LMFDB - Embedded newform 1014.2.i.b.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (of order $6$, degree $2$, 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.b.823.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(5.19615 - 3.00000i) q^{11} -1.00000 q^{12} -2.00000 q^{14} +(-2.59808 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000i q^{18} +(1.73205 + 1.00000i) q^{19} +(-2.59808 - 1.50000i) q^{20} +2.00000i q^{21} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.866025 + 0.500000i) q^{24} -4.00000 q^{25} +1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-1.50000 + 2.59808i) q^{30} +4.00000i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +3.00000i q^{34} +(-3.00000 + 5.19615i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} +2.00000 q^{38} -3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} -6.00000i q^{44} +(2.59808 + 1.50000i) q^{45} +(-5.19615 - 3.00000i) q^{46} +6.00000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-3.46410 + 2.00000i) q^{50} +3.00000 q^{51} +3.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-9.00000 - 15.5885i) q^{55} +(-1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 - 1.50000i) q^{58} +3.00000i q^{60} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(8.66025 - 5.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} +6.00000i q^{70} +(5.19615 + 3.00000i) q^{71} +(0.866025 + 0.500000i) q^{72} -13.0000i q^{73} +(-3.50000 + 6.06218i) q^{74} +(2.00000 + 3.46410i) q^{75} +(1.73205 - 1.00000i) q^{76} -12.0000 q^{77} -4.00000 q^{79} +(-2.59808 + 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000i q^{83} +(1.73205 + 1.00000i) q^{84} +(7.79423 + 4.50000i) q^{85} +10.0000i q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(15.5885 - 9.00000i) q^{89} +3.00000 q^{90} -6.00000 q^{92} +(3.46410 - 2.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +1.00000i q^{96} +(12.1244 + 7.00000i) q^{97} +(-2.59808 - 1.50000i) q^{98} +6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{10} - 4 q^{12} - 8 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{22} - 12 q^{23} - 16 q^{25} + 4 q^{27} - 6 q^{29} - 6 q^{30} - 12 q^{35} + 2 q^{36} + 8 q^{38} - 12 q^{40} + 4 q^{42} - 20 q^{43} - 2 q^{48} - 6 q^{49} + 12 q^{51} + 12 q^{53} - 36 q^{55} - 4 q^{56} + 14 q^{61} + 8 q^{62} - 4 q^{64} - 24 q^{66} + 6 q^{68} - 12 q^{69} - 14 q^{74} + 8 q^{75} - 48 q^{77} - 16 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{87} - 12 q^{88} + 12 q^{90} - 24 q^{92} + 12 q^{94} + 12 q^{95}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^10 - 4 * q^12 - 8 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^22 - 12 * q^23 - 16 * q^25 + 4 * q^27 - 6 * q^29 - 6 * q^30 - 12 * q^35 + 2 * q^36 + 8 * q^38 - 12 * q^40 + 4 * q^42 - 20 * q^43 - 2 * q^48 - 6 * q^49 + 12 * q^51 + 12 * q^53 - 36 * q^55 - 4 * q^56 + 14 * q^61 + 8 * q^62 - 4 * q^64 - 24 * q^66 + 6 * q^68 - 12 * q^69 - 14 * q^74 + 8 * q^75 - 48 * q^77 - 16 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^87 - 12 * q^88 + 12 * q^90 - 24 * q^92 + 12 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.00000i		−	1.34164i	−0.741620	−	0.670820i	$-0.765942\pi$
$5$		−	3.00000i		−	1.34164i	0.741620	−	0.670820i	$-0.234058\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	5.19615	−	3.00000i	1.56670	−	0.904534i	0.570149	−	0.821541i	$-0.306886\pi$
$11$	5.19615	−	3.00000i	1.56670	−	0.904534i	0.996550	−	0.0829925i	$-0.0264478\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−2.00000			−0.534522
$15$	−2.59808	+	1.50000i	−0.670820	+	0.387298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$			1.00000i			0.235702i
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	0.685344	−	0.728219i	$-0.259652\pi$
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	−0.287984	+	0.957635i	$0.592985\pi$
$20$	−2.59808	−	1.50000i	−0.580948	−	0.335410i
$21$			2.00000i			0.436436i
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	1.00000			0.192450
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$			3.00000i			0.514496i
$35$	−3.00000	+	5.19615i	−0.507093	+	0.878310i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	−3.00000			−0.474342
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		−	6.00000i		−	0.904534i
$45$	2.59808	+	1.50000i	0.387298	+	0.223607i
$46$	−5.19615	−	3.00000i	−0.766131	−	0.442326i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−3.46410	+	2.00000i	−0.489898	+	0.282843i
$51$	3.00000			0.420084
$52$		0			0
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−9.00000	−	15.5885i	−1.21356	−	2.10195i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$		−	2.00000i		−	0.264906i
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$			3.00000i			0.387298i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.133135	−	0.991098i	$-0.457496\pi$
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.924883	+	0.380251i	$0.124162\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$			6.00000i			0.717137i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	13.0000i		−	1.52153i	−0.649025	−	0.760767i	$-0.724823\pi$
$73$		−	13.0000i		−	1.52153i	0.649025	−	0.760767i	$-0.275177\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	1.73205	−	1.00000i	0.198680	−	0.114708i
$77$	−12.0000			−1.36753
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−2.59808	+	1.50000i	−0.290474	+	0.167705i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	1.73205	+	1.00000i	0.188982	+	0.109109i
$85$	7.79423	+	4.50000i	0.845403	+	0.488094i
$86$			10.0000i			1.07833i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	15.5885	−	9.00000i	1.65237	−	0.953998i	0.676280	−	0.736644i	$-0.263591\pi$
$89$	15.5885	−	9.00000i	1.65237	−	0.953998i	0.976093	−	0.217354i	$-0.0697425\pi$
$90$	3.00000			0.316228
$91$		0			0
$92$	−6.00000			−0.625543
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$			1.00000i			0.102062i
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.967247	−	0.253837i	$-0.0816925\pi$
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.263795	+	0.964579i	$0.415026\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$			6.00000i			0.603023i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$	2.59808	−	1.50000i	0.257248	−	0.148522i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$	6.00000			0.585540
