LMFDB - Embedded newform 966.2.h.b.827.19

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			827.19
Character	$\chi$	$=$	966.827
Dual form			966.2.h.b.827.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.656415 - 1.60285i) q^{3} -1.00000 q^{4} +0.252332 q^{5} +(1.60285 + 0.656415i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.13824 - 2.10426i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.656415 - 1.60285i) q^{3} -1.00000 q^{4} +0.252332 q^{5} +(1.60285 + 0.656415i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.13824 - 2.10426i) q^{9} +0.252332i q^{10} -5.50149 q^{11} +(-0.656415 + 1.60285i) q^{12} -3.10049 q^{13} -1.00000 q^{14} +(0.165634 - 0.404450i) q^{15} +1.00000 q^{16} +0.471124 q^{17} +(2.10426 - 2.13824i) q^{18} +2.38906i q^{19} -0.252332 q^{20} +(1.60285 + 0.656415i) q^{21} -5.50149i q^{22} +(-3.43621 - 3.34552i) q^{23} +(-1.60285 - 0.656415i) q^{24} -4.93633 q^{25} -3.10049i q^{26} +(-4.77639 + 2.04600i) q^{27} -1.00000i q^{28} -6.08436i q^{29} +(0.404450 + 0.165634i) q^{30} +1.40614 q^{31} +1.00000i q^{32} +(-3.61126 + 8.81805i) q^{33} +0.471124i q^{34} +0.252332i q^{35} +(2.13824 + 2.10426i) q^{36} +5.87175i q^{37} -2.38906 q^{38} +(-2.03521 + 4.96961i) q^{39} -0.252332i q^{40} -4.64674i q^{41} +(-0.656415 + 1.60285i) q^{42} +5.09258i q^{43} +5.50149 q^{44} +(-0.539546 - 0.530973i) q^{45} +(3.34552 - 3.43621i) q^{46} +4.02078i q^{47} +(0.656415 - 1.60285i) q^{48} -1.00000 q^{49} -4.93633i q^{50} +(0.309252 - 0.755139i) q^{51} +3.10049 q^{52} -1.95854 q^{53} +(-2.04600 - 4.77639i) q^{54} -1.38820 q^{55} +1.00000 q^{56} +(3.82930 + 1.56822i) q^{57} +6.08436 q^{58} +3.53472i q^{59} +(-0.165634 + 0.404450i) q^{60} -2.10168i q^{61} +1.40614i q^{62} +(2.10426 - 2.13824i) q^{63} -1.00000 q^{64} -0.782353 q^{65} +(-8.81805 - 3.61126i) q^{66} -5.88882i q^{67} -0.471124 q^{68} +(-7.61793 + 3.31167i) q^{69} -0.252332 q^{70} -15.2386i q^{71} +(-2.10426 + 2.13824i) q^{72} -3.34062 q^{73} -5.87175 q^{74} +(-3.24028 + 7.91218i) q^{75} -2.38906i q^{76} -5.50149i q^{77} +(-4.96961 - 2.03521i) q^{78} +13.9496i q^{79} +0.252332 q^{80} +(0.144138 + 8.99885i) q^{81} +4.64674 q^{82} -9.18343 q^{83} +(-1.60285 - 0.656415i) q^{84} +0.118880 q^{85} -5.09258 q^{86} +(-9.75230 - 3.99386i) q^{87} +5.50149i q^{88} -12.9856 q^{89} +(0.530973 - 0.539546i) q^{90} -3.10049i q^{91} +(3.43621 + 3.34552i) q^{92} +(0.923009 - 2.25382i) q^{93} -4.02078 q^{94} +0.602837i q^{95} +(1.60285 + 0.656415i) q^{96} -17.8515i q^{97} -1.00000i q^{98} +(11.7635 + 11.5766i) 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
$3$	0.656415	−	1.60285i	0.378981	−	0.925404i
$3$	0.656415	−	1.60285i	0.378981	−	0.925404i
$4$	−1.00000			−0.500000
$5$	0.252332			0.112846			0.0564231	−	0.998407i	$-0.482030\pi$
$5$	0.252332			0.112846			0.0564231	+	0.998407i	$0.482030\pi$
$6$	1.60285	+	0.656415i	0.654360	+	0.267980i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−2.13824	−	2.10426i	−0.712747	−	0.701422i
$10$			0.252332i			0.0797944i
$11$	−5.50149			−1.65876			−0.829381	−	0.558684i	$-0.811307\pi$
$11$	−5.50149			−1.65876			−0.829381	+	0.558684i	$0.811307\pi$
$12$	−0.656415	+	1.60285i	−0.189491	+	0.462702i
$13$	−3.10049			−0.859921			−0.429961	−	0.902848i	$-0.641473\pi$
$13$	−3.10049			−0.859921			−0.429961	+	0.902848i	$0.641473\pi$
$14$	−1.00000			−0.267261
$15$	0.165634	−	0.404450i	0.0427666	−	0.104428i
$16$	1.00000			0.250000
$17$	0.471124			0.114264			0.0571321	−	0.998367i	$-0.481804\pi$
$17$	0.471124			0.114264			0.0571321	+	0.998367i	$0.481804\pi$
$18$	2.10426	−	2.13824i	0.495980	−	0.503988i
$19$			2.38906i			0.548089i	0.961717	+	0.274044i	$0.0883615\pi$
$19$			2.38906i			0.548089i	−0.961717	+	0.274044i	$0.911638\pi$
$20$	−0.252332			−0.0564231
$21$	1.60285	+	0.656415i	0.349770	+	0.143241i
$22$		−	5.50149i		−	1.17292i
$23$	−3.43621	−	3.34552i	−0.716499	−	0.697589i
$23$	−3.43621	−	3.34552i	−0.716499	−	0.697589i
$24$	−1.60285	−	0.656415i	−0.327180	−	0.133990i
$25$	−4.93633			−0.987266
$26$		−	3.10049i		−	0.608056i
$27$	−4.77639	+	2.04600i	−0.919216	+	0.393753i
$28$		−	1.00000i		−	0.188982i
$29$		−	6.08436i		−	1.12984i	−0.825147	−	0.564918i	$-0.808908\pi$
$29$		−	6.08436i		−	1.12984i	0.825147	−	0.564918i	$-0.191092\pi$
$30$	0.404450	+	0.165634i	0.0738421	+	0.0302406i
$31$	1.40614			0.252550			0.126275	−	0.991995i	$-0.459698\pi$
$31$	1.40614			0.252550			0.126275	+	0.991995i	$0.459698\pi$
$32$			1.00000i			0.176777i
$33$	−3.61126	+	8.81805i	−0.628639	+	1.53503i
$34$			0.471124i			0.0807970i
$35$			0.252332i			0.0426519i
$36$	2.13824	+	2.10426i	0.356373	+	0.350711i
$37$			5.87175i			0.965310i	0.875811	+	0.482655i	$0.160328\pi$
$37$			5.87175i			0.965310i	−0.875811	+	0.482655i	$0.839672\pi$
$38$	−2.38906			−0.387557
$39$	−2.03521	+	4.96961i	−0.325894	+	0.795775i
$40$		−	0.252332i		−	0.0398972i
$41$		−	4.64674i		−	0.725699i	−0.931848	−	0.362850i	$-0.881804\pi$
$41$		−	4.64674i		−	0.725699i	0.931848	−	0.362850i	$-0.118196\pi$
$42$	−0.656415	+	1.60285i	−0.101287	+	0.247325i
$43$			5.09258i			0.776611i	0.921531	+	0.388305i	$0.126939\pi$
$43$			5.09258i			0.776611i	−0.921531	+	0.388305i	$0.873061\pi$
$44$	5.50149			0.829381
$45$	−0.539546	−	0.530973i	−0.0804308	−	0.0791528i
$46$	3.34552	−	3.43621i	0.493270	−	0.506641i
$47$			4.02078i			0.586492i	0.956037	+	0.293246i	$0.0947355\pi$
$47$			4.02078i			0.586492i	−0.956037	+	0.293246i	$0.905265\pi$
$48$	0.656415	−	1.60285i	0.0947453	−	0.231351i
$49$	−1.00000			−0.142857
$50$		−	4.93633i		−	0.698102i
$51$	0.309252	−	0.755139i	0.0433040	−	0.105741i
$52$	3.10049			0.429961
$53$	−1.95854			−0.269026			−0.134513	−	0.990912i	$-0.542947\pi$
$53$	−1.95854			−0.269026			−0.134513	+	0.990912i	$0.542947\pi$
$54$	−2.04600	−	4.77639i	−0.278426	−	0.649984i
$55$	−1.38820			−0.187185
$56$	1.00000			0.133631
$57$	3.82930	+	1.56822i	0.507204	+	0.207715i
$58$	6.08436			0.798915
$59$			3.53472i			0.460181i	0.973169	+	0.230091i	$0.0739023\pi$
$59$			3.53472i			0.460181i	−0.973169	+	0.230091i	$0.926098\pi$
$60$	−0.165634	+	0.404450i	−0.0213833	+	0.0522142i
$61$		−	2.10168i		−	0.269092i	−0.990907	−	0.134546i	$-0.957042\pi$
$61$		−	2.10168i		−	0.269092i	0.990907	−	0.134546i	$-0.0429577\pi$
$62$			1.40614i			0.178580i
$63$	2.10426	−	2.13824i	0.265112	−	0.269393i
$64$	−1.00000			−0.125000
$65$	−0.782353			−0.0970389
$66$	−8.81805	−	3.61126i	−1.08543	−	0.444515i
$67$		−	5.88882i		−	0.719434i	−0.933061	−	0.359717i	$-0.882873\pi$
$67$		−	5.88882i		−	0.719434i	0.933061	−	0.359717i	$-0.117127\pi$
$68$	−0.471124			−0.0571321
$69$	−7.61793	+	3.31167i	−0.917091	+	0.398678i
$70$	−0.252332			−0.0301594
$71$		−	15.2386i		−	1.80849i	−0.427019	−	0.904243i	$-0.640436\pi$
$71$		−	15.2386i		−	1.80849i	0.427019	−	0.904243i	$-0.359564\pi$
$72$	−2.10426	+	2.13824i	−0.247990	+	0.251994i
$73$	−3.34062			−0.390990			−0.195495	−	0.980705i	$-0.562631\pi$
$73$	−3.34062			−0.390990			−0.195495	+	0.980705i	$0.562631\pi$
$74$	−5.87175			−0.682577
$75$	−3.24028	+	7.91218i	−0.374155	+	0.913620i
$76$		−	2.38906i		−	0.274044i
$77$		−	5.50149i		−	0.626953i
$78$	−4.96961	−	2.03521i	−0.562698	−	0.230442i
$79$			13.9496i			1.56945i	0.619845	+	0.784725i	$0.287196\pi$
$79$			13.9496i			1.56945i	−0.619845	+	0.784725i	$0.712804\pi$
$80$	0.252332			0.0282116
