LMFDB - Embedded newform 966.2.h.b.827.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.15
Character	$\chi$	$=$	966.827
Dual form			966.2.h.b.827.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.01359 - 1.40450i) q^{3} -1.00000 q^{4} +1.51059 q^{5} +(1.40450 - 1.01359i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-0.945264 + 2.84719i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.01359 - 1.40450i) q^{3} -1.00000 q^{4} +1.51059 q^{5} +(1.40450 - 1.01359i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-0.945264 + 2.84719i) q^{9} +1.51059i q^{10} -1.20152 q^{11} +(1.01359 + 1.40450i) q^{12} -2.45816 q^{13} -1.00000 q^{14} +(-1.53112 - 2.12163i) q^{15} +1.00000 q^{16} -3.78965 q^{17} +(-2.84719 - 0.945264i) q^{18} +4.80264i q^{19} -1.51059 q^{20} +(1.40450 - 1.01359i) q^{21} -1.20152i q^{22} +(4.74822 - 0.674123i) q^{23} +(-1.40450 + 1.01359i) q^{24} -2.71811 q^{25} -2.45816i q^{26} +(4.95700 - 1.55826i) q^{27} -1.00000i q^{28} +9.64176i q^{29} +(2.12163 - 1.53112i) q^{30} -0.842474 q^{31} +1.00000i q^{32} +(1.21785 + 1.68754i) q^{33} -3.78965i q^{34} +1.51059i q^{35} +(0.945264 - 2.84719i) q^{36} -9.11097i q^{37} -4.80264 q^{38} +(2.49157 + 3.45250i) q^{39} -1.51059i q^{40} +8.42196i q^{41} +(1.01359 + 1.40450i) q^{42} -6.02163i q^{43} +1.20152 q^{44} +(-1.42791 + 4.30094i) q^{45} +(0.674123 + 4.74822i) q^{46} +12.1681i q^{47} +(-1.01359 - 1.40450i) q^{48} -1.00000 q^{49} -2.71811i q^{50} +(3.84116 + 5.32259i) q^{51} +2.45816 q^{52} -9.05644 q^{53} +(1.55826 + 4.95700i) q^{54} -1.81501 q^{55} +1.00000 q^{56} +(6.74533 - 4.86792i) q^{57} -9.64176 q^{58} +8.50654i q^{59} +(1.53112 + 2.12163i) q^{60} +5.57753i q^{61} -0.842474i q^{62} +(-2.84719 - 0.945264i) q^{63} -1.00000 q^{64} -3.71328 q^{65} +(-1.68754 + 1.21785i) q^{66} +13.3295i q^{67} +3.78965 q^{68} +(-5.75956 - 5.98560i) q^{69} -1.51059 q^{70} +4.48229i q^{71} +(2.84719 + 0.945264i) q^{72} -8.07349 q^{73} +9.11097 q^{74} +(2.75506 + 3.81760i) q^{75} -4.80264i q^{76} -1.20152i q^{77} +(-3.45250 + 2.49157i) q^{78} -9.34825i q^{79} +1.51059 q^{80} +(-7.21295 - 5.38269i) q^{81} -8.42196 q^{82} -8.00034 q^{83} +(-1.40450 + 1.01359i) q^{84} -5.72462 q^{85} +6.02163 q^{86} +(13.5419 - 9.77281i) q^{87} +1.20152i q^{88} +0.364537 q^{89} +(-4.30094 - 1.42791i) q^{90} -2.45816i q^{91} +(-4.74822 + 0.674123i) q^{92} +(0.853925 + 1.18326i) q^{93} -12.1681 q^{94} +7.25483i q^{95} +(1.40450 - 1.01359i) q^{96} +8.40421i q^{97} -1.00000i q^{98} +(1.13576 - 3.42096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.01359	−	1.40450i	−0.585197	−	0.810891i
$3$	−1.01359	−	1.40450i	−0.585197	−	0.810891i
$4$	−1.00000			−0.500000
$5$	1.51059			0.675557			0.337779	−	0.941226i	$-0.390325\pi$
$5$	1.51059			0.675557			0.337779	+	0.941226i	$0.390325\pi$
$6$	1.40450	−	1.01359i	0.573386	−	0.413797i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−0.945264	+	2.84719i	−0.315088	+	0.949062i
$10$			1.51059i			0.477691i
$11$	−1.20152			−0.362272			−0.181136	−	0.983458i	$-0.557977\pi$
$11$	−1.20152			−0.362272			−0.181136	+	0.983458i	$0.557977\pi$
$12$	1.01359	+	1.40450i	0.292599	+	0.405445i
$13$	−2.45816			−0.681772			−0.340886	−	0.940105i	$-0.610727\pi$
$13$	−2.45816			−0.681772			−0.340886	+	0.940105i	$0.610727\pi$
$14$	−1.00000			−0.267261
$15$	−1.53112	−	2.12163i	−0.395334	−	0.547803i
$16$	1.00000			0.250000
$17$	−3.78965			−0.919126			−0.459563	−	0.888145i	$-0.651994\pi$
$17$	−3.78965			−0.919126			−0.459563	+	0.888145i	$0.651994\pi$
$18$	−2.84719	−	0.945264i	−0.671088	−	0.222801i
$19$			4.80264i			1.10180i	0.834571	+	0.550901i	$0.185716\pi$
$19$			4.80264i			1.10180i	−0.834571	+	0.550901i	$0.814284\pi$
$20$	−1.51059			−0.337779
$21$	1.40450	−	1.01359i	0.306488	−	0.221184i
$22$		−	1.20152i		−	0.256165i
$23$	4.74822	−	0.674123i	0.990072	−	0.140564i
$23$	4.74822	−	0.674123i	0.990072	−	0.140564i
$24$	−1.40450	+	1.01359i	−0.286693	+	0.206899i
$25$	−2.71811			−0.543623
$26$		−	2.45816i		−	0.482086i
$27$	4.95700	−	1.55826i	0.953975	−	0.299887i
$28$		−	1.00000i		−	0.188982i
$29$			9.64176i			1.79043i	0.445634	+	0.895215i	$0.352978\pi$
$29$			9.64176i			1.79043i	−0.445634	+	0.895215i	$0.647022\pi$
$30$	2.12163	−	1.53112i	0.387355	−	0.279544i
$31$	−0.842474			−0.151313			−0.0756564	−	0.997134i	$-0.524105\pi$
$31$	−0.842474			−0.151313			−0.0756564	+	0.997134i	$0.524105\pi$
$32$			1.00000i			0.176777i
$33$	1.21785	+	1.68754i	0.212001	+	0.293763i
$34$		−	3.78965i		−	0.649920i
$35$			1.51059i			0.255337i
$36$	0.945264	−	2.84719i	0.157544	−	0.474531i
$37$		−	9.11097i		−	1.49783i	−0.662664	−	0.748917i	$-0.730574\pi$
$37$		−	9.11097i		−	1.49783i	0.662664	−	0.748917i	$-0.269426\pi$
$38$	−4.80264			−0.779091
$39$	2.49157	+	3.45250i	0.398971	+	0.552843i
$40$		−	1.51059i		−	0.238845i
$41$			8.42196i			1.31529i	0.753328	+	0.657644i	$0.228447\pi$
$41$			8.42196i			1.31529i	−0.753328	+	0.657644i	$0.771553\pi$
$42$	1.01359	+	1.40450i	0.156401	+	0.216720i
$43$		−	6.02163i		−	0.918291i	−0.888361	−	0.459145i	$-0.848156\pi$
$43$		−	6.02163i		−	0.918291i	0.888361	−	0.459145i	$-0.151844\pi$
$44$	1.20152			0.181136
$45$	−1.42791	+	4.30094i	−0.212860	+	0.641146i
$46$	0.674123	+	4.74822i	0.0993940	+	0.700086i
$47$			12.1681i			1.77489i	0.460909	+	0.887447i	$0.347523\pi$
$47$			12.1681i			1.77489i	−0.460909	+	0.887447i	$0.652477\pi$
$48$	−1.01359	−	1.40450i	−0.146299	−	0.202723i
$49$	−1.00000			−0.142857
$50$		−	2.71811i		−	0.384399i
$51$	3.84116	+	5.32259i	0.537870	+	0.745311i
$52$	2.45816			0.340886
$53$	−9.05644			−1.24400			−0.621999	−	0.783018i	$-0.713679\pi$
$53$	−9.05644			−1.24400			−0.621999	+	0.783018i	$0.713679\pi$
$54$	1.55826	+	4.95700i	0.212052	+	0.674562i
$55$	−1.81501			−0.244736
$56$	1.00000			0.133631
$57$	6.74533	−	4.86792i	0.893441	−	0.644771i
$58$	−9.64176			−1.26603
$59$			8.50654i			1.10746i	0.832697	+	0.553729i	$0.186796\pi$
$59$			8.50654i			1.10746i	−0.832697	+	0.553729i	$0.813204\pi$
$60$	1.53112	+	2.12163i	0.197667	+	0.273902i
$61$			5.57753i			0.714130i	0.934080	+	0.357065i	$0.116223\pi$
$61$			5.57753i			0.714130i	−0.934080	+	0.357065i	$0.883777\pi$
$62$		−	0.842474i		−	0.106994i
$63$	−2.84719	−	0.945264i	−0.358712	−	0.119092i
$64$	−1.00000			−0.125000
$65$	−3.71328			−0.460576
$66$	−1.68754	+	1.21785i	−0.207722	+	0.149907i
$67$			13.3295i			1.62846i	0.580544	+	0.814229i	$0.302840\pi$
$67$			13.3295i			1.62846i	−0.580544	+	0.814229i	$0.697160\pi$
$68$	3.78965			0.459563
$69$	−5.75956	−	5.98560i	−0.693370	−	0.720582i
$70$	−1.51059			−0.180550
$71$			4.48229i			0.531950i	0.963980	+	0.265975i	$0.0856939\pi$
$71$			4.48229i			0.531950i	−0.963980	+	0.265975i	$0.914306\pi$
$72$	2.84719	+	0.945264i	0.335544	+	0.111400i
$73$	−8.07349			−0.944930			−0.472465	−	0.881349i	$-0.656636\pi$
$73$	−8.07349			−0.944930			−0.472465	+	0.881349i	$0.656636\pi$
$74$	9.11097			1.05913
$75$	2.75506	+	3.81760i	0.318127	+	0.440819i
$76$		−	4.80264i		−	0.550901i
$77$		−	1.20152i		−	0.136926i
$78$	−3.45250	+	2.49157i	−0.390919	+	0.282115i
$79$		−	9.34825i		−	1.05176i	−0.850559	−	0.525880i	$-0.823736\pi$
$79$		−	9.34825i		−	1.05176i	0.850559	−	0.525880i	$-0.176264\pi$
$80$	1.51059			0.168889
$81$	−7.21295	−	5.38269i	−0.801439	−	0.598077i
$82$	−8.42196			−0.930050
