LMFDB - Embedded newform 841.2.e.j.267.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			267.3
Character	$\chi$	$=$	841.267
Dual form			841.2.e.j.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483198 + 0.385338i) q^{2} +(0.602539 + 0.137526i) q^{3} +(-0.360046 - 1.57747i) q^{4} +(-2.40299 + 3.01326i) q^{5} +(0.238152 + 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(0.970194 - 2.01463i) q^{8} +(-2.35877 - 1.13592i) q^{9} +O(q^{10})$	\(q+(0.483198 + 0.385338i) q^{2} +(0.602539 + 0.137526i) q^{3} +(-0.360046 - 1.57747i) q^{4} +(-2.40299 + 3.01326i) q^{5} +(0.238152 + 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(0.970194 - 2.01463i) q^{8} +(-2.35877 - 1.13592i) q^{9} +(-2.32225 + 0.530037i) q^{10} +(0.599613 + 1.24511i) q^{11} -1.00000i q^{12} +(-0.212690 + 0.102426i) q^{13} +(1.08046 - 0.861642i) q^{14} +(-1.86230 + 1.48513i) q^{15} +(-1.67049 + 0.804465i) q^{16} -4.38197i q^{17} +(-0.702039 - 1.45780i) q^{18} +(-4.73240 + 1.08014i) q^{19} +(5.61850 + 2.70573i) q^{20} +(0.599613 - 1.24511i) q^{21} +(-0.190056 + 0.832688i) q^{22} +(-0.770676 - 0.966397i) q^{23} +(0.861642 - 1.08046i) q^{24} +(-2.19274 - 9.60704i) q^{25} +(-0.142240 - 0.0324654i) q^{26} +(-2.71463 - 2.16484i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(-7.88881 - 6.29112i) q^{31} +(-5.47718 - 1.25013i) q^{32} +(0.190056 + 0.832688i) q^{33} +(1.68854 - 2.11736i) q^{34} +(5.37326 + 6.73785i) q^{35} +(-0.942614 + 4.12986i) q^{36} +(-2.04281 + 4.24195i) q^{37} +(-2.70291 - 1.30165i) q^{38} +(-0.142240 + 0.0324654i) q^{39} +(3.73922 + 7.76458i) q^{40} -3.85410i q^{41} +(0.769519 - 0.370581i) q^{42} +(5.65739 - 4.51161i) q^{43} +(1.74823 - 1.39417i) q^{44} +(9.09093 - 4.37796i) q^{45} -0.763932i q^{46} +(-3.03719 - 6.30678i) q^{47} +(-1.11717 + 0.254986i) q^{48} +(1.80194 + 0.867767i) q^{49} +(2.64243 - 5.48705i) q^{50} +(0.602632 - 2.64030i) q^{51} +(0.238152 + 0.298633i) q^{52} +(-1.24698 + 1.56366i) q^{53} +(-0.477507 - 2.09210i) q^{54} +(-5.19270 - 1.18520i) q^{55} +(-3.90916 - 3.11745i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(3.01326 + 2.40299i) q^{60} +(0.602539 + 0.137526i) q^{61} +(-1.38766 - 6.07972i) q^{62} +(-3.64997 + 4.57692i) q^{63} +(0.147186 + 0.184565i) q^{64} +(0.202456 - 0.887019i) q^{65} +(-0.229032 + 0.475589i) q^{66} +(-1.37656 - 0.662915i) q^{67} +(-6.91240 + 1.57771i) q^{68} +(-0.331458 - 0.688279i) q^{69} +5.32624i q^{70} +(9.43507 - 4.54369i) q^{71} +(-4.57692 + 3.64997i) q^{72} +(-10.7175 + 8.54693i) q^{73} +(-2.62167 + 1.26253i) q^{74} -6.09017i q^{75} +(3.40777 + 7.07630i) q^{76} +(3.01269 - 0.687628i) q^{77} +(-0.0812403 - 0.0391233i) q^{78} +(-2.64243 + 5.48705i) q^{79} +(1.59011 - 6.96674i) q^{80} +(3.55901 + 4.46285i) q^{81} +(1.48513 - 1.86230i) q^{82} +(2.21281 + 9.69495i) q^{83} +(-2.18001 - 0.497572i) q^{84} +(13.2040 + 10.5298i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(3.68102 + 2.93552i) q^{89} +(6.07972 + 1.38766i) q^{90} +(0.117461 + 0.514629i) q^{91} +(-1.24698 + 1.56366i) q^{92} +(-3.88812 - 4.87555i) q^{93} +(0.962679 - 4.21777i) q^{94} +(8.11719 - 16.8555i) q^{95} +(-3.12829 - 1.50650i) q^{96} +(-3.47299 + 0.792688i) q^{97} +(0.536310 + 1.11366i) q^{98} -3.61803i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	0.483198	+	0.385338i	0.341673	+	0.272475i	0.779260	−	0.626701i	$-0.215595\pi$
$2$	0.483198	+	0.385338i	0.341673	+	0.272475i	−0.437587	+	0.899176i	$0.644167\pi$
$3$	0.602539	+	0.137526i	0.347876	+	0.0794004i	0.392889	−	0.919586i	$-0.371476\pi$
$3$	0.602539	+	0.137526i	0.347876	+	0.0794004i	−0.0450129	+	0.998986i	$0.514333\pi$
$4$	−0.360046	−	1.57747i	−0.180023	−	0.788733i
$5$	−2.40299	+	3.01326i	−1.07465	+	1.34757i	−0.140748	+	0.990046i	$0.544951\pi$
$5$	−2.40299	+	3.01326i	−1.07465	+	1.34757i	−0.933904	+	0.357525i	$0.883621\pi$
$6$	0.238152	+	0.298633i	0.0972251	+	0.121916i
$7$	0.497572	−	2.18001i	0.188065	−	0.823964i	−0.789571	−	0.613659i	$-0.789697\pi$
$7$	0.497572	−	2.18001i	0.188065	−	0.823964i	0.977636	−	0.210306i	$-0.0674459\pi$
$8$	0.970194	−	2.01463i	0.343015	−	0.712278i
$9$	−2.35877	−	1.13592i	−0.786256	−	0.378641i
$10$	−2.32225	+	0.530037i	−0.734358	+	0.167613i
$11$	0.599613	+	1.24511i	0.180790	+	0.375414i	0.971594	−	0.236656i	$-0.0760513\pi$
$11$	0.599613	+	1.24511i	0.180790	+	0.375414i	−0.790804	+	0.612070i	$0.790337\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−0.212690	+	0.102426i	−0.0589896	+	0.0284079i	−0.463146	−	0.886282i	$-0.653279\pi$
$13$	−0.212690	+	0.102426i	−0.0589896	+	0.0284079i	0.404156	+	0.914690i	$0.367565\pi$
$14$	1.08046	−	0.861642i	0.288766	−	0.230283i
$15$	−1.86230	+	1.48513i	−0.480843	+	0.383459i
$16$	−1.67049	+	0.804465i	−0.417622	+	0.201116i
$17$		−	4.38197i		−	1.06278i	−0.847126	−	0.531391i	$-0.821669\pi$
$17$		−	4.38197i		−	1.06278i	0.847126	−	0.531391i	$-0.178331\pi$
$18$	−0.702039	−	1.45780i	−0.165472	−	0.343606i
$19$	−4.73240	+	1.08014i	−1.08569	+	0.247801i	−0.727679	−	0.685918i	$-0.759401\pi$
$19$	−4.73240	+	1.08014i	−1.08569	+	0.247801i	−0.358008	+	0.933719i	$0.616544\pi$
$20$	5.61850	+	2.70573i	1.25634	+	0.605019i
$21$	0.599613	−	1.24511i	0.130846	−	0.271705i
$22$	−0.190056	+	0.832688i	−0.0405200	+	0.177530i
$23$	−0.770676	−	0.966397i	−0.160697	−	0.201508i	0.694964	−	0.719045i	$-0.255420\pi$
$23$	−0.770676	−	0.966397i	−0.160697	−	0.201508i	−0.855661	+	0.517537i	$0.826849\pi$
$24$	0.861642	−	1.08046i	0.175882	−	0.220549i
$25$	−2.19274	−	9.60704i	−0.438549	−	1.92141i
$26$	−0.142240	−	0.0324654i	−0.0278956	−	0.00636698i
$27$	−2.71463	−	2.16484i	−0.522430	−	0.416624i
$28$	−3.61803			−0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	−7.88881	−	6.29112i	−1.41687	−	1.12992i	−0.972180	−	0.234235i	$-0.924742\pi$
$31$	−7.88881	−	6.29112i	−1.41687	−	1.12992i	−0.444693	−	0.895683i	$-0.646687\pi$
$32$	−5.47718	−	1.25013i	−0.968237	−	0.220994i
$33$	0.190056	+	0.832688i	0.0330844	+	0.144952i
$34$	1.68854	−	2.11736i	0.289582	−	0.363124i
$35$	5.37326	+	6.73785i	0.908246	+	1.13890i
$36$	−0.942614	+	4.12986i	−0.157102	+	0.688310i
$37$	−2.04281	+	4.24195i	−0.335836	+	0.697371i	−0.998679	−	0.0513875i	$-0.983636\pi$
$37$	−2.04281	+	4.24195i	−0.335836	+	0.697371i	0.662842	+	0.748759i	$0.269350\pi$
$38$	−2.70291	−	1.30165i	−0.438469	−	0.211156i
$39$	−0.142240	+	0.0324654i	−0.0227766	+	0.00519862i
$40$	3.73922	+	7.76458i	0.591223	+	1.22769i
$41$		−	3.85410i		−	0.601910i	−0.953638	−	0.300955i	$-0.902695\pi$
$41$		−	3.85410i		−	0.601910i	0.953638	−	0.300955i	$-0.0973053\pi$
$42$	0.769519	−	0.370581i	0.118739	−	0.0571819i
$43$	5.65739	−	4.51161i	0.862743	−	0.688015i	−0.0886269	−	0.996065i	$-0.528248\pi$
$43$	5.65739	−	4.51161i	0.862743	−	0.688015i	0.951370	+	0.308050i	$0.0996764\pi$
$44$	1.74823	−	1.39417i	0.263555	−	0.210178i
$45$	9.09093	−	4.37796i	1.35520	−	0.652628i
$46$		−	0.763932i		−	0.112636i
$47$	−3.03719	−	6.30678i	−0.443019	−	0.919939i	−0.996218	−	0.0868895i	$-0.972307\pi$
$47$	−3.03719	−	6.30678i	−0.443019	−	0.919939i	0.553199	−	0.833049i	$-0.313407\pi$
$48$	−1.11717	+	0.254986i	−0.161249	+	0.0368041i
