LMFDB - Embedded newform 1950.2.y.e.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (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:	$15.5708283941$
Analytic rank:	$1$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.e.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.23205 + 1.86603i) q^{11} -1.00000i q^{12} +(-3.50000 - 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(1.96410 + 1.13397i) q^{19} -3.00000i q^{21} +(-3.23205 - 1.86603i) q^{22} +(-3.00000 + 1.73205i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.50000 - 2.59808i) q^{28} +(-2.73205 - 4.73205i) q^{29} -8.92820i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.86603 - 3.23205i) q^{33} +4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(3.96410 + 6.86603i) q^{37} +2.26795i q^{38} +(3.46410 - 1.00000i) q^{39} +(3.46410 - 2.00000i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-5.19615 - 3.00000i) q^{43} -3.73205i q^{44} +(-3.00000 - 1.73205i) q^{46} +0.464102 q^{47} +(0.866025 + 0.500000i) q^{48} +(-1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -3.73205i q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.50000 - 2.59808i) q^{56} -2.26795 q^{57} +(2.73205 - 4.73205i) q^{58} +(-3.92820 - 2.26795i) q^{59} +(3.73205 - 6.46410i) q^{61} +(7.73205 - 4.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +3.73205 q^{66} +(-2.73205 - 4.73205i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(1.73205 - 3.00000i) q^{69} +(-0.803848 - 0.464102i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.92820 q^{73} +(-3.96410 + 6.86603i) q^{74} +(-1.96410 + 1.13397i) q^{76} -11.1962i q^{77} +(2.59808 + 2.50000i) q^{78} -16.9282 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.46410 + 2.00000i) q^{82} -2.53590 q^{83} +(2.59808 + 1.50000i) q^{84} -6.00000i q^{86} +(4.73205 + 2.73205i) q^{87} +(3.23205 - 1.86603i) q^{88} +(8.76795 - 5.06218i) q^{89} +(7.50000 - 7.79423i) q^{91} -3.46410i q^{92} +(4.46410 + 7.73205i) q^{93} +(0.232051 + 0.401924i) q^{94} +1.00000i q^{96} +(6.19615 - 10.7321i) q^{97} +(1.00000 - 1.73205i) q^{98} +3.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 6 q^{7} - 4 q^{8} + 2 q^{9} - 6 q^{11} - 14 q^{13} - 12 q^{14} - 2 q^{16} + 4 q^{18} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 4 q^{26} - 6 q^{28} - 4 q^{29} + 2 q^{32} + 4 q^{33} + 2 q^{36} + 2 q^{37} - 12 q^{46} - 12 q^{47} - 4 q^{49} - 16 q^{51} + 10 q^{52} + 6 q^{56} - 16 q^{57} + 4 q^{58} + 12 q^{59} + 8 q^{61} + 24 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{66} - 4 q^{67} - 24 q^{71} - 2 q^{72} - 2 q^{74} + 6 q^{76} - 40 q^{79} - 2 q^{81} - 24 q^{83} + 12 q^{87} + 6 q^{88} + 42 q^{89} + 30 q^{91} + 4 q^{93} - 6 q^{94} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^7 - 4 * q^8 + 2 * q^9 - 6 * q^11 - 14 * q^13 - 12 * q^14 - 2 * q^16 + 4 * q^18 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 4 * q^26 - 6 * q^28 - 4 * q^29 + 2 * q^32 + 4 * q^33 + 2 * q^36 + 2 * q^37 - 12 * q^46 - 12 * q^47 - 4 * q^49 - 16 * q^51 + 10 * q^52 + 6 * q^56 - 16 * q^57 + 4 * q^58 + 12 * q^59 + 8 * q^61 + 24 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^66 - 4 * q^67 - 24 * q^71 - 2 * q^72 - 2 * q^74 + 6 * q^76 - 40 * q^79 - 2 * q^81 - 24 * q^83 + 12 * q^87 + 6 * q^88 + 42 * q^89 + 30 * q^91 + 4 * q^93 - 6 * q^94 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.900605	−	0.434638i	$-0.856876\pi$
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.0738948	+	0.997266i	$0.523543\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$	1.00000			0.235702
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	0.708082	−	0.706130i	$-0.249561\pi$
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	−0.257486	+	0.966282i	$0.582894\pi$
$20$		0			0
$21$		−	3.00000i		−	0.654654i
$22$	−3.23205	−	1.86603i	−0.689076	−	0.397838i
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	−0.779024	−	0.626994i	$-0.784285\pi$
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	0.153481	+	0.988152i	$0.450952\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$			1.00000i			0.192450i
$28$	−1.50000	−	2.59808i	−0.283473	−	0.490990i
$29$	−2.73205	−	4.73205i	−0.507329	−	0.878720i	−0.999964	−	0.00848369i	$-0.997300\pi$
$29$	−2.73205	−	4.73205i	−0.507329	−	0.878720i	0.492635	−	0.870236i	$-0.336034\pi$
$30$		0			0
$31$		−	8.92820i		−	1.60355i	−0.597624	−	0.801776i	$-0.703889\pi$
$31$		−	8.92820i		−	1.60355i	0.597624	−	0.801776i	$-0.296111\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.86603	−	3.23205i	0.324833	−	0.562628i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	3.96410	+	6.86603i	0.651694	+	1.12877i	0.982712	+	0.185143i	$0.0592748\pi$
$37$	3.96410	+	6.86603i	0.651694	+	1.12877i	−0.331017	+	0.943625i	$0.607392\pi$
$38$			2.26795i			0.367910i
$39$	3.46410	−	1.00000i	0.554700	−	0.160128i
$40$		0			0
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	−0.204483	−	0.978870i	$-0.565551\pi$
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	0.745485	+	0.666523i	$0.232218\pi$
$42$	2.59808	−	1.50000i	0.400892	−	0.231455i
$43$	−5.19615	−	3.00000i	−0.792406	−	0.457496i	0.0484030	−	0.998828i	$-0.484587\pi$
$43$	−5.19615	−	3.00000i	−0.792406	−	0.457496i	−0.840809	+	0.541332i	$0.817920\pi$
$44$		−	3.73205i		−	0.562628i
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$	0.464102			0.0676962			0.0338481	−	0.999427i	$-0.489224\pi$
$47$	0.464102			0.0676962			0.0338481	+	0.999427i	$0.489224\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$		−	3.73205i		−	0.512637i	−0.966592	−	0.256318i	$-0.917490\pi$
$53$		−	3.73205i		−	0.512637i	0.966592	−	0.256318i	$-0.0825095\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−2.26795			−0.300397
$58$	2.73205	−	4.73205i	0.358736	−	0.621349i
$59$	−3.92820	−	2.26795i	−0.511409	−	0.295262i	0.222004	−	0.975046i	$-0.428740\pi$
$59$	−3.92820	−	2.26795i	−0.511409	−	0.295262i	−0.733412	+	0.679784i	$0.762074\pi$
$60$		0			0
$61$	3.73205	−	6.46410i	0.477840	−	0.827643i	−0.521837	−	0.853045i	$-0.674753\pi$
$61$	3.73205	−	6.46410i	0.477840	−	0.827643i	0.999677	+	0.0254017i	$0.00808648\pi$
$62$	7.73205	−	4.46410i	0.981971	−	0.566941i
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.73205			0.459384
$67$	−2.73205	−	4.73205i	−0.333773	−	0.578112i	0.649475	−	0.760383i	$-0.274989\pi$
$67$	−2.73205	−	4.73205i	−0.333773	−	0.578112i	−0.983248	+	0.182271i	$0.941655\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$	1.73205	−	3.00000i	0.208514	−	0.361158i
$70$		0			0
$71$	−0.803848	−	0.464102i	−0.0953992	−	0.0550787i	0.451541	−	0.892250i	$-0.350874\pi$
$71$	−0.803848	−	0.464102i	−0.0953992	−	0.0550787i	−0.546941	+	0.837171i	$0.684208\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−6.92820			−0.810885			−0.405442	−	0.914121i	$-0.632883\pi$
$73$	−6.92820			−0.810885			−0.405442	+	0.914121i	$0.632883\pi$
$74$	−3.96410	+	6.86603i	−0.460817	+	0.798159i
$75$		0			0
$76$	−1.96410	+	1.13397i	−0.225298	+	0.130076i
$77$		−	11.1962i		−	1.27592i
$78$	2.59808	+	2.50000i	0.294174	+	0.283069i
$79$	−16.9282			−1.90457			−0.952286	−	0.305208i	$-0.901274\pi$
$79$	−16.9282			−1.90457			−0.952286	+	0.305208i	$0.901274\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.46410	+	2.00000i	0.382546	+	0.220863i
$83$	−2.53590			−0.278351			−0.139176	−	0.990268i	$-0.544445\pi$
$83$	−2.53590			−0.278351			−0.139176	+	0.990268i	$0.544445\pi$
$84$	2.59808	+	1.50000i	0.283473	+	0.163663i
$85$		0			0
$86$		−	6.00000i		−	0.646997i
$87$	4.73205	+	2.73205i	0.507329	+	0.292907i
$88$	3.23205	−	1.86603i	0.344538	−	0.198919i
$89$	8.76795	−	5.06218i	0.929401	−	0.536590i	0.0427788	−	0.999085i	$-0.486379\pi$
