LMFDB - Embedded newform 1014.2.i.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.d.823.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(3.46410 - 2.00000i) q^{11} +1.00000 q^{12} -4.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(6.92820 + 4.00000i) q^{19} +(1.73205 + 1.00000i) q^{20} +4.00000i q^{21} +(-2.00000 + 3.46410i) q^{22} +(-0.866025 + 0.500000i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(3.46410 - 2.00000i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{30} -4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.46410 + 2.00000i) q^{33} +2.00000i q^{34} +(-4.00000 + 6.92820i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.73205 - 1.00000i) q^{37} -8.00000 q^{38} -2.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(2.00000 - 3.46410i) q^{43} -4.00000i q^{44} +(-1.73205 - 1.00000i) q^{45} -8.00000i q^{47} +(0.500000 - 0.866025i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.00000 q^{51} -10.0000 q^{53} +(0.866025 - 0.500000i) q^{54} +(4.00000 + 6.92820i) q^{55} +(-2.00000 + 3.46410i) q^{56} +8.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(3.46410 + 2.00000i) q^{59} +2.00000i q^{60} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-3.46410 + 2.00000i) q^{63} -1.00000 q^{64} -4.00000 q^{66} +(-13.8564 + 8.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000i q^{70} +(6.92820 + 4.00000i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(6.92820 - 4.00000i) q^{76} +16.0000 q^{77} +8.00000 q^{79} +(1.73205 - 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +12.0000i q^{83} +(3.46410 + 2.00000i) q^{84} +(3.46410 + 2.00000i) q^{85} +4.00000i q^{86} +(3.00000 - 5.19615i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-12.1244 + 7.00000i) q^{89} +2.00000 q^{90} +(3.46410 - 2.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +1.00000i q^{96} +(-8.66025 - 5.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{10} + 4 q^{12} - 16 q^{14} - 2 q^{16} + 4 q^{17} - 8 q^{22} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 4 q^{30} - 16 q^{35} + 2 q^{36} - 32 q^{38} - 8 q^{40} - 8 q^{42}+ \cdots - 32 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^10 + 4 * q^12 - 16 * q^14 - 2 * q^16 + 4 * q^17 - 8 * q^22 + 4 * q^25 - 4 * q^27 - 12 * q^29 + 4 * q^30 - 16 * q^35 + 2 * q^36 - 32 * q^38 - 8 * q^40 - 8 * q^42 + 8 * q^43 + 2 * q^48 + 18 * q^49 + 8 * q^51 - 40 * q^53 + 16 * q^55 - 8 * q^56 + 4 * q^61 + 8 * q^62 - 4 * q^64 - 16 * q^66 - 4 * q^68 - 4 * q^74 + 2 * q^75 + 64 * q^77 + 32 * q^79 - 2 * q^81 + 20 * q^82 + 12 * q^87 + 8 * q^88 + 8 * q^90 + 16 * q^94 - 32 * q^95

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.00000i			0.894427i	0.894427	+	0.447214i	$0.147584\pi$
$5$			2.00000i			0.894427i	−0.894427	+	0.447214i	$0.852416\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.123371	−	0.992361i	$-0.460630\pi$
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.921095	+	0.389338i	$0.127296\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	−1.73205	+	1.00000i	−0.447214	+	0.258199i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		−	1.00000i		−	0.235702i
$19$	6.92820	+	4.00000i	1.58944	+	0.917663i	0.993399	+	0.114708i	$0.0365932\pi$
$19$	6.92820	+	4.00000i	1.58944	+	0.917663i	0.596040	+	0.802955i	$0.296740\pi$
$20$	1.73205	+	1.00000i	0.387298	+	0.223607i
$21$			4.00000i			0.872872i
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	3.46410	−	2.00000i	0.654654	−	0.377964i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.46410	+	2.00000i	0.603023	+	0.348155i
$34$			2.00000i			0.342997i
$35$	−4.00000	+	6.92820i	−0.676123	+	1.17108i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	0.635571	+	0.772043i	$0.280765\pi$
$38$	−8.00000			−1.29777
$39$		0			0
$40$	−2.00000			−0.316228
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.988600	−	0.150567i	$-0.951890\pi$
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.363905	+	0.931436i	$0.618557\pi$
$42$	−2.00000	−	3.46410i	−0.308607	−	0.534522i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$		−	4.00000i		−	0.603023i
$45$	−1.73205	−	1.00000i	−0.258199	−	0.149071i
$46$		0			0
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	2.00000			0.280056
$52$		0			0
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$			8.00000i			1.05963i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	0.708247	−	0.705965i	$-0.249486\pi$
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	−0.257260	+	0.966342i	$0.582820\pi$
$60$			2.00000i			0.258199i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−3.46410	+	2.00000i	−0.436436	+	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	−13.8564	+	8.00000i	−1.69283	+	0.977356i	−0.740613	+	0.671932i	$0.765465\pi$
$67$	−13.8564	+	8.00000i	−1.69283	+	0.977356i	−0.952217	+	0.305424i	$0.901202\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		−	8.00000i		−	0.956183i
$71$	6.92820	+	4.00000i	0.822226	+	0.474713i	0.851184	−	0.524868i	$-0.175885\pi$
$71$	6.92820	+	4.00000i	0.822226	+	0.474713i	−0.0289572	+	0.999581i	$0.509219\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	6.92820	−	4.00000i	0.794719	−	0.458831i
$77$	16.0000			1.82337
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.73205	−	1.00000i	0.193649	−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	3.46410	+	2.00000i	0.377964	+	0.218218i
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$			4.00000i			0.431331i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−12.1244	+	7.00000i	−1.28518	+	0.741999i	−0.977790	−	0.209585i	$-0.932789\pi$
$89$	−12.1244	+	7.00000i	−1.28518	+	0.741999i	−0.307389	+	0.951584i	$0.599455\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$		0			0
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	−8.00000	+	13.8564i	−0.820783	+	1.42164i
$96$			1.00000i			0.102062i
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$	−7.79423	−	4.50000i	−0.787336	−	0.454569i
$99$			4.00000i			0.402015i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	−1.73205	+	1.00000i	−0.171499	+	0.0990148i
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	8.66025	−	5.00000i	0.841158	−	0.485643i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	−6.92820	−	4.00000i	−0.660578	−	0.381385i
$111$	1.73205	+	1.00000i	0.164399	+	0.0949158i
