LMFDB - Embedded newform 351.2.bd.e.80.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(80,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("351.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bd (of order $12$, degree $4$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 $ x^20 + 88x^16 - 6x^15 + 48x^13 + 1980x^12 - 204x^11 + 18x^10 + 2076x^9 + 8020x^8 + 2220x^7 + 792x^6 + 4350x^5 + 10936x^4 + 6648x^3 + 1800x^2 - 540*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.4
Root			$-0.606342 - 0.606342i$ of defining polynomial
Character	$\chi$	$=$	351.80
Dual form			351.2.bd.e.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221937 - 0.828279i) q^{2} +(1.09526 + 0.632349i) q^{4} +(2.06553 + 2.06553i) q^{5} +(-3.61723 + 0.969233i) q^{7} +(1.97952 - 1.97952i) q^{8} +O(q^{10})$	\(q+(0.221937 - 0.828279i) q^{2} +(1.09526 + 0.632349i) q^{4} +(2.06553 + 2.06553i) q^{5} +(-3.61723 + 0.969233i) q^{7} +(1.97952 - 1.97952i) q^{8} +(2.16926 - 1.25242i) q^{10} +(3.71193 + 0.994610i) q^{11} +(-2.69784 + 2.39199i) q^{13} +3.21118i q^{14} +(0.0644276 + 0.111592i) q^{16} +(1.19714 - 2.07351i) q^{17} +(0.734041 + 2.73948i) q^{19} +(0.956160 + 3.56844i) q^{20} +(1.64763 - 2.85378i) q^{22} +(-2.35699 - 4.08243i) q^{23} +3.53287i q^{25} +(1.38249 + 2.76544i) q^{26} +(-4.57470 - 1.22579i) q^{28} +(-1.36394 + 0.787471i) q^{29} +(4.61940 - 4.61940i) q^{31} +(5.51489 - 1.47771i) q^{32} +(-1.45175 - 1.45175i) q^{34} +(-9.47349 - 5.46952i) q^{35} +(2.34298 - 8.74410i) q^{37} +2.43196 q^{38} +8.17755 q^{40} +(-0.487872 + 1.82076i) q^{41} +(-7.15745 - 4.13236i) q^{43} +(3.43659 + 3.43659i) q^{44} +(-3.90449 + 1.04621i) q^{46} +(5.69829 - 5.69829i) q^{47} +(6.08273 - 3.51187i) q^{49} +(2.92620 + 0.784073i) q^{50} +(-4.46742 + 0.913877i) q^{52} +7.54342i q^{53} +(5.61273 + 9.72153i) q^{55} +(-5.24177 + 9.07901i) q^{56} +(0.349538 + 1.30449i) q^{58} +(-3.01505 - 11.2523i) q^{59} +(-4.13446 + 7.16109i) q^{61} +(-2.80094 - 4.85137i) q^{62} -4.63812i q^{64} +(-10.5132 - 0.631746i) q^{65} +(-8.43318 - 2.25966i) q^{67} +(2.62236 - 1.51402i) q^{68} +(-6.63281 + 6.63281i) q^{70} +(-10.4500 + 2.80006i) q^{71} +(7.13018 + 7.13018i) q^{73} +(-6.72257 - 3.88128i) q^{74} +(-0.928340 + 3.46461i) q^{76} -14.3909 q^{77} -10.8095 q^{79} +(-0.0974194 + 0.363574i) q^{80} +(1.39982 + 0.808189i) q^{82} +(-10.2967 - 10.2967i) q^{83} +(6.75564 - 1.81017i) q^{85} +(-5.01125 + 5.01125i) q^{86} +(9.31672 - 5.37901i) q^{88} +(10.7854 + 2.88995i) q^{89} +(7.44032 - 11.2672i) q^{91} -5.96176i q^{92} +(-3.45511 - 5.98443i) q^{94} +(-4.14230 + 7.17467i) q^{95} +(2.54792 + 9.50895i) q^{97} +(-1.55883 - 5.81761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5}+O(q^{10}) $ 20 * q + 6 * q^5	$ 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) $ 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.221937	−	0.828279i	0.156933	−	0.585682i	−0.841999	−	0.539479i	$-0.818621\pi$
$2$	0.221937	−	0.828279i	0.156933	−	0.585682i	0.998932	−	0.0462029i	$-0.0147121\pi$
$3$		0			0
$3$		0			0
$4$	1.09526	+	0.632349i	0.547630	+	0.316174i
$5$	2.06553	+	2.06553i	0.923735	+	0.923735i	0.997291	−	0.0735560i	$-0.0234348\pi$
$5$	2.06553	+	2.06553i	0.923735	+	0.923735i	−0.0735560	+	0.997291i	$0.523435\pi$
$6$		0			0
$7$	−3.61723	+	0.969233i	−1.36718	+	0.366336i	−0.866449	−	0.499266i	$-0.833603\pi$
$7$	−3.61723	+	0.969233i	−1.36718	+	0.366336i	−0.500734	+	0.865601i	$0.666937\pi$
$8$	1.97952	−	1.97952i	0.699868	−	0.699868i
$9$		0			0
$10$	2.16926	−	1.25242i	0.685979	−	0.396050i
$11$	3.71193	+	0.994610i	1.11919	+	0.299886i	0.770556	−	0.637373i	$-0.219979\pi$
$11$	3.71193	+	0.994610i	1.11919	+	0.299886i	0.348634	+	0.937259i	$0.386646\pi$
$12$		0			0
$13$	−2.69784	+	2.39199i	−0.748248	+	0.663420i
$13$	−2.69784	+	2.39199i	−0.748248	+	0.663420i
$14$			3.21118i			0.858224i
$15$		0			0
$16$	0.0644276	+	0.111592i	0.0161069	+	0.0278980i
$17$	1.19714	−	2.07351i	0.290349	−	0.502900i	−0.683543	−	0.729910i	$-0.739562\pi$
$17$	1.19714	−	2.07351i	0.290349	−	0.502900i	0.973892	+	0.227011i	$0.0728952\pi$
$18$		0			0
$19$	0.734041	+	2.73948i	0.168401	+	0.628479i	0.997582	+	0.0694998i	$0.0221403\pi$
$19$	0.734041	+	2.73948i	0.168401	+	0.628479i	−0.829181	+	0.558980i	$0.811193\pi$
$20$	0.956160	+	3.56844i	0.213804	+	0.797927i
$21$		0			0
$22$	1.64763	−	2.85378i	0.351276	−	0.608427i
$23$	−2.35699	−	4.08243i	−0.491466	−	0.851245i	0.508485	−	0.861071i	$-0.330206\pi$
$23$	−2.35699	−	4.08243i	−0.491466	−	0.851245i	−0.999952	+	0.00982587i	$0.996872\pi$
$24$		0			0
$25$			3.53287i			0.706573i
$26$	1.38249	+	2.76544i	0.271128	+	0.542347i
$27$		0			0
$28$	−4.57470	−	1.22579i	−0.864536	−	0.231652i
$29$	−1.36394	+	0.787471i	−0.253277	+	0.146230i	−0.621264	−	0.783601i	$-0.713381\pi$
$29$	−1.36394	+	0.787471i	−0.253277	+	0.146230i	0.367987	+	0.929831i	$0.380047\pi$
$30$		0			0
$31$	4.61940	−	4.61940i	0.829670	−	0.829670i	−0.157801	−	0.987471i	$-0.550441\pi$
$31$	4.61940	−	4.61940i	0.829670	−	0.829670i	0.987471	+	0.157801i	$0.0504406\pi$
$32$	5.51489	−	1.47771i	0.974904	−	0.261225i
$33$		0			0
$34$	−1.45175	−	1.45175i	−0.248974	−	0.248974i
$35$	−9.47349	−	5.46952i	−1.60131	−	0.924518i
$36$		0			0
$37$	2.34298	−	8.74410i	0.385183	−	1.43752i	−0.452696	−	0.891665i	$-0.649538\pi$
$37$	2.34298	−	8.74410i	0.385183	−	1.43752i	0.837879	−	0.545857i	$-0.183796\pi$
$38$	2.43196			0.394517
$39$		0			0
$40$	8.17755			1.29298
$41$	−0.487872	+	1.82076i	−0.0761929	+	0.284356i	−0.993501	−	0.113822i	$-0.963691\pi$
$41$	−0.487872	+	1.82076i	−0.0761929	+	0.284356i	0.917308	+	0.398178i	$0.130357\pi$
$42$		0			0
$43$	−7.15745	−	4.13236i	−1.09150	−	0.630178i	−0.157525	−	0.987515i	$-0.550352\pi$
$43$	−7.15745	−	4.13236i	−1.09150	−	0.630178i	−0.933976	+	0.357337i	$0.883685\pi$
$44$	3.43659	+	3.43659i	0.518086	+	0.518086i
$45$		0			0
$46$	−3.90449	+	1.04621i	−0.575686	+	0.154255i
$47$	5.69829	−	5.69829i	0.831180	−	0.831180i	−0.156498	−	0.987678i	$-0.550020\pi$
$47$	5.69829	−	5.69829i	0.831180	−	0.831180i	0.987678	+	0.156498i	$0.0500204\pi$
$48$		0			0
$49$	6.08273	−	3.51187i	0.868962	−	0.501695i
$50$	2.92620	+	0.784073i	0.413827	+	0.110885i
$51$		0			0
$52$	−4.46742	+	0.913877i	−0.619519	+	0.126732i
$53$			7.54342i			1.03617i	0.855330	+	0.518084i	$0.173355\pi$
$53$			7.54342i			1.03617i	−0.855330	+	0.518084i	$0.826645\pi$
$54$		0			0
$55$	5.61273	+	9.72153i	0.756820	+	1.31085i
$56$	−5.24177	+	9.07901i	−0.700461	+	1.21323i
$57$		0			0
$58$	0.349538	+	1.30449i	0.0458965	+	0.171288i
$59$	−3.01505	−	11.2523i	−0.392527	−	1.46493i	−0.825952	−	0.563740i	$-0.809362\pi$
$59$	−3.01505	−	11.2523i	−0.392527	−	1.46493i	0.433426	−	0.901189i	$-0.357305\pi$
$60$		0			0
$61$	−4.13446	+	7.16109i	−0.529363	+	0.916884i	0.470051	+	0.882639i	$0.344236\pi$
$61$	−4.13446	+	7.16109i	−0.529363	+	0.916884i	−0.999414	+	0.0342440i	$0.989098\pi$
$62$	−2.80094	−	4.85137i	−0.355720	−	0.616125i
$63$		0			0
$64$		−	4.63812i		−	0.579765i
$65$	−10.5132	−	0.631746i	−1.30401	−	0.0783585i
$66$		0			0
$67$	−8.43318	−	2.25966i	−1.03028	−	0.276062i	−0.296198	−	0.955126i	$-0.595719\pi$
$67$	−8.43318	−	2.25966i	−1.03028	−	0.276062i	−0.734078	+	0.679065i	$0.762386\pi$
$68$	2.62236	−	1.51402i	0.318008	−	0.183602i
$69$		0			0
$70$	−6.63281	+	6.63281i	−0.792772	+	0.792772i
$71$	−10.4500	+	2.80006i	−1.24018	+	0.332306i	−0.818536	−	0.574455i	$-0.805214\pi$
$71$	−10.4500	+	2.80006i	−1.24018	+	0.332306i	−0.421646	+	0.906761i	$0.638547\pi$
$72$		0			0
