LMFDB - Embedded newform 966.2.k.a.229.14

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			229.14
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.347206 - 0.601379i) q^{5} +1.00000i q^{6} +(2.64100 - 0.158433i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.347206 - 0.601379i) q^{5} +1.00000i q^{6} +(2.64100 - 0.158433i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.347206 + 0.601379i) q^{10} +(0.872588 - 0.503789i) q^{11} +(-0.866025 - 0.500000i) q^{12} -3.43640i q^{13} +(-1.18329 + 2.36639i) q^{14} -0.694412i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.19587 - 5.53541i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.60220 - 4.50715i) q^{19} -0.694412 q^{20} +(2.20796 - 1.45771i) q^{21} +1.00758i q^{22} +(-2.30073 + 4.20793i) q^{23} +(0.866025 - 0.500000i) q^{24} +(2.25890 + 3.91252i) q^{25} +(2.97601 + 1.71820i) q^{26} -1.00000i q^{27} +(-1.45771 - 2.20796i) q^{28} -2.86176 q^{29} +(0.601379 + 0.347206i) q^{30} +(-6.88110 + 3.97281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.503789 - 0.872588i) q^{33} +6.39174 q^{34} +(0.821694 - 1.64325i) q^{35} -1.00000 q^{36} +(2.39320 + 1.38171i) q^{37} +(2.60220 + 4.50715i) q^{38} +(-1.71820 - 2.97601i) q^{39} +(0.347206 - 0.601379i) q^{40} -5.92565i q^{41} +(0.158433 + 2.64100i) q^{42} -3.64760i q^{43} +(-0.872588 - 0.503789i) q^{44} +(-0.347206 - 0.601379i) q^{45} +(-2.49381 - 4.09645i) q^{46} +(5.01260 + 2.89402i) q^{47} +1.00000i q^{48} +(6.94980 - 0.836846i) q^{49} -4.51779 q^{50} +(-5.53541 - 3.19587i) q^{51} +(-2.97601 + 1.71820i) q^{52} +(3.05978 - 1.76656i) q^{53} +(0.866025 + 0.500000i) q^{54} -0.699674i q^{55} +(2.64100 - 0.158433i) q^{56} -5.20440i q^{57} +(1.43088 - 2.47836i) q^{58} +(-4.86530 + 2.80898i) q^{59} +(-0.601379 + 0.347206i) q^{60} +(5.86533 - 10.1590i) q^{61} -7.94561i q^{62} +(1.18329 - 2.36639i) q^{63} +1.00000 q^{64} +(-2.06658 - 1.19314i) q^{65} +(0.503789 + 0.872588i) q^{66} +(11.8024 - 6.81411i) q^{67} +(-3.19587 + 5.53541i) q^{68} +(0.111472 + 4.79454i) q^{69} +(1.01225 + 1.53323i) q^{70} +10.2071 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.25774 - 1.30351i) q^{73} +(-2.39320 + 1.38171i) q^{74} +(3.91252 + 2.25890i) q^{75} -5.20440 q^{76} +(2.22469 - 1.46875i) q^{77} +3.43640 q^{78} +(7.80205 + 4.50452i) q^{79} +(0.347206 + 0.601379i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.13176 + 2.96282i) q^{82} -8.72376 q^{83} +(-2.36639 - 1.18329i) q^{84} -4.43850 q^{85} +(3.15892 + 1.82380i) q^{86} +(-2.47836 + 1.43088i) q^{87} +(0.872588 - 0.503789i) q^{88} +(-7.07766 + 12.2589i) q^{89} +0.694412 q^{90} +(-0.544441 - 9.07555i) q^{91} +(4.79454 - 0.111472i) q^{92} +(-3.97281 + 6.88110i) q^{93} +(-5.01260 + 2.89402i) q^{94} +(-1.80700 - 3.12982i) q^{95} +(-0.866025 - 0.500000i) q^{96} +10.1563 q^{97} +(-2.75017 + 6.43712i) q^{98} -1.00758i 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} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 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 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	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
$5$	0.347206	−	0.601379i	0.155275	−	0.268945i	−0.777884	−	0.628408i	$-0.783707\pi$
$5$	0.347206	−	0.601379i	0.155275	−	0.268945i	0.933159	+	0.359463i	$0.117040\pi$
$6$			1.00000i			0.408248i
$7$	2.64100	−	0.158433i	0.998205	−	0.0598822i
$7$	2.64100	−	0.158433i	0.998205	−	0.0598822i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.347206	+	0.601379i	0.109796	+	0.190173i
$11$	0.872588	−	0.503789i	0.263095	−	0.151898i	−0.362651	−	0.931925i	$-0.618128\pi$
$11$	0.872588	−	0.503789i	0.263095	−	0.151898i	0.625746	+	0.780027i	$0.284795\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	3.43640i		−	0.953086i	−0.879151	−	0.476543i	$-0.841890\pi$
$13$		−	3.43640i		−	0.953086i	0.879151	−	0.476543i	$-0.158110\pi$
$14$	−1.18329	+	2.36639i	−0.316249	+	0.632445i
$15$		−	0.694412i		−	0.179296i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.19587	−	5.53541i	−0.775112	−	1.34253i	−0.934731	−	0.355355i	$-0.884360\pi$
$17$	−3.19587	−	5.53541i	−0.775112	−	1.34253i	0.159619	−	0.987179i	$-0.448973\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.60220	−	4.50715i	0.596986	−	1.03401i	−0.396277	−	0.918131i	$-0.629698\pi$
$19$	2.60220	−	4.50715i	0.596986	−	1.03401i	0.993263	−	0.115879i	$-0.0369685\pi$
$20$	−0.694412			−0.155275
$21$	2.20796	−	1.45771i	0.481816	−	0.318098i
$22$			1.00758i			0.214816i
$23$	−2.30073	+	4.20793i	−0.479735	+	0.877413i
$23$	−2.30073	+	4.20793i	−0.479735	+	0.877413i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	2.25890	+	3.91252i	0.451779	+	0.782505i
$26$	2.97601	+	1.71820i	0.583644	+	0.336967i
$27$		−	1.00000i		−	0.192450i
$28$	−1.45771	−	2.20796i	−0.275481	−	0.417265i
$29$	−2.86176			−0.531416			−0.265708	−	0.964054i	$-0.585606\pi$
$29$	−2.86176			−0.531416			−0.265708	+	0.964054i	$0.585606\pi$
$30$	0.601379	+	0.347206i	0.109796	+	0.0633909i
$31$	−6.88110	+	3.97281i	−1.23588	+	0.713537i	−0.968250	−	0.249984i	$-0.919575\pi$
$31$	−6.88110	+	3.97281i	−1.23588	+	0.713537i	−0.267632	+	0.963521i	$0.586241\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.503789	−	0.872588i	0.0876984	−	0.151898i
$34$	6.39174			1.09617
$35$	0.821694	−	1.64325i	0.138892	−	0.277760i
$36$	−1.00000			−0.166667
$37$	2.39320	+	1.38171i	0.393439	+	0.227152i	0.683649	−	0.729811i	$-0.260392\pi$
$37$	2.39320	+	1.38171i	0.393439	+	0.227152i	−0.290210	+	0.956963i	$0.593725\pi$
$38$	2.60220	+	4.50715i	0.422133	+	0.731155i
$39$	−1.71820	−	2.97601i	−0.275132	−	0.476543i
$40$	0.347206	−	0.601379i	0.0548981	−	0.0950863i
$41$		−	5.92565i		−	0.925431i	−0.886507	−	0.462716i	$-0.846875\pi$
$41$		−	5.92565i		−	0.925431i	0.886507	−	0.462716i	$-0.153125\pi$
$42$	0.158433	+	2.64100i	0.0244468	+	0.407516i
$43$		−	3.64760i		−	0.556254i	−0.960544	−	0.278127i	$-0.910286\pi$
$43$		−	3.64760i		−	0.556254i	0.960544	−	0.278127i	$-0.0897137\pi$
$44$	−0.872588	−	0.503789i	−0.131548	−	0.0759490i
$45$	−0.347206	−	0.601379i	−0.0517584	−	0.0896482i
$46$	−2.49381	−	4.09645i	−0.367692	−	0.603989i
$47$	5.01260	+	2.89402i	0.731162	+	0.422137i	0.818847	−	0.574012i	$-0.194614\pi$
$47$	5.01260	+	2.89402i	0.731162	+	0.422137i	−0.0876850	+	0.996148i	$0.527947\pi$
$48$			1.00000i			0.144338i
$49$	6.94980	−	0.836846i	0.992828	−	0.119549i
$50$	−4.51779			−0.638912
$51$	−5.53541	−	3.19587i	−0.775112	−	0.447511i
$52$	−2.97601	+	1.71820i	−0.412699	+	0.238272i
$53$	3.05978	−	1.76656i	0.420293	−	0.242656i	−0.274910	−	0.961470i	$-0.588648\pi$
$53$	3.05978	−	1.76656i	0.420293	−	0.242656i	0.695203	+	0.718814i	$0.255315\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		−	0.699674i		−	0.0943440i
$56$	2.64100	−	0.158433i	0.352919	−	0.0211716i
$57$		−	5.20440i		−	0.689340i
$58$	1.43088	−	2.47836i	0.187884	−	0.325424i
$59$	−4.86530	+	2.80898i	−0.633409	+	0.365699i	−0.782071	−	0.623189i	$-0.785837\pi$
$59$	−4.86530	+	2.80898i	−0.633409	+	0.365699i	0.148662	+	0.988888i	$0.452503\pi$
$60$	−0.601379	+	0.347206i	−0.0776376	+	0.0448241i
$61$	5.86533	−	10.1590i	0.750979	−	1.30073i	−0.196370	−	0.980530i	$-0.562915\pi$
$61$	5.86533	−	10.1590i	0.750979	−	1.30073i	0.947349	−	0.320203i	$-0.103751\pi$
$62$		−	7.94561i		−	1.00909i
$63$	1.18329	−	2.36639i	0.149081	−	0.298137i
$64$	1.00000			0.125000
$65$	−2.06658	−	1.19314i	−0.256328	−	0.147991i
$66$	0.503789	+	0.872588i	0.0620121	+	0.107408i
$67$	11.8024	−	6.81411i	1.44189	−	0.832476i	0.443915	−	0.896069i	$-0.353589\pi$
$67$	11.8024	−	6.81411i	1.44189	−	0.832476i	0.997976	+	0.0635928i	$0.0202559\pi$
$68$	−3.19587	+	5.53541i	−0.387556	+	0.671267i
$69$	0.111472	+	4.79454i	0.0134196	+	0.577194i
$70$	1.01225	+	1.53323i	0.120987	+	0.183256i
$71$	10.2071			1.21136			0.605681	−	0.795707i	$-0.292901\pi$
$71$	10.2071			1.21136			0.605681	+	0.795707i	$0.292901\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.25774	−	1.30351i	0.264249	−	0.152564i	−0.362022	−	0.932169i	$-0.617914\pi$
$73$	2.25774	−	1.30351i	0.264249	−	0.152564i	0.626271	+	0.779605i	$0.284580\pi$
$74$	−2.39320	+	1.38171i	−0.278203	+	0.160621i
$75$	3.91252	+	2.25890i	0.451779	+	0.260835i
$76$	−5.20440			−0.596986
$77$	2.22469	−	1.46875i	0.253527	−	0.167380i
$78$	3.43640			0.389096
$79$	7.80205	+	4.50452i	0.877799	+	0.506798i	0.869932	−	0.493171i	$-0.164162\pi$
$79$	7.80205	+	4.50452i	0.877799	+	0.506798i	0.00786702	+	0.999969i	$0.497496\pi$
$80$	0.347206	+	0.601379i	0.0388188	+	0.0672362i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.13176	+	2.96282i	0.566708	+	0.327189i
