LMFDB - Embedded newform 690.2.w.a.37.3

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			37.3
Character	$\chi$	$=$	690.37
Dual form			690.2.w.a.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-0.00639501 + 2.23606i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.30166 - 3.48989i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-0.00639501 + 2.23606i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.30166 - 3.48989i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.07724 - 1.95948i) q^{10} +(-0.225966 + 0.769570i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(1.22483 + 0.456836i) q^{13} +(-0.530084 + 3.68682i) q^{14} +(0.165897 - 2.22991i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-3.93060 + 0.855049i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-0.491542 + 0.315895i) q^{19} +(-1.88455 + 1.20352i) q^{20} +(1.04938 + 3.57385i) q^{21} +(0.567142 - 0.567142i) q^{22} +(3.71435 - 3.03375i) q^{23} +1.00000i q^{24} +(-4.99992 - 0.0285992i) q^{25} +(-0.856065 - 0.987952i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(2.23215 - 2.98180i) q^{28} +(2.74626 - 4.27327i) q^{29} +(-1.21428 + 1.87763i) q^{30} +(5.05025 - 5.82829i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.280291 - 0.751489i) q^{33} +(3.85958 + 1.13328i) q^{34} +(7.81191 - 2.88827i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-6.52609 - 8.71784i) q^{37} +(0.582809 - 0.0416833i) q^{38} +(-1.18911 - 0.543050i) q^{39} +(2.23082 - 0.153140i) q^{40} +(0.881991 + 6.13438i) q^{41} +(0.791748 - 3.63961i) q^{42} +(0.717812 - 10.0363i) q^{43} +(-0.769570 + 0.225966i) q^{44} +(-0.324554 + 2.21239i) q^{45} +(-4.71392 + 0.882560i) q^{46} +(-1.91485 - 1.91485i) q^{47} +(0.479249 - 0.877679i) q^{48} +(-5.19473 + 4.50126i) q^{49} +(4.37462 + 2.42131i) q^{50} +(3.98158 - 0.572465i) q^{51} +(0.277876 + 1.27737i) q^{52} +(9.70639 - 3.62029i) q^{53} +(0.755750 + 0.654861i) q^{54} +(-1.71936 - 0.510195i) q^{55} +(-3.38813 + 1.54731i) q^{56} +(0.512825 - 0.280024i) q^{57} +(-4.45829 + 2.43441i) q^{58} +(3.28291 - 1.49926i) q^{59} +(1.96561 - 1.06602i) q^{60} +(-11.5687 - 10.0243i) q^{61} +(-7.22570 + 2.69505i) q^{62} +(-0.791748 - 3.63961i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-1.02935 + 2.73586i) q^{65} +(-0.606156 + 0.525237i) q^{66} +(6.10572 - 11.1818i) q^{67} +(-2.84435 - 2.84435i) q^{68} +(-3.92131 + 2.76104i) q^{69} +(-8.24055 - 1.20888i) q^{70} +(-6.59515 + 1.93651i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-1.29853 + 5.96927i) q^{73} +(1.54980 + 10.7791i) q^{74} +(4.98514 + 0.385216i) q^{75} +(-0.531495 - 0.242726i) q^{76} +(2.97984 - 0.213123i) q^{77} +(0.783404 + 1.04651i) q^{78} +(-0.806153 - 1.76523i) q^{79} +(-2.03133 - 0.934710i) q^{80} +(0.959493 + 0.281733i) q^{81} +(2.16579 - 5.80671i) q^{82} +(-7.46240 + 5.58628i) q^{83} +(-2.43918 + 2.81496i) q^{84} +(-1.88680 - 8.79451i) q^{85} +(-5.43991 + 8.46466i) q^{86} +(-3.04412 + 4.06646i) q^{87} +(0.783730 + 0.170490i) q^{88} +(-5.95402 - 6.87131i) q^{89} +(1.34514 - 1.78622i) q^{90} -4.86915i q^{91} +(4.56028 + 1.48454i) q^{92} +(-5.45316 + 5.45316i) q^{93} +(0.762935 + 2.59832i) q^{94} +(-0.703216 - 1.10114i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-4.00761 - 3.00006i) q^{97} +(6.71653 - 1.46109i) q^{98} +(-0.333188 + 0.729579i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	−0.00639501	+	2.23606i	−0.00285994	+	0.999996i
$5$	−0.00639501	+	2.23606i	−0.00285994	+	0.999996i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−1.30166	−	3.48989i	−0.491981	−	1.31905i	−0.911498	−	0.411305i	$-0.865073\pi$
$7$	−1.30166	−	3.48989i	−0.491981	−	1.31905i	0.419517	−	0.907748i	$-0.362200\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	1.07724	−	1.95948i	0.340654	−	0.619641i
$11$	−0.225966	+	0.769570i	−0.0681314	+	0.232034i	−0.986519	−	0.163648i	$-0.947674\pi$
$11$	−0.225966	+	0.769570i	−0.0681314	+	0.232034i	0.918387	+	0.395683i	$0.129492\pi$
$12$	−0.479249	−	0.877679i	−0.138347	−	0.253364i
$13$	1.22483	+	0.456836i	0.339705	+	0.126704i	0.513527	−	0.858074i	$-0.328339\pi$
$13$	1.22483	+	0.456836i	0.339705	+	0.126704i	−0.173821	+	0.984777i	$0.555611\pi$
$14$	−0.530084	+	3.68682i	−0.141671	+	0.985344i
$15$	0.165897	−	2.22991i	0.0428345	−	0.575759i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−3.93060	+	0.855049i	−0.953310	+	0.207380i	−0.662214	−	0.749314i	$-0.730383\pi$
$17$	−3.93060	+	0.855049i	−0.953310	+	0.207380i	−0.291095	+	0.956694i	$0.594020\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	−0.491542	+	0.315895i	−0.112767	+	0.0724713i	−0.595809	−	0.803126i	$-0.703168\pi$
$19$	−0.491542	+	0.315895i	−0.112767	+	0.0724713i	0.483041	+	0.875598i	$0.339532\pi$
$20$	−1.88455	+	1.20352i	−0.421398	+	0.269116i
$21$	1.04938	+	3.57385i	0.228993	+	0.779879i
$22$	0.567142	−	0.567142i	0.120915	−	0.120915i
$23$	3.71435	−	3.03375i	0.774495	−	0.632580i
$23$	3.71435	−	3.03375i	0.774495	−	0.632580i
$24$			1.00000i			0.204124i
$25$	−4.99992	−	0.0285992i	−0.999984	−	0.00571985i
$26$	−0.856065	−	0.987952i	−0.167888	−	0.193753i
$27$	−0.977147	−	0.212565i	−0.188052	−	0.0409082i
$28$	2.23215	−	2.98180i	0.421836	−	0.563507i
$29$	2.74626	−	4.27327i	0.509968	−	0.793526i	−0.486829	−	0.873497i	$-0.661847\pi$
$29$	2.74626	−	4.27327i	0.509968	−	0.793526i	0.996797	+	0.0799716i	$0.0254830\pi$
$30$	−1.21428	+	1.87763i	−0.221697	+	0.342808i
$31$	5.05025	−	5.82829i	0.907051	−	1.04679i	−0.0916478	−	0.995791i	$-0.529213\pi$
$31$	5.05025	−	5.82829i	0.907051	−	1.04679i	0.998699	−	0.0510010i	$-0.0162412\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	0.280291	−	0.751489i	0.0487924	−	0.130818i
$34$	3.85958	+	1.13328i	0.661913	+	0.194355i
$35$	7.81191	−	2.88827i	1.32045	−	0.488207i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−6.52609	−	8.71784i	−1.07288	−	1.43320i	−0.893300	−	0.449461i	$-0.851616\pi$
$37$	−6.52609	−	8.71784i	−1.07288	−	1.43320i	−0.179582	−	0.983743i	$-0.557475\pi$
$38$	0.582809	−	0.0416833i	0.0945440	−	0.00676192i
$39$	−1.18911	−	0.543050i	−0.190411	−	0.0869577i
$40$	2.23082	−	0.153140i	0.352723	−	0.0242135i
$41$	0.881991	+	6.13438i	0.137744	+	0.958030i	0.935065	+	0.354475i	$0.115340\pi$
$41$	0.881991	+	6.13438i	0.137744	+	0.958030i	−0.797322	+	0.603555i	$0.793750\pi$
$42$	0.791748	−	3.63961i	0.122169	−	0.561604i
$43$	0.717812	−	10.0363i	0.109465	−	1.53053i	−0.585020	−	0.811019i	$-0.698914\pi$
$43$	0.717812	−	10.0363i	0.109465	−	1.53053i	0.694486	−	0.719506i	$-0.255632\pi$
$44$	−0.769570	+	0.225966i	−0.116017	+	0.0340657i
$45$	−0.324554	+	2.21239i	−0.0483817	+	0.329803i
$46$	−4.71392	+	0.882560i	−0.695030	+	0.130126i
$47$	−1.91485	−	1.91485i	−0.279310	−	0.279310i	0.553523	−	0.832834i	$-0.313283\pi$
$47$	−1.91485	−	1.91485i	−0.279310	−	0.279310i	−0.832834	+	0.553523i	$0.813283\pi$
$48$	0.479249	−	0.877679i	0.0691736	−	0.126682i
$49$	−5.19473	+	4.50126i	−0.742105	+	0.643037i
$50$	4.37462	+	2.42131i	0.618664	+	0.342424i
$51$	3.98158	−	0.572465i	0.557533	−	0.0801611i
$52$	0.277876	+	1.27737i	0.0385344	+	0.177140i
$53$	9.70639	−	3.62029i	1.33327	−	0.497286i	0.421073	−	0.907027i	$-0.361654\pi$
$53$	9.70639	−	3.62029i	1.33327	−	0.497286i	0.912202	+	0.409741i	$0.134381\pi$
$54$	0.755750	+	0.654861i	0.102844	+	0.0891153i
$55$	−1.71936	−	0.510195i	−0.231838	−	0.0687947i
$56$	−3.38813	+	1.54731i	−0.452758	+	0.206768i
$57$	0.512825	−	0.280024i	0.0679254	−	0.0370901i
$58$	−4.45829	+	2.43441i	−0.585403	+	0.319654i
$59$	3.28291	−	1.49926i	0.427399	−	0.195187i	−0.190089	−	0.981767i	$-0.560878\pi$
$59$	3.28291	−	1.49926i	0.427399	−	0.195187i	0.617488	+	0.786580i	$0.288150\pi$
$60$	1.96561	−	1.06602i	0.253759	−	0.137622i
$61$	−11.5687	−	10.0243i	−1.48122	−	1.28348i	−0.871037	−	0.491218i	$-0.836552\pi$
$61$	−11.5687	−	10.0243i	−1.48122	−	1.28348i	−0.610180	−	0.792263i	$-0.708903\pi$
$62$	−7.22570	+	2.69505i	−0.917665	+	0.342271i
$63$	−0.791748	−	3.63961i	−0.0997509	−	0.458548i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	−1.02935	+	2.73586i	−0.127675	+	0.339342i
$66$	−0.606156	+	0.525237i	−0.0746127	+	0.0646522i
$67$	6.10572	−	11.1818i	0.745933	−	1.36607i	−0.178197	−	0.983995i	$-0.557026\pi$
$67$	6.10572	−	11.1818i	0.745933	−	1.36607i	0.924130	−	0.382079i	$-0.124792\pi$
$68$	−2.84435	−	2.84435i	−0.344929	−	0.344929i
$69$	−3.92131	+	2.76104i	−0.472070	+	0.332390i
$70$	−8.24055	−	1.20888i	−0.984934	−	0.144488i
$71$	−6.59515	+	1.93651i	−0.782701	+	0.229822i	−0.648583	−	0.761144i	$-0.724638\pi$
$71$	−6.59515	+	1.93651i	−0.782701	+	0.229822i	−0.134118	+	0.990965i	$0.542820\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	−1.29853	+	5.96927i	−0.151982	+	0.698650i	0.836581	+	0.547843i	$0.184551\pi$
$73$	−1.29853	+	5.96927i	−0.151982	+	0.698650i	−0.988563	+	0.150807i	$0.951813\pi$
$74$	1.54980	+	10.7791i	0.180160	+	1.25304i
$75$	4.98514	+	0.385216i	0.575634	+	0.0444810i
$76$	−0.531495	−	0.242726i	−0.0609667	−	0.0278426i
$77$	2.97984	−	0.213123i	0.339585	−	0.0242876i
$78$	0.783404	+	1.04651i	0.0887031	+	0.118493i
$79$	−0.806153	−	1.76523i	−0.0906994	−	0.198604i	0.858846	−	0.512234i	$-0.171182\pi$
$79$	−0.806153	−	1.76523i	−0.0906994	−	0.198604i	−0.949545	+	0.313630i	$0.898455\pi$
$80$	−2.03133	−	0.934710i	−0.227110	−	0.104504i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	2.16579	−	5.80671i	0.239172	−	0.641244i
