LMFDB - Embedded newform 783.2.bf.a.4.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(4,783)] 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("783.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(126)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.bf (of order $126$, degree $36$, 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:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$88$ over $\Q(\zeta_{126})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{126}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	783.4
Dual form			783.2.bf.a.196.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59066 - 1.02736i) q^{2} +(-1.56230 - 0.747815i) q^{3} +(0.652159 + 1.44533i) q^{4} +(-3.66732 - 1.54591i) q^{5} +(1.71681 + 2.79455i) q^{6} +(0.987458 - 2.18843i) q^{7} +(-0.116938 + 0.775835i) q^{8} +(1.88155 + 2.33662i) q^{9} +(4.24526 + 6.22665i) q^{10} +(3.41430 + 3.01313i) q^{11} +(0.0619752 - 2.74573i) q^{12} +(-4.22734 - 2.58327i) q^{13} +(-3.81901 + 2.46658i) q^{14} +(4.57339 + 5.15764i) q^{15} +(3.08148 - 3.49174i) q^{16} +(4.07762 + 2.35422i) q^{17} +(-0.592357 - 5.64978i) q^{18} +(7.97879 - 0.597928i) q^{19} +(-0.157329 - 6.30867i) q^{20} +(-3.17925 + 2.68055i) q^{21} +(-2.33542 - 8.30056i) q^{22} +(-1.32451 + 2.58354i) q^{23} +(0.762874 - 1.12464i) q^{24} +(7.56823 + 7.75933i) q^{25} +(4.07031 + 8.45209i) q^{26} +(-1.19218 - 5.05754i) q^{27} +3.80699 q^{28} +(-5.18388 - 1.45854i) q^{29} +(-1.97597 - 12.9025i) q^{30} +(3.62214 + 4.78189i) q^{31} +(-6.97829 + 1.96339i) q^{32} +(-3.08088 - 7.26067i) q^{33} +(-4.06749 - 7.93393i) q^{34} +(-7.00444 + 6.49917i) q^{35} +(-2.15012 + 4.24331i) q^{36} +(-0.0532242 + 0.0208889i) q^{37} +(-13.3058 - 7.24596i) q^{38} +(4.67255 + 7.19711i) q^{39} +(1.62822 - 2.66446i) q^{40} +(0.898138 + 2.46761i) q^{41} +(7.81097 - 0.997615i) q^{42} +(1.43109 + 3.39496i) q^{43} +(-2.12832 + 6.89984i) q^{44} +(-3.28804 - 11.4778i) q^{45} +(4.76105 - 2.74880i) q^{46} +(1.18620 - 5.86780i) q^{47} +(-7.42536 + 3.15076i) q^{48} +(0.817638 + 0.926497i) q^{49} +(-4.06688 - 20.1177i) q^{50} +(-4.60994 - 6.72730i) q^{51} +(0.976793 - 7.79462i) q^{52} +(-0.218983 + 0.959425i) q^{53} +(-3.29955 + 9.26961i) q^{54} +(-7.86330 - 16.3283i) q^{55} +(1.58239 + 1.02202i) q^{56} +(-12.9124 - 5.03252i) q^{57} +(6.74734 + 7.64574i) q^{58} +(1.61980 - 9.18636i) q^{59} +(-4.47193 + 9.97368i) q^{60} +(-8.30196 - 3.74599i) q^{61} +(-0.848884 - 11.3276i) q^{62} +(6.97148 - 1.81032i) q^{63} +(4.21694 + 1.30075i) q^{64} +(11.5095 + 16.0088i) q^{65} +(-2.55867 + 14.7144i) q^{66} +(-0.470732 + 1.40106i) q^{67} +(-0.743368 + 7.42885i) q^{68} +(4.00128 - 3.04578i) q^{69} +(17.8186 - 3.14190i) q^{70} +(7.28785 - 1.09847i) q^{71} +(-2.03286 + 1.18653i) q^{72} +(-3.35158 - 3.61214i) q^{73} +(0.106122 + 0.0214530i) q^{74} +(-6.02129 - 17.7820i) q^{75} +(6.06765 + 11.1421i) q^{76} +(9.96552 - 4.49661i) q^{77} +(-0.0384385 - 16.2485i) q^{78} +(6.31420 + 10.3327i) q^{79} +(-16.6987 + 8.04165i) q^{80} +(-1.91957 + 8.79291i) q^{81} +(1.10649 - 4.84784i) q^{82} +(5.44509 + 5.58257i) q^{83} +(-5.94765 - 2.84693i) q^{84} +(-11.3146 - 14.9373i) q^{85} +(1.21145 - 6.87046i) q^{86} +(7.00805 + 6.15527i) q^{87} +(-2.73696 + 2.29658i) q^{88} +(-1.20237 - 3.89797i) q^{89} +(-6.56166 + 21.6353i) q^{90} +(-9.82764 + 6.70037i) q^{91} +(-4.59787 - 0.229470i) q^{92} +(-2.08289 - 10.1794i) q^{93} +(-7.91517 + 8.11502i) q^{94} +(-30.1851 - 10.1417i) q^{95} +(12.3704 + 2.15108i) q^{96} +(-3.47418 - 0.977483i) q^{97} +(-0.348741 - 2.31375i) q^{98} +(-0.616391 + 13.6473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) $ 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.59066	−	1.02736i	−1.12477	−	0.726450i	−0.159364	−	0.987220i	$-0.550944\pi$
$2$	−1.59066	−	1.02736i	−1.12477	−	0.726450i	−0.965401	+	0.260770i	$0.916024\pi$
$3$	−1.56230	−	0.747815i	−0.901993	−	0.431751i
$3$	−1.56230	−	0.747815i	−0.901993	−	0.431751i
$4$	0.652159	+	1.44533i	0.326079	+	0.722666i
$5$	−3.66732	−	1.54591i	−1.64008	−	0.691350i	−0.642864	−	0.765980i	$-0.722254\pi$
$5$	−3.66732	−	1.54591i	−1.64008	−	0.691350i	−0.997211	+	0.0746302i	$0.976222\pi$
$6$	1.71681	+	2.79455i	0.700884	+	1.14087i
$7$	0.987458	−	2.18843i	0.373224	−	0.827150i	−0.625668	−	0.780090i	$-0.715173\pi$
$7$	0.987458	−	2.18843i	0.373224	−	0.827150i	0.998892	−	0.0470602i	$-0.0149853\pi$
$8$	−0.116938	+	0.775835i	−0.0413440	+	0.274299i
$9$	1.88155	+	2.33662i	0.627182	+	0.778873i
$10$	4.24526	+	6.22665i	1.34247	+	1.96904i
$11$	3.41430	+	3.01313i	1.02945	+	0.908494i	0.995856	−	0.0909414i	$-0.0289876\pi$
$11$	3.41430	+	3.01313i	1.02945	+	0.908494i	0.0335928	+	0.999436i	$0.489305\pi$
$12$	0.0619752	−	2.74573i	0.0178907	−	0.792625i
$13$	−4.22734	−	2.58327i	−1.17245	−	0.716471i	−0.207331	−	0.978271i	$-0.566478\pi$
$13$	−4.22734	−	2.58327i	−1.17245	−	0.716471i	−0.965122	+	0.261799i	$0.915684\pi$
$14$	−3.81901	+	2.46658i	−1.02067	+	0.659220i
$15$	4.57339	+	5.15764i	1.18085	+	1.33170i
$16$	3.08148	−	3.49174i	0.770369	−	0.872935i
$17$	4.07762	+	2.35422i	0.988969	+	0.570982i	0.904966	−	0.425484i	$-0.139896\pi$
$17$	4.07762	+	2.35422i	0.988969	+	0.570982i	0.0840031	+	0.996465i	$0.473229\pi$
$18$	−0.592357	−	5.64978i	−0.139620	−	1.33167i
$19$	7.97879	−	0.597928i	1.83046	−	0.137174i	0.885559	−	0.464527i	$-0.153776\pi$
$19$	7.97879	−	0.597928i	1.83046	−	0.137174i	0.944902	+	0.327353i	$0.106157\pi$
$20$	−0.157329	−	6.30867i	−0.0351797	−	1.41066i
$21$	−3.17925	+	2.68055i	−0.693768	+	0.584943i
$22$	−2.33542	−	8.30056i	−0.497913	−	1.76969i
$23$	−1.32451	+	2.58354i	−0.276178	+	0.538706i	−0.986217	−	0.165457i	$-0.947090\pi$
$23$	−1.32451	+	2.58354i	−0.276178	+	0.538706i	0.710039	+	0.704163i	$0.248677\pi$
$24$	0.762874	−	1.12464i	0.155721	−	0.229566i
$25$	7.56823	+	7.75933i	1.51365	+	1.55187i
$26$	4.07031	+	8.45209i	0.798254	+	1.65759i
$27$	−1.19218	−	5.05754i	−0.229434	−	0.973324i
$28$	3.80699			0.719454
$29$	−5.18388	−	1.45854i	−0.962623	−	0.270845i
$29$	−5.18388	−	1.45854i	−0.962623	−	0.270845i
$30$	−1.97597	−	12.9025i	−0.360762	−	2.35567i
$31$	3.62214	+	4.78189i	0.650555	+	0.858852i	0.996853	−	0.0792726i	$-0.0252597\pi$
$31$	3.62214	+	4.78189i	0.650555	+	0.858852i	−0.346298	+	0.938125i	$0.612561\pi$
$32$	−6.97829	+	1.96339i	−1.23360	+	0.347081i
$33$	−3.08088	−	7.26067i	−0.536312	−	1.26392i
$34$	−4.06749	−	7.93393i	−0.697568	−	1.36066i
$35$	−7.00444	+	6.49917i	−1.18397	+	1.09856i
$36$	−2.15012	+	4.24331i	−0.358354	+	0.707218i
$37$	−0.0532242	+	0.0208889i	−0.00875000	+	0.00343412i	−0.369712	−	0.929146i	$-0.620544\pi$
$37$	−0.0532242	+	0.0208889i	−0.00875000	+	0.00343412i	0.360962	+	0.932581i	$0.382448\pi$
$38$	−13.3058	−	7.24596i	−2.15849	−	1.17545i
$39$	4.67255	+	7.19711i	0.748207	+	1.15246i
$40$	1.62822	−	2.66446i	0.257444	−	0.421288i
$41$	0.898138	+	2.46761i	0.140266	+	0.385376i	0.989857	−	0.142064i	$-0.0453739\pi$
$41$	0.898138	+	2.46761i	0.140266	+	0.385376i	−0.849592	+	0.527441i	$0.823152\pi$
$42$	7.81097	−	0.997615i	1.20526	−	0.153935i
$43$	1.43109	+	3.39496i	0.218240	+	0.517726i	0.993489	−	0.113930i	$-0.0363439\pi$
$43$	1.43109	+	3.39496i	0.218240	+	0.517726i	−0.775249	+	0.631656i	$0.782376\pi$
$44$	−2.12832	+	6.89984i	−0.320856	+	1.04019i
$45$	−3.28804	−	11.4778i	−0.490152	−	1.71101i
$46$	4.76105	−	2.74880i	0.701979	−	0.405288i
$47$	1.18620	−	5.86780i	0.173025	−	0.855907i	−0.795300	−	0.606216i	$-0.792687\pi$
$47$	1.18620	−	5.86780i	0.173025	−	0.855907i	0.968325	−	0.249691i	$-0.0803291\pi$
$48$	−7.42536	+	3.15076i	−1.07176	+	0.454773i
$49$	0.817638	+	0.926497i	0.116805	+	0.132357i
$50$	−4.06688	−	20.1177i	−0.575144	−	2.84507i
$51$	−4.60994	−	6.72730i	−0.645521	−	0.942010i
$52$	0.976793	−	7.79462i	0.135457	−	1.08092i
$53$	−0.218983	+	0.959425i	−0.0300796	+	0.131787i	−0.987738	−	0.156118i	$-0.950102\pi$
$53$	−0.218983	+	0.959425i	−0.0300796	+	0.131787i	0.957659	+	0.287906i	$0.0929590\pi$
$54$	−3.29955	+	9.26961i	−0.449012	+	1.26143i
$55$	−7.86330	−	16.3283i	−1.06029	−	2.20171i
$56$	1.58239	+	1.02202i	0.211456	+	0.136573i
$57$	−12.9124	−	5.03252i	−1.71029	−	0.666574i
$58$	6.74734	+	7.64574i	0.885969	+	1.00393i
$59$	1.61980	−	9.18636i	0.210880	−	1.19596i	−0.677033	−	0.735952i	$-0.736735\pi$
$59$	1.61980	−	9.18636i	0.210880	−	1.19596i	0.887914	−	0.460010i	$-0.152154\pi$
$60$	−4.47193	+	9.97368i	−0.577323	+	1.28760i
$61$	−8.30196	−	3.74599i	−1.06296	−	0.479624i	−0.197342	−	0.980335i	$-0.563231\pi$
$61$	−8.30196	−	3.74599i	−1.06296	−	0.479624i	−0.865615	+	0.500711i	$0.833072\pi$
$62$	−0.848884	−	11.3276i	−0.107808	−	1.43860i
$63$	6.97148	−	1.81032i	0.878324	−	0.228079i
$64$	4.21694	+	1.30075i	0.527118	+	0.162594i
$65$	11.5095	+	16.0088i	1.42758	+	1.98564i
$66$	−2.55867	+	14.7144i	−0.314951	+	1.81122i
$67$	−0.470732	+	1.40106i	−0.0575091	+	0.171167i	−0.972811	−	0.231602i	$-0.925603\pi$
$67$	−0.470732	+	1.40106i	−0.0575091	+	0.171167i	0.915301	+	0.402769i	$0.131952\pi$
$68$	−0.743368	+	7.42885i	−0.0901466	+	0.900880i
$69$	4.00128	−	3.04578i	0.481698	−	0.366669i
$70$	17.8186	−	3.14190i	2.12973	−	0.375529i
$71$	7.28785	−	1.09847i	0.864908	−	0.130364i	0.298421	−	0.954434i	$-0.403540\pi$
$71$	7.28785	−	1.09847i	0.864908	−	0.130364i	0.566487	+	0.824070i	$0.308302\pi$
$72$	−2.03286	+	1.18653i	−0.239574	+	0.139834i
$73$	−3.35158	−	3.61214i	−0.392272	−	0.422769i	0.505777	−	0.862664i	$-0.331206\pi$
$73$	−3.35158	−	3.61214i	−0.392272	−	0.422769i	−0.898049	+	0.439896i	$0.855015\pi$
