LMFDB - Embedded newform 192.2.s.a.59.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			59.24
Character	$\chi$	$=$	192.59
Dual form			192.2.s.a.179.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05577 - 0.940934i) q^{2} +(-1.24680 - 1.20229i) q^{3} +(0.229286 - 1.98681i) q^{4} +(0.128682 - 0.646927i) q^{5} +(-2.44760 - 0.0961797i) q^{6} +(0.120549 + 0.0499330i) q^{7} +(-1.62739 - 2.31335i) q^{8} +(0.109011 + 2.99802i) q^{9} +O(q^{10})$	\(q+(1.05577 - 0.940934i) q^{2} +(-1.24680 - 1.20229i) q^{3} +(0.229286 - 1.98681i) q^{4} +(0.128682 - 0.646927i) q^{5} +(-2.44760 - 0.0961797i) q^{6} +(0.120549 + 0.0499330i) q^{7} +(-1.62739 - 2.31335i) q^{8} +(0.109011 + 2.99802i) q^{9} +(-0.472858 - 0.804085i) q^{10} +(-1.51860 - 2.27274i) q^{11} +(-2.67459 + 2.20149i) q^{12} +(1.27159 - 0.252935i) q^{13} +(0.174255 - 0.0607110i) q^{14} +(-0.938232 + 0.651875i) q^{15} +(-3.89486 - 0.911097i) q^{16} +(1.71615 + 1.71615i) q^{17} +(2.93603 + 3.06264i) q^{18} +(1.38425 - 0.275345i) q^{19} +(-1.25582 - 0.403998i) q^{20} +(-0.0902664 - 0.207191i) q^{21} +(-3.74179 - 0.970585i) q^{22} +(3.71748 - 1.53983i) q^{23} +(-0.752291 + 4.84087i) q^{24} +(4.21744 + 1.74692i) q^{25} +(1.10451 - 1.46352i) q^{26} +(3.46856 - 3.86899i) q^{27} +(0.126848 - 0.228059i) q^{28} +(5.35197 + 3.57607i) q^{29} +(-0.377183 + 1.57104i) q^{30} -3.91687 q^{31} +(-4.96934 + 2.70290i) q^{32} +(-0.839104 + 4.65944i) q^{33} +(3.42664 + 0.197070i) q^{34} +(0.0478155 - 0.0715609i) q^{35} +(5.98150 + 0.470819i) q^{36} +(1.85070 - 9.30412i) q^{37} +(1.20237 - 1.59319i) q^{38} +(-1.88951 - 1.21346i) q^{39} +(-1.70599 + 0.755115i) q^{40} +(4.19808 + 10.1351i) q^{41} +(-0.290253 - 0.133810i) q^{42} +(4.03057 + 6.03217i) q^{43} +(-4.86371 + 2.49606i) q^{44} +(1.95353 + 0.315268i) q^{45} +(2.47591 - 5.12361i) q^{46} +(-3.94696 + 3.94696i) q^{47} +(3.76070 + 5.81869i) q^{48} +(-4.93771 - 4.93771i) q^{49} +(6.09637 - 2.12399i) q^{50} +(-0.0763875 - 4.20300i) q^{51} +(-0.210977 - 2.58440i) q^{52} +(-7.62801 + 5.09687i) q^{53} +(0.0215329 - 7.34844i) q^{54} +(-1.66572 + 0.689962i) q^{55} +(-0.0806672 - 0.360133i) q^{56} +(-2.05693 - 1.32097i) q^{57} +(9.01527 - 1.26035i) q^{58} +(-2.03231 - 0.404252i) q^{59} +(1.08003 + 2.01356i) q^{60} +(-7.97360 - 5.32779i) q^{61} +(-4.13530 + 3.68552i) q^{62} +(-0.136559 + 0.366851i) q^{63} +(-2.70321 + 7.52945i) q^{64} -0.855173i q^{65} +(3.49833 + 5.70883i) q^{66} +(3.96652 - 5.93631i) q^{67} +(3.80316 - 3.01618i) q^{68} +(-6.48627 - 2.54962i) q^{69} +(-0.0168521 - 0.120543i) q^{70} +(3.68758 - 8.90261i) q^{71} +(6.75808 - 5.13112i) q^{72} +(2.46777 + 5.95773i) q^{73} +(-6.80065 - 11.5644i) q^{74} +(-3.15800 - 7.24864i) q^{75} +(-0.229670 - 2.81339i) q^{76} +(-0.0695805 - 0.349805i) q^{77} +(-3.13667 + 0.496782i) q^{78} +(-10.3595 + 10.3595i) q^{79} +(-1.09061 + 2.40245i) q^{80} +(-8.97623 + 0.653634i) q^{81} +(13.9686 + 6.75014i) q^{82} +(2.59720 + 13.0570i) q^{83} +(-0.432346 + 0.131837i) q^{84} +(1.33106 - 0.889387i) q^{85} +(9.93121 + 2.57606i) q^{86} +(-2.37336 - 10.8932i) q^{87} +(-2.78631 + 7.21169i) q^{88} +(0.461388 - 1.11389i) q^{89} +(2.35911 - 1.50529i) q^{90} +(0.165918 + 0.0330032i) q^{91} +(-2.20699 - 7.73900i) q^{92} +(4.88354 + 4.70920i) q^{93} +(-0.453239 + 7.88090i) q^{94} -0.930943i q^{95} +(9.44542 + 2.60461i) q^{96} +4.33905i q^{97} +(-9.85913 - 0.567009i) q^{98} +(6.64818 - 4.80054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{16}\right)$

Coefficient data

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

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

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

$2$	1.05577	−	0.940934i	0.746540	−	0.665341i
$2$	1.05577	−	0.940934i	0.746540	−	0.665341i
$3$	−1.24680	−	1.20229i	−0.719839	−	0.694141i
$3$	−1.24680	−	1.20229i	−0.719839	−	0.694141i
$4$	0.229286	−	1.98681i	0.114643	−	0.993407i
$5$	0.128682	−	0.646927i	0.0575482	−	0.289315i	−0.941285	−	0.337614i	$-0.890380\pi$
$5$	0.128682	−	0.646927i	0.0575482	−	0.289315i	0.998833	+	0.0482994i	$0.0153802\pi$
$6$	−2.44760	−	0.0961797i	−0.999229	−	0.0392652i
$7$	0.120549	+	0.0499330i	0.0455632	+	0.0188729i	0.405349	−	0.914162i	$-0.367150\pi$
$7$	0.120549	+	0.0499330i	0.0455632	+	0.0188729i	−0.359785	+	0.933035i	$0.617150\pi$
$8$	−1.62739	−	2.31335i	−0.575369	−	0.817894i
$9$	0.109011	+	2.99802i	0.0363370	+	0.999340i
$10$	−0.472858	−	0.804085i	−0.149531	−	0.254274i
$11$	−1.51860	−	2.27274i	−0.457875	−	0.685258i	0.528656	−	0.848836i	$-0.322696\pi$
$11$	−1.51860	−	2.27274i	−0.457875	−	0.685258i	−0.986530	+	0.163578i	$0.947696\pi$
$12$	−2.67459	+	2.20149i	−0.772089	+	0.635515i
$13$	1.27159	−	0.252935i	0.352675	−	0.0701514i	−0.0155737	−	0.999879i	$-0.504957\pi$
$13$	1.27159	−	0.252935i	0.352675	−	0.0701514i	0.368249	+	0.929727i	$0.379957\pi$
$14$	0.174255	−	0.0607110i	0.0465717	−	0.0162257i
$15$	−0.938232	+	0.651875i	−0.242251	+	0.168313i
$16$	−3.89486	−	0.911097i	−0.973714	−	0.227774i
$17$	1.71615	+	1.71615i	0.416228	+	0.416228i	0.883901	−	0.467673i	$-0.154908\pi$
$17$	1.71615	+	1.71615i	0.416228	+	0.416228i	−0.467673	+	0.883901i	$0.654908\pi$
$18$	2.93603	+	3.06264i	0.692029	+	0.721870i
$19$	1.38425	−	0.275345i	0.317569	−	0.0631685i	−0.0337320	−	0.999431i	$-0.510739\pi$
$19$	1.38425	−	0.275345i	0.317569	−	0.0631685i	0.351301	+	0.936262i	$0.385739\pi$
$20$	−1.25582	−	0.403998i	−0.280810	−	0.0903367i
$21$	−0.0902664	−	0.207191i	−0.0196977	−	0.0452127i
$22$	−3.74179	−	0.970585i	−0.797752	−	0.206929i
$23$	3.71748	−	1.53983i	0.775148	−	0.321077i	0.0401925	−	0.999192i	$-0.487203\pi$
$23$	3.71748	−	1.53983i	0.775148	−	0.321077i	0.734956	+	0.678115i	$0.237203\pi$
$24$	−0.752291	+	4.84087i	−0.153561	+	0.988139i
$25$	4.21744	+	1.74692i	0.843488	+	0.349384i
$26$	1.10451	−	1.46352i	0.216611	−	0.287020i
$27$	3.46856	−	3.86899i	0.667526	−	0.744587i
$28$	0.126848	−	0.228059i	0.0239720	−	0.0430992i
$29$	5.35197	+	3.57607i	0.993835	+	0.664059i	0.942355	−	0.334615i	$-0.108606\pi$
$29$	5.35197	+	3.57607i	0.993835	+	0.664059i	0.0514801	+	0.998674i	$0.483606\pi$
$30$	−0.377183	+	1.57104i	−0.0688638	+	0.286832i
$31$	−3.91687			−0.703490			−0.351745	−	0.936096i	$-0.614412\pi$
$31$	−3.91687			−0.703490			−0.351745	+	0.936096i	$0.614412\pi$
$32$	−4.96934	+	2.70290i	−0.878464	+	0.477809i
$33$	−0.839104	+	4.65944i	−0.146069	+	0.811105i
$34$	3.42664	+	0.197070i	0.587664	+	0.0337972i
$35$	0.0478155	−	0.0715609i	0.00808229	−	0.0120960i
$36$	5.98150	+	0.470819i	0.996916	+	0.0784698i
$37$	1.85070	−	9.30412i	0.304254	−	1.52959i	−0.461900	−	0.886932i	$-0.652832\pi$
$37$	1.85070	−	9.30412i	0.304254	−	1.52959i	0.766154	−	0.642656i	$-0.222168\pi$
$38$	1.20237	−	1.59319i	0.195050	−	0.258450i
$39$	−1.88951	−	1.21346i	−0.302564	−	0.194308i
$40$	−1.70599	+	0.755115i	−0.269740	+	0.119394i
$41$	4.19808	+	10.1351i	0.655629	+	1.58283i	0.804487	+	0.593971i	$0.202441\pi$
$41$	4.19808	+	10.1351i	0.655629	+	1.58283i	−0.148857	+	0.988859i	$0.547559\pi$
$42$	−0.290253	−	0.133810i	−0.0447870	−	0.0206474i
$43$	4.03057	+	6.03217i	0.614656	+	0.919897i	0.999996	−	0.00287729i	$-0.000915872\pi$
$43$	4.03057	+	6.03217i	0.614656	+	0.919897i	−0.385340	+	0.922775i	$0.625916\pi$
$44$	−4.86371	+	2.49606i	−0.733232	+	0.376296i
$45$	1.95353	+	0.315268i	0.291215	+	0.0469974i
$46$	2.47591	−	5.12361i	0.365053	−	0.755435i
$47$	−3.94696	+	3.94696i	−0.575724	+	0.575724i	−0.933722	−	0.357999i	$-0.883459\pi$
$47$	−3.94696	+	3.94696i	−0.575724	+	0.575724i	0.357999	+	0.933722i	$0.383459\pi$
$48$	3.76070	+	5.81869i	0.542810	+	0.839855i
$49$	−4.93771	−	4.93771i	−0.705387	−	0.705387i
$50$	6.09637	−	2.12399i	0.862157	−	0.300378i
$51$	−0.0763875	−	4.20300i	−0.0106964	−	0.588538i
$52$	−0.210977	−	2.58440i	−0.0292572	−	0.358392i
$53$	−7.62801	+	5.09687i	−1.04779	+	0.700109i	−0.955310	−	0.295605i	$-0.904479\pi$
$53$	−7.62801	+	5.09687i	−1.04779	+	0.700109i	−0.0924776	+	0.995715i	$0.529479\pi$
$54$	0.0215329	−	7.34844i	0.00293026	−	0.999996i
$55$	−1.66572	+	0.689962i	−0.224605	+	0.0930344i
$56$	−0.0806672	−	0.360133i	−0.0107796	−	0.0481248i
$57$	−2.05693	−	1.32097i	−0.272447	−	0.174967i
$58$	9.01527	−	1.26035i	1.18376	−	0.165492i
$59$	−2.03231	−	0.404252i	−0.264584	−	0.0526291i	0.0610153	−	0.998137i	$-0.480566\pi$
$59$	−2.03231	−	0.404252i	−0.264584	−	0.0526291i	−0.325600	+	0.945508i	$0.605566\pi$
$60$	1.08003	+	2.01356i	0.139431	+	0.259949i
$61$	−7.97360	−	5.32779i	−1.02092	−	0.682154i	−0.0719091	−	0.997411i	$-0.522909\pi$
$61$	−7.97360	−	5.32779i	−1.02092	−	0.682154i	−0.949006	+	0.315257i	$0.897909\pi$
$62$	−4.13530	+	3.68552i	−0.525183	+	0.468061i
$63$	−0.136559	+	0.366851i	−0.0172048	+	0.0462189i
$64$	−2.70321	+	7.52945i	−0.337902	+	0.941181i
$65$		−	0.855173i		−	0.106071i
$66$	3.49833	+	5.70883i	0.430615	+	0.702708i
$67$	3.96652	−	5.93631i	0.484587	−	0.725236i	−0.505938	−	0.862570i	$-0.668853\pi$
$67$	3.96652	−	5.93631i	0.484587	−	0.725236i	0.990525	+	0.137334i	$0.0438534\pi$
$68$	3.80316	−	3.01618i	0.461201	−	0.365766i
$69$	−6.48627	−	2.54962i	−0.780855	−	0.306938i
$70$	−0.0168521	−	0.120543i	−0.00201421	−	0.0144076i
$71$	3.68758	−	8.90261i	0.437635	−	1.05655i	−0.539128	−	0.842224i	$-0.681246\pi$
$71$	3.68758	−	8.90261i	0.437635	−	1.05655i	0.976763	−	0.214321i	$-0.0687540\pi$
$72$	6.75808	−	5.13112i	0.796447	−	0.604709i
$73$	2.46777	+	5.95773i	0.288831	+	0.697299i	0.999984	−	0.00573816i	$-0.00182652\pi$
