LMFDB - Embedded newform 966.2.l.d.47.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, 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:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.845576 - 1.51162i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.37030 - 2.37343i) q^{5} +(-1.48810 + 0.886316i) q^{6} +(-2.52742 + 0.782396i) q^{7} -1.00000i q^{8} +(-1.57000 - 2.55638i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.845576 - 1.51162i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.37030 - 2.37343i) q^{5} +(-1.48810 + 0.886316i) q^{6} +(-2.52742 + 0.782396i) q^{7} -1.00000i q^{8} +(-1.57000 - 2.55638i) q^{9} +(-2.37343 + 1.37030i) q^{10} +(3.00395 - 1.73433i) q^{11} +(1.73189 - 0.0235212i) q^{12} -0.435804i q^{13} +(2.58001 + 0.586136i) q^{14} +(-2.42904 - 4.07829i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.760820 - 1.31778i) q^{17} +(0.0814724 + 2.99889i) q^{18} +(-1.05371 - 0.608361i) q^{19} +2.74060 q^{20} +(-0.954439 + 4.48208i) q^{21} -3.46866 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.51162 - 0.845576i) q^{24} +(-1.25545 - 2.17451i) q^{25} +(-0.217902 + 0.377417i) q^{26} +(-5.19184 + 0.211639i) q^{27} +(-1.94128 - 1.79761i) q^{28} -4.66508i q^{29} +(0.0644624 + 4.74643i) q^{30} +(0.180650 - 0.104298i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.0815872 - 6.00734i) q^{33} +1.52164i q^{34} +(-1.60637 + 7.07078i) q^{35} +(1.42889 - 2.63785i) q^{36} +(-0.00946499 + 0.0163938i) q^{37} +(0.608361 + 1.05371i) q^{38} +(-0.658771 - 0.368505i) q^{39} +(-2.37343 - 1.37030i) q^{40} -8.06897 q^{41} +(3.06761 - 3.40438i) q^{42} -4.20542 q^{43} +(3.00395 + 1.73433i) q^{44} +(-8.21878 + 0.223284i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.71464 - 2.96985i) q^{47} +(0.886316 + 1.48810i) q^{48} +(5.77571 - 3.95489i) q^{49} +2.51090i q^{50} +(-2.63531 + 0.0357908i) q^{51} +(0.377417 - 0.217902i) q^{52} +(-0.785507 + 0.453513i) q^{53} +(4.60209 + 2.41264i) q^{54} -9.50622i q^{55} +(0.782396 + 2.52742i) q^{56} +(-1.81061 + 1.07840i) q^{57} +(-2.33254 + 4.04008i) q^{58} +(3.25061 + 5.63022i) q^{59} +(2.31739 - 4.14276i) q^{60} +(8.95335 + 5.16922i) q^{61} -0.208596 q^{62} +(5.96816 + 5.23269i) q^{63} -1.00000 q^{64} +(-1.03435 - 0.597183i) q^{65} +(-2.93301 + 5.24330i) q^{66} +(1.36737 + 2.36835i) q^{67} +(0.760820 - 1.31778i) q^{68} +(-1.48810 + 0.886316i) q^{69} +(4.92654 - 5.32029i) q^{70} +3.46373i q^{71} +(-2.55638 + 1.57000i) q^{72} +(7.02012 - 4.05307i) q^{73} +(0.0163938 - 0.00946499i) q^{74} +(-4.34861 + 0.0590596i) q^{75} -1.21672i q^{76} +(-6.23531 + 6.73366i) q^{77} +(0.386260 + 0.648520i) q^{78} +(-1.10560 + 1.91495i) q^{79} +(1.37030 + 2.37343i) q^{80} +(-4.07018 + 8.02706i) q^{81} +(6.98793 + 4.03448i) q^{82} -8.99307 q^{83} +(-4.35882 + 1.41447i) q^{84} -4.17021 q^{85} +(3.64200 + 2.10271i) q^{86} +(-7.05184 - 3.94468i) q^{87} +(-1.73433 - 3.00395i) q^{88} +(2.28463 - 3.95710i) q^{89} +(7.22931 + 3.91602i) q^{90} +(0.340971 + 1.10146i) q^{91} -1.00000i q^{92} +(-0.00490644 - 0.361266i) q^{93} +(-2.96985 + 1.71464i) q^{94} +(-2.88781 + 1.66728i) q^{95} +(-0.0235212 - 1.73189i) q^{96} -13.7096i q^{97} +(-6.97936 + 0.537175i) q^{98} +(-9.14982 - 4.95633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.845576	−	1.51162i	0.488193	−	0.872736i
$3$	0.845576	−	1.51162i	0.488193	−	0.872736i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.37030	−	2.37343i	0.612817	−	1.06143i	−0.377946	−	0.925828i	$-0.623369\pi$
$5$	1.37030	−	2.37343i	0.612817	−	1.06143i	0.990763	−	0.135603i	$-0.0432972\pi$
$6$	−1.48810	+	0.886316i	−0.607515	+	0.361837i
$7$	−2.52742	+	0.782396i	−0.955275	+	0.295718i
$7$	−2.52742	+	0.782396i	−0.955275	+	0.295718i
$8$		−	1.00000i		−	0.353553i
$9$	−1.57000	−	2.55638i	−0.523335	−	0.852127i
$10$	−2.37343	+	1.37030i	−0.750545	+	0.433327i
$11$	3.00395	−	1.73433i	0.905724	−	0.522920i	0.0266714	−	0.999644i	$-0.491509\pi$
$11$	3.00395	−	1.73433i	0.905724	−	0.522920i	0.879053	+	0.476724i	$0.158176\pi$
$12$	1.73189	−	0.0235212i	0.499954	−	0.00679000i
$13$		−	0.435804i		−	0.120870i	−0.998172	−	0.0604351i	$-0.980751\pi$
$13$		−	0.435804i		−	0.120870i	0.998172	−	0.0604351i	$-0.0192488\pi$
$14$	2.58001	+	0.586136i	0.689536	+	0.156651i
$15$	−2.42904	−	4.07829i	−0.627175	−	1.05301i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.760820	−	1.31778i	−0.184526	−	0.319608i	0.758891	−	0.651218i	$-0.225742\pi$
$17$	−0.760820	−	1.31778i	−0.184526	−	0.319608i	−0.943417	+	0.331610i	$0.892408\pi$
$18$	0.0814724	+	2.99889i	0.0192032	+	0.706846i
$19$	−1.05371	−	0.608361i	−0.241738	−	0.139568i	0.374237	−	0.927333i	$-0.377905\pi$
$19$	−1.05371	−	0.608361i	−0.241738	−	0.139568i	−0.615975	+	0.787765i	$0.711238\pi$
$20$	2.74060			0.612817
$21$	−0.954439	+	4.48208i	−0.208276	+	0.978070i
$22$	−3.46866			−0.739521
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	−1.51162	−	0.845576i	−0.308559	−	0.172602i
$25$	−1.25545	−	2.17451i	−0.251090	−	0.434901i
$26$	−0.217902	+	0.377417i	−0.0427341	+	0.0740176i
$27$	−5.19184	+	0.211639i	−0.999170	+	0.0407300i
$28$	−1.94128	−	1.79761i	−0.366868	−	0.339717i
$29$		−	4.66508i		−	0.866284i	−0.901326	−	0.433142i	$-0.857405\pi$
$29$		−	4.66508i		−	0.866284i	0.901326	−	0.433142i	$-0.142595\pi$
$30$	0.0644624	+	4.74643i	0.0117692	+	0.866575i
$31$	0.180650	−	0.104298i	0.0324456	−	0.0187325i	−0.483689	−	0.875240i	$-0.660704\pi$
$31$	0.180650	−	0.104298i	0.0324456	−	0.0187325i	0.516135	+	0.856507i	$0.327370\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.0815872	−	6.00734i	−0.0142025	−	1.04574i
$34$			1.52164i			0.260959i
$35$	−1.60637	+	7.07078i	−0.271525	+	1.19518i
$36$	1.42889	−	2.63785i	0.238148	−	0.439642i
$37$	−0.00946499	+	0.0163938i	−0.00155603	+	0.00269513i	−0.866802	−	0.498652i	$-0.833829\pi$
$37$	−0.00946499	+	0.0163938i	−0.00155603	+	0.00269513i	0.865246	+	0.501347i	$0.167162\pi$
$38$	0.608361	+	1.05371i	0.0986892	+	0.170935i
$39$	−0.658771	−	0.368505i	−0.105488	−	0.0590080i
$40$	−2.37343	−	1.37030i	−0.375272	−	0.216664i
$41$	−8.06897			−1.26016			−0.630080	−	0.776530i	$-0.716978\pi$
$41$	−8.06897			−1.26016			−0.630080	+	0.776530i	$0.716978\pi$
$42$	3.06761	−	3.40438i	0.473342	−	0.525307i
$43$	−4.20542			−0.641321			−0.320660	−	0.947194i	$-0.603905\pi$
$43$	−4.20542			−0.641321			−0.320660	+	0.947194i	$0.603905\pi$
$44$	3.00395	+	1.73433i	0.452862	+	0.261460i
$45$	−8.21878	+	0.223284i	−1.22518	+	0.0332852i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	1.71464	−	2.96985i	0.250107	−	0.433197i	−0.713448	−	0.700708i	$-0.752868\pi$
$47$	1.71464	−	2.96985i	0.250107	−	0.433197i	0.963555	+	0.267510i	$0.0862010\pi$
$48$	0.886316	+	1.48810i	0.127929	+	0.214789i
$49$	5.77571	−	3.95489i	0.825102	−	0.564984i
$50$			2.51090i			0.355095i
$51$	−2.63531	+	0.0357908i	−0.369018	+	0.00501172i
$52$	0.377417	−	0.217902i	0.0523383	−	0.0302176i
$53$	−0.785507	+	0.453513i	−0.107898	+	0.0622948i	−0.552978	−	0.833196i	$-0.686509\pi$
$53$	−0.785507	+	0.453513i	−0.107898	+	0.0622948i	0.445080	+	0.895491i	$0.353175\pi$
$54$	4.60209	+	2.41264i	0.626264	+	0.328318i
$55$		−	9.50622i		−	1.28182i
$56$	0.782396	+	2.52742i	0.104552	+	0.337741i
$57$	−1.81061	+	1.07840i	−0.239821	+	0.142838i
$58$	−2.33254	+	4.04008i	−0.306278	+	0.530488i
$59$	3.25061	+	5.63022i	0.423193	+	0.732992i	0.996250	−	0.0865235i	$-0.0275758\pi$
$59$	3.25061	+	5.63022i	0.423193	+	0.732992i	−0.573056	+	0.819516i	$0.694242\pi$
$60$	2.31739	−	4.14276i	0.299173	−	0.534828i
$61$	8.95335	+	5.16922i	1.14636	+	0.661851i	0.947997	−	0.318278i	$-0.103105\pi$
$61$	8.95335	+	5.16922i	1.14636	+	0.661851i	0.198362	+	0.980129i	$0.436438\pi$
$62$	−0.208596			−0.0264918
$63$	5.96816	+	5.23269i	0.751918	+	0.659257i
$64$	−1.00000			−0.125000
$65$	−1.03435	−	0.597183i	−0.128295	−	0.0740714i
$66$	−2.93301	+	5.24330i	−0.361029	+	0.645406i
$67$	1.36737	+	2.36835i	0.167051	+	0.289340i	0.937382	−	0.348304i	$-0.113242\pi$
$67$	1.36737	+	2.36835i	0.167051	+	0.289340i	−0.770331	+	0.637644i	$0.779909\pi$
$68$	0.760820	−	1.31778i	0.0922629	−	0.159804i
$69$	−1.48810	+	0.886316i	−0.179146	+	0.106700i
$70$	4.92654	−	5.32029i	0.588835	−	0.635896i
$71$			3.46373i			0.411069i	0.978650	+	0.205534i	$0.0658932\pi$
$71$			3.46373i			0.411069i	−0.978650	+	0.205534i	$0.934107\pi$
$72$	−2.55638	+	1.57000i	−0.301272	+	0.185027i
$73$	7.02012	−	4.05307i	0.821643	−	0.474376i	−0.0293400	−	0.999569i	$-0.509341\pi$
$73$	7.02012	−	4.05307i	0.821643	−	0.474376i	0.850983	+	0.525194i	$0.176007\pi$
$74$	0.0163938	−	0.00946499i	0.00190574	−	0.00110028i
$75$	−4.34861	+	0.0590596i	−0.502134	+	0.00681961i
$76$		−	1.21672i		−	0.139568i
$77$	−6.23531	+	6.73366i	−0.710579	+	0.767372i
$78$	0.386260	+	0.648520i	0.0437353	+	0.0734304i
$79$	−1.10560	+	1.91495i	−0.124389	+	0.215449i	−0.921494	−	0.388392i	$-0.873031\pi$
