LMFDB - Embedded newform 195.2.bh.a.59.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(59,195)] 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("195.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bh (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.17
Character	$\chi$	$=$	195.59
Dual form			195.2.bh.a.119.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25247 - 0.335598i) q^{2} +(-1.65273 + 0.518148i) q^{3} +(-0.276000 + 0.159349i) q^{4} +(0.638573 + 2.14295i) q^{5} +(-1.89610 + 1.20362i) q^{6} +(-0.589843 + 2.20132i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(2.46304 - 1.71272i) q^{9} +(1.51896 + 2.46967i) q^{10} +(2.74441 - 0.735363i) q^{11} +(0.373587 - 0.406369i) q^{12} +(-2.68330 + 2.40830i) q^{13} +2.95504i q^{14} +(-2.16575 - 3.21084i) q^{15} +(-1.63052 + 2.82414i) q^{16} +(3.93313 - 2.27079i) q^{17} +(2.51010 - 2.97172i) q^{18} +(0.775797 - 2.89531i) q^{19} +(-0.517722 - 0.489697i) q^{20} +(-0.165760 - 3.94382i) q^{21} +(3.19050 - 1.84204i) q^{22} +(0.387540 + 0.223746i) q^{23} +(2.41206 - 4.61517i) q^{24} +(-4.18445 + 2.73686i) q^{25} +(-2.55253 + 3.91682i) q^{26} +(-3.18331 + 4.10689i) q^{27} +(-0.187981 - 0.701555i) q^{28} +(4.98037 + 2.87542i) q^{29} +(-3.79009 - 3.29466i) q^{30} +(-4.62601 - 4.62601i) q^{31} +(0.461902 - 1.72384i) q^{32} +(-4.15475 + 2.63737i) q^{33} +(4.16405 - 4.16405i) q^{34} +(-5.09398 + 0.141704i) q^{35} +(-0.406880 + 0.865193i) q^{36} +(10.2908 - 2.75740i) q^{37} -3.88664i q^{38} +(3.18693 - 5.37061i) q^{39} +(-5.91336 - 3.19822i) q^{40} +(-0.217322 - 0.811058i) q^{41} +(-1.53115 - 4.88389i) q^{42} +(-2.38402 - 4.12924i) q^{43} +(-0.640278 + 0.640278i) q^{44} +(5.24310 + 4.18448i) q^{45} +(0.560470 + 0.150177i) q^{46} +(-3.06335 + 3.06335i) q^{47} +(1.23149 - 5.51240i) q^{48} +(1.56426 + 0.903128i) q^{49} +(-4.32241 + 4.83212i) q^{50} +(-5.32380 + 5.79096i) q^{51} +(0.356833 - 1.09227i) q^{52} +8.28713 q^{53} +(-2.60873 + 6.21206i) q^{54} +(3.32835 + 5.41155i) q^{55} +(-3.42592 - 5.93387i) q^{56} +(0.218017 + 5.18715i) q^{57} +(7.20275 + 1.92997i) q^{58} +(-1.67660 + 6.25715i) q^{59} +(1.10939 + 0.541082i) q^{60} +(5.66303 + 9.80865i) q^{61} +(-7.34641 - 4.24145i) q^{62} +(2.31744 + 6.43220i) q^{63} -8.83615i q^{64} +(-6.87434 - 4.21230i) q^{65} +(-4.31860 + 4.69755i) q^{66} +(-2.40083 - 8.96003i) q^{67} +(-0.723695 + 1.25348i) q^{68} +(-0.756433 - 0.168989i) q^{69} +(-6.33249 + 1.88701i) q^{70} +(12.8138 + 3.43344i) q^{71} +(-1.59515 + 8.87745i) q^{72} +(-1.56653 - 1.56653i) q^{73} +(11.9635 - 6.90712i) q^{74} +(5.49767 - 6.69146i) q^{75} +(0.247244 + 0.922728i) q^{76} +6.47509i q^{77} +(2.18916 - 7.79605i) q^{78} -9.74173 q^{79} +(-7.09319 - 1.69070i) q^{80} +(3.13318 - 8.43701i) q^{81} +(-0.544379 - 0.942892i) q^{82} +(0.856250 + 0.856250i) q^{83} +(0.674192 + 1.06208i) q^{84} +(7.37778 + 6.97842i) q^{85} +(-4.37167 - 4.37167i) q^{86} +(-9.72112 - 2.17173i) q^{87} +(-4.27113 + 7.39781i) q^{88} +(-1.64453 + 0.440650i) q^{89} +(7.97112 + 3.48135i) q^{90} +(-3.71871 - 7.32734i) q^{91} -0.142614 q^{92} +(10.0425 + 5.24860i) q^{93} +(-2.80869 + 4.86480i) q^{94} +(6.69991 - 0.186378i) q^{95} +(0.129806 + 3.08838i) q^{96} +(-9.80988 - 2.62855i) q^{97} +(2.26228 + 0.606176i) q^{98} +(5.50014 - 6.51164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{4} - 4 q^{9} - 36 q^{10} + 10 q^{15} - 16 q^{21} - 28 q^{24} + 18 q^{30} - 40 q^{31} - 32 q^{34} - 60 q^{36} - 4 q^{39} + 40 q^{40} + 4 q^{45} - 128 q^{46} + 60 q^{54} + 28 q^{55} + 20 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) $ 96 * q - 24 * q^4 - 4 * q^9 - 36 * q^10 + 10 * q^15 - 16 * q^21 - 28 * q^24 + 18 * q^30 - 40 * q^31 - 32 * q^34 - 60 * q^36 - 4 * q^39 + 40 * q^40 + 4 * q^45 - 128 * q^46 + 60 * q^54 + 28 * q^55 + 20 * q^60 - 48 * q^61 - 8 * q^66 + 72 * q^69 + 168 * q^70 + 66 * q^75 - 80 * q^76 - 80 * q^79 + 48 * q^81 - 132 * q^84 - 20 * q^85 - 56 * q^91 + 72 * q^94 + 204 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$

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 $

$2$	1.25247	−	0.335598i	0.885629	−	0.237304i	0.212795	−	0.977097i	$-0.431743\pi$
$2$	1.25247	−	0.335598i	0.885629	−	0.237304i	0.672834	+	0.739793i	$0.265077\pi$
$3$	−1.65273	+	0.518148i	−0.954205	+	0.299153i
$3$	−1.65273	+	0.518148i	−0.954205	+	0.299153i
$4$	−0.276000	+	0.159349i	−0.138000	+	0.0796743i
$5$	0.638573	+	2.14295i	0.285579	+	0.958355i
$5$	0.638573	+	2.14295i	0.285579	+	0.958355i
$6$	−1.89610	+	1.20362i	−0.774082	+	0.491375i
$7$	−0.589843	+	2.20132i	−0.222940	+	0.832022i	0.760280	+	0.649596i	$0.225062\pi$
$7$	−0.589843	+	2.20132i	−0.222940	+	0.832022i	−0.983219	+	0.182427i	$0.941605\pi$
$8$	−2.12594	+	2.12594i	−0.751635	+	0.751635i
$9$	2.46304	−	1.71272i	0.821015	−	0.570907i
$10$	1.51896	+	2.46967i	0.480338	+	0.780978i
$11$	2.74441	−	0.735363i	0.827472	−	0.221720i	0.179861	−	0.983692i	$-0.442435\pi$
$11$	2.74441	−	0.735363i	0.827472	−	0.221720i	0.647610	+	0.761972i	$0.275768\pi$
$12$	0.373587	−	0.406369i	0.107845	−	0.117309i
$13$	−2.68330	+	2.40830i	−0.744214	+	0.667941i
$13$	−2.68330	+	2.40830i	−0.744214	+	0.667941i
$14$			2.95504i			0.789767i
$15$	−2.16575	−	3.21084i	−0.559196	−	0.829036i
$16$	−1.63052	+	2.82414i	−0.407630	+	0.706035i
$17$	3.93313	−	2.27079i	0.953924	−	0.550748i	0.0596262	−	0.998221i	$-0.481009\pi$
$17$	3.93313	−	2.27079i	0.953924	−	0.550748i	0.894298	+	0.447473i	$0.147676\pi$
$18$	2.51010	−	2.97172i	0.591636	−	0.700441i
$19$	0.775797	−	2.89531i	0.177980	−	0.664230i	−0.818045	−	0.575154i	$-0.804942\pi$
$19$	0.775797	−	2.89531i	0.177980	−	0.664230i	0.996025	−	0.0890759i	$-0.0283914\pi$
$20$	−0.517722	−	0.489697i	−0.115766	−	0.109500i
$21$	−0.165760	−	3.94382i	−0.0361718	−	0.860613i
$22$	3.19050	−	1.84204i	0.680218	−	0.392724i
$23$	0.387540	+	0.223746i	0.0808076	+	0.0466543i	0.539859	−	0.841755i	$-0.318477\pi$
$23$	0.387540	+	0.223746i	0.0808076	+	0.0466543i	−0.459052	+	0.888410i	$0.651811\pi$
$24$	2.41206	−	4.61517i	0.492360	−	0.942068i
$25$	−4.18445	+	2.73686i	−0.836890	+	0.547372i
$26$	−2.55253	+	3.91682i	−0.500593	+	0.768152i
$27$	−3.18331	+	4.10689i	−0.612628	+	0.790371i
$28$	−0.187981	−	0.701555i	−0.0355251	−	0.132582i
$29$	4.98037	+	2.87542i	0.924832	+	0.533952i	0.885173	−	0.465261i	$-0.154040\pi$
$29$	4.98037	+	2.87542i	0.924832	+	0.533952i	0.0396587	+	0.999213i	$0.487373\pi$
$30$	−3.79009	−	3.29466i	−0.691973	−	0.601519i
$31$	−4.62601	−	4.62601i	−0.830856	−	0.830856i	0.156778	−	0.987634i	$-0.449889\pi$
$31$	−4.62601	−	4.62601i	−0.830856	−	0.830856i	−0.987634	+	0.156778i	$0.949889\pi$
$32$	0.461902	−	1.72384i	0.0816535	−	0.304735i
$33$	−4.15475	+	2.63737i	−0.723249	+	0.459107i
$34$	4.16405	−	4.16405i	0.714128	−	0.714128i
$35$	−5.09398	+	0.141704i	−0.861040	+	0.0239524i
$36$	−0.406880	+	0.865193i	−0.0678134	+	0.144199i
$37$	10.2908	−	2.75740i	1.69179	−	0.453315i	0.720941	−	0.692996i	$-0.243710\pi$
$37$	10.2908	−	2.75740i	1.69179	−	0.453315i	0.970852	+	0.239682i	$0.0770430\pi$
$38$		−	3.88664i		−	0.630497i
$39$	3.18693	−	5.37061i	0.510317	−	0.859987i
$40$	−5.91336	−	3.19822i	−0.934984	−	0.505682i
$41$	−0.217322	−	0.811058i	−0.0339401	−	0.126666i	0.946877	−	0.321595i	$-0.104219\pi$
$41$	−0.217322	−	0.811058i	−0.0339401	−	0.126666i	−0.980817	+	0.194929i	$0.937552\pi$
$42$	−1.53115	−	4.88389i	−0.236261	−	0.753600i
$43$	−2.38402	−	4.12924i	−0.363559	−	0.629703i	0.624985	−	0.780637i	$-0.285105\pi$
$43$	−2.38402	−	4.12924i	−0.363559	−	0.629703i	−0.988544	+	0.150934i	$0.951772\pi$
$44$	−0.640278	+	0.640278i	−0.0965256	+	0.0965256i
$45$	5.24310	+	4.18448i	0.781596	+	0.623785i
$46$	0.560470	+	0.150177i	0.0826368	+	0.0221425i
$47$	−3.06335	+	3.06335i	−0.446835	+	0.446835i	−0.894301	−	0.447466i	$-0.852327\pi$
$47$	−3.06335	+	3.06335i	−0.446835	+	0.446835i	0.447466	+	0.894301i	$0.352327\pi$
$48$	1.23149	−	5.51240i	0.177750	−	0.795646i
$49$	1.56426	+	0.903128i	0.223466	+	0.129018i
$50$	−4.32241	+	4.83212i	−0.611280	+	0.683365i
$51$	−5.32380	+	5.79096i	−0.745481	+	0.810896i
$52$	0.356833	−	1.09227i	0.0494838	−	0.151470i
$53$	8.28713			1.13832			0.569162	−	0.822225i	$-0.307268\pi$
$53$	8.28713			1.13832			0.569162	+	0.822225i	$0.307268\pi$
$54$	−2.60873	+	6.21206i	−0.355003	+	0.845354i
$55$	3.32835	+	5.41155i	0.448795	+	0.729693i
$56$	−3.42592	−	5.93387i	−0.457808	−	0.792946i
$57$	0.218017	+	5.18715i	0.0288771	+	0.687055i
$58$	7.20275	+	1.92997i	0.945767	+	0.253417i
$59$	−1.67660	+	6.25715i	−0.218275	+	0.814612i	0.766714	+	0.641989i	$0.221891\pi$
$59$	−1.67660	+	6.25715i	−0.218275	+	0.814612i	−0.984988	+	0.172622i	$0.944776\pi$
$60$	1.10939	+	0.541082i	0.143222	+	0.0698533i
$61$	5.66303	+	9.80865i	0.725077	+	1.25587i	0.958942	+	0.283601i	$0.0915290\pi$
$61$	5.66303	+	9.80865i	0.725077	+	1.25587i	−0.233866	+	0.972269i	$0.575138\pi$
$62$	−7.34641	−	4.24145i	−0.932995	−	0.538665i
$63$	2.31744	+	6.43220i	0.291970	+	0.810381i
$64$		−	8.83615i		−	1.10452i
$65$	−6.87434	−	4.21230i	−0.852656	−	0.522472i
$66$	−4.31860	+	4.69755i	−0.531583	+	0.578228i
$67$	−2.40083	−	8.96003i	−0.293308	−	1.09464i	−0.942552	−	0.334061i	$-0.891581\pi$
$67$	−2.40083	−	8.96003i	−0.293308	−	1.09464i	0.649243	−	0.760581i	$-0.275086\pi$
$68$	−0.723695	+	1.25348i	−0.0877609	+	0.152006i
$69$	−0.756433	−	0.168989i	−0.0910638	−	0.0203439i
$70$	−6.33249	+	1.88701i	−0.756878	+	0.225541i
$71$	12.8138	+	3.43344i	1.52072	+	0.407474i	0.919977	−	0.391971i	$-0.128207\pi$