$112$		−	4.00000i		−	0.377964i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−4.00000	−	6.92820i	−0.374634	−	0.648886i
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−4.00000			−0.368230
$119$	6.92820	−	4.00000i	0.635107	−	0.366679i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$			2.00000i			0.181071i
$123$	−8.66025	−	5.00000i	−0.780869	−	0.450835i
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$			12.0000i			1.07331i
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$127$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.00000			0.352180
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	3.46410	−	2.00000i	0.301511	−	0.174078i
$133$	16.0000	+	27.7128i	1.38738	+	2.40301i
$134$	8.00000	−	13.8564i	0.691095	−	1.19701i
$135$		−	2.00000i		−	0.172133i
$136$	1.73205	+	1.00000i	0.148522	+	0.0857493i
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	0.0821359	−	0.996621i	$-0.473826\pi$
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	−0.822031	+	0.569442i	$0.807159\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	4.00000	+	6.92820i	0.338062	+	0.585540i
$141$	6.92820	−	4.00000i	0.583460	−	0.336861i
$142$	−8.00000			−0.671345
$143$		0			0
$144$	1.00000			0.0833333
$145$	10.3923	−	6.00000i	0.863034	−	0.498273i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	−4.50000	+	7.79423i	−0.371154	+	0.642857i
$148$		−	2.00000i		−	0.164399i
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	−4.00000	+	6.92820i	−0.324443	+	0.561951i
$153$	1.00000	+	1.73205i	0.0808452	+	0.140028i
$154$	−13.8564	+	8.00000i	−1.11658	+	0.644658i
$155$	8.00000			0.642575
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−6.92820	+	4.00000i	−0.551178	+	0.318223i
$159$	−5.00000	−	8.66025i	−0.396526	−	0.686803i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$		0			0
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−13.8564	−	8.00000i	−1.08532	−	0.626608i	−0.152992	−	0.988227i	$-0.548891\pi$
$163$	−13.8564	−	8.00000i	−1.08532	−	0.626608i	−0.932326	+	0.361619i	$0.882224\pi$
$164$			10.0000i			0.780869i
$165$	−4.00000	+	6.92820i	−0.311400	+	0.539360i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$	−4.00000			−0.308607
$169$		0			0
$170$	−4.00000			−0.306786
$171$	−6.92820	+	4.00000i	−0.529813	+	0.305888i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$			6.00000i			0.454859i
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$	−3.46410	−	2.00000i	−0.261116	−	0.150756i
$177$			4.00000i			0.300658i
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−1.73205	+	1.00000i	−0.129099	+	0.0745356i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		−	8.00000i		−	0.585018i
$188$	−6.92820	−	4.00000i	−0.505291	−	0.291730i
$189$	−3.46410	−	2.00000i	−0.251976	−	0.145479i
$190$		−	16.0000i		−	1.16076i
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.00447566	−	0.999990i	$-0.498575\pi$
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.868255	+	0.496119i	$0.165242\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	9.00000			0.642857
$197$	15.5885	−	9.00000i	1.11063	−	0.641223i	0.171639	−	0.985160i	$-0.445094\pi$
$197$	15.5885	−	9.00000i	1.11063	−	0.641223i	0.938993	+	0.343937i	$0.111761\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$			1.00000i			0.0707107i
$201$	−13.8564	−	8.00000i	−0.977356	−	0.564276i
$202$	1.73205	+	1.00000i	0.121867	+	0.0703598i
$203$		−	24.0000i		−	1.68447i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	13.8564	−	8.00000i	0.965422	−	0.557386i
$207$		0			0
$208$		0			0
$209$	32.0000			2.21349
$210$	6.92820	−	4.00000i	0.478091	−	0.276026i
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$			8.00000i			0.548151i
$214$	10.3923	+	6.00000i	0.710403	+	0.410152i
$215$	6.92820	+	4.00000i	0.472500	+	0.272798i
$216$		−	1.00000i		−	0.0680414i
$217$	8.00000	−	13.8564i	0.543075	−	0.940634i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	1.73205	−	1.00000i	0.117041	−	0.0675737i
$220$	8.00000			0.539360
$221$		0			0
$222$	−2.00000			−0.134231
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	−0.611482	−	0.791258i	$-0.709426\pi$
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	0.379509	+	0.925188i	$0.376093\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$			6.00000i			0.399114i
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.200812	−	0.979630i	$-0.564358\pi$
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.948790	+	0.315906i	$0.897691\pi$
$228$	6.92820	+	4.00000i	0.458831	+	0.264906i
$229$		−	22.0000i		−	1.45380i	−0.686743	−	0.726900i	$-0.740960\pi$
$229$		−	22.0000i		−	1.45380i	0.686743	−	0.726900i	$-0.259040\pi$
$230$		0			0
$231$	8.00000	+	13.8564i	0.526361	+	0.911685i
$232$	5.19615	−	3.00000i	0.341144	−	0.196960i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$	3.46410	−	2.00000i	0.225494	−	0.130189i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	1.73205	+	1.00000i	0.111803	+	0.0645497i
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	0.752285	−	0.658838i	$-0.228952\pi$
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	−0.194429	+	0.980917i	$0.562285\pi$
$242$			5.00000i			0.321412i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	−15.5885	+	9.00000i	−0.995910	+	0.574989i
$246$	10.0000			0.637577
$247$		0			0
$248$	4.00000			0.254000
$249$	−10.3923	+	6.00000i	−0.658586	+	0.380235i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	−0.795978	−	0.605326i	$-0.793043\pi$
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	0.922217	+	0.386674i	$0.126376\pi$
$252$			4.00000i			0.251976i
$253$		0			0
$254$		0			0
$255$			4.00000i			0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−3.46410	+	2.00000i	−0.215666	+	0.124515i
$259$	8.00000			0.497096
$260$		0			0
$261$	6.00000			0.371391
$262$	−3.46410	+	2.00000i	−0.214013	+	0.123560i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$		−	20.0000i		−	1.22859i
$266$	−27.7128	−	16.0000i	−1.69918	−	0.981023i
$267$	−12.1244	−	7.00000i	−0.741999	−	0.428393i
$268$			16.0000i			0.977356i
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	−0.131713	−	0.991288i	$-0.542048\pi$
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	0.924337	−	0.381577i	$-0.124619\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	3.46410	−	2.00000i	0.210429	−	0.121491i	−0.391082	−	0.920356i	$-0.627899\pi$
