LMFDB - Embedded newform 224.2.bd.a.165.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [224,2,Mod(37,224)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("224.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(224, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			165.4
Character	$\chi$	$=$	224.165
Dual form			224.2.bd.a.205.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29209 - 0.574893i) q^{2} +(2.00399 + 0.263830i) q^{3} +(1.33900 + 1.48563i) q^{4} +(0.0973086 + 0.739132i) q^{5} +(-2.43766 - 1.49297i) q^{6} +(1.49056 - 2.18592i) q^{7} +(-0.876026 - 2.68935i) q^{8} +(1.04859 + 0.280969i) q^{9} +(0.299191 - 1.01097i) q^{10} +(2.01082 + 2.62055i) q^{11} +(2.29138 + 3.33045i) q^{12} +(0.237482 - 0.0983684i) q^{13} +(-3.18260 + 1.96749i) q^{14} +1.50689i q^{15} +(-0.414181 + 3.97850i) q^{16} +(-0.237856 - 0.137326i) q^{17} +(-1.19335 - 0.965865i) q^{18} +(2.51396 + 1.92903i) q^{19} +(-0.967780 + 1.13426i) q^{20} +(3.56377 - 3.98730i) q^{21} +(-1.09163 - 4.54200i) q^{22} +(-5.44793 - 1.45977i) q^{23} +(-1.04602 - 5.62054i) q^{24} +(4.29278 - 1.15025i) q^{25} +(-0.363400 - 0.00942610i) q^{26} +(-3.57503 - 1.48082i) q^{27} +(5.24331 - 0.712523i) q^{28} +(0.801128 + 1.93409i) q^{29} +(0.866299 - 1.94703i) q^{30} +(1.52247 - 2.63700i) q^{31} +(2.82237 - 4.90247i) q^{32} +(3.33829 + 5.78208i) q^{33} +(0.228383 + 0.314179i) q^{34} +(1.76073 + 0.889010i) q^{35} +(0.986643 + 1.93403i) q^{36} +(-1.06556 - 8.09376i) q^{37} +(-2.13928 - 3.93774i) q^{38} +(0.501865 - 0.134474i) q^{39} +(1.90254 - 0.909196i) q^{40} +(-2.41053 + 2.41053i) q^{41} +(-6.89699 + 3.10317i) q^{42} +(-3.81560 + 9.21166i) q^{43} +(-1.20069 + 6.49624i) q^{44} +(-0.105636 + 0.802388i) q^{45} +(6.20000 + 5.01813i) q^{46} +(-8.91945 + 5.14965i) q^{47} +(-1.87966 + 7.86360i) q^{48} +(-2.55648 - 6.51647i) q^{49} +(-6.20793 - 0.981667i) q^{50} +(-0.440430 - 0.337954i) q^{51} +(0.464127 + 0.221096i) q^{52} +(-4.88818 - 6.37040i) q^{53} +(3.76794 + 3.96862i) q^{54} +(-1.74127 + 1.74127i) q^{55} +(-7.18446 - 2.09370i) q^{56} +(4.52901 + 4.52901i) q^{57} +(0.0767677 - 2.95959i) q^{58} +(-9.21225 + 7.06881i) q^{59} +(-2.23867 + 2.01771i) q^{60} +(3.85029 - 5.01779i) q^{61} +(-3.48317 + 2.53198i) q^{62} +(2.17716 - 1.87333i) q^{63} +(-6.46516 + 4.71187i) q^{64} +(0.0958163 + 0.165959i) q^{65} +(-0.989288 - 9.39013i) q^{66} +(-1.56667 - 0.206257i) q^{67} +(-0.114472 - 0.537244i) q^{68} +(-10.5325 - 4.36269i) q^{69} +(-1.76393 - 2.16091i) q^{70} +(-1.35162 - 1.35162i) q^{71} +(-0.162970 - 3.06616i) q^{72} +(0.236720 + 0.883450i) q^{73} +(-3.27624 + 11.0705i) q^{74} +(8.90616 - 1.17252i) q^{75} +(0.500361 + 6.31777i) q^{76} +(8.72556 - 0.489409i) q^{77} +(-0.725763 - 0.114766i) q^{78} +(-12.0051 + 6.93117i) q^{79} +(-2.98094 + 0.0810073i) q^{80} +(-9.59405 - 5.53913i) q^{81} +(4.50041 - 1.72882i) q^{82} +(15.5006 - 6.42056i) q^{83} +(10.6955 - 0.0445440i) q^{84} +(0.0783567 - 0.189170i) q^{85} +(10.2258 - 9.70874i) q^{86} +(1.09518 + 4.08727i) q^{87} +(5.28604 - 7.70347i) q^{88} +(-2.73728 + 10.2157i) q^{89} +(0.597779 - 0.976029i) q^{90} +(0.138956 - 0.665741i) q^{91} +(-5.12608 - 10.0482i) q^{92} +(3.74674 - 4.88285i) q^{93} +(14.4852 - 1.52608i) q^{94} +(-1.18118 + 2.04586i) q^{95} +(6.94942 - 9.07987i) q^{96} -0.0930782 q^{97} +(-0.443070 + 9.88957i) q^{98} +(1.37224 + 3.31287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.29209	−	0.574893i	−0.913646	−	0.406511i
$2$	−1.29209	−	0.574893i	−0.913646	−	0.406511i
$3$	2.00399	+	0.263830i	1.15700	+	0.152322i	0.684505	−	0.729009i	$-0.260019\pi$
$3$	2.00399	+	0.263830i	1.15700	+	0.152322i	0.472499	+	0.881331i	$0.343352\pi$
$4$	1.33900	+	1.48563i	0.669498	+	0.742814i
$5$	0.0973086	+	0.739132i	0.0435177	+	0.330550i	0.999331	+	0.0365752i	$0.0116448\pi$
$5$	0.0973086	+	0.739132i	0.0435177	+	0.330550i	−0.955813	+	0.293975i	$0.905022\pi$
$6$	−2.43766	−	1.49297i	−0.995171	−	0.609504i
$7$	1.49056	−	2.18592i	0.563377	−	0.826200i
$7$	1.49056	−	2.18592i	0.563377	−	0.826200i
$8$	−0.876026	−	2.68935i	−0.309722	−	0.950827i
$9$	1.04859	+	0.280969i	0.349530	+	0.0936564i
$10$	0.299191	−	1.01097i	0.0946124	−	0.319696i
$11$	2.01082	+	2.62055i	0.606286	+	0.790127i	0.991136	−	0.132852i	$-0.0424136\pi$
$11$	2.01082	+	2.62055i	0.606286	+	0.790127i	−0.384850	+	0.922979i	$0.625747\pi$
$12$	2.29138	+	3.33045i	0.661464	+	0.961418i
$13$	0.237482	−	0.0983684i	0.0658657	−	0.0272825i	−0.349507	−	0.936934i	$-0.613651\pi$
$13$	0.237482	−	0.0983684i	0.0658657	−	0.0272825i	0.415373	+	0.909651i	$0.363651\pi$
$14$	−3.18260	+	1.96749i	−0.850587	+	0.525835i
$15$			1.50689i			0.389076i
$16$	−0.414181	+	3.97850i	−0.103545	+	0.994625i
$17$	−0.237856	−	0.137326i	−0.0576885	−	0.0333065i	0.470878	−	0.882198i	$-0.343937\pi$
$17$	−0.237856	−	0.137326i	−0.0576885	−	0.0333065i	−0.528567	+	0.848892i	$0.677270\pi$
$18$	−1.19335	−	0.965865i	−0.281275	−	0.227657i
$19$	2.51396	+	1.92903i	0.576742	+	0.442549i	0.855493	−	0.517814i	$-0.173254\pi$
$19$	2.51396	+	1.92903i	0.576742	+	0.442549i	−0.278752	+	0.960363i	$0.589921\pi$
$20$	−0.967780	+	1.13426i	−0.216402	+	0.253628i
$21$	3.56377	−	3.98730i	0.777679	−	0.870101i
$22$	−1.09163	−	4.54200i	−0.232735	−	0.968358i
$23$	−5.44793	−	1.45977i	−1.13597	−	0.304383i	−0.358641	−	0.933476i	$-0.616760\pi$
$23$	−5.44793	−	1.45977i	−1.13597	−	0.304383i	−0.777330	+	0.629093i	$0.783426\pi$
$24$	−1.04602	−	5.62054i	−0.213517	−	1.14729i
$25$	4.29278	−	1.15025i	0.858556	−	0.230049i
$26$	−0.363400	−	0.00942610i	−0.0712686	−	0.00184861i
$27$	−3.57503	−	1.48082i	−0.688014	−	0.284985i
$28$	5.24331	−	0.712523i	0.990893	−	0.134654i
$29$	0.801128	+	1.93409i	0.148766	+	0.359152i	0.980642	−	0.195809i	$-0.0627332\pi$
$29$	0.801128	+	1.93409i	0.148766	+	0.359152i	−0.831876	+	0.554961i	$0.812733\pi$
$30$	0.866299	−	1.94703i	0.158164	−	0.355478i
$31$	1.52247	−	2.63700i	0.273444	−	0.473619i	−0.696297	−	0.717754i	$-0.745170\pi$
$31$	1.52247	−	2.63700i	0.273444	−	0.473619i	0.969741	+	0.244134i	$0.0785038\pi$
$32$	2.82237	−	4.90247i	0.498930	−	0.866643i
$33$	3.33829	+	5.78208i	0.581121	+	1.00653i
$34$	0.228383	+	0.314179i	0.0391674	+	0.0538813i
$35$	1.76073	+	0.889010i	0.297617	+	0.150270i
$36$	0.986643	+	1.93403i	0.164441	+	0.322339i
$37$	−1.06556	−	8.09376i	−0.175178	−	1.33061i	−0.822664	−	0.568528i	$-0.807513\pi$
$37$	−1.06556	−	8.09376i	−0.175178	−	1.33061i	0.647486	−	0.762077i	$-0.275820\pi$
$38$	−2.13928	−	3.93774i	−0.347036	−	0.638785i
$39$	0.501865	−	0.134474i	0.0803627	−	0.0215331i
$40$	1.90254	−	0.909196i	0.300818	−	0.143756i
$41$	−2.41053	+	2.41053i	−0.376461	+	0.376461i	−0.869824	−	0.493363i	$-0.835768\pi$
$41$	−2.41053	+	2.41053i	−0.376461	+	0.376461i	0.493363	+	0.869824i	$0.335768\pi$
$42$	−6.89699	+	3.10317i	−1.06423	+	0.478830i
$43$	−3.81560	+	9.21166i	−0.581873	+	1.40477i	0.309240	+	0.950984i	$0.399925\pi$
$43$	−3.81560	+	9.21166i	−0.581873	+	1.40477i	−0.891113	+	0.453781i	$0.850075\pi$
$44$	−1.20069	+	6.49624i	−0.181010	+	0.979346i
$45$	−0.105636	+	0.802388i	−0.0157473	+	0.119613i
$46$	6.20000	+	5.01813i	0.914141	+	0.739883i
$47$	−8.91945	+	5.14965i	−1.30104	+	0.751153i	−0.980582	−	0.196111i	$-0.937169\pi$
$47$	−8.91945	+	5.14965i	−1.30104	+	0.751153i	−0.320454	+	0.947264i	$0.603835\pi$
$48$	−1.87966	+	7.86360i	−0.271306	+	1.13501i
$49$	−2.55648	−	6.51647i	−0.365212	−	0.930925i
$50$	−6.20793	−	0.981667i	−0.877934	−	0.138829i
$51$	−0.440430	−	0.337954i	−0.0616725	−	0.0473230i
$52$	0.464127	+	0.221096i	0.0643628	+	0.0306604i
$53$	−4.88818	−	6.37040i	−0.671443	−	0.875042i	0.326083	−	0.945341i	$-0.394271\pi$
$53$	−4.88818	−	6.37040i	−0.671443	−	0.875042i	−0.997526	+	0.0702992i	$0.977605\pi$
$54$	3.76794	+	3.96862i	0.512752	+	0.540060i
$55$	−1.74127	+	1.74127i	−0.234792	+	0.234792i
$56$	−7.18446	−	2.09370i	−0.960063	−	0.279782i
$57$	4.52901	+	4.52901i	0.599882	+	0.599882i
$58$	0.0767677	−	2.95959i	0.0100801	−	0.388613i
$59$	−9.21225	+	7.06881i	−1.19933	+	0.920280i	−0.998241	−	0.0592921i	$-0.981116\pi$
$59$	−9.21225	+	7.06881i	−1.19933	+	0.920280i	−0.201092	+	0.979572i	$0.564449\pi$
$60$	−2.23867	+	2.01771i	−0.289011	+	0.260486i
$61$	3.85029	−	5.01779i	0.492979	−	0.642463i	−0.478921	−	0.877858i	$-0.658972\pi$
$61$	3.85029	−	5.01779i	0.492979	−	0.642463i	0.971900	+	0.235396i	$0.0756386\pi$
$62$	−3.48317	+	2.53198i	−0.442362	+	0.321562i
$63$	2.17716	−	1.87333i	0.274296	−	0.236018i
$64$	−6.46516	+	4.71187i	−0.808145	+	0.588984i
$65$	0.0958163	+	0.165959i	0.0118846	+	0.0205847i
$66$	−0.989288	−	9.39013i	−0.121773	−	1.15584i
$67$	−1.56667	−	0.206257i	−0.191400	−	0.0251982i	0.0342169	−	0.999414i	$-0.489106\pi$
$67$	−1.56667	−	0.206257i	−0.191400	−	0.0251982i	−0.225617	+	0.974216i	$0.572440\pi$
$68$	−0.114472	−	0.537244i	−0.0138818	−	0.0651504i
$69$	−10.5325	−	4.36269i	−1.26796	−	0.525206i
$70$	−1.76393	−	2.16091i	−0.210830	−	0.258278i
$71$	−1.35162	−	1.35162i	−0.160408	−	0.160408i	0.622340	−	0.782747i	$-0.286182\pi$
$71$	−1.35162	−	1.35162i	−0.160408	−	0.160408i	−0.782747	+	0.622340i	$0.786182\pi$
$72$	−0.162970	−	3.06616i	−0.0192062	−	0.361350i
$73$	0.236720	+	0.883450i	0.0277060	+	0.103400i	0.978394	−	0.206748i	$-0.0662880\pi$
$73$	0.236720	+	0.883450i	0.0277060	+	0.103400i	−0.950688	+	0.310148i	$0.899621\pi$
$74$	−3.27624	+	11.0705i	−0.380855	+	1.28691i
$75$	8.90616	−	1.17252i	1.02839	−	0.135391i
$76$	0.500361	+	6.31777i	0.0573953	+	0.724698i