$81$	0.144138	+	8.99885i	0.0160154	+	0.999872i
$82$	4.64674			0.513147
$83$	−9.18343			−1.00801			−0.504006	−	0.863700i	$-0.668141\pi$
$83$	−9.18343			−1.00801			−0.504006	+	0.863700i	$0.668141\pi$
$84$	−1.60285	−	0.656415i	−0.174885	−	0.0716207i
$85$	0.118880			0.0128943
$86$	−5.09258			−0.549147
$87$	−9.75230	−	3.99386i	−1.04556	−	0.428187i
$88$			5.50149i			0.586461i
$89$	−12.9856			−1.37647			−0.688235	−	0.725488i	$-0.741614\pi$
$89$	−12.9856			−1.37647			−0.688235	+	0.725488i	$0.741614\pi$
$90$	0.530973	−	0.539546i	0.0559695	−	0.0568732i
$91$		−	3.10049i		−	0.325020i
$92$	3.43621	+	3.34552i	0.358249	+	0.348794i
$93$	0.923009	−	2.25382i	0.0957116	−	0.233711i
$94$	−4.02078			−0.414712
$95$			0.602837i			0.0618498i
$96$	1.60285	+	0.656415i	0.163590	+	0.0669950i
$97$		−	17.8515i		−	1.81254i	−0.422695	−	0.906272i	$-0.638916\pi$
$97$		−	17.8515i		−	1.81254i	0.422695	−	0.906272i	$-0.361084\pi$
$98$		−	1.00000i		−	0.101015i
$99$	11.7635	+	11.5766i	1.18228	+	1.16349i
$100$	4.93633			0.493633
$101$		−	0.803060i		−	0.0799074i	−0.999202	−	0.0399537i	$-0.987279\pi$
$101$		−	0.803060i		−	0.0799074i	0.999202	−	0.0399537i	$-0.0127210\pi$
$102$	0.755139	+	0.309252i	0.0747699	+	0.0306205i
$103$		−	11.9640i		−	1.17885i	−0.807823	−	0.589425i	$-0.799354\pi$
$103$		−	11.9640i		−	1.17885i	0.807823	−	0.589425i	$-0.200646\pi$
$104$			3.10049i			0.304028i
$105$	0.404450	+	0.165634i	0.0394702	+	0.0161643i
$106$		−	1.95854i		−	0.190230i
$107$	11.6433			1.12560			0.562800	−	0.826593i	$-0.309724\pi$
$107$	11.6433			1.12560			0.562800	+	0.826593i	$0.309724\pi$
$108$	4.77639	−	2.04600i	0.459608	−	0.196877i
$109$		−	1.11725i		−	0.107013i	−0.998567	−	0.0535066i	$-0.982960\pi$
$109$		−	1.11725i		−	0.107013i	0.998567	−	0.0535066i	$-0.0170398\pi$
$110$		−	1.38820i		−	0.132360i
$111$	9.41152	+	3.85430i	0.893302	+	0.365834i
$112$			1.00000i			0.0944911i
$113$	10.4257			0.980770			0.490385	−	0.871506i	$-0.336856\pi$
$113$	10.4257			0.980770			0.490385	+	0.871506i	$0.336856\pi$
$114$	−1.56822	+	3.82930i	−0.146877	+	0.358647i
$115$	−0.867065	−	0.844181i	−0.0808542	−	0.0787203i
$116$			6.08436i			0.564918i
$117$	6.62959	+	6.52425i	0.612906	+	0.603167i
$118$	−3.53472			−0.325397
$119$			0.471124i			0.0431878i
$120$	−0.404450	−	0.165634i	−0.0369210	−	0.0151203i
$121$	19.2664			1.75149
$122$	2.10168			0.190277
$123$	−7.44802	−	3.05019i	−0.671565	−	0.275026i
$124$	−1.40614			−0.126275
$125$	−2.50725			−0.224256
$126$	2.13824	+	2.10426i	0.190490	+	0.187463i
$127$	0.430922			0.0382382			0.0191191	−	0.999817i	$-0.493914\pi$
$127$	0.430922			0.0382382			0.0191191	+	0.999817i	$0.493914\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	8.16263	+	3.34284i	0.718679	+	0.294321i
$130$		−	0.782353i		−	0.0686169i
$131$			11.1468i			0.973904i	0.873429	+	0.486952i	$0.161891\pi$
$131$			11.1468i			0.973904i	−0.873429	+	0.486952i	$0.838109\pi$
$132$	3.61126	−	8.81805i	0.314320	−	0.767513i
$133$	−2.38906			−0.207158
$134$	5.88882			0.508717
$135$	−1.20524	+	0.516272i	−0.103730	+	0.0444336i
$136$		−	0.471124i		−	0.0403985i
$137$	−13.0016			−1.11080			−0.555400	−	0.831583i	$-0.687435\pi$
$137$	−13.0016			−1.11080			−0.555400	+	0.831583i	$0.687435\pi$
$138$	−3.31167	−	7.61793i	−0.281908	−	0.648481i
$139$	18.5932			1.57705			0.788526	−	0.615001i	$-0.210844\pi$
$139$	18.5932			1.57705			0.788526	+	0.615001i	$0.210844\pi$
$140$		−	0.252332i		−	0.0213259i
$141$	6.44470	+	2.63930i	0.542742	+	0.222269i
$142$	15.2386			1.27879
$143$	17.0573			1.42640
$144$	−2.13824	−	2.10426i	−0.178187	−	0.175355i
$145$		−	1.53528i		−	0.127498i
$146$		−	3.34062i		−	0.276472i
$147$	−0.656415	+	1.60285i	−0.0541402	+	0.132201i
$148$		−	5.87175i		−	0.482655i
$149$	−11.4109			−0.934821			−0.467410	−	0.884040i	$-0.654813\pi$
$149$	−11.4109			−0.934821			−0.467410	+	0.884040i	$0.654813\pi$
$150$	−7.91218	−	3.24028i	−0.646027	−	0.264568i
$151$	2.55551			0.207964			0.103982	−	0.994579i	$-0.466841\pi$
$151$	2.55551			0.207964			0.103982	+	0.994579i	$0.466841\pi$
$152$	2.38906			0.193779
$153$	−1.00738	−	0.991369i	−0.0814415	−	0.0801474i
$154$	5.50149			0.443323
$155$	0.354813			0.0284993
$156$	2.03521	−	4.96961i	0.162947	−	0.397887i
$157$		−	12.5401i		−	1.00081i	−0.865792	−	0.500403i	$-0.833185\pi$
$157$		−	12.5401i		−	1.00081i	0.865792	−	0.500403i	$-0.166815\pi$
$158$	−13.9496			−1.10977
$159$	−1.28562	+	3.13924i	−0.101956	+	0.248958i
$160$			0.252332i			0.0199486i
$161$	3.34552	−	3.43621i	0.263664	−	0.270811i
$162$	−8.99885	+	0.144138i	−0.707016	+	0.0113246i
$163$	8.16445			0.639489			0.319745	−	0.947504i	$-0.396403\pi$
$163$	8.16445			0.639489			0.319745	+	0.947504i	$0.396403\pi$
$164$			4.64674i			0.362850i
$165$	−0.911236	+	2.22508i	−0.0709396	+	0.173222i
$166$		−	9.18343i		−	0.712772i
$167$			18.6643i			1.44429i	0.691743	+	0.722144i	$0.256843\pi$
$167$			18.6643i			1.44429i	−0.691743	+	0.722144i	$0.743157\pi$
$168$	0.656415	−	1.60285i	0.0506435	−	0.123662i
$169$	−3.38696			−0.260535
$170$			0.118880i			0.00911764i
$171$	5.02722	−	5.10839i	0.384441	−	0.390648i
$172$		−	5.09258i		−	0.388305i
$173$		−	3.66045i		−	0.278299i	−0.990271	−	0.139149i	$-0.955563\pi$
$173$		−	3.66045i		−	0.278299i	0.990271	−	0.139149i	$-0.0444368\pi$
$174$	3.99386	−	9.75230i	0.302774	−	0.739320i
$175$		−	4.93633i		−	0.373151i
$176$	−5.50149			−0.414690
$177$	5.66562	+	2.32024i	0.425854	+	0.174400i
$178$		−	12.9856i		−	0.973312i
$179$			17.2447i			1.28893i	0.764633	+	0.644466i	$0.222920\pi$
$179$			17.2447i			1.28893i	−0.764633	+	0.644466i	$0.777080\pi$
$180$	0.539546	+	0.530973i	0.0402154	+	0.0395764i
$181$		−	5.76109i		−	0.428219i	−0.976810	−	0.214109i	$-0.931315\pi$
$181$		−	5.76109i		−	0.428219i	0.976810	−	0.214109i	$-0.0686849\pi$
$182$	3.10049			0.229824
$183$	−3.36867	−	1.37957i	−0.249019	−	0.101981i
$184$	−3.34552	+	3.43621i	−0.246635	+	0.253321i
$185$			1.48163i			0.108932i
$186$	2.25382	+	0.923009i	0.165258	+	0.0676783i
$187$	−2.59188			−0.189537
$188$		−	4.02078i		−	0.293246i
$189$	−2.04600	−	4.77639i	−0.148825	−	0.347431i
$190$	−0.602837			−0.0437344
$191$	17.4889			1.26545			0.632725	−	0.774376i	$-0.281936\pi$
$191$	17.4889			1.26545			0.632725	+	0.774376i	$0.281936\pi$
$192$	−0.656415	+	1.60285i	−0.0473726	+	0.115676i
$193$	20.4201			1.46987			0.734934	−	0.678139i	$-0.237213\pi$
$193$	20.4201			1.46987			0.734934	+	0.678139i	$0.237213\pi$
$194$	17.8515			1.28166
$195$	−0.513548	+	1.25399i	−0.0367759	+	0.0898003i
$196$	1.00000			0.0714286
$197$			8.17726i			0.582606i	0.956631	+	0.291303i	$0.0940887\pi$
$197$			8.17726i			0.582606i	−0.956631	+	0.291303i	$0.905911\pi$
$198$	−11.5766	+	11.7635i	−0.822713	+	0.835996i
$199$		−	0.0625989i		−	0.00443752i	−0.999998	−	0.00221876i	$-0.999294\pi$
$199$		−	0.0625989i		−	0.00443752i	0.999998	−	0.00221876i	$-0.000706253\pi$
$200$			4.93633i			0.349051i
$201$	−9.43888	−	3.86551i	−0.665768	−	0.272652i
$202$	0.803060			0.0565031
$203$	6.08436			0.427038
$204$	−0.309252	+	0.755139i	−0.0216520	+	0.0528703i
$205$		−	1.17252i		−	0.0818925i
$206$	11.9640			0.833573
$207$	0.307579	+	14.3842i	0.0213782	+	0.999771i
$208$	−3.10049			−0.214980
$209$		−	13.1434i		−	0.909149i
$210$	−0.165634	+	0.404450i	−0.0114299	+	0.0279097i
$211$	2.20409			0.151736			0.0758680	−	0.997118i	$-0.475827\pi$
$211$	2.20409			0.151736			0.0758680	+	0.997118i	$0.475827\pi$