$83$	−8.72376			−0.957557			−0.478779	−	0.877936i	$-0.658920\pi$
$83$	−8.72376			−0.957557			−0.478779	+	0.877936i	$0.658920\pi$
$84$	−2.36639	−	1.18329i	−0.258195	−	0.129108i
$85$	−4.43850			−0.481423
$86$	3.15892	+	1.82380i	0.340635	+	0.196666i
$87$	−2.47836	+	1.43088i	−0.265708	+	0.153407i
$88$	0.872588	−	0.503789i	0.0930182	−	0.0537041i
$89$	−7.07766	+	12.2589i	−0.750230	+	1.29944i	0.197480	+	0.980307i	$0.436724\pi$
$89$	−7.07766	+	12.2589i	−0.750230	+	1.29944i	−0.947711	+	0.319130i	$0.896609\pi$
$90$	0.694412			0.0731975
$91$	−0.544441	−	9.07555i	−0.0570729	−	0.951376i
$92$	4.79454	−	0.111472i	0.499865	−	0.0116217i
$93$	−3.97281	+	6.88110i	−0.411961	+	0.713537i
$94$	−5.01260	+	2.89402i	−0.517010	+	0.298496i
$95$	−1.80700	−	3.12982i	−0.185394	−	0.321112i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	10.1563			1.03121			0.515606	−	0.856826i	$-0.327567\pi$
$97$	10.1563			1.03121			0.515606	+	0.856826i	$0.327567\pi$
$98$	−2.75017	+	6.43712i	−0.277809	+	0.650248i
$99$		−	1.00758i		−	0.101265i
$100$	2.25890	−	3.91252i	0.225890	−	0.391252i
$101$	−7.63683	+	4.40913i	−0.759893	+	0.438724i	−0.829257	−	0.558867i	$-0.811236\pi$
$101$	−7.63683	+	4.40913i	−0.759893	+	0.438724i	0.0693643	+	0.997591i	$0.477903\pi$
$102$	5.53541	−	3.19587i	0.548087	−	0.316438i
$103$	−1.51523	+	2.62445i	−0.149300	+	0.258595i	−0.930969	−	0.365099i	$-0.881035\pi$
$103$	−1.51523	+	2.62445i	−0.149300	+	0.258595i	0.781669	+	0.623693i	$0.214369\pi$
$104$		−	3.43640i		−	0.336967i
$105$	−0.110018	−	1.83394i	−0.0107367	−	0.178975i
$106$			3.53313i			0.343168i
$107$	−3.57490	−	2.06397i	−0.345599	−	0.199531i	0.317146	−	0.948377i	$-0.397275\pi$
$107$	−3.57490	−	2.06397i	−0.345599	−	0.199531i	−0.662745	+	0.748845i	$0.730609\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−7.01171	+	4.04821i	−0.671600	+	0.387749i	−0.796683	−	0.604398i	$-0.793414\pi$
$109$	−7.01171	+	4.04821i	−0.671600	+	0.387749i	0.125082	+	0.992146i	$0.460080\pi$
$110$	0.605935	+	0.349837i	0.0577737	+	0.0333556i
$111$	2.76342			0.262293
$112$	−1.18329	+	2.36639i	−0.111811	+	0.223603i
$113$			8.66865i			0.815478i	0.913099	+	0.407739i	$0.133683\pi$
$113$			8.66865i			0.815478i	−0.913099	+	0.407739i	$0.866317\pi$
$114$	4.50715	+	2.60220i	0.422133	+	0.243718i
$115$	1.73173	+	2.84463i	0.161485	+	0.265263i
$116$	1.43088	+	2.47836i	0.132854	+	0.230110i
$117$	−2.97601	−	1.71820i	−0.275132	−	0.158848i
$118$		−	5.61797i		−	0.517176i
$119$	−9.31729	−	14.1127i	−0.854115	−	1.29371i
$120$		−	0.694412i		−	0.0633909i
$121$	−4.99239	+	8.64708i	−0.453854	+	0.786098i
$122$	5.86533	+	10.1590i	0.531022	+	0.919757i
$123$	−2.96282	−	5.13176i	−0.267149	−	0.462716i
$124$	6.88110	+	3.97281i	0.617941	+	0.356768i
$125$	6.60927			0.591151
$126$	1.45771	+	2.20796i	0.129863	+	0.196701i
$127$	−3.44624			−0.305804			−0.152902	−	0.988241i	$-0.548862\pi$
$127$	−3.44624			−0.305804			−0.152902	+	0.988241i	$0.548862\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.82380	−	3.15892i	−0.160577	−	0.278127i
$130$	2.06658	−	1.19314i	0.181251	−	0.104645i
$131$	11.1799	+	6.45472i	0.976792	+	0.563951i	0.901300	−	0.433195i	$-0.142614\pi$
$131$	11.1799	+	6.45472i	0.976792	+	0.563951i	0.0754919	+	0.997146i	$0.475947\pi$
$132$	−1.00758			−0.0876984
$133$	6.15834	−	12.3157i	0.533996	−	1.06790i
$134$			13.6282i			1.17730i
$135$	−0.601379	−	0.347206i	−0.0517584	−	0.0298827i
$136$	−3.19587	−	5.53541i	−0.274044	−	0.474657i
$137$	−6.21414	+	3.58774i	−0.530910	+	0.306521i	−0.741387	−	0.671078i	$-0.765832\pi$
$137$	−6.21414	+	3.58774i	−0.530910	+	0.306521i	0.210477	+	0.977599i	$0.432498\pi$
$138$	−4.20793	−	2.30073i	−0.358202	−	0.195851i
$139$		−	11.3167i		−	0.959866i	−0.877305	−	0.479933i	$-0.840661\pi$
$139$		−	11.3167i		−	0.959866i	0.877305	−	0.479933i	$-0.159339\pi$
$140$	−1.83394	+	0.110018i	−0.154997	+	0.00929822i
$141$	5.78805			0.487441
$142$	−5.10356	+	8.83963i	−0.428281	+	0.741805i
$143$	−1.73122	−	2.99856i	−0.144772	−	0.250752i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−0.993621	+	1.72100i	−0.0825157	+	0.142921i
$146$			2.60702i			0.215758i
$147$	5.60028	−	4.19963i	0.461903	−	0.346380i
$148$		−	2.76342i		−	0.227152i
$149$	1.49367	+	0.862369i	0.122366	+	0.0706480i	0.559934	−	0.828537i	$-0.310827\pi$
$149$	1.49367	+	0.862369i	0.122366	+	0.0706480i	−0.437568	+	0.899185i	$0.644160\pi$
$150$	−3.91252	+	2.25890i	−0.319456	+	0.184438i
$151$	9.42401	+	16.3229i	0.766915	+	1.32834i	0.939228	+	0.343293i	$0.111542\pi$
$151$	9.42401	+	16.3229i	0.766915	+	1.32834i	−0.172314	+	0.985042i	$0.555124\pi$
$152$	2.60220	−	4.50715i	0.211066	−	0.365578i
$153$	−6.39174			−0.516741
$154$	0.159634	+	2.66102i	0.0128637	+	0.214431i
$155$			5.51753i			0.443179i
$156$	−1.71820	+	2.97601i	−0.137566	+	0.238272i
$157$	7.15677	+	12.3959i	0.571173	+	0.989300i	0.996446	+	0.0842351i	$0.0268447\pi$
$157$	7.15677	+	12.3959i	0.571173	+	0.989300i	−0.425273	+	0.905065i	$0.639822\pi$
$158$	−7.80205	+	4.50452i	−0.620698	+	0.358360i
$159$	1.76656	−	3.05978i	0.140098	−	0.242656i
$160$	−0.694412			−0.0548981
$161$	−5.40956	+	11.4777i	−0.426333	+	0.904566i
$162$	1.00000			0.0785674
$163$	−7.44069	+	12.8877i	−0.582800	+	1.00944i	0.412346	+	0.911027i	$0.364710\pi$
$163$	−7.44069	+	12.8877i	−0.582800	+	1.00944i	−0.995146	+	0.0984119i	$0.968624\pi$
$164$	−5.13176	+	2.96282i	−0.400723	+	0.231358i
$165$	−0.349837	−	0.605935i	−0.0272348	−	0.0471720i
$166$	4.36188	−	7.55500i	0.338548	−	0.586382i
$167$		−	5.74034i		−	0.444201i	−0.975024	−	0.222101i	$-0.928709\pi$
$167$		−	5.74034i		−	0.444201i	0.975024	−	0.222101i	$-0.0712913\pi$
$168$	2.20796	−	1.45771i	0.170348	−	0.112465i
$169$	1.19114			0.0916261
$170$	2.21925	−	3.84385i	0.170209	−	0.294810i
$171$	−2.60220	−	4.50715i	−0.198995	−	0.344670i
$172$	−3.15892	+	1.82380i	−0.240865	+	0.139064i
$173$	6.82088	+	3.93804i	0.518582	+	0.299403i	0.736354	−	0.676596i	$-0.236546\pi$
$173$	6.82088	+	3.93804i	0.518582	+	0.299403i	−0.217772	+	0.976000i	$0.569879\pi$
$174$		−	2.86176i		−	0.216950i
$175$	6.58563	+	9.97510i	0.497827	+	0.754047i
$176$			1.00758i			0.0759490i
$177$	−2.80898	+	4.86530i	−0.211136	+	0.365699i
$178$	−7.07766	−	12.2589i	−0.530493	−	0.918841i
$179$	3.29381	+	5.70505i	0.246191	+	0.426416i	0.962466	−	0.271403i	$-0.0874876\pi$
$179$	3.29381	+	5.70505i	0.246191	+	0.426416i	−0.716275	+	0.697818i	$0.754154\pi$
$180$	−0.347206	+	0.601379i	−0.0258792	+	0.0448241i
$181$	−8.62120			−0.640808			−0.320404	−	0.947281i	$-0.603819\pi$
$181$	−8.62120			−0.640808			−0.320404	+	0.947281i	$0.603819\pi$
$182$	8.13188	+	4.06628i	0.602775	+	0.301412i
$183$		−	11.7307i		−	0.867155i
$184$	−2.30073	+	4.20793i	−0.169612	+	0.310212i
$185$	1.66186	−	0.959478i	0.122183	−	0.0705422i
$186$	−3.97281	−	6.88110i	−0.291300	−	0.504547i
$187$	−5.57735	−	3.22009i	−0.407856	−	0.235476i
$188$		−	5.78805i		−	0.422137i
$189$	−0.158433	−	2.64100i	−0.0115243	−	0.192105i
$190$	3.61400			0.262187
$191$	−0.265560	−	0.153321i	−0.0192152	−	0.0110939i	0.490362	−	0.871519i	$-0.336865\pi$
$191$	−0.265560	−	0.153321i	−0.0192152	−	0.0110939i	−0.509577	+	0.860425i	$0.670198\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−10.5005	−	18.1873i	−0.755840	−	1.30915i	−0.944956	−	0.327198i	$-0.893896\pi$
$193$	−10.5005	−	18.1873i	−0.755840	−	1.30915i	0.189116	−	0.981955i	$-0.439438\pi$
$194$	−5.07813	+	8.79558i	−0.364589	+	0.631486i
$195$	−2.38628			−0.170885
$196$	−4.19963	−	5.60028i	−0.299974	−	0.400020i
$197$	−16.4674			−1.17325			−0.586626	−	0.809858i	$-0.699544\pi$
$197$	−16.4674			−1.17325			−0.586626	+	0.809858i	$0.699544\pi$
$198$	0.872588	+	0.503789i	0.0620121	+	0.0358027i
$199$	−6.10945	−	10.5819i	−0.433087	−	0.750129i	0.564050	−	0.825740i	$-0.309242\pi$
$199$	−6.10945	−	10.5819i	−0.433087	−	0.750129i	−0.997137	+	0.0756116i	$0.975909\pi$
$200$	2.25890	+	3.91252i	0.159728	+	0.276657i
$201$	6.81411	−	11.8024i	0.480630	−	0.832476i
$202$		−	8.81825i		−	0.620450i
$203$	−7.55792	+	0.453399i	−0.530462	+	0.0318224i
$204$			6.39174i			0.447511i
$205$	−3.56356	−	2.05742i	−0.248890	−	0.143697i
$206$	−1.51523	−	2.62445i	−0.105571	−	0.182854i
$207$	2.49381	+	4.09645i	0.173331	+	0.284723i
$208$	2.97601	+	1.71820i	0.206349	+	0.119136i
$209$		−	5.24384i		−	0.362724i
$210$	1.64325	+	0.821694i	0.113395	+	0.0567023i
$211$	19.7479			1.35950			0.679752	−	0.733442i	$-0.262087\pi$
$211$	19.7479			1.35950			0.679752	+	0.733442i	$0.262087\pi$
$212$	−3.05978	−	1.76656i	−0.210147	−	0.121328i
$213$	8.83963	−	5.10356i	0.605681	−	0.349690i
