LMFDB - Embedded newform 324.9.g.h.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,9,Mod(53,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("324.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$N$	$=$	$324 = 2^{2} \cdot 3^{4}$
Weight:	$k$	$=$	$9$
Character orbit:	$[\chi]$	$=$	324.g (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$131.990669660$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Character	$\chi$	$=$	324.269
Dual form			324.9.g.h.53.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-526.228 + 303.818i) q^{5} +(1374.73 - 2381.10i) q^{7} +(-706.002 - 407.611i) q^{11} +(10037.6 + 17385.6i) q^{13} -9333.81i q^{17} -140284. q^{19} +(344013. - 198616. i) q^{23} +(-10701.8 + 18536.1i) q^{25} +(576713. + 332966. i) q^{29} +(202106. + 350058. i) q^{31} +1.67067e6i q^{35} -2.94560e6 q^{37} +(2.72780e6 - 1.57489e6i) q^{41} +(-1.61650e6 + 2.79986e6i) q^{43} +(-4.13711e6 - 2.38856e6i) q^{47} +(-897368. - 1.55429e6i) q^{49} -3.24093e6i q^{53} +495358. q^{55} +(-8.50578e6 + 4.91081e6i) q^{59} +(-3.73253e6 + 6.46493e6i) q^{61} +(-1.05641e7 - 6.09918e6i) q^{65} +(-4.45359e6 - 7.71384e6i) q^{67} +7.42665e6i q^{71} +2.46273e7 q^{73} +(-1.94113e6 + 1.12071e6i) q^{77} +(9.31613e6 - 1.61360e7i) q^{79} +(5.63748e7 + 3.25480e7i) q^{83} +(2.83578e6 + 4.91171e6i) q^{85} -1.00580e8i q^{89} +5.51958e7 q^{91} +(7.38214e7 - 4.26208e7i) q^{95} +(4.88788e7 - 8.46606e7i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q - 3692 q^{7} + 50380 q^{13} + 370216 q^{19} + 1958288 q^{25} + 285568 q^{31} - 5820104 q^{37} + 8122852 q^{43} - 14602560 q^{49} + 76640328 q^{55} + 5700244 q^{61} + 6328540 q^{67} - 103457408 q^{73}+ \cdots + 181751968 q^{97}+O(q^{100})$ 32 * q - 3692 * q^7 + 50380 * q^13 + 370216 * q^19 + 1958288 * q^25 + 285568 * q^31 - 5820104 * q^37 + 8122852 * q^43 - 14602560 * q^49 + 76640328 * q^55 + 5700244 * q^61 + 6328540 * q^67 - 103457408 * q^73 - 168603092 * q^79 + 96322644 * q^85 - 399487432 * q^91 + 181751968 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$ .

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−526.228	+	303.818i	−0.841965	+	0.486109i	−0.857932	−	0.513764i	$-0.828251\pi$
$5$	−526.228	+	303.818i	−0.841965	+	0.486109i	0.0159667	+	0.999873i	$0.494917\pi$
$6$		0			0
$7$	1374.73	−	2381.10i	0.572566	−	0.991713i	−0.423736	−	0.905786i	$-0.639281\pi$
$7$	1374.73	−	2381.10i	0.572566	−	0.991713i	0.996301	−	0.0859272i	$-0.0273853\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−706.002	−	407.611i	−0.0482209	−	0.0278404i	0.475696	−	0.879610i	$-0.342196\pi$
$11$	−706.002	−	407.611i	−0.0482209	−	0.0278404i	−0.523917	+	0.851770i	$0.675530\pi$
$12$		0			0
$13$	10037.6	+	17385.6i	0.351443	+	0.608717i	0.986503	−	0.163746i	$-0.0523578\pi$
$13$	10037.6	+	17385.6i	0.351443	+	0.608717i	−0.635060	+	0.772463i	$0.719024\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	9333.81i		−	0.111754i	−0.998438	−	0.0558770i	$-0.982205\pi$
$17$		−	9333.81i		−	0.111754i	0.998438	−	0.0558770i	$-0.0177955\pi$
$18$		0			0
$19$	−140284.			−1.07645			−0.538225	−	0.842801i	$-0.680905\pi$
$19$	−140284.			−1.07645			−0.538225	+	0.842801i	$0.680905\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	344013.	−	198616.i	1.22932	−	0.709746i	0.262429	−	0.964951i	$-0.415476\pi$
$23$	344013.	−	198616.i	1.22932	−	0.709746i	0.966887	+	0.255206i	$0.0821431\pi$
$24$		0			0
$25$	−10701.8	+	18536.1i	−0.0273967	+	0.0474525i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	576713.	+	332966.i	0.815395	+	0.470768i	0.848826	−	0.528673i	$-0.177310\pi$
$29$	576713.	+	332966.i	0.815395	+	0.470768i	−0.0334311	+	0.999441i	$0.510643\pi$
$30$		0			0
$31$	202106.	+	350058.i	0.218843	+	0.379047i	0.954455	−	0.298356i	$-0.0964384\pi$
$31$	202106.	+	350058.i	0.218843	+	0.379047i	−0.735612	+	0.677404i	$0.763105\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			1.67067e6i			1.11332i
$36$		0			0
$37$	−2.94560e6			−1.57169			−0.785844	−	0.618425i	$-0.787771\pi$
$37$	−2.94560e6			−1.57169			−0.785844	+	0.618425i	$0.787771\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.72780e6	−	1.57489e6i	0.965332	−	0.557335i	0.0675221	−	0.997718i	$-0.478491\pi$
$41$	2.72780e6	−	1.57489e6i	0.965332	−	0.557335i	0.897810	+	0.440383i	$0.145157\pi$
$42$		0			0
$43$	−1.61650e6	+	2.79986e6i	−0.472827	+	0.818961i	−0.999516	−	0.0310972i	$-0.990100\pi$
$43$	−1.61650e6	+	2.79986e6i	−0.472827	+	0.818961i	0.526689	+	0.850058i	$0.323433\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.13711e6	−	2.38856e6i	−0.847824	−	0.489491i	0.0120923	−	0.999927i	$-0.496151\pi$
$47$	−4.13711e6	−	2.38856e6i	−0.847824	−	0.489491i	−0.859916	+	0.510436i	$0.829484\pi$
$48$		0			0
$49$	−897368.	−	1.55429e6i	−0.155663	−	0.269617i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	3.24093e6i		−	0.410739i	−0.978685	−	0.205369i	$-0.934160\pi$
$53$		−	3.24093e6i		−	0.410739i	0.978685	−	0.205369i	$-0.0658396\pi$
$54$		0			0
$55$	495358.			0.0541337
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.50578e6	+	4.91081e6i	−0.701950	+	0.405271i	−0.808073	−	0.589082i	$-0.799489\pi$
$59$	−8.50578e6	+	4.91081e6i	−0.701950	+	0.405271i	0.106124	+	0.994353i	$0.466156\pi$
$60$		0			0
$61$	−3.73253e6	+	6.46493e6i	−0.269578	+	0.466922i	−0.968753	−	0.248028i	$-0.920217\pi$
$61$	−3.73253e6	+	6.46493e6i	−0.269578	+	0.466922i	0.699175	+	0.714950i	$0.253551\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.05641e7	−	6.09918e6i	−0.591805	−	0.341679i
$66$		0			0
$67$	−4.45359e6	−	7.71384e6i	−0.221010	−	0.382800i	0.734105	−	0.679036i	$-0.237602\pi$
$67$	−4.45359e6	−	7.71384e6i	−0.221010	−	0.382800i	−0.955115	+	0.296236i	$0.904269\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.42665e6i			0.292253i	0.989266	+	0.146127i	$0.0466807\pi$
$71$			7.42665e6i			0.292253i	−0.989266	+	0.146127i	$0.953319\pi$
$72$		0			0
$73$	2.46273e7			0.867211			0.433606	−	0.901103i	$-0.357241\pi$
