LMFDB - Embedded newform 310.2.s.a.77.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(23,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 18]))

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

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

chi := DirichletCharacter("310.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.s (of order $20$, degree $8$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			77.12
Character	$\chi$	$=$	310.77
Dual form			310.2.s.a.153.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 + 0.156434i) q^{2} +(0.00539952 + 0.0340912i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.0723287 - 2.23490i) q^{5} +0.0345162i q^{6} +(-1.74013 + 0.886641i) q^{7} +(0.891007 + 0.453990i) q^{8} +(2.85204 - 0.926683i) q^{9} +O(q^{10})$	\(q+(0.987688 + 0.156434i) q^{2} +(0.00539952 + 0.0340912i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.0723287 - 2.23490i) q^{5} +0.0345162i q^{6} +(-1.74013 + 0.886641i) q^{7} +(0.891007 + 0.453990i) q^{8} +(2.85204 - 0.926683i) q^{9} +(0.421053 - 2.19607i) q^{10} +(5.39525 + 1.75302i) q^{11} +(-0.00539952 + 0.0340912i) q^{12} +(-0.472393 - 2.98257i) q^{13} +(-1.85741 + 0.603509i) q^{14} +(0.0765810 - 0.00960160i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.48361 - 1.26546i) q^{17} +(2.96189 - 0.469117i) q^{18} +(1.11652 + 1.53676i) q^{19} +(0.759410 - 2.10316i) q^{20} +(-0.0396226 - 0.0545358i) q^{21} +(5.05459 + 2.57544i) q^{22} +(-0.0200854 + 0.0394199i) q^{23} +(-0.0106661 + 0.0328268i) q^{24} +(-4.98954 - 0.323295i) q^{25} -3.01975i q^{26} +(0.0940015 + 0.184488i) q^{27} +(-1.92895 + 0.305516i) q^{28} +(-7.51695 + 5.46138i) q^{29} +(0.0771401 + 0.00249651i) q^{30} +(-5.31865 + 1.64679i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.0306310 + 0.193396i) q^{33} +(-2.25507 - 1.63840i) q^{34} +(1.85569 + 3.95315i) q^{35} +2.99881 q^{36} +(-2.60361 + 2.60361i) q^{37} +(0.862373 + 1.69250i) q^{38} +(0.0991289 - 0.0322089i) q^{39} +(1.07907 - 1.95847i) q^{40} +(4.10410 - 2.98180i) q^{41} +(-0.0306035 - 0.0600627i) q^{42} +(5.15631 + 0.816679i) q^{43} +(4.58948 + 3.33445i) q^{44} +(-1.86476 - 6.44104i) q^{45} +(-0.0260048 + 0.0357925i) q^{46} +(-0.394206 - 2.48892i) q^{47} +(-0.0156700 + 0.0307541i) q^{48} +(-1.87257 + 2.57738i) q^{49} +(-4.87753 - 1.09985i) q^{50} +(0.0297309 - 0.0915022i) q^{51} +(0.472393 - 2.98257i) q^{52} +(-5.59680 + 10.9843i) q^{53} +(0.0639838 + 0.196922i) q^{54} +(4.30806 - 11.9310i) q^{55} -1.95299 q^{56} +(-0.0463614 + 0.0463614i) q^{57} +(-8.27875 + 4.21824i) q^{58} +(-1.64659 + 2.26634i) q^{59} +(0.0757999 + 0.0145332i) q^{60} -6.54992i q^{61} +(-5.51079 + 0.794496i) q^{62} +(-4.14128 + 4.14128i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-6.69991 + 0.840025i) q^{65} +(-0.0605077 + 0.186224i) q^{66} +(-7.51327 - 7.51327i) q^{67} +(-1.97100 - 1.97100i) q^{68} +(-0.00145232 - 0.000471889i) q^{69} +(1.21444 + 4.19477i) q^{70} +(0.478046 + 1.47128i) q^{71} +(2.96189 + 0.469117i) q^{72} +(7.04944 - 3.59187i) q^{73} +(-2.97885 + 2.16426i) q^{74} +(-0.0159196 - 0.171845i) q^{75} +(0.586990 + 1.80657i) q^{76} +(-10.9428 + 1.73316i) q^{77} +(0.102947 - 0.0163052i) q^{78} +(0.636609 + 1.95928i) q^{79} +(1.37216 - 1.76556i) q^{80} +(7.27248 - 5.28377i) q^{81} +(4.52003 - 2.30307i) q^{82} +(-3.21962 - 0.509938i) q^{83} +(-0.0208308 - 0.0641107i) q^{84} +(-3.00781 + 5.45908i) q^{85} +(4.96507 + 1.61325i) q^{86} +(-0.226773 - 0.226773i) q^{87} +(4.01135 + 4.01135i) q^{88} +(-4.49739 + 13.8415i) q^{89} +(-0.834199 - 6.65345i) q^{90} +(3.46650 + 4.77122i) q^{91} +(-0.0312838 + 0.0312838i) q^{92} +(-0.0848593 - 0.172428i) q^{93} -2.51994i q^{94} +(3.51526 - 2.38416i) q^{95} +(-0.0202881 + 0.0279242i) q^{96} +(10.7549 - 5.47988i) q^{97} +(-2.25271 + 2.25271i) q^{98} +17.0120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 12 q^{7}+O(q^{10}) $ 128 * q + 12 * q^7	$ 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) $ 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$3$	0.00539952	+	0.0340912i	0.00311741	+	0.0196826i	0.989198	−	0.146585i	$-0.0468283\pi$
$3$	0.00539952	+	0.0340912i	0.00311741	+	0.0196826i	−0.986081	+	0.166268i	$0.946828\pi$
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	0.0723287	−	2.23490i	0.0323464	−	0.999477i
$5$	0.0723287	−	2.23490i	0.0323464	−	0.999477i
$6$			0.0345162i			0.0140912i
$7$	−1.74013	+	0.886641i	−0.657708	+	0.335119i	−0.750791	−	0.660539i	$-0.770328\pi$
$7$	−1.74013	+	0.886641i	−0.657708	+	0.335119i	0.0930836	+	0.995658i	$0.470328\pi$
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	2.85204	−	0.926683i	0.950679	−	0.308894i
$10$	0.421053	−	2.19607i	0.133149	−	0.694458i
$11$	5.39525	+	1.75302i	1.62673	+	0.528557i	0.973516	−	0.228617i	$-0.0734204\pi$
$11$	5.39525	+	1.75302i	1.62673	+	0.528557i	0.653213	+	0.757174i	$0.273420\pi$
$12$	−0.00539952	+	0.0340912i	−0.00155871	+	0.00984129i
$13$	−0.472393	−	2.98257i	−0.131018	−	0.827217i	−0.962424	−	0.271551i	$-0.912463\pi$
$13$	−0.472393	−	2.98257i	−0.131018	−	0.827217i	0.831406	−	0.555666i	$-0.187537\pi$
$14$	−1.85741	+	0.603509i	−0.496413	+	0.161294i
$15$	0.0765810	−	0.00960160i	0.0197731	−	0.00247912i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−2.48361	−	1.26546i	−0.602364	−	0.306920i	0.126086	−	0.992019i	$-0.459759\pi$
$17$	−2.48361	−	1.26546i	−0.602364	−	0.306920i	−0.728449	+	0.685100i	$0.759759\pi$
$18$	2.96189	−	0.469117i	0.698124	−	0.110572i
$19$	1.11652	+	1.53676i	0.256148	+	0.352557i	0.917652	−	0.397384i	$-0.130082\pi$
$19$	1.11652	+	1.53676i	0.256148	+	0.352557i	−0.661505	+	0.749941i	$0.730082\pi$
$20$	0.759410	−	2.10316i	0.169809	−	0.470282i
$21$	−0.0396226	−	0.0545358i	−0.00864635	−	0.0119007i
$22$	5.05459	+	2.57544i	1.07764	+	0.549087i
$23$	−0.0200854	+	0.0394199i	−0.00418810	+	0.00821962i	−0.893091	−	0.449876i	$-0.851468\pi$
$23$	−0.0200854	+	0.0394199i	−0.00418810	+	0.00821962i	0.888903	+	0.458095i	$0.151468\pi$
$24$	−0.0106661	+	0.0328268i	−0.00217721	+	0.00670075i
$25$	−4.98954	−	0.323295i	−0.997907	−	0.0646589i
$26$		−	3.01975i		−	0.592222i
$27$	0.0940015	+	0.184488i	0.0180906	+	0.0355048i
$28$	−1.92895	+	0.305516i	−0.364537	+	0.0577370i
$29$	−7.51695	+	5.46138i	−1.39586	+	1.01415i	−0.400670	+	0.916223i	$0.631222\pi$
$29$	−7.51695	+	5.46138i	−1.39586	+	1.01415i	−0.995193	+	0.0979310i	$0.968778\pi$
$30$	0.0771401	+	0.00249651i	0.0140838	+	0.000455799i
$31$	−5.31865	+	1.64679i	−0.955258	+	0.295772i
$31$	−5.31865	+	1.64679i	−0.955258	+	0.295772i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.0306310	+	0.193396i	−0.00533217	+	0.0336660i
$34$	−2.25507	−	1.63840i	−0.386741	−	0.280984i
$35$	1.85569	+	3.95315i	0.313669	+	0.668204i
$36$	2.99881			0.499801
$37$	−2.60361	+	2.60361i	−0.428031	+	0.428031i	−0.887957	−	0.459926i	$-0.847876\pi$
$37$	−2.60361	+	2.60361i	−0.428031	+	0.428031i	0.459926	+	0.887957i	$0.347876\pi$
$38$	0.862373	+	1.69250i	0.139895	+	0.274560i
$39$	0.0991289	−	0.0322089i	0.0158733	−	0.00515756i
$40$	1.07907	−	1.95847i	0.170616	−	0.309662i
$41$	4.10410	−	2.98180i	0.640953	−	0.465680i	−0.219224	−	0.975674i	$-0.570353\pi$
$41$	4.10410	−	2.98180i	0.640953	−	0.465680i	0.860177	+	0.509995i	$0.170353\pi$
$42$	−0.0306035	−	0.0600627i	−0.00472222	−	0.00926787i
$43$	5.15631	+	0.816679i	0.786329	+	0.124542i	0.536671	−	0.843792i	$-0.319682\pi$
$43$	5.15631	+	0.816679i	0.786329	+	0.124542i	0.249658	+	0.968334i	$0.419682\pi$
$44$	4.58948	+	3.33445i	0.691890	+	0.502687i
$45$	−1.86476	−	6.44104i	−0.277982	−	0.960173i
$46$	−0.0260048	+	0.0357925i	−0.00383420	+	0.00527732i
$47$	−0.394206	−	2.48892i	−0.0575008	−	0.363046i	−0.999615	−	0.0277531i	$-0.991165\pi$
$47$	−0.394206	−	2.48892i	−0.0575008	−	0.363046i	0.942114	−	0.335293i	$-0.108835\pi$
$48$	−0.0156700	+	0.0307541i	−0.00226177	+	0.00443898i
$49$	−1.87257	+	2.57738i	−0.267510	+	0.368196i
$50$	−4.87753	−	1.09985i	−0.689787	−	0.155542i
$51$	0.0297309	−	0.0915022i	0.00416315	−	0.0128129i
$52$	0.472393	−	2.98257i	0.0655091	−	0.413608i
$53$	−5.59680	+	10.9843i	−0.768780	+	1.50882i	0.0897000	+	0.995969i	$0.471409\pi$
$53$	−5.59680	+	10.9843i	−0.768780	+	1.50882i	−0.858480	+	0.512847i	$0.828591\pi$
$54$	0.0639838	+	0.196922i	0.00870709	+	0.0267977i
$55$	4.30806	−	11.9310i	0.580899	−	1.60878i
$56$	−1.95299			−0.260980
$57$	−0.0463614	+	0.0463614i	−0.00614072	+	0.00614072i
$58$	−8.27875	+	4.21824i	−1.08705	+	0.553881i
$59$	−1.64659	+	2.26634i	−0.214368	+	0.295053i	−0.902636	−	0.430404i	$-0.858371\pi$
$59$	−1.64659	+	2.26634i	−0.214368	+	0.295053i	0.688268	+	0.725456i	$0.258371\pi$
$60$	0.0757999	+	0.0145332i	0.00978572	+	0.00187622i
$61$		−	6.54992i		−	0.838631i	−0.907841	−	0.419316i	$-0.862270\pi$
$61$		−	6.54992i		−	0.838631i	0.907841	−	0.419316i	$-0.137730\pi$
$62$	−5.51079	+	0.794496i	−0.699871	+	0.100901i
$63$	−4.14128	+	4.14128i	−0.521753	+	0.521753i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−6.69991	+	0.840025i	−0.831022	+	0.104192i
$66$	−0.0605077	+	0.186224i	−0.00744798	+	0.0229225i
$67$	−7.51327	−	7.51327i	−0.917891	−	0.917891i	0.0789844	−	0.996876i	$-0.474832\pi$
$67$	−7.51327	−	7.51327i	−0.917891	−	0.917891i	−0.996876	+	0.0789844i	$0.974832\pi$
$68$	−1.97100	−	1.97100i	−0.239019	−	0.239019i
$69$	−0.00145232		0.000471889i	−0.000174839		5.68088e-5i
$70$	1.21444	+	4.19477i	0.145153	+	0.501371i
$71$	0.478046	+	1.47128i	0.0567337	+	0.174608i	0.975408	−	0.220408i	$-0.0707389\pi$
$71$	0.478046	+	1.47128i	0.0567337	+	0.174608i	−0.918674	+	0.395016i	$0.870739\pi$
