LMFDB - Embedded newform 195.2.bh.a.59.18

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			59.18
Character	$\chi$	$=$	195.59
Dual form			195.2.bh.a.119.18

$q$-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} +(0.377636 + 1.69038i) q^{3} +(-0.276000 + 0.159349i) q^{4} +(2.14295 + 0.638573i) q^{5} +(1.04027 + 1.99042i) q^{6} +(0.589843 - 2.20132i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(-2.71478 + 1.27670i) q^{9} +(2.89828 + 0.0806242i) q^{10} +(-2.74441 + 0.735363i) q^{11} +(-0.373587 - 0.406369i) q^{12} +(2.68330 - 2.40830i) q^{13} -2.95504i q^{14} +(-0.270178 + 3.86355i) q^{15} +(-1.63052 + 2.82414i) q^{16} +(3.93313 - 2.27079i) q^{17} +(-2.97172 + 2.51010i) q^{18} +(0.775797 - 2.89531i) q^{19} +(-0.693209 + 0.165229i) q^{20} +(3.94382 + 0.165760i) q^{21} +(-3.19050 + 1.84204i) q^{22} +(0.387540 + 0.223746i) q^{23} +(-4.39649 - 2.79082i) 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} +(0.958209 + 4.92964i) q^{30} +(-4.62601 - 4.62601i) q^{31} +(0.461902 - 1.72384i) q^{32} +(-2.27943 - 4.36141i) q^{33} +(4.16405 - 4.16405i) q^{34} +(2.66971 - 4.34066i) q^{35} +(0.545839 - 0.784965i) q^{36} +(-10.2908 + 2.75740i) q^{37} -3.88664i q^{38} +(5.08425 + 3.62635i) q^{39} +(-5.91336 + 3.19822i) q^{40} +(0.217322 + 0.811058i) q^{41} +(4.99514 - 1.11593i) q^{42} +(2.38402 + 4.12924i) q^{43} +(0.640278 - 0.640278i) q^{44} +(-6.63290 + 1.00231i) q^{45} +(0.560470 + 0.150177i) q^{46} +(-3.06335 + 3.06335i) q^{47} +(-5.38962 - 1.68970i) q^{48} +(1.56426 + 0.903128i) q^{49} +(6.15937 + 2.02354i) q^{50} +(5.32380 + 5.79096i) q^{51} +(-0.356833 + 1.09227i) q^{52} +8.28713 q^{53} +(-5.36526 - 4.07544i) q^{54} +(-6.35072 - 0.176664i) q^{55} +(3.42592 + 5.93387i) q^{56} +(5.18715 + 0.218017i) q^{57} +(-7.20275 - 1.92997i) q^{58} +(1.67660 - 6.25715i) q^{59} +(-0.541082 - 1.10939i) q^{60} +(5.66303 + 9.80865i) q^{61} +(-7.34641 - 4.24145i) q^{62} +(1.20913 + 6.72917i) q^{63} -8.83615i q^{64} +(7.28805 - 3.44736i) q^{65} +(-4.31860 - 4.69755i) q^{66} +(2.40083 + 8.96003i) q^{67} +(-0.723695 + 1.25348i) q^{68} +(-0.231867 + 0.739585i) q^{69} +(1.88701 - 6.33249i) q^{70} +(-12.8138 - 3.43344i) q^{71} +(3.05728 - 8.48567i) q^{72} +(1.56653 + 1.56653i) q^{73} +(-11.9635 + 6.90712i) q^{74} +(-3.04614 + 8.10685i) q^{75} +(0.247244 + 0.922728i) q^{76} +6.47509i q^{77} +(7.58486 + 2.83562i) q^{78} -9.74173 q^{79} +(-5.29754 + 5.01078i) q^{80} +(5.74008 - 6.93192i) q^{81} +(0.544379 + 0.942892i) q^{82} +(0.856250 + 0.856250i) q^{83} +(-1.11491 + 0.582693i) q^{84} +(9.87856 - 2.35460i) q^{85} +(4.37167 + 4.37167i) q^{86} +(2.97979 - 9.50460i) 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} +(6.07278 - 9.56668i) q^{93} +(-2.80869 + 4.86480i) q^{94} +(3.51136 - 5.70910i) q^{95} +(3.08838 + 0.129806i) q^{96} +(9.80988 + 2.62855i) q^{97} +(2.26228 + 0.606176i) q^{98} +(6.51164 - 5.50014i) 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	$0.265077\pi$
$3$	0.377636	+	1.69038i	0.218028	+	0.975942i
$3$	0.377636	+	1.69038i	0.218028	+	0.975942i
$4$	−0.276000	+	0.159349i	−0.138000	+	0.0796743i
$5$	2.14295	+	0.638573i	0.958355	+	0.285579i
$5$	2.14295	+	0.638573i	0.958355	+	0.285579i
$6$	1.04027	+	1.99042i	0.424687	+	0.812584i
$7$	0.589843	−	2.20132i	0.222940	−	0.832022i	−0.760280	−	0.649596i	$-0.774938\pi$
$7$	0.589843	−	2.20132i	0.222940	−	0.832022i	0.983219	−	0.182427i	$-0.0583952\pi$
$8$	−2.12594	+	2.12594i	−0.751635	+	0.751635i
$9$	−2.71478	+	1.27670i	−0.904927	+	0.425566i
$10$	2.89828	+	0.0806242i	0.916516	+	0.0254956i
$11$	−2.74441	+	0.735363i	−0.827472	+	0.221720i	−0.647610	−	0.761972i	$-0.724232\pi$
$11$	−2.74441	+	0.735363i	−0.827472	+	0.221720i	−0.179861	+	0.983692i	$0.557565\pi$
$12$	−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
$15$	−0.270178	+	3.86355i	−0.0697596	+	0.997564i
$16$	−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	$0.147676\pi$
$18$	−2.97172	+	2.51010i	−0.700441	+	0.591636i
$19$	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	$-0.0283914\pi$
$20$	−0.693209	+	0.165229i	−0.155006	+	0.0369464i
$21$	3.94382	+	0.165760i	0.860613	+	0.0361718i
$22$	−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	$0.651811\pi$
$24$	−4.39649	−	2.79082i	−0.897430	−	0.569675i
$25$	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	−0.0396587	−	0.999213i	$-0.512627\pi$
$29$	−4.98037	−	2.87542i	−0.924832	−	0.533952i	−0.885173	+	0.465261i	$0.845960\pi$
$30$	0.958209	+	4.92964i	0.174944	+	0.900026i
$31$	−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
$33$	−2.27943	−	4.36141i	−0.396799	−	0.759223i
$34$	4.16405	−	4.16405i	0.714128	−	0.714128i
$35$	2.66971	−	4.34066i	0.451263	−	0.733706i
$36$	0.545839	−	0.784965i	0.0909731	−	0.130827i
$37$	−10.2908	+	2.75740i	−1.69179	+	0.453315i	−0.970852	−	0.239682i	$-0.922957\pi$
$37$	−10.2908	+	2.75740i	−1.69179	+	0.453315i	−0.720941	+	0.692996i	$0.756290\pi$
$38$		−	3.88664i		−	0.630497i
$39$	5.08425	+	3.62635i	0.814132	+	0.580680i
$40$	−5.91336	+	3.19822i	−0.934984	+	0.505682i
$41$	0.217322	+	0.811058i	0.0339401	+	0.126666i	0.980817	−	0.194929i	$-0.0624477\pi$
$41$	0.217322	+	0.811058i	0.0339401	+	0.126666i	−0.946877	+	0.321595i	$0.895781\pi$
$42$	4.99514	−	1.11593i	0.770768	−	0.172192i
$43$	2.38402	+	4.12924i	0.363559	+	0.629703i	0.988544	−	0.150934i	$-0.0482282\pi$
$43$	2.38402	+	4.12924i	0.363559	+	0.629703i	−0.624985	+	0.780637i	$0.714895\pi$
$44$	0.640278	−	0.640278i	0.0965256	−	0.0965256i
$45$	−6.63290	+	1.00231i	−0.988774	+	0.149416i
$46$	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	$0.352327\pi$
$48$	−5.38962	−	1.68970i	−0.777925	−	0.243887i
$49$	1.56426	+	0.903128i	0.223466	+	0.129018i
$50$	6.15937	+	2.02354i	0.871067	+	0.286171i
$51$	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	$0.307268\pi$
$54$	−5.36526	−	4.07544i	−0.730119	−	0.554597i
$55$	−6.35072	−	0.176664i	−0.856330	−	0.0238214i
$56$	3.42592	+	5.93387i	0.457808	+	0.792946i
$57$	5.18715	+	0.218017i	0.687055	+	0.0288771i
$58$	−7.20275	−	1.92997i	−0.945767	−	0.253417i
$59$	1.67660	−	6.25715i	0.218275	−	0.814612i	−0.766714	−	0.641989i	$-0.778109\pi$
$59$	1.67660	−	6.25715i	0.218275	−	0.814612i	0.984988	−	0.172622i	$-0.0552240\pi$
$60$	−0.541082	−	1.10939i	−0.0698533	−	0.143222i
$61$	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
$63$	1.20913	+	6.72917i	0.152337	+	0.847795i
$64$		−	8.83615i		−	1.10452i
$65$	7.28805	−	3.44736i	0.903971	−	0.427593i
$66$	−4.31860	−	4.69755i	−0.531583	−	0.578228i
$67$	2.40083	+	8.96003i	0.293308	+	1.09464i	0.942552	+	0.334061i	$0.108419\pi$
$67$	2.40083	+	8.96003i	0.293308	+	1.09464i	−0.649243	+	0.760581i	$0.724914\pi$
$68$	−0.723695	+	1.25348i	−0.0877609	+	0.152006i
$69$	−0.231867	+	0.739585i	−0.0279136	+	0.0890355i
$70$	1.88701	−	6.33249i	0.225541	−	0.756878i
$71$	−12.8138	−	3.43344i	−1.52072	−	0.407474i	−0.600738	−	0.799446i	$-0.705127\pi$
$71$	−12.8138	−	3.43344i	−1.52072	−	0.407474i	−0.919977	+	0.391971i	$0.871793\pi$
$72$	3.05728	−	8.48567i	0.360304	−	1.00005i
$73$	1.56653	+	1.56653i	0.183349	+	0.183349i	0.792813	−	0.609464i	$-0.208615\pi$
$73$	1.56653	+	1.56653i	0.183349	+	0.183349i	−0.609464	+	0.792813i	$0.708615\pi$
$74$	−11.9635	+	6.90712i	−1.39073	+	0.802937i
$75$	−3.04614	+	8.10685i	−0.351737	+	0.936099i
