LMFDB - Embedded newform 930.2.o.b.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, 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:	$7.42608738798$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	930.491
Dual form			930.2.o.b.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.866025 - 1.50000i) q^{11} +(0.866025 - 1.50000i) q^{12} +(6.00000 - 3.46410i) q^{13} +(0.866025 + 0.500000i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(2.59808 - 1.50000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.866025 + 1.50000i) q^{21} +(1.50000 - 0.866025i) q^{22} +(1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.46410 + 6.00000i) q^{26} +5.19615 q^{27} +(-0.500000 + 0.866025i) q^{28} +5.19615 q^{29} +1.73205 q^{30} +(-5.50000 - 0.866025i) q^{31} +1.00000i q^{32} +3.00000 q^{33} +1.00000i q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.00000 - 1.73205i) q^{37} +(1.73205 + 1.00000i) q^{38} +12.0000i q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.50000 + 0.866025i) q^{42} +(3.00000 + 1.73205i) q^{43} +(0.866025 + 1.50000i) q^{44} +(2.59808 + 1.50000i) q^{45} -6.00000i q^{47} +(-0.866025 + 1.50000i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-6.00000 + 3.46410i) q^{52} +(-0.866025 - 1.50000i) q^{53} +5.19615i q^{54} +(1.50000 + 0.866025i) q^{55} +(-0.866025 - 0.500000i) q^{56} +(1.73205 + 3.00000i) q^{57} +5.19615i q^{58} +(2.59808 + 1.50000i) q^{59} +1.73205i q^{60} -3.46410i q^{61} +(0.866025 - 5.50000i) q^{62} -3.00000 q^{63} -1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +3.00000i q^{66} +(-2.00000 - 3.46410i) q^{67} -1.00000 q^{70} +(-2.59808 + 1.50000i) q^{72} +(6.00000 - 3.46410i) q^{73} +(1.73205 - 3.00000i) q^{74} +(0.866025 + 1.50000i) q^{75} +(-1.00000 + 1.73205i) q^{76} -1.73205 q^{77} -12.0000 q^{78} +(9.00000 + 5.19615i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.06218 - 10.5000i) q^{83} +(-0.866025 - 1.50000i) q^{84} +(-1.73205 + 3.00000i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 + 0.866025i) q^{88} +13.8564 q^{89} +(-1.50000 + 2.59808i) q^{90} -6.92820i q^{91} +(6.06218 - 7.50000i) q^{93} +6.00000 q^{94} +2.00000i q^{95} +(-1.50000 - 0.866025i) q^{96} -1.00000 q^{97} +(-5.19615 + 3.00000i) q^{98} +(-2.59808 + 4.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9	$ 4 q - 4 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9} - 2 q^{10} + 24 q^{13} + 4 q^{16} + 4 q^{19} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 2 q^{28} - 22 q^{31} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 2 q^{40} - 6 q^{42} + 12 q^{43} + 12 q^{49} - 24 q^{52} + 6 q^{55} - 12 q^{63} - 4 q^{64} - 8 q^{67} - 4 q^{70} + 24 q^{73} - 4 q^{76} - 48 q^{78} + 36 q^{79} - 18 q^{81} - 18 q^{87} - 6 q^{88} - 6 q^{90} + 24 q^{94} - 6 q^{96} - 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9 - 2 * q^10 + 24 * q^13 + 4 * q^16 + 4 * q^19 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 2 * q^28 - 22 * q^31 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 2 * q^40 - 6 * q^42 + 12 * q^43 + 12 * q^49 - 24 * q^52 + 6 * q^55 - 12 * q^63 - 4 * q^64 - 8 * q^67 - 4 * q^70 + 24 * q^73 - 4 * q^76 - 48 * q^78 + 36 * q^79 - 18 * q^81 - 18 * q^87 - 6 * q^88 - 6 * q^90 + 24 * q^94 - 6 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	−1.00000			−0.500000
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	0.705422	−	0.708787i	$-0.250757\pi$
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	−0.966539	+	0.256520i	$0.917424\pi$
$12$	0.866025	−	1.50000i	0.250000	−	0.433013i
$13$	6.00000	−	3.46410i	1.66410	−	0.960769i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	6.00000	−	3.46410i	1.66410	−	0.960769i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	0.866025	+	0.500000i	0.231455	+	0.133631i
$15$		−	1.73205i		−	0.447214i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	0.866025	+	1.50000i	0.188982	+	0.327327i
$22$	1.50000	−	0.866025i	0.319801	−	0.184637i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.46410	+	6.00000i	0.679366	+	1.17670i
$27$	5.19615			1.00000
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	5.19615			0.964901			0.482451	−	0.875923i	$-0.339747\pi$
$29$	5.19615			0.964901			0.482451	+	0.875923i	$0.339747\pi$
$30$	1.73205			0.316228
$31$	−5.50000	−	0.866025i	−0.987829	−	0.155543i
$31$	−5.50000	−	0.866025i	−0.987829	−	0.155543i
$32$			1.00000i			0.176777i
$33$	3.00000			0.522233
$34$		0			0
$35$			1.00000i			0.169031i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−3.00000	−	1.73205i	−0.493197	−	0.284747i	0.232703	−	0.972548i	$-0.425243\pi$
$37$	−3.00000	−	1.73205i	−0.493197	−	0.284747i	−0.725900	+	0.687800i	$0.758576\pi$
$38$	1.73205	+	1.00000i	0.280976	+	0.162221i
$39$			12.0000i			1.92154i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−1.50000	+	0.866025i	−0.231455	+	0.133631i
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	0.710991	−	0.703201i	$-0.248247\pi$
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	−0.253495	+	0.967337i	$0.581580\pi$
$44$	0.866025	+	1.50000i	0.130558	+	0.226134i
$45$	2.59808	+	1.50000i	0.387298	+	0.223607i
$46$		0			0
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	−0.866025	+	1.50000i	−0.125000	+	0.216506i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−6.00000	+	3.46410i	−0.832050	+	0.480384i
$53$	−0.866025	−	1.50000i	−0.118958	−	0.206041i	0.800397	−	0.599470i	$-0.204622\pi$
$53$	−0.866025	−	1.50000i	−0.118958	−	0.206041i	−0.919355	+	0.393429i	$0.871289\pi$
$54$			5.19615i			0.707107i
$55$	1.50000	+	0.866025i	0.202260	+	0.116775i
$56$	−0.866025	−	0.500000i	−0.115728	−	0.0668153i
$57$	1.73205	+	3.00000i	0.229416	+	0.397360i
$58$			5.19615i			0.682288i
$59$	2.59808	+	1.50000i	0.338241	+	0.195283i	0.659494	−	0.751710i	$-0.270771\pi$
$59$	2.59808	+	1.50000i	0.338241	+	0.195283i	−0.321253	+	0.946993i	$0.604104\pi$
$60$			1.73205i			0.223607i
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$	0.866025	−	5.50000i	0.109985	−	0.698501i
$63$	−3.00000			−0.377964
$64$	−1.00000			−0.125000
$65$	−3.46410	+	6.00000i	−0.429669	+	0.744208i
$66$			3.00000i			0.369274i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$		0			0
$69$		0			0
$70$	−1.00000			−0.119523
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$	1.73205	−	3.00000i	0.201347	−	0.348743i
$75$	0.866025	+	1.50000i	0.100000	+	0.173205i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−1.73205			−0.197386
$78$	−12.0000			−1.35873
$79$	9.00000	+	5.19615i	1.01258	+	0.584613i	0.911946	−	0.410311i	$-0.134580\pi$
$79$	9.00000	+	5.19615i	1.01258	+	0.584613i	0.100633	+	0.994924i	$0.467913\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−6.06218	−	10.5000i	−0.665410	−	1.15252i	−0.979174	−	0.203024i	$-0.934923\pi$
$83$	−6.06218	−	10.5000i	−0.665410	−	1.15252i	0.313763	−	0.949501i	$-0.398410\pi$
$84$	−0.866025	−	1.50000i	−0.0944911	−	0.163663i
$85$		0			0
$86$	−1.73205	+	3.00000i	−0.186772	+	0.323498i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−1.50000	+	0.866025i	−0.159901	+	0.0923186i
$89$	13.8564			1.46878			0.734388	−	0.678730i	$-0.237469\pi$
$89$	13.8564			1.46878			0.734388	+	0.678730i	$0.237469\pi$
$90$	−1.50000	+	2.59808i	−0.158114	+	0.273861i
$91$		−	6.92820i		−	0.726273i
$92$		0			0
$93$	6.06218	−	7.50000i	0.628619	−	0.777714i
