LMFDB - Embedded newform 234.3.bb.d.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(19,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("234.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.bb (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:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Root			$-4.04651 + 4.04651i$ of defining polynomial
Character	$\chi$	$=$	234.37
Dual form			234.3.bb.d.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(5.04651 + 5.04651i) q^{5} +(-1.34715 - 5.02764i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(5.04651 + 5.04651i) q^{5} +(-1.34715 - 5.02764i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.74082 - 5.04651i) q^{10} +(7.32323 + 1.96225i) q^{11} +(12.9213 - 1.42820i) q^{13} -7.36098 q^{14} +(2.00000 + 3.46410i) q^{16} +(13.9968 + 8.08105i) q^{17} +(9.87664 - 2.64644i) q^{19} +(-3.69431 - 13.7873i) q^{20} +(5.36098 - 9.28549i) q^{22} +(8.29191 - 4.78733i) q^{23} +25.9346i q^{25} +(2.77857 - 18.1736i) q^{26} +(-2.69431 + 10.0553i) q^{28} +(-16.5880 - 28.7312i) q^{29} +(-34.2312 - 34.2312i) q^{31} +(5.46410 - 1.46410i) q^{32} +(16.1621 - 16.1621i) q^{34} +(18.5736 - 32.1705i) q^{35} +(63.2267 + 16.9415i) q^{37} -14.4604i q^{38} -20.1861 q^{40} +(-14.0962 + 52.6079i) q^{41} +(-40.7432 - 23.5231i) q^{43} +(-10.7220 - 10.7220i) q^{44} +(-3.50457 - 13.0792i) q^{46} +(-47.8214 + 47.8214i) q^{47} +(18.9729 - 10.9540i) q^{49} +(35.4274 + 9.49273i) q^{50} +(-23.8086 - 10.4476i) q^{52} -67.5177 q^{53} +(27.0543 + 46.8594i) q^{55} +(12.7496 + 7.36098i) q^{56} +(-45.3192 + 12.1432i) q^{58} +(19.4918 + 72.7442i) q^{59} +(-35.2597 + 61.0716i) q^{61} +(-59.2902 + 34.2312i) q^{62} -8.00000i q^{64} +(72.4150 + 58.0001i) q^{65} +(11.1841 - 41.7395i) q^{67} +(-16.1621 - 27.9936i) q^{68} +(-37.1473 - 37.1473i) q^{70} +(106.797 - 28.6161i) q^{71} +(-36.8385 + 36.8385i) q^{73} +(46.2851 - 80.1682i) q^{74} +(-19.7533 - 5.29288i) q^{76} -39.4621i q^{77} -13.3867 q^{79} +(-7.38861 + 27.5747i) q^{80} +(66.7041 + 38.5116i) q^{82} +(-93.1237 - 93.1237i) q^{83} +(29.8539 + 111.416i) q^{85} +(-47.0461 + 47.0461i) q^{86} +(-18.5710 + 10.7220i) q^{88} +(-48.6137 - 13.0260i) q^{89} +(-24.5875 - 63.0397i) q^{91} -19.1493 q^{92} +(47.8214 + 82.8291i) q^{94} +(63.1979 + 36.4873i) q^{95} +(-52.5419 + 14.0786i) q^{97} +(-8.01888 - 29.9269i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	5.04651	+	5.04651i	1.00930	+	1.00930i	0.999956	+	0.00934664i	$0.00297517\pi$
$5$	5.04651	+	5.04651i	1.00930	+	1.00930i	0.00934664	+	0.999956i	$0.497025\pi$
$6$		0			0
$7$	−1.34715	−	5.02764i	−0.192450	−	0.718235i	−0.992912	−	0.118851i	$-0.962079\pi$
$7$	−1.34715	−	5.02764i	−0.192450	−	0.718235i	0.800462	−	0.599384i	$-0.204588\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	8.74082	−	5.04651i	0.874082	−	0.504651i
$11$	7.32323	+	1.96225i	0.665748	+	0.178387i	0.575839	−	0.817563i	$-0.304676\pi$
$11$	7.32323	+	1.96225i	0.665748	+	0.178387i	0.0899095	+	0.995950i	$0.471342\pi$
$12$		0			0
$13$	12.9213	−	1.42820i	0.993947	−	0.109862i
$13$	12.9213	−	1.42820i	0.993947	−	0.109862i
$14$	−7.36098			−0.525784
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	13.9968	+	8.08105i	0.823341	+	0.475356i	0.851567	−	0.524246i	$-0.175653\pi$
$17$	13.9968	+	8.08105i	0.823341	+	0.475356i	−0.0282265	+	0.999602i	$0.508986\pi$
$18$		0			0
$19$	9.87664	−	2.64644i	0.519823	−	0.139286i	0.0106384	−	0.999943i	$-0.496614\pi$
$19$	9.87664	−	2.64644i	0.519823	−	0.139286i	0.509185	+	0.860657i	$0.329947\pi$
$20$	−3.69431	−	13.7873i	−0.184715	−	0.689367i
$21$		0			0
$22$	5.36098	−	9.28549i	0.243681	−	0.422068i
$23$	8.29191	−	4.78733i	0.360518	−	0.208145i	−0.308790	−	0.951130i	$-0.599924\pi$
$23$	8.29191	−	4.78733i	0.360518	−	0.208145i	0.669308	+	0.742985i	$0.266591\pi$
$24$		0			0
$25$			25.9346i			1.03738i
$26$	2.77857	−	18.1736i	0.106868	−	0.698984i
$27$		0			0
$28$	−2.69431	+	10.0553i	−0.0962252	+	0.359117i
$29$	−16.5880	−	28.7312i	−0.571999	−	0.990731i	−0.996361	−	0.0852386i	$-0.972835\pi$
$29$	−16.5880	−	28.7312i	−0.571999	−	0.990731i	0.424362	−	0.905493i	$-0.360499\pi$
$30$		0			0
$31$	−34.2312	−	34.2312i	−1.10423	−	1.10423i	−0.993894	−	0.110338i	$-0.964807\pi$
$31$	−34.2312	−	34.2312i	−1.10423	−	1.10423i	−0.110338	−	0.993894i	$-0.535193\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$		0			0
$34$	16.1621	−	16.1621i	0.475356	−	0.475356i
$35$	18.5736	−	32.1705i	0.530676	−	0.919157i
$36$		0			0
$37$	63.2267	+	16.9415i	1.70883	+	0.457879i	0.975137	−	0.221603i	$-0.0711289\pi$
$37$	63.2267	+	16.9415i	1.70883	+	0.457879i	0.733692	+	0.679482i	$0.237796\pi$
$38$		−	14.4604i		−	0.380537i
$39$		0			0
$40$	−20.1861			−0.504651
$41$	−14.0962	+	52.6079i	−0.343811	+	1.28312i	0.550185	+	0.835043i	$0.314557\pi$
$41$	−14.0962	+	52.6079i	−0.343811	+	1.28312i	−0.893995	+	0.448076i	$0.852109\pi$
$42$		0			0
$43$	−40.7432	−	23.5231i	−0.947515	−	0.547048i	−0.0552070	−	0.998475i	$-0.517582\pi$
$43$	−40.7432	−	23.5231i	−0.947515	−	0.547048i	−0.892308	+	0.451427i	$0.850915\pi$
$44$	−10.7220	−	10.7220i	−0.243681	−	0.243681i
$45$		0			0
$46$	−3.50457	−	13.0792i	−0.0761864	−	0.284331i
$47$	−47.8214	+	47.8214i	−1.01748	+	1.01748i	−0.0176317	+	0.999845i	$0.505613\pi$
$47$	−47.8214	+	47.8214i	−1.01748	+	1.01748i	−0.999845	+	0.0176317i	$0.994387\pi$
$48$		0			0
$49$	18.9729	−	10.9540i	0.387202	−	0.223551i
$50$	35.4274	+	9.49273i	0.708547	+	0.189855i
$51$		0			0
$52$	−23.8086	−	10.4476i	−0.457857	−	0.200915i
$53$	−67.5177			−1.27392			−0.636959	−	0.770897i	$-0.719808\pi$
$53$	−67.5177			−1.27392			−0.636959	+	0.770897i	$0.719808\pi$
$54$		0			0
$55$	27.0543	+	46.8594i	0.491896	+	0.851988i
$56$	12.7496	+	7.36098i	0.227671	+	0.131446i
$57$		0			0
$58$	−45.3192	+	12.1432i	−0.781365	+	0.209366i
$59$	19.4918	+	72.7442i	0.330369	+	1.23295i	0.908804	+	0.417224i	$0.136997\pi$
$59$	19.4918	+	72.7442i	0.330369	+	1.23295i	−0.578435	+	0.815729i	$0.696336\pi$
$60$		0			0
$61$	−35.2597	+	61.0716i	−0.578028	+	1.00117i	0.417677	+	0.908596i	$0.362844\pi$
$61$	−35.2597	+	61.0716i	−0.578028	+	1.00117i	−0.995705	+	0.0925789i	$0.970489\pi$
$62$	−59.2902	+	34.2312i	−0.956293	+	0.552116i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	72.4150	+	58.0001i	1.11408	+	0.892310i
$66$		0			0
$67$	11.1841	−	41.7395i	0.166926	−	0.622977i	−0.830860	−	0.556481i	$-0.812151\pi$
$67$	11.1841	−	41.7395i	0.166926	−	0.622977i	0.997787	−	0.0664962i	$-0.0211820\pi$
$68$	−16.1621	−	27.9936i	−0.237678	−	0.411670i
$69$		0			0
$70$	−37.1473	−	37.1473i	−0.530676	−	0.530676i
$71$	106.797	−	28.6161i	1.50418	−	0.403044i	0.589682	−	0.807635i	$-0.299253\pi$
$71$	106.797	−	28.6161i	1.50418	−	0.403044i	0.914498	+	0.404591i	$0.132586\pi$
$72$		0			0
$73$	−36.8385	+	36.8385i	−0.504638	+	0.504638i	−0.912876	−	0.408238i	$-0.866143\pi$
$73$	−36.8385	+	36.8385i	−0.504638	+	0.504638i	0.408238	+	0.912876i	$0.366143\pi$
$74$	46.2851	−	80.1682i	0.625475	−	1.08335i
$75$		0			0
$76$	−19.7533	−	5.29288i	−0.259912	−	0.0696431i
$77$		−	39.4621i		−	0.512494i
$78$		0			0
$79$	−13.3867			−0.169452			−0.0847259	−	0.996404i	$-0.527001\pi$
$79$	−13.3867			−0.169452			−0.0847259	+	0.996404i	$0.527001\pi$
$80$	−7.38861	+	27.5747i	−0.0923576	+	0.344683i
$81$		0			0
$82$	66.7041	+	38.5116i	0.813465	+	0.469654i
$83$	−93.1237	−	93.1237i	−1.12197	−	1.12197i	−0.991445	−	0.130528i	$-0.958333\pi$