$106$	2.59808	−	1.50000i	0.252347	−	0.145693i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	14.0000i		−	1.34096i	−0.741929	−	0.670478i	$-0.766089\pi$
$109$		−	14.0000i		−	1.34096i	0.741929	−	0.670478i	$-0.233911\pi$
$110$	−15.5885	−	9.00000i	−1.48630	−	0.858116i
$111$	6.06218	+	3.50000i	0.575396	+	0.332205i
$112$			2.00000i			0.188982i
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−15.5885	+	9.00000i	−1.45363	+	0.839254i
$116$	−3.00000			−0.278543
$117$		0			0
$118$		0			0
$119$	5.19615	−	3.00000i	0.476331	−	0.275010i
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	12.5000	−	21.6506i	1.13636	−	1.96824i
$122$		−	7.00000i		−	0.633750i
$123$	−2.59808	−	1.50000i	−0.234261	−	0.135250i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		−	3.00000i		−	0.268328i
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	10.0000			0.880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−5.19615	+	3.00000i	−0.452267	+	0.261116i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	5.00000	−	8.66025i	0.431934	−	0.748132i
$135$		−	3.00000i		−	0.258199i
$136$	2.59808	+	1.50000i	0.222783	+	0.128624i
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$			6.00000i			0.510754i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	5.19615	−	3.00000i	0.437595	−	0.252646i
$142$	6.00000			0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$	−7.79423	+	4.50000i	−0.647275	+	0.373705i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$			7.00000i			0.575396i
$149$	−7.79423	−	4.50000i	−0.638528	−	0.368654i	0.145519	−	0.989355i	$-0.453515\pi$
$149$	−7.79423	−	4.50000i	−0.638528	−	0.368654i	−0.784047	+	0.620701i	$0.786848\pi$
$150$	3.46410	+	2.00000i	0.282843	+	0.163299i
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$	−10.3923	+	6.00000i	−0.837436	+	0.483494i
$155$	12.0000			0.963863
$156$		0			0
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$			12.0000i			0.945732i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$		−	3.00000i		−	0.234261i
$165$	−9.00000	+	15.5885i	−0.700649	+	1.21356i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$	2.00000			0.154303
$169$		0			0
$170$	9.00000			0.690268
$171$	−1.73205	+	1.00000i	−0.132453	+	0.0764719i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$			3.00000i			0.227429i
$175$	6.92820	+	4.00000i	0.523723	+	0.302372i
$176$	−5.19615	−	3.00000i	−0.391675	−	0.226134i
$177$		0			0
$178$	9.00000	−	15.5885i	0.674579	−	1.16840i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	2.59808	−	1.50000i	0.193649	−	0.111803i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$	−5.19615	+	3.00000i	−0.383065	+	0.221163i
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$			18.0000i			1.31629i
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	−1.73205	−	1.00000i	−0.125988	−	0.0727393i
$190$		−	6.00000i		−	0.435286i
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	19.9186	−	11.5000i	1.43377	−	0.827788i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	19.9186	−	11.5000i	1.43377	−	0.827788i	0.997406	+	0.0719816i	$0.0229323\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	3.00000	+	5.19615i	0.213201	+	0.369274i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$			4.00000i			0.282843i
$201$	−8.66025	−	5.00000i	−0.610847	−	0.352673i
$202$	12.9904	+	7.50000i	0.914000	+	0.527698i
$203$			6.00000i			0.421117i
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−12.1244	+	7.00000i	−0.844744	+	0.487713i
$207$	6.00000			0.417029
$208$		0			0
$209$	12.0000			0.830057
$210$	5.19615	−	3.00000i	0.358569	−	0.207020i
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		−	6.00000i		−	0.411113i
$214$	5.19615	+	3.00000i	0.355202	+	0.205076i
$215$	25.9808	+	15.0000i	1.77187	+	1.02299i
$216$		−	1.00000i		−	0.0680414i
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$	−11.2583	+	6.50000i	−0.760767	+	0.439229i
$220$	−18.0000			−1.21356
$221$		0			0
$222$	7.00000			0.469809
$223$	−6.92820	+	4.00000i	−0.463947	+	0.267860i	−0.713702	−	0.700449i	$-0.752983\pi$
$223$	−6.92820	+	4.00000i	−0.463947	+	0.267860i	0.249756	+	0.968309i	$0.419650\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$		−	3.00000i		−	0.199557i
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.918311	−	0.395860i	$-0.129553\pi$
$227$	15.5885	+	9.00000i	1.03464	+	0.597351i	0.116331	+	0.993210i	$0.462887\pi$
$228$	−1.73205	−	1.00000i	−0.114708	−	0.0662266i
$229$		−	22.0000i		−	1.45380i	−0.686743	−	0.726900i	$-0.740960\pi$
$229$		−	22.0000i		−	1.45380i	0.686743	−	0.726900i	$-0.259040\pi$
$230$	−9.00000	+	15.5885i	−0.593442	+	1.02787i
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	18.0000			1.17419
$236$		0			0
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$	3.00000	−	5.19615i	0.194461	−	0.336817i
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	2.59808	+	1.50000i	0.167705	+	0.0968246i
$241$	0.866025	+	0.500000i	0.0557856	+	0.0322078i	0.527633	−	0.849472i	$-0.323079\pi$
$241$	0.866025	+	0.500000i	0.0557856	+	0.0322078i	−0.471848	+	0.881680i	$0.656413\pi$
$242$		−	25.0000i		−	1.60706i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$	−7.79423	+	4.50000i	−0.497955	+	0.287494i
$246$	−3.00000			−0.191273
$247$		0			0
$248$	4.00000			0.254000
$249$	5.19615	−	3.00000i	0.329293	−	0.190117i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−31.1769	−	18.0000i	−1.96008	−	1.13165i
$254$	−3.46410	−	2.00000i	−0.217357	−	0.125491i
$255$		−	9.00000i		−	0.563602i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	8.66025	−	5.00000i	0.539164	−	0.311286i
$259$	14.0000			0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		−	9.00000i		−	0.552866i
$266$	−3.46410	−	2.00000i	−0.212398	−	0.122628i
$267$	−15.5885	−	9.00000i	−0.953998	−	0.550791i
$268$		−	10.0000i		−	0.610847i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−1.50000	−	2.59808i	−0.0912871	−	0.158114i
$271$	−13.8564	+	8.00000i	−0.841717	+	0.485965i	−0.857847	−	0.513905i	$-0.828199\pi$
$271$	−13.8564	+	8.00000i	−0.841717	+	0.485965i	0.0161307	+	0.999870i	$0.494865\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−9.00000			−0.543710