$83$	−7.46240	+	5.58628i	−0.819105	+	0.613174i	−0.924468	−	0.381260i	$-0.875490\pi$
$83$	−7.46240	+	5.58628i	−0.819105	+	0.613174i	0.105363	+	0.994434i	$0.466399\pi$
$84$	−2.43918	+	2.81496i	−0.266136	+	0.307138i
$85$	−1.88680	−	8.79451i	−0.204653	−	0.953899i
$86$	−5.43991	+	8.46466i	−0.586600	+	0.912768i
$87$	−3.04412	+	4.06646i	−0.326363	+	0.435971i
$88$	0.783730	+	0.170490i	0.0835459	+	0.0181743i
$89$	−5.95402	−	6.87131i	−0.631125	−	0.728357i	0.346655	−	0.937993i	$-0.387318\pi$
$89$	−5.95402	−	6.87131i	−0.631125	−	0.728357i	−0.977780	+	0.209636i	$0.932772\pi$
$90$	1.34514	−	1.78622i	0.141790	−	0.188285i
$91$		−	4.86915i		−	0.510425i
$92$	4.56028	+	1.48454i	0.475442	+	0.154774i
$93$	−5.45316	+	5.45316i	−0.565467	+	0.565467i
$94$	0.762935	+	2.59832i	0.0786907	+	0.267996i
$95$	−0.703216	−	1.10114i	−0.0721485	−	0.112974i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	−4.00761	−	3.00006i	−0.406912	−	0.304610i	0.376145	−	0.926561i	$-0.377250\pi$
$97$	−4.00761	−	3.00006i	−0.406912	−	0.304610i	−0.783056	+	0.621951i	$0.786340\pi$
$98$	6.71653	−	1.46109i	0.678472	−	0.147593i
$99$	−0.333188	+	0.729579i	−0.0334866	+	0.0733254i
$100$	−2.67910	−	4.22166i	−0.267910	−	0.422166i
$101$	0.917646	−	6.38237i	0.0913091	−	0.635069i	−0.891852	−	0.452328i	$-0.850594\pi$
$101$	0.917646	−	6.38237i	0.0913091	−	0.635069i	0.983161	−	0.182741i	$-0.0584971\pi$
$102$	−3.76890	−	1.40573i	−0.373177	−	0.139188i
$103$	2.84659	+	5.21314i	0.280483	+	0.513666i	0.979501	−	0.201437i	$-0.0645613\pi$
$103$	2.84659	+	5.21314i	0.280483	+	0.513666i	−0.699018	+	0.715104i	$0.746379\pi$
$104$	0.368294	−	1.25430i	0.0361142	−	0.122994i
$105$	−7.99806	+	2.32362i	−0.780530	+	0.226762i
$106$	−10.2541	−	1.47432i	−0.995968	−	0.143199i
$107$	−0.308894	−	4.31890i	−0.0298619	−	0.417524i	−0.990292	−	0.139003i	$-0.955610\pi$
$107$	−0.308894	−	4.31890i	−0.0298619	−	0.417524i	0.960430	−	0.278521i	$-0.0898443\pi$
$108$	−0.349464	−	0.936950i	−0.0336272	−	0.0901580i
$109$	11.4347	+	7.34864i	1.09525	+	0.703872i	0.958030	−	0.286669i	$-0.0925480\pi$
$109$	11.4347	+	7.34864i	1.09525	+	0.703872i	0.137217	+	0.990541i	$0.456184\pi$
$110$	1.26454	+	1.27179i	0.120569	+	0.121260i
$111$	5.88754	+	9.16119i	0.558821	+	0.869542i
$112$	3.71524	+	0.265719i	0.351057	+	0.0251081i
$113$	12.1295	+	6.62321i	1.14105	+	0.623059i	0.934706	−	0.355421i	$-0.115663\pi$
$113$	12.1295	+	6.62321i	1.14105	+	0.623059i	0.206341	+	0.978480i	$0.433844\pi$
$114$	−0.584297			−0.0547245
$115$	6.75989	+	8.32490i	0.630363	+	0.776301i
$116$	5.07964			0.471633
$117$	1.14734	+	0.626497i	0.106072	+	0.0579197i
$118$	−3.59986	−	0.257467i	−0.331394	−	0.0237018i
$119$	8.10032	+	12.6043i	0.742555	+	1.15544i
$120$	−2.23606	−	0.00639501i	−0.204123	−	0.000583782i
$121$	8.71261	+	5.59926i	0.792056	+	0.509023i
$122$	5.34944	+	14.3424i	0.484315	+	1.29850i
$123$	−0.442122	−	6.18167i	−0.0398648	−	0.557383i
$124$	7.63344	+	1.09752i	0.685503	+	0.0985605i
$125$	0.0959241	−	11.1799i	0.00857971	−	0.999963i
$126$	−1.04938	+	3.57385i	−0.0934860	+	0.318384i
$127$	−0.378849	−	0.693809i	−0.0336174	−	0.0615656i	0.860330	−	0.509737i	$-0.170257\pi$
$127$	−0.378849	−	0.693809i	−0.0336174	−	0.0615656i	−0.893948	+	0.448171i	$0.852075\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	−1.43197	+	9.95954i	−0.126078	+	0.876889i
$130$	2.21459	−	1.90789i	0.194233	−	0.167333i
$131$	5.73902	−	12.5667i	0.501421	−	1.09796i	−0.474584	−	0.880210i	$-0.657402\pi$
$131$	5.73902	−	12.5667i	0.501421	−	1.09796i	0.976005	−	0.217748i	$-0.0698711\pi$
$132$	0.783730	−	0.170490i	0.0682149	−	0.0148392i
$133$	1.74226	+	1.30424i	0.151073	+	0.113092i
$134$	−10.7177	+	6.88787i	−0.925871	+	0.595021i
$135$	0.481557	−	2.18360i	0.0414459	−	0.187934i
$136$	1.13328	+	3.85958i	0.0971776	+	0.330956i
$137$	−7.62269	+	7.62269i	−0.651250	+	0.651250i	−0.953294	−	0.302044i	$-0.902331\pi$
$137$	−7.62269	+	7.62269i	−0.651250	+	0.651250i	0.302044	+	0.953294i	$0.402331\pi$
$138$	4.76488	−	0.544024i	0.405613	−	0.0463104i
$139$			13.3292i			1.13057i	0.824896	+	0.565284i	$0.191233\pi$
$139$			13.3292i			1.13057i	−0.824896	+	0.565284i	$0.808767\pi$
$140$	6.65321	+	5.01028i	0.562299	+	0.423446i
$141$	1.77337	+	2.04658i	0.149345	+	0.172353i
$142$	6.71650	+	1.46108i	0.563636	+	0.122612i
$143$	−0.628337	+	0.839360i	−0.0525442	+	0.0701908i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	9.53771	+	6.16813i	0.792064	+	0.512235i
$146$	4.00046	−	4.61678i	0.331081	−	0.382087i
$147$	5.50261	−	4.11920i	0.453848	−	0.339746i
$148$	3.80564	−	10.2033i	0.312822	−	0.838707i
$149$	1.45074	+	0.425977i	0.118850	+	0.0348974i	0.340616	−	0.940202i	$-0.389364\pi$
$149$	1.45074	+	0.425977i	0.118850	+	0.0348974i	−0.221767	+	0.975100i	$0.571182\pi$
$150$	−4.19074	−	2.72722i	−0.342172	−	0.222677i
$151$	5.18856	+	11.3614i	0.422239	+	0.924574i	0.994523	+	0.104518i	$0.0333301\pi$
$151$	5.18856	+	11.3614i	0.422239	+	0.924574i	−0.572284	+	0.820055i	$0.693943\pi$
$152$	0.350156	+	0.467754i	0.0284014	+	0.0379399i
$153$	−4.01227	+	0.286964i	−0.324373	+	0.0231996i
$154$	−2.71748	−	1.24103i	−0.218981	−	0.100005i
$155$	13.0001	+	11.3299i	1.04419	+	0.910041i
$156$	−0.186041	−	1.29394i	−0.0148952	−	0.103598i
$157$	−0.810318	+	3.72497i	−0.0646704	+	0.297285i	−0.998110	−	0.0614489i	$-0.980428\pi$
$157$	−0.810318	+	3.72497i	−0.0646704	+	0.297285i	0.933440	+	0.358734i	$0.116792\pi$
$158$	−0.138441	+	1.93565i	−0.0110137	+	0.153992i
$159$	−9.93992	+	2.91862i	−0.788287	+	0.231462i
$160$	1.33490	+	1.79389i	0.105533	+	0.141819i
$161$	−15.4222	−	9.01373i	−1.21544	−	0.710382i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	5.29249	−	9.69247i	0.414540	−	0.759173i	−0.584080	−	0.811696i	$-0.698545\pi$
$163$	5.29249	−	9.69247i	0.414540	−	0.759173i	0.998620	+	0.0525234i	$0.0167264\pi$
$164$	−4.68373	+	4.05848i	−0.365738	+	0.316914i
$165$	1.67858	+	0.631553i	0.130677	+	0.0491663i
$166$	9.22681	−	1.32662i	0.716139	−	0.102965i
$167$	0.240622	+	1.10612i	0.0186199	+	0.0855941i	0.985519	−	0.169564i	$-0.0542360\pi$
$167$	0.240622	+	1.10612i	0.0186199	+	0.0855941i	−0.966899	+	0.255158i	$0.917872\pi$
$168$	3.48989	−	1.30166i	0.269250	−	0.100425i
$169$	−8.53325	−	7.39410i	−0.656404	−	0.568777i
$170$	−2.55875	+	8.62301i	−0.196247	+	0.661354i
$171$	−0.531495	+	0.242726i	−0.0406445	+	0.0185617i
$172$	8.83117	−	4.82218i	0.673371	−	0.367688i
$173$	−5.28012	+	2.88317i	−0.401440	+	0.219203i	−0.667268	−	0.744818i	$-0.732537\pi$
$173$	−5.28012	+	2.88317i	−0.401440	+	0.219203i	0.265828	+	0.964020i	$0.414355\pi$
$174$	4.62060	−	2.11016i	0.350287	−	0.159971i
$175$	6.40838	+	17.4864i	0.484428	+	1.32185i
$176$	−0.606156	−	0.525237i	−0.0456907	−	0.0395912i
$177$	−3.38150	+	1.26124i	−0.254169	+	0.0948003i
$178$	1.93265	+	8.88426i	0.144858	+	0.665903i
$179$	−15.1511	+	2.17841i	−1.13245	+	0.162822i	−0.682954	−	0.730461i	$-0.739305\pi$
$179$	−15.1511	+	2.17841i	−1.13245	+	0.162822i	−0.449495	+	0.893283i	$0.648396\pi$
$180$	−2.03665	+	0.923075i	−0.151803	+	0.0688020i
$181$	−6.98290	+	6.05072i	−0.519035	+	0.449746i	−0.874558	−	0.484921i	$-0.838848\pi$
$181$	−6.98290	+	6.05072i	−0.519035	+	0.449746i	0.355523	+	0.934668i	$0.384303\pi$
$182$	−2.33353	+	4.27355i	−0.172973	+	0.316776i
$183$	10.8241	+	10.8241i	0.800138	+	0.800138i
$184$	−3.29100	−	3.48846i	−0.242616	−	0.257173i
$185$	19.5353	−	14.5370i	1.43627	−	1.06878i
$186$	7.39955	−	2.17270i	0.542561	−	0.159310i
$187$	0.230162	−	3.21808i	0.0168311	−	0.235330i
$188$	0.575629	−	2.64613i	0.0419821	−	0.192989i
$189$	0.530084	+	3.68682i	0.0385580	+	0.268177i
$190$	0.0894792	+	1.30346i	0.00649150	+	0.0945630i
$191$	−7.76101	−	3.54434i	−0.561567	−	0.256459i	0.114345	−	0.993441i	$-0.463523\pi$
$191$	−7.76101	−	3.54434i	−0.561567	−	0.256459i	−0.675912	+	0.736982i	$0.736250\pi$
$192$	0.997452	−	0.0713392i	0.0719849	−	0.00514846i
$193$	0.596958	+	0.797443i	0.0429700	+	0.0574012i	0.821512	−	0.570192i	$-0.193131\pi$
$193$	0.596958	+	0.797443i	0.0429700	+	0.0574012i	−0.778542	+	0.627593i	$0.784040\pi$
$194$	2.07962	+	4.55374i	0.149308	+	0.326939i
$195$	1.22190	−	2.65546i	0.0875019	−	0.190161i
$196$	−6.59519	−	1.93652i	−0.471085	−	0.138323i
$197$	−6.01716	+	16.1326i	−0.428705	+	1.14940i	0.525643	+	0.850705i	$0.323825\pi$
$197$	−6.01716	+	16.1326i	−0.428705	+	1.14940i	−0.954348	+	0.298697i	$0.903448\pi$
$198$	0.642082	−	0.480656i	0.0456308	−	0.0341588i
$199$	2.02501	−	2.33699i	0.143549	−	0.165665i	−0.679422	−	0.733748i	$-0.737769\pi$
$199$	2.02501	−	2.33699i	0.143549	−	0.165665i	0.822971	+	0.568083i	$0.192315\pi$
$200$	0.328164	+	4.98922i	0.0232047	+	0.352791i
$201$	−6.88787	+	10.7177i	−0.485833	+	0.755970i
$202$	−3.86414	+	5.16189i	−0.271880	+	0.363189i
$203$	−18.4879	−	4.02180i	−1.29760	−	0.282275i
$204$	2.63419	+	3.04002i	0.184430	+	0.212844i
$205$	−13.7225	+	1.93295i	−0.958420	+	0.135003i
$206$		−	5.93969i		−	0.413838i
$207$	4.10829	−	2.47426i	0.285546	−	0.171973i
$208$	−0.924364	+	0.924364i	−0.0640931	+	0.0640931i
$209$	−0.132031	−	0.449658i	−0.00913281	−	0.0311035i
$210$	8.13332	+	1.79367i	0.561252	+	0.123775i
$211$	1.29447	−	0.831908i	0.0891153	−	0.0572709i	−0.495324	−	0.868708i	$-0.664951\pi$
$211$	1.29447	−	0.831908i	0.0891153	−	0.0572709i	0.584440	+	0.811437i	$0.301314\pi$
$212$	8.29325	+	6.20825i	0.569583	+	0.426385i
$213$	6.71650	−	1.46108i	0.460207	−	0.100112i
$214$	−1.79872	+	3.93865i	−0.122958	+	0.269240i