$49$	1.80194	+	0.867767i	0.257420	+	0.123967i
$50$	2.64243	−	5.48705i	0.373695	−	0.775987i
$51$	0.602632	−	2.64030i	0.0843854	−	0.369716i
$52$	0.238152	+	0.298633i	0.0330257	+	0.0414130i
$53$	−1.24698	+	1.56366i	−0.171286	+	0.214786i	−0.860064	−	0.510187i	$-0.829576\pi$
$53$	−1.24698	+	1.56366i	−0.171286	+	0.214786i	0.688778	+	0.724973i	$0.258148\pi$
$54$	−0.477507	−	2.09210i	−0.0649805	−	0.284698i
$55$	−5.19270	−	1.18520i	−0.700183	−	0.159812i
$56$	−3.90916	−	3.11745i	−0.522383	−	0.416587i
$57$	−3.00000			−0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	3.01326	+	2.40299i	0.389010	+	0.310225i
$61$	0.602539	+	0.137526i	0.0771472	+	0.0176083i	0.260920	−	0.965360i	$-0.415974\pi$
$61$	0.602539	+	0.137526i	0.0771472	+	0.0176083i	−0.183773	+	0.982969i	$0.558831\pi$
$62$	−1.38766	−	6.07972i	−0.176232	−	0.772125i
$63$	−3.64997	+	4.57692i	−0.459853	+	0.576638i
$64$	0.147186	+	0.184565i	0.0183982	+	0.0230707i
$65$	0.202456	−	0.887019i	0.0251116	−	0.110021i
$66$	−0.229032	+	0.475589i	−0.0281918	+	0.0585410i
$67$	−1.37656	−	0.662915i	−0.168173	−	0.0809880i	0.347903	−	0.937530i	$-0.386894\pi$
$67$	−1.37656	−	0.662915i	−0.168173	−	0.0809880i	−0.516077	+	0.856542i	$0.672608\pi$
$68$	−6.91240	+	1.57771i	−0.838252	+	0.191326i
$69$	−0.331458	−	0.688279i	−0.0399028	−	0.0828591i
$70$			5.32624i			0.636607i
$71$	9.43507	−	4.54369i	1.11974	−	0.539237i	0.219926	−	0.975517i	$-0.429419\pi$
$71$	9.43507	−	4.54369i	1.11974	−	0.539237i	0.899811	+	0.436280i	$0.143704\pi$
$72$	−4.57692	+	3.64997i	−0.539395	+	0.430153i
$73$	−10.7175	+	8.54693i	−1.25439	+	1.00034i	−0.254947	+	0.966955i	$0.582058\pi$
$73$	−10.7175	+	8.54693i	−1.25439	+	1.00034i	−0.999443	+	0.0333868i	$0.989371\pi$
$74$	−2.62167	+	1.26253i	−0.304763	+	0.146766i
$75$		−	6.09017i		−	0.703232i
$76$	3.40777	+	7.07630i	0.390898	+	0.811707i
$77$	3.01269	−	0.687628i	0.343328	−	0.0783624i
$78$	−0.0812403	−	0.0391233i	−0.00919865	−	0.00442984i
$79$	−2.64243	+	5.48705i	−0.297296	+	0.617342i	−0.995092	−	0.0989550i	$-0.968450\pi$
$79$	−2.64243	+	5.48705i	−0.297296	+	0.617342i	0.697796	+	0.716297i	$0.254164\pi$
$80$	1.59011	−	6.96674i	0.177780	−	0.778905i
$81$	3.55901	+	4.46285i	0.395445	+	0.495873i
$82$	1.48513	−	1.86230i	0.164005	−	0.205656i
$83$	2.21281	+	9.69495i	0.242887	+	1.06416i	0.938374	+	0.345620i	$0.112331\pi$
$83$	2.21281	+	9.69495i	0.242887	+	1.06416i	−0.695487	+	0.718539i	$0.744811\pi$
$84$	−2.18001	−	0.497572i	−0.237858	−	0.0542895i
$85$	13.2040	+	10.5298i	1.43217	+	1.14212i
$86$	4.47214			0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	3.68102	+	2.93552i	0.390188	+	0.311164i	0.798860	−	0.601517i	$-0.205437\pi$
$89$	3.68102	+	2.93552i	0.390188	+	0.311164i	−0.408673	+	0.912681i	$0.634008\pi$
$90$	6.07972	+	1.38766i	0.640858	+	0.146272i
$91$	0.117461	+	0.514629i	0.0123132	+	0.0539478i
$92$	−1.24698	+	1.56366i	−0.130007	+	0.163023i
$93$	−3.88812	−	4.87555i	−0.403180	−	0.505571i
$94$	0.962679	−	4.21777i	0.0992927	−	0.435030i
$95$	8.11719	−	16.8555i	0.832806	−	1.72934i
$96$	−3.12829	−	1.50650i	−0.319279	−	0.153757i
$97$	−3.47299	+	0.792688i	−0.352629	+	0.0804852i	−0.395166	−	0.918610i	$-0.629313\pi$
$97$	−3.47299	+	0.792688i	−0.352629	+	0.0804852i	0.0425373	+	0.999095i	$0.486456\pi$
$98$	0.536310	+	1.11366i	0.0541755	+	0.112497i
$99$		−	3.61803i		−	0.363626i
$100$	−14.3653	+	6.91796i	−1.43653	+	0.691796i
$101$	0.483198	−	0.385338i	0.0480800	−	0.0383426i	−0.599155	−	0.800633i	$-0.704497\pi$
$101$	0.483198	−	0.385338i	0.0480800	−	0.0383426i	0.647235	+	0.762291i	$0.275925\pi$
$102$	1.30860	−	1.04357i	0.129571	−	0.103329i
$103$	−8.27120	+	3.98320i	−0.814986	+	0.392476i	−0.794463	−	0.607313i	$-0.792247\pi$
$103$	−8.27120	+	3.98320i	−0.814986	+	0.392476i	−0.0205229	+	0.999789i	$0.506533\pi$
$104$			0.527864i			0.0517613i
$105$	2.31097	+	4.79877i	0.225527	+	0.468312i
$106$	−1.20508	+	0.275051i	−0.117047	+	0.0267153i
$107$	−6.09409	−	2.93476i	−0.589138	−	0.283714i	0.115470	−	0.993311i	$-0.463163\pi$
$107$	−6.09409	−	2.93476i	−0.589138	−	0.283714i	−0.704608	+	0.709597i	$0.748877\pi$
$108$	−2.43757	+	5.06167i	−0.234556	+	0.487060i
$109$	−3.20029	+	14.0214i	−0.306532	+	1.34300i	0.553536	+	0.832825i	$0.313278\pi$
$109$	−3.20029	+	14.0214i	−0.306532	+	1.34300i	−0.860068	+	0.510179i	$0.829579\pi$
$110$	−2.05240	−	2.57363i	−0.195689	−	0.245386i
$111$	−1.81425	+	2.27500i	−0.172201	+	0.215933i
$112$	0.922549	+	4.04195i	0.0871727	+	0.381929i
$113$	7.74509	+	1.76777i	0.728597	+	0.166298i	0.570701	−	0.821158i	$-0.306672\pi$
$113$	7.74509	+	1.76777i	0.728597	+	0.166298i	0.157896	+	0.987456i	$0.449529\pi$
$114$	−1.44960	−	1.15601i	−0.135767	−	0.108271i
$115$	4.76393			0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	2.94276	+	2.34677i	0.270903	+	0.216038i
$119$	−9.55271	−	2.18034i	−0.875695	−	0.199872i
$120$	1.18520	+	5.19270i	0.108193	+	0.474026i
$121$	5.66763	−	7.10698i	0.515239	−	0.646089i
$122$	0.238152	+	0.298633i	0.0215613	+	0.0270370i
$123$	0.530037	−	2.32225i	0.0477919	−	0.209390i
$124$	−7.08369	+	14.7094i	−0.636134	+	1.32095i
$125$	16.8555	+	8.11719i	1.50760	+	0.726023i
$126$	−3.52732	+	0.805088i	−0.314239	+	0.0717230i
$127$	−6.91796	−	14.3653i	−0.613870	−	1.27471i	−0.943740	−	0.330687i	$-0.892719\pi$
$127$	−6.91796	−	14.3653i	−0.613870	−	1.27471i	0.329871	−	0.944026i	$-0.392995\pi$
$128$			11.3820i			1.00603i
$129$	4.02926	−	1.94039i	0.354756	−	0.170842i
$130$	0.439628	−	0.350592i	0.0385580	−	0.0307490i
$131$	11.2007	−	8.93226i	0.978610	−	0.780415i	0.00301554	−	0.999995i	$-0.499040\pi$
$131$	11.2007	−	8.93226i	0.978610	−	0.780415i	0.975594	+	0.219580i	$0.0704687\pi$
$132$	1.24511	−	0.599613i	0.108373	−	0.0521896i
$133$			10.8541i			0.941170i
$134$	−0.409704	−	0.850760i	−0.0353931	−	0.0734944i
$135$	13.0465	−	2.97777i	1.12286	−	0.256285i
$136$	−8.82803	−	4.25136i	−0.756997	−	0.364551i
$137$	3.10049	−	6.43823i	0.264893	−	0.550055i	−0.725519	−	0.688202i	$-0.758400\pi$
$137$	3.10049	−	6.43823i	0.264893	−	0.550055i	0.990412	+	0.138147i	$0.0441146\pi$
$138$	0.105060	−	0.460299i	0.00894331	−	0.0391832i
$139$	0.805422	+	1.00997i	0.0683150	+	0.0856643i	0.814815	−	0.579721i	$-0.196839\pi$
$139$	0.805422	+	1.00997i	0.0683150	+	0.0856643i	−0.746500	+	0.665386i	$0.768267\pi$
$140$	8.69411	−	10.9021i	0.734787	−	0.921393i
$141$	−0.962679	−	4.21777i	−0.0810722	−	0.355200i
$142$	6.30987	+	1.44019i	0.529512	+	0.120858i
$143$	−0.255063	−	0.203406i	−0.0213294	−	0.0170097i
$144$	4.85410			0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	0.966397	+	0.770676i	0.0797071	+	0.0635643i
$148$	7.42703	+	1.69517i	0.610498	+	0.139342i
$149$	2.14021	+	9.37689i	0.175333	+	0.768185i	0.983746	+	0.179568i	$0.0574701\pi$
$149$	2.14021	+	9.37689i	0.175333	+	0.768185i	−0.808412	+	0.588617i	$0.799673\pi$
$150$	2.34677	−	2.94276i	0.191613	−	0.240275i
$151$	−1.66706	−	2.09043i	−0.135664	−	0.170117i	0.709359	−	0.704847i	$-0.248985\pi$
$151$	−1.66706	−	2.09043i	−0.135664	−	0.170117i	−0.845023	+	0.534731i	$0.820413\pi$
$152$	−2.41526	+	10.5820i	−0.195904	+	0.858311i
$153$	−4.97757	+	10.3360i	−0.402413	+	0.835619i