$275$	−20.7846	+	12.0000i	−1.25336	+	0.723627i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$		−	4.00000i		−	0.239904i
$279$	−3.46410	−	2.00000i	−0.207390	−	0.119737i
$280$	5.19615	+	3.00000i	0.310530	+	0.179284i
$281$			9.00000i			0.536895i	0.963294	+	0.268447i	$0.0865106\pi$
$281$			9.00000i			0.536895i	−0.963294	+	0.268447i	$0.913489\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$	−6.00000			−0.355409
$286$		0			0
$287$	−6.00000			−0.354169
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		−	14.0000i		−	0.820695i
$292$	−11.2583	−	6.50000i	−0.658844	−	0.380384i
$293$	18.1865	+	10.5000i	1.06247	+	0.613417i	0.926114	−	0.377244i	$-0.123128\pi$
$293$	18.1865	+	10.5000i	1.06247	+	0.613417i	0.136355	+	0.990660i	$0.456461\pi$
$294$			3.00000i			0.174964i
$295$		0			0
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$	5.19615	−	3.00000i	0.301511	−	0.174078i
$298$	−9.00000			−0.521356
$299$		0			0
$300$	4.00000			0.230940
$301$	17.3205	−	10.0000i	0.998337	−	0.576390i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$		−	2.00000i		−	0.114708i
$305$	−18.1865	−	10.5000i	−1.04136	−	0.601228i
$306$	−2.59808	−	1.50000i	−0.148522	−	0.0857493i
$307$		−	10.0000i		−	0.570730i	−0.958419	−	0.285365i	$-0.907885\pi$
$307$		−	10.0000i		−	0.570730i	0.958419	−	0.285365i	$-0.0921148\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	7.00000	+	12.1244i	0.398216	+	0.689730i
$310$	10.3923	−	6.00000i	0.590243	−	0.340777i
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	4.33013	−	2.50000i	0.244363	−	0.141083i
$315$	−3.00000	−	5.19615i	−0.169031	−	0.292770i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$		−	3.00000i		−	0.168497i	−0.996445	−	0.0842484i	$-0.973151\pi$
$317$		−	3.00000i		−	0.168497i	0.996445	−	0.0842484i	$-0.0268489\pi$
$318$	−2.59808	−	1.50000i	−0.145693	−	0.0841158i
$319$	−15.5885	−	9.00000i	−0.872786	−	0.503903i
$320$			3.00000i			0.167705i
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$	−5.19615	+	3.00000i	−0.289122	+	0.166924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	4.00000			0.221540
$327$	−12.1244	+	7.00000i	−0.670478	+	0.387101i
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$			18.0000i			0.990867i
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	0.401768	−	0.915742i	$-0.368396\pi$
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	−0.592172	+	0.805812i	$0.701729\pi$
$332$	5.19615	+	3.00000i	0.285176	+	0.164646i
$333$		−	7.00000i		−	0.383598i
$334$		0			0
$335$	−15.0000	−	25.9808i	−0.819538	−	1.41948i
$336$	1.73205	−	1.00000i	0.0944911	−	0.0545545i
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$		0			0
$339$	−3.00000			−0.162938
$340$	7.79423	−	4.50000i	0.422701	−	0.244047i
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$			20.0000i			1.07990i
$344$	8.66025	+	5.00000i	0.466930	+	0.269582i
$345$	15.5885	+	9.00000i	0.839254	+	0.484544i
$346$			6.00000i			0.322562i
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	−8.66025	+	5.00000i	−0.463573	+	0.267644i	−0.713545	−	0.700609i	$-0.752912\pi$
$349$	−8.66025	+	5.00000i	−0.463573	+	0.267644i	0.249973	+	0.968253i	$0.419578\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$	−6.00000			−0.319801
$353$	12.9904	−	7.50000i	0.691408	−	0.399185i	−0.112731	−	0.993626i	$-0.535960\pi$
$353$	12.9904	−	7.50000i	0.691408	−	0.399185i	0.804139	+	0.594441i	$0.202627\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$		−	18.0000i		−	0.953998i
$357$	−5.19615	−	3.00000i	−0.275010	−	0.158777i
$358$	5.19615	+	3.00000i	0.274625	+	0.158555i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$	6.06218	−	3.50000i	0.318621	−	0.183956i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	−39.0000			−2.04135
$366$	−6.06218	+	3.50000i	−0.316875	+	0.182948i
$367$	−1.00000	−	1.73205i	−0.0521996	−	0.0904123i	0.838745	−	0.544524i	$-0.183290\pi$
$367$	−1.00000	−	1.73205i	−0.0521996	−	0.0904123i	−0.890945	+	0.454112i	$0.849957\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$			3.00000i			0.156174i
$370$	18.1865	+	10.5000i	0.945473	+	0.545869i
$371$	−5.19615	−	3.00000i	−0.269771	−	0.155752i
$372$		−	4.00000i		−	0.207390i
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$	−2.59808	+	1.50000i	−0.134164	+	0.0774597i
$376$	6.00000			0.309426
$377$		0			0
$378$	−2.00000			−0.102869
$379$	−17.3205	+	10.0000i	−0.889695	+	0.513665i	−0.873843	−	0.486209i	$-0.838379\pi$
$379$	−17.3205	+	10.0000i	−0.889695	+	0.513665i	−0.0158521	+	0.999874i	$0.505046\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		−	12.0000i		−	0.613973i
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.925997	−	0.377531i	$-0.123227\pi$
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.136047	+	0.990702i	$0.456560\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			36.0000i			1.83473i
$386$	11.5000	−	19.9186i	0.585335	−	1.01383i
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	12.1244	−	7.00000i	0.615521	−	0.355371i
$389$	−39.0000			−1.97738			−0.988689	−	0.149979i	$-0.952080\pi$
$389$	−39.0000			−1.97738			−0.988689	+	0.149979i	$0.952080\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$			12.0000i			0.603786i
$396$	5.19615	+	3.00000i	0.261116	+	0.150756i
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	0.163876	−	0.986481i	$-0.447600\pi$
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	−0.772380	+	0.635161i	$0.780934\pi$
$398$			10.0000i			0.501255i
$399$	−2.00000	+	3.46410i	−0.100125	+	0.173422i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−2.59808	+	1.50000i	−0.129742	+	0.0749064i	−0.563466	−	0.826139i	$-0.690532\pi$
$401$	−2.59808	+	1.50000i	−0.129742	+	0.0749064i	0.433724	+	0.901046i	$0.357199\pi$
$402$	−10.0000			−0.498755
$403$		0			0
$404$	15.0000			0.746278
$405$	−2.59808	+	1.50000i	−0.129099	+	0.0745356i
$406$	3.00000	+	5.19615i	0.148888	+	0.257881i
$407$	−21.0000	+	36.3731i	−1.04093	+	1.80295i
$408$		−	3.00000i		−	0.148522i
$409$	−0.866025	−	0.500000i	−0.0428222	−	0.0247234i	0.478436	−	0.878122i	$-0.341204\pi$
$409$	−0.866025	−	0.500000i	−0.0428222	−	0.0247234i	−0.521258	+	0.853399i	$0.674537\pi$
$410$	−7.79423	−	4.50000i	−0.384930	−	0.222239i
$411$			9.00000i			0.443937i
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$		0			0
