LMFDB - Embedded newform 450.2.l.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	450.289
Dual form			450.2.l.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.44575 + 1.70582i) q^{5} +1.27346i q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.44575 + 1.70582i) q^{5} +1.27346i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.530249 - 2.17229i) q^{10} +(-3.52874 + 2.56378i) q^{11} +(-2.51812 + 3.46589i) q^{13} +(1.03025 - 0.748520i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.0930960 - 0.0302487i) q^{17} +(0.103198 + 0.317610i) q^{19} +(-2.06909 + 0.847859i) q^{20} +(4.14828 + 1.34786i) q^{22} +(-3.71113 - 5.10793i) q^{23} +(-0.819639 + 4.93236i) q^{25} +4.28408 q^{26} +(-1.21113 - 0.393520i) q^{28} +(-1.44575 + 4.44955i) q^{29} +(2.48459 + 7.64677i) q^{31} +1.00000i q^{32} +(-0.0791922 - 0.0575365i) q^{34} +(-2.17229 + 1.84110i) q^{35} +(2.41492 - 3.32385i) q^{37} +(0.196294 - 0.270175i) q^{38} +(1.90211 + 1.17557i) q^{40} +(9.24846 + 6.71940i) q^{41} -10.2093i q^{43} +(-1.34786 - 4.14828i) q^{44} +(-1.95106 + 6.00473i) q^{46} +(11.1323 + 3.61710i) q^{47} +5.37831 q^{49} +(4.47214 - 2.23607i) q^{50} +(-2.51812 - 3.46589i) q^{52} +(0.841616 + 0.273457i) q^{53} +(-9.47501 - 2.31282i) q^{55} +(0.393520 + 1.21113i) q^{56} +(4.44955 - 1.44575i) q^{58} +(-6.15537 - 4.47214i) q^{59} +(1.35645 - 0.985520i) q^{61} +(4.72597 - 6.50473i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-9.55275 + 0.715345i) q^{65} +(1.11179 - 0.361243i) q^{67} +0.0978870i q^{68} +(2.76632 + 0.675249i) q^{70} +(0.728373 - 2.24170i) q^{71} +(-0.945424 - 1.30127i) q^{73} -4.10851 q^{74} -0.333955 q^{76} +(-3.26486 - 4.49370i) q^{77} +(-2.51358 + 7.73601i) q^{79} +(-0.166977 - 2.22982i) q^{80} -11.4317i q^{82} +(-7.05722 + 2.29303i) q^{83} +(0.186192 + 0.115073i) q^{85} +(-8.25950 + 6.00088i) q^{86} +(-2.56378 + 3.52874i) q^{88} +(-1.38197 + 1.00406i) q^{89} +(-4.41367 - 3.20672i) q^{91} +(6.00473 - 1.95106i) q^{92} +(-3.61710 - 11.1323i) q^{94} +(-0.392588 + 0.635220i) q^{95} +(6.28402 + 2.04180i) q^{97} +(-3.16129 - 4.35114i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) $ 8 * q + 2 * q^4 + 10 * q^5	$ 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.44575	+	1.70582i	0.646557	+	0.762866i
$5$	1.44575	+	1.70582i	0.646557	+	0.762866i
$6$		0			0
$7$			1.27346i			0.481322i	0.970609	+	0.240661i	$0.0773642\pi$
$7$			1.27346i			0.481322i	−0.970609	+	0.240661i	$0.922636\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$		0			0
$10$	0.530249	−	2.17229i	0.167679	−	0.686938i
$11$	−3.52874	+	2.56378i	−1.06396	+	0.773009i	−0.974816	−	0.223011i	$-0.928412\pi$
$11$	−3.52874	+	2.56378i	−1.06396	+	0.773009i	−0.0891391	+	0.996019i	$0.528412\pi$
$12$		0			0
$13$	−2.51812	+	3.46589i	−0.698400	+	0.961266i	0.301569	+	0.953444i	$0.402490\pi$
$13$	−2.51812	+	3.46589i	−0.698400	+	0.961266i	−0.999969	+	0.00782134i	$0.997510\pi$
$14$	1.03025	−	0.748520i	0.275346	−	0.200050i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.0930960	−	0.0302487i	0.0225791	−	0.00733640i	−0.297706	−	0.954658i	$-0.596221\pi$
$17$	0.0930960	−	0.0302487i	0.0225791	−	0.00733640i	0.320285	+	0.947321i	$0.396221\pi$
$18$		0			0
$19$	0.103198	+	0.317610i	0.0236752	+	0.0728647i	0.962196	−	0.272358i	$-0.0878034\pi$
$19$	0.103198	+	0.317610i	0.0236752	+	0.0728647i	−0.938521	+	0.345223i	$0.887803\pi$
$20$	−2.06909	+	0.847859i	−0.462663	+	0.189587i
$21$		0			0
$22$	4.14828	+	1.34786i	0.884417	+	0.287364i
$23$	−3.71113	−	5.10793i	−0.773824	−	1.06508i	−0.995937	−	0.0900565i	$-0.971295\pi$
$23$	−3.71113	−	5.10793i	−0.773824	−	1.06508i	0.222113	−	0.975021i	$-0.428705\pi$
$24$		0			0
$25$	−0.819639	+	4.93236i	−0.163928	+	0.986472i
$26$	4.28408			0.840177
$27$		0			0
$28$	−1.21113	−	0.393520i	−0.228882	−	0.0743683i
$29$	−1.44575	+	4.44955i	−0.268468	+	0.826260i	0.722406	+	0.691469i	$0.243036\pi$
$29$	−1.44575	+	4.44955i	−0.268468	+	0.826260i	−0.990874	+	0.134791i	$0.956964\pi$
$30$		0			0
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	0.881113	+	0.472907i	$0.156795\pi$
$31$	2.48459	+	7.64677i	0.446245	+	1.37340i	−0.434867	+	0.900494i	$0.643205\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.0791922	−	0.0575365i	−0.0135814	−	0.00986743i
$35$	−2.17229	+	1.84110i	−0.367184	+	0.311202i
$36$		0			0
$37$	2.41492	−	3.32385i	0.397011	−	0.546438i	−0.562980	−	0.826470i	$-0.690345\pi$
$37$	2.41492	−	3.32385i	0.397011	−	0.546438i	0.959991	+	0.280032i	$0.0903452\pi$
$38$	0.196294	−	0.270175i	0.0318431	−	0.0438282i
$39$		0			0
$40$	1.90211	+	1.17557i	0.300750	+	0.185874i
$41$	9.24846	+	6.71940i	1.44437	+	1.04939i	0.987107	+	0.160061i	$0.0511692\pi$
$41$	9.24846	+	6.71940i	1.44437	+	1.04939i	0.457260	+	0.889333i	$0.348831\pi$
$42$		0			0
$43$		−	10.2093i		−	1.55690i	−0.627704	−	0.778452i	$-0.716005\pi$
$43$		−	10.2093i		−	1.55690i	0.627704	−	0.778452i	$-0.283995\pi$
$44$	−1.34786	−	4.14828i	−0.203197	−	0.625377i
$45$		0			0
$46$	−1.95106	+	6.00473i	−0.287668	+	0.885350i
$47$	11.1323	+	3.61710i	1.62381	+	0.527608i	0.972837	−	0.231491i	$-0.0743603\pi$
$47$	11.1323	+	3.61710i	1.62381	+	0.527608i	0.650975	+	0.759099i	$0.274360\pi$
$48$		0			0
$49$	5.37831			0.768329
$50$	4.47214	−	2.23607i	0.632456	−	0.316228i
$51$		0			0
$52$	−2.51812	−	3.46589i	−0.349200	−	0.480633i
$53$	0.841616	+	0.273457i	0.115605	+	0.0375623i	0.366248	−	0.930517i	$-0.380642\pi$
$53$	0.841616	+	0.273457i	0.115605	+	0.0375623i	−0.250643	+	0.968079i	$0.580642\pi$
$54$		0			0
$55$	−9.47501	−	2.31282i	−1.27761	−	0.311860i
$56$	0.393520	+	1.21113i	0.0525863	+	0.161844i
$57$		0			0
$58$	4.44955	−	1.44575i	0.584254	−	0.189836i
$59$	−6.15537	−	4.47214i	−0.801361	−	0.582223i	0.109952	−	0.993937i	$-0.464930\pi$
$59$	−6.15537	−	4.47214i	−0.801361	−	0.582223i	−0.911313	+	0.411714i	$0.864930\pi$
$60$		0			0
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	−0.497551	−	0.867434i	$-0.665767\pi$
$61$	1.35645	−	0.985520i	0.173676	−	0.126183i	0.671227	+	0.741252i	$0.265767\pi$
$62$	4.72597	−	6.50473i	0.600198	−	0.826102i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−9.55275	+	0.715345i	−1.18487	+	0.0887276i
$66$		0			0
$67$	1.11179	−	0.361243i	0.135827	−	0.0441328i	−0.240315	−	0.970695i	$-0.577251\pi$
$67$	1.11179	−	0.361243i	0.135827	−	0.0441328i	0.376142	+	0.926562i	$0.377251\pi$
$68$			0.0978870i			0.0118705i
$69$		0			0
$70$	2.76632	+	0.675249i	0.330638	+	0.0807077i
$71$	0.728373	−	2.24170i	0.0864419	−	0.266041i	−0.898487	−	0.439000i	$-0.855333\pi$
$71$	0.728373	−	2.24170i	0.0864419	−	0.266041i	0.984929	+	0.172959i	$0.0553328\pi$
$72$		0			0
$73$	−0.945424	−	1.30127i	−0.110654	−	0.152302i	0.750098	−	0.661326i	$-0.230006\pi$
$73$	−0.945424	−	1.30127i	−0.110654	−	0.152302i	−0.860752	+	0.509025i	$0.830006\pi$
$74$	−4.10851			−0.477604
$75$		0			0
$76$	−0.333955			−0.0383073
$77$	−3.26486	−	4.49370i	−0.372066	−	0.512105i
$78$		0			0
$79$	−2.51358	+	7.73601i	−0.282800	+	0.870369i	0.704249	+	0.709953i	$0.251284\pi$
$79$	−2.51358	+	7.73601i	−0.282800	+	0.870369i	−0.987049	+	0.160417i	$0.948716\pi$
$80$	−0.166977	−	2.22982i	−0.0186686	−	0.249302i
$81$		0			0
$82$		−	11.4317i		−	1.26242i
$83$	−7.05722	+	2.29303i	−0.774630	+	0.251693i	−0.669546	−	0.742771i	$-0.733511\pi$
$83$	−7.05722	+	2.29303i	−0.774630	+	0.251693i	−0.105084	+	0.994463i	$0.533511\pi$
$84$		0			0
$85$	0.186192	+	0.115073i	0.0201954	+	0.0124814i
$86$	−8.25950	+	6.00088i	−0.890644	+	0.647091i
$87$		0			0
