LMFDB - Embedded newform 350.2.q.b.81.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.7
Character	$\chi$	$=$	350.81
Dual form			350.2.q.b.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(0.143555 + 1.36584i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.23569 + 0.0410536i) q^{5} +(-1.11107 - 0.807241i) q^{6} +(2.33546 - 1.24323i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.08954 - 0.231589i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(0.143555 + 1.36584i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.23569 + 0.0410536i) q^{5} +(-1.11107 - 0.807241i) q^{6} +(2.33546 - 1.24323i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.08954 - 0.231589i) q^{9} +(-1.52648 + 1.63397i) q^{10} +(-1.24274 - 0.264153i) q^{11} +(1.34335 - 0.285538i) q^{12} +(2.12235 - 6.53193i) q^{13} +(-0.638824 + 2.56747i) q^{14} +(0.264873 + 3.05948i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.942895 + 0.419804i) q^{17} +(-0.556941 + 0.964650i) q^{18} +(-0.227918 + 2.16850i) q^{19} +(-0.192865 - 2.22773i) q^{20} +(2.03332 + 3.01138i) q^{21} +(1.02786 - 0.746783i) q^{22} +(0.670365 - 0.744516i) q^{23} +(-0.686680 + 1.18936i) q^{24} +(4.99663 + 0.183566i) q^{25} +(3.43404 + 5.94793i) q^{26} +(1.74590 + 5.37332i) q^{27} +(-1.48055 - 2.19271i) q^{28} +(-4.20837 + 3.05756i) q^{29} +(-2.45087 - 1.85035i) q^{30} +(-9.37236 + 4.17285i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.182387 - 1.73530i) q^{33} +(0.318945 - 0.981611i) q^{34} +(5.27240 - 2.68361i) q^{35} +(-0.344208 - 1.05936i) q^{36} +(-6.16968 + 1.31141i) q^{37} +(-1.45900 - 1.62039i) q^{38} +(9.22622 + 1.96109i) q^{39} +(1.78458 + 1.34732i) q^{40} +(-3.90343 + 12.0135i) q^{41} +(-3.59845 - 0.503955i) q^{42} +5.88162 q^{43} +(-0.132804 + 1.26354i) q^{44} +(2.44538 - 0.473032i) q^{45} +(0.104721 + 0.996356i) q^{46} +(-6.03949 - 2.68895i) q^{47} +(-0.424392 - 1.30614i) q^{48} +(3.90874 - 5.80705i) q^{49} +(-3.47981 + 3.59039i) q^{50} +(-0.708741 - 1.22758i) q^{51} +(-6.71799 - 1.42795i) q^{52} +(-0.817190 - 7.77504i) q^{53} +(-5.16139 - 2.29800i) q^{54} +(-2.76754 - 0.641582i) q^{55} +(2.62018 + 0.366950i) q^{56} -2.99453 q^{57} +(0.543739 - 5.17334i) q^{58} +(3.22894 + 3.58610i) q^{59} +(3.01504 - 0.583225i) q^{60} +(8.60114 - 9.55253i) q^{61} +(3.17031 - 9.75720i) q^{62} +(2.25666 - 1.89542i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.01308 - 14.5162i) q^{65} +(1.16754 + 1.29668i) q^{66} +(-9.36011 + 4.16739i) q^{67} +(0.516063 + 0.893848i) q^{68} +(1.11312 + 0.808730i) q^{69} +(-1.53362 + 5.71384i) q^{70} +(-2.35827 + 1.71338i) q^{71} +(1.01758 + 0.453056i) q^{72} +(0.455863 + 0.0968967i) q^{73} +(3.15376 - 5.46247i) q^{74} +(0.466571 + 6.85093i) q^{75} +2.18044 q^{76} +(-3.23077 + 0.928100i) q^{77} +(-7.63092 + 5.54419i) q^{78} +(-8.81268 - 3.92366i) q^{79} +(-2.19537 + 0.424670i) q^{80} +(-4.03570 + 1.79681i) q^{81} +(-6.31589 - 10.9394i) q^{82} +(10.5572 + 7.67025i) q^{83} +(2.78235 - 2.33696i) q^{84} +(-2.12526 + 0.899842i) q^{85} +(-3.93557 + 4.37090i) q^{86} +(-4.78026 - 5.30902i) q^{87} +(-0.850133 - 0.944168i) q^{88} +(5.95104 - 6.60929i) q^{89} +(-1.28475 + 2.13379i) q^{90} +(-3.16405 - 17.8936i) q^{91} +(-0.810509 - 0.588869i) q^{92} +(-7.04488 - 12.2021i) q^{93} +(6.03949 - 2.68895i) q^{94} +(-0.598580 + 4.83874i) q^{95} +(1.25463 + 0.558596i) q^{96} +(0.962506 - 0.699301i) q^{97} +(1.70002 + 6.79043i) q^{98} -1.41519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 9 q^{2} + q^{3} + 9 q^{4} + 2 q^{6} + 8 q^{7} + 18 q^{8} + 20 q^{9}+O(q^{10}) $ 72 * q - 9 * q^2 + q^3 + 9 * q^4 + 2 * q^6 + 8 * q^7 + 18 * q^8 + 20 * q^9	\( 72 q - 9 q^{2} + q^{3} + 9 q^{4} + 2 q^{6} + 8 q^{7} + 18 q^{8} + 20 q^{9} - 10 q^{10} - 12 q^{11} - 4 q^{12} - 8 q^{13} + 11 q^{14} + 16 q^{15} + 9 q^{16} - 30 q^{17} + 50 q^{18} + 2 q^{19} + 10 q^{20} - 20 q^{21} + 26 q^{22} - 10 q^{23} - 6 q^{24} - 8 q^{25} - 14 q^{26} + 46 q^{27} - 2 q^{28} - 10 q^{29} - 12 q^{30} + 9 q^{31} + 36 q^{32} - 13 q^{33} + 20 q^{34} + 6 q^{35} - 40 q^{36} + 11 q^{37} - 12 q^{38} - 27 q^{39} + 5 q^{40} - 34 q^{41} + 2 q^{42} - 32 q^{43} + 13 q^{44} - 7 q^{45} - 15 q^{46} + 8 q^{47} + 8 q^{48} + 64 q^{49} - 46 q^{50} - 86 q^{51} + 4 q^{52} - 33 q^{53} + 13 q^{54} - 38 q^{55} + 2 q^{56} - 108 q^{57} - 5 q^{58} - q^{59} + 2 q^{60} - 19 q^{61} - 22 q^{62} - 20 q^{63} - 18 q^{64} + 3 q^{65} + 8 q^{66} + 40 q^{68} + 64 q^{69} + 34 q^{70} - 10 q^{71} - 5 q^{72} - 14 q^{73} + 4 q^{74} - 16 q^{75} + 56 q^{76} - 70 q^{77} + 46 q^{78} + 2 q^{79} - 60 q^{81} + 28 q^{82} - 56 q^{83} - 28 q^{84} + 52 q^{85} + 19 q^{86} - 8 q^{87} + 12 q^{88} + 8 q^{89} - 164 q^{90} + 29 q^{91} - 30 q^{92} - 44 q^{93} - 8 q^{94} + 27 q^{95} - q^{96} + 14 q^{97} - 20 q^{98}+O(q^{100}) \) 72 * q - 9 * q^2 + q^3 + 9 * q^4 + 2 * q^6 + 8 * q^7 + 18 * q^8 + 20 * q^9 - 10 * q^10 - 12 * q^11 - 4 * q^12 - 8 * q^13 + 11 * q^14 + 16 * q^15 + 9 * q^16 - 30 * q^17 + 50 * q^18 + 2 * q^19 + 10 * q^20 - 20 * q^21 + 26 * q^22 - 10 * q^23 - 6 * q^24 - 8 * q^25 - 14 * q^26 + 46 * q^27 - 2 * q^28 - 10 * q^29 - 12 * q^30 + 9 * q^31 + 36 * q^32 - 13 * q^33 + 20 * q^34 + 6 * q^35 - 40 * q^36 + 11 * q^37 - 12 * q^38 - 27 * q^39 + 5 * q^40 - 34 * q^41 + 2 * q^42 - 32 * q^43 + 13 * q^44 - 7 * q^45 - 15 * q^46 + 8 * q^47 + 8 * q^48 + 64 * q^49 - 46 * q^50 - 86 * q^51 + 4 * q^52 - 33 * q^53 + 13 * q^54 - 38 * q^55 + 2 * q^56 - 108 * q^57 - 5 * q^58 - q^59 + 2 * q^60 - 19 * q^61 - 22 * q^62 - 20 * q^63 - 18 * q^64 + 3 * q^65 + 8 * q^66 + 40 * q^68 + 64 * q^69 + 34 * q^70 - 10 * q^71 - 5 * q^72 - 14 * q^73 + 4 * q^74 - 16 * q^75 + 56 * q^76 - 70 * q^77 + 46 * q^78 + 2 * q^79 - 60 * q^81 + 28 * q^82 - 56 * q^83 - 28 * q^84 + 52 * q^85 + 19 * q^86 - 8 * q^87 + 12 * q^88 + 8 * q^89 - 164 * q^90 + 29 * q^91 - 30 * q^92 - 44 * q^93 - 8 * q^94 + 27 * q^95 - q^96 + 14 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	0.143555	+	1.36584i	0.0828817	+	0.788566i	0.954466	+	0.298320i	$0.0964264\pi$
$3$	0.143555	+	1.36584i	0.0828817	+	0.788566i	−0.871584	+	0.490246i	$0.836907\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	2.23569	+	0.0410536i	0.999831	+	0.0183597i
$5$	2.23569	+	0.0410536i	0.999831	+	0.0183597i
$6$	−1.11107	−	0.807241i	−0.453593	−	0.329555i
$7$	2.33546	−	1.24323i	0.882720	−	0.469898i
$7$	2.33546	−	1.24323i	0.882720	−	0.469898i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.08954	−	0.231589i	0.363180	−	0.0771963i
$10$	−1.52648	+	1.63397i	−0.482715	+	0.516707i
$11$	−1.24274	−	0.264153i	−0.374700	−	0.0796450i	0.0167122	−	0.999860i	$-0.494680\pi$
$11$	−1.24274	−	0.264153i	−0.374700	−	0.0796450i	−0.391412	+	0.920215i	$0.628013\pi$
$12$	1.34335	−	0.285538i	0.387791	−	0.0824276i
$13$	2.12235	−	6.53193i	0.588634	−	1.81163i	0.00447723	−	0.999990i	$-0.498575\pi$
$13$	2.12235	−	6.53193i	0.588634	−	1.81163i	0.584157	−	0.811641i	$-0.301425\pi$
$14$	−0.638824	+	2.56747i	−0.170733	+	0.686185i
$15$	0.264873	+	3.05948i	0.0683898	+	0.789955i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−0.942895	+	0.419804i	−0.228686	+	0.101817i	−0.517881	−	0.855453i	$-0.673279\pi$
$17$	−0.942895	+	0.419804i	−0.228686	+	0.101817i	0.289195	+	0.957270i	$0.406612\pi$
$18$	−0.556941	+	0.964650i	−0.131272	+	0.227370i
$19$	−0.227918	+	2.16850i	−0.0522881	+	0.497488i	0.936768	+	0.349950i	$0.113801\pi$
$19$	−0.227918	+	2.16850i	−0.0522881	+	0.497488i	−0.989056	+	0.147538i	$0.952865\pi$
$20$	−0.192865	−	2.22773i	−0.0431258	−	0.498137i
$21$	2.03332	+	3.01138i	0.443707	+	0.657138i
$22$	1.02786	−	0.746783i	0.219140	−	0.159215i
$23$	0.670365	−	0.744516i	0.139781	−	0.155242i	−0.669190	−	0.743092i	$-0.733359\pi$
$23$	0.670365	−	0.744516i	0.139781	−	0.155242i	0.808970	+	0.587849i	$0.200025\pi$
$24$	−0.686680	+	1.18936i	−0.140168	+	0.242778i
$25$	4.99663	+	0.183566i	0.999326	+	0.0367133i
$26$	3.43404	+	5.94793i	0.673470	+	1.16648i
$27$	1.74590	+	5.37332i	0.335998	+	1.03410i
$28$	−1.48055	−	2.19271i	−0.279797	−	0.414384i
$29$	−4.20837	+	3.05756i	−0.781475	+	0.567775i	−0.905421	−	0.424514i	$-0.860445\pi$
$29$	−4.20837	+	3.05756i	−0.781475	+	0.567775i	0.123946	+	0.992289i	$0.460445\pi$
$30$	−2.45087	−	1.85035i	−0.447466	−	0.337827i
$31$	−9.37236	+	4.17285i	−1.68333	+	0.749465i	−0.683517	+	0.729935i	$0.739550\pi$
$31$	−9.37236	+	4.17285i	−1.68333	+	0.749465i	−0.999809	+	0.0195304i	$0.993783\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.182387	−	1.73530i	0.0317496	−	0.302077i
$34$	0.318945	−	0.981611i	0.0546986	−	0.168345i
$35$	5.27240	−	2.68361i	0.891199	−	0.453613i
$36$	−0.344208	−	1.05936i	−0.0573680	−	0.176561i
$37$	−6.16968	+	1.31141i	−1.01429	+	0.215594i	−0.684929	−	0.728610i	$-0.740167\pi$
$37$	−6.16968	+	1.31141i	−1.01429	+	0.215594i	−0.329361	+	0.944204i	$0.606833\pi$
$38$	−1.45900	−	1.62039i	−0.236681	−	0.262861i
$39$	9.22622	+	1.96109i	1.47738	+	0.314026i
$40$	1.78458	+	1.34732i	0.282167	+	0.213030i
$41$	−3.90343	+	12.0135i	−0.609614	+	1.87620i	−0.148351	+	0.988935i	$0.547396\pi$
$41$	−3.90343	+	12.0135i	−0.609614	+	1.87620i	−0.461263	+	0.887263i	$0.652604\pi$
$42$	−3.59845	−	0.503955i	−0.555253	−	0.0777620i
$43$	5.88162			0.896939			0.448469	−	0.893798i	$-0.351969\pi$
$43$	5.88162			0.896939			0.448469	+	0.893798i	$0.351969\pi$
$44$	−0.132804	+	1.26354i	−0.0200209	+	0.190486i
$45$	2.44538	−	0.473032i	0.364536	−	0.0705154i
$46$	0.104721	+	0.996356i	0.0154403	+	0.146905i
$47$	−6.03949	−	2.68895i	−0.880950	−	0.392224i	−0.0841401	−	0.996454i	$-0.526814\pi$
$47$	−6.03949	−	2.68895i	−0.880950	−	0.392224i	−0.796810	+	0.604230i	$0.793481\pi$
$48$	−0.424392	−	1.30614i	−0.0612557	−	0.188526i
$49$	3.90874	−	5.80705i	0.558391	−	0.829578i
$50$	−3.47981	+	3.59039i	−0.492120	+	0.507758i
$51$	−0.708741	−	1.22758i	−0.0992436	−	0.171895i
$52$	−6.71799	−	1.42795i	−0.931618	−	0.198021i
$53$	−0.817190	−	7.77504i	−0.112250	−	1.06798i	−0.895128	−	0.445810i	$-0.852916\pi$