$72$	2.96189	+	0.469117i	0.349062	+	0.0552860i
$73$	7.04944	−	3.59187i	0.825074	−	0.420396i	0.0101392	−	0.999949i	$-0.496773\pi$
$73$	7.04944	−	3.59187i	0.825074	−	0.420396i	0.814935	+	0.579552i	$0.196773\pi$
$74$	−2.97885	+	2.16426i	−0.346284	+	0.251590i
$75$	−0.0159196	−	0.171845i	−0.00183824	−	0.0198430i
$76$	0.586990	+	1.80657i	0.0673324	+	0.207228i
$77$	−10.9428	+	1.73316i	−1.24704	+	0.197512i
$78$	0.102947	−	0.0163052i	0.0116565	−	0.00184620i
$79$	0.636609	+	1.95928i	0.0716242	+	0.220437i	0.980460	−	0.196717i	$-0.0630279\pi$
$79$	0.636609	+	1.95928i	0.0716242	+	0.220437i	−0.908836	+	0.417153i	$0.863028\pi$
$80$	1.37216	−	1.76556i	0.153412	−	0.197395i
$81$	7.27248	−	5.28377i	0.808053	−	0.587085i
$82$	4.52003	−	2.30307i	0.499154	−	0.254332i
$83$	−3.21962	−	0.509938i	−0.353400	−	0.0559730i	−0.0227891	−	0.999740i	$-0.507255\pi$
$83$	−3.21962	−	0.509938i	−0.353400	−	0.0559730i	−0.330610	+	0.943767i	$0.607255\pi$
$84$	−0.0208308	−	0.0641107i	−0.00227283	−	0.00699505i
$85$	−3.00781	+	5.45908i	−0.326243	+	0.592121i
$86$	4.96507	+	1.61325i	0.535397	+	0.173961i
$87$	−0.226773	−	0.226773i	−0.0243126	−	0.0243126i
$88$	4.01135	+	4.01135i	0.427611	+	0.427611i
$89$	−4.49739	+	13.8415i	−0.476722	+	1.46720i	0.366899	+	0.930261i	$0.380420\pi$
$89$	−4.49739	+	13.8415i	−0.476722	+	1.46720i	−0.843621	+	0.536939i	$0.819580\pi$
$90$	−0.834199	−	6.65345i	−0.0879323	−	0.701335i
$91$	3.46650	+	4.77122i	0.363388	+	0.500160i
$92$	−0.0312838	+	0.0312838i	−0.00326156	+	0.00326156i
$93$	−0.0848593	−	0.172428i	−0.00879950	−	0.0178799i
$94$		−	2.51994i		−	0.259912i
$95$	3.51526	−	2.38416i	0.360658	−	0.244610i
$96$	−0.0202881	+	0.0279242i	−0.00207065	+	0.00285000i
$97$	10.7549	−	5.47988i	1.09199	−	0.556398i	0.187231	−	0.982316i	$-0.440049\pi$
$97$	10.7549	−	5.47988i	1.09199	−	0.556398i	0.904762	+	0.425918i	$0.140049\pi$
$98$	−2.25271	+	2.25271i	−0.227558	+	0.227558i
$99$	17.0120			1.70977
$100$	−4.64543	−	1.84932i	−0.464543	−	0.184932i
$101$	−0.227738	−	0.700904i	−0.0226607	−	0.0697426i	0.939087	−	0.343680i	$-0.111674\pi$
$101$	−0.227738	−	0.700904i	−0.0226607	−	0.0697426i	−0.961747	+	0.273938i	$0.911674\pi$
$102$	0.0436789	−	0.0857247i	0.00432486	−	0.00848801i
$103$	−1.36080	+	8.59175i	−0.134084	+	0.846570i	0.825347	+	0.564626i	$0.190979\pi$
$103$	−1.36080	+	8.59175i	−0.134084	+	0.846570i	−0.959431	+	0.281945i	$0.909021\pi$
$104$	0.933154	−	2.87195i	0.0915033	−	0.281618i
$105$	−0.124748	+	0.0846079i	−0.0121741	+	0.00825688i
$106$	−7.24623	+	9.97358i	−0.703816	+	0.968719i
$107$	−2.93810	+	5.76634i	−0.284037	+	0.557453i	−0.988307	−	0.152479i	$-0.951274\pi$
$107$	−2.93810	+	5.76634i	−0.284037	+	0.557453i	0.704270	+	0.709932i	$0.251274\pi$
$108$	0.0323907	+	0.204507i	0.00311680	+	0.0196787i
$109$	0.929272	−	1.27903i	0.0890081	−	0.122509i	−0.762191	−	0.647353i	$-0.775876\pi$
$109$	0.929272	−	1.27903i	0.0890081	−	0.122509i	0.851199	+	0.524843i	$0.175876\pi$
$110$	6.12145	−	11.1102i	0.583657	−	1.05932i
$111$	−0.102819	−	0.0747020i	−0.00975910	−	0.00709040i
$112$	−1.92895	−	0.305516i	−0.182269	−	0.0288685i
$113$	−7.62020	−	14.9555i	−0.716848	−	1.40689i	−0.905284	−	0.424808i	$-0.860342\pi$
$113$	−7.62020	−	14.9555i	−0.716848	−	1.40689i	0.188436	−	0.982086i	$-0.439658\pi$
$114$	−0.0530431	+	0.0385381i	−0.00496794	+	0.00360942i
$115$	0.0866467	+	0.0477401i	0.00807985	+	0.00445179i
$116$	−8.83671	+	2.87122i	−0.820468	+	0.266586i
$117$	−4.11118	−	8.06865i	−0.380079	−	0.745947i
$118$	−1.98086	+	1.98086i	−0.182352	+	0.182352i
$119$	5.44382			0.499034
$120$	0.0725932	+	0.0262119i	0.00662682	+	0.00239281i
$121$	17.1365	+	12.4504i	1.55786	+	1.13185i
$122$	1.02463	−	6.46928i	0.0927659	−	0.585701i
$123$	0.123814	+	0.123814i	0.0111639	+	0.0111639i
$124$	−5.56723	−	0.0773630i	−0.499952	−	0.00694740i
$125$	−1.08342	+	11.1277i	−0.0969038	+	0.995294i
$126$	−4.73814	+	3.44246i	−0.422107	+	0.306678i
$127$	13.8373	−	2.19161i	1.22786	−	0.194474i	0.491388	−	0.870941i	$-0.336490\pi$
$127$	13.8373	−	2.19161i	1.22786	−	0.194474i	0.736473	+	0.676467i	$0.236490\pi$
$128$	0.453990	+	0.891007i	0.0401275	+	0.0787546i
$129$			0.180195i			0.0158652i
$130$	−6.74883	−	0.218415i	−0.591912	−	0.0191562i
$131$	6.69245	−	20.5973i	0.584722	−	1.79959i	−0.0156598	−	0.999877i	$-0.504985\pi$
$131$	6.69245	−	20.5973i	0.584722	−	1.79959i	0.600382	−	0.799713i	$-0.295015\pi$
$132$	−0.0888945	+	0.174465i	−0.00773728	+	0.0151853i
$133$	−3.30545	−	1.68421i	−0.286619	−	0.146040i
$134$	−6.24543	−	8.59610i	−0.539523	−	0.742590i
$135$	0.419111	−	0.196740i	0.0360714	−	0.0169327i
$136$	−1.63840	−	2.25507i	−0.140492	−	0.193371i
$137$	−6.23606	+	0.987694i	−0.532782	+	0.0843844i	−0.417028	−	0.908893i	$-0.636928\pi$
$137$	−6.23606	+	0.987694i	−0.532782	+	0.0843844i	−0.115754	+	0.993278i	$0.536928\pi$
$138$	−0.00136062		0.000693273i	−0.000115824		5.90153e-5i
$139$	−4.12745	−	2.99877i	−0.350086	−	0.254352i	0.398819	−	0.917030i	$-0.369420\pi$
$139$	−4.12745	−	2.99877i	−0.350086	−	0.254352i	−0.748905	+	0.662677i	$0.769420\pi$
$140$	0.543278	+	4.33310i	0.0459154	+	0.366214i
$141$	0.0827217	−	0.0268779i	0.00696643	−	0.00226353i
$142$	0.242003	+	1.52794i	0.0203084	+	0.128222i
$143$	2.67984	−	16.9198i	0.224100	−	1.41491i
$144$	2.85204	+	0.926683i	0.237670	+	0.0772236i
$145$	11.6619	+	17.1946i	0.968472	+	1.42794i
$146$	7.52454	−	2.44487i	0.622735	−	0.202339i
$147$	−0.0979769	−	0.0499217i	−0.00808100	−	0.00411747i
$148$	−3.28074	+	1.67162i	−0.269675	+	0.137406i
$149$		−	18.0009i		−	1.47469i	−0.675514	−	0.737347i	$-0.736078\pi$
$149$		−	18.0009i		−	1.47469i	0.675514	−	0.737347i	$-0.263922\pi$
$150$	0.0111589	−	0.172220i	0.000911120	−	0.0140617i
$151$	1.48691	+	0.483127i	0.121003	+	0.0393163i	0.368893	−	0.929472i	$-0.379737\pi$
$151$	1.48691	+	0.483127i	0.121003	+	0.0393163i	−0.247890	+	0.968788i	$0.579737\pi$
$152$	0.297154	+	1.87615i	0.0241023	+	0.152176i
$153$	−8.25602	−	1.30763i	−0.667460	−	0.105715i
$154$	−11.0792			−0.892784
$155$	3.29572	+	12.0058i	0.264718	+	0.964326i
$156$	0.104230			0.00834510
$157$	3.06625	+	0.485647i	0.244714	+	0.0387588i	0.277586	−	0.960701i	$-0.410466\pi$
$157$	3.06625	+	0.485647i	0.244714	+	0.0387588i	−0.0328726	+	0.999460i	$0.510466\pi$
$158$	0.322272	+	2.03475i	0.0256386	+	0.161876i
$159$	−0.404690	−	0.131492i	−0.0320940	−	0.0104280i
$160$	1.63146	−	1.52917i	0.128978	−	0.120891i
$161$		−	0.0864044i		−	0.00680962i
$162$	8.00951	−	4.08105i	0.629286	−	0.320637i
$163$	21.1600	+	10.7815i	1.65738	+	0.844475i	0.995490	+	0.0948703i	$0.0302436\pi$
$163$	21.1600	+	10.7815i	1.65738	+	0.844475i	0.661886	+	0.749605i	$0.269756\pi$
$164$	4.82466	−	1.56763i	0.376743	−	0.122411i
$165$	0.430005	+	0.0824452i	0.0334759	+	0.00641835i
$166$	−3.10021	−	1.00732i	−0.240623	−	0.0781832i
$167$	−3.07460	+	19.4122i	−0.237920	+	1.50216i	0.522448	+	0.852671i	$0.325019\pi$
$167$	−3.07460	+	19.4122i	−0.237920	+	1.50216i	−0.760367	+	0.649493i	$0.774981\pi$
$168$	−0.0105452	−	0.0665800i	−0.000813583	−	0.00513676i
$169$	3.69115	−	1.19933i	0.283935	−	0.0922559i
$170$	−3.82477	+	4.92135i	−0.293347	+	0.377450i
$171$	4.60845	+	3.34824i	0.352417	+	0.256046i
$172$	4.65157	+	2.37009i	0.354679	+	0.180718i
$173$	−17.4080	+	2.75716i	−1.32351	+	0.209623i	−0.777883	−	0.628409i	$-0.783707\pi$
$173$	−17.4080	+	2.75716i	−1.32351	+	0.209623i	−0.545622	+	0.838031i	$0.683707\pi$
$174$	−0.188506	−	0.259456i	−0.0142906	−	0.0196693i
$175$	8.96910	−	3.86135i	0.678000	−	0.291891i
$176$	3.33445	+	4.58948i	0.251344	+	0.345945i
$177$	−0.0861532	−	0.0438972i	−0.00647567	−	0.00329952i
$178$	−6.60731	+	12.9676i	−0.495239	+	0.971961i
$179$	−4.12127	+	12.6840i	−0.308038	+	0.948043i	0.670488	+	0.741920i	$0.266085\pi$
$179$	−4.12127	+	12.6840i	−0.308038	+	0.948043i	−0.978526	+	0.206123i	$0.933915\pi$
$180$	0.216900	−	6.70203i	0.0161668	−	0.499540i
$181$		−	13.5096i		−	1.00416i	−0.864820	−	0.502082i	$-0.832568\pi$
$181$		−	13.5096i		−	1.00416i	0.864820	−	0.502082i	$-0.167432\pi$
$182$	2.67744	+	5.25476i	0.198465	+	0.389509i
$183$	0.223295	−	0.0353664i	0.0165064	−	0.00261436i
$184$	−0.0357925	+	0.0260048i	−0.00263866	+	0.00191710i
$185$	5.63049	+	6.00712i	0.413962	+	0.441652i
$186$	−0.0568409	−	0.183580i	−0.00416778	−	0.0134607i
$187$	−11.1813	−	11.1813i	−0.817658	−	0.817658i
$188$	0.394206	−	2.48892i	0.0287504	−	0.181523i
$189$	−0.327150	−	0.237688i	−0.0237966	−	0.0172893i
$190$	3.84495	−	1.80490i	0.278942	−	0.130941i
$191$	23.6172			1.70888			0.854441	−	0.519548i	$-0.173900\pi$
$191$	23.6172			1.70888			0.854441	+	0.519548i	$0.173900\pi$
$192$	−0.0244066	+	0.0244066i	−0.00176140	+	0.00176140i
$193$	−11.8109	−	23.1802i	−0.850169	−	1.66855i	−0.737938	−	0.674869i	$-0.764200\pi$
$193$	−11.8109	−	23.1802i	−0.850169	−	1.66855i	−0.112231	−	0.993682i	$-0.535800\pi$
$194$	11.4797	−	3.72998i	0.824195	−	0.267797i
$195$	−0.0648138	−	0.223873i	−0.00464141	−	0.0160318i
$196$	−2.57738	+	1.87257i	−0.184098	+	0.133755i
$197$	2.29549	+	4.50514i	0.163547	+	0.320978i	0.958207	−	0.286076i	$-0.0923510\pi$
$197$	2.29549	+	4.50514i	0.163547	+	0.320978i	−0.794660	+	0.607054i	$0.792351\pi$
$198$	16.8025	+	2.66126i	1.19410	+	0.189127i
$199$	2.78740	+	2.02517i	0.197594	+	0.143560i	0.682183	−	0.731182i	$-0.261031\pi$
$199$	2.78740	+	2.02517i	0.197594	+	0.143560i	−0.484589	+	0.874742i	$0.661031\pi$
$200$	−4.29894	−	2.55326i	−0.303981	−	0.180543i
$201$	0.215568	−	0.296705i	0.0152050	−	0.0209279i
$202$	−0.115288	−	0.727901i	−0.00811165	−	0.0512149i
$203$	8.23819	−	16.1684i	0.578208	−	1.13480i
$204$	0.0565515	−	0.0778364i	0.00395939	−	0.00544964i