$83$	−93.1237	−	93.1237i	−1.12197	−	1.12197i	−0.130528	−	0.991445i	$-0.541667\pi$
$84$		0			0
$85$	29.8539	+	111.416i	0.351222	+	1.31078i
$86$	−47.0461	+	47.0461i	−0.547048	+	0.547048i
$87$		0			0
$88$	−18.5710	+	10.7220i	−0.211034	+	0.121840i
$89$	−48.6137	−	13.0260i	−0.546222	−	0.146360i	−0.0248529	−	0.999691i	$-0.507912\pi$
$89$	−48.6137	−	13.0260i	−0.546222	−	0.146360i	−0.521369	+	0.853331i	$0.674578\pi$
$90$		0			0
$91$	−24.5875	−	63.0397i	−0.270192	−	0.692744i
$92$	−19.1493			−0.208145
$93$		0			0
$94$	47.8214	+	82.8291i	0.508738	+	0.881160i
$95$	63.1979	+	36.4873i	0.665241	+	0.384077i
$96$		0			0
$97$	−52.5419	+	14.0786i	−0.541669	+	0.145140i	−0.519271	−	0.854609i	$-0.673797\pi$
$97$	−52.5419	+	14.0786i	−0.541669	+	0.145140i	−0.0223976	+	0.999749i	$0.507130\pi$
$98$	−8.01888	−	29.9269i	−0.0818253	−	0.305376i
$99$		0			0
$100$	25.9346	−	44.9201i	0.259346	−	0.449201i
$101$	−19.5286	+	11.2749i	−0.193353	+	0.111632i	−0.593551	−	0.804796i	$-0.702275\pi$
$101$	−19.5286	+	11.2749i	−0.193353	+	0.111632i	0.400198	+	0.916428i	$0.368941\pi$
$102$		0			0
$103$			109.385i			1.06199i	0.847374	+	0.530996i	$0.178182\pi$
$103$			109.385i			1.06199i	−0.847374	+	0.530996i	$0.821818\pi$
$104$	−22.9862	+	28.6990i	−0.221021	+	0.275952i
$105$		0			0
$106$	−24.7132	+	92.2309i	−0.233143	+	0.870103i
$107$	−16.4375	−	28.4706i	−0.153621	−	0.266080i	0.778935	−	0.627105i	$-0.215760\pi$
$107$	−16.4375	−	28.4706i	−0.153621	−	0.266080i	−0.932556	+	0.361025i	$0.882427\pi$
$108$		0			0
$109$	−150.086	−	150.086i	−1.37693	−	1.37693i	−0.849752	−	0.527183i	$-0.823248\pi$
$109$	−150.086	−	150.086i	−1.37693	−	1.37693i	−0.527183	−	0.849752i	$-0.676752\pi$
$110$	73.9136	−	19.8051i	0.671942	−	0.180046i
$111$		0			0
$112$	14.7220	−	14.7220i	0.131446	−	0.131446i
$113$	−59.3938	+	102.873i	−0.525609	+	0.910382i	0.473946	+	0.880554i	$0.342829\pi$
$113$	−59.3938	+	102.873i	−0.525609	+	0.910382i	−0.999555	+	0.0298278i	$0.990504\pi$
$114$		0			0
$115$	66.0046	+	17.6859i	0.573953	+	0.153790i
$116$			66.3519i			0.571999i
$117$		0			0
$118$	106.505			0.902584
$119$	21.7728	−	81.2573i	0.182965	−	0.682834i
$120$		0			0
$121$	−55.0098	−	31.7599i	−0.454626	−	0.262479i
$122$	70.5195	+	70.5195i	0.578028	+	0.578028i
$123$		0			0
$124$	25.0590	+	93.5214i	0.202089	+	0.754205i
$125$	−4.71659	+	4.71659i	−0.0377327	+	0.0377327i
$126$		0			0
$127$	−57.5499	+	33.2265i	−0.453149	+	0.261626i	−0.709159	−	0.705048i	$-0.750925\pi$
$127$	−57.5499	+	33.2265i	−0.453149	+	0.261626i	0.256010	+	0.966674i	$0.417592\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	105.735	−	77.6912i	0.813349	−	0.597625i
$131$	28.3277			0.216242			0.108121	−	0.994138i	$-0.465517\pi$
$131$	28.3277			0.216242			0.108121	+	0.994138i	$0.465517\pi$
$132$		0			0
$133$	−26.6107	−	46.0911i	−0.200080	−	0.346549i
$134$	−52.9235	−	30.5554i	−0.394952	−	0.228025i
$135$		0			0
$136$	−44.1557	+	11.8315i	−0.324674	+	0.0869962i
$137$	−13.0272	−	48.6183i	−0.0950892	−	0.354878i	0.901944	−	0.431854i	$-0.142140\pi$
$137$	−13.0272	−	48.6183i	−0.0950892	−	0.354878i	−0.997033	+	0.0769757i	$0.975474\pi$
$138$		0			0
$139$	74.1420	−	128.418i	0.533396	−	0.923868i	−0.465844	−	0.884867i	$-0.654249\pi$
$139$	74.1420	−	128.418i	0.533396	−	0.923868i	0.999239	−	0.0390012i	$-0.0124176\pi$
$140$	−64.3410	+	37.1473i	−0.459579	+	0.265338i
$141$		0			0
$142$		−	156.361i		−	1.10114i
$143$	97.4283	+	14.8958i	0.681316	+	0.104167i
$144$		0			0
$145$	61.2810	−	228.704i	0.422628	−	1.57727i
$146$	36.8385	+	63.8062i	0.252319	+	0.437029i
$147$		0			0
$148$	−92.5703	−	92.5703i	−0.625475	−	0.625475i
$149$	40.4254	−	10.8320i	0.271312	−	0.0726977i	−0.120598	−	0.992701i	$-0.538481\pi$
$149$	40.4254	−	10.8320i	0.271312	−	0.0726977i	0.391910	+	0.920004i	$0.371815\pi$
$150$		0			0
$151$	−2.57635	+	2.57635i	−0.0170619	+	0.0170619i	−0.715586	−	0.698524i	$-0.753840\pi$
$151$	−2.57635	+	2.57635i	−0.0170619	+	0.0170619i	0.698524	+	0.715586i	$0.253840\pi$
$152$	−14.4604	+	25.0462i	−0.0951343	+	0.164777i
$153$		0			0
$154$	−53.9062	−	14.4441i	−0.350040	−	0.0937929i
$155$		−	345.497i		−	2.22901i
$156$		0			0
$157$	275.987			1.75788			0.878939	−	0.476934i	$-0.158252\pi$
$157$	275.987			1.75788			0.878939	+	0.476934i	$0.158252\pi$
$158$	−4.89987	+	18.2866i	−0.0310118	+	0.115738i
$159$		0			0
$160$	34.9633	+	20.1861i	0.218520	+	0.126163i
$161$	−35.2395	−	35.2395i	−0.218879	−	0.218879i
$162$		0			0
$163$	−36.3840	−	135.787i	−0.223214	−	0.833048i	−0.983112	−	0.183005i	$-0.941418\pi$
$163$	−36.3840	−	135.787i	−0.223214	−	0.833048i	0.759898	−	0.650043i	$-0.225249\pi$
$164$	77.0233	−	77.0233i	0.469654	−	0.469654i
$165$		0			0
$166$	−161.295	+	93.1237i	−0.971657	+	0.560986i
$167$	−189.805	−	50.8582i	−1.13656	−	0.304540i	−0.358992	−	0.933341i	$-0.616879\pi$
$167$	−189.805	−	50.8582i	−1.13656	−	0.304540i	−0.777566	+	0.628801i	$0.783546\pi$
$168$		0			0
$169$	164.920	−	36.9085i	0.975861	−	0.218394i
$170$	163.125			0.959556
$171$		0			0
$172$	47.0461	+	81.4863i	0.273524	+	0.473758i
$173$	−114.533	−	66.1255i	−0.662039	−	0.382228i	0.131015	−	0.991380i	$-0.458177\pi$
$173$	−114.533	−	66.1255i	−0.662039	−	0.382228i	−0.793053	+	0.609152i	$0.791510\pi$
$174$		0			0
$175$	130.390	−	34.9379i	0.745086	−	0.199645i
$176$	7.84902	+	29.2929i	0.0445967	+	0.166437i
$177$		0			0
$178$	−35.5877	+	61.6398i	−0.199931	+	0.346291i
$179$	−30.6843	+	17.7156i	−0.171421	+	0.0989697i	−0.583255	−	0.812289i	$-0.698221\pi$
$179$	−30.6843	+	17.7156i	−0.171421	+	0.0989697i	0.411835	+	0.911258i	$0.364888\pi$
$180$		0			0
$181$			121.119i			0.669163i	0.942367	+	0.334582i	$0.108595\pi$
$181$			121.119i			0.669163i	−0.942367	+	0.334582i	$0.891405\pi$
$182$	−95.1135	+	10.5130i	−0.522602	+	0.0577636i
$183$		0			0
$184$	−7.00914	+	26.1585i	−0.0380932	+	0.142166i
$185$	233.579	+	404.570i	1.26259	+	2.18686i
$186$		0			0
$187$	86.6447	+	86.6447i	0.463341	+	0.463341i
$188$	130.650	−	35.0077i	0.694949	−	0.186211i
$189$		0			0
$190$	72.9747	−	72.9747i	0.384077	−	0.384077i
$191$	100.282	−	173.693i	0.525036	−	0.909389i	−0.474539	−	0.880235i	$-0.657385\pi$
$191$	100.282	−	173.693i	0.525036	−	0.909389i	0.999575	−	0.0291545i	$-0.00928147\pi$
$192$		0			0
$193$	25.2721	+	6.77163i	0.130943	+	0.0350862i	0.323695	−	0.946161i	$-0.395075\pi$
$193$	25.2721	+	6.77163i	0.130943	+	0.0350862i	−0.192752	+	0.981247i	$0.561741\pi$
$194$			76.9267i			0.396529i
$195$		0			0
$196$	−43.8160			−0.223551
$197$	24.5163	−	91.4962i	0.124448	−	0.464448i	−0.875371	−	0.483452i	$-0.839383\pi$
$197$	24.5163	−	91.4962i	0.124448	−	0.464448i	0.999819	+	0.0190039i	$0.00604951\pi$
$198$		0			0
$199$	170.780	+	98.5996i	0.858188	+	0.495475i	0.863405	−	0.504511i	$-0.168327\pi$
$199$	170.780	+	98.5996i	0.858188	+	0.495475i	−0.00521676	+	0.999986i	$0.501661\pi$
$200$	−51.8692	−	51.8692i	−0.259346	−	0.259346i
$201$		0			0
$202$	8.25377	+	30.8035i	0.0408602	+	0.152492i
$203$	−122.104	+	122.104i	−0.601496	+	0.601496i
$204$		0			0
$205$	−336.623	+	194.350i	−1.64207	+	0.948047i
$206$	149.423	+	40.0378i	0.725354	+	0.194358i
$207$		0			0
$208$	30.7901	+	41.9043i	0.148029	+	0.201463i
$209$	77.5219			0.370918
$210$		0			0
$211$	97.4174	+	168.732i	0.461694	+	0.799677i	0.999046	−	0.0436812i	$-0.0139086\pi$
$211$	97.4174	+	168.732i	0.461694	+	0.799677i	−0.537352	+	0.843358i	$0.680575\pi$