$73$	2.46777	+	5.95773i	0.288831	+	0.697299i	−0.711153	+	0.703038i	$0.751827\pi$
$74$	−6.80065	−	11.5644i	−0.790560	−	1.34433i
$75$	−3.15800	−	7.24864i	−0.364654	−	0.837000i
$76$	−0.229670	−	2.81339i	−0.0263449	−	0.322717i
$77$	−0.0695805	−	0.349805i	−0.00792944	−	0.0398640i
$78$	−3.13667	+	0.496782i	−0.355158	+	0.0562495i
$79$	−10.3595	+	10.3595i	−1.16553	+	1.16553i	−0.182288	+	0.983245i	$0.558350\pi$
$79$	−10.3595	+	10.3595i	−1.16553	+	1.16553i	−0.983245	+	0.182288i	$0.941650\pi$
$80$	−1.09061	+	2.40245i	−0.121934	+	0.268602i
$81$	−8.97623	+	0.653634i	−0.997359	+	0.0726260i
$82$	13.9686	+	6.75014i	1.54257	+	0.745428i
$83$	2.59720	+	13.0570i	0.285079	+	1.43319i	0.812190	+	0.583394i	$0.198275\pi$
$83$	2.59720	+	13.0570i	0.285079	+	1.43319i	−0.527110	+	0.849797i	$0.676725\pi$
$84$	−0.432346	+	0.131837i	−0.0471729	+	0.0143845i
$85$	1.33106	−	0.889387i	0.144374	−	0.0964676i
$86$	9.93121	+	2.57606i	1.07091	+	0.277784i
$87$	−2.37336	−	10.8932i	−0.254451	−	1.16788i
$88$	−2.78631	+	7.21169i	−0.297022	+	0.768769i
$89$	0.461388	−	1.11389i	0.0489070	−	0.118072i	−0.897538	−	0.440937i	$-0.854646\pi$
$89$	0.461388	−	1.11389i	0.0489070	−	0.118072i	0.946445	+	0.322865i	$0.104646\pi$
$90$	2.35911	−	1.50529i	0.248673	−	0.158672i
$91$	0.165918	+	0.0330032i	0.0173930	+	0.00345968i
$92$	−2.20699	−	7.73900i	−0.230095	−	0.806847i
$93$	4.88354	+	4.70920i	0.506400	+	0.488321i
$94$	−0.453239	+	7.88090i	−0.0467480	+	0.812853i
$95$		−	0.930943i		−	0.0955127i
$96$	9.44542	+	2.60461i	0.964019	+	0.265832i
$97$			4.33905i			0.440563i	0.975436	+	0.220282i	$0.0706976\pi$
$97$			4.33905i			0.440563i	−0.975436	+	0.220282i	$0.929302\pi$
$98$	−9.85913	−	0.567009i	−0.995922	−	0.0572765i
$99$	6.64818	−	4.80054i	0.668168	−	0.482473i
$100$	4.43781	−	7.97873i	0.443781	−	0.797873i
$101$	−14.2891	−	2.84228i	−1.42182	−	0.282817i	−0.576507	−	0.817092i	$-0.695585\pi$
$101$	−14.2891	−	2.84228i	−1.42182	−	0.282817i	−0.845311	+	0.534275i	$0.820585\pi$
$102$	−4.03540	−	4.36551i	−0.399564	−	0.432250i
$103$	−5.09354	+	12.2969i	−0.501882	+	1.21165i	0.446576	+	0.894746i	$0.352643\pi$
$103$	−5.09354	+	12.2969i	−0.501882	+	1.21165i	−0.948458	+	0.316904i	$0.897357\pi$
$104$	−2.65450	−	2.53001i	−0.260295	−	0.248088i
$105$	−0.145653	+	0.0317341i	−0.0142143	+	0.00309693i
$106$	−3.25758	+	12.5586i	−0.316404	+	1.21980i
$107$	−2.45827	+	1.64256i	−0.237650	+	0.158792i	−0.668693	−	0.743539i	$-0.733146\pi$
$107$	−2.45827	+	1.64256i	−0.237650	+	0.158792i	0.431043	+	0.902331i	$0.358146\pi$
$108$	−6.89166	−	7.77850i	−0.663150	−	0.748486i
$109$	−1.12559	−	5.65875i	−0.107812	−	0.542010i	−0.996507	−	0.0835098i	$-0.973387\pi$
$109$	−1.12559	−	5.65875i	−0.107812	−	0.542010i	0.888695	−	0.458500i	$-0.151613\pi$
$110$	−1.10940	+	2.29577i	−0.105777	+	0.218893i
$111$	−13.4937	+	9.37528i	−1.28076	+	0.889862i
$112$	−0.424027	−	0.304314i	−0.0400668	−	0.0287549i
$113$	12.8274	−	12.8274i	1.20670	−	1.20670i	0.234611	−	0.972089i	$-0.424619\pi$
$113$	12.8274	−	12.8274i	1.20670	−	1.20670i	0.972089	−	0.234611i	$-0.0753815\pi$
$114$	−3.41458	+	0.540798i	−0.319805	+	0.0506504i
$115$	−0.517786	−	2.60309i	−0.0482838	−	0.242739i
$116$	8.33211	−	9.81342i	0.773617	−	0.911153i
$117$	0.896920	+	3.78467i	0.0829203	+	0.349893i
$118$	−2.52602	+	1.48547i	−0.232539	+	0.136749i
$119$	0.121188	+	0.292573i	0.0111093	+	0.0268201i
$120$	3.03489	+	1.10961i	0.277046	+	0.101293i
$121$	1.35030	−	3.25990i	0.122754	−	0.296355i
$122$	−13.4314	+	1.87773i	−1.21602	+	0.170002i
$123$	6.95109	−	17.6837i	0.626759	−	1.59448i
$124$	−0.898083	+	7.78209i	−0.0806502	+	0.698852i
$125$	3.50511	−	5.24577i	0.313507	−	0.469196i
$126$	0.201009	+	0.515802i	0.0179073	+	0.0459513i
$127$		−	7.46755i		−	0.662638i	−0.943519	−	0.331319i	$-0.892506\pi$
$127$		−	7.46755i		−	0.662638i	0.943519	−	0.331319i	$-0.107494\pi$
$128$	4.23075	+	10.4929i	0.373949	+	0.927449i
$129$	2.22710	−	12.3668i	0.196085	−	1.08884i
$130$	−0.804661	−	0.902863i	−0.0705735	−	0.0791863i
$131$	10.0212	+	6.69593i	0.875553	+	0.585026i	0.910105	−	0.414377i	$-0.136000\pi$
$131$	10.0212	+	6.69593i	0.875553	+	0.585026i	−0.0345520	+	0.999403i	$0.511000\pi$
$132$	9.06505	+	2.73549i	0.789011	+	0.238094i
$133$	0.180619	+	0.0359274i	0.0156617	+	0.00311530i
$134$	−1.39796	−	9.99959i	−0.120766	−	0.863833i
$135$	−2.05661	−	2.74178i	−0.177005	−	0.235975i
$136$	1.17722	−	6.76291i	0.100946	−	0.579915i
$137$	3.08098	−	1.27618i	0.263226	−	0.109032i	−0.247167	−	0.968973i	$-0.579500\pi$
$137$	3.08098	−	1.27618i	0.263226	−	0.109032i	0.510393	+	0.859941i	$0.329500\pi$
$138$	−9.24701	+	3.41135i	−0.787158	+	0.290393i
$139$	−13.1348	+	8.77641i	−1.11408	+	0.744405i	−0.969501	−	0.245088i	$-0.921183\pi$
$139$	−13.1348	+	8.77641i	−1.11408	+	0.744405i	−0.144580	+	0.989493i	$0.546183\pi$
$140$	−0.131215	−	0.111408i	−0.0110897	−	0.00941572i
$141$	9.66645	−	0.175683i	0.814062	−	0.0147952i
$142$	−4.48354	−	12.8688i	−0.376251	−	1.07993i
$143$	−2.50589	−	2.50589i	−0.209553	−	0.209553i
$144$	2.30690	−	11.7762i	0.192242	−	0.981348i
$145$	3.00216	−	3.00216i	0.249316	−	0.249316i
$146$	8.21122	+	3.96796i	0.679566	+	0.328391i
$147$	0.219782	+	12.0929i	0.0181273	+	0.997403i
$148$	−18.0612	−	5.81031i	−1.48462	−	0.477604i
$149$	−3.46343	−	5.18338i	−0.283735	−	0.424639i	0.662037	−	0.749471i	$-0.269692\pi$
$149$	−3.46343	−	5.18338i	−0.283735	−	0.424639i	−0.945772	+	0.324832i	$0.894692\pi$
$150$	−10.1546	−	4.68140i	−0.829119	−	0.382235i
$151$	−3.01311	−	7.27429i	−0.245204	−	0.591974i	0.752581	−	0.658499i	$-0.228809\pi$
$151$	−3.01311	−	7.27429i	−0.245204	−	0.591974i	−0.997785	+	0.0665258i	$0.978809\pi$
$152$	−2.88969	−	2.75417i	−0.234385	−	0.223393i
$153$	−4.95798	+	5.33213i	−0.400829	+	0.431078i
$154$	−0.402604	−	0.303842i	−0.0324428	−	0.0244843i
$155$	−0.504030	+	2.53393i	−0.0404846	+	0.203530i
$156$	−2.84415	+	3.47588i	−0.227714	+	0.278293i
$157$	−0.365699	+	0.547307i	−0.0291860	+	0.0436799i	−0.845776	−	0.533539i	$-0.820862\pi$
$157$	−0.365699	+	0.547307i	−0.0291860	+	0.0436799i	0.816590	+	0.577218i	$0.195862\pi$
$158$	−1.18960	+	20.6848i	−0.0946399	+	1.64559i
$159$	15.6385	+	2.81629i	1.24021	+	0.223346i
$160$	1.10911	+	3.56261i	0.0876831	+	0.281649i
$161$	0.525027			0.0413779
$162$	−8.86178	+	9.13613i	−0.696247	+	0.717802i
$163$	18.9538	+	12.6645i	1.48458	+	0.991962i	0.992610	+	0.121347i	$0.0387215\pi$
$163$	18.9538	+	12.6645i	1.48458	+	0.991962i	0.491966	+	0.870614i	$0.336278\pi$
$164$	21.0990	−	6.01697i	1.64756	−	0.469846i
$165$	2.90634	+	1.14242i	0.226258	+	0.0889377i
$166$	15.0278	+	11.3413i	1.16638	+	0.880259i
$167$	9.66775	+	4.00451i	0.748113	+	0.309879i	0.723971	−	0.689830i	$-0.242315\pi$
$167$	9.66775	+	4.00451i	0.748113	+	0.309879i	0.0241416	+	0.999709i	$0.492315\pi$
$168$	−0.332407	+	0.545998i	−0.0256458	+	0.0421247i
$169$	−10.4575	+	4.33163i	−0.804421	+	0.333202i
$170$	0.568436	−	2.19143i	0.0435971	−	0.168075i
$171$	0.976388	+	4.12000i	0.0746663	+	0.315064i
$172$	12.9089	−	6.62489i	0.984298	−	0.505143i
$173$	−9.93901	+	1.97699i	−0.755649	+	0.150308i	−0.557858	−	0.829936i	$-0.688377\pi$
$173$	−9.93901	+	1.97699i	−0.755649	+	0.150308i	−0.197791	+	0.980244i	$0.563377\pi$
$174$	−12.7555	−	9.26754i	−0.966994	−	0.702570i
$175$	0.421179	+	0.421179i	0.0318382	+	0.0318382i
$176$	3.84403	+	10.2356i	0.289755	+	0.771537i
$177$	2.04785	+	2.94744i	0.153926	+	0.221543i
$178$	−0.560978	−	1.61014i	−0.0420471	−	0.120685i
$179$	−3.13037	+	0.622669i	−0.233975	+	0.0465405i	−0.310685	−	0.950513i	$-0.600558\pi$
$179$	−3.13037	+	0.622669i	−0.233975	+	0.0465405i	0.0767101	+	0.997053i	$0.475558\pi$
$180$	1.07430	−	3.80901i	0.0800732	−	0.283907i
$181$	10.4594	+	15.6535i	0.777438	+	1.16352i	0.982771	+	0.184826i	$0.0591722\pi$
$181$	10.4594	+	15.6535i	0.777438	+	1.16352i	−0.205333	+	0.978692i	$0.565828\pi$
$182$	0.206225	−	0.121275i	0.0152864	−	0.00898947i
$183$	3.53594	+	16.2292i	0.261384	+	1.19970i
$184$	−9.61196	−	6.09395i	−0.708603	−	0.449252i
$185$	−5.78094	−	2.39454i	−0.425023	−	0.176050i
$186$	9.58693	+	0.376723i	0.702948	+	0.0276227i
$187$	1.29423	−	6.50652i	0.0946432	−	0.475804i
$188$	6.93690	+	8.74686i	0.505925	+	0.637930i
$189$	0.611322	−	0.293206i	0.0444671	−	0.0213276i
$190$	−0.875956	−	0.982858i	−0.0635485	−	0.0713040i
$191$	−9.07901			−0.656934			−0.328467	−	0.944515i	$-0.606532\pi$
$191$	−9.07901			−0.656934			−0.328467	+	0.944515i	$0.606532\pi$
$192$	12.4229	−	6.13766i	0.896547	−	0.442948i
$193$	17.6278			1.26888			0.634440	−	0.772972i	$-0.281231\pi$
$193$	17.6278			1.26888			0.634440	+	0.772972i	$0.281231\pi$
$194$	4.08276	+	4.58102i	0.293125	+	0.328898i
$195$	−1.02816	+	1.06623i	−0.0736283	+	0.0763542i
$196$	−10.9425	+	8.67816i	−0.781604	+	0.619869i
$197$	3.19278	−	16.0512i	0.227476	−	1.14360i	−0.683122	−	0.730305i	$-0.739378\pi$
$197$	3.19278	−	16.0512i	0.227476	−	1.14360i	0.910598	−	0.413294i	$-0.135622\pi$
$198$	2.50194	−	11.3238i	0.177805	−	0.804744i
$199$	20.6774	+	8.56486i	1.46578	+	0.607147i	0.965893	−	0.258943i	$-0.0833741\pi$
$199$	20.6774	+	8.56486i	1.46578	+	0.607147i	0.499889	+	0.866089i	$0.333374\pi$
$200$	−2.82217	−	12.5994i	−0.199557	−	0.890909i
$201$	−12.0826	+	2.63249i	−0.852241	+	0.185682i
$202$	−17.7603	+	10.4443i	−1.24961	+	0.734859i
$203$	0.466610	+	0.698331i	0.0327496	+	0.0490132i
$204$	−8.36810	−	0.811921i	−0.585884	−	0.0568459i
$205$	7.09686	−	1.41165i	0.495666	−	0.0985941i
$206$	6.19298	+	17.7753i	0.431485	+	1.23847i
$207$	5.02169	+	10.9772i	0.349032	+	0.762969i