$53$	−0.817190	−	7.77504i	−0.112250	−	1.06798i	0.782878	−	0.622175i	$-0.213751\pi$
$54$	−5.16139	−	2.29800i	−0.702376	−	0.312718i
$55$	−2.76754	−	0.641582i	−0.373175	−	0.0865110i
$56$	2.62018	+	0.366950i	0.350136	+	0.0490358i
$57$	−2.99453			−0.396636
$58$	0.543739	−	5.17334i	0.0713965	−	0.679292i
$59$	3.22894	+	3.58610i	0.420372	+	0.466871i	0.915716	−	0.401826i	$-0.131624\pi$
$59$	3.22894	+	3.58610i	0.420372	+	0.466871i	−0.495344	+	0.868697i	$0.664958\pi$
$60$	3.01504	−	0.583225i	0.389239	−	0.0752940i
$61$	8.60114	−	9.55253i	1.10126	−	1.22308i	0.128393	−	0.991723i	$-0.459018\pi$
$61$	8.60114	−	9.55253i	1.10126	−	1.22308i	0.972870	−	0.231353i	$-0.0743153\pi$
$62$	3.17031	−	9.75720i	0.402629	−	1.23917i
$63$	2.25666	−	1.89542i	0.284312	−	0.238801i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.01308	−	14.5162i	0.621796	−	1.80052i
$66$	1.16754	+	1.29668i	0.143714	+	0.159611i
$67$	−9.36011	+	4.16739i	−1.14352	+	0.509128i	−0.888985	−	0.457936i	$-0.848589\pi$
$67$	−9.36011	+	4.16739i	−1.14352	+	0.509128i	−0.254535	+	0.967064i	$0.581922\pi$
$68$	0.516063	+	0.893848i	0.0625819	+	0.108395i
$69$	1.11312	+	0.808730i	0.134004	+	0.0973596i
$70$	−1.53362	+	5.71384i	−0.183302	+	0.682935i
$71$	−2.35827	+	1.71338i	−0.279875	+	0.203341i	−0.718863	−	0.695152i	$-0.755337\pi$
$71$	−2.35827	+	1.71338i	−0.279875	+	0.203341i	0.438988	+	0.898493i	$0.355337\pi$
$72$	1.01758	+	0.453056i	0.119923	+	0.0533932i
$73$	0.455863	+	0.0968967i	0.0533547	+	0.0113409i	0.234512	−	0.972113i	$-0.424651\pi$
$73$	0.455863	+	0.0968967i	0.0533547	+	0.0113409i	−0.181157	+	0.983454i	$0.557984\pi$
$74$	3.15376	−	5.46247i	0.366617	−	0.634999i
$75$	0.466571	+	6.85093i	0.0538749	+	0.791078i
$76$	2.18044			0.250114
$77$	−3.23077	+	0.928100i	−0.368181	+	0.105767i
$78$	−7.63092	+	5.54419i	−0.864032	+	0.627756i
$79$	−8.81268	−	3.92366i	−0.991504	−	0.441446i	−0.154115	−	0.988053i	$-0.549253\pi$
$79$	−8.81268	−	3.92366i	−0.991504	−	0.441446i	−0.837389	+	0.546607i	$0.815919\pi$
$80$	−2.19537	+	0.424670i	−0.245450	+	0.0474795i
$81$	−4.03570	+	1.79681i	−0.448411	+	0.199646i
$82$	−6.31589	−	10.9394i	−0.697473	−	1.20806i
$83$	10.5572	+	7.67025i	1.15880	+	0.841919i	0.989626	−	0.143667i	$-0.0458893\pi$
$83$	10.5572	+	7.67025i	1.15880	+	0.841919i	0.169176	+	0.985586i	$0.445889\pi$
$84$	2.78235	−	2.33696i	0.303579	−	0.254983i
$85$	−2.12526	+	0.899842i	−0.230516	+	0.0976016i
$86$	−3.93557	+	4.37090i	−0.424384	+	0.471326i
$87$	−4.78026	−	5.30902i	−0.512498	−	0.569187i
$88$	−0.850133	−	0.944168i	−0.0906245	−	0.100649i
$89$	5.95104	−	6.60929i	0.630809	−	0.700584i	−0.340004	−	0.940424i	$-0.610428\pi$
$89$	5.95104	−	6.60929i	0.630809	−	0.700584i	0.970812	+	0.239840i	$0.0770951\pi$
$90$	−1.28475	+	2.13379i	−0.135425	+	0.224922i
$91$	−3.16405	−	17.8936i	−0.331683	−	1.87576i
$92$	−0.810509	−	0.588869i	−0.0845014	−	0.0613939i
$93$	−7.04488	−	12.2021i	−0.730520	−	1.26530i
$94$	6.03949	−	2.68895i	0.622926	−	0.277345i
$95$	−0.598580	+	4.83874i	−0.0614130	+	0.496444i
$96$	1.25463	+	0.558596i	0.128050	+	0.0570115i
$97$	0.962506	−	0.699301i	0.0977276	−	0.0710033i	−0.537848	−	0.843042i	$-0.680763\pi$
$97$	0.962506	−	0.699301i	0.0977276	−	0.0710033i	0.635576	+	0.772038i	$0.280763\pi$
$98$	1.70002	+	6.79043i	0.171728	+	0.685937i
$99$	−1.41519			−0.142232
$100$	−0.339729	−	4.98845i	−0.0339729	−	0.498845i
$101$	−7.35752	+	12.7436i	−0.732101	+	1.26804i	0.223883	+	0.974616i	$0.428127\pi$
$101$	−7.35752	+	12.7436i	−0.732101	+	1.26804i	−0.955984	+	0.293419i	$0.905207\pi$
$102$	1.38651	+	0.294711i	0.137285	+	0.0291807i
$103$	−7.63638	−	3.39993i	−0.752435	−	0.335005i	−0.00557253	−	0.999984i	$-0.501774\pi$
$103$	−7.63638	−	3.39993i	−0.752435	−	0.335005i	−0.746862	+	0.664979i	$0.768440\pi$
$104$	5.55639	−	4.03695i	0.544849	−	0.395856i
$105$	4.42225	+	6.81600i	0.431568	+	0.665173i
$106$	6.32479	+	4.59523i	0.614318	+	0.446328i
$107$	3.29735	+	5.71118i	0.318767	+	0.552121i	0.980231	−	0.197856i	$-0.0633978\pi$
$107$	3.29735	+	5.71118i	0.318767	+	0.552121i	−0.661464	+	0.749977i	$0.730065\pi$
$108$	5.16139	−	2.29800i	0.496655	−	0.221125i
$109$	−6.52727	−	7.24927i	−0.625199	−	0.694354i	0.344464	−	0.938800i	$-0.388061\pi$
$109$	−6.52727	−	7.24927i	−0.625199	−	0.694354i	−0.969663	+	0.244445i	$0.921394\pi$
$110$	2.32863	−	1.62738i	0.222026	−	0.155165i
$111$	−2.67686	−	8.23852i	−0.254076	−	0.781966i
$112$	−2.02594	+	1.70164i	−0.191433	+	0.160789i
$113$	2.58741	−	7.96322i	0.243403	−	0.749116i	−0.752492	−	0.658601i	$-0.771149\pi$
$113$	2.58741	−	7.96322i	0.243403	−	0.749116i	0.995895	−	0.0905155i	$-0.0288515\pi$
$114$	2.00373	−	2.22537i	0.187667	−	0.208425i
$115$	1.52929	−	1.63699i	0.142607	−	0.152650i
$116$	3.48070	+	3.86571i	0.323175	+	0.358923i
$117$	0.799666	−	7.60831i	0.0739291	−	0.703389i
$118$	−4.82558			−0.444230
$119$	−1.68018	+	2.15267i	−0.154022	+	0.197335i
$120$	−1.58403	+	2.63086i	−0.144602	+	0.240164i
$121$	−8.57437	−	3.81756i	−0.779489	−	0.347051i
$122$	1.34363	+	12.7838i	0.121647	+	1.15739i
$123$	−16.9689	−	3.60685i	−1.53003	−	0.325218i
$124$	5.12966	+	8.88484i	0.460657	+	0.797882i
$125$	11.1634	+	0.615527i	0.998483	+	0.0550544i
$126$	−0.101426	+	2.94531i	−0.00903578	+	0.262389i
$127$	−1.00560	−	3.09493i	−0.0892328	−	0.274630i	0.896475	−	0.443094i	$-0.146119\pi$
$127$	−1.00560	−	3.09493i	−0.0892328	−	0.274630i	−0.985708	+	0.168464i	$0.946119\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	0.844338	+	8.03334i	0.0743398	+	0.707296i
$130$	7.43326	+	13.4387i	0.651940	+	1.17865i
$131$	−0.971572	+	9.24389i	−0.0848867	+	0.807643i	0.866403	+	0.499345i	$0.166426\pi$
$131$	−0.971572	+	9.24389i	−0.0848867	+	0.807643i	−0.951290	+	0.308298i	$0.900241\pi$
$132$	−1.74486			−0.151870
$133$	2.16366	+	5.34780i	0.187613	+	0.463713i
$134$	3.16616	−	9.74445i	0.273515	−	0.841792i
$135$	3.68269	+	12.0848i	0.316956	+	1.04009i
$136$	−1.00957	−	0.214591i	−0.0865701	−	0.0184010i
$137$	1.90928	+	2.12047i	0.163121	+	0.181164i	0.819164	−	0.573559i	$-0.194438\pi$
$137$	1.90928	+	2.12047i	0.163121	+	0.181164i	−0.656043	+	0.754723i	$0.727771\pi$
$138$	−1.34583	+	0.286064i	−0.114564	+	0.0243514i
$139$	5.03124	+	15.4846i	0.426744	+	1.31338i	0.901314	+	0.433166i	$0.142604\pi$
$139$	5.03124	+	15.4846i	0.426744	+	1.31338i	−0.474570	+	0.880218i	$0.657396\pi$
$140$	−3.22002	−	4.96301i	−0.272142	−	0.419451i
$141$	2.80567	−	8.63497i	0.236280	−	0.727196i
$142$	0.304698	−	2.89901i	0.0255697	−	0.243280i
$143$	−4.36296	+	7.55686i	−0.364849	+	0.631937i
$144$	−1.01758	+	0.453056i	−0.0847984	+	0.0377547i
$145$	−9.53414	+	6.66299i	−0.791767	+	0.553331i
$146$	−0.377040	+	0.273936i	−0.0312041	+	0.0226711i
$147$	8.49260	+	4.50506i	0.700458	+	0.371571i
$148$	1.94913	+	5.99881i	0.160218	+	0.493099i
$149$	3.43287	+	5.94591i	0.281232	+	0.487108i	0.971688	−	0.236266i	$-0.0759237\pi$
$149$	3.43287	+	5.94591i	0.281232	+	0.487108i	−0.690457	+	0.723374i	$0.742590\pi$
$150$	−5.40343	−	4.23744i	−0.441188	−	0.345985i
$151$	0.842037	−	1.45845i	0.0685240	−	0.118687i	−0.829728	−	0.558168i	$-0.811504\pi$
$151$	0.842037	−	1.45845i	0.0685240	−	0.118687i	0.898252	+	0.439481i	$0.144838\pi$
$152$	−1.45900	+	1.62039i	−0.118341	+	0.131431i
$153$	−0.930100	+	0.675757i	−0.0751941	+	0.0546317i
$154$	1.47210	−	3.02195i	0.118625	−	0.243516i
$155$	−21.1250	+	8.94442i	−1.69680	+	0.718433i
$156$	0.985948	−	9.38067i	0.0789390	−	0.751055i
$157$	1.98063	−	3.43054i	0.158071	−	0.273787i	−0.776102	−	0.630607i	$-0.782806\pi$
$157$	1.98063	−	3.43054i	0.158071	−	0.273787i	0.934173	+	0.356820i	$0.116139\pi$
$158$	8.81268	−	3.92366i	0.701099	−	0.312150i
$159$	10.5021	−	2.23230i	0.832873	−	0.177033i
$160$	1.15340	−	1.91564i	0.0911842	−	0.151445i
$161$	0.640002	−	2.57221i	0.0504392	−	0.202718i
$162$	1.36512	−	4.20141i	0.107254	−	0.330094i
$163$	6.81356	−	1.44827i	0.533679	−	0.113437i	0.0668139	−	0.997765i	$-0.478717\pi$
$163$	6.81356	−	1.44827i	0.533679	−	0.113437i	0.466865	+	0.884328i	$0.345383\pi$
$164$	12.3557	+	2.62629i	0.964821	+	0.205079i
$165$	0.479002	−	3.87211i	0.0372903	−	0.301443i
$166$	−12.7642	+	2.71312i	−0.990698	+	0.210579i
$167$	9.11585	+	6.62305i	0.705406	+	0.512507i	0.881688	−	0.471832i	$-0.156407\pi$
$167$	9.11585	+	6.62305i	0.705406	+	0.512507i	−0.176283	+	0.984340i	$0.556407\pi$
$168$	−0.125054	+	3.63142i	−0.00964810	+	0.280170i
$169$	−27.6445	−	20.0849i	−2.12650	−	1.54499i
$170$	0.753360	−	2.18148i	0.0577801	−	0.167312i
$171$	0.253874	+	2.41545i	0.0194142	+	0.184714i
$172$	−0.614797	−	5.84940i	−0.0468778	−	0.446013i
$173$	−1.70100	+	1.88915i	−0.129325	+	0.143630i	−0.804329	−	0.594184i	$-0.797475\pi$
$173$	−1.70100	+	1.88915i	−0.129325	+	0.143630i	0.675004	+	0.737814i	$0.264142\pi$
$174$	7.14399			0.541584
$175$	11.8976	−	5.78327i	0.899377	−	0.437174i
$176$	1.27050			0.0957678
$177$	−4.43450	+	4.92501i	−0.333317	+	0.370186i
$178$	0.929643	+	8.84496i	0.0696797	+	0.662958i
$179$	−1.45255	−	13.8201i	−0.108569	−	1.03296i	−0.904179	−	0.427155i	$-0.859516\pi$
$179$	−1.45255	−	13.8201i	−0.108569	−	1.03296i	0.795610	−	0.605810i	$-0.207151\pi$
$180$	−0.726053	−	2.38254i	−0.0541168	−	0.177584i
$181$	13.5983	+	9.87975i	1.01075	+	0.734356i	0.964367	−	0.264567i	$-0.0852292\pi$
$181$	13.5983	+	9.87975i	1.01075	+	0.734356i	0.0463872	+	0.998924i	$0.485229\pi$
$182$	15.4147	+	9.62182i	1.14262	+	0.713217i
$183$	14.2819	+	10.3764i	1.05575	+	0.767048i
$184$	0.979952	−	0.208295i	0.0722430	−	0.0153557i
$185$	−13.8473	+	2.67861i	−1.01808	+	0.196936i
$186$	13.7819	+	2.92942i	1.01054	+	0.214796i
$187$	1.28267	−	0.272639i	0.0937978	−	0.0199373i
$188$	−2.04293	+	6.28748i	−0.148996	+	0.458562i
$189$	10.7578	+	10.3786i	0.782512	+	0.754932i
$190$	−3.19535	−	3.68258i	−0.231815	−	0.267162i
$191$	6.38942	−	1.35811i	0.462322	−	0.0982696i	0.0291386	−	0.999575i	$-0.490724\pi$
$191$	6.38942	−	1.35811i	0.462322	−	0.0982696i	0.433183	+	0.901306i	$0.357390\pi$
$192$	−1.25463	+	0.558596i	−0.0905449	+	0.0403132i