$74$	0.106122	+	0.0214530i	0.0123364	+	0.00249386i
$75$	−6.02129	−	17.7820i	−0.695279	−	2.05329i
$76$	6.06765	+	11.1421i	0.696007	+	1.27808i
$77$	9.96552	−	4.49661i	1.13568	−	0.512437i
$78$	−0.0384385	−	16.2485i	−0.00435230	−	1.83978i
$79$	6.31420	+	10.3327i	0.710403	+	1.16252i	0.979894	+	0.199519i	$0.0639381\pi$
$79$	6.31420	+	10.3327i	0.710403	+	1.16252i	−0.269491	+	0.963003i	$0.586856\pi$
$80$	−16.6987	+	8.04165i	−1.86697	+	0.899084i
$81$	−1.91957	+	8.79291i	−0.213286	+	0.976990i
$82$	1.10649	−	4.84784i	0.122191	−	0.535354i
$83$	5.44509	+	5.58257i	0.597676	+	0.612767i	0.945827	−	0.324671i	$-0.105254\pi$
$83$	5.44509	+	5.58257i	0.597676	+	0.612767i	−0.348151	+	0.937439i	$0.613190\pi$
$84$	−5.94765	−	2.84693i	−0.648942	−	0.310625i
$85$	−11.3146	−	14.9373i	−1.22724	−	1.62018i
$86$	1.21145	−	6.87046i	0.130634	−	0.740861i
$87$	7.00805	+	6.15527i	0.751341	+	0.659914i
$88$	−2.73696	+	2.29658i	−0.291761	+	0.244816i
$89$	−1.20237	−	3.89797i	−0.127451	−	0.413184i	0.869248	−	0.494376i	$-0.164604\pi$
$89$	−1.20237	−	3.89797i	−0.127451	−	0.413184i	−0.996698	+	0.0811919i	$0.974127\pi$
$90$	−6.56166	+	21.6353i	−0.691660	+	2.28056i
$91$	−9.82764	+	6.70037i	−1.03022	+	0.702390i
$92$	−4.59787	−	0.229470i	−0.479361	−	0.0239239i
$93$	−2.08289	−	10.1794i	−0.215986	−	1.05556i
$94$	−7.91517	+	8.11502i	−0.816387	+	0.837000i
$95$	−30.1851	−	10.1417i	−3.09693	−	1.04051i
$96$	12.3704	+	2.15108i	1.26255	+	0.219543i
$97$	−3.47418	−	0.977483i	−0.352750	−	0.0992484i	0.0898806	−	0.995953i	$-0.471351\pi$
$97$	−3.47418	−	0.977483i	−0.352750	−	0.0992484i	−0.442630	+	0.896704i	$0.645955\pi$
$98$	−0.348741	−	2.31375i	−0.0352282	−	0.233724i
$99$	−0.616391	+	13.6473i	−0.0619496	+	1.37160i
$100$	−6.27912	+	15.9989i	−0.627912	+	1.59989i
$101$	6.77069	−	8.93856i	0.673709	−	0.889420i	−0.324699	−	0.945817i	$-0.605263\pi$
$101$	6.77069	−	8.93856i	0.673709	−	0.889420i	0.998408	+	0.0563977i	$0.0179615\pi$
$102$	0.421515	+	15.4369i	0.0417362	+	1.52848i
$103$	−2.26306	+	1.23239i	−0.222986	+	0.121431i	−0.585877	−	0.810400i	$-0.699250\pi$
$103$	−2.26306	+	1.23239i	−0.222986	+	0.121431i	0.362892	+	0.931831i	$0.381790\pi$
$104$	2.49853	−	2.97764i	0.245001	−	0.291981i
$105$	15.8032	−	4.91561i	1.54223	−	0.479714i
$106$	1.33400	−	1.30114i	0.129569	−	0.126378i
$107$	5.36069	−	6.72209i	0.518237	−	0.649849i	−0.451997	−	0.892020i	$-0.649288\pi$
$107$	5.36069	−	6.72209i	0.518237	−	0.649849i	0.970234	+	0.242171i	$0.0778595\pi$
$108$	6.53234	−	5.02141i	0.628575	−	0.483185i
$109$	12.8114	−	6.16966i	1.22711	−	0.590946i	0.295828	−	0.955241i	$-0.404404\pi$
$109$	12.8114	−	6.16966i	1.22711	−	0.590946i	0.931284	+	0.364295i	$0.118690\pi$
$110$	−4.26716	+	34.0512i	−0.406858	+	3.24665i
$111$	0.0987730	+	0.00716708i	0.00937512	+	0.000680269i
$112$	−4.59860	−	10.1916i	−0.434527	−	0.963011i
$113$	−6.93067	+	1.94999i	−0.651982	+	0.183439i	−0.580828	−	0.814026i	$-0.697271\pi$
$113$	−6.93067	+	1.94999i	−0.651982	+	0.183439i	−0.0711538	+	0.997465i	$0.522668\pi$
$114$	15.3690	+	21.2706i	1.43944	+	1.99218i
$115$	8.85130	−	7.42712i	0.825388	−	0.692583i
$116$	−1.27263	−	8.44364i	−0.118161	−	0.783972i
$117$	−1.91781	−	14.7382i	−0.177302	−	1.36255i
$118$	−12.0142	+	12.9482i	−1.10600	+	1.19198i
$119$	9.17853	−	6.59891i	0.841394	−	0.604921i
$120$	−4.53629	+	2.94507i	−0.414104	+	0.268847i
$121$	1.21066	+	9.66084i	0.110060	+	0.878258i
$122$	9.35711	+	14.4876i	0.847153	+	1.31165i
$123$	0.442160	−	4.52679i	0.0398682	−	0.408167i
$124$	−4.54921	+	8.35374i	−0.408531	+	0.750188i
$125$	−8.48998	−	21.6321i	−0.759366	−	1.93483i
$126$	−12.9491	−	4.28259i	−1.15360	−	0.381523i
$127$	−1.72585	−	0.677345i	−0.153144	−	0.0601046i	0.287531	−	0.957771i	$-0.407166\pi$
$127$	−1.72585	−	0.677345i	−0.153144	−	0.0601046i	−0.440675	+	0.897667i	$0.645261\pi$
$128$	3.94806	+	4.70511i	0.348962	+	0.415877i
$129$	0.303005	−	6.37413i	0.0266781	−	0.561210i
$130$	−1.86101	−	37.2888i	−0.163221	−	3.27045i
$131$	1.69889	+	0.870972i	0.148433	+	0.0760972i	0.528838	−	0.848723i	$-0.322628\pi$
$131$	1.69889	+	0.870972i	0.148433	+	0.0760972i	−0.380405	+	0.924820i	$0.624215\pi$
$132$	8.48487	−	9.18801i	0.738513	−	0.799713i
$133$	6.57020	−	18.0515i	0.569709	−	1.56526i
$134$	2.18816	−	1.74500i	0.189029	−	0.150745i
$135$	−3.44639	+	20.3906i	−0.296618	+	1.75494i
$136$	−2.30332	+	2.88827i	−0.197508	+	0.247667i
$137$	3.52577	+	5.76967i	0.301227	+	0.492936i	0.967534	−	0.252742i	$-0.0813323\pi$
$137$	3.52577	+	5.76967i	0.301227	+	0.492936i	−0.666307	+	0.745678i	$0.732126\pi$
$138$	−9.49377	+	0.734049i	−0.808164	+	0.0624864i
$139$	−0.493679	+	0.962956i	−0.0418733	+	0.0816769i	−0.909871	−	0.414892i	$-0.863820\pi$
$139$	−0.493679	+	0.962956i	−0.0418733	+	0.0816769i	0.867998	+	0.496568i	$0.165407\pi$
$140$	−13.9615	−	5.88525i	−1.17996	−	0.497394i
$141$	−6.24123	+	8.28019i	−0.525607	+	0.697318i
$142$	−12.7210	−	5.73993i	−1.06752	−	0.481684i
$143$	−6.64964	−	21.5576i	−0.556071	−	1.80274i
$144$	13.9568	+	0.630372i	1.16307	+	0.0525310i
$145$	16.7562	+	13.3627i	1.39153	+	1.10972i
$146$	1.62026	+	9.18894i	0.134093	+	0.760482i
$147$	−0.584546	−	2.05891i	−0.0482125	−	0.169816i
$148$	−0.0649021	−	0.0633037i	−0.00533492	−	0.00520353i
$149$	4.45489	+	0.445779i	0.364959	+	0.0365196i	0.280359	−	0.959895i	$-0.409547\pi$
$149$	4.45489	+	0.445779i	0.364959	+	0.0365196i	0.0846002	+	0.996415i	$0.473039\pi$
$150$	−8.69064	+	34.4711i	−0.709588	+	2.81455i
$151$	−9.12198	+	3.84524i	−0.742336	+	0.312921i	−0.726698	−	0.686957i	$-0.758946\pi$
$151$	−9.12198	+	3.84524i	−0.742336	+	0.312921i	−0.0156380	+	0.999878i	$0.504978\pi$
$152$	−0.469134	+	6.26015i	−0.0380518	+	0.507765i
$153$	2.17133	+	13.9574i	0.175541	+	1.12839i
$154$	−20.4714	−	3.08556i	−1.64963	−	0.248641i
$155$	−5.89120	−	23.1362i	−0.473192	−	1.85834i
$156$	−7.35497	+	11.4471i	−0.588869	+	0.916498i
$157$	21.3142	+	3.75827i	1.70106	+	0.299943i	0.938065	−	0.346460i	$-0.112616\pi$
$157$	21.3142	+	3.75827i	1.70106	+	0.299943i	0.762996	+	0.646403i	$0.223728\pi$
$158$	0.571658	−	22.9228i	0.0454787	−	1.82364i
$159$	1.05959	−	1.33515i	0.0840308	−	0.105884i
$160$	28.6268	+	3.58741i	2.26315	+	0.283609i
$161$	4.34602	+	5.44973i	0.342514	+	0.429499i
$162$	12.0868	−	12.0144i	0.949631	−	0.943943i
$163$	−5.19772	+	4.14504i	−0.407116	+	0.324665i	−0.805545	−	0.592535i	$-0.798127\pi$
$163$	−5.19772	+	4.14504i	−0.407116	+	0.324665i	0.398428	+	0.917199i	$0.369556\pi$
$164$	−2.98079	+	2.90738i	−0.232761	+	0.227029i
$165$	0.0742580	+	31.3900i	0.00578098	+	2.44371i
$166$	−2.92598	−	14.4740i	−0.227100	−	1.12340i
$167$	2.91729	+	10.3687i	0.225747	+	0.802352i	0.987918	+	0.154977i	$0.0495303\pi$
$167$	2.91729	+	10.3687i	0.225747	+	0.802352i	−0.762171	+	0.647376i	$0.775867\pi$
$168$	−1.70789	−	2.78003i	−0.131766	−	0.214484i
$169$	5.26637	+	10.2724i	0.405105	+	0.790187i
$170$	2.65168	+	35.3842i	0.203375	+	2.71384i
$171$	16.4096	+	17.5184i	1.25487	+	1.33966i
$172$	−3.97354	+	4.28246i	−0.302980	+	0.326534i
$173$	3.41086	+	19.3440i	0.259323	+	1.47070i	0.784727	+	0.619842i	$0.212803\pi$
$173$	3.41086	+	19.3440i	0.259323	+	1.47070i	−0.525404	+	0.850853i	$0.676086\pi$
$174$	−4.82376	−	16.9907i	−0.365688	−	1.28806i
$175$	24.4541	−	8.90056i	1.84855	−	0.672819i
$176$	21.0422	−	2.63692i	1.58611	−	0.198766i
$177$	−9.40031	+	13.1405i	−0.706571	+	0.987701i
$178$	−2.09205	+	7.43560i	−0.156806	+	0.557322i
$179$	−10.7507	−	9.97521i	−0.803546	−	0.745582i	0.167140	−	0.985933i	$-0.446547\pi$
$179$	−10.7507	−	9.97521i	−0.803546	−	0.745582i	−0.970686	+	0.240351i	$0.922737\pi$
$180$	14.4449	−	12.2377i	1.07666	−	0.912142i
$181$	6.87880	+	4.68989i	0.511297	+	0.348597i	0.791325	−	0.611395i	$-0.209391\pi$
$181$	6.87880	+	4.68989i	0.511297	+	0.348597i	−0.280028	+	0.959992i	$0.590344\pi$
$182$	22.5161	−	0.561516i	1.66900	−	0.0416224i
$183$	10.1688	+	12.0607i	0.751701	+	0.891550i
$184$	−1.84952	−	1.32971i	−0.136348	−	0.0980278i
$185$	0.227482	+	0.00567306i	0.0167248	+	0.000417091i
$186$	−7.14472	+	18.3318i	−0.523876	+	1.34416i
$187$	6.82864	+	20.3244i	0.499360	+	1.48627i
$188$	9.25452	−	2.11228i	0.674955	−	0.154054i
$189$	−12.2453	−	2.38511i	−0.890715	−	0.173492i
$190$	37.5951	+	47.1428i	2.72744	+	3.42010i
$191$	5.74673	−	15.7890i	0.415819	−	1.14245i	−0.538229	−	0.842799i	$-0.680906\pi$
$191$	5.74673	−	15.7890i	0.415819	−	1.14245i	0.954048	−	0.299654i	$-0.0968713\pi$
$192$	−5.61540	−	5.18566i	−0.405256	−	0.374243i
$193$	12.8441	−	5.79547i	0.924537	−	0.417167i	0.107797	−	0.994173i	$-0.465620\pi$
$193$	12.8441	−	5.79547i	0.924537	−	0.417167i	0.816740	+	0.577006i	$0.195779\pi$
$194$	4.52201	+	5.12406i	0.324662	+	0.367886i
$195$	−6.00970	−	33.6174i	−0.430363	−	2.40739i
$196$	−0.805866	+	1.78598i	−0.0575619	+	0.127570i
$197$	14.6789	−	13.6201i	1.04583	−	0.970390i	0.0462391	−	0.998930i	$-0.485276\pi$
$197$	14.6789	−	13.6201i	1.04583	−	0.970390i	0.999593	+	0.0285404i	$0.00908592\pi$
$198$	15.0011	−	21.0749i	1.06608	−	1.49773i
$199$	14.2586	−	9.72137i	1.01077	−	0.689130i	0.0597329	−	0.998214i	$-0.480975\pi$
$199$	14.2586	−	9.72137i	1.01077	−	0.689130i	0.951034	+	0.309085i	$0.100023\pi$
$200$	−6.90498	+	4.96434i	−0.488256	+	0.351032i
$201$	1.78316	−	1.83686i	0.125774	−	0.129562i
$202$	−19.9529	+	7.26228i	−1.40388	+	0.510972i
$203$	−8.31079	+	9.90433i	−0.583303	+	0.695147i
$204$	6.71676	−	11.0502i	0.470268	−	0.773666i
$205$	0.520937	−	10.4380i	0.0363838	−	0.729019i
