LMFDB - Embedded newform 234.3.bb.d.19.2

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			19.2
Root			$-4.04651 - 4.04651i$ of defining polynomial
Character	$\chi$	$=$	234.19
Dual form			234.3.bb.d.37.2

$q$-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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$

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	0.00934664	−	0.999956i	$-0.497025\pi$
$5$	5.04651	−	5.04651i	1.00930	−	1.00930i	0.999956	−	0.00934664i	$-0.00297517\pi$
$6$		0			0
$7$	−1.34715	+	5.02764i	−0.192450	+	0.718235i	0.800462	+	0.599384i	$0.204588\pi$
$7$	−1.34715	+	5.02764i	−0.192450	+	0.718235i	−0.992912	+	0.118851i	$0.962079\pi$
$8$	−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	0.0899095	−	0.995950i	$-0.471342\pi$
$11$	7.32323	−	1.96225i	0.665748	−	0.178387i	0.575839	+	0.817563i	$0.304676\pi$
$12$		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	−0.0282265	−	0.999602i	$-0.508986\pi$
$17$	13.9968	−	8.08105i	0.823341	−	0.475356i	0.851567	+	0.524246i	$0.175653\pi$
$18$		0			0
$19$	9.87664	+	2.64644i	0.519823	+	0.139286i	0.509185	−	0.860657i	$-0.329947\pi$
$19$	9.87664	+	2.64644i	0.519823	+	0.139286i	0.0106384	+	0.999943i	$0.496614\pi$
$20$	−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	0.669308	−	0.742985i	$-0.266591\pi$
$23$	8.29191	+	4.78733i	0.360518	+	0.208145i	−0.308790	+	0.951130i	$0.599924\pi$
$24$		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	0.424362	+	0.905493i	$0.360499\pi$
$29$	−16.5880	+	28.7312i	−0.571999	+	0.990731i	−0.996361	+	0.0852386i	$0.972835\pi$
$30$		0			0
$31$	−34.2312	+	34.2312i	−1.10423	+	1.10423i	−0.110338	+	0.993894i	$0.535193\pi$
$31$	−34.2312	+	34.2312i	−1.10423	+	1.10423i	−0.993894	+	0.110338i	$0.964807\pi$
$32$	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	0.733692	−	0.679482i	$-0.237796\pi$
$37$	63.2267	−	16.9415i	1.70883	−	0.457879i	0.975137	+	0.221603i	$0.0711289\pi$
$38$			14.4604i			0.380537i
$39$		0			0
$40$	−20.1861			−0.504651
$41$	−14.0962	−	52.6079i	−0.343811	−	1.28312i	−0.893995	−	0.448076i	$-0.852109\pi$
$41$	−14.0962	−	52.6079i	−0.343811	−	1.28312i	0.550185	−	0.835043i	$-0.314557\pi$
$42$		0			0
$43$	−40.7432	+	23.5231i	−0.947515	+	0.547048i	−0.892308	−	0.451427i	$-0.850915\pi$
$43$	−40.7432	+	23.5231i	−0.947515	+	0.547048i	−0.0552070	+	0.998475i	$0.517582\pi$
$44$	−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	−0.999845	−	0.0176317i	$-0.994387\pi$
$47$	−47.8214	−	47.8214i	−1.01748	−	1.01748i	−0.0176317	−	0.999845i	$-0.505613\pi$
$48$		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	−0.578435	−	0.815729i	$-0.696336\pi$
$59$	19.4918	−	72.7442i	0.330369	−	1.23295i	0.908804	−	0.417224i	$-0.136997\pi$
$60$		0			0
$61$	−35.2597	−	61.0716i	−0.578028	−	1.00117i	−0.995705	−	0.0925789i	$-0.970489\pi$
$61$	−35.2597	−	61.0716i	−0.578028	−	1.00117i	0.417677	−	0.908596i	$-0.362844\pi$
$62$	−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	0.997787	+	0.0664962i	$0.0211820\pi$
$67$	11.1841	+	41.7395i	0.166926	+	0.622977i	−0.830860	+	0.556481i	$0.812151\pi$
$68$	−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	0.914498	−	0.404591i	$-0.132586\pi$
$71$	106.797	+	28.6161i	1.50418	+	0.403044i	0.589682	+	0.807635i	$0.299253\pi$
$72$		0			0
