$		−	8.33891e7i		−	0.590749i	0.955382	−	0.295375i	$-0.0954445\pi$
$110$		0			0
$111$	−1.50391e8			−0.990670
$112$	−7.01867e7	+	7.01867e7i	−0.446049	+	0.446049i
$113$	−1.32609e8	−	1.32609e8i	−0.813317	−	0.813317i	0.171813	−	0.985130i	$-0.445038\pi$
$113$	−1.32609e8	−	1.32609e8i	−0.813317	−	0.813317i	−0.985130	+	0.171813i	$0.945038\pi$
$114$		−	4.91892e6i		−	0.0291240i
$115$		0			0
$116$	2.72516e8			1.50508
$117$	−4.59903e7	+	4.59903e7i	−0.245427	+	0.245427i
$118$	−3.99525e7	−	3.99525e7i	−0.206070	−	0.206070i
$119$			7.25861e7i			0.361964i
$120$		0			0
$121$	1.03925e8			0.484819
$122$	−2.92406e8	+	2.92406e8i	−1.31992	+	1.31992i
$123$	1.74447e8	+	1.74447e8i	0.762156	+	0.762156i
$124$			4.18459e8i			1.76997i
$125$		0			0
$126$	−2.53838e8			−1.00710
$127$	−5.62627e7	+	5.62627e7i	−0.216275	+	0.216275i	−0.806927	−	0.590652i	$-0.798871\pi$
$127$	−5.62627e7	+	5.62627e7i	−0.216275	+	0.216275i	0.590652	+	0.806927i	$0.298871\pi$
$128$	−2.45128e8	−	2.45128e8i	−0.913175	−	0.913175i
$129$		−	8.67308e7i		−	0.313195i
$130$		0			0
$131$	−9.55354e7			−0.324399			−0.162199	−	0.986758i	$-0.551859\pi$
$131$	−9.55354e7			−0.324399			−0.162199	+	0.986758i	$0.551859\pi$
$132$	2.20571e8	−	2.20571e8i	0.726530	−	0.726530i
$133$	1.37050e7	+	1.37050e7i	0.0437999	+	0.0437999i
$134$		−	6.26143e8i		−	1.94202i
$135$		0			0
$136$	−4.64348e7			−0.135734
$137$	2.97508e8	−	2.97508e8i	0.844533	−	0.844533i	−0.144911	−	0.989445i	$-0.546290\pi$
$137$	2.97508e8	−	2.97508e8i	0.844533	−	0.844533i	0.989445	+	0.144911i	$0.0462897\pi$
$138$	2.27734e8	+	2.27734e8i	0.627930	+	0.627930i
$139$		−	9.41167e7i		−	0.252120i	−0.992023	−	0.126060i	$-0.959767\pi$
$139$		−	9.41167e7i		−	0.252120i	0.992023	−	0.126060i	$-0.0402332\pi$
$140$		0			0
$141$	−3.28465e7			−0.0831022
$142$	−1.29995e8	+	1.29995e8i	−0.319722	+	0.319722i
$143$	3.75168e8	+	3.75168e8i	0.897183	+	0.897183i
$144$			4.69397e7i			0.109167i
$145$		0			0
$146$	5.71960e8			1.25879
$147$	5.16608e8	−	5.16608e8i	1.10635	−	1.10635i
$148$	8.50186e8	+	8.50186e8i	1.77201	+	1.77201i
$149$		−	3.37303e8i		−	0.684345i	−0.939637	−	0.342173i	$-0.888837\pi$
$149$		−	3.37303e8i		−	0.684345i	0.939637	−	0.342173i	$-0.111163\pi$
$150$		0			0
$151$	2.38983e8			0.459683			0.229842	−	0.973228i	$-0.426179\pi$
$151$	2.38983e8			0.459683			0.229842	+	0.973228i	$0.426179\pi$
$152$	−8.76739e6	+	8.76739e6i	−0.0164246	+	0.0164246i
$153$	2.42722e7	+	2.42722e7i	0.0442938	+	0.0442938i
$154$			2.07069e9i			3.68156i
$155$		0			0
$156$	5.19983e8			0.877993
$157$	1.02581e8	−	1.02581e8i	0.168838	−	0.168838i	−0.617630	−	0.786468i	$-0.711907\pi$
$157$	1.02581e8	−	1.02581e8i	0.168838	−	0.168838i	0.786468	+	0.617630i	$0.211907\pi$
$158$	2.85195e8	+	2.85195e8i	0.457630	+	0.457630i
$159$		−	6.95921e7i		−	0.108886i
$160$		0			0
$161$	−1.26902e9			−1.88870
$162$	−8.48812e7	+	8.48812e7i	−0.123240	+	0.123240i
$163$	4.84778e8	+	4.84778e8i	0.686740	+	0.686740i	0.961510	−	0.274770i	$-0.0886017\pi$
$163$	4.84778e8	+	4.84778e8i	0.686740	+	0.686740i	−0.274770	+	0.961510i	$0.588602\pi$
$164$		−	1.97236e9i		−	2.72654i
$165$		0			0
$166$	2.31111e9			3.04360
$167$	−2.80865e7	+	2.80865e7i	−0.0361103	+	0.0361103i	−0.724931	−	0.688821i	$-0.758129\pi$
$167$	−2.80865e7	+	2.80865e7i	−0.0361103	+	0.0361103i	0.688821	+	0.724931i	$0.258129\pi$
$168$	4.52435e8	+	4.52435e8i	0.567962	+	0.567962i
$169$			6.87038e7i			0.0842236i
$170$		0			0
$171$	9.16569e6			0.0107197
$172$	−4.90305e8	+	4.90305e8i	−0.560212	+	0.560212i
$173$	−9.29590e8	−	9.29590e8i	−1.03778	−	1.03778i	−0.999258	−	0.0385268i	$-0.987734\pi$
$173$	−9.29590e8	−	9.29590e8i	−1.03778	−	1.03778i	−0.0385268	−	0.999258i	$-0.512266\pi$
$174$			8.55486e8i			0.933288i
$175$		0			0
$176$	3.82912e8			0.399069
$177$	7.44456e7	−	7.44456e7i	0.0758483	−	0.0758483i
$178$	−1.88097e9	−	1.88097e9i	−1.87370	−	1.87370i
$179$		−	7.99332e8i		−	0.778601i	−0.921111	−	0.389301i	$-0.872717\pi$
$179$		−	7.99332e8i		−	0.778601i	0.921111	−	0.389301i	$-0.127283\pi$
$180$		0			0
$181$	1.06852e9			0.995563			0.497781	−	0.867303i	$-0.334148\pi$
$181$	1.06852e9			0.995563			0.497781	+	0.867303i	$0.334148\pi$
$182$	−2.44076e9	+	2.44076e9i	−2.22454	+	2.22454i
$183$	−5.44857e8	−	5.44857e8i	−0.485823	−	0.485823i
$184$		−	8.11816e8i		−	0.708250i
$185$		0			0
$186$	−1.31363e9			−1.09754
$187$	1.98001e8	−	1.98001e8i	0.161920	−	0.161920i
$188$	1.85687e8	+	1.85687e8i	0.148645	+	0.148645i
$189$		−	4.72990e8i		−	0.370684i
$190$		0			0
$191$	3.95924e8			0.297494			0.148747	−	0.988875i	$-0.452476\pi$
$191$	3.95924e8			0.297494			0.148747	+	0.988875i	$0.452476\pi$
$192$	8.93919e8	−	8.93919e8i	0.657799	−	0.657799i
$193$	1.29834e9	+	1.29834e9i	0.935746	+	0.935746i	0.998057	−	0.0623104i	$-0.0198469\pi$
$193$	1.29834e9	+	1.29834e9i	0.935746	+	0.935746i	−0.0623104	+	0.998057i	$0.519847\pi$
$194$			8.65966e8i			0.611356i
$195$		0			0
$196$	−5.84095e9			−3.95785
$197$	1.40667e9	−	1.40667e9i	0.933957	−	0.933957i	−0.0639938	−	0.997950i	$-0.520384\pi$
$197$	1.40667e9	−	1.40667e9i	0.933957	−	0.933957i	0.997950	+	0.0639938i	$0.0203838\pi$
$198$	6.92421e8	+	6.92421e8i	0.450515	+	0.450515i
$199$		−	2.46731e9i		−	1.57330i	−0.617398	−	0.786651i	$-0.711813\pi$
$199$		−	2.46731e9i		−	1.57330i	0.617398	−	0.786651i	$-0.288187\pi$
$200$		0			0
$201$	1.16673e9			0.714801
$202$	−5.92323e8	+	5.92323e8i	−0.355757	+	0.355757i
$203$	−2.38354e9	−	2.38354e9i	−1.40358	−	1.40358i
$204$		−	2.74430e8i		−	0.158457i
$205$		0			0
$206$	1.17224e9			0.650951
$207$	−4.24349e8	+	4.24349e8i	−0.231122	+	0.231122i
$208$	4.51346e8	+	4.51346e8i	0.241133	+	0.241133i
$209$		−	7.47694e7i		−	0.0391867i
$210$		0			0
$211$	7.52155e8			0.379470			0.189735	−	0.981835i	$-0.439237\pi$
$211$	7.52155e8			0.379470			0.189735	+	0.981835i	$0.439237\pi$
$212$	−3.93417e8	+	3.93417e8i	−0.194764	+	0.194764i
$213$	−2.42227e8	−	2.42227e8i	−0.117680	−	0.117680i
$214$			3.29079e8i			0.156908i
$215$		0			0
$216$	3.02581e8			0.139004
$217$	3.66003e9	−	3.66003e9i	1.65061	−	1.65061i
$218$	−1.47987e9	−	1.47987e9i	−0.655235	−	0.655235i
$219$			1.06576e9i			0.463324i
$220$		0			0
$221$	4.66775e8			0.195677
$222$	−2.66892e9	+	2.66892e9i	−1.09881	+	1.09881i
$223$	−2.13030e9	−	2.13030e9i	−0.861433	−	0.861433i	0.130071	−	0.991505i	$-0.458479\pi$
$223$	−2.13030e9	−	2.13030e9i	−0.861433	−	0.861433i	−0.991505	+	0.130071i	$0.958479\pi$
$224$			5.99372e9i			2.38070i
$225$		0			0
$226$	−4.70671e9			−1.80420
$227$	8.44893e8	−	8.44893e8i	0.318199	−	0.318199i	−0.529876	−	0.848075i	$-0.677762\pi$
