LMFDB - Embedded newform 261.2.x.a.101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.7
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.694410 + 1.59161i) q^{2} +(0.725664 - 1.57271i) q^{3} +(-0.690656 - 0.744350i) q^{4} +(-3.95207 - 0.595679i) q^{5} +(1.99922 + 2.24708i) q^{6} +(-0.402428 - 0.373398i) q^{7} +(-1.61379 + 0.564688i) q^{8} +(-1.94682 - 2.28252i) q^{9} +(3.69245 - 5.87649i) q^{10} +(2.35239 - 2.02439i) q^{11} +(-1.67183 + 0.546052i) q^{12} +(0.226431 - 0.332113i) q^{13} +(0.873753 - 0.381215i) q^{14} +(-3.80471 + 5.78319i) q^{15} +(0.373633 - 4.98578i) q^{16} +(-2.69557 - 2.69557i) q^{17} +(4.98476 - 1.51357i) q^{18} +(-5.36550 - 3.37137i) q^{19} +(2.28613 + 3.35314i) q^{20} +(-0.879274 + 0.361940i) q^{21} +(1.58851 + 5.14983i) q^{22} +(-6.37987 - 2.50392i) q^{23} +(-0.282977 + 2.94779i) q^{24} +(10.4862 + 3.23456i) q^{25} +(0.371356 + 0.591010i) q^{26} +(-5.00247 + 1.40544i) q^{27} +0.557437i q^{28} +(4.01043 + 3.59394i) q^{29} +(-6.56253 - 10.0715i) q^{30} +(-1.39623 + 1.03046i) q^{31} +(4.65275 + 2.45905i) q^{32} +(-1.47674 - 5.16865i) q^{33} +(6.16211 - 2.41845i) q^{34} +(1.36800 + 1.71542i) q^{35} +(-0.354407 + 3.02555i) q^{36} +(2.74830 + 7.85418i) q^{37} +(9.09175 - 6.19865i) q^{38} +(-0.358004 - 0.597111i) q^{39} +(6.71417 - 1.27039i) q^{40} +(3.40625 + 0.912701i) q^{41} +(0.0345121 - 1.65079i) q^{42} +(0.908650 - 1.23118i) q^{43} +(-3.13155 - 0.352841i) q^{44} +(6.33434 + 10.1804i) q^{45} +(8.41550 - 8.41550i) q^{46} +(6.35885 + 7.38911i) q^{47} +(-7.57005 - 4.20562i) q^{48} +(-0.500589 - 6.67989i) q^{49} +(-12.4299 + 14.4437i) q^{50} +(-6.19542 + 2.28326i) q^{51} +(-0.403594 + 0.0608320i) q^{52} +(-2.20154 - 1.75567i) q^{53} +(1.23686 - 8.93792i) q^{54} +(-10.5027 + 6.59928i) q^{55} +(0.860286 + 0.375339i) q^{56} +(-9.19573 + 5.99189i) q^{57} +(-8.50503 + 3.88735i) q^{58} +(-1.88972 + 1.09103i) q^{59} +(6.93247 - 1.16216i) q^{60} +(-7.36347 + 0.275521i) q^{61} +(-0.670535 - 2.93781i) q^{62} +(-0.0688326 + 1.64549i) q^{63} +(0.673195 - 0.536855i) q^{64} +(-1.09270 + 1.17765i) q^{65} +(9.25191 + 1.23878i) q^{66} +(-8.04795 + 0.603111i) q^{67} +(-0.144736 + 3.86816i) q^{68} +(-8.56758 + 8.21668i) q^{69} +(-3.68022 + 0.986111i) q^{70} +(12.9810 - 6.25130i) q^{71} +(4.43066 + 2.58414i) q^{72} +(-0.0593993 + 0.527184i) q^{73} +(-14.4092 - 1.07982i) q^{74} +(12.6965 - 14.1445i) q^{75} +(1.19624 + 6.32227i) q^{76} +(-1.70257 - 0.0637057i) q^{77} +(1.19897 - 0.155160i) q^{78} +(2.22446 - 11.7566i) q^{79} +(-4.44655 + 19.4816i) q^{80} +(-1.41976 + 8.88731i) q^{81} +(-3.81799 + 4.78761i) q^{82} +(2.07398 - 6.72367i) q^{83} +(0.876686 + 0.404512i) q^{84} +(9.04738 + 12.2588i) q^{85} +(1.32857 + 2.30115i) q^{86} +(8.56245 - 3.69924i) q^{87} +(-2.65310 + 4.59530i) q^{88} +(0.918803 - 0.103524i) q^{89} +(-20.6017 + 3.01242i) q^{90} +(-0.215132 + 0.0491025i) q^{91} +(2.54251 + 6.47821i) q^{92} +(0.607425 + 2.94363i) q^{93} +(-16.1762 + 4.98970i) q^{94} +(19.1966 + 16.5200i) q^{95} +(7.24370 - 5.53297i) q^{96} +(-4.29748 - 8.13124i) q^{97} +(10.9794 + 3.84185i) q^{98} +(-9.20039 - 1.42823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.694410	+	1.59161i	−0.491022	+	1.12543i	0.477977	+	0.878372i	$0.341370\pi$
$2$	−0.694410	+	1.59161i	−0.491022	+	1.12543i	−0.968999	+	0.247063i	$0.920535\pi$
$3$	0.725664	−	1.57271i	0.418962	−	0.908004i
$3$	0.725664	−	1.57271i	0.418962	−	0.908004i
$4$	−0.690656	−	0.744350i	−0.345328	−	0.372175i
$5$	−3.95207	−	0.595679i	−1.76742	−	0.266396i	−0.816838	−	0.576867i	$-0.804275\pi$
$5$	−3.95207	−	0.595679i	−1.76742	−	0.266396i	−0.950583	+	0.310472i	$0.899513\pi$
$6$	1.99922	+	2.24708i	0.816179	+	0.917365i
$7$	−0.402428	−	0.373398i	−0.152103	−	0.141131i	0.600451	−	0.799662i	$-0.294988\pi$
$7$	−0.402428	−	0.373398i	−0.152103	−	0.141131i	−0.752554	+	0.658530i	$0.771178\pi$
$8$	−1.61379	+	0.564688i	−0.570559	+	0.199647i
$9$	−1.94682	−	2.28252i	−0.648941	−	0.760839i
$10$	3.69245	−	5.87649i	1.16765	−	1.85831i
$11$	2.35239	−	2.02439i	0.709272	−	0.610378i	−0.221852	−	0.975080i	$-0.571210\pi$
$11$	2.35239	−	2.02439i	0.709272	−	0.610378i	0.931124	+	0.364703i	$0.118829\pi$
$12$	−1.67183	+	0.546052i	−0.482616	+	0.157632i
$13$	0.226431	−	0.332113i	0.0628005	−	0.0921114i	−0.793554	−	0.608500i	$-0.791772\pi$
$13$	0.226431	−	0.332113i	0.0628005	−	0.0921114i	0.856354	+	0.516389i	$0.172724\pi$
$14$	0.873753	−	0.381215i	0.233520	−	0.101884i
$15$	−3.80471	+	5.78319i	−0.982371	+	1.49321i
$16$	0.373633	−	4.98578i	0.0934082	−	1.24645i
$17$	−2.69557	−	2.69557i	−0.653771	−	0.653771i	0.300128	−	0.953899i	$-0.402971\pi$
$17$	−2.69557	−	2.69557i	−0.653771	−	0.653771i	−0.953899	+	0.300128i	$0.902971\pi$
$18$	4.98476	−	1.51357i	1.17492	−	0.356752i
$19$	−5.36550	−	3.37137i	−1.23093	−	0.773445i	−0.250083	−	0.968224i	$-0.580458\pi$
$19$	−5.36550	−	3.37137i	−1.23093	−	0.773445i	−0.980847	+	0.194780i	$0.937601\pi$
$20$	2.28613	+	3.35314i	0.511194	+	0.749784i
$21$	−0.879274	+	0.361940i	−0.191873	+	0.0789817i
$22$	1.58851	+	5.14983i	0.338672	+	1.09795i
$23$	−6.37987	−	2.50392i	−1.33030	−	0.522103i	−0.409558	−	0.912284i	$-0.634317\pi$
$23$	−6.37987	−	2.50392i	−1.33030	−	0.522103i	−0.920738	+	0.390182i	$0.872412\pi$
$24$	−0.282977	+	2.94779i	−0.0577625	+	0.601715i
$25$	10.4862	+	3.23456i	2.09724	+	0.646912i
$26$	0.371356	+	0.591010i	0.0728290	+	0.115907i
$27$	−5.00247	+	1.40544i	−0.962726	+	0.270478i
$28$			0.557437i			0.105346i
$29$	4.01043	+	3.59394i	0.744719	+	0.667379i
$29$	4.01043	+	3.59394i	0.744719	+	0.667379i
$30$	−6.56253	−	10.0715i	−1.19815	−	1.83880i
$31$	−1.39623	+	1.03046i	−0.250770	+	0.185077i	−0.711950	−	0.702230i	$-0.752188\pi$
$31$	−1.39623	+	1.03046i	−0.250770	+	0.185077i	0.461181	+	0.887306i	$0.347426\pi$
$32$	4.65275	+	2.45905i	0.822497	+	0.434702i
$33$	−1.47674	−	5.16865i	−0.257067	−	0.899746i
$34$	6.16211	−	2.41845i	1.05679	−	0.414761i
$35$	1.36800	+	1.71542i	0.231234	+	0.289958i
$36$	−0.354407	+	3.02555i	−0.0590678	+	0.504259i
$37$	2.74830	+	7.85418i	0.451817	+	1.29122i	0.914460	+	0.404675i	$0.132615\pi$
$37$	2.74830	+	7.85418i	0.451817	+	1.29122i	−0.462643	+	0.886545i	$0.653099\pi$
$38$	9.09175	−	6.19865i	1.47488	−	1.00555i
$39$	−0.358004	−	0.597111i	−0.0573265	−	0.0956143i
$40$	6.71417	−	1.27039i	1.06160	−	0.200866i
$41$	3.40625	+	0.912701i	0.531966	+	0.142540i	0.514796	−	0.857313i	$-0.327868\pi$
$41$	3.40625	+	0.912701i	0.531966	+	0.142540i	0.0171701	+	0.999853i	$0.494534\pi$
$42$	0.0345121	−	1.65079i	0.00532534	−	0.254723i
$43$	0.908650	−	1.23118i	0.138568	−	0.187753i	−0.729819	−	0.683641i	$-0.760395\pi$
$43$	0.908650	−	1.23118i	0.138568	−	0.187753i	0.868386	+	0.495888i	$0.165157\pi$
$44$	−3.13155	−	0.352841i	−0.472099	−	0.0531928i
$45$	6.33434	+	10.1804i	0.944267	+	1.51760i
$46$	8.41550	−	8.41550i	1.24080	−	1.24080i
$47$	6.35885	+	7.38911i	0.927533	+	1.07781i	0.996778	+	0.0802131i	$0.0255601\pi$
$47$	6.35885	+	7.38911i	0.927533	+	1.07781i	−0.0692449	+	0.997600i	$0.522059\pi$
$48$	−7.57005	−	4.20562i	−1.09264	−	0.607029i
$49$	−0.500589	−	6.67989i	−0.0715127	−	0.954271i
$50$	−12.4299	+	14.4437i	−1.75785	+	2.04265i
$51$	−6.19542	+	2.28326i	−0.867532	+	0.319721i
$52$	−0.403594	+	0.0608320i	−0.0559684	+	0.00843588i
$53$	−2.20154	−	1.75567i	−0.302405	−	0.241160i	0.460517	−	0.887651i	$-0.347664\pi$
$53$	−2.20154	−	1.75567i	−0.302405	−	0.241160i	−0.762921	+	0.646491i	$0.776236\pi$
$54$	1.23686	−	8.93792i	0.168315	−	1.21630i
$55$	−10.5027	+	6.59928i	−1.41618	+	0.889847i
$56$	0.860286	+	0.375339i	0.114961	+	0.0501568i
$57$	−9.19573	+	5.99189i	−1.21800	+	0.793645i
$58$	−8.50503	+	3.88735i	−1.11676	+	0.510434i
$59$	−1.88972	+	1.09103i	−0.246021	+	0.142040i	−0.617941	−	0.786224i	$-0.712033\pi$
$59$	−1.88972	+	1.09103i	−0.246021	+	0.142040i	0.371920	+	0.928265i	$0.378700\pi$
$60$	6.93247	−	1.16216i	0.894978	−	0.150035i
$61$	−7.36347	+	0.275521i	−0.942795	+	0.0352769i	−0.504367	−	0.863489i	$-0.668274\pi$
$61$	−7.36347	+	0.275521i	−0.942795	+	0.0352769i	−0.438428	+	0.898766i	$0.644465\pi$
$62$	−0.670535	−	2.93781i	−0.0851580	−	0.373102i
$63$	−0.0688326	+	1.64549i	−0.00867209	+	0.207312i
$64$	0.673195	−	0.536855i	0.0841494	−	0.0671069i
$65$	−1.09270	+	1.17765i	−0.135533	+	0.146070i
$66$	9.25191	+	1.23878i	1.13883	+	0.152484i
$67$	−8.04795	+	0.603111i	−0.983214	+	0.0736817i	−0.556625	−	0.830764i	$-0.687904\pi$
$67$	−8.04795	+	0.603111i	−0.983214	+	0.0736817i	−0.426589	+	0.904446i	$0.640285\pi$
$68$	−0.144736	+	3.86816i	−0.0175518	+	0.469083i
$69$	−8.56758	+	8.21668i	−1.03141	+	0.989172i
$70$	−3.68022	+	0.986111i	−0.439870	+	0.117863i
$71$	12.9810	−	6.25130i	1.54056	−	0.741892i	0.545213	−	0.838297i	$-0.316449\pi$
$71$	12.9810	−	6.25130i	1.54056	−	0.741892i	0.995342	+	0.0964048i	$0.0307343\pi$
$72$	4.43066	+	2.58414i	0.522159	+	0.304544i
$73$	−0.0593993	+	0.527184i	−0.00695217	+	0.0617022i	−0.996709	−	0.0810594i	$-0.974170\pi$
$73$	−0.0593993	+	0.527184i	−0.00695217	+	0.0617022i	0.989757	+	0.142762i	$0.0455982\pi$
$74$	−14.4092	−	1.07982i	−1.67504	−	0.125527i
$75$	12.6965	−	14.1445i	1.46606	−	1.63327i
$76$	1.19624	+	6.32227i	0.137218	+	0.725214i
$77$	−1.70257	−	0.0637057i	−0.194026	−	0.00725994i
$78$	1.19897	−	0.155160i	0.135756	−	0.0175684i
$79$	2.22446	−	11.7566i	0.250271	−	1.32272i	−0.601530	−	0.798851i	$-0.705442\pi$
$79$	2.22446	−	11.7566i	0.250271	−	1.32272i	0.851801	−	0.523866i	$-0.175511\pi$
$80$	−4.44655	+	19.4816i	−0.497139	+	2.17811i
