LMFDB - Embedded newform 966.2.k.a.229.3

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			229.3
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.44868 + 2.50918i) q^{5} -1.00000i q^{6} +(2.53486 - 0.757941i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.44868 + 2.50918i) q^{5} -1.00000i q^{6} +(2.53486 - 0.757941i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.44868 - 2.50918i) q^{10} +(3.09371 - 1.78615i) q^{11} +(0.866025 + 0.500000i) q^{12} -0.427415i q^{13} +(-0.611034 + 2.57423i) q^{14} -2.89735i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.156845 + 0.271664i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.24579 - 5.62187i) q^{19} +2.89735 q^{20} +(-1.81628 + 1.92383i) q^{21} +3.57231i q^{22} +(-3.63453 - 3.12893i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.69733 - 2.93986i) q^{25} +(0.370152 + 0.213708i) q^{26} +1.00000i q^{27} +(-1.92383 - 1.81628i) q^{28} +9.17880 q^{29} +(2.50918 + 1.44868i) q^{30} +(7.49501 - 4.32724i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.78615 + 3.09371i) q^{33} -0.313691 q^{34} +(-1.77038 + 7.45844i) q^{35} -1.00000 q^{36} +(-6.85378 - 3.95703i) q^{37} +(3.24579 + 5.62187i) q^{38} +(0.213708 + 0.370152i) q^{39} +(-1.44868 + 2.50918i) q^{40} +11.7279i q^{41} +(-0.757941 - 2.53486i) q^{42} -0.154289i q^{43} +(-3.09371 - 1.78615i) q^{44} +(1.44868 + 2.50918i) q^{45} +(4.52700 - 1.58313i) q^{46} +(5.27800 + 3.04725i) q^{47} -1.00000i q^{48} +(5.85105 - 3.84255i) q^{49} +3.39466 q^{50} +(-0.271664 - 0.156845i) q^{51} +(-0.370152 + 0.213708i) q^{52} +(0.239685 - 0.138382i) q^{53} +(-0.866025 - 0.500000i) q^{54} +10.3502i q^{55} +(2.53486 - 0.757941i) q^{56} +6.49158i q^{57} +(-4.58940 + 7.94908i) q^{58} +(-11.4404 + 6.60511i) q^{59} +(-2.50918 + 1.44868i) q^{60} +(-6.11830 + 10.5972i) q^{61} +8.65449i q^{62} +(0.611034 - 2.57423i) q^{63} +1.00000 q^{64} +(1.07246 + 0.619187i) q^{65} +(-1.78615 - 3.09371i) q^{66} +(2.18498 - 1.26150i) q^{67} +(0.156845 - 0.271664i) q^{68} +(4.71206 + 0.892472i) q^{69} +(-5.57401 - 5.26242i) q^{70} +11.0265 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.01862 - 1.16545i) q^{73} +(6.85378 - 3.95703i) q^{74} +(2.93986 + 1.69733i) q^{75} -6.49158 q^{76} +(6.48833 - 6.87250i) q^{77} -0.427415 q^{78} +(2.40844 + 1.39051i) q^{79} +(-1.44868 - 2.50918i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.1567 - 5.86396i) q^{82} +8.97419 q^{83} +(2.57423 + 0.611034i) q^{84} -0.908872 q^{85} +(0.133618 + 0.0771443i) q^{86} +(-7.94908 + 4.58940i) q^{87} +(3.09371 - 1.78615i) q^{88} +(2.07047 - 3.58615i) q^{89} -2.89735 q^{90} +(-0.323956 - 1.08344i) q^{91} +(-0.892472 + 4.71206i) q^{92} +(-4.32724 + 7.49501i) q^{93} +(-5.27800 + 3.04725i) q^{94} +(9.40420 + 16.2886i) q^{95} +(0.866025 + 0.500000i) q^{96} +14.5174 q^{97} +(0.402224 + 6.98843i) q^{98} -3.57231i 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
$5$	−1.44868	+	2.50918i	−0.647868	+	1.12214i	0.335763	+	0.941946i	$0.391006\pi$
$5$	−1.44868	+	2.50918i	−0.647868	+	1.12214i	−0.983631	+	0.180194i	$0.942328\pi$
$6$		−	1.00000i		−	0.408248i
$7$	2.53486	−	0.757941i	0.958088	−	0.286475i
$7$	2.53486	−	0.757941i	0.958088	−	0.286475i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.44868	−	2.50918i	−0.458112	−	0.793473i
$11$	3.09371	−	1.78615i	0.932788	−	0.538546i	0.0450960	−	0.998983i	$-0.485641\pi$
$11$	3.09371	−	1.78615i	0.932788	−	0.538546i	0.887692	+	0.460437i	$0.152307\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	0.427415i		−	0.118544i	−0.998242	−	0.0592718i	$-0.981122\pi$
$13$		−	0.427415i		−	0.118544i	0.998242	−	0.0592718i	$-0.0188779\pi$
$14$	−0.611034	+	2.57423i	−0.163306	+	0.687991i
$15$		−	2.89735i		−	0.748094i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.156845	+	0.271664i	0.0380406	+	0.0658882i	0.884419	−	0.466694i	$-0.154555\pi$
$17$	0.156845	+	0.271664i	0.0380406	+	0.0658882i	−0.846378	+	0.532582i	$0.821222\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.24579	−	5.62187i	0.744635	−	1.28975i	−0.205730	−	0.978609i	$-0.565957\pi$
$19$	3.24579	−	5.62187i	0.744635	−	1.28975i	0.950365	−	0.311137i	$-0.100710\pi$
$20$	2.89735			0.647868
$21$	−1.81628	+	1.92383i	−0.396346	+	0.419814i
$22$			3.57231i			0.761618i
$23$	−3.63453	−	3.12893i	−0.757851	−	0.652428i
$23$	−3.63453	−	3.12893i	−0.757851	−	0.652428i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−1.69733	−	2.93986i	−0.339466	−	0.587972i
$26$	0.370152	+	0.213708i	0.0725929	+	0.0419115i
$27$			1.00000i			0.192450i
$28$	−1.92383	−	1.81628i	−0.363569	−	0.343245i
$29$	9.17880			1.70446			0.852230	−	0.523167i	$-0.175249\pi$
$29$	9.17880			1.70446			0.852230	+	0.523167i	$0.175249\pi$
$30$	2.50918	+	1.44868i	0.458112	+	0.264491i
$31$	7.49501	−	4.32724i	1.34614	−	0.777196i	0.358442	−	0.933552i	$-0.383308\pi$
$31$	7.49501	−	4.32724i	1.34614	−	0.777196i	0.987701	+	0.156356i	$0.0499747\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.78615	+	3.09371i	−0.310929	+	0.538546i
$34$	−0.313691			−0.0537975
$35$	−1.77038	+	7.45844i	−0.299249	+	1.26071i
$36$	−1.00000			−0.166667
$37$	−6.85378	−	3.95703i	−1.12675	−	0.650532i	−0.183638	−	0.982994i	$-0.558787\pi$
$37$	−6.85378	−	3.95703i	−1.12675	−	0.650532i	−0.943117	+	0.332462i	$0.892121\pi$
$38$	3.24579	+	5.62187i	0.526537	+	0.911988i
$39$	0.213708	+	0.370152i	0.0342206	+	0.0592718i
$40$	−1.44868	+	2.50918i	−0.229056	+	0.396736i
$41$			11.7279i			1.83159i	0.401642	+	0.915797i	$0.368440\pi$
$41$			11.7279i			1.83159i	−0.401642	+	0.915797i	$0.631560\pi$
$42$	−0.757941	−	2.53486i	−0.116953	−	0.391138i
$43$		−	0.154289i		−	0.0235288i	−0.999931	−	0.0117644i	$-0.996255\pi$
$43$		−	0.154289i		−	0.0235288i	0.999931	−	0.0117644i	$-0.00374481\pi$
$44$	−3.09371	−	1.78615i	−0.466394	−	0.269273i
$45$	1.44868	+	2.50918i	0.215956	+	0.374047i
$46$	4.52700	−	1.58313i	0.667469	−	0.233419i
$47$	5.27800	+	3.04725i	0.769875	+	0.444487i	0.832830	−	0.553529i	$-0.186719\pi$
$47$	5.27800	+	3.04725i	0.769875	+	0.444487i	−0.0629551	+	0.998016i	$0.520052\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.85105	−	3.84255i	0.835864	−	0.548936i
$50$	3.39466			0.480077
$51$	−0.271664	−	0.156845i	−0.0380406	−	0.0219627i
$52$	−0.370152	+	0.213708i	−0.0513309	+	0.0296359i
$53$	0.239685	−	0.138382i	0.0329233	−	0.0190083i	−0.483448	−	0.875373i	$-0.660616\pi$
$53$	0.239685	−	0.138382i	0.0329233	−	0.0190083i	0.516371	+	0.856365i	$0.327282\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$			10.3502i			1.39563i
$56$	2.53486	−	0.757941i	0.338735	−	0.101284i
$57$			6.49158i			0.859831i
$58$	−4.58940	+	7.94908i	−0.602618	+	1.04376i
$59$	−11.4404	+	6.60511i	−1.48941	+	0.859912i	−0.999927	−	0.0121009i	$-0.996148\pi$
$59$	−11.4404	+	6.60511i	−1.48941	+	0.859912i	−0.489484	+	0.872012i	$0.662815\pi$
$60$	−2.50918	+	1.44868i	−0.323934	+	0.187023i
$61$	−6.11830	+	10.5972i	−0.783368	+	1.35683i	0.146602	+	0.989196i	$0.453166\pi$
$61$	−6.11830	+	10.5972i	−0.783368	+	1.35683i	−0.929969	+	0.367637i	$0.880167\pi$
$62$			8.65449i			1.09912i
$63$	0.611034	−	2.57423i	0.0769831	−	0.324322i
$64$	1.00000			0.125000
$65$	1.07246	+	0.619187i	0.133023	+	0.0768006i
$66$	−1.78615	−	3.09371i	−0.219860	−	0.380809i
$67$	2.18498	−	1.26150i	0.266937	−	0.154116i	−0.360558	−	0.932737i	$-0.617414\pi$
$67$	2.18498	−	1.26150i	0.266937	−	0.154116i	0.627495	+	0.778621i	$0.284080\pi$
$68$	0.156845	−	0.271664i	0.0190203	−	0.0329441i
$69$	4.71206	+	0.892472i	0.567265	+	0.107441i
$70$	−5.57401	−	5.26242i	−0.666221	−	0.628979i
$71$	11.0265			1.30860			0.654302	−	0.756234i	$-0.272963\pi$
$71$	11.0265			1.30860			0.654302	+	0.756234i	$0.272963\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.01862	−	1.16545i	0.236262	−	0.136406i	−0.377196	−	0.926134i	$-0.623112\pi$
$73$	2.01862	−	1.16545i	0.236262	−	0.136406i	0.613457	+	0.789728i	$0.289778\pi$
$74$	6.85378	−	3.95703i	0.796736	−	0.459996i
$75$	2.93986	+	1.69733i	0.339466	+	0.195991i
$76$	−6.49158			−0.744635
$77$	6.48833	−	6.87250i	0.739413	−	0.783194i
$78$	−0.427415			−0.0483952
$79$	2.40844	+	1.39051i	0.270971	+	0.156445i	0.629329	−	0.777139i	$-0.283330\pi$
$79$	2.40844	+	1.39051i	0.270971	+	0.156445i	−0.358358	+	0.933584i	$0.616663\pi$
$80$	−1.44868	−	2.50918i	−0.161967	−	0.280535i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.1567	−	5.86396i	−1.12162	−	0.647566i
$83$	8.97419			0.985045			0.492523	−	0.870300i	$-0.336075\pi$
$83$	8.97419			0.985045			0.492523	+	0.870300i	$0.336075\pi$
