LMFDB - Embedded newform 966.2.k.b.367.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.3
Character	$\chi$	$=$	966.367
Dual form			966.2.k.b.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.320775 - 0.555599i) q^{5} -1.00000i q^{6} +(-2.04200 - 1.68233i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.320775 - 0.555599i) q^{5} -1.00000i q^{6} +(-2.04200 - 1.68233i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.320775 - 0.555599i) q^{10} +(1.26628 + 0.731086i) q^{11} +(0.866025 - 0.500000i) q^{12} +3.75315i q^{13} +(0.435938 - 2.60959i) q^{14} +0.641551i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.24804 - 2.16166i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.74685 + 3.02564i) q^{19} +0.641551 q^{20} +(0.927261 + 2.47794i) q^{21} +1.46217i q^{22} +(4.68603 + 1.02035i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.29421 - 3.97368i) q^{25} +(-3.25032 + 1.87658i) q^{26} -1.00000i q^{27} +(2.47794 - 0.927261i) q^{28} +3.12287 q^{29} +(-0.555599 + 0.320775i) q^{30} +(5.79664 + 3.34669i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.731086 - 1.26628i) q^{33} +2.49607 q^{34} +(-0.279676 + 1.67418i) q^{35} -1.00000 q^{36} +(8.00310 - 4.62059i) q^{37} +(-1.74685 + 3.02564i) q^{38} +(1.87658 - 3.25032i) q^{39} +(0.320775 + 0.555599i) q^{40} +11.5475i q^{41} +(-1.68233 + 2.04200i) q^{42} -5.63040i q^{43} +(-1.26628 + 0.731086i) q^{44} +(0.320775 - 0.555599i) q^{45} +(1.45936 + 4.56840i) q^{46} +(-1.64885 + 0.951961i) q^{47} +1.00000i q^{48} +(1.33954 + 6.87063i) q^{49} +4.58841 q^{50} +(-2.16166 + 1.24804i) q^{51} +(-3.25032 - 1.87658i) q^{52} +(11.9760 + 6.91435i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.938058i q^{55} +(2.04200 + 1.68233i) q^{56} -3.49371i q^{57} +(1.56143 + 2.70448i) q^{58} +(-10.4694 - 6.04453i) q^{59} +(-0.555599 - 0.320775i) q^{60} +(-4.60070 - 7.96865i) q^{61} +6.69338i q^{62} +(0.435938 - 2.60959i) q^{63} +1.00000 q^{64} +(2.08525 - 1.20392i) q^{65} +(0.731086 - 1.26628i) q^{66} +(6.42953 + 3.71209i) q^{67} +(1.24804 + 2.16166i) q^{68} +(-3.54804 - 3.22667i) q^{69} +(-1.58972 + 0.594885i) q^{70} -3.43645 q^{71} +(-0.500000 - 0.866025i) q^{72} +(7.21510 + 4.16564i) q^{73} +(8.00310 + 4.62059i) q^{74} +(-3.97368 + 2.29421i) q^{75} -3.49371 q^{76} +(-1.35582 - 3.62318i) q^{77} +3.75315 q^{78} +(-12.2606 + 7.07864i) q^{79} +(-0.320775 + 0.555599i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-10.0004 + 5.77374i) q^{82} -10.5288 q^{83} +(-2.60959 - 0.435938i) q^{84} -1.60136 q^{85} +(4.87607 - 2.81520i) q^{86} +(-2.70448 - 1.56143i) q^{87} +(-1.26628 - 0.731086i) q^{88} +(0.915023 + 1.58487i) q^{89} +0.641551 q^{90} +(6.31403 - 7.66394i) q^{91} +(-3.22667 + 3.54804i) q^{92} +(-3.34669 - 5.79664i) q^{93} +(-1.64885 - 0.951961i) q^{94} +(1.12070 - 1.94110i) q^{95} +(-0.866025 + 0.500000i) q^{96} +11.5594 q^{97} +(-5.28037 + 4.59540i) q^{98} +1.46217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.320775	−	0.555599i	−0.143455	−	0.248472i	0.785340	−	0.619064i	$-0.212488\pi$
$5$	−0.320775	−	0.555599i	−0.143455	−	0.248472i	−0.928796	+	0.370593i	$0.879155\pi$
$6$		−	1.00000i		−	0.408248i
$7$	−2.04200	−	1.68233i	−0.771804	−	0.635860i
$7$	−2.04200	−	1.68233i	−0.771804	−	0.635860i
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.320775	−	0.555599i	0.101438	−	0.175696i
$11$	1.26628	+	0.731086i	0.381797	+	0.220431i	0.678600	−	0.734508i	$-0.262587\pi$
$11$	1.26628	+	0.731086i	0.381797	+	0.220431i	−0.296803	+	0.954939i	$0.595920\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$			3.75315i			1.04094i	0.853881	+	0.520468i	$0.174243\pi$
$13$			3.75315i			1.04094i	−0.853881	+	0.520468i	$0.825757\pi$
$14$	0.435938	−	2.60959i	0.116509	−	0.697442i
$15$			0.641551i			0.165648i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.24804	−	2.16166i	0.302693	−	0.524280i	−0.674052	−	0.738684i	$-0.735448\pi$
$17$	1.24804	−	2.16166i	0.302693	−	0.524280i	0.976745	+	0.214404i	$0.0687809\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.74685	+	3.02564i	0.400756	+	0.694129i	0.993817	−	0.111028i	$-0.0354143\pi$
$19$	1.74685	+	3.02564i	0.400756	+	0.694129i	−0.593062	+	0.805157i	$0.702081\pi$
$20$	0.641551			0.143455
$21$	0.927261	+	2.47794i	0.202345	+	0.540731i
$22$			1.46217i			0.311736i
$23$	4.68603	+	1.02035i	0.977105	+	0.212759i
$23$	4.68603	+	1.02035i	0.977105	+	0.212759i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.29421	−	3.97368i	0.458841	−	0.794736i
$26$	−3.25032	+	1.87658i	−0.637441	+	0.368027i
$27$		−	1.00000i		−	0.192450i
$28$	2.47794	−	0.927261i	0.468287	−	0.175236i
$29$	3.12287			0.579902			0.289951	−	0.957042i	$-0.406361\pi$
$29$	3.12287			0.579902			0.289951	+	0.957042i	$0.406361\pi$
$30$	−0.555599	+	0.320775i	−0.101438	+	0.0585653i
$31$	5.79664	+	3.34669i	1.04111	+	0.601083i	0.920147	−	0.391574i	$-0.128069\pi$
$31$	5.79664	+	3.34669i	1.04111	+	0.601083i	0.120960	+	0.992657i	$0.461403\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.731086	−	1.26628i	−0.127266	−	0.220431i
$34$	2.49607			0.428073
$35$	−0.279676	+	1.67418i	−0.0472739	+	0.282989i
$36$	−1.00000			−0.166667
$37$	8.00310	−	4.62059i	1.31570	−	0.759621i	0.332668	−	0.943044i	$-0.392051\pi$
$37$	8.00310	−	4.62059i	1.31570	−	0.759621i	0.983034	+	0.183423i	$0.0587179\pi$
$38$	−1.74685	+	3.02564i	−0.283377	+	0.490824i
$39$	1.87658	−	3.25032i	0.300493	−	0.520468i
$40$	0.320775	+	0.555599i	0.0507190	+	0.0878479i
$41$			11.5475i			1.80341i	0.432350	+	0.901706i	$0.357685\pi$
$41$			11.5475i			1.80341i	−0.432350	+	0.901706i	$0.642315\pi$
$42$	−1.68233	+	2.04200i	−0.259589	+	0.315088i
$43$		−	5.63040i		−	0.858629i	−0.903155	−	0.429314i	$-0.858755\pi$
$43$		−	5.63040i		−	0.858629i	0.903155	−	0.429314i	$-0.141245\pi$
$44$	−1.26628	+	0.731086i	−0.190899	+	0.110215i
$45$	0.320775	−	0.555599i	0.0478184	−	0.0828238i
$46$	1.45936	+	4.56840i	0.215171	+	0.673574i
$47$	−1.64885	+	0.951961i	−0.240509	+	0.138858i	−0.615411	−	0.788207i	$-0.711010\pi$
$47$	−1.64885	+	0.951961i	−0.240509	+	0.138858i	0.374902	+	0.927065i	$0.377676\pi$
$48$			1.00000i			0.144338i
$49$	1.33954	+	6.87063i	0.191363	+	0.981519i
$50$	4.58841			0.648900
$51$	−2.16166	+	1.24804i	−0.302693	+	0.174760i
$52$	−3.25032	−	1.87658i	−0.450739	−	0.260234i
$53$	11.9760	+	6.91435i	1.64503	+	0.949759i	0.979007	+	0.203828i	$0.0653382\pi$
$53$	11.9760	+	6.91435i	1.64503	+	0.949759i	0.666023	+	0.745931i	$0.267995\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		−	0.938058i		−	0.126488i
$56$	2.04200	+	1.68233i	0.272874	+	0.224811i
$57$		−	3.49371i		−	0.462753i
$58$	1.56143	+	2.70448i	0.205026	+	0.355116i
$59$	−10.4694	−	6.04453i	−1.36300	−	0.786931i	−0.372981	−	0.927839i	$-0.621664\pi$
$59$	−10.4694	−	6.04453i	−1.36300	−	0.786931i	−0.990023	+	0.140908i	$0.954998\pi$
$60$	−0.555599	−	0.320775i	−0.0717276	−	0.0414119i
$61$	−4.60070	−	7.96865i	−0.589060	−	1.02028i	−0.994356	−	0.106096i	$-0.966165\pi$
$61$	−4.60070	−	7.96865i	−0.589060	−	1.02028i	0.405296	−	0.914186i	$-0.367168\pi$
$62$			6.69338i			0.850060i
$63$	0.435938	−	2.60959i	0.0549230	−	0.328777i
$64$	1.00000			0.125000
$65$	2.08525	−	1.20392i	0.258643	−	0.149328i
$66$	0.731086	−	1.26628i	0.0899905	−	0.155868i
$67$	6.42953	+	3.71209i	0.785492	+	0.453504i	0.838373	−	0.545097i	$-0.183507\pi$
$67$	6.42953	+	3.71209i	0.785492	+	0.453504i	−0.0528814	+	0.998601i	$0.516841\pi$
$68$	1.24804	+	2.16166i	0.151347	+	0.262140i
$69$	−3.54804	−	3.22667i	−0.427134	−	0.388445i
$70$	−1.58972	+	0.594885i	−0.190008	+	0.0711024i
$71$	−3.43645			−0.407831			−0.203916	−	0.978988i	$-0.565367\pi$
$71$	−3.43645			−0.407831			−0.203916	+	0.978988i	$0.565367\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	7.21510	+	4.16564i	0.844464	+	0.487552i	0.858779	−	0.512346i	$-0.171223\pi$
$73$	7.21510	+	4.16564i	0.844464	+	0.487552i	−0.0143151	+	0.999898i	$0.504557\pi$
$74$	8.00310	+	4.62059i	0.930342	+	0.537133i
$75$	−3.97368	+	2.29421i	−0.458841	+	0.264912i
$76$	−3.49371			−0.400756
$77$	−1.35582	−	3.62318i	−0.154510	−	0.412899i
$78$	3.75315			0.424961
$79$	−12.2606	+	7.07864i	−1.37942	+	0.796410i	−0.992090	−	0.125530i	$-0.959937\pi$
$79$	−12.2606	+	7.07864i	−1.37942	+	0.796410i	−0.387332	+	0.921940i	$0.626603\pi$
$80$	−0.320775	+	0.555599i	−0.0358638	+	0.0621179i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.0004	+	5.77374i	−1.10436	+	0.637602i
$83$	−10.5288			−1.15569			−0.577844	−	0.816147i	$-0.696106\pi$
$83$	−10.5288			−1.15569			−0.577844	+	0.816147i	$0.696106\pi$
