LMFDB - Embedded newform 23.2.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,2,Mod(2,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("23.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	23.c (of order $11$, degree $10$, 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:	$0.183655924649$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			3.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	23.3
Dual form			23.2.c.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.313607 - 2.18119i) q^{2} +(-1.04408 + 2.28621i) q^{3} +(-2.74024 + 0.804606i) q^{4} +(0.809721 - 0.934468i) q^{5} +(5.31408 + 1.56036i) q^{6} +(-1.99611 + 1.28282i) q^{7} +(0.783524 + 1.71568i) q^{8} +(-2.17208 - 2.50672i) q^{9} +O(q^{10})$	\(q+(-0.313607 - 2.18119i) q^{2} +(-1.04408 + 2.28621i) q^{3} +(-2.74024 + 0.804606i) q^{4} +(0.809721 - 0.934468i) q^{5} +(5.31408 + 1.56036i) q^{6} +(-1.99611 + 1.28282i) q^{7} +(0.783524 + 1.71568i) q^{8} +(-2.17208 - 2.50672i) q^{9} +(-2.29218 - 1.47310i) q^{10} +(0.272084 - 1.89238i) q^{11} +(1.02152 - 7.10483i) q^{12} +(0.165284 + 0.106222i) q^{13} +(3.42408 + 3.95159i) q^{14} +(1.29098 + 2.82685i) q^{15} +(-1.30862 + 0.840996i) q^{16} +(1.49672 + 0.439476i) q^{17} +(-4.78644 + 5.52384i) q^{18} +(7.66103 - 2.24948i) q^{19} +(-1.46695 + 3.21217i) q^{20} +(-0.848710 - 5.90291i) q^{21} -4.21297 q^{22} +(-4.66752 + 1.10192i) q^{23} -4.74046 q^{24} +(0.493992 + 3.43579i) q^{25} +(0.179855 - 0.393828i) q^{26} +(0.764125 - 0.224367i) q^{27} +(4.43766 - 5.12133i) q^{28} +(-4.77570 - 1.40227i) q^{29} +(5.76103 - 3.70239i) q^{30} +(0.740552 + 1.62158i) q^{31} +(4.71506 + 5.44146i) q^{32} +(4.04231 + 2.59784i) q^{33} +(0.489198 - 3.40244i) q^{34} +(-0.417537 + 2.90404i) q^{35} +(7.96894 + 5.12133i) q^{36} +(-2.54297 - 2.93475i) q^{37} +(-7.30909 - 16.0047i) q^{38} +(-0.415415 + 0.266971i) q^{39} +(2.23768 + 0.657043i) q^{40} +(-0.279295 + 0.322324i) q^{41} +(-12.6092 + 3.70239i) q^{42} +(1.84991 - 4.05075i) q^{43} +(0.777050 + 5.40450i) q^{44} -4.10123 q^{45} +(3.86725 + 9.83517i) q^{46} -2.58842 q^{47} +(-0.556399 - 3.86984i) q^{48} +(-0.569072 + 1.24609i) q^{49} +(7.33918 - 2.15498i) q^{50} +(-2.56743 + 2.96297i) q^{51} +(-0.538385 - 0.158084i) q^{52} +(8.26060 - 5.30876i) q^{53} +(-0.729022 - 1.59634i) q^{54} +(-1.54806 - 1.78656i) q^{55} +(-3.76492 - 2.41956i) q^{56} +(-2.85592 + 19.8634i) q^{57} +(-1.56092 + 10.8565i) q^{58} +(-6.07293 - 3.90283i) q^{59} +(-5.81210 - 6.70752i) q^{60} +(3.08639 + 6.75826i) q^{61} +(3.30473 - 2.12382i) q^{62} +(7.55141 + 2.21729i) q^{63} +(8.35283 - 9.63968i) q^{64} +(0.233095 - 0.0684429i) q^{65} +(4.39867 - 9.63174i) q^{66} +(-1.03413 - 7.19254i) q^{67} -4.45497 q^{68} +(2.35404 - 11.8214i) q^{69} +6.46519 q^{70} +(0.103930 + 0.722850i) q^{71} +(2.59884 - 5.69067i) q^{72} +(6.18330 - 1.81558i) q^{73} +(-5.60373 + 6.46705i) q^{74} +(-8.37071 - 2.45786i) q^{75} +(-19.1831 + 12.3282i) q^{76} +(1.88449 + 4.12645i) q^{77} +(0.712591 + 0.822373i) q^{78} +(-4.77671 - 3.06980i) q^{79} +(-0.273730 + 1.90383i) q^{80} +(1.13126 - 7.86810i) q^{81} +(0.790638 + 0.508112i) q^{82} +(8.44098 + 9.74141i) q^{83} +(7.07518 + 15.4925i) q^{84} +(1.62260 - 1.04278i) q^{85} +(-9.41558 - 2.76466i) q^{86} +(8.19209 - 9.45418i) q^{87} +(3.45991 - 1.01592i) q^{88} +(-5.77436 + 12.6441i) q^{89} +(1.28618 + 8.94555i) q^{90} -0.466190 q^{91} +(11.9035 - 6.77503i) q^{92} -4.48047 q^{93} +(0.811746 + 5.64582i) q^{94} +(4.10123 - 8.98044i) q^{95} +(-17.3632 + 5.09830i) q^{96} +(-2.83147 + 3.26769i) q^{97} +(2.89643 + 0.850468i) q^{98} +(-5.33466 + 3.42838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.313607	−	2.18119i	−0.221754	−	1.54233i	−0.731401	−	0.681948i	$-0.761133\pi$
$2$	−0.313607	−	2.18119i	−0.221754	−	1.54233i	0.509647	−	0.860384i	$-0.329776\pi$
$3$	−1.04408	+	2.28621i	−0.602799	+	1.31995i	0.324593	+	0.945854i	$0.394773\pi$
$3$	−1.04408	+	2.28621i	−0.602799	+	1.31995i	−0.927392	+	0.374091i	$0.877955\pi$
$4$	−2.74024	+	0.804606i	−1.37012	+	0.402303i
$5$	0.809721	−	0.934468i	0.362118	−	0.417907i	−0.545230	−	0.838287i	$-0.683558\pi$
$5$	0.809721	−	0.934468i	0.362118	−	0.417907i	0.907348	+	0.420380i	$0.138103\pi$
$6$	5.31408	+	1.56036i	2.16947	+	0.637013i
$7$	−1.99611	+	1.28282i	−0.754460	+	0.484862i	−0.860469	−	0.509503i	$-0.829829\pi$
$7$	−1.99611	+	1.28282i	−0.754460	+	0.484862i	0.106009	+	0.994365i	$0.466193\pi$
$8$	0.783524	+	1.71568i	0.277017	+	0.606584i
$9$	−2.17208	−	2.50672i	−0.724028	−	0.835573i
$10$	−2.29218	−	1.47310i	−0.724852	−	0.465834i
$11$	0.272084	−	1.89238i	0.0820363	−	0.570575i	−0.906799	−	0.421563i	$-0.861482\pi$
$11$	0.272084	−	1.89238i	0.0820363	−	0.570575i	0.988835	−	0.149012i	$-0.0476093\pi$
$12$	1.02152	−	7.10483i	0.294888	−	2.05099i
$13$	0.165284	+	0.106222i	0.0458416	+	0.0294606i	0.563361	−	0.826211i	$-0.309508\pi$
$13$	0.165284	+	0.106222i	0.0458416	+	0.0294606i	−0.517519	+	0.855672i	$0.673144\pi$
$14$	3.42408	+	3.95159i	0.915123	+	1.05611i
$15$	1.29098	+	2.82685i	0.333330	+	0.729890i
$16$	−1.30862	+	0.840996i	−0.327154	+	0.210249i
$17$	1.49672	+	0.439476i	0.363008	+	0.106589i	0.458150	−	0.888875i	$-0.348512\pi$
$17$	1.49672	+	0.439476i	0.363008	+	0.106589i	−0.0951421	+	0.995464i	$0.530331\pi$
$18$	−4.78644	+	5.52384i	−1.12817	+	1.30198i
$19$	7.66103	−	2.24948i	1.75756	−	0.516066i	0.765678	−	0.643224i	$-0.222403\pi$
$19$	7.66103	−	2.24948i	1.75756	−	0.516066i	0.991883	+	0.127157i	$0.0405853\pi$
$20$	−1.46695	+	3.21217i	−0.328020	+	0.718263i
$21$	−0.848710	−	5.90291i	−0.185204	−	1.28812i
$22$	−4.21297			−0.898208
$23$	−4.66752	+	1.10192i	−0.973246	+	0.229765i
$23$	−4.66752	+	1.10192i	−0.973246	+	0.229765i
$24$	−4.74046			−0.967643
$25$	0.493992	+	3.43579i	0.0987984	+	0.687158i
$26$	0.179855	−	0.393828i	0.0352725	−	0.0772359i
$27$	0.764125	−	0.224367i	0.147056	−	0.0431795i
$28$	4.43766	−	5.12133i	0.838638	−	0.967840i
$29$	−4.77570	−	1.40227i	−0.886825	−	0.260395i	−0.193569	−	0.981087i	$-0.562006\pi$
$29$	−4.77570	−	1.40227i	−0.886825	−	0.260395i	−0.693256	+	0.720691i	$0.743825\pi$
$30$	5.76103	−	3.70239i	1.05182	−	0.675961i
$31$	0.740552	+	1.62158i	0.133007	+	0.291245i	0.964404	−	0.264435i	$-0.0851854\pi$
$31$	0.740552	+	1.62158i	0.133007	+	0.291245i	−0.831397	+	0.555680i	$0.812458\pi$
$32$	4.71506	+	5.44146i	0.833512	+	0.961924i
$33$	4.04231	+	2.59784i	0.703677	+	0.452226i
$34$	0.489198	−	3.40244i	0.0838967	−	0.583514i
$35$	−0.417537	+	2.90404i	−0.0705767	+	0.490872i
$36$	7.96894	+	5.12133i	1.32816	+	0.853555i
$37$	−2.54297	−	2.93475i	−0.418062	−	0.482469i	0.507184	−	0.861838i	$-0.330687\pi$
$37$	−2.54297	−	2.93475i	−0.418062	−	0.482469i	−0.925246	+	0.379369i	$0.876141\pi$
$38$	−7.30909	−	16.0047i	−1.18569	−	2.59630i
$39$	−0.415415	+	0.266971i	−0.0665196	+	0.0427496i
$40$	2.23768	+	0.657043i	0.353809	+	0.103888i
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	−0.777140	−	0.629328i	$-0.783330\pi$
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	0.733521	+	0.679667i	$0.237876\pi$
$42$	−12.6092	+	3.70239i	−1.94564	+	0.571291i
$43$	1.84991	−	4.05075i	0.282109	−	0.617733i	−0.714534	−	0.699601i	$-0.753361\pi$
$43$	1.84991	−	4.05075i	0.282109	−	0.617733i	0.996643	+	0.0818677i	$0.0260885\pi$
$44$	0.777050	+	5.40450i	0.117145	+	0.814759i
$45$	−4.10123			−0.611375
$46$	3.86725	+	9.83517i	0.570195	+	1.45012i
$47$	−2.58842			−0.377559			−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842			−0.377559			−0.188780	+	0.982019i	$0.560453\pi$
$48$	−0.556399	−	3.86984i	−0.0803092	−	0.558563i
$49$	−0.569072	+	1.24609i	−0.0812960	+	0.178013i
$50$	7.33918	−	2.15498i	1.03792	−	0.304760i
$51$	−2.56743	+	2.96297i	−0.359512	+	0.414898i
$52$	−0.538385	−	0.158084i	−0.0746605	−	0.0219223i
$53$	8.26060	−	5.30876i	1.13468	−	0.729215i	0.168149	−	0.985762i	$-0.446221\pi$
$53$	8.26060	−	5.30876i	1.13468	−	0.729215i	0.966532	+	0.256547i	$0.0825848\pi$
$54$	−0.729022	−	1.59634i	−0.0992074	−	0.217234i
$55$	−1.54806	−	1.78656i	−0.208741	−	0.240899i
$56$	−3.76492	−	2.41956i	−0.503108	−	0.323328i
$57$	−2.85592	+	19.8634i	−0.378276	+	2.63097i
$58$	−1.56092	+	10.8565i	−0.204959	+	1.42552i
$59$	−6.07293	−	3.90283i	−0.790628	−	0.508106i	0.0819173	−	0.996639i	$-0.473896\pi$
$59$	−6.07293	−	3.90283i	−0.790628	−	0.508106i	−0.872545	+	0.488533i	$0.837532\pi$
$60$	−5.81210	−	6.70752i	−0.750338	−	0.865936i
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	0.997737	+	0.0672363i	$0.0214181\pi$
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	−0.602565	+	0.798070i	$0.705855\pi$
$62$	3.30473	−	2.12382i	0.419701	−	0.269726i
$63$	7.55141	+	2.21729i	0.951388	+	0.279353i
$64$	8.35283	−	9.63968i	1.04410	−	1.20496i
$65$	0.233095	−	0.0684429i	0.0289119	−	0.00848929i
$66$	4.39867	−	9.63174i	0.541439	−	1.18559i
$67$	−1.03413	−	7.19254i	−0.126339	−	0.878708i	−0.950139	−	0.311827i	$-0.899059\pi$
$67$	−1.03413	−	7.19254i	−0.126339	−	0.878708i	0.823800	−	0.566881i	$-0.191850\pi$
$68$	−4.45497			−0.540244
$69$	2.35404	−	11.8214i	0.283394	−	1.42313i
$70$	6.46519			0.772738
$71$	0.103930	+	0.722850i	0.0123342	+	0.0857866i	0.995059	−	0.0992879i	$-0.0316565\pi$
$71$	0.103930	+	0.722850i	0.0123342	+	0.0857866i	−0.982725	+	0.185074i	$0.940747\pi$
$72$	2.59884	−	5.69067i	0.306276	−	0.670652i
$73$	6.18330	−	1.81558i	0.723700	−	0.212498i	0.100920	−	0.994895i	$-0.467821\pi$
$73$	6.18330	−	1.81558i	0.723700	−	0.212498i	0.622780	+	0.782397i	$0.286003\pi$