$77$	8.72556	−	0.489409i	0.994370	−	0.0557733i
$78$	−0.725763	−	0.114766i	−0.0821765	−	0.0129947i
$79$	−12.0051	+	6.93117i	−1.35068	+	0.779818i	−0.988345	−	0.152229i	$-0.951355\pi$
$79$	−12.0051	+	6.93117i	−1.35068	+	0.779818i	−0.362339	+	0.932046i	$0.618022\pi$
$80$	−2.98094	+	0.0810073i	−0.333279	+	0.00905689i
$81$	−9.59405	−	5.53913i	−1.06601	−	0.615459i
$82$	4.50041	−	1.72882i	0.496987	−	0.190917i
$83$	15.5006	−	6.42056i	1.70141	−	0.704748i	0.701445	−	0.712724i	$-0.252539\pi$
$83$	15.5006	−	6.42056i	1.70141	−	0.704748i	0.999968	+	0.00797574i	$0.00253878\pi$
$84$	10.6955	−	0.0445440i	1.16698	−	0.00486015i
$85$	0.0783567	−	0.189170i	0.00849898	−	0.0205184i
$86$	10.2258	−	9.70874i	1.10268	−	1.04692i
$87$	1.09518	+	4.08727i	0.117416	+	0.438201i
$88$	5.28604	−	7.70347i	0.563494	−	0.821193i
$89$	−2.73728	+	10.2157i	−0.290151	+	1.08286i	0.654842	+	0.755766i	$0.272735\pi$
$89$	−2.73728	+	10.2157i	−0.290151	+	1.08286i	−0.944993	+	0.327092i	$0.893931\pi$
$90$	0.597779	−	0.976029i	0.0630115	−	0.102882i
$91$	0.138956	−	0.665741i	0.0145665	−	0.0697886i
$92$	−5.12608	−	10.0482i	−0.534431	−	1.04760i
$93$	3.74674	−	4.88285i	0.388519	−	0.506328i
$94$	14.4852	−	1.52608i	1.49404	−	0.157403i
$95$	−1.18118	+	2.04586i	−0.121186	+	0.209901i
$96$	6.94942	−	9.07987i	0.709273	−	0.926711i
$97$	−0.0930782			−0.00945066			−0.00472533	−	0.999989i	$-0.501504\pi$
$97$	−0.0930782			−0.00945066			−0.00472533	+	0.999989i	$0.501504\pi$
$98$	−0.443070	+	9.88957i	−0.0447569	+	0.998998i
$99$	1.37224	+	3.31287i	0.137915	+	0.332956i
$100$	7.45686	+	4.83730i	0.745686	+	0.483730i
$101$	9.61735	−	7.37966i	0.956963	−	0.734303i	−0.00710107	−	0.999975i	$-0.502260\pi$
$101$	9.61735	−	7.37966i	0.956963	−	0.734303i	0.964064	+	0.265672i	$0.0855937\pi$
$102$	0.374788	+	0.689867i	0.0371095	+	0.0683070i
$103$	−0.216727	+	0.808836i	−0.0213547	+	0.0796970i	−0.975781	−	0.218750i	$-0.929802\pi$
$103$	−0.216727	+	0.808836i	−0.0213547	+	0.0796970i	0.954426	+	0.298447i	$0.0964687\pi$
$104$	−0.472587	−	0.552499i	−0.0463410	−	0.0541770i
$105$	3.29393	+	2.24610i	0.321455	+	0.219197i
$106$	2.65367	+	11.0413i	0.257747	+	1.07243i
$107$	−0.174066	+	0.0229162i	−0.0168276	+	0.00221539i	−0.138935	−	0.990301i	$-0.544368\pi$
$107$	−0.174066	+	0.0229162i	−0.0168276	+	0.00221539i	0.122108	+	0.992517i	$0.461035\pi$
$108$	−2.58699	−	7.29398i	−0.248933	−	0.701863i
$109$	−1.17379	+	8.91585i	−0.112429	+	0.853983i	0.838571	+	0.544792i	$0.183392\pi$
$109$	−1.17379	+	8.91585i	−0.112429	+	0.853983i	−0.951000	+	0.309191i	$0.899942\pi$
$110$	3.25092	−	1.24883i	0.309963	−	0.119071i
$111$		−	16.5009i		−	1.56620i
$112$	8.07931	+	6.83555i	0.763423	+	0.645898i
$113$		−	8.13250i		−	0.765041i	−0.923947	−	0.382520i	$-0.875056\pi$
$113$		−	8.13250i		−	0.765041i	0.923947	−	0.382520i	$-0.124944\pi$
$114$	−3.24819	−	8.45559i	−0.304221	−	0.791938i
$115$	0.548831	−	4.16879i	0.0511788	−	0.388741i
$116$	−1.80064	+	3.77992i	−0.167185	+	0.350957i
$117$	0.276660	−	0.0364230i	0.0255773	−	0.00336731i
$118$	15.9669	−	3.83748i	1.46987	−	0.353269i
$119$	−0.654721	+	0.315241i	−0.0600182	+	0.0288981i
$120$	4.05254	−	1.32007i	0.369944	−	0.120506i
$121$	0.0231099	−	0.0862472i	0.00210090	−	0.00784065i
$122$	−7.85961	+	4.26994i	−0.711576	+	0.386582i
$123$	−5.46664	+	4.19470i	−0.492910	+	0.378223i
$124$	5.95619	−	1.26910i	0.534881	−	0.113969i
$125$	2.69438	+	6.50481i	0.240993	+	0.581808i
$126$	−3.89006	+	1.16888i	−0.346554	+	0.104132i
$127$	−13.8415			−1.22824			−0.614119	−	0.789213i	$-0.710489\pi$
$127$	−13.8415			−1.22824			−0.614119	+	0.789213i	$0.710489\pi$
$128$	11.0624	−	2.37139i	0.977786	−	0.209603i
$129$	−10.0767	+	17.4534i	−0.887207	+	1.53669i
$130$	−0.0283948	−	0.269518i	−0.00249039	−	0.0236383i
$131$	11.7684	−	15.3368i	1.02821	−	1.33998i	0.0892263	−	0.996011i	$-0.471561\pi$
$131$	11.7684	−	15.3368i	1.02821	−	1.33998i	0.938980	−	0.343973i	$-0.111773\pi$
$132$	−4.12007	+	12.7016i	−0.358606	+	1.10553i
$133$	7.96390	−	2.61998i	0.690557	−	0.227181i
$134$	1.90571	+	1.16717i	0.164628	+	0.100828i
$135$	0.746644	−	2.78651i	0.0642609	−	0.239825i
$136$	−0.160949	+	0.759978i	−0.0138013	+	0.0651675i
$137$	−3.24561	−	12.1128i	−0.277291	−	1.03487i	−0.954290	−	0.298881i	$-0.903386\pi$
$137$	−3.24561	−	12.1128i	−0.277291	−	1.03487i	0.676999	−	0.735984i	$-0.263280\pi$
$138$	11.1008	+	11.6920i	0.944964	+	0.995291i
$139$	7.47093	−	18.0364i	0.633676	−	1.52983i	−0.201293	−	0.979531i	$-0.564514\pi$
$139$	7.47093	−	18.0364i	0.633676	−	1.52983i	0.834969	−	0.550297i	$-0.185486\pi$
$140$	1.03687	+	3.80617i	0.0876313	+	0.321680i
$141$	−19.2331	+	7.96662i	−1.61972	+	0.670910i
$142$	0.969377	+	2.52345i	0.0813483	+	0.211763i
$143$	0.735314	+	0.424534i	0.0614901	+	0.0355013i
$144$	−1.55214	+	4.05545i	−0.129345	+	0.337954i
$145$	−1.35160	+	0.780344i	−0.112244	+	0.0648040i
$146$	0.202026	−	1.27759i	0.0167198	−	0.105734i
$147$	−3.40392	−	13.7334i	−0.280751	−	1.13271i
$148$	10.5975	−	12.4205i	0.871112	−	1.02096i
$149$	−12.1516	+	1.59979i	−0.995501	+	0.131060i	−0.610635	−	0.791912i	$-0.709086\pi$
$149$	−12.1516	+	1.59979i	−0.995501	+	0.131060i	−0.384866	+	0.922972i	$0.625752\pi$
$150$	−12.1816	−	3.60509i	−0.994627	−	0.294354i
$151$	5.23083	+	19.5217i	0.425679	+	1.58865i	0.762436	+	0.647063i	$0.224003\pi$
$151$	5.23083	+	19.5217i	0.425679	+	1.58865i	−0.336758	+	0.941591i	$0.609330\pi$
$152$	2.98553	−	8.45078i	0.242158	−	0.685449i
$153$	−0.210829	−	0.210829i	−0.0170445	−	0.0170445i
$154$	−11.5556	−	4.38391i	−0.931175	−	0.353265i
$155$	2.09724	+	0.868706i	0.168454	+	0.0697761i
$156$	0.871773	+	0.565524i	0.0697977	+	0.0452781i
$157$	17.9395	+	2.36178i	1.43173	+	0.188491i	0.806169	−	0.591685i	$-0.201537\pi$
$157$	17.9395	+	2.36178i	1.43173	+	0.188491i	0.625560	+	0.780176i	$0.284870\pi$
$158$	19.4964	−	2.05403i	1.55105	−	0.163410i
$159$	−8.11516	−	14.0559i	−0.643574	−	1.11470i
$160$	3.89822	+	1.60905i	0.308181	+	0.127207i
$161$	−11.3114	+	9.73286i	−0.891461	+	0.767057i
$162$	9.21198	+	12.6726i	0.723761	+	0.995654i
$163$	−7.93095	+	10.3358i	−0.621200	+	0.809563i	−0.992920	−	0.118781i	$-0.962101\pi$
$163$	−7.93095	+	10.3358i	−0.621200	+	0.809563i	0.371721	+	0.928345i	$0.378768\pi$
$164$	−6.80883	−	0.353461i	−0.531680	−	0.0276007i
$165$	−3.94888	+	3.03008i	−0.307420	+	0.235891i
$166$	−23.7193	−	0.615247i	−1.84098	−	0.0477524i
$167$	8.64632	+	8.64632i	0.669073	+	0.669073i	0.957501	−	0.288429i	$-0.0931328\pi$
$167$	8.64632	+	8.64632i	0.669073	+	0.669073i	−0.288429	+	0.957501i	$0.593133\pi$
$168$	−13.8452	−	6.09123i	−1.06818	−	0.469949i
$169$	−9.14567	+	9.14567i	−0.703513	+	0.703513i
$170$	−0.209997	+	0.199378i	−0.0161060	+	0.0152916i
$171$	2.09412	+	2.72911i	0.160141	+	0.208700i
$172$	−18.7942	+	6.66582i	−1.43304	+	0.508264i
$173$	2.17697	+	1.67045i	0.165512	+	0.127002i	0.688197	−	0.725524i	$-0.258403\pi$
$173$	2.17697	+	1.67045i	0.165512	+	0.127002i	−0.522684	+	0.852526i	$0.675069\pi$
$174$	0.934671	−	5.91073i	0.0708572	−	0.448091i
$175$	3.88429	−	11.0982i	0.293625	−	0.838944i
$176$	−11.2587	+	6.91467i	−0.848658	+	0.521213i
$177$	−20.3262	+	11.7353i	−1.52781	+	0.882083i
$178$	9.40973	−	11.6259i	0.705289	−	0.871399i
$179$	−0.122808	+	0.932819i	−0.00917910	+	0.0697222i	−0.995421	−	0.0955844i	$-0.969528\pi$
$179$	−0.122808	+	0.932819i	−0.00917910	+	0.0697222i	0.986242	+	0.165307i	$0.0528614\pi$
$180$	−1.33350	+	0.917458i	−0.0993930	+	0.0683833i
$181$	0.611795	−	1.47700i	0.0454744	−	0.109785i	−0.899510	−	0.436900i	$-0.856076\pi$
$181$	0.611795	−	1.47700i	0.0454744	−	0.109785i	0.944985	+	0.327115i	$0.106076\pi$
$182$	−0.562273	+	0.780313i	−0.0416784	+	0.0578406i
$183$	9.03978	−	9.03978i	0.668240	−	0.668240i
$184$	0.846706	+	15.9301i	0.0624200	+	1.17439i
$185$	5.87867	−	1.57518i	0.432208	−	0.115810i
$186$	−7.64824	+	4.15510i	−0.560796	+	0.304667i
$187$	−0.118415	−	0.899452i	−0.00865937	−	0.0657745i
$188$	−19.5936	−	6.35563i	−1.42901	−	0.463532i
$189$	−8.56574	+	5.60746i	−0.623066	+	0.407883i
$190$	2.70234	−	1.96438i	0.196048	−	0.142511i
$191$	6.41353	+	11.1086i	0.464067	+	0.803787i	0.999159	−	0.0410064i	$-0.0130564\pi$
$191$	6.41353	+	11.1086i	0.464067	+	0.803787i	−0.535092	+	0.844794i	$0.679723\pi$
$192$	−14.1992	+	7.73684i	−1.02474	+	0.558358i
$193$	5.48121	−	9.49374i	0.394546	−	0.683374i	−0.598497	−	0.801125i	$-0.704235\pi$
$193$	5.48121	−	9.49374i	0.394546	−	0.683374i	0.993043	+	0.117751i	$0.0375684\pi$
$194$	0.120266	+	0.0535100i	0.00863456	+	0.00384180i
$195$	0.148230	+	0.357859i	0.0106150	+	0.0256268i
$196$	6.25794	−	12.5235i	0.446995	−	0.894536i
$197$	21.5255	+	8.91616i	1.53363	+	0.635250i	0.980265	−	0.197690i	$-0.0633438\pi$
$197$	21.5255	+	8.91616i	1.53363	+	0.635250i	0.553364	+	0.832939i	$0.313344\pi$
$198$	0.131494	−	5.06942i	0.00934485	−	0.360268i
$199$	4.51855	−	1.21074i	0.320311	−	0.0858271i	−0.0950810	−	0.995470i	$-0.530311\pi$
$199$	4.51855	−	1.21074i	0.320311	−	0.0858271i	0.415392	+	0.909642i	$0.363644\pi$
$200$	−6.85400	−	10.5371i	−0.484651	−	0.745087i
$201$	−3.08518	−	0.826672i	−0.217612	−	0.0583089i
$202$	−16.6690	+	4.00623i	−1.17283	+	0.281877i
$203$	5.42190	+	1.13168i	0.380543	+	0.0794281i
$204$	−0.0876601	−	1.10683i	−0.00613744	−	0.0774938i
$205$	−2.01626	−	1.54713i	−0.140822	−	0.108056i
$206$	0.745025	−	0.920494i	0.0519083	−	0.0641339i
$207$	−5.30250	−	3.06140i	−0.368549	−	0.212782i
$208$	0.292998	+	0.985566i	0.0203157	+	0.0683367i
$209$			10.4669i			0.724010i
$210$	−2.96479	−	4.79582i	−0.204590	−	0.330943i
