LMFDB - Embedded newform 231.2.y.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	231.16
Dual form			231.2.y.a.130.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.957375 - 0.203496i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.951935 - 0.423829i) q^{4} +(2.18684 + 2.42873i) q^{5} +(-0.302455 + 0.930859i) q^{6} +(-0.413889 + 2.61318i) q^{7} +(2.40878 + 1.75008i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.957375 - 0.203496i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.951935 - 0.423829i) q^{4} +(2.18684 + 2.42873i) q^{5} +(-0.302455 + 0.930859i) q^{6} +(-0.413889 + 2.61318i) q^{7} +(2.40878 + 1.75008i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-1.59938 - 2.77022i) q^{10} +(-2.36814 - 2.32205i) q^{11} +(-0.521011 + 0.902418i) q^{12} +(1.80041 + 5.54110i) q^{13} +(0.928019 - 2.41757i) q^{14} +(2.64401 - 1.92098i) q^{15} +(-0.555475 - 0.616918i) q^{16} +(7.61127 - 1.61783i) q^{17} +(0.894145 + 0.398099i) q^{18} +(1.52028 - 0.676874i) q^{19} +(-1.05236 - 3.23883i) q^{20} +(2.55560 + 0.684773i) q^{21} +(1.79467 + 2.70498i) q^{22} +(-0.496102 + 0.859274i) q^{23} +(1.99228 - 2.21265i) q^{24} +(-0.593822 + 5.64984i) q^{25} +(-0.596076 - 5.67129i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50153 - 2.31216i) q^{28} +(3.42038 - 2.48505i) q^{29} +(-2.92222 + 1.30106i) q^{30} +(-5.41160 + 6.01019i) q^{31} +(-2.57116 - 4.45338i) q^{32} +(-2.55686 + 2.11245i) q^{33} -7.61606 q^{34} +(-7.25180 + 4.70937i) q^{35} +(0.843014 + 0.612485i) q^{36} +(-0.148708 - 1.41487i) q^{37} +(-1.59322 + 0.338650i) q^{38} +(5.69894 - 1.21135i) q^{39} +(1.01714 + 9.67742i) q^{40} +(-1.56148 - 1.13448i) q^{41} +(-2.30732 - 1.17564i) q^{42} -1.62091 q^{43} +(1.27017 + 3.21412i) q^{44} +(-1.63409 - 2.83032i) q^{45} +(0.649815 - 0.721693i) q^{46} +(3.11813 - 1.38828i) q^{47} +(-0.671601 + 0.487947i) q^{48} +(-6.65739 - 2.16313i) q^{49} +(1.71823 - 5.28818i) q^{50} +(-0.813368 - 7.73868i) q^{51} +(0.634602 - 6.03783i) q^{52} +(-1.56601 + 1.73923i) q^{53} +(0.489382 - 0.847634i) q^{54} +(0.460880 - 10.8295i) q^{55} +(-5.57025 + 5.57024i) q^{56} +(-0.514253 - 1.58271i) q^{57} +(-3.78029 + 1.68309i) q^{58} +(-0.641951 - 0.285815i) q^{59} +(-3.33109 + 0.708045i) q^{60} +(1.42053 + 1.57766i) q^{61} +(6.40399 - 4.65277i) q^{62} +(0.948155 - 2.47002i) q^{63} +(2.06838 + 6.36581i) q^{64} +(-9.52061 + 16.4902i) q^{65} +(2.87775 - 1.50209i) q^{66} +(-5.44002 - 9.42239i) q^{67} +(-7.93111 - 1.68581i) q^{68} +(0.802710 + 0.583203i) q^{69} +(7.90103 - 3.03291i) q^{70} +(-2.16721 + 6.66998i) q^{71} +(-1.99228 - 2.21265i) q^{72} +(-6.02383 - 2.68198i) q^{73} +(-0.145550 + 1.38482i) q^{74} +(5.55682 + 1.18114i) q^{75} -1.73409 q^{76} +(7.04807 - 5.22731i) q^{77} -5.70253 q^{78} +(8.29474 + 1.76310i) q^{79} +(0.283592 - 2.69820i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.26406 + 1.40388i) q^{82} +(-0.840730 + 2.58750i) q^{83} +(-2.14254 - 1.73500i) q^{84} +(20.5738 + 14.9478i) q^{85} +(1.55182 + 0.329849i) q^{86} +(-2.11391 - 3.66140i) q^{87} +(-1.64057 - 9.73775i) q^{88} +(7.28991 - 12.6265i) q^{89} +(0.988474 + 3.04221i) q^{90} +(-15.2250 + 2.41140i) q^{91} +(0.836442 - 0.607711i) q^{92} +(5.41160 + 6.01019i) q^{93} +(-3.26773 + 0.694577i) q^{94} +(4.96855 + 2.21214i) q^{95} +(-4.69775 + 2.09157i) q^{96} +(-4.78740 - 14.7341i) q^{97} +(5.93343 + 3.42568i) q^{98} +(1.83361 + 2.76367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.957375	−	0.203496i	−0.676966	−	0.143894i	−0.143417	−	0.989662i	$-0.545809\pi$
$2$	−0.957375	−	0.203496i	−0.676966	−	0.143894i	−0.533550	+	0.845769i	$0.679142\pi$
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	−0.951935	−	0.423829i	−0.475967	−	0.211914i
$5$	2.18684	+	2.42873i	0.977982	+	1.08616i	0.996267	+	0.0863267i	$0.0275129\pi$
$5$	2.18684	+	2.42873i	0.977982	+	1.08616i	−0.0182844	+	0.999833i	$0.505820\pi$
$6$	−0.302455	+	0.930859i	−0.123477	+	0.380022i
$7$	−0.413889	+	2.61318i	−0.156435	+	0.987688i
$7$	−0.413889	+	2.61318i	−0.156435	+	0.987688i
$8$	2.40878	+	1.75008i	0.851634	+	0.618748i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−1.59938	−	2.77022i	−0.505770	−	0.876019i
$11$	−2.36814	−	2.32205i	−0.714022	−	0.700123i
$11$	−2.36814	−	2.32205i	−0.714022	−	0.700123i
$12$	−0.521011	+	0.902418i	−0.150403	+	0.260506i
$13$	1.80041	+	5.54110i	0.499345	+	1.53682i	0.810075	+	0.586327i	$0.199426\pi$
$13$	1.80041	+	5.54110i	0.499345	+	1.53682i	−0.310730	+	0.950498i	$0.600574\pi$
$14$	0.928019	−	2.41757i	0.248024	−	0.646122i
$15$	2.64401	−	1.92098i	0.682680	−	0.495996i
$16$	−0.555475	−	0.616918i	−0.138869	−	0.154229i
$17$	7.61127	−	1.61783i	1.84600	−	0.392380i	0.854178	−	0.519980i	$-0.174061\pi$
$17$	7.61127	−	1.61783i	1.84600	−	0.392380i	0.991826	+	0.127600i	$0.0407274\pi$
$18$	0.894145	+	0.398099i	0.210752	+	0.0938328i
$19$	1.52028	−	0.676874i	0.348777	−	0.155285i	−0.224869	−	0.974389i	$-0.572195\pi$
$19$	1.52028	−	0.676874i	0.348777	−	0.155285i	0.573646	+	0.819104i	$0.305529\pi$
$20$	−1.05236	−	3.23883i	−0.235315	−	0.724225i
$21$	2.55560	+	0.684773i	0.557677	+	0.149430i
$22$	1.79467	+	2.70498i	0.382625	+	0.576703i
$23$	−0.496102	+	0.859274i	−0.103444	+	0.179171i	−0.913102	−	0.407732i	$-0.866320\pi$
$23$	−0.496102	+	0.859274i	−0.103444	+	0.179171i	0.809657	+	0.586903i	$0.199653\pi$
$24$	1.99228	−	2.21265i	0.406673	−	0.451656i
$25$	−0.593822	+	5.64984i	−0.118764	+	1.12997i
$26$	−0.596076	−	5.67129i	−0.116900	−	1.11223i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.50153	−	2.31216i	0.283763	−	0.436956i
$29$	3.42038	−	2.48505i	0.635149	−	0.461462i	−0.223031	−	0.974811i	$-0.571595\pi$
$29$	3.42038	−	2.48505i	0.635149	−	0.461462i	0.858180	+	0.513349i	$0.171595\pi$
$30$	−2.92222	+	1.30106i	−0.533522	+	0.237539i
$31$	−5.41160	+	6.01019i	−0.971953	+	1.07946i	0.0248606	+	0.999691i	$0.492086\pi$
$31$	−5.41160	+	6.01019i	−0.971953	+	1.07946i	−0.996813	+	0.0797717i	$0.974581\pi$
$32$	−2.57116	−	4.45338i	−0.454522	−	0.787254i
$33$	−2.55686	+	2.11245i	−0.445093	+	0.367730i
$34$	−7.61606			−1.30614
$35$	−7.25180	+	4.70937i	−1.22578	+	0.796028i
$36$	0.843014	+	0.612485i	0.140502	+	0.102081i
$37$	−0.148708	−	1.41487i	−0.0244475	−	0.232603i	−0.999922	−	0.0124900i	$-0.996024\pi$
$37$	−0.148708	−	1.41487i	−0.0244475	−	0.232603i	0.975474	−	0.220113i	$-0.0706425\pi$
$38$	−1.59322	+	0.338650i	−0.258455	+	0.0549363i
$39$	5.69894	−	1.21135i	0.912561	−	0.193971i
$40$	1.01714	+	9.67742i	0.160824	+	1.53013i
$41$	−1.56148	−	1.13448i	−0.243862	−	0.177176i	0.459140	−	0.888364i	$-0.348158\pi$
$41$	−1.56148	−	1.13448i	−0.243862	−	0.177176i	−0.703002	+	0.711188i	$0.748158\pi$
$42$	−2.30732	−	1.17564i	−0.356027	−	0.181405i
$43$	−1.62091			−0.247186			−0.123593	−	0.992333i	$-0.539442\pi$
$43$	−1.62091			−0.247186			−0.123593	+	0.992333i	$0.539442\pi$
$44$	1.27017	+	3.21412i	0.191485	+	0.484547i
$45$	−1.63409	−	2.83032i	−0.243595	−	0.421919i
$46$	0.649815	−	0.721693i	0.0958100	−	0.106408i
$47$	3.11813	−	1.38828i	0.454826	−	0.202501i	−0.166520	−	0.986038i	$-0.553253\pi$
$47$	3.11813	−	1.38828i	0.454826	−	0.202501i	0.621345	+	0.783537i	$0.286586\pi$
$48$	−0.671601	+	0.487947i	−0.0969373	+	0.0704291i
$49$	−6.65739	−	2.16313i	−0.951056	−	0.309019i
$50$	1.71823	−	5.28818i	0.242995	−	0.747861i
$51$	−0.813368	−	7.73868i	−0.113894	−	1.08363i
$52$	0.634602	−	6.03783i	0.0880034	−	0.837297i
$53$	−1.56601	+	1.73923i	−0.215108	+	0.238901i	−0.841036	−	0.540979i	$-0.818054\pi$
$53$	−1.56601	+	1.73923i	−0.215108	+	0.238901i	0.625928	+	0.779881i	$0.284720\pi$
$54$	0.489382	−	0.847634i	0.0665964	−	0.115348i
$55$	0.460880	−	10.8295i	0.0621450	−	1.46025i
$56$	−5.57025	+	5.57024i	−0.744356	+	0.744354i
$57$	−0.514253	−	1.58271i	−0.0681144	−	0.209635i
$58$	−3.78029	+	1.68309i	−0.496376	+	0.221001i
$59$	−0.641951	−	0.285815i	−0.0835749	−	0.0372099i	0.364523	−	0.931194i	$-0.381232\pi$
$59$	−0.641951	−	0.285815i	−0.0835749	−	0.0372099i	−0.448098	+	0.893984i	$0.647899\pi$
$60$	−3.33109	+	0.708045i	−0.430042	+	0.0914083i
$61$	1.42053	+	1.57766i	0.181881	+	0.201999i	0.827190	−	0.561923i	$-0.189938\pi$
$61$	1.42053	+	1.57766i	0.181881	+	0.201999i	−0.645309	+	0.763921i	$0.723271\pi$
$62$	6.40399	−	4.65277i	0.813307	−	0.590902i
$63$	0.948155	−	2.47002i	0.119456	−	0.311193i
$64$	2.06838	+	6.36581i	0.258547	+	0.795726i
$65$	−9.52061	+	16.4902i	−1.18089	+	2.04536i
$66$	2.87775	−	1.50209i	0.354227	−	0.184895i
$67$	−5.44002	−	9.42239i	−0.664604	−	1.15113i	−0.979393	−	0.201966i	$-0.935267\pi$
$67$	−5.44002	−	9.42239i	−0.664604	−	1.15113i	0.314789	−	0.949162i	$-0.398066\pi$
$68$	−7.93111	−	1.68581i	−0.961789	−	0.204434i
$69$	0.802710	+	0.583203i	0.0966350	+	0.0702094i
$70$	7.90103	−	3.03291i	0.944354	−	0.362503i
$71$	−2.16721	+	6.66998i	−0.257200	+	0.791581i	0.736188	+	0.676777i	$0.236624\pi$
$71$	−2.16721	+	6.66998i	−0.257200	+	0.791581i	−0.993388	+	0.114804i	$0.963376\pi$
$72$	−1.99228	−	2.21265i	−0.234793	−	0.260764i
$73$	−6.02383	−	2.68198i	−0.705037	−	0.313902i	0.0227163	−	0.999742i	$-0.492769\pi$
$73$	−6.02383	−	2.68198i	−0.705037	−	0.313902i	−0.727753	+	0.685839i	$0.759435\pi$
$74$	−0.145550	+	1.38482i	−0.0169199	+	0.160982i
$75$	5.55682	+	1.18114i	0.641646	+	0.136386i
$76$	−1.73409			−0.198914
$77$	7.04807	−	5.22731i	0.803202	−	0.595707i
$78$	−5.70253			−0.645684
