LMFDB - Embedded newform 690.2.w.b.37.1

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			37.1
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.21203 - 0.326962i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.672927 + 1.80419i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.21203 - 0.326962i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.672927 + 1.80419i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.78476 + 1.34708i) q^{10} +(1.31759 - 4.48731i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-3.13276 - 1.16846i) q^{13} +(0.274041 - 1.90600i) q^{14} +(-2.18307 - 0.483934i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(5.05370 - 1.09936i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-1.04118 + 0.669124i) q^{19} +(-0.920858 - 2.03765i) q^{20} +(0.542503 + 1.84760i) q^{21} +(-3.30696 + 3.30696i) q^{22} +(4.76203 - 0.568430i) q^{23} -1.00000i q^{24} +(4.78619 + 1.44650i) q^{25} +(2.18957 + 2.52690i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-1.15397 + 1.54152i) q^{28} +(4.64515 - 7.22800i) q^{29} +(1.68411 + 1.47097i) q^{30} +(0.562596 - 0.649271i) q^{31} +(0.800541 - 0.599278i) q^{32} +(1.63436 - 4.38188i) q^{33} +(-4.96239 - 1.45709i) q^{34} +(-0.898636 - 4.21095i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.85598 + 7.82268i) q^{37} +(1.23450 - 0.0882930i) q^{38} +(-3.04142 - 1.38897i) q^{39} +(-0.168325 + 2.22972i) q^{40} +(-0.209772 - 1.45899i) q^{41} +(0.409315 - 1.88159i) q^{42} +(0.844906 - 11.8133i) q^{43} +(4.48731 - 1.31759i) q^{44} +(-2.14299 - 0.638440i) q^{45} +(-4.45195 - 1.78330i) q^{46} +(3.86757 + 3.86757i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(2.48799 - 2.15585i) q^{49} +(-3.50750 - 3.56334i) q^{50} +(5.11925 - 0.736037i) q^{51} +(-0.710727 - 3.26716i) q^{52} +(-3.54250 + 1.32129i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-4.38175 + 9.49529i) q^{55} +(1.75158 - 0.799922i) q^{56} +(-1.08626 + 0.593143i) q^{57} +(-7.54096 + 4.11768i) q^{58} +(-9.22216 + 4.21162i) q^{59} +(-0.773147 - 2.09815i) q^{60} +(-0.718957 - 0.622980i) q^{61} +(-0.804941 + 0.300227i) q^{62} +(0.409315 + 1.88159i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(6.54772 + 3.60896i) q^{65} +(-3.53445 + 3.06262i) q^{66} +(5.62182 - 10.2956i) q^{67} +(3.65708 + 3.65708i) q^{68} +(4.79044 - 0.227262i) q^{69} +(-1.22938 + 4.12653i) q^{70} +(-4.97783 + 1.46162i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-0.322216 + 1.48120i) q^{73} +(-1.39066 - 9.67227i) q^{74} +(4.67080 + 1.78426i) q^{75} +(-1.12581 - 0.514138i) q^{76} +(8.98260 - 0.642448i) q^{77} +(2.00373 + 2.67667i) q^{78} +(0.824779 + 1.80601i) q^{79} +(1.21633 - 1.87631i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-0.515109 + 1.38106i) q^{82} +(-5.47302 + 4.09705i) q^{83} +(-1.26100 + 1.45527i) q^{84} +(-11.5384 + 0.779463i) q^{85} +(-6.40308 + 9.96339i) q^{86} +(5.14895 - 6.87820i) q^{87} +(-4.56988 - 0.994116i) q^{88} +(-11.7688 - 13.5819i) q^{89} +(1.57488 + 1.58737i) q^{90} -6.43837i q^{91} +(3.05274 + 3.69875i) q^{92} +(0.607481 - 0.607481i) q^{93} +(-1.54096 - 5.24802i) q^{94} +(2.52190 - 1.13970i) q^{95} +(0.841254 - 0.540641i) q^{96} +(11.8155 + 8.84497i) q^{97} +(-3.21684 + 0.699781i) q^{98} +(1.94279 - 4.25413i) 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} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$3$	0.997452	+	0.0713392i	0.575879	+	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	−2.21203	−	0.326962i	−0.989252	−	0.146222i
$5$	−2.21203	−	0.326962i	−0.989252	−	0.146222i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	0.672927	+	1.80419i	0.254343	+	0.681919i	0.999881	+	0.0154556i	$0.00491987\pi$
$7$	0.672927	+	1.80419i	0.254343	+	0.681919i	−0.745538	+	0.666463i	$0.767807\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	1.78476	+	1.34708i	0.564391	+	0.425985i
$11$	1.31759	−	4.48731i	0.397270	−	1.35298i	−0.481800	−	0.876281i	$-0.660017\pi$
$11$	1.31759	−	4.48731i	0.397270	−	1.35298i	0.879069	−	0.476694i	$-0.158165\pi$
$12$	0.479249	+	0.877679i	0.138347	+	0.253364i
$13$	−3.13276	−	1.16846i	−0.868870	−	0.324072i	−0.124807	−	0.992181i	$-0.539831\pi$
$13$	−3.13276	−	1.16846i	−0.868870	−	0.324072i	−0.744063	+	0.668109i	$0.767104\pi$
$14$	0.274041	−	1.90600i	0.0732405	−	0.509399i
$15$	−2.18307	−	0.483934i	−0.563667	−	0.124951i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	5.05370	−	1.09936i	1.22570	−	0.266635i	0.447290	−	0.894389i	$-0.352389\pi$
$17$	5.05370	−	1.09936i	1.22570	−	0.266635i	0.778412	+	0.627754i	$0.216026\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	−1.04118	+	0.669124i	−0.238863	+	0.153508i	−0.654596	−	0.755979i	$-0.727161\pi$
$19$	−1.04118	+	0.669124i	−0.238863	+	0.153508i	0.415734	+	0.909486i	$0.363525\pi$
$20$	−0.920858	−	2.03765i	−0.205910	−	0.455633i
$21$	0.542503	+	1.84760i	0.118384	+	0.403179i
$22$	−3.30696	+	3.30696i	−0.705047	+	0.705047i
$23$	4.76203	−	0.568430i	0.992951	−	0.118526i
$23$	4.76203	−	0.568430i	0.992951	−	0.118526i
$24$		−	1.00000i		−	0.204124i
$25$	4.78619	+	1.44650i	0.957238	+	0.289301i
$26$	2.18957	+	2.52690i	0.429411	+	0.495566i
$27$	0.977147	+	0.212565i	0.188052	+	0.0409082i
$28$	−1.15397	+	1.54152i	−0.218079	+	0.291320i
$29$	4.64515	−	7.22800i	0.862583	−	1.34221i	−0.0759846	−	0.997109i	$-0.524210\pi$
$29$	4.64515	−	7.22800i	0.862583	−	1.34221i	0.938567	−	0.345096i	$-0.112154\pi$
$30$	1.68411	+	1.47097i	0.307475	+	0.268562i
$31$	0.562596	−	0.649271i	0.101045	−	0.116612i	−0.702974	−	0.711215i	$-0.748145\pi$
$31$	0.562596	−	0.649271i	0.101045	−	0.116612i	0.804020	+	0.594603i	$0.202691\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	1.63436	−	4.38188i	0.284505	−	0.762788i
$34$	−4.96239	−	1.45709i	−0.851044	−	0.249889i
$35$	−0.898636	−	4.21095i	−0.151897	−	0.711780i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	5.85598	+	7.82268i	0.962717	+	1.28604i	0.958215	+	0.286050i	$0.0923424\pi$
$37$	5.85598	+	7.82268i	0.962717	+	1.28604i	0.00450274	+	0.999990i	$0.498567\pi$
$38$	1.23450	−	0.0882930i	0.200262	−	0.0143230i
$39$	−3.04142	−	1.38897i	−0.487017	−	0.222413i
$40$	−0.168325	+	2.22972i	−0.0266145	+	0.352550i
$41$	−0.209772	−	1.45899i	−0.0327608	−	0.227857i	0.966863	−	0.255297i	$-0.0821733\pi$
$41$	−0.209772	−	1.45899i	−0.0327608	−	0.227857i	−0.999623	+	0.0274407i	$0.991264\pi$
$42$	0.409315	−	1.88159i	0.0631587	−	0.290336i
$43$	0.844906	−	11.8133i	0.128847	−	1.80152i	−0.363998	−	0.931400i	$-0.618589\pi$
$43$	0.844906	−	11.8133i	0.128847	−	1.80152i	0.492845	−	0.870117i	$-0.335957\pi$
$44$	4.48731	−	1.31759i	0.676488	−	0.198635i
$45$	−2.14299	−	0.638440i	−0.319458	−	0.0951730i
$46$	−4.45195	−	1.78330i	−0.656404	−	0.262933i
$47$	3.86757	+	3.86757i	0.564144	+	0.564144i	0.930482	−	0.366338i	$-0.119389\pi$
$47$	3.86757	+	3.86757i	0.564144	+	0.564144i	−0.366338	+	0.930482i	$0.619389\pi$
$48$	−0.479249	+	0.877679i	−0.0691736	+	0.126682i
$49$	2.48799	−	2.15585i	0.355427	−	0.307979i
$50$	−3.50750	−	3.56334i	−0.496036	−	0.503933i
$51$	5.11925	−	0.736037i	0.716838	−	0.103066i
$52$	−0.710727	−	3.26716i	−0.0985601	−	0.453073i
$53$	−3.54250	+	1.32129i	−0.486600	+	0.181493i	−0.580777	−	0.814063i	$-0.697251\pi$
$53$	−3.54250	+	1.32129i	−0.486600	+	0.181493i	0.0941763	+	0.995556i	$0.469978\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−4.38175	+	9.49529i	−0.590834	+	1.28034i
$56$	1.75158	−	0.799922i	0.234065	−	0.106894i
$57$	−1.08626	+	0.593143i	−0.143879	+	0.0785637i
$58$	−7.54096	+	4.11768i	−0.990177	+	0.540677i
$59$	−9.22216	+	4.21162i	−1.20062	+	0.548306i	−0.912417	−	0.409262i	$-0.865786\pi$
$59$	−9.22216	+	4.21162i	−1.20062	+	0.548306i	−0.288206	+	0.957568i	$0.593059\pi$
$60$	−0.773147	−	2.09815i	−0.0998129	−	0.270870i
$61$	−0.718957	−	0.622980i	−0.0920530	−	0.0797644i	0.607619	−	0.794229i	$-0.292125\pi$
$61$	−0.718957	−	0.622980i	−0.0920530	−	0.0797644i	−0.699672	+	0.714465i	$0.746670\pi$
$62$	−0.804941	+	0.300227i	−0.102228	+	0.0381289i
$63$	0.409315	+	1.88159i	0.0515688	+	0.237058i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	6.54772	+	3.60896i	0.812145	+	0.447637i
$66$	−3.53445	+	3.06262i	−0.435061	+	0.376983i
$67$	5.62182	−	10.2956i	0.686814	−	1.25781i	−0.268803	−	0.963195i	$-0.586628\pi$
$67$	5.62182	−	10.2956i	0.686814	−	1.25781i	0.955617	−	0.294611i	$-0.0951901\pi$
$68$	3.65708	+	3.65708i	0.443486	+	0.443486i
$69$	4.79044	−	0.227262i	0.576702	−	0.0273592i
$70$	−1.22938	+	4.12653i	−0.146939	+	0.493215i
$71$	−4.97783	+	1.46162i	−0.590760	+	0.173463i	−0.563430	−	0.826164i	$-0.690519\pi$
$71$	−4.97783	+	1.46162i	−0.590760	+	0.173463i	−0.0273296	+	0.999626i	$0.508700\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	−0.322216	+	1.48120i	−0.0377125	+	0.173362i	−0.992151	−	0.125046i	$-0.960092\pi$
$73$	−0.322216	+	1.48120i	−0.0377125	+	0.173362i	0.954438	+	0.298408i	$0.0964556\pi$
$74$	−1.39066	−	9.67227i	−0.161661	−	1.12438i
$75$	4.67080	+	1.78426i	0.539338	+	0.206029i
$76$	−1.12581	−	0.514138i	−0.129139	−	0.0589757i
$77$	8.98260	−	0.642448i	1.02366	−	0.0732137i
$78$	2.00373	+	2.67667i	0.226877	+	0.303073i
$79$	0.824779	+	1.80601i	0.0927949	+	0.203193i	0.950338	−	0.311220i	$-0.100737\pi$
$79$	0.824779	+	1.80601i	0.0927949	+	0.203193i	−0.857543	+	0.514412i	$0.828010\pi$
$80$	1.21633	−	1.87631i	0.135990	−	0.209778i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	−0.515109	+	1.38106i	−0.0568843	+	0.152513i