$206$	4.86586	+	0.364646i	0.339020	+	0.0254061i
$207$	−8.52887	+	1.76619i	−0.592798	+	0.122759i
$208$	−22.0466	+	6.80047i	−1.52865	+	0.471528i
$209$	29.0436	+	21.9997i	2.00899	+	1.52175i
$210$	−30.1875	−	8.41644i	−2.08314	−	0.580790i
$211$	−10.8590	+	9.58314i	−0.747565	+	0.659730i	−0.947383	−	0.320103i	$-0.896283\pi$
$211$	−10.8590	+	9.58314i	−0.747565	+	0.659730i	0.199817	+	0.979833i	$0.435965\pi$
$212$	−1.52950	+	0.309195i	−0.105047	+	0.0212356i
$213$	−12.2072	−	3.73383i	−0.836426	−	0.255838i
$214$	−15.4330	+	5.18521i	−1.05498	+	0.354454i
$215$		−	14.6627i		−	0.999990i
$216$	4.06323	−	0.333511i	0.276468	−	0.0226926i
$217$	14.0415	−	3.20489i	0.953202	−	0.217562i
$218$	−26.7170	−	3.34808i	−1.80951	−	0.226760i
$219$	2.53495	+	8.14959i	0.171296	+	0.550698i
$220$	18.4717	−	22.0137i	1.24536	−	1.48417i
$221$	−11.1559	−	20.4857i	−0.750428	−	1.37802i
$222$	−0.149751	−	0.112875i	−0.0100506	−	0.00757570i
$223$	−0.344525	−	13.8150i	−0.0230711	−	0.925123i	−0.897772	−	0.440460i	$-0.854815\pi$
$223$	−0.344525	−	13.8150i	−0.0230711	−	0.925123i	0.874701	−	0.484663i	$-0.161058\pi$
$224$	−2.59403	+	17.2103i	−0.173321	+	1.14991i
$225$	−3.89061	+	32.2836i	−0.259374	+	2.15224i
$226$	13.0277	+	4.01850i	0.866587	+	0.267307i
$227$	−5.31115	−	0.265068i	−0.352513	−	0.0175932i	−0.127193	−	0.991878i	$-0.540597\pi$
$227$	−5.31115	−	0.265068i	−0.352513	−	0.0175932i	−0.225320	+	0.974285i	$0.572343\pi$
$228$	−1.14726	−	21.9447i	−0.0759794	−	1.45332i
$229$	17.4670	+	17.0369i	1.15425	+	1.12583i	0.990240	+	0.139370i	$0.0445079\pi$
$229$	17.4670	+	17.0369i	1.15425	+	1.12583i	0.164015	+	0.986458i	$0.447556\pi$
$230$	−21.7097	+	2.72058i	−1.43149	+	0.179390i
$231$	−18.9317	−	0.427317i	−1.24562	−	0.0281154i
$232$	1.73779	−	3.85128i	0.114091	−	0.252849i
$233$	1.65983	−	2.87490i	0.108739	−	0.188341i	−0.806521	−	0.591206i	$-0.798652\pi$
$233$	1.65983	−	2.87490i	0.108739	−	0.188341i	0.915260	+	0.402865i	$0.131985\pi$
$234$	−12.0908	+	25.4138i	−0.790402	+	1.66135i
$235$	−13.4213	+	19.6854i	−0.875506	+	1.28413i
$236$	14.3337	−	3.64981i	0.933045	−	0.237583i
$237$	−2.13769	−	20.8646i	−0.138858	−	1.35530i
$238$	−21.3793	+	1.06700i	−1.38582	+	0.0691632i
$239$	−20.2737	−	5.16233i	−1.31140	−	0.333923i	−0.474005	−	0.880522i	$-0.657192\pi$
$239$	−20.2737	−	5.16233i	−1.31140	−	0.333923i	−0.837395	+	0.546599i	$0.815922\pi$
$240$	32.1019	−	0.0759423i	2.07217	−	0.00490205i
$241$	−5.25982	+	3.21421i	−0.338815	+	0.207045i	−0.680463	−	0.732783i	$-0.738221\pi$
$241$	−5.25982	+	3.21421i	−0.338815	+	0.207045i	0.341648	+	0.939828i	$0.389015\pi$
$242$	7.99937	−	16.6109i	0.514219	−	1.06779i
$243$	9.57441	−	12.3017i	0.614199	−	0.789151i
$244$		−	14.4421i		−	0.924558i
$245$	−1.56627	−	4.66175i	−0.100065	−	0.297828i
$246$	−5.35395	+	6.74632i	−0.341355	+	0.430129i
$247$	−35.2737	−	18.0838i	−2.24441	−	1.15064i
$248$	−4.13352	+	2.25100i	−0.262479	+	0.142938i
$249$	−4.33212	−	12.7936i	−0.274537	−	0.810759i
$250$	−8.71922	+	43.1315i	−0.551452	+	2.72788i
$251$	−16.4819	+	1.23515i	−1.04033	+	0.0779620i	−0.583923	−	0.811809i	$-0.698483\pi$
$251$	−16.4819	+	1.23515i	−1.04033	+	0.0779620i	−0.456407	+	0.889771i	$0.650864\pi$
$252$	7.16303	+	8.89549i	0.451229	+	0.560363i
$253$	−12.3068	+	4.83007i	−0.773723	+	0.303664i
$254$	2.04936	+	2.85048i	0.128588	+	0.178855i
$255$	6.50637	+	31.7977i	0.407445	+	1.99125i
$256$	−2.54364	−	20.2978i	−0.158978	−	1.26861i
$257$	15.8811	+	1.58914i	0.990633	+	0.0991278i	0.581672	−	0.813424i	$-0.302399\pi$
$257$	15.8811	+	1.58914i	0.990633	+	0.0991278i	0.408962	+	0.912551i	$0.365891\pi$
$258$	−7.03047	+	9.82776i	−0.437698	+	0.611850i
$259$	−0.00684260	+	0.137104i	−0.000425178	+	0.00851926i
$260$	−15.6320	+	27.0753i	−0.969453	+	1.67914i
$261$	−6.34565	−	14.8571i	−0.392786	−	0.919630i
$262$	−1.80756	−	3.13079i	−0.111672	−	0.193421i
$263$	25.9355	−	13.2964i	1.59925	−	0.819889i	0.599443	−	0.800417i	$-0.295389\pi$
$263$	25.9355	−	13.2964i	1.59925	−	0.819889i	0.999810	−	0.0194720i	$-0.00619851\pi$
$264$	5.99336	−	1.54120i	0.368866	−	0.0948545i
$265$	2.28626	−	3.17999i	0.140444	−	0.195345i
$266$	−28.9962	+	21.9638i	−1.77787	+	1.34669i
$267$	−1.03651	+	6.98894i	−0.0634334	+	0.427716i
$268$	−2.33199	+	0.233351i	−0.142449	+	0.0142542i
$269$	−6.28263	−	5.01023i	−0.383059	−	0.305479i	0.412962	−	0.910748i	$-0.364494\pi$
$269$	−6.28263	−	5.01023i	−0.383059	−	0.305479i	−0.796021	+	0.605269i	$0.793066\pi$
$270$	26.4304	−	28.8938i	1.60851	−	1.75842i
$271$	1.15067	−	2.38939i	0.0698983	−	0.145145i	−0.863092	−	0.505047i	$-0.831475\pi$
$271$	1.15067	−	2.38939i	0.0698983	−	0.145145i	0.932990	+	0.359901i	$0.117190\pi$
$272$	20.7854	−	6.98353i	1.26030	−	0.423439i
$273$	20.3643	−	3.11872i	1.23251	−	0.188753i
$274$	0.319207	−	12.7998i	0.0192840	−	0.773263i
$275$	2.46030	+	49.2967i	0.148362	+	2.97271i
$276$	7.01163	+	3.79685i	0.422051	+	0.228544i
$277$	−8.58208	−	1.73490i	−0.515647	−	0.104240i	−0.0666551	−	0.997776i	$-0.521233\pi$
$277$	−8.58208	−	1.73490i	−0.515647	−	0.104240i	−0.448992	+	0.893536i	$0.648217\pi$
$278$	1.77457	−	1.02455i	0.106432	−	0.0614484i
$279$	−4.35823	+	17.4609i	−0.260920	+	1.04536i
$280$	−4.22320	−	6.19429i	−0.252384	−	0.370180i
$281$	−2.28514	−	1.24442i	−0.136320	−	0.0742361i	0.408651	−	0.912691i	$-0.365999\pi$
$281$	−2.28514	−	1.24442i	−0.136320	−	0.0742361i	−0.544972	+	0.838455i	$0.683460\pi$
$282$	18.4344	−	6.75899i	1.09775	−	0.402492i
$283$	18.8004	−	19.2751i	1.11757	−	1.14578i	0.129529	−	0.991576i	$-0.458654\pi$
$283$	18.8004	−	19.2751i	1.11757	−	1.14578i	0.988038	−	0.154209i	$-0.0492830\pi$
$284$	6.34048	+	9.81699i	0.376239	+	0.582531i
$285$	39.5741	+	38.4172i	2.34417	+	2.27564i
$286$	−11.5700	+	41.1223i	−0.684150	+	2.43162i
$287$	6.28708	+	0.471151i	0.371115	+	0.0278112i
$288$	−17.7177	−	12.6114i	−1.04402	−	0.743134i
$289$	2.58468	+	4.47679i	0.152040	+	0.263341i
$290$	−12.9251	−	38.4701i	−0.758987	−	2.25904i
$291$	4.69673	+	4.12517i	0.275327	+	0.241821i
$292$	3.03498	−	7.19983i	0.177609	−	0.421338i
$293$	7.72967	−	30.3563i	0.451572	−	1.77344i	−0.165165	−	0.986266i	$-0.552816\pi$
$293$	7.72967	−	30.3563i	0.451572	−	1.77344i	0.616737	−	0.787170i	$-0.288454\pi$
$294$	−1.18542	+	3.87555i	−0.0691349	+	0.226027i
$295$	−20.1416	+	31.1853i	−1.17269	+	1.81568i
$296$	−0.00998244	−	0.0437359i	−0.000580217	−	0.00254210i
$297$	11.1686	−	20.8601i	0.648068	−	1.21043i
$298$	−6.62823	−	5.28584i	−0.383963	−	0.306200i
$299$	12.2731	−	7.49996i	0.709774	−	0.433734i
$300$	21.7741	−	20.2995i	1.25713	−	1.17199i
$301$	8.84278	+	0.220525i	0.509689	+	0.0127109i
$302$	18.4604	+	3.25506i	1.06228	+	0.187308i
$303$	−17.2622	+	8.90146i	−0.991689	+	0.511375i
$304$	22.4987	−	29.7024i	1.29039	−	1.70355i
$305$	24.6550	+	26.5718i	1.41174	+	1.52149i
$306$	10.8854	−	24.4322i	0.622277	−	1.39670i
$307$	−21.5384	−	12.4352i	−1.22926	−	0.709716i	−0.262388	−	0.964963i	$-0.584510\pi$
$307$	−21.5384	−	12.4352i	−1.22926	−	0.709716i	−0.966876	+	0.255247i	$0.917843\pi$
$308$	12.9982	+	11.4710i	0.740641	+	0.653620i
$309$	4.45717	−	0.233020i	0.253560	−	0.0132560i
$310$	−14.3982	+	42.8541i	−0.817764	+	2.43395i
$311$	−13.4886	−	4.53193i	−0.764868	−	0.256982i	−0.0910170	−	0.995849i	$-0.529012\pi$
$311$	−13.4886	−	4.53193i	−0.764868	−	0.256982i	−0.673851	+	0.738867i	$0.735361\pi$
$312$	−6.13017	+	2.78351i	−0.347053	+	0.157585i
$313$	2.90030	−	1.22258i	0.163935	−	0.0691042i	−0.304928	−	0.952375i	$-0.598632\pi$
$313$	2.90030	−	1.22258i	0.163935	−	0.0691042i	0.468862	+	0.883271i	$0.344664\pi$
$314$	−30.0426	−	27.8754i	−1.69540	−	1.57310i
$315$	−28.3652	−	4.13821i	−1.59820	−	0.233162i
$316$	−10.8164	+	15.8647i	−0.608468	+	0.892459i
$317$	−24.0383	+	12.3237i	−1.35012	+	0.692168i	−0.972306	−	0.233713i	$-0.924912\pi$
$317$	−24.0383	+	12.3237i	−1.35012	+	0.692168i	−0.377817	+	0.925880i	$0.623325\pi$
$318$	−3.05712	+	1.03519i	−0.171435	+	0.0580507i
$319$	−13.3045	−	20.5996i	−0.744910	−	1.15336i
$320$	−13.4540	−	11.2893i	−0.752104	−	0.631090i
$321$	−13.4019	+	6.49310i	−0.748019	+	0.362409i
$322$	−1.31421	−	13.1336i	−0.0732381	−	0.731905i
$323$	33.9422	+	16.3457i	1.88859	+	0.909499i
$324$	−13.9605	+	2.95995i	−0.775586	+	0.164442i
$325$	−11.9490	−	52.3521i	−0.662813	−	2.90397i
$326$	12.5262	−	1.25344i	0.693763	−	0.0694215i
$327$	−24.6290	+	0.0582639i	−1.36199	+	0.00322200i
$328$	−2.01949	+	0.408248i	−0.111508	+	0.0225418i
$329$	−11.6700	−	8.39014i	−0.643386	−	0.462563i
$330$	32.1305	−	50.0070i	1.76873	−	2.75279i
$331$	9.89967	+	11.7980i	0.544135	+	0.648475i	0.966109	−	0.258133i	$-0.0831072\pi$
$331$	9.89967	+	11.7980i	0.544135	+	0.648475i	−0.421974	+	0.906608i	$0.638663\pi$
$332$	−4.51761	+	11.5107i	−0.247936	+	0.631731i
$333$	−0.148953	−	0.0850611i	−0.00816259	−	0.00466132i
$334$	6.01191	−	19.4901i	0.328957	−	1.06645i
$335$	3.89224	−	4.41044i	0.212656	−	0.240968i
$336$	−0.437009	+	19.3611i	−0.0238408	+	1.05624i
$337$	6.48865	−	10.6182i	0.353459	−	0.578411i	−0.626057	−	0.779778i	$-0.715332\pi$
$337$	6.48865	−	10.6182i	0.353459	−	0.578411i	0.979516	+	0.201367i	$0.0645384\pi$
$338$	2.17645	−	21.7504i	0.118383	−	1.18306i
$339$	12.2860	+	2.13640i	0.667284	+	0.116033i
$340$	14.2105	−	26.0948i	0.770671	−	1.41519i
$341$	−2.04141	+	27.2408i	−0.110549	+	1.47517i
$342$	−8.10446	−	44.7242i	−0.438239	−	2.41841i
$343$	18.8946	−	5.82821i	1.02021	−	0.314694i
$344$	−2.80128	+	0.713293i	−0.151035	+	0.0384582i
$345$	−19.3825	+	4.98424i	−1.04352	+	0.268342i
$346$	14.4476	−	34.2738i	0.776709	−	1.84257i