$76$	0.247244	+	0.922728i	0.0283608	+	0.105844i
$77$			6.47509i			0.737905i
$78$	7.58486	+	2.83562i	0.858816	+	0.321071i
$79$	−9.74173			−1.09603			−0.548015	−	0.836468i	$-0.684616\pi$
$79$	−9.74173			−1.09603			−0.548015	+	0.836468i	$0.684616\pi$
$80$	−5.29754	+	5.01078i	−0.592283	+	0.560222i
$81$	5.74008	−	6.93192i	0.637786	−	0.770213i
$82$	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	$0.728830\pi$
$84$	−1.11491	+	0.582693i	−0.121646	+	0.0635770i
$85$	9.87856	−	2.35460i	1.07148	−	0.255392i
$86$	4.37167	+	4.37167i	0.471409	+	0.471409i
$87$	2.97979	−	9.50460i	0.319467	−	1.01900i
$88$	4.27113	−	7.39781i	0.455304	−	0.788609i
$89$	1.64453	−	0.440650i	0.174320	−	0.0467088i	−0.170603	−	0.985340i	$-0.554572\pi$
$89$	1.64453	−	0.440650i	0.174320	−	0.0467088i	0.344923	+	0.938631i	$0.387905\pi$
$90$	−7.97112	+	3.48135i	−0.840230	+	0.366967i
$91$	−3.71871	−	7.32734i	−0.389827	−	0.768114i
$92$	−0.142614			−0.0148686
$93$	6.07278	−	9.56668i	0.629717	−	0.992018i
$94$	−2.80869	+	4.86480i	−0.289695	+	0.501766i
$95$	3.51136	−	5.70910i	0.360258	−	0.585741i
$96$	3.08838	+	0.129806i	0.315207	+	0.0132482i
$97$	9.80988	+	2.62855i	0.996042	+	0.266889i	0.719787	−	0.694195i	$-0.244240\pi$
$97$	9.80988	+	2.62855i	0.996042	+	0.266889i	0.276256	+	0.961084i	$0.410906\pi$
$98$	2.26228	+	0.606176i	0.228525	+	0.0612330i
$99$	6.51164	−	5.50014i	0.654445	−	0.552785i
$100$	−1.59102	−	0.0885864i	−0.159102	−	0.00885864i
$101$	−6.55756	+	11.3580i	−0.652502	+	1.13017i	0.330012	+	0.943977i	$0.392947\pi$
$101$	−6.55756	+	11.3580i	−0.652502	+	1.13017i	−0.982514	+	0.186189i	$0.940386\pi$
$102$	8.61132	+	5.46633i	0.852648	+	0.541248i
$103$	5.12642			0.505122			0.252561	−	0.967581i	$-0.418727\pi$
$103$	5.12642			0.505122			0.252561	+	0.967581i	$0.418727\pi$
$104$	−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	$0.274454\pi$
$108$	1.53302	+	0.626245i	0.147515	+	0.0602604i
$109$	−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	$0.765462\pi$
$110$	−8.01336	+	1.91002i	−0.764044	+	0.182113i
$111$	−8.54724	−	16.3540i	−0.811268	−	1.55226i
$112$	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	$0.923266\pi$
$114$	6.56991	−	1.46774i	0.615329	−	0.137466i
$115$	0.687599	+	0.726949i	0.0641189	+	0.0677883i
$116$	1.83278			0.170169
$117$	−4.20991	+	9.96377i	−0.389207	+	0.921150i
$118$		−	8.39955i		−	0.773241i
$119$	−2.67882	−	9.99750i	−0.245567	−	0.916470i
$120$	−7.63931	−	8.78807i	−0.697370	−	0.802238i
$121$	−2.53524	+	1.46372i	−0.230476	+	0.133065i
$122$	10.3845	+	10.3845i	0.940171	+	0.940171i
$123$	−1.28893	+	0.673643i	−0.116219	+	0.0607404i
$124$	2.01393	+	0.539630i	0.180856	+	0.0484602i
$125$	7.21937	+	8.53702i	0.645720	+	0.763574i
$126$	3.77270	+	8.02229i	0.336098	+	0.714682i
$127$	−6.13964	+	10.6342i	−0.544805	+	0.943630i	0.453814	+	0.891096i	$0.350063\pi$
$127$	−6.13964	+	10.6342i	−0.544805	+	0.943630i	−0.998619	+	0.0525335i	$0.983270\pi$
$128$	−2.04159	−	7.61931i	−0.180453	−	0.673458i
$129$	−6.07970	+	5.58925i	−0.535287	+	0.492106i
$130$	7.97112	−	6.76357i	0.699114	−	0.593204i
$131$			0.875714i			0.0765115i	0.999268	+	0.0382557i	$0.0121802\pi$
$131$			0.875714i			0.0765115i	−0.999268	+	0.0382557i	$0.987820\pi$
$132$	1.32411	+	0.840522i	0.115249	+	0.0731581i
$133$	−5.91592	−	3.41556i	−0.512976	−	0.296167i
$134$	6.01393	+	10.4164i	0.519525	+	0.899843i
$135$	−4.19912	−	10.8336i	−0.361402	−	0.932410i
$136$	−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	$0.670021\pi$
$138$	−0.0422035	+	1.00412i	−0.00359260	+	0.0854764i
$139$	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	$0.570099\pi$
$140$	−0.0451607	+	1.62344i	−0.00381677	+	0.137205i
$141$	−6.33506	−	4.02140i	−0.533508	−	0.338663i
$142$	−17.2011			−1.44348
$143$	−5.59312	+	8.58256i	−0.467720	+	0.717710i
$144$	0.820923	−	9.74861i	0.0684103	−	0.812384i
$145$	−8.83651	−	9.34221i	−0.733832	−	0.775828i
$146$	2.48776	+	1.43631i	0.205889	+	0.118870i
$147$	−0.935909	+	2.98526i	−0.0771925	+	0.246220i
$148$	2.40086	−	2.40086i	0.197350	−	0.197350i
$149$	21.4260	+	5.74107i	1.75528	+	0.470327i	0.985741	−	0.168269i	$-0.0538176\pi$
$149$	21.4260	+	5.74107i	1.75528	+	0.470327i	0.769543	+	0.638595i	$0.220484\pi$
$150$	−1.09455	+	11.1759i	−0.0893693	+	0.912505i
$151$	−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
$153$	−7.77847	+	11.1861i	−0.628852	+	0.904345i
$154$	2.17303	+	8.10985i	0.175108	+	0.653510i
$155$	−6.95925	−	12.8673i	−0.558981	−	1.03353i
$156$	−1.98110	−	0.190703i	−0.158615	−	0.0152685i
$157$		−	21.4749i		−	1.71388i	−0.515414	−	0.856941i	$-0.672362\pi$
$157$		−	21.4749i		−	1.71388i	0.515414	−	0.856941i	$-0.327638\pi$
$158$	−12.2012	+	3.26930i	−0.970676	+	0.260092i
$159$	3.12952	+	14.0084i	0.248187	+	1.11094i
$160$	2.09063	−	3.39914i	0.165279	−	0.268726i
$161$	0.721125	−	0.721125i	0.0568326	−	0.0568326i
$162$	4.86293	−	10.6084i	0.382068	−	0.833472i
$163$	−2.86667	+	10.6985i	−0.224535	+	0.837975i	0.758056	+	0.652190i	$0.226149\pi$
$163$	−2.86667	+	10.6985i	−0.224535	+	0.837975i	−0.982590	+	0.185785i	$0.940517\pi$
$164$	−0.189222	−	0.189222i	−0.0147757	−	0.0147757i
$165$	−2.09963	−	10.8019i	−0.163456	−	0.840923i
$166$	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
$171$	1.59033	+	8.85060i	0.121615	+	0.676822i
$172$	−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	$0.368805\pi$
$174$	0.542368	−	12.9042i	0.0411168	−	0.978266i
$175$	8.49288	−	7.59701i	0.642001	−	0.574280i
$176$	2.39805	−	8.94964i	0.180760	−	0.674604i
$177$	11.2101	+	0.471164i	0.842604	+	0.0354149i
$178$	1.91184	−	1.10380i	0.143298	−	0.0827333i
$179$	3.43112	−	5.94288i	0.256454	−	0.444192i	−0.708835	−	0.705374i	$-0.750779\pi$
$179$	3.43112	−	5.94288i	0.256454	−	0.444192i	0.965290	+	0.261182i	$0.0841124\pi$
$180$	1.67096	−	1.33358i	0.124546	−	0.0993992i
$181$		−	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
$185$	−23.8134	−	0.662440i	−1.75080	−	0.0487036i
$186$	4.39540	−	14.0200i	0.322287	−	1.02799i
$187$	−9.12427	+	9.12427i	−0.667233	+	0.667233i
$188$	0.357343	−	1.33362i	0.0260619	−	0.0972644i
$189$	−10.9182	+	4.58508i	−0.794186	+	0.333515i
$190$	2.48191	−	8.32887i	0.180056	−	0.604240i
$191$	−14.4065	+	8.31762i	−1.04242	+	0.601842i	−0.920518	−	0.390700i	$-0.872233\pi$
$191$	−14.4065	+	8.31762i	−1.04242	+	0.601842i	−0.121903	+	0.992542i	$0.538900\pi$
$192$	14.9365	−	3.33685i	1.07795	−	0.240816i
$193$	6.44208	−	1.72615i	0.463711	−	0.124251i	−0.0193966	−	0.999812i	$-0.506175\pi$
$193$	6.44208	−	1.72615i	0.463711	−	0.124251i	0.483108	+	0.875561i	$0.339508\pi$
$194$	13.1687			0.945457
$195$	8.57959	+	11.0177i	0.614398	+	0.788997i
$196$	−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	$0.282440\pi$
$198$	6.30979	−	9.07405i	0.448417	−	0.644864i
$199$	−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	$0.336622\pi$
$200$	−14.7143	+	3.07750i	−1.04046	+	0.217612i
$201$	−14.2392	+	7.44195i	−1.00436	+	0.524915i
$202$	−4.40141	+	16.4263i	−0.309682	+	1.15575i
$203$	−9.26737	+	9.26737i	−0.650442	+	0.650442i
$204$	−2.39215	−	0.749963i	−0.167484	−	0.0525079i
$205$	−0.0522096	+	1.87683i	−0.00364648	+	0.131084i
$206$	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
$210$	11.4169	+	0.798386i	0.787843	+	0.0550939i
$211$	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
$213$	0.964879	−	22.9568i	0.0661124	−	1.57297i