$83$	−5.47302	+	4.09705i	−0.600742	+	0.449710i	−0.855865	−	0.517199i	$-0.826975\pi$
$83$	−5.47302	+	4.09705i	−0.600742	+	0.449710i	0.255123	+	0.966909i	$0.417884\pi$
$84$	−1.26100	+	1.45527i	−0.137586	+	0.158783i
$85$	−11.5384	+	0.779463i	−1.25152	+	0.0845446i
$86$	−6.40308	+	9.96339i	−0.690462	+	1.07438i
$87$	5.14895	−	6.87820i	0.552026	−	0.737420i
$88$	−4.56988	−	0.994116i	−0.487150	−	0.105973i
$89$	−11.7688	−	13.5819i	−1.24749	−	1.43968i	−0.853939	−	0.520373i	$-0.825793\pi$
$89$	−11.7688	−	13.5819i	−1.24749	−	1.43968i	−0.393549	−	0.919304i	$-0.628753\pi$
$90$	1.57488	+	1.58737i	0.166007	+	0.167323i
$91$		−	6.43837i		−	0.674924i
$92$	3.05274	+	3.69875i	0.318270	+	0.385622i
$93$	0.607481	−	0.607481i	0.0629929	−	0.0629929i
$94$	−1.54096	−	5.24802i	−0.158938	−	0.541292i
$95$	2.52190	−	1.13970i	0.258741	−	0.116931i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	11.8155	+	8.84497i	1.19968	+	0.898071i	0.996705	−	0.0811128i	$-0.0258474\pi$
$97$	11.8155	+	8.84497i	1.19968	+	0.898071i	0.202977	+	0.979183i	$0.434938\pi$
$98$	−3.21684	+	0.699781i	−0.324950	+	0.0706886i
$99$	1.94279	−	4.25413i	0.195258	−	0.427556i
$100$	1.37073	+	4.80844i	0.137073	+	0.480844i
$101$	1.26700	−	8.81216i	0.126071	−	0.876843i	−0.824395	−	0.566015i	$-0.808485\pi$
$101$	1.26700	−	8.81216i	0.126071	−	0.876843i	0.950466	−	0.310828i	$-0.100606\pi$
$102$	−4.84580	−	1.80739i	−0.479806	−	0.178958i
$103$	5.67463	+	10.3923i	0.559138	+	1.02398i	0.992439	+	0.122735i	$0.0391667\pi$
$103$	5.67463	+	10.3923i	0.559138	+	1.02398i	−0.433302	+	0.901249i	$0.642652\pi$
$104$	−0.941993	+	3.20813i	−0.0923700	+	0.314583i
$105$	−0.595941	−	4.26432i	−0.0581579	−	0.416155i
$106$	3.74241	+	0.538077i	0.363495	+	0.0522626i
$107$	−0.678912	−	9.49243i	−0.0656329	−	0.917668i	−0.918470	−	0.395491i	$-0.870575\pi$
$107$	−0.678912	−	9.49243i	−0.0656329	−	0.917668i	0.852837	−	0.522177i	$-0.174880\pi$
$108$	0.349464	+	0.936950i	0.0336272	+	0.0901580i
$109$	−4.91117	−	3.15622i	−0.470405	−	0.302311i	0.283878	−	0.958860i	$-0.408379\pi$
$109$	−4.91117	−	3.15622i	−0.470405	−	0.302311i	−0.754283	+	0.656550i	$0.772015\pi$
$110$	8.39637	−	6.23387i	0.800563	−	0.594376i
$111$	5.28300	+	8.22051i	0.501440	+	0.780256i
$112$	−1.92069	−	0.137370i	−0.181488	−	0.0129803i
$113$	0.406605	+	0.222023i	0.0382502	+	0.0208862i	0.498260	−	0.867028i	$-0.333972\pi$
$113$	0.406605	+	0.222023i	0.0382502	+	0.0208862i	−0.460010	+	0.887914i	$0.652154\pi$
$114$	1.23765			0.115917
$115$	−10.7196	−	0.299618i	−0.999610	−	0.0279395i
$116$	8.59193			0.797741
$117$	−2.93458	−	1.60240i	−0.271302	−	0.148142i
$118$	10.1125	+	0.723261i	0.930932	+	0.0665816i
$119$	5.38423	+	8.37803i	0.493572	+	0.768012i
$120$	−0.326962	+	2.21203i	−0.0298475	+	0.201930i
$121$	−9.14613	−	5.87786i	−0.831467	−	0.534351i
$122$	0.332451	+	0.891336i	0.0300987	+	0.0806978i
$123$	−0.105154	−	1.47024i	−0.00948140	−	0.132567i
$124$	0.850364	+	0.122264i	0.0763649	+	0.0109796i
$125$	−10.1143	−	4.76462i	−0.904647	−	0.426161i
$126$	0.542503	−	1.84760i	0.0483300	−	0.164597i
$127$	1.57085	+	2.87679i	0.139390	+	0.255274i	0.938044	−	0.346517i	$-0.112636\pi$
$127$	1.57085	+	2.87679i	0.139390	+	0.255274i	−0.798653	+	0.601791i	$0.794454\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	1.68551	−	11.7230i	0.148401	−	1.03215i
$130$	−4.01721	−	6.30550i	−0.352332	−	0.553029i
$131$	0.0351975	−	0.0770717i	0.00307522	−	0.00673378i	−0.908088	−	0.418779i	$-0.862458\pi$
$131$	0.0351975	−	0.0770717i	0.00307522	−	0.00673378i	0.911163	+	0.412045i	$0.135185\pi$
$132$	4.56988	−	0.994116i	0.397757	−	0.0865267i
$133$	−1.90786	−	1.42821i	−0.165433	−	0.123841i
$134$	−9.86830	+	6.34197i	−0.852491	+	0.547863i
$135$	−2.09198	−	0.789692i	−0.180049	−	0.0679659i
$136$	−1.45709	−	4.96239i	−0.124944	−	0.425522i
$137$	−1.34493	+	1.34493i	−0.114905	+	0.114905i	−0.762222	−	0.647316i	$-0.775891\pi$
$137$	−1.34493	+	1.34493i	−0.114905	+	0.114905i	0.647316	+	0.762222i	$0.275891\pi$
$138$	−4.31339	−	2.09635i	−0.367180	−	0.178453i
$139$			8.41593i			0.713830i	0.934137	+	0.356915i	$0.116171\pi$
$139$			8.41593i			0.713830i	−0.934137	+	0.356915i	$0.883829\pi$
$140$	3.05663	−	3.03259i	0.258333	−	0.256301i
$141$	3.58181	+	4.13363i	0.301643	+	0.348114i
$142$	5.06942	+	1.10278i	0.425416	+	0.0925436i
$143$	−9.37094	+	12.5181i	−0.783637	+	1.04682i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−12.6385	+	14.4698i	−1.04957	+	1.20165i
$146$	0.992667	−	1.14560i	0.0821537	−	0.0948104i
$147$	2.63544	−	1.97287i	0.217368	−	0.162719i
$148$	−3.41487	+	9.15562i	−0.280701	+	0.752588i
$149$	2.76344	+	0.811418i	0.226389	+	0.0664739i	0.392960	−	0.919556i	$-0.371451\pi$
$149$	2.76344	+	0.811418i	0.226389	+	0.0664739i	−0.166570	+	0.986030i	$0.553269\pi$
$150$	−3.24436	−	3.80449i	−0.264901	−	0.310635i
$151$	0.763947	+	1.67281i	0.0621691	+	0.136131i	0.938166	−	0.346185i	$-0.112523\pi$
$151$	0.763947	+	1.67281i	0.0621691	+	0.136131i	−0.875997	+	0.482316i	$0.839796\pi$
$152$	0.741696	+	0.990790i	0.0601595	+	0.0803637i
$153$	5.15871	−	0.368959i	0.417057	−	0.0298285i
$154$	−8.19173	−	3.74104i	−0.660108	−	0.301461i
$155$	−1.45677	+	1.25226i	−0.117010	+	0.100584i
$156$	−0.475840	−	3.30954i	−0.0380977	−	0.264975i
$157$	−3.26607	+	15.0139i	−0.260661	+	1.19824i	0.641597	+	0.767042i	$0.278272\pi$
$157$	−3.26607	+	15.0139i	−0.260661	+	1.19824i	−0.902258	+	0.431197i	$0.858091\pi$
$158$	0.141639	−	1.98038i	0.0112682	−	0.157550i
$159$	−3.62774	+	1.06520i	−0.287698	+	0.0844758i
$160$	−1.96677	+	1.06388i	−0.155487	+	0.0841068i
$161$	4.23005	+	8.20907i	0.333375	+	0.646966i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−10.9636	+	20.0783i	−0.858732	+	1.57265i	−0.0394773	+	0.999220i	$0.512569\pi$
$163$	−10.9636	+	20.0783i	−0.858732	+	1.57265i	−0.819255	+	0.573430i	$0.805613\pi$
$164$	1.11397	−	0.965263i	0.0869867	−	0.0753744i
$165$	−5.04797	+	9.15850i	−0.392984	+	0.712988i
$166$	6.76706	−	0.972957i	0.525226	−	0.0755161i
$167$	4.27935	+	19.6719i	0.331146	+	1.52226i	0.778354	+	0.627825i	$0.216055\pi$
$167$	4.27935	+	19.6719i	0.331146	+	1.52226i	−0.447208	+	0.894430i	$0.647582\pi$
$168$	1.80419	−	0.672927i	0.139196	−	0.0519174i
$169$	−1.37587	−	1.19220i	−0.105836	−	0.0917077i
$170$	10.5006	+	4.84565i	0.805357	+	0.371644i
$171$	−1.12581	+	0.514138i	−0.0860926	+	0.0393172i
$172$	10.3948	−	5.67599i	0.792596	−	0.432790i
$173$	−18.1090	+	9.88826i	−1.37680	+	0.751790i	−0.985692	−	0.168554i	$-0.946090\pi$
$173$	−18.1090	+	9.88826i	−1.37680	+	0.751790i	−0.391108	+	0.920345i	$0.627908\pi$
$174$	−7.81550	+	3.56922i	−0.592491	+	0.270582i
$175$	0.610992	+	9.60858i	0.0461867	+	0.726340i
$176$	3.53445	+	3.06262i	0.266420	+	0.230854i
$177$	−9.49911	+	3.54299i	−0.713997	+	0.266307i
$178$	3.82010	+	17.5607i	0.286329	+	1.31623i
$179$	16.5282	−	2.37640i	1.23538	−	0.177621i	0.506485	−	0.862249i	$-0.330944\pi$
$179$	16.5282	−	2.37640i	1.23538	−	0.177621i	0.728893	+	0.684628i	$0.240035\pi$
$180$	−0.621497	−	2.14796i	−0.0463236	−	0.160100i
$181$	−1.96355	+	1.70143i	−0.145950	+	0.126466i	−0.724776	−	0.688985i	$-0.758057\pi$
$181$	−1.96355	+	1.70143i	−0.145950	+	0.126466i	0.578826	+	0.815451i	$0.303511\pi$
$182$	−3.08558	+	5.65082i	−0.228718	+	0.418867i
$183$	−0.672683	−	0.672683i	−0.0497261	−	0.0497261i
$184$	−0.906700	−	4.70934i	−0.0668428	−	0.347177i
$185$	−10.3959	−	19.2187i	−0.764323	−	1.41299i
$186$	−0.824308	+	0.242039i	−0.0604412	+	0.0177471i
$187$	1.72553	−	24.1260i	0.126183	−	1.76427i
$188$	−1.16264	+	5.34458i	−0.0847944	+	0.389794i
$189$	0.274041	+	1.90600i	0.0199335	+	0.138641i
$190$	−2.75962	−	0.208327i	−0.200204	−	0.0151136i
$191$	−5.67537	−	2.59185i	−0.410655	−	0.187540i	0.199366	−	0.979925i	$-0.436112\pi$
$191$	−5.67537	−	2.59185i	−0.410655	−	0.187540i	−0.610021	+	0.792385i	$0.708839\pi$
$192$	−0.997452	+	0.0713392i	−0.0719849	+	0.00514846i
$193$	5.10083	+	6.81391i	0.367166	+	0.490476i	0.945636	−	0.325227i	$-0.105441\pi$
$193$	5.10083	+	6.81391i	0.367166	+	0.490476i	−0.578470	+	0.815704i	$0.696350\pi$
$194$	−6.13127	−	13.4256i	−0.440200	−	0.963903i
$195$	6.27358	+	4.06688i	0.449260	+	0.291235i
$196$	3.15873	+	0.927485i	0.225623	+	0.0662490i
$197$	−8.29745	+	22.2463i	−0.591168	+	1.58498i	0.204247	+	0.978919i	$0.434525\pi$
$197$	−8.29745	+	22.2463i	−0.591168	+	1.58498i	−0.795415	+	0.606065i	$0.792747\pi$
$198$	−3.74393	+	2.80267i	−0.266070	+	0.199177i
$199$	10.9173	−	12.5992i	0.773907	−	0.893136i	−0.222747	−	0.974876i	$-0.571502\pi$
$199$	10.9173	−	12.5992i	0.773907	−	0.893136i	0.996654	+	0.0817405i	$0.0260479\pi$
$200$	1.10138	−	4.87719i	0.0778790	−	0.344869i
$201$	6.34197	−	9.86830i	0.447328	−	0.696056i
$202$	−5.33524	+	7.12704i	−0.375386	+	0.501457i
$203$	16.1665	+	3.51681i	1.13467	+	0.246832i
$204$	3.38687	+	3.90866i	0.237128	+	0.273661i
$205$	−0.0130142	+	3.29593i	−0.000908952	+	0.230198i
$206$		−	11.8407i		−	0.824978i
$207$	4.79445	+	0.115063i	0.333237	+	0.00799744i
$208$	2.36426	−	2.36426i	0.163932	−	0.163932i
$209$	1.63072	+	5.55372i	0.112799	+	0.384159i
$210$	−1.52063	+	4.02831i	−0.104933	+	0.277980i
$211$	−12.5855	+	8.08822i	−0.866423	+	0.556816i	−0.896657	−	0.442727i	$-0.854011\pi$
$211$	−12.5855	+	8.08822i	−0.866423	+	0.556816i	0.0302339	+	0.999543i	$0.490375\pi$
$212$	−3.02676	−	2.26580i	−0.207879	−	0.155616i
$213$	−5.06942	+	1.10278i	−0.347351	+	0.0755615i