$227$	8.44893e8	−	8.44893e8i	0.318199	−	0.318199i	0.848075	+	0.529876i	$0.177762\pi$
$228$	−5.18153e7	−	5.18153e7i	−0.0191743	−	0.0191743i
$229$			4.36795e8i			0.158831i	0.996842	+	0.0794155i	$0.0253054\pi$
$229$			4.36795e8i			0.158831i	−0.996842	+	0.0794155i	$0.974695\pi$
$230$		0			0
$231$	−3.85843e9			−1.35507
$232$	1.52480e9	−	1.52480e9i	0.526334	−	0.526334i
$233$	1.11369e9	+	1.11369e9i	0.377868	+	0.377868i	0.870332	−	0.492465i	$-0.163904\pi$
$233$	1.11369e9	+	1.11369e9i	0.377868	+	0.377868i	−0.492465	+	0.870332i	$0.663904\pi$
$234$			1.63234e9i			0.544436i
$235$		0			0
$236$	−8.41709e8			−0.271340
$237$	−5.31420e8	+	5.31420e8i	−0.168440	+	0.168440i
$238$	1.28815e9	+	1.28815e9i	0.401476	+	0.401476i
$239$			3.18931e9i			0.977474i	0.872431	+	0.488737i	$0.162542\pi$
$239$			3.18931e9i			0.977474i	−0.872431	+	0.488737i	$0.837458\pi$
$240$		0			0
$241$	1.44534e9			0.428453			0.214226	−	0.976784i	$-0.431277\pi$
$241$	1.44534e9			0.428453			0.214226	+	0.976784i	$0.431277\pi$
$242$	1.84431e9	−	1.84431e9i	0.537741	−	0.537741i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$			6.16035e9i			1.73798i
$245$		0			0
$246$	6.19168e9			1.69071
$247$	8.81321e7	−	8.81321e7i	0.0236781	−	0.0236781i
$248$	2.34139e9	+	2.34139e9i	0.618968	+	0.618968i
$249$			4.30641e9i			1.12026i
$250$		0			0
$251$	−1.75290e9			−0.441633			−0.220816	−	0.975315i	$-0.570872\pi$
$251$	−1.75290e9			−0.441633			−0.220816	+	0.975315i	$0.570872\pi$
$252$	−2.67389e9	+	2.67389e9i	−0.663044	+	0.663044i
$253$	3.46164e9	+	3.46164e9i	0.844889	+	0.844889i
$254$			1.99694e9i			0.479766i
$255$		0			0
$256$	−1.78001e9			−0.414440
$257$	3.01535e9	−	3.01535e9i	0.691203	−	0.691203i	−0.271293	−	0.962497i	$-0.587451\pi$
$257$	3.01535e9	−	3.01535e9i	0.691203	−	0.691203i	0.962497	+	0.271293i	$0.0874514\pi$
$258$	−1.53917e9	−	1.53917e9i	−0.347383	−	0.347383i
$259$		−	1.48722e10i		−	3.30503i
$260$		0			0
$261$	−1.59407e9			−0.343515
$262$	−1.69542e9	+	1.69542e9i	−0.359810	+	0.359810i
$263$	6.47109e9	+	6.47109e9i	1.35255	+	1.35255i	0.882795	+	0.469758i	$0.155659\pi$
$263$	6.47109e9	+	6.47109e9i	1.35255	+	1.35255i	0.469758	+	0.882795i	$0.344341\pi$
$264$		−	2.46832e9i		−	0.508142i
$265$		0			0
$266$	4.86434e8			0.0971621
$267$	3.50491e9	−	3.50491e9i	0.689655	−	0.689655i
$268$	−6.59572e9	−	6.59572e9i	−1.27857	−	1.27857i
$269$		−	6.45204e9i		−	1.23222i	−0.787660	−	0.616110i	$-0.788708\pi$
$269$		−	6.45204e9i		−	1.23222i	0.787660	−	0.616110i	$-0.211292\pi$
$270$		0			0
$271$	−1.51873e9			−0.281581			−0.140790	−	0.990039i	$-0.544964\pi$
$271$	−1.51873e9			−0.281581			−0.140790	+	0.990039i	$0.544964\pi$
$272$	2.38205e8	−	2.38205e8i	0.0435187	−	0.0435187i
$273$	−4.54800e9	−	4.54800e9i	−0.818785	−	0.818785i
$274$		−	1.05595e10i		−	1.87344i
$275$		0			0
$276$	4.79784e9			0.826817
$277$	−3.83205e9	+	3.83205e9i	−0.650896	+	0.650896i	−0.953209	−	0.302313i	$-0.902241\pi$
$277$	−3.83205e9	+	3.83205e9i	−0.650896	+	0.650896i	0.302313	+	0.953209i	$0.402241\pi$
$278$	−1.67025e9	−	1.67025e9i	−0.279641	−	0.279641i
$279$		−	2.44776e9i		−	0.403973i
$280$		0			0
$281$	−6.48414e9			−1.03999			−0.519993	−	0.854171i	$-0.674065\pi$
$281$	−6.48414e9			−1.03999			−0.519993	+	0.854171i	$0.674065\pi$
$282$	−5.82912e8	+	5.82912e8i	−0.0921736	+	0.0921736i
$283$	2.45964e9	+	2.45964e9i	0.383465	+	0.383465i	0.872349	−	0.488884i	$-0.162596\pi$
$283$	2.45964e9	+	2.45964e9i	0.383465	+	0.383465i	−0.488884	+	0.872349i	$0.662596\pi$
$284$			2.73870e9i			0.420989i
$285$		0			0
$286$	1.33159e10			1.99024
$287$	−1.72512e10	+	1.72512e10i	−2.54267	+	2.54267i
$288$	2.00425e9	+	2.00425e9i	0.291328	+	0.291328i
$289$			6.72941e9i			0.964685i
$290$		0			0
$291$	−1.61360e9			−0.225022
$292$	6.02496e9	−	6.02496e9i	0.828748	−	0.828748i
$293$	−1.67209e9	−	1.67209e9i	−0.226877	−	0.226877i	0.584510	−	0.811387i	$-0.301287\pi$
$293$	−1.67209e9	−	1.67209e9i	−0.226877	−	0.226877i	−0.811387	+	0.584510i	$0.801287\pi$
$294$		−	1.83360e10i		−	2.45423i
$295$		0			0
$296$	9.51405e9			1.23936
$297$	−1.29023e9	+	1.29023e9i	−0.165821	+	0.165821i
$298$	−5.98596e9	−	5.98596e9i	−0.759048	−	0.759048i
$299$			8.16060e9i			1.02103i
$300$		0			0
$301$	8.57684e9			1.04487
$302$	4.24112e9	−	4.24112e9i	0.509862	−	0.509862i
$303$	−1.10371e9	−	1.10371e9i	−0.130943	−	0.130943i
$304$		−	8.99514e7i		−	0.0105321i
$305$		0			0
$306$	8.61495e8			0.0982578
$307$	−1.63713e8	+	1.63713e8i	−0.0184302	+	0.0184302i	−0.716262	−	0.697832i	$-0.754148\pi$
$307$	−1.63713e8	+	1.63713e8i	−0.0184302	+	0.0184302i	0.697832	+	0.716262i	$0.254148\pi$
$308$	2.18124e10	+	2.18124e10i	2.42382	+	2.42382i
$309$			2.18430e9i			0.239595i
$310$		0			0
$311$	−3.31282e9			−0.354125			−0.177063	−	0.984200i	$-0.556660\pi$
$311$	−3.31282e9			−0.354125			−0.177063	+	0.984200i	$0.556660\pi$
$312$	2.90945e9	−	2.90945e9i	0.307038	−	0.307038i
$313$	−8.43413e8	−	8.43413e8i	−0.0878745	−	0.0878745i	0.661803	−	0.749678i	$-0.269791\pi$
$313$	−8.43413e8	−	8.43413e8i	−0.0878745	−	0.0878745i	−0.749678	+	0.661803i	$0.769791\pi$
$314$		−	3.64093e9i		−	0.374536i
$315$		0			0
$316$	6.00843e9			0.602577
$317$	7.84707e9	−	7.84707e9i	0.777088	−	0.777088i	−0.202247	−	0.979335i	$-0.564824\pi$
$317$	7.84707e9	−	7.84707e9i	0.777088	−	0.777088i	0.979335	+	0.202247i	$0.0648242\pi$
$318$	−1.23502e9	−	1.23502e9i	−0.120772	−	0.120772i
$319$			1.30037e10i			1.25575i
$320$		0			0
$321$	−6.13191e8			−0.0577532
$322$	−2.25207e10	+	2.25207e10i	−2.09487	+	2.09487i
$323$	−4.65132e7	−	4.65132e7i	−0.00427333	−	0.00427333i
$324$			1.78826e9i			0.162274i
$325$		0			0
$326$	1.72063e10			1.52341
$327$	2.75752e9	−	2.75752e9i	0.241172	−	0.241172i
$328$	−1.10359e10	−	1.10359e10i	−0.953484	−	0.953484i
$329$		−	3.24820e9i		−	0.277242i
$330$		0			0
$331$	9.40384e9			0.783418			0.391709	−	0.920089i	$-0.371884\pi$
$331$	9.40384e9			0.783418			0.391709	+	0.920089i	$0.371884\pi$
$332$	2.43449e10	−	2.43449e10i	2.00381	−	2.00381i
$333$	−4.97314e9	−	4.97314e9i	−0.404439	−	0.404439i
$334$			9.96876e8i			0.0801042i
$335$		0			0
$336$	−4.64188e9			−0.364198
$337$	−1.44199e10	+	1.44199e10i	−1.11800	+	1.11800i	−0.125968	+	0.992034i	$0.540204\pi$
$337$	−1.44199e10	+	1.44199e10i	−1.11800	+	1.11800i	−0.992034	+	0.125968i	$0.959796\pi$
$338$	1.21925e9	+	1.21925e9i	0.0934174	+	0.0934174i
$339$		−	8.77027e9i		−	0.664070i
$340$		0			0
$341$	−1.99677e10			−1.47676
$342$	1.62659e8	−	1.62659e8i	0.0118898	−	0.0118898i
$343$	3.22359e10	+	3.22359e10i	2.32897	+	2.32897i
$344$			5.48679e9i			0.391818i
$345$		0			0
$346$	−3.29940e10			−2.30214
