LMFDB - Embedded newform 429.2.bi.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12326 + 2.20452i) q^{2} +(-0.671689 - 1.59651i) q^{3} +(-2.42261 - 3.33444i) q^{4} +(0.958973 - 0.488621i) q^{5} +(4.27400 + 0.312539i) q^{6} +(-2.80706 - 0.444595i) q^{7} +(5.18460 - 0.821160i) q^{8} +(-2.09767 + 2.14471i) q^{9} +O(q^{10})$	\(q+(-1.12326 + 2.20452i) q^{2} +(-0.671689 - 1.59651i) q^{3} +(-2.42261 - 3.33444i) q^{4} +(0.958973 - 0.488621i) q^{5} +(4.27400 + 0.312539i) q^{6} +(-2.80706 - 0.444595i) q^{7} +(5.18460 - 0.821160i) q^{8} +(-2.09767 + 2.14471i) q^{9} +2.66292i q^{10} +(2.67171 - 1.96520i) q^{11} +(-3.69622 + 6.10743i) q^{12} +(1.98939 + 3.00705i) q^{13} +(4.13317 - 5.68882i) q^{14} +(-1.42422 - 1.20281i) q^{15} +(-1.46609 + 4.51217i) q^{16} +(-1.69227 + 5.20828i) q^{17} +(-2.37183 - 7.03341i) q^{18} +(-7.61147 + 1.20554i) q^{19} +(-3.95250 - 2.01390i) q^{20} +(1.17567 + 4.78013i) q^{21} +(1.33129 + 8.09724i) q^{22} -2.17952 q^{23} +(-4.79343 - 7.72569i) q^{24} +(-2.25805 + 3.10794i) q^{25} +(-8.86368 + 1.00795i) q^{26} +(4.83303 + 1.90837i) q^{27} +(5.31796 + 10.4371i) q^{28} +(-1.53249 - 2.10929i) q^{29} +(4.25137 - 1.78865i) q^{30} +(-7.46760 - 3.80493i) q^{31} +(-0.876821 - 0.876821i) q^{32} +(-4.93200 - 2.94540i) q^{33} +(-9.58088 - 9.58088i) q^{34} +(-2.90914 + 0.945237i) q^{35} +(12.2333 + 1.79875i) q^{36} +(-0.783474 - 0.124090i) q^{37} +(5.89201 - 18.1337i) q^{38} +(3.46452 - 5.19587i) q^{39} +(4.57066 - 3.32078i) q^{40} +(1.46708 + 9.26280i) q^{41} +(-11.8585 - 2.77752i) q^{42} +6.53820i q^{43} +(-13.0253 - 4.14774i) q^{44} +(-0.963657 + 3.08169i) q^{45} +(2.44816 - 4.80478i) q^{46} +(-1.22375 + 0.193823i) q^{47} +(8.18847 - 0.690146i) q^{48} +(1.02455 + 0.332897i) q^{49} +(-4.31513 - 8.46891i) q^{50} +(9.45174 - 0.796617i) q^{51} +(5.20730 - 13.9184i) q^{52} +(8.39111 - 2.72644i) q^{53} +(-9.63575 + 8.51090i) q^{54} +(1.60186 - 3.19002i) q^{55} -14.9186 q^{56} +(7.03719 + 11.3420i) q^{57} +(6.37134 - 1.00912i) q^{58} +(-0.906540 + 5.72367i) q^{59} +(-0.560356 + 7.66291i) q^{60} +(1.93467 - 5.95432i) q^{61} +(16.7761 - 12.1885i) q^{62} +(6.84182 - 5.08773i) q^{63} +(-6.10648 + 1.98412i) q^{64} +(3.37708 + 1.91162i) q^{65} +(12.0331 - 7.56424i) q^{66} +(2.77842 - 2.77842i) q^{67} +(21.4664 - 6.97487i) q^{68} +(1.46396 + 3.47961i) q^{69} +(1.18392 - 7.47499i) q^{70} +(-8.83781 + 4.50309i) q^{71} +(-9.11443 + 12.8420i) q^{72} +(-11.8686 - 1.87980i) q^{73} +(1.15360 - 1.58780i) q^{74} +(6.47854 + 1.51742i) q^{75} +(22.4595 + 22.4595i) q^{76} +(-8.37337 + 4.32860i) q^{77} +(7.56284 + 13.4739i) q^{78} +(0.0311643 + 0.0959138i) q^{79} +(0.798799 + 5.04342i) q^{80} +(-0.199571 - 8.99779i) q^{81} +(-22.0679 - 7.17030i) q^{82} +(6.28326 - 3.20148i) q^{83} +(13.0909 - 15.5006i) q^{84} +(0.922032 + 5.82148i) q^{85} +(-14.4136 - 7.34409i) q^{86} +(-2.33814 + 3.86341i) q^{87} +(12.2380 - 12.3827i) q^{88} +(-4.83163 + 4.83163i) q^{89} +(-5.71119 - 5.58592i) q^{90} +(-4.24743 - 9.32545i) q^{91} +(5.28013 + 7.26748i) q^{92} +(-1.05870 + 14.4778i) q^{93} +(0.947299 - 2.91549i) q^{94} +(-6.71014 + 4.87521i) q^{95} +(-0.810900 + 1.98880i) q^{96} +(-6.81967 - 3.47480i) q^{97} +(-1.88471 + 1.88471i) q^{98} +(-1.38958 + 9.85236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−1.12326	+	2.20452i	−0.794263	+	1.55883i	0.0346164	+	0.999401i	$0.488979\pi$
$2$	−1.12326	+	2.20452i	−0.794263	+	1.55883i	−0.828879	+	0.559428i	$0.811021\pi$
$3$	−0.671689	−	1.59651i	−0.387800	−	0.921744i
$3$	−0.671689	−	1.59651i	−0.387800	−	0.921744i
$4$	−2.42261	−	3.33444i	−1.21131	−	1.66722i
$5$	0.958973	−	0.488621i	0.428866	−	0.218518i	−0.226214	−	0.974078i	$-0.572635\pi$
$5$	0.958973	−	0.488621i	0.428866	−	0.218518i	0.655080	+	0.755559i	$0.272635\pi$
$6$	4.27400	+	0.312539i	1.74486	+	0.127594i
$7$	−2.80706	−	0.444595i	−1.06097	−	0.168041i	−0.398530	−	0.917155i	$-0.630479\pi$
$7$	−2.80706	−	0.444595i	−1.06097	−	0.168041i	−0.662441	+	0.749114i	$0.730479\pi$
$8$	5.18460	−	0.821160i	1.83303	−	0.290324i
$9$	−2.09767	+	2.14471i	−0.699223	+	0.714904i
$10$			2.66292i			0.842089i
$11$	2.67171	−	1.96520i	0.805549	−	0.592529i
$11$	2.67171	−	1.96520i	0.805549	−	0.592529i
$12$	−3.69622	+	6.10743i	−1.06701	+	1.76306i
$13$	1.98939	+	3.00705i	0.551757	+	0.834005i
$13$	1.98939	+	3.00705i	0.551757	+	0.834005i
$14$	4.13317	−	5.68882i	1.10464	−	1.52040i
$15$	−1.42422	−	1.20281i	−0.367732	−	0.310563i
$16$	−1.46609	+	4.51217i	−0.366523	+	1.12804i
$17$	−1.69227	+	5.20828i	−0.410436	+	1.26319i	0.505833	+	0.862631i	$0.331185\pi$
$17$	−1.69227	+	5.20828i	−0.410436	+	1.26319i	−0.916270	+	0.400562i	$0.868815\pi$
$18$	−2.37183	−	7.03341i	−0.559045	−	1.65779i
$19$	−7.61147	+	1.20554i	−1.74619	+	0.276569i	−0.946233	−	0.323487i	$-0.895145\pi$
$19$	−7.61147	+	1.20554i	−1.74619	+	0.276569i	−0.799958	+	0.600056i	$0.795145\pi$
$20$	−3.95250	−	2.01390i	−0.883807	−	0.450322i
$21$	1.17567	+	4.78013i	0.256553	+	1.04311i
$22$	1.33129	+	8.09724i	0.283833	+	1.72634i
$23$	−2.17952			−0.454461			−0.227230	−	0.973841i	$-0.572967\pi$
$23$	−2.17952			−0.454461			−0.227230	+	0.973841i	$0.572967\pi$
$24$	−4.79343	−	7.72569i	−0.978454	−	1.57700i
$25$	−2.25805	+	3.10794i	−0.451609	+	0.621587i
$26$	−8.86368	+	1.00795i	−1.73831	+	0.197676i
$27$	4.83303	+	1.90837i	0.930116	+	0.367265i
$28$	5.31796	+	10.4371i	1.00500	+	1.97242i
$29$	−1.53249	−	2.10929i	−0.284576	−	0.391685i	0.642667	−	0.766146i	$-0.277828\pi$
$29$	−1.53249	−	2.10929i	−0.284576	−	0.391685i	−0.927243	+	0.374461i	$0.877828\pi$
$30$	4.25137	−	1.78865i	0.776190	−	0.326562i
$31$	−7.46760	−	3.80493i	−1.34122	−	0.683386i	−0.371689	−	0.928357i	$-0.621221\pi$
$31$	−7.46760	−	3.80493i	−1.34122	−	0.683386i	−0.969530	+	0.244972i	$0.921221\pi$
$32$	−0.876821	−	0.876821i	−0.155002	−	0.155002i
$33$	−4.93200	−	2.94540i	−0.858551	−	0.512728i
$34$	−9.58088	−	9.58088i	−1.64311	−	1.64311i
$35$	−2.90914	+	0.945237i	−0.491734	+	0.159774i
$36$	12.2333	+	1.79875i	2.03888	+	0.299792i
$37$	−0.783474	−	0.124090i	−0.128802	−	0.0204003i	0.0917004	−	0.995787i	$-0.470770\pi$
$37$	−0.783474	−	0.124090i	−0.128802	−	0.0204003i	−0.220503	+	0.975386i	$0.570770\pi$
$38$	5.89201	−	18.1337i	0.955810	−	2.94168i
$39$	3.46452	−	5.19587i	0.554767	−	0.832006i
$40$	4.57066	−	3.32078i	0.722685	−	0.525061i
$41$	1.46708	+	9.26280i	0.229120	+	1.44661i	0.787138	+	0.616777i	$0.211562\pi$
$41$	1.46708	+	9.26280i	0.229120	+	1.44661i	−0.558018	+	0.829829i	$0.688438\pi$
$42$	−11.8585	−	2.77752i	−1.82980	−	0.428581i
$43$			6.53820i			0.997067i	0.866870	+	0.498533i	$0.166128\pi$
$43$			6.53820i			0.997067i	−0.866870	+	0.498533i	$0.833872\pi$
$44$	−13.0253	−	4.14774i	−1.96364	−	0.625295i
$45$	−0.963657	+	3.08169i	−0.143654	+	0.459391i
$46$	2.44816	−	4.80478i	0.360961	−	0.708426i
$47$	−1.22375	+	0.193823i	−0.178502	+	0.0282720i	−0.245046	−	0.969512i	$-0.578803\pi$
$47$	−1.22375	+	0.193823i	−0.178502	+	0.0282720i	0.0665434	+	0.997784i	$0.478803\pi$
$48$	8.18847	−	0.690146i	1.18190	−	0.0996139i
$49$	1.02455	+	0.332897i	0.146364	+	0.0475567i
$50$	−4.31513	−	8.46891i	−0.610251	−	1.19769i
$51$	9.45174	−	0.796617i	1.32351	−	0.111549i
$52$	5.20730	−	13.9184i	0.722123	−	1.93014i
$53$	8.39111	−	2.72644i	1.15261	−	0.374505i	0.330483	−	0.943812i	$-0.392788\pi$
$53$	8.39111	−	2.72644i	1.15261	−	0.374505i	0.822125	+	0.569307i	$0.192788\pi$
$54$	−9.63575	+	8.51090i	−1.31126	+	1.15819i
$55$	1.60186	−	3.19002i	0.215994	−	0.430142i
$56$	−14.9186			−1.99358
$57$	7.03719	+	11.3420i	0.932098	+	1.50229i
$58$	6.37134	−	1.00912i	0.836597	−	0.132504i
$59$	−0.906540	+	5.72367i	−0.118021	+	0.745158i	0.855710	+	0.517456i	$0.173121\pi$
$59$	−0.906540	+	5.72367i	−0.118021	+	0.745158i	−0.973731	+	0.227702i	$0.926879\pi$
$60$	−0.560356	+	7.66291i	−0.0723416	+	0.989278i
$61$	1.93467	−	5.95432i	0.247710	−	0.762372i	−0.747469	−	0.664296i	$-0.768731\pi$
$61$	1.93467	−	5.95432i	0.247710	−	0.762372i	0.995179	−	0.0980756i	$-0.0312687\pi$
$62$	16.7761	−	12.1885i	2.13056	−	1.54794i
$63$	6.84182	−	5.08773i	0.861988	−	0.640994i
$64$	−6.10648	+	1.98412i	−0.763310	+	0.248014i
$65$	3.37708	+	1.91162i	0.418875	+	0.237107i
$66$	12.0331	−	7.56424i	1.48117	−	0.931094i
$67$	2.77842	−	2.77842i	0.339438	−	0.339438i	−0.516718	−	0.856156i	$-0.672846\pi$
$67$	2.77842	−	2.77842i	0.339438	−	0.339438i	0.856156	+	0.516718i	$0.172846\pi$
$68$	21.4664	−	6.97487i	2.60319	−	0.845827i
$69$	1.46396	+	3.47961i	0.176240	+	0.418896i
$70$	1.18392	−	7.47499i	0.141506	−	0.893432i
$71$	−8.83781	+	4.50309i	−1.04885	+	0.534418i	−0.891451	−	0.453116i	$-0.850312\pi$
$71$	−8.83781	+	4.50309i	−1.04885	+	0.534418i	−0.157403	+	0.987534i	$0.550312\pi$
$72$	−9.11443	+	12.8420i	−1.07415	+	1.51344i
$73$	−11.8686	−	1.87980i	−1.38911	−	0.220014i	−0.583336	−	0.812231i	$-0.698253\pi$
$73$	−11.8686	−	1.87980i	−1.38911	−	0.220014i	−0.805778	+	0.592217i	$0.798253\pi$
$74$	1.15360	−	1.58780i	0.134103	−	0.184578i
$75$	6.47854	+	1.51742i	0.748078	+	0.175217i
$76$	22.4595	+	22.4595i	2.57628	+	2.57628i
$77$	−8.37337	+	4.32860i	−0.954234	+	0.493290i
$78$	7.56284	+	13.4739i	0.856323	+	1.52562i
$79$	0.0311643	+	0.0959138i	0.00350625	+	0.0107911i	0.952794	−	0.303616i	$-0.0981941\pi$
$79$	0.0311643	+	0.0959138i	0.00350625	+	0.0107911i	−0.949288	+	0.314408i	$0.898194\pi$
