LMFDB - Embedded newform 819.2.fn.e.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	819.73
Dual form			819.2.fn.e.460.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.697597 + 2.60347i) q^{2} +(-4.55935 - 2.63234i) q^{4} +(-2.44137 - 0.654162i) q^{5} +(0.722189 + 2.54528i) q^{7} +(6.22207 - 6.22207i) q^{8} +O(q^{10})$	\(q+(-0.697597 + 2.60347i) q^{2} +(-4.55935 - 2.63234i) q^{4} +(-2.44137 - 0.654162i) q^{5} +(0.722189 + 2.54528i) q^{7} +(6.22207 - 6.22207i) q^{8} +(3.40618 - 5.89968i) q^{10} +(-0.557615 - 2.08105i) q^{11} +(1.44703 - 3.30244i) q^{13} +(-7.13035 + 0.104617i) q^{14} +(6.59378 + 11.4208i) q^{16} +(0.700866 - 1.21393i) q^{17} +(2.02208 + 0.541814i) q^{19} +(9.40907 + 9.40907i) q^{20} +5.80693 q^{22} +(1.13887 - 0.657528i) q^{23} +(1.20221 + 0.694099i) q^{25} +(7.58836 + 6.07106i) q^{26} +(3.40733 - 13.5059i) q^{28} +4.56814 q^{29} +(1.88389 + 7.03077i) q^{31} +(-17.3344 + 4.64473i) q^{32} +(2.67152 + 2.67152i) q^{34} +(-0.0981036 - 6.68639i) q^{35} +(-2.20574 - 0.591026i) q^{37} +(-2.82119 + 4.88645i) q^{38} +(-19.2606 + 11.1201i) q^{40} +(2.69291 - 2.69291i) q^{41} +0.437721i q^{43} +(-2.93567 + 10.9561i) q^{44} +(0.917379 + 3.42370i) q^{46} +(-2.07440 + 7.74178i) q^{47} +(-5.95689 + 3.67635i) q^{49} +(-2.64573 + 2.64573i) q^{50} +(-15.2907 + 11.2479i) q^{52} +(-1.26798 + 2.19621i) q^{53} +5.44537i q^{55} +(20.3304 + 11.3434i) q^{56} +(-3.18672 + 11.8930i) q^{58} +(7.54086 - 2.02057i) q^{59} +(6.57067 - 3.79358i) q^{61} -19.6186 q^{62} -21.9945i q^{64} +(-5.69306 + 7.11588i) q^{65} +(-0.548339 + 0.146927i) q^{67} +(-6.39099 + 3.68984i) q^{68} +(17.4762 + 4.40899i) q^{70} +(10.7460 + 10.7460i) q^{71} +(11.8953 - 3.18733i) q^{73} +(3.07743 - 5.33027i) q^{74} +(-7.79312 - 7.79312i) q^{76} +(4.89414 - 2.92219i) q^{77} +(-7.19713 - 12.4658i) q^{79} +(-8.62680 - 32.1956i) q^{80} +(5.13234 + 8.88948i) q^{82} +(3.82648 - 3.82648i) q^{83} +(-2.50518 + 2.50518i) q^{85} +(-1.13959 - 0.305353i) q^{86} +(-16.4179 - 9.47890i) q^{88} +(0.0134247 - 0.0501018i) q^{89} +(9.45066 + 1.29810i) q^{91} -6.92335 q^{92} +(-18.7084 - 10.8013i) q^{94} +(-4.58220 - 2.64553i) q^{95} +(9.43761 - 9.43761i) q^{97} +(-5.41574 - 18.0732i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.697597	+	2.60347i	−0.493276	+	1.84093i	0.0462053	+	0.998932i	$0.485287\pi$
$2$	−0.697597	+	2.60347i	−0.493276	+	1.84093i	−0.539481	+	0.841998i	$0.681379\pi$
$3$		0			0
$3$		0			0
$4$	−4.55935	−	2.63234i	−2.27968	−	1.31617i
$5$	−2.44137	−	0.654162i	−1.09181	−	0.292550i	−0.332386	−	0.943143i	$-0.607854\pi$
$5$	−2.44137	−	0.654162i	−1.09181	−	0.292550i	−0.759426	+	0.650593i	$0.774520\pi$
$6$		0			0
$7$	0.722189	+	2.54528i	0.272962	+	0.962025i
$7$	0.722189	+	2.54528i	0.272962	+	0.962025i
$8$	6.22207	−	6.22207i	2.19983	−	2.19983i
$9$		0			0
$10$	3.40618	−	5.89968i	1.07713	−	1.86564i
$11$	−0.557615	−	2.08105i	−0.168127	−	0.627459i	−0.997621	−	0.0689427i	$-0.978037\pi$
$11$	−0.557615	−	2.08105i	−0.168127	−	0.627459i	0.829493	−	0.558516i	$-0.188629\pi$
$12$		0			0
$13$	1.44703	−	3.30244i	0.401333	−	0.915932i
$13$	1.44703	−	3.30244i	0.401333	−	0.915932i
$14$	−7.13035	+	0.104617i	−1.90567	+	0.0279602i
$15$		0			0
$16$	6.59378	+	11.4208i	1.64844	+	2.85519i
$17$	0.700866	−	1.21393i	0.169985	−	0.294422i	−0.768429	−	0.639935i	$-0.778961\pi$
$17$	0.700866	−	1.21393i	0.169985	−	0.294422i	0.938414	+	0.345512i	$0.112295\pi$
$18$		0			0
$19$	2.02208	+	0.541814i	0.463896	+	0.124301i	0.483194	−	0.875513i	$-0.339476\pi$
$19$	2.02208	+	0.541814i	0.463896	+	0.124301i	−0.0192980	+	0.999814i	$0.506143\pi$
$20$	9.40907	+	9.40907i	2.10393	+	2.10393i
$21$		0			0
$22$	5.80693			1.23804
$23$	1.13887	−	0.657528i	0.237471	−	0.137104i	−0.376543	−	0.926399i	$-0.622887\pi$
$23$	1.13887	−	0.657528i	0.237471	−	0.137104i	0.614014	+	0.789295i	$0.289554\pi$
$24$		0			0
$25$	1.20221	+	0.694099i	0.240443	+	0.138820i
$26$	7.58836	+	6.07106i	1.48820	+	1.19063i
$27$		0			0
$28$	3.40733	−	13.5059i	0.643925	−	2.55237i
$29$	4.56814			0.848282			0.424141	−	0.905596i	$-0.360576\pi$
$29$	4.56814			0.848282			0.424141	+	0.905596i	$0.360576\pi$
$30$		0			0
$31$	1.88389	+	7.03077i	0.338357	+	1.26276i	0.900184	+	0.435509i	$0.143432\pi$
$31$	1.88389	+	7.03077i	0.338357	+	1.26276i	−0.561828	+	0.827254i	$0.689902\pi$
$32$	−17.3344	+	4.64473i	−3.06431	+	0.821079i
$33$		0			0
$34$	2.67152	+	2.67152i	0.458162	+	0.458162i
$35$	−0.0981036	−	6.68639i	−0.0165825	−	1.13021i
$36$		0			0
$37$	−2.20574	−	0.591026i	−0.362621	−	0.0971640i	0.0729080	−	0.997339i	$-0.476772\pi$
$37$	−2.20574	−	0.591026i	−0.362621	−	0.0971640i	−0.435529	+	0.900175i	$0.643439\pi$
$38$	−2.82119	+	4.88645i	−0.457658	+	0.792686i
$39$		0			0
$40$	−19.2606	+	11.1201i	−3.04537	+	1.75824i
$41$	2.69291	−	2.69291i	0.420562	−	0.420562i	−0.464835	−	0.885397i	$-0.653886\pi$
$41$	2.69291	−	2.69291i	0.420562	−	0.420562i	0.885397	+	0.464835i	$0.153886\pi$
$42$		0			0
$43$			0.437721i			0.0667518i	0.999443	+	0.0333759i	$0.0106258\pi$
$43$			0.437721i			0.0667518i	−0.999443	+	0.0333759i	$0.989374\pi$
$44$	−2.93567	+	10.9561i	−0.442569	+	1.65169i
$45$		0			0
$46$	0.917379	+	3.42370i	0.135260	+	0.504798i
$47$	−2.07440	+	7.74178i	−0.302583	+	1.12926i	0.632423	+	0.774623i	$0.282060\pi$
$47$	−2.07440	+	7.74178i	−0.302583	+	1.12926i	−0.935006	+	0.354632i	$0.884606\pi$
$48$		0			0
$49$	−5.95689	+	3.67635i	−0.850984	+	0.525192i
$50$	−2.64573	+	2.64573i	−0.374162	+	0.374162i
$51$		0			0
$52$	−15.2907	+	11.2479i	−2.12043	+	1.55981i
$53$	−1.26798	+	2.19621i	−0.174171	+	0.301672i	−0.939874	−	0.341522i	$-0.889058\pi$
$53$	−1.26798	+	2.19621i	−0.174171	+	0.301672i	0.765703	+	0.643194i	$0.222391\pi$
$54$		0			0
$55$			5.44537i			0.734253i
$56$	20.3304	+	11.3434i	2.71677	+	1.51582i
$57$		0			0
$58$	−3.18672	+	11.8930i	−0.418437	+	1.56163i
$59$	7.54086	−	2.02057i	0.981737	−	0.263056i	0.267961	−	0.963430i	$-0.413650\pi$
$59$	7.54086	−	2.02057i	0.981737	−	0.263056i	0.713776	+	0.700374i	$0.246984\pi$
$60$		0			0
$61$	6.57067	−	3.79358i	0.841288	−	0.485718i	−0.0164139	−	0.999865i	$-0.505225\pi$
$61$	6.57067	−	3.79358i	0.841288	−	0.485718i	0.857702	+	0.514147i	$0.171892\pi$
$62$	−19.6186			−2.49156
$63$		0			0
$64$		−	21.9945i		−	2.74931i
$65$	−5.69306	+	7.11588i	−0.706137	+	0.882616i
$66$		0			0
$67$	−0.548339	+	0.146927i	−0.0669903	+	0.0179500i	−0.292159	−	0.956370i	$-0.594373\pi$
$67$	−0.548339	+	0.146927i	−0.0669903	+	0.0179500i	0.225168	+	0.974320i	$0.427707\pi$
$68$	−6.39099	+	3.68984i	−0.775021	+	0.447459i
$69$		0			0
$70$	17.4762	+	4.40899i	2.08881	+	0.526976i
$71$	10.7460	+	10.7460i	1.27531	+	1.27531i	0.943263	+	0.332048i	$0.107739\pi$
$71$	10.7460	+	10.7460i	1.27531	+	1.27531i	0.332048	+	0.943263i	$0.392261\pi$
$72$		0			0
$73$	11.8953	−	3.18733i	1.39224	−	0.373049i	0.516687	−	0.856174i	$-0.327165\pi$
$73$	11.8953	−	3.18733i	1.39224	−	0.373049i	0.875551	+	0.483125i	$0.160498\pi$
$74$	3.07743	−	5.33027i	0.357744	−	0.619631i
$75$		0			0
$76$	−7.79312	−	7.79312i	−0.893933	−	0.893933i
$77$	4.89414	−	2.92219i	0.557739	−	0.333015i
$78$		0			0
$79$	−7.19713	−	12.4658i	−0.809740	−	1.40251i	−0.913044	−	0.407862i	$-0.866275\pi$
$79$	−7.19713	−	12.4658i	−0.809740	−	1.40251i	0.103303	−	0.994650i	$-0.467059\pi$
$80$	−8.62680	−	32.1956i	−0.964505	−	3.59958i
$81$		0			0
$82$	5.13234	+	8.88948i	0.566773	+	0.981679i
$83$	3.82648	−	3.82648i	0.420010	−	0.420010i	−0.465197	−	0.885207i	$-0.654016\pi$