$74$	−5.60373	+	6.46705i	−0.651421	+	0.751780i
$75$	−8.37071	−	2.45786i	−0.966566	−	0.283809i
$76$	−19.1831	+	12.3282i	−2.20045	+	1.41414i
$77$	1.88449	+	4.12645i	0.214757	+	0.470253i
$78$	0.712591	+	0.822373i	0.0806850	+	0.0931154i
$79$	−4.77671	−	3.06980i	−0.537422	−	0.345380i	0.243608	−	0.969874i	$-0.421669\pi$
$79$	−4.77671	−	3.06980i	−0.537422	−	0.345380i	−0.781030	+	0.624494i	$0.785305\pi$
$80$	−0.273730	+	1.90383i	−0.0306039	+	0.212855i
$81$	1.13126	−	7.86810i	0.125696	−	0.874233i
$82$	0.790638	+	0.508112i	0.0873113	+	0.0561116i
$83$	8.44098	+	9.74141i	0.926518	+	1.06926i	0.997421	+	0.0717758i	$0.0228666\pi$
$83$	8.44098	+	9.74141i	0.926518	+	1.06926i	−0.0709025	+	0.997483i	$0.522588\pi$
$84$	7.07518	+	15.4925i	0.771966	+	1.69037i
$85$	1.62260	−	1.04278i	0.175996	−	0.113106i
$86$	−9.41558	−	2.76466i	−1.01531	−	0.298121i
$87$	8.19209	−	9.45418i	0.878284	−	1.01359i
$88$	3.45991	−	1.01592i	0.368827	−	0.108297i
$89$	−5.77436	+	12.6441i	−0.612081	+	1.34027i	0.309060	+	0.951043i	$0.399986\pi$
$89$	−5.77436	+	12.6441i	−0.612081	+	1.34027i	−0.921141	+	0.389228i	$0.872742\pi$
$90$	1.28618	+	8.94555i	0.135575	+	0.942944i
$91$	−0.466190			−0.0488700
$92$	11.9035	−	6.77503i	1.24103	−	0.706346i
$93$	−4.48047			−0.464603
$94$	0.811746	+	5.64582i	0.0837252	+	0.582322i
$95$	4.10123	−	8.98044i	0.420777	−	0.921374i
$96$	−17.3632	+	5.09830i	−1.77213	+	0.520343i
$97$	−2.83147	+	3.26769i	−0.287492	+	0.331783i	−0.881064	−	0.472998i	$-0.843172\pi$
$97$	−2.83147	+	3.26769i	−0.287492	+	0.331783i	0.593572	+	0.804781i	$0.297717\pi$
$98$	2.89643	+	0.850468i	0.292583	+	0.0859103i
$99$	−5.33466	+	3.42838i	−0.536154	+	0.344565i
$100$	−4.11811	−	9.01741i	−0.411811	−	0.901741i
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	0.811950	−	0.583727i	$-0.198406\pi$
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	−0.693338	+	0.720612i	$0.743861\pi$
$102$	7.26795	+	4.67083i	0.719634	+	0.462481i
$103$	2.17930	−	15.1574i	0.214733	−	1.49350i	−0.542335	−	0.840163i	$-0.682459\pi$
$103$	2.17930	−	15.1574i	0.214733	−	1.49350i	0.757067	−	0.653337i	$-0.226631\pi$
$104$	−0.0527381	+	0.366802i	−0.00517140	+	0.0359679i
$105$	−6.20330	−	3.98662i	−0.605380	−	0.389054i
$106$	−14.1700	−	16.3530i	−1.37631	−	1.58835i
$107$	0.825981	+	1.80865i	0.0798506	+	0.174848i	0.945346	−	0.326068i	$-0.105724\pi$
$107$	0.825981	+	1.80865i	0.0798506	+	0.174848i	−0.865496	+	0.500916i	$0.832996\pi$
$108$	−1.91336	+	1.22964i	−0.184113	+	0.118322i
$109$	−14.9631	−	4.39356i	−1.43320	−	0.420826i	−0.529253	−	0.848464i	$-0.677528\pi$
$109$	−14.9631	−	4.39356i	−1.43320	−	0.420826i	−0.903950	+	0.427638i	$0.859346\pi$
$110$	−3.41133	+	3.93689i	−0.325258	+	0.375367i
$111$	9.36451	−	2.74967i	0.888840	−	0.260987i
$112$	1.53330	−	3.35745i	0.144883	−	0.317249i
$113$	0.211799	+	1.47310i	0.0199244	+	0.138577i	0.997356	−	0.0726771i	$-0.0231542\pi$
$113$	0.211799	+	1.47310i	0.0199244	+	0.138577i	−0.977431	+	0.211254i	$0.932245\pi$
$114$	44.2213			4.14171
$115$	−2.74969	+	5.25390i	−0.256410	+	0.489929i
$116$	14.2148			1.31981
$117$	−0.0927432	−	0.645043i	−0.00857412	−	0.0596343i
$118$	−6.60829	+	14.4701i	−0.608343	+	1.33208i
$119$	−3.55139	+	1.04278i	−0.325556	+	0.0955917i
$120$	−3.83845	+	4.42981i	−0.350401	+	0.404385i
$121$	7.04733	+	2.06928i	0.640667	+	0.188117i
$122$	13.7731	−	8.85143i	1.24696	−	0.801371i
$123$	−0.445295	−	0.975060i	−0.0401509	−	0.0879182i
$124$	−3.33402	−	3.84767i	−0.299404	−	0.345531i
$125$	8.81159	+	5.66287i	0.788133	+	0.506502i
$126$	2.46815	−	17.1664i	0.219881	−	1.52930i
$127$	−0.853087	+	5.93335i	−0.0756993	+	0.526500i	0.916323	+	0.400439i	$0.131142\pi$
$127$	−0.853087	+	5.93335i	−0.0756993	+	0.526500i	−0.992023	+	0.126061i	$0.959767\pi$
$128$	−11.5312	−	7.41067i	−1.01923	−	0.655017i
$129$	7.32941	+	8.45859i	0.645319	+	0.744737i
$130$	−0.222387	−	0.486959i	−0.0195046	−	0.0427092i
$131$	−10.7418	+	6.90335i	−0.938517	+	0.603148i	−0.917974	−	0.396641i	$-0.870176\pi$
$131$	−10.7418	+	6.90335i	−0.938517	+	0.603148i	−0.0205431	+	0.999789i	$0.506540\pi$
$132$	−13.1671	−	3.86622i	−1.14605	−	0.336511i
$133$	−12.4066	+	14.3180i	−1.07579	+	1.24153i
$134$	−15.3640	+	4.51126i	−1.32724	+	0.389714i
$135$	0.409064	−	0.895726i	0.0352067	−	0.0770918i
$136$	0.418715	+	2.91223i	0.0359045	+	0.249721i
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$	−26.5230	−	1.42732i	−2.25779	−	0.121502i
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	−1.19245	−	8.29370i	−0.100781	−	0.700946i
$141$	2.70251	−	5.91767i	0.227592	−	0.498358i
$142$	1.54408	−	0.453382i	0.129576	−	0.0380470i
$143$	0.245983	−	0.283880i	0.0205702	−	0.0237392i
$144$	4.95056	+	1.45362i	0.412547	+	0.121135i
$145$	−5.17736	+	3.32729i	−0.429957	+	0.276316i
$146$	−5.89924	−	12.9175i	−0.488225	−	1.06906i
$147$	−2.25468	−	2.60204i	−0.185963	−	0.214613i
$148$	9.32966	+	5.99581i	0.766893	+	0.492852i
$149$	2.36798	−	16.4697i	0.193993	−	1.34925i	−0.627317	−	0.778764i	$-0.715847\pi$
$149$	2.36798	−	16.4697i	0.193993	−	1.34925i	0.821309	−	0.570483i	$-0.193244\pi$
$150$	−2.73594	+	19.0289i	−0.223388	+	1.55370i
$151$	11.0961	+	7.13103i	0.902988	+	0.580315i	0.907675	−	0.419674i	$-0.137855\pi$
$151$	11.0961	+	7.13103i	0.902988	+	0.580315i	−0.00468679	+	0.999989i	$0.501492\pi$
$152$	9.86198	+	11.3813i	0.799913	+	0.923148i
$153$	−2.14935	−	4.70643i	−0.173765	−	0.380492i
$154$	8.40957	−	5.40450i	0.677662	−	0.435507i
$155$	2.11496	+	0.621008i	0.169877	+	0.0498805i
$156$	0.923529	−	1.06581i	0.0739415	−	0.0853330i
$157$	−3.96143	+	1.16318i	−0.316157	+	0.0928320i	−0.435961	−	0.899965i	$-0.643591\pi$
$157$	−3.96143	+	1.16318i	−0.316157	+	0.0928320i	0.119804	+	0.992798i	$0.461773\pi$
$158$	−5.19780	+	11.3816i	−0.413515	+	0.905471i
$159$	3.51225	+	24.4282i	0.278540	+	1.93729i
$160$	8.90276			0.703825
$161$	7.90335	−	8.18717i	0.622871	−	0.645239i
$162$	−17.5166			−1.37623
$163$	2.10474	+	14.6388i	0.164856	+	1.14660i	0.889320	+	0.457285i	$0.151178\pi$
$163$	2.10474	+	14.6388i	0.164856	+	1.14660i	−0.724464	+	0.689312i	$0.757913\pi$
$164$	0.505992	−	1.10797i	0.0395113	−	0.0865177i
$165$	5.70075	−	1.67389i	0.443802	−	0.130312i
$166$	18.6007	−	21.4663i	1.44369	−	1.66611i
$167$	−1.27588	−	0.374632i	−0.0987306	−	0.0289899i	0.231994	−	0.972717i	$-0.425475\pi$
$167$	−1.27588	−	0.374632i	−0.0987306	−	0.0289899i	−0.330725	+	0.943727i	$0.607293\pi$
$168$	9.46250	−	6.08118i	0.730048	−	0.469173i
$169$	−5.38436	−	11.7901i	−0.414181	−	0.906931i
$170$	−2.78336	−	3.21217i	−0.213474	−	0.246362i
$171$	−22.2792	−	14.3180i	−1.70373	−	1.09492i
$172$	−1.80995	+	12.5885i	−0.138007	+	0.959861i
$173$	2.41025	−	16.7637i	0.183248	−	1.27452i	−0.665771	−	0.746156i	$-0.731897\pi$
$173$	2.41025	−	16.7637i	0.183248	−	1.27452i	0.849019	−	0.528362i	$-0.177194\pi$
$174$	−23.1904	−	14.9036i	−1.75806	−	1.12984i
$175$	−5.39358	−	6.22452i	−0.407716	−	0.470530i
$176$	1.23543	+	2.70522i	0.0931244	+	0.203914i
$177$	15.2633	−	9.80914i	1.14726	−	0.737300i
$178$	29.3900	+	8.62968i	2.20287	+	0.646822i
$179$	0.937335	−	1.08174i	0.0700597	−	0.0808532i	−0.719638	−	0.694350i	$-0.755692\pi$
$179$	0.937335	−	1.08174i	0.0700597	−	0.0808532i	0.789697	+	0.613497i	$0.210238\pi$
$180$	11.2383	−	3.29988i	0.837657	−	0.245958i
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	0.478986	+	0.877822i	$0.341004\pi$
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	−0.977083	+	0.212858i	$0.931723\pi$
$182$	0.146201	+	1.01685i	0.0108371	+	0.0753737i
$183$	−18.6732			−1.38037
$184$	−5.54765	−	7.14459i	−0.408978	−	0.526706i
$185$	−4.80153			−0.353015
$186$	1.40511	+	9.77275i	0.103028	+	0.716573i
$187$	1.23889	−	2.71279i	0.0905967	−	0.198379i
$188$	7.09288	−	2.08266i	0.517301	−	0.151893i
$189$	−1.23746	+	1.42810i	−0.0900118	+	0.103879i
$190$	−20.8742	−	6.12922i	−1.51437	−	0.444660i
$191$	−17.4514	+	11.2153i	−1.26274	+	0.811512i	−0.988656	−	0.150195i	$-0.952010\pi$
$191$	−17.4514	+	11.2153i	−1.26274	+	0.811512i	−0.274081	+	0.961707i	$0.588374\pi$
$192$	13.3173	+	29.1609i	0.961096	+	2.10451i
$193$	−9.59519	−	11.0734i	−0.690677	−	0.797083i	0.296785	−	0.954944i	$-0.404086\pi$
$193$	−9.59519	−	11.0734i	−0.690677	−	0.797083i	−0.987461	+	0.157861i	$0.949540\pi$
$194$	8.01540	+	5.15119i	0.575472	+	0.369834i
$195$	−0.0868945	+	0.604364i	−0.00622264	+	0.0432794i
$196$	0.556778	−	3.87247i	0.0397698	−	0.276605i
$197$	9.82407	+	6.31355i	0.699936	+	0.449822i	0.841606	−	0.540092i	$-0.181611\pi$
$197$	9.82407	+	6.31355i	0.699936	+	0.449822i	−0.141669	+	0.989914i	$0.545247\pi$
$198$	9.15092	+	10.5607i	0.650328	+	0.750518i
$199$	−2.37759	−	5.20620i	−0.168543	−	0.369057i	0.806447	−	0.591306i	$-0.201388\pi$
$199$	−2.37759	−	5.20620i	−0.168543	−	0.369057i	−0.974990	+	0.222249i	$0.928660\pi$
$200$	−5.50765	+	3.53955i	−0.389450	+	0.250284i
$201$	17.5234	+	5.14533i	1.23600	+	0.362923i
$202$	2.62677	−	3.03146i	0.184819	−	0.213293i
$203$	11.3317	−	3.32729i	0.795330	−	0.233530i
$204$	4.65133	−	10.1850i	0.325659	−	0.713093i
$205$	0.0750502	+	0.521985i	0.00524173	+	0.0364570i
$206$	−33.7445			−2.35109
$207$	12.9004	+	9.30671i	0.896643	+	0.646861i
$208$	−0.305626			−0.0211913
$209$	−2.17244	−	15.1097i	−0.150271	−	1.04516i
$210$	−6.75016	+	14.7808i	−0.465805	+	1.01997i
$211$	13.4979	−	3.96334i	0.929234	−	0.272848i	0.218118	−	0.975922i	$-0.430008\pi$
$211$	13.4979	−	3.96334i	0.929234	−	0.272848i	0.711116	+	0.703075i	$0.248190\pi$
