LMFDB - Embedded newform 297.2.t.a.8.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	297.8
Dual form			297.2.t.a.260.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.120408 - 1.14561i) q^{2} +(0.658378 - 0.139943i) q^{4} +(0.932459 + 0.0980053i) q^{5} +(0.644183 - 0.580025i) q^{7} +(-0.951517 - 2.92847i) q^{8} -1.08003i q^{10} +(1.72444 + 2.83308i) q^{11} +(0.479642 - 1.07729i) q^{13} +(-0.742046 - 0.668141i) q^{14} +(-2.01051 + 0.895139i) q^{16} +(-2.52191 - 1.83228i) q^{17} +(6.59786 - 2.14377i) q^{19} +(0.627625 - 0.0659661i) q^{20} +(3.03796 - 2.31665i) q^{22} +(-2.04949 + 1.18327i) q^{23} +(-4.03086 - 0.856787i) q^{25} +(-1.29191 - 0.419767i) q^{26} +(0.342946 - 0.472024i) q^{28} +(2.42248 + 2.69044i) q^{29} +(-5.80030 - 2.58246i) q^{31} +(-1.81162 - 3.13781i) q^{32} +(-1.79541 + 3.10974i) q^{34} +(0.657520 - 0.477716i) q^{35} +(-2.46847 + 7.59716i) q^{37} +(-3.25036 - 7.30042i) q^{38} +(-0.600245 - 2.82393i) q^{40} +(2.41108 - 2.67778i) q^{41} +(-3.31791 - 1.91560i) q^{43} +(1.53180 + 1.62391i) q^{44} +(1.60234 + 2.20543i) q^{46} +(-0.0333008 + 0.156668i) q^{47} +(-0.653156 + 6.21437i) q^{49} +(-0.496192 + 4.72095i) q^{50} +(0.165027 - 0.776389i) q^{52} +(5.71174 + 7.86153i) q^{53} +(1.33031 + 2.81073i) q^{55} +(-2.31154 - 1.33457i) q^{56} +(2.79050 - 3.09916i) q^{58} +(1.80800 + 8.50597i) q^{59} +(5.51908 + 12.3961i) q^{61} +(-2.26008 + 6.95581i) q^{62} +(-6.93750 + 5.04039i) q^{64} +(0.552827 - 0.957525i) q^{65} +(-3.32149 - 5.75299i) q^{67} +(-1.91678 - 0.853407i) q^{68} +(-0.626445 - 0.695738i) q^{70} +(6.53958 - 9.00097i) q^{71} +(3.29787 + 1.07154i) q^{73} +(9.00058 + 1.91313i) q^{74} +(4.04388 - 2.33473i) q^{76} +(2.75411 + 0.824803i) q^{77} +(-7.50645 + 0.788960i) q^{79} +(-1.96245 + 0.637639i) q^{80} +(-3.35800 - 2.43973i) q^{82} +(-13.1816 + 5.86883i) q^{83} +(-2.17201 - 1.95568i) q^{85} +(-1.79502 + 4.03167i) q^{86} +(6.65574 - 7.74568i) q^{88} +9.28531i q^{89} +(-0.315880 - 0.972179i) q^{91} +(-1.18375 + 1.06585i) q^{92} +(0.183489 + 0.0192855i) q^{94} +(6.36233 - 1.35236i) q^{95} +(1.27346 + 12.1162i) q^{97} +7.19787 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.120408	−	1.14561i	−0.0851414	−	0.810066i	−0.950878	−	0.309566i	$-0.899816\pi$
$2$	−0.120408	−	1.14561i	−0.0851414	−	0.810066i	0.865736	−	0.500500i	$-0.166851\pi$
$3$		0			0
$3$		0			0
$4$	0.658378	−	0.139943i	0.329189	−	0.0699713i
$5$	0.932459	+	0.0980053i	0.417008	+	0.0438293i	0.310709	−	0.950505i	$-0.399433\pi$
$5$	0.932459	+	0.0980053i	0.417008	+	0.0438293i	0.106299	+	0.994334i	$0.466100\pi$
$6$		0			0
$7$	0.644183	−	0.580025i	0.243478	−	0.219229i	−0.538352	−	0.842720i	$-0.680953\pi$
$7$	0.644183	−	0.580025i	0.243478	−	0.219229i	0.781830	+	0.623491i	$0.214286\pi$
$8$	−0.951517	−	2.92847i	−0.336412	−	1.03537i
$9$		0			0
$10$		−	1.08003i		−	0.341536i
$11$	1.72444	+	2.83308i	0.519937	+	0.854205i
$11$	1.72444	+	2.83308i	0.519937	+	0.854205i
$12$		0			0
$13$	0.479642	−	1.07729i	0.133029	−	0.298788i	−0.834733	−	0.550655i	$-0.814378\pi$
$13$	0.479642	−	1.07729i	0.133029	−	0.298788i	0.967762	+	0.251867i	$0.0810447\pi$
$14$	−0.742046	−	0.668141i	−0.198320	−	0.178568i
$15$		0			0
$16$	−2.01051	+	0.895139i	−0.502629	+	0.223785i
$17$	−2.52191	−	1.83228i	−0.611653	−	0.444392i	0.238343	−	0.971181i	$-0.423396\pi$
$17$	−2.52191	−	1.83228i	−0.611653	−	0.444392i	−0.849996	+	0.526789i	$0.823396\pi$
$18$		0			0
$19$	6.59786	−	2.14377i	1.51365	−	0.491816i	0.569688	−	0.821861i	$-0.307064\pi$
$19$	6.59786	−	2.14377i	1.51365	−	0.491816i	0.943965	+	0.330046i	$0.107064\pi$
$20$	0.627625	−	0.0659661i	0.140341	−	0.0147505i
$21$		0			0
$22$	3.03796	−	2.31665i	0.647694	−	0.493912i
$23$	−2.04949	+	1.18327i	−0.427348	+	0.246730i	−0.698216	−	0.715887i	$-0.746023\pi$
$23$	−2.04949	+	1.18327i	−0.427348	+	0.246730i	0.270868	+	0.962616i	$0.412689\pi$
$24$		0			0
$25$	−4.03086	−	0.856787i	−0.806173	−	0.171357i