$79$	−1.10560	+	1.91495i	−0.124389	+	0.215449i	0.797105	+	0.603841i	$0.206364\pi$
$80$	1.37030	+	2.37343i	0.153204	+	0.265358i
$81$	−4.07018	+	8.02706i	−0.452242	+	0.891895i
$82$	6.98793	+	4.03448i	0.771688	+	0.445534i
$83$	−8.99307			−0.987118			−0.493559	−	0.869712i	$-0.664304\pi$
$83$	−8.99307			−0.987118			−0.493559	+	0.869712i	$0.664304\pi$
$84$	−4.35882	+	1.41447i	−0.475586	+	0.154332i
$85$	−4.17021			−0.452323
$86$	3.64200	+	2.10271i	0.392727	+	0.226741i
$87$	−7.05184	−	3.94468i	−0.756037	−	0.422914i
$88$	−1.73433	−	3.00395i	−0.184880	−	0.320222i
$89$	2.28463	−	3.95710i	0.242171	−	0.419452i	−0.719162	−	0.694843i	$-0.755474\pi$
$89$	2.28463	−	3.95710i	0.242171	−	0.419452i	0.961332	+	0.275391i	$0.0888073\pi$
$90$	7.22931	+	3.91602i	0.762036	+	0.412785i
$91$	0.340971	+	1.10146i	0.0357435	+	0.115464i
$92$		−	1.00000i		−	0.104257i
$93$	−0.00490644	−	0.361266i	−0.000508775	−	0.0374616i
$94$	−2.96985	+	1.71464i	−0.306317	+	0.176852i
$95$	−2.88781	+	1.66728i	−0.296283	+	0.171059i
$96$	−0.0235212	−	1.73189i	−0.00240063	−	0.176760i
$97$		−	13.7096i		−	1.39200i	−0.718042	−	0.696000i	$-0.754962\pi$
$97$		−	13.7096i		−	1.39200i	0.718042	−	0.696000i	$-0.245038\pi$
$98$	−6.97936	+	0.537175i	−0.705022	+	0.0542628i
$99$	−9.14982	−	4.95633i	−0.919592	−	0.498130i
$100$	1.25545	−	2.17451i	0.125545	−	0.217451i
$101$	−5.31566	−	9.20699i	−0.528928	−	0.916130i	−0.999431	−	0.0337317i	$-0.989261\pi$
$101$	−5.31566	−	9.20699i	−0.528928	−	0.916130i	0.470503	−	0.882398i	$-0.344073\pi$
$102$	2.30014	+	1.28666i	0.227748	+	0.127398i
$103$	14.5965	+	8.42729i	1.43824	+	0.830366i	0.997727	−	0.0673824i	$-0.0214648\pi$
$103$	14.5965	+	8.42729i	1.43824	+	0.830366i	0.440509	+	0.897748i	$0.354798\pi$
$104$	−0.435804			−0.0427341
$105$	9.33004	+	8.40710i	0.910519	+	0.820449i
$106$	0.907026			0.0880981
$107$	−14.9112	−	8.60896i	−1.44152	−	0.832260i	−0.443565	−	0.896242i	$-0.646287\pi$
$107$	−14.9112	−	8.60896i	−1.44152	−	0.832260i	−0.997951	+	0.0639822i	$0.979620\pi$
$108$	−2.77921	−	4.39045i	−0.267429	−	0.422471i
$109$	−5.24940	−	9.09223i	−0.502801	−	0.870878i	−0.999995	−	0.00323780i	$-0.998969\pi$
$109$	−5.24940	−	9.09223i	−0.502801	−	0.870878i	0.497193	−	0.867640i	$-0.334364\pi$
$110$	−4.75311	+	8.23263i	−0.453191	+	0.784950i
$111$	0.0167779	+	0.0281697i	0.00159249	+	0.00267375i
$112$	0.586136	−	2.58001i	0.0553847	−	0.243788i
$113$			7.78724i			0.732562i	0.930504	+	0.366281i	$0.119369\pi$
$113$			7.78724i			0.732562i	−0.930504	+	0.366281i	$0.880631\pi$
$114$	2.10723	−	0.0286188i	0.197360	−	0.00268040i
$115$	−2.37343	+	1.37030i	−0.221324	+	0.127781i
$116$	4.04008	−	2.33254i	0.375112	−	0.216571i
$117$	−1.11408	+	0.684214i	−0.102997	+	0.0632556i
$118$		−	6.50122i		−	0.598486i
$119$	2.95394	+	2.73532i	0.270787	+	0.250746i
$120$	−4.07829	+	2.42904i	−0.372296	+	0.221740i
$121$	0.515802	−	0.893396i	0.0468911	−	0.0812178i
$122$	−5.16922	−	8.95335i	−0.467999	−	0.810598i
$123$	−6.82292	+	12.1972i	−0.615202	+	1.09979i
$124$	0.180650	+	0.104298i	0.0162228	+	0.00936625i
$125$	6.82162			0.610145
$126$	−2.55224	−	7.51572i	−0.227371	−	0.669554i
$127$	−8.98092			−0.796928			−0.398464	−	0.917184i	$-0.630457\pi$
$127$	−8.98092			−0.796928			−0.398464	+	0.917184i	$0.630457\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.55600	+	6.35701i	−0.313088	+	0.559703i
$130$	0.597183	+	1.03435i	0.0523764	+	0.0907185i
$131$	−3.72178	+	6.44632i	−0.325174	+	0.563217i	−0.981548	−	0.191218i	$-0.938756\pi$
$131$	−3.72178	+	6.44632i	−0.325174	+	0.563217i	0.656374	+	0.754436i	$0.272089\pi$
$132$	5.16172	−	3.07433i	0.449270	−	0.267586i
$133$	3.13915	+	0.713165i	0.272199	+	0.0618392i
$134$		−	2.73474i		−	0.236245i
$135$	−6.61208	+	12.6125i	−0.569077	+	1.08551i
$136$	−1.31778	+	0.760820i	−0.112999	+	0.0652397i
$137$	−0.531957	+	0.307126i	−0.0454482	+	0.0262395i	−0.522552	−	0.852607i	$-0.675020\pi$
$137$	−0.531957	+	0.307126i	−0.0454482	+	0.0262395i	0.477104	+	0.878847i	$0.341687\pi$
$138$	1.73189	−	0.0235212i	0.147428	−	0.00200226i
$139$		−	17.6028i		−	1.49305i	−0.665356	−	0.746526i	$-0.731720\pi$
$139$		−	17.6028i		−	1.49305i	0.665356	−	0.746526i	$-0.268280\pi$
$140$	−6.92666	+	2.14424i	−0.585409	+	0.181221i
$141$	−3.03943	−	5.10313i	−0.255966	−	0.429761i
$142$	1.73186	−	2.99967i	0.145335	−	0.251727i
$143$	−0.755828	−	1.30913i	−0.0632055	−	0.109475i
$144$	2.99889	−	0.0814724i	0.249908	−	0.00678937i
$145$	−11.0723	−	6.39257i	−0.919500	−	0.530874i
$146$	−8.10613			−0.670868
$147$	−1.09449	−	12.0749i	−0.0902721	−	0.995917i
$148$	−0.0189300			−0.00155603
$149$	5.50079	+	3.17588i	0.450642	+	0.260179i	0.708101	−	0.706111i	$-0.249552\pi$
$149$	5.50079	+	3.17588i	0.450642	+	0.260179i	−0.257459	+	0.966289i	$0.582885\pi$
$150$	3.79554	+	2.12316i	0.309904	+	0.173355i
$151$	11.4470	+	19.8269i	0.931548	+	1.61349i	0.780678	+	0.624934i	$0.214874\pi$
$151$	11.4470	+	19.8269i	0.931548	+	1.61349i	0.150870	+	0.988554i	$0.451793\pi$
$152$	−0.608361	+	1.05371i	−0.0493446	+	0.0854673i
$153$	−2.17425	+	4.01386i	−0.175778	+	0.324502i
$154$	8.76677	−	2.71386i	0.706446	−	0.218689i
$155$		−	0.571680i		−	0.0459184i
$156$	−0.0102506	−	0.754765i	−0.000820708	−	0.0604295i
$157$	3.14379	−	1.81507i	0.250902	−	0.144858i	−0.369275	−	0.929320i	$-0.620394\pi$
$157$	3.14379	−	1.81507i	0.250902	−	0.144858i	0.620177	+	0.784462i	$0.287061\pi$
$158$	1.91495	−	1.10560i	0.152345	−	0.0879567i
$159$	0.0213344	+	1.57087i	0.00169193	+	0.124578i
$160$		−	2.74060i		−	0.216664i
$161$	2.58001	+	0.586136i	0.203333	+	0.0461940i
$162$	7.53840	−	4.91655i	0.592273	−	0.386281i
$163$	−10.3727	+	17.9660i	−0.812452	+	1.40721i	0.0986911	+	0.995118i	$0.468534\pi$
$163$	−10.3727	+	17.9660i	−0.812452	+	1.40721i	−0.911143	+	0.412090i	$0.864799\pi$
$164$	−4.03448	−	6.98793i	−0.315040	−	0.545666i
$165$	−14.3698	−	8.03823i	−1.11869	−	0.625775i
$166$	7.78823	+	4.49654i	0.604484	+	0.348999i
$167$	25.6239			1.98284			0.991419	−	0.130719i	$-0.0417285\pi$
$167$	25.6239			1.98284			0.991419	+	0.130719i	$0.0417285\pi$
$168$	4.48208	+	0.954439i	0.345800	+	0.0736366i
$169$	12.8101			0.985390
$170$	3.61151	+	2.08510i	0.276990	+	0.159920i
$171$	0.0991293	+	3.64882i	0.00758061	+	0.279032i
$172$	−2.10271	−	3.64200i	−0.160330	−	0.277700i
$173$	5.11367	−	8.85714i	0.388785	−	0.673396i	−0.603501	−	0.797362i	$-0.706228\pi$
$173$	5.11367	−	8.85714i	0.388785	−	0.673396i	0.992286	+	0.123966i	$0.0395615\pi$
$174$	4.13473	+	6.94211i	0.313453	+	0.526280i
$175$	4.87438	+	4.51363i	0.368468	+	0.341199i
$176$			3.46866i			0.261460i
$177$	11.2594	−	0.152917i	0.846309	−	0.0114939i
$178$	−3.95710	+	2.28463i	−0.296597	+	0.171240i
$179$	17.8312	−	10.2948i	1.33276	−	0.769471i	0.347041	−	0.937850i	$-0.387187\pi$
$179$	17.8312	−	10.2948i	1.33276	−	0.769471i	0.985722	+	0.168379i	$0.0538533\pi$
$180$	−4.30276	−	7.00603i	−0.320709	−	0.522198i
$181$		−	9.82577i		−	0.730344i	−0.930940	−	0.365172i	$-0.881010\pi$
$181$		−	9.82577i		−	0.730344i	0.930940	−	0.365172i	$-0.118990\pi$
$182$	0.255440	−	1.12438i	0.0189345	−	0.0833444i
$183$	15.3846	−	9.16312i	1.13727	−	0.677357i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	0.0259398	+	0.0449290i	0.00190713	+	0.00330325i
$186$	−0.176384	+	0.315319i	−0.0129331	+	0.0231203i
$187$	−4.57092	−	2.63902i	−0.334259	−	0.192985i
$188$	3.42929			0.250107
$189$	12.9564	−	4.59697i	0.942438	−	0.334381i
$190$	3.33455			0.241914
$191$	15.8766	+	9.16635i	1.14879	+	0.663254i	0.948592	−	0.316501i	$-0.102508\pi$
$191$	15.8766	+	9.16635i	1.14879	+	0.663254i	0.200198	+	0.979755i	$0.435842\pi$
$192$	−0.845576	+	1.51162i	−0.0610242	+	0.109092i
$193$	−10.7816	−	18.6742i	−0.776075	−	1.34420i	−0.934188	−	0.356780i	$-0.883875\pi$
$193$	−10.7816	−	18.6742i	−0.776075	−	1.34420i	0.158113	−	0.987421i	$-0.449459\pi$
$194$	−6.85480	+	11.8729i	−0.492146	+	0.852422i
$195$	−1.77734	+	1.05858i	−0.127278	+	0.0758068i
$196$	6.31289	+	3.02447i	0.450921	+	0.216034i
$197$		−	6.82329i		−	0.486139i	−0.970009	−	0.243070i	$-0.921846\pi$
$197$		−	6.82329i		−	0.486139i	0.970009	−	0.243070i	$-0.0781543\pi$
$198$	5.44581	+	8.86722i	0.387017	+	0.630166i
$199$	21.2578	−	12.2732i	1.50692	−	0.870022i	0.506954	−	0.861973i	$-0.330771\pi$
$199$	21.2578	−	12.2732i	1.50692	−	0.870022i	0.999968	−	0.00804890i	$-0.00256207\pi$
$200$	−2.17451	+	1.25545i	−0.153761	+	0.0887738i
$201$	4.73627	−	0.0643244i	0.334071	−	0.00453709i
$202$			10.6313i			0.748017i
$203$	3.64994	+	11.7906i	0.256175	+	0.827540i
$204$	−1.34865	−	2.26435i	−0.0944246	−	0.158536i
$205$	−11.0569	+	19.1511i	−0.772249	+	1.33757i
$206$	−8.42729	−	14.5965i	−0.587157	−	1.01699i
$207$	0.0814724	+	2.99889i	0.00566273	+	0.208438i
$208$	0.377417	+	0.217902i	0.0261692	+	0.0151088i
$209$	−4.22040			−0.291931
$210$	−3.87651	−	11.9458i	−0.267504	−	0.824337i
$211$	7.16890			0.493527			0.246764	−	0.969076i	$-0.420633\pi$
$211$	7.16890			0.493527			0.246764	+	0.969076i	$0.420633\pi$