$83$	−8.00034			−0.878151			−0.439076	−	0.898450i	$-0.644694\pi$
$83$	−8.00034			−0.878151			−0.439076	+	0.898450i	$0.644694\pi$
$84$	−1.40450	+	1.01359i	−0.153244	+	0.110592i
$85$	−5.72462			−0.620922
$86$	6.02163			0.649330
$87$	13.5419	−	9.77281i	1.45184	−	1.04776i
$88$			1.20152i			0.128083i
$89$	0.364537			0.0386409			0.0193204	−	0.999813i	$-0.493850\pi$
$89$	0.364537			0.0386409			0.0193204	+	0.999813i	$0.493850\pi$
$90$	−4.30094	−	1.42791i	−0.453359	−	0.150515i
$91$		−	2.45816i		−	0.257686i
$92$	−4.74822	+	0.674123i	−0.495036	+	0.0702822i
$93$	0.853925	+	1.18326i	0.0885479	+	0.122698i
$94$	−12.1681			−1.25504
$95$			7.25483i			0.744330i
$96$	1.40450	−	1.01359i	0.143347	−	0.103449i
$97$			8.40421i			0.853318i	0.904413	+	0.426659i	$0.140310\pi$
$97$			8.40421i			0.853318i	−0.904413	+	0.426659i	$0.859690\pi$
$98$		−	1.00000i		−	0.101015i
$99$	1.13576	−	3.42096i	0.114148	−	0.343819i
$100$	2.71811			0.271811
$101$		−	1.22130i		−	0.121524i	−0.998152	−	0.0607618i	$-0.980647\pi$
$101$		−	1.22130i		−	0.121524i	0.998152	−	0.0607618i	$-0.0193530\pi$
$102$	−5.32259	+	3.84116i	−0.527015	+	0.380332i
$103$			5.85397i			0.576809i	0.957509	+	0.288404i	$0.0931247\pi$
$103$			5.85397i			0.576809i	−0.957509	+	0.288404i	$0.906875\pi$
$104$			2.45816i			0.241043i
$105$	2.12163	−	1.53112i	0.207050	−	0.149422i
$106$		−	9.05644i		−	0.879640i
$107$	17.3805			1.68023			0.840117	−	0.542405i	$-0.182486\pi$
$107$	17.3805			1.68023			0.840117	+	0.542405i	$0.182486\pi$
$108$	−4.95700	+	1.55826i	−0.476987	+	0.149943i
$109$		−	13.6354i		−	1.30604i	−0.757341	−	0.653019i	$-0.773502\pi$
$109$		−	13.6354i		−	1.30604i	0.757341	−	0.653019i	$-0.226498\pi$
$110$		−	1.81501i		−	0.173054i
$111$	−12.7964	+	9.23480i	−1.21458	+	0.876528i
$112$			1.00000i			0.0944911i
$113$	−0.757627			−0.0712716			−0.0356358	−	0.999365i	$-0.511346\pi$
$113$	−0.757627			−0.0712716			−0.0356358	+	0.999365i	$0.511346\pi$
$114$	4.86792	+	6.74533i	0.455922	+	0.631758i
$115$	7.17262	−	1.01832i	0.668850	−	0.0949592i
$116$		−	9.64176i		−	0.895215i
$117$	2.32361	−	6.99885i	0.214818	−	0.647044i
$118$	−8.50654			−0.783091
$119$		−	3.78965i		−	0.347397i
$120$	−2.12163	+	1.53112i	−0.193678	+	0.139772i
$121$	−9.55635			−0.868759
$122$	−5.57753			−0.504966
$123$	11.8287	−	8.53643i	1.06656	−	0.769704i
$124$	0.842474			0.0756564
$125$	−11.6589			−1.04281
$126$	0.945264	−	2.84719i	0.0842108	−	0.253648i
$127$	8.23173			0.730448			0.365224	−	0.930920i	$-0.380992\pi$
$127$	8.23173			0.730448			0.365224	+	0.930920i	$0.380992\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−8.45741	+	6.10348i	−0.744634	+	0.537381i
$130$		−	3.71328i		−	0.325676i
$131$		−	14.1266i		−	1.23425i	−0.786866	−	0.617123i	$-0.788298\pi$
$131$		−	14.1266i		−	1.23425i	0.786866	−	0.617123i	$-0.211702\pi$
$132$	−1.21785	−	1.68754i	−0.106000	−	0.146882i
$133$	−4.80264			−0.416442
$134$	−13.3295			−1.15149
$135$	7.48800	−	2.35389i	0.644464	−	0.202591i
$136$			3.78965i			0.324960i
$137$	20.6926			1.76789			0.883943	−	0.467595i	$-0.154879\pi$
$137$	20.6926			1.76789			0.883943	+	0.467595i	$0.154879\pi$
$138$	5.98560	−	5.75956i	0.509529	−	0.490286i
$139$	4.05261			0.343738			0.171869	−	0.985120i	$-0.445019\pi$
$139$	4.05261			0.343738			0.171869	+	0.985120i	$0.445019\pi$
$140$		−	1.51059i		−	0.127668i
$141$	17.0901	−	12.3334i	1.43925	−	1.03866i
$142$	−4.48229			−0.376145
$143$	2.95354			0.246987
$144$	−0.945264	+	2.84719i	−0.0787720	+	0.237266i
$145$			14.5648i			1.20954i
$146$		−	8.07349i		−	0.668167i
$147$	1.01359	+	1.40450i	0.0835996	+	0.115842i
$148$			9.11097i			0.748917i
$149$	8.66606			0.709952			0.354976	−	0.934875i	$-0.384489\pi$
$149$	8.66606			0.709952			0.354976	+	0.934875i	$0.384489\pi$
$150$	−3.81760	+	2.75506i	−0.311706	+	0.224949i
$151$	1.38581			0.112776			0.0563879	−	0.998409i	$-0.482042\pi$
$151$	1.38581			0.112776			0.0563879	+	0.998409i	$0.482042\pi$
$152$	4.80264			0.389546
$153$	3.58223	−	10.7899i	0.289606	−	0.872308i
$154$	1.20152			0.0968214
$155$	−1.27263			−0.102220
$156$	−2.49157	−	3.45250i	−0.199486	−	0.276421i
$157$		−	6.96520i		−	0.555883i	−0.960598	−	0.277942i	$-0.910348\pi$
$157$		−	6.96520i		−	0.555883i	0.960598	−	0.277942i	$-0.0896522\pi$
$158$	9.34825			0.743707
$159$	9.17954	+	12.7198i	0.727985	+	1.00875i
$160$			1.51059i			0.119423i
$161$	0.674123	+	4.74822i	0.0531283	+	0.374212i
$162$	5.38269	−	7.21295i	0.422904	−	0.566703i
$163$	22.3854			1.75336			0.876680	−	0.481075i	$-0.159753\pi$
$163$	22.3854			1.75336			0.876680	+	0.481075i	$0.159753\pi$
$164$		−	8.42196i		−	0.657644i
$165$	1.83968	+	2.54919i	0.143219	+	0.198454i
$166$		−	8.00034i		−	0.620947i
$167$		−	15.0321i		−	1.16322i	−0.813468	−	0.581610i	$-0.802423\pi$
$167$		−	15.0321i		−	1.16322i	0.813468	−	0.581610i	$-0.197577\pi$
$168$	−1.01359	−	1.40450i	−0.0782003	−	0.108360i
$169$	−6.95743			−0.535187
$170$		−	5.72462i		−	0.439058i
$171$	−13.6740	−	4.53976i	−1.04568	−	0.347164i
$172$			6.02163i			0.459145i
$173$		−	1.51312i		−	0.115040i	−0.998344	−	0.0575200i	$-0.981681\pi$
$173$		−	1.51312i		−	0.115040i	0.998344	−	0.0575200i	$-0.0183193\pi$
$174$	9.77281	+	13.5419i	0.740875	+	1.02661i
$175$		−	2.71811i		−	0.205470i
$176$	−1.20152			−0.0905681
$177$	11.9475	−	8.62216i	0.898027	−	0.648081i
$178$			0.364537i			0.0273232i
$179$			13.2168i			0.987869i	0.869499	+	0.493935i	$0.164442\pi$
$179$			13.2168i			0.987869i	−0.869499	+	0.493935i	$0.835558\pi$
$180$	1.42791	−	4.30094i	0.106430	−	0.320573i
$181$		−	9.48412i		−	0.704949i	−0.935821	−	0.352474i	$-0.885340\pi$
$181$		−	9.48412i		−	0.704949i	0.935821	−	0.352474i	$-0.114660\pi$
$182$	2.45816			0.182211
$183$	7.83367	−	5.65334i	0.579082	−	0.417907i
$184$	−0.674123	−	4.74822i	−0.0496970	−	0.350043i
$185$		−	13.7629i		−	1.01187i
$186$	−1.18326	+	0.853925i	−0.0867608	+	0.0626128i
$187$	4.55335			0.332974
$188$		−	12.1681i		−	0.887447i
$189$	1.55826	+	4.95700i	0.113347	+	0.360569i
$190$	−7.25483			−0.526320
$191$	−15.1833			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$191$	−15.1833			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$192$	1.01359	+	1.40450i	0.0731497	+	0.101361i
$193$	−23.4613			−1.68878			−0.844392	−	0.535726i	$-0.820038\pi$
$193$	−23.4613			−1.68878			−0.844392	+	0.535726i	$0.820038\pi$
$194$	−8.40421			−0.603387
$195$	3.76375	+	5.21532i	0.269528	+	0.373477i
$196$	1.00000			0.0714286
$197$		−	13.7209i		−	0.977570i	−0.872404	−	0.488785i	$-0.837440\pi$
$197$		−	13.7209i		−	0.977570i	0.872404	−	0.488785i	$-0.162560\pi$
$198$	3.42096	+	1.13576i	0.243117	+	0.0807146i
$199$		−	21.9013i		−	1.55255i	−0.630397	−	0.776273i	$-0.717108\pi$
$199$		−	21.9013i		−	1.55255i	0.630397	−	0.776273i	$-0.282892\pi$
$200$			2.71811i			0.192200i
$201$	18.7213	−	13.5107i	1.32050	−	0.952969i
$202$	1.22130			0.0859302
$203$	−9.64176			−0.676719
$204$	−3.84116	−	5.32259i	−0.268935	−	0.372656i
$205$			12.7221i			0.888553i
$206$	−5.85397			−0.407865
$207$	−2.56897	+	14.1563i	−0.178555	+	0.983930i
$208$	−2.45816			−0.170443
$209$		−	5.77048i		−	0.399152i
$210$	1.53112	+	2.12163i	0.105658	+	0.146407i
$211$	−3.86365			−0.265985			−0.132992	−	0.991117i	$-0.542459\pi$
$211$	−3.86365			−0.265985			−0.132992	+	0.991117i	$0.542459\pi$
$212$	9.05644			0.621999