$271$	3.46410	−	2.00000i	0.210429	−	0.121491i	0.601511	+	0.798865i	$0.294566\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	3.46410	−	2.00000i	0.208893	−	0.120605i
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$		−	12.0000i		−	0.719712i
$279$	3.46410	+	2.00000i	0.207390	+	0.119737i
$280$	−6.92820	−	4.00000i	−0.414039	−	0.239046i
$281$			26.0000i			1.55103i	0.631329	+	0.775515i	$0.282510\pi$
$281$			26.0000i			1.55103i	−0.631329	+	0.775515i	$0.717490\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	6.92820	−	4.00000i	0.411113	−	0.237356i
$285$	−16.0000			−0.947758
$286$		0			0
$287$	−40.0000			−2.36113
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−6.00000	+	10.3923i	−0.352332	+	0.610257i
$291$		−	10.0000i		−	0.586210i
$292$	−1.73205	−	1.00000i	−0.101361	−	0.0585206i
$293$	22.5167	+	13.0000i	1.31544	+	0.759468i	0.982991	−	0.183654i	$-0.0587926\pi$
$293$	22.5167	+	13.0000i	1.31544	+	0.759468i	0.332446	+	0.943122i	$0.392126\pi$
$294$		−	9.00000i		−	0.524891i
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	−3.46410	+	2.00000i	−0.201008	+	0.116052i
$298$	−6.00000			−0.347571
$299$		0			0
$300$	1.00000			0.0577350
$301$	13.8564	−	8.00000i	0.798670	−	0.461112i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$	1.00000	−	1.73205i	0.0574485	−	0.0995037i
$304$		−	8.00000i		−	0.458831i
$305$	3.46410	+	2.00000i	0.198354	+	0.114520i
$306$	−1.73205	−	1.00000i	−0.0990148	−	0.0571662i
$307$			8.00000i			0.456584i	0.973593	+	0.228292i	$0.0733141\pi$
$307$			8.00000i			0.456584i	−0.973593	+	0.228292i	$0.926686\pi$
$308$	8.00000	−	13.8564i	0.455842	−	0.789542i
$309$	−8.00000	−	13.8564i	−0.455104	−	0.788263i
$310$	−6.92820	+	4.00000i	−0.393496	+	0.227185i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−12.1244	+	7.00000i	−0.684217	+	0.395033i
$315$	−4.00000	−	6.92820i	−0.225374	−	0.390360i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$		−	6.00000i		−	0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$		−	6.00000i		−	0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	8.66025	+	5.00000i	0.485643	+	0.280386i
$319$	−20.7846	−	12.0000i	−1.16371	−	0.671871i
$320$		−	2.00000i		−	0.111803i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	13.8564	−	8.00000i	0.770991	−	0.445132i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	16.0000			0.886158
$327$	1.73205	−	1.00000i	0.0957826	−	0.0553001i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	16.0000	−	27.7128i	0.882109	−	1.52786i
$330$		−	8.00000i		−	0.440386i
$331$	−6.92820	−	4.00000i	−0.380808	−	0.219860i	0.297361	−	0.954765i	$-0.403893\pi$
$331$	−6.92820	−	4.00000i	−0.380808	−	0.219860i	−0.678170	+	0.734905i	$0.737227\pi$
$332$	10.3923	+	6.00000i	0.570352	+	0.329293i
$333$			2.00000i			0.109599i
$334$		0			0
$335$	−16.0000	−	27.7128i	−0.874173	−	1.51411i
$336$	3.46410	−	2.00000i	0.188982	−	0.109109i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$	4.00000	−	6.92820i	0.216295	−	0.374634i
$343$			8.00000i			0.431959i
$344$	3.46410	+	2.00000i	0.186772	+	0.107833i
$345$		0			0
$346$		−	10.0000i		−	0.537603i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−5.19615	+	3.00000i	−0.278144	+	0.160586i	−0.632583	−	0.774493i	$-0.718005\pi$
$349$	−5.19615	+	3.00000i	−0.278144	+	0.160586i	0.354439	+	0.935079i	$0.384672\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	4.00000			0.213201
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	−0.141344	−	0.989960i	$-0.545142\pi$
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	0.786659	+	0.617388i	$0.211809\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$			14.0000i			0.741999i
$357$	6.92820	+	4.00000i	0.366679	+	0.211702i
$358$	10.3923	+	6.00000i	0.549250	+	0.317110i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	22.5000	+	38.9711i	1.18421	+	2.05111i
$362$	−8.66025	+	5.00000i	−0.455173	+	0.262794i
$363$	5.00000			0.262432
$364$		0			0
$365$	4.00000			0.209370
$366$	−1.73205	+	1.00000i	−0.0905357	+	0.0522708i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		0			0
$369$		−	10.0000i		−	0.520579i
$370$	−3.46410	−	2.00000i	−0.180090	−	0.103975i
$371$	−34.6410	−	20.0000i	−1.79847	−	1.03835i
$372$		−	4.00000i		−	0.207390i
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$	−10.3923	+	6.00000i	−0.536656	+	0.309839i
$376$	8.00000			0.412568
$377$		0			0
$378$	4.00000			0.205738
$379$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$379$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$			8.00000i			0.409316i
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.925997	−	0.377531i	$-0.123227\pi$
$383$	20.7846	+	12.0000i	1.06204	+	0.613171i	0.136047	+	0.990702i	$0.456560\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			32.0000i			1.63087i
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	26.0000			1.31825			0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000			1.31825			0.659126	+	0.752032i	$0.270926\pi$
$390$		0			0
$391$		0			0
$392$	−7.79423	+	4.50000i	−0.393668	+	0.227284i
$393$	2.00000	+	3.46410i	0.100887	+	0.174741i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$			16.0000i			0.805047i
$396$	3.46410	+	2.00000i	0.174078	+	0.100504i
$397$	5.19615	+	3.00000i	0.260787	+	0.150566i	0.624694	−	0.780870i	$-0.285224\pi$
$397$	5.19615	+	3.00000i	0.260787	+	0.150566i	−0.363906	+	0.931436i	$0.618557\pi$
$398$		−	8.00000i		−	0.401004i
$399$	−16.0000	+	27.7128i	−0.801002	+	1.38738i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−5.19615	+	3.00000i	−0.259483	+	0.149813i	−0.624099	−	0.781345i	$-0.714534\pi$
$401$	−5.19615	+	3.00000i	−0.259483	+	0.149813i	0.364615	+	0.931158i	$0.381200\pi$
$402$	16.0000			0.798007
$403$		0			0
$404$	−2.00000			−0.0995037
$405$	1.73205	−	1.00000i	0.0860663	−	0.0496904i
$406$	12.0000	+	20.7846i	0.595550	+	1.03152i
$407$	4.00000	−	6.92820i	0.198273	−	0.343418i
$408$			2.00000i			0.0990148i
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	0.456566	−	0.889689i	$-0.349079\pi$
$409$	−1.73205	−	1.00000i	−0.0856444	−	0.0494468i	−0.542211	+	0.840243i	$0.682412\pi$
$410$	17.3205	+	10.0000i	0.855399	+	0.493865i
$411$		−	10.0000i		−	0.493264i
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	8.00000	+	13.8564i	0.393654	+	0.681829i
$414$		0			0
$415$	−24.0000			−1.17811
$416$		0			0