$211$	−4.01171	+	1.66171i	−0.276178	+	0.114397i	−0.516474	−	0.856303i	$-0.672756\pi$
$211$	−4.01171	+	1.66171i	−0.276178	+	0.114397i	0.240296	+	0.970700i	$0.422756\pi$
$212$	2.91879	−	15.7920i	0.200464	−	1.08460i
$213$	−2.35203	−	3.06523i	−0.161159	−	0.210026i
$214$	0.238083	+	0.0704595i	0.0162750	+	0.00481651i
$215$	−7.17993	−	1.92386i	−0.489667	−	0.131206i
$216$	−0.850632	+	10.9117i	−0.0578782	+	0.742448i
$217$	−3.49494	−	7.25860i	−0.237252	−	0.492746i
$218$	6.64231	−	10.8453i	0.449874	−	0.734535i
$219$	0.241303	+	1.83288i	0.0163058	+	0.123854i
$220$	−4.91842	−	0.255326i	−0.331600	−	0.0172141i
$221$	−0.0699951	−	0.00921503i	−0.00470838	−	0.000619870i
$222$	−9.48628	+	21.3207i	−0.636677	+	1.43095i
$223$	25.6197			1.71562			0.857810	−	0.513967i	$-0.171825\pi$
$223$	25.6197			1.71562			0.857810	+	0.513967i	$0.171825\pi$
$224$	−6.50950	−	13.4769i	−0.434934	−	0.900462i
$225$	4.82456			0.321637
$226$	−4.67532	+	10.5079i	−0.310997	+	0.698977i
$227$	24.3131	+	3.20087i	1.61371	+	0.212449i	0.882708	−	0.469922i	$-0.155718\pi$
$227$	24.3131	+	3.20087i	1.61371	+	0.212449i	0.731006	+	0.682371i	$0.239051\pi$
$228$	−0.664100	+	12.7928i	−0.0439811	+	0.847221i
$229$	1.48972	+	11.3155i	0.0984434	+	0.747752i	0.967470	+	0.252986i	$0.0814127\pi$
$229$	1.48972	+	11.3155i	0.0984434	+	0.747752i	−0.869026	+	0.494766i	$0.835254\pi$
$230$	−3.10575	+	5.07093i	−0.204787	+	0.334367i
$231$	17.6151	+	1.32130i	1.15899	+	0.0869350i
$232$	4.49964	−	3.84883i	0.295416	−	0.252688i
$233$	15.9522	+	4.27438i	1.04506	+	0.280024i	0.740211	−	0.672375i	$-0.234726\pi$
$233$	15.9522	+	4.27438i	1.04506	+	0.280024i	0.304854	+	0.952399i	$0.401392\pi$
$234$	−0.378410	−	0.111988i	−0.0247374	−	0.00732091i
$235$	−4.67421	−	6.09155i	−0.304912	−	0.397369i
$236$	−22.8368	−	4.22087i	−1.48655	−	0.274755i
$237$	−25.8868	+	10.7227i	−1.68153	+	0.696513i
$238$	1.02719	−	0.0309252i	0.0665828	−	0.00200458i
$239$		−	27.6751i		−	1.79015i	−0.445913	−	0.895077i	$-0.647121\pi$
$239$		−	27.6751i		−	1.79015i	0.445913	−	0.895077i	$-0.352879\pi$
$240$	−5.99515	−	0.624124i	−0.386985	−	0.0402871i
$241$	22.5676	+	13.0294i	1.45371	+	0.839298i	0.998689	−	0.0511845i	$-0.0162997\pi$
$241$	22.5676	+	13.0294i	1.45371	+	0.839298i	0.455018	+	0.890482i	$0.349633\pi$
$242$	−0.0794430	+	0.0981535i	−0.00510679	+	0.00630954i
$243$	−8.55516	−	6.56461i	−0.548814	−	0.421120i
$244$	12.6101	−	0.998707i	0.807278	−	0.0639357i
$245$	4.56777	−	2.52369i	0.291824	−	0.161232i
$246$	9.47490	−	2.27720i	0.604097	−	0.145189i
$247$	0.786776	+	0.210816i	0.0500614	+	0.0134139i
$248$	−8.42553	−	1.78437i	−0.535022	−	0.113308i
$249$	32.7570	−	8.77721i	2.07589	−	0.556233i
$250$	0.258188	−	9.95379i	0.0163292	−	0.629533i
$251$	11.7913	+	4.88413i	0.744262	+	0.308283i	0.722398	−	0.691478i	$-0.243040\pi$
$251$	11.7913	+	4.88413i	0.744262	+	0.308283i	0.0218640	+	0.999761i	$0.493040\pi$
$252$	5.69829	+	0.726064i	0.358958	+	0.0457377i
$253$	−7.12941	−	17.2119i	−0.448222	−	1.08210i
$254$	17.8845	+	7.95741i	1.12217	+	0.499292i
$255$	0.206935	−	0.358422i	0.0129588	−	0.0224452i
$256$	−15.6569	−	3.29564i	−0.978557	−	0.205978i
$257$	−6.19325	−	10.7270i	−0.386325	−	0.669134i	0.605627	−	0.795748i	$-0.292922\pi$
$257$	−6.19325	−	10.7270i	−0.386325	−	0.669134i	−0.991952	+	0.126615i	$0.959589\pi$
$258$	23.0539	−	16.7583i	1.43527	−	1.04333i
$259$	−19.2806	−	9.73497i	−1.19804	−	0.604902i
$260$	−0.118255	+	0.364566i	−0.00733389	+	0.0226094i
$261$	0.296635	+	2.25317i	0.0183612	+	0.139468i
$262$	−24.0228	+	13.0510i	−1.48413	+	0.806294i
$263$	7.47556	−	2.00307i	0.460963	−	0.123515i	−0.0208616	−	0.999782i	$-0.506641\pi$
$263$	7.47556	−	2.00307i	0.460963	−	0.123515i	0.481825	+	0.876268i	$0.339974\pi$
$264$	12.6256	−	14.0431i	0.777051	−	0.864290i
$265$	4.23291	−	4.23291i	0.260025	−	0.260025i
$266$	−11.7963	−	1.19313i	−0.723277	−	0.0731558i
$267$	−8.18068	+	19.7499i	−0.500649	+	1.20867i
$268$	−1.79135	−	2.60367i	−0.109424	−	0.159045i
$269$	1.12283	−	8.52875i	0.0684603	−	0.520007i	−0.922515	−	0.385961i	$-0.873870\pi$
$269$	1.12283	−	8.52875i	0.0684603	−	0.520007i	0.990975	−	0.134046i	$-0.0427969\pi$
$270$	−2.56668	+	3.17119i	−0.156203	+	0.192992i
$271$	−22.8091	+	13.1689i	−1.38556	+	0.799951i	−0.992811	−	0.119696i	$-0.961808\pi$
$271$	−22.8091	+	13.1689i	−1.38556	+	0.799951i	−0.392746	+	0.919647i	$0.628475\pi$
$272$	0.644867	−	0.889431i	0.0391008	−	0.0539297i
$273$	0.454108	−	1.29748i	0.0274839	−	0.0785269i
$274$	−2.76994	+	17.5167i	−0.167338	+	1.05822i
$275$	11.6463	+	8.93652i	0.702299	+	0.538893i
$276$	−7.62158	−	21.4889i	−0.458765	−	1.29348i
$277$	−4.31256	−	5.62024i	−0.259117	−	0.337687i	0.645620	−	0.763659i	$-0.276599\pi$
$277$	−4.31256	−	5.62024i	−0.259117	−	0.337687i	−0.904737	+	0.425972i	$0.859932\pi$
$278$	−20.0221	+	19.0097i	−1.20085	+	1.14013i
$279$	2.33737	−	2.33737i	0.139935	−	0.139935i
$280$	0.848412	−	5.51400i	0.0507023	−	0.329524i
$281$	3.43098	+	3.43098i	0.204675	+	0.204675i	0.802000	−	0.597324i	$-0.203770\pi$
$281$	3.43098	+	3.43098i	0.204675	+	0.204675i	−0.597324	+	0.802000i	$0.703770\pi$
$282$	29.4309	+	0.763397i	1.75258	+	0.0454596i
$283$	−18.0660	+	13.8626i	−1.07391	+	0.824043i	−0.985096	−	0.172005i	$-0.944976\pi$
$283$	−18.0660	+	13.8626i	−1.07391	+	0.824043i	−0.0888180	+	0.996048i	$0.528309\pi$
$284$	0.198191	−	3.81781i	0.0117605	−	0.226546i
$285$	−2.90683	+	3.78825i	−0.172186	+	0.224397i
$286$	−0.706031	−	0.971264i	−0.0417485	−	0.0574320i
$287$	1.67619	+	8.86224i	0.0989422	+	0.523121i
$288$	4.33696	−	4.34769i	0.255558	−	0.256190i
$289$	−8.46228	−	14.6571i	−0.497781	−	0.862183i
$290$	2.19500	−	0.231252i	0.128895	−	0.0135796i
$291$	−0.186528	−	0.0245569i	−0.0109345	−	0.00143955i
$292$	−0.995512	+	1.53461i	−0.0582579	+	0.0898065i
$293$	−7.79492	−	3.22876i	−0.455384	−	0.188626i	0.143187	−	0.989696i	$-0.454265\pi$
$293$	−7.79492	−	3.22876i	−0.455384	−	0.188626i	−0.598572	+	0.801069i	$0.704265\pi$
$294$	−3.49708	+	19.7017i	−0.203954	+	1.14903i
$295$	−6.12121	−	6.12121i	−0.356391	−	0.356391i
$296$	−20.8335	+	9.95601i	−1.21092	+	0.578681i
$297$	−3.30816	−	12.3462i	−0.191959	−	0.716401i
$298$	16.6207	+	4.91882i	0.962813	+	0.284940i
$299$	−1.43738	+	0.189235i	−0.0831259	+	0.0109437i
$300$	13.6672	+	11.6612i	0.789078	+	0.673262i
$301$	14.4486	+	22.0711i	0.832802	+	1.27216i
$302$	4.46420	−	28.2310i	0.256886	−	1.62451i
$303$	21.2201	−	12.2514i	1.21906	−	0.703825i
$304$	−8.71587	+	9.20281i	−0.499889	+	0.527817i
$305$	4.08348	+	2.35760i	0.233819	+	0.134996i
$306$	0.151206	+	0.393614i	0.00864387	+	0.0225014i
$307$	−16.3850	+	6.78688i	−0.935141	+	0.387348i	−0.797626	−	0.603152i	$-0.793911\pi$
$307$	−16.3850	+	6.78688i	−0.935141	+	0.387348i	−0.137514	+	0.990500i	$0.543911\pi$
$308$	12.4106	+	12.3076i	0.707158	+	0.701292i
$309$	−0.647714	+	1.56372i	−0.0368472	+	0.0889569i
$310$	−2.21041	−	2.32814i	−0.125543	−	0.132229i
$311$	4.55416	+	16.9964i	0.258243	+	0.963775i	0.966258	+	0.257577i	$0.0829242\pi$
$311$	4.55416	+	16.9964i	0.258243	+	0.963775i	−0.708015	+	0.706197i	$0.750409\pi$
$312$	−0.801294	−	1.23188i	−0.0453644	−	0.0697417i
$313$	6.57439	−	24.5359i	0.371606	−	1.38685i	−0.486634	−	0.873606i	$-0.661776\pi$
$313$	6.57439	−	24.5359i	0.371606	−	1.38685i	0.858240	−	0.513248i	$-0.171558\pi$
$314$	−21.8217	−	13.3649i	−1.23147	−	0.754228i
$315$	1.59650	+	1.42692i	0.0899525	+	0.0803977i
$316$	−26.3720	−	8.55437i	−1.48354	−	0.481221i
$317$	−3.20787	+	4.18058i	−0.180172	+	0.234805i	−0.874705	−	0.484657i	$-0.838945\pi$
$317$	−3.20787	+	4.18058i	−0.180172	+	0.234805i	0.694532	+	0.719461i	$0.255611\pi$
$318$	2.40490	+	22.8268i	0.134860	+	1.28006i
$319$	−3.45747	+	5.98852i	−0.193581	+	0.335293i
$320$	−4.11181	−	4.32010i	−0.229857	−	0.241501i
$321$	−0.354872			−0.0198070
$322$	20.2107	−	6.07290i	1.12630	−	0.338429i
$323$	−0.333054	−	0.804063i	−0.0185316	−	0.0447392i
$324$	−4.61731	−	21.6701i	−0.256517	−	1.20389i
$325$	0.906312	−	0.695438i	0.0502731	−	0.0385759i
$326$	16.1895	−	8.79536i	0.896653	−	0.487130i
$327$	−4.70454	+	17.5576i	−0.260162	+	0.970937i
$328$	8.59442	+	4.37105i	0.474547	+	0.241351i
$329$	−2.03824	+	27.1730i	−0.112372	+	1.49810i
$330$	6.84428	−	1.64496i	0.376765	−	0.0905518i
$331$	−5.25271	+	0.691533i	−0.288715	+	0.0380101i	−0.273493	−	0.961874i	$-0.588179\pi$
$331$	−5.25271	+	0.691533i	−0.288715	+	0.0380101i	−0.0152224	+	0.999884i	$0.504846\pi$
$332$	30.2938	+	14.4310i	1.66259	+	0.792006i
$333$	1.15676	−	8.78643i	0.0633898	−	0.481494i
$334$	−6.20112	−	16.1425i	−0.339310	−	0.883281i
$335$		−	1.17805i		−	0.0643637i
$336$	14.3874	+	15.8299i	0.784899	+	0.863594i
$337$		−	13.2457i		−	0.721540i	−0.932655	−	0.360770i	$-0.882514\pi$
$337$		−	13.2457i		−	0.721540i	0.932655	−	0.360770i	$-0.117486\pi$
$338$	17.0748	−	6.55925i	0.928747	−	0.356776i
$339$	2.14560	−	16.2974i	0.116533	−	0.885155i
$340$	0.385955	−	0.136889i	0.0209314	−	0.00742383i
$341$	9.97182	−	1.31282i	0.540005	−	0.0710929i
$342$	−1.13684	−	4.73015i	−0.0614735	−	0.255777i
$343$	−18.0551	−	4.12491i	−0.974881	−	0.222724i
$344$	28.1159	+	2.19180i	1.51591	+	0.118174i
$345$	2.19970	−	8.20941i	0.118428	−	0.441980i
$346$	−1.85252	−	3.40990i	−0.0995919	−	0.183317i
$347$	−2.06355	+	1.58342i	−0.110777	+	0.0850022i	−0.662665	−	0.748916i	$-0.730574\pi$
$347$	−2.06355	+	1.58342i	−0.110777	+	0.0850022i	0.551887	+	0.833919i	$0.313908\pi$
$348$	−4.60572	+	7.09986i	−0.246892	+	0.380593i