$212$	−18.3645	+	21.1938i	−1.26128	+	1.45560i
$213$	−1.76110	−	0.517106i	−0.120669	−	0.0354315i
$214$	3.68596	−	2.36882i	0.251967	−	0.161929i
$215$	−2.28738	−	5.00866i	−0.155998	−	0.341588i
$216$	0.983652	+	1.13520i	0.0669291	+	0.0772403i
$217$	−3.55843	−	2.28687i	−0.241562	−	0.155243i
$218$	−4.89064	+	34.0151i	−0.331236	+	2.30379i
$219$	−2.30504	+	16.0319i	−0.155760	+	1.08334i
$220$	5.67953	+	3.65001i	0.382914	+	0.246084i
$221$	0.200702	+	0.231623i	0.0135007	+	0.0155806i
$222$	−8.93432	−	19.5634i	−0.599632	−	1.31301i
$223$	−3.53628	+	2.27263i	−0.236807	+	0.152187i	−0.653663	−	0.756786i	$-0.726768\pi$
$223$	−3.53628	+	2.27263i	−0.236807	+	0.152187i	0.416856	+	0.908973i	$0.363132\pi$
$224$	−16.3922	−	4.81319i	−1.09525	−	0.321595i
$225$	7.53956	−	8.70112i	0.502638	−	0.580075i
$226$	3.14668	−	0.923948i	0.209314	−	0.0614601i
$227$	7.65642	−	16.7652i	0.508174	−	1.11275i	−0.465551	−	0.885021i	$-0.654144\pi$
$227$	7.65642	−	16.7652i	0.508174	−	1.11275i	0.973725	−	0.227726i	$-0.0731289\pi$
$228$	−8.15629	−	56.7282i	−0.540163	−	3.75692i
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$	12.3221	+	4.34992i	0.812492	+	0.286825i
$231$	−11.4015			−0.750163
$232$	−1.33603	−	9.29227i	−0.0877145	−	0.610068i
$233$	1.73013	−	3.78846i	0.113345	−	0.248190i	−0.844455	−	0.535626i	$-0.820076\pi$
$233$	1.73013	−	3.78846i	0.113345	−	0.248190i	0.957800	+	0.287436i	$0.0928029\pi$
$234$	−1.37787	+	0.404581i	−0.0900745	+	0.0264483i
$235$	−2.09590	+	2.41879i	−0.136721	+	0.157785i
$236$	19.7815	+	5.80837i	1.28767	+	0.378093i
$237$	12.0055	−	7.71545i	0.779839	−	0.501172i
$238$	3.38825	+	7.41922i	0.219627	+	0.480917i
$239$	14.7456	+	17.0173i	0.953813	+	1.10076i	0.994825	+	0.101601i	$0.0323964\pi$
$239$	14.7456	+	17.0173i	0.953813	+	1.10076i	−0.0410120	+	0.999159i	$0.513058\pi$
$240$	−4.06677	−	2.61355i	−0.262509	−	0.168704i
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	0.944429	+	0.328717i	$0.106616\pi$
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	−0.998783	+	0.0493250i	$0.984293\pi$
$242$	2.30340	−	16.0205i	0.148068	−	1.02984i
$243$	18.8169	+	12.0929i	1.20710	+	0.775759i
$244$	−13.8952	−	16.0359i	−0.889548	−	1.02659i
$245$	0.703646	+	1.54077i	0.0449543	+	0.0984361i
$246$	−1.98714	+	1.27706i	−0.126695	+	0.0814222i
$247$	1.50519	+	0.441964i	0.0957730	+	0.0281215i
$248$	−2.20187	+	2.54110i	−0.139819	+	0.161360i
$249$	−31.0840	+	9.12708i	−1.96987	+	0.578405i
$250$	9.58839	−	20.9956i	0.606423	−	1.32788i
$251$	0.220675	+	1.53483i	0.0139289	+	0.0968775i	0.995600	−	0.0937056i	$-0.0298712\pi$
$251$	0.220675	+	1.53483i	0.0139289	+	0.0968775i	−0.981671	+	0.190583i	$0.938962\pi$
$252$	−22.4767			−1.41590
$253$	0.815292	+	9.13256i	0.0512570	+	0.574159i
$254$	13.2093			0.828824
$255$	0.689900	+	4.79836i	0.0432032	+	0.300485i
$256$	−1.95044	+	4.27088i	−0.121903	+	0.266930i
$257$	−26.3456	+	7.73578i	−1.64340	+	0.482545i	−0.967166	−	0.254145i	$-0.918206\pi$
$257$	−26.3456	+	7.73578i	−1.64340	+	0.482545i	−0.676230	+	0.736690i	$0.736388\pi$
$258$	16.1512	−	18.6395i	1.00553	−	1.16044i
$259$	8.84083	+	2.59590i	0.549342	+	0.161301i
$260$	−0.583666	+	0.375099i	−0.0361974	+	0.0232627i
$261$	6.85812	+	15.0172i	0.424507	+	0.929540i
$262$	18.4262	+	21.2650i	1.13837	+	1.31375i
$263$	−10.8864	−	6.99627i	−0.671285	−	0.431408i	0.160104	−	0.987100i	$-0.448817\pi$
$263$	−10.8864	−	6.99627i	−0.671285	−	0.431408i	−0.831388	+	0.555692i	$0.812453\pi$
$264$	−1.28980	+	8.97078i	−0.0793819	+	0.552113i
$265$	1.72791	−	12.0179i	0.106145	−	0.738253i
$266$	35.1210	+	22.5709i	2.15341	+	1.38391i
$267$	−22.8782	−	26.4028i	−1.40012	−	1.61583i
$268$	8.62092	+	18.8772i	0.526607	+	1.15311i
$269$	−8.41057	+	5.40514i	−0.512801	+	0.329557i	−0.771319	−	0.636449i	$-0.780402\pi$
$269$	−8.41057	+	5.40514i	−0.512801	+	0.329557i	0.258517	+	0.966007i	$0.416766\pi$
$270$	−2.08203	−	0.611339i	−0.126708	−	0.0372049i
$271$	−2.88885	+	3.33391i	−0.175485	+	0.202520i	−0.836678	−	0.547696i	$-0.815505\pi$
$271$	−2.88885	+	3.33391i	−0.175485	+	0.202520i	0.661193	+	0.750216i	$0.270051\pi$
$272$	−2.32823	+	0.683629i	−0.141169	+	0.0414511i
$273$	0.486739	−	1.06581i	0.0294588	−	0.0645057i
$274$	−0.218760	−	1.52151i	−0.0132158	−	0.0919177i
$275$	6.63624			0.400180
$276$	3.06096	+	34.2876i	0.184248	+	2.06387i
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	−4.37667	−	30.4404i	−0.262495	−	1.82570i
$279$	2.45631	−	5.37857i	0.147055	−	0.322006i
$280$	−5.30954	+	1.55902i	−0.317306	+	0.0931694i
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	−0.681516	−	0.731803i	$-0.738679\pi$
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	0.821344	+	0.570433i	$0.193225\pi$
$282$	−13.7551	−	4.03885i	−0.819102	−	0.240510i
$283$	12.4341	−	7.99089i	0.739129	−	0.475009i	−0.116115	−	0.993236i	$-0.537044\pi$
$283$	12.4341	−	7.99089i	0.739129	−	0.475009i	0.855243	+	0.518227i	$0.173408\pi$
$284$	−0.866403	−	1.89716i	−0.0514116	−	0.112576i
$285$	16.2492	+	18.7526i	0.962519	+	1.11081i
$286$	−0.696337	−	0.447509i	−0.0411753	−	0.0264618i
$287$	0.144020	−	1.00168i	0.00850125	−	0.0591275i
$288$	3.39872	−	23.6386i	0.200272	−	1.39292i
$289$	−12.2543	−	7.87535i	−0.720840	−	0.463256i
$290$	8.88110	+	10.2493i	0.521516	+	0.601862i
$291$	−4.51435	−	9.88506i	−0.264636	−	0.579472i
$292$	−15.4829	+	9.95024i	−0.906067	+	0.582294i
$293$	−20.6420	−	6.06104i	−1.20592	−	0.354090i	−0.383806	−	0.923414i	$-0.625387\pi$
$293$	−20.6420	−	6.06104i	−1.20592	−	0.354090i	−0.822113	+	0.569324i	$0.807205\pi$
$294$	−4.96845	+	5.73389i	−0.289766	+	0.334408i
$295$	−8.56445	+	2.51475i	−0.498642	+	0.146414i
$296$	3.04260	−	6.66236i	0.176847	−	0.387242i
$297$	−0.216683	−	1.50707i	−0.0125732	−	0.0874488i
$298$	−36.6660			−2.12401
$299$	−0.888516	−	0.313663i	−0.0513842	−	0.0181396i
$300$	24.9153			1.43849
$301$	1.50376	+	10.4589i	0.0866752	+	0.602839i
$302$	12.0743	−	26.4390i	0.694797	−	1.52139i
$303$	−4.38965	+	1.28892i	−0.252179	+	0.0740464i
$304$	−8.13354	+	9.38660i	−0.466490	+	0.538359i
$305$	8.81450	+	2.58817i	0.504717	+	0.148198i
$306$	−9.59155	+	6.16411i	−0.548312	+	0.352379i
$307$	5.87602	+	12.8667i	0.335362	+	0.734341i	0.999917	−	0.0128989i	$-0.00410596\pi$
$307$	5.87602	+	12.8667i	0.335362	+	0.734341i	−0.664555	+	0.747240i	$0.731379\pi$
$308$	−8.48411	−	9.79118i	−0.483427	−	0.557904i
$309$	32.3776	+	20.8078i	1.84190	+	1.18371i
$310$	0.691267	−	4.80787i	0.0392613	−	0.273069i
$311$	−0.0811393	+	0.564336i	−0.00460099	+	0.0320006i	−0.991993	−	0.126296i	$-0.959691\pi$
$311$	−0.0811393	+	0.564336i	−0.00460099	+	0.0320006i	0.987392	+	0.158297i	$0.0506002\pi$
$312$	−0.783524	−	0.503540i	−0.0443583	−	0.0285073i
$313$	13.8390	+	15.9711i	0.782227	+	0.902738i	0.997268	−	0.0738672i	$-0.0235341\pi$
$313$	13.8390	+	15.9711i	0.782227	+	0.902738i	−0.215041	+	0.976605i	$0.568989\pi$
$314$	3.77945	+	8.27584i	0.213287	+	0.467033i
$315$	8.18653	−	5.26116i	0.461259	−	0.296433i
$316$	15.5593	+	4.56862i	0.875279	+	0.257005i
$317$	5.77072	−	6.65977i	0.324116	−	0.374050i	−0.570185	−	0.821517i	$-0.693128\pi$
$317$	5.77072	−	6.65977i	0.324116	−	0.374050i	0.894301	+	0.447467i	$0.147674\pi$
$318$	52.1811	−	15.3217i	2.92617	−	0.859201i
$319$	−3.95303	+	8.65592i	−0.221327	+	0.484639i
$320$	−2.24451	−	15.6109i	−0.125472	−	0.872676i
$321$	−4.99734			−0.278924
$322$	−20.3363	−	14.6711i	−1.13330	−	0.817589i
$323$	12.4550			0.693015
$324$	3.23080	+	22.4707i	0.179489	+	1.24837i
$325$	−0.283306	+	0.620354i	−0.0157150	+	0.0344111i
$326$	31.2698	−	9.18165i	1.73188	−	0.508525i
$327$	25.6672	−	29.6216i	1.41940	−	1.63808i
$328$	−0.771839	−	0.226632i	−0.0426177	−	0.0125137i
$329$	5.16678	−	3.32049i	0.284854	−	0.183064i
$330$	−5.43886	−	11.9094i	−0.299399	−	0.655593i
$331$	−19.7686	−	22.8142i	−1.08658	−	1.25398i	−0.965239	−	0.261371i	$-0.915826\pi$
$331$	−19.7686	−	22.8142i	−1.08658	−	1.25398i	−0.121342	−	0.992611i	$-0.538720\pi$
$332$	−30.9683	−	19.9021i	−1.69961	−	1.09227i
$333$	−1.83303	+	12.7490i	−0.100450	+	0.698642i
$334$	−0.417017	+	2.90042i	−0.0228182	+	0.158704i
$335$	−7.55856	−	4.85759i	−0.412968	−	0.265398i
$336$	6.07496	+	7.01088i	0.331416	+	0.382475i
$337$	−2.05870	−	4.50792i	−0.112145	−	0.245562i	0.845235	−	0.534394i	$-0.179460\pi$
$337$	−2.05870	−	4.50792i	−0.112145	−	0.245562i	−0.957380	+	0.288832i	$0.906733\pi$
$338$	−24.0278	+	15.4418i	−1.30694	+	0.839920i
$339$	−3.58895	−	1.05381i	−0.194925	−	0.0572351i
$340$	−3.60728	+	4.16303i	−0.195632	+	0.225772i
$341$	3.27015	−	0.960202i	0.177088	−	0.0519979i
$342$	−24.2433	+	53.0853i	−1.31093	+	2.87053i
$343$	−2.82637	−	19.6578i	−0.152609	−	1.06142i
$344$	8.39923			0.452856
$345$	−9.14064	−	11.7719i	−0.492115	−	0.633775i
$346$	−37.3205			−2.00636
$347$	0.963038	+	6.69808i	0.0516986	+	0.359572i	0.999206	+	0.0398383i	$0.0126843\pi$
$347$	0.963038	+	6.69808i	0.0516986	+	0.359572i	−0.947508	+	0.319733i	$0.896407\pi$
$348$	−14.8414	+	32.4981i	−0.795582	+	1.74208i
$349$	−9.68306	+	2.84320i	−0.518322	+	0.152193i	−0.530422	−	0.847734i	$-0.677967\pi$
$349$	−9.68306	+	2.84320i	−0.518322	+	0.152193i	0.0121000	+	0.999927i	$0.496148\pi$
$350$	−11.8854	+	13.7165i	−0.635300	+	0.733175i
$351$	0.150131	+	0.0440823i	0.00801338	+	0.00235294i
$352$	11.5802	−	7.44216i	0.617228	−	0.396669i
$353$	10.1649	+	22.2580i	0.541023	+	1.18468i	0.960850	+	0.277071i	$0.0893636\pi$
$353$	10.1649	+	22.2580i	0.541023	+	1.18468i	−0.419827	+	0.907604i	$0.637909\pi$