$414$	5.19615	−	3.00000i	0.255377	−	0.147442i
$415$	18.0000			0.883585
$416$		0			0
$417$	−4.00000			−0.195881
$418$	10.3923	−	6.00000i	0.508304	−	0.293470i
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	−0.994720	−	0.102628i	$-0.967275\pi$
$419$	−12.0000	−	20.7846i	−0.586238	−	1.01539i	0.408481	−	0.912767i	$-0.366058\pi$
$420$	3.00000	−	5.19615i	0.146385	−	0.253546i
$421$		−	29.0000i		−	1.41337i	−0.707527	−	0.706687i	$-0.750189\pi$
$421$		−	29.0000i		−	1.41337i	0.707527	−	0.706687i	$-0.249811\pi$
$422$	13.8564	+	8.00000i	0.674519	+	0.389434i
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$		−	3.00000i		−	0.145693i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−3.00000	−	5.19615i	−0.145350	−	0.251754i
$427$	−12.1244	+	7.00000i	−0.586739	+	0.338754i
$428$	6.00000			0.290021
$429$		0			0
$430$	30.0000			1.44673
$431$	5.19615	−	3.00000i	0.250290	−	0.144505i	−0.369607	−	0.929188i	$-0.620508\pi$
$431$	5.19615	−	3.00000i	0.250290	−	0.144505i	0.619897	+	0.784683i	$0.287174\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−6.50000	+	11.2583i	−0.312370	+	0.541041i	−0.978875	−	0.204460i	$-0.934456\pi$
$433$	−6.50000	+	11.2583i	−0.312370	+	0.541041i	0.666505	+	0.745501i	$0.267790\pi$
$434$		−	8.00000i		−	0.384012i
$435$	7.79423	+	4.50000i	0.373705	+	0.215758i
$436$	−12.1244	−	7.00000i	−0.580651	−	0.335239i
$437$		−	12.0000i		−	0.574038i
$438$	−6.50000	+	11.2583i	−0.310582	+	0.537944i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$	−15.5885	+	9.00000i	−0.743151	+	0.429058i
$441$	3.00000			0.142857
$442$		0			0
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	6.06218	−	3.50000i	0.287698	−	0.166103i
$445$	−27.0000	−	46.7654i	−1.27992	−	2.21689i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$			9.00000i			0.425685i
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	0.0848262	−	0.996396i	$-0.472967\pi$
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	−0.820491	+	0.571660i	$0.806300\pi$
$450$		−	4.00000i		−	0.188562i
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	−8.66025	+	5.00000i	−0.406894	+	0.234920i
$454$	18.0000			0.844782
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−9.52628	+	5.50000i	−0.445621	+	0.257279i	−0.705979	−	0.708233i	$-0.749493\pi$
$457$	−9.52628	+	5.50000i	−0.445621	+	0.257279i	0.260358	+	0.965512i	$0.416159\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$			18.0000i			0.839254i
$461$	12.9904	+	7.50000i	0.605022	+	0.349310i	0.771015	−	0.636817i	$-0.219749\pi$
$461$	12.9904	+	7.50000i	0.605022	+	0.349310i	−0.165992	+	0.986127i	$0.553083\pi$
$462$	10.3923	+	6.00000i	0.483494	+	0.279145i
$463$			38.0000i			1.76601i	0.469364	+	0.883005i	$0.344483\pi$
$463$			38.0000i			1.76601i	−0.469364	+	0.883005i	$0.655517\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$	5.19615	−	3.00000i	0.240707	−	0.138972i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$	15.5885	−	9.00000i	0.719042	−	0.415139i
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$		0			0
$473$			60.0000i			2.75880i
$474$	3.46410	+	2.00000i	0.159111	+	0.0918630i
$475$	−6.92820	−	4.00000i	−0.317888	−	0.183533i
$476$		−	6.00000i		−	0.275010i
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	1.00000			0.0455488
$483$	10.3923	−	6.00000i	0.472866	−	0.273009i
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	21.0000	−	36.3731i	0.953561	−	1.65162i
$486$			1.00000i			0.0453609i
$487$	1.73205	+	1.00000i	0.0784867	+	0.0453143i	0.538730	−	0.842479i	$-0.318904\pi$
$487$	1.73205	+	1.00000i	0.0784867	+	0.0453143i	−0.460243	+	0.887793i	$0.652238\pi$
$488$	−6.06218	−	3.50000i	−0.274422	−	0.158438i
$489$		−	4.00000i		−	0.180886i
$490$	−4.50000	+	7.79423i	−0.203289	+	0.352107i
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	0.588292	−	0.808649i	$-0.299801\pi$
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	−0.994456	+	0.105151i	$0.966467\pi$
$492$	−2.59808	+	1.50000i	−0.117130	+	0.0676252i
$493$	9.00000			0.405340
$494$		0			0
$495$	18.0000			0.809040
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$	−2.59808	−	1.50000i	−0.116190	−	0.0670820i
$501$		0			0
$502$			12.0000i			0.535586i
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	38.9711	−	22.5000i	1.73419	−	1.00124i
$506$	−36.0000			−1.60040
$507$		0			0
$508$	−4.00000			−0.177471
$509$	−2.59808	+	1.50000i	−0.115158	+	0.0664863i	−0.556473	−	0.830866i	$-0.687846\pi$
$509$	−2.59808	+	1.50000i	−0.115158	+	0.0664863i	0.441315	+	0.897352i	$0.354512\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	−13.0000	+	22.5167i	−0.575086	+	0.996078i
$512$			1.00000i			0.0441942i
$513$	1.73205	+	1.00000i	0.0764719	+	0.0441511i
$514$	−2.59808	−	1.50000i	−0.114596	−	0.0661622i
$515$			42.0000i			1.85074i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	12.1244	−	7.00000i	0.532714	−	0.307562i
$519$	6.00000			0.263371
$520$		0			0
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$	2.59808	−	1.50000i	0.113715	−	0.0656532i
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$		0			0
$525$		−	8.00000i		−	0.349149i
$526$	5.19615	+	3.00000i	0.226563	+	0.130806i
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$			6.00000i			0.261116i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$	−4.00000			−0.173422
$533$		0			0
$534$	−18.0000			−0.778936
$535$	15.5885	−	9.00000i	0.673948	−	0.389104i
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$			18.0000i			0.776035i
$539$	−15.5885	−	9.00000i	−0.671442	−	0.387657i
$540$	−2.59808	−	1.50000i	−0.111803	−	0.0645497i
$541$			29.0000i			1.24681i	0.781900	+	0.623404i	$0.214251\pi$
$541$			29.0000i			1.24681i	−0.781900	+	0.623404i	$0.785749\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	−3.50000	−	6.06218i	−0.150199	−	0.260153i
$544$	2.59808	−	1.50000i	0.111392	−	0.0643120i
$545$	−42.0000			−1.79908
$546$		0			0
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$	−7.79423	+	4.50000i	−0.332953	+	0.192230i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$		−	6.00000i		−	0.255609i
$552$	5.19615	+	3.00000i	0.221163	+	0.127688i
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$		−	17.0000i		−	0.722261i