$205$	−6.36718	−	9.38792i	−0.444703	−	0.655681i
$206$	−2.68809	+	8.27309i	−0.187288	+	0.576414i
$207$	−0.0207547	+	0.131040i	−0.00144255	+	0.00910790i
$208$	1.37094	−	2.69062i	0.0950575	−	0.186561i
$209$	3.32994	+	10.2485i	0.230337	+	0.708904i
$210$	−0.136447	+	0.0640514i	−0.00941577	+	0.00441996i
$211$	−5.48313			−0.377474			−0.188737	−	0.982028i	$-0.560439\pi$
$211$	−5.48313			−0.377474			−0.188737	+	0.982028i	$0.560439\pi$
$212$	−8.71723	+	8.71723i	−0.598701	+	0.598701i
$213$	−0.0475764	+	0.0242414i	−0.00325988	+	0.00166099i
$214$	−3.80398	+	5.23573i	−0.260035	+	0.357907i
$215$	2.19814	−	11.4647i	0.149912	−	0.781889i
$216$			0.207056i			0.0140884i
$217$	7.79504	−	7.58137i	0.529162	−	0.514657i
$218$	1.11792	−	1.11792i	0.0757148	−	0.0757148i
$219$	0.160515	+	0.220930i	0.0108466	+	0.0149290i
$220$	7.78411	−	10.0158i	0.524804	−	0.675267i
$221$	−2.60109	+	8.00534i	−0.174968	+	0.538497i
$222$	−0.0898667	−	0.0898667i	−0.00603146	−	0.00603146i
$223$	18.7462	+	18.7462i	1.25534	+	1.25534i	0.953295	+	0.302040i	$0.0976676\pi$
$223$	18.7462	+	18.7462i	1.25534	+	1.25534i	0.302040	+	0.953295i	$0.402332\pi$
$224$	−1.85741	−	0.603509i	−0.124103	−	0.0403236i
$225$	−14.5299	+	3.70167i	−0.968662	+	0.246778i
$226$	−5.18683	−	15.9634i	−0.345023	−	1.06187i
$227$	−21.2765	−	3.36987i	−1.41217	−	0.223666i	−0.596700	−	0.802464i	$-0.703522\pi$
$227$	−21.2765	−	3.36987i	−1.41217	−	0.223666i	−0.815471	+	0.578799i	$0.803522\pi$
$228$	−0.0584188	+	0.0297658i	−0.00386888	+	0.00197129i
$229$	17.5781	−	12.7713i	1.16160	−	0.843948i	0.171617	−	0.985164i	$-0.445101\pi$
$229$	17.5781	−	12.7713i	1.16160	−	0.843948i	0.989979	+	0.141215i	$0.0451010\pi$
$230$	0.0781117	+	0.0607069i	0.00515054	+	0.00400289i
$231$	−0.118171	−	0.363694i	−0.00777510	−	0.0239293i
$232$	−9.17707	+	1.45350i	−0.602504	+	0.0954273i
$233$	−7.68445	+	1.21710i	−0.503425	+	0.0797346i	−0.402981	−	0.915208i	$-0.632026\pi$
$233$	−7.68445	+	1.21710i	−0.503425	+	0.0797346i	−0.100443	+	0.994943i	$0.532026\pi$
$234$	−2.79835	−	8.61244i	−0.182934	−	0.563013i
$235$	−5.59099	+	0.700989i	−0.364716	+	0.0457275i
$236$	−2.26634	+	1.64659i	−0.147526	+	0.107184i
$237$	−0.0633570	+	0.0322820i	−0.00411548	+	0.00209694i
$238$	5.37679	+	0.851600i	0.348526	+	0.0552011i
$239$	−3.53760	−	10.8876i	−0.228828	−	0.704261i	−0.997880	−	0.0650748i	$-0.979271\pi$
$239$	−3.53760	−	10.8876i	−0.228828	−	0.704261i	0.769052	−	0.639186i	$-0.220729\pi$
$240$	0.0675990	+	0.0372453i	0.00436350	+	0.00240417i
$241$	−11.5827	−	3.76345i	−0.746108	−	0.242425i	−0.0888026	−	0.996049i	$-0.528304\pi$
$241$	−11.5827	−	3.76345i	−0.746108	−	0.242425i	−0.657306	+	0.753624i	$0.728304\pi$
$242$	14.9778	+	14.9778i	0.962811	+	0.962811i
$243$	0.658630	+	0.658630i	0.0422511	+	0.0422511i
$244$	2.02404	−	6.22934i	0.129576	−	0.398793i
$245$	5.62473	+	4.37143i	0.359351	+	0.279280i
$246$	0.102921	+	0.141658i	0.00656197	+	0.00903178i
$247$	4.05606	−	4.05606i	0.258081	−	0.258081i
$248$	−5.48658	−	0.947317i	−0.348398	−	0.0601547i
$249$		−	0.112514i		−	0.00713031i
$250$	−2.81084	+	10.8212i	−0.177773	+	0.684395i
$251$	−8.24981	+	11.3549i	−0.520724	+	0.716714i	−0.985681	−	0.168618i	$-0.946069\pi$
$251$	−8.24981	+	11.3549i	−0.520724	+	0.716714i	0.464958	+	0.885333i	$0.346069\pi$
$252$	−5.21832	+	2.65887i	−0.328723	+	0.167493i
$253$	−0.177470	+	0.177470i	−0.0111574	+	0.0111574i
$254$	14.0098			0.879051
$255$	−0.202348	−	0.0730637i	−0.0126715	−	0.00457542i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.53106	−	4.96749i	0.157883	−	0.309864i	−0.798491	−	0.602006i	$-0.794368\pi$
$257$	2.53106	−	4.96749i	0.157883	−	0.309864i	0.956375	+	0.292143i	$0.0943682\pi$
$258$	−0.0281886	+	0.177976i	−0.00175495	+	0.0110803i
$259$	2.22216	−	6.83909i	0.138078	−	0.424961i
$260$	−6.63158	−	1.27148i	−0.411273	−	0.0788536i
$261$	−16.3776	+	22.5419i	−1.01375	+	1.39531i
$262$	9.83218	−	19.2967i	0.607434	−	1.19216i
$263$	3.17891	+	20.0708i	0.196020	+	1.23762i	0.867816	+	0.496885i	$0.165523\pi$
$263$	3.17891	+	20.0708i	0.196020	+	1.23762i	−0.671797	+	0.740736i	$0.734477\pi$
$264$	−0.115092	+	0.158411i	−0.00708345	+	0.00974954i
$265$	24.1441	+	13.3028i	1.48316	+	0.817182i
$266$	−3.00129	−	2.18056i	−0.184021	−	0.133699i
$267$	−0.496159	−	0.0785838i	−0.0303644	−	0.00480925i
$268$	−4.82381	−	9.46727i	−0.294661	−	0.578305i
$269$	12.5847	−	9.14330i	0.767301	−	0.557477i	−0.133840	−	0.991003i	$-0.542731\pi$
$269$	12.5847	−	9.14330i	0.767301	−	0.557477i	0.901141	+	0.433526i	$0.142731\pi$
$270$	0.444728	−	0.128754i	0.0270653	−	0.00783573i
$271$	−14.7283	+	4.78550i	−0.894678	+	0.290699i	−0.720039	−	0.693934i	$-0.755876\pi$
$271$	−14.7283	+	4.78550i	−0.894678	+	0.290699i	−0.174640	+	0.984632i	$0.555876\pi$
$272$	−1.26546	−	2.48361i	−0.0767299	−	0.150591i
$273$	−0.143940	+	0.143940i	−0.00871162	+	0.00871162i
$274$	−6.31379			−0.381430
$275$	−26.3531	−	10.4910i	−1.58915	−	0.632633i
$276$	−0.00123542		0.000897586i	−7.43636e−5		5.40283e-5i
$277$	1.41777	−	8.95144i	0.0851855	−	0.537840i	−0.907781	−	0.419444i	$-0.862225\pi$
$277$	1.41777	−	8.95144i	0.0851855	−	0.537840i	0.992967	−	0.118396i	$-0.0377751\pi$
$278$	−3.60752	−	3.60752i	−0.216365	−	0.216365i
$279$	−13.6429	+	9.62541i	−0.816782	+	0.576258i
$280$	−0.141258	+	4.36474i	−0.00844176	+	0.260843i
$281$	−3.88307	+	2.82122i	−0.231645	+	0.168300i	−0.697553	−	0.716533i	$-0.745728\pi$
$281$	−3.88307	+	2.82122i	−0.231645	+	0.168300i	0.465908	+	0.884833i	$0.345728\pi$
$282$	0.0859079	−	0.0136065i	0.00511574	−	0.000810254i
$283$	−1.94332	−	3.81399i	−0.115519	−	0.226718i	0.826007	−	0.563660i	$-0.190607\pi$
$283$	−1.94332	−	3.81399i	−0.115519	−	0.226718i	−0.941525	+	0.336942i	$0.890607\pi$
$284$			1.54699i			0.0917970i
$285$	0.100260	+	0.106966i	0.00593887	+	0.00633613i
$286$	5.29370	−	16.2923i	0.313023	−	0.963385i
$287$	−4.49789	+	8.82760i	−0.265502	+	0.521077i
$288$	2.67196	+	1.36143i	0.157447	+	0.0802231i
$289$	−5.42543	−	7.46747i	−0.319143	−	0.439263i
$290$	8.82853	+	18.8073i	0.518429	+	1.10440i
$291$	0.244887	+	0.337058i	0.0143555	+	0.0197587i
$292$	7.81436	−	1.23767i	0.457301	−	0.0724294i
$293$	−3.30319	−	1.68306i	−0.192974	−	0.0983254i	0.354833	−	0.934930i	$-0.384538\pi$
$293$	−3.30319	−	1.68306i	−0.192974	−	0.0983254i	−0.547808	+	0.836604i	$0.684538\pi$
$294$	−0.0889612	−	0.0646341i	−0.00518832	−	0.00376953i
$295$	4.94595	+	3.84389i	0.287964	+	0.223800i
$296$	−3.50185	+	1.13782i	−0.203541	+	0.0661344i
$297$	0.183749	+	1.16015i	0.0106622	+	0.0673186i
$298$	2.81597	−	17.7793i	0.163125	−	1.02993i
$299$	0.127061	+	0.0412846i	0.00734812	+	0.00238755i
$300$	0.0379626	−	0.168354i	0.00219177	−	0.00971991i
$301$	−9.69675	+	3.15067i	−0.558911	+	0.181601i
$302$	1.39303	+	0.709783i	0.0801597	+	0.0408434i
$303$	0.0226650	−	0.0115484i	0.00130207	−	0.000663438i
$304$			1.89954i			0.108946i
$305$	−14.6384	−	0.473747i	−0.838192	−	0.0271267i
$306$	−7.94982	−	2.58305i	−0.454461	−	0.147663i
$307$	2.62571	+	16.5781i	0.149857	+	0.946160i	0.941948	+	0.335758i	$0.108992\pi$
$307$	2.62571	+	16.5781i	0.149857	+	0.946160i	−0.792091	+	0.610403i	$0.791008\pi$
$308$	−10.9428	−	1.73316i	−0.623521	−	0.0987560i
$309$	−0.300251			−0.0170807
$310$	1.37703	+	12.3735i	0.0782100	+	0.702768i
$311$	−28.5542			−1.61916			−0.809581	−	0.587009i	$-0.800305\pi$
$311$	−28.5542			−1.61916			−0.809581	+	0.587009i	$0.800305\pi$
$312$	0.102947	+	0.0163052i	0.00582823	+	0.000923101i
$313$	0.909303	+	5.74111i	0.0513968	+	0.324507i	0.999968	+	0.00794419i	$0.00252874\pi$
$313$	0.909303	+	5.74111i	0.0513968	+	0.324507i	−0.948572	+	0.316563i	$0.897471\pi$
$314$	2.95253	+	0.959336i	0.166621	+	0.0541384i
$315$	8.95581	+	9.55488i	0.504603	+	0.538356i
$316$			2.06011i			0.115890i
$317$	6.85728	−	3.49396i	0.385143	−	0.196240i	−0.250689	−	0.968068i	$-0.580657\pi$
$317$	6.85728	−	3.49396i	0.385143	−	0.196240i	0.635832	+	0.771827i	$0.280657\pi$
$318$	−0.379138	−	0.193180i	−0.0212610	−	0.0108330i
$319$	−50.1298	+	16.2882i	−2.80673	+	0.911962i
$320$	1.85058	−	1.25512i	0.103451	−	0.0701636i
$321$	−0.212446	−	0.0690279i	−0.0118576	−	0.00385276i
$322$	0.0135166	−	0.0853406i	0.000753252	−	0.00475585i
$323$	−0.828292	−	5.22963i	−0.0460874	−	0.290984i
$324$	8.54931	−	2.77784i	0.474962	−	0.154324i
$325$	1.39277	+	15.0344i	0.0772572	+	0.833957i
$326$	19.2128	+	13.9589i	1.06410	+	0.773114i
$327$	0.0486214	+	0.0247739i	0.00268877	+	0.00137000i
$328$	5.01049	−	0.793584i	0.276658	−	0.0438184i
$329$	2.89275	+	3.98152i	0.159482	+	0.219508i
$330$	0.411814	+	0.148698i	0.0226696	+	0.00818555i
$331$	−20.7682	−	28.5850i	−1.14153	−	1.57118i	−0.764051	−	0.645156i	$-0.776792\pi$
$331$	−20.7682	−	28.5850i	−1.14153	−	1.57118i	−0.377475	−	0.926020i	$-0.623208\pi$
$332$	−2.90446	−	1.47990i	−0.159403	−	0.0812200i
$333$	−5.01287	+	9.83831i	−0.274704	+	0.539136i
$334$	−6.07349	+	18.6923i	−0.332327	+	1.02280i
$335$	−17.3348	+	16.2480i	−0.947102	+	0.887721i
$336$		−	0.0674099i		−	0.00367751i
$337$	2.06777	+	4.05823i	0.112639	+	0.221066i	0.940443	−	0.339951i	$-0.110410\pi$
$337$	2.06777	+	4.05823i	0.112639	+	0.221066i	−0.827804	+	0.561017i	$0.810410\pi$
$338$	3.83332	−	0.607139i	0.208505	−	0.0330240i
$339$	0.468705	−	0.340534i	0.0254566	−	0.0184953i
$340$	−4.54755	+	4.26243i	−0.246626	+	0.231163i
$341$	−31.5823	−	0.438873i	−1.71028	−	0.0237663i
$342$	4.02793	+	4.02793i	0.217806	+	0.217806i
$343$	3.11193	−	19.6479i	0.168028	−	1.06089i
$344$	4.22354	+	3.06858i	0.227718	+	0.165447i
$345$	−0.00115967	+	0.00321167i	−6.24344e−5	+	0.000172910i
$346$	−17.6250			−0.947525
