LMFDB - Embedded newform 770.2.bv.a.313.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			313.19
Character	$\chi$	$=$	770.313
Dual form			770.2.bv.a.647.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.838671 + 0.544639i) q^{2} +(1.00437 + 1.24029i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-2.14634 + 0.627077i) q^{5} +(-1.51785 - 0.493179i) q^{6} +(-2.45321 + 0.990841i) q^{7} +(0.156434 + 0.987688i) q^{8} +(0.0941655 - 0.443014i) q^{9} +O(q^{10})$	\(q+(-0.838671 + 0.544639i) q^{2} +(1.00437 + 1.24029i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-2.14634 + 0.627077i) q^{5} +(-1.51785 - 0.493179i) q^{6} +(-2.45321 + 0.990841i) q^{7} +(0.156434 + 0.987688i) q^{8} +(0.0941655 - 0.443014i) q^{9} +(1.45854 - 1.69489i) q^{10} +(-0.687648 - 3.24456i) q^{11} +(1.54158 - 0.413065i) q^{12} +(0.930007 + 0.473862i) q^{13} +(1.51778 - 2.16710i) q^{14} +(-2.93348 - 2.03227i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(-4.12158 - 2.67659i) q^{17} +(0.162309 + 0.422829i) q^{18} +(-1.33765 + 0.595561i) q^{19} +(-0.300131 + 2.21583i) q^{20} +(-3.69286 - 2.04753i) q^{21} +(2.34382 + 2.34659i) q^{22} +(5.18961 - 1.39055i) q^{23} +(-1.06791 + 1.18603i) q^{24} +(4.21355 - 2.69184i) q^{25} +(-1.03805 + 0.109104i) q^{26} +(4.91008 - 2.50181i) q^{27} +(-0.0926312 + 2.64413i) q^{28} +(-0.541665 - 0.745537i) q^{29} +(3.56708 + 0.106721i) q^{30} +(-7.63479 - 6.87440i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.33355 - 4.11162i) q^{33} +4.91442 q^{34} +(4.64409 - 3.66503i) q^{35} +(-0.366413 - 0.266214i) q^{36} +(1.47996 + 1.19845i) q^{37} +(0.797484 - 1.22802i) q^{38} +(0.346343 + 1.62942i) q^{39} +(-0.955119 - 2.02182i) q^{40} +(2.93074 - 4.03382i) q^{41} +(4.21226 - 0.294076i) q^{42} +(5.11915 + 5.11915i) q^{43} +(-3.24374 - 0.691482i) q^{44} +(0.0756928 + 1.00991i) q^{45} +(-3.59503 + 3.99268i) q^{46} +(-10.3859 - 3.98679i) q^{47} +(0.249663 - 1.57631i) q^{48} +(5.03647 - 4.86148i) q^{49} +(-2.06770 + 4.55243i) q^{50} +(-0.819840 - 7.80025i) q^{51} +(0.811163 - 0.656867i) q^{52} +(-4.51846 + 0.236802i) q^{53} +(-2.75535 + 4.77241i) q^{54} +(3.51051 + 6.53271i) q^{55} +(-1.36241 - 2.26800i) q^{56} +(-2.08217 - 1.06092i) q^{57} +(0.860327 + 0.330249i) q^{58} +(-3.13516 - 1.39586i) q^{59} +(-3.04973 + 1.85327i) q^{60} +(-5.72083 + 5.15105i) q^{61} +(10.1471 + 1.60715i) q^{62} +(0.207949 + 1.18011i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.29326 - 0.433883i) q^{65} +(-0.556400 + 5.26388i) q^{66} +(2.42099 + 0.648703i) q^{67} +(-4.12158 + 2.67659i) q^{68} +(6.93699 + 5.04002i) q^{69} +(-1.89874 + 5.60311i) q^{70} +(1.76211 - 5.42322i) q^{71} +(0.452290 + 0.0237035i) q^{72} +(-8.20972 + 3.15142i) q^{73} +(-1.89392 - 0.199059i) q^{74} +(7.57064 + 2.52243i) q^{75} +1.46424i q^{76} +(4.90178 + 7.27822i) q^{77} +(-1.17791 - 1.17791i) q^{78} +(0.505287 - 2.37719i) q^{79} +(1.90219 + 1.17544i) q^{80} +(6.79325 + 3.02455i) q^{81} +(-0.260951 + 4.97925i) q^{82} +(-4.13319 - 8.11183i) q^{83} +(-3.37253 + 2.54079i) q^{84} +(10.5247 + 3.16031i) q^{85} +(-7.08137 - 1.50519i) q^{86} +(0.380654 - 1.42062i) q^{87} +(3.09704 - 1.18674i) q^{88} +(4.16476 - 7.21357i) q^{89} +(-0.613516 - 0.805754i) q^{90} +(-2.75102 - 0.240994i) q^{91} +(0.840473 - 5.30654i) q^{92} +(0.858116 - 16.3738i) q^{93} +(10.8817 - 2.31299i) q^{94} +(2.49759 - 2.11709i) q^{95} +(0.649135 + 1.45798i) q^{96} +(0.592364 - 1.16258i) q^{97} +(-1.57618 + 6.82024i) q^{98} +(-1.50214 - 0.000887499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$3$	1.00437	+	1.24029i	0.579873	+	0.716084i	0.979692	−	0.200510i	$-0.0642600\pi$
$3$	1.00437	+	1.24029i	0.579873	+	0.716084i	−0.399818	+	0.916595i	$0.630927\pi$
$4$	0.406737	−	0.913545i	0.203368	−	0.456773i
$5$	−2.14634	+	0.627077i	−0.959872	+	0.280438i
$5$	−2.14634	+	0.627077i	−0.959872	+	0.280438i
$6$	−1.51785	−	0.493179i	−0.619659	−	0.201339i
$7$	−2.45321	+	0.990841i	−0.927226	+	0.374503i
$7$	−2.45321	+	0.990841i	−0.927226	+	0.374503i
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	0.0941655	−	0.443014i	0.0313885	−	0.147671i
$10$	1.45854	−	1.69489i	0.461231	−	0.535972i
$11$	−0.687648	−	3.24456i	−0.207334	−	0.978270i
$11$	−0.687648	−	3.24456i	−0.207334	−	0.978270i
$12$	1.54158	−	0.413065i	0.445016	−	0.119242i
$13$	0.930007	+	0.473862i	0.257938	+	0.131426i	0.578178	−	0.815910i	$-0.303764\pi$
$13$	0.930007	+	0.473862i	0.257938	+	0.131426i	−0.320241	+	0.947336i	$0.603764\pi$
$14$	1.51778	−	2.16710i	0.405645	−	0.579183i
$15$	−2.93348	−	2.03227i	−0.757421	−	0.524731i
$16$	−0.669131	−	0.743145i	−0.167283	−	0.185786i
$17$	−4.12158	−	2.67659i	−0.999630	−	0.649167i	−0.0624625	−	0.998047i	$-0.519895\pi$
$17$	−4.12158	−	2.67659i	−0.999630	−	0.649167i	−0.937167	+	0.348880i	$0.886562\pi$
$18$	0.162309	+	0.422829i	0.0382565	+	0.0996617i
$19$	−1.33765	+	0.595561i	−0.306878	+	0.136631i	−0.554398	−	0.832252i	$-0.687051\pi$
$19$	−1.33765	+	0.595561i	−0.306878	+	0.136631i	0.247519	+	0.968883i	$0.420385\pi$
$20$	−0.300131	+	2.21583i	−0.0671114	+	0.495476i
$21$	−3.69286	−	2.04753i	−0.805849	−	0.446807i
$22$	2.34382	+	2.34659i	0.499705	+	0.500295i
$23$	5.18961	−	1.39055i	1.08211	−	0.289950i	0.326650	−	0.945145i	$-0.394080\pi$
$23$	5.18961	−	1.39055i	1.08211	−	0.289950i	0.755460	+	0.655195i	$0.227414\pi$
$24$	−1.06791	+	1.18603i	−0.217985	+	0.242097i
$25$	4.21355	−	2.69184i	0.842710	−	0.538368i
$26$	−1.03805	+	0.109104i	−0.203579	+	0.0213970i
$27$	4.91008	−	2.50181i	0.944945	−	0.481473i
$28$	−0.0926312	+	2.64413i	−0.0175057	+	0.499693i
$29$	−0.541665	−	0.745537i	−0.100585	−	0.138443i	0.755758	−	0.654851i	$-0.227269\pi$
$29$	−0.541665	−	0.745537i	−0.100585	−	0.138443i	−0.856342	+	0.516408i	$0.827269\pi$
$30$	3.56708	+	0.106721i	0.651257	+	0.0194845i
$31$	−7.63479	−	6.87440i	−1.37125	−	1.23468i	−0.943749	−	0.330662i	$-0.892728\pi$
$31$	−7.63479	−	6.87440i	−1.37125	−	1.23468i	−0.427500	−	0.904015i	$-0.640606\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	3.33355	−	4.11162i	0.580296	−	0.715741i
$34$	4.91442			0.842816
$35$	4.64409	−	3.66503i	0.784994	−	0.619504i
$36$	−0.366413	−	0.266214i	−0.0610688	−	0.0443691i
$37$	1.47996	+	1.19845i	0.243304	+	0.197024i	0.743214	−	0.669054i	$-0.233300\pi$
$37$	1.47996	+	1.19845i	0.243304	+	0.197024i	−0.499910	+	0.866077i	$0.666634\pi$
$38$	0.797484	−	1.22802i	0.129369	−	0.199211i
$39$	0.346343	+	1.62942i	0.0554593	+	0.260915i
$40$	−0.955119	−	2.02182i	−0.151018	−	0.319678i
$41$	2.93074	−	4.03382i	0.457705	−	0.629977i	−0.516326	−	0.856392i	$-0.672701\pi$
$41$	2.93074	−	4.03382i	0.457705	−	0.629977i	0.974031	+	0.226415i	$0.0727006\pi$
$42$	4.21226	−	0.294076i	0.649966	−	0.0453770i
$43$	5.11915	+	5.11915i	0.780664	+	0.780664i	0.979943	−	0.199279i	$-0.0638601\pi$
$43$	5.11915	+	5.11915i	0.780664	+	0.780664i	−0.199279	+	0.979943i	$0.563860\pi$
$44$	−3.24374	−	0.691482i	−0.489012	−	0.104245i
$45$	0.0756928	+	1.00991i	0.0112836	+	0.150548i
$46$	−3.59503	+	3.99268i	−0.530058	+	0.588689i
$47$	−10.3859	−	3.98679i	−1.51495	−	0.581533i	−0.547992	−	0.836484i	$-0.684607\pi$
$47$	−10.3859	−	3.98679i	−1.51495	−	0.581533i	−0.966954	+	0.254951i	$0.917941\pi$
$48$	0.249663	−	1.57631i	0.0360358	−	0.227521i
$49$	5.03647	−	4.86148i	0.719495	−	0.694497i
$50$	−2.06770	+	4.55243i	−0.292416	+	0.643811i
$51$	−0.819840	−	7.80025i	−0.114801	−	1.09225i
$52$	0.811163	−	0.656867i	0.112488	−	0.0910910i
$53$	−4.51846	+	0.236802i	−0.620658	+	0.0325273i	−0.360074	−	0.932924i	$-0.617248\pi$
$53$	−4.51846	+	0.236802i	−0.620658	+	0.0325273i	−0.260584	+	0.965451i	$0.583915\pi$
$54$	−2.75535	+	4.77241i	−0.374956	+	0.649443i
$55$	3.51051	+	6.53271i	0.473358	+	0.880870i
$56$	−1.36241	−	2.26800i	−0.182060	−	0.303075i
$57$	−2.08217	−	1.06092i	−0.275790	−	0.140522i
$58$	0.860327	+	0.330249i	0.112966	+	0.0433638i
$59$	−3.13516	−	1.39586i	−0.408163	−	0.181726i	0.192376	−	0.981321i	$-0.438381\pi$
$59$	−3.13516	−	1.39586i	−0.408163	−	0.181726i	−0.600539	+	0.799595i	$0.705047\pi$
$60$	−3.04973	+	1.85327i	−0.393718	+	0.239256i
$61$	−5.72083	+	5.15105i	−0.732477	+	0.659525i	−0.948469	−	0.316870i	$-0.897368\pi$
$61$	−5.72083	+	5.15105i	−0.732477	+	0.659525i	0.215992	+	0.976395i	$0.430701\pi$
$62$	10.1471	+	1.60715i	1.28869	+	0.204108i
$63$	0.207949	+	1.18011i	0.0261991	+	0.148680i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−2.29326	−	0.433883i	−0.284444	−	0.0538166i
$66$	−0.556400	+	5.26388i	−0.0684881	+	0.647938i
$67$	2.42099	+	0.648703i	0.295771	+	0.0792517i	0.403653	−	0.914912i	$-0.367740\pi$
$67$	2.42099	+	0.648703i	0.295771	+	0.0792517i	−0.107882	+	0.994164i	$0.534407\pi$
$68$	−4.12158	+	2.67659i	−0.499815	+	0.324584i
$69$	6.93699	+	5.04002i	0.835115	+	0.606747i
$70$	−1.89874	+	5.60311i	−0.226942	+	0.669699i
$71$	1.76211	−	5.42322i	0.209124	−	0.643618i	−0.790395	−	0.612598i	$-0.790125\pi$
$71$	1.76211	−	5.42322i	0.209124	−	0.643618i	0.999519	−	0.0310197i	$-0.00987546\pi$
$72$	0.452290	+	0.0237035i	0.0533029	+	0.00279349i
$73$	−8.20972	+	3.15142i	−0.960875	+	0.368845i	−0.787709	−	0.616047i	$-0.788733\pi$
$73$	−8.20972	+	3.15142i	−0.960875	+	0.368845i	−0.173166	+	0.984893i	$0.555400\pi$
$74$	−1.89392	−	0.199059i	−0.220164	−	0.0231401i
$75$	7.57064	+	2.52243i	0.874182	+	0.291265i
$76$			1.46424i			0.167960i
$77$	4.90178	+	7.27822i	0.558610	+	0.829430i
$78$	−1.17791	−	1.17791i	−0.133372	−	0.133372i
$79$	0.505287	−	2.37719i	0.0568492	−	0.267455i	−0.940539	−	0.339687i	$-0.889679\pi$
$79$	0.505287	−	2.37719i	0.0568492	−	0.267455i	0.997388	+	0.0722322i	$0.0230123\pi$