$94$	6.00000			0.618853
$95$			2.00000i			0.205196i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−5.19615	+	3.00000i	−0.524891	+	0.303046i
$99$	−2.59808	+	4.50000i	−0.261116	+	0.452267i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$			15.0000i			1.49256i	0.665635	+	0.746278i	$0.268161\pi$
$101$			15.0000i			1.49256i	−0.665635	+	0.746278i	$0.731839\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−3.46410	−	6.00000i	−0.339683	−	0.588348i
$105$	−1.50000	−	0.866025i	−0.146385	−	0.0845154i
$106$	1.50000	−	0.866025i	0.145693	−	0.0841158i
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	0.369132	−	0.929377i	$-0.379655\pi$
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	−0.620298	+	0.784366i	$0.712988\pi$
$108$	−5.19615			−0.500000
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−0.866025	+	1.50000i	−0.0825723	+	0.143019i
$111$	5.19615	−	3.00000i	0.493197	−	0.284747i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.467143	−	0.884182i	$-0.345283\pi$
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.999295	+	0.0375328i	$0.0119499\pi$
$114$	−3.00000	+	1.73205i	−0.280976	+	0.162221i
$115$		0			0
$116$	−5.19615			−0.482451
$117$	−18.0000	−	10.3923i	−1.66410	−	0.960769i
$118$	−1.50000	+	2.59808i	−0.138086	+	0.239172i
$119$		0			0
$120$	−1.73205			−0.158114
$121$	4.00000	−	6.92820i	0.363636	−	0.629837i
$122$	3.46410			0.313625
$123$		0			0
$124$	5.50000	+	0.866025i	0.493915	+	0.0777714i
$125$			1.00000i			0.0894427i
$126$		−	3.00000i		−	0.267261i
$127$	−7.50000	−	4.33013i	−0.665517	−	0.384237i	0.128859	−	0.991663i	$-0.458869\pi$
$127$	−7.50000	−	4.33013i	−0.665517	−	0.384237i	−0.794376	+	0.607426i	$0.792202\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.19615	+	3.00000i	−0.457496	+	0.264135i
$130$	−6.00000	−	3.46410i	−0.526235	−	0.303822i
$131$	−10.3923	−	6.00000i	−0.907980	−	0.524222i	−0.0281993	−	0.999602i	$-0.508977\pi$
$131$	−10.3923	−	6.00000i	−0.907980	−	0.524222i	−0.879781	+	0.475380i	$0.842311\pi$
$132$	−3.00000			−0.261116
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$	3.46410	−	2.00000i	0.299253	−	0.172774i
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	−3.46410	−	6.00000i	−0.295958	−	0.512615i	0.679249	−	0.733908i	$-0.262306\pi$
$137$	−3.46410	−	6.00000i	−0.295958	−	0.512615i	−0.975207	+	0.221293i	$0.928972\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		−	1.00000i		−	0.0845154i
$141$	9.00000	+	5.19615i	0.757937	+	0.437595i
$142$		0			0
$143$	−10.3923	−	6.00000i	−0.869048	−	0.501745i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$	−10.3923			−0.857143
$148$	3.00000	+	1.73205i	0.246598	+	0.142374i
$149$	−12.9904	−	7.50000i	−1.06421	−	0.614424i	−0.137619	−	0.990485i	$-0.543945\pi$
$149$	−12.9904	−	7.50000i	−1.06421	−	0.614424i	−0.926595	+	0.376061i	$0.877278\pi$
$150$	−1.50000	+	0.866025i	−0.122474	+	0.0707107i
$151$			12.1244i			0.986666i	0.869841	+	0.493333i	$0.164222\pi$
$151$			12.1244i			0.986666i	−0.869841	+	0.493333i	$0.835778\pi$
$152$	−1.73205	−	1.00000i	−0.140488	−	0.0811107i
$153$		0			0
$154$		−	1.73205i		−	0.139573i
$155$	5.19615	−	2.00000i	0.417365	−	0.160644i
$156$		−	12.0000i		−	0.960769i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−5.19615	+	9.00000i	−0.413384	+	0.716002i
$159$	3.00000			0.237915
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	−7.79423	−	4.50000i	−0.612372	−	0.353553i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$		0			0
$165$	−2.59808	+	1.50000i	−0.202260	+	0.116775i
$166$	10.5000	−	6.06218i	0.814958	−	0.470516i
$167$	10.3923	−	18.0000i	0.804181	−	1.39288i	−0.112662	−	0.993633i	$-0.535938\pi$
$167$	10.3923	−	18.0000i	0.804181	−	1.39288i	0.916843	−	0.399248i	$-0.130729\pi$
$168$	1.50000	−	0.866025i	0.115728	−	0.0668153i
$169$	17.5000	−	30.3109i	1.34615	−	2.33161i
$170$		0			0
$171$	−6.00000			−0.458831
$172$	−3.00000	−	1.73205i	−0.228748	−	0.132068i
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	−0.766119	−	0.642699i	$-0.777815\pi$
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	0.173534	+	0.984828i	$0.444481\pi$
$174$	−7.79423	−	4.50000i	−0.590879	−	0.341144i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−0.866025	−	1.50000i	−0.0652791	−	0.113067i
$177$	−4.50000	+	2.59808i	−0.338241	+	0.195283i
$178$			13.8564i			1.03858i
$179$	−7.79423	+	13.5000i	−0.582568	+	1.00904i	0.412606	+	0.910910i	$0.364619\pi$
$179$	−7.79423	+	13.5000i	−0.582568	+	1.00904i	−0.995174	+	0.0981277i	$0.968715\pi$
$180$	−2.59808	−	1.50000i	−0.193649	−	0.111803i
$181$	12.0000	−	6.92820i	0.891953	−	0.514969i	0.0173722	−	0.999849i	$-0.494470\pi$
$181$	12.0000	−	6.92820i	0.891953	−	0.514969i	0.874581	+	0.484880i	$0.161137\pi$
$182$	6.92820			0.513553
$183$	5.19615	+	3.00000i	0.384111	+	0.221766i
$184$		0			0
$185$	3.46410			0.254686
$186$	7.50000	+	6.06218i	0.549927	+	0.444500i
$187$		0			0
$188$			6.00000i			0.437595i
$189$	2.59808	−	4.50000i	0.188982	−	0.327327i
$190$	−2.00000			−0.145095
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	−0.676068	−	0.736839i	$-0.736317\pi$
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	0.300088	+	0.953912i	$0.402984\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$		−	1.00000i		−	0.0717958i
$195$	−6.00000	−	10.3923i	−0.429669	−	0.744208i
$196$	−3.00000	−	5.19615i	−0.214286	−	0.371154i
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$	−4.50000	−	2.59808i	−0.319801	−	0.184637i
$199$	−10.5000	+	6.06218i	−0.744325	+	0.429736i	−0.823640	−	0.567113i	$-0.808060\pi$
$199$	−10.5000	+	6.06218i	−0.744325	+	0.429736i	0.0793146	+	0.996850i	$0.474727\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	6.92820			0.488678
$202$	−15.0000			−1.05540
$203$	2.59808	−	4.50000i	0.182349	−	0.315838i
$204$		0			0
$205$		0			0
$206$	−4.33013	+	2.50000i	−0.301694	+	0.174183i
$207$		0			0
$208$	6.00000	−	3.46410i	0.416025	−	0.240192i
$209$	−3.46410			−0.239617
$210$	0.866025	−	1.50000i	0.0597614	−	0.103510i
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	0.866025	+	1.50000i	0.0594789	+	0.103020i
$213$		0			0
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	−3.46410			−0.236250
$216$		−	5.19615i		−	0.353553i
$217$	−3.50000	+	4.33013i	−0.237595	+	0.293948i
$218$			14.0000i			0.948200i
$219$			12.0000i			0.810885i
$220$	−1.50000	−	0.866025i	−0.101130	−	0.0583874i
$221$		0			0
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$	13.5000	+	7.79423i	0.904027	+	0.521940i	0.878504	−	0.477734i	$-0.158542\pi$
$223$	13.5000	+	7.79423i	0.904027	+	0.521940i	0.0255224	+	0.999674i	$0.491875\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	−3.00000			−0.200000
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	−0.411296	−	0.911502i	$-0.634924\pi$
$227$	2.59808	−	1.50000i	0.172440	−	0.0995585i	0.583736	+	0.811943i	$0.301590\pi$
$228$	−1.73205	−	3.00000i	−0.114708	−	0.198680i
$229$	3.00000	+	1.73205i	0.198246	+	0.114457i	0.595837	−	0.803105i	$-0.296820\pi$
$229$	3.00000	+	1.73205i	0.198246	+	0.114457i	−0.397591	+	0.917563i	$0.630154\pi$
$230$		0			0
$231$	1.50000	−	2.59808i	0.0986928	−	0.170941i
$232$		−	5.19615i		−	0.341144i
$233$		−	12.0000i		−	0.786146i	−0.919507	−	0.393073i	$-0.871412\pi$