$212$	1.95854			0.134513
$213$	−24.4251	−	10.0028i	−1.67358	−	0.685382i
$214$			11.6433i			0.795920i
$215$			1.28502i			0.0876377i
$216$	2.04600	+	4.77639i	0.139213	+	0.324992i
$217$			1.40614i			0.0954548i
$218$	1.11725			0.0756698
$219$	−2.19283	+	5.35451i	−0.148178	+	0.361824i
$220$	1.38820			0.0935925
$221$	−1.46071			−0.0982583
$222$	−3.85430	+	9.41152i	−0.258684	+	0.631660i
$223$	−25.4713			−1.70569			−0.852843	−	0.522168i	$-0.825124\pi$
$223$	−25.4713			−1.70569			−0.852843	+	0.522168i	$0.825124\pi$
$224$	−1.00000			−0.0668153
$225$	10.5551	+	10.3873i	0.703670	+	0.692490i
$226$			10.4257i			0.693509i
$227$	−17.5961			−1.16790			−0.583949	−	0.811791i	$-0.698493\pi$
$227$	−17.5961			−1.16790			−0.583949	+	0.811791i	$0.698493\pi$
$228$	−3.82930	−	1.56822i	−0.253602	−	0.103858i
$229$			8.59906i			0.568242i	0.958788	+	0.284121i	$0.0917017\pi$
$229$			8.59906i			0.568242i	−0.958788	+	0.284121i	$0.908298\pi$
$230$	0.844181	−	0.867065i	0.0556636	−	0.0571726i
$231$	−8.81805	−	3.61126i	−0.580185	−	0.237603i
$232$	−6.08436			−0.399458
$233$		−	2.93410i		−	0.192219i	−0.995371	−	0.0961097i	$-0.969360\pi$
$233$		−	2.93410i		−	0.192219i	0.995371	−	0.0961097i	$-0.0306400\pi$
$234$	−6.52425	+	6.62959i	−0.426504	+	0.433390i
$235$			1.01457i			0.0661834i
$236$		−	3.53472i		−	0.230091i
$237$	22.3590	+	9.15670i	1.45238	+	0.594792i
$238$	−0.471124			−0.0305384
$239$		−	1.13350i		−	0.0733199i	−0.999328	−	0.0366599i	$-0.988328\pi$
$239$		−	1.13350i		−	0.0733199i	0.999328	−	0.0366599i	$-0.0116718\pi$
$240$	0.165634	−	0.404450i	0.0106917	−	0.0261071i
$241$		−	21.7858i		−	1.40335i	−0.712499	−	0.701673i	$-0.752437\pi$
$241$		−	21.7858i		−	1.40335i	0.712499	−	0.701673i	$-0.247563\pi$
$242$			19.2664i			1.23849i
$243$	14.5184	+	5.67594i	0.931355	+	0.364112i
$244$			2.10168i			0.134546i
$245$	−0.252332			−0.0161209
$246$	3.05019	−	7.44802i	0.194473	−	0.474868i
$247$		−	7.40727i		−	0.471313i
$248$		−	1.40614i		−	0.0892898i
$249$	−6.02814	+	14.7196i	−0.382018	+	0.932819i
$250$		−	2.50725i		−	0.158573i
$251$	24.3418			1.53644			0.768220	−	0.640186i	$-0.221143\pi$
$251$	24.3418			1.53644			0.768220	+	0.640186i	$0.221143\pi$
$252$	−2.10426	+	2.13824i	−0.132556	+	0.134696i
$253$	18.9043	+	18.4053i	1.18850	+	1.15713i
$254$			0.430922i			0.0270385i
$255$	0.0780343	−	0.190546i	0.00488670	−	0.0119324i
$256$	1.00000			0.0625000
$257$		−	6.49482i		−	0.405135i	−0.979268	−	0.202568i	$-0.935071\pi$
$257$		−	6.49482i		−	0.405135i	0.979268	−	0.202568i	$-0.0649286\pi$
$258$	−3.34284	+	8.16263i	−0.208116	+	0.508183i
$259$	−5.87175			−0.364853
$260$	0.782353			0.0485195
$261$	−12.8031	+	13.0098i	−0.792492	+	0.805287i
$262$	−11.1468			−0.688654
$263$	−10.0922			−0.622309			−0.311155	−	0.950359i	$-0.600716\pi$
$263$	−10.0922			−0.622309			−0.311155	+	0.950359i	$0.600716\pi$
$264$	8.81805	+	3.61126i	0.542713	+	0.222258i
$265$	−0.494203			−0.0303586
$266$		−	2.38906i		−	0.146483i
$267$	−8.52394	+	20.8139i	−0.521656	+	1.27379i
$268$			5.88882i			0.359717i
$269$		−	15.0560i		−	0.917983i	−0.888441	−	0.458991i	$-0.848211\pi$
$269$		−	15.0560i		−	0.917983i	0.888441	−	0.458991i	$-0.151789\pi$
$270$	−0.516272	−	1.20524i	−0.0314193	−	0.0733483i
$271$	−21.4792			−1.30477			−0.652386	−	0.757887i	$-0.726232\pi$
$271$	−21.4792			−1.30477			−0.652386	+	0.757887i	$0.726232\pi$
$272$	0.471124			0.0285661
$273$	−4.96961	−	2.03521i	−0.300775	−	0.123176i
$274$		−	13.0016i		−	0.785454i
$275$	27.1572			1.63764
$276$	7.61793	−	3.31167i	0.458545	−	0.199339i
$277$	11.6898			0.702374			0.351187	−	0.936305i	$-0.385778\pi$
$277$	11.6898			0.702374			0.351187	+	0.936305i	$0.385778\pi$
$278$			18.5932i			1.11514i
$279$	−3.00666	−	2.95889i	−0.180004	−	0.177144i
$280$	0.252332			0.0150797
$281$	17.4066			1.03839			0.519194	−	0.854656i	$-0.326232\pi$
$281$	17.4066			1.03839			0.519194	+	0.854656i	$0.326232\pi$
$282$	−2.63930	+	6.44470i	−0.157168	+	0.383777i
$283$			20.2774i			1.20537i	0.797980	+	0.602683i	$0.205902\pi$
$283$			20.2774i			1.20537i	−0.797980	+	0.602683i	$0.794098\pi$
$284$			15.2386i			0.904243i
$285$	0.966256	+	0.395711i	0.0572361	+	0.0234399i
$286$			17.0573i			1.00862i
$287$	4.64674			0.274289
$288$	2.10426	−	2.13824i	0.123995	−	0.125997i
$289$	−16.7780			−0.986944
$290$	1.53528			0.0901546
$291$	−28.6132	−	11.7180i	−1.67734	−	0.686920i
$292$	3.34062			0.195495
$293$	−16.3179			−0.953301			−0.476650	−	0.879093i	$-0.658149\pi$
$293$	−16.3179			−0.953301			−0.476650	+	0.879093i	$0.658149\pi$
$294$	−1.60285	−	0.656415i	−0.0934800	−	0.0382829i
$295$			0.891923i			0.0519298i
$296$	5.87175			0.341289
$297$	26.2772	−	11.2561i	1.52476	−	0.653143i
$298$		−	11.4109i		−	0.661018i
$299$	10.6539	+	10.3727i	0.616132	+	0.599871i
$300$	3.24028	−	7.91218i	0.187078	−	0.456810i
$301$	−5.09258			−0.293531
$302$			2.55551i			0.147053i
$303$	−1.28718	−	0.527140i	−0.0739467	−	0.0302834i
$304$			2.38906i			0.137022i
$305$		−	0.530321i		−	0.0303661i
$306$	0.991369	−	1.00738i	0.0566728	−	0.0575878i
$307$	15.9791			0.911973			0.455987	−	0.889987i	$-0.349286\pi$
$307$	15.9791			0.911973			0.455987	+	0.889987i	$0.349286\pi$
$308$			5.50149i			0.313476i
$309$	−19.1765	−	7.85336i	−1.09091	−	0.446762i
$310$			0.354813i			0.0201520i
$311$		−	20.1658i		−	1.14350i	−0.820428	−	0.571750i	$-0.806265\pi$
$311$		−	20.1658i		−	1.14350i	0.820428	−	0.571750i	$-0.193735\pi$
$312$	4.96961	+	2.03521i	0.281349	+	0.115221i
$313$		−	0.269860i		−	0.0152534i	−0.999971	−	0.00762669i	$-0.997572\pi$
$313$		−	0.269860i		−	0.0152534i	0.999971	−	0.00762669i	$-0.00242767\pi$
$314$	12.5401			0.707677
$315$	0.530973	−	0.539546i	0.0299170	−	0.0304000i
$316$		−	13.9496i		−	0.784725i
$317$			8.37234i			0.470237i	0.971967	+	0.235119i	$0.0755479\pi$
$317$			8.37234i			0.470237i	−0.971967	+	0.235119i	$0.924452\pi$
$318$	−3.13924	−	1.28562i	−0.176040	−	0.0720937i
$319$			33.4730i			1.87413i
$320$	−0.252332			−0.0141058
$321$	7.64284	−	18.6624i	0.426581	−	1.04164i
$322$	3.43621	+	3.34552i	0.191492	+	0.186438i
$323$			1.12554i			0.0626269i
$324$	−0.144138	−	8.99885i	−0.00800768	−	0.499936i
$325$	15.3050			0.848971
$326$			8.16445i			0.452187i
$327$	−1.79078	−	0.733380i	−0.0990305	−	0.0405560i
$328$	−4.64674			−0.256573
$329$	−4.02078			−0.221673
$330$	−2.22508	−	0.911236i	−0.122486	−	0.0501619i
$331$	−7.84024			−0.430939			−0.215469	−	0.976511i	$-0.569128\pi$
$331$	−7.84024			−0.430939			−0.215469	+	0.976511i	$0.569128\pi$
$332$	9.18343			0.504006
$333$	12.3557	−	12.5552i	0.677089	−	0.688022i
$334$	−18.6643			−1.02127
$335$		−	1.48594i		−	0.0811855i
$336$	1.60285	+	0.656415i	0.0874425	+	0.0358104i
$337$		−	25.3403i		−	1.38037i	−0.723631	−	0.690187i	$-0.757528\pi$
$337$		−	25.3403i		−	1.38037i	0.723631	−	0.690187i	$-0.242472\pi$
$338$		−	3.38696i		−	0.184226i
$339$	6.84360	−	16.7109i	0.371693	−	0.907609i
$340$	−0.118880			−0.00644715
$341$	−7.73585			−0.418920
$342$	5.10839	+	5.02722i	0.276230	+	0.271841i
$343$		−	1.00000i		−	0.0539949i
$344$	5.09258			0.274573
$345$	−1.92225	+	0.835640i	−0.103490	+	0.0449893i
$346$	3.66045			0.196787
$347$			32.1330i			1.72499i	0.506065	+	0.862495i	$0.331100\pi$
$347$			32.1330i			1.72499i	−0.506065	+	0.862495i	$0.668900\pi$
$348$	9.75230	+	3.99386i	0.522778	+	0.214093i
$349$	−22.8049			−1.22072			−0.610360	−	0.792124i	$-0.708975\pi$