$214$	−2.30635	+	8.60742i	−0.157659	+	0.588391i
$215$	2.47200	+	10.3711i	0.168589	+	0.707304i
$216$	15.4986	+	1.96348i	1.05454	+	0.133598i
$217$	−12.9120	+	7.45473i	−0.876522	+	0.506060i
$218$	−1.13855	−	0.657343i	−0.0771125	−	0.0445209i
$219$	−2.05646	+	3.23962i	−0.138963	+	0.218913i
$220$	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	0.916767	−	0.399423i	$-0.130790\pi$
$223$	−1.14819	−	4.28509i	−0.0768882	−	0.286951i	−0.993655	+	0.112473i	$0.964123\pi$
$224$	−3.52229	−	2.03359i	−0.235343	−	0.135875i
$225$	−14.8540	−	2.08769i	−0.990267	−	0.139179i
$226$	−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	$-0.0638579\pi$
$228$	−1.46639	+	0.766392i	−0.0971143	+	0.0507556i
$229$	−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	$0.378443\pi$
$230$	1.10516	+	0.679724i	0.0728720	+	0.0448196i
$231$	−10.9454	+	2.44523i	−0.720153	+	0.160884i
$232$	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	$-0.130500\pi$
$234$	−1.92896	+	13.8921i	−0.126100	+	0.908158i
$235$	−8.52076	+	4.60842i	−0.555833	+	0.300620i
$236$	0.534327	+	1.99414i	0.0347817	+	0.129807i
$237$	−3.67883	−	16.4672i	−0.238966	−	1.06966i
$238$	−6.71028	−	11.6226i	−0.434963	−	0.753378i
$239$	15.4524	−	15.4524i	0.999531	−	0.999531i	−0.000468754	−	1.00000i	$-0.500149\pi$
$239$	15.4524	−	15.4524i	0.999531	−	0.999531i	1.00000		0.000468754i	$0.000149209\pi$
$240$	−10.4707	−	7.06261i	−0.675879	−	0.455889i
$241$	−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
$243$	13.8853	+	7.08518i	0.890739	+	0.454514i
$244$	−3.12599	−	1.80479i	−0.200121	−	0.115540i
$245$	2.77542	+	2.93425i	0.177315	+	0.187463i
$246$	−1.38827	+	1.27628i	−0.0885129	+	0.0813726i
$247$	−4.89107	−	9.63735i	−0.311211	−	0.613210i
$248$	19.6693			1.24900
$249$	−1.12404	+	1.77074i	−0.0712330	+	0.112216i
$250$	11.9070	+	8.26954i	0.753067	+	0.523012i
$251$	−1.55359	−	2.69089i	−0.0980614	−	0.169847i	0.812821	−	0.582514i	$-0.197931\pi$
$251$	−1.55359	−	2.69089i	−0.0980614	−	0.169847i	−0.910882	+	0.412666i	$0.864598\pi$
$252$	−1.40600	−	1.66457i	−0.0885699	−	0.104858i
$253$	−1.22810	−	0.329069i	−0.0772102	−	0.0206884i
$254$	−4.12090	+	15.3794i	−0.258568	+	0.964990i
$255$	7.71067	+	15.8094i	0.482861	+	0.990020i
$256$	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	$0.531821\pi$
$258$	−5.73889	+	9.04069i	−0.357288	+	0.562849i
$259$			24.2798i			1.50867i
$260$	−1.46217	+	2.11281i	−0.0906798	+	0.131031i
$261$	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	$0.135501\pi$
$264$	14.1181	+	4.42616i	0.868907	+	0.272411i
$265$	17.7589	+	5.29194i	1.09092	+	0.325081i
$266$	−8.55576	−	2.29251i	−0.524588	−	0.140563i
$267$	1.36590	+	2.61347i	0.0835917	+	0.159942i
$268$	−2.09040	−	2.09040i	−0.127691	−	0.127691i
$269$	−8.98175	+	5.18562i	−0.547627	+	0.316173i	−0.748164	−	0.663513i	$-0.769065\pi$
$269$	−8.98175	+	5.18562i	−0.547627	+	0.316173i	0.200537	+	0.979686i	$0.435731\pi$
$270$	−8.89500	−	12.1596i	−0.541332	−	0.740007i
$271$	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
$273$	10.9817	−	9.05311i	0.664641	−	0.547919i
$274$	−8.16467			−0.493246
$275$	−13.4964	−	4.43398i	−0.813866	−	0.267379i
$276$	−0.0538564	−	0.241073i	−0.00324177	−	0.0145109i
$277$	1.18949	+	2.06025i	0.0714694	+	0.123789i	0.899546	−	0.436827i	$-0.143898\pi$
$277$	1.18949	+	2.06025i	0.0714694	+	0.123789i	−0.828076	+	0.560616i	$0.810564\pi$
$278$	15.9095	+	15.9095i	0.954188	+	0.954188i
$279$	18.4646	+	6.65259i	1.10545	+	0.398280i
$280$	3.55236	+	14.9037i	0.212294	+	0.890665i
$281$	−7.28271	−	7.28271i	−0.434450	−	0.434450i	0.455689	−	0.890139i	$-0.349393\pi$
$281$	−7.28271	−	7.28271i	−0.434450	−	0.434450i	−0.890139	+	0.455689i	$0.849393\pi$
$282$	−9.28403	−	2.91064i	−0.552856	−	0.173326i
$283$	−6.97223	+	12.0763i	−0.414456	+	0.717859i	−0.995371	−	0.0961049i	$-0.969362\pi$
$283$	−6.97223	+	12.0763i	−0.414456	+	0.717859i	0.580915	+	0.813964i	$0.302695\pi$
$284$	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
$288$	0.946865	+	5.26956i	0.0557945	+	0.310512i
$289$	1.81300	−	3.14021i	0.106647	−	0.184718i
$290$	−14.2027	−	8.73530i	−0.834010	−	0.512955i
$291$	−0.738685	+	17.5751i	−0.0433025	+	1.03027i
$292$	−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	$0.285858\pi$
$294$	−0.170350	+	4.05303i	−0.00993501	+	0.236378i
$295$	7.58851	−	12.3381i	0.441820	−	0.718353i
$296$	16.0155	−	27.7397i	0.930884	−	1.61234i
$297$	11.7564	+	8.93011i	0.682174	+	0.518178i
$298$	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
$303$	−21.6758	−	6.79558i	−1.24524	−	0.390396i
$304$	6.91182	+	6.91182i	0.396420	+	0.396420i
$305$	5.87203	+	24.6357i	0.336231	+	1.41064i
$306$	−5.98824	+	16.6207i	−0.342325	+	0.950143i
$307$	−11.4213	−	11.4213i	−0.651847	−	0.651847i	0.301591	−	0.953437i	$-0.402482\pi$
$307$	−11.4213	−	11.4213i	−0.651847	−	0.651847i	−0.953437	+	0.301591i	$0.902482\pi$
$308$	−1.03180	−	1.78712i	−0.0587920	−	0.101831i
$309$	1.93592	+	8.66562i	0.110131	+	0.492970i
$310$	−13.0345	−	13.7804i	−0.740310	−	0.782676i
$311$	8.25099			0.467871			0.233935	−	0.972252i	$-0.424840\pi$
$311$	8.25099			0.467871			0.233935	+	0.972252i	$0.424840\pi$
$312$	−18.5183	+	3.09942i	−1.04839	+	0.175470i
$313$			12.5949i			0.711907i	0.934504	+	0.355954i	$0.115844\pi$
$313$			12.5949i			0.711907i	−0.934504	+	0.355954i	$0.884156\pi$
$314$	−7.20693	−	26.8966i	−0.406710	−	1.51786i
$315$	−1.70596	+	15.1924i	−0.0961197	+	0.855993i
$316$	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	$0.801151\pi$
$318$	8.62082	+	16.4948i	0.483432	+	0.924984i
$319$	15.7827	+	4.22896i	0.883660	+	0.236776i
$320$	5.64253	−	18.9354i	0.315427	−	1.05852i
$321$	−11.3582	−	3.56090i	−0.633952	−	0.198750i
$322$	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
$325$	17.8193	−	2.73357i	0.988437	−	0.151631i
$326$			14.3616i			0.795418i
$327$	0.941163	−	1.48265i	0.0520464	−	0.0819907i
$328$	−2.18628	−	1.26225i	−0.120717	−	0.0696961i
$329$	4.93653	+	8.55031i	0.272160	+	0.471394i
$330$	−6.25480	−	12.8243i	−0.344315	−	0.705957i
$331$	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
$333$	24.4168	−	20.6240i	1.33803	−	1.13019i
$334$	−15.6579	−	27.1202i	−0.856761	−	1.48395i
$335$	−0.576777	+	20.7340i	−0.0315127	+	1.13282i
$336$	−6.89861	+	10.8676i	−0.376350	+	0.592879i
$337$	7.02217			0.382522			0.191261	−	0.981539i	$-0.438742\pi$
$337$	7.02217			0.382522			0.191261	+	0.981539i	$0.438742\pi$
$338$	−2.58365	−	16.6573i	−0.140532	−	0.906037i
$339$	7.55760	−	6.94793i	0.410473	−	0.377360i
$340$	−2.35128	+	2.22400i	−0.127516	+	0.120613i
$341$	16.0975	+	9.29389i	0.871728	+	0.503292i
$342$	4.96208	+	10.5514i	0.268318	+	0.570554i
$343$	14.1911	−	14.1911i	0.766248	−	0.766248i
$344$	−13.8468	−	3.71024i	−0.746570	−	0.200043i
$345$	−0.969159	+	1.43683i	−0.0521777	+	0.0773562i
$346$	−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	$0.496662\pi$
$348$	0.692123	+	3.09809i	0.0371017	+	0.166075i
$349$	−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
$351$	−18.4324	−	3.35368i	−0.983848	−	0.179006i
$352$			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	$0.539554\pi$
$354$	14.1984	−	3.17197i	0.754639	−	0.168589i
$355$	−25.2667	−	15.5402i	−1.34102	−	0.824789i
$356$	−0.383672	+	0.383672i	−0.0203346	+	0.0203346i
$357$	15.8880	−	8.30365i	0.840881	−	0.439476i