$215$	22.4372	+	1.66925i	1.53021	+	0.113842i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−26.9138	−	10.0383i	−1.82703	−	0.681446i
$218$	−6.51417	−	11.9298i	−0.441196	−	0.807989i
$219$	1.72107	−	5.86142i	0.116299	−	0.396078i
$220$	−0.500352	−	1.72225i	−0.0337338	−	0.116114i
$221$	−5.20491	−	0.748353i	−0.350120	−	0.0503397i
$222$	−0.776879	−	10.8622i	−0.0521407	−	0.729022i
$223$	6.66871	+	17.8795i	0.446570	+	1.19730i	0.944044	+	0.329821i	$0.106988\pi$
$223$	6.66871	+	17.8795i	0.446570	+	1.19730i	−0.497474	+	0.867479i	$0.665739\pi$
$224$	−3.13344	−	2.01374i	−0.209362	−	0.134549i
$225$	−4.94496	−	0.739871i	−0.329664	−	0.0493247i
$226$	−7.47164	−	11.6261i	−0.497006	−	0.773357i
$227$	−22.0693	−	1.57843i	−1.46479	−	0.104764i	−0.683966	−	0.729514i	$-0.739746\pi$
$227$	−22.0693	−	1.57843i	−1.46479	−	0.104764i	−0.780825	+	0.624750i	$0.785201\pi$
$228$	0.512825	+	0.280024i	0.0339627	+	0.0185450i
$229$	27.3562			1.80775			0.903875	−	0.427797i	$-0.140710\pi$
$229$	27.3562			1.80775			0.903875	+	0.427797i	$0.140710\pi$
$230$	−1.94331	−	10.5463i	−0.128138	−	0.695400i
$231$	−2.98746			−0.196560
$232$	−4.45829	−	2.43441i	−0.292701	−	0.159827i
$233$	−27.1785	−	1.94385i	−1.78052	−	0.127346i	−0.858090	−	0.513500i	$-0.828349\pi$
$233$	−27.1785	−	1.94385i	−1.78052	−	0.127346i	−0.922434	+	0.386155i	$0.873803\pi$
$234$	−0.706752	−	1.09973i	−0.0462018	−	0.0718914i
$235$	4.29397	−	4.26948i	0.280108	−	0.278510i
$236$	3.03613	+	1.95120i	0.197635	+	0.127012i
$237$	0.678169	+	1.81824i	0.0440518	+	0.118108i
$238$	−1.06886	−	14.9446i	−0.0692840	−	0.968717i
$239$	9.67015	+	1.39036i	0.625510	+	0.0899348i	0.447779	−	0.894144i	$-0.352215\pi$
$239$	9.67015	+	1.39036i	0.625510	+	0.0899348i	0.177731	+	0.984079i	$0.443124\pi$
$240$	1.95948	+	1.07724i	0.126484	+	0.0695357i
$241$	4.98891	−	16.9907i	0.321364	−	1.09446i	−0.627458	−	0.778651i	$-0.715904\pi$
$241$	4.98891	−	16.9907i	0.321364	−	1.09446i	0.948821	−	0.315814i	$-0.102277\pi$
$242$	−4.96344	−	9.08986i	−0.319062	−	0.584318i
$243$	−0.936950	−	0.349464i	−0.0601054	−	0.0224181i
$244$	2.17849	−	15.1517i	0.139464	−	0.969990i
$245$	−10.0319	−	11.6445i	−0.640912	−	0.743941i
$246$	−2.57452	+	5.63741i	−0.164145	+	0.359428i
$247$	−0.746366	+	0.162362i	−0.0474901	+	0.0103308i
$248$	−6.17372	−	4.62159i	−0.392032	−	0.293471i
$249$	7.84191	−	5.03969i	0.496961	−	0.319377i
$250$	−5.44216	+	9.76642i	−0.344192	+	0.617682i
$251$	3.66328	+	12.4760i	0.231224	+	0.787477i	0.990596	+	0.136820i	$0.0436882\pi$
$251$	3.66328	+	12.4760i	0.231224	+	0.787477i	−0.759372	+	0.650657i	$0.774494\pi$
$252$	2.63378	−	2.63378i	0.165913	−	0.165913i
$253$	1.49537	+	3.54398i	0.0940129	+	0.222808i
$254$			0.790505i			0.0496007i
$255$	1.25460	+	8.90671i	0.0785663	+	0.557760i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	2.71866	+	0.591408i	0.169585	+	0.0368910i	0.296556	−	0.955015i	$-0.404162\pi$
$257$	2.71866	+	0.591408i	0.169585	+	0.0368910i	−0.126971	+	0.991906i	$0.540525\pi$
$258$	6.02991	−	8.05501i	0.375406	−	0.501483i
$259$	−21.9295	+	34.1230i	−1.36263	+	2.12030i
$260$	−2.85806	+	0.613177i	−0.177249	+	0.0380276i
$261$	3.32646	−	3.83894i	0.205903	−	0.237624i
$262$	−11.0596	+	8.27911i	−0.683264	+	0.511485i
$263$	−0.260844	+	0.699351i	−0.0160844	+	0.0431238i	−0.944744	−	0.327810i	$-0.893690\pi$
$263$	−0.260844	+	0.699351i	−0.0160844	+	0.0431238i	0.928659	+	0.370934i	$0.120962\pi$
$264$	−0.769570	−	0.225966i	−0.0473638	−	0.0139073i
$265$	8.03312	+	21.7272i	0.493471	+	1.33469i
$266$	−0.904088	−	1.97968i	−0.0554332	−	0.121382i
$267$	5.44866	+	7.27855i	0.333452	+	0.445440i
$268$	12.7077	−	0.908875i	0.776248	−	0.0555184i
$269$	2.43455	+	1.11182i	0.148437	+	0.0677889i	0.488248	−	0.872705i	$-0.337636\pi$
$269$	2.43455	+	1.11182i	0.148437	+	0.0677889i	−0.339811	+	0.940494i	$0.610363\pi$
$270$	−1.46914	+	1.68571i	−0.0894090	+	0.102589i
$271$	−1.11015	−	7.72126i	−0.0674368	−	0.469033i	−0.995357	−	0.0962538i	$-0.969314\pi$
$271$	−1.11015	−	7.72126i	−0.0674368	−	0.469033i	0.927920	−	0.372779i	$-0.121595\pi$
$272$	0.855049	−	3.93060i	0.0518449	−	0.238327i
$273$	−0.347361	+	4.85674i	−0.0210232	+	0.293943i
$274$	10.3434	−	3.03711i	0.624870	−	0.183478i
$275$	1.15182	−	3.84133i	0.0694575	−	0.231641i
$276$	−4.44275	−	1.80608i	−0.267422	−	0.108713i
$277$	−9.19203	−	9.19203i	−0.552296	−	0.552296i	0.374807	−	0.927103i	$-0.377709\pi$
$277$	−9.19203	−	9.19203i	−0.552296	−	0.552296i	−0.927103	+	0.374807i	$0.877709\pi$
$278$	6.38801	−	11.6988i	0.383127	−	0.701645i
$279$	5.82829	−	5.05025i	0.348931	−	0.302350i
$280$	−3.43821	−	7.58596i	−0.205472	−	0.453348i
$281$	15.5157	−	2.23082i	0.925590	−	0.133080i	0.336994	−	0.941507i	$-0.390590\pi$
$281$	15.5157	−	2.23082i	0.925590	−	0.133080i	0.588596	+	0.808427i	$0.299681\pi$
$282$	−0.575629	−	2.64613i	−0.0342782	−	0.157574i
$283$	16.8639	−	6.28991i	1.00246	−	0.373897i	0.205973	−	0.978558i	$-0.433964\pi$
$283$	16.8639	−	6.28991i	1.00246	−	0.373897i	0.796483	+	0.604661i	$0.206691\pi$
$284$	−5.19471	−	4.50124i	−0.308249	−	0.267099i
$285$	0.622870	+	1.14850i	0.0368957	+	0.0680312i
$286$	0.953741	−	0.435559i	0.0563959	−	0.0257551i
$287$	20.2602	−	11.0629i	1.19592	−	0.653024i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	−0.745268	+	0.340352i	−0.0438393	+	0.0200207i
$290$	−5.41498	−	9.98458i	−0.317979	−	0.586315i
$291$	3.78338	+	3.27832i	0.221786	+	0.192178i
$292$	−5.72371	+	2.13483i	−0.334955	+	0.124932i
$293$	0.0638569	+	0.293545i	0.00373056	+	0.0171491i	0.978975	−	0.203983i	$-0.0653886\pi$
$293$	0.0638569	+	0.293545i	0.00373056	+	0.0171491i	−0.975244	+	0.221132i	$0.929025\pi$
$294$	−6.80365	+	0.978218i	−0.396797	+	0.0570508i
$295$	3.33143	+	7.35037i	0.193963	+	0.427955i
$296$	−8.23006	+	7.13139i	−0.478362	+	0.414503i
$297$	0.384386	−	0.703951i	0.0223043	−	0.0408474i
$298$	−1.06914	−	1.06914i	−0.0619335	−	0.0619335i
$299$	5.93535	−	2.01896i	0.343250	−	0.116760i
$300$	2.37110	+	4.40203i	0.136896	+	0.254151i
$301$	−35.9600	+	10.5588i	−2.07270	+	0.608599i
$302$	0.891030	−	12.4582i	0.0512730	−	0.716891i
$303$	−1.37062	+	6.30064i	−0.0787401	+	0.361962i
$304$	−0.0831542	−	0.578350i	−0.00476922	−	0.0331706i
$305$	22.4889	−	25.8041i	1.28771	−	1.47754i
$306$	3.65902	+	1.67102i	0.209172	+	0.0955257i
$307$	6.59827	−	0.471918i	0.376583	−	0.0269338i	0.118235	−	0.992986i	$-0.462276\pi$
$307$	6.59827	−	0.471918i	0.376583	−	0.0269338i	0.258348	+	0.966052i	$0.416822\pi$
$308$	1.79032	+	2.39158i	0.102013	+	0.136273i
$309$	−2.46744	−	5.40293i	−0.140368	−	0.307362i
$310$	−5.98007	−	16.1743i	−0.339645	−	0.918640i
$311$	8.06691	+	2.36866i	0.457433	+	0.134314i	0.502328	−	0.864677i	$-0.332477\pi$
$311$	8.06691	+	2.36866i	0.457433	+	0.134314i	−0.0448950	+	0.998992i	$0.514295\pi$
$312$	−0.456836	+	1.22483i	−0.0258633	+	0.0693421i
$313$	2.24900	−	1.68358i	0.127121	−	0.0951614i	−0.533825	−	0.845595i	$-0.679246\pi$
$313$	2.24900	−	1.68358i	0.127121	−	0.0951614i	0.660946	+	0.750433i	$0.270155\pi$
$314$	2.49639	−	2.88099i	0.140879	−	0.162583i
$315$	8.14344	−	1.74712i	0.458831	−	0.0984391i
$316$	1.04917	−	1.63253i	0.0590202	−	0.0918373i
$317$	−4.39198	+	5.86699i	−0.246678	+	0.329523i	−0.906742	−	0.421686i	$-0.861438\pi$
$317$	−4.39198	+	5.86699i	−0.246678	+	0.329523i	0.660064	+	0.751210i	$0.270529\pi$
$318$	10.1228	+	2.20208i	0.567659	+	0.123487i
$319$	2.66802	+	3.07906i	0.149380	+	0.172394i
$320$	−0.311894	−	2.21421i	−0.0174354	−	0.123778i
$321$			4.32994i			0.241673i
$322$	9.21596	+	15.3023i	0.513585	+	0.852762i
$323$	1.66195	−	1.66195i	0.0924733	−	0.0924733i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−6.11096	−	2.31917i	−0.338975	−	0.128645i
$326$	−9.29021	+	5.97046i	−0.514537	+	0.330673i
$327$	−10.8813	−	8.14566i	−0.601739	−	0.450456i
$328$	6.05583	−	1.31737i	0.334377	−	0.0727394i
$329$	−4.19013	+	9.17511i	−0.231009	+	0.505840i
$330$	−1.17059	−	1.35876i	−0.0644386	−	0.0747973i
$331$	4.51517	−	31.4037i	0.248176	−	1.72610i	−0.360566	−	0.932734i	$-0.617416\pi$
$331$	4.51517	−	31.4037i	0.248176	−	1.72610i	0.608742	−	0.793368i	$-0.291675\pi$
$332$	−8.73396	−	3.25760i	−0.479338	−	0.178784i
$333$	−5.21899	−	9.55786i	−0.285999	−	0.523768i
$334$	0.318918	−	1.08614i	0.0174504	−	0.0594307i
$335$	24.9641	+	13.7243i	1.36393	+	0.749837i
$336$	−3.68682	−	0.530084i	−0.201132	−	0.0289185i
$337$	−1.20439	−	16.8395i	−0.0656071	−	0.917307i	−0.918551	−	0.395304i	$-0.870639\pi$
$337$	−1.20439	−	16.8395i	−0.0656071	−	0.917307i	0.852943	−	0.522003i	$-0.174815\pi$
$338$	3.94584	+	10.5792i	0.214625	+	0.575432i
$339$	−11.6261	−	7.47164i	−0.631443	−	0.405804i
$340$	6.37833	−	6.34195i	0.345914	−	0.343941i
$341$	3.34410	+	5.20352i	0.181093	+	0.281786i
$342$	0.582809	+	0.0416833i	0.0315147	+	0.00225397i
$343$	−0.413165	−	0.225605i	−0.0223088	−	0.0121815i
$344$	−10.0620			−0.542505
$345$	−6.14877	−	8.78593i	−0.331039	−	0.473019i
$346$	6.01601			0.323423
$347$	−14.8406	−	8.10356i	−0.796683	−	0.435022i	0.0287049	−	0.999588i	$-0.490862\pi$
$347$	−14.8406	−	8.10356i	−0.796683	−	0.435022i	−0.825388	+	0.564566i	$0.809044\pi$
$348$	−5.06670	−	0.362377i	−0.271604	−	0.0194255i
$349$	−10.8840	−	16.9358i	−0.582608	−	0.906555i	0.417390	−	0.908727i	$-0.362945\pi$
$349$	−10.8840	−	16.9358i	−0.582608	−	0.906555i	−0.999998	+	0.00217230i	$0.999309\pi$
$350$	2.75582	−	18.4186i	0.147305	−	0.984517i
$351$	−1.09973	−	0.706752i	−0.0586991	−	0.0377236i