$80$	1.90219	+	1.17544i	0.212671	+	0.131419i
$81$	6.79325	+	3.02455i	0.754806	+	0.336061i
$82$	−0.260951	+	4.97925i	−0.0288172	+	0.549866i
$83$	−4.13319	−	8.11183i	−0.453676	−	0.890389i	−0.998650	−	0.0519367i	$-0.983461\pi$
$83$	−4.13319	−	8.11183i	−0.453676	−	0.890389i	0.544974	−	0.838453i	$-0.316539\pi$
$84$	−3.37253	+	2.54079i	−0.367974	+	0.277223i
$85$	10.5247	+	3.16031i	1.14157	+	0.342784i
$86$	−7.08137	−	1.50519i	−0.763604	−	0.162309i
$87$	0.380654	−	1.42062i	0.0408104	−	0.152306i
$88$	3.09704	−	1.18674i	0.330145	−	0.126507i
$89$	4.16476	−	7.21357i	0.441463	−	0.764637i	−0.556335	−	0.830958i	$-0.687793\pi$
$89$	4.16476	−	7.21357i	0.441463	−	0.764637i	0.997798	+	0.0663211i	$0.0211262\pi$
$90$	−0.613516	−	0.805754i	−0.0646703	−	0.0849339i
$91$	−2.75102	−	0.240994i	−0.288386	−	0.0252630i
$92$	0.840473	−	5.30654i	0.0876254	−	0.553245i
$93$	0.858116	−	16.3738i	0.0889825	−	1.69789i
$94$	10.8817	−	2.31299i	1.12237	−	0.238566i
$95$	2.49759	−	2.11709i	0.256248	−	0.217209i
$96$	0.649135	+	1.45798i	0.0662521	+	0.148805i
$97$	0.592364	−	1.16258i	0.0601454	−	0.118042i	−0.858977	−	0.512014i	$-0.828899\pi$
$97$	0.592364	−	1.16258i	0.0601454	−	0.118042i	0.919122	+	0.393972i	$0.128899\pi$
$98$	−1.57618	+	6.82024i	−0.159219	+	0.688948i
$99$	−1.50214		0.000887499i	−0.150970		8.91970e-5i
$100$	−0.745316	−	4.94414i	−0.0745316	−	0.494414i
$101$	−7.15425	−	6.44172i	−0.711875	−	0.640975i	0.231450	−	0.972847i	$-0.425653\pi$
$101$	−7.15425	−	6.44172i	−0.711875	−	0.640975i	−0.943324	+	0.331872i	$0.892320\pi$
$102$	4.93590	+	6.09533i	0.488727	+	0.603527i
$103$	0.828289	+	0.670735i	0.0816137	+	0.0660895i	0.669259	−	0.743029i	$-0.266612\pi$
$103$	0.828289	+	0.670735i	0.0816137	+	0.0660895i	−0.587645	+	0.809119i	$0.699945\pi$
$104$	−0.322543	+	0.992686i	−0.0316280	+	0.0973408i
$105$	9.21010	+	2.07898i	0.898814	+	0.202888i
$106$	3.66052	−	2.65953i	0.355542	−	0.258316i
$107$	6.59696	−	17.1857i	0.637752	−	1.66140i	−0.107164	−	0.994241i	$-0.534177\pi$
$107$	6.59696	−	17.1857i	0.637752	−	1.66140i	0.744915	−	0.667159i	$-0.232490\pi$
$108$	−0.288408	−	5.50316i	−0.0277521	−	0.529541i
$109$	−3.94873	+	2.27980i	−0.378220	+	0.218365i	−0.677043	−	0.735943i	$-0.736739\pi$
$109$	−3.94873	+	2.27980i	−0.378220	+	0.218365i	0.298824	+	0.954308i	$0.403406\pi$
$110$	−6.50213	−	3.56683i	−0.619954	−	0.340084i
$111$			3.03927i			0.288475i
$112$	2.37786	+	1.16009i	0.224686	+	0.109618i
$113$	1.18961	+	7.51093i	0.111910	+	0.706569i	0.978299	+	0.207199i	$0.0664349\pi$
$113$	1.18961	+	7.51093i	0.111910	+	0.706569i	−0.866389	+	0.499369i	$0.833565\pi$
$114$	2.32407	−	0.244270i	0.217669	−	0.0228780i
$115$	−10.2667	+	6.23889i	−0.957374	+	0.581779i
$116$	−0.901397	+	0.191598i	−0.0836926	+	0.0177894i
$117$	0.297502	−	0.367385i	0.0275041	−	0.0339647i
$118$	3.38961	−	0.536862i	0.312039	−	0.0494221i
$119$	12.7632	+	2.48239i	1.17000	+	0.227560i
$120$	1.54836	−	3.21528i	0.141345	−	0.293514i
$121$	−10.0543	+	4.46223i	−0.914025	+	0.405657i
$122$	1.99242	−	7.43582i	0.180385	−	0.673208i
$123$	7.94668	−	0.416468i	0.716528	−	0.0375516i
$124$	−9.38542	+	4.17866i	−0.842836	+	0.375255i
$125$	−7.35571	+	8.41983i	−0.657915	+	0.753092i
$126$	−0.817134	−	0.876465i	−0.0727961	−	0.0780817i
$127$	4.24414	+	8.32959i	0.376606	+	0.739131i	0.999052	−	0.0435316i	$-0.0138609\pi$
$127$	4.24414	+	8.32959i	0.376606	+	0.739131i	−0.622446	+	0.782663i	$0.713861\pi$
$128$	0.629320	−	0.777146i	0.0556246	−	0.0686906i
$129$	−1.20773	+	11.4908i	−0.106335	+	1.01171i
$130$	2.15960	−	0.885114i	0.189409	−	0.0776296i
$131$	−9.63453	−	5.56250i	−0.841773	−	0.485998i	0.0160937	−	0.999870i	$-0.494877\pi$
$131$	−9.63453	−	5.56250i	−0.841773	−	0.485998i	−0.857866	+	0.513873i	$0.828210\pi$
$132$	−2.40028	−	4.71770i	−0.208917	−	0.410623i
$133$	2.69143	−	2.78644i	0.233377	−	0.241615i
$134$	−2.38373	+	0.774519i	−0.205922	+	0.0669083i
$135$	−8.96987	+	8.44873i	−0.772003	+	0.727151i
$136$	1.99887	−	4.48955i	0.171402	−	0.384975i
$137$	−0.394026	+	0.606748i	−0.0336640	+	0.0518379i	−0.855102	−	0.518460i	$-0.826506\pi$
$137$	−0.394026	+	0.606748i	−0.0336640	+	0.0518379i	0.821438	+	0.570298i	$0.193172\pi$
$138$	−8.56284	−	0.448759i	−0.728917	−	0.0382009i
$139$	−9.38916	+	6.82162i	−0.796378	+	0.578603i	−0.909849	−	0.414939i	$-0.863803\pi$
$139$	−9.38916	+	6.82162i	−0.796378	+	0.578603i	0.113471	+	0.993541i	$0.463803\pi$
$140$	−1.45926	−	5.73329i	−0.123330	−	0.484551i
$141$	−5.48654	−	16.8858i	−0.462050	−	1.42204i
$142$	1.47587	+	5.50801i	0.123852	+	0.462222i
$143$	0.897955	−	3.34331i	0.0750908	−	0.279582i
$144$	−0.392232	+	0.226456i	−0.0326860	+	0.0188713i
$145$	1.63011	+	1.26051i	0.135373	+	0.104680i
$146$	5.16887	−	7.11434i	0.427779	−	0.588787i
$147$	11.0881	+	1.36397i	0.914535	+	0.112498i
$148$	1.69679	−	0.864558i	0.139475	−	0.0710662i
$149$	−7.87350	+	7.08933i	−0.645022	+	0.580781i	−0.925345	−	0.379125i	$-0.876225\pi$
$149$	−7.87350	+	7.08933i	−0.645022	+	0.580781i	0.280323	+	0.959906i	$0.409558\pi$
$150$	−7.72309	+	2.00778i	−0.630587	+	0.163934i
$151$	−1.18989	+	11.3211i	−0.0968320	+	0.921295i	0.832991	+	0.553287i	$0.186627\pi$
$151$	−1.18989	+	11.3211i	−0.0968320	+	0.921295i	−0.929823	+	0.368008i	$0.880040\pi$
$152$	−0.797484	−	1.22802i	−0.0646845	−	0.0996053i
$153$	−1.57387	+	1.57387i	−0.127240	+	0.127240i
$154$	−8.07499	−	3.43433i	−0.650701	−	0.276746i
$155$	20.6976	+	9.96718i	1.66247	+	0.800583i
$156$	1.62942	+	0.346343i	0.130458	+	0.0277296i
$157$	3.76374	−	3.04782i	0.300379	−	0.243242i	−0.467267	−	0.884116i	$-0.654761\pi$
$157$	3.76374	−	3.04782i	0.300379	−	0.243242i	0.767646	+	0.640874i	$0.221428\pi$
$158$	0.870940	+	2.26888i	0.0692883	+	0.180502i
$159$	−4.83191	−	5.36638i	−0.383195	−	0.425581i
$160$	−2.23550	+	0.0501967i	−0.176732	+	0.00396840i
$161$	−11.3534	+	8.55340i	−0.894772	+	0.674102i
$162$	−7.34459	+	1.16327i	−0.577045	+	0.0913950i
$163$	−6.75669	−	10.4044i	−0.529225	−	0.814935i	0.468421	−	0.883505i	$-0.344823\pi$
$163$	−6.75669	−	10.4044i	−0.529225	−	0.814935i	−0.997646	+	0.0685704i	$0.978156\pi$
$164$	−2.49304	−	4.31807i	−0.194674	−	0.337185i
$165$	−4.57662	+	10.9153i	−0.356290	+	0.849757i
$166$	7.88440	+	4.55206i	0.611948	+	0.353309i
$167$	4.26522	−	8.37096i	0.330052	−	0.647764i	−0.665030	−	0.746817i	$-0.731581\pi$
$167$	4.26522	−	8.37096i	0.330052	−	0.647764i	0.995082	+	0.0990525i	$0.0315812\pi$
$168$	1.44463	−	3.96770i	0.111456	−	0.306115i
$169$	−7.00084	−	9.63583i	−0.538526	−	0.741218i
$170$	−10.5480	+	3.08172i	−0.808996	+	0.236357i
$171$	0.137881	+	0.648680i	0.0105440	+	0.0496058i
$172$	6.75873	−	2.59443i	0.515348	−	0.197824i
$173$	−4.08843	+	10.6507i	−0.310838	+	0.809760i	0.685797	+	0.727792i	$0.259454\pi$
$173$	−4.08843	+	10.6507i	−0.310838	+	0.809760i	−0.996635	+	0.0819672i	$0.973880\pi$
$174$	0.454482	+	1.39875i	0.0344542	+	0.106039i
$175$	−7.66952	+	10.7786i	−0.579762	+	0.814786i
$176$	−1.95105	+	2.68205i	−0.147066	+	0.202167i
$177$	−1.41758	−	5.29049i	−0.106552	−	0.397657i
$178$	0.435933	+	8.31810i	0.0326746	+	0.623468i
$179$	−19.0825	−	2.00566i	−1.42630	−	0.149910i	−0.640292	−	0.768131i	$-0.721187\pi$
$179$	−19.0825	−	2.00566i	−1.42630	−	0.149910i	−0.786004	+	0.618222i	$0.787853\pi$
$180$	0.953383	+	0.341617i	0.0710610	+	0.0254627i
$181$	22.9915	+	7.47038i	1.70894	+	0.555269i	0.990157	−	0.139962i	$-0.0446982\pi$
$181$	22.9915	+	7.47038i	1.70894	+	0.555269i	0.718786	+	0.695232i	$0.244698\pi$
$182$	2.43846	−	1.29620i	0.180750	−	0.0960808i
$183$	−12.1347	−	1.92194i	−0.897019	−	0.142074i
$184$	2.18527	+	4.90819i	0.161100	+	0.361837i
$185$	−3.92801	−	1.64423i	−0.288793	−	0.120886i
$186$	8.19815	+	14.1996i	0.601117	+	1.04117i
$187$	−5.85013	+	15.2132i	−0.427804	+	1.11250i
$188$	−7.86646	+	7.86646i	−0.573721	+	0.573721i
$189$	−9.56655	+	11.0026i	−0.695864	+	0.800319i
$190$	−0.941609	+	3.13583i	−0.0683115	+	0.227497i
$191$	−2.14377	−	20.3966i	−0.155118	−	1.47585i	−0.744298	−	0.667847i	$-0.767216\pi$
$191$	−2.14377	−	20.3966i	−0.155118	−	1.47585i	0.589180	−	0.808002i	$-0.299451\pi$
$192$	−1.33848	−	0.869222i	−0.0965968	−	0.0627307i
$193$	−1.07897	−	0.700690i	−0.0776658	−	0.0504368i	0.505222	−	0.862989i	$-0.331411\pi$
$193$	−1.07897	−	0.700690i	−0.0776658	−	0.0504368i	−0.582888	+	0.812553i	$0.698077\pi$
$194$	0.136388	+	1.29764i	0.00979209	+	0.0931655i
$195$	−1.76514	−	3.28010i	−0.126404	−	0.234893i
$196$	−2.39267	−	6.57838i	−0.170905	−	0.469885i
$197$	−11.7303	+	11.7303i	−0.835749	+	0.835749i	−0.988296	−	0.152548i	$-0.951252\pi$
$197$	−11.7303	+	11.7303i	−0.835749	+	0.835749i	0.152548	+	0.988296i	$0.451252\pi$
$198$	1.26028	−	0.817377i	0.0895642	−	0.0580885i
$199$	0.327870	+	0.567887i	0.0232421	+	0.0402564i	0.877412	−	0.479737i	$-0.159268\pi$
$199$	0.327870	+	0.567887i	0.0232421	+	0.0402564i	−0.854170	+	0.519993i	$0.825934\pi$
$200$	3.31785	+	3.74058i	0.234607	+	0.264499i
$201$	1.62699	+	3.65428i	0.114759	+	0.257753i
$202$	9.50847	+	1.50599i	0.669014	+	0.105961i
$203$	2.06753	+	1.29226i	0.145112	+	0.0906985i
$204$	−7.45934	−	2.42369i	−0.522259	−	0.169692i
$205$	−3.76085	+	10.4958i	−0.262669	+	0.733055i
$206$	−1.05997	−	0.111407i	−0.0738516	−	0.00776212i
$207$	−0.127352	−	2.43001i	−0.00885155	−	0.168898i
$208$	−0.270148	−	1.00821i	−0.0187314	−	0.0699065i
$209$	2.85216	+	3.93055i	0.197288	+	0.271882i
$210$	−8.85653	+	3.27260i	−0.611159	+	0.225831i
$211$	5.63475	+	17.3420i	0.387912	+	1.19387i	0.934346	+	0.356368i	$0.115985\pi$
$211$	5.63475	+	17.3420i	0.387912	+	1.19387i	−0.546434	+	0.837502i	$0.684015\pi$