$212$	116.944	+	67.5177i	0.551623	+	0.318480i
$213$		0			0
$214$	−44.9081	+	12.0331i	−0.209851	+	0.0562294i
$215$	−86.9014	−	324.320i	−0.404193	−	1.50847i
$216$		0			0
$217$	−125.988	+	218.217i	−0.580588	+	1.00561i
$218$	−259.956	+	150.086i	−1.19246	+	0.688467i
$219$		0			0
$220$		−	108.217i		−	0.491896i
$221$	192.398	+	84.4275i	0.870580	+	0.382025i
$222$		0			0
$223$	106.021	−	395.676i	0.475431	−	1.77433i	−0.144319	−	0.989531i	$-0.546099\pi$
$223$	106.021	−	395.676i	0.475431	−	1.77433i	0.619750	−	0.784800i	$-0.287234\pi$
$224$	−14.7220	−	25.4992i	−0.0657230	−	0.113836i
$225$		0			0
$226$	118.788	+	118.788i	0.525609	+	0.525609i
$227$	−241.186	+	64.6255i	−1.06249	+	0.284694i	−0.747405	−	0.664369i	$-0.768700\pi$
$227$	−241.186	+	64.6255i	−1.06249	+	0.284694i	−0.315087	+	0.949063i	$0.602034\pi$
$228$		0			0
$229$	−174.256	+	174.256i	−0.760945	+	0.760945i	−0.976493	−	0.215548i	$-0.930846\pi$
$229$	−174.256	+	174.256i	−0.760945	+	0.760945i	0.215548	+	0.976493i	$0.430846\pi$
$230$	48.3187	−	83.6905i	0.210081	−	0.363872i
$231$		0			0
$232$	90.6384	+	24.2865i	0.390683	+	0.104683i
$233$			290.609i			1.24725i	0.781724	+	0.623624i	$0.214340\pi$
$233$			290.609i			1.24725i	−0.781724	+	0.623624i	$0.785660\pi$
$234$		0			0
$235$	−482.663			−2.05388
$236$	38.9835	−	145.488i	0.165184	−	0.616476i
$237$		0			0
$238$	−103.030	−	59.4844i	−0.432899	−	0.249935i
$239$	−215.875	−	215.875i	−0.903243	−	0.903243i	0.0924720	−	0.995715i	$-0.470523\pi$
$239$	−215.875	−	215.875i	−0.903243	−	0.903243i	−0.995715	+	0.0924720i	$0.970523\pi$
$240$		0			0
$241$	−31.0933	−	116.042i	−0.129018	−	0.481502i	0.870933	−	0.491402i	$-0.163515\pi$
$241$	−31.0933	−	116.042i	−0.129018	−	0.481502i	−0.999951	+	0.00989998i	$0.996849\pi$
$242$	−63.5198	+	63.5198i	−0.262479	+	0.262479i
$243$		0			0
$244$	122.143	−	70.5195i	0.500587	−	0.289014i
$245$	151.026	+	40.4674i	0.616434	+	0.165173i
$246$		0			0
$247$	123.839	−	48.3013i	0.501374	−	0.195552i
$248$	136.925			0.552116
$249$		0			0
$250$	4.71659	+	8.16937i	0.0188663	+	0.0326775i
$251$	151.116	+	87.2471i	0.602057	+	0.347598i	0.769850	−	0.638224i	$-0.220331\pi$
$251$	151.116	+	87.2471i	0.602057	+	0.347598i	−0.167793	+	0.985822i	$0.553664\pi$
$252$		0			0
$253$	70.1175	−	18.7879i	0.277144	−	0.0742606i
$254$	24.3235	+	90.7764i	0.0957617	+	0.357387i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	4.02596	−	2.32439i	0.0156652	−	0.00904433i	−0.492147	−	0.870512i	$-0.663788\pi$
$257$	4.02596	−	2.32439i	0.0156652	−	0.00904433i	0.507812	+	0.861468i	$0.330454\pi$
$258$		0			0
$259$		−	340.704i		−	1.31546i
$260$	−67.4264	−	172.874i	−0.259332	−	0.664901i
$261$		0			0
$262$	10.3687	−	38.6964i	0.0395750	−	0.147696i
$263$	6.92157	+	11.9885i	0.0263177	+	0.0455837i	0.878884	−	0.477035i	$-0.158289\pi$
$263$	6.92157	+	11.9885i	0.0263177	+	0.0455837i	−0.852567	+	0.522619i	$0.824955\pi$
$264$		0			0
$265$	−340.729	−	340.729i	−1.28577	−	1.28577i
$266$	−72.7018	+	19.4804i	−0.273315	+	0.0732345i
$267$		0			0
$268$	−61.1108	+	61.1108i	−0.228025	+	0.228025i
$269$	−230.126	+	398.590i	−0.855487	+	1.48175i	0.0207059	+	0.999786i	$0.493409\pi$
$269$	−230.126	+	398.590i	−0.855487	+	1.48175i	−0.876193	+	0.481961i	$0.839925\pi$
$270$		0			0
$271$	143.260	+	38.3864i	0.528635	+	0.141647i	0.513258	−	0.858234i	$-0.328438\pi$
$271$	143.260	+	38.3864i	0.528635	+	0.141647i	0.0153773	+	0.999882i	$0.495105\pi$
$272$			64.6484i			0.237678i
$273$		0			0
$274$	−71.1821			−0.259789
$275$	−50.8903	+	189.925i	−0.185056	+	0.690637i
$276$		0			0
$277$	323.280	+	186.646i	1.16707	+	0.673811i	0.952989	−	0.303004i	$-0.0979896\pi$
$277$	323.280	+	186.646i	1.16707	+	0.673811i	0.214085	+	0.976815i	$0.431323\pi$
$278$	−148.284	−	148.284i	−0.533396	−	0.533396i
$279$		0			0
$280$	27.1937	+	101.488i	0.0971204	+	0.362458i
$281$	136.099	−	136.099i	0.484337	−	0.484337i	−0.422177	−	0.906514i	$-0.638734\pi$
$281$	136.099	−	136.099i	0.484337	−	0.484337i	0.906514	+	0.422177i	$0.138734\pi$
$282$		0			0
$283$	−329.692	+	190.347i	−1.16499	+	0.672606i	−0.952494	−	0.304557i	$-0.901492\pi$
$283$	−329.692	+	190.347i	−1.16499	+	0.672606i	−0.212493	+	0.977162i	$0.568158\pi$
$284$	−213.594	−	57.2322i	−0.752090	−	0.201522i
$285$		0			0
$286$	56.0093	−	127.637i	0.195837	−	0.446284i
$287$	283.483			0.987747
$288$		0			0
$289$	−13.8932	−	24.0638i	−0.0480735	−	0.0832657i
$290$	−289.985	−	167.423i	−0.999948	−	0.577320i
$291$		0			0
$292$	100.645	−	26.9677i	0.344674	−	0.0923551i
$293$	1.43061	+	5.33910i	0.00488262	+	0.0182222i	0.968324	−	0.249696i	$-0.0803308\pi$
$293$	1.43061	+	5.33910i	0.00488262	+	0.0182222i	−0.963442	+	0.267919i	$0.913664\pi$
$294$		0			0
$295$	−268.739	+	465.470i	−0.910981	+	1.57787i
$296$	−160.336	+	92.5703i	−0.541677	+	0.312737i
$297$		0			0
$298$		−	59.1870i		−	0.198614i
$299$	100.305	−	73.7012i	0.335468	−	0.246492i
$300$		0			0
$301$	−63.3783	+	236.531i	−0.210559	+	0.785818i
$302$	2.57635	+	4.46237i	0.00853096	+	0.0147760i
$303$		0			0
$304$	28.9208	+	28.9208i	0.0951343	+	0.0951343i
$305$	−486.138	+	130.260i	−1.59389	+	0.427083i
$306$		0			0
$307$	−227.287	+	227.287i	−0.740349	+	0.740349i	−0.972645	−	0.232296i	$-0.925376\pi$
$307$	−227.287	+	227.287i	−0.740349	+	0.740349i	0.232296	+	0.972645i	$0.425376\pi$
$308$	−39.4621	+	68.3503i	−0.128124	+	0.221916i
$309$		0			0
$310$	−471.957	−	126.461i	−1.52244	−	0.407937i
$311$			308.864i			0.993132i	0.867999	+	0.496566i	$0.165406\pi$
$311$			308.864i			0.993132i	−0.867999	+	0.496566i	$0.834594\pi$
$312$		0			0
$313$	2.51660			0.00804026			0.00402013	−	0.999992i	$-0.498720\pi$
$313$	2.51660			0.00804026			0.00402013	+	0.999992i	$0.498720\pi$
$314$	101.018	−	377.005i	0.321714	−	1.20065i
$315$		0			0
$316$	23.1864	+	13.3867i	0.0733748	+	0.0423630i
$317$	−46.8460	−	46.8460i	−0.147779	−	0.147779i	0.629346	−	0.777125i	$-0.283323\pi$
$317$	−46.8460	−	46.8460i	−0.147779	−	0.147779i	−0.777125	+	0.629346i	$0.783323\pi$
$318$		0			0
$319$	−65.0996	−	242.955i	−0.204074	−	0.761615i
$320$	40.3721	−	40.3721i	0.126163	−	0.126163i
$321$		0			0
$322$	−61.0366	+	35.2395i	−0.189555	+	0.109439i
$323$	159.627	+	42.7720i	0.494202	+	0.132421i
$324$		0			0
$325$	37.0399	+	335.109i	0.113969	+	1.03111i
$326$	−198.806			−0.609833
$327$		0			0
$328$	−77.0233	−	133.408i	−0.234827	−	0.406732i
$329$	304.852	+	176.006i	0.926600	+	0.534973i
$330$		0			0
$331$	232.042	−	62.1755i	0.701033	−	0.187841i	0.109340	−	0.994004i	$-0.465126\pi$
$331$	232.042	−	62.1755i	0.701033	−	0.187841i	0.591693	+	0.806163i	$0.298460\pi$
$332$	68.1713	+	254.419i	0.205335	+	0.766321i
$333$		0			0
$334$	−138.947	+	240.663i	−0.416009	+	0.720549i
$335$	267.079	−	154.198i	0.797252	−	0.460293i
$336$		0			0
$337$		−	5.72952i		−	0.0170015i	−0.999964	−	0.00850077i	$-0.997294\pi$
$337$		−	5.72952i		−	0.0170015i	0.999964	−	0.00850077i	$-0.00270591\pi$
$338$	9.94712	−	238.795i	0.0294293	−	0.706494i
$339$		0			0
$340$	59.7077	−	222.832i	0.175611	−	0.655389i
$341$	−183.513	−	317.853i	−0.538161	−	0.932121i
$342$		0			0
$343$	−260.976	−	260.976i	−0.760863	−	0.760863i
$344$	128.532	−	34.4402i	0.373641	−	0.100117i
$345$		0			0
$346$	−132.251	+	132.251i	−0.382228	+	0.382228i
$347$	−51.4856	+	89.1757i	−0.148373	+	0.256990i	−0.930626	−	0.365971i	$-0.880737\pi$
$347$	−51.4856	+	89.1757i	−0.148373	+	0.256990i	0.782253	+	0.622961i	$0.214070\pi$
$348$		0			0