$73$	7.13018	+	7.13018i	0.834524	+	0.834524i	0.988132	−	0.153608i	$-0.0490893\pi$
$73$	7.13018	+	7.13018i	0.834524	+	0.834524i	−0.153608	+	0.988132i	$0.549089\pi$
$74$	−6.72257	−	3.88128i	−0.781482	−	0.451189i
$75$		0			0
$76$	−0.928340	+	3.46461i	−0.106488	+	0.397418i
$77$	−14.3909			−1.64000
$78$		0			0
$79$	−10.8095			−1.21616			−0.608081	−	0.793875i	$-0.708061\pi$
$79$	−10.8095			−1.21616			−0.608081	+	0.793875i	$0.708061\pi$
$80$	−0.0974194	+	0.363574i	−0.0108918	+	0.0406488i
$81$		0			0
$82$	1.39982	+	0.808189i	0.154585	+	0.0892496i
$83$	−10.2967	−	10.2967i	−1.13021	−	1.13021i	−0.990142	−	0.140064i	$-0.955269\pi$
$83$	−10.2967	−	10.2967i	−1.13021	−	1.13021i	−0.140064	−	0.990142i	$-0.544731\pi$
$84$		0			0
$85$	6.75564	−	1.81017i	0.732752	−	0.196340i
$86$	−5.01125	+	5.01125i	−0.540377	+	0.540377i
$87$		0			0
$88$	9.31672	−	5.37901i	0.993166	−	0.573404i
$89$	10.7854	+	2.88995i	1.14325	+	0.306334i	0.780259	−	0.625457i	$-0.215087\pi$
$89$	10.7854	+	2.88995i	1.14325	+	0.306334i	0.362995	+	0.931791i	$0.381754\pi$
$90$		0			0
$91$	7.44032	−	11.2672i	0.779957	−	1.18113i
$92$		−	5.96176i		−	0.621556i
$93$		0			0
$94$	−3.45511	−	5.98443i	−0.356368	−	0.617247i
$95$	−4.14230	+	7.17467i	−0.424991	+	0.736106i
$96$		0			0
$97$	2.54792	+	9.50895i	0.258702	+	0.965488i	0.965994	+	0.258566i	$0.0832500\pi$
$97$	2.54792	+	9.50895i	0.258702	+	0.965488i	−0.707292	+	0.706922i	$0.750083\pi$
$98$	−1.55883	−	5.81761i	−0.157465	−	0.587668i
$99$		0			0
$100$	−2.23400	+	3.86941i	−0.223400	+	0.386941i
$101$	4.82867	+	8.36350i	0.480471	+	0.832199i	0.999749	−	0.0224057i	$-0.00713256\pi$
$101$	4.82867	+	8.36350i	0.480471	+	0.832199i	−0.519278	+	0.854605i	$0.673799\pi$
$102$		0			0
$103$			8.98232i			0.885054i	0.896755	+	0.442527i	$0.145918\pi$
$103$			8.98232i			0.885054i	−0.896755	+	0.442527i	$0.854082\pi$
$104$	−0.605440	+	10.0755i	−0.0593683	+	0.987980i
$105$		0			0
$106$	6.24806	+	1.67416i	0.606865	+	0.162609i
$107$	10.6757	−	6.16361i	1.03206	−	0.595859i	0.114485	−	0.993425i	$-0.463478\pi$
$107$	10.6757	−	6.16361i	1.03206	−	0.595859i	0.917574	+	0.397566i	$0.130145\pi$
$108$		0			0
$109$	−0.555468	+	0.555468i	−0.0532042	+	0.0532042i	−0.733208	−	0.680004i	$-0.761978\pi$
$109$	−0.555468	+	0.555468i	−0.0532042	+	0.0532042i	0.680004	+	0.733208i	$0.261978\pi$
$110$	9.29781	−	2.49134i	0.886511	−	0.237540i
$111$		0			0
$112$	−0.341208	−	0.341208i	−0.0322411	−	0.0322411i
$113$	2.80857	+	1.62153i	0.264208	+	0.152541i	0.626253	−	0.779620i	$-0.284588\pi$
$113$	2.80857	+	1.62153i	0.264208	+	0.152541i	−0.362045	+	0.932161i	$0.617921\pi$
$114$		0			0
$115$	3.56395	−	13.3008i	0.332340	−	1.24031i
$116$	−1.99183			−0.184936
$117$		0			0
$118$	−9.98923			−0.919583
$119$	−2.32062	+	8.66066i	−0.212731	+	0.793921i
$120$		0			0
$121$	3.26292	+	1.88385i	0.296629	+	0.171259i
$122$	5.01379	+	5.01379i	0.453928	+	0.453928i
$123$		0			0
$124$	7.98053	−	2.13838i	0.716672	−	0.192032i
$125$	3.03042	−	3.03042i	0.271049	−	0.271049i
$126$		0			0
$127$	−2.80335	+	1.61851i	−0.248757	+	0.143620i	−0.619195	−	0.785237i	$-0.712541\pi$
$127$	−2.80335	+	1.61851i	−0.248757	+	0.143620i	0.370438	+	0.928857i	$0.379208\pi$
$128$	7.18812	+	1.92605i	0.635346	+	0.170241i
$129$		0			0
$130$	−2.85654	+	8.56769i	−0.250535	+	0.751436i
$131$		−	15.5185i		−	1.35586i	−0.735128	−	0.677928i	$-0.762878\pi$
$131$		−	15.5185i		−	1.35586i	0.735128	−	0.677928i	$-0.237122\pi$
$132$		0			0
$133$	−5.31038	−	9.19786i	−0.460469	−	0.797555i
$134$	−3.74326	+	6.48352i	−0.323369	+	0.560091i
$135$		0			0
$136$	−1.73479	−	6.47433i	−0.148757	−	0.555169i
$137$	−4.83416	−	18.0413i	−0.413010	−	1.54137i	−0.788789	−	0.614664i	$-0.789292\pi$
$137$	−4.83416	−	18.0413i	−0.413010	−	1.54137i	0.375779	−	0.926709i	$-0.377375\pi$
$138$		0			0
$139$	−2.96898	+	5.14242i	−0.251825	+	0.436174i	−0.964028	−	0.265799i	$-0.914364\pi$
$139$	−2.96898	+	5.14242i	−0.251825	+	0.436174i	0.712203	+	0.701973i	$0.247697\pi$
$140$	−6.91729	−	11.9811i	−0.584618	−	1.01259i
$141$		0			0
$142$			9.27692i			0.778502i
$143$	−12.3933	+	6.19562i	−1.03638	+	0.518104i
$144$		0			0
$145$	−4.44381	−	1.19072i	−0.369039	−	0.0988836i
$146$	7.48823	−	4.32333i	0.619730	−	0.357801i
$147$		0			0
$148$	8.09549	−	8.09549i	0.665445	−	0.665445i
$149$	2.41084	−	0.645984i	0.197504	−	0.0529210i	−0.158711	−	0.987325i	$-0.550734\pi$
$149$	2.41084	−	0.645984i	0.197504	−	0.0529210i	0.356215	+	0.934404i	$0.384067\pi$
$150$		0			0
$151$	−0.312896	−	0.312896i	−0.0254631	−	0.0254631i	0.694261	−	0.719724i	$-0.255732\pi$
$151$	−0.312896	−	0.312896i	−0.0254631	−	0.0254631i	−0.719724	+	0.694261i	$0.755732\pi$
$152$	6.87592	+	3.96981i	0.557711	+	0.321994i
$153$		0			0
$154$	−3.19387	+	11.9197i	−0.257370	+	0.960516i
$155$	19.0831			1.53279
$156$		0			0
$157$	−12.3339			−0.984352			−0.492176	−	0.870496i	$-0.663798\pi$
$157$	−12.3339			−0.984352			−0.492176	+	0.870496i	$0.663798\pi$
$158$	−2.39902	+	8.95328i	−0.190856	+	0.712284i
$159$		0			0
$160$	14.4435	+	8.33893i	1.14186	+	0.659251i
$161$	12.4826	+	12.4826i	0.983766	+	0.983766i
$162$		0			0
$163$	−1.66782	+	0.446891i	−0.130634	+	0.0350032i	−0.323543	−	0.946213i	$-0.604874\pi$
$163$	−1.66782	+	0.446891i	−0.130634	+	0.0350032i	0.192910	+	0.981216i	$0.438208\pi$
$164$	−1.68571	+	1.68571i	−0.131631	+	0.131631i
$165$		0			0
$166$	−10.8137	+	6.24331i	−0.839308	+	0.484575i
$167$	12.2797	+	3.29032i	0.950228	+	0.254613i	0.700459	−	0.713693i	$-0.252979\pi$
$167$	12.2797	+	3.29032i	0.950228	+	0.254613i	0.249769	+	0.968305i	$0.419645\pi$
$168$		0			0
$169$	1.55673	−	12.9065i	0.119749	−	0.992804i
$170$		−	5.99730i		−	0.459972i
$171$		0			0
$172$	−5.22618	−	9.05201i	−0.398493	−	0.690209i
$173$	−12.4906	+	21.6344i	−0.949645	+	1.64483i	−0.203471	+	0.979081i	$0.565222\pi$
$173$	−12.4906	+	21.6344i	−0.949645	+	1.64483i	−0.746173	+	0.665752i	$0.768111\pi$
$174$		0			0
$175$	−3.42417	−	12.7792i	−0.258843	−	0.966015i
$176$	0.128161	+	0.478302i	0.00966047	+	0.0360533i
$177$		0			0
$178$	4.78737	−	8.29197i	0.358829	−	0.621509i
$179$	5.32804	+	9.22844i	0.398236	+	0.689766i	0.993508	−	0.113759i	$-0.0362890\pi$
$179$	5.32804	+	9.22844i	0.398236	+	0.689766i	−0.595272	+	0.803524i	$0.702956\pi$
$180$		0			0
$181$		−	17.3698i		−	1.29109i	−0.763722	−	0.645545i	$-0.776630\pi$
$181$		−	17.3698i		−	1.29109i	0.763722	−	0.645545i	$-0.223370\pi$
$182$	−7.68113	−	8.66327i	−0.569363	−	0.642164i
$183$		0			0
$184$	−12.7470	−	3.41554i	−0.939720	−	0.251797i
$185$	22.9007	−	13.2217i	1.68370	−	0.972082i
$186$		0			0
$187$	6.50604	−	6.50604i	0.475769	−	0.475769i
$188$	9.84441	−	2.63780i	0.717977	−	0.192381i
$189$		0			0
$190$	5.02330	+	5.02330i	0.364429	+	0.364429i
$191$	−3.50036	−	2.02093i	−0.253277	−	0.146230i	0.367987	−	0.929831i	$-0.380047\pi$
$191$	−3.50036	−	2.02093i	−0.253277	−	0.146230i	−0.621264	+	0.783601i	$0.713381\pi$
$192$		0			0
$193$	−1.47358	+	5.49948i	−0.106071	+	0.395861i	−0.998464	−	0.0553964i	$-0.982358\pi$
$193$	−1.47358	+	5.49948i	−0.106071	+	0.395861i	0.892394	+	0.451258i	$0.149024\pi$
$194$	8.44154			0.606068
$195$		0			0
$196$	8.88290			0.634493
$197$	0.0320509	−	0.119616i	0.00228353	−	0.00852226i	−0.964775	−	0.263078i	$-0.915262\pi$
$197$	0.0320509	−	0.119616i	0.00228353	−	0.00852226i	0.967058	+	0.254555i	$0.0819291\pi$
$198$		0			0
$199$	12.0336	+	6.94758i	0.853037	+	0.492501i	0.861674	−	0.507462i	$-0.169416\pi$
$199$	12.0336	+	6.94758i	0.853037	+	0.492501i	−0.00863759	+	0.999963i	$0.502749\pi$
