LMFDB - Embedded newform 690.2.w.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.14628 - 0.627266i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.236933 + 0.433910i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.14628 - 0.627266i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.236933 + 0.433910i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-2.18556 - 0.472554i) q^{10} +(-3.22211 + 2.79198i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-4.47532 + 2.44371i) q^{13} +(-0.205374 + 0.449707i) q^{14} +(1.06916 - 1.96390i) q^{15} +(0.959493 - 0.281733i) q^{16} +(4.21004 + 5.62395i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(1.01115 + 7.03273i) q^{19} +(-2.21371 - 0.315433i) q^{20} +(-0.373630 - 0.323752i) q^{21} +(-3.01472 + 3.01472i) q^{22} +(-1.95743 - 4.37818i) q^{23} +1.00000i q^{24} +(4.21307 + 2.69258i) q^{25} +(-4.28958 + 2.75675i) q^{26} +(0.599278 - 0.800541i) q^{27} +(-0.172769 + 0.463212i) q^{28} +(-4.61015 - 0.662840i) q^{29} +(0.926329 - 2.03517i) q^{30} +(0.0976994 + 0.0627876i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-2.04326 - 3.74195i) q^{33} +(4.60052 + 5.30928i) q^{34} +(0.780701 - 0.782674i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-1.46440 - 3.92621i) q^{37} +(1.51029 + 6.94268i) q^{38} +(-1.43657 - 4.89249i) q^{39} +(-2.23057 - 0.156705i) q^{40} +(-3.92166 - 8.58723i) q^{41} +(-0.395774 - 0.296273i) q^{42} +(7.47099 + 1.62521i) q^{43} +(-2.79198 + 3.22211i) q^{44} +(1.69175 + 1.46218i) q^{45} +(-2.26478 - 4.22738i) q^{46} +(0.867374 + 0.867374i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.65235 + 5.68316i) q^{49} +(4.39443 + 2.38516i) q^{50} +(-6.39034 + 2.91837i) q^{51} +(-4.08199 + 3.05574i) q^{52} +(-8.31202 - 4.53871i) q^{53} +(0.540641 - 0.841254i) q^{54} +(8.66688 - 3.97125i) q^{55} +(-0.139284 + 0.474357i) q^{56} +(-7.08695 - 0.506868i) q^{57} +(-4.64569 - 0.332266i) q^{58} +(-1.73857 + 5.92101i) q^{59} +(0.778782 - 2.09607i) q^{60} +(-2.51209 + 3.90888i) q^{61} +(0.101930 + 0.0556578i) q^{62} +(0.395774 - 0.296273i) q^{63} +(0.909632 - 0.415415i) q^{64} +(11.1382 - 2.43768i) q^{65} +(-2.30500 - 3.58665i) q^{66} +(-0.102805 - 1.43740i) q^{67} +(4.96756 + 4.96756i) q^{68} +(4.69421 - 0.982050i) q^{69} +(0.722877 - 0.836374i) q^{70} +(-0.855805 + 0.987652i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-4.89275 - 3.66267i) q^{73} +(-1.74076 - 3.81174i) q^{74} +(-3.52660 + 3.54444i) q^{75} +(2.00172 + 6.81724i) q^{76} +(-0.448042 - 2.05962i) q^{77} +(-1.78193 - 4.77754i) q^{78} +(6.31931 + 1.85552i) q^{79} +(-2.23607 + 0.00282101i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-4.52427 - 8.28559i) q^{82} +(15.1240 - 5.64096i) q^{83} +(-0.415902 - 0.267284i) q^{84} +(-5.50823 - 14.7114i) q^{85} +(7.56789 + 1.08810i) q^{86} +(1.62765 - 4.36390i) q^{87} +(-2.55500 + 3.41308i) q^{88} +(7.84941 - 5.04451i) q^{89} +(1.79175 + 1.33777i) q^{90} -2.52088i q^{91} +(-2.56059 - 4.05504i) q^{92} +(-0.0821202 + 0.0821202i) q^{93} +(0.927042 + 0.803286i) q^{94} +(2.24117 - 15.7285i) q^{95} +(0.142315 + 0.989821i) q^{96} +(17.2808 + 6.44540i) q^{97} +(4.04847 + 5.40812i) q^{98} +(4.09076 - 1.20116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

Coefficient data

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

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

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

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.14628	−	0.627266i	−0.959848	−	0.280522i
$5$	−2.14628	−	0.627266i	−0.959848	−	0.280522i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−0.236933	+	0.433910i	−0.0895521	+	0.164002i	−0.918616	−	0.395151i	$-0.870692\pi$
$7$	−0.236933	+	0.433910i	−0.0895521	+	0.164002i	0.829064	+	0.559154i	$0.188874\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	−2.18556	−	0.472554i	−0.691136	−	0.149435i
$11$	−3.22211	+	2.79198i	−0.971503	+	0.841812i	−0.987429	−	0.158061i	$-0.949476\pi$
$11$	−3.22211	+	2.79198i	−0.971503	+	0.841812i	0.0159262	+	0.999873i	$0.494930\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	−4.47532	+	2.44371i	−1.24123	+	0.677763i	−0.959494	−	0.281729i	$-0.909092\pi$
$13$	−4.47532	+	2.44371i	−1.24123	+	0.677763i	−0.281736	+	0.959492i	$0.590910\pi$
$14$	−0.205374	+	0.449707i	−0.0548885	+	0.120189i
$15$	1.06916	−	1.96390i	0.276055	−	0.507077i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	4.21004	+	5.62395i	1.02108	+	1.36401i	0.929751	+	0.368189i	$0.120022\pi$
$17$	4.21004	+	5.62395i	1.02108	+	1.36401i	0.0913334	+	0.995820i	$0.470887\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	1.01115	+	7.03273i	0.231975	+	1.61342i	0.689543	+	0.724244i	$0.257811\pi$
$19$	1.01115	+	7.03273i	0.231975	+	1.61342i	−0.457569	+	0.889174i	$0.651280\pi$
$20$	−2.21371	−	0.315433i	−0.495000	−	0.0705330i
$21$	−0.373630	−	0.323752i	−0.0815327	−	0.0706485i
$22$	−3.01472	+	3.01472i	−0.642741	+	0.642741i
$23$	−1.95743	−	4.37818i	−0.408153	−	0.912914i
$23$	−1.95743	−	4.37818i	−0.408153	−	0.912914i
$24$			1.00000i			0.204124i
$25$	4.21307	+	2.69258i	0.842615	+	0.538516i
$26$	−4.28958	+	2.75675i	−0.841257	+	0.540643i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	−0.172769	+	0.463212i	−0.0326503	+	0.0875389i
$29$	−4.61015	−	0.662840i	−0.856084	−	0.123086i	−0.299722	−	0.954027i	$-0.596894\pi$
$29$	−4.61015	−	0.662840i	−0.856084	−	0.123086i	−0.556362	+	0.830940i	$0.687803\pi$
$30$	0.926329	−	2.03517i	0.169124	−	0.371569i
$31$	0.0976994	+	0.0627876i	0.0175473	+	0.0112770i	0.549385	−	0.835569i	$-0.314862\pi$
$31$	0.0976994	+	0.0627876i	0.0175473	+	0.0112770i	−0.531838	+	0.846846i	$0.678498\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	−2.04326	−	3.74195i	−0.355686	−	0.651390i
$34$	4.60052	+	5.30928i	0.788983	+	0.910535i
$35$	0.780701	−	0.782674i	0.131963	−	0.132296i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−1.46440	−	3.92621i	−0.240746	−	0.645466i	0.759239	−	0.650811i	$-0.225571\pi$
$37$	−1.46440	−	3.92621i	−0.240746	−	0.645466i	−0.999986	+	0.00534568i	$0.998298\pi$
$38$	1.51029	+	6.94268i	0.245001	+	1.12625i
$39$	−1.43657	−	4.89249i	−0.230035	−	0.783426i
$40$	−2.23057	−	0.156705i	−0.352684	−	0.0247773i
$41$	−3.92166	−	8.58723i	−0.612460	−	1.34110i	−0.920878	−	0.389850i	$-0.872527\pi$
$41$	−3.92166	−	8.58723i	−0.612460	−	1.34110i	0.308418	−	0.951251i	$-0.400200\pi$
$42$	−0.395774	−	0.296273i	−0.0610693	−	0.0457159i
$43$	7.47099	+	1.62521i	1.13931	+	0.247843i	0.742364	−	0.669997i	$-0.233705\pi$
$43$	7.47099	+	1.62521i	1.13931	+	0.247843i	0.396951	+	0.917840i	$0.370068\pi$
$44$	−2.79198	+	3.22211i	−0.420906	+	0.485752i
$45$	1.69175	+	1.46218i	0.252192	+	0.217969i
$46$	−2.26478	−	4.22738i	−0.333924	−	0.623294i
$47$	0.867374	+	0.867374i	0.126519	+	0.126519i	0.767531	−	0.641012i	$-0.221485\pi$
$47$	0.867374	+	0.867374i	0.126519	+	0.126519i	−0.641012	+	0.767531i	$0.721485\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	3.65235	+	5.68316i	0.521764	+	0.811880i
$50$	4.39443	+	2.38516i	0.621466	+	0.337313i
$51$	−6.39034	+	2.91837i	−0.894826	+	0.408653i
$52$	−4.08199	+	3.05574i	−0.566070	+	0.423755i
$53$	−8.31202	−	4.53871i	−1.14174	−	0.623439i	−0.206852	−	0.978372i	$-0.566322\pi$
$53$	−8.31202	−	4.53871i	−1.14174	−	0.623439i	−0.934892	+	0.354933i	$0.884504\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	8.66688	−	3.97125i	1.16864	−	0.535484i
$56$	−0.139284	+	0.474357i	−0.0186126	+	0.0633886i
$57$	−7.08695	−	0.506868i	−0.938689	−	0.0671364i
$58$	−4.64569	−	0.332266i	−0.610009	−	0.0436287i
$59$	−1.73857	+	5.92101i	−0.226342	+	0.770850i	0.765507	+	0.643428i	$0.222488\pi$
$59$	−1.73857	+	5.92101i	−0.226342	+	0.770850i	−0.991849	+	0.127422i	$0.959330\pi$
$60$	0.778782	−	2.09607i	0.100540	−	0.270601i
$61$	−2.51209	+	3.90888i	−0.321640	+	0.500481i	−0.963993	−	0.265928i	$-0.914322\pi$
$61$	−2.51209	+	3.90888i	−0.321640	+	0.500481i	0.642353	+	0.766409i	$0.277958\pi$
$62$	0.101930	+	0.0556578i	0.0129451	+	0.00706855i
$63$	0.395774	−	0.296273i	0.0498628	−	0.0373269i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	11.1382	−	2.43768i	1.38152	−	0.302357i
$66$	−2.30500	−	3.58665i	−0.283726	−	0.441487i
$67$	−0.102805	−	1.43740i	−0.0125596	−	0.175606i	−0.999860	−	0.0167408i	$-0.994671\pi$
$67$	−0.102805	−	1.43740i	−0.0125596	−	0.175606i	0.987300	−	0.158865i	$-0.0507836\pi$
$68$	4.96756	+	4.96756i	0.602405	+	0.602405i
$69$	4.69421	−	0.982050i	0.565116	−	0.118225i
$70$	0.722877	−	0.836374i	0.0864003	−	0.0999658i
$71$	−0.855805	+	0.987652i	−0.101565	+	0.117213i	−0.804256	−	0.594282i	$-0.797436\pi$
$71$	−0.855805	+	0.987652i	−0.101565	+	0.117213i	0.702691	+	0.711495i	$0.251982\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	−4.89275	−	3.66267i	−0.572653	−	0.428683i	0.273309	−	0.961926i	$-0.411882\pi$
$73$	−4.89275	−	3.66267i	−0.572653	−	0.428683i	−0.845962	+	0.533244i	$0.820973\pi$
$74$	−1.74076	−	3.81174i	−0.202360	−	0.443106i
$75$	−3.52660	+	3.54444i	−0.407217	+	0.409277i
$76$	2.00172	+	6.81724i	0.229613	+	0.781992i
$77$	−0.448042	−	2.05962i	−0.0510591	−	0.234715i
$78$	−1.78193	−	4.77754i	−0.201764	−	0.540950i
$79$	6.31931	+	1.85552i	0.710978	+	0.208762i	0.617172	−	0.786829i	$-0.288278\pi$
$79$	6.31931	+	1.85552i	0.710978	+	0.208762i	0.0938062	+	0.995590i	$0.470097\pi$