$81$	−1.41976	+	8.88731i	−0.157752	+	0.987479i
$82$	−3.81799	+	4.78761i	−0.421627	+	0.528703i
$83$	2.07398	−	6.72367i	0.227649	−	0.738019i	−0.767624	−	0.640900i	$-0.778561\pi$
$83$	2.07398	−	6.72367i	0.227649	−	0.738019i	0.995273	−	0.0971187i	$-0.0309627\pi$
$84$	0.876686	+	0.404512i	0.0956543	+	0.0441359i
$85$	9.04738	+	12.2588i	0.981327	+	1.32965i
$86$	1.32857	+	2.30115i	0.143264	+	0.248140i
$87$	8.56245	−	3.69924i	0.917991	−	0.396600i
$88$	−2.65310	+	4.59530i	−0.282821	+	0.489861i
$89$	0.918803	−	0.103524i	0.0973929	−	0.0109735i	−0.0631335	−	0.998005i	$-0.520109\pi$
$89$	0.918803	−	0.103524i	0.0973929	−	0.0109735i	0.160526	+	0.987032i	$0.448681\pi$
$90$	−20.6017	+	3.01242i	−2.17161	+	0.317537i
$91$	−0.215132	+	0.0491025i	−0.0225520	+	0.00514734i
$92$	2.54251	+	6.47821i	0.265075	+	0.675400i
$93$	0.607425	+	2.94363i	0.0629870	+	0.305240i
$94$	−16.1762	+	4.98970i	−1.66845	+	0.514648i
$95$	19.1966	+	16.5200i	1.96953	+	1.69492i
$96$	7.24370	−	5.53297i	0.739307	−	0.564706i
$97$	−4.29748	−	8.13124i	−0.436343	−	0.825602i	0.563657	−	0.826009i	$-0.309394\pi$
$97$	−4.29748	−	8.13124i	−0.436343	−	0.825602i	−1.00000		0.000407346i	$0.999870\pi$
$98$	10.9794	+	3.84185i	1.10908	+	0.388085i
$99$	−9.20039	−	1.42823i	−0.924674	−	0.143542i
$100$	−4.83470	−	10.0394i	−0.483470	−	1.00394i
$101$	−11.2612	−	8.31116i	−1.12053	−	0.826992i	−0.134070	−	0.990972i	$-0.542805\pi$
$101$	−11.2612	−	8.31116i	−1.12053	−	0.826992i	−0.986464	+	0.163980i	$0.947567\pi$
$102$	0.668107	−	11.4462i	0.0661525	−	1.13334i
$103$	−4.20664	−	2.86804i	−0.414493	−	0.282596i	0.338065	−	0.941123i	$-0.390228\pi$
$103$	−4.20664	−	2.86804i	−0.414493	−	0.282596i	−0.752558	+	0.658527i	$0.771180\pi$
$104$	−0.177870	+	0.663821i	−0.0174416	+	0.0650930i
$105$	3.69056	−	0.906646i	0.360161	−	0.0884796i
$106$	4.32311	−	2.28483i	0.419897	−	0.221922i
$107$	−1.02857	+	2.13585i	−0.0994356	+	0.206480i	−0.944752	−	0.327786i	$-0.893698\pi$
$107$	−1.02857	+	2.13585i	−0.0994356	+	0.206480i	0.845316	+	0.534266i	$0.179412\pi$
$108$	4.50113	+	2.75291i	0.433122	+	0.264899i
$109$	0.343427	+	0.0783850i	0.0328943	+	0.00750792i	0.238936	−	0.971035i	$-0.423201\pi$
$109$	0.343427	+	0.0783850i	0.0328943	+	0.00750792i	−0.206042	+	0.978543i	$0.566058\pi$
$110$	−3.21027	−	21.2988i	−0.306087	−	2.03076i
$111$	14.3467	+	1.37723i	1.36173	+	0.130721i
$112$	−2.01204	+	1.86690i	−0.190120	+	0.176406i
$113$	9.15948	−	17.3306i	0.861652	−	1.63032i	0.0885239	−	0.996074i	$-0.471785\pi$
$113$	9.15948	−	17.3306i	0.861652	−	1.63032i	0.773128	−	0.634250i	$-0.218691\pi$
$114$	−3.15111	−	18.7968i	−0.295128	−	1.76048i
$115$	23.7222	+	13.6960i	2.21211	+	1.27716i
$116$	−0.0946761	−	5.46735i	−0.00879045	−	0.507630i
$117$	−1.19887	+	0.129733i	−0.110836	+	0.0119938i
$118$	−0.424250	−	3.76532i	−0.0390553	−	0.346626i
$119$	0.0782506	+	2.09129i	0.00717322	+	0.191708i
$120$	2.87428	−	11.4813i	0.262385	−	1.04810i
$121$	−0.203905	+	1.35282i	−0.0185368	+	0.122984i
$122$	4.67474	−	11.9111i	0.423232	−	1.07838i
$123$	3.90720	−	4.69472i	0.352301	−	0.423308i
$124$	1.73134	+	0.327587i	0.155479	+	0.0294182i
$125$	−21.5108	−	10.3591i	−1.92399	−	0.926543i
$126$	−2.57117	−	1.25220i	−0.229058	−	0.111555i
$127$	1.48514	−	4.24429i	0.131785	−	0.376620i	−0.859016	−	0.511949i	$-0.828924\pi$
$127$	1.48514	−	4.24429i	0.131785	−	0.376620i	0.990801	+	0.135329i	$0.0432093\pi$
$128$	3.11111	+	11.6108i	0.274986	+	1.02626i
$129$	−1.27691	−	2.32246i	−0.112425	−	0.204481i
$130$	−1.11557	−	2.55693i	−0.0978424	−	0.224257i
$131$	−6.92803	−	15.8792i	−0.605305	−	1.38737i	−0.901723	−	0.432315i	$-0.857697\pi$
$131$	−6.92803	−	15.8792i	−0.605305	−	1.38737i	0.296418	−	0.955058i	$-0.404208\pi$
$132$	−2.82737	+	4.66897i	−0.246091	+	0.406382i
$133$	0.900363	+	3.36020i	0.0780714	+	0.291366i
$134$	4.62867	−	13.2280i	0.399856	−	1.14272i
$135$	20.6073	−	2.57455i	1.77360	−	0.221582i
$136$	5.87222	+	2.82791i	0.503539	+	0.242492i
$137$	−2.60476	−	0.492848i	−0.222540	−	0.0421068i	0.0734457	−	0.997299i	$-0.476600\pi$
$137$	−2.60476	−	0.492848i	−0.222540	−	0.0421068i	−0.295986	+	0.955192i	$0.595648\pi$
$138$	−7.12829	−	19.3419i	−0.606801	−	1.64650i
$139$	−0.779990	+	1.98738i	−0.0661579	+	0.168568i	−0.960129	−	0.279557i	$-0.909813\pi$
$139$	−0.779990	+	1.98738i	−0.0661579	+	0.168568i	0.893971	+	0.448124i	$0.147908\pi$
$140$	0.332054	−	2.20303i	0.0280637	−	0.186190i
$141$	16.2353	−	4.63859i	1.36726	−	0.390640i
$142$	0.935491	+	25.0015i	0.0785046	+	2.09808i
$143$	−0.139674	−	1.23964i	−0.0116801	−	0.103664i
$144$	−12.1075	+	8.85361i	−1.00896	+	0.737801i
$145$	−13.7087	−	16.5925i	−1.13844	−	1.37793i
$146$	−0.797821	−	0.460622i	−0.0660281	−	0.0381214i
$147$	−10.8688	−	4.06008i	−0.896442	−	0.334870i
$148$	3.94814	−	7.47024i	0.324535	−	0.614050i
$149$	1.59177	−	1.47694i	0.130403	−	0.120996i	−0.612276	−	0.790644i	$-0.709746\pi$
$149$	1.59177	−	1.47694i	0.130403	−	0.120996i	0.742678	+	0.669649i	$0.233555\pi$
$150$	13.6959	+	30.0298i	1.11827	+	2.45193i
$151$	−0.145391	−	0.964603i	−0.0118317	−	0.0784983i	0.982136	−	0.188174i	$-0.0602569\pi$
$151$	−0.145391	−	0.964603i	−0.0118317	−	0.0784983i	−0.993967	+	0.109676i	$0.965019\pi$
$152$	10.5625	+	2.41083i	0.856735	+	0.195544i
$153$	−0.904886	+	11.4005i	−0.0731557	+	0.921673i
$154$	1.28368	−	2.66558i	0.103442	−	0.214799i
$155$	6.13182	−	3.24076i	0.492519	−	0.260304i
$156$	−0.197203	+	0.678879i	−0.0157888	+	0.0543538i
$157$	−0.982158	+	3.66546i	−0.0783848	+	0.292536i	−0.993979	−	0.109566i	$-0.965054\pi$
$157$	−0.982158	+	3.66546i	−0.0783848	+	0.292536i	0.915595	+	0.402102i	$0.131720\pi$
$158$	17.1671	+	11.7043i	1.36574	+	0.931147i
$159$	−4.35874	+	2.18835i	−0.345670	+	0.173548i
$160$	−16.9232	−	12.4899i	−1.33790	−	0.987412i
$161$	1.63248	+	3.38988i	0.128657	+	0.267160i
$162$	−13.1592	−	8.43114i	−1.03388	−	0.662413i
$163$	−0.141584	−	0.0495424i	−0.0110897	−	0.00388046i	0.324729	−	0.945807i	$-0.394727\pi$
$163$	−0.141584	−	0.0495424i	−0.0110897	−	0.00388046i	−0.335818	+	0.941927i	$0.609013\pi$
$164$	−1.67318	−	3.16580i	−0.130653	−	0.247208i
$165$	2.75731	+	21.3065i	0.214656	+	1.65871i
$166$	9.26124	+	7.96994i	0.718812	+	0.618588i
$167$	−13.7644	+	4.24577i	−1.06512	+	0.328547i	−0.777296	−	0.629135i	$-0.783409\pi$
$167$	−13.7644	+	4.24577i	−1.06512	+	0.328547i	−0.287828	+	0.957682i	$0.592933\pi$
$168$	1.21458	−	1.08061i	0.0937067	−	0.0833708i
$169$	4.69041	+	11.9510i	0.360800	+	0.919304i
$170$	−25.7937	+	5.88725i	−1.97829	+	0.451531i
$171$	2.75048	+	18.8103i	0.210334	+	1.43846i
$172$	−1.54399	+	0.173966i	−0.117728	+	0.0132648i
$173$	−4.19462	+	7.26529i	−0.318911	+	0.552370i	−0.980261	−	0.197707i	$-0.936650\pi$
$173$	−4.19462	+	7.26529i	−0.318911	+	0.552370i	0.661350	+	0.750077i	$0.269984\pi$
$174$	−0.0581217	+	16.1968i	−0.00440620	+	1.22788i
$175$	−3.01215	−	5.21720i	−0.227697	−	0.394383i
$176$	−9.21426	−	12.4849i	−0.694551	−	0.941083i
$177$	0.344571	+	3.76371i	0.0258995	+	0.282898i
$178$	−0.473256	+	1.53426i	−0.0354721	+	0.114998i
$179$	11.0513	−	13.8580i	0.826017	−	1.03579i	−0.172692	−	0.984976i	$-0.555246\pi$
$179$	11.0513	−	13.8580i	0.826017	−	1.03579i	0.998708	−	0.0508160i	$-0.0161822\pi$
$180$	3.20290	−	11.7461i	0.238730	−	0.875502i
$181$	4.32644	−	18.9554i	0.321582	−	1.40894i	−0.513156	−	0.858295i	$-0.671524\pi$
$181$	4.32644	−	18.9554i	0.321582	−	1.40894i	0.834738	−	0.550647i	$-0.185619\pi$
$182$	0.0712382	−	0.376503i	0.00528053	−	0.0279083i
$183$	−4.91009	+	11.7805i	−0.362964	+	0.870841i
$184$	11.7097	+	0.438145i	0.863249	+	0.0323005i
$185$	−6.18290	−	32.6774i	−0.454576	−	2.40249i
$186$	−5.10689	−	1.07730i	−0.374456	−	0.0789918i
$187$	−11.7979	−	0.884131i	−0.862749	−	0.0646541i
$188$	1.10831	−	9.83655i	0.0808320	−	0.717404i
$189$	2.53792	+	1.30233i	0.184607	+	0.0947303i
$190$	−39.6236	+	19.0817i	−2.87460	+	1.38434i
$191$	16.6622	−	4.46461i	1.20563	−	0.323048i	0.400585	−	0.916260i	$-0.368807\pi$
$191$	16.6622	−	4.46461i	1.20563	−	0.323048i	0.805046	+	0.593212i	$0.202140\pi$
$192$	−0.355803	−	1.44832i	−0.0256779	−	0.104523i
$193$	−0.0781564	+	2.08877i	−0.00562582	+	0.150353i	0.993656	+	0.112462i	$0.0358736\pi$
$193$	−0.0781564	+	2.08877i	−0.00562582	+	0.150353i	−0.999282	+	0.0378914i	$0.987936\pi$
$194$	15.9259	−	1.19348i	1.14342	−	0.0856871i
$195$	1.05917	+	2.57308i	0.0758487	+	0.184262i
$196$	−4.62645	+	4.98612i	−0.330461	+	0.356152i
$197$	−11.5562	+	9.21574i	−0.823343	+	0.656595i	−0.941729	−	0.336373i	$-0.890800\pi$
$197$	−11.5562	+	9.21574i	−0.823343	+	0.656595i	0.118385	+	0.992968i	$0.462228\pi$
$198$	8.66203	−	13.6516i	0.615583	−	0.970178i
$199$	3.86265	+	16.9234i	0.273816	+	1.19967i	0.905468	+	0.424415i	$0.139520\pi$
$199$	3.86265	+	16.9234i	0.273816	+	1.19967i	−0.631652	+	0.775252i	$0.717623\pi$
$200$	−18.7490	+	0.701537i	−1.32575	+	0.0496061i
$201$	−4.89159	+	13.0947i	−0.345026	+	0.923631i
$202$	21.0480	−	12.1521i	1.48093	−	0.855017i
$203$	−0.271936	−	2.94379i	−0.0190862	−	0.206614i
$204$	5.97845	+	3.03461i	0.418575	+	0.212465i
$205$	−12.9181	−	5.63609i	−0.902236	−	0.393642i
$206$	7.48592	−	4.70372i	0.521569	−	0.327723i
$207$	6.70525	+	19.4368i	0.466047	+	1.35095i
$208$	−1.57124	−	1.25302i	−0.108946	−	0.0868814i
$209$	−19.4467	+	2.93112i	−1.34516	+	0.202750i
$210$	−1.11974	+	6.50349i	−0.0772692	+	0.448784i
$211$	−0.661228	+	0.768361i	−0.0455208	+	0.0528961i	−0.780271	−	0.625442i	$-0.784919\pi$
$211$	−0.661228	+	0.768361i	−0.0455208	+	0.0528961i	0.734750	+	0.678338i	$0.237300\pi$
