LMFDB - Embedded newform 663.2.z.d.205.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.3
Root			$0.729584i$ of defining polynomial
Character	$\chi$	$=$	663.205
Dual form			663.2.z.d.511.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.631839 + 0.364792i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.733853 + 1.27107i) q^{4} +0.945208i q^{5} +(0.631839 + 0.364792i) q^{6} +(-0.308178 - 0.177927i) q^{7} -2.52998i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.631839 + 0.364792i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.733853 + 1.27107i) q^{4} +0.945208i q^{5} +(0.631839 + 0.364792i) q^{6} +(-0.308178 - 0.177927i) q^{7} -2.52998i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.344805 - 0.597219i) q^{10} +(-1.69592 + 0.979137i) q^{11} +1.46771 q^{12} +(-1.84829 - 3.09578i) q^{13} +0.259625 q^{14} +(0.818574 - 0.472604i) q^{15} +(-0.544788 - 0.943601i) q^{16} +(-0.500000 + 0.866025i) q^{17} -0.729584i q^{18} +(1.46367 + 0.845051i) q^{19} +(-1.20143 - 0.693644i) q^{20} +0.355853i q^{21} +(0.714363 - 1.23731i) q^{22} +(-0.606797 - 1.05100i) q^{23} +(-2.19103 + 1.26499i) q^{24} +4.10658 q^{25} +(2.29714 + 1.28179i) q^{26} +1.00000 q^{27} +(0.452315 - 0.261144i) q^{28} +(-3.62213 - 6.27372i) q^{29} +(-0.344805 + 0.597219i) q^{30} -8.01115i q^{31} +(5.07050 + 2.92745i) q^{32} +(1.69592 + 0.979137i) q^{33} -0.729584i q^{34} +(0.168178 - 0.291293i) q^{35} +(-0.733853 - 1.27107i) q^{36} +(1.00678 - 0.581264i) q^{37} -1.23307 q^{38} +(-1.75687 + 3.14855i) q^{39} +2.39136 q^{40} +(-1.05344 + 0.608202i) q^{41} +(-0.129813 - 0.224842i) q^{42} +(3.07754 - 5.33045i) q^{43} -2.87417i q^{44} +(-0.818574 - 0.472604i) q^{45} +(0.766796 + 0.442710i) q^{46} -5.16110i q^{47} +(-0.544788 + 0.943601i) q^{48} +(-3.43668 - 5.95251i) q^{49} +(-2.59470 + 1.49805i) q^{50} +1.00000 q^{51} +(5.29132 - 0.0774638i) q^{52} -9.92348 q^{53} +(-0.631839 + 0.364792i) q^{54} +(-0.925488 - 1.60299i) q^{55} +(-0.450152 + 0.779686i) q^{56} -1.69010i q^{57} +(4.57721 + 2.64265i) q^{58} +(-5.98501 - 3.45545i) q^{59} +1.38729i q^{60} +(3.54801 - 6.14533i) q^{61} +(2.92241 + 5.06176i) q^{62} +(0.308178 - 0.177927i) q^{63} -2.09250 q^{64} +(2.92615 - 1.74702i) q^{65} -1.42873 q^{66} +(5.58216 - 3.22286i) q^{67} +(-0.733853 - 1.27107i) q^{68} +(-0.606797 + 1.05100i) q^{69} +0.245400i q^{70} +(-5.61258 - 3.24042i) q^{71} +(2.19103 + 1.26499i) q^{72} +9.64552i q^{73} +(-0.424081 + 0.734531i) q^{74} +(-2.05329 - 3.55640i) q^{75} +(-2.14824 + 1.24029i) q^{76} +0.696859 q^{77} +(-0.0385066 - 2.63027i) q^{78} -2.63504 q^{79} +(0.891899 - 0.514938i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.443735 - 0.768571i) q^{82} -4.82358i q^{83} +(-0.452315 - 0.261144i) q^{84} +(-0.818574 - 0.472604i) q^{85} +4.49065i q^{86} +(-3.62213 + 6.27372i) q^{87} +(2.47720 + 4.29064i) q^{88} +(-11.2195 + 6.47759i) q^{89} +0.689609 q^{90} +(0.0187815 + 1.28291i) q^{91} +1.78120 q^{92} +(-6.93786 + 4.00558i) q^{93} +(1.88273 + 3.26098i) q^{94} +(-0.798749 + 1.38347i) q^{95} -5.85491i q^{96} +(5.44329 + 3.14269i) q^{97} +(4.34286 + 2.50735i) q^{98} -1.95827i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.631839	+	0.364792i	−0.446777	+	0.257947i	−0.706468	−	0.707745i	$-0.749713\pi$
$2$	−0.631839	+	0.364792i	−0.446777	+	0.257947i	0.259691	+	0.965692i	$0.416379\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.733853	+	1.27107i	−0.366927	+	0.635536i
$5$			0.945208i			0.422710i	0.977409	+	0.211355i	$0.0677876\pi$
$5$			0.945208i			0.422710i	−0.977409	+	0.211355i	$0.932212\pi$
$6$	0.631839	+	0.364792i	0.257947	+	0.148926i
$7$	−0.308178	−	0.177927i	−0.116480	−	0.0672500i	0.440628	−	0.897690i	$-0.354756\pi$
$7$	−0.308178	−	0.177927i	−0.116480	−	0.0672500i	−0.557108	+	0.830440i	$0.688089\pi$
$8$		−	2.52998i		−	0.894485i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.344805	−	0.597219i	−0.109037	−	0.188857i
$11$	−1.69592	+	0.979137i	−0.511338	+	0.295221i	−0.733383	−	0.679815i	$-0.762060\pi$
$11$	−1.69592	+	0.979137i	−0.511338	+	0.295221i	0.222046	+	0.975036i	$0.428727\pi$
$12$	1.46771			0.423690
$13$	−1.84829	−	3.09578i	−0.512623	−	0.858614i
$13$	−1.84829	−	3.09578i	−0.512623	−	0.858614i
$14$	0.259625			0.0693877
$15$	0.818574	−	0.472604i	0.211355	−	0.122026i
$16$	−0.544788	−	0.943601i	−0.136197	−	0.235900i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$		−	0.729584i		−	0.171965i
$19$	1.46367	+	0.845051i	0.335789	+	0.193868i	0.658408	−	0.752661i	$-0.271230\pi$
$19$	1.46367	+	0.845051i	0.335789	+	0.193868i	−0.322619	+	0.946529i	$0.604563\pi$
$20$	−1.20143	−	0.693644i	−0.268647	−	0.155104i
$21$			0.355853i			0.0776536i
$22$	0.714363	−	1.23731i	0.152303	−	0.263796i
$23$	−0.606797	−	1.05100i	−0.126526	−	0.219149i	0.795802	−	0.605556i	$-0.207049\pi$
$23$	−0.606797	−	1.05100i	−0.126526	−	0.219149i	−0.922328	+	0.386407i	$0.873716\pi$
$24$	−2.19103	+	1.26499i	−0.447242	+	0.258215i
$25$	4.10658			0.821316
$26$	2.29714	+	1.28179i	0.450505	+	0.251379i
$27$	1.00000			0.192450
$28$	0.452315	−	0.261144i	0.0854795	−	0.0493516i
$29$	−3.62213	−	6.27372i	−0.672613	−	1.16500i	−0.977160	−	0.212503i	$-0.931838\pi$
$29$	−3.62213	−	6.27372i	−0.672613	−	1.16500i	0.304547	−	0.952497i	$-0.401495\pi$
$30$	−0.344805	+	0.597219i	−0.0629524	+	0.109037i
$31$		−	8.01115i		−	1.43885i	−0.694572	−	0.719423i	$-0.744406\pi$
$31$		−	8.01115i		−	1.43885i	0.694572	−	0.719423i	$-0.255594\pi$
$32$	5.07050	+	2.92745i	0.896346	+	0.517506i
$33$	1.69592	+	0.979137i	0.295221	+	0.170446i
$34$		−	0.729584i		−	0.125123i
$35$	0.168178	−	0.291293i	0.0284272	−	0.0492374i
$36$	−0.733853	−	1.27107i	−0.122309	−	0.211845i
$37$	1.00678	−	0.581264i	0.165514	−	0.0955593i	−0.414955	−	0.909842i	$-0.636203\pi$
$37$	1.00678	−	0.581264i	0.165514	−	0.0955593i	0.580469	+	0.814283i	$0.302869\pi$
$38$	−1.23307			−0.200031
$39$	−1.75687	+	3.14855i	−0.281325	+	0.504172i
$40$	2.39136			0.378108
$41$	−1.05344	+	0.608202i	−0.164519	+	0.0949852i	−0.579999	−	0.814617i	$-0.696947\pi$
$41$	−1.05344	+	0.608202i	−0.164519	+	0.0949852i	0.415480	+	0.909602i	$0.363614\pi$
$42$	−0.129813	−	0.224842i	−0.0200305	−	0.0346939i
$43$	3.07754	−	5.33045i	0.469320	−	0.812886i	−0.530065	−	0.847957i	$-0.677832\pi$
$43$	3.07754	−	5.33045i	0.469320	−	0.812886i	0.999385	+	0.0350709i	$0.0111657\pi$
$44$		−	2.87417i		−	0.433298i
$45$	−0.818574	−	0.472604i	−0.122026	−	0.0704517i
$46$	0.766796	+	0.442710i	0.113058	+	0.0652740i
$47$		−	5.16110i		−	0.752824i	−0.926452	−	0.376412i	$-0.877158\pi$
$47$		−	5.16110i		−	0.752824i	0.926452	−	0.376412i	$-0.122842\pi$
$48$	−0.544788	+	0.943601i	−0.0786334	+	0.136197i
$49$	−3.43668	−	5.95251i	−0.490955	−	0.850359i
$50$	−2.59470	+	1.49805i	−0.366946	+	0.211856i
$51$	1.00000			0.140028
$52$	5.29132	−	0.0774638i	0.733775	−	0.0107423i
$53$	−9.92348			−1.36310			−0.681548	−	0.731774i	$-0.738693\pi$
$53$	−9.92348			−1.36310			−0.681548	+	0.731774i	$0.738693\pi$
$54$	−0.631839	+	0.364792i	−0.0859823	+	0.0496419i
$55$	−0.925488	−	1.60299i	−0.124793	−	0.216148i
$56$	−0.450152	+	0.779686i	−0.0601541	+	0.104190i
$57$		−	1.69010i		−	0.223859i
$58$	4.57721	+	2.64265i	0.601017	+	0.346997i
$59$	−5.98501	−	3.45545i	−0.779182	−	0.449861i	0.0569585	−	0.998377i	$-0.481860\pi$
$59$	−5.98501	−	3.45545i	−0.779182	−	0.449861i	−0.836140	+	0.548516i	$0.815193\pi$
$60$			1.38729i			0.179098i
$61$	3.54801	−	6.14533i	0.454276	−	0.786829i	−0.544370	−	0.838845i	$-0.683231\pi$
$61$	3.54801	−	6.14533i	0.454276	−	0.786829i	0.998646	+	0.0520160i	$0.0165647\pi$
$62$	2.92241	+	5.06176i	0.371146	+	0.642844i
$63$	0.308178	−	0.177927i	0.0388268	−	0.0224167i
$64$	−2.09250			−0.261562
$65$	2.92615	−	1.74702i	0.362944	−	0.216691i
$66$	−1.42873			−0.175864
$67$	5.58216	−	3.22286i	0.681969	−	0.393735i	−0.118627	−	0.992939i	$-0.537849\pi$
$67$	5.58216	−	3.22286i	0.681969	−	0.393735i	0.800597	+	0.599204i	$0.204516\pi$
$68$	−0.733853	−	1.27107i	−0.0889928	−	0.154140i
$69$	−0.606797	+	1.05100i	−0.0730498	+	0.126526i
$70$			0.245400i			0.0293309i
$71$	−5.61258	−	3.24042i	−0.666091	−	0.384568i	0.128503	−	0.991709i	$-0.458983\pi$
$71$	−5.61258	−	3.24042i	−0.666091	−	0.384568i	−0.794594	+	0.607141i	$0.792316\pi$
$72$	2.19103	+	1.26499i	0.258215	+	0.149081i
$73$			9.64552i			1.12892i	0.825459	+	0.564461i	$0.190916\pi$
$73$			9.64552i			1.12892i	−0.825459	+	0.564461i	$0.809084\pi$
$74$	−0.424081	+	0.734531i	−0.0492985	+	0.0853874i
$75$	−2.05329	−	3.55640i	−0.237094	−	0.410658i
$76$	−2.14824	+	1.24029i	−0.246420	+	0.142271i
$77$	0.696859			0.0794144
$78$	−0.0385066	−	2.63027i	−0.00436001	−	0.297820i