$347$	−17.0082	+	17.0082i	−0.913049	+	0.913049i	−0.996511	−	0.0834619i	$-0.973402\pi$
$347$	−17.0082	+	17.0082i	−0.913049	+	0.913049i	0.0834619	+	0.996511i	$0.473402\pi$
$348$	−0.145597	−	0.285751i	−0.00780484	−	0.0153179i
$349$	−3.52713	+	1.14603i	−0.188803	+	0.0613458i	−0.401892	−	0.915687i	$-0.631647\pi$
$349$	−3.52713	+	1.14603i	−0.188803	+	0.0613458i	0.213089	+	0.977033i	$0.431647\pi$
$350$	9.46272	−	2.41074i	0.505804	−	0.128859i
$351$	0.505844	−	0.367517i	0.0270000	−	0.0196166i
$352$	2.57544	+	5.05459i	0.137272	+	0.269411i
$353$	16.3827	+	2.59476i	0.871963	+	0.138105i	0.576350	−	0.817203i	$-0.304476\pi$
$353$	16.3827	+	2.59476i	0.871963	+	0.138105i	0.295612	+	0.955308i	$0.404476\pi$
$354$	−0.0782255	−	0.0568341i	−0.00415764	−	0.00302070i
$355$	3.32273	−	0.961970i	0.176352	−	0.0510560i
$356$	−8.55454	+	11.7743i	−0.453390	+	0.624037i
$357$	0.0293940	+	0.185586i	0.00155570	+	0.00982227i
$358$	−6.05473	+	11.8831i	−0.320003	+	0.628041i
$359$	16.9015	−	23.2629i	0.892026	−	1.22777i	−0.0809164	−	0.996721i	$-0.525785\pi$
$359$	16.9015	−	23.2629i	0.892026	−	1.22777i	0.972942	−	0.231048i	$-0.0742153\pi$
$360$	1.26266	−	6.58559i	0.0665479	−	0.347091i
$361$	4.75631	−	14.6384i	0.250332	−	0.770443i
$362$	2.11337	−	13.3433i	0.111076	−	0.701309i
$363$	−0.331920	+	0.651430i	−0.0174213	+	0.0341912i
$364$	1.82245	+	5.60891i	0.0955221	+	0.293987i
$365$	−7.51758	−	16.0146i	−0.393488	−	0.838241i
$366$	0.226078			0.0118173
$367$	11.6599	−	11.6599i	0.608644	−	0.608644i	−0.333948	−	0.942592i	$-0.608381\pi$
$367$	11.6599	−	11.6599i	0.608644	−	0.608644i	0.942592	+	0.333948i	$0.108381\pi$
$368$	−0.0394199	+	0.0200854i	−0.00205490	+	0.00104703i
$369$	8.94186	−	12.3074i	0.465495	−	0.640699i
$370$	4.62145	+	6.81396i	0.240258	+	0.354241i
$371$		−	24.0766i		−	1.24999i
$372$	−0.0274230	−	0.190211i	−0.00142181	−	0.00986200i
$373$	16.9373	−	16.9373i	0.876980	−	0.876980i	−0.116241	−	0.993221i	$-0.537084\pi$
$373$	16.9373	−	16.9373i	0.876980	−	0.876980i	0.993221	+	0.116241i	$0.0370845\pi$
$374$	−9.29451	−	12.7928i	−0.480608	−	0.661500i
$375$	−0.385208	+	0.0231493i	−0.0198920	+	0.00119543i
$376$	0.778705	−	2.39661i	0.0401586	−	0.123596i
$377$	19.8399	+	19.8399i	1.02181	+	1.02181i
$378$	−0.285939	−	0.285939i	−0.0147071	−	0.0147071i
$379$	−16.5201	−	5.36769i	−0.848579	−	0.275720i	−0.147728	−	0.989028i	$-0.547196\pi$
$379$	−16.5201	−	5.36769i	−0.848579	−	0.275720i	−0.700851	+	0.713308i	$0.747196\pi$
$380$	4.07996	−	1.18120i	0.209297	−	0.0605941i
$381$	0.149429	+	0.459896i	0.00765550	+	0.0235612i
$382$	23.3265	+	3.69455i	1.19349	+	0.189030i
$383$	24.1185	−	12.2890i	1.23240	−	0.627937i	0.288279	−	0.957547i	$-0.406917\pi$
$383$	24.1185	−	12.2890i	1.23240	−	0.627937i	0.944117	+	0.329609i	$0.106917\pi$
$384$	−0.0279242	+	0.0202881i	−0.00142500	+	0.00103532i
$385$	3.08196	+	24.5813i	0.157071	+	1.25278i
$386$	−8.03932	−	24.7425i	−0.409191	−	1.25936i
$387$	15.4628	−	2.44906i	0.786017	−	0.124493i
$388$	11.9219	−	1.88824i	0.605241	−	0.0958608i
$389$	−3.29079	−	10.1280i	−0.166850	−	0.513510i	0.832318	−	0.554298i	$-0.187013\pi$
$389$	−3.29079	−	10.1280i	−0.166850	−	0.513510i	−0.999168	+	0.0407877i	$0.987013\pi$
$390$	−0.0289944	−	0.231255i	−0.00146819	−	0.0117101i
$391$	0.0997688	−	0.0724862i	0.00504552	−	0.00366579i
$392$	−2.83858	+	1.44633i	−0.143370	+	0.0730506i
$393$	0.738322	+	0.116939i	0.0372434	+	0.00589878i
$394$	1.56246	+	4.80877i	0.0787158	+	0.242262i
$395$	4.42484	−	1.28104i	0.222638	−	0.0644564i
$396$	16.1793	+	5.25698i	0.813042	+	0.264173i
$397$	−22.1373	−	22.1373i	−1.11104	−	1.11104i	−0.993010	−	0.118027i	$-0.962343\pi$
$397$	−22.1373	−	22.1373i	−1.11104	−	1.11104i	−0.118027	−	0.993010i	$-0.537657\pi$
$398$	2.43628	+	2.43628i	0.122120	+	0.122120i
$399$	0.0395690	−	0.121781i	0.00198093	−	0.00609667i
$400$	−3.84659	−	3.19433i	−0.192330	−	0.159716i
$401$	15.2827	+	21.0348i	0.763181	+	1.05043i	0.996943	+	0.0781347i	$0.0248964\pi$
$401$	15.2827	+	21.0348i	0.763181	+	1.05043i	−0.233762	+	0.972294i	$0.575104\pi$
$402$	0.259329	−	0.259329i	0.0129342	−	0.0129342i
$403$	7.42417	+	15.0853i	0.369824	+	0.751454i
$404$		−	0.736974i		−	0.0366658i
$405$	−11.2827	−	16.6354i	−0.560640	−	0.826621i
$406$	10.6661	−	14.6806i	0.529347	−	0.728584i
$407$	−18.6113	+	9.48295i	−0.922529	+	0.470052i
$408$	0.0680315	−	0.0680315i	0.00336806	−	0.00336806i
$409$	−0.627954			−0.0310503			−0.0155252	−	0.999879i	$-0.504942\pi$
$409$	−0.627954			−0.0310503			−0.0155252	+	0.999879i	$0.504942\pi$
$410$	−4.82020	−	10.2684i	−0.238053	−	0.507119i
$411$	−0.0673434	−	0.207262i	−0.00332181	−	0.0102235i
$412$	−3.94919	+	7.75073i	−0.194563	+	0.381851i
$413$	0.855857	−	5.40367i	0.0421140	−	0.265897i
$414$	−0.0409983	+	0.126180i	−0.00201496	+	0.00620140i
$415$	−1.37253	+	7.15865i	−0.0673749	+	0.351404i
$416$	1.77497	−	2.44303i	0.0870248	−	0.119779i
$417$	0.0799455	−	0.156902i	0.00391495	−	0.00768351i
$418$	1.68572	+	10.6432i	0.0824515	+	0.520578i
$419$	−7.71708	+	10.6216i	−0.377004	+	0.518902i	−0.954788	−	0.297288i	$-0.903918\pi$
$419$	−7.71708	+	10.6216i	−0.377004	+	0.518902i	0.577784	+	0.816190i	$0.303918\pi$
$420$	−0.144787	+	0.0419177i	−0.00706490	+	0.00204537i
$421$	21.0200	+	15.2719i	1.02445	+	0.744307i	0.967191	−	0.254052i	$-0.0817634\pi$
$421$	21.0200	+	15.2719i	1.02445	+	0.744307i	0.0572606	+	0.998359i	$0.481763\pi$
$422$	−5.41563	−	0.857751i	−0.263629	−	0.0417547i
$423$	−3.43073	−	6.73318i	−0.166808	−	0.327378i
$424$	−9.97358	+	7.24623i	−0.484360	+	0.351908i
$425$	11.9829	+	7.11701i	0.581258	+	0.345225i
$426$	−0.0507828	+	0.0165003i	−0.00246044	+	0.000799444i
$427$	5.80743	+	11.3977i	0.281041	+	0.551574i
$428$	−4.57619	+	4.57619i	−0.221199	+	0.221199i
$429$	0.591288			0.0285477
$430$	3.96456	−	10.9797i	0.191188	−	0.529490i
$431$	2.40686	+	1.74869i	0.115934	+	0.0842313i	0.644242	−	0.764822i	$-0.277173\pi$
$431$	2.40686	+	1.74869i	0.115934	+	0.0842313i	−0.528307	+	0.849053i	$0.677173\pi$
$432$	−0.0323907	+	0.204507i	−0.00155840	+	0.00983934i
$433$	−8.08981	−	8.08981i	−0.388771	−	0.388771i	0.485478	−	0.874249i	$-0.338646\pi$
$433$	−8.08981	−	8.08981i	−0.388771	−	0.388771i	−0.874249	+	0.485478i	$0.838646\pi$
$434$	8.88506	−	6.26862i	0.426497	−	0.300903i
$435$	−0.523217	+	0.490413i	−0.0250864	+	0.0235135i
$436$	1.27903	−	0.929272i	0.0612546	−	0.0445040i
$437$	−0.0830048	+	0.0131467i	−0.00397066	+	0.000628890i
$438$	0.123978	+	0.243320i	0.00592388	+	0.0116263i
$439$		−	12.1121i		−	0.578079i	−0.957317	−	0.289039i	$-0.906664\pi$
$439$		−	12.1121i		−	0.578079i	0.957317	−	0.289039i	$-0.0933358\pi$
$440$	9.25509	−	8.67482i	0.441219	−	0.413556i
$441$	−2.95224	+	9.08605i	−0.140583	+	0.432669i
$442$	−3.82138	+	7.49988i	−0.181764	+	0.356733i
$443$	9.66840	+	4.92630i	0.459360	+	0.234055i	0.668328	−	0.743867i	$-0.267010\pi$
$443$	9.66840	+	4.92630i	0.459360	+	0.234055i	−0.208968	+	0.977922i	$0.567010\pi$
$444$	−0.0747020	−	0.102819i	−0.00354520	−	0.00487955i
$445$	30.6091	+	11.0523i	1.45101	+	0.523931i
$446$	15.5828	+	21.4479i	0.737868	+	1.01559i
$447$	0.613674	−	0.0971964i	0.0290258	−	0.00459723i
$448$	−1.74013	−	0.886641i	−0.0822135	−	0.0418899i
$449$	27.4106	+	19.9150i	1.29359	+	0.939845i	0.999871	−	0.0160475i	$-0.00510831\pi$
$449$	27.4106	+	19.9150i	1.29359	+	0.939845i	0.293715	+	0.955893i	$0.405108\pi$
$450$	−14.9301	+	1.38311i	−0.703812	+	0.0652006i
$451$	27.3698	−	8.89300i	1.28880	−	0.418755i
$452$	−2.62574	−	16.5783i	−0.123504	−	0.779777i
$453$	−0.00844178	+	0.0532993i	−0.000396629	+	0.00250422i
$454$	−20.4874	−	6.65675i	−0.961521	−	0.312417i
$455$	10.9139	−	7.40217i	0.511653	−	0.347019i
$456$	−0.0623559	+	0.0202607i	−0.00292008	+	0.000948793i
$457$	−8.31228	−	4.23532i	−0.388832	−	0.198120i	0.248635	−	0.968597i	$-0.420018\pi$
$457$	−8.31228	−	4.23532i	−0.388832	−	0.198120i	−0.637467	+	0.770477i	$0.720018\pi$
$458$	19.3596	−	9.86420i	0.904614	−	0.460924i
$459$		−	0.577152i		−	0.0269391i
$460$	0.0676534	+	0.0721788i	0.00315436	+	0.00336536i
$461$	−29.8079	−	9.68517i	−1.38829	−	0.451084i	−0.482906	−	0.875672i	$-0.660419\pi$
$461$	−29.8079	−	9.68517i	−1.38829	−	0.451084i	−0.905386	+	0.424589i	$0.860419\pi$
$462$	−0.0598221	−	0.377702i	−0.00278318	−	0.0175723i
$463$	−16.6209	−	2.63249i	−0.772439	−	0.122342i	−0.242241	−	0.970216i	$-0.577882\pi$
$463$	−16.6209	−	2.63249i	−0.772439	−	0.122342i	−0.530198	+	0.847874i	$0.677882\pi$
$464$	−9.29146			−0.431345
$465$	−0.391496	+	0.177180i	−0.0181552	+	0.00821655i
$466$	−7.78023			−0.360412
$467$	40.5256	+	6.41863i	1.87530	+	0.297019i	0.986811	−	0.161876i	$-0.0517545\pi$
$467$	40.5256	+	6.41863i	1.87530	+	0.297019i	0.888491	+	0.458895i	$0.151754\pi$
$468$	−1.41662	−	8.94416i	−0.0654831	−	0.413444i
$469$	19.7356	+	6.41250i	0.911307	+	0.296102i
$470$	−5.63181	−	0.182264i	−0.259776	−	0.00840722i
$471$			0.107155i			0.00493743i
$472$	−2.49602	+	1.27179i	−0.114889	+	0.0585388i
$473$	26.3879	+	13.4453i	1.21332	+	0.618216i
$474$	−0.0676270	+	0.0219733i	−0.00310621	+	0.00100927i
$475$	−5.07410	−	8.02869i	−0.232816	−	0.368382i
$476$	5.17738	+	1.68223i	0.237305	+	0.0771050i
$477$	−5.78328	+	36.5142i	−0.264798	+	1.67187i
$478$	−1.79085	−	11.3070i	−0.0819114	−	0.517169i
$479$	−0.656294	+	0.213243i	−0.0299868	+	0.00974332i	−0.323972	−	0.946067i	$-0.605018\pi$
$479$	−0.656294	+	0.213243i	−0.0299868	+	0.00974332i	0.293985	+	0.955810i	$0.405018\pi$
$480$	0.0609403	+	0.0473616i	0.00278153	+	0.00216175i
$481$	8.99539	+	6.53553i	0.410154	+	0.297995i
$482$	−10.8514	−	5.52906i	−0.494267	−	0.251842i
$483$	0.00294563		0.000466542i	0.000134031		2.12284e-5i