$212$	0.213674	+	2.85128i	0.0146752	+	0.195827i
$213$	−0.411653	−	24.9516i	−0.0282060	−	1.70966i
$214$	−2.68518	−	3.12023i	−0.183555	−	0.213295i
$215$	−4.32444	+	4.32444i	−0.294924	+	0.294924i
$216$	7.27928	−	5.09292i	0.495292	−	0.346529i
$217$	0.946654	+	0.106662i	0.0642630	+	0.00724071i
$218$	−0.363237	+	0.492169i	−0.0246015	+	0.0333339i
$219$	0.786002	+	0.475976i	0.0531131	+	0.0321635i
$220$	12.1659	+	3.25985i	0.820227	+	0.219779i
$221$	−1.50559	+	0.284873i	−0.101277	+	0.0191626i
$222$	−12.1545	+	21.8779i	−0.815756	+	1.46835i
$223$	12.9373	−	8.82049i	0.866344	−	0.590664i	−0.0465241	−	0.998917i	$-0.514814\pi$
$223$	12.9373	−	8.82049i	0.866344	−	0.590664i	0.912869	+	0.408253i	$0.133862\pi$
$224$	−0.954190	−	2.72692i	−0.0637545	−	0.182200i
$225$	−13.0318	−	30.2320i	−0.868787	−	2.01547i
$226$	21.2230	+	26.6128i	1.41173	+	1.77026i
$227$	−11.7593	+	4.61520i	−0.780494	+	0.306321i	−0.721933	−	0.691962i	$-0.756746\pi$
$227$	−11.7593	+	4.61520i	−0.780494	+	0.306321i	−0.0585607	+	0.998284i	$0.518651\pi$
$228$	10.8112	+	2.70651i	0.715986	+	0.179243i
$229$	−6.78100	−	3.58386i	−0.448101	−	0.236828i	0.227965	−	0.973669i	$-0.426793\pi$
$229$	−6.78100	−	3.58386i	−0.448101	−	0.236828i	−0.676066	+	0.736841i	$0.736317\pi$
$230$	−38.2716	+	28.2457i	−2.52355	+	1.86247i
$231$	−1.33569	+	2.63142i	−0.0878817	+	0.173135i
$232$	−8.50143	−	3.53521i	−0.558146	−	0.232098i
$233$			25.2517i			1.65429i	0.561985	+	0.827147i	$0.310038\pi$
$233$			25.2517i			1.65429i	−0.561985	+	0.827147i	$0.689962\pi$
$234$	0.626026	−	1.99822i	0.0409246	−	0.130628i
$235$	−20.7291	−	32.9901i	−1.35222	−	2.15204i
$236$	2.11726	+	0.653088i	0.137822	+	0.0425124i
$237$	−16.8754	−	12.0297i	−1.09618	−	0.781416i
$238$	−3.38285	−	1.32767i	−0.219278	−	0.0860601i
$239$	6.22294	+	20.1743i	0.402529	+	1.30497i	0.899394	+	0.437138i	$0.144008\pi$
$239$	6.22294	+	20.1743i	0.402529	+	1.30497i	−0.496866	+	0.867827i	$0.665516\pi$
$240$	27.4122	+	21.1302i	1.76945	+	1.36395i
$241$	13.3590	+	19.5940i	0.860528	+	1.26216i	0.963562	+	0.267485i	$0.0861926\pi$
$241$	13.3590	+	19.5940i	0.860528	+	1.26216i	−0.103034	+	0.994678i	$0.532855\pi$
$242$	−2.01157	−	1.26395i	−0.129308	−	0.0812498i
$243$	12.9469	+	8.68208i	0.830542	+	0.556956i
$244$	5.29071	+	5.29071i	0.338703	+	0.338703i
$245$	−2.00071	+	26.6976i	−0.127821	+	1.70565i
$246$	4.75893	+	9.47878i	0.303419	+	0.604345i
$247$	−2.33459	+	1.01857i	−0.148546	+	0.0648100i
$248$	1.67132	−	2.45138i	0.106129	−	0.155663i
$249$	−9.06937	−	8.14089i	−0.574748	−	0.515908i
$250$	31.4249	−	27.0433i	1.98748	−	1.71037i
$251$	10.9893	−	17.4894i	0.693642	−	1.10392i	−0.295269	−	0.955414i	$-0.595409\pi$
$251$	10.9893	−	17.4894i	0.693642	−	1.10392i	0.988911	−	0.148510i	$-0.0474478\pi$
$252$	1.27236	−	1.08523i	0.0801511	−	0.0683632i
$253$	−20.0768	+	7.02519i	−1.26222	+	0.441670i
$254$	5.72394	+	5.31104i	0.359152	+	0.333244i
$255$	25.8448	−	5.33314i	1.61847	−	0.333974i
$256$	−18.9374	−	2.85435i	−1.18359	−	0.178397i
$257$	−1.40423	−	1.51340i	−0.0875937	−	0.0944035i	0.687734	−	0.725963i	$-0.258606\pi$
$257$	−1.40423	−	1.51340i	−0.0875937	−	0.0944035i	−0.775327	+	0.631559i	$0.782415\pi$
$258$	4.58314	−	0.419591i	0.285334	−	0.0261226i
$259$	1.82675	−	4.18695i	0.113509	−	0.260165i
$260$	1.63127			0.101167
$261$	0.395638	−	16.1506i	0.0244893	−	0.999700i
$262$	30.0843			1.85862
$263$	3.73800	−	8.56758i	0.230495	−	0.528299i	−0.762426	−	0.647075i	$-0.775992\pi$
$263$	3.73800	−	8.56758i	0.230495	−	0.528299i	0.992921	+	0.118775i	$0.0378969\pi$
$264$	5.30181	+	7.50720i	0.326304	+	0.462036i
$265$	7.65483	+	8.24995i	0.470232	+	0.506790i
$266$	−5.97334	−	0.900336i	−0.366249	−	0.0552031i
$267$	0.503929	−	1.52013i	0.0308400	−	0.0930306i
$268$	6.00729	+	5.57395i	0.366954	+	0.340483i
$269$	16.5693	−	5.79784i	1.01025	−	0.353501i	0.226119	−	0.974100i	$-0.427396\pi$
$269$	16.5693	−	5.79784i	1.01025	−	0.353501i	0.784128	+	0.620599i	$0.213111\pi$
$270$	−10.2123	+	34.5865i	−0.621500	+	2.10487i
$271$	4.13972	−	6.58833i	0.251470	−	0.400213i	−0.697004	−	0.717067i	$-0.745484\pi$
$271$	4.13972	−	6.58833i	0.251470	−	0.400213i	0.948474	+	0.316855i	$0.102627\pi$
$272$	−14.4467	+	12.4324i	−0.875958	+	0.753823i
$273$	−0.0788898	+	0.373972i	−0.00477463	+	0.0226338i
$274$	2.59319	−	3.80352i	0.156661	−	0.229779i
$275$	31.2156	−	13.6192i	1.88237	−	0.821270i
$276$	12.0333	+	0.702379i	0.724322	+	0.0422782i
$277$	−0.587103	+	7.83435i	−0.0352756	+	0.470721i	0.951393	+	0.307979i	$0.0996527\pi$
$277$	−0.587103	+	7.83435i	−0.0352756	+	0.470721i	−0.986669	+	0.162741i	$0.947966\pi$
$278$	−2.62150	−	2.62150i	−0.157227	−	0.157227i
$279$	5.07025	+	1.18078i	0.303548	+	0.0706917i
$280$	−3.17633	−	1.99582i	−0.189822	−	0.119273i
$281$	−14.8554	−	21.7889i	−0.886200	−	1.29982i	−0.953286	−	0.302069i	$-0.902323\pi$
$281$	−14.8554	−	21.7889i	−0.886200	−	1.29982i	0.0670862	−	0.997747i	$-0.478630\pi$
$282$	−3.89115	+	29.0613i	−0.231715	+	1.73057i
$283$	−1.28092	−	4.15263i	−0.0761427	−	0.246848i	0.909497	−	0.415710i	$-0.136467\pi$
$283$	−1.28092	−	4.15263i	−0.0761427	−	0.246848i	−0.985640	+	0.168862i	$0.945991\pi$
$284$	−13.6185	−	5.34488i	−0.808111	−	0.317160i
$285$	39.9114	−	18.2027i	2.36415	−	1.07823i
$286$	2.07001	+	0.638514i	0.122402	+	0.0377561i
$287$	−1.02997	−	1.63918i	−0.0607970	−	0.0967579i
$288$	−3.44525	−	15.4073i	−0.203013	−	0.907884i
$289$		−	2.46783i		−	0.145167i
$290$	35.9281	−	10.2968i	2.10977	−	0.604651i
$291$	−15.9066	+	0.858140i	−0.932461	+	0.0503051i
$292$	0.433434	−	0.319889i	0.0253648	−	0.0187201i
$293$	18.7446	+	9.90681i	1.09507	+	0.578762i	0.914412	−	0.404784i	$-0.132653\pi$
$293$	18.7446	+	9.90681i	1.09507	+	0.578762i	0.180659	+	0.983546i	$0.442177\pi$
$294$	14.0094	−	14.4795i	0.817047	−	0.844459i
$295$	8.11823	−	3.18617i	0.472662	−	0.185506i
$296$	−8.87033	−	11.1230i	−0.515577	−	0.646513i
$297$	−8.92259	+	13.4331i	−0.517741	+	0.779469i
$298$	1.24537	+	3.55907i	0.0721424	+	0.206171i
$299$	−2.27618	+	1.55187i	−0.131635	+	0.0897471i
$300$	−19.2974	+	0.318369i	−1.11413	+	0.0183810i
$301$	−0.825386	+	0.156171i	−0.0475744	+	0.00900157i
$302$	1.63623	+	0.438426i	0.0941544	+	0.0252286i
$303$	−21.2429	+	11.6795i	−1.22037	+	0.670970i
$304$	−18.8136	+	25.4916i	−1.07904	+	1.46204i
$305$	29.2651	+	3.29738i	1.67571	+	0.188808i
$306$	−17.5167	−	9.35682i	−1.00136	−	0.534894i
$307$	1.42348	−	1.42348i	0.0812425	−	0.0812425i	−0.665318	−	0.746560i	$-0.731704\pi$
$307$	1.42348	−	1.42348i	0.0812425	−	0.0812425i	0.746560	+	0.665318i	$0.231704\pi$
$308$	1.12847	+	1.31131i	0.0643007	+	0.0747188i
$309$	−7.56320	+	4.53459i	−0.430255	+	0.257964i
$310$	0.900014	+	12.0098i	0.0511173	+	0.682113i
$311$	3.69667	−	4.29561i	0.209619	−	0.243581i	−0.643314	−	0.765603i	$-0.722441\pi$
$311$	3.69667	−	4.29561i	0.209619	−	0.243581i	0.852932	+	0.522021i	$0.174822\pi$
$312$	0.914923	+	0.761449i	0.0517973	+	0.0431086i
$313$	−30.1123	+	4.53870i	−1.70205	+	0.256542i	−0.926919	−	0.375262i	$-0.877553\pi$
$313$	−30.1123	+	4.53870i	−1.70205	+	0.256542i	−0.775128	+	0.631804i	$0.782315\pi$
$314$	−5.15195	−	4.10854i	−0.290741	−	0.231859i
$315$	1.25221	−	6.46209i	0.0705543	−	0.364097i
$316$	−10.2873	+	6.46396i	−0.578708	+	0.363626i
$317$	−31.7787	−	13.8649i	−1.78487	−	0.778730i	−0.983585	−	0.180444i	$-0.942246\pi$
$317$	−31.7787	−	13.8649i	−1.78487	−	0.778730i	−0.801283	−	0.598286i	$-0.795849\pi$
$318$	−0.456244	−	8.45700i	−0.0255849	−	0.474245i
$319$	16.7096	+	0.335658i	0.935561	+	0.0187933i
$320$	−2.98031	+	1.72068i	−0.166604	+	0.0961890i
$321$	2.61267	+	3.16755i	0.145825	+	0.176795i
$322$	−6.52896	+	0.244297i	−0.363845	+	0.0136141i
$323$	5.37532	+	23.5508i	0.299091	+	1.31040i
$324$	7.59584	−	5.08127i	0.421991	−	0.282293i
$325$	3.44863	−	2.75019i	0.191295	−	0.152553i
$326$	0.177169	−	0.190943i	0.00981250	−	0.0105754i
$327$	0.372489	−	0.483229i	0.0205987	−	0.0267226i
$328$	−6.01234	+	0.450563i	−0.331976	+	0.0248782i
$329$	0.200107	−	5.34797i	0.0110322	−	0.294843i
$330$	−35.8263	−	10.4069i	−1.97217	−	0.572882i
$331$	−1.35303	+	0.362543i	−0.0743692	+	0.0199272i	−0.295812	−	0.955246i	$-0.595590\pi$
$331$	−1.35303	+	0.362543i	−0.0743692	+	0.0199272i	0.221443	+	0.975173i	$0.428923\pi$
$332$	−6.43718	+	3.09998i	−0.353286	+	0.170134i
$333$	12.5769	−	21.5637i	0.689207	−	1.18169i
$334$	2.80058	−	24.8559i	0.153241	−	1.36005i
$335$	32.1653	+	2.41046i	1.75738	+	0.131697i
$336$	1.47603	+	4.51910i	0.0805238	+	0.246537i
$337$	−2.56085	−	13.5344i	−0.139498	−	0.737266i	−0.980544	−	0.196301i	$-0.937107\pi$
$337$	−2.56085	−	13.5344i	−0.139498	−	0.737266i	0.841045	−	0.540965i	$-0.181941\pi$
$338$	−22.2783	−	0.833594i	−1.21178	−	0.0453415i
$339$	−20.6092	−	26.9814i	−1.11934	−	1.46543i
$340$	2.87619	−	15.2010i	0.155983	−	0.824391i
$341$	−1.19841	+	5.25056i	−0.0648973	+	0.284334i
$342$	−31.8485	−	8.68439i	−1.72217	−	0.469598i
$343$	−4.68878	+	5.87954i	−0.253170	+	0.317465i
$344$	−0.771135	+	2.49996i	−0.0415768	+	0.134789i
$345$	38.7542	−	27.3694i	2.08646	−	1.47352i
$346$	−8.65069	−	11.7213i	−0.465064	−	0.630139i
$347$	−3.36991	−	5.83686i	−0.180907	−	0.313339i	0.761283	−	0.648420i	$-0.224570\pi$
$347$	−3.36991	−	5.83686i	−0.180907	−	0.313339i	−0.942189	+	0.335081i	$0.891236\pi$
$348$	−8.66724	−	3.81856i	−0.464613	−	0.204696i
$349$	8.53408	−	14.7815i	0.456819	−	0.791233i	−0.541972	−	0.840397i	$-0.682322\pi$
$349$	8.53408	−	14.7815i	0.456819	−	0.791233i	0.998791	+	0.0491632i	$0.0156554\pi$