$213$	6.29540	−	4.54321i	0.431353	−	0.311296i
$214$			17.3805i			1.18811i
$215$		−	9.09623i		−	0.620358i
$216$	−1.55826	−	4.95700i	−0.106026	−	0.337281i
$217$		−	0.842474i		−	0.0571909i
$218$	13.6354			0.923509
$219$	8.18322	+	11.3392i	0.552971	+	0.766235i
$220$	1.81501			0.122368
$221$	9.31559			0.626635
$222$	−9.23480	−	12.7964i	−0.619799	−	0.858837i
$223$	3.15003			0.210941			0.105471	−	0.994422i	$-0.466365\pi$
$223$	3.15003			0.210941			0.105471	+	0.994422i	$0.466365\pi$
$224$	−1.00000			−0.0668153
$225$	2.56934	−	7.73898i	0.171289	−	0.515932i
$226$		−	0.757627i		−	0.0503966i
$227$	−17.5785			−1.16672			−0.583362	−	0.812212i	$-0.698263\pi$
$227$	−17.5785			−1.16672			−0.583362	+	0.812212i	$0.698263\pi$
$228$	−6.74533	+	4.86792i	−0.446720	+	0.322386i
$229$			24.5597i			1.62295i	0.584385	+	0.811476i	$0.301336\pi$
$229$			24.5597i			1.62295i	−0.584385	+	0.811476i	$0.698664\pi$
$230$	1.01832	+	7.17262i	0.0671463	+	0.472948i
$231$	−1.68754	+	1.21785i	−0.111032	+	0.0801288i
$232$	9.64176			0.633013
$233$			3.69266i			0.241914i	0.992658	+	0.120957i	$0.0385963\pi$
$233$			3.69266i			0.241914i	−0.992658	+	0.120957i	$0.961404\pi$
$234$	6.99885	+	2.32361i	0.457529	+	0.151899i
$235$			18.3810i			1.19904i
$236$		−	8.50654i		−	0.553729i
$237$	−13.1297	+	9.47531i	−0.852863	+	0.615488i
$238$	3.78965			0.245647
$239$			20.1962i			1.30638i	0.757193	+	0.653191i	$0.226570\pi$
$239$			20.1962i			1.30638i	−0.757193	+	0.653191i	$0.773430\pi$
$240$	−1.53112	−	2.12163i	−0.0988336	−	0.136951i
$241$		−	11.6386i		−	0.749706i	−0.927084	−	0.374853i	$-0.877693\pi$
$241$		−	11.6386i		−	0.749706i	0.927084	−	0.374853i	$-0.122307\pi$
$242$		−	9.55635i		−	0.614305i
$243$	−0.249025	+	15.5865i	−0.0159750	+	0.999872i
$244$		−	5.57753i		−	0.357065i
$245$	−1.51059			−0.0965082
$246$	8.53643	+	11.8287i	0.544263	+	0.754169i
$247$		−	11.8057i		−	0.751177i
$248$			0.842474i			0.0534972i
$249$	8.10908	+	11.2365i	0.513892	+	0.712085i
$250$		−	11.6589i		−	0.737375i
$251$	20.6318			1.30227			0.651134	−	0.758963i	$-0.274294\pi$
$251$	20.6318			1.30227			0.651134	+	0.758963i	$0.274294\pi$
$252$	2.84719	+	0.945264i	0.179356	+	0.0595461i
$253$	−5.70508	+	0.809973i	−0.358676	+	0.0509226i
$254$			8.23173i			0.516505i
$255$	5.80243	+	8.04025i	0.363362	+	0.503500i
$256$	1.00000			0.0625000
$257$			5.07826i			0.316773i	0.987377	+	0.158387i	$0.0506292\pi$
$257$			5.07826i			0.316773i	−0.987377	+	0.158387i	$0.949371\pi$
$258$	−6.10348	−	8.45741i	−0.379986	−	0.526535i
$259$	9.11097			0.566128
$260$	3.71328			0.230288
$261$	−27.4519	−	9.11402i	−1.69923	−	0.564143i
$262$	14.1266			0.872744
$263$	16.6385			1.02597			0.512987	−	0.858396i	$-0.328539\pi$
$263$	16.6385			1.02597			0.512987	+	0.858396i	$0.328539\pi$
$264$	1.68754	−	1.21785i	0.103861	−	0.0749536i
$265$	−13.6806			−0.840392
$266$		−	4.80264i		−	0.294469i
$267$	−0.369492	−	0.511994i	−0.0226125	−	0.0313335i
$268$		−	13.3295i		−	0.814229i
$269$			3.71346i			0.226413i	0.993571	+	0.113207i	$0.0361122\pi$
$269$			3.71346i			0.226413i	−0.993571	+	0.113207i	$0.963888\pi$
$270$	2.35389	+	7.48800i	0.143253	+	0.455705i
$271$	−17.6250			−1.07064			−0.535321	−	0.844649i	$-0.679809\pi$
$271$	−17.6250			−1.07064			−0.535321	+	0.844649i	$0.679809\pi$
$272$	−3.78965			−0.229782
$273$	−3.45250	+	2.49157i	−0.208955	+	0.150797i
$274$			20.6926i			1.25008i
$275$	3.26587			0.196939
$276$	5.75956	+	5.98560i	0.346685	+	0.360291i
$277$	24.4165			1.46704			0.733522	−	0.679666i	$-0.237875\pi$
$277$	24.4165			1.46704			0.733522	+	0.679666i	$0.237875\pi$
$278$			4.05261i			0.243060i
$279$	0.796361	−	2.39868i	0.0476769	−	0.143605i
$280$	1.51059			0.0902751
$281$	−2.48761			−0.148399			−0.0741993	−	0.997243i	$-0.523640\pi$
$281$	−2.48761			−0.148399			−0.0741993	+	0.997243i	$0.523640\pi$
$282$	12.3334	+	17.0901i	0.734446	+	1.01770i
$283$		−	21.7122i		−	1.29066i	−0.763905	−	0.645329i	$-0.776720\pi$
$283$		−	21.7122i		−	1.29066i	0.763905	−	0.645329i	$-0.223280\pi$
$284$		−	4.48229i		−	0.265975i
$285$	10.1894	−	7.35343i	0.603570	−	0.435580i
$286$			2.95354i			0.174646i
$287$	−8.42196			−0.497132
$288$	−2.84719	−	0.945264i	−0.167772	−	0.0557002i
$289$	−2.63852			−0.155207
$290$	−14.5648			−0.855273
$291$	11.8037	−	8.51843i	0.691948	−	0.499359i
$292$	8.07349			0.472465
$293$	−14.3453			−0.838062			−0.419031	−	0.907972i	$-0.637630\pi$
$293$	−14.3453			−0.838062			−0.419031	+	0.907972i	$0.637630\pi$
$294$	−1.40450	+	1.01359i	−0.0819124	+	0.0591139i
$295$			12.8499i			0.748151i
$296$	−9.11097			−0.529564
$297$	−5.95594	+	1.87228i	−0.345599	+	0.108641i
$298$			8.66606i			0.502012i
$299$	−11.6719	+	1.65710i	−0.675003	+	0.0958328i
$300$	−2.75506	−	3.81760i	−0.159063	−	0.220409i
$301$	6.02163			0.347081
$302$			1.38581i			0.0797445i
$303$	−1.71532	+	1.23790i	−0.0985424	+	0.0711153i
$304$			4.80264i			0.275450i
$305$			8.42538i			0.482436i
$306$	10.7899	+	3.58223i	0.616815	+	0.204782i
$307$	11.0837			0.632580			0.316290	−	0.948663i	$-0.397563\pi$
$307$	11.0837			0.632580			0.316290	+	0.948663i	$0.397563\pi$
$308$			1.20152i			0.0684630i
$309$	8.22193	−	5.93353i	0.467729	−	0.337547i
$310$		−	1.27263i		−	0.0722808i
$311$		−	1.60732i		−	0.0911426i	−0.998961	−	0.0455713i	$-0.985489\pi$
$311$		−	1.60732i		−	0.0911426i	0.998961	−	0.0455713i	$-0.0145108\pi$
$312$	3.45250	−	2.49157i	0.195459	−	0.141058i
$313$			16.7780i			0.948350i	0.880431	+	0.474175i	$0.157254\pi$
$313$			16.7780i			0.948350i	−0.880431	+	0.474175i	$0.842746\pi$
$314$	6.96520			0.393069
$315$	−4.30094	−	1.42791i	−0.242330	−	0.0804535i
$316$			9.34825i			0.525880i
$317$		−	1.06304i		−	0.0597063i	−0.999554	−	0.0298531i	$-0.990496\pi$
$317$		−	1.06304i		−	0.0597063i	0.999554	−	0.0298531i	$-0.00950396\pi$
$318$	−12.7198	+	9.17954i	−0.713292	+	0.514763i
$319$		−	11.5848i		−	0.648624i
$320$	−1.51059			−0.0844446
$321$	−17.6167	−	24.4110i	−0.983269	−	1.36249i
$322$	−4.74822	+	0.674123i	−0.264608	+	0.0375674i
$323$		−	18.2003i		−	1.01269i
$324$	7.21295	+	5.38269i	0.400719	+	0.299038i
$325$	6.68157			0.370627
$326$			22.3854i			1.23981i
$327$	−19.1510	+	13.8208i	−1.05905	+	0.764290i
$328$	8.42196			0.465025
$329$	−12.1681			−0.670847
$330$	−2.54919	+	1.83968i	−0.140328	+	0.101271i
$331$	21.8473			1.20083			0.600417	−	0.799687i	$-0.295001\pi$
$331$	21.8473			1.20083			0.600417	+	0.799687i	$0.295001\pi$
$332$	8.00034			0.439076
$333$	25.9406	+	8.61227i	1.42154	+	0.471950i
$334$	15.0321			0.822521
$335$			20.1354i			1.10012i
$336$	1.40450	−	1.01359i	0.0766220	−	0.0552960i
$337$		−	19.2373i		−	1.04792i	−0.851743	−	0.523960i	$-0.824454\pi$
$337$		−	19.2373i		−	1.04792i	0.851743	−	0.523960i	$-0.175546\pi$
$338$		−	6.95743i		−	0.378434i
$339$	0.767925	+	1.06409i	0.0417079	+	0.0577935i
$340$	5.72462			0.310461
$341$	1.01225			0.0548165
$342$	4.53976	−	13.6740i	0.245482	−	0.739406i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.02163			−0.324665
$345$	−8.70034	−	9.04180i	−0.468411	−	0.486794i
$346$	1.51312			0.0813456
$347$		−	22.0215i		−	1.18218i	−0.806607	−	0.591088i	$-0.798698\pi$
$347$		−	22.0215i		−	1.18218i	0.806607	−	0.591088i	$-0.201302\pi$
$348$	−13.5419	+	9.77281i	−0.725922	+	0.523878i
$349$	9.40059			0.503202			0.251601	−	0.967831i	$-0.419043\pi$