$79$	−2.63504			−0.296465			−0.148233	−	0.988953i	$-0.547358\pi$
$79$	−2.63504			−0.296465			−0.148233	+	0.988953i	$0.547358\pi$
$80$	0.891899	−	0.514938i	0.0997174	−	0.0575718i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.443735	−	0.768571i	0.0490023	−	0.0848745i
$83$		−	4.82358i		−	0.529456i	−0.964323	−	0.264728i	$-0.914718\pi$
$83$		−	4.82358i		−	0.529456i	0.964323	−	0.264728i	$-0.0852822\pi$
$84$	−0.452315	−	0.261144i	−0.0493516	−	0.0284932i
$85$	−0.818574	−	0.472604i	−0.0887868	−	0.0512611i
$86$			4.49065i			0.484239i
$87$	−3.62213	+	6.27372i	−0.388333	+	0.672613i
$88$	2.47720	+	4.29064i	0.264071	+	0.457384i
$89$	−11.2195	+	6.47759i	−1.18927	+	0.686623i	−0.958140	−	0.286301i	$-0.907574\pi$
$89$	−11.2195	+	6.47759i	−1.18927	+	0.686623i	−0.231126	+	0.972924i	$0.574241\pi$
$90$	0.689609			0.0726912
$91$	0.0187815	+	1.28291i	0.00196884	+	0.134486i
$92$	1.78120			0.185703
$93$	−6.93786	+	4.00558i	−0.719423	+	0.415359i
$94$	1.88273	+	3.26098i	0.194189	+	0.336345i
$95$	−0.798749	+	1.38347i	−0.0819499	+	0.141941i
$96$		−	5.85491i		−	0.597564i
$97$	5.44329	+	3.14269i	0.552682	+	0.319091i	0.750203	−	0.661207i	$-0.229956\pi$
$97$	5.44329	+	3.14269i	0.552682	+	0.319091i	−0.197521	+	0.980299i	$0.563289\pi$
$98$	4.34286	+	2.50735i	0.438695	+	0.253281i
$99$		−	1.95827i		−	0.196814i
$100$	−3.01363	+	5.21976i	−0.301363	+	0.521976i
$101$	−0.379162	−	0.656728i	−0.0377280	−	0.0653468i	0.846545	−	0.532317i	$-0.178679\pi$
$101$	−0.379162	−	0.656728i	−0.0377280	−	0.0653468i	−0.884273	+	0.466971i	$0.845345\pi$
$102$	−0.631839	+	0.364792i	−0.0625613	+	0.0361198i
$103$	13.3813			1.31850			0.659249	−	0.751925i	$-0.270874\pi$
$103$	13.3813			1.31850			0.659249	+	0.751925i	$0.270874\pi$
$104$	−7.83226	+	4.67615i	−0.768017	+	0.458534i
$105$	−0.336356			−0.0328249
$106$	6.27004	−	3.62001i	0.609000	−	0.351606i
$107$	4.52244	+	7.83309i	0.437201	+	0.757254i	0.997472	−	0.0710551i	$-0.0226366\pi$
$107$	4.52244	+	7.83309i	0.437201	+	0.757254i	−0.560272	+	0.828309i	$0.689303\pi$
$108$	−0.733853	+	1.27107i	−0.0706151	+	0.122309i
$109$		−	0.942463i		−	0.0902716i	−0.998981	−	0.0451358i	$-0.985628\pi$
$109$		−	0.942463i		−	0.0902716i	0.998981	−	0.0451358i	$-0.0143721\pi$
$110$	1.16952	+	0.675222i	0.111509	+	0.0643799i
$111$	−1.00678	−	0.581264i	−0.0955593	−	0.0551712i
$112$			0.387730i			0.0366370i
$113$	−1.02464	+	1.77473i	−0.0963902	+	0.166953i	−0.910188	−	0.414195i	$-0.864063\pi$
$113$	−1.02464	+	1.77473i	−0.0963902	+	0.166953i	0.813798	+	0.581148i	$0.197396\pi$
$114$	0.616536	+	1.06787i	0.0577439	+	0.100015i
$115$	0.993418	−	0.573550i	0.0926367	−	0.0534838i
$116$	10.6325			0.987199
$117$	3.60516	−	0.0527788i	0.333298	−	0.00487940i
$118$	5.04208			0.464161
$119$	0.308178	−	0.177927i	0.0282506	−	0.0163105i
$120$	−1.19568	−	2.07098i	−0.109150	−	0.189054i
$121$	−3.58258	+	6.20521i	−0.325689	+	0.564110i
$122$			5.17714i			0.468716i
$123$	1.05344	+	0.608202i	0.0949852	+	0.0548397i
$124$	10.1827	+	5.87901i	0.914438	+	0.527951i
$125$			8.60762i			0.769889i
$126$	−0.129813	+	0.224842i	−0.0115646	+	0.0200305i
$127$	−7.96016	−	13.7874i	−0.706350	−	1.22343i	−0.966202	−	0.257786i	$-0.917007\pi$
$127$	−7.96016	−	13.7874i	−0.706350	−	1.22343i	0.259852	−	0.965648i	$-0.416326\pi$
$128$	−8.81888	+	5.09158i	−0.779486	+	0.450036i
$129$	−6.15508			−0.541924
$130$	−1.21156	+	2.17127i	−0.106261	+	0.190433i
$131$	0.373813			0.0326602			0.0163301	−	0.999867i	$-0.494802\pi$
$131$	0.373813			0.0326602			0.0163301	+	0.999867i	$0.494802\pi$
$132$	−2.48911	+	1.43709i	−0.216649	+	0.125082i
$133$	−0.300714	−	0.520852i	−0.0260752	−	0.0451636i
$134$	−2.35135	+	4.07266i	−0.203126	+	0.351824i
$135$			0.945208i			0.0813506i
$136$	2.19103	+	1.26499i	0.187879	+	0.108472i
$137$	19.1290	+	11.0441i	1.63430	+	0.943565i	0.982745	+	0.184967i	$0.0592177\pi$
$137$	19.1290	+	11.0441i	1.63430	+	0.943565i	0.651558	+	0.758599i	$0.274116\pi$
$138$		−	0.885420i		−	0.0753719i
$139$	3.99684	−	6.92273i	0.339008	−	0.587178i	−0.645239	−	0.763981i	$-0.723242\pi$
$139$	3.99684	−	6.92273i	0.339008	−	0.587178i	0.984246	+	0.176803i	$0.0565754\pi$
$140$	0.246836	+	0.427532i	0.0208614	+	0.0361330i
$141$	−4.46964	+	2.58055i	−0.376412	+	0.217321i
$142$	4.72833			0.396792
$143$	6.16573	+	3.44044i	0.515604	+	0.287704i
$144$	1.08958			0.0907980
$145$	5.92997	−	3.42367i	0.492457	−	0.284320i
$146$	−3.51861	−	6.09441i	−0.291202	−	0.504377i
$147$	−3.43668	+	5.95251i	−0.283453	+	0.490955i
$148$			1.70625i			0.140253i
$149$	−2.68718	−	1.55145i	−0.220143	−	0.127099i	0.385874	−	0.922552i	$-0.373900\pi$
$149$	−2.68718	−	1.55145i	−0.220143	−	0.127099i	−0.606016	+	0.795452i	$0.707233\pi$
$150$	2.59470	+	1.49805i	0.211856	+	0.122315i
$151$			1.60135i			0.130316i	0.997875	+	0.0651582i	$0.0207552\pi$
$151$			1.60135i			0.130316i	−0.997875	+	0.0651582i	$0.979245\pi$
$152$	2.13796	−	3.70306i	0.173412	−	0.300358i
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	−0.440302	+	0.254209i	−0.0354806	+	0.0204847i
$155$	7.57221			0.608214
$156$	−2.71275	−	4.54369i	−0.217194	−	0.363786i
$157$	8.62389			0.688261			0.344131	−	0.938922i	$-0.388174\pi$
$157$	8.62389			0.688261			0.344131	+	0.938922i	$0.388174\pi$
$158$	1.66492	−	0.961242i	0.132454	−	0.0764723i
$159$	4.96174	+	8.59399i	0.393492	+	0.681548i
$160$	−2.76705	+	4.79268i	−0.218755	+	0.378894i
$161$			0.431862i			0.0340355i
$162$	0.631839	+	0.364792i	0.0496419	+	0.0286608i
$163$	−7.66337	−	4.42445i	−0.600241	−	0.346549i	0.168895	−	0.985634i	$-0.445980\pi$
$163$	−7.66337	−	4.42445i	−0.600241	−	0.346549i	−0.769136	+	0.639085i	$0.779313\pi$
$164$		−	1.78532i		−	0.139410i
$165$	−0.925488	+	1.60299i	−0.0720492	+	0.124793i
$166$	1.75960	+	3.04772i	0.136572	+	0.236549i
$167$	−18.4575	+	10.6564i	−1.42828	+	0.824620i	−0.996985	−	0.0775901i	$-0.975277\pi$
$167$	−18.4575	+	10.6564i	−1.42828	+	0.824620i	−0.431298	+	0.902210i	$0.641944\pi$
$168$	0.900304			0.0694599
$169$	−6.16765	+	11.4438i	−0.474434	+	0.880291i
$170$	0.689609			0.0528906
$171$	−1.46367	+	0.845051i	−0.111930	+	0.0646226i
$172$	4.51692	+	7.82354i	0.344412	+	0.596539i
$173$	−2.01916	+	3.49728i	−0.153514	+	0.265893i	−0.932517	−	0.361127i	$-0.882392\pi$
$173$	−2.01916	+	3.49728i	−0.153514	+	0.265893i	0.779003	+	0.627020i	$0.215726\pi$
$174$		−	5.28530i		−	0.400678i
$175$	−1.26556	−	0.730671i	−0.0956673	−	0.0552335i
$176$	1.84783	+	1.06684i	0.139285	+	0.0804164i
$177$			6.91089i			0.519454i
$178$	4.72595	−	8.18558i	0.354225	−	0.613535i
$179$	−3.43377	−	5.94747i	−0.256652	−	0.444535i	0.708691	−	0.705519i	$-0.249286\pi$
$179$	−3.43377	−	5.94747i	−0.256652	−	0.444535i	−0.965343	+	0.260984i	$0.915953\pi$
$180$	1.20143	−	0.693644i	0.0895491	−	0.0517012i
$181$	−25.5232			−1.89713			−0.948564	−	0.316587i	$-0.897463\pi$
$181$	−25.5232			−1.89713			−0.948564	+	0.316587i	$0.897463\pi$
$182$	−0.479863	−	0.803741i	−0.0355698	−	0.0595772i
$183$	−7.09602			−0.524553
$184$	−2.65902	+	1.53519i	−0.196026	+	0.113176i
$185$	0.549416	+	0.951616i	0.0403939	+	0.0699642i
$186$	2.92241	−	5.06176i	0.214281	−	0.371146i
$187$		−	1.95827i		−	0.143203i
$188$	6.56012	+	3.78749i	0.478446	+	0.276231i
$189$	−0.308178	−	0.177927i	−0.0224167	−	0.0129423i
$190$		−	1.16551i		−	0.0845549i
$191$	9.18687	−	15.9121i	0.664739	−	1.15136i	−0.314617	−	0.949219i	$-0.601876\pi$
$191$	9.18687	−	15.9121i	0.664739	−	1.15136i	0.979356	−	0.202143i	$-0.0647905\pi$
$192$	1.04625	+	1.81215i	0.0755064	+	0.130781i
$193$	−20.7376	+	11.9728i	−1.49272	+	0.861824i	−0.999965	−	0.00834327i	$-0.997344\pi$
$193$	−20.7376	+	11.9728i	−1.49272	+	0.861824i	−0.492757	+	0.870167i	$0.664011\pi$
$194$	−4.58571			−0.329235
$195$	−2.97604	−	1.66061i	−0.213119	−	0.118919i
$196$	10.0881			0.720578
$197$	−16.2499	+	9.38189i	−1.15776	+	0.668432i	−0.950766	−	0.309910i	$-0.899701\pi$
$197$	−16.2499	+	9.38189i	−1.15776	+	0.668432i	−0.206993	+	0.978343i	$0.566368\pi$
$198$	0.714363	+	1.23731i	0.0507676	+	0.0879320i
$199$	−6.72578	+	11.6494i	−0.476778	+	0.825804i	−0.999646	−	0.0266098i	$-0.991529\pi$
$199$	−6.72578	+	11.6494i	−0.476778	+	0.825804i	0.522868	+	0.852414i	$0.324862\pi$
$200$		−	10.3896i		−	0.734655i
$201$	−5.58216	−	3.22286i	−0.393735	−	0.227323i
$202$	0.479138	+	0.276631i	0.0337120	+	0.0194637i
$203$			2.57790i			0.180933i
$204$	−0.733853	+	1.27107i	−0.0513800	+	0.0889928i
$205$	−0.574877	−	0.995717i	−0.0401512	−	0.0695439i
$206$	−8.45481	+	4.88139i	−0.589075	+	0.340102i
$207$	1.21359			0.0843507
$208$	−1.91425	+	3.43059i	−0.132729	+	0.237869i
$209$	−3.30968			−0.228935
$210$	0.212522	−	0.122700i	0.0146654	−	0.00846710i