$347$	1.29230e10	−	1.29230e10i	0.891344	−	0.891344i	−0.103306	−	0.994650i	$-0.532942\pi$
$347$	1.29230e10	−	1.29230e10i	0.891344	−	0.891344i	0.994650	+	0.103306i	$0.0329420\pi$
$348$	9.01158e9	+	9.01158e9i	0.614446	+	0.614446i
$349$		−	3.53041e9i		−	0.237971i	−0.992896	−	0.118985i	$-0.962036\pi$
$349$		−	3.53041e9i		−	0.237971i	0.992896	−	0.118985i	$-0.0379642\pi$
$350$		0			0
$351$	−3.04163e9			−0.200391
$352$	1.63497e10	−	1.63497e10i	1.06498	−	1.06498i
$353$	−1.30724e9	−	1.30724e9i	−0.0841890	−	0.0841890i	0.663758	−	0.747947i	$-0.268960\pi$
$353$	−1.30724e9	−	1.30724e9i	−0.0841890	−	0.0841890i	−0.747947	+	0.663758i	$0.768960\pi$
$354$		−	2.64231e9i		−	0.168256i
$355$		0			0
$356$	−3.96278e10			−2.46717
$357$	−2.40028e9	+	2.40028e9i	−0.147771	+	0.147771i
$358$	−1.41854e10	−	1.41854e10i	−0.863593	−	0.863593i
$359$			1.48400e10i			0.893419i	0.894679	+	0.446710i	$0.147404\pi$
$359$			1.48400e10i			0.893419i	−0.894679	+	0.446710i	$0.852596\pi$
$360$		0			0
$361$	1.69660e10			0.998966
$362$	1.89626e10	−	1.89626e10i	1.10424	−	1.10424i
$363$	3.43661e9	+	3.43661e9i	0.197926	+	0.197926i
$364$			5.14213e10i			2.92912i
$365$		0			0
$366$	−1.93387e10			−1.07771
$367$	−1.10240e10	+	1.10240e10i	−0.607677	+	0.607677i	−0.942339	−	0.334661i	$-0.891378\pi$
$367$	−1.10240e10	+	1.10240e10i	−0.607677	+	0.607677i	0.334661	+	0.942339i	$0.391378\pi$
$368$	4.16452e9	+	4.16452e9i	0.227078	+	0.227078i
$369$			1.15373e10i			0.622298i
$370$		0			0
$371$	6.88199e9			0.363261
$372$	−1.38377e10	+	1.38377e10i	−0.722588	+	0.722588i
$373$	−2.10750e10	−	2.10750e10i	−1.08876	−	1.08876i	−0.995657	−	0.0931014i	$-0.970322\pi$
$373$	−2.10750e10	−	2.10750e10i	−1.08876	−	1.08876i	−0.0931014	−	0.995657i	$-0.529678\pi$
$374$		−	7.02767e9i		−	0.359191i
$375$		0			0
$376$	2.07794e9			0.103964
$377$	−1.53277e10	+	1.53277e10i	−0.758773	+	0.758773i
$378$	−8.39393e9	−	8.39393e9i	−0.411148	−	0.411148i
$379$			5.11807e9i			0.248056i	0.992279	+	0.124028i	$0.0395813\pi$
$379$			5.11807e9i			0.248056i	−0.992279	+	0.124028i	$0.960419\pi$
$380$		0			0
$381$	−3.72100e9			−0.176588
$382$	7.02629e9	−	7.02629e9i	0.329969	−	0.329969i
$383$	−2.17344e10	−	2.17344e10i	−1.01007	−	1.01007i	−0.999949	−	0.0101236i	$-0.996778\pi$
$383$	−2.17344e10	−	2.17344e10i	−1.01007	−	1.01007i	−0.0101236	−	0.999949i	$-0.503222\pi$
$384$		−	1.62119e10i		−	0.745604i
$385$		0			0
$386$	4.60820e10			2.07578
$387$	2.86803e9	−	2.86803e9i	0.127861	−	0.127861i
$388$	9.12199e9	+	9.12199e9i	0.402497	+	0.402497i
$389$		−	9.67038e9i		−	0.422323i	−0.977451	−	0.211162i	$-0.932275\pi$
$389$		−	9.67038e9i		−	0.422323i	0.977451	−	0.211162i	$-0.0677246\pi$
$390$		0			0
$391$	4.30689e9			0.184271
$392$	−3.26818e10	+	3.26818e10i	−1.38408	+	1.38408i
$393$	−3.15918e9	−	3.15918e9i	−0.132435	−	0.132435i
$394$		−	4.99270e10i		−	2.07181i
$395$		0			0
$396$	1.45878e10			0.593209
$397$	−5.26957e9	+	5.26957e9i	−0.212135	+	0.212135i	−0.805174	−	0.593039i	$-0.797928\pi$
$397$	−5.26957e9	+	5.26957e9i	−0.212135	+	0.212135i	0.593039	+	0.805174i	$0.297928\pi$
$398$	−4.37863e10	−	4.37863e10i	−1.74504	−	1.74504i
$399$			9.06398e8i			0.0357625i
$400$		0			0
$401$	−2.27953e10			−0.881591			−0.440796	−	0.897607i	$-0.645304\pi$
$401$	−2.27953e10			−0.881591			−0.440796	+	0.897607i	$0.645304\pi$
$402$	2.07054e10	−	2.07054e10i	0.792828	−	0.792828i
$403$	−2.35363e10	−	2.35363e10i	−0.892316	−	0.892316i
$404$			1.24789e10i			0.468437i
$405$		0			0
$406$	−8.45993e10			−3.11360
$407$	−4.05685e10	+	4.05685e10i	−1.47847	+	1.47847i
$408$	−1.53551e9	−	1.53551e9i	−0.0554131	−	0.0554131i
$409$		−	2.54920e10i		−	0.910984i	−0.890240	−	0.455492i	$-0.849463\pi$
$409$		−	2.54920e10i		−	0.910984i	0.890240	−	0.455492i	$-0.150537\pi$
$410$		0			0
$411$	1.96761e10			0.689558
$412$	1.23482e10	−	1.23482e10i	0.428565	−	0.428565i
$413$	7.36195e9	+	7.36195e9i	0.253042	+	0.253042i
$414$			1.50614e10i			0.512702i
$415$		0			0
$416$	3.85435e10			1.28700
$417$	3.11226e9	−	3.11226e9i	0.102928	−	0.102928i
$418$	−1.32690e9	−	1.32690e9i	−0.0434643	−	0.0434643i
$419$			5.13406e10i			1.66573i	0.553475	+	0.832866i	$0.313301\pi$
$419$			5.13406e10i			1.66573i	−0.553475	+	0.832866i	$0.686699\pi$
$420$		0			0
$421$	3.01466e10			0.959642			0.479821	−	0.877366i	$-0.340702\pi$
$421$	3.01466e10			0.959642			0.479821	+	0.877366i	$0.340702\pi$
$422$	1.33481e10	−	1.33481e10i	0.420892	−	0.420892i
$423$	−1.08617e9	−	1.08617e9i	−0.0339263	−	0.0339263i
$424$			4.40255e9i			0.136220i
$425$		0			0
$426$	−8.59737e9			−0.261052
$427$	5.38811e10	−	5.38811e10i	1.62078	−	1.62078i
$428$	3.46648e9	+	3.46648e9i	0.103303	+	0.103303i
$429$			2.48122e10i			0.732547i
$430$		0			0
$431$	−2.04188e10			−0.591727			−0.295863	−	0.955230i	$-0.595607\pi$
$431$	−2.04188e10			−0.591727			−0.295863	+	0.955230i	$0.595607\pi$
$432$	−1.55221e9	+	1.55221e9i	−0.0445671	+	0.0445671i
$433$	−1.29331e10	−	1.29331e10i	−0.367917	−	0.367917i	0.498800	−	0.866717i	$-0.333774\pi$
$433$	−1.29331e10	−	1.29331e10i	−0.367917	−	0.367917i	−0.866717	+	0.498800i	$0.833774\pi$
$434$		−	1.29906e11i		−	3.66158i
$435$		0			0
$436$	−3.11775e10			−0.862771
$437$	8.13187e8	−	8.13187e8i	0.0222979	−	0.0222979i
$438$	1.89136e10	+	1.89136e10i	0.513900	+	0.513900i
$439$		−	4.31979e10i		−	1.16307i	−0.813523	−	0.581533i	$-0.802453\pi$
$439$		−	4.31979e10i		−	1.16307i	0.813523	−	0.581533i	$-0.197547\pi$
$440$		0			0
$441$	3.41665e10			0.903329
$442$	8.28365e9	−	8.28365e9i	0.217036	−	0.217036i
$443$	1.41532e10	+	1.41532e10i	0.367484	+	0.367484i	0.866559	−	0.499075i	$-0.166327\pi$
$443$	1.41532e10	+	1.41532e10i	0.367484	+	0.367484i	−0.499075	+	0.866559i	$0.666327\pi$
$444$			5.62281e10i			1.44684i
$445$		0			0
$446$	−7.56110e10			−1.91093
$447$	1.11540e10	−	1.11540e10i	0.279383	−	0.279383i
$448$	8.84000e10	+	8.84000e10i	2.19452	+	2.19452i
$449$			5.32009e9i			0.130898i	0.997856	+	0.0654491i	$0.0208480\pi$
$449$			5.32009e9i			0.130898i	−0.997856	+	0.0654491i	$0.979152\pi$
$450$		0			0
$451$	9.41158e10			2.27487
$452$	−4.95799e10	+	4.95799e10i	−1.18782	+	1.18782i
$453$	7.90271e9	+	7.90271e9i	0.187665	+	0.187665i
$454$		−	2.99879e10i		−	0.705866i
$455$		0			0
$456$	−5.79842e8			−0.0134107
$457$	4.39139e10	−	4.39139e10i	1.00679	−	1.00679i	0.00680936	−	0.999977i	$-0.497832\pi$
$457$	4.39139e10	−	4.39139e10i	1.00679	−	1.00679i	0.999977	−	0.00680936i	$-0.00216750\pi$
$458$	7.75159e9	+	7.75159e9i	0.176169	+	0.176169i
$459$			1.60527e9i			0.0361657i
$460$		0			0
$461$	4.79757e10			1.06223			0.531114	−	0.847300i	$-0.321774\pi$