$233$		−	12.0000i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$234$	10.3923	−	18.0000i	0.679366	−	1.17670i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	−2.59808	−	1.50000i	−0.169120	−	0.0976417i
$237$	−15.5885	+	9.00000i	−1.01258	+	0.584613i
$238$		0			0
$239$	−5.19615	−	9.00000i	−0.336111	−	0.582162i	0.647586	−	0.761992i	$-0.275778\pi$
$239$	−5.19615	−	9.00000i	−0.336111	−	0.582162i	−0.983698	+	0.179830i	$0.942445\pi$
$240$		−	1.73205i		−	0.111803i
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.00239235	−	0.999997i	$-0.500762\pi$
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.867219	+	0.497927i	$0.834095\pi$
$242$	6.92820	+	4.00000i	0.445362	+	0.257130i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$			3.46410i			0.221766i
$245$	−5.19615	−	3.00000i	−0.331970	−	0.191663i
$246$		0			0
$247$		−	13.8564i		−	0.881662i
$248$	−0.866025	+	5.50000i	−0.0549927	+	0.349250i
$249$	21.0000			1.33082
$250$	−1.00000			−0.0632456
$251$	−8.66025	+	15.0000i	−0.546630	+	0.946792i	0.451872	+	0.892083i	$0.350756\pi$
$251$	−8.66025	+	15.0000i	−0.546630	+	0.946792i	−0.998502	+	0.0547088i	$0.982577\pi$
$252$	3.00000			0.188982
$253$		0			0
$254$	4.33013	−	7.50000i	0.271696	−	0.470592i
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	−0.139533	−	0.990217i	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$	−3.00000	−	5.19615i	−0.186772	−	0.323498i
$259$	−3.00000	+	1.73205i	−0.186411	+	0.107624i
$260$	3.46410	−	6.00000i	0.214834	−	0.372104i
$261$	−7.79423	−	13.5000i	−0.482451	−	0.835629i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−24.2487			−1.49524			−0.747620	−	0.664127i	$-0.768803\pi$
$263$	−24.2487			−1.49524			−0.747620	+	0.664127i	$0.768803\pi$
$264$		−	3.00000i		−	0.184637i
$265$	1.50000	+	0.866025i	0.0921443	+	0.0531995i
$266$	1.73205	−	1.00000i	0.106199	−	0.0613139i
$267$	−12.0000	+	20.7846i	−0.734388	+	1.27200i
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−6.92820	−	12.0000i	−0.422420	−	0.731653i	0.573756	−	0.819027i	$-0.305486\pi$
$269$	−6.92820	−	12.0000i	−0.422420	−	0.731653i	−0.996176	+	0.0873736i	$0.972153\pi$
$270$	−2.59808	−	4.50000i	−0.158114	−	0.273861i
$271$			12.1244i			0.736502i	0.929726	+	0.368251i	$0.120043\pi$
$271$			12.1244i			0.736502i	−0.929726	+	0.368251i	$0.879957\pi$
$272$		0			0
$273$	10.3923	+	6.00000i	0.628971	+	0.363137i
$274$	6.00000	−	3.46410i	0.362473	−	0.209274i
$275$	−1.73205			−0.104447
$276$		0			0
$277$		−	10.3923i		−	0.624413i	−0.950014	−	0.312207i	$-0.898932\pi$
$277$		−	10.3923i		−	0.624413i	0.950014	−	0.312207i	$-0.101068\pi$
$278$		0			0
$279$	6.00000	+	15.5885i	0.359211	+	0.933257i
$280$	1.00000			0.0597614
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	−5.19615	+	9.00000i	−0.309426	+	0.535942i
$283$	−28.0000			−1.66443			−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000			−1.66443			−0.832214	+	0.554455i	$0.812927\pi$
$284$		0			0
$285$	−3.00000	−	1.73205i	−0.177705	−	0.102598i
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$		0			0
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−2.59808	−	4.50000i	−0.152564	−	0.264249i
$291$	0.866025	−	1.50000i	0.0507673	−	0.0879316i
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	12.9904	+	7.50000i	0.758906	+	0.438155i	0.828903	−	0.559393i	$-0.188966\pi$
$293$	12.9904	+	7.50000i	0.758906	+	0.438155i	−0.0699967	+	0.997547i	$0.522299\pi$
$294$		−	10.3923i		−	0.606092i
$295$	−3.00000			−0.174667
$296$	−1.73205	+	3.00000i	−0.100673	+	0.174371i
$297$	−4.50000	−	7.79423i	−0.261116	−	0.452267i
$298$	7.50000	−	12.9904i	0.434463	−	0.752513i
$299$		0			0
$300$	−0.866025	−	1.50000i	−0.0500000	−	0.0866025i
$301$	3.00000	−	1.73205i	0.172917	−	0.0998337i
$302$	−12.1244			−0.697678
$303$	−22.5000	−	12.9904i	−1.29259	−	0.746278i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	1.73205	+	3.00000i	0.0991769	+	0.171780i
$306$		0			0
$307$	−11.0000	+	19.0526i	−0.627803	+	1.08739i	0.360188	+	0.932880i	$0.382712\pi$
$307$	−11.0000	+	19.0526i	−0.627803	+	1.08739i	−0.987992	+	0.154507i	$0.950621\pi$
$308$	1.73205			0.0986928
$309$	−8.66025			−0.492665
$310$	2.00000	+	5.19615i	0.113592	+	0.295122i
$311$		−	24.0000i		−	1.36092i	−0.732787	−	0.680458i	$-0.761781\pi$
$311$		−	24.0000i		−	1.36092i	0.732787	−	0.680458i	$-0.238219\pi$
$312$	12.0000			0.679366
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	0.830395	−	0.557175i	$-0.188115\pi$
$313$	13.5000	+	7.79423i	0.763065	+	0.440556i	−0.0673300	+	0.997731i	$0.521448\pi$
$314$		−	14.0000i		−	0.790066i
$315$	2.59808	−	1.50000i	0.146385	−	0.0845154i
$316$	−9.00000	−	5.19615i	−0.506290	−	0.292306i
$317$	−12.9904	−	7.50000i	−0.729612	−	0.421242i	0.0886679	−	0.996061i	$-0.471739\pi$
$317$	−12.9904	−	7.50000i	−0.729612	−	0.421242i	−0.818280	+	0.574819i	$0.805072\pi$
$318$			3.00000i			0.168232i
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	4.50000	−	2.59808i	0.251166	−	0.145010i
$322$		0			0
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$		−	6.92820i		−	0.384308i
$326$			20.0000i			1.10770i
$327$	−12.1244	+	21.0000i	−0.670478	+	1.16130i
$328$		0			0
$329$	−5.19615	−	3.00000i	−0.286473	−	0.165395i
$330$	−1.50000	−	2.59808i	−0.0825723	−	0.143019i
$331$	−15.0000	+	8.66025i	−0.824475	+	0.476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−15.0000	+	8.66025i	−0.824475	+	0.476011i	0.0274825	+	0.999622i	$0.491251\pi$
$332$	6.06218	+	10.5000i	0.332705	+	0.576262i
$333$			10.3923i			0.569495i
$334$	18.0000	+	10.3923i	0.984916	+	0.568642i
$335$	3.46410	+	2.00000i	0.189264	+	0.109272i
$336$	0.866025	+	1.50000i	0.0472456	+	0.0818317i
$337$			12.1244i			0.660456i	0.943901	+	0.330228i	$0.107126\pi$
$337$			12.1244i			0.660456i	−0.943901	+	0.330228i	$0.892874\pi$
$338$	30.3109	+	17.5000i	1.64870	+	0.951875i
$339$			31.1769i			1.69330i
$340$		0			0
$341$	3.46410	+	9.00000i	0.187592	+	0.487377i
$342$		−	6.00000i		−	0.324443i
$343$	13.0000			0.701934
$344$	1.73205	−	3.00000i	0.0933859	−	0.161749i
$345$		0			0
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$	0.866025	−	1.50000i	0.0464907	−	0.0805242i	−0.841844	−	0.539721i	$-0.818530\pi$
$347$	0.866025	−	1.50000i	0.0464907	−	0.0805242i	0.888334	+	0.459197i	$0.151863\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$	0.866025	−	0.500000i	0.0462910	−	0.0267261i
$351$	31.1769	−	18.0000i	1.66410	−	0.960769i
$352$	1.50000	−	0.866025i	0.0799503	−	0.0461593i
$353$	−6.92820	+	12.0000i	−0.368751	+	0.638696i	−0.989371	−	0.145416i	$-0.953548\pi$
$353$	−6.92820	+	12.0000i	−0.368751	+	0.638696i	0.620620	+	0.784112i	$0.286881\pi$
$354$	−2.59808	−	4.50000i	−0.138086	−	0.239172i
$355$		0			0
$356$	−13.8564			−0.734388
$357$		0			0
$358$	−13.5000	−	7.79423i	−0.713497	−	0.411938i
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	6.92820	+	12.0000i	0.364138	+	0.630706i
$363$	6.92820	+	12.0000i	0.363636	+	0.629837i
$364$			6.92820i			0.363137i
$365$	−3.46410	+	6.00000i	−0.181319	+	0.314054i
$366$	−3.00000	+	5.19615i	−0.156813	+	0.271607i
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	−0.716154	−	0.697942i	$-0.754099\pi$
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	0.246358	+	0.969179i	$0.420766\pi$
$368$		0			0
$369$		0			0
$370$			3.46410i			0.180090i
$371$	−1.73205			−0.0899236
$372$	−6.06218	+	7.50000i	−0.314309	+	0.388857i
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	−6.00000			−0.309426