$208$	−5.18310	−	0.173396i	−0.359383	−	0.0120228i
$209$	−2.72791	−	2.72791i	−0.188694	−	0.188694i
$210$	−0.123916	+	0.170554i	−0.00855101	+	0.0117693i
$211$	−12.6809	+	2.52238i	−0.872988	+	0.173648i	−0.611199	−	0.791477i	$-0.709312\pi$
$211$	−12.6809	+	2.52238i	−0.872988	+	0.173648i	−0.261789	+	0.965125i	$0.584312\pi$
$212$	8.37754	+	16.3241i	0.575372	+	1.12114i
$213$	−15.3012	+	6.66622i	−1.04842	+	0.456762i
$214$	−1.04981	+	4.04723i	−0.0717638	+	0.276663i
$215$	4.42103	−	1.83125i	0.301512	−	0.124890i
$216$	−14.5950	−	1.72768i	−0.993067	−	0.117553i
$217$	−0.472174	−	0.195581i	−0.0320533	−	0.0132769i
$218$	−6.51287	−	4.91520i	−0.441107	−	0.332900i
$219$	4.08609	−	10.3951i	0.276112	−	0.702433i
$220$	0.988900	+	3.46766i	0.0666717	+	0.233790i
$221$	2.61631	+	1.74816i	0.175992	+	0.117594i
$222$	−5.42465	+	22.5948i	−0.364079	+	1.51646i
$223$	18.7420			1.25506			0.627529	−	0.778593i	$-0.284066\pi$
$223$	18.7420			1.25506			0.627529	+	0.778593i	$0.284066\pi$
$224$	−0.734013	+	0.0776973i	−0.0490433	+	0.00519137i
$225$	−4.77756	+	12.8344i	−0.318504	+	0.855627i
$226$	1.47300	−	25.6125i	0.0979825	−	1.70372i
$227$	−7.50992	+	11.2394i	−0.498451	+	0.745985i	−0.992340	−	0.123541i	$-0.960575\pi$
$227$	−7.50992	+	11.2394i	−0.498451	+	0.745985i	0.493889	+	0.869525i	$0.335575\pi$
$228$	−3.09615	+	3.78385i	−0.205047	+	0.250592i
$229$	0.913652	−	4.59324i	0.0603758	−	0.303530i	−0.938784	−	0.344505i	$-0.888047\pi$
$229$	0.913652	−	4.59324i	0.0603758	−	0.303530i	0.999160	+	0.0409757i	$0.0130466\pi$
$230$	−2.99599	−	2.26105i	−0.197550	−	0.149089i
$231$	−0.333813	+	0.519792i	−0.0219633	+	0.0341998i
$232$	−0.437012	−	18.2006i	−0.0286912	−	1.19493i
$233$	3.90294	+	9.42252i	0.255690	+	0.617290i	0.998644	−	0.0520519i	$-0.0165761\pi$
$233$	3.90294	+	9.42252i	0.255690	+	0.617290i	−0.742954	+	0.669342i	$0.766576\pi$
$234$	4.50807	+	3.15179i	0.294701	+	0.206039i
$235$	2.04549	+	3.06130i	0.133433	+	0.199697i
$236$	−1.26915	+	3.94513i	−0.0826148	+	0.256806i
$237$	25.3713	−	0.461110i	1.64804	−	0.0299523i
$238$	0.403238	+	0.194859i	0.0261380	+	0.0126308i
$239$	7.36008	−	7.36008i	0.476084	−	0.476084i	−0.427793	−	0.903877i	$-0.640709\pi$
$239$	7.36008	−	7.36008i	0.476084	−	0.476084i	0.903877	+	0.427793i	$0.140709\pi$
$240$	4.24820	−	1.68414i	0.274220	−	0.108711i
$241$	−18.8532	−	18.8532i	−1.21444	−	1.21444i	−0.969551	−	0.244889i	$-0.921249\pi$
$241$	−18.8532	−	18.8532i	−1.21444	−	1.21444i	−0.244889	−	0.969551i	$-0.578751\pi$
$242$	−1.64176	−	4.71224i	−0.105536	−	0.302914i
$243$	11.9774	+	9.97706i	0.768351	+	0.640029i
$244$	−12.4136	+	14.6205i	−0.794697	+	0.935980i
$245$	−3.82973	+	2.55894i	−0.244672	+	0.163485i
$246$	−9.30043	−	25.2103i	−0.592974	−	1.60735i
$247$	1.69056	−	0.700251i	0.107567	−	0.0445559i
$248$	6.37427	+	9.06110i	0.404766	+	0.575381i
$249$	12.4601	−	19.4020i	0.789625	−	1.22955i
$250$	−1.23535	−	8.83639i	−0.0781301	−	0.558862i
$251$	−20.1441	−	4.00691i	−1.27148	−	0.252914i	−0.487186	−	0.873298i	$-0.661977\pi$
$251$	−20.1441	−	4.00691i	−1.27148	−	0.252914i	−0.784298	+	0.620385i	$0.786977\pi$
$252$	0.697554	+	0.355431i	0.0439418	+	0.0223900i
$253$	−9.14500	−	6.11050i	−0.574941	−	0.384164i
$254$	−7.02647	−	7.88399i	−0.440880	−	0.494686i
$255$	−2.72886	−	0.491433i	−0.170888	−	0.0307747i
$256$	14.3398	+	7.09718i	0.896238	+	0.443574i
$257$		−	6.72076i		−	0.419230i	−0.977784	−	0.209615i	$-0.932779\pi$
$257$		−	6.72076i		−	0.419230i	0.977784	−	0.209615i	$-0.0672210\pi$
$258$	−9.28505	−	15.1520i	−0.578062	−	0.943322i
$259$	0.687683	−	1.02919i	0.0427306	−	0.0639508i
$260$	−1.69907	−	0.196079i	−0.105372	−	0.0121603i
$261$	−10.1377	+	16.4351i	−0.627508	+	1.01731i
$262$	16.8804	−	2.35992i	1.04288	−	0.145796i
$263$	3.23136	−	7.80118i	0.199254	−	0.481041i	−0.792395	−	0.610008i	$-0.791166\pi$
$263$	3.23136	−	7.80118i	0.199254	−	0.481041i	0.991649	+	0.128967i	$0.0411661\pi$
$264$	12.1445	−	5.64158i	0.747442	−	0.347215i
$265$	2.31572	+	5.59064i	0.142253	+	0.343430i
$266$	0.224497	−	0.132020i	0.0137648	−	0.00809465i
$267$	−1.91447	+	0.834074i	−0.117164	+	0.0510445i
$268$	−10.8849	−	9.24184i	−0.664900	−	0.564535i
$269$	−4.08830	−	20.5533i	−0.249268	−	1.25315i	−0.879181	−	0.476489i	$-0.841909\pi$
$269$	−4.08830	−	20.5533i	−0.249268	−	1.25315i	0.629913	−	0.776666i	$-0.283091\pi$
$270$	−4.75113	−	0.959540i	−0.289145	−	0.0583958i
$271$	5.66399	−	5.66399i	0.344063	−	0.344063i	−0.513829	−	0.857892i	$-0.671774\pi$
$271$	5.66399	−	5.66399i	0.344063	−	0.344063i	0.857892	+	0.513829i	$0.171774\pi$
$272$	−5.12058	−	8.24774i	−0.310481	−	0.500093i
$273$	−0.167187	−	0.240630i	−0.0101186	−	0.0145636i
$274$	2.05199	−	4.24635i	0.123965	−	0.256532i
$275$	−2.43430	−	12.2380i	−0.146794	−	0.737981i
$276$	−6.55283	+	12.3024i	−0.394434	+	0.740518i
$277$	−5.04782	+	3.37284i	−0.303294	+	0.202655i	−0.697899	−	0.716196i	$-0.745881\pi$
$277$	−5.04782	+	3.37284i	−0.303294	+	0.202655i	0.394605	+	0.918851i	$0.370881\pi$
$278$	−5.60928	+	21.6248i	−0.336422	+	1.29697i
$279$	−0.426982	−	11.7428i	−0.0255627	−	0.703026i
$280$	−0.243360	+	0.00584327i	−0.0145435	+	0.000349202i
$281$	−3.86027	+	9.31952i	−0.230284	+	0.555956i	−0.996211	−	0.0869726i	$-0.972281\pi$
$281$	−3.86027	+	9.31952i	−0.230284	+	0.555956i	0.765926	+	0.642928i	$0.222281\pi$
$282$	10.0402	−	9.28097i	0.597886	−	0.552674i
$283$	−16.4849	−	3.27904i	−0.979924	−	0.194919i	−0.320959	−	0.947093i	$-0.604005\pi$
$283$	−16.4849	−	3.27904i	−0.979924	−	0.194919i	−0.658964	+	0.752174i	$0.729005\pi$
$284$	−16.8423	−	9.36778i	−0.999408	−	0.555875i
$285$	−1.11926	+	1.16070i	−0.0662993	+	0.0687538i
$286$	−5.00351	−	0.287757i	−0.295864	−	0.0170154i
$287$			1.43139i			0.0844924i
$288$	−8.64505	−	14.6035i	−0.509415	−	0.860521i
$289$		−	11.1096i		−	0.653509i
$290$	0.344745	−	5.99441i	0.0202441	−	0.352004i
$291$	5.21678	−	5.40991i	0.305813	−	0.317135i
$292$	12.4027	−	3.53698i	0.725814	−	0.206986i
$293$	−4.20467	−	0.836360i	−0.245639	−	0.0488607i	0.0707350	−	0.997495i	$-0.477466\pi$
$293$	−4.20467	−	0.836360i	−0.245639	−	0.0488607i	−0.316374	+	0.948634i	$0.602466\pi$
$294$	11.6106	+	12.5604i	0.677146	+	0.732540i
$295$	−0.523043	+	1.26274i	−0.0304527	+	0.0735194i
$296$	−24.5355	+	10.8601i	−1.42610	+	0.631230i
$297$	−14.0606	−	2.00772i	−0.815877	−	0.116500i
$298$	−8.53379	−	2.21359i	−0.494349	−	0.128230i
$299$	4.33763	−	2.89831i	0.250852	−	0.167614i
$300$	−15.1258	+	4.61234i	−0.873287	+	0.266294i
$301$	0.184676	+	0.928430i	0.0106446	+	0.0535138i
$302$	−10.0258	−	4.84482i	−0.576918	−	0.278788i
$303$	14.3984	+	20.7233i	0.827165	+	1.19052i
$304$	−5.64233	−	0.188759i	−0.323610	−	0.0108261i
$305$	−4.47275	+	4.47275i	−0.256109	+	0.256109i
$306$	−0.217277	+	10.2946i	−0.0124209	+	0.588504i
$307$	−3.82639	−	19.2366i	−0.218384	−	1.09789i	−0.921965	−	0.387274i	$-0.873417\pi$
$307$	−3.82639	−	19.2366i	−0.218384	−	1.09789i	0.703581	−	0.710615i	$-0.251583\pi$
$308$	−0.710951	+	0.0580382i	−0.0405102	+	0.00330703i
$309$	21.1350	−	9.20785i	1.20233	−	0.523816i
$310$	1.85212	+	3.14949i	0.105193	+	0.178879i
$311$	−10.4354	−	25.1933i	−0.591737	−	1.42858i	−0.881823	−	0.471580i	$-0.843684\pi$
$311$	−10.4354	−	25.1933i	−0.591737	−	1.42858i	0.290086	−	0.957001i	$-0.406316\pi$
$312$	0.267820	+	6.34588i	0.0151623	+	0.359265i
$313$	5.06588	−	12.2301i	0.286341	−	0.691288i	−0.713617	−	0.700537i	$-0.752944\pi$
$313$	5.06588	−	12.2301i	0.286341	−	0.691288i	0.999957	+	0.00924891i	$0.00294406\pi$
$314$	0.128887	+	0.921927i	0.00727353	+	0.0520274i
$315$	0.219753	+	0.135551i	0.0123817	+	0.00763742i
$316$	18.2071	+	22.9577i	1.02423	+	1.29147i
$317$	−4.04908	+	6.05988i	−0.227419	+	0.340357i	−0.927577	−	0.373631i	$-0.878113\pi$
$317$	−4.04908	+	6.05988i	−0.227419	+	0.340357i	0.700158	+	0.713987i	$0.253113\pi$
$318$	19.1605	−	11.7415i	1.07447	−	0.658428i
$319$		−	17.5943i		−	0.985089i
$320$	4.52315	+	2.71769i	0.252852	+	0.151923i
$321$	5.03979	+	0.907600i	0.281294	+	0.0506573i
$322$	0.554306	−	0.494016i	0.0308903	−	0.0275304i
$323$	2.84812	+	1.90305i	0.158474	+	0.105889i
$324$	−0.759474	+	17.9840i	−0.0421930	+	0.999109i
$325$	5.80471	+	1.15463i	0.321987	+	0.0640472i
$326$	31.9273	−	4.46350i	1.76829	−	0.247210i
$327$	−5.40005	+	8.40860i	−0.298623	+	0.464997i
$328$	16.6141	−	26.2053i	0.917358	−	1.44695i
$329$	−0.672886	+	0.278718i	−0.0370974	+	0.0153662i
$330$	4.14337	−	1.52854i	0.228085	−	0.0841435i
$331$	−18.8829	+	12.6171i	−1.03790	+	0.693501i	−0.953025	−	0.302891i	$-0.902048\pi$
$331$	−18.8829	+	12.6171i	−1.03790	+	0.693501i	−0.0848726	+	0.996392i	$0.527048\pi$
$332$	26.5373	−	2.16636i	1.45642	−	0.118895i
$333$	28.0957	+	4.53420i	1.53963	+	0.248472i
$334$	13.9749	−	4.86889i	0.764671	−	0.266414i
$335$	−3.32994	−	3.32994i	−0.181934	−	0.181934i
$336$	0.162804	+	0.889220i	0.00888167	+	0.0485109i
$337$	1.73367	−	1.73367i	0.0944390	−	0.0944390i	−0.658309	−	0.752748i	$-0.728728\pi$
$337$	1.73367	−	1.73367i	0.0944390	−	0.0944390i	0.752748	+	0.658309i	$0.228728\pi$
$338$	−6.96487	+	14.4130i	−0.378839	+	0.783963i
$339$	−31.4154	+	0.570959i	−1.70625	+	0.0310102i
$340$	−1.46185	−	2.84850i	−0.0792801	−	0.154481i
$341$	5.94815	+	8.90204i	0.322110	+	0.482072i
$342$	4.90749	+	3.43104i	0.265367	+	0.185529i
$343$	−0.698212	−	1.68563i	−0.0376999	−	0.0910156i
$344$	7.39525	−	19.1408i	0.398725	−	1.03200i
$345$	−2.48408	+	3.86805i	−0.133739	+	0.208249i
$346$	−8.63306	+	11.4392i	−0.464116	+	0.614975i
$347$	−1.12387	+	5.65009i	−0.0603327	+	0.303313i	−0.999156	−	0.0410875i	$-0.986918\pi$