$71$	12.8138	+	3.43344i	1.52072	+	0.407474i	0.600738	+	0.799446i	$0.294873\pi$
$72$	−1.59515	+	8.87745i	−0.187990	+	1.04622i
$73$	−1.56653	−	1.56653i	−0.183349	−	0.183349i	0.609464	−	0.792813i	$-0.291385\pi$
$73$	−1.56653	−	1.56653i	−0.183349	−	0.183349i	−0.792813	+	0.609464i	$0.791385\pi$
$74$	11.9635	−	6.90712i	1.39073	−	0.802937i
$75$	5.49767	−	6.69146i	0.634817	−	0.772663i
$76$	0.247244	+	0.922728i	0.0283608	+	0.105844i
$77$			6.47509i			0.737905i
$78$	2.18916	−	7.79605i	0.247873	−	0.882729i
$79$	−9.74173			−1.09603			−0.548015	−	0.836468i	$-0.684616\pi$
$79$	−9.74173			−1.09603			−0.548015	+	0.836468i	$0.684616\pi$
$80$	−7.09319	−	1.69070i	−0.793043	−	0.189025i
$81$	3.13318	−	8.43701i	0.348131	−	0.937446i
$82$	−0.544379	−	0.942892i	−0.0601166	−	0.104125i
$83$	0.856250	+	0.856250i	0.0939856	+	0.0939856i	0.752536	−	0.658551i	$-0.228830\pi$
$83$	0.856250	+	0.856250i	0.0939856	+	0.0939856i	−0.658551	+	0.752536i	$0.728830\pi$
$84$	0.674192	+	1.06208i	0.0735604	+	0.115883i
$85$	7.37778	+	6.97842i	0.800233	+	0.756916i
$86$	−4.37167	−	4.37167i	−0.471409	−	0.471409i
$87$	−9.72112	−	2.17173i	−1.04221	−	0.232833i
$88$	−4.27113	+	7.39781i	−0.455304	+	0.788609i
$89$	−1.64453	+	0.440650i	−0.174320	+	0.0467088i	−0.344923	−	0.938631i	$-0.612095\pi$
$89$	−1.64453	+	0.440650i	−0.174320	+	0.0467088i	0.170603	+	0.985340i	$0.445428\pi$
$90$	7.97112	+	3.48135i	0.840230	+	0.366967i
$91$	−3.71871	−	7.32734i	−0.389827	−	0.768114i
$92$	−0.142614			−0.0148686
$93$	10.0425	+	5.24860i	1.04136	+	0.544254i
$94$	−2.80869	+	4.86480i	−0.289695	+	0.501766i
$95$	6.69991	−	0.186378i	0.687396	−	0.0191219i
$96$	0.129806	+	3.08838i	0.0132482	+	0.315207i
$97$	−9.80988	−	2.62855i	−0.996042	−	0.266889i	−0.276256	−	0.961084i	$-0.589094\pi$
$97$	−9.80988	−	2.62855i	−0.996042	−	0.266889i	−0.719787	+	0.694195i	$0.755760\pi$
$98$	2.26228	+	0.606176i	0.228525	+	0.0612330i
$99$	5.50014	−	6.51164i	0.552785	−	0.654445i
$100$	0.718792	−	1.42216i	0.0718792	−	0.142216i
$101$	6.55756	−	11.3580i	0.652502	−	1.13017i	−0.330012	−	0.943977i	$-0.607053\pi$
$101$	6.55756	−	11.3580i	0.652502	−	1.13017i	0.982514	−	0.186189i	$-0.0596138\pi$
$102$	−4.72446	+	9.03965i	−0.467791	+	0.895058i
$103$	−5.12642			−0.505122			−0.252561	−	0.967581i	$-0.581273\pi$
$103$	−5.12642			−0.505122			−0.252561	+	0.967581i	$0.581273\pi$
$104$	0.584652	−	10.8245i	0.0573298	−	1.06143i
$105$	8.34556	−	2.87364i	0.814443	−	0.280438i
$106$	10.3794	−	2.78114i	1.00813	−	0.270129i
$107$	−3.43618	+	5.95164i	−0.332188	+	0.575367i	−0.982941	−	0.183923i	$-0.941120\pi$
$107$	−3.43618	+	5.95164i	−0.332188	+	0.575367i	0.650752	+	0.759290i	$0.274454\pi$
$108$	0.224166	−	1.64076i	0.0215704	−	0.157882i
$109$	−0.716943	−	0.716943i	−0.0686706	−	0.0686706i	0.671937	−	0.740608i	$-0.265462\pi$
$109$	−0.716943	−	0.716943i	−0.0686706	−	0.0686706i	−0.740608	+	0.671937i	$0.765462\pi$
$110$	5.98476	+	5.66081i	0.570625	+	0.539737i
$111$	−15.5791	+	9.88940i	−1.47871	+	0.938660i
$112$	−5.25510	−	5.25510i	−0.496560	−	0.496560i
$113$	−2.96354	−	5.13301i	−0.278787	−	0.482873i	0.692297	−	0.721613i	$-0.256599\pi$
$113$	−2.96354	−	5.13301i	−0.278787	−	0.482873i	−0.971083	+	0.238740i	$0.923266\pi$
$114$	2.01386	+	6.42358i	0.188615	+	0.601623i
$115$	−0.232004	+	0.973356i	−0.0216345	+	0.0907659i
$116$	−1.83278			−0.170169
$117$	−2.48436	+	10.5275i	−0.229679	+	0.973266i
$118$			8.39955i			0.773241i
$119$	2.67882	+	9.99750i	0.245567	+	0.916470i
$120$	11.4303	+	2.22180i	1.04344	+	0.202821i
$121$	−2.53524	+	1.46372i	−0.230476	+	0.133065i
$122$	10.3845	+	10.3845i	0.940171	+	0.940171i
$123$	0.779424	+	1.22786i	0.0702783	+	0.110712i
$124$	2.01393	+	0.539630i	0.180856	+	0.0484602i
$125$	−8.53702	−	7.21937i	−0.763574	−	0.645720i
$126$	5.06116	+	7.27839i	0.450884	+	0.648411i
$127$	6.13964	−	10.6342i	0.544805	−	0.943630i	−0.453814	−	0.891096i	$-0.649937\pi$
$127$	6.13964	−	10.6342i	0.544805	−	0.943630i	0.998619	−	0.0525335i	$-0.0167296\pi$
$128$	−2.04159	−	7.61931i	−0.180453	−	0.673458i
$129$	6.07970	+	5.58925i	0.535287	+	0.492106i
$130$	−10.0235	−	2.96877i	−0.879122	−	0.260378i
$131$		−	0.875714i		−	0.0765115i	−0.999268	−	0.0382557i	$-0.987820\pi$
$131$		−	0.875714i		−	0.0765115i	0.999268	−	0.0382557i	$-0.0121802\pi$
$132$	0.726449	−	1.38997i	0.0632293	−	0.120981i
$133$	5.91592	+	3.41556i	0.512976	+	0.296167i
$134$	−6.01393	−	10.4164i	−0.519525	−	0.899843i
$135$	−10.8336	−	4.19912i	−0.932410	−	0.361402i
$136$	−3.53403	+	13.1892i	−0.303041	+	1.13096i
$137$	−6.08218	−	1.62972i	−0.519636	−	0.139236i	−0.0105378	−	0.999944i	$-0.503354\pi$
$137$	−6.08218	−	1.62972i	−0.519636	−	0.139236i	−0.509098	+	0.860708i	$0.670021\pi$
$138$	−1.00412	+	0.0422035i	−0.0854764	+	0.00359260i
$139$	8.67597	+	15.0272i	0.735886	+	1.27459i	0.954333	+	0.298744i	$0.0965676\pi$
$139$	8.67597	+	15.0272i	0.735886	+	1.27459i	−0.218447	+	0.975849i	$0.570099\pi$
$140$	1.38336	−	0.850828i	0.116915	−	0.0719081i
$141$	3.47562	−	6.65016i	0.292700	−	0.560044i
$142$	17.2011			1.44348
$143$	−5.59312	+	8.58256i	−0.467720	+	0.717710i
$144$	0.820923	+	9.74861i	0.0684103	+	0.812384i
$145$	−2.98154	+	12.5088i	−0.247603	+	1.03880i
$146$	−2.48776	−	1.43631i	−0.205889	−	0.118870i
$147$	−3.05326	−	0.682108i	−0.251829	−	0.0562593i
$148$	−2.40086	+	2.40086i	−0.197350	+	0.197350i
$149$	−21.4260	−	5.74107i	−1.75528	−	0.470327i	−0.769543	−	0.638595i	$-0.779516\pi$
$149$	−21.4260	−	5.74107i	−1.75528	−	0.470327i	−0.985741	+	0.168269i	$0.946182\pi$
$150$	4.64002	−	10.2258i	0.378856	−	0.834937i
$151$	−0.495344	+	0.495344i	−0.0403105	+	0.0403105i	−0.726975	−	0.686664i	$-0.759074\pi$
$151$	−0.495344	+	0.495344i	−0.0403105	+	0.0403105i	0.686664	+	0.726975i	$0.259074\pi$
$152$	4.50597	+	7.80458i	0.365483	+	0.633035i
$153$	5.79824	−	12.3294i	0.468760	−	0.996774i
$154$	2.17303	+	8.10985i	0.175108	+	0.653510i
$155$	6.95925	−	12.8673i	0.558981	−	1.03353i
$156$	−0.0237913	+	1.99012i	−0.00190483	+	0.159337i
$157$			21.4749i			1.71388i	0.515414	+	0.856941i	$0.327638\pi$
$157$			21.4749i			1.71388i	−0.515414	+	0.856941i	$0.672362\pi$
$158$	−12.2012	+	3.26930i	−0.970676	+	0.260092i
$159$	−13.6964	+	4.29396i	−1.08620	+	0.340533i
$160$	3.98906	−	0.110968i	0.315363	−	0.00877275i
$161$	−0.721125	+	0.721125i	−0.0568326	+	0.0568326i
$162$	1.09276	−	11.6186i	0.0858556	−	0.912842i
$163$	2.86667	−	10.6985i	0.224535	−	0.837975i	−0.758056	−	0.652190i	$-0.773851\pi$
$163$	2.86667	−	10.6985i	0.224535	−	0.837975i	0.982590	−	0.185785i	$-0.0594828\pi$
$164$	0.189222	+	0.189222i	0.0147757	+	0.0147757i
$165$	−8.30486	−	7.21926i	−0.646533	−	0.562019i
$166$	1.35978	+	0.785070i	0.105539	+	0.0609333i
$167$	−6.25081	−	23.3283i	−0.483702	−	1.80520i	−0.585835	−	0.810430i	$-0.699233\pi$
$167$	−6.25081	−	23.3283i	−0.483702	−	1.80520i	0.102133	−	0.994771i	$-0.467433\pi$
$168$	8.73675	+	8.03196i	0.674055	+	0.619679i
$169$	1.40023	−	12.9244i	0.107710	−	0.994182i
$170$	11.5824	+	6.26428i	0.888328	+	0.480449i
$171$	−3.04804	−	8.46001i	−0.233089	−	0.646953i
$172$	1.31598	+	0.759779i	0.100342	+	0.0579326i
$173$	−2.53344	+	1.46268i	−0.192614	+	0.111206i	−0.593206	−	0.805051i	$-0.702138\pi$
$173$	−2.53344	+	1.46268i	−0.192614	+	0.111206i	0.400592	+	0.916257i	$0.368805\pi$
$174$	−12.9042	+	0.542368i	−0.978266	+	0.0411168i
$175$	−3.55654	−	10.8256i	−0.268849	−	0.818342i
$176$	−2.39805	+	8.94964i	−0.180760	+	0.674604i
$177$	−0.471164	−	11.2101i	−0.0354149	−	0.842604i
$178$	−1.91184	+	1.10380i	−0.143298	+	0.0827333i
$179$	−3.43112	+	5.94288i	−0.256454	+	0.444192i	−0.965290	−	0.261182i	$-0.915888\pi$
$179$	−3.43112	+	5.94288i	−0.256454	+	0.444192i	0.708835	+	0.705374i	$0.249221\pi$
$180$	−2.11389	−	0.319434i	−0.157560	−	0.0238092i
$181$		−	22.0007i		−	1.63530i	−0.575717	−	0.817649i	$-0.695277\pi$
$181$		−	22.0007i		−	1.63530i	0.575717	−	0.817649i	$-0.304723\pi$
$182$	−7.11661	−	7.92927i	−0.527518	−	0.587756i
$183$	−14.4418	−	13.2768i	−1.06757	−	0.981448i
$184$	−1.29956	+	0.348216i	−0.0958048	+	0.0256708i
$185$	12.4804	+	20.2918i	0.917576	+	1.49188i
$186$	14.3394	+	3.20345i	1.05141	+	0.234889i
$187$	9.12427	−	9.12427i	0.667233	−	0.667233i
$188$	0.357343	−	1.33362i	0.0260619	−	0.0972644i
$189$	−7.16294	−	9.42992i	−0.521027	−	0.685925i
$190$	8.32887	−	2.48191i	0.604240	−	0.180056i
$191$	14.4065	−	8.31762i	1.04242	−	0.601842i	0.121903	−	0.992542i	$-0.461100\pi$
$191$	14.4065	−	8.31762i	1.04242	−	0.601842i	0.920518	+	0.390700i	$0.127767\pi$
$192$	4.57843	+	14.6038i	0.330420	+	1.05394i
$193$	−6.44208	+	1.72615i	−0.463711	+	0.124251i	−0.483108	−	0.875561i	$-0.660492\pi$
$193$	−6.44208	+	1.72615i	−0.463711	+	0.124251i	0.0193966	+	0.999812i	$0.493825\pi$
$194$	−13.1687			−0.945457
$195$	13.5440	+	3.39988i	0.969908	+	0.243471i
$196$	−0.575649			−0.0411178
$197$	11.0981	−	2.97372i	0.790706	−	0.211869i	0.159206	−	0.987245i	$-0.449106\pi$
$197$	11.0981	−	2.97372i	0.790706	−	0.211869i	0.631499	+	0.775376i	$0.282440\pi$
$198$	4.70346	−	10.0015i	0.334260	−	0.710773i
$199$	−0.252420	+	0.145735i	−0.0178936	+	0.0103309i	−0.508920	−	0.860814i	$-0.669955\pi$
$199$	−0.252420	+	0.145735i	−0.0178936	+	0.0103309i	0.491027	+	0.871145i	$0.336622\pi$
$200$	3.07750	−	14.7143i	0.217612	−	1.04046i
$201$	8.61055	+	13.5645i	0.607342	+	0.956768i
$202$	4.40141	−	16.4263i	0.309682	−	1.15575i
$203$	−9.26737	+	9.26737i	−0.650442	+	0.650442i
$204$	0.546587	−	2.44664i	0.0382687	−	0.171299i
$205$	1.59928	−	0.983631i	0.111699	−	0.0686998i
$206$	−6.42069	+	1.72042i	−0.447350	+	0.119867i
$207$	1.33774	−	0.112650i	0.0929795	−	0.00782974i