$377$	31.1769	−	18.0000i	1.60569	−	0.927047i
$378$	4.50000	+	2.59808i	0.231455	+	0.133631i
$379$	−16.0000	+	27.7128i	−0.821865	+	1.42351i	0.0824272	+	0.996597i	$0.473733\pi$
$379$	−16.0000	+	27.7128i	−0.821865	+	1.42351i	−0.904292	+	0.426914i	$0.859601\pi$
$380$		−	2.00000i		−	0.102598i
$381$	12.9904	−	7.50000i	0.665517	−	0.384237i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	17.3205	+	30.0000i	0.885037	+	1.53293i	0.845672	+	0.533703i	$0.179200\pi$
$383$	17.3205	+	30.0000i	0.885037	+	1.53293i	0.0393649	+	0.999225i	$0.487467\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	1.50000	−	0.866025i	0.0764471	−	0.0441367i
$386$	19.9186	+	11.5000i	1.01383	+	0.585335i
$387$		−	10.3923i		−	0.528271i
$388$	1.00000			0.0507673
$389$	−6.92820	+	12.0000i	−0.351274	+	0.608424i	−0.986473	−	0.163924i	$-0.947585\pi$
$389$	−6.92820	+	12.0000i	−0.351274	+	0.608424i	0.635199	+	0.772348i	$0.280918\pi$
$390$	10.3923	−	6.00000i	0.526235	−	0.303822i
$391$		0			0
$392$	5.19615	−	3.00000i	0.262445	−	0.151523i
$393$	18.0000	−	10.3923i	0.907980	−	0.524222i
$394$		0			0
$395$	−10.3923			−0.522894
$396$	2.59808	−	4.50000i	0.130558	−	0.226134i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	−6.06218	−	10.5000i	−0.303870	−	0.526317i
$399$	3.46410			0.173422
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−17.3205			−0.864945			−0.432472	−	0.901647i	$-0.642359\pi$
$401$	−17.3205			−0.864945			−0.432472	+	0.901647i	$0.642359\pi$
$402$			6.92820i			0.345547i
$403$	−36.0000	+	13.8564i	−1.79329	+	0.690237i
$404$		−	15.0000i		−	0.746278i
$405$		−	9.00000i		−	0.447214i
$406$	4.50000	+	2.59808i	0.223331	+	0.128940i
$407$			6.00000i			0.297409i
$408$		0			0
$409$	−28.5000	−	16.4545i	−1.40923	−	0.813622i	−0.413920	−	0.910313i	$-0.635841\pi$
$409$	−28.5000	−	16.4545i	−1.40923	−	0.813622i	−0.995314	+	0.0966915i	$0.969174\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$	2.59808	−	1.50000i	0.127843	−	0.0738102i
$414$		0			0
$415$	10.5000	+	6.06218i	0.515425	+	0.297581i
$416$	3.46410	+	6.00000i	0.169842	+	0.294174i
$417$		0			0
$418$		−	3.46410i		−	0.169435i
$419$		−	3.00000i		−	0.146560i	−0.997311	−	0.0732798i	$-0.976653\pi$
$419$		−	3.00000i		−	0.146560i	0.997311	−	0.0732798i	$-0.0233466\pi$
$420$	1.50000	+	0.866025i	0.0731925	+	0.0422577i
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	0.602539	−	0.798089i	$-0.294156\pi$
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	−0.992435	+	0.122769i	$0.960822\pi$
$422$	−6.92820	−	4.00000i	−0.337260	−	0.194717i
$423$	−15.5885	+	9.00000i	−0.757937	+	0.437595i
$424$	−1.50000	+	0.866025i	−0.0728464	+	0.0420579i
$425$		0			0
$426$		0			0
$427$	−3.00000	−	1.73205i	−0.145180	−	0.0838198i
$428$	2.59808	+	1.50000i	0.125583	+	0.0725052i
$429$	18.0000	−	10.3923i	0.869048	−	0.501745i
$430$		−	3.46410i		−	0.167054i
$431$	25.9808	+	15.0000i	1.25145	+	0.722525i	0.971397	−	0.237460i	$-0.0763149\pi$
$431$	25.9808	+	15.0000i	1.25145	+	0.722525i	0.280052	+	0.959985i	$0.409648\pi$
$432$	5.19615			0.250000
$433$			34.6410i			1.66474i	0.554220	+	0.832370i	$0.313017\pi$
$433$			34.6410i			1.66474i	−0.554220	+	0.832370i	$0.686983\pi$
$434$	−4.33013	−	3.50000i	−0.207853	−	0.168005i
$435$		−	9.00000i		−	0.431517i
$436$	−14.0000			−0.670478
$437$		0			0
$438$	−12.0000			−0.573382
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	0.545185	−	0.838316i	$-0.316459\pi$
$439$	−9.50000	−	16.4545i	−0.453410	−	0.785330i	−0.998595	+	0.0529862i	$0.983126\pi$
$440$	0.866025	−	1.50000i	0.0412861	−	0.0715097i
$441$	9.00000	−	15.5885i	0.428571	−	0.742307i
$442$		0			0
$443$	31.1769	−	18.0000i	1.48126	−	0.855206i	0.481486	−	0.876454i	$-0.340097\pi$
$443$	31.1769	−	18.0000i	1.48126	−	0.855206i	0.999774	+	0.0212481i	$0.00676401\pi$
$444$	−5.19615	+	3.00000i	−0.246598	+	0.142374i
$445$	−12.0000	+	6.92820i	−0.568855	+	0.328428i
$446$	−7.79423	+	13.5000i	−0.369067	+	0.639244i
$447$	22.5000	−	12.9904i	1.06421	−	0.614424i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	10.3923			0.490443			0.245222	−	0.969467i	$-0.421139\pi$
$449$	10.3923			0.490443			0.245222	+	0.969467i	$0.421139\pi$
$450$		−	3.00000i		−	0.141421i
$451$		0			0
$452$	−15.5885	+	9.00000i	−0.733219	+	0.423324i
$453$	−18.1865	−	10.5000i	−0.854478	−	0.493333i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$	3.46410	+	6.00000i	0.162400	+	0.281284i
$456$	3.00000	−	1.73205i	0.140488	−	0.0811107i
$457$			6.92820i			0.324088i	0.986784	+	0.162044i	$0.0518086\pi$
$457$			6.92820i			0.324088i	−0.986784	+	0.162044i	$0.948191\pi$
$458$	−1.73205	+	3.00000i	−0.0809334	+	0.140181i
$459$		0			0
$460$		0			0
$461$	−15.5885			−0.726027			−0.363013	−	0.931784i	$-0.618252\pi$
$461$	−15.5885			−0.726027			−0.363013	+	0.931784i	$0.618252\pi$
$462$	2.59808	+	1.50000i	0.120873	+	0.0697863i
$463$		−	12.1244i		−	0.563467i	−0.959493	−	0.281733i	$-0.909091\pi$
$463$		−	12.1244i		−	0.563467i	0.959493	−	0.281733i	$-0.0909093\pi$
$464$	5.19615			0.241225
$465$	−1.50000	+	9.52628i	−0.0695608	+	0.441771i
$466$	12.0000			0.555889
$467$			39.0000i			1.80470i	0.430999	+	0.902352i	$0.358161\pi$
$467$			39.0000i			1.80470i	−0.430999	+	0.902352i	$0.641839\pi$
$468$	18.0000	+	10.3923i	0.832050	+	0.480384i
$469$	−4.00000			−0.184703
$470$	−5.19615	+	3.00000i	−0.239681	+	0.138380i
$471$	12.1244	−	21.0000i	0.558661	−	0.967629i
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$		−	6.00000i		−	0.275880i
$474$	−9.00000	−	15.5885i	−0.413384	−	0.716002i
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$		0			0
$477$	−2.59808	+	4.50000i	−0.118958	+	0.206041i
$478$	9.00000	−	5.19615i	0.411650	−	0.237666i
$479$	15.5885	+	9.00000i	0.712255	+	0.411220i	0.811895	−	0.583803i	$-0.198436\pi$
$479$	15.5885	+	9.00000i	0.712255	+	0.411220i	−0.0996406	+	0.995023i	$0.531769\pi$
$480$	1.73205			0.0790569
$481$	−24.0000			−1.09431
$482$	7.79423	−	13.5000i	0.355017	−	0.614908i
$483$		0			0
$484$	−4.00000	+	6.92820i	−0.181818	+	0.314918i
$485$	0.866025	−	0.500000i	0.0393242	−	0.0227038i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	31.5000	−	18.1865i	1.42740	−	0.824110i	0.430486	−	0.902597i	$-0.358342\pi$
$487$	31.5000	−	18.1865i	1.42740	−	0.824110i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$	−3.46410			−0.156813
$489$	−17.3205	+	30.0000i	−0.783260	+	1.35665i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	−14.7224	−	25.5000i	−0.664414	−	1.15080i	−0.979444	−	0.201717i	$-0.935348\pi$
$491$	−14.7224	−	25.5000i	−0.664414	−	1.15080i	0.315030	−	0.949082i	$-0.397985\pi$
$492$		0			0
$493$		0			0
$494$	13.8564			0.623429
$495$		−	5.19615i		−	0.233550i
$496$	−5.50000	−	0.866025i	−0.246957	−	0.0388857i
$497$		0			0
$498$			21.0000i			0.941033i
$499$	−30.0000	−	17.3205i	−1.34298	−	0.775372i	−0.355740	−	0.934585i	$-0.615771\pi$
$499$	−30.0000	−	17.3205i	−1.34298	−	0.775372i	−0.987244	+	0.159212i	$0.949105\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	18.0000	+	31.1769i	0.804181	+	1.39288i
$502$	−15.0000	−	8.66025i	−0.669483	−	0.386526i
$503$	−5.19615	−	3.00000i	−0.231685	−	0.133763i	0.379664	−	0.925124i	$-0.376040\pi$
$503$	−5.19615	−	3.00000i	−0.231685	−	0.133763i	−0.611349	+	0.791361i	$0.709373\pi$
$504$			3.00000i			0.133631i
$505$	−7.50000	−	12.9904i	−0.333746	−	0.578064i
$506$		0			0
$507$	30.3109	+	52.5000i	1.34615	+	2.33161i