$212$	−1.62149	+	4.22413i	−0.111365	+	0.290115i
$213$	8.49620	−	3.26138i	0.582150	−	0.223466i
$214$	3.82731	+	18.0061i	0.261629	+	1.23087i
$215$	−14.1975	−	7.77734i	−0.968265	−	0.530410i
$216$	3.23911	+	4.45826i	0.220394	+	0.303346i
$217$	25.5412	+	9.29946i	1.73385	+	0.631289i
$218$	2.07002	−	4.06263i	0.140199	−	0.275156i
$219$	−12.1543	−	7.01728i	−0.821311	−	0.474184i
$220$	7.39578	−	0.549922i	0.498623	−	0.0370757i
$221$	−2.56477	−	4.44230i	−0.172525	−	0.298822i
$222$	−1.65530	−	2.54895i	−0.111097	−	0.171074i
$223$	−16.8094	+	2.66235i	−1.12564	+	0.178284i	−0.691371	−	0.722500i	$-0.742993\pi$
$223$	−16.8094	+	2.66235i	−1.12564	+	0.178284i	−0.434269	+	0.900783i	$0.642993\pi$
$224$	−2.62607	+	0.322142i	−0.175461	+	0.0215240i
$225$	−0.795752	−	2.12014i	−0.0530502	−	0.141343i
$226$	−5.08844	−	5.65128i	−0.338478	−	0.375918i
$227$	2.90243	+	7.56109i	0.192641	+	0.501847i	0.995548	−	0.0942575i	$-0.0300477\pi$
$227$	2.90243	+	7.56109i	0.192641	+	0.501847i	−0.802907	+	0.596105i	$0.796714\pi$
$228$	−1.81609	+	1.47064i	−0.120274	+	0.0973956i
$229$	26.0506	+	5.53723i	1.72147	+	0.365910i	0.959502	−	0.281701i	$-0.0908986\pi$
$229$	26.0506	+	5.53723i	1.72147	+	0.365910i	0.761971	+	0.647611i	$0.224232\pi$
$230$	5.21243	−	10.8240i	0.343697	−	0.713714i
$231$	−4.10393	+	13.3897i	−0.270019	+	0.880977i
$232$	0.651624	−	0.651624i	0.0427812	−	0.0427812i
$233$	9.97714	+	15.3634i	0.653624	+	1.00649i	0.997715	+	0.0675568i	$0.0215204\pi$
$233$	9.97714	+	15.3634i	0.653624	+	1.00649i	−0.344091	+	0.938936i	$0.611813\pi$
$234$	−0.0494143	+	0.470146i	−0.00323032	+	0.0307344i
$235$	24.7918	+	2.04422i	1.61724	+	0.133350i
$236$	−2.55037	+	2.29636i	−0.166015	+	0.149481i
$237$	3.45591	−	1.76087i	0.224485	−	0.114381i
$238$	−12.0561	+	4.86941i	−0.781481	+	0.315637i
$239$	−9.14792	+	12.5910i	−0.591730	+	0.814446i	−0.994920	−	0.100670i	$-0.967901\pi$
$239$	−9.14792	+	12.5910i	−0.591730	+	0.814446i	0.403190	+	0.915116i	$0.367901\pi$
$240$	0.452607	+	3.53986i	0.0292157	+	0.228497i
$241$	16.8410	−	9.72316i	1.08482	−	0.626324i	0.152631	−	0.988283i	$-0.451225\pi$
$241$	16.8410	−	9.72316i	1.08482	−	0.626324i	0.932194	+	0.361960i	$0.117892\pi$
$242$	6.00193	−	9.21829i	0.385818	−	0.592574i
$243$	−1.20722	−	4.50541i	−0.0774433	−	0.289022i
$244$	2.37885	+	7.32136i	0.152290	+	0.468702i
$245$	−7.76144	+	13.5926i	−0.495860	+	0.868402i
$246$	−6.43782	+	4.67735i	−0.410460	+	0.298217i
$247$	−1.52624	−	0.0799868i	−0.0971123	−	0.00508944i
$248$	5.59542	−	8.61619i	0.355309	−	0.547128i
$249$	5.90981	−	13.2737i	0.374519	−	0.841183i
$250$	1.58325	−	11.0677i	0.100134	−	0.699981i
$251$	−9.44419	+	3.06860i	−0.596112	+	0.193688i	−0.591505	−	0.806301i	$-0.701466\pi$
$251$	−9.44419	+	3.06860i	−0.596112	+	0.193688i	−0.00460618	+	0.999989i	$0.501466\pi$
$252$	1.16266	+	0.290023i	0.0732409	+	0.0182697i
$253$	−8.08035	−	15.8818i	−0.508008	−	0.998479i
$254$	−8.09605	−	4.67426i	−0.507991	−	0.293289i
$255$	6.65102	+	16.2279i	0.416503	+	1.01623i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−3.56472	+	4.40206i	−0.222361	+	0.274593i	−0.876102	−	0.482125i	$-0.839865\pi$
$257$	−3.56472	+	4.40206i	−0.222361	+	0.274593i	0.653741	+	0.756718i	$0.273198\pi$
$258$	−5.24544	−	10.2948i	−0.326567	−	0.640924i
$259$	−4.81812	−	1.47364i	−0.299383	−	0.0915673i
$260$	−1.32912	+	1.91852i	−0.0824288	+	0.118982i
$261$	−0.381290	+	0.169761i	−0.0236012	+	0.0105079i
$262$	11.1097	−	0.582237i	0.686363	−	0.0359707i
$263$	−4.57593	+	17.0776i	−0.282164	+	1.05305i	0.668723	+	0.743512i	$0.266841\pi$
$263$	−4.57593	+	17.0776i	−0.282164	+	1.05305i	−0.950887	+	0.309539i	$0.899825\pi$
$264$	4.58248	+	2.64931i	0.282032	+	0.163054i
$265$	9.54965	−	3.34168i	0.586630	−	0.205278i
$266$	−0.739624	+	3.80276i	−0.0453492	+	0.233162i
$267$	13.1299	−	2.07957i	0.803537	−	0.127268i
$268$	1.57733	−	1.94784i	0.0963506	−	0.118983i
$269$	12.2773	−	2.60962i	0.748560	−	0.159111i	0.182191	−	0.983263i	$-0.441681\pi$
$269$	12.2773	−	2.60962i	0.748560	−	0.159111i	0.566369	+	0.824152i	$0.308348\pi$
$270$	2.92125	−	11.9710i	0.177782	−	0.728534i
$271$	−20.5868	+	2.16376i	−1.25056	+	0.131439i	−0.706564	−	0.707649i	$-0.749756\pi$
$271$	−20.5868	+	2.16376i	−1.25056	+	0.131439i	−0.543995	+	0.839088i	$0.683089\pi$
$272$	0.768785	+	4.85392i	0.0466144	+	0.294312i
$273$	−2.46414	−	3.65413i	−0.149137	−	0.221158i
$274$		−	0.723464i		−	0.0437060i
$275$	−11.6313	−	11.8200i	−0.701392	−	0.712776i
$276$	7.42581	−	4.28729i	0.446981	−	0.258065i
$277$	−0.229486	−	4.37886i	−0.0137885	−	0.263100i	−0.996821	−	0.0796702i	$-0.974613\pi$
$277$	−0.229486	−	4.37886i	−0.0137885	−	0.263100i	0.983033	−	0.183430i	$-0.0587200\pi$
$278$	4.15909	−	10.8348i	0.249446	−	0.649828i
$279$	−3.76439	+	2.73499i	−0.225368	+	0.163739i
$280$	4.34641	+	4.01357i	0.259747	+	0.239857i
$281$	3.12517	−	9.61829i	0.186432	−	0.573779i	−0.813538	−	0.581512i	$-0.802461\pi$
$281$	3.12517	−	9.61829i	0.186432	−	0.573779i	0.999970	+	0.00773263i	$0.00246140\pi$
$282$	13.7981	+	11.1735i	0.821664	+	0.665371i
$283$	−14.0510	−	17.3515i	−0.835243	−	1.03144i	−0.998990	−	0.0449367i	$-0.985691\pi$
$283$	−14.0510	−	17.3515i	−0.835243	−	1.03144i	0.163747	−	0.986502i	$-0.447642\pi$
$284$	−4.23764	−	3.81559i	−0.251458	−	0.226414i
$285$	5.13432	+	0.971409i	0.304131	+	0.0575413i
$286$	1.06781	+	3.29300i	0.0631409	+	0.194719i
$287$	−3.19285	+	12.7997i	−0.188468	+	0.755543i
$288$	0.205617	−	0.403547i	0.0121161	−	0.0237792i
$289$	2.90879	+	6.53324i	0.171105	+	0.384308i
$290$	−2.05365	−	0.169334i	−0.120594	−	0.00994364i
$291$	2.03689	−	0.432955i	0.119405	−	0.0253803i
$292$	−0.460232	+	8.78175i	−0.0269330	+	0.513913i
$293$	−0.956585	+	6.03964i	−0.0558843	+	0.352840i	0.943863	+	0.330339i	$0.107163\pi$
$293$	−0.956585	+	6.03964i	−0.0558843	+	0.352840i	−0.999747	+	0.0225011i	$0.992837\pi$
$294$	−10.0422	+	4.89511i	−0.585671	+	0.285489i
$295$	7.60444	+	1.03001i	0.442748	+	0.0599695i
$296$	−0.952176	+	1.64922i	−0.0553441	+	0.0958588i
$297$	−11.4937	−	14.2107i	−0.666930	−	0.824586i
$298$	2.74215	−	10.2338i	0.158848	−	0.592830i
$299$	5.48531	+	1.16594i	0.317224	+	0.0674280i
$300$	5.38361	−	5.89016i	0.310823	−	0.340068i
$301$	−17.6306	−	7.48608i	−1.01621	−	0.431491i
$302$	−5.16796	−	10.1427i	−0.297383	−	0.583647i
$303$	0.804105	−	15.3432i	0.0461946	−	0.881446i
$304$	1.33765	+	0.595561i	0.0767196	+	0.0341578i
$305$	9.04873	−	14.6433i	0.518129	−	0.838474i
$306$	0.462769	−	2.17716i	0.0264547	−	0.124460i
$307$	−18.1202	−	18.1202i	−1.03418	−	1.03418i	−0.999395	−	0.0347821i	$-0.988926\pi$
$307$	−18.1202	−	18.1202i	−1.03418	−	1.03418i	−0.0347821	−	0.999395i	$-0.511074\pi$
$308$	8.64272	−	1.51768i	0.492465	−	0.0864781i
$309$			1.70099i			0.0967658i
$310$	−22.7870	+	2.91355i	−1.29422	+	0.165479i
$311$	−6.01981	−	0.632708i	−0.341352	−	0.0358776i	−0.0676984	−	0.997706i	$-0.521566\pi$
$311$	−6.01981	−	0.632708i	−0.341352	−	0.0358776i	−0.273654	+	0.961828i	$0.588232\pi$
$312$	−1.55517	+	0.596976i	−0.0880444	+	0.0337971i
$313$	5.82312	+	0.305177i	0.329142	+	0.0172496i	0.216192	−	0.976351i	$-0.430636\pi$
$313$	5.82312	+	0.305177i	0.329142	+	0.0172496i	0.112951	+	0.993601i	$0.463970\pi$
$314$	−1.49658	+	4.60599i	−0.0844568	+	0.259931i
$315$	−1.18635	−	2.40251i	−0.0668431	−	0.135366i
$316$	−1.96615	−	1.42849i	−0.110605	−	0.0803590i
$317$	12.9276	−	8.39526i	0.726084	−	0.471525i	−0.127924	−	0.991784i	$-0.540831\pi$
$317$	12.9276	−	8.39526i	0.726084	−	0.471525i	0.854008	+	0.520259i	$0.174165\pi$
$318$	6.97512	+	1.86898i	0.391145	+	0.104807i
$319$	−2.04646	+	2.27013i	−0.114580	+	0.127103i
$320$	1.84751	−	1.25964i	0.103279	−	0.0704161i
$321$	27.9411	−	9.07860i	1.55952	−	0.506718i
$322$	4.86324	−	13.3570i	0.271018	−	0.744356i
$323$	7.10731	+	1.12569i	0.395461	+	0.0626349i
$324$	5.52613	−	4.97575i	0.307007	−	0.276430i
$325$	5.19419	−	0.506791i	0.288122	−	0.0281117i
$326$	11.3333	+	5.04590i	0.627692	+	0.279466i
$327$	−6.79361	−	2.60782i	−0.375688	−	0.144213i
$328$	4.44263	+	2.26363i	0.245303	+	0.124988i
$329$	29.4292	−	0.510394i	1.62248	−	0.0281390i
$330$	−2.10663	−	11.6470i	−0.115966	−	0.641145i
$331$	17.2739	−	29.9192i	0.949458	−	1.64451i	0.202889	−	0.979202i	$-0.434967\pi$
$331$	17.2739	−	29.9192i	0.949458	−	1.64451i	0.746569	−	0.665308i	$-0.231700\pi$
$332$	−9.09165	+	0.476473i	−0.498969	+	0.0261499i
$333$	0.670290	−	0.542790i	0.0367317	−	0.0297447i
$334$	0.982039	+	9.34348i	0.0537348	+	0.511253i
$335$	−5.60306	+	0.125813i	−0.306128	+	0.00687389i
$336$	0.949399	+	4.11440i	0.0517939	+	0.224459i
$337$	1.46158	−	9.22805i	0.0796173	−	0.502684i	−0.915364	−	0.402626i	$-0.868097\pi$
$337$	1.46158	−	9.22805i	0.0796173	−	0.502684i	0.994982	−	0.100057i	$-0.0319026\pi$
$338$	11.1194	+	4.26836i	0.604818	+	0.232168i
$339$	−8.12095	+	9.01923i	−0.441069	+	0.489857i
$340$	7.16788	−	8.32941i	0.388733	−	0.451726i
$341$	−17.0543	+	29.4987i	−0.923543	+	1.59744i
$342$	−0.468933	−	0.468933i	−0.0253570	−	0.0253570i
$343$	−7.53855	+	16.9166i	−0.407043	+	0.913409i
$344$	−4.25532	+	5.85694i	−0.229431	+	0.315785i
$345$	−18.0496	−	6.46756i	−0.971759	−	0.348202i
$346$	−2.37195	−	11.1592i	−0.127517	−	0.599921i
$347$	18.0223	−	27.7518i	0.967486	−	1.48980i	0.0983930	−	0.995148i	$-0.468630\pi$
$347$	18.0223	−	27.7518i	0.967486	−	1.48980i	0.869093	−	0.494649i	$-0.164704\pi$
$348$	−1.14297	−	0.925562i	−0.0612699	−	0.0496154i
$349$	17.0080	+	12.3571i	0.910419	+	0.661458i	0.941121	−	0.338071i	$-0.109774\pi$
$349$	17.0080	+	12.3571i	0.910419	+	0.661458i	−0.0307021	+	0.999529i	$0.509774\pi$