$73$	2.46273e7			0.867211			0.433606	+	0.901103i	$0.357241\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.94113e6	+	1.12071e6i	−0.0552193	+	0.0318809i
$78$		0			0
$79$	9.31613e6	−	1.61360e7i	0.239181	−	0.414274i	−0.721298	−	0.692624i	$-0.756454\pi$
$79$	9.31613e6	−	1.61360e7i	0.239181	−	0.414274i	0.960480	+	0.278350i	$0.0897877\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.63748e7	+	3.25480e7i	1.18788	+	0.685823i	0.957824	−	0.287355i	$-0.0927759\pi$
$83$	5.63748e7	+	3.25480e7i	1.18788	+	0.685823i	0.230056	+	0.973177i	$0.426109\pi$
$84$		0			0
$85$	2.83578e6	+	4.91171e6i	0.0543246	+	0.0940930i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	1.00580e8i		−	1.60306i	−0.597955	−	0.801530i	$-0.704020\pi$
$89$		−	1.00580e8i		−	1.60306i	0.597955	−	0.801530i	$-0.295980\pi$
$90$		0			0
$91$	5.51958e7			0.804897
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.38214e7	−	4.26208e7i	0.906333	−	0.523272i
$96$		0			0
$97$	4.88788e7	−	8.46606e7i	0.552120	−	0.956301i	−0.446001	−	0.895032i	$-0.647152\pi$
$97$	4.88788e7	−	8.46606e7i	0.552120	−	0.956301i	0.998121	−	0.0612681i	$-0.0195145\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.29976e7	+	1.32777e7i	0.221003	+	0.127596i	0.606414	−	0.795149i	$-0.292607\pi$
$101$	2.29976e7	+	1.32777e7i	0.221003	+	0.127596i	−0.385412	+	0.922745i	$0.625941\pi$
$102$		0			0
$103$	2.08498e7	+	3.61129e7i	0.185248	+	0.320859i	0.943660	−	0.330917i	$-0.107358\pi$
$103$	2.08498e7	+	3.61129e7i	0.185248	+	0.320859i	−0.758412	+	0.651775i	$0.774025\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.22034e7i			0.398257i	0.979973	+	0.199129i	$0.0638112\pi$
$107$			5.22034e7i			0.398257i	−0.979973	+	0.199129i	$0.936189\pi$
$108$		0			0
$109$	−1.29431e8			−0.916923			−0.458461	−	0.888714i	$-0.651599\pi$
$109$	−1.29431e8			−0.916923			−0.458461	+	0.888714i	$0.651599\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.06299e7	−	3.50047e7i	0.371854	−	0.214690i	−0.302414	−	0.953177i	$-0.597792\pi$
$113$	6.06299e7	−	3.50047e7i	0.371854	−	0.214690i	0.674268	+	0.738486i	$0.264459\pi$
$114$		0			0
$115$	−1.20686e8	+	2.09035e8i	−0.690027	+	1.19516i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.22248e7	−	1.28315e7i	−0.110828	−	0.0639866i
$120$		0			0
$121$	−1.06847e8	−	1.85065e8i	−0.498450	−	0.863340i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	2.50363e8i		−	1.02549i
$126$		0			0
$127$	4.01056e8			1.54167			0.770833	−	0.637037i	$-0.219840\pi$
$127$	4.01056e8			1.54167			0.770833	+	0.637037i	$0.219840\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.57209e8	−	1.48500e8i	0.873374	−	0.504243i	0.00490632	−	0.999988i	$-0.498438\pi$
$131$	2.57209e8	−	1.48500e8i	0.873374	−	0.504243i	0.868468	+	0.495745i	$0.165105\pi$
$132$		0			0
$133$	−1.92853e8	+	3.34031e8i	−0.616338	+	1.06753i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.09109e8	−	1.78464e8i	−0.877465	−	0.506605i	−0.00764328	−	0.999971i	$-0.502433\pi$
$137$	−3.09109e8	−	1.78464e8i	−0.877465	−	0.506605i	−0.869822	+	0.493366i	$0.835766\pi$
$138$		0			0
$139$	−1.92690e8	−	3.33750e8i	−0.516180	−	0.894049i	−0.999824	−	0.0187846i	$-0.994020\pi$
$139$	−1.92690e8	−	3.33750e8i	−0.516180	−	0.894049i	0.483644	−	0.875265i	$-0.339313\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	1.63657e7i		−	0.0391372i
$144$		0			0
$145$	−4.04644e8			−0.915378
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.48905e8	−	1.43705e8i	0.504996	−	0.291559i	−0.225778	−	0.974179i	$-0.572493\pi$
$149$	2.48905e8	−	1.43705e8i	0.504996	−	0.291559i	0.730774	+	0.682619i	$0.239159\pi$
$150$		0			0
$151$	−2.98417e8	+	5.16874e8i	−0.574006	+	0.994207i	0.422143	+	0.906529i	$0.361278\pi$
$151$	−2.98417e8	+	5.16874e8i	−0.574006	+	0.994207i	−0.996149	+	0.0876777i	$0.972055\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.12708e8	−	1.22807e8i	−0.368516	−	0.212763i
$156$		0			0
$157$	−9.16720e7	−	1.58781e8i	−0.150882	−	0.261336i	0.780670	−	0.624944i	$-0.214878\pi$
$157$	−9.16720e7	−	1.58781e8i	−0.150882	−	0.261336i	−0.931552	+	0.363608i	$0.881545\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	1.09217e9i		−	1.62550i
$162$		0			0
$163$	7.33428e8			1.03898			0.519490	−	0.854476i	$-0.326122\pi$
$163$	7.33428e8			1.03898			0.519490	+	0.854476i	$0.326122\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.05069e9	−	6.06614e8i	1.35085	−	0.779914i	0.362482	−	0.931991i	$-0.381929\pi$
$167$	1.05069e9	−	6.06614e8i	1.35085	−	0.779914i	0.988369	+	0.152077i	$0.0485961\pi$
$168$		0			0
$169$	2.06360e8	−	3.57426e8i	0.252976	−	0.438167i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.14652e9	+	6.61946e8i	1.27997	+	0.738989i	0.976842	−	0.213962i	$-0.0686370\pi$
$173$	1.14652e9	+	6.61946e8i	1.27997	+	0.738989i	0.303124	+	0.952951i	$0.401970\pi$
$174$		0			0
$175$	2.94243e7	+	5.09644e7i	0.0313729	+	0.0543394i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	1.22618e9i		−	1.19438i	−0.802099	−	0.597191i	$-0.796283\pi$
$179$		−	1.22618e9i		−	1.19438i	0.802099	−	0.597191i	$-0.203717\pi$
$180$		0			0
$181$	1.37982e9			1.28561			0.642805	−	0.766030i	$-0.277771\pi$
$181$	1.37982e9			1.28561			0.642805	+	0.766030i	$0.277771\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.55006e9	−	8.94925e8i	1.32331	−	0.764011i
$186$		0			0
$187$	−3.80456e6	+	6.58969e6i	−0.00311127	+	0.00538888i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.15621e9	+	6.67539e8i	0.868768	+	0.501583i	0.866939	−	0.498415i	$-0.166084\pi$
$191$	1.15621e9	+	6.67539e8i	0.868768	+	0.501583i	0.00182941	+	0.999998i	$0.499418\pi$
$192$		0			0
$193$	−1.06394e9	−	1.84280e9i	−0.766810	−	1.32815i	−0.939285	−	0.343139i	$-0.888510\pi$
$193$	−1.06394e9	−	1.84280e9i	−0.766810	−	1.32815i	0.172475	−	0.985014i	$-0.444824\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.87294e9i		−	1.24354i	−0.783200	−	0.621770i	$-0.786414\pi$