$84$	2.57423	+	0.611034i	0.280871	+	0.0666693i
$85$	−0.908872			−0.0985810
$86$	0.133618	+	0.0771443i	0.0144084	+	0.00831868i
$87$	−7.94908	+	4.58940i	−0.852230	+	0.492035i
$88$	3.09371	−	1.78615i	0.329790	−	0.190405i
$89$	2.07047	−	3.58615i	0.219469	−	0.380131i	−0.735177	−	0.677875i	$-0.762901\pi$
$89$	2.07047	−	3.58615i	0.219469	−	0.380131i	0.954646	+	0.297744i	$0.0962342\pi$
$90$	−2.89735			−0.305408
$91$	−0.323956	−	1.08344i	−0.0339598	−	0.113575i
$92$	−0.892472	+	4.71206i	−0.0930467	+	0.491266i
$93$	−4.32724	+	7.49501i	−0.448714	+	0.777196i
$94$	−5.27800	+	3.04725i	−0.544384	+	0.314300i
$95$	9.40420	+	16.2886i	0.964851	+	1.67117i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	14.5174			1.47402			0.737010	−	0.675882i	$-0.236237\pi$
$97$	14.5174			1.47402			0.737010	+	0.675882i	$0.236237\pi$
$98$	0.402224	+	6.98843i	0.0406308	+	0.705938i
$99$		−	3.57231i		−	0.359030i
$100$	−1.69733	+	2.93986i	−0.169733	+	0.293986i
$101$	−8.32633	+	4.80721i	−0.828501	+	0.478335i	−0.853339	−	0.521356i	$-0.825426\pi$
$101$	−8.32633	+	4.80721i	−0.828501	+	0.478335i	0.0248384	+	0.999691i	$0.492093\pi$
$102$	0.271664	−	0.156845i	0.0268987	−	0.0155300i
$103$	−4.32674	+	7.49413i	−0.426326	+	0.738419i	−0.996543	−	0.0830752i	$-0.973526\pi$
$103$	−4.32674	+	7.49413i	−0.426326	+	0.738419i	0.570217	+	0.821494i	$0.306859\pi$
$104$		−	0.427415i		−	0.0419115i
$105$	−2.19602	−	7.34439i	−0.214310	−	0.716739i
$106$			0.276765i			0.0268818i
$107$	−10.4990	−	6.06159i	−1.01498	−	0.585996i	−0.102331	−	0.994750i	$-0.532630\pi$
$107$	−10.4990	−	6.06159i	−1.01498	−	0.585996i	−0.912645	+	0.408754i	$0.865963\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	9.66819	−	5.58193i	0.926044	−	0.534652i	0.0404859	−	0.999180i	$-0.487109\pi$
$109$	9.66819	−	5.58193i	0.926044	−	0.534652i	0.885558	+	0.464528i	$0.153776\pi$
$110$	−8.96357	−	5.17512i	−0.854643	−	0.493428i
$111$	7.91406			0.751170
$112$	−0.611034	+	2.57423i	−0.0577373	+	0.243241i
$113$		−	12.9648i		−	1.21963i	−0.792545	−	0.609814i	$-0.791244\pi$
$113$		−	12.9648i		−	1.21963i	0.792545	−	0.609814i	$-0.208756\pi$
$114$	−5.62187	−	3.24579i	−0.526537	−	0.303996i
$115$	13.1163	−	4.58687i	1.22310	−	0.427728i
$116$	−4.58940	−	7.94908i	−0.426115	−	0.738053i
$117$	−0.370152	−	0.213708i	−0.0342206	−	0.0197573i
$118$		−	13.2102i		−	1.21610i
$119$	0.603486	+	0.569751i	0.0553215	+	0.0522290i
$120$		−	2.89735i		−	0.264491i
$121$	0.880690	−	1.52540i	0.0800627	−	0.138673i
$122$	−6.11830	−	10.5972i	−0.553924	−	0.959425i
$123$	−5.86396	−	10.1567i	−0.528736	−	0.915797i
$124$	−7.49501	−	4.32724i	−0.673071	−	0.388598i
$125$	−4.65124			−0.416020
$126$	1.92383	+	1.81628i	0.171388	+	0.161807i
$127$	−21.1035			−1.87263			−0.936316	−	0.351158i	$-0.885788\pi$
$127$	−21.1035			−1.87263			−0.936316	+	0.351158i	$0.885788\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.0771443	+	0.133618i	0.00679217	+	0.0117644i
$130$	−1.07246	+	0.619187i	−0.0940612	+	0.0543063i
$131$	17.4134	+	10.0536i	1.52142	+	0.878391i	0.999680	+	0.0252843i	$0.00804911\pi$
$131$	17.4134	+	10.0536i	1.52142	+	0.878391i	0.521737	+	0.853106i	$0.325284\pi$
$132$	3.57231			0.310929
$133$	3.96658	−	16.7108i	0.343946	−	1.44901i
$134$			2.52299i			0.217953i
$135$	−2.50918	−	1.44868i	−0.215956	−	0.124682i
$136$	0.156845	+	0.271664i	0.0134494	+	0.0232950i
$137$	6.95562	−	4.01583i	0.594259	−	0.343096i	−0.172521	−	0.985006i	$-0.555191\pi$
$137$	6.95562	−	4.01583i	0.594259	−	0.343096i	0.766780	+	0.641910i	$0.221858\pi$
$138$	−3.12893	+	3.63453i	−0.266352	+	0.309391i
$139$		−	2.34108i		−	0.198568i	−0.995059	−	0.0992838i	$-0.968345\pi$
$139$		−	2.34108i		−	0.198568i	0.995059	−	0.0992838i	$-0.0316552\pi$
$140$	7.34439	−	2.19602i	0.620714	−	0.185598i
$141$	−6.09450			−0.513250
$142$	−5.51324	+	9.54922i	−0.462661	+	0.801353i
$143$	−0.763429	−	1.32230i	−0.0638412	−	0.110576i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−13.2971	+	23.0313i	−1.10427	+	1.91264i
$146$			2.33090i			0.192907i
$147$	−3.14588	+	6.25327i	−0.259468	+	0.515761i
$148$			7.91406i			0.650532i
$149$	−14.8366	−	8.56589i	−1.21546	−	0.701745i	−0.251515	−	0.967853i	$-0.580929\pi$
$149$	−14.8366	−	8.56589i	−1.21546	−	0.701745i	−0.963943	+	0.266108i	$0.914262\pi$
$150$	−2.93986	+	1.69733i	−0.240039	+	0.138586i
$151$	2.57529	+	4.46054i	0.209574	+	0.362993i	0.951580	−	0.307400i	$-0.0994588\pi$
$151$	2.57529	+	4.46054i	0.209574	+	0.362993i	−0.742006	+	0.670393i	$0.766126\pi$
$152$	3.24579	−	5.62187i	0.263268	−	0.455994i
$153$	0.313691			0.0253604
$154$	2.70760	+	9.05531i	0.218185	+	0.729697i
$155$			25.0751i			2.01408i
$156$	0.213708	−	0.370152i	0.0171103	−	0.0296359i
$157$	−1.16389	−	2.01591i	−0.0928884	−	0.160887i	0.815837	−	0.578282i	$-0.196277\pi$
$157$	−1.16389	−	2.01591i	−0.0928884	−	0.160887i	−0.908725	+	0.417395i	$0.862943\pi$
$158$	−2.40844	+	1.39051i	−0.191605	+	0.110623i
$159$	−0.138382	+	0.239685i	−0.0109744	+	0.0190083i
$160$	2.89735			0.229056
$161$	−11.5846	−	5.17665i	−0.912992	−	0.407978i
$162$	1.00000			0.0785674
$163$	2.61097	−	4.52233i	0.204507	−	0.354216i	−0.745469	−	0.666541i	$-0.767774\pi$
$163$	2.61097	−	4.52233i	0.204507	−	0.354216i	0.949975	+	0.312324i	$0.101108\pi$
$164$	10.1567	−	5.86396i	0.793103	−	0.457898i
$165$	−5.17512	−	8.96357i	−0.402882	−	0.697813i
$166$	−4.48709	+	7.77187i	−0.348266	+	0.603214i
$167$		−	14.3042i		−	1.10689i	−0.832885	−	0.553446i	$-0.813313\pi$
$167$		−	14.3042i		−	1.10689i	0.832885	−	0.553446i	$-0.186687\pi$
$168$	−1.81628	+	1.92383i	−0.140129	+	0.148427i
$169$	12.8173			0.985947
$170$	0.454436	−	0.787107i	0.0348537	−	0.0603683i
$171$	−3.24579	−	5.62187i	−0.248212	−	0.429915i
$172$	−0.133618	+	0.0771443i	−0.0101883	+	0.00588219i
$173$	−3.00276	−	1.73364i	−0.228296	−	0.131807i	0.381490	−	0.924373i	$-0.375411\pi$
$173$	−3.00276	−	1.73364i	−0.228296	−	0.131807i	−0.609786	+	0.792566i	$0.708744\pi$
$174$		−	9.17880i		−	0.695843i
$175$	−6.53074	−	6.16566i	−0.493677	−	0.466080i
$176$			3.57231i			0.269273i
$177$	6.60511	−	11.4404i	0.496470	−	0.859912i
$178$	2.07047	+	3.58615i	0.155188	+	0.268793i
$179$	7.16855	+	12.4163i	0.535802	+	0.928037i	0.999124	+	0.0418467i	$0.0133241\pi$
$179$	7.16855	+	12.4163i	0.535802	+	0.928037i	−0.463322	+	0.886190i	$0.653343\pi$
$180$	1.44868	−	2.50918i	0.107978	−	0.187023i
$181$	−12.1151			−0.900506			−0.450253	−	0.892901i	$-0.648666\pi$
$181$	−12.1151			−0.900506			−0.450253	+	0.892901i	$0.648666\pi$
$182$	1.10026	+	0.261165i	0.0815569	+	0.0193589i
$183$		−	12.2366i		−	0.904555i
$184$	−3.63453	−	3.12893i	−0.267941	−	0.230668i
$185$	19.8578	−	11.4649i	1.45998	−	0.842918i
$186$	−4.32724	−	7.49501i	−0.317289	−	0.549561i
$187$	0.970467	+	0.560299i	0.0709676	+	0.0409732i
$188$		−	6.09450i		−	0.444487i
$189$	0.757941	+	2.53486i	0.0551321	+	0.184384i
$190$	−18.8084			−1.36450
$191$	5.66023	+	3.26793i	0.409560	+	0.236459i	0.690601	−	0.723236i	$-0.257346\pi$
$191$	5.66023	+	3.26793i	0.409560	+	0.236459i	−0.281041	+	0.959696i	$0.590680\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−0.193593	−	0.335314i	−0.0139352	−	0.0241364i	0.858974	−	0.512020i	$-0.171103\pi$
$193$	−0.193593	−	0.335314i	−0.0139352	−	0.0241364i	−0.872909	+	0.487883i	$0.837769\pi$
$194$	−7.25871	+	12.5724i	−0.521145	+	0.902649i
$195$	−1.23837			−0.0886817
$196$	−6.25327	−	3.14588i	−0.446662	−	0.224706i
$197$	−12.8580			−0.916096			−0.458048	−	0.888928i	$-0.651451\pi$
$197$	−12.8580			−0.916096			−0.458048	+	0.888928i	$0.651451\pi$
$198$	3.09371	+	1.78615i	0.219860	+	0.126936i
$199$	9.32410	+	16.1498i	0.660968	+	1.14483i	0.980362	+	0.197208i	$0.0631873\pi$
$199$	9.32410	+	16.1498i	0.660968	+	1.14483i	−0.319394	+	0.947622i	$0.603479\pi$
$200$	−1.69733	−	2.93986i	−0.120019	−	0.207880i
$201$	−1.26150	+	2.18498i	−0.0889791	+	0.154116i
$202$		−	9.61441i		−	0.676468i
$203$	23.2670	−	6.95699i	1.63302	−	0.488285i
$204$			0.313691i			0.0219627i
$205$	−29.4275	−	16.9900i	−2.05531	−	1.18663i
$206$	−4.32674	−	7.49413i	−0.301458	−	0.522141i
$207$	−4.52700	+	1.58313i	−0.314648	+	0.110035i
$208$	0.370152	+	0.213708i	0.0256655	+	0.0148180i
$209$		−	23.1899i		−	1.60408i
$210$	7.45844	+	1.77038i	0.514681	+	0.122168i
$211$	2.71153			0.186669			0.0933347	−	0.995635i	$-0.470247\pi$
$211$	2.71153			0.186669			0.0933347	+	0.995635i	$0.470247\pi$
$212$	−0.239685	−	0.138382i	−0.0164617	−	0.00950414i
$213$	−9.54922	+	5.51324i	−0.654302	+	0.377761i
$214$	10.4990	−	6.06159i	0.717696	−	0.414362i
$215$	0.387138	+	0.223514i	0.0264026	+	0.0152435i
$216$			1.00000i			0.0680414i