$88$	−2.56378	+	3.52874i	−0.273300	+	0.376165i
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	−0.658615	−	0.752480i	$-0.728858\pi$
$89$	−1.38197	+	1.00406i	−0.146488	+	0.106430i	0.512127	+	0.858910i	$0.328858\pi$
$90$		0			0
$91$	−4.41367	−	3.20672i	−0.462678	−	0.336155i
$92$	6.00473	−	1.95106i	0.626037	−	0.203412i
$93$		0			0
$94$	−3.61710	−	11.1323i	−0.373076	−	1.14821i
$95$	−0.392588	+	0.635220i	−0.0402786	+	0.0651722i
$96$		0			0
$97$	6.28402	+	2.04180i	0.638046	+	0.207314i	0.610136	−	0.792297i	$-0.291115\pi$
$97$	6.28402	+	2.04180i	0.638046	+	0.207314i	0.0279099	+	0.999610i	$0.491115\pi$
$98$	−3.16129	−	4.35114i	−0.319338	−	0.439532i
$99$		0			0
$100$	−4.43767	−	2.30371i	−0.443767	−	0.230371i
$101$	7.02311			0.698825			0.349413	−	0.936969i	$-0.386381\pi$
$101$	7.02311			0.698825			0.349413	+	0.936969i	$0.386381\pi$
$102$		0			0
$103$	−12.1228	−	3.93893i	−1.19449	−	0.388114i	−0.356760	−	0.934196i	$-0.616119\pi$
$103$	−12.1228	−	3.93893i	−1.19449	−	0.388114i	−0.837732	+	0.546082i	$0.816119\pi$
$104$	−1.32385	+	4.07440i	−0.129814	+	0.399528i
$105$		0			0
$106$	−0.273457	−	0.841616i	−0.0265605	−	0.0817449i
$107$		−	12.2022i		−	1.17963i	−0.807537	−	0.589817i	$-0.799200\pi$
$107$		−	12.2022i		−	1.17963i	0.807537	−	0.589817i	$-0.200800\pi$
$108$		0			0
$109$	−4.08628	−	2.96885i	−0.391394	−	0.284365i	0.374632	−	0.927173i	$-0.377769\pi$
$109$	−4.08628	−	2.96885i	−0.391394	−	0.284365i	−0.766027	+	0.642809i	$0.777769\pi$
$110$	3.69816	+	9.02488i	0.352606	+	0.860489i
$111$		0			0
$112$	0.748520	−	1.03025i	0.0707284	−	0.0973494i
$113$	8.24962	−	11.3546i	0.776059	−	1.06815i	−0.219647	−	0.975579i	$-0.570491\pi$
$113$	8.24962	−	11.3546i	0.776059	−	1.06815i	0.995706	−	0.0925736i	$-0.0295093\pi$
$114$		0			0
$115$	3.34786	−	13.7153i	0.312189	−	1.27896i
$116$	−3.78501	−	2.74997i	−0.351429	−	0.255328i
$117$		0			0
$118$			7.60845i			0.700415i
$119$	0.0385205	+	0.118554i	0.00353117	+	0.0108678i
$120$		0			0
$121$	2.47985	−	7.63220i	0.225441	−	0.693837i
$122$	−1.59460	−	0.518118i	−0.144369	−	0.0469082i
$123$		0			0
$124$	−8.04029			−0.722040
$125$	−9.59871	+	5.73279i	−0.858534	+	0.512756i
$126$		0			0
$127$	0.775266	+	1.06706i	0.0687937	+	0.0946864i	0.842027	−	0.539435i	$-0.181362\pi$
$127$	0.775266	+	1.06706i	0.0687937	+	0.0946864i	−0.773234	+	0.634121i	$0.781362\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$		0			0
$130$	6.19369	+	7.30786i	0.543222	+	0.640942i
$131$	0.550197	+	1.69333i	0.0480710	+	0.147947i	0.972211	−	0.234107i	$-0.0752167\pi$
$131$	0.550197	+	1.69333i	0.0480710	+	0.147947i	−0.924140	+	0.382054i	$0.875217\pi$
$132$		0			0
$133$	−0.404463	+	0.131418i	−0.0350714	+	0.0113954i
$134$	−0.945746	−	0.687124i	−0.0817000	−	0.0593585i
$135$		0			0
$136$	0.0791922	−	0.0575365i	0.00679068	−	0.00493372i
$137$	−5.61986	+	7.73508i	−0.480137	+	0.660852i	−0.978531	−	0.206098i	$-0.933923\pi$
$137$	−5.61986	+	7.73508i	−0.480137	+	0.660852i	0.498394	+	0.866951i	$0.333923\pi$
$138$		0			0
$139$	−3.72123	+	2.70363i	−0.315631	+	0.229319i	−0.734309	−	0.678816i	$-0.762494\pi$
$139$	−3.72123	+	2.70363i	−0.315631	+	0.229319i	0.418678	+	0.908135i	$0.362494\pi$
$140$	−1.07971	−	2.63490i	−0.0912523	−	0.222690i
$141$		0			0
$142$	−2.24170	+	0.728373i	−0.188119	+	0.0611237i
$143$		−	18.6861i		−	1.56261i
$144$		0			0
$145$	−9.68031	+	3.96673i	−0.803906	+	0.329419i
$146$	−0.497039	+	1.52973i	−0.0411352	+	0.126601i
$147$		0			0
$148$	2.41492	+	3.32385i	0.198505	+	0.273219i
$149$	2.03186			0.166457			0.0832284	−	0.996530i	$-0.473477\pi$
$149$	2.03186			0.166457			0.0832284	+	0.996530i	$0.473477\pi$
$150$		0			0
$151$	18.9655			1.54339			0.771696	−	0.635992i	$-0.219409\pi$
$151$	18.9655			1.54339			0.771696	+	0.635992i	$0.219409\pi$
$152$	0.196294	+	0.270175i	0.0159215	+	0.0219141i
$153$		0			0
$154$	−1.71644	+	5.28266i	−0.138315	+	0.425689i
$155$	−9.45193	+	15.2935i	−0.759197	+	1.22841i
$156$		0			0
$157$			14.2430i			1.13672i	0.822781	+	0.568359i	$0.192421\pi$
$157$			14.2430i			1.13672i	−0.822781	+	0.568359i	$0.807579\pi$
$158$	7.73601	−	2.51358i	0.615444	−	0.199970i
$159$		0			0
$160$	−1.70582	+	1.44575i	−0.134857	+	0.114296i
$161$	6.50473	−	4.72597i	0.512645	−	0.372458i
$162$		0			0
$163$	11.5880	−	15.9495i	0.907641	−	1.24926i	−0.0603249	−	0.998179i	$-0.519214\pi$
$163$	11.5880	−	15.9495i	0.907641	−	1.24926i	0.967966	−	0.251082i	$-0.0807863\pi$
$164$	−9.24846	+	6.71940i	−0.722184	+	0.524697i
$165$		0			0
$166$	6.00323	+	4.36160i	0.465941	+	0.338526i
$167$	5.49885	−	1.78668i	0.425514	−	0.138258i	−0.0884287	−	0.996083i	$-0.528185\pi$
$167$	5.49885	−	1.78668i	0.425514	−	0.138258i	0.513942	+	0.857825i	$0.328185\pi$
$168$		0			0
$169$	−1.65427	−	5.09132i	−0.127252	−	0.391640i
$170$	−0.0163449	−	0.218271i	−0.00125360	−	0.0167406i
$171$		0			0
$172$	9.70962	+	3.15485i	0.740352	+	0.240555i
$173$	6.18806	+	8.51713i	0.470469	+	0.647545i	0.976639	−	0.214889i	$-0.0689389\pi$
$173$	6.18806	+	8.51713i	0.470469	+	0.647545i	−0.506169	+	0.862434i	$0.668939\pi$
$174$		0			0
$175$	−6.28115	−	1.04377i	−0.474811	−	0.0789020i
$176$	4.36176			0.328780
$177$		0			0
$178$	1.62460	+	0.527864i	0.121769	+	0.0395651i
$179$	3.35558	−	10.3274i	0.250808	−	0.771906i	−0.743819	−	0.668381i	$-0.766988\pi$
$179$	3.35558	−	10.3274i	0.250808	−	0.771906i	0.994627	−	0.103525i	$-0.0330123\pi$
$180$		0			0
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	−0.996953	−	0.0780101i	$-0.975143\pi$
$181$	−3.17848	−	9.78234i	−0.236254	−	0.727116i	0.760698	−	0.649106i	$-0.224857\pi$
$182$			5.45559i			0.404395i
$183$		0			0
$184$	−5.10793	−	3.71113i	−0.376562	−	0.273588i
$185$	9.16125	−	0.686028i	0.673549	−	0.0504378i
$186$		0			0
$187$	−0.250961	+	0.345418i	−0.0183521	+	0.0252594i
$188$	−6.88014	+	9.46969i	−0.501785	+	0.690648i
$189$		0			0
$190$	0.744661	−	0.0557630i	0.0540234	−	0.00404547i
$191$	−7.79944	−	5.66662i	−0.564347	−	0.410022i	0.268700	−	0.963224i	$-0.413406\pi$
$191$	−7.79944	−	5.66662i	−0.564347	−	0.410022i	−0.833047	+	0.553202i	$0.813406\pi$
$192$		0			0
$193$		−	6.00000i		−	0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−2.04180	−	6.28402i	−0.146593	−	0.451167i
$195$		0			0
$196$	−1.66199	+	5.11507i	−0.118713	+	0.365362i
$197$	19.7330	+	6.41164i	1.40592	+	0.456810i	0.911100	−	0.412186i	$-0.135235\pi$
$197$	19.7330	+	6.41164i	1.40592	+	0.456810i	0.494818	+	0.868997i	$0.335235\pi$
$198$		0			0
$199$	19.0629			1.35133			0.675666	−	0.737208i	$-0.263856\pi$
$199$	19.0629			1.35133			0.675666	+	0.737208i	$0.263856\pi$
$200$	0.744661	+	4.94424i	0.0526555	+	0.349610i
$201$		0			0
$202$	−4.12808	−	5.68181i	−0.290451	−	0.399771i
$203$	−5.66631	−	1.84110i	−0.397697	−	0.129220i
$204$		0			0
$205$	1.90884	+	25.4908i	0.133319	+	1.78035i
$206$	3.93893	+	12.1228i	0.274438	+	0.844633i
$207$		0			0
$208$	4.07440	−	1.32385i	0.282509	−	0.0917927i
$209$	−1.17844	−	0.856187i	−0.0815144	−	0.0592237i
$210$		0			0
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	−0.950311	−	0.311303i	$-0.899235\pi$
$211$	−13.7691	+	10.0039i	−0.947906	+	0.688694i	0.00240468	+	0.999997i	$0.499235\pi$
$212$	−0.520147	+	0.715921i	−0.0357238	+	0.0491697i
$213$		0			0
$214$	−9.87181	+	7.17229i	−0.674823	+	0.490288i
$215$	17.4152	−	14.7601i	1.18771	−	1.00663i
$216$		0			0
$217$	−9.73784	+	3.16402i	−0.661048	+	0.214787i
$218$			5.05092i			0.342091i
$219$		0			0
$220$	5.12756	−	8.29657i	0.345700	−	0.559354i
$221$	−0.129588	+	0.398831i	−0.00871703	+	0.0268283i
$222$		0			0