$417$	−12.0000			−0.587643
$418$	−27.7128	+	16.0000i	−1.35548	+	0.782586i
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	0.813029	−	0.582224i	$-0.197817\pi$
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	−0.910735	+	0.412991i	$0.864484\pi$
$420$	−4.00000	+	6.92820i	−0.195180	+	0.338062i
$421$			22.0000i			1.07221i	0.844150	+	0.536107i	$0.180106\pi$
$421$			22.0000i			1.07221i	−0.844150	+	0.536107i	$0.819894\pi$
$422$	10.3923	+	6.00000i	0.505889	+	0.292075i
$423$	6.92820	+	4.00000i	0.336861	+	0.194487i
$424$		−	10.0000i		−	0.485643i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	−4.00000	−	6.92820i	−0.193801	−	0.335673i
$427$	6.92820	−	4.00000i	0.335279	−	0.193574i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−8.00000			−0.385794
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	−0.657491	−	0.753462i	$-0.728382\pi$
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	0.323772	+	0.946135i	$0.395049\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−15.0000	+	25.9808i	−0.720854	+	1.24856i	0.239804	+	0.970821i	$0.422917\pi$
$433$	−15.0000	+	25.9808i	−0.720854	+	1.24856i	−0.960658	+	0.277734i	$0.910416\pi$
$434$			16.0000i			0.768025i
$435$	10.3923	+	6.00000i	0.498273	+	0.287678i
$436$	−1.73205	−	1.00000i	−0.0829502	−	0.0478913i
$437$		0			0
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−6.92820	+	4.00000i	−0.330289	+	0.190693i
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	1.73205	−	1.00000i	0.0821995	−	0.0474579i
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$			6.00000i			0.283790i
$448$	−3.46410	−	2.00000i	−0.163663	−	0.0944911i
$449$	5.19615	+	3.00000i	0.245222	+	0.141579i	0.617574	−	0.786513i	$-0.288115\pi$
$449$	5.19615	+	3.00000i	0.245222	+	0.141579i	−0.372353	+	0.928091i	$0.621449\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−20.0000	+	34.6410i	−0.941763	+	1.63118i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	10.3923	−	6.00000i	0.488273	−	0.281905i
$454$	20.0000			0.938647
$455$		0			0
$456$	−8.00000			−0.374634
$457$	−25.9808	+	15.0000i	−1.21533	+	0.701670i	−0.963915	−	0.266209i	$-0.914229\pi$
$457$	−25.9808	+	15.0000i	−1.21533	+	0.701670i	−0.251414	+	0.967880i	$0.580895\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	5.19615	+	3.00000i	0.242009	+	0.139724i	0.616100	−	0.787668i	$-0.288712\pi$
$461$	5.19615	+	3.00000i	0.242009	+	0.139724i	−0.374091	+	0.927392i	$0.622045\pi$
$462$	−13.8564	−	8.00000i	−0.644658	−	0.372194i
$463$			20.0000i			0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$			20.0000i			0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$	4.00000			0.185098			0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000			0.185098			0.0925490	+	0.995708i	$0.470499\pi$
$468$		0			0
$469$	−64.0000			−2.95525
$470$	−13.8564	+	8.00000i	−0.639148	+	0.369012i
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$		−	16.0000i		−	0.735681i
$474$	−6.92820	−	4.00000i	−0.318223	−	0.183726i
$475$	6.92820	+	4.00000i	0.317888	+	0.183533i
$476$		−	8.00000i		−	0.366679i
$477$	5.00000	−	8.66025i	0.228934	−	0.396526i
$478$		0			0
$479$	13.8564	−	8.00000i	0.633115	−	0.365529i	−0.148842	−	0.988861i	$-0.547555\pi$
$479$	13.8564	−	8.00000i	0.633115	−	0.365529i	0.781958	+	0.623332i	$0.214221\pi$
$480$	−2.00000			−0.0912871
$481$		0			0
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	10.0000	−	17.3205i	0.454077	−	0.786484i
$486$			1.00000i			0.0453609i
$487$	−3.46410	−	2.00000i	−0.156973	−	0.0906287i	0.419456	−	0.907776i	$-0.362221\pi$
$487$	−3.46410	−	2.00000i	−0.156973	−	0.0906287i	−0.576429	+	0.817147i	$0.695554\pi$
$488$	1.73205	+	1.00000i	0.0784063	+	0.0452679i
$489$		−	16.0000i		−	0.723545i
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$	−8.66025	+	5.00000i	−0.390434	+	0.225417i
$493$	−12.0000			−0.540453
$494$		0			0
$495$	−8.00000			−0.359573
$496$	−3.46410	+	2.00000i	−0.155543	+	0.0898027i
$497$	16.0000	+	27.7128i	0.717698	+	1.24309i
$498$	6.00000	−	10.3923i	0.268866	−	0.465690i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	10.3923	+	6.00000i	0.464758	+	0.268328i
$501$		0			0
$502$			4.00000i			0.178529i
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.0539870	+	0.998542i	$0.517193\pi$
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.837769	+	0.546025i	$0.816140\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$	3.46410	−	2.00000i	0.154150	−	0.0889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	36.3731	−	21.0000i	1.61221	−	0.930809i	0.623350	−	0.781943i	$-0.285771\pi$
$509$	36.3731	−	21.0000i	1.61221	−	0.930809i	0.988857	−	0.148866i	$-0.0475623\pi$
$510$	−2.00000	−	3.46410i	−0.0885615	−	0.153393i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.92820	−	4.00000i	−0.305888	−	0.176604i
$514$	5.19615	+	3.00000i	0.229192	+	0.132324i
$515$		−	32.0000i		−	1.41009i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−16.0000	−	27.7128i	−0.703679	−	1.21881i
$518$	−6.92820	+	4.00000i	−0.304408	+	0.175750i
$519$	−10.0000			−0.438951
$520$		0			0
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$			4.00000i			0.174574i
$526$	6.92820	+	4.00000i	0.302084	+	0.174408i
$527$	−6.92820	−	4.00000i	−0.301797	−	0.174243i
$528$		−	4.00000i		−	0.174078i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	10.0000	+	17.3205i	0.434372	+	0.752355i
$531$	−3.46410	+	2.00000i	−0.150329	+	0.0867926i
$532$	32.0000			1.38738
$533$		0			0
$534$	14.0000			0.605839
$535$	20.7846	−	12.0000i	0.898597	−	0.518805i
$536$	−8.00000	−	13.8564i	−0.345547	−	0.598506i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$			26.0000i			1.12094i
$539$	31.1769	+	18.0000i	1.34288	+	0.775315i
$540$	−1.73205	−	1.00000i	−0.0745356	−	0.0430331i
$541$			34.0000i			1.46177i	0.682498	+	0.730887i	$0.260893\pi$
$541$			34.0000i			1.46177i	−0.682498	+	0.730887i	$0.739107\pi$
$542$	−2.00000	+	3.46410i	−0.0859074	+	0.148796i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	1.73205	−	1.00000i	0.0742611	−	0.0428746i
$545$	4.00000			0.171341
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−8.66025	+	5.00000i	−0.369948	+	0.213589i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$		−	48.0000i		−	2.04487i
$552$		0			0
$553$	27.7128	+	16.0000i	1.17847	+	0.680389i
$554$			22.0000i			0.934690i
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	8.00000			0.338062