$154$	1.72070	+	0.828644i	0.138658	+	0.0667741i
$155$	37.9135	−	8.65352i	3.04529	−	0.695067i
$156$	0.102426	+	0.212690i	0.00820065	+	0.0170288i
$157$		−	14.5623i		−	1.16220i	−0.813833	−	0.581099i	$-0.802623\pi$
$157$		−	14.5623i		−	1.16220i	0.813833	−	0.581099i	$-0.197377\pi$
$158$	−3.39119	+	1.63311i	−0.269788	+	0.129923i
$159$	−0.966397	+	0.770676i	−0.0766403	+	0.0611186i
$160$	16.9286	−	13.5001i	1.33832	−	1.06728i
$161$	−2.49022	+	1.19923i	−0.196257	+	0.0945122i
$162$			3.52786i			0.277175i
$163$	−2.61825	−	5.43684i	−0.205077	−	0.425847i	0.772909	−	0.634517i	$-0.218801\pi$
$163$	−2.61825	−	5.43684i	−0.205077	−	0.425847i	−0.977986	+	0.208670i	$0.933087\pi$
$164$	−6.07972	+	1.38766i	−0.474746	+	0.108358i
$165$	−2.96581	−	1.42826i	−0.230888	−	0.111190i
$166$	−2.66661	+	5.53726i	−0.206969	+	0.429775i
$167$	2.34267	−	10.2639i	0.181281	−	0.794245i	−0.799740	−	0.600346i	$-0.795029\pi$
$167$	2.34267	−	10.2639i	0.181281	−	0.794245i	0.981022	−	0.193899i	$-0.0621134\pi$
$168$	−1.92669	−	2.41599i	−0.148647	−	0.186398i
$169$	−8.07062	+	10.1202i	−0.620817	+	0.778480i
$170$	2.32261	+	10.1760i	0.178136	+	0.780464i
$171$	12.3896	+	2.82784i	0.947455	+	0.216250i
$172$	−9.15384	−	7.29995i	−0.697974	−	0.556616i
$173$	−4.09017			−0.310970			−0.155485	−	0.987838i	$-0.549694\pi$
$173$	−4.09017			−0.310970			−0.155485	+	0.987838i	$0.549694\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	−2.00329	−	1.59757i	−0.151004	−	0.120421i
$177$	3.66956	+	0.837554i	0.275821	+	0.0629544i
$178$	0.647498	+	2.83687i	0.0485320	+	0.212633i
$179$	9.97584	−	12.5093i	0.745629	−	0.934989i	−0.253851	−	0.967243i	$-0.581697\pi$
$179$	9.97584	−	12.5093i	0.745629	−	0.934989i	0.999480	+	0.0322542i	$0.0102686\pi$
$180$	−10.1792	−	12.7644i	−0.758716	−	0.951400i
$181$	−1.32272	+	5.79524i	−0.0983174	+	0.430757i	−0.999999	−	0.00164474i	$-0.999476\pi$
$181$	−1.32272	+	5.79524i	−0.0983174	+	0.430757i	0.901681	+	0.432401i	$0.142334\pi$
$182$	−0.141549	+	0.293930i	−0.0104923	+	0.0217876i
$183$	0.344139	+	0.165729i	0.0254395	+	0.0122510i
$184$	−2.69463	+	0.615033i	−0.198651	+	0.0453408i
$185$	−7.87321	−	16.3489i	−0.578850	−	1.20199i
$186$		−	3.85410i		−	0.282596i
$187$	5.45602	−	2.62748i	0.398984	−	0.192141i
$188$	−8.85521	+	7.06179i	−0.645833	+	0.515034i
$189$	−6.07009	+	4.84073i	−0.441534	+	0.352111i
$190$	10.4173	−	5.01670i	0.755749	−	0.363949i
$191$			17.0344i			1.23257i	0.787524	+	0.616284i	$0.211363\pi$
$191$			17.0344i			1.23257i	−0.787524	+	0.616284i	$0.788637\pi$
$192$	0.0633028	+	0.131450i	0.00456848	+	0.00948656i
$193$	12.1594	−	2.77531i	0.875255	−	0.199771i	0.238785	−	0.971072i	$-0.423251\pi$
$193$	12.1594	−	2.77531i	0.875255	−	0.199771i	0.636470	+	0.771301i	$0.280394\pi$
$194$	−1.98360	−	0.955250i	−0.142414	−	0.0685829i
$195$	0.243975	−	0.506620i	0.0174714	−	0.0362798i
$196$	0.720093	−	3.15493i	0.0514352	−	0.225352i
$197$	−3.92287	−	4.91912i	−0.279493	−	0.350473i	0.622194	−	0.782863i	$-0.286242\pi$
$197$	−3.92287	−	4.91912i	−0.279493	−	0.350473i	−0.901687	+	0.432390i	$0.857670\pi$
$198$	1.39417	−	1.74823i	0.0990790	−	0.124241i
$199$	1.30266	+	5.70733i	0.0923431	+	0.404582i	0.999882	−	0.0153872i	$-0.00489810\pi$
$199$	1.30266	+	5.70733i	0.0923431	+	0.404582i	−0.907538	+	0.419969i	$0.862041\pi$
$200$	−21.4820	−	4.90312i	−1.51901	−	0.346703i
$201$	−0.738262	−	0.588744i	−0.0520730	−	0.0415268i
$202$	0.381966			0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	11.6134	+	9.26138i	0.811115	+	0.646843i
$206$	−5.53151	−	1.26253i	−0.385398	−	0.0879647i
$207$	0.720093	+	3.15493i	0.0500499	+	0.219283i
$208$	0.272898	−	0.342203i	0.0189221	−	0.0237275i
$209$	−4.18250	−	5.24469i	−0.289309	−	0.362782i
$210$	−0.732494	+	3.20926i	−0.0505469	+	0.221460i
$211$	5.05582	−	10.4985i	0.348057	−	0.722748i	−0.651292	−	0.758827i	$-0.725773\pi$
$211$	5.05582	−	10.4985i	0.348057	−	0.722748i	0.999349	+	0.0360795i	$0.0114869\pi$
$212$	2.91560	+	1.40408i	0.200244	+	0.0964324i
$213$	6.30987	−	1.44019i	0.432345	−	0.0986799i
$214$	−1.81378	−	3.76636i	−0.123988	−	0.257463i
$215$			27.8885i			1.90198i
$216$	−6.99506	+	3.36864i	−0.475954	+	0.229207i
$217$	−17.6399	+	14.0674i	−1.19748	+	0.954955i
$218$	−6.94934	+	5.54192i	−0.470669	+	0.375346i
$219$	−7.63313	+	3.67592i	−0.515799	+	0.248396i
$220$			8.61803i			0.581028i
$221$	0.448827	+	0.932000i	0.0301914	+	0.0626931i
$222$	−1.75328	+	0.400176i	−0.117673	+	0.0268580i
$223$	−2.40898	−	1.16010i	−0.161317	−	0.0776862i	0.351483	−	0.936194i	$-0.385677\pi$
$223$	−2.40898	−	1.16010i	−0.161317	−	0.0776862i	−0.512800	+	0.858508i	$0.671392\pi$
$224$	−5.45058	+	11.3182i	−0.364182	+	0.756232i
$225$	−5.74068	+	25.1516i	−0.382712	+	1.67677i
$226$	3.06123	+	3.83866i	0.203630	+	0.255344i
$227$	−13.0238	+	16.3313i	−0.864420	+	1.08395i	0.131284	+	0.991345i	$0.458090\pi$
$227$	−13.0238	+	16.3313i	−0.864420	+	1.08395i	−0.995703	+	0.0926030i	$0.970481\pi$
$228$	1.08014	+	4.73240i	0.0715340	+	0.313411i
$229$	2.23434	+	0.509973i	0.147649	+	0.0336999i	0.295707	−	0.955279i	$-0.404445\pi$
$229$	2.23434	+	0.509973i	0.147649	+	0.0336999i	−0.148058	+	0.988979i	$0.547302\pi$
$230$	2.30192	+	1.83572i	0.151784	+	0.121044i
$231$	1.90983			0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	0.298633	+	0.238152i	0.0195223	+	0.0155685i
$235$	26.3023	+	6.00333i	1.71577	+	0.391614i
$236$	−2.19274	−	9.60704i	−0.142735	−	0.625365i
$237$	−2.34677	+	2.94276i	−0.152439	+	0.191153i
$238$	−3.77568	−	4.73456i	−0.244741	−	0.306896i
$239$	6.17332	−	27.0471i	0.399319	−	1.74953i	−0.230771	−	0.973008i	$-0.574125\pi$
$239$	6.17332	−	27.0471i	0.399319	−	1.74953i	0.630090	−	0.776522i	$-0.283018\pi$
$240$	1.91621	−	3.97905i	0.123691	−	0.256846i
$241$	−4.19174	−	2.01863i	−0.270013	−	0.130032i	0.293978	−	0.955812i	$-0.405021\pi$
$241$	−4.19174	−	2.01863i	−0.270013	−	0.130032i	−0.563992	+	0.825781i	$0.690735\pi$
$242$	5.47718	−	1.25013i	0.352086	−	0.0803614i
$243$	6.05019	+	12.5634i	0.388120	+	0.805940i
$244$		−	1.00000i		−	0.0640184i
$245$	−6.94485	+	3.34446i	−0.443690	+	0.213670i
$246$	1.15096	−	0.917862i	0.0733827	−	0.0585207i
$247$	0.895899	−	0.714456i	0.0570047	−	0.0454597i
$248$	−20.3279	+	9.78942i	−1.29083	+	0.621629i
$249$			6.14590i			0.389480i
$250$	5.01670	+	10.4173i	0.317284	+	0.658846i
$251$	−19.1597	+	4.37309i	−1.20935	+	0.276027i	−0.779227	−	0.626742i	$-0.784388\pi$
$251$	−19.1597	+	4.37309i	−1.20935	+	0.276027i	−0.430126	+	0.902769i	$0.641531\pi$
$252$	8.53410	+	4.10981i	0.537598	+	0.258893i
$253$	0.741162	−	1.53904i	0.0465965	−	0.0967585i
$254$	2.19274	−	9.60704i	0.137585	−	0.602799i
$255$	6.50780	+	8.16052i	0.407534	+	0.511031i
$256$	−4.09153	+	5.13062i	−0.255721	+	0.320664i
$257$	5.15811	+	22.5992i	0.321754	+	1.40970i	0.834430	+	0.551114i	$0.185797\pi$
$257$	5.15811	+	22.5992i	0.321754	+	1.40970i	−0.512676	+	0.858582i	$0.671346\pi$
$258$	2.69463	+	0.615033i	0.167761	+	0.0382903i
$259$	8.23102	+	6.56402i	0.511450	+	0.407868i
$260$	−1.47214			−0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	−13.0630	−	10.4174i	−0.805499	−	0.642364i	0.131649	−	0.991296i	$-0.457973\pi$