$508$	7.50000	+	4.33013i	0.332759	+	0.192118i
$509$	16.4545	+	28.5000i	0.729332	+	1.26324i	0.957166	+	0.289540i	$0.0935024\pi$
$509$	16.4545	+	28.5000i	0.729332	+	1.26324i	−0.227834	+	0.973700i	$0.573164\pi$
$510$		0			0
$511$		−	6.92820i		−	0.306486i
$512$			1.00000i			0.0441942i
$513$	5.19615	−	9.00000i	0.229416	−	0.397360i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$	−4.33013	−	2.50000i	−0.190808	−	0.110163i
$516$	5.19615	−	3.00000i	0.228748	−	0.132068i
$517$	−9.00000	+	5.19615i	−0.395820	+	0.228527i
$518$	−1.73205	−	3.00000i	−0.0761019	−	0.131812i
$519$		−	15.5885i		−	0.684257i
$520$	6.00000	+	3.46410i	0.263117	+	0.151911i
$521$	25.9808	+	15.0000i	1.13824	+	0.657162i	0.945994	−	0.324185i	$-0.105090\pi$
$521$	25.9808	+	15.0000i	1.13824	+	0.657162i	0.192244	+	0.981347i	$0.438423\pi$
$522$	13.5000	−	7.79423i	0.590879	−	0.341144i
$523$			45.0333i			1.96917i	0.174908	+	0.984585i	$0.444037\pi$
$523$			45.0333i			1.96917i	−0.174908	+	0.984585i	$0.555963\pi$
$524$	10.3923	+	6.00000i	0.453990	+	0.262111i
$525$	1.73205			0.0755929
$526$		−	24.2487i		−	1.05729i
$527$		0			0
$528$	3.00000			0.130558
$529$	−23.0000			−1.00000
$530$	−0.866025	+	1.50000i	−0.0376177	+	0.0651558i
$531$		−	9.00000i		−	0.390567i
$532$	1.00000	+	1.73205i	0.0433555	+	0.0750939i
$533$		0			0
$534$	−20.7846	−	12.0000i	−0.899438	−	0.519291i
$535$	3.00000			0.129701
$536$	−3.46410	+	2.00000i	−0.149626	+	0.0863868i
$537$	−13.5000	−	23.3827i	−0.582568	−	1.00904i
$538$	12.0000	−	6.92820i	0.517357	−	0.298696i
$539$	5.19615	−	9.00000i	0.223814	−	0.387657i
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	−0.566933	−	0.823764i	$-0.691870\pi$
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	0.996867	+	0.0790969i	$0.0252036\pi$
$542$	−12.1244			−0.520786
$543$			24.0000i			1.02994i
$544$		0			0
$545$	−12.1244	+	7.00000i	−0.519350	+	0.299847i
$546$	−6.00000	+	10.3923i	−0.256776	+	0.444750i
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$	3.46410	+	6.00000i	0.147979	+	0.256307i
$549$	−9.00000	+	5.19615i	−0.384111	+	0.221766i
$550$		−	1.73205i		−	0.0738549i
$551$	5.19615	−	9.00000i	0.221364	−	0.383413i
$552$		0			0
$553$	9.00000	−	5.19615i	0.382719	−	0.220963i
$554$	10.3923			0.441527
$555$	−3.00000	+	5.19615i	−0.127343	+	0.220564i
$556$		0			0
$557$	19.0526			0.807283			0.403641	−	0.914917i	$-0.367744\pi$
$557$	19.0526			0.807283			0.403641	+	0.914917i	$0.367744\pi$
$558$	−15.5885	+	6.00000i	−0.659912	+	0.254000i
$559$	24.0000			1.01509
$560$			1.00000i			0.0422577i
$561$		0			0
$562$	−6.00000			−0.253095
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.426855	−	0.904320i	$-0.359622\pi$
$563$	33.7750	−	19.5000i	1.42345	−	0.821827i	0.996592	+	0.0824933i	$0.0262883\pi$
$564$	−9.00000	−	5.19615i	−0.378968	−	0.218797i
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$		−	28.0000i		−	1.17693i
$567$	4.50000	+	7.79423i	0.188982	+	0.327327i
$568$		0			0
$569$	8.66025	+	15.0000i	0.363057	+	0.628833i	0.988462	−	0.151467i	$-0.0483998\pi$
$569$	8.66025	+	15.0000i	0.363057	+	0.628833i	−0.625406	+	0.780300i	$0.715066\pi$
$570$	1.73205	−	3.00000i	0.0725476	−	0.125656i
$571$	−27.0000	+	15.5885i	−1.12991	+	0.652357i	−0.943913	−	0.330193i	$-0.892886\pi$
$571$	−27.0000	+	15.5885i	−1.12991	+	0.652357i	−0.186001	+	0.982549i	$0.559553\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$		−	10.3923i		−	0.434145i
$574$		0			0
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−17.0000	+	29.4449i	−0.707719	+	1.22581i	0.257982	+	0.966150i	$0.416942\pi$
$577$	−17.0000	+	29.4449i	−0.707719	+	1.22581i	−0.965701	+	0.259656i	$0.916391\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$	19.9186	+	34.5000i	0.827788	+	1.43377i
$580$	4.50000	−	2.59808i	0.186852	−	0.107879i
$581$	−12.1244			−0.503003
$582$	1.50000	+	0.866025i	0.0621770	+	0.0358979i
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$	−3.46410	−	6.00000i	−0.143346	−	0.248282i
$585$	20.7846			0.859338
$586$	−7.50000	+	12.9904i	−0.309822	+	0.536628i
$587$	−8.66025			−0.357447			−0.178723	−	0.983899i	$-0.557197\pi$
$587$	−8.66025			−0.357447			−0.178723	+	0.983899i	$0.557197\pi$
$588$	10.3923			0.428571
$589$	−7.00000	+	8.66025i	−0.288430	+	0.356840i
$590$		−	3.00000i		−	0.123508i
$591$		0			0
$592$	−3.00000	−	1.73205i	−0.123299	−	0.0711868i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	7.79423	−	4.50000i	0.319801	−	0.184637i
$595$		0			0
$596$	12.9904	+	7.50000i	0.532107	+	0.307212i
$597$		−	21.0000i		−	0.859473i
$598$		0			0
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	−0.146503	−	0.989210i	$-0.546802\pi$
$599$	15.5885	−	9.00000i	0.636927	−	0.367730i	0.783430	+	0.621480i	$0.213468\pi$
$600$	1.50000	−	0.866025i	0.0612372	−	0.0353553i
$601$	6.00000	+	3.46410i	0.244745	+	0.141304i	0.617356	−	0.786684i	$-0.288204\pi$
$601$	6.00000	+	3.46410i	0.244745	+	0.141304i	−0.372611	+	0.927988i	$0.621537\pi$
$602$	1.73205	+	3.00000i	0.0705931	+	0.122271i
$603$	−6.00000	+	10.3923i	−0.244339	+	0.423207i
$604$		−	12.1244i		−	0.493333i
$605$			8.00000i			0.325246i
$606$	12.9904	−	22.5000i	0.527698	−	0.914000i
$607$	−2.00000	−	3.46410i	−0.0811775	−	0.140604i	0.822578	−	0.568652i	$-0.192535\pi$
$607$	−2.00000	−	3.46410i	−0.0811775	−	0.140604i	−0.903756	+	0.428048i	$0.859201\pi$
$608$	1.73205	+	1.00000i	0.0702439	+	0.0405554i
$609$	4.50000	+	7.79423i	0.182349	+	0.315838i
$610$	−3.00000	+	1.73205i	−0.121466	+	0.0701287i
$611$	−20.7846	−	36.0000i	−0.840855	−	1.45640i
$612$		0			0
$613$	−15.0000	−	8.66025i	−0.605844	−	0.349784i	0.165493	−	0.986211i	$-0.447078\pi$
$613$	−15.0000	−	8.66025i	−0.605844	−	0.349784i	−0.771337	+	0.636427i	$0.780412\pi$
$614$	−19.0526	−	11.0000i	−0.768899	−	0.443924i
$615$		0			0
$616$			1.73205i			0.0697863i
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	0.600935	−	0.799298i	$-0.294795\pi$
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	−0.391745	+	0.920074i	$0.628129\pi$
$618$		−	8.66025i		−	0.348367i
$619$		−	10.3923i		−	0.417702i	−0.977947	−	0.208851i	$-0.933028\pi$
$619$		−	10.3923i		−	0.417702i	0.977947	−	0.208851i	$-0.0669724\pi$
$620$	−5.19615	+	2.00000i	−0.208683	+	0.0803219i
$621$		0			0
$622$	24.0000			0.962312
$623$	6.92820	−	12.0000i	0.277573	−	0.480770i
$624$			12.0000i			0.480384i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.79423	+	13.5000i	−0.311520	+	0.539569i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	14.0000			0.558661
$629$		0			0
$630$	1.50000	+	2.59808i	0.0597614	+	0.103510i
$631$	28.5000	−	16.4545i	1.13457	−	0.655043i	0.189488	−	0.981883i	$-0.439317\pi$
$631$	28.5000	−	16.4545i	1.13457	−	0.655043i	0.945080	+	0.326841i	$0.105984\pi$
$632$	5.19615	−	9.00000i	0.206692	−	0.358001i
$633$	−6.92820	−	12.0000i	−0.275371	−	0.476957i
$634$	7.50000	−	12.9904i	0.297863	−	0.515914i
$635$	8.66025			0.343672
$636$	−3.00000			−0.118958
$637$	36.0000	+	20.7846i	1.42637	+	0.823516i
$638$	7.79423	−	4.50000i	0.308576	−	0.178157i
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	8.66025	+	15.0000i	0.342059	+	0.592464i	0.984815	−	0.173607i	$-0.0555422\pi$
$641$	8.66025	+	15.0000i	0.342059	+	0.592464i	−0.642756	+	0.766071i	$0.722209\pi$
$642$	2.59808	+	4.50000i	0.102538	+	0.177601i
$643$			17.3205i			0.683054i	0.939872	+	0.341527i	$0.110944\pi$