$89$	8.76795	−	5.06218i	0.929401	−	0.536590i	0.886622	+	0.462495i	$0.153046\pi$
$90$		0			0
$91$	7.50000	−	7.79423i	0.786214	−	0.817057i
$92$		−	3.46410i		−	0.361158i
$93$	4.46410	+	7.73205i	0.462906	+	0.801776i
$94$	0.232051	+	0.401924i	0.0239342	+	0.0414553i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	6.19615	−	10.7321i	0.629124	−	1.08967i	−0.358604	−	0.933490i	$-0.616747\pi$
$97$	6.19615	−	10.7321i	0.629124	−	1.08967i	0.987728	−	0.156185i	$-0.0499196\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$			3.73205i			0.375085i
$100$		0			0
$101$	4.19615	+	7.26795i	0.417533	+	0.723188i	0.995691	−	0.0927369i	$-0.0295616\pi$
$101$	4.19615	+	7.26795i	0.417533	+	0.723188i	−0.578158	+	0.815925i	$0.696228\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$			19.5885i			1.93011i	0.262051	+	0.965054i	$0.415601\pi$
$103$			19.5885i			1.93011i	−0.262051	+	0.965054i	$0.584399\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	3.23205	−	1.86603i	0.313925	−	0.181244i
$107$	−0.803848	+	0.464102i	−0.0777109	+	0.0448664i	−0.538352	−	0.842720i	$-0.680953\pi$
$107$	−0.803848	+	0.464102i	−0.0777109	+	0.0448664i	0.460641	+	0.887587i	$0.347620\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$	−6.86603	−	3.96410i	−0.651694	−	0.376256i
$112$	3.00000			0.283473
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.901553	−	0.432670i	$-0.142428\pi$
$113$	10.3923	+	6.00000i	0.977626	+	0.564433i	0.0760733	+	0.997102i	$0.475762\pi$
$114$	−1.13397	−	1.96410i	−0.106206	−	0.183955i
$115$		0			0
$116$	5.46410			0.507329
$117$	−2.50000	+	2.59808i	−0.231125	+	0.240192i
$118$		−	4.53590i		−	0.417563i
$119$	−10.3923	+	6.00000i	−0.952661	+	0.550019i
$120$		0			0
$121$	1.46410	−	2.53590i	0.133100	−	0.230536i
$122$	7.46410			0.675768
$123$	−2.00000	+	3.46410i	−0.180334	+	0.312348i
$124$	7.73205	+	4.46410i	0.694359	+	0.400888i
$125$		0			0
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	−4.03590	+	2.33013i	−0.358128	+	0.206765i	−0.668259	−	0.743928i	$-0.732960\pi$
$127$	−4.03590	+	2.33013i	−0.358128	+	0.206765i	0.310131	+	0.950694i	$0.399627\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.00000			0.528271
$130$		0			0
$131$	−20.3205			−1.77541			−0.887706	−	0.460412i	$-0.847702\pi$
$131$	−20.3205			−1.77541			−0.887706	+	0.460412i	$0.847702\pi$
$132$	1.86603	+	3.23205i	0.162417	+	0.281314i
$133$	−5.89230	+	3.40192i	−0.510928	+	0.294984i
$134$	2.73205	−	4.73205i	0.236013	−	0.408787i
$135$		0			0
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	−3.26795	+	5.66025i	−0.279200	+	0.483588i	−0.971186	−	0.238322i	$-0.923402\pi$
$137$	−3.26795	+	5.66025i	−0.279200	+	0.483588i	0.691986	+	0.721911i	$0.256736\pi$
$138$	3.46410			0.294884
$139$	10.8923	−	18.8660i	0.923873	−	1.60020i	0.130510	−	0.991447i	$-0.458339\pi$
$139$	10.8923	−	18.8660i	0.923873	−	1.60020i	0.793363	−	0.608748i	$-0.208328\pi$
$140$		0			0
$141$	−0.401924	+	0.232051i	−0.0338481	+	0.0195422i
$142$		−	0.928203i		−	0.0778931i
$143$	12.9282	−	3.73205i	1.08111	−	0.312090i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$	1.73205	+	1.00000i	0.142857	+	0.0824786i
$148$	−7.92820			−0.651694
$149$	−19.7321	−	11.3923i	−1.61651	−	0.933294i	−0.987813	−	0.155646i	$-0.950254\pi$
$149$	−19.7321	−	11.3923i	−1.61651	−	0.933294i	−0.628700	−	0.777648i	$-0.716413\pi$
$150$		0			0
$151$		−	18.7846i		−	1.52867i	−0.644819	−	0.764335i	$-0.723067\pi$
$151$		−	18.7846i		−	1.52867i	0.644819	−	0.764335i	$-0.276933\pi$
$152$	−1.96410	−	1.13397i	−0.159310	−	0.0919775i
$153$	3.46410	−	2.00000i	0.280056	−	0.161690i
$154$	9.69615	−	5.59808i	0.781338	−	0.451106i
$155$		0			0
$156$	−0.866025	+	3.50000i	−0.0693375	+	0.280224i
$157$		−	10.8038i		−	0.862241i	−0.902294	−	0.431120i	$-0.858118\pi$
$157$		−	10.8038i		−	0.862241i	0.902294	−	0.431120i	$-0.141882\pi$
$158$	−8.46410	−	14.6603i	−0.673368	−	1.16631i
$159$	1.86603	+	3.23205i	0.147985	+	0.256318i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	5.46410	−	9.46410i	0.427981	−	0.741286i	−0.568712	−	0.822537i	$-0.692558\pi$
$163$	5.46410	−	9.46410i	0.427981	−	0.741286i	0.996694	+	0.0812509i	$0.0258915\pi$
$164$			4.00000i			0.312348i
$165$		0			0
$166$	−1.26795	−	2.19615i	−0.0984119	−	0.170454i
$167$	3.23205	+	5.59808i	0.250104	+	0.433192i	0.963554	−	0.267513i	$-0.0862020\pi$
$167$	3.23205	+	5.59808i	0.250104	+	0.433192i	−0.713451	+	0.700706i	$0.752869\pi$
$168$			3.00000i			0.231455i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	1.96410	−	1.13397i	0.150199	−	0.0867172i
$172$	5.19615	−	3.00000i	0.396203	−	0.228748i
$173$	−19.1603	−	11.0622i	−1.45673	−	0.841042i	−0.457879	−	0.889015i	$-0.651391\pi$
$173$	−19.1603	−	11.0622i	−1.45673	−	0.841042i	−0.998849	+	0.0479730i	$0.984724\pi$
$174$			5.46410i			0.414232i
$175$		0			0
$176$	3.23205	+	1.86603i	0.243625	+	0.140657i
$177$	4.53590			0.340939
$178$	8.76795	+	5.06218i	0.657186	+	0.379426i
$179$	11.4641	+	19.8564i	0.856867	+	1.48414i	0.874902	+	0.484300i	$0.160926\pi$
$179$	11.4641	+	19.8564i	0.856867	+	1.48414i	−0.0180347	+	0.999837i	$0.505741\pi$
$180$		0			0
$181$	3.07180			0.228325			0.114162	−	0.993462i	$-0.463582\pi$
$181$	3.07180			0.228325			0.114162	+	0.993462i	$0.463582\pi$
$182$	10.5000	+	2.59808i	0.778312	+	0.192582i
$183$			7.46410i			0.551762i
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$		0			0
$186$	−4.46410	+	7.73205i	−0.327324	+	0.566941i
$187$	−14.9282			−1.09166
$188$	−0.232051	+	0.401924i	−0.0169240	+	0.0293133i
$189$	−2.59808	−	1.50000i	−0.188982	−	0.109109i
$190$		0			0
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	0.361588	+	0.932338i	$0.382235\pi$
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	−0.988222	+	0.153024i	$0.951099\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−8.92820	−	15.4641i	−0.642666	−	1.11313i	−0.984835	−	0.173492i	$-0.944495\pi$
$193$	−8.92820	−	15.4641i	−0.642666	−	1.11313i	0.342169	−	0.939638i	$-0.388838\pi$
$194$	12.3923			0.889716
$195$		0			0
$196$	2.00000			0.142857
$197$	4.69615	+	8.13397i	0.334587	+	0.579522i	0.983405	−	0.181422i	$-0.0580699\pi$
$197$	4.69615	+	8.13397i	0.334587	+	0.579522i	−0.648818	+	0.760943i	$0.724737\pi$
$198$	−3.23205	+	1.86603i	−0.229692	+	0.132613i
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	−0.992769	−	0.120037i	$-0.961699\pi$
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	0.600340	+	0.799745i	$0.295032\pi$
$200$		0			0
$201$	4.73205	+	2.73205i	0.333773	+	0.192704i
$202$	−4.19615	+	7.26795i	−0.295240	+	0.511371i
$203$	16.3923			1.15051
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	−16.9641	+	9.79423i	−1.18194	+	0.682396i
$207$			3.46410i			0.240772i
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	−8.46410			−0.585474
$210$		0			0
$211$	10.9641	+	18.9904i	0.754800	+	1.30735i	0.945474	+	0.325698i	$0.105599\pi$
$211$	10.9641	+	18.9904i	0.754800	+	1.30735i	−0.190674	+	0.981653i	$0.561067\pi$
$212$	3.23205	+	1.86603i	0.221978	+	0.128159i
$213$	0.928203			0.0635994
$214$	−0.803848	−	0.464102i	−0.0549499	−	0.0317253i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	23.1962	+	13.3923i	1.57466	+	0.909129i
$218$	9.00000	−	5.19615i	0.609557	−	0.351928i
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$		0			0
$221$	−10.3923	−	10.0000i	−0.699062	−	0.672673i
$222$		−	7.92820i		−	0.532106i
$223$	−4.42820	−	7.66987i	−0.296534	−	0.513613i	0.678806	−	0.734317i	$-0.262498\pi$
$223$	−4.42820	−	7.66987i	−0.296534	−	0.513613i	−0.975341	+	0.220705i	$0.929164\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$		0			0
$226$			12.0000i			0.798228i
$227$	−6.73205	+	11.6603i	−0.446822	+	0.773918i	−0.998177	−	0.0603523i	$-0.980778\pi$