$263$	−13.0630	−	10.4174i	−0.805499	−	0.642364i	−0.937148	+	0.348932i	$0.886544\pi$
$264$	1.86195	+	0.424977i	0.114595	+	0.0261555i
$265$	−1.71524	−	7.51494i	−0.105366	−	0.461639i
$266$	−4.18250	+	5.24469i	−0.256445	+	0.321572i
$267$	1.81425	+	2.27500i	0.111030	+	0.139228i
$268$	−0.550102	+	2.41015i	−0.0336028	+	0.147224i
$269$	2.60330	−	5.40581i	0.158726	−	0.329598i	−0.806406	−	0.591363i	$-0.798590\pi$
$269$	2.60330	−	5.40581i	0.158726	−	0.329598i	0.965132	+	0.261765i	$0.0843044\pi$
$270$	7.45147	+	3.58844i	0.453482	+	0.218385i
$271$	−9.92510	+	2.26534i	−0.602907	+	0.137610i	−0.513070	−	0.858347i	$-0.671492\pi$
$271$	−9.92510	+	2.26534i	−0.602907	+	0.137610i	−0.0898370	+	0.995956i	$0.528635\pi$
$272$	3.52514	+	7.32002i	0.213743	+	0.443842i
$273$			0.326238i			0.0197448i
$274$	3.97905	−	1.91621i	0.240383	−	0.115762i
$275$	10.6470	−	8.49071i	0.642039	−	0.512009i
$276$	−0.966397	+	0.770676i	−0.0581703	+	0.0463892i
$277$	19.2645	−	9.27729i	1.15749	−	0.557418i	0.246215	−	0.969215i	$-0.420813\pi$
$277$	19.2645	−	9.27729i	1.15749	−	0.557418i	0.911276	+	0.411797i	$0.135099\pi$
$278$			0.798374i			0.0478833i
$279$	11.4616	+	23.8004i	0.686191	+	1.42489i
$280$	18.7874	−	4.28809i	1.12276	−	0.256263i
$281$	−20.8346	−	10.0334i	−1.24289	−	0.598542i	−0.307290	−	0.951616i	$-0.599422\pi$
$281$	−20.8346	−	10.0334i	−1.24289	−	0.598542i	−0.935595	+	0.353074i	$0.885136\pi$
$282$	1.16010	−	2.40898i	0.0690831	−	0.143452i
$283$	−1.16513	+	5.10479i	−0.0692601	+	0.303448i	−0.997679	−	0.0680857i	$-0.978311\pi$
$283$	−1.16513	+	5.10479i	−0.0692601	+	0.303448i	0.928419	+	0.371534i	$0.121168\pi$
$284$	−10.5646	−	13.2476i	−0.626893	−	0.786098i
$285$	7.20898	−	9.03977i	0.427023	−	0.535470i
$286$	−0.0448660	−	0.196571i	−0.00265298	−	0.0116235i
$287$	−8.40196	−	1.91769i	−0.495952	−	0.113198i
$288$	11.4993	+	9.17042i	0.677605	+	0.540372i
$289$	−2.20163			−0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	17.3413	+	13.8292i	1.01482	+	0.809294i
$293$	−8.31405	−	1.89763i	−0.485712	−	0.110861i	−0.0273496	−	0.999626i	$-0.508707\pi$
$293$	−8.31405	−	1.89763i	−0.485712	−	0.110861i	−0.458363	+	0.888765i	$0.651564\pi$
$294$	0.169991	+	0.744779i	0.00991407	+	0.0434364i
$295$	−14.6346	+	18.3513i	−0.852062	+	1.06845i
$296$	6.56402	+	8.23102i	0.381526	+	0.478418i
$297$	1.06774	−	4.67807i	0.0619565	−	0.271449i
$298$	−2.57912	+	5.35560i	−0.149405	+	0.310242i
$299$	0.262899	+	0.126606i	0.0152039	+	0.00732179i
$300$	−9.60704	+	2.19274i	−0.554663	+	0.126598i
$301$	−7.02039	−	14.5780i	−0.404648	−	0.840261i
$302$		−	1.65248i		−	0.0950893i
$303$	0.344139	−	0.165729i	0.0197703	−	0.00952087i
$304$	7.03648	−	5.61141i	0.403570	−	0.321836i
$305$	−1.86230	+	1.48513i	−0.106635	+	0.0850384i
$306$	−6.38802	+	3.07631i	−0.365179	+	0.175861i
$307$		−	19.1803i		−	1.09468i	−0.836910	−	0.547340i	$-0.815640\pi$
$307$		−	19.1803i		−	1.09468i	0.836910	−	0.547340i	$-0.184360\pi$
$308$	−2.16942	−	4.50484i	−0.123614	−	0.256687i
$309$	−5.53151	+	1.26253i	−0.314677	+	0.0718229i
$310$	21.6543	+	10.4282i	1.22988	+	0.592279i
$311$	0.906891	−	1.88318i	0.0514251	−	0.106785i	−0.873673	−	0.486514i	$-0.838268\pi$
$311$	0.906891	−	1.88318i	0.0514251	−	0.106785i	0.925098	+	0.379729i	$0.123983\pi$
$312$	−0.0725948	+	0.318058i	−0.00410987	+	0.0180065i
$313$	−8.04915	−	10.0933i	−0.454965	−	0.570508i	0.500454	−	0.865763i	$-0.333167\pi$
$313$	−8.04915	−	10.0933i	−0.454965	−	0.570508i	−0.955418	+	0.295256i	$0.904595\pi$
$314$	5.61141	−	7.03648i	0.316670	−	0.397092i
$315$	−5.02059	−	21.9966i	−0.282878	−	1.23937i
$316$	9.60704	+	2.19274i	0.540438	+	0.123351i
$317$	−21.6631	−	17.2758i	−1.21672	−	0.970305i	−0.216741	−	0.976229i	$-0.569543\pi$
$317$	−21.6631	−	17.2758i	−1.21672	−	0.970305i	−0.999982	+	0.00592451i	$0.998114\pi$
$318$	−0.763932			−0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	−3.26832	−	2.60640i	−0.182420	−	0.145475i
$322$	−1.66538	−	0.380111i	−0.0928078	−	0.0211828i
$323$	4.73313	+	20.7372i	0.263359	+	1.15385i
$324$	5.75859	−	7.22105i	0.319922	−	0.401169i
$325$	1.45039	+	1.81873i	0.0804529	+	0.100885i
$326$	0.829890	−	3.63598i	0.0459633	−	0.201379i
$327$	−3.85659	+	8.00830i	−0.213270	+	0.442860i
$328$	−7.76458	−	3.73922i	−0.428727	−	0.206464i
$329$	−15.2600	+	3.48300i	−0.841313	+	0.192024i
$330$	−0.882711	−	1.83297i	−0.0485917	−	0.100902i
$331$		−	21.1803i		−	1.16418i	−0.813126	−	0.582088i	$-0.802236\pi$
$331$		−	21.1803i		−	1.16418i	0.813126	−	0.582088i	$-0.197764\pi$
$332$	14.4967	−	6.98126i	0.795612	−	0.383147i
$333$	9.63704	−	7.68528i	0.528107	−	0.421151i
$334$	5.08705	−	4.05678i	0.278351	−	0.221977i
$335$	5.30539	−	2.55494i	0.289865	−	0.139591i
$336$			2.56231i			0.139785i
$337$	−14.7819	−	30.6950i	−0.805223	−	1.67206i	−0.738463	−	0.674294i	$-0.764448\pi$
$337$	−14.7819	−	30.6950i	−0.805223	−	1.67206i	−0.0667606	−	0.997769i	$-0.521266\pi$
$338$	−7.79942	+	1.78017i	−0.424233	+	0.0968283i
$339$	4.42360	+	2.13030i	0.240257	+	0.115702i
$340$	11.8564	−	24.6201i	0.643004	−	1.33521i
$341$	3.10289	−	13.5947i	0.168031	−	0.736192i
$342$	4.89695	+	6.14058i	0.264797	+	0.332045i
$343$	12.5475	−	15.7341i	0.677501	−	0.849559i
$344$	−3.60046	−	15.7747i	−0.194124	−	0.850513i
$345$	2.87045	+	0.655162i	0.154540	+	0.0352727i
$346$	−1.97636	−	1.57610i	−0.106250	−	0.0847315i
$347$	32.1246			1.72454			0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246			1.72454			0.862270	+	0.506449i	$0.169042\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	−10.6470	−	8.49071i	−0.569107	−	0.453847i
$351$	0.799110	+	0.182392i	0.0426533	+	0.00973534i
$352$	−1.72764	−	7.56927i	−0.0920834	−	0.403444i
$353$	11.9240	−	14.9522i	0.634651	−	0.795827i	−0.355672	−	0.934611i	$-0.615748\pi$
$353$	11.9240	−	14.9522i	0.634651	−	0.795827i	0.990323	+	0.138784i	$0.0443194\pi$
$354$	1.45039	+	1.81873i	0.0770871	+	0.0966642i
$355$	−8.98110	+	39.3488i	−0.476667	+	2.08841i
$356$	3.30534	−	6.86361i	0.175183	−	0.363771i
$357$	−5.45602	−	2.62748i	−0.288763	−	0.139061i
$358$	9.64062	−	2.20041i	0.509522	−	0.116295i
$359$	10.3108	+	21.4106i	0.544182	+	1.13001i	0.973886	+	0.227036i	$0.0729037\pi$
$359$	10.3108	+	21.4106i	0.544182	+	1.13001i	−0.429704	+	0.902970i	$0.641382\pi$
$360$		−	22.5623i		−	1.18914i
$361$	4.11050	−	1.97951i	0.216342	−	0.104185i
$362$	−2.87226	+	2.29055i	−0.150963	+	0.120389i
$363$	4.39236	−	3.50279i	0.230539	−	0.183849i
$364$	0.769519	−	0.370581i	0.0403338	−	0.0194237i
$365$		−	52.8328i		−	2.76540i
$366$	0.102426	+	0.212690i	0.00535390	+	0.0111175i
$367$	26.5868	−	6.06826i	1.38782	−	0.316761i	0.537604	−	0.843197i	$-0.319329\pi$
$367$	26.5868	−	6.06826i	1.38782	−	0.316761i	0.850214	+	0.526437i	$0.176472\pi$
$368$	2.06484	+	0.994373i	0.107637	+	0.0518353i
$369$	−4.37796	+	9.09093i	−0.227908	+	0.473255i
$370$	2.49552	−	10.9336i	0.129736	−	0.568411i
$371$	2.78833	+	3.49646i	0.144763	+	0.181527i
$372$	−6.29112	+	7.88881i	−0.326179	+	0.409016i
$373$	−4.58794	−	20.1011i	−0.237555	−	1.04080i	−0.943199	−	0.332229i	$-0.892199\pi$
$373$	−4.58794	−	20.1011i	−0.237555	−	1.04080i	0.705644	−	0.708566i	$-0.250658\pi$