$555$	10.5000	−	18.1865i	0.445700	−	0.771975i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	2.59808	−	1.50000i	0.110084	−	0.0635570i	−0.443947	−	0.896053i	$-0.646422\pi$
$557$	2.59808	−	1.50000i	0.110084	−	0.0635570i	0.554031	+	0.832496i	$0.313089\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	6.00000			0.253546
$561$	15.5885	−	9.00000i	0.658145	−	0.379980i
$562$	4.50000	+	7.79423i	0.189821	+	0.328780i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		−	6.00000i		−	0.252646i
$565$	−7.79423	−	4.50000i	−0.327906	−	0.189316i
$566$	12.1244	+	7.00000i	0.509625	+	0.294232i
$567$			2.00000i			0.0839921i
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−5.19615	+	3.00000i	−0.217643	+	0.125656i
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$	−5.19615	+	3.00000i	−0.216883	+	0.125218i
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	6.92820	+	4.00000i	0.288175	+	0.166378i
$579$	−19.9186	−	11.5000i	−0.827788	−	0.477924i
$580$			9.00000i			0.373705i
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−7.00000	−	12.1244i	−0.290159	−	0.502571i
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$	−13.0000			−0.537944
$585$		0			0
$586$	21.0000			0.867502
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$		0			0
$591$	5.19615	+	3.00000i	0.213741	+	0.123404i
$592$	6.06218	+	3.50000i	0.249154	+	0.143849i
$593$			9.00000i			0.369586i	0.982777	+	0.184793i	$0.0591614\pi$
$593$			9.00000i			0.369586i	−0.982777	+	0.184793i	$0.940839\pi$
$594$	3.00000	−	5.19615i	0.123091	−	0.213201i
$595$	−9.00000	−	15.5885i	−0.368964	−	0.639064i
$596$	−7.79423	+	4.50000i	−0.319264	+	0.184327i
$597$	10.0000			0.409273
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	3.46410	−	2.00000i	0.141421	−	0.0816497i
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$	10.0000	−	17.3205i	0.407570	−	0.705931i
$603$			10.0000i			0.407231i
$604$	−8.66025	−	5.00000i	−0.352381	−	0.203447i
$605$	−64.9519	−	37.5000i	−2.64067	−	1.52459i
$606$		−	15.0000i		−	0.609333i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	5.19615	−	3.00000i	0.210559	−	0.121566i
$610$	−21.0000			−0.850265
$611$		0			0
$612$	−3.00000			−0.121268
$613$	26.8468	−	15.5000i	1.08433	−	0.626039i	0.152270	−	0.988339i	$-0.451342\pi$
$613$	26.8468	−	15.5000i	1.08433	−	0.626039i	0.932062	+	0.362300i	$0.118008\pi$
$614$	−5.00000	−	8.66025i	−0.201784	−	0.349499i
$615$	−4.50000	+	7.79423i	−0.181458	+	0.314294i
$616$			12.0000i			0.483494i
$617$	−12.9904	−	7.50000i	−0.522973	−	0.301939i	0.215177	−	0.976575i	$-0.430967\pi$
$617$	−12.9904	−	7.50000i	−0.522973	−	0.301939i	−0.738150	+	0.674636i	$0.764300\pi$
$618$	12.1244	+	7.00000i	0.487713	+	0.281581i
$619$			8.00000i			0.321547i	0.986991	+	0.160774i	$0.0513989\pi$
$619$			8.00000i			0.321547i	−0.986991	+	0.160774i	$0.948601\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	25.9808	−	15.0000i	1.04173	−	0.601445i
$623$	−36.0000			−1.44231
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−8.66025	+	5.00000i	−0.346133	+	0.199840i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$		−	21.0000i		−	0.837325i
$630$	−5.19615	−	3.00000i	−0.207020	−	0.119523i
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	0.113913	−	0.993491i	$-0.463661\pi$
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	−0.803432	+	0.595397i	$0.796995\pi$
$632$			4.00000i			0.159111i
$633$	8.00000	−	13.8564i	0.317971	−	0.550743i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	−10.3923	+	6.00000i	−0.412406	+	0.238103i
$636$	−3.00000			−0.118958
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$642$		−	6.00000i		−	0.236801i
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	0.201243	−	0.979541i	$-0.435502\pi$
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	−0.747686	+	0.664052i	$0.768835\pi$
$644$	10.3923	+	6.00000i	0.409514	+	0.236433i
$645$		−	30.0000i		−	1.18125i
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	3.46410	−	2.00000i	0.135665	−	0.0783260i
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$		0			0
$656$	−2.59808	−	1.50000i	−0.101438	−	0.0585652i
$657$	11.2583	+	6.50000i	0.439229	+	0.253589i
$658$		−	12.0000i		−	0.467809i
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$	9.00000	+	15.5885i	0.350325	+	0.606780i
$661$	4.33013	−	2.50000i	0.168422	−	0.0972387i	−0.413419	−	0.910541i	$-0.635666\pi$
$661$	4.33013	−	2.50000i	0.168422	−	0.0972387i	0.581842	+	0.813302i	$0.302332\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	6.00000			0.232845
$665$	−10.3923	+	6.00000i	−0.402996	+	0.232670i
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$		0			0
$669$	6.92820	+	4.00000i	0.267860	+	0.154649i
$670$	−25.9808	−	15.0000i	−1.00372	−	0.579501i
$671$		−	42.0000i		−	1.62139i
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	0.713123	−	0.701039i	$-0.247280\pi$
$673$	−6.50000	−	11.2583i	−0.250557	−	0.433977i	−0.963679	+	0.267063i	$0.913947\pi$
$674$	−19.9186	+	11.5000i	−0.767235	+	0.442963i
$675$	−4.00000			−0.153960
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−2.59808	+	1.50000i	−0.0997785	+	0.0576072i
$679$	−14.0000	−	24.2487i	−0.537271	−	0.930580i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$		−	18.0000i		−	0.689761i
$682$	20.7846	+	12.0000i	0.795884	+	0.459504i
$683$	41.5692	+	24.0000i	1.59060	+	0.918334i	0.993204	+	0.116390i	$0.0371322\pi$
$683$	41.5692	+	24.0000i	1.59060	+	0.918334i	0.597398	+	0.801945i	$0.296201\pi$
$684$			2.00000i			0.0764719i
$685$	−13.5000	+	23.3827i	−0.515808	+	0.893407i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−19.0526	+	11.0000i	−0.726900	+	0.419676i
$688$	10.0000			0.381246
$689$		0			0
$690$	18.0000			0.685248
$691$	−22.5167	+	13.0000i	−0.856574	+	0.494543i	−0.862864	−	0.505437i	$-0.831331\pi$
$691$	−22.5167	+	13.0000i	−0.856574	+	0.494543i	0.00628943	+	0.999980i	$0.497998\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$		−	30.0000i		−	1.13878i
$695$	−10.3923	−	6.00000i	−0.394203	−	0.227593i
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$			9.00000i			0.340899i
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	6.92820	−	4.00000i	0.261861	−	0.151186i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−5.19615	+	3.00000i	−0.195837	+	0.113067i
$705$	−9.00000	−	15.5885i	−0.338960	−	0.587095i
