LMFDB - Embedded newform 756.2.o.a.359.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.11
Character	$\chi$	$=$	756.359
Dual form			756.2.o.a.179.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04560 + 0.952218i) q^{2} +(0.186562 - 1.99128i) q^{4} +0.501474i q^{5} +(2.46962 - 0.949199i) q^{7} +(1.70106 + 2.25973i) q^{8} +O(q^{10})$	\(q+(-1.04560 + 0.952218i) q^{2} +(0.186562 - 1.99128i) q^{4} +0.501474i q^{5} +(2.46962 - 0.949199i) q^{7} +(1.70106 + 2.25973i) q^{8} +(-0.477513 - 0.524342i) q^{10} +1.69699 q^{11} +(-1.89819 - 3.28776i) q^{13} +(-1.67839 + 3.34410i) q^{14} +(-3.93039 - 0.742994i) q^{16} +(4.12962 - 2.38424i) q^{17} +(0.0919457 + 0.0530849i) q^{19} +(0.998575 + 0.0935560i) q^{20} +(-1.77437 + 1.61590i) q^{22} -7.55994 q^{23} +4.74852 q^{25} +(5.11542 + 1.63020i) q^{26} +(-1.42938 - 5.09479i) q^{28} +(-6.33235 - 3.65598i) q^{29} +(3.51006 + 2.02653i) q^{31} +(4.81711 - 2.96571i) q^{32} +(-2.04762 + 6.42526i) q^{34} +(0.475999 + 1.23845i) q^{35} +(3.83900 - 6.64935i) q^{37} +(-0.146687 + 0.0320468i) q^{38} +(-1.13320 + 0.853039i) q^{40} +(2.60966 - 1.50669i) q^{41} +(3.98023 + 2.29799i) q^{43} +(0.316593 - 3.37917i) q^{44} +(7.90468 - 7.19871i) q^{46} +(2.03670 + 3.52768i) q^{47} +(5.19804 - 4.68832i) q^{49} +(-4.96506 + 4.52163i) q^{50} +(-6.90098 + 3.16646i) q^{52} +(8.79953 - 5.08041i) q^{53} +0.850995i q^{55} +(6.34591 + 3.96603i) q^{56} +(10.1024 - 2.20708i) q^{58} +(1.67896 - 2.90805i) q^{59} +(0.919402 + 1.59245i) q^{61} +(-5.59982 + 1.22340i) q^{62} +(-2.21277 + 7.68789i) q^{64} +(1.64873 - 0.951893i) q^{65} +(-3.38415 - 1.95384i) q^{67} +(-3.97726 - 8.66804i) q^{68} +(-1.67698 - 0.841670i) q^{70} +9.65339 q^{71} +(5.55175 + 9.61592i) q^{73} +(2.31756 + 10.6081i) q^{74} +(0.122860 - 0.173186i) q^{76} +(4.19091 - 1.61078i) q^{77} +(-4.07338 + 2.35177i) q^{79} +(0.372592 - 1.97099i) q^{80} +(-1.29397 + 4.06036i) q^{82} +(-6.75864 + 11.7063i) q^{83} +(1.19563 + 2.07090i) q^{85} +(-6.34992 + 1.38727i) q^{86} +(2.88668 + 3.83473i) q^{88} +(-4.73824 - 2.73562i) q^{89} +(-7.80855 - 6.31776i) q^{91} +(-1.41040 + 15.0540i) q^{92} +(-5.48870 - 1.74915i) q^{94} +(-0.0266207 + 0.0461084i) q^{95} +(6.45605 - 11.1822i) q^{97} +(-0.970771 + 9.85178i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.04560	+	0.952218i	−0.739351	+	0.673320i
$2$	−1.04560	+	0.952218i	−0.739351	+	0.673320i
$3$		0			0
$3$		0			0
$4$	0.186562	−	1.99128i	0.0932810	−	0.995640i
$5$			0.501474i			0.224266i	0.993693	+	0.112133i	$0.0357683\pi$
$5$			0.501474i			0.224266i	−0.993693	+	0.112133i	$0.964232\pi$
$6$		0			0
$7$	2.46962	−	0.949199i	0.933428	−	0.358764i
$7$	2.46962	−	0.949199i	0.933428	−	0.358764i
$8$	1.70106	+	2.25973i	0.601417	+	0.798936i
$9$		0			0
$10$	−0.477513	−	0.524342i	−0.151003	−	0.165811i
$11$	1.69699			0.511661			0.255830	−	0.966722i	$-0.417651\pi$
$11$	1.69699			0.511661			0.255830	+	0.966722i	$0.417651\pi$
$12$		0			0
$13$	−1.89819	−	3.28776i	−0.526463	−	0.911861i	−0.999525	−	0.0308317i	$-0.990184\pi$
$13$	−1.89819	−	3.28776i	−0.526463	−	0.911861i	0.473061	−	0.881030i	$-0.343149\pi$
$14$	−1.67839	+	3.34410i	−0.448569	+	0.893748i
$15$		0			0
$16$	−3.93039	−	0.742994i	−0.982597	−	0.185749i
$17$	4.12962	−	2.38424i	1.00158	−	0.578263i	0.0928651	−	0.995679i	$-0.470397\pi$
$17$	4.12962	−	2.38424i	1.00158	−	0.578263i	0.908716	+	0.417416i	$0.137064\pi$
$18$		0			0
$19$	0.0919457	+	0.0530849i	0.0210938	+	0.0121785i	0.510510	−	0.859872i	$-0.329457\pi$
$19$	0.0919457	+	0.0530849i	0.0210938	+	0.0121785i	−0.489416	+	0.872050i	$0.662790\pi$
$20$	0.998575	+	0.0935560i	0.223288	+	0.0209198i
$21$		0			0
$22$	−1.77437	+	1.61590i	−0.378297	+	0.344511i
$23$	−7.55994			−1.57636			−0.788178	−	0.615447i	$-0.788976\pi$
$23$	−7.55994			−1.57636			−0.788178	+	0.615447i	$0.788976\pi$
$24$		0			0
$25$	4.74852			0.949705
$26$	5.11542	+	1.63020i	1.00322	+	0.319708i
$27$		0			0
$28$	−1.42938	−	5.09479i	−0.270128	−	0.962824i
$29$	−6.33235	−	3.65598i	−1.17589	−	0.678899i	−0.220828	−	0.975313i	$-0.570876\pi$
$29$	−6.33235	−	3.65598i	−1.17589	−	0.678899i	−0.955060	+	0.296413i	$0.904209\pi$
$30$		0			0
$31$	3.51006	+	2.02653i	0.630425	+	0.363976i	0.780917	−	0.624635i	$-0.214752\pi$
$31$	3.51006	+	2.02653i	0.630425	+	0.363976i	−0.150492	+	0.988611i	$0.548086\pi$
$32$	4.81711	−	2.96571i	0.851553	−	0.524269i
$33$		0			0
$34$	−2.04762	+	6.42526i	−0.351164	+	1.10192i
$35$	0.475999	+	1.23845i	0.0804585	+	0.209336i
$36$		0			0
$37$	3.83900	−	6.64935i	0.631128	−	1.09315i	−0.356193	−	0.934412i	$-0.615926\pi$
$37$	3.83900	−	6.64935i	0.631128	−	1.09315i	0.987321	−	0.158734i	$-0.0507411\pi$
$38$	−0.146687	+	0.0320468i	−0.0237957	+	0.00519867i
$39$		0			0
$40$	−1.13320	+	0.853039i	−0.179174	+	0.134877i
$41$	2.60966	−	1.50669i	0.407560	−	0.235305i	−0.282181	−	0.959361i	$-0.591058\pi$
$41$	2.60966	−	1.50669i	0.407560	−	0.235305i	0.689741	+	0.724056i	$0.257724\pi$
$42$		0			0
$43$	3.98023	+	2.29799i	0.606980	+	0.350440i	0.771783	−	0.635887i	$-0.219365\pi$
$43$	3.98023	+	2.29799i	0.606980	+	0.350440i	−0.164803	+	0.986327i	$0.552699\pi$
$44$	0.316593	−	3.37917i	0.0477282	−	0.509430i
$45$		0			0
$46$	7.90468	−	7.19871i	1.16548	−	1.06139i
$47$	2.03670	+	3.52768i	0.297084	+	0.514564i	0.975467	−	0.220144i	$-0.0706526\pi$
$47$	2.03670	+	3.52768i	0.297084	+	0.514564i	−0.678384	+	0.734708i	$0.737319\pi$
$48$		0			0
$49$	5.19804	−	4.68832i	0.742577	−	0.669760i
$50$	−4.96506	+	4.52163i	−0.702166	+	0.639455i
$51$		0			0
$52$	−6.90098	+	3.16646i	−0.956994	+	0.439109i
$53$	8.79953	−	5.08041i	1.20871	−	0.697848i	0.246231	−	0.969211i	$-0.420808\pi$
$53$	8.79953	−	5.08041i	1.20871	−	0.697848i	0.962477	+	0.271363i	$0.0874745\pi$
$54$		0			0
$55$			0.850995i			0.114748i
$56$	6.34591	+	3.96603i	0.848008	+	0.529983i
$57$		0			0
$58$	10.1024	−	2.20708i	1.32651	−	0.289804i
$59$	1.67896	−	2.90805i	0.218582	−	0.378595i	−0.735793	−	0.677207i	$-0.763190\pi$
$59$	1.67896	−	2.90805i	0.218582	−	0.378595i	0.954375	+	0.298612i	$0.0965235\pi$
$60$		0			0
$61$	0.919402	+	1.59245i	0.117717	+	0.203893i	0.918863	−	0.394577i	$-0.129109\pi$
$61$	0.919402	+	1.59245i	0.117717	+	0.203893i	−0.801145	+	0.598470i	$0.795776\pi$
$62$	−5.59982	+	1.22340i	−0.711178	+	0.155371i
$63$		0			0
$64$	−2.21277	+	7.68789i	−0.276596	+	0.960986i
$65$	1.64873	−	0.951893i	0.204499	−	0.118068i
$66$		0			0
$67$	−3.38415	−	1.95384i	−0.413440	−	0.238699i	0.278827	−	0.960341i	$-0.410054\pi$
$67$	−3.38415	−	1.95384i	−0.413440	−	0.238699i	−0.692267	+	0.721642i	$0.743388\pi$
$68$	−3.97726	−	8.66804i	−0.482313	−	1.05115i
$69$		0			0
$70$	−1.67698	−	0.841670i	−0.200437	−	0.100599i
$71$	9.65339			1.14565			0.572823	−	0.819679i	$-0.305848\pi$
$71$	9.65339			1.14565			0.572823	+	0.819679i	$0.305848\pi$
$72$		0			0
$73$	5.55175	+	9.61592i	0.649784	+	1.12546i	0.983174	+	0.182670i	$0.0584738\pi$
$73$	5.55175	+	9.61592i	0.649784	+	1.12546i	−0.333391	+	0.942789i	$0.608193\pi$
$74$	2.31756	+	10.6081i	0.269411	+	1.23317i
$75$		0			0
$76$	0.122860	−	0.173186i	0.0140931	−	0.0198658i
$77$	4.19091	−	1.61078i	0.477599	−	0.183565i
$78$		0			0
$79$	−4.07338	+	2.35177i	−0.458291	+	0.264595i	−0.711326	−	0.702863i	$-0.751905\pi$
$79$	−4.07338	+	2.35177i	−0.458291	+	0.264595i	0.253034	+	0.967457i	$0.418572\pi$
$80$	0.372592	−	1.97099i	0.0416571	−	0.220363i
$81$		0			0
$82$	−1.29397	+	4.06036i	−0.142895	+	0.448392i
$83$	−6.75864	+	11.7063i	−0.741858	+	1.28494i	0.209791	+	0.977746i	$0.432722\pi$