$349$	9.40059			0.503202			0.251601	+	0.967831i	$0.419043\pi$
$350$	2.71811			0.145289
$351$	−12.1851	+	3.83045i	−0.650393	+	0.204454i
$352$		−	1.20152i		−	0.0640413i
$353$			16.7522i			0.891632i	0.895125	+	0.445816i	$0.147086\pi$
$353$			16.7522i			0.891632i	−0.895125	+	0.445816i	$0.852914\pi$
$354$	8.62216	+	11.9475i	0.458263	+	0.635001i
$355$			6.77091i			0.359363i
$356$	−0.364537			−0.0193204
$357$	−5.32259	+	3.84116i	−0.281701	+	0.203296i
$358$	−13.2168			−0.698529
$359$	−34.6427			−1.82837			−0.914185	−	0.405298i	$-0.867168\pi$
$359$	−34.6427			−1.82837			−0.914185	+	0.405298i	$0.867168\pi$
$360$	4.30094	+	1.42791i	0.226679	+	0.0752574i
$361$	−4.06535			−0.213966
$362$	9.48412			0.498474
$363$	9.68623	+	13.4219i	0.508395	+	0.704469i
$364$			2.45816i			0.128843i
$365$	−12.1957			−0.638354
$366$	5.65334	+	7.83367i	0.295505	+	0.409472i
$367$			19.8472i			1.03601i	0.855377	+	0.518007i	$0.173326\pi$
$367$			19.8472i			1.03601i	−0.855377	+	0.518007i	$0.826674\pi$
$368$	4.74822	−	0.674123i	0.247518	−	0.0351411i
$369$	−23.9789	−	7.96098i	−1.24829	−	0.414432i
$370$	13.7629			0.715502
$371$		−	9.05644i		−	0.470187i
$372$	−0.853925	−	1.18326i	−0.0442739	−	0.0613491i
$373$		−	14.6091i		−	0.756429i	−0.925718	−	0.378214i	$-0.876538\pi$
$373$		−	14.6091i		−	0.756429i	0.925718	−	0.378214i	$-0.123462\pi$
$374$			4.55335i			0.235448i
$375$	11.8174	+	16.3750i	0.610247	+	0.845601i
$376$	12.1681			0.627520
$377$		−	23.7010i		−	1.22067i
$378$	−4.95700	+	1.55826i	−0.254960	+	0.0801481i
$379$		−	27.6370i		−	1.41962i	−0.704393	−	0.709810i	$-0.748781\pi$
$379$		−	27.6370i		−	1.41962i	0.704393	−	0.709810i	$-0.251219\pi$
$380$		−	7.25483i		−	0.372165i
$381$	−8.34361	−	11.5615i	−0.427456	−	0.592314i
$382$		−	15.1833i		−	0.776847i
$383$	26.5565			1.35698			0.678488	−	0.734611i	$-0.262636\pi$
$383$	26.5565			1.35698			0.678488	+	0.734611i	$0.262636\pi$
$384$	−1.40450	+	1.01359i	−0.0716733	+	0.0517246i
$385$		−	1.81501i		−	0.0925014i
$386$		−	23.4613i		−	1.19415i
$387$	17.1447	+	5.69204i	0.871515	+	0.289342i
$388$		−	8.40421i		−	0.426659i
$389$	24.0674			1.22027			0.610133	−	0.792299i	$-0.291116\pi$
$389$	24.0674			1.22027			0.610133	+	0.792299i	$0.291116\pi$
$390$	−5.21532	+	3.76375i	−0.264088	+	0.190585i
$391$	−17.9941	+	2.55469i	−0.910001	+	0.129196i
$392$			1.00000i			0.0505076i
$393$	−19.8409	+	14.3186i	−1.00084	+	0.722278i
$394$	13.7209			0.691247
$395$		−	14.1214i		−	0.710524i
$396$	−1.13576	+	3.42096i	−0.0570739	+	0.171910i
$397$	−27.0284			−1.35652			−0.678258	−	0.734824i	$-0.737265\pi$
$397$	−27.0284			−1.35652			−0.678258	+	0.734824i	$0.737265\pi$
$398$	21.9013			1.09782
$399$	4.86792	+	6.74533i	0.243701	+	0.337689i
$400$	−2.71811			−0.135906
$401$	−1.21964			−0.0609061			−0.0304530	−	0.999536i	$-0.509695\pi$
$401$	−1.21964			−0.0609061			−0.0304530	+	0.999536i	$0.509695\pi$
$402$	13.5107	+	18.7213i	0.673851	+	0.933736i
$403$	2.07094			0.103161
$404$			1.22130i			0.0607618i
$405$	−10.8958	−	8.13105i	−0.541418	−	0.404035i
$406$		−	9.64176i		−	0.478513i
$407$			10.9470i			0.542624i
$408$	5.32259	−	3.84116i	0.263507	−	0.190166i
$409$	−16.0387			−0.793064			−0.396532	−	0.918021i	$-0.629786\pi$
$409$	−16.0387			−0.793064			−0.396532	+	0.918021i	$0.629786\pi$
$410$	−12.7221			−0.628302
$411$	−20.9738	−	29.0628i	−1.03456	−	1.43356i
$412$		−	5.85397i		−	0.288404i
$413$	−8.50654			−0.418580
$414$	−14.1563	−	2.56897i	−0.695743	−	0.126258i
$415$	−12.0852			−0.593241
$416$		−	2.45816i		−	0.120521i
$417$	−4.10769	−	5.69191i	−0.201155	−	0.278734i
$418$	5.77048			0.282243
$419$	20.0695			0.980460			0.490230	−	0.871593i	$-0.336913\pi$
$419$	20.0695			0.980460			0.490230	+	0.871593i	$0.336913\pi$
$420$	−2.12163	+	1.53112i	−0.103525	+	0.0747111i
$421$			33.5031i			1.63284i	0.577457	+	0.816421i	$0.304045\pi$
$421$			33.5031i			1.63284i	−0.577457	+	0.816421i	$0.695955\pi$
$422$		−	3.86365i		−	0.188080i
$423$	−34.6448	−	11.5020i	−1.68449	−	0.559248i
$424$			9.05644i			0.439820i
$425$	10.3007			0.499658
$426$	4.54321	+	6.29540i	0.220119	+	0.305013i
$427$	−5.57753			−0.269916
$428$	−17.3805			−0.840117
$429$	−2.99368	−	4.14826i	−0.144536	−	0.200280i
$430$	9.09623			0.438659
$431$	10.4912			0.505345			0.252673	−	0.967552i	$-0.418690\pi$
$431$	10.4912			0.505345			0.252673	+	0.967552i	$0.418690\pi$
$432$	4.95700	−	1.55826i	0.238494	−	0.0749717i
$433$			1.74284i			0.0837558i	0.999123	+	0.0418779i	$0.0133340\pi$
$433$			1.74284i			0.0837558i	−0.999123	+	0.0418779i	$0.986666\pi$
$434$	0.842474			0.0404401
$435$	20.4563	−	14.7627i	0.980803	−	0.707818i
$436$			13.6354i			0.653019i
$437$	3.23757	+	22.8040i	0.154874	+	1.09086i
$438$	−11.3392	+	8.18322i	−0.541810	+	0.391009i
$439$	−28.2931			−1.35036			−0.675179	−	0.737654i	$-0.735934\pi$
$439$	−28.2931			−1.35036			−0.675179	+	0.737654i	$0.735934\pi$
$440$			1.81501i			0.0865271i
$441$	0.945264	−	2.84719i	0.0450126	−	0.135580i
$442$			9.31559i			0.443098i
$443$		−	2.31636i		−	0.110054i	−0.998485	−	0.0550269i	$-0.982476\pi$
$443$		−	2.31636i		−	0.110054i	0.998485	−	0.0550269i	$-0.0175245\pi$
$444$	12.7964	−	9.23480i	0.607290	−	0.438264i
$445$	0.550667			0.0261041
$446$			3.15003i			0.149158i
$447$	−8.78385	−	12.1715i	−0.415462	−	0.575693i
$448$		−	1.00000i		−	0.0472456i
$449$		−	0.106904i		−	0.00504511i	−0.999997	−	0.00252256i	$-0.999197\pi$
$449$		−	0.106904i		−	0.00504511i	0.999997	−	0.00252256i	$-0.000802955\pi$
$450$	7.73898	+	2.56934i	0.364819	+	0.121120i
$451$		−	10.1192i		−	0.476493i
$452$	0.757627			0.0356358
$453$	−1.40465	−	1.94638i	−0.0659960	−	0.0914488i
$454$		−	17.5785i		−	0.824999i
$455$		−	3.71328i		−	0.174081i
$456$	−4.86792	−	6.74533i	−0.227961	−	0.315879i
$457$			7.20068i			0.336834i	0.985716	+	0.168417i	$0.0538655\pi$
$457$			7.20068i			0.336834i	−0.985716	+	0.168417i	$0.946135\pi$
$458$	−24.5597			−1.14760
$459$	−18.7853	+	5.90526i	−0.876823	+	0.275634i
$460$	−7.17262	+	1.01832i	−0.334425	+	0.0474796i
$461$			13.6071i			0.633744i	0.948468	+	0.316872i	$0.102633\pi$
$461$			13.6071i			0.633744i	−0.948468	+	0.316872i	$0.897367\pi$
$462$	−1.21785	−	1.68754i	−0.0566596	−	0.0785116i
$463$	3.22899			0.150064			0.0750319	−	0.997181i	$-0.476094\pi$
$463$	3.22899			0.150064			0.0750319	+	0.997181i	$0.476094\pi$
$464$			9.64176i			0.447608i
$465$	1.28993	+	1.78742i	0.0598192	+	0.0828897i
$466$	−3.69266			−0.171059
$467$	−0.200880			−0.00929564			−0.00464782	−	0.999989i	$-0.501479\pi$
$467$	−0.200880			−0.00929564			−0.00464782	+	0.999989i	$0.501479\pi$
$468$	−2.32361	+	6.99885i	−0.107409	+	0.323522i
$469$	−13.3295			−0.615499
$470$	−18.3810			−0.847851
$471$	−9.78265	+	7.05986i	−0.450761	+	0.325301i
$472$	8.50654			0.391545
$473$			7.23512i			0.332671i
$474$	−9.47531	−	13.1297i	−0.435215	−	0.603065i
$475$		−	13.0541i		−	0.598964i
$476$			3.78965i			0.173699i
$477$	8.56074	−	25.7854i	0.391969	−	1.18063i
$478$	−20.1962			−0.923752
$479$	13.5185			0.617678			0.308839	−	0.951114i	$-0.400060\pi$
$479$	13.5185			0.617678			0.308839	+	0.951114i	$0.400060\pi$
$480$	2.12163	−	1.53112i	0.0968388	−	0.0698859i
$481$			22.3962i			1.02118i
$482$	11.6386			0.530122
$483$	5.98560	−	5.75956i	0.272354	−	0.262069i
$484$	9.55635			0.434379
$485$			12.6953i			0.576465i
$486$	−15.5865	−	0.249025i	−0.707017	−	0.0112960i