$352$	0.280291	+	0.751489i	0.0149396	+	0.0400545i
$353$	2.07726	+	29.0439i	0.110561	+	1.54585i	0.685754	+	0.727833i	$0.259472\pi$
$353$	2.07726	+	29.0439i	0.110561	+	1.54585i	−0.575193	+	0.818018i	$0.695073\pi$
$354$	3.57232	+	0.513622i	0.189867	+	0.0272987i
$355$	−4.28798	−	14.7595i	−0.227582	−	0.783355i
$356$	2.56152	−	8.72375i	0.135760	−	0.462358i
$357$	−7.18050	−	13.1501i	−0.380032	−	0.695977i
$358$	14.3418	+	5.34923i	0.757990	+	0.282715i
$359$	3.03813	−	21.1306i	0.160346	−	1.11523i	−0.737635	−	0.675199i	$-0.764058\pi$
$359$	3.03813	−	21.1306i	0.160346	−	1.11523i	0.897982	−	0.440033i	$-0.145033\pi$
$360$	2.22991	+	0.165897i	0.117526	+	0.00874356i
$361$	−7.75106	+	16.9725i	−0.407951	+	0.893287i
$362$	9.02855	−	1.96404i	0.474530	−	0.103228i
$363$	−8.29097	−	6.20654i	−0.435163	−	0.325759i
$364$	4.09619	−	2.63246i	0.214698	−	0.137978i
$365$	−13.3393	−	2.94177i	−0.698212	−	0.153979i
$366$	−4.31263	−	14.6875i	−0.225425	−	0.767727i
$367$	−7.14254	+	7.14254i	−0.372837	+	0.372837i	−0.868510	−	0.495672i	$-0.834922\pi$
$367$	−7.14254	+	7.14254i	−0.372837	+	0.372837i	0.495672	+	0.868510i	$0.334922\pi$
$368$	1.21660	+	4.63895i	0.0634196	+	0.241822i
$369$			6.19746i			0.322627i
$370$	−24.1126	+	3.39651i	−1.25355	+	0.176576i
$371$	−25.2688	−	29.1618i	−1.31189	−	1.51400i
$372$	−7.53570	−	1.63929i	−0.390708	−	0.0849932i
$373$	−21.9839	+	29.3671i	−1.13828	+	1.52057i	−0.318478	+	0.947930i	$0.603172\pi$
$373$	−21.9839	+	29.3671i	−1.13828	+	1.52057i	−0.819807	+	0.572640i	$0.805919\pi$
$374$	−1.74427	+	2.71414i	−0.0901941	+	0.140345i
$375$	−0.893247	+	11.1446i	−0.0461271	+	0.575505i
$376$	−1.77337	+	2.04658i	−0.0914546	+	0.105544i
$377$	5.31587	−	3.97941i	0.273781	−	0.204950i
$378$	1.30166	−	3.48989i	0.0669502	−	0.179500i
$379$	6.20790	+	1.82280i	0.318878	+	0.0936311i	0.437255	−	0.899338i	$-0.355951\pi$
$379$	6.20790	+	1.82280i	0.318878	+	0.0936311i	−0.118377	+	0.992969i	$0.537769\pi$
$380$	0.546148	−	1.18690i	0.0280168	−	0.0608868i
$381$	0.328388	+	0.719068i	0.0168238	+	0.0368390i
$382$	5.11306	+	6.83025i	0.261607	+	0.349466i
$383$	−37.2438	+	2.66373i	−1.90307	+	0.136110i	−0.972931	−	0.231095i	$-0.925769\pi$
$383$	−37.2438	+	2.66373i	−1.90307	+	0.136110i	−0.930140	+	0.367205i	$0.880315\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	0.457499	+	6.66447i	0.0233163	+	0.339653i
$386$	−0.141764	−	0.985991i	−0.00721560	−	0.0501856i
$387$	2.13882	−	9.83201i	0.108723	−	0.499789i
$388$	0.357133	−	4.99338i	0.0181307	−	0.253500i
$389$	32.8781	−	9.65388i	1.66698	−	0.489471i	0.693930	−	0.720043i	$-0.255878\pi$
$389$	32.8781	−	9.65388i	1.66698	−	0.489471i	0.973055	+	0.230572i	$0.0740597\pi$
$390$	−2.34506	+	1.74505i	−0.118747	+	0.0883638i
$391$	−12.0056	+	15.1004i	−0.607149	+	0.763659i
$392$	4.86038	+	4.86038i	0.245486	+	0.245486i
$393$	−6.62090	+	12.1253i	−0.333980	+	0.611639i
$394$	13.0127	−	11.2755i	0.655569	−	0.568054i
$395$	3.95231	−	1.79132i	0.198862	−	0.0901310i
$396$	−0.793896	+	0.114145i	−0.0398948	+	0.00573600i
$397$	2.80975	+	12.9162i	0.141017	+	0.648246i	0.992333	+	0.123592i	$0.0394415\pi$
$397$	2.80975	+	12.9162i	0.141017	+	0.648246i	−0.851316	+	0.524653i	$0.824195\pi$
$398$	−2.89731	+	1.08064i	−0.145229	+	0.0541676i
$399$	−1.64478	−	1.42521i	−0.0823418	−	0.0713495i
$400$	2.10306	−	4.53621i	0.105153	−	0.226810i
$401$	−30.0512	+	13.7239i	−1.50069	+	0.685340i	−0.985176	−	0.171544i	$-0.945124\pi$
$401$	−30.0512	+	13.7239i	−1.50069	+	0.685340i	−0.515509	+	0.856884i	$0.672397\pi$
$402$	11.1818	−	6.10572i	0.557697	−	0.304526i
$403$	8.84825	−	4.83151i	0.440763	−	0.240675i
$404$	5.86530	−	2.67859i	0.291810	−	0.133265i
$405$	−0.636107	+	2.14368i	−0.0316084	+	0.106520i
$406$	14.2990	+	12.3902i	0.709648	+	0.614913i
$407$	8.18367	−	3.05235i	0.405649	−	0.151299i
$408$	−0.855049	−	3.93060i	−0.0423312	−	0.194593i
$409$	−26.2664	+	3.77654i	−1.29879	+	0.186738i	−0.756800	−	0.653647i	$-0.773238\pi$
$409$	−26.2664	+	3.77654i	−1.29879	+	0.186738i	−0.541990	+	0.840385i	$0.682329\pi$
$410$	12.9703	+	4.87997i	0.640558	+	0.241005i
$411$	8.14706	−	7.05947i	0.401865	−	0.348218i
$412$	−2.84659	+	5.21314i	−0.140242	+	0.256833i
$413$	−9.50547	−	9.50547i	−0.467733	−	0.467733i
$414$	−4.79155	+	0.202716i	−0.235492	+	0.00996294i
$415$	−12.4435	−	16.7221i	−0.610829	−	0.820855i
$416$	1.25430	−	0.368294i	0.0614969	−	0.0180571i
$417$	0.950894	−	13.2952i	0.0465655	−	0.651071i
$418$	−0.0996168	+	0.457931i	−0.00487242	+	0.0223981i
$419$	−4.34832	−	30.2433i	−0.212430	−	1.47748i	−0.765009	−	0.644019i	$-0.777266\pi$
$419$	−4.34832	−	30.2433i	−0.212430	−	1.47748i	0.552580	−	0.833460i	$-0.313644\pi$
$420$	−6.27883	−	5.47215i	−0.306375	−	0.267014i
$421$	27.7968	+	12.6944i	1.35473	+	0.618685i	0.954632	−	0.297787i	$-0.0962486\pi$
$421$	27.7968	+	12.6944i	1.35473	+	0.618685i	0.400099	+	0.916472i	$0.368976\pi$
$422$	−1.53482	+	0.109773i	−0.0747141	+	0.00534366i
$423$	−1.62285	−	2.16788i	−0.0789057	−	0.105406i
$424$	−4.30352	−	9.42339i	−0.208997	−	0.457640i
$425$	19.6771	−	4.16276i	0.954480	−	0.201924i
$426$	−6.59515	−	1.93651i	−0.319536	−	0.0938243i
$427$	−19.9252	+	53.4216i	−0.964249	+	2.58525i
$428$	3.46629	−	2.59483i	0.167550	−	0.125426i
$429$	0.686615	−	0.792396i	0.0331501	−	0.0382573i
$430$	−18.8927	−	12.2181i	−0.911086	−	0.589208i
$431$	10.6918	−	16.6368i	0.515006	−	0.801364i	−0.482201	−	0.876061i	$-0.660162\pi$
$431$	10.6918	−	16.6368i	0.515006	−	0.801364i	0.997206	+	0.0746965i	$0.0237988\pi$
$432$	0.599278	−	0.800541i	0.0288328	−	0.0385161i
$433$	39.5224	+	8.59757i	1.89933	+	0.413173i	0.999723	−	0.0235359i	$-0.00749242\pi$
$433$	39.5224	+	8.59757i	1.89933	+	0.413173i	0.899603	+	0.436709i	$0.143856\pi$
$434$	18.8108	+	21.7088i	0.902947	+	1.04206i
$435$	−9.07338	−	6.83283i	−0.435035	−	0.327609i
$436$			13.5925i			0.650961i
$437$	−0.867412	+	2.66456i	−0.0414939	+	0.127463i
$438$	−4.31963	+	4.31963i	−0.206400	+	0.206400i
$439$	−5.00436	−	17.0433i	−0.238845	−	0.813431i	−0.988450	−	0.151546i	$-0.951575\pi$
$439$	−5.00436	−	17.0433i	−0.238845	−	0.813431i	0.749605	−	0.661885i	$-0.230243\pi$
$440$	−0.386238	+	1.75138i	−0.0184132	+	0.0834936i
$441$	−5.78245	+	3.71616i	−0.275355	+	0.176960i
$442$	4.20959	+	3.15126i	0.200230	+	0.149890i
$443$	−15.7889	+	3.43466i	−0.750153	+	0.163186i	−0.571358	−	0.820701i	$-0.693583\pi$
$443$	−15.7889	+	3.43466i	−0.750153	+	0.163186i	−0.178795	+	0.983886i	$0.557220\pi$
$444$	−4.52384	+	9.90583i	−0.214692	+	0.470110i
$445$	15.4027	−	13.2696i	0.730159	−	0.629039i
$446$	2.71575	−	18.8884i	0.128594	−	0.894393i
$447$	−1.41666	−	0.528386i	−0.0670056	−	0.0249918i
$448$	1.78507	+	3.26912i	0.0843368	+	0.154451i
$449$	6.49193	−	22.1095i	0.306373	−	1.04341i	−0.652078	−	0.758152i	$-0.726102\pi$
$449$	6.49193	−	22.1095i	0.306373	−	1.04341i	0.958451	−	0.285258i	$-0.0920794\pi$
$450$	3.98550	+	3.01923i	0.187878	+	0.142328i
$451$	−4.92014	−	0.707409i	−0.231680	−	0.0333106i
$452$	0.985905	+	13.7848i	0.0463731	+	0.648380i
$453$	−4.36483	−	11.7026i	−0.205077	−	0.549834i
$454$	18.6133	+	11.9620i	0.873565	+	0.561406i
$455$	10.8877	+	0.0311382i	0.510423	+	0.00145978i
$456$	−0.315895	−	0.491542i	−0.0147931	−	0.0230186i
$457$	19.0231	+	1.36056i	0.889863	+	0.0636443i	0.508780	−	0.860896i	$-0.330097\pi$
$457$	19.0231	+	1.36056i	0.889863	+	0.0636443i	0.381083	+	0.924541i	$0.375551\pi$
$458$	−24.0100	−	13.1104i	−1.12191	−	0.612611i
$459$	4.02252			0.187755
$460$	−3.34868	+	10.1876i	−0.156133	+	0.474997i
$461$	10.4915			0.488640			0.244320	−	0.969695i	$-0.421435\pi$
$461$	10.4915			0.488640			0.244320	+	0.969695i	$0.421435\pi$
$462$	2.62203	+	1.43173i	0.121988	+	0.0666103i
$463$	−4.38952	−	0.313945i	−0.203998	−	0.0145902i	−0.0310339	−	0.999518i	$-0.509880\pi$
$463$	−4.38952	−	0.313945i	−0.203998	−	0.0145902i	−0.172964	+	0.984928i	$0.555335\pi$
$464$	2.74626	+	4.27327i	0.127492	+	0.198381i
$465$	−12.1587	−	12.2285i	−0.563847	−	0.567082i
$466$	22.9224	+	14.7313i	1.06186	+	0.682417i
$467$	1.21498	+	3.25749i	0.0562226	+	0.150739i	0.962025	−	0.272962i	$-0.0880035\pi$
$467$	1.21498	+	3.25749i	0.0562226	+	0.150739i	−0.905802	+	0.423701i	$0.860731\pi$
$468$	0.0932580	+	1.30392i	0.00431085	+	0.0602736i
$469$	−46.9708	−	6.75337i	−2.16891	−	0.311842i
$470$	−5.81487	+	1.68935i	−0.268220	+	0.0779240i
$471$	1.07399	−	3.65767i	0.0494868	−	0.168537i
$472$	−1.72964	−	3.16759i	−0.0796130	−	0.145800i
$473$	7.56146	+	2.82028i	0.347676	+	0.129677i
$474$	0.276176	−	1.92085i	0.0126852	−	0.0882273i
$475$	2.46670	−	1.56539i	0.113180	−	0.0718251i
$476$	−6.22409	+	13.6288i	−0.285281	+	0.624677i
$477$	10.1228	−	2.20208i	0.463492	−	0.100826i
$478$	−7.82096	−	5.85470i	−0.357722	−	0.267788i
$479$	−17.5394	+	11.2719i	−0.801394	+	0.515024i	−0.876070	−	0.482183i	$-0.839844\pi$
$479$	−17.5394	+	11.2719i	−0.801394	+	0.515024i	0.0746766	+	0.997208i	$0.476208\pi$
$480$	−1.20352	−	1.88455i	−0.0549331	−	0.0860175i
$481$	−4.01070	−	13.6592i	−0.182872	−	0.622805i
$482$	−12.5214	+	12.5214i	−0.570335	+	0.570335i
$483$	14.7399	+	10.0910i	0.670690	+	0.459155i
$484$			10.3567i			0.470759i
$485$	6.73394	−	8.94208i	0.305773	−	0.406039i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	32.4898	+	7.06772i	1.47225	+	0.320269i	0.875916	−	0.482464i	$-0.160258\pi$
$487$	32.4898	+	7.06772i	1.47225	+	0.320269i	0.596338	+	0.802734i	$0.296622\pi$
$488$	−9.17347	+	12.2543i	−0.415263	+	0.554727i