$83$	−6.75864	+	11.7063i	−0.741858	+	1.28494i	−0.951649	+	0.307189i	$0.900612\pi$
$84$		0			0
$85$	1.19563	+	2.07090i	0.129685	+	0.224621i
$86$	−6.34992	+	1.38727i	−0.684730	+	0.149593i
$87$		0			0
$88$	2.88668	+	3.83473i	0.307721	+	0.408784i
$89$	−4.73824	−	2.73562i	−0.502252	−	0.289975i	0.227391	−	0.973804i	$-0.426980\pi$
$89$	−4.73824	−	2.73562i	−0.502252	−	0.289975i	−0.729643	+	0.683828i	$0.760314\pi$
$90$		0			0
$91$	−7.80855	−	6.31776i	−0.818558	−	0.662281i
$92$	−1.41040	+	15.0540i	−0.147044	+	1.56948i
$93$		0			0
$94$	−5.48870	−	1.74915i	−0.566116	−	0.180411i
$95$	−0.0266207	+	0.0461084i	−0.00273122	+	0.00473062i
$96$		0			0
$97$	6.45605	−	11.1822i	0.655512	−	1.13538i	−0.326253	−	0.945283i	$-0.605786\pi$
$97$	6.45605	−	11.1822i	0.655512	−	1.13538i	0.981765	−	0.190098i	$-0.0608806\pi$
$98$	−0.970771	+	9.85178i	−0.0980627	+	0.995180i
$99$		0			0
$100$	0.885894	−	9.45564i	0.0885894	−	0.945564i
$101$		−	10.4778i		−	1.04258i	−0.853380	−	0.521289i	$-0.825451\pi$
$101$		−	10.4778i		−	1.04258i	0.853380	−	0.521289i	$-0.174549\pi$
$102$		0			0
$103$			19.0141i			1.87352i	0.349975	+	0.936759i	$0.386190\pi$
$103$			19.0141i			1.87352i	−0.349975	+	0.936759i	$0.613810\pi$
$104$	4.20052	−	9.88209i	0.411895	−	0.969019i
$105$		0			0
$106$	−4.36314	+	13.6911i	−0.423785	+	1.32980i
$107$	5.50504	−	9.53502i	0.532193	−	0.921785i	−0.467101	−	0.884204i	$-0.654702\pi$
$107$	5.50504	−	9.53502i	0.532193	−	0.921785i	0.999294	−	0.0375808i	$-0.0119652\pi$
$108$		0			0
$109$	2.16757	+	3.75434i	0.207615	+	0.359600i	0.950963	−	0.309305i	$-0.100096\pi$
$109$	2.16757	+	3.75434i	0.207615	+	0.359600i	−0.743348	+	0.668905i	$0.766763\pi$
$110$	−0.810332	−	0.889801i	−0.0772622	−	0.0848392i
$111$		0			0
$112$	−10.4118	+	1.89581i	−0.983824	+	0.179137i
$113$	−2.92804	+	1.69051i	−0.275447	+	0.159029i	−0.631360	−	0.775490i	$-0.717503\pi$
$113$	−2.92804	+	1.69051i	−0.275447	+	0.159029i	0.355913	+	0.934519i	$0.384170\pi$
$114$		0			0
$115$		−	3.79111i		−	0.353523i
$116$	−8.46146	+	11.9274i	−0.785627	+	1.10743i
$117$		0			0
$118$	1.01357	+	4.63939i	0.0933067	+	0.427091i
$119$	7.93548	−	9.80800i	0.727444	−	0.899098i
$120$		0			0
$121$	−8.12024			−0.738203
$122$	−2.47769	−	0.789597i	−0.224319	−	0.0714868i
$123$		0			0
$124$	4.69024	−	6.61143i	0.421196	−	0.593724i
$125$			4.88863i			0.437253i
$126$		0			0
$127$			8.51215i			0.755332i	0.925942	+	0.377666i	$0.123273\pi$
$127$			8.51215i			0.755332i	−0.925942	+	0.377666i	$0.876727\pi$
$128$	−5.00687	−	10.1455i	−0.442549	−	0.896744i
$129$		0			0
$130$	−0.817501	+	2.56525i	−0.0716996	+	0.224987i
$131$	8.42036			0.735690			0.367845	−	0.929887i	$-0.380096\pi$
$131$	8.42036			0.735690			0.367845	+	0.929887i	$0.380096\pi$
$132$		0			0
$133$	0.277459	+	0.0438246i	0.0240587	+	0.00380008i
$134$	5.39895	−	1.17951i	0.466398	−	0.101894i
$135$		0			0
$136$	12.4125	+	5.27610i	1.06436	+	0.452422i
$137$			4.25362i			0.363411i	0.983353	+	0.181706i	$0.0581618\pi$
$137$			4.25362i			0.363411i	−0.983353	+	0.181706i	$0.941838\pi$
$138$		0			0
$139$	−0.535435	+	0.309134i	−0.0454150	+	0.0262204i	−0.522536	−	0.852617i	$-0.675014\pi$
$139$	−0.535435	+	0.309134i	−0.0454150	+	0.0262204i	0.477121	+	0.878838i	$0.341680\pi$
$140$	2.55490	−	0.716799i	0.215929	−	0.0605806i
$141$		0			0
$142$	−10.0936	+	9.19213i	−0.847035	+	0.771386i
$143$	−3.22120	−	5.57929i	−0.269371	−	0.466564i
$144$		0			0
$145$	1.83338	−	3.17551i	0.152254	−	0.263712i
$146$	−14.9614	−	4.76793i	−1.23821	−	0.394597i
$147$		0			0
$148$	−12.5245	−	8.88504i	−1.02951	−	0.730346i
$149$		−	6.01223i		−	0.492541i	−0.969201	−	0.246270i	$-0.920795\pi$
$149$		−	6.01223i		−	0.492541i	0.969201	−	0.246270i	$-0.0792051\pi$
$150$		0			0
$151$		−	22.1543i		−	1.80289i	−0.432895	−	0.901444i	$-0.642508\pi$
$151$		−	22.1543i		−	1.80289i	0.432895	−	0.901444i	$-0.357492\pi$
$152$	0.0364479	+	0.298073i	0.00295631	+	0.0241769i
$153$		0			0
$154$	−2.84821	+	5.67489i	−0.229515	+	0.457296i
$155$	−1.01625	+	1.76020i	−0.0816275	+	0.141383i
$156$		0			0
$157$	−1.94908	+	3.37590i	−0.155553	+	0.269426i	−0.933260	−	0.359200i	$-0.883049\pi$
$157$	−1.94908	+	3.37590i	−0.155553	+	0.269426i	0.777707	+	0.628627i	$0.216383\pi$
$158$	2.01974	−	6.33776i	0.160682	−	0.504205i
$159$		0			0
$160$	1.48723	+	2.41566i	0.117576	+	0.190974i
$161$	−18.6702	+	7.17589i	−1.47142	+	0.565539i
$162$		0			0
$163$	−16.9101	−	9.76307i	−1.32450	−	0.764703i	−0.340060	−	0.940404i	$-0.610447\pi$
$163$	−16.9101	−	9.76307i	−1.32450	−	0.764703i	−0.984444	+	0.175701i	$0.943781\pi$
$164$	−2.51337	−	5.47765i	−0.196261	−	0.427733i
$165$		0			0
$166$	−4.08012	−	18.6758i	−0.316679	−	1.44953i
$167$	2.20243	+	3.81473i	0.170430	+	0.295193i	0.938570	−	0.345089i	$-0.112151\pi$
$167$	2.20243	+	3.81473i	0.170430	+	0.295193i	−0.768141	+	0.640281i	$0.778818\pi$
$168$		0			0
$169$	−0.706255	+	1.22327i	−0.0543273	+	0.0940976i
$170$	−3.22210	−	1.02683i	−0.247124	−	0.0787542i
$171$		0			0
$172$	5.31850	−	7.49704i	0.405532	−	0.571644i
$173$	−15.5563	+	8.98141i	−1.18272	+	0.682844i	−0.956642	−	0.291265i	$-0.905924\pi$
$173$	−15.5563	+	8.98141i	−1.18272	+	0.682844i	−0.226078	+	0.974109i	$0.572590\pi$
$174$		0			0
$175$	11.7270	−	4.50730i	0.886481	−	0.340720i
$176$	−6.66982	−	1.26085i	−0.502756	−	0.0950402i
$177$		0			0
$178$	7.55921	−	1.65146i	0.566587	−	0.123783i
$179$	4.24475	+	7.35212i	0.317267	+	0.549523i	0.979917	−	0.199406i	$-0.0639014\pi$
$179$	4.24475	+	7.35212i	0.317267	+	0.549523i	−0.662649	+	0.748930i	$0.730568\pi$
$180$		0			0
$181$	−24.6598			−1.83295			−0.916476	−	0.400090i	$-0.868979\pi$
$181$	−24.6598			−1.83295			−0.916476	+	0.400090i	$0.868979\pi$
$182$	14.1805	−	0.829586i	1.05113	−	0.0614930i
$183$		0			0
$184$	−12.8599	−	17.0834i	−0.948047	−	1.25941i
$185$	3.33447	+	1.92516i	0.245155	+	0.141541i
$186$		0			0
$187$	7.00791	−	4.04602i	0.512469	−	0.295874i
$188$	7.40456	−	3.39752i	0.540033	−	0.247789i
$189$		0			0
$190$	−0.0160706	−	0.0735596i	−0.00116589	−	0.00533658i
$191$	−2.96036	−	5.12749i	−0.214204	−	0.371012i	0.738822	−	0.673901i	$-0.235382\pi$
$191$	−2.96036	−	5.12749i	−0.214204	−	0.371012i	−0.953026	+	0.302888i	$0.902049\pi$
$192$		0			0
$193$	−8.24353	+	14.2782i	−0.593382	+	1.02777i	0.400391	+	0.916344i	$0.368874\pi$
$193$	−8.24353	+	14.2782i	−0.593382	+	1.02777i	−0.993773	+	0.111423i	$0.964459\pi$
$194$	3.89745	+	17.8397i	0.279820	+	1.28081i
$195$		0			0
$196$	−8.36600	−	11.2254i	−0.597572	−	0.801815i
$197$		−	4.24471i		−	0.302423i	−0.988501	−	0.151212i	$-0.951683\pi$
$197$		−	4.24471i		−	0.302423i	0.988501	−	0.151212i	$-0.0483175\pi$
$198$		0			0
$199$	−18.9984	+	10.9688i	−1.34676	+	0.777555i	−0.987790	−	0.155793i	$-0.950207\pi$
$199$	−18.9984	+	10.9688i	−1.34676	+	0.777555i	−0.358974	+	0.933347i	$0.616873\pi$
$200$	8.07754	+	10.7304i	0.571168	+	0.758753i
$201$		0			0
$202$	9.97713	+	10.9556i	0.701988	+	0.770831i
$203$	−19.1088	−	3.01823i	−1.34117	−	0.211838i
$204$		0			0
$205$	0.755565	+	1.30868i	0.0527709	+	0.0914019i
$206$	−18.1056	−	19.8812i	−1.26148	−	1.38519i
$207$		0			0
$208$	5.01784	+	14.3325i	0.347925	+	0.993782i
$209$	0.156031	+	0.0900843i	0.0107929	+	0.00623126i
$210$		0			0
$211$	8.25342	−	4.76511i	0.568189	−	0.328044i	−0.188237	−	0.982124i	$-0.560277\pi$
$211$	8.25342	−	4.76511i	0.568189	−	0.328044i	0.756426	+	0.654080i	$0.226944\pi$
$212$	−8.47486	−	18.4701i	−0.582056	−	1.26853i
$213$		0			0
$214$	3.32334	+	15.2118i	0.227179	+	1.03986i