$193$	2.15137	−	3.72628i	0.154859	−	0.268224i	−0.778149	−	0.628080i	$-0.783841\pi$
$193$	2.15137	−	3.72628i	0.154859	−	0.268224i	0.933008	+	0.359856i	$0.117174\pi$
$194$	−0.124360	+	1.18320i	−0.00892852	+	0.0849492i
$195$	20.5465	+	4.76317i	1.47136	+	0.341098i
$196$	−6.18381	−	3.28032i	−0.441701	−	0.234309i
$197$	−3.52079	+	2.55800i	−0.250846	+	0.182250i	−0.706102	−	0.708110i	$-0.749548\pi$
$197$	−3.52079	+	2.55800i	−0.250846	+	0.182250i	0.455256	+	0.890361i	$0.349548\pi$
$198$	0.946947	−	1.05169i	0.0672966	−	0.0747404i
$199$	1.75518	−	3.04005i	0.124421	−	0.215504i	−0.797085	−	0.603867i	$-0.793626\pi$
$199$	1.75518	−	3.04005i	0.124421	−	0.215504i	0.921506	+	0.388363i	$0.126959\pi$
$200$	3.93446	+	3.08545i	0.278208	+	0.218174i
$201$	−7.03567	−	12.1861i	−0.496258	−	0.859544i
$202$	−4.54720	−	13.9948i	−0.319940	−	0.984673i
$203$	−6.02721	+	12.3728i	−0.423027	+	0.868400i
$204$	−1.14677	+	0.833175i	−0.0802897	+	0.0583339i
$205$	−9.22007	+	26.6983i	−0.643957	+	1.86469i
$206$	7.63638	−	3.39993i	0.532052	−	0.236885i
$207$	0.557968	−	0.966429i	0.0387815	−	0.0671715i
$208$	−0.717909	+	6.83045i	−0.0497780	+	0.473607i
$209$	0.856058	−	2.63468i	0.0592148	−	0.182244i
$210$	−8.02434	−	1.27442i	−0.553732	−	0.0879432i
$211$	1.30392	+	4.01304i	0.0897653	+	0.276269i	0.985854	−	0.167606i	$-0.0536035\pi$
$211$	1.30392	+	4.01304i	0.0897653	+	0.276269i	−0.896089	+	0.443875i	$0.853603\pi$
$212$	−7.64703	+	1.62543i	−0.525200	+	0.111635i
$213$	−2.67874	−	2.97504i	−0.183544	−	0.203847i
$214$	−6.45060	−	1.37112i	−0.440954	−	0.0937276i
$215$	13.1495	+	0.241462i	0.896788	+	0.0164676i
$216$	−1.74590	+	5.37332i	−0.118793	+	0.365608i
$217$	−16.7009	+	21.3976i	−1.13373	+	1.45256i
$218$	9.75486			0.660682
$219$	−0.0669035	+	0.636544i	−0.00452092	+	0.0430137i
$220$	−0.348781	+	2.81944i	−0.0235148	+	0.190087i
$221$	0.740973	+	7.04989i	0.0498433	+	0.474227i
$222$	7.91358	+	3.52335i	0.531125	+	0.236472i
$223$	−6.10291	−	18.7828i	−0.408681	−	1.25779i	−0.917782	−	0.397084i	$-0.870022\pi$
$223$	−6.10291	−	18.7828i	−0.408681	−	1.25779i	0.509101	−	0.860707i	$-0.329978\pi$
$224$	0.0910567	−	2.64418i	0.00608398	−	0.176672i
$225$	5.48654	−	0.957161i	0.365769	−	0.0638107i
$226$	4.18651	+	7.25125i	0.278483	+	0.482346i
$227$	20.9468	+	4.45239i	1.39029	+	0.295515i	0.841415	−	0.540389i	$-0.181723\pi$
$227$	20.9468	+	4.45239i	1.39029	+	0.295515i	0.548875	+	0.835904i	$0.315056\pi$
$228$	0.313014	+	2.97813i	0.0207299	+	0.197232i
$229$	6.58655	+	2.93252i	0.435251	+	0.193786i	0.612653	−	0.790352i	$-0.290102\pi$
$229$	6.58655	+	2.93252i	0.435251	+	0.193786i	−0.177401	+	0.984139i	$0.556769\pi$
$230$	0.193220	+	2.23184i	0.0127406	+	0.147163i
$231$	−1.73143	−	4.27947i	−0.113920	−	0.281569i
$232$	−5.20183			−0.341517
$233$	0.865999	−	8.23943i	0.0567335	−	0.539783i	−0.928834	−	0.370497i	$-0.879187\pi$
$233$	0.865999	−	8.23943i	0.0567335	−	0.539783i	0.985567	−	0.169286i	$-0.0541461\pi$
$234$	5.11900	+	5.68522i	0.334639	+	0.371655i
$235$	−13.3920	−	6.25962i	−0.873601	−	0.408332i
$236$	3.22894	−	3.58610i	0.210186	−	0.233435i
$237$	4.09397	−	12.5999i	0.265932	−	0.818455i
$238$	−0.475490	−	2.68903i	−0.0308215	−	0.174304i
$239$	−3.45405	−	10.6305i	−0.223424	−	0.687628i	−0.998448	−	0.0556963i	$-0.982262\pi$
$239$	−3.45405	−	10.6305i	−0.223424	−	0.687628i	0.775024	−	0.631932i	$-0.217738\pi$
$240$	−0.895187	−	2.93756i	−0.0577841	−	0.189618i
$241$	5.85992	+	6.50811i	0.377471	+	0.419224i	0.901706	−	0.432350i	$-0.142315\pi$
$241$	5.85992	+	6.50811i	0.377471	+	0.419224i	−0.524235	+	0.851574i	$0.675649\pi$
$242$	8.57437	−	3.81756i	0.551182	−	0.245402i
$243$	5.44127	+	9.42455i	0.349057	+	0.604585i
$244$	−10.3993	−	7.55551i	−0.665745	−	0.483692i
$245$	8.97713	−	12.8223i	0.573528	−	0.819186i
$246$	14.0348	−	10.1969i	0.894827	−	0.650130i
$247$	13.6808	+	6.09106i	0.870486	+	0.387565i
$248$	−10.0351	−	2.13303i	−0.637232	−	0.135448i
$249$	−8.96077	+	15.5205i	−0.567866	+	0.983572i
$250$	−7.92719	+	7.88414i	−0.501359	+	0.498637i
$251$	−15.3256			−0.967342			−0.483671	−	0.875250i	$-0.660697\pi$
$251$	−15.3256			−0.967342			−0.483671	+	0.875250i	$0.660697\pi$
$252$	−2.12092	−	2.04617i	−0.133606	−	0.128897i
$253$	−1.02975	+	0.748161i	−0.0647401	+	0.0470365i
$254$	2.97286	+	1.32360i	0.186534	+	0.0830502i
$255$	−1.53413	−	2.77358i	−0.0960709	−	0.173688i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−9.83677	−	17.0378i	−0.613601	−	1.06279i	−0.990628	−	0.136585i	$-0.956387\pi$
$257$	−9.83677	−	17.0378i	−0.613601	−	1.06279i	0.377028	−	0.926202i	$-0.376946\pi$
$258$	−6.53490	−	4.74789i	−0.406845	−	0.295590i
$259$	−12.7787	+	10.7331i	−0.794027	+	0.666922i
$260$	−14.9607	−	3.46826i	−0.927825	−	0.215092i
$261$	−3.87709	+	4.30595i	−0.239986	+	0.266531i
$262$	−6.21944	−	6.90739i	−0.384239	−	0.426740i
$263$	−18.8719	−	20.9594i	−1.16369	−	1.29241i	−0.948837	−	0.315767i	$-0.897738\pi$
$263$	−18.8719	−	20.9594i	−1.16369	−	1.29241i	−0.214857	−	0.976646i	$-0.568928\pi$
$264$	1.16754	−	1.29668i	0.0718570	−	0.0798053i
$265$	−1.50779	−	17.4161i	−0.0926229	−	1.06987i
$266$	−5.42196	−	1.97046i	−0.332442	−	0.120817i
$267$	9.88152	+	7.17935i	0.604739	+	0.439369i
$268$	5.12296	+	8.87323i	0.312935	+	0.542019i
$269$	−12.4304	+	5.53435i	−0.757893	+	0.337436i	−0.749040	−	0.662525i	$-0.769485\pi$
$269$	−12.4304	+	5.53435i	−0.757893	+	0.337436i	−0.00885307	+	0.999961i	$0.502818\pi$
$270$	−11.4449	−	5.34951i	−0.696516	−	0.325561i
$271$	−10.1068	−	4.49982i	−0.613941	−	0.273344i	0.0761160	−	0.997099i	$-0.475748\pi$
$271$	−10.1068	−	4.49982i	−0.613941	−	0.273344i	−0.690057	+	0.723755i	$0.742415\pi$
$272$	0.835008	−	0.606669i	0.0506298	−	0.0367847i
$273$	23.9856	−	6.89030i	1.45167	−	0.417020i
$274$	−2.85338			−0.172379
$275$	−6.16102	−	1.54800i	−0.371524	−	0.0933478i
$276$	0.687947	−	1.19156i	0.0414095	−	0.0717234i
$277$	18.6515	+	3.96451i	1.12066	+	0.238204i	0.730748	−	0.682647i	$-0.239171\pi$
$277$	18.6515	+	3.96451i	1.12066	+	0.238204i	0.389914	+	0.920851i	$0.372505\pi$
$278$	−14.8738	−	6.62226i	−0.892074	−	0.397177i
$279$	−9.24518	+	6.71702i	−0.553495	+	0.402137i
$280$	5.84285	+	0.927956i	0.349177	+	0.0554560i
$281$	−16.6269	−	12.0801i	−0.991876	−	0.720640i	−0.0315449	−	0.999502i	$-0.510043\pi$
$281$	−16.6269	−	12.0801i	−0.991876	−	0.720640i	−0.960331	+	0.278862i	$0.910043\pi$
$282$	4.53967	+	7.86295i	0.270334	+	0.468232i
$283$	−1.14994	+	0.511986i	−0.0683567	+	0.0304344i	−0.440630	−	0.897689i	$-0.645245\pi$
$283$	−1.14994	+	0.511986i	−0.0683567	+	0.0304344i	0.372274	+	0.928123i	$0.378578\pi$
$284$	1.95050	+	2.16625i	0.115741	+	0.128543i
$285$	−6.69485	−	0.122936i	−0.396569	−	0.00728213i
$286$	−2.69646	−	8.29884i	−0.159445	−	0.490720i
$287$	5.81933	+	32.9100i	0.343504	+	1.94262i
$288$	0.344208	−	1.05936i	0.0202827	−	0.0624236i
$289$	−10.6624	+	11.8418i	−0.627200	+	0.696577i
$290$	1.42802	−	11.5437i	0.0838561	−	0.677867i
$291$	1.09330	+	1.21424i	0.0640906	+	0.0711799i
$292$	0.0487152	−	0.463494i	0.00285084	−	0.0271239i
$293$	−6.63727			−0.387753			−0.193877	−	0.981026i	$-0.562106\pi$
$293$	−6.63727			−0.387753			−0.193877	+	0.981026i	$0.562106\pi$
$294$	−9.03057	+	3.29675i	−0.526674	+	0.192271i
$295$	7.07169	+	8.14998i	0.411730	+	0.474510i
$296$	−5.76220	−	2.56550i	−0.334921	−	0.149117i
$297$	−0.750320	−	7.13882i	−0.0435380	−	0.414236i
$298$	−6.71571	−	1.42747i	−0.389031	−	0.0826910i
$299$	−3.44037	−	5.95890i	−0.198962	−	0.344612i
$300$	6.76463	−	1.18013i	0.390556	−	0.0681350i
$301$	13.7363	−	7.31224i	0.791746	−	0.421470i
$302$	0.520408	+	1.60165i	0.0299461	+	0.0921646i
$303$	−18.4619	−	8.21976i	−1.06061	−	0.472213i
$304$	−0.227918	−	2.16850i	−0.0130720	−	0.124372i
$305$	19.6217	−	21.0034i	1.12353	−	1.20265i
$306$	0.120173	−	1.14337i	0.00686983	−	0.0653620i
$307$	−10.4872			−0.598536			−0.299268	−	0.954169i	$-0.596742\pi$
$307$	−10.4872			−0.598536			−0.299268	+	0.954169i	$0.596742\pi$
$308$	1.26072	+	3.11606i	0.0718364	+	0.177554i
$309$	3.54751	−	10.9181i	0.201811	−	0.621110i
$310$	7.48840	−	21.6839i	0.425312	−	1.23156i
$311$	−5.01316	−	1.06558i	−0.284270	−	0.0604235i	0.0635697	−	0.997977i	$-0.479751\pi$
$311$	−5.01316	−	1.06558i	−0.284270	−	0.0604235i	−0.347840	+	0.937554i	$0.613085\pi$
$312$	6.31147	+	7.00960i	0.357317	+	0.396840i
$313$	13.3218	−	2.83164i	0.752995	−	0.160054i	0.184604	−	0.982813i	$-0.440900\pi$
$313$	13.3218	−	2.83164i	0.752995	−	0.160054i	0.568390	+	0.822759i	$0.307566\pi$
$314$	1.22409	+	3.76737i	0.0690796	+	0.212605i
$315$	5.12300	−	4.14493i	0.288648	−	0.233540i
$316$	−2.98099	+	9.17454i	−0.167694	+	0.516108i
$317$	1.59095	−	15.1369i	0.0893568	−	0.850173i	−0.854419	−	0.519585i	$-0.826086\pi$
$317$	1.59095	−	15.1369i	0.0893568	−	0.850173i	0.943775	−	0.330588i	$-0.107247\pi$
$318$	−5.36838	+	9.29830i	−0.301044	+	0.521423i
$319$	6.03757	−	2.68810i	0.338039	−	0.150505i
$320$	0.651822	+	2.13895i	0.0364380	+	0.119571i
$321$	−7.32719	+	5.32352i	−0.408964	+	0.297130i
$322$	1.48328	+	2.19676i	0.0826598	+	0.122420i
$323$	−0.695441	−	2.14035i	−0.0386954	−	0.119092i
$324$	2.20881	+	3.82577i	0.122712	+	0.212543i
$325$	11.8036	−	32.2480i	0.654748	−	1.78880i
$326$	−3.48289	+	6.03254i	−0.192899	+	0.334112i
$327$	8.96430	−	9.95586i	0.495727	−	0.550560i
$328$	−10.2193	+	7.42477i	−0.564268	+	0.409964i
$329$	−17.4480	+	1.22856i	−0.961939	+	0.0677328i
$330$	2.55702	+	2.94691i	0.140759	+	0.162222i
$331$	1.53497	−	14.6043i	0.0843697	−	0.802724i	−0.867750	−	0.497000i	$-0.834435\pi$
$331$	1.53497	−	14.6043i	0.0843697	−	0.802724i	0.952120	−	0.305724i	$-0.0988985\pi$
$332$	6.52470	−	11.3011i	0.358090	−	0.620229i
$333$	−6.41841	+	2.85766i	−0.351727	+	0.156599i
$334$	−11.0216	+	2.34271i	−0.603074	+	0.128187i
$335$	−21.0974	+	8.93273i	−1.15267	+	0.488047i
$336$	−2.61499	−	2.52283i	−0.142659	−	0.137631i
$337$	0.274373	−	0.844434i	0.0149461	−	0.0459992i	−0.943305	−	0.331926i	$-0.892301\pi$
$337$	0.274373	−	0.844434i	0.0149461	−	0.0459992i	0.958251	+	0.285927i	$0.0923015\pi$
$338$	33.4237	−	7.10443i	1.81801	−	0.386430i