$83$	3.82648	−	3.82648i	0.420010	−	0.420010i	0.885207	+	0.465197i	$0.154016\pi$
$84$		0			0
$85$	−2.50518	+	2.50518i	−0.271725	+	0.271725i
$86$	−1.13959	−	0.305353i	−0.122885	−	0.0329270i
$87$		0			0
$88$	−16.4179	−	9.47890i	−1.75016	−	1.01045i
$89$	0.0134247	−	0.0501018i	0.00142302	−	0.00531078i	−0.965211	−	0.261473i	$-0.915792\pi$
$89$	0.0134247	−	0.0501018i	0.00142302	−	0.00531078i	0.966634	+	0.256163i	$0.0824583\pi$
$90$		0			0
$91$	9.45066	+	1.29810i	0.990698	+	0.136078i
$92$	−6.92335			−0.721809
$93$		0			0
$94$	−18.7084	−	10.8013i	−1.92962	−	1.11407i
$95$	−4.58220	−	2.64553i	−0.470124	−	0.271426i
$96$		0			0
$97$	9.43761	−	9.43761i	0.958244	−	0.958244i	−0.0409188	−	0.999162i	$-0.513028\pi$
$97$	9.43761	−	9.43761i	0.958244	−	0.958244i	0.999162	+	0.0409188i	$0.0130285\pi$
$98$	−5.41574	−	18.0732i	−0.547072	−	1.82567i
$99$		0			0
$100$	−3.65421	−	6.32928i	−0.365421	−	0.632928i
$101$	7.17255	−	12.4232i	0.713696	−	1.23616i	−0.249765	−	0.968306i	$-0.580353\pi$
$101$	7.17255	−	12.4232i	0.713696	−	1.23616i	0.963461	−	0.267850i	$-0.0863133\pi$
$102$		0			0
$103$	4.50750	+	7.80723i	0.444138	+	0.769269i	0.997992	−	0.0633449i	$-0.0201768\pi$
$103$	4.50750	+	7.80723i	0.444138	+	0.769269i	−0.553854	+	0.832614i	$0.686843\pi$
$104$	−11.5445	−	29.5515i	−1.13203	−	2.89777i
$105$		0			0
$106$	−4.83321	−	4.83321i	−0.469443	−	0.469443i
$107$	2.15478	+	3.73220i	0.208311	+	0.360805i	0.951183	−	0.308629i	$-0.0998701\pi$
$107$	2.15478	+	3.73220i	0.208311	+	0.360805i	−0.742872	+	0.669434i	$0.766537\pi$
$108$		0			0
$109$	7.12483	−	1.90909i	0.682434	−	0.182858i	0.0990849	−	0.995079i	$-0.468408\pi$
$109$	7.12483	−	1.90909i	0.682434	−	0.182858i	0.583350	+	0.812221i	$0.301742\pi$
$110$	−14.1768	−	3.79867i	−1.35171	−	0.362189i
$111$		0			0
$112$	−24.3071	+	25.0309i	−2.29680	+	2.36520i
$113$	−10.1580			−0.955583			−0.477792	−	0.878473i	$-0.658563\pi$
$113$	−10.1580			−0.955583			−0.477792	+	0.878473i	$0.658563\pi$
$114$		0			0
$115$	−3.21053	+	0.860259i	−0.299384	+	0.0802196i
$116$	−20.8278	−	12.0249i	−1.93381	−	1.11649i
$117$		0			0
$118$			21.0419i			1.93707i
$119$	3.59596	+	0.907207i	0.329641	+	0.0831636i
$120$		0			0
$121$	5.50646	−	3.17915i	0.500587	−	0.289014i
$122$	5.29278	+	19.7529i	0.479186	+	1.78834i
$123$		0			0
$124$	9.91809	−	37.0148i	0.890671	−	3.32403i
$125$	6.45503	+	6.45503i	0.577355	+	0.577355i
$126$		0			0
$127$		−	8.50086i		−	0.754329i	−0.926146	−	0.377165i	$-0.876899\pi$
$127$		−	8.50086i		−	0.754329i	0.926146	−	0.377165i	$-0.123101\pi$
$128$	22.5932	+	6.05383i	1.99698	+	0.535088i
$129$		0			0
$130$	−14.5545	−	19.7857i	−1.27651	−	1.73532i
$131$	7.97433	−	4.60398i	0.696720	−	0.402252i	−0.109404	−	0.993997i	$-0.534894\pi$
$131$	7.97433	−	4.60398i	0.696720	−	0.402252i	0.806125	+	0.591746i	$0.201561\pi$
$132$		0			0
$133$	0.0812549	+	5.53804i	0.00704570	+	0.480209i
$134$		−	1.53008i		−	0.132179i
$135$		0			0
$136$	−3.19235	−	11.9140i	−0.273742	−	1.02162i
$137$	2.35513	+	8.78945i	0.201212	+	0.750934i	0.990571	+	0.137002i	$0.0437465\pi$
$137$	2.35513	+	8.78945i	0.201212	+	0.750934i	−0.789359	+	0.613932i	$0.789587\pi$
$138$		0			0
$139$		−	0.744275i		−	0.0631286i	−0.999502	−	0.0315643i	$-0.989951\pi$
$139$		−	0.744275i		−	0.0631286i	0.999502	−	0.0315643i	$-0.0100489\pi$
$140$	−17.1536	+	30.7438i	−1.44974	+	2.59833i
$141$		0			0
$142$	−35.4731	+	20.4804i	−2.97684	+	1.71868i
$143$	−7.67942	−	1.16984i	−0.642185	−	0.0978271i
$144$		0			0
$145$	−11.1525	−	2.98830i	−0.926165	−	0.248165i
$146$			33.1925i			2.74703i
$147$		0			0
$148$	8.50095	+	8.50095i	0.698774	+	0.698774i
$149$	3.87314	−	14.4547i	0.317300	−	1.18418i	−0.604530	−	0.796583i	$-0.706639\pi$
$149$	3.87314	−	14.4547i	0.317300	−	1.18418i	0.921829	−	0.387596i	$-0.126694\pi$
$150$		0			0
$151$	3.27408	+	12.2190i	0.266441	+	0.994372i	0.961362	+	0.275286i	$0.0887726\pi$
$151$	3.27408	+	12.2190i	0.266441	+	0.994372i	−0.694921	+	0.719086i	$0.744561\pi$
$152$	15.9527	−	9.21030i	1.29394	−	0.747054i
$153$		0			0
$154$	4.19370	+	14.7803i	0.337938	+	1.19103i
$155$		−	18.3971i		−	1.47769i
$156$		0			0
$157$	9.11258	+	5.26115i	0.727263	+	0.419886i	0.817420	−	0.576042i	$-0.195404\pi$
$157$	9.11258	+	5.26115i	0.727263	+	0.419886i	−0.0901569	+	0.995928i	$0.528737\pi$
$158$	37.4750	−	10.0414i	2.98135	−	0.798850i
$159$		0			0
$160$	45.3579			3.58586
$161$	2.49607	+	2.42388i	0.196718	+	0.191029i
$162$		0			0
$163$	−0.520357	−	0.139429i	−0.0407575	−	0.0109209i	0.238383	−	0.971171i	$-0.423383\pi$
$163$	−0.520357	−	0.139429i	−0.0407575	−	0.0109209i	−0.279140	+	0.960250i	$0.590049\pi$
$164$	−19.3666	+	5.18927i	−1.51228	+	0.405214i
$165$		0			0
$166$	7.29277	+	12.6314i	0.566029	+	0.980390i
$167$	4.43553	+	4.43553i	0.343232	+	0.343232i	0.857581	−	0.514349i	$-0.171966\pi$
$167$	4.43553	+	4.43553i	0.343232	+	0.343232i	−0.514349	+	0.857581i	$0.671966\pi$
$168$		0			0
$169$	−8.81222	−	9.55744i	−0.677863	−	0.735188i
$170$	−4.77455	−	8.26976i	−0.366191	−	0.634262i
$171$		0			0
$172$	1.15223	−	1.99572i	0.0878568	−	0.152172i
$173$	1.29813	+	2.24843i	0.0986952	+	0.170945i	0.911145	−	0.412086i	$-0.135200\pi$
$173$	1.29813	+	2.24843i	0.0986952	+	0.170945i	−0.812450	+	0.583031i	$0.801866\pi$
$174$		0			0
$175$	−0.898449	+	3.56124i	−0.0679163	+	0.269205i
$176$	20.0903	−	20.0903i	1.51437	−	1.51437i
$177$		0			0
$178$	0.121073	+	0.0699017i	0.00907482	+	0.00523935i
$179$	−1.39849	−	0.807419i	−0.104528	−	0.0603493i	0.446825	−	0.894622i	$-0.352555\pi$
$179$	−1.39849	−	0.807419i	−0.104528	−	0.0603493i	−0.551353	+	0.834272i	$0.685888\pi$
$180$		0			0
$181$	−2.49671			−0.185579			−0.0927895	−	0.995686i	$-0.529578\pi$
$181$	−2.49671			−0.185579			−0.0927895	+	0.995686i	$0.529578\pi$
$182$	−9.97232	+	23.6989i	−0.739197	+	1.75668i
$183$		0			0
$184$	2.99495	−	11.1773i	0.220791	−	0.824003i
$185$	4.99839	+	2.88582i	0.367489	+	0.212170i
$186$		0			0
$187$	−2.91707	−	0.781626i	−0.213317	−	0.0571582i
$188$	29.8370	−	29.8370i	2.17609	−	2.17609i
$189$		0			0
$190$	10.0841	−	10.0841i	0.731577	−	0.731577i
$191$	−5.46624	−	9.46781i	−0.395523	−	0.685066i	0.597645	−	0.801761i	$-0.296103\pi$
$191$	−5.46624	−	9.46781i	−0.395523	−	0.685066i	−0.993168	+	0.116695i	$0.962770\pi$
$192$		0			0
$193$	−1.61284	−	6.01922i	−0.116095	−	0.433273i	0.883271	−	0.468862i	$-0.155336\pi$
$193$	−1.61284	−	6.01922i	−0.116095	−	0.433273i	−0.999367	+	0.0355893i	$0.988669\pi$
$194$	17.9869	+	31.1542i	1.29138	+	2.23674i
$195$		0			0
$196$	36.8369	−	1.08119i	2.63121	−	0.0772276i
$197$	−11.4927	−	11.4927i	−0.818821	−	0.818821i	0.167116	−	0.985937i	$-0.446554\pi$
$197$	−11.4927	−	11.4927i	−0.818821	−	0.818821i	−0.985937	+	0.167116i	$0.946554\pi$
$198$		0			0
$199$	−9.02611	+	15.6337i	−0.639844	+	1.10824i	0.345623	+	0.938373i	$0.387668\pi$
$199$	−9.02611	+	15.6337i	−0.639844	+	1.10824i	−0.985467	+	0.169868i	$0.945666\pi$
$200$	11.7990	−	3.16153i	0.834315	−	0.223554i
$201$		0			0
$202$	27.3399	+	27.3399i	1.92363	+	1.92363i
$203$	3.29906	+	11.6272i	0.231549	+	0.816069i
$204$		0			0
$205$	−8.33599	+	4.81279i	−0.582211	+	0.336140i
$206$	−23.4703	+	6.28884i	−1.63525	+	0.438164i
$207$		0			0
$208$	47.2577	−	5.24941i	3.27673	−	0.363981i
$209$		−	4.51016i		−	0.311974i
$210$		0			0
$211$	2.78534			0.191750			0.0958752	−	0.995393i	$-0.469435\pi$
$211$	2.78534			0.191750			0.0958752	+	0.995393i	$0.469435\pi$
$212$	11.5623	−	6.67552i	0.794105	−	0.458477i
$213$		0			0
$214$	−11.2198	+	3.00634i	−0.766971	+	0.205509i
$215$	0.286340	−	1.06864i	0.0195282	−	0.0728804i
$216$		0			0