$80$	−2.23607	+	0.00282101i	−0.250000	+	0.000315399i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	−4.52427	−	8.28559i	−0.499622	−	0.914990i
$83$	15.1240	−	5.64096i	1.66008	−	0.619176i	0.667925	−	0.744229i	$-0.267183\pi$
$83$	15.1240	−	5.64096i	1.66008	−	0.619176i	0.992150	+	0.125053i	$0.0399100\pi$
$84$	−0.415902	−	0.267284i	−0.0453786	−	0.0291630i
$85$	−5.50823	−	14.7114i	−0.597451	−	1.59568i
$86$	7.56789	+	1.08810i	0.816067	+	0.117333i
$87$	1.62765	−	4.36390i	0.174502	−	0.467859i
$88$	−2.55500	+	3.41308i	−0.272364	+	0.363835i
$89$	7.84941	−	5.04451i	0.832036	−	0.534717i	−0.0538882	−	0.998547i	$-0.517161\pi$
$89$	7.84941	−	5.04451i	0.832036	−	0.534717i	0.885924	+	0.463830i	$0.153525\pi$
$90$	1.79175	+	1.33777i	0.188867	+	0.141013i
$91$		−	2.52088i		−	0.264260i
$92$	−2.56059	−	4.05504i	−0.266960	−	0.422768i
$93$	−0.0821202	+	0.0821202i	−0.00851547	+	0.00851547i
$94$	0.927042	+	0.803286i	0.0956170	+	0.0828526i
$95$	2.24117	−	15.7285i	0.229939	−	1.61371i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	17.2808	+	6.44540i	1.75460	+	0.654431i	0.999998	−	0.00175624i	$-0.000559030\pi$
$97$	17.2808	+	6.44540i	1.75460	+	0.654431i	0.754598	+	0.656187i	$0.227832\pi$
$98$	4.04847	+	5.40812i	0.408957	+	0.546303i
$99$	4.09076	−	1.20116i	0.411137	−	0.120721i
$100$	4.55339	+	2.06559i	0.455339	+	0.206559i
$101$	−3.88350	+	8.50369i	−0.386423	+	0.846149i	0.612045	+	0.790823i	$0.290347\pi$
$101$	−3.88350	+	8.50369i	−0.386423	+	0.846149i	−0.998468	+	0.0553258i	$0.982380\pi$
$102$	−6.16586	+	3.36681i	−0.610511	+	0.333364i
$103$	0.733116	−	10.2503i	0.0722361	−	1.00999i	−0.824050	−	0.566517i	$-0.808291\pi$
$103$	0.733116	−	10.2503i	0.0722361	−	1.00999i	0.896286	−	0.443476i	$-0.146255\pi$
$104$	−3.85360	+	3.33916i	−0.377876	+	0.327432i
$105$	0.598837	+	0.929229i	0.0584405	+	0.0906835i
$106$	−8.61463	−	3.93417i	−0.836727	−	0.382120i
$107$	0.672557	−	0.146306i	0.0650185	−	0.0141439i	−0.179938	−	0.983678i	$-0.557590\pi$
$107$	0.672557	−	0.146306i	0.0650185	−	0.0141439i	0.244957	+	0.969534i	$0.421226\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	−1.98714	+	13.8208i	−0.190333	+	1.32380i	0.640793	+	0.767713i	$0.278606\pi$
$109$	−1.98714	+	13.8208i	−0.190333	+	1.32380i	−0.831127	+	0.556083i	$0.812304\pi$
$110$	8.36149	−	4.57942i	0.797237	−	0.436631i
$111$	4.14777	−	0.596359i	0.393689	−	0.0566039i
$112$	−0.105089	+	0.483085i	−0.00992995	+	0.0456472i
$113$	−5.83590	+	0.417392i	−0.548996	+	0.0392649i	−0.343082	−	0.939305i	$-0.611471\pi$
$113$	−5.83590	+	0.417392i	−0.548996	+	0.0392649i	−0.205913	+	0.978570i	$0.566016\pi$
$114$	−7.10505			−0.665449
$115$	1.45492	+	10.6247i	0.135672	+	0.990754i
$116$	−4.65756			−0.432443
$117$	5.08605	−	0.363761i	0.470205	−	0.0336297i
$118$	−1.31174	+	6.02995i	−0.120755	+	0.555102i
$119$	−3.43778	+	0.494279i	−0.315141	+	0.0453104i
$120$	0.627266	−	2.14628i	0.0572613	−	0.195928i
$121$	1.02141	−	7.10408i	0.0928556	−	0.645825i
$122$	−2.22683	+	4.07813i	−0.201608	+	0.369217i
$123$	9.22460	−	2.00669i	0.831754	−	0.180937i
$124$	0.105641	+	0.0482444i	0.00948681	+	0.00433248i
$125$	−7.35349	−	8.42177i	−0.657716	−	0.753266i
$126$	0.373630	−	0.323752i	0.0332856	−	0.0288421i
$127$	0.0718953	−	1.00523i	0.00637968	−	0.0891996i	−0.993265	−	0.115868i	$-0.963035\pi$
$127$	0.0718953	−	1.00523i	0.00637968	−	0.0891996i	0.999644	+	0.0266680i	$0.00848971\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	−3.17614	+	6.95479i	−0.279644	+	0.612335i
$130$	10.9359	−	3.22606i	0.959140	−	0.282944i
$131$	−8.19505	+	2.40628i	−0.716005	+	0.210238i	−0.619390	−	0.785084i	$-0.712620\pi$
$131$	−8.19505	+	2.40628i	−0.716005	+	0.210238i	−0.0966155	+	0.995322i	$0.530802\pi$
$132$	−2.55500	−	3.41308i	−0.222384	−	0.297070i
$133$	−3.29114	−	1.22753i	−0.285378	−	0.106441i
$134$	−0.205086	−	1.42640i	−0.0177167	−	0.123222i
$135$	−1.78837	+	1.34228i	−0.153919	+	0.115525i
$136$	5.30928	+	4.60052i	0.455267	+	0.394491i
$137$	−14.7877	+	14.7877i	−1.26340	+	1.26340i	−0.313963	+	0.949435i	$0.601657\pi$
$137$	−14.7877	+	14.7877i	−1.26340	+	1.26340i	−0.949435	+	0.313963i	$0.898343\pi$
$138$	4.61219	−	1.31443i	0.392616	−	0.111892i
$139$		−	0.109697i		−	0.00930434i	−0.999989	−	0.00465217i	$-0.998519\pi$
$139$		−	0.109697i		−	0.00930434i	0.999989	−	0.00465217i	$-0.00148084\pi$
$140$	0.661369	−	0.885813i	0.0558959	−	0.0748648i
$141$	−1.03193	+	0.663178i	−0.0869038	+	0.0558497i
$142$	−0.783166	+	1.04619i	−0.0657219	+	0.0877941i
$143$	7.59720	−	20.3689i	0.635310	−	1.70333i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	9.47892	+	4.31443i	0.787182	+	0.358294i
$146$	−5.14158	−	3.30429i	−0.425520	−	0.273465i
$147$	−6.32964	+	2.36084i	−0.522060	+	0.194718i
$148$	−2.00826	−	3.67785i	−0.165078	−	0.302317i
$149$	11.4743	+	13.2421i	0.940014	+	1.08483i	0.996259	+	0.0864169i	$0.0275417\pi$
$149$	11.4743	+	13.2421i	0.940014	+	1.08483i	−0.0562452	+	0.998417i	$0.517913\pi$
$150$	−3.26476	+	3.78700i	−0.266566	+	0.309207i
$151$	−9.46791	−	2.78003i	−0.770488	−	0.226236i	−0.127217	−	0.991875i	$-0.540605\pi$
$151$	−9.46791	−	2.78003i	−0.770488	−	0.226236i	−0.643270	+	0.765639i	$0.722423\pi$
$152$	2.48296	+	6.65707i	0.201395	+	0.539960i
$153$	−1.49331	−	6.86464i	−0.120727	−	0.554973i
$154$	−0.593832	−	2.02240i	−0.0478523	−	0.162970i
$155$	−0.170306	−	0.196044i	−0.0136793	−	0.0157466i
$156$	−2.11822	−	4.63825i	−0.169593	−	0.371357i
$157$	10.7222	+	8.02656i	0.855727	+	0.640589i	0.934366	−	0.356314i	$-0.115967\pi$
$157$	10.7222	+	8.02656i	0.855727	+	0.640589i	−0.0786394	+	0.996903i	$0.525058\pi$
$158$	6.43558	+	1.39997i	0.511987	+	0.111376i
$159$	6.20183	−	7.15729i	0.491837	−	0.567610i
$160$	−2.23017	+	0.162333i	−0.176310	+	0.0128335i
$161$	2.36351	+	0.187985i	0.186271	+	0.0148153i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	0.117423	+	1.64179i	0.00919730	+	0.128595i	0.999976	−	0.00689326i	$-0.00219421\pi$
$163$	0.117423	+	1.64179i	0.00919730	+	0.128595i	−0.990779	+	0.135488i	$0.956740\pi$
$164$	−5.10383	−	7.94172i	−0.398542	−	0.620144i
$165$	2.03822	+	9.31296i	0.158675	+	0.725013i
$166$	14.6830	−	6.70552i	1.13963	−	0.520450i
$167$	10.5438	−	7.89300i	0.815905	−	0.610779i	−0.107675	−	0.994186i	$-0.534340\pi$
$167$	10.5438	−	7.89300i	0.815905	−	0.610779i	0.923579	+	0.383408i	$0.125250\pi$
$168$	−0.433910	−	0.236933i	−0.0334769	−	0.0182797i
$169$	7.02843	−	10.9365i	0.540649	−	0.841266i
$170$	−6.54369	−	14.2810i	−0.501878	−	1.09530i
$171$	2.00172	−	6.81724i	0.153076	−	0.521328i
$172$	7.62623	+	0.545439i	0.581495	+	0.0415893i
$173$	−2.92036	−	0.208869i	−0.222031	−	0.0158800i	−0.0401196	−	0.999195i	$-0.512774\pi$
$173$	−2.92036	−	0.208869i	−0.222031	−	0.0158800i	−0.181912	+	0.983315i	$0.558228\pi$
$174$	1.31219	−	4.46889i	0.0994766	−	0.338786i
$175$	−2.16655	+	1.19013i	−0.163776	+	0.0899656i
$176$	−2.30500	+	3.58665i	−0.173746	+	0.270354i
$177$	−5.41614	−	2.95743i	−0.407102	−	0.222294i
$178$	7.46954	−	5.59163i	0.559866	−	0.419110i
$179$	10.5319	−	4.80975i	0.787190	−	0.359498i	0.0190819	−	0.999818i	$-0.493926\pi$
$179$	10.5319	−	4.80975i	0.787190	−	0.359498i	0.768108	+	0.640320i	$0.221198\pi$
$180$	1.88262	+	1.20654i	0.140322	+	0.0899298i
$181$	12.1550	+	18.9135i	0.903471	+	1.40583i	0.913925	+	0.405882i	$0.133036\pi$
$181$	12.1550	+	18.9135i	0.903471	+	1.40583i	−0.0104548	+	0.999945i	$0.503328\pi$
$182$	−0.179837	−	2.51446i	−0.0133304	−	0.186384i
$183$	−3.28557	−	3.28557i	−0.242876	−	0.242876i
$184$	−2.84335	−	3.86204i	−0.209614	−	0.284714i
$185$	0.680244	+	9.34534i	0.0500125	+	0.687083i
$186$	−0.0760526	+	0.0877694i	−0.00557645	+	0.00643556i
$187$	−29.2672	−	6.36668i	−2.14023	−	0.465578i
$188$	0.981985	+	0.735105i	0.0716186	+	0.0536130i
$189$	0.205374	+	0.449707i	0.0149388	+	0.0327113i
$190$	1.11340	−	15.8483i	0.0807744	−	1.14976i
$191$	4.03747	+	13.7503i	0.292141	+	0.994940i	0.966528	+	0.256562i	$0.0825898\pi$
$191$	4.03747	+	13.7503i	0.292141	+	0.994940i	−0.674387	+	0.738378i	$0.735592\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	−0.915025	−	2.45328i	−0.0658650	−	0.176591i	0.899848	−	0.436204i	$-0.143678\pi$
$193$	−0.915025	−	2.45328i	−0.0658650	−	0.176591i	−0.965713	+	0.259614i	$0.916405\pi$
$194$	17.6966	+	5.19618i	1.27054	+	0.373064i
$195$	0.0143845	+	11.4018i	0.00103009	+	0.816499i
$196$	4.42397	+	5.10553i	0.315998	+	0.364681i
$197$	−7.01961	−	12.8555i	−0.500126	−	0.915913i	−0.998793	−	0.0491191i	$-0.984359\pi$
$197$	−7.01961	−	12.8555i	−0.500126	−	0.915913i	0.498667	−	0.866794i	$-0.333823\pi$
$198$	3.99465	−	1.48993i	0.283888	−	0.105885i
$199$	19.5276	+	12.5496i	1.38428	+	0.889620i	0.999443	−	0.0333660i	$-0.0106227\pi$
$199$	19.5276	+	12.5496i	1.38428	+	0.889620i	0.384833	+	0.922986i	$0.374259\pi$
$200$	4.68914	+	1.73549i	0.331572	+	0.122718i
$201$	1.42640	+	0.205086i	0.100611	+	0.0144656i
$202$	−3.26696	+	8.75907i	−0.229863	+	0.616286i
$203$	1.37991	−	1.84334i	0.0968505	−	0.129377i
$204$	−5.90997	+	3.79810i	−0.413780	+	0.265920i
$205$	3.03052	+	20.8906i	0.211660	+	1.45906i
$206$		−	10.2765i		−	0.715997i
$207$	−0.0382184	+	4.79568i	−0.00265636	+	0.333323i
$208$	−3.60556	+	3.60556i	−0.250001	+	0.250001i
$209$	−22.8933	−	19.8371i	−1.58356	−	1.37216i
$210$	0.663602	+	0.884141i	0.0457929	+	0.0610115i
$211$	−2.49144	−	17.3283i	−0.171518	−	1.19293i	−0.875680	−	0.482892i	$-0.839586\pi$
$211$	−2.49144	−	17.3283i	−0.171518	−	1.19293i	0.704163	−	0.710039i	$-0.251323\pi$
$212$	−8.87334	−	3.30959i	−0.609424	−	0.227303i