$339$	11.2479	+	2.39081i	0.610902	+	0.129851i
$340$	1.11706	+	2.01955i	0.0605812	+	0.109526i
$341$	12.7497	−	2.71003i	0.690434	−	0.146756i
$342$	−1.96490	−	1.42759i	−0.106250	−	0.0771951i
$343$	1.90917	−	18.4216i	0.103086	−	0.994672i
$344$	4.75833	+	3.45713i	0.256552	+	0.186396i
$345$	2.45539	+	1.85377i	0.132194	+	0.0998035i
$346$	−0.265722	−	2.52818i	−0.0142853	−	0.135916i
$347$	−0.833362	−	7.92891i	−0.0447372	−	0.425646i	−0.993852	−	0.110716i	$-0.964686\pi$
$347$	−0.833362	−	7.92891i	−0.0447372	−	0.425646i	0.949115	−	0.314930i	$-0.101981\pi$
$348$	−4.78026	+	5.30902i	−0.256249	+	0.284593i
$349$	8.86108			0.474323			0.237161	−	0.971470i	$-0.423783\pi$
$349$	8.86108			0.474323			0.237161	+	0.971470i	$0.423783\pi$
$350$	−3.66327	+	12.7114i	−0.195810	+	0.679455i
$351$	38.8035			2.07118
$352$	−0.850133	+	0.944168i	−0.0453122	+	0.0503243i
$353$	3.22877	+	30.7197i	0.171850	+	1.63504i	0.652257	+	0.757998i	$0.273822\pi$
$353$	3.22877	+	30.7197i	0.171850	+	1.63504i	−0.480407	+	0.877046i	$0.659511\pi$
$354$	−0.692737	−	6.59095i	−0.0368186	−	0.350305i
$355$	−5.34270	+	3.73378i	−0.283561	+	0.198168i
$356$	−7.19514	−	5.22758i	−0.381342	−	0.277061i
$357$	−3.18140	−	1.98582i	−0.168378	−	0.105101i
$358$	11.2423	+	8.16801i	0.594174	+	0.431693i
$359$	−12.5394	+	2.66532i	−0.661802	+	0.140670i	−0.526555	−	0.850141i	$-0.676516\pi$
$359$	−12.5394	+	2.66532i	−0.661802	+	0.140670i	−0.135248	+	0.990812i	$0.543183\pi$
$360$	2.25640	+	1.05467i	0.118923	+	0.0555860i
$361$	13.9344	+	2.96184i	0.733388	+	0.155886i
$362$	−16.4411	+	3.49467i	−0.864127	+	0.183676i
$363$	3.98326	−	12.2592i	0.209067	−	0.643443i
$364$	−17.4649	+	5.01711i	−0.915408	+	0.262968i
$365$	1.01519	+	0.235346i	0.0531375	+	0.0123186i
$366$	−17.2677	+	3.67036i	−0.902596	+	0.191853i
$367$	17.6333	−	7.85084i	0.920449	−	0.409810i	0.108872	−	0.994056i	$-0.465276\pi$
$367$	17.6333	−	7.85084i	0.920449	−	0.409810i	0.811577	+	0.584245i	$0.198609\pi$
$368$	−0.500922	+	0.867623i	−0.0261124	+	0.0452280i
$369$	−1.47075	+	13.9932i	−0.0765640	+	0.728458i
$370$	7.27509	−	12.0829i	0.378214	−	0.628161i
$371$	−11.5747	−	17.1423i	−0.600929	−	0.889986i
$372$	−11.3989	+	8.28175i	−0.591003	+	0.429389i
$373$	8.88591	−	9.86880i	0.460095	−	0.510987i	−0.467797	−	0.883836i	$-0.654952\pi$
$373$	8.88591	−	9.86880i	0.460095	−	0.510987i	0.927892	+	0.372849i	$0.121619\pi$
$374$	−0.655660	+	1.13564i	−0.0339034	+	0.0587224i
$375$	0.761852	+	15.3357i	0.0393419	+	0.791933i
$376$	−3.30552	−	5.72533i	−0.170469	−	0.295262i
$377$	11.0401	+	33.9780i	0.568595	+	1.74996i
$378$	−14.9112	+	1.04994i	−0.766947	+	0.0540029i
$379$	9.37895	−	6.81421i	0.481764	−	0.350022i	−0.320244	−	0.947335i	$-0.603765\pi$
$379$	9.37895	−	6.81421i	0.481764	−	0.350022i	0.802008	+	0.597313i	$0.203765\pi$
$380$	4.87480	+	0.0895151i	0.250072	+	0.00459203i
$381$	4.08281	−	1.81778i	0.209168	−	0.0931278i
$382$	−3.26608	+	5.65702i	−0.167107	+	0.289438i
$383$	−1.54172	+	14.6685i	−0.0787782	+	0.749524i	0.881821	+	0.471585i	$0.156318\pi$
$383$	−1.54172	+	14.6685i	−0.0787782	+	0.749524i	−0.960599	+	0.277939i	$0.910349\pi$
$384$	0.424392	−	1.30614i	0.0216571	−	0.0666538i
$385$	−7.26111	+	1.94231i	−0.370060	+	0.0989893i
$386$	1.32962	+	4.09215i	0.0676759	+	0.208285i
$387$	6.40826	−	1.36212i	0.325750	−	0.0692404i
$388$	−0.796080	−	0.884136i	−0.0404148	−	0.0448852i
$389$	3.32303	+	0.706332i	0.168484	+	0.0358124i	0.291381	−	0.956607i	$-0.405885\pi$
$389$	3.32303	+	0.706332i	0.168484	+	0.0358124i	−0.122897	+	0.992419i	$0.539218\pi$
$390$	−17.2880	+	12.0818i	−0.875412	+	0.611787i
$391$	−0.319533	+	0.983421i	−0.0161595	+	0.0497338i
$392$	6.57553	−	2.40050i	0.332114	−	0.121244i
$393$	−12.7651			−0.643915
$394$	0.454901	−	4.32810i	0.0229176	−	0.218046i
$395$	−19.5414	−	9.13388i	−0.983232	−	0.459575i
$396$	0.147928	+	1.40744i	0.00743364	+	0.0707264i
$397$	−11.4234	−	5.08604i	−0.573325	−	0.255261i	0.0995305	−	0.995035i	$-0.468266\pi$
$397$	−11.4234	−	5.08604i	−0.573325	−	0.255261i	−0.672856	+	0.739774i	$0.734933\pi$
$398$	1.08476	+	3.33854i	0.0543740	+	0.167346i
$399$	−6.99361	+	3.72291i	−0.350119	+	0.186379i
$400$	−4.92561	+	0.859303i	−0.246280	+	0.0429651i
$401$	−14.2405	−	24.6653i	−0.711137	−	1.23173i	−0.964431	−	0.264336i	$-0.914847\pi$
$401$	−14.2405	−	24.6653i	−0.711137	−	1.23173i	0.253294	−	0.967389i	$-0.418486\pi$
$402$	13.7638	+	2.92560i	0.686478	+	0.145915i
$403$	7.36527	+	70.0758i	0.366890	+	3.49073i
$404$	13.4429	+	5.98515i	0.668807	+	0.297772i
$405$	−9.09634	+	3.85143i	−0.452001	+	0.191379i
$406$	−5.16179	−	12.7581i	−0.256175	−	0.633174i
$407$	8.01372			0.397226
$408$	0.148167	−	1.40972i	0.00733537	−	0.0697914i
$409$	4.02491	+	4.47012i	0.199019	+	0.221033i	0.834391	−	0.551173i	$-0.185820\pi$
$409$	4.02491	+	4.47012i	0.199019	+	0.221033i	−0.635372	+	0.772207i	$0.719153\pi$
$410$	−13.6713	−	24.7165i	−0.675176	−	1.22066i
$411$	−2.62213	+	2.91217i	−0.129340	+	0.143647i
$412$	−2.58309	+	7.94993i	−0.127260	+	0.391665i
$413$	11.9994	+	4.36086i	0.590453	+	0.214584i
$414$	0.344843	+	1.06132i	0.0169481	+	0.0521609i
$415$	23.2877	+	17.5817i	1.14315	+	0.863052i
$416$	−4.59564	−	5.10397i	−0.225320	−	0.250243i
$417$	−20.4271	+	9.09475i	−1.00032	+	0.445372i
$418$	1.38513	+	2.39912i	0.0677490	+	0.117345i
$419$	−25.7532	−	18.7108i	−1.25813	−	0.914083i	−0.259463	−	0.965753i	$-0.583546\pi$
$419$	−25.7532	−	18.7108i	−1.25813	−	0.914083i	−0.998664	+	0.0516701i	$0.983546\pi$
$420$	6.31641	−	5.11049i	0.308209	−	0.249367i
$421$	23.5414	−	17.1038i	1.14734	−	0.833589i	0.159212	−	0.987244i	$-0.449105\pi$
$421$	23.5414	−	17.1038i	1.14734	−	0.833589i	0.988125	+	0.153655i	$0.0491045\pi$
$422$	−3.85476	−	1.71625i	−0.187647	−	0.0835458i
$423$	−7.20300	−	1.53105i	−0.350222	−	0.0744420i
$424$	3.90894	−	6.77048i	0.189835	−	0.328803i
$425$	−4.78836	+	1.92452i	−0.232269	+	0.0933529i
$426$	4.00332			0.193961
$427$	8.21157	−	33.0028i	0.397386	−	1.59712i
$428$	5.33523	−	3.87627i	0.257888	−	0.187367i
$429$	−10.9478	−	4.87426i	−0.528563	−	0.235331i
$430$	−8.97817	+	9.61041i	−0.432966	+	0.463455i
$431$	2.26813	−	1.00984i	0.109252	−	0.0486422i	−0.351383	−	0.936232i	$-0.614288\pi$
$431$	2.26813	−	1.00984i	0.109252	−	0.0486422i	0.460635	+	0.887590i	$0.347622\pi$
$432$	−2.82492	−	4.89291i	−0.135914	−	0.235410i
$433$	5.38758	+	3.91431i	0.258911	+	0.188110i	0.709667	−	0.704538i	$-0.248846\pi$
$433$	5.38758	+	3.91431i	0.258911	+	0.188110i	−0.450756	+	0.892647i	$0.648846\pi$
$434$	−4.72637	−	26.7290i	−0.226873	−	1.28303i
$435$	−10.4692	−	12.0656i	−0.501961	−	0.578500i
$436$	−6.52727	+	7.24927i	−0.312600	+	0.347177i
$437$	1.46169	+	1.62337i	0.0699222	+	0.0776565i
$438$	−0.428278	−	0.475650i	−0.0204639	−	0.0227275i
$439$	−15.1636	+	16.8409i	−0.723719	+	0.803772i	−0.986961	−	0.160958i	$-0.948542\pi$
$439$	−15.1636	+	16.8409i	−0.723719	+	0.803772i	0.263242	+	0.964730i	$0.415208\pi$
$440$	−1.86187	−	2.14577i	−0.0887613	−	0.102296i
$441$	2.91388	−	7.23223i	0.138756	−	0.344392i
$442$	−5.73490	−	4.16665i	−0.272781	−	0.198187i
$443$	8.05208	+	13.9466i	0.382566	+	0.662623i	0.991428	−	0.130652i	$-0.0417072\pi$
$443$	8.05208	+	13.9466i	0.382566	+	0.662623i	−0.608862	+	0.793276i	$0.708374\pi$
$444$	−7.91358	+	3.52335i	−0.375562	+	0.167211i
$445$	13.5760	−	14.5320i	0.643565	−	0.688884i
$446$	18.0420	+	8.03282i	0.854314	+	0.380365i
$447$	−7.62833	+	5.54231i	−0.360808	+	0.262142i
$448$	1.90408	+	1.83697i	0.0899595	+	0.0867888i
$449$	20.1219			0.949613			0.474807	−	0.880090i	$-0.342518\pi$
$449$	20.1219			0.949613			0.474807	+	0.880090i	$0.342518\pi$
$450$	−2.95990	+	4.71776i	−0.139531	+	0.222397i
$451$	8.02436	−	13.8986i	0.377852	−	0.654459i
$452$	−8.19005	−	1.74085i	−0.385228	−	0.0818827i
$453$	2.11289	+	0.940717i	0.0992720	+	0.0441988i
$454$	−17.3249	+	12.5873i	−0.813100	+	0.590752i
$455$	−6.33924	−	40.1345i	−0.297188	−	1.88154i
$456$	−2.42263	−	1.76014i	−0.113450	−	0.0824263i
$457$	13.5158	+	23.4100i	0.632240	+	1.09507i	0.987093	+	0.160150i	$0.0511978\pi$
$457$	13.5158	+	23.4100i	0.632240	+	1.09507i	−0.354852	+	0.934922i	$0.615469\pi$
$458$	−6.58655	+	2.93252i	−0.307769	+	0.137028i
$459$	−3.90194	−	4.33354i	−0.182127	−	0.202272i
$460$	−1.78787	−	1.34980i	−0.0833600	−	0.0629350i
$461$	7.64384	+	23.5253i	0.356009	+	1.09568i	0.955422	+	0.295243i	$0.0954007\pi$
$461$	7.64384	+	23.5253i	0.356009	+	1.09568i	−0.599413	+	0.800440i	$0.704599\pi$
$462$	4.33882	+	1.57683i	0.201860	+	0.0733606i
$463$	−10.5029	+	32.3247i	−0.488113	+	1.50226i	0.339308	+	0.940675i	$0.389807\pi$
$463$	−10.5029	+	32.3247i	−0.488113	+	1.50226i	−0.827421	+	0.561582i	$0.810193\pi$
$464$	3.48070	−	3.86571i	0.161588	−	0.179461i
$465$	−15.2492	−	27.5693i	−0.707166	−	1.27850i
$466$	5.54362	+	6.15682i	0.256803	+	0.285209i
$467$	1.48163	−	14.0967i	0.0685615	−	0.652319i	−0.905237	−	0.424907i	$-0.860307\pi$
$467$	1.48163	−	14.0967i	0.0685615	−	0.652319i	0.973799	−	0.227412i	$-0.0730265\pi$
$468$	−7.65022			−0.353632
$469$	−16.6791	+	21.3696i	−0.770170	+	0.986756i
$470$	13.6128	−	5.76373i	0.627913	−	0.265861i
$471$	4.96989	+	2.21274i	0.229001	+	0.101958i
$472$	0.504410	+	4.79914i	0.0232174	+	0.220898i
$473$	−7.30933	−	1.55365i	−0.336083	−	0.0714367i
$474$	6.62419	+	11.4734i	0.304259	+	0.526992i
$475$	−1.53689	+	10.7933i	−0.0705172	+	0.495233i
$476$	2.31651	+	1.44596i	0.106177	+	0.0662753i
$477$	−2.69098	−	8.28197i	−0.123211	−	0.379206i
$478$	10.2112	+	4.54632i	0.467049	+	0.207944i
$479$	0.230513	+	2.19319i	0.0105324	+	0.100209i	0.998525	−	0.0542911i	$-0.0172899\pi$
$479$	0.230513	+	2.19319i	0.0105324	+	0.100209i	−0.987993	+	0.154500i	$0.950623\pi$
$480$	2.78203	+	1.30035i	0.126982	+	0.0593528i
$481$	−4.52823	+	43.0832i	−0.206469	+	1.96442i
$482$	−8.75752			−0.398894
$483$	3.60509	+	0.504885i	0.164037	+	0.0229730i
$484$	−2.90038	+	8.92645i	−0.131835	+	0.405748i
$485$	2.18057	−	1.52391i	0.0990148	−	0.0691971i
$486$	−10.6447	−	2.26261i	−0.482855	−	0.102634i