$217$	15.7190	−	16.6497i	1.06708	−	1.13026i
$218$			11.1639i			0.756112i
$219$	−1.16545	+	2.01862i	−0.0787538	+	0.136406i
$220$	8.96357	−	5.17512i	0.604324	−	0.348906i
$221$	0.116113	−	0.0670381i	0.00781063	−	0.00450947i
$222$	−3.95703	+	6.85378i	−0.265579	+	0.459996i
$223$		−	26.0270i		−	1.74289i	−0.490490	−	0.871447i	$-0.663182\pi$
$223$		−	26.0270i		−	1.74289i	0.490490	−	0.871447i	$-0.336818\pi$
$224$	−1.92383	−	1.81628i	−0.128541	−	0.121356i
$225$	−3.39466			−0.226311
$226$	11.2279	+	6.48241i	0.746866	+	0.431203i
$227$	8.45618	+	14.6465i	0.561256	+	0.972125i	0.997387	+	0.0722413i	$0.0230152\pi$
$227$	8.45618	+	14.6465i	0.561256	+	0.972125i	−0.436131	+	0.899883i	$0.643652\pi$
$228$	5.62187	−	3.24579i	0.372318	−	0.214958i
$229$	4.85436	−	8.40800i	0.320785	−	0.555616i	−0.659865	−	0.751384i	$-0.729387\pi$
$229$	4.85436	−	8.40800i	0.320785	−	0.555616i	0.980650	+	0.195768i	$0.0627199\pi$
$230$	−2.58581	+	13.6525i	−0.170503	+	0.900219i
$231$	−2.18280	+	9.19592i	−0.143618	+	0.605047i
$232$	9.17880			0.602618
$233$	4.94268	−	8.56097i	0.323806	−	0.560848i	−0.657464	−	0.753486i	$-0.728371\pi$
$233$	4.94268	−	8.56097i	0.323806	−	0.560848i	0.981270	+	0.192638i	$0.0617043\pi$
$234$	0.370152	−	0.213708i	0.0241976	−	0.0139705i
$235$	−15.2922	+	8.82897i	−0.997555	+	0.575938i
$236$	11.4404	+	6.60511i	0.744705	+	0.429956i
$237$	−2.78103			−0.180647
$238$	−0.795162	+	0.237759i	−0.0515427	+	0.0154116i
$239$	5.55249			0.359161			0.179580	−	0.983743i	$-0.442526\pi$
$239$	5.55249			0.359161			0.179580	+	0.983743i	$0.442526\pi$
$240$	2.50918	+	1.44868i	0.161967	+	0.0935117i
$241$	−1.56971	−	2.71882i	−0.101114	−	0.175135i	0.811030	−	0.585005i	$-0.198907\pi$
$241$	−1.56971	−	2.71882i	−0.101114	−	0.175135i	−0.912144	+	0.409870i	$0.865574\pi$
$242$	0.880690	+	1.52540i	0.0566129	+	0.0980564i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	12.2366			0.783368
$245$	1.16539	+	20.2480i	0.0744537	+	1.29360i
$246$	11.7279			0.747745
$247$	−2.40287	−	1.38730i	−0.152891	−	0.0882718i
$248$	7.49501	−	4.32724i	0.475933	−	0.274780i
$249$	−7.77187	+	4.48709i	−0.492523	+	0.284358i
$250$	2.32562	−	4.02809i	0.147085	−	0.254759i
$251$	−8.42670			−0.531888			−0.265944	−	0.963988i	$-0.585684\pi$
$251$	−8.42670			−0.531888			−0.265944	+	0.963988i	$0.585684\pi$
$252$	−2.53486	+	0.757941i	−0.159681	+	0.0477458i
$253$	−16.8329	−	3.18818i	−1.05828	−	0.200439i
$254$	10.5517	−	18.2762i	0.662076	−	1.14675i
$255$	0.787107	−	0.454436i	0.0492905	−	0.0284579i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.1283	−	7.00225i	−0.756540	−	0.436789i	0.0715121	−	0.997440i	$-0.477218\pi$
$257$	−12.1283	−	7.00225i	−0.756540	−	0.436789i	−0.828052	+	0.560651i	$0.810551\pi$
$258$	−0.154289			−0.00960558
$259$	−20.3726	−	4.83577i	−1.26589	−	0.300480i
$260$		−	1.23837i		−	0.0768006i
$261$	4.58940	−	7.94908i	0.284077	−	0.492035i
$262$	−17.4134	+	10.0536i	−1.07580	+	0.621116i
$263$	−0.594082	+	0.342993i	−0.0366327	+	0.0211499i	−0.518204	−	0.855257i	$-0.673399\pi$
$263$	−0.594082	+	0.342993i	−0.0366327	+	0.0211499i	0.481572	+	0.876407i	$0.340066\pi$
$264$	−1.78615	+	3.09371i	−0.109930	+	0.190405i
$265$			0.801886i			0.0492594i
$266$	12.4887	+	11.7906i	0.765730	+	0.722925i
$267$			4.14093i			0.253421i
$268$	−2.18498	−	1.26150i	−0.133469	−	0.0770582i
$269$	3.27332	−	1.88985i	0.199578	−	0.115226i	−0.396881	−	0.917870i	$-0.629907\pi$
$269$	3.27332	−	1.88985i	0.199578	−	0.115226i	0.596459	+	0.802644i	$0.296574\pi$
$270$	2.50918	−	1.44868i	0.152704	−	0.0881637i
$271$	13.6509	+	7.88135i	0.829233	+	0.478758i	0.853590	−	0.520946i	$-0.174421\pi$
$271$	13.6509	+	7.88135i	0.829233	+	0.478758i	−0.0243571	+	0.999703i	$0.507754\pi$
$272$	−0.313691			−0.0190203
$273$	0.822273	+	0.776307i	0.0497662	+	0.0469843i
$274$			8.03166i			0.485211i
$275$	−10.5021	−	6.06338i	−0.633300	−	0.365636i
$276$	−1.58313	−	4.52700i	−0.0952930	−	0.272493i
$277$	8.15437	+	14.1238i	0.489949	+	0.848616i	0.999933	−	0.0115676i	$-0.00368217\pi$
$277$	8.15437	+	14.1238i	0.489949	+	0.848616i	−0.509984	+	0.860184i	$0.670349\pi$
$278$	2.02743	+	1.17054i	0.121597	+	0.0702043i
$279$		−	8.65449i		−	0.518131i
$280$	−1.77038	+	7.45844i	−0.105801	+	0.445727i
$281$		−	16.7860i		−	1.00137i	−0.865630	−	0.500685i	$-0.833082\pi$
$281$		−	16.7860i		−	1.00137i	0.865630	−	0.500685i	$-0.166918\pi$
$282$	3.04725	−	5.27800i	0.181461	−	0.314300i
$283$	−15.5403	−	26.9167i	−0.923778	−	1.60003i	−0.793515	−	0.608551i	$-0.791751\pi$
$283$	−15.5403	−	26.9167i	−0.923778	−	1.60003i	−0.130263	−	0.991479i	$-0.541582\pi$
$284$	−5.51324	−	9.54922i	−0.327151	−	0.566642i
$285$	−16.2886	−	9.40420i	−0.964851	−	0.557057i
$286$	1.52686			0.0902850
$287$	8.88908	+	29.7287i	0.524706	+	1.75483i
$288$	−1.00000			−0.0589256
$289$	8.45080	−	14.6372i	0.497106	−	0.861013i
$290$	−13.2971	−	23.0313i	−0.780834	−	1.35244i
$291$	−12.5724	+	7.25871i	−0.737010	+	0.425513i
$292$	−2.01862	−	1.16545i	−0.118131	−	0.0682028i
$293$	24.7265			1.44454			0.722270	−	0.691612i	$-0.243099\pi$
$293$	24.7265			1.44454			0.722270	+	0.691612i	$0.243099\pi$
$294$	−3.84255	−	5.85105i	−0.224102	−	0.341240i
$295$		−	38.2747i		−	2.22844i
$296$	−6.85378	−	3.95703i	−0.398368	−	0.229998i
$297$	1.78615	+	3.09371i	0.103643	+	0.179515i
$298$	14.8366	−	8.56589i	0.859459	−	0.496209i
$299$	−1.33735	+	1.55345i	−0.0773411	+	0.0898384i
$300$		−	3.39466i		−	0.195991i
$301$	−0.116942	−	0.391100i	−0.00674040	−	0.0225426i
$302$	−5.15059			−0.296383
$303$	4.80721	−	8.32633i	0.276167	−	0.478335i
$304$	3.24579	+	5.62187i	0.186159	+	0.322436i
$305$	−17.7269	−	30.7038i	−1.01504	−	1.75810i
$306$	−0.156845	+	0.271664i	−0.00896625	+	0.0155300i
$307$			19.0918i			1.08963i	0.838557	+	0.544814i	$0.183400\pi$
$307$			19.0918i			1.08963i	−0.838557	+	0.544814i	$0.816600\pi$
$308$	−9.19592	−	2.18280i	−0.523986	−	0.124377i
$309$		−	8.65348i		−	0.492279i
$310$	−21.7157	−	12.5376i	−1.23337	−	0.712085i
$311$	−6.07305	+	3.50628i	−0.344371	+	0.198823i	−0.662203	−	0.749324i	$-0.730379\pi$
$311$	−6.07305	+	3.50628i	−0.344371	+	0.198823i	0.317832	+	0.948147i	$0.397045\pi$
$312$	0.213708	+	0.370152i	0.0120988	+	0.0209558i
$313$	−6.22577	+	10.7834i	−0.351902	+	0.609511i	−0.986583	−	0.163263i	$-0.947798\pi$
$313$	−6.22577	+	10.7834i	−0.351902	+	0.609511i	0.634681	+	0.772774i	$0.281131\pi$
$314$	2.32778			0.131364
$315$	5.57401	+	5.26242i	0.314060	+	0.296504i
$316$		−	2.78103i		−	0.156445i
$317$	−16.9037	+	29.2780i	−0.949405	+	1.64442i	−0.202722	+	0.979236i	$0.564979\pi$
$317$	−16.9037	+	29.2780i	−0.949405	+	1.64442i	−0.746682	+	0.665181i	$0.768354\pi$
$318$	−0.138382	−	0.239685i	−0.00776010	−	0.0134409i
$319$	28.3965	−	16.3948i	1.58990	−	0.917930i
$320$	−1.44868	+	2.50918i	−0.0809835	+	0.140268i
$321$	12.1232			0.676650
$322$	10.2754	−	7.44420i	0.572626	−	0.414849i
$323$	2.03635			0.113305
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.25654	+	0.725464i	−0.0697004	+	0.0402415i
$326$	2.61097	+	4.52233i	0.144608	+	0.250469i
$327$	−5.58193	+	9.66819i	−0.308681	+	0.534652i
$328$			11.7279i			0.647566i
$329$	15.6886	+	3.72395i	0.864942	+	0.205308i
$330$	10.3502			0.569762
$331$	−6.12028	+	10.6006i	−0.336401	+	0.582664i	−0.983753	−	0.179527i	$-0.942543\pi$
$331$	−6.12028	+	10.6006i	−0.336401	+	0.582664i	0.647352	+	0.762191i	$0.275877\pi$
$332$	−4.48709	−	7.77187i	−0.246261	−	0.426537i
$333$	−6.85378	+	3.95703i	−0.375585	+	0.216844i
$334$	12.3878	+	7.15210i	0.677830	+	0.391345i
$335$			7.31000i			0.399388i
$336$	−0.757941	−	2.53486i	−0.0413491	−	0.138288i
$337$		−	8.32079i		−	0.453263i	−0.973981	−	0.226631i	$-0.927229\pi$
$337$		−	8.32079i		−	0.453263i	0.973981	−	0.226631i	$-0.0727712\pi$
$338$	−6.40866	+	11.1001i	−0.348585	+	0.603767i
$339$	6.48241	+	11.2279i	0.352076	+	0.609814i
$340$	0.454436	+	0.787107i	0.0246453	+	0.0426868i
$341$	15.4582	−	26.7745i	0.837111	−	1.44992i
$342$	6.49158			0.351024
$343$	11.9192	−	14.1751i	0.643575	−	0.765383i
$344$		−	0.154289i		−	0.00831868i
$345$	−9.06562	+	10.5305i	−0.488077	+	0.566943i
$346$	3.00276	−	1.73364i	0.161429	−	0.0932013i
$347$	−2.46565	−	4.27063i	−0.132363	−	0.229259i	0.792224	−	0.610230i	$-0.208923\pi$
$347$	−2.46565	−	4.27063i	−0.132363	−	0.229259i	−0.924587	+	0.380971i	$0.875590\pi$
$348$	7.94908	+	4.58940i	0.426115	+	0.246018i
$349$			3.40917i			0.182489i	0.995829	+	0.0912444i	$0.0290845\pi$
$349$			3.40917i			0.182489i	−0.995829	+	0.0912444i	$0.970916\pi$
$350$	8.60499	−	2.57295i	0.459956	−	0.137530i
$351$	0.427415			0.0228137