$349$	−2.18080	−	5.26491i	−0.116735	−	0.281824i	0.854703	−	0.519118i	$-0.173740\pi$
$349$	−2.18080	−	5.26491i	−0.116735	−	0.281824i	−0.971438	+	0.237294i	$0.923740\pi$
$350$	−11.3991	+	12.1068i	−0.609309	+	0.647136i
$351$	−0.994672			−0.0530917
$352$	18.5225	−	2.46182i	0.987251	−	0.131215i
$353$	−12.7963	+	22.1639i	−0.681079	+	1.17966i	0.293573	+	0.955937i	$0.405155\pi$
$353$	−12.7963	+	22.1639i	−0.681079	+	1.17966i	−0.974652	+	0.223726i	$0.928178\pi$
$354$	33.0099	−	3.47773i	1.75446	−	0.184839i
$355$	0.867501	−	1.13055i	0.0460422	−	0.0600033i
$356$	−18.8419	+	9.61215i	−0.998617	+	0.509443i
$357$	−1.39522	+	0.459005i	−0.0738431	+	0.0242931i
$358$	0.694951	−	1.13469i	0.0367293	−	0.0599700i
$359$	4.00253	−	14.9377i	0.211246	−	0.788380i	−0.776209	−	0.630476i	$-0.782860\pi$
$359$	4.00253	−	14.9377i	0.211246	−	0.788380i	0.987455	−	0.157904i	$-0.0504736\pi$
$360$	2.25044	−	0.418820i	0.118609	−	0.0220738i
$361$	−2.31873	−	8.65360i	−0.122038	−	0.455453i
$362$	−1.63961	+	1.55671i	−0.0861762	+	0.0818186i
$363$	0.0690665	−	0.166741i	0.00362505	−	0.00875165i
$364$	1.17510	−	0.684988i	0.0615922	−	0.0359031i
$365$	−0.629952	+	0.260935i	−0.0329732	+	0.0136579i
$366$	−16.8771	+	6.48331i	−0.882182	+	0.338888i
$367$	16.8198	+	9.71092i	0.877987	+	0.506906i	0.869994	−	0.493062i	$-0.164123\pi$
$367$	16.8198	+	9.71092i	0.877987	+	0.506906i	0.00799252	+	0.999968i	$0.497456\pi$
$368$	8.06411	−	21.0700i	0.420371	−	1.09835i
$369$	−3.20494	+	1.85037i	−0.166842	+	0.0963265i
$370$	−8.50134	−	1.34433i	−0.441963	−	0.0698882i
$371$	−21.2113	+	1.18972i	−1.10124	+	0.0617673i
$372$	12.2710	−	0.971848i	0.636220	−	0.0503880i
$373$	−15.9998	+	2.10641i	−0.828438	+	0.109066i	−0.532808	−	0.846236i	$-0.678863\pi$
$373$	−15.9998	+	2.10641i	−0.828438	+	0.109066i	−0.295631	+	0.955302i	$0.595530\pi$
$374$	−0.364086	+	1.23025i	−0.0188264	+	0.0636147i
$375$	3.68335	+	13.7464i	0.190207	+	0.709863i
$376$	21.6628	+	19.4763i	1.11718	+	1.00441i
$377$	0.380508	+	0.380508i	0.0195971	+	0.0195971i
$378$	14.2914	−	2.32096i	0.735070	−	0.119378i
$379$	8.51634	+	3.52758i	0.437455	+	0.181200i	0.590532	−	0.807015i	$-0.298918\pi$
$379$	8.51634	+	3.52758i	0.437455	+	0.181200i	−0.153077	+	0.988214i	$0.548918\pi$
$380$	−4.62098	+	0.984606i	−0.237051	+	0.0505092i
$381$	−27.7383	−	3.65182i	−1.42108	−	0.187088i
$382$	−1.90063	−	18.0404i	−0.0972445	−	0.923025i
$383$	−5.43130	−	9.40729i	−0.277526	−	0.480690i	0.693243	−	0.720704i	$-0.256181\pi$
$383$	−5.43130	−	9.40729i	−0.277526	−	0.480690i	−0.970769	+	0.240014i	$0.922848\pi$
$384$	22.7946	−	1.83365i	1.16323	−	0.0935731i
$385$	1.21081	+	6.40172i	0.0617086	+	0.326262i
$386$	−12.5401	+	9.11566i	−0.638275	+	0.463975i
$387$	−6.58919	+	8.58720i	−0.334947	+	0.436512i
$388$	−0.124631	−	0.138280i	−0.00632720	−	0.00702009i
$389$	−8.77205	+	6.73103i	−0.444760	+	0.341277i	−0.806737	−	0.590910i	$-0.798769\pi$
$389$	−8.77205	+	6.73103i	−0.444760	+	0.341277i	0.361977	+	0.932187i	$0.382102\pi$
$390$	0.0142041	−	0.547603i	0.000719251	−	0.0277289i
$391$	1.09536	+	1.09536i	0.0553946	+	0.0553946i
$392$	−15.2855	+	12.5839i	−0.772034	+	0.635581i
$393$	27.6300	−	27.6300i	1.39375	−	1.39375i
$394$	−22.6871	−	23.8953i	−1.14296	−	1.20383i
$395$	−6.29126	−	8.19893i	−0.316547	−	0.412533i
$396$	−3.08427	+	6.47455i	−0.154991	+	0.325358i
$397$	14.7402	+	11.3105i	0.739788	+	0.567659i	0.908439	−	0.418016i	$-0.137275\pi$
$397$	14.7402	+	11.3105i	0.739788	+	0.567659i	−0.168651	+	0.985676i	$0.553941\pi$
$398$	−6.53442	−	1.03329i	−0.327541	−	0.0517944i
$399$	16.6508	−	3.14930i	0.833582	−	0.157662i
$400$	2.79827	+	17.5552i	0.139913	+	0.877762i
$401$	−1.21956	+	0.704116i	−0.0609022	+	0.0351619i	−0.530142	−	0.847909i	$-0.677861\pi$
$401$	−1.21956	+	0.704116i	−0.0609022	+	0.0351619i	0.469240	+	0.883071i	$0.344528\pi$
$402$	3.51109	+	2.84179i	0.175117	+	0.141735i
$403$	0.102163	−	0.776004i	0.00508910	−	0.0386555i
$404$	23.8410	+	4.40649i	1.18614	+	0.219231i
$405$	3.16056	−	7.63028i	0.157050	−	0.379152i
$406$	−6.35499	−	4.57924i	−0.315393	−	0.227264i
$407$	19.0675	−	19.0675i	0.945140	−	0.945140i
$408$	−0.523046	+	1.48052i	−0.0258946	+	0.0732969i
$409$	−19.4066	+	5.19999i	−0.959596	+	0.257123i	−0.704429	−	0.709774i	$-0.748797\pi$
$409$	−19.4066	+	5.19999i	−0.959596	+	0.257123i	−0.255167	+	0.966897i	$0.582130\pi$
$410$	1.71576	+	3.15817i	0.0847352	+	0.155971i
$411$	−3.30845	−	25.1302i	−0.163194	−	1.23958i
$412$	−1.49183	+	0.761052i	−0.0734970	+	0.0374943i
$413$	1.72046	+	30.6737i	0.0846582	+	1.50935i
$414$	5.09133	+	7.00397i	0.250225	+	0.344227i
$415$	6.25399	+	10.8322i	0.306996	+	0.531733i
$416$	0.188015	−	1.44188i	0.00921821	−	0.0706941i
$417$	19.7302	−	34.1737i	0.966193	−	1.67349i
$418$	6.01735	−	13.5242i	0.294318	−	0.661489i
$419$	6.86208	+	16.5665i	0.335235	+	0.809328i	0.998160	+	0.0606421i	$0.0193148\pi$
$419$	6.86208	+	16.5665i	0.335235	+	0.809328i	−0.662925	+	0.748686i	$0.730685\pi$
$420$	1.07369	+	7.90107i	0.0523907	+	0.385533i
$421$	9.32287	+	3.86166i	0.454369	+	0.188206i	0.598117	−	0.801408i	$-0.295916\pi$
$421$	9.32287	+	3.86166i	0.454369	+	0.188206i	−0.143748	+	0.989614i	$0.545916\pi$
$422$	6.13880	+	0.159232i	0.298832	+	0.00775130i
$423$	−10.7997	+	2.89378i	−0.525102	+	0.140701i
$424$	−12.8500	+	18.7266i	−0.624053	+	0.909446i
$425$	−1.17902	−	0.315918i	−0.0571910	−	0.0153243i
$426$	1.27686	+	5.31272i	0.0618640	+	0.257402i
$427$	−5.22941	−	15.8957i	−0.253069	−	0.769248i
$428$	−0.267119	−	0.227913i	−0.0129117	−	0.0110166i
$429$	1.36156	+	1.04476i	0.0657366	+	0.0504415i
$430$	8.17110	+	6.61349i	0.394046	+	0.318931i
$431$	−18.6180	−	10.7491i	−0.896798	−	0.517766i	−0.0206379	−	0.999787i	$-0.506570\pi$
$431$	−18.6180	−	10.7491i	−0.896798	−	0.517766i	−0.876160	+	0.482021i	$0.839903\pi$
$432$	7.37217	−	13.6099i	0.354694	−	0.654807i
$433$		−	32.1640i		−	1.54570i	−0.634587	−	0.772852i	$-0.718830\pi$
$433$		−	32.1640i		−	1.54570i	0.634587	−	0.772852i	$-0.281170\pi$
$434$	0.342854	+	11.3880i	0.0164575	+	0.546641i
$435$	−2.91446	+	1.20721i	−0.139738	+	0.0578813i
$436$	−14.8173	+	10.1945i	−0.709622	+	0.488226i
$437$	−10.8799	−	14.1790i	−0.520457	−	0.678273i
$438$	0.741924	−	2.50697i	0.0354505	−	0.119788i
$439$	−10.5084	−	2.81571i	−0.501537	−	0.134386i	−0.000823632	−	1.00000i	$-0.500262\pi$
$439$	−10.5084	−	2.81571i	−0.501537	−	0.134386i	−0.500713	+	0.865613i	$0.666929\pi$
$440$	6.20826	+	3.15747i	0.295967	+	0.150527i
$441$	−0.849776	−	7.55141i	−0.0404655	−	0.359591i
$442$	0.0851423	+	0.0521464i	0.00404981	+	0.00248035i
$443$	−3.04856	−	23.1561i	−0.144841	−	1.10018i	−0.897262	−	0.441497i	$-0.854447\pi$
$443$	−3.04856	−	23.1561i	−0.144841	−	1.10018i	0.752421	−	0.658682i	$-0.228886\pi$
$444$	24.5143	−	22.0947i	1.16340	−	1.04857i
$445$	−7.81709	−	1.02914i	−0.370565	−	0.0487859i
$446$	−33.1029	−	14.7286i	−1.56747	−	0.697418i
$447$	−24.7738			−1.17176
$448$	0.663088	+	21.1556i	0.0313280	+	0.999509i
$449$	9.55987			0.451158			0.225579	−	0.974225i	$-0.427573\pi$
$449$	9.55987			0.451158			0.225579	+	0.974225i	$0.427573\pi$
$450$	−6.23376	−	2.77360i	−0.293862	−	0.130749i
$451$	−11.1641	−	1.46978i	−0.525695	−	0.0692090i
$452$	12.0819	−	10.8894i	0.568283	−	0.512193i
$453$	5.33211	+	40.5014i	0.250524	+	1.90292i
$454$	−29.5745	−	18.1132i	−1.38800	−	0.850096i
$455$	0.505592	+	0.0379242i	0.0237025	+	0.00177792i
$456$	8.21254	−	16.1476i	0.384588	−	0.756181i
$457$	8.12438	+	2.17692i	0.380043	+	0.101832i	0.443783	−	0.896134i	$-0.353636\pi$
$457$	8.12438	+	2.17692i	0.380043	+	0.101832i	−0.0637401	+	0.997967i	$0.520303\pi$
$458$	4.58037	−	15.4771i	0.214027	−	0.723199i
$459$	0.646985	+	0.843167i	0.0301987	+	0.0393557i
$460$	6.92815	−	4.76663i	0.323027	−	0.222245i
$461$	20.9004	−	8.65723i	0.973428	−	0.403207i	0.161441	−	0.986882i	$-0.448386\pi$
$461$	20.9004	−	8.65723i	0.973428	−	0.403207i	0.811987	+	0.583675i	$0.198386\pi$
$462$	−22.0006	−	11.8340i	−1.02356	−	0.550568i
$463$			33.6055i			1.56178i	0.624668	+	0.780891i	$0.285235\pi$
$463$			33.6055i			1.56178i	−0.624668	+	0.780891i	$0.714765\pi$
$464$	−8.02661	+	2.38622i	−0.372626	+	0.110778i
$465$	3.97366	+	2.29419i	0.184274	+	0.106391i
$466$	−18.1544	−	14.6937i	−0.840986	−	0.680673i
$467$	0.182812	+	0.140277i	0.00845953	+	0.00649123i	0.612983	−	0.790096i	$-0.289970\pi$
$467$	0.182812	+	0.140277i	0.00845953	+	0.00649123i	−0.604523	+	0.796588i	$0.706636\pi$
$468$	0.424558	+	0.362244i	0.0196252	+	0.0167447i
$469$	−2.78608	+	3.11718i	−0.128649	+	0.143938i
$470$	2.53751	+	10.5580i	0.117047	+	0.487004i
$471$	35.3275	+	9.46598i	1.62781	+	0.436169i
$472$	27.0806	+	18.5825i	1.24649	+	0.855327i
$473$	−31.8121	+	8.52404i	−1.46272	+	0.391936i
$474$	39.6125	+	1.02750i	1.81946	+	0.0471944i
$475$	13.0107	+	5.38922i	0.596973	+	0.247274i
$476$	−1.34500	−	0.550566i	−0.0616480	−	0.0252351i
$477$	−3.33582	−	8.05338i	−0.152737	−	0.368739i
$478$	−15.9102	+	35.7587i	−0.727717	+	1.63557i
$479$	2.98768	−	5.17482i	0.136511	−	0.236444i	−0.789663	−	0.613541i	$-0.789744\pi$
$479$	2.98768	−	5.17482i	0.136511	−	0.236444i	0.926174	+	0.377097i	$0.123078\pi$
$480$	7.38747	+	4.25299i	0.337190	+	0.194122i
$481$	−1.04922	−	1.81731i	−0.0478404	−	0.0828621i
$482$	−21.6689	−	29.8091i	−0.986990	−	1.35777i
$483$	−25.2357	+	16.5203i	−1.14826	+	0.751698i
$484$	0.159075	−	0.0811519i	0.00723069	−	0.00368872i
$485$	−0.00905731	−	0.0687971i	−0.000411271	−	0.00312392i
$486$	7.28009	+	13.4004i	0.330232	+	0.607853i
$487$	−20.8556	+	5.58824i	−0.945057	+	0.253227i	−0.698263	−	0.715841i	$-0.746044\pi$