$487$	−10.4483	−	11.6040i	−0.473456	−	0.525827i	0.458355	−	0.888769i	$-0.348439\pi$
$487$	−10.4483	−	11.6040i	−0.473456	−	0.525827i	−0.931812	+	0.362942i	$0.881772\pi$
$488$	12.5733	−	2.67254i	0.569167	−	0.120980i
$489$	2.95622	+	9.09831i	0.133685	+	0.411440i
$490$	3.52195	+	15.2511i	0.159106	+	0.688974i
$491$	3.75997	−	11.5720i	0.169685	−	0.522237i	−0.829666	−	0.558260i	$-0.811469\pi$
$491$	3.75997	−	11.5720i	0.169685	−	0.522237i	0.999351	+	0.0360235i	$0.0114691\pi$
$492$	−1.81336	+	17.2529i	−0.0817525	+	0.777823i
$493$	2.68447	−	4.64965i	0.120903	−	0.209410i
$494$	−13.6808	+	6.09106i	−0.615526	+	0.274050i
$495$	−3.16393	−	0.0580987i	−0.142208	−	0.00261134i
$496$	8.29997	−	6.03028i	0.372680	−	0.270768i
$497$	−3.37750	+	6.93341i	−0.151502	+	0.311006i
$498$	−5.53806	−	17.0444i	−0.248166	−	0.763778i
$499$	13.1695	+	22.8103i	0.589550	+	1.02113i	0.994291	+	0.106699i	$0.0340282\pi$
$499$	13.1695	+	22.8103i	0.589550	+	1.02113i	−0.404741	+	0.914431i	$0.632638\pi$
$500$	−0.554736	−	11.1666i	−0.0248085	−	0.499384i
$501$	−7.73738	+	13.4015i	−0.345681	+	0.598737i
$502$	10.2548	−	11.3891i	0.457695	−	0.508321i
$503$	30.4902	−	22.1524i	1.35949	−	0.987727i	0.361012	−	0.932561i	$-0.382431\pi$
$503$	30.4902	−	22.1524i	1.35949	−	0.987727i	0.998477	−	0.0551660i	$-0.0175688\pi$
$504$	2.93977	−	0.206998i	0.130948	−	0.00922041i
$505$	−16.9723	+	28.1887i	−0.755258	+	1.25438i
$506$	0.133049	−	1.26587i	0.00591474	−	0.0562750i
$507$	23.4642	−	40.6411i	1.04208	−	1.80494i
$508$	−2.97286	+	1.32360i	−0.131899	+	0.0587253i
$509$	21.4426	−	4.55776i	0.950425	−	0.202019i	0.293487	−	0.955963i	$-0.405184\pi$
$509$	21.4426	−	4.55776i	0.950425	−	0.202019i	0.656939	+	0.753944i	$0.271851\pi$
$510$	3.08770	+	0.715804i	0.136726	+	0.0316963i
$511$	1.18511	−	0.340446i	0.0524264	−	0.0150605i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−12.0500	+	2.56130i	−0.532019	+	0.113084i
$514$	19.2436	+	4.09036i	0.848800	+	0.180418i
$515$	−16.9330	−	7.91470i	−0.746157	−	0.348763i
$516$	7.90107	−	1.67942i	0.347825	−	0.0739325i
$517$	6.79522	+	4.93702i	0.298854	+	0.217130i
$518$	0.574342	−	16.6782i	0.0252351	−	0.732800i
$519$	−2.82446	−	2.05209i	−0.123980	−	0.0900768i
$520$	12.5881	−	8.79727i	0.552025	−	0.385786i
$521$	3.47215	+	33.0353i	0.152118	+	1.44730i	0.758263	+	0.651949i	$0.226048\pi$
$521$	3.47215	+	33.0353i	0.152118	+	1.44730i	−0.606145	+	0.795354i	$0.707285\pi$
$522$	−0.605661	−	5.76248i	−0.0265091	−	0.252217i
$523$	18.1167	−	20.1207i	0.792190	−	0.879816i	−0.202859	−	0.979208i	$-0.565023\pi$
$523$	18.1167	−	20.1207i	0.792190	−	0.879816i	0.995048	+	0.0993923i	$0.0316899\pi$
$524$	9.29481			0.406046
$525$	9.60697	+	15.4200i	0.419283	+	0.672985i
$526$	28.2037			1.22974
$527$	7.08538	−	7.86911i	0.308644	−	0.342784i
$528$	0.182387	+	1.73530i	0.00793739	+	0.0755193i
$529$	2.29924	+	21.8758i	0.0999670	+	0.951122i
$530$	13.9516	+	10.5332i	0.606020	+	0.457532i
$531$	4.34856	+	3.15942i	0.188712	+	0.137107i
$532$	5.09234	−	2.71080i	0.220781	−	0.117528i
$533$	70.1870	+	50.9939i	3.04014	+	2.20879i
$534$	−11.9473	+	2.53948i	−0.517011	+	0.109894i
$535$	7.13740	+	12.9038i	0.308577	+	0.557880i
$536$	−10.0220	−	2.13025i	−0.432885	−	0.0920126i
$537$	18.6675	−	3.96790i	0.805563	−	0.171228i
$538$	4.20471	−	12.9408i	0.181278	−	0.557916i
$539$	−6.39149	+	6.18415i	−0.275301	+	0.266370i
$540$	11.6336	−	4.92572i	0.500631	−	0.211969i
$541$	27.2838	−	5.79934i	1.17302	−	0.249333i	0.420121	−	0.907468i	$-0.361988\pi$
$541$	27.2838	−	5.79934i	1.17302	−	0.249333i	0.752900	+	0.658135i	$0.228654\pi$
$542$	10.1068	−	4.49982i	0.434122	−	0.193284i
$543$	−11.5420	+	19.9914i	−0.495315	+	0.857912i
$544$	−0.107887	+	1.02647i	−0.00462560	+	0.0440097i
$545$	−14.2954	−	16.4751i	−0.612346	−	0.705716i
$546$	−10.9290	+	22.4353i	−0.467717	+	0.960140i
$547$	−21.1922	+	15.3970i	−0.906114	+	0.658330i	−0.940029	−	0.341095i	$-0.889202\pi$
$547$	−21.1922	+	15.3970i	−0.906114	+	0.658330i	0.0339153	+	0.999425i	$0.489202\pi$
$548$	1.90928	−	2.12047i	0.0815605	−	0.0905821i
$549$	7.15903	−	12.3998i	0.305540	−	0.529211i
$550$	5.27291	−	3.54272i	0.224838	−	0.151062i
$551$	−5.67115	−	9.82272i	−0.241599	−	0.418462i
$552$	0.425174	+	1.30855i	0.0180966	+	0.0556957i
$553$	−25.4597	+	1.79269i	−1.08266	+	0.0762328i
$554$	−15.4265	+	11.2080i	−0.655410	+	0.476183i
$555$	−5.64641	−	18.5287i	−0.239677	−	0.786499i
$556$	14.8738	−	6.62226i	0.630791	−	0.280846i
$557$	−20.0659	+	34.7552i	−0.850220	+	1.47262i	0.0307896	+	0.999526i	$0.490198\pi$
$557$	−20.0659	+	34.7552i	−0.850220	+	1.47262i	−0.881010	+	0.473098i	$0.843136\pi$
$558$	1.19452	−	11.3651i	0.0505680	−	0.481122i
$559$	12.4829	−	38.4183i	0.527969	−	1.62492i
$560$	−4.59924	+	3.72116i	−0.194353	+	0.157248i
$561$	0.556514	+	1.71277i	0.0234960	+	0.0723133i
$562$	20.1028	−	4.27299i	0.847987	−	0.180245i
$563$	−22.9694	−	25.5101i	−0.968045	−	1.07512i	−0.997142	−	0.0755459i	$-0.975930\pi$
$563$	−22.9694	−	25.5101i	−0.968045	−	1.07512i	0.0290977	−	0.999577i	$-0.490737\pi$
$564$	−8.88094	−	1.88770i	−0.373955	−	0.0794866i
$565$	6.11156	−	17.6971i	0.257115	−	0.744521i
$566$	0.388980	−	1.19716i	0.0163500	−	0.0503202i
$567$	−7.19136	+	9.21370i	−0.302009	+	0.386939i
$568$	−2.91498			−0.122310
$569$	−2.52939	+	24.0655i	−0.106037	+	1.00888i	0.804078	+	0.594524i	$0.202659\pi$
$569$	−2.52939	+	24.0655i	−0.106037	+	1.00888i	−0.910116	+	0.414355i	$0.864007\pi$
$570$	4.57109	−	4.89299i	0.191462	−	0.204945i
$571$	−2.89841	−	27.5765i	−0.121295	−	1.15404i	−0.870661	−	0.491884i	$-0.836308\pi$
$571$	−2.89841	−	27.5765i	−0.121295	−	1.15404i	0.749366	−	0.662156i	$-0.230358\pi$
$572$	7.97152	+	3.54915i	0.333306	+	0.148397i
$573$	2.77219	+	8.53194i	0.115810	+	0.356427i
$574$	−28.3508	−	17.6965i	−1.18334	−	0.738637i
$575$	3.48623	−	3.59701i	0.145386	−	0.150006i
$576$	0.556941	+	0.964650i	0.0232059	+	0.0401937i
$577$	−30.7547	−	6.53712i	−1.28034	−	0.272144i	−0.482969	−	0.875637i	$-0.660442\pi$
$577$	−30.7547	−	6.53712i	−1.28034	−	0.272144i	−0.797368	+	0.603493i	$0.793775\pi$
$578$	−1.66563	−	15.8474i	−0.0692811	−	0.659166i
$579$	5.39834	+	2.40349i	0.224347	+	0.0998858i
$580$	7.62308	+	8.78544i	0.316531	+	0.364795i
$581$	34.1918	+	4.78848i	1.41851	+	0.198660i
$582$	−1.63392			−0.0677281
$583$	−1.03824	+	9.87822i	−0.0429996	+	0.409114i
$584$	0.311846	+	0.346341i	0.0129043	+	0.0143317i
$585$	2.10015	−	16.9770i	0.0868307	−	0.701913i
$586$	4.44120	−	4.93245i	0.183464	−	0.203758i
$587$	−5.30150	+	16.3164i	−0.218817	+	0.673448i	0.780044	+	0.625725i	$0.215197\pi$
$587$	−5.30150	+	16.3164i	−0.218817	+	0.673448i	−0.998861	+	0.0477234i	$0.984803\pi$
$588$	3.59267	−	8.91698i	0.148159	−	0.367730i
$589$	−6.91268	−	21.2750i	−0.284832	−	0.876622i
$590$	−10.7885	−	0.198107i	−0.444155	−	0.00815595i
$591$	−3.99924	−	4.44161i	−0.164507	−	0.182703i
$592$	5.76220	−	2.56550i	0.236825	−	0.105441i
$593$	4.07566	+	7.05924i	0.167367	+	0.289888i	0.937493	−	0.348003i	$-0.113140\pi$
$593$	4.07566	+	7.05924i	0.167367	+	0.289888i	−0.770126	+	0.637891i	$0.779807\pi$
$594$	5.80724	+	4.21921i	0.238274	+	0.173116i
$595$	−3.84473	+	4.74374i	−0.157619	+	0.194474i
$596$	5.55450	−	4.03558i	0.227521	−	0.165304i
$597$	4.40418	+	1.96087i	0.180251	+	0.0802530i
$598$	6.73038	+	1.43059i	0.275226	+	0.0585010i
$599$	3.78577	−	6.55715i	0.154682	−	0.267918i	−0.778261	−	0.627941i	$-0.783898\pi$
$599$	3.78577	−	6.55715i	0.154682	−	0.267918i	0.932943	+	0.360023i	$0.117231\pi$
$600$	−3.64941	+	5.81676i	−0.148987	+	0.237468i
$601$	−5.30238			−0.216289			−0.108144	−	0.994135i	$-0.534491\pi$
$601$	−5.30238			−0.216289			−0.108144	+	0.994135i	$0.534491\pi$
$602$	−3.75732	+	15.1009i	−0.153137	+	0.615466i
$603$	−9.23310	+	6.70824i	−0.376001	+	0.273181i
$604$	−1.53848	−	0.684975i	−0.0625998	−	0.0278712i
$605$	−19.0129	−	8.88689i	−0.772985	−	0.361303i
$606$	18.4619	−	8.21976i	0.749963	−	0.333905i
$607$	6.57576	+	11.3895i	0.266902	+	0.462288i	0.968060	−	0.250718i	$-0.0806667\pi$
$607$	6.57576	+	11.3895i	0.266902	+	0.462288i	−0.701158	+	0.713006i	$0.747333\pi$
$608$	1.76402	+	1.28163i	0.0715403	+	0.0519771i
$609$	−17.7645	−	6.45601i	−0.719852	−	0.261611i
$610$	2.47912	+	28.6358i	0.100377	+	1.15943i
$611$	−30.3820	+	33.7426i	−1.22912	+	1.36508i
$612$	0.769277	+	0.854369i	0.0310962	+	0.0345358i
$613$	2.97401	+	3.30297i	0.120119	+	0.133406i	0.800205	−	0.599727i	$-0.204724\pi$
$613$	2.97401	+	3.30297i	0.120119	+	0.133406i	−0.680086	+	0.733133i	$0.738057\pi$
$614$	7.01731	−	7.79351i	0.283195	−	0.314520i
$615$	−37.7891	−	8.76043i	−1.52380	−	0.353255i
$616$	−3.15927	−	1.14815i	−0.127291	−	0.0462603i
$617$	−36.5230	−	26.5355i	−1.47036	−	1.06828i	−0.980510	−	0.196471i	$-0.937052\pi$
$617$	−36.5230	−	26.5355i	−1.47036	−	1.06828i	−0.489849	−	0.871807i	$-0.662948\pi$
$618$	5.74000	+	9.94197i	0.230897	+	0.399925i
$619$	43.8861	−	19.5394i	1.76393	−	0.785353i	0.775949	−	0.630796i	$-0.217271\pi$
$619$	43.8861	−	19.5394i	1.76393	−	0.785353i	0.987984	−	0.154558i	$-0.0493952\pi$
$620$	11.1036	+	20.0743i	0.445931	+	0.806205i
$621$	5.17091	+	2.30224i	0.207501	+	0.0923856i
$622$	4.14634	−	3.01249i	0.166253	−	0.120790i
$623$	5.68150	−	22.8343i	0.227624	−	0.914836i
$624$	−9.43234			−0.377596
$625$	24.9326	+	1.83443i	0.997304	+	0.0733770i
$626$	−6.80973	+	11.7948i	−0.272171	+	0.471415i
$627$	3.72143	+	0.791014i	0.148620	+	0.0315901i
$628$	−3.61878	−	1.61119i	−0.144405	−	0.0642933i
$629$	5.26683	−	3.82657i	0.210002	−	0.152576i
$630$	−0.347674	+	6.58063i	−0.0138516	+	0.262179i
$631$	8.06487	+	5.85947i	0.321058	+	0.233262i	0.736627	−	0.676300i	$-0.236418\pi$
$631$	8.06487	+	5.85947i	0.321058	+	0.233262i	−0.415569	+	0.909562i	$0.636418\pi$
$632$	−4.82334	−	8.35427i	−0.191862	−	0.332315i
$633$	−5.29398	+	2.35703i	−0.210417	+	0.0936836i
$634$	10.1844	+	11.3109i	0.404472	+	0.449212i
$635$	−2.12116	−	6.96058i	−0.0841756	−	0.276222i
$636$	−3.31784	−	10.2113i	−0.131561	−	0.404903i
$637$	−29.6355	−	37.8562i	−1.17420	−	1.49992i
$638$	−2.04228	+	6.28548i	−0.0808545	+	0.248845i