$197$		−	1.87294e9i		−	1.24354i	0.783200	−	0.621770i	$-0.213586\pi$
$198$		0			0
$199$	1.35017e9			0.860944			0.430472	−	0.902604i	$-0.358347\pi$
$199$	1.35017e9			0.860944			0.430472	+	0.902604i	$0.358347\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.58565e9	−	9.15476e8i	0.933734	−	0.539092i
$204$		0			0
$205$	−9.56963e8	+	1.65751e9i	−0.541851	+	0.938513i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.90408e7	+	5.71813e7i	0.0519074	+	0.0299687i
$210$		0			0
$211$	5.50404e8	+	9.53328e8i	0.277685	+	0.480964i	0.970809	−	0.239854i	$-0.0770996\pi$
$211$	5.50404e8	+	9.53328e8i	0.277685	+	0.480964i	−0.693124	+	0.720818i	$0.743766\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	1.96449e9i		−	0.919382i
$216$		0			0
$217$	1.11137e9			0.501208
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.62274e8	−	9.36887e7i	0.0680266	−	0.0392752i
$222$		0			0
$223$	9.95275e7	−	1.72387e8i	0.0402461	−	0.0697083i	−0.845201	−	0.534449i	$-0.820519\pi$
$223$	9.95275e7	−	1.72387e8i	0.0402461	−	0.0697083i	0.885447	+	0.464741i	$0.153852\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.45727e9	−	1.99605e9i	−1.30206	−	0.751742i	−0.321299	−	0.946978i	$-0.604120\pi$
$227$	−3.45727e9	−	1.99605e9i	−1.30206	−	0.751742i	−0.980756	+	0.195235i	$0.937453\pi$
$228$		0			0
$229$	−2.42288e9	−	4.19656e9i	−0.881030	−	1.52599i	−0.850197	−	0.526465i	$-0.823517\pi$
$229$	−2.42288e9	−	4.19656e9i	−0.881030	−	1.52599i	−0.0308334	−	0.999525i	$-0.509816\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	3.48755e9i		−	1.18330i	−0.806193	−	0.591652i	$-0.798476\pi$
$233$		−	3.48755e9i		−	1.18330i	0.806193	−	0.591652i	$-0.201524\pi$
$234$		0			0
$235$	2.90275e9			0.951784
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.54856e9	−	2.04876e9i	1.08758	−	0.627914i	0.154648	−	0.987970i	$-0.450576\pi$
$239$	3.54856e9	−	2.04876e9i	1.08758	−	0.627914i	0.932931	+	0.360056i	$0.117242\pi$
$240$		0			0
$241$	−2.78446e9	+	4.82282e9i	−0.825415	+	1.42966i	0.0761871	+	0.997094i	$0.475725\pi$
$241$	−2.78446e9	+	4.82282e9i	−0.825415	+	1.42966i	−0.901602	+	0.432567i	$0.857608\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.44441e8	+	5.45273e8i	0.262126	+	0.151339i
$246$		0			0
$247$	−1.40811e9	−	2.43892e9i	−0.378311	−	0.655253i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	3.91007e9i		−	0.985122i	−0.870278	−	0.492561i	$-0.836061\pi$
$251$		−	3.91007e9i		−	0.985122i	0.870278	−	0.492561i	$-0.163939\pi$
$252$		0			0
$253$	−3.23832e8			−0.0790383
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.94160e9	−	3.43039e9i	1.36198	−	0.786340i	0.372094	−	0.928195i	$-0.378640\pi$
$257$	5.94160e9	−	3.43039e9i	1.36198	−	0.786340i	0.989887	+	0.141855i	$0.0453066\pi$
$258$		0			0
$259$	−4.04940e9	+	7.01377e9i	−0.899895	+	1.55866i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.80580e9	−	1.61993e9i	−0.586453	−	0.338589i	0.177241	−	0.984168i	$-0.443283\pi$
$263$	−2.80580e9	−	1.61993e9i	−0.586453	−	0.338589i	−0.763694	+	0.645579i	$0.776616\pi$
$264$		0			0
$265$	9.84652e8	+	1.70547e9i	0.199664	+	0.345828i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			7.38756e9i			1.41089i	0.708766	+	0.705443i	$0.249252\pi$
$269$			7.38756e9i			1.41089i	−0.708766	+	0.705443i	$0.750748\pi$
$270$		0			0
$271$	−5.67999e9			−1.05310			−0.526551	−	0.850144i	$-0.676515\pi$
$271$	−5.67999e9			−1.05310			−0.526551	+	0.850144i	$0.676515\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.51111e7	−	8.72437e6i	0.00264219	−	0.00152547i
$276$		0			0
$277$	2.31156e9	−	4.00373e9i	0.392632	−	0.680058i	−0.600164	−	0.799877i	$-0.704898\pi$
$277$	2.31156e9	−	4.00373e9i	0.392632	−	0.680058i	0.992796	+	0.119819i	$0.0382313\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.30888e9	+	3.64243e9i	1.01188	+	0.584206i	0.911740	−	0.410768i	$-0.134739\pi$
$281$	6.30888e9	+	3.64243e9i	1.01188	+	0.584206i	0.100135	+	0.994974i	$0.468073\pi$
$282$		0			0
$283$	−2.71039e9	−	4.69453e9i	−0.422557	−	0.731891i	0.573632	−	0.819113i	$-0.305534\pi$
$283$	−2.71039e9	−	4.69453e9i	−0.422557	−	0.731891i	−0.996189	+	0.0872227i	$0.972201\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	8.66022e9i		−	1.27644i
$288$		0			0
$289$	6.88864e9			0.987511
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.82731e9	−	3.36440e9i	0.790675	−	0.456496i	−0.0495251	−	0.998773i	$-0.515771\pi$
$293$	5.82731e9	−	3.36440e9i	0.790675	−	0.456496i	0.840200	+	0.542276i	$0.182437\pi$
$294$		0			0
$295$	2.98399e9	−	5.16841e9i	0.394011	−	0.682448i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.90610e9	+	3.98724e9i	0.864069	+	0.498870i
$300$		0			0
$301$	4.44451e9	+	7.69812e9i	0.541449	+	0.937818i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	4.53604e9i		−	0.524176i
$306$		0			0
$307$	2.97720e8			0.0335161			0.0167581	−	0.999860i	$-0.494665\pi$
$307$	2.97720e8			0.0335161			0.0167581	+	0.999860i	$0.494665\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.59723e9	−	1.49951e9i	0.277632	−	0.160291i	−0.354719	−	0.934973i	$-0.615423\pi$
$311$	2.59723e9	−	1.49951e9i	0.277632	−	0.160291i	0.632351	+	0.774682i	$0.282090\pi$
$312$		0			0
$313$	−8.82643e8	+	1.52878e9i	−0.0919619	+	0.159283i	−0.908337	−	0.418240i	$-0.862647\pi$
$313$	−8.82643e8	+	1.52878e9i	−0.0919619	+	0.159283i	0.816375	+	0.577523i	$0.195980\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.36397e9	−	5.40629e9i	−0.927306	−	0.535380i	−0.0413473	−	0.999145i	$-0.513165\pi$
$317$	−9.36397e9	−	5.40629e9i	−0.927306	−	0.535380i	−0.885958	+	0.463765i	$0.846498\pi$
$318$		0			0
$319$	−2.71441e8	−	4.70149e8i	−0.0262127	−	0.0454017i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.30938e9i			0.120298i
$324$		0			0
$325$	−4.29682e8			−0.0385136
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.13748e10	+	6.56726e9i	−0.970870	+	0.560532i
$330$		0			0
$331$	3.17028e9	−	5.49109e9i	0.264110	−	0.457453i	−0.703220	−	0.710973i	$-0.748255\pi$