$212$	−0.785507	−	0.453513i	−0.0539489	−	0.0311474i
$213$	5.23584	+	2.92884i	0.358754	+	0.200681i
$214$	8.60896	+	14.9112i	0.588497	+	1.01931i
$215$	−5.76269	+	9.98128i	−0.393013	+	0.680718i
$216$	0.211639	+	5.19184i	0.0144002	+	0.353260i
$217$	−0.374976	+	0.404945i	−0.0254550	+	0.0274895i
$218$			10.4988i			0.711069i
$219$	−0.190666	−	14.0389i	−0.0128840	−	0.948664i
$220$	8.23263	−	4.75311i	0.555044	−	0.320455i
$221$	−0.574293	+	0.331568i	−0.0386311	+	0.0223037i
$222$	−0.000445256	−	0.0327846i	−2.98836e−5	−	0.00220036i
$223$		−	21.5279i		−	1.44162i	−0.693134	−	0.720809i	$-0.743771\pi$
$223$		−	21.5279i		−	1.44162i	0.693134	−	0.720809i	$-0.256229\pi$
$224$	−1.79761	+	1.94128i	−0.120108	+	0.129708i
$225$	−3.58780	+	6.62340i	−0.239187	+	0.441560i
$226$	3.89362	−	6.74395i	0.259000	−	0.448601i
$227$	12.4069	+	21.4893i	0.823474	+	1.42630i	0.903080	+	0.429472i	$0.141300\pi$
$227$	12.4069	+	21.4893i	0.823474	+	1.42630i	−0.0796069	+	0.996826i	$0.525366\pi$
$228$	−1.83922	−	1.02883i	−0.121806	−	0.0681360i
$229$	7.00295	+	4.04316i	0.462768	+	0.267179i	0.713207	−	0.700953i	$-0.247242\pi$
$229$	7.00295	+	4.04316i	0.462768	+	0.267179i	−0.250439	+	0.968132i	$0.580575\pi$
$230$	2.74060			0.180710
$231$	4.90632	+	15.1192i	0.322812	+	0.994774i
$232$	−4.66508			−0.306278
$233$	−15.1865	−	8.76791i	−0.994899	−	0.574405i	−0.0881639	−	0.996106i	$-0.528100\pi$
$233$	−15.1865	−	8.76791i	−0.994899	−	0.574405i	−0.906735	+	0.421701i	$0.861433\pi$
$234$	1.30693	−	0.0355060i	0.0854366	−	0.00232110i
$235$	−4.69916	−	8.13918i	−0.306539	−	0.530942i
$236$	−3.25061	+	5.63022i	−0.211597	+	0.366496i
$237$	1.95982	+	3.29048i	0.127304	+	0.213740i
$238$	−1.19052	−	3.84582i	−0.0771702	−	0.249288i
$239$		−	10.5376i		−	0.681622i	−0.940132	−	0.340811i	$-0.889298\pi$
$239$		−	10.5376i		−	0.681622i	0.940132	−	0.340811i	$-0.110702\pi$
$240$	4.74643	−	0.0644624i	0.306380	−	0.00416103i
$241$	7.85333	−	4.53412i	0.505877	−	0.292068i	−0.225260	−	0.974299i	$-0.572323\pi$
$241$	7.85333	−	4.53412i	0.505877	−	0.292068i	0.731137	+	0.682230i	$0.238990\pi$
$242$	−0.893396	+	0.515802i	−0.0574297	+	0.0331570i
$243$	8.69224	+	12.9401i	0.557607	+	0.830105i
$244$			10.3384i			0.661851i
$245$	−1.47218	−	19.1276i	−0.0940543	−	1.22202i
$246$	12.0074	−	7.15165i	0.765566	−	0.455973i
$247$	−0.265126	+	0.459212i	−0.0168696	+	0.0292189i
$248$	−0.104298	−	0.180650i	−0.00662294	−	0.0114713i
$249$	−7.60432	+	13.5941i	−0.481904	+	0.861493i
$250$	−5.90770	−	3.41081i	−0.373636	−	0.215719i
$251$	12.9843			0.819563			0.409782	−	0.912184i	$-0.365605\pi$
$251$	12.9843			0.819563			0.409782	+	0.912184i	$0.365605\pi$
$252$	−1.54756	+	7.78493i	−0.0974871	+	0.490404i
$253$	−3.46866			−0.218073
$254$	7.77770	+	4.49046i	0.488017	+	0.281756i
$255$	−3.52623	+	6.30378i	−0.220821	+	0.394758i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.19925	+	2.07716i	−0.0748072	+	0.129570i	−0.901002	−	0.433814i	$-0.857167\pi$
$257$	−1.19925	+	2.07716i	−0.0748072	+	0.129570i	0.826195	+	0.563384i	$0.190501\pi$
$258$	6.25809	−	3.72733i	0.389612	−	0.232053i
$259$	0.0110955	−	0.0488395i	0.000689443	−	0.00303474i
$260$		−	1.19437i		−	0.0740714i
$261$	−11.9257	+	7.32420i	−0.738184	+	0.453356i
$262$	6.44632	−	3.72178i	0.398255	−	0.229933i
$263$	14.7688	−	8.52676i	0.910683	−	0.525783i	0.0300318	−	0.999549i	$-0.490439\pi$
$263$	14.7688	−	8.52676i	0.910683	−	0.525783i	0.880651	+	0.473766i	$0.157106\pi$
$264$	−6.00734	+	0.0815872i	−0.369726	+	0.00502134i
$265$			2.48580i			0.152701i
$266$	−2.36200	−	2.18720i	−0.144824	−	0.134106i
$267$	−4.04981	−	6.79953i	−0.247844	−	0.416124i
$268$	−1.36737	+	2.36835i	−0.0835254	+	0.144670i
$269$	−6.75121	−	11.6934i	−0.411628	−	0.712961i	0.583440	−	0.812157i	$-0.301706\pi$
$269$	−6.75121	−	11.6934i	−0.411628	−	0.712961i	−0.995068	+	0.0991953i	$0.968373\pi$
$270$	12.0325	−	7.61670i	0.732273	−	0.463537i
$271$	24.6557	+	14.2350i	1.49773	+	0.864715i	0.999997	−	0.00261508i	$-0.000832408\pi$
$271$	24.6557	+	14.2350i	1.49773	+	0.864715i	0.497734	+	0.867330i	$0.334166\pi$
$272$	1.52164			0.0922629
$273$	1.95331	+	0.415948i	0.118220	+	0.0251743i
$274$	0.614251			0.0371083
$275$	−7.54262	−	4.35474i	−0.454837	−	0.262600i
$276$	−1.51162	−	0.845576i	−0.0909890	−	0.0508977i
$277$	−3.00910	−	5.21192i	−0.180799	−	0.313154i	0.761354	−	0.648337i	$-0.224535\pi$
$277$	−3.00910	−	5.21192i	−0.180799	−	0.313154i	−0.942153	+	0.335183i	$0.891202\pi$
$278$	−8.80142	+	15.2445i	−0.527874	+	0.914304i
$279$	−0.550247	−	0.298061i	−0.0329424	−	0.0178445i
$280$	7.07078	+	1.60637i	0.422560	+	0.0959987i
$281$		−	3.00152i		−	0.179056i	−0.995984	−	0.0895278i	$-0.971464\pi$
$281$		−	3.00152i		−	0.179056i	0.995984	−	0.0895278i	$-0.0285358\pi$
$282$	0.0806611	+	5.93916i	0.00480330	+	0.353672i
$283$	−7.32745	+	4.23050i	−0.435572	+	0.251477i	−0.701717	−	0.712455i	$-0.747583\pi$
$283$	−7.32745	+	4.23050i	−0.435572	+	0.251477i	0.266146	+	0.963933i	$0.414250\pi$
$284$	−2.99967	+	1.73186i	−0.177998	+	0.102767i
$285$	0.0784328	+	5.77508i	0.00464596	+	0.342086i
$286$			1.51166i			0.0893861i
$287$	20.3937	−	6.31312i	1.20380	−	0.372652i
$288$	−2.63785	−	1.42889i	−0.155437	−	0.0841981i
$289$	7.34231	−	12.7172i	0.431900	−	0.748073i
$290$	6.39257	+	11.0723i	0.375384	+	0.650185i
$291$	−20.7237	−	11.5925i	−1.21485	−	0.679565i
$292$	7.02012	+	4.05307i	0.410821	+	0.237188i
$293$	−16.8122			−0.982177			−0.491088	−	0.871110i	$-0.663401\pi$
$293$	−16.8122			−0.982177			−0.491088	+	0.871110i	$0.663401\pi$
$294$	−5.08957	+	11.0044i	−0.296830	+	0.641788i
$295$	17.8173			1.03736
$296$	0.0163938	+	0.00946499i	0.000952872	+	0.000550141i
$297$	−15.2290	+	9.64012i	−0.883674	+	0.559376i
$298$	−3.17588	−	5.50079i	−0.183974	−	0.318652i
$299$	−0.217902	+	0.377417i	−0.0126016	+	0.0218266i
$300$	−2.22545	−	3.73648i	−0.128487	−	0.215726i
$301$	10.6289	−	3.29030i	0.612638	−	0.189650i
$302$		−	22.8941i		−	1.31741i
$303$	−18.4123	+	0.250062i	−1.05776	+	0.0143657i
$304$	1.05371	−	0.608361i	0.0604345	−	0.0348919i
$305$	24.5376	−	14.1668i	1.40502	−	0.811187i
$306$	3.88989	−	2.38898i	0.222370	−	0.136569i
$307$		−	24.6237i		−	1.40535i	−0.711510	−	0.702676i	$-0.751988\pi$
$307$		−	24.6237i		−	1.40535i	0.711510	−	0.702676i	$-0.248012\pi$
$308$	−8.94917	−	2.03311i	−0.509926	−	0.115847i
$309$	25.0813	−	14.9385i	1.42683	−	0.849821i
$310$	−0.285840	+	0.495089i	−0.0162346	+	0.0281192i
$311$	14.0970	+	24.4167i	0.799366	+	1.38454i	0.920029	+	0.391850i	$0.128165\pi$
$311$	14.0970	+	24.4167i	0.799366	+	1.38454i	−0.120663	+	0.992694i	$0.538502\pi$
$312$	−0.368505	+	0.658771i	−0.0208625	+	0.0372956i
$313$	23.5943	+	13.6222i	1.33363	+	0.769970i	0.985854	−	0.167609i	$-0.0536047\pi$
$313$	23.5943	+	13.6222i	1.33363	+	0.769970i	0.347773	+	0.937579i	$0.386938\pi$
$314$	−3.63014			−0.204861
$315$	20.5976	−	6.99467i	1.16054	−	0.394105i
$316$	−2.21120			−0.124389
$317$	4.97190	+	2.87053i	0.279250	+	0.161225i	0.633084	−	0.774083i	$-0.281789\pi$
$317$	4.97190	+	2.87053i	0.279250	+	0.161225i	−0.353834	+	0.935308i	$0.615122\pi$
$318$	0.766959	−	1.37108i	0.0430089	−	0.0768864i
$319$	−8.09079	−	14.0137i	−0.452997	−	0.784614i
$320$	−1.37030	+	2.37343i	−0.0766022	+	0.132679i
$321$	−25.6220	+	15.2605i	−1.43008	+	0.851759i
$322$	−1.94128	−	1.79761i	−0.108184	−	0.100177i
$323$			1.85141i			0.103015i
$324$	−8.98672	+	0.488654i	−0.499262	+	0.0271475i
$325$	−0.947658	+	0.547131i	−0.0525666	+	0.0303494i
$326$	17.9660	−	10.3727i	0.995046	−	0.574490i
$327$	−18.1828	+	0.246945i	−1.00551	+	0.0136561i
$328$			8.06897i			0.445534i
$329$	−2.01003	+	8.84760i	−0.110817	+	0.487784i
$330$	8.42551	+	14.1462i	0.463809	+	0.778724i
$331$	−3.41368	+	5.91267i	−0.187633	+	0.324990i	−0.944461	−	0.328625i	$-0.893415\pi$
$331$	−3.41368	+	5.91267i	−0.187633	+	0.324990i	0.756828	+	0.653614i	$0.226748\pi$
$332$	−4.49654	−	7.78823i	−0.246779	−	0.427435i
$333$	0.0567690	−	0.00154227i	0.00311092	−	8.45159e-5i
$334$	−22.1910	−	12.8120i	−1.21424	−	0.701039i
$335$	7.49483			0.409486
$336$	−3.40438	−	3.06761i	−0.185724	−	0.167352i
$337$	22.6179			1.23207			0.616037	−	0.787717i	$-0.288737\pi$
$337$	22.6179			1.23207			0.616037	+	0.787717i	$0.288737\pi$
$338$	−11.0939	−	6.40504i	−0.603426	−	0.348388i
$339$	11.7714	+	6.58470i	0.639333	+	0.357632i
$340$	−2.08510	−	3.61151i	−0.113081	−	0.195861i
$341$	0.361775	−	0.626613i	0.0195912	−	0.0339330i
$342$	1.73856	−	3.20954i	0.0940106	−	0.173552i
$343$	−11.5034	+	14.5146i	−0.621124	+	0.783712i
$344$			4.20542i			0.226741i
$345$	0.0644624	+	4.74643i	0.00347054	+	0.255539i
$346$	−8.85714	+	5.11367i	−0.476163	+	0.274913i
$347$	−13.8384	+	7.98958i	−0.742882	+	0.428903i	−0.823116	−	0.567873i	$-0.807766\pi$
$347$	−13.8384	+	7.98958i	−0.742882	+	0.428903i	0.0802344	+	0.996776i	$0.474433\pi$
$348$	−0.109728	−	8.07941i	−0.00588206	−	0.433102i
$349$			8.55471i			0.457923i	0.973435	+	0.228961i	$0.0735330\pi$