$489$	−5.97046	+	9.29021i	−0.269993	+	0.420118i
$490$	3.22414	+	15.0279i	0.145652	+	0.678892i
$491$	1.30681	−	1.50814i	0.0589756	−	0.0680615i	−0.725495	−	0.688227i	$-0.758389\pi$
$491$	1.30681	−	1.50814i	0.0589756	−	0.0680615i	0.784471	+	0.620166i	$0.212935\pi$
$492$	4.96133	−	3.71400i	0.223674	−	0.167440i
$493$	−7.14059	+	19.1447i	−0.321596	+	0.862233i
$494$	0.732881	+	0.215193i	0.0329739	+	0.00968201i
$495$	−1.62925	−	0.749693i	−0.0732294	−	0.0336962i
$496$	3.20365	+	7.01503i	0.143848	+	0.314984i
$497$	15.3428	+	20.4956i	0.688221	+	0.919355i
$498$	−9.29794	+	0.665002i	−0.416651	+	0.0297995i
$499$	23.9554	+	10.9401i	1.07239	+	0.489744i	0.871765	−	0.489924i	$-0.162975\pi$
$499$	23.9554	+	10.9401i	1.07239	+	0.489744i	0.200625	+	0.979668i	$0.435703\pi$
$500$	9.45701	−	5.96363i	0.422931	−	0.266702i
$501$	−0.161099	−	1.12047i	−0.00719736	−	0.0500588i
$502$	2.76392	−	12.7055i	0.123360	−	0.567076i
$503$	0.237174	−	3.31613i	0.0105751	−	0.147859i	−0.989421	−	0.145072i	$-0.953659\pi$
$503$	0.237174	−	3.31613i	0.0105751	−	0.147859i	0.999996	−	0.00278640i	$-0.000886939\pi$
$504$	−3.57385	+	1.04938i	−0.159192	+	0.0467430i
$505$	14.2655	+	2.09272i	0.634805	+	0.0931250i
$506$	0.385996	−	3.82713i	0.0171596	−	0.170137i
$507$	7.98402	+	7.98402i	0.354583	+	0.354583i
$508$	0.378849	−	0.693809i	0.0168087	−	0.0307828i
$509$	5.34901	−	4.63495i	0.237091	−	0.205440i	−0.528209	−	0.849114i	$-0.677136\pi$
$509$	5.34901	−	4.63495i	0.237091	−	0.205440i	0.765300	+	0.643674i	$0.222591\pi$
$510$	3.16739	−	8.41850i	0.140254	−	0.372777i
$511$	22.5223	−	3.23822i	0.996328	−	0.143250i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	0.547457	−	0.204191i	0.0241708	−	0.00901525i
$514$	−2.10268	−	1.82198i	−0.0927452	−	0.0803642i
$515$	−11.6751	+	6.33181i	−0.514466	+	0.279013i
$516$	−9.15268	+	4.17989i	−0.402924	+	0.184009i
$517$	1.90631	−	1.04092i	0.0838393	−	0.0457797i
$518$	35.6005	−	19.4393i	1.56419	−	0.854115i
$519$	5.47235	−	2.49914i	0.240210	−	0.109700i
$520$	2.80232	+	0.831549i	0.122890	+	0.0364658i
$521$	13.4344	+	11.6409i	0.588570	+	0.509999i	0.897458	−	0.441099i	$-0.145411\pi$
$521$	13.4344	+	11.6409i	0.588570	+	0.509999i	−0.308888	+	0.951098i	$0.599957\pi$
$522$	−4.75937	+	1.77515i	−0.208312	+	0.0776963i
$523$	−7.72520	−	35.5122i	−0.337799	−	1.55284i	−0.762187	−	0.647357i	$-0.775874\pi$
$523$	−7.72520	−	35.5122i	−0.337799	−	1.55284i	0.424387	−	0.905481i	$-0.360489\pi$
$524$	13.6745	−	1.96610i	0.597375	−	0.0858895i
$525$	−5.14459	−	17.8990i	−0.224528	−	0.781176i
$526$	0.564101	−	0.488796i	0.0245960	−	0.0213125i
$527$	−14.8670	+	27.2269i	−0.647617	+	1.18602i
$528$	0.567142	+	0.567142i	0.0246817	+	0.0246817i
$529$	4.59274	−	22.5368i	0.199684	−	0.979860i
$530$	3.36224	−	22.9194i	0.146046	−	0.995554i
$531$	3.46286	−	1.01679i	0.150275	−	0.0441249i
$532$	−0.155259	+	2.17080i	−0.00673133	+	0.0941163i
$533$	−1.72212	+	7.91648i	−0.0745935	+	0.342901i
$534$	−1.29393	−	8.99950i	−0.0559939	−	0.389446i
$535$	9.65930	−	0.663086i	0.417608	−	0.0286677i
$536$	−11.5889	−	5.29247i	−0.500563	−	0.228600i
$537$	15.2679	−	1.09198i	0.658860	−	0.0471226i
$538$	−1.60391	−	2.14258i	−0.0691496	−	0.0923730i
$539$	−2.29020	−	5.01485i	−0.0986460	−	0.216005i
$540$	2.09731	−	0.775431i	0.0902538	−	0.0333692i
$541$	−18.9914	−	5.57639i	−0.816505	−	0.239748i	−0.153295	−	0.988180i	$-0.548988\pi$
$541$	−18.9914	−	5.57639i	−0.816505	−	0.239748i	−0.663211	+	0.748433i	$0.730807\pi$
$542$	−2.72605	+	7.30882i	−0.117094	+	0.313941i
$543$	7.39676	−	5.53715i	0.317426	−	0.237622i
$544$	−2.63419	+	3.04002i	−0.112940	+	0.130340i
$545$	−16.5051	+	25.5217i	−0.707001	+	1.09323i
$546$	2.63246	−	4.09619i	0.112659	−	0.175301i
$547$	23.2587	−	31.0700i	0.994471	−	1.32846i	0.0503945	−	0.998729i	$-0.483952\pi$
$547$	23.2587	−	31.0700i	0.994471	−	1.32846i	0.944076	−	0.329728i	$-0.106957\pi$
$548$	−10.5337	−	2.29148i	−0.449979	−	0.0978870i
$549$	−10.0243	−	11.5687i	−0.427827	−	0.493739i
$550$	−2.85188	+	2.81944i	−0.121605	+	0.120221i
$551$			2.96802i			0.126442i
$552$	3.03375	+	3.71435i	0.129125	+	0.158093i
$553$	−5.11111	+	5.11111i	−0.217347	+	0.217347i
$554$	3.66238	+	12.4729i	0.155600	+	0.529924i
$555$	−20.5226	+	13.1063i	−0.871136	+	0.556331i
$556$	−11.2132	+	7.20631i	−0.475547	+	0.305616i
$557$	15.4627	+	11.5753i	0.655177	+	0.490459i	0.874394	−	0.485217i	$-0.161259\pi$
$557$	15.4627	+	11.5753i	0.655177	+	0.490459i	−0.219217	+	0.975676i	$0.570350\pi$
$558$	−7.53570	+	1.63929i	−0.319011	+	0.0693967i
$559$	5.46415	−	11.9648i	0.231109	−	0.506058i
$560$	−0.617923	+	8.30580i	−0.0261120	+	0.350984i
$561$	−0.459151	+	3.19346i	−0.0193854	+	0.134828i
$562$	−14.6869	−	5.47795i	−0.619531	−	0.231073i
$563$	−19.8724	−	36.3936i	−0.837521	−	1.53381i	−0.845587	−	0.533838i	$-0.820749\pi$
$563$	−19.8724	−	36.3936i	−0.837521	−	1.53381i	0.00806524	−	0.999967i	$-0.497433\pi$
$564$	−0.762935	+	2.59832i	−0.0321254	+	0.109409i
$565$	−14.8874	+	27.0799i	−0.626320	+	1.13926i
$566$	−17.8155	−	2.56149i	−0.748843	−	0.107667i
$567$	−0.265719	−	3.71524i	−0.0111592	−	0.156025i
$568$	2.40207	+	6.44020i	0.100789	+	0.270225i
$569$	−24.3303	−	15.6361i	−1.01998	−	0.655500i	−0.0800207	−	0.996793i	$-0.525499\pi$
$569$	−24.3303	−	15.6361i	−1.01998	−	0.655500i	−0.939957	+	0.341294i	$0.889135\pi$
$570$	0.00373659	−	1.30652i	0.000156508	−	0.0547242i
$571$	19.7366	+	30.7107i	0.825949	+	1.28520i	0.955903	+	0.293682i	$0.0948806\pi$
$571$	19.7366	+	30.7107i	0.825949	+	1.28520i	−0.129954	+	0.991520i	$0.541483\pi$
$572$	−1.04582	−	0.0747985i	−0.0437279	−	0.00312748i
$573$	7.48839	+	4.08897i	0.312832	+	0.170819i
$574$	−23.0839			−0.963503
$575$	−18.6582	+	15.0623i	−0.778100	+	0.628140i
$576$	−1.00000			−0.0416667
$577$	38.0765	+	20.7913i	1.58514	+	0.865554i	0.998445	+	0.0557500i	$0.0177550\pi$
$577$	38.0765	+	20.7913i	1.58514	+	0.865554i	0.586700	+	0.809804i	$0.300427\pi$
$578$	0.817219	+	0.0584487i	0.0339918	+	0.00243115i
$579$	−0.538548	−	0.837998i	−0.0223813	−	0.0348260i
$580$	−0.0324844	+	11.3584i	−0.00134884	+	0.471631i
$581$	29.2090	+	18.7715i	1.21179	+	0.778772i
$582$	−1.74946	−	4.69049i	−0.0725176	−	0.194427i
$583$	0.592756	+	8.28781i	0.0245494	+	0.343246i
$584$	6.04670	+	0.869384i	0.250214	+	0.0359753i
$585$	−1.40822	+	2.56152i	−0.0582228	+	0.105906i
$586$	0.0846355	−	0.288242i	0.00349626	−	0.0119072i
$587$	11.1524	+	20.4242i	0.460310	+	0.842995i	0.999999	+	0.00113090i	$0.000359977\pi$
$587$	11.1524	+	20.4242i	0.460310	+	0.842995i	−0.539689	+	0.841864i	$0.681458\pi$
$588$	6.44023	+	2.40208i	0.265591	+	0.0990602i
$589$	−0.641280	+	4.46020i	−0.0264235	+	0.183779i
$590$	0.598733	−	8.04785i	0.0246494	−	0.331325i
$591$	7.15272	−	15.6623i	0.294223	−	0.644259i
$592$	10.6411	−	2.31482i	0.437345	−	0.0951385i
$593$	4.32085	+	3.23455i	0.177436	+	0.132827i	0.684304	−	0.729197i	$-0.260106\pi$
$593$	4.32085	+	3.23455i	0.177436	+	0.132827i	−0.506868	+	0.862024i	$0.669197\pi$
$594$	−0.674735	+	0.433626i	−0.0276847	+	0.0177919i
$595$	−28.2359	+	18.0322i	−1.15756	+	0.739248i
$596$	0.425977	+	1.45074i	0.0174487	+	0.0594248i
$597$	−2.18657	+	2.18657i	−0.0894904	+	0.0894904i
$598$	−6.17692	−	1.07251i	−0.252593	−	0.0438582i
$599$		−	21.4395i		−	0.875995i	−0.898976	−	0.437997i	$-0.855688\pi$
$599$		−	21.4395i		−	0.875995i	0.898976	−	0.437997i	$-0.144312\pi$
$600$	0.0285992	−	4.99992i	0.00116756	−	0.204121i
$601$	17.5905	+	20.3005i	0.717531	+	0.828075i	0.991008	−	0.133803i	$-0.0427190\pi$
$601$	17.5905	+	20.3005i	0.717531	+	0.828075i	−0.273477	+	0.961879i	$0.588174\pi$
$602$	36.6216	+	7.96654i	1.49258	+	0.324692i
$603$	7.63491	−	10.1990i	0.310918	−	0.415337i
$604$	−6.75263	+	10.5073i	−0.274761	+	0.427536i
$605$	−12.5760	+	19.4461i	−0.511286	+	0.790597i
$606$	4.22254	−	4.87307i	0.171529	−	0.197955i
$607$	−6.11574	+	4.57819i	−0.248230	+	0.185823i	−0.716147	−	0.697950i	$-0.754096\pi$
$607$	−6.11574	+	4.57819i	−0.248230	+	0.185823i	0.467916	+	0.883773i	$0.345005\pi$
$608$	−0.204191	+	0.547457i	−0.00828104	+	0.0222023i
$609$	18.1539	+	5.33046i	0.735633	+	0.216001i
$610$	−32.1047	+	11.8699i	−1.29988	+	0.480600i
$611$	−1.47059	−	3.22014i	−0.0594936	−	0.130273i
$612$	−2.41061	−	3.22020i	−0.0974431	−	0.130169i
$613$	−7.46457	+	0.533876i	−0.301491	+	0.0215631i	−0.221265	−	0.975214i	$-0.571019\pi$
$613$	−7.46457	+	0.533876i	−0.301491	+	0.0215631i	−0.0802258	+	0.996777i	$0.525564\pi$
$614$	−6.01733	−	2.74802i	−0.242840	−	0.110901i
$615$	13.8254	−	0.949079i	0.557495	−	0.0382706i
$616$	−0.425159	−	2.95705i	−0.0171302	−	0.119143i
$617$	5.78496	−	26.5930i	0.232894	−	1.07059i	−0.701033	−	0.713129i	$-0.747277\pi$
$617$	5.78496	−	26.5930i	0.232894	−	1.07059i	0.933926	−	0.357465i	$-0.116359\pi$
$618$	−0.423733	+	5.92456i	−0.0170450	+	0.238321i
$619$	−20.7383	+	6.08931i	−0.833542	+	0.244750i	−0.670538	−	0.741875i	$-0.733937\pi$
$619$	−20.7383	+	6.08931i	−0.833542	+	0.244750i	−0.163004	+	0.986625i	$0.552118\pi$
$620$	−2.50294	+	17.0618i	−0.100521	+	0.685219i
$621$	−4.27433	+	2.17488i	−0.171523	+	0.0872748i
$622$	−5.94498	−	5.94498i	−0.238372	−	0.238372i
$623$	−16.2300	+	29.7229i	−0.650240	+	1.19082i
$624$	0.987952	−	0.856065i	0.0395497	−	0.0342700i
$625$	24.9984	+	0.285988i	0.999935	+	0.0114395i
$626$	−2.78075	+	0.399811i	−0.111141	+	0.0159797i
$627$	0.0996168	+	0.457931i	0.00397831	+	0.0182880i
$628$	−3.57174	+	1.33219i	−0.142528	+	0.0531601i