$331$	3.17028e9	−	5.49109e9i	0.264110	−	0.457453i	0.967330	+	0.253520i	$0.0815883\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.68721e9	+	2.70616e9i	0.372165	+	0.214869i
$336$		0			0
$337$	−1.46721e9	−	2.54129e9i	−0.113756	−	0.197031i	0.803526	−	0.595270i	$-0.202955\pi$
$337$	−1.46721e9	−	2.54129e9i	−0.113756	−	0.197031i	−0.917282	+	0.398239i	$0.869621\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	3.29522e8i		−	0.0243707i
$342$		0			0
$343$	1.09155e10			0.788622
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.95917e10	+	1.13113e10i	−1.35131	+	0.780178i	−0.988433	−	0.151660i	$-0.951538\pi$
$347$	−1.95917e10	+	1.13113e10i	−1.35131	+	0.780178i	−0.362875	+	0.931838i	$0.618205\pi$
$348$		0			0
$349$	5.09278e9	−	8.82096e9i	0.343284	−	0.594585i	−0.641756	−	0.766908i	$-0.721794\pi$
$349$	5.09278e9	−	8.82096e9i	0.343284	−	0.594585i	0.985040	+	0.172323i	$0.0551273\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.83827e9	−	1.63868e9i	−0.182791	−	0.105534i	0.405812	−	0.913956i	$-0.366989\pi$
$353$	−2.83827e9	−	1.63868e9i	−0.182791	−	0.105534i	−0.588603	+	0.808422i	$0.700322\pi$
$354$		0			0
$355$	−2.25635e9	−	3.90811e9i	−0.142067	−	0.246067i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			2.28030e10i			1.37282i	0.727214	+	0.686410i	$0.240815\pi$
$359$			2.28030e10i			1.37282i	−0.727214	+	0.686410i	$0.759185\pi$
$360$		0			0
$361$	2.69605e9			0.158744
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.29596e10	+	7.48221e9i	−0.730161	+	0.421559i
$366$		0			0
$367$	−2.58936e9	+	4.48491e9i	−0.142734	+	0.247223i	−0.928525	−	0.371269i	$-0.878923\pi$
$367$	−2.58936e9	+	4.48491e9i	−0.142734	+	0.247223i	0.785791	+	0.618492i	$0.212256\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.71698e9	−	4.45540e9i	−0.407335	−	0.235175i
$372$		0			0
$373$	1.13600e10	+	1.96762e10i	0.586873	+	1.01649i	0.994639	+	0.103408i	$0.0329747\pi$
$373$	1.13600e10	+	1.96762e10i	0.586873	+	1.01649i	−0.407766	+	0.913087i	$0.633692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1.33686e10i			0.661793i
$378$		0			0
$379$	−1.92617e10			−0.933552			−0.466776	−	0.884376i	$-0.654585\pi$
$379$	−1.92617e10			−0.933552			−0.466776	+	0.884376i	$0.654585\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.38104e10	+	1.37470e10i	−1.10655	+	0.638869i	−0.937934	−	0.346813i	$-0.887264\pi$
$383$	−2.38104e10	+	1.37470e10i	−1.10655	+	0.638869i	−0.168619	+	0.985681i	$0.553931\pi$
$384$		0			0
$385$	6.80983e8	−	1.17950e9i	0.0309951	−	0.0536851i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.34689e9	−	5.39643e9i	−0.408196	−	0.235672i	0.281818	−	0.959468i	$-0.409062\pi$
$389$	−9.34689e9	−	5.39643e9i	−0.408196	−	0.235672i	−0.690014	+	0.723796i	$0.742396\pi$
$390$		0			0
$391$	−1.85384e9	−	3.21095e9i	−0.0793170	−	0.137381i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			1.13216e10i			0.465072i
$396$		0			0
$397$	−3.93849e10			−1.58551			−0.792753	−	0.609543i	$-0.791353\pi$
$397$	−3.93849e10			−1.58551			−0.792753	+	0.609543i	$0.791353\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.72425e10	−	2.15020e10i	1.44033	−	0.831574i	0.442458	−	0.896789i	$-0.354107\pi$
$401$	3.72425e10	−	2.15020e10i	1.44033	−	0.831574i	0.997871	+	0.0652150i	$0.0207733\pi$
$402$		0			0
$403$	−4.05731e9	+	7.02746e9i	−0.153822	+	0.266427i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.07960e9	+	1.20066e9i	0.0757882	+	0.0437564i
$408$		0			0
$409$	1.21803e10	+	2.10969e10i	0.435277	+	0.753921i	0.997318	−	0.0731876i	$-0.0233172\pi$
$409$	1.21803e10	+	2.10969e10i	0.435277	+	0.753921i	−0.562041	+	0.827109i	$0.689984\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			2.70042e10i			0.928177i
$414$		0			0
$415$	−3.95547e10			−1.33354
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.36765e10	+	1.36696e10i	−0.768178	+	0.443508i	−0.832224	−	0.554439i	$-0.812933\pi$
$419$	−2.36765e10	+	1.36696e10i	−0.768178	+	0.443508i	0.0640464	+	0.997947i	$0.479599\pi$
$420$		0			0
$421$	2.37070e10	−	4.10617e10i	0.754654	−	1.30710i	−0.190892	−	0.981611i	$-0.561138\pi$
$421$	2.37070e10	−	4.10617e10i	0.754654	−	1.30710i	0.945546	−	0.325488i	$-0.105529\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.73013e8	+	9.98890e7i	0.00530301	+	0.00306170i
$426$		0			0
$427$	1.02624e10	+	1.77751e10i	0.308702	+	0.534688i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			6.57626e10i			1.90577i	0.303334	+	0.952884i	$0.401900\pi$
$431$			6.57626e10i			1.90577i	−0.303334	+	0.952884i	$0.598100\pi$
$432$		0			0
$433$	−1.59683e10			−0.454264			−0.227132	−	0.973864i	$-0.572935\pi$
$433$	−1.59683e10			−0.454264			−0.227132	+	0.973864i	$0.572935\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.82595e10	+	2.78626e10i	−1.32330	+	0.764006i
$438$		0			0
$439$	1.03916e10	−	1.79987e10i	0.279784	−	0.484600i	−0.691547	−	0.722332i	$-0.743070\pi$
$439$	1.03916e10	−	1.79987e10i	0.279784	−	0.484600i	0.971331	+	0.237731i	$0.0764038\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.28206e10	+	7.40199e9i	0.332885	+	0.192191i	0.657121	−	0.753785i	$-0.271774\pi$
$443$	1.28206e10	+	7.40199e9i	0.332885	+	0.192191i	−0.324236	+	0.945976i	$0.605107\pi$
$444$		0			0
$445$	3.05579e10	+	5.29278e10i	0.779261	+	1.34972i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			5.49600e9i			0.135226i	0.997712	+	0.0676132i	$0.0215384\pi$
$449$			5.49600e9i			0.135226i	−0.997712	+	0.0676132i	$0.978462\pi$
$450$		0			0
$451$	−2.56778e9			−0.0620656
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.90456e10	+	1.67695e10i	−0.677695	+	0.391267i
$456$		0			0
$457$	3.67217e9	−	6.36039e9i	0.0841896	−	0.145821i	−0.820856	−	0.571135i	$-0.806503\pi$
$457$	3.67217e9	−	6.36039e9i	0.0841896	−	0.145821i	0.905046	+	0.425315i	$0.139837\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.16460e10	+	2.40443e10i	0.922082	+	0.532364i	0.884299	−	0.466922i	$-0.154637\pi$