$227$	−6.73205	+	11.6603i	−0.446822	+	0.773918i	0.551355	+	0.834271i	$0.314111\pi$
$228$	1.13397	−	1.96410i	0.0750993	−	0.130076i
$229$		−	11.4641i		−	0.757569i	−0.925485	−	0.378785i	$-0.876342\pi$
$229$		−	11.4641i		−	0.757569i	0.925485	−	0.378785i	$-0.123658\pi$
$230$		0			0
$231$	5.59808	+	9.69615i	0.368326	+	0.637960i
$232$	2.73205	+	4.73205i	0.179368	+	0.310674i
$233$			18.0000i			1.17922i	0.807688	+	0.589610i	$0.200718\pi$
$233$			18.0000i			1.17922i	−0.807688	+	0.589610i	$0.799282\pi$
$234$	−3.50000	−	0.866025i	−0.228802	−	0.0566139i
$235$		0			0
$236$	3.92820	−	2.26795i	0.255704	−	0.147631i
$237$	14.6603	−	8.46410i	0.952286	−	0.549802i
$238$	−10.3923	−	6.00000i	−0.673633	−	0.388922i
$239$		−	3.46410i		−	0.224074i	−0.993704	−	0.112037i	$-0.964262\pi$
$239$		−	3.46410i		−	0.224074i	0.993704	−	0.112037i	$-0.0357375\pi$
$240$		0			0
$241$	12.8205	+	7.40192i	0.825842	+	0.476800i	0.852427	−	0.522847i	$-0.175130\pi$
$241$	12.8205	+	7.40192i	0.825842	+	0.476800i	−0.0265852	+	0.999647i	$0.508463\pi$
$242$	2.92820			0.188232
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.73205	+	6.46410i	0.238920	+	0.413822i
$245$		0			0
$246$	−4.00000			−0.255031
$247$	−5.89230	−	5.66987i	−0.374918	−	0.360765i
$248$			8.92820i			0.566941i
$249$	2.19615	−	1.26795i	0.139176	−	0.0803530i
$250$		0			0
$251$	−13.2321	+	22.9186i	−0.835200	+	1.44661i	0.0586681	+	0.998278i	$0.481315\pi$
$251$	−13.2321	+	22.9186i	−0.835200	+	1.44661i	−0.893868	+	0.448331i	$0.852019\pi$
$252$	−3.00000			−0.188982
$253$	6.46410	−	11.1962i	0.406395	−	0.703896i
$254$	−4.03590	−	2.33013i	−0.253235	−	0.146205i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.5885	+	10.7321i	−1.15952	+	0.669447i	−0.951188	−	0.308612i	$-0.900136\pi$
$257$	−18.5885	+	10.7321i	−1.15952	+	0.669447i	−0.208328	+	0.978059i	$0.566802\pi$
$258$	3.00000	+	5.19615i	0.186772	+	0.323498i
$259$	−23.7846			−1.47790
$260$		0			0
$261$	−5.46410			−0.338219
$262$	−10.1603	−	17.5981i	−0.627703	−	1.08721i
$263$	17.7679	−	10.2583i	1.09562	−	0.632556i	0.160552	−	0.987027i	$-0.448673\pi$
$263$	17.7679	−	10.2583i	1.09562	−	0.632556i	0.935067	+	0.354472i	$0.115339\pi$
$264$	−1.86603	+	3.23205i	−0.114846	+	0.198919i
$265$		0			0
$266$	−5.89230	−	3.40192i	−0.361280	−	0.208585i
$267$	−5.06218	+	8.76795i	−0.309800	+	0.536590i
$268$	5.46410			0.333773
$269$	−15.4641	+	26.7846i	−0.942863	+	1.63309i	−0.182888	+	0.983134i	$0.558545\pi$
$269$	−15.4641	+	26.7846i	−0.942863	+	1.63309i	−0.759975	+	0.649953i	$0.774789\pi$
$270$		0			0
$271$	−3.12436	+	1.80385i	−0.189791	+	0.109576i	−0.591885	−	0.806023i	$-0.701616\pi$
$271$	−3.12436	+	1.80385i	−0.189791	+	0.109576i	0.402094	+	0.915599i	$0.368283\pi$
$272$		−	4.00000i		−	0.242536i
$273$	−2.59808	+	10.5000i	−0.157243	+	0.635489i
$274$	−6.53590			−0.394848
$275$		0			0
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	−16.9641	−	9.79423i	−1.01927	−	0.588478i	−0.105380	−	0.994432i	$-0.533606\pi$
$277$	−16.9641	−	9.79423i	−1.01927	−	0.588478i	−0.913894	+	0.405954i	$0.866939\pi$
$278$	21.7846			1.30655
$279$	−7.73205	−	4.46410i	−0.462906	−	0.267259i
$280$		0			0
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$	−0.401924	−	0.232051i	−0.0239342	−	0.0138184i
$283$	12.4641	−	7.19615i	0.740914	−	0.427767i	−0.0814876	−	0.996674i	$-0.525967\pi$
$283$	12.4641	−	7.19615i	0.740914	−	0.427767i	0.822402	+	0.568907i	$0.192634\pi$
$284$	0.803848	−	0.464102i	0.0476996	−	0.0275394i
$285$		0			0
$286$	9.69615	+	9.33013i	0.573346	+	0.551702i
$287$			12.0000i			0.708338i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$			12.3923i			0.726450i
$292$	3.46410	−	6.00000i	0.202721	−	0.351123i
$293$	−9.62436	+	16.6699i	−0.562261	+	0.973864i	0.435038	+	0.900412i	$0.356735\pi$
$293$	−9.62436	+	16.6699i	−0.562261	+	0.973864i	−0.997299	+	0.0734522i	$0.976598\pi$
$294$			2.00000i			0.116642i
$295$		0			0
$296$	−3.96410	−	6.86603i	−0.230409	−	0.399080i
$297$	−1.86603	−	3.23205i	−0.108278	−	0.187543i
$298$		−	22.7846i		−	1.31988i
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$		0			0
$301$	15.5885	−	9.00000i	0.898504	−	0.518751i
$302$	16.2679	−	9.39230i	0.936115	−	0.540466i
$303$	−7.26795	−	4.19615i	−0.417533	−	0.241063i
$304$		−	2.26795i		−	0.130076i
$305$		0			0
$306$	3.46410	+	2.00000i	0.198030	+	0.114332i
$307$	−20.2487			−1.15565			−0.577827	−	0.816159i	$-0.696099\pi$
$307$	−20.2487			−1.15565			−0.577827	+	0.816159i	$0.696099\pi$
$308$	9.69615	+	5.59808i	0.552490	+	0.318980i
$309$	−9.79423	−	16.9641i	−0.557174	−	0.965054i
$310$		0			0
$311$	5.07180			0.287595			0.143798	−	0.989607i	$-0.454069\pi$
$311$	5.07180			0.287595			0.143798	+	0.989607i	$0.454069\pi$
$312$	−3.46410	+	1.00000i	−0.196116	+	0.0566139i
$313$			1.32051i			0.0746395i	0.999303	+	0.0373198i	$0.0118820\pi$
$313$			1.32051i			0.0746395i	−0.999303	+	0.0373198i	$0.988118\pi$
$314$	9.35641	−	5.40192i	0.528013	−	0.304848i
$315$		0			0
$316$	8.46410	−	14.6603i	0.476143	−	0.824704i
$317$	−23.5359			−1.32191			−0.660954	−	0.750427i	$-0.729848\pi$
$317$	−23.5359			−1.32191			−0.660954	+	0.750427i	$0.729848\pi$
$318$	−1.86603	+	3.23205i	−0.104642	+	0.181244i
$319$	17.6603	+	10.1962i	0.988784	+	0.570875i
$320$		0			0
$321$	0.464102	−	0.803848i	0.0259036	−	0.0448664i
$322$	9.00000	−	5.19615i	0.501550	−	0.289570i
$323$	4.53590	+	7.85641i	0.252384	+	0.437142i
$324$	1.00000			0.0555556
$325$		0			0
$326$	10.9282			0.605257
$327$	5.19615	+	9.00000i	0.287348	+	0.497701i
$328$	−3.46410	+	2.00000i	−0.191273	+	0.110432i
$329$	−0.696152	+	1.20577i	−0.0383801	+	0.0664763i
$330$		0			0
$331$	5.53590	+	3.19615i	0.304280	+	0.175676i	0.644364	−	0.764719i	$-0.277122\pi$
$331$	5.53590	+	3.19615i	0.304280	+	0.175676i	−0.340084	+	0.940395i	$0.610455\pi$
$332$	1.26795	−	2.19615i	0.0695878	−	0.120530i
$333$	7.92820			0.434463
$334$	−3.23205	+	5.59808i	−0.176850	+	0.306313i
$335$		0			0
$336$	−2.59808	+	1.50000i	−0.141737	+	0.0818317i
$337$			5.60770i			0.305471i	0.988267	+	0.152735i	$0.0488082\pi$
$337$			5.60770i			0.305471i	−0.988267	+	0.152735i	$0.951192\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	−12.0000			−0.651751
$340$		0			0
$341$	16.6603	+	28.8564i	0.902203	+	1.56266i
$342$	1.96410	+	1.13397i	0.106206	+	0.0613183i
$343$	−15.0000			−0.809924
$344$	5.19615	+	3.00000i	0.280158	+	0.161749i
$345$		0			0
$346$		−	22.1244i		−	1.18941i
$347$	−14.1962	−	8.19615i	−0.762089	−	0.439993i	0.0679560	−	0.997688i	$-0.478352\pi$
$347$	−14.1962	−	8.19615i	−0.762089	−	0.439993i	−0.830045	+	0.557696i	$0.811686\pi$
$348$	−4.73205	+	2.73205i	−0.253665	+	0.146453i
$349$	−15.1244	+	8.73205i	−0.809588	+	0.467416i	−0.846813	−	0.531891i	$-0.821482\pi$
$349$	−15.1244	+	8.73205i	−0.809588	+	0.467416i	0.0372247	+	0.999307i	$0.488148\pi$
$350$		0			0
$351$	0.866025	−	3.50000i	0.0462250	−	0.186816i
$352$			3.73205i			0.198919i
$353$	−14.1962	−	24.5885i	−0.755585	−	1.30871i	−0.945083	−	0.326830i	$-0.894019\pi$
$353$	−14.1962	−	24.5885i	−0.755585	−	1.30871i	0.189498	−	0.981881i	$-0.439314\pi$
$354$	2.26795	+	3.92820i	0.120540	+	0.208782i
$355$		0			0
$356$			10.1244i			0.536590i
$357$	6.00000	−	10.3923i	0.317554	−	0.550019i
$358$	−11.4641	+	19.8564i	−0.605897	+	1.04944i
$359$		−	12.9282i		−	0.682324i	−0.940004	−	0.341162i	$-0.889179\pi$
$359$		−	12.9282i		−	0.682324i	0.940004	−	0.341162i	$-0.110821\pi$
$360$		0			0
$361$	−6.92820	−	12.0000i	−0.364642	−	0.631579i
$362$	1.53590	+	2.66025i	0.0807250	+	0.139820i
$363$			2.92820i			0.153691i
$364$	3.00000	+	10.3923i	0.157243	+	0.544705i
$365$		0			0
$366$	−6.46410	+	3.73205i	−0.337884	+	0.195077i