$26$	−1.29191	−	0.419767i	−0.253364	−	0.0823230i
$27$		0			0
$28$	0.342946	−	0.472024i	0.0648106	−	0.0892042i
$29$	2.42248	+	2.69044i	0.449843	+	0.499601i	0.924824	−	0.380395i	$-0.124212\pi$
$29$	2.42248	+	2.69044i	0.449843	+	0.499601i	−0.474981	+	0.879996i	$0.657545\pi$
$30$		0			0
$31$	−5.80030	−	2.58246i	−1.04176	−	0.463823i	−0.186739	−	0.982410i	$-0.559792\pi$
$31$	−5.80030	−	2.58246i	−1.04176	−	0.463823i	−0.855025	+	0.518586i	$0.826458\pi$
$32$	−1.81162	−	3.13781i	−0.320251	−	0.554692i
$33$		0			0
$34$	−1.79541	+	3.10974i	−0.307910	+	0.533316i
$35$	0.657520	−	0.477716i	0.111141	−	0.0807487i
$36$		0			0
$37$	−2.46847	+	7.59716i	−0.405813	+	1.24897i	0.514401	+	0.857550i	$0.328014\pi$
$37$	−2.46847	+	7.59716i	−0.405813	+	1.24897i	−0.920214	+	0.391415i	$0.871986\pi$
$38$	−3.25036	−	7.30042i	−0.527278	−	1.18429i
$39$		0			0
$40$	−0.600245	−	2.82393i	−0.0949070	−	0.446503i
$41$	2.41108	−	2.67778i	0.376548	−	0.418199i	−0.524847	−	0.851197i	$-0.675878\pi$
$41$	2.41108	−	2.67778i	0.376548	−	0.418199i	0.901395	+	0.432998i	$0.142544\pi$
$42$		0			0
$43$	−3.31791	−	1.91560i	−0.505976	−	0.292126i	0.225202	−	0.974312i	$-0.427696\pi$
$43$	−3.31791	−	1.91560i	−0.505976	−	0.292126i	−0.731178	+	0.682187i	$0.761029\pi$
$44$	1.53180	+	1.62391i	0.230927	+	0.244814i
$45$		0			0
$46$	1.60234	+	2.20543i	0.236252	+	0.325174i
$47$	−0.0333008	+	0.156668i	−0.00485741	+	0.0228523i	−0.980510	−	0.196471i	$-0.937052\pi$
$47$	−0.0333008	+	0.156668i	−0.00485741	+	0.0228523i	0.975652	+	0.219324i	$0.0703851\pi$
$48$		0			0
$49$	−0.653156	+	6.21437i	−0.0933081	+	0.887767i
$50$	−0.496192	+	4.72095i	−0.0701721	+	0.667643i
$51$		0			0
$52$	0.165027	−	0.776389i	0.0228851	−	0.107666i
$53$	5.71174	+	7.86153i	0.784567	+	1.07986i	0.994763	+	0.102205i	$0.0325898\pi$
$53$	5.71174	+	7.86153i	0.784567	+	1.07986i	−0.210196	+	0.977659i	$0.567410\pi$
$54$		0			0
$55$	1.33031	+	2.81073i	0.179379	+	0.378999i
$56$	−2.31154	−	1.33457i	−0.308892	−	0.178339i
$57$		0			0
$58$	2.79050	−	3.09916i	0.366410	−	0.406940i
$59$	1.80800	+	8.50597i	0.235382	+	1.10738i	0.924039	+	0.382297i	$0.124867\pi$
$59$	1.80800	+	8.50597i	0.235382	+	1.10738i	−0.688658	+	0.725086i	$0.741800\pi$
$60$		0			0
$61$	5.51908	+	12.3961i	0.706646	+	1.58715i	0.805874	+	0.592087i	$0.201696\pi$
$61$	5.51908	+	12.3961i	0.706646	+	1.58715i	−0.0992283	+	0.995065i	$0.531637\pi$
$62$	−2.26008	+	6.95581i	−0.287030	+	0.883389i
$63$		0			0
$64$	−6.93750	+	5.04039i	−0.867188	+	0.630049i
$65$	0.552827	−	0.957525i	0.0685698	−	0.118766i
$66$		0			0
$67$	−3.32149	−	5.75299i	−0.405785	−	0.702840i	0.588628	−	0.808404i	$-0.299668\pi$
$67$	−3.32149	−	5.75299i	−0.405785	−	0.702840i	−0.994412	+	0.105565i	$0.966335\pi$
$68$	−1.91678	−	0.853407i	−0.232444	−	0.103491i
$69$		0			0
$70$	−0.626445	−	0.695738i	−0.0748745	−	0.0831566i
$71$	6.53958	−	9.00097i	0.776106	−	1.06822i	−0.219595	−	0.975591i	$-0.570474\pi$
$71$	6.53958	−	9.00097i	0.776106	−	1.06822i	0.995701	−	0.0926270i	$-0.0295264\pi$
$72$		0			0
$73$	3.29787	+	1.07154i	0.385987	+	0.125415i	0.495581	−	0.868562i	$-0.334955\pi$
$73$	3.29787	+	1.07154i	0.385987	+	0.125415i	−0.109594	+	0.993976i	$0.534955\pi$
$74$	9.00058	+	1.91313i	1.04630	+	0.222397i
$75$		0			0
$76$	4.04388	−	2.33473i	0.463865	−	0.267812i
$77$	2.75411	+	0.824803i	0.313860	+	0.0939950i
$78$		0			0
$79$	−7.50645	+	0.788960i	−0.844542	+	0.0887649i	−0.516909	−	0.856040i	$-0.672918\pi$
$79$	−7.50645	+	0.788960i	−0.844542	+	0.0887649i	−0.327633	+	0.944805i	$0.606251\pi$
$80$	−1.96245	+	0.637639i	−0.219409	+	0.0712902i
$81$		0			0
$82$	−3.35800	−	2.43973i	−0.370829	−	0.269423i
$83$	−13.1816	+	5.86883i	−1.44687	+	0.644188i	−0.971810	−	0.235765i	$-0.924240\pi$
$83$	−13.1816	+	5.86883i	−1.44687	+	0.644188i	−0.475060	+	0.879953i	$0.657574\pi$
$84$		0			0
$85$	−2.17201	−	1.95568i	−0.235587	−	0.212124i
$86$	−1.79502	+	4.03167i	−0.193562	+	0.434747i
$87$		0			0
$88$	6.65574	−	7.74568i	0.709505	−	0.825692i