$629$	33.1056	+	28.6862i	1.32001	+	1.14379i
$630$	−7.98463	−	2.36933i	−0.318115	−	0.0943962i
$631$	−10.0477	+	4.58864i	−0.399994	+	0.182671i	−0.605247	−	0.796038i	$-0.706926\pi$
$631$	−10.0477	+	4.58864i	−0.399994	+	0.182671i	0.205253	+	0.978709i	$0.434198\pi$
$632$	−1.70322	+	0.930030i	−0.0677505	+	0.0369946i
$633$	−1.35052	+	0.737442i	−0.0536785	+	0.0293107i
$634$	6.66650	−	3.04449i	0.264760	−	0.120912i
$635$	1.55382	−	0.842691i	0.0616615	−	0.0334412i
$636$	−7.82923	−	6.78407i	−0.310449	−	0.269006i
$637$	−8.41898	+	3.14012i	−0.333572	+	0.124416i
$638$	−0.866028	−	3.98107i	−0.0342864	−	0.157612i
$639$	−6.80362	+	0.978213i	−0.269147	+	0.0386975i
$640$	−0.787414	+	2.09284i	−0.0311253	+	0.0827268i
$641$	−6.93339	+	6.00782i	−0.273852	+	0.237295i	−0.780949	−	0.624595i	$-0.785264\pi$
$641$	−6.93339	+	6.00782i	−0.273852	+	0.237295i	0.507097	+	0.861889i	$0.330719\pi$
$642$	2.07512	−	3.80029i	0.0818983	−	0.149986i
$643$	−6.13550	−	6.13550i	−0.241960	−	0.241960i	0.575700	−	0.817661i	$-0.304729\pi$
$643$	−6.13550	−	6.13550i	−0.241960	−	0.241960i	−0.817661	+	0.575700i	$0.804729\pi$
$644$	−0.755062	−	17.8472i	−0.0297536	−	0.703279i
$645$	−22.2610	−	3.26565i	−0.876525	−	0.128585i
$646$	−2.25514	+	0.662170i	−0.0887274	+	0.0260527i
$647$	−0.705844	+	9.86899i	−0.0277496	+	0.387990i	0.964530	+	0.263972i	$0.0850326\pi$
$647$	−0.705844	+	9.86899i	−0.0277496	+	0.387990i	−0.992280	+	0.124018i	$0.960422\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	0.411956	+	2.86521i	0.0161707	+	0.112469i
$650$	4.25200	+	4.96416i	0.166777	+	0.194710i
$651$	26.1291	+	11.9328i	1.02408	+	0.467681i
$652$	11.0152	−	0.787820i	0.431387	−	0.0308534i
$653$	−16.2130	−	21.6581i	−0.634466	−	0.847547i	0.361945	−	0.932199i	$-0.382113\pi$
$653$	−16.2130	−	21.6581i	−0.634466	−	0.847547i	−0.996411	+	0.0846527i	$0.973022\pi$
$654$	5.64651	+	12.3641i	0.220796	+	0.483476i
$655$	28.0632	+	12.9132i	1.09652	+	0.504559i
$656$	−5.94642	−	1.74603i	−0.232169	−	0.0681709i
$657$	−2.13483	+	5.72371i	−0.0832878	+	0.223303i
$658$	8.07475	−	6.04468i	0.314787	−	0.235646i
$659$	6.90361	−	7.96719i	0.268927	−	0.310358i	−0.605183	−	0.796086i	$-0.706900\pi$
$659$	6.90361	−	7.96719i	0.268927	−	0.310358i	0.874110	+	0.485728i	$0.161446\pi$
$660$	0.376214	+	1.75356i	0.0146441	+	0.0682571i
$661$	−3.42664	+	5.33195i	−0.133281	+	0.207389i	−0.901479	−	0.432824i	$-0.857517\pi$
$661$	−3.42664	+	5.33195i	−0.133281	+	0.207389i	0.768198	+	0.640212i	$0.221154\pi$
$662$	−19.0130	+	25.3985i	−0.738963	+	0.987139i
$663$	5.13826	+	1.11776i	0.199554	+	0.0434102i
$664$	6.10441	+	7.04487i	0.236897	+	0.273394i
$665$	−2.92749	+	3.88745i	−0.113523	+	0.150749i
$666$			10.8899i			0.421976i
$667$	−2.76345	−	24.2039i	−0.107001	−	0.937177i
$668$	−0.800437	+	0.800437i	−0.0309698	+	0.0309698i
$669$	−5.37621	−	18.3097i	−0.207856	−	0.707893i
$670$	−15.3331	−	24.0095i	−0.592371	−	0.927569i
$671$	10.3285	−	6.63775i	0.398729	−	0.256247i
$672$	2.98180	+	2.23215i	0.115025	+	0.0861070i
$673$	−30.1136	+	6.55081i	−1.16079	+	0.252515i	−0.751403	−	0.659844i	$-0.770622\pi$
$673$	−30.1136	+	6.55081i	−1.16079	+	0.252515i	−0.409391	+	0.912359i	$0.634259\pi$
$674$	−7.01326	+	15.3569i	−0.270141	+	0.591525i
$675$	4.87958	+	1.09075i	0.187815	+	0.0419832i
$676$	1.60689	−	11.1762i	0.0618035	−	0.429853i
$677$	30.7088	+	11.4538i	1.18024	+	0.440205i	0.861559	−	0.507658i	$-0.169489\pi$
$677$	30.7088	+	11.4538i	1.18024	+	0.440205i	0.318677	+	0.947863i	$0.396761\pi$
$678$	6.62321	+	12.1295i	0.254363	+	0.465831i
$679$	−5.25332	+	17.8912i	−0.201604	+	0.686600i
$680$	−8.63750	+	2.50939i	−0.331233	+	0.0962307i
$681$	21.9005	+	3.14881i	0.839228	+	0.120663i
$682$	−0.441264	−	6.16967i	−0.0168969	−	0.236249i
$683$	16.1381	+	43.2678i	0.617505	+	1.65560i	0.747644	+	0.664100i	$0.231185\pi$
$683$	16.1381	+	43.2678i	0.617505	+	1.65560i	−0.130138	+	0.991496i	$0.541542\pi$
$684$	−0.491542	−	0.315895i	−0.0187946	−	0.0120785i
$685$	−16.9960	−	17.0935i	−0.649385	−	0.653110i
$686$	0.254505	+	0.396018i	0.00971705	+	0.0151200i
$687$	−27.2865	−	1.95157i	−1.04105	−	0.0744570i
$688$	8.83117	+	4.82218i	0.336685	+	0.183844i
$689$	13.5425			0.515929
$690$	1.18600	+	10.6580i	0.0451502	+	0.405744i
$691$	30.3168			1.15331			0.576653	−	0.816989i	$-0.304358\pi$
$691$	30.3168			1.15331			0.576653	+	0.816989i	$0.304358\pi$
$692$	−5.28012	−	2.88317i	−0.200720	−	0.109601i
$693$	2.97984	+	0.213123i	0.113195	+	0.00809586i
$694$	9.14163	+	14.2246i	0.347011	+	0.539960i
$695$	−29.8049	−	0.0852404i	−1.13056	−	0.00323335i
$696$	4.27327	+	2.74626i	0.161978	+	0.104097i
$697$	−8.71195	−	23.3576i	−0.329989	−	0.884734i
$698$	1.43618	+	20.0804i	0.0543601	+	0.760054i
$699$	26.9706	+	3.87779i	1.02012	+	0.146671i
$700$	−11.2458	+	14.8449i	−0.425053	+	0.561085i
$701$	10.7326	−	36.5520i	0.405366	−	1.38055i	−0.463760	−	0.885961i	$-0.653500\pi$
$701$	10.7326	−	36.5520i	0.405366	−	1.38055i	0.869126	−	0.494590i	$-0.164682\pi$
$702$	0.626497	+	1.14734i	0.0236456	+	0.0433037i
$703$	5.96177	+	2.22362i	0.224852	+	0.0838656i
$704$	0.114145	−	0.793896i	0.00430200	−	0.0299211i
$705$	−4.58761	+	3.95227i	−0.172779	+	0.148851i
$706$	12.0961	−	26.4867i	0.455242	−	0.996842i
$707$	−23.4682	+	5.10519i	−0.882612	+	0.192000i
$708$	−2.88920	−	2.16283i	−0.108583	−	0.0812840i
$709$	16.9238	−	10.8763i	0.635587	−	0.408467i	−0.182787	−	0.983152i	$-0.558512\pi$
$709$	16.9238	−	10.8763i	0.635587	−	0.408467i	0.818374	+	0.574685i	$0.194876\pi$
$710$	−3.31002	+	15.0091i	−0.124223	+	0.563283i
$711$	−0.546730	−	1.86199i	−0.0205040	−	0.0698301i
$712$	−6.42904	+	6.42904i	−0.240939	+	0.240939i
$713$	1.07678	−	36.9695i	0.0403259	−	1.38452i
$714$			14.9828i			0.560718i
$715$	−1.87284	−	1.41037i	−0.0700402	−	0.0527447i
$716$	−10.0239	−	11.5682i	−0.374611	−	0.432325i
$717$	−9.54632	−	2.07668i	−0.356514	−	0.0775549i
$718$	−12.7933	+	17.0899i	−0.477443	+	0.637789i
$719$	−1.77165	+	2.75675i	−0.0660715	+	0.102809i	−0.872717	−	0.488226i	$-0.837644\pi$
$719$	−1.77165	+	2.75675i	−0.0660715	+	0.102809i	0.806646	+	0.591035i	$0.201281\pi$
$720$	−1.87763	−	1.21428i	−0.0699753	−	0.0452537i
$721$	14.4880	−	16.7200i	0.539560	−	0.622686i
$722$	14.9370	−	11.1817i	0.555897	−	0.416139i
$723$	−6.18830	+	16.5915i	−0.230145	+	0.617043i
$724$	−8.86543	−	2.60313i	−0.329481	−	0.0967444i
$725$	−13.8533	+	21.2874i	−0.514498	+	0.790596i
$726$	4.30233	+	9.42079i	0.159674	+	0.349638i
$727$	−12.1057	−	16.1713i	−0.448974	−	0.599759i	0.517765	−	0.855523i	$-0.326764\pi$
$727$	−12.1057	−	16.1713i	−0.448974	−	0.599759i	−0.966739	+	0.255763i	$0.917673\pi$
$728$	−4.85674	+	0.347361i	−0.180003	+	0.0128741i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	10.2978	+	8.97479i	0.381139	+	0.332172i
$731$	5.76012	+	40.0625i	0.213046	+	1.48177i
$732$	−3.25385	+	14.9577i	−0.120266	+	0.552853i
$733$	−2.31240	+	32.3315i	−0.0854104	+	1.19419i	0.756286	+	0.654241i	$0.227012\pi$
$733$	−2.31240	+	32.3315i	−0.0854104	+	1.19419i	−0.841696	+	0.539952i	$0.818443\pi$
$734$	9.69191	−	2.84580i	0.357735	−	0.105040i
$735$	9.17559	+	12.3305i	0.338447	+	0.454818i
$736$	1.15543	−	4.65457i	0.0425897	−	0.171570i
$737$	7.22549	+	7.22549i	0.266154	+	0.266154i
$738$	2.97013	−	5.43938i	0.109332	−	0.200227i
$739$	−8.65934	+	7.50336i	−0.318539	+	0.276016i	−0.799423	−	0.600769i	$-0.794861\pi$
$739$	−8.65934	+	7.50336i	−0.318539	+	0.276016i	0.480884	+	0.876784i	$0.340316\pi$
$740$	22.7909	+	8.57488i	0.837809	+	0.315219i
$741$	0.756047	−	0.108703i	0.0277741	−	0.00399331i
$742$	8.20216	+	37.7047i	0.301111	+	1.38418i
$743$	23.3844	−	8.72192i	0.857890	−	0.319976i	0.118254	−	0.992983i	$-0.462270\pi$
$743$	23.3844	−	8.72192i	0.857890	−	0.319976i	0.739636	+	0.673007i	$0.234998\pi$
$744$	5.82829	+	5.05025i	0.213676	+	0.185151i
$745$	−0.961787	+	3.24122i	−0.0352371	+	0.118749i
$746$	33.3690	−	15.2391i	1.22173	−	0.557943i
$747$	−8.18145	+	4.46741i	−0.299344	+	0.163454i
$748$	2.83166	−	1.54620i	0.103536	−	0.0565348i
$749$	−14.6704	+	6.69975i	−0.536045	+	0.244803i
$750$	6.12502	−	9.35329i	0.223654	−	0.341534i
$751$	−9.55792	−	8.28198i	−0.348773	−	0.302214i	0.462802	−	0.886462i	$-0.346844\pi$
$751$	−9.55792	−	8.28198i	−0.348773	−	0.302214i	−0.811575	+	0.584248i	$0.801390\pi$
$752$	2.53727	−	0.946353i	0.0925247	−	0.0345099i
$753$	−2.76392	−	12.7055i	−0.100723	−	0.463015i
$754$	−6.57276	+	0.945020i	−0.239366	+	0.0344156i
$755$	−25.4378	+	11.5293i	−0.925778	+	0.419593i
$756$	−2.81496	+	2.43918i	−0.102379	+	0.0887121i
$757$	−7.46140	+	13.6645i	−0.271189	+	0.496646i	−0.977412	−	0.211344i	$-0.932216\pi$
$757$	−7.46140	+	13.6645i	−0.271189	+	0.496646i	0.706222	+	0.707990i	$0.250398\pi$
$758$	−4.57496	−	4.57496i	−0.166170	−	0.166170i
$759$	−1.23873	−	3.64162i	−0.0449631	−	0.132183i
$760$	−1.04816	+	0.779979i	−0.0380209	+	0.0282928i
$761$	−21.6135	+	6.34631i	−0.783490	+	0.230053i	−0.648926	−	0.760851i	$-0.724782\pi$
$761$	−21.6135	+	6.34631i	−0.783490	+	0.230053i	−0.134564	+	0.990905i	$0.542963\pi$
$762$	0.0563940	−	0.788491i	0.00204294	−	0.0285640i
$763$	10.7618	−	49.4712i	0.389604	−	1.79098i
$764$	−1.21424	−	8.44519i	−0.0439295	−	0.305536i
$765$	−0.616009	−	8.97352i	−0.0222718	−	0.324438i
$766$	33.9647	+	15.5112i	1.22720	+	0.560441i
$767$	4.70591	−	0.336573i	0.169921	−	0.0121530i
$768$	0.599278	+	0.800541i	0.0216246	+	0.0288870i
$769$	0.984953	+	2.15675i	0.0355183	+	0.0777742i	0.926560	−	0.376148i	$-0.122752\pi$