$354$	−26.1822	−	30.2159i	−1.39157	−	1.60596i
$355$	0.759635	+	0.488188i	0.0403173	+	0.0259103i
$356$	5.64961	−	39.2939i	0.299429	−	2.08257i
$357$	1.32391	−	9.20798i	0.0700686	−	0.487338i
$358$	−2.65343	−	1.70526i	−0.140238	−	0.0901257i
$359$	−0.274264	−	0.316518i	−0.0144751	−	0.0167052i	0.748466	−	0.663173i	$-0.230791\pi$
$359$	−0.274264	−	0.316518i	−0.0144751	−	0.0167052i	−0.762941	+	0.646468i	$0.776245\pi$
$360$	−3.21341	−	7.03639i	−0.169362	−	0.370850i
$361$	37.6474	−	24.1945i	1.98144	−	1.27340i
$362$	34.1074	+	10.0148i	1.79265	+	0.526368i
$363$	−12.0888	+	13.9512i	−0.634497	+	0.732248i
$364$	1.27747	−	0.375099i	0.0669577	−	0.0196606i
$365$	3.31015	−	7.24821i	0.173261	−	0.379389i
$366$	5.85606	+	40.7298i	0.306101	+	2.12898i
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$	5.18129	−	5.36735i	0.270093	−	0.279793i
$369$	1.41463			0.0736426
$370$	1.50579	+	10.4730i	0.0782825	+	0.544466i
$371$	−9.67888	+	21.1938i	−0.502503	+	1.10033i
$372$	12.2776	−	3.60502i	0.636562	−	0.186911i
$373$	−9.43508	+	10.8887i	−0.488530	+	0.563794i	−0.945472	−	0.325703i	$-0.894399\pi$
$373$	−9.43508	+	10.8887i	−0.488530	+	0.563794i	0.456942	+	0.889496i	$0.348945\pi$
$374$	−6.30563	−	1.85150i	−0.326056	−	0.0957388i
$375$	−22.1465	+	14.2327i	−1.14364	+	0.734973i
$376$	−2.02809	−	4.44089i	−0.104591	−	0.229021i
$377$	−0.640396	−	0.739056i	−0.0329821	−	0.0380633i
$378$	3.50303	+	2.25126i	0.180176	+	0.115792i
$379$	0.800823	−	5.56985i	0.0411355	−	0.286104i	−0.958862	−	0.283873i	$-0.908381\pi$
$379$	0.800823	−	5.56985i	0.0411355	−	0.286104i	0.999998	−	0.00223119i	$-0.000710211\pi$
$380$	−4.01263	+	27.9084i	−0.205843	+	1.43167i
$381$	−12.6742	−	8.14522i	−0.649320	−	0.417292i
$382$	29.9356	+	34.5475i	1.53164	+	1.76760i
$383$	0.0962350	+	0.210725i	0.00491738	+	0.0107676i	0.912075	−	0.410024i	$-0.134480\pi$
$383$	0.0962350	+	0.210725i	0.00491738	+	0.0107676i	−0.907157	+	0.420792i	$0.861752\pi$
$384$	28.9819	−	18.6255i	1.47898	−	0.950480i
$385$	5.38195	+	1.58028i	0.274289	+	0.0805386i
$386$	−21.1441	+	24.4016i	−1.07621	+	1.24201i
$387$	−14.1722	+	4.16135i	−0.720416	+	0.211533i
$388$	5.12969	−	11.2325i	0.260421	−	0.570241i
$389$	4.29361	+	29.8627i	0.217695	+	1.51410i	0.746516	+	0.665367i	$0.231725\pi$
$389$	4.29361	+	29.8627i	0.217695	+	1.51410i	−0.528821	+	0.848733i	$0.677366\pi$
$390$	1.34548			0.0681311
$391$	−7.47023	−	0.402007i	−0.377786	−	0.0203304i
$392$	−2.58378			−0.130500
$393$	−4.56722	−	31.7657i	−0.230386	−	1.60237i
$394$	10.6901	−	23.4081i	0.538561	−	1.17928i
$395$	−6.73644	+	1.97800i	−0.338947	+	0.0995238i
$396$	11.8597	−	13.6869i	0.595975	−	0.687791i
$397$	12.5168	+	3.67528i	0.628202	+	0.184457i	0.580310	−	0.814396i	$-0.302931\pi$
$397$	12.5168	+	3.67528i	0.628202	+	0.184457i	0.0478924	+	0.998853i	$0.484750\pi$
$398$	−10.6101	+	6.81867i	−0.531834	+	0.341789i
$399$	−19.7805	−	43.3132i	−0.990263	−	2.16837i
$400$	−3.53593	−	4.08068i	−0.176797	−	0.204034i
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	0.00967246	−	0.999953i	$-0.496921\pi$
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	−0.905571	+	0.424194i	$0.860557\pi$
$402$	5.72746	−	39.8354i	0.285660	−	1.98681i
$403$	−0.0498457	+	0.346685i	−0.00248299	+	0.0172696i
$404$	−4.37332	−	2.81056i	−0.217581	−	0.139831i
$405$	−6.43648	−	7.42810i	−0.319831	−	0.369105i
$406$	−10.8111	−	23.6731i	−0.536548	−	1.17488i
$407$	−6.24557	+	4.01378i	−0.309581	+	0.198956i
$408$	−7.09514	−	2.08332i	−0.351262	−	0.103140i
$409$	5.99134	−	6.91437i	0.296253	−	0.341894i	−0.588036	−	0.808835i	$-0.700099\pi$
$409$	5.99134	−	6.91437i	0.296253	−	0.341894i	0.884288	+	0.466941i	$0.154644\pi$
$410$	1.11501	−	0.327397i	0.0550665	−	0.0161690i
$411$	−0.728307	+	1.59477i	−0.0359247	+	0.0786642i
$412$	6.22391	+	43.2882i	0.306630	+	2.13266i
$413$	17.1289			0.842859
$414$	16.2540	−	31.0569i	0.798840	−	1.52636i
$415$	15.9379			0.782360
$416$	0.201323	+	1.40023i	0.00987065	+	0.0686519i
$417$	−14.5711	+	31.9062i	−0.713548	+	1.56245i
$418$	−32.2757	+	9.47700i	−1.57866	+	0.463535i
$419$	5.87685	−	6.78225i	0.287103	−	0.331334i	−0.593817	−	0.804600i	$-0.702380\pi$
$419$	5.87685	−	6.78225i	0.287103	−	0.331334i	0.880920	+	0.473266i	$0.156925\pi$
$420$	20.2062	+	5.93307i	0.985960	+	0.289504i
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.298241	−	0.954491i	$-0.403600\pi$
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.992129	+	0.125221i	$0.0399638\pi$
$422$	−12.8778	−	28.1985i	−0.626882	−	1.37268i
$423$	5.62226	+	6.48843i	0.273364	+	0.315478i
$424$	15.5805	+	10.0130i	0.756656	+	0.486273i
$425$	−0.770581	+	5.35951i	−0.0373787	+	0.259974i
$426$	−0.575610	+	4.00346i	−0.0278884	+	0.193968i
$427$	−14.8305	−	9.53095i	−0.717696	−	0.461235i
$428$	−3.71863	−	4.29153i	−0.179747	−	0.207439i
$429$	0.392184	+	0.858763i	0.0189348	+	0.0414615i
$430$	−10.2075	+	6.55995i	−0.492249	+	0.316349i
$431$	21.2071	+	6.22697i	1.02151	+	0.299942i	0.749254	−	0.662283i	$-0.230412\pi$
$431$	21.2071	+	6.22697i	1.02151	+	0.299942i	0.272256	+	0.962225i	$0.412230\pi$
$432$	−0.811254	+	0.936237i	−0.0390315	+	0.0450447i
$433$	−12.1810	+	3.57666i	−0.585382	+	0.171884i	−0.560995	−	0.827819i	$-0.689581\pi$
$433$	−12.1810	+	3.57666i	−0.585382	+	0.171884i	−0.0243864	+	0.999703i	$0.507763\pi$
$434$	−3.87213	+	8.47878i	−0.185868	+	0.406994i
$435$	−2.20132	−	15.3105i	−0.105545	−	0.734082i
$436$	44.5375			2.13296
$437$	−33.2793	+	18.9413i	−1.59196	+	0.906086i
$438$	35.6915			1.70541
$439$	−2.62158	−	18.2335i	−0.125121	−	0.870238i	−0.951615	−	0.307292i	$-0.900577\pi$
$439$	−2.62158	−	18.2335i	−0.125121	−	0.870238i	0.826494	−	0.562946i	$-0.190332\pi$
$440$	1.85221	−	4.05578i	0.0883009	−	0.193352i
$441$	4.35968	−	1.28012i	0.207604	−	0.0609580i
$442$	0.442270	−	0.510407i	0.0210366	−	0.0242776i
$443$	13.3492	+	3.91968i	0.634240	+	0.186230i	0.583020	−	0.812458i	$-0.301871\pi$
$443$	13.3492	+	3.91968i	0.634240	+	0.186230i	0.0512201	+	0.998687i	$0.483689\pi$
$444$	−23.4486	+	15.0695i	−1.11282	+	0.715166i
$445$	7.13988	+	15.6342i	0.338463	+	0.741130i
$446$	6.06603	+	7.00057i	0.287235	+	0.331487i
$447$	35.1808	+	22.6093i	1.66399	+	1.06938i
$448$	−4.30718	+	29.9571i	−0.203495	+	1.41534i
$449$	−4.28260	+	29.7862i	−0.202109	+	1.40570i	0.595904	+	0.803056i	$0.296794\pi$
$449$	−4.28260	+	29.7862i	−0.202109	+	1.40570i	−0.798013	+	0.602641i	$0.794115\pi$
$450$	−21.3432	−	13.7165i	−1.00613	−	0.646600i
$451$	0.533969	+	0.616233i	0.0251436	+	0.0290173i
$452$	−1.76564	−	3.86622i	−0.0830489	−	0.181852i
$453$	−27.8883	+	17.9227i	−1.31030	+	0.842082i
$454$	−38.9692	−	11.4424i	−1.82891	−	0.537017i
$455$	−0.377484	+	0.435640i	−0.0176967	+	0.0204231i
$456$	−36.3168	+	10.6636i	−1.70069	+	0.499368i
$457$	15.8055	−	34.6093i	0.739351	−	1.61895i	−0.0452680	−	0.998975i	$-0.514414\pi$
$457$	15.8055	−	34.6093i	0.739351	−	1.61895i	0.784619	−	0.619978i	$-0.212859\pi$
$458$	−3.42606	−	23.8287i	−0.160089	−	1.11344i
$459$	1.24228			0.0579849
$460$	3.30748	−	16.6093i	0.154212	−	0.774415i
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	3.57559	+	24.8688i	0.166352	+	1.15700i
$463$	−11.5638	+	25.3212i	−0.537415	+	1.17677i	0.425001	+	0.905193i	$0.360274\pi$
$463$	−11.5638	+	25.3212i	−0.537415	+	1.17677i	−0.962416	+	0.271581i	$0.912453\pi$
$464$	7.42886	−	2.18131i	0.344876	−	0.101265i
$465$	−3.62794	+	4.18686i	−0.168241	+	0.194161i
$466$	−8.80592	−	2.58565i	−0.407926	−	0.119778i
$467$	−14.6095	+	9.38895i	−0.676047	+	0.434469i	−0.833101	−	0.553121i	$-0.813437\pi$
$467$	−14.6095	+	9.38895i	−0.676047	+	0.434469i	0.157054	+	0.987590i	$0.449800\pi$
$468$	0.773144	+	1.69295i	0.0357386	+	0.0782566i
$469$	11.2910	+	13.0305i	0.521370	+	0.601693i
$470$	5.93313	+	3.81299i	0.273675	+	0.175880i
$471$	1.47677	−	10.2711i	0.0680458	−	0.473269i
$472$	1.93772	−	13.4771i	0.0891909	−	0.620336i
$473$	−7.16224	−	4.60289i	−0.329320	−	0.211641i
$474$	−20.5938	−	23.7666i	−0.945906	−	1.09163i
$475$	11.5132	+	25.2105i	0.528263	+	1.15674i
$476$	8.89263	−	5.71494i	0.407593	−	0.261944i
$477$	−31.2503	−	9.17591i	−1.43085	−	0.420136i
$478$	32.4936	−	37.4996i	1.48622	−	1.71519i
$479$	24.4458	−	7.17792i	1.11695	−	0.327968i	0.329387	−	0.944195i	$-0.393158\pi$
$479$	24.4458	−	7.17792i	1.11695	−	0.327968i	0.787568	+	0.616228i	$0.211340\pi$
$480$	−9.29517	+	20.3536i	−0.424265	+	0.929010i
$481$	−0.108579	−	0.755186i	−0.00495079	−	0.0344335i
$482$	13.0655			0.595119
$483$	10.4659	+	26.6168i	0.476214	+	1.21110i
$484$	−20.9763			−0.953469
$485$	0.760851	+	5.29183i	0.0345485	+	0.240290i
$486$	20.4757	−	44.8356i	0.928797	−	2.03378i
$487$	5.91151	−	1.73577i	0.267876	−	0.0786555i	−0.145036	−	0.989426i	$-0.546330\pi$
$487$	5.91151	−	1.73577i	0.267876	−	0.0786555i	0.412912	+	0.910771i	$0.364512\pi$
$488$	−9.17673	+	10.5905i	−0.415411	+	0.479410i
$489$	−35.6649	−	10.4721i	−1.61282	−	0.473567i
$490$	3.14004	−	2.01798i	0.141852	−	0.0911630i
$491$	−13.5623	−	29.6973i	−0.612058	−	1.34022i	−0.921157	−	0.389191i	$-0.872755\pi$
$491$	−13.5623	−	29.6973i	−0.612058	−	1.34022i	0.309099	−	0.951030i	$-0.399973\pi$
$492$	2.00475	+	2.31361i	0.0903812	+	0.104306i
$493$	−6.53161	−	4.19761i	−0.294169	−	0.189051i
$494$	0.491967	−	3.42171i	0.0221346	−	0.153950i
$495$	−1.11588	+	7.76111i	−0.0501550	+	0.348836i
$496$	−2.33284	−	1.49923i	−0.104748	−	0.0673172i
$497$	−1.13475	−	1.30957i	−0.0509004	−	0.0587421i
$498$	29.6560	+	64.9376i	1.32892	+	2.90992i
$499$	−7.21265	+	4.63529i	−0.322882	+	0.207504i	−0.692033	−	0.721866i	$-0.743285\pi$