$214$	−3.95337	+	8.65667i	−0.270247	+	0.591758i
$215$	−5.73148	+	25.8552i	−0.390884	+	1.76331i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	1.54999	+	0.578117i	0.105220	+	0.0392451i
$218$	2.79782	+	5.12382i	0.189492	+	0.347029i
$219$	−0.427063	+	1.45444i	−0.0288582	+	0.0982821i
$220$	−10.3569	+	1.44738i	−0.698262	+	0.0975823i
$221$	−17.1166	−	2.46099i	−1.15139	−	0.165544i
$222$	−0.697107	−	9.74684i	−0.0467868	−	0.654165i
$223$	−3.53332	−	9.47320i	−0.236609	−	0.634372i	0.763324	−	0.646016i	$-0.223566\pi$
$223$	−3.53332	−	9.47320i	−0.236609	−	0.634372i	−0.999932	+	0.0116441i	$0.996293\pi$
$224$	1.61991	+	1.04106i	0.108235	+	0.0695585i
$225$	4.53162	+	2.11293i	0.302108	+	0.140862i
$226$	−0.250464	−	0.389730i	−0.0166606	−	0.0259244i
$227$	25.2604	+	1.80666i	1.67659	+	0.119912i	0.876957	−	0.480570i	$-0.159570\pi$
$227$	25.2604	+	1.80666i	1.67659	+	0.119912i	0.799638	+	0.600482i	$0.205025\pi$
$228$	−1.08626	−	0.593143i	−0.0719393	−	0.0392818i
$229$	−2.49271			−0.164723			−0.0823616	−	0.996603i	$-0.526246\pi$
$229$	−2.49271			−0.164723			−0.0823616	+	0.996603i	$0.526246\pi$
$230$	9.26479	+	5.40033i	0.610902	+	0.356088i
$231$	9.00554			0.592521
$232$	−7.54096	−	4.11768i	−0.495088	−	0.270339i
$233$	−15.0189	−	1.07417i	−0.983919	−	0.0703713i	−0.429901	−	0.902876i	$-0.641452\pi$
$233$	−15.0189	−	1.07417i	−0.983919	−	0.0703713i	−0.554018	+	0.832505i	$0.686906\pi$
$234$	1.80767	+	2.81279i	0.118171	+	0.183878i
$235$	−7.29066	−	9.81976i	−0.475590	−	0.640570i
$236$	−8.52891	−	5.48120i	−0.555185	−	0.356796i
$237$	0.693838	+	1.86025i	0.0450696	+	0.120836i
$238$	−0.710465	−	9.93360i	−0.0460526	−	0.643900i
$239$	15.8835	+	2.28370i	1.02742	+	0.147720i	0.635356	−	0.772220i	$-0.280853\pi$
$239$	15.8835	+	2.28370i	1.02742	+	0.147720i	0.392060	+	0.919940i	$0.371763\pi$
$240$	1.34708	−	1.78476i	0.0869539	−	0.115206i
$241$	2.05802	−	7.00896i	0.132569	−	0.451487i	−0.866275	−	0.499568i	$-0.833492\pi$
$241$	2.05802	−	7.00896i	0.132569	−	0.451487i	0.998843	+	0.0480806i	$0.0153104\pi$
$242$	5.21041	+	9.54215i	0.334938	+	0.613393i
$243$	0.936950	+	0.349464i	0.0601054	+	0.0224181i
$244$	0.135386	−	0.941634i	0.00866723	−	0.0602819i
$245$	−6.20839	+	3.95534i	−0.396640	+	0.252697i
$246$	−0.612321	+	1.34080i	−0.0390401	+	0.0854860i
$247$	4.04360	−	0.879631i	0.257288	−	0.0559696i
$248$	−0.687751	−	0.514844i	−0.0436723	−	0.0326926i
$249$	−5.75136	+	3.69617i	−0.364477	+	0.234235i
$250$	6.59364	+	9.02906i	0.417018	+	0.571048i
$251$	1.53925	+	5.24219i	0.0971563	+	0.330884i	0.993700	−	0.112071i	$-0.0357484\pi$
$251$	1.53925	+	5.24219i	0.0971563	+	0.330884i	−0.896544	+	0.442955i	$0.853930\pi$
$252$	−1.36160	+	1.36160i	−0.0857729	+	0.0857729i
$253$	3.72369	−	22.1177i	0.234107	−	1.39053i
$254$		−	3.27773i		−	0.205663i
$255$	−11.5646	−	0.0456636i	−0.724204	−	0.00285957i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−24.2315	−	5.27124i	−1.51152	−	0.328811i	−0.621020	−	0.783795i	$-0.713281\pi$
$257$	−24.2315	−	5.27124i	−1.51152	−	0.328811i	−0.890500	+	0.454984i	$0.849645\pi$
$258$	−7.09755	+	9.48122i	−0.441874	+	0.590275i
$259$	−10.1729	+	15.8294i	−0.632115	+	0.983590i
$260$	0.503914	+	7.45945i	0.0312514	+	0.462615i
$261$	5.62652	−	6.49335i	0.348273	−	0.401928i
$262$	−0.0678286	+	0.0507759i	−0.00419046	+	0.00313694i
$263$	6.69063	−	17.9383i	0.412562	−	1.10612i	−0.550025	−	0.835148i	$-0.685382\pi$
$263$	6.69063	−	17.9383i	0.412562	−	1.10612i	0.962587	−	0.270973i	$-0.0873453\pi$
$264$	−4.48731	−	1.31759i	−0.276175	−	0.0810923i
$265$	8.26815	−	1.76446i	0.507908	−	0.108390i
$266$	0.990023	+	2.16785i	0.0607022	+	0.132919i
$267$	−10.7699	−	14.3869i	−0.659105	−	0.880461i
$268$	11.7006	−	0.836842i	0.714727	−	0.0511183i
$269$	−27.3302	−	12.4813i	−1.66635	−	0.760998i	−0.999880	−	0.0154701i	$-0.995076\pi$
$269$	−27.3302	−	12.4813i	−1.66635	−	0.760998i	−0.666474	−	0.745528i	$-0.732197\pi$
$270$	1.45763	+	1.69568i	0.0887085	+	0.103196i
$271$	2.91362	+	20.2647i	0.176990	+	1.23099i	0.863680	+	0.504041i	$0.168154\pi$
$271$	2.91362	+	20.2647i	0.176990	+	1.23099i	−0.686690	+	0.726950i	$0.740937\pi$
$272$	−1.09936	+	5.05370i	−0.0666588	+	0.306425i
$273$	0.459308	−	6.42196i	0.0277986	−	0.388675i
$274$	1.82498	−	0.535862i	0.110251	−	0.0323726i
$275$	12.7972	−	19.5712i	0.771699	−	1.18019i
$276$	2.78109	+	3.90711i	0.167402	+	0.235180i
$277$	−9.26656	−	9.26656i	−0.556773	−	0.556773i	0.371614	−	0.928387i	$-0.378805\pi$
$277$	−9.26656	−	9.26656i	−0.556773	−	0.556773i	−0.928387	+	0.371614i	$0.878805\pi$
$278$	4.03333	−	7.38649i	0.241903	−	0.443012i
$279$	0.649271	−	0.562596i	0.0388708	−	0.0336817i
$280$	−4.13611	+	1.19675i	−0.247180	+	0.0715196i
$281$	14.0330	−	2.01764i	0.837139	−	0.120362i	0.289605	−	0.957146i	$-0.406476\pi$
$281$	14.0330	−	2.01764i	0.837139	−	0.120362i	0.547533	+	0.836784i	$0.315567\pi$
$282$	−1.16264	−	5.34458i	−0.0692343	−	0.318265i
$283$	20.9528	−	7.81497i	1.24551	−	0.464552i	0.361656	−	0.932312i	$-0.382211\pi$
$283$	20.9528	−	7.81497i	1.24551	−	0.464552i	0.883856	+	0.467760i	$0.154939\pi$
$284$	−3.92081	−	3.39740i	−0.232657	−	0.201599i
$285$	2.59678	−	0.956886i	0.153820	−	0.0566810i
$286$	14.2240	−	6.49587i	0.841081	−	0.384109i
$287$	2.49114	−	1.36026i	0.147047	−	0.0802938i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	8.86752	−	4.04966i	0.521619	−	0.238215i
$290$	18.0272	−	6.64283i	1.05859	−	0.390080i
$291$	11.1544	+	9.66534i	0.653883	+	0.566592i
$292$	−1.42027	+	0.529733i	−0.0831150	+	0.0310003i
$293$	−4.28174	−	19.6828i	−0.250142	−	1.14988i	−0.915171	−	0.403067i	$-0.867944\pi$
$293$	−4.28174	−	19.6828i	−0.250142	−	1.14988i	0.665029	−	0.746818i	$-0.268419\pi$
$294$	−3.25857	+	0.468511i	−0.190044	+	0.0273241i
$295$	21.7768	−	6.30094i	1.26789	−	0.366855i
$296$	7.38498	−	6.39912i	0.429243	−	0.371942i
$297$	2.24133	−	4.10469i	0.130055	−	0.238178i
$298$	−2.03654	−	2.03654i	−0.117973	−	0.117973i
$299$	−15.5825	−	3.78347i	−0.901157	−	0.218804i
$300$	1.02421	+	4.89398i	0.0591328	+	0.282554i
$301$	21.8820	−	6.42514i	1.26126	−	0.370339i
$302$	0.131192	−	1.83431i	0.00754928	−	0.105553i
$303$	1.89242	−	8.69932i	0.108717	−	0.499763i
$304$	−0.176136	−	1.22505i	−0.0101021	−	0.0702616i
$305$	1.38667	+	1.61313i	0.0794003	+	0.0923673i
$306$	−4.70452	−	2.14848i	−0.268939	−	0.122821i
$307$	−9.08427	+	0.649719i	−0.518466	+	0.0370814i	−0.328121	−	0.944636i	$-0.606415\pi$
$307$	−9.08427	+	0.649719i	−0.518466	+	0.0370814i	−0.190345	+	0.981717i	$0.560961\pi$
$308$	5.39682	+	7.20931i	0.307512	+	0.410788i
$309$	4.91879	+	10.7707i	0.279820	+	0.612721i
$310$	1.87872	−	0.400928i	0.106704	−	0.0227712i
$311$	−11.7546	−	3.45146i	−0.666543	−	0.195715i	−0.0690797	−	0.997611i	$-0.522006\pi$
$311$	−11.7546	−	3.45146i	−0.666543	−	0.195715i	−0.597463	+	0.801897i	$0.703824\pi$
$312$	−1.16846	+	3.13276i	−0.0661509	+	0.177357i
$313$	17.0236	−	12.7437i	0.962229	−	0.720315i	0.00213615	−	0.999998i	$-0.499320\pi$
$313$	17.0236	−	12.7437i	0.962229	−	0.720315i	0.960093	+	0.279682i	$0.0902291\pi$
$314$	10.0620	−	11.6121i	0.567829	−	0.655310i
$315$	−0.290209	−	4.29597i	−0.0163514	−	0.242051i
$316$	−1.07341	+	1.67025i	−0.0603839	+	0.0939591i
$317$	3.92123	−	5.23815i	0.220238	−	0.294204i	−0.676791	−	0.736175i	$-0.736630\pi$
$317$	3.92123	−	5.23815i	0.220238	−	0.294204i	0.897029	+	0.441972i	$0.145721\pi$
$318$	3.69448	+	0.803686i	0.207176	+	0.0450685i
$319$	−26.3139	−	30.3678i	−1.47329	−	1.70027i
$320$	2.23605	+	0.00882919i	0.124999	+	0.000493567i
$321$		−	9.51667i		−	0.531169i
$322$	0.221565	−	9.23218i	0.0123473	−	0.514489i
$323$	−4.52619	+	4.52619i	−0.251844	+	0.251844i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−13.3038	−	10.1240i	−0.737962	−	0.561579i
$326$	19.2450	−	12.3680i	1.06588	−	0.685000i
$327$	−4.67349	−	3.49853i	−0.258445	−	0.193469i
$328$	−1.44031	+	0.313321i	−0.0795279	+	0.0173002i
$329$	−4.37523	+	9.58042i	−0.241214	+	0.528186i
$330$	8.81970	−	5.61899i	0.485508	−	0.309315i
$331$	0.699572	−	4.86563i	0.0384519	−	0.267439i	−0.961521	−	0.274730i	$-0.911412\pi$
$331$	0.699572	−	4.86563i	0.0384519	−	0.267439i	0.999973	+	0.00729064i	$0.00232070\pi$
$332$	−6.40560	−	2.38916i	−0.351553	−	0.131122i
$333$	4.68309	+	8.57644i	0.256632	+	0.469986i
$334$	5.67183	−	19.3165i	0.310349	−	1.05695i
$335$	−15.8019	+	20.9361i	−0.863351	+	1.14386i
$336$	−1.90600	−	0.274041i	−0.103981	−	0.0149502i
$337$	−2.39104	−	33.4311i	−0.130248	−	1.82111i	−0.472311	−	0.881432i	$-0.656580\pi$
$337$	−2.39104	−	33.4311i	−0.130248	−	1.82111i	0.342063	−	0.939677i	$-0.388874\pi$
$338$	0.636213	+	1.70575i	0.0346054	+	0.0927808i
$339$	0.389730	+	0.250464i	0.0211672	+	0.0136033i
$340$	−6.89386	−	9.28531i	−0.373872	−	0.503567i
$341$	−2.17221	−	3.38002i	−0.117632	−	0.183038i
$342$	1.23450	+	0.0882930i	0.0667539	+	0.00477434i
$343$	17.3942	+	9.49794i	0.939198	+	0.512841i
$344$	−11.8435			−0.638559
$345$	−10.6709	−	1.06358i	−0.574504	−	0.0572614i
$346$	20.6328			1.10923
$347$	19.2269	+	10.4987i	1.03215	+	0.563599i	0.903722	−	0.428120i	$-0.140824\pi$
$347$	19.2269	+	10.4987i	1.03215	+	0.563599i	0.128432	+	0.991718i	$0.459006\pi$
$348$	8.57004	+	0.612942i	0.459403	+	0.0328571i
$349$	14.3530	+	22.3337i	0.768299	+	1.19550i	0.976099	+	0.217326i	$0.0697334\pi$
$349$	14.3530	+	22.3337i	0.768299	+	1.19550i	−0.207800	+	0.978171i	$0.566630\pi$
$350$	4.06865	−	8.72606i	0.217478	−	0.466428i
$351$	−2.81279	−	1.80767i	−0.150136	−	0.0964863i