$79$	8.29474	+	1.76310i	0.933232	+	0.198365i	0.649346	−	0.760493i	$-0.275043\pi$
$79$	8.29474	+	1.76310i	0.933232	+	0.198365i	0.283886	+	0.958858i	$0.408376\pi$
$80$	0.283592	−	2.69820i	0.0317065	−	0.301667i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	1.26406	+	1.40388i	0.139592	+	0.155033i
$83$	−0.840730	+	2.58750i	−0.0922821	+	0.284015i	−0.986536	−	0.163545i	$-0.947707\pi$
$83$	−0.840730	+	2.58750i	−0.0922821	+	0.284015i	0.894254	+	0.447560i	$0.147707\pi$
$84$	−2.14254	−	1.73500i	−0.233770	−	0.189304i
$85$	20.5738	+	14.9478i	2.23155	+	1.62131i
$86$	1.55182	+	0.329849i	0.167337	+	0.0355685i
$87$	−2.11391	−	3.66140i	−0.226635	−	0.392543i
$88$	−1.64057	−	9.73775i	−0.174885	−	1.03805i
$89$	7.28991	−	12.6265i	0.772729	−	1.33841i	−0.163333	−	0.986571i	$-0.552224\pi$
$89$	7.28991	−	12.6265i	0.772729	−	1.33841i	0.936062	−	0.351835i	$-0.114442\pi$
$90$	0.988474	+	3.04221i	0.104194	+	0.320677i
$91$	−15.2250	+	2.41140i	−1.59602	+	0.252783i
$92$	0.836442	−	0.607711i	0.0872051	−	0.0633582i
$93$	5.41160	+	6.01019i	0.561157	+	0.623228i
$94$	−3.26773	+	0.694577i	−0.337040	+	0.0716401i
$95$	4.96855	+	2.21214i	0.509762	+	0.226961i
$96$	−4.69775	+	2.09157i	−0.479462	+	0.213470i
$97$	−4.78740	−	14.7341i	−0.486087	−	1.49602i	−0.830401	−	0.557167i	$-0.811888\pi$
$97$	−4.78740	−	14.7341i	−0.486087	−	1.49602i	0.344314	−	0.938855i	$-0.388112\pi$
$98$	5.93343	+	3.42568i	0.599367	+	0.346046i
$99$	1.83361	+	2.76367i	0.184285	+	0.277759i
$100$	2.95984	−	5.12660i	0.295984	−	0.512660i
$101$	1.92145	−	2.13399i	0.191192	−	0.212340i	−0.639926	−	0.768437i	$-0.721035\pi$
$101$	1.92145	−	2.13399i	0.191192	−	0.212340i	0.831118	+	0.556097i	$0.187702\pi$
$102$	−0.796095	+	7.57434i	−0.0788252	+	0.749971i
$103$	−0.734402	−	6.98737i	−0.0723628	−	0.688486i	−0.969225	−	0.246176i	$-0.920826\pi$
$103$	−0.734402	−	6.98737i	−0.0723628	−	0.688486i	0.896862	−	0.442310i	$-0.145841\pi$
$104$	−5.36058	+	16.4982i	−0.525649	+	1.61778i
$105$	3.92555	+	7.70434i	0.383094	+	0.751866i
$106$	1.85318	−	1.34642i	0.179997	−	0.130776i
$107$	2.38273	−	1.06086i	0.230347	−	0.102557i	−0.288318	−	0.957535i	$-0.593096\pi$
$107$	2.38273	−	1.06086i	0.230347	−	0.102557i	0.518665	+	0.854978i	$0.326429\pi$
$108$	0.697249	−	0.774373i	0.0670928	−	0.0745141i
$109$	6.05096	+	10.4806i	0.579577	+	1.00386i	0.995528	+	0.0944699i	$0.0301156\pi$
$109$	6.05096	+	10.4806i	0.579577	+	1.00386i	−0.415951	+	0.909387i	$0.636551\pi$
$110$	−2.64500	+	10.2741i	−0.252191	+	0.979598i
$111$	−1.42266			−0.135033
$112$	1.84202	−	1.19622i	0.174055	−	0.113032i
$113$	−4.04177	−	2.93651i	−0.380217	−	0.276244i	0.381218	−	0.924485i	$-0.375505\pi$
$113$	−4.04177	−	2.93651i	−0.380217	−	0.276244i	−0.761435	+	0.648241i	$0.775505\pi$
$114$	0.170258	+	1.61989i	0.0159461	+	0.151717i
$115$	−3.17184	+	0.674195i	−0.295775	+	0.0628690i
$116$	−4.30921	+	0.915952i	−0.400101	+	0.0850440i
$117$	−0.609010	−	5.79434i	−0.0563030	−	0.535687i
$118$	0.556425	+	0.404267i	0.0512231	+	0.0372158i
$119$	1.07744	+	20.5592i	0.0987691	+	1.88466i
$120$	9.73073			0.888290
$121$	0.216197	+	10.9979i	0.0196542	+	0.999807i
$122$	−1.03893	−	1.79949i	−0.0940607	−	0.162918i
$123$	−1.29149	+	1.43434i	−0.116449	+	0.129330i
$124$	7.69878	−	3.42772i	0.691371	−	0.307818i
$125$	−1.80047	+	1.30812i	−0.161039	+	0.117001i
$126$	−1.41038	+	2.17179i	−0.125647	+	0.193478i
$127$	4.34065	−	13.3591i	0.385170	−	1.18543i	−0.551186	−	0.834382i	$-0.685825\pi$
$127$	4.34065	−	13.3591i	0.385170	−	1.18543i	0.936357	−	0.351050i	$-0.114175\pi$
$128$	0.390245	+	3.71293i	0.0344931	+	0.328180i
$129$	−0.169431	+	1.61203i	−0.0149176	+	0.141931i
$130$	12.4705	−	13.8499i	1.09373	−	1.21471i
$131$	11.0583	−	19.1535i	0.966168	−	1.67345i	0.259723	−	0.965683i	$-0.416369\pi$
$131$	11.0583	−	19.1535i	0.966168	−	1.67345i	0.706445	−	0.707768i	$-0.250298\pi$
$132$	3.32928	−	0.927241i	0.289777	−	0.0807060i
$133$	1.13956	+	4.25292i	0.0988126	+	0.368775i
$134$	3.29072	+	10.1278i	0.284275	+	0.874907i
$135$	−2.98563	+	1.32929i	−0.256962	+	0.114407i
$136$	21.1652	+	9.42337i	1.81490	+	0.808047i
$137$	4.87333	−	1.03586i	0.416357	−	0.0884993i	0.00502994	−	0.999987i	$-0.498399\pi$
$137$	4.87333	−	1.03586i	0.416357	−	0.0884993i	0.411327	+	0.911488i	$0.365066\pi$
$138$	−0.649815	−	0.721693i	−0.0553159	−	0.0614346i
$139$	−3.08225	+	2.23938i	−0.261433	+	0.189942i	−0.710778	−	0.703416i	$-0.751657\pi$
$139$	−3.08225	+	2.23938i	−0.261433	+	0.189942i	0.449346	+	0.893358i	$0.351657\pi$
$140$	8.89920	−	1.40949i	0.752120	−	0.119123i
$141$	−1.05474	−	3.24616i	−0.0888252	−	0.273376i
$142$	3.43215	−	5.94465i	0.288019	−	0.498864i
$143$	8.60306	−	17.3028i	0.719424	−	1.44693i
$144$	0.415072	+	0.718927i	0.0345894	+	0.0599106i
$145$	13.5153	+	2.87277i	1.12239	+	0.238571i
$146$	5.22129	+	3.79349i	0.432117	+	0.313952i
$147$	−2.84717	+	6.39481i	−0.234830	+	0.527435i
$148$	−0.458100	+	1.40989i	−0.0376556	+	0.115892i
$149$	−10.8478	−	12.0477i	−0.888686	−	0.986986i	0.111291	−	0.993788i	$-0.464501\pi$
$149$	−10.8478	−	12.0477i	−0.888686	−	0.986986i	−0.999977	+	0.00680204i	$0.997835\pi$
$150$	−5.07960	−	2.26158i	−0.414748	−	0.184658i
$151$	−1.52291	+	14.4895i	−0.123933	+	1.17914i	0.738959	+	0.673751i	$0.235318\pi$
$151$	−1.52291	+	14.4895i	−0.123933	+	1.17914i	−0.862891	+	0.505390i	$0.831349\pi$
$152$	4.84662	+	1.03018i	0.393113	+	0.0835587i
$153$	−7.78131			−0.629082
$154$	−7.81138	+	3.57024i	−0.629459	+	0.287698i
$155$	−26.4314			−2.12302
$156$	−5.93842	−	1.26225i	−0.475454	−	0.101061i
$157$	−0.566398	+	5.38892i	−0.0452035	+	0.430082i	0.948393	+	0.317097i	$0.102708\pi$
$157$	−0.566398	+	5.38892i	−0.0452035	+	0.430082i	−0.993597	+	0.112986i	$0.963959\pi$
$158$	−7.58240	−	3.37590i	−0.603223	−	0.268572i
$159$	1.56601	+	1.73923i	0.124193	+	0.137930i
$160$	5.19334	−	15.9835i	0.410570	−	1.26360i
$161$	−2.04011	−	1.65205i	−0.160783	−	0.130200i
$162$	−0.791836	−	0.575303i	−0.0622125	−	0.0452000i
$163$	6.04274	+	1.28442i	0.473304	+	0.100604i	0.438387	−	0.898786i	$-0.355550\pi$
$163$	6.04274	+	1.28442i	0.473304	+	0.100604i	0.0349171	+	0.999390i	$0.488883\pi$
$164$	1.00560	+	1.74175i	0.0785244	+	0.136008i
$165$	−10.7220	−	1.59035i	−0.834707	−	0.123808i
$166$	1.33144	−	2.30612i	0.103340	−	0.178990i
$167$	0.811604	+	2.49786i	0.0628038	+	0.193290i	0.977535	−	0.210772i	$-0.0675978\pi$
$167$	0.811604	+	2.49786i	0.0628038	+	0.193290i	−0.914731	+	0.404063i	$0.867598\pi$
$168$	4.95747	+	6.12198i	0.382477	+	0.472321i
$169$	−16.9451	+	12.3113i	−1.30347	+	0.947025i
$170$	−16.6551	−	18.4973i	−1.27739	−	1.41868i
$171$	−1.62779	+	0.345998i	−0.124480	+	0.0264591i
$172$	1.54300	+	0.686987i	0.117652	+	0.0523822i
$173$	−12.2386	+	5.44897i	−0.930483	+	0.414278i	−0.815282	−	0.579065i	$-0.803418\pi$
$173$	−12.2386	+	5.44897i	−0.930483	+	0.414278i	−0.115201	+	0.993342i	$0.536751\pi$
$174$	1.27872	+	3.93551i	0.0969398	+	0.298350i
$175$	−14.5183	−	3.89017i	−1.09748	−	0.294069i
$176$	−0.117068	+	2.75079i	−0.00882430	+	0.207349i
$177$	−0.351351	+	0.608558i	−0.0264092	+	0.0457421i
$178$	−9.54863	+	10.6048i	−0.715700	+	0.794865i
$179$	1.98257	−	18.8629i	0.148184	−	1.40988i	−0.627430	−	0.778673i	$-0.715893\pi$
$179$	1.98257	−	18.8629i	0.148184	−	1.40988i	0.775614	−	0.631207i	$-0.217440\pi$
$180$	0.355973	+	3.38685i	0.0265326	+	0.252441i
$181$	3.33476	−	10.2633i	0.247871	−	0.762867i	−0.747280	−	0.664509i	$-0.768641\pi$
$181$	3.33476	−	10.2633i	0.247871	−	0.762867i	0.995151	−	0.0983584i	$-0.0313592\pi$
$182$	15.0668	+	0.789630i	1.11682	+	0.0585313i
$183$	1.71751	−	1.24784i	0.126962	−	0.0922430i
$184$	−2.69880	+	1.20159i	−0.198959	+	0.0885820i
$185$	3.11112	−	3.45525i	0.228734	−	0.254035i
$186$	−3.95788	−	6.85525i	−0.290206	−	0.502651i
$187$	−21.7812	−	13.8425i	−1.59280	−	1.01226i
$188$	−3.55665			−0.259395
$189$	−2.35738	−	1.20115i	−0.171474	−	0.0873707i
$190$	−4.30660	−	3.12893i	−0.312434	−	0.226996i
$191$	−0.864224	−	8.22255i	−0.0625331	−	0.594963i	−0.980255	−	0.197739i	$-0.936640\pi$
$191$	−0.864224	−	8.22255i	−0.0625331	−	0.594963i	0.917722	−	0.397224i	$-0.130026\pi$
$192$	6.54714	−	1.39164i	0.472499	−	0.100433i
$193$	13.4017	−	2.84862i	0.964676	−	0.205048i	0.301462	−	0.953478i	$-0.402525\pi$
$193$	13.4017	−	2.84862i	0.964676	−	0.205048i	0.663214	+	0.748430i	$0.269192\pi$
$194$	1.58500	+	15.0803i	0.113796	+	1.08270i
$195$	15.4047	+	11.1922i	1.10315	+	0.801487i
$196$	5.42061	+	4.88075i	0.387186	+	0.348625i
$197$	−3.57341			−0.254595			−0.127297	−	0.991865i	$-0.540630\pi$
$197$	−3.57341			−0.254595			−0.127297	+	0.991865i	$0.540630\pi$
$198$	−1.19306	−	3.01900i	−0.0847869	−	0.214551i
$199$	−11.1559	−	19.3226i	−0.790821	−	1.36974i	−0.925459	−	0.378848i	$-0.876320\pi$
$199$	−11.1559	−	19.3226i	−0.790821	−	1.36974i	0.134637	−	0.990895i	$-0.457013\pi$
$200$	−11.3181	+	12.5700i	−0.800309	+	0.888833i
$201$	−9.93941	+	4.42531i	−0.701072	+	0.312137i
$202$	−2.27381	+	1.65202i	−0.159985	+	0.116236i
$203$	5.07822	+	9.96659i	0.356421	+	0.699518i
$204$	−2.50560	+	7.71145i	−0.175427	+	0.539909i
$205$	−0.659355	−	6.27334i	−0.0460513	−	0.438149i
$206$	−0.718806	+	6.83898i	−0.0500816	+	0.476495i
$207$	0.663914	−	0.737352i	0.0461452	−	0.0512495i
$208$	2.41832	−	4.18865i	0.167680	−	0.290431i
$209$	−5.17198	−	1.92724i	−0.357753	−	0.133310i
$210$	−2.19042	−	8.17477i	−0.151153	−	0.564113i
$211$	−5.18329	−	15.9525i	−0.356832	−	1.09822i	−0.954940	−	0.296800i	$-0.904080\pi$