$347$	−1.12387	+	5.65009i	−0.0603327	+	0.303313i	0.938823	+	0.344400i	$0.111918\pi$
$348$	−22.1870	+	2.21776i	−1.18935	+	0.118884i
$349$	−17.7202	+	26.5202i	−0.948542	+	1.41959i	−0.0412234	+	0.999150i	$0.513126\pi$
$349$	−17.7202	+	26.5202i	−0.948542	+	1.41959i	−0.907319	+	0.420444i	$0.861874\pi$
$350$	0.840969	+	0.0483650i	0.0449517	+	0.00258522i
$351$	3.43199	−	5.79708i	0.183186	−	0.309425i
$352$	13.6894	+	7.18942i	0.729649	+	0.383197i
$353$	2.67300			0.142269			0.0711346	−	0.997467i	$-0.477338\pi$
$353$	2.67300			0.142269			0.0711346	+	0.997467i	$0.477338\pi$
$354$	4.93540	+	1.18491i	0.262314	+	0.0629774i
$355$	−5.28481	−	3.53120i	−0.280489	−	0.187417i
$356$	−2.10730	−	1.17209i	−0.111687	−	0.0621207i
$357$	0.200660	−	0.510482i	0.0106201	−	0.0270176i
$358$	−2.71905	+	3.60286i	−0.143706	+	0.190417i
$359$	10.0334	+	4.15595i	0.529540	+	0.219343i	0.631402	−	0.775456i	$-0.282480\pi$
$359$	10.0334	+	4.15595i	0.529540	+	0.219343i	−0.101862	+	0.994799i	$0.532480\pi$
$360$	−2.44982	−	5.03226i	−0.129117	−	0.265224i
$361$	−15.7134	+	6.50869i	−0.827019	+	0.342563i
$362$	25.7716	+	6.68491i	1.35452	+	0.351351i
$363$	−5.60289	+	2.44100i	−0.294075	+	0.128119i
$364$	0.103614	−	0.322082i	0.00543085	−	0.0168817i
$365$	4.17177	−	0.829817i	0.218361	−	0.0434346i
$366$	19.0038	+	13.8072i	0.993343	+	0.721714i
$367$	−24.8849	−	24.8849i	−1.29898	−	1.29898i	−0.929066	−	0.369913i	$-0.879388\pi$
$367$	−24.8849	−	24.8849i	−1.29898	−	1.29898i	−0.369913	−	0.929066i	$-0.620612\pi$
$368$	−15.8820	+	2.61044i	−0.827906	+	0.136078i
$369$	−29.9274	+	13.6907i	−1.55796	+	0.712712i
$370$	−8.35642	+	2.91140i	−0.434430	+	0.151357i
$371$	−1.17405	+	0.233533i	−0.0609537	+	0.0121244i
$372$	10.4760	−	8.62294i	0.543157	−	0.447079i
$373$	15.6143	+	23.3685i	0.808480	+	1.20998i	0.974618	+	0.223873i	$0.0718702\pi$
$373$	15.6143	+	23.3685i	0.808480	+	1.20998i	−0.166138	+	0.986102i	$0.553130\pi$
$374$	−4.75580	−	8.08715i	−0.245917	−	0.418176i
$375$	−10.6771	+	2.32627i	−0.551363	+	0.120128i
$376$	15.5540	+	2.70748i	0.802134	+	0.139628i
$377$	7.71001	+	3.19359i	0.397086	+	0.164478i
$378$	0.369525	−	0.884771i	0.0190063	−	0.0455077i
$379$	−0.250734	+	1.26053i	−0.0128794	+	0.0647489i	−0.986690	−	0.162610i	$-0.948009\pi$
$379$	−0.250734	+	1.26053i	−0.0128794	+	0.0647489i	0.973811	+	0.227358i	$0.0730089\pi$
$380$	−1.84961	−	0.213452i	−0.0948829	−	0.0109499i
$381$	−8.97814	+	9.31053i	−0.459964	+	0.476993i
$382$	−9.58532	+	8.54275i	−0.490428	+	0.437085i
$383$	−10.8069			−0.552209			−0.276104	−	0.961128i	$-0.589044\pi$
$383$	−10.8069			−0.552209			−0.276104	+	0.961128i	$0.589044\pi$
$384$	7.34057	−	18.1691i	0.374597	−	0.927188i
$385$	−0.235252			−0.0119896
$386$	18.6109	−	16.5866i	0.947270	−	0.844238i
$387$	−17.6452	+	12.7413i	−0.896955	+	0.647676i
$388$	8.62087	+	0.994882i	0.437659	+	0.0505075i
$389$	−1.99431	+	10.0261i	−0.101116	+	0.508343i	0.896721	+	0.442597i	$0.145943\pi$
$389$	−1.99431	+	10.0261i	−0.101116	+	0.508343i	−0.997836	+	0.0657460i	$0.979057\pi$
$390$	−0.0822502	+	2.09312i	−0.00416490	+	0.105989i
$391$	9.02234	+	3.73718i	0.456280	+	0.188997i
$392$	−3.38710	+	19.4582i	−0.171074	+	0.982789i
$393$	−4.44394	−	20.3968i	−0.224167	−	1.02888i
$394$	−11.7323	−	19.9505i	−0.591063	−	1.00509i
$395$	5.36875	+	8.03491i	0.270131	+	0.404280i
$396$	−8.01345	−	14.3094i	−0.402691	−	0.719074i
$397$	0.271922	−	0.0540887i	0.0136474	−	0.00271463i	−0.188262	−	0.982119i	$-0.560285\pi$
$397$	0.271922	−	0.0540887i	0.0136474	−	0.00271463i	0.201909	+	0.979404i	$0.435285\pi$
$398$	29.8895	−	10.4136i	1.49822	−	0.521985i
$399$	−0.182000	−	0.261950i	−0.00911142	−	0.0131139i
$400$	−14.8347	−	10.6465i	−0.741736	−	0.532325i
$401$	5.70249	+	5.70249i	0.284769	+	0.284769i	0.835007	−	0.550239i	$-0.185463\pi$
$401$	5.70249	+	5.70249i	0.284769	+	0.284769i	−0.550239	+	0.835007i	$0.685463\pi$
$402$	−10.2794	+	14.1482i	−0.512690	+	0.705649i
$403$	−4.98064	+	0.990712i	−0.248104	+	0.0493509i
$404$	−8.92336	+	27.7381i	−0.443954	+	1.38002i
$405$	−0.732224	+	5.89108i	−0.0363845	+	0.292730i
$406$	1.14971	+	0.298225i	0.0570594	+	0.0148007i
$407$	−23.9564	+	9.92305i	−1.18747	+	0.491867i
$408$	−9.59872	+	7.01663i	−0.475207	+	0.347375i
$409$	5.27970	+	2.18692i	0.261064	+	0.108136i	0.509377	−	0.860544i	$-0.329876\pi$
$409$	5.27970	+	2.18692i	0.261064	+	0.108136i	−0.248312	+	0.968680i	$0.579876\pi$
$410$	6.16435	−	8.16805i	0.304436	−	0.403391i
$411$	−5.37570	−	2.11308i	−0.265164	−	0.104231i
$412$	23.2638	+	12.9394i	1.14612	+	0.637480i
$413$	−0.224807	−	0.150211i	−0.0110620	−	0.00739142i
$414$	15.6306	+	6.86430i	0.768201	+	0.337362i
$415$	8.78113			0.431049
$416$	−5.63530	+	4.69389i	−0.276293	+	0.230137i
$417$	26.9282	+	4.84942i	1.31868	+	0.237477i
$418$	−5.44683	−	0.313253i	−0.266413	−	0.0153217i
$419$	−4.40488	+	6.59237i	−0.215193	+	0.322058i	−0.923324	−	0.384022i	$-0.874539\pi$
$419$	−4.40488	+	6.59237i	−0.215193	+	0.322058i	0.708131	+	0.706081i	$0.249539\pi$
$420$	0.0296535	+	0.296661i	0.00144694	+	0.0144756i
$421$	2.54628	−	12.8010i	0.124098	−	0.623884i	−0.867807	−	0.496902i	$-0.834471\pi$
$421$	2.54628	−	12.8010i	0.124098	−	0.623884i	0.991905	−	0.126982i	$-0.0405291\pi$
$422$	−11.0147	+	14.5949i	−0.536185	+	0.710470i
$423$	−12.2633	−	11.4028i	−0.596264	−	0.554423i
$424$	24.2046	+	9.35170i	1.17548	+	0.454159i
$425$	4.23979	+	10.2358i	0.205660	+	0.496507i
$426$	−9.88198	+	21.4354i	−0.478783	+	1.03855i
$427$	−0.695177	−	1.04041i	−0.0336420	−	0.0503488i
$428$	2.69982	+	5.26073i	0.130501	+	0.254287i
$429$	0.111539	+	6.13713i	0.00538517	+	0.296304i
$430$	2.94449	−	6.09328i	0.141996	−	0.293844i
$431$	28.2829	−	28.2829i	1.36234	−	1.36234i	0.491411	−	0.870928i	$-0.336481\pi$
$431$	28.2829	−	28.2829i	1.36234	−	1.36234i	0.870928	−	0.491411i	$-0.163519\pi$
$432$	−17.0346	+	11.9089i	−0.819577	+	0.572970i
$433$	−6.49657	−	6.49657i	−0.312205	−	0.312205i	0.533558	−	0.845763i	$-0.320855\pi$
$433$	−6.49657	−	6.49657i	−0.312205	−	0.312205i	−0.845763	+	0.533558i	$0.820855\pi$
$434$	−0.682535	+	0.237797i	−0.0327627	+	0.0114146i
$435$	−7.35254	+	0.133629i	−0.352527	+	0.00640701i
$436$	−11.5010	+	0.938876i	−0.550796	+	0.0449640i
$437$	4.72195	−	3.15511i	0.225881	−	0.150929i
$438$	−5.46711	−	14.8195i	−0.261229	−	0.708103i
$439$	16.5400	−	6.85111i	0.789413	−	0.326985i	0.0487053	−	0.998813i	$-0.484490\pi$
$439$	16.5400	−	6.85111i	0.789413	−	0.326985i	0.740707	+	0.671828i	$0.234490\pi$
$440$	4.30689	+	2.73055i	0.205323	+	0.130174i
$441$	14.2651	−	15.3416i	0.679289	−	0.730553i
$442$	4.40712	−	0.616125i	0.209625	−	0.0293061i
$443$	−5.03687	−	1.00190i	−0.239309	−	0.0476015i	0.0739786	−	0.997260i	$-0.476430\pi$
$443$	−5.03687	−	1.00190i	−0.239309	−	0.0476015i	−0.313288	+	0.949658i	$0.601430\pi$
$444$	15.5330	+	28.9590i	0.737165	+	1.37434i
$445$	−0.661233	−	0.441822i	−0.0313454	−	0.0209444i
$446$	19.7872	−	17.6350i	0.936951	−	0.835042i
$447$	−1.91372	+	10.6267i	−0.0905159	+	0.502624i
$448$	−0.701838	+	0.772688i	−0.0331587	+	0.0365061i
$449$			20.6619i			0.975093i	0.873097	+	0.487547i	$0.162108\pi$
$449$			20.6619i			0.975093i	−0.873097	+	0.487547i	$0.837892\pi$
$450$	7.03235	+	18.0455i	0.331508	+	0.850673i
$451$	16.6592	−	24.9322i	0.784450	−	1.17401i
$452$	−22.5445	−	28.4268i	−1.06040	−	1.33708i
$453$	−4.98905	+	12.6922i	−0.234406	+	0.596332i
$454$	2.64680	+	18.9325i	0.124221	+	0.888547i
$455$	0.0427014	−	0.103090i	0.00200187	−	0.00483294i
$456$	0.291549	+	6.90813i	0.0136530	+	0.323503i
$457$	8.62657	+	20.8264i	0.403534	+	0.974217i	0.986801	+	0.161936i	$0.0517740\pi$
$457$	8.62657	+	20.8264i	0.403534	+	0.974217i	−0.583267	+	0.812280i	$0.698226\pi$
$458$	−3.35733	−	5.70907i	−0.156878	−	0.266768i
$459$	12.5924	−	0.687185i	0.587761	−	0.0320750i
$460$	−5.29057	+	0.431893i	−0.246674	+	0.0201371i
$461$	5.95852	+	29.9555i	0.277516	+	1.39517i	0.828190	+	0.560447i	$0.189371\pi$
$461$	5.95852	+	29.9555i	0.277516	+	1.39517i	−0.550674	+	0.834720i	$0.685629\pi$
$462$	0.136661	+	0.862875i	0.00635806	+	0.0401446i
$463$	−15.5380	+	15.5380i	−0.722112	+	0.722112i	−0.969035	−	0.246923i	$-0.920580\pi$
$463$	−15.5380	+	15.5380i	−0.722112	+	0.722112i	0.246923	+	0.969035i	$0.420580\pi$
$464$	−17.5870	−	18.8044i	−0.816456	−	0.872974i
$465$	3.67493	−	2.55331i	0.170421	−	0.118407i
$466$	12.9866	+	6.27558i	0.601591	+	0.290711i
$467$	−3.82547	−	19.2319i	−0.177022	−	0.889948i	−0.962546	−	0.271118i	$-0.912607\pi$
$467$	−3.82547	−	19.2319i	−0.177022	−	0.889948i	0.785525	−	0.618831i	$-0.212393\pi$
$468$	7.72509	−	0.914241i	0.357092	−	0.0422608i
$469$	0.774578	−	0.517556i	0.0357667	−	0.0238985i
$470$	5.04004	+	1.30734i	0.232480	+	0.0603031i
$471$	1.11397	−	0.242706i	0.0513292	−	0.0111833i
$472$	2.37218	+	5.35933i	0.109188	+	0.246683i
$473$	7.58876	−	18.3209i	0.348932	−	0.842395i
$474$	26.3523	−	24.3595i	1.21040	−	1.11887i
$475$	6.31901	+	1.25693i	0.289936	+	0.0576719i
$476$	0.609074	−	0.173694i	0.0279169	−	0.00796127i
$477$	−16.1121	−	22.3133i	−0.737721	−	1.02166i
$478$	0.845175	−	14.6959i	0.0386574	−	0.672174i
$479$			15.8484i			0.724131i	0.932153	+	0.362066i	$0.117928\pi$
$479$			15.8484i			0.724131i	−0.932153	+	0.362066i	$0.882072\pi$
$480$	2.90044	−	5.77533i	0.132387	−	0.263607i
$481$		−	12.2991i		−	0.560792i
$482$	−37.6442	−	2.16496i	−1.71464	−	0.0986110i
$483$	−0.654602	−	0.631233i	−0.0297854	−	0.0287221i
$484$	−6.16722	−	3.43024i	−0.280328	−	0.155920i
$485$	2.80705	+	0.558356i	0.127461	+	0.0253536i