$349$	468.190	+	125.451i	1.34152	+	0.359459i	0.856997	−	0.515321i	$-0.172327\pi$
$349$	468.190	+	125.451i	1.34152	+	0.359459i	0.484521	+	0.874780i	$0.338994\pi$
$350$		−	190.904i		−	0.545441i
$351$		0			0
$352$	42.8878			0.121840
$353$	50.9642	−	190.201i	0.144375	−	0.538813i	−0.855408	−	0.517955i	$-0.826693\pi$
$353$	50.9642	−	190.201i	0.144375	−	0.538813i	0.999782	−	0.0208583i	$-0.00663989\pi$
$354$		0			0
$355$	683.363	+	394.540i	1.92497	+	1.11138i
$356$	71.1755	+	71.1755i	0.199931	+	0.199931i
$357$		0			0
$358$	12.9687	+	48.3998i	0.0362254	+	0.135195i
$359$	54.1215	−	54.1215i	0.150756	−	0.150756i	−0.627699	−	0.778456i	$-0.716003\pi$
$359$	54.1215	−	54.1215i	0.150756	−	0.150756i	0.778456	+	0.627699i	$0.216003\pi$
$360$		0			0
$361$	−222.091	+	128.224i	−0.615210	+	0.355192i
$362$	165.451	+	44.3325i	0.457047	+	0.122465i
$363$		0			0
$364$	−20.4530	+	133.775i	−0.0561895	+	0.367515i
$365$	−371.812			−1.01866
$366$		0			0
$367$	107.824	+	186.757i	0.293799	+	0.508875i	0.974705	−	0.223496i	$-0.0717470\pi$
$367$	107.824	+	186.757i	0.293799	+	0.508875i	−0.680906	+	0.732371i	$0.738414\pi$
$368$	33.1676	+	19.1493i	0.0901294	+	0.0520362i
$369$		0			0
$370$	638.149	−	170.991i	1.72473	−	0.462139i
$371$	90.9566	+	339.455i	0.245166	+	0.914972i
$372$		0			0
$373$	315.693	−	546.797i	0.846363	−	1.46594i	−0.0380693	−	0.999275i	$-0.512121\pi$
$373$	315.693	−	546.797i	0.846363	−	1.46594i	0.884432	−	0.466669i	$-0.154546\pi$
$374$	150.073	−	86.6447i	0.401265	−	0.231670i
$375$		0			0
$376$		−	191.286i		−	0.508738i
$377$	−255.372	−	347.554i	−0.677380	−	0.921894i
$378$		0			0
$379$	−64.5160	+	240.777i	−0.170227	+	0.635296i	0.827089	+	0.562072i	$0.189995\pi$
$379$	−64.5160	+	240.777i	−0.170227	+	0.635296i	−0.997316	+	0.0732240i	$0.976671\pi$
$380$	−72.9747	−	126.396i	−0.192039	−	0.332621i
$381$		0			0
$382$	−200.564	−	200.564i	−0.525036	−	0.525036i
$383$	−271.369	+	72.7131i	−0.708535	+	0.189851i	−0.595050	−	0.803688i	$-0.702868\pi$
$383$	−271.369	+	72.7131i	−0.708535	+	0.189851i	−0.113485	+	0.993540i	$0.536201\pi$
$384$		0			0
$385$	199.146	−	199.146i	0.517262	−	0.517262i
$386$	18.5004	−	32.0437i	0.0479286	−	0.0830148i
$387$		0			0
$388$	105.084	+	28.1571i	0.270835	+	0.0725699i
$389$		−	265.150i		−	0.681620i	−0.940132	−	0.340810i	$-0.889299\pi$
$389$		−	265.150i		−	0.681620i	0.940132	−	0.340810i	$-0.110701\pi$
$390$		0			0
$391$	154.747			0.395772
$392$	−16.0378	+	59.8538i	−0.0409127	+	0.152688i
$393$		0			0
$394$	−116.013	−	66.9799i	−0.294448	−	0.170000i
$395$	−67.5561	−	67.5561i	−0.171028	−	0.171028i
$396$		0			0
$397$	−32.5780	−	121.583i	−0.0820604	−	0.306253i	0.912681	−	0.408673i	$-0.134008\pi$
$397$	−32.5780	−	121.583i	−0.0820604	−	0.306253i	−0.994741	+	0.102419i	$0.967342\pi$
$398$	197.199	−	197.199i	0.495475	−	0.495475i
$399$		0			0
$400$	−89.8402	+	51.8692i	−0.224600	+	0.129673i
$401$	537.968	+	144.148i	1.34157	+	0.359472i	0.857015	−	0.515291i	$-0.172316\pi$
$401$	537.968	+	144.148i	1.34157	+	0.359472i	0.484551	+	0.874763i	$0.338983\pi$
$402$		0			0
$403$	−491.201	−	393.423i	−1.21886	−	0.976235i
$404$	45.0994			0.111632
$405$		0			0
$406$	122.104	+	211.490i	0.300748	+	0.520911i
$407$	429.780	+	248.134i	1.05597	+	0.609665i
$408$		0			0
$409$	199.444	−	53.4410i	0.487639	−	0.130663i	−0.00661830	−	0.999978i	$-0.502107\pi$
$409$	199.444	−	53.4410i	0.487639	−	0.130663i	0.494257	+	0.869316i	$0.335440\pi$
$410$	142.274	+	530.973i	0.347009	+	1.29506i
$411$		0			0
$412$	109.385	−	189.461i	0.265498	−	0.459856i
$413$	339.474	−	195.995i	0.821970	−	0.474564i
$414$		0			0
$415$		−	939.900i		−	2.26482i
$416$	68.5123	−	26.7220i	0.164693	−	0.0642355i
$417$		0			0
$418$	28.3750	−	105.897i	0.0678828	−	0.253342i
$419$	167.706	+	290.475i	0.400253	+	0.693259i	0.993756	−	0.111573i	$-0.0355889\pi$
$419$	167.706	+	290.475i	0.400253	+	0.693259i	−0.593503	+	0.804832i	$0.702256\pi$
$420$		0			0
$421$	274.627	+	274.627i	0.652321	+	0.652321i	0.953551	−	0.301230i	$-0.0973973\pi$
$421$	274.627	+	274.627i	0.652321	+	0.652321i	−0.301230	+	0.953551i	$0.597397\pi$
$422$	266.149	−	71.3145i	0.630685	−	0.168992i
$423$		0			0
$424$	135.035	−	135.035i	0.318480	−	0.318480i
$425$	−209.579	+	363.001i	−0.493127	+	0.854121i
$426$		0			0
$427$	354.547	+	95.0005i	0.830320	+	0.222484i
$428$			65.7500i			0.153621i
$429$		0			0
$430$	−474.838			−1.10427
$431$	−35.5849	+	132.805i	−0.0825635	+	0.308131i	−0.994842	−	0.101440i	$-0.967655\pi$
$431$	−35.5849	+	132.805i	−0.0825635	+	0.308131i	0.912278	+	0.409571i	$0.134322\pi$
$432$		0			0
$433$	−364.107	−	210.217i	−0.840893	−	0.485490i	0.0166746	−	0.999861i	$-0.494692\pi$
$433$	−364.107	−	210.217i	−0.840893	−	0.485490i	−0.857568	+	0.514371i	$0.828025\pi$
$434$	251.975	+	251.975i	0.580588	+	0.580588i
$435$		0			0
$436$	109.871	+	410.042i	0.251997	+	0.940464i
$437$	69.2268	−	69.2268i	0.158414	−	0.158414i
$438$		0			0
$439$	645.502	−	372.680i	1.47039	−	0.848930i	0.470943	−	0.882164i	$-0.343914\pi$
$439$	645.502	−	372.680i	1.47039	−	0.848930i	0.999448	+	0.0332332i	$0.0105804\pi$
$440$	−147.827	−	39.6102i	−0.335971	−	0.0900231i
$441$		0			0
$442$	185.753	−	231.918i	0.420255	−	0.524702i
$443$	−661.917			−1.49417			−0.747084	−	0.664729i	$-0.768547\pi$
$443$	−661.917			−1.49417			−0.747084	+	0.664729i	$0.768547\pi$
$444$		0			0
$445$	−179.594	−	311.066i	−0.403582	−	0.699025i
$446$	−501.697	−	289.655i	−1.12488	−	0.649450i
$447$		0			0
$448$	−40.2211	+	10.7772i	−0.0897793	+	0.0240563i
$449$	8.12050	+	30.3061i	0.0180857	+	0.0674969i	0.974379	−	0.224913i	$-0.0722096\pi$
$449$	8.12050	+	30.3061i	0.0180857	+	0.0674969i	−0.956293	+	0.292409i	$0.905543\pi$
$450$		0			0
$451$	−206.460	+	357.599i	−0.457783	+	0.792903i
$452$	205.746	−	118.788i	0.455191	−	0.262805i
$453$		0			0
$454$			353.120i			0.777798i
$455$	194.050	−	442.212i	0.426483	−	0.971894i
$456$		0			0
$457$	−42.0960	+	157.104i	−0.0921137	+	0.343773i	−0.996566	−	0.0828016i	$-0.973613\pi$
$457$	−42.0960	+	157.104i	−0.0921137	+	0.343773i	0.904452	+	0.426575i	$0.140280\pi$
$458$	174.256	+	301.821i	0.380472	+	0.658997i
$459$		0			0
$460$	−96.6374	−	96.6374i	−0.210081	−	0.210081i
$461$	77.8033	−	20.8473i	0.168771	−	0.0452220i	−0.173444	−	0.984844i	$-0.555490\pi$
$461$	77.8033	−	20.8473i	0.168771	−	0.0452220i	0.342215	+	0.939622i	$0.388823\pi$
$462$		0			0
$463$	−172.856	+	172.856i	−0.373338	+	0.373338i	−0.868692	−	0.495353i	$-0.835039\pi$
$463$	−172.856	+	172.856i	−0.373338	+	0.373338i	0.495353	+	0.868692i	$0.335039\pi$
$464$	66.3519	−	114.925i	0.143000	−	0.247683i
$465$		0			0
$466$	396.979	+	106.370i	0.851887	+	0.228262i
$467$			649.970i			1.39180i	0.718139	+	0.695899i	$0.244994\pi$
$467$			649.970i			1.39180i	−0.718139	+	0.695899i	$0.755006\pi$
$468$		0			0
$469$	−224.918			−0.479569
$470$	−176.667	+	659.329i	−0.375887	+	1.40283i
$471$		0			0
$472$	−184.472	−	106.505i	−0.390830	−	0.225646i
$473$	−252.213	−	252.213i	−0.533221	−	0.533221i
$474$		0			0
$475$	68.6344	+	256.147i	0.144493	+	0.539257i
$476$	−118.969	+	118.969i	−0.249935	+	0.249935i
$477$		0			0
$478$	−373.907	+	215.875i	−0.782232	+	0.451622i
$479$	490.789	+	131.507i	1.02461	+	0.274544i	0.731723	−	0.681602i	$-0.238717\pi$
$479$	490.789	+	131.507i	1.02461	+	0.274544i	0.292890	+	0.956146i	$0.405383\pi$
$480$		0			0
$481$	841.167	+	128.606i	1.74879	+	0.267373i
$482$	−169.897			−0.352484
$483$		0			0
$484$	63.5198	+	110.020i	0.131239	+	0.227313i