$352$	−1.63436	−	4.38188i	−0.0871116	−	0.233555i
$353$	0.923601	+	12.9136i	0.0491583	+	0.687323i	0.960959	+	0.276690i	$0.0892376\pi$
$353$	0.923601	+	12.9136i	0.0491583	+	0.687323i	−0.911801	+	0.410633i	$0.865308\pi$
$354$	10.0351	+	1.44284i	0.533362	+	0.0766859i
$355$	11.4890	−	1.60560i	0.609774	−	0.0852162i
$356$	5.06313	−	17.2434i	0.268345	−	0.913901i
$357$	4.77283	+	8.74079i	0.252605	+	0.462611i
$358$	−15.6454	−	5.83542i	−0.826883	−	0.308412i
$359$	−1.21970	+	8.48323i	−0.0643735	+	0.447728i	0.931987	+	0.362491i	$0.118074\pi$
$359$	−1.21970	+	8.48323i	−0.0643735	+	0.447728i	−0.996361	+	0.0852366i	$0.972835\pi$
$360$	−0.483934	+	2.18307i	−0.0255056	+	0.115058i
$361$	−7.25656	+	15.8897i	−0.381924	+	0.836298i
$362$	2.53878	−	0.552278i	0.133435	−	0.0290271i
$363$	−8.70351	−	6.51536i	−0.456816	−	0.341968i
$364$	5.41630	−	3.48084i	0.283891	−	0.182446i
$365$	1.19705	−	3.17112i	0.0626565	−	0.165984i
$366$	0.268017	+	0.912782i	0.0140095	+	0.0477119i
$367$	−22.3382	+	22.3382i	−1.16605	+	1.16605i	−0.182917	+	0.983128i	$0.558554\pi$
$367$	−22.3382	+	22.3382i	−1.16605	+	1.16605i	−0.983128	+	0.182917i	$0.941446\pi$
$368$	−1.46116	+	4.56783i	−0.0761680	+	0.238114i
$369$		−	1.47400i		−	0.0767332i
$370$	−0.0862765	+	21.8501i	−0.00448530	+	1.13593i
$371$	−4.76769	−	5.50221i	−0.247526	−	0.285661i
$372$	0.839475	+	0.182617i	0.0435247	+	0.00946823i
$373$	19.3102	−	25.7954i	0.999845	−	1.33564i	0.0584641	−	0.998290i	$-0.481380\pi$
$373$	19.3102	−	25.7954i	0.999845	−	1.33564i	0.941381	−	0.337347i	$-0.109529\pi$
$374$	−13.0768	+	20.3480i	−0.676187	+	1.05217i
$375$	−9.74859	−	5.47403i	−0.503415	−	0.282677i
$376$	3.58181	−	4.13363i	0.184718	−	0.213176i
$377$	−22.9977	+	17.2159i	−1.18444	+	0.886663i
$378$	0.672927	−	1.80419i	0.0346116	−	0.0927974i
$379$	30.6864	+	9.01033i	1.57625	+	0.462830i	0.948814	−	0.315836i	$-0.102285\pi$
$379$	30.6864	+	9.01033i	1.57625	+	0.462830i	0.627439	+	0.778666i	$0.284103\pi$
$380$	2.32222	+	1.50539i	0.119127	+	0.0772248i
$381$	1.36162	+	2.98153i	0.0697578	+	0.152748i
$382$	3.73901	+	4.99473i	0.191304	+	0.255553i
$383$	22.0721	−	1.57863i	1.12783	−	0.0806641i	0.505072	−	0.863077i	$-0.331466\pi$
$383$	22.0721	−	1.57863i	1.12783	−	0.0806641i	0.622760	+	0.782413i	$0.286011\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	−20.0799	−	1.51586i	−1.02336	−	0.0772551i
$386$	−1.21133	−	8.42500i	−0.0616552	−	0.428821i
$387$	2.51752	−	11.5728i	0.127973	−	0.588281i
$388$	−1.05292	+	14.7218i	−0.0534540	+	0.747385i
$389$	1.88848	−	0.554508i	0.0957497	−	0.0281147i	−0.233507	−	0.972355i	$-0.575020\pi$
$389$	1.88848	−	0.554508i	0.0957497	−	0.0281147i	0.329257	+	0.944241i	$0.393202\pi$
$390$	−3.55714	−	6.57602i	−0.180123	−	0.332990i
$391$	23.4409	−	8.10787i	1.18546	−	0.410033i
$392$	−2.32785	−	2.32785i	−0.117574	−	0.117574i
$393$	0.0406060	−	0.0743644i	0.00204830	−	0.00375119i
$394$	17.9440	−	15.5486i	0.904006	−	0.783326i
$395$	−1.23394	−	4.26464i	−0.0620863	−	0.214577i
$396$	4.62915	−	0.665571i	0.232624	−	0.0334462i
$397$	−1.78908	−	8.22426i	−0.0897912	−	0.412764i	0.910208	−	0.414152i	$-0.135922\pi$
$397$	−1.78908	−	8.22426i	−0.0897912	−	0.412764i	−0.999999	+	0.00138821i	$0.999558\pi$
$398$	−15.6200	+	5.82598i	−0.782962	+	0.292030i
$399$	−1.80111	−	1.56067i	−0.0901685	−	0.0781314i
$400$	−3.30404	+	3.75277i	−0.165202	+	0.187639i
$401$	−20.8422	+	9.51832i	−1.04081	+	0.475322i	−0.861121	−	0.508401i	$-0.830237\pi$
$401$	−20.8422	+	9.51832i	−1.04081	+	0.475322i	−0.179690	+	0.983723i	$0.557510\pi$
$402$	−10.2956	+	5.62182i	−0.513497	+	0.280391i
$403$	−2.52112	+	1.37664i	−0.125586	+	0.0685752i
$404$	8.09825	−	3.69835i	0.402903	−	0.184000i
$405$	−2.03032	−	0.936920i	−0.100887	−	0.0465559i
$406$	−12.5036	−	10.8344i	−0.620542	−	0.537703i
$407$	42.8186	−	15.9705i	2.12244	−	0.791629i
$408$	−1.09936	−	5.05370i	−0.0544267	−	0.250195i
$409$	−22.9030	+	3.29295i	−1.13248	+	0.162826i	−0.682968	−	0.730448i	$-0.739311\pi$
$409$	−22.9030	+	3.29295i	−1.13248	+	0.162826i	−0.449512	+	0.893274i	$0.648402\pi$
$410$	1.59099	−	2.88653i	0.0785736	−	0.142556i
$411$	−1.43745	+	1.24556i	−0.0709043	+	0.0614390i
$412$	−5.67463	+	10.3923i	−0.279569	+	0.511992i
$413$	−13.8044	−	13.8044i	−0.679270	−	0.679270i
$414$	−4.15285	−	2.39872i	−0.204101	−	0.117891i
$415$	13.4461	−	7.27335i	0.660043	−	0.357035i
$416$	−3.20813	+	0.941993i	−0.157292	+	0.0461850i
$417$	−0.600386	+	8.39449i	−0.0294010	+	0.411080i
$418$	1.23037	−	5.65591i	0.0601792	−	0.276639i
$419$	2.02897	+	14.1118i	0.0991219	+	0.689408i	0.977422	+	0.211298i	$0.0677690\pi$
$419$	2.02897	+	14.1118i	0.0991219	+	0.689408i	−0.878300	+	0.478110i	$0.841322\pi$
$420$	3.26519	−	2.80681i	0.159325	−	0.136958i
$421$	3.93299	+	1.79614i	0.191682	+	0.0875383i	0.508944	−	0.860800i	$-0.330036\pi$
$421$	3.93299	+	1.79614i	0.191682	+	0.0875383i	−0.317262	+	0.948338i	$0.602763\pi$
$422$	14.9223	−	1.06727i	0.726407	−	0.0519536i
$423$	3.27780	+	4.37862i	0.159372	+	0.212896i
$424$	1.57064	+	3.43922i	0.0762769	+	0.167023i
$425$	25.7782	+	2.04843i	1.25043	+	0.0993633i
$426$	4.97783	+	1.46162i	0.241177	+	0.0708158i
$427$	0.640167	−	1.71635i	0.0309798	−	0.0830602i
$428$	7.61849	−	5.70313i	0.368254	−	0.275671i
$429$	−10.2401	+	11.8177i	−0.494396	+	0.570564i
$430$	17.4215	−	19.9458i	0.840139	−	0.961872i
$431$	−20.9792	+	32.6442i	−1.01053	+	1.57242i	−0.205960	+	0.978560i	$0.566032\pi$
$431$	−20.9792	+	32.6442i	−1.01053	+	1.57242i	−0.804571	+	0.593856i	$0.797605\pi$
$432$	−0.599278	+	0.800541i	−0.0288328	+	0.0385161i
$433$	−1.94439	−	0.422976i	−0.0934413	−	0.0203269i	0.165602	−	0.986193i	$-0.447043\pi$
$433$	−1.94439	−	0.422976i	−0.0934413	−	0.0203269i	−0.259043	+	0.965866i	$0.583407\pi$
$434$	−1.08333	−	1.25023i	−0.0520017	−	0.0600131i
$435$	−13.6386	+	13.5313i	−0.653920	+	0.648776i
$436$		−	5.83792i		−	0.279586i
$437$	−4.57776	+	3.77822i	−0.218984	+	0.180737i
$438$	1.07186	−	1.07186i	0.0512156	−	0.0512156i
$439$	−4.95664	−	16.8808i	−0.236568	−	0.805675i	−0.989116	−	0.147138i	$-0.952994\pi$
$439$	−4.95664	−	16.8808i	−0.236568	−	0.805675i	0.752548	−	0.658537i	$-0.228824\pi$
$440$	9.78368	+	3.69320i	0.466419	+	0.176066i
$441$	2.76947	−	1.77983i	0.131880	−	0.0847539i
$442$	13.8434	+	10.3631i	0.658465	+	0.492920i
$443$	−32.3599	+	7.03948i	−1.53747	+	0.334456i	−0.899954	−	0.435984i	$-0.856400\pi$
$443$	−32.3599	+	7.03948i	−1.53747	+	0.334456i	−0.637513	+	0.770440i	$0.720037\pi$
$444$	−4.05932	+	8.88868i	−0.192647	+	0.421838i
$445$	21.5922	+	33.8915i	1.02357	+	1.60661i
$446$	−1.43890	+	10.0078i	−0.0681339	+	0.473881i
$447$	2.69851	+	1.00649i	0.127635	+	0.0476054i
$448$	−0.922840	−	1.69006i	−0.0436001	−	0.0798476i
$449$	9.90073	−	33.7188i	0.467244	−	1.59129i	−0.302641	−	0.953105i	$-0.597868\pi$
$449$	9.90073	−	33.7188i	0.467244	−	1.59129i	0.769885	−	0.638183i	$-0.220314\pi$
$450$	−2.96469	−	4.02624i	−0.139757	−	0.189799i
$451$	−6.82336	−	0.981051i	−0.321299	−	0.0461959i
$452$	0.0330495	+	0.462092i	0.00155452	+	0.0217350i
$453$	0.642663	+	1.72305i	0.0301950	+	0.0809558i
$454$	−21.3047	−	13.6917i	−0.999880	−	0.642584i
$455$	−2.10510	+	14.2419i	−0.0986888	+	0.667670i
$456$	0.669124	+	1.04118i	0.0313346	+	0.0487576i
$457$	−18.3283	−	1.31086i	−0.857361	−	0.0613197i	−0.364266	−	0.931295i	$-0.618680\pi$
$457$	−18.3283	−	1.31086i	−0.857361	−	0.0613197i	−0.493095	+	0.869975i	$0.664135\pi$
$458$	2.18780	+	1.19463i	0.102229	+	0.0558214i
$459$	5.17189			0.241403
$460$	−5.54341	−	9.17990i	−0.258463	−	0.428015i
$461$	19.2241			0.895354			0.447677	−	0.894195i	$-0.352251\pi$
$461$	19.2241			0.895354			0.447677	+	0.894195i	$0.352251\pi$
$462$	−7.90397	−	4.31590i	−0.367726	−	0.200794i
$463$	16.5366	+	1.18272i	0.768523	+	0.0549658i	0.450094	−	0.892981i	$-0.351390\pi$
$463$	16.5366	+	1.18272i	0.768523	+	0.0549658i	0.318429	+	0.947947i	$0.396845\pi$
$464$	4.64515	+	7.22800i	0.215646	+	0.335551i
$465$	−1.54239	+	1.14515i	−0.0715267	+	0.0531048i
$466$	12.6670	+	8.14056i	0.586786	+	0.377104i
$467$	10.3979	+	27.8778i	0.481157	+	1.29003i	0.920158	+	0.391546i	$0.128060\pi$
$467$	10.3979	+	27.8778i	0.481157	+	1.29003i	−0.439001	+	0.898486i	$0.644668\pi$
$468$	−0.238528	−	3.33505i	−0.0110259	−	0.154163i
$469$	22.3582	+	3.21463i	1.03241	+	0.148438i
$470$	1.69275	+	12.1126i	0.0780805	+	0.558714i
$471$	−4.32883	+	14.7426i	−0.199462	+	0.679305i
$472$	4.85879	+	8.89821i	0.223644	+	0.409573i
$473$	−51.8969	−	19.3565i	−2.38622	−	0.890014i
$474$	0.282557	−	1.96523i	0.0129783	−	0.0902658i
$475$	−5.95117	+	1.69649i	−0.273058	+	0.0778402i
$476$	−4.13711	+	9.05900i	−0.189624	+	0.415219i
$477$	−3.69448	+	0.803686i	−0.169159	+	0.0367982i
$478$	−12.8461	−	9.61649i	−0.587568	−	0.439848i
$479$	15.6884	−	10.0823i	0.716822	−	0.460673i	−0.130708	−	0.991421i	$-0.541725\pi$
$479$	15.6884	−	10.0823i	0.716822	−	0.460673i	0.847530	+	0.530748i	$0.178089\pi$
$480$	−2.03765	+	0.920858i	−0.0930056	+	0.0420312i
$481$	−9.20490	−	31.3490i	−0.419707	−	1.42939i
$482$	−5.16532	+	5.16532i	−0.235274	+	0.235274i
$483$	3.63364	+	8.48993i	0.165336	+	0.386305i
$484$		−	10.8720i		−	0.494183i
$485$	−23.2443	−	23.4286i	−1.05547	−	1.06384i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−31.9635	−	6.95323i	−1.44840	−	0.315081i	−0.581495	−	0.813550i	$-0.697532\pi$
$487$	−31.9635	−	6.95323i	−1.44840	−	0.315081i	−0.866907	+	0.498469i	$0.833896\pi$
$488$	−0.570103	+	0.761568i	−0.0258073	+	0.0344746i