$350$	0.561753	−	13.2168i	0.0300270	−	0.706469i
$351$	5.75192			0.307015
$352$	0.175536	−	3.31198i	0.00935608	−	0.176529i
$353$	28.5708	+	7.65553i	1.52067	+	0.407463i	0.919963	−	0.392005i	$-0.128218\pi$
$353$	28.5708	+	7.65553i	1.52067	+	0.407463i	0.600709	+	0.799468i	$0.294885\pi$
$354$	4.07029	+	3.66491i	0.216334	+	0.194788i
$355$	−0.381310	+	12.7450i	−0.0202378	+	0.676437i
$356$	−4.89597	−	6.73872i	−0.259486	−	0.357151i
$357$	9.74005	+	18.3233i	0.515498	+	0.969773i
$358$	17.0963	−	8.71101i	0.903569	−	0.460391i
$359$	−36.3168	+	3.81705i	−1.91673	+	0.201456i	−0.986294	−	0.165000i	$-0.947238\pi$
$359$	−36.3168	+	3.81705i	−1.91673	+	0.201456i	−0.930435	+	0.366456i	$0.880571\pi$
$360$	−0.985633	+	0.232745i	−0.0519474	+	0.0122667i
$361$	−11.2789	+	12.5264i	−0.593624	+	0.659287i
$362$	−23.3509	+	6.25686i	−1.22730	+	0.328853i
$363$	−15.6327	−	7.98854i	−0.820504	−	0.419289i
$364$	−1.33910	+	2.41516i	−0.0701880	+	0.126589i
$365$	15.6447	−	11.9121i	0.818879	−	0.623510i
$366$	11.2237	−	4.99713i	0.586674	−	0.261204i
$367$	11.7953	+	30.7279i	0.615712	+	1.60398i	0.785749	+	0.618546i	$0.212278\pi$
$367$	11.7953	+	30.7279i	0.615712	+	1.60398i	−0.170037	+	0.985438i	$0.554389\pi$
$368$	−4.50591	−	2.92617i	−0.234887	−	0.152537i
$369$	−1.51106	−	1.67821i	−0.0786629	−	0.0873640i
$370$	4.18982	−	0.760386i	0.217818	−	0.0395306i
$371$	10.8501	−	5.05800i	0.563308	−	0.262598i
$372$	−14.6092	−	7.44376i	−0.757452	−	0.385941i
$373$	30.7326	−	8.23479i	1.59128	−	0.426381i	0.648883	−	0.760888i	$-0.275236\pi$
$373$	30.7326	−	8.23479i	1.59128	−	0.426381i	0.942393	+	0.334507i	$0.108570\pi$
$374$	−3.37939	−	15.9451i	−0.174744	−	0.824502i
$375$	−17.8309	−	0.666619i	−0.920785	−	0.0344241i
$376$	2.31299	−	10.8817i	0.119283	−	0.561183i
$377$	−0.150470	−	0.950030i	−0.00774960	−	0.0489290i
$378$	2.03075	−	14.4378i	0.104451	−	0.742603i
$379$	4.29129	+	1.39433i	0.220429	+	0.0716217i	0.417149	−	0.908838i	$-0.363029\pi$
$379$	4.29129	+	1.39433i	0.220429	+	0.0716217i	−0.196721	+	0.980460i	$0.563029\pi$
$380$	−0.918193	−	3.14276i	−0.0471023	−	0.161220i
$381$	−6.06845	+	13.6300i	−0.310896	+	0.698284i
$382$	12.9067	+	15.9385i	0.660365	+	0.815483i
$383$	7.60745	−	4.94034i	0.388723	−	0.252439i	−0.335450	−	0.942058i	$-0.608888\pi$
$383$	7.60745	−	4.94034i	0.388723	−	0.252439i	0.724173	+	0.689619i	$0.242222\pi$
$384$	1.59596			0.0814435
$385$	−15.0849	−	12.5477i	−0.768798	−	0.639492i
$386$	1.28652			0.0654822
$387$	2.74990	−	1.78581i	0.139785	−	0.0907777i
$388$	−0.821133	−	1.01401i	−0.0416867	−	0.0514788i
$389$	11.5265	−	25.8890i	0.584418	−	1.31262i	−0.343259	−	0.939241i	$-0.611531\pi$
$389$	11.5265	−	25.8890i	0.584418	−	1.31262i	0.927677	−	0.373384i	$-0.121803\pi$
$390$	3.26684	+	1.78956i	0.165423	+	0.0906177i
$391$	−25.1113	−	8.15917i	−1.26994	−	0.412627i
$392$	5.58951	+	4.21396i	0.282313	+	0.212837i
$393$	−2.77750	−	17.5365i	−0.140106	−	0.884597i
$394$	3.44908	−	16.2266i	0.173762	−	0.817485i
$395$	0.406164	+	5.41911i	0.0204363	+	0.272665i
$396$	−0.611784	+	1.37191i	−0.0307433	+	0.0689410i
$397$	−0.882864	+	0.236563i	−0.0443097	+	0.0118727i	−0.280906	−	0.959735i	$-0.590635\pi$
$397$	−0.882864	+	0.236563i	−0.0443097	+	0.0118727i	0.236596	+	0.971608i	$0.423968\pi$
$398$	−0.584268	−	0.297699i	−0.0292867	−	0.0149223i
$399$	6.15920	+	0.539554i	0.308345	+	0.0270115i
$400$	−4.81984	−	1.33008i	−0.240992	−	0.0665041i
$401$	−6.38891	−	7.09561i	−0.319047	−	0.354338i	0.562193	−	0.827006i	$-0.309958\pi$
$401$	−6.38891	−	7.09561i	−0.319047	−	0.354338i	−0.881241	+	0.472668i	$0.843291\pi$
$402$	−3.35477	−	2.17862i	−0.167321	−	0.108659i
$403$	−3.84289	−	10.0111i	−0.191428	−	0.498687i
$404$	−8.79470	+	3.91565i	−0.437553	+	0.194811i
$405$	−16.4773	−	2.23182i	−0.818761	−	0.110900i
$406$	−2.43779	+	0.0422789i	−0.120985	+	0.00209827i
$407$	2.87074	−	5.62592i	0.142297	−	0.278867i
$408$	7.57597	−	2.02997i	0.375066	−	0.100499i
$409$	19.0333	−	21.1386i	0.941135	−	1.04524i	−0.0577646	−	0.998330i	$-0.518397\pi$
$409$	19.0333	−	21.1386i	0.941135	−	1.04524i	0.998899	−	0.0469057i	$-0.0149360\pi$
$410$	−2.56228	−	10.8508i	−0.126542	−	0.535882i
$411$	−1.14829	+	0.120691i	−0.0566412	+	0.00595323i
$412$	0.949642	−	0.483867i	0.0467855	−	0.0238384i
$413$	9.07429	+	0.317898i	0.446517	+	0.0156427i
$414$	1.43029	+	1.96862i	0.0702947	+	0.0967524i
$415$	13.9580	+	14.8189i	0.685170	+	0.727432i
$416$	0.775673	+	0.698419i	0.0380305	+	0.0342428i
$417$	−17.8910	−	4.79388i	−0.876127	−	0.234757i
$418$	−4.53276	−	1.74304i	−0.221704	−	0.0852547i
$419$	38.3664			1.87432			0.937162	−	0.348896i	$-0.113443\pi$
$419$	38.3664			1.87432			0.937162	+	0.348896i	$0.113443\pi$
$420$	5.64533	−	7.56825i	0.275464	−	0.369293i
$421$	30.6310	+	22.2547i	1.49286	+	1.08463i	0.973118	+	0.230306i	$0.0739727\pi$
$421$	30.6310	+	22.2547i	1.49286	+	1.08463i	0.519744	+	0.854322i	$0.326027\pi$
$422$	−14.1708	−	11.4753i	−0.689824	−	0.558609i
$423$	−2.74420	+	4.22570i	−0.133428	+	0.205461i
$424$	−0.940729	−	4.42578i	−0.0456858	−	0.214935i
$425$	−24.5714	−	0.183277i	−1.19189	−	0.00889026i
$426$	−5.34923	+	7.36259i	−0.259171	+	0.356719i
$427$	8.93050	−	18.3050i	0.432177	−	0.885843i
$428$	−13.0167	−	13.0167i	−0.629184	−	0.629184i
$429$	5.04857	−	2.24419i	0.243747	−	0.108351i
$430$	16.1429	−	1.20992i	0.778480	−	0.0583473i
$431$	8.08380	−	8.97797i	0.389383	−	0.432454i	−0.516301	−	0.856407i	$-0.672691\pi$
$431$	8.08380	−	8.97797i	0.389383	−	0.432454i	0.905684	+	0.423954i	$0.139358\pi$
$432$	−5.14469	−	1.97486i	−0.247524	−	0.0950156i
$433$	−2.06873	+	13.0614i	−0.0994168	+	0.627693i	0.886790	+	0.462173i	$0.152930\pi$
$433$	−2.06873	+	13.0614i	−0.0994168	+	0.627693i	−0.986206	+	0.165520i	$0.947070\pi$
$434$	−26.4855	+	6.11153i	−1.27134	+	0.293363i
$435$	0.0738259	+	3.28783i	0.00353968	+	0.157639i
$436$	0.476608	+	4.53462i	0.0228254	+	0.217169i
$437$	−6.11374	+	4.95081i	−0.292460	+	0.236829i
$438$	14.0153	−	0.734512i	0.669678	−	0.0350963i
$439$	16.4031	−	28.4110i	0.782878	−	1.35598i	−0.147380	−	0.989080i	$-0.547084\pi$
$439$	16.4031	−	28.4110i	0.782878	−	1.35598i	0.930258	−	0.366905i	$-0.119583\pi$
$440$	−5.90312	+	4.48923i	−0.281420	+	0.214016i
$441$	−1.67944	−	2.68901i	−0.0799734	−	0.128048i
$442$	4.57045	+	2.32876i	0.217394	+	0.110768i
$443$	10.9447	+	4.20126i	0.519996	+	0.199608i	0.604188	−	0.796842i	$-0.293497\pi$
$443$	10.9447	+	4.20126i	0.519996	+	0.199608i	−0.0841917	+	0.996450i	$0.526831\pi$
$444$	2.77651	+	1.23618i	0.131767	+	0.0586666i
$445$	−4.41552	+	18.0944i	−0.209316	+	0.857757i
$446$	12.6475	−	11.3879i	0.598877	−	0.539232i
$447$	−16.7008	−	2.64514i	−0.789919	−	0.125111i
$448$	2.02695	−	1.70043i	0.0957645	−	0.0803377i
$449$	17.5176	−	5.69182i	0.826708	−	0.268614i	0.135050	−	0.990839i	$-0.456881\pi$
$449$	17.5176	−	5.69182i	0.826708	−	0.268614i	0.691658	+	0.722225i	$0.256881\pi$
$450$	1.82208	+	1.34470i	0.0858939	+	0.0633898i
$451$	−15.1033	−	6.73511i	−0.711186	−	0.317144i
$452$	7.34544	+	1.96820i	0.345500	+	0.0925765i
$453$	−15.2365	+	9.89472i	−0.715875	+	0.464895i
$454$	−6.55225	−	4.76048i	−0.307512	−	0.223421i
$455$	6.05575	−	1.20785i	0.283898	−	0.0566249i
$456$	0.722133	−	2.22250i	0.0338170	−	0.104078i
$457$	−29.6329	−	1.55300i	−1.38617	−	0.0726461i	−0.655407	−	0.755276i	$-0.727503\pi$
$457$	−29.6329	−	1.55300i	−1.38617	−	0.0726461i	−0.730764	+	0.682630i	$0.760836\pi$
$458$	−24.8637	+	9.54427i	−1.16180	+	0.445974i
$459$	−26.9336	−	2.83083i	−1.25715	−	0.132132i
$460$	1.52367	+	11.9167i	0.0710414	+	0.555618i
$461$		−	8.81091i		−	0.410365i	−0.978724	−	0.205182i	$-0.934221\pi$
$461$		−	8.81091i		−	0.410365i	0.978724	−	0.205182i	$-0.0657788\pi$
$462$	−3.85070	−	13.4647i	−0.179151	−	0.626434i
$463$	−24.8683	−	24.8683i	−1.15573	−	1.15573i	−0.985384	−	0.170346i	$-0.945512\pi$
$463$	−24.8683	−	24.8683i	−1.15573	−	1.15573i	−0.170346	−	0.985384i	$-0.554488\pi$
$464$	−0.191598	+	0.901397i	−0.00889471	+	0.0418463i
$465$	8.42585	+	35.6819i	0.390739	+	1.65471i
$466$	−16.7351	−	7.45093i	−0.775237	−	0.345158i
$467$	−1.52726	+	29.1419i	−0.0706733	+	1.34853i	0.701297	+	0.712869i	$0.252604\pi$
$467$	−1.52726	+	29.1419i	−0.0706733	+	1.34853i	−0.771971	+	0.635658i	$0.780729\pi$
$468$	−0.214617	−	0.421210i	−0.00992070	−	0.0194705i
$469$	−6.58196	+	0.807416i	−0.303927	+	0.0372830i
$470$	−21.9055	+	11.7882i	−1.01043	+	0.543747i
$471$	7.56037	+	1.60701i	0.348364	+	0.0740470i
$472$	0.888231	−	3.31493i	0.0408842	−	0.152582i
$473$	13.0892	−	20.1296i	0.601842	−	0.925558i
$474$	−1.93933	+	3.35901i	−0.0890763	+	0.154285i
$475$	−4.03310	+	6.11017i	−0.185052	+	0.280354i
$476$	7.45902	−	10.6501i	0.341884	−	0.488144i
$477$	−0.320576	+	2.02404i	−0.0146782	+	0.0926743i
$478$	0.814524	−	15.5420i	0.0372555	−	0.710877i
$479$	40.2407	−	8.55343i	1.83865	−	0.390816i	0.848309	−	0.529501i	$-0.177621\pi$
$479$	40.2407	−	8.55343i	1.83865	−	0.390816i	0.990337	+	0.138685i	$0.0442877\pi$
$480$	−2.30753	−	2.72227i	−0.105324	−	0.124254i
$481$	0.808474	+	1.81586i	0.0368632	+	0.0827962i
$482$	−8.82844	+	17.3268i	−0.402125	+	0.789214i
$483$	−22.0117	−	5.49076i	−1.00157	−	0.249838i
$484$	−0.0129981	+	11.0000i	−0.000590825	+	0.500000i
$485$	−0.542386	+	2.86675i	−0.0246285	+	0.130172i
$486$	3.46628	+	3.12106i	0.157234	+	0.141574i
$487$	3.26660	+	4.03391i	0.148024	+	0.182794i	0.845765	−	0.533556i	$-0.179145\pi$
$487$	3.26660	+	4.03391i	0.148024	+	0.182794i	−0.697741	+	0.716350i	$0.745811\pi$
$488$	−5.98257	−	4.84459i	−0.270818	−	0.219304i
$489$	6.11828	−	18.8301i	0.276678	−	0.851528i