$73$	−36.8385	−	36.8385i	−0.504638	−	0.504638i	0.408238	−	0.912876i	$-0.366143\pi$
$73$	−36.8385	−	36.8385i	−0.504638	−	0.504638i	−0.912876	+	0.408238i	$0.866143\pi$
$74$	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	−0.130528	+	0.991445i	$0.541667\pi$
$83$	−93.1237	+	93.1237i	−1.12197	+	1.12197i	−0.991445	+	0.130528i	$0.958333\pi$
$84$		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	−0.521369	−	0.853331i	$-0.674578\pi$
$89$	−48.6137	+	13.0260i	−0.546222	+	0.146360i	−0.0248529	+	0.999691i	$0.507912\pi$
$90$		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	−0.0223976	−	0.999749i	$-0.507130\pi$
$97$	−52.5419	−	14.0786i	−0.541669	−	0.145140i	−0.519271	+	0.854609i	$0.673797\pi$
$98$	−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	0.400198	−	0.916428i	$-0.368941\pi$
$101$	−19.5286	−	11.2749i	−0.193353	−	0.111632i	−0.593551	+	0.804796i	$0.702275\pi$
$102$		0			0
$103$		−	109.385i		−	1.06199i	−0.847374	−	0.530996i	$-0.821818\pi$
$103$		−	109.385i		−	1.06199i	0.847374	−	0.530996i	$-0.178182\pi$
$104$	−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	−0.932556	−	0.361025i	$-0.882427\pi$
$107$	−16.4375	+	28.4706i	−0.153621	+	0.266080i	0.778935	+	0.627105i	$0.215760\pi$
$108$		0			0
$109$	−150.086	+	150.086i	−1.37693	+	1.37693i	−0.527183	+	0.849752i	$0.676752\pi$
$109$	−150.086	+	150.086i	−1.37693	+	1.37693i	−0.849752	+	0.527183i	$0.823248\pi$
$110$	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	−0.999555	−	0.0298278i	$-0.990504\pi$
$113$	−59.3938	−	102.873i	−0.525609	−	0.910382i	0.473946	−	0.880554i	$-0.342829\pi$
$114$		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	0.256010	−	0.966674i	$-0.417592\pi$
$127$	−57.5499	−	33.2265i	−0.453149	−	0.261626i	−0.709159	+	0.705048i	$0.750925\pi$
$128$	−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	−0.997033	−	0.0769757i	$-0.975474\pi$
$137$	−13.0272	+	48.6183i	−0.0950892	+	0.354878i	0.901944	+	0.431854i	$0.142140\pi$
$138$		0			0
$139$	74.1420	+	128.418i	0.533396	+	0.923868i	0.999239	+	0.0390012i	$0.0124176\pi$
$139$	74.1420	+	128.418i	0.533396	+	0.923868i	−0.465844	+	0.884867i	$0.654249\pi$
$140$	−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	0.391910	−	0.920004i	$-0.371815\pi$
$149$	40.4254	+	10.8320i	0.271312	+	0.0726977i	−0.120598	+	0.992701i	$0.538481\pi$
$150$		0			0
$151$	−2.57635	−	2.57635i	−0.0170619	−	0.0170619i	0.698524	−	0.715586i	$-0.253840\pi$
$151$	−2.57635	−	2.57635i	−0.0170619	−	0.0170619i	−0.715586	+	0.698524i	$0.753840\pi$
$152$	−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	0.759898	+	0.650043i	$0.225249\pi$
$163$	−36.3840	+	135.787i	−0.223214	+	0.833048i	−0.983112	+	0.183005i	$0.941418\pi$
$164$	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	−0.777566	−	0.628801i	$-0.783546\pi$
$167$	−189.805	+	50.8582i	−1.13656	+	0.304540i	−0.358992	+	0.933341i	$0.616879\pi$
$168$		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	−0.793053	−	0.609152i	$-0.791510\pi$
$173$	−114.533	+	66.1255i	−0.662039	+	0.382228i	0.131015	+	0.991380i	$0.458177\pi$
$174$		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	0.411835	−	0.911258i	$-0.364888\pi$
$179$	−30.6843	−	17.7156i	−0.171421	−	0.0989697i	−0.583255	+	0.812289i	$0.698221\pi$
$180$		0			0
$181$		−	121.119i		−	0.669163i	−0.942367	−	0.334582i	$-0.891405\pi$