$358$	2.30296	−	8.59475i	0.121715	−	0.454247i
$359$	−18.3546	−	18.3546i	−0.968720	−	0.968720i	0.0308058	−	0.999525i	$-0.490193\pi$
$359$	−18.3546	−	18.3546i	−0.968720	−	0.968720i	−0.999525	+	0.0308058i	$0.990193\pi$
$360$	11.9703	−	16.2320i	0.630891	−	0.855504i
$361$	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
$366$	−13.6322	+	21.4754i	−0.712569	+	1.12254i
$367$	11.4479	+	6.60945i	0.597575	+	0.345010i	0.768087	−	0.640345i	$-0.221209\pi$
$367$	11.4479	+	6.60945i	0.597575	+	0.345010i	−0.170512	+	0.985356i	$0.554542\pi$
$368$	−1.26378	+	0.729645i	−0.0658792	+	0.0380354i
$369$	−1.62546	−	1.92439i	−0.0846181	−	0.100180i
$370$	−30.0478	+	7.16204i	−1.56211	+	0.372337i
$371$	4.88811	−	18.2427i	0.253778	−	0.947112i
$372$	−0.151649	+	3.60809i	−0.00786263	+	0.187071i
$373$	−13.0651	+	7.54312i	−0.676483	+	0.390568i	−0.798529	−	0.601957i	$-0.794388\pi$
$373$	−13.0651	+	7.54312i	−0.676483	+	0.390568i	0.122045	+	0.992525i	$0.461055\pi$
$374$	−8.36578	+	14.4900i	−0.432584	+	0.749257i
$375$	−11.7045	+	15.4274i	−0.604419	+	0.796666i
$376$		−	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	$0.454118\pi$
$380$	−0.0593980	+	2.13524i	−0.00304705	+	0.109536i
$381$	−20.2944	−	6.36249i	−1.03971	−	0.325960i
$382$	−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	$0.956936\pi$
$384$	12.1086	−	6.32839i	0.617913	−	0.322944i
$385$	−4.13482	+	13.8758i	−0.210730	+	0.707175i
$386$	7.48921	−	4.32390i	0.381191	−	0.220081i
$387$	−11.7439	−	8.16630i	−0.596975	−	0.415117i
$388$	−3.12638	+	0.837711i	−0.158718	+	0.0425283i
$389$	−20.3601			−1.03230			−0.516150	−	0.856498i	$-0.672635\pi$
$389$	−20.3601			−1.03230			−0.516150	+	0.856498i	$0.672635\pi$
$390$	14.4432	+	10.9201i	0.731360	+	0.552959i
$391$	2.03232			0.102779
$392$	−5.24554	+	1.40554i	−0.264940	+	0.0709904i
$393$	−1.48029	+	0.330701i	−0.0746708	+	0.0166817i
$394$	12.9020	−	7.44899i	0.649995	−	0.375275i
$395$	−20.8760	−	6.22081i	−1.05039	−	0.313003i
$396$	−0.920773	+	2.55566i	−0.0462706	+	0.128427i
$397$	8.11051	−	30.2688i	0.407055	−	1.51915i	−0.393179	−	0.919462i	$-0.628625\pi$
$397$	8.11051	−	30.2688i	0.407055	−	1.51915i	0.800234	−	0.599688i	$-0.204709\pi$
$398$	−0.267240	+	0.267240i	−0.0133955	+	0.0133955i
$399$	3.53953	−	11.2900i	0.177198	−	0.565208i
$400$	−14.5521	+	7.35498i	−0.727605	+	0.367749i
$401$	13.7202	−	3.67631i	0.685154	−	0.183586i	0.100582	−	0.994929i	$-0.467929\pi$
$401$	13.7202	−	3.67631i	0.685154	−	0.183586i	0.584571	+	0.811342i	$0.301263\pi$
$402$	−15.3367	+	14.0995i	−0.764924	+	0.703217i
$403$	−23.5538	−	1.27219i	−1.17330	−	0.0633723i
$404$		−	4.17975i		−	0.207950i
$405$	16.7272	−	11.1893i	0.831182	−	0.556000i
$406$	−8.49698	+	14.7172i	−0.421698	+	0.730402i
$407$	26.2144	−	15.1349i	1.29940	−	0.750210i
$408$	−23.6294	−	0.993148i	−1.16983	−	0.0491682i
$409$	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	$-0.0867832\pi$
$410$	0.564470	+	2.36819i	0.0278772	+	0.116957i
$411$	0.457989	−	10.8967i	0.0225909	−	0.537492i
$412$	−1.41489	+	0.816888i	−0.0697067	+	0.0402452i
$413$	−12.7851	−	7.38148i	−0.629113	−	0.363219i
$414$	−1.71329	+	0.307853i	−0.0842034	+	0.0151301i
$415$	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	0.757311	−	0.653054i	$-0.226513\pi$
$419$	11.6759	+	6.74109i	0.570405	+	0.329324i	−0.186906	+	0.982378i	$0.559846\pi$
$420$	−2.76128	+	0.536730i	−0.134737	+	0.0261897i
$421$	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
$423$	4.40535	−	12.2273i	0.214195	−	0.594511i
$424$	−17.6180	+	17.6180i	−0.855605	+	0.855605i
$425$	22.6728	+	1.26240i	1.09979	+	0.0612354i
$426$	−6.49576	−	29.0764i	−0.314721	−	1.40876i
$427$	24.9323	−	6.68060i	1.20656	−	0.323297i
$428$		−	2.19020i		−	0.105867i
$429$	−16.6200	−	6.21342i	−0.802420	−	0.299987i
$430$	6.57662	+	12.1599i	0.317153	+	0.586402i
$431$	3.16022	+	11.7941i	0.152222	+	0.568102i	0.999327	+	0.0366759i	$0.0116769\pi$
$431$	3.16022	+	11.7941i	0.152222	+	0.568102i	−0.847105	+	0.531426i	$0.821656\pi$
$432$	16.7889	−	2.29376i	0.807756	−	0.110358i
$433$	8.46304	+	14.6584i	0.406708	+	0.704439i	0.994519	−	0.104560i	$-0.0333433\pi$
$433$	8.46304	+	14.6584i	0.406708	+	0.704439i	−0.587811	+	0.808999i	$0.700010\pi$
$434$	−13.6700	+	13.6700i	−0.656183	+	0.656183i
$435$	12.4549	−	18.4650i	0.597167	−	0.885331i
$436$	0.312120	+	0.0836322i	0.0149478	+	0.00400526i
$437$	0.948467	−	0.948467i	0.0453713	−	0.0453713i
$438$	−1.48844	+	4.74767i	−0.0711205	+	0.226852i
$439$	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	$0.645336\pi$
$440$	13.8769	−	13.1257i	0.661553	−	0.625743i
$441$	−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	$0.273527\pi$
$444$	4.96503	+	3.15172i	0.235630	+	0.149574i
$445$	3.80552	+	0.105862i	0.180399	+	0.00501833i
$446$	−2.87613	−	4.98160i	−0.136189	−	0.235886i
$447$	−1.61338	+	38.3861i	−0.0763102	+	1.81560i
$448$	−19.4512	−	5.21194i	−0.918984	−	0.246241i
$449$	−1.90550	+	7.11141i	−0.0899260	+	0.335608i	−0.996201	−	0.0870794i	$-0.972247\pi$
$449$	−1.90550	+	7.11141i	−0.0899260	+	0.335608i	0.906275	+	0.422688i	$0.138913\pi$
$450$	−19.3048	+	2.37021i	−0.910037	+	0.111733i
$451$	−1.19285	−	2.06607i	−0.0561689	−	0.0972874i
$452$	1.63587	+	0.944472i	0.0769450	+	0.0444242i
$453$	−1.02438	−	0.650260i	−0.0481296	−	0.0305519i
$454$		−	17.4304i		−	0.818051i
$455$	−3.28996	−	18.0768i	−0.154236	−	0.847452i
$456$	−11.4911	+	10.5641i	−0.538120	+	0.494710i
$457$	−0.0620628	−	0.231621i	−0.00290317	−	0.0108348i	0.964459	−	0.264232i	$-0.0851186\pi$
$457$	−0.0620628	−	0.231621i	−0.00290317	−	0.0108348i	−0.967362	+	0.253398i	$0.918452\pi$
$458$	−7.70462	+	13.3448i	−0.360013	+	0.623561i
$459$	−21.8463	−	8.92429i	−1.01970	−	0.416550i
$460$	−0.305615	−	0.0910698i	−0.0142494	−	0.00424615i
$461$	16.4008	+	4.39457i	0.763860	+	0.204676i	0.619657	−	0.784872i	$-0.287272\pi$
$461$	16.4008	+	4.39457i	0.763860	+	0.204676i	0.144203	+	0.989548i	$0.453938\pi$
$462$	−12.8881	+	6.73582i	−0.599610	+	0.313379i
$463$	−13.0393	−	13.0393i	−0.605988	−	0.605988i	0.335907	−	0.941895i	$-0.390957\pi$
$463$	−13.0393	−	13.0393i	−0.605988	−	0.605988i	−0.941895	+	0.335907i	$0.890957\pi$
$464$	16.2412	−	9.37685i	0.753978	−	0.435310i
$465$	19.1227	−	16.6230i	0.886792	−	0.770872i
$466$	−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	$0.880800\pi$
$468$	−0.425776	−	3.42084i	−0.0196815	−	0.158128i
$469$	21.1400			0.976156
$470$	−9.12541	+	8.63145i	−0.420924	+	0.398139i
$471$	36.3008	−	8.10970i	1.67265	−	0.373675i
$472$	9.73800	+	16.8667i	0.448228	+	0.776354i
$473$	−9.57921	−	9.57921i	−0.440453	−	0.440453i
$474$	−10.1340	−	19.3901i	−0.465470	−	0.890617i
$475$	11.1703	−	9.99204i	0.512530	−	0.458466i
$476$	2.33244	+	2.33244i	0.106907	+	0.106907i
$477$	−22.4977	+	10.5802i	−1.03010	+	0.484433i
$478$	14.1678	−	24.5394i	0.648021	−	1.12241i
$479$	−4.26159	+	1.14189i	−0.194717	+	0.0521742i	−0.354859	−	0.934920i	$-0.615471\pi$
$479$	−4.26159	+	1.14189i	−0.194717	+	0.0521742i	0.160143	+	0.987094i	$0.448805\pi$
$480$	6.53535	+	2.25032i	0.298297	+	0.102713i
$481$	−20.9726	+	32.1822i	−0.956269	+	1.46738i
$482$	−32.2609			−1.46944
$483$	1.49130	+	0.946654i	0.0678565	+	0.0430743i
$484$	0.466483	−	0.807972i	0.0212038	−	0.0367260i
$485$	19.3435	+	11.8972i	0.878345	+	0.540223i
$486$	19.7686	+	4.21410i	0.896722	+	0.191156i