$214$	3.57490	−	2.06397i	0.244375	−	0.141090i
$215$	−2.19359	−	1.26647i	−0.149602	−	0.0863726i
$216$		−	1.00000i		−	0.0680414i
$217$	−17.5436	+	11.5824i	−1.19094	+	0.786264i
$218$		−	8.09643i		−	0.548359i
$219$	1.30351	−	2.25774i	0.0880829	−	0.152564i
$220$	−0.605935	+	0.349837i	−0.0408522	+	0.0235860i
$221$	−19.0219	+	10.9823i	−1.27955	+	0.738749i
$222$	−1.38171	+	2.39320i	−0.0927344	+	0.160621i
$223$		−	14.4448i		−	0.967297i	−0.875262	−	0.483649i	$-0.839311\pi$
$223$		−	14.4448i		−	0.967297i	0.875262	−	0.483649i	$-0.160689\pi$
$224$	−1.45771	−	2.20796i	−0.0973973	−	0.147525i
$225$	4.51779			0.301186
$226$	−7.50727	−	4.33433i	−0.499376	−	0.288315i
$227$	7.70316	+	13.3423i	0.511277	+	0.885557i	0.999915	+	0.0130703i	$0.00416053\pi$
$227$	7.70316	+	13.3423i	0.511277	+	0.885557i	−0.488638	+	0.872487i	$0.662506\pi$
$228$	−4.50715	+	2.60220i	−0.298493	+	0.172335i
$229$	−11.6395	+	20.1602i	−0.769160	+	1.33222i	0.168860	+	0.985640i	$0.445992\pi$
$229$	−11.6395	+	20.1602i	−0.769160	+	1.33222i	−0.938019	+	0.346583i	$0.887342\pi$
$230$	−3.32938	+	0.0774073i	−0.219533	+	0.00510409i
$231$	1.19226	−	2.38432i	0.0784450	−	0.156877i
$232$	−2.86176			−0.187884
$233$	−13.8681	+	24.0203i	−0.908532	+	1.57362i	−0.0924277	+	0.995719i	$0.529463\pi$
$233$	−13.8681	+	24.0203i	−0.908532	+	1.57362i	−0.816104	+	0.577904i	$0.803871\pi$
$234$	2.97601	−	1.71820i	0.194548	−	0.112322i
$235$	3.48081	−	2.00964i	0.227063	−	0.131095i
$236$	4.86530	+	2.80898i	0.316704	+	0.182849i
$237$	9.00903			0.585199
$238$	16.8806	−	1.01266i	1.09421	−	0.0656413i
$239$	−9.23553			−0.597397			−0.298698	−	0.954348i	$-0.596552\pi$
$239$	−9.23553			−0.597397			−0.298698	+	0.954348i	$0.596552\pi$
$240$	0.601379	+	0.347206i	0.0388188	+	0.0224121i
$241$	−10.1848	−	17.6405i	−0.656058	−	1.13633i	−0.981627	−	0.190808i	$-0.938889\pi$
$241$	−10.1848	−	17.6405i	−0.656058	−	1.13633i	0.325569	−	0.945518i	$-0.394444\pi$
$242$	−4.99239	−	8.64708i	−0.320923	−	0.555855i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−11.7307			−0.750979
$245$	1.90975	−	4.47002i	0.122009	−	0.285579i
$246$	5.92565			0.377806
$247$	−15.4884	−	8.94221i	−0.985501	−	0.568979i
$248$	−6.88110	+	3.97281i	−0.436950	+	0.252273i
$249$	−7.55500	+	4.36188i	−0.478779	+	0.276423i
$250$	−3.30463	+	5.72380i	−0.209003	+	0.362005i
$251$	−0.953956			−0.0602132			−0.0301066	−	0.999547i	$-0.509585\pi$
$251$	−0.953956			−0.0602132			−0.0301066	+	0.999547i	$0.509585\pi$
$252$	−2.64100	+	0.158433i	−0.166368	+	0.00998037i
$253$	0.112316	+	4.83087i	0.00706127	+	0.303714i
$254$	1.72312	−	2.98453i	0.108118	−	0.187266i
$255$	−3.84385	+	2.21925i	−0.240711	+	0.138975i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	19.0256	+	10.9845i	1.18679	+	0.685192i	0.957575	−	0.288185i	$-0.0930518\pi$
$257$	19.0256	+	10.9845i	1.18679	+	0.685192i	0.229212	+	0.973377i	$0.426385\pi$
$258$	3.64760			0.227090
$259$	6.53935	+	3.26994i	0.406335	+	0.203184i
$260$			2.38628i			0.147991i
$261$	−1.43088	+	2.47836i	−0.0885693	+	0.153407i
$262$	−11.1799	+	6.45472i	−0.690696	+	0.398774i
$263$	−12.0696	+	6.96837i	−0.744242	+	0.429688i	−0.823609	−	0.567157i	$-0.808043\pi$
$263$	−12.0696	+	6.96837i	−0.744242	+	0.429688i	0.0793679	+	0.996845i	$0.474710\pi$
$264$	0.503789	−	0.872588i	0.0310061	−	0.0537041i
$265$		−	2.45345i		−	0.150714i
$266$	7.58651	+	11.4911i	0.465158	+	0.704565i
$267$			14.1553i			0.866291i
$268$	−11.8024	−	6.81411i	−0.720945	−	0.416238i
$269$	8.31929	−	4.80315i	0.507236	−	0.292853i	−0.224461	−	0.974483i	$-0.572062\pi$
$269$	8.31929	−	4.80315i	0.507236	−	0.292853i	0.731697	+	0.681630i	$0.238729\pi$
$270$	0.601379	−	0.347206i	0.0365987	−	0.0211303i
$271$	−13.1493	−	7.59173i	−0.798761	−	0.461165i	0.0442768	−	0.999019i	$-0.485902\pi$
$271$	−13.1493	−	7.59173i	−0.798761	−	0.461165i	−0.843038	+	0.537854i	$0.819235\pi$
$272$	6.39174			0.387556
$273$	−5.00927	−	7.58744i	−0.303175	−	0.459213i
$274$		−	7.17547i		−	0.433486i
$275$	3.94217	+	2.27601i	0.237722	+	0.137249i
$276$	4.09645	−	2.49381i	0.246578	−	0.150109i
$277$	−0.135465	−	0.234632i	−0.00813929	−	0.0140977i	0.861927	−	0.507032i	$-0.169258\pi$
$277$	−0.135465	−	0.234632i	−0.00813929	−	0.0140977i	−0.870066	+	0.492935i	$0.835924\pi$
$278$	9.80051	+	5.65833i	0.587796	+	0.339364i
$279$			7.94561i			0.475691i
$280$	0.821694	−	1.64325i	0.0491056	−	0.0982031i
$281$		−	28.3978i		−	1.69407i	−0.531536	−	0.847036i	$-0.678385\pi$
$281$		−	28.3978i		−	1.69407i	0.531536	−	0.847036i	$-0.321615\pi$
$282$	−2.89402	+	5.01260i	−0.172337	+	0.298496i
$283$	1.18894	+	2.05930i	0.0706751	+	0.122413i	0.899197	−	0.437543i	$-0.144151\pi$
$283$	1.18894	+	2.05930i	0.0706751	+	0.122413i	−0.828522	+	0.559956i	$0.810818\pi$
$284$	−5.10356	−	8.83963i	−0.302841	−	0.524535i
$285$	−3.12982	−	1.80700i	−0.185394	−	0.107037i
$286$	3.46244			0.204738
$287$	−0.938821	−	15.6497i	−0.0554168	−	0.923770i
$288$	−1.00000			−0.0589256
$289$	−11.9272	+	20.6584i	−0.701598	+	1.21520i
$290$	−0.993621	−	1.72100i	−0.0583474	−	0.101061i
$291$	8.79558	−	5.07813i	0.515606	−	0.297685i
$292$	−2.25774	−	1.30351i	−0.132124	−	0.0762821i
$293$	−24.0208			−1.40331			−0.701656	−	0.712515i	$-0.747556\pi$
$293$	−24.0208			−1.40331			−0.701656	+	0.712515i	$0.747556\pi$
$294$	0.836846	+	6.94980i	0.0488059	+	0.405320i
$295$			3.90119i			0.227136i
$296$	2.39320	+	1.38171i	0.139102	+	0.0803104i
$297$	−0.503789	−	0.872588i	−0.0292328	−	0.0506327i
$298$	−1.49367	+	0.862369i	−0.0865258	+	0.0499557i
$299$	14.4601	+	7.90624i	0.836251	+	0.457229i
$300$		−	4.51779i		−	0.260835i
$301$	−0.577902	−	9.63333i	−0.0333097	−	0.555256i
$302$	−18.8480			−1.08458
$303$	−4.40913	+	7.63683i	−0.253298	+	0.438724i
$304$	2.60220	+	4.50715i	0.149246	+	0.258503i
$305$	−4.07296	−	7.05457i	−0.233217	−	0.403943i
$306$	3.19587	−	5.53541i	0.182696	−	0.316438i
$307$			7.86777i			0.449038i	0.974470	+	0.224519i	$0.0720810\pi$
$307$			7.86777i			0.449038i	−0.974470	+	0.224519i	$0.927919\pi$
$308$	−2.38432	−	1.19226i	−0.135859	−	0.0679354i
$309$			3.03045i			0.172396i
$310$	−4.77832	−	2.75876i	−0.271390	−	0.156687i
$311$	19.0390	−	10.9922i	1.07960	−	0.623309i	0.148814	−	0.988865i	$-0.452454\pi$
$311$	19.0390	−	10.9922i	1.07960	−	0.623309i	0.930789	+	0.365556i	$0.119121\pi$
$312$	−1.71820	−	2.97601i	−0.0972740	−	0.168483i
$313$	−16.6808	+	28.8920i	−0.942854	+	1.63307i	−0.182863	+	0.983138i	$0.558536\pi$
$313$	−16.6808	+	28.8920i	−0.942854	+	1.63307i	−0.759991	+	0.649933i	$0.774797\pi$
$314$	−14.3135			−0.807760
$315$	−1.01225	−	1.53323i	−0.0570339	−	0.0863879i
$316$		−	9.00903i		−	0.506798i
$317$	−1.60246	+	2.77554i	−0.0900032	+	0.155890i	−0.907512	−	0.420026i	$-0.862021\pi$
$317$	−1.60246	+	2.77554i	−0.0900032	+	0.155890i	0.817509	+	0.575916i	$0.195354\pi$
$318$	1.76656	+	3.05978i	0.0990640	+	0.171584i
$319$	−2.49714	+	1.44172i	−0.139813	+	0.0807210i
$320$	0.347206	−	0.601379i	0.0194094	−	0.0336181i
$321$	−4.12794			−0.230399
$322$	−7.23516	−	10.4236i	−0.403200	−	0.580887i
$323$	−33.2652			−1.85092
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	13.4450	−	7.76247i	0.745794	−	0.430585i
$326$	−7.44069	−	12.8877i	−0.412102	−	0.713781i
$327$	−4.04821	+	7.01171i	−0.223867	+	0.387749i
$328$		−	5.92565i		−	0.327189i
$329$	13.6968	+	6.84896i	0.755129	+	0.377596i
$330$	0.699674			0.0385158
$331$	−3.79293	+	6.56955i	−0.208478	+	0.361095i	−0.951235	−	0.308466i	$-0.900184\pi$
$331$	−3.79293	+	6.56955i	−0.208478	+	0.361095i	0.742757	+	0.669561i	$0.233518\pi$
$332$	4.36188	+	7.55500i	0.239389	+	0.414634i
$333$	2.39320	−	1.38171i	0.131146	−	0.0757174i
$334$	4.97128	+	2.87017i	0.272017	+	0.157049i
$335$		−	9.46360i		−	0.517052i
$336$	0.158433	+	2.64100i	0.00864325	+	0.144079i
$337$			18.4331i			1.00412i	0.864834	+	0.502058i	$0.167424\pi$
$337$			18.4331i			1.00412i	−0.864834	+	0.502058i	$0.832576\pi$
$338$	−0.595570	+	1.03156i	−0.0323947	+	0.0561093i
$339$	4.33433	+	7.50727i	0.235408	+	0.407739i
$340$	2.21925	+	3.84385i	0.120356	+	0.208462i
$341$	−4.00291	+	6.93324i	−0.216770	+	0.375456i
$342$	5.20440			0.281422
$343$	18.2219	−	3.31119i	0.983888	−	0.178788i
$344$		−	3.64760i		−	0.196666i
$345$	2.92203	+	1.59766i	0.157317	+	0.0860149i
$346$	−6.82088	+	3.93804i	−0.366693	+	0.211710i
$347$	−3.63932	−	6.30349i	−0.195369	−	0.338389i	0.751652	−	0.659559i	$-0.229257\pi$
$347$	−3.63932	−	6.30349i	−0.195369	−	0.338389i	−0.947021	+	0.321170i	$0.895924\pi$
$348$	2.47836	+	1.43088i	0.132854	+	0.0767033i
$349$			20.1006i			1.07596i	0.842958	+	0.537979i	$0.180812\pi$
$349$			20.1006i			1.07596i	−0.842958	+	0.537979i	$0.819188\pi$