$489$	−12.3680	+	19.2450i	−0.559300	+	0.870287i
$490$	7.34457	−	0.496153i	0.331794	−	0.0224139i
$491$	−1.05111	+	1.21304i	−0.0474357	+	0.0547438i	−0.778972	−	0.627059i	$-0.784258\pi$
$491$	−1.05111	+	1.21304i	−0.0474357	+	0.0547438i	0.731536	+	0.681803i	$0.238804\pi$
$492$	1.18000	−	0.883334i	0.0531983	−	0.0398238i
$493$	15.5290	−	41.6348i	0.699390	−	1.87514i
$494$	−3.97055	−	1.16586i	−0.178643	−	0.0524544i
$495$	−5.68847	+	8.77505i	−0.255678	+	0.394409i
$496$	0.356886	+	0.781472i	0.0160247	+	0.0350891i
$497$	−5.98676	−	7.99737i	−0.268543	−	0.358731i
$498$	6.81923	−	0.487721i	0.305577	−	0.0218553i
$499$	11.5710	+	5.28429i	0.517988	+	0.236557i	0.657215	−	0.753703i	$-0.271734\pi$
$499$	11.5710	+	5.28429i	0.517988	+	0.236557i	−0.139227	+	0.990261i	$0.544462\pi$
$500$	−1.45993	−	11.0846i	−0.0652900	−	0.495719i
$501$	2.86508	+	19.9270i	0.128002	+	0.890274i
$502$	1.16135	−	5.33864i	0.0518336	−	0.238275i
$503$	−1.67227	+	23.3814i	−0.0745629	+	1.04253i	0.813128	+	0.582085i	$0.197763\pi$
$503$	−1.67227	+	23.3814i	−0.0745629	+	1.04253i	−0.887691	+	0.460441i	$0.847691\pi$
$504$	1.84760	−	0.542503i	0.0822985	−	0.0241650i
$505$	−5.68389	+	19.0785i	−0.252930	+	0.848984i
$506$	−13.8681	+	17.6276i	−0.616511	+	0.783644i
$507$	−1.28732	−	1.28732i	−0.0571717	−	0.0571717i
$508$	−1.57085	+	2.87679i	−0.0696951	+	0.127637i
$509$	15.7687	−	13.6636i	0.698935	−	0.605630i	−0.231175	−	0.972912i	$-0.574257\pi$
$509$	15.7687	−	13.6636i	0.698935	−	0.605630i	0.930110	+	0.367282i	$0.119712\pi$
$510$	10.1281	+	5.58241i	0.448481	+	0.247193i
$511$	−2.88920	+	0.415404i	−0.127810	+	0.0183764i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	−1.15962	+	0.432514i	−0.0511983	+	0.0190960i
$514$	18.7412	+	16.2394i	0.826641	+	0.716288i
$515$	−9.15458	−	24.8435i	−0.403399	−	1.09474i
$516$	10.7732	−	4.91997i	0.474265	−	0.216590i
$517$	22.4509	−	12.2591i	0.987390	−	0.539156i
$518$	16.5148	−	9.01775i	0.725617	−	0.396217i
$519$	−18.7683	+	8.57118i	−0.823836	+	0.376233i
$520$	3.13266	−	6.78850i	0.137376	−	0.297695i
$521$	4.40597	+	3.81779i	0.193029	+	0.167261i	0.746013	−	0.665931i	$-0.231966\pi$
$521$	4.40597	+	3.81779i	0.193029	+	0.167261i	−0.552984	+	0.833192i	$0.686511\pi$
$522$	−8.05021	+	3.00257i	−0.352348	+	0.131419i
$523$	−2.66596	−	12.2552i	−0.116574	−	0.535884i	−0.997980	−	0.0635243i	$-0.979766\pi$
$523$	−2.66596	−	12.2552i	−0.116574	−	0.535884i	0.881406	−	0.472360i	$-0.156598\pi$
$524$	0.0838660	−	0.0120581i	0.00366370	−	0.000526761i
$525$	−0.0760323	+	9.62768i	−0.00331832	+	0.420187i
$526$	−14.4691	+	12.5376i	−0.630883	+	0.546664i
$527$	2.12941	−	3.89972i	0.0927584	−	0.169874i
$528$	3.30696	+	3.30696i	0.143917	+	0.143917i
$529$	22.3538	−	5.41375i	0.971903	−	0.235381i
$530$	−8.10240	−	2.41387i	−0.351946	−	0.104852i
$531$	−9.72767	+	2.85630i	−0.422145	+	0.123953i
$532$	0.170017	−	2.37714i	0.00737115	−	0.103062i
$533$	−1.04761	+	4.81578i	−0.0453770	+	0.208595i
$534$	2.55760	+	17.7885i	0.110678	+	0.769783i
$535$	−1.60189	+	21.2196i	−0.0692558	+	0.917401i
$536$	−10.6704	−	4.87301i	−0.460892	−	0.210482i
$537$	16.6556	−	1.19124i	0.718744	−	0.0514056i
$538$	18.0055	+	24.0526i	0.776273	+	1.03698i
$539$	−6.39583	−	14.0049i	−0.275488	−	0.603234i
$540$	−0.466679	−	2.18683i	−0.0200827	−	0.0941060i
$541$	−21.5164	−	6.31778i	−0.925061	−	0.271622i	−0.215694	−	0.976461i	$-0.569201\pi$
$541$	−21.5164	−	6.31778i	−0.925061	−	0.271622i	−0.709368	+	0.704839i	$0.751019\pi$
$542$	7.15460	−	19.1822i	0.307316	−	0.823947i
$543$	−2.07993	+	1.55702i	−0.0892583	+	0.0668180i
$544$	3.38687	−	3.90866i	0.145211	−	0.167582i
$545$	9.83171	+	8.58743i	0.421144	+	0.367845i
$546$	−3.48084	+	5.41630i	−0.148966	+	0.231796i
$547$	−2.52026	+	3.36667i	−0.107758	+	0.143948i	−0.851178	−	0.524877i	$-0.824111\pi$
$547$	−2.52026	+	3.36667i	−0.107758	+	0.143948i	0.743420	+	0.668825i	$0.233202\pi$
$548$	−1.85856	−	0.404304i	−0.0793936	−	0.0172710i
$549$	−0.622980	−	0.718957i	−0.0265881	−	0.0306843i
$550$	−20.6113	+	11.0442i	−0.878869	+	0.470927i
$551$			10.6338i			0.453015i
$552$	−0.568430	−	4.76203i	−0.0241940	−	0.202685i
$553$	−2.70337	+	2.70337i	−0.114959	+	0.114959i
$554$	3.69207	+	12.5741i	0.156861	+	0.534220i
$555$	−8.99838	−	19.9114i	−0.381960	−	0.845191i
$556$	−7.07993	+	4.55000i	−0.300256	+	0.192963i
$557$	10.7229	+	8.02704i	0.454342	+	0.340116i	0.801814	−	0.597574i	$-0.203869\pi$
$557$	10.7229	+	8.02704i	0.454342	+	0.340116i	−0.347471	+	0.937691i	$0.612960\pi$
$558$	−0.839475	+	0.182617i	−0.0355378	+	0.00773077i
$559$	−16.4503	+	36.0211i	−0.695772	+	1.52353i
$560$	4.20372	+	0.931862i	0.177640	+	0.0393784i
$561$	3.44226	−	23.9415i	0.145332	−	1.01081i
$562$	−13.2834	−	4.95446i	−0.560327	−	0.208991i
$563$	−6.14890	−	11.2609i	−0.259145	−	0.474589i	0.715419	−	0.698695i	$-0.246236\pi$
$563$	−6.14890	−	11.2609i	−0.259145	−	0.474589i	−0.974565	+	0.224106i	$0.928054\pi$
$564$	−1.54096	+	5.24802i	−0.0648860	+	0.220982i
$565$	−0.826831	−	0.624067i	−0.0347850	−	0.0262547i
$566$	−22.1351	−	3.18255i	−0.930408	−	0.133772i
$567$	0.137370	+	1.92069i	0.00576902	+	0.0806614i
$568$	1.81301	+	4.86088i	0.0760723	+	0.203958i
$569$	−3.41359	−	2.19378i	−0.143105	−	0.0919682i	0.467129	−	0.884189i	$-0.345288\pi$
$569$	−3.41359	−	2.19378i	−0.143105	−	0.0919682i	−0.610234	+	0.792221i	$0.708925\pi$
$570$	−2.73772	−	0.404665i	−0.114671	−	0.0169496i
$571$	−0.759069	−	1.18113i	−0.0317661	−	0.0494289i	0.825007	−	0.565122i	$-0.191171\pi$
$571$	−0.759069	−	1.18113i	−0.0317661	−	0.0494289i	−0.856773	+	0.515693i	$0.827535\pi$
$572$	−15.5972	−	1.11553i	−0.652152	−	0.0466429i
$573$	−5.47601	−	2.99013i	−0.228764	−	0.124914i
$574$	−2.83832			−0.118469
$575$	23.6142	+	4.16768i	0.984780	+	0.173804i
$576$	−1.00000			−0.0416667
$577$	−10.7211	−	5.85414i	−0.446324	−	0.243711i	0.240337	−	0.970690i	$-0.422742\pi$
$577$	−10.7211	−	5.85414i	−0.446324	−	0.243711i	−0.686660	+	0.726978i	$0.740924\pi$
$578$	−9.72363	−	0.695448i	−0.404450	−	0.0289268i
$579$	4.60174	+	7.16044i	0.191242	+	0.297578i
$580$	−19.0057	−	2.80924i	−0.789167	−	0.116647i
$581$	−11.0748	−	7.11734i	−0.459460	−	0.295277i
$582$	−5.15788	−	13.8288i	−0.213801	−	0.573222i
$583$	1.26144	+	17.6372i	0.0522435	+	0.730460i
$584$	1.50042	+	0.215727i	0.0620876	+	0.00892685i
$585$	5.96747	+	4.50407i	0.246724	+	0.186220i
$586$	−5.67499	+	19.3272i	−0.234432	+	0.798401i
$587$	2.11538	+	3.87403i	0.0873110	+	0.159898i	0.917686	−	0.397307i	$-0.130055\pi$
$587$	2.11538	+	3.87403i	0.0873110	+	0.159898i	−0.830375	+	0.557206i	$0.811874\pi$
$588$	3.08451	+	1.15046i	0.127203	+	0.0474443i
$589$	−0.151320	+	1.05245i	−0.00623503	+	0.0433656i
$590$	−22.1327	−	4.90629i	−0.911190	−	0.201989i
$591$	−9.86334	+	21.5977i	−0.405724	+	0.888411i
$592$	−9.54842	+	2.07713i	−0.392438	+	0.0853696i
$593$	13.5970	+	10.1786i	0.558363	+	0.417985i	0.840836	−	0.541290i	$-0.182064\pi$
$593$	13.5970	+	10.1786i	0.558363	+	0.417985i	−0.282473	+	0.959275i	$0.591155\pi$
$594$	−3.93434	+	2.52844i	−0.161428	+	0.103743i
$595$	−9.17080	−	20.2929i	−0.375966	−	0.831929i
$596$	0.811418	+	2.76344i	0.0332370	+	0.113195i
$597$	11.7883	−	11.7883i	0.482463	−	0.482463i
$598$	11.8632	+	10.7886i	0.485121	+	0.441177i
$599$			3.37234i			0.137790i	0.997624	+	0.0688950i	$0.0219473\pi$
$599$			3.37234i			0.137790i	−0.997624	+	0.0688950i	$0.978053\pi$
$600$	1.44650	−	4.78619i	0.0590533	−	0.195395i
$601$	16.3669	+	18.8884i	0.667621	+	0.770476i	0.984002	−	0.178156i	$-0.0570133\pi$
$601$	16.3669	+	18.8884i	0.667621	+	0.770476i	−0.316381	+	0.948632i	$0.602468\pi$
$602$	−22.2846	−	4.84773i	−0.908254	−	0.197579i
$603$	7.02981	−	9.39073i	0.286276	−	0.382420i
$604$	−0.994236	+	1.54706i	−0.0404549	+	0.0629491i
$605$	18.3097	+	15.9925i	0.744396	+	0.650187i
$606$	−5.83008	+	6.72827i	−0.236831	+	0.273317i
$607$	26.8435	−	20.0948i	1.08954	−	0.815621i	0.105654	−	0.994403i	$-0.466306\pi$
$607$	26.8435	−	20.0948i	1.08954	−	0.815621i	0.983889	+	0.178781i	$0.0572155\pi$
$608$	−0.432514	+	1.15962i	−0.0175408	+	0.0470286i
$609$	15.8744	+	4.66115i	0.643264	+	0.188879i
$610$	−0.443960	−	2.08036i	−0.0179754	−	0.0842315i
$611$	−7.59707	−	16.6353i	−0.307345	−	0.672991i
$612$	3.09940	+	4.14031i	0.125286	+	0.167362i
$613$	−9.53526	+	0.681975i	−0.385126	+	0.0275447i	−0.262560	−	0.964916i	$-0.584567\pi$
$613$	−9.53526	+	0.681975i	−0.385126	+	0.0275447i	−0.122566	+	0.992460i	$0.539112\pi$
$614$	8.28445	+	3.78338i	0.334333	+	0.152685i
$615$	−0.248110	+	3.28661i	−0.0100048	+	0.132529i
$616$	−1.28162	−	8.91388i	−0.0516380	−	0.359150i
$617$	−3.30067	+	15.1729i	−0.132880	+	0.610839i	0.861749	+	0.507335i	$0.169369\pi$
$617$	−3.30067	+	15.1729i	−0.132880	+	0.610839i	−0.994629	+	0.103505i	$0.966994\pi$
$618$	0.844704	−	11.8105i	0.0339790	−	0.475088i
$619$	−4.15104	+	1.21886i	−0.166844	+	0.0489899i	−0.364088	−	0.931365i	$-0.618619\pi$
$619$	−4.15104	+	1.21886i	−0.166844	+	0.0489899i	0.197244	+	0.980355i	$0.436801\pi$
$620$	−1.84106	−	0.548489i	−0.0739387	−	0.0220278i
$621$	4.77403	+	0.456802i	0.191575	+	0.0183308i
$622$	8.66266	+	8.66266i	0.347341	+	0.347341i
$623$	16.5847	−	30.3727i	0.664454	−	1.21686i
$624$	2.52690	−	2.18957i	0.101157	−	0.0876531i
$625$	20.8152	+	13.8465i	0.832610	+	0.553860i
$626$	−21.0486	+	3.02633i	−0.841272	+	0.120957i
$627$	1.23037	+	5.65591i	0.0491361	+	0.225875i
$628$	−14.3963	+	5.36953i	−0.574473	+	0.214267i
$629$	38.1943	+	33.0956i	1.52291	+	1.31961i