$208$	−2.42619	−	11.5048i	−0.168226	−	0.797714i
$209$		−	8.51643i		−	0.589094i
$210$	9.48816	−	6.39989i	0.654745	−	0.441634i
$211$	7.95121	−	13.7719i	0.547384	−	0.948096i	−0.451069	−	0.892489i	$-0.648957\pi$
$211$	7.95121	−	13.7719i	0.547384	−	0.948096i	0.998453	−	0.0556073i	$-0.0177095\pi$
$212$	−2.28725	+	1.32054i	−0.157089	+	0.0906952i
$213$	−22.9568	+	0.964879i	−1.57297	+	0.0661124i
$214$	−2.30635	+	8.60742i	−0.157659	+	0.588391i
$215$	7.32637	−	7.74564i	0.499654	−	0.528248i
$216$	−1.96348	−	15.4986i	−0.133598	−	1.05454i
$217$	12.9120	−	7.45473i	0.876522	−	0.506060i
$218$	−1.13855	−	0.657343i	−0.0771125	−	0.0445209i
$219$	3.40076	+	1.77736i	0.229802	+	0.120103i
$220$	−1.78095	−	0.963218i	−0.120071	−	0.0649401i
$221$	−5.08504	+	15.5654i	−0.342057	+	1.04704i
$222$	−16.1935	+	17.6145i	−1.08684	+	1.18221i
$223$	1.14819	+	4.28509i	0.0768882	+	0.286951i	0.993655	−	0.112473i	$-0.0358771\pi$
$223$	1.14819	+	4.28509i	0.0768882	+	0.286951i	−0.916767	+	0.399423i	$0.869210\pi$
$224$	3.52229	+	2.03359i	0.235343	+	0.135875i
$225$	−5.61901	+	13.9078i	−0.374601	+	0.927186i
$226$	−5.43437	−	5.43437i	−0.361489	−	0.361489i
$227$	3.47922	−	12.9846i	0.230924	−	0.861820i	−0.749020	−	0.662547i	$-0.769475\pi$
$227$	3.47922	−	12.9846i	0.230924	−	0.861820i	0.979944	−	0.199273i	$-0.0638579\pi$
$228$	−0.886738	−	1.39691i	−0.0587257	−	0.0925128i
$229$	−8.40317	+	8.40317i	−0.555297	+	0.555297i	−0.927965	−	0.372668i	$-0.878443\pi$
$229$	−8.40317	+	8.40317i	−0.555297	+	0.555297i	0.372668	+	0.927965i	$0.378443\pi$
$230$	0.0360787	+	1.29696i	0.00237896	+	0.0855188i
$231$	−3.35506	−	10.7016i	−0.220747	−	0.704113i
$232$	−16.7010	+	4.47502i	−1.09647	+	0.293799i
$233$		−	12.1684i		−	0.797175i	−0.917130	−	0.398588i	$-0.869500\pi$
$233$		−	12.1684i		−	0.797175i	0.917130	−	0.398588i	$-0.130500\pi$
$234$	0.421420	+	14.0191i	0.0275491	+	0.916457i
$235$	−8.52076	−	4.60842i	−0.555833	−	0.300620i
$236$	−0.534327	−	1.99414i	−0.0347817	−	0.129807i
$237$	16.1005	−	5.04766i	1.04584	−	0.327881i
$238$	6.71028	+	11.6226i	0.434963	+	0.753378i
$239$	−15.4524	+	15.4524i	−0.999531	+	0.999531i	−1.00000		0.000468754i	$-0.999851\pi$
$239$	−15.4524	+	15.4524i	−0.999531	+	0.999531i	0.000468754		1.00000i	$0.499851\pi$
$240$	12.5992	−	0.881060i	0.813273	−	0.0568722i
$241$	−24.0324	−	6.43947i	−1.54806	−	0.414803i	−0.619203	−	0.785231i	$-0.712544\pi$
$241$	−24.0324	−	6.43947i	−1.54806	−	0.414803i	−0.928861	+	0.370428i	$0.879211\pi$
$242$	−2.68408	+	2.68408i	−0.172539	+	0.172539i
$243$	−0.806681	+	15.5676i	−0.0517486	+	0.998660i
$244$	−3.12599	−	1.80479i	−0.200121	−	0.115540i
$245$	−0.936459	+	3.92885i	−0.0598282	+	0.251005i
$246$	1.38827	+	1.27628i	0.0885129	+	0.0813726i
$247$	4.89107	+	9.63735i	0.311211	+	0.613210i
$248$	19.6693			1.24900
$249$	−1.85882	−	0.971487i	−0.117798	−	0.0615655i
$250$	−13.1152	−	6.17703i	−0.829475	−	0.390669i
$251$	1.55359	+	2.69089i	0.0980614	+	0.169847i	0.910882	−	0.412666i	$-0.135402\pi$
$251$	1.55359	+	2.69089i	0.0980614	+	0.169847i	−0.812821	+	0.582514i	$0.802069\pi$
$252$	−1.66457	−	1.40600i	−0.104858	−	0.0885699i
$253$	1.22810	+	0.329069i	0.0772102	+	0.0206884i
$254$	4.12090	−	15.3794i	0.258568	−	0.964990i
$255$	−15.8094	−	7.71067i	−0.990020	−	0.482861i
$256$	3.72210	+	6.44686i	0.232631	+	0.402929i
$257$	11.4142	+	6.58997i	0.711996	+	0.411071i	0.811800	−	0.583936i	$-0.198488\pi$
$257$	11.4142	+	6.58997i	0.711996	+	0.411071i	−0.0998036	+	0.995007i	$0.531821\pi$
$258$	9.49037	+	4.96002i	0.590844	+	0.308797i
$259$			24.2798i			1.50867i
$260$	2.56854	+	0.0671798i	0.159294	+	0.00416631i
$261$	17.1917	−	1.44770i	1.06414	−	0.0896103i
$262$	−0.293888	−	1.09680i	−0.0181564	−	0.0677608i
$263$	1.58530	−	2.74583i	0.0977540	−	0.169315i	−0.813001	−	0.582263i	$-0.802167\pi$
$263$	1.58530	−	2.74583i	0.0977540	−	0.169315i	0.910755	+	0.412948i	$0.135501\pi$
$264$	3.22587	−	14.4397i	0.198538	−	0.888701i
$265$	5.29194	+	17.7589i	0.325081	+	1.09092i
$266$	8.55576	+	2.29251i	0.524588	+	0.140563i
$267$	2.48964	−	1.58038i	0.152364	−	0.0967180i
$268$	2.09040	+	2.09040i	0.127691	+	0.127691i
$269$	8.98175	−	5.18562i	0.547627	−	0.316173i	−0.200537	−	0.979686i	$-0.564269\pi$
$269$	8.98175	−	5.18562i	0.547627	−	0.316173i	0.748164	+	0.663513i	$0.230935\pi$
$270$	−14.9780	−	1.62352i	−0.911531	−	0.0988041i
$271$	5.62575	+	20.9956i	0.341740	+	1.27539i	0.896375	+	0.443297i	$0.146191\pi$
$271$	5.62575	+	20.9956i	0.341740	+	1.27539i	−0.554635	+	0.832094i	$0.687142\pi$
$272$			14.8103i			0.898005i
$273$	9.94268	+	10.1833i	0.601758	+	0.616320i
$274$	−8.16467			−0.493246
$275$	−9.47127	+	10.5882i	−0.571139	+	0.638490i
$276$	0.235703	−	0.0738954i	0.0141877	−	0.00444798i
$277$	−1.18949	−	2.06025i	−0.0714694	−	0.123789i	0.828076	−	0.560616i	$-0.189436\pi$
$277$	−1.18949	−	2.06025i	−0.0714694	−	0.123789i	−0.899546	+	0.436827i	$0.856102\pi$
$278$	15.9095	+	15.9095i	0.954188	+	0.954188i
$279$	−19.3171	−	3.47101i	−1.15649	−	0.207804i
$280$	10.5283	−	11.1308i	0.629184	−	0.665191i
$281$	7.28271	+	7.28271i	0.434450	+	0.434450i	0.890139	−	0.455689i	$-0.150607\pi$
$281$	7.28271	+	7.28271i	0.434450	+	0.434450i	−0.455689	+	0.890139i	$0.650607\pi$
$282$	2.12133	−	9.49553i	0.126323	−	0.565450i
$283$	6.97223	−	12.0763i	0.414456	−	0.717859i	−0.580915	−	0.813964i	$-0.697305\pi$
$283$	6.97223	−	12.0763i	0.414456	−	0.717859i	0.995371	+	0.0961049i	$0.0306384\pi$
$284$	−4.08371	+	1.09423i	−0.242324	+	0.0649305i
$285$	−10.9766	+	3.77958i	−0.650196	+	0.223883i
$286$	−4.12492	+	12.6264i	−0.243911	+	0.746616i
$287$	1.91359			0.112956
$288$	−1.81477	−	5.03701i	−0.106937	−	0.296809i
$289$	1.81300	−	3.14021i	0.106647	−	0.184718i
$290$	0.463657	+	16.6675i	0.0272269	+	0.978751i
$291$	17.5751	−	0.738685i	1.03027	−	0.0433025i
$292$	0.681988	+	0.182738i	0.0399103	+	0.0106939i
$293$	26.5976	+	7.12679i	1.55385	+	0.416352i	0.930709	−	0.365761i	$-0.119191\pi$
$293$	26.5976	+	7.12679i	1.55385	+	0.416352i	0.623137	+	0.782113i	$0.285858\pi$
$294$	−4.05303	+	0.170350i	−0.236378	+	0.00993501i
$295$	−14.4794	+	0.402787i	−0.843022	+	0.0234511i
$296$	−16.0155	+	27.7397i	−0.930884	+	1.61234i
$297$	−5.71626	+	13.6119i	−0.331691	+	0.789842i
$298$	−28.7620			−1.66614
$299$	−1.57873	+	0.332931i	−0.0913005	+	0.0192539i
$300$	−0.451082	+	2.72289i	−0.0260433	+	0.157206i
$301$	10.4960	−	2.81239i	0.604978	−	0.162103i
$302$	−0.454166	+	0.786639i	−0.0261343	+	0.0452660i
$303$	−4.95275	+	22.1696i	−0.284528	+	1.27361i
$304$	6.91182	+	6.91182i	0.396420	+	0.396420i
$305$	−17.4032	+	18.3991i	−0.996503	+	1.05353i
$306$	3.12439	−	17.3881i	0.178609	−	0.994010i
$307$	11.4213	+	11.4213i	0.651847	+	0.651847i	0.953437	−	0.301591i	$-0.0975177\pi$
$307$	11.4213	+	11.4213i	0.651847	+	0.651847i	−0.301591	+	0.953437i	$0.597518\pi$
$308$	−1.03180	−	1.78712i	−0.0587920	−	0.101831i
$309$	8.47261	−	2.65625i	0.481990	−	0.151109i
$310$	4.39799	−	18.4515i	0.249789	−	1.04797i
$311$	−8.25099			−0.467871			−0.233935	−	0.972252i	$-0.575160\pi$
$311$	−8.25099			−0.467871			−0.233935	+	0.972252i	$0.575160\pi$
$312$	4.64240	+	18.1929i	0.262824	+	1.02997i
$313$		−	12.5949i		−	0.711907i	−0.934504	−	0.355954i	$-0.884156\pi$
$313$		−	12.5949i		−	0.711907i	0.934504	−	0.355954i	$-0.115844\pi$
$314$	7.20693	+	26.8966i	0.406710	+	1.51786i
$315$	−12.3040	+	9.07359i	−0.693252	+	0.511239i
$316$	2.68871	−	1.55233i	0.151252	−	0.0873254i
$317$	−4.02879	−	4.02879i	−0.226279	−	0.226279i	0.584857	−	0.811136i	$-0.301151\pi$
$317$	−4.02879	−	4.02879i	−0.226279	−	0.226279i	−0.811136	+	0.584857i	$0.801151\pi$
$318$	−15.7133	+	9.97453i	−0.881156	+	0.559344i
$319$	15.7827	+	4.22896i	0.883660	+	0.236776i
$320$	18.9354	−	5.64253i	1.05852	−	0.315427i
$321$	2.59526	−	11.6169i	0.144853	−	0.648393i
$322$	−0.661179	+	1.14520i	−0.0368460	+	0.0638192i
$323$	−3.52335	−	13.1493i	−0.196044	−	0.731647i
$324$	0.479669	+	2.82788i	0.0266483	+	0.157104i
$325$	4.63698	−	17.4212i	0.257213	−	0.966355i
$326$		−	14.3616i		−	0.795418i
$327$	1.55640	+	0.813431i	0.0860689	+	0.0449828i
$328$	2.18628	+	1.26225i	0.120717	+	0.0696961i
$329$	−4.93653	−	8.55031i	−0.272160	−	0.471394i
$330$	−12.8243	−	6.25480i	−0.705957	−	0.344315i
$331$	4.18246	−	15.6091i	0.229889	−	0.857956i	−0.750498	−	0.660873i	$-0.770186\pi$
$331$	4.18246	−	15.6091i	0.229889	−	0.857956i	0.980387	−	0.197083i	$-0.0631470\pi$
$332$	−0.372767	−	0.0998825i	−0.0204582	−	0.00548177i
$333$	20.6240	−	24.4168i	1.13019	−	1.33803i
$334$	−15.6579	−	27.1202i	−0.856761	−	1.48395i
$335$	17.6678	−	10.8665i	0.965293	−	0.593700i
$336$	11.4082	+	5.96235i	0.622368	+	0.325273i
$337$	−7.02217			−0.382522			−0.191261	−	0.981539i	$-0.561258\pi$
$337$	−7.02217			−0.382522			−0.191261	+	0.981539i	$0.561258\pi$
$338$	−2.58365	−	16.6573i	−0.140532	−	0.906037i
$339$	7.55760	+	6.94793i	0.410473	+	0.377360i
$340$	−3.14827	−	0.750404i	−0.170739	−	0.0406964i
$341$	−16.0975	−	9.29389i	−0.871728	−	0.503292i
$342$	−6.65673	−	9.57298i	−0.359955	−	0.517647i
$343$	−14.1911	+	14.1911i	−0.766248	+	0.766248i
$344$	13.8468	+	3.71024i	0.746570	+	0.200043i
$345$	−0.120902	−	1.72891i	−0.00650917	−	0.0930813i
$346$	−2.68218	+	2.68218i	−0.144195	+	0.144195i
$347$	16.2290	+	28.1095i	0.871221	+	1.50900i	0.860735	+	0.509054i	$0.170005\pi$
$347$	16.2290	+	28.1095i	0.871221	+	1.50900i	0.0104862	+	0.999945i	$0.496662\pi$
$348$	3.02909	−	0.949649i	0.162376	−	0.0509066i
$349$	−2.92829	−	10.9285i	−0.156748	−	0.584990i	−0.998949	−	0.0458273i	$-0.985408\pi$