$769$	0.984953	+	2.15675i	0.0355183	+	0.0777742i	−0.891041	+	0.453922i	$0.850024\pi$
$770$	2.79240	−	6.06852i	0.100631	−	0.218694i
$771$	−2.66954	−	0.783848i	−0.0961412	−	0.0282296i
$772$	−0.348112	+	0.933324i	−0.0125288	+	0.0335911i
$773$	7.19081	−	5.38297i	0.258635	−	0.193612i	−0.462089	−	0.886833i	$-0.652900\pi$
$773$	7.19081	−	5.38297i	0.258635	−	0.193612i	0.720725	+	0.693221i	$0.243809\pi$
$774$	−6.58918	+	7.60432i	−0.236843	+	0.273332i
$775$	−25.4175	+	28.9966i	−0.913024	+	1.04159i
$776$	−2.70652	+	4.21142i	−0.0971584	+	0.151181i
$777$	24.3079	−	32.4716i	0.872042	−	1.16491i
$778$	−33.4830	−	7.28378i	−1.20042	−	0.261136i
$779$	−2.37136	−	2.73669i	−0.0849627	−	0.0980521i
$780$	2.89452	−	0.407723i	0.103640	−	0.0145988i
$781$		−	5.51302i		−	0.197271i
$782$	17.7739	−	7.49962i	0.635593	−	0.268186i
$783$	−3.59185	+	3.59185i	−0.128362	+	0.128362i
$784$	−1.93652	−	6.59519i	−0.0691615	−	0.235542i
$785$	−8.32408	−	1.83574i	−0.297099	−	0.0655204i
$786$	11.6220	−	7.46903i	0.414545	−	0.266412i
$787$	−36.7890	−	27.5399i	−1.31139	−	0.981691i	−0.999502	−	0.0315711i	$-0.989949\pi$
$787$	−36.7890	−	27.5399i	−1.31139	−	0.981691i	−0.311884	−	0.950120i	$-0.600960\pi$
$788$	−16.8247	+	3.66000i	−0.599357	+	0.130382i
$789$	0.310071	−	0.678961i	0.0110388	−	0.0241716i
$790$	−4.32735	−	0.321940i	−0.153960	−	0.0114541i
$791$	7.32575	−	50.9517i	0.260474	−	1.81163i
$792$	0.751489	+	0.280291i	0.0267030	+	0.00995971i
$793$	−9.59013	−	17.5630i	−0.340556	−	0.623681i
$794$	3.72402	−	12.6828i	0.132161	−	0.450097i
$795$	−6.46265	−	22.2449i	−0.229207	−	0.788946i
$796$	3.06080	+	0.440077i	0.108487	+	0.0155981i
$797$	1.04053	+	14.5486i	0.0368576	+	0.515337i	0.982025	+	0.188751i	$0.0604438\pi$
$797$	1.04053	+	14.5486i	0.0368576	+	0.515337i	−0.945167	+	0.326586i	$0.894102\pi$
$798$	0.760556	+	2.03913i	0.0269234	+	0.0721844i
$799$	9.16381	+	5.88922i	0.324192	+	0.208346i
$800$	−4.01978	+	2.97344i	−0.142121	+	0.105127i
$801$	−4.91553	−	7.64871i	−0.173682	−	0.270254i
$802$	32.9525	+	2.35681i	1.16359	+	0.0832218i
$803$	−4.30035	−	2.34817i	−0.151756	−	0.0828650i
$804$	−12.7402			−0.449312
$805$	20.2539	−	34.4274i	0.713855	−	1.21341i
$806$	−10.0814			−0.355103
$807$	−2.34903	−	1.28267i	−0.0826897	−	0.0451520i
$808$	−6.43157	−	0.459995i	−0.226262	−	0.0161826i
$809$	−21.3298	−	33.1897i	−0.749914	−	1.16689i	−0.981010	−	0.193958i	$-0.937867\pi$
$809$	−21.3298	−	33.1897i	−0.749914	−	1.16689i	0.231096	−	0.972931i	$-0.425769\pi$
$810$	1.58565	−	1.57661i	0.0557142	−	0.0553964i
$811$	0.635205	+	0.408222i	0.0223051	+	0.0143346i	0.551746	−	0.834012i	$-0.313962\pi$
$811$	0.635205	+	0.408222i	0.0223051	+	0.0143346i	−0.529441	+	0.848347i	$0.677598\pi$
$812$	−6.61196	−	17.7274i	−0.232034	−	0.622109i
$813$	0.556493	+	7.78078i	0.0195170	+	0.272884i
$814$	−8.64547	−	1.24303i	−0.303023	−	0.0435682i
$815$	21.6391	+	11.8963i	0.757984	+	0.416709i
$816$	−1.13328	+	3.85958i	−0.0396726	+	0.135112i
$817$	2.81759	+	5.16003i	0.0985750	+	0.180527i
$818$	24.8634	+	9.27356i	0.869327	+	0.324242i
$819$	0.692952	−	4.81959i	0.0242137	−	0.168410i
$820$	−9.04504	−	10.4991i	−0.315866	−	0.366643i
$821$	0.343996	−	0.753245i	0.0120055	−	0.0262884i	−0.903534	−	0.428516i	$-0.859037\pi$
$821$	0.343996	−	0.753245i	0.0120055	−	0.0262884i	0.915540	+	0.402227i	$0.131764\pi$
$822$	−10.5337	+	2.29148i	−0.367407	+	0.0799244i
$823$	36.1905	+	27.0918i	1.26152	+	0.944362i	0.999784	−	0.0207776i	$-0.00661420\pi$
$823$	36.1905	+	27.0918i	1.26152	+	0.944362i	0.261736	+	0.965140i	$0.415705\pi$
$824$	4.99679	−	3.21124i	0.174071	−	0.111869i
$825$	−1.42292	+	3.74937i	−0.0495399	+	0.130536i
$826$	3.78726	+	12.8982i	0.131776	+	0.448787i
$827$	−31.7975	+	31.7975i	−1.10571	+	1.10571i	−0.111999	+	0.993708i	$0.535725\pi$
$827$	−31.7975	+	31.7975i	−1.10571	+	1.10571i	−0.993708	+	0.111999i	$0.964275\pi$
$828$	4.30259	+	2.11842i	0.149525	+	0.0736203i
$829$		−	27.8442i		−	0.967069i	−0.875325	−	0.483535i	$-0.839353\pi$
$829$		−	27.8442i		−	0.967069i	0.875325	−	0.483535i	$-0.160647\pi$
$830$	2.90738	+	20.6402i	0.100917	+	0.716431i
$831$	8.51286	+	9.82437i	0.295308	+	0.340803i
$832$	−1.27737	−	0.277876i	−0.0442849	−	0.00963360i
$833$	16.5696	−	22.1344i	0.574102	−	0.766911i
$834$	−7.20631	+	11.2132i	−0.249534	+	0.388283i
$835$	−2.47489	+	0.530970i	−0.0856470	+	0.0183750i
$836$	0.306895	−	0.354175i	0.0106142	−	0.0122494i
$837$	−6.17372	+	4.62159i	−0.213395	+	0.159746i
$838$	−10.6776	+	28.6278i	−0.368852	+	0.988931i
$839$	52.6047	+	15.4461i	1.81612	+	0.533260i	0.999062	−	0.0433026i	$-0.0137880\pi$
$839$	52.6047	+	15.4461i	1.81612	+	0.533260i	0.817053	+	0.576562i	$0.195606\pi$
$840$	2.88827	+	7.81191i	0.0996548	+	0.269537i
$841$	1.32818	+	2.90832i	0.0457994	+	0.100287i
$842$	−18.3129	−	24.4631i	−0.631103	−	0.843055i
$843$	−15.6353	+	1.11826i	−0.538509	+	0.0385150i
$844$	1.39969	+	0.639218i	0.0481794	+	0.0220028i
$845$	16.5882	−	19.0336i	0.570652	−	0.654774i
$846$	0.385390	+	2.68045i	0.0132500	+	0.0921557i
$847$	8.19990	−	37.6943i	0.281752	−	1.29519i
$848$	−0.739042	+	10.3332i	−0.0253788	+	0.354842i
$849$	−17.2697	+	5.07083i	−0.592693	+	0.174030i
$850$	−19.2652	−	5.77667i	−0.660790	−	0.198138i
$851$	−50.6879	−	12.5825i	−1.73756	−	0.431324i
$852$	4.86036	+	4.86036i	0.166513	+	0.166513i
$853$	13.9681	−	25.5806i	0.478258	−	0.875865i	−0.521486	−	0.853260i	$-0.674622\pi$
$853$	13.9681	−	25.5806i	0.478258	−	0.875865i	0.999744	−	0.0226049i	$-0.00719596\pi$
$854$	43.0902	−	37.3378i	1.47452	−	1.27767i
$855$	−0.539350	−	1.19001i	−0.0184454	−	0.0406974i
$856$	−4.28586	+	0.616214i	−0.146488	+	0.0210618i
$857$	4.04783	+	18.6076i	0.138271	+	0.635623i	0.993155	+	0.116803i	$0.0372647\pi$
$857$	4.04783	+	18.6076i	0.138271	+	0.635623i	−0.854884	+	0.518820i	$0.826372\pi$
$858$	−0.982383	+	0.366410i	−0.0335380	+	0.0125090i
$859$	−14.0740	−	12.1952i	−0.480197	−	0.416093i	0.380835	−	0.924643i	$-0.375636\pi$
$859$	−14.0740	−	12.1952i	−0.480197	−	0.416093i	−0.861033	+	0.508550i	$0.830182\pi$
$860$	10.7262	+	19.7779i	0.365761	+	0.674419i
$861$	−20.9978	+	9.58939i	−0.715605	+	0.326806i
$862$	−17.3571	+	9.47770i	−0.591185	+	0.322812i
$863$	19.9346	−	10.8851i	0.678583	−	0.370534i	−0.102699	−	0.994712i	$-0.532748\pi$
$863$	19.9346	−	10.8851i	0.678583	−	0.370534i	0.781282	+	0.624178i	$0.214566\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	−6.41316	−	11.8251i	−0.218054	−	0.402066i
$866$	−30.5676	−	26.4870i	−1.03873	−	0.900064i
$867$	0.767649	−	0.286318i	0.0260707	−	0.00972388i
$868$	−6.10591	−	28.0684i	−0.207248	−	0.952705i
$869$	1.54063	−	0.221509i	0.0522624	−	0.00751419i
$870$	4.68889	+	10.3454i	0.158968	+	0.350743i
$871$	12.5867	−	10.9064i	0.426484	−	0.369550i
$872$	6.51417	−	11.9298i	0.220598	−	0.403995i
$873$	−3.53987	−	3.53987i	−0.119806	−	0.119806i
$874$	2.03830	−	1.92292i	0.0689464	−	0.0650438i
$875$	−39.1415	+	14.2177i	−1.32323	+	0.480646i
$876$	5.86142	−	1.72107i	0.198039	−	0.0581495i
$877$	0.756955	−	10.5836i	0.0255606	−	0.357383i	−0.968535	−	0.248877i	$-0.919939\pi$
$877$	0.756955	−	10.5836i	0.0255606	−	0.357383i	0.994096	−	0.108507i	$-0.0346069\pi$
$878$	−3.77575	+	17.3569i	−0.127425	+	0.585765i
$879$	−0.0427529	−	0.297353i	−0.00144202	−	0.0100295i
$880$	1.17834	−	1.35204i	0.0397218	−	0.0455773i
$881$	26.1512	+	11.9429i	0.881057	+	0.402365i	0.803978	−	0.594660i	$-0.202713\pi$
$881$	26.1512	+	11.9429i	0.881057	+	0.402365i	0.0770796	+	0.997025i	$0.475440\pi$
$882$	6.85610	−	0.490358i	0.230857	−	0.0165112i
$883$	−10.7968	−	14.4228i	−0.363340	−	0.485365i	0.581201	−	0.813760i	$-0.302583\pi$
$883$	−10.7968	−	14.4228i	−0.363340	−	0.485365i	−0.944540	+	0.328395i	$0.893492\pi$
$884$	−2.18443	−	4.78324i	−0.0734704	−	0.160878i
$885$	−2.79857	−	7.56931i	−0.0940730	−	0.254439i
$886$	15.5036	+	4.55228i	0.520855	+	0.152937i
$887$	−13.1438	+	35.2400i	−0.441327	+	1.18324i	0.505876	+	0.862606i	$0.331169\pi$
$887$	−13.1438	+	35.2400i	−0.441327	+	1.18324i	−0.947202	+	0.320636i	$0.896103\pi$
$888$	8.71784	−	6.52609i	0.292551	−	0.219001i
$889$	−1.92818	+	2.22524i	−0.0646692	+	0.0746322i
$890$	−19.8781	+	4.26471i	−0.666315	+	0.142953i
$891$	−0.433626	+	0.674735i	−0.0145270	+	0.0226045i
$892$	−11.4358	+	15.2765i	−0.382899	+	0.511494i
$893$	1.54612	+	0.336339i	0.0517391	+	0.0112551i
$894$	0.990143	+	1.14269i	0.0331153	+	0.0382171i
$895$	−4.77415	−	33.8928i	−0.159582	−	1.13291i
$896$		−	3.72473i		−	0.124435i
$897$	−6.06426	+	1.59040i	−0.202480	+	0.0531018i
$898$	−16.2938	+	16.2938i	−0.543730	+	0.543730i
$899$	−11.0366	−	37.5871i	−0.368090	−	1.25360i
$900$	−2.05103	−	4.55997i	−0.0683675	−	0.151999i
$901$	−35.0564	+	22.5293i	−1.16790	+	0.750561i
$902$	3.97928	+	2.97885i	0.132495	+	0.0991849i
$903$	36.6216	−	7.96654i	1.21869	−	0.265110i
$904$	5.74102	−	12.5711i	0.190944	−	0.418108i
$905$	−13.4851	−	15.6529i	−0.448260	−	0.520319i
$906$	−1.77752	+	12.3629i	−0.0590541	+	0.410731i
$907$	−38.4989	−	14.3593i	−1.27833	−	0.476794i	−0.383644	−	0.923481i	$-0.625331\pi$
$907$	−38.4989	−	14.3593i	−1.27833	−	0.476794i	−0.894690	+	0.446687i	$0.852604\pi$
$908$	−10.6037	−	19.4192i	−0.351896	−	0.644450i
$909$	1.81661	−	6.18681i	0.0602532	−	0.205203i
$910$	−9.54098	−	5.24525i	−0.316280	−	0.173878i
$911$	−34.5610	−	4.96912i	−1.14506	−	0.164634i	−0.456436	−	0.889756i	$-0.650874\pi$
$911$	−34.5610	−	4.96912i	−1.14506	−	0.164634i	−0.688621	+	0.725122i	$0.741783\pi$