$630$	−1.80413	+	3.90957i	−0.0718783	+	0.155761i
$631$	−3.64400	+	1.66416i	−0.145065	+	0.0662492i	−0.486625	−	0.873611i	$-0.661772\pi$
$631$	−3.64400	+	1.66416i	−0.145065	+	0.0662492i	0.341560	+	0.939860i	$0.389045\pi$
$632$	1.74257	−	0.951518i	0.0693159	−	0.0378493i
$633$	−13.1305	+	7.16977i	−0.521889	+	0.284973i
$634$	−5.95196	+	2.71817i	−0.236382	+	0.107952i
$635$	−2.53417	−	6.87717i	−0.100565	−	0.272912i
$636$	−2.85741	−	2.47596i	−0.113304	−	0.0981780i
$637$	−10.3133	+	3.84665i	−0.408627	+	0.152410i
$638$	8.54138	+	39.2641i	0.338156	+	1.55448i
$639$	−5.13517	+	0.738326i	−0.203144	+	0.0292077i
$640$	−1.95830	−	1.07937i	−0.0774087	−	0.0426660i
$641$	21.5856	−	18.7040i	0.852580	−	0.738765i	−0.114450	−	0.993429i	$-0.536510\pi$
$641$	21.5856	−	18.7040i	0.852580	−	0.738765i	0.967030	+	0.254664i	$0.0819650\pi$
$642$	−4.56086	+	8.35259i	−0.180003	+	0.329650i
$643$	6.97098	+	6.97098i	0.274909	+	0.274909i	0.831073	−	0.556164i	$-0.187727\pi$
$643$	6.97098	+	6.97098i	0.274909	+	0.274909i	−0.556164	+	0.831073i	$0.687727\pi$
$644$	−4.61898	+	7.99670i	−0.182013	+	0.315114i
$645$	−7.56137	+	25.3805i	−0.297729	+	0.999356i
$646$	6.14171	−	1.80337i	0.241642	−	0.0709526i
$647$	1.10440	−	15.4415i	0.0434184	−	0.607069i	−0.928437	−	0.371490i	$-0.878847\pi$
$647$	1.10440	−	15.4415i	0.0434184	−	0.607069i	0.971855	−	0.235579i	$-0.0756986\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	6.74779	+	46.9319i	0.264874	+	1.84224i
$650$	6.82454	+	15.2615i	0.267680	+	0.598604i
$651$	1.50480	+	0.687219i	0.0589778	+	0.0269342i
$652$	−22.8182	+	1.63199i	−0.893632	+	0.0639138i
$653$	4.15753	+	5.55381i	0.162697	+	0.217337i	0.874480	−	0.485062i	$-0.161203\pi$
$653$	4.15753	+	5.55381i	0.162697	+	0.217337i	−0.711783	+	0.702399i	$0.752112\pi$
$654$	2.42516	+	5.31036i	0.0948312	+	0.207651i
$655$	−0.103058	+	0.158977i	−0.00402679	+	0.00621174i
$656$	1.41429	+	0.415273i	0.0552187	+	0.0162137i
$657$	−0.529733	+	1.42027i	−0.0206669	+	0.0554100i
$658$	8.43146	−	6.31171i	0.328692	−	0.246056i
$659$	20.2957	−	23.4225i	0.790609	−	0.912412i	−0.207218	−	0.978295i	$-0.566441\pi$
$659$	20.2957	−	23.4225i	0.790609	−	0.912412i	0.997827	+	0.0658832i	$0.0209865\pi$
$660$	−10.4338	+	0.704840i	−0.406134	+	0.0274359i
$661$	−8.47601	+	13.1889i	−0.329679	+	0.512990i	−0.966037	−	0.258403i	$-0.916804\pi$
$661$	−8.47601	+	13.1889i	−0.329679	+	0.512990i	0.636358	+	0.771394i	$0.280440\pi$
$662$	−2.94585	+	3.93519i	−0.114494	+	0.152946i
$663$	−16.8974	−	3.67580i	−0.656240	−	0.142756i
$664$	4.47705	+	5.16680i	0.173743	+	0.200511i
$665$	3.75329	+	3.78304i	0.145546	+	0.146700i
$666$		−	9.77173i		−	0.378647i
$667$	18.0117	−	37.0603i	0.697417	−	1.43498i
$668$	−14.2354	+	14.2354i	−0.550786	+	0.550786i
$669$	−2.84851	−	9.70112i	−0.110130	−	0.375067i
$670$	23.9026	−	10.8021i	0.923438	−	0.417321i
$671$	−3.74280	+	2.40535i	−0.144489	+	0.0928576i
$672$	1.54152	+	1.15397i	0.0594654	+	0.0445152i
$673$	−21.6620	+	4.71229i	−0.835010	+	0.181645i	−0.609690	−	0.792640i	$-0.708706\pi$
$673$	−21.6620	+	4.71229i	−0.835010	+	0.181645i	−0.225319	+	0.974285i	$0.572343\pi$
$674$	−13.9233	+	30.4877i	−0.536304	+	1.17434i
$675$	4.36933	+	2.43083i	0.168176	+	0.0935625i
$676$	0.259090	−	1.80201i	0.00996499	−	0.0693080i
$677$	−5.73354	−	2.13850i	−0.220358	−	0.0821892i	0.236861	−	0.971544i	$-0.423882\pi$
$677$	−5.73354	−	2.13850i	−0.220358	−	0.0821892i	−0.457218	+	0.889354i	$0.651154\pi$
$678$	−0.222023	−	0.406605i	−0.00852674	−	0.0156156i
$679$	−8.00702	+	27.2694i	−0.307281	+	1.04650i
$680$	1.60062	+	11.4534i	0.0613809	+	0.439218i
$681$	25.0672	+	3.60412i	0.960577	+	0.138110i
$682$	0.286629	+	4.00760i	0.0109756	+	0.153459i
$683$	5.35896	+	14.3679i	0.205055	+	0.549773i	0.998246	−	0.0591992i	$-0.0188547\pi$
$683$	5.35896	+	14.3679i	0.205055	+	0.549773i	−0.793191	+	0.608972i	$0.791582\pi$
$684$	−1.04118	−	0.669124i	−0.0398104	−	0.0255846i
$685$	3.41478	−	2.53530i	0.130472	−	0.0968687i
$686$	−10.7146	−	16.6723i	−0.409086	−	0.636551i
$687$	−2.48636	−	0.177828i	−0.0948607	−	0.00678457i
$688$	10.3948	+	5.67599i	0.396298	+	0.216395i
$689$	12.6417			0.481609
$690$	8.85593	+	6.04752i	0.337140	+	0.230225i
$691$	−17.9176			−0.681618			−0.340809	−	0.940133i	$-0.610701\pi$
$691$	−17.9176			−0.681618			−0.340809	+	0.940133i	$0.610701\pi$
$692$	−18.1090	−	9.88826i	−0.688400	−	0.375895i
$693$	8.98260	+	0.642448i	0.341221	+	0.0244046i
$694$	−11.8436	−	18.4289i	−0.449575	−	0.699553i
$695$	2.75169	−	18.6163i	0.104378	−	0.706158i
$696$	−7.22800	−	4.64515i	−0.273976	−	0.176074i
$697$	−2.66409	−	7.14270i	−0.100910	−	0.270549i
$698$	−1.89392	−	26.4805i	−0.0716861	−	1.00230i
$699$	−14.9040	−	2.14287i	−0.563720	−	0.0810507i
$700$	−7.75292	+	5.70879i	−0.293033	+	0.215772i
$701$	−10.7049	+	36.4576i	−0.404319	+	1.37698i	0.466126	+	0.884718i	$0.345649\pi$
$701$	−10.7049	+	36.4576i	−0.404319	+	1.37698i	−0.870445	+	0.492266i	$0.836169\pi$
$702$	1.60240	+	2.93458i	0.0604788	+	0.110759i
$703$	−11.3315	−	4.22642i	−0.427374	−	0.159402i
$704$	−0.665571	+	4.62915i	−0.0250847	+	0.174468i
$705$	−6.57155	−	10.3148i	−0.247499	−	0.388480i
$706$	5.37822	−	11.7767i	0.202412	−	0.443220i
$707$	16.7514	−	3.64404i	0.630001	−	0.137048i
$708$	−8.11616	−	6.07568i	−0.305024	−	0.228338i
$709$	−17.8564	+	11.4756i	−0.670613	+	0.430977i	−0.831146	−	0.556054i	$-0.812315\pi$
$709$	−17.8564	+	11.4756i	−0.670613	+	0.430977i	0.160534	+	0.987030i	$0.448679\pi$
$710$	−10.8532	−	4.09691i	−0.407312	−	0.153754i
$711$	0.559362	+	1.90501i	0.0209777	+	0.0714435i
$712$	−12.7077	+	12.7077i	−0.476242	+	0.476242i
$713$	2.31003	−	3.41164i	0.0865114	−	0.127767i
$714$		−	9.95898i		−	0.372705i
$715$	24.8218	−	24.6265i	0.928282	−	0.920980i
$716$	10.9350	+	12.6197i	0.408660	+	0.471619i
$717$	15.6801	+	3.41099i	0.585583	+	0.127386i
$718$	5.13609	−	6.86101i	0.191677	−	0.256051i
$719$	−18.5644	+	28.8867i	−0.692335	+	1.07729i	0.300027	+	0.953931i	$0.403004\pi$
$719$	−18.5644	+	28.8867i	−0.692335	+	1.07729i	−0.992362	+	0.123363i	$0.960632\pi$
$720$	1.47097	−	1.68411i	0.0548200	−	0.0627632i
$721$	−14.9311	+	17.2314i	−0.556062	+	0.641729i
$722$	13.9840	−	10.4683i	0.520432	−	0.389590i
$723$	2.55279	−	6.84429i	0.0949392	−	0.254542i
$724$	−2.49291	−	0.731985i	−0.0926483	−	0.0272040i
$725$	32.6879	−	27.8753i	1.21400	−	1.03526i
$726$	4.51640	+	9.88954i	0.167619	+	0.367035i
$727$	−15.3166	−	20.4605i	−0.568060	−	0.758839i	0.420886	−	0.907113i	$-0.361719\pi$
$727$	−15.3166	−	20.4605i	−0.568060	−	0.758839i	−0.988946	+	0.148274i	$0.952628\pi$
$728$	−6.42196	+	0.459308i	−0.238014	+	0.0170231i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	−2.57038	+	2.20954i	−0.0951341	+	0.0817787i
$731$	−8.71726	−	60.6299i	−0.322420	−	2.24248i
$732$	0.202217	−	0.929576i	0.00747415	−	0.0343581i
$733$	2.64091	−	36.9247i	0.0975442	−	1.36385i	−0.679164	−	0.733986i	$-0.737658\pi$
$733$	2.64091	−	36.9247i	0.0975442	−	1.36385i	0.776709	−	0.629860i	$-0.216888\pi$
$734$	30.3113	−	8.90022i	1.11881	−	0.328513i
$735$	−6.47475	+	3.50236i	−0.238825	+	0.129187i
$736$	3.47155	−	3.30883i	0.127963	−	0.121965i
$737$	−38.7923	−	38.7923i	−1.42893	−	1.42893i
$738$	−0.706412	+	1.29370i	−0.0260034	+	0.0476216i
$739$	−2.49817	+	2.16467i	−0.0918965	+	0.0796288i	−0.699598	−	0.714537i	$-0.746637\pi$
$739$	−2.49817	+	2.16467i	−0.0918965	+	0.0796288i	0.607701	+	0.794166i	$0.292092\pi$
$740$	10.5474	−	19.1360i	0.387729	−	0.703454i
$741$	4.09605	−	0.588923i	0.150472	−	0.0216346i
$742$	1.54757	+	7.11409i	0.0568133	+	0.261166i
$743$	−35.8185	+	13.3596i	−1.31405	+	0.490116i	−0.906168	−	0.422918i	$-0.861006\pi$
$743$	−35.8185	+	13.3596i	−1.31405	+	0.490116i	−0.407884	+	0.913034i	$0.633733\pi$
$744$	−0.649271	−	0.562596i	−0.0238034	−	0.0206258i
$745$	−5.84751	−	2.69842i	−0.214236	−	0.0988626i
$746$	−29.3106	+	13.3857i	−1.07314	+	0.490085i
$747$	−6.00039	+	3.27646i	−0.219543	+	0.119879i
$748$	21.2290	−	11.5919i	0.776209	−	0.423842i
$749$	16.6693	−	7.61260i	0.609081	−	0.278158i
$750$	5.93271	+	9.47644i	0.216632	+	0.346031i
$751$	−1.74858	−	1.51515i	−0.0638065	−	0.0552886i	0.622374	−	0.782720i	$-0.286168\pi$
$751$	−1.74858	−	1.51515i	−0.0638065	−	0.0552886i	−0.686180	+	0.727432i	$0.740714\pi$
$752$	−5.12472	+	1.91142i	−0.186879	+	0.0697024i
$753$	1.16135	+	5.33864i	0.0423220	+	0.194551i
$754$	28.4353	−	4.08838i	1.03555	−	0.148890i
$755$	−1.14293	−	3.95009i	−0.0415955	−	0.143759i
$756$	−1.45527	+	1.26100i	−0.0529276	+	0.0458620i
$757$	−19.9867	+	36.6029i	−0.726430	+	1.33036i	0.209374	+	0.977836i	$0.432857\pi$
$757$	−19.9867	+	36.6029i	−0.726430	+	1.33036i	−0.935804	+	0.352521i	$0.885324\pi$
$758$	−22.6146	−	22.6146i	−0.821399	−	0.821399i
$759$	5.29206	−	21.7957i	0.192090	−	0.791132i
$760$	−1.31671	−	2.43417i	−0.0477619	−	0.0882966i
$761$	−19.8268	+	5.82166i	−0.718720	+	0.211035i	−0.620586	−	0.784138i	$-0.713105\pi$
$761$	−19.8268	+	5.82166i	−0.718720	+	0.211035i	−0.0981334	+	0.995173i	$0.531287\pi$
$762$	0.233830	−	3.26938i	0.00847078	−	0.118437i
$763$	2.38955	−	10.9846i	0.0865074	−	0.397668i
$764$	−0.887930	−	6.17569i	−0.0321242	−	0.223429i
$765$	−11.5319	−	0.870557i	−0.416936	−	0.0314751i
$766$	−20.1288	−	9.19250i	−0.727282	−	0.332139i
$767$	33.8119	−	2.41827i	1.22088	−	0.0873188i
$768$	−0.599278	−	0.800541i	−0.0216246	−	0.0288870i
$769$	4.20220	+	9.20153i	0.151535	+	0.331816i	0.970142	−	0.242539i	$-0.0779803\pi$