$223$	2.92595	+	4.02723i	0.195936	+	0.269683i	0.895669	−	0.444722i	$-0.146697\pi$
$223$	2.92595	+	4.02723i	0.195936	+	0.269683i	−0.699732	+	0.714405i	$0.746697\pi$
$224$	−1.27346			−0.0850865
$225$		0			0
$226$	−14.0351			−0.933600
$227$	−0.603519	−	0.830673i	−0.0400570	−	0.0551337i	0.788519	−	0.615011i	$-0.210848\pi$
$227$	−0.603519	−	0.830673i	−0.0400570	−	0.0551337i	−0.828576	+	0.559877i	$0.810848\pi$
$228$		0			0
$229$	1.26236	−	3.88514i	0.0834189	−	0.256737i	−0.900644	−	0.434558i	$-0.856905\pi$
$229$	1.26236	−	3.88514i	0.0834189	−	0.256737i	0.984063	+	0.177821i	$0.0569047\pi$
$230$	−13.0637	+	5.35317i	−0.861396	+	0.352978i
$231$		0			0
$232$			4.67853i			0.307161i
$233$	4.19681	−	1.36363i	0.274942	−	0.0893342i	−0.168301	−	0.985736i	$-0.553828\pi$
$233$	4.19681	−	1.36363i	0.274942	−	0.0893342i	0.443243	+	0.896402i	$0.353828\pi$
$234$		0			0
$235$	9.92435	+	24.2191i	0.647393	+	1.57988i
$236$	6.15537	−	4.47214i	0.400680	−	0.291111i
$237$		0			0
$238$	0.0732703	−	0.100848i	0.00474941	−	0.00653700i
$239$	−17.5979	+	12.7856i	−1.13831	+	0.827032i	−0.986883	−	0.161437i	$-0.948387\pi$
$239$	−17.5979	+	12.7856i	−1.13831	+	0.827032i	−0.151428	+	0.988468i	$0.548387\pi$
$240$		0			0
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	0.918605	−	0.395177i	$-0.129317\pi$
$241$	12.8328	+	9.32358i	0.826633	+	0.600584i	−0.0919714	+	0.995762i	$0.529317\pi$
$242$	−7.63220	+	2.47985i	−0.490617	+	0.159411i
$243$		0			0
$244$	0.518118	+	1.59460i	0.0331691	+	0.102084i
$245$	7.77566	+	9.17442i	0.496769	+	0.586132i
$246$		0			0
$247$	−1.36067	−	0.442107i	−0.0865771	−	0.0281306i
$248$	4.72597	+	6.50473i	0.300099	+	0.413051i
$249$		0			0
$250$	10.2799	+	4.39587i	0.650158	+	0.278019i
$251$	8.49087			0.535939			0.267970	−	0.963427i	$-0.413647\pi$
$251$	8.49087			0.535939			0.267970	+	0.963427i	$0.413647\pi$
$252$		0			0
$253$	26.1912	+	8.51005i	1.64663	+	0.535022i
$254$	0.407581	−	1.25441i	0.0255739	−	0.0787085i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			9.98572i			0.622892i	0.950264	+	0.311446i	$0.100813\pi$
$257$			9.98572i			0.622892i	−0.950264	+	0.311446i	$0.899187\pi$
$258$		0			0
$259$	4.23279	+	3.07530i	0.263013	+	0.191090i
$260$	2.27163	−	9.30625i	0.140880	−	0.577149i
$261$		0			0
$262$	1.04654	−	1.44043i	0.0646553	−	0.0889904i
$263$	−4.54612	+	6.25720i	−0.280326	+	0.385836i	−0.925842	−	0.377911i	$-0.876642\pi$
$263$	−4.54612	+	6.25720i	−0.280326	+	0.385836i	0.645516	+	0.763747i	$0.276642\pi$
$264$		0			0
$265$	0.750293	+	1.83099i	0.0460901	+	0.112477i
$266$	0.344057	+	0.249972i	0.0210955	+	0.0153268i
$267$		0			0
$268$			1.16901i			0.0714084i
$269$	−2.26777	−	6.97948i	−0.138268	−	0.425546i	0.857816	−	0.513957i	$-0.171821\pi$
$269$	−2.26777	−	6.97948i	−0.138268	−	0.425546i	−0.996084	+	0.0884112i	$0.971821\pi$
$270$		0			0
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	−0.745198	−	0.666844i	$-0.767645\pi$
$271$	4.10960	−	12.6481i	0.249641	−	0.768315i	0.994838	−	0.101472i	$-0.0323551\pi$
$272$	−0.0930960	−	0.0302487i	−0.00564478	−	0.00183410i
$273$		0			0
$274$	9.56108			0.577606
$275$	−9.75320	−	19.5064i	−0.588140	−	1.17628i
$276$		0			0
$277$	−11.5165	−	15.8511i	−0.691959	−	0.952399i	−0.999999	−	0.00102623i	$-0.999673\pi$
$277$	−11.5165	−	15.8511i	−0.691959	−	0.952399i	0.308041	−	0.951373i	$-0.400327\pi$
$278$	4.37457	+	1.42138i	0.262369	+	0.0852489i
$279$		0			0
$280$	−1.49704	+	2.42226i	−0.0894652	+	0.144758i
$281$	3.55571	+	10.9433i	0.212116	+	0.652825i	0.999346	+	0.0361656i	$0.0115144\pi$
$281$	3.55571	+	10.9433i	0.212116	+	0.652825i	−0.787230	+	0.616659i	$0.788486\pi$
$282$		0			0
$283$	−18.6927	+	6.07363i	−1.11117	+	0.361040i	−0.806390	−	0.591384i	$-0.798582\pi$
$283$	−18.6927	+	6.07363i	−1.11117	+	0.361040i	−0.304776	+	0.952424i	$0.598582\pi$
$284$	1.90690	+	1.38545i	0.113154	+	0.0822111i
$285$		0			0
$286$	−15.1174	+	10.9834i	−0.893911	+	0.649464i
$287$	−8.55687	+	11.7775i	−0.505096	+	0.695205i
$288$		0			0
$289$	−13.7455	+	9.98672i	−0.808561	+	0.587454i
$290$	8.89910	+	5.49994i	0.522573	+	0.322968i
$291$		0			0
$292$	1.52973	−	0.497039i	0.0895206	−	0.0290870i
$293$			6.12203i			0.357653i	0.983881	+	0.178827i	$0.0572301\pi$
$293$			6.12203i			0.357653i	−0.983881	+	0.178827i	$0.942770\pi$
$294$		0			0
$295$	−1.27044	−	16.9655i	−0.0739679	−	0.987770i
$296$	1.26960	−	3.90742i	0.0737939	−	0.227114i
$297$		0			0
$298$	−1.19430	−	1.64381i	−0.0691839	−	0.0952235i
$299$	27.0486			1.56426
$300$		0			0
$301$	13.0011			0.749371
$302$	−11.1477	−	15.3434i	−0.641475	−	0.882915i
$303$		0			0
$304$	0.103198	−	0.317610i	0.00591880	−	0.0182162i
$305$	3.64220	+	0.889050i	0.208552	+	0.0509069i
$306$		0			0
$307$			14.1935i			0.810064i	0.914302	+	0.405032i	$0.132740\pi$
$307$			14.1935i			0.810064i	−0.914302	+	0.405032i	$0.867260\pi$
$308$	5.28266	−	1.71644i	0.301008	−	0.0978033i
$309$		0			0
$310$	17.9284	−	1.34255i	1.01827	−	0.0762516i
$311$	5.81375	−	4.22394i	0.329668	−	0.239518i	−0.410622	−	0.911806i	$-0.634688\pi$
$311$	5.81375	−	4.22394i	0.329668	−	0.239518i	0.740290	+	0.672288i	$0.234688\pi$
$312$		0			0
$313$	−0.367741	+	0.506152i	−0.0207859	+	0.0286094i	−0.819283	−	0.573389i	$-0.805629\pi$
$313$	−0.367741	+	0.506152i	−0.0207859	+	0.0286094i	0.798498	+	0.601998i	$0.205629\pi$
$314$	11.5229	−	8.37184i	0.650272	−	0.472450i
$315$		0			0
$316$	−6.58064	−	4.78112i	−0.370190	−	0.268959i
$317$	−6.85717	+	2.22803i	−0.385137	+	0.125139i	−0.495185	−	0.868788i	$-0.664900\pi$
$317$	−6.85717	+	2.22803i	−0.385137	+	0.125139i	0.110048	+	0.993926i	$0.464900\pi$
$318$		0			0
$319$	−6.30600	−	19.4079i	−0.353068	−	1.08663i
$320$	2.17229	+	0.530249i	0.121435	+	0.0296418i
$321$		0			0
$322$	−7.64677	−	2.48459i	−0.426138	−	0.138461i
$323$	0.0192146	+	0.0264466i	0.00106913	+	0.00147153i
$324$		0			0
$325$	−15.0311	−	15.2611i	−0.833775	−	0.846531i
$326$	−19.7147			−1.09189
$327$		0			0
$328$	10.8722	+	3.53260i	0.600318	+	0.195055i
$329$	−4.60623	+	14.1765i	−0.253949	+	0.781576i
$330$		0			0
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	−0.915533	−	0.402244i	$-0.868231\pi$
$331$	−7.48266	−	23.0292i	−0.411284	−	1.26580i	0.504249	−	0.863558i	$-0.331769\pi$
$332$		−	7.42040i		−	0.407247i
$333$		0			0
$334$	−4.67760	−	3.39847i	−0.255947	−	0.185956i
$335$	2.22358	+	1.37425i	0.121487	+	0.0750832i
$336$		0			0
$337$	−13.0498	+	17.9615i	−0.710866	+	0.978423i	0.288912	+	0.957356i	$0.406706\pi$
$337$	−13.0498	+	17.9615i	−0.710866	+	0.978423i	−0.999778	+	0.0210674i	$0.993294\pi$
$338$	−3.14661	+	4.33094i	−0.171153	+	0.235572i
$339$		0			0
$340$	−0.166977	+	0.141520i	−0.00905562	+	0.00767498i
$341$	−28.3721	−	20.6135i	−1.53644	−	1.11629i
$342$		0			0
$343$			15.7632i			0.851135i
$344$	−3.15485	−	9.70962i	−0.170098	−	0.523508i
$345$		0			0
$346$	3.25325	−	10.0125i	0.174896	−	0.538275i
$347$	−23.9270	−	7.77436i	−1.28447	−	0.417349i	−0.414317	−	0.910133i	$-0.635979\pi$
$347$	−23.9270	−	7.77436i	−1.28447	−	0.417349i	−0.870152	+	0.492783i	$0.835979\pi$
$348$		0			0
$349$	25.4708			1.36342			0.681710	−	0.731622i	$-0.261236\pi$
$349$	25.4708			1.36342			0.681710	+	0.731622i	$0.261236\pi$
$350$	2.84754	+	5.69507i	0.152207	+	0.304415i
$351$		0			0
$352$	−2.56378	−	3.52874i	−0.136650	−	0.188082i
$353$	−27.5059	−	8.93720i	−1.46399	−	0.475679i	−0.534703	−	0.845040i	$-0.679577\pi$
$353$	−27.5059	−	8.93720i	−1.46399	−	0.475679i	−0.929286	+	0.369361i	$0.879577\pi$
$354$		0			0
$355$	4.87698	−	1.99846i	0.258843	−	0.106067i