$89$			9.28531i			0.984241i	0.870527	+	0.492120i	$0.163778\pi$
$89$			9.28531i			0.984241i	−0.870527	+	0.492120i	$0.836222\pi$
$90$		0			0
$91$	−0.315880	−	0.972179i	−0.0331132	−	0.101912i
$92$	−1.18375	+	1.06585i	−0.123414	+	0.111123i
$93$		0			0
$94$	0.183489	+	0.0192855i	0.0189255	+	0.00198915i
$95$	6.36233	−	1.35236i	0.652761	−	0.138749i
$96$		0			0
$97$	1.27346	+	12.1162i	0.129300	+	1.23021i	0.846136	+	0.532968i	$0.178923\pi$
$97$	1.27346	+	12.1162i	0.129300	+	1.23021i	−0.716835	+	0.697243i	$0.754410\pi$
$98$	7.19787			0.727095
$99$		0			0
$100$	−2.77373			−0.277373
$101$	0.633258	+	6.02504i	0.0630115	+	0.599514i	0.979778	+	0.200090i	$0.0641234\pi$
$101$	0.633258	+	6.02504i	0.0630115	+	0.599514i	−0.916766	+	0.399425i	$0.869210\pi$
$102$		0			0
$103$	3.90142	−	0.829273i	0.384419	−	0.0817107i	−0.0116487	−	0.999932i	$-0.503708\pi$
$103$	3.90142	−	0.829273i	0.384419	−	0.0817107i	0.396067	+	0.918221i	$0.370375\pi$
$104$	−3.61121	−	0.379554i	−0.354108	−	0.0372183i
$105$		0			0
$106$	8.31848	−	7.49000i	0.807963	−	0.727493i
$107$	−1.90097	−	5.85057i	−0.183773	−	0.565596i	0.816152	−	0.577838i	$-0.196103\pi$
$107$	−1.90097	−	5.85057i	−0.183773	−	0.565596i	−0.999925	+	0.0122414i	$0.996103\pi$
$108$		0			0
$109$		−	16.9364i		−	1.62221i	−0.584897	−	0.811107i	$-0.698865\pi$
$109$		−	16.9364i		−	1.62221i	0.584897	−	0.811107i	$-0.301135\pi$
$110$	3.05981	−	1.86245i	0.291742	−	0.177577i
$111$		0			0
$112$	−0.775936	+	1.74278i	−0.0733191	+	0.164677i
$113$	−5.94960	−	5.35705i	−0.559691	−	0.503948i	0.340029	−	0.940415i	$-0.389563\pi$
$113$	−5.94960	−	5.35705i	−0.559691	−	0.503948i	−0.899721	+	0.436466i	$0.856230\pi$
$114$		0			0
$115$	−2.02703	+	0.902493i	−0.189022	+	0.0841579i
$116$	1.97141	+	1.43232i	0.183041	+	0.132987i
$117$		0			0
$118$	9.52681	−	3.09545i	0.877014	−	0.284959i
$119$	−2.68734	+	0.282451i	−0.246348	+	0.0258922i
$120$		0			0
$121$	−5.05264	+	9.77092i	−0.459331	+	0.888265i
$122$	13.5365	−	7.81528i	1.22553	−	0.707562i
$123$		0			0
$124$	−4.18018	−	0.888525i	−0.375392	−	0.0797919i
$125$	−8.13317	−	2.64263i	−0.727453	−	0.236364i
$126$		0			0
$127$	−3.73492	+	5.14068i	−0.331421	+	0.456161i	−0.941911	−	0.335862i	$-0.890972\pi$
$127$	−3.73492	+	5.14068i	−0.331421	+	0.456161i	0.610490	+	0.792024i	$0.290972\pi$
$128$	1.76081	+	1.95558i	0.155635	+	0.172850i
$129$		0			0
$130$	−1.16351	−	0.518029i	−0.102047	−	0.0454341i
$131$	−8.68698	−	15.0463i	−0.758985	−	1.31460i	−0.943369	−	0.331746i	$-0.892362\pi$
$131$	−8.68698	−	15.0463i	−0.758985	−	1.31460i	0.184384	−	0.982854i	$-0.440971\pi$
$132$		0			0
$133$	3.00679	−	5.20791i	0.260721	−	0.451583i
$134$	−6.19073	+	4.49783i	−0.534798	+	0.388553i
$135$		0			0
$136$	−2.96612	+	9.12878i	−0.254343	+	0.782787i
$137$	−7.19951	−	16.1704i	−0.615096	−	1.38153i	−0.905386	−	0.424589i	$-0.860419\pi$
$137$	−7.19951	−	16.1704i	−0.615096	−	1.38153i	0.290290	−	0.956939i	$-0.406248\pi$
$138$		0			0
$139$	1.28467	+	6.04390i	0.108964	+	0.512637i	0.998449	+	0.0556722i	$0.0177302\pi$
$139$	1.28467	+	6.04390i	0.108964	+	0.512637i	−0.889485	+	0.456965i	$0.848936\pi$
$140$	0.366044	−	0.406533i	0.0309363	−	0.0343583i
$141$		0			0
$142$	−11.0990	−	6.40800i	−0.931407	−	0.537748i
$143$	3.87917	−	0.498862i	0.324392	−	0.0417170i
$144$		0			0
$145$	1.99518	+	2.74614i	0.165691	+	0.228054i
$146$	0.830477	−	3.90709i	0.0687308	−	0.323353i
$147$		0			0
$148$	−0.562018	+	5.34724i	−0.0461976	+	0.439541i
$149$	0.771598	−	7.34127i	0.0632118	−	0.601420i	−0.916364	−	0.400346i	$-0.868890\pi$
$149$	0.771598	−	7.34127i	0.0632118	−	0.601420i	0.979576	−	0.201074i	$-0.0644433\pi$
$150$		0			0
$151$	2.80349	−	13.1894i	0.228145	−	1.07334i	−0.703704	−	0.710493i	$-0.748472\pi$
$151$	2.80349	−	13.1894i	0.228145	−	1.07334i	0.931849	−	0.362845i	$-0.118195\pi$
$152$	−12.5560	−	17.2818i	−1.01842	−	1.40174i
$153$		0			0
$154$	0.613283	−	3.25444i	0.0494198	−	0.262250i
$155$	−5.15544	−	2.97650i	−0.414095	−	0.239078i