$461$	4.79757e10			1.06223			0.531114	+	0.847300i	$0.321774\pi$
$462$	−6.84737e10	+	6.84737e10i	−1.50299	+	1.50299i
$463$	2.51559e10	+	2.51559e10i	0.547414	+	0.547414i	0.925692	−	0.378278i	$-0.123484\pi$
$463$	2.51559e10	+	2.51559e10i	0.547414	+	0.547414i	−0.378278	+	0.925692i	$0.623484\pi$
$464$			1.56441e10i			0.337504i
$465$		0			0
$466$	3.95282e10			0.838231
$467$	−3.06024e10	+	3.06024e10i	−0.643411	+	0.643411i	−0.951392	−	0.307981i	$-0.900347\pi$
$467$	−3.06024e10	+	3.06024e10i	−0.643411	+	0.643411i	0.307981	+	0.951392i	$0.400347\pi$
$468$	1.71949e10	+	1.71949e10i	0.358439	+	0.358439i
$469$			1.15378e11i			2.38469i
$470$		0			0
$471$	6.78435e9			0.137856
$472$	−4.70960e9	+	4.70960e9i	−0.0948889	+	0.0948889i
$473$	−2.33960e10	−	2.33960e10i	−0.467409	−	0.467409i
$474$			1.88617e10i			0.373653i
$475$		0			0
$476$	2.71385e10			0.528637
$477$	2.30128e9	−	2.30128e9i	0.0444525	−	0.0444525i
$478$	5.65992e10	+	5.65992e10i	1.08417	+	1.08417i
$479$		−	3.81001e10i		−	0.723743i	−0.932228	−	0.361871i	$-0.882138\pi$
$479$		−	3.81001e10i		−	0.723743i	0.932228	−	0.361871i	$-0.117862\pi$
$480$		0			0
$481$	−9.56378e10			−1.78669
$482$	2.56499e10	−	2.56499e10i	0.475222	−	0.475222i
$483$	−4.19640e10	−	4.19640e10i	−0.771060	−	0.771060i
$484$		−	3.88556e10i		−	0.708063i
$485$		0			0
$486$	−5.61372e9			−0.100625
$487$	−1.62003e10	+	1.62003e10i	−0.288009	+	0.288009i	−0.836293	−	0.548283i	$-0.815282\pi$
$487$	−1.62003e10	+	1.62003e10i	−0.288009	+	0.288009i	0.548283	+	0.836293i	$0.315282\pi$
$488$	3.44689e10	+	3.44689e10i	0.607782	+	0.607782i
$489$			3.20614e10i			0.560721i
$490$		0			0
$491$	1.12980e11			1.94390			0.971952	−	0.235181i	$-0.0755683\pi$
$491$	1.12980e11			1.94390			0.971952	+	0.235181i	$0.0755683\pi$
$492$	6.52224e10	−	6.52224e10i	1.11311	−	1.11311i
$493$	8.08946e9	+	8.08946e9i	0.136940	+	0.136940i
$494$		−	3.12808e9i		−	0.0525255i
$495$		0			0
$496$	−2.40222e10			−0.396904
$497$	2.39539e10	−	2.39539e10i	0.392600	−	0.392600i
$498$	7.64239e10	+	7.64239e10i	1.24254	+	1.24254i
$499$			6.81466e10i			1.09911i	0.835457	+	0.549556i	$0.185203\pi$
$499$			6.81466e10i			1.09911i	−0.835457	+	0.549556i	$0.814797\pi$
$500$		0			0
$501$	−1.85753e9			−0.0294840
$502$	−3.11079e10	+	3.11079e10i	−0.489841	+	0.489841i
$503$	3.44116e10	+	3.44116e10i	0.537567	+	0.537567i	0.922814	−	0.385246i	$-0.125884\pi$
$503$	3.44116e10	+	3.44116e10i	0.537567	+	0.537567i	−0.385246	+	0.922814i	$0.625884\pi$
$504$			2.99224e10i			0.463739i
$505$		0			0
$506$	1.22864e11			1.87423
$507$	−2.27190e9	+	2.27190e9i	−0.0343841	+	0.0343841i
$508$	2.10355e10	+	2.10355e10i	0.315863	+	0.315863i
$509$			7.46440e9i			0.111205i	0.998453	+	0.0556024i	$0.0177079\pi$
$509$			7.46440e9i			0.111205i	−0.998453	+	0.0556024i	$0.982292\pi$
$510$		0			0
$511$	−1.05394e11			−1.54572
$512$	3.11639e10	−	3.11639e10i	0.453495	−	0.453495i
$513$	3.03092e8	+	3.03092e8i	0.00437628	+	0.00437628i
$514$		−	1.07024e11i		−	1.53331i
$515$		0			0
$516$	−3.24269e10			−0.457411
$517$	−8.86048e9	+	8.86048e9i	−0.124021	+	0.124021i
$518$	−2.63930e11	−	2.63930e11i	−3.66581	−	3.66581i
$519$		−	6.14796e10i		−	0.847347i
$520$		0			0
$521$	−7.17794e10			−0.974201			−0.487101	−	0.873346i	$-0.661946\pi$
$521$	−7.17794e10			−0.974201			−0.487101	+	0.873346i	$0.661946\pi$
$522$	−2.82893e10	+	2.82893e10i	−0.381013	+	0.381013i
$523$	−5.00016e10	−	5.00016e10i	−0.668309	−	0.668309i	0.289016	−	0.957324i	$-0.406672\pi$
$523$	−5.00016e10	−	5.00016e10i	−0.668309	−	0.668309i	−0.957324	+	0.289016i	$0.906672\pi$
$524$			3.57188e10i			0.473774i
$525$		0			0
$526$	2.29679e11			3.00039
$527$	−1.24217e10	+	1.24217e10i	−0.161042	+	0.161042i
$528$	1.26622e10	+	1.26622e10i	0.162919	+	0.162919i
$529$		−	3.01392e9i		−	0.0384866i
$530$		0			0
$531$	4.92355e9			0.0619299
$532$	5.12403e9	−	5.12403e9i	0.0639684	−	0.0639684i
$533$	1.10936e11	+	1.10936e11i	1.37456	+	1.37456i
$534$		−	1.24400e11i		−	1.52987i
$535$		0			0
$536$	−7.38098e10			−0.894241
$537$	2.64324e10	−	2.64324e10i	0.317863	−	0.317863i
$538$	−1.14501e11	−	1.14501e11i	−1.36673	−	1.36673i
$539$		−	2.78714e11i		−	3.30220i
$540$		0			0
$541$	−7.79225e10			−0.909649			−0.454825	−	0.890581i	$-0.650298\pi$
$541$	−7.79225e10			−0.909649			−0.454825	+	0.890581i	$0.650298\pi$
$542$	−2.69522e10	+	2.69522e10i	−0.312318	+	0.312318i
$543$	3.53340e10	+	3.53340e10i	0.406437	+	0.406437i
$544$		−	2.03420e10i		−	0.232272i
$545$		0			0
$546$	−1.61423e11			−1.81633
$547$	1.72190e10	−	1.72190e10i	0.192335	−	0.192335i	−0.604369	−	0.796704i	$-0.706575\pi$
$547$	1.72190e10	−	1.72190e10i	0.192335	−	0.192335i	0.796704	+	0.604369i	$0.206575\pi$
$548$	−1.11232e11	−	1.11232e11i	−1.23341	−	1.23341i
$549$		−	3.60348e10i		−	0.396673i
$550$		0			0
$551$	3.05475e9			0.0331413
$552$	2.68452e10	−	2.68452e10i	0.289142	−	0.289142i
$553$	−5.25523e10	−	5.25523e10i	−0.561942	−	0.561942i
$554$			1.36011e11i			1.44389i
$555$		0			0
$556$	−3.51884e10			−0.368214
$557$	−8.67000e10	+	8.67000e10i	−0.900738	+	0.900738i	−0.995500	−	0.0947619i	$-0.969791\pi$
$557$	−8.67000e10	+	8.67000e10i	−0.900738	+	0.900738i	0.0947619	+	0.995500i	$0.469791\pi$
$558$	−4.34394e10	−	4.34394e10i	−0.448071	−	0.448071i
$559$		−	5.51546e10i		−	0.564852i
$560$		0			0
$561$	1.30950e10			0.132207
$562$	−1.15071e11	+	1.15071e11i	−1.15351	+	1.15351i
$563$	2.12366e10	+	2.12366e10i	0.211374	+	0.211374i	0.804851	−	0.593477i	$-0.202245\pi$
$563$	2.12366e10	+	2.12366e10i	0.211374	+	0.211374i	−0.593477	+	0.804851i	$0.702245\pi$
$564$			1.22806e10i			0.121368i
$565$		0			0
$566$	8.73002e10			0.850648
$567$	1.56409e10	−	1.56409e10i	0.151331	−	0.151331i
$568$	1.53238e10	+	1.53238e10i	0.147222	+	0.147222i
$569$			8.56235e10i			0.816853i	0.912791	+	0.408426i	$0.133922\pi$
$569$			8.56235e10i			0.816853i	−0.912791	+	0.408426i	$0.866078\pi$
$570$		0			0
$571$	1.17429e11			1.10466			0.552332	−	0.833624i	$-0.313738\pi$
$571$	1.17429e11			1.10466			0.552332	+	0.833624i	$0.313738\pi$
$572$	1.40268e11	−	1.40268e11i	1.31031	−	1.31031i
$573$	1.30925e10	+	1.30925e10i	0.121452	+	0.121452i
$574$			6.12297e11i			5.64046i
$575$		0			0
$576$	5.91204e10			0.537091
$577$	−8.97554e10	+	8.97554e10i	−0.809762	+	0.809762i	−0.984598	−	0.174836i	$-0.944061\pi$
$577$	−8.97554e10	+	8.97554e10i	−0.809762	+	0.809762i	0.174836	+	0.984598i	$0.444061\pi$
$578$	1.19424e11	+	1.19424e11i	1.06999	+	1.06999i
$579$			8.58671e10i			0.764034i
$580$		0			0
$581$	−4.25863e11			−3.73736
$582$	−2.86359e10	+	2.86359e10i	−0.249585	+	0.249585i
$583$	−1.87728e10	−	1.87728e10i	−0.162500	−	0.162500i