$356$	−0.527864	−	1.62460i	−0.0279767	−	0.0861035i
$357$		0			0
$358$	−10.3274	+	3.35558i	−0.545820	+	0.177348i
$359$	6.82792	+	4.96077i	0.360364	+	0.261820i	0.753204	−	0.657787i	$-0.228507\pi$
$359$	6.82792	+	4.96077i	0.360364	+	0.261820i	−0.392840	+	0.919607i	$0.628507\pi$
$360$		0			0
$361$	15.2811	−	11.1024i	0.804268	−	0.584335i
$362$	−6.04582	+	8.32136i	−0.317761	+	0.437361i
$363$		0			0
$364$	4.41367	−	3.20672i	0.231339	−	0.168078i
$365$	0.852880	−	3.49402i	0.0446418	−	0.182885i
$366$		0			0
$367$	−2.85041	+	0.926153i	−0.148790	+	0.0483448i	−0.382465	−	0.923970i	$-0.624925\pi$
$367$	−2.85041	+	0.926153i	−0.148790	+	0.0483448i	0.233675	+	0.972315i	$0.424925\pi$
$368$			6.31375i			0.329127i
$369$		0			0
$370$	−5.93986	−	7.00837i	−0.308799	−	0.364348i
$371$	−0.348236	+	1.07176i	−0.0180795	+	0.0556431i
$372$		0			0
$373$	−10.3080	−	14.1877i	−0.533728	−	0.734613i	0.453965	−	0.891019i	$-0.350009\pi$
$373$	−10.3080	−	14.1877i	−0.533728	−	0.734613i	−0.987693	+	0.156406i	$0.950009\pi$
$374$	0.426960			0.0220776
$375$		0			0
$376$	11.7052			0.603649
$377$	−11.7811	−	16.2153i	−0.606757	−	0.835130i
$378$		0			0
$379$	−9.82469	+	30.2373i	−0.504661	+	1.55319i	0.296680	+	0.954977i	$0.404121\pi$
$379$	−9.82469	+	30.2373i	−0.504661	+	1.55319i	−0.801340	+	0.598209i	$0.795879\pi$
$380$	−0.482814	−	0.569667i	−0.0247678	−	0.0292233i
$381$		0			0
$382$			9.64063i			0.493258i
$383$	18.6755	−	6.06804i	0.954273	−	0.310062i	0.209822	−	0.977740i	$-0.432711\pi$
$383$	18.6755	−	6.06804i	0.954273	−	0.310062i	0.744451	+	0.667677i	$0.232711\pi$
$384$		0			0
$385$	2.94528	−	12.0660i	0.150105	−	0.614941i
$386$	−4.85410	+	3.52671i	−0.247067	+	0.179505i
$387$		0			0
$388$	−3.88374	+	5.34551i	−0.197167	+	0.271377i
$389$	23.8930	−	17.3593i	1.21142	−	0.880150i	0.216063	−	0.976379i	$-0.430678\pi$
$389$	23.8930	−	17.3593i	1.21142	−	0.880150i	0.995359	+	0.0962298i	$0.0306784\pi$
$390$		0			0
$391$	−0.500000	−	0.363271i	−0.0252861	−	0.0183714i
$392$	5.11507	−	1.66199i	0.258350	−	0.0839431i
$393$		0			0
$394$	−6.41164	−	19.7330i	−0.323014	−	0.994134i
$395$	−16.8302	+	6.89659i	−0.846821	+	0.347005i
$396$		0			0
$397$	21.1823	+	6.88254i	1.06311	+	0.345425i	0.787800	−	0.615931i	$-0.211220\pi$
$397$	21.1823	+	6.88254i	1.06311	+	0.345425i	0.275308	+	0.961356i	$0.411220\pi$
$398$	−11.2049	−	15.4222i	−0.561650	−	0.773045i
$399$		0			0
$400$	3.56227	−	3.50859i	0.178114	−	0.175430i
$401$	−7.37458			−0.368269			−0.184134	−	0.982901i	$-0.558948\pi$
$401$	−7.37458			−0.368269			−0.184134	+	0.982901i	$0.558948\pi$
$402$		0			0
$403$	−32.7594	−	10.6442i	−1.63186	−	0.530224i
$404$	−2.17026	+	6.67937i	−0.107974	+	0.332311i
$405$		0			0
$406$	1.84110	+	5.66631i	0.0913720	+	0.281214i
$407$			17.9203i			0.888278i
$408$		0			0
$409$	−14.9117	−	10.8340i	−0.737335	−	0.535705i	0.154541	−	0.987986i	$-0.450610\pi$
$409$	−14.9117	−	10.8340i	−0.737335	−	0.535705i	−0.891875	+	0.452281i	$0.850610\pi$
$410$	19.5005	−	16.5274i	0.963059	−	0.816229i
$411$		0			0
$412$	7.49228	−	10.3122i	0.369118	−	0.508048i
$413$	5.69507	−	7.83860i	0.280236	−	0.385712i
$414$		0			0
$415$	−14.1144	−	8.72320i	−0.692850	−	0.428205i
$416$	−3.46589	−	2.51812i	−0.169929	−	0.123461i
$417$		0			0
$418$			1.45663i			0.0712462i
$419$	3.58315	+	11.0278i	0.175048	+	0.538744i	0.999636	−	0.0269911i	$-0.00859259\pi$
$419$	3.58315	+	11.0278i	0.175048	+	0.538744i	−0.824587	+	0.565735i	$0.808593\pi$
$420$		0			0
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	−0.970628	−	0.240585i	$-0.922661\pi$
$421$	−0.902012	+	2.77611i	−0.0439614	+	0.135299i	0.926667	+	0.375884i	$0.122661\pi$
$422$	16.1866	+	5.25934i	0.787951	+	0.256021i
$423$		0			0
$424$	0.884927			0.0429759
$425$	0.0728926	+	0.483976i	0.00353581	+	0.0234763i
$426$		0			0
$427$	1.25502	+	1.72738i	0.0607346	+	0.0835940i
$428$	11.6050	+	3.77070i	0.560949	+	0.182263i
$429$		0			0
$430$	−22.1775	−	5.41347i	−1.06950	−	0.261061i
$431$	−2.34092	−	7.20460i	−0.112758	−	0.347033i	0.878715	−	0.477347i	$-0.158402\pi$
$431$	−2.34092	−	7.20460i	−0.112758	−	0.347033i	−0.991473	+	0.130314i	$0.958402\pi$
$432$		0			0
$433$	27.3735	−	8.89418i	1.31548	−	0.427427i	0.434543	−	0.900651i	$-0.356910\pi$
$433$	27.3735	−	8.89418i	1.31548	−	0.427427i	0.880942	+	0.473224i	$0.156910\pi$
$434$	8.28350	+	6.01832i	0.397621	+	0.288888i
$435$		0			0
$436$	4.08628	−	2.96885i	0.195697	−	0.142182i
$437$	1.23935	−	1.70582i	0.0592862	−	0.0816004i
$438$		0			0
$439$	14.3588	−	10.4323i	0.685310	−	0.497907i	−0.189805	−	0.981822i	$-0.560786\pi$
$439$	14.3588	−	10.4323i	0.685310	−	0.497907i	0.875115	+	0.483915i	$0.160786\pi$
$440$	−9.72597	+	0.728316i	−0.463667	+	0.0347211i
$441$		0			0
$442$	0.398831	−	0.129588i	0.0189704	−	0.00616387i
$443$			19.3439i			0.919058i	0.888163	+	0.459529i	$0.151982\pi$
$443$			19.3439i			0.919058i	−0.888163	+	0.459529i	$0.848018\pi$
$444$		0			0
$445$	−3.71071	−	0.905773i	−0.175905	−	0.0429378i
$446$	1.53827	−	4.73429i	0.0728390	−	0.224175i
$447$		0			0
$448$	0.748520	+	1.03025i	0.0353642	+	0.0486747i
$449$	11.2932			0.532960			0.266480	−	0.963840i	$-0.414139\pi$
$449$	11.2932			0.532960			0.266480	+	0.963840i	$0.414139\pi$
$450$		0			0
$451$	−49.8625			−2.34793
$452$	8.24962	+	11.3546i	0.388029	+	0.534076i
$453$		0			0
$454$	−0.317289	+	0.976514i	−0.0148911	+	0.0458301i
$455$	−0.910961	−	12.1650i	−0.0427065	−	0.570305i
$456$		0			0
$457$		−	2.60741i		−	0.121970i	−0.998139	−	0.0609848i	$-0.980576\pi$
$457$		−	2.60741i		−	0.121970i	0.998139	−	0.0609848i	$-0.0194241\pi$
$458$	−3.88514	+	1.26236i	−0.181540	+	0.0589861i
$459$		0			0
$460$	12.0095	+	7.42226i	0.559944	+	0.346065i
$461$	−1.58366	+	1.15060i	−0.0737585	+	0.0535887i	−0.624053	−	0.781382i	$-0.714515\pi$
$461$	−1.58366	+	1.15060i	−0.0737585	+	0.0535887i	0.550295	+	0.834970i	$0.314515\pi$
$462$		0			0
$463$	−0.856972	+	1.17952i	−0.0398269	+	0.0548170i	−0.828466	−	0.560039i	$-0.810786\pi$
$463$	−0.856972	+	1.17952i	−0.0398269	+	0.0548170i	0.788639	+	0.614856i	$0.210786\pi$
$464$	3.78501	−	2.74997i	0.175715	−	0.127664i
$465$		0			0
$466$	−3.57002	−	2.59377i	−0.165378	−	0.120154i
$467$	−24.3331	+	7.90629i	−1.12600	+	0.365860i	−0.812055	−	0.583581i	$-0.801651\pi$
$467$	−24.3331	+	7.90629i	−1.12600	+	0.365860i	−0.313945	+	0.949441i	$0.601651\pi$
$468$		0			0
$469$	0.460027	+	1.41582i	0.0212421	+	0.0653764i
$470$	13.7603	−	22.2646i	0.634714	−	1.02699i
$471$		0			0
$472$	−7.23607	−	2.35114i	−0.333067	−	0.108220i
$473$	26.1744	+	36.0260i	1.20350	+	1.65648i
$474$		0			0
$475$	−1.65115	+	0.248683i	−0.0757601	+	0.0114104i
$476$	−0.124655			−0.00571355
$477$		0			0
$478$	20.6875	+	6.72179i	0.946226	+	0.307447i
$479$	−2.12209	+	6.53112i	−0.0969608	+	0.298415i	−0.987760	−	0.155983i	$-0.950145\pi$
$479$	−2.12209	+	6.53112i	−0.0969608	+	0.298415i	0.890799	+	0.454398i	$0.150145\pi$
$480$		0			0
$481$	5.43906	+	16.7397i	0.248000	+	0.763265i
$482$		−	15.8622i		−	0.722504i
$483$		0			0
$484$	6.49234	+	4.71696i	0.295106	+	0.214407i
$485$	5.60215	+	13.6713i	0.254381	+	0.620783i
$486$		0			0
$487$	24.8770	−	34.2403i	1.12728	−	1.55157i	0.334159	−	0.942517i	$-0.391548\pi$
$487$	24.8770	−	34.2403i	1.12728	−	1.55157i	0.793126	−	0.609058i	$-0.208452\pi$
$488$	0.985520	−	1.35645i	0.0446124	−	0.0614037i
$489$		0			0
$490$	2.85184	−	11.6832i	0.128833	−	0.527795i
$491$	10.4767	+	7.61178i	0.472808	+	0.343515i	0.798535	−	0.601949i	$-0.205609\pi$
$491$	10.4767	+	7.61178i	0.472808	+	0.343515i	−0.325727	+	0.945464i	$0.605609\pi$
$492$		0			0