$347$	−4.25240	−	3.56819i	−0.228281	−	0.191550i	0.521472	−	0.853268i	$-0.325383\pi$
$347$	−4.25240	−	3.56819i	−0.228281	−	0.191550i	−0.749753	+	0.661718i	$0.769828\pi$
$348$	−4.32605	+	14.1432i	−0.231900	+	0.758153i
$349$	−23.8437	−	8.67838i	−1.27632	−	0.464543i	−0.387108	−	0.922035i	$-0.626526\pi$
$349$	−23.8437	−	8.67838i	−1.27632	−	0.464543i	−0.889214	+	0.457492i	$0.848748\pi$
$350$	−48.0421	−	10.9653i	−2.56796	−	0.586120i
$351$	−8.02528	+	24.4597i	−0.428358	+	1.30556i
$352$	−29.7419	−	14.3229i	−1.58525	−	0.763415i
$353$	−0.222511	+	0.344515i	−0.0118431	+	0.0183367i	−0.845897	−	0.533346i	$-0.820935\pi$
$353$	−0.222511	+	0.344515i	−0.0118431	+	0.0183367i	0.834054	+	0.551682i	$0.186014\pi$
$354$	28.4527	−	11.2446i	1.51224	−	0.597644i
$355$	−28.4250	−	7.23789i	−1.50864	−	0.384148i
$356$	4.84974	−	4.27992i	0.257035	−	0.226835i
$357$	−19.2744	+	3.44562i	−1.02011	+	0.182362i
$358$	6.85263	+	26.9120i	0.362172	+	1.42234i
$359$	26.3656	+	10.3477i	1.39152	+	0.546133i	0.938473	−	0.345352i	$-0.112240\pi$
$359$	26.3656	+	10.3477i	1.39152	+	0.546133i	0.453051	+	0.891485i	$0.350336\pi$
$360$	9.28940	−	1.20878i	0.489594	−	0.0637083i
$361$	44.5159	−	6.70969i	2.34294	−	0.353141i
$362$	−6.12364	−	14.5270i	−0.321851	−	0.763522i
$363$	5.33311	−	15.9984i	0.279916	−	0.839701i
$364$	−16.0935	−	9.83451i	−0.843526	−	0.515468i
$365$	6.70728	+	18.4281i	0.351075	+	0.964570i
$366$	−3.78452	−	29.6314i	−0.197820	−	1.54886i
$367$	−25.8433	−	7.27119i	−1.34901	−	0.379553i	−0.481271	−	0.876572i	$-0.659825\pi$
$367$	−25.8433	−	7.27119i	−1.34901	−	0.379553i	−0.867740	+	0.497019i	$0.834428\pi$
$368$	4.93962	+	12.5860i	0.257496	+	0.656088i
$369$	−4.07598	+	6.74153i	−0.212187	+	0.350950i
$370$	−0.356019	−	0.242729i	−0.0185085	−	0.0126189i
$371$	1.88340	+	1.42662i	0.0977813	+	0.0740665i
$372$	13.3543	−	9.64907i	0.692386	−	0.500281i
$373$	1.30195	−	1.81090i	0.0674123	−	0.0937648i	−0.776877	−	0.629652i	$-0.783197\pi$
$373$	1.30195	−	1.81090i	0.0674123	−	0.0937648i	0.844289	+	0.535887i	$0.180023\pi$
$374$	10.0184	−	39.3447i	0.518038	−	2.03446i
$375$	−2.91294	+	40.1447i	−0.150424	+	2.07306i
$376$	4.41374	+	1.60647i	0.227621	+	0.0828473i
$377$	18.1462	+	19.5572i	0.934578	+	1.00724i
$378$	17.0277	+	16.3742i	0.875812	+	0.842198i
$379$	−17.1470	−	3.91369i	−0.880783	−	0.201033i	−0.241867	−	0.970309i	$-0.577760\pi$
$379$	−17.1470	−	3.91369i	−0.880783	−	0.201033i	−0.638916	+	0.769276i	$0.720617\pi$
$380$	−5.02742	−	50.2415i	−0.257901	−	2.57734i
$381$	2.18976	+	2.34883i	0.112185	+	0.120334i
$382$	−25.3620	+	19.2110i	−1.29763	+	0.982920i
$383$	−19.8606	+	0.991202i	−1.01483	+	0.0506481i	−0.550349	−	0.834935i	$-0.685505\pi$
$383$	−19.8606	+	0.991202i	−1.01483	+	0.0506481i	−0.464481	+	0.885583i	$0.653759\pi$
$384$	−2.64949	−	10.3032i	−0.135206	−	0.525783i
$385$	−43.4981	+	1.08477i	−2.21687	+	0.0552852i
$386$	−26.3846	−	3.97683i	−1.34294	−	0.202415i
$387$	−5.24005	+	9.73169i	−0.266367	+	0.494690i
$388$	−0.852930	−	5.65882i	−0.0433010	−	0.287283i
$389$	−8.51074	+	1.50067i	−0.431512	+	0.0760872i	−0.385185	−	0.922839i	$-0.625863\pi$
$389$	−8.51074	+	1.50067i	−0.431512	+	0.0760872i	−0.0463263	+	0.998926i	$0.514751\pi$
$390$	−24.9777	+	59.6480i	−1.26480	+	3.02039i
$391$	−11.4831	+	7.41654i	−0.580723	+	0.375071i
$392$	−0.814422	+	0.526010i	−0.0411345	+	0.0265675i
$393$	−2.00285	−	2.63118i	−0.101031	−	0.132725i
$394$	−37.3419	+	6.58438i	−1.88126	+	0.331716i
$395$	−7.18277	−	47.6546i	−0.361404	−	2.39776i
$396$	−20.1268	+	8.00929i	−1.01141	+	0.402482i
$397$	25.6535	+	3.86665i	1.28751	+	0.194062i	0.756888	−	0.653544i	$-0.226719\pi$
$397$	25.6535	+	3.86665i	1.28751	+	0.194062i	0.530626	+	0.847606i	$0.321957\pi$
$398$	−32.6679	+	0.814687i	−1.63749	+	0.0408366i
$399$	−23.7638	+	23.2885i	−1.18968	+	1.16588i
$400$	50.4149	−	2.51610i	2.52074	−	0.125805i
$401$	−18.7815	+	14.2265i	−0.937905	+	0.710435i	−0.957215	−	0.289378i	$-0.906551\pi$
$401$	−18.7815	+	14.2265i	−0.937905	+	0.710435i	0.0193099	+	0.999814i	$0.493853\pi$
$402$	−4.72350	+	1.08987i	−0.235587	+	0.0543578i
$403$	−2.95909	−	29.5716i	−0.147403	−	1.47307i
$404$	17.3348	+	3.95654i	0.862436	+	0.196845i
$405$	20.6327	−	29.2789i	1.02525	−	1.45488i
$406$	23.3949	−	7.21625i	1.16107	−	0.358137i
$407$	−0.244664	−	0.0890505i	−0.0121276	−	0.00441407i
$408$	5.75835	−	2.78988i	0.285081	−	0.138120i
$409$	1.99400	−	7.83094i	0.0985971	−	0.387215i	−0.900242	−	0.435390i	$-0.856610\pi$
$409$	1.99400	−	7.83094i	0.0985971	−	0.387215i	0.998839	+	0.0481752i	$0.0153406\pi$
$410$	−11.5521	+	16.0680i	−0.570520	+	0.793544i
$411$	−1.19366	−	11.6506i	−0.0588788	−	0.574680i
$412$	−3.25709	−	2.46715i	−0.160465	−	0.121548i
$413$	−18.5042	−	12.6160i	−0.910534	−	0.620792i
$414$	15.3810	+	5.95278i	0.755936	+	0.292563i
$415$	−11.3388	−	28.8907i	−0.556598	−	1.41819i
$416$	34.5716	+	9.72693i	1.69501	+	0.476902i
$417$	1.49139	−	1.13524i	0.0730335	−	0.0555931i
$418$	−23.5970	−	64.8321i	−1.15416	−	3.17104i
$419$	3.61854	+	2.21124i	0.176777	+	0.108026i	0.607019	−	0.794688i	$-0.292365\pi$
$419$	3.61854	+	2.21124i	0.176777	+	0.108026i	−0.430242	+	0.902714i	$0.641572\pi$
$420$	17.4109	+	19.6351i	0.849564	+	0.958095i
$421$	−0.475545	−	1.12813i	−0.0231767	−	0.0549815i	0.909478	−	0.415753i	$-0.136482\pi$
$421$	−0.475545	−	1.12813i	−0.0231767	−	0.0549815i	−0.932654	+	0.360771i	$0.882514\pi$
$422$	27.1183	−	4.08742i	1.32010	−	0.198973i
$423$	15.9427	−	8.26884i	0.775161	−	0.402045i
$424$	−0.718749	−	0.282088i	−0.0349055	−	0.0136994i
$425$	12.5933	+	49.4569i	0.610863	+	2.39901i
$426$	15.5816	+	18.4804i	0.754929	+	0.895379i
$427$	−16.3957	+	14.4693i	−0.793442	+	0.700217i
$428$	13.2117	+	3.36410i	0.638610	+	0.162610i
$429$	−5.73239	+	38.6521i	−0.276762	+	1.86614i
$430$	−15.0638	+	23.3234i	−0.726443	+	1.12475i
$431$	−0.990897	−	0.477191i	−0.0477298	−	0.0229855i	0.409867	−	0.912145i	$-0.365575\pi$
$431$	−0.990897	−	0.477191i	−0.0477298	−	0.0229855i	−0.457596	+	0.889160i	$0.651290\pi$
$432$	−21.3333	−	11.4219i	−1.02640	−	0.549538i
$433$	−0.177256	−	0.0404575i	−0.00851838	−	0.00194426i	0.218260	−	0.975891i	$-0.429962\pi$
$433$	−0.177256	−	0.0404575i	−0.00851838	−	0.00194426i	−0.226778	+	0.973946i	$0.572819\pi$
$434$	−25.6279	−	9.32778i	−1.23018	−	0.447748i
$435$	−16.1853	−	33.4071i	−0.776025	−	1.60175i
$436$	17.2723	+	14.4932i	0.827193	+	0.694097i
$437$	−9.02318	+	21.4055i	−0.431637	+	1.02396i
$438$	4.34030	−	15.5675i	0.207388	−	0.743844i
$439$	−23.7694	+	6.05243i	−1.13445	+	0.288867i	−0.767296	−	0.641293i	$-0.778398\pi$
$439$	−23.7694	+	6.05243i	−1.13445	+	0.288867i	−0.367155	+	0.930160i	$0.619668\pi$
$440$	13.5876	−	4.19122i	0.647763	−	0.199809i
$441$	−0.626446	+	3.65376i	−0.0298308	+	0.173988i
$442$	−3.30085	+	44.0468i	−0.157006	+	2.09509i
$443$	3.83620	−	7.04445i	0.182263	−	0.334692i	−0.770999	−	0.636837i	$-0.780242\pi$
$443$	3.83620	−	7.04445i	0.182263	−	0.334692i	0.953262	+	0.302145i	$0.0977028\pi$
$444$	0.0540569	+	0.147434i	0.00256543	+	0.00699691i
$445$	−1.61644	+	16.1539i	−0.0766265	+	0.765767i
$446$	−13.6449	+	22.3289i	−0.646106	+	1.05731i
$447$	−6.62650	−	4.02787i	−0.313423	−	0.190512i
$448$	7.01067	−	7.94405i	0.331223	−	0.375321i
$449$	5.77675	−	18.7278i	0.272622	−	0.883818i	−0.710941	−	0.703252i	$-0.751731\pi$
$449$	5.77675	−	18.7278i	0.272622	−	0.883818i	0.983563	−	0.180567i	$-0.0577932\pi$
$450$	39.3554	−	47.3551i	1.85523	−	2.23234i
$451$	−4.36874	+	11.1314i	−0.205716	+	0.524156i
$452$	−7.33828	−	8.74542i	−0.345164	−	0.411350i
$453$	17.1268	+	0.814150i	0.804686	+	0.0382521i
$454$	8.17590	+	5.87807i	0.383714	+	0.275871i
$455$	46.3993	−	9.37981i	2.17523	−	0.439732i
$456$	5.41436	−	9.42939i	0.253551	−	0.441572i
$457$	−26.0993	+	2.61163i	−1.22087	+	0.122167i	−0.689066	−	0.724699i	$-0.741979\pi$
$457$	−26.0993	+	2.61163i	−1.22087	+	0.122167i	−0.531807	+	0.846865i	$0.678487\pi$
$458$	−10.2812	−	45.0447i	−0.480407	−	2.10480i
$459$	7.04531	−	23.4294i	0.328847	−	1.09359i
$460$	16.5071	+	7.94941i	0.769648	+	0.370643i
$461$	3.60553	+	36.0319i	0.167926	+	1.67817i	0.618772	+	0.785570i	$0.287630\pi$
$461$	3.60553	+	36.0319i	0.167926	+	1.67817i	−0.450846	+	0.892602i	$0.648878\pi$
$462$	29.6749	+	20.1293i	1.38060	+	0.936502i
$463$	28.0507	+	23.5373i	1.30363	+	1.09387i	0.989507	+	0.144488i	$0.0461534\pi$
$463$	28.0507	+	23.5373i	1.30363	+	1.09387i	0.314118	+	0.949384i	$0.398291\pi$
$464$	−21.0669	+	13.6063i	−0.978005	+	0.631656i
$465$	−8.09779	+	40.5511i	−0.375526	+	1.88051i
$466$	−5.59376	+	2.86775i	−0.259126	+	0.132846i
$467$	17.6365	−	25.8680i	0.816119	−	1.19703i	−0.161548	−	0.986865i	$-0.551649\pi$
$467$	17.6365	−	25.8680i	0.816119	−	1.19703i	0.977667	−	0.210161i	$-0.0673989\pi$
$468$	20.0509	−	12.3835i	0.926855	−	0.572429i
$469$	2.60130	+	2.41366i	0.120117	+	0.111452i
$470$	41.5725	−	17.5243i	1.91760	−	0.808335i
$471$	−30.4887	−	21.8106i	−1.40484	−	1.00498i
$472$	6.93769	+	2.33094i	0.319333	+	0.107290i
$473$	−5.34328	+	15.9035i	−0.245684	+	0.731242i
$474$	−18.0351	+	35.3847i	−0.828379	+	1.62527i
$475$	65.0249	+	57.3848i	2.98355	+	2.63300i
$476$	15.5235	+	8.96249i	0.711518	+	0.410795i
$477$	−2.65384	+	1.29352i	−0.121511	+	0.0592264i
$478$	26.9451	+	29.0399i	1.23244	+	1.32825i
$479$	22.2411	−	29.3623i	1.01622	−	1.34160i	0.0774732	−	0.996994i	$-0.475315\pi$
$479$	22.2411	−	29.3623i	1.01622	−	1.34160i	0.938748	−	0.344604i	$-0.111987\pi$
$480$	−42.0409	−	27.0122i	−1.91890	−	1.23293i
$481$	0.278959	+	0.0491879i	0.0127194	+	0.00224278i