$350$	−11.9315	+	0.715769i	−0.637766	+	0.0382595i
$351$	−3.43640			−0.183422
$352$	−0.872588	−	0.503789i	−0.0465091	−	0.0268520i
$353$	24.6635	−	14.2395i	1.31271	−	0.757891i	0.330162	−	0.943924i	$-0.392897\pi$
$353$	24.6635	−	14.2395i	1.31271	−	0.757891i	0.982543	+	0.186033i	$0.0595632\pi$
$354$	−2.80898	−	4.86530i	−0.149296	−	0.258588i
$355$	3.54397	−	6.13834i	0.188095	−	0.325789i
$356$	14.1553			0.750230
$357$	−15.1254	−	7.56331i	−0.800519	−	0.400293i
$358$	−6.58763			−0.348167
$359$	18.6232	+	10.7521i	0.982892	+	0.567473i	0.903142	−	0.429342i	$-0.141254\pi$
$359$	18.6232	+	10.7521i	0.982892	+	0.567473i	0.0797503	+	0.996815i	$0.474588\pi$
$360$	−0.347206	−	0.601379i	−0.0182994	−	0.0316954i
$361$	−4.04291	−	7.00252i	−0.212784	−	0.368554i
$362$	4.31060	−	7.46617i	0.226560	−	0.392413i
$363$			9.98479i			0.524065i
$364$	−7.58744	+	5.00927i	−0.397690	+	0.262557i
$365$		−	1.81034i		−	0.0947577i
$366$	10.1590	+	5.86533i	0.531022	+	0.306586i
$367$	14.7720	+	25.5858i	0.771090	+	1.33557i	0.936966	+	0.349420i	$0.113621\pi$
$367$	14.7720	+	25.5858i	0.771090	+	1.33557i	−0.165876	+	0.986147i	$0.553045\pi$
$368$	−2.49381	−	4.09645i	−0.129999	−	0.213542i
$369$	−5.13176	−	2.96282i	−0.267149	−	0.154239i
$370$			1.91896i			0.0997617i
$371$	7.80101	−	5.15028i	0.405008	−	0.267389i
$372$	7.94561			0.411961
$373$	21.9702	+	12.6845i	1.13757	+	0.656778i	0.945828	−	0.324667i	$-0.105252\pi$
$373$	21.9702	+	12.6845i	1.13757	+	0.656778i	0.191745	+	0.981445i	$0.438585\pi$
$374$	5.57735	−	3.22009i	0.288398	−	0.166507i
$375$	5.72380	−	3.30463i	0.295576	−	0.170651i
$376$	5.01260	+	2.89402i	0.258505	+	0.149248i
$377$			9.83417i			0.506485i
$378$	2.36639	+	1.18329i	0.121714	+	0.0608621i
$379$		−	30.6715i		−	1.57549i	−0.616003	−	0.787744i	$-0.711249\pi$
$379$		−	30.6715i		−	1.57549i	0.616003	−	0.787744i	$-0.288751\pi$
$380$	−1.80700	+	3.12982i	−0.0926972	+	0.160556i
$381$	−2.98453	+	1.72312i	−0.152902	+	0.0882781i
$382$	0.265560	−	0.153321i	0.0135872	−	0.00784458i
$383$	1.52237	−	2.63682i	0.0777895	−	0.134735i	−0.824506	−	0.565853i	$-0.808547\pi$
$383$	1.52237	−	2.63682i	0.0777895	−	0.134735i	0.902296	+	0.431117i	$0.141880\pi$
$384$			1.00000i			0.0510310i
$385$	−0.110852	−	1.84784i	−0.00564953	−	0.0941747i
$386$	21.0009			1.06892
$387$	−3.15892	−	1.82380i	−0.160577	−	0.0927091i
$388$	−5.07813	−	8.79558i	−0.257803	−	0.446528i
$389$	18.2141	−	10.5159i	0.923490	−	0.533177i	0.0387431	−	0.999249i	$-0.487665\pi$
$389$	18.2141	−	10.5159i	0.923490	−	0.533177i	0.884747	+	0.466072i	$0.154331\pi$
$390$	1.19314	−	2.06658i	0.0604170	−	0.104645i
$391$	30.6454	−	0.712498i	1.54981	−	0.0360326i
$392$	6.94980	−	0.836846i	0.351018	−	0.0422671i
$393$	12.9094			0.651195
$394$	8.23369	−	14.2612i	0.414807	−	0.718467i
$395$	5.41784	−	3.12799i	0.272601	−	0.157386i
$396$	−0.872588	+	0.503789i	−0.0438492	+	0.0253163i
$397$	5.15363	+	2.97545i	0.258653	+	0.149334i	0.623720	−	0.781648i	$-0.285621\pi$
$397$	5.15363	+	2.97545i	0.258653	+	0.149334i	−0.365067	+	0.930981i	$0.618954\pi$
$398$	12.2189			0.612478
$399$	−0.824551	−	13.7448i	−0.0412792	−	0.688103i
$400$	−4.51779			−0.225890
$401$	−26.4645	−	15.2793i	−1.32157	−	0.763010i	−0.337593	−	0.941292i	$-0.609613\pi$
$401$	−26.4645	−	15.2793i	−1.32157	−	0.763010i	−0.983979	+	0.178282i	$0.942946\pi$
$402$	6.81411	+	11.8024i	0.339857	+	0.588650i
$403$	13.6522	+	23.6462i	0.680062	+	1.17790i
$404$	7.63683	+	4.40913i	0.379947	+	0.219362i
$405$	−0.694412			−0.0345056
$406$	3.38631	−	6.77205i	0.168060	−	0.336091i
$407$	2.78436			0.138016
$408$	−5.53541	−	3.19587i	−0.274044	−	0.158219i
$409$	−30.7466	+	17.7516i	−1.52032	+	0.877758i	−0.520609	+	0.853795i	$0.674295\pi$
$409$	−30.7466	+	17.7516i	−1.52032	+	0.877758i	−0.999713	+	0.0239633i	$0.992372\pi$
$410$	3.56356	−	2.05742i	0.175992	−	0.101609i
$411$	−3.58774	+	6.21414i	−0.176970	+	0.306521i
$412$	3.03045			0.149300
$413$	−12.4042	+	8.18936i	−0.610373	+	0.402972i
$414$	−4.79454	+	0.111472i	−0.235639	+	0.00547854i
$415$	−3.02894	+	5.24628i	−0.148685	+	0.257530i
$416$	−2.97601	+	1.71820i	−0.145911	+	0.0842417i
$417$	−5.65833	−	9.80051i	−0.277089	−	0.479933i
$418$	4.54130	+	2.62192i	0.222122	+	0.128242i
$419$	16.0891			0.786004			0.393002	−	0.919538i	$-0.371437\pi$
$419$	16.0891			0.786004			0.393002	+	0.919538i	$0.371437\pi$
$420$	−1.53323	+	1.01225i	−0.0748141	+	0.0493928i
$421$			36.0019i			1.75462i	0.479922	+	0.877311i	$0.340665\pi$
$421$			36.0019i			1.75462i	−0.479922	+	0.877311i	$0.659335\pi$
$422$	−9.87397	+	17.1022i	−0.480657	+	0.832523i
$423$	5.01260	−	2.89402i	0.243721	−	0.140712i
$424$	3.05978	−	1.76656i	0.148596	−	0.0857920i
$425$	14.4383	−	25.0078i	0.700359	−	1.21306i
$426$			10.2071i			0.494537i
$427$	13.8808	−	27.7593i	0.671740	−	1.34337i
$428$			4.12794i			0.199531i
$429$	−2.99856	−	1.73122i	−0.144772	−	0.0835841i
$430$	2.19359	−	1.26647i	0.105784	−	0.0610746i
$431$	25.5379	−	14.7443i	1.23012	−	0.710209i	0.263064	−	0.964778i	$-0.415267\pi$
$431$	25.5379	−	14.7443i	1.23012	−	0.710209i	0.967055	+	0.254569i	$0.0819337\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−35.9883			−1.72949			−0.864743	−	0.502215i	$-0.832519\pi$
$433$	−35.9883			−1.72949			−0.864743	+	0.502215i	$0.832519\pi$
$434$	−1.25885	−	20.9844i	−0.0604267	−	1.00728i
$435$			1.98724i			0.0952810i
$436$	7.01171	+	4.04821i	0.335800	+	0.193874i
$437$	12.9788	+	21.3196i	0.620859	+	1.01985i
$438$	1.30351	+	2.25774i	0.0622840	+	0.107879i
$439$	−11.1258	−	6.42349i	−0.531006	−	0.306576i	0.210420	−	0.977611i	$-0.432517\pi$
$439$	−11.1258	−	6.42349i	−0.531006	−	0.306576i	−0.741426	+	0.671035i	$0.765850\pi$
$440$		−	0.699674i		−	0.0333556i
$441$	2.75017	−	6.43712i	0.130960	−	0.306530i
$442$		−	21.9646i		−	1.04475i
$443$	3.36126	−	5.82188i	0.159698	−	0.276606i	−0.775061	−	0.631886i	$-0.782281\pi$
$443$	3.36126	−	5.82188i	0.159698	−	0.276606i	0.934760	+	0.355280i	$0.115614\pi$
$444$	−1.38171	−	2.39320i	−0.0655732	−	0.113576i
$445$	4.91481	+	8.51271i	0.232984	+	0.403541i
$446$	12.5096	+	7.22242i	0.592346	+	0.341991i
$447$	1.72474			0.0815773
$448$	2.64100	−	0.158433i	0.124776	−	0.00748528i
$449$	−32.4004			−1.52907			−0.764536	−	0.644581i	$-0.777032\pi$
$449$	−32.4004			−1.52907			−0.764536	+	0.644581i	$0.777032\pi$
$450$	−2.25890	+	3.91252i	−0.106485	+	0.184438i
$451$	−2.98528	−	5.17065i	−0.140571	−	0.243476i
$452$	7.50727	−	4.33433i	0.353112	−	0.203870i
$453$	16.3229	+	9.42401i	0.766915	+	0.442778i
$454$	−15.4063			−0.723054
$455$	−5.64687	−	2.82367i	−0.264730	−	0.132376i
$456$		−	5.20440i		−	0.243718i
$457$	9.43622	+	5.44801i	0.441408	+	0.254847i	0.704195	−	0.710007i	$-0.251308\pi$
$457$	9.43622	+	5.44801i	0.441408	+	0.254847i	−0.262787	+	0.964854i	$0.584642\pi$
$458$	−11.6395	−	20.1602i	−0.543878	−	0.942024i
$459$	−5.53541	+	3.19587i	−0.258371	+	0.149170i
$460$	1.59766	−	2.92203i	0.0744911	−	0.136241i
$461$		−	17.9167i		−	0.834463i	−0.908800	−	0.417232i	$-0.863000\pi$
$461$		−	17.9167i		−	0.834463i	0.908800	−	0.417232i	$-0.137000\pi$
$462$	1.46875	+	2.22469i	0.0683327	+	0.103502i
$463$	−16.4297			−0.763552			−0.381776	−	0.924255i	$-0.624687\pi$
$463$	−16.4297			−0.763552			−0.381776	+	0.924255i	$0.624687\pi$
$464$	1.43088	−	2.47836i	0.0664270	−	0.115055i
$465$	2.75876	+	4.77832i	0.127935	+	0.221589i
$466$	−13.8681	−	24.0203i	−0.642429	−	1.11272i
$467$	14.7664	−	25.5762i	0.683308	−	1.18352i	−0.290657	−	0.956827i	$-0.593874\pi$
$467$	14.7664	−	25.5762i	0.683308	−	1.18352i	0.973965	−	0.226698i	$-0.0727929\pi$
$468$			3.43640i			0.158848i
$469$	30.0906	−	19.8660i	1.38945	−	0.917326i
$470$			4.01929i			0.185396i
$471$	12.3959	+	7.15677i	0.571173	+	0.329767i
$472$	−4.86530	+	2.80898i	−0.223944	+	0.129294i
$473$	−1.83762	−	3.18285i	−0.0844939	−	0.146348i
$474$	−4.50452	+	7.80205i	−0.206899	+	0.358360i
$475$	23.5124			1.07882
$476$	−7.56331	+	15.1254i	−0.346664	+	0.693270i
$477$		−	3.53313i		−	0.161771i
$478$	4.61776	−	7.99820i	0.211212	−	0.365829i
$479$	−1.61672	−	2.80025i	−0.0738699	−	0.127946i	0.826724	−	0.562607i	$-0.190202\pi$
$479$	−1.61672	−	2.80025i	−0.0738699	−	0.127946i	−0.900594	+	0.434661i	$0.856868\pi$
$480$	−0.601379	+	0.347206i	−0.0274490	+	0.0158477i
$481$	4.74812	−	8.22398i	0.216496	−	0.374981i
$482$	20.3695			0.927806
$483$	1.05401	+	12.6447i	0.0479592	+	0.575355i
$484$	9.98479			0.453854
$485$	3.52632	−	6.10776i	0.160122	−	0.277339i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−0.504659	−	0.874096i	−0.0228683	−	0.0396091i	0.854365	−	0.519674i	$-0.173947\pi$