$374$	3.64881	+	0.832817i	0.188675	+	0.0430639i
$375$	9.03977	+	7.20898i	0.466812	+	0.372270i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	−18.9921	−	15.1457i	−0.975558	−	0.777982i	−0.000515656	−	1.00000i	$-0.500164\pi$
$379$	−18.9921	−	15.1457i	−0.975558	−	0.777982i	−0.975043	+	0.222018i	$0.928736\pi$
$380$	−29.5116	−	6.73582i	−1.51391	−	0.345540i
$381$	−2.19274	−	9.60704i	−0.112338	−	0.492184i
$382$	−6.56402	+	8.23102i	−0.335844	+	0.421135i
$383$	17.9902	+	22.5590i	0.919258	+	1.15271i	0.987903	+	0.155072i	$0.0495610\pi$
$383$	17.9902	+	22.5590i	0.919258	+	1.15271i	−0.0686449	+	0.997641i	$0.521868\pi$
$384$	−1.56531	+	6.85807i	−0.0798794	+	0.349975i
$385$	−5.16748	+	10.7304i	−0.263359	+	0.546871i
$386$	6.94485	+	3.34446i	0.353484	+	0.170229i
$387$	−18.4693	+	4.21550i	−0.938847	+	0.214286i
$388$	2.50088	+	5.19312i	0.126963	+	0.263641i
$389$			19.1246i			0.969656i	0.874609	+	0.484828i	$0.161118\pi$
$389$			19.1246i			0.969656i	−0.874609	+	0.484828i	$0.838882\pi$
$390$	0.313108	−	0.150785i	0.0158549	−	0.00763530i
$391$	−4.23472	+	3.37708i	−0.214159	+	0.170786i
$392$	3.49646	−	2.78833i	0.176598	−	0.140832i
$393$	7.97727	−	3.84165i	0.402400	−	0.193786i
$394$		−	3.88854i		−	0.195902i
$395$	−10.1842	−	21.1477i	−0.512422	−	1.06405i
$396$	−5.70733	+	1.30266i	−0.286804	+	0.0654611i
$397$	12.6638	+	6.09855i	0.635577	+	0.306078i	0.723786	−	0.690024i	$-0.242400\pi$
$397$	12.6638	+	6.09855i	0.635577	+	0.306078i	−0.0882095	+	0.996102i	$0.528115\pi$
$398$	−1.56981	+	3.25974i	−0.0786873	+	0.163396i
$399$	−1.49272	+	6.54002i	−0.0747293	+	0.327410i
$400$	11.3915	+	14.2845i	0.569574	+	0.714223i
$401$	15.6302	−	19.5996i	0.780535	−	0.978759i	−0.219460	−	0.975621i	$-0.570430\pi$
$401$	15.6302	−	19.5996i	0.780535	−	0.978759i	0.999995	−	0.00313805i	$-0.000998873\pi$
$402$	−0.129861	−	0.568960i	−0.00647690	−	0.0283772i
$403$	2.32225	+	0.530037i	0.115679	+	0.0264030i
$404$	−0.781831	−	0.623490i	−0.0388976	−	0.0310198i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	−4.73456	−	3.77568i	−0.234396	−	0.186924i
$409$	−26.7290	−	6.10072i	−1.32167	−	0.301661i	−0.497230	−	0.867619i	$-0.665650\pi$
$409$	−26.7290	−	6.10072i	−1.32167	−	0.301661i	−0.824435	+	0.565957i	$0.808507\pi$
$410$	2.04282	+	8.95017i	0.100888	+	0.442017i
$411$	2.75359	−	3.45289i	0.135824	−	0.170318i
$412$	9.26138	+	11.6134i	0.456275	+	0.572151i
$413$	3.03030	−	13.2766i	0.149111	−	0.653299i
$414$	−0.867767	+	1.80194i	−0.0426484	+	0.0885604i
$415$	−34.5307	−	16.6291i	−1.69505	−	0.816292i
$416$	1.29299	−	0.295116i	0.0633939	−	0.0144692i
$417$	0.346401	+	0.719310i	0.0169634	+	0.0352248i
$418$		−	4.14590i		−	0.202783i
$419$	−15.8231	+	7.62000i	−0.773009	+	0.372261i	−0.778436	−	0.627724i	$-0.783987\pi$
$419$	−15.8231	+	7.62000i	−0.773009	+	0.372261i	0.00542744	+	0.999985i	$0.498272\pi$
$420$	6.73785	−	5.37326i	0.328773	−	0.262188i
$421$	−24.2637	+	19.3497i	−1.18254	+	0.943045i	−0.999199	−	0.0400047i	$-0.987263\pi$
$421$	−24.2637	+	19.3497i	−1.18254	+	0.943045i	−0.183341	+	0.983049i	$0.558691\pi$
$422$	6.48844	−	3.12467i	0.315852	−	0.152106i
$423$			18.3262i			0.891052i
$424$	1.94039	+	4.02926i	0.0942335	+	0.195678i
$425$	−42.0977	+	9.60853i	−2.04204	+	0.466082i
$426$	3.60388	+	1.73553i	0.174608	+	0.0840869i
$427$	0.599613	−	1.24511i	0.0290173	−	0.0602550i
$428$	−2.43533	+	10.6699i	−0.117716	+	0.515748i
$429$	−0.125712	−	0.157638i	−0.00606942	−	0.00761082i
$430$	−10.7465	+	13.4757i	−0.518243	+	0.649856i
$431$	−3.24808	−	14.2308i	−0.156455	−	0.685472i	−0.990925	−	0.134419i	$-0.957083\pi$
$431$	−3.24808	−	14.2308i	−0.156455	−	0.685472i	0.834470	−	0.551053i	$-0.185774\pi$
$432$	6.27629	+	1.43252i	0.301968	+	0.0689222i
$433$	−8.11695	−	6.47305i	−0.390076	−	0.311075i	0.408740	−	0.912651i	$-0.365968\pi$
$433$	−8.11695	−	6.47305i	−0.390076	−	0.311075i	−0.798816	+	0.601576i	$0.794540\pi$
$434$	−13.9443			−0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	4.69099	+	3.74094i	0.224400	+	0.178953i
$438$	−5.10479	−	1.16513i	−0.243916	−	0.0556723i
$439$	−4.66054	−	20.4192i	−0.222435	−	0.974553i	−0.955638	−	0.294543i	$-0.904833\pi$
$439$	−4.66054	−	20.4192i	−0.222435	−	0.974553i	0.733203	−	0.680010i	$-0.238025\pi$
$440$	−7.42566	+	9.31148i	−0.354004	+	0.443907i
$441$	−3.26463	−	4.09372i	−0.155459	−	0.194939i
$442$	−0.142262	+	0.623291i	−0.00676672	+	0.0296469i
$443$	0.828644	−	1.72070i	0.0393701	−	0.0817528i	−0.880356	−	0.474313i	$-0.842696\pi$
$443$	0.828644	−	1.72070i	0.0393701	−	0.0817528i	0.919726	+	0.392561i	$0.128411\pi$
$444$	4.24195	+	2.04281i	0.201314	+	0.0969476i
$445$	−17.6909	+	4.03784i	−0.838631	+	0.191412i
$446$	−0.716982	−	1.48883i	−0.0339501	−	0.0704981i
$447$			5.94427i			0.281154i
$448$	0.475589	−	0.229032i	0.0224695	−	0.0108207i
$449$	20.4250	−	16.2884i	0.963917	−	0.768698i	−0.00897427	−	0.999960i	$-0.502857\pi$
$449$	20.4250	−	16.2884i	0.963917	−	0.768698i	0.972892	+	0.231261i	$0.0742852\pi$
$450$	−12.4657	+	9.94109i	−0.587640	+	0.468628i
$451$	4.79877	−	2.31097i	0.225965	−	0.108819i
$452$		−	12.8541i		−	0.604606i
$453$	−0.716982	−	1.48883i	−0.0336868	−	0.0699513i
$454$	−12.5862	+	2.87271i	−0.590697	+	0.134823i
$455$	−1.83297	−	0.882711i	−0.0859309	−	0.0413821i
$456$	−2.91058	+	6.04388i	−0.136300	+	0.283031i
$457$	4.16297	−	18.2392i	0.194735	−	0.853191i	−0.779274	−	0.626683i	$-0.784412\pi$
$457$	4.16297	−	18.2392i	0.194735	−	0.853191i	0.974009	−	0.226508i	$-0.0727309\pi$
$458$	0.883116	+	1.10739i	0.0412653	+	0.0517450i
$459$	−9.48626	+	11.8954i	−0.442781	+	0.555230i
$460$	−1.71524	−	7.51494i	−0.0799733	−	0.350386i
$461$	−38.0014	−	8.67358i	−1.76990	−	0.403969i	−0.791582	−	0.611063i	$-0.790742\pi$
$461$	−38.0014	−	8.67358i	−1.76990	−	0.403969i	−0.978321	+	0.207094i	$0.933599\pi$
$462$	0.922827	+	0.735930i	0.0429338	+	0.0342386i
$463$	−10.7082			−0.497652			−0.248826	−	0.968548i	$-0.580045\pi$
$463$	−10.7082			−0.497652			−0.248826	+	0.968548i	$0.580045\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	7.36204	+	5.87103i	0.341040	+	0.271970i
$467$	17.4944	+	3.99298i	0.809543	+	0.184773i	0.607207	−	0.794543i	$-0.292290\pi$
$467$	17.4944	+	3.99298i	0.809543	+	0.184773i	0.202336	+	0.979316i	$0.435147\pi$
$468$	−0.222521	−	0.974928i	−0.0102860	−	0.0450661i
$469$	−2.13010	+	2.67106i	−0.0983587	+	0.123338i
$470$	10.3959	+	13.0361i	0.479528	+	0.601309i
$471$	2.00269	−	8.77435i	0.0922790	−	0.404301i
$472$	5.90864	−	12.2694i	0.271967	−	0.564746i
$473$	9.00969	+	4.33884i	0.414266	+	0.199500i
$474$	−2.26791	+	0.517637i	−0.104169	+	0.0237758i
$475$	20.7539	+	43.0959i	0.952253	+	1.97737i
$476$			15.8541i			0.726672i
$477$	4.71753	−	2.27184i	0.216001	−	0.104021i
$478$	13.4052	−	10.6903i	0.613140	−	0.488963i
$479$	−8.74114	+	6.97083i	−0.399393	+	0.318505i	−0.802505	−	0.596645i	$-0.796500\pi$
$479$	−8.74114	+	6.97083i	−0.399393	+	0.318505i	0.403112	+	0.915151i	$0.367928\pi$
$480$	12.0567	−	5.80622i	0.550312	−	0.265016i
$481$		−	1.11146i		−	0.0506780i
$482$	−1.24758	−	2.59064i	−0.0568259	−	0.118000i
$483$	−1.66538	+	0.380111i	−0.0757772	+	0.0172957i