$487$	−20.8556	+	5.58824i	−0.945057	+	0.253227i	−0.246793	+	0.969068i	$0.579377\pi$
$488$	−16.8675	−	5.95904i	−0.763557	−	0.269753i
$489$	−18.6204	+	18.6204i	−0.842045	+	0.842045i
$490$	−7.35282	+	0.634853i	−0.332166	+	0.0286797i
$491$	−10.1495	+	24.5032i	−0.458043	+	1.10581i	0.511146	+	0.859494i	$0.329221\pi$
$491$	−10.1495	+	24.5032i	−0.458043	+	1.10581i	−0.969189	+	0.246319i	$0.920779\pi$
$492$	−13.5516	−	2.50471i	−0.610952	−	0.112921i
$493$	0.0750487	−	0.570051i	0.00338002	−	0.0256738i
$494$	−0.895389	−	0.724706i	−0.0402855	−	0.0326060i
$495$	−2.31512	+	1.33663i	−0.104057	+	0.0600772i
$496$	9.86072	+	7.14935i	0.442759	+	0.321015i
$497$	−4.96919	+	0.939864i	−0.222899	+	0.0421587i
$498$	−47.3710	−	7.49082i	−2.12274	−	0.335672i
$499$	−5.36750	−	4.11863i	−0.240282	−	0.184375i	0.481600	−	0.876391i	$-0.340056\pi$
$499$	−5.36750	−	4.11863i	−0.240282	−	0.184375i	−0.721882	+	0.692016i	$0.756723\pi$
$500$	−6.05597	+	12.7128i	−0.270831	+	0.568532i
$501$	15.0460	+	19.6083i	0.672205	+	0.876035i
$502$	−12.4276	−	13.0895i	−0.554671	−	0.584212i
$503$	−3.04175	+	3.04175i	−0.135625	+	0.135625i	−0.771660	−	0.636035i	$-0.780573\pi$
$503$	−3.04175	+	3.04175i	−0.135625	+	0.135625i	0.636035	+	0.771660i	$0.280573\pi$
$504$	−6.94529	−	4.21405i	−0.309368	−	0.187709i
$505$	6.39039	+	6.39039i	0.284369	+	0.284369i
$506$	−0.683172	+	26.3380i	−0.0303707	+	1.17087i
$507$	−20.7407	+	15.9149i	−0.921128	+	0.706806i
$508$	−18.5338	−	20.5634i	−0.822303	−	0.912352i
$509$	2.52422	−	3.28962i	0.111884	−	0.145810i	−0.734054	−	0.679091i	$-0.762374\pi$
$509$	2.52422	−	3.28962i	0.111884	−	0.145810i	0.845938	+	0.533281i	$0.179041\pi$
$510$	−0.473433	+	0.344148i	−0.0209640	+	0.0152391i
$511$	2.28399	+	0.799382i	0.101038	+	0.0353626i
$512$	18.3355	+	13.2593i	0.810322	+	0.585985i
$513$	−6.13091	−	10.6191i	−0.270686	−	0.468843i
$514$	1.83535	+	17.4208i	0.0809537	+	0.768397i
$515$	−0.618926	−	0.0814832i	−0.0272731	−	0.00359058i
$516$	−39.4220	+	8.39976i	−1.73546	+	0.369779i
$517$	−31.4304	−	13.0189i	−1.38231	−	0.572570i
$518$	19.3157	+	23.6627i	0.848683	+	1.03968i
$519$	3.92192	+	3.92192i	0.172153	+	0.172153i
$520$	0.362383	−	0.403067i	0.0158915	−	0.0176757i
$521$	−11.2996	−	42.1708i	−0.495046	−	1.84754i	−0.529775	−	0.848138i	$-0.677724\pi$
$521$	−11.2996	−	42.1708i	−0.495046	−	1.84754i	0.0347293	−	0.999397i	$-0.488943\pi$
$522$	0.912051	−	3.08183i	0.0399194	−	0.134888i
$523$	−13.6755	+	1.80041i	−0.597986	+	0.0787264i	−0.423442	−	0.905923i	$-0.639178\pi$
$523$	−13.6755	+	1.80041i	−0.597986	+	0.0787264i	−0.174544	+	0.984649i	$0.555845\pi$
$524$	38.5426	−	3.05253i	1.68374	−	0.133351i
$525$	10.7121	−	21.2158i	0.467515	−	0.925936i
$526$	−10.8107	−	1.70950i	−0.471367	−	0.0745378i
$527$	−0.724258	+	0.418150i	−0.0315492	+	0.0182149i
$528$	−24.3867	+	10.8865i	−1.06129	+	0.473776i
$529$	7.63040	+	4.40541i	0.331756	+	0.191540i
$530$	−7.90277	+	3.03583i	−0.343274	+	0.131868i
$531$	−11.6460	+	4.82393i	−0.505393	+	0.209341i
$532$	14.5559	+	8.32324i	0.631080	+	0.360858i
$533$	−0.335338	+	0.809577i	−0.0145251	+	0.0350667i
$534$	21.9243	−	20.8156i	0.948756	−	0.900781i
$535$	−0.0338762	−	0.126428i	−0.00146460	−	0.00546595i
$536$	0.817752	+	4.39401i	0.0353215	+	0.189792i
$537$	−0.492212	+	1.83696i	−0.0212405	+	0.0792707i
$538$	−6.35392	+	10.3744i	−0.273937	+	0.447273i
$539$	11.9361	−	19.8029i	0.514126	−	0.852970i
$540$	5.13948	−	2.62189i	0.221168	−	0.112828i
$541$	7.12245	−	9.28215i	0.306218	−	0.399071i	−0.614742	−	0.788728i	$-0.710740\pi$
$541$	7.12245	−	9.28215i	0.306218	−	0.399071i	0.920960	+	0.389657i	$0.127407\pi$
$542$	37.0422	−	3.90254i	1.59110	−	0.167629i
$543$	1.61571	−	2.79849i	0.0693367	−	0.120095i
$544$	−1.34455	+	0.778496i	−0.0576473	+	0.0333777i
$545$	−6.70421			−0.287177
$546$	−1.33266	+	1.41539i	−0.0570326	+	0.0605733i
$547$	4.82313	+	11.6441i	0.206222	+	0.497865i	0.992822	−	0.119598i	$-0.0381606\pi$
$547$	4.82313	+	11.6441i	0.206222	+	0.497865i	−0.786600	+	0.617463i	$0.788161\pi$
$548$	13.6492	−	21.0407i	0.583067	−	0.898816i
$549$	5.44722	−	4.17980i	0.232482	−	0.178390i
$550$	−9.91053	−	18.2422i	−0.422587	−	0.777849i
$551$	−1.71692	+	6.40763i	−0.0731432	+	0.272974i
$552$	−2.50606	+	32.1472i	−0.106665	+	1.36828i
$553$	−2.74337	+	36.5736i	−0.116660	+	1.55527i
$554$	2.34118	+	9.74111i	0.0994672	+	0.413860i
$555$	12.1964	−	1.60568i	0.517707	−	0.0681575i
$556$	36.7989	−	13.0517i	1.56062	−	0.553514i
$557$	1.51050	−	11.4734i	0.0640020	−	0.486143i	−0.929185	−	0.369614i	$-0.879490\pi$
$557$	1.51050	−	11.4734i	0.0640020	−	0.486143i	0.993187	−	0.116529i	$-0.0371768\pi$
$558$	−4.36383	+	1.67635i	−0.184735	+	0.0709657i
$559$			2.56294i			0.108401i
$560$	−4.26619	+	6.63684i	−0.180279	+	0.280458i
$561$		−	1.83373i		−	0.0774204i
$562$	−2.46069	−	6.40559i	−0.103798	−	0.270203i
$563$	1.41449	−	10.7441i	0.0596137	−	0.452811i	−0.935441	−	0.353483i	$-0.884997\pi$
$563$	1.41449	−	10.7441i	0.0596137	−	0.452811i	0.995055	−	0.0993282i	$-0.0316694\pi$
$564$	−37.5885	−	17.9060i	−1.58276	−	0.753978i
$565$	6.01099	−	0.791362i	0.252884	−	0.0332928i
$566$	31.3124	−	7.52564i	1.31616	−	0.316326i
$567$	−26.4086	+	12.7154i	−1.10906	+	0.533998i
$568$	−2.45092	+	4.81902i	−0.102838	+	0.202202i
$569$	−6.02563	+	22.4880i	−0.252608	+	0.942745i	0.716798	+	0.697281i	$0.245607\pi$
$569$	−6.02563	+	22.4880i	−0.252608	+	0.942745i	−0.969406	+	0.245464i	$0.921060\pi$
$570$	5.93372	−	3.22365i	0.248536	−	0.135024i
$571$	12.5012	−	9.59250i	0.523158	−	0.401434i	−0.313141	−	0.949707i	$-0.601381\pi$
$571$	12.5012	−	9.59250i	0.523158	−	0.401434i	0.836299	+	0.548273i	$0.184715\pi$
$572$	0.353883	+	1.66085i	0.0147966	+	0.0694438i
$573$	9.92188	+	23.9535i	0.414492	+	1.00067i
$574$	2.92905	−	12.4144i	0.122256	−	0.518169i
$575$	−25.0659			−1.04532
$576$	−8.10320	+	3.12432i	−0.337633	+	0.130180i
$577$	8.37214	−	14.5010i	0.348537	−	0.603683i	−0.637453	−	0.770489i	$-0.720012\pi$
$577$	8.37214	−	14.5010i	0.348537	−	0.603683i	0.985990	+	0.166806i	$0.0533454\pi$
$578$	2.50777	+	23.8032i	0.104309	+	0.990083i
$579$	13.4890	−	17.5792i	0.560585	−	0.730569i
$580$	−2.96908	−	0.963091i	−0.123284	−	0.0399902i
$581$	9.06971	−	43.4533i	0.376275	−	1.80275i
$582$	0.226893	+	0.138963i	0.00940503	+	0.00576021i
$583$	6.86472	−	25.6195i	0.284308	−	1.06105i
$584$	2.16853	−	1.41055i	0.0897344	−	0.0583688i
$585$	0.0538429	+	0.200944i	0.00222613	+	0.00830803i
$586$	8.21555	+	8.65310i	0.339381	+	0.357456i
$587$	−9.89537	+	23.8895i	−0.408426	+	0.986027i	0.577127	+	0.816655i	$0.304174\pi$
$587$	−9.89537	+	23.8895i	−0.408426	+	0.986027i	−0.985552	+	0.169372i	$0.945826\pi$
$588$	15.8449	−	23.4459i	0.653433	−	0.966895i
$589$	8.91428	−	3.69242i	0.367306	−	0.152143i
$590$	4.39012	+	11.4282i	0.180738	+	0.470492i
$591$	40.7845	+	23.5470i	1.67765	+	0.968593i
$592$	32.6423	−	0.887059i	1.34159	−	0.0364579i
$593$	28.7707	−	16.6108i	1.18147	−	0.682122i	0.225116	−	0.974332i	$-0.427724\pi$
$593$	28.7707	−	16.6108i	1.18147	−	0.682122i	0.956354	+	0.292210i	$0.0943905\pi$
$594$	−2.82332	+	17.8543i	−0.115842	+	0.732570i
$595$	−0.296715	−	0.453250i	−0.0121641	−	0.0185814i
$596$	−18.6477	−	15.9107i	−0.763839	−	0.651728i
$597$	9.37455	−	1.23418i	0.383675	−	0.0505117i
$598$	1.96602	+	0.581832i	0.0803964	+	0.0237929i
$599$	−4.85700	−	18.1266i	−0.198452	−	0.740631i	−0.991346	−	0.131273i	$-0.958094\pi$
$599$	−4.85700	−	18.1266i	−0.198452	−	0.740631i	0.792895	−	0.609359i	$-0.208573\pi$
$600$	−10.9553	−	22.9246i	−0.447250	−	0.935892i
$601$	−18.6060	−	18.6060i	−0.758956	−	0.758956i	0.217176	−	0.976132i	$-0.430315\pi$
$601$	−18.6060	−	18.6060i	−0.758956	−	0.758956i	−0.976132	+	0.217176i	$0.930315\pi$
$602$	−5.98036	−	36.8242i	−0.243741	−	1.50084i
$603$	−1.58485	−	0.656466i	−0.0645400	−	0.0267334i
$604$	−21.9980	+	33.9106i	−0.895084	+	1.37980i
$605$	0.0659969	+	0.00868865i	0.00268315	+	0.000353244i
$606$	−34.4615	+	3.63066i	−1.39990	+	0.147485i
$607$	19.6219	+	33.9861i	0.796427	+	1.37945i	0.921929	+	0.387359i	$0.126612\pi$
$607$	19.6219	+	33.9861i	0.796427	+	1.37945i	−0.125502	+	0.992093i	$0.540054\pi$
$608$	16.5523	−	6.88017i	0.671286	−	0.279028i
$609$	10.5669	+	3.69833i	0.428191	+	0.149864i
$610$	−3.92086	−	5.39379i	−0.158751	−	0.218388i
$611$	−1.61165	+	2.10034i	−0.0652003	+	0.0849707i
$612$	0.0309144	−	0.595513i	0.00124964	−	0.0240722i
$613$	−12.6740	+	9.72510i	−0.511898	+	0.392793i	−0.832160	−	0.554536i	$-0.812896\pi$
$613$	−12.6740	+	9.72510i	−0.511898	+	0.392793i	0.320262	+	0.947329i	$0.396229\pi$
$614$	25.0726	+	0.650350i	1.01185	+	0.0262460i
$615$	−3.63239	−	3.63239i	−0.146472	−	0.146472i
$616$	−8.96001	−	23.0373i	−0.361009	−	0.928200i
$617$	−13.0001	+	13.0001i	−0.523363	+	0.523363i	−0.918585	−	0.395223i	$-0.870667\pi$
$617$	−13.0001	+	13.0001i	−0.523363	+	0.523363i	0.395223	+	0.918585i	$0.370667\pi$
$618$	1.73588	−	1.64810i	0.0698272	−	0.0662963i
$619$	−21.6215	−	28.1777i	−0.869042	−	1.13256i	−0.990163	−	0.139919i	$-0.955316\pi$
$619$	−21.6215	−	28.1777i	−0.869042	−	1.13256i	0.121121	−	0.992638i	$-0.461351\pi$
$620$	1.51762	+	4.27891i	0.0609492	+	0.171845i
$621$	17.3148	+	13.2861i	0.694820	+	0.533154i
$622$	3.88670	−	24.5790i	0.155843	−	0.985527i
$623$	18.2505	+	21.2105i	0.731192	+	0.849780i
$624$	0.327143	+	2.05237i	0.0130962	+	0.0821604i
$625$	14.6983	−	8.48606i	0.587931	−	0.339442i
$626$	−22.6003	+	27.9231i	−0.903288	+	1.11603i
$627$	−2.76148	+	20.9756i	−0.110283	+	0.837683i