$349$	−2.92829	−	10.9285i	−0.156748	−	0.584990i	0.842202	−	0.539162i	$-0.181259\pi$
$350$	−8.08752	−	12.3652i	−0.432296	−	0.660948i
$351$	−1.34882	−	18.6864i	−0.0719946	−	0.997405i
$352$		−	5.07060i		−	0.270264i
$353$	−13.6671	+	3.66208i	−0.727425	+	0.194913i	−0.603482	−	0.797376i	$-0.706221\pi$
$353$	−13.6671	+	3.66208i	−0.727425	+	0.194913i	−0.123943	+	0.992289i	$0.539554\pi$
$354$	−4.35221	−	13.8822i	−0.231317	−	0.737831i
$355$	0.824851	+	29.6518i	0.0437786	+	1.57375i
$356$	0.383672	−	0.383672i	0.0203346	−	0.0203346i
$357$	−9.60757	−	15.1352i	−0.508486	−	0.801038i
$358$	−2.30296	+	8.59475i	−0.121715	+	0.454247i
$359$	18.3546	+	18.3546i	0.968720	+	0.968720i	0.999525	−	0.0308058i	$-0.00980733\pi$
$359$	18.3546	+	18.3546i	0.968720	+	0.968720i	−0.0308058	+	0.999525i	$0.509807\pi$
$360$	−20.0425	+	2.25058i	−1.05633	+	0.118616i
$361$	8.67351	+	5.00765i	0.456500	+	0.263561i
$362$	−7.38338	−	27.5552i	−0.388062	−	1.44827i
$363$	3.43164	−	3.73276i	0.180114	−	0.195919i
$364$	2.19396	+	1.42977i	0.114995	+	0.0749404i
$365$	2.35665	−	4.35735i	0.123353	−	0.228074i
$366$	−22.5436	−	11.7821i	−1.17837	−	0.615861i
$367$	−11.4479	−	6.60945i	−0.597575	−	0.345010i	0.170512	−	0.985356i	$-0.445458\pi$
$367$	−11.4479	−	6.60945i	−0.597575	−	0.345010i	−0.768087	+	0.640345i	$0.778791\pi$
$368$	−1.26378	+	0.729645i	−0.0658792	+	0.0380354i
$369$	−1.92439	−	1.62546i	−0.100180	−	0.0846181i
$370$	22.4412	+	21.2264i	1.16666	+	1.10351i
$371$	−4.88811	+	18.2427i	−0.253778	+	0.947112i
$372$	−3.60809	+	0.151649i	−0.187071	+	0.00786263i
$373$	13.0651	−	7.54312i	0.676483	−	0.390568i	−0.122045	−	0.992525i	$-0.538945\pi$
$373$	13.0651	−	7.54312i	0.676483	−	0.390568i	0.798529	+	0.601957i	$0.205612\pi$
$374$	8.36578	−	14.4900i	0.432584	−	0.749257i
$375$	17.8501	+	7.50824i	0.921776	+	0.387724i
$376$		−	13.0250i		−	0.671714i
$377$	−20.2887	+	4.27859i	−1.04492	+	0.220358i
$378$	−12.1360	−	9.40680i	−0.624209	−	0.483834i
$379$	−4.41475	+	1.18293i	−0.226771	+	0.0607630i	−0.370415	−	0.928866i	$-0.620785\pi$
$379$	−4.41475	+	1.18293i	−0.226771	+	0.0607630i	0.143644	+	0.989629i	$0.454118\pi$
$380$	−1.81947	+	1.11906i	−0.0933370	+	0.0574066i
$381$	−4.63710	+	20.7567i	−0.237566	+	1.06340i
$382$	15.2524	−	15.2524i	0.780379	−	0.780379i
$383$	−3.91778	+	14.6214i	−0.200189	+	0.747117i	0.790673	+	0.612239i	$0.209731\pi$
$383$	−3.91778	+	14.6214i	−0.200189	+	0.747117i	−0.990862	+	0.134878i	$0.956936\pi$
$384$	7.32213	+	11.5348i	0.373656	+	0.588634i
$385$	−13.8758	+	4.13482i	−0.707175	+	0.210730i
$386$	−7.48921	+	4.32390i	−0.381191	+	0.220081i
$387$	−12.9442	−	6.08734i	−0.657989	−	0.309437i
$388$	3.12638	−	0.837711i	0.158718	−	0.0425283i
$389$	20.3601			1.03230			0.516150	−	0.856498i	$-0.327365\pi$
$389$	20.3601			1.03230			0.516150	+	0.856498i	$0.327365\pi$
$390$	18.1045	−	0.287100i	0.916755	−	0.0145379i
$391$	2.03232			0.102779
$392$	−5.24554	+	1.40554i	−0.264940	+	0.0709904i
$393$	0.453750	+	1.44732i	0.0228886	+	0.0730077i
$394$	12.9020	−	7.44899i	0.649995	−	0.375275i
$395$	−6.22081	−	20.8760i	−0.313003	−	1.05039i
$396$	−0.480416	+	2.67365i	−0.0241418	+	0.134356i
$397$	−8.11051	+	30.2688i	−0.407055	+	1.51915i	0.393179	+	0.919462i	$0.371375\pi$
$397$	−8.11051	+	30.2688i	−0.407055	+	1.51915i	−0.800234	+	0.599688i	$0.795291\pi$
$398$	−0.267240	+	0.267240i	−0.0133955	+	0.0133955i
$399$	−11.5472	−	2.57968i	−0.578083	−	0.129146i
$400$	−0.906453	−	16.2800i	−0.0453226	−	0.813999i
$401$	−13.7202	+	3.67631i	−0.685154	+	0.183586i	−0.584571	−	0.811342i	$-0.698737\pi$
$401$	−13.7202	+	3.67631i	−0.685154	+	0.183586i	−0.100582	+	0.994929i	$0.532071\pi$
$402$	15.3367	+	14.0995i	0.764924	+	0.703217i
$403$	23.5538	+	1.27219i	1.17330	+	0.0633723i
$404$			4.17975i			0.207950i
$405$	20.0808	+	1.32659i	0.997825	+	0.0659186i
$406$	−8.49698	+	14.7172i	−0.421698	+	0.730402i
$407$	26.2144	−	15.1349i	1.29940	−	0.750210i
$408$	−0.993148	−	23.6294i	−0.0491682	−	1.16983i
$409$	5.33224	−	19.9002i	0.263662	−	0.984001i	−0.699402	−	0.714729i	$-0.746550\pi$
$409$	5.33224	−	19.9002i	0.263662	−	0.984001i	0.963064	−	0.269273i	$-0.0867832\pi$
$410$	1.67294	−	1.76868i	0.0826207	−	0.0873489i
$411$	10.8967	−	0.457989i	0.537492	−	0.0225909i
$412$	1.41489	−	0.816888i	0.0697067	−	0.0402452i
$413$	−12.7851	−	7.38148i	−0.629113	−	0.363219i
$414$	1.63767	−	0.590034i	0.0804873	−	0.0289986i
$415$	−1.28812	+	2.38168i	−0.0632313	+	0.116912i
$416$	2.91210	+	5.73799i	0.142777	+	0.281328i
$417$	−22.1254	−	20.3405i	−1.08348	−	0.996080i
$418$	−2.85810	−	10.6666i	−0.139794	−	0.521718i
$419$	−11.6759	−	6.74109i	−0.570405	−	0.329324i	0.186906	−	0.982378i	$-0.440154\pi$
$419$	−11.6759	−	6.74109i	−0.570405	−	0.329324i	−0.757311	+	0.653054i	$0.773487\pi$
$420$	−1.84546	+	2.12298i	−0.0900493	+	0.103591i
$421$	11.4321	+	11.4321i	0.557166	+	0.557166i	0.928500	−	0.371333i	$-0.121099\pi$
$421$	11.4321	+	11.4321i	0.557166	+	0.557166i	−0.371333	+	0.928500i	$0.621099\pi$
$422$	5.33682	−	19.9173i	0.259792	−	0.969558i
$423$	−2.29850	+	12.7918i	−0.111757	+	0.621959i
$424$	−17.6180	+	17.6180i	−0.855605	+	0.855605i
$425$	−10.2431	+	20.2664i	−0.496865	+	0.983066i
$426$	−28.4288	+	8.91272i	−1.37738	+	0.431823i
$427$	−24.9323	+	6.68060i	−1.20656	+	0.323297i
$428$		−	2.19020i		−	0.105867i
$429$	4.79689	−	17.0827i	0.231596	−	0.824762i
$430$	6.57662	−	12.1599i	0.317153	−	0.586402i
$431$	−3.16022	−	11.7941i	−0.152222	−	0.568102i	−0.999327	−	0.0366759i	$-0.988323\pi$
$431$	−3.16022	−	11.7941i	−0.152222	−	0.568102i	0.847105	−	0.531426i	$-0.178344\pi$
$432$	−6.40799	−	15.6865i	−0.308305	−	0.754716i
$433$	−8.46304	−	14.6584i	−0.406708	−	0.704439i	0.587811	−	0.808999i	$-0.299990\pi$
$433$	−8.46304	−	14.6584i	−0.406708	−	0.704439i	−0.994519	+	0.104560i	$0.966657\pi$
$434$	13.6700	−	13.6700i	0.656183	−	0.656183i
$435$	−1.55375	−	22.2186i	−0.0744966	−	1.06530i
$436$	0.312120	+	0.0836322i	0.0149478	+	0.00400526i
$437$	0.948467	−	0.948467i	0.0453713	−	0.0453713i
$438$	4.85582	+	1.08481i	0.232020	+	0.0518340i
$439$	2.43013	+	1.40303i	0.115984	+	0.0669631i	0.556870	−	0.830600i	$-0.312002\pi$
$439$	2.43013	+	1.40303i	0.115984	+	0.0669631i	−0.440886	+	0.897563i	$0.645336\pi$
$440$	−18.5806	−	4.42876i	−0.885793	−	0.211133i
$441$	5.39966	−	0.454701i	0.257127	−	0.0216524i
$442$	−1.14515	+	21.2017i	−0.0544690	+	1.00846i
$443$	27.4864			1.30592			0.652960	−	0.757393i	$-0.273527\pi$
$443$	27.4864			1.30592			0.652960	+	0.757393i	$0.273527\pi$
$444$	2.72398	−	5.21198i	0.129274	−	0.247350i
$445$	−1.99444	−	3.24275i	−0.0945455	−	0.153721i
$446$	2.87613	+	4.98160i	0.136189	+	0.235886i
$447$	38.3861	−	1.61338i	1.81560	−	0.0763102i
$448$	19.4512	+	5.21194i	0.918984	+	0.246241i
$449$	1.90550	−	7.11141i	0.0899260	−	0.335608i	−0.906275	−	0.422688i	$-0.861087\pi$
$449$	1.90550	−	7.11141i	0.0899260	−	0.335608i	0.996201	+	0.0870794i	$0.0277534\pi$
$450$	−2.37021	+	19.3048i	−0.111733	+	0.910037i
$451$	−1.19285	−	2.06607i	−0.0561689	−	0.0972874i
$452$	1.63587	+	0.944472i	0.0769450	+	0.0444242i
$453$	0.562009	−	1.07533i	0.0264055	−	0.0505235i
$454$		−	17.4304i		−	0.818051i
$455$	13.3274	−	12.6480i	0.624799	−	0.592949i
$456$	−11.4911	−	10.5641i	−0.538120	−	0.494710i
$457$	0.0620628	+	0.231621i	0.00290317	+	0.0108348i	0.967362	−	0.253398i	$-0.0815481\pi$
$457$	0.0620628	+	0.231621i	0.00290317	+	0.0108348i	−0.964459	+	0.264232i	$0.914881\pi$
$458$	−7.70462	+	13.3448i	−0.360013	+	0.623561i
$459$	−3.19447	+	23.3816i	−0.149105	+	1.09136i
$460$	−0.0910698	−	0.305615i	−0.00424615	−	0.0142494i
$461$	−16.4008	−	4.39457i	−0.763860	−	0.204676i	−0.144203	−	0.989548i	$-0.546062\pi$
$461$	−16.4008	−	4.39457i	−0.763860	−	0.204676i	−0.619657	+	0.784872i	$0.712728\pi$
$462$	−7.79353	−	12.2775i	−0.362588	−	0.571199i
$463$	13.0393	+	13.0393i	0.605988	+	0.605988i	0.941895	−	0.335907i	$-0.109043\pi$
$463$	13.0393	+	13.0393i	0.605988	+	0.605988i	−0.335907	+	0.941895i	$0.609043\pi$
$464$	−16.2412	+	9.37685i	−0.753978	+	0.435310i
$465$	−4.83458	+	24.8722i	−0.224198	+	1.15342i
$466$	−4.08367	−	15.2405i	−0.189173	−	0.706002i
$467$			15.8095i			0.731575i	0.930698	+	0.365788i	$0.119200\pi$
$467$			15.8095i			0.731575i	−0.930698	+	0.365788i	$0.880800\pi$
$468$	−0.991857	−	3.30146i	−0.0458486	−	0.152610i
$469$	21.1400			0.976156
$470$	−12.2186	−	2.91235i	−0.563600	−	0.134337i
$471$	−11.1272	−	35.4922i	−0.512713	−	1.63540i
$472$	−9.73800	−	16.8667i	−0.448228	−	0.776354i
$473$	−9.57921	−	9.57921i	−0.440453	−	0.440453i
$474$	18.4713	−	11.7253i	0.848417	−	0.538562i
$475$	4.67778	+	14.2385i	0.214631	+	0.653309i
$476$	−2.33244	−	2.33244i	−0.106907	−	0.106907i
$477$	20.4116	−	14.1935i	0.934582	−	0.649877i
$478$	−14.1678	+	24.5394i	−0.648021	+	1.12241i
$479$	4.26159	−	1.14189i	0.194717	−	0.0521742i	−0.160143	−	0.987094i	$-0.551195\pi$
$479$	4.26159	−	1.14189i	0.194717	−	0.0521742i	0.354859	+	0.934920i	$0.384529\pi$
$480$	−6.53535	+	2.25032i	−0.298297	+	0.102713i
$481$	−20.9726	+	32.1822i	−0.956269	+	1.46738i
$482$	−32.2609			−1.46944
$483$	0.818177	−	1.56548i	0.0372283	−	0.0712317i
$484$	0.466483	−	0.807972i	0.0212038	−	0.0367260i
$485$	−0.631484	−	22.7006i	−0.0286742	−	1.03078i
$486$	4.21410	+	19.7686i	0.191156	+	0.896722i
$487$	−38.6598	−	10.3589i	−1.75184	−	0.469405i	−0.766826	−	0.641855i	$-0.778165\pi$
$487$	−38.6598	−	10.3589i	−1.75184	−	0.469405i	−0.985018	+	0.172450i	$0.944832\pi$
$488$	−32.8919	−	8.81337i	−1.48895	−	0.398963i
$489$	0.805602	+	19.1672i	0.0364306	+	0.866770i
$490$	0.145628	+	5.23503i	0.00657880	+	0.236495i
