LMFDB - Embedded newform 405.2.p.a.289.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(19,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.p (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.11
Character	$\chi$	$=$	405.289
Dual form			405.2.p.a.199.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.795984 - 0.948617i) q^{2} +(0.0810128 + 0.459446i) q^{4} +(-2.17384 - 0.523837i) q^{5} +(2.24130 + 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.22727 + 1.64518i) q^{10} +(4.87230 - 1.77337i) q^{11} +(0.993836 + 1.18441i) q^{13} +(2.15894 - 1.81156i) q^{14} +(2.67745 - 0.974511i) q^{16} +(-4.61649 + 2.66533i) q^{17} +(2.28767 - 3.96236i) q^{19} +(0.0645661 - 1.04120i) q^{20} +(2.19602 - 6.03353i) q^{22} +(5.06318 - 0.892775i) q^{23} +(4.45119 + 2.27748i) q^{25} +1.91463 q^{26} +1.06177i q^{28} +(-4.94693 - 4.15097i) q^{29} +(-0.228069 - 1.29344i) q^{31} +(-0.882557 + 2.42480i) q^{32} +(-1.14627 + 6.50084i) q^{34} +(-4.66522 - 2.03319i) q^{35} +(-3.18754 + 1.84032i) q^{37} +(-1.93781 - 5.32410i) q^{38} +(-4.95020 - 4.70552i) q^{40} +(-3.26644 + 2.74087i) q^{41} +(2.88612 + 7.92956i) q^{43} +(1.20949 + 2.09490i) q^{44} +(3.18331 - 5.51365i) q^{46} +(-6.68721 - 1.17913i) q^{47} +(-1.71059 - 0.622605i) q^{49} +(5.70353 - 2.40964i) q^{50} +(-0.463658 + 0.552567i) q^{52} +6.64507i q^{53} +(-11.5206 + 1.30274i) q^{55} +(5.32509 + 4.46828i) q^{56} +(-7.87536 + 1.38864i) q^{58} +(-2.83430 - 1.03160i) q^{59} +(0.999796 - 5.67013i) q^{61} +(-1.40852 - 0.813210i) q^{62} +(4.44699 + 7.70241i) q^{64} +(-1.54001 - 3.09533i) q^{65} +(-2.22595 - 2.65278i) q^{67} +(-1.59857 - 1.90510i) q^{68} +(-5.64216 + 2.80712i) q^{70} +(0.0130487 + 0.0226011i) q^{71} +(-5.00704 - 2.89081i) q^{73} +(-0.791465 + 4.48862i) q^{74} +(2.00582 + 0.730059i) q^{76} +(11.6211 - 2.04912i) q^{77} +(-12.6845 - 10.6435i) q^{79} +(-6.33083 + 0.715887i) q^{80} +5.28029i q^{82} +(6.96279 - 8.29793i) q^{83} +(11.4317 - 3.37572i) q^{85} +(9.81943 + 3.57398i) q^{86} +(15.5964 + 2.75006i) q^{88} +(-2.32308 + 4.02369i) q^{89} +(1.75941 + 3.04738i) q^{91} +(0.820364 + 2.25393i) q^{92} +(-6.44146 + 5.40503i) q^{94} +(-7.04866 + 7.41518i) q^{95} +(-2.48117 - 6.81695i) q^{97} +(-1.95222 + 1.12712i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) $ 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.795984	−	0.948617i	0.562846	−	0.670774i	−0.407300	−	0.913294i	$-0.633530\pi$
$2$	0.795984	−	0.948617i	0.562846	−	0.670774i	0.970146	+	0.242521i	$0.0779742\pi$
$3$		0			0
$3$		0			0
$4$	0.0810128	+	0.459446i	0.0405064	+	0.229723i
$5$	−2.17384	−	0.523837i	−0.972172	−	0.234267i
$5$	−2.17384	−	0.523837i	−0.972172	−	0.234267i
$6$		0			0
$7$	2.24130	+	0.395202i	0.847133	+	0.149372i	0.580333	−	0.814379i	$-0.302923\pi$
$7$	2.24130	+	0.395202i	0.847133	+	0.149372i	0.266800	+	0.963752i	$0.414034\pi$
$8$	2.64518	+	1.52719i	0.935211	+	0.539945i
$9$		0			0
$10$	−2.22727	+	1.64518i	−0.704324	+	0.520251i
$11$	4.87230	−	1.77337i	1.46905	−	0.534692i	0.521211	−	0.853428i	$-0.325480\pi$
$11$	4.87230	−	1.77337i	1.46905	−	0.534692i	0.947844	+	0.318736i	$0.103258\pi$
$12$		0			0
$13$	0.993836	+	1.18441i	0.275641	+	0.328496i	0.886049	−	0.463591i	$-0.153439\pi$
$13$	0.993836	+	1.18441i	0.275641	+	0.328496i	−0.610409	+	0.792087i	$0.708995\pi$
$14$	2.15894	−	1.81156i	0.577000	−	0.484161i
$15$		0			0
$16$	2.67745	−	0.974511i	0.669361	−	0.243628i
$17$	−4.61649	+	2.66533i	−1.11966	+	0.646438i	−0.941315	−	0.337530i	$-0.890409\pi$
$17$	−4.61649	+	2.66533i	−1.11966	+	0.646438i	−0.178348	+	0.983967i	$0.557075\pi$
$18$		0			0
$19$	2.28767	−	3.96236i	0.524827	−	0.909027i	−0.474755	−	0.880118i	$-0.657463\pi$
$19$	2.28767	−	3.96236i	0.524827	−	0.909027i	0.999582	−	0.0289093i	$-0.00920339\pi$
$20$	0.0645661	−	1.04120i	0.0144374	−	0.232820i
$21$		0			0
$22$	2.19602	−	6.03353i	0.468194	−	1.28635i
$23$	5.06318	−	0.892775i	1.05575	−	0.186156i	0.381278	−	0.924461i	$-0.375484\pi$
$23$	5.06318	−	0.892775i	1.05575	−	0.186156i	0.674468	+	0.738304i	$0.264373\pi$
$24$		0			0
$25$	4.45119	+	2.27748i	0.890238	+	0.455496i
$26$	1.91463			0.375490
$27$		0			0
$28$			1.06177i			0.200657i
$29$	−4.94693	−	4.15097i	−0.918622	−	0.770816i	0.0551173	−	0.998480i	$-0.482447\pi$
$29$	−4.94693	−	4.15097i	−0.918622	−	0.770816i	−0.973740	+	0.227664i	$0.926891\pi$
$30$		0			0
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	0.957453	−	0.288591i	$-0.0931867\pi$
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	−0.998415	+	0.0562816i	$0.982076\pi$
$32$	−0.882557	+	2.42480i	−0.156015	+	0.428649i
$33$		0			0
$34$	−1.14627	+	6.50084i	−0.196584	+	1.11489i
$35$	−4.66522	−	2.03319i	−0.788566	−	0.343671i
$36$		0			0
$37$	−3.18754	+	1.84032i	−0.524028	+	0.302548i	−0.738581	−	0.674165i	$-0.764504\pi$
$37$	−3.18754	+	1.84032i	−0.524028	+	0.302548i	0.214553	+	0.976712i	$0.431170\pi$
$38$	−1.93781	−	5.32410i	−0.314355	−	0.863683i
$39$		0			0
$40$	−4.95020	−	4.70552i	−0.782695	−	0.744009i
$41$	−3.26644	+	2.74087i	−0.510132	+	0.428052i	−0.861176	−	0.508307i	$-0.830271\pi$
$41$	−3.26644	+	2.74087i	−0.510132	+	0.428052i	0.351044	+	0.936359i	$0.385827\pi$
$42$		0			0
$43$	2.88612	+	7.92956i	0.440130	+	1.20925i	0.939407	+	0.342804i	$0.111377\pi$
$43$	2.88612	+	7.92956i	0.440130	+	1.20925i	−0.499277	+	0.866442i	$0.666401\pi$
$44$	1.20949	+	2.09490i	0.182337	+	0.315817i
$45$		0			0
$46$	3.18331	−	5.51365i	0.469353	−	0.812944i
$47$	−6.68721	−	1.17913i	−0.975429	−	0.171995i	−0.336857	−	0.941556i	$-0.609364\pi$
$47$	−6.68721	−	1.17913i	−0.975429	−	0.171995i	−0.638573	+	0.769561i	$0.720475\pi$
$48$		0			0
$49$	−1.71059	−	0.622605i	−0.244371	−	0.0889436i
$50$	5.70353	−	2.40964i	0.806602	−	0.340774i
$51$		0			0
$52$	−0.463658	+	0.552567i	−0.0642979	+	0.0766272i
$53$			6.64507i			0.912771i	0.889782	+	0.456385i	$0.150856\pi$
$53$			6.64507i			0.912771i	−0.889782	+	0.456385i	$0.849144\pi$
$54$		0			0
$55$	−11.5206	+	1.30274i	−1.55343	+	0.175662i
$56$	5.32509	+	4.46828i	0.711596	+	0.597100i
$57$		0			0
$58$	−7.87536	+	1.38864i	−1.03409	+	0.182337i
$59$	−2.83430	−	1.03160i	−0.368995	−	0.134303i	0.150866	−	0.988554i	$-0.451794\pi$
$59$	−2.83430	−	1.03160i	−0.368995	−	0.134303i	−0.519861	+	0.854251i	$0.674016\pi$
$60$		0			0
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	−0.851463	−	0.524414i	$-0.824284\pi$
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	0.979474	−	0.201571i	$-0.0646046\pi$
$62$	−1.40852	−	0.813210i	−0.178882	−	0.103278i
$63$		0			0
$64$	4.44699	+	7.70241i	0.555874	+	0.962801i
$65$	−1.54001	−	3.09533i	−0.191014	−	0.383928i
$66$		0			0
$67$	−2.22595	−	2.65278i	−0.271943	−	0.324089i	0.612738	−	0.790286i	$-0.290068\pi$
$67$	−2.22595	−	2.65278i	−0.271943	−	0.324089i	−0.884681	+	0.466197i	$0.845624\pi$
$68$	−1.59857	−	1.90510i	−0.193855	−	0.231028i
$69$		0			0
$70$	−5.64216	+	2.80712i	−0.674367	+	0.335515i
$71$	0.0130487	+	0.0226011i	0.00154860	+	0.00268225i	0.866799	−	0.498658i	$-0.166174\pi$
$71$	0.0130487	+	0.0226011i	0.00154860	+	0.00268225i	−0.865250	+	0.501341i	$0.832840\pi$
$72$		0			0
$73$	−5.00704	−	2.89081i	−0.586029	−	0.338344i	0.177497	−	0.984121i	$-0.443200\pi$
$73$	−5.00704	−	2.89081i	−0.586029	−	0.338344i	−0.763526	+	0.645777i	$0.776533\pi$
$74$	−0.791465	+	4.48862i	−0.0920059	+	0.521792i
$75$		0			0
$76$	2.00582	+	0.730059i	0.230083	+	0.0837435i
$77$	11.6211	−	2.04912i	1.32435	−	0.233519i
$78$		0			0
$79$	−12.6845	−	10.6435i	−1.42712	−	1.19749i	−0.947393	−	0.320073i	$-0.896292\pi$
$79$	−12.6845	−	10.6435i	−1.42712	−	1.19749i	−0.479724	−	0.877420i	$-0.659263\pi$
$80$	−6.33083	+	0.715887i	−0.707809	+	0.0800386i