$80$	0.798799	+	5.04342i	0.0893084	+	0.563871i
$81$	−0.199571	−	8.99779i	−0.0221745	−	0.999754i
$82$	−22.0679	−	7.17030i	−2.43699	−	0.791827i
$83$	6.28326	−	3.20148i	0.689677	−	0.351408i	−0.0737729	−	0.997275i	$-0.523504\pi$
$83$	6.28326	−	3.20148i	0.689677	−	0.351408i	0.763450	+	0.645867i	$0.223504\pi$
$84$	13.0909	−	15.5006i	1.42833	−	1.69126i
$85$	0.922032	+	5.82148i	0.100008	+	0.631428i
$86$	−14.4136	−	7.34409i	−1.55426	−	0.791933i
$87$	−2.33814	+	3.86341i	−0.250675	+	0.414201i
$88$	12.2380	−	12.3827i	1.30457	−	1.32000i
$89$	−4.83163	+	4.83163i	−0.512152	+	0.512152i	−0.915185	−	0.403033i	$-0.867956\pi$
$89$	−4.83163	+	4.83163i	−0.512152	+	0.512152i	0.403033	+	0.915185i	$0.367956\pi$
$90$	−5.71119	−	5.58592i	−0.602013	−	0.588808i
$91$	−4.24743	−	9.32545i	−0.445251	−	0.977573i
$92$	5.28013	+	7.26748i	0.550492	+	0.757687i
$93$	−1.05870	+	14.4778i	−0.109782	+	1.50128i
$94$	0.947299	−	2.91549i	0.0977064	−	0.300710i
$95$	−6.71014	+	4.87521i	−0.688446	+	0.500185i
$96$	−0.810900	+	1.98880i	−0.0827622	+	0.202981i
$97$	−6.81967	−	3.47480i	−0.692433	−	0.352812i	0.0720996	−	0.997397i	$-0.477030\pi$
$97$	−6.81967	−	3.47480i	−0.692433	−	0.352812i	−0.764532	+	0.644585i	$0.777030\pi$
$98$	−1.88471	+	1.88471i	−0.190385	+	0.190385i
$99$	−1.38958	+	9.85236i	−0.139658	+	0.990200i
$100$	15.8336			1.58336
$101$	0.174122	+	0.535894i	0.0173258	+	0.0533234i	0.959346	−	0.282234i	$-0.0910754\pi$
$101$	0.174122	+	0.535894i	0.0173258	+	0.0533234i	−0.942020	+	0.335557i	$0.891075\pi$
$102$	−8.86057	+	21.7313i	−0.877328	+	2.15172i
$103$	10.6215	+	14.6192i	1.04657	+	1.44047i	0.891749	+	0.452530i	$0.149478\pi$
$103$	10.6215	+	14.6192i	1.04657	+	1.44047i	0.154816	+	0.987943i	$0.450522\pi$
$104$	12.7835	+	13.9567i	1.25352	+	1.36857i
$105$	3.46311	+	4.00956i	0.337965	+	0.391293i
$106$	−3.41490	+	21.5608i	−0.331684	+	2.09417i
$107$	−2.60239	+	3.58189i	−0.251583	+	0.346274i	−0.916065	−	0.401030i	$-0.868652\pi$
$107$	−2.60239	+	3.58189i	−0.251583	+	0.346274i	0.664482	+	0.747304i	$0.268652\pi$
$108$	−5.34523	−	20.7387i	−0.514345	−	1.99558i
$109$	−1.47880	+	1.47880i	−0.141643	+	0.141643i	−0.774373	−	0.632730i	$-0.781934\pi$
$109$	−1.47880	+	1.47880i	−0.141643	+	0.141643i	0.632730	+	0.774373i	$0.281934\pi$
$110$	5.23316	+	7.11454i	0.498962	+	0.678344i
$111$	0.328140	+	1.33417i	0.0311457	+	0.126634i
$112$	6.12151	−	12.0141i	0.578428	−	1.13523i
$113$	−0.203783	+	0.280483i	−0.0191703	+	0.0263856i	−0.818495	−	0.574514i	$-0.805191\pi$
$113$	−0.203783	+	0.280483i	−0.0191703	+	0.0263856i	0.799324	+	0.600900i	$0.205191\pi$
$114$	−32.9082	+	2.77359i	−3.08214	+	0.259771i
$115$	−2.09010	+	1.06496i	−0.194903	+	0.0993079i
$116$	−3.32067	+	10.2200i	−0.308317	+	0.948902i
$117$	−10.6223	−	2.04112i	−0.982034	−	0.188702i
$118$	−11.5996	−	8.42763i	−1.06783	−	0.775826i
$119$	7.06590	−	13.8676i	0.647730	−	1.27124i
$120$	−8.37171	−	5.06656i	−0.764229	−	0.462512i
$121$	3.27602	−	10.5008i	0.297820	−	0.954622i
$122$	10.9532	+	10.9532i	0.991661	+	0.991661i
$123$	13.8027	−	8.56393i	1.24455	−	0.772183i
$124$	5.40378	+	34.1182i	0.485274	+	3.06390i
$125$	−1.48864	+	9.39891i	−0.133148	+	0.840664i
$126$	3.53086	+	20.7977i	0.314554	+	1.85281i
$127$	−6.11643	−	1.98735i	−0.542745	−	0.176349i	0.0247975	−	0.999692i	$-0.492106\pi$
$127$	−6.11643	−	1.98735i	−0.542745	−	0.176349i	−0.567543	+	0.823344i	$0.692106\pi$
$128$	2.87309	−	18.1400i	0.253948	−	1.60336i
$129$	10.4383	−	4.39164i	0.919040	−	0.386662i
$130$	−8.00752	+	5.29758i	−0.702306	+	0.464629i
$131$		−	9.94336i		−	0.868756i	−0.900731	−	0.434378i	$-0.856968\pi$
$131$		−	9.94336i		−	0.868756i	0.900731	−	0.434378i	$-0.143032\pi$
$132$	2.12708	+	23.5810i	0.185139	+	2.05247i
$133$	21.9019			1.89913
$134$	3.00419	+	9.24596i	0.259523	+	0.798729i
$135$	5.56721	−	0.531448i	0.479149	−	0.0457398i
$136$	−4.49693	+	28.3925i	−0.385609	+	2.43464i
$137$	−7.92693	−	15.5575i	−0.677243	−	1.32916i	−0.932105	−	0.362187i	$-0.882030\pi$
$137$	−7.92693	−	15.5575i	−0.677243	−	1.32916i	0.254862	−	0.966977i	$-0.417970\pi$
$138$	−9.31527	−	0.681185i	−0.792968	−	0.0579863i
$139$	9.68627	−	7.03748i	0.821578	−	0.596912i	−0.0955858	−	0.995421i	$-0.530472\pi$
$139$	9.68627	−	7.03748i	0.821578	−	0.596912i	0.917164	+	0.398510i	$0.130472\pi$
$140$	10.1996	+	7.41041i	0.862020	+	0.626294i
$141$	1.13142	+	1.82353i	0.0952825	+	0.153569i
$142$		−	24.5412i		−	2.05945i
$143$	11.2245	+	4.12440i	0.938639	+	0.344900i
$144$	−6.60192	−	12.6094i	−0.550160	−	1.05078i
$145$	−2.50026	−	1.27394i	−0.207635	−	0.105795i
$146$	17.4755	−	24.0530i	1.44629	−	1.99064i
$147$	−0.156707	−	1.85931i	−0.0129250	−	0.153353i
$148$	1.48428	+	2.91307i	0.122007	+	0.239453i
$149$	−7.65205	+	3.89891i	−0.626880	+	0.319411i	−0.738412	−	0.674349i	$-0.764424\pi$
$149$	−7.65205	+	3.89891i	−0.626880	+	0.319411i	0.111532	+	0.993761i	$0.464424\pi$
$150$	−10.6223	+	12.5776i	−0.867304	+	1.02696i
$151$	−1.09169	−	6.89267i	−0.0888407	−	0.560918i	−0.991453	−	0.130464i	$-0.958353\pi$
$151$	−1.09169	−	6.89267i	−0.0888407	−	0.560918i	0.902612	−	0.430454i	$-0.141647\pi$
$152$	−38.4725	+	12.5005i	−3.12053	+	1.01392i
$153$	−7.62043	−	14.5547i	−0.616075	−	1.17668i
$154$	−0.137031	−	23.3214i	−0.0110423	−	1.87929i
$155$	−9.02039			−0.724536
$156$	−25.7185	+	1.03535i	−2.05913	+	0.0828943i
$157$	2.38518	+	1.73294i	0.190358	+	0.138303i	0.678882	−	0.734247i	$-0.262465\pi$
$157$	2.38518	+	1.73294i	0.190358	+	0.138303i	−0.488524	+	0.872550i	$0.662465\pi$
$158$	−0.246449	−	0.0390337i	−0.0196064	−	0.00310535i
$159$	−9.98899	−	11.5651i	−0.792178	−	0.917176i
$160$	−1.26928	−	0.412415i	−0.100346	−	0.0326042i
$161$	6.11805	+	0.969003i	0.482170	+	0.0763682i
$162$	20.0599	+	9.66687i	1.57606	+	0.759501i
$163$	6.44999	−	12.6588i	0.505202	−	0.991515i	−0.487748	−	0.872984i	$-0.662182\pi$
$163$	6.44999	−	12.6588i	0.505202	−	0.991515i	0.992950	−	0.118531i	$-0.0378184\pi$
$164$	27.3321	−	27.3321i	2.13428	−	2.13428i
$165$	−6.16884	−	0.414676i	−0.480244	−	0.0322825i
$166$			17.4476i			1.35420i
$167$	14.8075	+	7.54477i	1.14584	+	0.583832i	0.920613	−	0.390475i	$-0.127689\pi$
$167$	14.8075	+	7.54477i	1.14584	+	0.583832i	0.225222	+	0.974308i	$0.427689\pi$
$168$	10.0207	+	23.8176i	0.773110	+	1.83757i
$169$	−5.08466	+	11.9644i	−0.391128	+	0.920336i
$170$	−13.8692	−	4.50639i	−1.06372	−	0.345624i
$171$	13.3808	−	18.8532i	1.02326	−	1.44174i
$172$	21.8013	−	15.8396i	1.66233	−	1.20775i
$173$	7.44025	+	5.40566i	0.565672	+	0.410985i	0.833530	−	0.552474i	$-0.186316\pi$
$173$	7.44025	+	5.40566i	0.565672	+	0.410985i	−0.267859	+	0.963458i	$0.586316\pi$
$174$	−5.89062	−	9.49407i	−0.446567	−	0.719743i
$175$	7.72026	−	7.72026i	0.583597	−	0.583597i
$176$	4.95033	+	14.9363i	0.373145	+	1.12587i
$177$	9.74679	−	2.39722i	0.732613	−	0.180186i
$178$	−5.22425	−	16.0786i	−0.391574	−	1.20514i
$179$	−3.65475	−	2.65533i	−0.273169	−	0.198469i	0.442764	−	0.896638i	$-0.353998\pi$
$179$	−3.65475	−	2.65533i	−0.273169	−	0.198469i	−0.715932	+	0.698170i	$0.753998\pi$
$180$	12.6103	−	4.25248i	0.939915	−	0.316961i
$181$	11.0984	+	3.60608i	0.824935	+	0.268038i	0.690910	−	0.722940i	$-0.257210\pi$
$181$	11.0984	+	3.60608i	0.824935	+	0.268038i	0.134025	+	0.990978i	$0.457210\pi$
$182$	25.3291	+	1.11136i	1.87751	+	0.0823793i
$183$	−10.8056	+	0.910725i	−0.798773	+	0.0673227i
$184$	−11.2999	+	1.78973i	−0.833042	+	0.131941i
$185$	−0.811964	+	0.263823i	−0.0596968	+	0.0193967i
$186$	−30.7273	−	18.5962i	−2.25304	−	1.36354i
$187$	5.71403	+	17.2406i	0.417851	+	1.26076i
$188$	3.61096	+	3.61096i	0.263357	+	0.263357i
$189$	−12.7182	−	7.50564i	−0.925110	−	0.545955i
$190$	−3.21025	−	20.2687i	−0.232896	−	1.47045i
$191$	−2.17332	−	2.99131i	−0.157256	−	0.216444i	0.723118	−	0.690724i	$-0.242708\pi$
$191$	−2.17332	−	2.99131i	−0.157256	−	0.216444i	−0.880374	+	0.474281i	$0.842708\pi$
$192$	7.26931	+	8.41633i	0.524617	+	0.607396i
$193$	−1.86037	+	0.947904i	−0.133912	+	0.0682316i	−0.519663	−	0.854371i	$-0.673942\pi$
$193$	−1.86037	+	0.947904i	−0.133912	+	0.0682316i	0.385751	+	0.922603i	$0.373942\pi$
$194$	15.3205	−	11.1310i	1.09995	−	0.799158i
$195$	0.783569	−	6.67554i	0.0561125	−	0.478046i
$196$	−1.37207	−	4.22279i	−0.0980048	−	0.301628i
$197$	5.25386	+	5.25386i	0.374322	+	0.374322i	0.869049	−	0.494727i	$-0.164732\pi$
$197$	5.25386	+	5.25386i	0.374322	+	0.374322i	−0.494727	+	0.869049i	$0.664732\pi$
$198$	−20.1588	−	14.1301i	−1.43263	−	1.00418i
$199$		−	20.3826i		−	1.44489i	−0.691431	−	0.722443i	$-0.743019\pi$
$199$		−	20.3826i		−	1.44489i	0.691431	−	0.722443i	$-0.256981\pi$
$200$	−9.15496	+	17.9676i	−0.647354	+	1.27050i
$201$	−6.30201	−	2.56954i	−0.444509	−	0.181241i
$202$	−1.37697	−	0.218091i	−0.0968833	−	0.0153448i
$203$	3.36401	+	6.60224i	0.236107	+	0.463387i
$204$	−25.5542	−	29.5864i	−1.78915	−	2.07146i
$205$	5.93290	+	8.16593i	0.414371	+	0.570333i
$206$	−44.1589	+	6.99409i	−3.07670	+	0.487301i
$207$	4.57191	−	4.67444i	0.317769	−	0.324896i
$208$	−16.4849	+	4.56785i	−1.14302	+	0.316724i
$209$	−17.9665	+	18.1789i	−1.24277	+	1.25746i
$210$	−12.7291	+	3.13072i	−0.878391	+	0.216041i
$211$	−2.23873	−	6.89010i	−0.154120	−	0.474334i	0.843950	−	0.536421i	$-0.180224\pi$
$211$	−2.23873	−	6.89010i	−0.154120	−	0.474334i	−0.998071	+	0.0620874i	$0.980224\pi$
$212$	−29.4196	−	21.3746i	−2.02054	−	1.46801i