$156$		0			0
$157$	−1.96206	+	2.17909i	−0.156590	+	0.173910i	−0.816335	−	0.577579i	$-0.803998\pi$
$157$	−1.96206	+	2.17909i	−0.156590	+	0.173910i	0.659745	+	0.751489i	$0.270664\pi$
$158$	1.80768	+	8.50445i	0.143811	+	0.676578i
$159$		0			0
$160$	−1.38173	−	3.10343i	−0.109236	−	0.245347i
$161$	−0.633918	+	1.95100i	−0.0499598	+	0.153760i
$162$		0			0
$163$	17.8134	−	12.9422i	1.39525	−	1.01371i	0.399985	−	0.916522i	$-0.369015\pi$
$163$	17.8134	−	12.9422i	1.39525	−	1.01371i	0.995266	−	0.0971873i	$-0.0309846\pi$
$164$	1.21267	−	2.10040i	0.0946935	−	0.164014i
$165$		0			0
$166$	8.31055	+	14.3943i	0.645024	+	1.11721i
$167$	0.588990	+	0.262235i	0.0455774	+	0.0202924i	0.429399	−	0.903115i	$-0.358725\pi$
$167$	0.588990	+	0.262235i	0.0455774	+	0.0202924i	−0.383821	+	0.923407i	$0.625392\pi$
$168$		0			0
$169$	7.76819	+	8.62745i	0.597553	+	0.663650i
$170$	−1.97892	+	2.72374i	−0.151776	+	0.208902i
$171$		0			0
$172$	−2.45251	−	0.796869i	−0.187002	−	0.0607607i
$173$	13.1988	+	2.80550i	1.00349	+	0.213298i	0.680219	−	0.733009i	$-0.261885\pi$
$173$	13.1988	+	2.80550i	1.00349	+	0.213298i	0.323269	+	0.946307i	$0.395218\pi$
$174$		0			0
$175$	−3.09357	+	1.78607i	−0.233852	+	0.135015i
$176$	−6.00300	−	4.15233i	−0.452493	−	0.312994i
$177$		0			0
$178$	10.6373	−	1.11803i	0.797301	−	0.0837997i
$179$	−1.06341	+	0.345524i	−0.0794832	+	0.0258256i	−0.348489	−	0.937313i	$-0.613305\pi$
$179$	−1.06341	+	0.345524i	−0.0794832	+	0.0258256i	0.269005	+	0.963139i	$0.413305\pi$
$180$		0			0
$181$	−18.7897	−	13.6515i	−1.39663	−	1.01471i	−0.995101	−	0.0988656i	$-0.968479\pi$
$181$	−18.7897	−	13.6515i	−1.39663	−	1.01471i	−0.401530	−	0.915846i	$-0.631521\pi$
$182$	−1.07570	+	0.478933i	−0.0797362	+	0.0355009i
$183$		0			0
$184$	5.41530	+	4.87596i	0.399222	+	0.359461i
$185$	−3.04630	+	6.84211i	−0.223969	+	0.503042i
$186$		0			0
$187$	0.842101	−	10.3044i	0.0615805	−	0.753533i
$188$			0.107807i			0.00786262i
$189$		0			0
$190$	−2.31534	−	7.12590i	−0.167973	−	0.516967i
$191$	2.22298	−	2.00158i	0.160849	−	0.144829i	−0.584776	−	0.811195i	$-0.698818\pi$
$191$	2.22298	−	2.00158i	0.160849	−	0.144829i	0.745625	+	0.666365i	$0.232151\pi$
$192$		0			0
$193$	−9.83585	−	1.03379i	−0.708000	−	0.0744138i	−0.256318	−	0.966593i	$-0.582509\pi$
$193$	−9.83585	−	1.03379i	−0.708000	−	0.0744138i	−0.451682	+	0.892179i	$0.649176\pi$
$194$	13.7270	−	2.91777i	0.985543	−	0.209484i
$195$		0			0
$196$	0.439631	+	4.18281i	0.0314022	+	0.298772i
$197$	4.94568			0.352365			0.176183	−	0.984357i	$-0.443625\pi$
$197$	4.94568			0.352365			0.176183	+	0.984357i	$0.443625\pi$
$198$		0			0
$199$	−7.64868			−0.542200			−0.271100	−	0.962551i	$-0.587387\pi$
$199$	−7.64868			−0.542200			−0.271100	+	0.962551i	$0.587387\pi$
$200$	1.32636	+	12.6195i	0.0937881	+	0.892334i
$201$		0			0
$202$	6.82608	−	1.45093i	0.480282	−	0.102087i
$203$	3.12104	+	0.328035i	0.219054	+	0.0230235i
$204$		0			0
$205$	2.51067	−	2.26062i	0.175353	−	0.157888i
$206$	−1.41978	−	4.36965i	−0.0989211	−	0.304448i
$207$		0			0
$208$			2.59526i			0.179949i
$209$	17.4511	+	14.9954i	1.20712	+	1.03726i
$210$		0			0
$211$	9.56038	−	21.4730i	0.658163	−	1.47826i	−0.207810	−	0.978169i	$-0.566634\pi$
$211$	9.56038	−	21.4730i	0.658163	−	1.47826i	0.865973	−	0.500090i	$-0.166700\pi$
$212$	4.86064	+	4.37654i	0.333830	+	0.300582i
$213$		0			0
$214$	−6.47357	+	2.88222i	−0.442524	+	0.197024i
$215$	−2.90607	−	2.11139i	−0.198193	−	0.143995i
$216$		0			0
$217$	−5.23434	+	1.70074i	−0.355330	+	0.115454i
$218$	−19.4025	+	2.03928i	−1.31410	+	0.138118i
$219$		0			0
$220$	1.26919	+	1.66436i	0.0855686	+	0.112211i
$221$	−3.18352	+	1.83800i	−0.214146	+	0.123638i
$222$		0			0
$223$	20.4423	+	4.34515i	1.36892	+	0.290973i	0.832989	−	0.553290i	$-0.186628\pi$
$223$	20.4423	+	4.34515i	1.36892	+	0.290973i	0.535930	+	0.844263i	$0.319961\pi$
$224$	−2.98702	−	0.970542i	−0.199579	−	0.0648470i
$225$		0			0
$226$	−5.42069	+	7.46094i	−0.360579	+	0.496294i