$628$	20.5122	+	29.8139i	0.818526	+	1.18970i
$629$	−0.858034	+	2.07148i	−0.0342121	+	0.0825952i
$630$	−1.24250	−	2.76152i	−0.0495022	−	0.110022i
$631$	16.4788	−	16.4788i	0.656012	−	0.656012i	−0.298422	−	0.954434i	$-0.596460\pi$
$631$	16.4788	−	16.4788i	0.656012	−	0.656012i	0.954434	+	0.298422i	$0.0964604\pi$
$632$	29.1571	+	26.2141i	1.15981	+	1.04274i
$633$	−8.47784	+	2.27163i	−0.336964	+	0.0902892i
$634$	6.54825	−	3.55750i	0.260064	−	0.141287i
$635$	−1.34690	−	10.2307i	−0.0534501	−	0.405994i
$636$	10.0156	−	30.8769i	0.397146	−	1.22435i
$637$	−1.24813	−	1.29607i	−0.0494529	−	0.0513522i
$638$	7.91013	−	5.75003i	0.313165	−	0.227646i
$639$	−1.03753	−	1.79706i	−0.0410441	−	0.0710905i
$640$	2.82924	+	7.94581i	0.111835	+	0.314086i
$641$	−13.9878	+	24.2276i	−0.552484	+	0.956931i	0.445610	+	0.895227i	$0.352987\pi$
$641$	−13.9878	+	24.2276i	−0.552484	+	0.956931i	−0.998095	+	0.0617037i	$0.980347\pi$
$642$	0.458527	+	0.204014i	0.0180966	+	0.00805178i
$643$	0.627316	+	1.51447i	0.0247389	+	0.0597251i	0.935766	−	0.352621i	$-0.114709\pi$
$643$	0.627316	+	1.51447i	0.0247389	+	0.0597251i	−0.911027	+	0.412346i	$0.864709\pi$
$644$	−29.6053	−	3.77224i	−1.16661	−	0.148647i
$645$	−13.8809	−	5.74967i	−0.546561	−	0.226393i
$646$	−0.0319147	+	1.23039i	−0.00125567	+	0.0484091i
$647$	−34.4904	+	9.24168i	−1.35596	+	0.363328i	−0.862331	−	0.506346i	$-0.830996\pi$
$647$	−34.4904	+	9.24168i	−1.35596	+	0.363328i	−0.493627	+	0.869674i	$0.664329\pi$
$648$	−6.49199	+	30.6541i	−0.255029	+	1.20421i
$649$	−37.0484	−	9.92709i	−1.45428	−	0.389672i
$650$	−1.57084	+	0.377536i	−0.0616134	+	0.0148082i
$651$	−5.08878	−	15.4682i	−0.199445	−	0.606248i
$652$	−25.9747	+	2.05717i	−1.01725	+	0.0805649i
$653$	−26.9275	−	20.6622i	−1.05375	−	0.808574i	−0.0717475	−	0.997423i	$-0.522858\pi$
$653$	−26.9275	−	20.6622i	−1.05375	−	0.808574i	−0.982006	+	0.188849i	$0.939524\pi$
$654$	16.1724	−	19.9814i	0.632392	−	0.781334i
$655$	12.4811	+	7.20597i	0.487677	+	0.281560i
$656$	−8.59188	−	10.5887i	−0.335457	−	0.413418i
$657$			0.992889i			0.0387363i
$658$	18.2552	−	33.9382i	0.711661	−	1.32305i
$659$	36.6698	−	15.1891i	1.42845	−	0.591685i	0.471484	−	0.881875i	$-0.343719\pi$
$659$	36.6698	−	15.1891i	1.42845	−	0.591685i	0.956969	+	0.290190i	$0.0937185\pi$
$660$	−9.78910	−	1.80930i	−0.381040	−	0.0704269i
$661$	28.1714	+	36.7136i	1.09574	+	1.42799i	0.893727	+	0.448611i	$0.148081\pi$
$661$	28.1714	+	36.7136i	1.09574	+	1.42799i	0.202012	+	0.979383i	$0.435252\pi$
$662$	7.18454	+	2.12623i	0.279235	+	0.0826381i
$663$	−0.137838	−	0.0369337i	−0.00535319	−	0.00143438i
$664$	−30.8460	−	36.0619i	−1.19706	−	1.39947i
$665$	2.71147	+	5.63143i	0.105146	+	0.218377i
$666$	−6.54589	+	10.6879i	−0.253648	+	0.414146i
$667$	−1.54116	−	11.7063i	−0.0596739	−	0.453268i
$668$	−1.26783	+	24.4226i	−0.0490539	+	0.944939i
$669$	51.3416	+	6.75924i	1.98498	+	0.261327i
$670$	−0.677253	+	1.52215i	−0.0261646	+	0.0588057i
$671$	20.8916			0.806513
$672$	−9.48935	−	28.7249i	−0.366060	−	1.10809i
$673$	34.9075			1.34559			0.672793	−	0.739831i	$-0.265095\pi$
$673$	34.9075			1.34559			0.672793	+	0.739831i	$0.265095\pi$
$674$	−7.61488	+	17.1147i	−0.293314	+	0.659233i
$675$	−17.0501	−	2.24469i	−0.656259	−	0.0863982i
$676$	−25.8331	−	1.34105i	−0.993579	−	0.0515789i
$677$	0.758921	+	5.76457i	0.0291677	+	0.221551i	0.999821	−	0.0189336i	$-0.00602711\pi$
$677$	0.758921	+	5.76457i	0.0291677	+	0.221551i	−0.970653	+	0.240484i	$0.922694\pi$
$678$	−12.1416	+	19.8243i	−0.466295	+	0.761347i
$679$	−0.138738	+	0.203461i	−0.00532429	+	0.00780813i
$680$	−0.577386	−	0.0450106i	−0.0221417	−	0.00172608i
$681$	47.8786	+	12.8290i	1.83471	+	0.491610i
$682$	−13.6392	−	4.03646i	−0.522273	−	0.154564i
$683$	15.5513	+	20.2669i	0.595055	+	0.775491i	0.989671	−	0.143355i	$-0.0457892\pi$
$683$	15.5513	+	20.2669i	0.595055	+	0.775491i	−0.394616	+	0.918846i	$0.629123\pi$
$684$	−1.25042	+	6.76534i	−0.0478111	+	0.258679i
$685$	8.63713	−	3.57762i	0.330008	−	0.136694i
$686$	20.9574	+	15.7095i	0.800157	+	0.599791i
$687$			23.0693i			0.880147i
$688$	−35.0682	−	18.9956i	−1.33696	−	0.724202i
$689$	−1.78750	−	1.03202i	−0.0680985	−	0.0393167i
$690$	−7.56175	+	9.34270i	−0.287871	+	0.355671i
$691$	28.8549	+	22.1411i	1.09769	+	0.842288i	0.988423	−	0.151725i	$-0.0484827\pi$
$691$	28.8549	+	22.1411i	1.09769	+	0.842288i	0.109268	+	0.994012i	$0.465149\pi$
$692$	0.433290	+	5.47090i	0.0164712	+	0.207972i
$693$	9.28706	+	1.93842i	0.352786	+	0.0736347i
$694$	3.57659	−	0.859597i	0.135765	−	0.0326299i
$695$	14.0583	+	3.76690i	0.533261	+	0.142887i
$696$	10.0327	−	6.52587i	0.380287	−	0.247362i
$697$	0.904386	−	0.242329i	0.0342560	−	0.00917888i
$698$	−0.208974	+	8.05646i	−0.00790977	+	0.304942i
$699$	30.8404	+	12.7745i	1.16649	+	0.483176i
$700$	21.6888	−	9.08981i	0.819760	−	0.343562i
$701$	−8.73457	−	21.0871i	−0.329900	−	0.796449i	−0.998599	−	0.0529159i	$-0.983148\pi$
$701$	−8.73457	−	21.0871i	−0.329900	−	0.796449i	0.668699	−	0.743533i	$-0.266852\pi$
$702$	1.28521	+	0.571830i	0.0485070	+	0.0215823i
$703$	12.9343	−	22.4029i	0.487827	−	0.844940i
$704$	−25.3480	−	7.46756i	−0.955339	−	0.281444i
$705$	−7.75993	−	13.4406i	−0.292256	−	0.506202i
$706$	29.2758	−	21.2812i	1.10181	−	0.800928i
$707$	−1.79611	−	32.0225i	−0.0675498	−	1.20433i
$708$	−44.6511	−	14.4836i	−1.67809	−	0.544328i
$709$	−0.162748	−	1.23620i	−0.00611214	−	0.0464263i	0.988117	−	0.153704i	$-0.0491201\pi$
$709$	−0.162748	−	1.23620i	−0.00611214	−	0.0464263i	−0.994229	+	0.107277i	$0.965787\pi$
$710$	−1.77083	+	0.962051i	−0.0664582	+	0.0361051i
$711$	−14.5359	+	3.89489i	−0.545140	+	0.146070i
$712$	29.8714	−	1.58770i	1.11948	−	0.0595015i
$713$	−12.1437	+	12.1437i	−0.454786	+	0.454786i
$714$	2.06664	+	0.209030i	0.0773419	+	0.00782274i
$715$	−0.242234	+	0.584805i	−0.00905905	+	0.0218705i
$716$	−1.55026	+	1.06659i	−0.0579360	+	0.0398605i
$717$	7.30153	−	55.4606i	0.272681	−	2.07121i
$718$	−13.7592	+	16.9998i	−0.513489	+	0.634426i
$719$	0.246628	−	0.142391i	0.00919766	−	0.00531027i	−0.495394	−	0.868668i	$-0.664976\pi$
$719$	0.246628	−	0.142391i	0.00919766	−	0.00531027i	0.504592	+	0.863358i	$0.331643\pi$
$720$	−3.14855	−	0.752609i	−0.117339	−	0.0280481i
$721$	1.44501	+	1.67936i	0.0538148	+	0.0625427i
$722$	−1.97889	+	12.5143i	−0.0736468	+	0.465732i
$723$	41.7877	+	32.0648i	1.55410	+	1.19250i
$724$	3.01347	−	1.06880i	0.111995	−	0.0397217i
$725$	5.66376	+	7.38115i	0.210347	+	0.274129i
$726$	−0.185099	+	0.175739i	−0.00686966	+	0.00652229i
$727$	−2.93684	+	2.93684i	−0.108921	+	0.108921i	−0.759467	−	0.650546i	$-0.774540\pi$
$727$	−2.93684	+	2.93684i	−0.108921	+	0.108921i	0.650546	+	0.759467i	$0.274540\pi$
$728$	−1.91214	+	0.209507i	−0.0708685	+	0.00776484i
$729$	8.08802	+	8.08802i	0.299556	+	0.299556i
$730$	0.963964	+	0.0250039i	0.0356779	+	0.000925436i
$731$	2.17256	−	1.66707i	0.0803552	−	0.0616587i
$732$	25.5340	+	1.32553i	0.943763	+	0.0489928i
$733$	−0.0661780	+	0.0862448i	−0.00244434	+	0.00318552i	−0.794574	−	0.607167i	$-0.792306\pi$
$733$	−0.0661780	+	0.0862448i	−0.00244434	+	0.00318552i	0.792130	+	0.610353i	$0.208972\pi$
$734$	−16.1500	−	22.2170i	−0.596106	−	0.820043i
$735$	9.81958	−	3.85233i	0.362201	−	0.142095i
$736$	−22.5325	+	22.5883i	−0.830560	+	0.832615i
$737$	−2.60980	−	4.52030i	−0.0961331	−	0.166507i
$738$	5.20484	−	0.548351i	0.191593	−	0.0201851i
$739$	35.9133	+	4.72807i	1.32109	+	0.173925i	0.757883	−	0.652390i	$-0.226234\pi$
$739$	35.9133	+	4.72807i	1.32109	+	0.173925i	0.563208	+	0.826315i	$0.309567\pi$
$740$	10.2117	+	6.62435i	0.375388	+	0.243516i
$741$	1.52107	+	0.630048i	0.0558780	+	0.0231454i
$742$	28.0909	+	10.6570i	1.03125	+	0.391231i
$743$	−23.8662	−	23.8662i	−0.875568	−	0.875568i	0.117505	−	0.993072i	$-0.462511\pi$
$743$	−23.8662	−	23.8662i	−0.875568	−	0.875568i	−0.993072	+	0.117505i	$0.962511\pi$
$744$	−16.4139	−	5.79878i	−0.601763	−	0.212593i
$745$	−2.36492	−	8.82600i	−0.0866439	−	0.323360i
$746$	21.8841	+	6.47650i	0.801236	+	0.237121i
$747$	18.0578	−	2.37735i	0.660700	−	0.0869828i
$748$	1.17769	−	1.38028i	0.0430608	−	0.0504682i
$749$	−0.209362	+	0.414652i	−0.00764993	+	0.0151511i
$750$	3.14352	−	19.8792i	0.114785	−	0.725885i
$751$	−29.5087	+	17.0368i	−1.07679	+	0.621683i	−0.930028	−	0.367489i	$-0.880217\pi$
$751$	−29.5087	+	17.0368i	−1.07679	+	0.621683i	−0.146759	+	0.989172i	$0.546884\pi$
$752$	−16.7936	−	37.6189i	−0.612399	−	1.37182i
$753$	22.3411	+	12.8986i	0.814155	+	0.470053i
$754$	−0.272899	−	0.710401i	−0.00993840	−	0.0258713i
$755$	−13.9201	+	5.76590i	−0.506605	+	0.209843i
$756$	−19.8001	−	5.21713i	−0.720122	−	0.189745i
$757$	−15.0712	+	36.3851i	−0.547772	+	1.32244i	0.371360	+	0.928489i	$0.378892\pi$
$757$	−15.0712	+	36.3851i	−0.547772	+	1.32244i	−0.919132	+	0.393950i	$0.871108\pi$
$758$	−8.97590	−	9.45394i	−0.326019	−	0.343383i
$759$	−9.74624	−	36.3735i	−0.353766	−	1.32027i
$760$	6.53676	+	1.38437i	0.237113	+	0.0502163i
$761$	4.34164	−	16.2032i	0.157384	−	0.587366i	−0.841505	−	0.540249i	$-0.818330\pi$
$761$	4.34164	−	16.2032i	0.157384	−	0.587366i	0.998889	−	0.0471169i	$-0.0150033\pi$
$762$	33.7410	+	20.6650i	1.22231	+	0.748615i
$763$	17.7397	+	15.8554i	0.642221	+	0.574004i
$764$	−7.91550	+	24.4024i	−0.286373	+	0.882849i
$765$	0.135315	−	0.176346i	0.00489233	−	0.00637581i
$766$	1.60955	+	15.2775i	0.0581552	+	0.551998i
$767$	−1.49240	+	2.58491i	−0.0538874	+	0.0933357i
$768$	−30.5068	−	10.7352i	−1.10082	−	0.387373i
$769$	44.5030			1.60482			0.802410	−	0.596773i	$-0.203551\pi$