$81$		0			0
$82$			5.28029i			0.583110i
$83$	6.96279	−	8.29793i	0.764265	−	0.910816i	−0.233844	−	0.972274i	$-0.575131\pi$
$83$	6.96279	−	8.29793i	0.764265	−	0.910816i	0.998110	+	0.0614583i	$0.0195751\pi$
$84$		0			0
$85$	11.4317	−	3.37572i	1.23994	−	0.366149i
$86$	9.81943	+	3.57398i	1.05886	+	0.385392i
$87$		0			0
$88$	15.5964	+	2.75006i	1.66258	+	0.293158i
$89$	−2.32308	+	4.02369i	−0.246246	+	0.426510i	−0.962481	−	0.271349i	$-0.912530\pi$
$89$	−2.32308	+	4.02369i	−0.246246	+	0.426510i	0.716235	+	0.697859i	$0.245864\pi$
$90$		0			0
$91$	1.75941	+	3.04738i	0.184436	+	0.319453i
$92$	0.820364	+	2.25393i	0.0855289	+	0.234989i
$93$		0			0
$94$	−6.44146	+	5.40503i	−0.664386	+	0.557486i
$95$	−7.04866	+	7.41518i	−0.723178	+	0.760781i
$96$		0			0
$97$	−2.48117	−	6.81695i	−0.251924	−	0.692157i	−0.999605	−	0.0280982i	$-0.991055\pi$
$97$	−2.48117	−	6.81695i	−0.251924	−	0.692157i	0.747681	−	0.664058i	$-0.231167\pi$
$98$	−1.95222	+	1.12712i	−0.197204	+	0.113856i
$99$		0			0
$100$	−0.685777	+	2.22959i	−0.0685777	+	0.222959i
$101$	−0.0757615	+	0.429665i	−0.00753855	+	0.0427532i	−0.988345	−	0.152231i	$-0.951354\pi$
$101$	−0.0757615	+	0.429665i	−0.00753855	+	0.0427532i	0.980806	+	0.194984i	$0.0624655\pi$
$102$		0			0
$103$	0.775652	−	2.13109i	0.0764273	−	0.209982i	−0.895595	−	0.444870i	$-0.853250\pi$
$103$	0.775652	−	2.13109i	0.0764273	−	0.209982i	0.972023	+	0.234888i	$0.0754722\pi$
$104$	0.820053	+	4.65075i	0.0804128	+	0.456044i
$105$		0			0
$106$	6.30363	+	5.28937i	0.612263	+	0.513749i
$107$			4.36720i			0.422193i	0.977465	+	0.211097i	$0.0677034\pi$
$107$			4.36720i			0.422193i	−0.977465	+	0.211097i	$0.932297\pi$
$108$		0			0
$109$	−7.95224			−0.761686			−0.380843	−	0.924640i	$-0.624366\pi$
$109$	−7.95224			−0.761686			−0.380843	+	0.924640i	$0.624366\pi$
$110$	−7.93440	+	11.9656i	−0.756515	+	1.14087i
$111$		0			0
$112$	6.38610	−	1.12604i	0.603429	−	0.106401i
$113$	−5.38234	+	14.7879i	−0.506328	+	1.39112i	0.378671	+	0.925531i	$0.376381\pi$
$113$	−5.38234	+	14.7879i	−0.506328	+	1.39112i	−0.884999	+	0.465593i	$0.845841\pi$
$114$		0			0
$115$	−11.4742	−	0.711529i	−1.06998	−	0.0663504i
$116$	1.50638	−	2.60913i	0.139864	−	0.242252i
$117$		0			0
$118$	−3.23466	+	1.86753i	−0.297774	+	0.171920i
$119$	−11.4003	+	4.14937i	−1.04506	+	0.380372i
$120$		0			0
$121$	12.1680	−	10.2102i	1.10618	−	0.928196i
$122$	−4.58296	−	5.46176i	−0.414922	−	0.494484i
$123$		0			0
$124$	0.575791	−	0.209571i	0.0517075	−	0.0188200i
$125$	−8.48316	−	7.28258i	−0.758757	−	0.651374i
$126$		0			0
$127$	2.90443	+	1.67688i	0.257727	+	0.148799i	0.623297	−	0.781985i	$-0.285793\pi$
$127$	2.90443	+	1.67688i	0.257727	+	0.148799i	−0.365570	+	0.930784i	$0.619126\pi$
$128$	5.76393	+	1.01634i	0.509464	+	0.0898323i
$129$		0			0
$130$	−4.16210	−	1.00295i	−0.365040	−	0.0879649i
$131$	0.958255	+	5.43454i	0.0837231	+	0.474818i	0.997625	+	0.0688819i	$0.0219432\pi$
$131$	0.958255	+	5.43454i	0.0837231	+	0.474818i	−0.913902	+	0.405936i	$0.866946\pi$
$132$		0			0
$133$	6.69329	−	7.97675i	0.580382	−	0.691672i
$134$	−4.28829			−0.370452
$135$		0			0
$136$	−16.2819			−1.39616
$137$	3.81854	−	4.55076i	0.326240	−	0.388798i	−0.577848	−	0.816145i	$-0.696107\pi$
$137$	3.81854	−	4.55076i	0.326240	−	0.388798i	0.904088	+	0.427347i	$0.140552\pi$
$138$		0			0
$139$	2.76633	+	15.6886i	0.234637	+	1.33069i	0.843377	+	0.537323i	$0.180564\pi$
$139$	2.76633	+	15.6886i	0.234637	+	1.33069i	−0.608740	+	0.793370i	$0.708325\pi$
$140$	0.556197	−	2.30813i	0.0470072	−	0.195073i
$141$		0			0
$142$	0.0318263	+	0.00561184i	0.00267081	+	0.000470935i
$143$	6.94267	+	4.00835i	0.580575	+	0.335195i
$144$		0			0
$145$	8.57942	+	11.6149i	0.712482	+	0.964569i
$146$	−6.72780	+	2.44872i	−0.556796	+	0.202657i
$147$		0			0
$148$	−1.10376	−	1.31541i	−0.0907286	−	0.108126i
$149$	15.5994	−	13.0894i	1.27795	−	1.07233i	0.284430	−	0.958697i	$-0.408196\pi$
$149$	15.5994	−	13.0894i	1.27795	−	1.07233i	0.993523	−	0.113632i	$-0.0362486\pi$
$150$		0			0
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	−0.414394	−	0.910098i	$-0.636006\pi$
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	0.267555	+	0.963543i	$0.413784\pi$
$152$	12.1026	−	6.98743i	0.981649	−	0.566755i
$153$		0			0
$154$	7.30642	−	12.6551i	0.588768	−	1.01978i
$155$	−0.181768	+	2.93121i	−0.0145999	+	0.235441i
$156$		0			0
$157$	−4.36413	+	11.9904i	−0.348296	+	0.956935i	0.634611	+	0.772832i	$0.281160\pi$
$157$	−4.36413	+	11.9904i	−0.348296	+	0.956935i	−0.982907	+	0.184103i	$0.941062\pi$
$158$	−20.1933	+	3.56063i	−1.60649	+	0.283268i
$159$		0			0
$160$	3.18874	−	4.80883i	0.252092	−	0.380171i
$161$	11.7009			0.922163
$162$		0			0
$163$		−	24.6659i		−	1.93198i	−0.258578	−	0.965990i	$-0.583254\pi$
$163$		−	24.6659i		−	1.93198i	0.258578	−	0.965990i	$-0.416746\pi$
$164$	−1.52391	−	1.27871i	−0.118997	−	0.0998503i
$165$		0			0
$166$	−2.32929	−	13.2100i	−0.180788	−	1.02530i
$167$	1.83304	−	5.03625i	0.141845	−	0.389716i	−0.848345	−	0.529444i	$-0.822401\pi$
$167$	1.83304	−	5.03625i	0.141845	−	0.389716i	0.990190	+	0.139728i	$0.0446227\pi$
$168$		0			0
$169$	1.84231	−	10.4483i	0.141717	−	0.803714i
$170$	5.89720	−	13.5314i	0.452295	−	1.03781i
$171$		0			0
$172$	−3.40939	+	1.96841i	−0.259964	+	0.150090i
$173$	−4.89834	−	13.4581i	−0.372414	−	1.02320i	−0.974426	−	0.224711i	$-0.927856\pi$
$173$	−4.89834	−	13.4581i	−0.372414	−	1.02320i	0.602012	−	0.798487i	$-0.294366\pi$
$174$		0			0
$175$	9.07640	+	6.86364i	0.686111	+	0.518843i
$176$	11.3172	−	9.49622i	0.853063	−	0.715805i
$177$		0			0
$178$	1.96781	+	5.40651i	0.147493	+	0.405235i
$179$	2.84521	+	4.92805i	0.212661	+	0.368340i	0.952547	−	0.304393i	$-0.0984536\pi$
$179$	2.84521	+	4.92805i	0.212661	+	0.368340i	−0.739885	+	0.672733i	$0.765120\pi$
$180$		0			0
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	−0.613350	−	0.789811i	$-0.710178\pi$
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	0.990672	+	0.136271i	$0.0435117\pi$
$182$	4.29126	+	0.756665i	0.318090	+	0.0560878i
$183$		0			0
$184$	14.7564	+	5.37091i	1.08786	+	0.395948i
$185$	7.89323	−	2.33083i	0.580322	−	0.171366i
$186$		0			0
$187$	−17.7663	+	21.1731i	−1.29920	+	1.54833i
$188$		−	3.16794i		−	0.231046i
$189$		0			0
$190$	1.42354	+	12.5889i	0.103274	+	0.913291i
$191$	4.87022	+	4.08660i	0.352397	+	0.295696i	0.801752	−	0.597657i	$-0.203902\pi$
$191$	4.87022	+	4.08660i	0.352397	+	0.295696i	−0.449355	+	0.893353i	$0.648346\pi$
$192$		0			0
$193$	−19.2071	+	3.38673i	−1.38256	+	0.243782i	−0.814957	−	0.579521i	$-0.803240\pi$
$193$	−19.2071	+	3.38673i	−1.38256	+	0.243782i	−0.567601	+	0.823304i	$0.692128\pi$
$194$	−8.44165	−	3.07251i	−0.606075	−	0.220593i
$195$		0			0
$196$	0.147474	−	0.836365i	0.0105338	−	0.0597404i
$197$	−7.83426	−	4.52311i	−0.558168	−	0.322259i	0.194242	−	0.980954i	$-0.437775\pi$
$197$	−7.83426	−	4.52311i	−0.558168	−	0.322259i	−0.752410	+	0.658695i	$0.771109\pi$
$198$		0			0
$199$	5.04715	+	8.74191i	0.357783	+	0.619698i	0.987590	−	0.157054i	$-0.0501995\pi$
$199$	5.04715	+	8.74191i	0.357783	+	0.619698i	−0.629807	+	0.776751i	$0.716866\pi$
$200$	8.29603	+	12.8222i	0.586618	+	0.906664i
$201$		0			0
$202$	0.347282	+	0.413875i	0.0244347	+	0.0291201i
$203$	−9.44710	−	11.2586i	−0.663057	−	0.790200i
$204$		0			0
$205$	8.53650	−	4.24713i	0.596215	−	0.296633i
$206$	−1.40418	−	2.43211i	−0.0978338	−	0.169453i
$207$		0			0
$208$	3.81516	+	2.20268i	0.264534	+	0.152729i
$209$	4.11947	−	23.3627i	0.284950	−	1.61603i
$210$		0			0
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	0.454839	−	0.890573i	$-0.349697\pi$
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	−0.224022	+	0.974584i	$0.571919\pi$