$584$		−	6.74226e10i		−	0.579634i
$585$		0			0
$586$	−5.93477e10			−0.503285
$587$	4.65934e10	−	4.65934e10i	0.392439	−	0.392439i	−0.483117	−	0.875556i	$-0.660495\pi$
$587$	4.65934e10	−	4.65934e10i	0.392439	−	0.392439i	0.875556	+	0.483117i	$0.160495\pi$
$588$	−1.93149e11	−	1.93149e11i	−1.61579	−	1.61579i
$589$			4.69070e9i			0.0389741i
$590$		0			0
$591$	9.30317e10			0.762572
$592$	−4.88060e10	+	4.88060e10i	−0.397362	+	0.397362i
$593$	−4.13929e10	−	4.13929e10i	−0.334740	−	0.334740i	0.519644	−	0.854383i	$-0.326065\pi$
$593$	−4.13929e10	−	4.13929e10i	−0.334740	−	0.334740i	−0.854383	+	0.519644i	$0.826065\pi$
$594$			4.57941e10i			0.367844i
$595$		0			0
$596$	−1.26111e11			−0.999464
$597$	8.15894e10	−	8.15894e10i	0.642298	−	0.642298i
$598$	1.44822e11	+	1.44822e11i	1.13248	+	1.13248i
$599$			1.05447e10i			0.0819083i	0.999161	+	0.0409541i	$0.0130398\pi$
$599$			1.05447e10i			0.0819083i	−0.999161	+	0.0409541i	$0.986960\pi$
$600$		0			0
$601$	−1.12786e11			−0.864487			−0.432244	−	0.901757i	$-0.642278\pi$
$601$	−1.12786e11			−0.864487			−0.432244	+	0.901757i	$0.642278\pi$
$602$	1.52209e11	−	1.52209e11i	1.15893	−	1.15893i
$603$	3.85815e10	+	3.85815e10i	0.291816	+	0.291816i
$604$		−	8.93509e10i		−	0.671353i
$605$		0			0
$606$	−3.91740e10			−0.290474
$607$	1.13351e10	−	1.13351e10i	0.0834971	−	0.0834971i	−0.664125	−	0.747622i	$-0.731196\pi$
$607$	1.13351e10	−	1.13351e10i	0.0834971	−	0.0834971i	0.747622	+	0.664125i	$0.231196\pi$
$608$	−3.84078e9	−	3.84078e9i	−0.0281064	−	0.0281064i
$609$		−	1.57638e11i		−	1.14602i
$610$		0			0
$611$	−2.08880e10			−0.149876
$612$	9.07488e9	−	9.07488e9i	0.0646897	−	0.0646897i
$613$	−1.73159e11	−	1.73159e11i	−1.22632	−	1.22632i	−0.965348	−	0.260968i	$-0.915958\pi$
$613$	−1.73159e11	−	1.73159e11i	−1.22632	−	1.22632i	−0.260968	−	0.965348i	$-0.584042\pi$
$614$			5.81067e9i			0.0408840i
$615$		0			0
$616$	2.44093e11			1.69524
$617$	−1.28944e11	+	1.28944e11i	−0.889733	+	0.889733i	−0.994497	−	0.104764i	$-0.966591\pi$
$617$	−1.28944e11	+	1.28944e11i	−0.889733	+	0.889733i	0.104764	+	0.994497i	$0.466591\pi$
$618$	3.87638e10	+	3.87638e10i	0.265749	+	0.265749i
$619$			9.70728e10i			0.661203i	0.943770	+	0.330602i	$0.107252\pi$
$619$			9.70728e10i			0.661203i	−0.943770	+	0.330602i	$0.892748\pi$
$620$		0			0
$621$	−2.80648e10			−0.188710
$622$	−5.87912e10	+	5.87912e10i	−0.392781	+	0.392781i
$623$	3.46602e11	+	3.46602e11i	2.30080	+	2.30080i
$624$			2.98503e10i			0.196884i
$625$		0			0
$626$	−2.99353e10			−0.194934
$627$	2.47248e9	−	2.47248e9i	0.0159979	−	0.0159979i
$628$	−3.83531e10	−	3.83531e10i	−0.246583	−	0.246583i
$629$			5.04745e10i			0.322455i
$630$		0			0
$631$	6.43467e10			0.405890			0.202945	−	0.979190i	$-0.434949\pi$
$631$	6.43467e10			0.405890			0.202945	+	0.979190i	$0.434949\pi$
$632$	3.36188e10	−	3.36188e10i	0.210724	−	0.210724i
$633$	2.48723e10	+	2.48723e10i	0.154918	+	0.154918i
$634$		−	2.78517e11i		−	1.72383i
$635$		0			0
$636$	−2.60191e10			−0.159024
$637$	3.28526e11	−	3.28526e11i	1.99532	−	1.99532i
$638$	2.30771e11	+	2.30771e11i	1.39283	+	1.39283i
$639$		−	1.60199e10i		−	0.0960855i
$640$		0			0
$641$	9.91025e10			0.587020			0.293510	−	0.955956i	$-0.405177\pi$
$641$	9.91025e10			0.587020			0.293510	+	0.955956i	$0.405177\pi$
$642$	−1.08820e10	+	1.08820e10i	−0.0640575	+	0.0640575i
$643$	−3.17814e10	−	3.17814e10i	−0.185921	−	0.185921i	0.608009	−	0.793930i	$-0.291968\pi$
$643$	−3.17814e10	−	3.17814e10i	−0.185921	−	0.185921i	−0.793930	+	0.608009i	$0.791968\pi$
$644$			4.74460e11i			2.75839i
$645$		0			0
$646$	−1.65090e9			−0.00947960
$647$	3.03075e10	−	3.03075e10i	0.172955	−	0.172955i	−0.615321	−	0.788276i	$-0.710974\pi$
$647$	3.03075e10	−	3.03075e10i	0.172955	−	0.172955i	0.788276	+	0.615321i	$0.210974\pi$
$648$	1.00058e10	+	1.00058e10i	0.0567481	+	0.0567481i
$649$		−	4.01640e10i		−	0.226391i
$650$		0			0
$651$	2.42060e11			1.34772
$652$	1.81249e11	−	1.81249e11i	1.00296	−	1.00296i
$653$	−2.13983e11	−	2.13983e11i	−1.17686	−	1.17686i	−0.980539	−	0.196326i	$-0.937099\pi$
$653$	−2.13983e11	−	2.13983e11i	−1.17686	−	1.17686i	−0.196326	−	0.980539i	$-0.562901\pi$
$654$		−	9.78729e10i		−	0.534997i
$655$		0			0
$656$	1.13226e11			0.611408
$657$	−3.52428e10	+	3.52428e10i	−0.189151	+	0.189151i
$658$	−5.76444e10	−	5.76444e10i	−0.307506	−	0.307506i
$659$		−	2.44725e11i		−	1.29759i	−0.760964	−	0.648794i	$-0.775273\pi$
$659$		−	2.44725e11i		−	1.29759i	0.760964	−	0.648794i	$-0.224727\pi$
$660$		0			0
$661$	−9.38180e10			−0.491451			−0.245726	−	0.969339i	$-0.579026\pi$
$661$	−9.38180e10			−0.491451			−0.245726	+	0.969339i	$0.579026\pi$
$662$	1.66886e11	−	1.66886e11i	0.868935	−	0.868935i
$663$	1.54354e10	+	1.54354e10i	0.0798846	+	0.0798846i
$664$		−	2.72433e11i		−	1.40148i
$665$		0			0
$666$	−1.76512e11			−0.897176
$667$	−1.41427e11	+	1.41427e11i	−0.714546	+	0.714546i
$668$	1.05010e10	+	1.05010e10i	0.0527380	+	0.0527380i
$669$		−	1.40890e11i		−	0.703357i
$670$		0			0
$671$	−2.93955e11			−1.45008
$672$	−1.98201e11	+	1.98201e11i	−0.971915	+	0.971915i
$673$	1.91901e11	+	1.91901e11i	0.935443	+	0.935443i	0.998039	−	0.0625955i	$-0.0199378\pi$
$673$	1.91901e11	+	1.91901e11i	0.935443	+	0.935443i	−0.0625955	+	0.998039i	$0.519938\pi$
$674$			5.11807e11i			2.48009i
$675$		0			0
$676$	2.56870e10			0.123006
$677$	−2.28633e11	+	2.28633e11i	−1.08839	+	1.08839i	−0.0926971	+	0.995694i	$0.529549\pi$
$677$	−2.28633e11	+	2.28633e11i	−1.08839	+	1.08839i	−0.995694	+	0.0926971i	$0.970451\pi$
$678$	−1.55642e11	−	1.55642e11i	−0.736560	−	0.736560i
$679$		−	1.59570e11i		−	0.750709i
$680$		0			0
$681$	5.58781e10			0.259808
$682$	−3.54358e11	+	3.54358e11i	−1.63797	+	1.63797i
$683$	7.49280e10	+	7.49280e10i	0.344319	+	0.344319i	0.857988	−	0.513669i	$-0.171714\pi$
$683$	7.49280e10	+	7.49280e10i	0.344319	+	0.344319i	−0.513669	+	0.857988i	$0.671714\pi$
$684$		−	3.42687e9i		−	0.0156557i
$685$		0			0
$686$	1.14415e12			5.16640
$687$	−1.44440e10	+	1.44440e10i	−0.0648425	+	0.0648425i
$688$	−2.81466e10	−	2.81466e10i	−0.125624	−	0.125624i
$689$		−	4.42556e10i		−	0.196377i
$690$		0			0
$691$	−2.24658e11			−0.985394			−0.492697	−	0.870201i	$-0.663989\pi$
$691$	−2.24658e11			−0.985394			−0.492697	+	0.870201i	$0.663989\pi$
$692$	−3.47555e11	+	3.47555e11i	−1.51565	+	1.51565i
$693$	−1.27591e11	−	1.27591e11i	−0.553206	−	0.553206i
$694$		−	4.58677e11i		−	1.97728i
$695$		0			0
$696$	1.00845e11			0.429750
$697$	5.85484e10	−	5.85484e10i	0.248076	−	0.248076i
$698$	−6.26526e10	−	6.26526e10i	−0.263947	−	0.263947i
$699$			7.36551e10i			0.308528i