$639$	−2.17263	+	2.41295i	−0.0859478	+	0.0954547i
$640$	−2.02571	−	0.946842i	−0.0800731	−	0.0374272i
$641$	6.64656	+	7.38175i	0.262523	+	0.291562i	0.859967	−	0.510349i	$-0.170484\pi$
$641$	6.64656	+	7.38175i	0.262523	+	0.291562i	−0.597444	+	0.801910i	$0.703817\pi$
$642$	0.946705	−	9.00729i	0.0373635	−	0.355490i
$643$	−45.7152			−1.80283			−0.901416	−	0.432955i	$-0.857471\pi$
$643$	−45.7152			−1.80283			−0.901416	+	0.432955i	$0.857471\pi$
$644$	−2.62501	−	0.367627i	−0.103440	−	0.0144865i
$645$	1.55788	+	17.9947i	0.0613415	+	0.708541i
$646$	2.05593	+	0.915358i	0.0808894	+	0.0360143i
$647$	−3.88059	−	36.9214i	−0.152562	−	1.45153i	−0.756237	−	0.654298i	$-0.772964\pi$
$647$	−3.88059	−	36.9214i	−0.152562	−	1.45153i	0.603675	−	0.797230i	$-0.293702\pi$
$648$	−4.32109	−	0.918476i	−0.169748	−	0.0360811i
$649$	−3.06546	−	5.30953i	−0.120330	−	0.208417i
$650$	16.0668	+	30.3500i	0.630191	+	1.19042i
$651$	−31.6231	−	19.7390i	−1.23941	−	0.773634i
$652$	−2.15254	−	6.62485i	−0.0843001	−	0.259449i
$653$	15.4113	+	6.86157i	0.603093	+	0.268514i	0.685486	−	0.728086i	$-0.259590\pi$
$653$	15.4113	+	6.86157i	0.603093	+	0.268514i	−0.0823935	+	0.996600i	$0.526256\pi$
$654$	1.40036	+	13.3235i	0.0547584	+	0.520992i
$655$	−2.55163	+	20.6266i	−0.0997005	+	0.805948i
$656$	1.32038	−	12.5626i	0.0515522	−	0.490486i
$657$	0.519121			0.0202529
$658$	10.7620	−	13.7884i	0.419546	−	0.537530i
$659$	14.0167	−	43.1390i	0.546013	−	1.68045i	−0.172556	−	0.985000i	$-0.555203\pi$
$659$	14.0167	−	43.1390i	0.546013	−	1.68045i	0.718569	−	0.695455i	$-0.244797\pi$
$660$	−3.90097	−	0.0716328i	−0.151845	−	0.00278830i
$661$	8.12873	+	1.72781i	0.316171	+	0.0672042i	0.363264	−	0.931686i	$-0.381662\pi$
$661$	8.12873	+	1.72781i	0.316171	+	0.0672042i	−0.0470929	+	0.998891i	$0.514996\pi$
$662$	9.82600	+	10.9129i	0.381898	+	0.424141i
$663$	−9.52263	+	2.02410i	−0.369828	+	0.0786094i
$664$	4.03249	+	12.4107i	0.156491	+	0.481629i
$665$	4.61773	+	12.0448i	0.179068	+	0.467079i
$666$	2.17110	−	6.68196i	0.0841284	−	0.258921i
$667$	−0.544742	+	5.18288i	−0.0210925	+	0.200682i
$668$	5.63391	−	9.75821i	0.217982	−	0.377556i
$669$	24.7782	−	11.0320i	0.957979	−	0.426520i
$670$	7.47861	−	21.6556i	0.288924	−	0.836629i
$671$	−13.2123	+	9.59930i	−0.510055	+	0.370577i
$672$	3.62460	−	0.255218i	0.139822	−	0.00984524i
$673$	−1.93883	−	5.96709i	−0.0747362	−	0.230015i	0.906709	−	0.421757i	$-0.138586\pi$
$673$	−1.93883	−	5.96709i	−0.0747362	−	0.230015i	−0.981445	+	0.191742i	$0.938586\pi$
$674$	0.443945	+	0.768935i	0.0171001	+	0.0296183i
$675$	7.73724	+	27.1690i	0.297806	+	1.04573i
$676$	−17.0852	+	29.5925i	−0.657124	+	1.13817i
$677$	−28.9505	+	32.1528i	−1.11266	+	1.23573i	−0.143407	+	0.989664i	$0.545806\pi$
$677$	−28.9505	+	32.1528i	−1.11266	+	1.23573i	−0.969252	+	0.246069i	$0.920861\pi$
$678$	−9.30303	+	6.75905i	−0.357281	+	0.259580i
$679$	1.37850	−	2.82981i	0.0529019	−	0.108598i
$680$	−2.24828	−	0.521206i	−0.0862177	−	0.0199873i
$681$	−3.07421	+	29.2491i	−0.117804	+	1.12083i
$682$	−6.51726	+	11.2882i	−0.249559	+	0.432248i
$683$	23.8094	−	10.6006i	0.911040	−	0.405621i	0.102954	−	0.994686i	$-0.467170\pi$
$683$	23.8094	−	10.6006i	0.911040	−	0.405621i	0.808086	+	0.589065i	$0.200504\pi$
$684$	2.37568	−	0.504967i	0.0908365	−	0.0193079i
$685$	4.18151	+	4.81911i	0.159767	+	0.184129i
$686$	12.4124	+	13.7452i	0.473909	+	0.524796i
$687$	−3.05981	+	9.41713i	−0.116739	+	0.359286i
$688$	−5.75309	+	1.22286i	−0.219335	+	0.0466210i
$689$	−52.5204	−	11.1636i	−2.00087	−	0.425298i
$690$	−3.02060	+	0.584300i	−0.114992	+	0.0222439i
$691$	14.9208	−	3.17150i	0.567612	−	0.120650i	0.0848384	−	0.996395i	$-0.472963\pi$
$691$	14.9208	−	3.17150i	0.567612	−	0.120650i	0.482774	+	0.875745i	$0.339629\pi$
$692$	2.05661	+	1.49421i	0.0781805	+	0.0568014i
$693$	−3.30512	+	1.75941i	−0.125551	+	0.0668346i
$694$	6.44996	+	4.68617i	0.244837	+	0.177885i
$695$	10.6126	+	34.8253i	0.402559	+	1.32100i
$696$	−0.746750	−	7.10485i	−0.0283055	−	0.269309i
$697$	−1.36280	−	12.9662i	−0.0516197	−	0.491129i
$698$	−5.92922	+	6.58507i	−0.224424	+	0.249248i
$699$	11.3780			0.430357
$700$	−6.99523	−	11.2279i	−0.264395	−	0.424376i
$701$	−19.1850			−0.724608			−0.362304	−	0.932060i	$-0.618010\pi$
$701$	−19.1850			−0.724608			−0.362304	+	0.932060i	$0.618010\pi$
$702$	−25.9646	+	28.8366i	−0.979972	+	1.08837i
$703$	−1.43760	−	13.6778i	−0.0542201	−	0.515870i
$704$	−0.132804	−	1.26354i	−0.00500523	−	0.0476216i
$705$	6.62712	−	19.1900i	0.249592	−	0.722735i
$706$	−24.9896	−	18.1560i	−0.940497	−	0.683311i
$707$	−1.33990	+	38.9093i	−0.0503923	+	1.46333i
$708$	5.36156	+	3.89540i	0.201500	+	0.146398i
$709$	9.80779	−	2.08471i	0.368339	−	0.0782929i	−0.0200235	−	0.999800i	$-0.506374\pi$
$709$	9.80779	−	2.08471i	0.368339	−	0.0782929i	0.388363	+	0.921507i	$0.373041\pi$
$710$	0.800226	−	6.46878i	0.0300319	−	0.242769i
$711$	−10.5105	−	2.23407i	−0.394173	−	0.0837840i
$712$	8.69933	−	1.84910i	0.326021	−	0.0692980i
$713$	−3.17615	+	9.77520i	−0.118948	+	0.366084i
$714$	3.60452	−	1.03547i	0.134896	−	0.0387514i
$715$	−10.0645	+	16.7157i	−0.376389	+	0.625132i
$716$	−13.5926	+	2.88919i	−0.507979	+	0.107974i
$717$	14.0237	−	6.24373i	0.523723	−	0.233176i
$718$	6.40975	−	11.1020i	0.239210	−	0.414323i
$719$	4.67738	−	44.5023i	0.174437	−	1.65965i	−0.460925	−	0.887439i	$-0.652482\pi$
$719$	4.67738	−	44.5023i	0.174437	−	1.65965i	0.635361	−	0.772215i	$-0.280851\pi$
$720$	−2.29360	+	0.971119i	−0.0854773	+	0.0361915i
$721$	−22.0614	+	1.55340i	−0.821608	+	0.0578517i
$722$	−11.5250	+	8.37339i	−0.428916	+	0.311625i
$723$	−8.04779	+	8.93797i	−0.299300	+	0.332407i
$724$	8.40422	−	14.5565i	0.312340	−	0.540989i
$725$	−21.5889	+	14.5050i	−0.801793	+	0.538701i
$726$	6.44506	+	11.1632i	0.239198	+	0.414304i
$727$	−5.95488	−	18.3272i	−0.220854	−	0.679720i	−0.998686	−	0.0512471i	$-0.983680\pi$
$727$	−5.95488	−	18.3272i	−0.220854	−	0.679720i	0.777832	−	0.628473i	$-0.216320\pi$
$728$	7.95784	−	16.3360i	0.294937	−	0.605454i
$729$	−22.8131	+	16.5747i	−0.844929	+	0.613877i
$730$	−0.854191	+	0.596957i	−0.0316150	+	0.0220944i
$731$	−5.54575	+	2.46913i	−0.205117	+	0.0913240i
$732$	8.82672	−	15.2883i	0.326245	−	0.565073i
$733$	−3.03860	+	28.9104i	−0.112233	+	1.06783i	0.782936	+	0.622103i	$0.213721\pi$
$733$	−3.03860	+	28.9104i	−0.112233	+	1.06783i	−0.895169	+	0.445727i	$0.852945\pi$
$734$	−5.96465	+	18.3573i	−0.220159	+	0.677580i
$735$	18.8019	+	10.4206i	0.693518	+	0.384369i
$736$	−0.309587	−	0.952811i	−0.0114115	−	0.0351211i
$737$	12.7330	−	2.70649i	0.469027	−	0.0996947i
$738$	−9.41487	−	10.4563i	−0.346566	−	0.384901i
$739$	37.1186	+	7.88980i	1.36543	+	0.290231i	0.831606	−	0.555365i	$-0.187422\pi$
$739$	37.1186	+	7.88980i	1.36543	+	0.290231i	0.533823	+	0.845596i	$0.320755\pi$
$740$	4.11138	+	13.4915i	0.151137	+	0.495957i
$741$	−6.35546	+	19.5601i	−0.233474	+	0.718558i
$742$	20.4842	+	2.86877i	0.752000	+	0.105316i
$743$	−12.4748			−0.457656			−0.228828	−	0.973467i	$-0.573489\pi$
$743$	−12.4748			−0.457656			−0.228828	+	0.973467i	$0.573489\pi$
$744$	1.47278	−	14.0126i	0.0539948	−	0.513726i
$745$	7.43074	+	13.4341i	0.272241	+	0.492189i
$746$	1.38812	+	13.2070i	0.0508225	+	0.483544i
$747$	13.2788	+	5.91212i	0.485847	+	0.216313i
$748$	−0.405220	−	1.24714i	−0.0148163	−	0.0456000i
$749$	14.8012	+	9.23885i	0.540823	+	0.337580i
$750$	−11.9064	−	9.69544i	−0.434762	−	0.354027i
$751$	−18.0067	−	31.1885i	−0.657074	−	1.13809i	−0.981369	−	0.192130i	$-0.938460\pi$
$751$	−18.0067	−	31.1885i	−0.657074	−	1.13809i	0.324295	−	0.945956i	$-0.394873\pi$
$752$	6.46658	+	1.37451i	0.235812	+	0.0501234i
$753$	−2.20007	−	20.9322i	−0.0801749	−	0.762813i
$754$	−32.6378	−	14.5313i	−1.18860	−	0.529199i
$755$	1.94241	−	3.22608i	0.0706915	−	0.117409i
$756$	9.19726	−	11.7837i	0.334501	−	0.428569i
$757$	13.3430			0.484959			0.242480	−	0.970157i	$-0.422039\pi$
$757$	13.3430			0.484959			0.242480	+	0.970157i	$0.422039\pi$
$758$	−1.21180	+	11.5295i	−0.0440146	+	0.418771i
$759$	−1.16969	−	1.29907i	−0.0424571	−	0.0471534i
$760$	−3.32840	+	3.56278i	−0.120734	+	0.129236i
$761$	−3.38205	+	3.75615i	−0.122599	+	0.136160i	−0.801319	−	0.598237i	$-0.795868\pi$
$761$	−3.38205	+	3.75615i	−0.122599	+	0.136160i	0.678720	+	0.734397i	$0.262535\pi$
$762$	−1.38105	+	4.25045i	−0.0500303	+	0.153978i
$763$	−24.2567	−	8.81544i	−0.878152	−	0.319140i
$764$	−2.01855	−	6.21245i	−0.0730285	−	0.224759i
$765$	−2.10716	+	1.47260i	−0.0761845	+	0.0532420i
$766$	−9.86919	−	10.9608i	−0.356588	−	0.396031i
$767$	30.2771	−	13.4802i	1.09324	−	0.486743i
$768$	0.686680	+	1.18936i	0.0247784	+	0.0429175i
$769$	10.4674	+	7.60502i	0.377464	+	0.274244i	0.760299	−	0.649573i	$-0.225052\pi$
$769$	10.4674	+	7.60502i	0.377464	+	0.274244i	−0.382835	+	0.923817i	$0.625052\pi$
$770$	3.41521	−	6.69571i	0.123076	−	0.241297i
$771$	21.8587	−	15.8813i	0.787222	−	0.571950i
$772$	−3.93075	−	1.75008i	−0.141471	−	0.0629869i
$773$	−8.45126	−	1.79637i	−0.303971	−	0.0646109i	0.0534013	−	0.998573i	$-0.482994\pi$
$773$	−8.45126	−	1.79637i	−0.303971	−	0.0646109i	−0.357372	+	0.933962i	$0.616327\pi$
$774$	−3.27571	+	5.67370i	−0.117743	+	0.203937i
$775$	−47.5962	+	19.1297i	−1.70971	+	0.687159i
$776$	1.18972			0.0427085
$777$	−16.4941	−	15.9128i	−0.591723	−	0.570867i
$778$	−2.74845	+	1.99686i	−0.0985366	+	0.0715911i
$779$	−25.1617	−	11.2027i	−0.901510	−	0.401378i
$780$	2.58939	−	20.9318i	0.0927149	−	0.749479i
$781$	3.38331	−	1.50635i	0.121064	−	0.0539013i
$782$	−0.517015	−	0.895497i	−0.0184884	−	0.0320229i
$783$	−23.7766	−	17.2747i	−0.849707	−	0.617348i
$784$	−2.61597	+	6.49282i	−0.0934274	+	0.231886i
$785$	4.56890	−	7.58832i	0.163071	−	0.270839i
$786$	8.54154	−	9.48634i	0.304667	−	0.338366i
$787$	31.3268	+	34.7920i	1.11668	+	1.24020i	0.967902	+	0.251330i	$0.0808679\pi$
$787$	31.3268	+	34.7920i	1.11668	+	1.24020i	0.148780	+	0.988870i	$0.452465\pi$
$788$	2.91201	+	3.23412i	0.103736	+	0.115211i
$789$	25.9180	−	28.7848i	0.922704	−	1.02477i