$212$	−3.05305	+	0.538336i	−0.209685	+	0.0369730i
$213$		0			0
$214$	4.14280	+	3.47622i	0.283196	+	0.237630i
$215$	−2.12018	−	18.7495i	−0.144595	−	1.27870i
$216$		0			0
$217$		−	2.98913i		−	0.202915i
$218$	−6.32986	+	7.54363i	−0.428712	+	0.510919i
$219$		0			0
$220$	−1.53185	−	5.18755i	−0.103278	−	0.349745i
$221$	−7.74487	−	2.81890i	−0.520977	−	0.189620i
$222$		0			0
$223$	−18.2797	−	3.22320i	−1.22410	−	0.215842i	−0.476010	−	0.879440i	$-0.657917\pi$
$223$	−18.2797	−	3.22320i	−1.22410	−	0.215842i	−0.748089	+	0.663598i	$0.769029\pi$
$224$	−2.93637	+	5.08593i	−0.196194	+	0.339818i
$225$		0			0
$226$	9.74376	+	16.8767i	0.648145	+	1.12262i
$227$	8.41561	+	23.1217i	0.558564	+	1.53464i	0.821722	+	0.569888i	$0.193014\pi$
$227$	8.41561	+	23.1217i	0.558564	+	1.53464i	−0.263158	+	0.964753i	$0.584764\pi$
$228$		0			0
$229$	−1.56307	+	1.31157i	−0.103291	+	0.0866713i	−0.692971	−	0.720966i	$-0.743698\pi$
$229$	−1.56307	+	1.31157i	−0.103291	+	0.0866713i	0.589680	+	0.807637i	$0.299254\pi$
$230$	−9.80827	+	10.3183i	−0.646738	+	0.680367i
$231$		0			0
$232$	−6.74618	−	18.5350i	−0.442908	−	1.21688i
$233$	7.51547	−	4.33906i	0.492355	−	0.284261i	−0.233196	−	0.972430i	$-0.574918\pi$
$233$	7.51547	−	4.33906i	0.492355	−	0.284261i	0.725551	+	0.688169i	$0.241585\pi$
$234$		0			0
$235$	13.9193	+	6.06626i	0.907993	+	0.395719i
$236$	0.244351	−	1.38578i	0.0159059	−	0.0902068i
$237$		0			0
$238$	−5.13829	+	14.1173i	−0.333066	+	0.915092i
$239$	−0.654990	−	3.71463i	−0.0423678	−	0.240280i	0.956268	−	0.292491i	$-0.0944842\pi$
$239$	−0.654990	−	3.71463i	−0.0423678	−	0.240280i	−0.998636	+	0.0522114i	$0.983373\pi$
$240$		0			0
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	0.656652	−	0.754194i	$-0.271972\pi$
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	−0.628710	+	0.777640i	$0.716417\pi$
$242$		−	19.6699i		−	1.26443i
$243$		0			0
$244$	2.68612			0.171961
$245$	3.39242	+	2.24952i	0.216734	+	0.143717i
$246$		0			0
$247$	6.96662	−	1.22840i	0.443275	−	0.0781614i
$248$	1.37205	−	3.76969i	0.0871256	−	0.239375i
$249$		0			0
$250$	−13.6608	+	2.25045i	−0.863988	+	0.142331i
$251$	−0.425928	+	0.737730i	−0.0268844	+	0.0465651i	−0.879155	−	0.476537i	$-0.841892\pi$
$251$	−0.425928	+	0.737730i	−0.0268844	+	0.0465651i	0.852270	+	0.523102i	$0.175225\pi$
$252$		0			0
$253$	23.0861	−	13.3288i	1.45141	−	0.837973i
$254$	3.90260	−	1.42043i	0.244871	−	0.0891257i
$255$		0			0
$256$	−8.07425	+	6.77510i	−0.504641	+	0.423444i
$257$	11.8239	+	14.0912i	0.737553	+	0.878982i	0.996209	−	0.0869875i	$-0.0277240\pi$
$257$	11.8239	+	14.0912i	0.737553	+	0.878982i	−0.258656	+	0.965970i	$0.583280\pi$
$258$		0			0
$259$	−7.87153	+	2.86500i	−0.489113	+	0.178023i
$260$	1.29738	−	0.958312i	0.0804598	−	0.0594320i
$261$		0			0
$262$	5.91805	+	3.41679i	0.365618	+	0.211090i
$263$	−6.87408	−	1.21209i	−0.423874	−	0.0747404i	−0.0423576	−	0.999103i	$-0.513487\pi$
$263$	−6.87408	−	1.21209i	−0.423874	−	0.0747404i	−0.381516	+	0.924362i	$0.624598\pi$
$264$		0			0
$265$	3.48094	−	14.4453i	0.213832	−	0.887370i
$266$	−2.23913	−	12.6987i	−0.137290	−	0.778610i
$267$		0			0
$268$	1.03848	−	1.23761i	0.0634352	−	0.0755992i
$269$	9.05450			0.552062			0.276031	−	0.961149i	$-0.410981\pi$
$269$	9.05450			0.552062			0.276031	+	0.961149i	$0.410981\pi$
$270$		0			0
$271$	−2.68123			−0.162873			−0.0814364	−	0.996679i	$-0.525951\pi$
$271$	−2.68123			−0.162873			−0.0814364	+	0.996679i	$0.525951\pi$
$272$	−9.76300	+	11.6351i	−0.591969	+	0.705481i
$273$		0			0
$274$	−1.27743	−	7.24467i	−0.0771724	−	0.437667i
$275$	25.7264	+	3.20296i	1.55136	+	0.193146i
$276$		0			0
$277$	9.53431	+	1.68116i	0.572861	+	0.101011i	0.452572	−	0.891728i	$-0.350507\pi$
$277$	9.53431	+	1.68116i	0.572861	+	0.101011i	0.120289	+	0.992739i	$0.461618\pi$
$278$	17.0845	+	9.86372i	1.02466	+	0.591587i
$279$		0			0
$280$	−9.23526	−	12.5028i	−0.551913	−	0.747187i
$281$	12.4600	−	4.53506i	0.743300	−	0.270539i	0.0575163	−	0.998345i	$-0.481682\pi$
$281$	12.4600	−	4.53506i	0.743300	−	0.270539i	0.685784	+	0.727806i	$0.259460\pi$
$282$		0			0
$283$	12.5849	+	14.9981i	0.748094	+	0.891543i	0.997033	−	0.0769758i	$-0.0245264\pi$
$283$	12.5849	+	14.9981i	0.748094	+	0.891543i	−0.248939	+	0.968519i	$0.580082\pi$
$284$	−0.00932686	+	0.00782616i	−0.000553447	+	0.000464397i
$285$		0			0
$286$	9.32865	−	3.39535i	0.551615	−	0.200771i
$287$	−8.40428	+	4.85221i	−0.496089	+	0.286417i
$288$		0			0
$289$	5.70798	−	9.88651i	0.335763	−	0.581559i
$290$	17.8472	+	1.10673i	1.04803	+	0.0649892i
$291$		0			0
$292$	0.922540	−	2.53466i	0.0539875	−	0.148330i
$293$	−29.7888	+	5.25257i	−1.74028	+	0.306858i	−0.951462	−	0.307767i	$-0.900418\pi$
$293$	−29.7888	+	5.25257i	−1.74028	+	0.306858i	−0.788819	+	0.614625i	$0.789307\pi$
$294$		0			0
$295$	5.62094	+	3.72726i	0.327264	+	0.217009i
$296$	−11.2421			−0.653436
$297$		0			0
$298$		−	25.2169i		−	1.46077i
$299$	6.08938	+	5.10960i	0.352158	+	0.295496i
$300$		0			0
$301$	3.33490	+	18.9131i	0.192220	+	1.09014i
$302$	−0.813265	+	2.23443i	−0.0467982	+	0.128577i
$303$		0			0
$304$	2.26375	−	12.8384i	0.129835	−	0.736330i
$305$	−5.14363	+	11.8022i	−0.294523	+	0.675794i
$306$		0			0
$307$	15.8229	−	9.13533i	0.903058	−	0.521381i	0.0248672	−	0.999691i	$-0.492084\pi$
$307$	15.8229	−	9.13533i	0.903058	−	0.521381i	0.878191	+	0.478310i	$0.158750\pi$
$308$	1.88292	+	5.17329i	0.107289	+	0.294775i
$309$		0			0
$310$	2.63591	+	2.50563i	0.149710	+	0.142310i
$311$	−25.8479	+	21.6890i	−1.46570	+	1.22987i	−0.545681	+	0.837993i	$0.683729\pi$
$311$	−25.8479	+	21.6890i	−1.46570	+	1.22987i	−0.920018	+	0.391875i	$0.871826\pi$
$312$		0			0
$313$	0.953665	+	2.62017i	0.0539043	+	0.148101i	0.963723	−	0.266906i	$-0.0860014\pi$
$313$	0.953665	+	2.62017i	0.0539043	+	0.148101i	−0.909818	+	0.415007i	$0.863779\pi$
$314$	7.90048	+	13.6840i	0.445850	+	0.772235i
$315$		0			0
$316$	3.86253	−	6.69010i	0.217284	−	0.376348i
$317$	2.71702	+	0.479083i	0.152603	+	0.0269080i	0.249428	−	0.968393i	$-0.419758\pi$
$317$	2.71702	+	0.479083i	0.152603	+	0.0269080i	−0.0968248	+	0.995301i	$0.530869\pi$
$318$		0			0
$319$	−31.4642	−	11.4520i	−1.76166	−	0.641190i
$320$	−5.63225	−	19.0733i	−0.314852	−	1.06623i
$321$		0			0
$322$	9.31377	−	11.0997i	0.519036	−	0.618563i
$323$			24.3896i			1.35707i
$324$		0			0
$325$	1.72629	+	7.53547i	0.0957572	+	0.417993i
$326$	−23.3985	−	19.6337i	−1.29592	−	1.08741i
$327$		0			0
$328$	−12.8261	+	2.26160i	−0.708206	+	0.124876i
$329$	−14.5221	−	5.28560i	−0.800627	−	0.291404i
$330$		0			0
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	0.497902	+	0.867233i	$0.334104\pi$
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	−0.764486	+	0.644640i	$0.777007\pi$
$332$	4.37653	+	2.52679i	0.240193	+	0.138676i
$333$		0			0
$334$	−3.31840	−	5.74763i	−0.181575	−	0.314496i
$335$	3.44923	+	6.93276i	0.188452	+	0.378777i
$336$		0			0
$337$	9.17286	+	10.9318i	0.499677	+	0.595492i	0.955651	−	0.294501i	$-0.0951534\pi$
$337$	9.17286	+	10.9318i	0.499677	+	0.595492i	−0.455974	+	0.889993i	$0.650709\pi$
$338$	−8.44497	−	10.0643i	−0.459346	−	0.547427i
$339$		0			0
$340$	2.47708	+	4.97879i	0.134338	+	0.270013i
$341$	−3.40498	−	5.89759i	−0.184390	−	0.319372i
$342$		0			0
$343$	−17.3847	−	10.0371i	−0.938685	−	0.541950i
$344$	−4.47567	+	25.3828i	−0.241312	+	1.36855i
$345$		0			0
$346$	−16.6656	−	6.06577i	−0.895946	−	0.326098i
$347$	−17.3984	+	3.06781i	−0.933994	+	0.164688i	−0.619880	−	0.784697i	$-0.712819\pi$
$347$	−17.3984	+	3.06781i	−0.933994	+	0.164688i	−0.314114	+	0.949385i	$0.601708\pi$
$348$		0			0
$349$	18.7439	+	15.7280i	1.00334	+	0.841899i	0.987443	−	0.157975i	$-0.0504965\pi$