$213$	13.1255	+	11.0849i	0.899342	+	0.759528i
$214$	−4.97317	−	9.76040i	−0.339959	−	0.667207i
$215$	3.19471	+	6.26996i	0.217877	+	0.427608i
$216$	26.6244	+	5.92543i	1.81156	+	0.403174i
$217$	19.2704	+	14.0007i	1.30816	+	0.950432i
$218$	−1.59896	−	4.92110i	−0.108295	−	0.333299i
$219$	4.97089	+	20.2109i	0.335901	+	1.36573i
$220$	−14.5176	+	2.38689i	−0.978778	+	0.160924i
$221$	−19.0281	+	5.27255i	−1.27997	+	0.354670i
$222$	−3.30979	−	0.775228i	−0.222139	−	0.0520299i
$223$	−3.02031	+	0.478370i	−0.202255	+	0.0320340i	−0.256740	−	0.966481i	$-0.582648\pi$
$223$	−3.02031	+	0.478370i	−0.202255	+	0.0320340i	0.0544849	+	0.998515i	$0.482648\pi$
$224$	2.07146	+	2.85112i	0.138405	+	0.190499i
$225$	−1.92899	−	11.3623i	−0.128599	−	0.757485i
$226$	−0.389429	−	0.764298i	−0.0259044	−	0.0508403i
$227$	−28.9730	−	4.58886i	−1.92300	−	0.304574i	−0.925718	−	0.378216i	$-0.876538\pi$
$227$	−28.9730	−	4.58886i	−1.92300	−	0.304574i	−0.997285	+	0.0736420i	$0.976538\pi$
$228$	20.7709	−	50.9424i	1.37559	−	3.37375i
$229$	0.644424	−	1.26475i	0.0425848	−	0.0835773i	−0.868734	−	0.495280i	$-0.835066\pi$
$229$	0.644424	−	1.26475i	0.0425848	−	0.0835773i	0.911318	+	0.411702i	$0.135066\pi$
$230$		−	5.80388i		−	0.382697i
$231$	12.5349	+	10.4607i	0.824738	+	0.688261i
$232$	−9.67740	−	9.67740i	−0.635353	−	0.635353i
$233$	−1.38483	−	4.26207i	−0.0907233	−	0.279218i	0.895392	−	0.445278i	$-0.146895\pi$
$233$	−1.38483	−	4.26207i	−0.0907233	−	0.279218i	−0.986116	+	0.166061i	$0.946895\pi$
$234$	16.4313	−	21.1244i	1.07415	−	1.38094i
$235$	−1.07884	+	0.783821i	−0.0703755	+	0.0511308i
$236$	21.2814	−	10.8434i	1.38530	−	0.705848i
$237$	0.132194	−	0.114178i	0.00858694	−	0.00741667i
$238$	22.6345	+	31.1538i	1.46718	+	2.01940i
$239$	−2.81869	−	17.7965i	−0.182326	−	1.15116i	−0.893806	−	0.448453i	$-0.851975\pi$
$239$	−2.81869	−	17.7965i	−0.182326	−	1.15116i	0.711481	−	0.702706i	$-0.248025\pi$
$240$	7.51530	−	4.66289i	0.485111	−	0.300988i
$241$	−2.10829	−	2.10829i	−0.135807	−	0.135807i	0.635936	−	0.771742i	$-0.280614\pi$
$241$	−2.10829	−	2.10829i	−0.135807	−	0.135807i	−0.771742	+	0.635936i	$0.780614\pi$
$242$	19.4695	+	19.0172i	1.25155	+	1.22247i
$243$	−14.2310	+	6.36233i	−0.912918	+	0.408143i
$244$	−24.5413	+	7.97395i	−1.57110	+	0.510480i
$245$	1.14518	−	0.181378i	0.0731627	−	0.0115878i
$246$	3.37533	+	40.0478i	0.215203	+	2.55335i
$247$	−18.7673	−	20.4898i	−1.19413	−	1.30373i
$248$	−41.8410	−	13.5950i	−2.65690	−	0.863281i
$249$	−9.33157	−	7.88087i	−0.591365	−	0.499430i
$250$	−19.0479	−	13.8391i	−1.20470	−	0.875263i
$251$	−4.21055	−	12.9587i	−0.265768	−	0.817949i	−0.991516	−	0.129988i	$-0.958506\pi$
$251$	−4.21055	−	12.9587i	−0.265768	−	0.817949i	0.725748	−	0.687961i	$-0.241494\pi$
$252$	−33.5398	−	10.4881i	−2.11281	−	0.660685i
$253$	−5.82303	+	4.28318i	−0.366091	+	0.269281i
$254$	11.2515	−	11.2515i	0.705980	−	0.705980i
$255$	8.67472	−	5.38225i	0.543232	−	0.337050i
$256$	26.3737	+	19.1616i	1.64836	+	1.19760i
$257$	11.1667	−	8.11310i	0.696561	−	0.506081i	−0.182250	−	0.983252i	$-0.558338\pi$
$257$	11.1667	−	8.11310i	0.696561	−	0.506081i	0.878810	+	0.477171i	$0.158338\pi$
$258$	−2.04345	+	27.9443i	−0.127219	+	1.73974i
$259$	2.14409	+	0.696658i	0.133227	+	0.0432882i
$260$	−1.80717	−	15.8918i	−0.112076	−	0.985567i
$261$	7.73846	+	1.13784i	0.478999	+	0.0704308i
$262$	21.9203	+	11.1690i	1.35424	+	0.690020i
$263$			28.0053i			1.72688i	0.504450	+	0.863441i	$0.331695\pi$
$263$			28.0053i			1.72688i	−0.504450	+	0.863441i	$0.668305\pi$
$264$	−27.9891	−	11.2207i	−1.72261	−	0.690589i
$265$	6.71466	−	6.71466i	0.412478	−	0.412478i
$266$	−24.6014	+	48.2830i	−1.50841	+	2.96042i
$267$	10.9591	+	4.46838i	0.670685	+	0.273461i
$268$	−15.9955	−	2.53344i	−0.977083	−	0.154755i
$269$	17.4816	+	5.68013i	1.06587	+	0.346324i	0.788879	−	0.614548i	$-0.210662\pi$
$269$	17.4816	+	5.68013i	1.06587	+	0.346324i	0.276995	+	0.960871i	$0.410662\pi$
$270$	−5.08182	+	12.8700i	−0.309270	+	0.783241i
$271$	−27.1845	−	4.30560i	−1.65134	−	0.261547i	−0.739821	−	0.672804i	$-0.765090\pi$
$271$	−27.1845	−	4.30560i	−1.65134	−	0.261547i	−0.911519	+	0.411257i	$0.865090\pi$
$272$	−21.0196	−	15.2716i	−1.27450	−	0.925980i
$273$	−12.0352	+	13.0448i	−0.728403	+	0.789510i
$274$	43.2007			2.60985
$275$	0.0748631	+	12.7410i	0.00451442	+	0.768311i
$276$	8.05597	−	13.3112i	0.484913	−	0.801243i
$277$	−21.2736	+	6.91222i	−1.27821	+	0.415315i	−0.867949	−	0.496653i	$-0.834562\pi$
$277$	−21.2736	+	6.91222i	−1.27821	+	0.415315i	−0.410260	+	0.911969i	$0.634562\pi$
$278$	4.63408	+	29.2584i	0.277934	+	1.75480i
$279$	23.8250	−	8.03435i	1.42637	−	0.481004i
$280$	−14.3065	+	7.28955i	−0.854979	+	0.435634i
$281$	−4.00110	−	7.85261i	−0.238686	−	0.468447i	0.740327	−	0.672247i	$-0.234671\pi$
$281$	−4.00110	−	7.85261i	−0.238686	−	0.468447i	−0.979013	+	0.203800i	$0.934671\pi$
$282$	−5.29088	+	0.445930i	−0.315068	+	0.0265547i
$283$	−11.7175	+	16.1277i	−0.696532	+	0.958693i	0.303451	+	0.952847i	$0.401861\pi$
$283$	−11.7175	+	16.1277i	−0.696532	+	0.958693i	−0.999983	+	0.00584651i	$0.998139\pi$
$284$	36.4259	+	18.5599i	2.16148	+	1.10133i
$285$	12.2904	+	7.43817i	0.728022	+	0.440599i
$286$	−21.7003	+	20.1118i	−1.28317	+	1.18924i
$287$		−	26.6535i		−	1.57331i
$288$	3.71981	−	0.0412475i	0.219192	−	0.00243053i
$289$	−10.5091	−	7.63531i	−0.618183	−	0.449136i
$290$	5.61686	−	4.08089i	0.329834	−	0.239638i
$291$	−0.966841	+	13.2216i	−0.0566772	+	0.775066i
$292$	22.4849	+	44.1292i	1.31583	+	2.58247i
$293$	0.121352	−	0.766186i	0.00708946	−	0.0447611i	−0.983890	−	0.178775i	$-0.942787\pi$
$293$	0.121352	−	0.766186i	0.00708946	−	0.0447611i	0.990979	+	0.134014i	$0.0427866\pi$
$294$	4.27489	+	1.74301i	0.249317	+	0.101655i
$295$	1.92736	+	5.93180i	0.112215	+	0.345363i
$296$	−4.16390			−0.242022
$297$	16.6627	−	4.39925i	0.966870	−	0.255270i
$298$		−	21.2485i		−	1.23090i
$299$	−4.33591	−	6.55391i	−0.250752	−	0.379022i
$300$	−10.6353	−	25.2785i	−0.614027	−	1.45945i
$301$	2.90686	−	18.3532i	0.167548	−	1.05786i
$302$	16.4213	+	5.33559i	0.944938	+	0.307029i
$303$	0.738602	−	0.637941i	0.0424316	−	0.0366488i
$304$	5.71953	−	36.1117i	0.328037	−	2.07115i
$305$	−1.05410	−	6.65535i	−0.0603578	−	0.381084i
$306$	40.6457	−	0.450705i	2.32356	−	0.0257651i
$307$	0.518927	+	0.518927i	0.0296167	+	0.0296167i	0.721760	−	0.692143i	$-0.243333\pi$
$307$	0.518927	+	0.518927i	0.0296167	+	0.0296167i	−0.692143	+	0.721760i	$0.743333\pi$
$308$	34.7189	+	17.4340i	1.97829	+	0.993393i
$309$	16.2053	−	26.7768i	0.921890	−	1.52328i
$310$	10.1322	−	19.8856i	0.575472	−	1.12943i
$311$	17.5982	+	12.7858i	0.997902	+	0.725018i	0.961637	−	0.274324i	$-0.0884541\pi$
$311$	17.5982	+	12.7858i	0.997902	+	0.725018i	0.0362647	+	0.999342i	$0.488454\pi$
$312$	13.6955	−	29.7835i	0.775356	−	1.68616i
$313$	−9.78026	+	30.1005i	−0.552813	+	1.70138i	0.148838	+	0.988862i	$0.452447\pi$
$313$	−9.78026	+	30.1005i	−0.552813	+	1.70138i	−0.701651	+	0.712521i	$0.747553\pi$
$314$	−6.49946	+	3.31164i	−0.366786	+	0.186887i
$315$	4.07515	−	8.22206i	0.229609	−	0.463260i
$316$	0.244320	−	0.336278i	0.0137441	−	0.0189171i
$317$	9.10646	−	17.8724i	0.511470	−	1.00382i	−0.480459	−	0.877017i	$-0.659530\pi$
$317$	9.10646	−	17.8724i	0.511470	−	1.00382i	0.991928	−	0.126798i	$-0.0404702\pi$
$318$	36.7158	−	9.03025i	2.05892	−	0.506391i
$319$	−8.23952	−	2.62376i	−0.461324	−	0.146902i
$320$	−4.88647	+	4.88647i	−0.273162	+	0.273162i
$321$	7.46650	+	1.74883i	0.416740	+	0.0976099i
$322$	−9.00832	+	12.3989i	−0.502014	+	0.690963i
$323$	6.60190	−	41.6828i	0.367340	−	2.31929i
$324$	−29.5191	+	22.4636i	−1.63995	+	1.24798i
$325$	−13.8378	−	0.607160i	−0.767585	−	0.0336792i
$326$	20.6616	+	28.4382i	1.14434	+	1.57505i
$327$	3.35420	+	1.36762i	0.185488	+	0.0756294i
$328$	15.2125	+	46.8192i	0.839969	+	2.58516i
$329$	3.52131			0.194136
$330$	7.84335	−	13.1335i	0.431762	−	0.722977i
$331$	−16.9621	+	16.9621i	−0.932323	+	0.932323i	−0.997851	−	0.0655281i	$-0.979127\pi$
$331$	−16.9621	+	16.9621i	−0.932323	+	0.932323i	0.0655281	+	0.997851i	$0.479127\pi$
$332$	−25.8971	−	13.1952i	−1.42129	−	0.724181i
$333$	1.90961	−	1.42003i	0.104646	−	0.0778169i
$334$	−33.2652	+	24.1686i	−1.82019	+	1.32244i
$335$	1.30684	−	4.02203i	0.0714001	−	0.219747i
$336$	−23.2924	−	1.70327i	−1.27070	−	0.0929211i
$337$	5.37789	+	7.40203i	0.292952	+	0.403214i	0.929970	−	0.367635i	$-0.119832\pi$
$337$	5.37789	+	7.40203i	0.292952	+	0.403214i	−0.637018	+	0.770849i	$0.719832\pi$
$338$	−20.6643	−	24.6483i	−1.12399	−	1.34069i
$339$	0.584672	+	0.136944i	0.0317550	+	0.00743776i
$340$	17.1777	−	17.1777i	0.931590	−	0.931590i
$341$	−27.4286	+	4.50963i	−1.48534	+	0.244210i
$342$	26.5321	+	50.6752i	1.43469	+	2.74020i
$343$	14.9981	+	7.64189i	0.809819	+	0.412623i
$344$	5.36892	+	33.8980i	0.289473	+	1.82766i
$345$	3.10411	+	2.62154i	0.167120	+	0.141139i
$346$	−20.2742	+	10.3302i	−1.08995	+	0.555355i
$347$	25.2355	+	8.19952i	1.35471	+	0.440173i	0.894275	−	0.447518i	$-0.147692\pi$
$347$	25.2355	+	8.19952i	1.35471	+	0.440173i	0.460439	+	0.887691i	$0.347692\pi$
$348$	18.5467	−	1.56317i	0.994209	−	0.0837946i
$349$	−0.689093	−	4.35076i	−0.0368863	−	0.232891i	0.962357	−	0.271789i	$-0.0876152\pi$
$349$	−0.689093	−	4.35076i	−0.0368863	−	0.232891i	−0.999243	+	0.0388980i	$0.987615\pi$