$706$	7.50000	−	12.9904i	0.282266	−	0.488899i
$707$		−	30.0000i		−	1.12827i
$708$		0			0
$709$	−4.33013	−	2.50000i	−0.162621	−	0.0938895i	0.416481	−	0.909145i	$-0.363263\pi$
$709$	−4.33013	−	2.50000i	−0.162621	−	0.0938895i	−0.579102	+	0.815255i	$0.696597\pi$
$710$		−	18.0000i		−	0.675528i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	20.7846	−	12.0000i	0.778390	−	0.449404i
$714$	−6.00000			−0.224544
$715$		0			0
$716$	6.00000			0.224231
$717$	−5.19615	+	3.00000i	−0.194054	+	0.112037i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		−	3.00000i		−	0.111803i
$721$	24.2487	+	14.0000i	0.903069	+	0.521387i
$722$	−12.9904	−	7.50000i	−0.483452	−	0.279121i
$723$		−	1.00000i		−	0.0371904i
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$	−21.6506	+	12.5000i	−0.803530	+	0.463919i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−33.7750	+	19.5000i	−1.25007	+	0.721727i
$731$	−15.0000	−	25.9808i	−0.554795	−	0.960933i
$732$	−3.50000	+	6.06218i	−0.129364	+	0.224065i
$733$			31.0000i			1.14501i	0.819901	+	0.572506i	$0.194029\pi$
$733$			31.0000i			1.14501i	−0.819901	+	0.572506i	$0.805971\pi$
$734$	−1.73205	−	1.00000i	−0.0639312	−	0.0369107i
$735$	7.79423	+	4.50000i	0.287494	+	0.165985i
$736$			6.00000i			0.221163i
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	−13.8564	+	8.00000i	−0.509716	+	0.294285i	−0.732717	−	0.680534i	$-0.761748\pi$
$739$	−13.8564	+	8.00000i	−0.509716	+	0.294285i	0.223001	+	0.974818i	$0.428415\pi$
$740$	21.0000			0.771975
$741$		0			0
$742$	−6.00000			−0.220267
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.196409	−	0.980522i	$-0.437072\pi$
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.947361	+	0.320166i	$0.103739\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	−13.5000	+	23.3827i	−0.494602	+	0.856675i
$746$			29.0000i			1.06177i
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$	15.5885	+	9.00000i	0.569970	+	0.329073i
$749$		−	12.0000i		−	0.438470i
$750$	−1.50000	+	2.59808i	−0.0547723	+	0.0948683i
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	0.965013	−	0.262201i	$-0.0844484\pi$
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	−0.709580	+	0.704625i	$0.751115\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$	12.0000			0.437304
$754$		0			0
$755$	−30.0000			−1.09181
$756$	−1.73205	+	1.00000i	−0.0629941	+	0.0363696i
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	0.989873	+	0.141958i	$0.0453398\pi$
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	−0.371997	+	0.928234i	$0.621327\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$			36.0000i			1.30672i
$760$	−5.19615	−	3.00000i	−0.188484	−	0.108821i
$761$	25.9808	+	15.0000i	0.941802	+	0.543750i	0.890525	−	0.454935i	$-0.150337\pi$
$761$	25.9808	+	15.0000i	0.941802	+	0.543750i	0.0512772	+	0.998684i	$0.483671\pi$
$762$			4.00000i			0.144905i
$763$	−14.0000	+	24.2487i	−0.506834	+	0.877862i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$	−7.79423	+	4.50000i	−0.281801	+	0.162698i
$766$	24.0000			0.867155
$767$		0			0
$768$	1.00000			0.0360844
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	−0.702416	−	0.711767i	$-0.747895\pi$
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	0.265200	+	0.964193i	$0.414562\pi$
$770$	18.0000	+	31.1769i	0.648675	+	1.12354i
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$		−	23.0000i		−	0.827788i
$773$	−25.9808	−	15.0000i	−0.934463	−	0.539513i	−0.0462427	−	0.998930i	$-0.514725\pi$
$773$	−25.9808	−	15.0000i	−0.934463	−	0.539513i	−0.888220	+	0.459418i	$0.848058\pi$
$774$	−8.66025	−	5.00000i	−0.311286	−	0.179721i
$775$		−	16.0000i		−	0.574737i
$776$	7.00000	−	12.1244i	0.251285	−	0.435239i
$777$	−7.00000	−	12.1244i	−0.251124	−	0.434959i
$778$	−33.7750	+	19.5000i	−1.21089	+	0.699109i
$779$	6.00000			0.214972
$780$		0			0
$781$	36.0000			1.28818
$782$	15.5885	−	9.00000i	0.557442	−	0.321839i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		−	15.0000i		−	0.535373i
$786$		0			0
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$			6.00000i			0.213741i
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$	−5.19615	+	3.00000i	−0.184754	+	0.106668i
$792$	6.00000			0.213201
$793$		0			0
$794$	−14.0000			−0.496841
$795$	−7.79423	+	4.50000i	−0.276433	+	0.159599i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$			4.00000i			0.141598i
$799$	−15.5885	−	9.00000i	−0.551480	−	0.318397i
$800$	3.46410	+	2.00000i	0.122474	+	0.0707107i
$801$			18.0000i			0.635999i
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	−39.0000	−	67.5500i	−1.37628	−	2.38379i
$804$	−8.66025	+	5.00000i	−0.305424	+	0.176336i
$805$	36.0000			1.26883
$806$		0			0
$807$	18.0000			0.633630
$808$	12.9904	−	7.50000i	0.457000	−	0.263849i
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.831897	+	0.554930i	$0.187255\pi$
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.0646355	+	0.997909i	$0.479412\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$			4.00000i			0.140459i	0.997531	+	0.0702295i	$0.0223732\pi$
$811$			4.00000i			0.140459i	−0.997531	+	0.0702295i	$0.977627\pi$
$812$	5.19615	+	3.00000i	0.182349	+	0.105279i
$813$	13.8564	+	8.00000i	0.485965	+	0.280572i
$814$			42.0000i			1.47210i
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−17.3205	+	10.0000i	−0.605968	+	0.349856i
$818$	−1.00000			−0.0349642
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	−0.746715	−	0.665144i	$-0.768370\pi$
$821$	−15.5885	+	9.00000i	−0.544041	+	0.314102i	0.202674	+	0.979246i	$0.435037\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$			14.0000i			0.487713i
$825$	20.7846	+	12.0000i	0.723627	+	0.417786i
$826$		0			0
$827$		−	48.0000i		−	1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$		−	48.0000i		−	1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	0.975035	−	0.222049i	$-0.0712747\pi$
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	−0.679818	+	0.733381i	$0.737941\pi$
$830$	15.5885	−	9.00000i	0.541083	−	0.312395i
$831$	−17.0000			−0.589723
$832$		0			0
$833$	9.00000			0.311832
$834$	−3.46410	+	2.00000i	−0.119952	+	0.0692543i
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$			4.00000i			0.138260i
$838$	−20.7846	−	12.0000i	−0.717992	−	0.414533i