$227$	−7.94758	−	8.82668i	−0.527499	−	0.585847i	0.419229	−	0.907881i	$-0.362300\pi$
$227$	−7.94758	−	8.82668i	−0.527499	−	0.585847i	−0.946728	+	0.322033i	$0.895634\pi$
$228$		0			0
$229$	8.95362	+	3.98641i	0.591672	+	0.263429i	0.680655	−	0.732604i	$-0.261695\pi$
$229$	8.95362	+	3.98641i	0.591672	+	0.263429i	−0.0889834	+	0.996033i	$0.528362\pi$
$230$	1.27797	+	2.21351i	0.0842670	+	0.145955i
$231$		0			0
$232$	5.57383	−	9.65415i	0.365940	−	0.633826i
$233$	12.6222	−	9.17056i	0.826907	−	0.600783i	−0.0917755	−	0.995780i	$-0.529254\pi$
$233$	12.6222	−	9.17056i	0.826907	−	0.600783i	0.918683	+	0.394997i	$0.129254\pi$
$234$		0			0
$235$	−0.0464058	+	0.142823i	−0.00302718	+	0.00931671i
$236$	2.38070	+	5.34713i	0.154970	+	0.348068i
$237$		0			0
$238$	0.647155	+	3.04462i	0.0419488	+	0.197354i
$239$	−20.0566	+	22.2751i	−1.29736	+	1.44086i	−0.466343	+	0.884604i	$0.654429\pi$
$239$	−20.0566	+	22.2751i	−1.29736	+	1.44086i	−0.831012	+	0.556255i	$0.812238\pi$
$240$		0			0
$241$	1.64353	+	0.948892i	0.105869	+	0.0611235i	0.552000	−	0.833844i	$-0.313865\pi$
$241$	1.64353	+	0.948892i	0.105869	+	0.0611235i	−0.446131	+	0.894968i	$0.647198\pi$
$242$	11.8020	+	4.61184i	0.758662	+	0.296460i
$243$		0			0
$244$	5.36837	+	7.38893i	0.343675	+	0.473028i
$245$	−1.21808	+	5.73063i	−0.0778205	+	0.366116i
$246$		0			0
$247$	0.855136	−	8.13608i	0.0544110	−	0.517686i
$248$	−2.04357	+	19.4432i	−0.129767	+	1.23465i
$249$		0			0
$250$	−2.04811	+	9.63561i	−0.129534	+	0.609410i
$251$	−1.59530	−	2.19574i	−0.100694	−	0.138594i	0.755696	−	0.654922i	$-0.227299\pi$
$251$	−1.59530	−	2.19574i	−0.100694	−	0.138594i	−0.856391	+	0.516328i	$0.827299\pi$
$252$		0			0
$253$	−6.88652	−	3.76588i	−0.432952	−	0.236759i
$254$	6.33891	+	3.65977i	0.397739	+	0.229635i
$255$		0			0
$256$	−9.44758	+	10.4926i	−0.590474	+	0.655788i
$257$	1.77181	+	8.33571i	0.110522	+	0.519967i	0.998225	+	0.0595505i	$0.0189667\pi$
$257$	1.77181	+	8.33571i	0.110522	+	0.519967i	−0.887703	+	0.460417i	$0.847700\pi$
$258$		0			0
$259$	2.81640	+	6.32573i	0.175002	+	0.393062i
$260$	0.229971	−	0.707777i	0.0142622	−	0.0438945i
$261$		0			0
$262$	−16.1911	+	11.7636i	−1.00029	+	0.726755i
$263$	11.9263	−	20.6569i	0.735407	−	1.27376i	−0.219138	−	0.975694i	$-0.570324\pi$
$263$	11.9263	−	20.6569i	0.735407	−	1.27376i	0.954545	−	0.298068i	$-0.0963422\pi$
$264$		0			0
$265$	4.55549	+	7.89033i	0.279841	+	0.484699i
$266$	−6.32825	−	2.81752i	−0.388010	−	0.172753i
$267$		0			0
$268$	−2.99188	−	3.32282i	−0.182758	−	0.202974i
$269$	−14.1414	+	19.4640i	−0.862219	+	1.18674i	0.118817	+	0.992916i	$0.462090\pi$
$269$	−14.1414	+	19.4640i	−0.862219	+	1.18674i	−0.981036	+	0.193826i	$0.937910\pi$
$270$		0			0
$271$	12.2868	+	3.99222i	0.746370	+	0.242510i	0.657418	−	0.753526i	$-0.271648\pi$
$271$	12.2868	+	3.99222i	0.746370	+	0.242510i	0.0889514	+	0.996036i	$0.471648\pi$
$272$	6.71048	+	1.42636i	0.406883	+	0.0864856i
$273$		0			0
$274$	−17.6580	+	10.1949i	−1.06676	+	0.615894i
$275$	−4.52363	−	12.8972i	−0.272785	−	0.777731i
$276$		0			0
$277$	−6.63747	+	0.697626i	−0.398807	+	0.0419163i	−0.301809	−	0.953368i	$-0.597591\pi$
$277$	−6.63747	+	0.697626i	−0.398807	+	0.0419163i	−0.0969976	+	0.995285i	$0.530924\pi$
$278$	6.76925	−	2.19946i	0.405993	−	0.131915i
$279$		0			0
$280$	−2.02462	−	1.47097i	−0.120994	−	0.0879073i
$281$	−0.560682	+	0.249632i	−0.0334475	+	0.0148918i	−0.423392	−	0.905946i	$-0.639161\pi$
$281$	−0.560682	+	0.249632i	−0.0334475	+	0.0148918i	0.389945	+	0.920838i	$0.372494\pi$
$282$		0			0
$283$	−14.0498	−	12.6505i	−0.835176	−	0.751995i	0.135912	−	0.990721i	$-0.456604\pi$
$283$	−14.0498	−	12.6505i	−0.835176	−	0.751995i	−0.971087	+	0.238726i	$0.923270\pi$
$284$	3.04590	−	6.84120i	0.180741	−	0.405951i
$285$		0			0
$286$	−1.03858	−	4.38394i	−0.0614128	−	0.259228i
$287$		−	3.12347i		−	0.184372i
$288$		0			0
$289$	−2.25049	−	6.92628i	−0.132381	−	0.407428i
$290$	2.90576	−	2.61635i	0.170632	−	0.153638i