$349$	−22.8049			−1.22072			−0.610360	+	0.792124i	$0.708975\pi$
$350$	4.93633			0.263858
$351$	14.8091	−	6.34361i	0.790454	−	0.338597i
$352$		−	5.50149i		−	0.293230i
$353$			1.38461i			0.0736952i	0.999321	+	0.0368476i	$0.0117316\pi$
$353$			1.38461i			0.0736952i	−0.999321	+	0.0368476i	$0.988268\pi$
$354$	−2.32024	+	5.66562i	−0.123319	+	0.301124i
$355$		−	3.84518i		−	0.204081i
$356$	12.9856			0.688235
$357$	0.755139	+	0.309252i	0.0399662	+	0.0163674i
$358$	−17.2447			−0.911412
$359$	−24.6312			−1.29999			−0.649994	−	0.759940i	$-0.725229\pi$
$359$	−24.6312			−1.29999			−0.649994	+	0.759940i	$0.725229\pi$
$360$	−0.530973	+	0.539546i	−0.0279847	+	0.0284366i
$361$	13.2924			0.699599
$362$	5.76109			0.302796
$363$	12.6467	−	30.8811i	0.663782	−	1.62084i
$364$			3.10049i			0.162510i
$365$	−0.842946			−0.0441218
$366$	1.37957	−	3.36867i	0.0721114	−	0.176083i
$367$			28.4245i			1.48375i	0.670541	+	0.741873i	$0.266062\pi$
$367$			28.4245i			1.48375i	−0.670541	+	0.741873i	$0.733938\pi$
$368$	−3.43621	−	3.34552i	−0.179125	−	0.174397i
$369$	−9.77798	+	9.93585i	−0.509021	+	0.517240i
$370$	−1.48163			−0.0770263
$371$		−	1.95854i		−	0.101682i
$372$	−0.923009	+	2.25382i	−0.0478558	+	0.116855i
$373$		−	5.51022i		−	0.285309i	−0.989773	−	0.142654i	$-0.954436\pi$
$373$		−	5.51022i		−	0.285309i	0.989773	−	0.142654i	$-0.0455637\pi$
$374$		−	2.59188i		−	0.134023i
$375$	−1.64580	+	4.01874i	−0.0849886	+	0.207527i
$376$	4.02078			0.207356
$377$			18.8645i			0.971571i
$378$	4.77639	−	2.04600i	0.245671	−	0.105235i
$379$		−	27.8007i		−	1.42803i	−0.700131	−	0.714014i	$-0.746875\pi$
$379$		−	27.8007i		−	1.42803i	0.700131	−	0.714014i	$-0.253125\pi$
$380$		−	0.602837i		−	0.0309249i
$381$	0.282864	−	0.690703i	0.0144915	−	0.0353858i
$382$			17.4889i			0.894809i
$383$	−33.3811			−1.70570			−0.852848	−	0.522159i	$-0.825127\pi$
$383$	−33.3811			−1.70570			−0.852848	+	0.522159i	$0.825127\pi$
$384$	−1.60285	−	0.656415i	−0.0817950	−	0.0334975i
$385$		−	1.38820i		−	0.0707493i
$386$			20.4201i			1.03935i
$387$	10.7161	−	10.8892i	0.544732	−	0.553527i
$388$			17.8515i			0.906272i
$389$	4.72149			0.239389			0.119694	−	0.992811i	$-0.461809\pi$
$389$	4.72149			0.239389			0.119694	+	0.992811i	$0.461809\pi$
$390$	−1.25399	−	0.513548i	−0.0634984	−	0.0260045i
$391$	−1.61888	−	1.57615i	−0.0818702	−	0.0797094i
$392$			1.00000i			0.0505076i
$393$	17.8667	+	7.31695i	0.901255	+	0.369091i
$394$	−8.17726			−0.411964
$395$			3.51992i			0.177107i
$396$	−11.7635	−	11.5766i	−0.591138	−	0.581746i
$397$	7.48413			0.375618			0.187809	−	0.982206i	$-0.439861\pi$
$397$	7.48413			0.375618			0.187809	+	0.982206i	$0.439861\pi$
$398$	0.0625989			0.00313780
$399$	−1.56822	+	3.82930i	−0.0785090	+	0.191705i
$400$	−4.93633			−0.246816
$401$	−35.5877			−1.77716			−0.888582	−	0.458718i	$-0.848309\pi$
$401$	−35.5877			−1.77716			−0.888582	+	0.458718i	$0.848309\pi$
$402$	3.86551	−	9.43888i	0.192794	−	0.470769i
$403$	−4.35972			−0.217173
$404$			0.803060i			0.0399537i
$405$	0.0363707	+	2.27070i	0.00180727	+	0.112832i
$406$			6.08436i			0.301962i
$407$		−	32.3034i		−	1.60122i
$408$	−0.755139	−	0.309252i	−0.0373850	−	0.0153103i
$409$	31.9276			1.57872			0.789358	−	0.613933i	$-0.210413\pi$
$409$	31.9276			1.57872			0.789358	+	0.613933i	$0.210413\pi$
$410$	1.17252			0.0579067
$411$	−8.53443	+	20.8396i	−0.420972	+	1.02794i
$412$			11.9640i			0.589425i
$413$	−3.53472			−0.173932
$414$	−14.3842	+	0.307579i	−0.706945	+	0.0151167i
$415$	−2.31727			−0.113750
$416$		−	3.10049i		−	0.152014i
$417$	12.2048	−	29.8020i	0.597673	−	1.45941i
$418$	13.1434			0.642865
$419$	17.3290			0.846576			0.423288	−	0.905995i	$-0.360876\pi$
$419$	17.3290			0.846576			0.423288	+	0.905995i	$0.360876\pi$
$420$	−0.404450	−	0.165634i	−0.0197351	−	0.00808213i
$421$			25.2378i			1.23001i	0.788521	+	0.615007i	$0.210847\pi$
$421$			25.2378i			1.23001i	−0.788521	+	0.615007i	$0.789153\pi$
$422$			2.20409i			0.107294i
$423$	8.46080	−	8.59740i	0.411378	−	0.418020i
$424$			1.95854i			0.0951152i
$425$	−2.32562			−0.112809
$426$	10.0028	−	24.4251i	0.484638	−	1.18340i
$427$	2.10168			0.101707
$428$	−11.6433			−0.562800
$429$	11.1967	−	27.3403i	0.540580	−	1.32000i
$430$	−1.28502			−0.0619692
$431$	−26.1039			−1.25738			−0.628690	−	0.777656i	$-0.716409\pi$
$431$	−26.1039			−1.25738			−0.628690	+	0.777656i	$0.716409\pi$
$432$	−4.77639	+	2.04600i	−0.229804	+	0.0984383i
$433$		−	2.34431i		−	0.112660i	−0.998412	−	0.0563302i	$-0.982060\pi$
$433$		−	2.34431i		−	0.112660i	0.998412	−	0.0563302i	$-0.0179400\pi$
$434$	−1.40614			−0.0674968
$435$	−2.46082	−	1.00778i	−0.117987	−	0.0483193i
$436$			1.11725i			0.0535066i
$437$	7.99265	−	8.20932i	0.382340	−	0.392705i
$438$	−5.35451	−	2.19283i	−0.255848	−	0.104778i
$439$	−7.50867			−0.358369			−0.179185	−	0.983815i	$-0.557346\pi$
$439$	−7.50867			−0.358369			−0.179185	+	0.983815i	$0.557346\pi$
$440$			1.38820i			0.0661799i
$441$	2.13824	+	2.10426i	0.101821	+	0.100203i
$442$		−	1.46071i		−	0.0694791i
$443$		−	15.1702i		−	0.720760i	−0.932806	−	0.360380i	$-0.882647\pi$
$443$		−	15.1702i		−	0.720760i	0.932806	−	0.360380i	$-0.117353\pi$
$444$	−9.41152	−	3.85430i	−0.446651	−	0.182917i
$445$	−3.27668			−0.155330
$446$		−	25.4713i		−	1.20610i
$447$	−7.49031	+	18.2900i	−0.354279	+	0.865087i
$448$		−	1.00000i		−	0.0472456i
$449$		−	19.0138i		−	0.897318i	−0.893703	−	0.448659i	$-0.851902\pi$
$449$		−	19.0138i		−	0.897318i	0.893703	−	0.448659i	$-0.148098\pi$
$450$	−10.3873	+	10.5551i	−0.489664	+	0.497570i
$451$			25.5640i			1.20376i
$452$	−10.4257			−0.490385
$453$	1.67747	−	4.09609i	0.0788146	−	0.192451i
$454$		−	17.5961i		−	0.825828i
$455$		−	0.782353i		−	0.0366773i
$456$	1.56822	−	3.82930i	0.0734385	−	0.179324i
$457$		−	3.65320i		−	0.170890i	−0.996343	−	0.0854448i	$-0.972769\pi$
$457$		−	3.65320i		−	0.170890i	0.996343	−	0.0854448i	$-0.0272311\pi$
$458$	−8.59906			−0.401808
$459$	−2.25027	+	0.963920i	−0.105034	+	0.0449919i
$460$	0.867065	+	0.844181i	0.0404271	+	0.0393601i
$461$		−	41.7766i		−	1.94573i	−0.231374	−	0.972865i	$-0.574322\pi$
$461$		−	41.7766i		−	1.94573i	0.231374	−	0.972865i	$-0.425678\pi$
$462$	3.61126	−	8.81805i	0.168011	−	0.410253i
$463$	−19.4404			−0.903471			−0.451735	−	0.892152i	$-0.649195\pi$
$463$	−19.4404			−0.903471			−0.451735	+	0.892152i	$0.649195\pi$
$464$		−	6.08436i		−	0.282459i
$465$	0.232905	−	0.568712i	0.0108007	−	0.0263734i
$466$	2.93410			0.135920
$467$	−26.0964			−1.20760			−0.603798	−	0.797137i	$-0.706347\pi$
$467$	−26.0964			−1.20760			−0.603798	+	0.797137i	$0.706347\pi$
$468$	−6.62959	−	6.52425i	−0.306453	−	0.301584i
$469$	5.88882			0.271921
$470$	−1.01457			−0.0467987
$471$	−20.0998	−	8.23149i	−0.926151	−	0.379287i
$472$	3.53472			0.162699
$473$		−	28.0168i		−	1.28821i
$474$	−9.15670	+	22.3590i	−0.420581	+	1.02698i
$475$		−	11.7932i		−	0.541109i
$476$		−	0.471124i		−	0.0215939i
$477$	4.18783	+	4.12129i	0.191748	+	0.188701i
$478$	1.13350			0.0518450
$479$	−24.4346			−1.11645			−0.558224	−	0.829690i	$-0.688517\pi$
$479$	−24.4346			−1.11645			−0.558224	+	0.829690i	$0.688517\pi$
$480$	0.404450	+	0.165634i	0.0184605	+	0.00756014i
$481$		−	18.2053i		−	0.830091i
$482$	21.7858			0.992316
$483$	−3.31167	−	7.61793i	−0.150686	−	0.346628i
$484$	−19.2664			−0.875745
$485$		−	4.50450i		−	0.204539i