$213$	−0.783166	−	1.04619i	−0.0536617	−	0.0716836i
$214$	0.660406	−	0.193913i	0.0451444	−	0.0132556i
$215$	−15.0154	−	8.17446i	−1.02404	−	0.557494i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−0.0503923	+	0.0275163i	−0.00342085	+	0.00186793i
$218$	−0.996107	+	13.9274i	−0.0674649	+	0.943282i
$219$	4.61899	−	4.00238i	0.312123	−	0.270456i
$220$	8.01349	−	5.16426i	0.540270	−	0.348174i
$221$	−32.5846	−	14.8809i	−2.19188	−	1.00100i
$222$	4.09466	−	0.890738i	0.274815	−	0.0597824i
$223$	−7.45356	+	13.6502i	−0.499127	+	0.914083i	0.499725	+	0.866184i	$0.333434\pi$
$223$	−7.45356	+	13.6502i	−0.499127	+	0.914083i	−0.998852	+	0.0478990i	$0.984747\pi$
$224$	−0.0703580	+	0.489351i	−0.00470099	+	0.0326961i
$225$	−2.71381	−	4.19943i	−0.180921	−	0.279962i
$226$	−5.79126	+	0.832657i	−0.385229	+	0.0553875i
$227$	5.17078	−	23.7697i	0.343197	−	1.57765i	−0.405092	−	0.914276i	$-0.632761\pi$
$227$	5.17078	−	23.7697i	0.343197	−	1.57765i	0.748289	−	0.663373i	$-0.230876\pi$
$228$	−7.08695	+	0.506868i	−0.469344	+	0.0335682i
$229$	−22.3228			−1.47513			−0.737565	−	0.675276i	$-0.764024\pi$
$229$	−22.3228			−1.47513			−0.737565	+	0.675276i	$0.764024\pi$
$230$	2.20917	+	10.4938i	0.145668	+	0.691940i
$231$	2.10778			0.138682
$232$	−4.64569	+	0.332266i	−0.305005	+	0.0218144i
$233$	−0.114595	+	0.526783i	−0.00750734	+	0.0345107i	−0.980748	−	0.195277i	$-0.937439\pi$
$233$	−0.114595	+	0.526783i	−0.00750734	+	0.0345107i	0.973241	+	0.229787i	$0.0738031\pi$
$234$	5.04714	−	0.725669i	0.329942	−	0.0474385i
$235$	−1.31756	−	2.40570i	−0.0859479	−	0.156931i
$236$	−0.878222	+	6.10817i	−0.0571674	+	0.397608i
$237$	−3.15638	+	5.78047i	−0.205029	+	0.375482i
$238$	−3.39376	+	0.738268i	−0.219985	+	0.0478548i
$239$	−11.2960	−	5.15870i	−0.730676	−	0.333688i	0.0150995	−	0.999886i	$-0.495193\pi$
$239$	−11.2960	−	5.15870i	−0.730676	−	0.333688i	−0.745775	+	0.666198i	$0.767921\pi$
$240$	0.472554	−	2.18556i	0.0305032	−	0.141078i
$241$	11.0459	−	9.57136i	0.711531	−	0.616545i	−0.221998	−	0.975047i	$-0.571258\pi$
$241$	11.0459	−	9.57136i	0.711531	−	0.616545i	0.933529	+	0.358502i	$0.116712\pi$
$242$	0.512010	−	7.15884i	0.0329133	−	0.460188i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	−1.93022	+	4.22660i	−0.123570	+	0.270581i
$245$	−4.27412	−	14.4887i	−0.273063	−	0.925647i
$246$	9.05794	−	2.65965i	0.577513	−	0.169573i
$247$	−21.7112	−	29.0027i	−1.38145	−	1.84540i
$248$	0.108813	+	0.0405852i	0.00690964	+	0.00257716i
$249$	2.29721	+	15.9774i	0.145580	+	1.01253i
$250$	−7.93556	−	7.87572i	−0.501889	−	0.498104i
$251$	11.0395	+	9.56582i	0.696810	+	0.603789i	0.929526	−	0.368755i	$-0.120216\pi$
$251$	11.0395	+	9.56582i	0.696810	+	0.603789i	−0.232717	+	0.972545i	$0.574761\pi$
$252$	0.349582	−	0.349582i	0.0220216	−	0.0220216i
$253$	18.5308	+	8.64188i	1.16502	+	0.543310i
$254$		−	1.00780i		−	0.0632347i
$255$	15.5461	−	2.25521i	0.973533	−	0.141227i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−7.22501	+	9.65148i	−0.450684	+	0.602043i	−0.967132	−	0.254276i	$-0.918163\pi$
$257$	−7.22501	+	9.65148i	−0.450684	+	0.602043i	0.516448	+	0.856319i	$0.327254\pi$
$258$	−2.67190	+	7.16365i	−0.166345	+	0.445989i
$259$	2.05059	+	0.294830i	0.127417	+	0.0183198i
$260$	10.6779	−	3.99799i	0.662214	−	0.247945i
$261$	3.91819	+	2.51807i	0.242530	+	0.155864i
$262$	−8.00251	+	2.98478i	−0.494397	+	0.184400i
$263$	0.977446	+	1.79006i	0.0602719	+	0.110380i	0.906078	−	0.423111i	$-0.139062\pi$
$263$	0.977446	+	1.79006i	0.0602719	+	0.110380i	−0.845806	+	0.533490i	$0.820880\pi$
$264$	−2.79198	−	3.22211i	−0.171834	−	0.198307i
$265$	14.9930	+	14.9552i	0.921012	+	0.918691i
$266$	−3.37033	−	0.989618i	−0.206648	−	0.0606774i
$267$	3.26072	+	8.74232i	0.199553	+	0.535021i
$268$	−0.306321	−	1.40814i	−0.0187116	−	0.0860156i
$269$	−0.167546	−	0.570609i	−0.0102154	−	0.0347906i	0.954228	−	0.299082i	$-0.0966803\pi$
$269$	−0.167546	−	0.570609i	−0.0102154	−	0.0347906i	−0.964443	+	0.264291i	$0.914862\pi$
$270$	−1.68806	+	1.46644i	−0.102732	+	0.0892449i
$271$	6.93045	+	15.1756i	0.420995	+	0.921851i	0.994703	+	0.102791i	$0.0327772\pi$
$271$	6.93045	+	15.1756i	0.420995	+	0.921851i	−0.573708	+	0.819060i	$0.694496\pi$
$272$	5.62395	+	4.21004i	0.341002	+	0.255271i
$273$	2.46327	+	0.535851i	0.149084	+	0.0324312i
$274$	−13.6951	+	15.8050i	−0.827350	+	0.954813i
$275$	−21.0926	+	3.08700i	−1.27193	+	0.186153i
$276$	4.50667	−	1.64011i	0.271269	−	0.0987230i
$277$	16.0642	+	16.0642i	0.965203	+	0.965203i	0.999415	−	0.0342117i	$-0.0108921\pi$
$277$	16.0642	+	16.0642i	0.965203	+	0.965203i	−0.0342117	+	0.999415i	$0.510892\pi$
$278$	−0.00782566	−	0.109417i	−0.000469352	−	0.00656240i
$279$	−0.0627876	−	0.0976994i	−0.00375900	−	0.00584911i
$280$	0.596491	−	0.930737i	0.0356471	−	0.0556222i
$281$	−29.8138	+	13.6155i	−1.77854	+	0.812232i	−0.801867	+	0.597503i	$0.796160\pi$
$281$	−29.8138	+	13.6155i	−1.77854	+	0.812232i	−0.976674	+	0.214729i	$0.931113\pi$
$282$	−0.981985	+	0.735105i	−0.0584764	+	0.0437749i
$283$	−5.73483	−	3.13146i	−0.340900	−	0.186146i	0.299674	−	0.954042i	$-0.403122\pi$
$283$	−5.73483	−	3.13146i	−0.340900	−	0.186146i	−0.640575	+	0.767896i	$0.721304\pi$
$284$	−0.706537	+	1.09939i	−0.0419252	+	0.0652370i
$285$	14.8927	+	5.53328i	0.882165	+	0.327763i
$286$	6.12474	−	20.8590i	0.362164	−	1.23342i
$287$	4.65525	+	0.332950i	0.274791	+	0.0196534i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	−9.11497	+	31.0428i	−0.536175	+	1.82604i
$290$	9.76256	+	3.62722i	0.573277	+	0.212998i
$291$	−9.97139	+	15.5158i	−0.584533	+	0.909552i
$292$	−5.36420	−	2.92908i	−0.313916	−	0.171411i
$293$	2.80219	−	2.09769i	0.163706	−	0.122549i	−0.514284	−	0.857620i	$-0.671942\pi$
$293$	2.80219	−	2.09769i	0.163706	−	0.122549i	0.677990	+	0.735071i	$0.262851\pi$
$294$	−6.14510	+	2.80637i	−0.358389	+	0.163671i
$295$	7.44550	−	11.6176i	0.433494	−	0.676405i
$296$	−2.26551	−	3.52521i	−0.131680	−	0.204899i
$297$	0.304152	+	4.25260i	0.0176487	+	0.246761i
$298$	12.3898	+	12.3898i	0.717720	+	0.717720i
$299$	19.4591	+	14.8104i	1.12535	+	0.856505i
$300$	−2.98628	+	4.01025i	−0.172413	+	0.231532i
$301$	−2.47532	+	2.85667i	−0.142675	+	0.164656i
$302$	−9.64211	−	2.09751i	−0.554841	−	0.120698i
$303$	−7.48385	−	5.60234i	−0.429936	−	0.321846i
$304$	2.95154	+	6.46298i	0.169283	+	0.370677i
$305$	7.84356	−	6.81383i	0.449121	−	0.390159i
$306$	−1.97922	−	6.74062i	−0.113145	−	0.385336i
$307$	−7.13768	−	32.8114i	−0.407369	−	1.87264i	−0.483180	−	0.875521i	$-0.660518\pi$
$307$	−7.13768	−	32.8114i	−0.407369	−	1.87264i	0.0758111	−	0.997122i	$-0.475845\pi$
$308$	−0.736595	−	1.97489i	−0.0419714	−	0.112530i
$309$	9.86022	+	2.89522i	0.560928	+	0.164703i
$310$	−0.183858	−	0.183395i	−0.0104424	−	0.0104161i
$311$	16.8548	+	19.4515i	0.955747	+	1.10299i	0.994604	+	0.103746i	$0.0330829\pi$
$311$	16.8548	+	19.4515i	0.955747	+	1.10299i	−0.0388568	+	0.999245i	$0.512372\pi$
$312$	−2.44371	−	4.47532i	−0.138348	−	0.253365i
$313$	−11.7033	+	4.36512i	−0.661512	+	0.246731i	−0.657721	−	0.753262i	$-0.728479\pi$
$313$	−11.7033	+	4.36512i	−0.661512	+	0.246731i	−0.00379076	+	0.999993i	$0.501207\pi$
$314$	11.2675	+	7.24119i	0.635863	+	0.408644i
$315$	−1.03529	+	0.387630i	−0.0583317	+	0.0218405i
$316$	6.51906	+	0.937299i	0.366726	+	0.0527272i
$317$	4.30349	−	11.5381i	0.241708	−	0.648045i	−0.758284	−	0.651924i	$-0.773962\pi$
$317$	4.30349	−	11.5381i	0.241708	−	0.648045i	0.999992	+	0.00387908i	$0.00123475\pi$
$318$	5.67543	−	7.58149i	0.318262	−	0.425149i
$319$	16.7051	−	10.7357i	0.935303	−	0.601083i
$320$	−2.21290	+	0.321018i	−0.123705	+	0.0179454i
$321$			0.688286i			0.0384164i
$322$	2.37090	+	0.0188945i	0.132125	+	0.00105295i
$323$	−35.2947	+	35.2947i	−1.96385	+	1.96385i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−25.4347	−	1.75464i	−1.41087	−	0.0973296i
$326$	0.234248	+	1.62923i	0.0129738	+	0.0902348i
$327$	−13.0826	−	4.87956i	−0.723469	−	0.269840i
$328$	−5.65738	−	7.55738i	−0.312377	−	0.417287i
$329$	−0.581871	+	0.170853i	−0.0320796	+	0.00941942i
$330$	2.69741	+	9.14383i	0.148487	+	0.503351i
$331$	−3.34080	+	7.31533i	−0.183627	+	0.402087i	−0.978950	−	0.204099i	$-0.934574\pi$
$331$	−3.34080	+	7.31533i	−0.183627	+	0.402087i	0.795324	+	0.606185i	$0.207301\pi$
$332$	14.1673	−	7.73592i	0.777530	−	0.424563i
$333$	−0.298941	+	4.17975i	−0.0163819	+	0.229049i
$334$	9.95387	−	8.62508i	0.544651	−	0.471943i
$335$	−0.680982	+	3.14955i	−0.0372060	+	0.172078i
$336$	−0.449707	−	0.205374i	−0.0245335	−	0.0112041i
$337$	−13.0991	+	2.84953i	−0.713552	+	0.155224i	−0.554666	−	0.832073i	$-0.687154\pi$
$337$	−13.0991	+	2.84953i	−0.713552	+	0.155224i	−0.158886	+	0.987297i	$0.550790\pi$
$338$	6.23033	−	11.4100i	0.338885	−	0.620622i
$339$	0.832657	−	5.79126i	0.0452237	−	0.314538i
$340$	−7.54581	−	13.7778i	−0.409229	−	0.747205i
$341$	−0.490100	+	0.0704657i	−0.0265404	+	0.00381593i
$342$	1.51029	−	6.94268i	0.0816669	−	0.375417i
$343$	−6.78320	+	0.485144i	−0.366258	+	0.0261953i
$344$	7.64571			0.412229
$345$	−10.6911	−	0.836757i	−0.575590	−	0.0450495i
$346$	−2.92782			−0.157401
$347$	35.3623	−	2.52916i	1.89835	−	0.135773i	0.927248	−	0.374447i	$-0.122168\pi$
$347$	35.3623	−	2.52916i	1.89835	−	0.135773i	0.971100	+	0.238675i	$0.0767130\pi$
$348$	0.990035	−	4.55112i	0.0530715	−	0.243966i
$349$	7.21943	−	1.03800i	0.386447	−	0.0555627i	0.0536466	−	0.998560i	$-0.482916\pi$
$349$	7.21943	−	1.03800i	0.386447	−	0.0555627i	0.332800	+	0.942997i	$0.392006\pi$