$487$	−0.504659	−	0.874096i	−0.0228683	−	0.0396091i	−0.877233	+	0.480065i	$0.840613\pi$
$488$	5.86533	−	10.1590i	0.265511	−	0.459879i
$489$			14.8814i			0.672960i
$490$	2.91627	+	3.88890i	0.131744	+	0.175683i
$491$	−19.4647			−0.878431			−0.439215	−	0.898382i	$-0.644743\pi$
$491$	−19.4647			−0.878431			−0.439215	+	0.898382i	$0.644743\pi$
$492$	−2.96282	+	5.13176i	−0.133574	+	0.231358i
$493$	9.14582	+	15.8410i	0.411907	+	0.713444i
$494$	15.4884	−	8.94221i	0.696854	−	0.402329i
$495$	−0.605935	−	0.349837i	−0.0272348	−	0.0157240i
$496$		−	7.94561i		−	0.356768i
$497$	26.9570	−	1.61715i	1.20919	−	0.0725391i
$498$		−	8.72376i		−	0.390921i
$499$	−4.66018	+	8.07167i	−0.208618	+	0.361338i	−0.951280	−	0.308330i	$-0.900230\pi$
$499$	−4.66018	+	8.07167i	−0.208618	+	0.361338i	0.742661	+	0.669667i	$0.233563\pi$
$500$	−3.30463	−	5.72380i	−0.147788	−	0.255976i
$501$	−2.87017	−	4.97128i	−0.128230	−	0.222101i
$502$	0.476978	−	0.826151i	0.0212886	−	0.0368729i
$503$	15.2384			0.679445			0.339723	−	0.940526i	$-0.389667\pi$
$503$	15.2384			0.679445			0.339723	+	0.940526i	$0.389667\pi$
$504$	1.18329	−	2.36639i	0.0527081	−	0.105408i
$505$			6.12350i			0.272492i
$506$	−4.23981	−	2.31816i	−0.188483	−	0.103055i
$507$	1.03156	−	0.595570i	0.0458131	−	0.0264502i
$508$	1.72312	+	2.98453i	0.0764511	+	0.132417i
$509$	31.0109	+	17.9041i	1.37453	+	0.793586i	0.991495	−	0.130146i	$-0.0415448\pi$
$509$	31.0109	+	17.9041i	1.37453	+	0.793586i	0.383037	+	0.923733i	$0.374878\pi$
$510$		−	4.43850i		−	0.196540i
$511$	5.75619	−	3.80027i	0.254639	−	0.168114i
$512$	1.00000			0.0441942
$513$	−4.50715	−	2.60220i	−0.198995	−	0.114890i
$514$	−19.0256	+	10.9845i	−0.839185	+	0.484504i
$515$	1.05219	+	1.82245i	0.0463651	+	0.0803067i
$516$	−1.82380	+	3.15892i	−0.0802884	+	0.139064i
$517$	5.83191			0.256487
$518$	−6.10153	+	4.02827i	−0.268086	+	0.176992i
$519$	7.87607			0.345721
$520$	−2.06658	−	1.19314i	−0.0906255	−	0.0523226i
$521$	−8.89012	−	15.3981i	−0.389483	−	0.674605i	0.602897	−	0.797819i	$-0.294013\pi$
$521$	−8.89012	−	15.3981i	−0.389483	−	0.674605i	−0.992380	+	0.123214i	$0.960680\pi$
$522$	−1.43088	−	2.47836i	−0.0626280	−	0.108475i
$523$	16.2822	−	28.2017i	0.711973	−	1.23317i	−0.252142	−	0.967690i	$-0.581135\pi$
$523$	16.2822	−	28.2017i	0.711973	−	1.23317i	0.964115	−	0.265483i	$-0.0855315\pi$
$524$		−	12.9094i		−	0.563951i
$525$	10.6909	+	5.34588i	0.466588	+	0.233313i
$526$		−	13.9367i		−	0.607671i
$527$	43.9822	+	25.3931i	1.91589	+	1.10614i
$528$	0.503789	+	0.872588i	0.0219246	+	0.0379745i
$529$	−12.4133	−	19.3626i	−0.539708	−	0.841852i
$530$	2.12475	+	1.22672i	0.0922932	+	0.0532855i
$531$			5.61797i			0.243799i
$532$	−13.7448	+	0.824551i	−0.595915	+	0.0357488i
$533$	−20.3629			−0.882016
$534$	−12.2589	−	7.07766i	−0.530493	−	0.306280i
$535$	−2.48245	+	1.43325i	−0.107326	+	0.0619646i
$536$	11.8024	−	6.81411i	0.509785	−	0.294325i
$537$	5.70505	+	3.29381i	0.246191	+	0.142139i
$538$			9.60629i			0.414157i
$539$	5.64271	−	4.23145i	0.243049	−	0.182262i
$540$			0.694412i			0.0298827i
$541$	−7.95647	+	13.7810i	−0.342075	+	0.592492i	−0.984818	−	0.173590i	$-0.944463\pi$
$541$	−7.95647	+	13.7810i	−0.342075	+	0.592492i	0.642743	+	0.766082i	$0.277797\pi$
$542$	13.1493	−	7.59173i	0.564809	−	0.326093i
$543$	−7.46617	+	4.31060i	−0.320404	+	0.184985i
$544$	−3.19587	+	5.53541i	−0.137022	+	0.237329i
$545$			5.62226i			0.240831i
$546$	9.07555	−	0.544441i	0.388398	−	0.0232999i
$547$	0.261331			0.0111737			0.00558686	−	0.999984i	$-0.498222\pi$
$547$	0.261331			0.0111737			0.00558686	+	0.999984i	$0.498222\pi$
$548$	6.21414	+	3.58774i	0.265455	+	0.153261i
$549$	−5.86533	−	10.1590i	−0.250326	−	0.433578i
$550$	−3.94217	+	2.27601i	−0.168095	+	0.0970495i
$551$	−7.44688	+	12.8984i	−0.317248	+	0.549489i
$552$	0.111472	+	4.79454i	0.00474455	+	0.204069i
$553$	21.3189	+	10.6603i	0.906572	+	0.453324i
$554$	0.270930			0.0115107
$555$	0.959478	−	1.66186i	0.0407276	−	0.0705422i
$556$	−9.80051	+	5.65833i	−0.415634	+	0.239967i
$557$	31.6441	−	18.2697i	1.34080	−	0.774112i	0.353877	−	0.935292i	$-0.384863\pi$
$557$	31.6441	−	18.2697i	1.34080	−	0.774112i	0.986925	+	0.161180i	$0.0515300\pi$
$558$	−6.88110	−	3.97281i	−0.291300	−	0.168182i
$559$	−12.5346			−0.530159
$560$	1.01225	+	1.53323i	0.0427754	+	0.0647909i
$561$	−6.44017			−0.271904
$562$	24.5932	+	14.1989i	1.03740	+	0.598945i
$563$	−15.5863	−	26.9962i	−0.656882	−	1.13775i	−0.981418	−	0.191880i	$-0.938541\pi$
$563$	−15.5863	−	26.9962i	−0.656882	−	1.13775i	0.324536	−	0.945873i	$-0.394792\pi$
$564$	−2.89402	−	5.01260i	−0.121860	−	0.211068i
$565$	5.21314	+	3.00981i	0.219318	+	0.126624i
$566$	−2.37788			−0.0999497
$567$	−1.45771	−	2.20796i	−0.0612180	−	0.0927256i
$568$	10.2071			0.428281
$569$	−30.2138	−	17.4439i	−1.26663	−	0.731288i	−0.292280	−	0.956333i	$-0.594414\pi$
$569$	−30.2138	−	17.4439i	−1.26663	−	0.731288i	−0.974349	+	0.225044i	$0.927747\pi$
$570$	3.12982	−	1.80700i	0.131094	−	0.0756869i
$571$	−13.3024	+	7.68012i	−0.556687	+	0.321403i	−0.751815	−	0.659375i	$-0.770821\pi$
$571$	−13.3024	+	7.68012i	−0.556687	+	0.321403i	0.195128	+	0.980778i	$0.437488\pi$
$572$	−1.73122	+	2.99856i	−0.0723860	+	0.125376i
$573$	−0.306642			−0.0128102
$574$	14.0224	+	7.01179i	0.585284	+	0.292666i
$575$	−21.6607	+	0.503606i	−0.903314	+	0.0210018i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	35.0453	−	20.2334i	1.45895	−	0.842328i	0.459995	−	0.887922i	$-0.347851\pi$
$577$	35.0453	−	20.2334i	1.45895	−	0.842328i	0.998960	+	0.0455939i	$0.0145180\pi$
$578$	−11.9272	−	20.6584i	−0.496104	−	0.859278i
$579$	−18.1873	−	10.5005i	−0.755840	−	0.436384i
$580$	1.98724			0.0825157
$581$	−23.0395	+	1.38214i	−0.955839	+	0.0573406i
$582$			10.1563i			0.420991i
$583$	1.77995	−	3.08297i	0.0737180	−	0.127683i
$584$	2.25774	−	1.30351i	0.0934261	−	0.0539396i
$585$	−2.06658	+	1.19314i	−0.0854425	+	0.0493303i
$586$	12.0104	−	20.8027i	0.496146	−	0.859350i
$587$			44.0069i			1.81636i	0.418580	+	0.908180i	$0.362528\pi$
$587$			44.0069i			1.81636i	−0.418580	+	0.908180i	$0.637472\pi$
$588$	−6.43712	−	2.75017i	−0.265463	−	0.113415i
$589$			41.3522i			1.70389i
$590$	−3.37853	−	1.95059i	−0.139092	−	0.0803046i
$591$	−14.2612	+	8.23369i	−0.586626	+	0.338689i
$592$	−2.39320	+	1.38171i	−0.0983597	+	0.0567880i
$593$	18.9579	+	10.9453i	0.778507	+	0.449471i	0.835901	−	0.548880i	$-0.184946\pi$
$593$	18.9579	+	10.9453i	0.778507	+	0.449471i	−0.0573940	+	0.998352i	$0.518279\pi$
$594$	1.00758			0.0413414
$595$	−11.7221	+	0.703207i	−0.480559	+	0.0288287i
$596$		−	1.72474i		−	0.0706480i
$597$	−10.5819	−	6.10945i	−0.433087	−	0.250043i
$598$	−14.0771	+	8.56972i	−0.575654	+	0.350442i
$599$	18.3092	+	31.7125i	0.748094	+	1.29574i	0.948735	+	0.316072i	$0.102364\pi$
$599$	18.3092	+	31.7125i	0.748094	+	1.29574i	−0.200642	+	0.979665i	$0.564303\pi$
$600$	3.91252	+	2.25890i	0.159728	+	0.0922190i
$601$			13.3351i			0.543949i	0.962304	+	0.271975i	$0.0876767\pi$
$601$			13.3351i			0.543949i	−0.962304	+	0.271975i	$0.912323\pi$
$602$	8.63166	+	4.31619i	0.351800	+	0.175915i
$603$		−	13.6282i		−	0.554984i
$604$	9.42401	−	16.3229i	0.383457	−	0.664168i
$605$	3.46678	+	6.00464i	0.140945	+	0.244123i
$606$	−4.40913	−	7.63683i	−0.179109	−	0.310225i
$607$	12.3976	+	7.15777i	0.503204	+	0.290525i	0.730036	−	0.683409i	$-0.239503\pi$
$607$	12.3976	+	7.15777i	0.503204	+	0.290525i	−0.226832	+	0.973934i	$0.572837\pi$
$608$	−5.20440			−0.211066
$609$	−6.31865	+	4.17162i	−0.256045	+	0.169042i
$610$	8.14591			0.329818
$611$	9.94503	−	17.2253i	0.402333	−	0.696861i
$612$	3.19587	+	5.53541i	0.129185	+	0.223756i
$613$	−0.466489	+	0.269328i	−0.0188413	+	0.0108780i	−0.509391	−	0.860535i	$-0.670129\pi$
$613$	−0.466489	+	0.269328i	−0.0188413	+	0.0108780i	0.490550	+	0.871413i	$0.336796\pi$
$614$	−6.81369	−	3.93389i	−0.274978	−	0.158759i
$615$	−4.11484			−0.165926
$616$	2.22469	−	1.46875i	0.0896353	−	0.0591778i
$617$			29.8073i			1.20000i	0.800001	+	0.599998i	$0.204832\pi$
$617$			29.8073i			1.20000i	−0.800001	+	0.599998i	$0.795168\pi$
$618$	−2.62445	−	1.51523i	−0.105571	−	0.0609513i
$619$	0.144303	+	0.249939i	0.00580001	+	0.0100459i	0.868911	−	0.494969i	$-0.164820\pi$
$619$	0.144303	+	0.249939i	0.00580001	+	0.0100459i	−0.863111	+	0.505015i	$0.831487\pi$
$620$	4.77832	−	2.75876i	0.191902	−	0.110795i
$621$	4.20793	+	2.30073i	0.168858	+	0.0923251i
$622$			21.9844i			0.881493i
$623$	−16.7499	+	33.4970i	−0.671071	+	1.34203i
$624$	3.43640			0.137566
$625$	−8.99970	+	15.5879i	−0.359988	+	0.623518i
$626$	−16.6808	−	28.8920i	−0.666699	−	1.15476i
$627$	−2.62192	−	4.54130i	−0.104709	−	0.181362i