$486$	22.0331	−	0.736505i	0.999442	−	0.0334085i
$487$	−0.0367056	+	0.0886152i	−0.00166329	+	0.00401554i	−0.924709	−	0.380675i	$-0.875692\pi$
$487$	−0.0367056	+	0.0886152i	−0.00166329	+	0.00401554i	0.923046	+	0.384690i	$0.125692\pi$
$488$	0.651080	+	27.1162i	0.0294730	+	1.22749i
$489$	−8.40517	−	38.5780i	−0.380095	−	1.74456i
$490$	−1.63550	+	6.30517i	−0.0738845	+	0.284839i
$491$	32.9415	−	22.0108i	1.48663	−	0.993334i	0.494356	−	0.869260i	$-0.335404\pi$
$491$	32.9415	−	22.0108i	1.48663	−	0.993334i	0.992273	−	0.124074i	$-0.0395960\pi$
$492$	−33.5403	−	17.8651i	−1.51212	−	0.805422i
$493$	3.04771	+	15.3219i	0.137262	+	0.690062i
$494$	1.12594	−	2.33000i	0.0506585	−	0.104832i
$495$	−2.25010	−	4.91863i	−0.101134	−	0.221076i
$496$	15.2556	+	3.56865i	0.684998	+	0.160237i
$497$	0.889068	−	0.889068i	0.0398802	−	0.0398802i
$498$	−5.10108	−	32.2081i	−0.228585	−	1.44328i
$499$	−0.272080	−	1.36784i	−0.0121800	−	0.0612328i	0.974217	−	0.225612i	$-0.0724380\pi$
$499$	−0.272080	−	1.36784i	−0.0121800	−	0.0612328i	−0.986397	+	0.164379i	$0.947438\pi$
$500$	−9.61870	−	8.16679i	−0.430161	−	0.365230i
$501$	−7.23916	−	16.6162i	−0.323422	−	0.742359i
$502$	−25.0377	+	14.7239i	−1.11749	+	0.657160i
$503$	−3.58557	−	8.65633i	−0.159873	−	0.385967i	0.823563	−	0.567225i	$-0.191983\pi$
$503$	−3.58557	−	8.65633i	−0.159873	−	0.385967i	−0.983436	+	0.181258i	$0.941983\pi$
$504$	1.07089	−	0.281100i	0.0477013	−	0.0125212i
$505$	−3.67749	+	8.87825i	−0.163646	+	0.395077i
$506$	−15.4046	+	2.15359i	−0.684816	+	0.0957387i
$507$	18.2462	+	7.17222i	0.810343	+	0.318530i
$508$	−14.8366	−	1.71220i	−0.658269	−	0.0759668i
$509$	0.132412	−	0.198168i	0.00586904	−	0.00878365i	−0.828523	−	0.559954i	$-0.810819\pi$
$509$	0.132412	−	0.198168i	0.00586904	−	0.00878365i	0.834393	+	0.551171i	$0.185819\pi$
$510$	−3.34345	+	2.04884i	−0.148050	+	0.0907243i
$511$			0.841421i			0.0372223i
$512$	21.8175	−	5.99985i	0.964205	−	0.265158i
$513$	3.73606	−	6.31071i	0.164951	−	0.278625i
$514$	−6.32379	−	7.09556i	−0.278931	−	0.312972i
$515$	7.29975	+	4.87754i	0.321665	+	0.214930i
$516$	−24.0599	−	7.26036i	−1.05918	−	0.319619i
$517$	14.9643	+	2.97658i	0.658128	+	0.130910i
$518$	−0.242368	−	1.73365i	−0.0106490	−	0.0761722i
$519$	14.7689	+	9.48464i	0.648281	+	0.416329i
$520$	−1.97832	+	1.39170i	−0.0867550	+	0.0610300i
$521$	28.5978	−	11.8456i	1.25289	−	0.518964i	0.345170	−	0.938540i	$-0.387821\pi$
$521$	28.5978	−	11.8456i	1.25289	−	0.518964i	0.907720	+	0.419576i	$0.137821\pi$
$522$	4.76133	+	26.8906i	0.208398	+	1.17697i
$523$	2.09849	−	1.40217i	0.0917608	−	0.0613126i	−0.508843	−	0.860859i	$-0.669927\pi$
$523$	2.09849	−	1.40217i	0.0917608	−	0.0613126i	0.600604	+	0.799547i	$0.294927\pi$
$524$	15.6013	−	18.3749i	0.681545	−	0.802712i
$525$	−0.0187471	−	1.03150i	−0.000818189	−	0.0450185i
$526$	−3.92884	−	11.2767i	−0.171306	−	0.491688i
$527$	−6.72194	−	6.72194i	−0.292812	−	0.292812i
$528$	7.51339	−	17.3834i	0.326979	−	0.756514i
$529$	−4.81487	+	4.81487i	−0.209342	+	0.209342i
$530$	7.70528	+	3.72347i	0.334696	+	0.161737i
$531$	0.990410	−	6.13697i	0.0429801	−	0.266322i
$532$	0.112794	−	0.350619i	0.00489026	−	0.0152013i
$533$	7.90173	+	11.8258i	0.342262	+	0.512231i
$534$	−1.23643	+	2.68198i	−0.0535054	+	0.116061i
$535$	0.746283	+	1.80169i	0.0322646	+	0.0778937i
$536$	−20.1879	+	0.484727i	−0.871983	+	0.0209370i
$537$	4.65157	+	2.98726i	0.200730	+	0.128910i
$538$	−23.6556	−	17.8526i	−1.01986	−	0.769682i
$539$	−3.72375	+	18.7205i	−0.160393	+	0.806351i
$540$	−5.91895	+	3.45745i	−0.254711	+	0.148785i
$541$	−18.4168	+	27.5627i	−0.791800	+	1.18501i	0.187433	+	0.982277i	$0.439983\pi$
$541$	−18.4168	+	27.5627i	−0.791800	+	1.18501i	−0.979234	+	0.202736i	$0.935017\pi$
$542$	0.650410	−	11.3093i	0.0279375	−	0.485776i
$543$	5.77934	−	32.0920i	0.248015	−	1.37720i
$544$	−13.1667	−	3.88956i	−0.564519	−	0.166763i
$545$	−3.80564			−0.163016
$546$	−0.402928	−	0.0967367i	−0.0172437	−	0.00413995i
$547$	15.5866	+	10.4146i	0.666435	+	0.445298i	0.842222	−	0.539130i	$-0.181247\pi$
$547$	15.5866	+	10.4146i	0.666435	+	0.445298i	−0.175787	+	0.984428i	$0.556247\pi$
$548$	−1.82912	−	6.41395i	−0.0781359	−	0.273990i
$549$	15.1036	−	24.4858i	0.644606	−	1.04503i
$550$	−14.0852	−	10.6300i	−0.600596	−	0.453265i
$551$	8.39313	+	3.47655i	0.357559	+	0.148106i
$552$	4.65750	+	19.1543i	0.198236	+	0.815259i
$553$	−1.76611	+	0.731545i	−0.0751024	+	0.0311085i
$554$	−2.15569	+	8.31060i	−0.0915866	+	0.353084i
$555$	4.32873	+	9.93585i	0.183744	+	0.421754i
$556$	14.4255	+	28.1087i	0.611775	+	1.19208i
$557$	−34.3714	+	6.83689i	−1.45636	+	0.289688i	−0.858873	−	0.512189i	$-0.828835\pi$
$557$	−34.3714	+	6.83689i	−1.45636	+	0.289688i	−0.597489	+	0.801877i	$0.703835\pi$
$558$	−11.5000	−	11.9959i	−0.486835	−	0.507829i
$559$	6.65097	+	6.65097i	0.281306	+	0.281306i
$560$	−0.251433	+	0.235155i	−0.0106250	+	0.00993711i
$561$	−9.43634	+	6.55628i	−0.398403	+	0.276806i
$562$	4.69351	+	13.4715i	0.197984	+	0.568261i
$563$	−7.73138	+	1.53787i	−0.325839	+	0.0648134i	−0.355299	−	0.934753i	$-0.615621\pi$
$563$	−7.73138	+	1.53787i	−0.325839	+	0.0648134i	0.0294605	+	0.999566i	$0.490621\pi$
$564$	1.86733	−	19.2457i	0.0786288	−	0.810391i
$565$	−6.64774	−	9.94904i	−0.279672	−	0.418559i
$566$	−20.4895	+	12.0493i	−0.861239	+	0.506469i
$567$	−1.11471	−	0.369415i	−0.0468136	−	0.0155140i
$568$	−26.5960	+	5.95732i	−1.11594	+	0.249964i
$569$	−28.7698	−	11.9168i	−1.20609	−	0.499580i	−0.313130	−	0.949710i	$-0.601378\pi$
$569$	−28.7698	−	11.9168i	−1.20609	−	0.499580i	−0.892963	+	0.450130i	$0.851378\pi$
$570$	−0.0895377	+	2.27858i	−0.00375032	+	0.0954390i
$571$	0.525215	−	2.64043i	0.0219795	−	0.110499i	−0.968238	−	0.250030i	$-0.919560\pi$
$571$	0.525215	−	2.64043i	0.0219795	−	0.110499i	0.990218	+	0.139531i	$0.0445596\pi$
$572$	−5.55330	+	4.40417i	−0.232195	+	0.184147i
$573$	11.3197	+	10.9156i	0.472887	+	0.456005i
$574$	1.34685	+	1.51122i	0.0562163	+	0.0630770i
$575$	18.3682			0.766008
$576$	−22.8681	−	7.28349i	−0.952838	−	0.303479i
$577$	−14.0828			−0.586276			−0.293138	−	0.956070i	$-0.594700\pi$
$577$	−14.0828			−0.586276			−0.293138	+	0.956070i	$0.594700\pi$
$578$	−10.4534	−	11.7292i	−0.434806	−	0.487870i
$579$	−21.9784	−	21.1937i	−0.913390	−	0.880782i
$580$	−5.27637	−	6.65308i	−0.219089	−	0.276254i
$581$	−0.338885	+	1.70369i	−0.0140593	+	0.0706810i
$582$	0.417328	−	10.6202i	0.0172988	−	0.440224i
$583$	23.1678	+	9.59640i	0.959511	+	0.397442i
$584$	9.76631	−	15.4044i	0.404133	−	0.637437i
$585$	2.56382	−	0.0932233i	0.106001	−	0.00385431i
$586$	−5.22610	+	3.07331i	−0.215888	+	0.126957i
$587$	16.5811	+	24.8153i	0.684374	+	1.02424i	0.997226	+	0.0744364i	$0.0237158\pi$
$587$	16.5811	+	24.8153i	0.684374	+	1.02424i	−0.312851	+	0.949802i	$0.601284\pi$
$588$	24.0767	+	2.33606i	0.992905	+	0.0963374i
$589$	−5.42194	+	1.07849i	−0.223407	+	0.0444384i
$590$	0.635941	+	1.82530i	0.0261813	+	0.0751466i
$591$	−23.2789	+	16.1739i	−0.957565	+	0.665307i
$592$	−15.6852	+	34.5520i	−0.644657	+	1.42008i
$593$	1.51792	+	1.51792i	0.0623333	+	0.0623333i	0.737586	−	0.675253i	$-0.235966\pi$
$593$	1.51792	+	1.51792i	0.0623333	+	0.0623333i	−0.675253	+	0.737586i	$0.735966\pi$
$594$	−16.7338	+	11.1104i	−0.686597	+	0.455865i
$595$	0.204868	−	0.0407508i	0.00839877	−	0.00167062i
$596$	−11.0925	+	5.69270i	−0.454368	+	0.233182i
$597$	−15.4831	−	35.5388i	−0.633682	−	1.45451i
$598$	1.85240	−	7.14136i	0.0757504	−	0.292032i
$599$	−27.1829	+	11.2595i	−1.11066	+	0.460052i	−0.861167	−	0.508323i	$-0.830266\pi$
$599$	−27.1829	+	11.2595i	−1.11066	+	0.460052i	−0.249498	+	0.968375i	$0.580266\pi$
$600$	−11.6294	+	19.1019i	−0.474767	+	0.779832i
$601$	14.3135	+	5.92883i	0.583858	+	0.241842i	0.655006	−	0.755624i	$-0.272666\pi$
$601$	14.3135	+	5.92883i	0.583858	+	0.241842i	−0.0711476	+	0.997466i	$0.522666\pi$
$602$	1.06857	+	0.806437i	0.0435515	+	0.0328679i
$603$	18.2296	+	11.2446i	0.742366	+	0.457914i
$604$	−15.1435	+	4.31860i	−0.616181	+	0.175721i
$605$	−1.93516	−	1.29303i	−0.0786755	−	0.0525693i
$606$	34.7006	+	8.33108i	1.40962	+	0.338427i
$607$	−26.9760			−1.09492			−0.547460	−	0.836832i	$-0.684405\pi$
$607$	−26.9760			−1.09492			−0.547460	+	0.836832i	$0.684405\pi$
$608$	−6.13460	+	5.10978i	−0.248791	+	0.207229i
$609$	0.257826	−	1.43168i	0.0104476	−	0.0580145i
$610$	−0.513616	+	8.93074i	−0.0207957	+	0.361595i
$611$	−4.02059	+	6.01723i	−0.162656	+	0.243431i
$612$	9.45716	+	11.0732i	0.382283	+	0.447606i
$613$	−3.08394	+	15.5040i	−0.124559	+	0.626201i	0.867187	+	0.497983i	$0.165926\pi$
$613$	−3.08394	+	15.5040i	−0.124559	+	0.626201i	−0.991746	+	0.128218i	$0.959074\pi$
$614$	−22.1401	−	16.7089i	−0.893502	−	0.674318i
$615$	−10.5456	−	6.77241i	−0.425238	−	0.273090i
$616$	−0.695988	+	0.730233i	−0.0280422	+	0.0294219i
$617$	−13.4837	−	32.5525i	−0.542832	−	1.31051i	−0.922717	−	0.385479i	$-0.874036\pi$
$617$	−13.4837	−	32.5525i	−0.542832	−	1.31051i	0.379885	−	0.925034i	$-0.375964\pi$
$618$	13.6497	−	29.6080i	0.549070	−	1.19101i
$619$	12.0137	+	17.9798i	0.482873	+	0.722671i	0.990288	−	0.139031i	$-0.0443989\pi$
$619$	12.0137	+	17.9798i	0.482873	+	0.722671i	−0.507415	+	0.861702i	$0.669399\pi$
$620$	4.91888	+	1.58241i	0.197547	+	0.0635510i
$621$	6.93674	−	19.7239i	0.278362	−	0.791492i
$622$	−34.7226	−	16.7792i	−1.39225	−	0.672785i
$623$	0.111240	−	0.111240i	0.00445672	−	0.00445672i
$624$	6.25381	+	6.44777i	0.250353	+	0.258117i
$625$	13.1969	+	13.1969i	0.527875	+	0.527875i
$626$	−6.15935	−	17.6788i	−0.246177	−	0.706588i