$84$	−2.60959	−	0.435938i	−0.284730	−	0.0475647i
$85$	−1.60136			−0.173692
$86$	4.87607	−	2.81520i	0.525801	−	0.303571i
$87$	−2.70448	−	1.56143i	−0.289951	−	0.167403i
$88$	−1.26628	−	0.731086i	−0.134986	−	0.0779341i
$89$	0.915023	+	1.58487i	0.0969923	+	0.167996i	0.910438	−	0.413645i	$-0.135744\pi$
$89$	0.915023	+	1.58487i	0.0969923	+	0.167996i	−0.813446	+	0.581640i	$0.802411\pi$
$90$	0.641551			0.0676254
$91$	6.31403	−	7.66394i	0.661890	−	0.803399i
$92$	−3.22667	+	3.54804i	−0.336403	+	0.369909i
$93$	−3.34669	−	5.79664i	−0.347036	−	0.601083i
$94$	−1.64885	−	0.951961i	−0.170065	−	0.0981873i
$95$	1.12070	−	1.94110i	0.114981	−	0.199153i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	11.5594			1.17368			0.586841	−	0.809702i	$-0.300371\pi$
$97$	11.5594			1.17368			0.586841	+	0.809702i	$0.300371\pi$
$98$	−5.28037	+	4.59540i	−0.533398	+	0.464205i
$99$			1.46217i			0.146954i
$100$	2.29421	+	3.97368i	0.229421	+	0.397368i
$101$	14.3329	+	8.27511i	1.42618	+	0.823404i	0.996817	−	0.0797294i	$-0.0254056\pi$
$101$	14.3329	+	8.27511i	1.42618	+	0.823404i	0.429361	+	0.903133i	$0.358739\pi$
$102$	−2.16166	−	1.24804i	−0.214037	−	0.123574i
$103$	−4.77542	−	8.27128i	−0.470536	−	0.814993i	0.528896	−	0.848687i	$-0.322606\pi$
$103$	−4.77542	−	8.27128i	−0.470536	−	0.814993i	−0.999432	+	0.0336937i	$0.989273\pi$
$104$		−	3.75315i		−	0.368027i
$105$	1.07930	−	1.31005i	0.105329	−	0.127848i
$106$			13.8287i			1.34316i
$107$	−3.03603	+	1.75285i	−0.293504	+	0.169455i	−0.639521	−	0.768774i	$-0.720867\pi$
$107$	−3.03603	+	1.75285i	−0.293504	+	0.169455i	0.346017	+	0.938228i	$0.387534\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−13.6070	−	7.85601i	−1.30332	−	0.752470i	−0.322344	−	0.946622i	$-0.604471\pi$
$109$	−13.6070	−	7.85601i	−1.30332	−	0.752470i	−0.980971	+	0.194153i	$0.937804\pi$
$110$	0.812382	−	0.469029i	0.0774576	−	0.0447202i
$111$	−9.24119			−0.877135
$112$	−0.435938	+	2.60959i	−0.0411923	+	0.246583i
$113$			6.33088i			0.595559i	0.954635	+	0.297779i	$0.0962460\pi$
$113$			6.33088i			0.595559i	−0.954635	+	0.297779i	$0.903754\pi$
$114$	3.02564	−	1.74685i	0.283377	−	0.163608i
$115$	−0.936255	−	2.93086i	−0.0873062	−	0.273304i
$116$	−1.56143	+	2.70448i	−0.144975	+	0.251105i
$117$	−3.25032	+	1.87658i	−0.300493	+	0.173489i
$118$		−	12.0891i		−	1.11289i
$119$	−6.18512	+	2.31451i	−0.566989	+	0.212171i
$120$		−	0.641551i		−	0.0585653i
$121$	−4.43103	−	7.67476i	−0.402821	−	0.697706i
$122$	4.60070	−	7.96865i	0.416528	−	0.721448i
$123$	5.77374	−	10.0004i	0.520600	−	0.901706i
$124$	−5.79664	+	3.34669i	−0.520553	+	0.300542i
$125$	−6.15145			−0.550203
$126$	2.47794	−	0.927261i	0.220752	−	0.0826070i
$127$	20.0911			1.78280			0.891400	−	0.453217i	$-0.149724\pi$
$127$	20.0911			1.78280			0.891400	+	0.453217i	$0.149724\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.81520	+	4.87607i	−0.247865	+	0.429314i
$130$	2.08525	+	1.20392i	0.182888	+	0.105591i
$131$	2.29470	−	1.32484i	0.200489	−	0.115752i	−0.396395	−	0.918080i	$-0.629739\pi$
$131$	2.29470	−	1.32484i	0.200489	−	0.115752i	0.596883	+	0.802328i	$0.296405\pi$
$132$	1.46217			0.127266
$133$	1.52304	−	9.11714i	0.132064	−	0.790557i
$134$			7.42418i			0.641351i
$135$	−0.555599	+	0.320775i	−0.0478184	+	0.0276079i
$136$	−1.24804	+	2.16166i	−0.107018	+	0.185361i
$137$	19.8373	+	11.4530i	1.69481	+	0.978500i	0.950530	+	0.310634i	$0.100541\pi$
$137$	19.8373	+	11.4530i	1.69481	+	0.978500i	0.744281	+	0.667866i	$0.232792\pi$
$138$	1.02035	−	4.68603i	0.0868584	−	0.398901i
$139$		−	7.19533i		−	0.610300i	−0.952304	−	0.305150i	$-0.901293\pi$
$139$		−	7.19533i		−	0.610300i	0.952304	−	0.305150i	$-0.0987065\pi$
$140$	−1.31005	−	1.07930i	−0.110719	−	0.0912174i
$141$	1.90392			0.160339
$142$	−1.71822	−	2.97605i	−0.144190	−	0.249745i
$143$	−2.74388	+	4.75253i	−0.229455	+	0.397427i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−1.00174	−	1.73506i	−0.0831899	−	0.144089i
$146$			8.33128i			0.689502i
$147$	2.27524	−	6.61992i	0.187659	−	0.546001i
$148$			9.24119i			0.759621i
$149$	−4.73532	+	2.73394i	−0.387933	+	0.223973i	−0.681264	−	0.732038i	$-0.738569\pi$
$149$	−4.73532	+	2.73394i	−0.387933	+	0.223973i	0.293331	+	0.956011i	$0.405236\pi$
$150$	−3.97368	−	2.29421i	−0.324450	−	0.187321i
$151$	8.72726	−	15.1161i	0.710215	−	1.23013i	−0.254562	−	0.967057i	$-0.581931\pi$
$151$	8.72726	−	15.1161i	0.710215	−	1.23013i	0.964776	−	0.263071i	$-0.0847355\pi$
$152$	−1.74685	−	3.02564i	−0.141689	−	0.245412i
$153$	2.49607			0.201796
$154$	2.45985	−	2.98576i	0.198221	−	0.240599i
$155$		−	4.29414i		−	0.344914i
$156$	1.87658	+	3.25032i	0.150246	+	0.260234i
$157$	−2.89797	+	5.01943i	−0.231283	+	0.400594i	−0.958186	−	0.286146i	$-0.907626\pi$
$157$	−2.89797	+	5.01943i	−0.231283	+	0.400594i	0.726903	+	0.686740i	$0.240959\pi$
$158$	−12.2606	−	7.07864i	−0.975399	−	0.563147i
$159$	−6.91435	−	11.9760i	−0.548343	−	0.949759i
$160$	−0.641551			−0.0507190
$161$	−7.85231	−	9.96701i	−0.618849	−	0.785510i
$162$	−1.00000			−0.0785674
$163$	−0.565971	−	0.980291i	−0.0443303	−	0.0767823i	0.843009	−	0.537900i	$-0.180782\pi$
$163$	−0.565971	−	0.980291i	−0.0443303	−	0.0767823i	−0.887339	+	0.461117i	$0.847449\pi$
$164$	−10.0004	−	5.77374i	−0.780900	−	0.450853i
$165$	−0.469029	+	0.812382i	−0.0365139	+	0.0632438i
$166$	−5.26441	−	9.11823i	−0.408598	−	0.707712i
$167$			1.49172i			0.115433i	0.998333	+	0.0577164i	$0.0183819\pi$
$167$			1.49172i			0.115433i	−0.998333	+	0.0577164i	$0.981618\pi$
$168$	−0.927261	−	2.47794i	−0.0715398	−	0.191177i
$169$	−1.08614			−0.0835492
$170$	−0.800679	−	1.38682i	−0.0614093	−	0.106364i
$171$	−1.74685	+	3.02564i	−0.133585	+	0.231376i
$172$	4.87607	+	2.81520i	0.371797	+	0.214657i
$173$	−17.1380	+	9.89462i	−1.30298	+	0.752274i	−0.980914	−	0.194444i	$-0.937710\pi$
$173$	−17.1380	+	9.89462i	−1.30298	+	0.752274i	−0.322064	+	0.946718i	$0.604376\pi$
$174$		−	3.12287i		−	0.236744i
$175$	−11.3698	+	4.25466i	−0.859477	+	0.321622i
$176$		−	1.46217i		−	0.110215i
$177$	6.04453	+	10.4694i	0.454335	+	0.786931i
$178$	−0.915023	+	1.58487i	−0.0685839	+	0.118791i
$179$	11.2078	−	19.4125i	0.837713	−	1.45096i	−0.0540890	−	0.998536i	$-0.517225\pi$
$179$	11.2078	−	19.4125i	0.837713	−	1.45096i	0.891802	−	0.452426i	$-0.149441\pi$
$180$	0.320775	+	0.555599i	0.0239092	+	0.0414119i
$181$	−19.7000			−1.46429			−0.732145	−	0.681148i	$-0.761481\pi$
$181$	−19.7000			−1.46429			−0.732145	+	0.681148i	$0.761481\pi$
$182$	9.79418	+	1.63614i	0.725993	+	0.121279i
$183$			9.20141i			0.680188i
$184$	−4.68603	−	1.02035i	−0.345459	−	0.0752216i
$185$	−5.13440	−	2.96434i	−0.377488	−	0.217943i
$186$	3.34669	−	5.79664i	0.245391	−	0.425030i
$187$	3.16072	−	1.82484i	0.231135	−	0.133446i
$188$		−	1.90392i		−	0.138858i
$189$	−1.68233	+	2.04200i	−0.122371	+	0.148534i
$190$	2.24139			0.162608
$191$	−18.2187	+	10.5186i	−1.31826	+	0.761097i	−0.983448	−	0.181188i	$-0.942006\pi$
$191$	−18.2187	+	10.5186i	−1.31826	+	0.761097i	−0.334811	+	0.942285i	$0.608672\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	5.41719	−	9.38285i	0.389938	−	0.675392i	−0.602503	−	0.798117i	$-0.705830\pi$
$193$	5.41719	−	9.38285i	0.389938	−	0.675392i	0.992441	+	0.122724i	$0.0391631\pi$
$194$	5.77972	+	10.0108i	0.414960	+	0.718731i
$195$	−2.40784			−0.172429
$196$	−6.61992	−	2.27524i	−0.472851	−	0.162517i
$197$	−11.8314			−0.842956			−0.421478	−	0.906839i	$-0.638488\pi$
$197$	−11.8314			−0.842956			−0.421478	+	0.906839i	$0.638488\pi$
$198$	−1.26628	+	0.731086i	−0.0899905	+	0.0519560i
$199$	7.17383	−	12.4254i	0.508539	−	0.880816i	−0.491412	−	0.870927i	$-0.663519\pi$
$199$	7.17383	−	12.4254i	0.508539	−	0.880816i	0.999951	−	0.00988879i	$-0.00314775\pi$
$200$	−2.29421	+	3.97368i	−0.162225	+	0.280982i
$201$	−3.71209	−	6.42953i	−0.261831	−	0.453504i
$202$			16.5502i			1.16447i
$203$	−6.37690	−	5.25369i	−0.447571	−	0.368737i
$204$		−	2.49607i		−	0.174760i
$205$	6.41577	−	3.70414i	0.448097	−	0.258709i
$206$	4.77542	−	8.27128i	0.332720	−	0.576287i
$207$	1.45936	+	4.56840i	0.101433	+	0.317526i
$208$	3.25032	−	1.87658i	0.225369	−	0.130117i
$209$			5.10840i			0.353356i
$210$	1.67418	+	0.279676i	0.115530	+	0.0192995i
$211$	7.50209			0.516465			0.258233	−	0.966083i	$-0.416860\pi$
$211$	7.50209			0.516465			0.258233	+	0.966083i	$0.416860\pi$
$212$	−11.9760	+	6.91435i	−0.822515	+	0.474879i
$213$	2.97605	+	1.71822i	0.203916	+	0.117731i
$214$	−3.03603	−	1.75285i	−0.207539	−	0.119823i
$215$	−3.12825	+	1.80609i	−0.213345	+	0.123175i
$216$			1.00000i			0.0680414i
$217$	−6.20651	−	16.5858i	−0.421326	−	1.12592i