$628$	7.15677	−	12.3959i	0.285586	−	0.494650i
$629$		−	17.6631i		−	0.704273i
$630$	1.83394	−	0.110018i	0.0730661	−	0.00438323i
$631$		−	9.06755i		−	0.360973i	−0.983577	−	0.180487i	$-0.942233\pi$
$631$		−	9.06755i		−	0.360973i	0.983577	−	0.180487i	$-0.0577673\pi$
$632$	7.80205	+	4.50452i	0.310349	+	0.179180i
$633$	17.1022	−	9.87397i	0.679752	−	0.392455i
$634$	−1.60246	−	2.77554i	−0.0636418	−	0.110231i
$635$	−1.19655	+	2.07249i	−0.0474838	+	0.0822444i
$636$	−3.53313			−0.140098
$637$	−2.87574	−	23.8823i	−0.113941	−	0.946251i
$638$		−	2.88345i		−	0.114157i
$639$	5.10356	−	8.83963i	0.201894	−	0.349690i
$640$	0.347206	+	0.601379i	0.0137245	+	0.0237716i
$641$	−30.8179	+	17.7927i	−1.21723	+	0.702770i	−0.964325	−	0.264720i	$-0.914720\pi$
$641$	−30.8179	+	17.7927i	−1.21723	+	0.702770i	−0.252908	+	0.967490i	$0.581387\pi$
$642$	2.06397	−	3.57490i	0.0814584	−	0.141090i
$643$	35.8046			1.41200			0.705998	−	0.708214i	$-0.250499\pi$
$643$	35.8046			1.41200			0.705998	+	0.708214i	$0.250499\pi$
$644$	12.6447	−	1.05401i	0.498272	−	0.0415339i
$645$	−2.53294			−0.0997344
$646$	16.6326	−	28.8085i	0.654401	−	1.13345i
$647$	21.8874	−	12.6367i	0.860481	−	0.496799i	−0.00369223	−	0.999993i	$-0.501175\pi$
$647$	21.8874	−	12.6367i	0.860481	−	0.496799i	0.864173	+	0.503194i	$0.167842\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.83027	+	4.90217i	−0.111098	+	0.192427i
$650$			15.5249i			0.608939i
$651$	−9.40200	+	18.8024i	−0.368493	+	0.736926i
$652$	14.8814			0.582800
$653$	−1.22127	+	2.11529i	−0.0477918	+	0.0827779i	−0.888932	−	0.458040i	$-0.848552\pi$
$653$	−1.22127	+	2.11529i	−0.0477918	+	0.0827779i	0.841140	+	0.540818i	$0.181885\pi$
$654$	−4.04821	−	7.01171i	−0.158298	−	0.274180i
$655$	7.76345	−	4.48223i	0.303343	−	0.175135i
$656$	5.13176	+	2.96282i	0.200362	+	0.115679i
$657$		−	2.60702i		−	0.101709i
$658$	−12.7798	+	8.43729i	−0.498207	+	0.328920i
$659$		−	49.3984i		−	1.92429i	−0.272539	−	0.962145i	$-0.587863\pi$
$659$		−	49.3984i		−	1.92429i	0.272539	−	0.962145i	$-0.412137\pi$
$660$	−0.349837	+	0.605935i	−0.0136174	+	0.0235860i
$661$	−5.62710	−	9.74643i	−0.218869	−	0.379092i	0.735594	−	0.677423i	$-0.236903\pi$
$661$	−5.62710	−	9.74643i	−0.218869	−	0.379092i	−0.954462	+	0.298331i	$0.903570\pi$
$662$	−3.79293	−	6.56955i	−0.147416	−	0.255333i
$663$	−10.9823	+	19.0219i	−0.426517	+	0.738749i
$664$	−8.72376			−0.338548
$665$	−5.26816	−	7.97957i	−0.204291	−	0.309434i
$666$			2.76342i			0.107081i
$667$	6.58414	−	12.0421i	0.254939	−	0.466271i
$668$	−4.97128	+	2.87017i	−0.192345	+	0.111050i
$669$	−7.22242	−	12.5096i	−0.279235	−	0.483649i
$670$	8.19572	+	4.73180i	0.316628	+	0.182805i
$671$		−	11.8195i		−	0.456289i
$672$	−2.36639	−	1.18329i	−0.0912856	−	0.0456466i
$673$	−15.4129			−0.594122			−0.297061	−	0.954859i	$-0.596006\pi$
$673$	−15.4129			−0.594122			−0.297061	+	0.954859i	$0.596006\pi$
$674$	−15.9636	−	9.21657i	−0.614894	−	0.355009i
$675$	3.91252	−	2.25890i	0.150593	−	0.0869449i
$676$	−0.595570	−	1.03156i	−0.0229065	−	0.0396753i
$677$	0.964781	−	1.67105i	0.0370796	−	0.0642237i	−0.846890	−	0.531768i	$-0.821528\pi$
$677$	0.964781	−	1.67105i	0.0370796	−	0.0642237i	0.883970	+	0.467544i	$0.154861\pi$
$678$	−8.66865			−0.332918
$679$	26.8227	−	1.60909i	1.02936	−	0.0617513i
$680$	−4.43850			−0.170209
$681$	13.3423	+	7.70316i	0.511277	+	0.295186i
$682$	−4.00291	−	6.93324i	−0.153279	−	0.265488i
$683$	−7.37251	−	12.7696i	−0.282101	−	0.488613i	0.689801	−	0.723999i	$-0.257698\pi$
$683$	−7.37251	−	12.7696i	−0.282101	−	0.488613i	−0.971902	+	0.235386i	$0.924365\pi$
$684$	−2.60220	+	4.50715i	−0.0994977	+	0.172335i
$685$			4.98274i			0.190381i
$686$	−6.24335	+	17.4362i	−0.238372	+	0.665717i
$687$			23.2790i			0.888149i
$688$	3.15892	+	1.82380i	0.120433	+	0.0695318i
$689$	−6.07063	−	10.5146i	−0.231273	−	0.400576i
$690$	−2.84463	+	1.73173i	−0.108293	+	0.0659258i
$691$	−25.7188	−	14.8487i	−0.978388	−	0.564872i	−0.0766046	−	0.997062i	$-0.524408\pi$
$691$	−25.7188	−	14.8487i	−0.978388	−	0.564872i	−0.901783	+	0.432189i	$0.857741\pi$
$692$		−	7.87607i		−	0.299403i
$693$	−0.159634	−	2.66102i	−0.00606399	−	0.101084i
$694$	7.27864			0.276293
$695$	−6.80559	−	3.92921i	−0.258151	−	0.149043i
$696$	−2.47836	+	1.43088i	−0.0939419	+	0.0542374i
$697$	−32.8009	+	18.9376i	−1.24242	+	0.717313i
$698$	−17.4076	−	10.0503i	−0.658887	−	0.380409i
$699$			27.7363i			1.04908i
$700$	5.34588	−	10.6909i	0.202055	−	0.404077i
$701$		−	42.8066i		−	1.61678i	−0.588646	−	0.808391i	$-0.700339\pi$
$701$		−	42.8066i		−	1.61678i	0.588646	−	0.808391i	$-0.299661\pi$
$702$	1.71820	−	2.97601i	0.0648493	−	0.112322i
$703$	12.4552	−	7.19099i	0.469755	−	0.271213i
$704$	0.872588	−	0.503789i	0.0328869	−	0.0189873i
$705$	2.00964	−	3.48081i	0.0756876	−	0.131095i
$706$			28.4790i			1.07182i
$707$	−19.4703	+	12.8544i	−0.732258	+	0.483441i
$708$	5.61797			0.211136
$709$	0.830962	+	0.479756i	0.0312074	+	0.0180176i	0.515523	−	0.856876i	$-0.327598\pi$
$709$	0.830962	+	0.479756i	0.0312074	+	0.0180176i	−0.484315	+	0.874894i	$0.660931\pi$
$710$	3.54397	+	6.13834i	0.133003	+	0.230368i
$711$	7.80205	−	4.50452i	0.292600	−	0.168933i
$712$	−7.07766	+	12.2589i	−0.265247	+	0.459420i
$713$	−0.885711	−	38.0955i	−0.0331701	−	1.42669i
$714$	14.1127	−	9.31729i	0.528154	−	0.348691i
$715$	−2.40436			−0.0899180
$716$	3.29381	−	5.70505i	0.123096	−	0.213208i
$717$	−7.99820	+	4.61776i	−0.298698	+	0.172454i
$718$	−18.6232	+	10.7521i	−0.695010	+	0.401264i
$719$	19.9148	+	11.4978i	0.742699	+	0.428797i	0.823050	−	0.567969i	$-0.192271\pi$
$719$	19.9148	+	11.4978i	0.742699	+	0.428797i	−0.0803511	+	0.996767i	$0.525604\pi$
$720$	0.694412			0.0258792
$721$	−3.58592	+	7.17124i	−0.133546	+	0.267071i
$722$	8.08581			0.300923
$723$	−17.6405	−	10.1848i	−0.656058	−	0.378775i
$724$	4.31060	+	7.46617i	0.160202	+	0.277478i
$725$	−6.46442	−	11.1967i	−0.240083	−	0.415835i
$726$	−8.64708	−	4.99239i	−0.320923	−	0.185285i
$727$	−27.0355			−1.00269			−0.501345	−	0.865248i	$-0.667161\pi$
$727$	−27.0355			−1.00269			−0.501345	+	0.865248i	$0.667161\pi$
$728$	−0.544441	−	9.07555i	−0.0201783	−	0.336362i
$729$	−1.00000			−0.0370370
$730$	1.56780	+	0.905172i	0.0580270	+	0.0335019i
$731$	−20.1910	+	11.6573i	−0.746790	+	0.431160i
$732$	−10.1590	+	5.86533i	−0.375489	+	0.216789i
$733$	−3.87805	+	6.71697i	−0.143239	+	0.248097i	−0.928715	−	0.370796i	$-0.879085\pi$
$733$	−3.87805	+	6.71697i	−0.143239	+	0.248097i	0.785476	+	0.618893i	$0.212418\pi$
$734$	−29.5439			−1.09049
$735$	−0.581116	−	4.82602i	−0.0214348	−	0.178011i
$736$	4.79454	−	0.111472i	0.176729	−	0.00410890i
$737$	6.86574	−	11.8918i	0.252903	−	0.438041i
$738$	5.13176	−	2.96282i	0.188903	−	0.109063i
$739$	−5.27624	−	9.13872i	−0.194090	−	0.336173i	0.752512	−	0.658578i	$-0.228842\pi$
$739$	−5.27624	−	9.13872i	−0.194090	−	0.336173i	−0.946602	+	0.322405i	$0.895509\pi$
$740$	−1.66186	−	0.959478i	−0.0610913	−	0.0352711i
$741$	−17.8844			−0.657001
$742$	0.559766	+	9.33101i	0.0205497	+	0.342552i
$743$			6.14468i			0.225426i	0.993628	+	0.112713i	$0.0359541\pi$
$743$			6.14468i			0.225426i	−0.993628	+	0.112713i	$0.964046\pi$
$744$	−3.97281	+	6.88110i	−0.145650	+	0.252273i
$745$	1.03722	−	0.598840i	0.0380008	−	0.0219398i
$746$	−21.9702	+	12.6845i	−0.804386	+	0.464412i
$747$	−4.36188	+	7.55500i	−0.159593	+	0.276423i
$748$			6.44017i			0.235476i
$749$	−9.76832	−	4.88457i	−0.356927	−	0.178478i
$750$			6.60927i			0.241336i
$751$	−1.70564	−	0.984749i	−0.0622395	−	0.0359340i	0.468557	−	0.883433i	$-0.344774\pi$
$751$	−1.70564	−	0.984749i	−0.0622395	−	0.0359340i	−0.530797	+	0.847499i	$0.678107\pi$
$752$	−5.01260	+	2.89402i	−0.182791	+	0.105534i
$753$	−0.826151	+	0.476978i	−0.0301066	+	0.0173821i
$754$	−8.51664	−	4.91708i	−0.310158	−	0.179070i
$755$	13.0883			0.476332
$756$	−2.20796	+	1.45771i	−0.0803027	+	0.0530164i
$757$		−	9.75150i		−	0.354424i	−0.984173	−	0.177212i	$-0.943292\pi$
$757$		−	9.75150i		−	0.354424i	0.984173	−	0.177212i	$-0.0567079\pi$
$758$	26.5623	+	15.3357i	0.964786	+	0.557019i
$759$	2.51270	+	4.12749i	0.0912053	+	0.149819i
$760$	−1.80700	−	3.12982i	−0.0655468	−	0.113530i
$761$	−12.4257	−	7.17399i	−0.450432	−	0.260057i	0.257581	−	0.966257i	$-0.417075\pi$
$761$	−12.4257	−	7.17399i	−0.450432	−	0.260057i	−0.708013	+	0.706200i	$0.750408\pi$
$762$		−	3.44624i		−	0.124844i
$763$	−17.8766	+	11.8022i	−0.647176	+	0.427270i
$764$			0.306642i			0.0110939i
$765$	−2.21925	+	3.84385i	−0.0802372	+	0.138975i
$766$	1.52237	+	2.63682i	0.0550055	+	0.0952722i