$461$	4.16460e10	+	2.40443e10i	0.922082	+	0.532364i	0.0377832	+	0.999286i	$0.487970\pi$
$462$		0			0
$463$	−1.53055e10	−	2.65099e10i	−0.333060	−	0.576877i	0.650050	−	0.759891i	$-0.274748\pi$
$463$	−1.53055e10	−	2.65099e10i	−0.333060	−	0.576877i	−0.983110	+	0.183014i	$0.941415\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			8.47837e8i			0.0178256i	0.999960	+	0.00891282i	$0.00283708\pi$
$467$			8.47837e8i			0.0178256i	−0.999960	+	0.00891282i	$0.997163\pi$
$468$		0			0
$469$	−2.44899e10			−0.506170
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.28251e9	−	1.31781e9i	0.0456003	−	0.0263273i
$474$		0			0
$475$	1.50130e9	−	2.60032e9i	0.0294912	−	0.0510803i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.47487e10	−	4.89297e10i	−1.60987	−	0.929459i	−0.989398	−	0.145230i	$-0.953608\pi$
$479$	−8.47487e10	−	4.89297e10i	−1.60987	−	0.929459i	−0.620472	−	0.784229i	$-0.713059\pi$
$480$		0			0
$481$	−2.95666e10	−	5.12109e10i	−0.552359	−	0.956714i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			5.94010e10i			1.07356i
$486$		0			0
$487$	9.28211e10			1.65018			0.825089	−	0.565003i	$-0.191125\pi$
$487$	9.28211e10			1.65018			0.825089	+	0.565003i	$0.191125\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.81786e10	+	3.35894e10i	−1.00101	+	0.577932i	−0.908546	−	0.417784i	$-0.862807\pi$
$491$	−5.81786e10	+	3.35894e10i	−1.00101	+	0.577932i	−0.0924615	+	0.995716i	$0.529474\pi$
$492$		0			0
$493$	3.10784e9	−	5.38293e9i	0.0526103	−	0.0911237i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.76836e10	+	1.02096e10i	0.289832	+	0.167334i
$498$		0			0
$499$	4.99812e10	+	8.65701e10i	0.806130	+	1.39626i	0.915526	+	0.402259i	$0.131775\pi$
$499$	4.99812e10	+	8.65701e10i	0.806130	+	1.39626i	−0.109396	+	0.993998i	$0.534892\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	5.08201e10i		−	0.793895i	−0.917841	−	0.396948i	$-0.870069\pi$
$503$		−	5.08201e10i		−	0.793895i	0.917841	−	0.396948i	$-0.129931\pi$
$504$		0			0
$505$	−1.61360e10			−0.248102
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.10795e11	+	6.39676e10i	−1.65063	+	0.952992i	−0.673817	+	0.738898i	$0.735346\pi$
$509$	−1.10795e11	+	6.39676e10i	−1.65063	+	0.952992i	−0.976813	+	0.214094i	$0.931320\pi$
$510$		0			0
$511$	3.38559e10	−	5.86401e10i	0.496536	−	0.860025i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.19435e10	−	1.26691e10i	−0.311944	−	0.180101i
$516$		0			0
$517$	1.94721e9	+	3.37266e9i	0.0272552	+	0.0472074i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	4.07798e10i		−	0.553470i	−0.960946	−	0.276735i	$-0.910748\pi$
$521$		−	4.07798e10i		−	0.553470i	0.960946	−	0.276735i	$-0.0892524\pi$
$522$		0			0
$523$	4.12269e10			0.551028			0.275514	−	0.961297i	$-0.411152\pi$
$523$	4.12269e10			0.551028			0.275514	+	0.961297i	$0.411152\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.26738e9	−	1.88642e9i	0.0423601	−	0.0244566i
$528$		0			0
$529$	3.97411e10	−	6.88336e10i	0.507478	−	0.878978i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.47609e10	+	3.16162e10i	0.678518	+	0.391743i
$534$		0			0
$535$	−1.58603e10	−	2.74709e10i	−0.193596	−	0.335319i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			1.46311e9i			0.0173349i
$540$		0			0
$541$	−5.12506e10			−0.598288			−0.299144	−	0.954208i	$-0.596701\pi$
$541$	−5.12506e10			−0.598288			−0.299144	+	0.954208i	$0.596701\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.81103e10	−	3.93235e10i	0.772017	−	0.445724i
$546$		0			0
$547$	−6.79895e10	+	1.17761e11i	−0.759438	+	1.31539i	0.183699	+	0.982982i	$0.441193\pi$
$547$	−6.79895e10	+	1.17761e11i	−0.759438	+	1.31539i	−0.943138	+	0.332403i	$0.892141\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.09036e10	−	4.67097e10i	−0.877732	−	0.506759i
$552$		0			0
$553$	−2.56143e10	−	4.43653e10i	−0.273894	−	0.474398i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			9.57766e10i			0.995036i	0.867454	+	0.497518i	$0.165755\pi$
$557$			9.57766e10i			0.995036i	−0.867454	+	0.497518i	$0.834245\pi$
$558$		0			0
$559$	−6.49030e10			−0.664687
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.09169e11	−	6.30286e10i	1.08659	−	0.627342i	0.153922	−	0.988083i	$-0.450810\pi$
$563$	1.09169e11	−	6.30286e10i	1.08659	−	0.627342i	0.932666	+	0.360741i	$0.117476\pi$
$564$		0			0
$565$	−2.12701e10	+	3.68409e10i	−0.208726	+	0.361523i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.07480e11	+	6.20537e10i	1.02537	+	0.591995i	0.915654	−	0.401968i	$-0.131674\pi$
$569$	1.07480e11	+	6.20537e10i	1.02537	+	0.591995i	0.109712	+	0.993963i	$0.465007\pi$
$570$		0			0
$571$	3.83881e10	+	6.64902e10i	0.361121	+	0.625480i	0.988146	−	0.153520i	$-0.0490608\pi$
$571$	3.83881e10	+	6.64902e10i	0.361121	+	0.625480i	−0.627025	+	0.778999i	$0.715728\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			8.50223e9i			0.0777788i
$576$		0			0
$577$	1.17318e10			0.105843			0.0529214	−	0.998599i	$-0.483147\pi$
$577$	1.17318e10			0.105843			0.0529214	+	0.998599i	$0.483147\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.55000e11	−	8.94895e10i	1.36028	−	0.785357i
$582$		0			0
$583$	−1.32104e9	+	2.28810e9i	−0.0114351	+	0.0198062i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.57092e10	+	9.06970e9i	0.132313	+	0.0763907i	0.564695	−	0.825299i	$-0.308994\pi$
$587$	1.57092e10	+	9.06970e9i	0.132313	+	0.0763907i	−0.432383	+	0.901690i	$0.642327\pi$
$588$		0			0
$589$	−2.83523e10	−	4.91076e10i	−0.235574	−	0.408025i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1.58240e11i		−	1.27967i	−0.768514	−	0.639833i	$-0.779003\pi$
$593$		−	1.58240e11i		−	1.27967i	0.768514	−	0.639833i	$-0.220997\pi$
$594$		0			0
$595$	1.55937e10			0.124418
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.18786e10	−	1.26316e10i	0.169946	−	0.0981185i	−0.412614	−	0.910906i	$-0.635384\pi$
$599$	2.18786e10	−	1.26316e10i	0.169946	−	0.0981185i	0.582561	+	0.812787i	$0.302051\pi$
$600$		0			0