$181$		−	121.119i		−	0.669163i	0.942367	−	0.334582i	$-0.108595\pi$
$182$	−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	0.999575	+	0.0291545i	$0.00928147\pi$
$191$	100.282	+	173.693i	0.525036	+	0.909389i	−0.474539	+	0.880235i	$0.657385\pi$
$192$		0			0
$193$	25.2721	−	6.77163i	0.130943	−	0.0350862i	−0.192752	−	0.981247i	$-0.561741\pi$
$193$	25.2721	−	6.77163i	0.130943	−	0.0350862i	0.323695	+	0.946161i	$0.395075\pi$
$194$		−	76.9267i		−	0.396529i
$195$		0			0
$196$	−43.8160			−0.223551
$197$	24.5163	+	91.4962i	0.124448	+	0.464448i	0.999819	−	0.0190039i	$-0.00604951\pi$
$197$	24.5163	+	91.4962i	0.124448	+	0.464448i	−0.875371	+	0.483452i	$0.839383\pi$
$198$		0			0
$199$	170.780	−	98.5996i	0.858188	−	0.495475i	−0.00521676	−	0.999986i	$-0.501661\pi$
$199$	170.780	−	98.5996i	0.858188	−	0.495475i	0.863405	+	0.504511i	$0.168327\pi$
$200$	−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	−0.537352	−	0.843358i	$-0.680575\pi$
$211$	97.4174	−	168.732i	0.461694	−	0.799677i	0.999046	+	0.0436812i	$0.0139086\pi$
$212$	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	0.619750	+	0.784800i	$0.287234\pi$
$223$	106.021	+	395.676i	0.475431	+	1.77433i	−0.144319	+	0.989531i	$0.546099\pi$
$224$	−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	−0.315087	−	0.949063i	$-0.602034\pi$
$227$	−241.186	−	64.6255i	−1.06249	−	0.284694i	−0.747405	+	0.664369i	$0.768700\pi$
$228$		0			0
$229$	−174.256	−	174.256i	−0.760945	−	0.760945i	0.215548	−	0.976493i	$-0.430846\pi$
$229$	−174.256	−	174.256i	−0.760945	−	0.760945i	−0.976493	+	0.215548i	$0.930846\pi$
$230$	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	$-0.785660\pi$
$233$		−	290.609i		−	1.24725i	0.781724	−	0.623624i	$-0.214340\pi$
$234$		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	−0.995715	−	0.0924720i	$-0.970523\pi$
$239$	−215.875	+	215.875i	−0.903243	+	0.903243i	0.0924720	+	0.995715i	$0.470523\pi$
$240$		0			0
$241$	−31.0933	+	116.042i	−0.129018	+	0.481502i	−0.999951	−	0.00989998i	$-0.996849\pi$
$241$	−31.0933	+	116.042i	−0.129018	+	0.481502i	0.870933	+	0.491402i	$0.163515\pi$
$242$	−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	−0.167793	−	0.985822i	$-0.553664\pi$
$251$	151.116	−	87.2471i	0.602057	−	0.347598i	0.769850	+	0.638224i	$0.220331\pi$
$252$		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	0.507812	−	0.861468i	$-0.330454\pi$
$257$	4.02596	+	2.32439i	0.0156652	+	0.00904433i	−0.492147	+	0.870512i	$0.663788\pi$
$258$		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	−0.852567	−	0.522619i	$-0.824955\pi$
$263$	6.92157	−	11.9885i	0.0263177	−	0.0455837i	0.878884	+	0.477035i	$0.158289\pi$
$264$		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	−0.876193	−	0.481961i	$-0.839925\pi$
$269$	−230.126	−	398.590i	−0.855487	−	1.48175i	0.0207059	−	0.999786i	$-0.493409\pi$
$270$		0			0
$271$	143.260	−	38.3864i	0.528635	−	0.141647i	0.0153773	−	0.999882i	$-0.495105\pi$
$271$	143.260	−	38.3864i	0.528635	−	0.141647i	0.513258	+	0.858234i	$0.328438\pi$
$272$		−	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	0.214085	−	0.976815i	$-0.431323\pi$
$277$	323.280	−	186.646i	1.16707	−	0.673811i	0.952989	+	0.303004i	$0.0979896\pi$
$278$	−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	0.906514	−	0.422177i	$-0.138734\pi$