$350$	8.34760	+	25.6913i	0.446198	+	1.37326i
$351$	3.87623	+	18.3296i	0.206898	+	0.978363i
$352$	−4.06573	−	0.619483i	−0.216704	−	0.0330185i
$353$	−6.43700	−	6.43700i	−0.342607	−	0.342607i	0.514740	−	0.857347i	$-0.327889\pi$
$353$	−6.43700	−	6.43700i	−0.342607	−	0.342607i	−0.857347	+	0.514740i	$0.827889\pi$
$354$	−5.66343	+	24.1796i	−0.301008	+	1.28513i
$355$	−6.27492	+	8.63668i	−0.333038	+	0.458387i
$356$	27.8160	+	4.40562i	1.47424	+	0.233497i
$357$	−26.8858	−	1.96604i	−1.42295	−	0.104054i
$358$	9.95893	−	5.07433i	0.526346	−	0.268187i
$359$	−1.33940	+	8.45667i	−0.0706911	+	0.446326i	0.926801	+	0.375552i	$0.122547\pi$
$359$	−1.33940	+	8.45667i	−0.0706911	+	0.446326i	−0.997492	+	0.0707738i	$0.977453\pi$
$360$	−2.46562	+	16.7686i	−0.129950	+	0.883785i
$361$	38.4111	−	12.4805i	2.02163	−	0.656869i
$362$	−20.4160	+	20.4160i	−1.07304	+	1.07304i
$363$	−18.9651	+	1.82311i	−0.995411	+	0.0956887i
$364$	−20.8053	+	36.7548i	−1.09049	+	1.92647i
$365$	−12.3002	+	3.99657i	−0.643821	+	0.209190i
$366$	10.1298	−	24.8441i	0.529491	−	1.29862i
$367$	−8.88027	+	6.45189i	−0.463546	+	0.336786i	−0.794921	−	0.606713i	$-0.792488\pi$
$367$	−8.88027	+	6.45189i	−0.463546	+	0.336786i	0.331374	+	0.943499i	$0.392488\pi$
$368$	3.19538	−	9.83435i	0.166570	−	0.512651i
$369$	−22.9435	−	16.2838i	−1.19439	−	0.847702i
$370$	0.330442	−	2.08633i	0.0171789	−	0.108463i
$371$	−24.7665	+	3.92264i	−1.28582	+	0.203653i
$372$	50.8402	−	31.5440i	2.63594	−	1.63548i
$373$	−2.68379			−0.138961			−0.0694807	−	0.997583i	$-0.522134\pi$
$373$	−2.68379			−0.138961			−0.0694807	+	0.997583i	$0.522134\pi$
$374$	−44.4256	−	6.76899i	−2.29719	−	0.350016i
$375$	16.0053	−	3.93651i	0.826511	−	0.203281i
$376$	−6.18549	+	2.00979i	−0.318992	+	0.103647i
$377$	3.29401	−	8.80445i	0.169650	−	0.453452i
$378$	30.8321	−	19.6066i	1.58583	−	1.00846i
$379$	−7.21761	−	14.1653i	−0.370744	−	0.727625i	0.627975	−	0.778233i	$-0.283884\pi$
$379$	−7.21761	−	14.1653i	−0.370744	−	0.727625i	−0.998719	+	0.0506083i	$0.983884\pi$
$380$	32.5122	+	10.5639i	1.66784	+	0.541914i
$381$	0.935520	+	11.0998i	0.0479282	+	0.568660i
$382$	9.03560	−	1.43110i	0.462301	−	0.0732213i
$383$	1.45043	−	2.84663i	0.0741134	−	0.145456i	−0.850977	−	0.525203i	$-0.823989\pi$
$383$	1.45043	−	2.84663i	0.0741134	−	0.145456i	0.925090	+	0.379748i	$0.123989\pi$
$384$	−30.8905	+	7.59751i	−1.57637	+	0.387709i
$385$	−5.91479	+	8.24242i	−0.301445	+	0.420073i
$386$		−	5.16595i		−	0.262940i
$387$	−14.0226	−	13.7150i	−0.712807	−	0.697172i
$388$	4.93493	+	31.1579i	0.250533	+	1.58180i
$389$	−12.7113	+	9.23529i	−0.644487	+	0.468248i	−0.861389	−	0.507946i	$-0.830405\pi$
$389$	−12.7113	+	9.23529i	−0.644487	+	0.468248i	0.216901	+	0.976193i	$0.430405\pi$
$390$	13.8362	+	9.22574i	0.700623	+	0.467164i
$391$	3.68834	−	11.3515i	0.186527	−	0.574072i
$392$	5.58525	+	0.884617i	0.282098	+	0.0446799i
$393$	−15.8747	+	6.67884i	−0.800770	+	0.336903i
$394$	−17.4837	+	5.68078i	−0.880814	+	0.286194i
$395$	0.0767512	+	0.0767512i	0.00386177	+	0.00386177i
$396$	36.2186	−	19.2350i	1.82005	−	0.966596i
$397$	16.3307	+	16.3307i	0.819617	+	0.819617i	0.986052	−	0.166436i	$-0.0532258\pi$
$397$	16.3307	+	16.3307i	0.819617	+	0.819617i	−0.166436	+	0.986052i	$0.553226\pi$
$398$	44.9338	+	22.8949i	2.25233	+	1.14762i
$399$	−14.7112	−	34.9665i	−0.736483	−	1.75051i
$400$	−10.7130	−	14.7452i	−0.535651	−	0.737261i
$401$	−2.21006	−	4.33749i	−0.110365	−	0.216604i	0.829217	−	0.558926i	$-0.188787\pi$
$401$	−2.21006	−	4.33749i	−0.110365	−	0.216604i	−0.939583	+	0.342322i	$0.888787\pi$
$402$	12.7434	−	11.0066i	0.635581	−	0.548961i
$403$	−3.41435	−	30.0249i	−0.170081	−	1.49565i
$404$	1.36508	−	1.87887i	0.0679150	−	0.0934770i
$405$	−4.58789	−	8.53112i	−0.227974	−	0.423915i
$406$	−18.3334			−0.909871
$407$	−2.33707	+	1.20815i	−0.115844	+	0.0598856i
$408$	48.3494	−	11.8915i	2.39365	−	0.588719i
$409$	−12.2186	−	6.22569i	−0.604171	−	0.307841i	0.125016	−	0.992155i	$-0.460102\pi$
$409$	−12.2186	−	6.22569i	−0.604171	−	0.307841i	−0.729187	+	0.684314i	$0.760102\pi$
$410$	−24.6661	+	3.90673i	−1.21817	+	0.192939i
$411$	−19.5132	+	23.1052i	−0.962515	+	1.13969i
$412$	23.0152	−	70.8334i	1.13388	−	3.48971i
$413$	5.08943	−	15.6637i	0.250435	−	0.770758i
$414$	5.16944	+	15.3294i	0.254064	+	0.753401i
$415$	4.46116	−	6.14027i	0.218990	−	0.301414i
$416$	0.892304	−	4.38098i	0.0437488	−	0.214795i
$417$	−17.7415	−	10.7372i	−0.868807	−	0.525803i
$418$	−19.8946	−	60.0269i	−0.973078	−	2.93601i
$419$			13.3838i			0.653840i	0.945052	+	0.326920i	$0.106011\pi$
$419$			13.3838i			0.653840i	−0.945052	+	0.326920i	$0.893989\pi$
$420$	4.97985	−	21.2612i	0.242992	−	1.03744i
$421$	−7.88320	+	1.24858i	−0.384204	+	0.0608519i	−0.345549	−	0.938401i	$-0.612307\pi$
$421$	−7.88320	+	1.24858i	−0.384204	+	0.0608519i	−0.0386548	+	0.999253i	$0.512307\pi$
$422$	17.7040	+	2.80404i	0.861818	+	0.136498i
$423$	2.15133	−	3.03116i	0.104601	−	0.147380i
$424$	41.2657	−	21.0259i	2.00404	−	1.02111i
$425$	−12.3658	−	17.0200i	−0.599828	−	0.825592i
$426$	−39.1802	+	16.4841i	−1.89829	+	0.798655i
$427$	−8.07802	+	15.8540i	−0.390923	+	0.767229i
$428$	18.2482			0.882060
$429$	−0.954725	−	20.6903i	−0.0460946	−	0.998937i
$430$	−17.4107			−0.839619
$431$	0.636248	−	1.24871i	0.0306470	−	0.0601481i	−0.875175	−	0.483806i	$-0.839254\pi$
$431$	0.636248	−	1.24871i	0.0306470	−	0.0601481i	0.905822	+	0.423658i	$0.139254\pi$
$432$	−15.6965	+	19.0096i	−0.755200	+	0.914600i
$433$	−3.48067	−	4.79074i	−0.167271	−	0.230228i	0.717150	−	0.696919i	$-0.245446\pi$
$433$	−3.48067	−	4.79074i	−0.167271	−	0.230228i	−0.884421	+	0.466691i	$0.845446\pi$
$434$	−52.5104	+	26.7554i	−2.52058	+	1.28430i
$435$	−0.354467	+	4.84737i	−0.0169954	+	0.232414i
$436$	8.51351	+	1.34841i	0.407723	+	0.0645770i
$437$	16.5893	−	2.62749i	0.793575	−	0.125690i
$438$	−50.1389	−	11.7437i	−2.39573	−	0.561135i
$439$			24.2027i			1.15513i	0.816345	+	0.577565i	$0.195997\pi$
$439$			24.2027i			1.15513i	−0.816345	+	0.577565i	$0.804003\pi$
$440$	5.68548	−	17.8544i	0.271044	−	0.851174i
$441$	−2.86314	+	1.49906i	−0.136340	+	0.0713837i
$442$	9.75006	−	47.8703i	0.463763	−	2.27696i
$443$	−1.86532	+	2.56739i	−0.0886241	+	0.121981i	−0.851027	−	0.525122i	$-0.824020\pi$
$443$	−1.86532	+	2.56739i	−0.0886241	+	0.121981i	0.762403	+	0.647103i	$0.224020\pi$
$444$	3.65376	−	4.32635i	0.173400	−	0.205319i
$445$	−2.27257	+	6.99425i	−0.107730	+	0.331559i
$446$	2.33801	−	7.19566i	0.110708	−	0.340724i
$447$	11.3644	+	9.59769i	0.537519	+	0.453955i
$448$	18.0234	−	2.85463i	0.851526	−	0.134868i
$449$	26.0845	+	13.2907i	1.23100	+	0.627228i	0.943761	−	0.330630i	$-0.107261\pi$
$449$	26.0845	+	13.2907i	1.23100	+	0.627228i	0.287244	+	0.957858i	$0.407261\pi$
$450$	27.2151	+	8.51027i	1.28293	+	0.401178i
$451$	22.1228	+	21.8644i	1.04172	+	1.02955i
$452$	1.42894			0.0672118
$453$	−10.2709	+	6.37263i	−0.482570	+	0.299412i
$454$	42.6603	−	58.7169i	2.00215	−	2.75572i
$455$	−8.62978	−	6.86747i	−0.404570	−	0.321952i
$456$	45.7986	+	53.0252i	2.14472	+	2.48313i
$457$	0.0173949	+	0.0341394i	0.000813698	+	0.00159697i	0.891413	−	0.453192i	$-0.149715\pi$
$457$	0.0173949	+	0.0341394i	0.000813698	+	0.00159697i	−0.890599	+	0.454789i	$0.849715\pi$
$458$	2.06432	+	2.84129i	0.0964592	+	0.132765i
$459$	−18.1181	+	21.9423i	−0.845680	+	1.02418i
$460$	8.61455	+	4.38933i	0.401655	+	0.204654i
$461$	10.9046	+	10.9046i	0.507878	+	0.507878i	0.913875	−	0.405996i	$-0.133075\pi$
$461$	10.9046	+	10.9046i	0.507878	+	0.507878i	−0.405996	+	0.913875i	$0.633075\pi$
$462$	−37.1407	+	15.8835i	−1.72794	+	0.738965i
$463$	3.81940	+	3.81940i	0.177502	+	0.177502i	0.790266	−	0.612764i	$-0.209942\pi$
$463$	3.81940	+	3.81940i	0.177502	+	0.177502i	−0.612764	+	0.790266i	$0.709942\pi$
$464$	11.7642	−	3.82243i	0.546141	−	0.177452i
$465$	6.05890	+	14.4011i	0.280975	+	0.667836i
$466$	10.9513	+	1.73452i	0.507311	+	0.0803501i
$467$	6.16518	−	18.9745i	0.285291	−	0.878034i	−0.701021	−	0.713141i	$-0.747272\pi$
$467$	6.16518	−	18.9745i	0.285291	−	0.878034i	0.986311	−	0.164893i	$-0.0527280\pi$
$468$	18.9278	+	40.3644i	0.874938	+	1.86584i
$469$	−9.03449	+	6.56394i	−0.417174	+	0.303094i
$470$	−0.516134	−	3.25874i	−0.0238075	−	0.150315i
$471$	1.16455	−	4.97195i	0.0536594	−	0.229096i
$472$			30.4194i			1.40016i
$473$	12.8488	+	17.4682i	0.590791	+	0.803187i
$474$	0.103219	+	0.419676i	0.00474102	+	0.0192764i
$475$	13.4403	−	26.3781i	0.616684	−	1.21031i
$476$	−63.3587	+	10.0350i	−2.90404	+	0.459955i
$477$	−11.7544	+	23.7157i	−0.538195	+	1.08587i
$478$	42.3988	+	13.7762i	1.93927	+	0.630108i
$479$	10.2229	+	20.0635i	0.467095	+	0.916725i	0.997613	+	0.0690514i	$0.0219972\pi$
$479$	10.2229	+	20.0635i	0.467095	+	0.916725i	−0.530519	+	0.847673i	$0.678003\pi$
$480$	0.194139	+	2.30343i	0.00886120	+	0.105137i
$481$	−1.18549	−	2.60281i	−0.0540537	−	0.118678i
$482$	7.01590	−	2.27960i	0.319565	−	0.103833i
$483$	−2.56240	−	10.4184i	−0.116593	−	0.474052i
$484$	−42.9510	+	14.5158i	−1.95232	+	0.659809i
$485$	−8.23774			−0.374057
$486$	1.95920	−	38.5190i	0.0888710	−	1.74726i
$487$	−1.29536	+	0.205164i	−0.0586982	+	0.00929688i	−0.185714	−	0.982604i	$-0.559460\pi$
$487$	−1.29536	+	0.205164i	−0.0586982	+	0.00929688i	0.127016	+	0.991901i	$0.459460\pi$
$488$	5.14107	−	32.4594i	0.232725	−	1.46937i