$350$	−2.07613	+	1.34166i	−0.110974	+	0.0717148i
$351$	−0.725669	+	5.04714i	−0.0387333	+	0.269396i
$352$	−2.04326	+	3.74195i	−0.108906	+	0.199447i
$353$	8.17240	−	1.77780i	0.434973	−	0.0946225i	0.0102531	−	0.999947i	$-0.496736\pi$
$353$	8.17240	−	1.77780i	0.434973	−	0.0946225i	0.424720	+	0.905325i	$0.360373\pi$
$354$	−5.61332	−	2.56352i	−0.298345	−	0.136249i
$355$	2.45632	−	1.58296i	0.130368	−	0.0840150i
$356$	7.05161	−	6.11025i	0.373734	−	0.323843i
$357$	0.247771	−	3.46429i	0.0131134	−	0.183349i
$358$	10.1619	−	5.54883i	0.537074	−	0.293265i
$359$	2.58281	−	5.65557i	0.136316	−	0.298490i	−0.829147	−	0.559030i	$-0.811174\pi$
$359$	2.58281	−	5.65557i	0.136316	−	0.298490i	0.965463	+	0.260541i	$0.0839008\pi$
$360$	1.96390	+	1.06916i	0.103507	+	0.0563495i
$361$	−30.2065	+	8.86942i	−1.58981	+	0.466812i
$362$	13.4733	+	17.9982i	0.708139	+	0.945962i
$363$	6.72461	+	2.50815i	0.352950	+	0.131644i
$364$	−0.358758	−	2.49522i	−0.0188040	−	0.130785i
$365$	8.20377	+	10.9302i	0.429405	+	0.572112i
$366$	−3.51159	−	3.04281i	−0.183554	−	0.159050i
$367$	−11.6888	+	11.6888i	−0.610150	+	0.610150i	−0.942985	−	0.332835i	$-0.891995\pi$
$367$	−11.6888	+	11.6888i	−0.610150	+	0.610150i	0.332835	+	0.942985i	$0.391995\pi$
$368$	−3.11162	−	3.64936i	−0.162204	−	0.190236i
$369$			9.44034i			0.491444i
$370$	1.34520	+	9.27300i	0.0699336	+	0.482081i
$371$	3.93878	−	2.53130i	0.204491	−	0.131418i
$372$	−0.0695974	+	0.0929713i	−0.00360846	+	0.00482034i
$373$	1.72239	−	4.61792i	0.0891822	−	0.239107i	−0.884700	−	0.466161i	$-0.845637\pi$
$373$	1.72239	−	4.61792i	0.0891822	−	0.239107i	0.973882	+	0.227054i	$0.0729095\pi$
$374$	−29.6468	−	4.26256i	−1.53300	−	0.220412i
$375$	9.79240	−	5.39527i	0.505677	−	0.278610i
$376$	1.03193	+	0.663178i	0.0532175	+	0.0342008i
$377$	22.2517	−	8.29945i	1.14602	−	0.427443i
$378$	0.236933	+	0.433910i	0.0121865	+	0.0223179i
$379$	0.316306	+	0.365037i	0.0162476	+	0.0187507i	0.763815	−	0.645435i	$-0.223324\pi$
$379$	0.316306	+	0.365037i	0.0162476	+	0.0187507i	−0.747568	+	0.664186i	$0.768778\pi$
$380$	−0.0200434	−	15.8874i	−0.00102821	−	0.815004i
$381$	0.966973	+	0.283929i	0.0495395	+	0.0145461i
$382$	5.00812	+	13.4273i	0.256238	+	0.686999i
$383$	−2.78486	−	12.8018i	−0.142300	−	0.654142i	−0.991933	−	0.126767i	$-0.959540\pi$
$383$	−2.78486	−	12.8018i	−0.142300	−	0.654142i	0.849633	−	0.527375i	$-0.176824\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	−0.330301	+	4.70156i	−0.0168337	+	0.239614i
$386$	−1.08771	−	2.38175i	−0.0553629	−	0.121228i
$387$	−6.12071	−	4.58191i	−0.311133	−	0.232911i
$388$	18.0222	+	3.92048i	0.914936	+	0.199032i
$389$	−16.6136	+	19.1731i	−0.842341	+	0.972113i	−0.999881	−	0.0153993i	$-0.995098\pi$
$389$	−16.6136	+	19.1731i	−0.842341	+	0.972113i	0.157540	+	0.987513i	$0.449644\pi$
$390$	0.827742	+	11.3717i	0.0419143	+	0.575829i
$391$	16.3818	−	29.4408i	0.828464	−	1.48889i
$392$	4.77692	+	4.77692i	0.241271	+	0.241271i
$393$	−0.609310	−	8.51926i	−0.0307356	−	0.429740i
$394$	−7.91882	−	12.3219i	−0.398944	−	0.620770i
$395$	−12.3991	−	7.94635i	−0.623868	−	0.399824i
$396$	3.87818	−	1.77111i	0.194886	−	0.0890015i
$397$	−16.1413	+	12.0832i	−0.810108	+	0.606439i	−0.921960	−	0.387286i	$-0.873413\pi$
$397$	−16.1413	+	12.0832i	−0.810108	+	0.606439i	0.111852	+	0.993725i	$0.464322\pi$
$398$	20.3731	+	11.1246i	1.02121	+	0.557625i
$399$	1.89906	−	2.95500i	0.0950721	−	0.147935i
$400$	4.80100	+	1.39655i	0.240050	+	0.0698277i
$401$	−9.34882	+	31.8392i	−0.466858	+	1.58997i	0.303808	+	0.952733i	$0.401742\pi$
$401$	−9.34882	+	31.8392i	−0.466858	+	1.58997i	−0.770666	+	0.637239i	$0.780076\pi$
$402$	1.43740	+	0.102805i	0.0716909	+	0.00512743i
$403$	−0.590671	−	0.0422456i	−0.0294234	−	0.00210440i
$404$	−2.63377	+	8.96981i	−0.131035	+	0.446265i
$405$	−0.931462	−	2.03283i	−0.0462847	−	0.101012i
$406$	1.24489	−	1.93709i	0.0617828	−	0.0961359i
$407$	15.6804	+	8.56213i	0.777247	+	0.424409i
$408$	−5.62395	+	4.21004i	−0.278427	+	0.208428i
$409$	16.5934	−	7.57794i	0.820490	−	0.374705i	0.0394774	−	0.999220i	$-0.487431\pi$
$409$	16.5934	−	7.57794i	0.820490	−	0.374705i	0.781013	+	0.624515i	$0.214703\pi$
$410$	4.51311	+	20.6211i	0.222887	+	1.01841i
$411$	−11.3064	−	17.5931i	−0.557704	−	0.867804i
$412$	−0.733116	−	10.2503i	−0.0361181	−	0.504996i
$413$	−2.15726	−	2.15726i	−0.106152	−	0.106152i
$414$	0.303999	+	4.78619i	0.0149407	+	0.235228i
$415$	−35.9988	+	2.62034i	−1.76711	+	0.128627i
$416$	−3.33916	+	3.85360i	−0.163716	+	0.188938i
$417$	0.107190	+	0.0233177i	0.00524910	+	0.00114187i
$418$	−24.2501	−	18.1534i	−1.18611	−	0.887911i
$419$	0.547002	+	1.19777i	0.0267228	+	0.0585148i	0.922523	−	0.385943i	$-0.126124\pi$
$419$	0.547002	+	1.19777i	0.0267228	+	0.0585148i	−0.895800	+	0.444457i	$0.853396\pi$
$420$	0.724985	+	0.834548i	0.0353756	+	0.0407218i
$421$	−5.34094	−	18.1896i	−0.260301	−	0.886505i	−0.981123	−	0.193385i	$-0.938053\pi$
$421$	−5.34094	−	18.1896i	−0.260301	−	0.886505i	0.720822	−	0.693121i	$-0.243765\pi$
$422$	−3.72128	−	17.1064i	−0.181149	−	0.832728i
$423$	−0.428671	−	1.14931i	−0.0208427	−	0.0558814i
$424$	−9.08684	−	2.66814i	−0.441296	−	0.129576i
$425$	2.59425	+	35.0300i	0.125840	+	1.69921i
$426$	−0.855805	−	0.987652i	−0.0414639	−	0.0478519i
$427$	−1.10091	−	2.01616i	−0.0532766	−	0.0975688i
$428$	0.644890	−	0.240531i	0.0311719	−	0.0116265i
$429$	18.2885	+	11.7533i	0.882977	+	0.567455i
$430$	−15.5603	−	7.08245i	−0.750385	−	0.341546i
$431$	17.9944	+	2.58721i	0.866762	+	0.124621i	0.561330	−	0.827592i	$-0.310290\pi$
$431$	17.9944	+	2.58721i	0.866762	+	0.124621i	0.305432	+	0.952214i	$0.401199\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	−1.04727	+	1.39899i	−0.0503285	+	0.0672310i	−0.824999	−	0.565134i	$-0.808825\pi$
$433$	−1.04727	+	1.39899i	−0.0503285	+	0.0672310i	0.774671	+	0.632365i	$0.217916\pi$
$434$	−0.0483009	+	0.0310411i	−0.00231852	+	0.00149002i
$435$	−6.23072	+	8.34520i	−0.298740	+	0.400122i
$436$			13.9630i			0.668705i
$437$	28.8113	−	18.1931i	1.37823	−	0.870294i
$438$	4.32170	−	4.32170i	0.206499	−	0.206499i
$439$	−10.2550	−	8.88598i	−0.489443	−	0.424105i	0.374856	−	0.927083i	$-0.377692\pi$
$439$	−10.2550	−	8.88598i	−0.489443	−	0.424105i	−0.864299	+	0.502978i	$0.832238\pi$
$440$	7.62466	−	5.72278i	0.363492	−	0.272823i
$441$	−0.961420	−	6.68682i	−0.0457819	−	0.318420i
$442$	−33.5631	−	12.5184i	−1.59644	−	0.595440i
$443$	20.1027	+	26.8541i	0.955109	+	1.27588i	0.961188	+	0.275895i	$0.0889742\pi$
$443$	20.1027	+	26.8541i	0.955109	+	1.27588i	−0.00607853	+	0.999982i	$0.501935\pi$
$444$	4.02068	−	1.18058i	0.190813	−	0.0560278i
$445$	−20.0113	+	5.90329i	−0.948628	+	0.279843i
$446$	−6.46077	+	14.1471i	−0.305927	+	0.669886i
$447$	−15.3785	+	8.39730i	−0.727378	+	0.397179i
$448$	−0.0352689	+	0.493123i	−0.00166630	+	0.0232979i
$449$	−9.61216	+	8.32899i	−0.453626	+	0.393069i	−0.851486	−	0.524377i	$-0.824298\pi$
$449$	−9.61216	+	8.32899i	−0.453626	+	0.393069i	0.397860	+	0.917446i	$0.369753\pi$
$450$	−3.00648	−	3.99513i	−0.141727	−	0.188332i
$451$	36.6114	+	16.7199i	1.72396	+	0.787307i
$452$	−5.71710	+	1.24368i	−0.268910	+	0.0584977i
$453$	4.72905	−	8.66060i	0.222190	−	0.406911i
$454$	3.46189	−	24.0780i	0.162475	−	1.13004i
$455$	−1.58126	+	5.41052i	−0.0741307	+	0.253649i
$456$	−7.03273	+	1.01115i	−0.329338	+	0.0473516i
$457$	6.11563	−	28.1131i	0.286077	−	1.31508i	−0.579775	−	0.814777i	$-0.696860\pi$
$457$	6.11563	−	28.1131i	0.286077	−	1.31508i	0.865852	−	0.500299i	$-0.166777\pi$
$458$	−22.2659	+	1.59249i	−1.04042	+	0.0744121i
$459$	7.02519			0.327908
$460$	2.95216	+	10.3094i	0.137645	+	0.480681i
$461$	9.07788			0.422799			0.211399	−	0.977400i	$-0.432198\pi$
$461$	9.07788			0.422799			0.211399	+	0.977400i	$0.432198\pi$
$462$	2.10241	−	0.150368i	0.0978132	−	0.00699574i
$463$	7.58866	−	34.8845i	0.352675	−	1.62122i	−0.369306	−	0.929308i	$-0.620405\pi$
$463$	7.58866	−	34.8845i	0.352675	−	1.62122i	0.721981	−	0.691913i	$-0.243232\pi$
$464$	−4.61015	+	0.662840i	−0.214021	+	0.0307716i
$465$	0.227765	−	0.124742i	0.0105623	−	0.00578478i
$466$	−0.0767223	+	0.533616i	−0.00355409	+	0.0247193i
$467$	−16.5954	+	30.3922i	−0.767942	+	1.40638i	0.141237	+	0.989976i	$0.454892\pi$
$467$	−16.5954	+	30.3922i	−0.767942	+	1.40638i	−0.909179	+	0.416406i	$0.863290\pi$
$468$	4.98251	−	1.08388i	0.230317	−	0.0501023i
$469$	0.648058	+	0.295958i	0.0299246	+	0.0136661i
$470$	−1.48582	−	2.30558i	−0.0685358	−	0.106349i
$471$	−10.1223	+	8.77102i	−0.466411	+	0.404147i
$472$	−0.440233	+	6.15525i	−0.0202633	+	0.283319i
$473$	−28.6099	+	15.6222i	−1.31548	+	0.718309i
$474$	−2.73596	+	5.99092i	−0.125667	+	0.275172i
$475$	−14.6761	+	32.3520i	−0.673387	+	1.48441i
$476$	−3.33245	+	0.978495i	−0.152743	+	0.0448493i
$477$	5.67543	+	7.58149i	0.259860	+	0.347133i
$478$	−11.6352	−	4.33971i	−0.532182	−	0.198494i
$479$	3.52086	+	24.4881i	0.160872	+	1.11889i	0.896994	+	0.442042i	$0.145746\pi$
$479$	3.52086	+	24.4881i	0.160872	+	1.11889i	−0.736122	+	0.676849i	$0.763345\pi$
$480$	0.315433	−	2.21371i	0.0143975	−	0.101041i
$481$	16.1482	+	13.9925i	0.736294	+	0.638003i
$482$	10.3350	−	10.3350i	0.470745	−	0.470745i
$483$	−0.686090	+	2.26954i	−0.0312182	+	0.103268i
$484$		−	7.17713i		−	0.326233i
$485$	−33.0465	−	24.6733i	−1.50056	−	1.12036i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	3.07236	−	4.10419i	0.139222	−	0.185979i	−0.725511	−	0.688210i	$-0.758397\pi$