$352$	−3.09371	−	1.78615i	−0.164895	−	0.0952023i
$353$	−7.22650	+	4.17222i	−0.384628	+	0.222065i	−0.679830	−	0.733370i	$-0.737946\pi$
$353$	−7.22650	+	4.17222i	−0.384628	+	0.222065i	0.295202	+	0.955435i	$0.404613\pi$
$354$	6.60511	+	11.4404i	0.351057	+	0.608049i
$355$	−15.9738	+	27.6675i	−0.847802	+	1.46844i
$356$	−4.14093			−0.219469
$357$	−0.807510	−	0.191676i	−0.0427380	−	0.0101446i
$358$	−14.3371			−0.757739
$359$	−23.4259	−	13.5249i	−1.23637	−	0.713819i	−0.268020	−	0.963413i	$-0.586369\pi$
$359$	−23.4259	−	13.5249i	−1.23637	−	0.713819i	−0.968350	+	0.249595i	$0.919703\pi$
$360$	1.44868	+	2.50918i	0.0763520	+	0.132245i
$361$	−11.5703	−	20.0403i	−0.608963	−	1.05476i
$362$	6.05754	−	10.4920i	0.318377	−	0.551445i
$363$			1.76138i			0.0924485i
$364$	−0.776307	+	0.822273i	−0.0406896	+	0.0430988i
$365$			6.75344i			0.353491i
$366$	10.5972	+	6.11830i	0.553924	+	0.319808i
$367$	12.1381	+	21.0238i	0.633602	+	1.09743i	0.986809	+	0.161886i	$0.0517577\pi$
$367$	12.1381	+	21.0238i	0.633602	+	1.09743i	−0.353207	+	0.935545i	$0.614909\pi$
$368$	4.52700	−	1.58313i	0.235986	−	0.0825261i
$369$	10.1567	+	5.86396i	0.528736	+	0.305266i
$370$			22.9298i			1.19207i
$371$	0.502684	−	0.532448i	0.0260980	−	0.0276433i
$372$	8.65449			0.448714
$373$	21.0241	+	12.1383i	1.08859	+	0.628495i	0.933200	−	0.359358i	$-0.117004\pi$
$373$	21.0241	+	12.1383i	1.08859	+	0.628495i	0.155386	+	0.987854i	$0.450338\pi$
$374$	−0.970467	+	0.560299i	−0.0501817	+	0.0289724i
$375$	4.02809	−	2.32562i	0.208010	−	0.120095i
$376$	5.27800	+	3.04725i	0.272192	+	0.157150i
$377$		−	3.92316i		−	0.202053i
$378$	−2.57423	−	0.611034i	−0.132404	−	0.0314282i
$379$			24.8201i			1.27492i	0.770483	+	0.637461i	$0.220015\pi$
$379$			24.8201i			1.27492i	−0.770483	+	0.637461i	$0.779985\pi$
$380$	9.40420	−	16.2886i	0.482425	−	0.835585i
$381$	18.2762	−	10.5517i	0.936316	−	0.540582i
$382$	−5.66023	+	3.26793i	−0.289602	+	0.167202i
$383$	−13.9796	+	24.2134i	−0.714324	+	1.23725i	0.248895	+	0.968530i	$0.419933\pi$
$383$	−13.9796	+	24.2134i	−0.714324	+	1.23725i	−0.963220	+	0.268716i	$0.913401\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	7.84487	+	26.2364i	0.399812	+	1.33713i
$386$	0.387187			0.0197073
$387$	−0.133618	−	0.0771443i	−0.00679217	−	0.00392146i
$388$	−7.25871	−	12.5724i	−0.368505	−	0.638269i
$389$	−23.6834	+	13.6736i	−1.20080	+	0.693281i	−0.960733	−	0.277476i	$-0.910502\pi$
$389$	−23.6834	+	13.6736i	−1.20080	+	0.693281i	−0.240065	+	0.970757i	$0.577169\pi$
$390$	0.619187	−	1.07246i	0.0313537	−	0.0543063i
$391$	0.279960	−	1.47813i	0.0141582	−	0.0747521i
$392$	5.85105	−	3.84255i	0.295523	−	0.194078i
$393$	−20.1073			−1.01428
$394$	6.42901	−	11.1354i	0.323889	−	0.560992i
$395$	−6.97811	+	4.02881i	−0.351107	+	0.202711i
$396$	−3.09371	+	1.78615i	−0.155465	+	0.0897576i
$397$	1.53267	+	0.884890i	0.0769227	+	0.0444114i	0.537968	−	0.842965i	$-0.319192\pi$
$397$	1.53267	+	0.884890i	0.0769227	+	0.0444114i	−0.461045	+	0.887377i	$0.652525\pi$
$398$	−18.6482			−0.934749
$399$	4.92024	+	16.4553i	0.246320	+	0.823793i
$400$	3.39466			0.169733
$401$	−7.19640	−	4.15484i	−0.359371	−	0.207483i	0.309434	−	0.950921i	$-0.399860\pi$
$401$	−7.19640	−	4.15484i	−0.359371	−	0.207483i	−0.668805	+	0.743438i	$0.733194\pi$
$402$	−1.26150	−	2.18498i	−0.0629177	−	0.108977i
$403$	−1.84953	−	3.20348i	−0.0921316	−	0.159577i
$404$	8.32633	+	4.80721i	0.414250	+	0.239168i
$405$	2.89735			0.143971
$406$	−5.60856	+	23.6283i	−0.278348	+	1.17265i
$407$	−28.2715			−1.40136
$408$	−0.271664	−	0.156845i	−0.0134494	−	0.00776500i
$409$	12.8639	−	7.42700i	0.636081	−	0.367241i	−0.147022	−	0.989133i	$-0.546969\pi$
$409$	12.8639	−	7.42700i	0.636081	−	0.367241i	0.783103	+	0.621892i	$0.213636\pi$
$410$	29.4275	−	16.9900i	1.45332	−	0.839075i
$411$	−4.01583	+	6.95562i	−0.198086	+	0.343096i
$412$	8.65348			0.426326
$413$	−23.9935	+	25.4142i	−1.18064	+	1.25055i
$414$	0.892472	−	4.71206i	0.0438626	−	0.231585i
$415$	−13.0007	+	22.5179i	−0.638179	+	1.10536i
$416$	−0.370152	+	0.213708i	−0.0181482	+	0.0104779i
$417$	1.17054	+	2.02743i	0.0573215	+	0.0992838i
$418$	20.0831	+	11.5950i	0.982294	+	0.567128i
$419$	−3.55988			−0.173912			−0.0869559	−	0.996212i	$-0.527714\pi$
$419$	−3.55988			−0.173912			−0.0869559	+	0.996212i	$0.527714\pi$
$420$	−5.26242	+	5.57401i	−0.256780	+	0.271984i
$421$		−	7.49745i		−	0.365403i	−0.983168	−	0.182702i	$-0.941516\pi$
$421$		−	7.49745i		−	0.365403i	0.983168	−	0.182702i	$-0.0584843\pi$
$422$	−1.35576	+	2.34825i	−0.0659976	+	0.114311i
$423$	5.27800	−	3.04725i	0.256625	−	0.148162i
$424$	0.239685	−	0.138382i	0.0116402	−	0.00672044i
$425$	0.532436	−	0.922206i	0.0258269	−	0.0447336i
$426$		−	11.0265i		−	0.534235i
$427$	−7.47698	+	31.4997i	−0.361836	+	1.52438i
$428$			12.1232i			0.585996i
$429$	1.32230	+	0.763429i	0.0638412	+	0.0368587i
$430$	−0.387138	+	0.223514i	−0.0186694	+	0.0107788i
$431$	5.12954	−	2.96154i	0.247081	−	0.142652i	−0.371346	−	0.928495i	$-0.621104\pi$
$431$	5.12954	−	2.96154i	0.247081	−	0.142652i	0.618427	+	0.785842i	$0.287770\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	1.98204			0.0952509			0.0476254	−	0.998865i	$-0.484835\pi$
$433$	1.98204			0.0952509			0.0476254	+	0.998865i	$0.484835\pi$
$434$	6.55959	+	21.9379i	0.314871	+	1.05305i
$435$		−	26.5942i		−	1.27510i
$436$	−9.66819	−	5.58193i	−0.463022	−	0.267326i
$437$	−29.3874	+	10.2770i	−1.40579	+	0.491615i
$438$	−1.16545	−	2.01862i	−0.0556874	−	0.0964534i
$439$	8.95666	+	5.17113i	0.427478	+	0.246804i	0.698272	−	0.715833i	$-0.253953\pi$
$439$	8.95666	+	5.17113i	0.427478	+	0.246804i	−0.270794	+	0.962637i	$0.587286\pi$
$440$			10.3502i			0.493428i
$441$	−0.402224	−	6.98843i	−0.0191535	−	0.332783i
$442$			0.134076i			0.00637735i
$443$	−13.5384	+	23.4491i	−0.643227	+	1.11410i	0.341481	+	0.939889i	$0.389072\pi$
$443$	−13.5384	+	23.4491i	−0.643227	+	1.11410i	−0.984708	+	0.174213i	$0.944262\pi$
$444$	−3.95703	−	6.85378i	−0.187792	−	0.325266i
$445$	5.99887	+	10.3904i	0.284374	+	0.492550i
$446$	22.5400	+	13.0135i	1.06730	+	0.616206i
$447$	17.1318			0.810306
$448$	2.53486	−	0.757941i	0.119761	−	0.0358094i
$449$	24.8671			1.17355			0.586776	−	0.809749i	$-0.300397\pi$
$449$	24.8671			1.17355			0.586776	+	0.809749i	$0.300397\pi$
$450$	1.69733	−	2.93986i	0.0800129	−	0.138586i
$451$	20.9479	+	36.2828i	0.986397	+	1.70849i
$452$	−11.2279	+	6.48241i	−0.528114	+	0.304907i
$453$	−4.46054	−	2.57529i	−0.209574	−	0.120998i
$454$	−16.9124			−0.793736
$455$	3.18785	+	0.756689i	0.149449	+	0.0354741i
$456$			6.49158i			0.303996i
$457$	11.0578	+	6.38424i	0.517264	+	0.298642i	0.735814	−	0.677183i	$-0.236800\pi$
$457$	11.0578	+	6.38424i	0.517264	+	0.298642i	−0.218551	+	0.975826i	$0.570133\pi$
$458$	4.85436	+	8.40800i	0.226829	+	0.392880i
$459$	−0.271664	+	0.156845i	−0.0126802	+	0.00732091i
$460$	−10.5305	−	9.06562i	−0.490987	−	0.422687i
$461$		−	34.7356i		−	1.61780i	−0.587947	−	0.808899i	$-0.700064\pi$
$461$		−	34.7356i		−	1.61780i	0.587947	−	0.808899i	$-0.299936\pi$
$462$	−6.87250	−	6.48833i	−0.319738	−	0.301864i
$463$	14.0409			0.652537			0.326269	−	0.945277i	$-0.394209\pi$
$463$	14.0409			0.652537			0.326269	+	0.945277i	$0.394209\pi$
$464$	−4.58940	+	7.94908i	−0.213058	+	0.369027i
$465$	−12.5376	−	21.7157i	−0.581415	−	1.00704i
$466$	4.94268	+	8.56097i	0.228965	+	0.396579i
$467$	−0.571191	+	0.989331i	−0.0264316	+	0.0457808i	−0.878939	−	0.476935i	$-0.841748\pi$
$467$	−0.571191	+	0.989331i	−0.0264316	+	0.0457808i	0.852507	+	0.522716i	$0.175081\pi$
$468$			0.427415i			0.0197573i
$469$	4.58247	−	4.85380i	0.211599	−	0.224128i
$470$		−	17.6579i		−	0.814500i
$471$	2.01591	+	1.16389i	0.0928884	+	0.0536291i
$472$	−11.4404	+	6.60511i	−0.526586	+	0.304025i
$473$	−0.275583	−	0.477324i	−0.0126713	−	0.0219474i
$474$	1.39051	−	2.40844i	0.0638684	−	0.110623i
$475$	−22.0367			−1.01111
$476$	0.191676	−	0.807510i	0.00878544	−	0.0370122i
$477$		−	0.276765i		−	0.0126722i
$478$	−2.77625	+	4.80860i	−0.126982	+	0.219940i
$479$	−8.81884	−	15.2747i	−0.402943	−	0.697918i	0.591137	−	0.806571i	$-0.298679\pi$
$479$	−8.81884	−	15.2747i	−0.402943	−	0.697918i	−0.994080	+	0.108654i	$0.965346\pi$
$480$	−2.50918	+	1.44868i	−0.114528	+	0.0661227i
$481$	−1.69130	+	2.92941i	−0.0771164	+	0.133570i
$482$	3.13943			0.142997
$483$	12.6209	−	1.30917i	0.574269	−	0.0595693i
$484$	−1.76138			−0.0800627
$485$	−21.0310	+	36.4268i	−0.954970	+	1.65406i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	7.92306	+	13.7231i	0.359028	+	0.621855i	0.987799	−	0.155736i	$-0.0497749\pi$