$215$	−1.15238	+	1.99598i	−0.0785918	+	0.136125i
$216$		0			0
$217$	10.5921	+	1.67302i	0.719038	+	0.113572i
$218$	−5.84136	−	1.86154i	−0.395627	−	0.126079i
$219$		0			0
$220$	1.69457	+	0.158763i	0.114248	+	0.0107038i
$221$	−15.6776	−	9.05148i	−1.05459	−	0.608868i
$222$		0			0
$223$	9.02007	+	5.20774i	0.604029	+	0.348736i	0.770625	−	0.637289i	$-0.219944\pi$
$223$	9.02007	+	5.20774i	0.604029	+	0.348736i	−0.166596	+	0.986025i	$0.553278\pi$
$224$	9.08138	−	11.8966i	0.606775	−	0.794874i
$225$		0			0
$226$	1.45183	−	4.55573i	0.0965745	−	0.303042i
$227$	5.79790			0.384820			0.192410	−	0.981315i	$-0.438370\pi$
$227$	5.79790			0.384820			0.192410	+	0.981315i	$0.438370\pi$
$228$		0			0
$229$	−4.93361			−0.326022			−0.163011	−	0.986624i	$-0.552121\pi$
$229$	−4.93361			−0.326022			−0.163011	+	0.986624i	$0.552121\pi$
$230$	3.60997	+	3.96399i	0.238034	+	0.261378i
$231$		0			0
$232$	−2.51019	−	20.5285i	−0.164802	−	1.34776i
$233$	9.83606	+	5.67885i	0.644382	+	0.372034i	0.786300	−	0.617844i	$-0.211994\pi$
$233$	9.83606	+	5.67885i	0.644382	+	0.372034i	−0.141919	+	0.989878i	$0.545327\pi$
$234$		0			0
$235$	−1.76904	+	1.02135i	−0.115399	+	0.0666258i
$236$	−5.47750	−	3.88581i	−0.356555	−	0.252945i
$237$		0			0
$238$	1.04201	+	17.8116i	0.0675434	+	1.15455i
$239$	−7.21752	−	12.5011i	−0.466862	−	0.808629i	0.532421	−	0.846480i	$-0.321282\pi$
$239$	−7.21752	−	12.5011i	−0.466862	−	0.808629i	−0.999283	+	0.0378504i	$0.987949\pi$
$240$		0			0
$241$	−14.0809			−0.907030			−0.453515	−	0.891249i	$-0.649830\pi$
$241$	−14.0809			−0.907030			−0.453515	+	0.891249i	$0.649830\pi$
$242$	8.49053	−	7.73224i	0.545792	−	0.497047i
$243$		0			0
$244$	3.34254	−	1.53370i	0.213984	−	0.0981848i
$245$	2.35107	+	2.60668i	0.150204	+	0.166535i
$246$		0			0
$247$		−	0.403061i		−	0.0256461i
$248$	1.39141	+	11.3791i	0.0883546	+	0.722570i
$249$		0			0
$250$	−4.65504	−	5.11156i	−0.294411	−	0.323283i
$251$	−25.2044			−1.59089			−0.795445	−	0.606026i	$-0.792763\pi$
$251$	−25.2044			−1.59089			−0.795445	+	0.606026i	$0.792763\pi$
$252$		0			0
$253$	−12.8291			−0.806560
$254$	−8.10543	−	8.90031i	−0.508580	−	0.558455i
$255$		0			0
$256$	14.8959	+	5.84051i	0.930995	+	0.365032i
$257$			7.12209i			0.444264i	0.975017	+	0.222132i	$0.0713016\pi$
$257$			7.12209i			0.444264i	−0.975017	+	0.222132i	$0.928698\pi$
$258$		0			0
$259$	3.16932	−	20.0653i	0.196932	−	1.24680i
$260$	−1.58790	−	3.46066i	−0.0984771	−	0.214621i
$261$		0			0
$262$	−8.80433	+	8.01802i	−0.543934	+	0.495355i
$263$	−27.3916			−1.68904			−0.844520	−	0.535524i	$-0.820114\pi$
$263$	−27.3916			−1.68904			−0.844520	+	0.535524i	$0.820114\pi$
$264$		0			0
$265$	2.54769	+	4.41273i	0.156504	+	0.271072i
$266$	−0.331842	+	0.218378i	−0.0203465	+	0.0133896i
$267$		0			0
$268$	−4.52199	+	6.37427i	−0.276225	+	0.389371i
$269$	−4.90694	+	2.83302i	−0.299181	+	0.172732i	−0.642075	−	0.766642i	$-0.721926\pi$
$269$	−4.90694	+	2.83302i	−0.299181	+	0.172732i	0.342894	+	0.939374i	$0.388593\pi$
$270$		0			0
$271$	14.0632	+	8.11940i	0.854279	+	0.493218i	0.862092	−	0.506751i	$-0.169154\pi$
$271$	14.0632	+	8.11940i	0.854279	+	0.493218i	−0.00781341	+	0.999969i	$0.502487\pi$
$272$	−18.0025	+	6.30270i	−1.09156	+	0.382157i
$273$		0			0
$274$	−4.05037	−	4.44759i	−0.244692	−	0.268689i
$275$	8.05818			0.485927
$276$		0			0
$277$	−2.77634			−0.166814			−0.0834071	−	0.996516i	$-0.526580\pi$
$277$	−2.77634			−0.166814			−0.0834071	+	0.996516i	$0.526580\pi$
$278$	0.265489	−	0.833081i	0.0159230	−	0.0499649i
$279$		0			0
$280$	−1.98886	+	3.18231i	−0.118857	+	0.190179i
$281$	25.4336	+	14.6841i	1.51724	+	0.875981i	0.999795	+	0.0202663i	$0.00645142\pi$
$281$	25.4336	+	14.6841i	1.51724	+	0.875981i	0.517448	+	0.855714i	$0.326882\pi$
$282$		0			0
$283$	26.5510	+	15.3292i	1.57829	+	0.911227i	0.995098	+	0.0988943i	$0.0315306\pi$
$283$	26.5510	+	15.3292i	1.57829	+	0.911227i	0.583194	+	0.812333i	$0.301803\pi$
$284$	1.80095	−	19.2226i	0.106867	−	1.14065i
$285$		0			0
$286$	8.68079	+	2.76642i	0.513306	+	0.163582i
$287$	5.01472	−	6.19803i	0.296010	−	0.365858i
$288$		0			0
$289$	2.86919	−	4.96958i	0.168776	−	0.292328i
$290$	1.10679	+	5.06609i	0.0649931	+	0.297491i
$291$		0			0
$292$	20.1837	−	9.26113i	1.18116	−	0.541967i
$293$	1.86213	−	1.07510i	0.108787	−	0.0628079i	−0.444620	−	0.895720i	$-0.646661\pi$
$293$	1.86213	−	1.07510i	0.108787	−	0.0628079i	0.553406	+	0.832912i	$0.313328\pi$
$294$		0			0
$295$	1.45831	+	0.841955i	0.0849060	+	0.0490205i
$296$	21.5561	−	2.63584i	1.25292	−	0.153205i
$297$		0			0
$298$	5.72495	+	6.28639i	0.331637	+	0.364161i
$299$	14.3502	+	24.8553i	0.829894	+	1.43742i
$300$		0			0
$301$	12.0109	+	1.89712i	0.692297	+	0.109348i
$302$	21.0957	+	23.1645i	1.21392	+	1.33297i
$303$		0			0
$304$	−0.321941	−	0.276959i	−0.0184646	−	0.0158847i
$305$	−0.798573	+	0.461056i	−0.0457262	+	0.0264000i
$306$		0			0
$307$			19.1505i			1.09298i	0.837467	+	0.546488i	$0.184036\pi$
$307$			19.1505i			1.09298i	−0.837467	+	0.546488i	$0.815964\pi$
$308$	−2.42565	−	8.64579i	−0.138214	−	0.492639i
$309$		0			0
$310$	−0.613501	−	2.80817i	−0.0348445	−	0.159493i
$311$	2.84561	−	4.92873i	0.161360	−	0.279483i	−0.773997	−	0.633189i	$-0.781745\pi$
$311$	2.84561	−	4.92873i	0.161360	−	0.279483i	0.935357	+	0.353706i	$0.115079\pi$
$312$		0			0
$313$	12.3072	+	21.3167i	0.695645	+	1.20489i	0.969963	+	0.243254i	$0.0782147\pi$
$313$	12.3072	+	21.3167i	0.695645	+	1.20489i	−0.274318	+	0.961639i	$0.588452\pi$
$314$	−1.17664	−	5.38580i	−0.0664015	−	0.303938i
$315$		0			0
$316$	3.92309	+	8.55000i	0.220691	+	0.480975i
$317$	10.2861	−	5.93871i	0.577728	−	0.333551i	−0.182502	−	0.983205i	$-0.558420\pi$
$317$	10.2861	−	5.93871i	0.577728	−	0.333551i	0.760230	+	0.649654i	$0.225086\pi$
$318$		0			0
$319$	−10.7459	−	6.20416i	−0.601656	−	0.347366i
$320$	−3.85528	−	1.10965i	−0.215517	−	0.0620311i
$321$		0			0
$322$	12.6885	−	25.2812i	0.707105	−	1.40887i
$323$	0.506268			0.0281695
$324$		0			0
$325$	−9.01360	−	15.6120i	−0.499985	−	0.865999i
$326$	26.9778	−	5.89386i	1.49416	−	0.326431i
$327$		0			0
$328$	7.84390	+	3.33416i	0.433107	+	0.184098i
$329$	8.37835	+	6.77878i	0.461914	+	0.373726i
$330$		0			0
$331$	−13.8173	+	7.97740i	−0.759466	+	0.438478i	−0.829104	−	0.559094i	$-0.811149\pi$
$331$	−13.8173	+	7.97740i	−0.759466	+	0.438478i	0.0696381	+	0.997572i	$0.477816\pi$
$332$	22.0496	+	15.6423i	1.21013	+	0.858483i
$333$		0			0
$334$	−5.93532	−	1.89149i	−0.324766	−	0.103497i
$335$	0.979800	−	1.69706i	0.0535322	−	0.0927204i
$336$		0			0
$337$	6.26967	+	10.8594i	0.341531	+	0.591549i	0.984717	−	0.174161i	$-0.0557213\pi$
$337$	6.26967	+	10.8594i	0.341531	+	0.591549i	−0.643186	+	0.765710i	$0.722388\pi$
$338$	−0.426358	−	1.95156i	−0.0231908	−	0.106151i
$339$		0			0
$340$	4.34680	−	1.99449i	0.235738	−	0.108166i
$341$	5.95652	+	3.43900i	0.322564	+	0.186232i
$342$		0			0
$343$	8.38703	−	16.5123i	0.452857	−	0.891583i
$344$	1.57779	+	12.9033i	0.0850688	+	0.695698i
$345$		0			0
$346$	7.71338	−	24.2039i	0.414674	−	1.30121i
$347$	−11.6384	+	20.1584i	−0.624784	+	1.08216i	0.363799	+	0.931478i	$0.381480\pi$
$347$	−11.6384	+	20.1584i	−0.624784	+	1.08216i	−0.988583	+	0.150680i	$0.951854\pi$
$348$		0			0
$349$	−11.9434	+	20.6866i	−0.639317	+	1.10733i	0.346266	+	0.938136i	$0.387449\pi$
$349$	−11.9434	+	20.6866i	−0.639317	+	1.10733i	−0.985583	+	0.169193i	$0.945884\pi$
$350$	−7.96988	+	15.8795i	−0.426008	+	0.848797i
$351$		0			0
$352$	8.17457	−	5.03277i	0.435706	−	0.268248i