$627$	0.121422	+	6.68089i	0.00484912	+	0.266809i
$628$	1.00355	+	0.852066i	0.0400459	+	0.0340011i
$629$	19.1434	−	12.7912i	0.763296	−	0.510018i
$630$	0.359553	−	0.0636635i	0.0143249	−	0.00253641i
$631$	6.89332	−	2.85530i	0.274419	−	0.113668i	−0.241230	−	0.970468i	$-0.577551\pi$
$631$	6.89332	−	2.85530i	0.274419	−	0.113668i	0.515649	+	0.856800i	$0.327551\pi$
$632$	40.8241	+	7.10625i	1.62389	+	0.282672i
$633$	18.8431	+	12.1012i	0.748947	+	0.480978i
$634$	1.42706	+	10.2077i	0.0566758	+	0.405401i
$635$	−4.83096	−	0.960938i	−0.191711	−	0.0381337i
$636$	9.18112	−	30.4250i	0.364055	−	1.20643i
$637$	−7.52765	−	5.02981i	−0.298256	−	0.199289i
$638$	−16.5550	−	18.5754i	−0.655420	−	0.735408i
$639$	27.0922	+	10.0850i	1.07175	+	0.398955i
$640$	7.33255	−	1.38675i	0.289845	−	0.0548159i
$641$			31.6101i			1.24852i	0.781215	+	0.624262i	$0.214600\pi$
$641$			31.6101i			1.24852i	−0.781215	+	0.624262i	$0.785400\pi$
$642$	6.17484	−	3.78390i	0.243701	−	0.149339i
$643$	−3.02011	+	4.51991i	−0.119101	+	0.178248i	−0.886230	−	0.463246i	$-0.846685\pi$
$643$	−3.02011	+	4.51991i	−0.119101	+	0.178248i	0.767129	+	0.641493i	$0.221685\pi$
$644$	0.120381	−	1.04313i	0.00474369	−	0.0411051i
$645$	−7.71383	−	3.03215i	−0.303732	−	0.119391i
$646$	4.79760	−	0.670714i	0.188759	−	0.0263889i
$647$	−13.6254	+	32.8947i	−0.535671	+	1.29322i	0.392047	+	0.919945i	$0.371767\pi$
$647$	−13.6254	+	32.8947i	−0.535671	+	1.29322i	−0.927719	+	0.373280i	$0.878233\pi$
$648$	16.1199	+	19.7015i	0.633250	+	0.773948i
$649$	2.16750	+	5.23282i	0.0850819	+	0.205406i
$650$	7.21484	−	4.24283i	0.282989	−	0.166417i
$651$	0.353562	+	0.811539i	0.0138572	+	0.0318067i
$652$	29.5079	−	34.7539i	1.15562	−	1.36107i
$653$	−5.41220	−	27.2090i	−0.211796	−	1.06477i	−0.929613	−	0.368537i	$-0.879859\pi$
$653$	−5.41220	−	27.2090i	−0.211796	−	1.06477i	0.717817	−	0.696231i	$-0.245141\pi$
$654$	2.21075	+	13.9586i	0.0864472	+	0.545825i
$655$	5.62132	−	5.62132i	0.219643	−	0.219643i
$656$	−7.11689	−	43.2994i	−0.277868	−	1.69056i
$657$	−17.5924	+	8.04789i	−0.686344	+	0.313978i
$658$	−0.448155	+	0.927403i	−0.0174709	+	0.0361539i
$659$	−4.93829	−	24.8265i	−0.192369	−	0.967102i	−0.949483	−	0.313820i	$-0.898391\pi$
$659$	−4.93829	−	24.8265i	−0.192369	−	0.967102i	0.757114	−	0.653283i	$-0.226609\pi$
$660$	2.93617	−	5.51242i	0.114290	−	0.214571i
$661$	27.4496	−	18.3412i	1.06767	−	0.713391i	0.107891	−	0.994163i	$-0.465590\pi$
$661$	27.4496	−	18.3412i	1.06767	−	0.713391i	0.959775	+	0.280771i	$0.0905903\pi$
$662$	−8.06403	+	31.0883i	−0.313417	+	1.20828i
$663$	−1.16022	−	5.32517i	−0.0450591	−	0.206812i
$664$	25.9788	−	27.2570i	1.00817	−	1.05778i
$665$	0.0464848	−	0.112224i	0.00180260	−	0.00435187i
$666$	33.9289	−	21.6491i	1.31472	−	0.838887i
$667$	25.4024	+	5.05285i	0.983584	+	0.195647i
$668$	10.1729	−	18.2898i	0.393601	−	0.707655i
$669$	−23.3675	−	22.5333i	−0.903440	−	0.871187i
$670$	−6.64890	−	0.382385i	−0.256869	−	0.0147728i
$671$			26.2127i			1.01193i
$672$	1.00858	+	0.785621i	0.0389068	+	0.0303060i
$673$			16.0202i			0.617532i	0.951138	+	0.308766i	$0.0999161\pi$
$673$			16.0202i			0.617532i	−0.951138	+	0.308766i	$0.900084\pi$
$674$	0.199081	−	3.46162i	0.00766833	−	0.133337i
$675$	21.3873	−	10.2579i	0.823197	−	0.394827i
$676$	6.20838	+	21.7702i	0.238784	+	0.837317i
$677$	19.9234	+	3.96301i	0.765719	+	0.152311i	0.562472	−	0.826817i	$-0.309851\pi$
$677$	19.9234	+	3.96301i	0.765719	+	0.152311i	0.203247	+	0.979128i	$0.434851\pi$
$678$	−32.6301	+	30.1626i	−1.25315	+	1.15839i
$679$	−0.216662	+	0.523067i	−0.00831471	+	0.0200735i
$680$	−4.22362	−	1.63184i	−0.161969	−	0.0625782i
$681$	22.8763	−	4.98417i	0.876623	−	0.190994i
$682$	14.6561	+	3.80165i	0.561211	+	0.145573i
$683$	6.01014	−	4.01585i	0.229972	−	0.153662i	−0.435246	−	0.900311i	$-0.643339\pi$
$683$	6.01014	−	4.01585i	0.229972	−	0.153662i	0.665218	+	0.746649i	$0.268339\pi$
$684$	8.40955	−	0.995244i	0.321547	−	0.0380541i
$685$	−0.429132	−	2.15739i	−0.0163963	−	0.0824297i
$686$	−2.32322	−	1.12266i	−0.0887009	−	0.0428635i
$687$	−6.66153	+	4.62837i	−0.254153	+	0.176583i
$688$	−10.2026	−	27.1667i	−0.388970	−	1.03572i
$689$	−8.41051	+	8.41051i	−0.320415	+	0.320415i
$690$	1.01697	+	6.42112i	0.0387154	+	0.244448i
$691$	−5.84940	−	29.4069i	−0.222522	−	1.11869i	−0.916911	−	0.399092i	$-0.869325\pi$
$691$	−5.84940	−	29.4069i	−0.222522	−	1.11869i	0.694389	−	0.719599i	$-0.255675\pi$
$692$	1.64904	+	20.2003i	0.0626871	+	0.767899i
$693$	1.04114	−	0.246736i	0.0395495	−	0.00937274i
$694$	4.12982	+	7.02267i	0.156766	+	0.266577i
$695$	3.98748	+	9.62663i	0.151254	+	0.365159i
$696$	−21.3375	+	23.2179i	−0.808797	+	0.880074i
$697$	−10.1888	+	24.5978i	−0.385927	+	0.931709i
$698$	6.24533	+	44.6727i	0.236389	+	1.69089i
$699$	6.46241	−	16.4404i	0.244431	−	0.621834i
$700$	0.933375	−	0.740234i	0.0352783	−	0.0279782i
$701$	13.3731	−	20.0143i	0.505095	−	0.755928i	−0.488050	−	0.872816i	$-0.662292\pi$
$701$	13.3731	−	20.0143i	0.505095	−	0.755928i	0.993145	+	0.116887i	$0.0372917\pi$
$702$	−1.83129	−	9.34963i	−0.0691177	−	0.352879i
$703$		−	13.3888i		−	0.504970i
$704$	21.2176	−	5.29050i	0.799669	−	0.199393i
$705$	1.13024	−	6.27609i	0.0425674	−	0.236371i
$706$	2.82206	−	2.51511i	0.106210	−	0.0946575i
$707$	−1.58061	−	1.05613i	−0.0594450	−	0.0397199i
$708$	6.32556	−	3.39290i	0.237729	−	0.127513i
$709$	1.09653	+	0.218114i	0.0411811	+	0.00819144i	0.215638	−	0.976473i	$-0.430817\pi$
$709$	1.09653	+	0.218114i	0.0411811	+	0.00819144i	−0.174457	+	0.984665i	$0.555817\pi$
$710$	−8.90216	+	1.24454i	−0.334092	+	0.0467067i
$711$	−32.1872	−	29.9286i	−1.20712	−	1.12241i
$712$	−3.32768	+	0.745376i	−0.124710	+	0.0279342i
$713$	−14.5609	+	6.03132i	−0.545309	+	0.225875i
$714$	−0.268479	−	0.727757i	−0.0100476	−	0.0272356i
$715$	−1.94359	+	1.29866i	−0.0726861	+	0.0485673i
$716$	0.519378	+	6.36223i	0.0194101	+	0.237768i
$717$	−18.0255	+	0.327604i	−0.673173	+	0.0122346i
$718$	14.5034	−	5.05301i	0.541260	−	0.188577i
$719$	34.6451	+	34.6451i	1.29205	+	1.29205i	0.933520	+	0.358525i	$0.116720\pi$
$719$	34.6451	+	34.6451i	1.29205	+	1.29205i	0.358525	+	0.933520i	$0.383280\pi$
$720$	−7.32147	−	3.00778i	−0.272855	−	0.112093i
$721$	−1.22804	+	1.22804i	−0.0457347	+	0.0457347i
$722$	−10.4654	+	21.6569i	−0.389482	+	0.805986i
$723$	0.839172	+	46.1730i	0.0312092	+	1.71719i
$724$	33.4988	−	17.1917i	1.24497	−	0.638923i
$725$	16.3245	+	24.4313i	0.606277	+	0.907357i
$726$	−3.61852	+	7.84907i	−0.134296	+	0.291306i
$727$	−0.480494	−	1.16001i	−0.0178205	−	0.0430226i	0.914719	−	0.404091i	$-0.132412\pi$
$727$	−0.480494	−	1.16001i	−0.0178205	−	0.0430226i	−0.932539	+	0.361068i	$0.882412\pi$
$728$	−0.193666	−	0.437537i	−0.00717772	−	0.0162162i
$729$	−2.93812	−	26.8397i	−0.108819	−	0.994062i
$730$	3.62362	−	4.80146i	0.134116	−	0.177710i
$731$	−3.43505	+	17.2692i	−0.127050	+	0.638724i
$732$	33.0552	−	3.30411i	1.22176	−	0.122124i
$733$	20.0016	−	29.9345i	0.738775	−	1.10565i	−0.251679	−	0.967811i	$-0.580983\pi$
$733$	20.0016	−	29.9345i	0.738775	−	1.10565i	0.990454	−	0.137844i	$-0.0440173\pi$
$734$	−49.6876	−	2.85759i	−1.83400	−	0.105476i
$735$	7.85149	+	1.41395i	0.289606	+	0.0521543i
$736$	−14.3114	+	17.6999i	−0.527526	+	0.652428i
$737$	−19.5153			−0.718854
$738$	−18.7143	+	42.6140i	−0.688883	+	1.56864i
$739$	−16.4166	−	10.9692i	−0.603895	−	0.403510i	0.215695	−	0.976461i	$-0.430798\pi$
$739$	−16.4166	−	10.9692i	−0.603895	−	0.403510i	−0.819590	+	0.572951i	$0.805798\pi$
$740$	−6.08300	+	10.9366i	−0.223615	+	0.402038i
$741$	−2.94968	−	1.15946i	−0.108359	−	0.0425939i
$742$	−1.01978	+	1.35126i	−0.0374375	+	0.0496064i
$743$	17.3442	+	7.18421i	0.636297	+	0.263563i	0.677426	−	0.735591i	$-0.263095\pi$
$743$	17.3442	+	7.18421i	0.636297	+	0.263563i	−0.0411287	+	0.999154i	$0.513095\pi$
$744$	2.94663	−	18.9611i	0.108029	−	0.695146i
$745$	−3.79895	+	1.57358i	−0.139183	+	0.0576514i
$746$	38.4733	+	9.97963i	1.40861	+	0.365380i
$747$	−38.8620	+	9.20980i	−1.42188	+	0.336969i
$748$	−12.6305	−	4.06324i	−0.461816	−	0.148567i
$749$	−0.378360	+	0.0752604i	−0.0138250	+	0.00274995i
$750$	−9.08365	+	12.5024i	−0.331688	+	0.456524i
$751$	−23.8625	−	23.8625i	−0.870754	−	0.870754i	0.121800	−	0.992555i	$-0.461133\pi$
$751$	−23.8625	−	23.8625i	−0.870754	−	0.870754i	−0.992555	+	0.121800i	$0.961133\pi$
$752$	18.9689	−	11.7768i	0.691725	−	0.429455i
$753$	20.2982	+	29.2148i	0.739706	+	1.06465i
$754$	11.1449	−	3.88292i	0.405874	−	0.141408i
$755$	−5.09367	+	1.01319i	−0.185378	+	0.0368739i
$756$	−0.442379	−	1.28181i	−0.0160892	−	0.0466190i
$757$	−21.3248	−	31.9148i	−0.775063	−	1.15996i	−0.983319	−	0.181889i	$-0.941779\pi$
$757$	−21.3248	−	31.9148i	−0.775063	−	1.15996i	0.208256	−	0.978074i	$-0.433221\pi$
$758$	0.921356	+	1.56675i	0.0334651	+	0.0569068i
$759$	4.05540	+	18.6135i	0.147202	+	0.675626i
$760$	−2.15360	+	1.51500i	−0.0781193	+	0.0549550i
$761$	−1.76986	−	0.733099i	−0.0641573	−	0.0265748i	0.350374	−	0.936610i	$-0.386054\pi$
$761$	−1.76986	−	0.733099i	−0.0641573	−	0.0265748i	−0.414531	+	0.910035i	$0.636054\pi$
$762$	−0.718227	+	18.2776i	−0.0260186	+	0.662127i
$763$	0.146869	−	0.738360i	0.00531701	−	0.0267304i
$764$	−2.08169	+	18.0383i	−0.0753129	+	0.652603i
$765$	2.81150	+	3.89360i	0.101650	+	0.140773i
$766$	−11.4096	+	10.1686i	−0.412246	+	0.367407i
$767$	−2.68651			−0.0970043
$768$	−9.34599	−	26.0893i	−0.337245	−	0.941417i
$769$	16.6973			0.602118			0.301059	−	0.953605i	$-0.402660\pi$
$769$	16.6973			0.602118			0.301059	+	0.953605i	$0.402660\pi$