$486$	−5.67594	+	14.5184i	−0.257466	+	0.658568i
$487$	12.0770			0.547261			0.273631	−	0.961835i	$-0.411775\pi$
$487$	12.0770			0.547261			0.273631	+	0.961835i	$0.411775\pi$
$488$	−2.10168			−0.0951385
$489$	5.35927	−	13.0864i	0.242354	−	0.591786i
$490$		−	0.252332i		−	0.0113992i
$491$		−	7.93573i		−	0.358134i	−0.983837	−	0.179067i	$-0.942692\pi$
$491$		−	7.93573i		−	0.358134i	0.983837	−	0.179067i	$-0.0573080\pi$
$492$	7.44802	+	3.05019i	0.335783	+	0.137513i
$493$		−	2.86648i		−	0.129100i
$494$	7.40727			0.333269
$495$	2.96831	+	2.92114i	0.133416	+	0.131296i
$496$	1.40614			0.0631374
$497$	15.2386			0.683543
$498$	−14.7196	−	6.02814i	−0.659603	−	0.270127i
$499$	−23.7262			−1.06213			−0.531066	−	0.847330i	$-0.678208\pi$
$499$	−23.7262			−1.06213			−0.531066	+	0.847330i	$0.678208\pi$
$500$	2.50725			0.112128
$501$	29.9161	+	12.2515i	1.33655	+	0.547358i
$502$			24.3418i			1.08643i
$503$	−5.27424			−0.235167			−0.117583	−	0.993063i	$-0.537515\pi$
$503$	−5.27424			−0.235167			−0.117583	+	0.993063i	$0.537515\pi$
$504$	−2.13824	−	2.10426i	−0.0952448	−	0.0937314i
$505$		−	0.202638i		−	0.00901725i
$506$	−18.4053	+	18.9043i	−0.818217	+	0.840397i
$507$	−2.22325	+	5.42878i	−0.0987380	+	0.241100i
$508$	−0.430922			−0.0191191
$509$			7.73592i			0.342888i	0.985194	+	0.171444i	$0.0548433\pi$
$509$			7.73592i			0.342888i	−0.985194	+	0.171444i	$0.945157\pi$
$510$	0.190546	+	0.0780343i	0.00843751	+	0.00345542i
$511$		−	3.34062i		−	0.147780i
$512$			1.00000i			0.0441942i
$513$	−4.88803	−	11.4111i	−0.215812	−	0.503812i
$514$	6.49482			0.286474
$515$		−	3.01891i		−	0.133029i
$516$	−8.16263	−	3.34284i	−0.359340	−	0.147160i
$517$		−	22.1203i		−	0.972850i
$518$		−	5.87175i		−	0.257990i
$519$	−5.86714	−	2.40277i	−0.257539	−	0.105470i
$520$			0.782353i			0.0343084i
$521$	−32.8623			−1.43972			−0.719861	−	0.694118i	$-0.755795\pi$
$521$	−32.8623			−1.43972			−0.719861	+	0.694118i	$0.755795\pi$
$522$	−13.0098	−	12.8031i	−0.569424	−	0.560376i
$523$		−	41.1952i		−	1.80134i	−0.434501	−	0.900671i	$-0.643075\pi$
$523$		−	41.1952i		−	1.80134i	0.434501	−	0.900671i	$-0.356925\pi$
$524$		−	11.1468i		−	0.486952i
$525$	−7.91218	−	3.24028i	−0.345316	−	0.141417i
$526$		−	10.0922i		−	0.440039i
$527$	0.662465			0.0288574
$528$	−3.61126	+	8.81805i	−0.157160	+	0.383756i
$529$	0.615030	+	22.9918i	0.0267404	+	0.999642i
$530$		−	0.494203i		−	0.0214668i
$531$	7.43799	−	7.55808i	0.322781	−	0.327993i
$532$	2.38906			0.103579
$533$			14.4072i			0.624044i
$534$	−20.8139	−	8.52394i	−0.900707	−	0.368867i
$535$	2.93798			0.127020
$536$	−5.88882			−0.254358
$537$	27.6407	+	11.3197i	1.19278	+	0.488481i
$538$	15.0560			0.649112
$539$	5.50149			0.236966
$540$	1.20524	−	0.516272i	0.0518651	−	0.0222168i
$541$	11.6640			0.501473			0.250736	−	0.968055i	$-0.419327\pi$
$541$	11.6640			0.501473			0.250736	+	0.968055i	$0.419327\pi$
$542$		−	21.4792i		−	0.922612i
$543$	−9.23416	−	3.78167i	−0.396276	−	0.162287i
$544$			0.471124i			0.0201993i
$545$		−	0.281918i		−	0.0120760i
$546$	2.03521	−	4.96961i	0.0870988	−	0.212680i
$547$	−24.1526			−1.03269			−0.516346	−	0.856380i	$-0.672708\pi$
$547$	−24.1526			−1.03269			−0.516346	+	0.856380i	$0.672708\pi$
$548$	13.0016			0.555400
$549$	−4.42249	+	4.49389i	−0.188747	+	0.191795i
$550$			27.1572i			1.15799i
$551$	14.5359			0.619251
$552$	3.31167	+	7.61793i	0.140954	+	0.324241i
$553$	−13.9496			−0.593196
$554$			11.6898i			0.496654i
$555$	2.37483	+	0.972564i	0.100806	+	0.0412830i
$556$	−18.5932			−0.788526
$557$	33.0696			1.40120			0.700602	−	0.713553i	$-0.252915\pi$
$557$	33.0696			1.40120			0.700602	+	0.713553i	$0.252915\pi$
$558$	2.95889	−	3.00666i	0.125260	−	0.127282i
$559$		−	15.7895i		−	0.667824i
$560$			0.252332i			0.0106630i
$561$	−1.70135	+	4.15439i	−0.0718310	+	0.175399i
$562$			17.4066i			0.734252i
$563$	24.2673			1.02274			0.511371	−	0.859360i	$-0.329138\pi$
$563$	24.2673			1.02274			0.511371	+	0.859360i	$0.329138\pi$
$564$	−6.44470	−	2.63930i	−0.271371	−	0.111135i
$565$	2.63074			0.110676
$566$	−20.2774			−0.852323
$567$	−8.99885	+	0.144138i	−0.377916	+	0.00605324i
$568$	−15.2386			−0.639396
$569$	−44.1025			−1.84887			−0.924436	−	0.381338i	$-0.875464\pi$
$569$	−44.1025			−1.84887			−0.924436	+	0.381338i	$0.875464\pi$
$570$	−0.395711	+	0.966256i	−0.0165745	+	0.0404720i
$571$		−	5.02125i		−	0.210133i	−0.994465	−	0.105066i	$-0.966494\pi$
$571$		−	5.02125i		−	0.210133i	0.994465	−	0.105066i	$-0.0335055\pi$
$572$	−17.0573			−0.713202
$573$	11.4800	−	28.0320i	0.479582	−	1.17105i
$574$			4.64674i			0.193951i
$575$	16.9622	+	16.5146i	0.707374	+	0.688705i
$576$	2.13824	+	2.10426i	0.0890933	+	0.0876777i
$577$	−1.04410			−0.0434663			−0.0217331	−	0.999764i	$-0.506918\pi$
$577$	−1.04410			−0.0434663			−0.0217331	+	0.999764i	$0.506918\pi$
$578$		−	16.7780i		−	0.697875i
$579$	13.4040	−	32.7302i	0.557052	−	1.36022i
$580$			1.53528i			0.0637489i
$581$		−	9.18343i		−	0.380993i
$582$	11.7180	−	28.6132i	0.485726	−	1.18606i
$583$	10.7749			0.446251
$584$			3.34062i			0.138236i
$585$	1.67286	+	1.64628i	0.0691642	+	0.0680652i
$586$		−	16.3179i		−	0.674085i
$587$		−	14.4825i		−	0.597758i	−0.954291	−	0.298879i	$-0.903387\pi$
$587$		−	14.4825i		−	0.597758i	0.954291	−	0.298879i	$-0.0966127\pi$
$588$	0.656415	−	1.60285i	0.0270701	−	0.0661003i
$589$			3.35935i			0.138420i
$590$	−0.891923			−0.0367199
$591$	13.1069	+	5.36767i	0.539146	+	0.220797i
$592$			5.87175i			0.241328i
$593$		−	3.58230i		−	0.147107i	−0.997291	−	0.0735537i	$-0.976566\pi$
$593$		−	3.58230i		−	0.147107i	0.997291	−	0.0735537i	$-0.0234340\pi$
$594$	11.2561	+	26.2772i	0.461842	+	1.07817i
$595$			0.118880i			0.00487359i
$596$	11.4109			0.467410
$597$	−0.100336	−	0.0410908i	−0.00410650	−	0.00168174i
$598$	−10.3727	+	10.6539i	−0.424173	+	0.435671i
$599$		−	7.95060i		−	0.324853i	−0.986721	−	0.162426i	$-0.948068\pi$
$599$		−	7.95060i		−	0.324853i	0.986721	−	0.162426i	$-0.0519320\pi$
$600$	7.91218	+	3.24028i	0.323013	+	0.132284i
$601$	−23.9355			−0.976350			−0.488175	−	0.872746i	$-0.662337\pi$
$601$	−23.9355			−0.976350			−0.488175	+	0.872746i	$0.662337\pi$
$602$		−	5.09258i		−	0.207558i
$603$	−12.3916	+	12.5917i	−0.504627	+	0.512774i
$604$	−2.55551			−0.103982
$605$	4.86153			0.197649
$606$	0.527140	−	1.28718i	0.0214136	−	0.0522882i
$607$	−36.7347			−1.49102			−0.745508	−	0.666497i	$-0.767793\pi$
$607$	−36.7347			−1.49102			−0.745508	+	0.666497i	$0.767793\pi$
$608$	−2.38906			−0.0968893
$609$	3.99386	−	9.75230i	0.161839	−	0.395183i
$610$	0.530321			0.0214721
$611$		−	12.4664i		−	0.504337i
$612$	1.00738	+	0.991369i	0.0407207	+	0.0400737i
$613$			4.62698i			0.186882i	0.995625	+	0.0934410i	$0.0297866\pi$
$613$			4.62698i			0.186882i	−0.995625	+	0.0934410i	$0.970213\pi$
$614$			15.9791i			0.644862i
$615$	−1.87937	−	0.769660i	−0.0757836	−	0.0310357i
$616$	−5.50149			−0.221661
$617$	−5.21923			−0.210118			−0.105059	−	0.994466i	$-0.533503\pi$
$617$	−5.21923			−0.210118			−0.105059	+	0.994466i	$0.533503\pi$
$618$	7.85336	−	19.1765i	0.315908	−	0.771392i
$619$			19.6131i			0.788316i	0.919043	+	0.394158i	$0.128964\pi$
$619$			19.6131i			0.788316i	−0.919043	+	0.394158i	$0.871036\pi$
$620$	−0.354813			−0.0142497
$621$	23.2576	+	8.94900i	0.933295	+	0.359111i
$622$	20.1658			0.808577
$623$		−	12.9856i		−	0.520257i
$624$	−2.03521	+	4.96961i	−0.0814735	+	0.198944i