$700$		0			0
$701$	3.53033e11			1.46199			0.730993	−	0.682385i	$-0.239057\pi$
$701$	3.53033e11			1.46199			0.730993	+	0.682385i	$0.239057\pi$
$702$	−5.39784e10	+	5.39784e10i	−0.222265	+	0.222265i
$703$	9.53011e9	+	9.53011e9i	0.0390191	+	0.0390191i
$704$		−	4.82277e11i		−	1.96339i
$705$		0			0
$706$	−4.63979e10			−0.186758
$707$	1.09146e11	−	1.09146e11i	0.436848	−	0.436848i
$708$	−2.78337e10	−	2.78337e10i	−0.110774	−	0.110774i
$709$		−	2.18103e11i		−	0.863130i	−0.902082	−	0.431565i	$-0.857962\pi$
$709$		−	2.18103e11i		−	0.863130i	0.902082	−	0.431565i	$-0.142038\pi$
$710$		0			0
$711$	−3.51461e10			−0.137530
$712$	−2.21728e11	+	2.21728e11i	−0.862782	+	0.862782i
$713$	−2.17167e11	−	2.17167e11i	−0.840304	−	0.840304i
$714$			8.51935e10i			0.327804i
$715$		0			0
$716$	−2.98854e11			−1.13712
$717$	−1.05464e11	+	1.05464e11i	−0.399052	+	0.399052i
$718$	2.63358e11	+	2.63358e11i	0.990944	+	0.990944i
$719$			2.08604e11i			0.780562i	0.920696	+	0.390281i	$0.127622\pi$
$719$			2.08604e11i			0.780562i	−0.920696	+	0.390281i	$0.872378\pi$
$720$		0			0
$721$	−2.16006e11			−0.799328
$722$	3.01088e11	−	3.01088e11i	1.10801	−	1.10801i
$723$	4.77948e10	+	4.77948e10i	0.174915	+	0.174915i
$724$		−	3.99498e11i		−	1.45399i
$725$		0			0
$726$	1.21976e11			0.439064
$727$	3.27126e11	−	3.27126e11i	1.17105	−	1.17105i	0.189096	−	0.981959i	$-0.439444\pi$
$727$	3.27126e11	−	3.27126e11i	1.17105	−	1.17105i	0.981959	−	0.189096i	$-0.0605558\pi$
$728$	2.87717e11	+	2.87717e11i	1.02433	+	1.02433i
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−2.91088e10			−0.101942
$732$	−2.03711e11	+	2.03711e11i	−0.709529	+	0.709529i
$733$	−2.25912e11	−	2.25912e11i	−0.782571	−	0.782571i	0.197693	−	0.980264i	$-0.436655\pi$
$733$	−2.25912e11	−	2.25912e11i	−0.782571	−	0.782571i	−0.980264	+	0.197693i	$0.936655\pi$
$734$			3.91274e11i			1.34802i
$735$		0			0
$736$	3.55637e11			1.21198
$737$	3.14729e11	−	3.14729e11i	1.06676	−	1.06676i
$738$	2.04747e11	+	2.04747e11i	0.690228	+	0.690228i
$739$		−	1.16727e11i		−	0.391374i	−0.980666	−	0.195687i	$-0.937306\pi$
$739$		−	1.16727e11i		−	0.391374i	0.980666	−	0.195687i	$-0.0626936\pi$
$740$		0			0
$741$	5.82873e9			0.0193331
$742$	1.22132e11	−	1.22132e11i	0.402914	−	0.402914i
$743$	1.19853e11	+	1.19853e11i	0.393271	+	0.393271i	0.875852	−	0.482580i	$-0.160300\pi$
$743$	1.19853e11	+	1.19853e11i	0.393271	+	0.393271i	−0.482580	+	0.875852i	$0.660300\pi$
$744$			1.54851e11i			0.505385i
$745$		0			0
$746$	−7.48016e11			−2.41521
$747$	−1.42405e11	+	1.42405e11i	−0.457343	+	0.457343i
$748$	−7.40286e10	−	7.40286e10i	−0.236479	−	0.236479i
$749$		−	6.06387e10i		−	0.192674i
$750$		0			0
$751$	6.28712e11			1.97648			0.988238	−	0.152922i	$-0.0488683\pi$
$751$	6.28712e11			1.97648			0.988238	+	0.152922i	$0.0488683\pi$
$752$	−1.06596e10	+	1.06596e10i	−0.0333326	+	0.0333326i
$753$	−5.79650e10	−	5.79650e10i	−0.180296	−	0.180296i
$754$			5.44028e11i			1.68320i
$755$		0			0
$756$	−1.76841e11			−0.541373
$757$	2.17480e11	−	2.17480e11i	0.662272	−	0.662272i	−0.293643	−	0.955915i	$-0.594868\pi$
$757$	2.17480e11	−	2.17480e11i	0.662272	−	0.662272i	0.955915	+	0.293643i	$0.0948676\pi$
$758$	9.08281e10	+	9.08281e10i	0.275134	+	0.275134i
$759$			2.28940e11i			0.689849i
$760$		0			0
$761$	−4.15938e11			−1.24019			−0.620097	−	0.784525i	$-0.712907\pi$
$761$	−4.15938e11			−1.24019			−0.620097	+	0.784525i	$0.712907\pi$
$762$	−6.60350e10	+	6.60350e10i	−0.195864	+	0.195864i
$763$	2.72692e11	+	2.72692e11i	0.804589	+	0.804589i
$764$		−	1.48028e11i		−	0.434481i
$765$		0			0
$766$	−7.71421e11			−2.24066
$767$	4.73421e10	−	4.73421e10i	0.136794	−	0.136794i
$768$	−5.88614e10	−	5.88614e10i	−0.169194	−	0.169194i
$769$			5.68263e11i			1.62497i	0.582985	+	0.812483i	$0.301885\pi$
$769$			5.68263e11i			1.62497i	−0.582985	+	0.812483i	$0.698115\pi$
$770$		0			0
$771$	1.99424e11			0.564365
$772$	4.85422e11	−	4.85422e11i	1.36663	−	1.36663i
$773$	1.86021e11	+	1.86021e11i	0.521008	+	0.521008i	0.917876	−	0.396867i	$-0.129903\pi$
$773$	1.86021e11	+	1.86021e11i	0.521008	+	0.521008i	−0.396867	+	0.917876i	$0.629903\pi$
$774$		−	1.01795e11i		−	0.283637i
$775$		0			0
$776$	1.02080e11			0.281510
$777$	4.91795e11	−	4.91795e11i	1.34927	−	1.34927i
$778$	−1.71616e11	−	1.71616e11i	−0.468424	−	0.468424i
$779$		−	2.21091e10i		−	0.0600374i
$780$		0			0
$781$	−1.30683e11			−0.351249
$782$	7.64325e10	−	7.64325e10i	0.204386	−	0.204386i
$783$	−5.27130e10	−	5.27130e10i	−0.140240	−	0.140240i
$784$		−	3.35307e11i		−	0.887521i
$785$		0			0
$786$	−1.12129e11			−0.293784
$787$	−3.34091e11	+	3.34091e11i	−0.870894	+	0.870894i	−0.992570	−	0.121676i	$-0.961173\pi$
$787$	−3.34091e11	+	3.34091e11i	−0.870894	+	0.870894i	0.121676	+	0.992570i	$0.461173\pi$
$788$	−5.25925e11	−	5.25925e11i	−1.36401	−	1.36401i
$789$			4.27973e11i			1.10436i
$790$		0			0
$791$	8.67295e11			2.21544
$792$	8.16225e10	−	8.16225e10i	0.207448	−	0.207448i
$793$	−3.46490e11	−	3.46490e11i	−0.876190	−	0.876190i
$794$			1.87033e11i			0.470584i
$795$		0			0
$796$	−9.22479e11			−2.29776
$797$	−2.57385e11	+	2.57385e11i	−0.637895	+	0.637895i	−0.950036	−	0.312140i	$-0.898954\pi$
$797$	−2.57385e11	+	2.57385e11i	−0.637895	+	0.637895i	0.312140	+	0.950036i	$0.398954\pi$
$798$	1.60854e10	+	1.60854e10i	0.0396663	+	0.0396663i
$799$			1.10240e10i			0.0270491i
$800$		0			0
$801$	2.31801e11			0.563101
$802$	−4.04537e11	+	4.04537e11i	−0.977825	+	0.977825i
$803$	2.87494e11	+	2.87494e11i	0.691460	+	0.691460i
$804$		−	4.36216e11i		−	1.04394i
$805$		0			0
$806$	−8.35377e11			−1.97944
$807$	2.13357e11	−	2.13357e11i	0.503051	−	0.503051i
$808$	6.98230e10	+	6.98230e10i	0.163815	+	0.163815i
$809$			8.05063e11i			1.87947i	0.341900	+	0.939736i	$0.388930\pi$
$809$			8.05063e11i			1.87947i	−0.341900	+	0.939736i	$0.611070\pi$
$810$		0			0
$811$	6.53535e11			1.51072			0.755362	−	0.655307i	$-0.227461\pi$
$811$	6.53535e11			1.51072			0.755362	+	0.655307i	$0.227461\pi$
$812$	−8.91158e11	+	8.91158e11i	−2.04989	+	2.04989i
$813$	−5.02215e10	−	5.02215e10i	−0.114955	−	0.114955i
$814$			1.43990e12i			3.27971i
$815$		0			0
$816$	1.57540e10			0.0355329
$817$	−5.49605e9	+	5.49605e9i	−0.0123357	+	0.0123357i
$818$	−4.52395e11	−	4.52395e11i	−1.01043	−	1.01043i
$819$		−	3.00788e11i		−	0.668535i
$820$		0			0
$821$	1.37239e11			0.302068			0.151034	−	0.988529i	$-0.451740\pi$
$821$	1.37239e11			0.302068			0.151034	+	0.988529i	$0.451740\pi$
$822$	3.49182e11	−	3.49182e11i	0.764830	−	0.764830i
$823$	−8.37135e10	−	8.37135e10i	−0.182472	−	0.182472i	0.609960	−	0.792432i	$-0.291185\pi$