$484$	−13.2516	−	6.38165i	−0.602347	−	0.290075i
$485$	5.95700	−	12.3698i	0.270494	−	0.561686i
$486$	−1.91769	+	8.40196i	−0.0869883	+	0.381121i
$487$	26.5372	+	33.2766i	1.20251	+	1.50790i	0.808178	+	0.588938i	$0.200454\pi$
$487$	26.5372	+	33.2766i	1.20251	+	1.50790i	0.394335	+	0.918967i	$0.370975\pi$
$488$	0.861642	−	1.08046i	0.0390047	−	0.0489103i
$489$	−0.829890	−	3.63598i	−0.0375289	−	0.164425i
$490$	−4.64449	−	1.06007i	−0.209817	−	0.0478893i
$491$	11.8249	+	9.43004i	0.533650	+	0.425572i	0.852881	−	0.522105i	$-0.174853\pi$
$491$	11.8249	+	9.43004i	0.533650	+	0.425572i	−0.319231	+	0.947677i	$0.603425\pi$
$492$	−3.85410			−0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	10.9021	+	8.69411i	0.490012	+	0.390771i
$496$	18.2392	+	4.16297i	0.818962	+	0.186923i
$497$	−5.21064	−	22.8293i	−0.233729	−	1.02403i
$498$	−2.36825	+	2.96969i	−0.106124	+	0.133075i
$499$	−15.3920	−	19.3010i	−0.689042	−	0.864032i	0.307110	−	0.951674i	$-0.400638\pi$
$499$	−15.3920	−	19.3010i	−0.689042	−	0.864032i	−0.996152	+	0.0876423i	$0.972067\pi$
$500$	6.73582	−	29.5116i	0.301235	−	1.31980i
$501$	2.82310	−	5.86222i	0.126127	−	0.261905i
$502$	−10.9431	−	5.26991i	−0.488413	−	0.235207i
$503$	−13.9127	+	3.17549i	−0.620337	+	0.141588i	−0.521128	−	0.853479i	$-0.674489\pi$
$503$	−13.9127	+	3.17549i	−0.620337	+	0.141588i	−0.0992095	+	0.995067i	$0.531631\pi$
$504$	5.67961	+	11.7938i	0.252990	+	0.525339i
$505$			2.38197i			0.105996i
$506$	0.951178	−	0.458063i	0.0422850	−	0.0203634i
$507$	−6.25465	+	4.98792i	−0.277779	+	0.221521i
$508$	−20.1700	+	16.0850i	−0.894898	+	0.713657i
$509$	−28.4367	+	13.6944i	−1.26043	+	0.606992i	−0.940289	−	0.340377i	$-0.889445\pi$
$509$	−28.4367	+	13.6944i	−1.26043	+	0.606992i	−0.320143	+	0.947369i	$0.603731\pi$
$510$			6.45085i			0.285648i
$511$	13.2996	+	27.6169i	0.588340	+	1.22170i
$512$	18.2392	−	4.16297i	0.806064	−	0.183979i
$513$	15.1850	+	7.31272i	0.670435	+	0.322865i
$514$	−6.21592	+	12.9075i	−0.274173	+	0.569325i
$515$	7.87323	−	34.4949i	0.346936	−	1.52003i
$516$	−4.51161	−	5.65739i	−0.198613	−	0.249053i
$517$	6.03149	−	7.56325i	0.265265	−	0.332631i
$518$	1.44785	+	6.34344i	0.0636149	+	0.278715i
$519$	−2.46449	−	0.562503i	−0.108179	−	0.0246911i
$520$	−1.59059	−	1.26845i	−0.0697520	−	0.0556254i
$521$	−4.09017			−0.179194			−0.0895968	−	0.995978i	$-0.528558\pi$
$521$	−4.09017			−0.179194			−0.0895968	+	0.995978i	$0.528558\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	−18.1231	−	14.4527i	−0.791712	−	0.631369i
$525$	−13.2766	−	3.03030i	−0.579438	−	0.132253i
$526$	−2.29780	−	10.0673i	−0.100189	−	0.438957i
$527$	−27.5675	+	34.5685i	−1.20086	+	1.50583i
$528$	−0.987354	−	1.23810i	−0.0429690	−	0.0538815i
$529$	4.77800	−	20.9338i	0.207739	−	0.910165i
$530$	2.06699	−	4.29215i	0.0897844	−	0.186439i
$531$	−14.3653	−	6.91796i	−0.623401	−	0.300214i
$532$	17.1220	−	3.90798i	0.742332	−	0.169432i
$533$	0.394760	+	0.819729i	0.0170990	+	0.0355064i
$534$			1.79837i			0.0778232i
$535$	23.4873	−	11.3109i	1.01544	−	0.489011i
$536$	−2.67106	+	2.13010i	−0.115372	+	0.0920061i
$537$	7.73117	−	6.16541i	0.333625	−	0.266057i
$538$	3.34098	−	1.60893i	0.144040	−	0.0693659i
$539$			2.76393i			0.119051i
$540$	−9.39466	−	19.5082i	−0.404282	−	0.839500i
$541$	−14.2308	+	3.24808i	−0.611829	+	0.139646i	−0.517197	−	0.855866i	$-0.673025\pi$
$541$	−14.2308	+	3.24808i	−0.611829	+	0.139646i	−0.0946319	+	0.995512i	$0.530167\pi$
$542$	−5.66871	−	2.72991i	−0.243492	−	0.117260i
$543$	−1.59399	+	3.30995i	−0.0684045	+	0.142043i
$544$	−5.47803	+	24.0008i	−0.234869	+	1.02903i
$545$	−34.5598	−	43.3366i	−1.48038	−	1.85634i
$546$	−0.125712	+	0.157638i	−0.00537997	+	0.00674627i
$547$	−1.64264	−	7.19688i	−0.0702343	−	0.307717i	0.927594	−	0.373591i	$-0.121874\pi$
$547$	−1.64264	−	7.19688i	−0.0702343	−	0.307717i	−0.997828	+	0.0658742i	$0.979016\pi$
$548$	−11.2724	−	2.57286i	−0.481534	−	0.109907i
$549$	−1.26503	−	1.00883i	−0.0539902	−	0.0430557i
$550$	8.41641			0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	10.6470	+	8.49071i	0.452757	+	0.361062i
$554$	12.8835	+	2.94057i	0.547366	+	0.124933i
$555$	−2.49552	−	10.9336i	−0.105929	−	0.464106i
$556$	1.30320	−	1.63416i	0.0552680	−	0.0693038i
$557$	3.43330	+	4.30522i	0.145473	+	0.182418i	0.849230	−	0.528024i	$-0.177067\pi$
$557$	3.43330	+	4.30522i	0.145473	+	0.182418i	−0.703756	+	0.710441i	$0.748495\pi$
$558$	−3.63293	+	15.9169i	−0.153794	+	0.673816i
$559$	−0.741162	+	1.53904i	−0.0313478	+	0.0650944i
$560$	−14.3963	−	6.93290i	−0.608356	−	0.292969i
$561$	3.64881	−	0.832817i	0.154053	−	0.0351616i
$562$	−6.20098	−	12.8765i	−0.261572	−	0.543161i
$563$		−	28.3951i		−	1.19671i	−0.801230	−	0.598356i	$-0.795821\pi$
$563$		−	28.3951i		−	1.19671i	0.801230	−	0.598356i	$-0.204179\pi$
$564$	−6.30678	+	3.03719i	−0.265563	+	0.127889i
$565$	−23.9381	+	19.0900i	−1.00709	+	0.803124i
$566$	−2.53006	+	2.01766i	−0.106346	+	0.0848084i
$567$	11.4999	−	5.53806i	0.482951	−	0.232577i
$568$		−	23.4164i		−	0.982531i
$569$	−0.843588	−	1.75173i	−0.0353650	−	0.0734363i	0.882538	−	0.470241i	$-0.155833\pi$
$569$	−0.843588	−	1.75173i	−0.0353650	−	0.0734363i	−0.917903	+	0.396805i	$0.870119\pi$
$570$	6.96674	−	1.59011i	0.291804	−	0.0666025i
$571$	31.0894	+	14.9718i	1.30105	+	0.626552i	0.950713	−	0.310072i	$-0.100353\pi$
$571$	31.0894	+	14.9718i	1.30105	+	0.626552i	0.350336	+	0.936624i	$0.386067\pi$
$572$	−0.229032	+	0.475589i	−0.00957629	+	0.0198854i
$573$	−2.34267	+	10.2639i	−0.0978664	+	0.428781i
$574$	−3.32086	−	4.16422i	−0.138610	−	0.173811i
$575$	−7.59432	+	9.52297i	−0.316705	+	0.397135i
$576$	−0.137526	−	0.602539i	−0.00573023	−	0.0251058i
$577$	−2.69463	−	0.615033i	−0.112179	−	0.0256041i	0.166063	−	0.986115i	$-0.446895\pi$
$577$	−2.69463	−	0.615033i	−0.112179	−	0.0256041i	−0.278242	+	0.960511i	$0.589752\pi$
$578$	−1.06382	−	0.848370i	−0.0442492	−	0.0352875i
$579$	7.70820			0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	−1.06382	−	0.848370i	−0.0440969	−	0.0351661i
$583$	−2.69463	−	0.615033i	−0.111600	−	0.0254721i
$584$	6.82082	+	29.8840i	0.282247	+	1.23661i
$585$	−1.48513	+	1.86230i	−0.0614026	+	0.0769965i
$586$	−3.28611	−	4.12065i	−0.135748	−	0.170223i
$587$	−10.3735	+	45.4492i	−0.428160	+	1.87589i	0.0518966	+	0.998652i	$0.483473\pi$
$587$	−10.3735	+	45.4492i	−0.428160	+	1.87589i	−0.480056	+	0.877238i	$0.659384\pi$
$588$	0.867767	−	1.80194i	0.0357861	−	0.0743107i
$589$	44.1283	+	21.2511i	1.81827	+	0.875635i
$590$	−14.1429	+	3.22802i	−0.582253	+	0.132895i
$591$	−1.68718	−	3.50346i	−0.0694011	−	0.144113i
$592$		−	8.72949i		−	0.358780i
$593$	−13.0079	+	6.26428i	−0.534171	+	0.257243i	−0.681466	−	0.731849i	$-0.738657\pi$
$593$	−13.0079	+	6.26428i	−0.534171	+	0.257243i	0.147295	+	0.989093i	$0.452943\pi$
$594$	2.31857	−	1.84900i	0.0951319	−	0.0758652i
$595$	29.5250	−	23.5454i	1.21041	−	0.965268i
$596$	14.0212	−	6.75223i	0.574329	−	0.276582i
$597$			3.61803i			0.148076i
$598$	0.0782465	+	0.162481i	0.00319974	+	0.00664433i
$599$	12.7412	−	2.90810i	0.520592	−	0.118822i	0.0458528	−	0.998948i	$-0.485399\pi$