$491$	7.03573	−	12.1862i	0.317518	−	0.549957i	−0.662452	−	0.749105i	$-0.730484\pi$
$491$	7.03573	−	12.1862i	0.317518	−	0.549957i	0.979970	+	0.199147i	$0.0638173\pi$
$492$	−0.410778	−	0.214688i	−0.0185193	−	0.00967888i
$493$	26.1179			1.17629
$494$	9.36018	+	10.4290i	0.421135	+	0.469225i
$495$	17.4664	+	7.62835i	0.785054	+	0.342869i
$496$	20.6073	−	5.52171i	0.925296	−	0.247932i
$497$	−15.1162	+	26.1821i	−0.678056	+	1.17443i
$498$	−2.65414	−	0.592942i	−0.118935	−	0.0265704i
$499$	−12.8997	−	12.8997i	−0.577470	−	0.577470i	0.356735	−	0.934206i	$-0.383890\pi$
$499$	−12.8997	−	12.8997i	−0.577470	−	0.577470i	−0.934206	+	0.356735i	$0.883890\pi$
$500$	3.50661	+	0.632182i	0.156820	+	0.0282721i
$501$	22.4184	+	35.3166i	1.00158	+	1.57783i
$502$	2.84887	+	2.84887i	0.127151	+	0.127151i
$503$	−11.6042	−	20.0990i	−0.517405	−	0.896172i	−0.999796	−	0.0202156i	$-0.993565\pi$
$503$	−11.6042	−	20.0990i	−0.517405	−	0.896172i	0.482391	−	0.875956i	$-0.339769\pi$
$504$	−18.6013	−	8.74774i	−0.828566	−	0.389655i
$505$	28.5271	+	6.79957i	1.26944	+	0.302577i
$506$	1.64860			0.0732890
$507$	4.38254	+	22.0860i	0.194635	+	0.980876i
$508$			3.91337i			0.173628i
$509$	−2.71529	−	10.1336i	−0.120353	−	0.449165i	0.879278	−	0.476308i	$-0.158025\pi$
$509$	−2.71529	−	10.1336i	−0.120353	−	0.449165i	−0.999632	+	0.0271439i	$0.991359\pi$
$510$	−22.3884	−	4.35179i	−0.991375	−	0.192701i
$511$	4.37246	−	2.52444i	0.193426	−	0.111675i
$512$	17.9808	+	17.9808i	0.794647	+	0.794647i
$513$	9.42113	+	12.4028i	0.415953	+	0.547597i
$514$	16.5075	+	4.42316i	0.728113	+	0.195097i
$515$	−3.27360	−	10.9857i	−0.144252	−	0.484086i
$516$	−2.56863	−	0.573840i	−0.113078	−	0.0252619i
$517$	−6.15442	+	10.6598i	−0.270671	+	0.468816i
$518$	8.14824	+	30.4096i	0.358013	+	1.33612i
$519$	3.42921	−	3.73011i	0.150525	−	0.163734i
$520$	23.5696	−	5.65933i	1.03359	−	0.248178i
$521$		−	28.1221i		−	1.23205i	−0.787726	−	0.616026i	$-0.788741\pi$
$521$		−	28.1221i		−	1.23205i	0.787726	−	0.616026i	$-0.211259\pi$
$522$	21.0462	−	7.58269i	0.921166	−	0.331885i
$523$	−30.0865	−	17.3704i	−1.31559	−	0.759556i	−0.332574	−	0.943077i	$-0.607917\pi$
$523$	−30.0865	−	17.3704i	−1.31559	−	0.759556i	−0.983016	+	0.183521i	$0.941251\pi$
$524$	0.139544	+	0.241697i	0.00609600	+	0.0105586i
$525$	11.4873	+	16.0491i	0.501347	+	0.700439i
$526$	1.06405	−	3.97109i	0.0463948	−	0.173148i
$527$	−28.6994	−	7.68998i	−1.25017	−	0.334981i
$528$	−0.673909	−	16.0339i	−0.0293281	−	0.697786i
$529$	−11.3999	−	19.7452i	−0.495647	−	0.858485i
$530$	12.5878	+	20.4665i	0.546780	+	0.889007i
$531$	6.58721	+	18.2832i	0.285861	+	0.793423i
$532$	−2.17706			−0.0943874
$533$	2.53641	+	1.65294i	0.109864	+	0.0715967i
$534$	2.58782	−	2.81490i	0.111986	−	0.121813i
$535$	−14.9483	−	3.56300i	−0.646272	−	0.154042i
$536$	24.1526	+	13.9445i	1.04323	+	0.602310i
$537$	2.59143	−	11.5998i	0.111829	−	0.500569i
$538$	9.50908	−	9.50908i	0.409965	−	0.409965i
$539$	4.95711	+	1.32825i	0.213518	+	0.0572120i
$540$	3.65920	−	0.567367i	0.157467	−	0.0244156i
$541$	−17.6269	+	17.6269i	−0.757839	+	0.757839i	−0.975929	−	0.218090i	$-0.930017\pi$
$541$	−17.6269	+	17.6269i	−0.757839	+	0.757839i	0.218090	+	0.975929i	$0.430017\pi$
$542$	14.0922	+	24.4083i	0.605310	+	1.04843i
$543$	11.3996	+	36.3612i	0.489204	+	1.56041i
$544$	−2.09777	−	7.82898i	−0.0899411	−	0.335665i
$545$	1.07855	−	1.99419i	0.0462000	−	0.0854217i
$546$	15.8704	+	9.41749i	0.679189	+	0.403031i
$547$			7.60825i			0.325305i	0.986683	+	0.162653i	$0.0520050\pi$
$547$			7.60825i			0.325305i	−0.986683	+	0.162653i	$0.947995\pi$
$548$	1.93837	−	0.519386i	0.0828032	−	0.0221871i
$549$	30.7478	+	14.4600i	1.31228	+	0.617136i
$550$	−8.30910	+	16.4399i	−0.354301	+	0.700999i
$551$	12.1890	−	12.1890i	0.519269	−	0.519269i
$552$	1.96740	−	1.24887i	0.0837380	−	0.0531555i
$553$	5.74609	−	21.4447i	0.244349	−	0.911922i
$554$	−2.18121	−	2.18121i	−0.0926709	−	0.0926709i
$555$	−31.1409	−	27.0702i	−1.32186	−	1.14907i
$556$	−4.78913	−	2.76501i	−0.203104	−	0.117262i
$557$	−0.832532	−	3.10705i	−0.0352755	−	0.131650i	0.946043	−	0.324042i	$-0.105042\pi$
$557$	−0.832532	−	3.10705i	−0.0352755	−	0.131650i	−0.981318	+	0.192392i	$0.938375\pi$
$558$	−25.3590	+	2.13546i	−1.07353	+	0.0904012i
$559$	16.3415	+	5.33858i	0.691170	+	0.225798i
$560$	7.90564	−	14.6172i	0.334074	−	0.617688i
$561$	−10.3522	+	19.8077i	−0.437072	+	0.836282i
$562$	11.5654	+	6.67730i	0.487858	+	0.281665i
$563$	16.0712	−	9.27874i	0.677322	−	0.391052i	−0.121523	−	0.992589i	$-0.538778\pi$
$563$	16.0712	−	9.27874i	0.677322	−	0.391052i	0.798845	+	0.601536i	$0.205445\pi$
$564$	0.100422	+	2.38928i	0.00422853	+	0.100607i
$565$	9.10733	−	9.62852i	0.383148	−	0.405075i
$566$	4.67973	−	17.4650i	0.196704	−	0.734109i
$567$	16.7245	+	11.8737i	0.702364	+	0.498647i
$568$	−34.5407	+	19.9421i	−1.44930	+	0.836751i
$569$	−10.2020	+	17.6703i	−0.427688	+	0.740778i	−0.996667	−	0.0815741i	$-0.974005\pi$
$569$	−10.2020	+	17.6703i	−0.427688	+	0.740778i	0.568979	+	0.822352i	$0.307339\pi$
$570$	−12.4794	+	8.41752i	−0.522704	+	0.352571i
$571$			0.850329i			0.0355852i	0.999842	+	0.0177926i	$0.00566385\pi$
$571$			0.850329i			0.0355852i	−0.999842	+	0.0177926i	$0.994336\pi$
$572$	0.176082	−	3.26004i	0.00736234	−	0.136309i
$573$	−19.5004	+	21.2115i	−0.814640	+	0.886124i
$574$	2.39671	−	0.642196i	0.100037	−	0.0268048i
$575$	−2.23400	+	0.124387i	−0.0931643	+	0.00518729i
$576$	−15.1338	−	21.7638i	−0.630577	−	0.906826i
$577$	8.23663	−	8.23663i	0.342896	−	0.342896i	−0.514559	−	0.857455i	$-0.672044\pi$
$577$	8.23663	−	8.23663i	0.342896	−	0.342896i	0.857455	+	0.514559i	$0.172044\pi$
$578$	1.21688	−	4.54146i	0.0506155	−	0.188900i
$579$	9.75264	−	6.19082i	0.405306	−	0.257282i
$580$	−1.17036	−	3.92754i	−0.0485966	−	0.163082i
$581$	−2.38994	+	1.37983i	−0.0991513	+	0.0572450i
$582$	21.7643	−	6.82334i	0.902160	−	0.282836i
$583$	22.7433	−	6.09405i	0.941932	−	0.252390i
$584$	6.66073			0.275623
$585$	−24.1463	+	1.39872i	−0.998326	+	0.0578299i
$586$	35.7043			1.47493
$587$	−0.0816572	+	0.0218800i	−0.00337035	+	0.000903083i	−0.260504	−	0.965473i	$-0.583889\pi$
$587$	−0.0816572	+	0.0218800i	−0.00337035	+	0.000903083i	0.257133	+	0.966376i	$0.417222\pi$
$588$	0.951393	−	0.298271i	0.0392348	−	0.0123005i
$589$	−16.9826	+	9.80491i	−0.699756	+	0.404004i
$590$	−17.9998	+	5.36373i	−0.741040	+	0.220821i
$591$	−16.8013	+	10.6652i	−0.691114	+	0.438709i
$592$	−8.99200	+	33.5586i	−0.369569	+	1.37925i
$593$	−29.3266	+	29.3266i	−1.20430	+	1.20430i	−0.231451	+	0.972847i	$0.574347\pi$
$593$	−29.3266	+	29.3266i	−1.20430	+	1.20430i	−0.972847	+	0.231451i	$0.925653\pi$
$594$	−2.59131	+	18.9668i	−0.106323	+	0.778218i
$595$	−19.7135	+	12.1247i	−0.808175	+	0.497065i
$596$	6.82839	−	1.82966i	0.279702	−	0.0749459i
$597$	0.341671	−	0.371652i	0.0139837	−	0.0152107i
$598$	−1.86558	+	0.946805i	−0.0762893	+	0.0387178i
$599$		−	35.3223i		−	1.44323i	−0.692294	−	0.721615i	$-0.743400\pi$
$599$		−	35.3223i		−	1.44323i	0.692294	−	0.721615i	$-0.256600\pi$
$600$	2.53792	+	25.9134i	0.103610	+	1.05791i
$601$	−5.49445	+	9.51667i	−0.224123	+	0.388193i	−0.956056	−	0.293184i	$-0.905285\pi$
$601$	−5.49445	+	9.51667i	−0.224123	+	0.388193i	0.731933	+	0.681377i	$0.238619\pi$
$602$	12.2021	−	7.04486i	0.497319	−	0.287127i
$603$	−21.2594	−	17.9570i	−0.865749	−	0.731265i
$604$	0.0577824	−	0.215647i	0.00235113	−	0.00877455i
$605$	−4.75561	−	4.49818i	−0.193343	−	0.182877i
$606$	1.23690	+	29.4288i	0.0502456	+	1.19546i
$607$	−12.9895	+	7.49947i	−0.527226	+	0.304394i	−0.739886	−	0.672732i	$-0.765121\pi$
$607$	−12.9895	+	7.49947i	−0.527226	+	0.304394i	0.212660	+	0.977126i	$0.431787\pi$
$608$	−4.63272	−	2.67470i	−0.187882	−	0.108474i
$609$	10.5146	−	20.1184i	0.426073	−	0.815237i
$610$	−15.6222	+	28.8848i	−0.632525	+	1.16951i
$611$	0.842445	−	15.5973i	0.0340817	−	0.631001i
$612$	0.364361	+	4.32686i	0.0147284	+	0.174903i
$613$	−1.79972	−	6.71663i	−0.0726898	−	0.271282i	0.920010	−	0.391895i	$-0.128181\pi$
$613$	−1.79972	−	6.71663i	−0.0726898	−	0.271282i	−0.992700	+	0.120613i	$0.961514\pi$
$614$	18.1377	+	10.4718i	0.731980	+	0.422609i
$615$	−2.13351	+	2.45434i	−0.0860316	+	0.0989686i
$616$	−13.7657	−	13.7657i	−0.554635	−	0.554635i
$617$	−1.01846	+	3.80094i	−0.0410017	+	0.153020i	−0.983392	−	0.181496i	$-0.941906\pi$
$617$	−1.01846	+	3.80094i	−0.0410017	+	0.153020i	0.942390	+	0.334516i	$0.108573\pi$
$618$	9.72024	−	6.17026i	0.391005	−	0.248204i
$619$	21.4563	−	21.4563i	0.862401	−	0.862401i	−0.129216	−	0.991617i	$-0.541246\pi$
$619$	21.4563	−	21.4563i	0.862401	−	0.862401i	0.991617	+	0.129216i	$0.0412459\pi$
$620$	0.129641	+	4.66033i	0.00520650	+	0.187163i
$621$	−2.15256	+	0.879330i	−0.0863792	+	0.0352863i
$622$	−10.3341	+	2.76901i	−0.414360	+	0.111027i
$623$		−	3.88005i		−	0.155451i
$624$	9.97103	+	17.7572i	0.399161	+	0.710858i
$625$	10.0192	−	22.9045i	0.400769	−	0.916179i
$626$	−4.22683	−	15.7747i	−0.168938	−	0.630486i
$627$	4.41277	+	14.0754i	0.176229	+	0.562116i
$628$	−3.42199	−	5.92706i	−0.136552	−	0.236516i
$629$	34.2134	−	34.2134i	1.36418	−	1.36418i
$630$	−12.3653	+	15.4936i	−0.492645	+	0.617279i
$631$	−21.8951	−	5.86676i	−0.871628	−	0.233552i	−0.204837	−	0.978796i	$-0.565666\pi$
$631$	−21.8951	−	5.86676i	−0.871628	−	0.233552i	−0.666792	+	0.745244i	$0.732333\pi$
$632$	20.7104	−	20.7104i	0.823815	−	0.823815i
$633$	−6.00533	+	26.8812i	−0.238690	+	1.06843i
$634$	−6.39798	−	3.69388i	−0.254096	−	0.146703i
$635$	26.7091	+	6.36623i	1.05992	+	0.252636i