$493$			0.457967i			0.0206258i
$494$	0.442107	+	1.36067i	0.0198913	+	0.0612193i
$495$		0			0
$496$	2.48459	−	7.64677i	0.111561	−	0.343350i
$497$	2.85471	+	0.927551i	0.128051	+	0.0416064i
$498$		0			0
$499$	12.9767			0.580915			0.290458	−	0.956888i	$-0.406192\pi$
$499$	12.9767			0.580915			0.290458	+	0.956888i	$0.406192\pi$
$500$	−2.48604	−	10.9004i	−0.111179	−	0.487483i
$501$		0			0
$502$	−4.99081	−	6.86926i	−0.222751	−	0.306590i
$503$	20.2024	+	6.56414i	0.900778	+	0.292681i	0.722558	−	0.691310i	$-0.242966\pi$
$503$	20.2024	+	6.56414i	0.900778	+	0.292681i	0.178220	+	0.983991i	$0.442966\pi$
$504$		0			0
$505$	10.1536	+	11.9802i	0.451831	+	0.533110i
$506$	−8.51005	−	26.1912i	−0.378318	−	1.16434i
$507$		0			0
$508$	−1.25441	+	0.407581i	−0.0556553	+	0.0180835i
$509$	−11.5303	−	8.37728i	−0.511073	−	0.371317i	0.302157	−	0.953258i	$-0.402293\pi$
$509$	−11.5303	−	8.37728i	−0.511073	−	0.371317i	−0.813231	+	0.581942i	$0.802293\pi$
$510$		0			0
$511$	1.65711	−	1.20396i	0.0733060	−	0.0532600i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$		0			0
$514$	8.07862	−	5.86946i	0.356332	−	0.258891i
$515$	−10.8073	−	26.3739i	−0.476229	−	1.16217i
$516$		0			0
$517$	−48.5564	+	15.7769i	−2.13551	+	0.693869i
$518$		−	5.23201i		−	0.229881i
$519$		0			0
$520$	−8.86415	+	3.63229i	−0.388719	+	0.159287i
$521$	9.07543	−	27.9313i	0.397602	−	1.22369i	−0.529315	−	0.848426i	$-0.677551\pi$
$521$	9.07543	−	27.9313i	0.397602	−	1.22369i	0.926917	−	0.375268i	$-0.122449\pi$
$522$		0			0
$523$	8.95773	+	12.3293i	0.391694	+	0.539121i	0.958635	−	0.284638i	$-0.0918733\pi$
$523$	8.95773	+	12.3293i	0.391694	+	0.539121i	−0.566941	+	0.823758i	$0.691873\pi$
$524$	−1.78048			−0.0777804
$525$		0			0
$526$	7.73433			0.337233
$527$	0.462611	+	0.636729i	0.0201516	+	0.0277363i
$528$		0			0
$529$	−5.21110	+	16.0381i	−0.226569	+	0.697309i
$530$	1.04029	−	1.68323i	0.0451875	−	0.0731149i
$531$		0			0
$532$		−	0.425277i		−	0.0184381i
$533$	−46.5775	+	15.1339i	−2.01749	+	0.655523i
$534$		0			0
$535$	20.8148	−	17.6413i	0.899902	−	0.762701i
$536$	0.945746	−	0.687124i	0.0408500	−	0.0296793i
$537$		0			0
$538$	−4.31355	+	5.93710i	−0.185970	+	0.255966i
$539$	−18.9786	+	13.7888i	−0.817468	+	0.593925i
$540$		0			0
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.0818632	−	0.996644i	$-0.526087\pi$
$541$	−24.5392	−	17.8288i	−1.05502	−	0.766520i	−0.973161	+	0.230123i	$0.926087\pi$
$542$	−12.6481	+	4.10960i	−0.543281	+	0.176523i
$543$		0			0
$544$	0.0302487	+	0.0930960i	0.00129690	+	0.00399146i
$545$	−0.843389	−	11.2627i	−0.0361268	−	0.482439i
$546$		0			0
$547$	29.5288	+	9.59449i	1.26256	+	0.410231i	0.862406	−	0.506217i	$-0.168956\pi$
$547$	29.5288	+	9.59449i	1.26256	+	0.410231i	0.400155	+	0.916448i	$0.368956\pi$
$548$	−5.61986	−	7.73508i	−0.240069	−	0.330426i
$549$		0			0
$550$	−10.0482	+	19.3561i	−0.428458	+	0.825346i
$551$	−1.56242			−0.0665613
$552$		0			0
$553$	−9.85148	−	3.20094i	−0.418928	−	0.136118i
$554$	−6.05458	+	18.6341i	−0.257234	+	0.791686i
$555$		0			0
$556$	−1.42138	−	4.37457i	−0.0602801	−	0.185523i
$557$			28.0537i			1.18867i	0.804216	+	0.594337i	$0.202585\pi$
$557$			28.0537i			1.18867i	−0.804216	+	0.594337i	$0.797415\pi$
$558$		0			0
$559$	35.3843	+	25.7082i	1.49660	+	1.08734i
$560$	2.83959	−	0.212639i	0.119994	−	0.00898563i
$561$		0			0
$562$	6.76336	−	9.30896i	0.285295	−	0.392675i
$563$	−13.6142	+	18.7384i	−0.573772	+	0.789729i	−0.992995	−	0.118154i	$-0.962302\pi$
$563$	−13.6142	+	18.7384i	−0.573772	+	0.789729i	0.419223	+	0.907883i	$0.362302\pi$
$564$		0			0
$565$	31.2958	−	2.34354i	1.31662	−	0.0985936i
$566$	15.9010	+	11.5527i	0.668367	+	0.485597i
$567$		0			0
$568$		−	2.35706i		−	0.0989002i
$569$	−4.16602	−	12.8217i	−0.174649	−	0.537514i	0.824968	−	0.565179i	$-0.191193\pi$
$569$	−4.16602	−	12.8217i	−0.174649	−	0.537514i	−0.999617	+	0.0276651i	$0.991193\pi$
$570$		0			0
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	0.298945	+	0.954270i	$0.403365\pi$
$571$	−12.0389	+	37.0519i	−0.503813	+	1.55058i	−0.802758	+	0.596305i	$0.796635\pi$
$572$	17.7716	+	5.77433i	0.743067	+	0.241437i
$573$		0			0
$574$	14.5578			0.607632
$575$	28.2360	−	14.1180i	1.17752	−	0.588760i
$576$		0			0
$577$	−26.1132	−	35.9417i	−1.08711	−	1.49627i	−0.851449	−	0.524437i	$-0.824276\pi$
$577$	−26.1132	−	35.9417i	−1.08711	−	1.49627i	−0.235657	−	0.971836i	$-0.575724\pi$
$578$	16.1588	+	5.25033i	0.672119	+	0.218385i
$579$		0			0
$580$	−0.781209	−	10.4323i	−0.0324380	−	0.433178i
$581$	−2.92007	−	8.98706i	−0.121145	−	0.372846i
$582$		0			0
$583$	−3.67093	+	1.19276i	−0.152034	+	0.0493989i
$584$	−1.30127	−	0.945424i	−0.0538467	−	0.0391219i
$585$		0			0
$586$	4.95283	−	3.59844i	0.204600	−	0.148650i
$587$	23.0686	−	31.7512i	0.952144	−	1.31051i	0.00157480	−	0.999999i	$-0.499499\pi$
$587$	23.0686	−	31.7512i	0.952144	−	1.31051i	0.950569	−	0.310514i	$-0.100501\pi$
$588$		0			0
$589$	−2.17229	+	1.57826i	−0.0895076	+	0.0650311i
$590$	−12.9786	+	10.9999i	−0.534322	+	0.452858i
$591$		0			0
$592$	−3.90742	+	1.26960i	−0.160594	+	0.0521802i
$593$			23.5637i			0.967644i	0.875167	+	0.483822i	$0.160752\pi$
$593$			23.5637i			0.967644i	−0.875167	+	0.483822i	$0.839248\pi$
$594$		0			0
$595$	−0.146541	+	0.237108i	−0.00600758	+	0.00972047i
$596$	−0.627881	+	1.93242i	−0.0257190	+	0.0791549i
$597$		0			0
$598$	−15.8988	−	21.8828i	−0.650149	−	0.894854i
$599$	39.2513			1.60376			0.801882	−	0.597483i	$-0.203832\pi$
$599$	39.2513			1.60376			0.801882	+	0.597483i	$0.203832\pi$
$600$		0			0
$601$	−13.1067			−0.534635			−0.267317	−	0.963609i	$-0.586137\pi$
$601$	−13.1067			−0.534635			−0.267317	+	0.963609i	$0.586137\pi$
$602$	−7.64186	−	10.5181i	−0.311459	−	0.428687i
$603$		0			0
$604$	−5.86067	+	18.0373i	−0.238467	+	0.733926i
$605$	16.6044	−	6.80404i	0.675065	−	0.276624i
$606$		0			0
$607$			6.14712i			0.249504i	0.992188	+	0.124752i	$0.0398135\pi$
$607$			6.14712i			0.249504i	−0.992188	+	0.124752i	$0.960186\pi$
$608$	−0.317610	+	0.103198i	−0.0128808	+	0.00418522i
$609$		0			0
$610$	−1.42158	−	3.46917i	−0.0575579	−	0.140463i
$611$	−40.5689	+	29.4750i	−1.64124	+	1.19243i
$612$		0			0
$613$	−13.0198	+	17.9202i	−0.525865	+	0.723790i	−0.986493	−	0.163803i	$-0.947624\pi$
$613$	−13.0198	+	17.9202i	−0.525865	+	0.723790i	0.460629	+	0.887593i	$0.347624\pi$
$614$	11.4828	−	8.34271i	0.463406	−	0.336684i
$615$		0			0
$616$	−4.49370	−	3.26486i	−0.181056	−	0.131545i
$617$	−11.5313	+	3.74675i	−0.464233	+	0.150838i	−0.531789	−	0.846877i	$-0.678480\pi$
$617$	−11.5313	+	3.74675i	−0.464233	+	0.150838i	0.0675559	+	0.997715i	$0.478480\pi$
$618$		0			0
$619$	−4.06963	−	12.5250i	−0.163572	−	0.503424i	0.835356	−	0.549709i	$-0.185262\pi$
$619$	−4.06963	−	12.5250i	−0.163572	−	0.503424i	−0.998928	+	0.0462856i	$0.985262\pi$
$620$	−11.6242	−	13.7153i	−0.466840	−	0.550819i
$621$		0			0
$622$	−6.83447	−	2.22066i	−0.274037	−	0.0890402i
$623$	−1.27862	−	1.75987i	−0.0512270	−	0.0705079i
$624$		0			0
$625$	−23.6564	−	8.08551i	−0.946255	−	0.323420i
$626$	0.625638			0.0250055
$627$		0			0
$628$	−13.5459	−	4.40134i	−0.540541	−	0.175633i
$629$	0.124277	−	0.382486i	0.00495526	−	0.0152507i
$630$		0			0
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	0.926469	+	0.376371i	$0.122828\pi$
$631$	10.0018	+	30.7824i	0.398165	+	1.22543i	−0.528304	+	0.849055i	$0.677172\pi$
$632$			8.13412i			0.323558i
$633$		0			0
$634$	5.83306	+	4.23796i	0.231660	+	0.168311i
$635$	−0.699377	+	2.86516i	−0.0277539	+	0.113701i
$636$		0			0