$211$	−5.18329	−	15.9525i	−0.356832	−	1.09822i	0.598107	−	0.801416i	$-0.295920\pi$
$212$	2.22787	−	0.991912i	0.153011	−	0.0681248i
$213$	6.40690	+	2.85254i	0.438994	+	0.195453i
$214$	−2.49705	+	0.530764i	−0.170695	+	0.0362823i
$215$	−3.54466	−	3.93674i	−0.241743	−	0.268483i
$216$	−2.40878	+	1.75008i	−0.163897	+	0.119078i
$217$	−13.4659	−	16.6290i	−0.914125	−	1.12885i
$218$	−3.66028	−	11.2652i	−0.247906	−	0.762975i
$219$	−3.29695	+	5.71049i	−0.222788	+	0.385879i
$220$	−5.02858	+	10.1136i	−0.339027	+	0.681862i
$221$	22.6680	+	39.2621i	1.52481	+	2.64105i
$222$	1.36202	+	0.289506i	0.0914127	+	0.0194304i
$223$	18.3982	+	13.3670i	1.23203	+	0.895124i	0.997041	−	0.0768739i	$-0.0244939\pi$
$223$	18.3982	+	13.3670i	1.23203	+	0.895124i	0.234991	+	0.971998i	$0.424494\pi$
$224$	12.7017	−	4.87570i	0.848665	−	0.325771i
$225$	1.75551	−	5.40292i	0.117034	−	0.360194i
$226$	3.27192	+	3.63383i	0.217645	+	0.241719i
$227$	14.5193	+	6.46439i	0.963677	+	0.429056i	0.827399	−	0.561614i	$-0.189820\pi$
$227$	14.5193	+	6.46439i	0.963677	+	0.429056i	0.136277	+	0.990671i	$0.456486\pi$
$228$	−0.181262	+	1.72459i	−0.0120043	+	0.114214i
$229$	−27.2349	−	5.78895i	−1.79973	−	0.382545i	−0.818366	−	0.574698i	$-0.805120\pi$
$229$	−27.2349	−	5.78895i	−1.79973	−	0.382545i	−0.981365	+	0.192153i	$0.938453\pi$
$230$	3.17383			0.209276
$231$	−4.46195	−	7.55586i	−0.293575	−	0.497139i
$232$	12.5880			0.826443
$233$	−8.16481	−	1.73548i	−0.534895	−	0.113695i	−0.0674583	−	0.997722i	$-0.521489\pi$
$233$	−8.16481	−	1.73548i	−0.534895	−	0.113695i	−0.467436	+	0.884027i	$0.654822\pi$
$234$	−0.596076	+	5.67129i	−0.0389667	+	0.370744i
$235$	10.1906	+	4.53714i	0.664760	+	0.295970i
$236$	0.489959	+	0.544154i	0.0318936	+	0.0354214i
$237$	2.62048	−	8.06501i	0.170219	−	0.523879i
$238$	3.15220	−	19.9021i	0.204327	−	1.29006i
$239$	4.70883	+	3.42117i	0.304589	+	0.221297i	0.729571	−	0.683905i	$-0.239720\pi$
$239$	4.70883	+	3.42117i	0.304589	+	0.221297i	−0.424982	+	0.905202i	$0.639720\pi$
$240$	−2.65377	−	0.564077i	−0.171300	−	0.0364110i
$241$	8.79813	+	15.2388i	0.566737	+	0.981618i	0.996886	+	0.0788595i	$0.0251279\pi$
$241$	8.79813	+	15.2388i	0.566737	+	0.981618i	−0.430149	+	0.902758i	$0.641539\pi$
$242$	2.03105	−	10.5731i	0.130561	−	0.679664i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.683596	−	2.10389i	−0.0437628	−	0.134688i
$245$	−9.30497	−	20.8994i	−0.594473	−	1.33521i
$246$	1.52832	−	1.11039i	0.0974422	−	0.0707959i
$247$	6.48776	+	7.20539i	0.412806	+	0.458468i
$248$	−23.5537	+	5.00650i	−1.49566	+	0.317913i
$249$	2.48545	+	1.10659i	0.157509	+	0.0701274i
$250$	1.98992	−	0.885969i	0.125854	−	0.0560336i
$251$	2.55627	+	7.86739i	0.161350	+	0.496585i	0.998749	−	0.0500075i	$-0.0159245\pi$
$251$	2.55627	+	7.86739i	0.161350	+	0.496585i	−0.837398	+	0.546593i	$0.815925\pi$
$252$	−1.94945	+	1.94944i	−0.122804	+	0.122803i
$253$	3.17012	−	0.882911i	0.199303	−	0.0555082i
$254$	−6.87417	+	11.9064i	−0.431324	+	0.747075i
$255$	17.0164	−	18.8987i	1.06561	−	1.18348i
$256$	1.78126	−	16.9476i	0.111329	−	1.05922i
$257$	−0.130470	−	1.24134i	−0.00813851	−	0.0774327i	0.989699	−	0.143166i	$-0.0457281\pi$
$257$	−0.130470	−	1.24134i	−0.00813851	−	0.0774327i	−0.997837	+	0.0657329i	$0.979061\pi$
$258$	0.490250	−	1.50884i	0.0305217	−	0.0939360i
$259$	3.75884	+	0.196996i	0.233563	+	0.0122407i
$260$	16.0520	−	11.6625i	0.995504	−	0.723276i
$261$	−3.86231	+	1.71961i	−0.239071	+	0.106441i
$262$	−14.4846	+	16.0868i	−0.894862	+	0.993845i
$263$	−2.76257	−	4.78491i	−0.170347	−	0.295050i	0.768194	−	0.640217i	$-0.221156\pi$
$263$	−2.76257	−	4.78491i	−0.170347	−	0.295050i	−0.938541	+	0.345167i	$0.887822\pi$
$264$	−9.85590	+	0.613706i	−0.606588	+	0.0377710i
$265$	−7.64871			−0.469857
$266$	−0.225535	−	4.30354i	−0.0138284	−	0.263867i
$267$	−11.7953	−	8.56981i	−0.721862	−	0.524464i
$268$	1.18506	+	11.2751i	0.0723893	+	0.688738i
$269$	−16.3888	+	3.48354i	−0.999242	+	0.212395i	−0.678365	−	0.734725i	$-0.737311\pi$
$269$	−16.3888	+	3.48354i	−0.999242	+	0.212395i	−0.320877	+	0.947121i	$0.603978\pi$
$270$	3.12887	−	0.665061i	0.190417	−	0.0404744i
$271$	1.95529	+	18.6033i	0.118775	+	1.13007i	0.877806	+	0.479016i	$0.159007\pi$
$271$	1.95529	+	18.6033i	0.118775	+	1.13007i	−0.759031	+	0.651055i	$0.774327\pi$
$272$	−5.22594	−	3.79687i	−0.316869	−	0.230219i
$273$	0.806736	+	15.3937i	0.0488259	+	0.931669i
$274$	−4.87640			−0.294594
$275$	14.5255	−	12.0007i	0.875918	−	0.723672i
$276$	−0.516950	−	0.895383i	−0.0311167	−	0.0538957i
$277$	−0.470638	+	0.522696i	−0.0282779	+	0.0314058i	−0.757118	−	0.653278i	$-0.773393\pi$
$277$	−0.470638	+	0.522696i	−0.0282779	+	0.0314058i	0.728840	+	0.684684i	$0.240060\pi$
$278$	3.40657	−	1.51670i	0.204313	−	0.0909659i
$279$	6.54294	−	4.75372i	0.391715	−	0.284598i
$280$	−25.7098	−	1.34742i	−1.53645	−	0.0805235i
$281$	−7.73488	+	23.8055i	−0.461425	+	1.42012i	0.402000	+	0.915640i	$0.368315\pi$
$281$	−7.73488	+	23.8055i	−0.461425	+	1.42012i	−0.863424	+	0.504479i	$0.831685\pi$
$282$	0.349201	+	3.32243i	0.0207946	+	0.197848i
$283$	−0.634700	+	6.03877i	−0.0377290	+	0.358968i	0.959327	+	0.282296i	$0.0910960\pi$
$283$	−0.634700	+	6.03877i	−0.0377290	+	0.358968i	−0.997056	+	0.0766717i	$0.975571\pi$
$284$	4.88997	−	5.43086i	0.290166	−	0.322262i
$285$	2.71938	−	4.71010i	0.161082	−	0.279002i
$286$	−11.7574	+	14.8145i	−0.695230	+	0.876002i
$287$	3.61089	−	3.61088i	0.213144	−	0.213143i
$288$	1.58907	+	4.89064i	0.0936366	+	0.288184i
$289$	39.7838	−	17.7129i	2.34022	−	1.04193i
$290$	−12.3546	−	5.50064i	−0.725489	−	0.323008i
$291$	−15.1538	+	3.22104i	−0.888332	+	0.188821i
$292$	4.59760	+	5.10615i	0.269054	+	0.298815i
$293$	−10.3270	+	7.50299i	−0.603309	+	0.438329i	−0.847052	−	0.531510i	$-0.821625\pi$
$293$	−10.3270	+	7.50299i	−0.603309	+	0.438329i	0.243743	+	0.969840i	$0.421625\pi$
$294$	4.02713	−	5.54285i	0.234867	−	0.323265i
$295$	−0.709674	−	2.18415i	−0.0413188	−	0.127166i
$296$	2.11793	−	3.66836i	0.123102	−	0.213219i
$297$	2.94019	−	1.53469i	0.170607	−	0.0890515i
$298$	7.93375	+	13.7417i	0.459590	+	0.796033i
$299$	−5.65451	−	1.20190i	−0.327009	−	0.0695079i
$300$	−4.78913	−	3.47951i	−0.276500	−	0.200889i
$301$	0.670875	−	4.23572i	0.0386686	−	0.244143i
$302$	4.40656	−	13.5620i	0.253569	−	0.780405i
$303$	−1.92145	−	2.13399i	−0.110385	−	0.122595i
$304$	−1.26206	−	0.561903i	−0.0723838	−	0.0322274i
$305$	−0.725237	+	6.90017i	−0.0415270	+	0.395103i
$306$	7.44963	+	1.58347i	0.425867	+	0.0905208i
$307$	16.4189			0.937076			0.468538	−	0.883443i	$-0.344781\pi$
$307$	16.4189			0.937076			0.468538	+	0.883443i	$0.344781\pi$
$308$	−8.92478	+	1.98888i	−0.508537	+	0.113327i
$309$	−7.02586			−0.399687
$310$	25.3048	+	5.37869i	1.43721	+	0.305489i
$311$	0.964468	−	9.17630i	0.0546900	−	0.520340i	−0.932543	−	0.361058i	$-0.882415\pi$
$311$	0.964468	−	9.17630i	0.0546900	−	0.520340i	0.987233	−	0.159282i	$-0.0509178\pi$
$312$	15.8475	+	7.05575i	0.897186	+	0.399453i
$313$	17.4183	+	19.3450i	0.984540	+	1.09344i	0.995619	+	0.0935035i	$0.0298066\pi$
$313$	17.4183	+	19.3450i	0.984540	+	1.09344i	−0.0110792	+	0.999939i	$0.503527\pi$
$314$	1.63888	−	5.04396i	0.0924874	−	0.284647i
$315$	8.07246	−	3.09872i	0.454832	−	0.174593i
$316$	−7.14880	−	5.19391i	−0.402152	−	0.292180i
$317$	12.4922	+	2.65530i	0.701632	+	0.149136i	0.544895	−	0.838504i	$-0.316569\pi$
$317$	12.4922	+	2.65530i	0.701632	+	0.149136i	0.156737	+	0.987640i	$0.449903\pi$
$318$	−1.14533	−	1.98377i	−0.0642269	−	0.111244i
$319$	−13.8704	−	2.05733i	−0.776591	−	0.115188i
$320$	−10.9376	+	18.9445i	−0.611431	+	1.05903i
$321$	−0.805986	−	2.48057i	−0.0449858	−	0.138452i
$322$	1.61696	+	1.99678i	0.0901097	+	0.111276i
$323$	10.4762	−	7.61142i	0.582913	−	0.423511i
$324$	−0.697249	−	0.774373i	−0.0387361	−	0.0430207i
$325$	−32.3755	+	6.88162i	−1.79587	+	0.381723i
$326$	−5.52379	−	2.45935i	−0.305935	−	0.136211i
$327$	11.0557	−	4.92230i	0.611379	−	0.272204i
$328$	−1.77583	−	5.46545i	−0.0980539	−	0.301779i
$329$	2.33726	+	8.72281i	0.128857	+	0.480904i
$330$	9.94135	+	3.70445i	0.547253	+	0.203923i
$331$	−2.24139	+	3.88220i	−0.123198	+	0.213385i	−0.921027	−	0.389499i	$-0.872648\pi$
$331$	−2.24139	+	3.88220i	−0.123198	+	0.213385i	0.797829	+	0.602884i	$0.205982\pi$
$332$	1.89698	−	2.10681i	0.104110	−	0.115626i
$333$	−0.148708	+	1.41487i	−0.00814917	+	0.0775342i
$334$	−0.268704	−	2.55655i	−0.0147028	−	0.139888i
$335$	10.9880	−	33.8175i	0.600337	−	1.84765i
$336$	−0.997124	−	1.95697i	−0.0543976	−	0.106761i
$337$	−7.49955	+	5.44874i	−0.408527	+	0.296812i	−0.773005	−	0.634400i	$-0.781247\pi$
$337$	−7.49955	+	5.44874i	−0.408527	+	0.296812i	0.364478	+	0.931212i	$0.381247\pi$
$338$	18.7281	−	8.33829i	1.01867	−	0.453543i
$339$	−3.34291	+	3.71268i	−0.181562	+	0.201645i
$340$	−13.2497	−	22.9491i	−0.718564	−	1.24459i
$341$	26.7714	−	1.66700i	1.44975	−	0.0902731i
$342$	1.62882			0.0880763
$343$	8.40806	−	16.5016i	0.453993	−	0.891005i
$344$	−3.90441	−	2.83672i	−0.210512	−	0.152946i
$345$	0.338954	+	3.22493i	0.0182487	+	0.173625i
$346$	12.8258	−	2.72620i	0.689517	−	0.146561i
$347$	9.14151	−	1.94309i	0.490742	−	0.104310i	0.0441071	−	0.999027i	$-0.485956\pi$
$347$	9.14151	−	1.94309i	0.490742	−	0.104310i	0.446635	+	0.894716i	$0.352622\pi$
$348$	0.460499	+	4.38135i	0.0246853	+	0.234865i
$349$	−7.76854	−	5.64417i	−0.415840	−	0.302126i	0.360122	−	0.932905i	$-0.382735\pi$