$487$	−22.4796			−1.01865			−0.509324	−	0.860575i	$-0.670105\pi$
$487$	−22.4796			−1.01865			−0.509324	+	0.860575i	$0.670105\pi$
$488$	5.57753			0.252483
$489$	−22.6896	−	31.4404i	−1.02606	−	1.42178i
$490$		−	1.51059i		−	0.0682416i
$491$			6.85241i			0.309245i	0.987974	+	0.154622i	$0.0494161\pi$
$491$			6.85241i			0.309245i	−0.987974	+	0.154622i	$0.950584\pi$
$492$	−11.8287	+	8.53643i	−0.533278	+	0.384852i
$493$		−	36.5390i		−	1.64563i
$494$	11.8057			0.531162
$495$	1.71566	−	5.16767i	0.0771133	−	0.232269i
$496$	−0.842474			−0.0378282
$497$	−4.48229			−0.201058
$498$	−11.2365	+	8.10908i	−0.503520	+	0.363376i
$499$	−41.3050			−1.84907			−0.924534	−	0.381101i	$-0.875545\pi$
$499$	−41.3050			−1.84907			−0.924534	+	0.381101i	$0.875545\pi$
$500$	11.6589			0.521403
$501$	−21.1127	+	15.2364i	−0.943245	+	0.680714i
$502$			20.6318i			0.920842i
$503$	−20.9234			−0.932929			−0.466464	−	0.884540i	$-0.654472\pi$
$503$	−20.9234			−0.932929			−0.466464	+	0.884540i	$0.654472\pi$
$504$	−0.945264	+	2.84719i	−0.0421054	+	0.126824i
$505$		−	1.84488i		−	0.0820961i
$506$	−0.809973	−	5.70508i	−0.0360077	−	0.253622i
$507$	7.05199	+	9.77174i	0.313190	+	0.433978i
$508$	−8.23173			−0.365224
$509$			14.8383i			0.657697i	0.944383	+	0.328848i	$0.106661\pi$
$509$			14.8383i			0.657697i	−0.944383	+	0.328848i	$0.893339\pi$
$510$	−8.04025	+	5.80243i	−0.356028	+	0.256936i
$511$		−	8.07349i		−	0.357150i
$512$			1.00000i			0.0441942i
$513$	7.48375	+	23.8067i	0.330416	+	1.05109i
$514$	−5.07826			−0.223992
$515$			8.84296i			0.389667i
$516$	8.45741	−	6.10348i	0.372317	−	0.268691i
$517$		−	14.6202i		−	0.642995i
$518$			9.11097i			0.400313i
$519$	−2.12518	+	1.53368i	−0.0932849	+	0.0673211i
$520$			3.71328i			0.162838i
$521$	31.1956			1.36671			0.683353	−	0.730088i	$-0.260521\pi$
$521$	31.1956			1.36671			0.683353	+	0.730088i	$0.260521\pi$
$522$	9.11402	−	27.4519i	0.398910	−	1.20154i
$523$			34.2690i			1.49848i	0.662300	+	0.749238i	$0.269580\pi$
$523$			34.2690i			1.49848i	−0.662300	+	0.749238i	$0.730420\pi$
$524$			14.1266i			0.617123i
$525$	−3.81760	+	2.75506i	−0.166614	+	0.120241i
$526$			16.6385i			0.725473i
$527$	3.19269			0.139076
$528$	1.21785	+	1.68754i	0.0530002	+	0.0734408i
$529$	22.0911	−	6.40176i	0.960483	−	0.278338i
$530$		−	13.6806i		−	0.594247i
$531$	−24.2197	−	8.04093i	−1.05105	−	0.348947i
$532$	4.80264			0.208221
$533$		−	20.7026i		−	0.896727i
$534$	0.511994	−	0.369492i	0.0221562	−	0.0159895i
$535$	26.2548			1.13509
$536$	13.3295			0.575747
$537$	18.5630	−	13.3964i	0.801054	−	0.578098i
$538$	−3.71346			−0.160098
$539$	1.20152			0.0517532
$540$	−7.48800	+	2.35389i	−0.322232	+	0.101295i
$541$	16.6017			0.713762			0.356881	−	0.934150i	$-0.383840\pi$
$541$	16.6017			0.713762			0.356881	+	0.934150i	$0.383840\pi$
$542$		−	17.6250i		−	0.757058i
$543$	−13.3205	+	9.61302i	−0.571637	+	0.412534i
$544$		−	3.78965i		−	0.162480i
$545$		−	20.5976i		−	0.882304i
$546$	−2.49157	−	3.45250i	−0.106630	−	0.147753i
$547$	31.0055			1.32570			0.662850	−	0.748753i	$-0.269347\pi$
$547$	31.0055			1.32570			0.662850	+	0.748753i	$0.269347\pi$
$548$	−20.6926			−0.883943
$549$	−15.8803	−	5.27224i	−0.677754	−	0.225014i
$550$			3.26587i			0.139257i
$551$	−46.3059			−1.97270
$552$	−5.98560	+	5.75956i	−0.254764	+	0.245143i
$553$	9.34825			0.397528
$554$			24.4165i			1.03736i
$555$	−19.3301	+	13.9500i	−0.820518	+	0.592145i
$556$	−4.05261			−0.171869
$557$	27.4386			1.16261			0.581305	−	0.813685i	$-0.302542\pi$
$557$	27.4386			1.16261			0.581305	+	0.813685i	$0.302542\pi$
$558$	2.39868	+	0.796361i	0.101544	+	0.0337127i
$559$			14.8022i			0.626065i
$560$			1.51059i			0.0638341i
$561$	−4.61524	−	6.39520i	−0.194856	−	0.270006i
$562$		−	2.48761i		−	0.104934i
$563$	24.4274			1.02949			0.514746	−	0.857343i	$-0.327886\pi$
$563$	24.4274			1.02949			0.514746	+	0.857343i	$0.327886\pi$
$564$	−17.0901	+	12.3334i	−0.719623	+	0.519332i
$565$	−1.14447			−0.0481480
$566$	21.7122			0.912633
$567$	5.38269	−	7.21295i	0.226052	−	0.302915i
$568$	4.48229			0.188073
$569$	−13.9726			−0.585763			−0.292881	−	0.956149i	$-0.594614\pi$
$569$	−13.9726			−0.585763			−0.292881	+	0.956149i	$0.594614\pi$
$570$	7.35343	+	10.1894i	0.308001	+	0.426789i
$571$			20.9540i			0.876897i	0.898756	+	0.438448i	$0.144472\pi$
$571$			20.9540i			0.876897i	−0.898756	+	0.438448i	$0.855528\pi$
$572$	−2.95354			−0.123494
$573$	15.3897	+	21.3251i	0.642914	+	0.890867i
$574$		−	8.42196i		−	0.351526i
$575$	−12.9062	+	1.83234i	−0.538225	+	0.0764140i
$576$	0.945264	−	2.84719i	0.0393860	−	0.118633i
$577$	−25.3004			−1.05327			−0.526634	−	0.850092i	$-0.676546\pi$
$577$	−25.3004			−1.05327			−0.526634	+	0.850092i	$0.676546\pi$
$578$		−	2.63852i		−	0.109748i
$579$	23.7802	+	32.9515i	0.988272	+	1.36942i
$580$		−	14.5648i		−	0.604769i
$581$		−	8.00034i		−	0.331910i
$582$	8.51843	+	11.8037i	0.353100	+	0.489281i
$583$	10.8815			0.450666
$584$			8.07349i			0.334083i
$585$	3.51003	−	10.5724i	0.145122	−	0.437115i
$586$		−	14.3453i		−	0.592599i
$587$			27.2005i			1.12269i	0.827583	+	0.561343i	$0.189715\pi$
$587$			27.2005i			1.12269i	−0.827583	+	0.561343i	$0.810285\pi$
$588$	−1.01359	−	1.40450i	−0.0417998	−	0.0579208i
$589$		−	4.04610i		−	0.166717i
$590$	−12.8499			−0.529023
$591$	−19.2710	+	13.9073i	−0.792703	+	0.572071i
$592$		−	9.11097i		−	0.374458i
$593$		−	24.2179i		−	0.994508i	−0.867605	−	0.497254i	$-0.834342\pi$
$593$		−	24.2179i		−	0.994508i	0.867605	−	0.497254i	$-0.165658\pi$
$594$	−1.87228	−	5.95594i	−0.0768206	−	0.244375i
$595$		−	5.72462i		−	0.234687i
$596$	−8.66606			−0.354976
$597$	−30.7605	+	22.1990i	−1.25894	+	0.908545i
$598$	−1.65710	−	11.6719i	−0.0677640	−	0.477299i
$599$			17.2510i			0.704856i	0.935839	+	0.352428i	$0.114644\pi$
$599$			17.2510i			0.704856i	−0.935839	+	0.352428i	$0.885356\pi$
$600$	3.81760	−	2.75506i	0.155853	−	0.112475i
$601$	1.10880			0.0452287			0.0226144	−	0.999744i	$-0.492801\pi$
$601$	1.10880			0.0452287			0.0226144	+	0.999744i	$0.492801\pi$
$602$			6.02163i			0.245423i
$603$	−37.9516	−	12.5999i	−1.54551	−	0.513108i
$604$	−1.38581			−0.0563879
$605$	−14.4357			−0.586896
$606$	−1.23790	−	1.71532i	−0.0502861	−	0.0696800i
$607$	33.6534			1.36595			0.682974	−	0.730442i	$-0.260686\pi$
$607$	33.6534			1.36595			0.682974	+	0.730442i	$0.260686\pi$
$608$	−4.80264			−0.194773
$609$	9.77281	+	13.5419i	0.396014	+	0.548745i
$610$	−8.42538			−0.341133
$611$		−	29.9111i		−	1.21007i
$612$	−3.58223	+	10.7899i	−0.144803	+	0.436154i
$613$		−	28.0405i		−	1.13255i	−0.824218	−	0.566273i	$-0.808385\pi$
$613$		−	28.0405i		−	1.13255i	0.824218	−	0.566273i	$-0.191615\pi$
$614$			11.0837i			0.447302i
$615$	17.8683	−	12.8951i	0.720519	−	0.519979i
$616$	−1.20152			−0.0484107
$617$	−21.0698			−0.848239			−0.424119	−	0.905606i	$-0.639416\pi$
$617$	−21.0698			−0.848239			−0.424119	+	0.905606i	$0.639416\pi$
$618$	5.93353	+	8.22193i	0.238682	+	0.330734i
$619$			35.9494i			1.44493i	0.691409	+	0.722463i	$0.256990\pi$
$619$			35.9494i			1.44493i	−0.691409	+	0.722463i	$0.743010\pi$
$620$	1.27263			0.0511102
$621$	22.4864	−	10.7406i	0.902350	−	0.431004i
$622$	1.60732			0.0644475
$623$			0.364537i			0.0146049i
$624$	2.49157	+	3.45250i	0.0997428	+	0.138211i
$625$	−4.02130			−0.160852
$626$	−16.7780			−0.670585