$349$	18.7439	+	15.7280i	1.00334	+	0.841899i	0.0158927	+	0.999874i	$0.494941\pi$
$350$	13.7356	−	3.14667i	0.734201	−	0.168197i
$351$		0			0
$352$			13.3795i			0.713129i
$353$	20.5015	−	24.4328i	1.09119	−	1.30043i	0.140567	−	0.990071i	$-0.455108\pi$
$353$	20.5015	−	24.4328i	1.09119	−	1.30043i	0.950621	−	0.310355i	$-0.100448\pi$
$354$		0			0
$355$	−0.0165266	−	0.0559666i	−0.000877141	−	0.00297040i
$356$	−2.03687	−	0.741359i	−0.107954	−	0.0392920i
$357$		0			0
$358$	6.93958	+	1.22364i	0.366768	+	0.0646711i
$359$	4.13080	−	7.15476i	0.218015	−	0.377614i	−0.736186	−	0.676780i	$-0.763375\pi$
$359$	4.13080	−	7.15476i	0.218015	−	0.377614i	0.954201	+	0.299166i	$0.0967083\pi$
$360$		0			0
$361$	−0.966856	−	1.67464i	−0.0508871	−	0.0881391i
$362$	−4.30002	−	11.8142i	−0.226004	−	0.620941i
$363$		0			0
$364$	−1.25757	+	1.05523i	−0.0659148	+	0.0553091i
$365$	9.37019	+	8.90705i	0.490458	+	0.466216i
$366$		0			0
$367$	−7.40606	−	20.3480i	−0.386593	−	1.06216i	−0.968525	−	0.248918i	$-0.919925\pi$
$367$	−7.40606	−	20.3480i	−0.386593	−	1.06216i	0.581931	−	0.813238i	$-0.302297\pi$
$368$	12.6864	−	7.32448i	0.661323	−	0.381815i
$369$		0			0
$370$	4.07183	−	9.34296i	0.211684	−	0.485717i
$371$	−2.62615	+	14.8936i	−0.136343	+	0.773238i
$372$		0			0
$373$	−10.4509	+	28.7136i	−0.541126	+	1.48673i	0.304267	+	0.952587i	$0.401589\pi$
$373$	−10.4509	+	28.7136i	−0.541126	+	1.48673i	−0.845393	+	0.534145i	$0.820634\pi$
$374$	5.94343	+	33.7068i	0.307327	+	1.74294i
$375$		0			0
$376$	−15.8881	−	13.3317i	−0.819365	−	0.687529i
$377$		−	9.98457i		−	0.514232i
$378$		0			0
$379$	−6.49045			−0.333392			−0.166696	−	0.986008i	$-0.553310\pi$
$379$	−6.49045			−0.333392			−0.166696	+	0.986008i	$0.553310\pi$
$380$	−3.97791	−	2.63776i	−0.204062	−	0.135314i
$381$		0			0
$382$	7.75324	−	1.36711i	0.396690	−	0.0699472i
$383$	2.57705	−	7.08040i	0.131681	−	0.361791i	−0.856276	−	0.516519i	$-0.827228\pi$
$383$	2.57705	−	7.08040i	0.131681	−	0.361791i	0.987957	+	0.154727i	$0.0494499\pi$
$384$		0			0
$385$	−26.3360	−	1.63312i	−1.34220	−	0.0832316i
$386$	−12.0758	+	20.9160i	−0.614645	+	1.06460i
$387$		0			0
$388$	2.93102	−	1.69222i	0.148800	−	0.0859096i
$389$	7.42372	−	2.70201i	0.376398	−	0.136997i	−0.146892	−	0.989153i	$-0.546927\pi$
$389$	7.42372	−	2.70201i	0.376398	−	0.136997i	0.523289	+	0.852155i	$0.324705\pi$
$390$		0			0
$391$	−20.9946	+	17.6165i	−1.06174	+	0.890906i
$392$	−3.57399	−	4.25931i	−0.180514	−	0.215128i
$393$		0			0
$394$	−10.5267	+	3.83139i	−0.530325	+	0.193023i
$395$	21.9986	+	29.7820i	1.10687	+	1.49850i
$396$		0			0
$397$	1.40079	+	0.808746i	0.0703036	+	0.0405898i	0.534740	−	0.845017i	$-0.320410\pi$
$397$	1.40079	+	0.808746i	0.0703036	+	0.0405898i	−0.464436	+	0.885607i	$0.653743\pi$
$398$	12.3102	+	2.17062i	0.617054	+	0.108803i
$399$		0			0
$400$	14.1372	+	1.76010i	0.706862	+	0.0880050i
$401$	−2.06958	−	11.7372i	−0.103350	−	0.586127i	−0.991867	−	0.127282i	$-0.959375\pi$
$401$	−2.06958	−	11.7372i	−0.103350	−	0.586127i	0.888517	−	0.458844i	$-0.151736\pi$
$402$		0			0
$403$	1.30530	−	1.55560i	0.0650216	−	0.0774898i
$404$	−0.203545			−0.0101268
$405$		0			0
$406$	−18.1999			−0.903244
$407$	−12.2671	+	14.6193i	−0.608055	+	0.724652i
$408$		0			0
$409$	−1.98160	−	11.2382i	−0.0979836	−	0.555693i	−0.993792	−	0.111253i	$-0.964514\pi$
$409$	−1.98160	−	11.2382i	−0.0979836	−	0.555693i	0.895809	−	0.444440i	$-0.146597\pi$
$410$	2.76601	−	11.4785i	0.136604	−	0.566884i
$411$		0			0
$412$	1.04196	+	0.183725i	0.0513336	+	0.00905149i
$413$	−5.94484	−	3.43226i	−0.292527	−	0.168890i
$414$		0			0
$415$	−19.4828	+	14.3910i	−0.956372	+	0.706428i
$416$	−3.74908	+	1.36455i	−0.183814	+	0.0669027i
$417$		0			0
$418$	−18.8832	−	22.5041i	−0.923609	−	1.10071i
$419$	24.7402	−	20.7595i	1.20864	−	1.01417i	0.209296	−	0.977852i	$-0.432883\pi$
$419$	24.7402	−	20.7595i	1.20864	−	1.01417i	0.999340	−	0.0363142i	$-0.0115617\pi$
$420$		0			0
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	−0.631994	−	0.774974i	$-0.717763\pi$
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	0.0140082	+	0.999902i	$0.495541\pi$
$422$	3.82641	−	2.20918i	0.186267	−	0.107541i
$423$		0			0
$424$	−10.1483	+	17.5774i	−0.492846	+	0.853634i
$425$	−26.6191	+	1.34993i	−1.29122	+	0.0654811i
$426$		0			0
$427$	4.48169	−	12.3134i	0.216884	−	0.595885i
$428$	−2.00649	+	0.353799i	−0.0969875	+	0.0171015i
$429$		0			0
$430$	−19.4737	−	12.9131i	−0.939106	−	0.622723i
$431$	−23.0480			−1.11018			−0.555092	−	0.831789i	$-0.687317\pi$
$431$	−23.0480			−1.11018			−0.555092	+	0.831789i	$0.687317\pi$
$432$		0			0
$433$			28.7044i			1.37944i	0.724074	+	0.689722i	$0.242267\pi$
$433$			28.7044i			1.37944i	−0.724074	+	0.689722i	$0.757733\pi$
$434$	−2.83554	−	2.37930i	−0.136110	−	0.114210i
$435$		0			0
$436$	−0.644233	−	3.65363i	−0.0308532	−	0.174977i
$437$	8.04538	−	22.1045i	0.384863	−	1.05740i
$438$		0			0
$439$	−0.464755	+	2.63576i	−0.0221816	+	0.125798i	−0.993888	−	0.110395i	$-0.964789\pi$
$439$	−0.464755	+	2.63576i	−0.0221816	+	0.125798i	0.971706	+	0.236193i	$0.0758996\pi$
$440$	−32.4635	−	14.1482i	−1.54764	−	0.674488i
$441$		0			0
$442$	−8.83886	+	5.10312i	−0.420422	+	0.242731i
$443$	−0.954638	−	2.62285i	−0.0453562	−	0.124615i	0.914947	−	0.403575i	$-0.132233\pi$
$443$	−0.954638	−	2.62285i	−0.0453562	−	0.124615i	−0.960303	+	0.278960i	$0.910010\pi$
$444$		0			0
$445$	7.15777	−	7.52996i	0.339311	−	0.356954i
$446$	−17.6079	+	14.7748i	−0.833760	+	0.699608i
$447$		0			0
$448$	6.92304	+	19.0209i	0.327083	+	0.898653i
$449$	−12.0160	−	20.8123i	−0.567069	−	0.982192i	−0.996854	−	0.0792608i	$-0.974744\pi$
$449$	−12.0160	−	20.8123i	−0.567069	−	0.982192i	0.429785	−	0.902931i	$-0.358589\pi$
$450$		0			0
$451$	−11.0545	+	19.1470i	−0.520536	+	0.901595i
$452$	−7.23026	−	1.27489i	−0.340083	−	0.0599658i
$453$		0			0
$454$	28.6323	+	10.4213i	1.34378	+	0.489097i
$455$	−2.22834	−	7.54618i	−0.104466	−	0.353770i
$456$		0			0
$457$	−19.7351	+	23.5193i	−0.923167	+	1.10019i	0.0715399	+	0.997438i	$0.477209\pi$
$457$	−19.7351	+	23.5193i	−0.923167	+	1.10019i	−0.994707	+	0.102750i	$0.967236\pi$
$458$			2.52675i			0.118067i
$459$		0			0
$460$	−0.602649	−	5.32943i	−0.0280987	−	0.248486i
$461$	8.31123	+	6.97395i	0.387093	+	0.324809i	0.815479	−	0.578786i	$-0.196473\pi$
$461$	8.31123	+	6.97395i	0.387093	+	0.324809i	−0.428387	+	0.903595i	$0.640918\pi$
$462$		0			0
$463$	32.0801	−	5.65658i	1.49089	−	0.262884i	0.631968	−	0.774995i	$-0.282247\pi$
$463$	32.0801	−	5.65658i	1.49089	−	0.262884i	0.858919	+	0.512111i	$0.171136\pi$
$464$	−17.2903	−	6.29316i	−0.802682	−	0.292153i
$465$		0			0
$466$	1.86609	−	10.5831i	0.0864450	−	0.490254i
$467$	−11.8736	−	6.85522i	−0.549445	−	0.317222i	0.199453	−	0.979907i	$-0.436083\pi$
$467$	−11.8736	−	6.85522i	−0.549445	−	0.317222i	−0.748898	+	0.662685i	$0.769417\pi$
$468$		0			0
$469$	−3.94064	−	6.82538i	−0.181962	−	0.315167i
$470$	16.8341	−	8.37540i	0.776498	−	0.386329i
$471$		0			0
$472$	−5.92178	−	7.05730i	−0.272572	−	0.324839i
$473$	28.1241	+	33.5170i	1.29315	+	1.54111i
$474$		0			0
$475$	19.2070	−	12.4271i	0.881279	−	0.570194i
$476$	−2.82998	−	4.90167i	−0.129712	−	0.224668i
$477$		0			0
$478$	−4.04513	−	2.33545i	−0.185020	−	0.106821i
$479$	−2.05131	+	11.6335i	−0.0937266	+	0.531550i	0.901403	+	0.432980i	$0.142538\pi$
$479$	−2.05131	+	11.6335i	−0.0937266	+	0.531550i	−0.995130	+	0.0985701i	$0.968573\pi$
$480$		0			0
$481$	−5.34758	−	1.94636i	−0.243829	−	0.0887465i
$482$	0.690558	−	0.121764i	0.0314541	−	0.00554620i
$483$		0			0
$484$	5.67678	+	4.76339i	0.258036	+	0.216518i
$485$	1.82270	+	16.1187i	0.0827643	+	0.731913i