$211$	−5.87084	−	10.1686i	−0.404166	−	0.700035i	0.590058	−	0.807361i	$-0.299105\pi$
$211$	−5.87084	−	10.1686i	−0.404166	−	0.700035i	−0.994224	+	0.107325i	$0.965771\pi$
$212$	7.28238	−	12.6135i	0.500156	−	0.866296i
$213$			6.48085i			0.444060i
$214$	−5.71490	−	3.29950i	−0.390663	−	0.225549i
$215$	5.03839	+	2.90891i	0.343615	+	0.198386i
$216$		−	2.52998i		−	0.172144i
$217$	−1.42540	+	2.46886i	−0.0967624	+	0.167597i
$218$	0.343803	+	0.595484i	0.0232853	+	0.0403313i
$219$	8.35327	−	4.82276i	0.564461	−	0.325892i
$220$	2.71669			0.183159
$221$	3.60516	−	0.0527788i	0.242510	−	0.00355029i
$222$	0.848163			0.0569250
$223$	13.8436	−	7.99260i	0.927035	−	0.535224i	0.0411625	−	0.999152i	$-0.486894\pi$
$223$	13.8436	−	7.99260i	0.927035	−	0.535224i	0.885873	+	0.463928i	$0.153561\pi$
$224$	−1.04174	−	1.80435i	−0.0696045	−	0.120559i
$225$	−2.05329	+	3.55640i	−0.136886	+	0.237094i
$226$		−	1.49513i		−	0.0994543i
$227$	1.24446	+	0.718488i	0.0825976	+	0.0476877i	0.540730	−	0.841196i	$-0.318148\pi$
$227$	1.24446	+	0.718488i	0.0825976	+	0.0476877i	−0.458132	+	0.888884i	$0.651481\pi$
$228$	2.14824	+	1.24029i	0.142271	+	0.0821400i
$229$			13.2968i			0.878679i	0.898321	+	0.439340i	$0.144788\pi$
$229$			13.2968i			0.878679i	−0.898321	+	0.439340i	$0.855212\pi$
$230$	−0.418453	+	0.724782i	−0.0275920	+	0.0477907i
$231$	−0.348429	−	0.603497i	−0.0229250	−	0.0397072i
$232$	−15.8724	+	9.16394i	−1.04207	+	0.601642i
$233$	9.25528			0.606333			0.303167	−	0.952938i	$-0.401956\pi$
$233$	9.25528			0.606333			0.303167	+	0.952938i	$0.401956\pi$
$234$	−2.25863	+	1.34848i	−0.147651	+	0.0881531i
$235$	4.87831			0.318226
$236$	8.78424	−	5.07158i	0.571805	−	0.330132i
$237$	1.31752	+	2.28201i	0.0855821	+	0.148233i
$238$	−0.129813	+	0.224842i	−0.00841450	+	0.0145743i
$239$			13.1646i			0.851545i	0.904830	+	0.425772i	$0.139998\pi$
$239$			13.1646i			0.851545i	−0.904830	+	0.425772i	$0.860002\pi$
$240$	−0.891899	−	0.514938i	−0.0575718	−	0.0332391i
$241$	−2.90459	−	1.67697i	−0.187101	−	0.108023i	0.403524	−	0.914969i	$-0.367785\pi$
$241$	−2.90459	−	1.67697i	−0.187101	−	0.108023i	−0.590625	+	0.806946i	$0.701119\pi$
$242$		−	5.22759i		−	0.336042i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.20744	+	9.01954i	0.333372	+	0.577417i
$245$	5.62636	−	3.24838i	0.359455	−	0.207532i
$246$	−0.887469			−0.0565830
$247$	−0.0892015	−	6.09309i	−0.00567575	−	0.387694i
$248$	−20.2681			−1.28703
$249$	−4.17734	+	2.41179i	−0.264728	+	0.152841i
$250$	−3.13999	−	5.43862i	−0.198590	−	0.343969i
$251$	7.83186	−	13.5652i	0.494342	−	0.856226i	−0.505636	−	0.862747i	$-0.668742\pi$
$251$	7.83186	−	13.5652i	0.494342	−	0.856226i	0.999979	+	0.00652056i	$0.00207557\pi$
$252$			0.522289i			0.0329011i
$253$	2.05815	+	1.18828i	0.129395	+	0.0747063i
$254$	10.0591	+	5.80761i	0.631162	+	0.364402i
$255$			0.945208i			0.0591912i
$256$	5.80723	−	10.0584i	0.362952	−	0.628651i
$257$	−5.92643	−	10.2649i	−0.369681	−	0.640306i	0.619835	−	0.784732i	$-0.287200\pi$
$257$	−5.92643	−	10.2649i	−0.369681	−	0.640306i	−0.989516	+	0.144427i	$0.953866\pi$
$258$	3.88901	−	2.24532i	0.242119	−	0.139788i
$259$	−0.413690			−0.0257054
$260$	0.0732194	+	5.00140i	0.00454087	+	0.310174i
$261$	7.24427			0.448409
$262$	−0.236189	+	0.136364i	−0.0145918	+	0.00842459i
$263$	−6.71105	−	11.6239i	−0.413821	−	0.716759i	0.581483	−	0.813559i	$-0.302473\pi$
$263$	−6.71105	−	11.6239i	−0.413821	−	0.716759i	−0.995304	+	0.0967995i	$0.969139\pi$
$264$	2.47720	−	4.29064i	0.152461	−	0.264071i
$265$		−	9.37976i		−	0.576194i
$266$	0.380006	+	0.219396i	0.0232996	+	0.0134521i
$267$	11.2195	+	6.47759i	0.686623	+	0.396422i
$268$			9.46043i			0.577888i
$269$	3.34909	−	5.80080i	0.204198	−	0.353681i	−0.745679	−	0.666305i	$-0.767875\pi$
$269$	3.34909	−	5.80080i	0.204198	−	0.353681i	0.949877	+	0.312624i	$0.101208\pi$
$270$	−0.344805	−	0.597219i	−0.0209841	−	0.0363456i
$271$	12.6192	−	7.28571i	0.766563	−	0.442575i	−0.0650843	−	0.997880i	$-0.520732\pi$
$271$	12.6192	−	7.28571i	0.766563	−	0.442575i	0.831647	+	0.555305i	$0.187398\pi$
$272$	1.08958			0.0660653
$273$	1.10164	−	0.657721i	0.0666744	−	0.0398071i
$274$	−16.1153			−0.973559
$275$	−6.96441	+	4.02091i	−0.419970	+	0.242470i
$276$	−0.890601	−	1.54257i	−0.0536079	−	0.0928515i
$277$	−0.133476	+	0.231187i	−0.00801980	+	0.0138907i	−0.870007	−	0.493039i	$-0.835886\pi$
$277$	−0.133476	+	0.231187i	−0.00801980	+	0.0138907i	0.861988	+	0.506929i	$0.169219\pi$
$278$			5.83206i			0.349784i
$279$	6.93786	+	4.00558i	0.415359	+	0.239808i
$280$	−0.736966	−	0.425487i	−0.0440421	−	0.0254277i
$281$		−	16.1518i		−	0.963537i	−0.876299	−	0.481768i	$-0.839995\pi$
$281$		−	16.1518i		−	0.963537i	0.876299	−	0.481768i	$-0.160005\pi$
$282$	1.88273	−	3.26098i	0.112115	−	0.194189i
$283$	−14.5768	−	25.2478i	−0.866503	−	1.50083i	−0.865547	−	0.500828i	$-0.833029\pi$
$283$	−14.5768	−	25.2478i	−0.866503	−	1.50083i	−0.000956377	−	1.00000i	$-0.500304\pi$
$284$	8.23762	−	4.75599i	0.488813	−	0.282216i
$285$	1.59750			0.0946276
$286$	−5.15079	+	0.0754064i	−0.304573	+	0.00445888i
$287$	0.432862			0.0255510
$288$	−5.07050	+	2.92745i	−0.298782	+	0.172502i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.49786	+	4.32641i	−0.146679	+	0.254056i
$291$		−	6.28537i		−	0.368455i
$292$	−12.2601	−	7.07840i	−0.717471	−	0.414232i
$293$	9.02281	+	5.20932i	0.527118	+	0.304332i	0.739842	−	0.672781i	$-0.234900\pi$
$293$	9.02281	+	5.20932i	0.527118	+	0.304332i	−0.212724	+	0.977112i	$0.568234\pi$
$294$		−	5.01470i		−	0.292463i
$295$	3.26612	−	5.65708i	0.190161	−	0.329368i
$296$	−1.47059	−	2.54714i	−0.0854763	−	0.148049i
$297$	−1.69592	+	0.979137i	−0.0984070	+	0.0568153i
$298$	2.26382			0.131140
$299$	−2.13213	+	3.82107i	−0.123304	+	0.220978i
$300$	6.02726			0.347984
$301$	−1.89686	+	1.09515i	−0.109333	+	0.0631235i
$302$	−0.584161	−	1.01180i	−0.0336147	−	0.0582224i
$303$	−0.379162	+	0.656728i	−0.0217823	+	0.0377280i
$304$		−	1.84149i		−	0.105617i
$305$	5.80862	+	3.35361i	0.332600	+	0.192027i
$306$	0.631839	+	0.364792i	0.0361198	+	0.0208538i
$307$			30.5982i			1.74633i	0.487423	+	0.873166i	$0.337937\pi$
$307$			30.5982i			1.74633i	−0.487423	+	0.873166i	$0.662063\pi$
$308$	−0.511392	+	0.885757i	−0.0291393	+	0.0504707i
$309$	−6.69064	−	11.5885i	−0.380617	−	0.659249i
$310$	−4.78441	+	2.76228i	−0.271736	+	0.156887i
$311$	32.2214			1.82711			0.913553	−	0.406719i	$-0.133327\pi$
$311$	32.2214			1.82711			0.913553	+	0.406719i	$0.133327\pi$
$312$	7.96579	+	4.44487i	0.450974	+	0.251641i
$313$	10.9710			0.620120			0.310060	−	0.950717i	$-0.399651\pi$
$313$	10.9710			0.620120			0.310060	+	0.950717i	$0.399651\pi$
$314$	−5.44891	+	3.14593i	−0.307500	+	0.177535i
$315$	0.168178	+	0.291293i	0.00947575	+	0.0164125i
$316$	1.93373	−	3.34932i	0.108781	−	0.188414i
$317$		−	28.8913i		−	1.62270i	−0.584561	−	0.811350i	$-0.698733\pi$
$317$		−	28.8913i		−	1.62270i	0.584561	−	0.811350i	$-0.301267\pi$
$318$	−6.27004	−	3.62001i	−0.351606	−	0.203000i
$319$	12.2857	+	7.09313i	0.687865	+	0.397139i
$320$		−	1.97784i		−	0.110565i
$321$	4.52244	−	7.83309i	0.252418	−	0.437201i
$322$	−0.157540	−	0.272867i	−0.00877935	−	0.0152063i
$323$	−1.46367	+	0.845051i	−0.0814408	+	0.0470199i
$324$	1.46771			0.0815393
$325$	−7.59015	−	12.7131i	−0.421026	−	0.705193i
$326$	6.45601			0.357566
$327$	−0.816197	+	0.471231i	−0.0451358	+	0.0260592i
$328$	1.53874	+	2.66518i	0.0849628	+	0.147160i
$329$	−0.918298	+	1.59054i	−0.0506274	+	0.0876892i
$330$		−	1.35044i		−	0.0743395i
$331$	−19.7310	−	11.3917i	−1.08451	−	0.626145i	−0.152404	−	0.988318i	$-0.548701\pi$
$331$	−19.7310	−	11.3917i	−1.08451	−	0.626145i	−0.932111	+	0.362174i	$0.882035\pi$
$332$	6.13111	+	3.53980i	0.336488	+	0.194272i
$333$			1.16253i			0.0637062i
$334$	7.77477	−	13.4663i	0.425416	−	0.736843i
$335$	3.04627	+	5.27630i	0.166436	+	0.288275i
$336$	0.335784	−	0.193865i	0.0183185	−	0.0105762i
$337$	−8.37595			−0.456267			−0.228134	−	0.973630i	$-0.573262\pi$
$337$	−8.37595			−0.456267			−0.228134	+	0.973630i	$0.573262\pi$
$338$	−0.277645	−	9.48053i	−0.0151019	−	0.515673i
$339$	2.04928			0.111302
$340$	1.20143	−	0.693644i	0.0651565	−	0.0376181i
$341$	7.84402	+	13.5862i	0.424777	+	0.735736i
$342$	0.616536	−	1.06787i	0.0333384	−	0.0577439i
$343$			4.93689i			0.266567i
$344$	−13.4860	−	7.78612i	−0.727114	−	0.419800i
$345$	−0.993418	−	0.573550i	−0.0534838	−	0.0308789i
$346$		−	2.94629i		−	0.158393i
$347$	4.85756	−	8.41354i	0.260768	−	0.451663i	−0.705679	−	0.708532i	$-0.749358\pi$
$347$	4.85756	−	8.41354i	0.260768	−	0.451663i	0.966446	+	0.256869i	$0.0826910\pi$
$348$	−5.31623	−	9.20798i	−0.284980	−	0.493599i