$349$			8.55471i			0.457923i	−0.973435	+	0.228961i	$0.926467\pi$
$350$	−1.96452	−	6.34611i	−0.105008	−	0.339214i
$351$	0.0922331	+	2.26262i	0.00492304	+	0.120770i
$352$	1.73433	−	3.00395i	0.0924401	−	0.160111i
$353$	−1.19637	−	2.07217i	−0.0636764	−	0.110291i	0.832430	−	0.554131i	$-0.186949\pi$
$353$	−1.19637	−	2.07217i	−0.0636764	−	0.110291i	−0.896106	+	0.443840i	$0.853616\pi$
$354$	−9.82739	−	5.49727i	−0.522320	−	0.292177i
$355$	8.22092	+	4.74635i	0.436321	+	0.251910i
$356$	4.56926			0.242171
$357$	6.63254	−	2.15232i	0.351031	−	0.113913i
$358$	−20.5896			−1.08820
$359$	−10.3163	−	5.95610i	−0.544472	−	0.314351i	0.202417	−	0.979299i	$-0.435120\pi$
$359$	−10.3163	−	5.95610i	−0.544472	−	0.314351i	−0.746889	+	0.664948i	$0.768454\pi$
$360$	0.223284	+	8.21878i	0.0117681	+	0.433168i
$361$	−8.75979	−	15.1724i	−0.461042	−	0.798548i
$362$	−4.91289	+	8.50937i	−0.258216	+	0.447243i
$363$	−0.914327	−	1.53513i	−0.0479897	−	0.0805736i
$364$	−0.783407	+	0.846019i	−0.0410617	+	0.0443435i
$365$		−	22.2157i		−	1.16282i
$366$	−17.9051	+	0.243173i	−0.935912	+	0.0127109i
$367$	−18.7139	+	10.8045i	−0.976856	+	0.563988i	−0.901320	−	0.433155i	$-0.857400\pi$
$367$	−18.7139	+	10.8045i	−0.976856	+	0.563988i	−0.0755369	+	0.997143i	$0.524067\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	12.6683	+	20.6274i	0.659486	+	1.07382i
$370$		−	0.0518795i		−	0.00269709i
$371$	1.63048	−	1.76080i	0.0846504	−	0.0914159i
$372$	0.310412	−	0.184882i	0.0160941	−	0.00958569i
$373$	−5.41610	+	9.38096i	−0.280435	+	0.485728i	−0.971492	−	0.237073i	$-0.923812\pi$
$373$	−5.41610	+	9.38096i	−0.280435	+	0.485728i	0.691057	+	0.722800i	$0.257145\pi$
$374$	2.63902	+	4.57092i	0.136461	+	0.236357i
$375$	5.76820	−	10.3117i	0.297869	−	0.532495i
$376$	−2.96985	−	1.71464i	−0.153158	−	0.0884260i
$377$	−2.03306			−0.104708
$378$	−13.5190	−	2.49709i	−0.695345	−	0.128437i
$379$	−21.6669			−1.11295			−0.556477	−	0.830863i	$-0.687847\pi$
$379$	−21.6669			−1.11295			−0.556477	+	0.830863i	$0.687847\pi$
$380$	−2.88781	−	1.66728i	−0.148141	−	0.0855294i
$381$	−7.59405	+	13.5758i	−0.389055	+	0.695507i
$382$	−9.16635	−	15.8766i	−0.468992	−	0.812317i
$383$	−8.29154	+	14.3614i	−0.423678	+	0.733832i	−0.996296	−	0.0859904i	$-0.972595\pi$
$383$	−8.29154	+	14.3614i	−0.423678	+	0.733832i	0.572618	+	0.819822i	$0.305928\pi$
$384$	1.48810	−	0.886316i	0.0759393	−	0.0452296i
$385$	7.43762	+	24.0262i	0.379056	+	1.22449i
$386$			21.5632i			1.09754i
$387$	6.60253	+	10.7507i	0.335625	+	0.546487i
$388$	11.8729	−	6.85480i	0.602753	−	0.348000i
$389$	19.6980	−	11.3727i	0.998729	−	0.576617i	0.0908572	−	0.995864i	$-0.471039\pi$
$389$	19.6980	−	11.3727i	0.998729	−	0.576617i	0.907872	+	0.419247i	$0.137706\pi$
$390$	2.06851	−	0.0280929i	0.104743	−	0.00142254i
$391$			1.52164i			0.0769526i
$392$	−3.95489	−	5.77571i	−0.199752	−	0.291718i
$393$	6.59735	+	11.0768i	0.332792	+	0.558750i
$394$	−3.41164	+	5.90914i	−0.171876	+	0.297698i
$395$	3.03001	+	5.24812i	0.152456	+	0.264062i
$396$	−0.282600	−	10.4021i	−0.0142012	−	0.522727i
$397$	−16.9159	−	9.76642i	−0.848986	−	0.490162i	0.0113226	−	0.999936i	$-0.496396\pi$
$397$	−16.9159	−	9.76642i	−0.848986	−	0.490162i	−0.860309	+	0.509774i	$0.829729\pi$
$398$	−24.5463			−1.23040
$399$	3.73243	−	4.14218i	0.186855	−	0.207368i
$400$	2.51090			0.125545
$401$	12.3930	+	7.15511i	0.618877	+	0.357309i	0.776432	−	0.630201i	$-0.217028\pi$
$401$	12.3930	+	7.15511i	0.618877	+	0.357309i	−0.157554	+	0.987510i	$0.550361\pi$
$402$	−4.13389	−	2.31243i	−0.206180	−	0.115333i
$403$	−0.0454535	−	0.0787278i	−0.00226420	−	0.00392171i
$404$	5.31566	−	9.20699i	0.264464	−	0.458065i
$405$	13.4743	+	20.6598i	0.669544	+	1.02659i
$406$	2.73437	−	12.0359i	0.135705	−	0.597334i
$407$			0.0656616i			0.00325473i
$408$	0.0357908	+	2.63531i	0.00177191	+	0.130467i
$409$	1.19071	−	0.687456i	0.0588768	−	0.0339925i	−0.470273	−	0.882521i	$-0.655844\pi$
$409$	1.19071	−	0.687456i	0.0588768	−	0.0339925i	0.529149	+	0.848529i	$0.322511\pi$
$410$	19.1511	−	11.0569i	0.945807	−	0.546062i
$411$	0.0144479	+	1.06382i	0.000712665	+	0.0524742i
$412$			16.8546i			0.830366i
$413$	−12.6207	−	11.6867i	−0.621025	−	0.575064i
$414$	1.42889	−	2.63785i	0.0702261	−	0.129643i
$415$	−12.3232	+	21.3444i	−0.604923	+	1.04776i
$416$	−0.217902	−	0.377417i	−0.0106835	−	0.0185044i
$417$	−26.6088	−	14.8845i	−1.30304	−	0.728898i
$418$	3.65497	+	2.11020i	0.178770	+	0.103213i
$419$	−16.4251			−0.802421			−0.401210	−	0.915986i	$-0.631410\pi$
$419$	−16.4251			−0.802421			−0.401210	+	0.915986i	$0.631410\pi$
$420$	−2.61574	+	12.2836i	−0.127635	+	0.599378i
$421$	−11.5639			−0.563590			−0.281795	−	0.959475i	$-0.590930\pi$
$421$	−11.5639			−0.563590			−0.281795	+	0.959475i	$0.590930\pi$
$422$	−6.20845	−	3.58445i	−0.302222	−	0.174488i
$423$	−10.2841	+	0.279393i	−0.500029	+	0.0135845i
$424$	0.453513	+	0.785507i	0.0220245	+	0.0381476i
$425$	−1.91034	+	3.30881i	−0.0926653	+	0.160501i
$426$	−3.06995	−	5.15437i	−0.148740	−	0.249730i
$427$	−26.6733	−	6.05973i	−1.29081	−	0.293251i
$428$		−	17.2179i		−	0.832260i
$429$	−2.61802	+	0.0355560i	−0.126399	+	0.00171666i
$430$	9.98128	−	5.76269i	0.481340	−	0.277902i
$431$	2.68474	−	1.55004i	0.129319	−	0.0746626i	−0.433945	−	0.900940i	$-0.642879\pi$
$431$	2.68474	−	1.55004i	0.129319	−	0.0746626i	0.563264	+	0.826277i	$0.309545\pi$
$432$	2.41264	−	4.60209i	0.116078	−	0.221418i
$433$			21.8007i			1.04767i	0.851818	+	0.523837i	$0.175500\pi$
$433$			21.8007i			1.04767i	−0.851818	+	0.523837i	$0.824500\pi$
$434$	0.527211	−	0.163205i	0.0253069	−	0.00783408i
$435$	−19.0256	+	11.3317i	−0.912206	+	0.543312i
$436$	5.24940	−	9.09223i	0.251401	−	0.435439i
$437$	0.608361	+	1.05371i	0.0291019	+	0.0504059i
$438$	−6.85435	+	12.2534i	−0.327513	+	0.585491i
$439$	24.8166	+	14.3279i	1.18443	+	0.683833i	0.957036	−	0.289969i	$-0.0936449\pi$
$439$	24.8166	+	14.3279i	1.18443	+	0.683833i	0.227398	+	0.973802i	$0.426978\pi$
$440$	−9.50622			−0.453191
$441$	−19.1781	−	8.55574i	−0.913243	−	0.407416i
$442$	0.663136			0.0315422
$443$	25.5305	+	14.7401i	1.21299	+	0.700322i	0.963410	−	0.268032i	$-0.0863732\pi$
$443$	25.5305	+	14.7401i	1.21299	+	0.700322i	0.249583	+	0.968353i	$0.419707\pi$
$444$	−0.0160067	+	0.0286150i	−0.000759645	+	0.00135801i
$445$	−6.26127	−	10.8448i	−0.296813	−	0.514095i
$446$	−10.7640	+	18.6437i	−0.509689	+	0.882807i
$447$	9.45207	−	5.62967i	0.447068	−	0.266274i
$448$	2.52742	−	0.782396i	0.119409	−	0.0369647i
$449$		−	31.8252i		−	1.50193i	−0.660344	−	0.750963i	$-0.729590\pi$
$449$		−	31.8252i		−	1.50193i	0.660344	−	0.750963i	$-0.270410\pi$
$450$	6.41883	−	3.94213i	0.302586	−	0.185834i
$451$	−24.2388	+	13.9943i	−1.14136	+	0.658964i
$452$	−6.74395	+	3.89362i	−0.317209	+	0.183140i
$453$	39.6501	−	0.538497i	1.86292	−	0.0253008i
$454$		−	24.8138i		−	1.16457i
$455$	3.08147	+	0.700061i	0.144462	+	0.0328193i
$456$	1.07840	+	1.81061i	0.0505007	+	0.0847894i
$457$	−3.68965	+	6.39067i	−0.172595	+	0.298943i	−0.939326	−	0.343025i	$-0.888548\pi$
$457$	−3.68965	+	6.39067i	−0.172595	+	0.298943i	0.766732	+	0.641968i	$0.221882\pi$
$458$	−4.04316	−	7.00295i	−0.188924	−	0.327226i
$459$	4.22895	+	6.68068i	0.197390	+	0.311827i
$460$	−2.37343	−	1.37030i	−0.110662	−	0.0638906i
$461$	21.7224			1.01171			0.505856	−	0.862618i	$-0.331177\pi$
$461$	21.7224			1.01171			0.505856	+	0.862618i	$0.331177\pi$
$462$	3.31062	−	15.5468i	0.154024	−	0.723303i
$463$	−32.2342			−1.49805			−0.749025	−	0.662542i	$-0.769478\pi$
$463$	−32.2342			−1.49805			−0.749025	+	0.662542i	$0.769478\pi$
$464$	4.04008	+	2.33254i	0.187556	+	0.108285i
$465$	−0.864164	−	0.483398i	−0.0400746	−	0.0224171i
$466$	8.76791	+	15.1865i	0.406166	+	0.703500i
$467$	−0.354054	+	0.613240i	−0.0163837	+	0.0283774i	−0.874101	−	0.485744i	$-0.838549\pi$
$467$	−0.354054	+	0.613240i	−0.0163837	+	0.0283774i	0.857717	+	0.514122i	$0.171882\pi$
$468$	−1.14959	−	0.622716i	−0.0531397	−	0.0287850i
$469$	−5.30891	−	4.91600i	−0.245142	−	0.227000i
$470$			9.39832i			0.433512i
$471$	−0.0853854	−	6.28701i	−0.00393435	−	0.289690i
$472$	5.63022	−	3.25061i	0.259152	−	0.149621i
$473$	−12.6329	+	7.29359i	−0.580860	+	0.335360i
$474$	−0.0520101	−	3.82955i	−0.00238890	−	0.175897i
$475$			3.05507i			0.140176i
$476$	−0.891888	+	3.92584i	−0.0408796	+	0.179941i
$477$	2.39260	+	1.29604i	0.109550	+	0.0593416i
$478$	−5.26881	+	9.12585i	−0.240990	+	0.417407i
$479$	16.5330	+	28.6360i	0.755412	+	1.30841i	0.945169	+	0.326581i	$0.105897\pi$
$479$	16.5330	+	28.6360i	0.755412	+	1.30841i	−0.189757	+	0.981831i	$0.560770\pi$
$480$	−4.14276	−	2.31739i	−0.189090	−	0.105774i
$481$	0.00714450	+	0.00412488i	0.000325761	+	0.000188078i
$482$	−9.06824			−0.413047
$483$	3.06761	−	3.40438i	0.139581	−	0.154904i
$484$	1.03160			0.0468911
$485$	−32.5388	−	18.7863i	−1.47751	−	0.853041i
$486$	−1.05767	−	15.5525i	−0.0479771	−	0.705477i