$217$	−16.5347	+	9.87257i	−1.12245	+	0.670194i
$218$			19.8810i			1.34651i
$219$		0			0
$220$	14.3341	−	24.8274i	0.966403	−	1.67386i
$221$	−2.99478	−	4.07116i	−0.201450	−	0.273856i
$222$		0			0
$223$	12.1327	−	12.1327i	0.812463	−	0.812463i	−0.172540	−	0.985003i	$-0.555197\pi$
$223$	12.1327	−	12.1327i	0.812463	−	0.812463i	0.985003	+	0.172540i	$0.0551974\pi$
$224$	−24.3408	−	40.7664i	−1.62634	−	2.72382i
$225$		0			0
$226$	7.08618	−	26.4460i	0.471366	−	1.75916i
$227$	4.43867	+	16.5653i	0.294605	+	1.09948i	0.941531	+	0.336927i	$0.109388\pi$
$227$	4.43867	+	16.5653i	0.294605	+	1.09948i	−0.646926	+	0.762553i	$0.723946\pi$
$228$		0			0
$229$	−5.63884	+	21.0444i	−0.372625	+	1.39065i	0.484160	+	0.874980i	$0.339125\pi$
$229$	−5.63884	+	21.0444i	−0.372625	+	1.39065i	−0.856784	+	0.515675i	$0.827541\pi$
$230$		−	8.95863i		−	0.590715i
$231$		0			0
$232$	28.4233	−	28.4233i	1.86608	−	1.86608i
$233$	−26.1233	+	15.0823i	−1.71139	+	0.988073i	−0.778705	+	0.627390i	$0.784123\pi$
$233$	−26.1233	+	15.0823i	−1.71139	+	0.988073i	−0.932688	+	0.360683i	$0.882544\pi$
$234$		0			0
$235$	10.1288	−	17.5435i	0.660728	−	1.14441i
$236$	−39.7003	−	10.6377i	−2.58427	−	0.692453i
$237$		0			0
$238$	−4.87042	+	8.72910i	−0.315702	+	0.565823i
$239$	−10.1720	−	10.1720i	−0.657969	−	0.657969i	0.296930	−	0.954899i	$-0.404037\pi$
$239$	−10.1720	−	10.1720i	−0.657969	−	0.657969i	−0.954899	+	0.296930i	$0.904037\pi$
$240$		0			0
$241$	20.6397	−	5.53040i	1.32952	−	0.356245i	0.476986	−	0.878911i	$-0.341729\pi$
$241$	20.6397	−	5.53040i	1.32952	−	0.356245i	0.852537	+	0.522667i	$0.175063\pi$
$242$	4.43554	+	16.5537i	0.285127	+	1.06411i
$243$		0			0
$244$	−39.9440			−2.55715
$245$	16.9479	−	5.07854i	1.08276	−	0.324456i
$246$		0			0
$247$	4.71531	−	5.89377i	0.300028	−	0.375012i
$248$	55.4677	+	32.0243i	3.52220	+	2.03354i
$249$		0			0
$250$	−21.3085	+	12.3024i	−1.34767	+	0.778075i
$251$	−10.4531			−0.659791			−0.329896	−	0.944017i	$-0.607014\pi$
$251$	−10.4531			−0.659791			−0.329896	+	0.944017i	$0.607014\pi$
$252$		0			0
$253$	−2.00340	−	2.00340i	−0.125952	−	0.125952i
$254$	22.1317	+	5.93017i	1.38867	+	0.372092i
$255$		0			0
$256$	−9.52744	+	16.5020i	−0.595465	+	1.03138i
$257$	−7.01434	−	12.1492i	−0.437543	−	0.757846i	0.559957	−	0.828522i	$-0.310818\pi$
$257$	−7.01434	−	12.1492i	−0.437543	−	0.757846i	−0.997499	+	0.0706758i	$0.977484\pi$
$258$		0			0
$259$	−0.0886351	−	6.04105i	−0.00550752	−	0.375373i
$260$	44.6881	−	17.4577i	2.77144	−	1.08268i
$261$		0			0
$262$	6.42345	+	23.9726i	0.396842	+	1.48103i
$263$	1.26443	−	2.19006i	0.0779683	−	0.135045i	−0.824405	−	0.566000i	$-0.808490\pi$
$263$	1.26443	−	2.19006i	0.0779683	−	0.135045i	0.902373	+	0.430955i	$0.141823\pi$
$264$		0			0
$265$	4.53228	−	4.53228i	0.278416	−	0.278416i
$266$	−14.4748	−	3.65178i	−0.887507	−	0.223905i
$267$		0			0
$268$	2.88683	+	0.773525i	0.176341	+	0.0472505i
$269$	7.00983	+	4.04713i	0.427397	+	0.246758i	0.698237	−	0.715867i	$-0.253968\pi$
$269$	7.00983	+	4.04713i	0.427397	+	0.246758i	−0.270840	+	0.962624i	$0.587301\pi$
$270$		0			0
$271$	7.25276	−	27.0677i	0.440574	−	1.64424i	−0.286791	−	0.957993i	$-0.592588\pi$
$271$	7.25276	−	27.0677i	0.440574	−	1.64424i	0.727365	−	0.686251i	$-0.240745\pi$
$272$	18.4854			1.12084
$273$		0			0
$274$	−24.5260			−1.48167
$275$	0.774080	−	2.88891i	0.0466788	−	0.174208i
$276$		0			0
$277$	−7.99289	−	4.61469i	−0.480246	−	0.277270i	0.240273	−	0.970705i	$-0.422763\pi$
$277$	−7.99289	−	4.61469i	−0.480246	−	0.277270i	−0.720519	+	0.693435i	$0.756096\pi$
$278$	1.93770	+	0.519204i	0.116215	+	0.0311398i
$279$		0			0
$280$	−42.2136	−	40.9928i	−2.52274	−	2.44979i
$281$	−8.78641	+	8.78641i	−0.524153	+	0.524153i	−0.918823	−	0.394670i	$-0.870859\pi$
$281$	−8.78641	+	8.78641i	−0.524153	+	0.524153i	0.394670	+	0.918823i	$0.370859\pi$
$282$		0			0
$283$	−2.72067	+	4.71234i	−0.161727	+	0.280119i	−0.935488	−	0.353358i	$-0.885040\pi$
$283$	−2.72067	+	4.71234i	−0.161727	+	0.280119i	0.773761	+	0.633477i	$0.218373\pi$
$284$	−20.7076	−	77.2816i	−1.22877	−	4.58582i
$285$		0			0
$286$	8.40279	−	19.1770i	0.496867	−	1.13396i
$287$	8.79901	+	4.90942i	0.519389	+	0.289794i
$288$		0			0
$289$	7.51758	+	13.0208i	0.442210	+	0.765931i
$290$	15.5599	−	26.9506i	0.913709	−	1.58259i
$291$		0			0
$292$	−62.6250	−	16.7803i	−3.66485	−	0.981993i
$293$	8.39280	+	8.39280i	0.490313	+	0.490313i	0.908405	−	0.418092i	$-0.137301\pi$
$293$	8.39280	+	8.39280i	0.490313	+	0.490313i	−0.418092	+	0.908405i	$0.637301\pi$
$294$		0			0
$295$	−19.7318			−1.14883
$296$	−17.4017	+	10.0469i	−1.01145	+	0.583962i
$297$		0			0
$298$	34.9306	+	20.1672i	2.02347	+	1.16825i
$299$	−0.523468	−	4.71251i	−0.0302729	−	0.272532i
$300$		0			0
$301$	−1.11412	+	0.316117i	−0.0642168	+	0.0182207i
$302$	−34.0959			−1.96200
$303$		0			0
$304$	7.14520	+	26.6663i	0.409805	+	1.52941i
$305$	−18.5230	+	4.96323i	−1.06063	+	0.284194i
$306$		0			0
$307$	−1.45103	−	1.45103i	−0.0828145	−	0.0828145i	0.664486	−	0.747301i	$-0.268650\pi$
$307$	−1.45103	−	1.45103i	−0.0828145	−	0.0828145i	−0.747301	+	0.664486i	$0.768650\pi$
$308$	−30.0063	+	0.440257i	−1.70977	+	0.0250860i
$309$		0			0
$310$	47.8962	+	12.8337i	2.72032	+	0.728907i
$311$	1.64915	−	2.85641i	0.0935147	−	0.161972i	−0.815473	−	0.578795i	$-0.803523\pi$
$311$	1.64915	−	2.85641i	0.0935147	−	0.161972i	0.908988	+	0.416823i	$0.136856\pi$
$312$		0			0
$313$	−20.7394	+	11.9739i	−1.17226	+	0.676805i	−0.954212	−	0.299133i	$-0.903303\pi$
$313$	−20.7394	+	11.9739i	−1.17226	+	0.676805i	−0.218049	+	0.975938i	$0.569969\pi$
$314$	−20.0542	+	20.0542i	−1.13172	+	1.13172i
$315$		0			0
$316$			75.7813i			4.26303i
$317$	7.84293	−	29.2702i	0.440503	−	1.64398i	−0.287041	−	0.957918i	$-0.592672\pi$
$317$	7.84293	−	29.2702i	0.440503	−	1.64398i	0.727544	−	0.686061i	$-0.240662\pi$
$318$		0			0
$319$	−2.54726	−	9.50651i	−0.142619	−	0.532263i
$320$	−14.3880	+	53.6966i	−0.804311	+	3.00173i
$321$		0			0
$322$	−8.05176	+	4.80755i	−0.448707	+	0.267914i
$323$	2.07493	−	2.07493i	0.115452	−	0.115452i
$324$		0			0
$325$	4.03186	−	2.96586i	0.223647	−	0.164516i
$326$	0.725999	−	1.25747i	0.0402094	−	0.0696447i
$327$		0			0
$328$		−	33.5110i		−	1.85034i
$329$	−21.2031	+	0.311095i	−1.16897	+	0.0171512i
$330$		0			0
$331$	−2.47572	+	9.23949i	−0.136078	+	0.507849i	0.863914	+	0.503640i	$0.168006\pi$
$331$	−2.47572	+	9.23949i	−0.136078	+	0.507849i	−0.999991	+	0.00420839i	$0.998660\pi$
$332$	−27.5188	+	7.37365i	−1.51029	+	0.404682i
$333$		0			0
$334$	−14.6420	+	8.45355i	−0.801173	+	0.462557i
$335$	1.43481			0.0783921
$336$		0			0
$337$		−	24.0729i		−	1.31133i	−0.755050	−	0.655667i	$-0.772388\pi$
$337$		−	24.0729i		−	1.31133i	0.755050	−	0.655667i	$-0.227612\pi$
$338$	31.0299	−	16.2751i	1.68780	−	0.885249i
$339$		0			0
$340$	18.0165	−	4.82750i	0.977081	−	0.261808i
$341$	13.5809	−	7.84092i	0.735446	−	0.424610i
$342$		0			0
$343$	−13.6593	−	12.5069i	−0.737534	−	0.675310i
$344$	2.72353	+	2.72353i	0.146843	+	0.146843i
$345$		0			0
$346$	−6.75929	+	1.81115i	−0.363382	+	0.0973679i
$347$	−1.98989	+	3.44658i	−0.106823	+	0.185022i	−0.914481	−	0.404628i	$-0.867401\pi$
$347$	−1.98989	+	3.44658i	−0.106823	+	0.185022i	0.807659	+	0.589650i	$0.200734\pi$
$348$		0			0
$349$	−5.05995	−	5.05995i	−0.270853	−	0.270853i	0.558591	−	0.829443i	$-0.311342\pi$
$349$	−5.05995	−	5.05995i	−0.270853	−	0.270853i	−0.829443	+	0.558591i	$0.811342\pi$
$350$	−8.64482	−	4.82340i	−0.462085	−	0.257821i
$351$		0			0
$352$	19.3318	+	33.4836i	1.03039	+	1.78468i