$349$	−7.76854	−	5.64417i	−0.415840	−	0.302126i	−0.775962	+	0.630780i	$0.782735\pi$
$350$	13.1078	+	6.67876i	0.700641	+	0.356995i
$351$	−5.82626			−0.310983
$352$	−4.25209	+	16.5166i	−0.226637	+	0.880338i
$353$	5.95457	+	10.3136i	0.316930	+	0.548939i	0.979846	−	0.199755i	$-0.0640147\pi$
$353$	5.95457	+	10.3136i	0.316930	+	0.548939i	−0.662916	+	0.748694i	$0.730681\pi$
$354$	0.460214	−	0.511120i	0.0244601	−	0.0271657i
$355$	−20.9389	+	9.32259i	−1.11132	+	0.494792i
$356$	−12.2910	+	8.92993i	−0.651421	+	0.473285i
$357$	20.5592	+	1.07748i	1.08811	+	0.0570263i
$358$	−5.73660	+	17.6554i	−0.303189	+	0.933118i
$359$	0.764408	+	7.27286i	0.0403439	+	0.383847i	0.995999	+	0.0893598i	$0.0284821\pi$
$359$	0.764408	+	7.27286i	0.0403439	+	0.383847i	−0.955655	+	0.294487i	$0.904851\pi$
$360$	1.01714	−	9.67742i	0.0536079	−	0.510045i
$361$	−10.8604	+	12.0617i	−0.571599	+	0.634825i
$362$	−5.28116	+	9.14724i	−0.277572	+	0.480768i
$363$	10.9602	+	0.934579i	0.575263	+	0.0490527i
$364$	15.5153	+	4.15732i	0.813221	+	0.217903i
$365$	−6.65933	−	20.4953i	−0.348565	−	1.07277i
$366$	−1.89823	+	0.845145i	−0.0992219	+	0.0441765i
$367$	6.95866	+	3.09820i	0.363239	+	0.161724i	0.580237	−	0.814448i	$-0.302960\pi$
$367$	6.95866	+	3.09820i	0.363239	+	0.161724i	−0.216998	+	0.976172i	$0.569627\pi$
$368$	0.805674	−	0.171251i	0.0419987	−	0.00892710i
$369$	1.29149	+	1.43434i	0.0672321	+	0.0746689i
$370$	−3.68164	+	2.67487i	−0.191399	+	0.139060i
$371$	−3.89676	−	4.81210i	−0.202310	−	0.249832i
$372$	−2.60420	−	8.01490i	−0.135021	−	0.415553i
$373$	4.75727	−	8.23984i	0.246322	−	0.426643i	−0.716180	−	0.697915i	$-0.754111\pi$
$373$	4.75727	−	8.23984i	0.246322	−	0.426643i	0.962503	+	0.271273i	$0.0874445\pi$
$374$	18.0359	+	17.6848i	0.932615	+	0.914462i
$375$	1.11275	+	1.92734i	0.0574622	+	0.0995274i
$376$	9.94050	+	2.11292i	0.512642	+	0.108965i
$377$	19.9280	+	14.4785i	1.02634	+	0.745683i
$378$	2.01247	+	1.62967i	0.103510	+	0.0838210i
$379$	−10.8424	+	33.3696i	−0.556938	+	1.71408i	0.133831	+	0.991004i	$0.457272\pi$
$379$	−10.8424	+	33.3696i	−0.556938	+	1.71408i	−0.690769	+	0.723076i	$0.742728\pi$
$380$	−3.79217	−	4.21163i	−0.194534	−	0.216052i
$381$	−12.8322	−	5.71328i	−0.657416	−	0.292700i
$382$	−0.845871	+	8.04793i	−0.0432785	+	0.411768i
$383$	−30.3191	−	6.44452i	−1.54923	−	0.329300i	−0.647661	−	0.761929i	$-0.724253\pi$
$383$	−30.3191	−	6.44452i	−1.54923	−	0.329300i	−0.901572	+	0.432629i	$0.857586\pi$
$384$	3.73339			0.190519
$385$	28.1087	+	5.68657i	1.43255	+	0.289815i
$386$	−13.4101			−0.682558
$387$	1.58549	+	0.337005i	0.0805948	+	0.0171309i
$388$	−1.68744	+	16.0549i	−0.0856669	+	0.815066i
$389$	−13.6694	−	6.08603i	−0.693068	−	0.308574i	0.0298039	−	0.999556i	$-0.490512\pi$
$389$	−13.6694	−	6.08603i	−0.693068	−	0.308574i	−0.722872	+	0.690982i	$0.757178\pi$
$390$	−12.4705	−	13.8499i	−0.631468	−	0.701316i
$391$	−2.38581	+	7.34278i	−0.120656	+	0.371340i
$392$	−12.2506	−	16.8615i	−0.618746	−	0.851635i
$393$	−17.8927	−	12.9998i	−0.902567	−	0.655753i
$394$	3.42109	+	0.727176i	0.172352	+	0.0366346i
$395$	13.8571	+	24.0013i	0.697229	+	1.20764i
$396$	−0.574157	−	3.40797i	−0.0288525	−	0.171257i
$397$	18.9529	−	32.8275i	0.951221	−	1.64756i	0.208433	−	0.978037i	$-0.433164\pi$
$397$	18.9529	−	32.8275i	0.951221	−	1.64756i	0.742788	−	0.669527i	$-0.233503\pi$
$398$	6.74831	+	20.7692i	0.338262	+	1.04106i
$399$	4.34874	−	0.688769i	0.217709	−	0.0344816i
$400$	3.81534	−	2.77201i	0.190767	−	0.138600i
$401$	4.33318	+	4.81249i	0.216389	+	0.240324i	0.841560	−	0.540163i	$-0.181638\pi$
$401$	4.33318	+	4.81249i	0.216389	+	0.240324i	−0.625171	+	0.780488i	$0.714971\pi$
$402$	10.4163	−	2.21405i	0.519517	−	0.110427i
$403$	−43.0462	−	19.1654i	−2.14428	−	0.954697i
$404$	−2.73354	+	1.21705i	−0.135999	+	0.0605506i
$405$	1.00992	+	3.10822i	0.0501834	+	0.154449i
$406$	−2.83360	−	10.5752i	−0.140629	−	0.524837i
$407$	−2.93322	+	3.69591i	−0.145394	+	0.183200i
$408$	11.5841	−	20.0643i	0.573499	−	0.993330i
$409$	−10.0831	+	11.1984i	−0.498578	+	0.553727i	−0.938934	−	0.344096i	$-0.888185\pi$
$409$	−10.0831	+	11.1984i	−0.498578	+	0.553727i	0.440357	+	0.897823i	$0.354852\pi$
$410$	−0.645352	+	6.14012i	−0.0318717	+	0.303239i
$411$	−0.520782	−	4.95491i	−0.0256883	−	0.244408i
$412$	−2.26235	+	6.96278i	−0.111458	+	0.343032i
$413$	1.01258	−	1.55924i	0.0498259	−	0.0767250i
$414$	−0.785663	+	0.570818i	−0.0386133	+	0.0280542i
$415$	−8.12287	+	3.61653i	−0.398736	+	0.177529i
$416$	20.0475	−	22.2650i	0.982909	−	1.09163i
$417$	1.90493	+	3.29944i	0.0932850	+	0.161574i
$418$	4.55934	+	2.89757i	0.223005	+	0.141725i
$419$	17.4503			0.852505			0.426252	−	0.904604i	$-0.359834\pi$
$419$	17.4503			0.852505			0.426252	+	0.904604i	$0.359834\pi$
$420$	−0.471546	−	8.99779i	−0.0230091	−	0.439047i
$421$	10.9271	+	7.93899i	0.532553	+	0.386923i	0.821312	−	0.570479i	$-0.193243\pi$
$421$	10.9271	+	7.93899i	0.532553	+	0.386923i	−0.288759	+	0.957402i	$0.593243\pi$
$422$	1.71607	+	16.3273i	0.0835370	+	0.794801i
$423$	−3.33863	+	0.709647i	−0.162330	+	0.0345042i
$424$	−6.81597	+	1.44878i	−0.331013	+	0.0703589i
$425$	4.62071	+	43.9632i	0.224138	+	2.13253i
$426$	−5.55333	−	4.03473i	−0.269060	−	0.195483i
$427$	−4.71065	+	3.05913i	−0.227964	+	0.148042i
$428$	−2.71783			−0.131371
$429$	−16.3087	−	10.3646i	−0.787392	−	0.500406i
$430$	2.59245	+	4.49026i	0.125019	+	0.216540i
$431$	−20.5274	+	22.7979i	−0.988768	+	1.09814i	0.00640242	+	0.999980i	$0.497962\pi$
$431$	−20.5274	+	22.7979i	−0.988768	+	1.09814i	−0.995171	+	0.0981590i	$0.968705\pi$
$432$	0.758375	−	0.337650i	0.0364873	−	0.0162452i
$433$	−13.0154	+	9.45625i	−0.625481	+	0.454438i	−0.854832	−	0.518906i	$-0.826340\pi$
$433$	−13.0154	+	9.45625i	−0.625481	+	0.454438i	0.229351	+	0.973344i	$0.426340\pi$
$434$	9.50797	+	18.6605i	0.456397	+	0.895732i
$435$	4.26977	−	13.1410i	0.204720	−	0.630062i
$436$	−1.31815	−	12.5414i	−0.0631281	−	0.600624i
$437$	−0.172596	+	1.64214i	−0.00825637	+	0.0785542i
$438$	4.31849	−	4.79616i	0.206345	−	0.229170i
$439$	−17.8076	+	30.8436i	−0.849908	+	1.47208i	0.0313816	+	0.999507i	$0.490009\pi$
$439$	−17.8076	+	30.8436i	−0.849908	+	1.47208i	−0.881290	+	0.472576i	$0.843324\pi$
$440$	20.0627	−	25.2794i	0.956452	−	1.20515i
$441$	6.06217	+	3.50001i	0.288675	+	0.166667i
$442$	−13.7121	−	42.2014i	−0.652216	−	2.00731i
$443$	4.41154	−	1.96414i	0.209599	−	0.0933193i	−0.299252	−	0.954174i	$-0.596737\pi$
$443$	4.41154	−	1.96414i	0.209599	−	0.0933193i	0.508851	+	0.860855i	$0.330071\pi$
$444$	1.35428	+	0.602964i	0.0642712	+	0.0286154i
$445$	46.6082	−	9.90687i	2.20944	−	0.469631i
$446$	−14.8938	−	16.5412i	−0.705242	−	0.783250i
$447$	−13.1156	+	9.52904i	−0.620347	+	0.450708i
$448$	−17.4911	+	2.77030i	−0.826375	+	0.130884i
$449$	−4.66263	−	14.3501i	−0.220043	−	0.677223i	−0.998757	−	0.0498437i	$-0.984128\pi$
$449$	−4.66263	−	14.3501i	−0.220043	−	0.677223i	0.778714	−	0.627379i	$-0.215872\pi$
$450$	−2.78016	+	4.81538i	−0.131058	+	0.226999i
$451$	1.06349	+	6.31245i	0.0500777	+	0.297242i
$452$	2.60292	+	4.50839i	0.122431	+	0.212057i
$453$	14.2510	+	3.02913i	0.669568	+	0.142321i
$454$	−12.5849	−	9.14346i	−0.590638	−	0.429124i
$455$	−39.1513	−	31.7042i	−1.83544	−	1.48631i
$456$	1.53115	−	4.71238i	0.0717025	−	0.220678i
$457$	−19.7179	−	21.8989i	−0.922364	−	1.02439i	−0.999625	−	0.0273783i	$-0.991284\pi$
$457$	−19.7179	−	21.8989i	−0.922364	−	1.02439i	0.0772610	−	0.997011i	$-0.475383\pi$
$458$	24.8960	+	11.0844i	1.16331	+	0.517940i
$459$	−0.813368	+	7.73868i	−0.0379648	+	0.361211i
$460$	3.30512	+	0.702526i	0.154102	+	0.0327554i
$461$	0.00123942			5.77254e−5			2.88627e−5	−	1.00000i	$-0.499991\pi$
$461$	0.00123942			5.77254e−5			2.88627e−5		1.00000i	$0.499991\pi$
$462$	2.73417	+	8.14178i	0.127205	+	0.378790i
$463$	0.725133			0.0336998			0.0168499	−	0.999858i	$-0.494636\pi$
$463$	0.725133			0.0336998			0.0168499	+	0.999858i	$0.494636\pi$
$464$	−3.43301	−	0.729709i	−0.159373	−	0.0338759i
$465$	−2.76283	+	26.2866i	−0.128123	+	1.21901i
$466$	7.46362	+	3.32302i	0.345746	+	0.153936i
$467$	−15.9318	−	17.6941i	−0.737238	−	0.818785i	0.251592	−	0.967833i	$-0.419046\pi$
$467$	−15.9318	−	17.6941i	−0.737238	−	0.818785i	−0.988830	+	0.149048i	$0.952379\pi$
$468$	−1.87607	+	5.77395i	−0.0867214	+	0.266901i
$469$	26.8739	−	10.3159i	1.24092	−	0.476344i
$470$	−8.83292	−	6.41749i	−0.407432	−	0.296017i
$471$	5.30019	+	1.12659i	0.244220	+	0.0519106i
$472$	−1.04612	−	1.81193i	−0.0481516	−	0.0834010i
$473$	3.83854	+	3.76382i	0.176496	+	0.173061i
$474$	−4.14998	+	7.18798i	−0.190615	+	0.330155i
$475$	2.92145	+	8.99130i	0.134045	+	0.412549i
$476$	7.68792	−	20.0277i	0.352375	−	0.917967i
$477$	1.89339	−	1.37563i	0.0866925	−	0.0629858i
$478$	−3.81192	−	4.23357i	−0.174353	−	0.193639i
$479$	−2.29049	+	0.486858i	−0.104655	+	0.0222451i	−0.259941	−	0.965624i	$-0.583703\pi$
$479$	−2.29049	+	0.486858i	−0.104655	+	0.0222451i	0.155286	+	0.987869i	$0.450370\pi$
$480$	−15.3531	−	6.83562i	−0.700768	−	0.312002i
$481$	7.57218	−	3.37135i	0.345262	−	0.153720i
$482$	−5.32207	−	16.3796i	−0.242413	−	0.746072i
$483$	−1.85625	+	1.85624i	−0.0844621	+	0.0844620i
$484$	4.45541	−	10.5609i	0.202519	−	0.480040i
$485$	25.3158	−	43.8483i	1.14953	−	1.99105i
$486$	−0.654921	+	0.727363i	−0.0297078	+	0.0329939i
$487$	−1.65450	+	15.7415i	−0.0749725	+	0.713316i	0.890883	+	0.454233i	$0.150087\pi$
$487$	−1.65450	+	15.7415i	−0.0749725	+	0.713316i	−0.965855	+	0.259082i	$0.916580\pi$