$485$	−336.201	−	194.106i	−0.693198	−	0.400218i
$486$		0			0
$487$	−749.567	+	200.846i	−1.53915	+	0.412415i	−0.925992	−	0.377544i	$-0.876769\pi$
$487$	−749.567	+	200.846i	−1.53915	+	0.412415i	−0.613161	+	0.789958i	$0.710102\pi$
$488$	−51.6238	−	192.663i	−0.105787	−	0.394801i
$489$		0			0
$490$	110.559	−	191.494i	0.225631	−	0.390804i
$491$	108.265	−	62.5068i	0.220499	−	0.127305i	−0.385682	−	0.922632i	$-0.626034\pi$
$491$	108.265	−	62.5068i	0.220499	−	0.127305i	0.606181	+	0.795327i	$0.292701\pi$
$492$		0			0
$493$		−	536.193i		−	1.08761i
$494$	−20.6524	−	186.847i	−0.0418065	−	0.378234i
$495$		0			0
$496$	50.1180	−	187.043i	0.101044	−	0.377102i
$497$	−287.743	−	498.386i	−0.578960	−	1.00279i
$498$		0			0
$499$	151.406	+	151.406i	0.303419	+	0.303419i	0.842350	−	0.538931i	$-0.181172\pi$
$499$	151.406	+	151.406i	0.303419	+	0.303419i	−0.538931	+	0.842350i	$0.681172\pi$
$500$	12.8860	−	3.45278i	0.0257719	−	0.00690556i
$501$		0			0
$502$	174.494	−	174.494i	0.347598	−	0.347598i
$503$	263.256	−	455.973i	0.523372	−	0.906506i	−0.476258	−	0.879305i	$-0.658007\pi$
$503$	263.256	−	455.973i	0.523372	−	0.906506i	0.999630	−	0.0272010i	$-0.00865940\pi$
$504$		0			0
$505$	−155.450	−	41.6527i	−0.307822	−	0.0824807i
$506$		−	102.659i		−	0.202884i
$507$		0			0
$508$	132.906			0.261626
$509$	249.649	−	931.702i	0.490469	−	1.83046i	−0.0635873	−	0.997976i	$-0.520254\pi$
$509$	249.649	−	931.702i	0.490469	−	1.83046i	0.554056	−	0.832479i	$-0.313079\pi$
$510$		0			0
$511$	234.838	+	135.584i	0.459566	+	0.265330i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−1.70157	−	6.35036i	−0.00331045	−	0.0123548i
$515$	−552.014	+	552.014i	−1.07187	+	1.07187i
$516$		0			0
$517$	−444.045	+	256.369i	−0.858888	+	0.495879i
$518$	−465.410	−	124.706i	−0.898475	−	0.240746i
$519$		0			0
$520$	−260.830	+	28.8298i	−0.501597	+	0.0554419i
$521$	158.382			0.303997			0.151998	−	0.988381i	$-0.451429\pi$
$521$	158.382			0.303997			0.151998	+	0.988381i	$0.451429\pi$
$522$		0			0
$523$	114.739	+	198.734i	0.219386	+	0.379989i	0.954621	−	0.297825i	$-0.0962611\pi$
$523$	114.739	+	198.734i	0.219386	+	0.379989i	−0.735234	+	0.677813i	$0.762928\pi$
$524$	−49.0650	−	28.3277i	−0.0936356	−	0.0540605i
$525$		0			0
$526$	18.9101	−	5.06694i	0.0359507	−	0.00963296i
$527$	−202.503	−	755.751i	−0.384256	−	1.43406i
$528$		0			0
$529$	−218.663	+	378.735i	−0.413351	+	0.715945i
$530$	−590.160	+	340.729i	−1.11351	+	0.642885i
$531$		0			0
$532$			106.443i			0.200080i
$533$	−107.007	+	699.895i	−0.200764	+	1.31312i
$534$		0			0
$535$	60.7251	−	226.629i	0.113505	−	0.423606i
$536$	61.1108	+	105.847i	0.114013	+	0.197476i
$537$		0			0
$538$	460.252	+	460.252i	0.855487	+	0.855487i
$539$	160.437	−	42.9891i	0.297657	−	0.0797571i
$540$		0			0
$541$	606.240	−	606.240i	1.12059	−	1.12059i	0.128938	−	0.991653i	$-0.458843\pi$
$541$	606.240	−	606.240i	1.12059	−	1.12059i	0.991653	−	0.128938i	$-0.0411569\pi$
$542$	104.874	−	181.647i	0.193494	−	0.335141i
$543$		0			0
$544$	88.3114	+	23.6630i	0.162337	+	0.0434981i
$545$		−	1514.82i		−	2.77949i
$546$		0			0
$547$	−790.673			−1.44547			−0.722736	−	0.691124i	$-0.757116\pi$
$547$	−790.673			−1.44547			−0.722736	+	0.691124i	$0.757116\pi$
$548$	−26.0545	+	97.2365i	−0.0475446	+	0.177439i
$549$		0			0
$550$	240.816	+	139.035i	0.437847	+	0.252791i
$551$	−239.869	−	239.869i	−0.435334	−	0.435334i
$552$		0			0
$553$	18.0339	+	67.3035i	0.0326111	+	0.121706i
$554$	373.291	−	373.291i	0.673811	−	0.673811i
$555$		0			0
$556$	−256.835	+	148.284i	−0.461934	+	0.266698i
$557$	414.689	+	111.116i	0.744505	+	0.199490i	0.611080	−	0.791569i	$-0.290736\pi$
$557$	414.689	+	111.116i	0.744505	+	0.199490i	0.133426	+	0.991059i	$0.457402\pi$
$558$		0			0
$559$	−560.051	−	245.759i	−1.00188	−	0.439641i
$560$	148.589			0.265338
$561$		0			0
$562$	−136.099	−	235.730i	−0.242168	−	0.419448i
$563$	276.549	+	159.665i	0.491206	+	0.283598i	0.725074	−	0.688671i	$-0.241805\pi$
$563$	276.549	+	159.665i	0.491206	+	0.283598i	−0.233869	+	0.972268i	$0.575139\pi$
$564$		0			0
$565$	−818.883	+	219.419i	−1.44935	+	0.388352i
$566$	139.344	+	520.039i	0.246191	+	0.918797i
$567$		0			0
$568$	−156.361	+	270.826i	−0.275284	+	0.476806i
$569$	−687.019	+	396.650i	−1.20741	+	0.697101i	−0.962194	−	0.272366i	$-0.912194\pi$
$569$	−687.019	+	396.650i	−1.20741	+	0.697101i	−0.245221	+	0.969467i	$0.578860\pi$
$570$		0			0
$571$			852.111i			1.49231i	0.665771	+	0.746156i	$0.268103\pi$
$571$			852.111i			1.49231i	−0.665771	+	0.746156i	$0.731897\pi$
$572$	−153.855	−	123.229i	−0.268977	−	0.215435i
$573$		0			0
$574$	103.762	−	387.245i	0.180770	−	0.674644i
$575$	124.158	+	215.047i	0.215926	+	0.373996i
$576$		0			0
$577$	−186.391	−	186.391i	−0.323035	−	0.323035i	0.526895	−	0.849930i	$-0.323356\pi$
$577$	−186.391	−	186.391i	−0.323035	−	0.323035i	−0.849930	+	0.526895i	$0.823356\pi$
$578$	−37.9570	+	10.1706i	−0.0656696	+	0.0175961i
$579$		0			0
$580$	−334.846	+	334.846i	−0.577320	+	0.577320i
$581$	−342.741	+	593.644i	−0.589915	+	1.02176i
$582$		0			0
$583$	−494.448	−	132.487i	−0.848109	−	0.227250i
$584$		−	147.354i		−	0.252319i
$585$		0			0
$586$	7.81698			0.0133396
$587$	−203.087	+	757.931i	−0.345975	+	1.29119i	0.545495	+	0.838114i	$0.316342\pi$
$587$	−203.087	+	757.931i	−0.345975	+	1.29119i	−0.891469	+	0.453081i	$0.850325\pi$
$588$		0			0
$589$	−428.680	−	247.499i	−0.727810	−	0.420201i
$590$	537.479	+	537.479i	0.910981	+	0.910981i
$591$		0			0
$592$	67.7661	+	252.907i	0.114470	+	0.427207i
$593$	375.307	−	375.307i	0.632895	−	0.632895i	−0.315898	−	0.948793i	$-0.602306\pi$
$593$	375.307	−	375.307i	0.632895	−	0.632895i	0.948793	+	0.315898i	$0.102306\pi$
$594$		0			0
$595$	519.943	−	300.189i	0.873853	−	0.504520i
$596$	−80.8509	−	21.6639i	−0.135656	−	0.0363489i
$597$		0			0
$598$	−63.9635	−	163.996i	−0.106962	−	0.274240i
$599$	−320.645			−0.535300			−0.267650	−	0.963516i	$-0.586247\pi$
$599$	−320.645			−0.535300			−0.267650	+	0.963516i	$0.586247\pi$
$600$		0			0
$601$	29.2104	+	50.5939i	0.0486030	+	0.0841828i	0.889303	−	0.457318i	$-0.151190\pi$
$601$	29.2104	+	50.5939i	0.0486030	+	0.0841828i	−0.840700	+	0.541500i	$0.817856\pi$
$602$	299.909	+	173.153i	0.498188	+	0.287629i
$603$		0			0
$604$	7.03871	−	1.88602i	0.0116535	−	0.00312255i
$605$	−117.331	−	437.884i	−0.193935	−	0.723776i
$606$		0			0
$607$	327.926	−	567.984i	0.540240	−	0.935724i	−0.458649	−	0.888617i	$-0.651667\pi$
$607$	327.926	−	567.984i	0.540240	−	0.935724i	0.998890	−	0.0471065i	$-0.0150000\pi$
$608$	50.0923	−	28.9208i	0.0823887	−	0.0475671i
$609$		0			0
$610$			711.755i			1.16681i
$611$	−549.616	+	686.214i	−0.899536	+	1.12310i
$612$		0			0
$613$	−49.8176	+	185.922i	−0.0812686	+	0.303298i	−0.994581	−	0.103960i	$-0.966849\pi$
$613$	−49.8176	+	185.922i	−0.0812686	+	0.303298i	0.913313	+	0.407259i	$0.133515\pi$
$614$	227.287	+	393.673i	0.370174	+	0.641161i
$615$		0			0
$616$	78.9241	+	78.9241i	0.128124	+	0.128124i
$617$	−19.1730	+	5.13739i	−0.0310745	+	0.00832640i	−0.274323	−	0.961638i	$-0.588454\pi$
$617$	−19.1730	+	5.13739i	−0.0310745	+	0.00832640i	0.243248	+	0.969964i	$0.421787\pi$
$618$		0			0
$619$	−319.972	+	319.972i	−0.516917	+	0.516917i	−0.916637	−	0.399720i	$-0.869107\pi$
$619$	−319.972	+	319.972i	−0.516917	+	0.516917i	0.399720	+	0.916637i	$0.369107\pi$
$620$	−345.497	+	598.418i	−0.557252	+	0.965190i
$621$		0			0