$489$	−24.5423	−	1.79467i	−1.10984	−	0.0811578i
$490$	−0.886477	+	2.72830i	−0.0400470	+	0.123252i
$491$	8.94967	−	6.50232i	0.403893	−	0.293445i	−0.367232	−	0.930129i	$-0.619694\pi$
$491$	8.94967	−	6.50232i	0.403893	−	0.293445i	0.771125	+	0.636684i	$0.219694\pi$
$492$	−61.9946	−	25.2772i	−2.79493	−	1.13959i
$493$	13.5791	−	4.41213i	0.611574	−	0.198712i
$494$	66.2505	−	18.3575i	2.98075	−	0.825944i
$495$	3.48151	+	10.1271i	0.156482	+	0.455181i
$496$	28.1167	−	28.1167i	1.26248	−	1.26248i
$497$	26.8103	−	8.71121i	1.20261	−	0.390751i
$498$	27.8553	−	11.7194i	1.24822	−	0.525158i
$499$	2.48403	−	15.6835i	0.111200	−	0.702091i	−0.867598	−	0.497266i	$-0.834337\pi$
$499$	2.48403	−	15.6835i	0.111200	−	0.702091i	0.978799	−	0.204825i	$-0.0656626\pi$
$500$	34.9465	−	17.8061i	1.56286	−	0.796315i
$501$	2.09929	−	28.7079i	0.0937892	−	1.28258i
$502$	33.2973	+	5.27377i	1.48613	+	0.235380i
$503$	−24.7343	+	34.0439i	−1.10285	+	1.51794i	−0.271295	+	0.962496i	$0.587452\pi$
$503$	−24.7343	+	34.0439i	−1.10285	+	1.51794i	−0.831554	+	0.555444i	$0.812548\pi$
$504$	31.2943	−	31.9961i	1.39396	−	1.42522i
$505$	0.428828	+	0.428828i	0.0190826	+	0.0190826i
$506$	−2.90158	−	17.6481i	−0.128991	−	0.784552i
$507$	22.5165	+	0.0813631i	0.999993	+	0.00361346i
$508$	8.19105	+	25.2095i	0.363419	+	1.11849i
$509$	2.94485	+	18.5930i	0.130528	+	0.824122i	0.962891	+	0.269891i	$0.0869876\pi$
$509$	2.94485	+	18.5930i	0.130528	+	0.824122i	−0.832363	+	0.554231i	$0.813012\pi$
$510$	2.12133	+	25.1692i	0.0939340	+	1.11451i
$511$	32.4802	+	10.5534i	1.43684	+	0.466857i
$512$	−39.1380	+	19.9418i	−1.72967	+	0.881311i
$513$	−39.0870	−	8.69906i	−1.72573	−	0.384073i
$514$	5.34236	+	33.7303i	0.235641	+	1.48778i
$515$	17.3290	+	8.82955i	0.763606	+	0.389076i
$516$	−39.9316	−	24.1666i	−1.75789	−	1.06388i
$517$	−2.88860	+	2.92274i	−0.127040	+	0.128542i
$518$	−3.94416	+	3.94416i	−0.173296	+	0.173296i
$519$	3.63264	−	15.5093i	0.159455	−	0.680784i
$520$	19.0786	+	7.13787i	0.836650	+	0.313016i
$521$	−6.54308	−	9.00577i	−0.286657	−	0.394550i	0.641267	−	0.767318i	$-0.278409\pi$
$521$	−6.54308	−	9.00577i	−0.286657	−	0.394550i	−0.927925	+	0.372767i	$0.878409\pi$
$522$	−11.2007	+	15.7815i	−0.490240	+	0.690736i
$523$	7.41742	−	22.8285i	0.324341	−	0.998220i	−0.647396	−	0.762154i	$-0.724142\pi$
$523$	7.41742	−	22.8285i	0.324341	−	0.998220i	0.971737	−	0.236066i	$-0.0758581\pi$
$524$	−33.1556	+	24.0889i	−1.44841	+	1.05233i
$525$	−17.5111	−	7.13984i	−0.764245	−	0.311608i
$526$	−61.7382	−	31.4572i	−2.69191	−	1.37160i
$527$	32.4543	−	32.4543i	1.41373	−	1.41373i
$528$	20.5209	−	17.9358i	0.893058	−	0.780556i
$529$	−18.2497			−0.793465
$530$	7.26028	+	22.3449i	0.315367	+	0.970598i
$531$	−10.3740	−	13.9506i	−0.450193	−	0.605406i
$532$	−53.0598	−	73.0305i	−2.30043	−	3.16627i
$533$	−24.9351	+	22.8389i	−1.08006	+	0.989263i
$534$	−22.1605	+	19.1403i	−0.958979	+	0.828284i
$535$	−0.745439	+	4.70652i	−0.0322281	+	0.203481i
$536$	12.1235	−	16.6865i	0.523655	−	0.720749i
$537$	−1.78440	+	7.61838i	−0.0770025	+	0.328757i
$538$	−32.1583	+	32.1583i	−1.38644	+	1.38644i
$539$	3.39151	−	1.12404i	0.146082	−	0.0484159i
$540$	−15.2593	−	17.2761i	−0.656655	−	0.743443i
$541$	0.974600	−	1.91276i	0.0419013	−	0.0822360i	−0.869107	−	0.494625i	$-0.835305\pi$
$541$	0.974600	−	1.91276i	0.0419013	−	0.0822360i	0.911008	+	0.412389i	$0.135305\pi$
$542$	40.0269	−	55.0924i	1.71930	−	2.36642i
$543$	−1.69752	−	20.1408i	−0.0728474	−	0.864323i
$544$	6.05055	−	3.08291i	0.259415	−	0.132179i
$545$	−0.695555	+	2.14070i	−0.0297943	+	0.0916974i
$546$	−15.2389	−	41.1845i	−0.652167	−	1.76253i
$547$	−34.2446	−	24.8802i	−1.46419	−	1.06380i	−0.982246	−	0.187600i	$-0.939929\pi$
$547$	−34.2446	−	24.8802i	−1.46419	−	1.06380i	−0.481949	−	0.876199i	$-0.660071\pi$
$548$	−32.6716	+	64.1217i	−1.39566	+	2.73914i
$549$	8.71198	+	16.6395i	0.371818	+	0.710157i
$550$	−28.1718	−	14.1464i	−1.20125	−	0.603203i
$551$	14.2073	+	14.2073i	0.605252	+	0.605252i
$552$	10.4474	+	16.8383i	0.444669	+	0.716685i
$553$	−0.0448373	−	0.283092i	−0.00190668	−	0.0120383i
$554$	8.65765	−	54.6623i	0.367828	−	2.32238i
$555$	0.966582	+	1.11910i	0.0410291	+	0.0475031i
$556$	−46.9322	−	15.2492i	−1.99037	−	0.646710i
$557$	−4.73605	+	29.9022i	−0.200673	+	1.26700i	0.657428	+	0.753517i	$0.271644\pi$
$557$	−4.73605	+	29.9022i	−0.200673	+	1.26700i	−0.858101	+	0.513481i	$0.828356\pi$
$558$	−9.04976	+	61.5473i	−0.383107	+	2.60550i
$559$	−19.6607	+	13.0070i	−0.831558	+	0.550139i
$560$		−	14.5123i		−	0.613258i
$561$	23.6867	−	20.7028i	1.00006	−	0.874074i
$562$	21.8055			0.919808
$563$	−3.02472	−	9.30912i	−0.127477	−	0.392333i	0.866868	−	0.498538i	$-0.166130\pi$
$563$	−3.02472	−	9.30912i	−0.127477	−	0.392333i	−0.994344	+	0.106206i	$0.966130\pi$
$564$	3.33948	−	8.19037i	0.140618	−	0.344877i
$565$	−0.0583724	+	0.368549i	−0.00245574	+	0.0155050i
$566$	−22.3921	−	43.9469i	−0.941209	−	1.84723i
$567$	−3.44017	+	25.3461i	−0.144473	+	1.06444i
$568$	−42.1228	+	30.6040i	−1.76743	+	1.28411i
$569$	15.0326	+	10.9219i	0.630201	+	0.457868i	0.856470	−	0.516197i	$-0.172653\pi$
$569$	15.0326	+	10.9219i	0.630201	+	0.457868i	−0.226269	+	0.974065i	$0.572653\pi$
$570$	−30.2029	+	18.7395i	−1.26506	+	0.784910i
$571$		−	24.8769i		−	1.04106i	−0.853842	−	0.520532i	$-0.825733\pi$
$571$		−	24.8769i		−	1.04106i	0.853842	−	0.520532i	$-0.174267\pi$
$572$	−13.4400	−	47.4193i	−0.561956	−	1.98270i
$573$	−3.31586	+	5.47895i	−0.138522	+	0.228886i
$574$	58.7582	+	29.9388i	2.45252	+	1.24962i
$575$	4.92145	−	6.77380i	0.205239	−	0.282487i
$576$	8.55402	−	17.2586i	0.356417	−	0.719110i
$577$	16.1259	+	31.6488i	0.671329	+	1.31756i	0.935584	+	0.353105i	$0.114874\pi$
$577$	16.1259	+	31.6488i	0.671329	+	1.31756i	−0.264254	+	0.964453i	$0.585126\pi$
$578$	28.6366	−	14.5911i	1.19113	−	0.606909i
$579$	2.76292	+	2.33339i	0.114823	+	0.0969724i
$580$	1.80926	+	11.4232i	0.0751256	+	0.474324i
$581$	−19.0609	+	6.19325i	−0.790778	+	0.256939i
$582$	−28.0613	−	16.9827i	−1.16318	−	0.703956i
$583$	17.0606	−	23.7744i	0.706578	−	0.984635i
$584$	−63.0776			−2.61017
$585$	−11.1839	+	3.23291i	−0.462396	+	0.133664i
$586$	1.55276	+	1.12815i	0.0641439	+	0.0466033i
$587$	−46.1226	−	7.30510i	−1.90368	−	0.301514i	−0.910079	−	0.414436i	$-0.863979\pi$
$587$	−46.1226	−	7.30510i	−1.90368	−	0.301514i	−0.993604	+	0.112922i	$0.963979\pi$
$588$	−5.82011	+	5.02691i	−0.240017	+	0.207306i
$589$	61.4264	+	19.9586i	2.53103	+	0.822381i
$590$	−15.2417	−	2.41404i	−0.627489	−	0.0993846i
$591$	4.85887	−	11.9168i	0.199867	−	0.490191i
$592$	1.70856	−	3.35324i	0.0702215	−	0.137817i
$593$	−24.0919	+	24.0919i	−0.989337	+	0.989337i	−0.999944	−	0.0106070i	$-0.996624\pi$
$593$	−24.0919	+	24.0919i	−0.989337	+	0.989337i	0.0106070	+	0.999944i	$0.496624\pi$
$594$	−9.01831	+	41.6748i	−0.370026	+	1.70994i
$595$		−	16.7512i		−	0.686733i
$596$	31.5387	+	16.0698i	1.29187	+	0.658243i
$597$	−32.5410	+	13.6908i	−1.33181	+	0.560326i
$598$	19.3185	−	2.19685i	0.789994	−	0.0898360i
$599$	6.73113	+	2.18708i	0.275027	+	0.0893615i	0.443283	−	0.896382i	$-0.353814\pi$
$599$	6.73113	+	2.18708i	0.275027	+	0.0893615i	−0.168256	+	0.985743i	$0.553814\pi$
$600$	34.8347	+	2.54731i	1.42212	+	0.103994i
$601$	19.0837	−	13.8652i	0.778442	−	0.565571i	−0.126069	−	0.992021i	$-0.540236\pi$
$601$	19.0837	−	13.8652i	0.778442	−	0.565571i	0.904511	+	0.426450i	$0.140236\pi$
$602$	37.1947	+	27.0235i	1.51594	+	1.10140i
$603$	0.130703	+	11.7871i	0.00532263	+	0.480009i
$604$	−20.3385	+	20.3385i	−0.827561	+	0.827561i
$605$	−1.98932	−	11.6708i	−0.0808775	−	0.474484i
$606$	0.576712	+	2.34483i	0.0234273	+	0.0952523i
$607$	9.39526	+	28.9156i	0.381342	+	1.17365i	0.939099	+	0.343646i	$0.111662\pi$
$607$	9.39526	+	28.9156i	0.381342	+	1.17365i	−0.557758	+	0.830004i	$0.688338\pi$
$608$	7.73094	+	5.61686i	0.313531	+	0.227794i
$609$	8.28096	−	9.80532i	0.335561	−	0.397332i
$610$	15.8559	+	5.15188i	0.641985	+	0.208594i
$611$	−3.01735	−	3.29428i	−0.122069	−	0.133272i
$612$	−30.0704	+	60.6703i	−1.21552	+	2.45245i
$613$	−30.6248	+	4.85049i	−1.23692	+	0.195910i	−0.740432	−	0.672131i	$-0.765379\pi$
$613$	−30.6248	+	4.85049i	−1.23692	+	0.195910i	−0.496493	+	0.868041i	$0.665379\pi$
$614$	−1.72687	+	0.561095i	−0.0696909	+	0.0226439i
$615$	9.05191	−	14.9569i	0.365008	−	0.603119i
$616$	−39.8581	+	29.3180i	−1.60593	+	1.18125i
$617$	−1.95568	−	1.95568i	−0.0787325	−	0.0787325i	0.666644	−	0.745376i	$-0.267730\pi$
$617$	−1.95568	−	1.95568i	−0.0787325	−	0.0787325i	−0.745376	+	0.666644i	$0.767730\pi$
$618$	40.8272	+	65.8022i	1.64231	+	2.64695i
$619$	6.70728	+	42.3481i	0.269588	+	1.70211i	0.636022	+	0.771671i	$0.280579\pi$
$619$	6.70728	+	42.3481i	0.269588	+	1.70211i	−0.366434	+	0.930444i	$0.619421\pi$
$620$	21.8529	+	30.0780i	0.877635	+	1.20796i
$621$	−10.5337	−	4.15932i	−0.422701	−	0.166908i
$622$	−47.9539	+	24.4337i	−1.92278	+	0.979703i
$623$	15.7108	−	11.4146i	0.629441	−	0.457316i
$624$	18.3654	+	23.2501i	0.735203	+	0.930751i
$625$	−2.77069	−	8.52730i	−0.110828	−	0.341092i
$626$	−55.3714	−	55.3714i	−2.21309	−	2.21309i
$627$	41.0906	+	16.4731i	1.64100	+	0.657871i
$628$		−	12.1515i		−	0.484897i
$629$	1.97215	−	3.87056i	0.0786347	−	0.154329i
$630$	13.5482	+	18.2192i	0.539774	+	0.725871i
$631$	29.0291	+	4.59776i	1.15563	+	0.183034i	0.704687	−	0.709519i	$-0.251088\pi$