$488$	0.660716	+	6.28630i	0.0299092	+	0.284567i
$489$	1.90903	−	5.87538i	0.0863292	−	0.265694i
$490$	4.65539	+	21.9021i	0.210309	+	0.989435i
$491$	20.8755	−	15.1669i	0.942096	−	0.684473i	−0.00682814	−	0.999977i	$-0.502173\pi$
$491$	20.8755	−	15.1669i	0.942096	−	0.684473i	0.948924	+	0.315504i	$0.102173\pi$
$492$	1.83733	−	0.818031i	0.0828331	−	0.0368797i
$493$	22.0131	−	24.4480i	0.991418	−	1.10108i
$494$	−4.74495	−	8.21850i	−0.213485	−	0.369768i
$495$	−2.70239	+	10.4970i	−0.121463	+	0.471806i
$496$	6.71381			0.301459
$497$	−16.5328	−	8.42392i	−0.741600	−	0.377865i
$498$	−2.15432	−	1.56520i	−0.0965372	−	0.0701384i
$499$	−0.961777	−	9.15070i	−0.0430551	−	0.409641i	−0.994730	−	0.102533i	$-0.967305\pi$
$499$	−0.961777	−	9.15070i	−0.0430551	−	0.409641i	0.951675	−	0.307108i	$-0.0993614\pi$
$500$	2.26835	−	0.482152i	0.101443	−	0.0215625i
$501$	2.56901	−	0.546061i	0.114775	−	0.0243962i
$502$	−0.846324	−	8.05224i	−0.0377733	−	0.359389i
$503$	4.63336	+	3.36633i	0.206591	+	0.150097i	0.686270	−	0.727347i	$-0.259247\pi$
$503$	4.63336	+	3.36633i	0.206591	+	0.150097i	−0.479679	+	0.877444i	$0.659247\pi$
$504$	6.60664	−	4.29040i	0.294283	−	0.191109i
$505$	9.38478			0.417617
$506$	−3.21466	+	0.200170i	−0.142909	+	0.00889865i
$507$	10.4726	+	18.1391i	0.465106	+	0.805588i
$508$	−9.79401	+	10.8773i	−0.434539	+	0.482604i
$509$	7.76305	−	3.45633i	0.344091	−	0.153199i	−0.227413	−	0.973798i	$-0.573027\pi$
$509$	7.76305	−	3.45633i	0.344091	−	0.153199i	0.571504	+	0.820599i	$0.306360\pi$
$510$	−20.1369	+	14.6303i	−0.891678	+	0.647842i
$511$	9.50170	−	14.6313i	0.420330	−	0.647251i
$512$	−2.84674	+	8.76138i	−0.125809	+	0.387202i
$513$	0.173952	+	1.65504i	0.00768016	+	0.0730718i
$514$	−0.127699	+	1.21498i	−0.00563258	+	0.0535904i
$515$	15.3644	−	17.0639i	0.677036	−	0.751925i
$516$	0.844510	−	1.46273i	0.0371775	−	0.0643933i
$517$	−10.6078	−	3.95279i	−0.466531	−	0.173844i
$518$	−3.55854	−	0.953510i	−0.156353	−	0.0418948i
$519$	4.13984	+	12.7411i	0.181719	+	0.559273i
$520$	−51.7923	+	23.0594i	−2.27124	+	1.01122i
$521$	−35.5297	−	15.8188i	−1.55658	−	0.693036i	−0.565313	−	0.824877i	$-0.691244\pi$
$521$	−35.5297	−	15.8188i	−1.55658	−	0.693036i	−0.991271	+	0.131841i	$0.957911\pi$
$522$	4.04761	−	0.860346i	0.177159	−	0.0376563i
$523$	5.25330	+	5.83438i	0.229711	+	0.255119i	0.846971	−	0.531640i	$-0.178424\pi$
$523$	5.25330	+	5.83438i	0.229711	+	0.255119i	−0.617260	+	0.786759i	$0.711757\pi$
$524$	−18.6446	+	13.5461i	−0.814492	+	0.591763i
$525$	−5.38643	+	14.0321i	−0.235083	+	0.612411i
$526$	1.67110	+	5.14313i	0.0728636	+	0.224251i
$527$	−31.4657	+	54.5002i	−1.37067	+	2.37407i
$528$	2.72348	+	0.403962i	0.118524	+	0.0175802i
$529$	11.0078	+	19.0660i	0.478598	+	0.828957i
$530$	7.32268	+	1.55648i	0.318077	+	0.0676094i
$531$	0.568498	+	0.413038i	0.0246707	+	0.0179243i
$532$	0.717720	−	4.53148i	0.0311171	−	0.196465i
$533$	3.47497	−	10.6949i	0.150518	−	0.463246i
$534$	9.54863	+	10.6048i	0.413210	+	0.458916i
$535$	7.78719	+	3.46708i	0.336669	+	0.149895i
$536$	3.38614	−	32.2170i	0.146259	−	1.39156i
$537$	−18.5523	−	3.94342i	−0.800593	−	0.170171i
$538$	16.3991			0.707016
$539$	10.7428	+	20.5814i	0.462723	+	0.886503i
$540$	3.40551			0.146550
$541$	6.98671	+	1.48507i	0.300382	+	0.0638482i	0.355637	−	0.934624i	$-0.384264\pi$
$541$	6.98671	+	1.48507i	0.300382	+	0.0638482i	−0.0552551	+	0.998472i	$0.517597\pi$
$542$	1.91376	−	18.2082i	0.0822032	−	0.782111i
$543$	−9.85853	−	4.38930i	−0.423070	−	0.188363i
$544$	−26.7746	−	29.7362i	−1.14795	−	1.27493i
$545$	−12.2220	+	37.6154i	−0.523533	+	1.61127i
$546$	2.36021	−	14.9017i	0.101008	−	0.637735i
$547$	−17.6795	−	12.8449i	−0.755922	−	0.549210i	0.141735	−	0.989905i	$-0.454732\pi$
$547$	−17.6795	−	12.8449i	−0.755922	−	0.549210i	−0.897657	+	0.440695i	$0.854732\pi$
$548$	−5.07812	−	1.07939i	−0.216926	−	0.0461091i
$549$	−1.06148	−	1.83853i	−0.0453027	−	0.0784666i
$550$	−16.3484	+	8.53334i	−0.697099	+	0.363863i
$551$	3.51788	−	6.09315i	0.149867	−	0.259577i
$552$	0.912901	+	2.80962i	0.0388556	+	0.119585i
$553$	−8.04040	+	20.9459i	−0.341913	+	0.890711i
$554$	0.556944	−	0.404643i	0.0236623	−	0.0171917i
$555$	−3.11112	−	3.45525i	−0.132060	−	0.146667i
$556$	3.88321	−	0.825403i	0.164685	−	0.0350049i
$557$	−26.9559	−	12.0015i	−1.14216	−	0.508522i	−0.253611	−	0.967306i	$-0.581618\pi$
$557$	−26.9559	−	12.0015i	−1.14216	−	0.508522i	−0.888548	+	0.458785i	$0.848285\pi$
$558$	−7.23141	+	3.21963i	−0.306130	+	0.136298i
$559$	−2.91830	−	8.98160i	−0.123431	−	0.379881i
$560$	6.93349	+	1.85783i	0.292993	+	0.0785076i
$561$	−16.0434	+	20.2150i	−0.677353	+	0.853477i
$562$	12.2495	−	21.2168i	0.516715	−	0.894976i
$563$	22.5317	−	25.0240i	0.949600	−	1.05464i	−0.0488404	−	0.998807i	$-0.515553\pi$
$563$	22.5317	−	25.0240i	0.949600	−	1.05464i	0.998440	−	0.0558309i	$-0.0177808\pi$
$564$	−0.371771	+	3.53716i	−0.0156544	+	0.148941i
$565$	−1.70668	−	16.2380i	−0.0718008	−	0.683139i
$566$	1.83651	−	5.65221i	0.0771945	−	0.237580i
$567$	−1.44098	+	2.21891i	−0.0605155	+	0.0931856i
$568$	−16.8933	+	12.2737i	−0.708829	+	0.514994i
$569$	−23.4638	+	10.4468i	−0.983654	+	0.437951i	−0.834587	−	0.550876i	$-0.814294\pi$
$569$	−23.4638	+	10.4468i	−0.983654	+	0.437951i	−0.149067	+	0.988827i	$0.547627\pi$
$570$	−3.56195	+	3.95595i	−0.149194	+	0.165696i
$571$	−6.48717	−	11.2361i	−0.271480	−	0.470217i	0.697761	−	0.716330i	$-0.254180\pi$
$571$	−6.48717	−	11.2361i	−0.271480	−	0.470217i	−0.969241	+	0.246114i	$0.920846\pi$
$572$	−15.5230	+	12.8249i	−0.649047	+	0.536235i
$573$	−8.26784			−0.345394
$574$	−4.19177	+	2.72216i	−0.174961	+	0.113621i
$575$	−4.56017	−	3.31316i	−0.190172	−	0.138168i
$576$	−0.699652	−	6.65674i	−0.0291522	−	0.277364i
$577$	23.0630	−	4.90220i	0.960127	−	0.204081i	0.298914	−	0.954280i	$-0.403376\pi$
$577$	23.0630	−	4.90220i	0.960127	−	0.204081i	0.661212	+	0.750199i	$0.270042\pi$
$578$	−41.6925	+	8.86202i	−1.73418	+	0.368611i
$579$	−1.43216	−	13.6260i	−0.0595183	−	0.566279i
$580$	−11.6481	−	8.46287i	−0.483663	−	0.351401i
$581$	−6.41363	−	3.26791i	−0.266082	−	0.135576i
$582$	15.1633			0.628541
$583$	7.74710	−	0.482396i	0.320852	−	0.0199788i
$584$	−9.81642	−	17.0025i	−0.406206	−	0.703570i
$585$	12.7411	−	14.1504i	0.526778	−	0.585046i
$586$	11.4136	−	5.08167i	0.471493	−	0.209922i
$587$	2.16252	−	1.57116i	0.0892568	−	0.0648489i	−0.542262	−	0.840210i	$-0.682432\pi$
$587$	2.16252	−	1.57116i	0.0892568	−	0.0648489i	0.631519	+	0.775361i	$0.282432\pi$
$588$	5.42062	−	4.88073i	0.223543	−	0.201278i
$589$	−4.15903	+	12.8002i	−0.171370	+	0.527422i
$590$	0.234957	+	2.23547i	0.00967304	+	0.0920329i
$591$	−0.373523	+	3.55383i	−0.0153647	+	0.146185i
$592$	−0.790252	+	0.877664i	−0.0324792	+	0.0360718i
$593$	6.70372	−	11.6112i	0.275289	−	0.476814i	−0.694919	−	0.719088i	$-0.744560\pi$
$593$	6.70372	−	11.6112i	0.275289	−	0.476814i	0.970208	+	0.242274i	$0.0778932\pi$
$594$	−3.12717	+	0.870951i	−0.128309	+	0.0357355i
$595$	−47.5765	+	47.5764i	−1.95045	+	1.95044i
$596$	5.22023	+	16.0662i	0.213829	+	0.658098i
$597$	−20.3829	+	9.07503i	−0.834215	+	0.371416i
$598$	5.16891	+	2.30135i	0.211372	+	0.0941090i
$599$	13.9118	−	2.95704i	0.568420	−	0.120821i	0.0852683	−	0.996358i	$-0.472825\pi$
$599$	13.9118	−	2.95704i	0.568420	−	0.120821i	0.483152	+	0.875537i	$0.339492\pi$
$600$	11.3181	+	12.5700i	0.462059	+	0.513168i
$601$	23.1951	−	16.8522i	0.946146	−	0.687415i	−0.00374617	−	0.999993i	$-0.501192\pi$
$601$	23.1951	−	16.8522i	0.946146	−	0.687415i	0.949892	+	0.312578i	$0.101192\pi$
$602$	−1.50423	+	3.91865i	−0.0613079	+	0.159712i
$603$	3.36212	+	10.3475i	0.136916	+	0.421384i
$604$	7.59078	−	13.1476i	0.308865	−	0.534969i
$605$	−26.2380	+	24.5756i	−1.06673	+	0.999141i
$606$	1.40529	+	2.43404i	0.0570861	+	0.0988760i
$607$	23.2913	+	4.95071i	0.945363	+	0.200943i	0.654706	−	0.755884i	$-0.272793\pi$
$607$	23.2913	+	4.95071i	0.945363	+	0.200943i	0.290658	+	0.956827i	$0.406126\pi$
$608$	−6.92327	−	5.03005i	−0.280776	−	0.203996i
$609$	10.4428	−	4.00861i	0.423164	−	0.162437i
$610$	2.09848	−	6.45847i	0.0849651	−	0.261496i
$611$	13.3065	+	14.7784i	0.538324	+	0.597869i
$612$	7.40730	+	3.29794i	0.299422	+	0.133311i
$613$	1.73767	−	16.5328i	0.0701838	−	0.667755i	−0.901711	−	0.432339i	$-0.857688\pi$
$613$	1.73767	−	16.5328i	0.0701838	−	0.667755i	0.971895	−	0.235415i	$-0.0756450\pi$
$614$	−15.7190	−	3.34118i	−0.634369	−	0.134839i
$615$	−6.30790			−0.254359
$616$	26.1255	−	0.256741i	1.05263	−	0.0103444i
$617$	29.2087			1.17590			0.587949	−	0.808898i	$-0.299935\pi$
$617$	29.2087			1.17590			0.587949	+	0.808898i	$0.299935\pi$
$618$	6.72638	+	1.42974i	0.270575	+	0.0575125i
$619$	0.770361	−	7.32950i	0.0309634	−	0.294597i	−0.968071	−	0.250674i	$-0.919348\pi$
$619$	0.770361	−	7.32950i	0.0309634	−	0.294597i	0.999035	−	0.0439231i	$-0.0139857\pi$
$620$	25.1610	+	11.2024i	1.01049	+	0.449899i
$621$	−0.663914	−	0.737352i	−0.0266420	−	0.0295889i
$622$	−2.79070	+	8.58889i	−0.111897	+	0.344383i
$623$	29.9781	+	24.2758i	1.20105	+	0.972590i
$624$	−3.91292	−	2.84290i	−0.156642	−	0.113807i
$625$	20.6697	+	4.39348i	0.826788	+	0.175739i
$626$	−12.7392	−	22.0649i	−0.509161	−	0.881893i
$627$	−2.45730	+	4.94220i	−0.0981350	+	0.197372i
$628$	2.82315	−	4.88984i	0.112656	−	0.195126i
$629$	−3.42087	−	10.5283i	−0.136399	−	0.419792i
$630$	−8.35895	+	1.32392i	−0.333029	+	0.0527463i