$499$	−7.21265	+	4.63529i	−0.322882	+	0.207504i	0.369151	+	0.929369i	$0.379649\pi$
$500$	−28.7022	−	8.42774i	−1.28360	−	0.376900i
$501$	2.18861	−	2.52579i	0.0977797	−	0.112844i
$502$	3.27854	−	0.962667i	0.146329	−	0.0429659i
$503$	2.80635	−	6.14505i	0.125129	−	0.273994i	−0.836692	−	0.547674i	$-0.815513\pi$
$503$	2.80635	−	6.14505i	0.125129	−	0.273994i	0.961821	+	0.273679i	$0.0882408\pi$
$504$	2.11255	+	14.6931i	0.0941003	+	0.654482i
$505$	2.25073			0.100156
$506$	19.6641	−	4.64234i	0.874177	−	0.206377i
$507$	32.5764			1.44677
$508$	−2.43635	−	16.9452i	−0.108096	−	0.751821i
$509$	17.0206	−	37.2699i	0.754425	−	1.65196i	−0.00382066	−	0.999993i	$-0.501216\pi$
$509$	17.0206	−	37.2699i	0.754425	−	1.65196i	0.758246	−	0.651968i	$-0.226057\pi$
$510$	10.2498	−	3.00960i	0.453867	−	0.133267i
$511$	−10.0135	+	11.5562i	−0.442971	+	0.511216i
$512$	−16.3767	−	4.80863i	−0.723754	−	0.212513i
$513$	5.34928	−	3.43777i	0.236176	−	0.151781i
$514$	25.1354	+	55.0388i	1.10867	+	2.42766i
$515$	−12.3995	−	14.3097i	−0.546385	−	0.630562i
$516$	−26.8902	−	17.2813i	−1.18377	−	0.760765i
$517$	−0.704266	+	4.89828i	−0.0309736	+	0.215426i
$518$	2.88960	−	20.0976i	0.126962	−	0.883037i
$519$	35.8088	+	23.0129i	1.57183	+	1.01016i
$520$	0.300061	+	0.346289i	0.0131586	+	0.0151858i
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	0.659162	−	0.752001i	$-0.270911\pi$
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	−0.999984	+	0.00570487i	$0.998184\pi$
$522$	30.6045	−	19.6683i	1.33952	−	0.860859i
$523$	−22.6095	−	6.63875i	−0.988644	−	0.290292i	−0.252856	−	0.967504i	$-0.581370\pi$
$523$	−22.6095	−	6.63875i	−0.988644	−	0.290292i	−0.735788	+	0.677212i	$0.763188\pi$
$524$	23.8807	−	27.5597i	1.04323	−	1.20395i
$525$	19.8619	−	5.83198i	0.866844	−	0.254528i
$526$	−11.8461	+	25.9394i	−0.516515	+	1.13101i
$527$	0.395751	+	2.75251i	0.0172392	+	0.119901i
$528$	−7.47461			−0.325291
$529$	20.5716	−	10.2864i	0.894416	−	0.447237i
$530$	−26.7551			−1.16217
$531$	3.40760	+	23.7004i	0.147877	+	1.02851i
$532$	22.4767	−	49.2171i	0.974488	−	2.13383i
$533$	−0.0804009	+	0.0236078i	−0.00348255	+	0.00102257i
$534$	−50.4147	+	58.1817i	−2.18166	+	2.51777i
$535$	2.35894	+	0.692647i	0.101986	+	0.0299457i
$536$	11.5298	−	7.40976i	0.498012	−	0.320053i
$537$	1.49444	+	3.27237i	0.0644899	+	0.141213i
$538$	14.4272	+	16.6499i	0.622002	+	0.717829i
$539$	2.20325	+	1.41595i	0.0949009	+	0.0609891i
$540$	−0.400227	+	2.78364i	−0.0172230	+	0.119789i
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	−0.992530	−	0.122001i	$-0.961069\pi$
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	0.986697	+	0.162569i	$0.0519780\pi$
$542$	8.17784	+	5.25558i	0.351268	+	0.225746i
$543$	−26.5504	−	30.6408i	−1.13939	−	1.31492i
$544$	4.66572	+	10.2165i	0.200041	+	0.438029i
$545$	−16.2216	+	10.4250i	−0.694856	+	0.446557i
$546$	−2.47737	−	0.727422i	−0.106022	−	0.0311308i
$547$	−19.5057	+	22.5108i	−0.834003	+	0.962491i	−0.999720	−	0.0236827i	$-0.992461\pi$
$547$	−19.5057	+	22.5108i	−0.834003	+	0.962491i	0.165717	+	0.986173i	$0.447006\pi$
$548$	−1.91148	+	0.561261i	−0.0816544	+	0.0239759i
$549$	10.2371	−	22.4162i	0.436911	−	0.956701i
$550$	−2.08117	−	14.4749i	−0.0887415	−	0.617211i
$551$	−39.7412			−1.69303
$552$	22.1262	−	5.22359i	0.941754	−	0.222331i
$553$	13.4729			0.572925
$554$	9.66043	+	67.1897i	0.410432	+	2.85462i
$555$	5.01317	−	10.9773i	0.212797	−	0.465961i
$556$	−38.2425	+	11.2290i	−1.62184	+	0.476216i
$557$	3.93487	−	4.54108i	0.166726	−	0.192412i	−0.666238	−	0.745739i	$-0.732097\pi$
$557$	3.93487	−	4.54108i	0.166726	−	0.192412i	0.832964	+	0.553327i	$0.186642\pi$
$558$	−12.5020	−	3.67091i	−0.529251	−	0.155402i
$559$	0.736039	−	0.473023i	0.0311311	−	0.0200068i
$560$	−1.89589	−	4.15141i	−0.0801159	−	0.175429i
$561$	4.90852	+	5.66473i	0.207238	+	0.239165i
$562$	−6.63532	−	4.26426i	−0.279894	−	0.179877i
$563$	−0.0126931	+	0.0882822i	−0.000534949	+	0.00372065i	−0.990087	−	0.140454i	$-0.955144\pi$
$563$	−0.0126931	+	0.0882822i	−0.000534949	+	0.00372065i	0.989552	+	0.144175i	$0.0460528\pi$
$564$	−2.64412	+	18.3903i	−0.111338	+	0.774370i
$565$	1.54806	+	0.994879i	0.0651274	+	0.0418549i
$566$	−21.3290	−	24.6150i	−0.896526	−	1.03465i
$567$	7.83526	+	17.1568i	0.329050	+	0.720519i
$568$	−1.15875	+	0.744681i	−0.0486199	+	0.0312461i
$569$	39.6842	+	11.6523i	1.66365	+	0.488491i	0.972243	−	0.233975i	$-0.0751733\pi$
$569$	39.6842	+	11.6523i	1.66365	+	0.488491i	0.691406	+	0.722466i	$0.256991\pi$
$570$	35.8070	−	41.3235i	1.49979	−	1.73085i
$571$	−24.7458	+	7.26602i	−1.03558	+	0.304073i	−0.754977	−	0.655751i	$-0.772352\pi$
$571$	−24.7458	+	7.26602i	−1.03558	+	0.304073i	−0.280602	+	0.959824i	$0.590534\pi$
$572$	−0.445641	+	0.975819i	−0.0186332	+	0.0408010i
$573$	−7.42000	−	51.6072i	−0.309975	−	2.15592i
$574$	−2.23002			−0.0930793
$575$	−6.09167	−	15.4923i	−0.254040	−	0.646073i
$576$	−42.3070			−1.76279
$577$	−3.86302	−	26.8679i	−0.160820	−	1.11853i	−0.897093	−	0.441842i	$-0.854325\pi$
$577$	−3.86302	−	26.8679i	−0.160820	−	1.11853i	0.736273	−	0.676684i	$-0.236584\pi$
$578$	−13.3346	+	29.1986i	−0.554645	+	1.21450i
$579$	35.3343	−	10.3751i	1.46845	−	0.431174i
$580$	11.5100	−	13.2833i	0.477929	−	0.551559i
$581$	−29.3457	−	8.61667i	−1.21746	−	0.357480i
$582$	−20.1454	+	12.9467i	−0.835054	+	0.536657i
$583$	−7.79865	−	17.0767i	−0.322987	−	0.707243i
$584$	7.95971	+	9.18600i	0.329375	+	0.380119i
$585$	−0.677869	−	0.435640i	−0.0280264	−	0.0180115i
$586$	−6.74678	+	46.9249i	−0.278707	+	1.93845i
$587$	−4.50210	+	31.3128i	−0.185822	+	1.29242i	0.656863	+	0.754010i	$0.271883\pi$
$587$	−4.50210	+	31.3128i	−0.185822	+	1.29242i	−0.842685	+	0.538407i	$0.819026\pi$
$588$	8.27197	+	5.31608i	0.341130	+	0.219231i
$589$	9.32111	+	10.7571i	0.384070	+	0.443240i
$590$	8.17101	+	17.8920i	0.336395	+	0.736603i
$591$	−24.6912	+	15.8681i	−1.01566	+	0.652726i
$592$	5.79588	+	1.70182i	0.238209	+	0.0699446i
$593$	16.8600	−	19.4575i	0.692358	−	0.799024i	−0.295341	−	0.955392i	$-0.595433\pi$
$593$	16.8600	−	19.4575i	0.692358	−	0.799024i	0.987699	+	0.156368i	$0.0499786\pi$
$594$	−3.21924	+	0.945253i	−0.132087	+	0.0387842i
$595$	−1.90119	+	4.16303i	−0.0779412	+	0.170667i
$596$	6.76277	+	47.0361i	0.277014	+	1.92667i
$597$	14.3849			0.588733
$598$	−0.405513	+	2.03638i	−0.0165826	+	0.0832740i
$599$	16.9434			0.692289			0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434			0.692289			0.346144	+	0.938181i	$0.387491\pi$
$600$	−2.34175	−	16.2872i	−0.0956015	−	0.664923i
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	−0.973624	−	0.228159i	$-0.926729\pi$
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	0.810019	+	0.586403i	$0.199457\pi$
$602$	22.3411	−	6.55995i	0.910557	−	0.267364i
$603$	−15.7834	+	18.2151i	−0.642752	+	0.741775i
$604$	−36.1436	−	10.6127i	−1.47066	−	0.431826i
$605$	7.64006	−	4.90997i	0.310613	−	0.199619i
$606$	4.18800	+	9.17043i	0.170126	+	0.372523i
$607$	−2.12520	−	2.45261i	−0.0862592	−	0.0995484i	0.710979	−	0.703213i	$-0.248252\pi$
$607$	−2.12520	−	2.45261i	−0.0862592	−	0.0995484i	−0.797238	+	0.603665i	$0.793707\pi$
$608$	48.3627	+	31.0808i	1.96136	+	1.26049i
$609$	−4.22430	+	29.3806i	−0.171177	+	1.19056i
$610$	2.88099	−	20.0377i	0.116648	−	0.811304i
$611$	−0.427825	−	0.274946i	−0.0173079	−	0.0111231i
$612$	9.67656	+	11.1673i	0.391152	+	0.451413i
$613$	−13.6731	−	29.9399i	−0.552251	−	1.20926i	−0.955723	−	0.294269i	$-0.904924\pi$
$613$	−13.6731	−	29.9399i	−0.552251	−	1.20926i	0.403471	−	0.914992i	$-0.367803\pi$
$614$	26.2219	−	16.8518i	1.05823	−	0.680083i
$615$	−1.27173	−	0.373413i	−0.0512810	−	0.0150575i
$616$	−5.60312	+	6.46634i	−0.225756	+	0.260536i
$617$	−2.90191	+	0.852079i	−0.116827	+	0.0343034i	−0.339623	−	0.940562i	$-0.610300\pi$
$617$	−2.90191	+	0.852079i	−0.116827	+	0.0343034i	0.222797	+	0.974865i	$0.428481\pi$
$618$	35.2319	−	77.1470i	1.41723	−	3.10331i
$619$	−1.48326	−	10.3163i	−0.0596172	−	0.414647i	−0.997674	−	0.0681655i	$-0.978285\pi$
$619$	−1.48326	−	10.3163i	−0.0596172	−	0.414647i	0.938057	−	0.346482i	$-0.112624\pi$
$620$	−6.29515			−0.252819
$621$	−3.31934	+	1.88924i	−0.133200	+	0.0758127i
$622$	1.25637			0.0503758
$623$	−4.69386	−	32.6465i	−0.188056	−	1.30796i
$624$	0.319097	−	0.698725i	0.0127741	−	0.0279714i
$625$	−4.22587	+	1.24083i	−0.169035	+	0.0496331i
$626$	30.4958	−	35.1941i	1.21886	−	1.40664i
$627$	36.8121	+	10.8090i	1.47013	+	0.431670i
$628$	9.91937	−	6.37479i	0.395826	−	0.254382i
$629$	−2.51636	−	5.51006i	−0.100334	−	0.219701i
$630$	−14.0429	−	16.2064i	−0.559484	−	0.645678i
$631$	28.6878	+	18.4366i	1.14205	+	0.733948i	0.968040	−	0.250797i	$-0.0806926\pi$
$631$	28.6878	+	18.4366i	1.14205	+	0.733948i	0.174005	+	0.984745i	$0.444329\pi$
$632$	1.52413	−	10.6006i	0.0606266	−	0.421667i
$633$	−5.03182	+	34.9971i	−0.199997	+	1.39101i
$634$	−16.3359	−	10.4985i	−0.648783	−	0.416947i
$635$	4.85377	+	5.60155i	0.192616	+	0.222291i
$636$	−29.2795	−	64.1132i	−1.16101	−	2.54225i
$637$	−0.226421	+	0.145512i	−0.00897113	+	0.00576539i
$638$	20.1199	+	5.90773i	0.796553	+	0.233889i
$639$	1.58624	−	1.83062i	0.0627506	−	0.0724180i
$640$	−16.2621	+	4.77499i	−0.642817	+	0.188748i
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	−0.969012	−	0.247013i	$-0.920551\pi$
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	0.821248	+	0.570571i	$0.193278\pi$
$642$	1.56720	+	10.9001i	0.0618525	+	0.430194i