$353$	2.53408	+	9.45731i	0.134875	+	0.503362i	0.999998	+	0.00180195i	$0.000573578\pi$
$353$	2.53408	+	9.45731i	0.134875	+	0.503362i	−0.865123	+	0.501560i	$0.832760\pi$
$354$		0			0
$355$	−19.2052	−	33.2644i	−1.01931	−	1.76549i
$356$	−0.193093	+	0.193093i	−0.0102339	+	0.0102339i
$357$		0			0
$358$	3.07767	−	3.07767i	0.162660	−	0.162660i
$359$	35.9441	+	9.63119i	1.89706	+	0.508315i	0.997429	+	0.0716576i	$0.0228289\pi$
$359$	35.9441	+	9.63119i	1.89706	+	0.508315i	0.899628	+	0.436657i	$0.143838\pi$
$360$		0			0
$361$	−12.6592	−	7.30882i	−0.666276	−	0.384675i
$362$	1.74170	−	6.50011i	0.0915416	−	0.341638i
$363$		0			0
$364$	−39.6718	−	30.7959i	−2.07937	−	1.61414i
$365$	−31.1258			−1.62920
$366$		0			0
$367$	24.6834	+	14.2510i	1.28846	+	0.743895i	0.978380	−	0.206814i	$-0.0663097\pi$
$367$	24.6834	+	14.2510i	1.28846	+	0.743895i	0.310083	+	0.950709i	$0.399643\pi$
$368$	15.0189	+	8.67118i	0.782915	+	0.452016i
$369$		0			0
$370$	−11.0000	+	11.0000i	−0.571863	+	0.571863i
$371$	−6.50568	−	1.64129i	−0.337758	−	0.0852114i
$372$		0			0
$373$	2.36014	+	4.08789i	0.122204	+	0.211663i	0.920636	−	0.390421i	$-0.127671\pi$
$373$	2.36014	+	4.08789i	0.122204	+	0.211663i	−0.798433	+	0.602084i	$0.794337\pi$
$374$	4.06988	−	7.04923i	0.210448	−	0.364507i
$375$		0			0
$376$	35.2628	+	61.0770i	1.81854	+	3.14981i
$377$	6.61022	−	15.0860i	0.340444	−	0.776969i
$378$		0			0
$379$	4.79288	+	4.79288i	0.246193	+	0.246193i	0.819406	−	0.573213i	$-0.194303\pi$
$379$	4.79288	+	4.79288i	0.246193	+	0.246193i	−0.573213	+	0.819406i	$0.694303\pi$
$380$	13.9279	+	24.1238i	0.714486	+	1.23753i
$381$		0			0
$382$	28.4624	−	7.62647i	1.45626	−	0.390204i
$383$	−5.13388	−	1.37562i	−0.262329	−	0.0702908i	0.125257	−	0.992124i	$-0.460024\pi$
$383$	−5.13388	−	1.37562i	−0.262329	−	0.0702908i	−0.387586	+	0.921833i	$0.626691\pi$
$384$		0			0
$385$	−13.8600	+	3.93259i	−0.706370	+	0.200423i
$386$	16.7960			0.854892
$387$		0			0
$388$	−67.8724	+	18.1864i	−3.44570	+	0.923272i
$389$	30.2004	+	17.4362i	1.53122	+	0.884050i	0.999306	+	0.0372510i	$0.0118601\pi$
$389$	30.2004	+	17.4362i	1.53122	+	0.884050i	0.531913	+	0.846799i	$0.321473\pi$
$390$		0			0
$391$		−	1.84335i		−	0.0932224i
$392$	−14.1897	+	59.9386i	−0.716687	+	3.02736i
$393$		0			0
$394$	37.9381	−	21.9036i	1.91130	−	1.10349i
$395$	9.41618	+	35.1417i	0.473779	+	1.76817i
$396$		0			0
$397$	−9.42978	+	35.1924i	−0.473267	+	1.76626i	0.154643	+	0.987970i	$0.450577\pi$
$397$	−9.42978	+	35.1924i	−0.473267	+	1.76626i	−0.627910	+	0.778286i	$0.716090\pi$
$398$	−34.4052	−	34.4052i	−1.72458	−	1.72458i
$399$		0			0
$400$			18.3069i			0.915347i
$401$	−14.2063	−	3.80657i	−0.709430	−	0.190091i	−0.113979	−	0.993483i	$-0.536360\pi$
$401$	−14.2063	−	3.80657i	−0.709430	−	0.190091i	−0.595451	+	0.803392i	$0.703026\pi$
$402$		0			0
$403$	25.9447	+	3.95229i	1.29240	+	0.196877i
$404$	−65.4044	+	37.7612i	−3.25399	+	1.87869i
$405$		0			0
$406$	−32.5724	+	0.477907i	−1.61654	+	0.0237181i
$407$			4.91981i			0.243866i
$408$		0			0
$409$	0.568872	+	2.12306i	0.0281289	+	0.104979i	0.978563	−	0.205947i	$-0.0660276\pi$
$409$	0.568872	+	2.12306i	0.0281289	+	0.104979i	−0.950434	+	0.310926i	$0.899361\pi$
$410$	−6.71477	−	25.0599i	−0.331619	−	1.23762i
$411$		0			0
$412$		−	47.4612i		−	2.33825i
$413$	10.5888	+	17.7344i	0.521043	+	0.872651i
$414$		0			0
$415$	−11.8450	+	6.83869i	−0.581446	+	0.335698i
$416$	−9.74435	+	63.9667i	−0.477756	+	3.13623i
$417$		0			0
$418$	11.7421	+	3.14628i	0.574323	+	0.153889i
$419$		−	31.5129i		−	1.53951i	−0.638342	−	0.769753i	$-0.720380\pi$
$419$		−	31.5129i		−	1.53951i	0.638342	−	0.769753i	$-0.279620\pi$
$420$		0			0
$421$	−10.0626	−	10.0626i	−0.490422	−	0.490422i	0.418017	−	0.908439i	$-0.362725\pi$
$421$	−10.0626	−	10.0626i	−0.490422	−	0.490422i	−0.908439	+	0.418017i	$0.862725\pi$
$422$	−1.94304	+	7.25153i	−0.0945858	+	0.352999i
$423$		0			0
$424$	5.77549	+	21.5544i	0.280483	+	1.04678i
$425$	1.68518	−	0.972940i	0.0817433	−	0.0471945i
$426$		0			0
$427$	14.4010	+	13.9845i	0.696912	+	0.676757i
$428$		−	22.6885i		−	1.09669i
$429$		0			0
$430$	2.58241	+	1.49096i	0.124535	+	0.0719002i
$431$	12.8581	−	3.44532i	0.619353	−	0.165955i	0.0645192	−	0.997916i	$-0.479449\pi$
$431$	12.8581	−	3.44532i	0.619353	−	0.165955i	0.554834	+	0.831961i	$0.312782\pi$
$432$		0			0
$433$	−29.1175			−1.39930			−0.699648	−	0.714488i	$-0.746660\pi$
$433$	−29.1175			−1.39930			−0.699648	+	0.714488i	$0.746660\pi$
$434$	−14.1683	−	49.9348i	−0.680102	−	2.39695i
$435$		0			0
$436$	−37.5100	−	10.0508i	−1.79640	−	0.481344i
$437$	2.65914	−	0.712515i	0.127204	−	0.0340842i
$438$		0			0
$439$	−5.15668	−	8.93164i	−0.246115	−	0.426284i	0.716329	−	0.697762i	$-0.245821\pi$
$439$	−5.15668	−	8.93164i	−0.246115	−	0.426284i	−0.962445	+	0.271478i	$0.912487\pi$
$440$	33.8815	+	33.8815i	1.61524	+	1.61524i
$441$		0			0
$442$	12.6883	−	4.95677i	0.603520	−	0.235769i
$443$	0.307483	+	0.532577i	0.0146090	+	0.0253035i	0.873237	−	0.487295i	$-0.162016\pi$
$443$	0.307483	+	0.532577i	0.0146090	+	0.0253035i	−0.858628	+	0.512598i	$0.828683\pi$
$444$		0			0
$445$	−0.0655493	+	0.113535i	−0.00310734	+	0.00538207i
$446$	23.1233	+	40.0507i	1.09492	+	1.89645i
$447$		0			0
$448$	55.9821	−	15.8842i	2.64490	−	0.750457i
$449$	−8.66406	+	8.66406i	−0.408882	+	0.408882i	−0.881349	−	0.472466i	$-0.843364\pi$
$449$	−8.66406	+	8.66406i	−0.408882	+	0.408882i	0.472466	+	0.881349i	$0.343364\pi$
$450$		0			0
$451$	−7.10569	−	4.10247i	−0.334594	−	0.193178i
$452$	46.3139	+	26.7393i	2.17842	+	1.25771i
$453$		0			0
$454$	−46.2237			−2.16939
$455$	−22.2234	−	9.35140i	−1.04185	−	0.438401i
$456$		0			0
$457$	−4.78572	+	17.8605i	−0.223866	+	0.835481i	0.758989	+	0.651103i	$0.225694\pi$
$457$	−4.78572	+	17.8605i	−0.223866	+	0.835481i	−0.982855	+	0.184378i	$0.940973\pi$
$458$	−50.8548	−	29.3611i	−2.37629	−	1.37195i
$459$		0			0
$460$	16.9024	+	4.52900i	0.788080	+	0.211165i
$461$	5.20251	−	5.20251i	0.242305	−	0.242305i	−0.575498	−	0.817803i	$-0.695192\pi$
$461$	5.20251	−	5.20251i	0.242305	−	0.242305i	0.817803	+	0.575498i	$0.195192\pi$
$462$		0			0
$463$	−13.9818	+	13.9818i	−0.649788	+	0.649788i	−0.952942	−	0.303154i	$-0.901960\pi$
$463$	−13.9818	+	13.9818i	−0.649788	+	0.649788i	0.303154	+	0.952942i	$0.401960\pi$
$464$	30.1213	+	52.1716i	1.39835	+	2.42201i
$465$		0			0
$466$	−21.0427	−	78.5325i	−0.974785	−	3.63795i
$467$	−4.94463	−	8.56435i	−0.228810	−	0.396311i	0.728646	−	0.684891i	$-0.240150\pi$
$467$	−4.94463	−	8.56435i	−0.228810	−	0.396311i	−0.957456	+	0.288580i	$0.906817\pi$
$468$		0			0
$469$	−0.769975	−	1.28957i	−0.0355541	−	0.0595467i
$470$	38.6082	+	38.6082i	1.78086	+	1.78086i
$471$		0			0
$472$	34.3477	−	59.4919i	1.58098	−	2.73834i
$473$	0.910917	−	0.244079i	0.0418840	−	0.0112228i
$474$		0			0
$475$	2.05490	+	2.05490i	0.0942852	+	0.0942852i
$476$	−14.0072	−	13.6021i	−0.642017	−	0.623450i
$477$		0			0
$478$	33.5783	−	19.3864i	1.53584	−	0.886715i
$479$	−13.1156	+	3.51431i	−0.599267	+	0.160573i	−0.545685	−	0.837990i	$-0.683730\pi$
$479$	−13.1156	+	3.51431i	−0.599267	+	0.160573i	−0.0535818	+	0.998563i	$0.517064\pi$
$480$		0			0
$481$	−5.14359	+	6.42909i	−0.234528	+	0.293141i
$482$			57.5929i			2.62328i
$483$		0			0
$484$	−33.4745			−1.52157
$485$	−29.2144	+	16.8669i	−1.32656	+	0.765888i
$486$		0			0
$487$	−5.93329	+	1.58982i	−0.268863	+	0.0720416i	−0.390732	−	0.920505i	$-0.627778\pi$
$487$	−5.93329	+	1.58982i	−0.268863	+	0.0720416i	0.121869	+	0.992546i	$0.461111\pi$