$643$			17.3205i			0.683054i	−0.939872	+	0.341527i	$0.889056\pi$
$644$		0			0
$645$	3.00000	−	5.19615i	0.118125	−	0.204598i
$646$		0			0
$647$	−20.7846			−0.817127			−0.408564	−	0.912730i	$-0.633970\pi$
$647$	−20.7846			−0.817127			−0.408564	+	0.912730i	$0.633970\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$		−	5.19615i		−	0.203967i
$650$	6.92820			0.271746
$651$	−3.46410	−	9.00000i	−0.135769	−	0.352738i
$652$	−20.0000			−0.783260
$653$		−	27.0000i		−	1.05659i	−0.849060	−	0.528296i	$-0.822831\pi$
$653$		−	27.0000i		−	1.05659i	0.849060	−	0.528296i	$-0.177169\pi$
$654$	−21.0000	−	12.1244i	−0.821165	−	0.474100i
$655$	12.0000			0.468879
$656$		0			0
$657$	−18.0000	−	10.3923i	−0.702247	−	0.405442i
$658$	3.00000	−	5.19615i	0.116952	−	0.202567i
$659$			39.0000i			1.51922i	0.650376	+	0.759612i	$0.274611\pi$
$659$			39.0000i			1.51922i	−0.650376	+	0.759612i	$0.725389\pi$
$660$	2.59808	−	1.50000i	0.101130	−	0.0583874i
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−8.66025	−	15.0000i	−0.336590	−	0.582992i
$663$		0			0
$664$	−10.5000	+	6.06218i	−0.407479	+	0.235258i
$665$	1.73205	+	1.00000i	0.0671660	+	0.0387783i
$666$	−10.3923			−0.402694
$667$		0			0
$668$	−10.3923	+	18.0000i	−0.402090	+	0.696441i
$669$	−23.3827	+	13.5000i	−0.904027	+	0.521940i
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	−5.19615	+	3.00000i	−0.200595	+	0.115814i
$672$	−1.50000	+	0.866025i	−0.0578638	+	0.0334077i
$673$	22.5000	−	12.9904i	0.867311	−	0.500742i	0.000857451	−	1.00000i	$-0.499727\pi$
$673$	22.5000	−	12.9904i	0.867311	−	0.500742i	0.866454	+	0.499257i	$0.166394\pi$
$674$	−12.1244			−0.467013
$675$	2.59808	−	4.50000i	0.100000	−	0.173205i
$676$	−17.5000	+	30.3109i	−0.673077	+	1.16580i
$677$	−14.7224	−	25.5000i	−0.565829	−	0.980045i	−0.996972	−	0.0777610i	$-0.975223\pi$
$677$	−14.7224	−	25.5000i	−0.565829	−	0.980045i	0.431143	−	0.902284i	$-0.358110\pi$
$678$	−31.1769			−1.19734
$679$	−0.500000	+	0.866025i	−0.0191882	+	0.0332350i
$680$		0			0
$681$			5.19615i			0.199117i
$682$	−9.00000	+	3.46410i	−0.344628	+	0.132647i
$683$		−	51.0000i		−	1.95146i	−0.218975	−	0.975730i	$-0.570271\pi$
$683$		−	51.0000i		−	1.95146i	0.218975	−	0.975730i	$-0.429729\pi$
$684$	6.00000			0.229416
$685$	6.00000	+	3.46410i	0.229248	+	0.132357i
$686$			13.0000i			0.496342i
$687$	−5.19615	+	3.00000i	−0.198246	+	0.114457i
$688$	3.00000	+	1.73205i	0.114374	+	0.0660338i
$689$	−10.3923	−	6.00000i	−0.395915	−	0.228582i
$690$		0			0
$691$	26.0000	+	45.0333i	0.989087	+	1.71315i	0.622139	+	0.782907i	$0.286264\pi$
$691$	26.0000	+	45.0333i	0.989087	+	1.71315i	0.366947	+	0.930242i	$0.380403\pi$
$692$	7.79423	−	4.50000i	0.296292	−	0.171064i
$693$	2.59808	+	4.50000i	0.0986928	+	0.170941i
$694$	1.50000	+	0.866025i	0.0569392	+	0.0328739i
$695$		0			0
$696$	7.79423	+	4.50000i	0.295439	+	0.170572i
$697$		0			0
$698$			22.0000i			0.832712i
$699$	18.0000	+	10.3923i	0.680823	+	0.393073i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	−23.3827	−	13.5000i	−0.883152	−	0.509888i	−0.0114555	−	0.999934i	$-0.503646\pi$
$701$	−23.3827	−	13.5000i	−0.883152	−	0.509888i	−0.871696	+	0.490046i	$0.836980\pi$
$702$	18.0000	+	31.1769i	0.679366	+	1.17670i
$703$	−6.00000	+	3.46410i	−0.226294	+	0.130651i
$704$	0.866025	+	1.50000i	0.0326396	+	0.0565334i
$705$	−10.3923			−0.391397
$706$	−12.0000	−	6.92820i	−0.451626	−	0.260746i
$707$	12.9904	+	7.50000i	0.488554	+	0.282067i
$708$	4.50000	−	2.59808i	0.169120	−	0.0976417i
$709$			6.92820i			0.260194i	0.991501	+	0.130097i	$0.0415289\pi$
$709$			6.92820i			0.260194i	−0.991501	+	0.130097i	$0.958471\pi$
$710$		0			0
$711$		−	31.1769i		−	1.16923i
$712$		−	13.8564i		−	0.519291i
$713$		0			0
$714$		0			0
$715$	12.0000			0.448775
$716$	7.79423	−	13.5000i	0.291284	−	0.504519i
$717$	18.0000			0.672222
$718$		0			0
$719$	−6.92820	+	12.0000i	−0.258378	+	0.447524i	−0.965808	−	0.259260i	$-0.916521\pi$
$719$	−6.92820	+	12.0000i	−0.258378	+	0.447524i	0.707429	+	0.706784i	$0.249855\pi$
$720$	2.59808	+	1.50000i	0.0968246	+	0.0559017i
$721$	5.00000			0.186210
$722$	−12.9904	+	7.50000i	−0.483452	+	0.279121i
$723$	23.3827	−	13.5000i	0.869611	−	0.502070i
$724$	−12.0000	+	6.92820i	−0.445976	+	0.257485i
$725$	2.59808	−	4.50000i	0.0964901	−	0.167126i
$726$	−12.0000	+	6.92820i	−0.445362	+	0.257130i
$727$	0.500000	−	0.866025i	0.0185440	−	0.0321191i	−0.856605	−	0.515974i	$-0.827430\pi$
$727$	0.500000	−	0.866025i	0.0185440	−	0.0321191i	0.875148	+	0.483854i	$0.160764\pi$
$728$	−6.92820			−0.256776
$729$	27.0000			1.00000
$730$	−6.00000	−	3.46410i	−0.222070	−	0.128212i
$731$		0			0
$732$	−5.19615	−	3.00000i	−0.192055	−	0.110883i
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$	−5.19615	−	9.00000i	−0.191793	−	0.332196i
$735$	9.00000	−	5.19615i	0.331970	−	0.191663i
$736$		0			0
$737$	−3.46410	+	6.00000i	−0.127602	+	0.221013i
$738$		0			0
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.997470	−	0.0710909i	$-0.977352\pi$
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.437168	+	0.899380i	$0.644019\pi$
$740$	−3.46410			−0.127343
$741$	20.7846	+	12.0000i	0.763542	+	0.440831i
$742$		−	1.73205i		−	0.0635856i
$743$	−17.3205			−0.635428			−0.317714	−	0.948187i	$-0.602915\pi$
$743$	−17.3205			−0.635428			−0.317714	+	0.948187i	$0.602915\pi$
$744$	−7.50000	−	6.06218i	−0.274963	−	0.222250i
$745$	15.0000			0.549557
$746$		−	10.0000i		−	0.366126i
$747$	−18.1865	+	31.5000i	−0.665410	+	1.15252i
$748$		0			0
$749$	−2.59808	+	1.50000i	−0.0949316	+	0.0548088i
$750$	0.866025	−	1.50000i	0.0316228	−	0.0547723i
$751$	−3.50000	+	6.06218i	−0.127717	+	0.221212i	−0.922792	−	0.385299i	$-0.874098\pi$
$751$	−3.50000	+	6.06218i	−0.127717	+	0.221212i	0.795075	+	0.606511i	$0.207432\pi$
$752$		−	6.00000i		−	0.218797i
$753$	−15.0000	−	25.9808i	−0.546630	−	0.946792i
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	−6.06218	−	10.5000i	−0.220625	−	0.382134i
$756$	−2.59808	+	4.50000i	−0.0944911	+	0.163663i
$757$	33.0000	−	19.0526i	1.19941	−	0.692477i	0.238983	−	0.971024i	$-0.423186\pi$
$757$	33.0000	−	19.0526i	1.19941	−	0.692477i	0.960423	+	0.278547i	$0.0898527\pi$
$758$	−27.7128	−	16.0000i	−1.00657	−	0.581146i
$759$		0			0
$760$	2.00000			0.0725476
$761$	−20.7846	+	36.0000i	−0.753442	+	1.30500i	0.192704	+	0.981257i	$0.438274\pi$
$761$	−20.7846	+	36.0000i	−0.753442	+	1.30500i	−0.946145	+	0.323742i	$0.895059\pi$
$762$	7.50000	+	12.9904i	0.271696	+	0.470592i
$763$	7.00000	−	12.1244i	0.253417	−	0.438931i
$764$	5.19615	−	3.00000i	0.187990	−	0.108536i
$765$		0			0
$766$	−30.0000	+	17.3205i	−1.08394	+	0.625815i
$767$	20.7846			0.750489
$768$	−0.866025	+	1.50000i	−0.0312500	+	0.0541266i
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$	0.866025	+	1.50000i	0.0312094	+	0.0540562i
$771$			20.7846i			0.748539i
$772$	−11.5000	+	19.9186i	−0.413894	+	0.716886i
$773$	−27.7128			−0.996761			−0.498380	−	0.866959i	$-0.666072\pi$
$773$	−27.7128			−0.996761			−0.498380	+	0.866959i	$0.666072\pi$
$774$	10.3923			0.373544
$775$	−3.50000	+	4.33013i	−0.125724	+	0.155543i
$776$			1.00000i			0.0358979i
$777$		−	6.00000i		−	0.215249i
$778$	−12.0000	−	6.92820i	−0.430221	−	0.248388i
$779$		0			0
$780$	6.00000	+	10.3923i	0.214834	+	0.372104i
$781$		0			0
$782$		0			0
$783$	27.0000			0.964901
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	12.1244	−	7.00000i	0.432737	−	0.249841i