$353$			30.4841i			1.62251i	0.584695	+	0.811253i	$0.301214\pi$
$353$			30.4841i			1.62251i	−0.584695	+	0.811253i	$0.698786\pi$
$354$		0			0
$355$			4.84092i			0.256930i
$356$	−6.33136	+	8.92479i	−0.335561	+	0.473013i
$357$		0			0
$358$	−11.4391	−	3.64546i	−0.604577	−	0.192668i
$359$	−8.47002	+	14.6705i	−0.447031	+	0.774280i	−0.998191	−	0.0601193i	$-0.980852\pi$
$359$	−8.47002	+	14.6705i	−0.447031	+	0.774280i	0.551160	+	0.834399i	$0.314185\pi$
$360$		0			0
$361$	−9.49436	−	16.4447i	−0.499703	−	0.865512i
$362$	25.7844	−	23.4815i	1.35520	−	1.23416i
$363$		0			0
$364$	−14.0372	+	14.3704i	−0.735750	+	0.753211i
$365$	−4.82213	+	2.78406i	−0.252402	+	0.145724i
$366$		0			0
$367$		−	14.1754i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$367$		−	14.1754i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$368$	29.7135	+	5.61699i	1.54892	+	0.292806i
$369$		0			0
$370$	−5.31970	+	1.16220i	−0.276558	+	0.0604198i
$371$	16.9092	−	20.8992i	0.877880	−	1.08503i
$372$		0			0
$373$	−2.71462			−0.140558			−0.0702790	−	0.997527i	$-0.522389\pi$
$373$	−2.71462			−0.140558			−0.0702790	+	0.997527i	$0.522389\pi$
$374$	−3.47479	+	10.9036i	−0.179677	+	0.563811i
$375$		0			0
$376$	−4.50704	+	10.6032i	−0.232433	+	0.546818i
$377$			27.7590i			1.42966i
$378$		0			0
$379$		−	14.5807i		−	0.748961i	−0.927235	−	0.374480i	$-0.877821\pi$
$379$		−	14.5807i		−	0.748961i	0.927235	−	0.374480i	$-0.122179\pi$
$380$	0.0868483	+	0.0616113i	0.00445522	+	0.00316059i
$381$		0			0
$382$	7.97784	+	2.54240i	0.408182	+	0.130081i
$383$	22.2221			1.13549			0.567747	−	0.823203i	$-0.307815\pi$
$383$	22.2221			1.13549			0.567747	+	0.823203i	$0.307815\pi$
$384$		0			0
$385$	0.807764	+	2.10163i	0.0411674	+	0.107109i
$386$	−4.97653	−	22.7789i	−0.253299	−	1.15942i
$387$		0			0
$388$	−21.0624	−	14.9420i	−1.06928	−	0.758564i
$389$		−	8.11722i		−	0.411560i	−0.978598	−	0.205780i	$-0.934027\pi$
$389$		−	8.11722i		−	0.411560i	0.978598	−	0.205780i	$-0.0659731\pi$
$390$		0			0
$391$	−31.2197	+	18.0247i	−1.57885	+	0.911549i
$392$	19.4365	+	3.77104i	0.981694	+	0.190467i
$393$		0			0
$394$	4.04189	+	4.43827i	0.203627	+	0.223597i
$395$	−1.17935	−	2.04270i	−0.0593396	−	0.102779i
$396$		0			0
$397$	8.63142	−	14.9501i	0.433199	−	0.750322i	−0.563948	−	0.825810i	$-0.690718\pi$
$397$	8.63142	−	14.9501i	0.433199	−	0.750322i	0.997147	+	0.0754882i	$0.0240515\pi$
$398$	9.42014	−	29.5596i	0.472189	−	1.48169i
$399$		0			0
$400$	−18.6635	−	3.52812i	−0.933177	−	0.176406i
$401$			0.908634i			0.0453750i	0.999743	+	0.0226875i	$0.00722228\pi$
$401$			0.908634i			0.0453750i	−0.999743	+	0.0226875i	$0.992778\pi$
$402$		0			0
$403$		−	15.3870i		−	0.766480i
$404$	−20.8642	−	1.95475i	−1.03803	−	0.0972527i
$405$		0			0
$406$	22.8541	−	15.0398i	1.13423	−	0.746415i
$407$	6.51473	−	11.2839i	0.322923	−	0.559320i
$408$		0			0
$409$	17.3097	−	29.9813i	0.855909	−	1.48248i	−0.0198905	−	0.999802i	$-0.506332\pi$
$409$	17.3097	−	29.9813i	0.855909	−	1.48248i	0.875799	−	0.482675i	$-0.160335\pi$
$410$	−2.03616	−	0.648891i	−0.100559	−	0.0320464i
$411$		0			0
$412$	37.8625	+	3.54731i	1.86535	+	0.174764i
$413$	1.38608	−	8.77543i	0.0682045	−	0.431811i
$414$		0			0
$415$	−5.87041	−	3.38929i	−0.288167	−	0.166373i
$416$	−18.8944	−	10.2080i	−0.926372	−	0.500490i
$417$		0			0
$418$	−0.248926	+	0.0543829i	−0.0121753	+	0.00265996i
$419$	18.7089	+	32.4047i	0.913989	+	1.58308i	0.808375	+	0.588668i	$0.200347\pi$
$419$	18.7089	+	32.4047i	0.913989	+	1.58308i	0.105614	+	0.994407i	$0.466319\pi$
$420$		0			0
$421$	−2.84045	+	4.91981i	−0.138435	+	0.239777i	−0.926904	−	0.375297i	$-0.877541\pi$
$421$	−2.84045	+	4.91981i	−0.138435	+	0.239777i	0.788469	+	0.615074i	$0.210874\pi$
$422$	−4.09235	+	12.8415i	−0.199213	+	0.625113i
$423$		0			0
$424$	26.4489	+	11.2425i	1.28447	+	0.545983i
$425$	19.6096	−	11.3216i	0.951206	−	0.549179i
$426$		0			0
$427$	3.78213	+	3.06005i	0.183030	+	0.148086i
$428$	−17.9599	−	12.7410i	−0.868122	−	0.615857i
$429$		0			0
$430$	−0.695680	−	3.18432i	−0.0335487	−	0.153562i
$431$	5.53553	+	9.58782i	0.266637	+	0.461829i	0.967991	−	0.250984i	$-0.0807541\pi$
$431$	5.53553	+	9.58782i	0.266637	+	0.461829i	−0.701354	+	0.712813i	$0.747421\pi$
$432$		0			0
$433$	13.1104			0.630044			0.315022	−	0.949084i	$-0.397988\pi$
$433$	13.1104			0.630044			0.315022	+	0.949084i	$0.397988\pi$
$434$	−12.6682	+	8.33667i	−0.608092	+	0.400173i
$435$		0			0
$436$	7.88032	−	3.61582i	0.377399	−	0.173166i
$437$	−0.695104	−	0.401318i	−0.0332513	−	0.0191977i
$438$		0			0
$439$	−30.8719	+	17.8239i	−1.47343	+	0.850687i	−0.999553	−	0.0299023i	$-0.990480\pi$
$439$	−30.8719	+	17.8239i	−1.47343	+	0.850687i	−0.473880	+	0.880589i	$0.657147\pi$
$440$	−1.92302	+	1.44760i	−0.0916763	+	0.0690114i
$441$		0			0
$442$	25.0115	−	5.46428i	1.18968	−	0.259909i
$443$	−5.98203	−	10.3612i	−0.284215	−	0.492275i	0.688204	−	0.725518i	$-0.258400\pi$
$443$	−5.98203	−	10.3612i	−0.284215	−	0.492275i	−0.972419	+	0.233243i	$0.925066\pi$
$444$		0			0
$445$	1.37184	−	2.37610i	0.0650316	−	0.112638i
$446$	−14.3903	+	3.14386i	−0.681400	+	0.148866i
$447$		0			0
$448$	1.83264	+	21.0865i	0.0865841	+	0.996245i
$449$		−	2.61389i		−	0.123357i	−0.998096	−	0.0616786i	$-0.980355\pi$
$449$		−	2.61389i		−	0.123357i	0.998096	−	0.0616786i	$-0.0196454\pi$
$450$		0			0
$451$	4.42856	−	2.55683i	0.208533	−	0.120396i
$452$	2.82001	+	6.14593i	0.132642	+	0.289080i
$453$		0			0
$454$	−6.06229	+	5.52087i	−0.284517	+	0.259107i
$455$	3.16819	−	3.91579i	0.148527	−	0.183575i
$456$		0			0
$457$	−8.89303	−	15.4032i	−0.415998	−	0.720530i	0.579534	−	0.814948i	$-0.303234\pi$
$457$	−8.89303	−	15.4032i	−0.415998	−	0.720530i	−0.995533	+	0.0944176i	$0.969901\pi$
$458$	5.15859	−	4.69787i	0.241045	−	0.219517i
$459$		0			0
$460$	−7.54917	−	0.707278i	−0.351982	−	0.0329770i
$461$	−28.0337	−	16.1853i	−1.30566	−	0.753824i	−0.324293	−	0.945957i	$-0.605126\pi$
$461$	−28.0337	−	16.1853i	−1.30566	−	0.753824i	−0.981369	+	0.192133i	$0.938460\pi$
$462$		0			0
$463$	20.5925	−	11.8891i	0.957015	−	0.552533i	0.0617618	−	0.998091i	$-0.480328\pi$
$463$	20.5925	−	11.8891i	0.957015	−	0.552533i	0.895253	+	0.445558i	$0.146995\pi$
$464$	22.1722	+	19.0743i	1.02932	+	0.885504i
$465$		0			0
$466$	−15.6921	+	3.42826i	−0.726922	+	0.158811i
$467$	−3.53691	+	6.12611i	−0.163669	+	0.283483i	−0.936182	−	0.351516i	$-0.885666\pi$
$467$	−3.53691	+	6.12611i	−0.163669	+	0.283483i	0.772513	+	0.634999i	$0.219000\pi$
$468$		0			0
$469$	−10.2121	−	1.61301i	−0.471553	−	0.0744818i
$470$	0.877155	−	2.75244i	0.0404602	−	0.126961i
$471$		0			0
$472$	9.42742	−	1.15277i	0.433932	−	0.0530604i
$473$	6.75440	+	3.89966i	0.310568	+	0.179306i
$474$		0			0
$475$	0.436606	+	0.252075i	0.0200329	+	0.0115660i
$476$	−18.0500	−	17.6316i	−0.827321	−	0.808141i
$477$		0			0
$478$	19.4504	+	6.19852i	0.889641	+	0.283514i
$479$	−15.2543			−0.696985			−0.348492	−	0.937312i	$-0.613306\pi$
$479$	−15.2543			−0.696985			−0.348492	+	0.937312i	$0.613306\pi$
$480$		0			0
$481$	−29.1486			−1.32906
$482$	14.7230	−	13.4081i	0.670614	−	0.610721i
$483$		0			0
$484$	−1.51493	+	16.1697i	−0.0688603	+	0.734985i
$485$	5.60759	+	3.23754i	0.254627	+	0.147009i
$486$		0			0
$487$	−11.0078	+	6.35536i	−0.498811	+	0.287989i	−0.728222	−	0.685341i	$-0.759653\pi$
$487$	−11.0078	+	6.35536i	−0.498811	+	0.287989i	0.229411	+	0.973330i	$0.426320\pi$
$488$	−2.03455	+	4.78646i	−0.0920998	+	0.216673i
$489$		0			0
$490$	−4.94041	−	0.486817i	−0.223185	−	0.0219921i