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$	−15.0696	+	28.7939i	−0.593825	+	1.13464i
$645$	13.8391			0.544913
$646$	−3.90598	−	27.1667i	−0.153679	−	1.06886i
$647$	−18.6747	+	40.8919i	−0.734178	+	1.60763i	0.0587216	+	0.998274i	$0.481298\pi$
$647$	−18.6747	+	40.8919i	−0.734178	+	1.60763i	−0.792900	+	0.609352i	$0.791430\pi$
$648$	14.3855	−	4.22396i	0.565115	−	0.165933i
$649$	−9.03801	+	10.4304i	−0.354773	+	0.409430i
$650$	1.44196	+	0.423396i	0.0565581	+	0.0166070i
$651$	8.94354	−	5.74766i	0.350525	−	0.225269i
$652$	−17.5459	−	38.4202i	−0.687152	−	1.50465i
$653$	19.2289	+	22.1914i	0.752486	+	0.868415i	0.994807	−	0.101781i	$-0.0324542\pi$
$653$	19.2289	+	22.1914i	0.752486	+	0.868415i	−0.242321	+	0.970196i	$0.577909\pi$
$654$	−72.6596	−	46.6955i	−2.84121	−	1.82594i
$655$	−2.24692	+	15.6277i	−0.0877945	+	0.610624i
$656$	0.0944170	−	0.656685i	0.00368636	−	0.0256392i
$657$	−17.9818	−	11.5562i	−0.701536	−	0.450850i
$658$	−8.86294	−	10.2284i	−0.345513	−	0.398744i
$659$	−16.6805	−	36.5251i	−0.649778	−	1.42282i	−0.891748	−	0.452532i	$-0.850521\pi$
$659$	−16.6805	−	36.5251i	−0.649778	−	1.42282i	0.241970	−	0.970284i	$-0.422206\pi$
$660$	−14.2746	+	9.17371i	−0.555637	+	0.357086i
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	0.0904132	−	0.995904i	$-0.471181\pi$
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	−0.462366	+	0.886689i	$0.652999\pi$
$662$	−43.5624	+	50.2737i	−1.69310	+	1.95394i
$663$	−0.739087	+	0.217015i	−0.0287037	+	0.00842818i
$664$	−10.0994	+	22.1146i	−0.391933	+	0.858214i
$665$	3.33381	+	23.1872i	0.129280	+	0.899159i
$666$	28.3829			1.09981
$667$	23.8359	+	1.28272i	0.922929	+	0.0496669i
$668$	3.79764			0.146935
$669$	−1.50356	−	10.4575i	−0.0581310	−	0.404310i
$670$	−8.22489	+	18.0100i	−0.317755	+	0.695787i
$671$	13.6290	−	4.00183i	0.526141	−	0.154489i
$672$	28.1188	−	32.4508i	1.08470	−	1.25182i
$673$	32.6772	+	9.59489i	1.25961	+	0.369856i	0.842351	−	0.538930i	$-0.181171\pi$
$673$	32.6772	+	9.59489i	1.25961	+	0.369856i	0.417263	+	0.908786i	$0.362989\pi$
$674$	−9.18700	+	5.90412i	−0.353870	+	0.227418i
$675$	1.14835	+	2.51454i	0.0442000	+	0.0967846i
$676$	24.2408	+	27.9754i	0.932339	+	1.07598i
$677$	−21.0239	−	13.5112i	−0.808012	−	0.519278i	0.0702091	−	0.997532i	$-0.477633\pi$
$677$	−21.0239	−	13.5112i	−0.808012	−	0.519278i	−0.878221	+	0.478254i	$0.841270\pi$
$678$	−1.17304	+	8.15864i	−0.0450502	+	0.313331i
$679$	1.46006	−	10.1550i	0.0560320	−	0.389711i
$680$	3.06043	+	1.96682i	0.117362	+	0.0754240i
$681$	30.3349	+	35.0084i	1.16244	+	1.34152i
$682$	−3.11992	−	6.83168i	−0.119468	−	0.261598i
$683$	29.0032	−	18.6392i	1.10978	−	0.713210i	0.148532	−	0.988908i	$-0.452545\pi$
$683$	29.0032	−	18.6392i	1.10978	−	0.713210i	0.961244	+	0.275698i	$0.0889088\pi$
$684$	72.5707	+	21.3087i	2.77481	+	0.814757i
$685$	0.564829	−	0.651848i	0.0215810	−	0.0249058i
$686$	−41.9910	+	12.3297i	−1.60322	+	0.470749i
$687$	−11.4062	+	24.9761i	−0.435174	+	0.952898i
$688$	0.985836	+	6.85664i	0.0375846	+	0.261407i
$689$	1.92925			0.0734987
$690$	−22.8100	+	23.6292i	−0.868363	+	0.899547i
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	6.88349	+	47.8757i	0.261671	+	1.81996i
$693$	6.25059	−	13.6869i	0.237440	−	0.519921i
$694$	14.3077	−	4.20113i	0.543114	−	0.159473i
$695$	11.3004	−	13.0414i	0.428649	−	0.494687i
$696$	22.6390	+	6.64742i	0.858130	+	0.251970i
$697$	−0.559680	+	0.359685i	−0.0211994	+	0.0136240i
$698$	9.23823	+	20.2289i	0.349672	+	0.765675i
$699$	6.85483	+	7.91090i	0.259274	+	0.299218i
$700$	19.7880	+	12.7170i	0.747915	+	0.480656i
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	−0.816275	−	0.577664i	$-0.803965\pi$
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	0.945957	−	0.324293i	$-0.105126\pi$
$702$	0.0490697	−	0.341287i	0.00185202	−	0.0128811i
$703$	−26.0834	−	16.7628i	−0.983756	−	0.632221i
$704$	−15.9693	−	18.4296i	−0.601866	−	0.694590i
$705$	−3.34160	−	7.31707i	−0.125852	−	0.275577i
$706$	45.3611	−	29.1518i	1.70719	−	1.09714i
$707$	−4.14417	−	1.21684i	−0.155858	−	0.0457639i
$708$	−33.9326	+	39.1603i	−1.27527	+	1.47173i
$709$	−6.75188	+	1.98253i	−0.253572	+	0.0744556i	−0.406048	−	0.913852i	$-0.633094\pi$
$709$	−6.75188	+	1.98253i	−0.253572	+	0.0744556i	0.152476	+	0.988307i	$0.451275\pi$
$710$	0.826602	−	1.81001i	0.0310218	−	0.0679283i
$711$	2.68028	+	18.6417i	0.100518	+	0.699119i
$712$	−26.2175			−0.982544
$713$	−5.24339	−	6.75275i	−0.196367	−	0.252892i
$714$	−20.4995			−0.767175
$715$	−0.0660988	−	0.459728i	−0.00247196	−	0.0171928i
$716$	−1.69814	+	3.71841i	−0.0634626	+	0.138964i
$717$	−54.3008	+	15.9441i	−2.02790	+	0.595445i
$718$	−0.604373	+	0.697483i	−0.0225550	+	0.0260298i
$719$	−25.4920	−	7.48514i	−0.950693	−	0.279149i	−0.230618	−	0.973044i	$-0.574075\pi$
$719$	−25.4920	−	7.48514i	−0.950693	−	0.279149i	−0.720075	+	0.693896i	$0.755893\pi$
$720$	5.36693	−	3.44912i	0.200014	−	0.128541i
$721$	15.0941	+	33.0515i	0.562134	+	1.23090i
$722$	−64.5792	−	74.5284i	−2.40339	−	2.77366i
$723$	−12.5363	−	8.05658i	−0.466230	−	0.299628i
$724$	6.55643	−	45.6010i	0.243668	−	1.69475i
$725$	2.45875	−	17.1010i	0.0913158	−	0.635115i
$726$	34.2213	+	21.9927i	1.27007	+	0.816226i
$727$	3.42332	+	3.95072i	0.126964	+	0.146524i	0.815672	−	0.578514i	$-0.196367\pi$
$727$	3.42332	+	3.95072i	0.126964	+	0.146524i	−0.688708	+	0.725039i	$0.741822\pi$
$728$	−0.365271	−	0.799832i	−0.0135378	−	0.0296437i
$729$	−27.2318	+	17.5008i	−1.00859	+	0.648179i
$730$	−16.8478	−	4.94696i	−0.623564	−	0.183095i
$731$	4.54901	−	5.24983i	0.168251	−	0.194172i
$732$	51.1691	−	15.0246i	1.89126	−	0.555325i
$733$	−11.0870	+	24.2771i	−0.409506	+	0.896694i	0.586711	+	0.809796i	$0.300422\pi$
$733$	−11.0870	+	24.2771i	−0.409506	+	0.896694i	−0.996217	+	0.0868973i	$0.972305\pi$
$734$	−8.95920	−	62.3126i	−0.330690	−	2.30000i
$735$	−4.25719			−0.157029
$736$	−28.0037	−	20.2026i	−1.03223	−	0.744677i
$737$	−13.8924			−0.511734
$738$	−0.443638	−	3.08557i	−0.0163305	−	0.113581i
$739$	−0.930342	+	2.03716i	−0.0342232	+	0.0749383i	−0.925972	−	0.377593i	$-0.876752\pi$
$739$	−0.930342	+	2.03716i	−0.0342232	+	0.0749383i	0.891748	+	0.452532i	$0.149479\pi$
$740$	13.1573	−	3.86334i	0.483673	−	0.142019i
$741$	−2.58196	+	2.97974i	−0.0948507	+	0.109464i
$742$	49.2630	+	14.4649i	1.80850	+	0.531024i
$743$	15.2605	−	9.80730i	0.559852	−	0.359795i	−0.229907	−	0.973213i	$-0.573842\pi$
$743$	15.2605	−	9.80730i	0.559852	−	0.359795i	0.789759	+	0.613418i	$0.210206\pi$
$744$	−3.51056	−	7.68705i	−0.128703	−	0.281821i
$745$	−13.4730	−	15.5486i	−0.493612	−	0.569658i
$746$	26.7091	+	17.1649i	0.977890	+	0.628452i
$747$	6.08446	−	42.3183i	0.222619	−	1.54835i
$748$	−1.21212	+	8.43051i	−0.0443197	+	0.308250i
$749$	−3.96893	−	2.55068i	−0.145022	−	0.0931997i
$750$	37.9895	+	43.8422i	1.38718	+	1.60089i
$751$	11.7258	+	25.6759i	0.427880	+	0.936927i	0.993666	+	0.112375i	$0.0358457\pi$
$751$	11.7258	+	25.6759i	0.427880	+	0.936927i	−0.565786	+	0.824552i	$0.691427\pi$
$752$	3.38724	−	2.17685i	0.123520	−	0.0793815i
$753$	−3.73935	−	1.09797i	−0.136269	−	0.0400123i
$754$	−1.41119	+	1.62860i	−0.0513924	+	0.0593100i
$755$	15.6485	−	4.59481i	0.569507	−	0.167222i
$756$	2.24187	−	4.90900i	0.0815359	−	0.178539i
$757$	−0.0173643	−	0.120772i	−0.000631118	−	0.00438952i	0.989503	−	0.144509i	$-0.0461603\pi$
$757$	−0.0173643	−	0.120772i	−0.000631118	−	0.00438952i	−0.990135	+	0.140120i	$0.955251\pi$
$758$	−12.4000			−0.450389
$759$	−21.7302	−	7.67118i	−0.788756	−	0.278446i
$760$	18.6210			0.675453
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	0.935027	+	0.354576i	$0.115375\pi$
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	−0.797257	+	0.603640i	$0.793716\pi$
$762$	−13.7915	+	30.1992i	−0.499614	+	1.09400i
$763$	35.5042	−	10.4250i	1.28534	−	0.377409i
$764$	38.7970	−	44.7741i	1.40363	−	1.61987i
$765$	−6.13839	−	1.80239i	−0.221934	−	0.0651657i
$766$	0.429451	−	0.275992i	0.0155167	−	0.00997198i
$767$	−0.589194	−	1.29015i	−0.0212745	−	0.0465848i
$768$	−7.72771	−	8.91825i	−0.278850	−	0.321810i
$769$	−6.60471	−	4.24459i	−0.238172	−	0.153064i	0.416111	−	0.909314i	$-0.363393\pi$
$769$	−6.60471	−	4.24459i	−0.238172	−	0.153064i	−0.654283	+	0.756250i	$0.727029\pi$
$770$	1.75907	−	12.2346i	0.0633926	−	0.440905i
$771$	9.82128	−	68.3085i	0.353705	−	2.46007i
$772$	35.2028	+	22.6235i	1.26698	+	0.814237i
$773$	22.4497	+	25.9084i	0.807460	+	0.931859i	0.998766	−	0.0496716i	$-0.0158175\pi$
$773$	22.4497	+	25.9084i	0.807460	+	0.931859i	−0.191305	+	0.981531i	$0.561272\pi$
$774$	13.5212	+	29.6073i	0.486009	+	1.06421i
$775$	−5.20559	+	3.34543i	−0.186990	+	0.120171i
$776$	−7.82482	−	2.29757i	−0.280895	−	0.0824781i
$777$	−15.1653	+	17.5017i	−0.544052	+	0.627869i
$778$	63.7897	−	18.7303i	2.28697	−	0.671515i
$779$	−1.41463	+	3.09760i	−0.0506843	+	0.110983i
$780$	−0.248164	−	1.72602i	−0.00888569	−	0.0618013i
$781$	1.39619			0.0499596
$782$	1.46587	+	16.4200i	0.0524193	+	0.587180i
$783$	−3.96386			−0.141657
$784$	−0.303264	−	2.10925i	−0.0108308	−	0.0753302i
$785$	−2.12070	+	4.64369i	−0.0756911	+	0.165740i
$786$	−67.8546	+	19.9239i	−2.42029	+	0.710662i
$787$	−10.4860	+	12.1015i	−0.373785	+	0.431370i	−0.911211	−	0.411940i	$-0.864851\pi$
$787$	−10.4860	+	12.1015i	−0.373785	+	0.431370i	0.537426	+	0.843311i	$0.319397\pi$
$788$	−32.0002	−	9.39611i	−1.13996	−	0.334723i
$789$	27.3612	−	17.5840i	0.974085	−	0.626006i
$790$	6.42697	+	14.0731i	0.228661	+	0.500699i