$486$		0			0
$487$		−	31.6087i		−	1.43233i	−0.697933	−	0.716163i	$-0.745897\pi$
$487$		−	31.6087i		−	1.43233i	0.697933	−	0.716163i	$-0.254103\pi$
$488$	11.3040	−	13.4716i	0.511709	−	0.609831i
$489$		0			0
$490$	4.83425	−	1.42753i	0.218389	−	0.0644890i
$491$	15.3997	+	5.60502i	0.694977	+	0.252951i	0.665265	−	0.746608i	$-0.268319\pi$
$491$	15.3997	+	5.60502i	0.694977	+	0.252951i	0.0297121	+	0.999558i	$0.490541\pi$
$492$		0			0
$493$	33.9012	+	5.97769i	1.52683	+	0.269222i
$494$	4.38004	−	7.58644i	0.197067	−	0.341330i
$495$		0			0
$496$	−1.87111	−	3.24087i	−0.0840155	−	0.145519i
$497$	0.0203142	+	0.0558127i	0.000911215	+	0.00250354i
$498$		0			0
$499$	30.4626	−	25.5612i	1.36369	−	1.14427i	0.388871	−	0.921292i	$-0.372865\pi$
$499$	30.4626	−	25.5612i	1.36369	−	1.14427i	0.974823	−	0.222982i	$-0.0715791\pi$
$500$	2.65871	−	4.48754i	0.118901	−	0.200689i
$501$		0			0
$502$	0.360791	+	0.991264i	0.0161029	+	0.0442423i
$503$	5.13479	−	2.96457i	0.228949	−	0.132184i	−0.381138	−	0.924518i	$-0.624468\pi$
$503$	5.13479	−	2.96457i	0.228949	−	0.132184i	0.610087	+	0.792334i	$0.291134\pi$
$504$		0			0
$505$	0.389768	−	0.894337i	0.0173444	−	0.0397975i
$506$	5.73228	−	32.5094i	0.254831	−	1.44522i
$507$		0			0
$508$	−0.535138	+	1.47028i	−0.0237429	+	0.0652331i
$509$	7.53016	+	42.7057i	0.333768	+	1.89290i	0.439067	+	0.898454i	$0.355309\pi$
$509$	7.53016	+	42.7057i	0.333768	+	1.89290i	−0.105298	+	0.994441i	$0.533580\pi$
$510$		0			0
$511$	−10.0798	−	8.45798i	−0.445905	−	0.374159i
$512$			24.7579i			1.09416i
$513$		0			0
$514$	22.7787			1.00473
$515$	−2.80249	+	4.22633i	−0.123492	+	0.186235i
$516$		0			0
$517$	−34.6731	+	6.11381i	−1.52492	+	0.268885i
$518$	−3.54783	+	9.74757i	−0.155883	+	0.428284i
$519$		0			0
$520$	0.653571	−	10.5396i	0.0286610	−	0.462191i
$521$	16.3247	−	28.2751i	0.715196	−	1.23876i	−0.247688	−	0.968840i	$-0.579671\pi$
$521$	16.3247	−	28.2751i	0.715196	−	1.23876i	0.962884	−	0.269916i	$-0.0869959\pi$
$522$		0			0
$523$	−15.2548	+	8.80738i	−0.667047	+	0.385120i	−0.794957	−	0.606666i	$-0.792507\pi$
$523$	−15.2548	+	8.80738i	−0.667047	+	0.385120i	0.127910	+	0.991786i	$0.459173\pi$
$524$	−2.41925	+	0.880534i	−0.105685	+	0.0384663i
$525$		0			0
$526$	−6.62147	+	5.55607i	−0.288710	+	0.242256i
$527$	4.50033	+	5.36328i	0.196037	+	0.233628i
$528$		0			0
$529$	3.22579	−	1.17409i	0.140252	−	0.0510475i
$530$	−10.9323	−	14.8003i	−0.474870	−	0.642886i
$531$		0			0
$532$	4.20713	+	2.42899i	0.182402	+	0.105310i
$533$	−6.49261	−	1.14482i	−0.281226	−	0.0495878i
$534$		0			0
$535$	2.28770	−	9.49361i	0.0989060	−	0.410444i
$536$	−1.83671	−	10.4165i	−0.0793340	−	0.449925i
$537$		0			0
$538$	7.20724	−	8.58925i	0.310726	−	0.370309i
$539$	−9.43865			−0.406551
$540$		0			0
$541$	40.8023			1.75423			0.877113	−	0.480284i	$-0.159466\pi$
$541$	40.8023			1.75423			0.877113	+	0.480284i	$0.159466\pi$
$542$	−2.13421	+	2.54346i	−0.0916723	+	0.109251i
$543$		0			0
$544$	−2.38859	−	13.5464i	−0.102410	−	0.580797i
$545$	17.2869	+	4.16568i	0.740490	+	0.178438i
$546$		0			0
$547$	29.8441	+	5.26232i	1.27604	+	0.225000i	0.770298	−	0.637684i	$-0.220107\pi$
$547$	29.8441	+	5.26232i	1.27604	+	0.225000i	0.505743	+	0.862684i	$0.331219\pi$
$548$	2.40018	+	1.38575i	0.102531	+	0.0591961i
$549$		0			0
$550$	23.5162	−	21.8550i	1.00273	−	0.931899i
$551$	−27.7646	+	10.1055i	−1.18281	+	0.430508i
$552$		0			0
$553$	−24.2234	−	28.8684i	−1.03008	−	1.22761i
$554$	9.18393	−	7.70623i	0.390188	−	0.327407i
$555$		0			0
$556$	−6.98398	+	2.54196i	−0.296187	+	0.107803i
$557$	−24.6008	+	14.2033i	−1.04237	+	0.601812i	−0.920503	−	0.390735i	$-0.872221\pi$
$557$	−24.6008	+	14.2033i	−1.04237	+	0.601812i	−0.121865	+	0.992547i	$0.538888\pi$
$558$		0			0
$559$	−6.52350	+	11.2990i	−0.275915	+	0.477898i
$560$	−14.4722	−	0.897439i	−0.611563	−	0.0379237i
$561$		0			0
$562$	5.61591	−	15.4296i	0.236893	−	0.650858i
$563$	6.21863	−	1.09651i	0.262084	−	0.0462124i	−0.0410621	−	0.999157i	$-0.513074\pi$
$563$	6.21863	−	1.09651i	0.262084	−	0.0462124i	0.303146	+	0.952944i	$0.401963\pi$
$564$		0			0
$565$	19.4468	−	29.3270i	0.818133	−	1.23380i
$566$	24.2448			1.01909
$567$		0			0
$568$			0.0797117i			0.00334463i
$569$	−2.76710	−	2.32188i	−0.116003	−	0.0973381i	0.582941	−	0.812515i	$-0.301902\pi$
$569$	−2.76710	−	2.32188i	−0.116003	−	0.0973381i	−0.698944	+	0.715176i	$0.746346\pi$
$570$		0			0
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	0.802147	+	0.597127i	$0.203691\pi$
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	−0.549542	+	0.835466i	$0.685198\pi$
$572$	−1.27918	+	3.51451i	−0.0534851	+	0.146949i
$573$		0			0
$574$	−2.08678	+	11.8347i	−0.0871006	+	0.493972i
$575$	24.5704	+	7.55738i	1.02466	+	0.315165i
$576$		0			0
$577$	−19.6374	+	11.3377i	−0.817517	+	0.471994i	−0.849559	−	0.527493i	$-0.823132\pi$
$577$	−19.6374	+	11.3377i	−0.817517	+	0.471994i	0.0320424	+	0.999487i	$0.489799\pi$
$578$	−4.83505	−	13.2842i	−0.201112	−	0.552550i
$579$		0			0
$580$	−4.64140	+	4.88274i	−0.192724	+	0.202745i
$581$	18.8851	−	15.8465i	0.783485	−	0.657422i
$582$		0			0
$583$	11.7842	+	32.3768i	0.488051	+	1.34091i
$584$	−8.82966	−	15.2934i	−0.365374	−	0.632847i
$585$		0			0
$586$	−18.7288	+	32.4391i	−0.773678	+	1.34005i
$587$	18.6058	+	3.28071i	0.767946	+	0.135410i	0.543878	−	0.839164i	$-0.316955\pi$
$587$	18.6058	+	3.28071i	0.767946	+	0.135410i	0.224067	+	0.974574i	$0.428066\pi$
$588$		0			0
$589$	−5.64683	−	2.05528i	−0.232673	−	0.0846862i
$590$	8.00992	−	2.36528i	0.329763	−	0.0973772i
$591$		0			0
$592$	−6.74104	+	8.03366i	−0.277055	+	0.330181i
$593$		−	8.73461i		−	0.358688i	−0.983786	−	0.179344i	$-0.942603\pi$
$593$		−	8.73461i		−	0.358688i	0.983786	−	0.179344i	$-0.0573974\pi$
$594$		0			0
$595$	26.9560	−	3.04817i	1.10509	−	0.124963i
$596$	7.27765	+	6.10667i	0.298104	+	0.250139i
$597$		0			0
$598$	9.69410	−	1.70933i	0.396421	−	0.0698998i
$599$	−6.00796	−	2.18672i	−0.245479	−	0.0893469i	0.216351	−	0.976316i	$-0.430585\pi$
$599$	−6.00796	−	2.18672i	−0.245479	−	0.0893469i	−0.461829	+	0.886969i	$0.652807\pi$
$600$		0			0
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	−0.900880	−	0.434068i	$-0.857078\pi$
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	0.995010	−	0.0997716i	$-0.0318112\pi$
$602$	20.5959	+	11.8910i	0.839425	+	0.484642i
$603$		0			0
$604$	−0.447916	−	0.775814i	−0.0182255	−	0.0315674i
$605$	−31.7998	+	15.8212i	−1.29284	+	0.643225i
$606$		0			0
$607$	2.88515	+	3.43839i	0.117105	+	0.139560i	0.821412	−	0.570335i	$-0.193187\pi$
$607$	2.88515	+	3.43839i	0.117105	+	0.139560i	−0.704307	+	0.709895i	$0.748742\pi$
$608$	7.58895	+	9.04416i	0.307773	+	0.366789i
$609$		0			0
$610$	7.10156	+	14.2737i	0.287534	+	0.577926i
$611$	−5.24941	−	9.09225i	−0.212369	−	0.367833i
$612$		0			0
$613$	20.1066	+	11.6086i	0.812100	+	0.468866i	0.847685	−	0.530501i	$-0.177996\pi$
$613$	20.1066	+	11.6086i	0.812100	+	0.468866i	−0.0355848	+	0.999367i	$0.511329\pi$
$614$	3.92882	−	22.2814i	0.158554	−	0.899205i
$615$		0			0
$616$	33.8694	+	12.3275i	1.36464	+	0.496687i
$617$	43.5312	−	7.67572i	1.75250	−	0.309013i	0.796993	−	0.603988i	$-0.206423\pi$
$617$	43.5312	−	7.67572i	1.75250	−	0.309013i	0.955505	+	0.294975i	$0.0953114\pi$
$618$		0			0
$619$	−3.65944	−	3.07064i	−0.147085	−	0.123419i	0.566276	−	0.824216i	$-0.308384\pi$
$619$	−3.65944	−	3.07064i	−0.147085	−	0.123419i	−0.713361	+	0.700796i	$0.752828\pi$
$620$	−1.36146	+	0.153953i	−0.0546775	+	0.00618291i
$621$		0			0
$622$			41.7838i			1.67538i
$623$	−6.79689	+	8.10022i	−0.272312	+	0.324529i
$624$		0			0
$625$	14.6262	+	20.2750i	0.585047	+	0.811000i
$626$	3.24464	+	1.18095i	0.129682	+	0.0472004i