$491$	−12.0966	−	20.9519i	−0.545911	−	0.945546i	−0.998549	−	0.0538515i	$-0.982850\pi$
$491$	−12.0966	−	20.9519i	−0.545911	−	0.945546i	0.452638	−	0.891695i	$-0.350483\pi$
$492$		0			0
$493$	−34.8670			−1.57033
$494$	0.383802	+	0.421441i	0.0172681	+	0.0189615i
$495$		0			0
$496$	−12.2902	−	10.5730i	−0.551846	−	0.474743i
$497$	23.8402	−	9.16299i	1.06938	−	0.411016i
$498$		0			0
$499$			16.1724i			0.723977i	0.932182	+	0.361989i	$0.117902\pi$
$499$			16.1724i			0.723977i	−0.932182	+	0.361989i	$0.882098\pi$
$500$	9.73463	+	0.912033i	0.435346	+	0.0407873i
$501$		0			0
$502$	26.3538	−	24.0001i	1.17623	−	1.07118i
$503$	5.44592			0.242822			0.121411	−	0.992602i	$-0.461258\pi$
$503$	5.44592			0.242822			0.121411	+	0.992602i	$0.461258\pi$
$504$		0			0
$505$	5.25433			0.233815
$506$	13.4141	−	12.2161i	0.596331	−	0.543073i
$507$		0			0
$508$	16.9501	+	1.58804i	0.752038	+	0.0704581i
$509$			7.37130i			0.326727i	0.986566	+	0.163364i	$0.0522343\pi$
$509$			7.37130i			0.326727i	−0.986566	+	0.163364i	$0.947766\pi$
$510$		0			0
$511$	22.8381	+	18.4779i	1.01030	+	0.817416i
$512$	−21.1366	+	8.07732i	−0.934116	+	0.356970i
$513$		0			0
$514$	−6.78178	−	7.44687i	−0.299132	−	0.328467i
$515$	−9.53510			−0.420166
$516$		0			0
$517$	3.45626	+	5.98642i	0.152006	+	0.263282i
$518$	15.7927	+	23.9982i	0.693893	+	1.05442i
$519$		0			0
$520$	4.95561	+	2.10645i	0.217318	+	0.0923740i
$521$	0.235443	−	0.135933i	0.0103150	−	0.00595534i	−0.494834	−	0.868988i	$-0.664771\pi$
$521$	0.235443	−	0.135933i	0.0103150	−	0.00595534i	0.505149	+	0.863032i	$0.331438\pi$
$522$		0			0
$523$	−7.10967	−	4.10477i	−0.310884	−	0.179489i	0.336438	−	0.941706i	$-0.390778\pi$
$523$	−7.10967	−	4.10477i	−0.310884	−	0.179489i	−0.647322	+	0.762217i	$0.724111\pi$
$524$	1.57092	−	16.7673i	0.0686259	−	0.732482i
$525$		0			0
$526$	28.6407	−	26.0828i	1.24879	−	1.13726i
$527$	19.3270			0.841896
$528$		0			0
$529$	34.1527			1.48490
$530$	−6.86576	−	2.18800i	−0.298229	−	0.0950406i
$531$		0			0
$532$	0.139030	−	0.544322i	0.00602773	−	0.0235994i
$533$	−9.90726	−	5.71996i	−0.429131	−	0.247759i
$534$		0			0
$535$	4.78156	+	2.76064i	0.206725	+	0.119353i
$536$	−1.34150	−	10.9709i	−0.0579439	−	0.473869i
$537$		0			0
$538$	2.43304	−	7.63468i	0.104896	−	0.329154i
$539$	8.82101	−	7.95602i	0.379948	−	0.342690i
$540$		0			0
$541$	−14.2672	+	24.7116i	−0.613396	+	1.06243i	0.377267	+	0.926104i	$0.376864\pi$
$541$	−14.2672	+	24.7116i	−0.613396	+	1.06243i	−0.990664	+	0.136329i	$0.956469\pi$
$542$	−22.4359	+	4.90159i	−0.963706	+	0.210541i
$543$		0			0
$544$	12.8219	−	23.7324i	0.549734	−	1.01752i
$545$	−1.88270	+	1.08698i	−0.0806461	+	0.0465611i
$546$		0			0
$547$	9.56519	+	5.52246i	0.408978	+	0.236123i	0.690350	−	0.723475i	$-0.257456\pi$
$547$	9.56519	+	5.52246i	0.408978	+	0.236123i	−0.281373	+	0.959599i	$0.590790\pi$
$548$	8.47015	+	0.793564i	0.361827	+	0.0338994i
$549$		0			0
$550$	−8.42564	+	7.67314i	−0.359271	+	0.327184i
$551$	−0.388155	−	0.672304i	−0.0165360	−	0.0286411i
$552$		0			0
$553$	−7.82741	+	9.67443i	−0.332855	+	0.411399i
$554$	2.90295	−	2.64368i	0.123334	−	0.112319i
$555$		0			0
$556$	0.515680	+	1.12387i	0.0218697	+	0.0476629i
$557$	−4.13074	+	2.38488i	−0.175025	+	0.101051i	−0.584953	−	0.811067i	$-0.698887\pi$
$557$	−4.13074	+	2.38488i	−0.175025	+	0.101051i	0.409928	+	0.912118i	$0.365554\pi$
$558$		0			0
$559$		−	17.4481i		−	0.737975i
$560$	−0.950700	−	5.22126i	−0.0401744	−	0.220638i
$561$		0			0
$562$	−40.5759	+	8.86464i	−1.71159	+	0.373932i
$563$	−6.00983	+	10.4093i	−0.253284	+	0.438701i	−0.964428	−	0.264346i	$-0.914844\pi$
$563$	−6.00983	+	10.4093i	−0.253284	+	0.438701i	0.711144	+	0.703046i	$0.248177\pi$
$564$		0			0
$565$	−0.847745	−	1.46834i	−0.0356649	−	0.0617734i
$566$	−42.3585	+	9.25408i	−1.78046	+	0.388978i
$567$		0			0
$568$	16.4210	+	21.8141i	0.689011	+	0.915298i
$569$	−11.9089	+	6.87561i	−0.499247	+	0.288240i	−0.728403	−	0.685149i	$-0.759737\pi$
$569$	−11.9089	+	6.87561i	−0.499247	+	0.288240i	0.229156	+	0.973390i	$0.426404\pi$
$570$		0			0
$571$	−36.8309	−	21.2643i	−1.54133	−	0.889885i	−0.998755	−	0.0498746i	$-0.984118\pi$
$571$	−36.8309	−	21.2643i	−1.54133	−	0.889885i	−0.542570	−	0.840010i	$-0.682549\pi$
$572$	−11.7109	+	5.37343i	−0.489656	+	0.224675i
$573$		0			0
$574$	0.658483	+	11.2558i	0.0274846	+	0.469807i
$575$	−35.8986			−1.49707
$576$		0			0
$577$	22.8935	+	39.6527i	0.953069	+	1.65076i	0.738727	+	0.674004i	$0.235427\pi$
$577$	22.8935	+	39.6527i	0.953069	+	1.65076i	0.214341	+	0.976759i	$0.431240\pi$
$578$	1.73210	+	7.92829i	0.0720458	+	0.329774i
$579$		0			0
$580$	−5.98129	−	4.24320i	−0.248360	−	0.176189i
$581$	−5.57965	+	35.3254i	−0.231483	+	1.46555i
$582$		0			0
$583$	14.9327	−	8.62139i	0.618448	−	0.357061i
$584$	−12.2855	+	28.9028i	−0.508378	+	1.19600i
$585$		0			0
$586$	−0.923312	+	2.89727i	−0.0381416	+	0.119685i
$587$	−5.33958	+	9.24842i	−0.220388	+	0.381723i	−0.954926	−	0.296845i	$-0.904066\pi$
$587$	−5.33958	+	9.24842i	−0.220388	+	0.381723i	0.734538	+	0.678568i	$0.237399\pi$
$588$		0			0
$589$	0.215157	+	0.372662i	0.00886537	+	0.0153553i
$590$	−2.32653	+	0.508279i	−0.0957819	+	0.0209255i
$591$		0			0
$592$	−20.0292	+	23.2822i	−0.823195	+	0.956891i
$593$	−29.7776	−	17.1921i	−1.22282	−	0.705995i	−0.257301	−	0.966331i	$-0.582833\pi$
$593$	−29.7776	−	17.1921i	−1.22282	−	0.705995i	−0.965518	+	0.260336i	$0.916167\pi$
$594$		0			0
$595$	4.91846	+	3.97944i	0.201637	+	0.163141i
$596$	−11.9720	−	1.12165i	−0.490393	−	0.0459447i
$597$		0			0
$598$	−38.6722	−	12.3242i	−1.58143	−	0.503973i
$599$	10.8778	−	18.8409i	0.444454	−	0.769818i	−0.553560	−	0.832810i	$-0.686731\pi$
$599$	10.8778	−	18.8409i	0.444454	−	0.769818i	0.998014	+	0.0629918i	$0.0200642\pi$
$600$		0			0
$601$	17.5245	−	30.3533i	0.714839	−	1.23814i	−0.248183	−	0.968713i	$-0.579833\pi$
$601$	17.5245	−	30.3533i	0.714839	−	1.23814i	0.963022	−	0.269424i	$-0.0868334\pi$
$602$	−14.3651	+	9.45337i	−0.585477	+	0.385291i
$603$		0			0
$604$	−44.1153	−	4.13314i	−1.79503	−	0.168175i
$605$		−	4.07209i		−	0.165554i
$606$		0			0
$607$		−	3.60667i		−	0.146390i	−0.997318	−	0.0731951i	$-0.976680\pi$
$607$		−	3.60667i		−	0.146390i	0.997318	−	0.0731951i	$-0.0233196\pi$
$608$	0.600347	−	0.0169688i	0.0243473	−	0.000688175i
$609$		0			0
$610$	0.395962	−	1.24250i	0.0160321	−	0.0503072i
$611$	7.73211	−	13.3924i	0.312808	−	0.541799i
$612$		0			0
$613$	−4.90678	−	8.49879i	−0.198183	−	0.343263i	0.749756	−	0.661714i	$-0.230171\pi$
$613$	−4.90678	−	8.49879i	−0.198183	−	0.343263i	−0.947939	+	0.318451i	$0.896837\pi$
$614$	−18.2354	−	20.0238i	−0.735923	−	0.808094i
$615$		0			0
$616$	10.7689	+	6.73030i	0.433893	+	0.271171i
$617$	18.4047	−	10.6260i	0.740945	−	0.427785i	−0.0814679	−	0.996676i	$-0.525961\pi$
$617$	18.4047	−	10.6260i	0.740945	−	0.427785i	0.822413	+	0.568891i	$0.192627\pi$
$618$		0			0
$619$			28.4810i			1.14475i	0.819992	+	0.572374i	$0.193978\pi$
$619$			28.4810i			1.14475i	−0.819992	+	0.572374i	$0.806022\pi$
$620$	3.31546	+	2.35203i	0.133152	+	0.0944599i
$621$		0			0
$622$	1.71786	+	7.86313i	0.0688800	+	0.315283i
$623$	−14.2983	−	2.25841i	−0.572849	−	0.0904815i
$624$		0			0
$625$	21.2911			0.851644
$626$	−33.1666	−	10.5696i	−1.32560	−	0.422448i
$627$		0			0
$628$	6.35875	+	4.51098i	0.253742	+	0.180008i
$629$		−	36.6124i		−	1.45983i
$630$		0			0
$631$		−	21.2573i		−	0.846239i	−0.906074	−	0.423119i	$-0.860935\pi$
$631$		−	21.2573i		−	0.846239i	0.906074	−	0.423119i	$-0.139065\pi$