$218$		−	15.7120i		−	1.06415i
$219$	−4.16564	−	7.21510i	−0.281488	−	0.487552i
$220$	0.812382	+	0.469029i	0.0547708	+	0.0316219i
$221$	8.11305	+	4.68407i	0.545743	+	0.315085i
$222$	−4.62059	−	8.00310i	−0.310114	−	0.537133i
$223$		−	15.4435i		−	1.03417i	−0.855933	−	0.517087i	$-0.827016\pi$
$223$		−	15.4435i		−	1.03417i	0.855933	−	0.517087i	$-0.172984\pi$
$224$	−2.47794	+	0.927261i	−0.165564	+	0.0619553i
$225$	4.58841			0.305894
$226$	−5.48270	+	3.16544i	−0.364704	+	0.210562i
$227$	−5.87255	+	10.1715i	−0.389775	+	0.675109i	−0.992419	−	0.122900i	$-0.960780\pi$
$227$	−5.87255	+	10.1715i	−0.389775	+	0.675109i	0.602644	+	0.798010i	$0.294114\pi$
$228$	3.02564	+	1.74685i	0.200378	+	0.115688i
$229$	1.20025	+	2.07889i	0.0793146	+	0.137377i	0.902954	−	0.429736i	$-0.141394\pi$
$229$	1.20025	+	2.07889i	0.0793146	+	0.137377i	−0.823640	+	0.567113i	$0.808060\pi$
$230$	2.07007	−	2.27625i	0.136496	−	0.150091i
$231$	−0.637417	+	3.81567i	−0.0419389	+	0.251053i
$232$	−3.12287			−0.205026
$233$	11.5129	+	19.9410i	0.754236	+	1.30638i	0.945753	+	0.324887i	$0.105326\pi$
$233$	11.5129	+	19.9410i	0.754236	+	1.30638i	−0.191517	+	0.981489i	$0.561341\pi$
$234$	−3.25032	−	1.87658i	−0.212480	−	0.122676i
$235$	1.05782	+	0.610731i	0.0690044	+	0.0398397i
$236$	10.4694	−	6.04453i	0.681502	−	0.393465i
$237$	14.1573			0.919615
$238$	−5.09699	−	4.19921i	−0.330389	−	0.272195i
$239$	−24.8829			−1.60954			−0.804772	−	0.593584i	$-0.797713\pi$
$239$	−24.8829			−1.60954			−0.804772	+	0.593584i	$0.797713\pi$
$240$	0.555599	−	0.320775i	0.0358638	−	0.0207060i
$241$	3.92849	−	6.80434i	0.253056	−	0.438306i	−0.711310	−	0.702879i	$-0.751898\pi$
$241$	3.92849	−	6.80434i	0.253056	−	0.438306i	0.964366	+	0.264573i	$0.0852309\pi$
$242$	4.43103	−	7.67476i	0.284837	−	0.493352i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	9.20141			0.589060
$245$	3.38763	−	2.94818i	0.216428	−	0.188352i
$246$	11.5475			0.736240
$247$	−11.3557	+	6.55620i	−0.722545	+	0.417161i
$248$	−5.79664	−	3.34669i	−0.368087	−	0.212515i
$249$	9.11823	+	5.26441i	0.577844	+	0.333619i
$250$	−3.07573	−	5.32731i	−0.194526	−	0.336929i
$251$	20.1145			1.26961			0.634807	−	0.772671i	$-0.281080\pi$
$251$	20.1145			1.26961			0.634807	+	0.772671i	$0.281080\pi$
$252$	2.04200	+	1.68233i	0.128634	+	0.105977i
$253$	5.18785	+	4.71795i	0.326157	+	0.296615i
$254$	10.0456	+	17.3994i	0.630315	+	1.09174i
$255$	1.38682	+	0.800679i	0.0868458	+	0.0501405i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.6917	−	9.05958i	0.978819	−	0.565121i	0.0769055	−	0.997038i	$-0.475496\pi$
$257$	15.6917	−	9.05958i	0.978819	−	0.565121i	0.901913	+	0.431917i	$0.142163\pi$
$258$	−5.63040			−0.350534
$259$	−24.1157	−	4.02859i	−1.49848	−	0.250324i
$260$			2.40784i			0.149328i
$261$	1.56143	+	2.70448i	0.0966503	+	0.167403i
$262$	2.29470	+	1.32484i	0.141767	+	0.0818492i
$263$	−2.45403	−	1.41683i	−0.151322	−	0.0873657i	0.422427	−	0.906397i	$-0.361178\pi$
$263$	−2.45403	−	1.41683i	−0.151322	−	0.0873657i	−0.573749	+	0.819031i	$0.694512\pi$
$264$	0.731086	+	1.26628i	0.0449952	+	0.0779341i
$265$		−	8.87181i		−	0.544991i
$266$	8.65720	−	3.23958i	0.530807	−	0.198631i
$267$		−	1.83005i		−	0.111997i
$268$	−6.42953	+	3.71209i	−0.392746	+	0.226752i
$269$	−9.06271	−	5.23236i	−0.552563	−	0.319023i	0.197592	−	0.980284i	$-0.436688\pi$
$269$	−9.06271	−	5.23236i	−0.552563	−	0.319023i	−0.750155	+	0.661262i	$0.770021\pi$
$270$	−0.555599	−	0.320775i	−0.0338127	−	0.0195218i
$271$	0.476714	−	0.275231i	0.0289583	−	0.0167191i	−0.485451	−	0.874264i	$-0.661345\pi$
$271$	0.476714	−	0.275231i	0.0289583	−	0.0167191i	0.514409	+	0.857545i	$0.328011\pi$
$272$	−2.49607			−0.151347
$273$	−9.30008	+	3.48015i	−0.562867	+	0.210628i
$274$			22.9061i			1.38381i
$275$	5.81021	−	3.35453i	0.350369	−	0.202286i
$276$	4.56840	−	1.45936i	0.274985	−	0.0878433i
$277$	−2.25153	+	3.89976i	−0.135281	+	0.234314i	−0.925705	−	0.378247i	$-0.876527\pi$
$277$	−2.25153	+	3.89976i	−0.135281	+	0.234314i	0.790424	+	0.612561i	$0.209860\pi$
$278$	6.23134	−	3.59766i	0.373731	−	0.215773i
$279$			6.69338i			0.400722i
$280$	0.279676	−	1.67418i	0.0167139	−	0.100052i
$281$		−	11.9701i		−	0.714079i	−0.934089	−	0.357040i	$-0.883786\pi$
$281$		−	11.9701i		−	0.714079i	0.934089	−	0.357040i	$-0.116214\pi$
$282$	0.951961	+	1.64885i	0.0566885	+	0.0981873i
$283$	−10.7059	+	18.5431i	−0.636398	+	1.10227i	0.349819	+	0.936817i	$0.386243\pi$
$283$	−10.7059	+	18.5431i	−0.636398	+	1.10227i	−0.986217	+	0.165457i	$0.947090\pi$
$284$	1.71822	−	2.97605i	0.101958	−	0.176596i
$285$	−1.94110	+	1.12070i	−0.114981	+	0.0663843i
$286$	−5.48775			−0.324498
$287$	19.4266	−	23.5800i	1.14672	−	1.39188i
$288$	1.00000			0.0589256
$289$	5.38481	+	9.32676i	0.316753	+	0.548633i
$290$	1.00174	−	1.73506i	0.0588241	−	0.101886i
$291$	−10.0108	−	5.77972i	−0.586841	−	0.338813i
$292$	−7.21510	+	4.16564i	−0.422232	+	0.243776i
$293$	−5.03581			−0.294195			−0.147098	−	0.989122i	$-0.546993\pi$
$293$	−5.03581			−0.294195			−0.147098	+	0.989122i	$0.546993\pi$
$294$	6.87063	−	1.33954i	0.400704	−	0.0781237i
$295$			7.75575i			0.451557i
$296$	−8.00310	+	4.62059i	−0.465171	+	0.268567i
$297$	0.731086	−	1.26628i	0.0424219	−	0.0734769i
$298$	−4.73532	−	2.73394i	−0.274310	−	0.158373i
$299$	−3.82955	+	17.5874i	−0.221468	+	1.01710i
$300$		−	4.58841i		−	0.264912i
$301$	−9.47219	+	11.4973i	−0.545968	+	0.662693i
$302$	17.4545			1.00440
$303$	−8.27511	−	14.3329i	−0.475392	−	0.823404i
$304$	1.74685	−	3.02564i	0.100189	−	0.173532i
$305$	−2.95159	+	5.11230i	−0.169007	+	0.292729i
$306$	1.24804	+	2.16166i	0.0713455	+	0.123574i
$307$		−	9.89753i		−	0.564882i	−0.959285	−	0.282441i	$-0.908856\pi$
$307$		−	9.89753i		−	0.564882i	0.959285	−	0.282441i	$-0.0911441\pi$
$308$	3.81567	+	0.637417i	0.217418	+	0.0363202i
$309$			9.55085i			0.543329i
$310$	3.71884	−	2.14707i	0.211216	−	0.121945i
$311$	22.5520	+	13.0204i	1.27880	+	0.738318i	0.976629	−	0.214934i	$-0.0689535\pi$
$311$	22.5520	+	13.0204i	1.27880	+	0.738318i	0.302176	+	0.953252i	$0.402287\pi$
$312$	−1.87658	+	3.25032i	−0.106240	+	0.184013i
$313$	−6.92894	−	12.0013i	−0.391647	−	0.678352i	0.601020	−	0.799234i	$-0.294761\pi$
$313$	−6.92894	−	12.0013i	−0.391647	−	0.678352i	−0.992667	+	0.120882i	$0.961428\pi$
$314$	−5.79594			−0.327084
$315$	−1.58972	+	0.594885i	−0.0895708	+	0.0335180i
$316$		−	14.1573i		−	0.796410i
$317$	5.09880	+	8.83138i	0.286377	+	0.496020i	0.972942	−	0.231049i	$-0.0742157\pi$
$317$	5.09880	+	8.83138i	0.286377	+	0.496020i	−0.686565	+	0.727068i	$0.740882\pi$
$318$	6.91435	−	11.9760i	0.387737	−	0.671581i
$319$	3.95442	+	2.28309i	0.221405	+	0.127828i
$320$	−0.320775	−	0.555599i	−0.0179319	−	0.0310589i
$321$	3.50571			0.195670
$322$	4.70553	−	11.7838i	0.262229	−	0.656686i
$323$	8.72055			0.485224
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	14.9138	+	8.61050i	0.827270	+	0.477625i
$326$	0.565971	−	0.980291i	0.0313462	−	0.0542933i
$327$	7.85601	+	13.6070i	0.434439	+	0.752470i
$328$		−	11.5475i		−	0.637602i
$329$	4.96846	+	0.829992i	0.273920	+	0.0457590i
$330$	−0.938058			−0.0516384
$331$	4.96632	+	8.60191i	0.272973	+	0.472804i	0.969622	−	0.244609i	$-0.0786595\pi$
$331$	4.96632	+	8.60191i	0.272973	+	0.472804i	−0.696648	+	0.717413i	$0.745326\pi$
$332$	5.26441	−	9.11823i	0.288922	−	0.500428i
$333$	8.00310	+	4.62059i	0.438567	+	0.253207i
$334$	−1.29187	+	0.745861i	−0.0706879	+	0.0408117i
$335$		−	4.76299i		−	0.260230i
$336$	1.68233	−	2.04200i	0.0917785	−	0.111400i
$337$		−	25.7788i		−	1.40426i	−0.712049	−	0.702130i	$-0.752233\pi$
$337$		−	25.7788i		−	1.40426i	0.712049	−	0.702130i	$-0.247767\pi$
$338$	−0.543069	−	0.940624i	−0.0295391	−	0.0511632i
$339$	3.16544	−	5.48270i	0.171923	−	0.297779i
$340$	0.800679	−	1.38682i	0.0434229	−	0.0752107i
$341$	4.89344	+	8.47568i	0.264995	+	0.458984i
$342$	−3.49371			−0.188918
$343$	8.82331	−	16.2834i	0.476414	−	0.879221i
$344$			5.63040i			0.303571i
$345$	−0.654609	+	3.00633i	−0.0352430	+	0.161855i
$346$	−17.1380	−	9.89462i	−0.921344	−	0.531938i
$347$	2.22541	−	3.85452i	0.119466	−	0.206921i	−0.800090	−	0.599880i	$-0.795215\pi$
$347$	2.22541	−	3.85452i	0.119466	−	0.206921i	0.919556	+	0.392958i	$0.128548\pi$
$348$	2.70448	−	1.56143i	0.144975	−	0.0837016i
$349$			22.9293i			1.22738i	0.789548	+	0.613689i	$0.210315\pi$
$349$			22.9293i			1.22738i	−0.789548	+	0.613689i	$0.789685\pi$
$350$	−9.36955	−	7.71922i	−0.500823	−	0.412609i
$351$	3.75315			0.200328
$352$	1.26628	−	0.731086i	0.0674929	−	0.0389670i
$353$	−2.19435	−	1.26691i	−0.116794	−	0.0674308i	0.440465	−	0.897770i	$-0.354814\pi$