$636$	3.09597	−	3.36763i	0.122763	−	0.133535i
$637$	−6.37239	+	1.34384i	−0.252483	+	0.0532450i
$638$	21.1865			0.838783
$639$	37.4414	−	13.4897i	1.48116	−	0.533644i
$640$	15.0241	−	9.24051i	0.593879	−	0.365263i
$641$	0.623490	+	1.07992i	0.0246264	+	0.0426542i	0.878076	−	0.478521i	$-0.158827\pi$
$641$	0.623490	+	1.07992i	0.0246264	+	0.0426542i	−0.853450	+	0.521175i	$0.825494\pi$
$642$	−0.648140	−	15.4208i	−0.0255800	−	0.608610i
$643$	−2.91685	−	0.781568i	−0.115029	−	0.0308220i	0.200845	−	0.979623i	$-0.435631\pi$
$643$	−2.91685	−	0.781568i	−0.115029	−	0.0308220i	−0.315875	+	0.948801i	$0.602298\pi$
$644$	0.0841202	−	0.313941i	0.00331480	−	0.0123710i
$645$	−8.09513	+	16.5976i	−0.318746	+	0.653530i
$646$	−8.82576	−	15.2867i	−0.347245	−	0.601446i
$647$	−4.37664	−	2.52686i	−0.172064	−	0.0993410i	0.411495	−	0.911412i	$-0.365007\pi$
$647$	−4.37664	−	2.52686i	−0.172064	−	0.0993410i	−0.583559	+	0.812071i	$0.698340\pi$
$648$	11.2757	+	24.5976i	0.442950	+	0.966285i
$649$			18.4051i			0.722464i
$650$	−0.0388475	−	23.3757i	−0.00152373	−	0.916869i
$651$	−17.4774	+	19.0110i	−0.684992	+	0.745099i
$652$	0.913598	+	3.40959i	0.0357793	+	0.133530i
$653$	4.45799	−	7.72146i	0.174454	−	0.302164i	−0.765518	−	0.643415i	$-0.777517\pi$
$653$	4.45799	−	7.72146i	0.174454	−	0.302164i	0.939972	+	0.341251i	$0.110850\pi$
$654$	2.22232	+	0.496474i	0.0868997	+	0.0194137i
$655$	1.87661	−	0.559208i	0.0733252	−	0.0218500i
$656$	2.64489	+	0.708697i	0.103266	+	0.0276700i
$657$	−6.54148	−	1.17541i	−0.255208	−	0.0458571i
$658$	−9.05231	−	9.05231i	−0.352896	−	0.352896i
$659$	−26.8813	+	15.5199i	−1.04715	+	0.604570i	−0.921849	−	0.387549i	$-0.873322\pi$
$659$	−26.8813	+	15.5199i	−1.04715	+	0.604570i	−0.125297	+	0.992119i	$0.539988\pi$
$660$	3.44252	+	0.669146i	0.134000	+	0.0260465i
$661$	−3.97807	−	14.8464i	−0.154729	−	0.577456i	−0.999128	−	0.0417423i	$-0.986709\pi$
$661$	−3.97807	−	14.8464i	−0.154729	−	0.577456i	0.844399	−	0.535714i	$-0.179958\pi$
$662$		−	20.9536i		−	0.814384i
$663$	0.339038	−	28.3602i	0.0131671	−	1.10142i
$664$	−3.64068			−0.141286
$665$	−3.54162	+	14.8586i	−0.137338	+	0.576192i
$666$	17.6366	−	37.5027i	0.683406	−	1.45320i
$667$	1.28673	+	2.22868i	0.0498223	+	0.0862948i
$668$	5.44256	+	5.44256i	0.210579	+	0.210579i
$669$	−4.11795	−	6.48717i	−0.159209	−	0.250808i
$670$	18.4815	−	19.5392i	0.714004	−	0.754865i
$671$	22.7546	+	22.7546i	0.878432	+	0.878432i
$672$	−6.87510	−	1.53592i	−0.265213	−	0.0592493i
$673$	5.27490	−	9.13640i	0.203333	−	0.352182i	−0.746268	−	0.665646i	$-0.768156\pi$
$673$	5.27490	−	9.13640i	0.203333	−	0.352182i	0.949600	+	0.313464i	$0.101489\pi$
$674$	−8.79505	+	2.35663i	−0.338773	+	0.0907739i
$675$	2.08042	−	25.8973i	0.0800754	−	0.996789i
$676$	1.67302	+	3.79025i	0.0643468	+	0.145779i
$677$	−39.8150			−1.53021			−0.765107	−	0.643904i	$-0.777314\pi$
$677$	−39.8150			−1.53021			−0.765107	+	0.643904i	$0.777314\pi$
$678$	11.7974	+	6.16575i	0.453075	+	0.236794i
$679$	11.5726	−	20.0443i	0.444115	−	0.769229i
$680$	−30.5205	+	0.849018i	−1.17041	+	0.0325583i
$681$	0.977744	+	23.2628i	0.0374672	+	0.891434i
$682$	−23.2806	−	6.23802i	−0.891460	−	0.238866i
$683$	11.4193	+	3.05980i	0.436949	+	0.117080i	0.470586	−	0.882354i	$-0.344042\pi$
$683$	11.4193	+	3.05980i	0.436949	+	0.117080i	−0.0336375	+	0.999434i	$0.510709\pi$
$684$	2.18935	+	1.84926i	0.0837118	+	0.0707082i
$685$	−0.391524	−	14.0745i	−0.0149594	−	0.537759i
$686$	−13.0114	+	22.5364i	−0.496778	+	0.860445i
$687$	9.53410	−	18.2423i	0.363748	−	0.695986i
$688$	15.5487			0.592790
$689$	−22.2369	+	19.9579i	−0.847158	+	0.760334i
$690$	−0.731644	−	2.12483i	−0.0278532	−	0.0808908i
$691$	−13.1578	+	3.52563i	−0.500547	+	0.134121i	−0.500254	−	0.865879i	$-0.666760\pi$
$691$	−13.1578	+	3.52563i	−0.500547	+	0.134121i	−0.000293354		1.00000i	$0.500093\pi$
$692$	0.466152	−	0.807399i	0.0177204	−	0.0306927i
$693$	11.0900	+	15.9484i	0.421275	+	0.605831i
$694$	29.7599	+	29.7599i	1.12967	+	1.12967i
$695$	−26.6623	+	28.1881i	−1.01136	+	1.06924i
$696$	25.2835	−	16.0496i	0.958370	−	0.608358i
$697$	−2.69650	−	2.69650i	−0.102137	−	0.102137i
$698$	−7.33517	−	12.7049i	−0.277640	−	0.480887i
$699$	6.30501	+	20.1110i	0.238477	+	0.760669i
$700$	2.70666	+	2.42114i	0.102302	+	0.0915107i
$701$	−30.0152			−1.13366			−0.566829	−	0.823836i	$-0.691830\pi$
$701$	−30.0152			−1.13366			−0.566829	+	0.823836i	$0.691830\pi$
$702$	−7.96046	−	22.9514i	−0.300448	−	0.866246i
$703$		−	31.9342i		−	1.20442i
$704$	−6.49778	−	24.2500i	−0.244894	−	0.913958i
$705$	16.4704	+	3.20146i	0.620310	+	0.120574i
$706$	−15.8886	+	9.17328i	−0.597975	+	0.345241i
$707$	21.1348	+	21.1348i	0.794855	+	0.794855i
$708$	1.91636	+	3.01891i	0.0720211	+	0.113458i
$709$	−35.0441	−	9.39004i	−1.31611	−	0.352650i	−0.468590	−	0.883416i	$-0.655238\pi$
$709$	−35.0441	−	9.39004i	−1.31611	−	0.352650i	−0.847519	+	0.530765i	$0.821905\pi$
$710$	10.9842	+	36.8611i	0.412228	+	1.38337i
$711$	−23.9943	+	16.6849i	−0.899857	+	0.625731i
$712$	2.55938	−	4.43297i	0.0959167	−	0.166133i
$713$	−0.757711	−	2.82782i	−0.0283765	−	0.105903i
$714$	−17.1125	−	15.7320i	−0.640419	−	0.588757i
$715$	−21.9636	−	6.50517i	−0.821392	−	0.243280i
$716$		−	2.18698i		−	0.0817312i
$717$	17.5320	−	33.5453i	0.654745	−	1.25277i
$718$	29.1483	+	16.8288i	1.08781	+	0.628045i
$719$	23.2174	+	40.2137i	0.865863	+	1.49972i	0.866188	+	0.499719i	$0.166563\pi$
$719$	23.2174	+	40.2137i	0.865863	+	1.49972i	−0.000324371		1.00000i	$0.500103\pi$
$720$	−20.3665	+	7.98440i	−0.759016	+	0.297561i
$721$	3.02379	−	11.2849i	0.112612	−	0.420273i
$722$	12.5438	+	3.36111i	0.466834	+	0.125088i
$723$	43.0557	−	1.80964i	1.60126	−	0.0673014i
$724$	3.50578	+	6.07218i	0.130291	+	0.225671i
$725$	−28.7097	+	1.59853i	−1.06625	+	0.0593679i
$726$	3.04531	−	5.82682i	0.113022	−	0.216254i
$727$	51.6317			1.91491			0.957457	−	0.288575i	$-0.0931814\pi$
$727$	51.6317			1.91491			0.957457	+	0.288575i	$0.0931814\pi$
$728$	23.4833	+	7.67174i	0.870348	+	0.284334i
$729$	−6.73308	−	26.1470i	−0.249373	−	0.968407i
$730$	1.48932	−	6.24833i	0.0551221	−	0.231261i
$731$	−18.7533	−	10.8272i	−0.693615	−	0.400459i
$732$	6.10157	+	1.36311i	0.225521	+	0.0503820i
$733$	6.10483	−	6.10483i	0.225487	−	0.225487i	−0.585317	−	0.810804i	$-0.699030\pi$
$733$	6.10483	−	6.10483i	0.225487	−	0.225487i	0.810804	+	0.585317i	$0.199030\pi$
$734$	−16.5562	−	4.43623i	−0.611102	−	0.163744i
$735$	−0.488010	−	6.97856i	−0.0180005	−	0.257408i
$736$	0.564708	−	0.564708i	0.0208154	−	0.0208154i
$737$	−13.1777	−	22.8245i	−0.485409	−	0.840752i
$738$	−2.95574	−	1.39002i	−0.108802	−	0.0511672i
$739$	4.11405	+	15.3538i	0.151338	+	0.564800i	0.999391	+	0.0348893i	$0.0111079\pi$
$739$	4.11405	+	15.3538i	0.151338	+	0.564800i	−0.848054	+	0.529911i	$0.822225\pi$
$740$	−6.67805	−	3.61180i	−0.245490	−	0.132772i
$741$	−13.0772	−	13.3937i	−0.480403	−	0.492028i
$742$			24.4888i			0.899012i
$743$	7.79514	−	2.08870i	0.285976	−	0.0766270i	−0.112980	−	0.993597i	$-0.536039\pi$
$743$	7.79514	−	2.08870i	0.285976	−	0.0766270i	0.398955	+	0.916970i	$0.369373\pi$
$744$	−32.5081	+	10.1916i	−1.19180	+	0.373642i
$745$	−1.37924	−	49.5808i	−0.0505313	−	1.81650i
$746$	13.8321	−	13.8321i	0.506430	−	0.506430i
$747$	3.57550	+	0.642465i	0.130821	+	0.0235066i
$748$	−1.06436	+	3.97224i	−0.0389168	+	0.145239i
$749$	−11.0747	−	11.0747i	−0.404660	−	0.404660i
$750$	24.8764	+	3.41337i	0.908359	+	0.124639i
$751$	26.3089	+	15.1894i	0.960025	+	0.554271i	0.896181	−	0.443689i	$-0.146331\pi$
$751$	26.3089	+	15.1894i	0.960025	+	0.554271i	0.0638441	+	0.997960i	$0.479664\pi$
$752$	−3.65648	−	13.6462i	−0.133338	−	0.497625i
$753$	−3.96194	−	3.64233i	−0.144381	−	0.132734i
$754$	−23.9751	+	12.1676i	−0.873121	+	0.443119i
$755$	−1.37781	−	0.745182i	−0.0501436	−	0.0271200i
$756$	3.47961	+	1.46125i	0.126552	+	0.0531451i
$757$	25.1140	+	14.4995i	0.912782	+	0.526995i	0.881325	−	0.472510i	$-0.156652\pi$
$757$	25.1140	+	14.4995i	0.912782	+	0.526995i	0.0314569	+	0.999505i	$0.489985\pi$
$758$	−5.13235	+	2.96316i	−0.186415	+	0.107627i
$759$	−2.20023	+	0.0924764i	−0.0798634	+	0.00335668i
$760$	−13.8474	+	14.6399i	−0.502298	+	0.531044i
$761$	−1.91474	+	7.14590i	−0.0694092	+	0.259039i	−0.991908	−	0.126962i	$-0.959477\pi$
$761$	−1.91474	+	7.14590i	−0.0694092	+	0.259039i	0.922498	+	0.386001i	$0.126144\pi$
$762$	1.15807	+	27.5533i	0.0419525	+	0.998150i
$763$	2.00111	−	1.15534i	0.0724449	−	0.0418261i
$764$	−2.65080	+	4.59132i	−0.0959026	+	0.166108i
$765$	30.1239	+	4.55209i	1.08913	+	0.164581i
$766$			19.6276i			0.709174i
$767$	−10.5702	−	20.8276i	−0.381669	−	0.752040i
$768$	−9.49206	−	8.72634i	−0.342515	−	0.314885i
$769$	−39.8453	+	10.6765i	−1.43686	+	0.385005i	−0.891433	−	0.453153i	$-0.850299\pi$
$769$	−39.8453	+	10.6765i	−1.43686	+	0.385005i	−0.545427	+	0.838158i	$0.683632\pi$
$770$	−15.9913	+	9.83542i	−0.576288	+	0.354444i
$771$	−22.2791	−	4.97723i	−0.802364	−	0.179250i
$772$	1.50295	−	1.50295i	0.0540925	−	0.0540925i
$773$	5.37414	−	20.0566i	0.193294	−	0.721385i	−0.799407	−	0.600789i	$-0.794853\pi$
$773$	5.37414	−	20.0566i	0.193294	−	0.721385i	0.992702	−	0.120595i	$-0.0384803\pi$
$774$	−18.2551	−	3.28017i	−0.656164	−	0.117903i
$775$	32.0180	+	6.69657i	1.15012	+	0.240548i
$776$	26.4434	−	15.2671i	0.949263	−	0.548057i
$777$	−12.5805	−	40.1279i	−0.451324	−	1.43958i
$778$	25.5004	−	6.83282i	0.914235	−	0.244968i
$779$	−2.51687			−0.0901761
$780$	−4.27992	+	1.21985i	−0.153246	+	0.0436778i
$781$	37.6911			1.34869
$782$	2.54542	−	0.682044i	0.0910241	−	0.0243898i