$487$	3.07236	−	4.10419i	0.139222	−	0.185979i	0.864733	+	0.502232i	$0.167488\pi$
$488$	−1.62378	+	4.35353i	−0.0735053	+	0.197075i
$489$	−1.62923	−	0.234248i	−0.0736764	−	0.0105931i
$490$	−5.29684	−	14.1468i	−0.239287	−	0.639089i
$491$	6.21789	+	3.99600i	0.280609	+	0.180337i	0.673373	−	0.739303i	$-0.264845\pi$
$491$	6.21789	+	3.99600i	0.280609	+	0.180337i	−0.392764	+	0.919639i	$0.628481\pi$
$492$	8.84512	−	3.29906i	0.398769	−	0.148733i
$493$	−15.6811	−	28.7179i	−0.706243	−	1.29339i
$494$	−23.7249	−	27.3800i	−1.06743	−	1.23188i
$495$	−9.53339	+	0.0120273i	−0.428494	+	0.000540586i
$496$	0.111431	+	0.0327192i	0.00500341	+	0.00146913i
$497$	−0.225784	−	0.605349i	−0.0101278	−	0.0271536i
$498$	3.43117	+	15.7729i	0.153755	+	0.706799i
$499$	−3.85411	−	13.1259i	−0.172534	−	0.587596i	−0.999672	−	0.0255979i	$-0.991851\pi$
$499$	−3.85411	−	13.1259i	−0.172534	−	0.587596i	0.827139	−	0.561998i	$-0.189967\pi$
$500$	−8.47719	−	7.28953i	−0.379111	−	0.325998i
$501$	5.47137	+	11.9806i	0.244443	+	0.535255i
$502$	11.6938	+	8.75389i	0.521921	+	0.390705i
$503$	−20.1236	−	4.37762i	−0.897267	−	0.195188i	−0.259797	−	0.965663i	$-0.583656\pi$
$503$	−20.1236	−	4.37762i	−0.897267	−	0.195188i	−0.637470	+	0.770475i	$0.720019\pi$
$504$	0.323752	−	0.373630i	0.0144211	−	0.0166428i
$505$	13.6692	−	15.8153i	0.608270	−	0.703774i
$506$	19.1001	+	7.29789i	0.849104	+	0.324431i
$507$	9.19252	+	9.19252i	0.408254	+	0.408254i
$508$	−0.0718953	−	1.00523i	−0.00318984	−	0.0445998i
$509$	1.25267	+	1.94919i	0.0555235	+	0.0863962i	0.867905	−	0.496729i	$-0.165466\pi$
$509$	1.25267	+	1.94919i	0.0555235	+	0.0863962i	−0.812382	+	0.583126i	$0.801830\pi$
$510$	15.3456	−	3.35851i	0.679514	−	0.148717i
$511$	2.74852	−	1.25521i	0.121587	−	0.0555271i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	6.23595	+	3.40509i	0.275324	+	0.150338i
$514$	−6.51807	+	10.1423i	−0.287500	+	0.447359i
$515$	−8.00315	+	21.5402i	−0.352661	+	0.949175i
$516$	−2.15405	+	7.33601i	−0.0948266	+	0.322950i
$517$	−5.21646	−	0.373089i	−0.229420	−	0.0164084i
$518$	2.06640	+	0.147792i	0.0907922	+	0.00649359i
$519$	0.824863	−	2.80923i	0.0362075	−	0.123311i
$520$	10.3655	−	4.74956i	0.454555	−	0.208282i
$521$	15.9114	−	24.7587i	0.697092	−	1.08470i	−0.294545	−	0.955638i	$-0.595168\pi$
$521$	15.9114	−	24.7587i	0.697092	−	1.08470i	0.991637	−	0.129059i	$-0.0411956\pi$
$522$	4.08784	+	2.23213i	0.178920	+	0.0976977i
$523$	−0.628295	+	0.470336i	−0.0274734	+	0.0205664i	−0.612926	−	0.790140i	$-0.710008\pi$
$523$	−0.628295	+	0.470336i	−0.0274734	+	0.0205664i	0.585453	+	0.810707i	$0.300917\pi$
$524$	−7.76919	+	3.54807i	−0.339399	+	0.154998i
$525$	−0.702401	−	2.37002i	−0.0306553	−	0.103436i
$526$	1.10266	+	1.71577i	0.0480781	+	0.0748110i
$527$	0.0582038	+	0.813795i	0.00253540	+	0.0354495i
$528$	−3.01472	−	3.01472i	−0.131199	−	0.131199i
$529$	−15.3369	+	17.1400i	−0.666822	+	0.745217i
$530$	16.0217	+	13.8475i	0.695937	+	0.601497i
$531$	4.04113	−	4.66371i	0.175370	−	0.202388i
$532$	−3.43234	−	0.746660i	−0.148811	−	0.0323718i
$533$	38.5354	+	28.8472i	1.66915	+	1.24951i
$534$	3.87608	+	8.48743i	0.167734	+	0.367287i
$535$	−1.53527	−	0.107858i	−0.0663755	−	0.00466311i
$536$	−0.405996	−	1.38270i	−0.0175364	−	0.0597234i
$537$	2.46112	+	11.3136i	0.106205	+	0.488217i
$538$	−0.207826	−	0.557202i	−0.00896000	−	0.0240227i
$539$	−27.6355	−	8.11452i	−1.19035	−	0.349517i
$540$	−1.57914	+	1.58313i	−0.0679555	+	0.0681272i
$541$	−10.9554	−	12.6433i	−0.471011	−	0.543576i	0.469681	−	0.882836i	$-0.344369\pi$
$541$	−10.9554	−	12.6433i	−0.471011	−	0.543576i	−0.940693	+	0.339260i	$0.889823\pi$
$542$	7.99541	+	14.6425i	0.343432	+	0.628949i
$543$	−21.0650	+	7.85683i	−0.903984	+	0.337169i
$544$	5.90997	+	3.79810i	0.253388	+	0.162842i
$545$	12.9343	−	28.4170i	0.554045	−	1.21725i
$546$	2.49522	+	0.358758i	0.106786	+	0.0153534i
$547$	6.54432	−	17.5460i	0.279815	−	0.750212i	−0.718679	−	0.695342i	$-0.755253\pi$
$547$	6.54432	−	17.5460i	0.279815	−	0.750212i	0.998494	−	0.0548701i	$-0.0174745\pi$
$548$	−12.5327	+	16.7417i	−0.535369	+	0.715170i
$549$	3.90888	−	2.51209i	0.166827	−	0.107213i
$550$	−20.8187	+	4.58387i	−0.887710	+	0.195457i
$551$		−	33.0922i		−	1.40977i
$552$	4.37818	−	1.95743i	0.186348	−	0.0833139i
$553$	−2.30238	+	2.30238i	−0.0979070	+	0.0979070i
$554$	17.1693	+	14.8772i	0.729452	+	0.632073i
$555$	−9.27637	−	1.32180i	−0.393760	−	0.0561072i
$556$	−0.0156114	−	0.108580i	−0.000662073	−	0.00460482i
$557$	6.68006	+	2.49153i	0.283043	+	0.105570i	0.486976	−	0.873415i	$-0.338100\pi$
$557$	6.68006	+	2.49153i	0.283043	+	0.105570i	−0.203933	+	0.978985i	$0.565373\pi$
$558$	−0.0695974	−	0.0929713i	−0.00294629	−	0.00393579i
$559$	−37.4066	+	10.9836i	−1.58213	+	0.464555i
$560$	0.528573	−	0.970919i	0.0223363	−	0.0410288i
$561$	12.4424	−	27.2450i	0.525317	−	1.15028i
$562$	−28.7665	+	15.7077i	−1.21344	+	0.662589i
$563$	1.23449	−	17.2605i	0.0520277	−	0.727442i	−0.902758	−	0.430148i	$-0.858461\pi$
$563$	1.23449	−	17.2605i	0.0520277	−	0.727442i	0.954786	−	0.297294i	$-0.0960842\pi$
$564$	−0.927042	+	0.803286i	−0.0390355	+	0.0338244i
$565$	12.7873	+	2.76482i	0.537967	+	0.116317i
$566$	−5.94362	−	2.71436i	−0.249829	−	0.114093i
$567$	−0.483085	+	0.105089i	−0.0202877	+	0.00441331i
$568$	−0.626307	+	1.14700i	−0.0262793	+	0.0481269i
$569$	5.88070	−	40.9012i	0.246532	−	1.71467i	−0.371433	−	0.928460i	$-0.621133\pi$
$569$	5.88070	−	40.9012i	0.246532	−	1.71467i	0.617965	−	0.786206i	$-0.287957\pi$
$570$	15.2495	+	4.45675i	0.638729	+	0.186673i
$571$	−12.8451	+	1.84685i	−0.537550	+	0.0772881i	−0.405743	−	0.913987i	$-0.632987\pi$
$571$	−12.8451	+	1.84685i	−0.537550	+	0.0772881i	−0.131807	+	0.991275i	$0.542078\pi$
$572$	4.62108	−	21.2428i	0.193217	−	0.888204i
$573$	−14.2943	+	1.02235i	−0.597154	+	0.0427093i
$574$	4.66714			0.194803
$575$	3.54180	−	23.7161i	0.147703	−	0.989032i
$576$	−1.00000			−0.0416667
$577$	16.6828	−	1.19318i	0.694515	−	0.0496727i	0.280381	−	0.959889i	$-0.409539\pi$
$577$	16.6828	−	1.19318i	0.694515	−	0.0496727i	0.414134	+	0.910216i	$0.364085\pi$
$578$	−6.87719	+	31.6139i	−0.286053	+	1.31497i
$579$	2.59172	−	0.372632i	0.107708	−	0.0154861i
$580$	9.99645	+	2.92153i	0.415080	+	0.121310i
$581$	−1.13570	+	7.89898i	−0.0471168	+	0.327705i
$582$	−8.83910	+	16.1876i	−0.366393	+	0.670998i
$583$	39.4542	−	8.58274i	1.63403	−	0.355461i
$584$	−5.55949	−	2.53893i	−0.230053	−	0.105062i
$585$	−11.1443	−	2.40957i	−0.460759	−	0.0996234i
$586$	2.64540	−	2.29226i	0.109281	−	0.0946922i
$587$	−2.22934	+	31.1702i	−0.0920147	+	1.28653i	0.716304	+	0.697788i	$0.245832\pi$
$587$	−2.22934	+	31.1702i	−0.0920147	+	1.28653i	−0.808319	+	0.588745i	$0.799622\pi$
$588$	−5.92924	+	3.23761i	−0.244518	+	0.133517i
$589$	−0.342779	+	0.750582i	−0.0141240	+	0.0309272i
$590$	6.59774	−	12.1192i	0.271625	−	0.498939i
$591$	14.0538	−	4.12656i	0.578096	−	0.169744i
$592$	−2.51123	−	3.35461i	−0.103211	−	0.137873i
$593$	35.2141	+	13.1342i	1.44607	+	0.539356i	0.945293	−	0.326221i	$-0.105775\pi$
$593$	35.2141	+	13.1342i	1.44607	+	0.539356i	0.500776	+	0.865577i	$0.333048\pi$
$594$	0.606754	+	4.22007i	0.0248954	+	0.173152i
$595$	7.68851	+	1.09554i	0.315198	+	0.0449128i
$596$	13.2421	+	11.4743i	0.542417	+	0.470007i
$597$	−16.4137	+	16.4137i	−0.671769	+	0.671769i
$598$	20.4661	+	13.3844i	0.836922	+	0.547330i
$599$		−	32.8294i		−	1.34137i	−0.741742	−	0.670686i	$-0.766000\pi$
$599$		−	32.8294i		−	1.34137i	0.741742	−	0.670686i	$-0.234000\pi$
$600$	−2.69258	+	4.21307i	−0.109924	+	0.171998i
$601$	9.48094	−	6.09303i	0.386736	−	0.248540i	−0.332797	−	0.942998i	$-0.607992\pi$
$601$	9.48094	−	6.09303i	0.386736	−	0.248540i	0.719533	+	0.694459i	$0.244356\pi$
$602$	−2.26522	+	3.02597i	−0.0923233	+	0.123330i
$603$	−0.503602	+	1.35021i	−0.0205083	+	0.0549848i
$604$	−9.76718	−	1.40431i	−0.397421	−	0.0571405i
$605$	−6.64839	+	14.6067i	−0.270295	+	0.593846i
$606$	−7.86445	−	5.05418i	−0.319472	−	0.205312i
$607$	−15.4177	+	5.75052i	−0.625787	+	0.233406i	−0.642295	−	0.766457i	$-0.722018\pi$
$607$	−15.4177	+	5.75052i	−0.625787	+	0.233406i	0.0165086	+	0.999864i	$0.494745\pi$
$608$	3.40509	+	6.23595i	0.138095	+	0.252901i
$609$	1.50789	+	1.74020i	0.0611030	+	0.0705166i
$610$	7.33748	−	7.35602i	0.297086	−	0.297837i
$611$	−6.00138	−	1.76217i	−0.242790	−	0.0712896i
$612$	−2.45505	−	6.58225i	−0.0992396	−	0.266072i
$613$	−1.98105	−	9.10674i	−0.0800139	−	0.367818i	0.919677	−	0.392675i	$-0.128450\pi$
$613$	−1.98105	−	9.10674i	−0.0800139	−	0.367818i	−0.999691	+	0.0248576i	$0.992087\pi$
$614$	−9.46022	−	32.2186i	−0.381784	−	1.30024i
$615$	−21.0573	−	1.47935i	−0.849114	−	0.0596532i
$616$	−0.875605	−	1.91731i	−0.0352791	−	0.0772506i
$617$	11.5869	+	8.67384i	0.466471	+	0.349195i	0.806515	−	0.591214i	$-0.201351\pi$
$617$	11.5869	+	8.67384i	0.466471	+	0.349195i	−0.340044	+	0.940409i	$0.610442\pi$
$618$	10.0416	+	2.18443i	0.403934	+	0.0878705i
$619$	−7.20691	+	8.31722i	−0.289670	+	0.334297i	−0.881869	−	0.471495i	$-0.843715\pi$
$619$	−7.20691	+	8.31722i	−0.289670	+	0.334297i	0.592199	+	0.805792i	$0.298260\pi$
$620$	−0.196473	−	0.169811i	−0.00789053	−	0.00681978i
$621$	−4.67796	−	1.05674i	−0.187720	−	0.0424055i
$622$	18.1995	+	18.1995i	0.729733	+	0.729733i
$623$	0.329080	+	4.60114i	0.0131843	+	0.184341i
$624$	−2.75675	−	4.28958i	−0.110358	−	0.171721i
$625$	10.5000	+	22.6881i	0.420000	+	0.907524i
$626$	−11.3621	+	5.18890i	−0.454121	+	0.207390i