$601$	−6.35697e10	+	1.10106e11i	−0.487250	+	0.843942i	−0.999893	−	0.0146601i	$-0.995333\pi$
$601$	−6.35697e10	+	1.10106e11i	−0.487250	+	0.843942i	0.512642	+	0.858602i	$0.328667\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.12452e11	+	6.49242e10i	0.839355	+	0.484602i
$606$		0			0
$607$	−6.84595e10	−	1.18575e11i	−0.504289	−	0.873454i	−0.999988	−	0.00495926i	$-0.998421\pi$
$607$	−6.84595e10	−	1.18575e11i	−0.504289	−	0.873454i	0.495699	−	0.868494i	$-0.334912\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	9.59013e10i		−	0.688113i
$612$		0			0
$613$	−7.59376e10			−0.537793			−0.268896	−	0.963169i	$-0.586659\pi$
$613$	−7.59376e10			−0.537793			−0.268896	+	0.963169i	$0.586659\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.98217e11	−	1.14440e11i	1.36773	−	0.789657i	0.377089	−	0.926177i	$-0.376925\pi$
$617$	1.98217e11	−	1.14440e11i	1.36773	−	0.789657i	0.990637	+	0.136520i	$0.0435918\pi$
$618$		0			0
$619$	−3.12175e10	+	5.40703e10i	−0.212635	+	0.368295i	−0.952538	−	0.304418i	$-0.901538\pi$
$619$	−3.12175e10	+	5.40703e10i	−0.212635	+	0.368295i	0.739903	+	0.672713i	$0.234871\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.39490e11	−	1.38270e11i	−1.58978	−	0.917857i
$624$		0			0
$625$	7.18845e10	+	1.24508e11i	0.471102	+	0.815973i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.74937e10i			0.175643i
$630$		0			0
$631$	1.56990e11			0.990274			0.495137	−	0.868815i	$-0.335118\pi$
$631$	1.56990e11			0.990274			0.495137	+	0.868815i	$0.335118\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.11047e11	+	1.21848e11i	−1.29803	+	0.749418i
$636$		0			0
$637$	1.80148e10	−	3.12025e10i	0.109414	−	0.189510i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.83107e10	+	1.63452e10i	0.167694	+	0.0968183i	0.581498	−	0.813548i	$-0.302467\pi$
$641$	2.83107e10	+	1.63452e10i	0.167694	+	0.0968183i	−0.413804	+	0.910366i	$0.635800\pi$
$642$		0			0
$643$	−1.10841e11	−	1.91982e11i	−0.648420	−	1.12310i	−0.983500	−	0.180907i	$-0.942097\pi$
$643$	−1.10841e11	−	1.91982e11i	−0.648420	−	1.12310i	0.335080	−	0.942190i	$-0.391237\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.43253e11i		−	0.817498i	−0.912647	−	0.408749i	$-0.865965\pi$
$647$		−	1.43253e11i		−	0.817498i	0.912647	−	0.408749i	$-0.134035\pi$
$648$		0			0
$649$	8.00680e9			0.0451315
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.92869e11	−	1.69088e11i	1.61072	−	0.929949i	0.621516	−	0.783401i	$-0.286517\pi$
$653$	2.92869e11	−	1.69088e11i	1.61072	−	0.929949i	0.989204	−	0.146548i	$-0.0468163\pi$
$654$		0			0
$655$	−9.02336e10	+	1.56289e11i	−0.490234	+	0.849110i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.88265e10	−	5.12840e10i	−0.470978	−	0.271919i	0.245671	−	0.969353i	$-0.420992\pi$
$659$	−8.88265e10	−	5.12840e10i	−0.470978	−	0.271919i	−0.716649	+	0.697434i	$0.754325\pi$
$660$		0			0
$661$	−4.38284e10	−	7.59130e10i	−0.229588	−	0.397659i	0.728098	−	0.685473i	$-0.240405\pi$
$661$	−4.38284e10	−	7.59130e10i	−0.229588	−	0.397659i	−0.957686	+	0.287815i	$0.907071\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	2.34368e11i		−	1.19843i
$666$		0			0
$667$	2.64529e11			1.33650
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.27035e9	−	3.04284e9i	0.0259986	−	0.0150103i
$672$		0			0
$673$	−1.52990e10	+	2.64987e10i	−0.0745768	+	0.129171i	−0.900902	−	0.434022i	$-0.857094\pi$
$673$	−1.52990e10	+	2.64987e10i	−0.0745768	+	0.129171i	0.826325	+	0.563193i	$0.190427\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.03946e9	−	4.64158e9i	−0.0382712	−	0.0220959i	0.480742	−	0.876862i	$-0.340367\pi$
$677$	−8.03946e9	−	4.64158e9i	−0.0382712	−	0.0220959i	−0.519014	+	0.854766i	$0.673701\pi$
$678$		0			0
$679$	−1.34390e11	−	2.32771e11i	−0.632251	−	1.09509i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	2.87449e11i		−	1.32092i	−0.750859	−	0.660462i	$-0.770360\pi$
$683$		−	2.87449e11i		−	1.32092i	0.750859	−	0.660462i	$-0.229640\pi$
$684$		0			0
$685$	2.16883e11			0.985060
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.63454e10	−	3.25310e10i	0.250024	−	0.144351i
$690$		0			0
$691$	−1.75801e11	+	3.04496e11i	−0.771095	+	1.33558i	0.165868	+	0.986148i	$0.446958\pi$
$691$	−1.75801e11	+	3.04496e11i	−0.771095	+	1.33558i	−0.936963	+	0.349428i	$0.886376\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.02798e11	+	1.17086e11i	0.869210	+	0.501839i
$696$		0			0
$697$	−1.46998e10	−	2.54608e10i	−0.0622844	−	0.107880i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	3.49664e11i		−	1.44803i	−0.689783	−	0.724016i	$-0.742294\pi$
$701$		−	3.49664e11i		−	1.44803i	0.689783	−	0.724016i	$-0.257706\pi$
$702$		0			0
$703$	4.13220e11			1.69184
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.32311e10	−	3.65065e10i	0.253077	−	0.146114i
$708$		0			0
$709$	2.07733e11	−	3.59805e11i	0.822093	−	1.42391i	−0.0820274	−	0.996630i	$-0.526140\pi$
$709$	2.07733e11	−	3.59805e11i	0.822093	−	1.42391i	0.904121	−	0.427277i	$-0.140527\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.39054e11	+	8.02830e10i	0.538054	+	0.310646i
$714$		0			0
$715$	4.97218e9	+	8.61207e9i	0.0190249	+	0.0329521i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			3.28416e11i			1.22888i	0.788965	+	0.614438i	$0.210617\pi$
$719$			3.28416e11i			1.22888i	−0.788965	+	0.614438i	$0.789383\pi$
$720$		0			0
$721$	1.14651e11			0.424266
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.23438e10	+	7.12669e9i	−0.0446783	+	0.0257950i
$726$		0			0
$727$	9.86413e10	−	1.70852e11i	0.353119	−	0.611620i	−0.633675	−	0.773599i	$-0.718454\pi$
$727$	9.86413e10	−	1.70852e11i	0.353119	−	0.611620i	0.986794	+	0.161979i	$0.0517878\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.61334e10	+	1.50881e10i	0.0915222	+	0.0528404i
$732$		0			0
$733$	8.77015e10	+	1.51903e11i	0.303802	+	0.526201i	0.976994	−	0.213267i	$-0.0684105\pi$
$733$	8.77015e10	+	1.51903e11i	0.303802	+	0.526201i	−0.673192	+	0.739468i	$0.735077\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			7.26132e9i			0.0246119i