$769$	4.20220	+	9.20153i	0.151535	+	0.331816i	−0.818606	+	0.574355i	$0.805253\pi$
$770$	16.8972	+	10.9537i	0.608933	+	0.394744i
$771$	−23.7937	−	6.98647i	−0.856910	−	0.251611i
$772$	−2.97451	+	7.97497i	−0.107055	+	0.287026i
$773$	0.212390	−	0.158993i	0.00763912	−	0.00571857i	−0.595451	−	0.803391i	$-0.703027\pi$
$773$	0.212390	−	0.158993i	0.00763912	−	0.00571857i	0.603090	+	0.797673i	$0.293936\pi$
$774$	−7.75585	+	8.95073i	−0.278778	+	0.321727i
$775$	3.63187	−	2.29373i	0.130460	−	0.0823934i
$776$	7.97953	−	12.4164i	0.286448	−	0.445722i
$777$	−11.2763	+	15.0633i	−0.404534	+	0.540394i
$778$	−1.92323	−	0.418372i	−0.0689510	−	0.0149994i
$779$	1.19466	+	1.37871i	0.0428031	+	0.0493974i
$780$	−0.0295210	+	7.47639i	−0.00105702	+	0.267698i
$781$			24.2629i			0.868195i
$782$	−24.4593	−	4.11793i	−0.874663	−	0.147257i
$783$	6.07542	−	6.07542i	0.217118	−	0.217118i
$784$	0.927485	+	3.15873i	0.0331245	+	0.112812i
$785$	12.1336	−	32.1434i	0.433068	−	1.14725i
$786$	−0.0712781	+	0.0458076i	−0.00254241	+	0.00163390i
$787$	−11.0926	−	8.30384i	−0.395409	−	0.296000i	0.383010	−	0.923744i	$-0.374887\pi$
$787$	−11.0926	−	8.30384i	−0.395409	−	0.296000i	−0.778420	+	0.627744i	$0.783978\pi$
$788$	−23.2007	+	5.04701i	−0.826492	+	0.179792i
$789$	7.95328	−	17.4153i	0.283144	−	0.619999i
$790$	−0.960820	+	4.33435i	−0.0341844	+	0.154209i
$791$	−0.126956	+	0.882997i	−0.00451403	+	0.0313957i
$792$	−4.38188	−	1.63436i	−0.155703	−	0.0580744i
$793$	1.52439	+	2.79172i	0.0541328	+	0.0991368i
$794$	−2.37123	+	8.07567i	−0.0841518	+	0.286595i
$795$	8.37296	−	1.17012i	0.296958	−	0.0415000i
$796$	16.5015	+	2.37255i	0.584880	+	0.0840930i
$797$	3.78322	+	52.8964i	0.134009	+	1.87369i	0.409403	+	0.912354i	$0.365737\pi$
$797$	3.78322	+	52.8964i	0.134009	+	1.87369i	−0.275394	+	0.961331i	$0.588808\pi$
$798$	0.832848	+	2.23295i	0.0294825	+	0.0790457i
$799$	23.7974	+	15.2937i	0.841893	+	0.541051i
$800$	4.69840	−	1.71027i	0.166114	−	0.0604672i
$801$	−9.71608	−	15.1185i	−0.343301	−	0.534186i
$802$	22.8544	+	1.63458i	0.807018	+	0.0577191i
$803$	6.22207	+	3.39751i	0.219572	+	0.119895i
$804$	11.7305			0.413702
$805$	−6.67295	−	19.5418i	−0.235191	−	0.688759i
$806$	2.87249			0.101179
$807$	−26.3702	−	14.3992i	−0.928275	−	0.506877i
$808$	−8.88010	−	0.635117i	−0.312401	−	0.0223433i
$809$	18.6172	+	28.9689i	0.654545	+	1.01849i	0.996881	+	0.0789139i	$0.0251452\pi$
$809$	18.6172	+	28.9689i	0.654545	+	1.01849i	−0.342337	+	0.939577i	$0.611218\pi$
$810$	1.33295	+	1.79534i	0.0468350	+	0.0630819i
$811$	24.4366	+	15.7044i	0.858084	+	0.551457i	0.894086	−	0.447895i	$-0.147826\pi$
$811$	24.4366	+	15.7044i	0.858084	+	0.551457i	−0.0360025	+	0.999352i	$0.511462\pi$
$812$	5.78175	+	15.5015i	0.202899	+	0.543995i
$813$	1.46053	+	20.4209i	0.0512230	+	0.716192i
$814$	−45.2348	−	6.50379i	−1.58548	−	0.227958i
$815$	30.8166	−	40.8291i	1.07946	−	1.43018i
$816$	−1.45709	+	4.96239i	−0.0510084	+	0.173719i
$817$	7.02489	+	12.8651i	0.245770	+	0.450094i
$818$	21.6796	+	8.08608i	0.758010	+	0.282723i
$819$	0.916275	−	6.37283i	0.0320172	−	0.222685i
$820$	−2.77975	+	1.77097i	−0.0970731	+	0.0618449i
$821$	0.235349	−	0.515342i	0.00821373	−	0.0179856i	−0.905481	−	0.424387i	$-0.860489\pi$
$821$	0.235349	−	0.515342i	0.00821373	−	0.0179856i	0.913694	+	0.406402i	$0.133217\pi$
$822$	1.85856	−	0.404304i	0.0648246	−	0.0141017i
$823$	−15.4456	−	11.5624i	−0.538399	−	0.403041i	0.295179	−	0.955442i	$-0.404621\pi$
$823$	−15.4456	−	11.5624i	−0.538399	−	0.403041i	−0.833578	+	0.552401i	$0.813712\pi$
$824$	9.96100	−	6.40155i	0.347008	−	0.223009i
$825$	14.1608	−	18.6084i	0.493015	−	0.647862i
$826$	5.50008	+	18.7316i	0.191372	+	0.651754i
$827$	−32.6438	+	32.6438i	−1.13514	+	1.13514i	−0.145825	+	0.989310i	$0.546584\pi$
$827$	−32.6438	+	32.6438i	−1.13514	+	1.13514i	−0.989310	+	0.145825i	$0.953416\pi$
$828$	2.49528	+	4.09556i	0.0867169	+	0.142330i
$829$			17.3711i			0.603324i	0.953415	+	0.301662i	$0.0975414\pi$
$829$			17.3711i			0.603324i	−0.953415	+	0.301662i	$0.902459\pi$
$830$	−15.2871	−	0.0603621i	−0.530623	−	0.00209520i
$831$	−8.58188	−	9.90402i	−0.297702	−	0.343567i
$832$	3.26716	+	0.710727i	0.113268	+	0.0246400i
$833$	10.2035	−	13.6302i	0.353529	−	0.472260i
$834$	4.55000	−	7.07993i	0.157553	−	0.245158i
$835$	−3.03411	−	44.9140i	−0.105000	−	1.55431i
$836$	−3.79046	+	4.37442i	−0.131096	+	0.151292i
$837$	0.687751	−	0.514844i	0.0237722	−	0.0177956i
$838$	4.98229	−	13.3580i	0.172110	−	0.461446i
$839$	−22.3023	−	6.54854i	−0.769960	−	0.226081i	−0.126920	−	0.991913i	$-0.540509\pi$
$839$	−22.3023	−	6.54854i	−0.769960	−	0.226081i	−0.643040	+	0.765832i	$0.722327\pi$
$840$	−4.21095	+	0.898636i	−0.145291	+	0.0310059i
$841$	−18.6195	−	40.7709i	−0.642050	−	1.40589i
$842$	−2.59111	−	3.46131i	−0.0892954	−	0.119285i
$843$	14.1412	−	1.01140i	0.487048	−	0.0348344i
$844$	−13.6085	−	6.21479i	−0.468423	−	0.213922i
$845$	2.65367	+	3.08704i	0.0912890	+	0.106198i
$846$	−0.778402	−	5.41390i	−0.0267620	−	0.186134i
$847$	4.45008	−	20.4567i	0.152907	−	0.702901i
$848$	0.269726	−	3.77126i	0.00926241	−	0.129505i
$849$	21.4569	−	6.30031i	0.736398	−	0.216226i
$850$	−21.6433	−	14.1520i	−0.742358	−	0.485411i
$851$	32.3330	+	33.9231i	1.10836	+	1.16287i
$852$	−3.66845	−	3.66845i	−0.125679	−	0.125679i
$853$	−0.0122498	+	0.0224338i	−0.000419424	+	0.000768118i	−0.877889	−	0.478865i	$-0.841048\pi$
$853$	−0.0122498	+	0.0224338i	−0.000419424	+	0.000768118i	0.877469	+	0.479633i	$0.159230\pi$
$854$	−1.38442	+	1.19961i	−0.0473739	+	0.0410497i
$855$	2.65843	−	0.769195i	0.0909162	−	0.0263059i
$856$	−9.41981	+	1.35436i	−0.321962	+	0.0462912i
$857$	0.377782	+	1.73664i	0.0129048	+	0.0593224i	0.983149	−	0.182806i	$-0.0585181\pi$
$857$	0.377782	+	1.73664i	0.0129048	+	0.0593224i	−0.970244	+	0.242129i	$0.922154\pi$
$858$	14.6511	−	5.46459i	0.500181	−	0.186558i
$859$	12.4988	+	10.8303i	0.426455	+	0.369526i	0.841483	−	0.540283i	$-0.181683\pi$
$859$	12.4988	+	10.8303i	0.426455	+	0.369526i	−0.415028	+	0.909809i	$0.636228\pi$
$860$	−24.8495	+	9.15678i	−0.847361	+	0.312243i
$861$	2.58183	−	1.17908i	0.0879885	−	0.0401830i
$862$	34.0577	−	18.5969i	1.16001	−	0.633413i
$863$	−22.8719	+	12.4890i	−0.778570	+	0.425131i	−0.818814	−	0.574059i	$-0.805368\pi$
$863$	−22.8719	+	12.4890i	−0.778570	+	0.425131i	0.0402443	+	0.999190i	$0.487186\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	43.2908	−	15.9522i	1.47193	−	0.542391i
$866$	1.50384	+	1.30308i	0.0511025	+	0.0442806i
$867$	9.13382	−	3.40674i	0.310201	−	0.115699i
$868$	0.351646	+	1.61649i	0.0119356	+	0.0548672i
$869$	9.19088	−	1.32145i	0.311779	−	0.0448271i
$870$	18.4552	−	5.33986i	0.625688	−	0.181038i
$871$	−29.6417	+	25.6847i	−1.00437	+	0.870294i
$872$	−2.79782	+	5.12382i	−0.0947460	+	0.173514i
$873$	10.4365	+	10.4365i	0.353221	+	0.353221i
$874$	5.82852	−	1.12218i	0.197153	−	0.0379582i
$875$	1.79011	−	21.4543i	0.0605167	−	0.725287i
$876$	−1.45444	+	0.427063i	−0.0491411	+	0.0144291i
$877$	−1.65711	+	23.1694i	−0.0559566	+	0.782375i	0.889563	+	0.456812i	$0.151009\pi$
$877$	−1.65711	+	23.1694i	−0.0559566	+	0.782375i	−0.945520	+	0.325564i	$0.894446\pi$
$878$	−3.73975	+	17.1914i	−0.126210	+	0.580180i
$879$	−2.86667	−	19.9382i	−0.0966905	−	0.672497i
$880$	−6.81697	−	7.93026i	−0.229800	−	0.267329i
$881$	22.6385	+	10.3386i	0.762710	+	0.348318i	0.758500	−	0.651673i	$-0.225933\pi$
$881$	22.6385	+	10.3386i	0.762710	+	0.348318i	0.00421003	+	0.999991i	$0.498660\pi$
$882$	−3.28369	+	0.234854i	−0.110568	+	0.00790795i
$883$	22.0943	+	29.5145i	0.743532	+	0.993242i	0.999646	+	0.0265959i	$0.00846674\pi$
$883$	22.0943	+	29.5145i	0.743532	+	0.993242i	−0.256114	+	0.966646i	$0.582442\pi$
$884$	−7.18360	−	15.7299i	−0.241611	−	0.529053i
$885$	22.1708	−	4.73135i	0.745263	−	0.159043i
$886$	31.7753	+	9.33007i	1.06751	+	0.313450i
$887$	−14.2747	+	38.2719i	−0.479297	+	1.28505i	0.442290	+	0.896872i	$0.354166\pi$
$887$	−14.2747	+	38.2719i	−0.479297	+	1.28505i	−0.921587	+	0.388173i	$0.873106\pi$
$888$	7.82268	−	5.85598i	0.262512	−	0.196514i
$889$	−4.13321	+	4.76998i	−0.138623	+	0.159980i
$890$	−2.70850	−	40.0939i	−0.0907890	−	1.34395i
$891$	2.52844	−	3.93434i	0.0847061	−	0.131805i
$892$	6.05910	−	8.09401i	0.202874	−	0.271008i
$893$	−6.61472	−	1.43894i	−0.221353	−	0.0481524i
$894$	−1.88606	−	2.17663i	−0.0630794	−	0.0727975i
$895$	−37.3380	−	0.147432i	−1.24807	−	0.00492809i
$896$			1.92560i			0.0643297i
$897$	−15.2728	−	4.88547i	−0.509945	−	0.163121i
$898$	−24.8494	+	24.8494i	−0.829234	+	0.829234i
$899$	−2.07958	−	7.08240i	−0.0693579	−	0.236211i
$900$	0.672469	+	4.95457i	0.0224156	+	0.165152i
$901$	−16.4502	+	10.5719i	−0.548035	+	0.352200i
$902$	5.51855	+	4.13113i	0.183748	+	0.137552i
$903$	22.2846	−	4.84773i	0.741586	−	0.161322i
$904$	0.192450	−	0.421408i	0.00640081	−	0.0140158i
$905$	4.89975	−	3.12161i	0.162873	−	0.103766i
$906$	0.261716	−	1.82028i	0.00869495	−	0.0604747i
$907$	−18.5004	−	6.90028i	−0.614295	−	0.229120i	0.0230059	−	0.999735i	$-0.492676\pi$
$907$	−18.5004	−	6.90028i	−0.614295	−	0.229120i	−0.637301	+	0.770615i	$0.719949\pi$
$908$	12.1370	+	22.2272i	0.402779	+	0.737635i
$909$	2.50820	−	8.54216i	0.0831919	−	0.283325i
$910$	8.67302	−	11.4909i	0.287508	−	0.380921i
$911$	54.1049	+	7.77911i	1.79258	+	0.257733i	0.956677	−	0.291151i	$-0.0940382\pi$
$911$	54.1049	+	7.77911i	1.79258	+	0.257733i	0.835898	+	0.548884i	$0.184947\pi$
$912$	−0.0882930	−	1.23450i	−0.00292367	−	0.0408783i