$350$	10.3954	−	1.17128i	0.555657	−	0.0626075i
$351$	−0.665947	+	1.97962i	−0.0355456	+	0.105664i
$352$	15.9231	−	3.63435i	0.848706	−	0.193712i
$353$	5.89936	+	15.0313i	0.313991	+	0.800037i	0.997538	+	0.0701298i	$0.0223413\pi$
$353$	5.89936	+	15.0313i	0.313991	+	0.800037i	−0.683547	+	0.729907i	$0.739563\pi$
$354$	−6.22961	−	2.06514i	−0.331100	−	0.109761i
$355$	−55.0254	+	16.9731i	−2.92045	+	0.900839i
$356$	−0.711635	−	0.612412i	−0.0377166	−	0.0324578i
$357$	3.34578	+	1.39451i	0.177077	+	0.0738053i
$358$	14.3822	+	27.2125i	0.760124	+	1.43822i
$359$	26.6079	+	9.31051i	1.40431	+	0.491390i	0.922878	−	0.385092i	$-0.125830\pi$
$359$	26.6079	+	9.31051i	1.40431	+	0.491390i	0.481434	+	0.876482i	$0.340116\pi$
$360$	−15.9710	−	12.8520i	−0.841745	−	0.677359i
$361$	9.17869	+	19.0597i	0.483089	+	1.00314i
$362$	27.1652	+	20.0488i	1.42777	+	1.05374i
$363$	1.97963	+	1.30238i	0.103904	+	0.0683571i
$364$	0.185132	+	0.126221i	0.00970355	+	0.00661577i
$365$	0.548783	−	2.04809i	0.0287246	−	0.107202i
$366$	−15.3403	−	15.9954i	−0.801851	−	0.836095i
$367$	6.65792	−	3.51881i	0.347540	−	0.183680i	−0.284384	−	0.958710i	$-0.591789\pi$
$367$	6.65792	−	3.51881i	0.347540	−	0.183680i	0.631924	+	0.775030i	$0.282265\pi$
$368$	−14.8677	+	30.8731i	−0.775033	+	1.60937i
$369$	−4.54810	−	9.55168i	−0.236765	−	0.497241i
$370$	56.3030	+	12.8508i	2.92705	+	0.668081i
$371$	0.230397	+	1.52858i	0.0119616	+	0.0793600i
$372$	1.77157	−	2.48517i	0.0918516	−	0.128850i
$373$	−24.7379	+	22.9534i	−1.28088	+	1.18848i	−0.309515	+	0.950894i	$0.600167\pi$
$373$	−24.7379	+	22.9534i	−1.28088	+	1.18848i	−0.971366	+	0.237589i	$0.923643\pi$
$374$	9.59978	−	18.1637i	0.496393	−	0.939221i
$375$	−31.9014	+	26.3130i	−1.64738	+	1.35880i
$376$	−14.4344	−	8.33368i	−0.744395	−	0.429777i
$377$	2.10168	−	0.518136i	0.108242	−	0.0266854i
$378$	−3.83515	+	3.13503i	−0.197259	+	0.161248i
$379$	−0.332817	−	2.95383i	−0.0170957	−	0.151728i	0.982264	−	0.187502i	$-0.0600391\pi$
$379$	−0.332817	−	2.95383i	−0.0170957	−	0.151728i	−0.999360	+	0.0357736i	$0.988610\pi$
$380$	−0.961575	−	25.6986i	−0.0493278	−	1.31831i
$381$	−5.59732	−	5.41562i	−0.286759	−	0.277451i
$382$	−4.46447	+	29.6198i	−0.228422	+	1.51548i
$383$	5.19011	−	13.2242i	0.265202	−	0.675724i	−0.734794	−	0.678290i	$-0.762721\pi$
$383$	5.19011	−	13.2242i	0.265202	−	0.675724i	0.999997	+	0.00256543i	$0.000816604\pi$
$384$	20.5181	+	3.53269i	1.04706	+	0.180277i
$385$	6.69074	+	1.26596i	0.340992	+	0.0645191i
$386$	−3.27023	−	1.57486i	−0.166450	−	0.0801583i
$387$	−4.57916	+	0.322875i	−0.232772	+	0.0164126i
$388$	−3.08440	+	8.81472i	−0.156587	+	0.447500i
$389$	3.21643	+	12.0039i	0.163080	+	0.608621i	0.998277	+	0.0586716i	$0.0186865\pi$
$389$	3.21643	+	12.0039i	0.163080	+	0.608621i	−0.835198	+	0.549950i	$0.814647\pi$
$390$	−4.83083	−	0.100995i	−0.244619	−	0.00511409i
$391$	10.4479	+	23.9469i	0.528373	+	1.21104i
$392$	4.57990	+	10.4972i	0.231320	+	0.530191i
$393$	−30.0008	−	0.627209i	−1.51334	−	0.0316385i
$394$	−6.64310	−	24.7924i	−0.334674	−	1.24902i
$395$	−15.7944	+	45.1377i	−0.794701	+	2.27112i
$396$	5.29121	+	7.83473i	0.265893	+	0.393710i
$397$	−8.19230	−	3.94521i	−0.411160	−	0.198004i	0.216858	−	0.976203i	$-0.430419\pi$
$397$	−8.19230	−	3.94521i	−0.411160	−	0.198004i	−0.628018	+	0.778199i	$0.716133\pi$
$398$	−29.6176	−	5.60395i	−1.48460	−	0.280901i
$399$	5.93798	+	1.02237i	0.297271	+	0.0511825i
$400$	20.0448	−	51.0733i	1.00224	−	2.55366i
$401$	−3.13676	+	20.8111i	−0.156643	+	1.03926i	0.762972	+	0.646432i	$0.223740\pi$
$401$	−3.13676	+	20.8111i	−0.156643	+	1.03926i	−0.919614	+	0.392823i	$0.871498\pi$
$402$	−17.4449	−	16.8786i	−0.870071	−	0.841828i
$403$	0.0260811	+	0.697033i	0.00129919	+	0.0347217i
$404$	1.59122	+	14.1225i	0.0791661	+	0.702618i
$405$	10.9050	−	34.2776i	0.541873	−	1.70327i
$406$	4.87419	+	1.61138i	0.241902	+	0.0799717i
$407$	22.3650	+	12.9124i	1.10859	+	0.640046i
$408$	8.70874	−	7.18318i	0.431147	−	0.355620i
$409$	11.0335	−	20.8764i	0.545571	−	1.03227i	−0.445033	−	0.895514i	$-0.646808\pi$
$409$	11.0335	−	20.8764i	0.545571	−	1.03227i	0.990605	−	0.136757i	$-0.0436680\pi$
$410$	17.9409	−	16.6467i	0.886036	−	0.822121i
$411$	−2.66529	+	3.73889i	−0.131469	+	0.184426i
$412$	0.770517	+	5.11204i	0.0379606	+	0.251852i
$413$	1.16787	+	0.266558i	0.0574670	+	0.0131165i
$414$	−35.5920	−	2.82503i	−1.74925	−	0.138843i
$415$	−12.2017	+	25.3370i	−0.598956	+	1.24375i
$416$	1.87020	−	0.988432i	0.0916943	−	0.0484619i
$417$	2.55956	+	2.66887i	0.125342	+	0.130695i
$418$	8.83881	−	32.9869i	0.432320	−	1.61344i
$419$	−17.0844	−	11.6480i	−0.834629	−	0.569040i	0.0688726	−	0.997625i	$-0.478060\pi$
$419$	−17.0844	−	11.6480i	−0.834629	−	0.569040i	−0.903501	+	0.428585i	$0.859012\pi$
$420$	−3.22377	−	2.12089i	−0.157304	−	0.103489i
$421$	−9.34466	−	6.89667i	−0.455431	−	0.336123i	0.341826	−	0.939763i	$-0.388955\pi$
$421$	−9.34466	−	6.89667i	−0.455431	−	0.336123i	−0.797257	+	0.603640i	$0.793716\pi$
$422$	−0.763764	−	1.58597i	−0.0371794	−	0.0772039i
$423$	4.48623	−	28.8995i	0.218128	−	1.40514i
$424$	4.54422	+	1.59009i	0.220687	+	0.0772216i
$425$	−19.5472	−	36.9852i	−0.948180	−	1.79404i
$426$	39.9989	+	16.6715i	1.93796	+	0.807735i
$427$	3.06614	+	2.63863i	0.148381	+	0.127692i
$428$	2.30021	−	0.709520i	0.111185	−	0.0342960i
$429$	−2.05095	−	0.679897i	−0.0990209	−	0.0328258i
$430$	−3.87986	−	9.88573i	−0.187104	−	0.476732i
$431$	−25.2984	+	5.77421i	−1.21858	+	0.278134i	−0.783004	−	0.622017i	$-0.786314\pi$
$431$	−25.2984	+	5.77421i	−1.21858	+	0.278134i	−0.435579	+	0.900150i	$0.643456\pi$
$432$	5.13815	+	25.4664i	0.247209	+	1.22525i
$433$	16.3402	−	1.84110i	0.785261	−	0.0884777i	0.289777	−	0.957094i	$-0.406419\pi$
$433$	16.3402	−	1.84110i	0.785261	−	0.0884777i	0.495485	+	0.868617i	$0.334990\pi$
$434$	−0.827130	+	1.43263i	−0.0397035	+	0.0687685i
$435$	−36.0430	+	9.51920i	−1.72813	+	0.456411i
$436$	−0.178844	−	0.309767i	−0.00856508	−	0.0148352i
$437$	25.7896	+	34.9437i	1.23368	+	1.67158i
$438$	−1.30337	+	0.920483i	−0.0622776	+	0.0439824i
$439$	4.81744	−	15.6177i	0.229924	−	0.745394i	−0.764934	−	0.644109i	$-0.777228\pi$
$439$	4.81744	−	15.6177i	0.229924	−	0.745394i	0.994857	−	0.101285i	$-0.0322955\pi$
$440$	13.2226	−	16.5806i	0.630361	−	0.790448i
$441$	−14.2724	+	14.1472i	−0.679639	+	0.673675i
$442$	0.592092	−	2.59412i	0.0281629	−	0.123390i
$443$	1.78732	−	9.44621i	0.0849181	−	0.448803i	−0.914139	−	0.405400i	$-0.867132\pi$
$443$	1.78732	−	9.44621i	0.0849181	−	0.448803i	0.999058	−	0.0434034i	$-0.0138201\pi$
$444$	−8.88348	−	11.6302i	−0.421591	−	0.551943i
$445$	−3.69284	−	0.138176i	−0.175058	−	0.00655019i
$446$	5.05496	+	26.7161i	0.239359	+	1.26504i
$447$	−1.16771	−	3.57515i	−0.0552309	−	0.169099i
$448$	−0.471373	−	0.0353245i	−0.0222703	−	0.00166893i
$449$	0.173703	−	1.54165i	0.00819753	−	0.0727551i	−0.988947	−	0.148267i	$-0.952631\pi$
$449$	0.173703	−	1.54165i	0.00819753	−	0.0727551i	0.997145	+	0.0755119i	$0.0240591\pi$
$450$	57.1668	+	0.251924i	2.69487	+	0.0118758i
$451$	9.86048	−	4.74856i	0.464312	−	0.223601i
$452$	−19.2261	+	5.15161i	−0.904319	+	0.242312i
$453$	−1.62254	−	0.471321i	−0.0762338	−	0.0221446i
$454$	0.820228	−	21.9211i	0.0384952	−	1.02881i
$455$	0.879468	−	0.0659070i	0.0412301	−	0.00308977i
$456$	11.4564	−	14.8623i	0.536495	−	0.695993i
$457$	9.77712	−	10.5372i	0.457355	−	0.492911i	−0.461703	−	0.887035i	$-0.652761\pi$
$457$	9.77712	−	10.5372i	0.457355	−	0.492911i	0.919057	+	0.394124i	$0.128952\pi$
$458$	10.4129	−	8.30400i	0.486563	−	0.388021i
$459$	17.2730	+	9.69603i	0.806233	+	0.452572i
$460$	−6.18925	−	27.1169i	−0.288575	−	1.26433i
$461$	−34.5836	+	1.29403i	−1.61072	+	0.0602689i	−0.827497	−	0.561470i	$-0.810236\pi$
$461$	−34.5836	+	1.29403i	−1.61072	+	0.0602689i	−0.783224	+	0.621739i	$0.786426\pi$
$462$	−3.26067	−	3.95317i	−0.151700	−	0.183918i
$463$	13.6253	−	7.86655i	0.633220	−	0.365589i	−0.148778	−	0.988871i	$-0.547534\pi$
$463$	13.6253	−	7.86655i	0.633220	−	0.365589i	0.781998	+	0.623281i	$0.214201\pi$
$464$	19.4171	−	18.6523i	0.901414	−	0.865912i
$465$	−0.647129	−	11.9953i	−0.0300099	−	0.556267i
$466$	−40.1908	−	17.5350i	−1.86180	−	0.812295i
$467$	0.946636	−	0.594811i	0.0438051	−	0.0275246i	−0.509952	−	0.860203i	$-0.670337\pi$
$467$	0.946636	−	0.594811i	0.0438051	−	0.0275246i	0.553757	+	0.832679i	$0.313194\pi$
$468$	0.924575	+	0.802780i	0.0427385	+	0.0371085i
$469$	3.46392	+	2.76238i	0.159949	+	0.127555i
$470$	66.9018	−	10.0838i	3.08595	−	0.465132i
$471$	5.05199	+	4.20454i	0.232783	+	0.193735i
$472$	2.43352	−	2.82780i	0.112012	−	0.130160i
$473$	−0.354889	−	4.73567i	−0.0163178	−	0.217746i
$474$	30.8651	−	18.5054i	1.41768	−	0.849983i
$475$	−45.3587	−	52.7078i	−2.08120	−	2.41840i
$476$	1.50261	−	1.50261i	0.0688720	−	0.0688720i
$477$	0.278663	+	8.44303i	0.0127591	+	0.386580i
$478$	−36.4308	−	4.10476i	−1.66630	−	0.187747i
$479$	−23.2220	+	31.4647i	−1.06104	+	1.43766i	−0.169046	+	0.985608i	$0.554069\pi$
$479$	−23.2220	+	31.4647i	−1.06104	+	1.43766i	−0.891993	+	0.452049i	$0.850693\pi$
$480$	−31.9235	+	17.5518i	−1.45710	+	0.801125i
$481$	3.23077	+	0.865683i	0.147310	+	0.0394717i
$482$	−40.4626	+	7.65594i	−1.84302	+	0.348718i
$483$	6.51593	−	0.107500i	0.296485	−	0.00489142i
$484$	1.14780	−	0.782558i	0.0521728	−	0.0355708i
$485$	12.1404	+	34.6952i	0.551265	+	1.57543i
$486$	−22.8089	+	14.5774i	−1.03463	+	0.661244i
$487$	3.07673	+	3.85810i	0.139420	+	0.174827i	0.846639	−	0.532167i	$-0.178622\pi$