$291$		0			0
$292$	2.32120	+	0.243968i	0.135838	+	0.0142771i
$293$	2.05683	−	0.437193i	0.120161	−	0.0255411i	−0.147438	−	0.989071i	$-0.547103\pi$
$293$	2.05683	−	0.437193i	0.120161	−	0.0255411i	0.267600	+	0.963530i	$0.413769\pi$
$294$		0			0
$295$	0.852255	+	8.10866i	0.0496202	+	0.472105i
$296$	24.5968			1.42966
$297$		0			0
$298$	−8.50312			−0.492572
$299$	0.291712	+	2.77545i	0.0168701	+	0.160509i
$300$		0			0
$301$	−3.24843	+	0.690476i	−0.187237	+	0.0397984i
$302$	−15.4474	−	1.62359i	−0.888900	−	0.0934272i
$303$		0			0
$304$	−11.3461	+	10.2161i	−0.650744	+	0.585933i
$305$	3.93143	+	12.0997i	0.225113	+	0.692827i
$306$		0			0
$307$			17.6110i			1.00511i	0.864545	+	0.502556i	$0.167607\pi$
$307$			17.6110i			1.00511i	−0.864545	+	0.502556i	$0.832393\pi$
$308$	1.92867	+	0.157615i	0.109896	+	0.00898096i
$309$		0			0
$310$	−2.78914	+	6.26450i	−0.158412	+	0.355800i
$311$	8.17812	+	7.36361i	0.463739	+	0.417552i	0.867596	−	0.497270i	$-0.165664\pi$
$311$	8.17812	+	7.36361i	0.463739	+	0.417552i	−0.403857	+	0.914822i	$0.632331\pi$
$312$		0			0
$313$	−3.56418	+	1.58687i	−0.201459	+	0.0896954i	−0.504986	−	0.863127i	$-0.668502\pi$
$313$	−3.56418	+	1.58687i	−0.201459	+	0.0896954i	0.303527	+	0.952823i	$0.401836\pi$
$314$	2.73263	+	1.98537i	0.154211	+	0.112041i
$315$		0			0
$316$	−4.83167	+	1.56991i	−0.271803	+	0.0883141i
$317$	21.4837	−	2.25803i	1.20665	−	0.126824i	0.520227	−	0.854028i	$-0.325847\pi$
$317$	21.4837	−	2.25803i	1.20665	−	0.126824i	0.686421	+	0.727204i	$0.259181\pi$
$318$		0			0
$319$	−3.44480	+	11.5026i	−0.192872	+	0.644019i
$320$	−6.96292	+	4.02004i	−0.389239	+	0.224727i
$321$		0			0
$322$	2.31141	+	0.491305i	0.128810	+	0.0273794i
$323$	−20.5672	−	6.68269i	−1.14439	−	0.371835i
$324$		0			0
$325$	−2.85638	+	3.93148i	−0.158444	+	0.218079i
$326$	−16.9715	−	18.8488i	−0.939965	−	1.04394i
$327$		0			0
$328$	−10.1360	−	4.51283i	−0.559666	−	0.249179i
$329$	0.0694194	+	0.120238i	0.00382722	+	0.00662893i
$330$		0			0
$331$	3.42603	−	5.93405i	0.188311	−	0.326165i	−0.756376	−	0.654137i	$-0.773032\pi$
$331$	3.42603	−	5.93405i	0.188311	−	0.326165i	0.944687	+	0.327972i	$0.106365\pi$
$332$	−7.85719	+	5.70858i	−0.431219	+	0.313299i
$333$		0			0
$334$	0.229499	−	0.706326i	0.0125576	−	0.0386485i
$335$	−2.53333	−	5.68995i	−0.138411	−	0.310875i
$336$		0			0
$337$	−0.153680	−	0.723009i	−0.00837150	−	0.0393848i	0.973764	−	0.227562i	$-0.0730754\pi$
$337$	−0.153680	−	0.723009i	−0.00837150	−	0.0393848i	−0.982135	+	0.188177i	$0.939742\pi$
$338$	8.94831	−	9.93811i	0.486724	−	0.540562i
$339$		0			0
$340$	−1.70368	−	0.983622i	−0.0923952	−	0.0533444i
$341$	−2.68594	−	20.8860i	−0.145452	−	1.13104i
$342$		0			0
$343$	6.75032	+	9.29102i	0.364483	+	0.501668i
$344$	−2.45272	+	11.5391i	−0.132242	+	0.622147i
$345$		0			0
$346$	1.62475	−	15.4585i	0.0873472	−	0.831053i
$347$	1.24436	−	11.8393i	0.0668008	−	0.635567i	−0.908984	−	0.416832i	$-0.863140\pi$
$347$	1.24436	−	11.8393i	0.0668008	−	0.635567i	0.975784	−	0.218735i	$-0.0701930\pi$
$348$		0			0
$349$	−2.11800	+	9.96440i	−0.113374	+	0.533382i	0.884402	+	0.466726i	$0.154566\pi$
$349$	−2.11800	+	9.96440i	−0.113374	+	0.533382i	−0.997776	+	0.0666564i	$0.978767\pi$
$350$	2.41863	+	3.32896i	0.129281	+	0.177940i
$351$		0			0
$352$	5.76564	−	10.5434i	0.307310	−	0.561965i
$353$	−27.2712	−	15.7451i	−1.45150	−	0.838025i	−0.452935	−	0.891544i	$-0.649623\pi$
$353$	−27.2712	−	15.7451i	−1.45150	−	0.838025i	−0.998567	+	0.0535191i	$0.982956\pi$
$354$		0			0
$355$	6.98003	−	7.75211i	0.370462	−	0.411439i
$356$	1.29941	+	6.11324i	0.0688686	+	0.324001i
$357$		0			0
$358$	0.523878	+	1.17665i	0.0276878	+	0.0621878i
$359$	−8.57599	+	26.3942i	−0.452624	+	1.39303i	0.421279	+	0.906931i	$0.361581\pi$
$359$	−8.57599	+	26.3942i	−0.452624	+	1.39303i	−0.873903	+	0.486101i	$0.838419\pi$
$360$		0			0
$361$	23.5646	−	17.1207i	1.24024	−	0.901090i
$362$	−13.3769	+	23.1694i	−0.703073	+	1.21776i