$622$	421.916	+	113.052i	0.678322	+	0.181756i
$623$			261.961i			0.420482i
$624$		0			0
$625$	600.761			0.961217
$626$	0.921140	−	3.43774i	0.00147147	−	0.00549160i
$627$		0			0
$628$	−478.023	−	275.987i	−0.761184	−	0.439470i
$629$	748.065	+	748.065i	1.18929	+	1.18929i
$630$		0			0
$631$	113.387	+	423.167i	0.179695	+	0.670629i	0.995704	+	0.0925909i	$0.0295149\pi$
$631$	113.387	+	423.167i	0.179695	+	0.670629i	−0.816010	+	0.578038i	$0.803818\pi$
$632$	26.7734	−	26.7734i	0.0423630	−	0.0423630i
$633$		0			0
$634$	−81.1397	+	46.8460i	−0.127981	+	0.0738896i
$635$	−458.104	−	122.749i	−0.721424	−	0.193305i
$636$		0			0
$637$	229.510	−	168.637i	0.360298	−	0.264736i
$638$	−355.711			−0.557541
$639$		0			0
$640$	−40.3721	−	69.9266i	−0.0630814	−	0.109260i
$641$	536.275	+	309.618i	0.836622	+	0.483024i	0.856115	−	0.516786i	$-0.172872\pi$
$641$	536.275	+	309.618i	0.836622	+	0.483024i	−0.0194927	+	0.999810i	$0.506205\pi$
$642$		0			0
$643$	−389.853	+	104.461i	−0.606304	+	0.162459i	−0.548894	−	0.835892i	$-0.684951\pi$
$643$	−389.853	+	104.461i	−0.606304	+	0.162459i	−0.0574099	+	0.998351i	$0.518284\pi$
$644$	25.7971	+	96.2760i	0.0400576	+	0.149497i
$645$		0			0
$646$	116.855	−	202.399i	0.180891	−	0.313312i
$647$	216.586	−	125.046i	0.334754	−	0.193270i	−0.323196	−	0.946332i	$-0.604757\pi$
$647$	216.586	−	125.046i	0.334754	−	0.193270i	0.657950	+	0.753062i	$0.271424\pi$
$648$		0			0
$649$			570.971i			0.879770i
$650$	471.325	+	72.0611i	0.725116	+	0.110863i
$651$		0			0
$652$	−72.7679	+	271.574i	−0.111607	+	0.416524i
$653$	−195.830	−	339.188i	−0.299894	−	0.519431i	0.676218	−	0.736702i	$-0.263618\pi$
$653$	−195.830	−	339.188i	−0.299894	−	0.519431i	−0.976111	+	0.217271i	$0.930284\pi$
$654$		0			0
$655$	142.956	+	142.956i	0.218254	+	0.218254i
$656$	−210.432	+	56.3850i	−0.320780	+	0.0859527i
$657$		0			0
$658$	352.012	−	352.012i	0.534973	−	0.534973i
$659$	−305.994	+	529.997i	−0.464330	+	0.804244i	−0.999171	−	0.0407093i	$-0.987038\pi$
$659$	−305.994	+	529.997i	−0.464330	+	0.804244i	0.534841	+	0.844953i	$0.320372\pi$
$660$		0			0
$661$	−585.429	−	156.865i	−0.885671	−	0.237315i	−0.212819	−	0.977092i	$-0.568264\pi$
$661$	−585.429	−	156.865i	−0.885671	−	0.237315i	−0.672852	+	0.739777i	$0.734931\pi$
$662$		−	339.733i		−	0.513192i
$663$		0			0
$664$	372.495			0.560986
$665$	98.3080	−	366.890i	0.147832	−	0.551715i
$666$		0			0
$667$	−275.092	−	158.824i	−0.412432	−	0.238117i
$668$	277.894	+	277.894i	0.416009	+	0.416009i
$669$		0			0
$670$	−112.881	−	421.278i	−0.168479	−	0.628773i
$671$	−378.053	+	378.053i	−0.563418	+	0.563418i
$672$		0			0
$673$	680.049	−	392.627i	1.01047	−	0.583398i	0.0991438	−	0.995073i	$-0.468390\pi$
$673$	680.049	−	392.627i	1.01047	−	0.583398i	0.911331	+	0.411675i	$0.135056\pi$
$674$	−7.82667	−	2.09715i	−0.0116123	−	0.00311150i
$675$		0			0
$676$	−322.559	−	100.993i	−0.477159	−	0.149398i
$677$	622.197			0.919051			0.459525	−	0.888165i	$-0.348020\pi$
$677$	622.197			0.919051			0.459525	+	0.888165i	$0.348020\pi$
$678$		0			0
$679$	141.564	+	245.196i	0.208489	+	0.361113i
$680$	−282.540	−	163.125i	−0.415500	−	0.239889i
$681$		0			0
$682$	−501.366	+	134.341i	−0.735141	+	0.196980i
$683$	−218.794	−	816.549i	−0.320342	−	1.19553i	−0.918912	−	0.394462i	$-0.870931\pi$
$683$	−218.794	−	816.549i	−0.320342	−	1.19553i	0.598570	−	0.801071i	$-0.295736\pi$
$684$		0			0
$685$	179.611	−	311.095i	0.262205	−	0.454153i
$686$	−452.024	+	260.976i	−0.658927	+	0.380432i
$687$		0			0
$688$		−	188.185i		−	0.273524i
$689$	−872.417	+	96.4290i	−1.26621	+	0.139955i
$690$		0			0
$691$	172.573	−	644.052i	0.249744	−	0.932058i	−0.721195	−	0.692732i	$-0.756407\pi$
$691$	172.573	−	644.052i	0.249744	−	0.932058i	0.970939	−	0.239326i	$-0.0769264\pi$
$692$	132.251	+	229.065i	0.191114	+	0.331019i
$693$		0			0
$694$	102.971	+	102.971i	0.148373	+	0.148373i
$695$	1022.22	−	273.903i	1.47082	−	0.394105i
$696$		0			0
$697$	−622.429	+	622.429i	−0.893012	+	0.893012i
$698$	342.739	−	593.641i	0.491030	−	0.850488i
$699$		0			0
$700$	−260.780	−	69.8758i	−0.372543	−	0.0998226i
$701$			299.776i			0.427640i	0.976873	+	0.213820i	$0.0685907\pi$
$701$			299.776i			0.427640i	−0.976873	+	0.213820i	$0.931409\pi$
$702$		0			0
$703$	669.302			0.952065
$704$	15.6980	−	58.5859i	0.0222983	−	0.0832186i
$705$		0			0
$706$	−241.165	−	139.237i	−0.341594	−	0.197219i
$707$	82.9940	+	82.9940i	0.117389	+	0.117389i
$708$		0			0
$709$	−88.7405	−	331.184i	−0.125163	−	0.467114i	0.874683	−	0.484696i	$-0.161070\pi$
$709$	−88.7405	−	331.184i	−0.125163	−	0.467114i	−0.999845	+	0.0175820i	$0.994403\pi$
$710$	789.080	−	789.080i	1.11138	−	1.11138i
$711$		0			0
$712$	123.280	−	71.1755i	0.173145	−	0.0999655i
$713$	−447.718	−	119.966i	−0.627936	−	0.168255i
$714$		0			0
$715$	416.501	+	566.845i	0.582519	+	0.792790i
$716$	70.8623			0.0989697
$717$		0			0
$718$	−54.1215	−	93.7412i	−0.0753781	−	0.130559i
$719$	−551.827	−	318.597i	−0.767492	−	0.443112i	0.0644873	−	0.997919i	$-0.479459\pi$
$719$	−551.827	−	318.597i	−0.767492	−	0.443112i	−0.831979	+	0.554807i	$0.812792\pi$
$720$		0			0
$721$	549.950	−	147.359i	0.762759	−	0.204381i
$722$	93.8666	+	350.315i	0.130009	+	0.485201i
$723$		0			0
$724$	121.119	−	209.783i	0.167291	−	0.289756i
$725$	745.133	−	430.203i	1.02777	−	0.593383i
$726$		0			0
$727$			617.181i			0.848943i	0.905441	+	0.424471i	$0.139540\pi$
$727$			617.181i			0.848943i	−0.905441	+	0.424471i	$0.860460\pi$
$728$	175.254	+	76.9045i	0.240734	+	0.105638i
$729$		0			0
$730$	−136.093	+	507.905i	−0.186429	+	0.695761i
$731$	−380.182	−	658.495i	−0.520085	−	0.900814i
$732$		0			0
$733$	−932.866	−	932.866i	−1.27267	−	1.27267i	−0.944683	−	0.327985i	$-0.893631\pi$
$733$	−932.866	−	932.866i	−1.27267	−	1.27267i	−0.327985	−	0.944683i	$-0.606369\pi$
$734$	294.581	−	78.9329i	0.401337	−	0.107538i
$735$		0			0
$736$	38.2987	−	38.2987i	0.0520362	−	0.0520362i
$737$	163.807	−	283.722i	0.222262	−	0.384969i
$738$		0			0
$739$	195.134	+	52.2859i	0.264051	+	0.0707523i	0.388416	−	0.921484i	$-0.373023\pi$
$739$	195.134	+	52.2859i	0.264051	+	0.0707523i	−0.124364	+	0.992237i	$0.539689\pi$
$740$		−	934.314i		−	1.26259i
$741$		0			0
$742$	496.996			0.669806
$743$	271.553	−	1013.45i	0.365482	−	1.36400i	−0.501283	−	0.865283i	$-0.667139\pi$
$743$	271.553	−	1013.45i	0.365482	−	1.36400i	0.866766	−	0.498716i	$-0.166195\pi$
$744$		0			0
$745$	258.671	+	149.344i	0.347210	+	0.200462i
$746$	−631.387	−	631.387i	−0.846363	−	0.846363i
$747$		0			0
$748$	−63.4283	−	236.718i	−0.0847972	−	0.316467i
$749$	−120.996	+	120.996i	−0.161543	+	0.161543i
$750$		0			0
$751$	1272.00	−	734.389i	1.69374	−	0.977881i	0.742288	−	0.670080i	$-0.233740\pi$
$751$	1272.00	−	734.389i	1.69374	−	0.977881i	0.951451	−	0.307800i	$-0.0995929\pi$
$752$	−261.301	−	70.0154i	−0.347475	−	0.0931055i
$753$		0			0
$754$	−568.240	+	221.632i	−0.753634	+	0.293941i
$755$	−26.0032			−0.0344413
$756$		0			0
$757$	427.864	+	741.082i	0.565210	+	0.978972i	0.997030	+	0.0770121i	$0.0245380\pi$
$757$	427.864	+	741.082i	0.565210	+	0.978972i	−0.431821	+	0.901960i	$0.642129\pi$
$758$	305.293	+	176.261i	0.402761	+	0.232534i
$759$		0			0
$760$	−199.370	+	53.4212i	−0.262330	+	0.0702910i
$761$	−111.078	−	414.549i	−0.145963	−	0.544743i	−0.999711	−	0.0240550i	$-0.992342\pi$
$761$	−111.078	−	414.549i	−0.145963	−	0.544743i	0.853747	−	0.520688i	$-0.174324\pi$
$762$		0			0