$367$	11.5359	−	6.66025i	0.602169	−	0.347662i	−0.167725	−	0.985834i	$-0.553642\pi$
$367$	11.5359	−	6.66025i	0.602169	−	0.347662i	0.769894	+	0.638171i	$0.220309\pi$
$368$	3.00000	+	1.73205i	0.156386	+	0.0902894i
$369$		−	4.00000i		−	0.208232i
$370$		0			0
$371$	9.69615	+	5.59808i	0.503399	+	0.290638i
$372$	−8.92820			−0.462906
$373$	−19.8564	−	11.4641i	−1.02813	−	0.593589i	−0.111679	−	0.993744i	$-0.535623\pi$
$373$	−19.8564	−	11.4641i	−1.02813	−	0.593589i	−0.916447	+	0.400156i	$0.868956\pi$
$374$	−7.46410	−	12.9282i	−0.385960	−	0.668501i
$375$		0			0
$376$	−0.464102			−0.0239342
$377$	5.46410	+	18.9282i	0.281416	+	0.974852i
$378$		−	3.00000i		−	0.154303i
$379$	−5.42820	+	3.13397i	−0.278828	+	0.160981i	−0.632893	−	0.774239i	$-0.718133\pi$
$379$	−5.42820	+	3.13397i	−0.278828	+	0.160981i	0.354065	+	0.935221i	$0.384799\pi$
$380$		0			0
$381$	2.33013	−	4.03590i	0.119376	−	0.206765i
$382$	−17.3205			−0.886194
$383$	−18.3923	+	31.8564i	−0.939803	+	1.62779i	−0.173966	+	0.984752i	$0.555658\pi$
$383$	−18.3923	+	31.8564i	−0.939803	+	1.62779i	−0.765837	+	0.643035i	$0.777675\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	8.92820	−	15.4641i	0.454434	−	0.787102i
$387$	−5.19615	+	3.00000i	−0.264135	+	0.152499i
$388$	6.19615	+	10.7321i	0.314562	+	0.544837i
$389$	9.85641			0.499740			0.249870	−	0.968279i	$-0.419612\pi$
$389$	9.85641			0.499740			0.249870	+	0.968279i	$0.419612\pi$
$390$		0			0
$391$	−13.8564			−0.700749
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	17.5981	−	10.1603i	0.887706	−	0.512517i
$394$	−4.69615	+	8.13397i	−0.236589	+	0.409784i
$395$		0			0
$396$	−3.23205	−	1.86603i	−0.162417	−	0.0937713i
$397$	−3.96410	+	6.86603i	−0.198953	+	0.344596i	−0.948189	−	0.317707i	$-0.897087\pi$
$397$	−3.96410	+	6.86603i	−0.198953	+	0.344596i	0.749237	+	0.662303i	$0.230421\pi$
$398$	−11.0718			−0.554979
$399$	3.40192	−	5.89230i	0.170309	−	0.294984i
$400$		0			0
$401$	−1.83975	+	1.06218i	−0.0918725	+	0.0530426i	−0.545232	−	0.838285i	$-0.683559\pi$
$401$	−1.83975	+	1.06218i	−0.0918725	+	0.0530426i	0.453360	+	0.891328i	$0.350225\pi$
$402$			5.46410i			0.272525i
$403$	−7.73205	+	31.2487i	−0.385161	+	1.55661i
$404$	−8.39230			−0.417533
$405$		0			0
$406$	8.19615	+	14.1962i	0.406768	+	0.704543i
$407$	−25.6244	−	14.7942i	−1.27015	−	0.733323i
$408$	4.00000			0.198030
$409$	−0.820508	−	0.473721i	−0.0405715	−	0.0234240i	0.479577	−	0.877500i	$-0.340790\pi$
$409$	−0.820508	−	0.473721i	−0.0405715	−	0.0234240i	−0.520149	+	0.854076i	$0.674123\pi$
$410$		0			0
$411$		−	6.53590i		−	0.322392i
$412$	−16.9641	−	9.79423i	−0.835761	−	0.482527i
$413$	11.7846	−	6.80385i	0.579883	−	0.334795i
$414$	−3.00000	+	1.73205i	−0.147442	+	0.0851257i
$415$		0			0
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$			21.7846i			1.06680i
$418$	−4.23205	−	7.33013i	−0.206996	−	0.358528i
$419$	−8.92820	−	15.4641i	−0.436171	−	0.755471i	0.561219	−	0.827667i	$-0.310332\pi$
$419$	−8.92820	−	15.4641i	−0.436171	−	0.755471i	−0.997390	+	0.0721964i	$0.976999\pi$
$420$		0			0
$421$			5.85641i			0.285424i	0.989764	+	0.142712i	$0.0455822\pi$
$421$			5.85641i			0.285424i	−0.989764	+	0.142712i	$0.954418\pi$
$422$	−10.9641	+	18.9904i	−0.533724	+	0.924437i
$423$	0.232051	−	0.401924i	0.0112827	−	0.0195422i
$424$			3.73205i			0.181244i
$425$		0			0
$426$	0.464102	+	0.803848i	0.0224858	+	0.0389465i
$427$	11.1962	+	19.3923i	0.541820	+	0.938459i
$428$		−	0.928203i		−	0.0448664i
$429$	−9.33013	+	9.69615i	−0.450463	+	0.468135i
$430$		0			0
$431$	−12.0000	+	6.92820i	−0.578020	+	0.333720i	−0.760346	−	0.649518i	$-0.774971\pi$
$431$	−12.0000	+	6.92820i	−0.578020	+	0.333720i	0.182326	+	0.983238i	$0.441637\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−28.3923	−	16.3923i	−1.36445	−	0.787764i	−0.374235	−	0.927334i	$-0.622095\pi$
$433$	−28.3923	−	16.3923i	−1.36445	−	0.787764i	−0.990212	+	0.139570i	$0.955428\pi$
$434$			26.7846i			1.28570i
$435$		0			0
$436$	9.00000	+	5.19615i	0.431022	+	0.248851i
$437$	−7.85641			−0.375823
$438$	6.00000	+	3.46410i	0.286691	+	0.165521i
$439$	10.6603	+	18.4641i	0.508786	+	0.881243i	0.999948	+	0.0101753i	$0.00323895\pi$
$439$	10.6603	+	18.4641i	0.508786	+	0.881243i	−0.491162	+	0.871068i	$0.663428\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$	3.46410	−	14.0000i	0.164771	−	0.665912i
$443$			7.85641i			0.373269i	0.982429	+	0.186635i	$0.0597580\pi$
$443$			7.85641i			0.373269i	−0.982429	+	0.186635i	$0.940242\pi$
$444$	6.86603	−	3.96410i	0.325847	−	0.188128i
$445$		0			0
$446$	4.42820	−	7.66987i	0.209682	−	0.363179i
$447$	22.7846			1.07768
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	15.6962	+	9.06218i	0.740747	+	0.427671i	0.822341	−	0.568995i	$-0.192668\pi$
$449$	15.6962	+	9.06218i	0.740747	+	0.427671i	−0.0815937	+	0.996666i	$0.526001\pi$
$450$		0			0
$451$	−7.46410	+	12.9282i	−0.351471	+	0.608765i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	9.39230	+	16.2679i	0.441289	+	0.764335i
$454$	−13.4641			−0.631902
$455$		0			0
$456$	2.26795			0.106206
$457$	−0.267949	−	0.464102i	−0.0125341	−	0.0217098i	0.859690	−	0.510816i	$-0.170657\pi$
$457$	−0.267949	−	0.464102i	−0.0125341	−	0.0217098i	−0.872224	+	0.489106i	$0.837323\pi$
$458$	9.92820	−	5.73205i	0.463914	−	0.267841i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	28.0526	+	16.1962i	1.30654	+	0.754330i	0.981517	−	0.191377i	$-0.0612952\pi$
$461$	28.0526	+	16.1962i	1.30654	+	0.754330i	0.325021	+	0.945707i	$0.394629\pi$
$462$	−5.59808	+	9.69615i	−0.260446	+	0.451106i
$463$	0.784610			0.0364639			0.0182320	−	0.999834i	$-0.494196\pi$
$463$	0.784610			0.0364639			0.0182320	+	0.999834i	$0.494196\pi$
$464$	−2.73205	+	4.73205i	−0.126832	+	0.219680i
$465$		0			0
$466$	−15.5885	+	9.00000i	−0.722121	+	0.416917i
$467$		−	3.60770i		−	0.166944i	−0.996510	−	0.0834721i	$-0.973399\pi$
$467$		−	3.60770i		−	0.166944i	0.996510	−	0.0834721i	$-0.0266010\pi$
$468$	−1.00000	−	3.46410i	−0.0462250	−	0.160128i
$469$	16.3923			0.756926
$470$		0			0
$471$	5.40192	+	9.35641i	0.248908	+	0.431120i
$472$	3.92820	+	2.26795i	0.180810	+	0.104391i
$473$	22.3923			1.02960
$474$	14.6603	+	8.46410i	0.673368	+	0.388769i
$475$		0			0
$476$		−	12.0000i		−	0.550019i
$477$	−3.23205	−	1.86603i	−0.147985	−	0.0854394i
$478$	3.00000	−	1.73205i	0.137217	−	0.0792222i
$479$	22.7321	−	13.1244i	1.03865	−	0.599667i	0.119202	−	0.992870i	$-0.461966\pi$
$479$	22.7321	−	13.1244i	1.03865	−	0.599667i	0.919452	+	0.393203i	$0.128633\pi$
$480$		0			0
$481$	−7.92820	−	27.4641i	−0.361495	−	1.25226i
$482$			14.8038i			0.674297i
$483$	5.19615	+	9.00000i	0.236433	+	0.409514i
$484$	1.46410	+	2.53590i	0.0665501	+	0.115268i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−10.5000	+	18.1865i	−0.475800	+	0.824110i	−0.999616	−	0.0277214i	$-0.991175\pi$
$487$	−10.5000	+	18.1865i	−0.475800	+	0.824110i	0.523815	+	0.851832i	$0.324508\pi$
$488$	−3.73205	+	6.46410i	−0.168942	+	0.292616i
$489$			10.9282i			0.494190i
$490$		0			0
$491$	7.69615	+	13.3301i	0.347322	+	0.601580i	0.985773	−	0.168083i	$-0.0537576\pi$
$491$	7.69615	+	13.3301i	0.347322	+	0.601580i	−0.638450	+	0.769663i	$0.720424\pi$
$492$	−2.00000	−	3.46410i	−0.0901670	−	0.156174i
$493$		−	21.8564i		−	0.984363i
$494$	1.96410	−	7.93782i	0.0883691	−	0.357140i
$495$		0			0
$496$	−7.73205	+	4.46410i	−0.347179	+	0.200444i
$497$	2.41154	−	1.39230i	0.108172	−	0.0624534i
$498$	2.19615	+	1.26795i	0.0984119	+	0.0568182i
$499$		−	1.32051i		−	0.0591141i	−0.999563	−	0.0295570i	$-0.990590\pi$
$499$		−	1.32051i		−	0.0591141i	0.999563	−	0.0295570i	$-0.00940967\pi$
$500$		0			0
$501$	−5.59808	−	3.23205i	−0.250104	−	0.144397i
$502$	−26.4641			−1.18115
$503$	−0.232051	−	0.133975i	−0.0103466	−	0.00597363i	0.494818	−	0.868997i	$-0.335235\pi$