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	0.668546	−	0.743670i	$-0.266917\pi$
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	−0.309764	+	0.950813i	$0.600250\pi$
$840$		−	6.00000i		−	0.207020i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−14.5000	−	25.1147i	−0.499703	−	0.865511i
$843$	7.79423	−	4.50000i	0.268447	−	0.154988i
$844$	16.0000			0.550743
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−43.3013	+	25.0000i	−1.48785	+	0.859010i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	7.00000	−	12.1244i	0.240239	−	0.416107i
$850$		−	12.0000i		−	0.411597i
$851$	36.3731	+	21.0000i	1.24685	+	0.719871i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$	−7.00000	+	12.1244i	−0.239535	+	0.414887i
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$	5.19615	−	3.00000i	0.177601	−	0.102538i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$		0			0
$859$	26.0000			0.887109			0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000			0.887109			0.443554	+	0.896248i	$0.353717\pi$
$860$	25.9808	−	15.0000i	0.885937	−	0.511496i
$861$	3.00000	+	5.19615i	0.102240	+	0.177084i
$862$	3.00000	−	5.19615i	0.102180	−	0.176982i
$863$		−	18.0000i		−	0.612727i	−0.951915	−	0.306364i	$-0.900888\pi$
$863$		−	18.0000i		−	0.612727i	0.951915	−	0.306364i	$-0.0991123\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	15.5885	+	9.00000i	0.530023	+	0.306009i
$866$			13.0000i			0.441758i
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	−20.7846	+	12.0000i	−0.705070	+	0.407072i
$870$	9.00000			0.305129
$871$		0			0
$872$	−14.0000			−0.474100
$873$	−12.1244	+	7.00000i	−0.410347	+	0.236914i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−3.00000	+	5.19615i	−0.101419	+	0.175662i
$876$			13.0000i			0.439229i
$877$	35.5070	+	20.5000i	1.19899	+	0.692236i	0.960329	−	0.278868i	$-0.0899591\pi$
$877$	35.5070	+	20.5000i	1.19899	+	0.692236i	0.238658	+	0.971104i	$0.423292\pi$
$878$	12.1244	+	7.00000i	0.409177	+	0.236239i
$879$		−	21.0000i		−	0.708312i
$880$	−9.00000	+	15.5885i	−0.303390	+	0.525487i
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	0.997833	+	0.0657979i	$0.0209593\pi$
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	−0.441934	+	0.897048i	$0.645707\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$		0			0
$886$	−31.1769	+	18.0000i	−1.04741	+	0.604722i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$			8.00000i			0.268311i
$890$	−46.7654	−	27.0000i	−1.56758	−	0.905042i
$891$	−5.19615	−	3.00000i	−0.174078	−	0.100504i
$892$			8.00000i			0.267860i
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$	4.50000	+	7.79423i	0.150503	+	0.260678i
$895$	15.5885	−	9.00000i	0.521065	−	0.300837i
$896$	2.00000			0.0668153
$897$		0			0
$898$	−18.0000			−0.600668
$899$	10.3923	−	6.00000i	0.346603	−	0.200111i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$		−	18.0000i		−	0.599334i
$903$	−17.3205	−	10.0000i	−0.576390	−	0.332779i
$904$	−2.59808	−	1.50000i	−0.0864107	−	0.0498893i
$905$		−	21.0000i		−	0.698064i
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	15.5885	−	9.00000i	0.517321	−	0.298675i
$909$	−15.0000			−0.497519
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−5.50000	+	9.52628i	−0.181924	+	0.315101i
$915$			21.0000i			0.694239i
$916$	−19.0526	−	11.0000i	−0.629514	−	0.363450i
$917$		0			0
$918$			3.00000i			0.0990148i
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	9.00000	+	15.5885i	0.296721	+	0.513936i
$921$	−8.66025	+	5.00000i	−0.285365	+	0.164756i
$922$	15.0000			0.493999
$923$		0			0
$924$	12.0000			0.394771
$925$	24.2487	−	14.0000i	0.797293	−	0.460317i
$926$	19.0000	+	32.9090i	0.624379	+	1.08146i
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$			3.00000i			0.0984798i
$929$	28.5788	+	16.5000i	0.937641	+	0.541347i	0.889220	−	0.457480i	$-0.151248\pi$
$929$	28.5788	+	16.5000i	0.937641	+	0.541347i	0.0484211	+	0.998827i	$0.484581\pi$
$930$	−10.3923	−	6.00000i	−0.340777	−	0.196748i
$931$		−	6.00000i		−	0.196642i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	−15.0000	−	25.9808i	−0.491078	−	0.850572i
$934$	15.5885	−	9.00000i	0.510070	−	0.294489i
$935$	54.0000			1.76599
$936$		0			0
$937$	47.0000			1.53542			0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000			1.53542			0.767712	+	0.640796i	$0.221395\pi$
$938$	−17.3205	+	10.0000i	−0.565535	+	0.326512i
$939$	5.00000	+	8.66025i	0.163169	+	0.282617i
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$		−	42.0000i		−	1.36916i	−0.728937	−	0.684580i	$-0.759985\pi$
$941$		−	42.0000i		−	1.36916i	0.728937	−	0.684580i	$-0.240015\pi$
$942$	−4.33013	−	2.50000i	−0.141083	−	0.0814544i
$943$	−15.5885	−	9.00000i	−0.507630	−	0.293080i
$944$		0			0
$945$	−3.00000	+	5.19615i	−0.0975900	+	0.169031i
$946$	30.0000	+	51.9615i	0.975384	+	1.68941i
$947$	20.7846	−	12.0000i	0.675409	−	0.389948i	−0.122714	−	0.992442i	$-0.539160\pi$
$947$	20.7846	−	12.0000i	0.675409	−	0.389948i	0.798123	+	0.602494i	$0.205826\pi$
$948$	4.00000			0.129914
$949$		0			0
$950$	−8.00000			−0.259554
$951$	−2.59808	+	1.50000i	−0.0842484	+	0.0486408i
$952$	−3.00000	−	5.19615i	−0.0972306	−	0.168408i
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.0174443	−	0.999848i	$-0.494447\pi$
$953$	27.0000	−	46.7654i	0.874616	−	1.51488i	0.857171	−	0.515031i	$-0.172220\pi$
$954$			3.00000i			0.0971286i
$955$	−31.1769	−	18.0000i	−1.00886	−	0.582466i
$956$	−5.19615	−	3.00000i	−0.168056	−	0.0970269i
$957$			18.0000i			0.581857i
$958$		0			0
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$	2.59808	−	1.50000i	0.0838525	−	0.0484123i
$961$	15.0000			0.483871
$962$		0			0
$963$	−6.00000			−0.193347
$964$	0.866025	−	0.500000i	0.0278928	−	0.0161039i
$965$	−34.5000	−	59.7558i	−1.11059	−	1.92361i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	−21.6506	−	12.5000i	−0.695878	−	0.401765i
$969$	5.19615	+	3.00000i	0.166924	+	0.0963739i
$970$		−	42.0000i		−	1.34854i
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.247193	+	0.968966i	$0.579508\pi$
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.715553	+	0.698558i	$0.753825\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−6.92820	+	4.00000i	−0.222108	+	0.128234i
$974$	2.00000			0.0640841
$975$		0			0
$976$	−7.00000			−0.224065