$767$	9.65280	+	16.7191i	0.348542	+	0.603693i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−11.4878			−0.414261			−0.207130	−	0.978313i	$-0.566412\pi$
$769$	−11.4878			−0.414261			−0.207130	+	0.978313i	$0.566412\pi$
$770$	1.65570	+	0.827920i	0.0596674	+	0.0298362i
$771$	21.9689			0.791191
$772$	−10.5005	+	18.1873i	−0.377920	+	0.654576i
$773$	10.4851	+	18.1607i	0.377123	+	0.653196i	0.990642	−	0.136483i	$-0.0435800\pi$
$773$	10.4851	+	18.1607i	0.377123	+	0.653196i	−0.613519	+	0.789680i	$0.710247\pi$
$774$	3.15892	−	1.82380i	0.113545	−	0.0655552i
$775$	−31.0874	−	17.9483i	−1.11669	−	0.644722i
$776$	10.1563			0.364589
$777$	7.29821	−	0.437819i	0.261822	−	0.0157067i
$778$			21.0318i			0.754026i
$779$	−26.7078	−	15.4197i	−0.956905	−	0.552469i
$780$	1.19314	+	2.06658i	0.0427213	+	0.0739954i
$781$	8.90661	−	5.14223i	0.318704	−	0.184004i
$782$	−14.7057	+	26.8960i	−0.525874	+	0.961798i
$783$			2.86176i			0.102271i
$784$	−2.75017	+	6.43712i	−0.0982203	+	0.229897i
$785$	9.93950			0.354756
$786$	−6.45472	+	11.1799i	−0.230232	+	0.398774i
$787$	16.1817	+	28.0275i	0.576816	+	0.999074i	0.995842	+	0.0910998i	$0.0290382\pi$
$787$	16.1817	+	28.0275i	0.576816	+	0.999074i	−0.419026	+	0.907974i	$0.637628\pi$
$788$	8.23369	+	14.2612i	0.293313	+	0.508033i
$789$	−6.96837	+	12.0696i	−0.248081	+	0.429688i
$790$			6.25598i			0.222578i
$791$	1.37340	+	22.8939i	0.0488326	+	0.814015i
$792$		−	1.00758i		−	0.0358027i
$793$	−34.9106	−	20.1556i	−1.23971	−	0.715748i
$794$	−5.15363	+	2.97545i	−0.182895	+	0.105595i
$795$	−1.22672	−	2.12475i	−0.0435074	−	0.0753571i
$796$	−6.10945	+	10.5819i	−0.216544	+	0.375064i
$797$	21.6891			0.768269			0.384135	−	0.923277i	$-0.374500\pi$
$797$	21.6891			0.768269			0.384135	+	0.923277i	$0.374500\pi$
$798$	12.3157	+	6.15834i	0.435970	+	0.218003i
$799$		−	36.9957i		−	1.30881i
$800$	2.25890	−	3.91252i	0.0798640	−	0.138329i
$801$	7.07766	+	12.2589i	0.250077	+	0.433146i
$802$	26.4645	−	15.2793i	0.934493	−	0.539530i
$803$	1.31339	−	2.27485i	0.0463484	−	0.0802777i
$804$	−13.6282			−0.480630
$805$	5.02418	+	7.23831i	0.177079	+	0.255117i
$806$	−27.3043			−0.961754
$807$	4.80315	−	8.31929i	0.169079	−	0.292853i
$808$	−7.63683	+	4.40913i	−0.268663	+	0.155113i
$809$	14.7809	+	25.6013i	0.519670	+	0.900094i	0.999739	+	0.0228635i	$0.00727831\pi$
$809$	14.7809	+	25.6013i	0.519670	+	0.900094i	−0.480069	+	0.877231i	$0.659388\pi$
$810$	0.347206	−	0.601379i	0.0121996	−	0.0211303i
$811$		−	42.1095i		−	1.47866i	−0.673342	−	0.739332i	$-0.735142\pi$
$811$		−	42.1095i		−	1.47866i	0.673342	−	0.739332i	$-0.264858\pi$
$812$	4.17162	+	6.31865i	0.146395	+	0.221741i
$813$	−15.1835			−0.532507
$814$	−1.39218	+	2.41133i	−0.0487960	+	0.0845171i
$815$	5.16691	+	8.94935i	0.180989	+	0.313482i
$816$	5.53541	−	3.19587i	0.193778	−	0.111878i
$817$	−16.4403	−	9.49180i	−0.575173	−	0.332076i
$818$		−	35.5031i		−	1.24134i
$819$	−8.13188	−	4.06628i	−0.284151	−	0.142087i
$820$			4.11484i			0.143697i
$821$	−4.02090	+	6.96441i	−0.140330	+	0.243059i	−0.927621	−	0.373523i	$-0.878150\pi$
$821$	−4.02090	+	6.96441i	−0.140330	+	0.243059i	0.787291	+	0.616582i	$0.211483\pi$
$822$	−3.58774	−	6.21414i	−0.125137	−	0.216743i
$823$	15.5077	+	26.8602i	0.540566	+	0.936287i	0.998872	+	0.0474928i	$0.0151231\pi$
$823$	15.5077	+	26.8602i	0.540566	+	0.936287i	−0.458306	+	0.888795i	$0.651544\pi$
$824$	−1.51523	+	2.62445i	−0.0527854	+	0.0914270i
$825$	4.55203			0.158481
$826$	−0.890074	−	14.8371i	−0.0309696	−	0.516248i
$827$			53.3319i			1.85453i	0.374401	+	0.927267i	$0.377848\pi$
$827$			53.3319i			1.85453i	−0.374401	+	0.927267i	$0.622152\pi$
$828$	2.30073	−	4.20793i	0.0799559	−	0.146236i
$829$	7.55260	−	4.36050i	0.262313	−	0.151446i	−0.363076	−	0.931759i	$-0.618274\pi$
$829$	7.55260	−	4.36050i	0.262313	−	0.151446i	0.625389	+	0.780313i	$0.284940\pi$
$830$	−3.02894	−	5.24628i	−0.105136	−	0.182101i
$831$	−0.234632	−	0.135465i	−0.00813929	−	0.00469922i
$832$		−	3.43640i		−	0.119136i
$833$	−26.8429	−	35.7955i	−0.930052	−	1.24024i
$834$	11.3167			0.391864
$835$	−3.45212	−	1.99308i	−0.119466	−	0.0689734i
$836$	−4.54130	+	2.62192i	−0.157064	+	0.0906810i
$837$	3.97281	+	6.88110i	0.137320	+	0.237846i
$838$	−8.04455	+	13.9336i	−0.277894	+	0.481327i
$839$	−17.3777			−0.599944			−0.299972	−	0.953948i	$-0.596977\pi$
$839$	−17.3777			−0.599944			−0.299972	+	0.953948i	$0.596977\pi$
$840$	−0.110018	−	1.83394i	−0.00379598	−	0.0632771i
$841$	−20.8103			−0.717597
$842$	−31.1785	−	18.0009i	−1.07448	−	0.620353i
$843$	−14.1989	−	24.5932i	−0.489036	−	0.847036i
$844$	−9.87397	−	17.1022i	−0.339876	−	0.588683i
$845$	0.413571	−	0.716326i	0.0142273	−	0.0246424i
$846$			5.78805i			0.198997i
$847$	−11.8149	+	23.6279i	−0.405966	+	0.811865i
$848$			3.53313i			0.121328i
$849$	2.05930	+	1.18894i	0.0706751	+	0.0408043i
$850$	14.4383	+	25.0078i	0.495229	+	0.857761i
$851$	−11.3202	+	6.89144i	−0.388053	+	0.236236i
$852$	−8.83963	−	5.10356i	−0.302841	−	0.174845i
$853$			24.1191i			0.825822i	0.910771	+	0.412911i	$0.135488\pi$
$853$			24.1191i			0.825822i	−0.910771	+	0.412911i	$0.864512\pi$
$854$	17.0999	+	25.9008i	0.585146	+	0.886308i
$855$	−3.61400			−0.123596
$856$	−3.57490	−	2.06397i	−0.122188	−	0.0705450i
$857$	13.0736	−	7.54805i	0.446586	−	0.257837i	−0.259801	−	0.965662i	$-0.583657\pi$
$857$	13.0736	−	7.54805i	0.446586	−	0.257837i	0.706387	+	0.707825i	$0.250324\pi$
$858$	2.99856	−	1.73122i	0.102369	−	0.0591029i
$859$	−22.5393	−	13.0131i	−0.769032	−	0.444001i	0.0634969	−	0.997982i	$-0.479775\pi$
$859$	−22.5393	−	13.0131i	−0.769032	−	0.444001i	−0.832529	+	0.553981i	$0.813108\pi$
$860$			2.53294i			0.0863726i
$861$	−8.63787	−	13.0836i	−0.294378	−	0.445888i
$862$			29.4887i			1.00439i
$863$	3.57515	−	6.19233i	0.121699	−	0.210789i	−0.798739	−	0.601678i	$-0.794499\pi$
$863$	3.57515	−	6.19233i	0.121699	−	0.210789i	0.920438	+	0.390889i	$0.127832\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	4.73650	−	2.73462i	0.161046	−	0.0929799i
$866$	17.9941	−	31.1668i	0.611466	−	1.05909i
$867$			23.8543i			0.810135i
$868$	18.8024	+	9.40200i	0.638196	+	0.319125i
$869$	9.07730			0.307926
$870$	−1.72100	−	0.993621i	−0.0583474	−	0.0336869i
$871$	−23.4160	−	40.5577i	−0.793422	−	1.37425i
$872$	−7.01171	+	4.04821i	−0.237447	+	0.137090i
$873$	5.07813	−	8.79558i	0.171869	−	0.297685i
$874$	−24.9527	+	0.580144i	−0.844038	+	0.0196237i
$875$	17.4551	−	1.04713i	0.590090	−	0.0353994i
$876$	−2.60702			−0.0880829
$877$	−12.2462	+	21.2110i	−0.413524	+	0.716245i	−0.995272	−	0.0971238i	$-0.969036\pi$
$877$	−12.2462	+	21.2110i	−0.413524	+	0.716245i	0.581748	+	0.813369i	$0.302369\pi$
$878$	11.1258	−	6.42349i	0.375478	−	0.216782i
$879$	−20.8027	+	12.0104i	−0.701656	+	0.405102i
$880$	0.605935	+	0.349837i	0.0204261	+	0.0117930i
$881$	−29.8450			−1.00550			−0.502752	−	0.864431i	$-0.667679\pi$
$881$	−29.8450			−1.00550			−0.502752	+	0.864431i	$0.667679\pi$
$882$	4.19963	+	5.60028i	0.141409	+	0.188571i
$883$	−4.17779			−0.140594			−0.0702969	−	0.997526i	$-0.522395\pi$
$883$	−4.17779			−0.140594			−0.0702969	+	0.997526i	$0.522395\pi$
$884$	19.0219	+	10.9823i	0.639775	+	0.369374i
$885$	1.95059	+	3.37853i	0.0655685	+	0.113568i
$886$	3.36126	+	5.82188i	0.112924	+	0.195590i
$887$	−6.90434	−	3.98622i	−0.231825	−	0.133844i	0.379589	−	0.925155i	$-0.376066\pi$
$887$	−6.90434	−	3.98622i	−0.231825	−	0.133844i	−0.611414	+	0.791311i	$0.709399\pi$
$888$	2.76342			0.0927344
$889$	−9.10153	+	0.545999i	−0.305255	+	0.0183122i
$890$	−9.82963			−0.329490
$891$	−0.872588	−	0.503789i	−0.0292328	−	0.0168776i
$892$	−12.5096	+	7.22242i	−0.418852	+	0.241824i
$893$	26.0876	−	15.0617i	0.872987	−	0.504019i
$894$	−0.862369	+	1.49367i	−0.0288419	+	0.0499557i
$895$	4.57453			0.152910
$896$	−1.18329	+	2.36639i	−0.0395311	+	0.0790556i
$897$	16.4760	−	0.383062i	0.550116	−	0.0127901i
$898$	16.2002	−	28.0596i	0.540608	−	0.936361i
$899$	19.6921	−	11.3692i	0.656767	−	0.379185i
$900$	−2.25890	−	3.91252i	−0.0752965	−	0.130417i
$901$	−19.5573	−	11.2914i	−0.651549	−	0.376172i
$902$	5.97055			0.198798
$903$	−5.31715	−	8.05376i	−0.176944	−	0.268012i
$904$			8.66865i			0.288315i
$905$	−2.99333	+	5.18460i	−0.0995017	+	0.172342i
$906$	−16.3229	+	9.42401i	−0.542291	+	0.313092i
$907$	16.6110	−	9.59038i	0.551560	−	0.318443i	−0.198191	−	0.980163i	$-0.563507\pi$
$907$	16.6110	−	9.59038i	0.551560	−	0.318443i	0.749751	+	0.661720i	$0.230173\pi$
$908$	7.70316	−	13.3423i	0.255638	−	0.442778i
$909$			8.81825i			0.292483i
$910$	5.26881	−	3.47850i	0.174659	−	0.115311i
$911$		−	24.1810i		−	0.801152i	−0.916264	−	0.400576i	$-0.868810\pi$
$911$		−	24.1810i		−	0.801152i	0.916264	−	0.400576i	$-0.131190\pi$