$503$	−0.232051	−	0.133975i	−0.0103466	−	0.00597363i	−0.505164	+	0.863023i	$0.668568\pi$
$504$	−1.50000	−	2.59808i	−0.0668153	−	0.115728i
$505$		0			0
$506$	12.9282			0.574729
$507$	−12.9904	+	0.500000i	−0.576923	+	0.0222058i
$508$		−	4.66025i		−	0.206765i
$509$	−4.60770	+	2.66025i	−0.204232	+	0.117914i	−0.598628	−	0.801027i	$-0.704287\pi$
$509$	−4.60770	+	2.66025i	−0.204232	+	0.117914i	0.394396	+	0.918941i	$0.370954\pi$
$510$		0			0
$511$	10.3923	−	18.0000i	0.459728	−	0.796273i
$512$	−1.00000			−0.0441942
$513$	−1.13397	+	1.96410i	−0.0500662	+	0.0867172i
$514$	−18.5885	−	10.7321i	−0.819902	−	0.473370i
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	−1.50000	+	0.866025i	−0.0659699	+	0.0380878i
$518$	−11.8923	−	20.5981i	−0.522518	−	0.905028i
$519$	22.1244			0.971151
$520$		0			0
$521$	−27.3923			−1.20008			−0.600039	−	0.799970i	$-0.704848\pi$
$521$	−27.3923			−1.20008			−0.600039	+	0.799970i	$0.704848\pi$
$522$	−2.73205	−	4.73205i	−0.119579	−	0.207116i
$523$	11.8756	−	6.85641i	0.519286	−	0.299810i	−0.217357	−	0.976092i	$-0.569743\pi$
$523$	11.8756	−	6.85641i	0.519286	−	0.299810i	0.736642	+	0.676283i	$0.236410\pi$
$524$	10.1603	−	17.5981i	0.443853	−	0.768776i
$525$		0			0
$526$	17.7679	+	10.2583i	0.774719	+	0.447284i
$527$	17.8564	−	30.9282i	0.777837	−	1.34725i
$528$	−3.73205			−0.162417
$529$	−5.50000	+	9.52628i	−0.239130	+	0.414186i
$530$		0			0
$531$	−3.92820	+	2.26795i	−0.170470	+	0.0984206i
$532$		−	6.80385i		−	0.294984i
$533$	−13.8564	+	4.00000i	−0.600188	+	0.173259i
$534$	−10.1244			−0.438124
$535$		0			0
$536$	2.73205	+	4.73205i	0.118007	+	0.204393i
$537$	−19.8564	−	11.4641i	−0.856867	−	0.494713i
$538$	−30.9282			−1.33341
$539$	6.46410	+	3.73205i	0.278429	+	0.160751i
$540$		0			0
$541$			26.7846i			1.15156i	0.817605	+	0.575780i	$0.195302\pi$
$541$			26.7846i			1.15156i	−0.817605	+	0.575780i	$0.804698\pi$
$542$	−3.12436	−	1.80385i	−0.134203	−	0.0774819i
$543$	−2.66025	+	1.53590i	−0.114162	+	0.0659117i
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$		0			0
$546$	−10.3923	+	3.00000i	−0.444750	+	0.128388i
$547$		−	29.3205i		−	1.25365i	−0.779158	−	0.626827i	$-0.784353\pi$
$547$		−	29.3205i		−	1.25365i	0.779158	−	0.626827i	$-0.215647\pi$
$548$	−3.26795	−	5.66025i	−0.139600	−	0.241794i
$549$	−3.73205	−	6.46410i	−0.159280	−	0.275881i
$550$		0			0
$551$		−	12.3923i		−	0.527930i
$552$	−1.73205	+	3.00000i	−0.0737210	+	0.127688i
$553$	25.3923	−	43.9808i	1.07979	−	1.87025i
$554$		−	19.5885i		−	0.832234i
$555$		0			0
$556$	10.8923	+	18.8660i	0.461937	+	0.800098i
$557$	−21.6962	−	37.5788i	−0.919295	−	1.59227i	−0.800488	−	0.599349i	$-0.795426\pi$
$557$	−21.6962	−	37.5788i	−0.919295	−	1.59227i	−0.118808	−	0.992917i	$-0.537907\pi$
$558$		−	8.92820i		−	0.377961i
$559$	15.5885	+	15.0000i	0.659321	+	0.634432i
$560$		0			0
$561$	12.9282	−	7.46410i	0.545829	−	0.315135i
$562$	−6.00000	+	3.46410i	−0.253095	+	0.146124i
$563$	−16.7321	−	9.66025i	−0.705172	−	0.407131i	0.104099	−	0.994567i	$-0.466804\pi$
$563$	−16.7321	−	9.66025i	−0.705172	−	0.407131i	−0.809271	+	0.587436i	$0.800137\pi$
$564$		−	0.464102i		−	0.0195422i
$565$		0			0
$566$	12.4641	+	7.19615i	0.523905	+	0.302477i
$567$	3.00000			0.125988
$568$	0.803848	+	0.464102i	0.0337287	+	0.0194733i
$569$	9.16025	+	15.8660i	0.384018	+	0.665138i	0.991632	−	0.129094i	$-0.0412068\pi$
$569$	9.16025	+	15.8660i	0.384018	+	0.665138i	−0.607615	+	0.794232i	$0.707873\pi$
$570$		0			0
$571$	−16.8564			−0.705419			−0.352709	−	0.935733i	$-0.614740\pi$
$571$	−16.8564			−0.705419			−0.352709	+	0.935733i	$0.614740\pi$
$572$	−3.23205	+	13.0622i	−0.135139	+	0.546157i
$573$		−	17.3205i		−	0.723575i
$574$	−10.3923	+	6.00000i	−0.433766	+	0.250435i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−25.3205			−1.05411			−0.527053	−	0.849832i	$-0.676703\pi$
$577$	−25.3205			−1.05411			−0.527053	+	0.849832i	$0.676703\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	15.4641	+	8.92820i	0.642666	+	0.371043i
$580$		0			0
$581$	3.80385	−	6.58846i	0.157810	−	0.273335i
$582$	−10.7321	+	6.19615i	−0.444858	+	0.256839i
$583$	6.96410	+	12.0622i	0.288424	+	0.499564i
$584$	6.92820			0.286691
$585$		0			0
$586$	−19.2487			−0.795157
$587$	2.46410	+	4.26795i	0.101704	+	0.176157i	0.912387	−	0.409329i	$-0.134237\pi$
$587$	2.46410	+	4.26795i	0.101704	+	0.176157i	−0.810683	+	0.585486i	$0.800904\pi$
$588$	−1.73205	+	1.00000i	−0.0714286	+	0.0412393i
$589$	10.1244	−	17.5359i	0.417167	−	0.722554i
$590$		0			0
$591$	−8.13397	−	4.69615i	−0.334587	−	0.193174i
$592$	3.96410	−	6.86603i	0.162924	−	0.282192i
$593$	−3.21539			−0.132040			−0.0660201	−	0.997818i	$-0.521030\pi$
$593$	−3.21539			−0.132040			−0.0660201	+	0.997818i	$0.521030\pi$
$594$	1.86603	−	3.23205i	0.0765639	−	0.132613i
$595$		0			0
$596$	19.7321	−	11.3923i	0.808256	−	0.466647i
$597$		−	11.0718i		−	0.453138i
$598$	9.00000	+	8.66025i	0.368037	+	0.354144i
$599$	−15.0718			−0.615817			−0.307908	−	0.951416i	$-0.599629\pi$
$599$	−15.0718			−0.615817			−0.307908	+	0.951416i	$0.599629\pi$
$600$		0			0
$601$	12.3564	+	21.4019i	0.504028	+	0.873003i	0.999989	+	0.00465778i	$0.00148262\pi$
$601$	12.3564	+	21.4019i	0.504028	+	0.873003i	−0.495961	+	0.868345i	$0.665184\pi$
$602$	15.5885	+	9.00000i	0.635338	+	0.366813i
$603$	−5.46410			−0.222515
$604$	16.2679	+	9.39230i	0.661933	+	0.382167i
$605$		0			0
$606$		−	8.39230i		−	0.340914i
$607$	32.4282	+	18.7224i	1.31622	+	0.759920i	0.983118	−	0.182971i	$-0.0585714\pi$
$607$	32.4282	+	18.7224i	1.31622	+	0.759920i	0.333102	+	0.942891i	$0.391905\pi$
$608$	1.96410	−	1.13397i	0.0796548	−	0.0459887i
$609$	−14.1962	+	8.19615i	−0.575257	+	0.332125i
$610$		0			0
$611$	−1.62436	−	0.401924i	−0.0657144	−	0.0162601i
$612$			4.00000i			0.161690i
$613$	−22.5000	−	38.9711i	−0.908766	−	1.57403i	−0.815780	−	0.578362i	$-0.803692\pi$
$613$	−22.5000	−	38.9711i	−0.908766	−	1.57403i	−0.0929864	−	0.995667i	$-0.529641\pi$
$614$	−10.1244	−	17.5359i	−0.408586	−	0.707691i
$615$		0			0
$616$			11.1962i			0.451106i
$617$	14.2679	−	24.7128i	0.574406	−	0.994900i	−0.421700	−	0.906735i	$-0.638566\pi$
$617$	14.2679	−	24.7128i	0.574406	−	0.994900i	0.996106	−	0.0881649i	$-0.0281003\pi$
$618$	9.79423	−	16.9641i	0.393982	−	0.682396i
$619$		−	42.5167i		−	1.70889i	−0.519543	−	0.854444i	$-0.673898\pi$
$619$		−	42.5167i		−	1.70889i	0.519543	−	0.854444i	$-0.326102\pi$
$620$		0			0
$621$	−1.73205	−	3.00000i	−0.0695048	−	0.120386i
$622$	2.53590	+	4.39230i	0.101680	+	0.176115i
$623$			30.3731i			1.21687i
$624$	−2.59808	−	2.50000i	−0.104006	−	0.100080i
$625$		0			0
$626$	−1.14359	+	0.660254i	−0.0457072	+	0.0263891i
$627$	7.33013	−	4.23205i	0.292737	−	0.169012i
$628$	9.35641	+	5.40192i	0.373361	+	0.215560i
$629$			31.7128i			1.26447i
$630$		0			0
$631$	6.92820	+	4.00000i	0.275807	+	0.159237i	0.631524	−	0.775356i	$-0.282430\pi$
$631$	6.92820	+	4.00000i	0.275807	+	0.159237i	−0.355716	+	0.934594i	$0.615763\pi$
$632$	16.9282			0.673368
$633$	−18.9904	−	10.9641i	−0.754800	−	0.435784i
$634$	−11.7679	−	20.3827i	−0.467365	−	0.809500i
$635$		0			0
$636$	−3.73205			−0.147985
$637$	2.00000	+	6.92820i	0.0792429	+	0.274505i
$638$			20.3923i			0.807339i
$639$	−0.803848	+	0.464102i	−0.0317997	+	0.0183596i
$640$		0			0
$641$	−3.76795	+	6.52628i	−0.148825	+	0.257773i	−0.930793	−	0.365546i	$-0.880882\pi$
$641$	−3.76795	+	6.52628i	−0.148825	+	0.257773i	0.781968	+	0.623318i	$0.214216\pi$
$642$	0.928203			0.0366333
$643$	−14.3923	+	24.9282i	−0.567577	+	0.983072i	0.429228	+	0.903196i	$0.358786\pi$
$643$	−14.3923	+	24.9282i	−0.567577	+	0.983072i	−0.996805	+	0.0798761i	$0.974548\pi$
$644$	9.00000	+	5.19615i	0.354650	+	0.204757i