$791$	−2.31250	−	2.66877i	−0.0822231	−	0.0948905i
$792$	−10.0618	−	6.46634i	−0.357531	−	0.229772i
$793$	−0.207742	+	1.44488i	−0.00737712	+	0.0513090i
$794$	4.09109	−	28.4542i	0.145187	−	1.00980i
$795$	25.6714	+	16.4980i	0.910469	+	0.585123i
$796$	10.7041	+	12.3532i	0.379397	+	0.437847i
$797$	8.94128	+	19.5787i	0.316716	+	0.693512i	0.999304	−	0.0372914i	$-0.0118730\pi$
$797$	8.94128	+	19.5787i	0.316716	+	0.693512i	−0.682588	+	0.730803i	$0.739146\pi$
$798$	−88.2709	+	56.7282i	−3.12475	+	2.00816i
$799$	−3.87413	−	1.13755i	−0.137057	−	0.0402435i
$800$	−16.3665	+	18.8880i	−0.578644	+	0.667791i
$801$	44.2376	−	12.9893i	1.56306	−	0.458955i
$802$	−19.5219	+	42.7470i	−0.689343	+	1.50945i
$803$	−1.75340	−	12.1952i	−0.0618761	−	0.430358i
$804$	−52.1582			−1.83948
$805$	−1.25114	−	14.0148i	−0.0440969	−	0.493955i
$806$	0.771816			0.0271860
$807$	−3.57601	−	24.8717i	−0.125882	−	0.875526i
$808$	−1.42623	+	3.12301i	−0.0501746	+	0.109867i
$809$	−23.1479	+	6.79683i	−0.813836	+	0.238964i	−0.662060	−	0.749451i	$-0.730318\pi$
$809$	−23.1479	+	6.79683i	−0.813836	+	0.238964i	−0.151776	+	0.988415i	$0.548499\pi$
$810$	−14.1835	+	16.3687i	−0.498359	+	0.575136i
$811$	−13.7575	−	4.03956i	−0.483091	−	0.141848i	0.0311137	−	0.999516i	$-0.490095\pi$
$811$	−13.7575	−	4.03956i	−0.483091	−	0.141848i	−0.514205	+	0.857668i	$0.671913\pi$
$812$	−28.3744	+	18.2351i	−0.995747	+	0.639927i
$813$	−4.60584	−	10.0854i	−0.161534	−	0.353710i
$814$	10.7135	+	12.3640i	0.375507	+	0.433358i
$815$	15.3837	+	9.88652i	0.538868	+	0.346310i
$816$	0.867929	−	6.03658i	0.0303836	−	0.211323i
$817$	5.06017	−	35.1942i	0.177033	−	1.23129i
$818$	−16.9605	−	10.8998i	−0.593008	−	0.381103i
$819$	1.01260	+	1.16861i	0.0353832	+	0.0408344i
$820$	−0.625648	−	1.36998i	−0.0218486	−	0.0478417i
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	−0.315180	−	0.949032i	$-0.602065\pi$
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	0.732339	+	0.680940i	$0.238428\pi$
$822$	3.70689	+	1.08844i	0.129293	+	0.0379638i
$823$	−10.4929	+	12.1095i	−0.365760	+	0.422109i	−0.908561	−	0.417752i	$-0.862818\pi$
$823$	−10.4929	+	12.1095i	−0.365760	+	0.422109i	0.542802	+	0.839861i	$0.317364\pi$
$824$	27.7127	−	8.13718i	0.965417	−	0.283472i
$825$	−6.92875	+	15.1719i	−0.241228	+	0.528216i
$826$	−5.37175	−	37.3613i	−0.186907	−	1.29997i
$827$	35.1240			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$827$	35.1240			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$828$	−42.8385	−	15.1228i	−1.48874	−	0.525554i
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	−4.99824	−	34.7635i	−0.173491	−	1.20666i
$831$	32.1620	−	70.4250i	1.11569	−	2.44302i
$832$	2.40453	−	0.706035i	0.0833622	−	0.0244774i
$833$	−1.39937	+	1.61496i	−0.0484853	+	0.0559550i
$834$	74.1629	+	21.7762i	2.56805	+	0.754048i
$835$	−1.38319	+	0.888922i	−0.0478672	+	0.0307624i
$836$	18.1103	+	39.6561i	0.626359	+	1.37153i
$837$	0.929704	+	1.07294i	0.0321353	+	0.0370861i
$838$	−16.6364	−	10.6915i	−0.574694	−	0.369333i
$839$	−5.49501	+	38.2187i	−0.189709	+	1.31945i	0.643052	+	0.765822i	$0.277668\pi$
$839$	−5.49501	+	38.2187i	−0.189709	+	1.31945i	−0.832761	+	0.553632i	$0.813241\pi$
$840$	1.97932	−	13.7665i	0.0682930	−	0.474989i
$841$	−3.55542	−	2.28493i	−0.122601	−	0.0787906i
$842$	−45.4164	−	52.4134i	−1.56515	−	1.80628i
$843$	3.73708	+	8.18306i	0.128712	+	0.281839i
$844$	−33.7985	+	21.7210i	−1.16339	+	0.747667i
$845$	−15.3773	−	4.51519i	−0.528996	−	0.155327i
$846$	12.3893	−	14.2980i	0.425953	−	0.491576i
$847$	−16.7218	+	4.90997i	−0.574568	+	0.168708i
$848$	−6.34530	+	13.8943i	−0.217898	+	0.477131i
$849$	5.28673	+	36.7700i	0.181440	+	1.26194i
$850$	11.9317			0.409255
$851$	15.1032	+	10.8959i	0.517732	+	0.373505i
$852$	5.24190			0.179584
$853$	5.46907	+	38.0382i	0.187257	+	1.30240i	0.839070	+	0.544024i	$0.183100\pi$
$853$	5.46907	+	38.0382i	0.187257	+	1.30240i	−0.651812	+	0.758380i	$0.725991\pi$
$854$	−16.1378	+	35.3369i	−0.552226	+	1.20921i
$855$	−31.4197	+	9.22564i	−1.07453	+	0.315510i
$856$	−2.45588	+	2.83423i	−0.0839402	+	0.0968721i
$857$	48.8281	+	14.3372i	1.66794	+	0.489750i	0.973286	−	0.229598i	$-0.0737411\pi$
$857$	48.8281	+	14.3372i	1.66794	+	0.489750i	0.694650	+	0.719348i	$0.255559\pi$
$858$	1.75013	−	1.12474i	0.0597485	−	0.0383980i
$859$	3.79985	+	8.32050i	0.129649	+	0.283892i	0.963313	−	0.268380i	$-0.0864883\pi$
$859$	3.79985	+	8.32050i	0.129649	+	0.283892i	−0.833664	+	0.552272i	$0.813761\pi$
$860$	10.2980	+	11.8845i	0.351158	+	0.405257i
$861$	2.13969	+	1.37510i	0.0729205	+	0.0468631i
$862$	6.93147	−	48.2094i	0.236087	−	1.64202i
$863$	−1.75600	+	12.2133i	−0.0597750	+	0.415744i	0.937860	+	0.347013i	$0.112804\pi$
$863$	−1.75600	+	12.2133i	−0.0597750	+	0.415744i	−0.997635	+	0.0687310i	$0.978105\pi$
$864$	4.82378	+	3.10006i	0.164108	+	0.105466i
$865$	−13.7135	−	15.8262i	−0.466272	−	0.538107i
$866$	11.6214	+	25.4474i	0.394912	+	0.864737i
$867$	30.7991	−	19.7934i	1.04599	−	0.672219i
$868$	11.5910	+	3.40342i	0.393423	+	0.115519i
$869$	−7.10891	+	8.20412i	−0.241153	+	0.278306i
$870$	−32.7047	+	9.60297i	−1.10879	+	0.325571i
$871$	0.593078	−	1.29866i	0.0200957	−	0.0440034i
$872$	−4.18600	−	29.1143i	−0.141756	−	0.985934i
$873$	14.3414			0.485381
$874$	51.7512	+	66.6482i	1.75051	+	2.25441i
$875$	−24.8534			−0.840199
$876$	−6.58303	−	45.7860i	−0.222420	−	1.54696i
$877$	0.958445	−	2.09870i	0.0323644	−	0.0708681i	−0.892759	−	0.450534i	$-0.851234\pi$
$877$	0.958445	−	2.09870i	0.0323644	−	0.0708681i	0.925124	+	0.379666i	$0.123961\pi$
$878$	−38.9485	+	11.4363i	−1.31445	+	0.385957i
$879$	35.4087	−	40.8638i	1.19431	−	1.37830i
$880$	3.52831	+	1.03600i	0.118939	+	0.0349237i
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.937135	−	0.348966i	$-0.886533\pi$
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.0718697	+	0.997414i	$0.522897\pi$
$882$	−4.15940	−	9.10782i	−0.140054	−	0.306676i
$883$	−19.9566	−	23.0311i	−0.671592	−	0.775059i	0.313032	−	0.949742i	$-0.398655\pi$
$883$	−19.9566	−	23.0311i	−0.671592	−	0.775059i	−0.984625	+	0.174684i	$0.944110\pi$
$884$	−0.736336	−	0.473214i	−0.0247657	−	0.0159159i
$885$	3.19271	−	22.2058i	0.107322	−	0.746438i
$886$	4.36315	−	30.3464i	0.146583	−	1.01951i
$887$	17.4906	+	11.2405i	0.587278	+	0.377421i	0.800276	−	0.599632i	$-0.204686\pi$
$887$	17.4906	+	11.2405i	0.587278	+	0.377421i	−0.212998	+	0.977053i	$0.568323\pi$
$888$	12.0549	+	13.9121i	0.404535	+	0.466858i
$889$	−5.90859	−	12.9380i	−0.198168	−	0.433927i
$890$	31.8619	−	20.4764i	1.06801	−	0.686370i
$891$	−14.5817	−	4.28156i	−0.488504	−	0.143438i
$892$	7.86168	−	9.07286i	0.263228	−	0.303782i
$893$	−19.8299	+	5.82260i	−0.663584	+	0.194846i
$894$	38.2822	−	83.8263i	1.28035	−	2.80357i
$895$	−0.251874	−	1.75182i	−0.00841920	−	0.0585569i
$896$	32.5243			1.08656
$897$	1.64478	−	1.70385i	0.0549176	−	0.0568898i
$898$	66.3122			2.21287
$899$	−1.26275	−	8.78264i	−0.0421152	−	0.292918i
$900$	−13.6592	+	29.9095i	−0.455307	+	0.996984i
$901$	14.6969	−	4.31539i	0.489624	−	0.143766i
$902$	1.17666	−	1.35794i	0.0391786	−	0.0452145i
$903$	−25.4812	−	7.48196i	−0.847962	−	0.248984i
$904$	−2.36141	+	1.51759i	−0.0785393	+	0.0504742i
$905$	8.28590	+	18.1436i	0.275433	+	0.603114i
$906$	47.8387	+	55.2088i	1.58933	+	1.83419i
$907$	−19.1064	−	12.2789i	−0.634417	−	0.407715i	0.183525	−	0.983015i	$-0.441249\pi$
$907$	−19.1064	−	12.2789i	−0.634417	−	0.407715i	−0.817943	+	0.575300i	$0.804885\pi$
$908$	−7.49100	+	52.1011i	−0.248598	+	1.72903i
$909$	0.859242	−	5.97616i	0.0284992	−	0.198217i
$910$	1.06859	+	0.686743i	0.0354235	+	0.0227653i
$911$	−0.546182	−	0.630328i	−0.0180958	−	0.0208837i	0.746630	−	0.665240i	$-0.231671\pi$
$911$	−0.546182	−	0.630328i	−0.0180958	−	0.0208837i	−0.764725	+	0.644356i	$0.777125\pi$
$912$	−12.9677	−	28.3953i	−0.429404	−	0.940264i
$913$	20.7312	−	13.3231i	0.686101	−	0.440930i
$914$	−80.4460	−	23.6211i	−2.66092	−	0.781315i
$915$	−15.1201	+	17.4496i	−0.499856	+	0.576864i
$916$	−29.9362	+	8.79006i	−0.989120	+	0.290432i
$917$	12.5861	−	27.5597i	0.415630	−	0.910103i
$918$	−0.389589	−	2.70965i	−0.0128584	−	0.0894319i
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$	−11.1684	−	0.601024i	−0.368213	−	0.0198152i
$921$	−35.5510			−1.17145
$922$	−2.74725	−	19.1075i	−0.0904758	−	0.629273i
$923$	−0.0596044	+	0.130515i	−0.00196190	+	0.00429597i
$924$	31.2428	−	9.17371i	1.02781	−	0.301793i
$925$	8.82696	−	10.1869i	0.290229	−	0.334942i
$926$	58.8566	+	17.2819i	1.93415	+	0.567918i
$927$	−42.7289	+	27.4602i	−1.40340	+	0.901910i
$928$	−14.8873	−	32.5986i	−0.488699	−	1.07010i
$929$	11.5958	+	13.3822i	0.380445	+	0.439056i	0.913385	−	0.407096i	$-0.133459\pi$
$929$	11.5958	+	13.3822i	0.380445	+	0.439056i	−0.532941	+	0.846153i	$0.678913\pi$
$930$	10.2701	+	6.60017i	0.336769	+	0.216428i
$931$	−1.55661	+	10.8265i	−0.0510159	+	0.354824i
$932$	−1.69275	+	11.7734i	−0.0554480	+	0.385649i
$933$	−1.20548	−	0.774713i	−0.0394655	−	0.0253630i
$934$	25.0607	+	28.9216i	0.820011	+	0.946343i
$935$	−1.53186	−	3.35431i	−0.0500972	−	0.109698i
$936$	1.03402	−	0.664524i	0.0337980	−	0.0217207i
$937$	22.3812	+	6.57170i	0.731161	+	0.214688i	0.626062	−	0.779774i	$-0.284666\pi$
$937$	22.3812	+	6.57170i	0.731161	+	0.214688i	0.105099	+	0.994462i	$0.466484\pi$
$938$	24.8810	−	28.7143i	0.812395	−	0.937554i
$939$	−50.9622	+	14.9639i	−1.66309	+	0.488327i
$940$	3.79708	−	8.31444i	0.123847	−	0.271187i