$490$	−0.893792	−	15.6269i	−0.0403774	−	0.705953i
$491$	28.0351	−	20.3687i	1.26521	−	0.919227i	0.266206	−	0.963916i	$-0.414230\pi$
$491$	28.0351	−	20.3687i	1.26521	−	0.919227i	0.999001	+	0.0446892i	$0.0142297\pi$
$492$	2.85174	−	7.42904i	0.128566	−	0.334927i
$493$	0.237020	+	4.52260i	0.0106748	+	0.203688i
$494$	1.32358	−	0.764167i	0.0595505	−	0.0343815i
$495$	3.22465	−	0.940050i	0.144937	−	0.0422521i
$496$			10.2736i			0.461299i
$497$	1.05072	+	15.0503i	0.0471314	+	0.675096i
$498$	2.27296	+	14.3509i	0.101854	+	0.643081i
$499$	−6.72494	+	0.706819i	−0.301050	+	0.0316416i	−0.253849	−	0.967244i	$-0.581697\pi$
$499$	−6.72494	+	0.706819i	−0.301050	+	0.0316416i	−0.0472005	+	0.998885i	$0.515030\pi$
$500$	4.70006	+	10.1444i	0.210193	+	0.453673i
$501$	14.6663	−	3.11742i	0.655242	−	0.139276i
$502$	6.24928	−	7.71722i	0.278919	−	0.344436i
$503$	−41.9732	+	6.64790i	−1.87149	+	0.296415i	−0.985809	−	0.167873i	$-0.946310\pi$
$503$	−41.9732	+	6.64790i	−1.87149	+	0.296415i	−0.885684	+	0.464289i	$0.846310\pi$
$504$	−1.13305	+	0.389998i	−0.0504700	+	0.0173719i
$505$	19.3949	+	9.33984i	0.863062	+	0.415618i
$506$	15.4266	+	8.91870i	0.685796	+	0.396485i
$507$	4.91983	−	18.3610i	0.218497	−	0.815443i
$508$	9.33570	−	0.489263i	0.414205	−	0.0217076i
$509$	9.17317	−	4.08416i	0.406594	−	0.181027i	−0.193241	−	0.981151i	$-0.561900\pi$
$509$	9.17317	−	4.08416i	0.406594	−	0.181027i	0.599834	+	0.800124i	$0.295233\pi$
$510$	−14.4164	−	9.98745i	−0.638367	−	0.442252i
$511$	17.0176	−	15.8656i	0.752815	−	0.701854i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	−5.07799	+	6.27080i	−0.224199	+	0.276863i
$514$	0.592090	−	5.63336i	0.0261160	−	0.248477i
$515$	−2.19839	−	0.920224i	−0.0968727	−	0.0405499i
$516$	10.0061	+	5.77704i	0.440495	+	0.254320i
$517$	−5.79349	+	36.4393i	−0.254797	+	1.60260i
$518$	4.84342	−	1.38824i	0.212807	−	0.0609958i
$519$	−17.3163	+	5.62642i	−0.760103	+	0.246972i
$520$	0.0697963	−	2.33290i	0.00306077	−	0.102304i
$521$	−12.4854	+	28.0426i	−0.546995	+	1.22857i	0.402682	+	0.915340i	$0.368078\pi$
$521$	−12.4854	+	28.0426i	−0.546995	+	1.22857i	−0.949677	+	0.313231i	$0.898589\pi$
$522$	0.227318	−	0.350039i	0.00994943	−	0.0153208i
$523$	23.8437	+	1.24960i	1.04261	+	0.0546410i	0.565945	−	0.824443i	$-0.308511\pi$
$523$	23.8437	+	1.24960i	1.04261	+	0.0546410i	0.476667	+	0.879084i	$0.341845\pi$
$524$	−9.00031	+	6.53911i	−0.393180	+	0.285662i
$525$	−21.0717	+	1.31325i	−0.919644	+	0.0573149i
$526$	−5.46344	−	16.8147i	−0.238217	−	0.733157i
$527$	13.0675	+	48.7685i	0.569229	+	2.12439i
$528$	−5.28611	+	0.273902i	−0.230048	+	0.0119200i
$529$	5.07987	−	2.93286i	0.220864	−	0.127516i
$530$	−6.18900	+	8.00368i	−0.268833	+	0.347658i
$531$	−0.913611	+	1.25748i	−0.0396474	+	0.0545699i
$532$	−1.45083	−	3.59209i	−0.0629015	−	0.155737i
$533$	4.63709	−	2.36271i	0.200855	−	0.102341i
$534$	−9.87905	+	8.89514i	−0.427508	+	0.384930i
$535$	−3.38257	+	41.0231i	−0.146241	+	1.77358i
$536$	−0.261990	+	2.49267i	−0.0113162	+	0.107667i
$537$	−16.6783	−	25.6824i	−0.719723	−	1.10828i
$538$	−8.87531	+	8.87531i	−0.382642	+	0.382642i
$539$	−19.2367	−	12.9981i	−0.828582	−	0.559868i
$540$	4.06993	+	11.6308i	0.175142	+	0.500509i
$541$	28.9078	+	6.14453i	1.24284	+	0.264174i	0.781983	−	0.623299i	$-0.214208\pi$
$541$	28.9078	+	6.14453i	1.24284	+	0.264174i	0.460859	+	0.887474i	$0.347542\pi$
$542$	16.0871	−	13.0271i	0.690999	−	0.559560i
$543$	13.8265	+	36.0192i	0.593351	+	1.54573i
$544$	−3.28839	−	3.65213i	−0.140989	−	0.156584i
$545$	7.04571	−	7.36939i	0.301805	−	0.315670i
$546$	4.05678	+	1.72254i	0.173614	+	0.0737178i
$547$	8.11698	−	1.28560i	0.347057	−	0.0549684i	0.0195274	−	0.999809i	$-0.493784\pi$
$547$	8.11698	−	1.28560i	0.347057	−	0.0549684i	0.327530	+	0.944841i	$0.393784\pi$
$548$	0.394026	+	0.606748i	0.0168320	+	0.0259190i
$549$	1.74328	+	3.01946i	0.0744016	+	0.128867i
$550$	16.1925	+	3.57828i	0.690449	+	0.152579i
$551$	1.16857	+	0.674675i	0.0497828	+	0.0287421i
$552$	−3.89278	+	7.64001i	−0.165688	+	0.325181i
$553$	1.11584	+	6.33240i	0.0474504	+	0.269281i
$554$	2.57736	+	3.54743i	0.109502	+	0.150716i
$555$	−1.90586	−	6.52331i	−0.0808991	−	0.276899i
$556$	2.41295	+	11.3520i	0.102332	+	0.481433i
$557$	−7.16772	+	2.75143i	−0.303706	+	0.116582i	−0.505448	−	0.862857i	$-0.668673\pi$
$557$	−7.16772	+	2.75143i	−0.303706	+	0.116582i	0.201743	+	0.979439i	$0.435340\pi$
$558$	1.66750	−	4.34398i	0.0705909	−	0.183896i
$559$	2.33508	+	7.18662i	0.0987632	+	0.303962i
$560$	−5.83115	−	0.998841i	−0.246411	−	0.0422087i
$561$	−24.7446	+	8.02385i	−1.04472	+	0.338767i
$562$	2.61751	+	9.76867i	0.110413	+	0.412066i
$563$	2.24190	+	42.7780i	0.0944848	+	1.80288i	0.476975	+	0.878917i	$0.341733\pi$
$563$	2.24190	+	42.7780i	0.0944848	+	1.80288i	−0.382490	+	0.923960i	$0.624933\pi$
$564$	−17.6576	−	1.85588i	−0.743517	−	0.0781468i
$565$	−7.26325	−	15.3750i	−0.305567	−	0.646832i
$566$	21.2344	+	6.89948i	0.892550	+	0.290007i
$567$	−19.6621	−	0.688819i	−0.825731	−	0.0289277i
$568$	5.63210	+	0.892038i	0.236318	+	0.0374291i
$569$	−0.160825	−	0.361219i	−0.00674213	−	0.0151431i	0.910143	−	0.414294i	$-0.135972\pi$
$569$	−0.160825	−	0.361219i	−0.00674213	−	0.0151431i	−0.916885	+	0.399151i	$0.869305\pi$
$570$	−4.83507	+	1.98166i	−0.202519	+	0.0830025i
$571$	0.0383424	+	0.0664110i	0.00160458	+	0.00277921i	0.866827	−	0.498610i	$-0.166156\pi$
$571$	0.0383424	+	0.0664110i	0.00160458	+	0.00277921i	−0.865222	+	0.501389i	$0.832823\pi$
$572$	−2.68903	−	2.18017i	−0.112434	−	0.0911575i
$573$	23.1447	−	23.1447i	0.966883	−	0.966883i
$574$	−4.29347	−	12.4737i	−0.179206	−	0.520642i
$575$	18.1235	−	19.8288i	0.755804	−	0.826917i
$576$	0.0473421	+	0.450430i	0.00197259	+	0.0187679i
$577$	−37.9074	−	24.6173i	−1.57810	−	1.02483i	−0.973609	−	0.228224i	$-0.926708\pi$
$577$	−37.9074	−	24.6173i	−1.57810	−	1.02483i	−0.604495	−	0.796609i	$-0.706625\pi$
$578$	−5.99777	−	3.89500i	−0.249475	−	0.162011i
$579$	−0.214622	−	2.04199i	−0.00891938	−	0.0848622i
$580$	1.81456	−	0.976480i	0.0753454	−	0.0405461i
$581$	18.1771	+	15.8047i	0.754114	+	0.655689i
$582$	−1.47248	+	1.47248i	−0.0610361	+	0.0610361i
$583$	3.87543	+	14.4975i	0.160504	+	0.600427i
$584$	−4.39690	−	7.61566i	−0.181945	−	0.315138i
$585$	−0.408162	+	0.975089i	−0.0168754	+	0.0403150i
$586$	−2.48717	−	5.58626i	−0.102744	−	0.230766i
$587$	14.0039	+	2.21800i	0.578002	+	0.0915466i	0.438589	−	0.898688i	$-0.355478\pi$
$587$	14.0039	+	2.21800i	0.578002	+	0.0915466i	0.139413	+	0.990234i	$0.455478\pi$
$588$	5.75600	−	9.57475i	0.237374	−	0.394856i
$589$	14.3068	+	4.64857i	0.589502	+	0.191541i
$590$	−6.93860	+	3.27784i	−0.285658	+	0.134946i
$591$	−26.3306	−	2.76745i	−1.08309	−	0.113838i
$592$	−0.0996661	−	1.90174i	−0.00409625	−	0.0781611i
$593$	5.21522	+	19.4635i	0.214163	+	0.799269i	0.986459	+	0.164006i	$0.0524416\pi$
$593$	5.21522	+	19.4635i	0.214163	+	0.799269i	−0.772296	+	0.635263i	$0.780892\pi$
$594$	17.3791	+	5.65816i	0.713072	+	0.232157i
$595$	−28.9507	+	2.67544i	−1.18686	+	0.109682i
$596$	3.27398	+	10.0763i	0.134108	+	0.412741i
$597$	−0.375044	+	0.977024i	−0.0153495	+	0.0399869i
$598$	−5.23538	+	2.00968i	−0.214091	+	0.0821817i
$599$	−6.55217	−	30.8255i	−0.267714	−	1.25950i	−0.882315	−	0.470659i	$-0.844016\pi$
$599$	−6.55217	−	30.8255i	−0.267714	−	1.25950i	0.614601	−	0.788838i	$-0.289317\pi$
$600$	−1.30707	+	7.87203i	−0.0533608	+	0.321374i
$601$	0.442779	+	0.609433i	0.0180613	+	0.0248593i	0.817952	−	0.575286i	$-0.195109\pi$
$601$	0.442779	+	0.609433i	0.0180613	+	0.0248593i	−0.799891	+	0.600146i	$0.795109\pi$
$602$	18.8635	−	3.32397i	0.768819	−	0.135475i
$603$	0.515359	−	1.01145i	0.0209870	−	0.0411894i
$604$	9.85833	+	5.69171i	0.401130	+	0.231592i
$605$	18.7817	−	15.8823i	0.763586	−	0.645706i
$606$	7.68215	+	13.3059i	0.312066	+	0.540514i
$607$	−13.3753	−	20.5962i	−0.542888	−	0.835974i	0.455643	−	0.890163i	$-0.349410\pi$
$607$	−13.3753	−	20.5962i	−0.542888	−	0.835974i	−0.998531	+	0.0541884i	$0.982743\pi$
$608$	−1.44622	+	0.229058i	−0.0586518	+	0.00928953i
$609$	0.473785	+	3.86224i	0.0191987	+	0.156506i
$610$	0.386421	+	17.2092i	0.0156457	+	0.696780i
$611$	−7.76981	−	8.62925i	−0.314333	−	0.349102i
$612$	0.797654	+	2.07796i	0.0322432	+	0.0839965i
$613$	25.4892	−	20.6407i	1.02950	−	0.833671i	0.0432699	−	0.999063i	$-0.486222\pi$
$613$	25.4892	−	20.6407i	1.02950	−	0.833671i	0.986228	+	0.165393i	$0.0528891\pi$
$614$	25.0659	+	5.32792i	1.01158	+	0.215017i
$615$	−16.7951	+	5.87706i	−0.677244	+	0.236986i
$616$	−6.42181	+	5.98000i	−0.258742	+	0.240941i
$617$	6.63131	−	6.63131i	0.266966	−	0.266966i	−0.560910	−	0.827877i	$-0.689549\pi$
$617$	6.63131	−	6.63131i	0.266966	−	0.266966i	0.827877	+	0.560910i	$0.189549\pi$
$618$	−0.926424	−	1.42657i	−0.0372663	−	0.0573850i
$619$	1.98212	−	18.8586i	0.0796680	−	0.757990i	−0.879642	−	0.475636i	$-0.842218\pi$
$619$	1.98212	−	18.8586i	0.0796680	−	0.757990i	0.959310	−	0.282354i	$-0.0911154\pi$
$620$	17.5240	−	14.8542i	0.703779	−	0.596559i
$621$	22.0025	−	19.8111i	0.882930	−	0.794994i
$622$	5.39324	−	2.74799i	0.216249	−	0.110184i
$623$	−3.06951	+	21.8230i	−0.122977	+	0.874321i
$624$	0.979143	−	1.34767i	0.0391971	−	0.0539502i
$625$	10.5080	−	22.6844i	0.420319	−	0.907376i
$626$	−5.04989	+	2.91556i	−0.201834	+	0.116529i
$627$	−2.01041	+	7.48525i	−0.0802879	+	0.298932i
$628$	−1.25347	−	4.67800i	−0.0500188	−	0.186673i
$629$	−2.89202	−	8.90073i	−0.115313	−	0.354895i
$630$	2.30346	+	1.36879i	0.0917720	+	0.0545337i
$631$	−10.3967	+	7.55364i	−0.413886	+	0.300705i	−0.775173	−	0.631749i	$-0.782337\pi$