$482$	11.6687	+	0.291000i	0.531495	+	0.0132547i
$483$	−2.71438	−	11.7641i	−0.123508	−	0.535286i
$484$	−13.1736	+	8.05021i	−0.598799	+	0.365918i
$485$	11.2298	+	8.95550i	0.509921	+	0.406648i
$486$	−27.8678	+	9.73140i	−1.26411	+	0.441425i
$487$	8.12883	+	35.6147i	0.368353	+	1.61386i	0.731305	+	0.682051i	$0.238912\pi$
$487$	8.12883	+	35.6147i	0.368353	+	1.61386i	−0.362952	+	0.931808i	$0.618231\pi$
$488$	3.87709	−	6.00290i	0.175507	−	0.271739i
$489$	11.2201	−	2.58886i	0.507390	−	0.117072i
$490$	−2.29789	+	9.02437i	−0.103808	+	0.407679i
$491$	16.1954	−	38.4201i	0.730890	−	1.73388i	0.0531372	−	0.998587i	$-0.483078\pi$
$491$	16.1954	−	38.4201i	0.730890	−	1.73388i	0.677753	−	0.735290i	$-0.262954\pi$
$492$	6.83107	−	2.31312i	0.307968	−	0.104283i
$493$	−17.7042	−	18.1514i	−0.797357	−	0.817497i
$494$	37.5299	+	65.0037i	1.68855	+	2.92466i
$495$	23.3579	−	49.0960i	1.04986	−	2.20670i
$496$	27.8586	+	2.08772i	1.25089	+	0.0937412i
$497$	4.79253	−	17.0337i	0.214974	−	0.764064i
$498$	−6.25262	+	24.8008i	−0.280187	+	1.11135i
$499$	−1.15013	−	1.78075i	−0.0514869	−	0.0797174i	0.813336	−	0.581794i	$-0.197649\pi$
$499$	−1.15013	−	1.78075i	−0.0514869	−	0.0797174i	−0.864823	+	0.502076i	$0.832570\pi$
$500$	25.7288	−	26.3784i	1.15063	−	1.17968i
$501$	3.19617	−	18.3805i	0.142794	−	0.821182i
$502$	27.4861	+	14.9681i	1.22676	+	0.668059i
$503$	13.5858	+	19.9268i	0.605762	+	0.888490i	0.999528	−	0.0307205i	$-0.00978019\pi$
$503$	13.5858	+	19.9268i	0.605762	+	0.888490i	−0.393766	+	0.919211i	$0.628828\pi$
$504$	0.589279	+	5.62042i	0.0262486	+	0.250353i
$505$	−38.6485	+	22.3137i	−1.71983	+	0.992947i
$506$	24.5381	+	4.96049i	1.09085	+	0.220521i
$507$	−0.545756	−	19.9869i	−0.0242379	−	0.887648i
$508$	−0.146538	−	2.93616i	−0.00650156	−	0.130271i
$509$	−0.556436	+	22.3124i	−0.0246636	+	0.988978i	0.856494	+	0.516156i	$0.172638\pi$
$509$	−0.556436	+	22.3124i	−0.0246636	+	0.988978i	−0.881158	+	0.472822i	$0.843235\pi$
$510$	22.3181	−	57.2636i	0.988263	−	2.53568i
$511$	−11.2145	+	3.76786i	−0.496099	+	0.166680i
$512$	−11.4771	+	23.8324i	−0.507220	+	1.05325i
$513$	−12.5362	−	39.6402i	−0.553485	−	1.75016i
$514$	−23.6287	−	18.8433i	−1.04222	−	0.831142i
$515$	10.2045	−	1.02112i	0.449665	−	0.0449957i
$516$	9.41034	−	3.71900i	0.414267	−	0.163720i
$517$	21.7305	−	16.4602i	0.955708	−	0.723920i
$518$	0.151739	−	0.211057i	0.00666704	−	0.00927329i
$519$	9.13693	−	32.7717i	0.401067	−	1.43852i
$520$	−13.7661	+	7.05745i	−0.603682	+	0.309490i
$521$	−10.4949	−	18.1777i	−0.459789	−	0.796377i	0.539161	−	0.842203i	$-0.318742\pi$
$521$	−10.4949	−	18.1777i	−0.459789	−	0.796377i	−0.998949	+	0.0458255i	$0.985408\pi$
$522$	−5.16974	+	30.1518i	−0.226273	+	1.31971i
$523$	−8.45793	+	14.6496i	−0.369839	+	0.640581i	−0.989540	−	0.144257i	$-0.953921\pi$
$523$	−8.45793	+	14.6496i	−0.369839	+	0.640581i	0.619701	+	0.784838i	$0.287254\pi$
$524$	−0.150896	+	3.02348i	−0.00659191	+	0.132081i
$525$	−44.8605	−	4.38181i	−1.95787	−	0.191238i
$526$	−54.9147	−	5.49504i	−2.39439	−	0.239595i
$527$	3.51212	+	28.0260i	0.152990	+	1.22083i
$528$	−34.8460	−	11.6160i	−1.51648	−	0.505521i
$529$	8.50572	+	11.8307i	0.369814	+	0.514380i
$530$	−6.90364	+	2.70948i	−0.299875	+	0.117692i
$531$	24.5128	−	13.4997i	1.06376	−	0.585837i
$532$	30.3752	−	2.27631i	1.31693	−	0.0986904i
$533$	2.57779	−	12.7516i	0.111656	−	0.552332i
$534$	8.82886	−	10.0522i	0.382062	−	0.434999i
$535$	−30.0511	+	16.3649i	−1.29922	+	0.707518i
$536$	−1.03195	−	0.529049i	−0.0445734	−	0.0228514i
$537$	9.33620	+	23.6238i	0.402887	+	1.01944i
$538$	4.84623	+	14.4241i	0.208936	+	0.621866i
$539$			5.62699i			0.242372i
$540$	−31.7188	+	8.31674i	−1.36496	+	0.357896i
$541$	−17.3416	+	36.0101i	−0.745572	+	1.54820i	0.0882103	+	0.996102i	$0.471885\pi$
$541$	−17.3416	+	36.0101i	−0.745572	+	1.54820i	−0.833782	+	0.552094i	$0.813829\pi$
$542$	−4.28508	+	2.61856i	−0.184060	+	0.112477i
$543$	−7.23957	−	12.4711i	−0.310680	−	0.535185i
$544$	−33.0771	−	8.42246i	−1.41817	−	0.361110i
$545$	−56.5213	+	2.82086i	−2.42111	+	0.120832i
$546$	−35.5967	−	15.9606i	−1.52340	−	0.683051i
$547$	6.93218	−	1.76515i	0.296398	−	0.0754723i	−0.0956556	−	0.995414i	$-0.530495\pi$
$547$	6.93218	−	1.76515i	0.296398	−	0.0754723i	0.392054	+	0.919942i	$0.371765\pi$
$548$	−6.03972	+	8.85865i	−0.258004	+	0.378423i
$549$	−6.86757	−	26.4467i	−0.293101	−	1.12872i
$550$	46.7318	−	80.9419i	1.99265	−	3.45137i
$551$	−42.2332	−	8.53784i	−1.79920	−	0.363724i
$552$	1.89512	+	3.46051i	0.0806616	+	0.147289i
$553$	28.8475	−	3.61506i	1.22672	−	0.153728i
$554$	11.8688	+	11.5765i	0.504257	+	0.491838i
$555$	−0.351153	−	0.178978i	−0.0149056	−	0.00759718i
$556$	−1.71375	−	0.0855296i	−0.0726791	−	0.00362726i
$557$	29.9126	+	9.22682i	1.26744	+	0.390953i	0.854331	−	0.519730i	$-0.173967\pi$
$557$	29.9126	+	9.22682i	1.26744	+	0.390953i	0.413107	+	0.910682i	$0.364444\pi$
$558$	24.8710	−	23.2969i	1.05287	−	0.986235i
$559$	2.72038	−	18.0486i	0.115060	−	0.763372i
$560$	1.10938	+	44.4847i	0.0468798	+	1.87982i
$561$	4.53054	−	36.8594i	0.191279	−	1.55620i
$562$	2.35642	+	4.32711i	0.0993995	+	0.182528i
$563$	0.302100	−	0.360029i	0.0127320	−	0.0151734i	−0.759641	−	0.650343i	$-0.774625\pi$
$563$	0.302100	−	0.360029i	0.0127320	−	0.0151734i	0.772373	+	0.635169i	$0.219070\pi$
$564$	−16.0379	−	3.62065i	−0.675318	−	0.152457i
$565$	28.4315	+	3.56293i	1.19612	+	0.149893i
$566$	−49.7074	+	11.3454i	−2.08936	+	0.476882i
$567$	17.3472	+	12.8835i	0.728513	+	0.541055i
$568$			5.78262i			0.242633i
$569$	27.1741	−	9.13000i	1.13920	−	0.382750i	0.315021	−	0.949085i	$-0.397988\pi$
$569$	27.1741	−	9.13000i	1.13920	−	0.382750i	0.824175	+	0.566335i	$0.191639\pi$
$570$	−23.4807	−	101.765i	−0.983498	−	4.26248i
$571$	−21.7010	+	4.38696i	−0.908160	+	0.183588i	−0.629681	−	0.776854i	$-0.716814\pi$
$571$	−21.7010	+	4.38696i	−0.908160	+	0.183588i	−0.278479	+	0.960442i	$0.589830\pi$
$572$	26.8213	−	23.6699i	1.12145	−	0.989690i
$573$	−20.7854	+	20.3696i	−0.868321	+	0.850954i
$574$	−9.51655	−	7.20851i	−0.397213	−	0.300877i
$575$	−30.0707	+	9.27559i	−1.25404	+	0.386819i
$576$	4.89500	+	12.3008i	0.203958	+	0.512534i
$577$	22.3824	+	1.67733i	0.931791	+	0.0698281i	0.531968	−	0.846764i	$-0.321453\pi$
$577$	22.3824	+	1.67733i	0.931791	+	0.0698281i	0.399823	+	0.916592i	$0.369072\pi$
$578$	0.487921	−	9.77643i	0.0202949	−	0.406646i
$579$	−24.4002	−	0.550748i	−1.01404	−	0.0228883i
$580$	−8.38591	+	32.9329i	−0.348206	+	1.36746i
$581$	17.5939	−	6.40365i	0.729917	−	0.265668i
$582$	−3.23288	−	11.3869i	−0.134007	−	0.472004i
$583$	−3.63855	+	2.61594i	−0.150693	+	0.108341i
$584$	3.19435	−	2.17787i	0.132183	−	0.0901210i
$585$	−15.7507	+	57.0146i	−0.651211	+	2.35726i
$586$	−43.4820	+	40.3454i	−1.79623	+	1.66665i
$587$	−5.61354	+	12.4409i	−0.231696	+	0.513490i	−0.990448	−	0.137889i	$-0.955968\pi$
$587$	−5.61354	+	12.4409i	−0.231696	+	0.513490i	0.758752	+	0.651380i	$0.225809\pi$
$588$	2.59459	−	2.18760i	0.106999	−	0.0902150i
$589$	31.7595	+	35.9879i	1.30863	+	1.48286i
$590$	64.0767	−	28.9125i	2.63800	−	1.19031i
$591$	−33.1182	+	10.3015i	−1.36230	+	0.423746i
$592$	−0.0910703	+	0.250214i	−0.00374297	+	0.0102837i
$593$	6.55444	+	8.21901i	0.269159	+	0.337514i	0.897981	−	0.440035i	$-0.145034\pi$
$593$	6.55444	+	8.21901i	0.269159	+	0.337514i	−0.628822	+	0.777549i	$0.716463\pi$
$594$	−39.1962	+	21.7072i	−1.60824	+	0.890657i
$595$	−43.8619	+	10.0112i	−1.79816	+	0.410419i
$596$	2.26100	+	6.72952i	0.0926141	+	0.275652i
$597$	−29.5460	+	4.52485i	−1.20924	+	0.185190i
$598$	−27.2275	−	0.679011i	−1.11341	−	0.0277668i
$599$	−1.27178	−	0.914344i	−0.0519633	−	0.0373591i	0.557463	−	0.830202i	$-0.311775\pi$
$599$	−1.27178	−	0.914344i	−0.0519633	−	0.0373591i	−0.609426	+	0.792843i	$0.708600\pi$
$600$	14.5000	−	2.59213i	0.591961	−	0.105823i
$601$	37.7947	−	0.942542i	1.54168	−	0.0384471i	0.754965	−	0.655765i	$-0.227654\pi$
$601$	37.7947	−	0.942542i	1.54168	−	0.0384471i	0.786714	+	0.617318i	$0.211781\pi$
$602$	−13.8393	−	9.43546i	−0.564047	−	0.384561i
$603$	−4.15945	+	1.53624i	−0.169386	+	0.0625606i
$604$	−11.5066	−	10.6766i	−0.468198	−	0.434424i
$605$	10.4949	−	37.3009i	0.426677	−	1.51650i
$606$	36.6033	+	3.57527i	1.48691	+	0.145235i
$607$	21.8934	−	2.74360i	0.888627	−	0.111359i	0.333133	−	0.942880i	$-0.391894\pi$
$607$	21.8934	−	2.74360i	0.888627	−	0.111359i	0.555494	+	0.831520i	$0.312529\pi$
$608$	−54.5044	+	19.8380i	−2.21044	+	0.804536i
$609$	20.3905	−	9.25857i	0.826266	−	0.375176i
$610$	−11.9190	−	67.5961i	−0.482587	−	2.73688i
$611$	−20.1726	+	21.7409i	−0.816097	+	0.879544i
$612$	−18.7571	+	12.2407i	−0.758209	+	0.494803i
$613$	−3.16401	−	42.2208i	−0.127793	−	1.70528i	−0.581023	−	0.813887i	$-0.697347\pi$
$613$	−3.16401	−	42.2208i	−0.127793	−	1.70528i	0.453229	−	0.891394i	$-0.350272\pi$
$614$	21.4849	+	41.9078i	0.867060	+	1.69126i
$615$	−8.61953	+	15.9176i	−0.347573	+	0.641861i
$616$	2.32328	+	8.25743i	0.0936076	+	0.332701i
$617$	−3.72922	−	18.4474i	−0.150133	−	0.742664i	−0.982178	−	0.187955i	$-0.939814\pi$
$617$	−3.72922	−	18.4474i	−0.150133	−	0.742664i	0.832045	−	0.554708i	$-0.187170\pi$
$618$	−7.32923	−	4.20844i	−0.294825	−	0.169288i
$619$	21.2238	−	20.7011i	0.853056	−	0.832047i	−0.134239	−	0.990949i	$-0.542859\pi$
$619$	21.2238	−	20.7011i	0.853056	−	0.832047i	0.987294	+	0.158902i	$0.0507953\pi$
$620$	29.5975	−	23.6032i	1.18866	−	0.947928i
$621$	14.6454	+	3.61870i	0.587700	+	0.145214i
$622$	16.7998	+	21.0663i	0.673612	+	0.844683i