$625$	24.0490			0.961959
$626$	0.269860			0.0107858
$627$	−21.0669	−	8.62753i	−0.841330	−	0.344550i
$628$			12.5401i			0.500403i
$629$			2.76632i			0.110300i
$630$	0.539546	+	0.530973i	0.0214960	+	0.0211545i
$631$			23.2849i			0.926958i	0.886108	+	0.463479i	$0.153399\pi$
$631$			23.2849i			0.926958i	−0.886108	+	0.463479i	$0.846601\pi$
$632$	13.9496			0.554884
$633$	1.44680	−	3.53283i	0.0575051	−	0.140417i
$634$	−8.37234			−0.332508
$635$	0.108735			0.00431504
$636$	1.28562	−	3.13924i	0.0509780	−	0.124479i
$637$	3.10049			0.122846
$638$	−33.4730			−1.32521
$639$	−32.0660	+	32.5837i	−1.26851	+	1.28899i
$640$		−	0.252332i		−	0.00997430i
$641$	−19.5620			−0.772653			−0.386327	−	0.922362i	$-0.626256\pi$
$641$	−19.5620			−0.772653			−0.386327	+	0.922362i	$0.626256\pi$
$642$	18.6624	+	7.64284i	0.736548	+	0.301639i
$643$			47.1630i			1.85993i	0.367651	+	0.929964i	$0.380162\pi$
$643$			47.1630i			1.85993i	−0.367651	+	0.929964i	$0.619838\pi$
$644$	−3.34552	+	3.43621i	−0.131832	+	0.135406i
$645$	2.05969	+	0.843506i	0.0811003	+	0.0332130i
$646$	−1.12554			−0.0442839
$647$			20.4000i			0.802006i	0.916077	+	0.401003i	$0.131338\pi$
$647$			20.4000i			0.802006i	−0.916077	+	0.401003i	$0.868662\pi$
$648$	8.99885	−	0.144138i	0.353508	−	0.00566229i
$649$		−	19.4462i		−	0.763331i
$650$			15.3050i			0.600313i
$651$	2.25382	+	0.923009i	0.0883343	+	0.0361756i
$652$	−8.16445			−0.319745
$653$		−	2.53918i		−	0.0993660i	−0.998765	−	0.0496830i	$-0.984179\pi$
$653$		−	2.53918i		−	0.0993660i	0.998765	−	0.0496830i	$-0.0158211\pi$
$654$	0.733380	−	1.79078i	0.0286774	−	0.0700251i
$655$			2.81270i			0.109901i
$656$		−	4.64674i		−	0.181425i
$657$	7.14305	+	7.02955i	0.278677	+	0.274249i
$658$		−	4.02078i		−	0.156747i
$659$	32.5218			1.26687			0.633435	−	0.773796i	$-0.281644\pi$
$659$	32.5218			1.26687			0.633435	+	0.773796i	$0.281644\pi$
$660$	0.911236	−	2.22508i	0.0354698	−	0.0866109i
$661$			26.2380i			1.02054i	0.860014	+	0.510270i	$0.170455\pi$
$661$			26.2380i			1.02054i	−0.860014	+	0.510270i	$0.829545\pi$
$662$		−	7.84024i		−	0.304720i
$663$	−0.958834	+	2.34130i	−0.0372380	+	0.0909286i
$664$			9.18343i			0.356386i
$665$	−0.602837			−0.0233770
$666$	12.5552	+	12.3557i	0.486505	+	0.478775i
$667$	−20.3553	+	20.9071i	−0.788161	+	0.809526i
$668$		−	18.6643i		−	0.722144i
$669$	−16.7197	+	40.8266i	−0.646423	+	1.57845i
$670$	1.48594			0.0574068
$671$			11.5624i			0.446360i
$672$	−0.656415	+	1.60285i	−0.0253217	+	0.0618312i
$673$	6.70202			0.258344			0.129172	−	0.991622i	$-0.458768\pi$
$673$	6.70202			0.258344			0.129172	+	0.991622i	$0.458768\pi$
$674$	25.3403			0.976071
$675$	23.5778	−	10.0997i	0.907511	−	0.388739i
$676$	3.38696			0.130268
$677$	12.0244			0.462137			0.231068	−	0.972938i	$-0.425778\pi$
$677$	12.0244			0.462137			0.231068	+	0.972938i	$0.425778\pi$
$678$	16.7109	+	6.84360i	0.641776	+	0.262827i
$679$	17.8515			0.685077
$680$		−	0.118880i		−	0.00455882i
$681$	−11.5504	+	28.2039i	−0.442611	+	1.08078i
$682$		−	7.73585i		−	0.296221i
$683$			30.3967i			1.16310i	0.813512	+	0.581548i	$0.197553\pi$
$683$			30.3967i			1.16310i	−0.813512	+	0.581548i	$0.802447\pi$
$684$	−5.02722	+	5.10839i	−0.192221	+	0.195324i
$685$	−3.28072			−0.125350
$686$	1.00000			0.0381802
$687$	13.7830	+	5.64455i	0.525854	+	0.215353i
$688$			5.09258i			0.194153i
$689$	6.07244			0.231342
$690$	−0.835640	−	1.92225i	−0.0318123	−	0.0731787i
$691$	−17.3792			−0.661137			−0.330568	−	0.943782i	$-0.607240\pi$
$691$	−17.3792			−0.661137			−0.330568	+	0.943782i	$0.607240\pi$
$692$			3.66045i			0.139149i
$693$	−11.5766	+	11.7635i	−0.439758	+	0.446859i
$694$	−32.1330			−1.21975
$695$	4.69165			0.177965
$696$	−3.99386	+	9.75230i	−0.151387	+	0.369660i
$697$		−	2.18919i		−	0.0829215i
$698$		−	22.8049i		−	0.863180i
$699$	−4.70292	−	1.92599i	−0.177881	−	0.0728476i
$700$			4.93633i			0.186576i
$701$	−29.2013			−1.10292			−0.551459	−	0.834202i	$-0.685929\pi$
$701$	−29.2013			−1.10292			−0.551459	+	0.834202i	$0.685929\pi$
$702$	6.34361	+	14.8091i	0.239424	+	0.558935i
$703$	−14.0280			−0.529076
$704$	5.50149			0.207345
$705$	1.62620	+	0.665980i	0.0612464	+	0.0250823i
$706$	−1.38461			−0.0521103
$707$	0.803060			0.0302022
$708$	−5.66562	−	2.32024i	−0.212927	−	0.0872001i
$709$			12.6452i			0.474900i	0.971400	+	0.237450i	$0.0763117\pi$
$709$			12.6452i			0.474900i	−0.971400	+	0.237450i	$0.923688\pi$
$710$	3.84518			0.144307
$711$	29.3536	−	29.8275i	1.10085	−	1.11862i
$712$			12.9856i			0.486656i
$713$	−4.83178	−	4.70426i	−0.180952	−	0.176176i
$714$	−0.309252	+	0.755139i	−0.0115735	+	0.0282604i
$715$	4.30411			0.160964
$716$		−	17.2447i		−	0.644466i
$717$	−1.81682	−	0.744045i	−0.0678505	−	0.0277869i
$718$		−	24.6312i		−	0.919230i
$719$			29.1016i			1.08531i	0.839957	+	0.542654i	$0.182580\pi$
$719$			29.1016i			1.08531i	−0.839957	+	0.542654i	$0.817420\pi$
$720$	−0.539546	−	0.530973i	−0.0201077	−	0.0197882i
$721$	11.9640			0.445564
$722$			13.2924i			0.494691i
$723$	−34.9193	−	14.3005i	−1.29866	−	0.531842i
$724$			5.76109i			0.214109i
$725$			30.0344i			1.11545i
$726$	30.8811	+	12.6467i	1.14610	+	0.469365i
$727$			48.1236i			1.78480i	0.451240	+	0.892402i	$0.350982\pi$
$727$			48.1236i			1.78480i	−0.451240	+	0.892402i	$0.649018\pi$
$728$	−3.10049			−0.114912
$729$	18.6278	−	19.5450i	0.689917	−	0.723889i
$730$		−	0.842946i		−	0.0311988i
$731$			2.39923i			0.0887389i
$732$	3.36867	+	1.37957i	0.124510	+	0.0509905i
$733$		−	10.4367i		−	0.385487i	−0.981249	−	0.192743i	$-0.938261\pi$
$733$		−	10.4367i		−	0.385487i	0.981249	−	0.192743i	$-0.0617385\pi$
$734$	−28.4245			−1.04917
$735$	−0.165634	+	0.404450i	−0.00610952	+	0.0149183i
$736$	3.34552	−	3.43621i	0.123317	−	0.126660i
$737$			32.3973i			1.19337i
$738$	−9.93585	−	9.77798i	−0.365744	−	0.359932i
$739$	0.383508			0.0141076			0.00705379	−	0.999975i	$-0.497755\pi$
$739$	0.383508			0.0141076			0.00705379	+	0.999975i	$0.497755\pi$
$740$		−	1.48163i		−	0.0544658i
$741$	−11.8727	−	4.86224i	−0.436155	−	0.178619i
$742$	1.95854			0.0719003
$743$	4.50514			0.165278			0.0826389	−	0.996580i	$-0.473665\pi$
$743$	4.50514			0.165278			0.0826389	+	0.996580i	$0.473665\pi$
$744$	−2.25382	−	0.923009i	−0.0826292	−	0.0338392i
$745$	−2.87935			−0.105491
$746$	5.51022			0.201744
$747$	19.6364	+	19.3244i	0.718457	+	0.707042i
$748$	2.59188			0.0947686
$749$			11.6433i			0.425437i
$750$	−4.01874	−	1.64580i	−0.146744	−	0.0600960i
$751$		−	39.9527i		−	1.45790i	−0.684569	−	0.728948i	$-0.740010\pi$
$751$		−	39.9527i		−	1.45790i	0.684569	−	0.728948i	$-0.259990\pi$
$752$			4.02078i			0.146623i
$753$	15.9783	−	39.0162i	0.582282	−	1.42183i
$754$	−18.8645			−0.687004
$755$	0.644837			0.0234680
$756$	2.04600	+	4.77639i	0.0744124	+	0.173716i
$757$			7.19221i			0.261405i	0.991422	+	0.130703i	$0.0417233\pi$
$757$			7.19221i			0.261405i	−0.991422	+	0.130703i	$0.958277\pi$
$758$	27.8007			1.00977
$759$	41.9100	−	18.2191i	1.52124	−	0.661312i
$760$	0.602837			0.0218672
$761$			2.47057i			0.0895580i	0.998997	+	0.0447790i	$0.0142584\pi$
$761$			2.47057i			0.0895580i	−0.998997	+	0.0447790i	$0.985742\pi$
$762$	0.690703	+	0.282864i	0.0250215	+	0.0102471i
$763$	1.11725			0.0404472
$764$	−17.4889			−0.632725
$765$	−0.254193	−	0.250154i	−0.00919037	−	0.00904434i
$766$		−	33.3811i		−	1.20611i
$767$		−	10.9594i		−	0.395720i