$353$	−2.19435	−	1.26691i	−0.116794	−	0.0674308i	−0.557259	+	0.830339i	$0.688147\pi$
$354$	−6.04453	+	10.4694i	−0.321263	+	0.556444i
$355$	1.10233	+	1.90929i	0.0585055	+	0.101334i
$356$	−1.83005			−0.0969923
$357$	6.51373	+	1.08813i	0.344743	+	0.0575901i
$358$	22.4157			1.18471
$359$	−9.78344	+	5.64847i	−0.516350	+	0.298115i	−0.735440	−	0.677590i	$-0.763025\pi$
$359$	−9.78344	+	5.64847i	−0.516350	+	0.298115i	0.219090	+	0.975705i	$0.429691\pi$
$360$	−0.320775	+	0.555599i	−0.0169063	+	0.0292826i
$361$	3.39700	−	5.88378i	0.178790	−	0.309673i
$362$	−9.85001	−	17.0607i	−0.517705	−	0.896691i
$363$			8.86205i			0.465137i
$364$	3.48015	+	9.30008i	0.182409	+	0.487457i
$365$		−	5.34494i		−	0.279767i
$366$	−7.96865	+	4.60070i	−0.416528	+	0.240483i
$367$	−9.30564	+	16.1178i	−0.485751	+	0.841345i	−0.999866	−	0.0163765i	$-0.994787\pi$
$367$	−9.30564	+	16.1178i	−0.485751	+	0.841345i	0.514115	+	0.857721i	$0.328120\pi$
$368$	−1.45936	−	4.56840i	−0.0760745	−	0.238144i
$369$	−10.0004	+	5.77374i	−0.520600	+	0.300569i
$370$		−	5.92869i		−	0.308218i
$371$	−12.8228	−	34.2667i	−0.665727	−	1.77904i
$372$	6.69338			0.347036
$373$	12.2660	−	7.08177i	0.635109	−	0.366680i	−0.147619	−	0.989044i	$-0.547161\pi$
$373$	12.2660	−	7.08177i	0.635109	−	0.366680i	0.782728	+	0.622364i	$0.213828\pi$
$374$	3.16072	+	1.82484i	0.163437	+	0.0943605i
$375$	5.32731	+	3.07573i	0.275101	+	0.158830i
$376$	1.64885	−	0.951961i	0.0850327	−	0.0490936i
$377$			11.7206i			0.603641i
$378$	−2.60959	−	0.435938i	−0.134223	−	0.0224222i
$379$			29.9100i			1.53638i	0.640224	+	0.768188i	$0.278841\pi$
$379$			29.9100i			1.53638i	−0.640224	+	0.768188i	$0.721159\pi$
$380$	1.12070	+	1.94110i	0.0574905	+	0.0995764i
$381$	−17.3994	−	10.0456i	−0.891400	−	0.514650i
$382$	−18.2187	−	10.5186i	−0.932150	−	0.538177i
$383$	−15.3684	−	26.6188i	−0.785287	−	1.36016i	−0.928828	−	0.370512i	$-0.879182\pi$
$383$	−15.3684	−	26.6188i	−0.785287	−	1.36016i	0.143541	−	0.989644i	$-0.454151\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−1.57812	+	1.91552i	−0.0804285	+	0.0976237i
$386$	10.8344			0.551456
$387$	4.87607	−	2.81520i	0.247865	−	0.143105i
$388$	−5.77972	+	10.0108i	−0.293421	+	0.508220i
$389$	19.7850	+	11.4229i	1.00314	+	0.579163i	0.909176	−	0.416412i	$-0.136713\pi$
$389$	19.7850	+	11.4229i	1.00314	+	0.579163i	0.0939645	+	0.995576i	$0.470046\pi$
$390$	−1.20392	−	2.08525i	−0.0609628	−	0.105591i
$391$	8.05400	−	8.85618i	0.407308	−	0.447876i
$392$	−1.33954	−	6.87063i	−0.0676571	−	0.347019i
$393$	−2.64969			−0.133659
$394$	−5.91572	−	10.2463i	−0.298030	−	0.516203i
$395$	7.86578	+	4.54131i	0.395770	+	0.228498i
$396$	−1.26628	−	0.731086i	−0.0636329	−	0.0367385i
$397$	−2.75666	+	1.59156i	−0.138353	+	0.0798780i	−0.567579	−	0.823319i	$-0.692120\pi$
$397$	−2.75666	+	1.59156i	−0.138353	+	0.0798780i	0.429226	+	0.903197i	$0.358786\pi$
$398$	14.3477			0.719183
$399$	−5.87756	+	7.13416i	−0.294246	+	0.357155i
$400$	−4.58841			−0.229421
$401$	−7.09790	+	4.09797i	−0.354452	+	0.204643i	−0.666644	−	0.745376i	$-0.732270\pi$
$401$	−7.09790	+	4.09797i	−0.354452	+	0.204643i	0.312192	+	0.950019i	$0.398937\pi$
$402$	3.71209	−	6.42953i	0.185142	−	0.320676i
$403$	−12.5606	+	21.7557i	−0.625690	+	1.08373i
$404$	−14.3329	+	8.27511i	−0.713089	+	0.411702i
$405$	0.641551			0.0318789
$406$	1.36138	−	8.14940i	0.0675640	−	0.404448i
$407$	13.5122			0.669775
$408$	2.16166	−	1.24804i	0.107018	−	0.0617870i
$409$	−14.7694	−	8.52713i	−0.730301	−	0.421639i	0.0882313	−	0.996100i	$-0.471879\pi$
$409$	−14.7694	−	8.52713i	−0.730301	−	0.421639i	−0.818532	+	0.574461i	$0.805212\pi$
$410$	6.41577	+	3.70414i	0.316852	+	0.182935i
$411$	−11.4530	−	19.8373i	−0.564937	−	0.978500i
$412$	9.55085			0.470536
$413$	11.2097	+	29.9560i	0.551594	+	1.47404i
$414$	−3.22667	+	3.54804i	−0.158582	+	0.174377i
$415$	3.37739	+	5.84981i	0.165789	+	0.287156i
$416$	3.25032	+	1.87658i	0.159360	+	0.0920067i
$417$	−3.59766	+	6.23134i	−0.176178	+	0.305150i
$418$	−4.42401	+	2.55420i	−0.216385	+	0.124930i
$419$	−26.4920			−1.29422			−0.647110	−	0.762397i	$-0.724022\pi$
$419$	−26.4920			−1.29422			−0.647110	+	0.762397i	$0.724022\pi$
$420$	0.594885	+	1.58972i	0.0290274	+	0.0775706i
$421$			27.2139i			1.32632i	0.748476	+	0.663162i	$0.230786\pi$
$421$			27.2139i			1.32632i	−0.748476	+	0.663162i	$0.769214\pi$
$422$	3.75105	+	6.49700i	0.182598	+	0.316269i
$423$	−1.64885	−	0.951961i	−0.0801696	−	0.0462859i
$424$	−11.9760	−	6.91435i	−0.581606	−	0.335790i
$425$	−5.72651	−	9.91860i	−0.277776	−	0.481123i
$426$			3.43645i			0.166496i
$427$	−4.01125	+	24.0119i	−0.194118	+	1.16202i
$428$		−	3.50571i		−	0.169455i
$429$	4.75253	−	2.74388i	0.229455	−	0.132476i
$430$	−3.12825	−	1.80609i	−0.150858	−	0.0870976i
$431$	7.87094	+	4.54429i	0.379130	+	0.218891i	0.677440	−	0.735578i	$-0.263090\pi$
$431$	7.87094	+	4.54429i	0.379130	+	0.218891i	−0.298310	+	0.954469i	$0.596423\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	38.2940			1.84029			0.920147	−	0.391572i	$-0.128069\pi$
$433$	38.2940			1.84029			0.920147	+	0.391572i	$0.128069\pi$
$434$	11.2605	−	13.6679i	0.540520	−	0.656080i
$435$			2.00348i			0.0960594i
$436$	13.6070	−	7.85601i	0.651658	−	0.376235i
$437$	5.09858	+	15.9606i	0.243898	+	0.763501i
$438$	4.16564	−	7.21510i	0.199042	−	0.344751i
$439$	−8.56977	+	4.94776i	−0.409013	+	0.236144i	−0.690366	−	0.723461i	$-0.742550\pi$
$439$	−8.56977	+	4.94776i	−0.409013	+	0.236144i	0.281353	+	0.959604i	$0.409217\pi$
$440$			0.938058i			0.0447202i
$441$	−5.28037	+	4.59540i	−0.251446	+	0.218828i
$442$			9.36814i			0.445597i
$443$	−0.732011	−	1.26788i	−0.0347789	−	0.0602388i	0.848112	−	0.529817i	$-0.177739\pi$
$443$	−0.732011	−	1.26788i	−0.0347789	−	0.0602388i	−0.882891	+	0.469578i	$0.844406\pi$
$444$	4.62059	−	8.00310i	0.219284	−	0.379810i
$445$	0.587034	−	1.01677i	0.0278281	−	0.0481996i
$446$	13.3745	−	7.72176i	0.633300	−	0.365636i
$447$	5.46788			0.258622
$448$	−2.04200	−	1.68233i	−0.0964755	−	0.0794825i
$449$	−14.7310			−0.695198			−0.347599	−	0.937643i	$-0.613003\pi$
$449$	−14.7310			−0.695198			−0.347599	+	0.937643i	$0.613003\pi$
$450$	2.29421	+	3.97368i	0.108150	+	0.187321i
$451$	−8.44220	+	14.6223i	−0.397528	+	0.688538i
$452$	−5.48270	−	3.16544i	−0.257885	−	0.148890i
$453$	−15.1161	+	8.72726i	−0.710215	+	0.410043i
$454$	−11.7451			−0.551224
$455$	−6.28346	−	1.04967i	−0.294573	−	0.0492092i
$456$			3.49371i			0.163608i
$457$	−13.3608	+	7.71386i	−0.624992	+	0.360839i	−0.778810	−	0.627260i	$-0.784176\pi$
$457$	−13.3608	+	7.71386i	−0.624992	+	0.360839i	0.153818	+	0.988099i	$0.450843\pi$
$458$	−1.20025	+	2.07889i	−0.0560839	+	0.0971401i
$459$	−2.16166	−	1.24804i	−0.100898	−	0.0582534i
$460$	3.00633	+	0.654609i	0.140171	+	0.0305213i
$461$			4.48982i			0.209112i	0.994519	+	0.104556i	$0.0333421\pi$
$461$			4.48982i			0.209112i	−0.994519	+	0.104556i	$0.966658\pi$
$462$	−3.62318	+	1.35582i	−0.168565	+	0.0630783i
$463$	−30.3409			−1.41006			−0.705031	−	0.709177i	$-0.749067\pi$
$463$	−30.3409			−1.41006			−0.705031	+	0.709177i	$0.749067\pi$
$464$	−1.56143	−	2.70448i	−0.0724877	−	0.125552i
$465$	−2.14707	+	3.71884i	−0.0995681	+	0.172457i
$466$	−11.5129	+	19.9410i	−0.533326	+	0.923747i
$467$	8.55783	+	14.8226i	0.396009	+	0.685908i	0.993229	−	0.116169i	$-0.0370614\pi$
$467$	8.55783	+	14.8226i	0.396009	+	0.685908i	−0.597220	+	0.802077i	$0.703728\pi$
$468$		−	3.75315i		−	0.173489i
$469$	−6.88415	−	18.3967i	−0.317881	−	0.849479i
$470$			1.22146i			0.0563419i
$471$	5.01943	−	2.89797i	0.231283	−	0.133531i
$472$	10.4694	+	6.04453i	0.481895	+	0.278222i
$473$	4.11631	−	7.12966i	0.189268	−	0.327822i
$474$	7.07864	+	12.2606i	0.325133	+	0.563147i
$475$	16.0306			0.735533
$476$	1.08813	−	6.51373i	0.0498745	−	0.298556i
$477$			13.8287i			0.633172i
$478$	−12.4415	−	21.5493i	−0.569060	−	0.985641i
$479$	−9.60766	+	16.6409i	−0.438985	+	0.760344i	−0.997611	−	0.0690750i	$-0.977995\pi$
$479$	−9.60766	+	16.6409i	−0.438985	+	0.760344i	0.558626	+	0.829419i	$0.311329\pi$
$480$	0.555599	+	0.320775i	0.0253595	+	0.0146413i
$481$	17.3418	+	30.0368i	0.790717	+	1.36956i
$482$	7.85698			0.357875
$483$	1.81680	+	12.5578i	0.0826671	+	0.571401i
$484$	8.86205			0.402821
$485$	−3.70798	−	6.42241i	−0.168371	−	0.291627i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−0.744901	+	1.29021i	−0.0337547	+	0.0584649i	−0.882409	−	0.470483i	$-0.844080\pi$
$487$	−0.744901	+	1.29021i	−0.0337547	+	0.0584649i	0.848655	+	0.528948i	$0.177413\pi$
$488$	4.60070	+	7.96865i	0.208264	+	0.360724i