$487$	3.07673	+	3.85810i	0.139420	+	0.174827i	−0.707219	+	0.706994i	$0.750051\pi$
$488$	11.7275	−	4.60269i	0.530878	−	0.208354i
$489$	−0.180658	+	0.186719i	−0.00816964	+	0.00844373i
$490$	−41.1028	−	21.7234i	−1.85683	−	0.981365i
$491$	−8.00688	+	5.90935i	−0.361346	+	0.266685i	−0.759328	−	0.650708i	$-0.774472\pi$
$491$	−8.00688	+	5.90935i	−0.361346	+	0.266685i	0.397983	+	0.917393i	$0.369710\pi$
$492$	−6.19305	+	0.334107i	−0.279204	+	0.0150627i
$493$	−1.12267	−	20.4981i	−0.0505626	−	0.923188i
$494$		−	4.42305i		−	0.199002i
$495$	35.5099	+	11.1249i	1.59605	+	0.500029i
$496$	4.61598	+	7.34630i	0.207264	+	0.329859i
$497$	−7.55812	−	2.33137i	−0.339028	−	0.104576i
$498$	19.2550	−	8.78173i	0.862835	−	0.393519i
$499$	38.6977	+	15.1877i	1.73235	+	0.679896i	0.999999	−	0.00103675i	$-0.000330006\pi$
$499$	38.6977	+	15.1877i	1.73235	+	0.679896i	0.732346	+	0.680932i	$0.238425\pi$
$500$	7.14581	+	23.1661i	0.319570	+	1.03602i
$501$	−3.31101	+	24.7284i	−0.147925	+	1.10479i
$502$	20.2052	+	29.6356i	0.901801	+	1.32270i
$503$	−23.6134	−	14.8373i	−1.05287	−	0.661563i	−0.109732	−	0.993961i	$-0.534999\pi$
$503$	−23.6134	−	14.8373i	−1.05287	−	0.661563i	−0.943139	+	0.332398i	$0.892142\pi$
$504$	−0.818107	−	2.69433i	−0.0364414	−	0.120015i
$505$	39.5544	+	39.5544i	1.76015	+	1.76015i
$506$	2.76024	−	36.8328i	0.122707	−	1.63742i
$507$	22.1990	+	1.29574i	0.985894	+	0.0575460i
$508$	−4.18496	+	1.82588i	−0.185678	+	0.0810103i
$509$	−13.7055	+	20.1023i	−0.607487	+	0.891020i	−0.999582	−	0.0289051i	$-0.990798\pi$
$509$	−13.7055	+	20.1023i	−0.607487	+	0.891020i	0.392095	+	0.919925i	$0.371750\pi$
$510$	−9.45866	+	44.8382i	−0.418836	+	1.98547i
$511$	0.220754	−	0.189974i	0.00976556	−	0.00840395i
$512$	4.90282	−	7.80279i	0.216676	−	0.344838i
$513$	31.5790	+	9.32427i	1.39425	+	0.411676i
$514$	3.38386	−	1.18406i	0.149255	−	0.0522267i
$515$	14.9165	+	13.8405i	0.657300	+	0.609886i
$516$	−0.846822	+	2.55449i	−0.0372793	+	0.112455i
$517$	29.9169	+	4.50925i	1.31575	+	0.198317i
$518$	5.39546	+	5.81493i	0.237063	+	0.255493i
$519$	8.38230	+	11.8691i	0.367942	+	0.520995i
$520$	1.09838	−	2.51752i	0.0481672	−	0.110400i
$521$	2.60813			0.114264			0.0571322	−	0.998367i	$-0.481804\pi$
$521$	2.60813			0.114264			0.0571322	+	0.998367i	$0.481804\pi$
$522$	25.4307	+	11.8449i	1.11307	+	0.518436i
$523$	21.7770			0.952240			0.476120	−	0.879380i	$-0.342043\pi$
$523$	21.7770			0.952240			0.476120	+	0.879380i	$0.342043\pi$
$524$	−7.03481	+	16.1240i	−0.307317	+	0.704379i
$525$	−10.3909	+	0.951300i	−0.453498	+	0.0415181i
$526$	11.0405	+	11.8988i	0.481389	+	0.518813i
$527$	6.54130	+	0.985943i	0.284944	+	0.0429484i
$528$	−26.3215	+	5.43151i	−1.14550	+	0.236376i
$529$	17.5730	+	16.3054i	0.764043	+	0.708929i
$530$	−18.4462	+	6.45462i	−0.801254	+	0.280371i
$531$	6.16926	+	2.18928i	0.267723	+	0.0950066i
$532$	1.87933	−	2.99093i	0.0814791	−	0.129673i
$533$	1.07440	−	0.924594i	0.0465373	−	0.0400486i
$534$	2.06952	+	1.85765i	0.0895568	+	0.0803885i
$535$	5.33726	−	7.82833i	0.230750	−	0.338448i
$536$	12.6471	−	5.51787i	0.546271	−	0.238336i
$537$	−13.7749	−	27.4368i	−0.594433	−	1.18398i
$538$	−2.27800	+	30.3978i	−0.0982116	+	1.31054i
$539$	−14.7003	−	14.7003i	−0.633187	−	0.633187i
$540$	−16.1489	−	13.5609i	−0.694940	−	0.583570i
$541$	−13.9221	−	8.74785i	−0.598559	−	0.376099i	0.198411	−	0.980119i	$-0.436422\pi$
$541$	−13.9221	−	8.74785i	−0.598559	−	0.376099i	−0.796969	+	0.604020i	$0.793565\pi$
$542$	7.61136	+	11.1638i	0.326936	+	0.479527i
$543$	−26.6717	−	20.5595i	−1.14459	−	0.882291i
$544$	−5.91326	−	19.1703i	−0.253529	−	0.821921i
$545$	−1.31056	−	0.514355i	−0.0561381	−	0.0220326i
$546$	−0.540434	−	0.385252i	−0.0231285	−	0.0164872i
$547$	18.3373	+	5.65632i	0.784047	+	0.241847i	0.660832	−	0.750533i	$-0.270203\pi$
$547$	18.3373	+	5.65632i	0.784047	+	0.241847i	0.123215	+	0.992380i	$0.460680\pi$
$548$	1.43214	+	2.27925i	0.0611782	+	0.0973645i
$549$	14.9642	+	16.2708i	0.638658	+	0.694423i
$550$			59.1402i			2.52175i
$551$	−9.40147	−	32.8040i	−0.400516	−	1.39750i
$552$	9.18637	−	18.0980i	0.390998	−	0.770300i
$553$	−5.28507	+	3.90056i	−0.224744	+	0.165868i
$554$	−12.0615	−	6.37469i	−0.512444	−	0.270835i
$555$	−55.8787	−	13.9889i	−2.37192	−	0.593797i
$556$	2.01801	−	0.792012i	0.0855829	−	0.0335888i
$557$	−8.87207	−	11.1252i	−0.375922	−	0.471391i	0.557498	−	0.830179i	$-0.311762\pi$
$557$	−8.87207	−	11.1252i	−0.375922	−	0.471391i	−0.933419	+	0.358788i	$0.883190\pi$
$558$	−5.40018	+	7.24989i	−0.228608	+	0.306912i
$559$	−0.203143	−	0.580550i	−0.00859204	−	0.0245547i
$560$	9.06382	−	6.17961i	0.383016	−	0.261136i
$561$	−9.95180	+	17.9131i	−0.420165	+	0.756291i
$562$	44.9951	−	8.51353i	1.89800	−	0.359121i
$563$	15.6119	+	4.18320i	0.657963	+	0.176301i	0.572327	−	0.820026i	$-0.306041\pi$
$563$	15.6119	+	4.18320i	0.657963	+	0.176301i	0.0856366	+	0.996326i	$0.472708\pi$
$564$	−14.6658	−	8.88108i	−0.617540	−	0.373961i
$565$	−46.5224	+	63.0356i	−1.95721	+	2.65193i
$566$	7.49884	+	0.844916i	0.315200	+	0.0355145i
$567$	3.88986	−	3.04636i	0.163359	−	0.127935i
$568$	−17.4184	+	17.4184i	−0.730862	+	0.730862i
$569$	27.4902	+	31.9442i	1.15245	+	1.33917i	0.931439	+	0.363897i	$0.118554\pi$
$569$	27.4902	+	31.9442i	1.15245	+	1.33917i	0.221008	+	0.975272i	$0.429065\pi$
$570$	1.25655	+	76.1634i	0.0526310	+	3.19013i
$571$	−0.556275	−	7.42298i	−0.0232794	−	0.310642i	−0.996673	−	0.0815029i	$-0.974028\pi$
$571$	−0.556275	−	7.42298i	−0.0232794	−	0.310642i	0.973394	−	0.229139i	$-0.0735910\pi$
$572$	−0.826261	+	0.960133i	−0.0345477	+	0.0401452i
$573$	5.06960	−	29.4445i	0.211786	−	1.23006i
$574$	3.32415	−	0.501035i	0.138747	−	0.0209128i
$575$	−58.8014	−	46.8926i	−2.45219	−	1.95556i
$576$	−2.53597	−	0.491417i	−0.105665	−	0.0204757i
$577$	26.0769	−	16.3852i	1.08560	−	0.682125i	0.134467	−	0.990918i	$-0.457068\pi$
$577$	26.0769	−	16.3852i	1.08560	−	0.682125i	0.951129	+	0.308793i	$0.0999249\pi$
$578$	3.92782	+	1.71369i	0.163376	+	0.0712800i
$579$	3.22832	+	1.63867i	0.134164	+	0.0681006i
$580$	−2.88262	+	21.6637i	−0.119694	+	0.899538i
$581$	−3.34524	+	1.93137i	−0.138784	+	0.0801269i
$582$	9.67988	−	25.9129i	0.401244	−	1.07412i
$583$	−8.73304	+	0.326767i	−0.361686	+	0.0135333i
$584$	−0.201837	−	0.884304i	−0.00835205	−	0.0365927i
$585$	4.81531	+	0.201430i	0.199089	+	0.00832809i
$586$	−28.7842	+	22.9546i	−1.18906	+	0.948246i
$587$	−11.7143	+	12.6250i	−0.483499	+	0.521088i	−0.926937	−	0.375217i	$-0.877568\pi$
$587$	−11.7143	+	12.6250i	−0.483499	+	0.521088i	0.443438	+	0.896305i	$0.353759\pi$
$588$	4.48447	+	10.8943i	0.184936	+	0.449274i
$589$	10.9655	−	0.821752i	0.451827	−	0.0338597i
$590$	−0.566257	+	15.1335i	−0.0233124	+	0.623038i
$591$	6.10777	+	24.8620i	0.251240	+	1.02269i
$592$	40.1861	−	10.7678i	1.65164	−	0.442555i
$593$	6.27585	−	3.02229i	0.257718	−	0.124111i	−0.300564	−	0.953762i	$-0.597175\pi$
$593$	6.27585	−	3.02229i	0.257718	−	0.124111i	0.558282	+	0.829651i	$0.311461\pi$
$594$	−15.1843	−	23.5293i	−0.623019	−	0.965420i
$595$	0.936487	−	8.31155i	0.0383922	−	0.340740i
$596$	−2.19873	−	0.164772i	−0.0900633	−	0.00674931i
$597$	29.4185	+	6.20587i	1.20402	+	0.253989i
$598$	−0.889367	−	4.70042i	−0.0363689	−	0.192214i
$599$	−46.5579	−	1.74207i	−1.90231	−	0.0711792i	−0.939686	−	0.342038i	$-0.888883\pi$
$599$	−46.5579	−	1.74207i	−1.90231	−	0.0711792i	−0.962619	+	0.270859i	$0.912692\pi$
$600$	−12.5021	+	29.9957i	−0.510398	+	1.22457i
$601$	7.96700	−	42.1066i	0.324981	−	1.71756i	−0.314930	−	0.949115i	$-0.601981\pi$
$601$	7.96700	−	42.1066i	0.324981	−	1.71756i	0.639911	−	0.768449i	$-0.278971\pi$
$602$	0.324593	−	1.42214i	0.0132294	−	0.0579619i
$603$	17.0445	+	17.1954i	0.694107	+	0.700252i
$604$	−0.617588	+	0.774431i	−0.0251293	+	0.0315111i
$605$	1.61170	−	5.22499i	0.0655248	−	0.212426i
$606$	−3.83788	−	41.9207i	−0.155903	−	1.70291i
$607$	−21.3151	−	28.8809i	−0.865152	−	1.17224i	−0.983794	−	0.179303i	$-0.942616\pi$
$607$	−21.3151	−	28.8809i	−0.865152	−	1.17224i	0.118642	−	0.992937i	$-0.462146\pi$
$608$	−16.6740	−	28.8801i	−0.676218	−	1.17124i
$609$	−4.82706	−	1.70853i	−0.195602	−	0.0692331i
$610$	−25.5701	+	44.2887i	−1.03530	+	1.79320i
$611$	3.89385	−	0.438732i	0.157528	−	0.0177492i
$612$	9.11091	−	7.20025i	0.368287	−	0.291053i
$613$	−36.7355	+	8.38463i	−1.48373	+	0.338652i	−0.886241	−	0.463224i	$-0.846693\pi$
$613$	−36.7355	+	8.38463i	−1.48373	+	0.338652i	−0.597491	+	0.801876i	$0.703835\pi$
$614$	1.27714	+	3.25411i	0.0515413	+	0.131325i
$615$	−18.2381	+	16.2264i	−0.735431	+	0.654312i
$616$	2.78356	−	0.858614i	0.112153	−	0.0345946i
$617$	−26.2704	−	22.6075i	−1.05761	−	0.910144i	−0.0614830	−	0.998108i	$-0.519583\pi$
$617$	−26.2704	−	22.6075i	−1.05761	−	0.910144i	−0.996124	+	0.0879640i	$0.971964\pi$
$618$	−1.96531	−	15.1865i	−0.0790562	−	0.610890i
$619$	6.68970	+	12.6575i	0.268882	+	0.508749i	0.981172	−	0.193136i	$-0.0618659\pi$
$619$	6.68970	+	12.6575i	0.268882	+	0.508749i	−0.712290	+	0.701885i	$0.752342\pi$
$620$	−6.64724	−	2.32597i	−0.266959	−	0.0934132i
$621$	35.4343	+	3.55922i	1.42193	+	0.142827i
$622$	4.26991	+	8.86655i	0.171208	+	0.355516i
$623$	−0.408408	−	0.301419i	−0.0163625	−	0.0120761i
$624$	−3.11083	+	1.56183i	−0.124533	+	0.0625231i
$625$	33.5071	+	22.8448i	1.34028	+	0.913790i
$626$	13.6865	−	51.0786i	0.547021	−	2.04151i
$627$	−9.50199	+	32.7110i	−0.379473	+	1.30635i
$628$	3.40672	−	1.80051i	0.135943	−	0.0718480i
$629$	13.7633	−	28.5797i	0.548777	−	1.13955i