$632$	−12.2434	−	5.20424i	−0.487018	−	0.207014i
$633$		0			0
$634$	−5.10026	+	16.0042i	−0.202557	+	0.635607i
$635$	−4.26862			−0.169395
$636$		0			0
$637$	−25.2810	−	8.19060i	−1.00167	−	0.324523i
$638$	17.1436	−	3.74538i	0.678723	−	0.148281i
$639$		0			0
$640$	5.08771	−	2.51082i	0.201109	−	0.0992487i
$641$			36.7687i			1.45228i	0.687548	+	0.726138i	$0.258687\pi$
$641$			36.7687i			1.45228i	−0.687548	+	0.726138i	$0.741313\pi$
$642$		0			0
$643$	0.592243	−	0.341931i	0.0233558	−	0.0134845i	−0.488277	−	0.872689i	$-0.662374\pi$
$643$	0.592243	−	0.341931i	0.0233558	−	0.0134845i	0.511632	+	0.859204i	$0.329041\pi$
$644$	10.8061	+	38.5163i	0.425818	+	1.51775i
$645$		0			0
$646$	−0.529354	+	0.482078i	−0.0208272	+	0.0189671i
$647$	20.1867	+	34.9643i	0.793619	+	1.37459i	0.923712	+	0.383087i	$0.125139\pi$
$647$	20.1867	+	34.9643i	0.793619	+	1.37459i	−0.130093	+	0.991502i	$0.541528\pi$
$648$		0			0
$649$	2.84917	−	4.93491i	0.111840	−	0.193712i
$650$	24.2907	+	7.74102i	0.952759	+	0.303628i
$651$		0			0
$652$	−22.5958	+	31.8514i	−0.884919	+	1.24740i
$653$			0.765132i			0.0299419i	0.999888	+	0.0149710i	$0.00476558\pi$
$653$			0.765132i			0.0299419i	−0.999888	+	0.0149710i	$0.995234\pi$
$654$		0			0
$655$			4.22259i			0.164990i
$656$	−11.3764	+	3.98291i	−0.444175	+	0.155506i
$657$		0			0
$658$	−15.2153	+	0.890122i	−0.593154	+	0.0347006i
$659$	20.6707	−	35.8027i	0.805215	−	1.39467i	−0.110930	−	0.993828i	$-0.535383\pi$
$659$	20.6707	−	35.8027i	0.805215	−	1.39467i	0.916146	−	0.400845i	$-0.131284\pi$
$660$		0			0
$661$	13.5001	−	23.3829i	0.525093	−	0.909488i	−0.474480	−	0.880266i	$-0.657364\pi$
$661$	13.5001	−	23.3829i	0.525093	−	0.909488i	0.999573	−	0.0292215i	$-0.00930282\pi$
$662$	6.85112	−	21.4982i	0.266276	−	0.835553i
$663$		0			0
$664$	−37.9500	+	4.64046i	−1.47275	+	0.180085i
$665$	−0.0219769	+	0.139138i	−0.000852228	+	0.00539556i
$666$		0			0
$667$	47.8722	+	27.6390i	1.85362	+	1.07019i
$668$	8.00708	−	3.67398i	0.309803	−	0.142151i
$669$		0			0
$670$	0.591494	+	2.70743i	0.0228514	+	0.104597i
$671$	1.56021	+	2.70237i	0.0602314	+	0.104324i
$672$		0			0
$673$	14.7318	−	25.5163i	0.567871	−	0.983581i	−0.428906	−	0.903349i	$-0.641101\pi$
$673$	14.7318	−	25.5163i	0.567871	−	0.983581i	0.996776	−	0.0802316i	$-0.0255660\pi$
$674$	−16.8961	−	5.38449i	−0.650813	−	0.207403i
$675$		0			0
$676$	2.30411	+	1.63457i	0.0886196	+	0.0628679i
$677$	14.9223	−	8.61540i	0.573511	−	0.331117i	−0.185040	−	0.982731i	$-0.559241\pi$
$677$	14.9223	−	8.61540i	0.573511	−	0.331117i	0.758550	+	0.651615i	$0.225908\pi$
$678$		0			0
$679$	5.32984	−	33.7439i	0.204541	−	1.29497i
$680$	−2.64583	+	6.22454i	−0.101463	+	0.238700i
$681$		0			0
$682$	−9.50282	+	2.07609i	−0.363882	+	0.0794975i
$683$	−16.6012	−	28.7542i	−0.635228	−	1.10025i	−0.986467	−	0.163962i	$-0.947573\pi$
$683$	−16.6012	−	28.7542i	−0.635228	−	1.10025i	0.351238	−	0.936286i	$-0.385761\pi$
$684$		0			0
$685$	−2.13308			−0.0815008
$686$	6.95387	+	25.2516i	0.265500	+	0.964111i
$687$		0			0
$688$	−13.9365	−	11.9893i	−0.531323	−	0.457087i
$689$	−33.4064	−	19.2872i	−1.27268	−	0.734783i
$690$		0			0
$691$	−9.20826	+	5.31639i	−0.350299	+	0.202245i	−0.664817	−	0.747006i	$-0.731490\pi$
$691$	−9.20826	+	5.31639i	−0.350299	+	0.202245i	0.314518	+	0.949251i	$0.398157\pi$
$692$	14.9823	+	32.6524i	0.569541	+	1.24126i
$693$		0			0
$694$	−7.02599	−	32.1599i	−0.266703	−	1.22077i
$695$	−0.155022	−	0.268507i	−0.00588034	−	0.0101850i
$696$		0			0
$697$	7.18461	−	12.4441i	0.272136	−	0.471354i
$698$	−7.21012	−	33.0027i	−0.272907	−	1.24917i
$699$		0			0
$700$	−6.78747	−	24.1927i	−0.256542	−	0.914399i
$701$		−	14.3639i		−	0.542518i	−0.962506	−	0.271259i	$-0.912560\pi$
$701$		−	14.3639i		−	0.542518i	0.962506	−	0.271259i	$-0.0874399\pi$
$702$		0			0
$703$	0.705959	−	0.407586i	0.0266258	−	0.0153724i
$704$	−3.75504	+	13.0462i	−0.141523	+	0.491699i
$705$		0			0
$706$	−29.0275	−	31.8742i	−1.09247	−	1.19960i
$707$	−9.94550	−	25.8761i	−0.374039	−	0.973172i
$708$		0			0
$709$	11.1763	+	19.3579i	0.419734	+	0.727000i	0.995912	−	0.0903237i	$-0.0287902\pi$
$709$	11.1763	+	19.3579i	0.419734	+	0.727000i	−0.576179	+	0.817324i	$0.695457\pi$
$710$	−4.60961	−	5.06167i	−0.172996	−	0.189961i
$711$		0			0
$712$	−1.87827	−	15.3606i	−0.0703910	−	0.575663i
$713$	−26.5358	−	15.3205i	−0.993775	−	0.573756i
$714$		0			0
$715$	2.79787	−	1.61535i	0.104634	−	0.0604107i
$716$	15.4320	−	7.08086i	0.576722	−	0.264624i
$717$		0			0
$718$	−5.11326	−	23.4048i	−0.190825	−	0.873460i
$719$	−6.77863	+	11.7409i	−0.252800	+	0.437863i	−0.964296	−	0.264828i	$-0.914685\pi$
$719$	−6.77863	+	11.7409i	−0.252800	+	0.437863i	0.711496	+	0.702691i	$0.248018\pi$
$720$		0			0
$721$	18.0482	+	46.9577i	0.672150	+	1.74880i
$722$	25.5863	+	8.15391i	0.952222	+	0.303457i
$723$		0			0
$724$	−4.60059	+	49.1046i	−0.170980	+	1.82496i
$725$	−30.0693	−	17.3605i	−1.11675	−	0.644754i
$726$		0			0
$727$	−18.9137	−	10.9198i	−0.701469	−	0.404993i	0.106425	−	0.994321i	$-0.466059\pi$
$727$	−18.9137	−	10.9198i	−0.701469	−	0.404993i	−0.807894	+	0.589327i	$0.799393\pi$
$728$	0.993607	−	28.3921i	0.0368255	−	1.05228i
$729$		0			0
$730$	2.39099	−	7.50274i	0.0884947	−	0.277689i
$731$	21.9158			0.810586
$732$		0			0
$733$	−47.7005			−1.76186			−0.880929	−	0.473248i	$-0.843081\pi$
$733$	−47.7005			−1.76186			−0.880929	+	0.473248i	$0.843081\pi$
$734$	13.4981	+	14.8219i	0.498225	+	0.547085i
$735$		0			0
$736$	−36.4171	+	22.4206i	−1.34235	+	0.826435i
$737$	−5.74285	−	3.31564i	−0.211541	−	0.122133i
$738$		0			0
$739$	−1.03773	+	0.599135i	−0.0381736	+	0.0220395i	−0.518965	−	0.854795i	$-0.673683\pi$
$739$	−1.03773	+	0.599135i	−0.0381736	+	0.0220395i	0.480792	+	0.876835i	$0.340349\pi$
$740$	4.45562	−	6.28071i	0.163792	−	0.230884i
$741$		0			0
$742$	2.22034	+	37.9534i	0.0815114	+	1.39331i
$743$	14.0688	+	24.3679i	0.516134	+	0.893970i	0.999825	+	0.0187314i	$0.00596273\pi$
$743$	14.0688	+	24.3679i	0.516134	+	0.893970i	−0.483690	+	0.875239i	$0.660704\pi$
$744$		0			0
$745$	3.01497			0.110460
$746$	2.83841	−	2.58491i	0.103922	−	0.0946404i
$747$		0			0
$748$	−6.74935	−	14.7096i	−0.246781	−	0.537834i
$749$	4.54473	−	28.7732i	0.166061	−	1.05135i
$750$		0			0
$751$		−	3.29885i		−	0.120377i	−0.998187	−	0.0601884i	$-0.980830\pi$
$751$		−	3.29885i		−	0.120377i	0.998187	−	0.0601884i	$-0.0191702\pi$
$752$	−5.38400	−	15.3784i	−0.196334	−	0.560792i
$753$		0			0
$754$	−26.4326	−	29.0249i	−0.962620	−	1.05702i
$755$	11.1098			0.404327
$756$		0			0
$757$	5.01338			0.182215			0.0911073	−	0.995841i	$-0.470959\pi$
$757$	5.01338			0.182215			0.0911073	+	0.995841i	$0.470959\pi$
$758$	13.8840	+	15.2456i	0.504290	+	0.553745i
$759$		0			0
$760$	−0.149476	+	0.0182777i	−0.00542206	+	0.000663000i
$761$			12.1178i			0.439269i	0.975582	+	0.219634i	$0.0704864\pi$
$761$			12.1178i			0.439269i	−0.975582	+	0.219634i	$0.929514\pi$
$762$		0			0
$763$	8.91668	+	7.21433i	0.322806	+	0.261176i
$764$	−10.7626	+	4.93831i	−0.389376	+	0.178662i
$765$		0			0
$766$	−23.2354	+	21.1603i	−0.839530	+	0.764551i
$767$	−12.7479			−0.460302
$768$		0			0
$769$	6.90320	+	11.9567i	0.248936	+	0.431170i	0.963231	−	0.268675i	$-0.0865858\pi$
$769$	6.90320	+	11.9567i	0.248936	+	0.431170i	−0.714295	+	0.699845i	$0.753252\pi$
$770$	−2.84581	−	1.42830i	−0.102556	−	0.0514724i
$771$		0			0
$772$	26.8940	+	19.0789i	0.967935	+	0.686666i
$773$	13.5671	−	7.83300i	0.487976	−	0.281733i	−0.235758	−	0.971812i	$-0.575757\pi$