$627$	−8.10466	+	5.84891i	−0.323669	+	0.233583i
$628$			6.96520i			0.277942i
$629$			34.5274i			1.37670i
$630$	1.42791	−	4.30094i	0.0568892	−	0.171353i
$631$		−	13.5649i		−	0.540012i	−0.962859	−	0.270006i	$-0.912974\pi$
$631$		−	13.5649i		−	0.540012i	0.962859	−	0.270006i	$-0.0870257\pi$
$632$	−9.34825			−0.371854
$633$	3.91616	+	5.42651i	0.155653	+	0.215685i
$634$	1.06304			0.0422187
$635$	12.4348			0.493459
$636$	−9.17954	−	12.7198i	−0.363992	−	0.504373i
$637$	2.45816			0.0973960
$638$	11.5848			0.458646
$639$	−12.7619	−	4.23695i	−0.504854	−	0.167611i
$640$		−	1.51059i		−	0.0597114i
$641$	4.96720			0.196193			0.0980964	−	0.995177i	$-0.468725\pi$
$641$	4.96720			0.196193			0.0980964	+	0.995177i	$0.468725\pi$
$642$	24.4110	−	17.6167i	0.963424	−	0.695276i
$643$			44.0972i			1.73902i	0.493914	+	0.869511i	$0.335566\pi$
$643$			44.0972i			1.73902i	−0.493914	+	0.869511i	$0.664434\pi$
$644$	−0.674123	−	4.74822i	−0.0265642	−	0.187106i
$645$	−12.7757	+	9.21986i	−0.503042	+	0.363032i
$646$	18.2003			0.716083
$647$			4.16947i			0.163919i	0.996636	+	0.0819593i	$0.0261178\pi$
$647$			4.16947i			0.163919i	−0.996636	+	0.0819593i	$0.973882\pi$
$648$	−5.38269	+	7.21295i	−0.211452	+	0.283351i
$649$		−	10.2208i		−	0.401201i
$650$			6.68157i			0.262073i
$651$	−1.18326	+	0.853925i	−0.0463756	+	0.0334680i
$652$	−22.3854			−0.876680
$653$			32.4362i			1.26933i	0.772789	+	0.634663i	$0.218861\pi$
$653$			32.4362i			1.26933i	−0.772789	+	0.634663i	$0.781139\pi$
$654$	−13.8208	−	19.1510i	−0.540435	−	0.748865i
$655$		−	21.3395i		−	0.833804i
$656$			8.42196i			0.328822i
$657$	7.63158	−	22.9867i	0.297736	−	0.896798i
$658$		−	12.1681i		−	0.474361i
$659$	0.367264			0.0143066			0.00715329	−	0.999974i	$-0.497723\pi$
$659$	0.367264			0.0143066			0.00715329	+	0.999974i	$0.497723\pi$
$660$	−1.83968	−	2.54919i	−0.0716093	−	0.0992270i
$661$		−	7.74682i		−	0.301316i	−0.988586	−	0.150658i	$-0.951861\pi$
$661$		−	7.74682i		−	0.301316i	0.988586	−	0.150658i	$-0.0481393\pi$
$662$			21.8473i			0.849118i
$663$	−9.44220	−	13.0838i	−0.366705	−	0.508132i
$664$			8.00034i			0.310473i
$665$	−7.25483			−0.281330
$666$	−8.61227	+	25.9406i	−0.333719	+	1.00518i
$667$	6.49973	+	45.7812i	0.251671	+	1.77265i
$668$			15.0321i			0.581610i
$669$	−3.19284	−	4.42423i	−0.123442	−	0.171051i
$670$	−20.1354			−0.777900
$671$		−	6.70153i		−	0.258710i
$672$	1.01359	+	1.40450i	0.0391001	+	0.0541799i
$673$	45.7621			1.76400			0.882000	−	0.471250i	$-0.156197\pi$
$673$	45.7621			1.76400			0.882000	+	0.471250i	$0.156197\pi$
$674$	19.2373			0.740992
$675$	−13.4737	+	4.23552i	−0.518602	+	0.163025i
$676$	6.95743			0.267593
$677$	−16.6859			−0.641292			−0.320646	−	0.947199i	$-0.603900\pi$
$677$	−16.6859			−0.641292			−0.320646	+	0.947199i	$0.603900\pi$
$678$	−1.06409	+	0.767925i	−0.0408662	+	0.0294920i
$679$	−8.40421			−0.322524
$680$			5.72462i			0.219529i
$681$	17.8174	+	24.6891i	0.682764	+	0.946087i
$682$			1.01225i			0.0387611i
$683$		−	20.6005i		−	0.788257i	−0.919055	−	0.394128i	$-0.871047\pi$
$683$		−	20.6005i		−	0.788257i	0.919055	−	0.394128i	$-0.128953\pi$
$684$	13.6740	+	4.53976i	0.522839	+	0.173582i
$685$	31.2580			1.19431
$686$	1.00000			0.0381802
$687$	34.4942	−	24.8935i	1.31604	−	0.949748i
$688$		−	6.02163i		−	0.229573i
$689$	22.2622			0.848123
$690$	9.04180	−	8.70034i	0.344216	−	0.331216i
$691$	11.7689			0.447712			0.223856	−	0.974622i	$-0.428136\pi$
$691$	11.7689			0.447712			0.223856	+	0.974622i	$0.428136\pi$
$692$			1.51312i			0.0575200i
$693$	3.42096	+	1.13576i	0.129951	+	0.0431438i
$694$	22.0215			0.835925
$695$	6.12184			0.232215
$696$	−9.77281	−	13.5419i	−0.370437	−	0.513304i
$697$		−	31.9163i		−	1.20892i
$698$			9.40059i			0.355817i
$699$	5.18635	−	3.74285i	0.196166	−	0.141567i
$700$			2.71811i			0.102735i
$701$	5.12177			0.193447			0.0967233	−	0.995311i	$-0.469164\pi$
$701$	5.12177			0.193447			0.0967233	+	0.995311i	$0.469164\pi$
$702$	−3.83045	−	12.1851i	−0.144571	−	0.459898i
$703$	43.7567			1.65031
$704$	1.20152			0.0452841
$705$	25.8162	−	18.6308i	0.972293	−	0.701677i
$706$	−16.7522			−0.630479
$707$	1.22130			0.0459316
$708$	−11.9475	+	8.62216i	−0.449014	+	0.324041i
$709$			23.7258i			0.891041i	0.895272	+	0.445521i	$0.146981\pi$
$709$			23.7258i			0.891041i	−0.895272	+	0.445521i	$0.853019\pi$
$710$	−6.77091			−0.254108
$711$	26.6162	+	8.83657i	0.998187	+	0.331397i
$712$		−	0.364537i		−	0.0136616i
$713$	−4.00025	+	0.567931i	−0.149811	+	0.0212692i
$714$	−3.84116	−	5.32259i	−0.143752	−	0.199193i
$715$	4.46159			0.166854
$716$		−	13.2168i		−	0.493935i
$717$	28.3656	−	20.4707i	1.05933	−	0.764492i
$718$		−	34.6427i		−	1.29285i
$719$			51.0374i			1.90338i	0.307068	+	0.951688i	$0.400652\pi$
$719$			51.0374i			1.90338i	−0.307068	+	0.951688i	$0.599348\pi$
$720$	−1.42791	+	4.30094i	−0.0532150	+	0.160286i
$721$	−5.85397			−0.218013
$722$		−	4.06535i		−	0.151297i
$723$	−16.3464	+	11.7967i	−0.607930	+	0.438726i
$724$			9.48412i			0.352474i
$725$		−	26.2074i		−	0.973319i
$726$	−13.4219	+	9.68623i	−0.498134	+	0.359490i
$727$			19.0158i			0.705258i	0.935763	+	0.352629i	$0.114712\pi$
$727$			19.0158i			0.705258i	−0.935763	+	0.352629i	$0.885288\pi$
$728$	−2.45816			−0.0911056
$729$	22.1437	−	15.4486i	0.820136	−	0.572169i
$730$		−	12.1957i		−	0.451385i
$731$			22.8199i			0.844025i
$732$	−7.83367	+	5.65334i	−0.289541	+	0.208953i
$733$			4.20189i			0.155201i	0.996985	+	0.0776003i	$0.0247258\pi$
$733$			4.20189i			0.155201i	−0.996985	+	0.0776003i	$0.975274\pi$
$734$	−19.8472			−0.732572
$735$	1.53112	+	2.12163i	0.0564763	+	0.0782576i
$736$	0.674123	+	4.74822i	0.0248485	+	0.175022i
$737$		−	16.0157i		−	0.589945i
$738$	7.96098	−	23.9789i	0.293048	−	0.882675i
$739$	−0.372973			−0.0137200			−0.00686002	−	0.999976i	$-0.502184\pi$
$739$	−0.372973			−0.0137200			−0.00686002	+	0.999976i	$0.502184\pi$
$740$			13.7629i			0.505936i
$741$	−16.5811	+	11.9661i	−0.609123	+	0.439587i
$742$	9.05644			0.332473
$743$	2.28963			0.0839984			0.0419992	−	0.999118i	$-0.486627\pi$
$743$	2.28963			0.0839984			0.0419992	+	0.999118i	$0.486627\pi$
$744$	1.18326	−	0.853925i	0.0433804	−	0.0313064i
$745$	13.0909			0.479613
$746$	14.6091			0.534876
$747$	7.56244	−	22.7785i	0.276695	−	0.833421i
$748$	−4.55335			−0.166487
$749$			17.3805i			0.635069i
$750$	−16.3750	+	11.8174i	−0.597930	+	0.431510i
$751$			11.5045i			0.419806i	0.977722	+	0.209903i	$0.0673148\pi$
$751$			11.5045i			0.419806i	−0.977722	+	0.209903i	$0.932685\pi$
$752$			12.1681i			0.443724i
$753$	−20.9122	−	28.9774i	−0.762083	−	1.05600i
$754$	23.7010			0.863141
$755$	2.09339			0.0761864
$756$	−1.55826	−	4.95700i	−0.0566733	−	0.180284i
$757$			39.5263i			1.43661i	0.695729	+	0.718304i	$0.255081\pi$
$757$			39.5263i			1.43661i	−0.695729	+	0.718304i	$0.744919\pi$
$758$	27.6370			1.00382
$759$	6.92024	+	7.19183i	0.251189	+	0.261047i
$760$	7.25483			0.263160
$761$			15.2443i			0.552605i	0.961071	+	0.276303i	$0.0891092\pi$
$761$			15.2443i			0.552605i	−0.961071	+	0.276303i	$0.910891\pi$
$762$	11.5615	−	8.34361i	0.418829	−	0.302257i
$763$	13.6354			0.493636
$764$	15.1833			0.549314
$765$	5.41128	−	16.2991i	0.195645	−	0.589294i
$766$			26.5565i			0.959527i
$767$		−	20.9105i		−	0.755034i
$768$	−1.01359	−	1.40450i	−0.0365748	−	0.0506807i