$630$	9.41554	+	6.48037i	0.375124	+	0.258184i
$631$	−14.4465	−	3.29732i	−0.575106	−	0.131264i	−0.0749315	−	0.997189i	$-0.523874\pi$
$631$	−14.4465	−	3.29732i	−0.575106	−	0.131264i	−0.500175	+	0.865924i	$0.666731\pi$
$632$	3.04898	+	20.2287i	0.121282	+	0.804654i
$633$	0.728578	+	1.59749i	0.0289584	+	0.0634946i
$634$	44.1349	−	40.9512i	1.75282	−	1.62638i
$635$	−8.39762	+	15.8891i	−0.333249	+	0.630539i
$636$	4.63929	+	1.73303i	0.183960	+	0.0687190i
$637$	−2.33183	−	1.34628i	−0.0923903	−	0.0533416i
$638$	−12.1376	+	26.3621i	−0.480532	+	1.04368i
$639$	−39.5403	−	17.4591i	−1.56419	−	0.690670i
$640$	−5.37901	−	47.7400i	−0.212624	−	1.88709i
$641$	−0.986052	−	26.3528i	−0.0389467	−	1.04087i	−0.872555	−	0.488516i	$-0.837538\pi$
$641$	−0.986052	−	26.3528i	−0.0389467	−	1.04087i	0.833608	−	0.552357i	$-0.186271\pi$
$642$	−6.85575	+	1.95876i	−0.270575	+	0.0773061i
$643$	4.60367	−	30.5434i	0.181551	−	1.20451i	−0.693491	−	0.720466i	$-0.743928\pi$
$643$	4.60367	−	30.5434i	0.181551	−	1.20451i	0.875042	−	0.484048i	$-0.160834\pi$
$644$	1.39578	−	3.55638i	0.0550013	−	0.140141i
$645$	3.66299	+	9.93917i	0.144230	+	0.391354i
$646$	−41.2163	−	7.79854i	−1.62163	−	0.306830i
$647$	21.5212	+	10.3641i	0.846087	+	0.407454i	0.806124	−	0.591747i	$-0.201562\pi$
$647$	21.5212	+	10.3641i	0.846087	+	0.407454i	0.0399631	+	0.999201i	$0.487276\pi$
$648$	−2.72736	−	15.1439i	−0.107141	−	0.594910i
$649$	−2.23668	+	6.39208i	−0.0877976	+	0.250911i
$650$	1.98245	+	7.39861i	0.0777582	+	0.290198i
$651$	0.854701	−	1.41141i	0.0334984	−	0.0553175i
$652$	0.0609090	+	0.139605i	0.00238538	+	0.00546735i
$653$	1.50185	+	3.44227i	0.0587717	+	0.134706i	0.943470	−	0.331458i	$-0.107540\pi$
$653$	1.50185	+	3.44227i	0.0587717	+	0.134706i	−0.884698	+	0.466164i	$0.845636\pi$
$654$	0.510450	+	0.928416i	0.0199602	+	0.0363039i
$655$	17.9212	+	66.8827i	0.700238	+	2.61332i
$656$	5.82321	−	16.6418i	0.227358	−	0.649753i
$657$	1.31895	−	0.890753i	0.0514570	−	0.0347516i
$658$	8.37290	+	4.03217i	0.326409	+	0.157191i
$659$	36.6937	+	6.94282i	1.42938	+	0.270454i	0.842272	−	0.539052i	$-0.181217\pi$
$659$	36.6937	+	6.94282i	1.42938	+	0.270454i	0.587111	+	0.809506i	$0.300265\pi$
$660$	13.9552	−	16.7679i	0.543205	−	0.652690i
$661$	−10.8477	+	27.6396i	−0.421928	+	1.07506i	0.549029	+	0.835803i	$0.314998\pi$
$661$	−10.8477	+	27.6396i	−0.421928	+	1.07506i	−0.970957	+	0.239253i	$0.923098\pi$
$662$	0.362532	−	2.40524i	0.0140902	−	0.0934824i
$663$	−0.644531	+	2.57458i	−0.0250315	+	0.0999883i
$664$	0.449821	+	12.0217i	0.0174564	+	0.466533i
$665$	−1.55670	−	13.8161i	−0.0603662	−	0.535765i
$666$	25.5875	+	34.9915i	0.991494	+	1.35589i
$667$	−16.5871	−	32.9707i	−0.642256	−	1.27663i
$668$	12.6668	+	7.31320i	0.490094	+	0.282956i
$669$	−4.48393	−	26.7473i	−0.173359	−	1.03411i
$670$	−26.1724	+	49.5207i	−1.01113	+	1.91315i
$671$	−16.7640	+	15.5547i	−0.647166	+	0.600482i
$672$	−4.98107	−	0.478165i	−0.192149	−	0.0184456i
$673$	5.35938	+	35.5572i	0.206589	+	1.37063i	0.816128	+	0.577871i	$0.196116\pi$
$673$	5.35938	+	35.5572i	0.206589	+	1.37063i	−0.609539	+	0.792756i	$0.708645\pi$
$674$	23.3197	+	5.32257i	0.898242	+	0.205018i
$675$	−57.0028	−	1.44306i	−2.19404	−	0.0555433i
$676$	5.65624	−	11.7453i	0.217548	−	0.451743i
$677$	−2.79278	+	1.47603i	−0.107335	+	0.0567283i	−0.520074	−	0.854121i	$-0.674096\pi$
$677$	−2.79278	+	1.47603i	−0.107335	+	0.0567283i	0.412739	+	0.910849i	$0.364572\pi$
$678$	57.2550	−	14.0656i	2.19886	−	0.540188i
$679$	−1.30676	+	4.87691i	−0.0501490	+	0.187159i
$680$	−21.5229	−	14.6741i	−0.825366	−	0.562725i
$681$	−1.27497	+	21.8431i	−0.0488569	+	0.837029i
$682$	−7.52463	−	5.55343i	−0.288133	−	0.212652i
$683$	−10.4087	−	21.6139i	−0.398279	−	0.827035i	−0.999607	−	0.0280324i	$-0.991076\pi$
$683$	−10.4087	−	21.6139i	−0.398279	−	0.827035i	0.601328	−	0.799002i	$-0.294638\pi$
$684$	12.1018	−	15.0388i	0.462725	−	0.575022i
$685$	10.0006	+	3.49937i	0.382105	+	0.133704i
$686$	−6.10197	−	11.5455i	−0.232974	−	0.440809i
$687$	−10.5571	+	8.06385i	−0.402779	+	0.307655i
$688$	−5.79888	−	4.99034i	−0.221080	−	0.190255i
$689$	−1.08158	+	0.333622i	−0.0412048	+	0.0127100i
$690$	16.6499	+	80.6869i	0.633853	+	3.07170i
$691$	−17.5854	−	44.8068i	−0.668979	−	1.70453i	−0.708882	−	0.705327i	$-0.750800\pi$
$691$	−17.5854	−	44.8068i	−0.668979	−	1.70453i	0.0399028	−	0.999204i	$-0.487295\pi$
$692$	8.30496	−	1.89555i	0.315707	−	0.0720581i
$693$	3.16920	+	4.01017i	0.120388	+	0.152334i
$694$	11.6301	−	1.31040i	0.441472	−	0.0497420i
$695$	4.26642	−	7.38966i	0.161835	−	0.280306i
$696$	−11.7290	+	10.8049i	−0.444588	+	0.409559i
$697$	−6.72152	−	11.6420i	−0.254596	−	0.440973i
$698$	17.6001	+	23.8473i	0.666173	+	0.902633i
$699$	39.7136	+	18.3243i	1.50211	+	0.693087i
$700$	−1.80306	+	5.84539i	−0.0681494	+	0.220935i
$701$	−16.4837	+	20.6699i	−0.622580	+	0.780691i	−0.988705	−	0.149875i	$-0.952113\pi$
$701$	−16.4837	+	20.6699i	−0.622580	+	0.780691i	0.366125	+	0.930566i	$0.380684\pi$
$702$	−2.68833	−	2.43459i	−0.101465	−	0.0918878i
$703$	11.7333	−	51.4072i	0.442532	−	1.93886i
$704$	0.496810	−	2.62570i	0.0187242	−	0.0989599i
$705$	−66.9262	+	8.66103i	−2.52059	+	0.326193i
$706$	−28.0205	−	1.04845i	−1.05457	−	0.0394591i
$707$	1.42846	+	7.54957i	0.0537226	+	0.283931i
$708$	2.56354	−	2.85591i	0.0963437	−	0.107332i
$709$	12.9353	+	0.969365i	0.485795	+	0.0364053i	0.315377	−	0.948967i	$-0.397869\pi$
$709$	12.9353	+	0.969365i	0.485795	+	0.0364053i	0.170418	+	0.985372i	$0.445488\pi$
$710$	11.1958	−	99.3651i	0.420169	−	3.72910i
$711$	−31.1652	+	17.8106i	−1.16879	+	0.667948i
$712$	−1.42429	+	0.685903i	−0.0533776	+	0.0257053i
$713$	11.4879	−	3.07818i	0.430227	−	0.115279i
$714$	−4.54285	+	4.35679i	−0.170012	+	0.163049i
$715$	−0.186427	+	4.98236i	−0.00697196	+	0.186330i
$716$	−17.9479	+	1.34501i	−0.670743	+	0.0502652i
$717$	36.2440	+	4.85288i	1.35356	+	0.181234i
$718$	−33.2955	+	35.8840i	−1.24258	+	1.33918i
$719$	27.3782	−	21.8334i	1.02104	−	0.814248i	0.0383000	−	0.999266i	$-0.487806\pi$
$719$	27.3782	−	21.8334i	1.02104	−	0.814248i	0.982735	+	0.185018i	$0.0592343\pi$
$720$	53.1237	−	27.7779i	1.97980	−	1.03522i
$721$	0.621948	+	2.72493i	0.0231626	+	0.101482i
$722$	−36.7094	+	1.37357i	−1.36618	+	0.0511189i
$723$	40.5099	−	6.79110i	1.50658	−	0.252564i
$724$	−17.0975	+	9.87126i	−0.635425	+	0.366863i
$725$	30.4293	+	50.6587i	1.13012	+	1.88142i
$726$	−3.44755	+	2.24640i	−0.127950	+	0.0833718i
$727$	27.9148	+	12.1791i	1.03530	+	0.451698i	0.847660	−	0.530540i	$-0.178011\pi$
$727$	27.9148	+	12.1791i	1.03530	+	0.451698i	0.187642	+	0.982237i	$0.439915\pi$
$728$	0.319450	−	0.200724i	0.0118396	−	0.00743931i
$729$	23.0495	−	14.0614i	0.853684	−	0.520792i
$730$	2.87866	+	2.29566i	0.106544	+	0.0849661i
$731$	−5.76805	+	0.869393i	−0.213339	+	0.0321557i
$732$	12.1600	−	4.48146i	0.449447	−	0.165640i
$733$	8.48000	−	9.85393i	0.313216	−	0.363963i	−0.579194	−	0.815190i	$-0.696632\pi$
$733$	8.48000	−	9.85393i	0.313216	−	0.363963i	0.892409	+	0.451227i	$0.149013\pi$
$734$	0.977234	+	13.0403i	0.0360703	+	0.481325i
$735$	40.5357	+	22.5200i	1.49518	+	0.830664i
$736$	−23.5267	−	27.3385i	−0.867205	−	1.00771i
$737$	−17.7110	+	17.7110i	−0.652392	+	0.652392i
$738$	18.3608	−	0.605998i	0.675869	−	0.0223071i
$739$	4.48512	+	0.505351i	0.164988	+	0.0185896i	0.194072	−	0.980987i	$-0.437831\pi$
$739$	4.48512	+	0.505351i	0.164988	+	0.0185896i	−0.0290842	+	0.999577i	$0.509259\pi$
$740$	−20.0532	+	27.1711i	−0.737170	+	0.998829i
$741$	−0.0922132	+	4.41076i	−0.00338754	+	0.162033i
$742$	−2.59289	−	0.694763i	−0.0951879	−	0.0255055i
$743$	4.79620	−	0.907490i	0.175956	−	0.0332926i	−0.0971871	−	0.995266i	$-0.530985\pi$
$743$	4.79620	−	0.907490i	0.175956	−	0.0332926i	0.273143	+	0.961974i	$0.411937\pi$
$744$	−2.64248	−	4.40738i	−0.0968782	−	0.161582i
$745$	−7.17056	+	4.88880i	−0.262709	+	0.179112i
$746$	−19.3545	−	55.3121i	−0.708620	−	2.02512i
$747$	−19.3846	+	8.35591i	−0.709244	+	0.305727i
$748$	7.49020	+	9.39241i	0.273869	+	0.343420i
$749$	1.21145	−	0.475458i	0.0442653	−	0.0173729i
$750$	−19.7273	−	69.0465i	−0.720339	−	2.52122i
$751$	−8.55458	−	4.52123i	−0.312161	−	0.164982i	0.303849	−	0.952720i	$-0.401728\pi$
$751$	−8.55458	−	4.52123i	−0.312161	−	0.164982i	−0.616010	+	0.787738i	$0.711252\pi$
$752$	39.2164	−	28.9430i	1.43007	−	1.05544i
$753$	−19.5312	−	29.9745i	−0.711757	−	1.09233i
$754$	−0.634759	+	3.70484i	−0.0231165	+	0.134922i
$755$			3.89879i			0.141891i
$756$	−0.783446	−	2.78856i	−0.0284937	−	0.101419i
$757$	11.6705	+	18.5734i	0.424170	+	0.675063i	0.988625	−	0.150401i	$-0.0480564\pi$
$757$	11.6705	+	18.5734i	0.424170	+	0.675063i	−0.564455	+	0.825464i	$0.690914\pi$
$758$	4.93245	+	1.52146i	0.179155	+	0.0552619i
$759$	−3.52047	+	36.6730i	−0.127785	+	1.33114i
$760$	−40.3078	−	15.8197i	−1.46212	−	0.573839i
$761$	4.77532	+	15.4812i	0.173105	+	0.561194i	0.999999	−	0.00116420i	$-0.000370576\pi$
$761$	4.77532	+	15.4812i	0.173105	+	0.561194i	−0.826894	+	0.562358i	$0.809894\pi$
$762$	12.5064	−	5.14805i	0.453058	−	0.186494i
$763$	−0.108936	−	0.159779i	−0.00394374	−	0.00578440i
$764$	−14.8311	−	9.31897i	−0.536569	−	0.337149i
$765$	10.3672	−	44.5165i	0.374827	−	1.60950i
$766$	17.4436	+	17.4436i	0.630264	+	0.630264i
$767$	−0.0655455	+	0.874644i	−0.00236671	+	0.0315816i
$768$	−18.2312	+	27.7117i	−0.657863	+	0.999958i
$769$	−15.0637	+	6.57221i	−0.543210	+	0.237000i	−0.653536	−	0.756895i	$-0.726715\pi$
$769$	−15.0637	+	6.57221i	−0.543210	+	0.237000i	0.110326	+	0.993895i	$0.464810\pi$