$645$		0			0
$646$	−4.53590	+	7.85641i	−0.178463	+	0.309106i
$647$	27.9449	−	16.1340i	1.09863	−	0.634292i	0.162766	−	0.986665i	$-0.447958\pi$
$647$	27.9449	−	16.1340i	1.09863	−	0.634292i	0.935860	+	0.352373i	$0.114625\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	16.9282			0.664490
$650$		0			0
$651$	−26.7846			−1.04977
$652$	5.46410	+	9.46410i	0.213991	+	0.370643i
$653$	25.6244	−	14.7942i	1.00276	−	0.578943i	0.0936952	−	0.995601i	$-0.470132\pi$
$653$	25.6244	−	14.7942i	1.00276	−	0.578943i	0.909063	+	0.416658i	$0.136799\pi$
$654$	−5.19615	+	9.00000i	−0.203186	+	0.351928i
$655$		0			0
$656$	−3.46410	−	2.00000i	−0.135250	−	0.0780869i
$657$	−3.46410	+	6.00000i	−0.135147	+	0.234082i
$658$	−1.39230			−0.0542777
$659$	7.85641	−	13.6077i	0.306042	−	0.530081i	−0.671451	−	0.741049i	$-0.734328\pi$
$659$	7.85641	−	13.6077i	0.306042	−	0.530081i	0.977493	+	0.210969i	$0.0676618\pi$
$660$		0			0
$661$	36.7128	−	21.1962i	1.42796	−	0.824435i	0.431003	−	0.902351i	$-0.358160\pi$
$661$	36.7128	−	21.1962i	1.42796	−	0.824435i	0.996960	+	0.0779157i	$0.0248265\pi$
$662$			6.39230i			0.248444i
$663$	14.0000	+	3.46410i	0.543715	+	0.134535i
$664$	2.53590			0.0984119
$665$		0			0
$666$	3.96410	+	6.86603i	0.153606	+	0.266053i
$667$	16.3923	+	9.46410i	0.634713	+	0.366451i
$668$	−6.46410			−0.250104
$669$	7.66987	+	4.42820i	0.296534	+	0.171204i
$670$		0			0
$671$			27.8564i			1.07538i
$672$	−2.59808	−	1.50000i	−0.100223	−	0.0578638i
$673$	21.4641	−	12.3923i	0.827380	−	0.477688i	−0.0255746	−	0.999673i	$-0.508142\pi$
$673$	21.4641	−	12.3923i	0.827380	−	0.477688i	0.852955	+	0.521985i	$0.174808\pi$
$674$	−4.85641	+	2.80385i	−0.187062	+	0.108000i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$			2.92820i			0.112540i	0.998416	+	0.0562700i	$0.0179208\pi$
$677$			2.92820i			0.112540i	−0.998416	+	0.0562700i	$0.982079\pi$
$678$	−6.00000	−	10.3923i	−0.230429	−	0.399114i
$679$	18.5885	+	32.1962i	0.713360	+	1.23557i
$680$		0			0
$681$		−	13.4641i		−	0.515945i
$682$	−16.6603	+	28.8564i	−0.637954	+	1.10497i
$683$	3.33975	−	5.78461i	0.127792	−	0.221342i	−0.795029	−	0.606571i	$-0.792544\pi$
$683$	3.33975	−	5.78461i	0.127792	−	0.221342i	0.922821	+	0.385230i	$0.125878\pi$
$684$			2.26795i			0.0867172i
$685$		0			0
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	5.73205	+	9.92820i	0.218691	+	0.378785i
$688$			6.00000i			0.228748i
$689$	−3.23205	+	13.0622i	−0.123131	+	0.497629i
$690$		0			0
$691$	19.9641	−	11.5263i	0.759470	−	0.438480i	−0.0696353	−	0.997573i	$-0.522184\pi$
$691$	19.9641	−	11.5263i	0.759470	−	0.438480i	0.829106	+	0.559092i	$0.188850\pi$
$692$	19.1603	−	11.0622i	0.728364	−	0.420521i
$693$	−9.69615	−	5.59808i	−0.368326	−	0.212653i
$694$		−	16.3923i		−	0.622243i
$695$		0			0
$696$	−4.73205	−	2.73205i	−0.179368	−	0.103558i
$697$	16.0000			0.606043
$698$	−15.1244	−	8.73205i	−0.572465	−	0.330513i
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$		0			0
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	3.46410	−	1.00000i	0.130744	−	0.0377426i
$703$			17.9808i			0.678157i
$704$	−3.23205	+	1.86603i	−0.121812	+	0.0703285i
$705$		0			0
$706$	14.1962	−	24.5885i	0.534279	−	0.925399i
$707$	−25.1769			−0.946875
$708$	−2.26795	+	3.92820i	−0.0852348	+	0.147631i
$709$	6.33975	+	3.66025i	0.238094	+	0.137464i	0.614300	−	0.789072i	$-0.289438\pi$
$709$	6.33975	+	3.66025i	0.238094	+	0.137464i	−0.376206	+	0.926536i	$0.622772\pi$
$710$		0			0
$711$	−8.46410	+	14.6603i	−0.317429	+	0.549802i
$712$	−8.76795	+	5.06218i	−0.328593	+	0.189713i
$713$	15.4641	+	26.7846i	0.579135	+	1.00309i
$714$	12.0000			0.449089
$715$		0			0
$716$	−22.9282			−0.856867
$717$	1.73205	+	3.00000i	0.0646846	+	0.112037i
$718$	11.1962	−	6.46410i	0.417837	−	0.241238i
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	−0.677409	−	0.735607i	$-0.736897\pi$
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	0.975759	+	0.218850i	$0.0702305\pi$
$720$		0			0
$721$	−50.8923	−	29.3827i	−1.89533	−	1.09427i
$722$	6.92820	−	12.0000i	0.257841	−	0.446594i
$723$	−14.8038			−0.550561
$724$	−1.53590	+	2.66025i	−0.0570812	+	0.0988676i
$725$		0			0
$726$	−2.53590	+	1.46410i	−0.0941160	+	0.0543379i
$727$		−	12.6603i		−	0.469543i	−0.972051	−	0.234771i	$-0.924566\pi$
$727$		−	12.6603i		−	0.469543i	0.972051	−	0.234771i	$-0.0754342\pi$
$728$	−7.50000	+	7.79423i	−0.277968	+	0.288873i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	−6.46410	−	3.73205i	−0.238920	−	0.137941i
$733$	−6.85641			−0.253247			−0.126624	−	0.991951i	$-0.540414\pi$
$733$	−6.85641			−0.253247			−0.126624	+	0.991951i	$0.540414\pi$
$734$	11.5359	+	6.66025i	0.425798	+	0.245834i
$735$		0			0
$736$			3.46410i			0.127688i
$737$	17.6603	+	10.1962i	0.650524	+	0.375580i
$738$	3.46410	−	2.00000i	0.127515	−	0.0736210i
$739$	−37.9641	+	21.9186i	−1.39653	+	0.806288i	−0.994028	−	0.109130i	$-0.965194\pi$
$739$	−37.9641	+	21.9186i	−1.39653	+	0.806288i	−0.402505	+	0.915418i	$0.631860\pi$
$740$		0			0
$741$	7.93782	+	1.96410i	0.291603	+	0.0721531i
$742$			11.1962i			0.411024i
$743$	−1.46410	−	2.53590i	−0.0537127	−	0.0930331i	0.837919	−	0.545795i	$-0.183772\pi$
$743$	−1.46410	−	2.53590i	−0.0537127	−	0.0930331i	−0.891632	+	0.452762i	$0.850439\pi$
$744$	−4.46410	−	7.73205i	−0.163662	−	0.283471i
$745$		0			0
$746$		−	22.9282i		−	0.839461i
$747$	−1.26795	+	2.19615i	−0.0463918	+	0.0803530i
$748$	7.46410	−	12.9282i	0.272915	−	0.472702i
$749$		−	2.78461i		−	0.101747i
$750$		0			0
$751$	−20.5885	−	35.6603i	−0.751283	−	1.30126i	−0.947201	−	0.320641i	$-0.896102\pi$
$751$	−20.5885	−	35.6603i	−0.751283	−	1.30126i	0.195917	−	0.980620i	$-0.437232\pi$
$752$	−0.232051	−	0.401924i	−0.00846202	−	0.0146567i
$753$		−	26.4641i		−	0.964405i
$754$	−13.6603	+	14.1962i	−0.497477	+	0.516993i
$755$		0			0
$756$	2.59808	−	1.50000i	0.0944911	−	0.0545545i
$757$	−15.8205	+	9.13397i	−0.575006	+	0.331980i	−0.759146	−	0.650920i	$-0.774383\pi$
$757$	−15.8205	+	9.13397i	−0.575006	+	0.331980i	0.184140	+	0.982900i	$0.441050\pi$
$758$	−5.42820	−	3.13397i	−0.197161	−	0.113831i
$759$			12.9282i			0.469264i
$760$		0			0
$761$	38.0885	+	21.9904i	1.38071	+	0.797151i	0.992243	−	0.124314i	$-0.0396730\pi$
$761$	38.0885	+	21.9904i	1.38071	+	0.797151i	0.388463	+	0.921465i	$0.373006\pi$
$762$	4.66025			0.168823
$763$	27.0000	+	15.5885i	0.977466	+	0.564340i
$764$	−8.66025	−	15.0000i	−0.313317	−	0.542681i
$765$		0			0
$766$	−36.7846			−1.32908
$767$	11.7846	+	11.3397i	0.425518	+	0.409454i
$768$		−	1.00000i		−	0.0360844i
$769$	−34.3923	+	19.8564i	−1.24022	+	0.716040i	−0.969139	−	0.246517i	$-0.920714\pi$
$769$	−34.3923	+	19.8564i	−1.24022	+	0.716040i	−0.271080	+	0.962557i	$0.587381\pi$
$770$		0			0
$771$	10.7321	−	18.5885i	0.386505	−	0.669447i
$772$	17.8564			0.642666
$773$	−26.6962	+	46.2391i	−0.960194	+	1.66310i	−0.238186	+	0.971220i	$0.576553\pi$
$773$	−26.6962	+	46.2391i	−0.960194	+	1.66310i	−0.722008	+	0.691885i	$0.756780\pi$
$774$	−5.19615	−	3.00000i	−0.186772	−	0.107833i
$775$		0			0
$776$	−6.19615	+	10.7321i	−0.222429	+	0.385258i
$777$	20.5981	−	11.8923i	0.738952	−	0.426634i
$778$	4.92820	+	8.53590i	0.176685	+	0.306027i
$779$	9.07180			0.325031
$780$		0			0
$781$	3.46410			0.123955
$782$	−6.92820	−	12.0000i	−0.247752	−	0.429119i
$783$	4.73205	−	2.73205i	0.169110	−	0.0976355i
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$		0			0
$786$	17.5981	+	10.1603i	0.627703	+	0.362404i
$787$	2.73205	−	4.73205i	0.0973871	−	0.168679i	−0.813215	−	0.581963i	$-0.802285\pi$
$787$	2.73205	−	4.73205i	0.0973871	−	0.168679i	0.910602	+	0.413284i	$0.135618\pi$
$788$	−9.39230			−0.334587
$789$	−10.2583	+	17.7679i	−0.365206	+	0.632556i
$790$		0			0