$823$	−8.37135e10	−	8.37135e10i	−0.182472	−	0.182472i	−0.792432	+	0.609960i	$0.791185\pi$
$824$		−	1.38184e11i		−	0.299742i
$825$		0			0
$826$	2.61299e11			0.561328
$827$	−1.81569e11	+	1.81569e11i	−0.388167	+	0.388167i	−0.874033	−	0.485866i	$-0.838504\pi$
$827$	−1.81569e11	+	1.81569e11i	−0.388167	+	0.388167i	0.485866	+	0.874033i	$0.338504\pi$
$828$	1.58655e11	+	1.58655e11i	0.337547	+	0.337547i
$829$			7.14030e11i			1.51181i	0.654679	+	0.755907i	$0.272804\pi$
$829$			7.14030e11i			1.51181i	−0.654679	+	0.755907i	$0.727196\pi$
$830$		0			0
$831$	−2.53437e11			−0.531454
$832$	5.68469e11	−	5.68469e11i	1.18635	−	1.18635i
$833$	−1.73385e11	−	1.73385e11i	−0.360107	−	0.360107i
$834$		−	1.10464e11i		−	0.228326i
$835$		0			0
$836$	−2.79548e10			−0.0572310
$837$	8.09429e10	−	8.09429e10i	0.164921	−	0.164921i
$838$	9.11119e11	+	9.11119e11i	1.84756	+	1.84756i
$839$		−	7.82380e11i		−	1.57896i	−0.613779	−	0.789478i	$-0.710352\pi$
$839$		−	7.82380e11i		−	1.57896i	0.613779	−	0.789478i	$-0.289648\pi$
$840$		0			0
$841$	−3.10278e10			−0.0620250
$842$	5.34997e11	−	5.34997e11i	1.06440	−	1.06440i
$843$	−2.14418e11	−	2.14418e11i	−0.424572	−	0.424572i
$844$		−	2.81216e11i		−	0.554204i
$845$		0			0
$846$	−3.85516e10			−0.0752594
$847$	−3.39848e11	+	3.39848e11i	−0.660314	+	0.660314i
$848$	−2.25846e10	−	2.25846e10i	−0.0436746	−	0.0436746i
$849$			1.62671e11i			0.313098i
$850$		0			0
$851$	−8.82441e11			−1.68255
$852$	−9.05636e10	+	9.05636e10i	−0.171868	+	0.171868i
$853$	−5.41750e11	−	5.41750e11i	−1.02330	−	1.02330i	−0.999722	−	0.0235778i	$-0.992494\pi$
$853$	−5.41750e11	−	5.41750e11i	−1.02330	−	1.02330i	−0.0235778	−	0.999722i	$-0.507506\pi$
$854$		−	1.91241e12i		−	3.59541i
$855$		0			0
$856$	3.87919e10			0.0722513
$857$	−2.04162e11	+	2.04162e11i	−0.378487	+	0.378487i	−0.870556	−	0.492069i	$-0.836241\pi$
$857$	−2.04162e11	+	2.04162e11i	−0.378487	+	0.378487i	0.492069	+	0.870556i	$0.336241\pi$
$858$	4.40330e11	+	4.40330e11i	0.812511	+	0.812511i
$859$		−	6.27859e11i		−	1.15316i	−0.817041	−	0.576580i	$-0.804387\pi$
$859$		−	6.27859e11i		−	1.15316i	0.817041	−	0.576580i	$-0.195613\pi$
$860$		0			0
$861$	−1.14093e12			−2.07609
$862$	−3.62363e11	+	3.62363e11i	−0.656319	+	0.656319i
$863$	−3.36990e11	−	3.36990e11i	−0.607538	−	0.607538i	0.334764	−	0.942302i	$-0.391343\pi$
$863$	−3.36990e11	−	3.36990e11i	−0.607538	−	0.607538i	−0.942302	+	0.334764i	$0.891343\pi$
$864$			1.32553e11i			0.237868i
$865$		0			0
$866$	−4.59034e11			−0.816157
$867$	−2.22529e11	+	2.22529e11i	−0.393831	+	0.393831i
$868$	−1.36841e12	−	1.36841e12i	−2.41067	−	2.41067i
$869$			2.86706e11i			0.502756i
$870$		0			0
$871$	7.41955e11			1.28916
$872$	−1.74447e11	+	1.74447e11i	−0.301715	+	0.301715i
$873$	−5.33588e10	−	5.33588e10i	−0.0918648	−	0.0918648i
$874$		−	2.88625e10i		−	0.0494639i
$875$		0			0
$876$	3.98468e11			0.676670
$877$	−2.22371e10	+	2.22371e10i	−0.0375906	+	0.0375906i	−0.725652	−	0.688062i	$-0.758462\pi$
$877$	−2.22371e10	+	2.22371e10i	−0.0375906	+	0.0375906i	0.688062	+	0.725652i	$0.258462\pi$
$878$	−7.66613e11	−	7.66613e11i	−1.29002	−	1.29002i
$879$		−	1.10586e11i		−	0.185244i
$880$		0			0
$881$	−3.70200e11			−0.614515			−0.307257	−	0.951626i	$-0.599411\pi$
$881$	−3.70200e11			−0.614515			−0.307257	+	0.951626i	$0.599411\pi$
$882$	6.06337e11	−	6.06337e11i	1.00194	−	1.00194i
$883$	4.44102e11	+	4.44102e11i	0.730533	+	0.730533i	0.970725	−	0.240192i	$-0.0772105\pi$
$883$	4.44102e11	+	4.44102e11i	0.730533	+	0.730533i	−0.240192	+	0.970725i	$0.577210\pi$
$884$		−	1.74518e11i		−	0.285779i
$885$		0			0
$886$	5.02340e11			0.815197
$887$	−4.96877e11	+	4.96877e11i	−0.802702	+	0.802702i	−0.983517	−	0.180815i	$-0.942126\pi$
$887$	−4.96877e11	+	4.96877e11i	−0.802702	+	0.802702i	0.180815	+	0.983517i	$0.442126\pi$
$888$	3.14612e11	+	3.14612e11i	0.505968	+	0.505968i
$889$		−	3.67971e11i		−	0.589125i
$890$		0			0
$891$	−8.53306e10			−0.135392
$892$	−7.96477e11	+	7.96477e11i	−1.25810	+	1.25810i
$893$	2.08145e9	+	2.08145e9i	0.00327311	+	0.00327311i
$894$		−	3.95889e11i		−	0.619760i
$895$		0			0
$896$	1.60320e12			2.48745
$897$	−2.69855e11	+	2.69855e11i	−0.416832	+	0.416832i
$898$	9.44133e10	+	9.44133e10i	0.145187	+	0.145187i
$899$		−	8.15793e11i		−	1.24894i
$900$		0			0
$901$	−2.33566e10			−0.0354414
$902$	1.67023e12	−	1.67023e12i	2.52319	−	2.52319i
$903$	2.83620e11	+	2.83620e11i	0.426566	+	0.426566i
$904$			5.54827e11i			0.830775i
$905$		0			0
$906$	2.80492e11			0.416301
$907$	−6.49222e11	+	6.49222e11i	−0.959322	+	0.959322i	−0.999204	−	0.0398827i	$-0.987302\pi$
$907$	−6.49222e11	+	6.49222e11i	−0.959322	+	0.959322i	0.0398827	+	0.999204i	$0.487302\pi$
$908$	−3.15889e11	−	3.15889e11i	−0.464719	−	0.464719i
$909$		−	7.29951e10i		−	0.106915i
$910$		0			0
$911$	8.02188e11			1.16467			0.582335	−	0.812949i	$-0.302139\pi$
$911$	8.02188e11			1.16467			0.582335	+	0.812949i	$0.302139\pi$
$912$	2.97452e9	−	2.97452e9i	0.00429970	−	0.00429970i
$913$	1.16167e12	+	1.16167e12i	1.67186	+	1.67186i
$914$		−	1.55864e12i		−	2.23337i
$915$		0			0
$916$	1.63309e11			0.231968
$917$	3.12412e11	−	3.12412e11i	0.441825	−	0.441825i
$918$	2.84880e10	+	2.84880e10i	0.0401136	+	0.0401136i
$919$			1.01545e12i			1.42363i	0.702369	+	0.711813i	$0.252126\pi$
$919$			1.01545e12i			1.42363i	−0.702369	+	0.711813i	$0.747874\pi$
$920$		0			0
$921$	−1.08273e10			−0.0150482
$922$	8.51403e11	−	8.51403e11i	1.17818	−	1.17818i
$923$	−1.54039e11	−	1.54039e11i	−0.212238	−	0.212238i
$924$			1.44259e12i			1.97904i
$925$		0			0
$926$	8.92861e11			1.21434
$927$	−7.22307e10	+	7.22307e10i	−0.0978144	+	0.0978144i
$928$	6.67978e11	+	6.67978e11i	0.900679	+	0.900679i
$929$			2.60786e11i			0.350124i	0.984557	+	0.175062i	$0.0560125\pi$
$929$			2.60786e11i			0.350124i	−0.984557	+	0.175062i	$0.943987\pi$
$930$		0			0
$931$	−6.54739e10			−0.0871504
$932$	4.16386e11	−	4.16386e11i	0.551864	−	0.551864i
$933$	−1.09549e11	−	1.09549e11i	−0.144571	−	0.144571i
$934$			1.08617e12i			1.42729i
$935$		0			0
$936$	1.92420e11			0.250696
$937$	−7.07133e11	+	7.07133e11i	−0.917367	+	0.917367i	−0.996837	−	0.0794706i	$-0.974677\pi$
$937$	−7.07133e11	+	7.07133e11i	−0.917367	+	0.917367i	0.0794706	+	0.996837i	$0.474677\pi$
$938$	2.04756e12	+	2.04756e12i	2.64500	+	2.64500i
$939$		−	5.57801e10i		−	0.0717492i
$940$		0			0
$941$	2.53626e11			0.323471			0.161736	−	0.986834i	$-0.448291\pi$
$941$	2.53626e11			0.323471			0.161736	+	0.986834i	$0.448291\pi$
$942$	1.20399e11	−	1.20399e11i	0.152904	−	0.152904i
$943$	1.02360e12	+	1.02360e12i	1.29444	+	1.29444i