$599$	12.7412	−	2.90810i	0.520592	−	0.118822i	0.474739	+	0.880126i	$0.342542\pi$
$600$	−12.2694	−	5.90864i	−0.500897	−	0.241219i
$601$	12.6516	−	26.2714i	0.516071	−	1.07163i	−0.466289	−	0.884633i	$-0.654409\pi$
$601$	12.6516	−	26.2714i	0.516071	−	1.07163i	0.982360	−	0.187000i	$-0.0598765\pi$
$602$	2.22521	−	9.74928i	0.0906928	−	0.397351i
$603$	2.49396	+	3.12733i	0.101562	+	0.127355i
$604$	−2.69737	+	3.38239i	−0.109754	+	0.137627i
$605$	7.79590	+	34.1561i	0.316948	+	1.38864i
$606$	0.230149	+	0.0525301i	0.00934917	+	0.00213389i
$607$	−8.58350	−	6.84512i	−0.348394	−	0.277835i	0.433620	−	0.901096i	$-0.357236\pi$
$607$	−8.58350	−	6.84512i	−0.348394	−	0.277835i	−0.782014	+	0.623261i	$0.785807\pi$
$608$	27.2705			1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	1.29196	+	1.03030i	0.0522670	+	0.0416816i
$612$	18.0969	+	4.13050i	0.731524	+	0.166966i
$613$	6.12845	+	26.8505i	0.247526	+	1.08448i	0.933985	+	0.357313i	$0.116307\pi$
$613$	6.12845	+	26.8505i	0.247526	+	1.08448i	−0.686459	+	0.727169i	$0.740836\pi$
$614$	7.39091	−	9.26791i	0.298273	−	0.374022i
$615$	5.72385	+	7.17748i	0.230808	+	0.289424i
$616$	1.53758	−	6.73659i	0.0619509	−	0.271425i
$617$	6.15262	−	12.7760i	0.247695	−	0.514344i	−0.739638	−	0.673005i	$-0.765003\pi$
$617$	6.15262	−	12.7760i	0.247695	−	0.514344i	0.987333	+	0.158661i	$0.0507176\pi$
$618$	−3.15932	−	1.52145i	−0.127086	−	0.0612016i
$619$	−6.87883	+	1.57005i	−0.276483	+	0.0631055i	−0.358514	−	0.933524i	$-0.616717\pi$
$619$	−6.87883	+	1.57005i	−0.276483	+	0.0631055i	0.0820308	+	0.996630i	$0.473859\pi$
$620$	−27.3013	−	56.6917i	−1.09644	−	2.27679i
$621$			4.29180i			0.172224i
$622$	1.16387	−	0.560489i	0.0466669	−	0.0224736i
$623$	8.23102	−	6.56402i	0.329769	−	0.262982i
$624$	0.211493	−	0.168660i	0.00846650	−	0.00675181i
$625$	−20.5717	+	9.90679i	−0.822866	+	0.396271i
$626$		−	7.97871i		−	0.318894i
$627$	−1.79884	−	3.73533i	−0.0718387	−	0.149175i
$628$	−22.9715	+	5.24311i	−0.916665	+	0.209223i
$629$	18.5881	+	8.95154i	0.741154	+	0.356921i
$630$	6.05019	−	12.5634i	0.241045	−	0.500536i
$631$	−6.27838	+	27.5074i	−0.249938	+	1.09505i	0.681691	+	0.731641i	$0.261245\pi$
$631$	−6.27838	+	27.5074i	−0.249938	+	1.09505i	−0.931629	+	0.363411i	$0.881612\pi$
$632$	8.49071	+	10.6470i	0.337742	+	0.423515i
$633$	4.49014	−	5.63046i	0.178467	−	0.223791i
$634$	−3.81058	−	16.6953i	−0.151338	−	0.663054i
$635$	59.9101	+	13.6741i	2.37746	+	0.542640i
$636$	1.56366	+	1.24698i	0.0620033	+	0.0494460i
$637$	−0.472136			−0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	−34.2968	−	27.3508i	−1.35570	−	1.08113i
$641$	−10.7785	−	2.46013i	−0.425727	−	0.0971693i	0.00428892	−	0.999991i	$-0.498635\pi$
$641$	−10.7785	−	2.46013i	−0.425727	−	0.0971693i	−0.430016	+	0.902821i	$0.641492\pi$
$642$	−0.574903	−	2.51882i	−0.0226896	−	0.0994097i
$643$	23.3287	−	29.2533i	0.919996	−	1.15364i	−0.0677709	−	0.997701i	$-0.521589\pi$
$643$	23.3287	−	29.2533i	0.919996	−	1.15364i	0.987767	−	0.155938i	$-0.0498399\pi$
$644$	2.78833	+	3.49646i	0.109876	+	0.137780i
$645$	−3.83539	+	16.8039i	−0.151018	+	0.661654i
$646$	−5.70379	+	11.8440i	−0.224413	+	0.465998i
$647$	−27.5047	−	13.2455i	−1.08132	−	0.520736i	−0.193581	−	0.981084i	$-0.562010\pi$
$647$	−27.5047	−	13.2455i	−1.08132	−	0.520736i	−0.887738	+	0.460348i	$0.847725\pi$
$648$	12.4439	−	2.84024i	0.488843	−	0.111575i
$649$	3.65174	+	7.58292i	0.143343	+	0.297656i
$650$			1.43769i			0.0563910i
$651$	−12.5634	+	6.05019i	−0.492397	+	0.237126i
$652$	−7.63375	+	6.08771i	−0.298961	+	0.238413i
$653$	37.5382	−	29.9357i	1.46898	−	1.17147i	0.520830	−	0.853660i	$-0.325622\pi$
$653$	37.5382	−	29.9357i	1.46898	−	1.17147i	0.948153	−	0.317815i	$-0.102949\pi$
$654$	−4.94940	+	2.38351i	−0.193537	+	0.0932025i
$655$			55.2148i			2.15742i
$656$	3.10049	+	6.43823i	0.121054	+	0.251371i
$657$	34.9887	−	7.98595i	1.36504	−	0.311562i
$658$	−8.71576	−	4.19729i	−0.339776	−	0.163627i
$659$	−3.06137	+	6.35699i	−0.119254	+	0.247633i	−0.952047	−	0.305950i	$-0.901026\pi$
$659$	−3.06137	+	6.35699i	−0.119254	+	0.247633i	0.832794	+	0.553584i	$0.186740\pi$
$660$	−1.18520	+	5.19270i	−0.0461338	+	0.202125i
$661$	−23.3502	−	29.2803i	−0.908218	−	1.13887i	−0.989837	−	0.142206i	$-0.954580\pi$
$661$	−23.3502	−	29.2803i	−0.908218	−	1.13887i	0.0816186	−	0.996664i	$-0.473991\pi$
$662$	8.16159	−	10.2343i	0.317209	−	0.397768i
$663$	0.142262	+	0.623291i	0.00552500	+	0.0242066i
$664$	21.6786	+	4.94799i	0.841291	+	0.192019i
$665$	−32.7062	−	26.0823i	−1.26829	−	1.01143i
$666$	7.61803			0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	−1.29196	−	1.03030i	−0.0499500	−	0.0398338i
$670$	3.54807	+	0.809825i	0.137074	+	0.0312863i
$671$	0.190056	+	0.832688i	0.00733701	+	0.0321456i
$672$	−4.84073	+	6.07009i	−0.186735	+	0.234159i
$673$	4.03531	+	5.06012i	0.155550	+	0.195053i	0.853500	−	0.521093i	$-0.174476\pi$
$673$	4.03531	+	5.06012i	0.155550	+	0.195053i	−0.697950	+	0.716147i	$0.745904\pi$
$674$	4.68534	−	20.5278i	0.180473	−	0.790702i
$675$	−14.8452	+	30.8265i	−0.571393	+	1.18651i
$676$	18.8701	+	9.08738i	0.725774	+	0.349515i
$677$	39.8091	−	9.08616i	1.52999	−	0.349209i	0.627048	−	0.778980i	$-0.284263\pi$
$677$	39.8091	−	9.08616i	1.52999	−	0.349209i	0.902938	+	0.429771i	$0.141406\pi$
$678$	1.31659	+	2.73394i	0.0505635	+	0.104996i
$679$			7.96556i			0.305690i
$680$	34.0241	−	16.3852i	1.30477	−	0.628342i
$681$	−10.0933	+	8.04915i	−0.386777	+	0.308444i
$682$	6.73785	−	5.37326i	0.258006	−	0.205753i
$683$	−18.7889	+	9.04826i	−0.718937	+	0.346222i	−0.757322	−	0.653041i	$-0.773493\pi$
$683$	−18.7889	+	9.04826i	−0.718937	+	0.346222i	0.0383853	+	0.999263i	$0.487779\pi$
$684$		−	20.5623i		−	0.786219i
$685$	11.9496	+	24.8136i	0.456571	+	0.948079i
$686$	12.1259	−	2.76765i	0.462967	−	0.105669i
$687$	1.27614	+	0.614556i	0.0486878	+	0.0234468i
$688$	−5.82116	+	12.0878i	−0.221930	+	0.460842i
$689$	0.105060	−	0.460299i	0.00400247	−	0.0175360i
$690$	1.13454	+	1.42267i	0.0431912	+	0.0541600i
$691$	7.37764	−	9.25127i	0.280659	−	0.351935i	−0.621442	−	0.783460i	$-0.713453\pi$
$691$	7.37764	−	9.25127i	0.280659	−	0.351935i	0.902101	+	0.431525i	$0.142024\pi$
$692$	1.47265	+	6.45211i	0.0559818	+	0.245272i
$693$	−7.88733	−	1.80023i	−0.299615	−	0.0683852i
$694$	15.5226	+	12.3788i	0.589228	+	0.469894i
$695$	−4.97871			−0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	2.18786	+	1.74476i	0.0828116	+	0.0660400i
$699$	9.18032	+	2.09535i	0.347232	+	0.0792533i
$700$	7.93342	+	34.7586i	0.299855	+	1.31375i
$701$	13.1280	−	16.4620i	0.495839	−	0.621762i	−0.469446	−	0.882961i	$-0.655546\pi$
$701$	13.1280	−	16.4620i	0.495839	−	0.621762i	0.965285	+	0.261199i	$0.0841178\pi$
$702$	0.315846	+	0.396058i	0.0119208	+	0.0149483i
$703$	5.08552	−	22.2811i	0.191804	−	0.840348i
$704$	−0.141549	+	0.293930i	−0.00533484	+	0.0110779i
$705$	15.0225	+	7.23447i	0.565782	+	0.272466i
$706$	11.5233	−	2.63012i	0.433686	−	0.0989859i
$707$	−0.599613	−	1.24511i	−0.0225508	−	0.0468271i
$708$		−	6.09017i		−	0.228883i
$709$	−37.3961	+	18.0090i	−1.40444	+	0.676343i	−0.974057	−	0.226302i	$-0.927336\pi$