$627$	24.2501	−	18.1534i	0.968455	−	0.724977i
$628$	11.7554	+	6.41893i	0.469091	+	0.256143i
$629$	15.9157	−	24.7652i	0.634599	−	0.987455i
$630$	−1.00499	+	0.460499i	−0.0400399	+	0.0183467i
$631$	5.82708	−	19.8452i	0.231972	−	0.790025i	−0.758423	−	0.651762i	$-0.774030\pi$
$631$	5.82708	−	19.8452i	0.231972	−	0.790025i	0.990396	−	0.138263i	$-0.0441518\pi$
$632$	6.56931	+	0.469846i	0.261313	+	0.0186895i
$633$	17.4619	+	1.24890i	0.694048	+	0.0496393i
$634$	3.46941	−	11.8157i	0.137788	−	0.469262i
$635$	−0.784853	+	2.11241i	−0.0311460	+	0.0838284i
$636$	5.12012	−	7.96705i	0.203026	−	0.315914i
$637$	−30.2334	−	16.5087i	−1.19789	−	0.654098i
$638$	15.8966	−	11.9001i	0.629353	−	0.471128i
$639$	1.18875	−	0.542885i	0.0470264	−	0.0214762i
$640$	−2.18437	+	0.478067i	−0.0863446	+	0.0188972i
$641$	−1.80524	−	2.80900i	−0.0713026	−	0.110949i	0.803771	−	0.594939i	$-0.202824\pi$
$641$	−1.80524	−	2.80900i	−0.0713026	−	0.110949i	−0.875074	+	0.483990i	$0.839187\pi$
$642$	0.0491018	+	0.686533i	0.00193789	+	0.0270953i
$643$	−9.93736	−	9.93736i	−0.391891	−	0.391891i	0.483470	−	0.875361i	$-0.339376\pi$
$643$	−9.93736	−	9.93736i	−0.391891	−	0.391891i	−0.875361	+	0.483470i	$0.839376\pi$
$644$	2.36621	−	0.150292i	0.0932417	−	0.00592233i
$645$	11.1794	−	12.9347i	0.440189	−	0.509302i
$646$	−32.6869	+	37.7227i	−1.28605	+	1.48418i
$647$	32.5683	+	7.08479i	1.28039	+	0.278532i	0.800785	−	0.598952i	$-0.204416\pi$
$647$	32.5683	+	7.08479i	1.28039	+	0.278532i	0.479606	+	0.877484i	$0.340780\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	−10.9295	−	23.9322i	−0.429019	−	0.939420i
$650$	−25.4951	+	0.0643292i	−1.00000	+	0.00252320i
$651$	−0.0161758	−	0.0550897i	−0.000633980	−	0.00215914i
$652$	0.349879	+	1.60837i	0.0137023	+	0.0629886i
$653$	−12.5420	−	33.6265i	−0.490807	−	1.31591i	−0.912467	−	0.409151i	$-0.865825\pi$
$653$	−12.5420	−	33.6265i	−0.490807	−	1.31591i	0.421659	−	0.906754i	$-0.361448\pi$
$654$	−13.3974	−	3.93382i	−0.523879	−	0.153825i
$655$	19.0983	−	0.0240943i	0.746232	−	0.000941444i
$656$	−6.18211	−	7.13453i	−0.241371	−	0.278557i
$657$	2.92908	+	5.36420i	0.114274	+	0.209277i
$658$	−0.568200	+	0.211928i	−0.0221507	+	0.00826180i
$659$	5.29764	+	3.40459i	0.206367	+	0.132624i	0.639742	−	0.768590i	$-0.279041\pi$
$659$	5.29764	+	3.40459i	0.206367	+	0.132624i	−0.433375	+	0.901214i	$0.642678\pi$
$660$	3.34285	+	8.92810i	0.130120	+	0.347526i
$661$	−16.2026	−	2.32959i	−0.630209	−	0.0906104i	−0.180194	−	0.983631i	$-0.557672\pi$
$661$	−16.2026	−	2.32959i	−0.630209	−	0.0906104i	−0.450016	+	0.893021i	$0.648582\pi$
$662$	−2.81042	+	7.53502i	−0.109230	+	0.292857i
$663$	21.4672	−	28.6768i	0.833715	−	1.11371i
$664$	13.5793	−	8.72689i	0.526979	−	0.338669i
$665$	6.29374	+	4.69906i	0.244061	+	0.182222i
$666$			4.19042i			0.162376i
$667$	6.12203	+	21.4815i	0.237046	+	0.831768i
$668$	9.31320	−	9.31320i	0.360339	−	0.360339i
$669$	−11.7539	−	10.1848i	−0.454430	−	0.393766i
$670$	−0.454561	+	3.19011i	−0.0175612	+	0.123245i
$671$	−2.81928	−	19.6085i	−0.108837	−	0.756979i
$672$	−0.463212	−	0.172769i	−0.0178688	−	0.00666472i
$673$	1.81545	+	2.42516i	0.0699805	+	0.0934831i	0.834166	−	0.551514i	$-0.185950\pi$
$673$	1.81545	+	2.42516i	0.0699805	+	0.0934831i	−0.764185	+	0.644997i	$0.776859\pi$
$674$	−12.8624	+	3.77675i	−0.495442	+	0.145475i
$675$	4.68032	−	1.75914i	0.180146	−	0.0677092i
$676$	5.40047	−	11.8254i	0.207711	−	0.454823i
$677$	10.4293	−	5.69480i	0.400829	−	0.218869i	−0.266173	−	0.963925i	$-0.585759\pi$
$677$	10.4293	−	5.69480i	0.400829	−	0.218869i	0.667002	+	0.745056i	$0.267577\pi$
$678$	0.417392	−	5.83590i	0.0160298	−	0.224127i
$679$	−6.89110	+	5.97117i	−0.264456	+	0.229152i
$680$	−8.50948	−	13.2044i	−0.326324	−	0.506364i
$681$	22.1273	+	10.1052i	0.847922	+	0.387233i
$682$	−0.483824	+	0.105250i	−0.0185266	+	0.00403021i
$683$	5.12457	−	9.38495i	0.196086	−	0.359105i	−0.761073	−	0.648666i	$-0.775327\pi$
$683$	5.12457	−	9.38495i	0.196086	−	0.359105i	0.957160	+	0.289561i	$0.0935092\pi$
$684$	1.01115	−	7.03273i	0.0386624	−	0.268903i
$685$	41.0144	−	22.4628i	1.56708	−	0.858259i
$686$	−6.73131	+	0.967816i	−0.257003	+	0.0369514i
$687$	4.74504	−	21.8126i	0.181035	−	0.832203i
$688$	7.62623	−	0.545439i	0.290747	−	0.0207947i
$689$	48.2902			1.83971
$690$	−10.7236	−	0.0719301i	−0.408239	−	0.00273833i
$691$	13.8122			0.525442			0.262721	−	0.964872i	$-0.415380\pi$
$691$	13.8122			0.525442			0.262721	+	0.964872i	$0.415380\pi$
$692$	−2.92036	+	0.208869i	−0.111016	+	0.00793999i
$693$	−0.448042	+	2.05962i	−0.0170197	+	0.0782383i
$694$	35.0918	−	5.04543i	1.33207	−	0.191522i
$695$	−0.0688089	+	0.235440i	−0.00261007	+	0.00893075i
$696$	0.662840	−	4.61015i	0.0251249	−	0.174747i
$697$	31.7839	−	58.2078i	1.20390	−	2.20478i
$698$	7.12698	−	1.55038i	0.269760	−	0.0586827i
$699$	−0.490385	−	0.223951i	−0.0185481	−	0.00847062i
$700$	−1.97513	+	1.48635i	−0.0746527	+	0.0561788i
$701$	−9.98141	+	8.64894i	−0.376992	+	0.326666i	−0.822661	−	0.568532i	$-0.807511\pi$
$701$	−9.98141	+	8.64894i	−0.376992	+	0.326666i	0.445669	+	0.895198i	$0.352966\pi$
$702$	−0.363761	+	5.08605i	−0.0137293	+	0.191960i
$703$	26.1313	−	14.2688i	0.985559	−	0.538156i
$704$	−1.77111	+	3.87818i	−0.0667511	+	0.146165i
$705$	2.63079	−	0.776077i	0.0990814	−	0.0292288i
$706$	8.02475	−	2.35628i	0.302015	−	0.0886797i
$707$	−2.76970	−	3.69989i	−0.104165	−	0.139149i
$708$	−5.78190	−	2.15654i	−0.217297	−	0.0810476i
$709$	−6.52545	−	45.3855i	−0.245068	−	1.70449i	−0.625949	−	0.779864i	$-0.715288\pi$
$709$	−6.52545	−	45.3855i	−0.245068	−	1.70449i	0.380880	−	0.924624i	$-0.375621\pi$
$710$	2.33714	−	1.75416i	0.0877112	−	0.0658326i
$711$	−4.97744	−	4.31297i	−0.186668	−	0.161749i
$712$	6.59774	−	6.59774i	0.247261	−	0.247261i
$713$	0.0836554	−	0.550648i	0.00313292	−	0.0206219i
$714$		−	3.47313i		−	0.129979i
$715$	−29.0825	+	38.9520i	−1.08762	+	1.45672i
$716$	9.74019	−	6.25964i	0.364008	−	0.233934i
$717$	7.44194	−	9.94127i	0.277924	−	0.371263i
$718$	2.17277	−	5.82542i	0.0810870	−	0.217403i
$719$	−8.26669	−	1.18857i	−0.308295	−	0.0443262i	−0.0135692	−	0.999908i	$-0.504319\pi$
$719$	−8.26669	−	1.18857i	−0.308295	−	0.0443262i	−0.294726	+	0.955582i	$0.595228\pi$
$720$	2.03517	+	0.926329i	0.0758463	+	0.0345223i
$721$	4.27401	+	2.74674i	0.159172	+	0.102294i
$722$	−29.4968	+	11.0017i	−1.09776	+	0.409442i
$723$	7.00464	+	12.8280i	0.260505	+	0.477080i
$724$	14.7229	+	16.9911i	0.547172	+	0.631471i
$725$	−17.6382	−	15.2058i	−0.655065	−	0.564729i
$726$	6.88640	+	2.02203i	0.255578	+	0.0750446i
$727$	13.7394	+	36.8368i	0.509566	+	1.36620i	0.896070	+	0.443913i	$0.146410\pi$
$727$	13.7394	+	36.8368i	0.509566	+	1.36620i	−0.386504	+	0.922288i	$0.626317\pi$
$728$	−0.535851	−	2.46327i	−0.0198600	−	0.0912948i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	8.96262	+	10.3171i	0.331721	+	0.381852i
$731$	22.3130	+	48.8587i	0.825277	+	1.80710i
$732$	−3.71971	−	2.78454i	−0.137485	−	0.102920i
$733$	23.6714	+	5.14939i	0.874321	+	0.190197i	0.627267	−	0.778805i	$-0.284174\pi$
$733$	23.6714	+	5.14939i	0.874321	+	0.190197i	0.247055	+	0.969002i	$0.420537\pi$
$734$	−10.8251	+	12.4929i	−0.399563	+	0.461121i
$735$	15.0661	−	1.09665i	0.555721	−	0.0404507i
$736$	−3.36403	−	3.41808i	−0.124000	−	0.125992i
$737$	4.34443	+	4.34443i	0.160029	+	0.160029i
$738$	0.673466	+	9.41629i	0.0247906	+	0.346618i
$739$	−15.7837	−	24.5600i	−0.580614	−	0.903454i	0.419376	−	0.907813i	$-0.362249\pi$
$739$	−15.7837	−	24.5600i	−0.580614	−	0.903454i	−0.999991	+	0.00435888i	$0.998613\pi$
$740$	2.00330	+	9.15341i	0.0736428	+	0.336486i
$741$	32.9550	−	15.0500i	1.21063	−	0.552877i
$742$	3.74816	−	2.80584i	0.137599	−	0.103006i
$743$	−14.2175	−	7.76333i	−0.521588	−	0.284809i	0.196809	−	0.980442i	$-0.436942\pi$
$743$	−14.2175	−	7.76333i	−0.521588	−	0.284809i	−0.718397	+	0.695633i	$0.755124\pi$
$744$	−0.0627876	+	0.0976994i	−0.00230191	+	0.00358184i
$745$	−16.3209	−	35.6187i	−0.597951	−	1.30497i
$746$	1.38857	−	4.72902i	0.0508390	−	0.173142i
$747$	−16.1006	−	1.15154i	−0.589091	−	0.0421326i
$748$	−29.8753	−	2.13673i	−1.09235	−	0.0781264i
$749$	−0.0958671	+	0.326493i	−0.00350291	+	0.0119298i
$750$	9.38256	−	6.08010i	0.342602	−	0.222014i
$751$	16.7656	−	26.0878i	0.611785	−	0.951956i	−0.387759	−	0.921761i	$-0.626751\pi$
$751$	16.7656	−	26.0878i	0.611785	−	0.951956i	0.999544	−	0.0301953i	$-0.00961293\pi$
$752$	1.07661	+	0.587872i	0.0392598	+	0.0214375i
$753$	−11.6938	+	8.75389i	−0.426147	+	0.319010i
$754$	21.6029	−	9.86572i	0.786732	−	0.359288i
$755$	18.5770	+	11.9056i	0.676087	+	0.433290i
$756$	0.267284	+	0.415902i	0.00972101	+	0.0151262i
$757$	1.33216	+	18.6261i	0.0484183	+	0.676976i	0.962472	+	0.271382i	$0.0874807\pi$
$757$	1.33216	+	18.6261i	0.0484183	+	0.676976i	−0.914053	+	0.405594i	$0.867065\pi$
$758$	0.341542	+	0.341542i	0.0124054	+	0.0124054i
$759$	−12.3834	+	16.2704i	−0.449489	+	0.590578i
$760$	−1.15338	−	15.8454i	−0.0418376	−	0.574775i
$761$	−7.74211	+	8.93487i	−0.280651	+	0.323889i	−0.878520	−	0.477705i	$-0.841469\pi$
$761$	−7.74211	+	8.93487i	−0.280651	+	0.323889i	0.597869	+	0.801594i	$0.296014\pi$
$762$	0.984765	+	0.214222i	0.0356743	+	0.00776046i
$763$	−5.52618	−	4.13685i	−0.200061	−	0.149764i
$764$	5.95325	+	13.0358i	0.215381	+	0.471618i
$765$	−1.10088	+	15.6702i	−0.0398026	+	0.566556i
$766$	−3.69104	−	12.5705i	−0.133363	−	0.454191i