$489$			1.13194i			0.0511882i
$490$	4.24701	+	1.45968i	0.191860	+	0.0659417i
$491$	−10.2935			−0.464537			−0.232269	−	0.972652i	$-0.574615\pi$
$491$	−10.2935			−0.464537			−0.232269	+	0.972652i	$0.574615\pi$
$492$	5.77374	+	10.0004i	0.260300	+	0.450853i
$493$	3.89745	−	6.75059i	0.175532	−	0.304031i
$494$	−11.3557	−	6.55620i	−0.510916	−	0.294978i
$495$	0.812382	−	0.469029i	0.0365139	−	0.0210813i
$496$		−	6.69338i		−	0.300542i
$497$	7.01723	+	5.78123i	0.314766	+	0.259324i
$498$			10.5288i			0.471808i
$499$	6.36607	+	11.0264i	0.284984	+	0.493608i	0.972605	−	0.232462i	$-0.0746782\pi$
$499$	6.36607	+	11.0264i	0.284984	+	0.493608i	−0.687621	+	0.726070i	$0.741345\pi$
$500$	3.07573	−	5.32731i	0.137551	−	0.238245i
$501$	0.745861	−	1.29187i	0.0333226	−	0.0577164i
$502$	10.0572	+	17.4196i	0.448876	+	0.777476i
$503$	−22.8522			−1.01893			−0.509465	−	0.860491i	$-0.670157\pi$
$503$	−22.8522			−1.01893			−0.509465	+	0.860491i	$0.670157\pi$
$504$	−0.435938	+	2.60959i	−0.0194182	+	0.116240i
$505$		−	10.6178i		−	0.472486i
$506$	−1.49193	+	6.85178i	−0.0663246	+	0.304599i
$507$	0.940624	+	0.543069i	0.0417746	+	0.0241186i
$508$	−10.0456	+	17.3994i	−0.445700	+	0.771975i
$509$	−3.25906	+	1.88162i	−0.144455	+	0.0834012i	−0.570486	−	0.821308i	$-0.693245\pi$
$509$	−3.25906	+	1.88162i	−0.144455	+	0.0834012i	0.426030	+	0.904709i	$0.359912\pi$
$510$			1.60136i			0.0709093i
$511$	−7.72528	−	20.6444i	−0.341746	−	0.913255i
$512$	−1.00000			−0.0441942
$513$	3.02564	−	1.74685i	0.133585	−	0.0771255i
$514$	15.6917	+	9.05958i	0.692129	+	0.399601i
$515$	−3.06368	+	5.30644i	−0.135002	+	0.233830i
$516$	−2.81520	−	4.87607i	−0.123932	−	0.214657i
$517$	−2.78386			−0.122434
$518$	−8.56899	−	22.8991i	−0.376500	−	1.00613i
$519$	19.7892			0.868651
$520$	−2.08525	+	1.20392i	−0.0914442	+	0.0527953i
$521$	14.6312	−	25.3419i	0.641003	−	1.11025i	−0.344206	−	0.938894i	$-0.611852\pi$
$521$	14.6312	−	25.3419i	0.641003	−	1.11025i	0.985209	−	0.171356i	$-0.0548147\pi$
$522$	−1.56143	+	2.70448i	−0.0683421	+	0.118372i
$523$	−19.2011	−	33.2572i	−0.839603	−	1.45424i	−0.890227	−	0.455518i	$-0.849454\pi$
$523$	−19.2011	−	33.2572i	−0.839603	−	1.45424i	0.0506233	−	0.998718i	$-0.483879\pi$
$524$			2.64969i			0.115752i
$525$	11.9739	+	2.00026i	0.522583	+	0.0872987i
$526$		−	2.83367i		−	0.123554i
$527$	14.4688	−	8.35358i	0.630272	−	0.363888i
$528$	−0.731086	+	1.26628i	−0.0318164	+	0.0551077i
$529$	20.9178	+	9.56283i	0.909467	+	0.415775i
$530$	7.68321	−	4.43590i	0.333737	−	0.192683i
$531$		−	12.0891i		−	0.524621i
$532$	7.13416	+	5.87756i	0.309305	+	0.254825i
$533$	−43.3394			−1.87724
$534$	1.58487	−	0.915023i	0.0685839	−	0.0395969i
$535$	1.94777	+	1.12454i	0.0842094	+	0.0486183i
$536$	−6.42953	−	3.71209i	−0.277713	−	0.160338i
$537$	−19.4125	+	11.2078i	−0.837713	+	0.483654i
$538$		−	10.4647i		−	0.451166i
$539$	−3.32679	+	9.67946i	−0.143295	+	0.416924i
$540$		−	0.641551i		−	0.0276079i
$541$	3.78930	+	6.56326i	0.162915	+	0.282177i	0.935913	−	0.352232i	$-0.114577\pi$
$541$	3.78930	+	6.56326i	0.162915	+	0.282177i	−0.772998	+	0.634408i	$0.781244\pi$
$542$	0.476714	+	0.275231i	0.0204766	+	0.0118222i
$543$	17.0607	+	9.85001i	0.732145	+	0.422704i
$544$	−1.24804	−	2.16166i	−0.0535091	−	0.0926805i
$545$			10.0801i			0.431782i
$546$	−7.66394	−	6.31403i	−0.327986	−	0.270216i
$547$	−14.8688			−0.635746			−0.317873	−	0.948133i	$-0.602968\pi$
$547$	−14.8688			−0.635746			−0.317873	+	0.948133i	$0.602968\pi$
$548$	−19.8373	+	11.4530i	−0.847406	+	0.489250i
$549$	4.60070	−	7.96865i	0.196353	−	0.340094i
$550$	5.81021	+	3.35453i	0.247748	+	0.143037i
$551$	5.45519	+	9.44867i	0.232399	+	0.402527i
$552$	3.54804	+	3.22667i	0.151015	+	0.137336i
$553$	36.9447	+	6.17170i	1.57105	+	0.262447i
$554$	−4.50306			−0.191317
$555$	2.96434	+	5.13440i	0.125829	+	0.217943i
$556$	6.23134	+	3.59766i	0.264267	+	0.152575i
$557$	−7.57642	−	4.37425i	−0.321023	−	0.185343i	0.330825	−	0.943692i	$-0.392673\pi$
$557$	−7.57642	−	4.37425i	−0.321023	−	0.185343i	−0.651849	+	0.758349i	$0.726006\pi$
$558$	−5.79664	+	3.34669i	−0.245391	+	0.141677i
$559$	21.1318			0.893778
$560$	1.58972	−	0.594885i	0.0671781	−	0.0251385i
$561$	−3.64969			−0.154090
$562$	10.3665	−	5.98507i	0.437282	−	0.252465i
$563$	−7.69223	+	13.3233i	−0.324189	+	0.561512i	−0.981348	−	0.192240i	$-0.938425\pi$
$563$	−7.69223	+	13.3233i	−0.324189	+	0.561512i	0.657159	+	0.753752i	$0.271758\pi$
$564$	−0.951961	+	1.64885i	−0.0400848	+	0.0694289i
$565$	3.51743	−	2.03079i	0.147979	−	0.0854359i
$566$	−21.4118			−0.900003
$567$	2.47794	−	0.927261i	0.104064	−	0.0389413i
$568$	3.43645			0.144190
$569$	9.48688	−	5.47725i	0.397711	−	0.229618i	−0.287785	−	0.957695i	$-0.592919\pi$
$569$	9.48688	−	5.47725i	0.397711	−	0.229618i	0.685496	+	0.728077i	$0.259586\pi$
$570$	−1.94110	−	1.12070i	−0.0813038	−	0.0469408i
$571$	12.1074	+	6.99022i	0.506680	+	0.292532i	0.731468	−	0.681876i	$-0.238836\pi$
$571$	12.1074	+	6.99022i	0.506680	+	0.292532i	−0.224788	+	0.974408i	$0.572169\pi$
$572$	−2.74388	−	4.75253i	−0.114727	−	0.198713i
$573$	21.0371			0.878840
$574$	30.1342	+	5.03398i	1.25778	+	0.210114i
$575$	14.8053	−	16.2799i	0.617423	−	0.678918i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	37.3087	+	21.5402i	1.55318	+	0.896731i	0.997880	+	0.0650829i	$0.0207312\pi$
$577$	37.3087	+	21.5402i	1.55318	+	0.896731i	0.555303	+	0.831648i	$0.312602\pi$
$578$	−5.38481	+	9.32676i	−0.223979	+	0.387942i
$579$	−9.38285	+	5.41719i	−0.389938	+	0.225131i
$580$	2.00348			0.0831899
$581$	21.4999	+	17.7129i	0.891966	+	0.734857i
$582$		−	11.5594i		−	0.479154i
$583$	10.1100	+	17.5110i	0.418712	+	0.725231i
$584$	−7.21510	−	4.16564i	−0.298563	−	0.172375i
$585$	2.08525	+	1.20392i	0.0862144	+	0.0497759i
$586$	−2.51791	−	4.36114i	−0.104014	−	0.180157i
$587$			1.59131i			0.0656803i	0.999461	+	0.0328402i	$0.0104552\pi$
$587$			1.59131i			0.0656803i	−0.999461	+	0.0328402i	$0.989545\pi$
$588$	4.59540	+	5.28037i	0.189511	+	0.217759i
$589$			23.3847i			0.963550i
$590$	−6.71667	+	3.87787i	−0.276521	+	0.159649i
$591$	10.2463	+	5.91572i	0.421478	+	0.243340i
$592$	−8.00310	−	4.62059i	−0.328925	−	0.189905i
$593$	−3.60850	+	2.08337i	−0.148183	+	0.0855538i	−0.572259	−	0.820073i	$-0.693933\pi$
$593$	−3.60850	+	2.08337i	−0.148183	+	0.0855538i	0.424075	+	0.905627i	$0.360599\pi$
$594$	1.46217			0.0599937
$595$	3.26998	+	2.69401i	0.134056	+	0.110444i
$596$		−	5.46788i		−	0.223973i
$597$	−12.4254	+	7.17383i	−0.508539	+	0.293605i
$598$	−17.1459	+	5.47720i	−0.701147	+	0.223980i
$599$	17.4240	−	30.1793i	0.711925	−	1.23309i	−0.252208	−	0.967673i	$-0.581157\pi$
$599$	17.4240	−	30.1793i	0.711925	−	1.23309i	0.964133	−	0.265418i	$-0.0855099\pi$
$600$	3.97368	−	2.29421i	0.162225	−	0.0936606i
$601$		−	13.8276i		−	0.564041i	−0.959408	−	0.282020i	$-0.908995\pi$
$601$		−	13.8276i		−	0.564041i	0.959408	−	0.282020i	$-0.0910046\pi$
$602$	−14.6930	−	2.45451i	−0.598844	−	0.100038i
$603$			7.42418i			0.302336i
$604$	8.72726	+	15.1161i	0.355107	+	0.615064i
$605$	−2.84273	+	4.92375i	−0.115573	+	0.200179i
$606$	8.27511	−	14.3329i	0.336153	−	0.582234i
$607$	−31.8009	+	18.3602i	−1.29076	+	0.745219i	−0.978789	−	0.204873i	$-0.934322\pi$
$607$	−31.8009	+	18.3602i	−1.29076	+	0.745219i	−0.311969	+	0.950092i	$0.600989\pi$
$608$	3.49371			0.141689
$609$	2.89571	+	7.73828i	0.117340	+	0.313571i
$610$	−5.90317			−0.239012
$611$	−3.57285	−	6.18836i	−0.144542	−	0.250354i
$612$	−1.24804	+	2.16166i	−0.0504489	+	0.0873800i
$613$	−25.6063	−	14.7838i	−1.03423	−	0.597112i	−0.116036	−	0.993245i	$-0.537019\pi$
$613$	−25.6063	−	14.7838i	−1.03423	−	0.597112i	−0.918193	+	0.396133i	$0.870352\pi$
$614$	8.57151	−	4.94877i	0.345918	−	0.199716i
$615$	−7.40829			−0.298731
$616$	1.35582	+	3.62318i	0.0546274	+	0.145982i
$617$		−	21.0301i		−	0.846639i	−0.905981	−	0.423319i	$-0.860865\pi$
$617$		−	21.0301i		−	0.846639i	0.905981	−	0.423319i	$-0.139135\pi$
$618$	−8.27128	+	4.77542i	−0.332720	+	0.192096i
$619$	−0.785602	+	1.36070i	−0.0315760	+	0.0546912i	−0.881382	−	0.472405i	$-0.843386\pi$
$619$	−0.785602	+	1.36070i	−0.0315760	+	0.0546912i	0.849806	+	0.527096i	$0.176719\pi$
$620$	3.71884	+	2.14707i	0.149352	+	0.0862285i
$621$	1.02035	−	4.68603i	0.0409454	−	0.188044i
$622$			26.0408i			1.04414i
$623$	0.797787	−	4.77567i	0.0319627	−	0.191333i
$624$	−3.75315			−0.150246
$625$	−9.49780	−	16.4507i	−0.379912	−	0.658027i
$626$	6.92894	−	12.0013i	0.276936	−	0.479667i
$627$	2.55420	−	4.42401i	0.102005	−	0.176678i
$628$	−2.89797	−	5.01943i	−0.115642	−	0.200297i
$629$		−	23.0667i		−	0.919729i