$631$	−11.9021	+	8.64741i	−0.473817	+	0.344248i	−0.798927	−	0.601428i	$-0.794599\pi$
$631$	−11.9021	+	8.64741i	−0.473817	+	0.344248i	0.325110	+	0.945676i	$0.394599\pi$
$632$	16.8947	+	18.7634i	0.672034	+	0.746369i
$633$	−16.4069	+	3.48740i	−0.652117	+	0.138612i
$634$	−11.4194	−	5.08424i	−0.453521	−	0.201921i
$635$	41.9380	−	18.6720i	1.66426	−	0.740976i
$636$	−0.753603	−	2.31935i	−0.0298823	−	0.0919682i
$637$	7.06606e−5	−	40.7838i	2.79967e−6	−	1.61591i
$638$	12.8605	+	4.79220i	0.509151	+	0.189725i
$639$	3.50661	−	6.07363i	0.138720	−	0.240269i
$640$	−8.16430	+	9.06737i	−0.322722	+	0.358419i
$641$	−2.64825	+	25.1964i	−0.104600	+	0.995200i	0.808786	+	0.588104i	$0.200125\pi$
$641$	−2.64825	+	25.1964i	−0.104600	+	0.995200i	−0.913385	+	0.407096i	$0.866541\pi$
$642$	0.266844	+	2.53885i	0.0105315	+	0.100200i
$643$	5.70088	−	17.5455i	0.224821	−	0.691927i	−0.773489	−	0.633810i	$-0.781490\pi$
$643$	5.70088	−	17.5455i	0.224821	−	0.691927i	0.998310	−	0.0581174i	$-0.0185098\pi$
$644$	1.24186	+	2.43730i	0.0489362	+	0.0960429i
$645$	−4.28569	+	3.11374i	−0.168749	+	0.122603i
$646$	−11.5786	+	5.15511i	−0.455553	+	0.202825i
$647$	−28.4723	+	31.6217i	−1.11936	+	1.24318i	−0.152384	+	0.988321i	$0.548695\pi$
$647$	−28.4723	+	31.6217i	−1.11936	+	1.24318i	−0.966979	+	0.254857i	$0.917972\pi$
$648$	1.48871	+	2.57852i	0.0584821	+	0.101294i
$649$	0.856555	+	2.16749i	0.0336227	+	0.0850814i
$650$	32.3958			1.27067
$651$	−17.9455	+	11.6539i	−0.703340	+	0.456753i
$652$	−5.20792	−	3.78378i	−0.203958	−	0.148184i
$653$	−1.55081	−	14.7550i	−0.0606880	−	0.577408i	−0.982039	−	0.188677i	$-0.939580\pi$
$653$	−1.55081	−	14.7550i	−0.0606880	−	0.577408i	0.921351	−	0.388731i	$-0.127086\pi$
$654$	−11.5861	+	2.46270i	−0.453052	+	0.0962991i
$655$	70.7013	−	15.0280i	2.76253	−	0.587194i
$656$	0.167482	+	1.59348i	0.00653907	+	0.0622151i
$657$	5.33458	+	3.87580i	0.208122	+	0.151209i
$658$	−0.462576	−	8.82663i	−0.0180331	−	0.344098i
$659$	31.4056			1.22339			0.611695	−	0.791094i	$-0.290488\pi$
$659$	31.4056			1.22339			0.611695	+	0.791094i	$0.290488\pi$
$660$	9.53261	+	6.05820i	0.371056	+	0.235815i
$661$	−5.65773	−	9.79948i	−0.220060	−	0.381156i	0.734766	−	0.678321i	$-0.237292\pi$
$661$	−5.65773	−	9.79948i	−0.220060	−	0.381156i	−0.954826	+	0.297165i	$0.903959\pi$
$662$	2.93586	−	3.26061i	0.114106	−	0.126727i
$663$	41.4164	−	18.4398i	1.60848	−	0.716142i
$664$	−6.55348	+	4.76138i	−0.254324	+	0.184777i
$665$	−7.83714	+	12.0681i	−0.303911	+	0.467982i
$666$	0.430290	−	1.32430i	0.0166734	−	0.0513154i
$667$	0.438483	+	4.17188i	0.0169781	+	0.161536i
$668$	0.286071	−	2.72178i	0.0110684	−	0.105309i
$669$	15.2170	−	16.9001i	0.588321	−	0.653397i
$670$	−17.4014	+	30.1400i	−0.672273	+	1.16441i
$671$	0.299380	−	7.03467i	0.0115574	−	0.271570i
$672$	−3.52130	−	13.1417i	−0.135837	−	0.506953i
$673$	−8.09843	−	24.9244i	−0.312171	−	0.960765i	−0.976903	−	0.213683i	$-0.931454\pi$
$673$	−8.09843	−	24.9244i	−0.312171	−	0.960765i	0.664732	−	0.747082i	$-0.268546\pi$
$674$	8.28868	−	3.69036i	0.319268	−	0.142147i
$675$	−5.18982	−	2.31066i	−0.199756	−	0.0889372i
$676$	21.3485	−	4.53776i	0.821096	−	0.174529i
$677$	−1.26060	−	1.40003i	−0.0484487	−	0.0538077i	0.718433	−	0.695596i	$-0.244860\pi$
$677$	−1.26060	−	1.40003i	−0.0484487	−	0.0538077i	−0.766882	+	0.641788i	$0.778193\pi$
$678$	3.95593	−	2.87415i	0.151927	−	0.110381i
$679$	40.4843	−	6.41204i	1.55364	−	0.246072i
$680$	23.3981	+	72.0119i	0.897276	+	2.76153i
$681$	7.94665	−	13.7640i	0.304516	−	0.527438i
$682$	−25.9695	−	3.85194i	−0.994423	−	0.147498i
$683$	10.6427	+	18.4337i	0.407232	+	0.705347i	0.994578	−	0.103989i	$-0.0331607\pi$
$683$	10.6427	+	18.4337i	0.407232	+	0.705347i	−0.587346	+	0.809336i	$0.699827\pi$
$684$	1.69619	+	0.360537i	0.0648556	+	0.0137855i
$685$	13.1730	+	9.57073i	0.503314	+	0.365679i
$686$	−11.4077	+	14.0873i	−0.435548	+	0.537854i
$687$	−8.60406	+	26.4806i	−0.328265	+	1.01030i
$688$	0.900374	+	0.999966i	0.0343264	+	0.0381234i
$689$	−12.4567	−	5.54608i	−0.474562	−	0.211289i
$690$	0.331756	−	3.15645i	0.0126297	−	0.120164i
$691$	15.7577	+	3.34940i	0.599451	+	0.127417i	0.497636	−	0.867386i	$-0.334202\pi$
$691$	15.7577	+	3.34940i	0.599451	+	0.127417i	0.101815	+	0.994803i	$0.467535\pi$
$692$	13.9598			0.530671
$693$	−7.98087	+	3.64770i	−0.303168	+	0.138565i
$694$	−9.14726			−0.347225
$695$	−12.1792	−	2.58877i	−0.461984	−	0.0981978i
$696$	1.31580	−	12.5190i	0.0498754	−	0.474533i
$697$	−13.7203	−	6.10865i	−0.519692	−	0.231382i
$698$	6.28883	+	6.98446i	0.238036	+	0.264366i
$699$	−2.57943	+	7.93868i	−0.0975631	+	0.300268i
$700$	12.1717	+	9.85644i	0.460046	+	0.372538i
$701$	−41.1034	−	29.8634i	−1.55246	−	1.12792i	−0.941872	−	0.335973i	$-0.890935\pi$
$701$	−41.1034	−	29.8634i	−1.55246	−	1.12792i	−0.610584	−	0.791952i	$-0.709065\pi$
$702$	5.57791	+	1.18562i	0.210525	+	0.0447484i
$703$	−1.18376	−	2.05034i	−0.0446465	−	0.0773300i
$704$	9.88350	−	19.8780i	0.372498	−	0.749181i
$705$	5.57749	−	9.66050i	0.210060	−	0.363835i
$706$	−3.60197	−	11.0857i	−0.135562	−	0.417217i
$707$	4.78123	+	5.90433i	0.179817	+	0.222055i
$708$	0.592388	−	0.430395i	0.0222633	−	0.0161752i
$709$	−14.3281	−	15.9130i	−0.538103	−	0.597624i	0.411372	−	0.911468i	$-0.365050\pi$
$709$	−14.3281	−	15.9130i	−0.538103	−	0.597624i	−0.949475	+	0.313844i	$0.898383\pi$
$710$	21.9435	−	4.66423i	0.823524	−	0.175045i
$711$	−7.74692	−	3.44915i	−0.290532	−	0.129353i
$712$	39.6573	−	17.6565i	1.48622	−	0.661707i
$713$	−2.47970	−	7.63172i	−0.0928654	−	0.285810i
$714$	−19.4636	−	5.21527i	−0.728407	−	0.195177i
$715$	60.8371	−	16.9438i	2.27518	−	0.633662i
$716$	−9.88192	+	17.1160i	−0.369305	+	0.639654i
$717$	3.89463	−	4.32543i	0.145448	−	0.161536i
$718$	0.748175	−	7.11841i	0.0279216	−	0.265657i
$719$	4.00956	+	38.1484i	0.149531	+	1.42270i	0.769790	+	0.638298i	$0.220361\pi$
$719$	4.00956	+	38.1484i	0.149531	+	1.42270i	−0.620258	+	0.784398i	$0.712972\pi$
$720$	−0.838381	+	2.58027i	−0.0312446	+	0.0961611i
$721$	18.5632	+	0.972872i	0.691330	+	0.0362317i
$722$	12.8520	−	9.33750i	0.478300	−	0.347506i
$723$	16.0750	−	7.15704i	0.597835	−	0.266173i
$724$	−7.52436	+	8.35665i	−0.279641	+	0.310573i
$725$	12.0090	+	20.8003i	0.446005	+	0.772503i
$726$	−10.3029	−	3.12511i	−0.382375	−	0.115984i
$727$	16.5965			0.615531			0.307765	−	0.951462i	$-0.400419\pi$
$727$	16.5965			0.615531			0.307765	+	0.951462i	$0.400419\pi$
$728$	−40.8940	−	20.8366i	−1.51563	−	0.772255i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	2.20475	+	20.9768i	0.0816016	+	0.776388i
$731$	−12.3372	+	2.62234i	−0.456306	+	0.0969909i
$732$	−2.16382	+	0.459935i	−0.0799772	+	0.0169997i
$733$	0.526136	+	5.00585i	0.0194333	+	0.184895i	0.999932	−	0.0116282i	$-0.00370144\pi$
$733$	0.526136	+	5.00585i	0.0194333	+	0.184895i	−0.980499	+	0.196524i	$0.937035\pi$
$734$	−6.03158	−	4.38220i	−0.222630	−	0.161750i
$735$	−21.7575	+	7.06941i	−0.802539	+	0.260759i
$736$	5.10224			0.188071
$737$	−8.99649	+	34.9455i	−0.331390	+	1.28724i
$738$	−0.944554	−	1.63602i	−0.0347695	−	0.0602226i
$739$	−10.6551	+	11.8337i	−0.391954	+	0.435310i	−0.906534	−	0.422133i	$-0.861281\pi$
$739$	−10.6551	+	11.8337i	−0.391954	+	0.435310i	0.514579	+	0.857443i	$0.327948\pi$
$740$	−4.42602	+	1.97059i	−0.162704	+	0.0724404i
$741$	7.84407	−	5.69905i	0.288159	−	0.209360i
$742$	2.75141	+	5.39996i	0.101008	+	0.198239i
$743$	−10.6331	+	32.7254i	−0.390092	+	1.20058i	0.542627	+	0.839974i	$0.317430\pi$
$743$	−10.6331	+	32.7254i	−0.390092	+	1.20058i	−0.932719	+	0.360605i	$0.882570\pi$
$744$	2.51704	+	23.9480i	0.0922791	+	0.877977i
$745$	5.53822	−	52.6927i	0.202905	−	1.93051i
$746$	−6.23127	+	6.92053i	−0.228143	+	0.253379i
$747$	1.36033	−	2.35616i	0.0497718	−	0.0862074i
$748$	14.8675	+	22.4087i	0.543609	+	0.819341i
$749$	1.78603	+	6.66558i	0.0652602	+	0.243555i
$750$	−0.673113	−	2.07163i	−0.0245786	−	0.0756452i
$751$	−33.4821	+	14.9072i	−1.22178	+	0.543971i	−0.913311	−	0.407264i	$-0.866483\pi$
$751$	−33.4821	+	14.9072i	−1.22178	+	0.543971i	−0.308468	+	0.951235i	$0.599816\pi$
$752$	−2.58850	−	1.15247i	−0.0943928	−	0.0420264i
$753$	8.09150	−	1.71990i	0.294871	−	0.0626767i
$754$	−16.1323	−	17.9167i	−0.587502	−	0.652487i
$755$	−38.5214	+	27.9875i	−1.40194	+	1.01857i
$756$	1.73499	+	2.14254i	0.0631010	+	0.0779234i
$757$	12.5629	+	38.6648i	0.456608	+	1.40529i	0.869237	+	0.494396i	$0.164611\pi$
$757$	12.5629	+	38.6648i	0.456608	+	1.40529i	−0.412629	+	0.910899i	$0.635389\pi$
$758$	17.1709	−	29.7408i	0.623674	−	1.08023i
$759$	−0.546707	−	3.24504i	−0.0198442	−	0.117787i
$760$	8.09673	+	14.0239i	0.293699	+	0.508702i
$761$	11.4914	+	2.44257i	0.416563	+	0.0885431i	0.411425	−	0.911444i	$-0.365031\pi$
$761$	11.4914	+	2.44257i	0.416563	+	0.0885431i	0.00513784	+	0.999987i	$0.498365\pi$
$762$	11.1226	+	8.08107i	0.402931	+	0.292746i
$763$	−29.8920	+	11.4744i	−1.08216	+	0.415403i
$764$	−2.66227	+	8.19361i	−0.0963174	+	0.296434i
$765$	−17.0164	−	18.8987i	−0.615231	−	0.683283i
$766$	27.7153	+	12.3396i	1.00139	+	0.445850i
$767$	0.427953	−	4.07170i	0.0154525	−	0.147021i
$768$	−16.6685	−	3.54301i	−0.601474	−	0.127847i
$769$	4.97197			0.179294			0.0896469	−	0.995974i	$-0.471426\pi$
$769$	4.97197			0.179294			0.0896469	+	0.995974i	$0.471426\pi$
$770$	−25.7533	−	11.1642i	−0.928086	−	0.402330i
$771$	−1.24818			−0.0449521
$772$	−13.9649	−	2.96833i	−0.502607	−	0.106832i
$773$	2.71032	−	25.7869i	0.0974833	−	0.927491i	−0.831039	−	0.556214i	$-0.812253\pi$