$487$	7.92306	+	13.7231i	0.359028	+	0.621855i	−0.628771	+	0.777591i	$0.716442\pi$
$488$	−6.11830	+	10.5972i	−0.276962	+	0.479713i
$489$			5.22194i			0.236144i
$490$	−18.1179	−	9.11473i	−0.818485	−	0.411762i
$491$	−0.346828			−0.0156521			−0.00782607	−	0.999969i	$-0.502491\pi$
$491$	−0.346828			−0.0156521			−0.00782607	+	0.999969i	$0.502491\pi$
$492$	−5.86396	+	10.1567i	−0.264368	+	0.457898i
$493$	1.43965	+	2.49355i	0.0648387	+	0.112304i
$494$	2.40287	−	1.38730i	0.108110	−	0.0624176i
$495$	8.96357	+	5.17512i	0.402882	+	0.232604i
$496$			8.65449i			0.388598i
$497$	27.9506	−	8.35743i	1.25376	−	0.374882i
$498$		−	8.97419i		−	0.402143i
$499$	15.7401	−	27.2627i	0.704624	−	1.22044i	−0.262203	−	0.965013i	$-0.584449\pi$
$499$	15.7401	−	27.2627i	0.704624	−	1.22044i	0.966827	−	0.255432i	$-0.0822176\pi$
$500$	2.32562	+	4.02809i	0.104005	+	0.180142i
$501$	7.15210	+	12.3878i	0.319532	+	0.553446i
$502$	4.21335	−	7.29773i	0.188051	−	0.325714i
$503$	−42.1803			−1.88072			−0.940362	−	0.340174i	$-0.889514\pi$
$503$	−42.1803			−1.88072			−0.940362	+	0.340174i	$0.889514\pi$
$504$	0.611034	−	2.57423i	0.0272176	−	0.114665i
$505$		−	27.8564i		−	1.23959i
$506$	11.1775	−	12.9836i	0.496901	−	0.577193i
$507$	−11.1001	+	6.40866i	−0.492974	+	0.284618i
$508$	10.5517	+	18.2762i	0.468158	+	0.810874i
$509$	−34.3900	−	19.8551i	−1.52431	−	0.880060i	−0.999586	−	0.0287873i	$-0.990835\pi$
$509$	−34.3900	−	19.8551i	−1.52431	−	0.880060i	−0.524723	−	0.851273i	$-0.675831\pi$
$510$			0.908872i			0.0402455i
$511$	4.23358	−	4.48425i	0.187282	−	0.198372i
$512$	1.00000			0.0441942
$513$	5.62187	+	3.24579i	0.248212	+	0.143305i
$514$	12.1283	−	7.00225i	0.534955	−	0.308856i
$515$	−12.5361	−	21.7132i	−0.552406	−	0.956796i
$516$	0.0771443	−	0.133618i	0.00339609	−	0.00588219i
$517$	21.7714			0.957507
$518$	14.3742	−	15.2253i	0.631565	−	0.668961i
$519$	3.46729			0.152197
$520$	1.07246	+	0.619187i	0.0470306	+	0.0271531i
$521$	5.45273	+	9.44441i	0.238889	+	0.413767i	0.960396	−	0.278640i	$-0.0898836\pi$
$521$	5.45273	+	9.44441i	0.238889	+	0.413767i	−0.721507	+	0.692407i	$0.756550\pi$
$522$	4.58940	+	7.94908i	0.200873	+	0.347922i
$523$	1.11073	−	1.92384i	0.0485689	−	0.0841238i	−0.840719	−	0.541472i	$-0.817867\pi$
$523$	1.11073	−	1.92384i	0.0485689	−	0.0841238i	0.889288	+	0.457348i	$0.151201\pi$
$524$		−	20.1073i		−	0.878391i
$525$	8.73862	+	2.07425i	0.381384	+	0.0905278i
$526$		−	0.685987i		−	0.0299105i
$527$	2.35111	+	1.35742i	0.102416	+	0.0591299i
$528$	−1.78615	−	3.09371i	−0.0777324	−	0.134636i
$529$	3.41956	+	22.7444i	0.148677	+	0.988886i
$530$	−0.694453	−	0.400943i	−0.0301651	−	0.0174158i
$531$			13.2102i			0.573274i
$532$	−16.4553	+	4.92024i	−0.713426	+	0.213319i
$533$	5.01269			0.217124
$534$	−3.58615	−	2.07047i	−0.155188	−	0.0895978i
$535$	30.4193	−	17.5626i	1.31514	−	0.759297i
$536$	2.18498	−	1.26150i	0.0943766	−	0.0544884i
$537$	−12.4163	−	7.16855i	−0.535802	−	0.309346i
$538$			3.77970i			0.162955i
$539$	11.2381	−	22.3386i	0.484057	−	0.962192i
$540$			2.89735i			0.124682i
$541$	−12.8206	+	22.2059i	−0.551201	+	0.954707i	0.446988	+	0.894540i	$0.352497\pi$
$541$	−12.8206	+	22.2059i	−0.551201	+	0.954707i	−0.998188	+	0.0601673i	$0.980837\pi$
$542$	−13.6509	+	7.88135i	−0.586356	+	0.338533i
$543$	10.4920	−	6.05754i	0.450253	−	0.259954i
$544$	0.156845	−	0.271664i	0.00672468	−	0.0116475i
$545$			32.3456i			1.38554i
$546$	−1.08344	+	0.323956i	−0.0463669	+	0.0138640i
$547$	−33.1347			−1.41674			−0.708368	−	0.705843i	$-0.750568\pi$
$547$	−33.1347			−1.41674			−0.708368	+	0.705843i	$0.750568\pi$
$548$	−6.95562	−	4.01583i	−0.297130	−	0.171548i
$549$	6.11830	+	10.5972i	0.261123	+	0.452277i
$550$	10.5021	−	6.06338i	0.447810	−	0.258543i
$551$	29.7925	−	51.6021i	1.26920	−	2.19832i
$552$	4.71206	+	0.892472i	0.200559	+	0.0379861i
$553$	7.15899	+	1.69930i	0.304431	+	0.0722618i
$554$	−16.3087			−0.692892
$555$	−11.4649	+	19.8578i	−0.486659	+	0.842918i
$556$	−2.02743	+	1.17054i	−0.0859823	+	0.0496419i
$557$	−9.52469	+	5.49908i	−0.403574	+	0.233004i	−0.688025	−	0.725687i	$-0.741522\pi$
$557$	−9.52469	+	5.49908i	−0.403574	+	0.233004i	0.284451	+	0.958691i	$0.408189\pi$
$558$	7.49501	+	4.32724i	0.317289	+	0.183187i
$559$	−0.0659453			−0.00278919
$560$	−5.57401	−	5.26242i	−0.235545	−	0.222378i
$561$	−1.12060			−0.0473117
$562$	14.5371	+	8.39301i	0.613211	+	0.354038i
$563$	−1.70395	−	2.95134i	−0.0718131	−	0.124384i	0.827883	−	0.560901i	$-0.189545\pi$
$563$	−1.70395	−	2.95134i	−0.0718131	−	0.124384i	−0.899696	+	0.436517i	$0.856212\pi$
$564$	3.04725	+	5.27800i	0.128312	+	0.222244i
$565$	32.5311	+	18.7818i	1.36859	+	0.790158i
$566$	31.0807			1.30642
$567$	−1.92383	−	1.81628i	−0.0807932	−	0.0762768i
$568$	11.0265			0.462661
$569$	−17.7037	−	10.2212i	−0.742176	−	0.428496i	0.0806837	−	0.996740i	$-0.474290\pi$
$569$	−17.7037	−	10.2212i	−0.742176	−	0.428496i	−0.822860	+	0.568244i	$0.807623\pi$
$570$	16.2886	−	9.40420i	0.682252	−	0.393899i
$571$	21.9891	−	12.6954i	0.920216	−	0.531287i	0.0365117	−	0.999333i	$-0.488375\pi$
$571$	21.9891	−	12.6954i	0.920216	−	0.531287i	0.883704	+	0.468047i	$0.155042\pi$
$572$	−0.763429	+	1.32230i	−0.0319206	+	0.0552881i
$573$	−6.53587			−0.273040
$574$	−30.1903	−	7.16616i	−1.26012	−	0.299110i
$575$	−3.02964	+	15.9958i	−0.126345	+	0.667072i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−22.4330	+	12.9517i	−0.933899	+	0.539187i	−0.888043	−	0.459761i	$-0.847935\pi$
$577$	−22.4330	+	12.9517i	−0.933899	+	0.539187i	−0.0458565	+	0.998948i	$0.514602\pi$
$578$	8.45080	+	14.6372i	0.351507	+	0.608828i
$579$	0.335314	+	0.193593i	0.0139352	+	0.00804547i
$580$	26.5942			1.10427
$581$	22.7483	−	6.80191i	0.943760	−	0.282191i
$582$		−	14.5174i		−	0.601766i
$583$	0.494345	−	0.856230i	0.0204737	−	0.0354614i
$584$	2.01862	−	1.16545i	0.0835311	−	0.0482267i
$585$	1.07246	−	0.619187i	0.0443409	−	0.0256002i
$586$	−12.3633	+	21.4138i	−0.510722	+	0.884596i
$587$		−	5.53944i		−	0.228637i	−0.993444	−	0.114319i	$-0.963532\pi$
$587$		−	5.53944i		−	0.228637i	0.993444	−	0.114319i	$-0.0364685\pi$
$588$	6.98843	−	0.402224i	0.288198	−	0.0165874i
$589$		−	56.1813i		−	2.31491i
$590$	33.1468	+	19.1373i	1.36463	+	0.787871i
$591$	11.1354	−	6.42901i	0.458048	−	0.264454i
$592$	6.85378	−	3.95703i	0.281689	−	0.162633i
$593$	−25.2957	−	14.6045i	−1.03877	−	0.599734i	−0.119285	−	0.992860i	$-0.538060\pi$
$593$	−25.2957	−	14.6045i	−1.03877	−	0.599734i	−0.919485	+	0.393126i	$0.871394\pi$
$594$	−3.57231			−0.146574
$595$	−2.30387	+	0.688872i	−0.0944493	+	0.0282410i
$596$			17.1318i			0.701745i
$597$	−16.1498	−	9.32410i	−0.660968	−	0.381610i
$598$	−0.676652	−	1.93491i	−0.0276704	−	0.0791243i
$599$	13.3770	+	23.1696i	0.546569	+	0.946686i	0.998506	+	0.0546359i	$0.0173998\pi$
$599$	13.3770	+	23.1696i	0.546569	+	0.946686i	−0.451937	+	0.892050i	$0.649267\pi$
$600$	2.93986	+	1.69733i	0.120019	+	0.0692932i
$601$			23.5442i			0.960387i	0.877163	+	0.480194i	$0.159434\pi$
$601$			23.5442i			0.960387i	−0.877163	+	0.480194i	$0.840566\pi$
$602$	0.397173	+	0.0942756i	0.0161876	+	0.00384239i
$603$		−	2.52299i		−	0.102744i
$604$	2.57529	−	4.46054i	0.104787	−	0.181497i
$605$	2.55167	+	4.41962i	0.103740	+	0.179683i
$606$	4.80721	+	8.32633i	0.195279	+	0.338234i
$607$	−3.11144	−	1.79639i	−0.126290	−	0.0729133i	0.435524	−	0.900177i	$-0.356563\pi$
$607$	−3.11144	−	1.79639i	−0.126290	−	0.0729133i	−0.561814	+	0.827264i	$0.689896\pi$
$608$	−6.49158			−0.263268
$609$	−16.6713	+	17.6584i	−0.675556	+	0.715556i
$610$	35.4537			1.43548
$611$	1.30244	−	2.25590i	0.0526912	−	0.0912638i
$612$	−0.156845	−	0.271664i	−0.00634009	−	0.0109814i
$613$	−13.8200	+	7.97899i	−0.558185	+	0.322268i	−0.752417	−	0.658687i	$-0.771112\pi$
$613$	−13.8200	+	7.97899i	−0.558185	+	0.322268i	0.194232	+	0.980956i	$0.437779\pi$
$614$	−16.5340	−	9.54592i	−0.667258	−	0.385242i
$615$	33.9799			1.37020
$616$	6.48833	−	6.87250i	0.261422	−	0.276901i
$617$		−	9.35371i		−	0.376566i	−0.982115	−	0.188283i	$-0.939708\pi$
$617$		−	9.35371i		−	0.376566i	0.982115	−	0.188283i	$-0.0602922\pi$
$618$	7.49413	+	4.32674i	0.301458	+	0.174047i
$619$	−19.2975	−	33.4242i	−0.775631	−	1.34343i	−0.934439	−	0.356124i	$-0.884098\pi$
$619$	−19.2975	−	33.4242i	−0.775631	−	1.34343i	0.158807	−	0.987310i	$-0.449235\pi$
$620$	21.7157	−	12.5376i	0.872123	−	0.503520i
$621$	3.12893	−	3.63453i	0.125560	−	0.145849i
$622$		−	7.01256i		−	0.281178i
$623$	2.53025	−	10.6597i	0.101372	−	0.427072i
$624$	−0.427415			−0.0171103
$625$	15.2248	−	26.3701i	0.608992	−	1.05480i
$626$	−6.22577	−	10.7834i	−0.248832	−	0.430990i