$637$	−13.5432	+	18.6406i	−0.536602	+	0.738569i
$638$	−11.9947	+	16.5093i	−0.474876	+	0.653610i
$639$		0			0
$640$	−0.847859	−	2.06909i	−0.0335146	−	0.0817880i
$641$	−11.5106	−	8.36292i	−0.454640	−	0.330315i	0.336785	−	0.941582i	$-0.390660\pi$
$641$	−11.5106	−	8.36292i	−0.454640	−	0.330315i	−0.791425	+	0.611266i	$0.790660\pi$
$642$		0			0
$643$			18.7825i			0.740708i	0.928891	+	0.370354i	$0.120764\pi$
$643$			18.7825i			0.740708i	−0.928891	+	0.370354i	$0.879236\pi$
$644$	2.48459	+	7.64677i	0.0979065	+	0.301325i
$645$		0			0
$646$	0.0101017	−	0.0310899i	0.000397447	−	0.00122322i
$647$	14.3035	+	4.64749i	0.562328	+	0.182712i	0.576369	−	0.817190i	$-0.304469\pi$
$647$	14.3035	+	4.64749i	0.562328	+	0.182712i	−0.0140402	+	0.999901i	$0.504469\pi$
$648$		0			0
$649$	33.1863			1.30267
$650$	−3.51140	+	21.1306i	−0.137728	+	0.828811i
$651$		0			0
$652$	11.5880	+	15.9495i	0.453820	+	0.624630i
$653$	22.5809	+	7.33698i	0.883659	+	0.287118i	0.715476	−	0.698637i	$-0.246210\pi$
$653$	22.5809	+	7.33698i	0.883659	+	0.287118i	0.168183	+	0.985756i	$0.446210\pi$
$654$		0			0
$655$	−2.09307	+	3.38667i	−0.0817832	+	0.132328i
$656$	−3.53260	−	10.8722i	−0.137925	−	0.424489i
$657$		0			0
$658$	14.1765	−	4.60623i	0.552658	−	0.179569i
$659$	5.30922	+	3.85737i	0.206818	+	0.150262i	0.686373	−	0.727250i	$-0.259202\pi$
$659$	5.30922	+	3.85737i	0.206818	+	0.150262i	−0.479555	+	0.877512i	$0.659202\pi$
$660$		0			0
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.0441853	−	0.999023i	$-0.485931\pi$
$661$	25.9148	−	18.8282i	1.00797	−	0.732331i	0.963782	+	0.266692i	$0.0859308\pi$
$662$	−14.2329	+	19.5898i	−0.553176	+	0.761381i
$663$		0			0
$664$	−6.00323	+	4.36160i	−0.232970	+	0.169263i
$665$	−0.808926	−	0.499944i	−0.0313688	−	0.0193870i
$666$		0			0
$667$	28.0933	−	9.12808i	1.08778	−	0.353441i
$668$			5.78183i			0.223706i
$669$		0			0
$670$	−0.195198	−	2.60668i	−0.00754114	−	0.100705i
$671$	−2.25991	+	6.95529i	−0.0872429	+	0.268506i
$672$		0			0
$673$	29.2455	+	40.2530i	1.12733	+	1.55164i	0.793039	+	0.609171i	$0.208498\pi$
$673$	29.2455	+	40.2530i	1.12733	+	1.55164i	0.334294	+	0.942469i	$0.391502\pi$
$674$	22.2016			0.855173
$675$		0			0
$676$	5.35333			0.205897
$677$	−16.8590	−	23.2044i	−0.647943	−	0.891818i	0.351064	−	0.936351i	$-0.385820\pi$
$677$	−16.8590	−	23.2044i	−0.647943	−	0.891818i	−0.999008	+	0.0445337i	$0.985820\pi$
$678$		0			0
$679$	−2.60015	+	8.00244i	−0.0997846	+	0.307105i
$680$	0.212639	+	0.0519044i	0.00815432	+	0.00199044i
$681$		0			0
$682$			35.0699i			1.34289i
$683$	−33.3619	+	10.8399i	−1.27656	+	0.414779i	−0.867367	−	0.497670i	$-0.834189\pi$
$683$	−33.3619	+	10.8399i	−1.27656	+	0.414779i	−0.409192	+	0.912449i	$0.634189\pi$
$684$		0			0
$685$	−21.3195	+	1.59649i	−0.814578	+	0.0609986i
$686$	12.7527	−	9.26540i	0.486902	−	0.353755i
$687$		0			0
$688$	−6.00088	+	8.25950i	−0.228781	+	0.314890i
$689$	−3.06706	+	2.22835i	−0.116846	+	0.0848934i
$690$		0			0
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	0.613663	−	0.789568i	$-0.289696\pi$
$691$	1.37666	+	1.00020i	0.0523704	+	0.0380493i	−0.561292	+	0.827618i	$0.689696\pi$
$692$	−10.0125	+	3.25325i	−0.380618	+	0.123670i
$693$		0			0
$694$	7.77436	+	23.9270i	0.295110	+	0.908257i
$695$	−9.99186	−	2.43898i	−0.379013	−	0.0925159i
$696$		0			0
$697$	1.06425	+	0.345795i	0.0403113	+	0.0130979i
$698$	−14.9714	−	20.6063i	−0.566674	−	0.779960i
$699$		0			0
$700$	2.93367	−	5.65119i	0.110882	−	0.213595i
$701$	5.26104			0.198707			0.0993534	−	0.995052i	$-0.468323\pi$
$701$	5.26104			0.198707			0.0993534	+	0.995052i	$0.468323\pi$
$702$		0			0
$703$	1.30490	+	0.423989i	0.0492154	+	0.0159910i
$704$	−1.34786	+	4.14828i	−0.0507993	+	0.156344i
$705$		0			0
$706$	8.93720	+	27.5059i	0.336356	+	1.03520i
$707$			8.94363i			0.336360i
$708$		0			0
$709$	−35.0458	−	25.4622i	−1.31617	−	0.956254i	−0.999971	−	0.00756154i	$-0.997593\pi$
$709$	−35.0458	−	25.4622i	−1.31617	−	0.956254i	−0.316200	−	0.948693i	$-0.602407\pi$
$710$	−4.48340	−	2.77089i	−0.168259	−	0.103990i
$711$		0			0
$712$	−1.00406	+	1.38197i	−0.0376286	+	0.0517914i
$713$	29.8386	−	41.0693i	1.11746	−	1.53806i
$714$		0			0
$715$	31.8752	−	27.0154i	1.19206	−	1.01032i
$716$	8.78501	+	6.38268i	0.328311	+	0.238532i
$717$		0			0
$718$		−	8.43977i		−	0.314970i
$719$	7.61145	+	23.4256i	0.283859	+	0.873629i	0.986738	+	0.162319i	$0.0518974\pi$
$719$	7.61145	+	23.4256i	0.283859	+	0.873629i	−0.702879	+	0.711309i	$0.748103\pi$
$720$		0			0
$721$	5.01606	−	15.4378i	0.186808	−	0.574935i
$722$	−17.9640	−	5.83686i	−0.668551	−	0.217225i
$723$		0			0
$724$	10.2858			0.382267
$725$	−20.7618	−	10.7780i	−0.771074	−	0.400283i
$726$		0			0
$727$	8.26374	+	11.3741i	0.306485	+	0.421841i	0.934281	−	0.356537i	$-0.116043\pi$
$727$	8.26374	+	11.3741i	0.306485	+	0.421841i	−0.627796	+	0.778378i	$0.716043\pi$
$728$	−5.18858	−	1.68587i	−0.192301	−	0.0624825i
$729$		0			0
$730$	−3.32803	+	1.36374i	−0.123176	+	0.0504743i
$731$	−0.308818	−	0.950445i	−0.0114221	−	0.0351535i
$732$		0			0
$733$	−26.8518	+	8.72468i	−0.991794	+	0.322253i	−0.759582	−	0.650412i	$-0.774596\pi$
$733$	−26.8518	+	8.72468i	−0.991794	+	0.322253i	−0.232212	+	0.972665i	$0.574596\pi$
$734$	2.42470	+	1.76165i	0.0894974	+	0.0650236i
$735$		0			0
$736$	5.10793	−	3.71113i	0.188281	−	0.136794i
$737$	−2.99707	+	4.12512i	−0.110399	+	0.151951i
$738$		0			0
$739$	−28.0840	+	20.4042i	−1.03309	+	0.750582i	−0.968924	−	0.247357i	$-0.920438\pi$
$739$	−28.0840	+	20.4042i	−1.03309	+	0.750582i	−0.0641632	+	0.997939i	$0.520438\pi$
$740$	−2.17853	+	8.92486i	−0.0800844	+	0.328085i
$741$		0			0
$742$	1.07176	−	0.348236i	0.0393456	−	0.0127842i
$743$		−	35.3024i		−	1.29512i	−0.762015	−	0.647559i	$-0.775790\pi$
$743$		−	35.3024i		−	1.29512i	0.762015	−	0.647559i	$-0.224210\pi$
$744$		0			0
$745$	2.93756	+	3.46599i	0.107624	+	0.126984i
$746$	−5.41923	+	16.6787i	−0.198412	+	0.610650i
$747$		0			0
$748$	−0.250961	−	0.345418i	−0.00917603	−	0.0126297i
$749$	15.5390			0.567783
$750$		0			0
$751$	14.5513			0.530983			0.265491	−	0.964113i	$-0.414466\pi$
$751$	14.5513			0.530983			0.265491	+	0.964113i	$0.414466\pi$
$752$	−6.88014	−	9.46969i	−0.250893	−	0.345324i
$753$		0			0
$754$	−6.19369	+	19.0622i	−0.225561	+	0.694205i
$755$	27.4193	+	32.3517i	0.997891	+	1.17740i
$756$		0			0
$757$		−	23.9496i		−	0.870462i	−0.900319	−	0.435231i	$-0.856667\pi$
$757$		−	23.9496i		−	0.870462i	0.900319	−	0.435231i	$-0.143333\pi$
$758$	30.2373	−	9.82469i	1.09827	−	0.356849i
$759$		0			0
$760$	−0.177079	+	0.725446i	−0.00642334	+	0.0263147i
$761$	−17.4988	+	12.7137i	−0.634333	+	0.460870i	−0.857899	−	0.513819i	$-0.828230\pi$
$761$	−17.4988	+	12.7137i	−0.634333	+	0.460870i	0.223566	+	0.974689i	$0.428230\pi$
$762$		0			0
$763$	3.78071	−	5.20370i	0.136871	−	0.188387i
$764$	7.79944	−	5.66662i	0.282174	−	0.205011i
$765$		0			0
$766$	−15.8863	−	11.5421i	−0.573996	−	0.417033i
$767$	30.9999	−	10.0725i	1.11934	−	0.363696i
$768$		0			0
$769$	−13.7177	−	42.2187i	−0.494672	−	1.52244i	−0.817467	−	0.575975i	$-0.804623\pi$
$769$	−13.7177	−	42.2187i	−0.494672	−	1.52244i	0.322795	−	0.946469i	$-0.395377\pi$
$770$	−11.4928	+	4.70945i	−0.414172	+	0.169717i
$771$		0			0
$772$	5.70634	+	1.85410i	0.205376	+	0.0667306i
$773$	−6.81261	−	9.37675i	−0.245032	−	0.337258i	0.668731	−	0.743504i	$-0.266838\pi$
$773$	−6.81261	−	9.37675i	−0.245032	−	0.337258i	−0.913764	+	0.406246i	$0.866838\pi$
$774$		0			0
$775$	−39.7531	+	5.98729i	−1.42797	+	0.215070i
$776$	6.60741			0.237192