$488$	17.2793	−	64.4871i	0.782195	−	2.91919i
$489$		0			0
$490$	1.39903	+	47.6660i	0.0632015	+	2.15333i
$491$		−	22.4430i		−	1.01284i	−0.862287	−	0.506420i	$-0.830968\pi$
$491$		−	22.4430i		−	1.01284i	0.862287	−	0.506420i	$-0.169032\pi$
$492$		0			0
$493$	3.20165	−	5.54542i	0.144195	−	0.249753i
$494$	12.0549	+	16.3876i	0.542374	+	0.737315i
$495$		0			0
$496$	−67.8748	+	67.8748i	−3.04767	+	3.04767i
$497$	−19.5908	+	35.1121i	−0.878769	+	1.57499i
$498$		0			0
$499$	9.64734	−	36.0044i	0.431874	−	1.61178i	−0.316563	−	0.948571i	$-0.602529\pi$
$499$	9.64734	−	36.0044i	0.431874	−	1.61178i	0.748438	−	0.663205i	$-0.230804\pi$
$500$	−12.4389	−	46.4226i	−0.556284	−	2.07608i
$501$		0			0
$502$	7.29203	−	27.2142i	0.325459	−	1.21463i
$503$			22.9063i			1.02134i	0.859776	+	0.510671i	$0.170603\pi$
$503$			22.9063i			1.02134i	−0.859776	+	0.510671i	$0.829397\pi$
$504$		0			0
$505$	−25.6376	+	25.6376i	−1.14086	+	1.14086i
$506$	6.61334	−	3.81822i	0.293999	−	0.169740i
$507$		0			0
$508$	−22.3772	+	38.7584i	−0.992827	+	1.71963i
$509$	−40.3870	−	10.8217i	−1.79012	−	0.479661i	−0.797754	−	0.602984i	$-0.793978\pi$
$509$	−40.3870	−	10.8217i	−1.79012	−	0.479661i	−0.992367	+	0.123322i	$0.960645\pi$
$510$		0			0
$511$	16.7033	+	27.9750i	0.738910	+	1.23754i
$512$	−3.23738	−	3.23738i	−0.143073	−	0.143073i
$513$		0			0
$514$	36.5232	−	9.78637i	1.61097	−	0.431658i
$515$	−5.89728	−	22.0089i	−0.259865	−	0.969830i
$516$		0			0
$517$	17.2677			0.759434
$518$	15.7895	+	3.98346i	0.693751	+	0.175023i
$519$		0			0
$520$	8.85289	+	79.6981i	0.388225	+	3.49499i
$521$	−9.76857	−	5.63989i	−0.427969	−	0.247088i	0.270512	−	0.962717i	$-0.412807\pi$
$521$	−9.76857	−	5.63989i	−0.427969	−	0.247088i	−0.698481	+	0.715629i	$0.746140\pi$
$522$		0			0
$523$	27.4072	−	15.8235i	1.19843	−	0.691915i	0.238226	−	0.971210i	$-0.423434\pi$
$523$	27.4072	−	15.8235i	1.19843	−	0.691915i	0.960205	+	0.279295i	$0.0901008\pi$
$524$	−48.4770			−2.11773
$525$		0			0
$526$	4.81969	+	4.81969i	0.210149	+	0.210149i
$527$	9.85525	+	2.64071i	0.429301	+	0.115031i
$528$		0			0
$529$	−10.6353	+	18.4209i	−0.462405	+	0.800909i
$530$	8.63794	+	14.9614i	0.375208	+	0.649880i
$531$		0			0
$532$	14.2076	−	25.4638i	0.615976	−	1.10399i
$533$	−4.99647	−	12.7899i	−0.216421	−	0.553992i
$534$		0			0
$535$	−2.81916	−	10.5212i	−0.121883	−	0.454873i
$536$	−2.49761	+	4.32600i	−0.107881	+	0.186855i
$537$		0			0
$538$	−15.4266	+	15.4266i	−0.665088	+	0.665088i
$539$	10.9723	+	10.3466i	0.472610	+	0.445658i
$540$		0			0
$541$	−30.8404	−	8.26367i	−1.32593	−	0.355283i	−0.474736	−	0.880128i	$-0.657457\pi$
$541$	−30.8404	−	8.26367i	−1.32593	−	0.355283i	−0.851198	+	0.524845i	$0.824123\pi$
$542$	65.4103	+	37.7647i	2.80961	+	1.62213i
$543$		0			0
$544$	−6.51066	+	24.2981i	−0.279142	+	1.04177i
$545$	−18.6432			−0.798585
$546$		0			0
$547$	−10.5664			−0.451787			−0.225893	−	0.974152i	$-0.572530\pi$
$547$	−10.5664			−0.451787			−0.225893	+	0.974152i	$0.572530\pi$
$548$	12.3990	−	46.2737i	0.529659	−	1.97672i
$549$		0			0
$550$	6.98118	+	4.03058i	0.297678	+	0.171865i
$551$	9.23713	+	2.47508i	0.393515	+	0.105442i
$552$		0			0
$553$	26.5312	−	27.3214i	1.12822	−	1.16182i
$554$	17.5900	−	17.5900i	0.747328	−	0.747328i
$555$		0			0
$556$	−1.95919	+	3.39341i	−0.0830881	+	0.143913i
$557$	−1.25353	−	4.67823i	−0.0531136	−	0.198223i	0.934271	−	0.356564i	$-0.116052\pi$
$557$	−1.25353	−	4.67823i	−0.0531136	−	0.198223i	−0.987384	+	0.158342i	$0.949385\pi$
$558$		0			0
$559$	1.44555	+	0.633394i	0.0611401	+	0.0267897i
$560$	75.7167	−	45.2090i	3.19962	−	1.91043i
$561$		0			0
$562$	−16.7458	−	29.0045i	−0.706378	−	1.22348i
$563$	5.27248	−	9.13221i	0.222209	−	0.384877i	−0.733270	−	0.679938i	$-0.762007\pi$
$563$	5.27248	−	9.13221i	0.222209	−	0.384877i	0.955478	+	0.295061i	$0.0953400\pi$
$564$		0			0
$565$	24.7994	+	6.64497i	1.04332	+	0.279556i
$566$	−10.3705	−	10.3705i	−0.435904	−	0.435904i
$567$		0			0
$568$	133.724			5.61094
$569$	−9.51695	+	5.49461i	−0.398971	+	0.230346i	−0.686040	−	0.727564i	$-0.740653\pi$
$569$	−9.51695	+	5.49461i	−0.398971	+	0.230346i	0.287069	+	0.957910i	$0.407319\pi$
$570$		0			0
$571$	−13.0863	−	7.55535i	−0.547643	−	0.316182i	0.200528	−	0.979688i	$-0.435734\pi$
$571$	−13.0863	−	7.55535i	−0.547643	−	0.316182i	−0.748171	+	0.663506i	$0.769068\pi$
$572$	31.9337	+	25.5486i	1.33522	+	1.06824i
$573$		0			0
$574$	−18.9197	+	19.4831i	−0.789692	+	0.813210i
$575$	1.82556			0.0761310
$576$		0			0
$577$	1.22540	+	4.57325i	0.0510140	+	0.190387i	0.986731	−	0.162366i	$-0.0519124\pi$
$577$	1.22540	+	4.57325i	0.0510140	+	0.190387i	−0.935717	+	0.352753i	$0.885246\pi$
$578$	−39.1435	+	10.4885i	−1.62816	+	0.436263i
$579$		0			0
$580$	42.9819	+	42.9819i	1.78473	+	1.78473i
$581$	12.5029	+	6.97601i	0.518707	+	0.289414i
$582$		0			0
$583$	5.27745	+	1.41409i	0.218570	+	0.0585656i
$584$	54.1815	−	93.8451i	2.24205	−	3.88334i
$585$		0			0
$586$	−27.7052	+	15.9956i	−1.14449	+	0.660772i
$587$	7.44792	−	7.44792i	0.307409	−	0.307409i	−0.536495	−	0.843904i	$-0.680252\pi$
$587$	7.44792	−	7.44792i	0.307409	−	0.307409i	0.843904	+	0.536495i	$0.180252\pi$
$588$		0			0
$589$			15.2375i			0.627850i
$590$	13.7648	−	51.3711i	0.566689	−	2.11491i
$591$		0			0
$592$	−7.79418	−	29.0883i	−0.320339	−	1.19552i
$593$	5.83377	−	21.7719i	0.239564	−	0.894066i	−0.736474	−	0.676466i	$-0.763510\pi$
$593$	5.83377	−	21.7719i	0.239564	−	0.894066i	0.976038	−	0.217600i	$-0.0698228\pi$
$594$		0			0
$595$	−8.18559	−	4.56717i	−0.335577	−	0.187236i
$596$	−55.7089	+	55.7089i	−2.28192	+	2.28192i
$597$		0			0
$598$	12.6340	+	1.92460i	0.516645	+	0.0787029i
$599$	23.0340	−	39.8961i	0.941146	−	1.63011i	0.177855	−	0.984057i	$-0.443084\pi$
$599$	23.0340	−	39.8961i	0.941146	−	1.63011i	0.763291	−	0.646055i	$-0.223582\pi$
$600$		0			0
$601$		−	1.03260i		−	0.0421204i	−0.999778	−	0.0210602i	$-0.993296\pi$
$601$		−	1.03260i		−	0.0421204i	0.999778	−	0.0210602i	$-0.00670417\pi$
$602$	−0.0457932	−	3.12110i	−0.00186639	−	0.127207i
$603$		0			0
$604$	17.2370	−	64.3295i	0.701365	−	2.61753i
$605$	−15.5230	+	4.15937i	−0.631098	+	0.169102i
$606$		0			0
$607$	23.6563	−	13.6580i	0.960180	−	0.554360i	0.0639518	−	0.997953i	$-0.479630\pi$
$607$	23.6563	−	13.6580i	0.960180	−	0.554360i	0.896229	+	0.443593i	$0.146296\pi$
$608$	−37.5680			−1.52358
$609$		0			0
$610$		−	51.6864i		−	2.09272i
$611$	22.5651	+	18.0532i	0.912885	+	0.730353i
$612$		0			0
$613$	26.8783	−	7.20201i	1.08560	−	0.290887i	0.328714	−	0.944430i	$-0.393385\pi$
$613$	26.8783	−	7.20201i	1.08560	−	0.290887i	0.756889	+	0.653543i	$0.226718\pi$
$614$	4.78994	−	2.76547i	0.193306	−	0.111605i
$615$		0			0
$616$	12.2696	−	48.6338i	0.494356	−	1.95951i
$617$	−11.4818	−	11.4818i	−0.462241	−	0.462241i	0.437148	−	0.899390i	$-0.355989\pi$
$617$	−11.4818	−	11.4818i	−0.462241	−	0.462241i	−0.899390	+	0.437148i	$0.855989\pi$
$618$		0			0
$619$	36.3384	−	9.73685i	1.46056	−	0.391357i	0.560880	−	0.827897i	$-0.310463\pi$
$619$	36.3384	−	9.73685i	1.46056	−	0.391357i	0.899685	+	0.436540i	$0.143796\pi$
$620$	−48.4274	+	83.8787i	−1.94489	+	3.36865i
$621$		0			0
$622$	6.28613	+	6.28613i	0.252051	+	0.252051i
$623$	0.137218	−	0.00201328i	0.00549753	−	8.06605e-5i
$624$		0			0
$625$	−15.0069	−	25.9928i	−0.600278	−	1.03971i
$626$	−16.7059	−	62.3474i	−0.667703	−	2.49190i
$627$		0			0
$628$	−27.6983	−	47.9749i	−1.10528	−	1.91441i
$629$	−2.26339	+	2.26339i	−0.0902474	+	0.0902474i
$630$		0			0
$631$	1.20311	−	1.20311i	0.0478949	−	0.0478949i	−0.682754	−	0.730649i	$-0.739218\pi$