$627$	11.5950	+	20.0831i	0.463058	+	0.802040i
$628$	−1.16389	+	2.01591i	−0.0464442	+	0.0804437i
$629$		−	2.48257i		−	0.0989864i
$630$	−7.34439	+	2.19602i	−0.292608	+	0.0874917i
$631$		−	9.46971i		−	0.376983i	−0.982075	−	0.188492i	$-0.939640\pi$
$631$		−	9.46971i		−	0.376983i	0.982075	−	0.188492i	$-0.0603598\pi$
$632$	2.40844	+	1.39051i	0.0958026	+	0.0553117i
$633$	−2.34825	+	1.35576i	−0.0933347	+	0.0538868i
$634$	−16.9037	−	29.2780i	−0.671330	−	1.16278i
$635$	30.5721	−	52.9525i	1.21322	−	2.10136i
$636$	0.276765			0.0109744
$637$	−1.64237	−	2.50083i	−0.0650729	−	0.0990864i
$638$			32.7895i			1.29815i
$639$	5.51324	−	9.54922i	0.218101	−	0.377761i
$640$	−1.44868	−	2.50918i	−0.0572640	−	0.0991841i
$641$	1.09594	−	0.632739i	0.0432869	−	0.0249917i	−0.478200	−	0.878251i	$-0.658711\pi$
$641$	1.09594	−	0.632739i	0.0432869	−	0.0249917i	0.521487	+	0.853259i	$0.325377\pi$
$642$	−6.06159	+	10.4990i	−0.239232	+	0.414362i
$643$	23.4585			0.925114			0.462557	−	0.886590i	$-0.346932\pi$
$643$	23.4585			0.925114			0.462557	+	0.886590i	$0.346932\pi$
$644$	1.30917	+	12.6209i	0.0515885	+	0.497332i
$645$	−0.447028			−0.0176017
$646$	−1.01817	+	1.76353i	−0.0400595	+	0.0693851i
$647$	16.0942	−	9.29197i	0.632727	−	0.365305i	−0.149080	−	0.988825i	$-0.547631\pi$
$647$	16.0942	−	9.29197i	0.632727	−	0.365305i	0.781807	+	0.623520i	$0.214298\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−23.5955	+	40.8686i	−0.926203	+	1.60423i
$650$		−	1.45093i		−	0.0569101i
$651$	−5.28819	+	22.2786i	−0.207261	+	0.873167i
$652$	−5.22194			−0.204507
$653$	21.9568	−	38.0302i	0.859235	−	1.48824i	−0.0134251	−	0.999910i	$-0.504273\pi$
$653$	21.9568	−	38.0302i	0.859235	−	1.48824i	0.872660	−	0.488329i	$-0.162393\pi$
$654$	−5.58193	−	9.66819i	−0.218271	−	0.378056i
$655$	−50.4528	+	29.1290i	−1.97136	+	1.13816i
$656$	−10.1567	−	5.86396i	−0.396552	−	0.228949i
$657$		−	2.33090i		−	0.0909371i
$658$	−11.0694	+	11.7248i	−0.431528	+	0.457079i
$659$		−	3.82764i		−	0.149103i	−0.997217	−	0.0745517i	$-0.976247\pi$
$659$		−	3.82764i		−	0.149103i	0.997217	−	0.0745517i	$-0.0237526\pi$
$660$	−5.17512	+	8.96357i	−0.201441	+	0.348906i
$661$	21.4389	+	37.1333i	0.833877	+	1.44432i	0.894941	+	0.446184i	$0.147217\pi$
$661$	21.4389	+	37.1333i	0.833877	+	1.44432i	−0.0610639	+	0.998134i	$0.519449\pi$
$662$	−6.12028	−	10.6006i	−0.237872	−	0.412006i
$663$	−0.0670381	+	0.116113i	−0.00260354	+	0.00450947i
$664$	8.97419			0.348266
$665$	36.1841	+	34.1614i	1.40316	+	1.32472i
$666$		−	7.91406i		−	0.306664i
$667$	−33.3606	−	28.7199i	−1.29173	−	1.11204i
$668$	−12.3878	+	7.15210i	−0.479298	+	0.276723i
$669$	13.0135	+	22.5400i	0.503130	+	0.871447i
$670$	−6.33065	−	3.65500i	−0.244574	−	0.141205i
$671$			43.7129i			1.68752i
$672$	2.57423	+	0.611034i	0.0993029	+	0.0235712i
$673$	19.0943			0.736033			0.368016	−	0.929819i	$-0.380037\pi$
$673$	19.0943			0.736033			0.368016	+	0.929819i	$0.380037\pi$
$674$	7.20602	+	4.16040i	0.277565	+	0.160253i
$675$	2.93986	−	1.69733i	0.113155	−	0.0653302i
$676$	−6.40866	−	11.1001i	−0.246487	−	0.426928i
$677$	−16.5644	+	28.6904i	−0.636621	+	1.10266i	0.349548	+	0.936919i	$0.386335\pi$
$677$	−16.5644	+	28.6904i	−0.636621	+	1.10266i	−0.986169	+	0.165742i	$0.946998\pi$
$678$	−12.9648			−0.497911
$679$	36.7996	−	11.0033i	1.41224	−	0.422270i
$680$	−0.908872			−0.0348537
$681$	−14.6465	−	8.45618i	−0.561256	−	0.324042i
$682$	15.4582	+	26.7745i	0.591927	+	1.02525i
$683$	1.26572	+	2.19229i	0.0484314	+	0.0838856i	0.889225	−	0.457470i	$-0.151244\pi$
$683$	1.26572	+	2.19229i	0.0484314	+	0.0838856i	−0.840793	+	0.541356i	$0.817911\pi$
$684$	−3.24579	+	5.62187i	−0.124106	+	0.214958i
$685$			23.2706i			0.889123i
$686$	6.31641	+	17.4099i	0.241161	+	0.664711i
$687$			9.70872i			0.370411i
$688$	0.133618	+	0.0771443i	0.00509413	+	0.00294110i
$689$	−0.0591468	−	0.102445i	−0.00225331	−	0.00390285i
$690$	−4.58687	−	13.1163i	−0.174619	−	0.499330i
$691$	−32.2979	−	18.6472i	−1.22867	−	0.709373i	−0.261918	−	0.965090i	$-0.584355\pi$
$691$	−32.2979	−	18.6472i	−1.22867	−	0.709373i	−0.966752	+	0.255718i	$0.917688\pi$
$692$			3.46729i			0.131807i
$693$	−2.70760	−	9.05531i	−0.102853	−	0.343983i
$694$	4.93130			0.187189
$695$	5.87419	+	3.39147i	0.222821	+	0.128646i
$696$	−7.94908	+	4.58940i	−0.301309	+	0.173961i
$697$	−3.18605	+	1.83947i	−0.120680	+	0.0696749i
$698$	−2.95243	−	1.70459i	−0.111751	−	0.0645196i
$699$			9.88535i			0.373898i
$700$	−2.07425	+	8.73862i	−0.0783994	+	0.330289i
$701$			38.1696i			1.44164i	0.693120	+	0.720822i	$0.256236\pi$
$701$			38.1696i			1.44164i	−0.693120	+	0.720822i	$0.743764\pi$
$702$	−0.213708	+	0.370152i	−0.00806587	+	0.0139705i
$703$	−44.4918	+	25.6874i	−1.67804	+	0.968818i
$704$	3.09371	−	1.78615i	0.116599	−	0.0673182i
$705$	8.82897	−	15.2922i	0.332518	−	0.575938i
$706$		−	8.34444i		−	0.314047i
$707$	−17.4625	+	18.4965i	−0.656745	+	0.695632i
$708$	−13.2102			−0.496470
$709$	−14.9067	−	8.60639i	−0.559833	−	0.323220i	0.193245	−	0.981150i	$-0.438099\pi$
$709$	−14.9067	−	8.60639i	−0.559833	−	0.323220i	−0.753079	+	0.657931i	$0.771432\pi$
$710$	−15.9738	−	27.6675i	−0.599487	−	1.03834i
$711$	2.40844	−	1.39051i	0.0903236	−	0.0521484i
$712$	2.07047	−	3.58615i	0.0775940	−	0.134397i
$713$	−40.7805	−	7.72389i	−1.52724	−	0.289262i
$714$	0.569751	−	0.603486i	0.0213224	−	0.0225849i
$715$	4.42385			0.165443
$716$	7.16855	−	12.4163i	0.267901	−	0.464018i
$717$	−4.80860	+	2.77625i	−0.179580	+	0.103681i
$718$	23.4259	−	13.5249i	0.874246	−	0.504746i
$719$	−0.847035	−	0.489036i	−0.0315891	−	0.0182380i	0.484122	−	0.875000i	$-0.339139\pi$
$719$	−0.847035	−	0.489036i	−0.0315891	−	0.0182380i	−0.515711	+	0.856762i	$0.672472\pi$
$720$	−2.89735			−0.107978
$721$	−5.28757	+	22.2760i	−0.196920	+	0.829602i
$722$	23.1406			0.861204
$723$	2.71882	+	1.56971i	0.101114	+	0.0583783i
$724$	6.05754	+	10.4920i	0.225127	+	0.389931i
$725$	−15.5795	−	26.9844i	−0.578606	−	1.00218i
$726$	−1.52540	−	0.880690i	−0.0566129	−	0.0326855i
$727$	−9.69979			−0.359745			−0.179873	−	0.983690i	$-0.557569\pi$
$727$	−9.69979			−0.359745			−0.179873	+	0.983690i	$0.557569\pi$
$728$	−0.323956	−	1.08344i	−0.0120066	−	0.0401549i
$729$	−1.00000			−0.0370370
$730$	−5.84865	−	3.37672i	−0.216468	−	0.124978i
$731$	0.0419146	−	0.0241994i	0.00155027	−	0.000895048i
$732$	−10.5972	+	6.11830i	−0.391684	+	0.226139i
$733$	−6.50853	+	11.2731i	−0.240398	+	0.416382i	−0.960828	−	0.277146i	$-0.910611\pi$
$733$	−6.50853	+	11.2731i	−0.240398	+	0.416382i	0.720430	+	0.693528i	$0.243945\pi$
$734$	−24.2761			−0.896049
$735$	−11.1332	−	16.9526i	−0.410656	−	0.625305i
$736$	−0.892472	+	4.71206i	−0.0328970	+	0.173689i
$737$	4.50645	−	7.80541i	0.165997	−	0.287516i
$738$	−10.1567	+	5.86396i	−0.373872	+	0.215855i
$739$	−12.6119	−	21.8445i	−0.463937	−	0.803562i	0.535216	−	0.844715i	$-0.320230\pi$
$739$	−12.6119	−	21.8445i	−0.463937	−	0.803562i	−0.999153	+	0.0411533i	$0.986897\pi$
$740$	−19.8578	−	11.4649i	−0.729988	−	0.421459i
$741$	2.77460			0.101927
$742$	0.209772	+	0.701561i	0.00770095	+	0.0257551i
$743$			5.52396i			0.202655i	0.994853	+	0.101327i	$0.0323089\pi$
$743$			5.52396i			0.202655i	−0.994853	+	0.101327i	$0.967691\pi$
$744$	−4.32724	+	7.49501i	−0.158644	+	0.274780i
$745$	42.9868	−	24.8184i	1.57491	−	0.909277i
$746$	−21.0241	+	12.1383i	−0.769746	+	0.444413i
$747$	4.48709	−	7.77187i	0.164174	−	0.284358i
$748$		−	1.12060i		−	0.0409732i
$749$	−31.2078	−	7.40769i	−1.14031	−	0.270671i
$750$			4.65124i			0.169839i
$751$	5.29901	+	3.05938i	0.193363	+	0.111638i	0.593556	−	0.804793i	$-0.297723\pi$
$751$	5.29901	+	3.05938i	0.193363	+	0.111638i	−0.400193	+	0.916431i	$0.631057\pi$
$752$	−5.27800	+	3.04725i	−0.192469	+	0.111122i
$753$	7.29773	−	4.21335i	0.265944	−	0.153543i
$754$	3.39756	+	1.96158i	0.123732	+	0.0714365i
$755$	−14.9231			−0.543106
$756$	1.81628	−	1.92383i	0.0660576	−	0.0699689i
$757$		−	4.45031i		−	0.161749i	−0.996724	−	0.0808745i	$-0.974229\pi$
$757$		−	4.45031i		−	0.161749i	0.996724	−	0.0808745i	$-0.0257713\pi$
$758$	−21.4948	−	12.4100i	−0.780727	−	0.450753i
$759$	16.1718	−	5.65541i	0.587000	−	0.205278i
$760$	9.40420	+	16.2886i	0.341126	+	0.590848i
$761$	5.83642	+	3.36966i	0.211570	+	0.122150i	0.602041	−	0.798465i	$-0.294354\pi$
$761$	5.83642	+	3.36966i	0.211570	+	0.122150i	−0.390471	+	0.920615i	$0.627688\pi$
$762$			21.1035i			0.764499i
$763$	20.2767	−	21.4773i	0.734067	−	0.777532i
$764$		−	6.53587i		−	0.236459i
$765$	−0.454436	+	0.787107i	−0.0164302	+	0.0284579i
$766$	−13.9796	−	24.2134i	−0.505104	−	0.874865i