$631$	29.0291	+	4.59776i	1.15563	+	0.183034i	0.450944	+	0.892552i	$0.351088\pi$
$632$	0.240335	+	0.471684i	0.00956001	+	0.0187626i
$633$	−9.49636	+	8.20215i	−0.377447	+	0.326006i
$634$	29.1712	+	40.1507i	1.15854	+	1.59459i
$635$	−6.83655	+	1.08280i	−0.271300	+	0.0429698i
$636$	−14.3639	+	61.3256i	−0.569564	+	2.43172i
$637$	1.03719	+	3.74313i	0.0410951	+	0.148308i
$638$	15.0392	−	15.2170i	0.595408	−	0.602446i
$639$	8.88097	−	28.4005i	0.351326	−	1.12351i
$640$	−6.10837	−	18.7996i	−0.241454	−	0.743120i
$641$	−19.8012	−	14.3864i	−0.782102	−	0.568231i	0.123507	−	0.992344i	$-0.460586\pi$
$641$	−19.8012	−	14.3864i	−0.782102	−	0.568231i	−0.905609	+	0.424113i	$0.860586\pi$
$642$	−12.2421	+	14.4956i	−0.483158	+	0.572098i
$643$	22.4634	+	44.0869i	0.885870	+	1.73862i	0.638370	+	0.769729i	$0.279609\pi$
$643$	22.4634	+	44.0869i	0.885870	+	1.73862i	0.247500	+	0.968888i	$0.420391\pi$
$644$	−11.5906	−	22.7478i	−0.456733	−	0.896389i
$645$	7.86419	−	9.31183i	0.309652	−	0.366653i
$646$	84.4747	+	61.3745i	3.32361	+	2.41475i
$647$	7.06052	+	21.7300i	0.277578	+	0.854296i	0.988526	+	0.151052i	$0.0482660\pi$
$647$	7.06052	+	21.7300i	0.277578	+	0.854296i	−0.710948	+	0.703244i	$0.751734\pi$
$648$	−8.42332	−	46.4861i	−0.330899	−	1.82615i
$649$	8.82612	+	17.0735i	0.346455	+	0.670193i
$650$	16.8819	−	29.8237i	0.662165	−	1.16978i
$651$	9.40860	−	40.1694i	0.368752	−	1.57436i
$652$	−57.8360	+	9.16032i	−2.26503	+	0.358746i
$653$	−8.92041	−	12.2779i	−0.349083	−	0.480471i	0.597984	−	0.801508i	$-0.295969\pi$
$653$	−8.92041	−	12.2779i	−0.349083	−	0.480471i	−0.947067	+	0.321037i	$0.895969\pi$
$654$	−6.78256	+	5.85820i	−0.265219	+	0.229074i
$655$	−4.85854	−	9.53542i	−0.189839	−	0.372580i
$656$	−43.9462	−	6.96040i	−1.71581	−	0.271758i
$657$	28.9280	−	21.5115i	1.12859	−	0.839244i
$658$	−3.95534	+	7.76279i	−0.154195	+	0.302625i
$659$			36.6282i			1.42683i	0.700741	+	0.713416i	$0.252853\pi$
$659$			36.6282i			1.42683i	−0.700741	+	0.713416i	$0.747147\pi$
$660$	13.5620	+	21.5743i	0.527901	+	0.839777i
$661$	−18.6569	−	18.6569i	−0.725669	−	0.725669i	0.244085	−	0.969754i	$-0.421513\pi$
$661$	−18.6569	−	18.6569i	−0.725669	−	0.725669i	−0.969754	+	0.244085i	$0.921513\pi$
$662$	−18.3405	−	56.4461i	−0.712822	−	2.19384i
$663$	21.1986	+	26.8370i	0.823287	+	1.04226i
$664$	29.9473	−	21.7580i	1.16218	−	0.844373i
$665$	21.0033	−	10.7017i	0.814473	−	0.414995i
$666$	0.985490	+	5.80481i	0.0381870	+	0.224932i
$667$	3.34008	+	4.59723i	0.129329	+	0.178005i
$668$	−10.7151	−	67.6527i	−0.414581	−	2.61756i
$669$	2.79243	+	4.50063i	0.107962	+	0.174004i
$670$	7.39872	+	7.39872i	0.285837	+	0.285837i
$671$	−6.53251	−	19.7102i	−0.252185	−	0.760903i
$672$	3.16046	−	5.22217i	0.121917	−	0.201450i
$673$	12.9876	−	4.21993i	0.500636	−	0.162666i	−0.0478037	−	0.998857i	$-0.515222\pi$
$673$	12.9876	−	4.21993i	0.500636	−	0.162666i	0.548439	+	0.836190i	$0.315222\pi$
$674$	−22.3586	+	3.54126i	−0.861223	+	0.136404i
$675$	−16.8443	+	10.7116i	−0.648336	+	0.412288i
$676$	52.2127	−	12.0306i	2.00818	−	0.462714i
$677$	38.8399	+	12.6198i	1.49274	+	0.485020i	0.937890	−	0.346933i	$-0.112777\pi$
$677$	38.8399	+	12.6198i	1.49274	+	0.485020i	0.554847	+	0.831952i	$0.312777\pi$
$678$	−0.958632	+	1.13510i	−0.0368160	+	0.0435931i
$679$	17.5984	+	12.7860i	0.675364	+	0.490681i
$680$	9.56074	+	29.4249i	0.366638	+	1.12840i
$681$	12.1346	+	49.3378i	0.465001	+	1.89063i
$682$	20.8679	−	65.5324i	0.799072	−	2.50936i
$683$	4.16252	−	4.16252i	0.159274	−	0.159274i	−0.622971	−	0.782245i	$-0.714074\pi$
$683$	4.16252	−	4.16252i	0.159274	−	0.159274i	0.782245	+	0.622971i	$0.214074\pi$
$684$	−95.2815	+	1.05654i	−3.64318	+	0.0403978i
$685$	−15.2034	−	11.0459i	−0.580893	−	0.422044i
$686$	−33.6933	+	24.4796i	−1.28642	+	0.934637i
$687$	−2.45204	−	0.179307i	−0.0935512	−	0.00684099i
$688$	−29.5015	−	9.58562i	−1.12473	−	0.365448i
$689$	24.8917	+	19.8085i	0.948299	+	0.754644i
$690$	−9.26594	+	3.89840i	−0.352748	+	0.148410i
$691$	31.2803	+	15.9381i	1.18996	+	0.606314i	0.932919	−	0.360087i	$-0.117253\pi$
$691$	31.2803	+	15.9381i	1.18996	+	0.606314i	0.257040	+	0.966401i	$0.417253\pi$
$692$		−	37.9049i		−	1.44093i
$693$	8.28095	−	27.0384i	0.314567	−	1.02710i
$694$	−46.4220	+	46.4220i	−1.76215	+	1.76215i
$695$	5.85021	−	11.4817i	0.221911	−	0.435525i
$696$	−8.94984	+	21.9502i	−0.339243	+	0.832022i
$697$	−50.7260	−	8.03420i	−1.92138	−	0.304317i
$698$	10.3653	+	3.36791i	0.392334	+	0.127477i
$699$	−5.87425	+	5.07368i	−0.222185	+	0.191904i
$700$	−44.4460	−	7.03955i	−1.67990	−	0.266070i
$701$	−36.1628	−	26.2738i	−1.36585	−	0.992348i	−0.998048	−	0.0624436i	$-0.980111\pi$
$701$	−36.1628	−	26.2738i	−1.36585	−	0.992348i	−0.367801	−	0.929904i	$-0.619889\pi$
$702$	−44.7619	−	12.0437i	−1.68943	−	0.454559i
$703$	6.11298			0.230556
$704$	−12.4155	+	17.3014i	−0.467928	+	0.652071i
$705$	1.97602	+	1.19589i	0.0744211	+	0.0450397i
$706$	21.4209	−	6.96006i	0.806185	−	0.261945i
$707$	−0.250517	−	1.58170i	−0.00942166	−	0.0594860i
$708$	−31.6061	−	26.6926i	−1.18783	−	1.00317i
$709$	−15.2629	+	7.77684i	−0.573210	+	0.292065i	−0.716468	−	0.697620i	$-0.754242\pi$
$709$	−15.2629	+	7.77684i	−0.573210	+	0.292065i	0.143257	+	0.989685i	$0.454242\pi$
$710$	−11.9914	−	23.5344i	−0.450028	−	0.883229i
$711$	−0.271080	−	0.134357i	−0.0101663	−	0.00503878i
$712$	−21.0826	+	29.0176i	−0.790102	+	1.08748i
$713$	16.2758	+	8.29291i	0.609532	+	0.310572i
$714$	34.5338	−	57.0618i	1.29240	−	2.13549i
$715$	12.7793	−	1.52933i	0.477917	−	0.0571939i
$716$			18.6194i			0.695839i
$717$	−26.5189	+	16.4538i	−0.990368	+	0.614477i
$718$	−17.1384	−	12.4518i	−0.639598	−	0.464695i
$719$	4.57866	−	3.32659i	0.170755	−	0.124061i	−0.499125	−	0.866530i	$-0.666345\pi$
$719$	4.57866	−	3.32659i	0.170755	−	0.124061i	0.669881	+	0.742469i	$0.266345\pi$
$720$	−12.4923	−	8.86622i	−0.465560	−	0.330425i
$721$	−23.3155	−	45.7593i	−0.868316	−	1.70417i
$722$	−15.6320	+	98.6966i	−0.581763	+	3.67311i
$723$	−1.94978	+	4.78200i	−0.0725131	+	0.177845i
$724$	−14.8628	−	45.7430i	−0.552372	−	1.70003i
$725$	10.0160			0.371983
$726$	17.2836	−	43.8568i	0.641456	−	1.62768i
$727$		−	6.56045i		−	0.243314i	−0.992572	−	0.121657i	$-0.961179\pi$
$727$		−	6.56045i		−	0.243314i	0.992572	−	0.121657i	$-0.0388207\pi$
$728$	−29.6789	−	44.8609i	−1.09997	−	1.66266i
$729$	19.7163	+	18.4464i	0.730233	+	0.683198i
$730$	5.00576	−	31.6051i	0.185271	−	1.16976i
$731$	−34.0528	−	11.0644i	−1.25949	−	0.409233i
$732$	29.2146	+	33.8243i	1.07980	+	1.25018i
$733$	5.20242	−	32.8468i	0.192156	−	1.21322i	−0.683377	−	0.730066i	$-0.739489\pi$
$733$	5.20242	−	32.8468i	0.192156	−	1.21322i	0.875533	−	0.483159i	$-0.160511\pi$
$734$	−4.24848	−	26.8238i	−0.156814	−	0.990086i
$735$	−1.05877	−	1.70645i	−0.0390535	−	0.0629435i
$736$	1.91105	+	1.91105i	0.0704421	+	0.0704421i
$737$	1.96298	−	12.8833i	0.0723074	−	0.474561i
$738$	61.6694	−	32.2884i	2.27008	−	1.18855i
$739$	−7.09702	+	13.9287i	−0.261068	+	0.512375i	−0.983916	−	0.178632i	$-0.942833\pi$
$739$	−7.09702	+	13.9287i	−0.261068	+	0.512375i	0.722848	+	0.691007i	$0.242833\pi$
$740$	2.84678	+	2.06831i	0.104650	+	0.0760324i
$741$	−20.1063	+	43.7248i	−0.738622	+	1.60627i
$742$	19.1717	−	59.0044i	0.703815	−	2.16612i
$743$	−30.2439	+	15.4100i	−1.10954	+	0.565339i	−0.910024	−	0.414556i	$-0.863937\pi$
$743$	−30.2439	+	15.4100i	−1.10954	+	0.565339i	−0.199516	+	0.979895i	$0.563937\pi$
$744$	6.39966	+	75.9310i	0.234623	+	2.78377i
$745$	−5.43302	+	7.47791i	−0.199050	+	0.273969i
$746$	3.01458	−	5.91646i	0.110372	−	0.216617i
$747$	−6.31394	+	20.1914i	−0.231015	+	0.738765i
$748$	43.6450	−	60.8205i	1.59582	−	2.22382i
$749$	8.89757	−	8.89757i	0.325110	−	0.325110i
$750$	−9.29999	+	39.7057i	−0.339587	+	1.44985i
$751$	1.94937	−	2.68308i	0.0711336	−	0.0979069i	−0.771968	−	0.635662i	$-0.780727\pi$
$751$	1.94937	−	2.68308i	0.0711336	−	0.0979069i	0.843101	+	0.537755i	$0.180727\pi$
$752$	0.919568	−	5.80593i	0.0335332	−	0.211720i
$753$	−17.8606	+	15.4264i	−0.650875	+	0.562170i
$754$	15.7095	+	17.1514i	0.572108	+	0.624616i
$755$	−4.41481	−	6.07647i	−0.160671	−	0.221145i
$756$	5.78407	+	60.5913i	0.210365	+	2.20368i
$757$	3.19765	+	9.84135i	0.116221	+	0.357690i	0.992200	−	0.124659i	$-0.0397837\pi$
$757$	3.19765	+	9.84135i	0.116221	+	0.357690i	−0.875979	+	0.482349i	$0.839784\pi$
$758$	39.3350			1.42871
$759$	10.7494	+	6.41954i	0.390178	+	0.233015i
$760$	−30.7861	+	30.7861i	−1.11673	+	1.11673i
$761$	47.1222	+	24.0100i	1.70818	+	0.870361i	0.983416	+	0.181363i	$0.0580509\pi$
$761$	47.1222	+	24.0100i	1.70818	+	0.870361i	0.724763	+	0.688998i	$0.241949\pi$
$762$	−25.5205	−	10.4056i	−0.924511	−	0.376954i
$763$	4.80854	−	3.49361i	0.174081	−	0.126477i
$764$	−4.70926	+	14.4936i	−0.170375	+	0.524360i
$765$	−14.4195	−	10.2341i	−0.521339	−	0.370013i
$766$	4.64623	+	6.39498i	0.167875	+	0.231060i
$767$	−19.0148	+	8.66059i	−0.686584	+	0.312716i
$768$	12.8768	−	54.9765i	0.464650	−	1.98379i
$769$	27.3795	−	27.3795i	0.987330	−	0.987330i	−0.0125911	−	0.999921i	$-0.504008\pi$
$769$	27.3795	−	27.3795i	0.987330	−	0.987330i	0.999921	+	0.0125911i	$0.00400797\pi$
$770$	−11.5267	−	22.2976i	−0.415394	−	0.803550i
$771$	−20.4532	−	12.3783i	−0.736603	−	0.445793i
$772$	7.66768	+	3.90688i	0.275966	+	0.140612i
$773$	−6.16497	−	38.9241i	−0.221739	−	1.40000i	−0.807667	−	0.589639i	$-0.799270\pi$