$200$	6.99340	+	6.99340i	0.494508	+	0.494508i
$201$		0			0
$202$	7.99897	−	2.14332i	0.562806	−	0.150803i
$203$	4.17044	−	4.17044i	0.292707	−	0.292707i
$204$		0			0
$205$	−4.76857	+	2.75313i	−0.333051	+	0.192287i
$206$	7.43987	+	1.99351i	0.518360	+	0.138894i
$207$		0			0
$208$	−0.440743	−	0.146947i	−0.0305600	−	0.0101889i
$209$			10.8988i			0.753889i
$210$		0			0
$211$	3.54501	+	6.14014i	0.244049	+	0.422705i	0.961864	−	0.273529i	$-0.0881910\pi$
$211$	3.54501	+	6.14014i	0.244049	+	0.422705i	−0.717815	+	0.696234i	$0.754858\pi$
$212$	−4.77007	+	8.26201i	−0.327610	+	0.567437i
$213$		0			0
$214$	−2.73587	−	10.2104i	−0.187020	−	0.697968i
$215$	−6.24844	−	23.3195i	−0.426140	−	1.59038i
$216$		0			0
$217$	−12.2322	+	21.1867i	−0.830373	+	1.43825i
$218$	0.336804	+	0.583361i	0.0228112	+	0.0395102i
$219$		0			0
$220$			14.1968i			0.957148i
$221$	1.73012	+	8.45756i	0.116380	+	0.568917i
$222$		0			0
$223$	16.1266	+	4.32112i	1.07992	+	0.289363i	0.754563	−	0.656228i	$-0.227849\pi$
$223$	16.1266	+	4.32112i	1.07992	+	0.289363i	0.325356	+	0.945591i	$0.394516\pi$
$224$	−18.5164	+	10.6904i	−1.23718	+	0.714284i
$225$		0			0
$226$	1.96640	−	1.96640i	0.130803	−	0.130803i
$227$	−5.91485	+	1.58488i	−0.392582	+	0.105192i	−0.449710	−	0.893175i	$-0.648473\pi$
$227$	−5.91485	+	1.58488i	−0.392582	+	0.105192i	0.0571274	+	0.998367i	$0.481806\pi$
$228$		0			0
$229$	−10.8935	−	10.8935i	−0.719864	−	0.719864i	0.248713	−	0.968577i	$-0.419992\pi$
$229$	−10.8935	−	10.8935i	−0.719864	−	0.719864i	−0.968577	+	0.248713i	$0.919992\pi$
$230$	−10.2258	−	5.90389i	−0.674272	−	0.389291i
$231$		0			0
$232$	−1.14113	+	4.25877i	−0.0749192	+	0.279602i
$233$	6.63769			0.434850			0.217425	−	0.976077i	$-0.430234\pi$
$233$	6.63769			0.434850			0.217425	+	0.976077i	$0.430234\pi$
$234$		0			0
$235$	23.5400			1.53558
$236$	3.81313	−	14.2308i	0.248214	−	0.926346i
$237$		0			0
$238$	6.65841	+	3.84424i	0.431601	+	0.249185i
$239$	10.5799	+	10.5799i	0.684354	+	0.684354i	0.960978	−	0.276624i	$-0.0892158\pi$
$239$	10.5799	+	10.5799i	0.684354	+	0.684354i	−0.276624	+	0.960978i	$0.589216\pi$
$240$		0			0
$241$	18.2954	−	4.90225i	1.17851	−	0.315782i	0.384176	−	0.923260i	$-0.374485\pi$
$241$	18.2954	−	4.90225i	1.17851	−	0.315782i	0.794336	+	0.607478i	$0.207819\pi$
$242$	2.28451	−	2.28451i	0.146854	−	0.146854i
$243$		0			0
$244$	−9.05661	+	5.22884i	−0.579790	+	0.334742i
$245$	19.8180	+	5.31021i	1.26612	+	0.339257i
$246$		0			0
$247$	−8.53314	−	5.63487i	−0.542951	−	0.358538i
$248$		−	18.2885i		−	1.16132i
$249$		0			0
$250$	−1.83747	−	3.18259i	−0.116212	−	0.201285i
$251$	−0.192472	+	0.333372i	−0.0121488	+	0.0210423i	−0.872036	−	0.489442i	$-0.837200\pi$
$251$	−0.192472	+	0.333372i	−0.0121488	+	0.0210423i	0.859887	+	0.510484i	$0.170534\pi$
$252$		0			0
$253$	−4.68857	−	17.4980i	−0.294768	−	1.10009i
$254$	0.718415	+	2.68116i	0.0450774	+	0.168231i
$255$		0			0
$256$	7.82874	−	13.5598i	0.489296	−	0.847485i
$257$	−4.94982	−	8.57334i	−0.308761	−	0.534790i	0.669330	−	0.742965i	$-0.266581\pi$
$257$	−4.94982	−	8.57334i	−0.308761	−	0.534790i	−0.978092	+	0.208175i	$0.933248\pi$
$258$		0			0
$259$			33.9003i			2.10646i
$260$	−11.1152	−	7.33996i	−0.689338	−	0.455205i
$261$		0			0
$262$	−12.8536	−	3.44412i	−0.794101	−	0.212779i
$263$	−13.8582	+	8.00104i	−0.854534	+	0.493365i	−0.862178	−	0.506605i	$-0.830900\pi$
$263$	−13.8582	+	8.00104i	−0.854534	+	0.493365i	0.00764424	+	0.999971i	$0.497567\pi$
$264$		0			0
$265$	−15.5812	+	15.5812i	−0.957145	+	0.957145i
$266$	−8.79696	+	2.35714i	−0.539376	+	0.144525i
$267$		0			0
$268$	−7.80763	−	7.80763i	−0.476927	−	0.476927i
$269$	−7.23225	−	4.17554i	−0.440958	−	0.254587i	0.263046	−	0.964783i	$-0.415273\pi$
$269$	−7.23225	−	4.17554i	−0.440958	−	0.254587i	−0.704004	+	0.710196i	$0.748606\pi$
$270$		0			0
$271$	−3.89219	+	14.5258i	−0.236433	+	0.882382i	0.741064	+	0.671434i	$0.234322\pi$
$271$	−3.89219	+	14.5258i	−0.236433	+	0.882382i	−0.977497	+	0.210947i	$0.932345\pi$
$272$	0.308516			0.0187065
$273$		0			0
$274$	−16.0161			−0.967569
$275$	−3.51382	+	13.1138i	−0.211891	+	0.790790i
$276$		0			0
$277$	−7.76356	−	4.48229i	−0.466467	−	0.269315i	0.248293	−	0.968685i	$-0.420131\pi$
$277$	−7.76356	−	4.48229i	−0.466467	−	0.269315i	−0.714760	+	0.699370i	$0.753464\pi$
$278$	3.60043	+	3.60043i	0.215940	+	0.215940i
$279$		0			0
$280$	−29.5801	+	7.92595i	−1.76775	+	0.473666i
$281$	14.4402	−	14.4402i	0.861428	−	0.861428i	−0.130076	−	0.991504i	$-0.541522\pi$
$281$	14.4402	−	14.4402i	0.861428	−	0.861428i	0.991504	+	0.130076i	$0.0415222\pi$
$282$		0			0
$283$	−9.61260	+	5.54984i	−0.571410	+	0.329904i	−0.757712	−	0.652589i	$-0.773683\pi$
$283$	−9.61260	+	5.54984i	−0.571410	+	0.329904i	0.186302	+	0.982492i	$0.440350\pi$
$284$	−13.2160	−	3.54123i	−0.784228	−	0.210133i
$285$		0			0
$286$	2.38117	+	11.6402i	0.140801	+	0.688297i
$287$		−	7.05898i		−	0.416678i
$288$		0			0
$289$	5.63371	+	9.75787i	0.331395	+	0.573992i
$290$	−1.97249	+	3.41646i	−0.115829	+	0.200621i
$291$		0			0
$292$	3.30064	+	12.3182i	0.193155	+	0.720866i
$293$	5.12188	+	19.1151i	0.299223	+	1.11672i	0.937805	+	0.347162i	$0.112855\pi$
$293$	5.12188	+	19.1151i	0.299223	+	1.11672i	−0.638582	+	0.769554i	$0.720479\pi$
$294$		0			0
$295$	17.0144	−	29.4698i	0.990616	−	1.71580i
$296$	−12.6712	−	21.9471i	−0.736498	−	1.27565i
$297$		0			0
$298$		−	2.14022i		−	0.123980i
$299$	16.1239	+	5.37585i	0.932471	+	0.310893i
$300$		0			0
$301$	29.8953	+	8.01043i	1.72314	+	0.461713i
$302$	−0.328608	+	0.189722i	−0.0189093	+	0.0109173i
$303$		0			0
$304$	−0.258411	+	0.258411i	−0.0148209	+	0.0148209i
$305$	−23.3313	+	6.25161i	−1.33595	+	0.357966i
$306$		0			0
$307$	16.9419	+	16.9419i	0.966928	+	0.966928i	0.999470	−	0.0325425i	$-0.0103604\pi$
$307$	16.9419	+	16.9419i	0.966928	+	0.966928i	−0.0325425	+	0.999470i	$0.510360\pi$
$308$	−15.7618	−	9.10007i	−0.898111	−	0.518525i
$309$		0			0
$310$	4.23524	−	15.8061i	0.240545	−	0.897727i
$311$	−12.2575			−0.695060			−0.347530	−	0.937669i	$-0.612979\pi$
$311$	−12.2575			−0.695060			−0.347530	+	0.937669i	$0.612979\pi$
$312$		0			0
$313$	−4.70672			−0.266040			−0.133020	−	0.991113i	$-0.542467\pi$
$313$	−4.70672			−0.266040			−0.133020	+	0.991113i	$0.542467\pi$
$314$	−2.73734	+	10.2159i	−0.154477	+	0.576517i
$315$		0			0
$316$	−11.8392	−	6.83537i	−0.666007	−	0.384520i
$317$	12.7204	+	12.7204i	0.714449	+	0.714449i	0.967463	−	0.253014i	$-0.0814217\pi$
$317$	12.7204	+	12.7204i	0.714449	+	0.714449i	−0.253014	+	0.967463i	$0.581422\pi$
$318$		0			0
$319$	−5.84608	+	1.56645i	−0.327318	+	0.0877045i
$320$	9.58019	−	9.58019i	0.535549	−	0.535549i
$321$		0			0
$322$	13.1094	−	7.56872i	0.730559	−	0.421788i
$323$	6.55908	+	1.75750i	0.364957	+	0.0977900i
$324$		0			0
$325$	−8.45059	−	9.53112i	−0.468754	−	0.528692i
$326$			1.48060i			0.0820029i
$327$		0			0
$328$	2.63849	+	4.57000i	0.145686	+	0.252336i
$329$	−15.0890	+	26.1350i	−0.831885	+	1.44087i
$330$		0			0
$331$	3.94967	+	14.7404i	0.217093	+	0.810204i	0.985419	+	0.170145i	$0.0544234\pi$
$331$	3.94967	+	14.7404i	0.217093	+	0.810204i	−0.768326	+	0.640059i	$0.778910\pi$
$332$	−4.76645	−	17.7886i	−0.261593	−	0.976277i
$333$		0			0
$334$	5.45061	−	9.44074i	0.298244	−	0.516574i
$335$	−12.7516	−	22.0864i	−0.696695	−	1.20671i
$336$		0			0
$337$		−	24.0050i		−	1.30764i	−0.756652	−	0.653818i	$-0.773166\pi$
$337$		−	24.0050i		−	1.30764i	0.756652	−	0.653818i	$-0.226834\pi$
$338$	−10.3447	−	4.15383i	−0.562675	−	0.225938i
$339$		0			0
$340$	8.54384	+	2.28932i	0.463355	+	0.124156i