$631$	−10.3967	+	7.55364i	−0.413886	+	0.300705i	0.361287	+	0.932455i	$0.382337\pi$
$632$	2.42697	+	0.127192i	0.0965395	+	0.00505942i
$633$	−15.8498	+	24.4065i	−0.629972	+	0.970071i
$634$	−6.26958	+	14.0817i	−0.248997	+	0.559256i
$635$	−14.3327	−	15.2167i	−0.568774	−	0.603857i
$636$	−6.86774	+	2.23146i	−0.272324	+	0.0884833i
$637$	6.98762	−	2.13462i	0.276860	−	0.0845768i
$638$	0.479908	−	3.01847i	0.0189997	−	0.119503i
$639$	−2.23663	−	1.29132i	−0.0884797	−	0.0510838i
$640$	−0.863405	+	2.06265i	−0.0341291	+	0.0815335i
$641$	−1.03313	+	9.82957i	−0.0408062	+	0.388245i	0.954989	+	0.296640i	$0.0958662\pi$
$641$	−1.03313	+	9.82957i	−0.0408062	+	0.388245i	−0.995795	+	0.0916045i	$0.970800\pi$
$642$	−18.4888	+	22.8317i	−0.729694	+	0.901097i
$643$	9.33470	+	18.3204i	0.368124	+	0.722485i	0.998554	−	0.0537617i	$-0.0171211\pi$
$643$	9.33470	+	18.3204i	0.368124	+	0.722485i	−0.630429	+	0.776247i	$0.717121\pi$
$644$	3.19608	+	13.8508i	0.125943	+	0.545799i
$645$	−4.61341	−	25.4205i	−0.181653	−	1.00093i
$646$	−6.57378	+	2.92684i	−0.258642	+	0.115155i
$647$	−39.7955	+	2.08560i	−1.56452	+	0.0819932i	−0.814794	−	0.579750i	$-0.803150\pi$
$647$	−39.7955	+	2.08560i	−1.56452	+	0.0819932i	−0.749730	+	0.661744i	$0.769817\pi$
$648$	−1.92461	+	7.18276i	−0.0756060	+	0.282165i
$649$	−2.37307	+	11.1321i	−0.0931512	+	0.436972i
$650$	−4.08020	+	3.25399i	−0.160039	+	0.127632i
$651$	14.1187	+	41.0187i	0.553356	+	1.60765i
$652$	−12.2531	+	1.94070i	−0.479868	+	0.0760035i
$653$	−26.6742	+	32.9399i	−1.04384	+	1.28904i	−0.0876961	+	0.996147i	$0.527950\pi$
$653$	−26.6742	+	32.9399i	−1.04384	+	1.28904i	−0.956146	+	0.292890i	$0.905383\pi$
$654$	7.11792	−	1.51296i	0.278333	−	0.0591615i
$655$	24.1671	+	5.89741i	0.944286	+	0.230431i
$656$	−4.95876	+	0.521187i	−0.193607	+	0.0203489i
$657$	0.623049	+	3.93378i	0.0243074	+	0.153471i
$658$	−24.4034	+	16.4563i	−0.951344	+	0.641534i
$659$		−	41.3001i		−	1.60882i	−0.594073	−	0.804411i	$-0.702481\pi$
$659$		−	41.3001i		−	1.60882i	0.594073	−	0.804411i	$-0.297519\pi$
$660$	8.11017	+	8.62062i	0.315688	+	0.335557i
$661$	−18.2894	+	10.5594i	−0.711375	+	0.410712i	−0.811570	−	0.584255i	$-0.801387\pi$
$661$	−18.2894	+	10.5594i	−0.711375	+	0.410712i	0.100195	+	0.994968i	$0.468053\pi$
$662$	1.80809	+	34.5004i	0.0702734	+	1.34090i
$663$	2.93379	−	7.64278i	0.113939	−	0.296821i
$664$	7.36539	−	5.35127i	0.285833	−	0.207670i
$665$	−4.02942	+	7.66838i	−0.156254	+	0.297367i
$666$	−0.266528	+	0.820288i	−0.0103277	+	0.0317855i
$667$	−3.84774	−	3.11584i	−0.148985	−	0.120646i
$668$	−5.91243	−	7.30125i	−0.228759	−	0.282494i
$669$	−20.1849	−	18.1746i	−0.780395	−	0.702671i
$670$	4.63060	−	3.15716i	0.178896	−	0.121972i
$671$	20.6468	+	15.0194i	0.797061	+	0.579818i
$672$	−3.03709	−	2.93354i	−0.117158	−	0.113164i
$673$	−7.84874	+	15.4040i	−0.302547	+	0.593782i	−0.991362	−	0.131156i	$-0.958131\pi$
$673$	−7.84874	+	15.4040i	−0.302547	+	0.593782i	0.688815	+	0.724937i	$0.258131\pi$
$674$	3.80017	+	8.53532i	0.146377	+	0.328768i
$675$	13.9544	−	23.7586i	0.537104	−	0.914471i
$676$	−11.6503	+	2.47634i	−0.448087	+	0.0952439i
$677$	2.10168	−	40.1025i	0.0807742	−	1.54126i	−0.594741	−	0.803918i	$-0.702745\pi$
$677$	2.10168	−	40.1025i	0.0807742	−	1.54126i	0.675515	−	0.737346i	$-0.263921\pi$
$678$	1.89858	−	11.9871i	0.0729144	−	0.460364i
$679$	−0.301260	+	3.43899i	−0.0115613	+	0.131976i
$680$	−1.47497	+	10.8895i	−0.0565626	+	0.417595i
$681$	−6.46286	+	11.1940i	−0.247657	+	0.428955i
$682$	−1.76318	−	34.0281i	−0.0675156	−	1.30300i
$683$	−8.70817	+	32.4993i	−0.333209	+	1.24355i	0.572589	+	0.819842i	$0.305939\pi$
$683$	−8.70817	+	32.4993i	−0.333209	+	1.24355i	−0.905798	+	0.423709i	$0.860728\pi$
$684$	0.648680	+	0.137881i	0.0248029	+	0.00527202i
$685$	0.465237	−	1.54937i	0.0177758	−	0.0591984i
$686$	−2.89107	−	18.2932i	−0.110381	−	0.698438i
$687$	19.2967	+	37.8718i	0.736214	+	1.44490i
$688$	0.378890	−	7.22965i	0.0144451	−	0.275628i
$689$	−4.31441	−	1.92090i	−0.164366	−	0.0731804i
$690$	18.6602	−	4.40637i	0.710380	−	0.167748i
$691$	2.84204	−	13.3708i	0.108116	−	0.508648i	−0.890448	−	0.455085i	$-0.849609\pi$
$691$	2.84204	−	13.3708i	0.108116	−	0.508648i	0.998564	−	0.0535629i	$-0.0170578\pi$
$692$	8.06701	+	8.06701i	0.306662	+	0.306662i
$693$	3.68593	−	1.48620i	0.140017	−	0.0564561i
$694$			33.0903i			1.25609i
$695$	15.8746	−	20.5293i	0.602159	−	0.778719i
$696$	1.46268	+	0.153733i	0.0554426	+	0.00582725i
$697$	−22.8762	+	8.78134i	−0.866496	+	0.332617i
$698$	−20.9943	−	1.10026i	−0.794645	−	0.0416456i
$699$	−9.03445	+	27.8052i	−0.341714	+	1.05169i
$700$	6.72727	+	11.3905i	0.254267	+	0.430521i
$701$	−24.0897	−	17.5022i	−0.909854	−	0.661048i	0.0311237	−	0.999516i	$-0.490091\pi$
$701$	−24.0897	−	17.5022i	−0.909854	−	0.661048i	−0.940978	+	0.338468i	$0.890091\pi$
$702$	−4.82397	+	3.13272i	−0.182069	+	0.118237i
$703$	−2.69342	−	0.721699i	−0.101584	−	0.0272194i
$704$	1.65662	+	2.87326i	0.0624360	+	0.108290i
$705$	22.3647	+	32.8023i	0.842304	+	1.23540i
$706$	−28.1310	+	9.14032i	−1.05873	+	0.344001i
$707$	23.9336	+	8.71415i	0.900115	+	0.327729i
$708$	−5.40968	−	0.856810i	−0.203308	−	0.0322009i
$709$	12.9108	−	11.6249i	0.484874	−	0.436583i	−0.390085	−	0.920779i	$-0.627554\pi$
$709$	12.9108	−	11.6249i	0.484874	−	0.436583i	0.874960	+	0.484196i	$0.160888\pi$
$710$	−6.62166	−	10.8966i	−0.248506	−	0.408941i
$711$	−1.00555	−	0.447698i	−0.0377109	−	0.0167900i
$712$	7.77627	+	2.98503i	0.291428	+	0.111869i
$713$	−49.1808	−	25.0589i	−1.84184	−	0.938462i
$714$	−18.1483	−	10.0624i	−0.679183	−	0.376576i
$715$	0.169198	+	7.73897i	0.00632766	+	0.289421i
$716$	−9.59383	+	16.6170i	−0.358538	+	0.621006i
$717$	−24.8045	+	1.29995i	−0.926341	+	0.0485475i
$718$	28.3789	−	22.9808i	1.05909	−	0.857636i
$719$	1.45874	+	13.8790i	0.0544017	+	0.517598i	0.987460	+	0.157872i	$0.0504632\pi$
$719$	1.45874	+	13.8790i	0.0544017	+	0.517598i	−0.933058	+	0.359726i	$0.882870\pi$
$720$	0.699859	−	0.732011i	0.0260822	−	0.0272804i
$721$	−2.69656	−	0.824750i	−0.100425	−	0.0307153i
$722$	2.63686	−	16.6485i	0.0981337	−	0.619592i
$723$	28.9742	+	11.1221i	1.07756	+	0.413637i
$724$	16.1760	−	17.9653i	0.601177	−	0.667674i
$725$	−4.28920	−	1.68328i	−0.159297	−	0.0625155i
$726$	17.4615	−	1.81442i	0.648059	−	0.0673396i
$727$	−8.56078	−	8.56078i	−0.317502	−	0.317502i	0.530305	−	0.847807i	$-0.322077\pi$
$727$	−8.56078	−	8.56078i	−0.317502	−	0.317502i	−0.847807	+	0.530305i	$0.822077\pi$
$728$	−0.192328	−	2.75485i	−0.00712817	−	0.102102i
$729$	17.4881	−	24.0703i	0.647707	−	0.891492i
$730$	−6.63291	+	18.5111i	−0.245495	+	0.685125i
$731$	−7.39715	−	34.8008i	−0.273593	−	1.28716i
$732$	−6.69139	+	10.3038i	−0.247321	+	0.380841i
$733$	35.7869	+	28.9797i	1.32182	+	1.07039i	0.991986	+	0.126350i	$0.0403263\pi$
$733$	35.7869	+	28.9797i	1.32182	+	1.07039i	0.329834	+	0.944039i	$0.393007\pi$
$734$	−26.6280	−	19.3464i	−0.982858	−	0.714088i
$735$	−24.6542	+	4.02558i	−0.909385	+	0.148486i
$736$	5.37268			0.198040
$737$	0.439962	−	8.30113i	0.0162062	−	0.305776i
$738$	2.18130	+	0.584478i	0.0802948	+	0.0215149i
$739$	−13.9901	−	12.5968i	−0.514636	−	0.463380i	0.370421	−	0.928864i	$-0.379214\pi$
$739$	−13.9901	−	12.5968i	−0.514636	−	0.463380i	−0.885056	+	0.465484i	$0.845880\pi$
$740$	−3.09974	+	2.91965i	−0.113949	+	0.107329i
$741$	−1.43370	−	1.97332i	−0.0526684	−	0.0724918i
$742$	−6.34486	+	10.1514i	−0.232927	+	0.372669i
$743$	18.8182	−	9.58836i	0.690374	−	0.351763i	−0.0733500	−	0.997306i	$-0.523369\pi$
$743$	18.8182	−	9.58836i	0.690374	−	0.351763i	0.763724	+	0.645543i	$0.223369\pi$
$744$	16.3065	−	1.71388i	0.597824	−	0.0628339i
$745$	12.4536	−	20.1534i	0.456266	−	0.738364i
$746$	−21.2896	+	23.6445i	−0.779467	+	0.865686i
$747$	−3.98286	+	1.06720i	−0.145725	+	0.0390469i
$748$	11.5185	+	11.5321i	0.421159	+	0.421657i
$749$	0.844551	+	48.6965i	0.0308592	+	1.77933i
$750$	15.3173	−	9.15234i	0.559310	−	0.334196i
$751$	−22.8195	+	10.1599i	−0.832694	+	0.370739i	−0.778387	−	0.627785i	$-0.783962\pi$
$751$	−22.8195	+	10.1599i	−0.832694	+	0.370739i	−0.0543072	+	0.998524i	$0.517295\pi$
$752$	3.98679	+	10.3859i	0.145383	+	0.378736i
$753$	−13.2914	−	8.63155i	−0.484367	−	0.314551i
$754$	0.643618	+	0.714810i	0.0234392	+	0.0260318i
$755$	−4.54527	−	25.0450i	−0.165419	−	0.911481i
$756$	6.16028	+	13.2146i	0.224047	+	0.480611i
$757$	−29.4112	−	14.9857i	−1.06897	−	0.544666i	−0.171245	−	0.985228i	$-0.554779\pi$
$757$	−29.4112	−	14.9857i	−1.06897	−	0.544666i	−0.897722	+	0.440562i	$0.854779\pi$
$758$	−4.35838	+	1.16783i	−0.158304	+	0.0424173i
$759$	11.5824	−	25.9732i	0.420415	−	0.942768i
$760$	2.48173	+	2.13566i	0.0900219	+	0.0774684i
$761$	−0.477924	+	2.24846i	−0.0173247	+	0.0815064i	−0.985961	−	0.166978i	$-0.946599\pi$
$761$	−0.477924	+	2.24846i	−0.0173247	+	0.0815064i	0.968636	+	0.248484i	$0.0799325\pi$
$762$	−2.33398	−	14.7362i	−0.0845512	−	0.533835i
$763$	7.42814	−	9.50539i	0.268917	−	0.344118i
$764$	−19.5052	−	6.33763i	−0.705674	−	0.229287i
$765$	2.39113	−	4.36501i	0.0864514	−	0.157817i
$766$	−3.68945	+	8.28663i	−0.133305	+	0.299408i
$767$	−2.25428	−	2.78380i	−0.0813972	−	0.100517i
$768$	−1.33848	+	0.869222i	−0.0482984	+	0.0313654i
$769$	−17.3647			−0.626188			−0.313094	−	0.949722i	$-0.601365\pi$
$769$	−17.3647			−0.626188			−0.313094	+	0.949722i	$0.601365\pi$
$770$	19.4853	+	2.30759i	0.702200	+	0.0831598i
$771$	−9.04015			−0.325573
$772$	−1.07897	+	0.700690i	−0.0388329	+	0.0252184i
$773$	−2.94113	−	3.63200i	−0.105785	−	0.130634i	0.721504	−	0.692411i	$-0.243451\pi$