$630$	−1.31005	−	1.07930i	−0.0521936	−	0.0430003i
$631$		−	37.7541i		−	1.50297i	−0.659752	−	0.751484i	$-0.729339\pi$
$631$		−	37.7541i		−	1.50297i	0.659752	−	0.751484i	$-0.270661\pi$
$632$	12.2606	−	7.07864i	0.487699	−	0.281573i
$633$	−6.49700	−	3.75105i	−0.258233	−	0.149091i
$634$	−5.09880	+	8.83138i	−0.202499	+	0.350739i
$635$	−6.44474	−	11.1626i	−0.255752	−	0.442975i
$636$	13.8287			0.548343
$637$	−25.7865	+	5.02751i	−1.02170	+	0.199197i
$638$			4.56617i			0.180776i
$639$	−1.71822	−	2.97605i	−0.0679719	−	0.117731i
$640$	0.320775	−	0.555599i	0.0126798	−	0.0219620i
$641$	−20.0875	−	11.5975i	−0.793408	−	0.458074i	0.0477531	−	0.998859i	$-0.484794\pi$
$641$	−20.0875	−	11.5975i	−0.793408	−	0.458074i	−0.841161	+	0.540785i	$0.818127\pi$
$642$	1.75285	+	3.03603i	0.0691796	+	0.119823i
$643$	40.1024			1.58148			0.790742	−	0.612150i	$-0.209695\pi$
$643$	40.1024			1.58148			0.790742	+	0.612150i	$0.209695\pi$
$644$	12.5578	−	1.81680i	0.494848	−	0.0715918i
$645$	3.61219			0.142230
$646$	4.36027	+	7.55222i	0.171553	+	0.297138i
$647$	19.8504	+	11.4606i	0.780400	+	0.450564i	0.836572	−	0.547857i	$-0.184556\pi$
$647$	19.8504	+	11.4606i	0.780400	+	0.450564i	−0.0561717	+	0.998421i	$0.517889\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−8.83815	−	15.3081i	−0.346928	−	0.600896i
$650$			17.2210i			0.675463i
$651$	−2.91790	+	17.4670i	−0.114362	+	0.684585i
$652$	1.13194			0.0443303
$653$	−9.19997	−	15.9348i	−0.360023	−	0.623577i	0.627942	−	0.778261i	$-0.283898\pi$
$653$	−9.19997	−	15.9348i	−0.360023	−	0.623577i	−0.987964	+	0.154683i	$0.950564\pi$
$654$	−7.85601	+	13.6070i	−0.307194	+	0.532076i
$655$	−1.47217	−	0.849955i	−0.0575223	−	0.0332105i
$656$	10.0004	−	5.77374i	0.390450	−	0.225427i
$657$			8.33128i			0.325034i
$658$	1.76543	+	4.71781i	0.0688238	+	0.183919i
$659$		−	31.2706i		−	1.21813i	−0.793120	−	0.609065i	$-0.791545\pi$
$659$		−	31.2706i		−	1.21813i	0.793120	−	0.609065i	$-0.208455\pi$
$660$	−0.469029	−	0.812382i	−0.0182569	−	0.0316219i
$661$	−10.2933	+	17.8285i	−0.400362	+	0.693447i	−0.993769	−	0.111455i	$-0.964449\pi$
$661$	−10.2933	+	17.8285i	−0.400362	+	0.693447i	0.593408	+	0.804902i	$0.297782\pi$
$662$	−4.96632	+	8.60191i	−0.193021	+	0.334323i
$663$	−4.68407	−	8.11305i	−0.181914	−	0.315085i
$664$	10.5288			0.408598
$665$	−5.55403	+	2.07835i	−0.215376	+	0.0805951i
$666$			9.24119i			0.358089i
$667$	14.6338	+	3.18643i	0.566625	+	0.123379i
$668$	−1.29187	−	0.745861i	−0.0499839	−	0.0288582i
$669$	−7.72176	+	13.3745i	−0.298541	+	0.517087i
$670$	4.12487	−	2.38149i	0.159358	−	0.0920051i
$671$		−	13.4540i		−	0.519388i
$672$	2.60959	+	0.435938i	0.100667	+	0.0168167i
$673$	47.3232			1.82418			0.912088	−	0.409993i	$-0.134469\pi$
$673$	47.3232			1.82418			0.912088	+	0.409993i	$0.134469\pi$
$674$	22.3251	−	12.8894i	0.859930	−	0.496481i
$675$	−3.97368	−	2.29421i	−0.152947	−	0.0883040i
$676$	0.543069	−	0.940624i	0.0208873	−	0.0361778i
$677$	0.689148	+	1.19364i	0.0264861	+	0.0458753i	0.878965	−	0.476887i	$-0.158235\pi$
$677$	0.689148	+	1.19364i	0.0264861	+	0.0458753i	−0.852479	+	0.522762i	$0.824902\pi$
$678$	6.33088			0.243136
$679$	−23.6044	−	19.4468i	−0.905853	−	0.746298i
$680$	1.60136			0.0614093
$681$	10.1715	−	5.87255i	0.389775	−	0.225036i
$682$	−4.89344	+	8.47568i	−0.187379	+	0.324551i
$683$	−11.0026	+	19.0571i	−0.421004	+	0.729201i	−0.996038	−	0.0889287i	$-0.971656\pi$
$683$	−11.0026	+	19.0571i	−0.421004	+	0.729201i	0.575034	+	0.818130i	$0.304989\pi$
$684$	−1.74685	−	3.02564i	−0.0667926	−	0.115688i
$685$		−	14.6954i		−	0.561483i
$686$	18.5135	−	0.500486i	0.706849	−	0.0191086i
$687$		−	2.40050i		−	0.0915846i
$688$	−4.87607	+	2.81520i	−0.185899	+	0.107329i
$689$	−25.9506	+	44.9477i	−0.988638	+	1.71237i
$690$	−2.93086	+	0.936255i	−0.111576	+	0.0356426i
$691$	−8.91888	+	5.14932i	−0.339290	+	0.195889i	−0.659958	−	0.751302i	$-0.729426\pi$
$691$	−8.91888	+	5.14932i	−0.339290	+	0.195889i	0.320668	+	0.947192i	$0.396093\pi$
$692$		−	19.7892i		−	0.752274i
$693$	2.45985	−	2.98576i	0.0934421	−	0.113420i
$694$	4.45082			0.168951
$695$	−3.99772	+	2.30808i	−0.151642	+	0.0875506i
$696$	2.70448	+	1.56143i	0.102513	+	0.0591860i
$697$	24.9617	+	14.4117i	0.945493	+	0.545881i
$698$	−19.8574	+	11.4646i	−0.751612	+	0.433943i
$699$		−	23.0258i		−	0.870917i
$700$	2.00026	−	11.9739i	0.0756029	−	0.452570i
$701$		−	43.7655i		−	1.65300i	−0.562936	−	0.826500i	$-0.690328\pi$
$701$		−	43.7655i		−	1.65300i	0.562936	−	0.826500i	$-0.309672\pi$
$702$	1.87658	+	3.25032i	0.0708268	+	0.122676i
$703$	27.9605	+	16.1430i	1.05455	+	0.608845i
$704$	1.26628	+	0.731086i	0.0477247	+	0.0275539i
$705$	−0.610731	−	1.05782i	−0.0230015	−	0.0398397i
$706$		−	2.53382i		−	0.0953615i
$707$	−15.3464	−	41.0104i	−0.577160	−	1.54236i
$708$	−12.0891			−0.454335
$709$	−44.5820	+	25.7394i	−1.67431	+	0.966664i	−0.709132	+	0.705075i	$0.750913\pi$
$709$	−44.5820	+	25.7394i	−1.67431	+	0.966664i	−0.965179	+	0.261589i	$0.915753\pi$
$710$	−1.10233	+	1.90929i	−0.0413696	+	0.0716543i
$711$	−12.2606	−	7.07864i	−0.459807	−	0.265470i
$712$	−0.915023	−	1.58487i	−0.0342920	−	0.0593954i
$713$	23.7484	+	21.5973i	0.889385	+	0.808826i
$714$	2.31451	+	6.18512i	0.0866184	+	0.231472i
$715$	3.52067			0.131666
$716$	11.2078	+	19.4125i	0.418857	+	0.725481i
$717$	21.5493	+	12.4415i	0.804772	+	0.464635i
$718$	−9.78344	−	5.64847i	−0.365115	−	0.210799i
$719$	15.8322	−	9.14071i	0.590440	−	0.340891i	−0.174831	−	0.984598i	$-0.555938\pi$
$719$	15.8322	−	9.14071i	0.590440	−	0.340891i	0.765272	+	0.643708i	$0.222605\pi$
$720$	−0.641551			−0.0239092
$721$	−4.16358	+	24.9238i	−0.155060	+	0.928211i
$722$	6.79401			0.252847
$723$	−6.80434	+	3.92849i	−0.253056	+	0.146102i
$724$	9.85001	−	17.0607i	0.366073	−	0.634057i
$725$	7.16450	−	12.4093i	0.266083	−	0.460869i
$726$	−7.67476	+	4.43103i	−0.284837	+	0.164451i
$727$	38.4180			1.42484			0.712422	−	0.701751i	$-0.247598\pi$
$727$	38.4180			1.42484			0.712422	+	0.701751i	$0.247598\pi$
$728$	−6.31403	+	7.66394i	−0.234014	+	0.284045i
$729$	−1.00000			−0.0370370
$730$	4.62886	−	2.67247i	0.171322	−	0.0989126i
$731$	−12.1710	−	7.02695i	−0.450162	−	0.259901i
$732$	−7.96865	−	4.60070i	−0.294530	−	0.170047i
$733$	2.37885	+	4.12028i	0.0878647	+	0.152186i	0.906608	−	0.421973i	$-0.138662\pi$
$733$	2.37885	+	4.12028i	0.0878647	+	0.152186i	−0.818744	+	0.574159i	$0.805329\pi$
$734$	−18.6113			−0.686955
$735$	−4.40786	+	0.859385i	−0.162586	+	0.0316989i
$736$	3.22667	−	3.54804i	0.118937	−	0.130783i
$737$	5.42771	+	9.40108i	0.199932	+	0.346293i
$738$	−10.0004	−	5.77374i	−0.368120	−	0.212534i
$739$	−12.4961	+	21.6439i	−0.459676	+	0.796182i	−0.998944	−	0.0459523i	$-0.985368\pi$
$739$	−12.4961	+	21.6439i	−0.459676	+	0.796182i	0.539268	+	0.842134i	$0.318701\pi$
$740$	5.13440	−	2.96434i	0.188744	−	0.108971i
$741$	13.1124			0.481696
$742$	23.2644	−	28.2382i	0.854063	−	1.03666i
$743$		−	8.94675i		−	0.328224i	−0.986442	−	0.164112i	$-0.947524\pi$
$743$		−	8.94675i		−	0.328224i	0.986442	−	0.164112i	$-0.0524759\pi$
$744$	3.34669	+	5.79664i	0.122696	+	0.212515i
$745$	3.03795	+	1.75396i	0.111302	+	0.0642602i
$746$	12.2660	+	7.08177i	0.449090	+	0.259282i
$747$	−5.26441	−	9.11823i	−0.192615	−	0.333619i
$748$			3.64969i			0.133446i
$749$	9.14846	+	1.52827i	0.334277	+	0.0558418i
$750$			6.15145i			0.224619i
$751$	1.84512	−	1.06528i	0.0673294	−	0.0388727i	−0.465957	−	0.884807i	$-0.654290\pi$
$751$	1.84512	−	1.06528i	0.0673294	−	0.0388727i	0.533287	+	0.845935i	$0.320957\pi$
$752$	1.64885	+	0.951961i	0.0601272	+	0.0347145i
$753$	−17.4196	−	10.0572i	−0.634807	−	0.366506i
$754$	−10.1503	+	5.86030i	−0.369653	+	0.213419i
$755$	−11.1980			−0.407536
$756$	−0.927261	−	2.47794i	−0.0337242	−	0.0901218i
$757$		−	22.6608i		−	0.823622i	−0.911269	−	0.411811i	$-0.864896\pi$
$757$		−	22.6608i		−	0.823622i	0.911269	−	0.411811i	$-0.135104\pi$
$758$	−25.9029	+	14.9550i	−0.940834	+	0.543191i
$759$	−2.13384	−	6.67979i	−0.0774534	−	0.242461i
$760$	−1.12070	+	1.94110i	−0.0406519	+	0.0704111i
$761$	25.7830	−	14.8858i	0.934634	−	0.539611i	0.0463598	−	0.998925i	$-0.485238\pi$
$761$	25.7830	−	14.8858i	0.934634	−	0.539611i	0.888274	+	0.459314i	$0.151905\pi$
$762$		−	20.0911i		−	0.727825i
$763$	14.5692	+	38.9335i	0.527439	+	1.40949i
$764$		−	21.0371i		−	0.761097i
$765$	−0.800679	−	1.38682i	−0.0289486	−	0.0501405i
$766$	15.3684	−	26.6188i	0.555282	−	0.961776i
$767$	22.6860	−	39.2934i	0.819145	−	1.41880i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−12.3151			−0.444093			−0.222047	−	0.975036i	$-0.571274\pi$