$561$	6.92820	−	4.00000i	0.292509	−	0.168880i
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		−	8.00000i		−	0.336861i
$565$	10.3923	+	6.00000i	0.437208	+	0.252422i
$566$	3.46410	+	2.00000i	0.145607	+	0.0840663i
$567$		−	4.00000i		−	0.167984i
$568$	−4.00000	+	6.92820i	−0.167836	+	0.290701i
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$	13.8564	−	8.00000i	0.580381	−	0.335083i
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$	34.6410	−	20.0000i	1.44589	−	0.834784i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			18.0000i			0.749350i	0.927156	+	0.374675i	$0.122246\pi$
$577$			18.0000i			0.749350i	−0.927156	+	0.374675i	$0.877754\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$	12.1244	+	7.00000i	0.503871	+	0.290910i
$580$		−	12.0000i		−	0.498273i
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$	5.00000	+	8.66025i	0.207257	+	0.358979i
$583$	−34.6410	+	20.0000i	−1.43468	+	0.828315i
$584$	2.00000			0.0827606
$585$		0			0
$586$	−26.0000			−1.07405
$587$	3.46410	−	2.00000i	0.142979	−	0.0825488i	−0.426804	−	0.904344i	$-0.640361\pi$
$587$	3.46410	−	2.00000i	0.142979	−	0.0825488i	0.569783	+	0.821795i	$0.307027\pi$
$588$	4.50000	+	7.79423i	0.185577	+	0.321429i
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$		−	8.00000i		−	0.329355i
$591$	15.5885	+	9.00000i	0.641223	+	0.370211i
$592$	−1.73205	−	1.00000i	−0.0711868	−	0.0410997i
$593$			42.0000i			1.72473i	0.506284	+	0.862367i	$0.331019\pi$
$593$			42.0000i			1.72473i	−0.506284	+	0.862367i	$0.668981\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	8.00000	+	13.8564i	0.327968	+	0.568057i
$596$	5.19615	−	3.00000i	0.212843	−	0.122885i
$597$	−8.00000			−0.327418
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	−0.866025	+	0.500000i	−0.0353553	+	0.0204124i
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	−8.00000	+	13.8564i	−0.326056	+	0.564745i
$603$		−	16.0000i		−	0.651570i
$604$	−10.3923	−	6.00000i	−0.422857	−	0.244137i
$605$	8.66025	+	5.00000i	0.352089	+	0.203279i
$606$			2.00000i			0.0812444i
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	4.00000	+	6.92820i	0.162221	+	0.280976i
$609$	20.7846	−	12.0000i	0.842235	−	0.486265i
$610$	−4.00000			−0.161955
$611$		0			0
$612$	2.00000			0.0808452
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	−0.534570	−	0.845124i	$-0.679527\pi$
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	0.464614	+	0.885514i	$0.346193\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$	10.0000	−	17.3205i	0.403239	−	0.698430i
$616$			16.0000i			0.644658i
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	0.391745	−	0.920074i	$-0.371871\pi$
$617$	−5.19615	−	3.00000i	−0.209189	−	0.120775i	−0.600935	+	0.799298i	$0.705205\pi$
$618$	13.8564	+	8.00000i	0.557386	+	0.321807i
$619$		−	32.0000i		−	1.28619i	−0.765787	−	0.643094i	$-0.777650\pi$
$619$		−	32.0000i		−	1.28619i	0.765787	−	0.643094i	$-0.222350\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$		0			0
$622$		0			0
$623$	−56.0000			−2.24359
$624$		0			0
$625$	−19.0000			−0.760000
$626$	5.19615	−	3.00000i	0.207680	−	0.119904i
$627$	16.0000	+	27.7128i	0.638978	+	1.10674i
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$		−	4.00000i		−	0.159490i
$630$	6.92820	+	4.00000i	0.276026	+	0.159364i
$631$	−31.1769	−	18.0000i	−1.24113	−	0.716569i	−0.271808	−	0.962351i	$-0.587622\pi$
$631$	−31.1769	−	18.0000i	−1.24113	−	0.716569i	−0.969325	+	0.245783i	$0.920955\pi$
$632$			8.00000i			0.318223i
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$		0			0
$636$	−10.0000			−0.396526
$637$		0			0
$638$	24.0000			0.950169
$639$	−6.92820	+	4.00000i	−0.274075	+	0.158238i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$			12.0000i			0.473602i
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	0.747686	−	0.664052i	$-0.231165\pi$
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	−0.201243	+	0.979541i	$0.564498\pi$
$644$		0			0
$645$			8.00000i			0.315000i
$646$	−8.00000	+	13.8564i	−0.314756	+	0.545173i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	16.0000			0.628055
$650$		0			0
$651$	16.0000			0.627089
$652$	−13.8564	+	8.00000i	−0.542659	+	0.313304i
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	0.947118	−	0.320884i	$-0.103980\pi$
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	−0.751453	+	0.659786i	$0.770647\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$			8.00000i			0.312586i
$656$	8.66025	+	5.00000i	0.338126	+	0.195217i
$657$	1.73205	+	1.00000i	0.0675737	+	0.0390137i
$658$			32.0000i			1.24749i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	4.00000	+	6.92820i	0.155700	+	0.269680i
$661$	1.73205	−	1.00000i	0.0673690	−	0.0388955i	−0.465937	−	0.884818i	$-0.654283\pi$
$661$	1.73205	−	1.00000i	0.0673690	−	0.0388955i	0.533306	+	0.845922i	$0.320949\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−55.4256	+	32.0000i	−2.14931	+	1.24091i
$666$	−1.00000	−	1.73205i	−0.0387492	−	0.0671156i
$667$		0			0
$668$		0			0
$669$	−3.46410	−	2.00000i	−0.133930	−	0.0773245i
$670$	27.7128	+	16.0000i	1.07064	+	0.618134i
$671$		−	8.00000i		−	0.308837i
$672$	−2.00000	+	3.46410i	−0.0771517	+	0.133631i
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	15.5885	−	9.00000i	0.600445	−	0.346667i
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$	−5.19615	+	3.00000i	−0.199557	+	0.115214i
$679$	−20.0000	−	34.6410i	−0.767530	−	1.32940i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		−	20.0000i		−	0.766402i
$682$	13.8564	+	8.00000i	0.530589	+	0.306336i
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.998916	−	0.0465592i	$-0.0148256\pi$
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.459136	+	0.888366i	$0.348159\pi$
$684$			8.00000i			0.305888i
$685$	10.0000	−	17.3205i	0.382080	−	0.661783i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	19.0526	−	11.0000i	0.726900	−	0.419676i
$688$	−4.00000			−0.152499
$689$		0			0
$690$		0			0
$691$	−27.7128	+	16.0000i	−1.05425	+	0.608669i	−0.923835	−	0.382791i	$-0.874963\pi$
$691$	−27.7128	+	16.0000i	−1.05425	+	0.608669i	−0.130410	+	0.991460i	$0.541629\pi$
$692$	5.00000	+	8.66025i	0.190071	+	0.329213i
$693$	−8.00000	+	13.8564i	−0.303895	+	0.526361i
$694$			12.0000i			0.455514i
$695$	−20.7846	−	12.0000i	−0.788405	−	0.455186i