$769$	44.5030			1.60482			0.802410	+	0.596773i	$0.203551\pi$
$770$	2.11583	−	8.96769i	0.0762492	−	0.323173i
$771$	−9.58110	−	23.1308i	−0.345055	−	0.833037i
$772$	21.4435	−	4.56903i	0.771768	−	0.164443i
$773$	0.324325	−	0.248864i	0.0116652	−	0.00895100i	−0.602912	−	0.797807i	$-0.705993\pi$
$773$	0.324325	−	0.248864i	0.0116652	−	0.00895100i	0.614578	+	0.788856i	$0.289326\pi$
$774$	13.4506	−	7.30736i	0.483470	−	0.262658i
$775$	3.50244	−	13.0713i	0.125811	−	0.469534i
$776$	0.0815390	+	0.250320i	0.00292708	+	0.00898595i
$777$	−36.0697	−	24.5956i	−1.29399	−	0.882362i
$778$	15.2039	−	3.65411i	0.545086	−	0.131006i
$779$	−10.7099	+	1.40999i	−0.383723	+	0.0505181i
$780$	−0.333166	+	0.699386i	−0.0119293	+	0.0250420i
$781$	0.824125	−	6.25985i	0.0294895	−	0.223995i
$782$	−0.785587	−	2.04501i	−0.0280925	−	0.0731295i
$783$		−	8.10077i		−	0.289498i
$784$	26.9846	−	7.47196i	0.963737	−	0.266856i
$785$			13.4895i			0.481461i
$786$	−51.5847	+	19.8161i	−1.83997	+	0.706819i
$787$	1.80857	−	13.7374i	0.0644684	−	0.489686i	−0.928502	−	0.371326i	$-0.878903\pi$
$787$	1.80857	−	13.7374i	0.0644684	−	0.489686i	0.992971	−	0.118360i	$-0.0377636\pi$
$788$	15.5765	+	43.9176i	0.554889	+	1.56450i
$789$	15.5094	−	2.04185i	0.552150	−	0.0726919i
$790$	3.41537	+	14.2106i	0.121513	+	0.505589i
$791$	−17.7770	−	12.1219i	−0.632077	−	0.431007i
$792$	7.70734	−	6.59257i	0.273868	−	0.234257i
$793$	0.420783	−	1.57038i	0.0149424	−	0.0557660i
$794$	−12.5433	−	23.0883i	−0.445145	−	0.819371i
$795$	9.59947	−	7.36594i	0.340458	−	0.261243i
$796$	7.84902	+	5.09170i	0.278201	+	0.180471i
$797$	11.9672	+	28.8914i	0.423901	+	1.02339i	0.981186	+	0.193065i	$0.0618430\pi$
$797$	11.9672	+	28.8914i	0.423901	+	1.02339i	−0.557285	+	0.830321i	$0.688157\pi$
$798$	−23.3248	−	5.50325i	−0.825691	−	0.194813i
$799$	2.82872			0.100073
$800$	6.47677	−	24.2917i	0.228988	−	0.858840i
$801$	−5.74057	+	9.94296i	−0.202833	+	0.351317i
$802$	1.98058	−	0.208662i	0.0699367	−	0.00736812i
$803$	−1.83913	+	2.39680i	−0.0649014	+	0.0845812i
$804$	−2.90292	−	5.69034i	−0.102378	−	0.200683i
$805$	−8.29456	−	7.41351i	−0.292345	−	0.261292i
$806$	−0.578123	+	0.943935i	−0.0203635	+	0.0332487i
$807$	4.50029	−	16.7953i	0.158418	−	0.591222i
$808$	−28.2715	−	19.3996i	−0.994588	−	0.682476i
$809$	12.3827	+	46.2127i	0.435351	+	1.62475i	0.740225	+	0.672359i	$0.234719\pi$
$809$	12.3827	+	46.2127i	0.435351	+	1.62475i	−0.304874	+	0.952393i	$0.598614\pi$
$810$	−8.47033	+	8.04202i	−0.297617	+	0.282568i
$811$	6.70708	−	16.1923i	0.235517	−	0.568589i	−0.761292	−	0.648409i	$-0.775435\pi$
$811$	6.70708	−	16.1923i	0.235517	−	0.568589i	0.996809	+	0.0798201i	$0.0254346\pi$
$812$	5.57865	+	9.57024i	0.195772	+	0.335849i
$813$	−49.1836	+	20.3725i	−1.72494	+	0.714496i
$814$	−35.5987	+	13.6751i	−1.24773	+	0.479313i
$815$	−8.41128	−	4.85626i	−0.294634	−	0.170107i
$816$	1.52697	−	1.61228i	0.0534545	−	0.0564409i
$817$	−27.3618	+	15.7973i	−0.957268	+	0.552679i
$818$	28.0646	+	4.43788i	0.981255	+	0.155167i
$819$	0.332760	−	0.659048i	0.0116276	−	0.0230290i
$820$	−0.401303	−	5.06702i	−0.0140141	−	0.176948i
$821$	11.1450	−	1.46727i	0.388964	−	0.0512081i	0.0664919	−	0.997787i	$-0.478819\pi$
$821$	11.1450	−	1.46727i	0.388964	−	0.0512081i	0.322473	+	0.946579i	$0.395486\pi$
$822$	−10.1724	+	34.3725i	−0.354802	+	1.19888i
$823$	−10.4965	−	39.1733i	−0.365884	−	1.36550i	−0.866219	−	0.499665i	$-0.833456\pi$
$823$	−10.4965	−	39.1733i	−0.365884	−	1.36550i	0.500335	−	0.865832i	$-0.333210\pi$
$824$	2.36510	−	0.125708i	0.0823921	−	0.00437924i
$825$	20.9814	+	20.9814i	0.730477	+	0.730477i
$826$	15.4111	−	40.6223i	0.536221	−	1.41343i
$827$	−17.2925	−	7.16278i	−0.601319	−	0.249074i	0.0611930	−	0.998126i	$-0.480509\pi$
$827$	−17.2925	−	7.16278i	−0.601319	−	0.249074i	−0.662512	+	0.749052i	$0.730509\pi$
$828$	−2.55192	−	11.9767i	−0.0886854	−	0.416220i
$829$	−50.5327	−	6.65276i	−1.75507	−	0.231060i	−0.816792	−	0.576932i	$-0.804250\pi$
$829$	−50.5327	−	6.65276i	−1.75507	−	0.231060i	−0.938282	+	0.345872i	$0.887583\pi$
$830$	−1.85335	−	17.5916i	−0.0643306	−	0.610613i
$831$	−7.15953	−	12.4007i	−0.248362	−	0.430175i
$832$	−1.07186	+	1.75495i	−0.0371601	+	0.0608421i
$833$	−0.286808	+	1.90105i	−0.00993730	+	0.0658676i
$834$	−45.1395	+	32.8128i	−1.56305	+	1.13621i
$835$	−5.54942	+	7.23214i	−0.192045	+	0.250278i
$836$	−15.5499	+	14.0151i	−0.537805	+	0.484723i
$837$	−9.34781	+	7.17283i	−0.323108	+	0.247929i
$838$	0.657555	−	25.3504i	0.0227149	−	0.875716i
$839$	3.61471	+	3.61471i	0.124794	+	0.124794i	0.766745	−	0.641951i	$-0.221875\pi$
$839$	3.61471	+	3.61471i	0.124794	+	0.124794i	−0.641951	+	0.766745i	$0.721875\pi$
$840$	3.15497	−	10.8262i	0.108857	−	0.373538i
$841$	17.4072	−	17.4072i	0.600248	−	0.600248i
$842$	−9.82595	−	10.3493i	−0.338625	−	0.356659i
$843$	5.97045	+	7.78085i	0.205633	+	0.267987i
$844$	−7.84034	−	3.73490i	−0.269876	−	0.128560i
$845$	−7.64981	−	5.86991i	−0.263161	−	0.201931i
$846$	15.6179	+	2.46967i	0.536953	+	0.0849090i
$847$	−0.154083	−	0.179073i	−0.00529435	−	0.00615301i
$848$	27.3692	−	16.8091i	0.939863	−	0.577228i
$849$	−39.8615	+	23.0141i	−1.36804	+	0.789840i
$850$	1.34178	+	1.08601i	0.0460228	+	0.0372497i
$851$	−6.00989	+	45.6497i	−0.206017	+	1.56485i
$852$	1.40443	−	7.59857i	0.0481149	−	0.260323i
$853$	−16.8601	+	40.7039i	−0.577279	+	1.39368i	0.317966	+	0.948102i	$0.397000\pi$
$853$	−16.8601	+	40.7039i	−0.577279	+	1.39368i	−0.895245	+	0.445573i	$0.853000\pi$
$854$	−2.38146	+	23.5451i	−0.0814921	+	0.805696i
$855$	−1.81339	+	1.81339i	−0.0620168	+	0.0620168i
$856$	0.214116	+	0.448048i	0.00731833	+	0.0153140i
$857$	−52.9396	+	14.1851i	−1.80838	+	0.484555i	−0.995235	−	0.0975024i	$-0.968915\pi$
$857$	−52.9396	+	14.1851i	−1.80838	+	0.484555i	−0.813148	+	0.582057i	$0.802248\pi$
$858$	−1.15863	−	2.13267i	−0.0395550	−	0.0728083i
$859$	3.09027	+	23.4729i	0.105439	+	0.800885i	0.959697	+	0.281037i	$0.0906783\pi$
$859$	3.09027	+	23.4729i	0.105439	+	0.800885i	−0.854259	+	0.519848i	$0.825988\pi$
$860$	−6.75576	−	13.2427i	−0.230369	−	0.451574i
$861$	1.02094	+	18.2021i	0.0347934	+	0.620325i
$862$	17.8766	+	24.5922i	0.608878	+	0.837613i
$863$	−7.71814	−	13.3682i	−0.262728	−	0.455059i	0.704238	−	0.709964i	$-0.251289\pi$
$863$	−7.71814	−	13.3682i	−0.262728	−	0.455059i	−0.966966	+	0.254905i	$0.917956\pi$
$864$	−17.3497	+	13.3470i	−0.590250	+	0.454075i
$865$	−1.02285	+	1.77162i	−0.0347778	+	0.0602369i
$866$	−18.4909	+	41.5588i	−0.628345	+	1.41223i
$867$	−13.0913	−	31.6053i	−0.444605	−	1.07337i
$868$	6.10388	−	14.9114i	0.207179	−	0.506126i
$869$	−42.3037	−	17.5228i	−1.43506	−	0.594419i
$870$	4.45976	+	0.115680i	0.151200	+	0.00392193i
$871$	−0.392347	+	0.105129i	−0.0132942	+	0.00356216i
$872$	25.0061	−	4.65378i	0.846812	−	0.157597i
$873$	−0.0976010	−	0.0261521i	−0.00330329	−	0.000885115i
$874$	5.90644	+	24.5753i	0.199788	+	0.831273i
$875$	18.2351	+	3.80609i	0.616460	+	0.128669i
$876$	−2.39987	+	2.81270i	−0.0810842	+	0.0950324i
$877$	−2.83944	−	2.17878i	−0.0958811	−	0.0735721i	0.559708	−	0.828690i	$-0.310913\pi$
$877$	−2.83944	−	2.17878i	−0.0958811	−	0.0735721i	−0.655589	+	0.755117i	$0.727580\pi$
$878$	11.9590	+	9.67933i	0.403597	+	0.326662i
$879$	−14.7691	−	8.52695i	−0.498149	−	0.287607i
$880$	−6.20642	−	7.64882i	−0.209219	−	0.257842i
$881$			35.8359i			1.20734i	0.797234	+	0.603671i	$0.206296\pi$
$881$			35.8359i			1.20734i	−0.797234	+	0.603671i	$0.793704\pi$
$882$	−3.24326	+	10.2456i	−0.109206	+	0.344988i
$883$	−32.8847	+	13.6213i	−1.10666	+	0.458393i	−0.859786	−	0.510655i	$-0.829403\pi$
$883$	−32.8847	+	13.6213i	−1.10666	+	0.458393i	−0.246872	+	0.969048i	$0.579403\pi$
$884$	−0.0800330	−	0.116326i	−0.00269180	−	0.00391245i
$885$	−10.6519	−	13.8818i	−0.358059	−	0.466632i
$886$	−9.37327	+	31.6724i	−0.314901	+	1.06405i
$887$	5.99300	+	1.60582i	0.201225	+	0.0539181i	0.358024	−	0.933712i	$-0.383451\pi$
$887$	5.99300	+	1.60582i	0.201225	+	0.0539181i	−0.156799	+	0.987631i	$0.550117\pi$
$888$	−44.3767	+	14.4553i	−1.48919	+	0.485086i
$889$	−20.6316	+	30.2565i	−0.691962	+	1.01477i
$890$	9.50874	+	5.82373i	0.318734	+	0.195212i
$891$	−4.77634	−	36.2799i	−0.160014	−	1.21542i
$892$	34.3046	+	38.0613i	1.14860	+	1.27439i
$893$	−32.3569	−	4.25987i	−1.08278	−	0.142551i
$894$	32.0100	+	14.2423i	1.07058	+	0.476334i
$895$	−0.701427			−0.0234461
$896$	11.3055	−	27.7162i	0.377689	−	0.925933i
$897$	−2.93042			−0.0978440
$898$	−12.3522	−	5.49591i	−0.412199	−	0.183401i
$899$	6.31990	+	0.832031i	0.210781	+	0.0277498i
$900$	6.46006	+	7.16750i	0.215335	+	0.238917i
$901$	0.287860	+	2.18651i	0.00959000	+	0.0728433i
$902$	13.5800	+	8.31722i	0.452165	+	0.276933i
$903$	23.1318	+	48.0422i	0.769778	+	1.59874i
$904$	−21.8711	+	7.12428i	−0.727422	+	0.236950i
$905$	1.15123	+	0.308472i	0.0382683	+	0.0102540i
$906$	16.3944	−	55.3968i	0.544667	−	1.84044i
$907$	1.57015	+	2.04626i	0.0521360	+	0.0679449i	0.818694	−	0.574231i	$-0.194699\pi$
$907$	1.57015	+	2.04626i	0.0521360	+	0.0679449i	−0.766558	+	0.642176i	$0.778032\pi$
$908$	27.7998	+	40.4061i	0.922568	+	1.34092i
$909$	12.1581	−	5.03606i	0.403260	−	0.167036i
$910$	−0.631468	−	0.339663i	−0.0209330	−	0.0112597i
$911$		−	28.7357i		−	0.952055i	−0.879430	−	0.476027i	$-0.842076\pi$
$911$		−	28.7357i		−	0.952055i	0.879430	−	0.476027i	$-0.157924\pi$
$912$	−19.8945	+	16.1428i	−0.658773	+	0.534543i
$913$	47.9944	+	27.7096i	1.58838	+	0.917053i
$914$	−9.24594	−	7.48343i	−0.305828	−	0.247530i