$349$	3.34488	−	1.93117i	0.179047	−	0.103373i	−0.407798	−	0.913072i	$-0.633703\pi$
$349$	3.34488	−	1.93117i	0.179047	−	0.103373i	0.586845	+	0.809699i	$0.300370\pi$
$350$	1.06617			0.0569893
$351$	−1.84829	−	3.09578i	−0.0986544	−	0.165240i
$352$	−11.4655			−0.611114
$353$	3.71156	−	2.14287i	0.197546	−	0.114053i	−0.397964	−	0.917401i	$-0.630283\pi$
$353$	3.71156	−	2.14287i	0.197546	−	0.114053i	0.595510	+	0.803348i	$0.296950\pi$
$354$	−2.52104	−	4.36657i	−0.133992	−	0.232080i
$355$	3.06288	−	5.30506i	0.162561	−	0.281563i
$356$		−	19.0144i		−	1.00776i
$357$	−0.308178	−	0.177927i	−0.0163105	−	0.00941688i
$358$	4.33918	+	2.50523i	0.229333	+	0.132405i
$359$			9.22830i			0.487051i	0.969895	+	0.243525i	$0.0783039\pi$
$359$			9.22830i			0.487051i	−0.969895	+	0.243525i	$0.921696\pi$
$360$	−1.19568	+	2.07098i	−0.0630179	+	0.109150i
$361$	−8.07178	−	13.9807i	−0.424830	−	0.735828i
$362$	16.1266	−	9.31068i	0.847593	−	0.489358i
$363$	7.16516			0.376073
$364$	−1.64445	−	0.917596i	−0.0861928	−	0.0480951i
$365$	−9.11703			−0.477207
$366$	4.48354	−	2.58857i	0.234358	−	0.135307i
$367$	−10.6165	−	18.3884i	−0.554179	−	0.959866i	−0.997967	−	0.0637340i	$-0.979699\pi$
$367$	−10.6165	−	18.3884i	−0.554179	−	0.959866i	0.443788	−	0.896132i	$-0.353634\pi$
$368$	−0.661152	+	1.14515i	−0.0344649	+	0.0596950i
$369$		−	1.21640i		−	0.0633235i
$370$	−0.694284	−	0.400845i	−0.0360941	−	0.0208390i
$371$	3.05820	+	1.76565i	0.158774	+	0.0916681i
$372$		−	11.7580i		−	0.609625i
$373$	13.5017	−	23.3857i	0.699093	−	1.21087i	−0.269688	−	0.962948i	$-0.586921\pi$
$373$	13.5017	−	23.3857i	0.699093	−	1.21087i	0.968781	−	0.247917i	$-0.0797461\pi$
$374$	0.714363	+	1.23731i	0.0369388	+	0.0639799i
$375$	7.45441	−	4.30381i	0.384944	−	0.222248i
$376$	−13.0575			−0.673389
$377$	−12.7273	+	22.8090i	−0.655488	+	1.17472i
$378$	0.259625			0.0133537
$379$	10.3953	−	6.00175i	0.533973	−	0.308289i	−0.208660	−	0.977988i	$-0.566910\pi$
$379$	10.3953	−	6.00175i	0.533973	−	0.308289i	0.742633	+	0.669699i	$0.233577\pi$
$380$	−1.17233	−	2.03053i	−0.0601392	−	0.104164i
$381$	−7.96016	+	13.7874i	−0.407811	+	0.706350i
$382$			13.4052i			0.685870i
$383$	18.7705	+	10.8371i	0.959126	+	0.553752i	0.895904	−	0.444248i	$-0.146529\pi$
$383$	18.7705	+	10.8371i	0.959126	+	0.553752i	0.0632222	+	0.997999i	$0.479862\pi$
$384$	8.81888	+	5.09158i	0.450036	+	0.259829i
$385$			0.658677i			0.0335693i
$386$	8.73519	−	15.1298i	0.444610	−	0.770087i
$387$	3.07754	+	5.33045i	0.156440	+	0.270962i
$388$	−7.98915	+	4.61254i	−0.405588	+	0.234166i
$389$	11.1925			0.567483			0.283742	−	0.958901i	$-0.408424\pi$
$389$	11.1925			0.567483			0.283742	+	0.958901i	$0.408424\pi$
$390$	2.48615	−	0.0363967i	0.125891	−	0.00184302i
$391$	1.21359			0.0613741
$392$	−15.0598	+	8.69476i	−0.760633	+	0.439152i
$393$	−0.186906	−	0.323731i	−0.00942817	−	0.0163301i
$394$	6.84488	−	11.8557i	0.344840	−	0.597281i
$395$		−	2.49066i		−	0.125319i
$396$	2.48911	+	1.43709i	0.125082	+	0.0722163i
$397$	14.7825	+	8.53466i	0.741910	+	0.428342i	0.822764	−	0.568384i	$-0.192431\pi$
$397$	14.7825	+	8.53466i	0.741910	+	0.428342i	−0.0808531	+	0.996726i	$0.525764\pi$
$398$		−	9.81405i		−	0.491934i
$399$	−0.300714	+	0.520852i	−0.0150545	+	0.0260752i
$400$	−2.23722	−	3.87497i	−0.111861	−	0.193749i
$401$	1.91790	−	1.10730i	0.0957752	−	0.0552958i	−0.451347	−	0.892348i	$-0.649056\pi$
$401$	1.91790	−	1.10730i	0.0957752	−	0.0552958i	0.547123	+	0.837052i	$0.315723\pi$
$402$	4.70270			0.234549
$403$	−24.8007	+	14.8069i	−1.23541	+	0.737586i
$404$	1.11300			0.0553737
$405$	0.818574	−	0.472604i	0.0406753	−	0.0234839i
$406$	−0.940397	−	1.62881i	−0.0466711	−	0.0808367i
$407$	−1.13828	+	1.97155i	−0.0564222	+	0.0977261i
$408$		−	2.52998i		−	0.125253i
$409$	20.8809	+	12.0556i	1.03249	+	0.596110i	0.917698	−	0.397280i	$-0.130046\pi$
$409$	20.8809	+	12.0556i	1.03249	+	0.596110i	0.114794	+	0.993389i	$0.463379\pi$
$410$	0.726460	+	0.419422i	0.0358773	+	0.0207138i
$411$		−	22.0883i		−	1.08954i
$412$	−9.81990	+	17.0086i	−0.483792	+	0.837952i
$413$	1.22963	+	2.12979i	0.0605063	+	0.104800i
$414$	−0.766796	+	0.442710i	−0.0376860	+	0.0217580i
$415$	4.55928			0.223806
$416$	−0.309015	−	21.1079i	−0.0151507	−	1.03490i
$417$	−7.99368			−0.391452
$418$	2.09118	−	1.20735i	0.102283	−	0.0590532i
$419$	−0.489565	−	0.847951i	−0.0239168	−	0.0414251i	0.853819	−	0.520570i	$-0.174280\pi$
$419$	−0.489565	−	0.847951i	−0.0239168	−	0.0414251i	−0.877736	+	0.479144i	$0.840947\pi$
$420$	0.246836	−	0.427532i	0.0120443	−	0.0208614i
$421$			12.0306i			0.586335i	0.956061	+	0.293167i	$0.0947094\pi$
$421$			12.0306i			0.586335i	−0.956061	+	0.293167i	$0.905291\pi$
$422$	7.41885	+	4.28328i	0.361144	+	0.208507i
$423$	4.46964	+	2.58055i	0.217321	+	0.125471i
$424$			25.1063i			1.21927i
$425$	−2.05329	+	3.55640i	−0.0995992	+	0.172511i
$426$	−2.36416	−	4.09485i	−0.114544	−	0.198396i
$427$	−2.18684	+	1.26257i	−0.105828	+	0.0611001i
$428$	−13.2752			−0.641682
$429$	−0.103355	−	7.05990i	−0.00499004	−	0.340855i
$430$	−4.24460			−0.204693
$431$	23.4046	−	13.5127i	1.12736	−	0.650882i	0.184091	−	0.982909i	$-0.441066\pi$
$431$	23.4046	−	13.5127i	1.12736	−	0.650882i	0.943270	+	0.332027i	$0.107732\pi$
$432$	−0.544788	−	0.943601i	−0.0262111	−	0.0453990i
$433$	−7.54771	+	13.0730i	−0.362720	+	0.628249i	−0.988407	−	0.151825i	$-0.951485\pi$
$433$	−7.54771	+	13.0730i	−0.362720	+	0.628249i	0.625688	+	0.780074i	$0.284818\pi$
$434$		−	2.07990i		−	0.0998382i
$435$	−5.92997	−	3.42367i	−0.284320	−	0.164152i
$436$	1.19794	+	0.691630i	0.0573708	+	0.0331231i
$437$		−	2.05110i		−	0.0981173i
$438$	−3.51861	+	6.09441i	−0.168126	+	0.291202i
$439$	−9.92747	−	17.1949i	−0.473812	−	0.820667i	0.525738	−	0.850646i	$-0.323789\pi$
$439$	−9.92747	−	17.1949i	−0.473812	−	0.820667i	−0.999551	+	0.0299794i	$0.990456\pi$
$440$	−4.05555	+	2.34147i	−0.193341	+	0.111625i
$441$	6.87337			0.327303
$442$	−2.25863	+	1.34848i	−0.107432	+	0.0641408i
$443$	9.28873			0.441321			0.220660	−	0.975351i	$-0.429179\pi$
$443$	9.28873			0.441321			0.220660	+	0.975351i	$0.429179\pi$
$444$	1.47766	−	0.853126i	0.0701265	−	0.0404876i
$445$	−6.12267	−	10.6048i	−0.290242	−	0.502715i
$446$	−5.83128	+	10.1001i	−0.276119	+	0.478252i
$447$			3.10289i			0.146762i
$448$	0.644861	+	0.372311i	0.0304668	+	0.0175900i
$449$	−23.3563	−	13.4848i	−1.10225	−	0.636385i	−0.165440	−	0.986220i	$-0.552904\pi$
$449$	−23.3563	−	13.4848i	−1.10225	−	0.636385i	−0.936811	+	0.349835i	$0.886238\pi$
$450$		−	2.99610i		−	0.141237i
$451$	1.19103	−	2.06292i	0.0560832	−	0.0971390i
$452$	−1.50387	−	2.60479i	−0.0707363	−	0.122519i
$453$	1.38681	−	0.800677i	0.0651582	−	0.0376191i
$454$	−1.04840			−0.0492036
$455$	−1.21262	+	0.0177524i	−0.0568484	+	0.000832247i
$456$	−4.27593			−0.200239
$457$	−29.5209	+	17.0439i	−1.38093	+	0.797279i	−0.992269	−	0.124103i	$-0.960395\pi$
$457$	−29.5209	+	17.0439i	−1.38093	+	0.797279i	−0.388658	+	0.921382i	$0.627061\pi$
$458$	−4.85058	−	8.40145i	−0.226653	−	0.392574i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$			1.68361i			0.0784985i
$461$	−25.2453	−	14.5754i	−1.17579	−	0.678844i	−0.220755	−	0.975329i	$-0.570852\pi$
$461$	−25.2453	−	14.5754i	−1.17579	−	0.678844i	−0.955037	+	0.296486i	$0.904185\pi$
$462$	0.440302	+	0.254209i	0.0204847	+	0.0118269i
$463$			17.0260i			0.791263i	0.918409	+	0.395632i	$0.129474\pi$
$463$			17.0260i			0.791263i	−0.918409	+	0.395632i	$0.870526\pi$
$464$	−3.94659	+	6.83569i	−0.183216	+	0.317339i
$465$	−3.78610	−	6.55772i	−0.175576	−	0.304107i
$466$	−5.84784	+	3.37625i	−0.270896	+	0.156402i
$467$	21.4682			0.993430			0.496715	−	0.867914i	$-0.334539\pi$
$467$	21.4682			0.993430			0.496715	+	0.867914i	$0.334539\pi$
$468$	−2.57858	+	4.62115i	−0.119195	+	0.213613i
$469$	−2.29373			−0.105915
$470$	−3.08231	+	1.77957i	−0.142176	+	0.0820855i
$471$	−4.31195	−	7.46851i	−0.198684	−	0.344131i
$472$	−8.74223	+	15.1420i	−0.402394	+	0.696966i
$473$			12.0533i			0.554212i
$474$	−1.66492	−	0.961242i	−0.0764723	−	0.0441513i
$475$	6.01068	+	3.47027i	0.275789	+	0.159227i
$476$			0.522289i			0.0239391i
$477$	4.96174	−	8.59399i	0.227183	−	0.393492i
$478$	−4.80233	−	8.31788i	−0.219653	−	0.380451i
$479$	5.35808	−	3.09349i	0.244817	−	0.141345i	−0.372572	−	0.928003i	$-0.621524\pi$
$479$	5.35808	−	3.09349i	0.244817	−	0.141345i	0.617389	+	0.786658i	$0.288191\pi$
$480$	5.53411			0.252596
$481$	−3.66028	−	2.04242i	−0.166895	−	0.0931262i
$482$	2.44698			0.111457
$483$	0.374003	−	0.215931i	0.0170177	−	0.00982520i
$484$	−5.25818	−	9.10743i	−0.239008	−	0.413974i
$485$	−2.97049	+	5.14504i	−0.134883	+	0.233624i