$738$		0			0
$739$	−2.71136e11			−0.909096			−0.454548	−	0.890722i	$-0.650199\pi$
$739$	−2.71136e11			−0.909096			−0.454548	+	0.890722i	$0.650199\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.93494e11	−	1.69449e11i	0.963038	−	0.556010i	0.0659310	−	0.997824i	$-0.478998\pi$
$743$	2.93494e11	−	1.69449e11i	0.963038	−	0.556010i	0.897107	+	0.441814i	$0.145665\pi$
$744$		0			0
$745$	−8.73204e10	+	1.51243e11i	−0.283459	+	0.490966i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.24302e11	+	7.17657e10i	0.394957	+	0.228029i
$750$		0			0
$751$	−1.59569e11	−	2.76382e11i	−0.501637	−	0.868861i	−0.999998	−	0.00189143i	$-0.999398\pi$
$751$	−1.59569e11	−	2.76382e11i	−0.501637	−	0.868861i	0.498361	−	0.866970i	$-0.333935\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	3.62658e11i		−	1.11612i
$756$		0			0
$757$	−3.74679e11			−1.14097			−0.570487	−	0.821307i	$-0.693245\pi$
$757$	−3.74679e11			−1.14097			−0.570487	+	0.821307i	$0.693245\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.45694e11	−	3.15056e11i	1.62708	−	0.939398i	0.642128	−	0.766597i	$-0.278052\pi$
$761$	5.45694e11	−	3.15056e11i	1.62708	−	0.939398i	0.984957	−	0.172801i	$-0.0552816\pi$
$762$		0			0
$763$	−1.77933e11	+	3.08189e11i	−0.524999	+	0.909325i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.70755e11	−	9.85852e10i	−0.493391	−	0.284859i
$768$		0			0
$769$	2.08754e11	+	3.61573e11i	0.596939	+	1.03393i	0.993270	+	0.115821i	$0.0369497\pi$
$769$	2.08754e11	+	3.61573e11i	0.596939	+	1.03393i	−0.396332	+	0.918107i	$0.629717\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	9.25620e10i		−	0.259248i	−0.991563	−	0.129624i	$-0.958623\pi$
$773$		−	9.25620e10i		−	0.259248i	0.991563	−	0.129624i	$-0.0413770\pi$
$774$		0			0
$775$	−8.65164e9			−0.0239823
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.82666e11	+	2.20933e11i	−1.03913	+	0.599943i
$780$		0			0
$781$	3.02718e9	−	5.24323e9i	0.00813644	−	0.0140927i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.64807e10	+	5.57032e10i	0.254075	+	0.146690i
$786$		0			0
$787$	−1.89908e11	−	3.28930e11i	−0.495044	−	0.857442i	0.504940	−	0.863155i	$-0.331515\pi$
$787$	−1.89908e11	−	3.28930e11i	−0.495044	−	0.857442i	−0.999984	+	0.00571313i	$0.998181\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1.92488e11i		−	0.491697i
$792$		0			0
$793$	−1.49862e11			−0.378965
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.38154e11	−	3.10704e11i	1.33375	−	0.770039i	0.347876	−	0.937541i	$-0.386903\pi$
$797$	5.38154e11	−	3.10704e11i	1.33375	−	0.770039i	0.985872	+	0.167501i	$0.0535698\pi$
$798$		0			0
$799$	−2.22944e10	+	3.86150e10i	−0.0547026	+	0.0947477i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.73869e10	−	1.00383e10i	−0.0418177	−	0.0241435i
$804$		0			0
$805$	3.31822e11	+	5.74733e11i	0.790172	+	1.36862i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			6.64937e11i			1.55234i	0.630525	+	0.776169i	$0.282840\pi$
$809$			6.64937e11i			1.55234i	−0.630525	+	0.776169i	$0.717160\pi$
$810$		0			0
$811$	1.73636e11			0.401381			0.200690	−	0.979655i	$-0.435682\pi$
$811$	1.73636e11			0.401381			0.200690	+	0.979655i	$0.435682\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.85951e11	+	2.22829e11i	−0.874785	+	0.505057i
$816$		0			0
$817$	2.26769e11	−	3.92776e11i	0.508975	−	0.881570i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00043e11	−	5.77601e10i	−0.220199	−	0.127132i	0.385843	−	0.922564i	$-0.373911\pi$
$821$	−1.00043e11	−	5.77601e10i	−0.220199	−	0.127132i	−0.606043	+	0.795432i	$0.707244\pi$
$822$		0			0
$823$	−3.97564e11	−	6.88602e11i	−0.866579	−	1.50096i	−0.865471	−	0.500959i	$-0.832981\pi$
$823$	−3.97564e11	−	6.88602e11i	−0.866579	−	1.50096i	−0.00110803	−	0.999999i	$-0.500353\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			2.68441e11i			0.573888i	0.957947	+	0.286944i	$0.0926394\pi$
$827$			2.68441e11i			0.573888i	−0.957947	+	0.286944i	$0.907361\pi$
$828$		0			0
$829$	1.67579e11			0.354815			0.177407	−	0.984138i	$-0.443229\pi$
$829$	1.67579e11			0.354815			0.177407	+	0.984138i	$0.443229\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.45074e10	+	8.37587e9i	−0.0301308	+	0.0173960i
$834$		0			0
$835$	−3.68601e11	+	6.38435e11i	−0.758246	+	1.31332i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.79429e11	−	3.92269e11i	−1.37119	−	0.791655i	−0.380109	−	0.924942i	$-0.624113\pi$
$839$	−6.79429e11	−	3.92269e11i	−1.37119	−	0.791655i	−0.991077	+	0.133287i	$0.957447\pi$
$840$		0			0
$841$	−2.83912e10	−	4.91749e10i	−0.0567543	−	0.0983014i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			2.50783e11i			0.491895i
$846$		0			0
$847$	−5.87544e11			−1.14158
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.01332e12	+	5.85043e11i	−1.93210	+	1.11550i
$852$		0			0
$853$	−1.93777e11	+	3.35631e11i	−0.366020	+	0.633966i	−0.988939	−	0.148320i	$-0.952613\pi$
$853$	−1.93777e11	+	3.35631e11i	−0.366020	+	0.633966i	0.622919	+	0.782286i	$0.285947\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.21737e11	+	1.85755e11i	0.596455	+	0.344363i	0.767646	−	0.640874i	$-0.221428\pi$
$857$	3.21737e11	+	1.85755e11i	0.596455	+	0.344363i	−0.171191	+	0.985238i	$0.554761\pi$
$858$		0			0
$859$	2.13870e11	+	3.70434e11i	0.392805	+	0.680358i	0.992818	−	0.119632i	$-0.0381714\pi$
$859$	2.13870e11	+	3.70434e11i	0.392805	+	0.680358i	−0.600013	+	0.799990i	$0.704838\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.10371e11i			0.198981i	0.995039	+	0.0994904i	$0.0317213\pi$
$863$			1.10371e11i			0.198981i	−0.995039	+	0.0994904i	$0.968279\pi$
$864$		0			0
$865$	−8.04444e11			−1.43692
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.31544e10	+	7.59470e9i	−0.0230671	+	0.0133178i
$870$		0			0
$871$	8.94064e10	−	1.54856e11i	0.155344	−	0.269065i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.96141e11	−	3.44182e11i	−1.01699	−	0.587160i