$363$		0			0
$364$	−0.344018	−	0.595856i	−0.0180314	−	0.0312313i
$365$	2.97011	+	1.32238i	0.155463	+	0.0692165i
$366$		0			0
$367$	−11.2990	−	12.5488i	−0.589800	−	0.655040i	0.372179	−	0.928161i	$-0.378611\pi$
$367$	−11.2990	−	12.5488i	−0.589800	−	0.655040i	−0.961980	+	0.273121i	$0.911944\pi$
$368$	3.06133	−	4.21357i	0.159583	−	0.219647i
$369$		0			0
$370$	8.20517	+	2.66602i	0.426567	+	0.138600i
$371$	8.23929	+	1.75131i	0.427762	+	0.0909237i
$372$		0			0
$373$	5.20412	−	3.00460i	0.269459	−	0.155572i	−0.359183	−	0.933267i	$-0.616944\pi$
$373$	5.20412	−	3.00460i	0.269459	−	0.155572i	0.628642	+	0.777695i	$0.283611\pi$
$374$	−11.9062	+	0.276019i	−0.615655	+	0.0142726i
$375$		0			0
$376$	0.490483	−	0.0515518i	0.0252947	−	0.00265858i
$377$	4.06031	−	1.31928i	0.209117	−	0.0679462i
$378$		0			0
$379$	−6.88315	−	5.00090i	−0.353563	−	0.256879i	0.396799	−	0.917906i	$-0.370121\pi$
$379$	−6.88315	−	5.00090i	−0.353563	−	0.256879i	−0.750362	+	0.661027i	$0.770121\pi$
$380$	3.99957	−	1.78072i	0.205173	−	0.0913491i
$381$		0			0
$382$	−2.56069	−	2.30566i	−0.131016	−	0.117968i
$383$	4.11794	−	9.24903i	0.210417	−	0.472604i	−0.777247	−	0.629196i	$-0.783384\pi$
$383$	4.11794	−	9.24903i	0.210417	−	0.472604i	0.987663	+	0.156592i	$0.0500509\pi$
$384$		0			0
$385$	2.48726	+	1.03901i	0.126762	+	0.0529530i
$386$			11.3925i			0.579863i
$387$		0			0
$388$	2.53398	+	7.79880i	0.128644	+	0.395924i
$389$	6.93488	−	6.24419i	0.351612	−	0.316593i	−0.474331	−	0.880347i	$-0.657310\pi$
$389$	6.93488	−	6.24419i	0.351612	−	0.316593i	0.825943	+	0.563754i	$0.190643\pi$
$390$		0			0
$391$	7.33672	+	0.771120i	0.371034	+	0.0389972i
$392$	18.8201	−	4.00033i	0.950557	−	0.202047i
$393$		0			0
$394$	−0.595501	−	5.66581i	−0.0300009	−	0.285439i
$395$	−7.07678			−0.356071
$396$		0			0
$397$	10.3328			0.518587			0.259294	−	0.965799i	$-0.416510\pi$
$397$	10.3328			0.518587			0.259294	+	0.965799i	$0.416510\pi$
$398$	0.920963	+	8.76238i	0.0461637	+	0.439218i
$399$		0			0
$400$	8.87105	−	1.88560i	0.443553	−	0.0942800i
$401$	14.7518	+	1.55048i	0.736671	+	0.0774273i	0.465431	−	0.885084i	$-0.345899\pi$
$401$	14.7518	+	1.55048i	0.736671	+	0.0774273i	0.271241	+	0.962512i	$0.412566\pi$
$402$		0			0
$403$	−5.56414	+	5.00997i	−0.277169	+	0.249564i
$404$	1.26008	+	3.87814i	0.0626915	+	0.192944i
$405$		0			0
$406$		−	3.61498i		−	0.179409i
$407$	−25.7800	+	6.10747i	−1.27787	+	0.302736i
$408$		0			0
$409$	3.55322	−	7.98066i	0.175695	−	0.394618i	−0.804136	−	0.594446i	$-0.797371\pi$
$409$	3.55322	−	7.98066i	0.175695	−	0.394618i	0.979831	+	0.199827i	$0.0640381\pi$
$410$	−2.89209	−	2.60405i	−0.142830	−	0.128605i
$411$		0			0
$412$	2.45256	−	1.09195i	0.120829	−	0.0537965i
$413$	6.09836	+	4.43072i	0.300081	+	0.218021i
$414$		0			0
$415$	−12.8665	+	4.18058i	−0.631591	+	0.205216i
$416$	−4.24927	+	0.446616i	−0.208338	+	0.0218972i
$417$		0			0
$418$	15.0776	−	21.7976i	0.737471	−	1.06616i
$419$	30.4601	−	17.5861i	1.48807	−	0.859139i	0.488165	−	0.872752i	$-0.337667\pi$
$419$	30.4601	−	17.5861i	1.48807	−	0.859139i	0.999907	+	0.0136128i	$0.00433321\pi$
$420$		0			0
$421$	1.56053	+	0.331701i	0.0760557	+	0.0161661i	0.245782	−	0.969325i	$-0.420955\pi$
$421$	1.56053	+	0.331701i	0.0760557	+	0.0161661i	−0.169727	+	0.985491i	$0.554288\pi$
$422$	−25.7507	−	8.36692i	−1.25353	−	0.407295i
$423$		0			0
$424$	17.5874	−	24.2070i	0.854121	−	1.17560i
$425$	8.59561	+	9.54640i	0.416949	+	0.463068i
$426$		0			0
$427$	10.7453	+	4.78412i	0.520002	+	0.231520i
$428$	−2.07030	−	3.58586i	−0.100072	−	0.173329i
$429$		0			0
$430$	−2.06890	+	3.58345i	−0.0997714	+	0.172809i
$431$	23.8660	−	17.3397i	1.14959	−	0.835223i	0.161160	−	0.986928i	$-0.448477\pi$
$431$	23.8660	−	17.3397i	1.14959	−	0.835223i	0.988426	+	0.151706i	$0.0484766\pi$
$432$		0			0
$433$	3.54190	−	10.9008i	0.170213	−	0.523861i	−0.829170	−	0.558997i	$-0.811186\pi$
$433$	3.54190	−	10.9008i	0.170213	−	0.523861i	0.999383	+	0.0351356i	$0.0111863\pi$