$631$	1.20311	−	1.20311i	0.0478949	−	0.0478949i	0.730649	+	0.682754i	$0.239218\pi$
$632$	−122.344	−	32.7820i	−4.86659	−	1.30400i
$633$		0			0
$634$	70.7329	+	40.8377i	2.80916	+	1.62187i
$635$	−5.56094	+	20.7537i	−0.220679	+	0.823586i
$636$		0			0
$637$	3.52113	+	24.9920i	0.139512	+	0.990220i
$638$	26.5269			1.05021
$639$		0			0
$640$	−51.1981	−	29.5593i	−2.02378	−	1.16843i
$641$	1.30393	+	0.752823i	0.0515020	+	0.0297347i	0.525530	−	0.850775i	$-0.323867\pi$
$641$	1.30393	+	0.752823i	0.0515020	+	0.0297347i	−0.474028	+	0.880510i	$0.657200\pi$
$642$		0			0
$643$	−27.5811	+	27.5811i	−1.08769	+	1.08769i	−0.0919256	+	0.995766i	$0.529302\pi$
$643$	−27.5811	+	27.5811i	−1.08769	+	1.08769i	−0.995766	+	0.0919256i	$0.970698\pi$
$644$	−4.99997	−	17.6219i	−0.197026	−	0.694399i
$645$		0			0
$646$	3.95455	+	6.84948i	0.155590	+	0.269489i
$647$	−3.94074	+	6.82555i	−0.154926	+	0.268340i	−0.933032	−	0.359793i	$-0.882847\pi$
$647$	−3.94074	+	6.82555i	−0.154926	+	0.268340i	0.778106	+	0.628133i	$0.216181\pi$
$648$		0			0
$649$	−8.40979	−	14.5662i	−0.330113	−	0.571773i
$650$	4.90891	+	12.5658i	0.192543	+	0.492871i
$651$		0			0
$652$	2.00546	+	2.00546i	0.0785401	+	0.0785401i
$653$	3.18315	+	5.51337i	0.124566	+	0.215755i	0.921563	−	0.388228i	$-0.126913\pi$
$653$	3.18315	+	5.51337i	0.124566	+	0.215755i	−0.796997	+	0.603983i	$0.793579\pi$
$654$		0			0
$655$	−22.4800	+	6.02350i	−0.878367	+	0.235358i
$656$	48.5116	+	12.9986i	1.89406	+	0.507511i
$657$		0			0
$658$	13.9813	−	55.4186i	0.545048	−	2.16044i
$659$	25.8902			1.00854			0.504270	−	0.863546i	$-0.331762\pi$
$659$	25.8902			1.00854			0.504270	+	0.863546i	$0.331762\pi$
$660$		0			0
$661$	−37.1246	+	9.94751i	−1.44398	+	0.386913i	−0.893925	−	0.448216i	$-0.852060\pi$
$661$	−37.1246	+	9.94751i	−1.44398	+	0.386913i	−0.550054	+	0.835129i	$0.685393\pi$
$662$	−22.3277	−	12.8909i	−0.867790	−	0.501019i
$663$		0			0
$664$		−	47.6172i		−	1.84791i
$665$	3.42440	−	13.5735i	0.132793	−	0.526360i
$666$		0			0
$667$	5.20252	−	3.00368i	0.201442	−	0.116303i
$668$	−8.54731	−	31.8990i	−0.330705	−	1.23421i
$669$		0			0
$670$	−1.00092	+	3.73548i	−0.0386689	+	0.144314i
$671$	−11.5585	−	11.5585i	−0.446212	−	0.446212i
$672$		0			0
$673$		−	5.66768i		−	0.218473i	−0.994016	−	0.109236i	$-0.965159\pi$
$673$		−	5.66768i		−	0.218473i	0.994016	−	0.109236i	$-0.0348406\pi$
$674$	62.6730	+	16.7932i	2.41407	+	0.646849i
$675$		0			0
$676$	15.0196	+	66.7725i	0.577675	+	2.56817i
$677$	−2.32654	+	1.34323i	−0.0894161	+	0.0516244i	−0.544041	−	0.839058i	$-0.683107\pi$
$677$	−2.32654	+	1.34323i	−0.0894161	+	0.0516244i	0.454625	+	0.890683i	$0.349773\pi$
$678$		0			0
$679$	30.8371	+	17.2056i	1.18342	+	0.660290i
$680$			31.1748i			1.19550i
$681$		0			0
$682$	10.9396	+	40.8272i	0.418899	+	1.56335i
$683$	−3.37609	−	12.5998i	−0.129183	−	0.482116i	0.870772	−	0.491688i	$-0.163620\pi$
$683$	−3.37609	−	12.5998i	−0.129183	−	0.482116i	−0.999954	+	0.00957166i	$0.996953\pi$
$684$		0			0
$685$		−	22.9989i		−	0.878743i
$686$	42.0901	−	26.8368i	1.60701	−	1.02463i
$687$		0			0
$688$	−4.99910	+	2.88623i	−0.190589	+	0.110037i
$689$	5.41804	+	7.36540i	0.206411	+	0.280599i
$690$		0			0
$691$	2.50901	+	0.672287i	0.0954472	+	0.0255750i	0.306227	−	0.951959i	$-0.400933\pi$
$691$	2.50901	+	0.672287i	0.0954472	+	0.0255750i	−0.210779	+	0.977534i	$0.567600\pi$
$692$		−	13.6685i		−	0.519599i
$693$		0			0
$694$	−7.58493	−	7.58493i	−0.287920	−	0.287920i
$695$	−0.486877	+	1.81705i	−0.0184683	+	0.0689246i
$696$		0			0
$697$	−1.38165	−	5.15639i	−0.0523338	−	0.195312i
$698$	16.7032	−	9.64360i	0.632226	−	0.365016i
$699$		0			0
$700$	13.4708	−	13.8719i	0.509147	−	0.524310i
$701$			42.5214i			1.60601i	0.595972	+	0.803005i	$0.296767\pi$
$701$			42.5214i			1.60601i	−0.595972	+	0.803005i	$0.703233\pi$
$702$		0			0
$703$	−4.13995	−	2.39020i	−0.156141	−	0.0901481i
$704$	−45.7715	+	12.2644i	−1.72508	+	0.462234i
$705$		0			0
$706$	−26.3896			−0.993184
$707$	36.8005	+	9.28422i	1.38403	+	0.349169i
$708$		0			0
$709$	46.1184	+	12.3574i	1.73201	+	0.464091i	0.980645	−	0.195793i	$-0.0627280\pi$
$709$	46.1184	+	12.3574i	1.73201	+	0.464091i	0.751367	+	0.659884i	$0.229395\pi$
$710$	100.000	−	26.7950i	3.75295	−	1.00560i
$711$		0			0
$712$	−0.228207	−	0.395266i	−0.00855242	−	0.0148132i
$713$	6.76843	+	6.76843i	0.253480	+	0.253480i
$714$		0			0
$715$	17.9830	+	7.87960i	0.672526	+	0.294680i
$716$	4.25081	+	7.36261i	0.158860	+	0.275154i
$717$		0			0
$718$	−50.1490	+	86.8606i	−1.87154	+	3.24161i
$719$	9.27940	+	16.0724i	0.346063	+	0.599399i	0.985546	−	0.169406i	$-0.0541850\pi$
$719$	9.27940	+	16.0724i	0.346063	+	0.599399i	−0.639483	+	0.768805i	$0.720852\pi$
$720$		0			0
$721$	−16.6163	+	17.1111i	−0.618823	+	0.637252i
$722$	27.8593	−	27.8593i	1.03682	−	1.03682i
$723$		0			0
$724$	11.3834	+	6.57220i	0.423060	+	0.244254i
$725$	5.49189	+	3.17074i	0.203964	+	0.117758i
$726$		0			0
$727$	32.8685			1.21903			0.609513	−	0.792776i	$-0.291365\pi$
$727$	32.8685			1.21903			0.609513	+	0.792776i	$0.291365\pi$
$728$	66.8795	−	50.7258i	2.47872	−	1.88002i
$729$		0			0
$730$	21.7133	−	81.0350i	0.803644	−	2.99924i
$731$	0.531364	+	0.306783i	0.0196532	+	0.0113468i
$732$		0			0
$733$	36.2185	+	9.70471i	1.33776	+	0.358452i	0.855603	−	0.517633i	$-0.173187\pi$
$733$	36.2185	+	9.70471i	1.33776	+	0.358452i	0.482157	+	0.876085i	$0.339853\pi$
$734$	−54.3210	+	54.3210i	−2.00503	+	2.00503i
$735$		0			0
$736$	−16.6876	+	16.6876i	−0.615112	+	0.615112i
$737$	0.611524	+	1.05919i	0.0225258	+	0.0390158i
$738$		0			0
$739$	−1.37878	−	5.14567i	−0.0507191	−	0.189286i	0.935918	−	0.352217i	$-0.114572\pi$
$739$	−1.37878	−	5.14567i	−0.0507191	−	0.189286i	−0.986638	+	0.162930i	$0.947905\pi$
$740$	−15.1929	−	26.3149i	−0.558504	−	0.967357i
$741$		0			0
$742$	8.81138	−	15.7924i	0.323476	−	0.579756i
$743$	12.3984	+	12.3984i	0.454854	+	0.454854i	0.896962	−	0.442108i	$-0.145769\pi$
$743$	12.3984	+	12.3984i	0.454854	+	0.454854i	−0.442108	+	0.896962i	$0.645769\pi$
$744$		0			0
$745$	−18.9115	+	32.7557i	−0.692864	+	1.20007i
$746$	−12.2891	+	3.29286i	−0.449936	+	0.120560i
$747$		0			0
$748$	11.2424	+	11.2424i	0.411064	+	0.411064i
$749$	−7.94332	+	8.17988i	−0.290243	+	0.298886i
$750$		0			0
$751$	−27.4170	+	15.8292i	−1.00046	+	0.577615i	−0.908384	−	0.418137i	$-0.862683\pi$
$751$	−27.4170	+	15.8292i	−1.00046	+	0.577615i	−0.0920748	+	0.995752i	$0.529350\pi$
$752$	−102.095	+	27.3563i	−3.72303	+	0.997582i
$753$		0			0
$754$	34.6647	+	27.7335i	1.26241	+	1.00999i
$755$		−	31.9730i		−	1.16361i
$756$		0			0
$757$	−20.0484			−0.728670			−0.364335	−	0.931268i	$-0.618704\pi$
$757$	−20.0484			−0.728670			−0.364335	+	0.931268i	$0.618704\pi$
$758$	−15.8216	+	9.13460i	−0.574666	+	0.331784i
$759$		0			0
$760$	−44.9715	+	12.0501i	−1.63129	+	0.437102i
$761$	−11.8816	+	44.3428i	−0.430708	+	1.60743i	0.320424	+	0.947274i	$0.396175\pi$
$761$	−11.8816	+	44.3428i	−0.430708	+	1.60743i	−0.751133	+	0.660151i	$0.770492\pi$
$762$		0			0
$763$	10.0046	+	16.7559i	0.362192	+	0.606606i
$764$			57.5561i			2.08231i
$765$		0			0
$766$	7.16275	−	12.4063i	0.258801	−	0.448256i
$767$	4.23903	−	27.8271i	0.153062	−	1.00478i
$768$		0			0
$769$	−4.10750	+	4.10750i	−0.148120	+	0.148120i	−0.777278	−	0.629158i	$-0.783400\pi$
$769$	−4.10750	+	4.10750i	−0.148120	+	0.148120i	0.629158	+	0.777278i	$0.283400\pi$
$770$	−0.569681	−	38.8274i	−0.0205299	−	1.39924i
$771$		0			0
$772$	−8.49112	+	31.6893i	−0.305602	+	1.14052i