$696$	5.19615	+	3.00000i	0.196960	+	0.113715i
$697$			20.0000i			0.757554i
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$	3.46410	−	2.00000i	0.130931	−	0.0755929i
$701$	50.0000			1.88847			0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000			1.88847			0.944237	+	0.329267i	$0.106802\pi$
$702$		0			0
$703$	16.0000			0.603451
$704$	−3.46410	+	2.00000i	−0.130558	+	0.0753778i
$705$	8.00000	+	13.8564i	0.301297	+	0.521862i
$706$	−7.00000	+	12.1244i	−0.263448	+	0.456306i
$707$		−	8.00000i		−	0.300871i
$708$	3.46410	+	2.00000i	0.130189	+	0.0751646i
$709$	5.19615	+	3.00000i	0.195146	+	0.112667i	0.594389	−	0.804178i	$-0.297394\pi$
$709$	5.19615	+	3.00000i	0.195146	+	0.112667i	−0.399244	+	0.916845i	$0.630727\pi$
$710$		−	16.0000i		−	0.600469i
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$		0			0
$714$	−8.00000			−0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$		0			0
$718$		0			0
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$			2.00000i			0.0745356i
$721$	−55.4256	−	32.0000i	−2.06416	−	1.19174i
$722$	−38.9711	−	22.5000i	−1.45036	−	0.837363i
$723$			10.0000i			0.371904i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−4.33013	+	2.50000i	−0.160706	+	0.0927837i
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.46410	+	2.00000i	−0.128212	+	0.0740233i
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$		−	2.00000i		−	0.0738717i	−0.999318	−	0.0369358i	$-0.988240\pi$
$733$		−	2.00000i		−	0.0738717i	0.999318	−	0.0369358i	$-0.0117597\pi$
$734$	13.8564	+	8.00000i	0.511449	+	0.295285i
$735$	−15.5885	−	9.00000i	−0.574989	−	0.331970i
$736$		0			0
$737$	−32.0000	+	55.4256i	−1.17874	+	2.04163i
$738$	5.00000	+	8.66025i	0.184053	+	0.318788i
$739$	−34.6410	+	20.0000i	−1.27429	+	0.735712i	−0.975793	−	0.218698i	$-0.929819\pi$
$739$	−34.6410	+	20.0000i	−1.27429	+	0.735712i	−0.298498	+	0.954410i	$0.596486\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	40.0000			1.46845
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	−0.830197	−	0.557470i	$-0.811772\pi$
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	0.0676840	+	0.997707i	$0.478439\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$		−	6.00000i		−	0.219676i
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$	−6.92820	−	4.00000i	−0.253320	−	0.146254i
$749$		−	48.0000i		−	1.75388i
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	−6.92820	+	4.00000i	−0.252646	+	0.145865i
$753$	4.00000			0.145768
$754$		0			0
$755$	24.0000			0.873449
$756$	−3.46410	+	2.00000i	−0.125988	+	0.0727393i
$757$	−27.0000	−	46.7654i	−0.981332	−	1.69972i	−0.657222	−	0.753697i	$-0.728269\pi$
$757$	−27.0000	−	46.7654i	−0.981332	−	1.69972i	−0.324109	−	0.946020i	$-0.605065\pi$
$758$		0			0
$759$		0			0
$760$	−13.8564	−	8.00000i	−0.502625	−	0.290191i
$761$	−22.5167	−	13.0000i	−0.816228	−	0.471250i	0.0328858	−	0.999459i	$-0.489530\pi$
$761$	−22.5167	−	13.0000i	−0.816228	−	0.471250i	−0.849114	+	0.528209i	$0.822864\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	−3.46410	+	2.00000i	−0.125245	+	0.0723102i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	1.73205	−	1.00000i	0.0624593	−	0.0360609i	−0.468445	−	0.883493i	$-0.655186\pi$
$769$	1.73205	−	1.00000i	0.0624593	−	0.0360609i	0.530904	+	0.847432i	$0.321852\pi$
$770$	−16.0000	−	27.7128i	−0.576600	−	0.998700i
$771$	3.00000	−	5.19615i	0.108042	−	0.187135i
$772$		−	14.0000i		−	0.503871i
$773$	46.7654	+	27.0000i	1.68203	+	0.971123i	0.960307	+	0.278944i	$0.0899843\pi$
$773$	46.7654	+	27.0000i	1.68203	+	0.971123i	0.721726	+	0.692179i	$0.243349\pi$
$774$	−3.46410	−	2.00000i	−0.124515	−	0.0718885i
$775$		−	4.00000i		−	0.143684i
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	4.00000	+	6.92820i	0.143499	+	0.248548i
$778$	−22.5167	+	13.0000i	−0.807261	+	0.466073i
$779$	−80.0000			−2.86630
$780$		0			0
$781$	32.0000			1.14505
$782$		0			0
$783$	3.00000	+	5.19615i	0.107211	+	0.185695i
$784$	4.50000	−	7.79423i	0.160714	−	0.278365i
$785$			28.0000i			0.999363i
$786$	−3.46410	−	2.00000i	−0.123560	−	0.0713376i
$787$	34.6410	+	20.0000i	1.23482	+	0.712923i	0.968031	−	0.250832i	$-0.0807042\pi$
$787$	34.6410	+	20.0000i	1.23482	+	0.712923i	0.266788	+	0.963755i	$0.414038\pi$
$788$		−	18.0000i		−	0.641223i
$789$	4.00000	−	6.92820i	0.142404	−	0.246651i
$790$	−8.00000	−	13.8564i	−0.284627	−	0.492989i
$791$	20.7846	−	12.0000i	0.739016	−	0.426671i
$792$	−4.00000			−0.142134
$793$		0			0
$794$	−6.00000			−0.212932
$795$	17.3205	−	10.0000i	0.614295	−	0.354663i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		−	32.0000i		−	1.13279i
$799$	−13.8564	−	8.00000i	−0.490204	−	0.283020i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		−	14.0000i		−	0.494666i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−4.00000	−	6.92820i	−0.141157	−	0.244491i
$804$	−13.8564	+	8.00000i	−0.488678	+	0.282138i
$805$		0			0
$806$		0			0
$807$	26.0000			0.915243
$808$	1.73205	−	1.00000i	0.0609333	−	0.0351799i
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	0.847911	−	0.530139i	$-0.177860\pi$
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	−0.883069	+	0.469243i	$0.844527\pi$
$810$	−1.00000	+	1.73205i	−0.0351364	+	0.0608581i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−20.7846	−	12.0000i	−0.729397	−	0.421117i
$813$	3.46410	+	2.00000i	0.121491	+	0.0701431i
$814$			8.00000i			0.280400i
$815$	16.0000	−	27.7128i	0.560456	−	0.970737i
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	27.7128	−	16.0000i	0.969549	−	0.559769i
$818$	2.00000			0.0699284
$819$		0			0
$820$	−20.0000			−0.698430
$821$	36.3731	−	21.0000i	1.26943	−	0.732905i	0.294549	−	0.955636i	$-0.404831\pi$
$821$	36.3731	−	21.0000i	1.26943	−	0.732905i	0.974880	+	0.222731i	$0.0714973\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		−	16.0000i		−	0.557386i
$825$	3.46410	+	2.00000i	0.120605	+	0.0696311i
$826$	−13.8564	−	8.00000i	−0.482126	−	0.278356i
$827$		−	28.0000i		−	0.973655i	−0.873498	−	0.486828i	$-0.838154\pi$
$827$		−	28.0000i		−	0.973655i	0.873498	−	0.486828i	$-0.161846\pi$
$828$		0			0
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$	20.7846	−	12.0000i	0.721444	−	0.416526i
$831$	22.0000			0.763172
$832$		0			0
$833$	18.0000			0.623663
$834$	10.3923	−	6.00000i	0.359856	−	0.207763i
$835$		0			0
$836$	16.0000	−	27.7128i	0.553372	−	0.958468i