$486$		−	0.729584i		−	0.0330946i
$487$	15.1564	+	8.75052i	0.686800	+	0.396524i	0.802412	−	0.596770i	$-0.203550\pi$
$487$	15.1564	+	8.75052i	0.686800	+	0.396524i	−0.115612	+	0.993294i	$0.536883\pi$
$488$	−15.5476	−	8.97641i	−0.703806	−	0.406343i
$489$			8.84889i			0.400161i
$490$	−2.36997	+	4.10491i	−0.107064	+	0.185441i
$491$	1.68438	+	2.91743i	0.0760150	+	0.131662i	0.901527	−	0.432722i	$-0.142447\pi$
$491$	1.68438	+	2.91743i	0.0760150	+	0.131662i	−0.825512	+	0.564384i	$0.809114\pi$
$492$	−1.54614	+	0.892662i	−0.0697052	+	0.0402443i
$493$	7.24427			0.326265
$494$	2.27907	+	3.81731i	0.102540	+	0.171749i
$495$	1.85098			0.0831952
$496$	−7.55933	+	4.36438i	−0.339424	+	0.195967i
$497$	1.15312	+	1.99726i	0.0517243	+	0.0895892i
$498$	1.75960	−	3.04772i	0.0788497	−	0.136572i
$499$			28.3938i			1.27108i	0.772067	+	0.635541i	$0.219223\pi$
$499$			28.3938i			1.27108i	−0.772067	+	0.635541i	$0.780777\pi$
$500$	−10.9409	−	6.31673i	−0.489292	−	0.282493i
$501$	18.4575	+	10.6564i	0.824620	+	0.476094i
$502$			11.4280i			0.510057i
$503$	−19.1863	+	33.2317i	−0.855476	+	1.48173i	0.0207273	+	0.999785i	$0.493402\pi$
$503$	−19.1863	+	33.2317i	−0.855476	+	1.48173i	−0.876203	+	0.481942i	$0.839932\pi$
$504$	−0.450152	−	0.779686i	−0.0200514	−	0.0347300i
$505$	0.620744	−	0.358387i	0.0276228	−	0.0159480i
$506$	−1.73389			−0.0770810
$507$	12.9944	−	0.380552i	0.577103	−	0.0169009i
$508$	23.3664			1.03671
$509$	−21.1059	+	12.1855i	−0.935503	+	0.540113i	−0.888548	−	0.458784i	$-0.848285\pi$
$509$	−21.1059	+	12.1855i	−0.935503	+	0.540113i	−0.0469550	+	0.998897i	$0.514952\pi$
$510$	−0.344805	−	0.597219i	−0.0152682	−	0.0264453i
$511$	1.71620	−	2.97254i	0.0759201	−	0.131497i
$512$		−	11.8926i		−	0.525583i
$513$	1.46367	+	0.845051i	0.0646226	+	0.0373099i
$514$	7.48910	+	4.32383i	0.330330	+	0.190716i
$515$			12.6481i			0.557342i
$516$	4.51692	−	7.82354i	0.198846	−	0.344412i
$517$	5.05342	+	8.75279i	0.222249	+	0.384947i
$518$	0.261385	−	0.150911i	0.0114846	−	0.00663064i
$519$	4.03831			0.177262
$520$	−4.41993	−	7.40312i	−0.193827	−	0.324648i
$521$	−40.9321			−1.79327			−0.896634	−	0.442773i	$-0.853995\pi$
$521$	−40.9321			−1.79327			−0.896634	+	0.442773i	$0.853995\pi$
$522$	−4.57721	+	2.64265i	−0.200339	+	0.115666i
$523$	0.880108	+	1.52439i	0.0384844	+	0.0666570i	0.884626	−	0.466301i	$-0.154414\pi$
$523$	0.880108	+	1.52439i	0.0384844	+	0.0666570i	−0.846142	+	0.532958i	$0.821080\pi$
$524$	−0.274324	+	0.475142i	−0.0119839	+	0.0207567i
$525$			1.46134i			0.0637782i
$526$	8.48060	+	4.89628i	0.369772	+	0.213488i
$527$	6.93786	+	4.00558i	0.302218	+	0.174486i
$528$		−	2.13369i		−	0.0928569i
$529$	10.7636	−	18.6431i	0.467982	−	0.810569i
$530$	3.42166	+	5.92649i	0.148627	+	0.257430i
$531$	5.98501	−	3.45545i	0.259727	−	0.149954i
$532$	0.882720			0.0382708
$533$	3.82991	+	2.13707i	0.165892	+	0.0925667i
$534$	−9.45189			−0.409023
$535$	−7.40390	+	4.27465i	−0.320099	+	0.184809i
$536$	−8.15379	−	14.1228i	−0.352190	−	0.610011i
$537$	−3.43377	+	5.94747i	−0.148178	+	0.256652i
$538$			4.88689i			0.210689i
$539$	11.6567	+	6.72997i	0.502087	+	0.289880i
$540$	−1.20143	−	0.693644i	−0.0517012	−	0.0298497i
$541$		−	2.10668i		−	0.0905733i	−0.998974	−	0.0452867i	$-0.985580\pi$
$541$		−	2.10668i		−	0.0905733i	0.998974	−	0.0452867i	$-0.0144201\pi$
$542$	−5.31554	+	9.20678i	−0.228322	+	0.395465i
$543$	12.7616	+	22.1038i	0.547653	+	0.948564i
$544$	−5.07050	+	2.92745i	−0.217396	+	0.125514i
$545$	0.890824			0.0381587
$546$	−0.456129	+	0.817444i	−0.0195205	+	0.0349834i
$547$	−22.7513			−0.972774			−0.486387	−	0.873743i	$-0.661685\pi$
$547$	−22.7513			−0.972774			−0.486387	+	0.873743i	$0.661685\pi$
$548$	−28.0758	+	16.2096i	−1.19934	+	0.692439i
$549$	3.54801	+	6.14533i	0.151425	+	0.262276i
$550$	2.93359	−	5.08113i	0.125089	−	0.216660i
$551$		−	12.2435i		−	0.521592i
$552$	2.65902	+	1.53519i	0.113176	+	0.0653419i
$553$	0.812061	+	0.468844i	0.0345324	+	0.0199373i
$554$		−	0.194764i		−	0.00827474i
$555$	0.549416	−	0.951616i	0.0233214	−	0.0403939i
$556$	5.86619	+	10.1605i	0.248782	+	0.430903i
$557$	19.3845	−	11.1916i	0.821347	−	0.474205i	−0.0295338	−	0.999564i	$-0.509402\pi$
$557$	19.3845	−	11.1916i	0.821347	−	0.474205i	0.850881	+	0.525359i	$0.176069\pi$
$558$	−5.84481			−0.247431
$559$	−22.1901	+	0.324857i	−0.938540	+	0.0137400i
$560$	−0.366485			−0.0154868
$561$	−1.69592	+	0.979137i	−0.0716016	+	0.0413392i
$562$	5.89206	+	10.2053i	0.248541	+	0.430486i
$563$	15.7520	−	27.2833i	0.663868	−	1.14985i	−0.315723	−	0.948852i	$-0.602247\pi$
$563$	15.7520	−	27.2833i	0.663868	−	1.14985i	0.979591	−	0.201002i	$-0.0644197\pi$
$564$		−	7.57498i		−	0.318964i
$565$	−1.67749	−	0.968500i	−0.0705726	−	0.0407451i
$566$	18.4204	+	10.6350i	0.774268	+	0.447024i
$567$			0.355853i			0.0149444i
$568$	−8.19822	+	14.1997i	−0.343990	+	0.595808i
$569$	−19.4172	−	33.6316i	−0.814013	−	1.40991i	−0.910035	−	0.414532i	$-0.863945\pi$
$569$	−19.4172	−	33.6316i	−0.814013	−	1.40991i	0.0960220	−	0.995379i	$-0.469388\pi$
$570$	−1.00936	+	0.582755i	−0.0422775	+	0.0244089i
$571$	−14.9944			−0.627496			−0.313748	−	0.949506i	$-0.601585\pi$
$571$	−14.9944			−0.627496			−0.313748	+	0.949506i	$0.601585\pi$
$572$	−8.89779	+	5.31230i	−0.372035	+	0.222119i
$573$	−18.3737			−0.767574
$574$	−0.273499	+	0.157905i	−0.0114156	+	0.00659081i
$575$	−2.49186	−	4.31603i	−0.103918	−	0.179991i
$576$	1.04625	−	1.81215i	0.0435937	−	0.0755064i
$577$			0.0168293i			0.000700613i	1.00000		0.000350306i	$0.000111506\pi$
$577$			0.0168293i			0.000700613i	−1.00000		0.000350306i	$0.999888\pi$
$578$	0.631839	+	0.364792i	0.0262810	+	0.0151734i
$579$	20.7376	+	11.9728i	0.861824	+	0.497574i
$580$			10.0499i			0.417299i
$581$	−0.858243	+	1.48652i	−0.0356059	+	0.0616713i
$582$	2.29285	+	3.97134i	0.0950418	+	0.164617i
$583$	16.8294	−	9.71645i	0.697002	−	0.402414i
$584$	24.4030			1.00980
$585$	0.0498869	+	3.40763i	0.00206257	+	0.140888i
$586$	−7.60128			−0.314006
$587$	8.64477	−	4.99106i	0.356808	−	0.206003i	−0.310872	−	0.950452i	$-0.600621\pi$
$587$	8.64477	−	4.99106i	0.356808	−	0.206003i	0.667680	+	0.744449i	$0.267288\pi$
$588$	−5.04404	−	8.73654i	−0.208013	−	0.360289i
$589$	6.76983	−	11.7257i	0.278946	−	0.483149i
$590$			4.76581i			0.196205i
$591$	16.2499	+	9.38189i	0.668432	+	0.385919i
$592$	−1.09696	−	0.633332i	−0.0450849	−	0.0260298i
$593$			28.2801i			1.16133i	0.814144	+	0.580663i	$0.197206\pi$
$593$			28.2801i			1.16133i	−0.814144	+	0.580663i	$0.802794\pi$
$594$	0.714363	−	1.23731i	0.0293107	−	0.0507676i
$595$	0.168178	+	0.291293i	0.00689462	+	0.0119418i
$596$	3.94400	−	2.27707i	0.161552	−	0.0932723i
$597$	13.4516			0.550536
$598$	−0.0467314	−	3.19208i	−0.00191099	−	0.130534i
$599$	−0.0137095			−0.000560157			−0.000280078	−	1.00000i	$-0.500089\pi$
$599$	−0.0137095			−0.000560157			−0.000280078		1.00000i	$0.500089\pi$
$600$	−8.99765	+	5.19479i	−0.367327	+	0.212077i
$601$	13.8663	+	24.0172i	0.565619	+	0.979681i	0.996992	+	0.0775074i	$0.0246961\pi$
$601$	13.8663	+	24.0172i	0.565619	+	0.979681i	−0.431373	+	0.902174i	$0.641971\pi$
$602$	0.799006	−	1.38392i	0.0325651	−	0.0564043i
$603$			6.44572i			0.262490i
$604$	−2.03543	−	1.17516i	−0.0828207	−	0.0478165i
$605$	−5.86522	−	3.38628i	−0.238455	−	0.137672i
$606$		−	0.553261i		−	0.0224747i
$607$	18.8717	−	32.6867i	0.765977	−	1.32671i	−0.173751	−	0.984790i	$-0.555589\pi$
$607$	18.8717	−	32.6867i	0.765977	−	1.32671i	0.939728	−	0.341922i	$-0.111078\pi$
$608$	4.94769	+	8.56965i	0.200655	+	0.347545i
$609$	2.23252	−	1.28895i	0.0904665	−	0.0522308i
$610$	−4.89348			−0.198131
$611$	−15.9776	+	9.53921i	−0.646385	+	0.385915i
$612$	1.46771			0.0593285
$613$	34.0049	−	19.6327i	1.37344	−	0.792958i	0.382084	−	0.924128i	$-0.375207\pi$
$613$	34.0049	−	19.6327i	1.37344	−	0.792958i	0.991360	+	0.131169i	$0.0418732\pi$
$614$	−11.1620	−	19.3331i	−0.450461	−	0.780222i
$615$	−0.574877	+	0.995717i	−0.0231813	+	0.0401512i
$616$		−	1.76304i		−	0.0710350i
$617$	13.9176	+	8.03531i	0.560300	+	0.323490i	0.753266	−	0.657716i	$-0.228477\pi$
$617$	13.9176	+	8.03531i	0.560300	+	0.323490i	−0.192966	+	0.981205i	$0.561811\pi$
$618$	8.45481	+	4.88139i	0.340102	+	0.196358i
$619$			32.1824i			1.29352i	0.762693	+	0.646761i	$0.223877\pi$
$619$			32.1824i			1.29352i	−0.762693	+	0.646761i	$0.776123\pi$
$620$	−5.55689	+	9.62482i	−0.223170	+	0.386542i
$621$	−0.606797	−	1.05100i	−0.0243499	−	0.0421753i
$622$	−20.3587	+	11.7541i	−0.816310	+	0.471297i
$623$	4.61014			0.184702
$624$	3.92810	−	0.0575065i	0.157250	−	0.00230210i
$625$	12.3969			0.495877
$626$	−6.93193	+	4.00215i	−0.277056	+	0.159958i