$915$	7.56124	+	5.80195i	0.249967	+	0.191806i
$916$	−14.8160	+	17.3646i	−0.489533	+	0.573743i
$917$	−15.9836	−	48.5851i	−0.527826	−	1.60442i
$918$	−0.351232	−	1.46140i	−0.0115924	−	0.0482332i
$919$	−16.2729	−	4.36031i	−0.536794	−	0.143833i	−0.0197702	−	0.999805i	$-0.506293\pi$
$919$	−16.2729	−	4.36031i	−0.536794	−	0.143833i	−0.517024	+	0.855971i	$0.672960\pi$
$920$	−11.6921	+	2.17597i	−0.385477	+	0.0717396i
$921$	−34.6259	+	9.27799i	−1.14096	+	0.305720i
$922$	−31.9822	−	0.829574i	−1.05328	−	0.0273206i
$923$	−0.453942	−	0.188029i	−0.0149417	−	0.00618905i
$924$	21.6235	+	27.9386i	0.711362	+	0.919114i
$925$	−13.8841	−	33.5191i	−0.456505	−	1.10210i
$926$	19.3196	−	43.4214i	0.634881	−	1.42692i
$927$	−0.454516	+	0.787244i	−0.0149283	+	0.0258565i
$928$	11.7429	+	1.53123i	0.385480	+	0.0502650i
$929$	−19.9628	−	34.5767i	−0.654960	−	1.13442i	−0.981904	−	0.189380i	$-0.939352\pi$
$929$	−19.9628	−	34.5767i	−0.654960	−	1.13442i	0.326944	−	0.945044i	$-0.393981\pi$
$930$	−3.81541	−	5.24874i	−0.125112	−	0.172113i
$931$	6.14357	−	21.3137i	0.201347	−	0.698527i
$932$	15.0098	+	29.4224i	0.491662	+	0.963764i
$933$	4.64234	+	35.2620i	0.151983	+	1.15443i
$934$	−0.155566	−	0.286347i	−0.00509026	−	0.00936957i
$935$	0.653292	−	0.175049i	0.0213649	−	0.00572471i
$936$	−0.340316	−	0.712128i	−0.0111236	−	0.0232766i
$937$	−7.07585	+	7.07585i	−0.231158	+	0.231158i	−0.813176	−	0.582018i	$-0.802263\pi$
$937$	−7.07585	+	7.07585i	−0.231158	+	0.231158i	0.582018	+	0.813176i	$0.302263\pi$
$938$	5.39191	−	2.42599i	0.176052	−	0.0792113i
$939$	19.6483	−	47.4353i	0.641199	−	1.54799i
$940$	2.79103	−	15.1007i	0.0910333	−	0.492530i
$941$	−2.41243	+	18.3242i	−0.0786429	+	0.597352i	0.906065	+	0.423139i	$0.139072\pi$
$941$	−2.41243	+	18.3242i	−0.0786429	+	0.597352i	−0.984708	+	0.174214i	$0.944262\pi$
$942$	−40.2044	−	32.5404i	−1.30993	−	1.06022i
$943$	16.6512	−	9.61356i	0.542237	−	0.313061i
$944$	−24.3077	−	39.5787i	−0.791148	−	1.28818i
$945$	−4.97818	−	5.78556i	−0.161940	−	0.188204i
$946$	46.0046	+	7.27476i	1.49574	+	0.236523i
$947$	15.8334	+	12.1494i	0.514518	+	0.394804i	0.833126	−	0.553083i	$-0.186549\pi$
$947$	15.8334	+	12.1494i	0.514518	+	0.394804i	−0.318608	+	0.947886i	$0.603215\pi$
$948$	−50.5923	−	24.1006i	−1.64316	−	0.782751i
$949$	0.143120	+	0.186518i	0.00464588	+	0.00605463i
$950$	−13.7128	−	14.4431i	−0.444903	−	0.468597i
$951$	−7.53151	+	7.53151i	−0.244226	+	0.244226i
$952$	1.42135	+	1.48461i	0.0460661	+	0.0481166i
$953$	−4.20814	−	4.20814i	−0.136315	−	0.136315i	0.635657	−	0.771972i	$-0.280729\pi$
$953$	−4.20814	−	4.20814i	−0.136315	−	0.136315i	−0.771972	+	0.635657i	$0.780729\pi$
$954$	−0.319653	+	12.3234i	−0.0103491	+	0.398986i
$955$	−7.58661	+	5.82141i	−0.245497	+	0.188376i
$956$	41.1149	−	37.0568i	1.32975	−	1.19850i
$957$	−8.50869	+	11.0887i	−0.275047	+	0.358448i
$958$	−6.83533	+	4.96874i	−0.220839	+	0.160533i
$959$	−31.3153	−	10.9602i	−1.01123	−	0.353922i
$960$	−7.10026	−	9.74226i	−0.229160	−	0.314430i
$961$	10.8642	+	18.8173i	0.350457	+	0.607009i
$962$	0.310933	+	2.95132i	0.0100249	+	0.0951542i
$963$	−0.188963	−	0.0248774i	−0.00608924	−	0.000801664i
$964$	10.8611	+	50.9734i	0.349811	+	1.64174i
$965$	7.55050	+	3.12752i	0.243059	+	0.100678i
$966$	42.1042	−	6.83784i	1.35468	−	0.220004i
$967$	−20.1730	−	20.1730i	−0.648720	−	0.648720i	0.303964	−	0.952684i	$-0.401690\pi$
$967$	−20.1730	−	20.1730i	−0.648720	−	0.648720i	−0.952684	+	0.303964i	$0.901690\pi$
$968$	−0.252193	+	0.0134044i	−0.00810580	+	0.000430833i
$969$	−0.455300	−	1.69920i	−0.0146263	−	0.0545863i
$970$	−0.0278481	+	0.0940991i	−0.000894150	+	0.00302134i
$971$	24.3053	−	3.19986i	0.779995	−	0.102688i	0.269994	−	0.962862i	$-0.412978\pi$
$971$	24.3053	−	3.19986i	0.779995	−	0.102688i	0.510001	+	0.860174i	$0.329645\pi$
$972$	−1.70276	−	21.4998i	−0.0546161	−	0.689605i
$973$	−28.2903	−	43.2151i	−0.906945	−	1.38541i
$974$	30.1599	+	4.76923i	0.966387	+	0.152816i
$975$	1.99972	−	1.15454i	0.0640422	−	0.0369748i
$976$	18.3686	+	17.3966i	0.587963	+	0.556853i
$977$	−33.3963	−	19.2814i	−1.06844	−	0.616865i	−0.140687	−	0.990054i	$-0.544931\pi$
$977$	−33.3963	−	19.2814i	−1.06844	−	0.616865i	−0.927755	+	0.373189i	$0.878264\pi$
$978$	34.7641	−	13.3545i	1.11163	−	0.427031i
$979$	−32.2749	+	13.3687i	−1.03151	+	0.427265i
$980$	9.86548	+	3.40680i	0.315141	+	0.108826i
$981$	−3.73591	+	9.01928i	−0.119278	+	0.287963i
$982$	27.2008	−	25.8254i	0.868014	−	0.824122i
$983$	−15.1562	−	56.5639i	−0.483409	−	1.80411i	−0.587119	−	0.809500i	$-0.699738\pi$
$983$	−15.1562	−	56.5639i	−0.483409	−	1.80411i	0.103710	−	0.994608i	$-0.466929\pi$
$984$	16.0699	+	11.0270i	0.512290	+	0.351528i
$985$	−4.49560	+	16.7778i	−0.143242	+	0.534586i
$986$	−0.424688	+	0.693413i	−0.0135248	+	0.0220828i
$987$	−11.2537	+	53.9167i	−0.358208	+	1.71619i
$988$	0.740296	+	1.45114i	0.0235519	+	0.0461669i
$989$	34.2340	−	44.6146i	1.08858	−	1.41866i
$990$	3.75976	−	0.396106i	0.119493	−	0.0125891i
$991$	12.2087	−	21.1461i	0.387823	−	0.671729i	−0.604333	−	0.796732i	$-0.706560\pi$
$991$	12.2087	−	21.1461i	0.387823	−	0.671729i	0.992156	+	0.125002i	$0.0398938\pi$
$992$	−8.63083	−	14.9065i	−0.274029	−	0.473281i
$993$	−10.7088			−0.339834
$994$	6.96097	+	1.64237i	0.220788	+	0.0520927i
$995$	1.33459	+	3.22199i	0.0423094	+	0.102144i
$996$	56.9011	+	36.9121i	1.80298	+	1.16960i
$997$	36.7591	−	28.2062i	1.16417	−	0.893301i	0.168451	−	0.985710i	$-0.446123\pi$
$997$	36.7591	−	28.2062i	1.16417	−	0.893301i	0.995721	+	0.0924091i	$0.0294568\pi$
$998$	4.56752	+	8.40738i	0.144582	+	0.266131i
$999$	−8.17602	+	30.5133i	−0.258678	+	0.965398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.165.4	yes	240
4.3	odd	2		896.2.bh.a.753.6		240
7.2	even	3	inner	224.2.bd.a.37.17	✓	240
28.23	odd	6		896.2.bh.a.625.25		240
32.13	even	8	inner	224.2.bd.a.109.17	yes	240
32.19	odd	8		896.2.bh.a.529.25		240
224.51	odd	24		896.2.bh.a.401.6		240
224.205	even	24	inner	224.2.bd.a.205.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.17	✓	240	7.2	even	3	inner
224.2.bd.a.109.17	yes	240	32.13	even	8	inner
224.2.bd.a.165.4	yes	240	1.1	even	1	trivial
224.2.bd.a.205.4	yes	240	224.205	even	24	inner
896.2.bh.a.401.6		240	224.51	odd	24
896.2.bh.a.529.25		240	32.19	odd	8
896.2.bh.a.625.25		240	28.23	odd	6
896.2.bh.a.753.6		240	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29209 - 0.574893i) q^{2} +(2.00399 + 0.263830i) q^{3} +(1.33900 + 1.48563i) q^{4} +(0.0973086 + 0.739132i) q^{5} +(-2.43766 - 1.49297i) q^{6} +(1.49056 - 2.18592i) q^{7} +(-0.876026 - 2.68935i) q^{8} +(1.04859 + 0.280969i) q^{9} +(0.299191 - 1.01097i) q^{10} +(2.01082 + 2.62055i) q^{11} +(2.29138 + 3.33045i) q^{12} +(0.237482 - 0.0983684i) q^{13} +(-3.18260 + 1.96749i) q^{14} +1.50689i q^{15} +(-0.414181 + 3.97850i) q^{16} +(-0.237856 - 0.137326i) q^{17} +(-1.19335 - 0.965865i) q^{18} +(2.51396 + 1.92903i) q^{19} +(-0.967780 + 1.13426i) q^{20} +(3.56377 - 3.98730i) q^{21} +(-1.09163 - 4.54200i) q^{22} +(-5.44793 - 1.45977i) q^{23} +(-1.04602 - 5.62054i) q^{24} +(4.29278 - 1.15025i) q^{25} +(-0.363400 - 0.00942610i) q^{26} +(-3.57503 - 1.48082i) q^{27} +(5.24331 - 0.712523i) q^{28} +(0.801128 + 1.93409i) q^{29} +(0.866299 - 1.94703i) q^{30} +(1.52247 - 2.63700i) q^{31} +(2.82237 - 4.90247i) q^{32} +(3.33829 + 5.78208i) q^{33} +(0.228383 + 0.314179i) q^{34} +(1.76073 + 0.889010i) q^{35} +(0.986643 + 1.93403i) q^{36} +(-1.06556 - 8.09376i) q^{37} +(-2.13928 - 3.93774i) q^{38} +(0.501865 - 0.134474i) q^{39} +(1.90254 - 0.909196i) q^{40} +(-2.41053 + 2.41053i) q^{41} +(-6.89699 + 3.10317i) q^{42} +(-3.81560 + 9.21166i) q^{43} +(-1.20069 + 6.49624i) q^{44} +(-0.105636 + 0.802388i) q^{45} +(6.20000 + 5.01813i) q^{46} +(-8.91945 + 5.14965i) q^{47} +(-1.87966 + 7.86360i) q^{48} +(-2.55648 - 6.51647i) q^{49} +(-6.20793 - 0.981667i) q^{50} +(-0.440430 - 0.337954i) q^{51} +(0.464127 + 0.221096i) q^{52} +(-4.88818 - 6.37040i) q^{53} +(3.76794 + 3.96862i) q^{54} +(-1.74127 + 1.74127i) q^{55} +(-7.18446 - 2.09370i) q^{56} +(4.52901 + 4.52901i) q^{57} +(0.0767677 - 2.95959i) q^{58} +(-9.21225 + 7.06881i) q^{59} +(-2.23867 + 2.01771i) q^{60} +(3.85029 - 5.01779i) q^{61} +(-3.48317 + 2.53198i) q^{62} +(2.17716 - 1.87333i) q^{63} +(-6.46516 + 4.71187i) q^{64} +(0.0958163 + 0.165959i) q^{65} +(-0.989288 - 9.39013i) q^{66} +(-1.56667 - 0.206257i) q^{67} +(-0.114472 - 0.537244i) q^{68} +(-10.5325 - 4.36269i) q^{69} +(-1.76393 - 2.16091i) q^{70} +(-1.35162 - 1.35162i) q^{71} +(-0.162970 - 3.06616i) q^{72} +(0.236720 + 0.883450i) q^{73} +(-3.27624 + 11.0705i) q^{74} +(8.90616 - 1.17252i) q^{75} +(0.500361 + 6.31777i) q^{76} +(8.72556 - 0.489409i) q^{77} +(-0.725763 - 0.114766i) q^{78} +(-12.0051 + 6.93117i) q^{79} +(-2.98094 + 0.0810073i) q^{80} +(-9.59405 - 5.53913i) q^{81} +(4.50041 - 1.72882i) q^{82} +(15.5006 - 6.42056i) q^{83} +(10.6955 - 0.0445440i) q^{84} +(0.0783567 - 0.189170i) q^{85} +(10.2258 - 9.70874i) q^{86} +(1.09518 + 4.08727i) q^{87} +(5.28604 - 7.70347i) q^{88} +(-2.73728 + 10.2157i) q^{89} +(0.597779 - 0.976029i) q^{90} +(0.138956 - 0.665741i) q^{91} +(-5.12608 - 10.0482i) q^{92} +(3.74674 - 4.88285i) q^{93} +(14.4852 - 1.52608i) q^{94} +(-1.18118 + 2.04586i) q^{95} +(6.94942 - 9.07987i) q^{96} -0.0930782 q^{97} +(-0.443070 + 9.88957i) q^{98} +(1.37224 + 3.31287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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