$623$	−9.71774	−	1.21779i	−0.389333	−	0.0487897i
$624$	39.5288	+	5.86241i	1.58242	+	0.234684i
$625$	−0.954596	+	38.2781i	−0.0381838	+	1.53112i
$626$	−5.86941	−	1.03493i	−0.234589	−	0.0413643i
$627$	−28.9231	−	56.0893i	−1.15508	−	2.23999i
$628$	8.46831	+	33.2571i	0.337922	+	1.32710i
$629$	−0.266205	−	0.0401240i	−0.0106143	−	0.00159985i
$630$	40.8680	+	35.7237i	1.62822	+	1.42327i
$631$	0.0462192	−	0.616753i	0.00183996	−	0.0245525i	−0.996208	−	0.0870007i	$-0.972272\pi$
$631$	0.0462192	−	0.616753i	0.00183996	−	0.0245525i	0.998048	+	0.0624482i	$0.0198908\pi$
$632$	−8.75487	+	3.69049i	−0.348250	+	0.146800i
$633$	24.1314	−	6.85118i	0.959138	−	0.272310i
$634$	50.8975	+	5.09306i	2.02140	+	0.202271i
$635$	5.28212	+	5.15204i	0.209615	+	0.204452i
$636$	2.62075	+	0.660728i	0.103920	+	0.0261996i
$637$	−1.06304	−	6.02880i	−0.0421192	−	0.238870i
$638$	−0.000213762		46.4355i	−8.46292e−6		1.83840i
$639$	16.2791	+	14.9621i	0.643992	+	0.591892i
$640$	−7.20514	−	23.3585i	−0.284808	−	0.923325i
$641$	13.7065	+	6.18462i	0.541375	+	0.244278i	0.663421	−	0.748247i	$-0.269104\pi$
$641$	13.7065	+	6.18462i	0.541375	+	0.244278i	−0.122045	+	0.992525i	$0.538945\pi$
$642$	27.9885	+	3.44018i	1.10462	+	0.135773i
$643$	37.8089	+	15.9378i	1.49104	+	0.628525i	0.973818	−	0.227328i	$-0.0729988\pi$
$643$	37.8089	+	15.9378i	1.49104	+	0.628525i	0.517220	+	0.855853i	$0.326967\pi$
$644$	−5.04238	+	9.83553i	−0.198698	+	0.387574i
$645$	−10.9650	+	22.9075i	−0.431747	+	0.901984i
$646$	−37.1976	−	60.8711i	−1.46352	−	2.39494i
$647$	−7.91424	+	9.92414i	−0.311141	+	0.390158i	−0.912673	−	0.408690i	$-0.865986\pi$
$647$	−7.91424	+	9.92414i	−0.311141	+	0.390158i	0.601532	+	0.798848i	$0.294557\pi$
$648$	−6.59738	−	2.51750i	−0.259170	−	0.0988967i
$649$	33.2102	−	26.4843i	1.30362	−	1.03960i
$650$	−34.7775	+	95.5503i	−1.36408	+	3.74779i
$651$	−24.3337	−	5.49348i	−0.953714	−	0.215307i
$652$	−9.38070	−	4.80920i	−0.367376	−	0.188343i
$653$	0.0729549	+	1.46179i	0.00285494	+	0.0572042i	0.999775	−	0.0212233i	$-0.00675610\pi$
$653$	0.0729549	+	1.46179i	0.00285494	+	0.0572042i	−0.996920	+	0.0784276i	$0.975010\pi$
$654$	39.2362	+	25.2101i	1.53426	+	0.985792i
$655$	−4.88395	−	5.82046i	−0.190832	−	0.227424i
$656$	11.3839	+	4.46783i	0.444465	+	0.174440i
$657$	2.13405	−	14.6278i	0.0832572	−	0.570683i
$658$	9.94327	+	25.3350i	0.387629	+	0.987663i
$659$	4.11316	−	7.55303i	0.160226	−	0.294224i	−0.785699	−	0.618608i	$-0.787697\pi$
$659$	4.11316	−	7.55303i	0.160226	−	0.294224i	0.945925	+	0.324384i	$0.105157\pi$
$660$	−45.3205	+	20.5786i	−1.76410	+	0.801020i
$661$	−20.6172	−	31.9216i	−0.801915	−	1.24161i	−0.966861	−	0.255305i	$-0.917824\pi$
$661$	−20.6172	−	31.9216i	−0.801915	−	1.24161i	0.164945	−	0.986303i	$-0.447255\pi$
$662$	−3.62628	−	28.9370i	−0.140939	−	1.12467i
$663$	2.10935	+	40.3473i	0.0819203	+	1.56696i
$664$	−4.96790	+	3.57168i	−0.192792	+	0.138608i
$665$	−52.0009	+	56.0437i	−2.01651	+	2.17328i
$666$	0.149546	+	0.288331i	0.00579478	+	0.0111726i
$667$	10.6343	−	11.4609i	0.411761	−	0.443769i
$668$	−13.0836	+	10.9785i	−0.506222	+	0.424770i
$669$	−9.79283	+	21.8408i	−0.378613	+	0.844415i
$670$	−10.7223	+	3.01679i	−0.414239	+	0.116549i
$671$	−17.0582	−	37.8048i	−0.658524	−	1.45944i
$672$	16.9227	−	24.9477i	0.652809	−	0.962379i
$673$	3.04869	−	24.3279i	0.117518	−	0.937773i	−0.815703	−	0.578471i	$-0.803650\pi$
$673$	3.04869	−	24.3279i	0.117518	−	0.937773i	0.933221	−	0.359302i	$-0.116985\pi$
$674$	−21.2299	+	10.2238i	−0.817745	+	0.393805i
$675$	30.2204	−	47.5271i	1.16319	−	1.82932i
$676$	−11.4126	+	14.3109i	−0.438945	+	0.550420i
$677$	15.4161	−	15.0364i	0.592487	−	0.577895i	−0.339401	−	0.940642i	$-0.610224\pi$
$677$	15.4161	−	15.0364i	0.592487	−	0.577895i	0.931888	+	0.362746i	$0.118161\pi$
$678$	−17.3480	−	16.0204i	−0.666245	−	0.615258i
$679$	−5.56977	+	6.63779i	−0.213748	+	0.254735i
$680$	12.9120	−	7.03149i	0.495152	−	0.269645i
$681$	8.09937	+	4.38587i	0.310368	+	0.168067i
$682$	31.2332	−	41.2335i	1.19598	−	1.57891i
$683$	−3.45814	+	8.81120i	−0.132322	+	0.337151i	−0.981644	−	0.190725i	$-0.938916\pi$
$683$	−3.45814	+	8.81120i	−0.132322	+	0.337151i	0.849321	+	0.527876i	$0.177011\pi$
$684$	−14.6182	+	35.1421i	−0.558941	+	1.34369i
$685$	−4.01077	−	26.6097i	−0.153244	−	1.01671i
$686$	−36.0425	−	10.1408i	−1.37611	−	0.387177i
$687$	−14.5483	−	39.6788i	−0.555052	−	1.51384i
$688$	16.2642	+	5.46448i	0.620066	+	0.208331i
$689$	3.40417	−	3.49013i	0.129689	−	0.132963i
$690$	35.9515	+	11.9845i	1.36865	+	0.456241i
$691$	18.9217	+	0.944342i	0.719815	+	0.0359245i	0.406404	−	0.913693i	$-0.366782\pi$
$691$	18.9217	+	0.944342i	0.719815	+	0.0359245i	0.313411	+	0.949618i	$0.398528\pi$
$692$	−25.7341	+	17.5452i	−0.978262	+	0.666968i
$693$	29.2574	+	14.8250i	1.11140	+	0.563156i
$694$	3.09832	+	10.0445i	0.117610	+	0.381284i
$695$	3.29912	−	2.76829i	0.125143	−	0.105007i
$696$	−5.59498	+	4.71730i	−0.212077	+	0.178809i
$697$	−2.14703	+	12.1764i	−0.0813246	+	0.461214i
$698$	29.0113	+	38.3003i	1.09809	+	1.44969i
$699$	−4.74303	+	3.25021i	−0.179398	+	0.122934i
$700$	28.8122	+	29.5397i	1.08900	+	1.11650i
$701$	3.52427	−	15.4408i	0.133110	−	0.583192i	−0.863744	−	0.503931i	$-0.831887\pi$
$701$	3.52427	−	15.4408i	0.133110	−	0.583192i	0.996854	−	0.0792614i	$-0.0252562\pi$
$702$	37.8943	−	30.6621i	1.43023	−	1.15727i
$703$	−0.412175	+	0.198493i	−0.0155455	+	0.00748630i
$704$	10.4785	+	17.1474i	0.394925	+	0.646266i
$705$	35.6890	−	20.7178i	1.34413	−	0.780277i
$706$	0.707879	−	0.319407i	0.0266414	−	0.0120211i
$707$	−12.8756	−	23.6437i	−0.484239	−	0.889211i
$708$	−25.1229	−	5.01687i	−0.944177	−	0.188546i
$709$	−21.0554	−	4.25643i	−0.790750	−	0.159854i	−0.214064	−	0.976820i	$-0.568670\pi$
$709$	−21.0554	−	4.25643i	−0.790750	−	0.159854i	−0.576686	+	0.816966i	$0.695654\pi$
$710$	37.7786	+	40.7156i	1.41780	+	1.52803i
$711$	−12.2632	+	34.1954i	−0.459905	+	1.28243i
$712$	3.16479	−	0.477015i	0.118605	−	0.0178769i
$713$	−17.1517	+	3.02432i	−0.642338	+	0.113262i
$714$	34.1988	+	14.3208i	1.27986	+	0.535943i
$715$	−8.93965	+	89.3384i	−0.334324	+	3.34107i
$716$	7.40632	−	22.0438i	0.276787	−	0.823815i
$717$	27.8132	+	23.2261i	1.03870	+	0.867395i
$718$	−31.3079	−	43.5466i	−1.16840	−	1.62514i
$719$	−4.30054	−	1.32654i	−0.160383	−	0.0494716i	0.213524	−	0.976938i	$-0.431506\pi$
$719$	−4.30054	−	1.32654i	−0.160383	−	0.0494716i	−0.373907	+	0.927466i	$0.621982\pi$
$720$	−50.2096	−	23.8877i	−1.87120	−	0.890241i
$721$	0.462339	+	6.16948i	0.0172184	+	0.229764i
$722$	−77.7027	−	35.0608i	−2.89180	−	1.30483i
$723$	10.6210	−	1.08818i	0.395001	−	0.0404698i
$724$	−2.29238	+	13.0007i	−0.0851955	+	0.483168i
$725$	−27.9155	−	51.2620i	−1.03676	−	1.90382i
$726$	−24.9193	+	19.9691i	−0.924840	+	0.741121i
$727$	−4.14607	−	2.67782i	−0.153769	−	0.0993147i	0.463384	−	0.886157i	$-0.346635\pi$
$727$	−4.14607	−	2.67782i	−0.153769	−	0.0993147i	−0.617154	+	0.786843i	$0.711714\pi$
$728$	−4.04916	−	8.40817i	−0.150072	−	0.311627i
$729$	−24.1574	+	12.0590i	−0.894720	+	0.446628i
$730$	8.26322	−	36.2036i	0.305836	−	1.33995i
$731$	−2.15700	+	17.2125i	−0.0797796	+	0.636626i
$732$	−10.8000	+	22.5628i	−0.399179	+	0.833945i
$733$	4.47195	+	22.1215i	0.165175	+	0.817074i	0.973562	+	0.228423i	$0.0733569\pi$
$733$	4.47195	+	22.1215i	0.165175	+	0.817074i	−0.808387	+	0.588652i	$0.799659\pi$
$734$	33.6378	+	38.1163i	1.24159	+	1.40690i
$735$	−1.03916	+	8.45432i	−0.0383298	+	0.311842i
$736$	4.17029	−	20.6292i	0.153719	−	0.760403i
$737$	−5.82881	+	3.36527i	−0.214707	+	0.123961i
$738$	13.4095	−	6.53599i	0.493609	−	0.240593i
$739$	−5.29357	+	17.1613i	−0.194727	+	0.631290i	0.804572	+	0.593855i	$0.202395\pi$
$739$	−5.29357	+	17.1613i	−0.194727	+	0.631290i	−0.999299	+	0.0374345i	$0.988081\pi$
$740$	0.140155	+	0.332488i	0.00515221	+	0.0122225i
$741$	41.5847	+	54.6304i	1.52765	+	2.00690i
$742$	−1.53020	−	4.20419i	−0.0561754	−	0.154341i
$743$	−6.98519	+	11.4308i	−0.256262	+	0.419354i	−0.955259	−	0.295771i	$-0.904424\pi$
$743$	−6.98519	+	11.4308i	−0.256262	+	0.419354i	0.698997	+	0.715124i	$0.253630\pi$
$744$	8.14112	−	0.425616i	0.298468	−	0.0156038i
$745$	−15.6484	−	8.52165i	−0.573312	−	0.312209i
$746$	−3.93139	+	1.54296i	−0.143938	+	0.0564917i
$747$	−2.79916	+	23.2270i	−0.102416	+	0.849830i
$748$	−24.9222	+	23.1244i	−0.911246	+	0.845512i
$749$	−9.41738	−	18.3693i	−0.344104	−	0.671199i
$750$	45.8764	−	60.8639i	1.67517	−	2.22243i
$751$	−1.98288	+	0.557895i	−0.0723562	+	0.0203579i	−0.306827	−	0.951765i	$-0.599267\pi$
$751$	−1.98288	+	0.557895i	−0.0723562	+	0.0203579i	0.234471	+	0.972123i	$0.424664\pi$
$752$	−16.8336	−	22.2234i	−0.613858	−	0.810405i
$753$	26.6733	+	10.3958i	0.972030	+	0.378843i
$754$	−8.77228	−	49.7514i	−0.319467	−	1.81184i
$755$	39.3976			1.43383
$756$	−4.53860	−	19.2540i	−0.165067	−	0.700262i
$757$	11.7944	+	24.4913i	0.428674	+	0.890150i	0.997697	+	0.0678288i	$0.0216072\pi$
$757$	11.7944	+	24.4913i	0.428674	+	0.890150i	−0.569023	+	0.822321i	$0.692679\pi$
$758$	23.2543	+	23.8414i	0.844634	+	0.865960i
$759$	22.8389	+	1.65722i	0.829000	+	0.0601531i
$760$	11.3981	−	22.2327i	0.413451	−	0.806467i
$761$	6.04768	+	21.4947i	0.219228	+	0.779183i	0.989878	+	0.141924i	$0.0453288\pi$
$761$	6.04768	+	21.4947i	0.219228	+	0.779183i	−0.770649	+	0.637259i	$0.780068\pi$
$762$	−1.07007	−	5.98584i	−0.0387646	−	0.216844i
$763$	−0.851129	−	34.1292i	−0.0308130	−	1.23556i
$764$	26.5682	−	1.99101i	0.961202	−	0.0720322i
$765$	13.6139	−	54.5430i	0.492211	−	1.97201i