$281$	136.099	+	136.099i	0.484337	+	0.484337i	−0.422177	+	0.906514i	$0.638734\pi$
$282$		0			0
$283$	−329.692	−	190.347i	−1.16499	−	0.672606i	−0.212493	−	0.977162i	$-0.568158\pi$
$283$	−329.692	−	190.347i	−1.16499	−	0.672606i	−0.952494	+	0.304557i	$0.901492\pi$
$284$	−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	−0.963442	−	0.267919i	$-0.913664\pi$
$293$	1.43061	−	5.33910i	0.00488262	−	0.0182222i	0.968324	+	0.249696i	$0.0803308\pi$
$294$		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	0.232296	−	0.972645i	$-0.425376\pi$
$307$	−227.287	−	227.287i	−0.740349	−	0.740349i	−0.972645	+	0.232296i	$0.925376\pi$
$308$	−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	$-0.834594\pi$
$311$		−	308.864i		−	0.993132i	0.867999	−	0.496566i	$-0.165406\pi$
$312$		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	−0.777125	−	0.629346i	$-0.783323\pi$
$317$	−46.8460	+	46.8460i	−0.147779	+	0.147779i	0.629346	+	0.777125i	$0.283323\pi$
$318$		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	0.591693	−	0.806163i	$-0.298460\pi$
$331$	232.042	+	62.1755i	0.701033	+	0.187841i	0.109340	+	0.994004i	$0.465126\pi$
$332$	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	$0.00270591\pi$
$337$			5.72952i			0.0170015i	−0.999964	+	0.00850077i	$0.997294\pi$
$338$	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	0.782253	−	0.622961i	$-0.214070\pi$
$347$	−51.4856	−	89.1757i	−0.148373	−	0.256990i	−0.930626	+	0.365971i	$0.880737\pi$
$348$		0			0
$349$	468.190	−	125.451i	1.34152	−	0.359459i	0.484521	−	0.874780i	$-0.338994\pi$
$349$	468.190	−	125.451i	1.34152	−	0.359459i	0.856997	+	0.515321i	$0.172327\pi$
$350$			190.904i			0.545441i
$351$		0			0
$352$	42.8878			0.121840
$353$	50.9642	+	190.201i	0.144375	+	0.538813i	0.999782	+	0.0208583i	$0.00663989\pi$
$353$	50.9642	+	190.201i	0.144375	+	0.538813i	−0.855408	+	0.517955i	$0.826693\pi$
$354$		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	0.778456	−	0.627699i	$-0.216003\pi$
$359$	54.1215	+	54.1215i	0.150756	+	0.150756i	−0.627699	+	0.778456i	$0.716003\pi$
$360$		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	−0.680906	−	0.732371i	$-0.738414\pi$
$367$	107.824	−	186.757i	0.293799	−	0.508875i	0.974705	+	0.223496i	$0.0717470\pi$
$368$	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	0.884432	+	0.466669i	$0.154546\pi$
$373$	315.693	+	546.797i	0.846363	+	1.46594i	−0.0380693	+	0.999275i	$0.512121\pi$
$374$	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	−0.997316	−	0.0732240i	$-0.976671\pi$
$379$	−64.5160	−	240.777i	−0.170227	−	0.635296i	0.827089	−	0.562072i	$-0.189995\pi$
$380$	−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	−0.113485	−	0.993540i	$-0.536201\pi$
$383$	−271.369	−	72.7131i	−0.708535	−	0.189851i	−0.595050	+	0.803688i	$0.702868\pi$
$384$		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	$0.110701\pi$
$389$			265.150i			0.681620i	−0.940132	+	0.340810i	$0.889299\pi$
$390$		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	−0.994741	−	0.102419i	$-0.967342\pi$
$397$	−32.5780	+	121.583i	−0.0820604	+	0.306253i	0.912681	+	0.408673i	$0.134008\pi$
$398$	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	0.484551	−	0.874763i	$-0.338983\pi$