$773$	2.71032	−	25.7869i	0.0974833	−	0.927491i	0.928522	−	0.371277i	$-0.121080\pi$
$774$	−1.44933	−	0.645281i	−0.0520949	−	0.0231942i
$775$	−30.7431	−	34.1437i	−1.10433	−	1.22648i
$776$	14.2541	−	43.8696i	0.511692	−	1.57483i
$777$	0.588823	−	3.71766i	0.0211239	−	0.133370i
$778$	11.8483	+	8.60829i	0.424782	+	0.308622i
$779$	−3.14180	−	0.667809i	−0.112567	−	0.0239268i
$780$	−9.92069	−	17.1831i	−0.355218	−	0.615255i
$781$	20.6203	−	10.7631i	0.737851	−	0.385134i
$782$	3.77835	−	6.54429i	0.135113	−	0.234023i
$783$	1.30647	+	4.02090i	0.0466894	+	0.143695i
$784$	2.36354	+	5.30863i	0.0844123	+	0.189594i
$785$	−14.3268	+	10.4090i	−0.511346	+	0.371515i
$786$	14.4846	+	16.0868i	0.516649	+	0.573797i
$787$	9.76692	−	2.07602i	0.348153	−	0.0740022i	−0.0305162	−	0.999534i	$-0.509715\pi$
$787$	9.76692	−	2.07602i	0.348153	−	0.0740022i	0.378669	+	0.925532i	$0.376382\pi$
$788$	3.40165	+	1.51451i	0.121179	+	0.0539523i
$789$	−5.04747	+	2.24728i	−0.179695	+	0.0800052i
$790$	−8.38231	−	25.7981i	−0.298229	−	0.917855i
$791$	9.34648	−	9.34646i	0.332322	−	0.332322i
$792$	−0.419877	+	9.86605i	−0.0149197	+	0.350575i
$793$	−6.18444	+	10.7118i	−0.219616	+	0.380386i
$794$	−24.8253	+	27.5713i	−0.881019	+	0.978470i
$795$	−0.799508	+	7.60681i	−0.0283556	+	0.269786i
$796$	2.43023	+	23.1221i	0.0861371	+	0.819539i
$797$	0.379597	−	1.16828i	0.0134460	−	0.0413825i	−0.944108	−	0.329635i	$-0.893074\pi$
$797$	0.379597	−	1.16828i	0.0134460	−	0.0413825i	0.957554	+	0.288253i	$0.0930743\pi$
$798$	−4.30354	−	0.225542i	−0.152344	−	0.00798412i
$799$	21.4869	−	15.6112i	0.760152	−	0.552283i
$800$	26.6877	−	11.8821i	0.943553	−	0.420097i
$801$	−9.75581	+	10.8349i	−0.344705	+	0.382833i
$802$	−3.16916	−	5.48914i	−0.111907	−	0.193828i
$803$	8.03761	+	20.3389i	0.283641	+	0.717746i
$804$	11.3372			0.399834
$805$	−0.449002	−	8.56761i	−0.0158252	−	0.301969i
$806$	37.3113	+	27.1082i	1.31423	+	0.954846i
$807$	1.75137	+	16.6631i	0.0616510	+	0.586570i
$808$	8.36303	−	1.77762i	0.294210	−	0.0625363i
$809$	38.2385	−	8.12784i	1.34439	−	0.285759i	0.521158	−	0.853460i	$-0.325500\pi$
$809$	38.2385	−	8.12784i	1.34439	−	0.285759i	0.823235	+	0.567701i	$0.192167\pi$
$810$	−0.334362	−	3.18125i	−0.0117483	−	0.111778i
$811$	−20.5953	−	14.9634i	−0.723200	−	0.525436i	0.164205	−	0.986426i	$-0.447494\pi$
$811$	−20.5953	−	14.9634i	−0.723200	−	0.525436i	−0.887405	+	0.460991i	$0.847494\pi$
$812$	−0.610008	−	11.6398i	−0.0214071	−	0.408478i
$813$	18.7058			0.656041
$814$	3.56030	−	2.94147i	0.124788	−	0.103099i
$815$	10.0950	+	17.4850i	0.353611	+	0.612473i
$816$	−4.32233	+	4.80043i	−0.151312	+	0.168049i
$817$	−2.46424	+	1.09715i	−0.0862127	+	0.0383844i
$818$	11.9322	−	8.66922i	0.417198	−	0.303112i
$819$	15.3937	+	0.806763i	0.537899	+	0.0281906i
$820$	−2.03116	+	6.25126i	−0.0709311	+	0.218304i
$821$	−4.43620	−	42.2076i	−0.154824	−	1.47306i	−0.745694	−	0.666289i	$-0.767882\pi$
$821$	−4.43620	−	42.2076i	−0.154824	−	1.47306i	0.590870	−	0.806767i	$-0.298785\pi$
$822$	−0.509722	+	4.84968i	−0.0177786	+	0.169152i
$823$	−28.3785	+	31.5175i	−0.989213	+	1.09863i	0.00590939	+	0.999983i	$0.498119\pi$
$823$	−28.3785	+	31.5175i	−0.989213	+	1.09863i	−0.995122	+	0.0986496i	$0.968548\pi$
$824$	10.4595	−	18.1163i	0.364373	−	0.631112i
$825$	−10.4167	−	15.7003i	−0.362662	−	0.546614i
$826$	−1.28672	+	1.28672i	−0.0447707	+	0.0447706i
$827$	7.03348	+	21.6468i	0.244578	+	0.752734i	0.995706	+	0.0925768i	$0.0295104\pi$
$827$	7.03348	+	21.6468i	0.244578	+	0.752734i	−0.751127	+	0.660157i	$0.770490\pi$
$828$	−0.944514	+	0.420525i	−0.0328241	+	0.0146142i
$829$	−30.2692	−	13.4767i	−1.05129	−	0.468066i	−0.192986	−	0.981202i	$-0.561817\pi$
$829$	−30.2692	−	13.4767i	−1.05129	−	0.468066i	−0.858307	+	0.513136i	$0.828484\pi$
$830$	8.51258	−	1.80941i	0.295476	−	0.0628054i
$831$	0.470638	+	0.522696i	0.0163263	+	0.0181321i
$832$	−31.5497	+	22.9222i	−1.09379	+	0.794683i
$833$	−54.1708	−	5.69367i	−1.87691	−	0.197274i
$834$	−1.15231	−	3.54645i	−0.0399013	−	0.122804i
$835$	−4.29178	+	7.43358i	−0.148523	+	0.257250i
$836$	4.10657	+	4.02664i	0.142029	+	0.139264i
$837$	−4.04376	−	7.00399i	−0.139773	−	0.242093i
$838$	−16.7065	−	3.55108i	−0.577117	−	0.122670i
$839$	−20.1321	−	14.6268i	−0.695036	−	0.504973i	0.183276	−	0.983062i	$-0.441330\pi$
$839$	−20.1321	−	14.6268i	−0.695036	−	0.504973i	−0.878312	+	0.478088i	$0.841330\pi$
$840$	−4.02744	+	25.4281i	−0.138960	+	0.877353i
$841$	−3.43797	+	10.5810i	−0.118551	+	0.364862i
$842$	−8.84576	−	9.82421i	−0.304845	−	0.338565i
$843$	22.8666	+	10.1809i	0.787568	+	0.350648i
$844$	−1.82698	+	17.3826i	−0.0628873	+	0.598333i
$845$	−66.9569	−	14.2321i	−2.30339	−	0.489600i
$846$	3.34073			0.114857
$847$	−28.8289	−	3.98694i	−0.990572	−	0.136993i
$848$	1.94284			0.0667174
$849$	5.93935	+	1.26245i	0.203838	+	0.0433271i
$850$	4.52259	−	43.0295i	0.155123	−	1.47590i
$851$	1.28953	+	0.574137i	0.0442046	+	0.0196812i
$852$	−4.88997	−	5.43086i	−0.167527	−	0.186058i
$853$	−6.45402	+	19.8634i	−0.220981	+	0.680111i	0.777693	+	0.628644i	$0.216390\pi$
$853$	−6.45402	+	19.8634i	−0.220981	+	0.680111i	−0.998675	+	0.0514670i	$0.983610\pi$
$854$	5.13238	−	1.97013i	0.175627	−	0.0674165i
$855$	−4.40004	−	3.19682i	−0.150478	−	0.109329i
$856$	7.59608	+	1.61460i	0.259629	+	0.0551858i
$857$	−13.4354	−	23.2707i	−0.458944	−	0.794914i	0.539962	−	0.841689i	$-0.318439\pi$
$857$	−13.4354	−	23.2707i	−0.458944	−	0.794914i	−0.998905	+	0.0467759i	$0.985105\pi$
$858$	13.5044	+	13.2415i	0.461032	+	0.452059i
$859$	−6.19007	+	10.7215i	−0.211202	+	0.365813i	−0.952091	−	0.305815i	$-0.901071\pi$
$859$	−6.19007	+	10.7215i	−0.211202	+	0.365813i	0.740889	+	0.671628i	$0.234405\pi$
$860$	1.70578	+	5.24984i	0.0581665	+	0.179018i
$861$	−3.21366	−	3.96854i	−0.109521	−	0.135248i
$862$	24.2917	−	17.6489i	0.827378	−	0.601125i
$863$	−11.5399	−	12.8164i	−0.392823	−	0.436274i	0.513997	−	0.857792i	$-0.328164\pi$
$863$	−11.5399	−	12.8164i	−0.392823	−	0.436274i	−0.906820	+	0.421518i	$0.861497\pi$
$864$	5.02995	−	1.06915i	0.171122	−	0.0363732i
$865$	−39.9978	−	17.8082i	−1.35997	−	0.605496i
$866$	14.3849	−	6.40459i	0.488820	−	0.217637i
$867$	−13.4573	−	41.4173i	−0.457034	−	1.40661i
$868$	5.77080	+	21.5370i	0.195874	+	0.731013i
$869$	−15.5491	−	23.4361i	−0.527468	−	0.795014i
$870$	−6.76191	+	11.7120i	−0.229250	+	0.397073i
$871$	42.4161	−	47.1079i	1.43722	−	1.59619i
$872$	−3.76642	+	35.8351i	−0.127547	+	1.21353i
$873$	1.61939	+	15.4075i	0.0548081	+	0.521464i
$874$	0.499408	−	1.53702i	0.0168927	−	0.0519905i
$875$	−2.67315	−	5.24636i	−0.0903688	−	0.177359i
$876$	5.55876	−	4.03867i	0.187813	−	0.136454i
$877$	−50.7701	+	22.6043i	−1.71439	+	0.763294i	−0.716550	+	0.697536i	$0.754280\pi$
$877$	−50.7701	+	22.6043i	−1.71439	+	0.763294i	−0.997836	+	0.0657578i	$0.979054\pi$
$878$	23.3251	−	25.9051i	0.787183	−	0.874255i
$879$	6.38243	+	11.0547i	0.215274	+	0.372865i
$880$	−6.93692	+	5.73120i	−0.233844	+	0.193199i
$881$	−51.9944			−1.75174			−0.875869	−	0.482549i	$-0.839711\pi$
$881$	−51.9944			−1.75174			−0.875869	+	0.482549i	$0.839711\pi$
$882$	−5.09153	−	4.58445i	−0.171441	−	0.154367i
$883$	−42.2139	−	30.6702i	−1.42061	−	1.03213i	−0.991670	−	0.128801i	$-0.958887\pi$
$883$	−42.2139	−	30.6702i	−1.42061	−	1.03213i	−0.428940	−	0.903333i	$-0.641113\pi$
$884$	−4.93803	−	46.9822i	−0.166084	−	1.58018i
$885$	−2.24637	+	0.477481i	−0.0755109	+	0.0160503i
$886$	−4.62319	+	0.982690i	−0.155319	+	0.0330141i
$887$	−0.640629	−	6.09518i	−0.0215102	−	0.204656i	0.978488	−	0.206302i	$-0.0661428\pi$
$887$	−0.640629	−	6.09518i	−0.0215102	−	0.204656i	−0.999999	+	0.00164568i	$0.999476\pi$
$888$	−3.42688	−	2.48977i	−0.114999	−	0.0835513i
$889$	33.1133	+	16.8721i	1.11058	+	0.565872i
$890$	−46.6375			−1.56329
$891$	−1.21894	−	3.08451i	−0.0408362	−	0.103335i
$892$	−11.8485	−	20.5222i	−0.396717	−	0.687135i
$893$	3.80075	−	4.22116i	0.127187	−	0.141256i
$894$	14.4957	−	6.45389i	0.484808	−	0.215850i
$895$	50.1484	−	36.4349i	1.67628	−	1.21789i
$896$	−9.86407	−	0.516963i	−0.329536	−	0.0172705i
$897$	−1.78638	+	5.49790i	−0.0596454	+	0.183570i
$898$	1.54369	+	14.6872i	0.0515137	+	0.490120i
$899$	−3.57410	+	34.0053i	−0.119203	+	1.13414i
$900$	−3.96104	+	4.39919i	−0.132035	+	0.146640i
$901$	−9.10554	+	15.7713i	−0.303350	+	0.525417i
$902$	0.266403	−	6.25980i	0.00887026	−	0.208429i
$903$	−4.14239	−	1.10995i	−0.137850	−	0.0369369i
$904$	−4.59659	−	14.1469i	−0.152880	−	0.470517i
$905$	32.2194	−	14.3450i	1.07101	−	0.476844i
$906$	−13.0271	−	5.80004i	−0.432796	−	0.192693i
$907$	−50.7227	+	10.7814i	−1.68422	+	0.357992i	−0.947882	−	0.318622i	$-0.896780\pi$
$907$	−50.7227	+	10.7814i	−1.68422	+	0.357992i	−0.736338	+	0.676614i	$0.763447\pi$
$908$	−11.0816	−	12.3073i	−0.367755	−	0.408434i
$909$	−2.32315	+	1.68786i	−0.0770539	+	0.0559829i
$910$	31.0308	+	38.3199i	1.02866	+	1.27029i
$911$	10.6702	+	32.8394i	0.353519	+	1.08802i	0.956863	+	0.290538i	$0.0938343\pi$
$911$	10.6702	+	32.8394i	0.353519	+	1.08802i	−0.603345	+	0.797480i	$0.706166\pi$
$912$	−0.690746	+	1.19641i	−0.0228729	+	0.0396170i
$913$	7.99926	−	4.17535i	0.264737	−	0.138184i
$914$	14.4211	+	24.9780i	0.477006	+	0.826199i
$915$	6.78656	+	1.44253i	0.224357	+	0.0476885i
$916$	23.4723	+	17.0536i	0.775546	+	0.563467i
$917$	45.4747	+	36.8247i	1.50171	+	1.21606i
$918$	2.35349	−	7.24330i	0.0776768	−	0.239065i