$627$	1.65484	+	2.86627i	0.0660880	+	0.114468i
$628$	−6.32867	+	10.9616i	−0.252541	+	0.437415i
$629$			1.16253i			0.0463531i
$630$	−0.212522	−	0.122700i	−0.00846710	−	0.00488848i
$631$	8.29715	+	4.79036i	0.330304	+	0.190701i	0.655976	−	0.754782i	$-0.272257\pi$
$631$	8.29715	+	4.79036i	0.330304	+	0.190701i	−0.325672	+	0.945483i	$0.605590\pi$
$632$			6.66661i			0.265183i
$633$	−5.87084	+	10.1686i	−0.233345	+	0.404166i
$634$	10.5393	+	18.2547i	0.418570	+	0.724985i
$635$	13.0320	−	7.52401i	0.517158	−	0.298581i
$636$	−14.5648			−0.577530
$637$	−12.0756	+	21.6412i	−0.478455	+	0.857454i
$638$	−10.3501			−0.409763
$639$	5.61258	−	3.24042i	0.222030	−	0.128189i
$640$	−4.81260	−	8.33567i	−0.190235	−	0.329496i
$641$	−0.155237	+	0.268878i	−0.00613149	+	0.0106200i	−0.869075	−	0.494681i	$-0.835285\pi$
$641$	−0.155237	+	0.268878i	−0.00613149	+	0.0106200i	0.862943	+	0.505301i	$0.168618\pi$
$642$			6.59900i			0.260442i
$643$	−18.7747	−	10.8396i	−0.740401	−	0.427471i	0.0818143	−	0.996648i	$-0.473929\pi$
$643$	−18.7747	−	10.8396i	−0.740401	−	0.427471i	−0.822215	+	0.569177i	$0.807262\pi$
$644$	−0.548927	−	0.316923i	−0.0216308	−	0.0124885i
$645$		−	5.81783i		−	0.229077i
$646$	0.616536	−	1.06787i	0.0242573	−	0.0420148i
$647$	11.7476	+	20.3474i	0.461846	+	0.799940i	0.999053	−	0.0435099i	$-0.0138540\pi$
$647$	11.7476	+	20.3474i	0.461846	+	0.799940i	−0.537207	+	0.843450i	$0.680521\pi$
$648$	−2.19103	+	1.26499i	−0.0860718	+	0.0496936i
$649$	13.5334			0.531233
$650$	9.43337	+	5.26377i	0.370007	+	0.206462i
$651$	2.85080			0.111732
$652$	11.2476	−	6.49379i	0.440489	−	0.254316i
$653$	13.4698	+	23.3304i	0.527115	+	0.912990i	0.999501	+	0.0315980i	$0.0100596\pi$
$653$	13.4698	+	23.3304i	0.527115	+	0.912990i	−0.472386	+	0.881392i	$0.656607\pi$
$654$	0.343803	−	0.595484i	0.0134438	−	0.0232853i
$655$			0.353331i			0.0138058i
$656$	1.14780	+	0.662682i	0.0448140	+	0.0258734i
$657$	−8.35327	−	4.82276i	−0.325892	−	0.188154i
$658$		−	1.33995i		−	0.0522367i
$659$	15.9067	−	27.5512i	0.619637	−	1.07324i	−0.369915	−	0.929066i	$-0.620613\pi$
$659$	15.9067	−	27.5512i	0.619637	−	1.07324i	0.989552	−	0.144177i	$-0.0460536\pi$
$660$	−1.35835	−	2.35272i	−0.0528735	−	0.0915796i
$661$	13.2865	−	7.67095i	0.516784	−	0.298365i	−0.218834	−	0.975762i	$-0.570225\pi$
$661$	13.2865	−	7.67095i	0.516784	−	0.298365i	0.735618	+	0.677397i	$0.236892\pi$
$662$	16.6224			0.646049
$663$	−1.84829	−	3.09578i	−0.0717816	−	0.120230i
$664$	−12.2036			−0.473591
$665$	0.492314	−	0.284238i	0.0190911	−	0.0110223i
$666$	−0.424081	−	0.734531i	−0.0164328	−	0.0284625i
$667$	−4.39580	+	7.61375i	−0.170206	+	0.294806i
$668$		−	31.2810i		−	1.21030i
$669$	−13.8436	−	7.99260i	−0.535224	−	0.309012i
$670$	−3.84951	−	2.22251i	−0.148719	−	0.0858632i
$671$			13.8959i			0.536447i
$672$	−1.04174	+	1.80435i	−0.0401862	+	0.0696045i
$673$	17.3088	+	29.9798i	0.667207	+	1.15564i	0.978682	+	0.205382i	$0.0658436\pi$
$673$	17.3088	+	29.9798i	0.667207	+	1.15564i	−0.311475	+	0.950254i	$0.600823\pi$
$674$	5.29225	−	3.05548i	0.203850	−	0.117693i
$675$	4.10658			0.158062
$676$	−10.0197	−	16.2376i	−0.385374	−	0.624522i
$677$	−30.6553			−1.17818			−0.589090	−	0.808067i	$-0.700514\pi$
$677$	−30.6553			−1.17818			−0.589090	+	0.808067i	$0.700514\pi$
$678$	−1.29482	+	0.747563i	−0.0497271	+	0.0287100i
$679$	−1.11834	−	1.93701i	−0.0429178	−	0.0743358i
$680$	−1.19568	+	2.07098i	−0.0458523	+	0.0794185i
$681$		−	1.43698i		−	0.0550650i
$682$	−9.91231	−	5.72287i	−0.379562	−	0.219140i
$683$	8.14658	+	4.70343i	0.311720	+	0.179972i	0.647696	−	0.761899i	$-0.275733\pi$
$683$	8.14658	+	4.70343i	0.311720	+	0.179972i	−0.335976	+	0.941871i	$0.609066\pi$
$684$		−	2.48057i		−	0.0948471i
$685$	−10.4390	+	18.0809i	−0.398854	+	0.690836i
$686$	−1.80094	−	3.11932i	−0.0687601	−	0.119096i
$687$	11.5154	−	6.64841i	0.439340	−	0.253653i
$688$	−6.70642			−0.255680
$689$	18.3415	+	30.7209i	0.698755	+	1.17037i
$690$	0.836906			0.0318605
$691$	34.0888	−	19.6812i	1.29680	−	0.748707i	0.316949	−	0.948443i	$-0.397342\pi$
$691$	34.0888	−	19.6812i	1.29680	−	0.748707i	0.979850	+	0.199736i	$0.0640084\pi$
$692$	−2.96353	−	5.13298i	−0.112656	−	0.195127i
$693$	−0.348429	+	0.603497i	−0.0132357	+	0.0229250i
$694$			7.08800i			0.269057i
$695$	6.54342	+	3.77785i	0.248206	+	0.143302i
$696$	15.8724	+	9.16394i	0.601642	+	0.347358i
$697$		−	1.21640i		−	0.0460746i
$698$	−1.40895	+	2.44037i	−0.0533295	+	0.0923693i
$699$	−4.62764	−	8.01530i	−0.175033	−	0.303167i
$700$	1.85747	−	1.07241i	0.0702057	−	0.0405333i
$701$	25.1347			0.949325			0.474662	−	0.880168i	$-0.342570\pi$
$701$	25.1347			0.949325			0.474662	+	0.880168i	$0.342570\pi$
$702$	2.29714	+	1.28179i	0.0866998	+	0.0483780i
$703$	1.96479			0.0741035
$704$	3.54870	−	2.04884i	0.133746	−	0.0772186i
$705$	−2.43916	−	4.22474i	−0.0918639	−	0.159113i
$706$	−1.56340	+	2.70789i	−0.0588395	+	0.101913i
$707$			0.269852i			0.0101488i
$708$	−8.78424	−	5.07158i	−0.330132	−	0.190602i
$709$	−20.5082	−	11.8404i	−0.770203	−	0.444677i	0.0627440	−	0.998030i	$-0.480015\pi$
$709$	−20.5082	−	11.8404i	−0.770203	−	0.444677i	−0.832947	+	0.553353i	$0.813348\pi$
$710$			4.46925i			0.167728i
$711$	1.31752	−	2.28201i	0.0494108	−	0.0855821i
$712$	16.3882	+	28.3852i	0.614174	+	1.06378i
$713$	−8.41975	+	4.86115i	−0.315322	+	0.182051i
$714$	0.259625			0.00971623
$715$	−3.25193	+	5.82790i	−0.121615	+	0.217951i
$716$	10.0795			0.376690
$717$	11.4008	−	6.58228i	0.425772	−	0.245820i
$718$	−3.36641	−	5.83079i	−0.125633	−	0.217603i
$719$	−15.6904	+	27.1765i	−0.585153	+	1.01351i	0.409704	+	0.912219i	$0.365632\pi$
$719$	−15.6904	+	27.1765i	−0.585153	+	1.01351i	−0.994856	+	0.101295i	$0.967701\pi$
$720$			1.02988i			0.0383812i
$721$	−4.12382	−	2.38089i	−0.153579	−	0.0886689i
$722$	10.2001	+	5.88904i	0.379609	+	0.219168i
$723$			3.35394i			0.124734i
$724$	18.7303	−	32.4419i	0.696107	−	1.20569i
$725$	−14.8746	−	25.7635i	−0.552428	−	0.956834i
$726$	−4.52723	+	2.61379i	−0.168021	+	0.0970070i
$727$	−2.13113			−0.0790392			−0.0395196	−	0.999219i	$-0.512583\pi$
$727$	−2.13113			−0.0790392			−0.0395196	+	0.999219i	$0.512583\pi$
$728$	3.24574	−	0.0475169i	0.120295	−	0.00176110i
$729$	1.00000			0.0370370
$730$	5.76049	−	3.32582i	0.213205	−	0.123094i
$731$	3.07754	+	5.33045i	0.113827	+	0.197154i
$732$	5.20744	−	9.01954i	0.192472	−	0.333372i
$733$			11.6882i			0.431714i	0.976425	+	0.215857i	$0.0692544\pi$
$733$			11.6882i			0.431714i	−0.976425	+	0.215857i	$0.930746\pi$
$734$	13.4159	+	7.74566i	0.495189	+	0.285898i
$735$	−5.62636	−	3.24838i	−0.207532	−	0.119818i
$736$		−	7.10548i		−	0.261912i
$737$	−6.31125	+	10.9314i	−0.232478	+	0.402663i
$738$	0.443735	+	0.768571i	0.0163341	+	0.0282915i
$739$	−29.7512	+	17.1768i	−1.09441	+	0.631860i	−0.934748	−	0.355311i	$-0.884375\pi$
$739$	−29.7512	+	17.1768i	−1.09441	+	0.631860i	−0.159666	+	0.987171i	$0.551042\pi$
$740$	−1.61276			−0.0592863
$741$	−5.23217	+	3.12380i	−0.192209	+	0.114756i
$742$	−2.57639			−0.0945821
$743$	8.01005	−	4.62461i	0.293860	−	0.169660i	−0.345821	−	0.938300i	$-0.612400\pi$
$743$	8.01005	−	4.62461i	0.293860	−	0.169660i	0.639681	+	0.768640i	$0.279066\pi$
$744$	10.1340	+	17.5527i	0.371532	+	0.643513i
$745$	1.46644	−	2.53995i	0.0537262	−	0.0930565i
$746$			19.7013i			0.721316i
$747$	4.17734	+	2.41179i	0.152841	+	0.0882427i
$748$	2.48911	+	1.43709i	0.0910107	+	0.0525451i
$749$		−	3.21865i		−	0.117607i
$750$	−3.13999	+	5.43862i	−0.114656	+	0.198590i
$751$	−0.479680	−	0.830830i	−0.0175038	−	0.0303174i	0.857141	−	0.515082i	$-0.172239\pi$
$751$	−0.479680	−	0.830830i	−0.0175038	−	0.0303174i	−0.874645	+	0.484765i	$0.838905\pi$
$752$	−4.87002	+	2.81171i	−0.177591	+	0.102532i
$753$	−15.6637			−0.570817
$754$	−0.278952	−	19.0544i	−0.0101588	−	0.693920i
$755$	−1.51361			−0.0550860
$756$	0.452315	−	0.261144i	0.0164505	−	0.00949773i
$757$	−12.0617	−	20.8915i	−0.438391	−	0.759315i	0.559175	−	0.829050i	$-0.311118\pi$
$757$	−12.0617	−	20.8915i	−0.438391	−	0.759315i	−0.997566	+	0.0697349i	$0.977785\pi$
$758$	−4.37879	+	7.58428i	−0.159045	+	0.275473i
$759$		−	2.37655i		−	0.0862634i
$760$	3.50017	+	2.02082i	0.126964	+	0.0733029i
$761$	8.01435	+	4.62709i	0.290520	+	0.167732i	0.638176	−	0.769890i	$-0.279689\pi$
$761$	8.01435	+	4.62709i	0.290520	+	0.167732i	−0.347656	+	0.937622i	$0.613022\pi$
$762$		−	11.6152i		−	0.420775i
$763$	−0.167689	+	0.290447i	−0.00607076	+	0.0105149i
$764$	13.4836	+	23.3543i	0.487821	+	0.844930i
$765$	0.818574	−	0.472604i	0.0295956	−	0.0170870i
$766$	−15.8132			−0.571354
$767$	0.364749	+	24.9149i	0.0131703	+	0.899625i
$768$	−11.6145			−0.419101