$484$	12.4504	+	17.1365i	0.565926	+	0.778931i
$485$	−11.4691	−	24.4324i	−0.520785	−	1.10942i
$486$	0.547489	+	0.753554i	0.0248346	+	0.0341819i
$487$	5.15917	+	2.62873i	0.233784	+	0.119119i	0.566959	−	0.823746i	$-0.308120\pi$
$487$	5.15917	+	2.62873i	0.233784	+	0.119119i	−0.333175	+	0.942865i	$0.608120\pi$
$488$	2.97360	−	5.83602i	0.134609	−	0.264184i
$489$	−0.253302	+	0.779584i	−0.0114547	+	0.0352540i
$490$	4.87164	+	5.19751i	0.220078	+	0.234800i
$491$		−	17.7599i		−	0.801493i	−0.916189	−	0.400746i	$-0.868751\pi$
$491$		−	17.7599i		−	0.801493i	0.916189	−	0.400746i	$-0.131249\pi$
$492$	0.0794932	+	0.156014i	0.00358383	+	0.00703366i
$493$	25.5803	−	4.05153i	1.15208	−	0.182472i
$494$	4.64063	−	3.37162i	0.208792	−	0.151696i
$495$	1.23045	−	38.0200i	0.0553047	−	1.70887i
$496$	−5.27084	−	1.79394i	−0.236668	−	0.0805505i
$497$	−2.13636	−	2.13636i	−0.0958287	−	0.0958287i
$498$	0.0176011	−	0.111129i	0.000788725	−	0.00497982i
$499$	−15.8163	−	11.4912i	−0.708035	−	0.514417i	0.174504	−	0.984656i	$-0.444168\pi$
$499$	−15.8163	−	11.4912i	−0.708035	−	0.514417i	−0.882539	+	0.470239i	$0.844168\pi$
$500$	−4.46905	+	10.2483i	−0.199862	+	0.458318i
$501$	−0.678389			−0.0303082
$502$	−9.92454	+	9.92454i	−0.442954	+	0.442954i
$503$	−1.87749	−	3.68478i	−0.0837130	−	0.164296i	0.845355	−	0.534205i	$-0.179389\pi$
$503$	−1.87749	−	3.68478i	−0.0837130	−	0.164296i	−0.929068	+	0.369909i	$0.879389\pi$
$504$	−5.57001	+	1.80981i	−0.248108	+	0.0806152i
$505$	−1.58292	+	0.458275i	−0.0704391	+	0.0203930i
$506$	−0.203048	+	0.147523i	−0.00902656	+	0.00655818i
$507$	0.0608170	+	0.119360i	0.00270098	+	0.00530097i
$508$	13.8373	+	2.19161i	0.613930	+	0.0972370i
$509$	−4.51246	−	3.27849i	−0.200011	−	0.145317i	0.483272	−	0.875471i	$-0.339448\pi$
$509$	−4.51246	−	3.27849i	−0.200011	−	0.145317i	−0.683283	+	0.730154i	$0.739448\pi$
$510$	−0.188427	−	0.103818i	−0.00834367	−	0.00459715i
$511$	−9.08225	+	12.5006i	−0.401775	+	0.552996i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−0.178560	+	0.350443i	−0.00788360	+	0.0154724i
$514$	3.27699	−	4.51039i	0.144542	−	0.198945i
$515$	19.1033	+	3.66268i	0.841790	+	0.161397i
$516$	−0.0556832	+	0.171375i	−0.00245131	+	0.00754437i
$517$	2.23629	−	14.1194i	0.0983520	−	0.620970i
$518$	3.26467	−	6.40727i	0.143441	−	0.281519i
$519$	−0.187990	−	0.578573i	−0.00825183	−	0.0253965i
$520$	−6.35103	−	2.29323i	−0.278511	−	0.100565i
$521$	18.6021			0.814972			0.407486	−	0.913212i	$-0.366406\pi$
$521$	18.6021			0.814972			0.407486	+	0.913212i	$0.366406\pi$
$522$	−19.7023	+	19.7023i	−0.862348	+	0.862348i
$523$	26.7183	−	13.6136i	1.16831	−	0.595283i	0.241346	−	0.970439i	$-0.422411\pi$
$523$	26.7183	−	13.6136i	1.16831	−	0.595283i	0.926962	+	0.375156i	$0.122411\pi$
$524$	12.7298	−	17.5211i	0.556104	−	0.765412i
$525$	0.180067	+	0.284918i	0.00785877	+	0.0124348i
$526$			20.3210i			0.886039i
$527$	15.2934	+	2.64057i	0.666191	+	0.115025i
$528$	−0.138456	+	0.138456i	−0.00602554	+	0.00602554i
$529$	13.5179	+	18.6058i	0.587735	+	0.808948i
$530$	21.7658	+	16.9160i	0.945447	+	0.734782i
$531$	−2.59596	+	7.98956i	−0.112655	+	0.346717i
$532$	−2.62322	−	2.62322i	−0.113731	−	0.113731i
$533$	−10.8322	−	10.8322i	−0.469195	−	0.469195i
$534$	−0.477757	−	0.155233i	−0.0206746	−	0.00671758i
$535$	12.6747	+	6.98342i	0.547974	+	0.301920i
$536$	−3.28342	−	10.1053i	−0.141822	−	0.436483i
$537$	−0.454665	−	0.0720118i	−0.0196202	−	0.00310754i
$538$	13.8601	−	7.06206i	0.597550	−	0.304467i
$539$	−14.6212	+	10.6229i	−0.629780	+	0.457562i
$540$	0.459395	−	0.0575982i	0.0197692	−	0.00247863i
$541$	−3.23443	−	9.95456i	−0.139059	−	0.427980i	0.857140	−	0.515083i	$-0.172239\pi$
$541$	−3.23443	−	9.95456i	−0.139059	−	0.427980i	−0.996199	+	0.0871034i	$0.972239\pi$
$542$	−15.2956	+	2.42258i	−0.657000	+	0.104059i
$543$	0.460560	−	0.0729455i	0.0197645	−	0.00313039i
$544$	−0.861360	−	2.65099i	−0.0369305	−	0.113660i
$545$	−2.79129	−	2.16934i	−0.119566	−	0.0929242i
$546$	−0.164684	+	0.119650i	−0.00704785	+	0.00512056i
$547$	5.74997	−	2.92976i	0.245851	−	0.125267i	−0.326724	−	0.945120i	$-0.605945\pi$
$547$	5.74997	−	2.92976i	0.245851	−	0.125267i	0.572575	+	0.819853i	$0.305945\pi$
$548$	−6.23606	−	0.987694i	−0.266391	−	0.0421922i
$549$	−6.06970	−	18.6806i	−0.259048	−	0.797269i
$550$	−24.3875	−	14.4844i	−1.03988	−	0.617617i
$551$	−16.7857	−	5.45400i	−0.715094	−	0.232348i
$552$	−0.00107980	−	0.00107980i	−4.59592e−5	−	4.59592e-5i
$553$	−2.84496	−	2.84496i	−0.120980	−	0.120980i
$554$	2.80063	−	8.61945i	0.118987	−	0.366205i
$555$	−0.174388	+	0.224386i	−0.00740237	+	0.00952465i
$556$	−2.99877	−	4.12745i	−0.127176	−	0.175043i
$557$	19.1191	−	19.1191i	0.810104	−	0.810104i	−0.174545	−	0.984649i	$-0.555845\pi$
$557$	19.1191	−	19.1191i	0.810104	−	0.810104i	0.984649	+	0.174545i	$0.0558454\pi$
$558$	−14.9807	+	7.37268i	−0.634184	+	0.312111i
$559$		−	15.7649i		−	0.666782i
$560$	−0.822315	+	4.28891i	−0.0347491	+	0.181240i
$561$	0.320811	−	0.441558i	0.0135446	−	0.0186426i
$562$	−4.27660	+	2.17904i	−0.180397	+	0.0919171i
$563$	−4.58638	+	4.58638i	−0.193293	+	0.193293i	−0.797117	−	0.603824i	$-0.793643\pi$
$563$	−4.58638	+	4.58638i	−0.193293	+	0.193293i	0.603824	+	0.797117i	$0.293643\pi$
$564$	0.0869788			0.00366247
$565$	−33.9751	+	15.9487i	−1.42934	+	0.670965i
$566$	−1.32276	−	4.07104i	−0.0555997	−	0.171118i
$567$	−7.97026	+	15.6425i	−0.334720	+	0.656924i
$568$	−0.242003	+	1.52794i	−0.0101542	+	0.0641111i
$569$	1.71123	−	5.26663i	0.0717386	−	0.220789i	−0.908758	−	0.417322i	$-0.862969\pi$
$569$	1.71123	−	5.26663i	0.0717386	−	0.220789i	0.980497	+	0.196534i	$0.0629686\pi$
$570$	0.0822921	+	0.121333i	0.00344684	+	0.00508210i
$571$	−18.1616	+	24.9974i	−0.760041	+	1.04611i	0.237170	+	0.971468i	$0.423780\pi$
$571$	−18.1616	+	24.9974i	−0.760041	+	1.04611i	−0.997211	+	0.0746385i	$0.976220\pi$
$572$	7.77720	−	15.2636i	0.325181	−	0.638204i
$573$	0.127522	+	0.805141i	0.00532730	+	0.0336352i
$574$	−5.82345	+	8.01529i	−0.243066	+	0.334552i
$575$	0.112961	−	0.190194i	0.00471081	−	0.00793162i
$576$	2.42609	+	1.76266i	0.101087	+	0.0734440i
$577$	27.4091	+	4.34118i	1.14106	+	0.180726i	0.698224	−	0.715879i	$-0.253974\pi$
$577$	27.4091	+	4.34118i	1.14106	+	0.180726i	0.442832	+	0.896605i	$0.353974\pi$
$578$	−4.19047	−	8.22425i	−0.174300	−	0.342084i
$579$	0.726470	−	0.527811i	0.0301911	−	0.0219351i
$580$	5.77774	+	19.9568i	0.239907	+	0.828661i
$581$	6.05470	−	1.96729i	0.251191	−	0.0816170i
$582$	0.189145	+	0.371217i	0.00784030	+	0.0153875i
$583$	−49.4520	+	49.4520i	−2.04809	+	2.04809i
$584$	7.91177			0.327391
$585$	−18.3300	+	8.60448i	−0.757851	+	0.355751i
$586$	−2.99923	−	2.17907i	−0.123897	−	0.0900166i
$587$	−0.512027	+	3.23281i	−0.0211336	+	0.133432i	−0.995999	−	0.0893610i	$-0.971518\pi$
$587$	−0.512027	+	3.23281i	−0.0211336	+	0.133432i	0.974866	+	0.222793i	$0.0715175\pi$
$588$	−0.0777549	−	0.0777549i	−0.00320656	−	0.00320656i
$589$	−8.46912	−	6.33482i	−0.348964	−	0.261022i
$590$	4.28374	+	4.57028i	0.176359	+	0.188156i
$591$	−0.141191	+	0.102582i	−0.00580784	+	0.00421964i
$592$	−3.63673	+	0.576001i	−0.149469	+	0.0236735i
$593$	1.73148	+	3.39823i	0.0711036	+	0.139549i	0.923822	−	0.382822i	$-0.125048\pi$
$593$	1.73148	+	3.39823i	0.0711036	+	0.139549i	−0.852719	+	0.522371i	$0.825048\pi$
$594$			1.17461i			0.0481948i
$595$	0.393744	−	12.1664i	0.0161419	−	0.498773i
$596$	5.56259	−	17.1199i	0.227853	−	0.701259i
$597$	−0.0539898	+	0.105961i	−0.00220965	+	0.00433669i
$598$	0.119038	+	0.0606530i	0.00486784	+	0.00248029i
$599$	19.1192	+	26.3153i	0.781190	+	1.07522i	0.995150	+	0.0983730i	$0.0313638\pi$
$599$	19.1192	+	26.3153i	0.781190	+	1.07522i	−0.213960	+	0.976842i	$0.568636\pi$
$600$	0.0638316	−	0.160342i	0.00260591	−	0.00654595i
$601$	−0.678554	−	0.933950i	−0.0276788	−	0.0380966i	0.794953	−	0.606671i	$-0.207495\pi$
$601$	−0.678554	−	0.933950i	−0.0276788	−	0.0380966i	−0.822632	+	0.568574i	$0.807495\pi$
$602$	−10.0702	+	1.59497i	−0.410432	+	0.0650061i
$603$	−28.3905	−	14.4657i	−1.15615	−	0.589089i
$604$	1.26484	+	0.918962i	0.0514657	+	0.0373920i
$605$	29.0648	−	37.3977i	1.18165	−	1.52043i
$606$	0.0241925	−	0.00786063i	0.000982755	−	0.000319316i
$607$	−5.67260	−	35.8154i	−0.230244	−	1.45370i	−0.783864	−	0.620933i	$-0.786754\pi$
$607$	−5.67260	−	35.8154i	−0.230244	−	1.45370i	0.553620	−	0.832769i	$-0.313246\pi$
$608$	−0.297154	+	1.87615i	−0.0120512	+	0.0760881i
$609$	0.595682	+	0.193549i	0.0241382	+	0.00784299i
$610$	−14.3841	−	2.75786i	−0.582394	−	0.111663i
$611$	−7.23716	+	2.35149i	−0.292784	+	0.0951313i
$612$	−7.44787	−	3.79488i	−0.301062	−	0.153399i
$613$	−30.9411	+	15.7653i	−1.24970	+	0.636753i	−0.948491	−	0.316805i	$-0.897390\pi$
$613$	−30.9411	+	15.7653i	−1.24970	+	0.636753i	−0.301208	+	0.953558i	$0.597390\pi$
$614$			16.7847i			0.677376i
$615$	0.285666	−	0.267755i	0.0115192	−	0.0107969i
$616$	−10.5369	−	3.42365i	−0.424544	−	0.137943i
$617$	3.58854	+	22.6571i	0.144469	+	0.912141i	0.948321	+	0.317312i	$0.102780\pi$
$617$	3.58854	+	22.6571i	0.144469	+	0.912141i	−0.803852	+	0.594829i	$0.797220\pi$
$618$	−0.296554	−	0.0469696i	−0.0119292	−	0.00188939i
$619$	−5.60182			−0.225156			−0.112578	−	0.993643i	$-0.535911\pi$
$619$	−5.60182			−0.225156			−0.112578	+	0.993643i	$0.535911\pi$
$620$	−0.575569	+	12.4366i	−0.0231154	+	0.499465i
$621$	−0.00916057			−0.000367601
$622$	−28.2027	−	4.46686i	−1.13082	−	0.179105i
$623$	−4.44643	−	28.0737i	−0.178143	−	1.12475i
$624$	0.0991289	+	0.0322089i	0.00396833	+	0.00128939i
$625$	24.7910	+	3.22618i	0.991638	+	0.129047i