$769$	−12.3151			−0.444093			−0.222047	+	0.975036i	$0.571274\pi$
$770$	−2.44795	−	0.408935i	−0.0882179	−	0.0147370i
$771$	−18.1192			−0.652546
$772$	5.41719	+	9.38285i	0.194969	+	0.337696i
$773$	1.77489	−	3.07420i	0.0638383	−	0.110571i	−0.832340	−	0.554266i	$-0.812999\pi$
$773$	1.77489	−	3.07420i	0.0638383	−	0.110571i	0.896178	+	0.443695i	$0.146332\pi$
$774$	4.87607	+	2.81520i	0.175267	+	0.101190i
$775$	26.5974	−	15.3560i	0.955406	−	0.551604i
$776$	−11.5594			−0.414960
$777$	18.8705	+	15.5467i	0.676976	+	0.557735i
$778$			22.8458i			0.819061i
$779$	−34.9385	+	20.1717i	−1.25180	+	0.722728i
$780$	1.20392	−	2.08525i	0.0431072	−	0.0746638i
$781$	−4.35150	−	2.51234i	−0.155709	−	0.0898985i
$782$	11.6967	+	2.54688i	0.418272	+	0.0910763i
$783$		−	3.12287i		−	0.111602i
$784$	5.28037	−	4.59540i	0.188585	−	0.164121i
$785$	3.71839			0.132715
$786$	−1.32484	−	2.29470i	−0.0472557	−	0.0818492i
$787$	23.6118	−	40.8968i	0.841668	−	1.45781i	−0.0468152	−	0.998904i	$-0.514907\pi$
$787$	23.6118	−	40.8968i	0.841668	−	1.45781i	0.888483	−	0.458909i	$-0.151759\pi$
$788$	5.91572	−	10.2463i	0.210739	−	0.365010i
$789$	1.41683	+	2.45403i	0.0504406	+	0.0873657i
$790$			9.08262i			0.323145i
$791$	10.6506	−	12.9277i	0.378692	−	0.459655i
$792$		−	1.46217i		−	0.0519560i
$793$	29.9076	−	17.2671i	1.06205	−	0.613174i
$794$	−2.75666	−	1.59156i	−0.0978302	−	0.0564823i
$795$	−4.43590	+	7.68321i	−0.157325	+	0.272495i
$796$	7.17383	+	12.4254i	0.254270	+	0.440408i
$797$	−34.7174			−1.22975			−0.614877	−	0.788623i	$-0.710794\pi$
$797$	−34.7174			−1.22975			−0.614877	+	0.788623i	$0.710794\pi$
$798$	−9.11714	−	1.52304i	−0.322743	−	0.0539150i
$799$			4.75233i			0.168125i
$800$	−2.29421	−	3.97368i	−0.0811124	−	0.140491i
$801$	−0.915023	+	1.58487i	−0.0323308	+	0.0559985i
$802$	−7.09790	−	4.09797i	−0.250636	−	0.144705i
$803$	6.09089	+	10.5497i	0.214943	+	0.372292i
$804$	7.42418			0.261831
$805$	−3.01883	+	7.55991i	−0.106400	+	0.266452i
$806$	−25.1213			−0.884859
$807$	5.23236	+	9.06271i	0.184188	+	0.319023i
$808$	−14.3329	−	8.27511i	−0.504230	−	0.291117i
$809$	3.74043	−	6.47861i	0.131506	−	0.227776i	−0.792751	−	0.609546i	$-0.791352\pi$
$809$	3.74043	−	6.47861i	0.131506	−	0.227776i	0.924257	+	0.381770i	$0.124685\pi$
$810$	0.320775	+	0.555599i	0.0112709	+	0.0195218i
$811$		−	33.4013i		−	1.17288i	−0.809994	−	0.586438i	$-0.800530\pi$
$811$		−	33.4013i		−	1.17288i	0.809994	−	0.586438i	$-0.199470\pi$
$812$	7.73828	−	2.89571i	0.271560	−	0.101620i
$813$	−0.550462			−0.0193056
$814$	6.75610	+	11.7019i	0.236801	+	0.410152i
$815$	−0.363099	+	0.628906i	−0.0127188	+	0.0220296i
$816$	2.16166	+	1.24804i	0.0756733	+	0.0436900i
$817$	17.0356	−	9.83549i	0.595999	−	0.344100i
$818$		−	17.0543i		−	0.596288i
$819$	9.79418	+	1.63614i	0.342236	+	0.0571714i
$820$			7.40829i			0.258709i
$821$	−9.50836	−	16.4690i	−0.331844	−	0.574771i	0.651029	−	0.759053i	$-0.274337\pi$
$821$	−9.50836	−	16.4690i	−0.331844	−	0.574771i	−0.982873	+	0.184282i	$0.941004\pi$
$822$	11.4530	−	19.8373i	0.399471	−	0.691904i
$823$	−2.20184	+	3.81370i	−0.0767514	+	0.132937i	−0.901847	−	0.432056i	$-0.857788\pi$
$823$	−2.20184	+	3.81370i	−0.0767514	+	0.132937i	0.825095	+	0.564994i	$0.191121\pi$
$824$	4.77542	+	8.27128i	0.166360	+	0.288144i
$825$	−6.70905			−0.233579
$826$	−20.3378	+	24.6859i	−0.707641	+	0.858932i
$827$			29.6423i			1.03076i	0.856961	+	0.515381i	$0.172350\pi$
$827$			29.6423i			1.03076i	−0.856961	+	0.515381i	$0.827650\pi$
$828$	−4.68603	−	1.02035i	−0.162851	−	0.0354598i
$829$	−40.6106	−	23.4466i	−1.41047	−	0.814333i	−0.415034	−	0.909806i	$-0.636230\pi$
$829$	−40.6106	−	23.4466i	−1.41047	−	0.814333i	−0.995432	+	0.0954730i	$0.969564\pi$
$830$	−3.37739	+	5.84981i	−0.117231	+	0.203050i
$831$	3.89976	−	2.25153i	0.135281	−	0.0781047i
$832$			3.75315i			0.130117i
$833$	16.5238	+	5.67916i	0.572516	+	0.196771i
$834$	−7.19533			−0.249154
$835$	0.828799	−	0.478507i	0.0286818	−	0.0165594i
$836$	−4.42401	−	2.55420i	−0.153007	−	0.0883389i
$837$	3.34669	−	5.79664i	0.115679	−	0.200361i
$838$	−13.2460	−	22.9427i	−0.457576	−	0.792544i
$839$	−44.9952			−1.55341			−0.776703	−	0.629867i	$-0.783110\pi$
$839$	−44.9952			−1.55341			−0.776703	+	0.629867i	$0.783110\pi$
$840$	−1.07930	+	1.31005i	−0.0372394	+	0.0452009i
$841$	−19.2477			−0.663714
$842$	−23.5679	+	13.6070i	−0.812205	+	0.468927i
$843$	−5.98507	+	10.3665i	−0.206137	+	0.357040i
$844$	−3.75105	+	6.49700i	−0.129116	+	0.223636i
$845$	0.348407	+	0.603458i	0.0119856	+	0.0207596i
$846$		−	1.90392i		−	0.0654582i
$847$	−3.86331	+	23.1263i	−0.132745	+	0.794630i
$848$		−	13.8287i		−	0.474879i
$849$	18.5431	−	10.7059i	0.636398	−	0.367425i
$850$	5.72651	−	9.91860i	0.196418	−	0.340205i
$851$	42.2174	−	13.4862i	1.44719	−	0.462302i
$852$	−2.97605	+	1.71822i	−0.101958	+	0.0588654i
$853$		−	48.3358i		−	1.65499i	−0.561476	−	0.827493i	$-0.689766\pi$
$853$		−	48.3358i		−	1.65499i	0.561476	−	0.827493i	$-0.310234\pi$
$854$	−22.8005	+	8.53211i	−0.780218	+	0.291963i
$855$	2.24139			0.0766539
$856$	3.03603	−	1.75285i	0.103769	−	0.0599113i
$857$	−25.5120	−	14.7294i	−0.871474	−	0.503145i	−0.00363592	−	0.999993i	$-0.501157\pi$
$857$	−25.5120	−	14.7294i	−0.871474	−	0.503145i	−0.867838	+	0.496848i	$0.834491\pi$
$858$	4.75253	+	2.74388i	0.162249	+	0.0936744i
$859$	−8.29866	+	4.79123i	−0.283147	+	0.163475i	−0.634847	−	0.772638i	$-0.718937\pi$
$859$	−8.29866	+	4.79123i	−0.283147	+	0.163475i	0.351700	+	0.936113i	$0.385604\pi$
$860$		−	3.61219i		−	0.123175i
$861$	−28.6139	+	10.7075i	−0.975161	+	0.364911i
$862$			9.08858i			0.309558i
$863$	1.00927	+	1.74811i	0.0343560	+	0.0595063i	0.882692	−	0.469952i	$-0.155729\pi$
$863$	1.00927	+	1.74811i	0.0343560	+	0.0595063i	−0.848336	+	0.529458i	$0.822395\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	10.9949	+	6.34790i	0.373837	+	0.215835i
$866$	19.1470	+	33.1636i	0.650642	+	1.12695i
$867$		−	10.7696i		−	0.365755i
$868$	17.4670	+	2.91790i	0.592868	+	0.0990400i
$869$	−20.7004			−0.702213
$870$	−1.73506	+	1.00174i	−0.0588241	+	0.0339621i
$871$	−13.9320	+	24.1310i	−0.472069	+	0.817647i
$872$	13.6070	+	7.85601i	0.460792	+	0.266038i
$873$	5.77972	+	10.0108i	0.195614	+	0.338813i
$874$	−11.2730	+	12.3958i	−0.381316	+	0.419295i
$875$	12.5613	+	10.3488i	0.424649	+	0.349852i
$876$	8.33128			0.281488
$877$	−5.11265	−	8.85537i	−0.172642	−	0.299024i	0.766701	−	0.642005i	$-0.221897\pi$
$877$	−5.11265	−	8.85537i	−0.172642	−	0.299024i	−0.939343	+	0.342980i	$0.888564\pi$
$878$	−8.56977	−	4.94776i	−0.289216	−	0.166979i
$879$	4.36114	+	2.51791i	0.147098	+	0.0849268i
$880$	−0.812382	+	0.469029i	−0.0273854	+	0.0158110i
$881$	11.0718			0.373019			0.186509	−	0.982453i	$-0.440282\pi$
$881$	11.0718			0.373019			0.186509	+	0.982453i	$0.440282\pi$
$882$	−6.61992	−	2.27524i	−0.222904	−	0.0766113i
$883$	9.94740			0.334757			0.167378	−	0.985893i	$-0.446470\pi$
$883$	9.94740			0.334757			0.167378	+	0.985893i	$0.446470\pi$
$884$	−8.11305	+	4.68407i	−0.272871	+	0.157542i
$885$	3.87787	−	6.71667i	0.130353	−	0.225778i
$886$	0.732011	−	1.26788i	0.0245924	−	0.0425953i
$887$	−11.8399	+	6.83578i	−0.397546	+	0.229523i	−0.685424	−	0.728144i	$-0.740383\pi$
$887$	−11.8399	+	6.83578i	−0.397546	+	0.229523i	0.287879	+	0.957667i	$0.407050\pi$
$888$	9.24119			0.310114
$889$	−41.0262	−	33.7999i	−1.37597	−	1.13361i
$890$	1.17407			0.0393548
$891$	−1.26628	+	0.731086i	−0.0424219	+	0.0244923i
$892$	13.3745	+	7.72176i	0.447811	+	0.258544i
$893$	−5.76058	−	3.32587i	−0.192771	−	0.111296i
$894$	2.73394	+	4.73532i	0.0914367	+	0.158373i
$895$	−14.3808			−0.480697
$896$	0.435938	−	2.60959i	0.0145637	−	0.0871803i
$897$	12.1102	−	13.3163i	0.404347	−	0.444620i
$898$	−7.36550	−	12.7574i	−0.245790	−	0.425720i
$899$	18.1021	+	10.4513i	0.603740	+	0.348569i
$900$	−2.29421	+	3.97368i	−0.0764735	+	0.132456i
$901$	29.8930	−	17.2587i	0.995879	−	0.574971i
$902$	−16.8844			−0.562189
$903$	13.9518	−	5.22086i	0.464287	−	0.173739i
$904$		−	6.33088i		−	0.210562i
$905$	6.31928	+	10.9453i	0.210060	+	0.363835i
$906$	−15.1161	−	8.72726i	−0.502198	−	0.289944i
$907$	6.76394	+	3.90516i	0.224593	+	0.129669i	0.608075	−	0.793879i	$-0.291942\pi$
$907$	6.76394	+	3.90516i	0.224593	+	0.129669i	−0.383482	+	0.923548i	$0.625275\pi$
$908$	−5.87255	−	10.1715i	−0.194887	−	0.337555i
$909$			16.5502i			0.548936i
$910$	−2.23269	−	5.96647i	−0.0740131	−	0.197787i
$911$			17.1377i			0.567798i	0.958854	+	0.283899i	$0.0916280\pi$
$911$			17.1377i			0.567798i	−0.958854	+	0.283899i	$0.908372\pi$
$912$	−3.02564	+	1.74685i	−0.100189	+	0.0578441i