$401$	537.968	−	144.148i	1.34157	−	0.359472i	0.857015	+	0.515291i	$0.172316\pi$
$402$		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	0.494257	−	0.869316i	$-0.335440\pi$
$409$	199.444	+	53.4410i	0.487639	+	0.130663i	−0.00661830	+	0.999978i	$0.502107\pi$
$410$	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	−0.593503	−	0.804832i	$-0.702256\pi$
$419$	167.706	−	290.475i	0.400253	−	0.693259i	0.993756	+	0.111573i	$0.0355889\pi$
$420$		0			0
$421$	274.627	−	274.627i	0.652321	−	0.652321i	−0.301230	−	0.953551i	$-0.597397\pi$
$421$	274.627	−	274.627i	0.652321	−	0.652321i	0.953551	+	0.301230i	$0.0973973\pi$
$422$	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	0.912278	−	0.409571i	$-0.134322\pi$
$431$	−35.5849	−	132.805i	−0.0825635	−	0.308131i	−0.994842	+	0.101440i	$0.967655\pi$
$432$		0			0
$433$	−364.107	+	210.217i	−0.840893	+	0.485490i	−0.857568	−	0.514371i	$-0.828025\pi$
$433$	−364.107	+	210.217i	−0.840893	+	0.485490i	0.0166746	+	0.999861i	$0.494692\pi$
$434$	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	0.999448	−	0.0332332i	$-0.0105804\pi$
$439$	645.502	+	372.680i	1.47039	+	0.848930i	0.470943	+	0.882164i	$0.343914\pi$
$440$	−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	−0.956293	−	0.292409i	$-0.905543\pi$
$449$	8.12050	−	30.3061i	0.0180857	−	0.0674969i	0.974379	+	0.224913i	$0.0722096\pi$
$450$		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	0.904452	−	0.426575i	$-0.140280\pi$
$457$	−42.0960	−	157.104i	−0.0921137	−	0.343773i	−0.996566	+	0.0828016i	$0.973613\pi$
$458$	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	0.342215	−	0.939622i	$-0.388823\pi$
$461$	77.8033	+	20.8473i	0.168771	+	0.0452220i	−0.173444	+	0.984844i	$0.555490\pi$
$462$		0			0
$463$	−172.856	−	172.856i	−0.373338	−	0.373338i	0.495353	−	0.868692i	$-0.335039\pi$
$463$	−172.856	−	172.856i	−0.373338	−	0.373338i	−0.868692	+	0.495353i	$0.835039\pi$
$464$	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	$-0.755006\pi$
$467$		−	649.970i		−	1.39180i	0.718139	−	0.695899i	$-0.244994\pi$
$468$		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	0.292890	−	0.956146i	$-0.405383\pi$
$479$	490.789	−	131.507i	1.02461	−	0.274544i	0.731723	+	0.681602i	$0.238717\pi$
$480$		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	−0.613161	−	0.789958i	$-0.710102\pi$
$487$	−749.567	−	200.846i	−1.53915	−	0.412415i	−0.925992	+	0.377544i	$0.876769\pi$
$488$	−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	0.606181	−	0.795327i	$-0.292701\pi$
$491$	108.265	+	62.5068i	0.220499	+	0.127305i	−0.385682	+	0.922632i	$0.626034\pi$
$492$		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	−0.538931	−	0.842350i	$-0.681172\pi$
$499$	151.406	−	151.406i	0.303419	−	0.303419i	0.842350	+	0.538931i	$0.181172\pi$
$500$	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	0.999630	+	0.0272010i	$0.00865940\pi$
$503$	263.256	+	455.973i	0.523372	+	0.906506i	−0.476258	+	0.879305i	$0.658007\pi$
$504$		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	0.554056	+	0.832479i	$0.313079\pi$
$509$	249.649	+	931.702i	0.490469	+	1.83046i	−0.0635873	+	0.997976i	$0.520254\pi$
$510$		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	−0.735234	−	0.677813i	$-0.762928\pi$
$523$	114.739	−	198.734i	0.219386	−	0.379989i	0.954621	+	0.297825i	$0.0962611\pi$