$341$	21.7414	−	12.5524i	1.17736	−	0.679752i
$342$		0			0
$343$	−0.0628530	+	0.0628530i	−0.00339374	+	0.00339374i
$344$	−22.3485	+	5.98825i	−1.20495	+	0.322865i
$345$		0			0
$346$	15.1472	+	15.1472i	0.814318	+	0.814318i
$347$	−29.0822	−	16.7906i	−1.56121	−	0.901367i	−0.997135	−	0.0756449i	$-0.975898\pi$
$347$	−29.0822	−	16.7906i	−1.56121	−	0.901367i	−0.564078	−	0.825722i	$-0.690768\pi$
$348$		0			0
$349$	1.27507	−	4.75862i	0.0682529	−	0.254723i	−0.923366	−	0.383921i	$-0.874573\pi$
$349$	1.27507	−	4.75862i	0.0682529	−	0.254723i	0.991619	+	0.129198i	$0.0412402\pi$
$350$	−11.3447			−0.606398
$351$		0			0
$352$	21.9407			1.16944
$353$	−7.67945	+	28.6601i	−0.408736	+	1.52542i	0.388324	+	0.921523i	$0.373054\pi$
$353$	−7.67945	+	28.6601i	−0.408736	+	1.52542i	−0.797060	+	0.603900i	$0.793613\pi$
$354$		0			0
$355$	−27.3684	−	15.8011i	−1.45256	−	0.838637i
$356$	9.98541	+	9.98541i	0.529225	+	0.529225i
$357$		0			0
$358$	8.82621	−	2.36498i	0.466480	−	0.124993i
$359$	−5.65693	+	5.65693i	−0.298561	+	0.298561i	−0.840450	−	0.541889i	$-0.817709\pi$
$359$	−5.65693	+	5.65693i	−0.298561	+	0.298561i	0.541889	+	0.840450i	$0.317709\pi$
$360$		0			0
$361$	9.48856	−	5.47822i	0.499398	−	0.288327i
$362$	−14.3871	−	3.85501i	−0.756168	−	0.202615i
$363$		0			0
$364$	15.2739	−	7.63566i	0.800570	−	0.400218i
$365$			29.4553i			1.54176i
$366$		0			0
$367$	3.95028	+	6.84208i	0.206203	+	0.357154i	0.950515	−	0.310678i	$-0.100556\pi$
$367$	3.95028	+	6.84208i	0.206203	+	0.357154i	−0.744312	+	0.667832i	$0.767223\pi$
$368$	0.303710	−	0.526042i	0.0158320	−	0.0274218i
$369$		0			0
$370$	−5.86878	−	21.9026i	−0.305104	−	1.13866i
$371$	−7.31133	−	27.2863i	−0.379585	−	1.41663i
$372$		0			0
$373$	−8.34242	+	14.4495i	−0.431954	+	0.748166i	−0.997042	−	0.0768648i	$-0.975509\pi$
$373$	−8.34242	+	14.4495i	−0.431954	+	0.748166i	0.565088	+	0.825031i	$0.308842\pi$
$374$	−3.94489	−	6.83275i	−0.203985	−	0.353313i
$375$		0			0
$376$		−	22.5598i		−	1.16343i
$377$	1.79607	−	5.38701i	0.0925025	−	0.277445i
$378$		0			0
$379$	−9.55825	−	2.56113i	−0.490974	−	0.131556i	0.00483368	−	0.999988i	$-0.498461\pi$
$379$	−9.55825	−	2.56113i	−0.490974	−	0.131556i	−0.495808	+	0.868432i	$0.665128\pi$
$380$	−9.07379	+	5.23876i	−0.465476	+	0.268743i
$381$		0			0
$382$	−2.45076	+	2.45076i	−0.125392	+	0.125392i
$383$	19.8396	−	5.31600i	1.01375	−	0.271635i	0.286557	−	0.958063i	$-0.407489\pi$
$383$	19.8396	−	5.31600i	1.01375	−	0.271635i	0.727197	+	0.686428i	$0.240823\pi$
$384$		0			0
$385$	−29.7249	−	29.7249i	−1.51492	−	1.51492i
$386$	4.22806	+	2.44107i	0.215203	+	0.124247i
$387$		0			0
$388$	−3.22234	+	12.0259i	−0.163590	+	0.610525i
$389$	−15.8332			−0.802777			−0.401388	−	0.915908i	$-0.631472\pi$
$389$	−15.8332			−0.802777			−0.401388	+	0.915908i	$0.631472\pi$
$390$		0			0
$391$	−11.2866			−0.570788
$392$	5.08909	−	18.9928i	0.257038	−	0.959279i
$393$		0			0
$394$	−0.0919618	−	0.0530942i	−0.00463297	−	0.00267485i
$395$	−22.3274	−	22.3274i	−1.12341	−	1.12341i
$396$		0			0
$397$	−20.7258	+	5.55347i	−1.04020	+	0.278721i	−0.738196	−	0.674586i	$-0.764322\pi$
$397$	−20.7258	+	5.55347i	−1.04020	+	0.278721i	−0.302003	+	0.953307i	$0.597655\pi$
$398$	8.42523	−	8.42523i	0.422318	−	0.422318i
$399$		0			0
$400$	−0.394239	+	0.227614i	−0.0197119	+	0.0113807i
$401$	−13.8013	−	3.69806i	−0.689206	−	0.184672i	−0.102815	−	0.994701i	$-0.532785\pi$
$401$	−13.8013	−	3.69806i	−0.689206	−	0.184672i	−0.586391	+	0.810028i	$0.699452\pi$
$402$		0			0
$403$	−1.41285	+	23.5120i	−0.0703791	+	1.17122i
$404$			12.2136i			0.607650i
$405$		0			0
$406$	−2.52871	−	4.37986i	−0.125498	−	0.217369i
$407$	17.3939	−	30.1272i	0.862185	−	1.49335i
$408$		0			0
$409$	4.65950	+	17.3895i	0.230397	+	0.859854i	0.980170	+	0.198159i	$0.0634961\pi$
$409$	4.65950	+	17.3895i	0.230397	+	0.859854i	−0.749773	+	0.661695i	$0.769837\pi$
$410$	1.22204	+	4.56073i	0.0603524	+	0.225238i
$411$		0			0
$412$	−5.67996	+	9.83798i	−0.279831	+	0.484682i
$413$	21.8123	+	37.7799i	1.07331	+	1.85903i
$414$		0			0
$415$		−	42.5363i		−	2.08802i
$416$	−11.3436	+	17.1782i	−0.556168	+	0.842231i
$417$		0			0
$418$	9.02729	+	2.41885i	0.441539	+	0.118310i
$419$	2.77094	−	1.59980i	0.135369	−	0.0781554i	−0.430786	−	0.902454i	$-0.641764\pi$
$419$	2.77094	−	1.59980i	0.135369	−	0.0781554i	0.566155	+	0.824299i	$0.308430\pi$
$420$		0			0
$421$	−9.48739	+	9.48739i	−0.462387	+	0.462387i	−0.899437	−	0.437050i	$-0.856023\pi$
$421$	−9.48739	+	9.48739i	−0.462387	+	0.462387i	0.437050	+	0.899437i	$0.356023\pi$
$422$	5.87252	−	1.57354i	0.285870	−	0.0765986i
$423$		0			0
$424$	14.9324	+	14.9324i	0.725181	+	0.725181i
$425$	7.32543	+	4.22934i	0.355335	+	0.205153i
$426$		0			0
$427$	8.01450	−	29.9105i	0.387849	−	1.44747i
$428$	15.5902			0.753582
$429$		0			0
$430$	−20.7018			−0.998330
$431$	−1.62474	+	6.06362i	−0.0782611	+	0.292075i	−0.993953	−	0.109807i	$-0.964977\pi$
$431$	−1.62474	+	6.06362i	−0.0782611	+	0.292075i	0.915692	+	0.401881i	$0.131644\pi$
$432$		0			0
$433$	23.2783	+	13.4397i	1.11868	+	0.645872i	0.941064	−	0.338228i	$-0.109827\pi$
$433$	23.2783	+	13.4397i	1.11868	+	0.645872i	0.177618	+	0.984099i	$0.443161\pi$
$434$	14.8337	+	14.8337i	0.712043	+	0.712043i
$435$		0			0
$436$	−0.959631	+	0.257132i	−0.0459580	+	0.0123144i
$437$	9.45359	−	9.45359i	0.452227	−	0.452227i
$438$		0			0
$439$	−19.5214	+	11.2707i	−0.931706	+	0.537921i	−0.887351	−	0.461095i	$-0.847457\pi$
$439$	−19.5214	+	11.2707i	−0.931706	+	0.537921i	−0.0443556	+	0.999016i	$0.514123\pi$
$440$	30.3545	+	8.13347i	1.44710	+	0.387748i
$441$		0			0
$442$	7.38920	+	0.444021i	0.351468	+	0.0211199i
$443$			6.98762i			0.331992i	0.986126	+	0.165996i	$0.0530838\pi$
$443$			6.98762i			0.331992i	−0.986126	+	0.165996i	$0.946916\pi$
$444$		0			0
$445$	16.3084	+	28.2470i	0.773093	+	1.33904i
$446$	7.15818	−	12.3983i	0.338950	−	0.587078i
$447$		0			0
$448$	4.49542	+	16.7771i	0.212388	+	0.792644i
$449$	2.44458	+	9.12331i	0.115367	+	0.430556i	0.999314	−	0.0370313i	$-0.0117901\pi$
$449$	2.44458	+	9.12331i	0.115367	+	0.430556i	−0.883947	+	0.467587i	$0.845123\pi$
$450$		0			0
$451$	−3.62190	+	6.27331i	−0.170549	+	0.295399i
$452$	2.05074	+	3.55199i	0.0964588	+	0.167072i
$453$		0			0
$454$			5.25089i			0.246436i
$455$	38.6411	−	7.90460i	1.81152	−	0.370574i
$456$		0			0
$457$	−11.1523	−	2.98826i	−0.521684	−	0.139785i	−0.0116383	−	0.999932i	$-0.503705\pi$
$457$	−11.1523	−	2.98826i	−0.521684	−	0.139785i	−0.510045	+	0.860148i	$0.670371\pi$
$458$	−11.4405	+	6.60520i	−0.534582	+	0.308641i
$459$		0			0
$460$	12.3142	−	12.3142i	0.574153	−	0.574153i
$461$	−0.328123	+	0.0879202i	−0.0152822	+	0.00409485i	−0.266452	−	0.963848i	$-0.585851\pi$
$461$	−0.328123	+	0.0879202i	−0.0152822	+	0.00409485i	0.251170	+	0.967943i	$0.419185\pi$
$462$		0			0
$463$	−18.2604	−	18.2604i	−0.848631	−	0.848631i	0.141332	−	0.989962i	$-0.454862\pi$
$463$	−18.2604	−	18.2604i	−0.848631	−	0.848631i	−0.989962	+	0.141332i	$0.954862\pi$
$464$	−0.175751	−	0.101470i	−0.00815902	−	0.00471061i
$465$		0			0
$466$	1.47315	−	5.49786i	0.0682423	−	0.254684i
$467$	21.8775			1.01237			0.506185	−	0.862425i	$-0.331055\pi$
$467$	21.8775			1.01237			0.506185	+	0.862425i	$0.331055\pi$
$468$		0			0
$469$	32.6948			1.50971
$470$	5.22439	−	19.4977i	0.240983	−	0.899362i
$471$		0			0
$472$	−28.2427	−	16.3059i	−1.29997	−	0.750540i
$473$	−22.4579	−	22.4579i	−1.03262	−	1.03262i
$474$		0			0
$475$	−9.67821	+	2.59327i	−0.444067	+	0.118987i
$476$	−8.01823	+	8.01823i	−0.367515	+	0.367515i