$768$	0.656415	−	1.60285i	0.0236863	−	0.0578378i
$769$		−	47.0485i		−	1.69661i	−0.529505	−	0.848307i	$-0.677622\pi$
$769$		−	47.0485i		−	1.69661i	0.529505	−	0.848307i	$-0.322378\pi$
$770$	1.38820			0.0500273
$771$	−10.4102	−	4.26329i	−0.374914	−	0.153539i
$772$	−20.4201			−0.734934
$773$	42.5654			1.53097			0.765486	−	0.643453i	$-0.222499\pi$
$773$	42.5654			1.53097			0.765486	+	0.643453i	$0.222499\pi$
$774$	10.8892	+	10.7161i	0.391403	+	0.385183i
$775$	−6.94116			−0.249334
$776$	−17.8515			−0.640831
$777$	−3.85430	+	9.41152i	−0.138272	+	0.337637i
$778$			4.72149i			0.169273i
$779$	11.1014			0.397748
$780$	0.513548	−	1.25399i	0.0183880	−	0.0449001i
$781$			83.8348i			2.99985i
$782$	1.57615	−	1.61888i	0.0563631	−	0.0578910i
$783$	12.4486	+	29.0612i	0.444877	+	1.03856i
$784$	−1.00000			−0.0357143
$785$		−	3.16426i		−	0.112937i
$786$	−7.31695	+	17.8667i	−0.260987	+	0.637283i
$787$		−	42.2758i		−	1.50697i	−0.657464	−	0.753486i	$-0.728371\pi$
$787$		−	42.2758i		−	1.50697i	0.657464	−	0.753486i	$-0.271629\pi$
$788$		−	8.17726i		−	0.291303i
$789$	−6.62464	+	16.1762i	−0.235843	+	0.575888i
$790$	−3.51992			−0.125233
$791$			10.4257i			0.370696i
$792$	11.5766	−	11.7635i	0.411356	−	0.417998i
$793$			6.51624i			0.231398i
$794$			7.48413i			0.265602i
$795$	−0.324402	+	0.792131i	−0.0115053	+	0.0280940i
$796$			0.0625989i			0.00221876i
$797$	10.6019			0.375540			0.187770	−	0.982213i	$-0.439874\pi$
$797$	10.6019			0.375540			0.187770	+	0.982213i	$0.439874\pi$
$798$	−3.82930	−	1.56822i	−0.135556	−	0.0555143i
$799$			1.89429i			0.0670150i
$800$		−	4.93633i		−	0.174526i
$801$	27.7663	+	27.3251i	0.981075	+	0.965486i
$802$		−	35.5877i		−	1.25664i
$803$	18.3784			0.648560
$804$	9.43888	+	3.86551i	0.332884	+	0.136326i
$805$	0.844181	−	0.867065i	0.0297535	−	0.0305600i
$806$		−	4.35972i		−	0.153564i
$807$	−24.1325	−	9.88300i	−0.849505	−	0.347898i
$808$	−0.803060			−0.0282515
$809$		−	22.8185i		−	0.802256i	−0.916022	−	0.401128i	$-0.868618\pi$
$809$		−	22.8185i		−	0.802256i	0.916022	−	0.401128i	$-0.131382\pi$
$810$	−2.27070	+	0.0363707i	−0.0797841	+	0.00127794i
$811$	−46.9286			−1.64789			−0.823943	−	0.566673i	$-0.808230\pi$
$811$	−46.9286			−1.64789			−0.823943	+	0.566673i	$0.808230\pi$
$812$	−6.08436			−0.213519
$813$	−14.0993	+	34.4279i	−0.494484	+	1.20744i
$814$	32.3034			1.13223
$815$	2.06015			0.0721640
$816$	0.309252	−	0.755139i	0.0108260	−	0.0264352i
$817$	−12.1665			−0.425652
$818$			31.9276i			1.11632i
$819$	−6.52425	+	6.62959i	−0.227976	+	0.231657i
$820$			1.17252i			0.0409462i
$821$			45.8336i			1.59960i	0.600265	+	0.799801i	$0.295062\pi$
$821$			45.8336i			1.59960i	−0.600265	+	0.799801i	$0.704938\pi$
$822$	−20.8396	−	8.53443i	−0.726863	−	0.297672i
$823$	54.7532			1.90858			0.954288	−	0.298889i	$-0.0966161\pi$
$823$	54.7532			1.90858			0.954288	+	0.298889i	$0.0966161\pi$
$824$	−11.9640			−0.416787
$825$	17.8264	−	43.5288i	0.620634	−	1.51548i
$826$		−	3.53472i		−	0.122989i
$827$	35.4582			1.23300			0.616502	−	0.787353i	$-0.288549\pi$
$827$	35.4582			1.23300			0.616502	+	0.787353i	$0.288549\pi$
$828$	−0.307579	−	14.3842i	−0.0106891	−	0.499886i
$829$	−24.2004			−0.840514			−0.420257	−	0.907405i	$-0.638060\pi$
$829$	−24.2004			−0.840514			−0.420257	+	0.907405i	$0.638060\pi$
$830$		−	2.31727i		−	0.0804337i
$831$	7.67338	−	18.7370i	0.266187	−	0.649980i
$832$	3.10049			0.107490
$833$	−0.471124			−0.0163235
$834$	29.8020	+	12.2048i	1.03196	+	0.422619i
$835$			4.70960i			0.162983i
$836$			13.1434i			0.454574i
$837$	−6.71626	+	2.87696i	−0.232148	+	0.0994423i
$838$			17.3290i			0.598619i
$839$	−56.4665			−1.94944			−0.974720	−	0.223431i	$-0.928274\pi$
$839$	−56.4665			−1.94944			−0.974720	+	0.223431i	$0.928274\pi$
$840$	0.165634	−	0.404450i	0.00571493	−	0.0139548i
$841$	−8.01939			−0.276531
$842$	−25.2378			−0.869752
$843$	11.4259	−	27.9001i	0.393530	−	0.960930i
$844$	−2.20409			−0.0758680
$845$	−0.854638			−0.0294004
$846$	8.59740	+	8.46080i	0.295585	+	0.290888i
$847$			19.2664i			0.662001i
$848$	−1.95854			−0.0672566
$849$	32.5016	+	13.3104i	1.11545	+	0.456811i
$850$		−	2.32562i		−	0.0797681i
$851$	19.6440	−	20.1766i	0.673389	−	0.691643i
$852$	24.4251	+	10.0028i	0.836790	+	0.342691i
$853$	−28.7879			−0.985679			−0.492840	−	0.870120i	$-0.664041\pi$
$853$	−28.7879			−0.985679			−0.492840	+	0.870120i	$0.664041\pi$
$854$			2.10168i			0.0719180i
$855$	1.26853	−	1.28901i	0.0433828	−	0.0440832i
$856$		−	11.6433i		−	0.397960i
$857$			10.2674i			0.350728i	0.984504	+	0.175364i	$0.0561103\pi$
$857$			10.2674i			0.350728i	−0.984504	+	0.175364i	$0.943890\pi$
$858$	27.3403	+	11.1967i	0.933382	+	0.382248i
$859$	−47.6303			−1.62512			−0.812562	−	0.582875i	$-0.801928\pi$
$859$	−47.6303			−1.62512			−0.812562	+	0.582875i	$0.801928\pi$
$860$		−	1.28502i		−	0.0438188i
$861$	3.05019	−	7.44802i	0.103950	−	0.253828i
$862$		−	26.1039i		−	0.889102i
$863$			6.69188i			0.227794i	0.993493	+	0.113897i	$0.0363334\pi$
$863$			6.69188i			0.227794i	−0.993493	+	0.113897i	$0.963667\pi$
$864$	−2.04600	−	4.77639i	−0.0696064	−	0.162496i
$865$		−	0.923648i		−	0.0314050i
$866$	2.34431			0.0796630
$867$	−11.0134	+	26.8926i	−0.374033	+	0.913322i
$868$		−	1.40614i		−	0.0477274i
$869$		−	76.7434i		−	2.60334i
$870$	1.00778	−	2.46082i	0.0341669	−	0.0834295i
$871$			18.2582i			0.618657i
$872$	−1.11725			−0.0378349
$873$	−37.5643	+	38.1708i	−1.27136	+	1.29188i
$874$	8.20932	+	7.99265i	0.277684	+	0.270356i
$875$		−	2.50725i		−	0.0847606i
$876$	2.19283	−	5.35451i	0.0740890	−	0.180912i
$877$	14.7866			0.499307			0.249653	−	0.968335i	$-0.419683\pi$
$877$	14.7866			0.499307			0.249653	+	0.968335i	$0.419683\pi$
$878$		−	7.50867i		−	0.253405i
$879$	−10.7113	+	26.1551i	−0.361283	+	0.882189i
$880$	−1.38820			−0.0467963
$881$	13.0104			0.438331			0.219165	−	0.975688i	$-0.429667\pi$
$881$	13.0104			0.438331			0.219165	+	0.975688i	$0.429667\pi$
$882$	−2.10426	+	2.13824i	−0.0708543	+	0.0719983i
$883$	45.8305			1.54232			0.771160	−	0.636641i	$-0.219677\pi$
$883$	45.8305			1.54232			0.771160	+	0.636641i	$0.219677\pi$
$884$	1.46071			0.0491291
$885$	1.42962	+	0.585471i	0.0480560	+	0.0196804i
$886$	15.1702			0.509654
$887$			4.88742i			0.164104i	0.996628	+	0.0820518i	$0.0261473\pi$
$887$			4.88742i			0.164104i	−0.996628	+	0.0820518i	$0.973853\pi$
$888$	3.85430	−	9.41152i	0.129342	−	0.315830i
$889$			0.430922i			0.0144527i
$890$		−	3.27668i		−	0.109835i
$891$	−0.792975	−	49.5071i	−0.0265657	−	1.65855i
$892$	25.4713			0.852843
$893$	−9.60591			−0.321450
$894$	−18.2900	−	7.49031i	−0.611709	−	0.250513i
$895$			4.35140i			0.145451i
$896$	1.00000			0.0334077
$897$	23.6193	−	10.2678i	0.788626	−	0.342832i
$898$	19.0138			0.634500
$899$		−	8.55544i		−	0.285340i
$900$	−10.5551	−	10.3873i	−0.351835	−	0.346245i
$901$	−0.922715			−0.0307401
$902$	−25.5640			−0.851188
$903$	−3.34284	+	8.16263i	−0.111243	+	0.271635i
$904$		−	10.4257i		−	0.346755i
$905$		−	1.45371i		−	0.0483229i
$906$	4.09609	+	1.67747i	0.136084	+	0.0557303i
$907$			2.27033i			0.0753852i	0.999289	+	0.0376926i	$0.0120008\pi$
$907$			2.27033i			0.0753852i	−0.999289	+	0.0376926i	$0.987999\pi$
$908$	17.5961			0.583949
$909$	−1.68985	+	1.71713i	−0.0560488	+	0.0569537i
$910$	0.782353			0.0259347
$911$	9.42780			0.312357			0.156178	−	0.987729i	$-0.450083\pi$
$911$	9.42780			0.312357			0.156178	+	0.987729i	$0.450083\pi$