$913$	−13.3324	−	7.69748i	−0.441239	−	0.254749i
$914$	−13.3608	−	7.71386i	−0.441936	−	0.255152i
$915$	5.11230	−	2.95159i	0.169007	−	0.0975764i
$916$	−2.40050			−0.0793146
$917$	−6.91460	−	1.15510i	−0.228340	−	0.0381448i
$918$		−	2.49607i		−	0.0823827i
$919$	10.1476	−	5.85873i	0.334739	−	0.193262i	−0.323204	−	0.946329i	$-0.604760\pi$
$919$	10.1476	−	5.85873i	0.334739	−	0.193262i	0.657943	+	0.753068i	$0.271427\pi$
$920$	0.936255	+	2.93086i	0.0308674	+	0.0966276i
$921$	−4.94877	+	8.57151i	−0.163067	+	0.282441i
$922$	−3.88829	+	2.24491i	−0.128054	+	0.0739321i
$923$		−	12.8975i		−	0.424526i
$924$	−2.98576	−	2.45985i	−0.0982243	−	0.0809233i
$925$		−	42.4024i		−	1.39418i
$926$	−15.1705	−	26.2760i	−0.498532	−	0.863483i
$927$	4.77542	−	8.27128i	0.156845	−	0.271664i
$928$	1.56143	−	2.70448i	0.0512566	−	0.0887790i
$929$	23.3818	−	13.4995i	0.767130	−	0.442903i	−0.0647195	−	0.997903i	$-0.520615\pi$
$929$	23.3818	−	13.4995i	0.767130	−	0.442903i	0.831850	+	0.555001i	$0.187282\pi$
$930$	−4.29414			−0.140811
$931$	−18.4481	+	16.0550i	−0.604611	+	0.526180i
$932$	−23.0258			−0.754236
$933$	−13.0204	−	22.5520i	−0.426268	−	0.738318i
$934$	−8.55783	+	14.8226i	−0.280021	+	0.485010i
$935$	−2.02776	−	1.17073i	−0.0663150	−	0.0382870i
$936$	3.25032	−	1.87658i	0.106240	−	0.0613378i
$937$	−30.4938			−0.996190			−0.498095	−	0.867122i	$-0.665967\pi$
$937$	−30.4938			−0.996190			−0.498095	+	0.867122i	$0.665967\pi$
$938$	12.4899	−	15.1602i	0.407810	−	0.494998i
$939$			13.8579i			0.452235i
$940$	−1.05782	+	0.610731i	−0.0345022	+	0.0199199i
$941$	3.43393	−	5.94774i	0.111943	−	0.193891i	−0.804611	−	0.593803i	$-0.797626\pi$
$941$	3.43393	−	5.94774i	0.111943	−	0.193891i	0.916554	+	0.399912i	$0.130959\pi$
$942$	5.01943	+	2.89797i	0.163542	+	0.0944209i
$943$	−11.7825	+	54.1118i	−0.383692	+	1.76212i
$944$			12.0891i			0.393465i
$945$	1.67418	+	0.279676i	0.0544612	+	0.00909787i
$946$	8.23262			0.267666
$947$	−9.11070	−	15.7802i	−0.296058	−	0.512787i	0.679173	−	0.733979i	$-0.262339\pi$
$947$	−9.11070	−	15.7802i	−0.296058	−	0.512787i	−0.975230	+	0.221191i	$0.929005\pi$
$948$	−7.07864	+	12.2606i	−0.229904	+	0.398205i
$949$	−15.6343	+	27.0794i	−0.507510	+	0.879034i
$950$	8.01529	+	13.8829i	0.260050	+	0.450420i
$951$		−	10.1976i		−	0.330680i
$952$	6.18512	−	2.31451i	0.200461	−	0.0750138i
$953$			35.2554i			1.14204i	0.820938	+	0.571018i	$0.193451\pi$
$953$			35.2554i			1.14204i	−0.820938	+	0.571018i	$0.806549\pi$
$954$	−11.9760	+	6.91435i	−0.387737	+	0.223860i
$955$	11.6882	+	6.74820i	0.378222	+	0.218367i
$956$	12.4415	−	21.5493i	0.402386	−	0.696953i
$957$	−2.28309	−	3.95442i	−0.0738017	−	0.127828i
$958$	−19.2153			−0.620819
$959$	−21.2399	−	56.7599i	−0.685873	−	1.83287i
$960$			0.641551i			0.0207060i
$961$	6.90067	+	11.9523i	0.222602	+	0.385559i
$962$	−17.3418	+	30.0368i	−0.559121	+	0.968427i
$963$	−3.03603	−	1.75285i	−0.0978348	−	0.0564849i
$964$	3.92849	+	6.80434i	0.126528	+	0.219153i
$965$	−6.95081			−0.223754
$966$	−9.96701	+	7.85231i	−0.320683	+	0.252644i
$967$	−20.1479			−0.647913			−0.323956	−	0.946072i	$-0.605013\pi$
$967$	−20.1479			−0.647913			−0.323956	+	0.946072i	$0.605013\pi$
$968$	4.43103	+	7.67476i	0.142419	+	0.246676i
$969$	−7.55222	−	4.36027i	−0.242612	−	0.140072i
$970$	3.70798	−	6.42241i	0.119056	−	0.206211i
$971$	−20.4746	−	35.4630i	−0.657061	−	1.13806i	−0.981373	−	0.192113i	$-0.938466\pi$
$971$	−20.4746	−	35.4630i	−0.657061	−	1.13806i	0.324312	−	0.945950i	$-0.394867\pi$
$972$			1.00000i			0.0320750i
$973$	−12.1049	+	14.6929i	−0.388065	+	0.471032i
$974$	−1.48980			−0.0477364
$975$	−8.61050	−	14.9138i	−0.275757	−	0.477625i
$976$	−4.60070	+	7.96865i	−0.147265	+	0.255070i
$977$	−44.2956	−	25.5741i	−1.41714	−	0.818186i	−0.421094	−	0.907017i	$-0.638354\pi$
$977$	−44.2956	−	25.5741i	−1.41714	−	0.818186i	−0.996047	+	0.0888306i	$0.971687\pi$
$978$	−0.980291	+	0.565971i	−0.0313462	+	0.0180978i
$979$			2.67584i			0.0855203i
$980$	0.859385	+	4.40786i	0.0274520	+	0.140804i
$981$		−	15.7120i		−	0.501646i
$982$	−5.14673	−	8.91440i	−0.164239	−	0.284470i
$983$	−8.45720	+	14.6483i	−0.269743	+	0.467208i	−0.968795	−	0.247862i	$-0.920272\pi$
$983$	−8.45720	+	14.6483i	−0.269743	+	0.467208i	0.699052	+	0.715070i	$0.253605\pi$
$984$	−5.77374	+	10.0004i	−0.184060	+	0.318801i
$985$	3.79524	+	6.57354i	0.120926	+	0.209450i
$986$	7.79491			0.248240
$987$	−3.88781	−	3.20302i	−0.123750	−	0.101953i
$988$		−	13.1124i		−	0.417161i
$989$	5.74501	−	26.3842i	0.182681	−	0.838970i
$990$	0.812382	+	0.469029i	0.0258192	+	0.0149067i
$991$	−2.62618	+	4.54868i	−0.0834233	+	0.144493i	−0.904718	−	0.426010i	$-0.859919\pi$
$991$	−2.62618	+	4.54868i	−0.0834233	+	0.144493i	0.821295	+	0.570504i	$0.193252\pi$
$992$	5.79664	−	3.34669i	0.184043	−	0.106258i
$993$		−	9.93263i		−	0.315203i
$994$	−1.49808	+	8.96771i	−0.0475161	+	0.284439i
$995$	−9.20475			−0.291810
$996$	−9.11823	+	5.26441i	−0.288922	+	0.166809i
$997$	−6.38803	−	3.68813i	−0.202311	−	0.116804i	0.395422	−	0.918500i	$-0.370598\pi$
$997$	−6.38803	−	3.68813i	−0.202311	−	0.116804i	−0.597733	+	0.801695i	$0.703932\pi$
$998$	−6.36607	+	11.0264i	−0.201514	+	0.349033i
$999$	−4.62059	−	8.00310i	−0.146189	−	0.253207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.367.3	yes	32
7.5	odd	6	inner	966.2.k.b.229.6	yes	32
23.22	odd	2	inner	966.2.k.b.367.6	yes	32
161.68	even	6	inner	966.2.k.b.229.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.3	✓	32	161.68	even	6	inner
966.2.k.b.229.6	yes	32	7.5	odd	6	inner
966.2.k.b.367.3	yes	32	1.1	even	1	trivial
966.2.k.b.367.6	yes	32	23.22	odd	2	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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.320775 - 0.555599i) q^{5} -1.00000i q^{6} +(-2.04200 - 1.68233i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.320775 - 0.555599i) q^{5} -1.00000i q^{6} +(-2.04200 - 1.68233i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.320775 - 0.555599i) q^{10} +(1.26628 + 0.731086i) q^{11} +(0.866025 - 0.500000i) q^{12} +3.75315i q^{13} +(0.435938 - 2.60959i) q^{14} +0.641551i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.24804 - 2.16166i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.74685 + 3.02564i) q^{19} +0.641551 q^{20} +(0.927261 + 2.47794i) q^{21} +1.46217i q^{22} +(4.68603 + 1.02035i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.29421 - 3.97368i) q^{25} +(-3.25032 + 1.87658i) q^{26} -1.00000i q^{27} +(2.47794 - 0.927261i) q^{28} +3.12287 q^{29} +(-0.555599 + 0.320775i) q^{30} +(5.79664 + 3.34669i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.731086 - 1.26628i) q^{33} +2.49607 q^{34} +(-0.279676 + 1.67418i) q^{35} -1.00000 q^{36} +(8.00310 - 4.62059i) q^{37} +(-1.74685 + 3.02564i) q^{38} +(1.87658 - 3.25032i) q^{39} +(0.320775 + 0.555599i) q^{40} +11.5475i q^{41} +(-1.68233 + 2.04200i) q^{42} -5.63040i q^{43} +(-1.26628 + 0.731086i) q^{44} +(0.320775 - 0.555599i) q^{45} +(1.45936 + 4.56840i) q^{46} +(-1.64885 + 0.951961i) q^{47} +1.00000i q^{48} +(1.33954 + 6.87063i) q^{49} +4.58841 q^{50} +(-2.16166 + 1.24804i) q^{51} +(-3.25032 - 1.87658i) q^{52} +(11.9760 + 6.91435i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.938058i q^{55} +(2.04200 + 1.68233i) q^{56} -3.49371i q^{57} +(1.56143 + 2.70448i) q^{58} +(-10.4694 - 6.04453i) q^{59} +(-0.555599 - 0.320775i) q^{60} +(-4.60070 - 7.96865i) q^{61} +6.69338i q^{62} +(0.435938 - 2.60959i) q^{63} +1.00000 q^{64} +(2.08525 - 1.20392i) q^{65} +(0.731086 - 1.26628i) q^{66} +(6.42953 + 3.71209i) q^{67} +(1.24804 + 2.16166i) q^{68} +(-3.54804 - 3.22667i) q^{69} +(-1.58972 + 0.594885i) q^{70} -3.43645 q^{71} +(-0.500000 - 0.866025i) q^{72} +(7.21510 + 4.16564i) q^{73} +(8.00310 + 4.62059i) q^{74} +(-3.97368 + 2.29421i) q^{75} -3.49371 q^{76} +(-1.35582 - 3.62318i) q^{77} +3.75315 q^{78} +(-12.2606 + 7.07864i) q^{79} +(-0.320775 + 0.555599i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-10.0004 + 5.77374i) q^{82} -10.5288 q^{83} +(-2.60959 - 0.435938i) q^{84} -1.60136 q^{85} +(4.87607 - 2.81520i) q^{86} +(-2.70448 - 1.56143i) q^{87} +(-1.26628 - 0.731086i) q^{88} +(0.915023 + 1.58487i) q^{89} +0.641551 q^{90} +(6.31403 - 7.66394i) q^{91} +(-3.22667 + 3.54804i) q^{92} +(-3.34669 - 5.79664i) q^{93} +(-1.64885 - 0.951961i) q^{94} +(1.12070 - 1.94110i) q^{95} +(-0.866025 + 0.500000i) q^{96} +11.5594 q^{97} +(-5.28037 + 4.59540i) q^{98} +1.46217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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