$786$	10.3923	+	18.0000i	0.370681	+	0.642039i
$787$	9.00000	+	5.19615i	0.320815	+	0.185223i	0.651756	−	0.758429i	$-0.274033\pi$
$787$	9.00000	+	5.19615i	0.320815	+	0.185223i	−0.330941	+	0.943652i	$0.607366\pi$
$788$		0			0
$789$	21.0000	−	36.3731i	0.747620	−	1.29492i
$790$		−	10.3923i		−	0.369742i
$791$		−	18.0000i		−	0.640006i
$792$	4.50000	+	2.59808i	0.159901	+	0.0923186i
$793$	−12.0000	−	20.7846i	−0.426132	−	0.738083i
$794$	−1.73205	−	1.00000i	−0.0614682	−	0.0354887i
$795$	−2.59808	+	1.50000i	−0.0921443	+	0.0531995i
$796$	10.5000	−	6.06218i	0.372163	−	0.214868i
$797$	−19.9186	−	34.5000i	−0.705552	−	1.22205i	−0.966492	−	0.256697i	$-0.917366\pi$
$797$	−19.9186	−	34.5000i	−0.705552	−	1.22205i	0.260939	−	0.965355i	$-0.415968\pi$
$798$			3.46410i			0.122628i
$799$		0			0
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−20.7846	−	36.0000i	−0.734388	−	1.27200i
$802$		−	17.3205i		−	0.611608i
$803$	−10.3923	−	6.00000i	−0.366736	−	0.211735i
$804$	−6.92820			−0.244339
$805$		0			0
$806$	−13.8564	−	36.0000i	−0.488071	−	1.26805i
$807$	24.0000			0.844840
$808$	15.0000			0.527698
$809$	−19.0526	+	33.0000i	−0.669852	+	1.16022i	0.308093	+	0.951356i	$0.400309\pi$
$809$	−19.0526	+	33.0000i	−0.669852	+	1.16022i	−0.977945	+	0.208862i	$0.933024\pi$
$810$	9.00000			0.316228
$811$	−20.0000	−	34.6410i	−0.702295	−	1.21641i	−0.967659	−	0.252262i	$-0.918825\pi$
$811$	−20.0000	−	34.6410i	−0.702295	−	1.21641i	0.265364	−	0.964148i	$-0.414508\pi$
$812$	−2.59808	+	4.50000i	−0.0911746	+	0.157919i
$813$	−18.1865	−	10.5000i	−0.637830	−	0.368251i
$814$	−6.00000			−0.210300
$815$	−17.3205	+	10.0000i	−0.606711	+	0.350285i
$816$		0			0
$817$	6.00000	−	3.46410i	0.209913	−	0.121194i
$818$	16.4545	−	28.5000i	0.575317	−	0.996479i
$819$	−18.0000	+	10.3923i	−0.628971	+	0.363137i
$820$		0			0
$821$	−39.8372			−1.39033			−0.695163	−	0.718852i	$-0.744668\pi$
$821$	−39.8372			−1.39033			−0.695163	+	0.718852i	$0.744668\pi$
$822$			12.0000i			0.418548i
$823$	−34.5000	−	19.9186i	−1.20259	−	0.694318i	−0.241463	−	0.970410i	$-0.577627\pi$
$823$	−34.5000	−	19.9186i	−1.20259	−	0.694318i	−0.961131	+	0.276092i	$0.910961\pi$
$824$	4.33013	−	2.50000i	0.150847	−	0.0870916i
$825$	1.50000	−	2.59808i	0.0522233	−	0.0904534i
$826$	1.50000	+	2.59808i	0.0521917	+	0.0903986i
$827$	−8.66025	−	15.0000i	−0.301147	−	0.521601i	0.675249	−	0.737589i	$-0.264036\pi$
$827$	−8.66025	−	15.0000i	−0.301147	−	0.521601i	−0.976396	+	0.215988i	$0.930703\pi$
$828$		0			0
$829$			34.6410i			1.20313i	0.798823	+	0.601566i	$0.205456\pi$
$829$			34.6410i			1.20313i	−0.798823	+	0.601566i	$0.794544\pi$
$830$	−6.06218	+	10.5000i	−0.210421	+	0.364460i
$831$	15.5885	+	9.00000i	0.540758	+	0.312207i
$832$	−6.00000	+	3.46410i	−0.208013	+	0.120096i
$833$		0			0
$834$		0			0
$835$			20.7846i			0.719281i
$836$	3.46410			0.119808
$837$	−28.5788	−	4.50000i	−0.987829	−	0.155543i
$838$	3.00000			0.103633
$839$		−	30.0000i		−	1.03572i	−0.855467	−	0.517858i	$-0.826730\pi$
$839$		−	30.0000i		−	1.03572i	0.855467	−	0.517858i	$-0.173270\pi$
$840$	−0.866025	+	1.50000i	−0.0298807	+	0.0517549i
$841$	−2.00000			−0.0689655
$842$	13.8564	−	8.00000i	0.477523	−	0.275698i
$843$	−9.00000	−	5.19615i	−0.309976	−	0.178965i
$844$	4.00000	−	6.92820i	0.137686	−	0.238479i
$845$			35.0000i			1.20404i
$846$	−9.00000	−	15.5885i	−0.309426	−	0.535942i
$847$	−4.00000	−	6.92820i	−0.137442	−	0.238056i
$848$	−0.866025	−	1.50000i	−0.0297394	−	0.0515102i
$849$	24.2487	−	42.0000i	0.832214	−	1.44144i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$	1.73205	−	3.00000i	0.0592696	−	0.102658i
$855$	5.19615	−	3.00000i	0.177705	−	0.102598i
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	46.7654	−	27.0000i	1.59747	−	0.922302i	0.605503	−	0.795843i	$-0.292972\pi$
$857$	46.7654	−	27.0000i	1.59747	−	0.922302i	0.991972	−	0.126459i	$-0.0403613\pi$
$858$	10.3923	+	18.0000i	0.354787	+	0.614510i
$859$	6.00000	−	3.46410i	0.204717	−	0.118194i	−0.394137	−	0.919052i	$-0.628956\pi$
$859$	6.00000	−	3.46410i	0.204717	−	0.118194i	0.598854	+	0.800858i	$0.295623\pi$
$860$	3.46410			0.118125
$861$		0			0
$862$	−15.0000	+	25.9808i	−0.510902	+	0.884908i
$863$	−3.46410	−	6.00000i	−0.117919	−	0.204242i	0.801024	−	0.598633i	$-0.204289\pi$
$863$	−3.46410	−	6.00000i	−0.117919	−	0.204242i	−0.918943	+	0.394390i	$0.870956\pi$
$864$			5.19615i			0.176777i
$865$	4.50000	−	7.79423i	0.153005	−	0.265012i
$866$	−34.6410			−1.17715
$867$	−29.4449			−1.00000
$868$	3.50000	−	4.33013i	0.118798	−	0.146974i
$869$		−	18.0000i		−	0.610608i
$870$	9.00000			0.305129
$871$	−24.0000	−	13.8564i	−0.813209	−	0.469506i
$872$		−	14.0000i		−	0.474100i
$873$	1.50000	+	2.59808i	0.0507673	+	0.0879316i
$874$		0			0
$875$	0.866025	+	0.500000i	0.0292770	+	0.0169031i
$876$		−	12.0000i		−	0.405442i
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$	16.4545	−	9.50000i	0.555312	−	0.320609i
$879$	−22.5000	+	12.9904i	−0.758906	+	0.438155i
$880$	1.50000	+	0.866025i	0.0505650	+	0.0291937i
$881$	29.4449	+	51.0000i	0.992023	+	1.71823i	0.605182	+	0.796087i	$0.293100\pi$
$881$	29.4449	+	51.0000i	0.992023	+	1.71823i	0.386840	+	0.922147i	$0.373566\pi$
$882$	15.5885	+	9.00000i	0.524891	+	0.303046i
$883$		−	10.3923i		−	0.349729i	−0.984593	−	0.174864i	$-0.944051\pi$
$883$		−	10.3923i		−	0.349729i	0.984593	−	0.174864i	$-0.0559487\pi$
$884$		0			0
$885$	2.59808	−	4.50000i	0.0873334	−	0.151266i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−25.9808	−	15.0000i	−0.872349	−	0.503651i	−0.00422062	−	0.999991i	$-0.501343\pi$
$887$	−25.9808	−	15.0000i	−0.872349	−	0.503651i	−0.868128	+	0.496340i	$0.834677\pi$
$888$	−3.00000	−	5.19615i	−0.100673	−	0.174371i
$889$	−7.50000	+	4.33013i	−0.251542	+	0.145228i
$890$	−6.92820	−	12.0000i	−0.232234	−	0.402241i
$891$	15.5885			0.522233
$892$	−13.5000	−	7.79423i	−0.452013	−	0.260970i
$893$	−10.3923	−	6.00000i	−0.347765	−	0.200782i
$894$	12.9904	+	22.5000i	0.434463	+	0.752513i
$895$		−	15.5885i		−	0.521065i
$896$	−0.866025	−	0.500000i	−0.0289319	−	0.0167038i
$897$		0			0
$898$			10.3923i			0.346796i
$899$	−28.5788	−	4.50000i	−0.953158	−	0.150083i
$900$	3.00000			0.100000
$901$		0			0
$902$		0			0
$903$			6.00000i			0.199667i
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	−6.92820	+	12.0000i	−0.230301	+	0.398893i
$906$	10.5000	−	18.1865i	0.348839	−	0.604207i
$907$	10.0000			0.332045			0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000			0.332045			0.166022	+	0.986122i	$0.446908\pi$
$908$	−2.59808	+	1.50000i	−0.0862202	+	0.0497792i
$909$	38.9711	−	22.5000i	1.29259	−	0.746278i
$910$	−6.00000	+	3.46410i	−0.198898	+	0.114834i
$911$	15.5885	−	27.0000i	0.516469	−	0.894550i	−0.483349	−	0.875428i	$-0.660580\pi$
$911$	15.5885	−	27.0000i	0.516469	−	0.894550i	0.999817	−	0.0191219i	$-0.00608706\pi$
$912$	1.73205	+	3.00000i	0.0573539	+	0.0993399i
$913$	−10.5000	+	18.1865i	−0.347499	+	0.601886i
$914$	−6.92820			−0.229165
$915$	−6.00000			−0.198354
$916$	−3.00000	−	1.73205i	−0.0991228	−	0.0572286i
$917$	−10.3923	+	6.00000i	−0.343184	+	0.198137i
$918$		0			0
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$		0			0
$921$	−19.0526	−	33.0000i	−0.627803	−	1.08739i
$922$		−	15.5885i		−	0.513378i
$923$		0			0
$924$	−1.50000	+	2.59808i	−0.0493464	+	0.0854704i
$925$	−3.00000	+	1.73205i	−0.0986394	+	0.0569495i