$919$	−1.78193	−	1.97904i	−0.0587806	−	0.0652824i	0.713037	−	0.701126i	$-0.247319\pi$
$919$	−1.78193	−	1.97904i	−0.0587806	−	0.0652824i	−0.771818	+	0.635844i	$0.780652\pi$
$920$	−8.82016	−	3.92699i	−0.290792	−	0.129469i
$921$	1.71624	−	16.3289i	0.0565521	−	0.538057i
$922$	−0.00118659		0.000252217i	−3.90781e−5		8.30632e-6i
$923$	−40.8609			−1.34495
$924$	1.04509	+	9.08379i	0.0343810	+	0.298835i
$925$	8.08207			0.265737
$926$	−0.694225	−	0.147562i	−0.0228136	−	0.00484919i
$927$	−0.734402	+	6.98737i	−0.0241209	+	0.229495i
$928$	−19.8612	−	8.84279i	−0.651977	−	0.290279i
$929$	20.3082	+	22.5545i	0.666291	+	0.739991i	0.977636	−	0.210306i	$-0.0674461\pi$
$929$	20.3082	+	22.5545i	0.666291	+	0.739991i	−0.311345	+	0.950297i	$0.600779\pi$
$930$	7.99430	−	24.6039i	0.262143	−	0.806794i
$931$	−11.5853	+	1.21764i	−0.379692	+	0.0399066i
$932$	7.03682	+	5.11255i	0.230499	+	0.167467i
$933$	−9.02522	−	1.91837i	−0.295472	−	0.0628046i
$934$	11.6521	+	20.1820i	0.381267	+	0.660374i
$935$	−14.0124	−	83.1719i	−0.458253	−	2.72001i
$936$	8.67361	−	15.0231i	0.283506	−	0.491046i
$937$	3.69220	+	11.3634i	0.120619	+	0.371227i	0.993077	−	0.117461i	$-0.0374756\pi$
$937$	3.69220	+	11.3634i	0.120619	+	0.371227i	−0.872459	+	0.488688i	$0.837476\pi$
$938$	−27.8277	+	4.40745i	−0.908606	+	0.143908i
$939$	21.0597	−	15.3008i	0.687257	−	0.499322i
$940$	−7.77780	−	8.63812i	−0.253684	−	0.281744i
$941$	26.3683	−	5.60476i	0.859583	−	0.182710i	0.243026	−	0.970020i	$-0.421860\pi$
$941$	26.3683	−	5.60476i	0.859583	−	0.182710i	0.616558	+	0.787310i	$0.288527\pi$
$942$	−4.84501	−	2.15714i	−0.157859	−	0.0702834i
$943$	1.74949	−	0.778922i	0.0569711	−	0.0253652i
$944$	0.180264	+	0.554794i	0.00586708	+	0.0180570i
$945$	−2.23794	−	8.35215i	−0.0728003	−	0.271695i
$946$	−2.90900	−	4.38452i	−0.0945796	−	0.142553i
$947$	5.87245	−	10.1714i	0.190829	−	0.330526i	−0.754696	−	0.656074i	$-0.772216\pi$
$947$	5.87245	−	10.1714i	0.190829	−	0.330526i	0.945525	+	0.325549i	$0.105549\pi$
$948$	−5.91271	+	6.56673i	−0.192036	+	0.213277i
$949$	4.01575	−	38.2073i	0.130357	−	1.24026i
$950$	−0.967227	−	9.20255i	−0.0313810	−	0.298570i
$951$	3.94654	−	12.1462i	0.127975	−	0.393868i
$952$	−33.3850	+	51.4083i	−1.08201	+	1.66615i
$953$	7.21786	−	5.24408i	0.233809	−	0.169872i	−0.464711	−	0.885462i	$-0.653842\pi$
$953$	7.21786	−	5.24408i	0.233809	−	0.169872i	0.698521	+	0.715590i	$0.253842\pi$
$954$	−2.09262	+	0.931696i	−0.0677512	+	0.0301648i
$955$	18.0804	−	20.0803i	0.585068	−	0.649784i
$956$	−3.03251	−	5.25246i	−0.0980784	−	0.169877i
$957$	−3.49590	+	13.5793i	−0.113007	+	0.438957i
$958$	2.29193			0.0740488
$959$	0.689864	+	13.1636i	0.0222769	+	0.425075i
$960$	17.6974	+	12.8579i	0.571182	+	0.414988i
$961$	−3.59660	−	34.2194i	−0.116019	−	1.10385i
$962$	−7.93547	+	1.68674i	−0.255850	+	0.0543826i
$963$	−2.55123	+	0.542281i	−0.0822122	+	0.0174748i
$964$	−1.91660	−	18.2352i	−0.0617296	−	0.587318i
$965$	36.2258	+	26.3196i	1.16615	+	0.847258i
$966$	2.15486	−	1.39938i	0.0693316	−	0.0450244i
$967$	−3.63781			−0.116984			−0.0584921	−	0.998288i	$-0.518629\pi$
$967$	−3.63781			−0.116984			−0.0584921	+	0.998288i	$0.518629\pi$
$968$	−18.7264	+	26.8699i	−0.601890	+	0.863630i
$969$	−6.47466	−	11.2144i	−0.207996	−	0.360260i
$970$	−33.1597	+	36.8276i	−1.06469	+	1.18246i
$971$	−17.4333	+	7.76180i	−0.559461	+	0.249088i	−0.666930	−	0.745120i	$-0.732392\pi$
$971$	−17.4333	+	7.76180i	−0.559461	+	0.249088i	0.107469	+	0.994208i	$0.465725\pi$
$972$	−0.843014	+	0.612485i	−0.0270397	+	0.0196455i
$973$	−4.57620	−	8.98132i	−0.146706	−	0.287928i
$974$	4.78731	−	14.7338i	0.153395	−	0.472103i
$975$	3.45976	+	32.9174i	0.110801	+	1.05420i
$976$	0.184217	−	1.75270i	0.00589663	−	0.0561027i
$977$	31.2075	−	34.6594i	0.998415	−	1.10885i	0.00435838	−	0.999991i	$-0.498613\pi$
$977$	31.2075	−	34.6594i	0.998415	−	1.10885i	0.994057	−	0.108862i	$-0.0347207\pi$
$978$	−3.02327	+	5.23646i	−0.0966736	+	0.167444i
$979$	−46.5829	+	12.9738i	−1.48880	+	0.414645i
$980$	−4.13019e−5		23.8386i	−1.31934e−6		0.761495i
$981$	−3.73970	−	11.5096i	−0.119399	−	0.367474i
$982$	−23.0721	+	10.2723i	−0.736259	+	0.327804i
$983$	−19.8015	−	8.81621i	−0.631571	−	0.281194i	0.0658783	−	0.997828i	$-0.479015\pi$
$983$	−19.8015	−	8.81621i	−0.631571	−	0.281194i	−0.697449	+	0.716634i	$0.745682\pi$
$984$	−5.62113	+	1.19481i	−0.179195	+	0.0380891i
$985$	−7.81446	−	8.67883i	−0.248989	−	0.276531i
$986$	−26.0498	+	18.9263i	−0.829595	+	0.602736i
$987$	8.91934	−	1.41268i	0.283906	−	0.0449660i
$988$	−3.12208	−	9.60876i	−0.0993264	−	0.305695i
$989$	0.804135	−	1.39280i	0.0255700	−	0.0442886i
$990$	4.72331	−	9.49967i	0.150117	−	0.301919i
$991$	16.3268	+	28.2789i	0.518638	+	0.898307i	0.999765	+	0.0216568i	$0.00689411\pi$
$991$	16.3268	+	28.2789i	0.518638	+	0.898307i	−0.481127	+	0.876651i	$0.659773\pi$
$992$	40.6798	+	8.64676i	1.29159	+	0.274535i
$993$	3.62664	+	2.63491i	0.115088	+	0.0836163i
$994$	14.1139	+	11.4292i	0.447666	+	0.362513i
$995$	22.5332	−	69.3500i	0.714350	−	2.19854i
$996$	−1.89698	−	2.10681i	−0.0601080	−	0.0667567i
$997$	−8.13044	−	3.61990i	−0.257494	−	0.114644i	0.273930	−	0.961750i	$-0.411676\pi$
$997$	−8.13044	−	3.61990i	−0.257494	−	0.114644i	−0.531424	+	0.847106i	$0.678343\pi$
$998$	−0.941352	+	8.95637i	−0.0297980	+	0.283509i
$999$	1.39157	+	0.295788i	0.0440274	+	0.00935830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.16.3	✓	64
3.2	odd	2		693.2.by.d.478.6		64
7.4	even	3	inner	231.2.y.a.214.6	yes	64
11.9	even	5	inner	231.2.y.a.163.6	yes	64
21.11	odd	6		693.2.by.d.676.3		64
33.20	odd	10		693.2.by.d.163.3		64
77.53	even	15	inner	231.2.y.a.130.3	yes	64
231.53	odd	30		693.2.by.d.361.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.3	✓	64	1.1	even	1	trivial
231.2.y.a.130.3	yes	64	77.53	even	15	inner
231.2.y.a.163.6	yes	64	11.9	even	5	inner
231.2.y.a.214.6	yes	64	7.4	even	3	inner
693.2.by.d.163.3		64	33.20	odd	10
693.2.by.d.361.6		64	231.53	odd	30
693.2.by.d.478.6		64	3.2	odd	2
693.2.by.d.676.3		64	21.11	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.957375 - 0.203496i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.951935 - 0.423829i) q^{4} +(2.18684 + 2.42873i) q^{5} +(-0.302455 + 0.930859i) q^{6} +(-0.413889 + 2.61318i) q^{7} +(2.40878 + 1.75008i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.957375 - 0.203496i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.951935 - 0.423829i) q^{4} +(2.18684 + 2.42873i) q^{5} +(-0.302455 + 0.930859i) q^{6} +(-0.413889 + 2.61318i) q^{7} +(2.40878 + 1.75008i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-1.59938 - 2.77022i) q^{10} +(-2.36814 - 2.32205i) q^{11} +(-0.521011 + 0.902418i) q^{12} +(1.80041 + 5.54110i) q^{13} +(0.928019 - 2.41757i) q^{14} +(2.64401 - 1.92098i) q^{15} +(-0.555475 - 0.616918i) q^{16} +(7.61127 - 1.61783i) q^{17} +(0.894145 + 0.398099i) q^{18} +(1.52028 - 0.676874i) q^{19} +(-1.05236 - 3.23883i) q^{20} +(2.55560 + 0.684773i) q^{21} +(1.79467 + 2.70498i) q^{22} +(-0.496102 + 0.859274i) q^{23} +(1.99228 - 2.21265i) q^{24} +(-0.593822 + 5.64984i) q^{25} +(-0.596076 - 5.67129i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50153 - 2.31216i) q^{28} +(3.42038 - 2.48505i) q^{29} +(-2.92222 + 1.30106i) q^{30} +(-5.41160 + 6.01019i) q^{31} +(-2.57116 - 4.45338i) q^{32} +(-2.55686 + 2.11245i) q^{33} -7.61606 q^{34} +(-7.25180 + 4.70937i) q^{35} +(0.843014 + 0.612485i) q^{36} +(-0.148708 - 1.41487i) q^{37} +(-1.59322 + 0.338650i) q^{38} +(5.69894 - 1.21135i) q^{39} +(1.01714 + 9.67742i) q^{40} +(-1.56148 - 1.13448i) q^{41} +(-2.30732 - 1.17564i) q^{42} -1.62091 q^{43} +(1.27017 + 3.21412i) q^{44} +(-1.63409 - 2.83032i) q^{45} +(0.649815 - 0.721693i) q^{46} +(3.11813 - 1.38828i) q^{47} +(-0.671601 + 0.487947i) q^{48} +(-6.65739 - 2.16313i) q^{49} +(1.71823 - 5.28818i) q^{50} +(-0.813368 - 7.73868i) q^{51} +(0.634602 - 6.03783i) q^{52} +(-1.56601 + 1.73923i) q^{53} +(0.489382 - 0.847634i) q^{54} +(0.460880 - 10.8295i) q^{55} +(-5.57025 + 5.57024i) q^{56} +(-0.514253 - 1.58271i) q^{57} +(-3.78029 + 1.68309i) q^{58} +(-0.641951 - 0.285815i) q^{59} +(-3.33109 + 0.708045i) q^{60} +(1.42053 + 1.57766i) q^{61} +(6.40399 - 4.65277i) q^{62} +(0.948155 - 2.47002i) q^{63} +(2.06838 + 6.36581i) q^{64} +(-9.52061 + 16.4902i) q^{65} +(2.87775 - 1.50209i) q^{66} +(-5.44002 - 9.42239i) q^{67} +(-7.93111 - 1.68581i) q^{68} +(0.802710 + 0.583203i) q^{69} +(7.90103 - 3.03291i) q^{70} +(-2.16721 + 6.66998i) q^{71} +(-1.99228 - 2.21265i) q^{72} +(-6.02383 - 2.68198i) q^{73} +(-0.145550 + 1.38482i) q^{74} +(5.55682 + 1.18114i) q^{75} -1.73409 q^{76} +(7.04807 - 5.22731i) q^{77} -5.70253 q^{78} +(8.29474 + 1.76310i) q^{79} +(0.283592 - 2.69820i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.26406 + 1.40388i) q^{82} +(-0.840730 + 2.58750i) q^{83} +(-2.14254 - 1.73500i) q^{84} +(20.5738 + 14.9478i) q^{85} +(1.55182 + 0.329849i) q^{86} +(-2.11391 - 3.66140i) q^{87} +(-1.64057 - 9.73775i) q^{88} +(7.28991 - 12.6265i) q^{89} +(0.988474 + 3.04221i) q^{90} +(-15.2250 + 2.41140i) q^{91} +(0.836442 - 0.607711i) q^{92} +(5.41160 + 6.01019i) q^{93} +(-3.26773 + 0.694577i) q^{94} +(4.96855 + 2.21214i) q^{95} +(-4.69775 + 2.09157i) q^{96} +(-4.78740 - 14.7341i) q^{97} +(5.93343 + 3.42568i) q^{98} +(1.83361 + 2.76367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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