$487$	38.6598	+	10.3589i	1.75184	+	0.469405i	0.985018	−	0.172450i	$-0.0551683\pi$
$487$	38.6598	+	10.3589i	1.75184	+	0.469405i	0.766826	+	0.641855i	$0.221835\pi$
$488$	−32.8919	−	8.81337i	−1.48895	−	0.398963i
$489$	−19.1672	−	0.805602i	−0.866770	−	0.0364306i
$490$	4.46086	+	2.74363i	0.201521	+	0.123945i
$491$	−7.03573	+	12.1862i	−0.317518	+	0.549957i	−0.979970	−	0.199147i	$-0.936183\pi$
$491$	−7.03573	+	12.1862i	−0.317518	+	0.549957i	0.662452	+	0.749105i	$0.269516\pi$
$492$	0.248400	−	0.391314i	0.0111987	−	0.0176418i
$493$	−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
$498$	−0.813565	+	2.59502i	−0.0364567	+	0.116286i
$499$	−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	$0.883890\pi$
$500$	−3.35291	−	1.20582i	−0.149946	−	0.0539259i
$501$	37.0733	−	19.3759i	1.65631	−	0.865651i
$502$	−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	$-0.339769\pi$
$504$	−16.8764	−	11.7353i	−0.751734	−	0.522731i
$505$	−21.3054	+	20.1522i	−0.948080	+	0.896760i
$506$	−1.64860			−0.0732890
$507$	22.3759	−	2.51379i	0.993749	−	0.111641i
$508$		−	3.91337i		−	0.173628i
$509$	2.71529	+	10.1336i	0.120353	+	0.449165i	0.999632	−	0.0271439i	$-0.00864124\pi$
$509$	2.71529	+	10.1336i	0.120353	+	0.449165i	−0.879278	+	0.476308i	$0.841975\pi$
$510$	14.9630	+	17.2130i	0.662571	+	0.762206i
$511$	4.37246	−	2.52444i	0.193426	−	0.111675i
$512$	17.9808	+	17.9808i	0.794647	+	0.794647i
$513$	−14.3603	+	6.03057i	−0.634024	+	0.266256i
$514$	16.5075	+	4.42316i	0.728113	+	0.195097i
$515$	10.9857	+	3.27360i	0.484086	+	0.144252i
$516$	0.787356	−	2.51142i	0.0346614	−	0.110559i
$517$	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
$520$	−8.16509	+	22.8229i	−0.358063	+	1.00085i
$521$			28.1221i			1.23205i	0.787726	+	0.616026i	$0.211259\pi$
$521$			28.1221i			1.23205i	−0.787726	+	0.616026i	$0.788741\pi$
$522$	22.0179	−	3.95629i	0.963696	−	0.173162i
$523$	30.0865	+	17.3704i	1.31559	+	0.759556i	0.983016	−	0.183521i	$-0.0587495\pi$
$523$	30.0865	+	17.3704i	1.31559	+	0.759556i	0.332574	+	0.943077i	$0.392083\pi$
$524$	−0.139544	−	0.241697i	−0.00609600	−	0.0105586i
$525$	16.0491	+	11.4873i	0.700439	+	0.501347i
$526$	1.06405	−	3.97109i	0.0463948	−	0.173148i
$527$	−28.6994	−	7.68998i	−1.25017	−	0.334981i
$528$	16.0339	+	0.673909i	0.697786	+	0.0293281i
$529$	−11.3999	−	19.7452i	−0.495647	−	0.858485i
$530$	24.0184	+	0.668143i	1.04329	+	0.0290223i
$531$	3.43690	+	19.1273i	0.149149	+	0.830055i
$532$	2.17706			0.0943874
$533$	2.53641	+	1.65294i	0.109864	+	0.0715967i
$534$	2.58782	+	2.81490i	0.111986	+	0.121813i
$535$	−11.1641	+	10.5598i	−0.482667	+	0.456540i
$536$	−24.1526	−	13.9445i	−1.04323	−	0.602310i
$537$	11.3415	+	3.55566i	0.489420	+	0.153438i
$538$	−9.50908	+	9.50908i	−0.409965	+	0.409965i
$539$	−4.95711	−	1.32825i	−0.213518	−	0.0572120i
$540$	2.88528	+	2.32095i	0.124163	+	0.0998780i
$541$	−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
$543$	37.1895	−	8.30826i	1.59596	−	0.356541i
$544$	−2.09777	−	7.82898i	−0.0899411	−	0.335665i
$545$	−1.07855	−	1.99419i	−0.0462000	−	0.0854217i
$546$	10.7160	−	15.0242i	0.458602	−	0.642975i
$547$		−	7.60825i		−	0.325305i	−0.986683	−	0.162653i	$-0.947995\pi$
$547$		−	7.60825i		−	0.325305i	0.986683	−	0.162653i	$-0.0520050\pi$
$548$	1.93837	−	0.519386i	0.0828032	−	0.0221871i
$549$	−27.8966	−	19.3984i	−1.19060	−	0.827902i
$550$	−18.3919	−	1.02404i	−0.784233	−	0.0436653i
$551$	−12.1890	+	12.1890i	−0.519269	+	0.519269i
$552$	−1.07938	−	2.06525i	−0.0459414	−	0.0879030i
$553$	−5.74609	+	21.4447i	−0.244349	+	0.911922i
$554$	2.18121	+	2.18121i	0.0926709	+	0.0926709i
$555$	−7.87303	−	40.5039i	−0.334191	−	1.71929i
$556$	−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
$561$	−18.8692	−	11.9778i	−0.796657	−	0.505705i
$562$	−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	$0.205445\pi$
$564$	2.38928	+	0.100422i	0.100607	+	0.00422853i
$565$	−3.07292	−	12.8922i	−0.129279	−	0.542379i
$566$	−4.67973	+	17.4650i	−0.196704	+	0.734109i
$567$	−11.8737	−	16.7245i	−0.498647	−	0.702364i
$568$	34.5407	−	19.9421i	1.44930	−	0.836751i
$569$	10.2020	−	17.6703i	0.427688	−	0.740778i	−0.568979	−	0.822352i	$-0.692661\pi$
$569$	10.2020	−	17.6703i	0.427688	−	0.740778i	0.996667	+	0.0815741i	$0.0259947\pi$
$570$	15.0162	+	1.05008i	0.628961	+	0.0439832i
$571$			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
$575$	1.00928	+	1.99690i	0.0420898	+	0.0832763i
$576$	11.2811	+	23.9882i	0.470046	+	0.999509i
$577$	−8.23663	+	8.23663i	−0.342896	+	0.342896i	−0.857455	−	0.514559i	$-0.827956\pi$
$577$	−8.23663	+	8.23663i	−0.342896	+	0.342896i	0.514559	+	0.857455i	$0.327956\pi$
$578$	1.21688	−	4.54146i	0.0506155	−	0.188900i
$579$	5.35062	+	10.2377i	0.222364	+	0.425465i
$580$	3.92754	+	1.17036i	0.163082	+	0.0485966i
$581$	2.38994	−	1.37983i	0.0991513	−	0.0572450i
$582$	4.97298	+	22.2601i	0.206137	+	0.922712i
$583$	−22.7433	+	6.09405i	−0.941932	+	0.252390i
$584$	−6.66073			−0.275623
$585$	−15.3842	+	18.6635i	−0.636059	+	0.771640i
$586$	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	$0.417222\pi$
$588$	−0.217386	−	0.973066i	−0.00896484	−	0.0401286i
$589$	−16.9826	+	9.80491i	−0.699756	+	0.404004i
$590$	5.36373	−	17.9998i	0.220821	−	0.741040i
$591$	9.21777	+	17.6370i	0.379168	+	0.725490i
$592$	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	$0.925653\pi$
$594$	17.7214	+	7.23927i	0.727118	+	0.297031i
$595$	0.643561	−	23.1348i	0.0263834	−	0.948432i
$596$	−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	$0.256600\pi$
$599$			35.3223i			1.44323i	−0.692294	+	0.721615i	$0.743400\pi$
$600$	−10.7588	−	23.7106i	−0.439226	−	0.967983i
$601$	−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
$603$	−17.9570	−	21.2594i	−0.731265	−	0.865749i
$604$	0.0577824	−	0.215647i	0.00235113	−	0.00877455i
$605$	−6.36757	+	1.51774i	−0.258878	+	0.0617049i
$606$	−29.4288	−	1.23690i	−1.19546	−	0.0502456i
$607$	12.9895	−	7.49947i	0.527226	−	0.304394i	−0.212660	−	0.977126i	$-0.568213\pi$
$607$	12.9895	−	7.49947i	0.527226	−	0.304394i	0.739886	+	0.672732i	$0.234879\pi$
$608$	−4.63272	−	2.67470i	−0.187882	−	0.108474i
$609$	−19.1651	−	12.1657i	−0.776609	−	0.492979i
$610$	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	0.992700	−	0.120613i	$-0.0384861\pi$
$613$	1.79972	+	6.71663i	0.0726898	+	0.271282i	−0.920010	+	0.391895i	$0.871819\pi$
$614$	−18.1377	−	10.4718i	−0.731980	−	0.422609i
$615$	−3.19228	+	0.620506i	−0.128725	+	0.0250212i
$616$	−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	$0.108573\pi$
$618$	5.33285	+	10.2037i	0.214519	+	0.410454i
$619$	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	$0.0412459\pi$
$620$	3.97114	+	2.44244i	0.159485	+	0.0980906i
$621$	−0.314758	−	2.30384i	−0.0126308	−	0.0924498i
$622$	10.3341	−	2.76901i	0.414360	−	0.111027i
$623$		−	3.88005i		−	0.155451i
$624$	−18.5313	+	8.44582i	−0.741845	+	0.338103i
$625$	10.0192	+	22.9045i	0.400769	+	0.916179i
$626$	4.22683	+	15.7747i	0.168938	+	0.630486i
$627$	−14.3960	+	3.21611i	−0.574921	+	0.128439i
$628$	3.42199	+	5.92706i	0.136552	+	0.236516i
$629$	−34.2134	+	34.2134i	−1.36418	+	1.36418i
$630$	2.96187	+	19.6005i	0.118004	+	0.780902i
$631$	−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
$633$	26.2824	+	8.23981i	1.04463	+	0.327503i
$634$	−6.39798	−	3.69388i	−0.254096	−	0.146703i
$635$	−19.9476	+	18.8679i	−0.791597	+	0.748748i