$627$		0			0
$628$	−5.86248	−	1.03371i	−0.233938	−	0.0412496i
$629$	9.81015	−	16.9917i	0.391156	−	0.677502i
$630$		0			0
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	−0.960140	−	0.279518i	$-0.909825\pi$
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	0.238000	−	0.971265i	$-0.423508\pi$
$632$	−17.2980	−	47.5258i	−0.688076	−	1.89047i
$633$		0			0
$634$	2.61717	−	2.19607i	0.103941	−	0.0872169i
$635$	−5.43538	−	5.16672i	−0.215696	−	0.205035i
$636$		0			0
$637$	−0.962632	−	2.64481i	−0.0381409	−	0.104791i
$638$	−35.9086	+	20.7318i	−1.42163	+	0.820781i
$639$		0			0
$640$	−11.9975	−	5.22872i	−0.474242	−	0.206683i
$641$	−3.91713	+	22.2151i	−0.154717	+	0.877445i	0.804327	+	0.594187i	$0.202526\pi$
$641$	−3.91713	+	22.2151i	−0.154717	+	0.877445i	−0.959044	+	0.283258i	$0.908585\pi$
$642$		0			0
$643$	1.31828	−	3.62196i	0.0519881	−	0.142836i	−0.910981	−	0.412449i	$-0.864674\pi$
$643$	1.31828	−	3.62196i	0.0519881	−	0.142836i	0.962969	+	0.269613i	$0.0868957\pi$
$644$	0.947926	+	5.37595i	0.0373535	+	0.211842i
$645$		0			0
$646$	23.1364	+	19.4137i	0.910288	+	0.763823i
$647$		−	16.5713i		−	0.651486i	−0.945458	−	0.325743i	$-0.894386\pi$
$647$		−	16.5713i		−	0.651486i	0.945458	−	0.325743i	$-0.105614\pi$
$648$		0			0
$649$	−15.6390			−0.613884
$650$	8.52237	+	4.36053i	0.334275	+	0.171034i
$651$		0			0
$652$	11.3326	−	1.99825i	0.443821	−	0.0782576i
$653$	1.76642	−	4.85320i	0.0691254	−	0.189920i	−0.900320	−	0.435230i	$-0.856667\pi$
$653$	1.76642	−	4.85320i	0.0691254	−	0.189920i	0.969445	+	0.245309i	$0.0788894\pi$
$654$		0			0
$655$	0.763716	−	12.3158i	0.0298409	−	0.481218i
$656$	−6.07471	+	10.5217i	−0.237178	+	0.410804i
$657$		0			0
$658$	−16.5733	+	9.56862i	−0.646096	+	0.373024i
$659$	33.9146	−	12.3439i	1.32113	−	0.480850i	0.417307	−	0.908766i	$-0.362974\pi$
$659$	33.9146	−	12.3439i	1.32113	−	0.480850i	0.903819	+	0.427915i	$0.140752\pi$
$660$		0			0
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.149833	−	0.988711i	$-0.452127\pi$
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.999709	+	0.0241316i	$0.00768206\pi$
$662$	22.2322	+	26.4953i	0.864079	+	1.02977i
$663$		0			0
$664$	31.0903	−	11.3160i	1.20654	−	0.439144i
$665$	−18.7287	+	13.8340i	−0.726267	+	0.536460i
$666$		0			0
$667$	−28.7531	−	16.6006i	−1.11332	−	0.642778i
$668$	2.46238	+	0.434185i	0.0952725	+	0.0167991i
$669$		0			0
$670$	9.32207	+	2.24637i	0.360143	+	0.0867847i
$671$	−5.18394	−	29.3996i	−0.200124	−	1.13496i
$672$		0			0
$673$	6.19702	−	7.38532i	0.238878	−	0.284683i	−0.633265	−	0.773935i	$-0.718286\pi$
$673$	6.19702	−	7.38532i	0.238878	−	0.284683i	0.872143	+	0.489252i	$0.162730\pi$
$674$	17.6715			0.680682
$675$		0			0
$676$	4.94968			0.190372
$677$	15.8761	−	18.9204i	0.610167	−	0.727169i	−0.369179	−	0.929358i	$-0.620361\pi$
$677$	15.8761	−	18.9204i	0.610167	−	0.727169i	0.979346	+	0.202189i	$0.0648056\pi$
$678$		0			0
$679$	−2.86697	−	16.2594i	−0.110024	−	0.623979i
$680$	35.3943	+	8.52907i	1.35731	+	0.327075i
$681$		0			0
$682$	−8.30486	−	1.46437i	−0.318010	−	0.0560737i
$683$	17.9981	+	10.3912i	0.688678	+	0.397609i	0.803117	−	0.595822i	$-0.203174\pi$
$683$	17.9981	+	10.3912i	0.688678	+	0.397609i	−0.114438	+	0.993430i	$0.536507\pi$
$684$		0			0
$685$	−10.6848	+	7.89235i	−0.408244	+	0.301551i
$686$	−23.3593	+	8.50208i	−0.891861	+	0.324611i
$687$		0			0
$688$	15.4549	+	18.4184i	0.589212	+	0.702195i
$689$	−7.87048	+	6.60411i	−0.299841	+	0.251597i
$690$		0			0
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	−0.564456	−	0.825463i	$-0.690914\pi$
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	0.0981988	+	0.995167i	$0.468692\pi$
$692$	5.78643	−	3.34080i	0.219967	−	0.126998i
$693$		0			0
$694$	−10.9387	+	18.9463i	−0.415226	+	0.719193i
$695$	2.20473	−	35.5537i	0.0836300	−	1.34863i
$696$		0			0
$697$	7.77416	−	21.3593i	0.294467	−	0.809042i
$698$	29.8396	−	5.26153i	1.12945	−	0.199152i
$699$		0			0
$700$	−2.41817	+	4.72616i	−0.0913983	+	0.178632i
$701$	−25.6062			−0.967135			−0.483567	−	0.875307i	$-0.660659\pi$
$701$	−25.6062			−0.967135			−0.483567	+	0.875307i	$0.660659\pi$
$702$		0			0
$703$			16.8402i			0.635141i
$704$	35.3263	+	29.6423i	1.33141	+	1.11719i
$705$		0			0
$706$	−6.85846	−	38.8962i	−0.258121	−	1.46388i
$707$	−0.339609	+	0.933067i	−0.0127723	+	0.0350916i
$708$		0			0
$709$	−2.06567	+	11.7150i	−0.0775777	+	0.439965i	0.921135	+	0.389243i	$0.127263\pi$
$709$	−2.06567	+	11.7150i	−0.0775777	+	0.439965i	−0.998713	+	0.0507221i	$0.983848\pi$
$710$	−0.0662458	−	0.0288711i	−0.00248616	−	0.00108351i
$711$		0			0
$712$	−12.2899	+	7.09558i	−0.460584	+	0.265918i
$713$	−2.30951	−	6.34531i	−0.0864917	−	0.237634i
$714$		0			0
$715$	−12.9926	−	12.3504i	−0.485894	−	0.461877i
$716$	−2.03368	+	1.70646i	−0.0760021	+	0.0637733i
$717$		0			0
$718$	−3.49908	−	9.61363i	−0.130584	−	0.358777i
$719$	−3.31070	−	5.73431i	−0.123468	−	0.213854i	0.797665	−	0.603101i	$-0.206068\pi$
$719$	−3.31070	−	5.73431i	−0.123468	−	0.213854i	−0.921133	+	0.389247i	$0.872735\pi$
$720$		0			0
$721$	2.58068	−	4.46987i	0.0961096	−	0.166467i
$722$	−2.35820	−	0.415814i	−0.0877630	−	0.0154750i
$723$		0			0
$724$	4.45093	+	1.62000i	0.165417	+	0.0602070i
$725$	−12.5660	−	29.7433i	−0.466689	−	1.10464i
$726$		0			0
$727$	7.62291	−	9.08463i	0.282718	−	0.336930i	−0.605932	−	0.795517i	$-0.707200\pi$
$727$	7.62291	−	9.08463i	0.282718	−	0.336930i	0.888650	+	0.458586i	$0.151644\pi$
$728$			10.7478i			0.398341i
$729$		0			0
$730$	15.9079	−	1.79886i	0.588778	−	0.0665787i
$731$	−34.4587	−	28.9142i	−1.27450	−	1.06943i
$732$		0			0
$733$	−12.6872	+	2.23709i	−0.468612	+	0.0826289i	−0.402968	−	0.915214i	$-0.632021\pi$
$733$	−12.6872	+	2.23709i	−0.468612	+	0.0826289i	−0.0656441	+	0.997843i	$0.520910\pi$
$734$	−25.1976	−	9.17116i	−0.930059	−	0.338514i
$735$		0			0
$736$	−2.30374	+	13.0651i	−0.0849169	+	0.481588i
$737$	−15.5499	−	8.97771i	−0.572786	−	0.330698i
$738$		0			0
$739$	−12.2765	−	21.2636i	−0.451600	−	0.782194i	0.546886	−	0.837207i	$-0.315813\pi$
$739$	−12.2765	−	21.2636i	−0.451600	−	0.782194i	−0.998486	+	0.0550133i	$0.982480\pi$
$740$	1.71034	+	3.43769i	0.0628734	+	0.126372i
$741$		0			0
$742$	12.0380	+	14.3463i	0.441928	+	0.526669i
$743$	−26.5027	−	31.5847i	−0.972291	−	1.15873i	−0.987304	−	0.158844i	$-0.949223\pi$
$743$	−26.5027	−	31.5847i	−0.972291	−	1.15873i	0.0150131	−	0.999887i	$-0.495221\pi$
$744$		0			0
$745$	−40.7674	+	20.2829i	−1.49360	+	0.743107i
$746$	18.9194	+	32.7694i	0.692690	+	1.19977i
$747$		0			0
$748$	−11.1672	−	6.44737i	−0.408313	−	0.235739i
$749$	−1.72593	+	9.78822i	−0.0630640	+	0.357654i
$750$		0			0
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	0.119648	−	0.992816i	$-0.461823\pi$
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	−0.546514	+	0.837450i	$0.684045\pi$
$752$	−19.0537	+	3.35968i	−0.694817	+	0.122515i
$753$		0			0
$754$	−9.47154	−	7.94756i	−0.344933	−	0.289433i
$755$	4.26648	−	0.482451i	0.155273	−	0.0175582i
$756$		0			0
$757$			11.3137i			0.411203i	0.978636	+	0.205602i	$0.0659152\pi$
$757$			11.3137i			0.411203i	−0.978636	+	0.205602i	$0.934085\pi$
$758$	−5.16630	+	6.15696i	−0.187648	+	0.223631i
$759$		0			0
$760$	−29.9694	+	8.84979i	−1.08710	+	0.321016i
$761$	21.2994	+	7.75233i	0.772101	+	0.281022i	0.697875	−	0.716220i	$-0.254129\pi$
$761$	21.2994	+	7.75233i	0.772101	+	0.281022i	0.0742262	+	0.997241i	$0.476351\pi$
$762$		0			0
$763$	−17.8234	−	3.14274i	−0.645250	−	0.113775i
$764$	−1.48302	+	2.56867i	−0.0536539	+	0.0929313i
$765$		0			0
$766$	−4.66529	−	8.08053i	−0.168564	−	0.291961i
$767$	−1.59500	−	4.38222i	−0.0575920	−	0.158233i