$477$		0			0
$478$	11.1111	−	6.41501i	0.508211	−	0.293416i
$479$	12.2273	+	3.27631i	0.558682	+	0.149698i	0.527101	−	0.849803i	$-0.323279\pi$
$479$	12.2273	+	3.27631i	0.558682	+	0.149698i	0.0315811	+	0.999501i	$0.489946\pi$
$480$		0			0
$481$	14.5949	+	29.1946i	0.665468	+	1.33116i
$482$		−	16.2417i		−	0.739790i
$483$		0			0
$484$	2.38250	+	4.12661i	0.108295	+	0.187573i
$485$	−14.3783	+	24.9039i	−0.652883	+	1.13083i
$486$		0			0
$487$	9.24551	+	34.5047i	0.418954	+	1.56356i	0.776781	+	0.629770i	$0.216851\pi$
$487$	9.24551	+	34.5047i	0.418954	+	1.56356i	−0.357827	+	0.933788i	$0.616482\pi$
$488$	5.99129	+	22.3598i	0.271213	+	1.01218i
$489$		0			0
$490$	8.79668	−	15.2363i	0.397393	−	0.688305i
$491$	−2.07552	−	3.59490i	−0.0936668	−	0.162236i	0.815385	−	0.578920i	$-0.196525\pi$
$491$	−2.07552	−	3.59490i	−0.0936668	−	0.162236i	−0.909051	+	0.416684i	$0.863192\pi$
$492$		0			0
$493$			3.77086i			0.169831i
$494$	−6.56106	+	5.81724i	−0.295196	+	0.261730i
$495$		0			0
$496$	0.813105	+	0.217871i	0.0365095	+	0.00978269i
$497$	35.0860	−	20.2569i	1.57382	−	0.908646i
$498$		0			0
$499$	8.80069	−	8.80069i	0.393973	−	0.393973i	−0.482128	−	0.876101i	$-0.660136\pi$
$499$	8.80069	−	8.80069i	0.393973	−	0.393973i	0.876101	+	0.482128i	$0.160136\pi$
$500$	5.23538	−	1.40281i	0.234133	−	0.0627358i
$501$		0			0
$502$	0.233408	+	0.233408i	0.0104175	+	0.0104175i
$503$	0.683869	+	0.394832i	0.0304922	+	0.0176047i	0.515169	−	0.857089i	$-0.327729\pi$
$503$	0.683869	+	0.394832i	0.0304922	+	0.0176047i	−0.484676	+	0.874694i	$0.661063\pi$
$504$		0			0
$505$	−7.30132	+	27.2489i	−0.324904	+	1.21256i
$506$	−15.5338			−0.690561
$507$		0			0
$508$	−4.09386			−0.181636
$509$	−3.15103	+	11.7598i	−0.139667	+	0.521244i	0.860268	+	0.509842i	$0.170296\pi$
$509$	−3.15103	+	11.7598i	−0.139667	+	0.521244i	−0.999935	+	0.0114022i	$0.996370\pi$
$510$		0			0
$511$	−32.7023	−	18.8807i	−1.44666	−	0.835231i
$512$	1.03036	+	1.03036i	0.0455357	+	0.0455357i
$513$		0			0
$514$	−8.19967	+	2.19709i	−0.361672	+	0.0969097i
$515$	−18.5533	+	18.5533i	−0.817556	+	0.817556i
$516$		0			0
$517$	26.8192	−	15.4841i	1.17951	−	0.680989i
$518$	28.0789	+	7.52372i	1.23372	+	0.330573i
$519$		0			0
$520$	−22.0618	+	19.5607i	−0.967473	+	0.857792i
$521$		−	3.69559i		−	0.161907i	−0.996718	−	0.0809535i	$-0.974203\pi$
$521$		−	3.69559i		−	0.161907i	0.996718	−	0.0809535i	$-0.0257965\pi$
$522$		0			0
$523$	−18.8740	−	32.6907i	−0.825302	−	1.42947i	−0.901688	−	0.432387i	$-0.857671\pi$
$523$	−18.8740	−	32.6907i	−0.825302	−	1.42947i	0.0763859	−	0.997078i	$-0.475662\pi$
$524$	9.81310	−	16.9968i	0.428687	−	0.742508i
$525$		0			0
$526$	3.55145	+	13.2542i	0.154851	+	0.577910i
$527$	−4.04830	−	15.1085i	−0.176347	−	0.658135i
$528$		0			0
$529$	0.389195	−	0.674106i	0.0169215	−	0.0293090i
$530$	9.44754	+	16.3636i	0.410375	+	0.710790i
$531$		0			0
$532$		−	13.4321i		−	0.582354i
$533$	−3.03905	−	6.07913i	−0.131636	−	0.263316i
$534$		0			0
$535$	34.7822	+	9.31985i	1.50376	+	0.402932i
$536$	−21.1667	+	12.2206i	−0.914264	+	0.527851i
$537$		0			0
$538$	−5.06362	+	5.06362i	−0.218308	+	0.218308i
$539$	26.0716	−	6.98587i	1.12299	−	0.300903i
$540$		0			0
$541$	−18.1983	−	18.1983i	−0.782406	−	0.782406i	0.197830	−	0.980236i	$-0.436611\pi$
$541$	−18.1983	−	18.1983i	−0.782406	−	0.782406i	−0.980236	+	0.197830i	$0.936611\pi$
$542$	11.1676	+	6.44763i	0.479691	+	0.276950i
$543$		0			0
$544$	3.53805	−	13.2042i	0.151693	−	0.566125i
$545$	−2.29468			−0.0982931
$546$		0			0
$547$	19.0359			0.813915			0.406957	−	0.913447i	$-0.366590\pi$
$547$	19.0359			0.813915			0.406957	+	0.913447i	$0.366590\pi$
$548$	6.11374	−	22.8168i	0.261166	−	0.974686i
$549$		0			0
$550$	10.0820	+	5.82085i	0.429898	+	0.248202i
$551$	−3.15845	−	3.15845i	−0.134554	−	0.134554i
$552$		0			0
$553$	39.1004	−	10.4769i	1.66272	−	0.445524i
$554$	−5.43561	+	5.43561i	−0.230937	+	0.230937i
$555$		0			0
$556$	−6.50360	+	3.75486i	−0.275814	+	0.159241i
$557$	−34.7408	−	9.30877i	−1.47201	−	0.394425i	−0.568393	−	0.822757i	$-0.692435\pi$
$557$	−34.7408	−	9.30877i	−1.47201	−	0.394425i	−0.903621	+	0.428332i	$0.859101\pi$
$558$		0			0
$559$	29.1943	−	5.97212i	1.23479	−	0.252594i
$560$		−	1.40955i		−	0.0595644i
$561$		0			0
$562$	−8.75568	−	15.1653i	−0.369336	−	0.639709i
$563$	−21.3875	+	37.0442i	−0.901374	+	1.56122i	−0.0756612	+	0.997134i	$0.524107\pi$
$563$	−21.3875	+	37.0442i	−0.901374	+	1.56122i	−0.825712	+	0.564091i	$0.809227\pi$
$564$		0			0
$565$	2.45187	+	9.15052i	0.103151	+	0.384965i
$566$	2.46343	+	9.19363i	0.103545	+	0.386437i
$567$		0			0
$568$	−15.1432	+	26.2287i	−0.635393	+	1.10053i
$569$	0.541703	+	0.938257i	0.0227094	+	0.0393338i	0.877157	−	0.480204i	$-0.159437\pi$
$569$	0.541703	+	0.938257i	0.0227094	+	0.0393338i	−0.854447	+	0.519538i	$0.826104\pi$
$570$		0			0
$571$			1.13164i			0.0473579i	0.999720	+	0.0236789i	$0.00753794\pi$
$571$			1.13164i			0.0473579i	−0.999720	+	0.0236789i	$0.992462\pi$
$572$	−17.4917	−	1.05109i	−0.731365	−	0.0439481i
$573$		0			0
$574$	−5.84681	−	1.56665i	−0.244041	−	0.0653906i
$575$	14.4227	−	8.32693i	0.601467	−	0.347257i
$576$		0			0
$577$	−8.17115	+	8.17115i	−0.340169	+	0.340169i	−0.856431	−	0.516262i	$-0.827323\pi$
$577$	−8.17115	+	8.17115i	−0.340169	+	0.340169i	0.516262	+	0.856431i	$0.327323\pi$
$578$	9.33257	−	2.50065i	0.388184	−	0.104013i
$579$		0			0
$580$	−4.11419	−	4.11419i	−0.170832	−	0.170832i
$581$	47.2253	+	27.2655i	1.95923	+	1.13116i
$582$		0			0
$583$	−7.50276	+	28.0007i	−0.310732	+	1.15967i
$584$	28.2287			1.16811
$585$		0			0
$586$	16.9694			0.700999
$587$	−0.214121	+	0.799109i	−0.00883771	+	0.0329828i	−0.970204	−	0.242290i	$-0.922101\pi$
$587$	−0.214121	+	0.799109i	−0.00883771	+	0.0329828i	0.961366	+	0.275273i	$0.0887681\pi$
$588$		0			0
$589$	16.0456	+	9.26393i	0.661147	+	0.381713i
$590$	−20.6331	−	20.6331i	−0.849451	−	0.849451i
$591$		0			0
$592$	1.12672	−	0.301904i	0.0463080	−	0.0124082i
$593$	22.3242	−	22.3242i	0.916745	−	0.916745i	−0.0800462	−	0.996791i	$-0.525507\pi$
$593$	22.3242	−	22.3242i	0.916745	−	0.916745i	0.996791	+	0.0800462i	$0.0255068\pi$
$594$		0			0
$595$	−22.6822	+	13.0956i	−0.929880	+	0.536866i
$596$	3.04899	+	0.816974i	0.124891	+	0.0334646i
$597$		0			0
$598$	8.03120	−	12.1620i	0.328420	−	0.497342i
$599$			2.87145i			0.117324i	0.998278	+	0.0586621i	$0.0186835\pi$
$599$			2.87145i			0.117324i	−0.998278	+	0.0586621i	$0.981317\pi$
$600$		0			0
$601$	−12.7301	−	22.0492i	−0.519273	−	0.899407i	−0.999749	−	0.0223993i	$-0.992869\pi$
$601$	−12.7301	−	22.0492i	−0.519273	−	0.899407i	0.480476	−	0.877008i	$-0.340464\pi$
$602$	13.2697	−	22.9839i	0.540834	−	0.936753i
$603$		0			0
$604$	−0.144843	−	0.540561i	−0.00589358	−	0.0219951i
$605$	2.84852	+	10.6308i	0.115809	+	0.432205i
$606$		0			0
$607$	−1.00317	+	1.73755i	−0.0407175	+	0.0705248i	−0.885666	−	0.464323i	$-0.846298\pi$
$607$	−1.00317	+	1.73755i	−0.0407175	+	0.0705248i	0.844948	+	0.534848i	$0.179631\pi$
$608$	8.09631	+	14.0232i	0.328349	+	0.568717i
$609$		0			0
$610$			20.7123i			0.838618i
$611$	−1.74283	+	29.0034i	−0.0705073	+	1.17335i
$612$		0			0
$613$	−45.5010	−	12.1920i	−1.83777	−	0.492429i	−0.839099	−	0.543979i	$-0.816917\pi$
$613$	−45.5010	−	12.1920i	−1.83777	−	0.492429i	−0.998670	+	0.0515496i	$0.983584\pi$
$614$	17.7927	−	10.2726i	0.718055	−	0.414569i
$615$		0			0
$616$	−28.4872	+	28.4872i	−1.14778	+	1.14778i
$617$	41.3793	−	11.0876i	1.66587	−	0.446368i	0.701877	−	0.712298i	$-0.252345\pi$