$876$		0			0
$877$	−1.11245e10	−	1.92682e10i	−0.0188054	−	0.0325719i	0.856470	−	0.516198i	$-0.172653\pi$
$877$	−1.11245e10	−	1.92682e10i	−0.0188054	−	0.0325719i	−0.875275	+	0.483626i	$0.839320\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			6.11657e11i			1.01532i	0.861557	+	0.507661i	$0.169490\pi$
$881$			6.11657e11i			1.01532i	−0.861557	+	0.507661i	$0.830510\pi$
$882$		0			0
$883$	1.03070e12			1.69547			0.847735	−	0.530420i	$-0.177966\pi$
$883$	1.03070e12			1.69547			0.847735	+	0.530420i	$0.177966\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.29180e11	+	2.47787e11i	−0.693337	+	0.400298i	−0.804861	−	0.593463i	$-0.797760\pi$
$887$	−4.29180e11	+	2.47787e11i	−0.693337	+	0.400298i	0.111524	+	0.993762i	$0.464427\pi$
$888$		0			0
$889$	5.51344e11	−	9.54957e11i	0.882706	−	1.52889i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.80370e11	+	3.35077e11i	0.912640	+	0.526913i
$894$		0			0
$895$	3.72537e11	+	6.45252e11i	0.580600	+	1.00563i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			2.69177e11i			0.412097i
$900$		0			0
$901$	−3.02502e10			−0.0459018
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.26102e11	+	4.19215e11i	−1.08244	+	0.624946i
$906$		0			0
$907$	3.10687e11	−	5.38125e11i	0.459086	−	0.795159i	−0.539827	−	0.841776i	$-0.681510\pi$
$907$	3.10687e11	−	5.38125e11i	0.459086	−	0.795159i	0.998913	+	0.0466163i	$0.0148438\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.86965e11	−	2.23414e11i	−0.561821	−	0.324368i	0.192055	−	0.981384i	$-0.438485\pi$
$911$	−3.86965e11	−	2.23414e11i	−0.561821	−	0.324368i	−0.753876	+	0.657016i	$0.771818\pi$
$912$		0			0
$913$	−2.65338e10	−	4.59579e10i	−0.0381871	−	0.0661420i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	8.16587e11i		−	1.15485i
$918$		0			0
$919$	−1.63883e11			−0.229758			−0.114879	−	0.993379i	$-0.536648\pi$
$919$	−1.63883e11			−0.229758			−0.114879	+	0.993379i	$0.536648\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.29117e11	+	7.45455e10i	−0.177900	+	0.102710i
$924$		0			0
$925$	3.15233e10	−	5.46000e10i	0.0430591	−	0.0745806i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.67226e11	+	5.58428e11i	1.29857	+	0.749729i	0.980157	−	0.198223i	$-0.0635171\pi$
$929$	9.67226e11	+	5.58428e11i	1.29857	+	0.749729i	0.318412	+	0.947952i	$0.396850\pi$
$930$		0			0
$931$	1.25886e11	+	2.18042e11i	0.167564	+	0.290229i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	4.62357e9i		−	0.00604967i
$936$		0			0
$937$	1.38175e11			0.179255			0.0896274	−	0.995975i	$-0.471432\pi$
$937$	1.38175e11			0.179255			0.0896274	+	0.995975i	$0.471432\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.55174e11	−	1.47325e11i	0.325445	−	0.187896i	−0.328372	−	0.944549i	$-0.606500\pi$
$941$	2.55174e11	−	1.47325e11i	0.325445	−	0.187896i	0.653817	+	0.756653i	$0.273167\pi$
$942$		0			0
$943$	6.25599e11	−	1.08357e12i	0.791132	−	1.37028i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.23306e11	−	2.44396e11i	−0.526326	−	0.303875i	0.213193	−	0.977010i	$-0.431614\pi$
$947$	−4.23306e11	−	2.44396e11i	−0.526326	−	0.303875i	−0.739519	+	0.673136i	$0.764947\pi$
$948$		0			0
$949$	2.47198e11	+	4.28159e11i	0.304775	+	0.527886i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1.11594e12i			1.35291i	0.736486	+	0.676453i	$0.236484\pi$
$953$			1.11594e12i			1.35291i	−0.736486	+	0.676453i	$0.763516\pi$
$954$		0			0
$955$	−8.11241e11			−0.975296
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.49884e11	+	4.90681e11i	−1.00481	+	0.580129i
$960$		0			0
$961$	3.44752e11	−	5.97128e11i	0.404215	−	0.700122i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.11975e12	+	6.46487e11i	1.29125	+	0.745506i
$966$		0			0
$967$	4.19811e11	+	7.27134e11i	0.480118	+	0.831589i	0.999740	−	0.0228073i	$-0.00726042\pi$
$967$	4.19811e11	+	7.27134e11i	0.480118	+	0.831589i	−0.519622	+	0.854396i	$0.673927\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1.01392e12i			1.14058i	0.821444	+	0.570289i	$0.193169\pi$
$971$			1.01392e12i			1.14058i	−0.821444	+	0.570289i	$0.806831\pi$
$972$		0			0
$973$	−1.05959e12			−1.18219
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.06240e11	+	3.50013e11i	−0.665374	+	0.384154i	−0.794322	−	0.607497i	$-0.792174\pi$
$977$	−6.06240e11	+	3.50013e11i	−0.665374	+	0.384154i	0.128947	+	0.991651i	$0.458840\pi$
$978$		0			0
$979$	−4.09973e10	+	7.10094e10i	−0.0446298	+	0.0773010i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.64623e11	−	1.52780e11i	−0.283409	−	0.163626i	0.351557	−	0.936167i	$-0.385652\pi$
$983$	−2.64623e11	−	1.52780e11i	−0.283409	−	0.163626i	−0.634966	+	0.772540i	$0.718986\pi$
$984$		0			0
$985$	5.69033e11	+	9.85595e11i	0.604495	+	1.04702i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1.28425e12i			1.34235i
$990$		0			0
$991$	4.77081e11			0.494650			0.247325	−	0.968933i	$-0.420449\pi$
$991$	4.77081e11			0.494650			0.247325	+	0.968933i	$0.420449\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.10495e11	+	4.10205e11i	−0.724884	+	0.418512i
$996$		0			0
$997$	1.73423e11	−	3.00378e11i	0.175520	−	0.304010i	−0.764821	−	0.644243i	$-0.777173\pi$
$997$	1.73423e11	−	3.00378e11i	0.175520	−	0.304010i	0.940341	+	0.340233i	$0.110506\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.9.g.h.269.4		32
3.2	odd	2	inner	324.9.g.h.269.13		32
9.2	odd	6		324.9.c.b.161.13	yes	16
9.4	even	3	inner	324.9.g.h.53.13		32
9.5	odd	6	inner	324.9.g.h.53.4		32
9.7	even	3		324.9.c.b.161.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.9.c.b.161.4	✓	16	9.7	even	3
324.9.c.b.161.13	yes	16	9.2	odd	6
324.9.g.h.53.4		32	9.5	odd	6	inner
324.9.g.h.53.13		32	9.4	even	3	inner
324.9.g.h.269.4		32	1.1	even	1	trivial
324.9.g.h.269.13		32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	324.9.g.h.269.4

Level	$324$
Weight	$9$
Character	324.269
Analytic conductor	$131.991$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$