$487$	−2.98815	−	5.17563i	−0.135406	−	0.234530i	0.790346	−	0.612660i	$-0.209901\pi$
$487$	−2.98815	−	5.17563i	−0.135406	−	0.234530i	−0.925753	+	0.378130i	$0.876567\pi$
$488$	5.16922	−	8.95335i	0.234000	−	0.405299i
$489$	18.3870	+	30.8712i	0.831487	+	1.39605i
$490$	−8.28888	+	17.3011i	−0.374453	+	0.781585i
$491$			5.24711i			0.236799i	0.992966	+	0.118399i	$0.0377763\pi$
$491$			5.24711i			0.236799i	−0.992966	+	0.118399i	$0.962224\pi$
$492$	−13.9746	+	0.189792i	−0.630022	+	0.00855649i
$493$	−6.14754	+	3.54929i	−0.276871	+	0.159852i
$494$	0.459212	−	0.265126i	0.0206609	−	0.0119286i
$495$	−24.3015	+	14.9248i	−1.09227	+	0.670820i
$496$			0.208596i			0.00936625i
$497$	−2.71000	−	8.75429i	−0.121560	−	0.392684i
$498$	13.3826	−	7.97070i	0.599689	−	0.357176i
$499$	18.0190	−	31.2098i	0.806641	−	1.39714i	−0.108537	−	0.994092i	$-0.534617\pi$
$499$	18.0190	−	31.2098i	0.806641	−	1.39714i	0.915178	−	0.403050i	$-0.132050\pi$
$500$	3.41081	+	5.90770i	0.152536	+	0.264200i
$501$	21.6670	−	38.7337i	0.968009	−	1.73049i
$502$	−11.2448	−	6.49216i	−0.501878	−	0.289759i
$503$	−27.3783			−1.22074			−0.610369	−	0.792117i	$-0.708979\pi$
$503$	−27.3783			−1.22074			−0.610369	+	0.792117i	$0.708979\pi$
$504$	5.23269	−	5.96816i	0.233082	−	0.265843i
$505$	−29.1362			−1.29655
$506$	3.00395	+	1.73433i	0.133542	+	0.0771004i
$507$	10.8319	−	19.3640i	0.481061	−	0.859985i
$508$	−4.49046	−	7.77770i	−0.199232	−	0.345080i
$509$	0.828354	−	1.43475i	0.0367161	−	0.0635942i	−0.847083	−	0.531460i	$-0.821644\pi$
$509$	0.828354	−	1.43475i	0.0367161	−	0.0635942i	0.883800	+	0.467866i	$0.154977\pi$
$510$	6.20569	−	3.69612i	0.274793	−	0.163667i
$511$	−14.5717	+	15.7363i	−0.644614	+	0.696134i
$512$			1.00000i			0.0441942i
$513$	5.59946	+	2.93551i	0.247222	+	0.129606i
$514$	2.07716	−	1.19925i	0.0916198	−	0.0528967i
$515$	40.0032	−	23.0959i	1.76275	−	1.01773i
$516$	−7.28333	+	0.0989167i	−0.320631	+	0.00435457i
$517$		−	11.8950i		−	0.523143i
$518$	−0.0340288	+	0.0367485i	−0.00149514	+	0.00161464i
$519$	−9.06465	−	15.2193i	−0.397894	−	0.668054i
$520$	−0.597183	+	1.03435i	−0.0261882	+	0.0453593i
$521$	2.85673	+	4.94801i	0.125156	+	0.216776i	0.921794	−	0.387680i	$-0.126724\pi$
$521$	2.85673	+	4.94801i	0.125156	+	0.216776i	−0.796638	+	0.604457i	$0.793390\pi$
$522$	13.9901	−	0.380076i	0.612329	−	0.0166355i
$523$	−0.405946	−	0.234373i	−0.0177508	−	0.0102484i	0.491098	−	0.871104i	$-0.336596\pi$
$523$	−0.405946	−	0.234373i	−0.0177508	−	0.0102484i	−0.508849	+	0.860856i	$0.669929\pi$
$524$	−7.44357			−0.325174
$525$	10.9446	−	3.55160i	0.477660	−	0.155005i
$526$	−17.0535			−0.743569
$527$	−0.274884	−	0.158704i	−0.0119741	−	0.00691326i
$528$	5.24330	+	2.93301i	0.228186	+	0.127643i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	1.24290	−	2.15276i	0.0539881	−	0.0935101i
$531$	9.28952	−	17.1493i	0.403131	−	0.744215i
$532$	0.951958	+	3.07517i	0.0412726	+	0.133325i
$533$			3.51649i			0.152316i
$534$	0.107475	+	7.91347i	0.00465089	+	0.342449i
$535$	−40.8656	+	23.5937i	−1.76677	+	1.02005i
$536$	2.36835	−	1.36737i	0.102297	−	0.0590613i
$537$	−0.484294	−	35.6590i	−0.0208988	−	1.53880i
$538$			13.5024i			0.582130i
$539$	10.4909	−	21.8973i	0.451874	−	0.943182i
$540$	−14.2288	+	0.580019i	−0.612309	+	0.0249600i
$541$	−16.5701	+	28.7003i	−0.712405	+	1.23392i	0.251547	+	0.967845i	$0.419061\pi$
$541$	−16.5701	+	28.7003i	−0.712405	+	1.23392i	−0.963952	+	0.266077i	$0.914273\pi$
$542$	−14.2350	−	24.6557i	−0.611446	−	1.05906i
$543$	−14.8529	−	8.30843i	−0.637397	−	0.356549i
$544$	−1.31778	−	0.760820i	−0.0564993	−	0.0326199i
$545$	−28.7730			−1.23250
$546$	−1.48364	−	1.33688i	−0.0634939	−	0.0572130i
$547$	−30.6968			−1.31250			−0.656249	−	0.754544i	$-0.727858\pi$
$547$	−30.6968			−1.31250			−0.656249	+	0.754544i	$0.727858\pi$
$548$	−0.531957	−	0.307126i	−0.0227241	−	0.0131198i
$549$	−0.842298	−	31.0039i	−0.0359484	−	1.32321i
$550$	4.35474	+	7.54262i	0.185687	+	0.321619i
$551$	−2.83805	+	4.91565i	−0.120905	+	0.209414i
$552$	0.886316	+	1.48810i	0.0377241	+	0.0633378i
$553$	1.29606	−	5.70490i	0.0551142	−	0.242597i
$554$			6.01820i			0.255689i
$555$	0.0898497	−	0.00122027i	0.00381391	−	5.17976e-5i
$556$	15.2445	−	8.80142i	0.646511	−	0.373263i
$557$	−10.5510	+	6.09161i	−0.447060	+	0.258110i	−0.706588	−	0.707626i	$-0.749766\pi$
$557$	−10.5510	+	6.09161i	−0.447060	+	0.258110i	0.259528	+	0.965736i	$0.416433\pi$
$558$	0.327497	+	0.533252i	0.0138641	+	0.0225744i
$559$			1.83274i			0.0775166i
$560$	−5.32029	−	4.92654i	−0.224823	−	0.208184i
$561$	−7.85427	+	4.67802i	−0.331608	+	0.197506i
$562$	−1.50076	+	2.59939i	−0.0633057	+	0.109649i
$563$	−6.35275	−	11.0033i	−0.267737	−	0.463733i	0.700540	−	0.713613i	$-0.252942\pi$
$563$	−6.35275	−	11.0033i	−0.267737	−	0.463733i	−0.968277	+	0.249879i	$0.919609\pi$
$564$	2.89972	−	5.18379i	0.122100	−	0.218277i
$565$	18.4825	+	10.6709i	0.777564	+	0.448927i
$566$	8.46101			0.355643
$567$	4.00671	−	23.4722i	0.168266	−	0.985742i
$568$	3.46373			0.145335
$569$	−25.7753	−	14.8814i	−1.08056	−	0.623859i	−0.149510	−	0.988760i	$-0.547770\pi$
$569$	−25.7753	−	14.8814i	−1.08056	−	0.623859i	−0.931046	+	0.364901i	$0.881103\pi$
$570$	2.81962	−	5.04058i	0.118101	−	0.211127i
$571$	10.6920	+	18.5190i	0.447445	+	0.774997i	0.998219	−	0.0596575i	$-0.0190009\pi$
$571$	10.6920	+	18.5190i	0.447445	+	0.774997i	−0.550774	+	0.834654i	$0.685668\pi$
$572$	0.755828	−	1.30913i	0.0316027	−	0.0547376i
$573$	27.2809	−	16.2486i	1.13968	−	0.678794i
$574$	−20.8180	−	4.72951i	−0.868927	−	0.197406i
$575$			2.51090i			0.104712i
$576$	1.57000	+	2.55638i	0.0654168	+	0.106516i
$577$	2.79488	−	1.61362i	0.116352	−	0.0671760i	−0.440694	−	0.897657i	$-0.645268\pi$
$577$	2.79488	−	1.61362i	0.116352	−	0.0671760i	0.557047	+	0.830481i	$0.311934\pi$
$578$	−12.7172	+	7.34231i	−0.528968	+	0.305400i
$579$	−37.3450	+	0.507192i	−1.55201	+	0.0210782i
$580$		−	12.7851i		−	0.530874i
$581$	22.7293	−	7.03614i	0.942969	−	0.291908i
$582$	12.1510	+	20.4013i	0.503676	+	0.845660i
$583$	−1.57308	+	2.72466i	−0.0651504	+	0.112844i
$584$	−4.05307	−	7.02012i	−0.167717	−	0.290495i
$585$	0.0973078	+	3.58177i	0.00402318	+	0.148088i
$586$	14.5598	+	8.40608i	0.601458	+	0.347252i
$587$	−30.8413			−1.27296			−0.636479	−	0.771294i	$-0.719610\pi$
$587$	−30.8413			−1.27296			−0.636479	+	0.771294i	$0.719610\pi$
$588$	9.90988	−	6.98528i	0.408677	−	0.288068i
$589$	−0.253804			−0.0104578
$590$	−15.4302	−	8.90863i	−0.635251	−	0.366762i
$591$	−10.3142	−	5.76961i	−0.424271	−	0.237330i
$592$	−0.00946499	−	0.0163938i	−0.000389009	−	0.000673783i
$593$	13.7391	−	23.7969i	0.564199	−	0.977221i	−0.432925	−	0.901430i	$-0.642518\pi$
$593$	13.7391	−	23.7969i	0.564199	−	0.977221i	0.997124	−	0.0757913i	$-0.0241483\pi$
$594$	18.0087	−	0.734104i	0.738907	−	0.0301207i
$595$	10.5399	−	3.26275i	0.432093	−	0.133760i
$596$			6.35177i			0.260179i
$597$	−0.577360	−	42.5116i	−0.0236298	−	1.73988i
$598$	0.377417	−	0.217902i	0.0154337	−	0.00891067i
$599$	17.0476	−	9.84243i	0.696546	−	0.402151i	−0.109514	−	0.993985i	$-0.534929\pi$
$599$	17.0476	−	9.84243i	0.696546	−	0.402151i	0.806060	+	0.591834i	$0.201596\pi$
$600$	0.0590596	+	4.34861i	0.00241110	+	0.177531i
$601$			9.65964i			0.394025i	0.980401	+	0.197013i	$0.0631240\pi$
$601$			9.65964i			0.394025i	−0.980401	+	0.197013i	$0.936876\pi$
$602$	−10.8500	−	2.46495i	−0.442214	−	0.100464i
$603$	3.90764	−	7.21384i	0.159131	−	0.293770i
$604$	−11.4470	+	19.8269i	−0.465774	+	0.806744i
$605$	−1.41361	−	2.44844i	−0.0574714	−	0.0995434i
$606$	16.0705	+	8.98959i	0.652821	+	0.365177i
$607$	−12.7673	−	7.37122i	−0.518210	−	0.299189i	0.217992	−	0.975951i	$-0.430049\pi$
$607$	−12.7673	−	7.37122i	−0.518210	−	0.299189i	−0.736202	+	0.676762i	$0.763383\pi$
$608$	−1.21672			−0.0493446
$609$	20.9093	+	4.45253i	0.847286	+	0.180426i
$610$	−28.3336			−1.14719
$611$	−1.29427	−	0.747249i	−0.0523607	−	0.0302304i
$612$	−4.56323	+	0.123972i	−0.184458	+	0.00501126i
$613$	13.4281	+	23.2582i	0.542356	+	0.939389i	0.998768	+	0.0496200i	$0.0158010\pi$
$613$	13.4281	+	23.2582i	0.542356	+	0.939389i	−0.456412	+	0.889769i	$0.650866\pi$
$614$	−12.3119	+	21.3248i	−0.496867	+	0.860599i
$615$	19.5998	+	32.9076i	0.790342	+	1.32696i
$616$	6.73366	+	6.23531i	0.271307	+	0.251228i
$617$			18.1042i			0.728846i	0.931234	+	0.364423i	$0.118734\pi$
$617$			18.1042i			0.728846i	−0.931234	+	0.364423i	$0.881266\pi$
$618$	−29.1903	+	0.396441i	−1.17421	+	0.0159472i
$619$	−24.1494	+	13.9427i	−0.970646	+	0.560403i	−0.899433	−	0.437058i	$-0.856020\pi$
$619$	−24.1494	+	13.9427i	−0.970646	+	0.560403i	−0.0712131	+	0.997461i	$0.522687\pi$
$620$	0.495089	−	0.285840i	0.0198833	−	0.0114796i
$621$	4.60209	+	2.41264i	0.184675	+	0.0968157i
$622$		−	28.1940i		−	1.13047i
$623$	−2.67821	+	11.7887i	−0.107300	+	0.472306i
$624$	0.648520	−	0.386260i	0.0259616	−	0.0154628i
$625$	15.6249	−	27.0632i	0.624998	−	1.08253i
$626$	−13.6222	−	23.5943i	−0.544451	−	0.943016i