$763$	−552.390	+	956.767i	−0.723971	+	1.25395i
$764$	−347.387	+	200.564i	−0.454694	+	0.262518i
$765$		0			0
$766$			397.312i			0.518684i
$767$	355.753	+	912.112i	0.463823	+	1.18919i
$768$		0			0
$769$	114.020	−	425.529i	0.148271	−	0.553354i	−0.851317	−	0.524651i	$-0.824196\pi$
$769$	114.020	−	425.529i	0.148271	−	0.553354i	0.999588	−	0.0287025i	$-0.00913755\pi$
$770$	−199.146	−	344.931i	−0.258631	−	0.447962i
$771$		0			0
$772$	−37.0009	−	37.0009i	−0.0479286	−	0.0479286i
$773$	−1154.86	+	309.443i	−1.49399	+	0.400315i	−0.911084	−	0.412221i	$-0.864753\pi$
$773$	−1154.86	+	309.443i	−1.49399	+	0.400315i	−0.582911	+	0.812536i	$0.698086\pi$
$774$		0			0
$775$	887.773	−	887.773i	1.14551	−	1.14551i
$776$	76.9267	−	133.241i	0.0991323	−	0.171702i
$777$		0			0
$778$	−362.202	−	97.0517i	−0.465555	−	0.124745i
$779$			556.894i			0.714883i
$780$		0			0
$781$	838.250			1.07330
$782$	56.6413	−	211.388i	0.0724313	−	0.270317i
$783$		0			0
$784$	75.8915	+	43.8160i	0.0968004	+	0.0558877i
$785$	1392.77	+	1392.77i	1.77423	+	1.77423i
$786$		0			0
$787$	84.2515	+	314.431i	0.107054	+	0.399531i	0.998570	−	0.0534580i	$-0.0170243\pi$
$787$	84.2515	+	314.431i	0.107054	+	0.399531i	−0.891516	+	0.452989i	$0.850358\pi$
$788$	−133.960	+	133.960i	−0.170000	+	0.170000i
$789$		0			0
$790$	−117.011	+	67.5561i	−0.148115	+	0.0855141i
$791$	597.222	+	160.025i	0.755021	+	0.202307i
$792$		0			0
$793$	−368.379	+	839.484i	−0.464539	+	1.05862i
$794$	−178.009			−0.224193
$795$		0			0
$796$	−197.199	−	341.559i	−0.247738	−	0.429094i
$797$	−2.24946	−	1.29872i	−0.00282241	−	0.00162952i	0.498588	−	0.866839i	$-0.333852\pi$
$797$	−2.24946	−	1.29872i	−0.00282241	−	0.00162952i	−0.501411	+	0.865209i	$0.667185\pi$
$798$		0			0
$799$	−1055.79	+	282.899i	−1.32139	+	0.354066i
$800$	37.9709	+	141.709i	0.0474637	+	0.177137i
$801$		0			0
$802$	393.820	−	682.116i	0.491047	−	0.850519i
$803$	−342.064	+	197.491i	−0.425982	+	0.245941i
$804$		0			0
$805$		−	355.673i		−	0.441830i
$806$	−717.218	+	526.990i	−0.889848	+	0.653834i
$807$		0			0
$808$	16.5075	−	61.6069i	0.0204301	−	0.0762462i
$809$	−56.2400	−	97.4105i	−0.0695179	−	0.120409i	0.829171	−	0.558995i	$-0.188813\pi$
$809$	−56.2400	−	97.4105i	−0.0695179	−	0.120409i	−0.898689	+	0.438586i	$0.855479\pi$
$810$		0			0
$811$	725.545	+	725.545i	0.894630	+	0.894630i	0.994955	−	0.100324i	$-0.0319881\pi$
$811$	725.545	+	725.545i	0.894630	+	0.894630i	−0.100324	+	0.994955i	$0.531988\pi$
$812$	333.594	−	89.3861i	0.410829	−	0.110081i
$813$		0			0
$814$	496.267	−	496.267i	0.609665	−	0.609665i
$815$	501.638	−	868.862i	0.615506	−	1.06609i
$816$		0			0
$817$	−464.658	−	124.505i	−0.568737	−	0.152393i
$818$		−	292.007i		−	0.356977i
$819$		0			0
$820$	777.398			0.948047
$821$	143.499	−	535.547i	0.174786	−	0.652311i	−0.821802	−	0.569773i	$-0.807031\pi$
$821$	143.499	−	535.547i	0.174786	−	0.652311i	0.996588	−	0.0825373i	$-0.0263024\pi$
$822$		0			0
$823$	−96.1533	−	55.5142i	−0.116833	−	0.0674534i	0.440445	−	0.897780i	$-0.354821\pi$
$823$	−96.1533	−	55.5142i	−0.116833	−	0.0674534i	−0.557278	+	0.830326i	$0.688154\pi$
$824$	−218.770	−	218.770i	−0.265498	−	0.265498i
$825$		0			0
$826$	−143.478	−	535.469i	−0.173703	−	0.648267i
$827$	−878.475	+	878.475i	−1.06224	+	1.06224i	−0.0643137	+	0.997930i	$0.520486\pi$
$827$	−878.475	+	878.475i	−1.06224	+	1.06224i	−0.997930	+	0.0643137i	$0.979514\pi$
$828$		0			0
$829$	715.780	−	413.256i	0.863425	−	0.498499i	−0.00173250	−	0.999998i	$-0.500551\pi$
$829$	715.780	−	413.256i	0.863425	−	0.498499i	0.865158	+	0.501500i	$0.167218\pi$
$830$	−1283.93	−	344.027i	−1.54690	−	0.414491i
$831$		0			0
$832$	−11.4256	−	103.370i	−0.0137327	−	0.124243i
$833$	354.079			0.425065
$834$		0			0
$835$	−701.199	−	1214.51i	−0.839759	−	1.45450i
$836$	−134.272	−	77.5219i	−0.160612	−	0.0927296i
$837$		0			0
$838$	458.181	−	122.769i	0.546756	−	0.146503i
$839$	80.6696	+	301.063i	0.0961497	+	0.358836i	0.997191	−	0.0748971i	$-0.0238628\pi$
$839$	80.6696	+	301.063i	0.0961497	+	0.358836i	−0.901042	+	0.433733i	$0.857196\pi$
$840$		0			0
$841$	−129.822	+	224.858i	−0.154366	+	0.267369i
$842$	475.668	−	274.627i	0.564927	−	0.326161i
$843$		0			0
$844$		−	389.670i		−	0.461694i
$845$	1018.53	+	646.014i	1.20536	+	0.764514i
$846$		0			0
$847$	−85.5709	+	319.355i	−0.101028	+	0.377042i
$848$	−135.035	−	233.888i	−0.159240	−	0.275811i
$849$		0			0
$850$	419.158	+	419.158i	0.493127	+	0.493127i
$851$	605.374	−	162.210i	0.711368	−	0.190611i
$852$		0			0
$853$	724.409	−	724.409i	0.849249	−	0.849249i	−0.140791	−	0.990039i	$-0.544964\pi$
$853$	724.409	−	724.409i	0.849249	−	0.849249i	0.990039	+	0.140791i	$0.0449645\pi$
$854$	259.546	−	449.547i	0.303918	−	0.526402i
$855$		0			0
$856$	89.8161	+	24.0662i	0.104925	+	0.0281147i
$857$			49.0244i			0.0572047i	0.999591	+	0.0286023i	$0.00910565\pi$
$857$			49.0244i			0.0572047i	−0.999591	+	0.0286023i	$0.990894\pi$
$858$		0			0
$859$	−584.617			−0.680578			−0.340289	−	0.940321i	$-0.610525\pi$
$859$	−584.617			−0.680578			−0.340289	+	0.940321i	$0.610525\pi$
$860$	−173.803	+	648.641i	−0.202096	+	0.754234i
$861$		0			0
$862$	168.389	+	97.2197i	0.195347	+	0.112784i
$863$	−458.022	−	458.022i	−0.530732	−	0.530732i	0.390058	−	0.920790i	$-0.372455\pi$
$863$	−458.022	−	458.022i	−0.530732	−	0.530732i	−0.920790	+	0.390058i	$0.872455\pi$
$864$		0			0
$865$	−244.288	−	911.694i	−0.282414	−	1.05398i
$866$	−420.434	+	420.434i	−0.485490	+	0.485490i
$867$		0			0
$868$	436.434	−	251.975i	0.502804	−	0.290294i
$869$	−98.0339	−	26.2681i	−0.112812	−	0.0302280i
$870$		0			0
$871$	84.9002	−	555.302i	0.0974744	−	0.637545i
$872$	600.344			0.688467
$873$		0			0
$874$	−69.2268	−	119.904i	−0.0792069	−	0.137190i
$875$	30.0673	+	17.3593i	0.0343626	+	0.0198393i
$876$		0			0
$877$	−311.620	+	83.4983i	−0.355325	+	0.0952090i	−0.432066	−	0.901842i	$-0.642215\pi$
$877$	−311.620	+	83.4983i	−0.355325	+	0.0952090i	0.0767411	+	0.997051i	$0.475549\pi$
$878$	−272.821	−	1018.18i	−0.310730	−	1.15966i
$879$		0			0
$880$	−108.217	+	187.437i	−0.122974	+	0.212997i
$881$	1090.72	−	629.725i	1.23804	−	0.714785i	0.269349	−	0.963043i	$-0.413191\pi$
$881$	1090.72	−	629.725i	1.23804	−	0.714785i	0.968694	+	0.248258i	$0.0798580\pi$
$882$		0			0
$883$		−	213.692i		−	0.242007i	−0.992652	−	0.121003i	$-0.961389\pi$
$883$		−	213.692i		−	0.242007i	0.992652	−	0.121003i	$-0.0386112\pi$
$884$	−248.816	−	338.631i	−0.281466	−	0.383067i
$885$		0			0
$886$	−242.278	+	904.195i	−0.273452	+	1.02054i
$887$	−133.786	−	231.725i	−0.150830	−	0.261245i	0.780703	−	0.624903i	$-0.214861\pi$
$887$	−133.786	−	231.725i	−0.150830	−	0.261245i	−0.931533	+	0.363657i	$0.881528\pi$
$888$		0			0
$889$	244.579	+	244.579i	0.275117	+	0.275117i
$890$	−490.660	+	131.472i	−0.551303	+	0.147721i
$891$		0			0
$892$	−579.310	+	579.310i	−0.649450	+	0.649450i
$893$	−345.758	+	598.871i	−0.387187	+	0.670628i
$894$		0			0
$895$	−244.251	−	65.4467i	−0.272906	−	0.0731248i
$896$			58.8878i			0.0657230i
$897$		0			0
$898$	44.3712			0.0494112
$899$	−415.678	+	1551.33i	−0.462378	+	1.72562i
$900$		0			0
$901$	−945.031	−	545.614i	−1.04887	−	0.605565i
$902$	412.920	+	412.920i	0.457783	+	0.457783i
$903$		0			0
$904$	−86.9586	−	324.534i	−0.0961932	−	0.358998i
$905$	−611.226	+	611.226i	−0.675388	+	0.675388i
$906$		0			0
$907$	43.1528	−	24.9143i	0.0475776	−	0.0274689i	−0.476023	−	0.879433i	$-0.657922\pi$