$926$	12.1244			0.398431
$927$	7.50000	−	12.9904i	0.246332	−	0.426660i
$928$			5.19615i			0.170572i
$929$	20.7846			0.681921			0.340960	−	0.940078i	$-0.389248\pi$
$929$	20.7846			0.681921			0.340960	+	0.940078i	$0.389248\pi$
$930$	−9.52628	−	1.50000i	−0.312379	−	0.0491869i
$931$	12.0000			0.393284
$932$			12.0000i			0.393073i
$933$	36.0000	+	20.7846i	1.17859	+	0.680458i
$934$	−39.0000			−1.27612
$935$		0			0
$936$	−10.3923	+	18.0000i	−0.339683	+	0.588348i
$937$	1.00000	−	1.73205i	0.0326686	−	0.0565836i	−0.849229	−	0.528025i	$-0.822933\pi$
$937$	1.00000	−	1.73205i	0.0326686	−	0.0565836i	0.881897	+	0.471441i	$0.156266\pi$
$938$		−	4.00000i		−	0.130605i
$939$	−23.3827	+	13.5000i	−0.763065	+	0.440556i
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	9.52628	+	16.5000i	0.310548	+	0.537885i	0.978481	−	0.206337i	$-0.0661542\pi$
$941$	9.52628	+	16.5000i	0.310548	+	0.537885i	−0.667933	+	0.744221i	$0.732821\pi$
$942$	21.0000	+	12.1244i	0.684217	+	0.395033i
$943$		0			0
$944$	2.59808	+	1.50000i	0.0845602	+	0.0488208i
$945$			5.19615i			0.169031i
$946$	6.00000			0.195077
$947$	8.66025	−	15.0000i	0.281420	−	0.487435i	−0.690314	−	0.723510i	$-0.742528\pi$
$947$	8.66025	−	15.0000i	0.281420	−	0.487435i	0.971735	+	0.236075i	$0.0758611\pi$
$948$	15.5885	−	9.00000i	0.506290	−	0.292306i
$949$	24.0000	−	41.5692i	0.779073	−	1.34939i
$950$	1.73205	−	1.00000i	0.0561951	−	0.0324443i
$951$	22.5000	−	12.9904i	0.729612	−	0.421242i
$952$		0			0
$953$	−31.1769			−1.00992			−0.504960	−	0.863143i	$-0.668493\pi$
$953$	−31.1769			−1.00992			−0.504960	+	0.863143i	$0.668493\pi$
$954$	−4.50000	−	2.59808i	−0.145693	−	0.0841158i
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	5.19615	+	9.00000i	0.168056	+	0.291081i
$957$	15.5885			0.503903
$958$	−9.00000	+	15.5885i	−0.290777	+	0.503640i
$959$	−6.92820			−0.223723
$960$			1.73205i			0.0559017i
$961$	29.5000	+	9.52628i	0.951613	+	0.307299i
$962$		−	24.0000i		−	0.773791i
$963$			9.00000i			0.290021i
$964$	13.5000	+	7.79423i	0.434806	+	0.251035i
$965$			23.0000i			0.740396i
$966$		0			0
$967$	9.00000	+	5.19615i	0.289420	+	0.167097i	0.637680	−	0.770301i	$-0.279894\pi$
$967$	9.00000	+	5.19615i	0.289420	+	0.167097i	−0.348260	+	0.937398i	$0.613227\pi$
$968$	−6.92820	−	4.00000i	−0.222681	−	0.128565i
$969$		0			0
$970$	0.500000	+	0.866025i	0.0160540	+	0.0278064i
$971$	−7.79423	+	4.50000i	−0.250129	+	0.144412i	−0.619823	−	0.784741i	$-0.712796\pi$
$971$	−7.79423	+	4.50000i	−0.250129	+	0.144412i	0.369694	+	0.929153i	$0.379462\pi$
$972$	7.79423	+	13.5000i	0.250000	+	0.433013i
$973$		0			0
$974$	18.1865	+	31.5000i	0.582734	+	1.00933i
$975$	10.3923	+	6.00000i	0.332820	+	0.192154i
$976$		−	3.46410i		−	0.110883i
$977$			24.0000i			0.767828i	0.923369	+	0.383914i	$0.125424\pi$
$977$			24.0000i			0.767828i	−0.923369	+	0.383914i	$0.874576\pi$
$978$	−30.0000	−	17.3205i	−0.959294	−	0.553849i
$979$	−12.0000	−	20.7846i	−0.383522	−	0.664279i
$980$	5.19615	+	3.00000i	0.165985	+	0.0958315i
$981$	−21.0000	−	36.3731i	−0.670478	−	1.16130i
$982$	25.5000	−	14.7224i	0.813738	−	0.469812i
$983$	10.3923	+	18.0000i	0.331463	+	0.574111i	0.982799	−	0.184679i	$-0.0591244\pi$
$983$	10.3923	+	18.0000i	0.331463	+	0.574111i	−0.651336	+	0.758790i	$0.725791\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	9.00000	−	5.19615i	0.286473	−	0.165395i
$988$			13.8564i			0.440831i
$989$		0			0
$990$	5.19615			0.165145
$991$		−	17.3205i		−	0.550204i	−0.961415	−	0.275102i	$-0.911288\pi$
$991$		−	17.3205i		−	0.550204i	0.961415	−	0.275102i	$-0.0887116\pi$
$992$	0.866025	−	5.50000i	0.0274963	−	0.174625i
$993$		−	30.0000i		−	0.952021i
$994$		0			0
$995$	6.06218	−	10.5000i	0.192184	−	0.332872i
$996$	−21.0000			−0.665410
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$	17.3205	−	30.0000i	0.548271	−	0.949633i
$999$	−15.5885	−	9.00000i	−0.493197	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.b.491.2	yes	4
3.2	odd	2	inner	930.2.o.b.491.1	yes	4
31.6	odd	6	inner	930.2.o.b.161.2	yes	4
93.68	even	6	inner	930.2.o.b.161.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.b.161.1	✓	4	93.68	even	6	inner
930.2.o.b.161.2	yes	4	31.6	odd	6	inner
930.2.o.b.491.1	yes	4	3.2	odd	2	inner
930.2.o.b.491.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.866025 - 1.50000i) q^{11} +(0.866025 - 1.50000i) q^{12} +(6.00000 - 3.46410i) q^{13} +(0.866025 + 0.500000i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(2.59808 - 1.50000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.866025 + 1.50000i) q^{21} +(1.50000 - 0.866025i) q^{22} +(1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.46410 + 6.00000i) q^{26} +5.19615 q^{27} +(-0.500000 + 0.866025i) q^{28} +5.19615 q^{29} +1.73205 q^{30} +(-5.50000 - 0.866025i) q^{31} +1.00000i q^{32} +3.00000 q^{33} +1.00000i q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.00000 - 1.73205i) q^{37} +(1.73205 + 1.00000i) q^{38} +12.0000i q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.50000 + 0.866025i) q^{42} +(3.00000 + 1.73205i) q^{43} +(0.866025 + 1.50000i) q^{44} +(2.59808 + 1.50000i) q^{45} -6.00000i q^{47} +(-0.866025 + 1.50000i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-6.00000 + 3.46410i) q^{52} +(-0.866025 - 1.50000i) q^{53} +5.19615i q^{54} +(1.50000 + 0.866025i) q^{55} +(-0.866025 - 0.500000i) q^{56} +(1.73205 + 3.00000i) q^{57} +5.19615i q^{58} +(2.59808 + 1.50000i) q^{59} +1.73205i q^{60} -3.46410i q^{61} +(0.866025 - 5.50000i) q^{62} -3.00000 q^{63} -1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +3.00000i q^{66} +(-2.00000 - 3.46410i) q^{67} -1.00000 q^{70} +(-2.59808 + 1.50000i) q^{72} +(6.00000 - 3.46410i) q^{73} +(1.73205 - 3.00000i) q^{74} +(0.866025 + 1.50000i) q^{75} +(-1.00000 + 1.73205i) q^{76} -1.73205 q^{77} -12.0000 q^{78} +(9.00000 + 5.19615i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.06218 - 10.5000i) q^{83} +(-0.866025 - 1.50000i) q^{84} +(-1.73205 + 3.00000i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(-1.50000 + 0.866025i) q^{88} +13.8564 q^{89} +(-1.50000 + 2.59808i) q^{90} -6.92820i q^{91} +(6.06218 - 7.50000i) q^{93} +6.00000 q^{94} +2.00000i q^{95} +(-1.50000 - 0.866025i) q^{96} -1.00000 q^{97} +(-5.19615 + 3.00000i) q^{98} +(-2.59808 + 4.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9	\( 4 q - 4 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9} - 2 q^{10} + 24 q^{13} + 4 q^{16} + 4 q^{19} + 6 q^{22} + 6 q^{24} + 2 q^{25} - 2 q^{28} - 22 q^{31} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 2 q^{40} - 6 q^{42} + 12 q^{43} + 12 q^{49} - 24 q^{52} + 6 q^{55} - 12 q^{63} - 4 q^{64} - 8 q^{67} - 4 q^{70} + 24 q^{73} - 4 q^{76} - 48 q^{78} + 36 q^{79} - 18 q^{81} - 18 q^{87} - 6 q^{88} - 6 q^{90} + 24 q^{94} - 6 q^{96} - 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9 - 2 * q^10 + 24 * q^13 + 4 * q^16 + 4 * q^19 + 6 * q^22 + 6 * q^24 + 2 * q^25 - 2 * q^28 - 22 * q^31 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 2 * q^40 - 6 * q^42 + 12 * q^43 + 12 * q^49 - 24 * q^52 + 6 * q^55 - 12 * q^63 - 4 * q^64 - 8 * q^67 - 4 * q^70 + 24 * q^73 - 4 * q^76 - 48 * q^78 + 36 * q^79 - 18 * q^81 - 18 * q^87 - 6 * q^88 - 6 * q^90 + 24 * q^94 - 6 * q^96 - 4 * q^97

Introduction

L-functions

Modular forms

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