$912$	4.50715	+	2.60220i	0.149246	+	0.0861675i
$913$	−7.61225	+	4.39493i	−0.251929	+	0.145451i
$914$	−9.43622	+	5.44801i	−0.312123	+	0.180204i
$915$	−7.05457	−	4.07296i	−0.233217	−	0.134648i
$916$	23.2790			0.769160
$917$	30.5488	+	15.2757i	1.00881	+	0.504447i
$918$		−	6.39174i		−	0.210959i
$919$	4.37694	+	2.52703i	0.144382	+	0.0833589i	0.570451	−	0.821332i	$-0.306769\pi$
$919$	4.37694	+	2.52703i	0.144382	+	0.0833589i	−0.426069	+	0.904691i	$0.640102\pi$
$920$	1.73173	+	2.84463i	0.0570934	+	0.0937846i
$921$	3.93389	+	6.81369i	0.129626	+	0.224519i
$922$	15.5163	+	8.95835i	0.511002	+	0.295027i
$923$		−	35.0758i		−	1.15453i
$924$	−2.66102	+	0.159634i	−0.0875410	+	0.00525157i
$925$			12.4846i			0.410490i
$926$	8.21484	−	14.2285i	0.269956	−	0.467578i
$927$	1.51523	+	2.62445i	0.0497665	+	0.0861982i
$928$	1.43088	+	2.47836i	0.0469710	+	0.0813561i
$929$	6.98922	+	4.03523i	0.229309	+	0.132392i	0.610253	−	0.792206i	$-0.291068\pi$
$929$	6.98922	+	4.03523i	0.229309	+	0.132392i	−0.380944	+	0.924598i	$0.624401\pi$
$930$	−5.51753			−0.180927
$931$	14.3130	−	33.5014i	0.469089	−	1.09796i
$932$	27.7363			0.908532
$933$	10.9922	−	19.0390i	0.359868	−	0.623309i
$934$	14.7664	+	25.5762i	0.483172	+	0.836878i
$935$	−3.87298	+	2.23607i	−0.126660	+	0.0731272i
$936$	−2.97601	−	1.71820i	−0.0972740	−	0.0561612i
$937$	−28.8866			−0.943685			−0.471842	−	0.881683i	$-0.656411\pi$
$937$	−28.8866			−0.943685			−0.471842	+	0.881683i	$0.656411\pi$
$938$	2.15917	+	35.9922i	0.0704993	+	1.17519i
$939$			33.3616i			1.08871i
$940$	−3.48081	−	2.00964i	−0.113531	−	0.0655474i
$941$	13.6739	+	23.6839i	0.445756	+	0.772073i	0.998105	−	0.0615409i	$-0.0196015\pi$
$941$	13.6739	+	23.6839i	0.445756	+	0.772073i	−0.552348	+	0.833613i	$0.686268\pi$
$942$	−12.3959	+	7.15677i	−0.403880	+	0.233180i
$943$	24.9347	+	13.6333i	0.811985	+	0.443962i
$944$		−	5.61797i		−	0.182849i
$945$	−1.64325	−	0.821694i	−0.0534550	−	0.0267297i
$946$	3.67524			0.119492
$947$	8.90406	−	15.4223i	0.289343	−	0.501157i	−0.684310	−	0.729191i	$-0.739896\pi$
$947$	8.90406	−	15.4223i	0.289343	−	0.501157i	0.973653	+	0.228034i	$0.0732298\pi$
$948$	−4.50452	−	7.80205i	−0.146300	−	0.253399i
$949$	−4.47938	−	7.75851i	−0.145407	−	0.251852i
$950$	−11.7562	+	20.3623i	−0.381422	+	0.660642i
$951$			3.20492i			0.103927i
$952$	−9.31729	−	14.1127i	−0.301975	−	0.457395i
$953$		−	24.9501i		−	0.808213i	−0.914712	−	0.404106i	$-0.867583\pi$
$953$		−	24.9501i		−	0.808213i	0.914712	−	0.404106i	$-0.132417\pi$
$954$	3.05978	+	1.76656i	0.0990640	+	0.0571947i
$955$	−0.184408	+	0.106468i	−0.00596730	+	0.00344522i
$956$	4.61776	+	7.99820i	0.149349	+	0.258680i
$957$	−1.44172	+	2.49714i	−0.0466043	+	0.0807210i
$958$	3.23344			0.104468
$959$	−15.8432	+	10.4598i	−0.511602	+	0.337763i
$960$		−	0.694412i		−	0.0224121i
$961$	16.0664	−	27.8278i	0.518270	−	0.897670i
$962$	4.74812	+	8.22398i	0.153085	+	0.265152i
$963$	−3.57490	+	2.06397i	−0.115200	+	0.0665105i
$964$	−10.1848	+	17.6405i	−0.328029	+	0.568163i
$965$	−14.5833			−0.469453
$966$	−11.4777	−	5.40956i	−0.369288	−	0.174050i
$967$	−3.97534			−0.127838			−0.0639191	−	0.997955i	$-0.520360\pi$
$967$	−3.97534			−0.127838			−0.0639191	+	0.997955i	$0.520360\pi$
$968$	−4.99239	+	8.64708i	−0.160462	+	0.277928i
$969$	−28.8085	+	16.6326i	−0.925462	+	0.534316i
$970$	3.52632	+	6.10776i	0.113223	+	0.196108i
$971$	−10.3084	+	17.8546i	−0.330811	+	0.572982i	−0.982671	−	0.185358i	$-0.940656\pi$
$971$	−10.3084	+	17.8546i	−0.330811	+	0.572982i	0.651860	+	0.758339i	$0.273989\pi$
$972$			1.00000i			0.0320750i
$973$	−1.79294	−	29.8873i	−0.0574789	−	0.958144i
$974$	1.00932			0.0323407
$975$	7.76247	−	13.4450i	0.248598	−	0.430585i
$976$	5.86533	+	10.1590i	0.187745	+	0.325183i
$977$	28.3384	−	16.3612i	0.906626	−	0.523441i	0.0272818	−	0.999628i	$-0.491315\pi$
$977$	28.3384	−	16.3612i	0.906626	−	0.523441i	0.879344	+	0.476187i	$0.157982\pi$
$978$	−12.8877	−	7.44069i	−0.412102	−	0.237927i
$979$			14.2626i			0.455834i
$980$	−4.82602	+	0.581116i	−0.154162	+	0.0185631i
$981$			8.09643i			0.258499i
$982$	9.73236	−	16.8569i	0.310572	−	0.537927i
$983$	−10.0371	−	17.3847i	−0.320133	−	0.554487i	0.660382	−	0.750930i	$-0.270394\pi$
$983$	−10.0371	−	17.3847i	−0.320133	−	0.554487i	−0.980515	+	0.196443i	$0.937061\pi$
$984$	−2.96282	−	5.13176i	−0.0944514	−	0.163595i
$985$	−5.71757	+	9.90312i	−0.182177	+	0.315540i
$986$	−18.2916			−0.582524
$987$	15.2863	−	0.917020i	0.486567	−	0.0291891i
$988$			17.8844i			0.568979i
$989$	15.3488	+	8.39215i	0.488065	+	0.266855i
$990$	0.605935	−	0.349837i	0.0192579	−	0.0111185i
$991$	12.4101	+	21.4949i	0.394219	+	0.682808i	0.993001	−	0.118104i	$-0.0376817\pi$
$991$	12.4101	+	21.4949i	0.394219	+	0.682808i	−0.598782	+	0.800912i	$0.704348\pi$
$992$	6.88110	+	3.97281i	0.218475	+	0.126137i
$993$			7.58586i			0.240730i
$994$	−12.0780	+	24.1541i	−0.383092	+	0.766120i
$995$	−8.48495			−0.268991
$996$	7.55500	+	4.36188i	0.239389	+	0.138211i
$997$	−13.3802	+	7.72506i	−0.423755	+	0.244655i	−0.696683	−	0.717379i	$-0.745341\pi$
$997$	−13.3802	+	7.72506i	−0.423755	+	0.244655i	0.272927	+	0.962035i	$0.412008\pi$
$998$	−4.66018	−	8.07167i	−0.147515	−	0.255504i
$999$	1.38171	−	2.39320i	0.0437154	−	0.0757174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.14	yes	32
7.3	odd	6	inner	966.2.k.a.367.11	yes	32
23.22	odd	2	inner	966.2.k.a.229.11	✓	32
161.45	even	6	inner	966.2.k.a.367.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.11	✓	32	23.22	odd	2	inner
966.2.k.a.229.14	yes	32	1.1	even	1	trivial
966.2.k.a.367.11	yes	32	7.3	odd	6	inner
966.2.k.a.367.14	yes	32	161.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.347206 - 0.601379i) q^{5} +1.00000i q^{6} +(2.64100 - 0.158433i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.347206 - 0.601379i) q^{5} +1.00000i q^{6} +(2.64100 - 0.158433i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.347206 + 0.601379i) q^{10} +(0.872588 - 0.503789i) q^{11} +(-0.866025 - 0.500000i) q^{12} -3.43640i q^{13} +(-1.18329 + 2.36639i) q^{14} -0.694412i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.19587 - 5.53541i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.60220 - 4.50715i) q^{19} -0.694412 q^{20} +(2.20796 - 1.45771i) q^{21} +1.00758i q^{22} +(-2.30073 + 4.20793i) q^{23} +(0.866025 - 0.500000i) q^{24} +(2.25890 + 3.91252i) q^{25} +(2.97601 + 1.71820i) q^{26} -1.00000i q^{27} +(-1.45771 - 2.20796i) q^{28} -2.86176 q^{29} +(0.601379 + 0.347206i) q^{30} +(-6.88110 + 3.97281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.503789 - 0.872588i) q^{33} +6.39174 q^{34} +(0.821694 - 1.64325i) q^{35} -1.00000 q^{36} +(2.39320 + 1.38171i) q^{37} +(2.60220 + 4.50715i) q^{38} +(-1.71820 - 2.97601i) q^{39} +(0.347206 - 0.601379i) q^{40} -5.92565i q^{41} +(0.158433 + 2.64100i) q^{42} -3.64760i q^{43} +(-0.872588 - 0.503789i) q^{44} +(-0.347206 - 0.601379i) q^{45} +(-2.49381 - 4.09645i) q^{46} +(5.01260 + 2.89402i) q^{47} +1.00000i q^{48} +(6.94980 - 0.836846i) q^{49} -4.51779 q^{50} +(-5.53541 - 3.19587i) q^{51} +(-2.97601 + 1.71820i) q^{52} +(3.05978 - 1.76656i) q^{53} +(0.866025 + 0.500000i) q^{54} -0.699674i q^{55} +(2.64100 - 0.158433i) q^{56} -5.20440i q^{57} +(1.43088 - 2.47836i) q^{58} +(-4.86530 + 2.80898i) q^{59} +(-0.601379 + 0.347206i) q^{60} +(5.86533 - 10.1590i) q^{61} -7.94561i q^{62} +(1.18329 - 2.36639i) q^{63} +1.00000 q^{64} +(-2.06658 - 1.19314i) q^{65} +(0.503789 + 0.872588i) q^{66} +(11.8024 - 6.81411i) q^{67} +(-3.19587 + 5.53541i) q^{68} +(0.111472 + 4.79454i) q^{69} +(1.01225 + 1.53323i) q^{70} +10.2071 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.25774 - 1.30351i) q^{73} +(-2.39320 + 1.38171i) q^{74} +(3.91252 + 2.25890i) q^{75} -5.20440 q^{76} +(2.22469 - 1.46875i) q^{77} +3.43640 q^{78} +(7.80205 + 4.50452i) q^{79} +(0.347206 + 0.601379i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.13176 + 2.96282i) q^{82} -8.72376 q^{83} +(-2.36639 - 1.18329i) q^{84} -4.43850 q^{85} +(3.15892 + 1.82380i) q^{86} +(-2.47836 + 1.43088i) q^{87} +(0.872588 - 0.503789i) q^{88} +(-7.07766 + 12.2589i) q^{89} +0.694412 q^{90} +(-0.544441 - 9.07555i) q^{91} +(4.79454 - 0.111472i) q^{92} +(-3.97281 + 6.88110i) q^{93} +(-5.01260 + 2.89402i) q^{94} +(-1.80700 - 3.12982i) q^{95} +(-0.866025 - 0.500000i) q^{96} +10.1563 q^{97} +(-2.75017 + 6.43712i) q^{98} -1.00758i 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	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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