$767$	−6.68859	−	30.7470i	−0.241511	−	1.11021i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	−44.2399	−	12.9900i	−1.59533	−	0.468432i	−0.641089	−	0.767466i	$-0.721517\pi$
$769$	−44.2399	−	12.9900i	−1.59533	−	0.468432i	−0.954242	+	0.299035i	$0.903335\pi$
$770$	0.00594609	+	4.71315i	0.000214282	+	0.169850i
$771$	−7.89513	−	9.11147i	−0.284336	−	0.328141i
$772$	−1.25485	−	2.29809i	−0.0451630	−	0.0827099i
$773$	−43.0735	+	16.0656i	−1.54925	+	0.577840i	−0.971221	−	0.238179i	$-0.923450\pi$
$773$	−43.0735	+	16.0656i	−1.54925	+	0.577840i	−0.578026	+	0.816018i	$0.696177\pi$
$774$	−6.43198	−	4.13358i	−0.231193	−	0.148579i
$775$	0.242554	+	0.527593i	0.00871281	+	0.0189517i
$776$	18.2559	+	2.62481i	0.655349	+	0.0942250i
$777$	−0.723976	+	1.94105i	−0.0259725	+	0.0696349i
$778$	−15.2034	+	20.3094i	−0.545070	+	0.728128i
$779$	56.4263	−	36.2630i	2.02168	−	1.29926i
$780$	1.63688	+	11.2837i	0.0586098	+	0.404021i
$781$		−	5.57171i		−	0.199372i
$782$	14.2398	−	30.5345i	0.509214	−	1.09191i
$783$	−3.29339	+	3.29339i	−0.117696	+	0.117696i
$784$	5.10553	+	4.42397i	0.182340	+	0.157999i
$785$	−17.9782	−	23.9530i	−0.641668	−	0.854918i
$786$	−1.21551	−	8.45409i	−0.0433560	−	0.301547i
$787$	29.1513	+	10.8729i	1.03913	+	0.387576i	0.810377	−	0.585909i	$-0.199262\pi$
$787$	29.1513	+	10.8729i	1.03913	+	0.387576i	0.228753	+	0.973484i	$0.426535\pi$
$788$	−8.77768	−	11.7256i	−0.312692	−	0.417707i
$789$	−1.95692	+	0.574604i	−0.0696682	+	0.0204564i
$790$	−12.9344	−	7.04156i	−0.460186	−	0.250528i
$791$	1.20161	−	2.63115i	0.0427242	−	0.0935529i
$792$	3.74195	−	2.04326i	0.132965	−	0.0726041i
$793$	1.69022	−	23.6323i	0.0600213	−	0.839208i
$794$	−15.2382	+	13.2039i	−0.540782	+	0.468590i
$795$	−17.8004	+	11.4714i	−0.631316	+	0.406848i
$796$	21.1149	+	9.64283i	0.748396	+	0.341781i
$797$	−0.324225	+	0.0705309i	−0.0114846	+	0.00249833i	−0.218304	−	0.975881i	$-0.570052\pi$
$797$	−0.324225	+	0.0705309i	−0.0114846	+	0.00249833i	0.206819	+	0.978379i	$0.433689\pi$
$798$	1.68342	−	3.08295i	0.0595923	−	0.109135i
$799$	−1.22639	+	8.52975i	−0.0433867	+	0.301761i
$800$	4.88840	+	1.05050i	0.172831	+	0.0371406i
$801$	−9.23564	+	1.32788i	−0.326325	+	0.0469185i
$802$	−7.05362	+	32.4250i	−0.249072	+	1.14497i
$803$	25.9911	−	1.85892i	0.917205	−	0.0655998i
$804$	1.44107			0.0508226
$805$	−4.95486	−	1.88602i	−0.174636	−	0.0664735i
$806$	−0.592180			−0.0208586
$807$	0.593183	−	0.0424253i	0.0208810	−	0.00149344i
$808$	−1.98717	+	9.13485i	−0.0699082	+	0.321363i
$809$	3.67752	−	0.528747i	0.129295	−	0.0185898i	−0.0773637	−	0.997003i	$-0.524650\pi$
$809$	3.67752	−	0.528747i	0.129295	−	0.0185898i	0.206658	+	0.978413i	$0.433741\pi$
$810$	−1.07411	−	1.96120i	−0.0377403	−	0.0689094i
$811$	−0.463899	+	3.22649i	−0.0162897	+	0.113297i	−0.996344	−	0.0854329i	$-0.972773\pi$
$811$	−0.463899	+	3.22649i	−0.0162897	+	0.113297i	0.980054	+	0.198730i	$0.0636818\pi$
$812$	1.10353	−	2.02096i	0.0387262	−	0.0709218i
$813$	−16.3019	+	3.54627i	−0.571734	+	0.124373i
$814$	16.2512	+	7.42169i	0.569605	+	0.260130i
$815$	0.777816	−	3.59741i	0.0272457	−	0.126012i
$816$	−5.30928	+	4.60052i	−0.185862	+	0.161050i
$817$	−3.87537	+	54.1848i	−0.135582	+	1.89568i
$818$	16.0105	−	8.74239i	0.559794	−	0.305671i
$819$	−1.04721	+	2.29307i	−0.0365925	+	0.0801264i
$820$	5.97271	+	20.2466i	0.208576	+	0.707044i
$821$	1.29350	−	0.379805i	0.0451433	−	0.0132553i	−0.259083	−	0.965855i	$-0.583420\pi$
$821$	1.29350	−	0.379805i	0.0451433	−	0.0132553i	0.304226	+	0.952600i	$0.401602\pi$
$822$	−12.5327	−	16.7417i	−0.437127	−	0.583933i
$823$	12.6415	+	4.71502i	0.440653	+	0.164355i	0.559991	−	0.828499i	$-0.310804\pi$
$823$	12.6415	+	4.71502i	0.440653	+	0.164355i	−0.119338	+	0.992854i	$0.538077\pi$
$824$	−1.46250	−	10.1719i	−0.0509485	−	0.354355i
$825$	1.46710	−	21.2668i	0.0510780	−	0.740414i
$826$	−2.30566	−	1.99787i	−0.0802242	−	0.0695147i
$827$	13.5933	−	13.5933i	0.472685	−	0.472685i	−0.430097	−	0.902783i	$-0.641521\pi$
$827$	13.5933	−	13.5933i	0.472685	−	0.472685i	0.902783	+	0.430097i	$0.141521\pi$
$828$	0.644667	+	4.75231i	0.0224037	+	0.165154i
$829$			20.9469i			0.727516i	0.931494	+	0.363758i	$0.118506\pi$
$829$			20.9469i			0.727516i	−0.931494	+	0.363758i	$0.881494\pi$
$830$	−35.7201	+	5.18179i	−1.23986	+	0.179862i
$831$	−19.1117	+	12.2824i	−0.662979	+	0.426071i
$832$	−3.05574	+	4.08199i	−0.105939	+	0.141518i
$833$	−16.5853	+	44.4669i	−0.574647	+	1.54069i
$834$	0.108580	+	0.0156114i	0.00375982	+	0.000540580i
$835$	−27.5810	+	10.3268i	−0.954481	+	0.357375i
$836$	−25.4834	−	16.3772i	−0.881360	−	0.566416i
$837$	0.108813	−	0.0405852i	0.00376113	−	0.00140283i
$838$	0.631056	+	1.15569i	0.0217995	+	0.0399228i
$839$	23.6901	+	27.3399i	0.817874	+	0.943876i	0.999218	−	0.0395432i	$-0.0125903\pi$
$839$	23.6901	+	27.3399i	0.817874	+	0.943876i	−0.181344	+	0.983420i	$0.558045\pi$
$840$	0.782674	+	0.780701i	0.0270048	+	0.0269368i
$841$	−7.01115	−	2.05866i	−0.241764	−	0.0709883i
$842$	−6.62496	−	17.7622i	−0.228311	−	0.612126i
$843$	−6.96696	−	32.0266i	−0.239955	−	1.10306i
$844$	−4.93215	−	16.7974i	−0.169772	−	0.578189i
$845$	−21.9451	+	19.0641i	−0.754934	+	0.655823i
$846$	−0.509570	−	1.11580i	−0.0175194	−	0.0383621i
$847$	2.84052	+	2.12639i	0.0976015	+	0.0730635i
$848$	−9.25403	−	2.01309i	−0.317785	−	0.0691298i
$849$	4.27892	−	4.93814i	0.146852	−	0.169476i
$850$	5.08665	+	34.7557i	0.174471	+	1.19211i
$851$	−14.3232	+	14.0967i	−0.490993	+	0.483229i
$852$	−0.924083	−	0.924083i	−0.0316586	−	0.0316586i
$853$	0.820759	+	11.4757i	0.0281022	+	0.392921i	0.991964	+	0.126519i	$0.0403804\pi$
$853$	0.820759	+	11.4757i	0.0281022	+	0.392921i	−0.963862	+	0.266402i	$0.914165\pi$
$854$	−1.24193	−	1.93249i	−0.0424981	−	0.0661283i
$855$	−8.57249	+	13.3761i	−0.293173	+	0.457454i
$856$	0.626087	−	0.285924i	0.0213992	−	0.00977270i
$857$	−19.6222	+	14.6890i	−0.670281	+	0.501766i	−0.879375	−	0.476130i	$-0.842039\pi$
$857$	−19.6222	+	14.6890i	−0.670281	+	0.501766i	0.209095	+	0.977895i	$0.432948\pi$
$858$	19.0804	+	10.4187i	0.651393	+	0.355687i
$859$	19.5646	−	30.4431i	0.667535	−	1.03871i	−0.328033	−	0.944666i	$-0.606386\pi$
$859$	19.5646	−	30.4431i	0.667535	−	1.03871i	0.995568	−	0.0940392i	$-0.0299779\pi$
$860$	−16.0259	−	5.95434i	−0.546480	−	0.203041i
$861$	−1.31489	+	4.47809i	−0.0448112	+	0.152613i
$862$	18.1332	+	1.29691i	0.617618	+	0.0441729i
$863$	6.26137	+	0.447822i	0.213140	+	0.0152440i	0.177501	−	0.984121i	$-0.443199\pi$
$863$	6.26137	+	0.447822i	0.213140	+	0.0152440i	0.0356389	+	0.999365i	$0.488653\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	6.13692	+	2.28014i	0.208661	+	0.0775269i
$866$	−0.944798	+	1.47013i	−0.0321055	+	0.0499572i
$867$	−28.3958	−	15.5053i	−0.964372	−	0.526587i
$868$	−0.0459634	+	0.0344078i	−0.00156010	+	0.00116788i
$869$	−25.5421	+	11.6647i	−0.866456	+	0.395697i
$870$	−5.61951	+	8.76843i	−0.190519	+	0.297278i
$871$	3.97267	+	6.18159i	0.134609	+	0.209455i
$872$	0.996107	+	13.9274i	0.0337324	+	0.471641i
$873$	−13.0416	−	13.0416i	−0.441392	−	0.441392i
$874$	27.4400	−	20.2021i	0.928172	−	0.683347i
$875$	5.39657	−	1.19536i	0.182437	−	0.0404106i
$876$	4.00238	−	4.61899i	0.135228	−	0.156061i
$877$	33.7515	+	7.34220i	1.13971	+	0.247928i	0.742530	−	0.669813i	$-0.233626\pi$
$877$	33.7515	+	7.34220i	1.13971	+	0.247928i	0.397178	+	0.917741i	$0.369989\pi$
$878$	−10.8628	−	8.13176i	−0.366600	−	0.274433i
$879$	1.45411	+	3.18405i	0.0490458	+	0.107395i
$880$	7.19698	−	6.25213i	0.242610	−	0.210759i
$881$	−3.73913	−	12.7343i	−0.125975	−	0.429030i	0.872219	−	0.489116i	$-0.162681\pi$
$881$	−3.73913	−	12.7343i	−0.125975	−	0.429030i	−0.998193	+	0.0600862i	$0.980862\pi$
$882$	−1.43600	−	6.60120i	−0.0483527	−	0.222274i
$883$	15.5976	+	41.8188i	0.524902	+	1.40732i	0.881111	+	0.472910i	$0.156796\pi$
$883$	15.5976	+	41.8188i	0.524902	+	1.40732i	−0.356209	+	0.934406i	$0.615931\pi$
$884$	−34.3707	−	10.0921i	−1.15601	−	0.339435i
$885$	9.76947	+	9.74486i	0.328397	+	0.327570i
$886$	21.9673	+	25.3516i	0.738004	+	0.851702i
$887$	15.1386	+	27.7243i	0.508305	+	0.930891i	0.998250	+	0.0591375i	$0.0188350\pi$
$887$	15.1386	+	27.7243i	0.508305	+	0.930891i	−0.489945	+	0.871753i	$0.662983\pi$
$888$	3.92621	−	1.46440i	0.131755	−	0.0491421i
$889$	0.419144	+	0.269367i	0.0140576	+	0.00903429i
$890$	−19.5392	+	7.31584i	−0.654956	+	0.245227i
$891$	−4.22007	−	0.606754i	−0.141378	−	0.0203270i
$892$	−5.43507	+	14.5720i	−0.181980	+	0.487906i
$893$	−5.22296	+	6.97705i	−0.174780	+	0.233478i
$894$	−14.7403	+	9.47299i	−0.492988	+	0.316824i
$895$	−25.6214	+	3.71680i	−0.856429	+	0.124239i
$896$			0.494383i			0.0165162i
$897$	−18.6082	+	15.8663i	−0.621311	+	0.529759i
$898$	−8.99349	+	8.99349i	−0.300117	+	0.300117i
$899$	−0.408791	−	0.354219i	−0.0136339	−	0.0118139i
$900$	−3.28383	−	3.77047i	−0.109461	−	0.125682i
$901$	−9.46845	−	65.8545i	−0.315440	−	2.19393i
$902$	37.7109	+	14.0654i	1.25563	+	0.468327i
$903$	−2.26522	−	3.02597i	−0.0753817	−	0.100698i
$904$	−5.61381	+	1.64836i	−0.186713	+	0.0548238i
$905$	−14.2242	−	48.2181i	−0.472829	−	1.60282i
$906$	4.09916	−	8.97590i	0.136185	−	0.298204i
$907$	14.3427	−	7.83169i	0.476241	−	0.260047i	−0.223153	−	0.974783i	$-0.571635\pi$
$907$	14.3427	−	7.83169i	0.476241	−	0.260047i	0.699394	+	0.714736i	$0.253453\pi$
$908$	1.73537	−	24.2636i	0.0575902	−	0.805216i
$909$	7.06512	−	6.12196i	0.234335	−	0.203053i
$910$	−1.19125	+	5.50954i	−0.0394895	+	0.182640i
$911$	31.0181	+	14.1655i	1.02767	+	0.469323i	0.856625	−	0.515940i	$-0.172557\pi$