$977$	2.59808	−	1.50000i	0.0831198	−	0.0479893i	−0.457864	−	0.889022i	$-0.651385\pi$
$977$	2.59808	−	1.50000i	0.0831198	−	0.0479893i	0.540984	+	0.841033i	$0.318052\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	54.0000	−	93.5307i	1.72585	−	2.98926i
$980$			9.00000i			0.287494i
$981$	12.1244	+	7.00000i	0.387101	+	0.223493i
$982$	−15.5885	−	9.00000i	−0.497448	−	0.287202i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$	−1.50000	+	2.59808i	−0.0478183	+	0.0828236i
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$	7.79423	−	4.50000i	0.248219	−	0.143309i
$987$	−12.0000			−0.381964
$988$		0			0
$989$	60.0000			1.90789
$990$	15.5885	−	9.00000i	0.495434	−	0.286039i
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	−0.992278	−	0.124033i	$-0.960417\pi$
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	0.388723	−	0.921355i	$-0.372916\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$			4.00000i			0.126936i
$994$	−10.3923	−	6.00000i	−0.329624	−	0.190308i
$995$	25.9808	+	15.0000i	0.823646	+	0.475532i
$996$		−	6.00000i		−	0.190117i
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	−6.06218	+	3.50000i	−0.191799	+	0.110735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.b.361.2		4
13.2	odd	12		1014.2.a.f.1.1		1
13.3	even	3		1014.2.b.c.337.2		2
13.4	even	6	inner	1014.2.i.b.823.2		4
13.5	odd	4		1014.2.e.a.991.1		2
13.6	odd	12		1014.2.e.a.529.1		2
13.7	odd	12		78.2.e.a.61.1	yes	2
13.8	odd	4		78.2.e.a.55.1	✓	2
13.9	even	3	inner	1014.2.i.b.823.1		4
13.10	even	6		1014.2.b.c.337.1		2
13.11	odd	12		1014.2.a.c.1.1		1
13.12	even	2	inner	1014.2.i.b.361.1		4
39.2	even	12		3042.2.a.h.1.1		1
39.8	even	4		234.2.h.a.55.1		2
39.11	even	12		3042.2.a.i.1.1		1
39.20	even	12		234.2.h.a.217.1		2
39.23	odd	6		3042.2.b.h.1351.2		2
39.29	odd	6		3042.2.b.h.1351.1		2
52.7	even	12		624.2.q.g.529.1		2
52.11	even	12		8112.2.a.m.1.1		1
52.15	even	12		8112.2.a.c.1.1		1
52.47	even	4		624.2.q.g.289.1		2
65.7	even	12		1950.2.z.g.1699.2		4
65.8	even	4		1950.2.z.g.1849.2		4
65.33	even	12		1950.2.z.g.1699.1		4
65.34	odd	4		1950.2.i.m.601.1		2
65.47	even	4		1950.2.z.g.1849.1		4
65.59	odd	12		1950.2.i.m.451.1		2
156.47	odd	4		1872.2.t.c.289.1		2
156.59	odd	12		1872.2.t.c.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.a.55.1	✓	2	13.8	odd	4
78.2.e.a.61.1	yes	2	13.7	odd	12
234.2.h.a.55.1		2	39.8	even	4
234.2.h.a.217.1		2	39.20	even	12
624.2.q.g.289.1		2	52.47	even	4
624.2.q.g.529.1		2	52.7	even	12
1014.2.a.c.1.1		1	13.11	odd	12
1014.2.a.f.1.1		1	13.2	odd	12
1014.2.b.c.337.1		2	13.10	even	6
1014.2.b.c.337.2		2	13.3	even	3
1014.2.e.a.529.1		2	13.6	odd	12
1014.2.e.a.991.1		2	13.5	odd	4
1014.2.i.b.361.1		4	13.12	even	2	inner
1014.2.i.b.361.2		4	1.1	even	1	trivial
1014.2.i.b.823.1		4	13.9	even	3	inner
1014.2.i.b.823.2		4	13.4	even	6	inner
1872.2.t.c.289.1		2	156.47	odd	4
1872.2.t.c.1153.1		2	156.59	odd	12
1950.2.i.m.451.1		2	65.59	odd	12
1950.2.i.m.601.1		2	65.34	odd	4
1950.2.z.g.1699.1		4	65.33	even	12
1950.2.z.g.1699.2		4	65.7	even	12
1950.2.z.g.1849.1		4	65.47	even	4
1950.2.z.g.1849.2		4	65.8	even	4
3042.2.a.h.1.1		1	39.2	even	12
3042.2.a.i.1.1		1	39.11	even	12
3042.2.b.h.1351.1		2	39.29	odd	6
3042.2.b.h.1351.2		2	39.23	odd	6
8112.2.a.c.1.1		1	52.15	even	12
8112.2.a.m.1.1		1	52.11	even	12

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(5.19615 - 3.00000i) q^{11} -1.00000 q^{12} -2.00000 q^{14} +(-2.59808 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000i q^{18} +(1.73205 + 1.00000i) q^{19} +(-2.59808 - 1.50000i) q^{20} +2.00000i q^{21} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.866025 + 0.500000i) q^{24} -4.00000 q^{25} +1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-1.50000 + 2.59808i) q^{30} +4.00000i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +3.00000i q^{34} +(-3.00000 + 5.19615i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} +2.00000 q^{38} -3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} -6.00000i q^{44} +(2.59808 + 1.50000i) q^{45} +(-5.19615 - 3.00000i) q^{46} +6.00000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-3.46410 + 2.00000i) q^{50} +3.00000 q^{51} +3.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-9.00000 - 15.5885i) q^{55} +(-1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 - 1.50000i) q^{58} +3.00000i q^{60} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(8.66025 - 5.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} +6.00000i q^{70} +(5.19615 + 3.00000i) q^{71} +(0.866025 + 0.500000i) q^{72} -13.0000i q^{73} +(-3.50000 + 6.06218i) q^{74} +(2.00000 + 3.46410i) q^{75} +(1.73205 - 1.00000i) q^{76} -12.0000 q^{77} -4.00000 q^{79} +(-2.59808 + 1.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000i q^{83} +(1.73205 + 1.00000i) q^{84} +(7.79423 + 4.50000i) q^{85} +10.0000i q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(15.5885 - 9.00000i) q^{89} +3.00000 q^{90} -6.00000 q^{92} +(3.46410 - 2.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +1.00000i q^{96} +(12.1244 + 7.00000i) q^{97} +(-2.59808 - 1.50000i) q^{98} +6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{10} - 4 q^{12} - 8 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{22} - 12 q^{23} - 16 q^{25} + 4 q^{27} - 6 q^{29} - 6 q^{30} - 12 q^{35} + 2 q^{36} + 8 q^{38} - 12 q^{40} + 4 q^{42} - 20 q^{43} - 2 q^{48} - 6 q^{49} + 12 q^{51} + 12 q^{53} - 36 q^{55} - 4 q^{56} + 14 q^{61} + 8 q^{62} - 4 q^{64} - 24 q^{66} + 6 q^{68} - 12 q^{69} - 14 q^{74} + 8 q^{75} - 48 q^{77} - 16 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{87} - 12 q^{88} + 12 q^{90} - 24 q^{92} + 12 q^{94} + 12 q^{95}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^10 - 4 * q^12 - 8 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^22 - 12 * q^23 - 16 * q^25 + 4 * q^27 - 6 * q^29 - 6 * q^30 - 12 * q^35 + 2 * q^36 + 8 * q^38 - 12 * q^40 + 4 * q^42 - 20 * q^43 - 2 * q^48 - 6 * q^49 + 12 * q^51 + 12 * q^53 - 36 * q^55 - 4 * q^56 + 14 * q^61 + 8 * q^62 - 4 * q^64 - 24 * q^66 + 6 * q^68 - 12 * q^69 - 14 * q^74 + 8 * q^75 - 48 * q^77 - 16 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^87 - 12 * q^88 + 12 * q^90 - 24 * q^92 + 12 * q^94 + 12 * q^95

Introduction

L-functions

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