$617$	41.3793	−	11.0876i	1.66587	−	0.446368i	0.963993	+	0.265929i	$0.0856788\pi$
$618$		0			0
$619$	7.87348	+	7.87348i	0.316462	+	0.316462i	0.847407	−	0.530945i	$-0.178163\pi$
$619$	7.87348	+	7.87348i	0.316462	+	0.316462i	−0.530945	+	0.847407i	$0.678163\pi$
$620$	20.9009	+	12.0672i	0.839402	+	0.484629i
$621$		0			0
$622$	−2.72039	+	10.1526i	−0.109078	+	0.407084i
$623$	−41.8144			−1.67526
$624$		0			0
$625$	30.1832			1.20733
$626$	−1.04459	+	3.89848i	−0.0417504	+	0.155815i
$627$		0			0
$628$	−13.5088	−	7.79932i	−0.539061	−	0.311227i
$629$	−15.3261	−	15.3261i	−0.611092	−	0.611092i
$630$		0			0
$631$	−30.6521	+	8.21321i	−1.22024	+	0.326963i	−0.810772	−	0.585362i	$-0.800953\pi$
$631$	−30.6521	+	8.21321i	−1.22024	+	0.326963i	−0.409469	+	0.912324i	$0.634286\pi$
$632$	−21.3977	+	21.3977i	−0.851153	+	0.851153i
$633$		0			0
$634$	13.3592	−	7.71292i	0.530561	−	0.306319i
$635$	−9.13351	−	2.44732i	−0.362452	−	0.0971188i
$636$		0			0
$637$	−8.00991	+	24.0243i	−0.317364	+	0.951879i
$638$			5.18984i			0.205468i
$639$		0			0
$640$	10.8690	+	18.8256i	0.429635	+	0.744149i
$641$	21.4777	−	37.2004i	0.848317	−	1.46933i	−0.0343914	−	0.999408i	$-0.510949\pi$
$641$	21.4777	−	37.2004i	0.848317	−	1.46933i	0.882709	−	0.469920i	$-0.155717\pi$
$642$		0			0
$643$	−7.89423	−	29.4617i	−0.311318	−	1.16185i	−0.927369	−	0.374148i	$-0.877935\pi$
$643$	−7.89423	−	29.4617i	−0.311318	−	1.16185i	0.616051	−	0.787706i	$-0.288732\pi$
$644$	5.77833	+	21.5650i	0.227698	+	0.849781i
$645$		0			0
$646$	2.91140	−	5.04270i	0.114548	−	0.198402i
$647$	−5.21299	−	9.02916i	−0.204944	−	0.354973i	0.745171	−	0.666873i	$-0.232368\pi$
$647$	−5.21299	−	9.02916i	−0.204944	−	0.354973i	−0.950115	+	0.311901i	$0.899034\pi$
$648$		0			0
$649$		−	44.7667i		−	1.75725i
$650$	−9.76993	+	4.88414i	−0.383208	+	0.191572i
$651$		0			0
$652$	−2.10929	−	0.565181i	−0.0826060	−	0.0221342i
$653$	−18.8372	+	10.8757i	−0.737157	+	0.425598i	−0.821035	−	0.570878i	$-0.806603\pi$
$653$	−18.8372	+	10.8757i	−0.737157	+	0.425598i	0.0838777	+	0.996476i	$0.473269\pi$
$654$		0			0
$655$	32.0540	−	32.0540i	1.25245	−	1.25245i
$656$	−0.234615	+	0.0628649i	−0.00916017	+	0.00245446i
$657$		0			0
$658$	18.2982	+	18.2982i	0.713339	+	0.713339i
$659$	4.86607	+	2.80943i	0.189555	+	0.109440i	0.591774	−	0.806104i	$-0.298428\pi$
$659$	4.86607	+	2.80943i	0.189555	+	0.109440i	−0.402219	+	0.915543i	$0.631761\pi$
$660$		0			0
$661$	−6.62357	+	24.7195i	−0.257627	+	0.961477i	0.708983	+	0.705225i	$0.249154\pi$
$661$	−6.62357	+	24.7195i	−0.257627	+	0.961477i	−0.966610	+	0.256252i	$0.917512\pi$
$662$	13.0857			0.508591
$663$		0			0
$664$	−40.7650			−1.58199
$665$	8.02971	−	29.9673i	0.311379	−	1.16208i
$666$		0			0
$667$	6.42959	+	3.71212i	0.248955	+	0.143734i
$668$	11.3688	+	11.3688i	0.439871	+	0.439871i
$669$		0			0
$670$	−21.1238	+	5.66010i	−0.816083	+	0.218669i
$671$	−22.4693	+	22.4693i	−0.867418	+	0.867418i
$672$		0			0
$673$	−13.6958	+	7.90729i	−0.527935	+	0.304804i	−0.740175	−	0.672414i	$-0.765257\pi$
$673$	−13.6958	+	7.90729i	−0.527935	+	0.304804i	0.212240	+	0.977218i	$0.431924\pi$
$674$	−19.8828	−	5.32759i	−0.765859	−	0.205211i
$675$		0			0
$676$	9.86641	−	13.1515i	0.379477	−	0.505828i
$677$		−	28.5914i		−	1.09886i	−0.835541	−	0.549429i	$-0.814845\pi$
$677$		−	28.5914i		−	1.09886i	0.835541	−	0.549429i	$-0.185155\pi$
$678$		0			0
$679$	−18.4328	−	31.9265i	−0.707385	−	1.22523i
$680$	9.78968	−	16.9562i	0.375417	−	0.650242i
$681$		0			0
$682$	−5.57169	−	20.7938i	−0.213351	−	0.796236i
$683$	6.90821	+	25.7818i	0.264335	+	0.986512i	0.962656	+	0.270727i	$0.0872642\pi$
$683$	6.90821	+	25.7818i	0.264335	+	0.986512i	−0.698321	+	0.715785i	$0.746069\pi$
$684$		0			0
$685$	27.2798	−	47.2501i	1.04231	−	1.80533i
$686$	0.0381105	+	0.0660092i	0.00145506	+	0.00252024i
$687$		0			0
$688$		−	1.06495i		−	0.0406009i
$689$	−18.0438	−	20.3510i	−0.687414	−	0.775310i
$690$		0			0
$691$	3.32273	+	0.890322i	0.126403	+	0.0338695i	0.321466	−	0.946921i	$-0.395825\pi$
$691$	3.32273	+	0.890322i	0.126403	+	0.0338695i	−0.195063	+	0.980791i	$0.562491\pi$
$692$	−27.3610	+	15.7969i	−1.04011	+	0.600507i
$693$		0			0
$694$	−20.3617	+	20.3617i	−0.772920	+	0.772920i
$695$	−16.7544	+	4.48932i	−0.635529	+	0.170290i
$696$		0			0
$697$	3.19132	+	3.19132i	0.120880	+	0.120880i
$698$	−3.65849	−	2.11223i	−0.138476	−	0.0799490i
$699$		0			0
$700$	4.33054	−	16.1618i	0.163679	−	0.610858i
$701$	−45.1455			−1.70512			−0.852560	−	0.522629i	$-0.824951\pi$
$701$	−45.1455			−1.70512			−0.852560	+	0.522629i	$0.824951\pi$
$702$		0			0
$703$	25.6741			0.968318
$704$	4.61312	−	17.2164i	0.173863	−	0.648867i
$705$		0			0
$706$	22.0342	+	12.7215i	0.829268	+	0.478778i
$707$	−25.5726	−	25.5726i	−0.961755	−	0.961755i
$708$		0			0
$709$	50.8953	−	13.6374i	1.91141	−	0.512162i	0.918157	−	0.396216i	$-0.129677\pi$
$709$	50.8953	−	13.6374i	1.91141	−	0.512162i	0.993256	−	0.115945i	$-0.0369897\pi$
$710$	−19.1618	+	19.1618i	−0.719130	+	0.719130i
$711$		0			0
$712$	27.0708	−	15.6293i	1.01452	−	0.585733i
$713$	−29.7463	−	7.97049i	−1.11401	−	0.298497i
$714$		0			0
$715$	−38.3961	−	12.8016i	−1.43593	−	0.478751i
$716$			13.4767i			0.503649i
$717$		0			0
$718$	3.43004	+	5.94100i	0.128008	+	0.221716i
$719$	13.2296	−	22.9144i	0.493382	−	0.854563i	−0.506589	−	0.862188i	$-0.669094\pi$
$719$	13.2296	−	22.9144i	0.493382	−	0.854563i	0.999971	+	0.00762491i	$0.00242711\pi$
$720$		0			0
$721$	−8.70596	−	32.4911i	−0.324227	−	1.21003i
$722$	−2.43164	−	9.07499i	−0.0904962	−	0.337736i
$723$		0			0
$724$	10.9838	−	19.0245i	0.408210	−	0.707040i
$725$	−2.78203	−	4.81862i	−0.103322	−	0.178959i
$726$		0			0
$727$			25.7880i			0.956422i	0.878245	+	0.478211i	$0.158715\pi$
$727$			25.7880i			0.956422i	−0.878245	+	0.478211i	$0.841285\pi$
$728$	−7.57545	−	37.0320i	−0.280765	−	1.37250i
$729$		0			0
$730$	24.3972	+	6.53720i	0.902980	+	0.241953i
$731$	−17.1370	+	9.89402i	−0.633833	+	0.365944i
$732$		0			0
$733$	15.9394	−	15.9394i	0.588737	−	0.588737i	−0.348552	−	0.937289i	$-0.613327\pi$
$733$	15.9394	−	15.9394i	0.588737	−	0.588737i	0.937289	+	0.348552i	$0.113327\pi$
$734$	6.54387	−	1.75342i	0.241539	−	0.0647201i
$735$		0			0
$736$	−19.0312	−	19.0312i	−0.701499	−	0.701499i
$737$	−29.0559	−	16.7754i	−1.07029	−	0.617931i
$738$		0			0
$739$	−4.06064	+	15.1545i	−0.149373	+	0.557468i	0.850148	+	0.526543i	$0.176512\pi$
$739$	−4.06064	+	15.1545i	−0.149373	+	0.557468i	−0.999522	+	0.0309254i	$0.990155\pi$
$740$	33.4430			1.22939
$741$		0			0
$742$	−24.2233			−0.889265
$743$	−0.171821	+	0.641243i	−0.00630349	+	0.0235249i	−0.969006	−	0.247037i	$-0.920543\pi$
$743$	−0.171821	+	0.641243i	−0.00630349	+	0.0235249i	0.962702	+	0.270562i	$0.0872096\pi$
$744$		0			0
$745$	6.31398	+	3.64538i	0.231326	+	0.133556i
$746$	10.1167	+	10.1167i	0.370400	+	0.370400i
$747$		0			0
$748$	11.2399	−	3.01172i	0.410971	−	0.110119i
$749$	−32.6424	+	32.6424i	−1.19273	+	1.19273i
$750$		0			0
$751$	−14.6930	+	8.48301i	−0.536155	+	0.309549i	−0.743519	−	0.668715i	$-0.766845\pi$
$751$	−14.6930	+	8.48301i	−0.536155	+	0.309549i	0.207364	+	0.978264i	$0.433512\pi$
$752$	1.00301	+	0.268755i	0.0365760	+	0.00980050i
$753$		0			0
$754$	−4.06334	−	2.68323i	−0.147978	−	0.0977173i
$755$		−	1.29259i		−	0.0470423i
$756$		0			0
$757$	22.7933	+	39.4791i	0.828435	+	1.43489i	0.899265	+	0.437404i	$0.144102\pi$
$757$	22.7933	+	39.4791i	0.828435	+	1.43489i	−0.0708297	+	0.997488i	$0.522565\pi$
$758$	−4.24265	+	7.34849i	−0.154100	+	0.266909i
$759$		0			0