$773$	13.5671	−	7.83300i	0.487976	−	0.281733i	0.723735	+	0.690078i	$0.242424\pi$
$774$		0			0
$775$	16.6676	+	9.62304i	0.598718	+	0.345670i
$776$	36.2509	−	4.43270i	1.30133	−	0.159125i
$777$		0			0
$778$	7.72937	+	8.48737i	0.277111	+	0.304287i
$779$	0.319929			0.0114627
$780$		0			0
$781$	16.3817			0.586182
$782$	15.4799	−	48.5746i	0.553560	−	1.73702i
$783$		0			0
$784$	−23.9137	+	14.5648i	−0.854061	+	0.520172i
$785$	−1.69293	−	0.977413i	−0.0604232	−	0.0348854i
$786$		0			0
$787$	−37.8289	−	21.8405i	−1.34845	−	0.778530i	−0.360423	−	0.932789i	$-0.617368\pi$
$787$	−37.8289	−	21.8405i	−1.34845	−	0.778530i	−0.988030	+	0.154259i	$0.950701\pi$
$788$	−8.45240	−	0.791901i	−0.301104	−	0.0282103i
$789$		0			0
$790$	3.17822	+	1.01285i	0.113076	+	0.0360354i
$791$	−5.62652	+	6.95420i	−0.200056	+	0.247263i
$792$		0			0
$793$	3.49040	−	6.04555i	0.123948	−	0.214684i
$794$	5.21070	+	23.8508i	0.184921	+	0.846433i
$795$		0			0
$796$	18.2975	+	39.8776i	0.648537	+	1.41342i
$797$	44.7621	−	25.8434i	1.58556	−	0.915422i	0.591530	−	0.806283i	$-0.298524\pi$
$797$	44.7621	−	25.8434i	1.58556	−	0.915422i	0.994027	−	0.109139i	$-0.0348092\pi$
$798$		0			0
$799$	16.8216	+	9.71198i	0.595107	+	0.343585i
$800$	22.8742	−	14.0828i	0.808724	−	0.497901i
$801$		0			0
$802$	−0.865218	−	0.950068i	−0.0305519	−	0.0335481i
$803$	9.42125	+	16.3181i	0.332469	+	0.575853i
$804$		0			0
$805$	−3.59852	−	9.36261i	−0.126831	−	0.329989i
$806$	14.6518	+	16.0886i	0.516086	+	0.566698i
$807$		0			0
$808$	23.6770	−	17.8234i	0.832952	−	0.627023i
$809$	18.7111	−	10.8029i	0.657848	−	0.379809i	−0.133608	−	0.991034i	$-0.542656\pi$
$809$	18.7111	−	10.8029i	0.657848	−	0.379809i	0.791457	+	0.611225i	$0.209323\pi$
$810$		0			0
$811$		−	1.10006i		−	0.0386283i	−0.999813	−	0.0193141i	$-0.993852\pi$
$811$		−	1.10006i		−	0.0386283i	0.999813	−	0.0193141i	$-0.00614826\pi$
$812$	−9.57510	+	37.4878i	−0.336020	+	1.31556i
$813$		0			0
$814$	3.93287	+	18.0019i	0.137847	+	0.630965i
$815$	4.89593	−	8.47999i	0.171497	−	0.297041i
$816$		0			0
$817$	0.243977	+	0.422580i	0.00853567	+	0.0147842i
$818$	10.4497	+	47.8310i	0.365364	+	1.67237i
$819$		0			0
$820$	2.74690	−	1.26039i	0.0959259	−	0.0440148i
$821$	−27.2968	+	15.7598i	−0.952666	+	0.550022i	−0.893908	−	0.448250i	$-0.852047\pi$
$821$	−27.2968	+	15.7598i	−0.952666	+	0.550022i	−0.0587579	+	0.998272i	$0.518714\pi$
$822$		0			0
$823$	−17.4069	−	10.0499i	−0.606767	−	0.350317i	0.164932	−	0.986305i	$-0.447260\pi$
$823$	−17.4069	−	10.0499i	−0.606767	−	0.350317i	−0.771699	+	0.635988i	$0.780593\pi$
$824$	−42.9668	+	32.3442i	−1.49682	+	1.12676i
$825$		0			0
$826$	6.90684	+	10.4954i	0.240320	+	0.365183i
$827$	14.3246			0.498114			0.249057	−	0.968489i	$-0.419879\pi$
$827$	14.3246			0.498114			0.249057	+	0.968489i	$0.419879\pi$
$828$		0			0
$829$	15.2497	+	26.4133i	0.529646	+	0.917373i	0.999402	+	0.0345771i	$0.0110084\pi$
$829$	15.2497	+	26.4133i	0.529646	+	0.917373i	−0.469756	+	0.882796i	$0.655658\pi$
$830$	9.36545	−	2.04607i	0.325079	−	0.0710203i
$831$		0			0
$832$	29.4762	−	7.31802i	1.02190	−	0.253707i
$833$	10.2879	−	31.7544i	0.356454	−	1.10022i
$834$		0			0
$835$	−1.91299	+	1.10446i	−0.0662017	+	0.0382215i
$836$	0.208492	−	0.293894i	0.00721086	−	0.0101645i
$837$		0			0
$838$	−50.4184	−	16.0675i	−1.74167	−	0.555042i
$839$	5.36379	−	9.29036i	0.185179	−	0.320739i	−0.758458	−	0.651722i	$-0.774047\pi$
$839$	5.36379	−	9.29036i	0.185179	−	0.320739i	0.943637	+	0.330983i	$0.107380\pi$
$840$		0			0
$841$	12.2325	+	21.1872i	0.421809	+	0.730594i
$842$	−1.71475	−	7.84889i	−0.0590942	−	0.270491i
$843$		0			0
$844$	−7.94890	−	17.3239i	−0.273612	−	0.596312i
$845$	−0.613438	−	0.354168i	−0.0211029	−	0.0121838i
$846$		0			0
$847$	−20.0539	+	7.70772i	−0.689060	+	0.264841i
$848$	−38.3603	+	13.4300i	−1.31730	+	0.461188i
$849$		0			0
$850$	−9.72318	+	30.5105i	−0.333502	+	1.04650i
$851$	−29.0226	+	50.2687i	−0.994883	+	1.72319i
$852$		0			0
$853$	−4.00604	+	6.93866i	−0.137164	+	0.237575i	−0.926422	−	0.376487i	$-0.877132\pi$
$853$	−4.00604	+	6.93866i	−0.137164	+	0.237575i	0.789258	+	0.614062i	$0.210465\pi$
$854$	−6.86843	+	0.401816i	−0.235033	+	0.0137499i
$855$		0			0
$856$	30.9110	−	3.77974i	1.05652	−	0.129189i
$857$		−	9.40860i		−	0.321392i	−0.987004	−	0.160696i	$-0.948626\pi$
$857$		−	9.40860i		−	0.321392i	0.987004	−	0.160696i	$-0.0513738\pi$
$858$		0			0
$859$			8.19858i			0.279732i	0.990170	+	0.139866i	$0.0446672\pi$
$859$			8.19858i			0.279732i	−0.990170	+	0.139866i	$0.955333\pi$
$860$	3.75957	+	2.66709i	0.128200	+	0.0909470i
$861$		0			0
$862$	−14.9177	−	4.75400i	−0.508097	−	0.161922i
$863$	−14.3575	+	24.8680i	−0.488736	+	0.846516i	−0.999916	−	0.0129580i	$-0.995875\pi$
$863$	−14.3575	+	24.8680i	−0.488736	+	0.846516i	0.511180	+	0.859474i	$0.329209\pi$
$864$		0			0
$865$	−4.50394	−	7.80106i	−0.153139	−	0.265244i
$866$	−13.7082	+	12.4839i	−0.465824	+	0.424221i
$867$		0			0
$868$	5.30753	−	20.7797i	0.180149	−	0.705309i
$869$	−6.91248	+	3.99092i	−0.234490	+	0.135383i
$870$		0			0
$871$			14.8350i			0.502666i
$872$	−4.79662	+	11.2845i	−0.162434	+	0.382141i
$873$		0			0
$874$	1.10894	−	0.242272i	0.0375106	−	0.00819496i
$875$	4.64029	+	12.0731i	0.156870	+	0.408144i
$876$		0			0
$877$	−5.94951			−0.200901			−0.100450	−	0.994942i	$-0.532028\pi$
$877$	−5.94951			−0.200901			−0.100450	+	0.994942i	$0.532028\pi$
$878$	15.3074	−	48.0334i	0.516600	−	1.62105i
$879$		0			0
$880$	0.632284	−	3.34474i	0.0213143	−	0.112751i
$881$			20.0536i			0.675622i	0.941214	+	0.337811i	$0.109686\pi$
$881$			20.0536i			0.675622i	−0.941214	+	0.337811i	$0.890314\pi$
$882$		0			0
$883$			1.14562i			0.0385533i	0.999814	+	0.0192766i	$0.00613632\pi$
$883$			1.14562i			0.0385533i	−0.999814	+	0.0192766i	$0.993864\pi$
$884$	−20.9489	+	29.5299i	−0.704587	+	0.993197i
$885$		0			0
$886$	16.1209	+	5.13746i	0.541593	+	0.172596i
$887$	−14.8477			−0.498536			−0.249268	−	0.968435i	$-0.580190\pi$
$887$	−14.8477			−0.498536			−0.249268	+	0.968435i	$0.580190\pi$
$888$		0			0
$889$	8.07973	+	21.0218i	0.270985	+	0.705048i
$890$	0.828167	+	3.79075i	0.0277602	+	0.127066i
$891$		0			0
$892$	12.0529	−	16.9899i	0.403560	−	0.568865i
$893$			0.432473i			0.0144721i
$894$		0			0
$895$	−3.68690	+	2.12863i	−0.123239	+	0.0711523i
$896$	−21.9952	−	20.3030i	−0.734807	−	0.678276i
$897$		0			0
$898$	2.48899	+	2.73309i	0.0830588	+	0.0912043i
$899$	−14.8180	−	25.6654i	−0.494206	−	0.855990i
$900$		0			0
$901$	24.2258	−	41.9603i	0.807079	−	1.39790i
$902$	−2.19584	+	6.89037i	−0.0731136	+	0.229424i
$903$		0			0
$904$	−8.80087	−	3.74093i	−0.292713	−	0.124421i
$905$		−	12.3663i		−	0.411069i
$906$		0			0
$907$			38.9167i			1.29221i	0.763249	+	0.646104i	$0.223603\pi$
$907$			38.9167i			1.29221i	−0.763249	+	0.646104i	$0.776397\pi$
$908$	1.08167	−	11.5452i	0.0358964	−	0.383142i
$909$		0			0
$910$	0.416016	+	7.11116i	0.0137908	+	0.235733i
$911$	−10.5139	+	18.2107i	−0.348342	+	0.603346i	−0.985955	−	0.167010i	$-0.946589\pi$
$911$	−10.5139	+	18.2107i	−0.348342	+	0.603346i	0.637613	+	0.770357i	$0.279922\pi$
$912$		0			0
$913$	−11.4693	+	19.8655i	−0.379579	+	0.657451i
$914$	23.9657	+	7.63747i	0.792716	+	0.252625i
$915$		0			0
$916$	−0.920424	+	9.82420i	−0.0304117	+	0.324601i
$917$	20.7951	−	7.99260i	0.686714	−	0.263939i
$918$		0			0
$919$	16.2723	+	9.39484i	0.536775	+	0.309907i	0.743771	−	0.668435i	$-0.233035\pi$
$919$	16.2723	+	9.39484i	0.536775	+	0.309907i	−0.206996	+	0.978342i	$0.566369\pi$