$770$	−6.66102	+	9.76992i	−0.240047	+	0.352084i
$771$	−3.39914	+	1.11023i	−0.122417	+	0.0399838i
$772$	1.60876	−	1.38445i	0.0579005	−	0.0498274i
$773$	−2.74554	+	4.36951i	−0.0987504	+	0.157160i	−0.892445	−	0.451156i	$-0.851012\pi$
$773$	−2.74554	+	4.36951i	−0.0987504	+	0.157160i	0.793695	+	0.608316i	$0.208155\pi$
$774$	2.66593	−	7.51243i	0.0958248	−	0.270029i
$775$	−17.9742	+	6.28944i	−0.645651	+	0.225923i
$776$	11.5268	+	10.6953i	0.413789	+	0.383940i
$777$	−5.25925	−	5.91126i	−0.188674	−	0.212065i
$778$	−21.3390	−	3.21633i	−0.765039	−	0.115311i
$779$	−15.1992	−	16.3808i	−0.544567	−	0.586903i
$780$	1.18375	−	2.56551i	0.0423852	−	0.0918600i
$781$	17.8811	−	40.9840i	0.639838	−	1.46652i
$782$	−45.3691			−1.62239
$783$	−25.1132	−	12.3422i	−0.897471	−	0.441073i
$784$	−33.4915			−1.19613
$785$	6.06500	−	13.9011i	0.216469	−	0.496153i
$786$	21.8311	−	47.3139i	0.778691	−	1.68763i
$787$	−9.05888	−	9.76315i	−0.322914	−	0.348019i	0.550643	−	0.834741i	$-0.314383\pi$
$787$	−9.05888	−	9.76315i	−0.322914	−	0.348019i	−0.873557	+	0.486723i	$0.838192\pi$
$788$	14.8411	+	2.23693i	0.528692	+	0.0796875i
$789$	−10.7618	−	12.0960i	−0.383129	−	0.430628i
$790$	−60.8736	−	56.4825i	−2.16579	−	2.00956i
$791$	−10.1572	+	3.55417i	−0.361150	+	0.126372i
$792$	15.6540	−	2.89050i	0.556239	−	0.102709i
$793$	−1.57581	+	2.50789i	−0.0559586	+	0.0890576i
$794$	11.9680	−	10.2993i	0.424730	−	0.365509i
$795$	18.5296	−	6.05212i	0.657177	−	0.214647i
$796$	9.92916	−	14.5634i	0.351930	−	0.516186i
$797$	−16.5156	+	7.20570i	−0.585014	+	0.255239i	−0.671488	−	0.741015i	$-0.734345\pi$
$797$	−16.5156	+	7.20570i	−0.585014	+	0.255239i	0.0864743	+	0.996254i	$0.472440\pi$
$798$	−5.75060	+	8.74097i	−0.203569	+	0.309427i
$799$	2.77715	−	37.0585i	0.0982486	−	1.31104i
$800$	40.8356	+	40.8356i	1.44376	+	1.44376i
$801$	−2.02504	−	1.89564i	−0.0715513	−	0.0669791i
$802$	−30.9448	−	19.4439i	−1.09270	−	0.686588i
$803$	0.927497	+	1.36039i	0.0327307	+	0.0480071i
$804$	13.1255	−	5.40290i	0.462900	−	0.190546i
$805$	−4.43240	−	14.3695i	−0.156222	−	0.506458i
$806$	−1.12751	−	0.442516i	−0.0397149	−	0.0155870i
$807$	2.90542	−	30.2659i	0.102276	−	1.06541i
$808$	22.8664	+	7.05335i	0.804438	+	0.248136i
$809$	−9.46657	−	15.0660i	−0.332827	−	0.529691i	0.637825	−	0.770182i	$-0.279834\pi$
$809$	−9.46657	−	15.0660i	−0.332827	−	0.529691i	−0.970651	+	0.240491i	$0.922692\pi$
$810$	46.9838	+	41.1591i	1.65084	+	1.44618i
$811$			20.1055i			0.705999i	0.935623	+	0.353000i	$0.114838\pi$
$811$			20.1055i			0.705999i	−0.935623	+	0.353000i	$0.885162\pi$
$812$	−2.00340	+	2.23556i	−0.0703055	+	0.0784529i
$813$	−7.35748	−	11.2915i	−0.258038	−	0.396010i
$814$	−36.0820	+	26.6297i	−1.26467	+	0.933372i
$815$	0.530039	+	0.280134i	0.0185664	+	0.00981265i
$816$	9.06905	+	31.7421i	0.317480	+	1.11120i
$817$	−9.02611	+	3.54249i	−0.315784	+	0.123936i
$818$	25.5652	+	32.0578i	0.893866	+	1.12087i
$819$	0.530902	+	0.395449i	0.0185512	+	0.0138181i
$820$	4.72671	+	13.5082i	0.165064	+	0.471725i
$821$	−11.7736	+	8.02707i	−0.410900	+	0.280147i	−0.751077	−	0.660215i	$-0.770465\pi$
$821$	−11.7736	+	8.02707i	−0.410900	+	0.280147i	0.340177	+	0.940361i	$0.389513\pi$
$822$	−4.10003	−	6.83841i	−0.143005	−	0.238517i
$823$	21.7683	−	4.11878i	0.758794	−	0.143572i	0.207904	−	0.978149i	$-0.433336\pi$
$823$	21.7683	−	4.11878i	0.758794	−	0.143572i	0.550890	+	0.834578i	$0.314288\pi$
$824$	8.40816	+	2.25296i	0.292912	+	0.0784856i
$825$	1.23298	−	58.9760i	0.0429267	−	2.05328i
$826$	−1.23523	+	1.67368i	−0.0429793	+	0.0582349i
$827$	44.4380	+	5.00696i	1.54526	+	0.174109i	0.843040	−	0.537850i	$-0.180763\pi$
$827$	44.4380	+	5.00696i	1.54526	+	0.174109i	0.702221	+	0.711959i	$0.252192\pi$
$828$	9.83680	−	18.4152i	0.341852	−	0.639974i
$829$	−11.9822	+	11.9822i	−0.416158	+	0.416158i	−0.883877	−	0.467719i	$-0.845076\pi$
$829$	−11.9822	+	11.9822i	−0.416158	+	0.416158i	0.467719	+	0.883877i	$0.345076\pi$
$830$	−31.8536	−	37.0145i	−1.10565	−	1.28479i
$831$	11.8951	+	6.60845i	0.412637	+	0.229245i
$832$	−0.0258644	−	0.345137i	−0.000896688	−	0.0119655i
$833$	−16.6567	+	19.3555i	−0.577122	+	0.670628i
$834$	−6.02517	+	2.22052i	−0.208635	+	0.0768904i
$835$	56.9272	−	8.58039i	1.97005	−	0.296937i
$836$	15.6128	+	12.4508i	0.539979	+	0.430619i
$837$	5.53633	−	7.11718i	0.191364	−	0.246006i
$838$	30.4026	−	19.1032i	1.05024	−	0.659909i
$839$	8.79361	+	3.83661i	0.303589	+	0.132455i	0.546164	−	0.837678i	$-0.316087\pi$
$839$	8.79361	+	3.83661i	0.303589	+	0.132455i	−0.242575	+	0.970133i	$0.577992\pi$
$840$	−5.44379	+	3.54715i	−0.187829	+	0.122388i
$841$	3.16713	+	28.8265i	0.109211	+	0.994019i
$842$	17.4658	−	10.0839i	0.601911	−	0.347514i
$843$	−45.0476	+	7.55181i	−1.55152	+	0.260098i
$844$	1.02861	−	0.0384879i	0.0354063	−	0.00132481i
$845$	−11.4179	−	50.0250i	−0.392787	−	1.72091i
$846$	42.8813	+	27.2084i	1.47429	+	0.935444i
$847$	0.587199	−	0.468275i	0.0201764	−	0.0160901i
$848$	−9.57595	+	10.3204i	−0.328840	+	0.354405i
$849$	−7.46040	−	0.998908i	−0.256040	−	0.0342824i
$850$	72.4396	−	5.42860i	2.48466	−	0.186199i
$851$	2.13242	−	56.9902i	0.0730985	−	1.95360i
$852$	−18.2884	+	17.5394i	−0.626551	+	0.600890i
$853$	−5.45398	+	1.46139i	−0.186741	+	0.0500370i	−0.350977	−	0.936384i	$-0.614151\pi$
$853$	−5.45398	+	1.46139i	−0.186741	+	0.0500370i	0.164237	+	0.986421i	$0.447484\pi$
$854$	−6.32882	+	3.04780i	−0.216568	+	0.104293i
$855$	0.334822	−	75.9781i	0.0114507	−	2.59840i
$856$	0.453804	−	4.02762i	0.0155107	−	0.137661i
$857$	54.4449	+	4.08008i	1.85980	+	0.139373i	0.956890	−	0.290451i	$-0.0938054\pi$
$857$	54.4449	+	4.08008i	1.85980	+	0.139373i	0.902913	+	0.429824i	$0.141424\pi$
$858$	2.50633	−	2.79218i	0.0855647	−	0.0953234i
$859$	8.70772	+	46.0214i	0.297103	+	1.57023i	0.739341	+	0.673332i	$0.235137\pi$
$859$	8.70772	+	46.0214i	0.297103	+	1.57023i	−0.442237	+	0.896898i	$0.645815\pi$
$860$	6.20560	+	0.232197i	0.211609	+	0.00791785i
$861$	−3.32537	+	0.430341i	−0.113328	+	0.0146660i
$862$	8.37725	−	44.2748i	0.285330	−	1.50801i
$863$	0.932385	−	4.08505i	0.0317388	−	0.139057i	−0.956576	−	0.291483i	$-0.905851\pi$
$863$	0.932385	−	4.08505i	0.0317388	−	0.139057i	0.988315	+	0.152426i	$0.0487086\pi$
$864$	−26.7313	−	5.76215i	−0.909417	−	0.196032i
$865$	20.9052	−	26.2143i	0.710799	−	0.891313i
$866$	−8.41652	+	27.2857i	−0.286005	+	0.927205i
$867$	−3.88118	−	1.79082i	−0.131812	−	0.0608194i
$868$	−0.574418	−	0.778309i	−0.0194970	−	0.0264175i
$869$	−18.5671	−	32.1592i	−0.629846	−	1.09092i
$870$	9.87782	−	63.9765i	0.334889	−	2.16900i
$871$	−1.62200	+	2.80939i	−0.0549594	+	0.0951925i
$872$	−0.598481	+	0.0674326i	−0.0202671	+	0.00228356i
$873$	−10.1932	+	25.6392i	−0.344989	+	0.867754i
$874$	−73.5251	+	16.7816i	−2.48702	+	0.567647i
$875$	4.78849	+	12.2009i	0.161881	+	0.412465i
$876$	−0.188564	−	0.913797i	−0.00637100	−	0.0308743i
$877$	20.4988	−	6.32305i	0.692196	−	0.213514i	0.0713551	−	0.997451i	$-0.477268\pi$
$877$	20.4988	−	6.32305i	0.692196	−	0.213514i	0.620841	+	0.783937i	$0.286791\pi$
$878$	21.5120	+	18.5126i	0.725995	+	0.624769i
$879$	29.1828	−	22.2908i	0.984312	−	0.751849i
$880$	28.9784	+	54.8299i	0.976863	+	1.84831i
$881$	5.61368	+	1.96431i	0.189130	+	0.0661794i	0.423182	−	0.906045i	$-0.360913\pi$
$881$	5.61368	+	1.96431i	0.189130	+	0.0661794i	−0.234052	+	0.972224i	$0.575199\pi$
$882$	−12.6058	−	32.5400i	−0.424460	−	1.09568i
$883$	−3.41041	−	7.08180i	−0.114770	−	0.238321i	0.835669	−	0.549233i	$-0.185080\pi$
$883$	−3.41041	−	7.08180i	−0.114770	−	0.238321i	−0.950439	+	0.310911i	$0.899366\pi$
$884$	1.25189	+	0.923938i	0.0421056	+	0.0310754i
$885$	0.880194	−	15.0797i	0.0295874	−	0.506899i
$886$	13.7935	+	9.40426i	0.463402	+	0.315942i
$887$	−4.59235	+	17.1389i	−0.154196	+	0.575467i	0.844977	+	0.534803i	$0.179614\pi$
$887$	−4.59235	+	17.1389i	−0.154196	+	0.575467i	−0.999173	+	0.0406644i	$0.987053\pi$
$888$	−23.9302	+	5.87884i	−0.803044	+	0.197281i
$889$	−2.18247	+	1.15347i	−0.0731978	+	0.0386862i
$890$	2.78427	−	5.78160i	0.0933289	−	0.193800i
$891$	14.6516	+	23.7806i	0.490846	+	0.796679i
$892$	−15.5008	−	3.53795i	−0.519004	−	0.118459i
$893$	−9.20698	−	61.0843i	−0.308100	−	2.04411i
$894$	6.50109	+	0.624082i	0.217429	+	0.0208724i
$895$	−51.9306	+	48.1846i	−1.73585	+	1.61063i
$896$	3.08347	−	5.83420i	0.103011	−	0.194907i
$897$	0.788901	+	4.70591i	0.0263406	+	0.157126i
$898$	2.33308	+	1.34701i	0.0778560	+	0.0449502i
$899$	−9.30290	−	0.885362i	−0.310269	−	0.0295285i
$900$	−13.5027	+	30.5801i	−0.450090	+	1.01934i
$901$	1.20187	+	10.6669i	0.0400402	+	0.355367i
$902$	0.710609	+	18.9914i	0.0236607	+	0.632346i
$903$	−0.353341	+	1.41142i	−0.0117584	+	0.0469691i
$904$	−4.99507	+	33.1401i	−0.166133	+	1.10222i
$905$	−28.3897	+	72.3358i	−0.943707	+	2.40452i
$906$	1.87687	−	2.25516i	0.0623548	−	0.0749227i
$907$	−7.34084	−	1.38896i	−0.243749	−	0.0461197i	0.0626016	−	0.998039i	$-0.480060\pi$
$907$	−7.34084	−	1.38896i	−0.243749	−	0.0461197i	−0.306350	+	0.951919i	$0.599108\pi$
$908$	11.5570	+	5.56555i	0.383532	+	0.184699i
$909$	2.95324	+	41.8843i	0.0979528	+	1.38921i
$910$	−0.505813	+	1.44553i	−0.0167676	+	0.0479189i
$911$	−6.47302	−	24.1576i	−0.214461	−	0.800378i	−0.986356	−	0.164628i	$-0.947358\pi$
$911$	−6.47302	−	24.1576i	−0.214461	−	0.800378i	0.771895	−	0.635750i	$-0.219309\pi$
$912$	26.4384	+	48.0867i	0.875463	+	1.59231i
$913$	−8.73256	−	20.0152i	−0.289006	−	0.662408i
$914$	9.98178	+	22.8785i	0.330168	+	0.756753i