$760$	6.00266	+	22.4022i	0.217739	+	0.812614i
$761$	−3.36957	−	12.5754i	−0.122147	−	0.455859i	0.877575	−	0.479439i	$-0.159160\pi$
$761$	−3.36957	−	12.5754i	−0.122147	−	0.455859i	−0.999722	+	0.0235808i	$0.992493\pi$
$762$		0			0
$763$	1.47088	−	2.54763i	0.0532493	−	0.0922304i
$764$	−2.55587	−	4.42690i	−0.0924682	−	0.160160i
$765$		0			0
$766$		−	17.6125i		−	0.636366i
$767$	35.0497	+	23.1451i	1.26557	+	0.835720i
$768$		0			0
$769$	8.34703	+	2.23658i	0.301001	+	0.0806531i	0.406159	−	0.913802i	$-0.366868\pi$
$769$	8.34703	+	2.23658i	0.301001	+	0.0806531i	−0.105157	+	0.994456i	$0.533535\pi$
$770$	−31.2176	+	18.0235i	−1.12500	+	0.649521i
$771$		0			0
$772$	−5.09154	+	5.09154i	−0.183249	+	0.183249i
$773$	−48.1428	+	12.8998i	−1.73157	+	0.463974i	−0.980545	−	0.196294i	$-0.937109\pi$
$773$	−48.1428	+	12.8998i	−1.73157	+	0.463974i	−0.751030	+	0.660268i	$0.770443\pi$
$774$		0			0
$775$	16.3197	+	16.3197i	0.586222	+	0.586222i
$776$	23.8669	+	13.7795i	0.856771	+	0.494657i
$777$		0			0
$778$	−3.51398	+	13.1143i	−0.125982	+	0.470172i
$779$	−5.34606			−0.191543
$780$		0			0
$781$	−41.5745			−1.48765
$782$	−2.50491	+	9.34845i	−0.0895754	+	0.334300i
$783$		0			0
$784$	0.783792	+	0.452522i	0.0279926	+	0.0161615i
$785$	−25.4761	−	25.4761i	−0.909280	−	0.909280i
$786$		0			0
$787$	3.29048	−	0.881683i	0.117293	−	0.0314286i	−0.199695	−	0.979858i	$-0.563995\pi$
$787$	3.29048	−	0.881683i	0.117293	−	0.0314286i	0.316988	+	0.948430i	$0.397328\pi$
$788$	0.110743	−	0.110743i	0.00394505	−	0.00394505i
$789$		0			0
$790$	−23.4486	+	13.5380i	−0.834263	+	0.481662i
$791$	−11.7309	−	3.14328i	−0.417102	−	0.111762i
$792$		0			0
$793$	−5.97516	−	29.2091i	−0.212184	−	1.03725i
$794$			18.3993i			0.652966i
$795$		0			0
$796$	8.78659	+	15.2188i	0.311432	+	0.539417i
$797$	22.0737	−	38.2327i	0.781890	−	1.35427i	−0.148950	−	0.988845i	$-0.547589\pi$
$797$	22.0737	−	38.2327i	0.781890	−	1.35427i	0.930840	−	0.365428i	$-0.119077\pi$
$798$		0			0
$799$	−4.99379	−	18.6371i	−0.176668	−	0.659333i
$800$	5.22055	+	19.4834i	0.184574	+	0.688841i
$801$		0			0
$802$	−6.12604	+	10.6106i	−0.216318	+	0.374674i
$803$	19.3750	+	33.5585i	0.683729	+	1.18425i
$804$		0			0
$805$			51.5664i			1.81748i
$806$	19.1610	+	6.38842i	0.674916	+	0.225022i
$807$		0			0
$808$	26.1142	+	6.99729i	0.918695	+	0.246164i
$809$	−2.10393	+	1.21470i	−0.0739702	+	0.0427067i	−0.536529	−	0.843882i	$-0.680265\pi$
$809$	−2.10393	+	1.21470i	−0.0739702	+	0.0427067i	0.462559	+	0.886589i	$0.346931\pi$
$810$		0			0
$811$	2.38676	−	2.38676i	0.0838103	−	0.0838103i	−0.663959	−	0.747769i	$-0.731125\pi$
$811$	2.38676	−	2.38676i	0.0838103	−	0.0838103i	0.747769	+	0.663959i	$0.231125\pi$
$812$	7.20488	−	1.93054i	0.252842	−	0.0677488i
$813$		0			0
$814$	−21.0934	−	21.0934i	−0.739322	−	0.739322i
$815$	−4.36800	−	2.52187i	−0.153005	−	0.0883372i
$816$		0			0
$817$	6.06664	−	22.6410i	0.212245	−	0.792108i
$818$	15.4375			0.539758
$819$		0			0
$820$	−6.96377			−0.243185
$821$	−0.839428	+	3.13279i	−0.0292962	+	0.109335i	−0.979026	−	0.203737i	$-0.934691\pi$
$821$	−0.839428	+	3.13279i	−0.0292962	+	0.109335i	0.949729	+	0.313072i	$0.101358\pi$
$822$		0			0
$823$	−16.5110	−	9.53265i	−0.575538	−	0.332287i	0.183820	−	0.982960i	$-0.441154\pi$
$823$	−16.5110	−	9.53265i	−0.575538	−	0.332287i	−0.759358	+	0.650673i	$0.774487\pi$
$824$	17.7807	+	17.7807i	0.619421	+	0.619421i
$825$		0			0
$826$	36.1333	−	9.68189i	1.25724	−	0.336876i
$827$	4.73777	−	4.73777i	0.164748	−	0.164748i	−0.619918	−	0.784666i	$-0.712834\pi$
$827$	4.73777	−	4.73777i	0.164748	−	0.164748i	0.784666	+	0.619918i	$0.212834\pi$
$828$		0			0
$829$	−41.5310	+	23.9780i	−1.44243	+	0.832789i	−0.998012	−	0.0630295i	$-0.979924\pi$
$829$	−41.5310	+	23.9780i	−1.44243	+	0.832789i	−0.444421	+	0.895818i	$0.646590\pi$
$830$	−35.2319	−	9.44036i	−1.22292	−	0.327680i
$831$		0			0
$832$	11.0943	+	12.5129i	0.384627	+	0.433807i
$833$		−	16.8168i		−	0.582668i
$834$		0			0
$835$	18.5678	+	32.1603i	0.642564	+	1.11295i
$836$	−6.89187	+	11.9371i	−0.238360	+	0.412852i
$837$		0			0
$838$	−0.710109	−	2.65016i	−0.0245303	−	0.0915484i
$839$	−2.54487	−	9.49760i	−0.0878588	−	0.327894i	0.907981	−	0.419011i	$-0.137623\pi$
$839$	−2.54487	−	9.49760i	−0.0878588	−	0.327894i	−0.995840	+	0.0911170i	$0.970956\pi$
$840$		0			0
$841$	−13.2598	+	22.9666i	−0.457234	+	0.791952i
$842$	5.75261	+	9.96381i	0.198248	+	0.343376i
$843$		0			0
$844$			8.96674i			0.308648i
$845$	29.8742	−	23.4432i	1.02770	−	0.806472i
$846$		0			0
$847$	−13.6286	−	3.65178i	−0.468285	−	0.125476i
$848$	−0.841784	+	0.486004i	−0.0289070	+	0.0166895i
$849$		0			0
$850$	5.12885	−	5.12885i	0.175918	−	0.175918i
$851$	−41.2195	+	11.0447i	−1.41299	+	0.378609i
$852$		0			0
$853$	9.42766	+	9.42766i	0.322797	+	0.322797i	0.849839	−	0.527042i	$-0.176699\pi$
$853$	9.42766	+	9.42766i	0.322797	+	0.322797i	−0.527042	+	0.849839i	$0.676699\pi$
$854$	−22.9956	−	13.2765i	−0.786892	−	0.454312i
$855$		0			0
$856$	8.93177	−	33.3338i	0.305282	−	1.13933i
$857$	−28.5912			−0.976657			−0.488328	−	0.872660i	$-0.662393\pi$
$857$	−28.5912			−0.976657			−0.488328	+	0.872660i	$0.662393\pi$
$858$		0			0
$859$	−6.22456			−0.212379			−0.106190	−	0.994346i	$-0.533865\pi$
$859$	−6.22456			−0.212379			−0.106190	+	0.994346i	$0.533865\pi$
$860$	7.90238	−	29.4921i	0.269469	−	1.00567i
$861$		0			0
$862$	4.66178	+	2.69148i	0.158781	+	0.0916723i
$863$	−19.4242	−	19.4242i	−0.661208	−	0.661208i	0.294457	−	0.955665i	$-0.404861\pi$
$863$	−19.4242	−	19.4242i	−0.661208	−	0.661208i	−0.955665	+	0.294457i	$0.904861\pi$
$864$		0			0
$865$	−70.4864	+	18.8868i	−2.39661	+	0.642170i
$866$	16.2981	−	16.2981i	0.553834	−	0.553834i
$867$		0			0
$868$	−26.7948	+	15.4700i	−0.909474	+	0.525085i
$869$	−40.1241	−	10.7512i	−1.36112	−	0.364710i
$870$		0			0
$871$	28.1565	−	14.0759i	0.954047	−	0.476943i
$872$			2.19913i			0.0744718i
$873$		0			0
$874$	−5.73211	−	9.92831i	−0.193892	−	0.335830i
$875$	−8.02452	+	13.8989i	−0.271278	+	0.469868i
$876$		0			0
$877$	−2.11305	−	7.88600i	−0.0713525	−	0.266291i	0.921029	−	0.389494i	$-0.127350\pi$
$877$	−2.11305	−	7.88600i	−0.0713525	−	0.266291i	−0.992382	+	0.123203i	$0.960683\pi$
$878$	5.00276	+	18.6706i	0.168835	+	0.630101i
$879$		0			0
$880$	−0.723229	+	1.25267i	−0.0243800	+	0.0422275i
$881$	−16.2839	−	28.2046i	−0.548620	−	0.950237i	−0.998369	−	0.0570827i	$-0.981820\pi$
$881$	−16.2839	−	28.2046i	−0.548620	−	0.950237i	0.449750	−	0.893155i	$-0.351513\pi$
$882$		0			0
$883$			35.2731i			1.18704i	0.804821	+	0.593518i	$0.202261\pi$
$883$			35.2731i			1.18704i	−0.804821	+	0.593518i	$0.797739\pi$
$884$	−3.45320	+	10.3573i	−0.116144	+	0.348353i
$885$		0			0
$886$	5.78770	+	1.55081i	0.194441	+	0.0521004i
$887$	23.5439	−	13.5931i	0.790525	−	0.456410i	−0.0496222	−	0.998768i	$-0.515802\pi$
$887$	23.5439	−	13.5931i	0.790525	−	0.456410i	0.840147	+	0.542358i	$0.182468\pi$
$888$		0			0
$889$	8.57162	−	8.57162i	0.287483	−	0.287483i
$890$	27.0158	−	7.23887i	0.905573	−	0.242647i
$891$		0			0
$892$	14.9304	+	14.9304i	0.499907	+	0.499907i
$893$	19.7931	+	11.4276i	0.662351	+	0.382409i
$894$		0			0
$895$	−8.05640	+	30.0669i	−0.269296	+	1.00503i
$896$	−27.8679			−0.931000
$897$		0			0
$898$	8.09919			0.270274
$899$	−2.66294	+	9.93824i	−0.0888141	+	0.331459i
$900$		0			0
$901$	15.6413	+	9.03053i	0.521089	+	0.300851i
$902$	4.39222	+	4.39222i	0.146245	+	0.146245i
$903$		0			0
$904$	8.76949	−	2.34978i	0.291669	−	0.0781524i
$905$	35.8780	−	35.8780i	1.19263	−	1.19263i
$906$		0			0