$627$	−3.56866	+	6.37964i	−0.142519	+	0.254778i
$628$	3.14379	+	1.81507i	0.125451	+	0.0724292i
$629$	0.0288046			0.00114851
$630$	−21.3354	−	4.24125i	−0.850022	−	0.168975i
$631$	0.895993			0.0356689			0.0178345	−	0.999841i	$-0.494323\pi$
$631$	0.895993			0.0356689			0.0178345	+	0.999841i	$0.494323\pi$
$632$	1.91495	+	1.10560i	0.0761727	+	0.0439783i
$633$	6.06184	−	10.8367i	0.240937	−	0.430719i
$634$	−2.87053	−	4.97190i	−0.114003	−	0.197459i
$635$	−12.3066	+	21.3156i	−0.488371	+	0.845884i
$636$	−1.34975	+	0.803911i	−0.0535209	+	0.0318771i
$637$	−1.72355	−	2.51708i	−0.0682897	−	0.0997303i
$638$			16.1816i			0.640635i
$639$	8.85460	−	5.43806i	0.350283	−	0.215126i
$640$	2.37343	−	1.37030i	0.0938181	−	0.0541659i
$641$	−13.6094	+	7.85740i	−0.537539	+	0.310349i	−0.744081	−	0.668089i	$-0.767112\pi$
$641$	−13.6094	+	7.85740i	−0.537539	+	0.310349i	0.206542	+	0.978438i	$0.433779\pi$
$642$	29.8196	−	0.404987i	1.17688	−	0.0159836i
$643$		−	31.5591i		−	1.24457i	−0.782791	−	0.622285i	$-0.786204\pi$
$643$		−	31.5591i		−	1.24457i	0.782791	−	0.622285i	$-0.213796\pi$
$644$	0.782396	+	2.52742i	0.0308307	+	0.0995943i
$645$	10.2151	+	17.1509i	0.402220	+	0.675318i
$646$	0.925706	−	1.60337i	0.0364214	−	0.0630837i
$647$	4.68937	+	8.12222i	0.184358	+	0.319318i	0.943360	−	0.331771i	$-0.107646\pi$
$647$	4.68937	+	8.12222i	0.184358	+	0.319318i	−0.759002	+	0.651088i	$0.774313\pi$
$648$	8.02706	+	4.07018i	0.315333	+	0.159892i
$649$	19.5293	+	11.2753i	0.766593	+	0.442593i
$650$	1.09426			0.0429205
$651$	0.295054	+	0.909233i	0.0115641	+	0.0356356i
$652$	−20.7454			−0.812452
$653$	−12.6574	−	7.30776i	−0.495323	−	0.285975i	0.231457	−	0.972845i	$-0.425651\pi$
$653$	−12.6574	−	7.30776i	−0.495323	−	0.285975i	−0.726780	+	0.686870i	$0.758984\pi$
$654$	15.8702	+	8.87753i	0.620575	+	0.347139i
$655$	10.1999	+	17.6668i	0.398544	+	0.690299i
$656$	4.03448	−	6.98793i	0.157520	−	0.272833i
$657$	−21.3828	−	11.5828i	−0.834222	−	0.451887i
$658$	6.16453	−	6.65723i	0.240319	−	0.259526i
$659$			19.9758i			0.778146i	0.921207	+	0.389073i	$0.127205\pi$
$659$			19.9758i			0.778146i	−0.921207	+	0.389073i	$0.872795\pi$
$660$	−0.223598	−	16.4637i	−0.00870354	−	0.640850i
$661$	40.4552	−	23.3568i	1.57353	−	0.908475i	0.577793	−	0.816183i	$-0.303914\pi$
$661$	40.4552	−	23.3568i	1.57353	−	0.908475i	0.995732	−	0.0922918i	$-0.0294193\pi$
$662$	5.91267	−	3.41368i	0.229802	−	0.132676i
$663$	0.0155978	+	1.14848i	0.000605768	+	0.0446033i
$664$			8.99307i			0.348999i
$665$	5.99423	−	6.47331i	0.232446	−	0.251024i
$666$	−0.0499345	−	0.0270488i	−0.00193492	−	0.00104812i
$667$	−2.33254	+	4.04008i	−0.0903163	+	0.156432i
$668$	12.8120	+	22.1910i	0.495710	+	0.858594i
$669$	−32.5421	−	18.2035i	−1.25815	−	0.703788i
$670$	−6.49071	−	3.74742i	−0.250758	−	0.144775i
$671$	35.8605			1.38438
$672$	1.41447	+	4.35882i	0.0545644	+	0.168145i
$673$	5.80197			0.223649			0.111825	−	0.993728i	$-0.464330\pi$
$673$	5.80197			0.223649			0.111825	+	0.993728i	$0.464330\pi$
$674$	−19.5876	−	11.3089i	−0.754488	−	0.435604i
$675$	6.97832	+	11.0240i	0.268596	+	0.424313i
$676$	6.40504	+	11.0939i	0.246348	+	0.426687i
$677$	4.48469	−	7.76771i	0.172361	−	0.298537i	−0.766884	−	0.641786i	$-0.778194\pi$
$677$	4.48469	−	7.76771i	0.172361	−	0.298537i	0.939245	+	0.343248i	$0.111527\pi$
$678$	−6.90195	−	11.5882i	−0.265068	−	0.445042i
$679$	10.7263	+	34.6499i	0.411639	+	1.32974i
$680$			4.17021i			0.159920i
$681$	42.9747	−	0.583650i	1.64680	−	0.0223655i
$682$	−0.626613	+	0.361775i	−0.0239942	+	0.0138531i
$683$	−36.4099	+	21.0212i	−1.39318	+	0.804355i	−0.993666	−	0.112370i	$-0.964156\pi$
$683$	−36.4099	+	21.0212i	−1.39318	+	0.804355i	−0.399518	+	0.916725i	$0.630822\pi$
$684$	−3.11041	+	1.91026i	−0.118929	+	0.0730406i
$685$			1.68342i			0.0643201i
$686$	17.2195	−	6.81829i	0.657443	−	0.260323i
$687$	12.0333	−	7.16702i	0.459097	−	0.273439i
$688$	2.10271	−	3.64200i	0.0801651	−	0.138850i
$689$	0.197643	+	0.342327i	0.00752958	+	0.0130416i
$690$	2.31739	−	4.14276i	0.0882214	−	0.157712i
$691$	6.83426	+	3.94576i	0.259987	+	0.150104i	0.624329	−	0.781162i	$-0.285373\pi$
$691$	6.83426	+	3.94576i	0.259987	+	0.150104i	−0.364341	+	0.931265i	$0.618706\pi$
$692$	10.2273			0.388785
$693$	27.0033	+	5.36796i	1.02577	+	0.203912i
$694$	15.9792			0.606560
$695$	−41.7791	−	24.1212i	−1.58477	−	0.914969i
$696$	−3.94468	+	7.05184i	−0.149523	+	0.267299i
$697$	6.13903	+	10.6331i	0.232532	+	0.402758i
$698$	4.27735	−	7.40859i	0.161900	−	0.280419i
$699$	−26.0951	+	15.5423i	−0.987007	+	0.587863i
$700$	−1.47173	+	6.47815i	−0.0556262	+	0.244851i
$701$			34.0720i			1.28688i	0.765496	+	0.643441i	$0.222494\pi$
$701$			34.0720i			1.28688i	−0.765496	+	0.643441i	$0.777506\pi$
$702$	1.05144	−	2.00561i	0.0396839	−	0.0756967i
$703$	0.0199467	−	0.0115163i	0.000752306	−	0.000434344i
$704$	−3.00395	+	1.73433i	−0.113216	+	0.0653650i
$705$	−16.2769	+	0.221060i	−0.613022	+	0.00832560i
$706$			2.39274i			0.0900520i
$707$	20.6384	+	19.1110i	0.776188	+	0.718743i
$708$	5.76213	+	9.67447i	0.216554	+	0.363589i
$709$	−15.9712	+	27.6629i	−0.599811	+	1.03890i	0.393037	+	0.919523i	$0.371424\pi$
$709$	−15.9712	+	27.6629i	−0.599811	+	1.03890i	−0.992848	+	0.119381i	$0.961909\pi$
$710$	−4.74635	−	8.22092i	−0.178127	−	0.308525i
$711$	6.63114	−	0.180152i	0.248687	−	0.00675621i
$712$	−3.95710	−	2.28463i	−0.148299	−	0.0856202i
$713$	−0.208596			−0.00781199
$714$	−6.82011	−	1.45231i	−0.255236	−	0.0543514i
$715$	−4.14285			−0.154934
$716$	17.8312	+	10.2948i	0.666381	+	0.384735i
$717$	−15.9289	−	8.91036i	−0.594876	−	0.332763i
$718$	5.95610	+	10.3163i	0.222280	+	0.385000i
$719$	−7.33232	+	12.7000i	−0.273449	+	0.473628i	−0.969743	−	0.244129i	$-0.921498\pi$
$719$	−7.33232	+	12.7000i	−0.273449	+	0.473628i	0.696293	+	0.717757i	$0.254831\pi$
$720$	3.91602	−	7.22931i	0.145941	−	0.269420i
$721$	−43.4850	−	9.87908i	−1.61947	−	0.367916i
$722$			17.5196i			0.652012i
$723$	−0.213296	−	15.7052i	−0.00793257	−	0.584083i
$724$	8.50937	−	4.91289i	0.316248	−	0.182586i
$725$	−10.1442	+	5.85678i	−0.376748	+	0.217516i
$726$	0.0242646	+	1.78663i	0.000900545	+	0.0663080i
$727$			42.0245i			1.55860i	0.626650	+	0.779301i	$0.284426\pi$
$727$			42.0245i			1.55860i	−0.626650	+	0.779301i	$0.715574\pi$
$728$	1.10146	−	0.340971i	0.0408228	−	0.0126372i
$729$	26.9104	−	2.19759i	0.996682	−	0.0813923i
$730$	−11.1078	+	19.2394i	−0.411120	+	0.712080i
$731$	3.19957	+	5.54181i	0.118340	+	0.204971i
$732$	15.6278	+	8.74193i	0.577621	+	0.323111i
$733$	25.3917	+	14.6599i	0.937865	+	0.541476i	0.889290	−	0.457343i	$-0.151199\pi$
$733$	25.3917	+	14.6599i	0.937865	+	0.541476i	0.0485743	+	0.998820i	$0.484532\pi$
$734$	21.6089			0.797600
$735$	−30.1586	−	13.9485i	−1.11242	−	0.514498i
$736$	−1.00000			−0.0368605
$737$	8.21501	+	4.74294i	0.302604	+	0.174708i
$738$	−0.657398	−	24.1980i	−0.0241992	−	0.890740i
$739$	13.7002	+	23.7295i	0.503971	+	0.872903i	0.999989	+	0.00459102i	$0.00146137\pi$
$739$	13.7002	+	23.7295i	0.503971	+	0.872903i	−0.496019	+	0.868312i	$0.665205\pi$
$740$	−0.0259398	+	0.0449290i	−0.000953565	+	0.00165162i
$741$	0.469971	+	0.789069i	0.0172648	+	0.0289872i
$742$	−2.29244	+	0.709653i	−0.0841580	+	0.0260522i
$743$			52.7110i			1.93378i	0.255193	+	0.966890i	$0.417861\pi$
$743$			52.7110i			1.93378i	−0.255193	+	0.966890i	$0.582139\pi$
$744$	−0.361266	+	0.00490644i	−0.0132447	+	0.000179879i
$745$	15.0755	−	8.70384i	0.552323	−	0.318884i
$746$	9.38096	−	5.41610i	0.343461	−	0.198298i
$747$	14.1192	+	22.9897i	0.516593	+	0.841150i
$748$		−	5.27805i		−	0.192985i
$749$	44.4224	+	10.0920i	1.62316	+	0.368755i
$750$	−10.1513	+	6.04611i	−0.370672	+	0.220773i
$751$	20.5369	−	35.5709i	0.749401	−	1.29800i	−0.198709	−	0.980058i	$-0.563675\pi$
$751$	20.5369	−	35.5709i	0.749401	−	1.29800i	0.948110	−	0.317942i	$-0.102992\pi$
$752$	1.71464	+	2.96985i	0.0625267	+	0.108299i
$753$	10.9792	−	19.6274i	0.400105	−	0.715262i
$754$	1.76068	+	1.01653i	0.0641203	+	0.0370198i
$755$	62.7436			2.28347
$756$	10.4593	+	8.92207i	0.380401	+	0.324492i
$757$	−13.8131			−0.502045			−0.251023	−	0.967981i	$-0.580767\pi$
$757$	−13.8131			−0.502045			−0.251023	+	0.967981i	$0.580767\pi$
$758$	18.7641	+	10.8335i	0.681543	+	0.393489i
$759$	−2.93301	+	5.24330i	−0.106462	+	0.190320i
$760$	1.66728	+	2.88781i	0.0604785	+	0.104752i
$761$	16.4281	−	28.4543i	0.595517	−	1.03147i	−0.397956	−	0.917404i	$-0.630280\pi$
$761$	16.4281	−	28.4543i	0.595517	−	1.03147i	0.993474	−	0.114062i	$-0.0363862\pi$
$762$	13.3645	−	7.95993i	0.484145	−	0.288358i
$763$	20.3812	+	18.8728i	0.737848	+	0.683241i
$764$			18.3327i			0.663254i
$765$	6.54724	+	10.6606i	0.236716	+	0.385436i
$766$	14.3614	−	8.29154i	0.518898	−	0.299586i
$767$	2.45367	−	1.41663i	0.0885970	−	0.0511515i
$768$	−1.73189	+	0.0235212i	−0.0624942	+	0.000848750i
$769$			50.0765i			1.80580i	0.429847	+	0.902902i	$0.358568\pi$