$769$			20.4555i			0.737644i	0.929500	+	0.368822i	$0.120239\pi$
$769$			20.4555i			0.737644i	−0.929500	+	0.368822i	$0.879761\pi$
$770$	1.81501			0.0654084
$771$	7.13244	−	5.14728i	0.256868	−	0.185375i
$772$	23.4613			0.844392
$773$	−15.1044			−0.543267			−0.271633	−	0.962401i	$-0.587564\pi$
$773$	−15.1044			−0.543267			−0.271633	+	0.962401i	$0.587564\pi$
$774$	−5.69204	+	17.1447i	−0.204596	+	0.616254i
$775$	2.28994			0.0822571
$776$	8.40421			0.301693
$777$	−9.23480	−	12.7964i	−0.331297	−	0.459068i
$778$			24.0674i			0.862859i
$779$	−40.4476			−1.44919
$780$	−3.76375	−	5.21532i	−0.134764	−	0.186738i
$781$		−	5.38557i		−	0.192711i
$782$	−2.55469	−	17.9941i	−0.0913556	−	0.643468i
$783$	15.0243	+	47.7942i	0.536926	+	1.70803i
$784$	−1.00000			−0.0357143
$785$		−	10.5216i		−	0.375531i
$786$	−14.3186	−	19.8409i	−0.510728	−	0.707700i
$787$		−	50.2880i		−	1.79258i	−0.443473	−	0.896288i	$-0.646254\pi$
$787$		−	50.2880i		−	1.79258i	0.443473	−	0.896288i	$-0.353746\pi$
$788$			13.7209i			0.488785i
$789$	−16.8646	−	23.3688i	−0.600397	−	0.831953i
$790$	14.1214			0.502417
$791$		−	0.757627i		−	0.0269381i
$792$	−3.42096	−	1.13576i	−0.121558	−	0.0403573i
$793$		−	13.7105i		−	0.486874i
$794$		−	27.0284i		−	0.959201i
$795$	13.8665	+	19.2144i	0.491795	+	0.681466i
$796$			21.9013i			0.776273i
$797$	27.0117			0.956804			0.478402	−	0.878141i	$-0.341216\pi$
$797$	27.0117			0.956804			0.478402	+	0.878141i	$0.341216\pi$
$798$	−6.74533	+	4.86792i	−0.238782	+	0.172322i
$799$		−	46.1128i		−	1.63135i
$800$		−	2.71811i		−	0.0960998i
$801$	−0.344584	+	1.03791i	−0.0121753	+	0.0366726i
$802$		−	1.21964i		−	0.0430671i
$803$	9.70047			0.342322
$804$	−18.7213	+	13.5107i	−0.660251	+	0.476485i
$805$	1.01832	+	7.17262i	0.0358912	+	0.252801i
$806$			2.07094i			0.0729458i
$807$	5.21557	−	3.76393i	0.183597	−	0.132497i
$808$	−1.22130			−0.0429651
$809$			26.6228i			0.936007i	0.883727	+	0.468004i	$0.155027\pi$
$809$			26.6228i			0.936007i	−0.883727	+	0.468004i	$0.844973\pi$
$810$	8.13105	−	10.8958i	0.285696	−	0.382840i
$811$	−31.4687			−1.10501			−0.552507	−	0.833508i	$-0.686329\pi$
$811$	−31.4687			−1.10501			−0.552507	+	0.833508i	$0.686329\pi$
$812$	9.64176			0.338360
$813$	17.8645	+	24.7544i	0.626536	+	0.868173i
$814$	−10.9470			−0.383693
$815$	33.8152			1.18449
$816$	3.84116	+	5.32259i	0.134468	+	0.186328i
$817$	28.9197			1.01177
$818$		−	16.0387i		−	0.560781i
$819$	6.99885	+	2.32361i	0.244560	+	0.0811937i
$820$		−	12.7221i		−	0.444276i
$821$			49.1868i			1.71663i	0.513123	+	0.858315i	$0.328488\pi$
$821$			49.1868i			1.71663i	−0.513123	+	0.858315i	$0.671512\pi$
$822$	29.0628	−	20.9738i	1.01368	−	0.731546i
$823$	13.6206			0.474783			0.237392	−	0.971414i	$-0.423708\pi$
$823$	13.6206			0.474783			0.237392	+	0.971414i	$0.423708\pi$
$824$	5.85397			0.203933
$825$	−3.31026	−	4.58693i	−0.115248	−	0.159696i
$826$		−	8.50654i		−	0.295980i
$827$	−24.0601			−0.836653			−0.418326	−	0.908297i	$-0.637383\pi$
$827$	−24.0601			−0.836653			−0.418326	+	0.908297i	$0.637383\pi$
$828$	2.56897	−	14.1563i	0.0892777	−	0.491965i
$829$	−11.5244			−0.400258			−0.200129	−	0.979770i	$-0.564136\pi$
$829$	−11.5244			−0.400258			−0.200129	+	0.979770i	$0.564136\pi$
$830$		−	12.0852i		−	0.419485i
$831$	−24.7483	−	34.2930i	−0.858510	−	1.18961i
$832$	2.45816			0.0852215
$833$	3.78965			0.131304
$834$	5.69191	−	4.10769i	0.197095	−	0.142238i
$835$		−	22.7074i		−	0.785822i
$836$			5.77048i			0.199576i
$837$	−4.17614	+	1.31279i	−0.144349	+	0.0453767i
$838$			20.0695i			0.693290i
$839$	11.4278			0.394531			0.197266	−	0.980350i	$-0.436794\pi$
$839$	11.4278			0.394531			0.197266	+	0.980350i	$0.436794\pi$
$840$	−1.53112	−	2.12163i	−0.0528288	−	0.0732033i
$841$	−63.9636			−2.20564
$842$	−33.5031			−1.15459
$843$	2.52142	+	3.49386i	0.0868425	+	0.120335i
$844$	3.86365			0.132992
$845$	−10.5098			−0.361549
$846$	11.5020	−	34.6448i	0.395448	−	1.19111i
$847$		−	9.55635i		−	0.328360i
$848$	−9.05644			−0.311000
$849$	−30.4949	+	22.0073i	−1.04658	+	0.755290i
$850$			10.3007i			0.353311i
$851$	−6.14191	−	43.2608i	−0.210542	−	1.48296i
$852$	−6.29540	+	4.54321i	−0.215677	+	0.155648i
$853$	34.7292			1.18910			0.594552	−	0.804057i	$-0.297329\pi$
$853$	34.7292			1.18910			0.594552	+	0.804057i	$0.297329\pi$
$854$		−	5.57753i		−	0.190859i
$855$	−20.6559	−	6.85773i	−0.706415	−	0.234529i
$856$		−	17.3805i		−	0.594053i
$857$		−	28.1828i		−	0.962705i	−0.876527	−	0.481353i	$-0.840146\pi$
$857$		−	28.1828i		−	0.962705i	0.876527	−	0.481353i	$-0.159854\pi$
$858$	4.14826	−	2.99368i	0.141619	−	0.102203i
$859$	−14.6962			−0.501429			−0.250714	−	0.968061i	$-0.580665\pi$
$859$	−14.6962			−0.501429			−0.250714	+	0.968061i	$0.580665\pi$
$860$			9.09623i			0.310179i
$861$	8.53643	+	11.8287i	0.290921	+	0.403120i
$862$			10.4912i			0.357333i
$863$		−	12.6587i		−	0.430908i	−0.976514	−	0.215454i	$-0.930877\pi$
$863$		−	12.6587i		−	0.430908i	0.976514	−	0.215454i	$-0.0691231\pi$
$864$	1.55826	+	4.95700i	0.0530130	+	0.168641i
$865$		−	2.28570i		−	0.0777161i
$866$	−1.74284			−0.0592243
$867$	2.67438	+	3.70581i	0.0908267	+	0.125856i
$868$			0.842474i			0.0285954i
$869$			11.2321i			0.381024i
$870$	14.7627	+	20.4563i	0.500503	+	0.693533i
$871$		−	32.7661i		−	1.11024i
$872$	−13.6354			−0.461754
$873$	−23.9283	−	7.94420i	−0.809852	−	0.268870i
$874$	−22.8040	+	3.23757i	−0.771356	+	0.109512i
$875$		−	11.6589i		−	0.394143i
$876$	−8.18322	−	11.3392i	−0.276485	−	0.383118i
$877$	28.6282			0.966706			0.483353	−	0.875426i	$-0.339419\pi$
$877$	28.6282			0.966706			0.483353	+	0.875426i	$0.339419\pi$
$878$		−	28.2931i		−	0.954847i
$879$	14.5403	+	20.1480i	0.490431	+	0.679577i
$880$	−1.81501			−0.0611839
$881$	−20.1878			−0.680144			−0.340072	−	0.940399i	$-0.610451\pi$
$881$	−20.1878			−0.680144			−0.340072	+	0.940399i	$0.610451\pi$
$882$	2.84719	+	0.945264i	0.0958698	+	0.0318287i
$883$	24.0102			0.808008			0.404004	−	0.914757i	$-0.367618\pi$
$883$	24.0102			0.808008			0.404004	+	0.914757i	$0.367618\pi$
$884$	−9.31559			−0.313317
$885$	18.0478	−	13.0246i	0.606669	−	0.437816i
$886$	2.31636			0.0778198
$887$		−	14.0356i		−	0.471270i	−0.971842	−	0.235635i	$-0.924283\pi$
$887$		−	14.0356i		−	0.471270i	0.971842	−	0.235635i	$-0.0757169\pi$
$888$	9.23480	+	12.7964i	0.309899	+	0.429419i
$889$			8.23173i			0.276083i
$890$			0.550667i			0.0184584i
$891$	8.66652	+	6.46742i	0.290339	+	0.216667i
$892$	−3.15003			−0.105471
$893$	−58.4388			−1.95558
$894$	12.1715	−	8.78385i	0.407077	−	0.293776i
$895$			19.9652i			0.667362i
$896$	1.00000			0.0334077
$897$	14.1579	+	14.7136i	0.472720	+	0.491273i
$898$	0.106904			0.00356743
$899$		−	8.12294i		−	0.270915i
$900$	−2.56934	+	7.73898i	−0.0856445	+	0.257966i
$901$	34.3208			1.14339
$902$	10.1192			0.336931
$903$	−6.10348	−	8.45741i	−0.203111	−	0.281445i
$904$			0.757627i			0.0251983i
$905$		−	14.3266i		−	0.476233i
$906$	1.94638	−	1.40465i	0.0646641	−	0.0466662i
$907$		−	4.35089i		−	0.144469i	−0.997388	−	0.0722345i	$-0.976987\pi$
$907$		−	4.35089i		−	0.144469i	0.997388	−	0.0722345i	$-0.0230130\pi$
$908$	17.5785			0.583362
$909$	3.47726	+	1.15445i	0.115334	+	0.0382907i
$910$	3.71328			0.123094
$911$	3.21247			0.106434			0.0532170	−	0.998583i	$-0.483053\pi$
$911$	3.21247			0.106434			0.0532170	+	0.998583i	$0.483053\pi$