$915$	26.4224	−	43.6326i	0.873499	−	1.44245i
$916$	2.01569	+	7.52266i	0.0666003	+	0.248556i
$917$	−3.14124	+	8.97715i	−0.103733	+	0.296452i
$918$	−27.4268	+	20.7587i	−0.905219	+	0.685140i
$919$	31.6896	+	15.2609i	1.04534	+	0.503410i	0.876082	−	0.482161i	$-0.160148\pi$
$919$	31.6896	+	15.2609i	1.04534	+	0.503410i	0.169260	+	0.985572i	$0.445862\pi$
$920$	−46.0165	−	8.70679i	−1.51712	−	0.287054i
$921$	−1.20575	−	3.27170i	−0.0397309	−	0.107806i
$922$	21.9557	−	55.9421i	0.723071	−	1.84236i
$923$	0.863149	−	5.72662i	0.0284109	−	0.188494i
$924$	2.88120	−	0.823188i	0.0947845	−	0.0270809i
$925$	3.41433	+	91.2499i	0.112262	+	3.00028i
$926$	3.05892	+	27.1486i	0.100522	+	0.892160i
$927$	1.64324	+	15.1853i	0.0539710	+	0.498750i
$928$	9.82184	+	26.5836i	0.322418	+	0.872648i
$929$	−4.85046	−	2.80041i	−0.159138	−	0.0918786i	0.418316	−	0.908302i	$-0.362621\pi$
$929$	−4.85046	−	2.80041i	−0.159138	−	0.0918786i	−0.577454	+	0.816423i	$0.695954\pi$
$930$	19.5411	+	7.29966i	0.640778	+	0.239365i
$931$	−19.8345	+	37.5287i	−0.650049	+	1.22995i
$932$	18.7961	−	17.4403i	0.615687	−	0.571274i
$933$	−4.07320	−	8.93095i	−0.133350	−	0.292386i
$934$	0.289350	+	1.91971i	0.00946783	+	0.0628150i
$935$	46.0995	+	10.5219i	1.50762	+	0.344103i
$936$	1.86146	−	0.886350i	0.0608439	−	0.0289712i
$937$	−10.7173	+	22.2548i	−0.350120	+	0.727033i	−0.999439	−	0.0334837i	$-0.989340\pi$
$937$	−10.7173	+	22.2548i	−0.350120	+	0.727033i	0.649319	+	0.760516i	$0.275054\pi$
$938$	−6.80201	+	3.59497i	−0.222093	+	0.117380i
$939$	−14.7134	+	50.6514i	−0.480153	+	1.65295i
$940$	−10.2396	+	38.2145i	−0.333977	+	1.24642i
$941$	−7.83727	−	5.34336i	−0.255488	−	0.174188i	0.428803	−	0.903398i	$-0.358936\pi$
$941$	−7.83727	−	5.34336i	−0.255488	−	0.174188i	−0.684290	+	0.729210i	$0.739888\pi$
$942$	−10.2001	+	5.12109i	−0.332338	+	0.166854i
$943$	−19.4461	−	14.3519i	−0.633252	−	0.467361i
$944$	4.73359	+	9.82940i	0.154065	+	0.319920i
$945$	−9.25429	−	6.65868i	−0.301042	−	0.216607i
$946$	7.78376	+	2.72365i	0.253072	+	0.0885536i
$947$	−27.7644	−	52.5329i	−0.902223	−	1.70709i	−0.681594	−	0.731731i	$-0.738713\pi$
$947$	−27.7644	−	52.5329i	−0.902223	−	1.70709i	−0.220629	−	0.975358i	$-0.570811\pi$
$948$	2.70077	+	20.8696i	0.0877170	+	0.677815i
$949$	0.161635	+	0.139098i	0.00524688	+	0.00451530i
$950$	115.388	−	35.5923i	3.74367	−	1.15477i
$951$	−44.8661	+	39.9173i	−1.45488	+	1.29441i
$952$	−1.30721	−	3.33071i	−0.0423668	−	0.107949i
$953$	15.1319	−	3.45376i	0.490170	−	0.111878i	0.0297101	−	0.999559i	$-0.490542\pi$
$953$	15.1319	−	3.45376i	0.490170	−	0.111878i	0.460460	+	0.887680i	$0.347684\pi$
$954$	−13.6315	−	5.41940i	−0.441335	−	0.175460i
$955$	−68.5095	+	7.71917i	−2.21692	+	0.249786i
$956$	10.7188	−	18.5655i	0.346671	−	0.600452i
$957$	12.6535	−	26.0358i	0.409029	−	0.841619i
$958$	−33.9537	−	58.8096i	−1.09700	−	1.90005i
$959$	0.864201	+	1.17095i	0.0279065	+	0.0378120i
$960$	0.543427	+	5.93579i	0.0175390	+	0.191577i
$961$	−8.24981	+	26.7452i	−0.266123	+	0.862750i
$962$	−3.62131	+	4.54097i	−0.116756	+	0.146407i
$963$	6.87755	−	1.81039i	0.221626	−	0.0583390i
$964$	5.35836	−	23.4765i	0.172581	−	0.756128i
$965$	1.55312	−	8.20843i	0.0499966	−	0.264239i
$966$	−4.35363	+	10.4454i	−0.140076	+	0.336076i
$967$	−44.0976	−	1.65002i	−1.41808	−	0.0530609i	−0.682693	−	0.730705i	$-0.739192\pi$
$967$	−44.0976	−	1.65002i	−1.41808	−	0.0530609i	−0.735390	+	0.677644i	$0.763001\pi$
$968$	−0.434863	−	2.29831i	−0.0139770	−	0.0738704i
$969$	40.9392	+	8.63618i	1.31516	+	0.277434i
$970$	−63.6514	−	4.77001i	−2.04372	−	0.153156i
$971$	−5.19866	+	46.1394i	−0.166833	+	1.48068i	0.579424	+	0.815027i	$0.303278\pi$
$971$	−5.19866	+	46.1394i	−0.166833	+	1.48068i	−0.746257	+	0.665658i	$0.768151\pi$
$972$	−2.47933	−	15.6333i	−0.0795246	−	0.501440i
$973$	1.05598	−	0.508531i	0.0338530	−	0.0163028i
$974$	−8.27708	+	2.21784i	−0.265215	+	0.0710641i
$975$	−1.82270	−	7.41940i	−0.0583731	−	0.237611i
$976$	−1.37754	+	36.8156i	−0.0440940	+	1.17844i
$977$	−2.49453	+	0.186939i	−0.0798072	+	0.00598072i	−0.114574	−	0.993415i	$-0.536550\pi$
$977$	−2.49453	+	0.186939i	−0.0798072	+	0.00598072i	0.0347667	+	0.999395i	$0.488931\pi$
$978$	−0.171732	−	0.417196i	−0.00549139	−	0.0133405i
$979$	1.95181	−	2.10355i	0.0623800	−	0.0672297i
$980$	21.2542	−	16.9496i	0.678940	−	0.541437i
$981$	−0.489677	−	0.936480i	−0.0156342	−	0.0298995i
$982$	−3.84529	−	16.8473i	−0.122708	−	0.537619i
$983$	60.7050	−	2.27142i	1.93619	−	0.0724470i	0.958822	−	0.284006i	$-0.0916636\pi$
$983$	60.7050	−	2.27142i	1.93619	−	0.0724470i	0.977365	+	0.211559i	$0.0678541\pi$
$984$	−3.65434	+	9.78262i	−0.116496	+	0.311858i
$985$	51.1605	−	29.5375i	1.63011	−	0.941143i
$986$	33.4045	+	12.4472i	1.06382	+	0.396401i
$987$	−8.26558	−	4.19554i	−0.263096	−	0.133545i
$988$	2.37057	+	1.03427i	0.0754179	+	0.0329045i
$989$	−8.87984	+	5.57957i	−0.282362	+	0.177420i
$990$	−42.3649	+	48.7924i	−1.34645	+	1.55072i
$991$	0.911519	+	0.726912i	0.0289554	+	0.0230911i	0.637861	−	0.770152i	$-0.279820\pi$
$991$	0.911519	+	0.726912i	0.0289554	+	0.0230911i	−0.608905	+	0.793243i	$0.708391\pi$
$992$	−9.03025	+	1.36109i	−0.286711	+	0.0432147i
$993$	−0.411670	+	2.39100i	−0.0130640	+	0.0758762i
$994$	8.95906	−	10.4106i	0.284164	−	0.330205i
$995$	−5.18457	−	69.1833i	−0.164362	−	2.19326i
$996$	0.204136	+	12.3733i	0.00646830	+	0.392064i
$997$	14.7562	+	17.1471i	0.467335	+	0.543053i	0.941336	−	0.337471i	$-0.109572\pi$
$997$	14.7562	+	17.1471i	0.467335	+	0.543053i	−0.474001	+	0.880524i	$0.657191\pi$
$998$	−51.0449	+	51.0449i	−1.61580	+	1.61580i
$999$	−24.7869	−	35.4278i	−0.784223	−	1.12088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.7	yes	672
3.2	odd	2		783.2.be.a.710.22		672
9.4	even	3		783.2.be.a.449.7		672
9.5	odd	6	inner	261.2.x.a.14.22	✓	672
29.27	odd	28	inner	261.2.x.a.56.22	yes	672
87.56	even	28		783.2.be.a.143.7		672
261.85	odd	84		783.2.be.a.665.22		672
261.230	even	84	inner	261.2.x.a.230.7	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.22	✓	672	9.5	odd	6	inner
261.2.x.a.56.22	yes	672	29.27	odd	28	inner
261.2.x.a.101.7	yes	672	1.1	even	1	trivial
261.2.x.a.230.7	yes	672	261.230	even	84	inner
783.2.be.a.143.7		672	87.56	even	28
783.2.be.a.449.7		672	9.4	even	3
783.2.be.a.665.22		672	261.85	odd	84
783.2.be.a.710.22		672	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.694410 + 1.59161i) q^{2} +(0.725664 - 1.57271i) q^{3} +(-0.690656 - 0.744350i) q^{4} +(-3.95207 - 0.595679i) q^{5} +(1.99922 + 2.24708i) q^{6} +(-0.402428 - 0.373398i) q^{7} +(-1.61379 + 0.564688i) q^{8} +(-1.94682 - 2.28252i) q^{9} +(3.69245 - 5.87649i) q^{10} +(2.35239 - 2.02439i) q^{11} +(-1.67183 + 0.546052i) q^{12} +(0.226431 - 0.332113i) q^{13} +(0.873753 - 0.381215i) q^{14} +(-3.80471 + 5.78319i) q^{15} +(0.373633 - 4.98578i) q^{16} +(-2.69557 - 2.69557i) q^{17} +(4.98476 - 1.51357i) q^{18} +(-5.36550 - 3.37137i) q^{19} +(2.28613 + 3.35314i) q^{20} +(-0.879274 + 0.361940i) q^{21} +(1.58851 + 5.14983i) q^{22} +(-6.37987 - 2.50392i) q^{23} +(-0.282977 + 2.94779i) q^{24} +(10.4862 + 3.23456i) q^{25} +(0.371356 + 0.591010i) q^{26} +(-5.00247 + 1.40544i) q^{27} +0.557437i q^{28} +(4.01043 + 3.59394i) q^{29} +(-6.56253 - 10.0715i) q^{30} +(-1.39623 + 1.03046i) q^{31} +(4.65275 + 2.45905i) q^{32} +(-1.47674 - 5.16865i) q^{33} +(6.16211 - 2.41845i) q^{34} +(1.36800 + 1.71542i) q^{35} +(-0.354407 + 3.02555i) q^{36} +(2.74830 + 7.85418i) q^{37} +(9.09175 - 6.19865i) q^{38} +(-0.358004 - 0.597111i) q^{39} +(6.71417 - 1.27039i) q^{40} +(3.40625 + 0.912701i) q^{41} +(0.0345121 - 1.65079i) q^{42} +(0.908650 - 1.23118i) q^{43} +(-3.13155 - 0.352841i) q^{44} +(6.33434 + 10.1804i) q^{45} +(8.41550 - 8.41550i) q^{46} +(6.35885 + 7.38911i) q^{47} +(-7.57005 - 4.20562i) q^{48} +(-0.500589 - 6.67989i) q^{49} +(-12.4299 + 14.4437i) q^{50} +(-6.19542 + 2.28326i) q^{51} +(-0.403594 + 0.0608320i) q^{52} +(-2.20154 - 1.75567i) q^{53} +(1.23686 - 8.93792i) q^{54} +(-10.5027 + 6.59928i) q^{55} +(0.860286 + 0.375339i) q^{56} +(-9.19573 + 5.99189i) q^{57} +(-8.50503 + 3.88735i) q^{58} +(-1.88972 + 1.09103i) q^{59} +(6.93247 - 1.16216i) q^{60} +(-7.36347 + 0.275521i) q^{61} +(-0.670535 - 2.93781i) q^{62} +(-0.0688326 + 1.64549i) q^{63} +(0.673195 - 0.536855i) q^{64} +(-1.09270 + 1.17765i) q^{65} +(9.25191 + 1.23878i) q^{66} +(-8.04795 + 0.603111i) q^{67} +(-0.144736 + 3.86816i) q^{68} +(-8.56758 + 8.21668i) q^{69} +(-3.68022 + 0.986111i) q^{70} +(12.9810 - 6.25130i) q^{71} +(4.43066 + 2.58414i) q^{72} +(-0.0593993 + 0.527184i) q^{73} +(-14.4092 - 1.07982i) q^{74} +(12.6965 - 14.1445i) q^{75} +(1.19624 + 6.32227i) q^{76} +(-1.70257 - 0.0637057i) q^{77} +(1.19897 - 0.155160i) q^{78} +(2.22446 - 11.7566i) q^{79} +(-4.44655 + 19.4816i) q^{80} +(-1.41976 + 8.88731i) q^{81} +(-3.81799 + 4.78761i) q^{82} +(2.07398 - 6.72367i) q^{83} +(0.876686 + 0.404512i) q^{84} +(9.04738 + 12.2588i) q^{85} +(1.32857 + 2.30115i) q^{86} +(8.56245 - 3.69924i) q^{87} +(-2.65310 + 4.59530i) q^{88} +(0.918803 - 0.103524i) q^{89} +(-20.6017 + 3.01242i) q^{90} +(-0.215132 + 0.0491025i) q^{91} +(2.54251 + 6.47821i) q^{92} +(0.607425 + 2.94363i) q^{93} +(-16.1762 + 4.98970i) q^{94} +(19.1966 + 16.5200i) q^{95} +(7.24370 - 5.53297i) q^{96} +(-4.29748 - 8.13124i) q^{97} +(10.9794 + 3.84185i) q^{98} +(-9.20039 - 1.42823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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