$773$	10.8746	+	40.5845i	0.391132	+	1.45972i	0.828270	+	0.560329i	$0.189325\pi$
$773$	10.8746	+	40.5845i	0.391132	+	1.45972i	−0.437138	+	0.899394i	$0.644008\pi$
$774$		0			0
$775$	−2.61521	+	9.76010i	−0.0939412	+	0.350593i
$776$		−	117.443i		−	4.21595i
$777$		0			0
$778$	−66.4622	+	66.4622i	−2.38279	+	2.38279i
$779$	6.90434	−	3.98622i	0.247374	−	0.142821i
$780$		0			0
$781$	16.3707	−	28.3549i	0.585791	−	1.01462i
$782$	4.79911	+	1.28592i	0.171616	+	0.0459843i
$783$		0			0
$784$	−81.2650	−	43.7911i	−2.90232	−	1.56397i
$785$	−18.8055	−	18.8055i	−0.671197	−	0.671197i
$786$		0			0
$787$	−13.7338	+	3.67997i	−0.489558	+	0.131177i	−0.495150	−	0.868808i	$-0.664887\pi$
$787$	−13.7338	+	3.67997i	−0.489558	+	0.131177i	0.00559167	+	0.999984i	$0.498220\pi$
$788$	22.1465	+	82.6520i	0.788938	+	2.94436i
$789$		0			0
$790$	−98.0589			−3.48878
$791$	−7.33599	−	25.8549i	−0.260838	−	0.919295i
$792$		0			0
$793$	−3.02013	−	27.1887i	−0.107248	−	0.965497i
$794$	−85.0441	−	49.1002i	−3.01810	−	1.74250i
$795$		0			0
$796$	82.3064	−	47.5196i	2.91727	−	1.68429i
$797$	31.4048			1.11241			0.556207	−	0.831044i	$-0.312256\pi$
$797$	31.4048			1.11241			0.556207	+	0.831044i	$0.312256\pi$
$798$		0			0
$799$	7.94414	+	7.94414i	0.281044	+	0.281044i
$800$	−24.0635	−	6.44780i	−0.850774	−	0.227964i
$801$		0			0
$802$	19.8206	−	34.3303i	0.699889	−	1.21224i
$803$	−13.2660	−	22.9773i	−0.468146	−	0.810853i
$804$		0			0
$805$	−4.50821	−	7.55043i	−0.158894	−	0.266118i
$806$	−28.3886	+	64.7892i	−0.999947	+	2.28210i
$807$		0			0
$808$	−32.6701	−	121.926i	−1.14933	−	4.28935i
$809$	−14.9036	+	25.8137i	−0.523981	+	0.907562i	0.475629	+	0.879646i	$0.342220\pi$
$809$	−14.9036	+	25.8137i	−0.523981	+	0.907562i	−0.999610	+	0.0279158i	$0.991113\pi$
$810$		0			0
$811$	7.04429	−	7.04429i	0.247359	−	0.247359i	−0.572527	−	0.819886i	$-0.694037\pi$
$811$	7.04429	−	7.04429i	0.247359	−	0.247359i	0.819886	+	0.572527i	$0.194037\pi$
$812$	15.5652	−	61.6967i	0.546230	−	2.16513i
$813$		0			0
$814$	−12.8086	−	3.43204i	−0.448940	−	0.120293i
$815$	1.17917	+	0.680796i	0.0413046	+	0.0238472i
$816$		0			0
$817$	−0.237163	+	0.885105i	−0.00829729	+	0.0309659i
$818$	−5.92416			−0.207133
$819$		0			0
$820$	50.6756			1.76967
$821$	−6.25043	+	23.3269i	−0.218142	+	0.814116i	0.766895	+	0.641772i	$0.221801\pi$
$821$	−6.25043	+	23.3269i	−0.218142	+	0.814116i	−0.985037	+	0.172343i	$0.944866\pi$
$822$		0			0
$823$	−11.7031	−	6.75677i	−0.407943	−	0.235526i	0.281962	−	0.959425i	$-0.409015\pi$
$823$	−11.7031	−	6.75677i	−0.407943	−	0.235526i	−0.689906	+	0.723899i	$0.742348\pi$
$824$	76.6231	+	20.5311i	2.66929	+	0.715235i
$825$		0			0
$826$	−53.5576	+	15.1963i	−1.86351	+	0.528746i
$827$	−29.8965	+	29.8965i	−1.03960	+	1.03960i	−0.0404191	+	0.999183i	$0.512869\pi$
$827$	−29.8965	+	29.8965i	−1.03960	+	1.03960i	−0.999183	+	0.0404191i	$0.987131\pi$
$828$		0			0
$829$	27.4075	−	47.4712i	0.951903	−	1.64874i	0.210601	−	0.977572i	$-0.432458\pi$
$829$	27.4075	−	47.4712i	0.951903	−	1.64874i	0.741302	−	0.671172i	$-0.234209\pi$
$830$	−9.54131	−	35.6086i	−0.331184	−	1.23599i
$831$		0			0
$832$	−72.6355	−	31.8266i	−2.51818	−	1.10339i
$833$	0.287868	+	9.80789i	0.00997402	+	0.339823i
$834$		0			0
$835$	−7.92720	−	13.7303i	−0.274332	−	0.475157i
$836$	−11.8723	+	20.5634i	−0.410612	+	0.711201i
$837$		0			0
$838$	82.0428	+	21.9833i	2.83412	+	0.759401i
$839$	−1.27402	−	1.27402i	−0.0439842	−	0.0439842i	0.684773	−	0.728757i	$-0.259902\pi$
$839$	−1.27402	−	1.27402i	−0.0439842	−	0.0439842i	−0.728757	+	0.684773i	$0.759902\pi$
$840$		0			0
$841$	−8.13210			−0.280417
$842$	33.2173	−	19.1780i	1.14474	−	0.660919i
$843$		0			0
$844$	−12.6993	−	7.33196i	−0.437129	−	0.252376i
$845$	15.2617	+	29.0978i	0.525020	+	1.00100i
$846$		0			0
$847$	12.0685	+	11.7195i	0.414680	+	0.402687i
$848$	−33.4431			−1.14844
$849$		0			0
$850$	1.35744	+	5.06604i	0.0465598	+	0.173764i
$851$	−2.90067	+	0.777231i	−0.0994336	+	0.0266431i
$852$		0			0
$853$	−2.51606	−	2.51606i	−0.0861481	−	0.0861481i	0.662720	−	0.748868i	$-0.269402\pi$
$853$	−2.51606	−	2.51606i	−0.0861481	−	0.0861481i	−0.748868	+	0.662720i	$0.769402\pi$
$854$	−46.4543	+	27.7369i	−1.58963	+	0.949138i
$855$		0			0
$856$	36.6292	+	9.81477i	1.25196	+	0.335462i
$857$	10.5909	−	18.3440i	0.361778	−	0.626618i	−0.626476	−	0.779441i	$-0.715503\pi$
$857$	10.5909	−	18.3440i	0.361778	−	0.626618i	0.988254	+	0.152823i	$0.0488365\pi$
$858$		0			0
$859$	−7.46703	+	4.31109i	−0.254772	+	0.147093i	−0.621947	−	0.783059i	$-0.713658\pi$
$859$	−7.46703	+	4.31109i	−0.254772	+	0.147093i	0.367175	+	0.930152i	$0.380325\pi$
$860$	−4.11854	+	4.11854i	−0.140441	+	0.140441i
$861$		0			0
$862$			35.8791i			1.22205i
$863$	−9.40233	+	35.0900i	−0.320059	+	1.19448i	0.599127	+	0.800654i	$0.295514\pi$
$863$	−9.40233	+	35.0900i	−0.320059	+	1.19448i	−0.919186	+	0.393823i	$0.871152\pi$
$864$		0			0
$865$	−1.69838	−	6.33844i	−0.0577466	−	0.215513i
$866$	20.3123	−	75.8064i	0.690239	−	2.57601i
$867$		0			0
$868$	101.376	−	1.48740i	3.44092	−	0.0504856i
$869$	−21.9287	+	21.9287i	−0.743879	+	0.743879i
$870$		0			0
$871$	−0.308244	+	2.02346i	−0.0104444	+	0.0685625i
$872$	32.4527	−	56.2097i	1.09899	−	1.90350i
$873$		0			0
$874$			7.42004i			0.250987i
$875$	−11.7681	+	21.0916i	−0.397834	+	0.713026i
$876$		0			0
$877$	−9.14311	+	34.1226i	−0.308741	+	1.15224i	0.620936	+	0.783861i	$0.286753\pi$
$877$	−9.14311	+	34.1226i	−0.308741	+	1.15224i	−0.929677	+	0.368376i	$0.879914\pi$
$878$	26.8505	−	7.19458i	0.906161	−	0.242805i
$879$		0			0
$880$	−62.1902	+	35.9055i	−2.09643	+	1.21038i
$881$	−48.8409			−1.64549			−0.822747	−	0.568408i	$-0.807559\pi$
$881$	−48.8409			−1.64549			−0.822747	+	0.568408i	$0.807559\pi$
$882$		0			0
$883$			56.2857i			1.89417i	0.320989	+	0.947083i	$0.395985\pi$
$883$			56.2857i			1.89417i	−0.320989	+	0.947083i	$0.604015\pi$
$884$	2.93754	+	26.4451i	0.0988000	+	0.889446i
$885$		0			0
$886$	−1.60105	+	0.428999i	−0.0537882	+	0.0144125i
$887$	24.3132	−	14.0372i	0.816357	−	0.471324i	−0.0328019	−	0.999462i	$-0.510443\pi$
$887$	24.3132	−	14.0372i	0.816357	−	0.471324i	0.849158	+	0.528138i	$0.177110\pi$
$888$		0			0
$889$	21.6370	−	6.13923i	0.725683	−	0.205903i
$890$	−0.249857	−	0.249857i	−0.00837523	−	0.00837523i
$891$		0			0
$892$	−87.2544	+	23.3797i	−2.92149	+	0.782811i
$893$	−8.38921	+	14.5305i	−0.280734	+	0.486246i
$894$		0			0
$895$	2.88604	+	2.88604i	0.0964698	+	0.0964698i
$896$	0.907883	+	61.8780i	0.0303303	+	2.06720i
$897$		0			0
$898$	−16.5126	−	28.6006i	−0.551032	−	0.954415i
$899$	8.60587	+	32.1175i	0.287022	+	1.07118i
$900$		0			0
$901$	1.77737	+	3.07849i	0.0592127	+	0.102559i
$902$	15.6376	−	15.6376i	0.520674	−	0.520674i
$903$		0			0
$904$	−63.2037	+	63.2037i	−2.10212	+	2.10212i
$905$	6.09539	+	1.63325i	0.202617	+	0.0542912i
$906$		0			0
$907$	40.1518	+	23.1816i	1.33322	+	0.769733i	0.985791	−	0.167974i	$-0.0537225\pi$
$907$	40.1518	+	23.1816i	1.33322	+	0.769733i	0.347426	+	0.937707i	$0.387056\pi$
$908$	23.3682	−	87.2113i	0.775501	−	2.89421i
$909$		0			0
$910$	39.8490	−	51.3343i	1.32098	−	1.70171i
$911$	23.8152			0.789032			0.394516	−	0.918889i	$-0.370912\pi$
$911$	23.8152			0.789032			0.394516	+	0.918889i	$0.370912\pi$
$912$		0			0
$913$	−10.0968	−	5.82938i	−0.334154	−	0.192924i
$914$	−43.1609	−	24.9189i	−1.42763	−	0.824245i
$915$		0			0
$916$	81.1056	−	81.1056i	2.67980	−	2.67980i
$917$	17.4774	+	16.9719i	0.577154	+	0.560463i
$918$		0			0
$919$	28.8769	+	50.0162i	0.952561	+	1.64988i	0.739854	+	0.672768i	$0.234895\pi$