$709$	−37.3961	+	18.0090i	−1.40444	+	0.676343i	−0.430384	+	0.902646i	$0.641622\pi$
$710$	−19.5022	+	15.5525i	−0.731905	+	0.583675i
$711$	12.4657	−	9.94109i	0.467502	−	0.372820i
$712$	9.48528	−	4.56787i	0.355476	−	0.171188i
$713$			12.4721i			0.467085i
$714$	−1.62387	−	3.37201i	−0.0607719	−	0.126194i
$715$	1.22583	−	0.279788i	0.0458434	−	0.0104635i
$716$	−23.3248	−	11.2326i	−0.871688	−	0.419783i
$717$	7.43933	−	15.4479i	0.277827	−	0.576913i
$718$	−3.26815	+	14.3187i	−0.121966	+	0.534369i
$719$	5.30376	+	6.65071i	0.197797	+	0.248030i	0.870832	−	0.491581i	$-0.163581\pi$
$719$	5.30376	+	6.65071i	0.197797	+	0.248030i	−0.673035	+	0.739611i	$0.735010\pi$
$720$	−11.6644	+	14.6267i	−0.434706	+	0.545104i
$721$	4.56788	+	20.0132i	0.170117	+	0.745330i
$722$	2.74897	+	0.627433i	0.102306	+	0.0233507i
$723$	−2.24807	−	1.79278i	−0.0836066	−	0.0666740i
$724$	9.61803			0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	21.9349	+	17.4925i	0.813519	+	0.648759i	0.939223	−	0.343308i	$-0.111548\pi$
$727$	21.9349	+	17.4925i	0.813519	+	0.648759i	−0.125704	+	0.992068i	$0.540119\pi$
$728$	1.15075	+	0.262650i	0.0426495	+	0.00973447i
$729$	−1.89289	−	8.29330i	−0.0701071	−	0.307159i
$730$	20.3585	−	25.5287i	0.753501	−	0.944861i
$731$	−19.7697	−	24.7905i	−0.731210	−	0.916909i
$732$	0.137526	−	0.602539i	0.00508309	−	0.0222705i
$733$	−6.43001	+	13.3521i	−0.237498	+	0.493169i	−0.985317	−	0.170733i	$-0.945387\pi$
$733$	−6.43001	+	13.3521i	−0.237498	+	0.493169i	0.747820	+	0.663902i	$0.231101\pi$
$734$	15.1850	+	7.31272i	0.560489	+	0.269917i
$735$	−4.64449	+	1.06007i	−0.171315	+	0.0391014i
$736$	3.01301	+	6.25657i	0.111061	+	0.230620i
$737$		−	2.11146i		−	0.0777765i
$738$	−5.61850	+	2.70573i	−0.206820	+	0.0995992i
$739$	39.1454	−	31.2174i	1.43999	−	1.14835i	0.476968	−	0.878920i	$-0.341736\pi$
$739$	39.1454	−	31.2174i	1.43999	−	1.14835i	0.963020	−	0.269432i	$-0.0868358\pi$
$740$	−22.9551	+	18.3061i	−0.843846	+	0.672945i
$741$	0.638070	−	0.307278i	0.0234401	−	0.0112881i
$742$			2.76393i			0.101467i
$743$	15.2884	+	31.7466i	0.560875	+	1.16467i	0.967919	+	0.251261i	$0.0808453\pi$
$743$	15.2884	+	31.7466i	0.560875	+	1.16467i	−0.407044	+	0.913409i	$0.633440\pi$
$744$	−13.5947	+	3.10289i	−0.498404	+	0.113758i
$745$	−33.3979	−	16.0836i	−1.22360	−	0.589257i
$746$	5.52883	−	11.4807i	0.202425	−	0.420339i
$747$	5.79321	−	25.3817i	0.211962	−	0.928668i
$748$	−6.10919	−	7.66068i	−0.223374	−	0.280102i
$749$	−9.43004	+	11.8249i	−0.344566	+	0.432072i
$750$	1.59011	+	6.96674i	0.0580627	+	0.254389i
$751$	−18.0633	−	4.12284i	−0.659140	−	0.150444i	−0.120149	−	0.992756i	$-0.538337\pi$
$751$	−18.0633	−	4.12284i	−0.659140	−	0.150444i	−0.538991	+	0.842311i	$0.681194\pi$
$752$	10.1472	+	8.09210i	0.370029	+	0.295088i
$753$	−12.1459			−0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	9.82161	+	7.83247i	0.357208	+	0.284864i
$757$	0.0207525	+	0.00473663i	0.000754264	+	0.000172156i	0.222898	−	0.974842i	$-0.428448\pi$
$757$	0.0207525	+	0.00473663i	0.000754264	+	0.000172156i	−0.222144	+	0.975014i	$0.571305\pi$
$758$	−3.34074	−	14.6367i	−0.121341	−	0.531630i
$759$	0.658236	−	0.825401i	0.0238924	−	0.0299602i
$760$	−26.0823	−	32.7062i	−0.946106	−	1.18638i
$761$	−5.60789	+	24.5698i	−0.203286	+	0.890653i	0.765634	+	0.643277i	$0.222426\pi$
$761$	−5.60789	+	24.5698i	−0.203286	+	0.890653i	−0.968919	+	0.247377i	$0.920432\pi$
$762$	2.64243	−	5.48705i	0.0957250	−	0.198775i
$763$	28.9743	+	13.9533i	1.04894	+	0.505143i
$764$	26.8713	−	6.13319i	0.972168	−	0.221891i
$765$	−19.1841	−	39.8361i	−0.693602	−	1.44028i
$766$			17.8328i			0.644326i
$767$	−1.29532	+	0.623792i	−0.0467712	+	0.0225238i
$768$	−3.17090	+	2.52871i	−0.114420	+	0.0912468i
$769$	−15.1368	+	12.0712i	−0.545847	+	0.435298i	−0.857191	−	0.514999i	$-0.827792\pi$
$769$	−15.1368	+	12.0712i	−0.545847	+	0.435298i	0.311344	+	0.950297i	$0.399221\pi$
$770$	−6.63174	+	3.19368i	−0.238991

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.483198 + 0.385338i) q^{2} +(0.602539 + 0.137526i) q^{3} +(-0.360046 - 1.57747i) q^{4} +(-2.40299 + 3.01326i) q^{5} +(0.238152 + 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(0.970194 - 2.01463i) q^{8} +(-2.35877 - 1.13592i) q^{9} +O(q^{10})\)	\(q+(0.483198 + 0.385338i) q^{2} +(0.602539 + 0.137526i) q^{3} +(-0.360046 - 1.57747i) q^{4} +(-2.40299 + 3.01326i) q^{5} +(0.238152 + 0.298633i) q^{6} +(0.497572 - 2.18001i) q^{7} +(0.970194 - 2.01463i) q^{8} +(-2.35877 - 1.13592i) q^{9} +(-2.32225 + 0.530037i) q^{10} +(0.599613 + 1.24511i) q^{11} -1.00000i q^{12} +(-0.212690 + 0.102426i) q^{13} +(1.08046 - 0.861642i) q^{14} +(-1.86230 + 1.48513i) q^{15} +(-1.67049 + 0.804465i) q^{16} -4.38197i q^{17} +(-0.702039 - 1.45780i) q^{18} +(-4.73240 + 1.08014i) q^{19} +(5.61850 + 2.70573i) q^{20} +(0.599613 - 1.24511i) q^{21} +(-0.190056 + 0.832688i) q^{22} +(-0.770676 - 0.966397i) q^{23} +(0.861642 - 1.08046i) q^{24} +(-2.19274 - 9.60704i) q^{25} +(-0.142240 - 0.0324654i) q^{26} +(-2.71463 - 2.16484i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(-7.88881 - 6.29112i) q^{31} +(-5.47718 - 1.25013i) q^{32} +(0.190056 + 0.832688i) q^{33} +(1.68854 - 2.11736i) q^{34} +(5.37326 + 6.73785i) q^{35} +(-0.942614 + 4.12986i) q^{36} +(-2.04281 + 4.24195i) q^{37} +(-2.70291 - 1.30165i) q^{38} +(-0.142240 + 0.0324654i) q^{39} +(3.73922 + 7.76458i) q^{40} -3.85410i q^{41} +(0.769519 - 0.370581i) q^{42} +(5.65739 - 4.51161i) q^{43} +(1.74823 - 1.39417i) q^{44} +(9.09093 - 4.37796i) q^{45} -0.763932i q^{46} +(-3.03719 - 6.30678i) q^{47} +(-1.11717 + 0.254986i) q^{48} +(1.80194 + 0.867767i) q^{49} +(2.64243 - 5.48705i) q^{50} +(0.602632 - 2.64030i) q^{51} +(0.238152 + 0.298633i) q^{52} +(-1.24698 + 1.56366i) q^{53} +(-0.477507 - 2.09210i) q^{54} +(-5.19270 - 1.18520i) q^{55} +(-3.90916 - 3.11745i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(3.01326 + 2.40299i) q^{60} +(0.602539 + 0.137526i) q^{61} +(-1.38766 - 6.07972i) q^{62} +(-3.64997 + 4.57692i) q^{63} +(0.147186 + 0.184565i) q^{64} +(0.202456 - 0.887019i) q^{65} +(-0.229032 + 0.475589i) q^{66} +(-1.37656 - 0.662915i) q^{67} +(-6.91240 + 1.57771i) q^{68} +(-0.331458 - 0.688279i) q^{69} +5.32624i q^{70} +(9.43507 - 4.54369i) q^{71} +(-4.57692 + 3.64997i) q^{72} +(-10.7175 + 8.54693i) q^{73} +(-2.62167 + 1.26253i) q^{74} -6.09017i q^{75} +(3.40777 + 7.07630i) q^{76} +(3.01269 - 0.687628i) q^{77} +(-0.0812403 - 0.0391233i) q^{78} +(-2.64243 + 5.48705i) q^{79} +(1.59011 - 6.96674i) q^{80} +(3.55901 + 4.46285i) q^{81} +(1.48513 - 1.86230i) q^{82} +(2.21281 + 9.69495i) q^{83} +(-2.18001 - 0.497572i) q^{84} +(13.2040 + 10.5298i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(3.68102 + 2.93552i) q^{89} +(6.07972 + 1.38766i) q^{90} +(0.117461 + 0.514629i) q^{91} +(-1.24698 + 1.56366i) q^{92} +(-3.88812 - 4.87555i) q^{93} +(0.962679 - 4.21777i) q^{94} +(8.11719 - 16.8555i) q^{95} +(-3.12829 - 1.50650i) q^{96} +(-3.47299 + 0.792688i) q^{97} +(0.536310 + 1.11366i) q^{98} -3.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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