$944$		−	4.83194e10i		−	0.0608462i
$945$		0			0
$946$	−8.30397e11			−1.03686
$947$	−4.52515e11	+	4.52515e11i	−0.562643	+	0.562643i	−0.930057	−	0.367414i	$-0.880243\pi$
$947$	−4.52515e11	+	4.52515e11i	−0.562643	+	0.562643i	0.367414	+	0.930057i	$0.380243\pi$
$948$	1.98687e11	+	1.98687e11i	0.246001	+	0.246001i
$949$			6.77750e11i			0.835612i
$950$		0			0
$951$	5.18975e11			0.634490
$952$	1.51847e11	−	1.51847e11i	0.184867	−	0.184867i
$953$	−8.87265e11	−	8.87265e11i	−1.07568	−	1.07568i	−0.996892	−	0.0787851i	$-0.974896\pi$
$953$	−8.87265e11	−	8.87265e11i	−1.07568	−	1.07568i	−0.0787851	−	0.996892i	$-0.525104\pi$
$954$		−	8.16795e10i		−	0.0986097i
$955$		0			0
$956$	1.19242e12			1.42757
$957$	−4.30008e11	+	4.30008e11i	−0.512659	+	0.512659i
$958$	−6.76145e11	−	6.76145e11i	−0.802746	−	0.802746i
$959$			1.94577e12i			2.30048i
$960$		0			0
$961$	3.99793e11			0.468750
$962$	−1.69724e12	+	1.69724e12i	−1.98172	+	1.98172i
$963$	−2.02771e10	−	2.02771e10i	−0.0235776	−	0.0235776i
$964$		−	5.40385e11i		−	0.625742i
$965$		0			0
$966$	−1.48943e12			−1.71046
$967$	5.33086e11	−	5.33086e11i	0.609666	−	0.609666i	−0.333193	−	0.942859i	$-0.608126\pi$
$967$	5.33086e11	−	5.33086e11i	0.609666	−	0.609666i	0.942859	+	0.333193i	$0.108126\pi$
$968$	−2.17408e11	−	2.17408e11i	−0.247613	−	0.247613i
$969$		−	3.07621e9i		−	0.00348916i
$970$		0			0
$971$	−8.16337e11			−0.918317			−0.459158	−	0.888354i	$-0.651849\pi$
$971$	−8.16337e11			−0.918317			−0.459158	+	0.888354i	$0.651849\pi$
$972$	−5.91343e10	+	5.91343e10i	−0.0662482	+	0.0662482i
$973$	3.07773e11	+	3.07773e11i	0.343383	+	0.343383i
$974$			5.74998e11i			0.638897i
$975$		0			0
$976$	−3.53643e11			−0.389731
$977$	9.39049e11	−	9.39049e11i	1.03065	−	1.03065i	0.0311316	−	0.999515i	$-0.490089\pi$
$977$	9.39049e11	−	9.39049e11i	1.03065	−	1.03065i	0.999515	−	0.0311316i	$-0.00991110\pi$
$978$	5.68979e11	+	5.68979e11i	0.621929	+	0.621929i
$979$		−	1.89093e12i		−	2.05847i
$980$		0			0
$981$	1.82372e11			0.196916
$982$	2.00500e12	−	2.00500e12i	2.15610	−	2.15610i
$983$	−4.56361e11	−	4.56361e11i	−0.488759	−	0.488759i	0.419155	−	0.907914i	$-0.362326\pi$
$983$	−4.56361e11	−	4.56361e11i	−0.488759	−	0.488759i	−0.907914	+	0.419155i	$0.862326\pi$
$984$		−	7.29875e11i		−	0.778517i
$985$		0			0
$986$	2.87120e11			0.303777
$987$	1.07412e11	−	1.07412e11i	0.113184	−	0.113184i
$988$	−3.29508e10	−	3.29508e10i	−0.0345811	−	0.0345811i
$989$		−	5.08907e11i		−	0.531928i
$990$		0			0
$991$	−7.18030e11			−0.744471			−0.372236	−	0.928138i	$-0.621409\pi$
$991$	−7.18030e11			−0.744471			−0.372236	+	0.928138i	$0.621409\pi$
$992$	−1.02571e12	+	1.02571e12i	−1.05920	+	1.05920i
$993$	3.10967e11	+	3.10967e11i	0.319829	+	0.319829i
$994$		−	8.50197e11i		−	0.870911i
$995$		0			0
$996$	1.61008e12			1.63610
$997$	1.49528e11	−	1.49528e11i	0.151335	−	0.151335i	−0.627379	−	0.778714i	$-0.715872\pi$
$997$	1.49528e11	−	1.49528e11i	0.151335	−	0.151335i	0.778714	+	0.627379i	$0.215872\pi$
$998$	1.20937e12	+	1.20937e12i	1.21909	+	1.21909i
$999$		−	3.28905e11i		−	0.330223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.c.43.4	yes	8
5.2	odd	4	inner	75.9.f.c.7.4	yes	8
5.3	odd	4	inner	75.9.f.c.7.1	✓	8
5.4	even	2	inner	75.9.f.c.43.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.c.7.1	✓	8	5.3	odd	4	inner
75.9.f.c.7.4	yes	8	5.2	odd	4	inner
75.9.f.c.43.1	yes	8	5.4	even	2	inner
75.9.f.c.43.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.7465 - 17.7465i) q^{2} +(33.0681 + 33.0681i) q^{3} -373.880i q^{4} +1173.69 q^{6} +(-3270.12 + 3270.12i) q^{7} +(-2091.96 - 2091.96i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(17.7465 - 17.7465i) q^{2} +(33.0681 + 33.0681i) q^{3} -373.880i q^{4} +1173.69 q^{6} +(-3270.12 + 3270.12i) q^{7} +(-2091.96 - 2091.96i) q^{8} +2187.00i q^{9} +17840.5 q^{11} +(12363.5 - 12363.5i) q^{12} +(21029.0 + 21029.0i) q^{13} +116067. i q^{14} +21463.0 q^{16} +(11098.4 - 11098.4i) q^{17} +(38811.7 + 38811.7i) q^{18} -4190.99i q^{19} -216273. q^{21} +(316608. - 316608. i) q^{22} +(194032. + 194032. i) q^{23} -138354. i q^{24} +746383. q^{26} +(-72320.0 + 72320.0i) q^{27} +(1.22263e6 + 1.22263e6i) q^{28} +728886. i q^{29} -1.11923e6 q^{31} +(916437. - 916437. i) q^{32} +(589952. + 589952. i) q^{33} -393916. i q^{34} +817675. q^{36} +(-2.27395e6 + 2.27395e6i) q^{37} +(-74375.6 - 74375.6i) q^{38} +1.39078e6i q^{39} +5.27540e6 q^{41} +(-3.83810e6 + 3.83810e6i) q^{42} +(-1.31140e6 - 1.31140e6i) q^{43} -6.67021e6i q^{44} +6.88681e6 q^{46} +(-496649. + 496649. i) q^{47} +(709743. + 709743. i) q^{48} -1.56225e7i q^{49} +734006. q^{51} +(7.86231e6 - 7.86231e6i) q^{52} +(-1.05225e6 - 1.05225e6i) q^{53} +2.56686e6i q^{54} +1.36819e7 q^{56} +(138588. - 138588. i) q^{57} +(1.29352e7 + 1.29352e7i) q^{58} -2.25128e6i q^{59} -1.64768e7 q^{61} +(-1.98625e7 + 1.98625e7i) q^{62} +(-7.15175e6 - 7.15175e6i) q^{63} -2.70327e7i q^{64} +2.09392e7 q^{66} +(1.76413e7 - 1.76413e7i) q^{67} +(-4.14947e6 - 4.14947e6i) q^{68} +1.28326e7i q^{69} -7.32508e6 q^{71} +(4.57512e6 - 4.57512e6i) q^{72} +(1.61147e7 + 1.61147e7i) q^{73} +8.07097e7i q^{74} -1.56693e6 q^{76} +(-5.83406e7 + 5.83406e7i) q^{77} +(2.46815e7 + 2.46815e7i) q^{78} +1.60705e7i q^{79} -4.78297e6 q^{81} +(9.36201e7 - 9.36201e7i) q^{82} +(6.51143e7 + 6.51143e7i) q^{83} +8.08602e7i q^{84} -4.65455e7 q^{86} +(-2.41029e7 + 2.41029e7i) q^{87} +(-3.73217e7 - 3.73217e7i) q^{88} -1.05991e8i q^{89} -1.37534e8 q^{91} +(7.25448e7 - 7.25448e7i) q^{92} +(-3.70109e7 - 3.70109e7i) q^{93} +1.76276e7i q^{94} +6.06097e7 q^{96} +(-2.43982e7 + 2.43982e7i) q^{97} +(-2.77246e8 - 2.77246e8i) q^{98} +3.90172e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 1296 q^{6}+O(q^{10}) \) 8 * q + 1296 * q^6	\( 8 q + 1296 q^{6} + 107952 q^{11} + 401920 q^{16} - 953208 q^{21} + 4257936 q^{26} - 2908312 q^{31} + 3919104 q^{36} + 33914208 q^{41} + 50759328 q^{46} + 854064 q^{51} + 60954240 q^{56} + 29647000 q^{61} + 52666848 q^{66} - 28246944 q^{71} - 59323136 q^{76} - 38263752 q^{81} - 432922128 q^{86} - 517149432 q^{91} + 132129792 q^{96}+O(q^{100}) \) 8 * q + 1296 * q^6 + 107952 * q^11 + 401920 * q^16 - 953208 * q^21 + 4257936 * q^26 - 2908312 * q^31 + 3919104 * q^36 + 33914208 * q^41 + 50759328 * q^46 + 854064 * q^51 + 60954240 * q^56 + 29647000 * q^61 + 52666848 * q^66 - 28246944 * q^71 - 59323136 * q^76 - 38263752 * q^81 - 432922128 * q^86 - 517149432 * q^91 + 132129792 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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