$790$	19.8635	−	8.41030i	0.706712	−	0.299225i
$791$	−3.85737	−	21.8145i	−0.137152	−	0.775635i
$792$	−1.14491	−	0.831828i	−0.0406827	−	0.0295577i
$793$	−44.1418	−	76.4558i	−1.56752	−	2.71503i
$794$	11.4234	−	5.08604i	0.405402	−	0.180497i
$795$	23.5712	−	4.55958i	0.835983	−	0.161711i
$796$	−3.20686	−	1.42779i	−0.113664	−	0.0506066i
$797$	22.4253	−	16.2929i	0.794344	−	0.577125i	−0.114905	−	0.993376i	$-0.536656\pi$
$797$	22.4253	−	16.2929i	0.794344	−	0.577125i	0.909249	+	0.416252i	$0.136656\pi$
$798$	1.91298	−	7.68838i	0.0677188	−	0.272166i
$799$	6.82344			0.241396
$800$	2.65729	−	4.23542i	0.0939493	−	0.149745i
$801$	4.95325	−	8.57929i	0.175015	−	0.303134i
$802$	27.8586	+	5.92154i	0.983723	+	0.209097i
$803$	−0.540924	−	0.240835i	−0.0190888	−	0.00849887i
$804$	−11.3840	+	8.27093i	−0.401481	+	0.291693i
$805$	1.53645	−	5.72438i	0.0541526	−	0.201758i
$806$	−57.0048	−	41.4164i	−2.00791	−	1.45883i
$807$	−9.34347	−	16.1834i	−0.328906	−	0.569681i
$808$	−13.4429	+	5.98515i	−0.472918	+	0.210557i
$809$	9.07761	+	10.0817i	0.319152	+	0.354454i	0.881279	−	0.472597i	$-0.156683\pi$
$809$	9.07761	+	10.0817i	0.319152	+	0.354454i	−0.562127	+	0.827051i	$0.690017\pi$
$810$	3.22447	−	9.33701i	0.113296	−	0.328069i
$811$	−8.17891	−	25.1721i	−0.287201	−	0.883912i	−0.985730	−	0.168331i	$-0.946162\pi$
$811$	−8.17891	−	25.1721i	−0.287201	−	0.883912i	0.698530	−	0.715581i	$-0.253838\pi$
$812$	12.9350	+	4.70088i	0.453931	+	0.164969i
$813$	4.69514	−	14.4501i	0.164666	−	0.506789i
$814$	−5.36223	+	5.95536i	−0.187946	+	0.208735i
$815$	15.2925	−	2.95816i	0.535672	−	0.103620i
$816$	0.948481	+	1.05339i	0.0332035	+	0.0368762i
$817$	−1.34053	+	12.7543i	−0.0468992	+	0.446216i
$818$	−6.01514			−0.210314
$819$	−7.59133	−	18.7631i	−0.265262	−	0.655635i
$820$	27.5158	+	6.37883i	0.960893	+	0.222758i
$821$	1.66670	+	0.742061i	0.0581681	+	0.0258981i	0.435615	−	0.900133i	$-0.356531\pi$
$821$	1.66670	+	0.742061i	0.0581681	+	0.0258981i	−0.377446	+	0.926031i	$0.623198\pi$
$822$	−0.409617	−	3.89725i	−0.0142871	−	0.135932i
$823$	−1.39924	−	0.297418i	−0.0487745	−	0.0103673i	0.183460	−	0.983027i	$-0.441270\pi$
$823$	−1.39924	−	0.297418i	−0.0487745	−	0.0103673i	−0.232234	+	0.972660i	$0.574604\pi$
$824$	−4.17953	−	7.23915i	−0.145601	−	0.252188i
$825$	1.22987	−	8.63717i	0.0428184	−	0.300708i
$826$	−11.2699	+	5.99932i	−0.392131	+	0.208743i
$827$	−6.75433	−	20.7877i	−0.234871	−	0.722859i	−0.997138	−	0.0755964i	$-0.975914\pi$
$827$	−6.75433	−	20.7877i	−0.234871	−	0.722859i	0.762268	−	0.647262i	$-0.224086\pi$
$828$	−1.01946	−	0.453892i	−0.0354286	−	0.0157738i
$829$	4.16916	+	39.6669i	0.144801	+	1.37769i	0.789734	+	0.613450i	$0.210219\pi$
$829$	4.16916	+	39.6669i	0.144801	+	1.37769i	−0.644933	+	0.764239i	$0.723115\pi$
$830$	−28.6483	+	5.54169i	−0.994397	+	0.192355i
$831$	−2.73734	+	26.0441i	−0.0949574	+	0.903460i
$832$	6.86807			0.238108
$833$	−1.24771	+	7.11633i	−0.0432305	+	0.246566i
$834$	6.90971	−	21.2659i	0.239264	−	0.736378i
$835$	20.1083	+	15.1813i	0.695877	+	0.525372i
$836$	−2.70972	−	0.575970i	−0.0937178	−	0.0199203i
$837$	−38.7852	−	43.0753i	−1.34061	−	1.48890i
$838$	31.1371	−	6.61840i	1.07561	−	0.228629i
$839$	11.7352	+	36.1171i	0.405143	+	1.24690i	0.920776	+	0.390092i	$0.127557\pi$
$839$	11.7352	+	36.1171i	0.405143	+	1.24690i	−0.515633	+	0.856810i	$0.672443\pi$
$840$	−0.428664	+	8.11359i	−0.0147903	+	0.279946i
$841$	−0.599785	+	1.84595i	−0.0206822	+	0.0636534i
$842$	−3.04165	+	28.9393i	−0.104822	+	0.997316i
$843$	14.1126	−	24.4438i	0.486064	−	0.841888i
$844$	3.85476	−	1.71625i	0.132686	−	0.0590758i
$845$	−60.9799	−	46.0385i	−2.09777	−	1.58377i
$846$	5.95754	−	4.32840i	0.204824	−	0.148814i
$847$	−24.7712	+	1.74421i	−0.851149	+	0.0599318i
$848$	2.41586	+	7.43524i	0.0829608	+	0.255327i
$849$	−0.864368	−	1.49713i	−0.0296650	−	0.0513814i
$850$	1.77384	−	4.84620i	0.0608422	−	0.166223i
$851$	−3.15958	+	5.47255i	−0.108309	+	0.187596i
$852$	−2.67874	+	2.97504i	−0.0917722	+	0.101923i
$853$	3.90539	−	2.83743i	0.133718	−	0.0971517i	−0.518916	−	0.854825i	$-0.673664\pi$
$853$	3.90539	−	2.83743i	0.133718	−	0.0971517i	0.652634	+	0.757674i	$0.273664\pi$
$854$	19.0312	+	28.1856i	0.651235	+	0.964490i
$855$	0.468421	+	5.41062i	0.0160197	+	0.185039i
$856$	−0.689335	+	6.55858i	−0.0235610	+	0.224168i
$857$	12.6472	−	21.9056i	0.432020	−	0.748281i	−0.565027	−	0.825073i	$-0.691134\pi$
$857$	12.6472	−	21.9056i	0.432020	−	0.748281i	0.997047	+	0.0767912i	$0.0244675\pi$
$858$	10.9478	−	4.87426i	0.373751	−	0.166404i
$859$	31.0576	−	6.60150i	1.05967	−	0.225240i	0.355068	−	0.934841i	$-0.384458\pi$
$859$	31.0576	−	6.60150i	1.05967	−	0.225240i	0.704604	+	0.709600i	$0.251124\pi$
$860$	−1.13436	−	13.1027i	−0.0386812	−	0.446798i
$861$	−44.1143	+	12.6727i	−1.50341	+	0.431883i
$862$	−0.767221	+	2.36126i	−0.0261317	+	0.0804250i
$863$	−29.0366	+	6.17191i	−0.988416	+	0.210094i	−0.673631	−	0.739068i	$-0.735266\pi$
$863$	−29.0366	+	6.17191i	−0.988416	+	0.210094i	−0.314786	+	0.949163i	$0.601933\pi$
$864$	5.52638	+	1.17467i	0.188011	+	0.0399630i
$865$	−3.88047	+	4.15373i	−0.131940	+	0.141231i
$866$	−6.51389	+	1.38457i	−0.221351	+	0.0470496i
$867$	−17.7046	−	12.8632i	−0.601280	−	0.436856i
$868$	23.0261	+	14.3728i	0.781555	+	0.487845i
$869$	9.91543	+	7.20398i	0.336358	+	0.244378i
$870$	15.9718	+	0.293287i	0.541493	+	0.00994334i
$871$	7.35564	+	69.9842i	0.249236	+	2.37133i
$872$	−1.01966	−	9.70142i	−0.0345301	−	0.328532i
$873$	0.886738	−	0.984823i	0.0300115	−	0.0333312i
$874$	−2.18447			−0.0738907
$875$	26.8369	−	12.4412i	0.907252	−	0.420588i
$876$	0.640051			0.0216253
$877$	9.19005	−	10.2066i	0.310326	−	0.344652i	−0.567726	−	0.823218i	$-0.692177\pi$
$877$	9.19005	−	10.2066i	0.310326	−	0.344652i	0.878052	+	0.478566i	$0.158843\pi$
$878$	−2.36879	−	22.5375i	−0.0799427	−	0.760604i
$879$	−0.952814	−	9.06542i	−0.0321376	−	0.305769i
$880$	2.84045	+	0.0521588i	0.0957517	+	0.00175827i
$881$	−33.0243	−	23.9936i	−1.11262	−	0.808364i	−0.129544	−	0.991574i	$-0.541351\pi$
$881$	−33.0243	−	23.9936i	−1.11262	−	0.808364i	−0.983074	+	0.183210i	$0.941351\pi$
$882$	3.42483	+	7.00474i	0.115320	+	0.235862i
$883$	−15.1428	−	11.0019i	−0.509596	−	0.370243i	0.303075	−	0.952967i	$-0.401987\pi$
$883$	−15.1428	−	11.0019i	−0.509596	−	0.370243i	−0.812670	+	0.582724i	$0.801987\pi$
$884$	6.93382	−	1.47383i	0.233210	−	0.0495702i
$885$	−10.1164	+	10.8288i	−0.340058	+	0.364004i
$886$	−15.7522	−	3.34824i	−0.529207	−	0.112486i
$887$	−5.65768	+	1.20258i	−0.189966	+	0.0403786i	−0.301912	−	0.953336i	$-0.597625\pi$
$887$	−5.65768	+	1.20258i	−0.189966	+	0.0403786i	0.111946	+	0.993714i	$0.464292\pi$
$888$	2.67686	−	8.23852i	0.0898295	−	0.276467i
$889$	−6.19626	−	5.97787i	−0.207816	−	0.200491i
$890$	1.71528	+	19.8128i	0.0574962	+	0.664126i
$891$	5.48996	−	1.16693i	0.183921	−	0.0390935i
$892$	−18.0420	+	8.03282i	−0.604091	+	0.268959i
$893$	7.20751	−	12.4838i	0.241190	−	0.417753i
$894$	0.985613	−	9.37748i	0.0329638	−	0.313630i
$895$	−2.68010	−	30.9572i	−0.0895857	−	1.03478i
$896$	−2.63922	+	0.185835i	−0.0881700	+	0.00620830i
$897$	7.64500	−	5.55442i	0.255259	−	0.185457i
$898$	−13.4642	+	14.9535i	−0.449306	+	0.499005i
$899$	26.6837	−	46.2174i	0.889950	−	1.54144i
$900$	−1.52542	−	5.35643i	−0.0508473	−	0.178548i
$901$	4.03452	+	6.98799i	0.134409	+	0.232804i
$902$	4.95932	+	15.2632i	0.165127	+	0.508210i
$903$	11.9592	+	17.7118i	0.397978	+	0.589412i
$904$	6.77392	−	4.92154i	0.225297	−	0.163688i
$905$	29.9960	+	22.6463i	0.997101	+	0.752789i
$906$	−2.11289	+	0.940717i	−0.0701959	+	0.0312532i
$907$	−26.1835	+	45.3512i	−0.869410	+	1.50586i	−0.00681032	+	0.999977i	$0.502168\pi$
$907$	−26.1835	+	45.3512i	−0.869410	+	1.50586i	−0.862600	+	0.505886i	$0.831166\pi$
$908$	2.23846	−	21.2975i	0.0742858	−	0.706782i
$909$	−5.06504	+	15.5886i	−0.167997	+	0.517041i
$910$	34.0675	+	22.1443i	1.12933	+	0.734075i
$911$	15.7869	+	48.5871i	0.523044	+	1.60976i	0.768151	+	0.640268i	$0.221177\pi$
$911$	15.7869	+	48.5871i	0.523044	+	1.60976i	−0.245107	+	0.969496i	$0.578823\pi$
$912$	2.92910	−	0.622599i	0.0969921	−	0.0206163i
$913$	−11.0937	−	12.3208i	−0.367149	−	0.407760i
$914$	−26.4408	−	5.62017i	−0.874584	−	0.185899i
$915$	31.5040	+	23.7848i	1.04149	+	0.786302i
$916$	2.22797	−	6.85700i	0.0736143	−	0.226562i
$917$	9.22326	+	22.7966i	0.304579	+	0.752811i
$918$	5.83135			0.192463
$919$	−1.17887	+	11.2162i	−0.0388872	+	0.369987i	0.957721	+	0.287698i	$0.0928899\pi$
$919$	−1.17887	+	11.2162i	−0.0388872	+	0.369987i	−0.996608	+	0.0822895i	$0.973777\pi$
$920$	2.19942	−	0.425453i	0.0725128	−	0.0140268i
$921$	−1.50549	−	14.3238i	−0.0496077	−	0.471985i
$922$	−22.5974	−	10.0610i	−0.744207	−	0.331342i
$923$	6.18661	+	19.0404i	0.203635	+	0.626723i
$924$	−4.07505	+	2.16927i	−0.134059	+	0.0713637i
$925$	−31.0684	+	5.42007i	−1.02152	+	0.178211i
$926$	−16.9941	−	29.4347i	−0.558461	−	0.967283i
$927$	−9.10753	−	1.93586i	−0.299130	−	0.0635821i
$928$	0.543739	+	5.17334i	0.0178491	+	0.169823i
$929$	31.9149	+	14.2094i	1.04709	+	0.466196i	0.856863	−	0.515544i	$-0.172410\pi$
$929$	31.9149	+	14.2094i	1.04709	+	0.466196i	0.190230	+	0.981740i	$0.439077\pi$
$930$	30.6917	+	7.11508i	1.00642	+	0.233313i
$931$	11.7017	+	9.79962i	0.383508	+	0.321170i
$932$	−8.28482			−0.271378
$933$	0.735744	−	7.00013i	0.0240872	−	0.229174i
$934$	9.48452	+	10.5336i	0.310343	+	0.344671i
$935$	2.87884	−	0.556878i	0.0941480	−	0.0182119i
$936$	5.11900	−	5.68522i	0.167320	−	0.185827i
$937$	−0.226693	+	0.697691i	−0.00740575	+	0.0227926i	−0.954691	−	0.297599i	$-0.903814\pi$
$937$	−0.226693	+	0.697691i	−0.00740575	+	0.0227926i	0.947285	+	0.320391i	$0.103814\pi$
$938$	−4.72019	−	26.6940i	−0.154120	−	0.871591i
$939$	5.77998	+	17.7890i	0.188623	+	0.580521i
$940$	−4.82547	+	13.9730i	−0.157390	+	0.455749i
$941$	21.2535	+	23.6044i	0.692844	+	0.769481i	0.982220	−	0.187734i	$-0.0601144\pi$
$941$	21.2535	+	23.6044i	0.692844	+	0.769481i	−0.289376	+	0.957216i	$0.593448\pi$