$524$	−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	0.991653	+	0.128938i	$0.0411569\pi$
$541$	606.240	+	606.240i	1.12059	+	1.12059i	0.128938	+	0.991653i	$0.458843\pi$
$542$	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	0.133426	−	0.991059i	$-0.457402\pi$
$557$	414.689	−	111.116i	0.744505	−	0.199490i	0.611080	+	0.791569i	$0.290736\pi$
$558$		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	−0.233869	−	0.972268i	$-0.575139\pi$
$563$	276.549	−	159.665i	0.491206	−	0.283598i	0.725074	+	0.688671i	$0.241805\pi$
$564$		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	−0.245221	−	0.969467i	$-0.578860\pi$
$569$	−687.019	−	396.650i	−1.20741	−	0.697101i	−0.962194	+	0.272366i	$0.912194\pi$
$570$		0			0
$571$		−	852.111i		−	1.49231i	−0.665771	−	0.746156i	$-0.731897\pi$
$571$		−	852.111i		−	1.49231i	0.665771	−	0.746156i	$-0.268103\pi$
$572$	−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	−0.849930	−	0.526895i	$-0.823356\pi$
$577$	−186.391	+	186.391i	−0.323035	+	0.323035i	0.526895	+	0.849930i	$0.323356\pi$
$578$	−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	−0.891469	−	0.453081i	$-0.850325\pi$
$587$	−203.087	−	757.931i	−0.345975	−	1.29119i	0.545495	−	0.838114i	$-0.316342\pi$
$588$		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	0.948793	−	0.315898i	$-0.102306\pi$
$593$	375.307	+	375.307i	0.632895	+	0.632895i	−0.315898	+	0.948793i	$0.602306\pi$
$594$		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	−0.840700	−	0.541500i	$-0.817856\pi$
$601$	29.2104	−	50.5939i	0.0486030	−	0.0841828i	0.889303	+	0.457318i	$0.151190\pi$
$602$	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	0.998890	+	0.0471065i	$0.0150000\pi$
$607$	327.926	+	567.984i	0.540240	+	0.935724i	−0.458649	+	0.888617i	$0.651667\pi$
$608$	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	0.913313	−	0.407259i	$-0.133515\pi$
$613$	−49.8176	−	185.922i	−0.0812686	−	0.303298i	−0.994581	+	0.103960i	$0.966849\pi$
$614$	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	0.243248	−	0.969964i	$-0.421787\pi$
$617$	−19.1730	−	5.13739i	−0.0310745	−	0.00832640i	−0.274323	+	0.961638i	$0.588454\pi$
$618$		0			0
$619$	−319.972	−	319.972i	−0.516917	−	0.516917i	0.399720	−	0.916637i	$-0.369107\pi$
$619$	−319.972	−	319.972i	−0.516917	−	0.516917i	−0.916637	+	0.399720i	$0.869107\pi$
$620$	−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	−0.816010	−	0.578038i	$-0.803818\pi$
$631$	113.387	−	423.167i	0.179695	−	0.670629i	0.995704	−	0.0925909i	$-0.0295149\pi$
$632$	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	−0.0194927	−	0.999810i	$-0.506205\pi$
$641$	536.275	−	309.618i	0.836622	−	0.483024i	0.856115	+	0.516786i	$0.172872\pi$
$642$		0			0
$643$	−389.853	−	104.461i	−0.606304	−	0.162459i	−0.0574099	−	0.998351i	$-0.518284\pi$
$643$	−389.853	−	104.461i	−0.606304	−	0.162459i	−0.548894	+	0.835892i	$0.684951\pi$
$644$	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	0.657950	−	0.753062i	$-0.271424\pi$
$647$	216.586	+	125.046i	0.334754	+	0.193270i	−0.323196	+	0.946332i	$0.604757\pi$
$648$		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	−0.976111	−	0.217271i	$-0.930284\pi$
$653$	−195.830	+	339.188i	−0.299894	+	0.519431i	0.676218	+	0.736702i	$0.263618\pi$