$766$	32.6098	+	18.8273i	1.17824	+	0.680256i
$767$	−30.5783	+	34.6495i	−1.10412	+	1.25112i
$768$	−11.2051	+	33.6134i	−0.404328	+	1.21292i
$769$	14.5325	−	9.38607i	0.524054	−	0.338470i	−0.253449	−	0.967349i	$-0.581565\pi$
$769$	14.5325	−	9.38607i	0.524054	−	0.338470i	0.777504	+	0.628878i	$0.216486\pi$
$770$	70.3050	+	42.9625i	2.53362	+	1.54826i
$771$	−23.6226	−	14.3588i	−0.850746	−	0.517120i
$772$	16.7528	+	14.7844i	0.602945	+	0.532102i
$773$	23.4741	+	34.4302i	0.844304	+	1.23837i	0.969219	+	0.246199i	$0.0791817\pi$
$773$	23.4741	+	34.4302i	0.844304	+	1.23837i	−0.124915	+	0.992167i	$0.539866\pi$
$774$	18.3330	−	10.0964i	0.658967	−	0.362907i
$775$	−9.69103	+	64.2958i	−0.348112	+	2.30957i
$776$	1.16463	−	2.58109i	0.0418078	−	0.0926557i
$777$	0.113219	−	0.209081i	0.00406171	−	0.00750074i
$778$	15.0794	+	6.35650i	0.540623	+	0.227892i
$779$	8.64151	+	19.1516i	0.309614	+	0.686176i
$780$	44.6691	−	30.6099i	1.59941	−	1.09601i
$781$	28.1927	+	18.2088i	1.00881	+	0.651561i
$782$	25.8850			0.925647
$783$	−1.19655	+	27.9565i	−0.0427611	+	0.999085i
$784$	5.75462			0.205522
$785$	−72.3562	−	46.7326i	−2.58250	−	1.66796i
$786$	0.482698	+	6.24294i	0.0172173	+	0.222678i
$787$	14.6037	+	32.3652i	0.520567	+	1.15370i	0.966038	+	0.258399i	$0.0831950\pi$
$787$	14.6037	+	32.3652i	0.520567	+	1.15370i	−0.445471	+	0.895296i	$0.646964\pi$
$788$	29.2585	+	12.3335i	1.04229	+	0.439363i
$789$	−50.4622	+	1.37791i	−1.79650	+	0.0490548i
$790$	−37.5329	+	83.1814i	−1.33536	+	2.95946i
$791$	−2.57633	+	17.0928i	−0.0916037	+	0.607751i
$792$	−10.5159	−	2.07411i	−0.373668	−	0.0737001i
$793$	25.4183	+	37.2818i	0.902630	+	1.32392i
$794$	−36.8336	−	32.5058i	−1.30718	−	1.15359i
$795$	−5.94986	+	3.25840i	−0.211020	+	0.115563i
$796$	23.3495	+	14.2686i	0.827601	+	0.505737i
$797$	27.7847	−	17.9453i	0.984186	−	0.635655i	0.0523861	−	0.998627i	$-0.483317\pi$
$797$	27.7847	−	17.9453i	0.984186	−	0.635655i	0.931800	+	0.362972i	$0.118238\pi$
$798$	61.7256	−	12.6302i	2.18506	−	0.447103i
$799$	18.6510	−	21.1341i	0.659824	−	0.747671i
$800$	−68.0479	−	39.2875i	−2.40586	−	1.38902i
$801$	6.84577	−	10.1437i	0.241883	−	0.358409i
$802$	44.4906	−	3.33411i	1.57102	−	0.117732i
$803$	−0.559411	−	22.4317i	−0.0197412	−	0.791596i
$804$	3.81777	+	1.37934i	0.134642	+	0.0486454i
$805$	−7.51346	−	26.7044i	−0.264815	−	0.941208i
$806$	−25.6737	+	50.0784i	−0.904318	+	1.76394i
$807$	6.06862	+	12.5257i	0.213625	+	0.440926i
$808$	6.14309	+	6.29820i	0.216113	+	0.221570i
$809$	8.20268	+	17.0330i	0.288391	+	0.598850i	0.993954	−	0.109797i	$-0.0350201\pi$
$809$	8.20268	+	17.0330i	0.288391	+	0.598850i	−0.705563	+	0.708647i	$0.749306\pi$
$810$	−62.8994	+	25.3757i	−2.21006	+	0.891610i
$811$	−36.0934			−1.26741			−0.633706	−	0.773574i	$-0.718467\pi$
$811$	−36.0934			−1.26741			−0.633706	+	0.773574i	$0.718467\pi$
$812$	−19.7350	−	5.55267i	−0.692563	−	0.194860i
$813$	−3.58451	+	2.87245i	−0.125714	+	0.100741i
$814$	0.297691	+	0.393006i	0.0104341	+	0.0137749i
$815$	25.4695	−	7.16601i	0.892159	−	0.251015i
$816$	−37.6954	−	4.63330i	−1.31960	−	0.162198i
$817$	13.4483	+	26.2320i	0.470498	+	0.917741i
$818$	−11.2169	+	10.4078i	−0.392191	+	0.363900i
$819$	−34.1474	−	10.3564i	−1.19321	−	0.361882i
$820$	15.4261	−	6.05429i	0.538702	−	0.211425i
$821$	27.2991	+	14.8663i	0.952744	+	0.518837i	0.878154	−	0.478378i	$-0.158775\pi$
$821$	27.2991	+	14.8663i	0.952744	+	0.518837i	0.0745895	+	0.997214i	$0.476235\pi$
$822$	−10.0706	+	19.7584i	−0.351251	+	0.689152i
$823$	−28.5801	+	46.7692i	−0.996239	+	1.63027i	−0.245815	+	0.969317i	$0.579055\pi$
$823$	−28.5801	+	46.7692i	−0.996239	+	1.63027i	−0.750425	+	0.660956i	$0.770151\pi$
$824$	−0.691497	−	1.89987i	−0.0240894	−	0.0661852i
$825$	33.0211	−	78.8560i	1.14965	−	2.74541i
$826$	16.4728	+	39.0781i	0.573163	+	1.35970i
$827$	−6.81904	+	22.1068i	−0.237121	+	0.768728i	0.756301	+	0.654223i	$0.227004\pi$
$827$	−6.81904	+	22.1068i	−0.237121	+	0.768728i	−0.993423	+	0.114505i	$0.963472\pi$
$828$	−8.11491	−	11.1752i	−0.282013	−	0.388366i
$829$	2.35137	−	1.35757i	0.0816666	−	0.0471502i	−0.458611	−	0.888637i	$-0.651653\pi$
$829$	2.35137	−	1.35757i	0.0816666	−	0.0471502i	0.540277	+	0.841487i	$0.318319\pi$
$830$	−11.6449	+	57.6041i	−0.404201	+	1.99947i
$831$	12.1104	+	9.12824i	0.420104	+	0.316655i
$832$	−14.4663	−	16.3923i	−0.501527	−	0.568299i
$833$	1.15285	+	5.70280i	0.0399438	+	0.197590i
$834$	−3.53858	+	0.273600i	−0.122531	+	0.00947399i
$835$	5.33034	−	42.5351i	0.184464	−	1.47199i
$836$	−12.8558	+	56.3250i	−0.444627	+	1.94804i
$837$	19.8664	−	24.0200i	0.686682	−	0.830251i
$838$	−3.48412	−	7.23486i	−0.120357	−	0.249924i
$839$	32.7684	+	21.1640i	1.13129	+	0.730664i	0.966754	−	0.255707i	$-0.0823083\pi$
$839$	32.7684	+	21.1640i	1.13129	+	0.730664i	0.164535	+	0.986371i	$0.447388\pi$
$840$	1.96570	+	12.8355i	0.0678233	+	0.442867i
$841$	24.7453	+	15.1218i	0.853286	+	0.521443i
$842$	−0.402558	+	2.28302i	−0.0138731	+	0.0786780i
$843$	2.63948	+	3.65302i	0.0909084	+	0.125817i
$844$	−20.9326	−	9.44516i	−0.720531	−	0.325116i
$845$	−3.43326	−	45.8136i	−0.118108	−	1.57604i
$846$	−33.8544	−	3.22594i	−1.16394	−	0.110910i
$847$	22.3376	+	6.89023i	0.767528	+	0.236751i
$848$	2.67527	+	3.72108i	0.0918692	+	0.127782i
$849$	−43.7860	+	16.0542i	−1.50273	+	0.550979i
$850$	30.7782	−	91.6068i	1.05568	−	3.14209i
$851$	0.0165282	−	0.165174i	0.000566579	−	0.00566211i
$852$	−2.56443	−	20.0786i	−0.0878559	−	0.687880i
$853$	−21.8562	+	3.85383i	−0.748341	+	0.131953i	−0.534797	−	0.844981i	$-0.679612\pi$
$853$	−21.8562	+	3.85383i	−0.748341	+	0.131953i	−0.213544	+	0.976933i	$0.568501\pi$
$854$	40.9450	−	6.17146i	1.40111	−	0.211183i
$855$	−33.0975	−	89.6132i	−1.13191	−	3.06471i
$856$	4.58836	+	4.94508i	0.156827	+	0.169019i
$857$	−40.1787	−	8.12231i	−1.37248	−	0.277453i	−0.544759	−	0.838593i	$-0.683379\pi$
$857$	−40.1787	−	8.12231i	−1.37248	−	0.277453i	−0.827721	+	0.561140i	$0.810363\pi$
$858$	48.8277	−	55.5931i	1.66695	−	1.89792i
$859$	−23.5556	−	43.2553i	−0.803705	−	1.47585i	−0.878024	−	0.478616i	$-0.841139\pi$
$859$	−23.5556	−	43.2553i	−0.803705	−	1.47585i	0.0743187	−	0.997235i	$-0.476322\pi$
$860$	21.1925	−	9.56243i	0.722659	−	0.326076i
$861$	−9.46995	−	5.43765i	−0.322735	−	0.185315i
$862$	1.08593	+	1.77705i	0.0369870	+	0.0605266i
$863$	−27.8330	+	13.4037i	−0.947445	+	0.456266i	−0.842790	−	0.538243i	$-0.819088\pi$
$863$	−27.8330	+	13.4037i	−0.947445	+	0.456266i	−0.104656	+	0.994509i	$0.533374\pi$
$864$	18.2492	+	32.9523i	0.620852	+	1.12106i
$865$	17.3952	−	76.2134i	0.591455	−	2.59133i
$866$	0.240389	+	0.246459i	0.00816877	+	0.00837502i
$867$	−0.690222	−	8.92694i	−0.0234412	−	0.303175i
$868$	13.7895	+	18.2046i	0.468044	+	0.617905i
$869$	−9.57535	+	54.3045i	−0.324821	+	1.84215i
$870$	−8.57572	+	69.7673i	−0.290744	+	2.36533i
$871$	5.60928	−	4.70674i	0.190063	−	0.159482i
$872$	3.28849	+	10.6610i	0.111362	+	0.361028i
$873$	−4.25283	−	9.95702i	−0.143936	−	0.336994i
$874$	36.3439	−	24.7788i	1.22935	−	0.838157i
$875$	−55.7239	−	2.78106i	−1.88381	−	0.0940171i
$876$	−10.1257	+	8.97867i	−0.342115	+	0.303361i
$877$	38.8610	−	39.8422i	1.31224	−	1.34538i	0.411263	−	0.911517i	$-0.365088\pi$
$877$	38.8610	−	39.8422i	1.31224	−	1.34538i	0.900980	−	0.433860i	$-0.142849\pi$
$878$	44.0270	+	14.7923i	1.48584	+	0.499215i
$879$	−34.7770	+	41.6452i	−1.17300	+	1.40466i
$880$	−81.2448	−	22.8587i	−2.73876	−	0.770568i
$881$	6.37410	+	42.2894i	0.214749	+	1.42477i	0.793156	+	0.609018i	$0.208436\pi$
$881$	6.37410	+	42.2894i	0.214749	+	1.42477i	−0.578407	+	0.815748i	$0.696325\pi$
$882$	4.75017	−	5.16829i	0.159946	−	0.174025i
$883$	7.78307	−	19.8309i	0.261921	−	0.667364i	−0.738052	−	0.674744i	$-0.764254\pi$
$883$	7.78307	−	19.8309i	0.261921	−	0.667364i	0.999973	+	0.00738017i	$0.00234920\pi$
$884$	22.3332	−	29.4839i	0.751148	−	0.991652i
$885$	54.7879	−	33.6585i	1.84168	−	1.13142i
$886$	−13.3392	+	7.26416i	−0.448140	+	0.244044i
$887$	27.9451	−	33.3037i	0.938305	−	1.11823i	−0.0545033	−	0.998514i	$-0.517358\pi$
$887$	27.9451	−	33.3037i	0.938305	−	1.11823i	0.992808	−	0.119715i	$-0.0381980\pi$
$888$	−0.0171108	+	0.0757935i	−0.000574202	+	0.00254346i
$889$	−3.18653	+	3.10805i	−0.106873	+	0.104241i
$890$	19.1670	−	24.0346i	0.642478	−	0.805642i
$891$	−33.0482	+	24.2377i	−1.10716	+	0.811992i
$892$	19.7426	−	9.50755i	0.661032	−	0.318336i
$893$	5.95594	−	47.5273i	0.199308	−	1.59044i
$894$	6.40244	+	13.2147i	0.214130	+	0.441967i
$895$	24.0056	+	53.2019i	0.802419	+	1.77834i
$896$	14.1954	−	3.99396i	0.474234	−	0.133429i
$897$	−24.7829	+	2.53913i	−0.827476	+	0.0847791i
$898$	−28.4289	+	23.8547i	−0.948686	+	0.796042i
$899$	−11.8021	−	30.0718i	−0.393624	−	1.00295i
$900$	−49.1978	+	15.4308i	−1.63993	+	0.514361i
$901$	−3.15162	+	3.39664i	−0.104996	+	0.113159i
$902$	18.3851	−	13.2180i	0.612156	−	0.440110i
$903$	−13.6501	−	6.95729i	−0.454248	−	0.231524i
$904$	−0.702408	−	5.60509i	−0.0233618	−	0.186422i
$905$	−17.9767	−	27.8333i	−0.597564	−	0.925210i
$906$	−26.4064	−	18.8903i	−0.877295	−	0.627589i
$907$	−10.6412	+	19.5405i	−0.353334	+	0.648830i	−0.992772	−	0.120012i	$-0.961707\pi$
$907$	−10.6412	+	19.5405i	−0.353334	+	0.648830i	0.639438	+	0.768842i	$0.279167\pi$
$908$	−3.08060	−	7.84924i	−0.102233	−	0.260486i
$909$	33.6254	−	0.997775i	1.11528	−	0.0330941i
$910$	−83.4418	−	32.7485i	−2.76607	−	1.08560i
$911$	16.4988	+	19.6625i	0.546631	+	0.651449i	0.966661	−	0.256061i	$-0.0824248\pi$