$942$	−4.96989	+	2.21274i	−0.161928	+	0.0720949i
$943$	6.32754	+	10.9596i	0.206053	+	0.356894i
$944$	−3.90397	−	2.83640i	−0.127064	−	0.0923171i
$945$	23.6250	+	23.6450i	0.768520	+	0.769172i
$946$	6.04548	−	4.39230i	0.196555	−	0.142806i
$947$	7.64834	+	3.40526i	0.248538	+	0.110656i	0.527225	−	0.849726i	$-0.323233\pi$
$947$	7.64834	+	3.40526i	0.248538	+	0.110656i	−0.278687	+	0.960382i	$0.589899\pi$
$948$	−12.9589	−	2.75449i	−0.420884	−	0.0894617i
$949$	1.60042	−	2.77201i	0.0519519	−	0.0899834i
$950$	−6.99264	−	8.36429i	−0.226871	−	0.271373i
$951$	20.9029			0.677824
$952$	−2.62460	+	0.753966i	−0.0850638	+	0.0244362i
$953$	−5.70116	+	4.14214i	−0.184679	+	0.134177i	−0.676283	−	0.736642i	$-0.736411\pi$
$953$	−5.70116	+	4.14214i	−0.184679	+	0.134177i	0.491605	+	0.870818i	$0.336411\pi$
$954$	7.95532	+	3.54194i	0.257563	+	0.114674i
$955$	14.3405	−	2.77401i	0.464048	−	0.0897649i
$956$	−10.2112	+	4.54632i	−0.330254	+	0.147038i
$957$	4.53823	+	7.86045i	0.146700	+	0.254092i
$958$	−1.78410	−	1.29622i	−0.0576416	−	0.0418791i
$959$	7.09530	+	2.57859i	0.229119	+	0.0832671i
$960$	−2.82789	+	1.19734i	−0.0912698	+	0.0386440i
$961$	49.6855	−	55.1814i	1.60276	−	1.78004i
$962$	−28.9871	−	32.1934i	−0.934581	−	1.03796i
$963$	4.91525	+	5.45894i	0.158392	+	0.175912i
$964$	5.85992	−	6.50811i	0.188735	−	0.209612i
$965$	4.96278	−	8.24250i	0.159758	−	0.265335i
$966$	−2.78748	+	2.34127i	−0.0896856	+	0.0753291i
$967$	−14.4412	−	10.4921i	−0.464397	−	0.337404i	0.330857	−	0.943681i	$-0.392662\pi$
$967$	−14.4412	−	10.4921i	−0.464397	−	0.337404i	−0.795254	+	0.606277i	$0.792662\pi$
$968$	−4.69291	−	8.12836i	−0.150836	−	0.261255i
$969$	2.82353	−	1.25712i	0.0907049	−	0.0403844i
$970$	−0.326605	+	2.64018i	−0.0104867	+	0.0847709i
$971$	−34.2044	−	15.2288i	−1.09767	−	0.488715i	−0.223683	−	0.974662i	$-0.571808\pi$
$971$	−34.2044	−	15.2288i	−1.09767	−	0.488715i	−0.873988	+	0.485947i	$0.838475\pi$
$972$	8.80416	−	6.39659i	0.282393	−	0.205171i
$973$	31.0012	+	29.9086i	0.993853	+	0.958825i
$974$	15.6147			0.500327
$975$	45.7400	+	11.4925i	1.46485	+	0.368054i
$976$	−6.42710	+	11.1321i	−0.205726	+	0.356329i
$977$	−4.76782	−	1.01343i	−0.152536	−	0.0324225i	0.131011	−	0.991381i	$-0.458178\pi$
$977$	−4.76782	−	1.01343i	−0.152536	−	0.0324225i	−0.283547	+	0.958958i	$0.591511\pi$
$978$	−8.73946	−	3.89106i	−0.279457	−	0.124422i
$979$	−9.14145	+	6.64165i	−0.292162	+	0.212268i
$980$	−13.6904	−	7.58765i	−0.437324	−	0.242379i
$981$	−8.79058	−	6.38673i	−0.280662	−	0.203913i
$982$	6.08376	+	10.5374i	0.194140	+	0.336261i
$983$	−1.41623	+	0.630546i	−0.0451707	+	0.0201113i	−0.429198	−	0.903211i	$-0.641204\pi$
$983$	−1.41623	+	0.630546i	−0.0451707	+	0.0201113i	0.384027	+	0.923322i	$0.374537\pi$
$984$	−11.6081	−	12.8921i	−0.370051	−	0.410984i
$985$	−7.97642	+	5.57437i	−0.254150	+	0.177614i
$986$	1.65910	+	5.10617i	0.0528364	+	0.162614i
$987$	−4.18276	−	23.6547i	−0.133139	−	0.752939i
$988$	4.62767	−	14.2425i	0.147226	−	0.453114i
$989$	3.94283	−	4.37896i	0.125375	−	0.139243i
$990$	2.16026	−	2.31238i	0.0686575	−	0.0734923i
$991$	28.4651	+	31.6137i	0.904224	+	1.00424i	0.999961	+	0.00883557i	$0.00281249\pi$
$991$	28.4651	+	31.6137i	0.904224	+	1.00424i	−0.0957372	+	0.995407i	$0.530521\pi$
$992$	−1.07239	+	10.2031i	−0.0340485	+	0.323950i
$993$	20.1674			0.639994
$994$	−2.89254	−	7.14933i	−0.0917458	−	0.226763i
$995$	4.04883	−	6.72456i	0.128357	−	0.213183i
$996$	16.3721	+	7.28935i	0.518771	+	0.230972i
$997$	0.792020	+	7.53557i	0.0250835	+	0.238654i	0.999879	+	0.0155536i	$0.00495107\pi$
$997$	0.792020	+	7.53557i	0.0250835	+	0.238654i	−0.974795	+	0.223100i	$0.928382\pi$
$998$	−25.7635	−	5.47621i	−0.815530	−	0.173346i
$999$	−17.8182	−	30.8621i	−0.563744	−	0.976433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.b.81.7	✓	72
7.2	even	3	inner	350.2.q.b.331.3	yes	72
25.21	even	5	inner	350.2.q.b.221.3	yes	72
175.121	even	15	inner	350.2.q.b.121.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.b.81.7	✓	72	1.1	even	1	trivial
350.2.q.b.121.7	yes	72	175.121	even	15	inner
350.2.q.b.221.3	yes	72	25.21	even	5	inner
350.2.q.b.331.3	yes	72	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.143555 + 1.36584i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.23569 + 0.0410536i) q^{5} +(-1.11107 - 0.807241i) q^{6} +(2.33546 - 1.24323i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.08954 - 0.231589i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.143555 + 1.36584i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(2.23569 + 0.0410536i) q^{5} +(-1.11107 - 0.807241i) q^{6} +(2.33546 - 1.24323i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.08954 - 0.231589i) q^{9} +(-1.52648 + 1.63397i) q^{10} +(-1.24274 - 0.264153i) q^{11} +(1.34335 - 0.285538i) q^{12} +(2.12235 - 6.53193i) q^{13} +(-0.638824 + 2.56747i) q^{14} +(0.264873 + 3.05948i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.942895 + 0.419804i) q^{17} +(-0.556941 + 0.964650i) q^{18} +(-0.227918 + 2.16850i) q^{19} +(-0.192865 - 2.22773i) q^{20} +(2.03332 + 3.01138i) q^{21} +(1.02786 - 0.746783i) q^{22} +(0.670365 - 0.744516i) q^{23} +(-0.686680 + 1.18936i) q^{24} +(4.99663 + 0.183566i) q^{25} +(3.43404 + 5.94793i) q^{26} +(1.74590 + 5.37332i) q^{27} +(-1.48055 - 2.19271i) q^{28} +(-4.20837 + 3.05756i) q^{29} +(-2.45087 - 1.85035i) q^{30} +(-9.37236 + 4.17285i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.182387 - 1.73530i) q^{33} +(0.318945 - 0.981611i) q^{34} +(5.27240 - 2.68361i) q^{35} +(-0.344208 - 1.05936i) q^{36} +(-6.16968 + 1.31141i) q^{37} +(-1.45900 - 1.62039i) q^{38} +(9.22622 + 1.96109i) q^{39} +(1.78458 + 1.34732i) q^{40} +(-3.90343 + 12.0135i) q^{41} +(-3.59845 - 0.503955i) q^{42} +5.88162 q^{43} +(-0.132804 + 1.26354i) q^{44} +(2.44538 - 0.473032i) q^{45} +(0.104721 + 0.996356i) q^{46} +(-6.03949 - 2.68895i) q^{47} +(-0.424392 - 1.30614i) q^{48} +(3.90874 - 5.80705i) q^{49} +(-3.47981 + 3.59039i) q^{50} +(-0.708741 - 1.22758i) q^{51} +(-6.71799 - 1.42795i) q^{52} +(-0.817190 - 7.77504i) q^{53} +(-5.16139 - 2.29800i) q^{54} +(-2.76754 - 0.641582i) q^{55} +(2.62018 + 0.366950i) q^{56} -2.99453 q^{57} +(0.543739 - 5.17334i) q^{58} +(3.22894 + 3.58610i) q^{59} +(3.01504 - 0.583225i) q^{60} +(8.60114 - 9.55253i) q^{61} +(3.17031 - 9.75720i) q^{62} +(2.25666 - 1.89542i) q^{63} +(0.309017 + 0.951057i) q^{64} +(5.01308 - 14.5162i) q^{65} +(1.16754 + 1.29668i) q^{66} +(-9.36011 + 4.16739i) q^{67} +(0.516063 + 0.893848i) q^{68} +(1.11312 + 0.808730i) q^{69} +(-1.53362 + 5.71384i) q^{70} +(-2.35827 + 1.71338i) q^{71} +(1.01758 + 0.453056i) q^{72} +(0.455863 + 0.0968967i) q^{73} +(3.15376 - 5.46247i) q^{74} +(0.466571 + 6.85093i) q^{75} +2.18044 q^{76} +(-3.23077 + 0.928100i) q^{77} +(-7.63092 + 5.54419i) q^{78} +(-8.81268 - 3.92366i) q^{79} +(-2.19537 + 0.424670i) q^{80} +(-4.03570 + 1.79681i) q^{81} +(-6.31589 - 10.9394i) q^{82} +(10.5572 + 7.67025i) q^{83} +(2.78235 - 2.33696i) q^{84} +(-2.12526 + 0.899842i) q^{85} +(-3.93557 + 4.37090i) q^{86} +(-4.78026 - 5.30902i) q^{87} +(-0.850133 - 0.944168i) q^{88} +(5.95104 - 6.60929i) q^{89} +(-1.28475 + 2.13379i) q^{90} +(-3.16405 - 17.8936i) q^{91} +(-0.810509 - 0.588869i) q^{92} +(-7.04488 - 12.2021i) q^{93} +(6.03949 - 2.68895i) q^{94} +(-0.598580 + 4.83874i) q^{95} +(1.25463 + 0.558596i) q^{96} +(0.962506 - 0.699301i) q^{97} +(1.70002 + 6.79043i) q^{98} -1.41519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 9 q^{2} + q^{3} + 9 q^{4} + 2 q^{6} + 8 q^{7} + 18 q^{8} + 20 q^{9}+O(q^{10}) \) 72 * q - 9 * q^2 + q^3 + 9 * q^4 + 2 * q^6 + 8 * q^7 + 18 * q^8 + 20 * q^9	\( 72 q - 9 q^{2} + q^{3} + 9 q^{4} + 2 q^{6} + 8 q^{7} + 18 q^{8} + 20 q^{9} - 10 q^{10} - 12 q^{11} - 4 q^{12} - 8 q^{13} + 11 q^{14} + 16 q^{15} + 9 q^{16} - 30 q^{17} + 50 q^{18} + 2 q^{19} + 10 q^{20} - 20 q^{21} + 26 q^{22} - 10 q^{23} - 6 q^{24} - 8 q^{25} - 14 q^{26} + 46 q^{27} - 2 q^{28} - 10 q^{29} - 12 q^{30} + 9 q^{31} + 36 q^{32} - 13 q^{33} + 20 q^{34} + 6 q^{35} - 40 q^{36} + 11 q^{37} - 12 q^{38} - 27 q^{39} + 5 q^{40} - 34 q^{41} + 2 q^{42} - 32 q^{43} + 13 q^{44} - 7 q^{45} - 15 q^{46} + 8 q^{47} + 8 q^{48} + 64 q^{49} - 46 q^{50} - 86 q^{51} + 4 q^{52} - 33 q^{53} + 13 q^{54} - 38 q^{55} + 2 q^{56} - 108 q^{57} - 5 q^{58} - q^{59} + 2 q^{60} - 19 q^{61} - 22 q^{62} - 20 q^{63} - 18 q^{64} + 3 q^{65} + 8 q^{66} + 40 q^{68} + 64 q^{69} + 34 q^{70} - 10 q^{71} - 5 q^{72} - 14 q^{73} + 4 q^{74} - 16 q^{75} + 56 q^{76} - 70 q^{77} + 46 q^{78} + 2 q^{79} - 60 q^{81} + 28 q^{82} - 56 q^{83} - 28 q^{84} + 52 q^{85} + 19 q^{86} - 8 q^{87} + 12 q^{88} + 8 q^{89} - 164 q^{90} + 29 q^{91} - 30 q^{92} - 44 q^{93} - 8 q^{94} + 27 q^{95} - q^{96} + 14 q^{97} - 20 q^{98}+O(q^{100}) \) 72 * q - 9 * q^2 + q^3 + 9 * q^4 + 2 * q^6 + 8 * q^7 + 18 * q^8 + 20 * q^9 - 10 * q^10 - 12 * q^11 - 4 * q^12 - 8 * q^13 + 11 * q^14 + 16 * q^15 + 9 * q^16 - 30 * q^17 + 50 * q^18 + 2 * q^19 + 10 * q^20 - 20 * q^21 + 26 * q^22 - 10 * q^23 - 6 * q^24 - 8 * q^25 - 14 * q^26 + 46 * q^27 - 2 * q^28 - 10 * q^29 - 12 * q^30 + 9 * q^31 + 36 * q^32 - 13 * q^33 + 20 * q^34 + 6 * q^35 - 40 * q^36 + 11 * q^37 - 12 * q^38 - 27 * q^39 + 5 * q^40 - 34 * q^41 + 2 * q^42 - 32 * q^43 + 13 * q^44 - 7 * q^45 - 15 * q^46 + 8 * q^47 + 8 * q^48 + 64 * q^49 - 46 * q^50 - 86 * q^51 + 4 * q^52 - 33 * q^53 + 13 * q^54 - 38 * q^55 + 2 * q^56 - 108 * q^57 - 5 * q^58 - q^59 + 2 * q^60 - 19 * q^61 - 22 * q^62 - 20 * q^63 - 18 * q^64 + 3 * q^65 + 8 * q^66 + 40 * q^68 + 64 * q^69 + 34 * q^70 - 10 * q^71 - 5 * q^72 - 14 * q^73 + 4 * q^74 - 16 * q^75 + 56 * q^76 - 70 * q^77 + 46 * q^78 + 2 * q^79 - 60 * q^81 + 28 * q^82 - 56 * q^83 - 28 * q^84 + 52 * q^85 + 19 * q^86 - 8 * q^87 + 12 * q^88 + 8 * q^89 - 164 * q^90 + 29 * q^91 - 30 * q^92 - 44 * q^93 - 8 * q^94 + 27 * q^95 - q^96 + 14 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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