$770$	−0.248371	+	0.221357i	−0.00895068	+	0.00797714i
$771$	−8.08029	+	8.37943i	−0.291004	+	0.301778i
$772$	4.04182	−	35.0232i	0.145468	−	1.26051i
$773$	9.01117	−	45.3022i	0.324109	−	1.62941i	−0.384021	−	0.923325i	$-0.625461\pi$
$773$	9.01117	−	45.3022i	0.324109	−	1.62941i	0.708130	−	0.706082i	$-0.249539\pi$
$774$	−6.64048	+	30.0548i	−0.238687	+	1.08030i
$775$	−16.5192	−	6.84246i	−0.593386	−	0.245789i
$776$	10.0377	−	7.06131i	0.360334	−	0.253486i
$777$	−2.09479	+	0.456400i	−0.0751500	+	0.0163733i
$778$	7.32836	+	12.4617i	0.262734	+	0.446775i
$779$	8.60184	+	12.8736i	0.308193	+	0.461243i
$780$	1.88265	+	2.28724i	0.0674098	+	0.0818963i
$781$	−25.8333	+	5.13856i	−0.924388	+	0.183872i
$782$	13.0419	−	4.54385i	0.466378	−	0.162488i
$783$	32.3994	−	8.30286i	1.15786	−	0.296720i
$784$	14.7329	+	23.7304i	0.526176	+	0.847514i
$785$	0.307009	+	0.307009i	0.0109576	+	0.0109576i
$786$	−23.8838	−	17.3528i	−0.851907	−	0.618954i
$787$	49.8203	−	9.90988i	1.77590	−	0.353249i	0.805103	−	0.593135i	$-0.202110\pi$
$787$	49.8203	−	9.90988i	1.77590	−	0.353249i	0.970801	+	0.239886i	$0.0771102\pi$
$788$	−31.1586	−	10.0238i	−1.10998	−	0.357082i
$789$	−13.4081	+	5.84148i	−0.477341	+	0.207962i
$790$	13.2285	+	3.43134i	0.470648	+	0.122082i
$791$	2.18684	−	0.905819i	0.0777551	−	0.0322072i
$792$	−21.9245	−	7.56726i	−0.779054	−	0.268891i
$793$	−11.4867	−	4.75796i	−0.407905	−	0.168960i
$794$	0.236192	−	0.312966i	0.00838215	−	0.0111067i
$795$	3.83432	−	9.75456i	0.135989	−	0.345959i
$796$	21.7578	−	39.1183i	0.771185	−	1.38651i
$797$	2.51856	+	1.68284i	0.0892118	+	0.0596094i	0.599376	−	0.800468i	$-0.295415\pi$
$797$	2.51856	+	1.68284i	0.0892118	+	0.0596094i	−0.510164	+	0.860077i	$0.670415\pi$
$798$	−0.438628	−	0.105308i	−0.0155273	−	0.00372785i
$799$	−13.5472			−0.479265
$800$	−25.6797	+	2.71827i	−0.907913	+	0.0961052i
$801$	3.38976	+	1.26182i	0.119771	+	0.0445843i
$802$	11.3862	+	0.654830i	0.402059	+	0.0231229i
$803$	9.79283	−	14.6560i	0.345582	−	0.517199i
$804$	2.45990	+	24.6095i	0.0867539	+	0.867909i
$805$	0.0675614	−	0.339654i	0.00238123	−	0.0119712i
$806$	−4.32620	+	5.73242i	−0.152384	+	0.201916i
$807$	−19.6136	+	30.5411i	−0.690433	+	1.07510i
$808$	16.6787	+	37.6812i	0.586755	+	1.32562i
$809$	12.3905	+	29.9133i	0.435627	+	1.05170i	0.977443	+	0.211200i	$0.0677371\pi$
$809$	12.3905	+	29.9133i	0.435627	+	1.05170i	−0.541816	+	0.840497i	$0.682263\pi$
$810$	4.77006	+	6.90858i	0.167603	+	0.242743i
$811$	−13.7998	−	20.6529i	−0.484577	−	0.725221i	0.505946	−	0.862565i	$-0.331143\pi$
$811$	−13.7998	−	20.6529i	−0.484577	−	0.725221i	−0.990523	+	0.137344i	$0.956143\pi$
$812$	1.49444	−	0.766950i	0.0524446	−	0.0269147i
$813$	−13.8716	+	0.252110i	−0.486498	+	0.00884187i
$814$	−15.9554	+	33.0178i	−0.559236	+	1.15727i
$815$	10.6320	−	10.6320i	0.372424	−	0.372424i
$816$	−3.53182	+	16.4397i	−0.123639	+	0.575504i
$817$	7.24025	+	7.24025i	0.253304	+	0.253304i
$818$	7.63188	−	2.65897i	0.266842	−	0.0929687i
$819$	−0.0808573	+	0.501024i	−0.00282538	+	0.0175072i
$820$	−1.17748	−	14.4238i	−0.0411194	−	0.503701i
$821$	−19.1645	+	12.8053i	−0.668845	+	0.446908i	−0.843074	−	0.537797i	$-0.819257\pi$
$821$	−19.1645	+	12.8053i	−0.668845	+	0.446908i	0.174229	+	0.984705i	$0.444257\pi$
$822$	−7.66376	+	2.82726i	−0.267304	+	0.0986121i
$823$	−46.0915	+	19.0917i	−1.60665	+	0.665495i	−0.992336	−	0.123569i	$-0.960566\pi$
$823$	−46.0915	+	19.0917i	−1.60665	+	0.665495i	−0.614311	+	0.789064i	$0.710566\pi$
$824$	36.7362	−	8.22866i	1.27977	−	0.286659i
$825$	−11.6786	+	18.1851i	−0.406595	+	0.633123i
$826$	−0.378683	+	0.0529407i	−0.0131761	+	0.00184204i
$827$	3.97592	+	0.790860i	0.138256	+	0.0275009i	0.263733	−	0.964596i	$-0.415046\pi$
$827$	3.97592	+	0.790860i	0.138256	+	0.0275009i	−0.125477	+	0.992097i	$0.540046\pi$
$828$	22.9611	−	7.46024i	0.797953	−	0.259261i
$829$	−17.5609	−	11.7338i	−0.609917	−	0.407533i	0.211895	−	0.977292i	$-0.432036\pi$
$829$	−17.5609	−	11.7338i	−0.609917	−	0.407533i	−0.821812	+	0.569759i	$0.807036\pi$
$830$	9.27082	−	8.26246i	0.321795	−	0.286794i
$831$	10.3487	+	1.86367i	0.358994	+	0.0646500i
$832$	−1.53292	+	10.2581i	−0.0531443	+	0.355636i
$833$		−	16.9477i		−	0.587203i
$834$	32.9929	−	20.2178i	1.14245	−	0.700086i
$835$	3.83469	−	5.73902i	0.132705	−	0.198607i
$836$	−6.04533	+	4.79438i	−0.209082	+	0.165817i
$837$	−13.5859	+	15.1543i	−0.469598	+	0.523810i
$838$	1.55246	+	11.1047i	0.0536289	+	0.383606i
$839$	−19.5581	+	47.2175i	−0.675222	+	1.63013i	0.0973851	+	0.995247i	$0.468952\pi$
$839$	−19.5581	+	47.2175i	−0.675222	+	1.63013i	−0.772607	+	0.634884i	$0.781048\pi$
$840$	0.310446	+	0.285303i	0.0107114	+	0.00984390i
$841$	4.75745	+	11.4855i	0.164050	+	0.396052i
$842$	−9.35665	−	15.9108i	−0.322451	−	0.548322i
$843$	16.0177	−	6.97840i	0.551679	−	0.240349i
$844$	2.10396	+	25.7729i	0.0724213	+	0.887140i
$845$	1.45656	+	7.32262i	0.0501072	+	0.251906i
$846$	−23.6765	−	0.499714i	−0.814015	−	0.0171805i
$847$	0.325554	−	0.325554i	0.0111862	−	0.0111862i
$848$	34.3537	−	12.9017i	1.17971	−	0.443047i
$849$	16.6110	+	23.9079i	0.570086	+	0.820515i
$850$	14.1074	+	6.81720i	0.483880	+	0.233828i
$851$	−7.44682	−	37.4377i	−0.255274	−	1.28335i
$852$	9.73620	+	31.9290i	0.333557	+	1.09387i
$853$	−14.3936	+	9.61749i	−0.492827	+	0.329296i	−0.777026	−	0.629469i	$-0.783272\pi$
$853$	−14.3936	+	9.61749i	−0.492827	+	0.329296i	0.284199	+	0.958765i	$0.408272\pi$
$854$	−1.71290	−	0.444310i	−0.0586141	−	0.0152040i
$855$	2.79098	−	0.101483i	0.0954496	−	0.00347065i
$856$	7.80038	+	3.01376i	0.266612	+	0.103008i
$857$	21.9971	−	53.1056i	0.751405	−	1.81405i	0.200043	−	0.979787i	$-0.435892\pi$
$857$	21.9971	−	53.1056i	0.751405	−	1.81405i	0.551362	−	0.834266i	$-0.314108\pi$
$858$	5.89240	+	6.37443i	0.201163	+	0.217619i
$859$	−43.2845	−	8.60982i	−1.47685	−	0.293763i	−0.610026	−	0.792382i	$-0.708841\pi$
$859$	−43.2845	−	8.60982i	−1.47685	−	0.293763i	−0.866822	+	0.498619i	$0.833841\pi$
$860$	−2.62468	−	9.20365i	−0.0895007	−	0.313842i
$861$	1.72095	−	1.78466i	0.0586497	−	0.0608210i
$862$	3.24779	−	56.4725i	0.110620	−	1.92346i
$863$		−	18.7780i		−	0.639211i	−0.947551	−	0.319605i	$-0.896450\pi$
$863$		−	18.7780i		−	0.639211i	0.947551	−	0.319605i	$-0.103550\pi$
$864$	−6.77900	+	28.6015i	−0.230626	+	0.973042i
$865$			6.68422i			0.227270i
$866$	−12.9717	−	0.746017i	−0.440797	−	0.0253507i
$867$	−13.3570	+	13.8515i	−0.453627	+	0.470421i
$868$	−0.496846	+	0.893279i	−0.0168641	+	0.0303198i
$869$	39.2764	+	7.81255i	1.33236	+	0.265023i
$870$	−7.63683	+	7.05933i	−0.258913	+	0.239334i
$871$	3.54228	−	8.55182i	0.120026	−	0.289767i
$872$	−11.2589	+	11.8129i	−0.381275	+	0.400034i
$873$	−13.0085	+	0.473004i	−0.440272	+	0.0160088i
$874$	2.01653	−	7.77410i	0.0682101	−	0.262963i
$875$	0.684475	−	0.457351i	0.0231395	−	0.0154613i
$876$	−19.7162	−	10.5017i	−0.666147	−	0.354821i
$877$	−6.57996	−	33.0797i	−0.222189	−	1.11702i	−0.917324	−	0.398142i	$-0.869655\pi$
$877$	−6.57996	−	33.0797i	−0.222189	−	1.11702i	0.695134	−	0.718880i	$-0.255345\pi$
$878$	11.0160	−	22.7963i	0.371771	−	0.769336i
$879$	4.23682	+	6.09799i	0.142905	+	0.205680i
$880$	7.11634	−	1.16967i	0.239892	−	0.0394297i
$881$	13.0510	−	13.0510i	0.439698	−	0.439698i	−0.452212	−	0.891910i	$-0.649365\pi$
$881$	13.0510	−	13.0510i	0.439698	−	0.439698i	0.891910	+	0.452212i	$0.149365\pi$
$882$	0.625150	−	29.6197i	0.0210499	−	0.997346i
$883$	10.4090	+	52.3294i	0.350290	+	1.76103i	0.607160	+	0.794580i	$0.292309\pi$
$883$	10.4090	+	52.3294i	0.350290	+	1.76103i	−0.256870	+	0.966446i	$0.582691\pi$
$884$	4.07316	−	4.79730i	0.136995	−	0.161351i
$885$	2.17030	−	0.945530i	0.0729538	−	0.0317836i
$886$	−6.26048	+	3.68160i	−0.210325	+	0.123686i
$887$	5.27915	+	12.7450i	0.177256	+	0.427935i	0.987389	−	0.158312i	$-0.0506050\pi$
$887$	5.27915	+	12.7450i	0.177256	+	0.427935i	−0.810133	+	0.586246i	$0.800605\pi$
$888$	43.6478	+	15.9584i	1.46472	+	0.535530i
$889$	0.372877	−	0.900206i	0.0125059	−	0.0301919i
$890$	−1.11383	+	0.155716i	−0.0373357	+	0.00521961i
$891$	15.1168	+	19.4081i	0.506433	+	0.650195i
$892$	4.29728	−	37.2369i	0.143884	−	1.24678i
$893$	−4.37682	+	6.55037i	−0.146465	+	0.219200i
$894$	7.97855	+	13.0200i	0.266842	+	0.435453i
$895$			2.10525i			0.0703706i
$896$	−0.0139286	+	1.47616i	−0.000465322	+	0.0493151i
$897$	−8.89275	−	1.60147i	−0.296920	−	0.0534714i
$898$	19.4414	+	21.8141i	0.648770	+	0.727946i
$899$	−20.9629	−	14.0070i	−0.699153	−	0.467159i
$900$	24.4041	+	12.4349i	0.813471	+	0.414495i
$901$	−21.8378	−	4.34381i	−0.727524	−	0.144713i
$902$	−5.87138	−	41.9978i	−0.195496	−	1.39837i
$903$	0.885986	−	1.37960i	0.0294838	−	0.0459102i
$904$	−50.5495	−	8.79916i	−1.68125	−	0.292656i
$905$	11.4726	−	4.75212i	0.381363	−	0.157966i
$906$	6.67525	+	18.0944i	0.221770	+	0.601145i
$907$	39.6779	−	26.5119i	1.31748	−	0.880314i	0.319743	−	0.947504i	$-0.396403\pi$
$907$	39.6779	−	26.5119i	1.31748	−	0.880314i	0.997740	+	0.0671898i	$0.0214033\pi$
$908$	20.6087	+	17.4978i	0.683922	+	0.580686i
$909$	6.96353	−	43.1488i	0.230966	−	1.43116i
$910$	−0.0519184	−	0.149018i	−0.00172108	−	0.00493991i
$911$	−26.2030	−	26.2030i	−0.868146	−	0.868146i	0.124122	−	0.992267i	$-0.460389\pi$
$911$	−26.2030	−	26.2030i	−0.868146	−	0.868146i	−0.992267	+	0.124122i	$0.960389\pi$
$912$	6.80791	+	7.01905i	0.225432	+	0.232424i
$913$	25.7311	−	25.7311i	0.851574	−	0.851574i
$914$	28.7039	+	13.8708i	0.949440	+	0.458804i
$915$	10.9541	−	0.199086i	0.362133	−	0.00658159i