$767$	2.82312	+	4.88979i	0.101937	+	0.176560i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	8.74800			0.315461			0.157730	−	0.987482i	$-0.449582\pi$
$769$	8.74800			0.315461			0.157730	+	0.987482i	$0.449582\pi$
$770$	−26.6438	−	6.32435i	−0.960178	−	0.227914i
$771$	14.0045			0.504360
$772$	−0.193593	+	0.335314i	−0.00696758	+	0.0120682i
$773$	−20.2537	−	35.0804i	−0.728474	−	1.26175i	−0.957528	−	0.288340i	$-0.906897\pi$
$773$	−20.2537	−	35.0804i	−0.728474	−	1.26175i	0.229054	−	0.973414i	$-0.426437\pi$
$774$	0.133618	−	0.0771443i	0.00480279	−	0.00277289i
$775$	−25.4430	−	14.6895i	−0.913939	−	0.527663i
$776$	14.5174			0.521145
$777$	20.0611	−	5.99840i	0.719686	−	0.215191i
$778$		−	27.3473i		−	0.980447i
$779$	65.9329	+	38.0664i	2.36229	+	1.36387i
$780$	0.619187	+	1.07246i	0.0221704	+	0.0384003i
$781$	34.1127	−	19.6950i	1.22065	−	0.704742i
$782$	1.14012	+	0.981517i	0.0407705	+	0.0350990i
$783$			9.17880i			0.328024i
$784$	0.402224	+	6.98843i	0.0143651	+	0.249587i
$785$	6.74439			0.240718
$786$	10.0536	−	17.4134i	0.358602	−	0.621116i
$787$	16.9918	+	29.4306i	0.605691	+	1.04909i	0.991942	+	0.126694i	$0.0404367\pi$
$787$	16.9918	+	29.4306i	0.605691	+	1.04909i	−0.386251	+	0.922394i	$0.626230\pi$
$788$	6.42901	+	11.1354i	0.229024	+	0.396681i
$789$	0.342993	−	0.594082i	0.0122109	−	0.0211499i
$790$		−	8.05762i		−	0.286677i
$791$	−9.82657	−	32.8640i	−0.349393	−	1.16851i
$792$		−	3.57231i		−	0.126936i
$793$	4.52940	+	2.61505i	0.160844	+	0.0928633i
$794$	−1.53267	+	0.884890i	−0.0543926	+	0.0314036i
$795$	−0.400943	−	0.694453i	−0.0142200	−	0.0246297i
$796$	9.32410	−	16.1498i	0.330484	−	0.572415i
$797$	−33.9054			−1.20099			−0.600495	−	0.799629i	$-0.705030\pi$
$797$	−33.9054			−1.20099			−0.600495	+	0.799629i	$0.705030\pi$
$798$	−16.7108	−	3.96658i	−0.591555	−	0.140415i
$799$			1.91179i			0.0676342i
$800$	−1.69733	+	2.93986i	−0.0600096	+	0.103940i
$801$	−2.07047	−	3.58615i	−0.0731563	−	0.126710i
$802$	7.19640	−	4.15484i	0.254114	−	0.146713i
$803$	4.16335	−	7.21113i	0.146921	−	0.254475i
$804$	2.52299			0.0889791
$805$	29.7715	−	21.5685i	1.04931	−	0.760189i
$806$	3.69906			0.130294
$807$	−1.88985	+	3.27332i	−0.0665260	+	0.115226i
$808$	−8.32633	+	4.80721i	−0.292919	+	0.169117i
$809$	−21.9735	−	38.0593i	−0.772548	−	1.33809i	−0.936162	−	0.351568i	$-0.885649\pi$
$809$	−21.9735	−	38.0593i	−0.772548	−	1.33809i	0.163614	−	0.986524i	$-0.447685\pi$
$810$	−1.44868	+	2.50918i	−0.0509013	+	0.0881637i
$811$		−	28.9382i		−	1.01616i	−0.861310	−	0.508080i	$-0.830356\pi$
$811$		−	28.9382i		−	1.01616i	0.861310	−	0.508080i	$-0.169644\pi$
$812$	−17.6584	−	16.6713i	−0.619690	−	0.585048i
$813$	−15.7627			−0.552822
$814$	14.1357	−	24.4838i	0.495457	−	0.858157i
$815$	7.56490	+	13.1028i	0.264987	+	0.458971i
$816$	0.271664	−	0.156845i	0.00951014	−	0.00549068i
$817$	−0.867390	−	0.500788i	−0.0303461	−	0.0175204i
$818$			14.8540i			0.519358i
$819$	−1.10026	−	0.261165i	−0.0384463	−	0.00912586i
$820$			33.9799i			1.18663i
$821$	−19.7130	+	34.1439i	−0.687989	+	1.19163i	0.284499	+	0.958676i	$0.408173\pi$
$821$	−19.7130	+	34.1439i	−0.687989	+	1.19163i	−0.972488	+	0.232955i	$0.925161\pi$
$822$	−4.01583	−	6.95562i	−0.140068	−	0.242605i
$823$	−24.9198	−	43.1624i	−0.868650	−	1.50455i	−0.863376	−	0.504560i	$-0.831655\pi$
$823$	−24.9198	−	43.1624i	−0.868650	−	1.50455i	−0.00527375	−	0.999986i	$-0.501679\pi$
$824$	−4.32674	+	7.49413i	−0.150729	+	0.261071i
$825$	12.1268			0.422200
$826$	−10.0126	−	33.4861i	−0.348382	−	1.16513i
$827$		−	34.3434i		−	1.19424i	−0.802154	−	0.597118i	$-0.796313\pi$
$827$		−	34.3434i		−	1.19424i	0.802154	−	0.597118i	$-0.203687\pi$
$828$	3.63453	+	3.12893i	0.126309	+	0.108738i
$829$	−46.2243	+	26.6876i	−1.60544	+	0.926900i	−0.615064	+	0.788477i	$0.710870\pi$
$829$	−46.2243	+	26.6876i	−1.60544	+	0.926900i	−0.990373	+	0.138422i	$0.955797\pi$
$830$	−13.0007	−	22.5179i	−0.451261	−	0.781607i
$831$	−14.1238	−	8.15437i	−0.489949	−	0.282872i
$832$		−	0.427415i		−	0.0148180i
$833$	1.96159	+	0.986833i	0.0679652	+	0.0341917i
$834$	−2.34108			−0.0810649
$835$	35.8918	+	20.7222i	1.24209	+	0.717120i
$836$	−20.0831	+	11.5950i	−0.694587	+	0.401020i
$837$	4.32724	+	7.49501i	0.149571	+	0.259065i
$838$	1.77994	−	3.08295i	0.0614871	−	0.106499i
$839$	−17.1623			−0.592509			−0.296254	−	0.955109i	$-0.595738\pi$
$839$	−17.1623			−0.592509			−0.296254	+	0.955109i	$0.595738\pi$
$840$	−2.19602	−	7.34439i	−0.0757700	−	0.253406i
$841$	55.2504			1.90519
$842$	6.49298	+	3.74873i	0.223763	+	0.129190i
$843$	8.39301	+	14.5371i	0.289071	+	0.500685i
$844$	−1.35576	−	2.34825i	−0.0466673	−	0.0808302i
$845$	−18.5681	+	32.1610i	−0.638764	+	1.10637i
$846$			6.09450i			0.209533i
$847$	1.07626	−	4.53419i	0.0369809	−	0.155797i
$848$			0.276765i			0.00950414i
$849$	26.9167	+	15.5403i	0.923778	+	0.533343i
$850$	0.532436	+	0.922206i	0.0182624	+	0.0316314i
$851$	12.5290	+	35.8269i	0.429487	+	1.22813i
$852$	9.54922	+	5.51324i	0.327151	+	0.188881i
$853$		−	45.8302i		−	1.56920i	−0.620005	−	0.784598i	$-0.712869\pi$
$853$		−	45.8302i		−	1.56920i	0.620005	−	0.784598i	$-0.287131\pi$
$854$	−23.5411	−	22.2251i	−0.805560	−	0.760528i
$855$	18.8084			0.643234
$856$	−10.4990	−	6.06159i	−0.358848	−	0.207181i
$857$	−12.8686	+	7.42967i	−0.439582	+	0.253793i	−0.703420	−	0.710774i	$-0.748345\pi$
$857$	−12.8686	+	7.42967i	−0.439582	+	0.253793i	0.263838	+	0.964567i	$0.415011\pi$
$858$	−1.32230	+	0.763429i	−0.0451425	+	0.0260630i
$859$	−12.5258	−	7.23178i	−0.427375	−	0.246745i	0.270853	−	0.962621i	$-0.412694\pi$
$859$	−12.5258	−	7.23178i	−0.427375	−	0.246745i	−0.698228	+	0.715876i	$0.746028\pi$
$860$		−	0.447028i		−	0.0152435i
$861$	−22.5625	−	21.3012i	−0.768928	−	0.725944i
$862$			5.92308i			0.201741i
$863$	18.6209	−	32.2523i	0.633862	−	1.09788i	−0.352893	−	0.935664i	$-0.614802\pi$
$863$	18.6209	−	32.2523i	0.633862	−	1.09788i	0.986755	−	0.162218i	$-0.0518647\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	8.70006	−	5.02298i	0.295811	−	0.170786i
$866$	−0.991021	+	1.71650i	−0.0336763	+	0.0583290i
$867$			16.9016i			0.574008i
$868$	−22.2786	−	5.28819i	−0.756185	−	0.179493i
$869$	9.93469			0.337011
$870$	23.0313	+	13.2971i	0.780834	+	0.450815i
$871$	−0.539183	−	0.933892i	−0.0182695	−	0.0316437i
$872$	9.66819	−	5.58193i	0.327406	−	0.189028i
$873$	7.25871	−	12.5724i	0.245670	−	0.425513i
$874$	5.79355	−	30.5887i	0.195970	−	1.03468i
$875$	−11.7903	+	3.52537i	−0.398583	+	0.119179i
$876$	2.33090			0.0787538
$877$	−21.2289	+	36.7696i	−0.716850	+	1.24162i	0.245392	+	0.969424i	$0.421083\pi$
$877$	−21.2289	+	36.7696i	−0.716850	+	1.24162i	−0.962242	+	0.272196i	$0.912250\pi$
$878$	−8.95666	+	5.17113i	−0.302273	+	0.174517i
$879$	−21.4138	+	12.3633i	−0.722270	+	0.417003i
$880$	−8.96357	−	5.17512i	−0.302162	−	0.174453i
$881$	−17.2921			−0.582587			−0.291293	−	0.956634i	$-0.594086\pi$
$881$	−17.2921			−0.582587			−0.291293	+	0.956634i	$0.594086\pi$
$882$	6.25327	+	3.14588i	0.210559	+	0.105927i
$883$	28.3956			0.955587			0.477794	−	0.878472i	$-0.341437\pi$
$883$	28.3956			0.955587			0.477794	+	0.878472i	$0.341437\pi$
$884$	−0.116113	−	0.0670381i	−0.00390531	−	0.00225473i
$885$	19.1373	+	33.1468i	0.643294	+	1.11422i
$886$	−13.5384	−	23.4491i	−0.454830	−	0.787789i
$887$	−3.24993	−	1.87635i	−0.109122	−	0.0630015i	0.444446	−	0.895806i	$-0.353401\pi$
$887$	−3.24993	−	1.87635i	−0.109122	−	0.0630015i	−0.553568	+	0.832804i	$0.686734\pi$
$888$	7.91406			0.265579
$889$	−53.4945	+	15.9952i	−1.79415	+	0.536462i
$890$	−11.9977			−0.402165
$891$	−3.09371	−	1.78615i	−0.103643	−	0.0598384i
$892$	−22.5400	+	13.0135i	−0.754695	+	0.435723i
$893$	34.2625	−	19.7815i	1.14655	−	0.661962i
$894$	−8.56589	+	14.8366i	−0.286486	+	0.496209i
$895$	−41.5396			−1.38852
$896$	−0.611034	+	2.57423i	−0.0204132	+	0.0859988i
$897$	0.381456	−	2.01401i	0.0127365	−	0.0672457i
$898$	−12.4336	+	21.5356i	−0.414913	+	0.718651i
$899$	68.7952	−	39.7189i	2.29445	−	1.32470i
$900$	1.69733	+	2.93986i	0.0565776	+	0.0979953i
$901$	0.0751870	+	0.0434093i	0.00250484	+	0.00144617i
$902$	−41.8957			−1.39498
$903$	0.296824	+	0.280232i	0.00987770	+	0.00932553i
$904$		−	12.9648i		−	0.431203i
$905$	17.5508	−	30.3989i	0.583409	−	1.01049i
$906$	4.46054	−	2.57529i	0.148191	−	0.0855584i
$907$	−16.6152	+	9.59280i	−0.551699	+	0.318524i	−0.749807	−	0.661657i	$-0.769854\pi$
$907$	−16.6152	+	9.59280i	−0.551699	+	0.318524i	0.198108	+	0.980180i	$0.436520\pi$
$908$	8.45618	−	14.6465i	0.280628	−	0.486062i
$909$			9.61441i			0.318890i