$919$	28.8769	+	50.0162i	0.952561	+	1.64988i	0.212707	+	0.977116i	$0.431772\pi$
$920$	−14.6236	+	25.3287i	−0.482124	+	0.835064i
$921$		0			0
$922$	9.91531	+	17.1738i	0.326543	+	0.565590i
$923$	51.0376	−	19.9382i	1.67992	−	0.656273i
$924$		0			0
$925$	−2.24154	−	2.24154i	−0.0737014	−	0.0737014i
$926$	−26.6475	−	46.1547i	−0.875690	−	1.51674i
$927$		0			0
$928$	−79.1858	+	21.2178i	−2.59940	+	0.696507i
$929$	−18.4822	−	4.95230i	−0.606383	−	0.162480i	−0.0574529	−	0.998348i	$-0.518298\pi$
$929$	−18.4822	−	4.95230i	−0.606383	−	0.162480i	−0.548930	+	0.835868i	$0.684965\pi$
$930$		0			0
$931$	−14.0372	+	4.20633i	−0.460050	+	0.137857i
$932$	158.807			5.20190
$933$		0			0
$934$	25.7464	−	6.89872i	0.842447	−	0.225733i
$935$	6.61032	+	3.81647i	0.216181	+	0.124812i
$936$		0			0
$937$		−	8.53986i		−	0.278985i	−0.990223	−	0.139492i	$-0.955453\pi$
$937$		−	8.53986i		−	0.278985i	0.990223	−	0.139492i	$-0.0445471\pi$
$938$	3.89448	−	1.10501i	0.127159	−	0.0360797i
$939$		0			0
$940$	−92.3612	+	53.3248i	−3.01249	+	1.73926i
$941$	−6.94674	−	25.9256i	−0.226457	−	0.845149i	−0.981816	−	0.189838i	$-0.939204\pi$
$941$	−6.94674	−	25.9256i	−0.226457	−	0.845149i	0.755358	−	0.655312i	$-0.227463\pi$
$942$		0			0
$943$	1.29622	−	4.83755i	0.0422106	−	0.157532i
$944$	72.7992	+	72.7992i	2.36941	+	2.36941i
$945$		0			0
$946$			2.54181i			0.0826414i
$947$	−35.2734	−	9.45147i	−1.14623	−	0.307132i	−0.364777	−	0.931095i	$-0.618855\pi$
$947$	−35.2734	−	9.45147i	−1.14623	−	0.307132i	−0.781454	+	0.623963i	$0.785521\pi$
$948$		0			0
$949$	6.68683	−	43.8956i	0.217064	−	1.42491i
$950$	−6.78335	+	3.91637i	−0.220081	+	0.127064i
$951$		0			0
$952$	28.0190	−	16.7296i	0.908102	−	0.542210i
$953$		−	41.8966i		−	1.35716i	−0.734525	−	0.678581i	$-0.762595\pi$
$953$		−	41.8966i		−	1.35716i	0.734525	−	0.678581i	$-0.237405\pi$
$954$		0			0
$955$	7.15162	+	26.6902i	0.231421	+	0.863674i
$956$	19.6015	+	73.1536i	0.633956	+	2.36596i
$957$		0			0
$958$		−	36.5976i		−	1.18241i
$959$	−20.6708	+	12.3421i	−0.667494	+	0.398547i
$960$		0			0
$961$	−19.0359	+	10.9904i	−0.614062	+	0.354529i
$962$	−13.1498	−	17.8761i	−0.423966	−	0.576348i
$963$		0			0
$964$	−108.662	−	29.1158i	−3.49976	−	0.937758i
$965$			15.7502i			0.507016i
$966$		0			0
$967$	−26.8795	−	26.8795i	−0.864388	−	0.864388i	0.127456	−	0.991844i	$-0.459319\pi$
$967$	−26.8795	−	26.8795i	−0.864388	−	0.864388i	−0.991844	+	0.127456i	$0.959319\pi$
$968$	14.4806	−	54.0425i	0.465426	−	1.73699i
$969$		0			0
$970$	−23.5326	−	87.8250i	−0.755588	−	2.81989i
$971$	−35.4794	+	20.4840i	−1.13859	+	0.657364i	−0.946081	−	0.323932i	$-0.894995\pi$
$971$	−35.4794	+	20.4840i	−1.13859	+	0.657364i	−0.192507	+	0.981296i	$0.561662\pi$
$972$		0			0
$973$	1.89439	−	0.537508i	0.0607313	−	0.0172317i
$974$		−	16.5562i		−	0.530494i
$975$		0			0
$976$	86.6510	+	50.0280i	2.77363	+	1.60136i
$977$	−25.5649	+	6.85008i	−0.817892	+	0.219154i	−0.643425	−	0.765509i	$-0.722487\pi$
$977$	−25.5649	+	6.85008i	−0.817892	+	0.219154i	−0.174467	+	0.984663i	$0.555820\pi$
$978$		0			0
$979$	−0.111750			−0.00357154
$980$	−90.6397	−	21.4578i	−2.89538	−	0.685443i
$981$		0			0
$982$	58.4297	+	15.6562i	1.86457	+	0.499609i
$983$	−45.4290	+	12.1727i	−1.44896	+	0.388247i	−0.895661	−	0.444737i	$-0.853297\pi$
$983$	−45.4290	+	12.1727i	−1.44896	+	0.388247i	−0.553297	+	0.832984i	$0.686631\pi$
$984$		0			0
$985$	20.5398	+	35.5760i	0.654452	+	1.13354i
$986$	12.2039	+	12.2039i	0.388650	+	0.388650i
$987$		0			0
$988$	−37.0132	+	14.4595i	−1.17755	+	0.460017i
$989$	0.287813	+	0.498507i	0.00915193	+	0.0158516i
$990$		0			0
$991$	12.0292	−	20.8351i	0.382119	−	0.661850i	−0.609246	−	0.792981i	$-0.708528\pi$
$991$	12.0292	−	20.8351i	0.382119	−	0.661850i	0.991365	+	0.131132i	$0.0418610\pi$
$992$	−65.3120	−	113.124i	−2.07366	−	3.59168i
$993$		0			0
$994$	−77.7466	−	75.4982i	−2.46597	−	2.39466i
$995$	32.2630	−	32.2630i	1.02281	−	1.02281i
$996$		0			0
$997$	5.76234	+	3.32689i	0.182495	+	0.105364i	0.588464	−	0.808523i	$-0.299733\pi$
$997$	5.76234	+	3.32689i	0.182495	+	0.105364i	−0.405969	+	0.913887i	$0.633066\pi$
$998$	87.0062	+	50.2331i	2.75413	+	1.59010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.73.1		32
3.2	odd	2		91.2.bb.a.73.8	yes	32
7.5	odd	6	inner	819.2.fn.e.775.8		32
13.5	odd	4	inner	819.2.fn.e.577.8		32
21.2	odd	6		637.2.bc.b.411.1		32
21.5	even	6		91.2.bb.a.47.1	yes	32
21.11	odd	6		637.2.i.a.489.16		32
21.17	even	6		637.2.i.a.489.15		32
21.20	even	2		637.2.bc.b.619.8		32
39.5	even	4		91.2.bb.a.31.1	yes	32
91.5	even	12	inner	819.2.fn.e.460.1		32
273.5	odd	12		91.2.bb.a.5.8	✓	32
273.44	even	12		637.2.bc.b.460.8		32
273.83	odd	4		637.2.bc.b.31.1		32
273.122	odd	12		637.2.i.a.538.15		32
273.200	even	12		637.2.i.a.538.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.8	✓	32	273.5	odd	12
91.2.bb.a.31.1	yes	32	39.5	even	4
91.2.bb.a.47.1	yes	32	21.5	even	6
91.2.bb.a.73.8	yes	32	3.2	odd	2
637.2.i.a.489.15		32	21.17	even	6
637.2.i.a.489.16		32	21.11	odd	6
637.2.i.a.538.15		32	273.122	odd	12
637.2.i.a.538.16		32	273.200	even	12
637.2.bc.b.31.1		32	273.83	odd	4
637.2.bc.b.411.1		32	21.2	odd	6
637.2.bc.b.460.8		32	273.44	even	12
637.2.bc.b.619.8		32	21.20	even	2
819.2.fn.e.73.1		32	1.1	even	1	trivial
819.2.fn.e.460.1		32	91.5	even	12	inner
819.2.fn.e.577.8		32	13.5	odd	4	inner
819.2.fn.e.775.8		32	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.697597 + 2.60347i) q^{2} +(-4.55935 - 2.63234i) q^{4} +(-2.44137 - 0.654162i) q^{5} +(0.722189 + 2.54528i) q^{7} +(6.22207 - 6.22207i) q^{8} +O(q^{10})\)	\(q+(-0.697597 + 2.60347i) q^{2} +(-4.55935 - 2.63234i) q^{4} +(-2.44137 - 0.654162i) q^{5} +(0.722189 + 2.54528i) q^{7} +(6.22207 - 6.22207i) q^{8} +(3.40618 - 5.89968i) q^{10} +(-0.557615 - 2.08105i) q^{11} +(1.44703 - 3.30244i) q^{13} +(-7.13035 + 0.104617i) q^{14} +(6.59378 + 11.4208i) q^{16} +(0.700866 - 1.21393i) q^{17} +(2.02208 + 0.541814i) q^{19} +(9.40907 + 9.40907i) q^{20} +5.80693 q^{22} +(1.13887 - 0.657528i) q^{23} +(1.20221 + 0.694099i) q^{25} +(7.58836 + 6.07106i) q^{26} +(3.40733 - 13.5059i) q^{28} +4.56814 q^{29} +(1.88389 + 7.03077i) q^{31} +(-17.3344 + 4.64473i) q^{32} +(2.67152 + 2.67152i) q^{34} +(-0.0981036 - 6.68639i) q^{35} +(-2.20574 - 0.591026i) q^{37} +(-2.82119 + 4.88645i) q^{38} +(-19.2606 + 11.1201i) q^{40} +(2.69291 - 2.69291i) q^{41} +0.437721i q^{43} +(-2.93567 + 10.9561i) q^{44} +(0.917379 + 3.42370i) q^{46} +(-2.07440 + 7.74178i) q^{47} +(-5.95689 + 3.67635i) q^{49} +(-2.64573 + 2.64573i) q^{50} +(-15.2907 + 11.2479i) q^{52} +(-1.26798 + 2.19621i) q^{53} +5.44537i q^{55} +(20.3304 + 11.3434i) q^{56} +(-3.18672 + 11.8930i) q^{58} +(7.54086 - 2.02057i) q^{59} +(6.57067 - 3.79358i) q^{61} -19.6186 q^{62} -21.9945i q^{64} +(-5.69306 + 7.11588i) q^{65} +(-0.548339 + 0.146927i) q^{67} +(-6.39099 + 3.68984i) q^{68} +(17.4762 + 4.40899i) q^{70} +(10.7460 + 10.7460i) q^{71} +(11.8953 - 3.18733i) q^{73} +(3.07743 - 5.33027i) q^{74} +(-7.79312 - 7.79312i) q^{76} +(4.89414 - 2.92219i) q^{77} +(-7.19713 - 12.4658i) q^{79} +(-8.62680 - 32.1956i) q^{80} +(5.13234 + 8.88948i) q^{82} +(3.82648 - 3.82648i) q^{83} +(-2.50518 + 2.50518i) q^{85} +(-1.13959 - 0.305353i) q^{86} +(-16.4179 - 9.47890i) q^{88} +(0.0134247 - 0.0501018i) q^{89} +(9.45066 + 1.29810i) q^{91} -6.92335 q^{92} +(-18.7084 - 10.8013i) q^{94} +(-4.58220 - 2.64553i) q^{95} +(9.43761 - 9.43761i) q^{97} +(-5.41574 - 18.0732i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more