$769$	4.11711	−	2.37701i	0.148467	−	0.0857173i	−0.423926	−	0.905697i	$-0.639348\pi$
$769$	4.11711	−	2.37701i	0.148467	−	0.0857173i	0.572393	+	0.819979i	$0.306015\pi$
$770$	−0.240280	−	0.416177i	−0.00865909	−	0.0149980i
$771$	−5.92643	+	10.2649i	−0.213435	+	0.369681i
$772$		−	35.1452i		−	1.26490i
$773$	−19.8718	−	11.4730i	−0.714740	−	0.412655i	0.0980736	−	0.995179i	$-0.468732\pi$
$773$	−19.8718	−	11.4730i	−0.714740	−	0.412655i	−0.812814	+	0.582524i	$0.802065\pi$
$774$	−3.88901	−	2.24532i	−0.139788	−	0.0807065i
$775$		−	32.8985i		−	1.18175i
$776$	7.95094	−	13.7714i	0.285422	−	0.494366i
$777$	0.206845	+	0.358266i	0.00742052	+	0.0128527i
$778$	−7.07187	+	4.08294i	−0.253539	+	0.146381i
$779$	−2.05585			−0.0736583
$780$	4.29473	−	2.56411i	0.153776	−	0.0918099i
$781$	12.6913			0.454130
$782$	−0.766796	+	0.442710i	−0.0274206	+	0.0158313i
$783$	−3.62213	−	6.27372i	−0.129444	−	0.224204i
$784$	−3.74453	+	6.48572i	−0.133733	+	0.231633i
$785$			8.15137i			0.290935i
$786$	0.236189	+	0.136364i	0.00842459	+	0.00486394i
$787$	−34.2535	−	19.7763i	−1.22101	−	0.704949i	−0.255874	−	0.966710i	$-0.582363\pi$
$787$	−34.2535	−	19.7763i	−1.22101	−	0.704949i	−0.965133	+	0.261761i	$0.915697\pi$
$788$		−	27.5397i		−	0.981062i
$789$	−6.71105	+	11.6239i	−0.238920	+	0.413821i
$790$	0.908573	+	1.57370i	0.0323256	+	0.0559896i
$791$	0.631544	−	0.364622i	0.0224551	−	0.0129645i
$792$	−4.95440			−0.176047
$793$	−25.5823	+	0.374519i	−0.908454	+	0.0132996i
$794$	−12.4535			−0.441958
$795$	−8.12311	+	4.68988i	−0.288097	+	0.166333i
$796$	−9.87148	−	17.0979i	−0.349885	−	0.606019i
$797$	−4.29099	+	7.43222i	−0.151995	+	0.263263i	−0.931961	−	0.362559i	$-0.881903\pi$
$797$	−4.29099	+	7.43222i	−0.151995	+	0.263263i	0.779966	+	0.625822i	$0.215236\pi$
$798$		−	0.438793i		−	0.0155331i
$799$	4.46964	+	2.58055i	0.158125	+	0.0912933i
$800$	20.8224	+	12.0218i	0.736183	+	0.425036i
$801$		−	12.9552i		−	0.457749i
$802$	−0.807867	+	1.39927i	−0.0285268	+	0.0494098i
$803$	−9.44429	−	16.3580i	−0.333282	−	0.577261i
$804$	8.19297	−	4.73021i	0.288944	−	0.166822i
$805$	−0.408199			−0.0143871
$806$	10.2686	−	18.4027i	0.361696	−	0.648208i
$807$	−6.69819			−0.235787
$808$	−1.66151	+	0.959274i	−0.0584517	+	0.0337471i
$809$	8.86387	+	15.3527i	0.311637	+	0.539771i	0.978717	−	0.205215i	$-0.0657893\pi$
$809$	8.86387	+	15.3527i	0.311637	+	0.539771i	−0.667080	+	0.744986i	$0.732456\pi$
$810$	−0.344805	+	0.597219i	−0.0121152	+	0.0209841i
$811$			8.69589i			0.305354i	0.988276	+	0.152677i	$0.0487894\pi$
$811$			8.69589i			0.305354i	−0.988276	+	0.152677i	$0.951211\pi$
$812$	−3.27669	−	1.89180i	−0.114989	−	0.0663891i
$813$	−12.6192	−	7.28571i	−0.442575	−	0.255521i
$814$		−	1.66094i		−	0.0582158i
$815$	4.18202	−	7.24348i	0.146490	−	0.253728i
$816$	−0.544788	−	0.943601i	−0.0190714	−	0.0330326i
$817$	9.00900	−	5.20135i	0.315185	−	0.181972i
$818$	−17.5911			−0.615059
$819$	−1.12042	−	0.625190i	−0.0391508	−	0.0218459i
$820$	1.68750			0.0589302
$821$	13.1869	−	7.61344i	0.460225	−	0.265711i	−0.251914	−	0.967750i	$-0.581060\pi$
$821$	13.1869	−	7.61344i	0.460225	−	0.265711i	0.712139	+	0.702039i	$0.247727\pi$
$822$	8.05764	+	13.9562i	0.281042	+	0.486780i
$823$	22.5823	−	39.1136i	0.787169	−	1.36342i	−0.140526	−	0.990077i	$-0.544879\pi$
$823$	22.5823	−	39.1136i	0.787169	−	1.36342i	0.927695	−	0.373339i	$-0.121787\pi$
$824$		−	33.8544i		−	1.17938i
$825$	6.96441	+	4.02091i	0.242470	+	0.139990i
$826$	−1.55386	−	0.897121i	−0.0540657	−	0.0312148i
$827$			8.24974i			0.286872i	0.989660	+	0.143436i	$0.0458151\pi$
$827$			8.24974i			0.286872i	−0.989660	+	0.143436i	$0.954185\pi$
$828$	−0.890601	+	1.54257i	−0.0309505	+	0.0536079i
$829$	26.7784	+	46.3816i	0.930054	+	1.61090i	0.783225	+	0.621738i	$0.213573\pi$
$829$	26.7784	+	46.3816i	0.930054	+	1.61090i	0.146828	+	0.989162i	$0.453093\pi$
$830$	−2.88073	+	1.66319i	−0.0999917	+	0.0577302i
$831$	0.266952			0.00926047
$832$	3.86754	+	6.47790i	0.134083	+	0.224581i
$833$	6.87337			0.238148
$834$	5.05072	−	2.91603i	0.174892	−	0.100974i
$835$	−10.0725	−	17.4462i	−0.348575	−	0.603749i
$836$	2.42882	−	4.20684i	0.0840025	−	0.145497i
$837$		−	8.01115i		−	0.276906i
$838$	0.618652	+	0.357179i	0.0213710	+	0.0123385i
$839$	−22.3441	−	12.9004i	−0.771405	−	0.445371i	0.0619709	−	0.998078i	$-0.480261\pi$
$839$	−22.3441	−	12.9004i	−0.771405	−	0.445371i	−0.833375	+	0.552707i	$0.813595\pi$
$840$			0.850975i			0.0293614i
$841$	−11.7397	+	20.3337i	−0.404817	+	0.701164i
$842$	−4.38866	−	7.60139i	−0.151243	−	0.261961i
$843$	−13.9879	+	8.07591i	−0.481768	+	0.278149i
$844$	17.2334			0.593197
$845$	−10.8168	−	5.82971i	−0.372108	−	0.200548i
$846$	−3.76546			−0.129459
$847$	2.20815	−	1.27487i	0.0758728	−	0.0438052i
$848$	5.40620	+	9.36381i	0.185650	+	0.321554i
$849$	−14.5768	+	25.2478i	−0.500276	+	0.866503i
$850$		−	2.99610i		−	0.102765i
$851$	−1.22182	−	0.705420i	−0.0418835	−	0.0241815i
$852$	−8.23762	−	4.75599i	−0.282216	−	0.162938i
$853$		−	14.6909i		−	0.503008i	−0.967856	−	0.251504i	$-0.919075\pi$
$853$		−	14.6909i		−	0.503008i	0.967856	−	0.251504i	$-0.0809252\pi$
$854$	0.921152	−	1.59548i	0.0315212	−	0.0545963i
$855$	−0.798749	−	1.38347i	−0.0273166	−	0.0473138i
$856$	19.8176	−	11.4417i	0.677352	−	0.391069i
$857$	−46.6568			−1.59377			−0.796883	−	0.604134i	$-0.793519\pi$
$857$	−46.6568			−1.59377			−0.796883	+	0.604134i	$0.793519\pi$
$858$	2.64070	+	4.42302i	0.0901520	+	0.150999i
$859$	56.6349			1.93236			0.966179	−	0.257874i	$-0.0830218\pi$
$859$	56.6349			1.93236			0.966179	+	0.257874i	$0.0830218\pi$
$860$	−7.39487	+	4.26943i	−0.252163	+	0.145586i
$861$	−0.216431	−	0.374869i	−0.00737594	−	0.0127755i
$862$	−9.85863	+	17.0757i	−0.335786	+	0.581599i
$863$		−	41.3019i		−	1.40593i	−0.711223	−	0.702966i	$-0.751859\pi$
$863$		−	41.3019i		−	1.40593i	0.711223	−	0.702966i	$-0.248141\pi$
$864$	5.07050	+	2.92745i	0.172502	+	0.0995940i
$865$	−3.30566	−	1.90852i	−0.112396	−	0.0648917i
$866$		−	11.0134i		−	0.374250i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	−2.09207	−	3.62357i	−0.0710094	−	0.122992i
$869$	4.46880	−	2.58006i	0.151594	−	0.0875227i
$870$	4.99571			0.169370
$871$	−20.2947	−	11.3243i	−0.687660	−	0.383710i
$872$	−2.38442			−0.0807465
$873$	−5.44329	+	3.14269i	−0.184227	+	0.106364i
$874$	0.748224	+	1.29596i	0.0253091	+	0.0438366i
$875$	1.53153	−	2.65268i	0.0517750	−	0.0896769i
$876$			14.1568i			0.478314i
$877$	−21.8457	−	12.6126i	−0.737678	−	0.425899i	0.0835464	−	0.996504i	$-0.473375\pi$
$877$	−21.8457	−	12.6126i	−0.737678	−	0.425899i	−0.821225	+	0.570605i	$0.806709\pi$
$878$	12.5451	+	7.24293i	0.423377	+	0.244437i
$879$		−	10.4186i		−	0.351412i
$880$	−1.00839	+	1.74658i	−0.0339928	+	0.0588773i
$881$	−2.03846	−	3.53072i	−0.0686776	−	0.118953i	0.829642	−	0.558296i	$-0.188545\pi$
$881$	−2.03846	−	3.53072i	−0.0686776	−	0.118953i	−0.898319	+	0.439343i	$0.855211\pi$
$882$	−4.34286	+	2.50735i	−0.146232	+	0.0844269i
$883$	−7.26539			−0.244500			−0.122250	−	0.992499i	$-0.539011\pi$
$883$	−7.26539			−0.244500			−0.122250	+	0.992499i	$0.539011\pi$
$884$	−2.57858	+	4.62115i	−0.0867269	+	0.155426i
$885$	−6.53223			−0.219579
$886$	−5.86898	+	3.38846i	−0.197172	+	0.113837i
$887$	26.5444	+	45.9762i	0.891273	+	1.54373i	0.838351	+	0.545131i	$0.183520\pi$
$887$	26.5444	+	45.9762i	0.891273	+	1.54373i	0.0529224	+	0.998599i	$0.483146\pi$
$888$	−1.47059	+	2.54714i	−0.0493498	+	0.0854763i
$889$			5.66530i			0.190008i
$890$	7.73708	+	4.46700i	0.259347	+	0.149734i
$891$	1.69592	+	0.979137i	0.0568153	+	0.0328023i
$892$			23.4616i			0.785552i
$893$	4.36139	−	7.55415i	0.145948	−	0.252790i
$894$	−1.13191	−	1.96053i	−0.0378568	−	0.0655698i
$895$	5.62160	−	3.24563i	0.187909	−	0.108490i
$896$	3.62371			0.121060
$897$	4.37521	−	0.0640521i	0.146084	−	0.00213864i
$898$	19.6765			0.656614
$899$	−50.2597	+	29.0175i	−1.67626	+	0.967786i
$900$	−3.01363	−	5.21976i	−0.100454	−	0.173992i
$901$	4.96174	−	8.59399i	0.165300	−	0.286307i
$902$			1.73791i			0.0578660i
$903$	1.89686	+	1.09515i	0.0631235	+	0.0364444i
$904$	4.49004	+	2.59233i	0.149337	+	0.0862195i
$905$		−	24.1248i		−	0.801935i
$906$	−0.584161	+	1.01180i	−0.0194075	+	0.0336147i
$907$	11.6317	+	20.1467i	0.386224	+	0.668960i	0.991938	−	0.126723i	$-0.0404458\pi$
$907$	11.6317	+	20.1467i	0.386224	+	0.668960i	−0.605714	+	0.795682i	$0.707113\pi$
$908$	−1.82650	+	1.05453i	−0.0606145	+	0.0349958i
$909$	0.758324			0.0251520
$910$	0.759703	−	0.453570i	0.0251839	−	0.0150357i
$911$	2.98419			0.0988706			0.0494353	−	0.998777i	$-0.484258\pi$
$911$	2.98419			0.0988706			0.0494353	+	0.998777i	$0.484258\pi$
$912$	−1.59478	+	0.920747i	−0.0528085	+	0.0304890i