$837$			4.00000i			0.138260i
$838$	3.46410	+	2.00000i	0.119665	+	0.0690889i
$839$	−34.6410	−	20.0000i	−1.19594	−	0.690477i	−0.236293	−	0.971682i	$-0.575933\pi$
$839$	−34.6410	−	20.0000i	−1.19594	−	0.690477i	−0.959648	+	0.281205i	$0.909266\pi$
$840$		−	8.00000i		−	0.276026i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−11.0000	−	19.0526i	−0.379085	−	0.656595i
$843$	−22.5167	+	13.0000i	−0.775515	+	0.447744i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	−8.00000			−0.275046
$847$	17.3205	−	10.0000i	0.595140	−	0.343604i
$848$	5.00000	+	8.66025i	0.171701	+	0.297394i
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$			2.00000i			0.0685994i
$851$		0			0
$852$	6.92820	+	4.00000i	0.237356	+	0.137038i
$853$			2.00000i			0.0684787i	0.999414	+	0.0342393i	$0.0109009\pi$
$853$			2.00000i			0.0684787i	−0.999414	+	0.0342393i	$0.989099\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	−8.00000	−	13.8564i	−0.273594	−	0.473879i
$856$	10.3923	−	6.00000i	0.355202	−	0.205076i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$	6.92820	−	4.00000i	0.236250	−	0.136399i
$861$	−20.0000	−	34.6410i	−0.681598	−	1.18056i
$862$	4.00000	−	6.92820i	0.136241	−	0.235976i
$863$			40.0000i			1.36162i	0.732462	+	0.680808i	$0.238371\pi$
$863$			40.0000i			1.36162i	−0.732462	+	0.680808i	$0.761629\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−17.3205	−	10.0000i	−0.588915	−	0.340010i
$866$		−	30.0000i		−	1.01944i
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	27.7128	−	16.0000i	0.940093	−	0.542763i
$870$	−12.0000			−0.406838
$871$		0			0
$872$	2.00000			0.0677285
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$	−24.0000	+	41.5692i	−0.811348	+	1.40530i
$876$		−	2.00000i		−	0.0675737i
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	0.142548	−	0.989788i	$-0.454470\pi$
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	−0.785907	+	0.618344i	$0.787804\pi$
$878$	−13.8564	−	8.00000i	−0.467631	−	0.269987i
$879$			26.0000i			0.876958i
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	13.0000	+	22.5167i	0.437981	+	0.758606i	0.997534	−	0.0701893i	$-0.0223603\pi$
$881$	13.0000	+	22.5167i	0.437981	+	0.758606i	−0.559553	+	0.828795i	$0.689027\pi$
$882$	7.79423	−	4.50000i	0.262445	−	0.151523i
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	3.46410	−	2.00000i	0.116379	−	0.0671913i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−1.00000	+	1.73205i	−0.0335578	+	0.0581238i
$889$		0			0
$890$	24.2487	+	14.0000i	0.812819	+	0.469281i
$891$	−3.46410	−	2.00000i	−0.116052	−	0.0670025i
$892$			4.00000i			0.133930i
$893$	32.0000	−	55.4256i	1.07084	−	1.85475i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	20.7846	−	12.0000i	0.694753	−	0.401116i
$896$	4.00000			0.133631
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−20.7846	+	12.0000i	−0.693206	+	0.400222i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	−10.0000	+	17.3205i	−0.333148	+	0.577030i
$902$		−	40.0000i		−	1.33185i
$903$	13.8564	+	8.00000i	0.461112	+	0.266223i
$904$	5.19615	+	3.00000i	0.172821	+	0.0997785i
$905$			20.0000i			0.664822i
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−17.3205	+	10.0000i	−0.574801	+	0.331862i
$909$	2.00000			0.0663358
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	6.92820	−	4.00000i	0.229416	−	0.132453i
$913$	24.0000	+	41.5692i	0.794284	+	1.37574i
$914$	15.0000	−	25.9808i	0.496156	−	0.859367i
$915$			4.00000i			0.132236i
$916$	−19.0526	−	11.0000i	−0.629514	−	0.363450i
$917$	13.8564	+	8.00000i	0.457579	+	0.264183i
$918$		−	2.00000i		−	0.0660098i
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−6.92820	+	4.00000i	−0.228292	+	0.131804i
$922$	−6.00000			−0.197599
$923$		0			0
$924$	16.0000			0.526361
$925$	1.73205	−	1.00000i	0.0569495	−	0.0328798i
$926$	−10.0000	−	17.3205i	−0.328620	−	0.569187i
$927$	8.00000	−	13.8564i	0.262754	−	0.455104i
$928$		−	6.00000i		−	0.196960i
$929$	−39.8372	−	23.0000i	−1.30702	−	0.754606i	−0.325418	−	0.945570i	$-0.605505\pi$
$929$	−39.8372	−	23.0000i	−1.30702	−	0.754606i	−0.981597	+	0.190965i	$0.938838\pi$
$930$	−6.92820	−	4.00000i	−0.227185	−	0.131165i
$931$			72.0000i			2.35970i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$		0			0
$934$	−3.46410	+	2.00000i	−0.113349	+	0.0654420i
$935$	16.0000			0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	55.4256	−	32.0000i	1.80971	−	1.04484i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$	8.00000	−	13.8564i	0.260931	−	0.451946i
$941$		−	46.0000i		−	1.49956i	−0.661689	−	0.749779i	$-0.730160\pi$
$941$		−	46.0000i		−	1.49956i	0.661689	−	0.749779i	$-0.269840\pi$
$942$	−12.1244	−	7.00000i	−0.395033	−	0.228072i
$943$		0			0
$944$		−	4.00000i		−	0.130189i
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	8.00000	+	13.8564i	0.260102	+	0.450511i
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	−0.442659	−	0.896690i	$-0.645965\pi$
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	0.555227	+	0.831699i	$0.312631\pi$
$948$	8.00000			0.259828
$949$		0			0
$950$	−8.00000			−0.259554
$951$	5.19615	−	3.00000i	0.168497	−	0.0972817i
$952$	4.00000	+	6.92820i	0.129641	+	0.224544i
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	−0.999869	−	0.0162081i	$-0.994841\pi$
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	0.513971	+	0.857808i	$0.328174\pi$
$954$			10.0000i			0.323762i
$955$	13.8564	+	8.00000i	0.448383	+	0.258874i
$956$		0			0
$957$		−	24.0000i		−	0.775810i
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	−20.0000	−	34.6410i	−0.645834	−	1.11862i
$960$	1.73205	−	1.00000i	0.0559017	−	0.0322749i
$961$	15.0000			0.483871
$962$		0			0
$963$	12.0000			0.386695
$964$	8.66025	−	5.00000i	0.278928	−	0.161039i
$965$	14.0000	+	24.2487i	0.450676	+	0.780594i
$966$		0			0
$967$			4.00000i			0.128631i	0.997930	+	0.0643157i	$0.0204865\pi$
$967$			4.00000i			0.128631i	−0.997930	+	0.0643157i	$0.979514\pi$
$968$	4.33013	+	2.50000i	0.139176	+	0.0803530i
$969$	13.8564	+	8.00000i	0.445132	+	0.256997i
$970$			20.0000i			0.642161i
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	−0.549058	−	0.835784i	$-0.685013\pi$
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	0.998339	+	0.0576061i	$0.0183467\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−41.5692	+	24.0000i	−1.33265	+	0.769405i
$974$	4.00000			0.128168