$768$		0			0
$769$	−11.6191	+	9.74955i	−0.418994	+	0.351578i	−0.827780	−	0.561052i	$-0.810397\pi$
$769$	−11.6191	+	9.74955i	−0.418994	+	0.351578i	0.408786	+	0.912630i	$0.365952\pi$
$770$	−22.5122	+	23.6828i	−0.811284	+	0.853469i
$771$		0			0
$772$	−3.11204	−	8.55027i	−0.112005	−	0.307731i
$773$	−4.20823	+	2.42962i	−0.151359	+	0.0873874i	−0.573767	−	0.819019i	$-0.694518\pi$
$773$	−4.20823	+	2.42962i	−0.151359	+	0.0873874i	0.422407	+	0.906406i	$0.361185\pi$
$774$		0			0
$775$	1.93061	−	6.27678i	0.0693496	−	0.225468i
$776$	3.84768	−	21.8213i	0.138124	−	0.783338i
$777$		0			0
$778$	3.34599	−	9.19303i	0.119960	−	0.329586i
$779$	3.38777	+	19.2130i	0.121379	+	0.688377i
$780$		0			0
$781$	0.103657	+	0.0869789i	0.00370916	+	0.00311235i
$782$			33.9383i			1.21363i
$783$		0			0
$784$	−5.18676			−0.185241
$785$	15.7679	−	23.7791i	0.562782	−	0.848711i
$786$		0			0
$787$	−4.82676	+	0.851088i	−0.172055	+	0.0303380i	−0.259012	−	0.965874i	$-0.583397\pi$
$787$	−4.82676	+	0.851088i	−0.172055	+	0.0303380i	0.0869567	+	0.996212i	$0.472286\pi$
$788$	1.44345	−	3.96585i	0.0514209	−	0.141278i
$789$		0			0
$790$	45.7623	+	2.83777i	1.62815	+	0.100963i
$791$	−17.9076	+	31.0170i	−0.636723	+	1.10284i
$792$		0			0
$793$	7.70938	−	4.45101i	0.273768	−	0.158060i
$794$	1.88220	−	0.685063i	0.0667966	−	0.0243120i
$795$		0			0
$796$	−3.60756	+	3.02710i	−0.127866	+	0.107293i
$797$	−35.8673	−	42.7450i	−1.27049	−	1.51411i	−0.752270	−	0.658855i	$-0.771041\pi$
$797$	−35.8673	−	42.7450i	−1.27049	−	1.51411i	−0.518215	−	0.855250i	$-0.673403\pi$
$798$		0			0
$799$	34.0142	−	12.3802i	1.20334	−	0.437978i
$800$	−9.45087	+	8.78326i	−0.334139	+	0.310535i
$801$		0			0
$802$	−12.7814	−	7.37937i	−0.451328	−	0.260575i
$803$	−29.5223	−	5.20557i	−1.04182	−	0.183701i
$804$		0			0
$805$	−25.4360	−	6.12939i	−0.896502	−	0.216033i
$806$	−0.436667	−	2.47646i	−0.0153809	−	0.0872296i
$807$		0			0
$808$	−0.856584	+	1.02084i	−0.0301345	+	0.0359129i
$809$	−25.0205			−0.879673			−0.439837	−	0.898078i	$-0.644964\pi$
$809$	−25.0205			−0.879673			−0.439837	+	0.898078i	$0.644964\pi$
$810$		0			0
$811$	22.4129			0.787024			0.393512	−	0.919320i	$-0.371260\pi$
$811$	22.4129			0.787024			0.393512	+	0.919320i	$0.371260\pi$
$812$	4.40739	−	5.25253i	0.154669	−	0.184328i
$813$		0			0
$814$	4.10374	+	23.2735i	0.143836	+	0.815735i
$815$	−12.9209	+	53.6198i	−0.452600	+	1.87822i
$816$		0			0
$817$	38.0222	+	6.70435i	1.33023	+	0.234555i
$818$	−12.2381	−	7.06565i	−0.427894	−	0.247045i
$819$		0			0
$820$	2.64290	+	3.57799i	0.0922939	+	0.124949i
$821$	37.8576	−	13.7790i	1.32124	−	0.480892i	0.417384	−	0.908730i	$-0.362947\pi$
$821$	37.8576	−	13.7790i	1.32124	−	0.480892i	0.903855	+	0.427838i	$0.140725\pi$
$822$		0			0
$823$	8.96086	+	10.6791i	0.312356	+	0.372251i	0.899267	−	0.437400i	$-0.144101\pi$
$823$	8.96086	+	10.6791i	0.312356	+	0.372251i	−0.586911	+	0.809651i	$0.699656\pi$
$824$	5.30632	−	4.45253i	0.184854	−	0.155111i
$825$		0			0
$826$	−7.98790	+	2.90736i	−0.277935	+	0.101160i
$827$	30.3778	−	17.5386i	1.05634	−	0.609878i	0.131922	−	0.991260i	$-0.457885\pi$
$827$	30.3778	−	17.5386i	1.05634	−	0.609878i	0.924418	+	0.381382i	$0.124552\pi$
$828$		0			0
$829$	−16.3803	+	28.3716i	−0.568912	+	0.985385i	0.427762	+	0.903892i	$0.359302\pi$
$829$	−16.3803	+	28.3716i	−0.568912	+	0.985385i	−0.996674	+	0.0814933i	$0.974031\pi$
$830$	−1.85641	+	29.9367i	−0.0644369	+	1.03912i
$831$		0			0
$832$	−4.70322	+	12.9220i	−0.163055	+	0.447989i
$833$	9.55639	−	1.68505i	0.331109	−	0.0583835i
$834$		0			0
$835$	−6.62292	+	9.98779i	−0.229196	+	0.345642i
$836$	11.0676			0.382782
$837$		0			0
$838$		−	39.9932i		−	1.38154i
$839$	13.1790	+	11.0585i	0.454991	+	0.381783i	0.841284	−	0.540593i	$-0.181800\pi$
$839$	13.1790	+	11.0585i	0.454991	+	0.381783i	−0.386293	+	0.922376i	$0.626245\pi$
$840$		0			0
$841$	2.20580	+	12.5097i	0.0760621	+	0.431370i
$842$	−5.71508	+	15.7021i	−0.196955	+	0.541128i
$843$		0			0
$844$	−0.289053	+	1.63930i	−0.00994960	+	0.0564270i
$845$	−9.47810	+	21.7479i	−0.326057	+	0.748149i
$846$		0			0
$847$	31.3072	−	18.0752i	1.07573	−	0.621073i
$848$	6.47569	+	17.7918i	0.222376	+	0.610973i
$849$		0			0
$850$	−19.9078	+	26.3259i	−0.682833	+	0.902970i
$851$	−14.4961	+	12.1636i	−0.496919	+	0.416964i
$852$		0			0
$853$	−16.6428	−	45.7258i	−0.569840	−	1.56562i	−0.804756	−	0.593606i	$-0.797704\pi$
$853$	−16.6428	−	45.7258i	−0.569840	−	1.56562i	0.234916	−	0.972016i	$-0.424518\pi$
$854$	−8.11330	−	14.0526i	−0.277631	−	0.480872i
$855$		0			0
$856$	−6.66956	+	11.5520i	−0.227961	+	0.394840i
$857$	9.48011	+	1.67160i	0.323835	+	0.0571008i	0.333202	−	0.942855i	$-0.391871\pi$
$857$	9.48011	+	1.67160i	0.323835	+	0.0571008i	−0.00936777	+	0.999956i	$0.502982\pi$
$858$		0			0
$859$	−30.1158	−	10.9613i	−1.02754	−	0.373993i	−0.227395	−	0.973803i	$-0.573021\pi$
$859$	−30.1158	−	10.9613i	−1.02754	−	0.373993i	−0.800143	+	0.599809i	$0.795243\pi$
$860$	8.44262	−	2.49306i	0.287891	−	0.0850125i
$861$		0			0
$862$	−18.3459	+	21.8638i	−0.624863	+	0.744682i
$863$		−	11.1232i		−	0.378637i	−0.981916	−	0.189319i	$-0.939372\pi$
$863$		−	11.1232i		−	0.378637i	0.981916	−	0.189319i	$-0.0606279\pi$
$864$		0			0
$865$	3.59838	+	31.8217i	0.122348	+	1.08197i
$866$	27.2295	+	22.8482i	0.925295	+	0.776415i
$867$		0			0
$868$	1.37334	−	0.242158i	0.0466143	−	0.00821936i
$869$	−80.6777	−	29.3643i	−2.73680	−	0.996114i
$870$		0			0
$871$	0.929747	−	5.27286i	0.0315033	−	0.178664i
$872$	−21.0351	−	12.1446i	−0.712338	−	0.411268i
$873$		0			0
$874$	−14.5647	−	25.2268i	−0.492659	−	0.853310i
$875$	−16.1352	−	19.6750i	−0.545470	−	0.665138i
$876$		0			0
$877$	−34.3783	−	40.9704i	−1.16087	−	1.38347i	−0.909563	−	0.415567i	$-0.863583\pi$
$877$	−34.3783	−	40.9704i	−1.16087	−	1.38347i	−0.251309	−	0.967907i	$-0.580861\pi$
$878$	2.13039	+	2.53890i	0.0718971	+	0.0856836i
$879$		0			0
$880$	−29.5762	+	14.7149i	−0.997013	+	0.496041i
$881$	12.0656	+	20.8982i	0.406500	+	0.704078i	0.994495	−	0.104787i	$-0.0334160\pi$
$881$	12.0656	+	20.8982i	0.406500	+	0.704078i	−0.587995	+	0.808864i	$0.700083\pi$
$882$		0			0
$883$	−15.3713	−	8.87464i	−0.517286	−	0.298655i	0.218537	−	0.975829i	$-0.429871\pi$
$883$	−15.3713	−	8.87464i	−0.517286	−	0.298655i	−0.735824	+	0.677173i	$0.763205\pi$
$884$	0.667701	−	3.78672i	0.0224572	−	0.127361i
$885$		0			0
$886$	−3.24795	−	1.18216i	−0.109117	−	0.0397154i
$887$	2.06559	−	0.364220i	0.0693559	−	0.0122293i	−0.138863	−	0.990312i	$-0.544345\pi$
$887$	2.06559	−	0.364220i	0.0693559	−	0.0122293i	0.208218	+	0.978082i	$0.433234\pi$
$888$		0			0
$889$	5.84701	+	4.90623i	0.196103	+	0.164550i
$890$	−1.44557	−	12.7837i	−0.0484558	−	0.428511i
$891$		0			0
$892$		−	8.65966i		−	0.289947i
$893$	−19.9703	+	23.7996i	−0.668280	+	0.796425i
$894$		0			0
$895$	−3.60355	−	12.2032i	−0.120453	−	0.407909i
$896$	12.5171	+	4.55584i	0.418166	+	0.152200i
$897$		0			0
$898$	−29.3074	−	5.16769i	−0.978001	−	0.172448i
$899$	−4.24080	+	7.34528i	−0.141439	+	0.244979i
$900$		0			0
$901$	−17.7113	−	30.6769i	−0.590049	−	1.02200i
$902$	9.36392	+	25.7272i	0.311785	+	0.856621i
$903$		0			0
$904$	−36.8212	+	30.8966i	−1.22465	+	1.02761i
$905$	−15.6410	+	16.4543i	−0.519925	+	0.546960i
$906$		0			0
$907$	14.6217	+	40.1727i	0.485504	+	1.33391i	0.904713	+	0.426022i	$0.140085\pi$
$907$	14.6217	+	40.1727i	0.485504	+	1.33391i	−0.419208	+	0.907890i	$0.637692\pi$
$908$	−9.94141	+	5.73967i	−0.329917	+	0.190478i
$909$		0			0
$910$	−8.93216	−	3.89280i	−0.296098	−	0.129045i
$911$	−3.61639	+	20.5096i	−0.119816	+	0.679513i	0.864436	+	0.502743i	$0.167676\pi$
$911$	−3.61639	+	20.5096i	−0.119816	+	0.679513i	−0.984252	+	0.176770i	$0.943435\pi$