$912$	6.74533	−	4.86792i	0.223360	−	0.161193i
$913$	9.61258			0.318130
$914$	−7.20068			−0.238177
$915$	11.8335	−	8.53989i	0.391203	−	0.282320i
$916$		−	24.5597i		−	0.811476i
$917$	14.1266			0.466501
$918$	−5.90526	−	18.7853i	−0.194902	−	0.620008i
$919$			25.5301i			0.842161i	0.907023	+	0.421080i	$0.138349\pi$
$919$			25.5301i			0.842161i	−0.907023	+	0.421080i	$0.861651\pi$
$920$	−1.01832	−	7.17262i	−0.0335732	−	0.236474i
$921$	−11.2343	−	15.5671i	−0.370184	−	0.512954i
$922$	−13.6071			−0.448124
$923$		−	11.0182i		−	0.362669i
$924$	1.68754	−	1.21785i	0.0555161	−	0.0400644i
$925$			24.7646i			0.814256i
$926$			3.22899i			0.106111i
$927$	−16.6673	−	5.53355i	−0.547428	−	0.181746i
$928$	−9.64176			−0.316506
$929$		−	27.2380i		−	0.893650i	−0.894621	−	0.446825i	$-0.852555\pi$
$929$		−	27.2380i		−	0.893650i	0.894621	−	0.446825i	$-0.147445\pi$
$930$	−1.78742	+	1.28993i	−0.0586118	+	0.0422985i
$931$		−	4.80264i		−	0.157400i
$932$		−	3.69266i		−	0.120957i
$933$	−2.25748	+	1.62916i	−0.0739067	+	0.0533364i
$934$		−	0.200880i		−	0.00657301i
$935$	6.87825			0.224943
$936$	−6.99885	−	2.32361i	−0.228765	−	0.0759497i
$937$		−	6.58240i		−	0.215037i	−0.994203	−	0.107519i	$-0.965709\pi$
$937$		−	6.58240i		−	0.215037i	0.994203	−	0.107519i	$-0.0342906\pi$
$938$		−	13.3295i		−	0.435224i
$939$	23.5648	−	17.0061i	0.769008	−	0.554972i
$940$		−	18.3810i		−	0.599521i
$941$	−43.3092			−1.41184			−0.705920	−	0.708292i	$-0.749466\pi$
$941$	−43.3092			−1.41184			−0.705920	+	0.708292i	$0.749466\pi$
$942$	−7.05986	−	9.78265i	−0.230023	−	0.318736i
$943$	5.67743	+	39.9893i	0.184883	+	1.30223i
$944$			8.50654i			0.276864i
$945$	2.35389	+	7.48800i	0.0765720	+	0.243585i
$946$	−7.23512			−0.235234
$947$			4.18809i			0.136095i	0.997682	+	0.0680474i	$0.0216769\pi$
$947$			4.18809i			0.136095i	−0.997682	+	0.0680474i	$0.978323\pi$
$948$	13.1297	−	9.47531i	0.426432	−	0.307744i
$949$	19.8460			0.644227
$950$	13.0541			0.423532
$951$	−1.49304	+	1.07749i	−0.0484153	+	0.0349400i
$952$	−3.78965			−0.122823
$953$	46.7055			1.51294			0.756470	−	0.654029i	$-0.226922\pi$
$953$	46.7055			1.51294			0.756470	+	0.654029i	$0.226922\pi$
$954$	25.7854	+	8.56074i	0.834833	+	0.277164i
$955$	−22.9358			−0.742186
$956$		−	20.1962i		−	0.653191i
$957$	−16.2709	+	11.7422i	−0.525963	+	0.379573i
$958$			13.5185i			0.436764i
$959$			20.6926i			0.668198i
$960$	1.53112	+	2.12163i	0.0494168	+	0.0684754i
$961$	−30.2902			−0.977104
$962$	−22.3962			−0.722084
$963$	−16.4292	+	49.4855i	−0.529422	+	1.59465i
$964$			11.6386i			0.374853i
$965$	−35.4405			−1.14087
$966$	5.75956	+	5.98560i	0.185311	+	0.192584i
$967$	−35.5908			−1.14452			−0.572261	−	0.820072i	$-0.693934\pi$
$967$	−35.5908			−1.14452			−0.572261	+	0.820072i	$0.693934\pi$
$968$			9.55635i			0.307153i
$969$	−25.5625	+	18.4477i	−0.821185	+	0.592626i
$970$	−12.6953			−0.407622
$971$	37.1705			1.19286			0.596428	−	0.802666i	$-0.296586\pi$
$971$	37.1705			1.19286			0.596428	+	0.802666i	$0.296586\pi$
$972$	0.249025	−	15.5865i	0.00798749	−	0.499936i
$973$			4.05261i			0.129921i
$974$		−	22.4796i		−	0.720293i
$975$	−6.77238	−	9.38429i	−0.216890	−	0.300538i
$976$			5.57753i			0.178532i
$977$	−8.93720			−0.285927			−0.142963	−	0.989728i	$-0.545663\pi$
$977$	−8.93720			−0.285927			−0.142963	+	0.989728i	$0.545663\pi$
$978$	31.4404	−	22.6896i	1.00535	−	0.725535i
$979$	−0.437999			−0.0139985
$980$	1.51059			0.0482541
$981$	38.8227	+	12.8891i	1.23951	+	0.411517i
$982$	−6.85241			−0.218669
$983$	54.1690			1.72772			0.863861	−	0.503730i	$-0.168040\pi$
$983$	54.1690			1.72772			0.863861	+	0.503730i	$0.168040\pi$
$984$	−8.53643	−	11.8287i	−0.272131	−	0.377084i
$985$		−	20.7266i		−	0.660404i
$986$	36.5390			1.16364
$987$	12.3334	+	17.0901i	0.392578	+	0.543984i
$988$			11.8057i			0.375589i
$989$	−4.05932	−	28.5920i	−0.129079	−	0.909173i
$990$	5.16767	+	1.71566i	0.164239	+	0.0545273i
$991$	19.1479			0.608252			0.304126	−	0.952632i	$-0.401636\pi$
$991$	19.1479			0.608252			0.304126	+	0.952632i	$0.401636\pi$
$992$		−	0.842474i		−	0.0267486i
$993$	−22.1442	−	30.6846i	−0.702725	−	0.973745i
$994$		−	4.48229i		−	0.142170i
$995$		−	33.0840i		−	1.04883i
$996$	−8.10908	−	11.2365i	−0.256946	−	0.356043i
$997$	−8.46389			−0.268054			−0.134027	−	0.990978i	$-0.542791\pi$
$997$	−8.46389			−0.268054			−0.134027	+	0.990978i	$0.542791\pi$
$998$		−	41.3050i		−	1.30749i
$999$	−14.1972	−	45.1630i	−0.449180	−	1.42890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.b.827.15	yes	24
3.2	odd	2		966.2.h.a.827.3	✓	24
23.22	odd	2		966.2.h.a.827.15	yes	24
69.68	even	2	inner	966.2.h.b.827.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.3	✓	24	3.2	odd	2
966.2.h.a.827.15	yes	24	23.22	odd	2
966.2.h.b.827.3	yes	24	69.68	even	2	inner
966.2.h.b.827.15	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.01359 - 1.40450i) q^{3} -1.00000 q^{4} +1.51059 q^{5} +(1.40450 - 1.01359i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-0.945264 + 2.84719i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.01359 - 1.40450i) q^{3} -1.00000 q^{4} +1.51059 q^{5} +(1.40450 - 1.01359i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-0.945264 + 2.84719i) q^{9} +1.51059i q^{10} -1.20152 q^{11} +(1.01359 + 1.40450i) q^{12} -2.45816 q^{13} -1.00000 q^{14} +(-1.53112 - 2.12163i) q^{15} +1.00000 q^{16} -3.78965 q^{17} +(-2.84719 - 0.945264i) q^{18} +4.80264i q^{19} -1.51059 q^{20} +(1.40450 - 1.01359i) q^{21} -1.20152i q^{22} +(4.74822 - 0.674123i) q^{23} +(-1.40450 + 1.01359i) q^{24} -2.71811 q^{25} -2.45816i q^{26} +(4.95700 - 1.55826i) q^{27} -1.00000i q^{28} +9.64176i q^{29} +(2.12163 - 1.53112i) q^{30} -0.842474 q^{31} +1.00000i q^{32} +(1.21785 + 1.68754i) q^{33} -3.78965i q^{34} +1.51059i q^{35} +(0.945264 - 2.84719i) q^{36} -9.11097i q^{37} -4.80264 q^{38} +(2.49157 + 3.45250i) q^{39} -1.51059i q^{40} +8.42196i q^{41} +(1.01359 + 1.40450i) q^{42} -6.02163i q^{43} +1.20152 q^{44} +(-1.42791 + 4.30094i) q^{45} +(0.674123 + 4.74822i) q^{46} +12.1681i q^{47} +(-1.01359 - 1.40450i) q^{48} -1.00000 q^{49} -2.71811i q^{50} +(3.84116 + 5.32259i) q^{51} +2.45816 q^{52} -9.05644 q^{53} +(1.55826 + 4.95700i) q^{54} -1.81501 q^{55} +1.00000 q^{56} +(6.74533 - 4.86792i) q^{57} -9.64176 q^{58} +8.50654i q^{59} +(1.53112 + 2.12163i) q^{60} +5.57753i q^{61} -0.842474i q^{62} +(-2.84719 - 0.945264i) q^{63} -1.00000 q^{64} -3.71328 q^{65} +(-1.68754 + 1.21785i) q^{66} +13.3295i q^{67} +3.78965 q^{68} +(-5.75956 - 5.98560i) q^{69} -1.51059 q^{70} +4.48229i q^{71} +(2.84719 + 0.945264i) q^{72} -8.07349 q^{73} +9.11097 q^{74} +(2.75506 + 3.81760i) q^{75} -4.80264i q^{76} -1.20152i q^{77} +(-3.45250 + 2.49157i) q^{78} -9.34825i q^{79} +1.51059 q^{80} +(-7.21295 - 5.38269i) q^{81} -8.42196 q^{82} -8.00034 q^{83} +(-1.40450 + 1.01359i) q^{84} -5.72462 q^{85} +6.02163 q^{86} +(13.5419 - 9.77281i) q^{87} +1.20152i q^{88} +0.364537 q^{89} +(-4.30094 - 1.42791i) q^{90} -2.45816i q^{91} +(-4.74822 + 0.674123i) q^{92} +(0.853925 + 1.18326i) q^{93} -12.1681 q^{94} +7.25483i q^{95} +(1.40450 - 1.01359i) q^{96} +8.40421i q^{97} -1.00000i q^{98} +(1.13576 - 3.42096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

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