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	5.19615	−	3.00000i	0.166240	−	0.0959785i	−0.414572	−	0.910017i	$-0.636069\pi$
$977$	5.19615	−	3.00000i	0.166240	−	0.0959785i	0.580812	+	0.814038i	$0.302735\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$	−28.0000	+	48.4974i	−0.894884	+	1.54998i
$980$			18.0000i			0.574989i
$981$	1.73205	+	1.00000i	0.0553001	+	0.0319275i
$982$	−31.1769	−	18.0000i	−0.994895	−	0.574403i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	5.00000	−	8.66025i	0.159394	−	0.276079i
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$	10.3923	−	6.00000i	0.330958	−	0.191079i
$987$	32.0000			1.01857
$988$		0			0
$989$		0			0
$990$	6.92820	−	4.00000i	0.220193	−	0.127128i
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	0.941618	+	0.336683i	$0.109305\pi$
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	−0.179233	+	0.983807i	$0.557362\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		−	8.00000i		−	0.253872i
$994$	−27.7128	−	16.0000i	−0.878997	−	0.507489i
$995$	−13.8564	−	8.00000i	−0.439278	−	0.253617i
$996$			12.0000i			0.380235i
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$		0			0
$999$	−1.73205	+	1.00000i	−0.0547997	+	0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.d.361.1		4
13.2	odd	12		78.2.a.a.1.1	✓	1
13.3	even	3		1014.2.b.b.337.1		2
13.4	even	6	inner	1014.2.i.d.823.1		4
13.5	odd	4		1014.2.e.f.991.1		2
13.6	odd	12		1014.2.e.f.529.1		2
13.7	odd	12		1014.2.e.c.529.1		2
13.8	odd	4		1014.2.e.c.991.1		2
13.9	even	3	inner	1014.2.i.d.823.2		4
13.10	even	6		1014.2.b.b.337.2		2
13.11	odd	12		1014.2.a.d.1.1		1
13.12	even	2	inner	1014.2.i.d.361.2		4
39.2	even	12		234.2.a.c.1.1		1
39.11	even	12		3042.2.a.f.1.1		1
39.23	odd	6		3042.2.b.g.1351.1		2
39.29	odd	6		3042.2.b.g.1351.2		2
52.11	even	12		8112.2.a.v.1.1		1
52.15	even	12		624.2.a.h.1.1		1
65.2	even	12		1950.2.e.i.1249.1		2
65.28	even	12		1950.2.e.i.1249.2		2
65.54	odd	12		1950.2.a.w.1.1		1
91.41	even	12		3822.2.a.j.1.1		1
104.67	even	12		2496.2.a.b.1.1		1
104.93	odd	12		2496.2.a.t.1.1		1
117.2	even	12		2106.2.e.j.1405.1		2
117.41	even	12		2106.2.e.j.703.1		2
117.67	odd	12		2106.2.e.q.703.1		2
117.106	odd	12		2106.2.e.q.1405.1		2
143.54	even	12		9438.2.a.t.1.1		1
156.119	odd	12		1872.2.a.c.1.1		1
195.2	odd	12		5850.2.e.bb.5149.2		2
195.119	even	12		5850.2.a.d.1.1		1
195.158	odd	12		5850.2.e.bb.5149.1		2
312.197	even	12		7488.2.a.bz.1.1		1
312.275	odd	12		7488.2.a.bk.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.a.a.1.1	✓	1	13.2	odd	12
234.2.a.c.1.1		1	39.2	even	12
624.2.a.h.1.1		1	52.15	even	12
1014.2.a.d.1.1		1	13.11	odd	12
1014.2.b.b.337.1		2	13.3	even	3
1014.2.b.b.337.2		2	13.10	even	6
1014.2.e.c.529.1		2	13.7	odd	12
1014.2.e.c.991.1		2	13.8	odd	4
1014.2.e.f.529.1		2	13.6	odd	12
1014.2.e.f.991.1		2	13.5	odd	4
1014.2.i.d.361.1		4	1.1	even	1	trivial
1014.2.i.d.361.2		4	13.12	even	2	inner
1014.2.i.d.823.1		4	13.4	even	6	inner
1014.2.i.d.823.2		4	13.9	even	3	inner
1872.2.a.c.1.1		1	156.119	odd	12
1950.2.a.w.1.1		1	65.54	odd	12
1950.2.e.i.1249.1		2	65.2	even	12
1950.2.e.i.1249.2		2	65.28	even	12
2106.2.e.j.703.1		2	117.41	even	12
2106.2.e.j.1405.1		2	117.2	even	12
2106.2.e.q.703.1		2	117.67	odd	12
2106.2.e.q.1405.1		2	117.106	odd	12
2496.2.a.b.1.1		1	104.67	even	12
2496.2.a.t.1.1		1	104.93	odd	12
3042.2.a.f.1.1		1	39.11	even	12
3042.2.b.g.1351.1		2	39.23	odd	6
3042.2.b.g.1351.2		2	39.29	odd	6
3822.2.a.j.1.1		1	91.41	even	12
5850.2.a.d.1.1		1	195.119	even	12
5850.2.e.bb.5149.1		2	195.158	odd	12
5850.2.e.bb.5149.2		2	195.2	odd	12
7488.2.a.bk.1.1		1	312.275	odd	12
7488.2.a.bz.1.1		1	312.197	even	12
8112.2.a.v.1.1		1	52.11	even	12
9438.2.a.t.1.1		1	143.54	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(3.46410 - 2.00000i) q^{11} +1.00000 q^{12} -4.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(6.92820 + 4.00000i) q^{19} +(1.73205 + 1.00000i) q^{20} +4.00000i q^{21} +(-2.00000 + 3.46410i) q^{22} +(-0.866025 + 0.500000i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(3.46410 - 2.00000i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{30} -4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.46410 + 2.00000i) q^{33} +2.00000i q^{34} +(-4.00000 + 6.92820i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.73205 - 1.00000i) q^{37} -8.00000 q^{38} -2.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(2.00000 - 3.46410i) q^{43} -4.00000i q^{44} +(-1.73205 - 1.00000i) q^{45} -8.00000i q^{47} +(0.500000 - 0.866025i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.00000 q^{51} -10.0000 q^{53} +(0.866025 - 0.500000i) q^{54} +(4.00000 + 6.92820i) q^{55} +(-2.00000 + 3.46410i) q^{56} +8.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(3.46410 + 2.00000i) q^{59} +2.00000i q^{60} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-3.46410 + 2.00000i) q^{63} -1.00000 q^{64} -4.00000 q^{66} +(-13.8564 + 8.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000i q^{70} +(6.92820 + 4.00000i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(6.92820 - 4.00000i) q^{76} +16.0000 q^{77} +8.00000 q^{79} +(1.73205 - 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +12.0000i q^{83} +(3.46410 + 2.00000i) q^{84} +(3.46410 + 2.00000i) q^{85} +4.00000i q^{86} +(3.00000 - 5.19615i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-12.1244 + 7.00000i) q^{89} +2.00000 q^{90} +(3.46410 - 2.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +1.00000i q^{96} +(-8.66025 - 5.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{10} + 4 q^{12} - 16 q^{14} - 2 q^{16} + 4 q^{17} - 8 q^{22} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 4 q^{30} - 16 q^{35} + 2 q^{36} - 32 q^{38} - 8 q^{40} - 8 q^{42}+ \cdots - 32 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^10 + 4 * q^12 - 16 * q^14 - 2 * q^16 + 4 * q^17 - 8 * q^22 + 4 * q^25 - 4 * q^27 - 12 * q^29 + 4 * q^30 - 16 * q^35 + 2 * q^36 - 32 * q^38 - 8 * q^40 - 8 * q^42 + 8 * q^43 + 2 * q^48 + 18 * q^49 + 8 * q^51 - 40 * q^53 + 16 * q^55 - 8 * q^56 + 4 * q^61 + 8 * q^62 - 4 * q^64 - 16 * q^66 - 4 * q^68 - 4 * q^74 + 2 * q^75 + 64 * q^77 + 32 * q^79 - 2 * q^81 + 20 * q^82 + 12 * q^87 + 8 * q^88 + 8 * q^90 + 16 * q^94 - 32 * q^95

Introduction

L-functions

Modular forms

Varieties

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