$912$	0.0416833	+	0.582809i	0.00138027	+	0.0192987i
$913$	−2.61279	−	7.00515i	−0.0864706	−	0.231837i
$914$	−16.0441	−	10.3109i	−0.530693	−	0.341056i
$915$	−24.2725	+	24.1340i	−0.802423	+	0.797846i
$916$	14.7899	+	23.0135i	0.488672	+	0.760388i
$917$	−51.3266	−	3.67095i	−1.69495	−	0.121225i
$918$	−3.53048	−	1.92779i	−0.116523	−	0.0636266i
$919$	−4.12239			−0.135985			−0.0679926	−	0.997686i	$-0.521659\pi$
$919$	−4.12239			−0.135985			−0.0679926	+	0.997686i	$0.521659\pi$
$920$	7.82144	−	7.33655i	0.257865	−	0.241879i
$921$	−6.61513			−0.217976
$922$	−9.20820	−	5.02806i	−0.303256	−	0.165590i
$923$	−8.96258	−	0.641016i	−0.295007	−	0.0210993i
$924$	−1.61514	−	2.51321i	−0.0531342	−	0.0826784i
$925$	32.3806	+	43.7751i	1.06467	+	1.43932i
$926$	3.70213	+	2.37922i	0.121660	+	0.0781859i
$927$	2.07571	+	5.56519i	0.0681753	+	0.182785i
$928$	−0.362377	−	5.06670i	−0.0118956	−	0.166323i
$929$	−0.872634	−	0.125466i	−0.0286302	−	0.00411640i	0.127985	−	0.991776i	$-0.459149\pi$
$929$	−0.872634	−	0.125466i	−0.0286302	−	0.00411640i	−0.156615	+	0.987660i	$0.550058\pi$
$930$	4.81097	+	16.5597i	0.157758	+	0.543015i
$931$	1.13150	−	3.85355i	0.0370835	−	0.126295i
$932$	−13.0585	−	23.9149i	−0.427747	−	0.783360i
$933$	−7.87738	−	2.93811i	−0.257894	−	0.0961895i
$934$	0.494785	−	3.44131i	0.0161899	−	0.112603i
$935$	7.19435	+	0.535235i	0.235280	+	0.0175041i
$936$	0.543050	−	1.18911i	0.0177502	−	0.0388674i
$937$	28.9386	−	6.29520i	0.945382	−	0.205655i	0.286652	−	0.958035i	$-0.407458\pi$
$937$	28.9386	−	6.29520i	0.945382	−	0.205655i	0.658730	+	0.752380i	$0.271094\pi$
$938$	37.9887	+	28.4380i	1.24037	+	0.928533i
$939$	−2.36337	+	1.51885i	−0.0771257	+	0.0495657i
$940$	5.91321	+	1.30406i	0.192868	+	0.0425338i
$941$	8.85998	+	30.1743i	0.288827	+	0.983655i	0.968266	+	0.249923i	$0.0804052\pi$
$941$	8.85998	+	30.1743i	0.288827	+	0.983655i	−0.679439	+	0.733732i	$0.737777\pi$
$942$	−2.69556	+	2.69556i	−0.0878259	+	0.0878259i
$943$	21.8862	+	20.1095i	0.712713	+	0.654855i
$944$			3.60906i			0.117465i
$945$	−8.24733	+	1.16172i	−0.268286	+	0.0377908i
$946$	−5.28492	−	6.09912i	−0.171827	−	0.198299i
$947$	17.3528	+	3.77487i	0.563890	+	0.122667i	0.485469	−	0.874254i	$-0.338649\pi$
$947$	17.3528	+	3.77487i	0.563890	+	0.122667i	0.0784205	+	0.996920i	$0.475012\pi$
$948$	−1.16296	+	1.55353i	−0.0377711	+	0.0504563i
$949$	−4.31746	+	6.71809i	−0.140151	+	0.218079i
$950$	−2.91519	+	0.191745i	−0.0945812	+	0.00622103i
$951$	4.79933	−	5.53872i	0.155629	−	0.179605i
$952$	11.9944	−	8.97887i	0.388739	−	0.291007i
$953$	10.2826	−	27.5688i	0.333088	−	0.893042i	−0.657163	−	0.753748i	$-0.728244\pi$
$953$	10.2826	−	27.5688i	0.333088	−	0.893042i	0.990251	−	0.139294i	$-0.0444834\pi$
$954$	−9.93992	−	2.91862i	−0.321817	−	0.0944940i
$955$	7.97498	−	17.3314i	0.258064	−	0.560832i
$956$	4.05843	+	8.88673i	0.131259	+	0.287417i
$957$	−2.44156	−	3.26154i	−0.0789245	−	0.105431i
$958$	20.7960	−	1.48736i	0.671887	−	0.0480543i
$959$	36.5244	+	16.6802i	1.17944	+	0.538630i
$960$	0.153140	+	2.23082i	0.00494257	+	0.0719993i
$961$	−4.05227	−	28.1842i	−0.130718	−	0.909167i
$962$	−3.02604	+	13.9105i	−0.0975636	+	0.448493i
$963$	0.308894	−	4.31890i	0.00995397	−	0.139175i
$964$	16.9907	−	4.98891i	0.547232	−	0.160682i
$965$	−1.78695	+	1.32973i	−0.0575239	+	0.0428057i
$966$	−8.10083	−	15.9207i	−0.260640	−	0.512241i
$967$	−10.1871	−	10.1871i	−0.327594	−	0.327594i	0.524077	−	0.851671i	$-0.324410\pi$
$967$	−10.1871	−	10.1871i	−0.327594	−	0.327594i	−0.851671	+	0.524077i	$0.824410\pi$
$968$	4.96344	−	9.08986i	0.159531	−	0.292159i
$969$	−1.77628	+	1.53915i	−0.0570622	+	0.0494447i
$970$	−10.1957	+	4.62104i	−0.327365	+	0.148373i
$971$	52.0924	−	7.48975i	1.67172	−	0.240358i	0.759634	−	0.650350i	$-0.225378\pi$
$971$	52.0924	−	7.48975i	1.67172	−	0.240358i	0.912089	+	0.409993i	$0.134469\pi$
$972$	−0.212565	−	0.977147i	−0.00681803	−	0.0313420i
$973$	46.5174	−	17.3501i	1.49128	−	0.556218i
$974$	−25.1284	−	21.7739i	−0.805166	−	0.697681i
$975$	5.92994	+	2.74922i	0.189910	+	0.0880454i
$976$	13.9242	−	6.35898i	0.445704	−	0.203546i
$977$	46.4437	−	25.3602i	1.48586	−	0.811343i	0.487765	−	0.872975i	$-0.337812\pi$
$977$	46.4437	−	25.3602i	1.48586	−	0.811343i	0.998099	+	0.0616317i	$0.0196304\pi$
$978$	9.69247	−	5.29249i	0.309931	−	0.169235i
$979$	6.63336	−	3.02935i	0.212003	−	0.0968186i
$980$	4.37235	−	14.7348i	0.139670	−	0.470687i
$981$	10.2725	+	8.90117i	0.327976	+	0.284192i
$982$	−1.86974	+	0.697376i	−0.0596657	+	0.0222542i
$983$	12.2388	+	56.2607i	0.390356	+	1.79444i	0.582237	+	0.813019i	$0.302177\pi$
$983$	12.2388	+	56.2607i	0.390356	+	1.79444i	−0.191882	+	0.981418i	$0.561459\pi$
$984$	−6.13438	+	0.881991i	−0.195557	+	0.0281169i
$985$	−36.0350	−	13.5579i	−1.14817	−	0.431990i
$986$	15.4422	−	13.3808i	0.491780	−	0.426130i
$987$	4.83400	−	8.85281i	0.153868	−	0.281788i
$988$	−0.540103	−	0.540103i	−0.0171830	−	0.0171830i
$989$	−27.7815	−	39.4560i	−0.883400	−	1.25463i
$990$	1.07067	+	1.43881i	0.0340281	+	0.0457283i
$991$	24.3061	−	7.13690i	0.772108	−	0.226711i	0.128132	−	0.991757i	$-0.459102\pi$
$991$	24.3061	−	7.13690i	0.772108	−	0.226711i	0.643976	+	0.765046i	$0.277284\pi$
$992$	0.550163	−	7.69229i	0.0174677	−	0.244230i
$993$	−6.74398	+	31.0016i	−0.214014	+	0.983805i
$994$	−3.64358	−	25.3416i	−0.115567	−	0.803788i
$995$	5.21269	+	4.54299i	0.165253	+	0.144022i
$996$	8.47931	+	3.87237i	0.268677	+	0.122701i
$997$	54.9921	−	3.93311i	1.74162	−	0.124563i	0.836019	−	0.548700i	$-0.184877\pi$
$997$	54.9921	−	3.93311i	1.74162	−	0.124563i	0.905598	+	0.424137i	$0.139423\pi$
$998$	−15.7821	−	21.0825i	−0.499575	−	0.667353i
$999$	4.52384	+	9.90583i	0.143128	+	0.313406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.37.3	✓	240
5.3	odd	4	inner	690.2.w.a.313.3	yes	240
23.5	odd	22	inner	690.2.w.a.97.3	yes	240
115.28	even	44	inner	690.2.w.a.373.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.3	✓	240	1.1	even	1	trivial
690.2.w.a.97.3	yes	240	23.5	odd	22	inner
690.2.w.a.313.3	yes	240	5.3	odd	4	inner
690.2.w.a.373.3	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)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-0.00639501 + 2.23606i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.30166 - 3.48989i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-0.00639501 + 2.23606i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-1.30166 - 3.48989i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.07724 - 1.95948i) q^{10} +(-0.225966 + 0.769570i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(1.22483 + 0.456836i) q^{13} +(-0.530084 + 3.68682i) q^{14} +(0.165897 - 2.22991i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-3.93060 + 0.855049i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-0.491542 + 0.315895i) q^{19} +(-1.88455 + 1.20352i) q^{20} +(1.04938 + 3.57385i) q^{21} +(0.567142 - 0.567142i) q^{22} +(3.71435 - 3.03375i) q^{23} +1.00000i q^{24} +(-4.99992 - 0.0285992i) q^{25} +(-0.856065 - 0.987952i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(2.23215 - 2.98180i) q^{28} +(2.74626 - 4.27327i) q^{29} +(-1.21428 + 1.87763i) q^{30} +(5.05025 - 5.82829i) q^{31} +(0.800541 - 0.599278i) q^{32} +(0.280291 - 0.751489i) q^{33} +(3.85958 + 1.13328i) q^{34} +(7.81191 - 2.88827i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-6.52609 - 8.71784i) q^{37} +(0.582809 - 0.0416833i) q^{38} +(-1.18911 - 0.543050i) q^{39} +(2.23082 - 0.153140i) q^{40} +(0.881991 + 6.13438i) q^{41} +(0.791748 - 3.63961i) q^{42} +(0.717812 - 10.0363i) q^{43} +(-0.769570 + 0.225966i) q^{44} +(-0.324554 + 2.21239i) q^{45} +(-4.71392 + 0.882560i) q^{46} +(-1.91485 - 1.91485i) q^{47} +(0.479249 - 0.877679i) q^{48} +(-5.19473 + 4.50126i) q^{49} +(4.37462 + 2.42131i) q^{50} +(3.98158 - 0.572465i) q^{51} +(0.277876 + 1.27737i) q^{52} +(9.70639 - 3.62029i) q^{53} +(0.755750 + 0.654861i) q^{54} +(-1.71936 - 0.510195i) q^{55} +(-3.38813 + 1.54731i) q^{56} +(0.512825 - 0.280024i) q^{57} +(-4.45829 + 2.43441i) q^{58} +(3.28291 - 1.49926i) q^{59} +(1.96561 - 1.06602i) q^{60} +(-11.5687 - 10.0243i) q^{61} +(-7.22570 + 2.69505i) q^{62} +(-0.791748 - 3.63961i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-1.02935 + 2.73586i) q^{65} +(-0.606156 + 0.525237i) q^{66} +(6.10572 - 11.1818i) q^{67} +(-2.84435 - 2.84435i) q^{68} +(-3.92131 + 2.76104i) q^{69} +(-8.24055 - 1.20888i) q^{70} +(-6.59515 + 1.93651i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-1.29853 + 5.96927i) q^{73} +(1.54980 + 10.7791i) q^{74} +(4.98514 + 0.385216i) q^{75} +(-0.531495 - 0.242726i) q^{76} +(2.97984 - 0.213123i) q^{77} +(0.783404 + 1.04651i) q^{78} +(-0.806153 - 1.76523i) q^{79} +(-2.03133 - 0.934710i) q^{80} +(0.959493 + 0.281733i) q^{81} +(2.16579 - 5.80671i) q^{82} +(-7.46240 + 5.58628i) q^{83} +(-2.43918 + 2.81496i) q^{84} +(-1.88680 - 8.79451i) q^{85} +(-5.43991 + 8.46466i) q^{86} +(-3.04412 + 4.06646i) q^{87} +(0.783730 + 0.170490i) q^{88} +(-5.95402 - 6.87131i) q^{89} +(1.34514 - 1.78622i) q^{90} -4.86915i q^{91} +(4.56028 + 1.48454i) q^{92} +(-5.45316 + 5.45316i) q^{93} +(0.762935 + 2.59832i) q^{94} +(-0.703216 - 1.10114i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-4.00761 - 3.00006i) q^{97} +(6.71653 - 1.46109i) q^{98} +(-0.333188 + 0.729579i) 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

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