$636$	−3.09597	−	3.36763i	−0.122763	−	0.133535i
$637$	6.37239	−	1.34384i	0.252483	−	0.0532450i
$638$	21.1865			0.838783
$639$	39.1701	−	7.03830i	1.54954	−	0.278431i
$640$	0.490472	−	17.6315i	0.0193876	−	0.696946i
$641$	−0.623490	−	1.07992i	−0.0246264	−	0.0426542i	0.853450	−	0.521175i	$-0.174506\pi$
$641$	−0.623490	−	1.07992i	−0.0246264	−	0.0426542i	−0.878076	+	0.478521i	$0.841173\pi$
$642$	−15.4208	−	0.648140i	−0.608610	−	0.0255800i
$643$	2.91685	+	0.781568i	0.115029	+	0.0308220i	0.315875	−	0.948801i	$-0.397702\pi$
$643$	2.91685	+	0.781568i	0.115029	+	0.0308220i	−0.200845	+	0.979623i	$0.564369\pi$
$644$	−0.0841202	+	0.313941i	−0.00331480	+	0.0123710i
$645$	−16.5976	+	8.09513i	−0.653530	+	0.318746i
$646$	−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	$0.698340\pi$
$648$	2.53379	+	26.9400i	0.0995366	+	1.05830i
$649$			18.4051i			0.722464i
$650$	21.4007	−	9.40383i	0.839406	−	0.368848i
$651$	−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	$0.110850\pi$
$654$	0.681203	−	2.17282i	0.0266371	−	0.0849642i
$655$	−0.559208	+	1.87661i	−0.0218500	+	0.0733252i
$656$	−2.64489	−	0.708697i	−0.103266	−	0.0276700i
$657$	−6.25279	−	2.25281i	−0.243945	−	0.0878903i
$658$	9.05231	+	9.05231i	0.352896	+	0.352896i
$659$	26.8813	−	15.5199i	1.04715	−	0.604570i	0.125297	−	0.992119i	$-0.460012\pi$
$659$	26.8813	−	15.5199i	1.04715	−	0.604570i	0.921849	+	0.387549i	$0.126678\pi$
$660$	2.30076	+	2.64673i	0.0895568	+	0.103024i
$661$	−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
$663$	28.2317	+	2.71761i	1.09643	+	0.105543i
$664$	−3.64068			−0.141286
$665$	−10.4964	−	11.0971i	−0.407034	−	0.430328i
$666$	23.6599	−	34.0251i	0.916804	−	1.31845i
$667$	−1.28673	−	2.22868i	−0.0498223	−	0.0862948i
$668$	5.44256	+	5.44256i	0.210579	+	0.210579i
$669$	6.80983	−	3.55907i	0.263283	−	0.137602i
$670$	6.23588	+	26.1622i	0.240913	+	1.01073i
$671$	−22.7546	−	22.7546i	−0.878432	−	0.878432i
$672$	2.10740	−	6.72197i	0.0812949	−	0.259305i
$673$	−5.27490	+	9.13640i	−0.203333	+	0.352182i	−0.949600	−	0.313464i	$-0.898511\pi$
$673$	−5.27490	+	9.13640i	−0.203333	+	0.352182i	0.746268	+	0.665646i	$0.231844\pi$
$674$	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	$0.777314\pi$
$678$	7.13395	−	11.2384i	0.273978	−	0.431607i
$679$	11.5726	−	20.0443i	0.444115	−	0.769229i
$680$	−15.9955	+	26.0070i	−0.613400	+	0.997324i
$681$	23.2628	+	0.977744i	0.891434	+	0.0374672i
$682$	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	$0.510709\pi$
$684$	−1.84926	−	2.18935i	−0.0707082	−	0.0837118i
$685$	−11.9931	−	7.37632i	−0.458233	−	0.281835i
$686$	13.0114	−	22.5364i	0.496778	−	0.860445i
$687$	−17.3779	−	11.0312i	−0.663008	−	0.420867i
$688$	−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
$693$	−8.26674	−	17.5785i	−0.314028	−	0.667751i
$694$	29.7599	+	29.7599i	1.12967	+	1.12967i
$695$	8.99617	+	37.7428i	0.341244	+	1.43167i
$696$	13.8714	+	26.5411i	0.525793	+	1.00604i
$697$	2.69650	+	2.69650i	0.102137	+	0.102137i
$698$	−7.33517	−	12.7049i	−0.277640	−	0.480887i
$699$	20.5692	−	4.59521i	0.777997	−	0.173807i
$700$	−1.13346	+	3.45010i	−0.0428408	+	0.130402i
$701$	30.0152			1.13366			0.566829	−	0.823836i	$-0.308170\pi$
$701$	30.0152			1.13366			0.566829	+	0.823836i	$0.308170\pi$
$702$	−24.2115	+	1.98549i	−0.913803	+	0.0749375i
$703$			31.9342i			1.20442i
$704$	6.49778	+	24.2500i	0.244894	+	0.913958i
$705$	−11.0077	−	12.6630i	−0.414575	−	0.476918i
$706$	−15.8886	+	9.17328i	−0.597975	+	0.345241i
$707$	21.1348	+	21.1348i	0.794855	+	0.794855i
$708$	−3.16907	+	1.65627i	−0.119101	+	0.0622466i
$709$	−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	$0.821905\pi$
$710$	−36.8611	−	10.9842i	−1.38337	−	0.412228i
$711$	26.4467	−	12.4373i	0.991828	−	0.466434i
$712$	−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
$715$	−17.4664	+	14.8204i	−0.653205	+	0.554250i
$716$			2.18698i			0.0817312i
$717$	31.9558	+	20.2850i	1.19341	+	0.757559i
$718$	−29.1483	−	16.8288i	−1.08781	−	0.628045i
$719$	−23.2174	−	40.2137i	−0.865863	−	1.49972i	−0.866188	−	0.499719i	$-0.833437\pi$
$719$	−23.2174	−	40.2137i	−0.865863	−	1.49972i	0.000324371	−	1.00000i	$-0.499897\pi$
$720$	7.98440	−	20.3665i	0.297561	−	0.759016i
$721$	3.02379	−	11.2849i	0.112612	−	0.420273i
$722$	12.5438	+	3.36111i	0.466834	+	0.125088i
$723$	1.80964	−	43.0557i	0.0673014	−	1.60126i
$724$	3.50578	+	6.07218i	0.130291	+	0.225671i
$725$	−12.9705	−	25.6626i	−0.481712	−	0.953086i
$726$	−5.55073	−	3.52352i	−0.206007	−	0.130770i
$727$	−51.6317			−1.91491			−0.957457	−	0.288575i	$-0.906819\pi$
$727$	−51.6317			−1.91491			−0.957457	+	0.288575i	$0.906819\pi$
$728$	23.4833	+	7.67174i	0.870348	+	0.284334i
$729$	−6.73308	+	26.1470i	−0.249373	+	0.968407i
$730$	4.41395	+	4.66655i	0.163368	+	0.172717i
$731$	18.7533	+	10.8272i	0.693615	+	0.400459i
$732$	1.87030	−	5.96567i	0.0691282	−	0.220497i
$733$	−6.10483	+	6.10483i	−0.225487	+	0.225487i	−0.810804	−	0.585317i	$-0.800970\pi$
$733$	−6.10483	+	6.10483i	−0.225487	+	0.225487i	0.585317	+	0.810804i	$0.300970\pi$
$734$	16.5562	+	4.43623i	0.611102	+	0.163744i
$735$	−3.91191	+	5.79960i	−0.144293	+	0.213922i
$736$	0.564708	−	0.564708i	0.0208154	−	0.0208154i
$737$	−13.1777	−	22.8245i	−0.485409	−	0.840752i
$738$	−2.68166	−	1.86474i	−0.0987133	−	0.0686420i
$739$	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
$741$	14.4438	−	11.9072i	0.530605	−	0.437422i
$742$		−	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	$0.369373\pi$
$744$	7.42784	+	33.2486i	0.272318	+	1.21895i
$745$	42.2486	+	25.9849i	1.54787	+	0.952012i
$746$	−13.8321	+	13.8321i	−0.506430	+	0.506430i
$747$	−3.41770	−	1.23136i	−0.125047	−	0.0450530i
$748$	1.06436	−	3.97224i	0.0389168	−	0.145239i
$749$	11.0747	+	11.0747i	0.404660	+	0.404660i
$750$	−9.48216	+	23.2503i	−0.346239	+	0.848982i
$751$	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
$756$	2.28281	−	3.00529i	0.0830249	−	0.109301i
$757$	−25.1140	−	14.4995i	−0.912782	−	0.526995i	−0.0314569	−	0.999505i	$-0.510015\pi$
$757$	−25.1140	−	14.4995i	−0.912782	−	0.526995i	−0.881325	+	0.472510i	$0.843348\pi$
$758$	−5.13235	+	2.96316i	−0.186415	+	0.107627i
$759$	0.0924764	−	2.20023i	0.00335668	−	0.0798634i
$760$	4.67227	+	19.6022i	0.169481	+	0.711046i
$761$	1.91474	−	7.14590i	0.0694092	−	0.259039i	−0.922498	−	0.386001i	$-0.873856\pi$
$761$	1.91474	−	7.14590i	0.0694092	−	0.259039i	0.991908	+	0.126962i	$0.0405228\pi$
$762$	−27.5533	−	1.15807i	−0.998150	−	0.0419525i
$763$	−2.00111	+	1.15534i	−0.0724449	+	0.0418261i
$764$	2.65080	−	4.59132i	0.0959026	−	0.166108i
$765$	−23.8120	+	19.0042i	−0.860925	+	0.687097i
$766$			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	$0.683632\pi$
$770$	−0.522049	+	18.7666i	−0.0188133	+	0.676302i
$771$	−6.82916	+	21.7829i	−0.245946	+	0.784492i
$772$	−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	$-0.0384803\pi$
$774$	−17.4494	−	6.28682i	−0.627207	−	0.225975i
$775$	−6.69657	−	32.0180i	−0.240548	−	1.15012i
$776$	−26.4434	+	15.2671i	−0.949263	+	0.548057i
$777$	−41.0421	+	9.16892i	−1.47238	+	0.328933i
$778$	−25.5004	+	6.83282i	−0.914235	+	0.244968i
$779$	2.51687			0.0901761
$780$	−4.12363	−	1.67375i	−0.147649	−	0.0599298i
$781$	37.6911			1.34869
$782$	2.54542	−	0.682044i	0.0910241	−	0.0243898i
$783$	4.04504	+	29.6072i	0.144558	+	1.05807i