$773$	−2.94113	−	3.63200i	−0.105785	−	0.130634i	−0.827289	+	0.561777i	$0.810118\pi$
$774$	−1.33364	+	2.99541i	−0.0479368	+	0.107668i
$775$	−50.6743	−	8.41395i	−1.82028	−	0.302238i
$776$	1.24093	+	0.403203i	0.0445469	+	0.0144741i
$777$	−3.01143	−	7.45596i	−0.108035	−	0.267481i
$778$	4.43320	+	27.9901i	0.158938	+	1.00350i
$779$	−1.51793	+	7.14129i	−0.0543854	+	0.255863i
$780$	−3.71446	+	0.278400i	−0.132999	+	0.00996832i
$781$	−18.8076	−	1.98800i	−0.672990	−	0.0711362i
$782$	25.5039	−	6.83376i	0.912019	−	0.244375i
$783$	−4.52481	−	2.30550i	−0.161703	−	0.0823920i
$784$	−6.98284	−	0.489858i	−0.249387	−	0.0174949i
$785$	−6.16704	+	8.90180i	−0.220111	+	0.317719i
$786$	11.8804	+	13.1946i	0.423762	+	0.470635i
$787$	−6.16259	−	4.00203i	−0.219673	−	0.142657i	0.430112	−	0.902776i	$-0.358474\pi$
$787$	−6.16259	−	4.00203i	−0.219673	−	0.142657i	−0.649784	+	0.760119i	$0.725141\pi$
$788$	5.94501	+	15.4873i	0.211782	+	0.551712i
$789$	−25.7772	+	11.4767i	−0.917693	+	0.408583i
$790$	−3.29209	−	4.32363i	−0.117127	−	0.153828i
$791$	−10.3605	−	17.2472i	−0.368377	−	0.613238i
$792$	−0.234109	−	1.48378i	−0.00831871	−	0.0527239i
$793$	−7.76130	+	2.07963i	−0.275612	+	0.0738500i
$794$	0.611591	−	0.679241i	0.0217046	−	0.0241053i
$795$	13.7360	+	8.48809i	0.487167	+	0.301041i
$796$	0.652147	−	0.0685434i	0.0231147	−	0.00242946i
$797$	15.3960	−	7.84464i	0.545353	−	0.277871i	−0.159532	−	0.987193i	$-0.550998\pi$
$797$	15.3960	−	7.84464i	0.545353	−	0.277871i	0.704885	+	0.709321i	$0.250998\pi$
$798$	−5.45940	+	2.90203i	−0.193261	+	0.102731i
$799$	32.1355	+	44.2307i	1.13687	+	1.56477i
$800$	4.76667	−	1.50957i	0.168527	−	0.0533715i
$801$	−2.80354	−	2.52431i	−0.0990581	−	0.0891923i
$802$	9.22274	+	2.47123i	0.325666	+	0.0872620i
$803$	15.8703	+	24.4698i	0.560052	+	0.863522i
$804$	4.00011			0.141073
$805$	19.0046	−	25.4780i	0.669824	−	0.897980i
$806$	8.67534	+	6.30301i	0.305576	+	0.222014i
$807$	15.5677	+	12.6064i	0.548007	+	0.443768i
$808$	5.24324	−	8.07388i	0.184456	−	0.284038i
$809$	2.69078	+	12.6591i	0.0946029	+	0.445072i	0.999798	+	0.0200764i	$0.00639096\pi$
$809$	2.69078	+	12.6591i	0.0946029	+	0.445072i	−0.905196	+	0.424995i	$0.860276\pi$
$810$	15.0345	−	7.10239i	0.528259	−	0.249553i
$811$	17.7360	−	24.4115i	0.622795	−	0.857204i	−0.374757	−	0.927123i	$-0.622274\pi$
$811$	17.7360	−	24.4115i	0.622795	−	0.857204i	0.997553	+	0.0699188i	$0.0222740\pi$
$812$	2.02147	−	1.36317i	0.0709398	−	0.0478379i
$813$	−23.3605	−	23.3605i	−0.819288	−	0.819288i
$814$	0.656493	+	6.28181i	0.0230101	+	0.220177i
$815$	21.0265	+	18.0944i	0.736527	+	0.633819i
$816$	−5.24814	+	5.82865i	−0.183722	+	0.204043i
$817$	−9.89641	−	3.79888i	−0.346232	−	0.132906i
$818$	−4.44974	+	28.0946i	−0.155582	+	0.982304i
$819$	−0.365815	+	1.19605i	−0.0127826	+	0.0417933i
$820$	8.05867	+	7.70472i	0.281421	+	0.269060i
$821$	0.123261	+	1.17275i	0.00430182	+	0.0409291i	0.996462	−	0.0840418i	$-0.0267829\pi$
$821$	0.123261	+	1.17275i	0.00430182	+	0.0409291i	−0.992160	+	0.124971i	$0.960116\pi$
$822$	0.897308	−	0.726625i	0.0312972	−	0.0253440i
$823$	16.7336	−	0.876971i	0.583297	−	0.0305693i	0.241594	−	0.970377i	$-0.422330\pi$
$823$	16.7336	−	0.876971i	0.583297	−	0.0305693i	0.341703	+	0.939808i	$0.388996\pi$
$824$	−0.532904	+	0.923017i	−0.0185646	+	0.0321548i
$825$	2.97823	−	26.2979i	0.103689	−	0.915575i
$826$	−7.78348	+	4.67560i	−0.270822	+	0.162685i
$827$	−38.0637	−	19.3944i	−1.32361	−	0.674411i	−0.357830	−	0.933787i	$-0.616483\pi$
$827$	−38.0637	−	19.3944i	−1.32361	−	0.674411i	−0.965776	+	0.259376i	$0.916483\pi$
$828$	−2.27173	−	0.872034i	−0.0789479	−	0.0303053i
$829$	−18.3597	−	8.17429i	−0.637660	−	0.283905i	0.0623315	−	0.998056i	$-0.480146\pi$
$829$	−18.3597	−	8.17429i	−0.637660	−	0.283905i	−0.699992	+	0.714151i	$0.746813\pi$
$830$	−19.7771	−	4.82614i	−0.686473	−	0.167518i
$831$	5.20058	−	4.68263i	0.180406	−	0.162438i
$832$	−1.03092	−	0.163282i	−0.0357408	−	0.00566078i
$833$	−33.7704	+	6.55645i	−1.17007	+	0.227168i
$834$	17.6156	−	5.72366i	0.609978	−	0.198194i
$835$	−3.90536	+	20.6415i	−0.135151	+	0.714330i
$836$	4.75082	−	1.00688i	0.164310	−	0.0348238i
$837$	−54.6858	−	14.6530i	−1.89022	−	0.506483i
$838$	−32.1768	+	20.8959i	−1.11153	+	0.721836i
$839$	13.0700	+	9.49588i	0.451225	+	0.327834i	0.790079	−	0.613005i	$-0.210039\pi$
$839$	13.0700	+	9.49588i	0.451225	+	0.327834i	−0.338854	+	0.940839i	$0.610039\pi$
$840$	−0.612607	+	9.42193i	−0.0211369	+	0.325088i
$841$	8.69907	−	26.7730i	0.299968	−	0.923206i
$842$	−37.8101	−	1.98154i	−1.30302	−	0.0682885i
$843$	15.0683	−	5.78419i	0.518981	−	0.199218i
$844$	18.1345	+	1.90602i	0.624216	+	0.0656078i
$845$	21.0686	+	16.2917i	0.724782	+	0.560451i
$846$		−	5.03857i		−	0.173230i
$847$	20.2439	−	20.9090i	0.695588	−	0.718441i
$848$	3.19942	+	3.19942i	0.109868	+	0.109868i
$849$	7.40858	−	34.8546i	0.254262	−	1.19621i
$850$	20.7071	−	13.2288i	0.710249	−	0.453746i
$851$	9.34692	+	4.16152i	0.320408	+	0.142655i
$852$	0.476292	−	9.08819i	0.0163175	−	0.311356i
$853$	0.279089	+	0.547743i	0.00955583	+	0.0187544i	0.895735	−	0.444588i	$-0.146650\pi$
$853$	0.279089	+	0.547743i	0.00955583	+	0.0187544i	−0.886179	+	0.463343i	$0.846650\pi$
$854$	2.47989	+	20.2158i	0.0848602	+	0.691771i
$855$	−0.702712	−	1.30582i	−0.0240322	−	0.0446583i
$856$	18.0061	+	3.82731i	0.615435	+	0.130815i
$857$	0.994450	−	3.71134i	0.0339698	−	0.126777i	−0.946859	−	0.321650i	$-0.895763\pi$
$857$	0.994450	−	3.71134i	0.0339698	−	0.126777i	0.980829	+	0.194873i	$0.0624294\pi$
$858$	−3.01181	+	4.63179i	−0.102821	+	0.158127i
$859$	13.1158	−	22.7173i	0.447506	−	0.775104i	−0.550717	−	0.834692i	$-0.685645\pi$
$859$	13.1158	−	22.7173i	0.447506	−	0.775104i	0.998223	+	0.0595884i	$0.0189788\pi$
$860$	−12.8796	+	9.80678i	−0.439191	+	0.334408i
$861$	−19.0822	+	8.89558i	−0.650320	+	0.303161i
$862$	−1.88989	+	11.9323i	−0.0643700	+	0.406416i
$863$	−2.24134	+	42.7673i	−0.0762961	+	1.45582i	0.645527	+	0.763738i	$0.276638\pi$
$863$	−2.24134	+	42.7673i	−0.0762961	+	1.45582i	−0.721823	+	0.692078i	$0.756695\pi$
$864$	5.39029	−	1.14574i	0.183381	−	0.0389789i
$865$	2.09633	−	25.4238i	0.0712774	−	0.864436i
$866$	−5.37879	−	12.0810i	−0.182779	−	0.410528i
$867$	−5.18164	+	10.1695i	−0.175978	+	0.345376i
$868$	18.8840	−	19.5506i	0.640965	−	0.663590i
$869$	−8.06038	−	0.00476227i	−0.273430	−	0.000161549i
$870$	−1.85260	−	2.71720i	−0.0628089	−	0.0921216i
$871$	1.94415	+	1.75052i	0.0658749	+	0.0593140i
$872$	−2.86945	−	3.54348i	−0.0971718	−	0.119997i
$873$	−0.459258	−	0.371900i	−0.0155435	−	0.0125869i
$874$	2.43101	−	7.48188i	0.0822301	−	0.253078i
$875$	9.70238	−	27.9439i	0.328000	−	0.944678i
$876$	−11.3542	+	8.24931i	−0.383623	+	0.278718i
$877$	−1.81094	+	4.71765i	−0.0611509	+	0.159304i	−0.960752	−	0.277409i	$-0.910524\pi$
$877$	−1.81094	+	4.71765i	−0.0611509	+	0.159304i	0.899601	+	0.436713i	$0.143857\pi$
$878$	1.71695	+	32.7613i	0.0579441	+	1.10564i
$879$	−8.45170	+	4.87959i	−0.285069	+	0.164585i
$880$	2.50576	−	6.98006i	0.0844690	−	0.235298i
$881$			25.6088i			0.862781i	0.902165	+	0.431390i	$0.141977\pi$
$881$			25.6088i			0.862781i	−0.902165	+	0.431390i	$0.858023\pi$
$882$	2.87304	+	1.34050i	0.0967402	+	0.0451371i
$883$	5.29862	+	33.4542i	0.178313	+	1.12582i	0.900734	+	0.434370i	$0.143029\pi$
$883$	5.29862	+	33.4542i	0.178313	+	1.12582i	−0.722421	+	0.691453i	$0.756971\pi$
$884$	−5.10143	+	0.536182i	−0.171580	+	0.0180338i
$885$	6.36016	+	10.4663i	0.213794	+	0.351819i
$886$	−11.4671	+	2.43741i	−0.385246	+	0.0818866i
$887$	3.87581	−	4.78623i	0.130137	−	0.160706i	−0.707912	−	0.706300i	$-0.750363\pi$
$887$	3.87581	−	4.78623i	0.130137	−	0.160706i	0.838049	+	0.545595i	$0.183696\pi$
$888$	−3.00185	+	0.475447i	−0.100736	+	0.0159549i
$889$	−18.6651	−	16.2289i	−0.626006	−	0.544301i
$890$	−6.15175	−	17.5801i	−0.206207	−	0.589286i
$891$	5.14195	−	24.1209i	0.172262	−	0.808081i
$892$	−4.40482	+	16.4390i	−0.147484	+	0.550419i
$893$	16.2672	−	0.852526i	0.544360	−	0.0285287i
$894$	15.4471	−	6.87749i	0.516628	−	0.230018i
$895$	42.2153	−	7.66141i	1.41110	−	0.256093i
$896$	−0.773826	+	2.53006i	−0.0258517	+	0.0845233i
$897$	4.06317	+	7.97443i	0.135665	+	0.266258i
$898$	−11.5915	+	14.3143i	−0.386814	+	0.477676i
$899$	−0.989624	+	9.41564i	−0.0330058	+	0.314029i
$900$	−2.26050	−	0.135382i	−0.0753502	−	0.00451273i
$901$	19.2570	+	11.1180i	0.641544	+	0.370395i
$902$	16.3349	−	2.57730i	0.543892	−	0.0858147i
$903$	−8.42273	−	29.3860i	−0.280291	−	0.977903i
$904$	−7.23236	+	2.34994i	−0.240545	+	0.0781577i
$905$	−54.0320	−	1.61654i	−1.79608	−	0.0537358i
$906$	7.38938	−	16.5968i	0.245496	−	0.551393i
$907$	−31.7574	+	48.9021i	−1.05449	+	1.62377i	−0.316977	+	0.948433i	$0.602668\pi$
$907$	−31.7574	+	48.9021i	−1.05449	+	1.62377i	−0.737511	+	0.675335i	$0.763999\pi$
$908$	8.08792	+	0.423870i	0.268407	+	0.0140666i
$909$	−3.52745	+	2.56284i	−0.116998	+	0.0850042i
$910$	−4.42094	+	4.31119i	−0.146553	+	0.142915i
$911$	−10.2433	−	31.5257i	−0.339376	−	1.04449i	−0.964526	−	0.263987i	$-0.914962\pi$
$911$	−10.2433	−	31.5257i	−0.339376	−	1.04449i	0.625150	−	0.780504i	$-0.285038\pi$
$912$	0.604827	+	2.25725i	0.0200278	+	0.0747449i
$913$	−23.4771	+	18.9884i	−0.776979	+	0.628426i
$914$	25.6981	−	14.8368i	0.850018	−	0.490758i
$915$	27.2503	−	3.48423i	0.900867	−	0.115185i
$916$	15.6542	−	21.5462i	0.517231	−	0.711907i
$917$	29.1471	+	4.09968i	0.962521	+	0.135383i
$918$	24.1302	−	12.2949i	0.796415	−	0.405794i
$919$	22.6942	−	20.4340i	0.748614	−	0.674055i	−0.203749	−	0.979023i	$-0.565313\pi$
$919$	22.6942	−	20.4340i	0.748614	−	0.674055i	0.952362	+	0.304968i	$0.0986459\pi$