$783$	−27.6631	+	11.3005i	−0.988599	+	0.403847i
$784$	−5.10113	+	2.94514i	−0.182183	+	0.105183i
$785$	−46.0196	+	13.7133i	−1.64251	+	0.489448i
$786$	1.05402	+	1.66045i	0.0375958	+	0.0592261i
$787$	3.89237	−	14.5265i	0.138748	−	0.517815i	−0.861206	−	0.508256i	$-0.830290\pi$
$787$	3.89237	−	14.5265i	0.138748	−	0.517815i	0.999954	−	0.00955922i	$-0.00304284\pi$
$788$	−2.58921	+	2.58921i	−0.0922368	+	0.0922368i
$789$	−1.19734	+	5.35954i	−0.0426263	+	0.190805i
$790$	−14.7973	−	24.0589i	−0.526465	−	0.855976i
$791$	13.0474	−	3.49605i	0.463913	−	0.124305i
$792$	2.15040	+	25.5364i	0.0764112	+	0.907396i
$793$	−38.8178	−	12.6813i	−1.37846	−	0.450328i
$794$			40.6326i			1.44200i
$795$	−17.9479	−	26.6087i	−0.636546	−	0.943712i
$796$	0.0464453	−	0.0804456i	0.00164621	−	0.00285132i
$797$	25.0339	−	14.4534i	0.886748	−	0.511964i	0.0138705	−	0.999904i	$-0.495585\pi$
$797$	25.0339	−	14.4534i	0.886748	−	0.511964i	0.872877	+	0.487940i	$0.162251\pi$
$798$	−15.3282	+	0.644250i	−0.542614	+	0.0228062i
$799$	−5.09231	+	19.0048i	−0.180153	+	0.672340i
$800$	2.78511	+	8.47749i	0.0984684	+	0.299724i
$801$	−3.29583	+	3.90195i	−0.116453	+	0.137869i
$802$	−15.9503	+	9.20894i	−0.563226	+	0.325179i
$803$	−5.45119	−	3.14725i	−0.192368	−	0.111064i
$804$	−4.53800	−	2.37173i	−0.160043	−	0.0836444i
$805$	−2.00583	−	1.08484i	−0.0706961	−	0.0382357i
$806$	29.9273	−	6.31122i	1.05414	−	0.222303i
$807$	−12.1575	+	13.2243i	−0.427964	+	0.465518i
$808$	10.2055	+	38.0875i	0.359029	+	1.33992i
$809$	−6.32927	−	3.65421i	−0.222525	−	0.128475i	0.384594	−	0.923086i	$-0.374342\pi$
$809$	−6.32927	−	3.65421i	−0.222525	−	0.128475i	−0.607119	+	0.794611i	$0.707675\pi$
$810$	25.5958	−	5.07758i	0.899345	−	0.178408i
$811$	−21.0431	−	21.0431i	−0.738922	−	0.738922i	0.233447	−	0.972369i	$-0.424999\pi$
$811$	−21.0431	−	21.0431i	−0.738922	−	0.738922i	−0.972369	+	0.233447i	$0.924999\pi$
$812$	1.08105	−	4.03453i	0.0379374	−	0.141584i
$813$	−20.1767	−	31.7851i	−0.707627	−	1.11475i
$814$	27.7535	−	27.7535i	0.972760	−	0.972760i
$815$	24.7570	−	0.688689i	0.867200	−	0.0241237i
$816$	−7.67392	−	24.4774i	−0.268641	−	0.856881i
$817$	−13.8049	+	3.69902i	−0.482974	+	0.129412i
$818$		−	26.7139i		−	0.934028i
$819$	−21.7090	−	11.6784i	−0.758575	−	0.408078i
$820$	−0.284661	+	0.526325i	−0.00994078	+	0.0183801i
$821$	13.1364	+	49.0257i	0.458464	+	1.71101i	0.677700	+	0.735339i	$0.262977\pi$
$821$	13.1364	+	49.0257i	0.458464	+	1.71101i	−0.219236	+	0.975672i	$0.570357\pi$
$822$	13.4940	−	4.23051i	0.470658	−	0.147556i
$823$	20.6525	+	35.7712i	0.719901	+	1.24690i	0.961039	+	0.276414i	$0.0891460\pi$
$823$	20.6525	+	35.7712i	0.719901	+	1.24690i	−0.241138	+	0.970491i	$0.577521\pi$
$824$	10.8985	−	10.8985i	0.379667	−	0.379667i
$825$	10.1672	−	22.4069i	0.353978	−	0.780108i
$826$	−18.4901	−	4.95442i	−0.643354	−	0.172386i
$827$	−1.56771	+	1.56771i	−0.0545146	+	0.0545146i	−0.733839	−	0.679324i	$-0.762273\pi$
$827$	−1.56771	+	1.56771i	−0.0545146	+	0.0545146i	0.679324	+	0.733839i	$0.262273\pi$
$828$	−0.351266	+	0.244259i	−0.0122073	+	0.00848858i
$829$	−40.6816	−	23.4875i	−1.41293	−	0.815756i	−0.417267	−	0.908784i	$-0.637012\pi$
$829$	−40.6816	−	23.4875i	−1.41293	−	0.815756i	−0.995663	+	0.0930281i	$0.970345\pi$
$830$	−0.814044	+	3.41526i	−0.0282559	+	0.118546i
$831$	3.03342	+	2.78872i	0.105228	+	0.0967395i
$832$	21.2801	+	23.7101i	0.737753	+	0.821998i
$833$	8.20327			0.284226
$834$	−34.5376	−	18.0506i	−1.19594	−	0.625043i
$835$	45.9998	−	28.2920i	1.59189	−	0.979085i
$836$	1.35708	+	2.35053i	0.0469356	+	0.0812948i
$837$	33.7245	−	4.27249i	1.16569	−	0.147679i
$838$	−16.8860	−	4.52459i	−0.583317	−	0.156299i
$839$	−2.91462	+	10.8775i	−0.100624	+	0.375534i	−0.997812	−	0.0661149i	$-0.978940\pi$
$839$	−2.91462	+	10.8775i	−0.100624	+	0.375534i	0.897188	+	0.441649i	$0.145606\pi$
$840$	−11.6330	+	23.8514i	−0.401377	+	0.822951i
$841$	2.03608	+	3.52660i	0.0702097	+	0.121607i
$842$	18.1549	+	10.4818i	0.625660	+	0.361225i
$843$	−15.8099	−	8.26284i	−0.544521	−	0.284587i
$844$			5.06805i			0.174450i
$845$	28.5904	−	5.25254i	0.983540	−	0.180693i
$846$	1.41410	+	16.7927i	0.0486179	+	0.577346i
$847$	−1.72673	−	6.44424i	−0.0593311	−	0.221427i
$848$	−13.5123	+	23.4040i	−0.464015	+	0.803698i
$849$	−5.26594	+	23.5715i	−0.180727	+	0.808971i
$850$	−6.02783	+	28.8206i	−0.206753	+	0.988540i
$851$	4.60504	+	1.23392i	0.157859	+	0.0422981i
$852$	6.18231	−	3.92443i	0.211802	−	0.134449i
$853$	−21.6293	−	21.6293i	−0.740573	−	0.740573i	0.232115	−	0.972688i	$-0.425435\pi$
$853$	−21.6293	−	21.6293i	−0.740573	−	0.740573i	−0.972688	+	0.232115i	$0.925435\pi$
$854$	−28.9850	+	16.7345i	−0.991845	+	0.572642i
$855$	16.1830	−	11.9341i	0.553445	−	0.408138i
$856$	−5.34773	−	19.9580i	−0.182782	−	0.682151i
$857$			27.4580i			0.937948i	0.883212	+	0.468974i	$0.155376\pi$
$857$			27.4580i			0.937948i	−0.883212	+	0.468974i	$0.844624\pi$
$858$	0.275023	−	23.0054i	0.00938914	−	0.785392i
$859$	27.6237			0.942508			0.471254	−	0.881998i	$-0.343802\pi$
$859$	27.6237			0.942508			0.471254	+	0.881998i	$0.343802\pi$
$860$	−0.787819	+	3.30524i	−0.0268644	+	0.112708i
$861$	−3.16265	+	0.991523i	−0.107783	+	0.0337910i
$862$	−7.91615	−	13.7112i	−0.269625	−	0.467004i
$863$	14.7595	+	14.7595i	0.502418	+	0.502418i	0.912188	−	0.409771i	$-0.134391\pi$
$863$	14.7595	+	14.7595i	0.502418	+	0.502418i	−0.409771	+	0.912188i	$0.634391\pi$
$864$	5.60925	+	7.38450i	0.190831	+	0.251226i
$865$	−4.75223	−	4.49499i	−0.161581	−	0.152834i
$866$	−15.5190	−	15.5190i	−0.527358	−	0.527358i
$867$	−1.36931	+	6.12933i	−0.0465042	+	0.208163i
$868$	−2.37580	+	4.11501i	−0.0806399	+	0.139672i
$869$	−26.7353	+	7.16371i	−0.906934	+	0.243012i
$870$	−9.40255	−	27.3067i	−0.318776	−	0.925784i
$871$	28.0205	+	18.2606i	0.949440	+	0.618735i
$872$	3.04836			0.103231
$873$	−28.6641	+	10.3273i	−0.970134	+	0.349528i
$874$	0.869622	−	1.50623i	0.0294154	−	0.0509490i
$875$	20.9277	−	14.5345i	0.707485	−	0.491354i
$876$	−1.22183	+	0.0513538i	−0.0412818	+	0.00173508i
$877$	−14.0324	−	3.75997i	−0.473841	−	0.126965i	0.0139924	−	0.999902i	$-0.495546\pi$
$877$	−14.0324	−	3.75997i	−0.473841	−	0.126965i	−0.487833	+	0.872937i	$0.662213\pi$
$878$	3.51451	+	0.941710i	0.118609	+	0.0317812i
$879$	−47.6514	+	2.00280i	−1.60724	+	0.0675527i
$880$	−20.7099	+	0.576108i	−0.698132	+	0.0194206i
$881$	19.4302	−	33.6541i	0.654619	−	1.13383i	−0.327370	−	0.944896i	$-0.606162\pi$
$881$	19.4302	−	33.6541i	0.654619	−	1.13383i	0.981989	−	0.188938i	$-0.0605045\pi$
$882$	6.61031	−	2.38161i	0.222581	−	0.0801931i
$883$	−8.78225			−0.295546			−0.147773	−	0.989021i	$-0.547211\pi$
$883$	−8.78225			−0.295546			−0.147773	+	0.989021i	$0.547211\pi$
$884$	−1.07685	−	5.10633i	−0.0362183	−	0.171744i
$885$	23.7218	−	8.16816i	0.797401	−	0.274570i
$886$	34.4259	−	9.22439i	1.15656	−	0.309899i
$887$	17.0075	−	29.4578i	0.571055	−	0.989097i	−0.425403	−	0.905004i	$-0.639868\pi$
$887$	17.0075	−	29.4578i	0.571055	−	0.989097i	0.996458	−	0.0840926i	$-0.0267991\pi$
$888$	12.0961	−	54.1447i	0.405918	−	1.81698i
$889$	19.7878	+	19.7878i	0.663662	+	0.663662i
$890$	−3.58623	−	3.39211i	−0.120211	−	0.113704i
$891$	2.39447	−	25.4587i	0.0802177	−	0.852898i
$892$	−0.999721	−	0.999721i	−0.0334731	−	0.0334731i
$893$	6.49281	+	11.2459i	0.217274	+	0.376329i
$894$	47.5359	−	14.9030i	1.58984	−	0.498431i
$895$	−14.9263	−	3.55775i	−0.498931	−	0.118923i
$896$	17.9768			0.600562
$897$	2.43671	−	1.36826i	0.0813595	−	0.0456850i
$898$		−	9.54630i		−	0.318564i
$899$	−9.73754	−	36.3410i	−0.324765	−	1.21204i
$900$	−0.665341	−	4.73393i	−0.0221780	−	0.157798i
$901$	32.5943	−	18.8184i	1.08588	−	0.626930i
$902$	−2.18737	−	2.18737i	−0.0728314	−	0.0728314i
$903$	−15.8898	+	10.0866i	−0.528780	+	0.335661i
$904$	17.2128	+	4.61216i	0.572490	+	0.153398i
$905$	47.1463	−	14.0490i	1.56720	−	0.467006i
$906$	0.343019	−	1.53543i	0.0113961	−	0.0510112i
$907$	−19.4826	+	33.7449i	−0.646911	+	1.12048i	0.336946	+	0.941524i	$0.390606\pi$
$907$	−19.4826	+	33.7449i	−0.646911	+	1.12048i	−0.983857	+	0.178958i	$0.942727\pi$
$908$	1.10882	+	4.13816i	0.0367974	+	0.137330i
$909$	−3.30156	−	39.2066i	−0.109506	−	1.30040i
$910$	12.4475	−	20.3139i	0.412631	−	0.673400i
$911$			54.4600i			1.80434i	0.431379	+	0.902171i	$0.358027\pi$
$911$			54.4600i			1.80434i	−0.431379	+	0.902171i	$0.641973\pi$
$912$	−15.0047	−	7.84204i	−0.496857	−	0.259676i
$913$	2.97956	+	1.72025i	0.0986090	+	0.0569319i
$914$	0.155463	+	0.269270i	0.00514227	+	0.00890667i
$915$	19.2293	−	39.4262i	0.635701	−	1.30339i
$916$	0.980240	−	3.65830i	0.0323880	−	0.120874i
$917$	1.92773	+	0.516534i	0.0636593	+	0.0170574i
$918$	3.84583	+	30.3567i	0.126931	+	1.00192i
$919$	15.1481	+	26.2373i	0.499690	+	0.865488i	1.00000		0.000358010i	$-0.000113958\pi$
$919$	15.1481	+	26.2373i	0.499690	+	0.865488i	−0.500310	+	0.865846i	$0.666781\pi$
$920$	−1.57607	−	2.56253i	−0.0519616	−	0.0844840i
$921$	−24.7942	−	12.9584i	−0.816997	−	0.426993i
$922$	−22.0163			−0.725067
$923$	−42.6520	+	21.6464i	−1.40391	+	0.712500i
$924$	2.63128	+	2.41901i	0.0865627	+	0.0795797i
$925$	−35.5146	+	39.7026i	−1.16771	+	1.30541i
$926$	20.7073	+	11.9553i	0.680483	+	0.392877i
$927$	−12.6266	+	8.78013i	−0.414712	+	0.288377i
$928$	7.25722	−	7.25722i	0.238230	−	0.238230i
$929$	47.5492	+	12.7408i	1.56004	+	0.418011i	0.932675	−	0.360717i	$-0.117468\pi$
$929$	47.5492	+	12.7408i	1.56004	+	0.418011i	0.627362	+	0.778728i	$0.284135\pi$
$930$	2.29189	+	32.7741i	0.0751541	+	1.07471i
$931$	3.82839	−	3.82839i	0.125470	−	0.125470i