$777$		0			0
$778$	−28.0879	−	9.12631i	−1.00700	−	0.327194i
$779$	−1.17973	+	3.63083i	−0.0422682	+	0.130088i
$780$		0			0
$781$	3.17699	+	9.77776i	0.113682	+	0.349876i
$782$			0.618034i			0.0221009i
$783$		0			0
$784$	−4.35114	−	3.16129i	−0.155398	−	0.112903i
$785$	−24.2960	+	20.5918i	−0.867163	+	0.734953i
$786$		0			0
$787$	4.55658	−	6.27159i	0.162424	−	0.223558i	−0.720045	−	0.693927i	$-0.755879\pi$
$787$	4.55658	−	6.27159i	0.162424	−	0.223558i	0.882470	+	0.470369i	$0.155879\pi$
$788$	−12.1957	+	16.7859i	−0.434452	+	0.597972i
$789$		0			0
$790$	15.4720	+	9.56224i	0.550470	+	0.340209i
$791$	14.4596	+	10.5055i	0.514125	+	0.373534i
$792$		0			0
$793$			7.18297i			0.255075i
$794$	−6.88254	−	21.1823i	−0.244252	−	0.751731i
$795$		0			0
$796$	−5.89076	+	18.1299i	−0.208792	+	0.642597i
$797$	−38.4237	−	12.4846i	−1.36104	−	0.442228i	−0.464649	−	0.885495i	$-0.653819\pi$
$797$	−38.4237	−	12.4846i	−1.36104	−	0.442228i	−0.896390	+	0.443267i	$0.853819\pi$
$798$		0			0
$799$	1.14579			0.0405350
$800$	−4.93236	−	0.819639i	−0.174385	−	0.0289786i
$801$		0			0
$802$	4.33467	+	5.96616i	0.153062	+	0.210672i
$803$	6.67231	+	2.16797i	0.235461	+	0.0765059i
$804$		0			0
$805$	17.4658	+	4.26336i	0.615590	+	0.150264i
$806$	10.6442	+	32.7594i	0.374925	+	1.15390i
$807$		0			0
$808$	6.67937	−	2.17026i	0.234980	−	0.0763495i
$809$	−7.99707	−	5.81021i	−0.281162	−	0.204276i	0.438262	−	0.898847i	$-0.355594\pi$
$809$	−7.99707	−	5.81021i	−0.281162	−	0.204276i	−0.719424	+	0.694571i	$0.755594\pi$
$810$		0			0
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	−0.665059	−	0.746791i	$-0.731594\pi$
$811$	−4.56597	+	3.31737i	−0.160333	+	0.116489i	0.504726	+	0.863280i	$0.331594\pi$
$812$	3.50197	−	4.82005i	0.122895	−	0.169151i
$813$		0			0
$814$	14.4979	−	10.5333i	0.508150	−	0.369192i
$815$	43.9602	−	3.29190i	1.53986	−	0.115310i
$816$		0			0
$817$	3.24258	−	1.05358i	0.113443	−	0.0368600i
$818$			18.4318i			0.644454i
$819$		0			0
$820$	−24.8330	−	6.06166i	−0.867206	−	0.211682i
$821$	2.57398	−	7.92189i	0.0898325	−	0.276476i	−0.896040	−	0.443973i	$-0.853569\pi$
$821$	2.57398	−	7.92189i	0.0898325	−	0.276476i	0.985873	+	0.167497i	$0.0535685\pi$
$822$		0			0
$823$	−5.29439	−	7.28710i	−0.184551	−	0.254012i	0.706710	−	0.707503i	$-0.250178\pi$
$823$	−5.29439	−	7.28710i	−0.184551	−	0.254012i	−0.891261	+	0.453491i	$0.850178\pi$
$824$	−12.7466			−0.444050
$825$		0			0
$826$	−9.68904			−0.337125
$827$	27.7260	+	38.1615i	0.964126	+	1.32701i	0.944959	+	0.327189i	$0.106101\pi$
$827$	27.7260	+	38.1615i	0.964126	+	1.32701i	0.0191672	+	0.999816i	$0.493899\pi$
$828$		0			0
$829$	8.20305	−	25.2464i	0.284904	−	0.876844i	−0.701524	−	0.712646i	$-0.747497\pi$
$829$	8.20305	−	25.2464i	0.284904	−	0.876844i	0.986427	−	0.164197i	$-0.0525034\pi$
$830$	1.23904	+	16.5462i	0.0430077	+	0.574326i
$831$		0			0
$832$			4.28408i			0.148524i
$833$	0.500699	−	0.162687i	0.0173482	−	0.00563677i
$834$		0			0
$835$	10.9977	+	6.79695i	0.380591	+	0.235218i
$836$	1.17844	−	0.856187i	0.0407572	−	0.0296118i
$837$		0			0
$838$	6.81556	−	9.38081i	0.235440	−	0.324055i
$839$	−0.237312	+	0.172417i	−0.00819291	+	0.00595250i	−0.591874	−	0.806030i	$-0.701612\pi$
$839$	−0.237312	+	0.172417i	−0.00819291	+	0.00595250i	0.583681	+	0.811983i	$0.301612\pi$
$840$		0			0
$841$	5.75320	+	4.17994i	0.198386	+	0.144136i
$842$	2.77611	−	0.902012i	0.0956710	−	0.0310854i
$843$		0			0
$844$	−5.25934	−	16.1866i	−0.181034	−	0.557165i
$845$	6.29322	−	10.1826i	0.216493	−	0.350294i
$846$		0			0
$847$	9.71929	+	3.15799i	0.333959	+	0.108510i
$848$	−0.520147	−	0.715921i	−0.0178619	−	0.0245848i
$849$		0			0
$850$	0.348700	−	0.343446i	0.0119603	−	0.0117801i
$851$	−25.9401			−0.889215
$852$		0			0
$853$	47.9683	+	15.5859i	1.64240	+	0.533650i	0.977074	−	0.212899i	$-0.0682906\pi$
$853$	47.9683	+	15.5859i	1.64240	+	0.533650i	0.665330	+	0.746549i	$0.268291\pi$
$854$	0.659802	−	2.03066i	0.0225780	−	0.0694878i
$855$		0			0
$856$	−3.77070	−	11.6050i	−0.128880	−	0.396651i
$857$		−	42.6554i		−	1.45708i	−0.685003	−	0.728540i	$-0.740199\pi$
$857$		−	42.6554i		−	1.45708i	0.685003	−	0.728540i	$-0.259801\pi$
$858$		0			0
$859$	−24.0952	−	17.5062i	−0.822118	−	0.597304i	0.0952006	−	0.995458i	$-0.469651\pi$
$859$	−24.0952	−	17.5062i	−0.822118	−	0.597304i	−0.917318	+	0.398155i	$0.869651\pi$
$860$	8.65604	+	21.1240i	0.295169	+	0.720321i
$861$		0			0
$862$	−4.45269	+	6.12860i	−0.151659	+	0.208741i
$863$	16.1142	−	22.1793i	0.548534	−	0.754992i	−0.441278	−	0.897370i	$-0.645475\pi$
$863$	16.1142	−	22.1793i	0.548534	−	0.754992i	0.989812	+	0.142378i	$0.0454749\pi$
$864$		0			0
$865$	−5.58233	+	22.8693i	−0.189805	+	0.777580i
$866$	−23.2853	−	16.9177i	−0.791265	−	0.574888i
$867$		0			0
$868$		−	10.2390i		−	0.347533i
$869$	−10.9637	−	33.7426i	−0.371916	−	1.14464i
$870$		0			0
$871$	−1.54759	+	4.76300i	−0.0524382	+	0.161388i
$872$	−4.80371	−	1.56082i	−0.162674	−	0.0528560i
$873$		0			0
$874$	−2.10851			−0.0713214
$875$	−7.30046	−	12.2235i	−0.246801	−	0.413231i
$876$		0			0
$877$	1.95893	+	2.69624i	0.0661484	+	0.0910455i	0.840809	−	0.541331i	$-0.182079\pi$
$877$	1.95893	+	2.69624i	0.0661484	+	0.0910455i	−0.774661	+	0.632377i	$0.782079\pi$
$878$	−16.8798	−	5.48459i	−0.569666	−	0.185096i
$879$		0			0
$880$	6.30600	+	7.44038i	0.212575	+	0.250815i
$881$	2.40321	+	7.39632i	0.0809662	+	0.249188i	0.983343	−	0.181760i	$-0.0581793\pi$
$881$	2.40321	+	7.39632i	0.0809662	+	0.249188i	−0.902377	+	0.430948i	$0.858179\pi$
$882$		0			0
$883$	−5.35794	+	1.74090i	−0.180309	+	0.0585859i	−0.397780	−	0.917481i	$-0.630219\pi$
$883$	−5.35794	+	1.74090i	−0.180309	+	0.0585859i	0.217471	+	0.976067i	$0.430219\pi$
$884$	−0.339266	−	0.246491i	−0.0114107	−	0.00829039i
$885$		0			0
$886$	15.6496	−	11.3701i	0.525758	−	0.381985i
$887$	12.9554	−	17.8316i	0.435001	−	0.598728i	−0.534091	−	0.845427i	$-0.679346\pi$
$887$	12.9554	−	17.8316i	0.435001	−	0.598728i	0.969092	+	0.246699i	$0.0793460\pi$
$888$		0			0
$889$	−1.35886	+	0.987268i	−0.0455746	+	0.0331119i
$890$	1.44832	+	3.53443i	0.0485477	+	0.118474i
$891$		0			0
$892$	−4.73429	+	1.53827i	−0.158516	+	0.0515049i
$893$			3.90900i			0.130810i
$894$		0			0
$895$	22.4680	−	9.20679i	0.751022	−	0.307749i
$896$	0.393520	−	1.21113i	0.0131466	−	0.0404610i
$897$		0			0
$898$	−6.63799	−	9.13641i	−0.221513	−	0.304886i
$899$	−37.6168			−1.25459
$900$		0			0
$901$	0.0866228			0.00288582
$902$	29.3084	+	40.3396i	0.975864	+	1.34316i
$903$		0			0
$904$	4.33708	−	13.3482i	0.144249	−	0.443953i
$905$	12.0916	−	19.5647i	0.401940	−	0.650352i
$906$		0			0
$907$		−	10.7033i		−	0.355398i	−0.984085	−	0.177699i	$-0.943135\pi$
$907$		−	10.7033i		−	0.355398i	0.984085	−	0.177699i	$-0.0568653\pi$
$908$	0.976514	−	0.317289i	0.0324068	−	0.0105296i
$909$		0			0
$910$	−9.30625	+	7.88740i	−0.308499	+	0.261465i
$911$	44.2253	−	32.1316i	1.46525	−	1.06457i	0.483294	−	0.875458i	$-0.339440\pi$
$911$	44.2253	−	32.1316i	1.46525	−	1.06457i	0.981956	−	0.189108i	$-0.0605597\pi$
$912$		0			0
$913$	19.0243	−	26.1846i	0.629611	−	0.866585i
$914$	−2.10944	+	1.53260i	−0.0697741	+	0.0506939i
$915$		0			0
$916$	3.30489	+	2.40115i	0.109197	+	0.0793361i
$917$	−2.15639	+	0.700653i	−0.0712102	+	0.0231376i
$918$		0			0
$919$	13.9687	+	42.9912i	0.460785	+	1.41815i	0.864207	+	0.503136i	$0.167821\pi$
$919$	13.9687	+	42.9912i	0.460785	+	1.41815i	−0.403422	+	0.915014i	$0.632179\pi$
$920$	−1.05425	−	14.0786i	−0.0347577	−	0.464156i
$921$		0			0
$922$	1.86171	+	0.604905i	0.0613120	+	0.0199215i