$626$			5.81268i			0.232321i
$627$	−0.331404	+	0.168859i	−0.0132350	+	0.00674357i
$628$	2.76611	+	1.40940i	0.110380	+	0.0562413i
$629$	9.76112	−	3.17158i	0.389201	−	0.126459i
$630$	7.35084	+	10.8382i	0.292864	+	0.431806i
$631$	25.9756	+	8.43999i	1.03407	+	0.335991i	0.776399	−	0.630241i	$-0.217044\pi$
$631$	25.9756	+	8.43999i	1.03407	+	0.335991i	0.257674	+	0.966232i	$0.417044\pi$
$632$	−0.322272	+	2.03475i	−0.0128193	+	0.0809379i
$633$	−0.0296063	−	0.186927i	−0.00117674	−	0.00742967i
$634$	7.31944	−	2.37823i	0.290692	−	0.0944515i
$635$	−3.89719	−	31.0834i	−0.154655	−	1.23351i
$636$	−0.344250	−	0.250112i	−0.0136504	−	0.00991759i
$637$	8.57180	+	4.36755i	0.339627	+	0.173049i
$638$	−52.0606	+	8.24559i	−2.06110	+	0.326446i
$639$	2.72681	+	3.75313i	0.107871	+	0.148472i
$640$	2.02415	−	0.950177i	0.0800114	−	0.0375590i
$641$	23.4107	+	32.2221i	0.924667	+	1.27270i	0.961904	+	0.273389i	$0.0881445\pi$
$641$	23.4107	+	32.2221i	0.924667	+	1.27270i	−0.0372366	+	0.999306i	$0.511856\pi$
$642$	−0.199032	−	0.101412i	−0.00785517	−	0.00400241i
$643$	−16.4824	+	32.3484i	−0.650001	+	1.27570i	0.297126	+	0.954838i	$0.403972\pi$
$643$	−16.4824	+	32.3484i	−0.650001	+	1.27570i	−0.947127	+	0.320860i	$0.896028\pi$
$644$	0.0267004	−	0.0821755i	0.00105214	−	0.00323817i
$645$	0.402716	+	0.0130332i	0.0158569	+	0.000513183i
$646$		−	5.29482i		−	0.208322i
$647$	−5.60337	−	10.9972i	−0.220291	−	0.432346i	0.754240	−	0.656599i	$-0.228006\pi$
$647$	−5.60337	−	10.9972i	−0.220291	−	0.432346i	−0.974531	+	0.224253i	$0.928006\pi$
$648$	8.87861	−	1.40623i	0.348785	−	0.0552421i
$649$	−12.8567	+	9.34097i	−0.504671	+	0.366665i
$650$	−0.976269	+	15.0672i	−0.0382924	+	0.590983i
$651$	0.300548	+	0.224807i	0.0117794	+	0.00881088i
$652$	16.7926	+	16.7926i	0.657650	+	0.657650i
$653$	−3.17876	+	20.0699i	−0.124395	+	0.785396i	0.844068	+	0.536237i	$0.180154\pi$
$653$	−3.17876	+	20.0699i	−0.124395	+	0.785396i	−0.968462	+	0.249160i	$0.919846\pi$
$654$	0.0441473	+	0.0320749i	0.00172630	+	0.00125423i
$655$	−45.5487	−	16.4467i	−1.77974	−	0.642627i
$656$	5.07295			0.198065
$657$	16.7767	−	16.7767i	0.654523	−	0.654523i
$658$	2.23428	+	4.38503i	0.0871015	+	0.170946i
$659$	10.9403	−	3.55473i	0.426175	−	0.138473i	−0.0880735	−	0.996114i	$-0.528071\pi$
$659$	10.9403	−	3.55473i	0.426175	−	0.138473i	0.514248	+	0.857641i	$0.328071\pi$
$660$	0.383483	+	0.211289i	0.0149270	+	0.00822441i
$661$	−4.65235	+	3.38013i	−0.180956	+	0.131472i	−0.674576	−	0.738206i	$-0.735673\pi$
$661$	−4.65235	+	3.38013i	−0.180956	+	0.131472i	0.493620	+	0.869678i	$0.335673\pi$
$662$	−16.0409	−	31.4820i	−0.623446	−	1.22358i
$663$	−0.286957	−	0.0454495i	−0.0111445	−	0.00176511i
$664$	−2.63720	−	1.91604i	−0.102343	−	0.0743567i
$665$	−4.00312	+	7.26553i	−0.155234	+	0.281745i
$666$	−6.49021	+	8.93300i	−0.251490	+	0.346147i
$667$	−0.0643060	−	0.406012i	−0.00248994	−	0.0157208i
$668$	−8.92283	+	17.5120i	−0.345235	+	0.677561i
$669$	−0.537859	+	0.740300i	−0.0207948	+	0.0286216i
$670$	−19.6631	+	13.3362i	−0.759653	+	0.515221i
$671$	11.4822	−	35.3385i	0.443264	−	1.36423i
$672$	0.0105452	−	0.0665800i	0.000406791	−	0.00256838i
$673$	1.68614	−	3.30924i	0.0649960	−	0.127562i	−0.856223	−	0.516607i	$-0.827195\pi$
$673$	1.68614	−	3.30924i	0.0649960	−	0.127562i	0.921219	+	0.389045i	$0.127195\pi$
$674$	1.40747	+	4.33174i	0.0542136	+	0.166852i
$675$	−0.409380	−	0.950901i	−0.0157570	−	0.0366002i
$676$	3.88110			0.149273
$677$	27.2168	−	27.2168i	1.04603	−	1.04603i	0.0471380	−	0.998888i	$-0.484990\pi$
$677$	27.2168	−	27.2168i	1.04603	−	1.04603i	0.998888	−	0.0471380i	$-0.0150101\pi$
$678$	0.516206	−	0.263020i	0.0198248	−	0.0101012i
$679$	−13.8562	+	19.0714i	−0.531752	+	0.731894i
$680$	−5.15835	+	3.49856i	−0.197814	+	0.134164i
$681$		−	0.743538i		−	0.0284924i
$682$	−31.1249	−	5.37404i	−1.19183	−	0.205783i
$683$	−25.6664	+	25.6664i	−0.982096	+	0.982096i	−0.999843	−	0.0177469i	$-0.994351\pi$
$683$	−25.6664	+	25.6664i	−0.982096	+	0.982096i	0.0177469	+	0.999843i	$0.494351\pi$
$684$	3.34824	+	4.60845i	0.128023	+	0.176209i
$685$	1.75635	+	14.0084i	0.0671067	+	0.535233i
$686$	6.14722	−	18.9192i	0.234702	−	0.722339i
$687$	0.530301	+	0.530301i	0.0202323	+	0.0202323i
$688$	3.69151	+	3.69151i	0.140737	+	0.140737i
$689$	35.4055	+	11.5039i	1.34884	+	0.438265i
$690$	−0.00164781	+	0.00299071i	−6.27309e−5	+	0.000113855i
$691$	11.7796	+	36.2539i	0.448117	+	1.37916i	0.879029	+	0.476769i	$0.158192\pi$
$691$	11.7796	+	36.2539i	0.448117	+	1.37916i	−0.430912	+	0.902394i	$0.641808\pi$
$692$	−17.4080	−	2.75716i	−0.661753	−	0.104811i
$693$	−29.6030	+	15.0835i	−1.12453	+	0.572975i
$694$	−19.4595	+	14.1381i	−0.738672	+	0.536677i
$695$	−7.00047	+	9.00753i	−0.265543	+	0.341675i
$696$	−0.0991036	−	0.305009i	−0.00375651	−	0.0115614i
$697$	−13.9663	+	2.21205i	−0.529013	+	0.0837874i
$698$	−3.66299	+	0.580160i	−0.138646	+	0.0219594i
$699$	−0.0829846	−	0.255400i	−0.00313877	−	0.00966013i
$700$	9.72334	−	0.900763i	0.367508	−	0.0340456i
$701$	−4.31349	+	3.13393i	−0.162918	+	0.118367i	−0.666257	−	0.745722i	$-0.732105\pi$
$701$	−4.31349	+	3.13393i	−0.162918	+	0.118367i	0.503339	+	0.864089i	$0.332105\pi$
$702$	0.557109	−	0.283861i	0.0210267	−	0.0107136i
$703$	−6.90811	−	1.09414i	−0.260544	−	0.0412662i
$704$	1.75302	+	5.39525i	0.0660696	+	0.203341i
$705$	−0.0540862	−	0.186819i	−0.00203701	−	0.00703600i
$706$	15.7751	+	5.12564i	0.593703	+	0.192906i
$707$	1.01774	+	1.01774i	0.0382762	+	0.0382762i
$708$	−0.0683716	−	0.0683716i	−0.00256956	−	0.00256956i
$709$	−0.0256596	+	0.0789722i	−0.000963667	+	0.00296586i	−0.951537	−	0.307534i	$-0.900496\pi$
$709$	−0.0256596	+	0.0789722i	−0.000963667	+	0.00296586i	0.950574	+	0.310500i	$0.100496\pi$
$710$	3.43230	−	0.430337i	0.128812	−	0.0161503i
$711$	3.63127	+	4.99801i	0.136183	+	0.187440i
$712$	−10.2911	+	10.2911i	−0.385676	+	0.385676i
$713$	0.0419112	−	0.242737i	0.00156959	−	0.00909059i
$714$			0.187900i			0.00703197i
$715$	−37.6203	−	7.21296i	−1.40692	−	0.269749i
$716$	−7.83912	+	10.7896i	−0.292961	+	0.403227i
$717$	0.352071	−	0.179389i	0.0131483	−	0.00669940i
$718$	20.3325	−	20.3325i	0.758803	−	0.758803i
$719$	−42.7233			−1.59331			−0.796655	−	0.604435i	$-0.793399\pi$
$719$	−42.7233			−1.59331			−0.796655	+	0.604435i	$0.793399\pi$
$720$	2.27733	−	6.30698i	0.0848709	−	0.235047i
$721$	−5.24983	−	16.1573i	−0.195514	−	0.601730i
$722$	6.98771	−	13.7141i	0.260055	−	0.510388i
$723$	0.0657596	−	0.415190i	0.00244563	−	0.0154411i
$724$	4.17471	−	12.8484i	0.155152	−	0.477508i
$725$	39.2717	−	24.8196i	1.45852	−	0.921776i
$726$	−0.429739	+	0.591486i	−0.0159491	+	0.0219521i
$727$	−13.3424	+	26.1859i	−0.494841	+	0.971180i	0.499637	+	0.866235i	$0.333467\pi$
$727$	−13.3424	+	26.1859i	−0.494841	+	0.971180i	−0.994478	+	0.104945i	$0.966533\pi$
$728$	0.922581	+	5.82495i	0.0341931	+	0.215887i
$729$	15.8324	−	21.7914i	0.586385	−	0.807090i
$730$	−4.91980	−	16.9934i	−0.182090	−	0.628954i
$731$	−11.7728	−	8.55342i	−0.435432	−	0.316360i
$732$	0.223295	+	0.0353664i	0.00825321	+	0.00130718i
$733$	13.2230	+	25.9516i	0.488403	+	0.958544i	0.995328	+	0.0965539i	$0.0307820\pi$
$733$	13.2230	+	25.9516i	0.488403	+	0.958544i	−0.506925	+	0.861990i	$0.669218\pi$
$734$	13.3404	−	9.69237i	0.492403	−	0.357752i
$735$	−0.118656	+	0.215358i	−0.00437671	+	0.00794358i
$736$	−0.0420766	+	0.0136715i	−0.00155097	+	0.000503939i
$737$	−27.3650	−	53.7069i	−1.00800	−	1.97832i
$738$	10.7571	−	10.7571i	0.395973	−	0.395973i
$739$	−16.6028			−0.610745			−0.305373	−	0.952233i	$-0.598781\pi$
$739$	−16.6028			−0.610745			−0.305373	+	0.952233i	$0.598781\pi$
$740$	3.49861	+	7.45303i	0.128611	+	0.273979i
$741$	0.160177	+	0.116375i	0.00588425	+	0.00427516i
$742$	3.76640	−	23.7801i	0.138269	−	0.872996i
$743$	24.9154	+	24.9154i	0.914056	+	0.914056i	0.996588	−	0.0825327i	$-0.0263009\pi$
$743$	24.9154	+	24.9154i	0.914056	+	0.914056i	−0.0825327	+	0.996588i	$0.526301\pi$
$744$	0.00267028	−	0.192159i	9.78971e−5	−	0.00704491i
$745$	−40.2303	−	1.30198i	−1.47392	−	0.0477010i
$746$	19.3784	−	14.0792i	0.709492	−	0.515476i
$747$	−9.65504	+	1.52921i	−0.353259	+	0.0559508i
$748$	−7.17884	−	14.0893i	−0.262485	−	0.515155i
$749$		−	12.6392i		−	0.461827i
$750$	−0.384087	−	0.0373954i	−0.0140249	−	0.00136549i
$751$	13.1028	−	40.3263i	0.478128	−	1.47153i	−0.363564	−	0.931569i	$-0.618440\pi$
$751$	13.1028	−	40.3263i	0.478128	−	1.47153i	0.841692	−	0.539958i	$-0.181560\pi$
$752$	1.14403	−	2.24528i	0.0417185	−	0.0818771i
$753$	−0.431647	−	0.219935i	−0.0157301	−	0.00801489i
$754$	16.4920	+	22.6993i	0.600604	+	0.826660i
$755$	1.18729	−	3.28815i	0.0432097	−	0.119668i
$756$	−0.237688	−	0.327150i	−0.00864464	−	0.0118983i
$757$	9.43363	−	1.49414i	0.342871	−	0.0543055i	0.0173757	−	0.999849i	$-0.494469\pi$
$757$	9.43363	−	1.49414i	0.342871	−	0.0543055i	0.325496	+	0.945544i	$0.394469\pi$
$758$	−15.4770	−	7.88592i	−0.562149	−	0.286429i
$759$	−0.00700843	−	0.00509192i	−0.000254390	−	0.000184825i
$760$	4.21451	−	0.528408i	0.152876	−	0.0191674i
$761$	42.2928	−	13.7418i	1.53311	−	0.498138i	0.583646	−	0.812008i	$-0.301625\pi$
$761$	42.2928	−	13.7418i	1.53311	−	0.498138i	0.949466	+	0.313869i	$0.101625\pi$
$762$	0.0756460	+	0.477610i	0.00274037	+	0.0173020i
$763$	−0.483012	+	3.04962i	−0.0174862	+	0.110403i
$764$	22.4613	+	7.29813i	0.812622	+	0.264037i
$765$	−3.51956	+	18.3568i	−0.127250	+	0.663691i
$766$	25.7439	−	8.36471i	0.930167	−	0.302229i
$767$	7.53737	+	3.84048i	0.272159	+	0.138672i
$768$	−0.0307541	+	0.0156700i	−0.00110974	+	0.000565443i
$769$			14.3245i			0.516554i	0.966071	+	0.258277i	$0.0831547\pi$