$910$	−2.24924	+	2.38242i	−0.0745615	+	0.0789763i
$911$			14.1913i			0.470178i	0.971974	+	0.235089i	$0.0755381\pi$
$911$			14.1913i			0.470178i	−0.971974	+	0.235089i	$0.924462\pi$
$912$	−5.62187	−	3.24579i	−0.186159	−	0.107479i
$913$	27.7635	−	16.0293i	0.918839	−	0.530492i
$914$	−11.0578	+	6.38424i	−0.365761	+	0.211172i
$915$	30.7038	+	17.7269i	1.01504	+	0.586032i
$916$	−9.70872			−0.320785
$917$	51.7607	+	12.2862i	1.70929	+	0.405727i
$918$		−	0.313691i		−	0.0103533i
$919$	27.4284	+	15.8358i	0.904779	+	0.522374i	0.878747	−	0.477287i	$-0.158380\pi$
$919$	27.4284	+	15.8358i	0.904779	+	0.522374i	0.0260311	+	0.999661i	$0.491713\pi$
$920$	13.1163	−	4.58687i	0.432432	−	0.151225i
$921$	−9.54592	−	16.5340i	−0.314549	−	0.544814i
$922$	30.0819	+	17.3678i	0.990695	+	0.571978i
$923$		−	4.71289i		−	0.155127i
$924$	9.05531	−	2.70760i	0.297898	−	0.0890735i
$925$			26.8655i			0.883333i
$926$	−7.02046	+	12.1598i	−0.230707	+	0.399596i
$927$	4.32674	+	7.49413i	0.142109	+	0.246140i
$928$	−4.58940	−	7.94908i	−0.150654	−	0.260941i
$929$	−10.1746	−	5.87431i	−0.333818	−	0.192730i	0.323717	−	0.946154i	$-0.395067\pi$
$929$	−10.1746	−	5.87431i	−0.333818	−	0.192730i	−0.657535	+	0.753424i	$0.728401\pi$
$930$	25.0751			0.822245
$931$	−2.61107	−	45.3660i	−0.0855743	−	1.48681i
$932$	−9.88535			−0.323806
$933$	3.50628	−	6.07305i	0.114790	−	0.198823i
$934$	−0.571191	−	0.989331i	−0.0186899	−	0.0323719i
$935$	−2.81179	+	1.62339i	−0.0919553	+	0.0530904i
$936$	−0.370152	−	0.213708i	−0.0120988	−	0.00698525i
$937$	−33.5214			−1.09509			−0.547547	−	0.836775i	$-0.684438\pi$
$937$	−33.5214			−1.09509			−0.547547	+	0.836775i	$0.684438\pi$
$938$	1.91228	+	6.39544i	0.0624382	+	0.208818i
$939$		−	12.4515i		−	0.406341i
$940$	15.2922	+	8.82897i	0.498777	+	0.287969i
$941$	−26.8936	−	46.5811i	−0.876706	−	1.51850i	−0.854934	−	0.518737i	$-0.826402\pi$
$941$	−26.8936	−	46.5811i	−0.876706	−	1.51850i	−0.0217725	−	0.999763i	$-0.506931\pi$
$942$	−2.01591	+	1.16389i	−0.0656820	+	0.0379215i
$943$	36.6959	−	42.6254i	1.19498	−	1.38808i
$944$		−	13.2102i		−	0.429956i
$945$	−7.45844	−	1.77038i	−0.242623	−	0.0575906i
$946$	0.551166			0.0179200
$947$	−13.1205	+	22.7253i	−0.426357	+	0.738473i	−0.996546	−	0.0830410i	$-0.973537\pi$
$947$	−13.1205	+	22.7253i	−0.426357	+	0.738473i	0.570189	+	0.821514i	$0.306870\pi$
$948$	1.39051	+	2.40844i	0.0451618	+	0.0782225i
$949$	−0.498131	−	0.862789i	−0.0161700	−	0.0280073i
$950$	11.0183	−	19.0843i	0.357482	−	0.619178i
$951$		−	33.8073i		−	1.09628i
$952$	0.603486	+	0.569751i	0.0195591	+	0.0184657i
$953$			23.3997i			0.757991i	0.925399	+	0.378995i	$0.123730\pi$
$953$			23.3997i			0.757991i	−0.925399	+	0.378995i	$0.876270\pi$
$954$	0.239685	+	0.138382i	0.00776010	+	0.00448030i
$955$	−16.3997	+	9.46836i	−0.530681	+	0.306389i
$956$	−2.77625	−	4.80860i	−0.0897902	−	0.155521i
$957$	−16.3948	+	28.3965i	−0.529967	+	0.917930i
$958$	17.6377			0.569847
$959$	14.5878	−	15.4515i	0.471064	−	0.498956i
$960$		−	2.89735i		−	0.0935117i
$961$	21.9501	−	38.0187i	0.708067	−	1.22641i
$962$	−1.69130	−	2.92941i	−0.0545296	−	0.0944480i
$963$	−10.4990	+	6.06159i	−0.338325	+	0.195332i
$964$	−1.56971	+	2.71882i	−0.0505571	+	0.0875674i
$965$	1.12182			0.0361126
$966$	−5.17665	+	11.5846i	−0.166556	+	0.372727i
$967$	−9.84480			−0.316587			−0.158294	−	0.987392i	$-0.550599\pi$
$967$	−9.84480			−0.316587			−0.158294	+	0.987392i	$0.550599\pi$
$968$	0.880690	−	1.52540i	0.0283064	−	0.0490282i
$969$	−1.76353	+	1.01817i	−0.0566527	+	0.0327084i
$970$	−21.0310	−	36.4268i	−0.675266	−	1.16960i
$971$	24.5235	−	42.4760i	0.786997	−	1.36312i	−0.140802	−	0.990038i	$-0.544968\pi$
$971$	24.5235	−	42.4760i	0.786997	−	1.36312i	0.927799	−	0.373081i	$-0.121699\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−1.77440	−	5.93431i	−0.0568847	−	0.190245i
$974$	−15.8461			−0.507742
$975$	0.725464	−	1.25654i	0.0232335	−	0.0402415i
$976$	−6.11830	−	10.5972i	−0.195842	−	0.339208i
$977$	3.04108	−	1.75577i	0.0972928	−	0.0561720i	−0.450564	−	0.892744i	$-0.648777\pi$
$977$	3.04108	−	1.75577i	0.0972928	−	0.0561720i	0.547857	+	0.836572i	$0.315444\pi$
$978$	−4.52233	−	2.61097i	−0.144608	−	0.0834896i
$979$		−	14.7927i		−	0.472776i
$980$	16.9526	−	11.1332i	0.541530	−	0.355638i
$981$		−	11.1639i		−	0.356435i
$982$	0.173414	−	0.300362i	0.00553387	−	0.00958494i
$983$	16.6098	+	28.7690i	0.529771	+	0.917590i	0.999397	+	0.0347244i	$0.0110553\pi$
$983$	16.6098	+	28.7690i	0.529771	+	0.917590i	−0.469626	+	0.882865i	$0.655611\pi$
$984$	−5.86396	−	10.1567i	−0.186936	−	0.323783i
$985$	18.6271	−	32.2631i	0.593509	−	1.02799i
$986$	−2.87930			−0.0916957
$987$	−15.4487	+	4.61928i	−0.491738	+	0.147033i
$988$			2.77460i			0.0882718i
$989$	−0.482758	+	0.560766i	−0.0153508	+	0.0178313i
$990$	−8.96357	+	5.17512i	−0.284881	+	0.164476i
$991$	−27.8734	−	48.2782i	−0.885429	−	1.53361i	−0.845221	−	0.534417i	$-0.820531\pi$
$991$	−27.8734	−	48.2782i	−0.885429	−	1.53361i	−0.0402085	−	0.999191i	$-0.512802\pi$
$992$	−7.49501	−	4.32724i	−0.237967	−	0.137390i
$993$		−	12.2406i		−	0.388443i
$994$	−6.73756	+	28.3847i	−0.213703	+	0.900307i
$995$	−54.0304			−1.71288
$996$	7.77187	+	4.48709i	0.246261	+	0.142179i
$997$	−23.3893	+	13.5038i	−0.740748	+	0.427671i	−0.822341	−	0.568995i	$-0.807332\pi$
$997$	−23.3893	+	13.5038i	−0.740748	+	0.427671i	0.0815935	+	0.996666i	$0.473999\pi$
$998$	15.7401	+	27.2627i	0.498244	+	0.862985i
$999$	3.95703	−	6.85378i	0.125195	−	0.216844i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.3	✓	32	1.1	even	1	trivial
966.2.k.a.229.6	yes	32	23.22	odd	2	inner
966.2.k.a.367.3	yes	32	161.45	even	6	inner
966.2.k.a.367.6	yes	32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.44868 + 2.50918i) q^{5} -1.00000i q^{6} +(2.53486 - 0.757941i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.44868 + 2.50918i) q^{5} -1.00000i q^{6} +(2.53486 - 0.757941i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.44868 - 2.50918i) q^{10} +(3.09371 - 1.78615i) q^{11} +(0.866025 + 0.500000i) q^{12} -0.427415i q^{13} +(-0.611034 + 2.57423i) q^{14} -2.89735i q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.156845 + 0.271664i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.24579 - 5.62187i) q^{19} +2.89735 q^{20} +(-1.81628 + 1.92383i) q^{21} +3.57231i q^{22} +(-3.63453 - 3.12893i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.69733 - 2.93986i) q^{25} +(0.370152 + 0.213708i) q^{26} +1.00000i q^{27} +(-1.92383 - 1.81628i) q^{28} +9.17880 q^{29} +(2.50918 + 1.44868i) q^{30} +(7.49501 - 4.32724i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.78615 + 3.09371i) q^{33} -0.313691 q^{34} +(-1.77038 + 7.45844i) q^{35} -1.00000 q^{36} +(-6.85378 - 3.95703i) q^{37} +(3.24579 + 5.62187i) q^{38} +(0.213708 + 0.370152i) q^{39} +(-1.44868 + 2.50918i) q^{40} +11.7279i q^{41} +(-0.757941 - 2.53486i) q^{42} -0.154289i q^{43} +(-3.09371 - 1.78615i) q^{44} +(1.44868 + 2.50918i) q^{45} +(4.52700 - 1.58313i) q^{46} +(5.27800 + 3.04725i) q^{47} -1.00000i q^{48} +(5.85105 - 3.84255i) q^{49} +3.39466 q^{50} +(-0.271664 - 0.156845i) q^{51} +(-0.370152 + 0.213708i) q^{52} +(0.239685 - 0.138382i) q^{53} +(-0.866025 - 0.500000i) q^{54} +10.3502i q^{55} +(2.53486 - 0.757941i) q^{56} +6.49158i q^{57} +(-4.58940 + 7.94908i) q^{58} +(-11.4404 + 6.60511i) q^{59} +(-2.50918 + 1.44868i) q^{60} +(-6.11830 + 10.5972i) q^{61} +8.65449i q^{62} +(0.611034 - 2.57423i) q^{63} +1.00000 q^{64} +(1.07246 + 0.619187i) q^{65} +(-1.78615 - 3.09371i) q^{66} +(2.18498 - 1.26150i) q^{67} +(0.156845 - 0.271664i) q^{68} +(4.71206 + 0.892472i) q^{69} +(-5.57401 - 5.26242i) q^{70} +11.0265 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.01862 - 1.16545i) q^{73} +(6.85378 - 3.95703i) q^{74} +(2.93986 + 1.69733i) q^{75} -6.49158 q^{76} +(6.48833 - 6.87250i) q^{77} -0.427415 q^{78} +(2.40844 + 1.39051i) q^{79} +(-1.44868 - 2.50918i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.1567 - 5.86396i) q^{82} +8.97419 q^{83} +(2.57423 + 0.611034i) q^{84} -0.908872 q^{85} +(0.133618 + 0.0771443i) q^{86} +(-7.94908 + 4.58940i) q^{87} +(3.09371 - 1.78615i) q^{88} +(2.07047 - 3.58615i) q^{89} -2.89735 q^{90} +(-0.323956 - 1.08344i) q^{91} +(-0.892472 + 4.71206i) q^{92} +(-4.32724 + 7.49501i) q^{93} +(-5.27800 + 3.04725i) q^{94} +(9.40420 + 16.2886i) q^{95} +(0.866025 + 0.500000i) q^{96} +14.5174 q^{97} +(0.402224 + 6.98843i) q^{98} -3.57231i 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

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