$791$	−31.1769	+	18.0000i	−1.10852	+	0.640006i
$792$		−	3.73205i		−	0.132613i
$793$	−18.6603	+	19.3923i	−0.662645	+	0.688641i
$794$	−7.92820			−0.281361
$795$		0			0
$796$	−5.53590	−	9.58846i	−0.196215	−	0.339854i
$797$	−32.7846	−	18.9282i	−1.16129	−	0.670471i	−0.209678	−	0.977771i	$-0.567241\pi$
$797$	−32.7846	−	18.9282i	−1.16129	−	0.670471i	−0.951613	+	0.307299i	$0.900575\pi$
$798$	6.80385			0.240854
$799$	1.60770	+	0.928203i	0.0568762	+	0.0328375i
$800$		0			0
$801$		−	10.1244i		−	0.357727i
$802$	−1.83975	−	1.06218i	−0.0649637	−	0.0375068i
$803$	22.3923	−	12.9282i	0.790207	−	0.456226i
$804$	−4.73205	+	2.73205i	−0.166887	+	0.0963520i
$805$		0			0
$806$	−30.9282	+	8.92820i	−1.08940	+	0.314483i
$807$		−	30.9282i		−	1.08872i
$808$	−4.19615	−	7.26795i	−0.147620	−	0.255686i
$809$	17.3923	+	30.1244i	0.611481	+	1.05912i	0.990991	+	0.133928i	$0.0427592\pi$
$809$	17.3923	+	30.1244i	0.611481	+	1.05912i	−0.379510	+	0.925188i	$0.623907\pi$
$810$		0			0
$811$			7.58846i			0.266467i	0.991085	+	0.133233i	$0.0425360\pi$
$811$			7.58846i			0.266467i	−0.991085	+	0.133233i	$0.957464\pi$
$812$	−8.19615	+	14.1962i	−0.287629	+	0.498187i
$813$	1.80385	−	3.12436i	0.0632637	−	0.109576i
$814$		−	29.5885i		−	1.03707i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−6.80385	−	11.7846i	−0.238036	−	0.412291i
$818$		−	0.947441i		−	0.0331265i
$819$	−3.00000	−	10.3923i	−0.104828	−	0.363137i
$820$		0			0
$821$	42.7128	−	24.6603i	1.49069	−	0.860649i	0.490744	−	0.871304i	$-0.336725\pi$
$821$	42.7128	−	24.6603i	1.49069	−	0.860649i	0.999943	+	0.0106549i	$0.00339162\pi$
$822$	5.66025	−	3.26795i	0.197424	−	0.113983i
$823$	34.2846	+	19.7942i	1.19509	+	0.689983i	0.959456	−	0.281859i	$-0.0909511\pi$
$823$	34.2846	+	19.7942i	1.19509	+	0.689983i	0.235631	+	0.971843i	$0.424284\pi$
$824$		−	19.5885i		−	0.682396i
$825$		0			0
$826$	11.7846	+	6.80385i	0.410039	+	0.236736i
$827$	50.4974			1.75597			0.877984	−	0.478690i	$-0.158888\pi$
$827$	50.4974			1.75597			0.877984	+	0.478690i	$0.158888\pi$
$828$	−3.00000	−	1.73205i	−0.104257	−	0.0601929i
$829$	−19.6603	−	34.0526i	−0.682829	−	1.18269i	−0.974114	−	0.226058i	$-0.927416\pi$
$829$	−19.6603	−	34.0526i	−0.682829	−	1.18269i	0.291285	−	0.956636i	$-0.405917\pi$
$830$		0			0
$831$	19.5885			0.679516
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$		−	8.00000i		−	0.277184i
$834$	−18.8660	+	10.8923i	−0.653277	+	0.377170i
$835$		0			0
$836$	4.23205	−	7.33013i	0.146369	−	0.253518i
$837$	8.92820			0.308604
$838$	8.92820	−	15.4641i	0.308420	−	0.534199i
$839$	−37.3923	−	21.5885i	−1.29093	−	0.745316i	−0.312107	−	0.950047i	$-0.601035\pi$
$839$	−37.3923	−	21.5885i	−1.29093	−	0.745316i	−0.978818	+	0.204731i	$0.934368\pi$
$840$		0			0
$841$	−0.428203	+	0.741670i	−0.0147656	+	0.0255748i
$842$	−5.07180	+	2.92820i	−0.174786	+	0.100913i
$843$	−3.46410	−	6.00000i	−0.119310	−	0.206651i
$844$	−21.9282			−0.754800
$845$		0			0
$846$	0.464102			0.0159561
$847$	4.39230	+	7.60770i	0.150921	+	0.261403i
$848$	−3.23205	+	1.86603i	−0.110989	+	0.0640796i
$849$	−7.19615	+	12.4641i	−0.246971	+	0.427767i
$850$		0			0
$851$	−23.7846	−	13.7321i	−0.815326	−	0.470729i
$852$	−0.464102	+	0.803848i	−0.0158999	+	0.0275394i
$853$	44.6410			1.52848			0.764240	−	0.644932i	$-0.223114\pi$
$853$	44.6410			1.52848			0.764240	+	0.644932i	$0.223114\pi$
$854$	−11.1962	+	19.3923i	−0.383124	+	0.663591i
$855$		0			0
$856$	0.803848	−	0.464102i	0.0274749	−	0.0158627i
$857$			15.0718i			0.514843i	0.966299	+	0.257421i	$0.0828728\pi$
$857$			15.0718i			0.514843i	−0.966299	+	0.257421i	$0.917127\pi$
$858$	−13.0622	−	3.23205i	−0.445935	−	0.110340i
$859$	19.9282			0.679942			0.339971	−	0.940436i	$-0.389583\pi$
$859$	19.9282			0.679942			0.339971	+	0.940436i	$0.389583\pi$
$860$		0			0
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	−12.0000	−	6.92820i	−0.408722	−	0.235976i
$863$	−10.9282			−0.372000			−0.186000	−	0.982550i	$-0.559553\pi$
$863$	−10.9282			−0.372000			−0.186000	+	0.982550i	$0.559553\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$		−	32.7846i		−	1.11407i
$867$	0.866025	+	0.500000i	0.0294118	+	0.0169809i
$868$	−23.1962	+	13.3923i	−0.787329	+	0.454564i
$869$	54.7128	−	31.5885i	1.85601	−	1.07157i
$870$		0			0
$871$	5.46410	+	18.9282i	0.185144	+	0.641358i
$872$			10.3923i			0.351928i
$873$	−6.19615	−	10.7321i	−0.209708	−	0.363225i
$874$	−3.92820	−	6.80385i	−0.132873	−	0.230144i
$875$		0			0
$876$			6.92820i			0.234082i
$877$	16.8564	−	29.1962i	0.569200	−	0.985884i	−0.427445	−	0.904041i	$-0.640586\pi$
$877$	16.8564	−	29.1962i	0.569200	−	0.985884i	0.996645	−	0.0818426i	$-0.0260805\pi$
$878$	−10.6603	+	18.4641i	−0.359766	+	0.623133i
$879$		−	19.2487i		−	0.649243i
$880$		0			0
$881$	18.5526	+	32.1340i	0.625052	+	1.08262i	0.988531	+	0.151019i	$0.0482554\pi$
$881$	18.5526	+	32.1340i	0.625052	+	1.08262i	−0.363479	+	0.931602i	$0.618411\pi$
$882$	−1.00000	−	1.73205i	−0.0336718	−	0.0583212i
$883$			21.3205i			0.717492i	0.933435	+	0.358746i	$0.116796\pi$
$883$			21.3205i			0.717492i	−0.933435	+	0.358746i	$0.883204\pi$
$884$	13.8564	−	4.00000i	0.466041	−	0.134535i
$885$		0			0
$886$	−6.80385	+	3.92820i	−0.228580	+	0.131971i
$887$	−45.2654	+	26.1340i	−1.51986	+	0.877493i	−0.520136	+	0.854083i	$0.674119\pi$
$887$	−45.2654	+	26.1340i	−1.51986	+	0.877493i	−0.999726	+	0.0234098i	$0.992548\pi$
$888$	6.86603	+	3.96410i	0.230409	+	0.133027i
$889$		−	13.9808i		−	0.468900i
$890$		0			0
$891$	3.23205	+	1.86603i	0.108278	+	0.0625142i
$892$	8.85641			0.296534
$893$	0.911543	+	0.526279i	0.0305036	+	0.0176113i
$894$	11.3923	+	19.7321i	0.381016	+	0.659939i
$895$		0			0
$896$	−3.00000			−0.100223
$897$	−8.66025	+	9.00000i	−0.289157	+	0.300501i
$898$			18.1244i			0.604818i
$899$	−42.2487	+	24.3923i	−1.40907	+	0.813529i
$900$		0			0
$901$	7.46410	−	12.9282i	0.248665	−	0.430701i
$902$	−14.9282			−0.497055
$903$	−9.00000	+	15.5885i	−0.299501	+	0.518751i
$904$	−10.3923	−	6.00000i	−0.345643	−	0.199557i
$905$		0			0
$906$	−9.39230	+	16.2679i	−0.312038	+	0.540466i
$907$	−6.12436	+	3.53590i	−0.203356	+	0.117408i	−0.598220	−	0.801332i	$-0.704125\pi$
$907$	−6.12436	+	3.53590i	−0.203356	+	0.117408i	0.394864	+	0.918740i	$0.370792\pi$
$908$	−6.73205	−	11.6603i	−0.223411	−	0.386959i
$909$	8.39230			0.278355
$910$		0			0
$911$	−28.7846			−0.953677			−0.476838	−	0.878991i	$-0.658217\pi$
$911$	−28.7846			−0.953677			−0.476838	+	0.878991i	$0.658217\pi$
$912$	1.13397	+	1.96410i	0.0375497	+	0.0650379i
$913$	8.19615	−	4.73205i	0.271253	−	0.156608i
$914$	0.267949	−	0.464102i	0.00886297	−	0.0153511i
$915$		0			0
$916$	9.92820	+	5.73205i	0.328037	+	0.189392i
$917$	30.4808	−	52.7942i	1.00656	−	1.74342i
$918$	−4.00000			−0.132020
$919$	27.9808	−	48.4641i	0.923000	−	1.59868i	0.128254	−	0.991741i	$-0.459063\pi$
$919$	27.9808	−	48.4641i	0.923000	−	1.59868i	0.794746	−	0.606942i	$-0.207604\pi$
$920$		0			0
$921$	17.5359	−	10.1244i	0.577827	−	0.333609i
$922$			32.3923i			1.06678i
$923$	2.41154	+	2.32051i	0.0793769	+	0.0763805i
$924$	−11.1962			−0.368326
$925$		0			0
$926$	0.392305	+	0.679492i	0.0128919	+	0.0223295i
$927$	16.9641	+	9.79423i	0.557174	+	0.321685i
$928$	−5.46410			−0.179368
$929$	26.1051	+	15.0718i	0.856481	+	0.494490i	0.862832	−	0.505490i	$-0.168688\pi$
$929$	26.1051	+	15.0718i	0.856481	+	0.494490i	−0.00635120	+	0.999980i	$0.502022\pi$
$930$		0			0
$931$		−	4.53590i		−	0.148658i
$932$	−15.5885	−	9.00000i	−0.510617	−	0.294805i
$933$	−4.39230	+	2.53590i	−0.143798	+	0.0830216i
$934$	3.12436	−	1.80385i	0.102232	−	0.0590237i
$935$		0			0
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$		−	33.7128i		−	1.10135i	−0.834720	−	0.550675i	$-0.814370\pi$