$920$	8.56690	−	6.44892i	0.282442	−	0.212615i
$921$		0			0
$922$	44.7240	−	9.77088i	1.47291	−	0.321787i
$923$	−18.3240	−	31.7380i	−0.603141	−	1.04467i
$924$		0			0
$925$	18.2296	−	31.5746i	0.599385	−	1.03817i
$926$	−10.2105	+	32.0398i	−0.335539	+	1.05289i
$927$		0			0
$928$	−41.3462	+	1.16865i	−1.35726	+	0.0383628i
$929$	26.6151	−	15.3663i	0.873215	−	0.504151i	0.00479946	−	0.999988i	$-0.498472\pi$
$929$	26.6151	−	15.3663i	0.873215	−	0.504151i	0.868415	+	0.495838i	$0.165139\pi$
$930$		0			0
$931$	0.726816	−	0.155134i	0.0238204	−	0.00508430i
$932$	13.1432	−	18.5269i	0.430520	−	0.606868i
$933$		0			0
$934$	−2.13520	−	9.77338i	−0.0698658	−	0.319795i
$935$	2.02897	+	3.51429i	0.0663546	+	0.114929i
$936$		0			0
$937$	23.7669			0.776431			0.388215	−	0.921569i	$-0.373092\pi$
$937$	23.7669			0.776431			0.388215	+	0.921569i	$0.373092\pi$
$938$	12.2138	−	8.03762i	0.398793	−	0.262438i
$939$		0			0
$940$	1.70377	+	3.71319i	0.0555708	+	0.121111i
$941$	4.75086	+	2.74291i	0.154874	+	0.0894164i	0.575434	−	0.817848i	$-0.304833\pi$
$941$	4.75086	+	2.74291i	0.154874	+	0.0894164i	−0.420560	+	0.907265i	$0.638166\pi$
$942$		0			0
$943$	−19.7289	+	11.3905i	−0.642460	+	0.370925i
$944$	−8.75963	+	10.1823i	−0.285102	+	0.331405i
$945$		0			0
$946$	−10.7757	+	2.35418i	−0.350349	+	0.0765410i
$947$	16.7543	+	29.0194i	0.544443	+	0.943003i	0.998642	+	0.0521027i	$0.0165923\pi$
$947$	16.7543	+	29.0194i	0.544443	+	0.943003i	−0.454199	+	0.890900i	$0.650074\pi$
$948$		0			0
$949$	21.0766	−	36.5057i	0.684175	−	1.18503i
$950$	−0.696546	+	0.152175i	−0.0225989	+	0.00493720i
$951$		0			0
$952$	35.6622	+	1.24803i	1.15582	+	0.0404488i
$953$			21.1120i			0.683884i	0.939721	+	0.341942i	$0.111085\pi$
$953$			21.1120i			0.683884i	−0.939721	+	0.341942i	$0.888915\pi$
$954$		0			0
$955$	2.57130	−	1.48454i	0.0832054	−	0.0480387i
$956$	−26.2397	+	12.0399i	−0.848653	+	0.389397i
$957$		0			0
$958$	15.9499	−	14.5254i	0.515317	−	0.469294i
$959$	4.03753	+	10.5048i	0.130379	+	0.339218i
$960$		0			0
$961$	−7.28632	−	12.6203i	−0.235043	−	0.407106i
$962$	30.4778	−	27.7558i	0.982645	−	0.894884i
$963$		0			0
$964$	−2.62696	+	28.0390i	−0.0846086	+	0.903075i
$965$	−7.16015	−	4.13392i	−0.230493	−	0.133075i
$966$		0			0
$967$	19.5455	−	11.2846i	0.628540	−	0.362888i	−0.151646	−	0.988435i	$-0.548457\pi$
$967$	19.5455	−	11.2846i	0.628540	−	0.362888i	0.780186	+	0.625547i	$0.215124\pi$
$968$	−13.8130	−	18.3496i	−0.443968	−	0.589777i
$969$		0			0
$970$	−8.94614	+	1.95447i	−0.287243	+	0.0627542i
$971$	26.7170	−	46.2752i	0.857388	−	1.48504i	−0.0170228	−	0.999855i	$-0.505419\pi$
$971$	26.7170	−	46.2752i	0.857388	−	1.48504i	0.874411	−	0.485185i	$-0.161248\pi$
$972$		0			0
$973$	−1.02889	+	1.27168i	−0.0329847	+	0.0407681i
$974$	5.45808	−	17.1270i	0.174888	−	0.548784i
$975$		0			0
$976$	−2.43043	−	6.94206i	−0.0777961	−	0.222210i
$977$	22.7320	+	13.1243i	0.727260	+	0.419884i	0.817419	−	0.576044i	$-0.195404\pi$
$977$	22.7320	+	13.1243i	0.727260	+	0.419884i	−0.0901590	+	0.995927i	$0.528738\pi$
$978$		0			0
$979$	−8.04072	−	4.64231i	−0.256983	−	0.148369i
$980$	5.62926	−	4.19533i	0.179820	−	0.134015i
$981$		0			0
$982$	32.5990	+	10.3887i	1.04028	+	0.331518i
$983$	28.7580			0.917239			0.458620	−	0.888633i	$-0.348344\pi$
$983$	28.7580			0.917239			0.458620	+	0.888633i	$0.348344\pi$
$984$		0			0
$985$	2.12861			0.0678232
$986$	36.4569	−	33.2010i	1.16103	−	1.05733i
$987$		0			0
$988$	−0.802607	−	0.0751958i	−0.0255343	−	0.00239230i
$989$	−30.0903	−	17.3727i	−0.956817	−	0.552418i
$990$		0			0
$991$	26.2389	−	15.1490i	0.833506	−	0.481225i	−0.0215459	−	0.999768i	$-0.506859\pi$
$991$	26.2389	−	15.1490i	0.833506	−	0.481225i	0.855051	+	0.518543i	$0.173525\pi$
$992$	22.9185	−	0.647789i	0.727662	−	0.0205673i
$993$		0			0
$994$	−16.2022	+	32.2819i	−0.513901	+	1.02392i
$995$	−5.50055	−	9.52723i	−0.174379	−	0.302033i
$996$		0			0
$997$	20.2489			0.641290			0.320645	−	0.947199i	$-0.396100\pi$
$997$	20.2489			0.641290			0.320645	+	0.947199i	$0.396100\pi$
$998$	−15.3997	−	16.9099i	−0.487468	−	0.535274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.359.11		88
3.2	odd	2		252.2.o.a.191.34	yes	88
4.3	odd	2	inner	756.2.o.a.359.5		88
7.4	even	3		756.2.bb.a.683.18		88
9.4	even	3		252.2.bb.a.23.18	yes	88
9.5	odd	6		756.2.bb.a.611.27		88
12.11	even	2		252.2.o.a.191.40	yes	88
21.11	odd	6		252.2.bb.a.11.27	yes	88
28.11	odd	6		756.2.bb.a.683.27		88
36.23	even	6		756.2.bb.a.611.18		88
36.31	odd	6		252.2.bb.a.23.27	yes	88
63.4	even	3		252.2.o.a.95.40	yes	88
63.32	odd	6	inner	756.2.o.a.179.5		88
84.11	even	6		252.2.bb.a.11.18	yes	88
252.67	odd	6		252.2.o.a.95.34	✓	88
252.95	even	6	inner	756.2.o.a.179.11		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.34	✓	88	252.67	odd	6
252.2.o.a.95.40	yes	88	63.4	even	3
252.2.o.a.191.34	yes	88	3.2	odd	2
252.2.o.a.191.40	yes	88	12.11	even	2
252.2.bb.a.11.18	yes	88	84.11	even	6
252.2.bb.a.11.27	yes	88	21.11	odd	6
252.2.bb.a.23.18	yes	88	9.4	even	3
252.2.bb.a.23.27	yes	88	36.31	odd	6
756.2.o.a.179.5		88	63.32	odd	6	inner
756.2.o.a.179.11		88	252.95	even	6	inner
756.2.o.a.359.5		88	4.3	odd	2	inner
756.2.o.a.359.11		88	1.1	even	1	trivial
756.2.bb.a.611.18		88	36.23	even	6
756.2.bb.a.611.27		88	9.5	odd	6
756.2.bb.a.683.18		88	7.4	even	3
756.2.bb.a.683.27		88	28.11	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04560 + 0.952218i) q^{2} +(0.186562 - 1.99128i) q^{4} +0.501474i q^{5} +(2.46962 - 0.949199i) q^{7} +(1.70106 + 2.25973i) q^{8} +O(q^{10})\)	\(q+(-1.04560 + 0.952218i) q^{2} +(0.186562 - 1.99128i) q^{4} +0.501474i q^{5} +(2.46962 - 0.949199i) q^{7} +(1.70106 + 2.25973i) q^{8} +(-0.477513 - 0.524342i) q^{10} +1.69699 q^{11} +(-1.89819 - 3.28776i) q^{13} +(-1.67839 + 3.34410i) q^{14} +(-3.93039 - 0.742994i) q^{16} +(4.12962 - 2.38424i) q^{17} +(0.0919457 + 0.0530849i) q^{19} +(0.998575 + 0.0935560i) q^{20} +(-1.77437 + 1.61590i) q^{22} -7.55994 q^{23} +4.74852 q^{25} +(5.11542 + 1.63020i) q^{26} +(-1.42938 - 5.09479i) q^{28} +(-6.33235 - 3.65598i) q^{29} +(3.51006 + 2.02653i) q^{31} +(4.81711 - 2.96571i) q^{32} +(-2.04762 + 6.42526i) q^{34} +(0.475999 + 1.23845i) q^{35} +(3.83900 - 6.64935i) q^{37} +(-0.146687 + 0.0320468i) q^{38} +(-1.13320 + 0.853039i) q^{40} +(2.60966 - 1.50669i) q^{41} +(3.98023 + 2.29799i) q^{43} +(0.316593 - 3.37917i) q^{44} +(7.90468 - 7.19871i) q^{46} +(2.03670 + 3.52768i) q^{47} +(5.19804 - 4.68832i) q^{49} +(-4.96506 + 4.52163i) q^{50} +(-6.90098 + 3.16646i) q^{52} +(8.79953 - 5.08041i) q^{53} +0.850995i q^{55} +(6.34591 + 3.96603i) q^{56} +(10.1024 - 2.20708i) q^{58} +(1.67896 - 2.90805i) q^{59} +(0.919402 + 1.59245i) q^{61} +(-5.59982 + 1.22340i) q^{62} +(-2.21277 + 7.68789i) q^{64} +(1.64873 - 0.951893i) q^{65} +(-3.38415 - 1.95384i) q^{67} +(-3.97726 - 8.66804i) q^{68} +(-1.67698 - 0.841670i) q^{70} +9.65339 q^{71} +(5.55175 + 9.61592i) q^{73} +(2.31756 + 10.6081i) q^{74} +(0.122860 - 0.173186i) q^{76} +(4.19091 - 1.61078i) q^{77} +(-4.07338 + 2.35177i) q^{79} +(0.372592 - 1.97099i) q^{80} +(-1.29397 + 4.06036i) q^{82} +(-6.75864 + 11.7063i) q^{83} +(1.19563 + 2.07090i) q^{85} +(-6.34992 + 1.38727i) q^{86} +(2.88668 + 3.83473i) q^{88} +(-4.73824 - 2.73562i) q^{89} +(-7.80855 - 6.31776i) q^{91} +(-1.41040 + 15.0540i) q^{92} +(-5.48870 - 1.74915i) q^{94} +(-0.0266207 + 0.0461084i) q^{95} +(6.45605 - 11.1822i) q^{97} +(-0.970771 + 9.85178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more