$916$	−8.91642	−	2.86842i	−0.294607	−	0.0947753i
$917$	0.873693	+	1.30757i	0.0288519	+	0.0431799i
$918$	12.6480	−	12.5741i	0.417446	−	0.415006i
$919$	14.1445	+	34.1479i	0.466585	+	1.12644i	0.965644	+	0.259867i	$0.0836789\pi$
$919$	14.1445	+	34.1479i	0.466585	+	1.12644i	−0.499060	+	0.866568i	$0.666321\pi$
$920$	−5.17922	+	5.43406i	−0.170754	+	0.179156i
$921$	−18.3571	+	28.5845i	−0.604888	+	0.941892i
$922$	34.4770	+	26.0194i	1.13544	+	0.856905i
$923$	2.43731	−	12.2532i	0.0802249	−	0.403318i
$924$	0.956191	+	0.782406i	0.0314564	+	0.0257393i
$925$	24.0588	−	36.0066i	0.791049	−	1.18389i
$926$	−1.78427	+	31.0247i	−0.0586346	+	1.01954i
$927$	−37.4216	−	13.9300i	−1.22909	−	0.457522i
$928$	−36.2615	−	3.30489i	−1.19034	−	0.108488i
$929$	−52.3068			−1.71613			−0.858065	−	0.513541i	$-0.828333\pi$
$929$	−52.3068			−1.71613			−0.858065	+	0.513541i	$0.828333\pi$
$930$	1.47738	−	6.15357i	0.0484451	−	0.201783i
$931$	−8.19461	−	5.47546i	−0.268568	−	0.179451i
$932$	19.6157	−	5.59396i	0.642533	−	0.183236i
$933$	−17.2787	+	43.9573i	−0.565680	+	1.43910i
$934$	−22.1348	−	16.7049i	−0.724273	−	0.546602i
$935$	−4.04270	−	1.67454i	−0.132210	−	0.0547633i
$936$	7.29565	−	8.23403i	0.238466	−	0.269138i
$937$	−0.210887	+	0.0873524i	−0.00688939	+	0.00285368i	−0.386125	−	0.922446i	$-0.626187\pi$
$937$	−0.210887	+	0.0873524i	−0.00688939	+	0.00285368i	0.379236	+	0.925300i	$0.376187\pi$
$938$	0.330787	−	1.27524i	0.0108006	−	0.0416382i
$939$	−21.0203	+	9.15785i	−0.685970	+	0.298855i
$940$	6.55123	−	3.36210i	0.213678	−	0.109660i
$941$	−43.4652	+	8.64577i	−1.41693	+	0.281844i	−0.843375	−	0.537325i	$-0.819435\pi$
$941$	−43.4652	+	8.64577i	−1.41693	+	0.281844i	−0.573551	+	0.819170i	$0.694435\pi$
$942$	0.947725	−	1.30442i	0.0308785	−	0.0425002i
$943$	31.2125	+	31.2125i	1.01642	+	1.01642i
$944$	7.54724	+	3.42613i	0.245642	+	0.111511i
$945$	−0.111017	−	0.433211i	−0.00361139	−	0.0140924i
$946$	−9.22679	−	26.4831i	−0.299989	−	0.861040i
$947$	10.1237	−	2.01372i	0.328975	−	0.0654372i	−0.0278397	−	0.999612i	$-0.508863\pi$
$947$	10.1237	−	2.01372i	0.328975	−	0.0654372i	0.356815	+	0.934175i	$0.383863\pi$
$948$	4.90113	−	50.5137i	0.159181	−	1.64061i
$949$	4.64491	+	6.95159i	0.150780	+	0.225658i
$950$	7.85409	−	4.61875i	0.254820	−	0.149852i
$951$	12.3341	−	2.68729i	0.399960	−	0.0871412i
$952$	0.479605	−	0.756480i	0.0155441	−	0.0245176i
$953$	−50.4642	−	20.9029i	−1.63469	−	0.677113i	−0.638949	−	0.769249i	$-0.720630\pi$
$953$	−50.4642	−	20.9029i	−1.63469	−	0.677113i	−0.995746	+	0.0921366i	$0.970630\pi$
$954$	−38.0059	−	8.39725i	−1.23049	−	0.271871i
$955$	−1.16830	+	5.87346i	−0.0378054	+	0.190061i
$956$	−12.9355	−	16.3107i	−0.418365	−	0.527525i
$957$	−21.1534	+	21.9365i	−0.683791	+	0.709106i
$958$	14.9123	+	16.7322i	0.481794	+	0.540593i
$959$	0.435133			0.0140512
$960$	−2.37202	−	8.82653i	−0.0765565	−	0.284875i
$961$	−15.6581			−0.505101
$962$	−11.5727	−	12.9850i	−0.373118	−	0.418653i
$963$	−5.19241	−	7.19087i	−0.167323	−	0.231723i
$964$	−41.7805	+	33.1350i	−1.34566	+	1.06721i
$965$	2.26838	−	11.4039i	0.0730218	−	0.367106i
$966$	−1.28506	−	0.0504969i	−0.0413460	−	0.00162471i
$967$	−38.3116	−	15.8692i	−1.23202	−	0.510318i	−0.330807	−	0.943699i	$-0.607321\pi$
$967$	−38.3116	−	15.8692i	−1.23202	−	0.510318i	−0.901211	+	0.433380i	$0.857321\pi$
$968$	−9.73877	+	2.18142i	−0.313016	+	0.0701134i
$969$	−1.26302	−	5.79699i	−0.0405739	−	0.186226i
$970$	3.48896	−	2.05175i	0.112024	−	0.0658778i
$971$	−23.3072	−	34.8817i	−0.747963	−	1.11941i	−0.988859	−	0.148855i	$-0.952441\pi$
$971$	−23.3072	−	34.8817i	−0.747963	−	1.11941i	0.240896	−	0.970551i	$-0.422559\pi$
$972$	22.5688	−	21.5093i	0.723895	−	0.689910i
$973$	−2.02162	+	0.402125i	−0.0648102	+	0.0128915i
$974$	0.0446285	+	0.128095i	0.00142999	+	0.00410442i
$975$	−5.84910	−	8.41851i	−0.187321	−	0.269608i
$976$	26.2019	+	28.0157i	0.838702	+	0.896761i
$977$	−1.16173	−	1.16173i	−0.0371671	−	0.0371671i	0.688279	−	0.725446i	$-0.258367\pi$
$977$	−1.16173	−	1.16173i	−0.0371671	−	0.0371671i	−0.725446	+	0.688279i	$0.758367\pi$
$978$	−45.1733	−	32.8207i	−1.44448	−	1.04949i
$979$	−3.23225	+	0.642934i	−0.103303	+	0.0205483i
$980$	4.20604	+	8.19569i	0.134357	+	0.261802i
$981$	16.8423	−	3.99142i	0.537734	−	0.127436i
$982$	14.0678	−	54.2340i	0.448922	−	1.73068i
$983$	−10.0402	+	4.15877i	−0.320232	+	0.132644i	−0.537008	−	0.843577i	$-0.680446\pi$
$983$	−10.0402	+	4.15877i	−0.320232	+	0.132644i	0.216777	+	0.976221i	$0.430446\pi$
$984$	−52.2207	+	12.6978i	−1.66473	+	0.404793i
$985$	−9.97308	−	4.13099i	−0.317769	−	0.131624i
$986$	17.6345	+	13.3086i	0.561598	+	0.423833i
$987$	1.17405	+	0.461496i	0.0373705	+	0.0146896i
$988$	−1.00365	−	3.51938i	−0.0319303	−	0.111966i
$989$	24.2721	+	16.2181i	0.771807	+	0.515705i
$990$	−7.00369	−	3.07573i	−0.222592	−	0.0977531i
$991$	−15.2599			−0.484747			−0.242374	−	0.970183i	$-0.577926\pi$
$991$	−15.2599			−0.484747			−0.242374	+	0.970183i	$0.577926\pi$
$992$	19.4643	−	10.5869i	0.617991	−	0.336134i
$993$	38.7126	+	6.97163i	1.22851	+	0.221238i
$994$	0.102094	−	1.77520i	0.00323822	−	0.0563060i
$995$	8.20164	−	12.2746i	0.260010	−	0.389132i
$996$	−35.6912	−	29.2044i	−1.13092	−	0.925378i
$997$	7.68549	−	38.6376i	0.243402	−	1.22366i	−0.644851	−	0.764309i	$-0.723080\pi$
$997$	7.68549	−	38.6376i	0.243402	−	1.22366i	0.888252	−	0.459356i	$-0.151920\pi$
$998$	−1.57430	−	1.18811i	−0.0498335	−	0.0376089i
$999$	−29.5782	−	39.4323i	−0.935814	−	1.24758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.59.24	yes	240
3.2	odd	2	inner	192.2.s.a.59.7	✓	240
4.3	odd	2		768.2.s.a.143.24		240
12.11	even	2		768.2.s.a.143.4		240
64.13	even	16		768.2.s.a.623.4		240
64.51	odd	16	inner	192.2.s.a.179.7	yes	240
192.77	odd	16		768.2.s.a.623.24		240
192.179	even	16	inner	192.2.s.a.179.24	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.59.7	✓	240	3.2	odd	2	inner
192.2.s.a.59.24	yes	240	1.1	even	1	trivial
192.2.s.a.179.7	yes	240	64.51	odd	16	inner
192.2.s.a.179.24	yes	240	192.179	even	16	inner
768.2.s.a.143.4		240	12.11	even	2
768.2.s.a.143.24		240	4.3	odd	2
768.2.s.a.623.4		240	64.13	even	16
768.2.s.a.623.24		240	192.77	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05577 - 0.940934i) q^{2} +(-1.24680 - 1.20229i) q^{3} +(0.229286 - 1.98681i) q^{4} +(0.128682 - 0.646927i) q^{5} +(-2.44760 - 0.0961797i) q^{6} +(0.120549 + 0.0499330i) q^{7} +(-1.62739 - 2.31335i) q^{8} +(0.109011 + 2.99802i) q^{9} +O(q^{10})\)	\(q+(1.05577 - 0.940934i) q^{2} +(-1.24680 - 1.20229i) q^{3} +(0.229286 - 1.98681i) q^{4} +(0.128682 - 0.646927i) q^{5} +(-2.44760 - 0.0961797i) q^{6} +(0.120549 + 0.0499330i) q^{7} +(-1.62739 - 2.31335i) q^{8} +(0.109011 + 2.99802i) q^{9} +(-0.472858 - 0.804085i) q^{10} +(-1.51860 - 2.27274i) q^{11} +(-2.67459 + 2.20149i) q^{12} +(1.27159 - 0.252935i) q^{13} +(0.174255 - 0.0607110i) q^{14} +(-0.938232 + 0.651875i) q^{15} +(-3.89486 - 0.911097i) q^{16} +(1.71615 + 1.71615i) q^{17} +(2.93603 + 3.06264i) q^{18} +(1.38425 - 0.275345i) q^{19} +(-1.25582 - 0.403998i) q^{20} +(-0.0902664 - 0.207191i) q^{21} +(-3.74179 - 0.970585i) q^{22} +(3.71748 - 1.53983i) q^{23} +(-0.752291 + 4.84087i) q^{24} +(4.21744 + 1.74692i) q^{25} +(1.10451 - 1.46352i) q^{26} +(3.46856 - 3.86899i) q^{27} +(0.126848 - 0.228059i) q^{28} +(5.35197 + 3.57607i) q^{29} +(-0.377183 + 1.57104i) q^{30} -3.91687 q^{31} +(-4.96934 + 2.70290i) q^{32} +(-0.839104 + 4.65944i) q^{33} +(3.42664 + 0.197070i) q^{34} +(0.0478155 - 0.0715609i) q^{35} +(5.98150 + 0.470819i) q^{36} +(1.85070 - 9.30412i) q^{37} +(1.20237 - 1.59319i) q^{38} +(-1.88951 - 1.21346i) q^{39} +(-1.70599 + 0.755115i) q^{40} +(4.19808 + 10.1351i) q^{41} +(-0.290253 - 0.133810i) q^{42} +(4.03057 + 6.03217i) q^{43} +(-4.86371 + 2.49606i) q^{44} +(1.95353 + 0.315268i) q^{45} +(2.47591 - 5.12361i) q^{46} +(-3.94696 + 3.94696i) q^{47} +(3.76070 + 5.81869i) q^{48} +(-4.93771 - 4.93771i) q^{49} +(6.09637 - 2.12399i) q^{50} +(-0.0763875 - 4.20300i) q^{51} +(-0.210977 - 2.58440i) q^{52} +(-7.62801 + 5.09687i) q^{53} +(0.0215329 - 7.34844i) q^{54} +(-1.66572 + 0.689962i) q^{55} +(-0.0806672 - 0.360133i) q^{56} +(-2.05693 - 1.32097i) q^{57} +(9.01527 - 1.26035i) q^{58} +(-2.03231 - 0.404252i) q^{59} +(1.08003 + 2.01356i) q^{60} +(-7.97360 - 5.32779i) q^{61} +(-4.13530 + 3.68552i) q^{62} +(-0.136559 + 0.366851i) q^{63} +(-2.70321 + 7.52945i) q^{64} -0.855173i q^{65} +(3.49833 + 5.70883i) q^{66} +(3.96652 - 5.93631i) q^{67} +(3.80316 - 3.01618i) q^{68} +(-6.48627 - 2.54962i) q^{69} +(-0.0168521 - 0.120543i) q^{70} +(3.68758 - 8.90261i) q^{71} +(6.75808 - 5.13112i) q^{72} +(2.46777 + 5.95773i) q^{73} +(-6.80065 - 11.5644i) q^{74} +(-3.15800 - 7.24864i) q^{75} +(-0.229670 - 2.81339i) q^{76} +(-0.0695805 - 0.349805i) q^{77} +(-3.13667 + 0.496782i) q^{78} +(-10.3595 + 10.3595i) q^{79} +(-1.09061 + 2.40245i) q^{80} +(-8.97623 + 0.653634i) q^{81} +(13.9686 + 6.75014i) q^{82} +(2.59720 + 13.0570i) q^{83} +(-0.432346 + 0.131837i) q^{84} +(1.33106 - 0.889387i) q^{85} +(9.93121 + 2.57606i) q^{86} +(-2.37336 - 10.8932i) q^{87} +(-2.78631 + 7.21169i) q^{88} +(0.461388 - 1.11389i) q^{89} +(2.35911 - 1.50529i) q^{90} +(0.165918 + 0.0330032i) q^{91} +(-2.20699 - 7.73900i) q^{92} +(4.88354 + 4.70920i) q^{93} +(-0.453239 + 7.88090i) q^{94} -0.930943i q^{95} +(9.44542 + 2.60461i) q^{96} +4.33905i q^{97} +(-9.85913 - 0.567009i) q^{98} +(6.64818 - 4.80054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more