$769$			14.3245i			0.516554i	−0.966071	+	0.258277i	$0.916845\pi$
$770$	−0.801341	+	24.7608i	−0.0288783	+	0.892316i
$771$	0.183015	+	0.0594650i	0.00659111	+	0.00214158i
$772$	−4.06977	−	25.6955i	−0.146474	−	0.924801i
$773$	−12.4820	−	1.97695i	−0.448945	−	0.0711059i	−0.0721317	−	0.997395i	$-0.522980\pi$
$773$	−12.4820	−	1.97695i	−0.448945	−	0.0711059i	−0.376813	+	0.926289i	$0.622980\pi$
$774$	15.6555			0.562726
$775$	27.0700	−	6.49723i	0.972384	−	0.233388i
$776$	12.0705			0.433305
$777$	0.245152	+	0.0388282i	0.00879477	+	0.00139295i
$778$	−1.66590	−	10.5181i	−0.0597256	−	0.377092i
$779$	9.16464	+	2.97777i	0.328357	+	0.106690i
$780$	0.00753884	−	0.232944i	0.000269934	−	0.00834073i
$781$			8.77593i			0.314027i
$782$	0.109880	−	0.0559866i	0.00392929	−	0.00200207i
$783$	−1.71417	−	0.873411i	−0.0612593	−	0.0312132i
$784$	−3.02989	+	0.984470i	−0.108210	+	0.0351596i
$785$	1.30715	−	6.81764i	0.0466542	−	0.243332i
$786$	0.710939	+	0.230998i	0.0253583	+	0.00823943i
$787$	2.70603	−	17.0852i	0.0964595	−	0.609021i	−0.891346	−	0.453325i	$-0.850238\pi$
$787$	2.70603	−	17.0852i	0.0964595	−	0.609021i	0.987805	−	0.155696i	$-0.0497622\pi$
$788$	0.790970	+	4.99399i	0.0281772	+	0.177904i
$789$	−0.667075	+	0.216746i	−0.0237485	+	0.00771635i
$790$	4.57076	−	0.573075i	0.162620	−	0.0203891i
$791$	26.5203	+	19.2681i	0.942953	+	0.685095i
$792$	15.1578	+	7.72327i	0.538608	+	0.274434i
$793$	−19.5356	+	3.09414i	−0.693730	+	0.109876i
$794$	−18.4017	−	25.3278i	−0.653052	−	0.898848i
$795$	−0.323141	+	0.894930i	−0.0114606	+	0.0317399i
$796$	2.02517	+	2.78740i	0.0717801	+	0.0987969i
$797$	−31.7709	−	16.1881i	−1.12538	−	0.573411i	−0.210686	−	0.977554i	$-0.567570\pi$
$797$	−31.7709	−	16.1881i	−1.12538	−	0.573411i	−0.914696	+	0.404143i	$0.867570\pi$
$798$	0.0581325	−	0.114092i	0.00205787	−	0.00403880i
$799$	−2.17058	+	6.68035i	−0.0767895	+	0.236334i
$800$	−3.29953	−	3.75674i	−0.116656	−	0.132821i
$801$			43.6442i			1.54209i
$802$	11.8040	+	23.1666i	0.416812	+	0.818040i
$803$	44.3301	−	7.02120i	1.56438	−	0.247773i
$804$	0.296705	−	0.215568i	0.0104640	−	0.00760251i
$805$	−0.193105	−	0.00624952i	−0.00680606	−	0.000220267i
$806$	4.97290	+	16.0610i	0.175163	+	0.565725i
$807$	0.379658	+	0.379658i	0.0133646	+	0.0133646i
$808$	0.115288	−	0.727901i	0.00405582	−	0.0256075i
$809$	−15.4769	−	11.2446i	−0.544138	−	0.395339i	0.281482	−	0.959567i	$-0.409174\pi$
$809$	−15.4769	−	11.2446i	−0.544138	−	0.395339i	−0.825620	+	0.564227i	$0.809174\pi$
$810$	−8.54141	−	18.1956i	−0.300114	−	0.639328i
$811$	−39.0122			−1.36990			−0.684952	−	0.728589i	$-0.740177\pi$
$811$	−39.0122			−1.36990			−0.684952	+	0.728589i	$0.740177\pi$
$812$	12.8313	−	12.8313i	0.450290	−	0.450290i
$813$	−0.242669	−	0.476265i	−0.00851078	−	0.0167034i
$814$	−19.8657	+	6.45474i	−0.696291	+	0.226239i
$815$	25.6261	−	46.5105i	0.897643	−	1.62919i
$816$	0.0778364	−	0.0565515i	0.00272482	−	0.00197970i
$817$	4.50209	+	8.83585i	0.157508	+	0.309127i
$818$	−0.620223	−	0.0982336i	−0.0216856	−	0.00343466i
$819$	14.3080	+	10.3954i	0.499962	+	0.363243i
$820$	−3.15453	−	10.8960i	−0.110161	−	0.380505i
$821$	−12.2496	+	16.8601i	−0.427513	+	0.588421i	−0.967380	−	0.253329i	$-0.918474\pi$
$821$	−12.2496	+	16.8601i	−0.427513	+	0.588421i	0.539868	+	0.841750i	$0.318474\pi$
$822$	−0.0340914	−	0.215245i	−0.00118908	−	0.00750753i
$823$	1.89138	−	3.71205i	0.0659294	−	0.129394i	−0.855690	−	0.517489i	$-0.826867\pi$
$823$	1.89138	−	3.71205i	0.0659294	−	0.129394i	0.921619	+	0.388095i	$0.126867\pi$
$824$	−5.11305	+	7.03751i	−0.178122	+	0.245163i
$825$	0.215358	−	0.955055i	0.00749781	−	0.0332508i
$826$	1.69064	−	5.20326i	0.0588249	−	0.181044i
$827$	−6.22128	+	39.2796i	−0.216335	+	1.36589i	0.605357	+	0.795954i	$0.293030\pi$
$827$	−6.22128	+	39.2796i	−0.216335	+	1.36589i	−0.821692	+	0.569932i	$0.806970\pi$
$828$	−0.0602324	+	0.118213i	−0.00209322	+	0.00410818i
$829$	1.47597	+	4.54258i	0.0512626	+	0.157770i	0.973411	−	0.229067i	$-0.0735675\pi$
$829$	1.47597	+	4.54258i	0.0512626	+	0.157770i	−0.922148	+	0.386837i	$0.873568\pi$
$830$	−2.47549	+	6.85580i	−0.0859256	+	0.237968i
$831$	0.312821			0.0108516
$832$	2.13529	−	2.13529i	0.0740277	−	0.0740277i
$833$	7.91231	−	4.03152i	0.274145	−	0.139684i
$834$	0.103506	−	0.142464i	0.00358412	−	0.00493312i
$835$	43.1620	+	8.27548i	1.49368	+	0.286385i
$836$			10.7759i			0.372693i
$837$	−0.803775	−	0.826428i	−0.0277825	−	0.0285655i
$838$	−9.28366	+	9.28366i	−0.320699	+	0.320699i
$839$	12.2154	+	16.8131i	0.421722	+	0.580451i	0.966028	−	0.258436i	$-0.0832070\pi$
$839$	12.2154	+	16.8131i	0.421722	+	0.580451i	−0.544306	+	0.838887i	$0.683207\pi$
$840$	−0.149562	+	0.0187519i	−0.00516039	+	0.000647001i
$841$	17.7163	−	54.5253i	0.610908	−	1.88018i
$842$	18.3721	+	18.3721i	0.633146	+	0.633146i
$843$	−0.117145	−	0.117145i	−0.00403470	−	0.00403470i
$844$	−5.21477	−	1.69438i	−0.179500	−	0.0583230i
$845$	−2.41340	−	8.33609i	−0.0830234	−	0.286770i
$846$	−2.33519	−	7.18697i	−0.0802854	−	0.247093i
$847$	−40.8587	−	6.47139i	−1.40392	−	0.222359i
$848$	−10.9843	+	5.59680i	−0.377204	+	0.192195i
$849$	0.119531	−	0.0868440i	0.00410228	−	0.00298048i
$850$	10.7221	+	8.90393i	0.367764	+	0.305402i
$851$	−0.0503394	−	0.154929i	−0.00172561	−	0.00531089i
$852$	−0.0527388	+	0.00835301i	−0.00180680	+	0.000286169i
$853$	−38.1643	+	6.04464i	−1.30672	+	0.206964i	−0.770677	−	0.637225i	$-0.780082\pi$
$853$	−38.1643	+	6.04464i	−1.30672	+	0.206964i	−0.536044	+	0.844190i	$0.680082\pi$
$854$	3.95293	+	12.1659i	0.135267	+	0.416308i
$855$	7.81629	−	10.0572i	0.267311	−	0.343951i
$856$	−5.23573	+	3.80398i	−0.178953	+	0.130017i
$857$	−16.8690	+	8.59517i	−0.576233	+	0.293605i	−0.717717	−	0.696335i	$-0.754813\pi$
$857$	−16.8690	+	8.59517i	−0.576233	+	0.293605i	0.141484	+	0.989941i	$0.454813\pi$
$858$	0.584009	+	0.0924979i	0.0199377	+	0.00315783i
$859$	−8.68131	−	26.7183i	−0.296202	−	0.911617i	−0.982815	−	0.184594i	$-0.940903\pi$
$859$	−8.68131	−	26.7183i	−0.296202	−	0.911617i	0.686612	−	0.727024i	$-0.259097\pi$
$860$	5.63336	−	10.2244i	0.192096	−	0.348648i
$861$	−0.325230	−	0.105674i	−0.0110838	−	0.00360135i
$862$	2.10367	+	2.10367i	0.0716514	+	0.0716514i
$863$	1.67208	+	1.67208i	0.0569184	+	0.0569184i	0.734993	−	0.678075i	$-0.237185\pi$
$863$	1.67208	+	1.67208i	0.0569184	+	0.0569184i	−0.678075	+	0.734993i	$0.737185\pi$
$864$	−0.0639838	+	0.196922i	−0.00217677	+	0.00669942i
$865$	4.90286	+	39.1045i	0.166702	+	1.32959i
$866$	−6.72468	−	9.25573i	−0.228514	−	0.314523i
$867$	0.225280	−	0.225280i	0.00765092	−	0.00765092i
$868$	9.75630	−	4.80151i	0.331150	−	0.162974i
$869$			11.6868i			0.396448i
$870$	−0.593493	+	0.402526i	−0.0201213	+	0.0136469i
$871$	−18.8596	+	25.9581i	−0.639035	+	0.879556i
$872$	1.40866	−	0.717746i	0.0477031	−	0.0243059i
$873$	25.5952	−	25.5952i	0.866266	−	0.866266i
$874$	−0.0840395			−0.00284268
$875$	−7.98101	−	20.3243i	−0.269807	−	0.687087i
$876$	0.0843876	+	0.259718i	0.00285119	+	0.00877507i
$877$	12.7259	−	24.9760i	0.429723	−	0.843378i	−0.570041	−	0.821616i	$-0.693073\pi$
$877$	12.7259	−	24.9760i	0.429723	−	0.843378i	0.999763	−	0.0217615i	$-0.00692743\pi$
$878$	1.89475	−	11.9630i	0.0639447	−	0.403731i
$879$	0.0395419	−	0.121698i	0.00133372	−	0.00410476i
$880$	10.4982	−	7.12020i	0.353894	−	0.240022i
$881$	−17.3543	+	23.8862i	−0.584683	+	0.804747i	−0.994199	−	0.107556i	$-0.965697\pi$
$881$	−17.3543	+	23.8862i	−0.584683	+	0.804747i	0.409516	+	0.912303i	$0.365697\pi$
$882$	−4.33726	+	8.51235i	−0.146043	+	0.286626i
$883$	0.785105	+	4.95696i	0.0264209	+	0.166815i	0.997371	−	0.0724682i	$-0.0230876\pi$
$883$	0.785105	+	4.95696i	0.0264209	+	0.166815i	−0.970950	+	0.239283i	$0.923088\pi$
$884$	−4.94757	+	6.80975i	−0.166405	+	0.229037i
$885$	−0.104337	+	0.189369i	−0.00350726	+	0.00636555i
$886$	8.77873	+	6.37812i	0.294927	+	0.214277i
$887$	39.9671	+	6.33016i	1.34196	+	0.212546i	0.785776	−	0.618512i	$-0.212264\pi$
$887$	39.9671	+	6.33016i	1.34196	+	0.212546i	0.556187	+	0.831057i	$0.312264\pi$
$888$	−0.0576980	−	0.113239i	−0.00193622	−	0.00380004i
$889$	−22.1355	+	16.0824i	−0.742402	+	0.539386i
$890$	28.5033	+	15.7046i	0.955433	+	0.526419i
$891$	48.4994	−	15.7584i	1.62479	−	0.527927i
$892$	12.0358	+	23.6215i	0.402987	+	0.790907i
$893$	3.38473	−	3.38473i	0.113266	−	0.113266i
$894$	0.621324			0.0207802
$895$	28.0493	+	10.1280i	0.937583	+	0.338543i
$896$	−1.58001	−	1.14794i	−0.0527843	−	0.0383500i
$897$	−0.000721375		0.00455458i	−2.40860e−5		0.000152073i
$898$	23.9577	+	23.9577i	0.799480	+	0.799480i
$899$	30.9863	−	41.4261i	1.03345	−	1.38164i
$900$	−14.9627	−	0.969499i	−0.498756	−	0.0323166i
$901$	27.8005	−	20.1983i	0.926170	−	0.672902i
$902$	28.4240	−	4.50193i	0.946417	−	0.149898i
$903$	−0.159768	−	0.313562i	−0.00531674	−	0.0104347i
$904$		−	16.7849i		−	0.558258i
$905$	−30.1926	−	0.977134i	−1.00364	−	0.0324810i
$906$	−0.0166757	+	0.0513225i	−0.000554013	+	0.00170508i
$907$	−7.82568	+	15.3588i	−0.259848	+	0.509980i	−0.983664	−	0.180013i	$-0.942386\pi$
$907$	−7.82568	+	15.3588i	−0.259848	+	0.509980i	0.723817	+	0.689992i	$0.242386\pi$
$908$	−19.1938	−	9.77973i	−0.636969	−	0.324552i
$909$	−1.29903	−	1.78796i	−0.0430862	−	0.0593030i
$910$	11.9375	−	5.60372i	0.395725	−	0.185762i
$911$	8.86607	+	12.2031i	0.293746	+	0.404307i	0.930226	−	0.366986i	$-0.119610\pi$
$911$	8.86607	+	12.2031i	0.293746	+	0.404307i	−0.636480	+	0.771293i	$0.719610\pi$
$912$	−0.0647577	+	0.0102566i	−0.00214434	+	0.000339630i
$913$	−16.4768	−	8.39532i	−0.545301	−	0.277845i
$914$	−7.54739	−	5.48350i	−0.249645	−	0.181378i