$784$	−5.10113	+	2.94514i	−0.182183	+	0.105183i
$785$	13.7133	−	46.0196i	0.489448	−	1.64251i
$786$	−1.74304	+	0.910976i	−0.0621720	+	0.0324934i
$787$	−3.89237	+	14.5265i	−0.138748	+	0.517815i	0.861206	+	0.508256i	$0.169710\pi$
$787$	−3.89237	+	14.5265i	−0.138748	+	0.517815i	−0.999954	+	0.00955922i	$0.996957\pi$
$788$	−2.58921	+	2.58921i	−0.0922368	+	0.0922368i
$789$	5.24017	+	1.64285i	0.186555	+	0.0584868i
$790$	−28.2342	−	0.785419i	−1.00453	−	0.0279440i
$791$	−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
$795$	−2.23900	+	32.0177i	−0.0794091	+	1.13555i
$796$	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	$0.162251\pi$
$798$	0.644250	−	15.3282i	0.0228062	−	0.542614i
$799$	−5.09231	+	19.0048i	−0.180153	+	0.672340i
$800$	6.65072	−	5.94917i	0.235138	−	0.210335i
$801$	−3.90195	+	3.29583i	−0.137869	+	0.116453i
$802$	15.9503	−	9.20894i	0.563226	−	0.325179i
$803$	−5.45119	−	3.14725i	−0.192368	−	0.111064i
$804$	2.74416	−	4.32298i	0.0967790	−	0.152460i
$805$	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	0.607119	−	0.794611i	$-0.292325\pi$
$809$	6.32927	+	3.65421i	0.222525	+	0.128475i	−0.384594	+	0.923086i	$0.625658\pi$
$810$	17.1952	−	19.6278i	0.604179	−	0.689652i
$811$	−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
$813$	−33.3661	+	17.4384i	−1.17020	+	0.611590i
$814$	27.7535	−	27.7535i	0.972760	−	0.972760i
$815$	−12.9749	+	21.0958i	−0.454492	+	0.738955i
$816$	−25.0350	+	5.59290i	−0.876402	+	0.195791i
$817$	13.8049	−	3.69902i	0.482974	−	0.129412i
$818$		−	26.7139i		−	0.934028i
$819$	19.4503	+	15.1444i	0.679648	+	0.529190i
$820$	−0.284661	−	0.526325i	−0.00994078	−	0.0183801i
$821$	−13.1364	−	49.0257i	−0.458464	−	1.71101i	−0.677700	−	0.735339i	$-0.737023\pi$
$821$	−13.1364	−	49.0257i	−0.458464	−	1.71101i	0.219236	−	0.975672i	$-0.429643\pi$
$822$	−3.08328	−	13.8014i	−0.107542	−	0.481380i
$823$	−20.6525	−	35.7712i	−0.719901	−	1.24690i	−0.961039	−	0.276414i	$-0.910854\pi$
$823$	−20.6525	−	35.7712i	−0.719901	−	1.24690i	0.241138	−	0.970491i	$-0.422479\pi$
$824$	−10.8985	+	10.8985i	−0.379667	+	0.379667i
$825$	2.39837	−	24.4886i	0.0835006	−	0.852583i
$826$	−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	$0.262273\pi$
$828$	0.387167	−	0.182076i	0.0134550	−	0.00632757i
$829$	−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	$0.970345\pi$
$830$	2.41261	+	2.55068i	0.0837431	+	0.0885355i
$831$	−3.03342	+	2.78872i	−0.105228	+	0.0967395i
$832$	−21.2801	−	23.7101i	−0.737753	−	0.821998i
$833$	8.20327			0.284226
$834$	−20.8851	+	32.9011i	−0.723192	+	1.13927i
$835$	1.50170	−	53.9830i	0.0519684	−	1.86816i
$836$	−1.35708	−	2.35053i	−0.0469356	−	0.0812948i
$837$	−4.27249	+	33.7245i	−0.147679	+	1.16569i
$838$	16.8860	+	4.52459i	0.583317	+	0.156299i
$839$	2.91462	−	10.8775i	0.100624	−	0.375534i	−0.897188	−	0.441649i	$-0.854394\pi$
$839$	2.91462	−	10.8775i	0.100624	−	0.375534i	0.997812	+	0.0661149i	$0.0210604\pi$
$840$	−23.8514	+	11.6330i	−0.822951	+	0.401377i
$841$	2.03608	+	3.52660i	0.0702097	+	0.121607i
$842$	18.1549	+	10.4818i	0.625660	+	0.361225i
$843$	9.56034	−	15.0608i	0.329276	−	0.518721i
$844$			5.06805i			0.174450i
$845$	11.2538	−	26.8021i	0.387142	−	0.922020i
$846$	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
$849$	−23.0465	−	7.22530i	−0.790953	−	0.247972i
$850$	28.8206	−	6.02783i	0.988540	−	0.206753i
$851$	−4.60504	−	1.23392i	−0.157859	−	0.0422981i
$852$	3.39182	+	6.48981i	0.116202	+	0.222337i
$853$	21.6293	+	21.6293i	0.740573	+	0.740573i	0.972688	−	0.232115i	$-0.0745646\pi$
$853$	21.6293	+	21.6293i	0.740573	+	0.740573i	−0.232115	+	0.972688i	$0.574565\pi$
$854$	28.9850	−	16.7345i	0.991845	−	0.572642i
$855$	−2.24377	+	19.9819i	−0.0767355	+	0.683367i
$856$	−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	$0.844624\pi$
$858$	−22.9012	−	2.20449i	−0.781834	−	0.0752600i
$859$	27.6237			0.942508			0.471254	−	0.881998i	$-0.343802\pi$
$859$	27.6237			0.942508			0.471254	+	0.881998i	$0.343802\pi$
$860$	−2.33489	−	2.46851i	−0.0796192	−	0.0841756i
$861$	0.722641	+	3.23470i	0.0246275	+	0.110238i
$862$	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	$0.634391\pi$
$864$	−8.55001	+	3.59054i	−0.290877	+	0.122153i
$865$	−6.36305	+	1.51666i	−0.216350	+	0.0515681i
$866$	15.5190	+	15.5190i	0.527358	+	0.527358i
$867$	5.99281	+	1.87881i	0.203527	+	0.0638077i
$868$	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
$873$	−29.9875	+	5.38833i	−1.01492	+	0.182367i
$874$	0.869622	−	1.50623i	0.0294154	−	0.0509490i
$875$	23.0510	−	10.8567i	0.779268	−	0.367022i
$876$	0.0513538	−	1.22183i	0.00173508	−	0.0412818i
$877$	14.0324	+	3.75997i	0.473841	+	0.126965i	0.487833	−	0.872937i	$-0.337787\pi$
$877$	14.0324	+	3.75997i	0.473841	+	0.126965i	−0.0139924	+	0.999902i	$0.504454\pi$
$878$	3.51451	+	0.941710i	0.118609	+	0.0317812i
$879$	−2.00280	+	47.6514i	−0.0675527	+	1.60724i
$880$	10.8539	−	17.6473i	0.365885	−	0.594889i
$881$	−19.4302	+	33.6541i	−0.654619	+	1.13383i	0.327370	+	0.944896i	$0.393838\pi$
$881$	−19.4302	+	33.6541i	−0.654619	+	1.13383i	−0.981989	+	0.188938i	$0.939496\pi$
$882$	−6.91550	+	1.24262i	−0.232857	+	0.0418410i
$883$	8.78225			0.295546			0.147773	−	0.989021i	$-0.452789\pi$
$883$	8.78225			0.295546			0.147773	+	0.989021i	$0.452789\pi$
$884$	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	$-0.0267991\pi$
$888$	52.9387	+	16.5968i	1.77651	+	0.556953i
$889$	19.7878	+	19.7878i	0.663662	+	0.663662i
$890$	4.80182	−	1.14454i	0.160957	−	0.0383650i
$891$	−10.6557	+	23.2451i	−0.356978	+	0.778740i
$892$	0.999721	+	0.999721i	0.0334731	+	0.0334731i
$893$	6.49281	+	11.2459i	0.217274	+	0.376329i
$894$	10.8616	+	48.6188i	0.363266	+	1.62606i
$895$	11.1477	−	10.5443i	0.372626	−	0.352456i
$896$	−17.9768			−0.600562
$897$	1.15897	+	2.54294i	0.0386968	+	0.0849061i
$898$			9.54630i			0.318564i
$899$	9.73754	+	36.3410i	0.324765	+	1.21204i
$900$	4.43237	−	1.79076i	0.147746	−	0.0596921i
$901$	32.5943	−	18.8184i	1.08588	−	0.626930i
$902$	−2.18737	−	2.18737i	−0.0728314	−	0.0728314i
$903$	8.71768	+	16.6802i	0.290106	+	0.555081i
$904$	17.2128	+	4.61216i	0.572490	+	0.153398i
$905$	14.0490	−	47.1463i	0.467006	−	1.56720i
$906$	−1.50123	−	0.470651i	−0.0498750	−	0.0156363i
$907$	19.4826	−	33.7449i	0.646911	−	1.12048i	−0.336946	−	0.941524i	$-0.609394\pi$
$907$	19.4826	−	33.7449i	0.646911	−	1.12048i	0.983857	−	0.178958i	$-0.0572726\pi$
$908$	1.10882	+	4.13816i	0.0367974	+	0.137330i
$909$	3.30156	−	39.2066i	0.109506	−	1.30040i
$910$	−10.1871	−	21.5365i	−0.337699	−	0.713927i
$911$		−	54.4600i		−	1.80434i	−0.431379	−	0.902171i	$-0.641973\pi$
$911$		−	54.4600i		−	1.80434i	0.431379	−	0.902171i	$-0.358027\pi$
$912$	−9.07347	+	14.2938i	−0.300452	+	0.473314i
$913$	−2.97956	−	1.72025i	−0.0986090	−	0.0569319i
$914$	−0.155463	−	0.269270i	−0.00514227	−	0.00890667i
$915$	−39.4262	+	19.2293i	−1.30339	+	0.635701i
$916$	0.980240	−	3.65830i	0.0323880	−	0.120874i
$917$	1.92773	+	0.516534i	0.0636593	+	0.0170574i
$918$	−30.3567	−	3.84583i	−1.00192	−	0.126931i
$919$	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	$0.666781\pi$
$920$	−3.00725	−	0.0836556i	−0.0991461	−	0.00275804i
$921$	14.9932	−	23.6194i	0.494044	−	0.778286i
$922$	22.0163			0.725067
$923$	−42.6520	+	21.6464i	−1.40391	+	0.712500i
$924$	2.63128	−	2.41901i	0.0865627	−	0.0795797i