$912$		0			0
$913$	19.2095	−	52.7776i	0.635741	−	1.74668i
$914$	6.60204	+	37.4420i	0.218376	+	1.23847i
$915$		0			0
$916$	−0.729227	−	0.611894i	−0.0240943	−	0.0202175i
$917$			12.5591i			0.414739i
$918$		0			0
$919$	14.9586			0.493438			0.246719	−	0.969087i	$-0.420648\pi$
$919$	14.9586			0.493438			0.246719	+	0.969087i	$0.420648\pi$
$920$	−29.2647	−	19.4055i	−0.964829	−	0.639780i
$921$		0			0
$922$	13.2312	−	2.33302i	0.435747	−	0.0768340i
$923$	−0.0138006	+	0.0379168i	−0.000454252	+	0.00124805i
$924$		0			0
$925$	−18.3796	+	0.932081i	−0.604318	+	0.0306467i
$926$	20.1693	−	34.9343i	0.662804	−	1.14801i
$927$		0			0
$928$	14.4312	−	8.33188i	0.473729	−	0.273507i
$929$	−25.6422	+	9.33300i	−0.841294	+	0.306206i	−0.726486	−	0.687182i	$-0.758848\pi$
$929$	−25.6422	+	9.33300i	−0.841294	+	0.306206i	−0.114808	+	0.993388i	$0.536625\pi$
$930$		0			0
$931$	−6.38026	+	5.35367i	−0.209105	+	0.175460i
$932$	2.60241	+	3.10144i	0.0852449	+	0.101591i
$933$		0			0
$934$	−15.9542	+	5.80685i	−0.522037	+	0.190006i
$935$	49.7124	−	36.7203i	1.62577	−	1.20088i
$936$		0			0
$937$	47.0967	+	27.1913i	1.53858	+	0.888300i	0.998922	+	0.0464165i	$0.0147801\pi$
$937$	47.0967	+	27.1913i	1.53858	+	0.888300i	0.539659	+	0.841884i	$0.318553\pi$
$938$	−9.61136	−	1.69474i	−0.313822	−	0.0553353i
$939$		0			0
$940$	−1.65948	+	6.88660i	−0.0541264	+	0.224616i
$941$	8.21935	+	46.6142i	0.267943	+	1.51958i	0.760522	+	0.649313i	$0.224943\pi$
$941$	8.21935	+	46.6142i	0.267943	+	1.51958i	−0.492579	+	0.870268i	$0.663946\pi$
$942$		0			0
$943$	−14.0916	+	16.7937i	−0.458885	+	0.546878i
$944$	−8.59400			−0.279711
$945$		0			0
$946$	54.1812			1.76158
$947$	−26.0639	+	31.0617i	−0.846962	+	1.00937i	0.152815	+	0.988255i	$0.451166\pi$
$947$	−26.0639	+	31.0617i	−0.846962	+	1.00937i	−0.999777	+	0.0211155i	$0.993278\pi$
$948$		0			0
$949$	−1.55227	−	8.80337i	−0.0503889	−	0.285769i
$950$	3.49996	−	28.1119i	0.113554	−	0.912070i
$951$		0			0
$952$	−36.4927	−	6.43465i	−1.18273	−	0.208548i
$953$	−23.2862	−	13.4443i	−0.754315	−	0.435504i	0.0729359	−	0.997337i	$-0.476763\pi$
$953$	−23.2862	−	13.4443i	−0.754315	−	0.435504i	−0.827251	+	0.561833i	$0.810096\pi$
$954$		0			0
$955$	−8.44638	−	11.4348i	−0.273319	−	0.370023i
$956$	1.65361	−	0.601865i	0.0534816	−	0.0194657i
$957$		0			0
$958$	9.40297	+	11.2060i	0.303796	+	0.362050i
$959$	10.3570	−	8.69054i	0.334444	−	0.280632i
$960$		0			0
$961$	27.5095	−	10.0126i	0.887403	−	0.322988i
$962$	−6.10295	+	3.52354i	−0.196767	+	0.113603i
$963$		0			0
$964$	−0.132088	+	0.228784i	−0.00425428	+	0.00736864i
$965$	43.5273	+	2.69918i	1.40119	+	0.0868896i
$966$		0			0
$967$	−13.0453	+	35.8418i	−0.419510	+	1.15259i	0.532474	+	0.846446i	$0.321262\pi$
$967$	−13.0453	+	35.8418i	−0.419510	+	1.15259i	−0.951984	+	0.306147i	$0.900960\pi$
$968$	47.7794	−	8.42480i	1.53569	−	0.270783i
$969$		0			0
$970$	16.7413	+	11.1012i	0.537532	+	0.356438i
$971$	52.8853			1.69717			0.848585	−	0.529059i	$-0.177455\pi$
$971$	52.8853			1.69717			0.848585	+	0.529059i	$0.177455\pi$
$972$		0			0
$973$			36.2562i			1.16232i
$974$	−29.9846	−	25.1600i	−0.960767	−	0.806179i
$975$		0			0
$976$	−2.84870	−	16.1558i	−0.0911846	−	0.517134i
$977$	−7.16089	+	19.6744i	−0.229097	+	0.629439i	−0.999972	−	0.00754795i	$-0.997597\pi$
$977$	−7.16089	+	19.6744i	−0.229097	+	0.629439i	0.770874	+	0.636987i	$0.219820\pi$
$978$		0			0
$979$	−4.18324	+	23.7243i	−0.133697	+	0.758233i
$980$	−0.758704	+	1.74087i	−0.0242359	+	0.0556102i
$981$		0			0
$982$	17.5749	−	10.1469i	0.560838	−	0.323800i
$983$	12.7694	+	35.0835i	0.407279	+	1.11899i	0.958615	+	0.284707i	$0.0918963\pi$
$983$	12.7694	+	35.0835i	0.407279	+	1.11899i	−0.551335	+	0.834284i	$0.685881\pi$
$984$		0			0
$985$	14.6611	+	13.9364i	0.467141	+	0.444051i
$986$	32.6553	−	27.4011i	1.03996	−	0.872628i
$987$		0			0
$988$	1.12877	+	3.10127i	0.0359110	+	0.0986646i
$989$	21.6923	+	37.5721i	0.689774	+	1.19472i
$990$		0			0
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	−0.441566	−	0.897229i	$-0.645577\pi$
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	0.997806	−	0.0662071i	$-0.0210898\pi$
$992$	3.33763	+	0.588514i	0.105970	+	0.0186853i
$993$		0			0
$994$	0.0691147	+	0.0251557i	0.00219218	+	0.000797890i
$995$	−6.39236	−	21.6474i	−0.202652	−	0.686270i
$996$		0			0
$997$	30.6391	−	36.5143i	0.970351	−	1.15642i	−0.0173159	−	0.999850i	$-0.505512\pi$
$997$	30.6391	−	36.5143i	0.970351	−	1.15642i	0.987667	−	0.156569i	$-0.0500435\pi$
$998$		−	49.2436i		−	1.55878i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.p.a.289.11		96
3.2	odd	2		135.2.p.a.124.6	yes	96
5.4	even	2	inner	405.2.p.a.289.6		96
15.2	even	4		675.2.l.h.151.6		96
15.8	even	4		675.2.l.h.151.11		96
15.14	odd	2		135.2.p.a.124.11	yes	96
27.5	odd	18		135.2.p.a.49.11	yes	96
27.22	even	9	inner	405.2.p.a.199.6		96
135.32	even	36		675.2.l.h.76.6		96
135.49	even	18	inner	405.2.p.a.199.11		96
135.59	odd	18		135.2.p.a.49.6	✓	96
135.113	even	36		675.2.l.h.76.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.6	✓	96	135.59	odd	18
135.2.p.a.49.11	yes	96	27.5	odd	18
135.2.p.a.124.6	yes	96	3.2	odd	2
135.2.p.a.124.11	yes	96	15.14	odd	2
405.2.p.a.199.6		96	27.22	even	9	inner
405.2.p.a.199.11		96	135.49	even	18	inner
405.2.p.a.289.6		96	5.4	even	2	inner
405.2.p.a.289.11		96	1.1	even	1	trivial
675.2.l.h.76.6		96	135.32	even	36
675.2.l.h.76.11		96	135.113	even	36
675.2.l.h.151.6		96	15.2	even	4
675.2.l.h.151.11		96	15.8	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.795984 - 0.948617i) q^{2} +(0.0810128 + 0.459446i) q^{4} +(-2.17384 - 0.523837i) q^{5} +(2.24130 + 0.395202i) q^{7} +(2.64518 + 1.52719i) q^{8} +(-2.22727 + 1.64518i) q^{10} +(4.87230 - 1.77337i) q^{11} +(0.993836 + 1.18441i) q^{13} +(2.15894 - 1.81156i) q^{14} +(2.67745 - 0.974511i) q^{16} +(-4.61649 + 2.66533i) q^{17} +(2.28767 - 3.96236i) q^{19} +(0.0645661 - 1.04120i) q^{20} +(2.19602 - 6.03353i) q^{22} +(5.06318 - 0.892775i) q^{23} +(4.45119 + 2.27748i) q^{25} +1.91463 q^{26} +1.06177i q^{28} +(-4.94693 - 4.15097i) q^{29} +(-0.228069 - 1.29344i) q^{31} +(-0.882557 + 2.42480i) q^{32} +(-1.14627 + 6.50084i) q^{34} +(-4.66522 - 2.03319i) q^{35} +(-3.18754 + 1.84032i) q^{37} +(-1.93781 - 5.32410i) q^{38} +(-4.95020 - 4.70552i) q^{40} +(-3.26644 + 2.74087i) q^{41} +(2.88612 + 7.92956i) q^{43} +(1.20949 + 2.09490i) q^{44} +(3.18331 - 5.51365i) q^{46} +(-6.68721 - 1.17913i) q^{47} +(-1.71059 - 0.622605i) q^{49} +(5.70353 - 2.40964i) q^{50} +(-0.463658 + 0.552567i) q^{52} +6.64507i q^{53} +(-11.5206 + 1.30274i) q^{55} +(5.32509 + 4.46828i) q^{56} +(-7.87536 + 1.38864i) q^{58} +(-2.83430 - 1.03160i) q^{59} +(0.999796 - 5.67013i) q^{61} +(-1.40852 - 0.813210i) q^{62} +(4.44699 + 7.70241i) q^{64} +(-1.54001 - 3.09533i) q^{65} +(-2.22595 - 2.65278i) q^{67} +(-1.59857 - 1.90510i) q^{68} +(-5.64216 + 2.80712i) q^{70} +(0.0130487 + 0.0226011i) q^{71} +(-5.00704 - 2.89081i) q^{73} +(-0.791465 + 4.48862i) q^{74} +(2.00582 + 0.730059i) q^{76} +(11.6211 - 2.04912i) q^{77} +(-12.6845 - 10.6435i) q^{79} +(-6.33083 + 0.715887i) q^{80} +5.28029i q^{82} +(6.96279 - 8.29793i) q^{83} +(11.4317 - 3.37572i) q^{85} +(9.81943 + 3.57398i) q^{86} +(15.5964 + 2.75006i) q^{88} +(-2.32308 + 4.02369i) q^{89} +(1.75941 + 3.04738i) q^{91} +(0.820364 + 2.25393i) q^{92} +(-6.44146 + 5.40503i) q^{94} +(-7.04866 + 7.41518i) q^{95} +(-2.48117 - 6.81695i) q^{97} +(-1.95222 + 1.12712i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) \) 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Introduction

L-functions

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