$923$	5.93536	+	8.16933i	0.195365	+	0.268897i
$924$		0			0
$925$	14.4151	+	14.6356i	0.473965	+	0.481216i
$926$	1.45797			0.0479118
$927$		0			0
$928$	−4.44955	−	1.44575i	−0.146064	−	0.0474589i
$929$	11.4615	−	35.2748i	0.376039	−	1.15733i	−0.566736	−	0.823899i	$-0.691794\pi$
$929$	11.4615	−	35.2748i	0.376039	−	1.15733i	0.942775	−	0.333429i	$-0.108206\pi$
$930$		0			0
$931$	0.555029	+	1.70820i	0.0181903	+	0.0559841i
$932$			4.41279i			0.144546i
$933$		0			0
$934$	20.6989	+	15.0387i	0.677290	+	0.492080i
$935$	−0.952045	+	0.0712927i	−0.0311352	+	0.00233152i
$936$		0			0
$937$	26.3755	−	36.3028i	0.861651	−	1.18596i	−0.119522	−	0.992831i	$-0.538136\pi$
$937$	26.3755	−	36.3028i	0.861651	−	1.18596i	0.981173	−	0.193129i	$-0.0618636\pi$
$938$	0.875024	−	1.20437i	0.0285705	−	0.0393240i
$939$		0			0
$940$	−26.1005	+	1.95450i	−0.851305	+	0.0637488i
$941$	37.8128	+	27.4726i	1.23266	+	0.895582i	0.997087	−	0.0762745i	$-0.0243025\pi$
$941$	37.8128	+	27.4726i	1.23266	+	0.895582i	0.235575	+	0.971856i	$0.424303\pi$
$942$		0			0
$943$		−	72.1771i		−	2.35041i
$944$	2.35114	+	7.23607i	0.0765231	+	0.235514i
$945$		0			0
$946$	13.7607	−	42.3511i	0.447399	−	1.37695i
$947$	32.6851	+	10.6200i	1.06212	+	0.345105i	0.787415	−	0.616423i	$-0.211419\pi$
$947$	32.6851	+	10.6200i	1.06212	+	0.345105i	0.274708	+	0.961528i	$0.411419\pi$
$948$		0			0
$949$	6.89074			0.223683
$950$	1.17171	+	1.18964i	0.0380154	+	0.0385970i
$951$		0			0
$952$	0.0732703	+	0.100848i	0.00237470	+	0.00326850i
$953$	−14.4287	−	4.68815i	−0.467390	−	0.151864i	0.0658477	−	0.997830i	$-0.479025\pi$
$953$	−14.4287	−	4.68815i	−0.467390	−	0.151864i	−0.533238	+	0.845965i	$0.679025\pi$
$954$		0			0
$955$	−1.60977	−	21.4969i	−0.0520909	−	0.695624i
$956$	−6.72179	−	20.6875i	−0.217398	−	0.669083i
$957$		0			0
$958$	6.53112	−	2.12209i	0.211011	−	0.0685617i
$959$	−9.85029	−	7.15666i	−0.318083	−	0.231101i
$960$		0			0
$961$	−27.2205	+	19.7768i	−0.878079	+	0.637962i
$962$	10.3457	−	14.2396i	0.333559	−	0.459105i
$963$		0			0
$964$	−12.8328	+	9.32358i	−0.413317	+	0.300292i
$965$	10.2349	−	8.67447i	0.329474	−	0.279241i
$966$		0			0
$967$	−50.8143	+	16.5106i	−1.63408	+	0.530944i	−0.975204	−	0.221309i	$-0.928967\pi$
$967$	−50.8143	+	16.5106i	−1.63408	+	0.530944i	−0.658874	+	0.752253i	$0.728967\pi$
$968$		−	8.02497i		−	0.257932i
$969$		0			0
$970$	7.76748	−	12.5680i	0.249399	−	0.403536i
$971$	−8.39505	+	25.8373i	−0.269410	+	0.829159i	0.721234	+	0.692691i	$0.243575\pi$
$971$	−8.39505	+	25.8373i	−0.269410	+	0.829159i	−0.990645	+	0.136468i	$0.956425\pi$
$972$		0			0
$973$	−3.44296	−	4.73883i	−0.110376	−	0.151920i
$974$	−42.3233			−1.35613
$975$		0			0
$976$	−1.67667			−0.0536688
$977$	6.69674	+	9.21727i	0.214248	+	0.294886i	0.902592	−	0.430498i	$-0.141662\pi$
$977$	6.69674	+	9.21727i	0.214248	+	0.294886i	−0.688344	+	0.725384i	$0.741662\pi$
$978$		0			0
$979$	2.30242	−	7.08611i	0.0735856	−	0.226473i
$980$	−11.1282	+	4.56004i	−0.355477	+	0.145665i
$981$		0			0
$982$		−	12.9499i		−	0.413249i
$983$	−8.65482	+	2.81212i	−0.276046	+	0.0896927i	−0.443768	−	0.896142i	$-0.646359\pi$
$983$	−8.65482	+	2.81212i	−0.276046	+	0.0896927i	0.167723	+	0.985834i	$0.446359\pi$
$984$		0			0
$985$	17.5918	+	42.9305i	0.560521	+	1.36788i
$986$	0.370503	−	0.269186i	0.0117992	−	0.00857264i
$987$		0			0
$988$	0.840938	−	1.15745i	0.0267538	−	0.0368235i
$989$	−52.1484	+	37.8880i	−1.65822	+	1.20477i
$990$		0			0
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	0.521680	−	0.853141i	$-0.325306\pi$
$991$	−4.04514	−	2.93897i	−0.128498	−	0.0933594i	−0.650178	+	0.759782i	$0.725306\pi$
$992$	−7.64677	+	2.48459i	−0.242785	+	0.0788857i
$993$		0			0
$994$	−0.927551	−	2.85471i	−0.0294201	−	0.0905459i
$995$	27.5601	+	32.5178i	0.873714	+	1.03089i
$996$		0			0
$997$	−46.9380	−	15.2511i	−1.48654	−	0.483006i	−0.550481	−	0.834848i	$-0.685556\pi$
$997$	−46.9380	−	15.2511i	−1.48654	−	0.483006i	−0.936060	+	0.351841i	$0.885556\pi$
$998$	−7.62749	−	10.4983i	−0.241444	−	0.332319i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.b.289.1		8
3.2	odd	2		50.2.e.a.39.2	yes	8
12.11	even	2		400.2.y.a.289.2		8
15.2	even	4		250.2.d.b.51.2		8
15.8	even	4		250.2.d.c.51.1		8
15.14	odd	2		250.2.e.a.199.1		8
25.9	even	10	inner	450.2.l.b.109.1		8
75.29	odd	10		1250.2.b.c.1249.6		8
75.38	even	20		250.2.d.c.201.1		8
75.41	odd	10		250.2.e.a.49.1		8
75.47	even	20		1250.2.a.i.1.3		4
75.53	even	20		1250.2.a.h.1.2		4
75.59	odd	10		50.2.e.a.9.2	✓	8
75.62	even	20		250.2.d.b.201.2		8
75.71	odd	10		1250.2.b.c.1249.3		8
300.47	odd	20		10000.2.a.bb.1.2		4
300.59	even	10		400.2.y.a.209.2		8
300.203	odd	20		10000.2.a.o.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.9.2	✓	8	75.59	odd	10
50.2.e.a.39.2	yes	8	3.2	odd	2
250.2.d.b.51.2		8	15.2	even	4
250.2.d.b.201.2		8	75.62	even	20
250.2.d.c.51.1		8	15.8	even	4
250.2.d.c.201.1		8	75.38	even	20
250.2.e.a.49.1		8	75.41	odd	10
250.2.e.a.199.1		8	15.14	odd	2
400.2.y.a.209.2		8	300.59	even	10
400.2.y.a.289.2		8	12.11	even	2
450.2.l.b.109.1		8	25.9	even	10	inner
450.2.l.b.289.1		8	1.1	even	1	trivial
1250.2.a.h.1.2		4	75.53	even	20
1250.2.a.i.1.3		4	75.47	even	20
1250.2.b.c.1249.3		8	75.71	odd	10
1250.2.b.c.1249.6		8	75.29	odd	10
10000.2.a.o.1.3		4	300.203	odd	20
10000.2.a.bb.1.2		4	300.47	odd	20

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.44575 + 1.70582i) q^{5} +1.27346i q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.44575 + 1.70582i) q^{5} +1.27346i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.530249 - 2.17229i) q^{10} +(-3.52874 + 2.56378i) q^{11} +(-2.51812 + 3.46589i) q^{13} +(1.03025 - 0.748520i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.0930960 - 0.0302487i) q^{17} +(0.103198 + 0.317610i) q^{19} +(-2.06909 + 0.847859i) q^{20} +(4.14828 + 1.34786i) q^{22} +(-3.71113 - 5.10793i) q^{23} +(-0.819639 + 4.93236i) q^{25} +4.28408 q^{26} +(-1.21113 - 0.393520i) q^{28} +(-1.44575 + 4.44955i) q^{29} +(2.48459 + 7.64677i) q^{31} +1.00000i q^{32} +(-0.0791922 - 0.0575365i) q^{34} +(-2.17229 + 1.84110i) q^{35} +(2.41492 - 3.32385i) q^{37} +(0.196294 - 0.270175i) q^{38} +(1.90211 + 1.17557i) q^{40} +(9.24846 + 6.71940i) q^{41} -10.2093i q^{43} +(-1.34786 - 4.14828i) q^{44} +(-1.95106 + 6.00473i) q^{46} +(11.1323 + 3.61710i) q^{47} +5.37831 q^{49} +(4.47214 - 2.23607i) q^{50} +(-2.51812 - 3.46589i) q^{52} +(0.841616 + 0.273457i) q^{53} +(-9.47501 - 2.31282i) q^{55} +(0.393520 + 1.21113i) q^{56} +(4.44955 - 1.44575i) q^{58} +(-6.15537 - 4.47214i) q^{59} +(1.35645 - 0.985520i) q^{61} +(4.72597 - 6.50473i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-9.55275 + 0.715345i) q^{65} +(1.11179 - 0.361243i) q^{67} +0.0978870i q^{68} +(2.76632 + 0.675249i) q^{70} +(0.728373 - 2.24170i) q^{71} +(-0.945424 - 1.30127i) q^{73} -4.10851 q^{74} -0.333955 q^{76} +(-3.26486 - 4.49370i) q^{77} +(-2.51358 + 7.73601i) q^{79} +(-0.166977 - 2.22982i) q^{80} -11.4317i q^{82} +(-7.05722 + 2.29303i) q^{83} +(0.186192 + 0.115073i) q^{85} +(-8.25950 + 6.00088i) q^{86} +(-2.56378 + 3.52874i) q^{88} +(-1.38197 + 1.00406i) q^{89} +(-4.41367 - 3.20672i) q^{91} +(6.00473 - 1.95106i) q^{92} +(-3.61710 - 11.1323i) q^{94} +(-0.392588 + 0.635220i) q^{95} +(6.28402 + 2.04180i) q^{97} +(-3.16129 - 4.35114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) \) 8 * q + 2 * q^4 + 10 * q^5	\( 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

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