$907$	31.1474	−	17.9830i	1.03423	−	0.597114i	0.116038	−	0.993245i	$-0.462981\pi$
$907$	31.1474	−	17.9830i	1.03423	−	0.597114i	0.918194	+	0.396131i	$0.129647\pi$
$908$	−7.48050	−	2.00439i	−0.248249	−	0.0665181i
$909$		0			0
$910$	2.02865	−	33.7599i	0.0672492	−	1.11913i
$911$			23.7902i			0.788204i	0.919067	+	0.394102i	$0.128944\pi$
$911$			23.7902i			0.788204i	−0.919067	+	0.394102i	$0.871056\pi$
$912$		0			0
$913$	−27.9794	−	48.4617i	−0.925983	−	1.60385i
$914$	−4.95022	+	8.57403i	−0.163739	+	0.283604i
$915$		0			0
$916$	−5.04274	−	18.8197i	−0.166617	−	0.621822i
$917$	15.0410	+	56.1339i	0.496699	+	1.85370i
$918$		0			0
$919$	−24.8139	+	42.9789i	−0.818535	+	1.41774i	0.0882264	+	0.996100i	$0.471880\pi$
$919$	−24.8139	+	42.9789i	−0.818535	+	1.41774i	−0.906761	+	0.421644i	$0.861453\pi$
$920$	−19.2744	−	33.3843i	−0.635459	−	1.10065i
$921$		0			0
$922$			0.291290i			0.00959312i
$923$	21.4946	−	32.5504i	0.707505	−	1.07141i
$924$		0			0
$925$	30.8917	+	8.27742i	1.01571	+	0.272160i
$926$	−19.1773	+	11.0720i	−0.630206	+	0.363849i
$927$		0			0
$928$	−6.35833	+	6.35833i	−0.208722	+	0.208722i
$929$	11.0703	−	2.96628i	0.363205	−	0.0973204i	−0.0726012	−	0.997361i	$-0.523130\pi$
$929$	11.0703	−	2.96628i	0.363205	−	0.0973204i	0.435806	+	0.900041i	$0.356463\pi$
$930$		0			0
$931$	14.0857	+	14.0857i	0.461639	+	0.461639i
$932$	7.27000	+	4.19734i	0.238137	+	0.137488i
$933$		0			0
$934$	4.85543	−	18.1207i	0.158874	−	0.592927i
$935$	26.8769			0.878968
$936$		0			0
$937$	−25.5819			−0.835723			−0.417862	−	0.908511i	$-0.637220\pi$
$937$	−25.5819			−0.835723			−0.417862	+	0.908511i	$0.637220\pi$
$938$	7.25619	−	27.0805i	0.236923	−	0.884209i
$939$		0			0
$940$	25.7824	+	14.8855i	0.840930	+	0.485511i
$941$	−3.10076	−	3.10076i	−0.101082	−	0.101082i	0.654757	−	0.755839i	$-0.272771\pi$
$941$	−3.10076	−	3.10076i	−0.101082	−	0.101082i	−0.755839	+	0.654757i	$0.772771\pi$
$942$		0			0
$943$	8.58305	−	2.29982i	0.279503	−	0.0748925i
$944$	1.06142	−	1.06142i	0.0345462	−	0.0345462i
$945$		0			0
$946$	−23.5856	+	13.6172i	−0.766835	+	0.442733i
$947$	−2.43662	−	0.652890i	−0.0791795	−	0.0212161i	0.219012	−	0.975722i	$-0.429717\pi$
$947$	−2.43662	−	0.652890i	−0.0791795	−	0.0212161i	−0.298191	+	0.954506i	$0.596383\pi$
$948$		0			0
$949$	−36.2914	−	2.18077i	−1.17807	−	0.0707909i
$950$			8.59180i			0.278755i
$951$		0			0
$952$	12.5503	+	21.7377i	0.406757	+	0.704523i
$953$	21.0547	−	36.4678i	0.682028	−	1.18131i	−0.292333	−	0.956317i	$-0.594431\pi$
$953$	21.0547	−	36.4678i	0.682028	−	1.18131i	0.974361	−	0.224991i	$-0.0722352\pi$
$954$		0			0
$955$	−3.05581	−	11.4044i	−0.0988836	−	0.369039i
$956$	4.89753	+	18.2778i	0.158398	+	0.591148i
$957$		0			0
$958$	5.42739	−	9.40052i	0.175351	−	0.303717i
$959$	34.9725	+	60.5741i	1.12932	+	1.95604i
$960$		0			0
$961$		−	11.6778i		−	0.376703i
$962$	27.4204	−	5.60926i	0.884070	−	0.180850i
$963$		0			0
$964$	23.1382	+	6.19986i	0.745231	+	0.199684i
$965$	−14.4031	+	8.31563i	−0.463652	+	0.267690i
$966$		0			0
$967$	10.5472	−	10.5472i	0.339176	−	0.339176i	−0.516881	−	0.856057i	$-0.672907\pi$
$967$	10.5472	−	10.5472i	0.339176	−	0.339176i	0.856057	+	0.516881i	$0.172907\pi$
$968$	10.1882	−	2.72991i	0.327460	−	0.0877426i
$969$		0			0
$970$	17.4363	+	17.4363i	0.559846	+	0.559846i
$971$	34.8544	+	20.1232i	1.11853	+	0.645784i	0.941026	−	0.338335i	$-0.109864\pi$
$971$	34.8544	+	20.1232i	1.11853	+	0.645784i	0.177506	+	0.984120i	$0.443197\pi$
$972$		0			0
$973$	5.75526	−	21.4789i	0.184505	−	0.688582i
$974$	30.6315			0.981495
$975$		0			0
$976$	−1.06549			−0.0341056
$977$	−9.53918	+	35.6007i	−0.305185	+	1.13897i	0.627600	+	0.778536i	$0.284037\pi$
$977$	−9.53918	+	35.6007i	−0.305185	+	1.13897i	−0.932786	+	0.360432i	$0.882629\pi$
$978$		0			0
$979$	37.1605	+	21.4546i	1.18765	+	0.685692i
$980$	18.3479	+	18.3479i	0.586103	+	0.586103i
$981$		0			0
$982$	−3.43821	+	0.921267i	−0.109718	+	0.0293988i
$983$	13.4493	−	13.4493i	0.428965	−	0.428965i	−0.459311	−	0.888276i	$-0.651904\pi$
$983$	13.4493	−	13.4493i	0.428965	−	0.428965i	0.888276	+	0.459311i	$0.151904\pi$
$984$		0			0
$985$	0.313272	−	0.180868i	0.00998169	−	0.00576293i
$986$	3.12332	+	0.836891i	0.0994668	+	0.0266521i
$987$		0			0
$988$	−5.78281	−	11.5676i	−0.183976	−	0.368013i
$989$			38.9597i			1.23885i
$990$		0			0
$991$	−6.94341	−	12.0263i	−0.220565	−	0.382029i	0.734415	−	0.678701i	$-0.237457\pi$
$991$	−6.94341	−	12.0263i	−0.220565	−	0.382029i	−0.954980	+	0.296672i	$0.904123\pi$
$992$	18.6494	−	32.3017i	0.592118	−	1.02558i
$993$		0			0
$994$	−8.99150	−	33.5567i	−0.285193	−	1.06435i
$995$	10.5053	+	39.2062i	0.333040	+	1.24292i
$996$		0			0
$997$	14.7376	−	25.5262i	0.466743	−	0.808422i	−0.532535	−	0.846408i	$-0.678761\pi$
$997$	14.7376	−	25.5262i	0.466743	−	0.808422i	0.999278	+	0.0379853i	$0.0120940\pi$
$998$	−5.33623	−	9.24263i	−0.168916	−	0.292570i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.e.80.4	yes	20
3.2	odd	2		351.2.bd.d.80.2	✓	20
13.7	odd	12		351.2.bd.d.215.2	yes	20
39.20	even	12	inner	351.2.bd.e.215.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.80.2	✓	20	3.2	odd	2
351.2.bd.d.215.2	yes	20	13.7	odd	12
351.2.bd.e.80.4	yes	20	1.1	even	1	trivial
351.2.bd.e.215.4	yes	20	39.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221937 - 0.828279i) q^{2} +(1.09526 + 0.632349i) q^{4} +(2.06553 + 2.06553i) q^{5} +(-3.61723 + 0.969233i) q^{7} +(1.97952 - 1.97952i) q^{8} +O(q^{10})\)	\(q+(0.221937 - 0.828279i) q^{2} +(1.09526 + 0.632349i) q^{4} +(2.06553 + 2.06553i) q^{5} +(-3.61723 + 0.969233i) q^{7} +(1.97952 - 1.97952i) q^{8} +(2.16926 - 1.25242i) q^{10} +(3.71193 + 0.994610i) q^{11} +(-2.69784 + 2.39199i) q^{13} +3.21118i q^{14} +(0.0644276 + 0.111592i) q^{16} +(1.19714 - 2.07351i) q^{17} +(0.734041 + 2.73948i) q^{19} +(0.956160 + 3.56844i) q^{20} +(1.64763 - 2.85378i) q^{22} +(-2.35699 - 4.08243i) q^{23} +3.53287i q^{25} +(1.38249 + 2.76544i) q^{26} +(-4.57470 - 1.22579i) q^{28} +(-1.36394 + 0.787471i) q^{29} +(4.61940 - 4.61940i) q^{31} +(5.51489 - 1.47771i) q^{32} +(-1.45175 - 1.45175i) q^{34} +(-9.47349 - 5.46952i) q^{35} +(2.34298 - 8.74410i) q^{37} +2.43196 q^{38} +8.17755 q^{40} +(-0.487872 + 1.82076i) q^{41} +(-7.15745 - 4.13236i) q^{43} +(3.43659 + 3.43659i) q^{44} +(-3.90449 + 1.04621i) q^{46} +(5.69829 - 5.69829i) q^{47} +(6.08273 - 3.51187i) q^{49} +(2.92620 + 0.784073i) q^{50} +(-4.46742 + 0.913877i) q^{52} +7.54342i q^{53} +(5.61273 + 9.72153i) q^{55} +(-5.24177 + 9.07901i) q^{56} +(0.349538 + 1.30449i) q^{58} +(-3.01505 - 11.2523i) q^{59} +(-4.13446 + 7.16109i) q^{61} +(-2.80094 - 4.85137i) q^{62} -4.63812i q^{64} +(-10.5132 - 0.631746i) q^{65} +(-8.43318 - 2.25966i) q^{67} +(2.62236 - 1.51402i) q^{68} +(-6.63281 + 6.63281i) q^{70} +(-10.4500 + 2.80006i) q^{71} +(7.13018 + 7.13018i) q^{73} +(-6.72257 - 3.88128i) q^{74} +(-0.928340 + 3.46461i) q^{76} -14.3909 q^{77} -10.8095 q^{79} +(-0.0974194 + 0.363574i) q^{80} +(1.39982 + 0.808189i) q^{82} +(-10.2967 - 10.2967i) q^{83} +(6.75564 - 1.81017i) q^{85} +(-5.01125 + 5.01125i) q^{86} +(9.31672 - 5.37901i) q^{88} +(10.7854 + 2.88995i) q^{89} +(7.44032 - 11.2672i) q^{91} -5.96176i q^{92} +(-3.45511 - 5.98443i) q^{94} +(-4.14230 + 7.17467i) q^{95} +(2.54792 + 9.50895i) q^{97} +(-1.55883 - 5.81761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5}+O(q^{10}) \) 20 * q + 6 * q^5	\( 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) \) 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more