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	−0.998864	−	0.0476470i	$-0.984828\pi$
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	0.944980	−	0.327130i	$-0.106081\pi$
$942$	−22.8664			−0.745027
$943$	0.948444	−	1.81222i	0.0308856	−	0.0590139i
$944$	11.2294			0.365486
$945$	0.332520	+	2.31273i	0.0108169	+	0.0752331i
$946$	−7.79363	+	17.0657i	−0.253393	+	0.554853i
$947$	−5.75498	+	1.68981i	−0.187012	+	0.0549116i	−0.373897	−	0.927470i	$-0.621979\pi$
$947$	−5.75498	+	1.68981i	−0.187012	+	0.0549116i	0.186886	+	0.982382i	$0.440161\pi$
$948$	−26.6899	+	30.8018i	−0.866849	+	1.00040i
$949$	1.21486	+	0.356714i	0.0394359	+	0.0115794i
$950$	51.3781	−	33.0187i	1.66692	−	1.07127i
$951$	9.20056	+	20.1464i	0.298348	+	0.653292i
$952$	−4.57168	−	5.27600i	−0.148169	−	0.170996i
$953$	−15.0640	−	9.68107i	−0.487972	−	0.313601i	0.273417	−	0.961896i	$-0.411846\pi$
$953$	−15.0640	−	9.68107i	−0.487972	−	0.313601i	−0.761389	+	0.648295i	$0.775482\pi$
$954$	−10.2141	+	71.0403i	−0.330692	+	2.30002i
$955$	−3.65039	+	25.3890i	−0.118124	+	0.821570i
$956$	−54.0987	−	34.7671i	−1.74968	−	1.12445i
$957$	−15.6620	−	18.0749i	−0.506281	−	0.584279i
$958$	−23.3227	−	51.0697i	−0.753524	−	1.64999i
$959$	−1.39241	+	0.894847i	−0.0449632	+	0.0288961i
$960$	38.0333	+	11.1676i	1.22752	+	0.360432i
$961$	18.2196	−	21.0265i	0.587728	−	0.678274i
$962$	−1.61315	+	0.473664i	−0.0520101	+	0.0152715i
$963$	2.73967	−	5.99903i	0.0882845	−	0.193316i
$964$	−2.40984	−	16.7608i	−0.0776156	−	0.539829i
$965$	−18.1172			−0.583213
$966$	54.7739	−	31.1753i	1.76232	−	1.00305i
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	1.97153	+	13.7123i	0.0633673	+	0.440730i
$969$	−13.0040	+	28.4748i	−0.417748	+	0.914741i
$970$	11.3039	−	3.31911i	0.362945	−	0.106570i
$971$	−38.8241	+	44.8054i	−1.24592	+	1.43787i	−0.389964	+	0.920830i	$0.627513\pi$
$971$	−38.8241	+	44.8054i	−1.24592	+	1.43787i	−0.855960	+	0.517042i	$0.827033\pi$
$972$	−61.2928	−	17.9972i	−1.96597	−	0.577260i
$973$	−27.8576	+	17.9030i	−0.893073	+	0.573943i
$974$	−5.63994	−	12.3497i	−0.180715	−	0.395711i
$975$	−1.12247	−	1.29540i	−0.0359477	−	0.0414859i
$976$	−9.72257	−	6.24832i	−0.311212	−	0.200004i
$977$	1.79914	−	12.5133i	0.0575596	−	0.400336i	−0.940591	−	0.339542i	$-0.889728\pi$
$977$	1.79914	−	12.5133i	0.0575596	−	0.400336i	0.998150	−	0.0607934i	$-0.0193631\pi$
$978$	−11.6569	+	81.0758i	−0.372748	+	2.59252i
$979$	22.3564	+	14.3676i	0.714513	+	0.459189i
$980$	−3.16787	−	3.65592i	−0.101194	−	0.116784i
$981$	21.4877	+	47.0514i	0.686048	+	1.50224i
$982$	−60.5221	+	38.8952i	−1.93134	+	1.24120i
$983$	56.0008	+	16.4433i	1.78615	+	0.524461i	0.996072	−	0.0885469i	$-0.0282223\pi$
$983$	56.0008	+	16.4433i	1.78615	+	0.524461i	0.790077	+	0.613008i	$0.210040\pi$
$984$	1.32399	−	1.52797i	0.0422072	−	0.0487097i
$985$	13.8546	−	4.06807i	0.441444	−	0.129620i
$986$	−7.10741	+	15.5631i	−0.226346	+	0.495629i
$987$	2.19682	+	15.2792i	0.0699254	+	0.486342i
$988$	−4.48019			−0.142534
$989$	−4.17093	+	20.9454i	−0.132628	+	0.666025i
$990$	17.2784			0.549142
$991$	6.51675	+	45.3250i	0.207011	+	1.43980i	0.782839	+	0.622224i	$0.213771\pi$
$991$	6.51675	+	45.3250i	0.207011	+	1.43980i	−0.575828	+	0.817571i	$0.695320\pi$
$992$	−5.33204	+	11.6755i	−0.169292	+	0.370699i
$993$	72.7980	−	21.3754i	2.31018	−	0.678329i
$994$	−2.50055	+	2.88578i	−0.0793125	+	0.0915315i
$995$	−6.79021	−	1.99379i	−0.215264	−	0.0632073i
$996$	77.8338	−	50.0207i	2.46626	−	1.58497i
$997$	−16.3475	−	35.7959i	−0.517729	−	1.13367i	−0.970292	−	0.241936i	$-0.922218\pi$
$997$	−16.3475	−	35.7959i	−0.517729	−	1.13367i	0.452563	−	0.891732i	$-0.350510\pi$
$998$	12.3724	+	14.2785i	0.391640	+	0.451977i
$999$	−2.60161	−	1.67195i	−0.0823113	−	0.0528983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.2.c.a.3.1	✓	10
3.2	odd	2		207.2.i.c.118.1		10
4.3	odd	2		368.2.m.c.49.1		10
5.2	odd	4		575.2.p.b.49.2		20
5.3	odd	4		575.2.p.b.49.1		20
5.4	even	2		575.2.k.b.26.1		10
23.2	even	11		529.2.c.i.334.1		10
23.3	even	11		529.2.c.g.487.1		10
23.4	even	11		529.2.c.i.255.1		10
23.5	odd	22		529.2.c.f.466.1		10
23.6	even	11		529.2.c.d.177.1		10
23.7	odd	22		529.2.c.c.170.1		10
23.8	even	11	inner	23.2.c.a.8.1	yes	10
23.9	even	11		529.2.c.d.266.1		10
23.10	odd	22		529.2.a.j.1.5		5
23.11	odd	22		529.2.c.c.501.1		10
23.12	even	11		529.2.c.b.501.1		10
23.13	even	11		529.2.a.i.1.5		5
23.14	odd	22		529.2.c.e.266.1		10
23.15	odd	22		529.2.c.a.399.1		10
23.16	even	11		529.2.c.b.170.1		10
23.17	odd	22		529.2.c.e.177.1		10
23.18	even	11		529.2.c.g.466.1		10
23.19	odd	22		529.2.c.h.255.1		10
23.20	odd	22		529.2.c.f.487.1		10
23.21	odd	22		529.2.c.h.334.1		10
23.22	odd	2		529.2.c.a.118.1		10
69.8	odd	22		207.2.i.c.100.1		10
69.56	even	22		4761.2.a.bn.1.1		5
69.59	odd	22		4761.2.a.bo.1.1		5
92.31	odd	22		368.2.m.c.353.1		10
92.59	odd	22		8464.2.a.bs.1.5		5
92.79	even	22		8464.2.a.bt.1.5		5
115.8	odd	44		575.2.p.b.399.2		20
115.54	even	22		575.2.k.b.376.1		10
115.77	odd	44		575.2.p.b.399.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	1.1	even	1	trivial
23.2.c.a.8.1	yes	10	23.8	even	11	inner
207.2.i.c.100.1		10	69.8	odd	22
207.2.i.c.118.1		10	3.2	odd	2
368.2.m.c.49.1		10	4.3	odd	2
368.2.m.c.353.1		10	92.31	odd	22
529.2.a.i.1.5		5	23.13	even	11
529.2.a.j.1.5		5	23.10	odd	22
529.2.c.a.118.1		10	23.22	odd	2
529.2.c.a.399.1		10	23.15	odd	22
529.2.c.b.170.1		10	23.16	even	11
529.2.c.b.501.1		10	23.12	even	11
529.2.c.c.170.1		10	23.7	odd	22
529.2.c.c.501.1		10	23.11	odd	22
529.2.c.d.177.1		10	23.6	even	11
529.2.c.d.266.1		10	23.9	even	11
529.2.c.e.177.1		10	23.17	odd	22
529.2.c.e.266.1		10	23.14	odd	22
529.2.c.f.466.1		10	23.5	odd	22
529.2.c.f.487.1		10	23.20	odd	22
529.2.c.g.466.1		10	23.18	even	11
529.2.c.g.487.1		10	23.3	even	11
529.2.c.h.255.1		10	23.19	odd	22
529.2.c.h.334.1		10	23.21	odd	22
529.2.c.i.255.1		10	23.4	even	11
529.2.c.i.334.1		10	23.2	even	11
575.2.k.b.26.1		10	5.4	even	2
575.2.k.b.376.1		10	115.54	even	22
575.2.p.b.49.1		20	5.3	odd	4
575.2.p.b.49.2		20	5.2	odd	4
575.2.p.b.399.1		20	115.77	odd	44
575.2.p.b.399.2		20	115.8	odd	44
4761.2.a.bn.1.1		5	69.56	even	22
4761.2.a.bo.1.1		5	69.59	odd	22
8464.2.a.bs.1.5		5	92.59	odd	22
8464.2.a.bt.1.5		5	92.79	even	22

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.313607 - 2.18119i) q^{2} +(-1.04408 + 2.28621i) q^{3} +(-2.74024 + 0.804606i) q^{4} +(0.809721 - 0.934468i) q^{5} +(5.31408 + 1.56036i) q^{6} +(-1.99611 + 1.28282i) q^{7} +(0.783524 + 1.71568i) q^{8} +(-2.17208 - 2.50672i) q^{9} +O(q^{10})\)	\(q+(-0.313607 - 2.18119i) q^{2} +(-1.04408 + 2.28621i) q^{3} +(-2.74024 + 0.804606i) q^{4} +(0.809721 - 0.934468i) q^{5} +(5.31408 + 1.56036i) q^{6} +(-1.99611 + 1.28282i) q^{7} +(0.783524 + 1.71568i) q^{8} +(-2.17208 - 2.50672i) q^{9} +(-2.29218 - 1.47310i) q^{10} +(0.272084 - 1.89238i) q^{11} +(1.02152 - 7.10483i) q^{12} +(0.165284 + 0.106222i) q^{13} +(3.42408 + 3.95159i) q^{14} +(1.29098 + 2.82685i) q^{15} +(-1.30862 + 0.840996i) q^{16} +(1.49672 + 0.439476i) q^{17} +(-4.78644 + 5.52384i) q^{18} +(7.66103 - 2.24948i) q^{19} +(-1.46695 + 3.21217i) q^{20} +(-0.848710 - 5.90291i) q^{21} -4.21297 q^{22} +(-4.66752 + 1.10192i) q^{23} -4.74046 q^{24} +(0.493992 + 3.43579i) q^{25} +(0.179855 - 0.393828i) q^{26} +(0.764125 - 0.224367i) q^{27} +(4.43766 - 5.12133i) q^{28} +(-4.77570 - 1.40227i) q^{29} +(5.76103 - 3.70239i) q^{30} +(0.740552 + 1.62158i) q^{31} +(4.71506 + 5.44146i) q^{32} +(4.04231 + 2.59784i) q^{33} +(0.489198 - 3.40244i) q^{34} +(-0.417537 + 2.90404i) q^{35} +(7.96894 + 5.12133i) q^{36} +(-2.54297 - 2.93475i) q^{37} +(-7.30909 - 16.0047i) q^{38} +(-0.415415 + 0.266971i) q^{39} +(2.23768 + 0.657043i) q^{40} +(-0.279295 + 0.322324i) q^{41} +(-12.6092 + 3.70239i) q^{42} +(1.84991 - 4.05075i) q^{43} +(0.777050 + 5.40450i) q^{44} -4.10123 q^{45} +(3.86725 + 9.83517i) q^{46} -2.58842 q^{47} +(-0.556399 - 3.86984i) q^{48} +(-0.569072 + 1.24609i) q^{49} +(7.33918 - 2.15498i) q^{50} +(-2.56743 + 2.96297i) q^{51} +(-0.538385 - 0.158084i) q^{52} +(8.26060 - 5.30876i) q^{53} +(-0.729022 - 1.59634i) q^{54} +(-1.54806 - 1.78656i) q^{55} +(-3.76492 - 2.41956i) q^{56} +(-2.85592 + 19.8634i) q^{57} +(-1.56092 + 10.8565i) q^{58} +(-6.07293 - 3.90283i) q^{59} +(-5.81210 - 6.70752i) q^{60} +(3.08639 + 6.75826i) q^{61} +(3.30473 - 2.12382i) q^{62} +(7.55141 + 2.21729i) q^{63} +(8.35283 - 9.63968i) q^{64} +(0.233095 - 0.0684429i) q^{65} +(4.39867 - 9.63174i) q^{66} +(-1.03413 - 7.19254i) q^{67} -4.45497 q^{68} +(2.35404 - 11.8214i) q^{69} +6.46519 q^{70} +(0.103930 + 0.722850i) q^{71} +(2.59884 - 5.69067i) q^{72} +(6.18330 - 1.81558i) q^{73} +(-5.60373 + 6.46705i) q^{74} +(-8.37071 - 2.45786i) q^{75} +(-19.1831 + 12.3282i) q^{76} +(1.88449 + 4.12645i) q^{77} +(0.712591 + 0.822373i) q^{78} +(-4.77671 - 3.06980i) q^{79} +(-0.273730 + 1.90383i) q^{80} +(1.13126 - 7.86810i) q^{81} +(0.790638 + 0.508112i) q^{82} +(8.44098 + 9.74141i) q^{83} +(7.07518 + 15.4925i) q^{84} +(1.62260 - 1.04278i) q^{85} +(-9.41558 - 2.76466i) q^{86} +(8.19209 - 9.45418i) q^{87} +(3.45991 - 1.01592i) q^{88} +(-5.77436 + 12.6441i) q^{89} +(1.28618 + 8.94555i) q^{90} -0.466190 q^{91} +(11.9035 - 6.77503i) q^{92} -4.48047 q^{93} +(0.811746 + 5.64582i) q^{94} +(4.10123 - 8.98044i) q^{95} +(-17.3632 + 5.09830i) q^{96} +(-2.83147 + 3.26769i) q^{97} +(2.89643 + 0.850468i) q^{98} +(-5.33466 + 3.42838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more