$911$	31.0181	+	14.1655i	1.02767	+	0.469323i	0.171049	+	0.985263i	$0.445284\pi$
$912$	−6.94268	+	1.51029i	−0.229895	+	0.0500106i
$913$	−32.9818	+	60.4017i	−1.09154	+	1.99900i
$914$	4.09449	−	28.4778i	0.135434	−	0.941961i
$915$	4.99084	+	9.11269i	0.164992	+	0.301256i
$916$	−22.0956	+	3.17686i	−0.730058	+	0.104966i
$917$	0.897565	−	4.12604i	0.0296402	−	0.136254i
$918$	7.00729	−	0.501171i	0.231275	−	0.0165411i
$919$	−19.1375			−0.631289			−0.315644	−	0.948878i	$-0.602221\pi$
$919$	−19.1375			−0.631289			−0.315644	+	0.948878i	$0.602221\pi$
$920$	3.68011	+	10.0726i	0.121330	+	0.332083i
$921$	33.5787			1.10646
$922$	9.05475	−	0.647608i	0.298202	−	0.0213278i
$923$	1.41647	−	6.51140i	0.0466236	−	0.214325i
$924$	2.08633	−	0.299969i	0.0686352	−	0.00986826i
$925$	4.40202	−	20.4845i	0.144737	−	0.673525i
$926$	5.08069	−	35.3370i	0.166962	−	1.16125i
$927$	−4.92500	+	9.01946i	−0.161758	+	0.296238i
$928$	−4.55112	+	0.990035i	−0.149398	+	0.0324995i
$929$	−8.93771	−	4.08172i	−0.293237	−	0.133917i	0.263365	−	0.964696i	$-0.415168\pi$
$929$	−8.93771	−	4.08172i	−0.293237	−	0.133917i	−0.556602	+	0.830780i	$0.687895\pi$
$930$	0.218285	−	0.140673i	0.00715786	−	0.00461285i
$931$	−36.2750	+	31.4325i	−1.18887	+	1.03016i
$932$	−0.0384592	+	0.537729i	−0.00125977	+	0.0176139i
$933$	−22.5897	+	12.3349i	−0.739553	+	0.403826i
$934$	−14.3849	+	31.4986i	−0.470690	+	1.03067i
$935$	58.8220	+	32.0230i	1.92369	+	1.04726i
$936$	4.89249	−	1.43657i	0.159916	−	0.0469556i
$937$	14.9339	+	19.9493i	0.487869	+	0.651717i	0.975154	−	0.221526i	$-0.0711038\pi$
$937$	14.9339	+	19.9493i	0.487869	+	0.651717i	−0.487286	+	0.873243i	$0.662013\pi$
$938$	0.667521	+	0.248972i	0.0217953	+	0.00812924i
$939$	−1.77764	−	12.3638i	−0.0580111	−	0.403476i
$940$	−1.64651	−	2.19371i	−0.0537034	−	0.0715509i
$941$	16.1312	+	13.9777i	0.525861	+	0.455661i	0.876882	−	0.480707i	$-0.159620\pi$
$941$	16.1312	+	13.9777i	0.525861	+	0.455661i	−0.351020	+	0.936368i	$0.614165\pi$
$942$	−9.47079	+	9.47079i	−0.308575	+	0.308575i
$943$	−29.9201	+	33.9787i	−0.974332	+	1.10650i
$944$			6.17098i			0.200848i
$945$	−0.158706	−	1.09402i	−0.00516270	−	0.0355886i
$946$	−27.4225	+	17.6234i	−0.891583	+	0.572986i
$947$	−30.4368	+	40.6588i	−0.989064	+	1.32123i	−0.0423697	+	0.999102i	$0.513491\pi$
$947$	−30.4368	+	40.6588i	−0.989064	+	1.32123i	−0.946694	+	0.322133i	$0.895600\pi$
$948$	−2.30160	+	6.17084i	−0.0747526	+	0.200419i
$949$	30.8471	+	4.43514i	1.00134	+	0.143971i
$950$	−12.3308	+	33.3166i	−0.400063	+	1.08093i
$951$	10.3597	+	6.65775i	0.335935	+	0.215892i
$952$	−3.25415	+	1.21374i	−0.105468	+	0.0393374i
$953$	−13.4516	−	24.6348i	−0.435741	−	0.798001i	0.563870	−	0.825863i	$-0.309312\pi$
$953$	−13.4516	−	24.6348i	−0.435741	−	0.798001i	−0.999612	+	0.0278625i	$0.991130\pi$
$954$	6.20183	+	7.15729i	0.200792	+	0.231726i
$955$	−0.0404275	−	32.0447i	−0.00130820	−	1.03694i
$956$	−11.9152	−	3.49861i	−0.385364	−	0.113153i
$957$	6.93943	+	18.6053i	0.224320	+	0.601425i
$958$	5.25885	+	24.1746i	0.169906	+	0.781045i
$959$	−2.91284	−	9.92021i	−0.0940604	−	0.320340i
$960$	0.156705	−	2.23057i	0.00505764	−	0.0719913i
$961$	−12.8723	−	28.1863i	−0.415234	−	0.909236i
$962$	17.1053	+	12.8048i	0.551496	+	0.412845i
$963$	−0.672557	−	0.146306i	−0.0216728	−	0.00471464i
$964$	9.57136	−	11.0459i	0.308273	−	0.355766i
$965$	0.425047	+	5.83940i	0.0136828	+	0.187977i
$966$	−0.522434	+	2.31270i	−0.0168090	+	0.0744100i
$967$	−4.59885	−	4.59885i	−0.147889	−	0.147889i	0.629285	−	0.777174i	$-0.283348\pi$
$967$	−4.59885	−	4.59885i	−0.147889	−	0.147889i	−0.777174	+	0.629285i	$0.783348\pi$
$968$	−0.512010	−	7.15884i	−0.0164566	−	0.230094i
$969$	−26.9857	−	41.9906i	−0.866906	−	1.34893i
$970$	−34.7225	−	22.2529i	−1.11487	−	0.714498i
$971$	−30.7798	+	14.0567i	−0.987772	+	0.451100i	−0.842737	−	0.538326i	$-0.819057\pi$
$971$	−30.7798	+	14.0567i	−0.987772	+	0.451100i	−0.145036	+	0.989426i	$0.546330\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	0.0475984	+	0.0259907i	0.00152593	+	0.000833223i
$974$	2.77174	−	4.31291i	0.0888123	−	0.138195i
$975$	7.12108	−	24.4805i	0.228057	−	0.784004i
$976$	−1.30907	+	4.45828i	−0.0419023	+	0.142706i
$977$	33.5890	+	2.40233i	1.07461	+	0.0768575i	0.597408	−	0.801937i	$-0.296197\pi$
$977$	33.5890	+	2.40233i	1.07461	+	0.0768575i	0.477200	+	0.878795i	$0.341652\pi$
$978$	−1.64179	−	0.117423i	−0.0524987	−	0.00375478i
$979$	−11.2075	+	38.1693i	−0.358194	+	1.21990i
$980$	−6.29257	−	13.7329i	−0.201009	−	0.438682i
$981$	7.54895	−	11.7464i	0.241019	−	0.375034i
$982$	6.48712	+	3.54223i	0.207012	+	0.113037i
$983$	−11.6619	+	8.72998i	−0.371957	+	0.278443i	−0.768860	−	0.639417i	$-0.779176\pi$
$983$	−11.6619	+	8.72998i	−0.371957	+	0.278443i	0.396903	+	0.917860i	$0.370085\pi$
$984$	8.58723	−	3.92166i	0.273751	−	0.125018i
$985$	7.00229	+	31.9946i	0.223111	+	1.01943i
$986$	−17.6899	−	27.5260i	−0.563361	−	0.876607i
$987$	−0.0432626	−	0.604891i	−0.00137706	−	0.0192539i
$988$	−25.6177	−	25.6177i	−0.815008	−	0.815008i
$989$	−7.50847	−	35.8906i	−0.238756	−	1.14125i
$990$	−9.50824	+	0.692101i	−0.302192	+	0.0219964i
$991$	34.7957	−	40.1564i	1.10532	−	1.27561i	0.147245	−	0.989100i	$-0.452960\pi$
$991$	34.7957	−	40.1564i	1.10532	−	1.27561i	0.958077	−	0.286509i	$-0.0924950\pi$
$992$	0.113481	+	0.0246864i	0.00360304	+	0.000783794i
$993$	−6.43801	−	4.81943i	−0.204304	−	0.152940i
$994$	−0.268393	−	0.587699i	−0.00851292	−	0.0186407i
$995$	−34.0399	−	39.1841i	−1.07914	−	1.24222i
$996$	4.54766	+	15.4879i	0.144098	+	0.490753i
$997$	5.48607	+	25.2191i	0.173746	+	0.798695i	0.978690	+	0.205345i	$0.0658316\pi$
$997$	5.48607	+	25.2191i	0.173746	+	0.798695i	−0.804944	+	0.593351i	$0.797805\pi$
$998$	−4.78068	−	12.8175i	−0.151330	−	0.405731i
$999$	−4.02068	−	1.18058i	−0.127209	−	0.0373518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.7	✓	240
5.3	odd	4	inner	690.2.w.a.283.3	yes	240
23.10	odd	22	inner	690.2.w.a.217.3	yes	240
115.33	even	44	inner	690.2.w.a.493.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.7	✓	240	1.1	even	1	trivial
690.2.w.a.217.3	yes	240	23.10	odd	22	inner
690.2.w.a.283.3	yes	240	5.3	odd	4	inner
690.2.w.a.493.7	yes	240	115.33	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.14628 - 0.627266i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.236933 + 0.433910i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.14628 - 0.627266i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.236933 + 0.433910i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-2.18556 - 0.472554i) q^{10} +(-3.22211 + 2.79198i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-4.47532 + 2.44371i) q^{13} +(-0.205374 + 0.449707i) q^{14} +(1.06916 - 1.96390i) q^{15} +(0.959493 - 0.281733i) q^{16} +(4.21004 + 5.62395i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(1.01115 + 7.03273i) q^{19} +(-2.21371 - 0.315433i) q^{20} +(-0.373630 - 0.323752i) q^{21} +(-3.01472 + 3.01472i) q^{22} +(-1.95743 - 4.37818i) q^{23} +1.00000i q^{24} +(4.21307 + 2.69258i) q^{25} +(-4.28958 + 2.75675i) q^{26} +(0.599278 - 0.800541i) q^{27} +(-0.172769 + 0.463212i) q^{28} +(-4.61015 - 0.662840i) q^{29} +(0.926329 - 2.03517i) q^{30} +(0.0976994 + 0.0627876i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-2.04326 - 3.74195i) q^{33} +(4.60052 + 5.30928i) q^{34} +(0.780701 - 0.782674i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-1.46440 - 3.92621i) q^{37} +(1.51029 + 6.94268i) q^{38} +(-1.43657 - 4.89249i) q^{39} +(-2.23057 - 0.156705i) q^{40} +(-3.92166 - 8.58723i) q^{41} +(-0.395774 - 0.296273i) q^{42} +(7.47099 + 1.62521i) q^{43} +(-2.79198 + 3.22211i) q^{44} +(1.69175 + 1.46218i) q^{45} +(-2.26478 - 4.22738i) q^{46} +(0.867374 + 0.867374i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.65235 + 5.68316i) q^{49} +(4.39443 + 2.38516i) q^{50} +(-6.39034 + 2.91837i) q^{51} +(-4.08199 + 3.05574i) q^{52} +(-8.31202 - 4.53871i) q^{53} +(0.540641 - 0.841254i) q^{54} +(8.66688 - 3.97125i) q^{55} +(-0.139284 + 0.474357i) q^{56} +(-7.08695 - 0.506868i) q^{57} +(-4.64569 - 0.332266i) q^{58} +(-1.73857 + 5.92101i) q^{59} +(0.778782 - 2.09607i) q^{60} +(-2.51209 + 3.90888i) q^{61} +(0.101930 + 0.0556578i) q^{62} +(0.395774 - 0.296273i) q^{63} +(0.909632 - 0.415415i) q^{64} +(11.1382 - 2.43768i) q^{65} +(-2.30500 - 3.58665i) q^{66} +(-0.102805 - 1.43740i) q^{67} +(4.96756 + 4.96756i) q^{68} +(4.69421 - 0.982050i) q^{69} +(0.722877 - 0.836374i) q^{70} +(-0.855805 + 0.987652i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-4.89275 - 3.66267i) q^{73} +(-1.74076 - 3.81174i) q^{74} +(-3.52660 + 3.54444i) q^{75} +(2.00172 + 6.81724i) q^{76} +(-0.448042 - 2.05962i) q^{77} +(-1.78193 - 4.77754i) q^{78} +(6.31931 + 1.85552i) q^{79} +(-2.23607 + 0.00282101i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-4.52427 - 8.28559i) q^{82} +(15.1240 - 5.64096i) q^{83} +(-0.415902 - 0.267284i) q^{84} +(-5.50823 - 14.7114i) q^{85} +(7.56789 + 1.08810i) q^{86} +(1.62765 - 4.36390i) q^{87} +(-2.55500 + 3.41308i) q^{88} +(7.84941 - 5.04451i) q^{89} +(1.79175 + 1.33777i) q^{90} -2.52088i q^{91} +(-2.56059 - 4.05504i) q^{92} +(-0.0821202 + 0.0821202i) q^{93} +(0.927042 + 0.803286i) q^{94} +(2.24117 - 15.7285i) q^{95} +(0.142315 + 0.989821i) q^{96} +(17.2808 + 6.44540i) q^{97} +(4.04847 + 5.40812i) q^{98} +(4.09076 - 1.20116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more