$773$	−6.16497	−	38.9241i	−0.221739	−	1.40000i	0.585928	−	0.810363i	$-0.300730\pi$
$774$	45.9859	−	15.5075i	1.65293	−	0.557406i
$775$	28.6877	−	14.6171i	1.03049	−	0.525061i
$776$	−38.2107	−	12.4154i	−1.37168	−	0.445687i
$777$	−0.327943	−	3.89100i	−0.0117649	−	0.139589i
$778$	−6.08130	−	38.3958i	−0.218025	−	1.37656i
$779$	−22.3333	−	68.7349i	−0.800174	−	2.46268i
$780$	−24.1575	+	13.5595i	−0.864977	+	0.485508i
$781$	−14.7626	+	29.3989i	−0.528246	+	1.05198i
$782$	20.8817	+	20.8817i	0.746728	+	0.746728i
$783$	−3.38126	−	13.1188i	−0.120836	−	0.468827i
$784$	−3.00417	+	4.13489i	−0.107292	+	0.147675i
$785$	3.13408	+	0.496389i	0.111860	+	0.0177169i
$786$	3.10769	−	42.4980i	0.110848	−	1.51585i
$787$	−43.3002	+	22.0626i	−1.54349	+	0.786446i	−0.998642	−	0.0520918i	$-0.983411\pi$
$787$	−43.3002	+	22.0626i	−1.54349	+	0.786446i	−0.544844	+	0.838537i	$0.683411\pi$
$788$	4.79062	−	30.2468i	0.170659	−	1.07750i
$789$	44.7107	−	18.8109i	1.59174	−	0.669684i
$790$	−0.255411	+	0.0829880i	−0.00908710	+	0.00295258i
$791$	0.696734	−	0.696734i	0.0247730	−	0.0247730i
$792$	0.885966	+	52.2217i	0.0314814	+	1.85562i
$793$	21.7537	−	6.02780i	0.772497	−	0.214053i
$794$	−54.3450	+	17.6578i	−1.92863	+	0.626651i
$795$	−15.2302	−	6.20984i	−0.540158	−	0.220240i
$796$	−67.9647	+	49.3792i	−2.40894	+	1.75020i
$797$	1.78783	−	5.50239i	0.0633284	−	0.194905i	−0.914386	−	0.404843i	$-0.867326\pi$
$797$	1.78783	−	5.50239i	0.0633284	−	0.194905i	0.977715	+	0.209938i	$0.0673263\pi$
$798$	93.6087	+	6.84519i	3.31371	+	0.242317i
$799$	1.06143	−	6.70163i	0.0375508	−	0.237087i
$800$	4.70501	−	0.745200i	0.166347	−	0.0263468i
$801$	−0.227290	−	20.4976i	−0.00803091	−	0.724248i
$802$	12.0445			0.425308
$803$	−35.4036	+	18.3018i	−1.24936	+	0.645858i
$804$	6.69936	+	27.2387i	0.236268	+	0.960634i
$805$	6.34052	−	2.06016i	0.223474	−	0.0726111i
$806$	70.0256	+	26.1987i	2.46655	+	0.922809i
$807$	−2.67385	−	31.7248i	−0.0941240	−	1.11677i
$808$	1.34281	+	2.63541i	0.0472399	+	0.0927135i
$809$	−23.5484	−	7.65134i	−0.827918	−	0.269007i	−0.135750	−	0.990743i	$-0.543344\pi$
$809$	−23.5484	−	7.65134i	−0.827918	−	0.269007i	−0.692168	+	0.721736i	$0.743344\pi$
$810$	23.9604	−	0.531440i	0.841882	−	0.0186729i
$811$	11.6504	−	1.84524i	0.409100	−	0.0647951i	0.0515070	−	0.998673i	$-0.483598\pi$
$811$	11.6504	−	1.84524i	0.409100	−	0.0647951i	0.357593	+	0.933878i	$0.383598\pi$
$812$	13.8651	−	27.2118i	0.486570	−	0.954947i
$813$	11.3856	+	46.2922i	0.399310	+	1.62354i
$814$	−0.0382464	−	6.50918i	−0.00134054	−	0.228147i
$815$		−	15.2911i		−	0.535623i
$816$	−10.2627	+	43.8158i	−0.359265	+	1.53386i
$817$	−7.88206	−	49.7653i	−0.275758	−	1.74107i
$818$	27.4493	−	19.9431i	0.959742	−	0.697293i
$819$	28.9101	+	10.4522i	1.01020	+	0.365229i
$820$	12.8557	−	39.5658i	0.448941	−	1.38170i
$821$	−18.1391	−	2.87295i	−0.633058	−	0.100267i	−0.168346	−	0.985728i	$-0.553842\pi$
$821$	−18.1391	−	2.87295i	−0.633058	−	0.100267i	−0.464713	+	0.885461i	$0.653842\pi$
$822$	−29.0174	−	68.9702i	−1.01210	−	2.40561i
$823$	18.3252	−	5.95422i	0.638776	−	0.207551i	0.0283174	−	0.999599i	$-0.490985\pi$
$823$	18.3252	−	5.95422i	0.638776	−	0.207551i	0.610459	+	0.792048i	$0.290985\pi$
$824$	67.0729	+	67.0729i	2.33659	+	2.33659i
$825$	20.2908	−	8.67750i	0.706435	−	0.302112i
$826$	28.8141	+	28.8141i	1.00257	+	1.00257i
$827$	−33.0049	−	16.8168i	−1.14769	−	0.584778i	−0.226548	−	0.974000i	$-0.572744\pi$
$827$	−33.0049	−	16.8168i	−1.14769	−	0.584778i	−0.921144	+	0.389222i	$0.872744\pi$
$828$	−26.6626	−	3.92041i	−0.926590	−	0.136244i
$829$	−17.7389	−	24.4156i	−0.616099	−	0.847987i	0.380963	−	0.924590i	$-0.375593\pi$
$829$	−17.7389	−	24.4156i	−0.616099	−	0.847987i	−0.997062	+	0.0766030i	$0.975593\pi$
$830$	8.52528	+	16.7318i	0.295917	+	0.580769i
$831$	25.3247	+	29.3206i	0.878503	+	1.01712i
$832$	−18.1145	−	14.4153i	−0.628007	−	0.499760i
$833$	−3.46764	+	4.77280i	−0.120147	+	0.165368i
$834$	43.5986	−	27.0509i	1.50970	−	0.936696i
$835$	17.8865			0.618988
$836$	104.142	+	15.8678i	3.60184	+	0.548800i
$837$	−28.8299	−	32.6402i	−0.996507	−	1.12821i
$838$	−29.5047	−	15.0334i	−1.01922	−	0.519321i
$839$	28.4970	−	4.51348i	0.983826	−	0.155823i	0.356261	−	0.934387i	$-0.384051\pi$
$839$	28.4970	−	4.51348i	0.983826	−	0.155823i	0.627566	+	0.778564i	$0.284051\pi$
$840$	21.2474	+	17.9442i	0.733103	+	0.619133i
$841$	6.86092	−	21.1157i	0.236583	−	0.728129i
$842$	6.10236	−	18.7811i	0.210301	−	0.647240i
$843$	−9.84925	+	11.6623i	−0.339226	+	0.401671i
$844$	−17.5511	+	24.1570i	−0.604133	+	0.831517i
$845$	0.969994	+	13.9580i	0.0333688	+	0.480169i
$846$	4.26576	+	8.14741i	0.146660	+	0.280114i
$847$	−13.8646	+	28.0200i	−0.476394	+	0.962780i
$848$			41.8593i			1.43746i
$849$	33.6185	+	7.87422i	1.15378	+	0.270243i
$850$	51.4108	−	8.14268i	1.76338	−	0.279292i
$851$	1.70760	+	0.270457i	0.0585356	+	0.00927113i
$852$	5.16418	−	70.6207i	0.176922	−	2.41942i
$853$	−23.3604	+	11.9027i	−0.799846	+	0.407542i	−0.805613	−	0.592442i	$-0.798164\pi$
$853$	−23.3604	+	11.9027i	−0.799846	+	0.407542i	0.00576770	+	0.999983i	$0.498164\pi$
$854$	−25.8767	−	35.6162i	−0.885483	−	1.21876i
$855$	3.61975	−	24.6179i	0.123793	−	0.841914i
$856$	−10.5511	+	20.7076i	−0.360628	+	0.707773i
$857$	18.6030			0.635466			0.317733	−	0.948180i	$-0.397078\pi$
$857$	18.6030			0.635466			0.317733	+	0.948180i	$0.397078\pi$
$858$	46.6845	+	21.1358i	1.59378	+	0.721565i
$859$	−26.9534			−0.919639			−0.459819	−	0.888012i	$-0.652086\pi$
$859$	−26.9534			−0.919639			−0.459819	+	0.888012i	$0.652086\pi$
$860$	13.1673	−	25.8423i	0.449001	−	0.881214i
$861$	−42.5526	+	17.9029i	−1.45019	+	0.610128i
$862$	2.03812	+	2.80524i	0.0694188	+	0.0955468i
$863$	−28.6654	+	14.6058i	−0.975783	+	0.497186i	−0.867772	−	0.496963i	$-0.834448\pi$
$863$	−28.6654	+	14.6058i	−0.975783	+	0.497186i	−0.108012	+	0.994150i	$0.534448\pi$
$864$	−2.56440	−	5.91099i	−0.0872428	−	0.201096i
$865$	9.77632	+	1.54842i	0.332405	+	0.0526478i
$866$	14.4710	−	2.29197i	0.491743	−	0.0778844i
$867$	−5.13098	+	21.9064i	−0.174257	+	0.743981i
$868$		−	98.1743i		−	3.33225i
$869$	0.271751	+	0.195009i	0.00921852	+	0.00661524i
$870$	−10.2880	−	6.22627i	−0.348794	−	0.211090i
$871$	13.8822	+	2.82748i	0.470381	+	0.0958056i
$872$	−6.45264	+	8.88130i	−0.218514	+	0.300759i
$873$	21.7578	−	7.33725i	0.736392	−	0.248328i
$874$	−12.8417	+	39.5228i	−0.434378	+	1.33688i
$875$	8.35742	−	25.7215i	0.282532	−	0.869545i
$876$	55.3497	−	65.5384i	1.87009	−	2.21434i
$877$	49.0257	−	7.76491i	1.65548	−	0.262202i	0.742393	−	0.669965i	$-0.233691\pi$
$877$	49.0257	−	7.76491i	1.65548	−	0.262202i	0.913088	+	0.407762i	$0.133691\pi$
$878$	−53.3552	−	27.1858i	−1.80065	−	0.917477i
$879$	−1.30473	+	0.320899i	−0.0440075	+	0.0108237i
$880$	12.0454	+	11.9047i	0.406052	+	0.401308i
$881$	−22.5542			−0.759871			−0.379936	−	0.925013i	$-0.624054\pi$
$881$	−22.5542			−0.759871			−0.379936	+	0.925013i	$0.624054\pi$
$882$	−0.0886608	−	7.99566i	−0.00298536	−	0.269228i
$883$	−19.2455	+	26.4891i	−0.647661	+	0.891429i	−0.998995	−	0.0448211i	$-0.985728\pi$
$883$	−19.2455	+	26.4891i	−0.647661	+	0.891429i	0.351334	+	0.936250i	$0.385728\pi$
$884$	63.6789	+	50.6749i	2.14175	+	1.70438i
$885$	8.17557	−	7.06136i	0.274819	−	0.237365i
$886$	−3.56463	−	6.99597i	−0.119756	−	0.235034i
$887$	21.9368	+	30.1934i	0.736565	+	1.01379i	0.998809	+	0.0487930i	$0.0155375\pi$
$887$	21.9368	+	30.1934i	0.736565	+	1.01379i	−0.262244	+	0.965002i	$0.584463\pi$
$888$	2.79684	+	6.64770i	0.0938560	+	0.223082i
$889$	16.2856	+	8.29795i	0.546203	+	0.278304i
$890$	−12.8663	−	12.8663i	−0.431278	−	0.431278i
$891$	−18.2156	−	23.6472i	−0.610246	−	0.792212i
$892$	8.91215	+	8.91215i	0.298401	+	0.298401i
$893$	9.08086	−	2.95055i	0.303880	−	0.0987365i
$894$	−33.9234	+	14.2724i	−1.13457	+	0.477341i
$895$	−4.80225	−	0.760602i	−0.160522	−	0.0254241i
$896$	−16.1299	+	49.6428i	−0.538863	+	1.65845i
$897$	−7.55098	+	11.3245i	−0.252120	+	0.378114i
$898$	−58.5992	+	42.5748i	−1.95548	+	1.42074i
$899$	3.41830	+	21.5823i	0.114007	+	0.719810i
$900$	−33.2137	+	33.9585i	−1.10712	+	1.13195i
$901$			48.3171i			1.60968i
$902$	−73.0500	+	24.2108i	−2.43230	+	0.806132i
$903$	−31.2535	+	7.68680i	−1.04005	+	0.255801i
$904$	−0.826212	+	1.62153i	−0.0274794	+	0.0539314i
$905$	12.4050	−	1.96477i	0.412358	−	0.0653110i
$906$	−2.51167	−	29.8005i	−0.0834445	−	0.990056i
$907$	48.5680	+	15.7807i	1.61267	+	0.523989i	0.970197	−	0.242317i	$-0.0779073\pi$
$907$	48.5680	+	15.7807i	1.61267	+	0.523989i	0.642476	+	0.766306i	$0.277907\pi$
$908$	54.8890	+	107.726i	1.82156	+	3.57500i
$909$	−1.51459	−	0.750685i	−0.0502357	−	0.0248987i
$910$	24.8329	−	11.3106i	0.823203	−	0.374941i
$911$	11.4063	−	3.70614i	0.377908	−	0.122790i	−0.113903	−	0.993492i	$-0.536335\pi$
$911$	11.4063	−	3.70614i	0.377908	−	0.122790i	0.491811	+	0.870702i	$0.336335\pi$
$912$	−61.4943	+	15.1245i	−2.03628	+	0.500823i
$913$	10.4955	−	20.9012i	0.347350	−	0.691730i
$914$	−0.0947997			−0.00313570
$915$	−9.91729	+	6.15321i	−0.327855	+	0.203419i
$916$	−5.77844	+	0.915215i	−0.190925	+	0.0302396i
$917$	−4.42077	+	27.9117i	−0.145987	+	0.921724i
$918$	−28.0208	−	64.5885i	−0.924825	−	2.13174i
$919$	5.24381	−	16.1388i	0.172977	−	0.532369i	−0.826558	−	0.562851i	$-0.809704\pi$