$769$			50.0765i			1.80580i	−0.429847	+	0.902902i	$0.641432\pi$
$770$	5.57194	−	24.5261i	0.200799	−	0.883860i
$771$	2.12583	+	3.56921i	0.0765599	+	0.128542i
$772$	10.7816	−	18.6742i	0.388037	−	0.672101i
$773$	13.1154	+	22.7165i	0.471728	+	0.817056i	0.999477	−	0.0323439i	$-0.0102972\pi$
$773$	13.1154	+	22.7165i	0.471728	+	0.817056i	−0.527749	+	0.849400i	$0.676964\pi$
$774$	−0.342626	−	12.6116i	−0.0123154	−	0.453315i
$775$	−0.453594	−	0.261883i	−0.0162936	−	0.00940710i
$776$	−13.7096			−0.492146
$777$	−0.0644447	−	0.0580697i	−0.00231194	−	0.00208324i
$778$	−22.7453			−0.815459
$779$	8.50237	+	4.90884i	0.304629	+	0.175878i
$780$	−1.80543	−	1.00993i	−0.0646447	−	0.0361612i
$781$	6.00724	+	10.4049i	0.214956	+	0.372315i
$782$	0.760820	−	1.31778i	0.0272069	−	0.0471237i
$783$	0.987313	+	24.2204i	0.0352837	+	0.865565i
$784$	0.537175	+	6.97936i	0.0191848	+	0.249263i
$785$		−	9.94877i		−	0.355087i
$786$	−0.175082	−	12.8914i	−0.00624496	−	0.459823i
$787$	−34.3324	+	19.8218i	−1.22382	+	0.706571i	−0.965730	−	0.259550i	$-0.916426\pi$
$787$	−34.3324	+	19.8218i	−1.22382	+	0.706571i	−0.258088	+	0.966121i	$0.583092\pi$
$788$	5.90914	−	3.41164i	0.210504	−	0.121535i
$789$	−0.401120	−	29.5349i	−0.0142803	−	1.05147i
$790$		−	6.06001i		−	0.215605i
$791$	−6.09270	−	19.6816i	−0.216632	−	0.699798i
$792$	−4.95633	+	9.14982i	−0.176116	+	0.325125i
$793$	2.25277	−	3.90191i	0.0799981	−	0.138561i
$794$	9.76642	+	16.9159i	0.346597	+	0.600324i
$795$	3.75759	+	2.10193i	0.133268	+	0.0745477i
$796$	21.2578	+	12.2732i	0.753461	+	0.435011i
$797$	29.5869			1.04802			0.524012	−	0.851711i	$-0.324435\pi$
$797$	29.5869			1.04802			0.524012	+	0.851711i	$0.324435\pi$
$798$	−5.30347	+	1.72102i	−0.187741	+	0.0609234i
$799$	−5.21814			−0.184605
$800$	−2.17451	−	1.25545i	−0.0768804	−	0.0443869i
$801$	−13.7027	+	0.372269i	−0.484162	+	0.0131535i
$802$	−7.15511	−	12.3930i	−0.252656	−	0.437612i
$803$	14.0587	−	24.3504i	0.496121	−	0.859307i
$804$	2.42384	+	4.06957i	0.0854823	+	0.143523i
$805$	4.92654	−	5.32029i	0.173638	−	0.187516i
$806$			0.0909071i			0.00320207i
$807$	−23.3847	+	0.317593i	−0.823181	+	0.0111798i
$808$	−9.20699	+	5.31566i	−0.323901	+	0.187004i
$809$	−42.3111	+	24.4283i	−1.48758	+	0.858853i	−0.999900	−	0.0141701i	$-0.995489\pi$
$809$	−42.3111	+	24.4283i	−1.48758	+	0.858853i	−0.487678	+	0.873024i	$0.662156\pi$
$810$	−1.33921	−	24.6290i	−0.0470550	−	0.865376i
$811$			28.8582i			1.01335i	0.862137	+	0.506675i	$0.169125\pi$
$811$			28.8582i			1.01335i	−0.862137	+	0.506675i	$0.830875\pi$
$812$	−8.38601	+	9.05625i	−0.294291	+	0.317812i
$813$	42.3662	−	25.2334i	1.48585	−	0.884974i
$814$	0.0328308	−	0.0568647i	0.00115072	−	0.00199310i
$815$	28.4274	+	49.2378i	0.995770	+	1.72472i
$816$	1.28666	−	2.30014i	0.0450421	−	0.0805211i
$817$	4.43130	+	2.55841i	0.155032	+	0.0895076i
$818$	−1.37491			−0.0480727
$819$	2.28043	−	2.60095i	0.0796845	−	0.0908845i
$820$	−22.1138			−0.772249
$821$	−5.48431	−	3.16637i	−0.191404	−	0.110507i	0.401236	−	0.915975i	$-0.368581\pi$
$821$	−5.48431	−	3.16637i	−0.191404	−	0.110507i	−0.592640	+	0.805468i	$0.701914\pi$
$822$	0.519396	−	0.928516i	0.0181160	−	0.0323857i
$823$	−10.0015	−	17.3231i	−0.348631	−	0.603847i	0.637375	−	0.770553i	$-0.280020\pi$
$823$	−10.0015	−	17.3231i	−0.348631	−	0.603847i	−0.986007	+	0.166706i	$0.946687\pi$
$824$	8.42729	−	14.5965i	0.293579	−	0.508493i
$825$	−12.9606	+	7.71934i	−0.451229	+	0.268753i
$826$	5.08653	+	16.4313i	0.176983	+	0.571719i
$827$		−	33.4355i		−	1.16267i	−0.813665	−	0.581334i	$-0.802531\pi$
$827$		−	33.4355i		−	1.16267i	0.813665	−	0.581334i	$-0.197469\pi$
$828$	−2.55638	+	1.57000i	−0.0888404	+	0.0545614i
$829$	12.3131	−	7.10895i	0.427650	−	0.246904i	−0.270695	−	0.962665i	$-0.587253\pi$
$829$	12.3131	−	7.10895i	0.427650	−	0.246904i	0.698345	+	0.715761i	$0.253920\pi$
$830$	21.3444	−	12.3232i	0.740876	−	0.427745i
$831$	−10.4229	+	0.141556i	−0.361565	+	0.00491051i
$832$			0.435804i			0.0151088i
$833$	−9.60594	−	4.60216i	−0.332826	−	0.159455i
$834$	15.6017	+	26.1948i	0.540242	+	0.907052i
$835$	35.1125	−	60.8166i	1.21512	−	2.10465i
$836$	−2.11020	−	3.65497i	−0.0729827	−	0.126410i
$837$	−0.915831	+	0.579732i	−0.0316558	+	0.0200385i
$838$	14.2246	+	8.21257i	0.491380	+	0.283699i
$839$	−48.1274			−1.66154			−0.830771	−	0.556615i	$-0.812100\pi$
$839$	−48.1274			−1.66154			−0.830771	+	0.556615i	$0.812100\pi$
$840$	8.40710	−	9.33004i	0.290072	−	0.321917i
$841$	7.23702			0.249552
$842$	10.0146	+	5.78195i	0.345127	+	0.199259i
$843$	−4.53716	−	2.53801i	−0.156268	−	0.0874137i
$844$	3.58445	+	6.20845i	0.123382	+	0.213704i
$845$	17.5537	−	30.4038i	0.603864	−	1.04592i
$846$	9.04596	+	4.90008i	0.311007	+	0.168468i
$847$	−0.604661	+	2.66155i	−0.0207764	+	0.0914519i
$848$		−	0.907026i		−	0.0311474i
$849$	0.199013	+	14.6535i	0.00683012	+	0.502908i
$850$	3.30881	−	1.91034i	0.113491	−	0.0655243i
$851$	0.0163938	−	0.00946499i	0.000561973	−	0.000324456i
$852$	0.0814711	+	5.99880i	0.00279115	+	0.205515i
$853$		−	34.4704i		−	1.18024i	−0.807314	−	0.590122i	$-0.799080\pi$
$853$		−	34.4704i		−	1.18024i	0.807314	−	0.590122i	$-0.200920\pi$
$854$	20.0699	+	18.5845i	0.686776	+	0.635949i
$855$	8.79606	+	4.76471i	0.300819	+	0.162950i
$856$	−8.60896	+	14.9112i	−0.294248	+	0.509653i
$857$	17.2980	+	29.9609i	0.590887	+	1.02345i	0.994113	+	0.108346i	$0.0345554\pi$
$857$	17.2980	+	29.9609i	0.590887	+	1.02345i	−0.403226	+	0.915100i	$0.632111\pi$
$858$	2.28505	+	1.27822i	0.0780104	+	0.0436377i
$859$	−31.9259	−	18.4324i	−1.08930	−	0.628906i	−0.155908	−	0.987772i	$-0.549830\pi$
$859$	−31.9259	−	18.4324i	−1.08930	−	0.628906i	−0.933389	+	0.358865i	$0.883164\pi$
$860$	−11.5254			−0.393013
$861$	7.70134	−	36.1658i	0.262461	−	1.23253i
$862$	−3.10007			−0.105589
$863$	−41.4048	−	23.9051i	−1.40943	−	0.813738i	−0.414101	−	0.910231i	$-0.635904\pi$
$863$	−41.4048	−	23.9051i	−1.40943	−	0.813738i	−0.995334	+	0.0964932i	$0.969237\pi$
$864$	−4.39045	+	2.77921i	−0.149366	+	0.0945505i
$865$	−14.0145	−	24.2739i	−0.476509	−	0.825337i
$866$	10.9003	−	18.8800i	0.370409	−	0.641567i
$867$	−13.0152	−	21.8522i	−0.442019	−	0.742139i
$868$	−0.538180	−	0.122266i	−0.0182670	−	0.00414997i
$869$			7.66989i			0.260183i
$870$	22.1425	−	0.300722i	0.750700	−	0.0101954i
$871$	1.03214	−	0.595905i	0.0349726	−	0.0201915i
$872$	−9.09223	+	5.24940i	−0.307902	+	0.177767i
$873$	−35.0470	+	21.5241i	−1.18616	+	0.728481i
$874$		−	1.21672i		−	0.0411562i
$875$	−17.2411	+	5.33721i	−0.582856	+	0.180431i
$876$	12.0627	−	7.18459i	0.407562	−	0.242745i
$877$	−4.79681	+	8.30831i	−0.161977	+	0.280552i	−0.935578	−	0.353121i	$-0.885120\pi$
$877$	−4.79681	+	8.30831i	−0.161977	+	0.280552i	0.773601	+	0.633673i	$0.218454\pi$
$878$	−14.3279	−	24.8166i	−0.483543	−	0.837521i
$879$	−14.2159	+	25.4136i	−0.479492	+	0.857180i
$880$	8.23263	+	4.75311i	0.277522	+	0.160227i
$881$	−15.8094			−0.532632			−0.266316	−	0.963886i	$-0.585806\pi$
$881$	−15.8094			−0.532632			−0.266316	+	0.963886i	$0.585806\pi$
$882$	12.3308	+	16.9985i	0.415201	+	0.572371i
$883$	8.65292			0.291194			0.145597	−	0.989344i	$-0.453490\pi$
$883$	8.65292			0.291194			0.145597	+	0.989344i	$0.453490\pi$
$884$	−0.574293	−	0.331568i	−0.0193156	−	0.0111518i
$885$	15.0658	−	26.9330i	0.506433	−	0.905342i
$886$	−14.7401	−	25.5305i	−0.495202	−	0.857716i
$887$	9.71462	−	16.8262i	0.326185	−	0.564969i	−0.655566	−	0.755138i	$-0.727570\pi$
$887$	9.71462	−	16.8262i	0.326185	−	0.564969i	0.981751	+	0.190168i	$0.0609034\pi$
$888$	0.0281697	−	0.0167779i	0.000945314	−	0.000563030i
$889$	22.6986	−	7.02663i	0.761285	−	0.235666i
$890$			12.5225i			0.419756i
$891$	1.69498	+	31.1719i	0.0567838	+	1.04430i
$892$	18.6437	−	10.7640i	0.624239	−	0.360404i
$893$	−3.61348	+	2.08625i	−0.120921	+	0.0698136i
$894$	−11.0006	+	0.149401i	−0.367914	+	0.00499673i
$895$		−	56.4280i		−	1.88618i
$896$	−2.58001	−	0.586136i	−0.0861920	−	0.0195814i
$897$	0.386260	+	0.648520i	0.0128968	+	0.0216535i
$898$	−15.9126	+	27.5615i	−0.531011	+	0.919738i
$899$	−0.486559	−	0.842746i	−0.0162277	−	0.0281071i
$900$	−7.52993	+	0.204569i	−0.250998	+	0.00681898i
$901$	1.19526	+	0.690083i	0.0398198	+	0.0229900i
$902$	27.9885			0.931915
$903$	4.01382	−	18.8490i	0.133571	−	0.627257i
$904$	7.78724			0.259000
$905$	−23.3208	−	13.4643i	−0.775210	−	0.447567i
$906$	−34.6072	−	19.3587i	−1.14975	−	0.643149i
$907$	12.3931	+	21.4654i	0.411506	+	0.712748i	0.995055	−	0.0993294i	$-0.0316698\pi$
$907$	12.3931	+	21.4654i	0.411506	+	0.712748i	−0.583549	+	0.812078i	$0.698336\pi$
$908$	−12.4069	+	21.4893i	−0.411737	+	0.713149i
$909$	−15.1910	+	28.0439i	−0.503853	+	0.930157i
$910$	−2.31860	−	2.14701i	−0.0768609	−	0.0711726i
$911$		−	19.7681i		−	0.654948i	−0.944860	−	0.327474i	$-0.893803\pi$
$911$		−	19.7681i		−	0.654948i	0.944860	−	0.327474i	$-0.106197\pi$
$912$	−0.0286188	−	2.10723i	−0.000947663	−	0.0697774i