$907$	43.1528	−	24.9143i	0.0475776	−	0.0274689i	0.523600	+	0.851964i	$0.324589\pi$
$908$	482.371	+	129.251i	0.531246	+	0.142347i
$909$		0			0
$910$	−533.045	−	426.938i	−0.585764	−	0.469162i
$911$	465.226			0.510676			0.255338	−	0.966852i	$-0.417813\pi$
$911$	465.226			0.510676			0.255338	+	0.966852i	$0.417813\pi$
$912$		0			0
$913$	−499.234	−	864.699i	−0.546806	−	0.947096i
$914$	199.200	+	115.008i	0.217943	+	0.125830i
$915$		0			0
$916$	476.077	−	127.564i	0.519735	−	0.139263i
$917$	−38.1618	−	142.422i	−0.0416159	−	0.155313i
$918$		0			0
$919$	−334.402	+	579.201i	−0.363876	+	0.630251i	−0.988595	−	0.150598i	$-0.951880\pi$
$919$	−334.402	+	579.201i	−0.363876	+	0.630251i	0.624719	+	0.780849i	$0.285213\pi$
$920$	−167.381	+	96.6374i	−0.181936	+	0.105041i
$921$		0			0
$922$		−	113.912i		−	0.123549i
$923$	1339.08	−	522.285i	1.45080	−	0.565856i
$924$		0			0
$925$	−439.372	+	1639.76i	−0.474997	+	1.77271i
$926$	172.856	+	299.395i	0.186669	+	0.323321i
$927$		0			0
$928$	−132.704	−	132.704i	−0.143000	−	0.143000i
$929$	655.978	−	175.769i	0.706112	−	0.189202i	0.112145	−	0.993692i	$-0.464228\pi$
$929$	655.978	−	175.769i	0.706112	−	0.189202i	0.593966	+	0.804490i	$0.297561\pi$
$930$		0			0
$931$	158.399	−	158.399i	0.170139	−	0.170139i
$932$	290.609	−	503.349i	0.311812	−	0.540074i
$933$		0			0
$934$	887.875	+	237.906i	0.950616	+	0.254717i
$935$			874.507i			0.935302i
$936$		0			0
$937$	−210.517			−0.224671			−0.112336	−	0.993670i	$-0.535833\pi$
$937$	−210.517			−0.224671			−0.112336	+	0.993670i	$0.535833\pi$
$938$	−82.3256	+	307.243i	−0.0877671	+	0.327551i
$939$		0			0
$940$	835.996	+	482.663i	0.889358	+	0.513471i
$941$	−447.841	−	447.841i	−0.475920	−	0.475920i	0.427904	−	0.903824i	$-0.359252\pi$
$941$	−447.841	−	447.841i	−0.475920	−	0.475920i	−0.903824	+	0.427904i	$0.859252\pi$
$942$		0			0
$943$	134.967	+	503.703i	0.143125	+	0.534150i
$944$	−213.010	+	213.010i	−0.225646	+	0.225646i
$945$		0			0
$946$	−436.846	+	252.213i	−0.461783	+	0.266610i
$947$	−569.069	−	152.482i	−0.600918	−	0.161015i	−0.0544795	−	0.998515i	$-0.517350\pi$
$947$	−569.069	−	152.482i	−0.600918	−	0.161015i	−0.546438	+	0.837500i	$0.684017\pi$
$948$		0			0
$949$	−423.389	+	528.615i	−0.446143	+	0.557023i
$950$	375.025			0.394763
$951$		0			0
$952$	118.969	+	206.060i	0.124967	+	0.216450i
$953$	−333.275	−	192.416i	−0.349711	−	0.201906i	0.314847	−	0.949142i	$-0.398047\pi$
$953$	−333.275	−	192.416i	−0.349711	−	0.201906i	−0.664558	+	0.747237i	$0.731380\pi$
$954$		0			0
$955$	1382.62	−	370.472i	1.44777	−	0.387929i
$956$	158.032	+	589.782i	0.165305	+	0.616927i
$957$		0			0
$958$	359.283	−	622.296i	0.375034	−	0.649578i
$959$	−226.886	+	130.992i	−0.236586	+	0.136593i
$960$		0			0
$961$			1382.55i			1.43866i
$962$	483.568	−	1101.98i	0.502669	−	1.14551i
$963$		0			0
$964$	−62.1867	+	232.084i	−0.0645090	+	0.240751i
$965$	93.3627	+	161.709i	0.0967490	+	0.167574i
$966$		0			0
$967$	1196.08	+	1196.08i	1.23690	+	1.23690i	0.961262	+	0.275638i	$0.0888891\pi$
$967$	1196.08	+	1196.08i	1.23690	+	1.23690i	0.275638	+	0.961262i	$0.411111\pi$
$968$	173.539	−	46.4997i	0.179276	−	0.0480369i
$969$		0			0
$970$	−388.212	+	388.212i	−0.400218	+	0.400218i
$971$	149.962	−	259.741i	0.154440	−	0.267499i	−0.778415	−	0.627750i	$-0.783976\pi$
$971$	149.962	−	259.741i	0.154440	−	0.267499i	0.932855	+	0.360252i	$0.117309\pi$
$972$		0			0
$973$	−745.519	−	199.761i	−0.766206	−	0.205304i
$974$			1097.44i			1.12674i
$975$		0			0
$976$	−282.078			−0.289014
$977$	−62.1492	+	231.944i	−0.0636123	+	0.237404i	−0.990411	−	0.138155i	$-0.955883\pi$
$977$	−62.1492	+	231.944i	−0.0636123	+	0.237404i	0.926798	+	0.375559i	$0.122549\pi$
$978$		0			0
$979$	−330.449	−	190.785i	−0.337538	−	0.194877i
$980$	−221.118	−	221.118i	−0.225631	−	0.225631i
$981$		0			0
$982$	−45.7581	−	170.772i	−0.0465969	−	0.173902i
$983$	503.122	−	503.122i	0.511823	−	0.511823i	−0.403261	−	0.915085i	$-0.632123\pi$
$983$	503.122	−	503.122i	0.511823	−	0.511823i	0.915085	+	0.403261i	$0.132123\pi$
$984$		0			0
$985$	585.459	−	338.015i	0.594375	−	0.343162i
$986$	−732.453	−	196.260i	−0.742853	−	0.199047i
$987$		0			0
$988$	−262.798	−	40.1792i	−0.265989	−	0.0406672i
$989$	−450.451			−0.455461
$990$		0			0
$991$	268.482	+	465.025i	0.270921	+	0.469249i	0.969098	−	0.246677i	$-0.0793385\pi$
$991$	268.482	+	465.025i	0.270921	+	0.469249i	−0.698177	+	0.715925i	$0.746005\pi$
$992$	−237.161	−	136.925i	−0.239073	−	0.138029i
$993$		0			0
$994$	−786.129	+	210.643i	−0.790874	+	0.211914i
$995$	364.257	+	1359.43i	0.366087	+	1.36626i
$996$		0			0
$997$	509.605	−	882.662i	0.511139	−	0.885318i	−0.488778	−	0.872408i	$-0.662557\pi$
$997$	509.605	−	882.662i	0.511139	−	0.885318i	0.999917	−	0.0129099i	$-0.00410948\pi$
$998$	262.243	−	151.406i	0.262768	−	0.151709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.bb.d.37.2		8
3.2	odd	2		78.3.l.c.37.1	yes	8
13.6	odd	12	inner	234.3.bb.d.19.2		8
39.2	even	12		1014.3.f.h.577.3		8
39.11	even	12		1014.3.f.j.577.4		8
39.23	odd	6		1014.3.f.j.775.4		8
39.29	odd	6		1014.3.f.h.775.3		8
39.32	even	12		78.3.l.c.19.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.19.1	✓	8	39.32	even	12
78.3.l.c.37.1	yes	8	3.2	odd	2
234.3.bb.d.19.2		8	13.6	odd	12	inner
234.3.bb.d.37.2		8	1.1	even	1	trivial
1014.3.f.h.577.3		8	39.2	even	12
1014.3.f.h.775.3		8	39.29	odd	6
1014.3.f.j.577.4		8	39.11	even	12
1014.3.f.j.775.4		8	39.23	odd	6

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(5.04651 + 5.04651i) q^{5} +(-1.34715 - 5.02764i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(5.04651 + 5.04651i) q^{5} +(-1.34715 - 5.02764i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.74082 - 5.04651i) q^{10} +(7.32323 + 1.96225i) q^{11} +(12.9213 - 1.42820i) q^{13} -7.36098 q^{14} +(2.00000 + 3.46410i) q^{16} +(13.9968 + 8.08105i) q^{17} +(9.87664 - 2.64644i) q^{19} +(-3.69431 - 13.7873i) q^{20} +(5.36098 - 9.28549i) q^{22} +(8.29191 - 4.78733i) q^{23} +25.9346i q^{25} +(2.77857 - 18.1736i) q^{26} +(-2.69431 + 10.0553i) q^{28} +(-16.5880 - 28.7312i) q^{29} +(-34.2312 - 34.2312i) q^{31} +(5.46410 - 1.46410i) q^{32} +(16.1621 - 16.1621i) q^{34} +(18.5736 - 32.1705i) q^{35} +(63.2267 + 16.9415i) q^{37} -14.4604i q^{38} -20.1861 q^{40} +(-14.0962 + 52.6079i) q^{41} +(-40.7432 - 23.5231i) q^{43} +(-10.7220 - 10.7220i) q^{44} +(-3.50457 - 13.0792i) q^{46} +(-47.8214 + 47.8214i) q^{47} +(18.9729 - 10.9540i) q^{49} +(35.4274 + 9.49273i) q^{50} +(-23.8086 - 10.4476i) q^{52} -67.5177 q^{53} +(27.0543 + 46.8594i) q^{55} +(12.7496 + 7.36098i) q^{56} +(-45.3192 + 12.1432i) q^{58} +(19.4918 + 72.7442i) q^{59} +(-35.2597 + 61.0716i) q^{61} +(-59.2902 + 34.2312i) q^{62} -8.00000i q^{64} +(72.4150 + 58.0001i) q^{65} +(11.1841 - 41.7395i) q^{67} +(-16.1621 - 27.9936i) q^{68} +(-37.1473 - 37.1473i) q^{70} +(106.797 - 28.6161i) q^{71} +(-36.8385 + 36.8385i) q^{73} +(46.2851 - 80.1682i) q^{74} +(-19.7533 - 5.29288i) q^{76} -39.4621i q^{77} -13.3867 q^{79} +(-7.38861 + 27.5747i) q^{80} +(66.7041 + 38.5116i) q^{82} +(-93.1237 - 93.1237i) q^{83} +(29.8539 + 111.416i) q^{85} +(-47.0461 + 47.0461i) q^{86} +(-18.5710 + 10.7220i) q^{88} +(-48.6137 - 13.0260i) q^{89} +(-24.5875 - 63.0397i) q^{91} -19.1493 q^{92} +(47.8214 + 82.8291i) q^{94} +(63.1979 + 36.4873i) q^{95} +(-52.5419 + 14.0786i) q^{97} +(-8.01888 - 29.9269i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more