$932$	1.93901	+	3.35846i	0.0635144	+	0.110010i
$933$	13.6367	−	4.27524i	0.446445	−	0.139965i
$934$	5.30563	+	19.8009i	0.173605	+	0.647904i
$935$	25.3794	+	13.7263i	0.829994	+	0.448899i
$936$	−17.0992	−	27.6625i	−0.558906	−	0.904176i
$937$			36.4014i			1.18918i	0.804029	+	0.594590i	$0.202686\pi$
$937$			36.4014i			1.18918i	−0.804029	+	0.594590i	$0.797314\pi$
$938$	26.4772	−	7.09455i	0.864512	−	0.231645i
$939$	6.52604	+	20.8160i	0.212969	+	0.679306i
$940$	3.08607	−	0.0858482i	0.100657	−	0.00280006i
$941$	−0.425527	+	0.425527i	−0.0138718	+	0.0138718i	−0.714009	−	0.700137i	$-0.753122\pi$
$941$	−0.425527	+	0.425527i	−0.0138718	+	0.0138718i	0.700137	+	0.714009i	$0.253122\pi$
$942$	−25.8476	−	40.7186i	−0.842159	−	1.32669i
$943$	0.0972501	−	0.362942i	0.00316690	−	0.0118190i
$944$	−14.9374	−	14.9374i	−0.486170	−	0.486170i
$945$	15.6338	−	21.3715i	0.508566	−	0.695215i
$946$	−15.2124	−	8.78290i	−0.494599	−	0.285557i
$947$	8.92637	+	33.3137i	0.290068	+	1.08255i	0.945056	+	0.326909i	$0.106007\pi$
$947$	8.92637	+	33.3137i	0.290068	+	1.08255i	−0.654988	+	0.755640i	$0.727326\pi$
$948$	−3.63939	+	3.95874i	−0.118202	+	0.128574i
$949$	7.97617	+	0.430810i	0.258917	+	0.0139847i
$950$	10.6372	+	16.2635i	0.345116	+	0.527656i
$951$	8.74601	+	4.57100i	0.283609	+	0.148225i
$952$	−26.9492	−	15.5591i	−0.873428	−	0.504274i
$953$	−44.6938	+	25.8040i	−1.44778	+	0.835873i	−0.998349	−	0.0574438i	$-0.981705\pi$
$953$	−44.6938	+	25.8040i	−1.44778	+	0.835873i	−0.449427	+	0.893317i	$0.648372\pi$
$954$	20.8015	−	24.6270i	0.673474	−	0.797330i
$955$	27.0239	+	25.5610i	0.874471	+	0.827136i
$956$	1.80254	−	6.72716i	0.0582983	−	0.217572i
$957$	−28.2758	+	1.18844i	−0.914026	+	0.0384167i
$958$	4.95429	−	2.86036i	0.160066	−	0.0924140i
$959$	7.17507	−	12.4276i	0.231695	−	0.401308i
$960$	−28.3715	+	19.1369i	−0.915685	+	0.617642i
$961$			11.8000i			0.380644i
$962$	−15.4673	+	47.3455i	−0.498685	+	1.52648i
$963$	1.73003	+	20.5444i	0.0557494	+	0.662034i
$964$	7.65906	−	2.05224i	0.246682	−	0.0660982i
$965$	−7.81279	−	12.7028i	−0.251503	−	0.408917i
$966$	0.499370	−	2.23529i	0.0160670	−	0.0719192i
$967$	−13.6221	+	13.6221i	−0.438057	+	0.438057i	−0.891358	−	0.453300i	$-0.850246\pi$
$967$	−13.6221	+	13.6221i	−0.438057	+	0.438057i	0.453300	+	0.891358i	$0.350246\pi$
$968$	2.27799	−	8.50156i	0.0732172	−	0.273250i
$969$	12.6364	+	19.9067i	0.405941	+	0.639494i
$970$	−8.40918	−	28.2198i	−0.270002	−	0.906084i
$971$	−34.7333	+	20.0533i	−1.11465	+	0.643541i	−0.940029	−	0.341096i	$-0.889202\pi$
$971$	−34.7333	+	20.0533i	−1.11465	+	0.643541i	−0.174617	+	0.984637i	$0.555869\pi$
$972$	−2.25803	−	4.42519i	−0.0724262	−	0.141938i
$973$	−38.1973	+	10.2349i	−1.22455	+	0.328117i
$974$	−51.8966			−1.66288
$975$	1.36308	+	31.1952i	0.0436535	+	0.999047i
$976$	−36.9347			−1.18225
$977$	1.49732	−	0.401205i	0.0479034	−	0.0128357i	−0.234788	−	0.972047i	$-0.575440\pi$
$977$	1.49732	−	0.401205i	0.0479034	−	0.0128357i	0.282691	+	0.959211i	$0.408773\pi$
$978$	7.44146	+	23.7359i	0.237952	+	0.758992i
$979$	−4.18922	+	2.41865i	−0.133888	+	0.0773004i
$980$	−0.367594	−	1.23358i	−0.0117424	−	0.0394054i
$981$	−2.99378	−	0.537940i	−0.0955842	−	0.0171751i
$982$	4.72235	−	17.6241i	0.150696	−	0.562406i
$983$	7.26168	−	7.26168i	0.231611	−	0.231611i	−0.581754	−	0.813365i	$-0.697633\pi$
$983$	7.26168	−	7.26168i	0.231611	−	0.231611i	0.813365	+	0.581754i	$0.197633\pi$
$984$	−4.26737	−	0.953343i	−0.136039	−	0.0303915i
$985$	13.4595	+	21.8837i	0.428854	+	0.697272i
$986$	32.7119	−	8.76512i	1.04176	−	0.279138i
$987$	12.5891	+	11.5735i	0.400715	+	0.368389i
$988$	−2.88563	−	1.88052i	−0.0918042	−	0.0598273i
$989$		−	2.13366i		−	0.0678464i
$990$	24.4361	+	3.69260i	0.776631	+	0.117358i
$991$	−26.1268	+	45.2530i	−0.829946	+	1.43751i	0.0681339	+	0.997676i	$0.478295\pi$
$991$	−26.1268	+	45.2530i	−0.829946	+	1.43751i	−0.898080	+	0.439832i	$0.855038\pi$
$992$	−10.1113	+	5.83775i	−0.321033	+	0.185349i
$993$	1.17537	+	27.9649i	0.0372992	+	0.887438i
$994$	−10.1460	+	37.8652i	−0.321810	+	1.20101i
$995$	−0.473491	−	0.447861i	−0.0150107	−	0.0141982i
$996$	0.667837	−	0.0280694i	0.0211612	−	0.000889412i
$997$	0.313621	−	0.181069i	0.00993247	−	0.00573451i	−0.495026	−	0.868878i	$-0.664841\pi$
$997$	0.313621	−	0.181069i	0.00993247	−	0.00573451i	0.504958	+	0.863144i	$0.331508\pi$
$998$	−20.4856	−	11.8274i	−0.648460	−	0.374389i
$999$	−21.4344	+	51.0407i	−0.678153	+	1.61486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bh.a.59.17	yes	96
3.2	odd	2	inner	195.2.bh.a.59.7	✓	96
5.2	odd	4		975.2.bo.h.176.17		96
5.3	odd	4		975.2.bo.h.176.8		96
5.4	even	2	inner	195.2.bh.a.59.8	yes	96
13.2	odd	12	inner	195.2.bh.a.119.18	yes	96
15.2	even	4		975.2.bo.h.176.7		96
15.8	even	4		975.2.bo.h.176.18		96
15.14	odd	2	inner	195.2.bh.a.59.18	yes	96
39.2	even	12	inner	195.2.bh.a.119.8	yes	96
65.2	even	12		975.2.bo.h.626.7		96
65.28	even	12		975.2.bo.h.626.18		96
65.54	odd	12	inner	195.2.bh.a.119.7	yes	96
195.2	odd	12		975.2.bo.h.626.17		96
195.119	even	12	inner	195.2.bh.a.119.17	yes	96
195.158	odd	12		975.2.bo.h.626.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.7	✓	96	3.2	odd	2	inner
195.2.bh.a.59.8	yes	96	5.4	even	2	inner
195.2.bh.a.59.17	yes	96	1.1	even	1	trivial
195.2.bh.a.59.18	yes	96	15.14	odd	2	inner
195.2.bh.a.119.7	yes	96	65.54	odd	12	inner
195.2.bh.a.119.8	yes	96	39.2	even	12	inner
195.2.bh.a.119.17	yes	96	195.119	even	12	inner
195.2.bh.a.119.18	yes	96	13.2	odd	12	inner
975.2.bo.h.176.7		96	15.2	even	4
975.2.bo.h.176.8		96	5.3	odd	4
975.2.bo.h.176.17		96	5.2	odd	4
975.2.bo.h.176.18		96	15.8	even	4
975.2.bo.h.626.7		96	65.2	even	12
975.2.bo.h.626.8		96	195.158	odd	12
975.2.bo.h.626.17		96	195.2	odd	12
975.2.bo.h.626.18		96	65.28	even	12

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25247 - 0.335598i) q^{2} +(-1.65273 + 0.518148i) q^{3} +(-0.276000 + 0.159349i) q^{4} +(0.638573 + 2.14295i) q^{5} +(-1.89610 + 1.20362i) q^{6} +(-0.589843 + 2.20132i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(2.46304 - 1.71272i) q^{9} +(1.51896 + 2.46967i) q^{10} +(2.74441 - 0.735363i) q^{11} +(0.373587 - 0.406369i) q^{12} +(-2.68330 + 2.40830i) q^{13} +2.95504i q^{14} +(-2.16575 - 3.21084i) q^{15} +(-1.63052 + 2.82414i) q^{16} +(3.93313 - 2.27079i) q^{17} +(2.51010 - 2.97172i) q^{18} +(0.775797 - 2.89531i) q^{19} +(-0.517722 - 0.489697i) q^{20} +(-0.165760 - 3.94382i) q^{21} +(3.19050 - 1.84204i) q^{22} +(0.387540 + 0.223746i) q^{23} +(2.41206 - 4.61517i) q^{24} +(-4.18445 + 2.73686i) q^{25} +(-2.55253 + 3.91682i) q^{26} +(-3.18331 + 4.10689i) q^{27} +(-0.187981 - 0.701555i) q^{28} +(4.98037 + 2.87542i) q^{29} +(-3.79009 - 3.29466i) q^{30} +(-4.62601 - 4.62601i) q^{31} +(0.461902 - 1.72384i) q^{32} +(-4.15475 + 2.63737i) q^{33} +(4.16405 - 4.16405i) q^{34} +(-5.09398 + 0.141704i) q^{35} +(-0.406880 + 0.865193i) q^{36} +(10.2908 - 2.75740i) q^{37} -3.88664i q^{38} +(3.18693 - 5.37061i) q^{39} +(-5.91336 - 3.19822i) q^{40} +(-0.217322 - 0.811058i) q^{41} +(-1.53115 - 4.88389i) q^{42} +(-2.38402 - 4.12924i) q^{43} +(-0.640278 + 0.640278i) q^{44} +(5.24310 + 4.18448i) q^{45} +(0.560470 + 0.150177i) q^{46} +(-3.06335 + 3.06335i) q^{47} +(1.23149 - 5.51240i) q^{48} +(1.56426 + 0.903128i) q^{49} +(-4.32241 + 4.83212i) q^{50} +(-5.32380 + 5.79096i) q^{51} +(0.356833 - 1.09227i) q^{52} +8.28713 q^{53} +(-2.60873 + 6.21206i) q^{54} +(3.32835 + 5.41155i) q^{55} +(-3.42592 - 5.93387i) q^{56} +(0.218017 + 5.18715i) q^{57} +(7.20275 + 1.92997i) q^{58} +(-1.67660 + 6.25715i) q^{59} +(1.10939 + 0.541082i) q^{60} +(5.66303 + 9.80865i) q^{61} +(-7.34641 - 4.24145i) q^{62} +(2.31744 + 6.43220i) q^{63} -8.83615i q^{64} +(-6.87434 - 4.21230i) q^{65} +(-4.31860 + 4.69755i) q^{66} +(-2.40083 - 8.96003i) q^{67} +(-0.723695 + 1.25348i) q^{68} +(-0.756433 - 0.168989i) q^{69} +(-6.33249 + 1.88701i) q^{70} +(12.8138 + 3.43344i) q^{71} +(-1.59515 + 8.87745i) q^{72} +(-1.56653 - 1.56653i) q^{73} +(11.9635 - 6.90712i) q^{74} +(5.49767 - 6.69146i) q^{75} +(0.247244 + 0.922728i) q^{76} +6.47509i q^{77} +(2.18916 - 7.79605i) q^{78} -9.74173 q^{79} +(-7.09319 - 1.69070i) q^{80} +(3.13318 - 8.43701i) q^{81} +(-0.544379 - 0.942892i) q^{82} +(0.856250 + 0.856250i) q^{83} +(0.674192 + 1.06208i) q^{84} +(7.37778 + 6.97842i) q^{85} +(-4.37167 - 4.37167i) q^{86} +(-9.72112 - 2.17173i) q^{87} +(-4.27113 + 7.39781i) q^{88} +(-1.64453 + 0.440650i) q^{89} +(7.97112 + 3.48135i) q^{90} +(-3.71871 - 7.32734i) q^{91} -0.142614 q^{92} +(10.0425 + 5.24860i) q^{93} +(-2.80869 + 4.86480i) q^{94} +(6.69991 - 0.186378i) q^{95} +(0.129806 + 3.08838i) q^{96} +(-9.80988 - 2.62855i) q^{97} +(2.26228 + 0.606176i) q^{98} +(5.50014 - 6.51164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{4} - 4 q^{9} - 36 q^{10} + 10 q^{15} - 16 q^{21} - 28 q^{24} + 18 q^{30} - 40 q^{31} - 32 q^{34} - 60 q^{36} - 4 q^{39} + 40 q^{40} + 4 q^{45} - 128 q^{46} + 60 q^{54} + 28 q^{55} + 20 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) \) 96 * q - 24 * q^4 - 4 * q^9 - 36 * q^10 + 10 * q^15 - 16 * q^21 - 28 * q^24 + 18 * q^30 - 40 * q^31 - 32 * q^34 - 60 * q^36 - 4 * q^39 + 40 * q^40 + 4 * q^45 - 128 * q^46 + 60 * q^54 + 28 * q^55 + 20 * q^60 - 48 * q^61 - 8 * q^66 + 72 * q^69 + 168 * q^70 + 66 * q^75 - 80 * q^76 - 80 * q^79 + 48 * q^81 - 132 * q^84 - 20 * q^85 - 56 * q^91 + 72 * q^94 + 204 * q^96 - 48 * q^99

Introduction

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