$915$	−0.0628897	−	0.501599i	−0.00207907	−	0.0165824i
$916$	20.6643	−	6.71425i	0.682769	−	0.221845i
$917$	6.61663	+	41.7757i	0.218500	+	1.37956i
$918$	0.0902864	−	0.570046i	0.00297990	−	0.0188143i
$919$	12.6128	+	4.09815i	0.416058	+	0.135185i	0.509563	−	0.860433i	$-0.329807\pi$
$919$	12.6128	+	4.09815i	0.416058	+	0.135185i	−0.0935051	+	0.995619i	$0.529807\pi$
$920$	0.0555292	+	0.0818735i	0.00183074	+	0.00269929i
$921$	−0.550989	+	0.179027i	−0.0181557	+	0.00589915i
$922$	−27.9258	−	14.2289i	−0.919688	−	0.468604i
$923$	4.16236	−	2.12083i	0.137006	−	0.0698079i
$924$		−	0.382410i		−	0.0125804i
$925$	13.8325	−	12.1491i	0.454811	−	0.399459i
$926$	−16.0045	−	5.20016i	−0.525939	−	0.170888i
$927$	4.08078	+	25.7650i	0.134030	+	0.846234i
$928$	−9.17707	−	1.45350i	−0.301252	−	0.0477136i
$929$	−33.3045			−1.09268			−0.546342	−	0.837562i	$-0.683980\pi$
$929$	−33.3045			−1.09268			−0.546342	+	0.837562i	$0.683980\pi$
$930$	−0.414393	+	0.113756i	−0.0135885	+	0.00373019i
$931$	−6.05158			−0.198332
$932$	−7.68445	−	1.21710i	−0.251712	−	0.0398673i
$933$	−0.154179	−	0.973448i	−0.00504760	−	0.0318693i
$934$	39.0226	+	12.6792i	1.27686	+	0.414876i
$935$	−25.7978	+	24.1804i	−0.843679	+	0.790782i
$936$		−	9.05566i		−	0.295993i
$937$	32.5468	−	16.5834i	1.06326	−	0.541756i	0.167303	−	0.985905i	$-0.446494\pi$
$937$	32.5468	−	16.5834i	1.06326	−	0.541756i	0.895953	+	0.444149i	$0.146494\pi$
$938$	18.4895	+	9.42088i	0.603704	+	0.307603i
$939$	−0.190812	+	0.0619985i	−0.00622691	+	0.00202324i
$940$	−5.53396	−	1.06103i	−0.180498	−	0.0346070i
$941$	−23.7269	−	7.70932i	−0.773473	−	0.251317i	−0.104422	−	0.994533i	$-0.533299\pi$
$941$	−23.7269	−	7.70932i	−0.773473	−	0.251317i	−0.669051	+	0.743216i	$0.733299\pi$
$942$	−0.0167627	+	0.105835i	−0.000546158	+	0.00344830i
$943$	0.0351097	+	0.221674i	0.00114333	+	0.00721870i
$944$	−2.66424	+	0.865665i	−0.0867138	+	0.0281750i
$945$	−0.554871	+	0.713955i	−0.0180500	+	0.0232249i
$946$	23.9597	+	17.4078i	0.778998	+	0.565975i
$947$	−42.5088	−	21.6593i	−1.38135	−	0.703834i	−0.403862	−	0.914820i	$-0.632332\pi$
$947$	−42.5088	−	21.6593i	−1.38135	−	0.703834i	−0.977489	+	0.210986i	$0.932332\pi$
$948$	−0.0702317	+	0.0111236i	−0.00228102	+	0.000361278i
$949$	−14.0431	−	19.3287i	−0.455859	−	0.627436i
$950$	−3.75567	−	8.72361i	−0.121850	−	0.283031i
$951$	0.156139	+	0.214908i	0.00506317	+	0.00696885i
$952$	4.85048	+	2.47144i	0.157205	+	0.0800998i
$953$	7.84904	−	15.4046i	0.254255	−	0.499004i	−0.728233	−	0.685330i	$-0.759658\pi$
$953$	7.84904	−	15.4046i	0.254255	−	0.499004i	0.982488	+	0.186326i	$0.0596580\pi$
$954$	−11.4242	+	35.1600i	−0.369871	+	1.13835i
$955$	1.70820	−	52.7821i	0.0552762	−	1.70799i
$956$		−	11.4479i		−	0.370252i
$957$	−0.825960	−	1.62104i	−0.0266995	−	0.0524007i
$958$	−0.681573	+	0.107950i	−0.0220206	+	0.00348772i
$959$	9.97583	−	7.24786i	0.322136	−	0.234046i
$960$	0.0527810	+	0.0563116i	0.00170350	+	0.00181745i
$961$	25.5762	−	17.5174i	0.825037	−	0.565078i
$962$	7.86226	+	7.86226i	0.253489	+	0.253489i
$963$	−3.03599	+	19.1685i	−0.0978335	+	0.617696i
$964$	−9.85285	−	7.15851i	−0.317339	−	0.230560i
$965$	−52.6598	+	24.7196i	−1.69518	+	0.795753i
$966$	0.00298235			9.59555e−5
$967$	16.8000	−	16.8000i	0.540252	−	0.540252i	−0.383351	−	0.923603i	$-0.625230\pi$
$967$	16.8000	−	16.8000i	0.540252	−	0.540252i	0.923603	+	0.383351i	$0.125230\pi$
$968$	9.61636	+	18.8732i	0.309081	+	0.606606i
$969$	0.173812	−	0.0564750i	0.00558365	−	0.00181424i
$970$	−7.50582	−	25.9258i	−0.240997	−	0.832426i
$971$	−19.6694	+	14.2907i	−0.631222	+	0.458609i	−0.856823	−	0.515610i	$-0.827565\pi$
$971$	−19.6694	+	14.2907i	−0.631222	+	0.458609i	0.225602	+	0.974220i	$0.427565\pi$
$972$	0.422867	+	0.829922i	0.0135635	+	0.0266198i
$973$	9.84114	+	1.55868i	0.315492	+	0.0499691i
$974$	4.68443	+	3.40344i	0.150099	+	0.109053i
$975$	−0.505020	+	0.128660i	−0.0161736	+	0.00412041i
$976$	3.84995	−	5.29900i	0.123234	−	0.169617i
$977$	−0.323800	−	2.04439i	−0.0103593	−	0.0654059i	0.981967	−	0.189052i	$-0.0605414\pi$
$977$	−0.323800	−	2.04439i	−0.0103593	−	0.0654059i	−0.992326	+	0.123646i	$0.960541\pi$
$978$	−0.372137	+	0.730361i	−0.0118996	+	0.0233544i
$979$	−48.5291	+	66.7946i	−1.55100	+	2.13476i
$980$	3.99859	+	5.89561i	0.127730	+	0.188328i
$981$	1.46506	−	4.50899i	0.0467757	−	0.143961i
$982$	2.77826	−	17.5412i	0.0886578	−	0.559764i
$983$	4.91818	−	9.65247i	0.156866	−	0.307866i	−0.799176	−	0.601097i	$-0.794730\pi$
$983$	4.91818	−	9.65247i	0.156866	−	0.307866i	0.956042	+	0.293231i	$0.0947305\pi$
$984$	0.0541085	+	0.166529i	0.00172492	+	0.00530875i
$985$	10.2346	−	4.80432i	0.326100	−	0.153079i
$986$	25.8992			0.824799
$987$	−0.120116	+	0.120116i	−0.00382332	+	0.00382332i
$988$	5.11094	−	2.60415i	0.162601	−	0.0828491i
$989$	−0.135760	+	0.186858i	−0.00431692	+	0.00594173i
$990$	7.16294	−	37.3594i	0.227653	−	1.18736i
$991$		−	18.9885i		−	0.603188i	−0.953436	−	0.301594i	$-0.902481\pi$
$991$		−	18.9885i		−	0.603188i	0.953436	−	0.301594i	$-0.0975187\pi$
$992$	−4.92531	−	2.59640i	−0.156379	−	0.0824358i
$993$	0.862361	−	0.862361i	0.0273662	−	0.0273662i
$994$	−1.77586	−	2.44425i	−0.0563267	−	0.0775271i
$995$	4.72765	−	6.08308i	0.149877	−	0.192847i
$996$	0.0347689	−	0.107008i	0.00110169	−	0.00339066i
$997$	3.26083	+	3.26083i	0.103272	+	0.103272i	0.756855	−	0.653583i	$-0.226735\pi$
$997$	3.26083	+	3.26083i	0.103272	+	0.103272i	−0.653583	+	0.756855i	$0.726735\pi$
$998$	−13.8239	−	13.8239i	−0.437589	−	0.437589i
$999$	−0.725079	−	0.235592i	−0.0229405	−	0.00745381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.s.a.77.12	✓	128
5.3	odd	4	inner	310.2.s.a.263.13	yes	128
31.29	odd	10	inner	310.2.s.a.277.13	yes	128
155.153	even	20	inner	310.2.s.a.153.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.12	✓	128	1.1	even	1	trivial
310.2.s.a.153.12	yes	128	155.153	even	20	inner
310.2.s.a.263.13	yes	128	5.3	odd	4	inner
310.2.s.a.277.13	yes	128	31.29	odd	10	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 + 0.156434i) q^{2} +(0.00539952 + 0.0340912i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.0723287 - 2.23490i) q^{5} +0.0345162i q^{6} +(-1.74013 + 0.886641i) q^{7} +(0.891007 + 0.453990i) q^{8} +(2.85204 - 0.926683i) q^{9} +O(q^{10})\)	\(q+(0.987688 + 0.156434i) q^{2} +(0.00539952 + 0.0340912i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.0723287 - 2.23490i) q^{5} +0.0345162i q^{6} +(-1.74013 + 0.886641i) q^{7} +(0.891007 + 0.453990i) q^{8} +(2.85204 - 0.926683i) q^{9} +(0.421053 - 2.19607i) q^{10} +(5.39525 + 1.75302i) q^{11} +(-0.00539952 + 0.0340912i) q^{12} +(-0.472393 - 2.98257i) q^{13} +(-1.85741 + 0.603509i) q^{14} +(0.0765810 - 0.00960160i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.48361 - 1.26546i) q^{17} +(2.96189 - 0.469117i) q^{18} +(1.11652 + 1.53676i) q^{19} +(0.759410 - 2.10316i) q^{20} +(-0.0396226 - 0.0545358i) q^{21} +(5.05459 + 2.57544i) q^{22} +(-0.0200854 + 0.0394199i) q^{23} +(-0.0106661 + 0.0328268i) q^{24} +(-4.98954 - 0.323295i) q^{25} -3.01975i q^{26} +(0.0940015 + 0.184488i) q^{27} +(-1.92895 + 0.305516i) q^{28} +(-7.51695 + 5.46138i) q^{29} +(0.0771401 + 0.00249651i) q^{30} +(-5.31865 + 1.64679i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.0306310 + 0.193396i) q^{33} +(-2.25507 - 1.63840i) q^{34} +(1.85569 + 3.95315i) q^{35} +2.99881 q^{36} +(-2.60361 + 2.60361i) q^{37} +(0.862373 + 1.69250i) q^{38} +(0.0991289 - 0.0322089i) q^{39} +(1.07907 - 1.95847i) q^{40} +(4.10410 - 2.98180i) q^{41} +(-0.0306035 - 0.0600627i) q^{42} +(5.15631 + 0.816679i) q^{43} +(4.58948 + 3.33445i) q^{44} +(-1.86476 - 6.44104i) q^{45} +(-0.0260048 + 0.0357925i) q^{46} +(-0.394206 - 2.48892i) q^{47} +(-0.0156700 + 0.0307541i) q^{48} +(-1.87257 + 2.57738i) q^{49} +(-4.87753 - 1.09985i) q^{50} +(0.0297309 - 0.0915022i) q^{51} +(0.472393 - 2.98257i) q^{52} +(-5.59680 + 10.9843i) q^{53} +(0.0639838 + 0.196922i) q^{54} +(4.30806 - 11.9310i) q^{55} -1.95299 q^{56} +(-0.0463614 + 0.0463614i) q^{57} +(-8.27875 + 4.21824i) q^{58} +(-1.64659 + 2.26634i) q^{59} +(0.0757999 + 0.0145332i) q^{60} -6.54992i q^{61} +(-5.51079 + 0.794496i) q^{62} +(-4.14128 + 4.14128i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-6.69991 + 0.840025i) q^{65} +(-0.0605077 + 0.186224i) q^{66} +(-7.51327 - 7.51327i) q^{67} +(-1.97100 - 1.97100i) q^{68} +(-0.00145232 - 0.000471889i) q^{69} +(1.21444 + 4.19477i) q^{70} +(0.478046 + 1.47128i) q^{71} +(2.96189 + 0.469117i) q^{72} +(7.04944 - 3.59187i) q^{73} +(-2.97885 + 2.16426i) q^{74} +(-0.0159196 - 0.171845i) q^{75} +(0.586990 + 1.80657i) q^{76} +(-10.9428 + 1.73316i) q^{77} +(0.102947 - 0.0163052i) q^{78} +(0.636609 + 1.95928i) q^{79} +(1.37216 - 1.76556i) q^{80} +(7.27248 - 5.28377i) q^{81} +(4.52003 - 2.30307i) q^{82} +(-3.21962 - 0.509938i) q^{83} +(-0.0208308 - 0.0641107i) q^{84} +(-3.00781 + 5.45908i) q^{85} +(4.96507 + 1.61325i) q^{86} +(-0.226773 - 0.226773i) q^{87} +(4.01135 + 4.01135i) q^{88} +(-4.49739 + 13.8415i) q^{89} +(-0.834199 - 6.65345i) q^{90} +(3.46650 + 4.77122i) q^{91} +(-0.0312838 + 0.0312838i) q^{92} +(-0.0848593 - 0.172428i) q^{93} -2.51994i q^{94} +(3.51526 - 2.38416i) q^{95} +(-0.0202881 + 0.0279242i) q^{96} +(10.7549 - 5.47988i) q^{97} +(-2.25271 + 2.25271i) q^{98} +17.0120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 12 q^{7}+O(q^{10}) \) 128 * q + 12 * q^7	\( 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) \) 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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