$920$	−7.76814	−	9.16431i	−0.256108	−	0.302138i
$921$	4.27500	−	40.6739i	0.140866	−	1.34025i
$922$	4.79876	+	7.38945i	0.158039	+	0.243358i
$923$	4.20863	−	4.20863i	0.138529	−	0.138529i
$924$	10.5629	+	9.19520i	0.347493	+	0.302500i
$925$	9.46191	+	1.06590i	0.311106	+	0.0350465i
$926$	34.4006	+	7.31208i	1.13047	+	0.240290i
$927$	0.375141	−	0.303783i	0.0123213	−	0.00997755i
$928$	−0.330249	−	0.860327i	−0.0108409	−	0.0282416i
$929$	18.4176	+	20.4548i	0.604261	+	0.671100i	0.965207	−	0.261487i	$-0.0842128\pi$
$929$	18.4176	+	20.4548i	0.604261	+	0.671100i	−0.360946	+	0.932587i	$0.617546\pi$
$930$	−26.5003	−	25.3363i	−0.868978	−	0.830810i
$931$	−3.84173	+	9.50249i	−0.125908	+	0.311432i
$932$	18.0933	−	2.86569i	0.592665	−	0.0938689i
$933$	−5.26138	−	8.10181i	−0.172250	−	0.265241i
$934$	−14.5910	−	25.2723i	−0.477431	−	0.826934i
$935$	3.01649	−	36.3213i	0.0986497	−	1.18783i
$936$	0.409401	+	0.236368i	0.0133817	+	0.00772592i
$937$	5.82793	−	11.4380i	0.190390	−	0.373662i	−0.776003	−	0.630729i	$-0.782756\pi$
$937$	5.82793	−	11.4380i	0.190390	−	0.373662i	0.966394	+	0.257067i	$0.0827560\pi$
$938$	5.08035	−	4.26195i	0.165879	−	0.139158i
$939$	5.47006	+	7.52890i	0.178509	+	0.245696i
$940$	11.9512	−	21.8170i	0.389806	−	0.711591i
$941$	5.42043	+	25.5011i	0.176701	+	0.831313i	0.973790	+	0.227451i	$0.0730391\pi$
$941$	5.42043	+	25.5011i	0.176701	+	0.831313i	−0.797089	+	0.603862i	$0.793628\pi$
$942$	−7.21590	+	2.76993i	−0.235107	+	0.0902490i
$943$	9.60018	−	25.0093i	0.312625	−	0.814416i
$944$	1.06050	+	3.26390i	0.0345165	+	0.106231i
$945$	13.6336	−	29.6142i	0.443501	−	0.963351i
$946$	−0.0141863	+	24.0110i	−0.000461235	+	0.780663i
$947$	−8.14584	−	30.4007i	−0.264704	−	0.987890i	−0.962431	−	0.271526i	$-0.912472\pi$
$947$	−8.14584	−	30.4007i	−0.264704	−	0.987890i	0.697727	−	0.716364i	$-0.254195\pi$
$948$	−0.202993	−	3.87334i	−0.00659291	−	0.125800i
$949$	−9.12844	−	0.959438i	−0.296322	−	0.0311447i
$950$	0.0546071	−	7.32101i	0.00177169	−	0.237525i
$951$	23.3966	+	7.60203i	0.758688	+	0.246513i
$952$	−0.455229	+	12.9944i	−0.0147540	+	0.421150i
$953$	−3.46020	−	0.548042i	−0.112087	−	0.0177528i	0.100139	−	0.994973i	$-0.468071\pi$
$953$	−3.46020	−	0.548042i	−0.112087	−	0.0177528i	−0.212226	+	0.977221i	$0.568071\pi$
$954$	−0.833512	−	1.87210i	−0.0269859	−	0.0606114i
$955$	17.3915	+	42.4338i	0.562777	+	1.37313i
$956$	7.78169	+	13.4783i	0.251678	+	0.435919i
$957$	−4.87103	−	0.258166i	−0.157458	−	0.00834532i
$958$	−29.0902	+	29.0902i	−0.939861	+	0.939861i
$959$	0.365439	−	1.87890i	0.0118006	−	0.0606727i
$960$	3.41791	+	1.02631i	0.110313	+	0.0331241i
$961$	7.79232	+	74.1390i	0.251365	+	2.39158i
$962$	−1.66703	−	1.08258i	−0.0537473	−	0.0349039i
$963$	−6.99228	−	4.54084i	−0.225323	−	0.146326i
$964$	−2.03269	−	19.3398i	−0.0654687	−	0.622893i
$965$	2.75522	+	0.827322i	0.0886936	+	0.0266325i
$966$	21.4511	−	7.38351i	0.690177	−	0.237561i
$967$	−14.4218	+	14.4218i	−0.463773	+	0.463773i	−0.899890	−	0.436117i	$-0.856353\pi$
$967$	−14.4218	+	14.4218i	−0.463773	+	0.463773i	0.436117	+	0.899890i	$0.356353\pi$
$968$	−5.98012	−	9.23245i	−0.192208	−	0.296742i
$969$	5.74219	+	9.94576i	0.184466	+	0.319504i
$970$	−1.10646	−	2.69966i	−0.0355263	−	0.0866809i
$971$	−6.03482	−	13.5544i	−0.193667	−	0.434982i	0.790445	−	0.612533i	$-0.209849\pi$
$971$	−6.03482	−	13.5544i	−0.193667	−	0.434982i	−0.984112	+	0.177551i	$0.943183\pi$
$972$	−4.60692	−	0.729664i	−0.147767	−	0.0234040i
$973$	16.2744	−	26.0380i	0.521734	−	0.834741i
$974$	−4.93663	−	1.60401i	−0.158180	−	0.0513957i
$975$	5.84546	+	5.93332i	0.187205	+	0.190018i
$976$	7.65596	+	0.804674i	0.245061	+	0.0257570i
$977$	2.55652	+	48.7813i	0.0817903	+	1.56065i	0.664075	+	0.747666i	$0.268826\pi$
$977$	2.55652	+	48.7813i	0.0817903	+	1.56065i	−0.582284	+	0.812985i	$0.697841\pi$
$978$	5.12441	+	19.1245i	0.163860	+	0.611535i
$979$	−26.2687	−	8.55239i	−0.839552	−	0.273335i
$980$	9.26064	+	12.6191i	0.295820	+	0.403101i
$981$	0.638149	+	1.96402i	0.0203745	+	0.0627064i
$982$	−12.4186	+	32.3517i	−0.396295	+	1.03238i
$983$	31.3521	−	12.0349i	0.999976	−	0.383855i	0.197347	−	0.980334i	$-0.436767\pi$
$983$	31.3521	−	12.0349i	0.999976	−	0.383855i	0.802629	+	0.596479i	$0.203434\pi$
$984$	1.65447	+	7.78369i	0.0527427	+	0.248135i
$985$	17.8214	−	32.5330i	0.567837	−	1.03659i
$986$	−2.66197	−	3.66388i	−0.0847743	−	0.116682i
$987$	30.1908	+	35.9882i	0.960985	+	1.14552i
$988$	−0.693849	+	1.36176i	−0.0220743	+	0.0433232i
$989$	33.6849	+	19.4480i	1.07112	+	0.618410i
$990$	−2.19243	+	2.54466i	−0.0696800	+	0.0808747i
$991$	−0.607212	−	1.05172i	−0.0192887	−	0.0334090i	0.856220	−	0.516611i	$-0.172807\pi$
$991$	−0.607212	−	1.05172i	−0.0192887	−	0.0334090i	−0.875509	+	0.483202i	$0.839474\pi$
$992$	−5.59542	−	8.61619i	−0.177655	−	0.273564i
$993$	54.4580	−	8.62530i	1.72817	−	0.273716i
$994$	−9.07817	−	12.0499i	−0.287942	−	0.382201i
$995$	−1.05983	−	1.01328i	−0.0335988	−	0.0321231i
$996$	−9.72235	−	10.7978i	−0.308064	−	0.342140i
$997$	−1.67404	−	4.36103i	−0.0530175	−	0.138115i	0.904514	−	0.426444i	$-0.140234\pi$
$997$	−1.67404	−	4.36103i	−0.0530175	−	0.138115i	−0.957532	+	0.288329i	$0.906900\pi$
$998$	5.25505	−	4.25545i	0.166346	−	0.134704i
$999$	10.2650	+	2.18189i	0.324770	+	0.0690321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.313.19	✓	768
5.2	odd	4	inner	770.2.bv.a.467.19	yes	768
7.3	odd	6	inner	770.2.bv.a.423.6	yes	768
11.9	even	5	inner	770.2.bv.a.383.43	yes	768
35.17	even	12	inner	770.2.bv.a.577.43	yes	768
55.42	odd	20	inner	770.2.bv.a.537.6	yes	768
77.31	odd	30	inner	770.2.bv.a.493.19	yes	768
385.262	even	60	inner	770.2.bv.a.647.19	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.19	✓	768	1.1	even	1	trivial
770.2.bv.a.383.43	yes	768	11.9	even	5	inner
770.2.bv.a.423.6	yes	768	7.3	odd	6	inner
770.2.bv.a.467.19	yes	768	5.2	odd	4	inner
770.2.bv.a.493.19	yes	768	77.31	odd	30	inner
770.2.bv.a.537.6	yes	768	55.42	odd	20	inner
770.2.bv.a.577.43	yes	768	35.17	even	12	inner
770.2.bv.a.647.19	yes	768	385.262	even	60	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.838671 + 0.544639i) q^{2} +(1.00437 + 1.24029i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-2.14634 + 0.627077i) q^{5} +(-1.51785 - 0.493179i) q^{6} +(-2.45321 + 0.990841i) q^{7} +(0.156434 + 0.987688i) q^{8} +(0.0941655 - 0.443014i) q^{9} +O(q^{10})\)	\(q+(-0.838671 + 0.544639i) q^{2} +(1.00437 + 1.24029i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-2.14634 + 0.627077i) q^{5} +(-1.51785 - 0.493179i) q^{6} +(-2.45321 + 0.990841i) q^{7} +(0.156434 + 0.987688i) q^{8} +(0.0941655 - 0.443014i) q^{9} +(1.45854 - 1.69489i) q^{10} +(-0.687648 - 3.24456i) q^{11} +(1.54158 - 0.413065i) q^{12} +(0.930007 + 0.473862i) q^{13} +(1.51778 - 2.16710i) q^{14} +(-2.93348 - 2.03227i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(-4.12158 - 2.67659i) q^{17} +(0.162309 + 0.422829i) q^{18} +(-1.33765 + 0.595561i) q^{19} +(-0.300131 + 2.21583i) q^{20} +(-3.69286 - 2.04753i) q^{21} +(2.34382 + 2.34659i) q^{22} +(5.18961 - 1.39055i) q^{23} +(-1.06791 + 1.18603i) q^{24} +(4.21355 - 2.69184i) q^{25} +(-1.03805 + 0.109104i) q^{26} +(4.91008 - 2.50181i) q^{27} +(-0.0926312 + 2.64413i) q^{28} +(-0.541665 - 0.745537i) q^{29} +(3.56708 + 0.106721i) q^{30} +(-7.63479 - 6.87440i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.33355 - 4.11162i) q^{33} +4.91442 q^{34} +(4.64409 - 3.66503i) q^{35} +(-0.366413 - 0.266214i) q^{36} +(1.47996 + 1.19845i) q^{37} +(0.797484 - 1.22802i) q^{38} +(0.346343 + 1.62942i) q^{39} +(-0.955119 - 2.02182i) q^{40} +(2.93074 - 4.03382i) q^{41} +(4.21226 - 0.294076i) q^{42} +(5.11915 + 5.11915i) q^{43} +(-3.24374 - 0.691482i) q^{44} +(0.0756928 + 1.00991i) q^{45} +(-3.59503 + 3.99268i) q^{46} +(-10.3859 - 3.98679i) q^{47} +(0.249663 - 1.57631i) q^{48} +(5.03647 - 4.86148i) q^{49} +(-2.06770 + 4.55243i) q^{50} +(-0.819840 - 7.80025i) q^{51} +(0.811163 - 0.656867i) q^{52} +(-4.51846 + 0.236802i) q^{53} +(-2.75535 + 4.77241i) q^{54} +(3.51051 + 6.53271i) q^{55} +(-1.36241 - 2.26800i) q^{56} +(-2.08217 - 1.06092i) q^{57} +(0.860327 + 0.330249i) q^{58} +(-3.13516 - 1.39586i) q^{59} +(-3.04973 + 1.85327i) q^{60} +(-5.72083 + 5.15105i) q^{61} +(10.1471 + 1.60715i) q^{62} +(0.207949 + 1.18011i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.29326 - 0.433883i) q^{65} +(-0.556400 + 5.26388i) q^{66} +(2.42099 + 0.648703i) q^{67} +(-4.12158 + 2.67659i) q^{68} +(6.93699 + 5.04002i) q^{69} +(-1.89874 + 5.60311i) q^{70} +(1.76211 - 5.42322i) q^{71} +(0.452290 + 0.0237035i) q^{72} +(-8.20972 + 3.15142i) q^{73} +(-1.89392 - 0.199059i) q^{74} +(7.57064 + 2.52243i) q^{75} +1.46424i q^{76} +(4.90178 + 7.27822i) q^{77} +(-1.17791 - 1.17791i) q^{78} +(0.505287 - 2.37719i) q^{79} +(1.90219 + 1.17544i) q^{80} +(6.79325 + 3.02455i) q^{81} +(-0.260951 + 4.97925i) q^{82} +(-4.13319 - 8.11183i) q^{83} +(-3.37253 + 2.54079i) q^{84} +(10.5247 + 3.16031i) q^{85} +(-7.08137 - 1.50519i) q^{86} +(0.380654 - 1.42062i) q^{87} +(3.09704 - 1.18674i) q^{88} +(4.16476 - 7.21357i) q^{89} +(-0.613516 - 0.805754i) q^{90} +(-2.75102 - 0.240994i) q^{91} +(0.840473 - 5.30654i) q^{92} +(0.858116 - 16.3738i) q^{93} +(10.8817 - 2.31299i) q^{94} +(2.49759 - 2.11709i) q^{95} +(0.649135 + 1.45798i) q^{96} +(0.592364 - 1.16258i) q^{97} +(-1.57618 + 6.82024i) q^{98} +(-1.50214 - 0.000887499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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