$913$	−27.0147	+	15.5970i	−0.894057	+	0.516184i
$914$	6.39067	−	3.68965i	0.211385	−	0.122043i
$915$	−0.666440	−	49.0706i	−0.0220318	−	1.62223i
$916$			8.08631i			0.267179i
$917$	4.36294	−	19.2045i	0.144077	−	0.634187i
$918$	−0.322038	−	7.90011i	−0.0106288	−	0.260742i
$919$	28.4915	−	49.3487i	0.939848	−	1.62786i	0.174096	−	0.984729i	$-0.444300\pi$
$919$	28.4915	−	49.3487i	0.939848	−	1.62786i	0.765752	−	0.643136i	$-0.222367\pi$
$920$	1.37030	+	2.37343i	0.0451775	+	0.0782497i
$921$	−37.2218	−	20.8212i	−1.22650	−	0.686083i
$922$	−18.8121	−	10.8612i	−0.619544	−	0.357694i
$923$	1.50950			0.0496860
$924$	−10.6405	+	11.8086i	−0.350047	+	0.388475i
$925$	0.0475313			0.00156282
$926$	27.9156	+	16.1171i	0.917364	+	0.529641i
$927$	−1.37318	−	50.5451i	−0.0451013	−	1.66012i
$928$	−2.33254	−	4.04008i	−0.0765694	−	0.132622i
$929$	−11.5068	+	19.9304i	−0.377527	+	0.653896i	−0.990702	−	0.136051i	$-0.956559\pi$
$929$	−11.5068	+	19.9304i	−0.377527	+	0.653896i	0.613175	+	0.789947i	$0.289892\pi$
$930$	0.506689	+	0.850717i	0.0166150	+	0.0278961i
$931$	−8.49194	+	0.653592i	−0.278312	+	0.0214206i
$932$		−	17.5358i		−	0.574405i
$933$	48.8289	−	0.663157i	1.59859	−	0.0217108i
$934$	0.613240	−	0.354054i	0.0200658	−	0.0115850i
$935$	−12.5271	+	7.23252i	−0.409680	+	0.236529i
$936$	0.684214	+	1.11408i	0.0223642	+	0.0364149i
$937$		−	48.8411i		−	1.59557i	−0.602943	−	0.797784i	$-0.706005\pi$
$937$		−	48.8411i		−	1.59557i	0.602943	−	0.797784i	$-0.293995\pi$
$938$	2.13965	+	6.91183i	0.0698620	+	0.225679i
$939$	40.5423	−	24.1470i	1.32305	−	0.788009i
$940$	4.69916	−	8.13918i	0.153270	−	0.265471i
$941$	−6.22520	−	10.7824i	−0.202936	−	0.351495i	0.746537	−	0.665343i	$-0.231715\pi$
$941$	−6.22520	−	10.7824i	−0.202936	−	0.351495i	−0.949473	+	0.313849i	$0.898382\pi$
$942$	−3.06956	+	5.48740i	−0.100012	+	0.178789i
$943$	6.98793	+	4.03448i	0.227558	+	0.131381i
$944$	−6.50122			−0.211597
$945$	6.84354	−	37.0503i	0.222621	−	1.20525i
$946$	14.5872			0.474270
$947$	21.9466	+	12.6709i	0.713168	+	0.411748i	0.812233	−	0.583333i	$-0.198252\pi$
$947$	21.9466	+	12.6709i	0.713168	+	0.411748i	−0.0990648	+	0.995081i	$0.531585\pi$
$948$	−1.86973	+	3.34249i	−0.0607261	+	0.108559i
$949$	−1.76634	−	3.05939i	−0.0573379	−	0.0993121i
$950$	1.52754	−	2.64577i	0.0495598	−	0.0858401i
$951$	8.54327	−	5.08839i	0.277034	−	0.165002i
$952$	2.73532	−	2.95394i	0.0886522	−	0.0957376i
$953$			19.1366i			0.619895i	0.950754	+	0.309948i	$0.100311\pi$
$953$			19.1366i			0.619895i	−0.950754	+	0.309948i	$0.899689\pi$
$954$	−1.42403	−	2.31870i	−0.0461048	−	0.0750708i
$955$	43.5114	−	25.1213i	1.40800	−	0.812907i
$956$	9.12585	−	5.26881i	0.295151	−	0.170406i
$957$	−28.0247	+	0.380611i	−0.905911	+	0.0123034i
$958$		−	33.0660i		−	1.06831i
$959$	1.10419	−	1.19244i	0.0356560	−	0.0385058i
$960$	2.42904	+	4.07829i	0.0783969	+	0.131626i
$961$	−15.4782	+	26.8091i	−0.499298	+	0.864810i
$962$	−0.00412488	−	0.00714450i	−0.000132991	−	0.000230348i
$963$	1.40279	+	51.6347i	0.0452042	+	1.66391i
$964$	7.85333	+	4.53412i	0.252939	+	0.146034i
$965$	−59.0960			−1.90237
$966$	−4.35882	+	1.41447i	−0.140243	+	0.0455099i
$967$	10.1605			0.326740			0.163370	−	0.986565i	$-0.447764\pi$
$967$	10.1605			0.326740			0.163370	+	0.986565i	$0.447764\pi$
$968$	−0.893396	−	0.515802i	−0.0287148	−	0.0165785i
$969$	2.79864	+	1.56551i	0.0899051	+	0.0502914i
$970$	18.7863	+	32.5388i	0.603191	+	1.04476i
$971$	−15.3800	+	26.6389i	−0.493567	+	0.854882i	−0.999973	−	0.00741287i	$-0.997640\pi$
$971$	−15.3800	+	26.6389i	−0.493567	+	0.854882i	0.506406	+	0.862295i	$0.330974\pi$
$972$	−6.86029	+	13.9977i	−0.220044	+	0.448977i
$973$	13.7724	+	44.4898i	0.441522	+	1.42628i
$974$			5.97631i			0.191493i
$975$	0.0257384	+	1.89514i	0.000824288	+	0.0606931i
$976$	−8.95335	+	5.16922i	−0.286590	+	0.165463i
$977$	−39.0475	+	22.5441i	−1.24924	+	0.721248i	−0.970958	−	0.239251i	$-0.923098\pi$
$977$	−39.0475	+	22.5441i	−1.24924	+	0.721248i	−0.278281	+	0.960500i	$0.589765\pi$
$978$	−0.487957	−	35.9288i	−0.0156031	−	1.14887i
$979$		−	15.8492i		−	0.506543i
$980$	15.8289	−	10.8388i	0.505637	−	0.346232i
$981$	−15.0016	+	27.6943i	−0.478965	+	0.884211i
$982$	2.62356	−	4.54413i	0.0837211	−	0.145009i
$983$	29.0607	+	50.3345i	0.926891	+	1.60542i	0.788491	+	0.615046i	$0.210862\pi$
$983$	29.0607	+	50.3345i	0.926891	+	1.60542i	0.138399	+	0.990376i	$0.455804\pi$
$984$	12.1972	+	6.82292i	0.388834	+	0.217507i
$985$	−16.1946	−	9.34996i	−0.516003	−	0.297915i
$986$	7.09857			0.226065
$987$	11.6746	+	10.5197i	0.371606	+	0.334846i
$988$	−0.530252			−0.0168696
$989$	3.64200	+	2.10271i	0.115809	+	0.0668623i
$990$	28.5081	−	0.774495i	0.906048	−	0.0246151i
$991$	−19.7502	−	34.2083i	−0.627384	−	1.08666i	−0.988075	−	0.153976i	$-0.950792\pi$
$991$	−19.7502	−	34.2083i	−0.627384	−	1.08666i	0.360690	−	0.932686i	$-0.382541\pi$
$992$	0.104298	−	0.180650i	0.00331147	−	0.00573563i
$993$	6.05120	+	10.1598i	0.192029	+	0.322412i
$994$	−2.03021	+	8.93644i	−0.0643945	+	0.283447i
$995$		−	67.2718i		−	2.13266i
$996$	−15.5750	+	0.211528i	−0.493513	+	0.00670253i
$997$	46.2678	−	26.7127i	1.46532	−	0.846001i	0.466067	−	0.884749i	$-0.345671\pi$
$997$	46.2678	−	26.7127i	1.46532	−	0.846001i	0.999249	+	0.0387487i	$0.0123372\pi$
$998$	−31.2098	+	18.0190i	−0.987929	+	0.570381i
$999$	0.0456711	−	0.0871173i	0.00144497	−	0.00275627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.9	✓	56
3.2	odd	2	inner	966.2.l.d.47.28	yes	56
7.3	odd	6	inner	966.2.l.d.185.28	yes	56
21.17	even	6	inner	966.2.l.d.185.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.9	✓	56	1.1	even	1	trivial
966.2.l.d.47.28	yes	56	3.2	odd	2	inner
966.2.l.d.185.9	yes	56	21.17	even	6	inner
966.2.l.d.185.28	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.845576 - 1.51162i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.37030 - 2.37343i) q^{5} +(-1.48810 + 0.886316i) q^{6} +(-2.52742 + 0.782396i) q^{7} -1.00000i q^{8} +(-1.57000 - 2.55638i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.845576 - 1.51162i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.37030 - 2.37343i) q^{5} +(-1.48810 + 0.886316i) q^{6} +(-2.52742 + 0.782396i) q^{7} -1.00000i q^{8} +(-1.57000 - 2.55638i) q^{9} +(-2.37343 + 1.37030i) q^{10} +(3.00395 - 1.73433i) q^{11} +(1.73189 - 0.0235212i) q^{12} -0.435804i q^{13} +(2.58001 + 0.586136i) q^{14} +(-2.42904 - 4.07829i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.760820 - 1.31778i) q^{17} +(0.0814724 + 2.99889i) q^{18} +(-1.05371 - 0.608361i) q^{19} +2.74060 q^{20} +(-0.954439 + 4.48208i) q^{21} -3.46866 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.51162 - 0.845576i) q^{24} +(-1.25545 - 2.17451i) q^{25} +(-0.217902 + 0.377417i) q^{26} +(-5.19184 + 0.211639i) q^{27} +(-1.94128 - 1.79761i) q^{28} -4.66508i q^{29} +(0.0644624 + 4.74643i) q^{30} +(0.180650 - 0.104298i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.0815872 - 6.00734i) q^{33} +1.52164i q^{34} +(-1.60637 + 7.07078i) q^{35} +(1.42889 - 2.63785i) q^{36} +(-0.00946499 + 0.0163938i) q^{37} +(0.608361 + 1.05371i) q^{38} +(-0.658771 - 0.368505i) q^{39} +(-2.37343 - 1.37030i) q^{40} -8.06897 q^{41} +(3.06761 - 3.40438i) q^{42} -4.20542 q^{43} +(3.00395 + 1.73433i) q^{44} +(-8.21878 + 0.223284i) q^{45} +(0.500000 + 0.866025i) q^{46} +(1.71464 - 2.96985i) q^{47} +(0.886316 + 1.48810i) q^{48} +(5.77571 - 3.95489i) q^{49} +2.51090i q^{50} +(-2.63531 + 0.0357908i) q^{51} +(0.377417 - 0.217902i) q^{52} +(-0.785507 + 0.453513i) q^{53} +(4.60209 + 2.41264i) q^{54} -9.50622i q^{55} +(0.782396 + 2.52742i) q^{56} +(-1.81061 + 1.07840i) q^{57} +(-2.33254 + 4.04008i) q^{58} +(3.25061 + 5.63022i) q^{59} +(2.31739 - 4.14276i) q^{60} +(8.95335 + 5.16922i) q^{61} -0.208596 q^{62} +(5.96816 + 5.23269i) q^{63} -1.00000 q^{64} +(-1.03435 - 0.597183i) q^{65} +(-2.93301 + 5.24330i) q^{66} +(1.36737 + 2.36835i) q^{67} +(0.760820 - 1.31778i) q^{68} +(-1.48810 + 0.886316i) q^{69} +(4.92654 - 5.32029i) q^{70} +3.46373i q^{71} +(-2.55638 + 1.57000i) q^{72} +(7.02012 - 4.05307i) q^{73} +(0.0163938 - 0.00946499i) q^{74} +(-4.34861 + 0.0590596i) q^{75} -1.21672i q^{76} +(-6.23531 + 6.73366i) q^{77} +(0.386260 + 0.648520i) q^{78} +(-1.10560 + 1.91495i) q^{79} +(1.37030 + 2.37343i) q^{80} +(-4.07018 + 8.02706i) q^{81} +(6.98793 + 4.03448i) q^{82} -8.99307 q^{83} +(-4.35882 + 1.41447i) q^{84} -4.17021 q^{85} +(3.64200 + 2.10271i) q^{86} +(-7.05184 - 3.94468i) q^{87} +(-1.73433 - 3.00395i) q^{88} +(2.28463 - 3.95710i) q^{89} +(7.22931 + 3.91602i) q^{90} +(0.340971 + 1.10146i) q^{91} -1.00000i q^{92} +(-0.00490644 - 0.361266i) q^{93} +(-2.96985 + 1.71464i) q^{94} +(-2.88781 + 1.66728i) q^{95} +(-0.0235212 - 1.73189i) q^{96} -13.7096i q^{97} +(-6.97936 + 0.537175i) q^{98} +(-9.14982 - 4.95633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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