$912$	3.82930	+	1.56822i	0.126801	+	0.0519288i
$913$	50.5225			1.67205
$914$	3.65320			0.120837
$915$	−0.850023	−	0.348110i	−0.0281009	−	0.0115082i
$916$		−	8.59906i		−	0.284121i
$917$	−11.1468			−0.368101
$918$	−0.963920	−	2.25027i	−0.0318141	−	0.0742699i
$919$			12.6728i			0.418038i	0.977912	+	0.209019i	$0.0670271\pi$
$919$			12.6728i			0.418038i	−0.977912	+	0.209019i	$0.932973\pi$
$920$	−0.844181	+	0.867065i	−0.0278318	+	0.0285863i
$921$	10.4889	−	25.6120i	0.345621	−	0.843944i
$922$	41.7766			1.37584
$923$			47.2470i			1.55516i
$924$	8.81805	+	3.61126i	0.290093	+	0.118802i
$925$		−	28.9849i		−	0.953018i
$926$		−	19.4404i		−	0.638850i
$927$	−25.1755	+	25.5820i	−0.826871	+	0.840222i
$928$	6.08436			0.199729
$929$		−	57.5072i		−	1.88675i	−0.331730	−	0.943375i	$-0.607632\pi$
$929$		−	57.5072i		−	1.88675i	0.331730	−	0.943375i	$-0.392368\pi$
$930$	0.568712	+	0.232905i	0.0186488	+	0.00763725i
$931$		−	2.38906i		−	0.0782984i
$932$			2.93410i			0.0961097i
$933$	−32.3228	−	13.2372i	−1.05820	−	0.433365i
$934$		−	26.0964i		−	0.853900i
$935$	−0.654015			−0.0213886
$936$	6.52425	−	6.62959i	0.213252	−	0.216695i
$937$			11.1132i			0.363053i	0.983386	+	0.181526i	$0.0581038\pi$
$937$			11.1132i			0.363053i	−0.983386	+	0.181526i	$0.941896\pi$
$938$			5.88882i			0.192277i
$939$	−0.432544	−	0.177140i	−0.0141155	−	0.00578074i
$940$		−	1.01457i		−	0.0330917i
$941$	−27.8230			−0.907003			−0.453502	−	0.891255i	$-0.649825\pi$
$941$	−27.8230			−0.907003			−0.453502	+	0.891255i	$0.649825\pi$
$942$	8.23149	−	20.0998i	0.268196	−	0.654888i
$943$	−15.5458	+	15.9672i	−0.506239	+	0.519962i
$944$			3.53472i			0.115045i
$945$	−0.516272	−	1.20524i	−0.0167943	−	0.0392063i
$946$	28.0168			0.910904
$947$			21.5751i			0.701096i	0.936545	+	0.350548i	$0.114005\pi$
$947$			21.5751i			0.701096i	−0.936545	+	0.350548i	$0.885995\pi$
$948$	−22.3590	−	9.15670i	−0.726188	−	0.297396i
$949$	10.3576			0.336221
$950$	11.7932			0.382622
$951$	13.4196	+	5.49573i	0.435160	+	0.178211i
$952$	0.471124			0.0152692
$953$	0.898982			0.0291209			0.0145604	−	0.999894i	$-0.495365\pi$
$953$	0.898982			0.0291209			0.0145604	+	0.999894i	$0.495365\pi$
$954$	−4.12129	+	4.18783i	−0.133432	+	0.135586i
$955$	4.41300			0.142801
$956$			1.13350i			0.0366599i
$957$	53.6522	+	21.9722i	1.73433	+	0.710260i
$958$		−	24.4346i		−	0.789448i
$959$		−	13.0016i		−	0.419843i
$960$	−0.165634	+	0.404450i	−0.00534583	+	0.0130536i
$961$	−29.0228			−0.936219
$962$	18.2053			0.586963
$963$	−24.8962	−	24.5006i	−0.802268	−	0.789521i
$964$			21.7858i			0.701673i
$965$	5.15263			0.165869
$966$	7.61793	−	3.31167i	0.245103	−	0.106551i
$967$	24.7064			0.794504			0.397252	−	0.917710i	$-0.369964\pi$
$967$	24.7064			0.794504			0.397252	+	0.917710i	$0.369964\pi$
$968$		−	19.2664i		−	0.619245i
$969$	1.80408	+	0.738824i	0.0579553	+	0.0237344i
$970$	4.50450			0.144631
$971$	35.9227			1.15281			0.576407	−	0.817163i	$-0.304454\pi$
$971$	35.9227			1.15281			0.576407	+	0.817163i	$0.304454\pi$
$972$	−14.5184	−	5.67594i	−0.465678	−	0.182056i
$973$			18.5932i			0.596070i
$974$			12.0770i			0.386972i
$975$	10.0465	−	24.5316i	0.321744	−	0.785641i
$976$		−	2.10168i		−	0.0672731i
$977$	−8.43803			−0.269956			−0.134978	−	0.990849i	$-0.543096\pi$
$977$	−8.43803			−0.269956			−0.134978	+	0.990849i	$0.543096\pi$
$978$	13.0864	+	5.35927i	0.418456	+	0.171370i
$979$	71.4401			2.28324
$980$	0.252332			0.00806045
$981$	−2.35099	+	2.38895i	−0.0750614	+	0.0762733i
$982$	7.93573			0.253239
$983$	19.1227			0.609920			0.304960	−	0.952365i	$-0.401357\pi$
$983$	19.1227			0.609920			0.304960	+	0.952365i	$0.401357\pi$
$984$	−3.05019	+	7.44802i	−0.0972365	+	0.237434i
$985$			2.06338i			0.0657449i
$986$	2.86648			0.0912874
$987$	−2.63930	+	6.44470i	−0.0840099	+	0.205137i
$988$			7.40727i			0.235657i
$989$	17.0373	−	17.4992i	0.541755	−	0.556441i
$990$	−2.92114	+	2.96831i	−0.0928401	+	0.0943390i
$991$	−22.4016			−0.711609			−0.355805	−	0.934560i	$-0.615793\pi$
$991$	−22.4016			−0.711609			−0.355805	+	0.934560i	$0.615793\pi$
$992$			1.40614i			0.0446449i
$993$	−5.14645	+	12.5667i	−0.163318	+	0.398792i
$994$			15.2386i			0.483338i
$995$		−	0.0157957i		−	0.000500757i
$996$	6.02814	−	14.7196i	0.191009	−	0.466409i
$997$	−40.4484			−1.28102			−0.640508	−	0.767952i	$-0.721276\pi$
$997$	−40.4484			−1.28102			−0.640508	+	0.767952i	$0.721276\pi$
$998$		−	23.7262i		−	0.751041i
$999$	−12.0136	−	28.0458i	−0.380094	−	0.887329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.b.827.19	yes	24
3.2	odd	2		966.2.h.a.827.7	✓	24
23.22	odd	2		966.2.h.a.827.19	yes	24
69.68	even	2	inner	966.2.h.b.827.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.7	✓	24	3.2	odd	2
966.2.h.a.827.19	yes	24	23.22	odd	2
966.2.h.b.827.7	yes	24	69.68	even	2	inner
966.2.h.b.827.19	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.656415 - 1.60285i) q^{3} -1.00000 q^{4} +0.252332 q^{5} +(1.60285 + 0.656415i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.13824 - 2.10426i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.656415 - 1.60285i) q^{3} -1.00000 q^{4} +0.252332 q^{5} +(1.60285 + 0.656415i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.13824 - 2.10426i) q^{9} +0.252332i q^{10} -5.50149 q^{11} +(-0.656415 + 1.60285i) q^{12} -3.10049 q^{13} -1.00000 q^{14} +(0.165634 - 0.404450i) q^{15} +1.00000 q^{16} +0.471124 q^{17} +(2.10426 - 2.13824i) q^{18} +2.38906i q^{19} -0.252332 q^{20} +(1.60285 + 0.656415i) q^{21} -5.50149i q^{22} +(-3.43621 - 3.34552i) q^{23} +(-1.60285 - 0.656415i) q^{24} -4.93633 q^{25} -3.10049i q^{26} +(-4.77639 + 2.04600i) q^{27} -1.00000i q^{28} -6.08436i q^{29} +(0.404450 + 0.165634i) q^{30} +1.40614 q^{31} +1.00000i q^{32} +(-3.61126 + 8.81805i) q^{33} +0.471124i q^{34} +0.252332i q^{35} +(2.13824 + 2.10426i) q^{36} +5.87175i q^{37} -2.38906 q^{38} +(-2.03521 + 4.96961i) q^{39} -0.252332i q^{40} -4.64674i q^{41} +(-0.656415 + 1.60285i) q^{42} +5.09258i q^{43} +5.50149 q^{44} +(-0.539546 - 0.530973i) q^{45} +(3.34552 - 3.43621i) q^{46} +4.02078i q^{47} +(0.656415 - 1.60285i) q^{48} -1.00000 q^{49} -4.93633i q^{50} +(0.309252 - 0.755139i) q^{51} +3.10049 q^{52} -1.95854 q^{53} +(-2.04600 - 4.77639i) q^{54} -1.38820 q^{55} +1.00000 q^{56} +(3.82930 + 1.56822i) q^{57} +6.08436 q^{58} +3.53472i q^{59} +(-0.165634 + 0.404450i) q^{60} -2.10168i q^{61} +1.40614i q^{62} +(2.10426 - 2.13824i) q^{63} -1.00000 q^{64} -0.782353 q^{65} +(-8.81805 - 3.61126i) q^{66} -5.88882i q^{67} -0.471124 q^{68} +(-7.61793 + 3.31167i) q^{69} -0.252332 q^{70} -15.2386i q^{71} +(-2.10426 + 2.13824i) q^{72} -3.34062 q^{73} -5.87175 q^{74} +(-3.24028 + 7.91218i) q^{75} -2.38906i q^{76} -5.50149i q^{77} +(-4.96961 - 2.03521i) q^{78} +13.9496i q^{79} +0.252332 q^{80} +(0.144138 + 8.99885i) q^{81} +4.64674 q^{82} -9.18343 q^{83} +(-1.60285 - 0.656415i) q^{84} +0.118880 q^{85} -5.09258 q^{86} +(-9.75230 - 3.99386i) q^{87} +5.50149i q^{88} -12.9856 q^{89} +(0.530973 - 0.539546i) q^{90} -3.10049i q^{91} +(3.43621 + 3.34552i) q^{92} +(0.923009 - 2.25382i) q^{93} -4.02078 q^{94} +0.602837i q^{95} +(1.60285 + 0.656415i) q^{96} -17.8515i q^{97} -1.00000i q^{98} +(11.7635 + 11.5766i) 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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