$911$	16.4988	+	19.6625i	0.546631	+	0.651449i	−0.420030	+	0.907510i	$0.637980\pi$
$912$	−57.3615	+	29.5791i	−1.89943	+	0.979461i
$913$	1.77010	+	35.4673i	0.0585818	+	1.17380i
$914$	44.1981	+	22.6591i	1.46194	+	0.749495i
$915$	−18.6477	−	59.9504i	−0.616473	−	1.98190i
$916$	−13.2327	+	36.3564i	−0.437219	+	1.20125i
$917$	3.58365	−	2.85787i	0.118343	−	0.0943751i
$918$	−35.2770	+	30.0301i	−1.16431	+	0.991141i
$919$	13.0268	−	16.3351i	0.429715	−	0.538845i	−0.519085	−	0.854722i	$-0.673727\pi$
$919$	13.0268	−	16.3351i	0.429715	−	0.538845i	0.948800	+	0.315877i	$0.102299\pi$
$920$	4.72717	+	7.73567i	0.155850	+	0.255037i
$921$	24.3502	+	35.5343i	0.802366	+	1.17089i
$922$	31.2824	−	61.0186i	1.03023	−	2.00954i
$923$	−33.6459	−	14.1829i	−1.10747	−	0.466836i
$924$	−11.7289	−	27.6413i	−0.385852	−	0.909333i
$925$	−0.564897	−	0.254891i	−0.0185737	−	0.00838077i
$926$	−20.4378	−	66.2578i	−0.671629	−	2.17737i
$927$	−7.13768	−	2.96909i	−0.234432	−	0.0975178i
$928$	39.0383		0.000179710i	1.28150		5.89926e-6i
$929$	−1.63208	−	9.25601i	−0.0535470	−	0.303680i	0.946258	−	0.323412i	$-0.104830\pi$
$929$	−1.63208	−	9.25601i	−0.0535470	−	0.303680i	−0.999805	+	0.0197318i	$0.993719\pi$
$930$	54.5413	−	56.1837i	1.78848	−	1.84234i
$931$	7.07775	+	6.90344i	0.231964	+	0.226251i
$932$	5.23766	+	0.524107i	0.171565	+	0.0171677i
$933$	17.6841	+	17.1672i	0.578953	+	0.562028i
$934$	−54.6292	+	23.0281i	−1.78752	+	0.753504i
$935$	6.37681	−	85.0926i	0.208544	−	2.78283i
$936$	11.6587	+	0.235561i	0.381077	+	0.00769955i
$937$	−38.4789	−	5.79976i	−1.25705	−	0.189470i	−0.513465	−	0.858111i	$-0.671638\pi$
$937$	−38.4789	−	5.79976i	−1.25705	−	0.189470i	−0.743585	+	0.668641i	$0.766876\pi$
$938$	−1.65810	−	6.51177i	−0.0541389	−	0.212617i
$939$	−5.44539	−	0.258856i	−0.177704	−	0.00844743i
$940$	−37.2047	−	6.56019i	−1.21348	−	0.213970i
$941$	−0.534152	+	21.4188i	−0.0174129	+	0.698234i	0.928041	+	0.372478i	$0.121492\pi$
$941$	−0.534152	+	21.4188i	−0.0174129	+	0.698234i	−0.945454	+	0.325756i	$0.894381\pi$
$942$	26.0898	+	66.0160i	0.850050	+	2.15092i
$943$	−7.56477	−	0.947989i	−0.246343	−	0.0308708i
$944$	−27.0850	−	33.9635i	−0.881541	−	1.10542i
$945$	41.2203	+	27.6771i	1.34090	+	0.900335i
$946$	24.8379	−	19.8075i	0.807548	−	0.643998i
$947$	−11.7396	+	11.4504i	−0.381484	+	0.372089i	−0.863737	−	0.503943i	$-0.831882\pi$
$947$	−11.7396	+	11.4504i	−0.381484	+	0.372089i	0.482253	+	0.876032i	$0.339819\pi$
$948$	28.7622	−	16.6967i	0.934154	−	0.542285i
$949$	4.83711	+	23.9278i	0.157019	+	0.776729i
$950$	−44.4778	−	158.083i	−1.44305	−	5.12890i
$951$	46.7707	−	1.27711i	1.51664	−	0.0414131i
$952$	4.04635	+	7.89269i	0.131143	+	0.255804i
$953$	−2.62255	−	34.9955i	−0.0849528	−	1.13362i	−0.862930	−	0.505323i	$-0.831373\pi$
$953$	−2.62255	−	34.9955i	−0.0849528	−	1.13362i	0.777977	−	0.628292i	$-0.216246\pi$
$954$	5.55026	+	0.668881i	0.179696	+	0.0216558i
$955$	−45.4834	+	49.0195i	−1.47181	+	1.58623i
$956$	−5.76042	−	32.6690i	−0.186305	−	1.05659i
$957$	5.38090	+	42.1321i	0.173940	+	1.36194i
$958$	−65.5435	+	23.8559i	−2.11762	+	0.770749i
$959$	16.1081	−	2.01860i	0.520157	−	0.0651841i
$960$	12.5769	+	27.6983i	0.405918	+	0.893960i
$961$	−1.35050	+	4.79995i	−0.0435644	+	0.154837i
$962$	−0.393194	−	0.364831i	−0.0126771	−	0.0117626i
$963$	25.7933	−	0.122037i	0.831178	−	0.00393259i
$964$	−8.07584	−	5.50602i	−0.260105	−	0.177337i
$965$	−56.0626	+	1.39811i	−1.80472	+	0.0450069i
$966$	−7.76829	+	21.5013i	−0.249941	+	0.691794i
$967$	−8.88449	−	6.38751i	−0.285706	−	0.205408i	0.431785	−	0.901977i	$-0.357884\pi$
$967$	−8.88449	−	6.38751i	−0.285706	−	0.205408i	−0.717491	+	0.696568i	$0.754709\pi$
$968$	−7.63679	−	0.190450i	−0.245456	−	0.00612128i
$969$	−40.8042	−	50.9193i	−1.31082	−	1.63576i
$970$	−8.66236	−	25.7822i	−0.278131	−	0.827816i
$971$	−5.95730	+	1.35972i	−0.191179	+	0.0436354i	−0.317038	−	0.948413i	$-0.602688\pi$
$971$	−5.95730	+	1.35972i	−0.191179	+	0.0436354i	0.125859	+	0.992048i	$0.459831\pi$
$972$	24.0240	+	5.81557i	0.770571	+	0.186535i
$973$	1.61988	+	2.03126i	0.0519309	+	0.0651192i
$974$	23.6588	−	65.0021i	0.758078	−	2.08280i
$975$	−20.4818	+	90.7253i	−0.655942	+	2.90553i
$976$	−38.6623	+	17.4451i	−1.23755	+	0.558404i
$977$	6.67629	+	7.56516i	0.213593	+	0.242031i	0.846747	−	0.531995i	$-0.178557\pi$
$977$	6.67629	+	7.56516i	0.213593	+	0.242031i	−0.633154	+	0.774026i	$0.718240\pi$
$978$	−20.5070	−	7.40905i	−0.655742	−	0.236915i
$979$	7.63989	−	16.9317i	0.244172	−	0.541140i
$980$	5.71633	−	5.30398i	0.182601	−	0.169429i
$981$	38.5214	+	18.3269i	1.22989	+	0.585134i
$982$	−65.2326	+	44.4748i	−2.08166	+	1.41925i
$983$	23.2465	−	16.7131i	0.741449	−	0.533066i	−0.148618	−	0.988895i	$-0.547483\pi$
$983$	23.2465	−	16.7131i	0.741449	−	0.533066i	0.890067	+	0.455829i	$0.150657\pi$
$984$	3.46034	+	0.872398i	0.110311	+	0.0278110i
$985$	−74.8878	+	27.2569i	−2.38612	+	0.868477i
$986$	9.51339	+	47.0612i	0.302968	+	1.49873i
$987$	11.9577	+	21.8349i	0.380617	+	0.695011i
$988$	3.13301	−	62.7757i	0.0996742	−	1.99716i
$989$	−10.6665	−	0.799344i	−0.339175	−	0.0254177i
$990$	−87.5934	+	54.0981i	−2.78390	+	1.71935i
$991$	−27.2749	+	8.41318i	−0.866415	+	0.267253i	−0.695932	−	0.718107i	$-0.745009\pi$
$991$	−27.2749	+	8.41318i	−0.866415	+	0.267253i	−0.170482	+	0.985361i	$0.554533\pi$
$992$	−34.6650	−	26.2577i	−1.10062	−	0.833684i
$993$	−6.64353	−	25.8351i	−0.210826	−	0.819851i
$994$	−25.1229	+	22.1711i	−0.796850	+	0.703224i
$995$	−67.3193	+	13.6089i	−2.13416	+	0.431431i
$996$	15.6657	−	14.6048i	0.496387	−	0.462770i
$997$	−41.4095	+	13.9129i	−1.31145	+	0.440625i	−0.885718	−	0.464224i	$-0.846333\pi$
$997$	−41.4095	+	13.9129i	−1.31145	+	0.440625i	−0.425734	+	0.904848i	$0.639984\pi$
$998$			4.01416i			0.127066i
$999$	0.169099	+	0.244280i	0.00535006	+	0.00772868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.bf.a.4.17	✓	3168
27.7	even	9	inner	783.2.bf.a.439.17	yes	3168
29.22	even	14	inner	783.2.bf.a.544.17	yes	3168
783.196	even	126	inner	783.2.bf.a.196.17	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.17	✓	3168	1.1	even	1	trivial
783.2.bf.a.196.17	yes	3168	783.196	even	126	inner
783.2.bf.a.439.17	yes	3168	27.7	even	9	inner
783.2.bf.a.544.17	yes	3168	29.22	even	14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.bf (of order \(126\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59066 - 1.02736i) q^{2} +(-1.56230 - 0.747815i) q^{3} +(0.652159 + 1.44533i) q^{4} +(-3.66732 - 1.54591i) q^{5} +(1.71681 + 2.79455i) q^{6} +(0.987458 - 2.18843i) q^{7} +(-0.116938 + 0.775835i) q^{8} +(1.88155 + 2.33662i) q^{9} +(4.24526 + 6.22665i) q^{10} +(3.41430 + 3.01313i) q^{11} +(0.0619752 - 2.74573i) q^{12} +(-4.22734 - 2.58327i) q^{13} +(-3.81901 + 2.46658i) q^{14} +(4.57339 + 5.15764i) q^{15} +(3.08148 - 3.49174i) q^{16} +(4.07762 + 2.35422i) q^{17} +(-0.592357 - 5.64978i) q^{18} +(7.97879 - 0.597928i) q^{19} +(-0.157329 - 6.30867i) q^{20} +(-3.17925 + 2.68055i) q^{21} +(-2.33542 - 8.30056i) q^{22} +(-1.32451 + 2.58354i) q^{23} +(0.762874 - 1.12464i) q^{24} +(7.56823 + 7.75933i) q^{25} +(4.07031 + 8.45209i) q^{26} +(-1.19218 - 5.05754i) q^{27} +3.80699 q^{28} +(-5.18388 - 1.45854i) q^{29} +(-1.97597 - 12.9025i) q^{30} +(3.62214 + 4.78189i) q^{31} +(-6.97829 + 1.96339i) q^{32} +(-3.08088 - 7.26067i) q^{33} +(-4.06749 - 7.93393i) q^{34} +(-7.00444 + 6.49917i) q^{35} +(-2.15012 + 4.24331i) q^{36} +(-0.0532242 + 0.0208889i) q^{37} +(-13.3058 - 7.24596i) q^{38} +(4.67255 + 7.19711i) q^{39} +(1.62822 - 2.66446i) q^{40} +(0.898138 + 2.46761i) q^{41} +(7.81097 - 0.997615i) q^{42} +(1.43109 + 3.39496i) q^{43} +(-2.12832 + 6.89984i) q^{44} +(-3.28804 - 11.4778i) q^{45} +(4.76105 - 2.74880i) q^{46} +(1.18620 - 5.86780i) q^{47} +(-7.42536 + 3.15076i) q^{48} +(0.817638 + 0.926497i) q^{49} +(-4.06688 - 20.1177i) q^{50} +(-4.60994 - 6.72730i) q^{51} +(0.976793 - 7.79462i) q^{52} +(-0.218983 + 0.959425i) q^{53} +(-3.29955 + 9.26961i) q^{54} +(-7.86330 - 16.3283i) q^{55} +(1.58239 + 1.02202i) q^{56} +(-12.9124 - 5.03252i) q^{57} +(6.74734 + 7.64574i) q^{58} +(1.61980 - 9.18636i) q^{59} +(-4.47193 + 9.97368i) q^{60} +(-8.30196 - 3.74599i) q^{61} +(-0.848884 - 11.3276i) q^{62} +(6.97148 - 1.81032i) q^{63} +(4.21694 + 1.30075i) q^{64} +(11.5095 + 16.0088i) q^{65} +(-2.55867 + 14.7144i) q^{66} +(-0.470732 + 1.40106i) q^{67} +(-0.743368 + 7.42885i) q^{68} +(4.00128 - 3.04578i) q^{69} +(17.8186 - 3.14190i) q^{70} +(7.28785 - 1.09847i) q^{71} +(-2.03286 + 1.18653i) q^{72} +(-3.35158 - 3.61214i) q^{73} +(0.106122 + 0.0214530i) q^{74} +(-6.02129 - 17.7820i) q^{75} +(6.06765 + 11.1421i) q^{76} +(9.96552 - 4.49661i) q^{77} +(-0.0384385 - 16.2485i) q^{78} +(6.31420 + 10.3327i) q^{79} +(-16.6987 + 8.04165i) q^{80} +(-1.91957 + 8.79291i) q^{81} +(1.10649 - 4.84784i) q^{82} +(5.44509 + 5.58257i) q^{83} +(-5.94765 - 2.84693i) q^{84} +(-11.3146 - 14.9373i) q^{85} +(1.21145 - 6.87046i) q^{86} +(7.00805 + 6.15527i) q^{87} +(-2.73696 + 2.29658i) q^{88} +(-1.20237 - 3.89797i) q^{89} +(-6.56166 + 21.6353i) q^{90} +(-9.82764 + 6.70037i) q^{91} +(-4.59787 - 0.229470i) q^{92} +(-2.08289 - 10.1794i) q^{93} +(-7.91517 + 8.11502i) q^{94} +(-30.1851 - 10.1417i) q^{95} +(12.3704 + 2.15108i) q^{96} +(-3.47418 - 0.977483i) q^{97} +(-0.348741 - 2.31375i) q^{98} +(-0.616391 + 13.6473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) \) 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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