$919$	5.24381	−	16.1388i	0.172977	−	0.532369i	0.999535	+	0.0304823i	$0.00970433\pi$
$920$	−9.96183	+	7.23770i	−0.328432	+	0.238620i
$921$	0.479913	−	1.17703i	0.0158137	−	0.0387844i
$922$	−36.2881	+	11.7907i	−1.19508	+	0.388306i
$923$	−31.1228	−	17.6173i	−1.02442	−	0.579881i
$924$	4.51316	−	67.1392i	0.148472	−	2.20872i
$925$	2.15479	−	2.15479i	0.0708489	−	0.0708489i
$926$	−12.7101	+	4.12976i	−0.417679	+	0.135712i
$927$	−53.6343	−	7.88626i	−1.76158	−	0.259019i
$928$	−0.505751	+	3.19319i	−0.0166021	+	0.104821i
$929$	45.2983	−	23.0806i	1.48619	−	0.757250i	0.492594	−	0.870259i	$-0.336049\pi$
$929$	45.2983	−	23.0806i	1.48619	−	0.757250i	0.993594	+	0.113009i	$0.0360489\pi$
$930$	−38.5532	−	2.81923i	−1.26421	−	0.0924462i
$931$	−8.19966	−	1.29870i	−0.268733	−	0.0425631i
$932$	−10.8567	+	14.9430i	−0.355624	+	0.489474i
$933$	8.59217	−	36.6837i	0.281295	−	1.20097i
$934$	34.9045	+	34.9045i	1.14211	+	1.14211i
$935$	13.9037	+	13.7413i	0.454701	+	0.449389i
$936$	−56.7486	−	1.85978i	−1.85489	−	0.0607888i
$937$	5.78920	+	17.8173i	0.189125	+	0.582067i	0.999995	−	0.00315962i	$-0.00100574\pi$
$937$	5.78920	+	17.8173i	0.189125	+	0.582067i	−0.810870	+	0.585226i	$0.801006\pi$
$938$	−4.32226	−	27.2897i	−0.141127	−	0.891039i
$939$	54.6250	−	4.60394i	1.78262	−	0.150244i
$940$	5.22721	+	1.69842i	0.170493	+	0.0553965i
$941$	21.3153	−	10.8607i	0.694859	−	0.354048i	−0.0706256	−	0.997503i	$-0.522500\pi$
$941$	21.3153	−	10.8607i	0.694859	−	0.354048i	0.765484	+	0.643455i	$0.222500\pi$
$942$	9.65267	+	8.15204i	0.314501	+	0.265608i
$943$	−3.19753	−	20.1884i	−0.104126	−	0.657426i
$944$	−24.4971	−	12.4819i	−0.797312	−	0.406251i
$945$	−15.8638	−	0.983346i	−0.516049	−	0.0319883i
$946$	−52.9414	+	8.70426i	−1.72127	+	0.283000i
$947$	12.7452	−	12.7452i	0.414163	−	0.414163i	−0.469023	−	0.883186i	$-0.655394\pi$
$947$	12.7452	−	12.7452i	0.414163	−	0.414163i	0.883186	+	0.469023i	$0.155394\pi$
$948$	−0.700976	−	0.164185i	−0.0227667	−	0.00533247i
$949$	−17.9586	−	39.4291i	−0.582961	−	1.27992i
$950$	43.0540	+	59.2588i	1.39686	+	1.92261i
$951$	−34.6502	−	2.53382i	−1.12361	−	0.0821646i
$952$	25.2463	−	77.7003i	0.818239	−	2.51828i
$953$	22.9075	−	16.6433i	0.742048	−	0.539129i	−0.151304	−	0.988487i	$-0.548347\pi$
$953$	22.9075	−	16.6433i	0.742048	−	0.539129i	0.893352	+	0.449358i	$0.148347\pi$
$954$	−39.0784	−	52.5515i	−1.26521	−	1.70142i
$955$	−3.54577	−	1.80666i	−0.114739	−	0.0584622i
$956$	−52.5128	+	52.5128i	−1.69838	+	1.69838i
$957$	1.34554	+	14.9168i	0.0434951	+	0.482191i
$958$	−55.7132			−1.80001
$959$	15.3346	+	47.1951i	0.495181	+	1.52401i
$960$	11.0835	+	4.51910i	0.357717	+	0.145853i
$961$	23.0661	+	31.7478i	0.744069	+	1.02412i
$962$	7.06954	+	0.310189i	0.227931	+	0.0100009i
$963$	−2.22315	−	13.0950i	−0.0716401	−	0.421980i
$964$	−1.92239	+	12.1375i	−0.0619162	+	0.390923i
$965$	−1.32088	+	1.81803i	−0.0425205	+	0.0585244i
$966$	25.8457	+	6.05366i	0.831572	+	0.194773i
$967$	18.9926	−	18.9926i	0.610761	−	0.610761i	−0.332383	−	0.943144i	$-0.607853\pi$
$967$	18.9926	−	18.9926i	0.610761	−	0.610761i	0.943144	+	0.332383i	$0.107853\pi$
$968$	8.36197	−	57.1328i	0.268764	−	1.83632i
$969$	−70.9812	+	17.4579i	−2.28025	+	0.560827i
$970$	9.25310	−	18.1602i	0.297099	−	0.583090i
$971$	13.4751	−	18.5469i	0.432437	−	0.595199i	−0.536073	−	0.844171i	$-0.680093\pi$
$971$	13.4751	−	18.5469i	0.432437	−	0.595199i	0.968511	+	0.248973i	$0.0800929\pi$
$972$	55.6910	+	32.0389i	1.78629	+	1.02765i
$973$	−30.3188	+	15.4482i	−0.971976	+	0.495247i
$974$	1.00273	−	3.08609i	0.0321296	−	0.0988846i
$975$	8.32538	+	22.5000i	0.266626	+	0.720578i
$976$	24.0305	+	17.4592i	0.769197	+	0.558854i
$977$	1.12586	−	2.20962i	0.0360194	−	0.0706921i	−0.872295	−	0.488979i	$-0.837369\pi$
$977$	1.12586	−	2.20962i	0.0360194	−	0.0706921i	0.908315	+	0.418287i	$0.137369\pi$
$978$	31.5237	−	52.0880i	1.00802	−	1.66559i
$979$	−3.41360	+	22.4038i	−0.109099	+	0.716029i
$980$	−3.37912	−	3.37912i	−0.107942	−	0.107942i
$981$	−0.0695657	−	6.27361i	−0.00222106	−	0.200301i
$982$	4.28168	+	27.0335i	0.136634	+	0.862673i
$983$	−0.912987	+	5.76437i	−0.0291198	+	0.183855i	−0.997961	−	0.0638280i	$-0.979669\pi$
$983$	−0.912987	+	5.76437i	−0.0291198	+	0.183855i	0.968841	+	0.247683i	$0.0796691\pi$
$984$	64.5292	−	55.7348i	2.05712	−	1.77676i
$985$	7.60546	+	2.47116i	0.242330	+	0.0787378i
$986$	−5.52626	+	34.8914i	−0.175992	+	1.11117i
$987$	−2.36523	−	5.62180i	−0.0752860	−	0.178944i
$988$	−22.8560	+	112.217i	−0.727147	+	3.57011i
$989$		−	14.2501i		−	0.453128i
$990$	−26.2361	−	3.70033i	−0.833837	−	0.117604i
$991$	10.1488			0.322387			0.161194	−	0.986923i	$-0.448466\pi$
$991$	10.1488			0.322387			0.161194	+	0.986923i	$0.448466\pi$
$992$	3.21150	+	9.88399i	0.101965	+	0.313817i
$993$	38.4734	+	15.6869i	1.22092	+	0.497808i
$994$	−10.9109	+	68.8888i	−0.346073	+	2.18502i
$995$	−9.95938	−	19.5464i	−0.315734	−	0.619662i
$996$	−3.67149	+	50.2079i	−0.116335	+	1.59090i
$997$	19.3223	−	14.0385i	0.611944	−	0.444603i	−0.238155	−	0.971227i	$-0.576542\pi$
$997$	19.3223	−	14.0385i	0.611944	−	0.444603i	0.850098	+	0.526624i	$0.176542\pi$
$998$	31.7844	+	23.0927i	1.00612	+	0.730987i
$999$	−3.54974	−	2.09489i	−0.112309	−	0.0662792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.5	✓	416
3.2	odd	2	inner	429.2.bi.a.5.48	yes	416
11.9	even	5	inner	429.2.bi.a.317.48	yes	416
13.8	odd	4	inner	429.2.bi.a.203.5	yes	416
33.20	odd	10	inner	429.2.bi.a.317.5	yes	416
39.8	even	4	inner	429.2.bi.a.203.48	yes	416
143.86	odd	20	inner	429.2.bi.a.86.48	yes	416
429.86	even	20	inner	429.2.bi.a.86.5	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.5	✓	416	1.1	even	1	trivial
429.2.bi.a.5.48	yes	416	3.2	odd	2	inner
429.2.bi.a.86.5	yes	416	429.86	even	20	inner
429.2.bi.a.86.48	yes	416	143.86	odd	20	inner
429.2.bi.a.203.5	yes	416	13.8	odd	4	inner
429.2.bi.a.203.48	yes	416	39.8	even	4	inner
429.2.bi.a.317.5	yes	416	33.20	odd	10	inner
429.2.bi.a.317.48	yes	416	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12326 + 2.20452i) q^{2} +(-0.671689 - 1.59651i) q^{3} +(-2.42261 - 3.33444i) q^{4} +(0.958973 - 0.488621i) q^{5} +(4.27400 + 0.312539i) q^{6} +(-2.80706 - 0.444595i) q^{7} +(5.18460 - 0.821160i) q^{8} +(-2.09767 + 2.14471i) q^{9} +O(q^{10})\)	\(q+(-1.12326 + 2.20452i) q^{2} +(-0.671689 - 1.59651i) q^{3} +(-2.42261 - 3.33444i) q^{4} +(0.958973 - 0.488621i) q^{5} +(4.27400 + 0.312539i) q^{6} +(-2.80706 - 0.444595i) q^{7} +(5.18460 - 0.821160i) q^{8} +(-2.09767 + 2.14471i) q^{9} +2.66292i q^{10} +(2.67171 - 1.96520i) q^{11} +(-3.69622 + 6.10743i) q^{12} +(1.98939 + 3.00705i) q^{13} +(4.13317 - 5.68882i) q^{14} +(-1.42422 - 1.20281i) q^{15} +(-1.46609 + 4.51217i) q^{16} +(-1.69227 + 5.20828i) q^{17} +(-2.37183 - 7.03341i) q^{18} +(-7.61147 + 1.20554i) q^{19} +(-3.95250 - 2.01390i) q^{20} +(1.17567 + 4.78013i) q^{21} +(1.33129 + 8.09724i) q^{22} -2.17952 q^{23} +(-4.79343 - 7.72569i) q^{24} +(-2.25805 + 3.10794i) q^{25} +(-8.86368 + 1.00795i) q^{26} +(4.83303 + 1.90837i) q^{27} +(5.31796 + 10.4371i) q^{28} +(-1.53249 - 2.10929i) q^{29} +(4.25137 - 1.78865i) q^{30} +(-7.46760 - 3.80493i) q^{31} +(-0.876821 - 0.876821i) q^{32} +(-4.93200 - 2.94540i) q^{33} +(-9.58088 - 9.58088i) q^{34} +(-2.90914 + 0.945237i) q^{35} +(12.2333 + 1.79875i) q^{36} +(-0.783474 - 0.124090i) q^{37} +(5.89201 - 18.1337i) q^{38} +(3.46452 - 5.19587i) q^{39} +(4.57066 - 3.32078i) q^{40} +(1.46708 + 9.26280i) q^{41} +(-11.8585 - 2.77752i) q^{42} +6.53820i q^{43} +(-13.0253 - 4.14774i) q^{44} +(-0.963657 + 3.08169i) q^{45} +(2.44816 - 4.80478i) q^{46} +(-1.22375 + 0.193823i) q^{47} +(8.18847 - 0.690146i) q^{48} +(1.02455 + 0.332897i) q^{49} +(-4.31513 - 8.46891i) q^{50} +(9.45174 - 0.796617i) q^{51} +(5.20730 - 13.9184i) q^{52} +(8.39111 - 2.72644i) q^{53} +(-9.63575 + 8.51090i) q^{54} +(1.60186 - 3.19002i) q^{55} -14.9186 q^{56} +(7.03719 + 11.3420i) q^{57} +(6.37134 - 1.00912i) q^{58} +(-0.906540 + 5.72367i) q^{59} +(-0.560356 + 7.66291i) q^{60} +(1.93467 - 5.95432i) q^{61} +(16.7761 - 12.1885i) q^{62} +(6.84182 - 5.08773i) q^{63} +(-6.10648 + 1.98412i) q^{64} +(3.37708 + 1.91162i) q^{65} +(12.0331 - 7.56424i) q^{66} +(2.77842 - 2.77842i) q^{67} +(21.4664 - 6.97487i) q^{68} +(1.46396 + 3.47961i) q^{69} +(1.18392 - 7.47499i) q^{70} +(-8.83781 + 4.50309i) q^{71} +(-9.11443 + 12.8420i) q^{72} +(-11.8686 - 1.87980i) q^{73} +(1.15360 - 1.58780i) q^{74} +(6.47854 + 1.51742i) q^{75} +(22.4595 + 22.4595i) q^{76} +(-8.37337 + 4.32860i) q^{77} +(7.56284 + 13.4739i) q^{78} +(0.0311643 + 0.0959138i) q^{79} +(0.798799 + 5.04342i) q^{80} +(-0.199571 - 8.99779i) q^{81} +(-22.0679 - 7.17030i) q^{82} +(6.28326 - 3.20148i) q^{83} +(13.0909 - 15.5006i) q^{84} +(0.922032 + 5.82148i) q^{85} +(-14.4136 - 7.34409i) q^{86} +(-2.33814 + 3.86341i) q^{87} +(12.2380 - 12.3827i) q^{88} +(-4.83163 + 4.83163i) q^{89} +(-5.71119 - 5.58592i) q^{90} +(-4.24743 - 9.32545i) q^{91} +(5.28013 + 7.26748i) q^{92} +(-1.05870 + 14.4778i) q^{93} +(0.947299 - 2.91549i) q^{94} +(-6.71014 + 4.87521i) q^{95} +(-0.810900 + 1.98880i) q^{96} +(-6.81967 - 3.47480i) q^{97} +(-1.88471 + 1.88471i) q^{98} +(-1.38958 + 9.85236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

Modular forms

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