$913$	4.72294	+	8.18038i	0.156307	+	0.270731i
$914$	12.4349	−	21.5380i	0.411311	−	0.712412i
$915$		−	6.70721i		−	0.221734i
$916$	−16.9012	−	9.75792i	−0.558432	−	0.322411i
$917$	−0.115201	−	0.0665113i	−0.00380427	−	0.00219640i
$918$		−	0.729584i		−	0.0240799i
$919$	15.4853	−	26.8213i	0.510813	−	0.884754i	−0.489108	−	0.872223i	$-0.662678\pi$
$919$	15.4853	−	26.8213i	0.510813	−	0.884754i	0.999921	−	0.0125312i	$-0.00398890\pi$
$920$	−1.45107	−	2.51333i	−0.0478404	−	0.0828621i
$921$	26.4988	−	15.2991i	0.873166	−	0.504123i
$922$	21.2680			0.700423
$923$	0.342051	+	23.3645i	0.0112588	+	0.769053i
$924$	1.02278			0.0336471
$925$	4.13442	−	2.38701i	0.135939	−	0.0784844i
$926$	−6.21093	−	10.7577i	−0.204104	−	0.353518i
$927$	−6.69064	+	11.5885i	−0.219750	+	0.380617i
$928$		−	42.4145i		−	1.39232i
$929$	20.4138	+	11.7859i	0.669756	+	0.386684i	0.795984	−	0.605317i	$-0.206954\pi$
$929$	20.4138	+	11.7859i	0.669756	+	0.386684i	−0.126228	+	0.992001i	$0.540287\pi$
$930$	4.78441	+	2.76228i	0.156887	+	0.0905788i
$931$		−	11.6167i		−	0.380722i
$932$	−6.79201	+	11.7641i	−0.222480	+	0.385346i
$933$	−16.1107	−	27.9045i	−0.527440	−	0.913553i
$934$	−13.5644	+	7.83143i	−0.443842	+	0.256252i
$935$	1.85098			0.0605334
$936$	−0.133530	−	9.12101i	−0.00436455	−	0.298130i
$937$	17.6698			0.577248			0.288624	−	0.957443i	$-0.406802\pi$
$937$	17.6698			0.577248			0.288624	+	0.957443i	$0.406802\pi$
$938$	1.44927	−	0.836736i	0.0473203	−	0.0273204i
$939$	−5.48552	−	9.50121i	−0.179013	−	0.310060i
$940$	−3.57997	+	6.20068i	−0.116766	+	0.202244i
$941$		−	6.09600i		−	0.198724i	−0.995051	−	0.0993619i	$-0.968320\pi$
$941$		−	6.09600i		−	0.198724i	0.995051	−	0.0993619i	$-0.0316802\pi$
$942$	5.44891	+	3.14593i	0.177535	+	0.102500i
$943$	1.27845	+	0.738111i	0.0416319	+	0.0240362i
$944$			7.52994i			0.245079i
$945$	0.168178	−	0.291293i	0.00547082	−	0.00947575i
$946$	−4.39696	−	7.61576i	−0.142957	−	0.247610i
$947$	−5.90079	+	3.40682i	−0.191750	+	0.110707i	−0.592801	−	0.805349i	$-0.701978\pi$
$947$	−5.90079	+	3.40682i	−0.191750	+	0.110707i	0.401052	+	0.916055i	$0.368645\pi$
$948$	−3.86746			−0.125609
$949$	29.8604	−	17.8277i	0.969308	−	0.578712i
$950$	−5.06371			−0.164288
$951$	−25.0206	+	14.4457i	−0.811350	+	0.468433i
$952$	−0.450152	−	0.779686i	−0.0145895	−	0.0252698i
$953$	−6.42025	+	11.1202i	−0.207972	+	0.360218i	−0.951076	−	0.308958i	$-0.900020\pi$
$953$	−6.42025	+	11.1202i	−0.207972	+	0.360218i	0.743103	+	0.669177i	$0.233353\pi$
$954$			7.24002i			0.234404i
$955$	15.0403	+	8.68351i	0.486692	+	0.280992i
$956$	−16.7331	−	9.66086i	−0.541187	−	0.312454i
$957$		−	14.1863i		−	0.458577i
$958$	−2.25696	+	3.90917i	−0.0729191	+	0.126300i
$959$	−3.93010	−	6.80713i	−0.126910	−	0.219814i
$960$	−1.71286	+	0.988922i	−0.0552824	+	0.0319173i
$961$	−33.1786			−1.07028
$962$	3.05777	−	0.0447650i	0.0985864	−	0.00144328i
$963$	−9.04488			−0.291467
$964$	4.26309	−	2.46130i	0.137305	−	0.0792730i
$965$	−11.3168	−	19.6013i	−0.364301	−	0.630989i
$966$	−0.157540	+	0.272867i	−0.00506876	+	0.00877935i
$967$			7.77971i			0.250179i	0.992145	+	0.125089i	$0.0399217\pi$
$967$			7.77971i			0.250179i	−0.992145	+	0.125089i	$0.960078\pi$
$968$	15.6991	+	9.06387i	0.504588	+	0.291324i
$969$	1.46367	+	0.845051i	0.0470199	+	0.0271469i
$970$		−	4.33445i		−	0.139171i
$971$	21.8844	−	37.9050i	0.702305	−	1.21643i	−0.265350	−	0.964152i	$-0.585487\pi$
$971$	21.8844	−	37.9050i	0.702305	−	1.21643i	0.967655	−	0.252276i	$-0.0811792\pi$
$972$	−0.733853	−	1.27107i	−0.0235384	−	0.0407696i
$973$	−2.46348	+	1.42229i	−0.0789755	+	0.0455965i
$974$	−12.7685			−0.409129
$975$	−7.21475	+	12.9298i	−0.231057	+	0.414085i
$976$	−7.73165			−0.247484
$977$	23.6623	−	13.6614i	0.757024	−	0.437068i	−0.0712025	−	0.997462i	$-0.522684\pi$
$977$	23.6623	−	13.6614i	0.757024	−	0.437068i	0.828226	+	0.560394i	$0.189350\pi$
$978$	−3.22801	−	5.59107i	−0.103220	−	0.178783i
$979$	12.6849	−	21.9709i	0.405411	−	0.702192i
$980$			9.53534i			0.304595i
$981$	0.816197	+	0.471231i	0.0260592	+	0.0150453i
$982$	−2.12851	−	1.22890i	−0.0679235	−	0.0392157i
$983$			43.5653i			1.38952i	0.719242	+	0.694759i	$0.244489\pi$
$983$			43.5653i			1.38952i	−0.719242	+	0.694759i	$0.755511\pi$
$984$	1.53874	−	2.66518i	0.0490533	−	0.0849628i
$985$	−8.86784	−	15.3596i	−0.282553	−	0.489396i
$986$	−4.57721	+	2.64265i	−0.145768	+	0.0841592i
$987$	1.83660			0.0584595
$988$	7.81022	+	4.35806i	0.248476	+	0.138648i
$989$	−7.46977			−0.237525
$990$	−1.16952	+	0.675222i	−0.0371697	+	0.0214600i
$991$	−23.5034	−	40.7091i	−0.746610	−	1.29317i	−0.949439	−	0.313952i	$-0.898347\pi$
$991$	−23.5034	−	40.7091i	−0.746610	−	1.29317i	0.202829	−	0.979214i	$-0.434987\pi$
$992$	23.4523	−	40.6205i	0.744611	−	1.28970i
$993$			22.7834i			0.723010i
$994$	−1.45717	−	0.841296i	−0.0462185	−	0.0266843i
$995$	−11.0111	−	6.35727i	−0.349076	−	0.201539i
$996$		−	7.07960i		−	0.224326i
$997$	14.7423	−	25.5345i	0.466895	−	0.808685i	−0.532390	−	0.846499i	$-0.678706\pi$
$997$	14.7423	−	25.5345i	0.466895	−	0.808685i	0.999285	+	0.0378137i	$0.0120394\pi$
$998$	−10.3578	−	17.9403i	−0.327872	−	0.567891i
$999$	1.00678	−	0.581264i	0.0318531	−	0.0183904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.205.3	✓	16
13.2	odd	12		8619.2.a.bn.1.6		16
13.4	even	6	inner	663.2.z.d.511.3	yes	16
13.11	odd	12		8619.2.a.bn.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.3	✓	16	1.1	even	1	trivial
663.2.z.d.511.3	yes	16	13.4	even	6	inner
8619.2.a.bn.1.6		16	13.2	odd	12
8619.2.a.bn.1.11		16	13.11	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631839 + 0.364792i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.733853 + 1.27107i) q^{4} +0.945208i q^{5} +(0.631839 + 0.364792i) q^{6} +(-0.308178 - 0.177927i) q^{7} -2.52998i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.631839 + 0.364792i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.733853 + 1.27107i) q^{4} +0.945208i q^{5} +(0.631839 + 0.364792i) q^{6} +(-0.308178 - 0.177927i) q^{7} -2.52998i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.344805 - 0.597219i) q^{10} +(-1.69592 + 0.979137i) q^{11} +1.46771 q^{12} +(-1.84829 - 3.09578i) q^{13} +0.259625 q^{14} +(0.818574 - 0.472604i) q^{15} +(-0.544788 - 0.943601i) q^{16} +(-0.500000 + 0.866025i) q^{17} -0.729584i q^{18} +(1.46367 + 0.845051i) q^{19} +(-1.20143 - 0.693644i) q^{20} +0.355853i q^{21} +(0.714363 - 1.23731i) q^{22} +(-0.606797 - 1.05100i) q^{23} +(-2.19103 + 1.26499i) q^{24} +4.10658 q^{25} +(2.29714 + 1.28179i) q^{26} +1.00000 q^{27} +(0.452315 - 0.261144i) q^{28} +(-3.62213 - 6.27372i) q^{29} +(-0.344805 + 0.597219i) q^{30} -8.01115i q^{31} +(5.07050 + 2.92745i) q^{32} +(1.69592 + 0.979137i) q^{33} -0.729584i q^{34} +(0.168178 - 0.291293i) q^{35} +(-0.733853 - 1.27107i) q^{36} +(1.00678 - 0.581264i) q^{37} -1.23307 q^{38} +(-1.75687 + 3.14855i) q^{39} +2.39136 q^{40} +(-1.05344 + 0.608202i) q^{41} +(-0.129813 - 0.224842i) q^{42} +(3.07754 - 5.33045i) q^{43} -2.87417i q^{44} +(-0.818574 - 0.472604i) q^{45} +(0.766796 + 0.442710i) q^{46} -5.16110i q^{47} +(-0.544788 + 0.943601i) q^{48} +(-3.43668 - 5.95251i) q^{49} +(-2.59470 + 1.49805i) q^{50} +1.00000 q^{51} +(5.29132 - 0.0774638i) q^{52} -9.92348 q^{53} +(-0.631839 + 0.364792i) q^{54} +(-0.925488 - 1.60299i) q^{55} +(-0.450152 + 0.779686i) q^{56} -1.69010i q^{57} +(4.57721 + 2.64265i) q^{58} +(-5.98501 - 3.45545i) q^{59} +1.38729i q^{60} +(3.54801 - 6.14533i) q^{61} +(2.92241 + 5.06176i) q^{62} +(0.308178 - 0.177927i) q^{63} -2.09250 q^{64} +(2.92615 - 1.74702i) q^{65} -1.42873 q^{66} +(5.58216 - 3.22286i) q^{67} +(-0.733853 - 1.27107i) q^{68} +(-0.606797 + 1.05100i) q^{69} +0.245400i q^{70} +(-5.61258 - 3.24042i) q^{71} +(2.19103 + 1.26499i) q^{72} +9.64552i q^{73} +(-0.424081 + 0.734531i) q^{74} +(-2.05329 - 3.55640i) q^{75} +(-2.14824 + 1.24029i) q^{76} +0.696859 q^{77} +(-0.0385066 - 2.63027i) q^{78} -2.63504 q^{79} +(0.891899 - 0.514938i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.443735 - 0.768571i) q^{82} -4.82358i q^{83} +(-0.452315 - 0.261144i) q^{84} +(-0.818574 - 0.472604i) q^{85} +4.49065i q^{86} +(-3.62213 + 6.27372i) q^{87} +(2.47720 + 4.29064i) q^{88} +(-11.2195 + 6.47759i) q^{89} +0.689609 q^{90} +(0.0187815 + 1.28291i) q^{91} +1.78120 q^{92} +(-6.93786 + 4.00558i) q^{93} +(1.88273 + 3.26098i) q^{94} +(-0.798749 + 1.38347i) q^{95} -5.85491i q^{96} +(5.44329 + 3.14269i) q^{97} +(4.34286 + 2.50735i) q^{98} -1.95827i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

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