$913$	11.1735	+	29.9574i	0.369790	+	0.991446i
$914$	15.4581	+	9.93433i	0.511309	+	0.328598i
$915$	1.26805	+	1.70794i	0.0419206	+	0.0564627i
$916$	−1.34766	−	2.09700i	−0.0445280	−	0.0692870i
$917$	0.162737	+	0.0116392i	0.00537405	+	0.000384360i
$918$	−4.53926	−	2.47862i	−0.149818	−	0.0818068i
$919$	10.4227			0.343813			0.171907	−	0.985113i	$-0.445007\pi$
$919$	10.4227			0.343813			0.171907	+	0.985113i	$0.445007\pi$
$920$	0.465874	+	10.7137i	0.0153594	+	0.353220i
$921$	−9.10747			−0.300101
$922$	−16.8726	−	9.21311i	−0.555668	−	0.303418i
$923$	17.3022	+	1.23748i	0.569508	+	0.0407320i
$924$	4.86876	+	7.57594i	0.160171	+	0.249230i
$925$	16.7123	+	45.9115i	0.549497	+	1.50956i
$926$	−13.9470	−	8.96322i	−0.458328	−	0.294550i
$927$	4.13789	+	11.0941i	0.135906	+	0.364378i
$928$	−0.612942	−	8.57004i	−0.0201208	−	0.281325i
$929$	−30.8625	−	4.43736i	−1.01257	−	0.145585i	−0.383993	−	0.923336i	$-0.625451\pi$
$929$	−30.8625	−	4.43736i	−1.01257	−	0.145585i	−0.628573	+	0.777751i	$0.716361\pi$
$930$	1.90254	−	0.265880i	0.0623866	−	0.00871855i
$931$	−1.14790	+	3.90940i	−0.0376210	+	0.128125i
$932$	−7.21617	−	13.2154i	−0.236373	−	0.432886i
$933$	−11.4784	−	4.28123i	−0.375787	−	0.140161i
$934$	4.23441	−	29.4510i	0.138554	−	0.963665i
$935$	−11.7052	+	52.8034i	−0.382802	+	1.72686i
$936$	−1.38897	+	3.04142i	−0.0453999	+	0.0994119i
$937$	45.1911	−	9.83072i	1.47633	−	0.321155i	0.598884	−	0.800835i	$-0.295611\pi$
$937$	45.1911	−	9.83072i	1.47633	−	0.321155i	0.877444	+	0.479680i	$0.159247\pi$
$938$	−18.0828	−	13.5366i	−0.590423	−	0.441985i
$939$	17.8893	−	11.4968i	0.583796	−	0.375183i
$940$	4.31928	−	11.4423i	0.140879	−	0.373205i
$941$	−14.4804	−	49.3156i	−0.472046	−	1.60764i	−0.759949	−	0.649983i	$-0.774776\pi$
$941$	−14.4804	−	49.3156i	−0.472046	−	1.60764i	0.287902	−	0.957660i	$-0.407042\pi$
$942$	10.8647	−	10.8647i	0.353992	−	0.353992i
$943$	−1.82827	−	6.82853i	−0.0595368	−	0.222367i
$944$		−	10.1383i		−	0.329975i
$945$	0.0170015	−	4.30573i	0.000553058	−	0.140065i
$946$	36.2722	+	41.8604i	1.17931	+	1.36100i
$947$	20.7202	+	4.50741i	0.673317	+	0.146471i	0.536209	−	0.844085i	$-0.319856\pi$
$947$	20.7202	+	4.50741i	0.673317	+	0.146471i	0.137108	+	0.990556i	$0.456219\pi$
$948$	−1.18983	+	1.58942i	−0.0386438	+	0.0516220i
$949$	2.74015	−	4.26375i	0.0889490	−	0.138407i
$950$	6.03625	+	1.36312i	0.195842	+	0.0442254i
$951$	4.28492	−	4.94506i	0.138948	−	0.160355i
$952$	7.97257	−	5.96819i	0.258393	−	0.193430i
$953$	15.5878	−	41.7925i	0.504939	−	1.35379i	−0.395362	−	0.918525i	$-0.629381\pi$
$953$	15.5878	−	41.7925i	0.504939	−	1.35379i	0.900301	−	0.435268i	$-0.143346\pi$
$954$	3.62774	+	1.06520i	0.117452	+	0.0344871i
$955$	11.7067	+	7.58890i	0.378819	+	0.245571i
$956$	6.66608	+	14.5967i	0.215596	+	0.472090i
$957$	−24.0804	−	32.1676i	−0.778409	−	1.03983i
$958$	−18.6013	+	1.33039i	−0.600982	+	0.0429831i
$959$	−3.33155	−	1.52147i	−0.107581	−	0.0491308i
$960$	2.22972	+	0.168325i	0.0719640	+	0.00543266i
$961$	4.30672	+	29.9539i	0.138927	+	0.966255i
$962$	−6.94503	+	31.9258i	−0.223917	+	1.02933i
$963$	0.678912	−	9.49243i	0.0218776	−	0.305889i
$964$	7.00896	−	2.05802i	0.225743	−	0.0662843i
$965$	−9.05532	−	16.7404i	−0.291501	−	0.538892i
$966$	0.879617	−	9.19285i	0.0283012	−	0.295775i
$967$	−1.96505	−	1.96505i	−0.0631917	−	0.0631917i	0.674805	−	0.737996i	$-0.264228\pi$
$967$	−1.96505	−	1.96505i	−0.0631917	−	0.0631917i	−0.737996	+	0.674805i	$0.764228\pi$
$968$	−5.21041	+	9.54215i	−0.167469	+	0.306696i
$969$	−4.83755	+	4.19176i	−0.155404	+	0.134659i
$970$	9.17291	+	31.7026i	0.294524	+	1.01791i
$971$	−13.0021	+	1.86942i	−0.417258	+	0.0599927i	−0.347747	−	0.937588i	$-0.613053\pi$
$971$	−13.0021	+	1.86942i	−0.417258	+	0.0599927i	−0.0695114	+	0.997581i	$0.522144\pi$
$972$	0.212565	+	0.977147i	0.00681803	+	0.0313420i
$973$	−15.1839	+	5.66331i	−0.486774	+	0.181557i
$974$	24.7213	+	21.4212i	0.792123	+	0.686378i
$975$	−12.5477	−	11.0473i	−0.401847	−	0.353797i
$976$	0.865348	−	0.395191i	0.0276991	−	0.0126498i
$977$	−35.0515	+	19.1395i	−1.12140	+	0.612328i	−0.929402	−	0.369068i	$-0.879677\pi$
$977$	−35.0515	+	19.1395i	−1.12140	+	0.612328i	−0.191993	+	0.981396i	$0.561495\pi$
$978$	20.0783	−	10.9636i	0.642032	−	0.350576i
$979$	−76.4526	+	34.9148i	−2.44344	+	1.11588i
$980$	−6.68396	−	3.08441i	−0.213511	−	0.0985280i
$981$	−4.41200	−	3.82302i	−0.140864	−	0.122060i
$982$	1.50388	−	0.560919i	0.0479908	−	0.0178996i
$983$	−3.58035	−	16.4586i	−0.114195	−	0.524948i	−0.998333	−	0.0577209i	$-0.981617\pi$
$983$	−3.58035	−	16.4586i	−0.114195	−	0.524948i	0.884137	−	0.467227i	$-0.154747\pi$
$984$	−1.45899	+	0.209772i	−0.0465110	+	0.00668728i
$985$	25.6279	−	46.4966i	0.816574	−	1.48151i
$986$	−33.5829	+	29.0998i	−1.06950	+	0.926725i
$987$	−5.04755	+	9.24389i	−0.160665	+	0.294236i
$988$	2.92613	+	2.92613i	0.0930925	+	0.0930925i
$989$	−2.69158	−	56.7357i	−0.0855874	−	1.80409i
$990$	9.19808	−	4.97549i	0.292334	−	0.158131i
$991$	46.2357	−	13.5760i	1.46873	−	0.431257i	0.553041	−	0.833154i	$-0.313467\pi$
$991$	46.2357	−	13.5760i	1.46873	−	0.431257i	0.915685	+	0.401897i	$0.131649\pi$
$992$	0.0612881	−	0.856919i	0.00194590	−	0.0272072i
$993$	1.04490	−	4.80332i	0.0331589	−	0.152429i
$994$	1.42172	+	9.88827i	0.0450942	+	0.313637i
$995$	−28.2689	+	24.3004i	−0.896185	+	0.770374i
$996$	−6.21884	−	2.84005i	−0.197051	−	0.0899904i
$997$	−24.4409	+	1.74805i	−0.774050	+	0.0553611i	−0.452775	−	0.891625i	$-0.649566\pi$
$997$	−24.4409	+	1.74805i	−0.774050	+	0.0553611i	−0.321275	+	0.946986i	$0.604111\pi$
$998$	−7.62312	−	10.1833i	−0.241306	−	0.322347i
$999$	4.05932	+	8.88868i	0.128431	+	0.281225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.1	✓	240
5.3	odd	4	inner	690.2.w.b.313.1	yes	240
23.5	odd	22	inner	690.2.w.b.97.1	yes	240
115.28	even	44	inner	690.2.w.b.373.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.1	✓	240	1.1	even	1	trivial
690.2.w.b.97.1	yes	240	23.5	odd	22	inner
690.2.w.b.313.1	yes	240	5.3	odd	4	inner
690.2.w.b.373.1	yes	240	115.28	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)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.21203 - 0.326962i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.672927 + 1.80419i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(0.997452 + 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.21203 - 0.326962i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.672927 + 1.80419i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.78476 + 1.34708i) q^{10} +(1.31759 - 4.48731i) q^{11} +(0.479249 + 0.877679i) q^{12} +(-3.13276 - 1.16846i) q^{13} +(0.274041 - 1.90600i) q^{14} +(-2.18307 - 0.483934i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(5.05370 - 1.09936i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-1.04118 + 0.669124i) q^{19} +(-0.920858 - 2.03765i) q^{20} +(0.542503 + 1.84760i) q^{21} +(-3.30696 + 3.30696i) q^{22} +(4.76203 - 0.568430i) q^{23} -1.00000i q^{24} +(4.78619 + 1.44650i) q^{25} +(2.18957 + 2.52690i) q^{26} +(0.977147 + 0.212565i) q^{27} +(-1.15397 + 1.54152i) q^{28} +(4.64515 - 7.22800i) q^{29} +(1.68411 + 1.47097i) q^{30} +(0.562596 - 0.649271i) q^{31} +(0.800541 - 0.599278i) q^{32} +(1.63436 - 4.38188i) q^{33} +(-4.96239 - 1.45709i) q^{34} +(-0.898636 - 4.21095i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.85598 + 7.82268i) q^{37} +(1.23450 - 0.0882930i) q^{38} +(-3.04142 - 1.38897i) q^{39} +(-0.168325 + 2.22972i) q^{40} +(-0.209772 - 1.45899i) q^{41} +(0.409315 - 1.88159i) q^{42} +(0.844906 - 11.8133i) q^{43} +(4.48731 - 1.31759i) q^{44} +(-2.14299 - 0.638440i) q^{45} +(-4.45195 - 1.78330i) q^{46} +(3.86757 + 3.86757i) q^{47} +(-0.479249 + 0.877679i) q^{48} +(2.48799 - 2.15585i) q^{49} +(-3.50750 - 3.56334i) q^{50} +(5.11925 - 0.736037i) q^{51} +(-0.710727 - 3.26716i) q^{52} +(-3.54250 + 1.32129i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-4.38175 + 9.49529i) q^{55} +(1.75158 - 0.799922i) q^{56} +(-1.08626 + 0.593143i) q^{57} +(-7.54096 + 4.11768i) q^{58} +(-9.22216 + 4.21162i) q^{59} +(-0.773147 - 2.09815i) q^{60} +(-0.718957 - 0.622980i) q^{61} +(-0.804941 + 0.300227i) q^{62} +(0.409315 + 1.88159i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(6.54772 + 3.60896i) q^{65} +(-3.53445 + 3.06262i) q^{66} +(5.62182 - 10.2956i) q^{67} +(3.65708 + 3.65708i) q^{68} +(4.79044 - 0.227262i) q^{69} +(-1.22938 + 4.12653i) q^{70} +(-4.97783 + 1.46162i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-0.322216 + 1.48120i) q^{73} +(-1.39066 - 9.67227i) q^{74} +(4.67080 + 1.78426i) q^{75} +(-1.12581 - 0.514138i) q^{76} +(8.98260 - 0.642448i) q^{77} +(2.00373 + 2.67667i) q^{78} +(0.824779 + 1.80601i) q^{79} +(1.21633 - 1.87631i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-0.515109 + 1.38106i) q^{82} +(-5.47302 + 4.09705i) q^{83} +(-1.26100 + 1.45527i) q^{84} +(-11.5384 + 0.779463i) q^{85} +(-6.40308 + 9.96339i) q^{86} +(5.14895 - 6.87820i) q^{87} +(-4.56988 - 0.994116i) q^{88} +(-11.7688 - 13.5819i) q^{89} +(1.57488 + 1.58737i) q^{90} -6.43837i q^{91} +(3.05274 + 3.69875i) q^{92} +(0.607481 - 0.607481i) q^{93} +(-1.54096 - 5.24802i) q^{94} +(2.52190 - 1.13970i) q^{95} +(0.841254 - 0.540641i) q^{96} +(11.8155 + 8.84497i) q^{97} +(-3.21684 + 0.699781i) q^{98} +(1.94279 - 4.25413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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