$925$	−50.6078	−	16.6262i	−1.66398	−	0.546665i
$926$	−20.7073	−	11.9553i	−0.680483	−	0.392877i
$927$	−13.9171	+	6.54490i	−0.457098	+	0.214963i
$928$	−7.25722	+	7.25722i	−0.238230	+	0.238230i
$929$	−47.5492	−	12.7408i	−1.56004	−	0.418011i	−0.627362	−	0.778728i	$-0.715865\pi$
$929$	−47.5492	−	12.7408i	−1.56004	−	0.418011i	−0.932675	+	0.360717i	$0.882532\pi$
$930$	18.3719	−	27.2373i	0.602438	−	0.893145i
$931$	3.82839	−	3.82839i	0.125470	−	0.125470i
$932$	1.93901	+	3.35846i	0.0635144	+	0.110010i
$933$	3.11587	+	13.9473i	0.102009	+	0.456615i
$934$	5.30563	+	19.8009i	0.173605	+	0.647904i
$935$	−25.3794	+	13.7263i	−0.829994	+	0.448899i
$936$	−12.2324	−	30.1325i	−0.399828	−	0.984910i
$937$		−	36.4014i		−	1.18918i	−0.804029	−	0.594590i	$-0.797314\pi$
$937$		−	36.4014i		−	1.18918i	0.804029	−	0.594590i	$-0.202686\pi$
$938$	26.4772	−	7.09455i	0.864512	−	0.231645i
$939$	−21.2902	+	4.75630i	−0.694781	+	0.155216i
$940$	1.61738	−	2.62969i	0.0527532	−	0.0857712i
$941$	0.425527	−	0.425527i	0.0138718	−	0.0138718i	−0.700137	−	0.714009i	$-0.746878\pi$
$941$	0.425527	−	0.425527i	0.0138718	−	0.0138718i	0.714009	+	0.700137i	$0.246878\pi$
$942$	42.7440	−	22.3396i	1.39267	−	0.727864i
$943$	−0.0972501	+	0.362942i	−0.00316690	+	0.0118190i
$944$	14.9374	+	14.9374i	0.486170	+	0.486170i
$945$	−26.3251	+	2.85348i	−0.856357	+	0.0928236i
$946$	−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
$951$	5.28877	−	8.33160i	0.171500	−	0.270171i
$952$	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	$0.648372\pi$
$954$	−24.6270	+	20.8015i	−0.797330	+	0.673474i
$955$	−36.1839	+	8.62459i	−1.17088	+	0.279085i
$956$	−1.80254	+	6.72716i	−0.0582983	+	0.217572i
$957$	−1.18844	+	28.2758i	−0.0384167	+	0.914026i
$958$	−4.95429	+	2.86036i	−0.160066	+	0.0924140i
$959$	−7.17507	+	12.4276i	−0.231695	+	0.401308i
$960$	34.1389	+	2.38733i	1.10183	+	0.0770508i
$961$			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
$965$	14.9073	+	0.414691i	0.479884	+	0.0133494i
$966$	2.18550	+	0.685177i	0.0703174	+	0.0220452i
$967$	13.6221	−	13.6221i	0.438057	−	0.438057i	−0.453300	−	0.891358i	$-0.649754\pi$
$967$	13.6221	−	13.6221i	0.438057	−	0.438057i	0.891358	+	0.453300i	$0.149754\pi$
$968$	2.27799	−	8.50156i	0.0732172	−	0.273250i
$969$	20.8968	−	10.9215i	0.671302	−	0.350848i
$970$	28.2198	+	8.40918i	0.906084	+	0.270002i
$971$	34.7333	−	20.0533i	1.11465	−	0.643541i	0.174617	−	0.984637i	$-0.444131\pi$
$971$	34.7333	−	20.0533i	1.11465	−	0.643541i	0.940029	+	0.341096i	$0.110798\pi$
$972$	−4.96134	+	0.257087i	−0.159135	+	0.00824606i
$973$	38.1973	−	10.2349i	1.22455	−	0.328117i
$974$	51.8966			1.66288
$975$	11.3500	+	29.0891i	0.363491	+	0.931598i
$976$	−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	$0.408773\pi$
$978$	−24.2767	+	5.42348i	−0.776282	+	0.173424i
$979$	−4.18922	+	2.41865i	−0.133888	+	0.0773004i
$980$	−1.23358	−	0.367594i	−0.0394054	−	0.0117424i
$981$	2.86166	+	1.03102i	0.0913658	+	0.0329180i
$982$	−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	$0.197633\pi$
$984$	1.30807	−	4.17232i	0.0416996	−	0.133009i
$985$	25.6816	+	0.714408i	0.818282	+	0.0227629i
$986$	−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
$990$	19.3160	−	15.4159i	0.613903	−	0.489951i
$991$	−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
$993$	27.9649	+	1.17537i	0.887438	+	0.0372992i
$994$	−10.1460	+	37.8652i	−0.321810	+	1.20101i
$995$	−0.633986	+	0.151114i	−0.0200987	+	0.00479062i
$996$	0.0280694	−	0.667837i	0.000889412	−	0.0211612i
$997$	−0.313621	+	0.181069i	−0.00993247	+	0.00573451i	−0.504958	−	0.863144i	$-0.668492\pi$
$997$	−0.313621	+	0.181069i	−0.00993247	+	0.00573451i	0.495026	+	0.868878i	$0.335159\pi$
$998$	−20.4856	−	11.8274i	−0.648460	−	0.374389i
$999$	44.0831	+	33.4854i	1.39473	+	1.05943i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.7	✓	96	5.4	even	2	inner
195.2.bh.a.59.8	yes	96	3.2	odd	2	inner
195.2.bh.a.59.17	yes	96	15.14	odd	2	inner
195.2.bh.a.59.18	yes	96	1.1	even	1	trivial
195.2.bh.a.119.7	yes	96	39.2	even	12	inner
195.2.bh.a.119.8	yes	96	65.54	odd	12	inner
195.2.bh.a.119.17	yes	96	13.2	odd	12	inner
195.2.bh.a.119.18	yes	96	195.119	even	12	inner
975.2.bo.h.176.7		96	5.3	odd	4
975.2.bo.h.176.8		96	15.2	even	4
975.2.bo.h.176.17		96	15.8	even	4
975.2.bo.h.176.18		96	5.2	odd	4
975.2.bo.h.626.7		96	195.158	odd	12
975.2.bo.h.626.8		96	65.2	even	12
975.2.bo.h.626.17		96	65.28	even	12
975.2.bo.h.626.18		96	195.2	odd	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} +(0.377636 + 1.69038i) q^{3} +(-0.276000 + 0.159349i) q^{4} +(2.14295 + 0.638573i) q^{5} +(1.04027 + 1.99042i) q^{6} +(0.589843 - 2.20132i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(-2.71478 + 1.27670i) q^{9} +(2.89828 + 0.0806242i) q^{10} +(-2.74441 + 0.735363i) q^{11} +(-0.373587 - 0.406369i) q^{12} +(2.68330 - 2.40830i) q^{13} -2.95504i q^{14} +(-0.270178 + 3.86355i) q^{15} +(-1.63052 + 2.82414i) q^{16} +(3.93313 - 2.27079i) q^{17} +(-2.97172 + 2.51010i) q^{18} +(0.775797 - 2.89531i) q^{19} +(-0.693209 + 0.165229i) q^{20} +(3.94382 + 0.165760i) q^{21} +(-3.19050 + 1.84204i) q^{22} +(0.387540 + 0.223746i) q^{23} +(-4.39649 - 2.79082i) 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} +(0.958209 + 4.92964i) q^{30} +(-4.62601 - 4.62601i) q^{31} +(0.461902 - 1.72384i) q^{32} +(-2.27943 - 4.36141i) q^{33} +(4.16405 - 4.16405i) q^{34} +(2.66971 - 4.34066i) q^{35} +(0.545839 - 0.784965i) q^{36} +(-10.2908 + 2.75740i) q^{37} -3.88664i q^{38} +(5.08425 + 3.62635i) q^{39} +(-5.91336 + 3.19822i) q^{40} +(0.217322 + 0.811058i) q^{41} +(4.99514 - 1.11593i) q^{42} +(2.38402 + 4.12924i) q^{43} +(0.640278 - 0.640278i) q^{44} +(-6.63290 + 1.00231i) q^{45} +(0.560470 + 0.150177i) q^{46} +(-3.06335 + 3.06335i) q^{47} +(-5.38962 - 1.68970i) q^{48} +(1.56426 + 0.903128i) q^{49} +(6.15937 + 2.02354i) q^{50} +(5.32380 + 5.79096i) q^{51} +(-0.356833 + 1.09227i) q^{52} +8.28713 q^{53} +(-5.36526 - 4.07544i) q^{54} +(-6.35072 - 0.176664i) q^{55} +(3.42592 + 5.93387i) q^{56} +(5.18715 + 0.218017i) q^{57} +(-7.20275 - 1.92997i) q^{58} +(1.67660 - 6.25715i) q^{59} +(-0.541082 - 1.10939i) q^{60} +(5.66303 + 9.80865i) q^{61} +(-7.34641 - 4.24145i) q^{62} +(1.20913 + 6.72917i) q^{63} -8.83615i q^{64} +(7.28805 - 3.44736i) q^{65} +(-4.31860 - 4.69755i) q^{66} +(2.40083 + 8.96003i) q^{67} +(-0.723695 + 1.25348i) q^{68} +(-0.231867 + 0.739585i) q^{69} +(1.88701 - 6.33249i) q^{70} +(-12.8138 - 3.43344i) q^{71} +(3.05728 - 8.48567i) q^{72} +(1.56653 + 1.56653i) q^{73} +(-11.9635 + 6.90712i) q^{74} +(-3.04614 + 8.10685i) q^{75} +(0.247244 + 0.922728i) q^{76} +6.47509i q^{77} +(7.58486 + 2.83562i) q^{78} -9.74173 q^{79} +(-5.29754 + 5.01078i) q^{80} +(5.74008 - 6.93192i) q^{81} +(0.544379 + 0.942892i) q^{82} +(0.856250 + 0.856250i) q^{83} +(-1.11491 + 0.582693i) q^{84} +(9.87856 - 2.35460i) q^{85} +(4.37167 + 4.37167i) q^{86} +(2.97979 - 9.50460i) 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} +(6.07278 - 9.56668i) q^{93} +(-2.80869 + 4.86480i) q^{94} +(3.51136 - 5.70910i) q^{95} +(3.08838 + 0.129806i) q^{96} +(9.80988 + 2.62855i) q^{97} +(2.26228 + 0.606176i) q^{98} +(6.51164 - 5.50014i) 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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