$654$		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	0.534841	−	0.844953i	$-0.320372\pi$
$659$	−305.994	−	529.997i	−0.464330	−	0.804244i	−0.999171	+	0.0407093i	$0.987038\pi$
$660$		0			0
$661$	−585.429	+	156.865i	−0.885671	+	0.237315i	−0.672852	−	0.739777i	$-0.734931\pi$
$661$	−585.429	+	156.865i	−0.885671	+	0.237315i	−0.212819	+	0.977092i	$0.568264\pi$
$662$			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	0.911331	−	0.411675i	$-0.135056\pi$
$673$	680.049	+	392.627i	1.01047	+	0.583398i	0.0991438	+	0.995073i	$0.468390\pi$
$674$	−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	0.598570	+	0.801071i	$0.295736\pi$
$683$	−218.794	+	816.549i	−0.320342	+	1.19553i	−0.918912	+	0.394462i	$0.870931\pi$
$684$		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	0.970939	+	0.239326i	$0.0769264\pi$
$691$	172.573	+	644.052i	0.249744	+	0.932058i	−0.721195	+	0.692732i	$0.756407\pi$
$692$	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	$-0.931409\pi$
$701$		−	299.776i		−	0.427640i	0.976873	−	0.213820i	$-0.0685907\pi$
$702$		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	−0.999845	−	0.0175820i	$-0.994403\pi$
$709$	−88.7405	+	331.184i	−0.125163	+	0.467114i	0.874683	+	0.484696i	$0.161070\pi$
$710$	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	−0.831979	−	0.554807i	$-0.812792\pi$
$719$	−551.827	+	318.597i	−0.767492	+	0.443112i	0.0644873	+	0.997919i	$0.479459\pi$
$720$		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	$-0.860460\pi$
$727$		−	617.181i		−	0.848943i	0.905441	−	0.424471i	$-0.139540\pi$
$728$	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	−0.327985	+	0.944683i	$0.606369\pi$
$733$	−932.866	+	932.866i	−1.27267	+	1.27267i	−0.944683	+	0.327985i	$0.893631\pi$
$734$	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	−0.124364	−	0.992237i	$-0.539689\pi$
$739$	195.134	−	52.2859i	0.264051	−	0.0707523i	0.388416	+	0.921484i	$0.373023\pi$
$740$			934.314i			1.26259i
$741$		0			0
$742$	496.996			0.669806
$743$	271.553	+	1013.45i	0.365482	+	1.36400i	0.866766	+	0.498716i	$0.166195\pi$
$743$	271.553	+	1013.45i	0.365482	+	1.36400i	−0.501283	+	0.865283i	$0.667139\pi$
$744$		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	0.951451	+	0.307800i	$0.0995929\pi$
$751$	1272.00	+	734.389i	1.69374	+	0.977881i	0.742288	+	0.670080i	$0.233740\pi$
$752$	−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	−0.431821	−	0.901960i	$-0.642129\pi$
$757$	427.864	−	741.082i	0.565210	−	0.978972i	0.997030	−	0.0770121i	$-0.0245380\pi$
$758$	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	0.853747	+	0.520688i	$0.174324\pi$
$761$	−111.078	+	414.549i	−0.145963	+	0.544743i	−0.999711	+	0.0240550i	$0.992342\pi$
$762$		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	0.999588	+	0.0287025i	$0.00913755\pi$
$769$	114.020	+	425.529i	0.148271	+	0.553354i	−0.851317	+	0.524651i	$0.824196\pi$
$770$	−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	−0.582911	−	0.812536i	$-0.698086\pi$
$773$	−1154.86	−	309.443i	−1.49399	−	0.400315i	−0.911084	+	0.412221i	$0.864753\pi$
$774$		0			0
$775$	887.773	+	887.773i	1.14551	+	1.14551i
$776$	76.9267	+	133.241i	0.0991323	+	0.171702i
$777$		0			0
$778$

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

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