$937$		−	33.7128i		−	1.10135i	0.834720	−	0.550675i	$-0.185630\pi$
$938$	8.19615	+	14.1962i	0.267614	+	0.463521i
$939$	−0.660254	−	1.14359i	−0.0215466	−	0.0373198i
$940$		0			0
$941$		−	36.4974i		−	1.18978i	−0.803806	−	0.594891i	$-0.797195\pi$
$941$		−	36.4974i		−	1.18978i	0.803806	−	0.594891i	$-0.202805\pi$
$942$	−5.40192	+	9.35641i	−0.176004	+	0.304848i
$943$	−6.92820	+	12.0000i	−0.225613	+	0.390774i
$944$			4.53590i			0.147631i
$945$		0			0
$946$	11.1962	+	19.3923i	0.364018	+	0.630498i
$947$	6.80385	+	11.7846i	0.221095	+	0.382948i	0.955141	−	0.296152i	$-0.0957035\pi$
$947$	6.80385	+	11.7846i	0.221095	+	0.382948i	−0.734046	+	0.679100i	$0.762370\pi$
$948$			16.9282i			0.549802i
$949$	24.2487	+	6.00000i	0.787146	+	0.194768i
$950$		0			0
$951$	20.3827	−	11.7679i	0.660954	−	0.381602i
$952$	10.3923	−	6.00000i	0.336817	−	0.194461i
$953$	16.1769	+	9.33975i	0.524022	+	0.302544i	0.738579	−	0.674167i	$-0.235497\pi$
$953$	16.1769	+	9.33975i	0.524022	+	0.302544i	−0.214557	+	0.976711i	$0.568831\pi$
$954$		−	3.73205i		−	0.120830i
$955$		0			0
$956$	3.00000	+	1.73205i	0.0970269	+	0.0560185i
$957$	−20.3923			−0.659190
$958$	22.7321	+	13.1244i	0.734439	+	0.424029i
$959$	−9.80385	−	16.9808i	−0.316583	−	0.548337i
$960$		0			0
$961$	−48.7128			−1.57138
$962$	19.8205	−	20.5981i	0.639039	−	0.664109i
$963$			0.928203i			0.0299109i
$964$	−12.8205	+	7.40192i	−0.412921	+	0.238400i
$965$		0			0
$966$	−5.19615	+	9.00000i	−0.167183	+	0.289570i
$967$	28.8564			0.927959			0.463980	−	0.885846i	$-0.346421\pi$
$967$	28.8564			0.927959			0.463980	+	0.885846i	$0.346421\pi$
$968$	−1.46410	+	2.53590i	−0.0470580	+	0.0815069i
$969$	−7.85641	−	4.53590i	−0.252384	−	0.145714i
$970$		0			0
$971$	10.3038	−	17.8468i	0.330666	−	0.572731i	−0.651976	−	0.758239i	$-0.726060\pi$
$971$	10.3038	−	17.8468i	0.330666	−	0.572731i	0.982643	+	0.185509i	$0.0593932\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	32.6769	+	56.5981i	1.04757	+	1.81445i
$974$	−21.0000			−0.672883
$975$		0			0
$976$	−7.46410			−0.238920
$977$	0.732051	+	1.26795i	0.0234204	+	0.0405653i	0.877498	−	0.479580i	$-0.159211\pi$
$977$	0.732051	+	1.26795i	0.0234204	+	0.0405653i	−0.854078	+	0.520145i	$0.825878\pi$
$978$	−9.46410	+	5.46410i	−0.302629	+	0.174723i
$979$	−18.8923	+	32.7224i	−0.603801	+	1.04581i
$980$		0			0
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$	−7.69615	+	13.3301i	−0.245594	+	0.425381i
$983$	−16.1769			−0.515963			−0.257982	−	0.966150i	$-0.583057\pi$
$983$	−16.1769			−0.515963			−0.257982	+	0.966150i	$0.583057\pi$
$984$	2.00000	−	3.46410i	0.0637577	−	0.110432i
$985$		0			0
$986$	18.9282	−	10.9282i	0.602797	−	0.348025i
$987$		−	1.39230i		−	0.0443176i
$988$	7.85641	−	2.26795i	0.249946	−	0.0721531i
$989$	20.7846			0.660912
$990$		0			0
$991$	11.5885	+	20.0718i	0.368119	+	0.637602i	0.989272	−	0.146088i	$-0.0466684\pi$
$991$	11.5885	+	20.0718i	0.368119	+	0.637602i	−0.621152	+	0.783690i	$0.713335\pi$
$992$	−7.73205	−	4.46410i	−0.245493	−	0.141735i
$993$	−6.39230			−0.202854
$994$	2.41154	+	1.39230i	0.0764895	+	0.0441612i
$995$		0			0
$996$			2.53590i			0.0803530i
$997$	8.67691	+	5.00962i	0.274801	+	0.158656i	0.631067	−	0.775728i	$-0.282617\pi$
$997$	8.67691	+	5.00962i	0.274801	+	0.158656i	−0.356267	+	0.934384i	$0.615951\pi$
$998$	1.14359	−	0.660254i	0.0361998	−	0.0209000i
$999$	−6.86603	+	3.96410i	−0.217231	+	0.125419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.e.49.1		4
5.2	odd	4		390.2.bb.a.361.1	yes	4
5.3	odd	4		1950.2.bc.a.751.2		4
5.4	even	2		1950.2.y.d.49.2		4
13.4	even	6		1950.2.y.d.199.2		4
15.2	even	4		1170.2.bs.d.361.2		4
65.2	even	12		5070.2.a.ba.1.2		2
65.4	even	6	inner	1950.2.y.e.199.1		4
65.17	odd	12		390.2.bb.a.121.1	✓	4
65.37	even	12		5070.2.a.be.1.1		2
65.42	odd	12		5070.2.b.p.1351.1		4
65.43	odd	12		1950.2.bc.a.901.2		4
65.62	odd	12		5070.2.b.p.1351.4		4
195.17	even	12		1170.2.bs.d.901.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.1	✓	4	65.17	odd	12
390.2.bb.a.361.1	yes	4	5.2	odd	4
1170.2.bs.d.361.2		4	15.2	even	4
1170.2.bs.d.901.2		4	195.17	even	12
1950.2.y.d.49.2		4	5.4	even	2
1950.2.y.d.199.2		4	13.4	even	6
1950.2.y.e.49.1		4	1.1	even	1	trivial
1950.2.y.e.199.1		4	65.4	even	6	inner
1950.2.bc.a.751.2		4	5.3	odd	4
1950.2.bc.a.901.2		4	65.43	odd	12
5070.2.a.ba.1.2		2	65.2	even	12
5070.2.a.be.1.1		2	65.37	even	12
5070.2.b.p.1351.1		4	65.42	odd	12
5070.2.b.p.1351.4		4	65.62	odd	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.23205 + 1.86603i) q^{11} -1.00000i q^{12} +(-3.50000 - 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(1.96410 + 1.13397i) q^{19} -3.00000i q^{21} +(-3.23205 - 1.86603i) q^{22} +(-3.00000 + 1.73205i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.50000 - 2.59808i) q^{28} +(-2.73205 - 4.73205i) q^{29} -8.92820i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.86603 - 3.23205i) q^{33} +4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(3.96410 + 6.86603i) q^{37} +2.26795i q^{38} +(3.46410 - 1.00000i) q^{39} +(3.46410 - 2.00000i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-5.19615 - 3.00000i) q^{43} -3.73205i q^{44} +(-3.00000 - 1.73205i) q^{46} +0.464102 q^{47} +(0.866025 + 0.500000i) q^{48} +(-1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -3.73205i q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.50000 - 2.59808i) q^{56} -2.26795 q^{57} +(2.73205 - 4.73205i) q^{58} +(-3.92820 - 2.26795i) q^{59} +(3.73205 - 6.46410i) q^{61} +(7.73205 - 4.46410i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +3.73205 q^{66} +(-2.73205 - 4.73205i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(1.73205 - 3.00000i) q^{69} +(-0.803848 - 0.464102i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.92820 q^{73} +(-3.96410 + 6.86603i) q^{74} +(-1.96410 + 1.13397i) q^{76} -11.1962i q^{77} +(2.59808 + 2.50000i) q^{78} -16.9282 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.46410 + 2.00000i) q^{82} -2.53590 q^{83} +(2.59808 + 1.50000i) q^{84} -6.00000i q^{86} +(4.73205 + 2.73205i) q^{87} +(3.23205 - 1.86603i) q^{88} +(8.76795 - 5.06218i) q^{89} +(7.50000 - 7.79423i) q^{91} -3.46410i q^{92} +(4.46410 + 7.73205i) q^{93} +(0.232051 + 0.401924i) q^{94} +1.00000i q^{96} +(6.19615 - 10.7321i) q^{97} +(1.00000 - 1.73205i) q^{98} +3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 6 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 6 q^{7} - 4 q^{8} + 2 q^{9} - 6 q^{11} - 14 q^{13} - 12 q^{14} - 2 q^{16} + 4 q^{18} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 4 q^{26} - 6 q^{28} - 4 q^{29} + 2 q^{32} + 4 q^{33} + 2 q^{36} + 2 q^{37} - 12 q^{46} - 12 q^{47} - 4 q^{49} - 16 q^{51} + 10 q^{52} + 6 q^{56} - 16 q^{57} + 4 q^{58} + 12 q^{59} + 8 q^{61} + 24 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{66} - 4 q^{67} - 24 q^{71} - 2 q^{72} - 2 q^{74} + 6 q^{76} - 40 q^{79} - 2 q^{81} - 24 q^{83} + 12 q^{87} + 6 q^{88} + 42 q^{89} + 30 q^{91} + 4 q^{93} - 6 q^{94} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 6 * q^7 - 4 * q^8 + 2 * q^9 - 6 * q^11 - 14 * q^13 - 12 * q^14 - 2 * q^16 + 4 * q^18 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 4 * q^26 - 6 * q^28 - 4 * q^29 + 2 * q^32 + 4 * q^33 + 2 * q^36 + 2 * q^37 - 12 * q^46 - 12 * q^47 - 4 * q^49 - 16 * q^51 + 10 * q^52 + 6 * q^56 - 16 * q^57 + 4 * q^58 + 12 * q^59 + 8 * q^61 + 24 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^66 - 4 * q^67 - 24 * q^71 - 2 * q^72 - 2 * q^74 + 6 * q^76 - 40 * q^79 - 2 * q^81 - 24 * q^83 + 12 * q^87 + 6 * q^88 + 42 * q^89 + 30 * q^91 + 4 * q^93 - 6 * q^94 + 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

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