$434$	2.57864	+	5.79172i	0.123779	+	0.278011i
$435$		0			0
$436$	−2.37013	−	11.1506i	−0.113508	−	0.534015i
$437$	−10.9856	+	12.2007i	−0.525511	+	0.583639i
$438$		0			0
$439$	2.63084	+	1.51891i	0.125563	+	0.0724938i	0.561466	−	0.827500i	$-0.310238\pi$
$439$	2.63084	+	1.51891i	0.125563	+	0.0724938i	−0.435903	+	0.899994i	$0.643571\pi$
$440$	6.96532	−	6.57023i	0.332059	−	0.313223i
$441$		0			0
$442$	2.48895	+	3.42575i	0.118387	+	0.162946i
$443$	3.44135	−	16.1903i	0.163503	−	0.769223i	−0.817607	−	0.575776i	$-0.804700\pi$
$443$	3.44135	−	16.1903i	0.163503	−	0.769223i	0.981111	−	0.193447i	$-0.0619667\pi$
$444$		0			0
$445$	−0.910010	+	8.65817i	−0.0431386	+	0.410436i
$446$	2.51641	−	23.9420i	0.119155	−	1.13369i
$447$		0			0
$448$	−1.54547	+	7.27086i	−0.0730165	+	0.343516i
$449$	0.152765	+	0.210263i	0.00720943	+	0.00992293i	0.812606	−	0.582813i	$-0.198048\pi$
$449$	0.152765	+	0.210263i	0.00720943	+	0.00992293i	−0.805397	+	0.592736i	$0.798048\pi$
$450$		0			0
$451$	11.7441	+	2.21312i	0.553009	+	0.104212i
$452$	−4.66676	−	2.69436i	−0.219506	−	0.126732i
$453$		0			0
$454$	−9.15496	+	10.1676i	−0.429663	+	0.477190i
$455$	−0.199266	−	0.937475i	−0.00934175	−	0.0439495i
$456$		0			0
$457$	−2.21261	−	4.96960i	−0.103501	−	0.232468i	0.854370	−	0.519665i	$-0.173943\pi$
$457$	−2.21261	−	4.96960i	−0.103501	−	0.232468i	−0.957872	+	0.287197i	$0.907277\pi$
$458$	3.48877	−	10.7373i	0.163019	−	0.501722i
$459$		0			0
$460$	−1.20826	+	0.877849i	−0.0563352	+	0.0409299i
$461$	−14.6816	+	25.4292i	−0.683789	+	1.18436i	0.290026	+	0.957019i	$0.406336\pi$
$461$	−14.6816	+	25.4292i	−0.683789	+	1.18436i	−0.973816	+	0.227339i	$0.926997\pi$
$462$		0			0
$463$	−10.1913	−	17.6519i	−0.473632	−	0.820354i	0.525913	−	0.850539i	$-0.323724\pi$
$463$	−10.1913	−	17.6519i	−0.473632	−	0.820354i	−0.999544	+	0.0301843i	$0.990391\pi$
$464$	−7.27874	−	3.24070i	−0.337907	−	0.150446i
$465$		0			0
$466$	−12.0257	−	13.3559i	−0.557078	−	0.618698i
$467$	−0.293731	+	0.404285i	−0.0135922	+	0.0187081i	−0.815759	−	0.578392i	$-0.803680\pi$
$467$	−0.293731	+	0.404285i	−0.0135922	+	0.0187081i	0.802167	+	0.597100i	$0.203680\pi$
$468$		0			0
$469$	−5.47653	−	1.77943i	−0.252882	−	0.0821665i
$470$	0.169206	+	0.0359659i	0.00780490	+	0.00165898i
$471$		0			0
$472$	23.1891	−	13.3883i	1.06737	−	0.616244i
$473$	−0.294496	−	12.7032i	−0.0135409	−	0.584094i
$474$		0			0
$475$	−28.4318	+	2.98831i	−1.30454	+	0.137113i
$476$	−1.72976	+	0.562032i	−0.0792833	+	0.0257607i
$477$		0			0
$478$	27.9335	+	20.2949i	1.27765	+	0.928267i
$479$	−9.81779	+	4.37116i	−0.448586	+	0.199724i	−0.618580	−	0.785722i	$-0.712292\pi$
$479$	−9.81779	+	4.37116i	−0.448586	+	0.199724i	0.169994	+	0.985445i	$0.445625\pi$
$480$		0			0
$481$	7.00039	+	6.30318i	0.319190	+	0.287400i
$482$	0.889163	−	1.99709i	0.0405003	−	0.0909651i
$483$		0			0
$484$	−1.95918	+	7.14004i	−0.0890535	+	0.324547i
$485$			11.4226i			0.518675i
$486$		0			0
$487$	9.43244	+	29.0301i	0.427425	+	1.31548i	0.900653	+	0.434539i	$0.143089\pi$
$487$	9.43244	+	29.0301i	0.427425	+	1.31548i	−0.473228	+	0.880940i	$0.656911\pi$
$488$	31.0500	−	27.9575i	1.40557	−	1.26558i
$489$		0			0
$490$	6.71172	+	0.705430i	0.303204	+	0.0318681i
$491$	−24.5241	+	5.21275i	−1.10676	+	0.235248i	−0.724818	−	0.688940i	$-0.758076\pi$
$491$	−24.5241	+	5.21275i	−1.10676	+	0.235248i	−0.381937	+	0.924188i	$0.624743\pi$
$492$		0			0
$493$	−1.17966	−	11.2237i	−0.0531291	−	0.505490i
$494$	−9.42371			−0.423993
$495$		0			0
$496$	13.9732			0.627417
$497$	−1.00810	−	9.59139i	−0.0452193	−	0.430233i
$498$		0			0
$499$	−4.86170	+	1.03339i	−0.217640	+	0.0462607i	−0.315441	−	0.948945i	$-0.602152\pi$
$499$	−4.86170	+	1.03339i	−0.217640	+	0.0462607i	0.0978013	+	0.995206i	$0.468819\pi$
$500$	−5.72452	−	0.601671i	−0.256008	−	0.0269075i
$501$		0			0
$502$	−2.32337	+	2.09197i	−0.103697	+	0.0933693i
$503$	−11.3085	−	34.8039i	−0.504219	−	1.55183i	−0.802079	−	0.597218i	$-0.796273\pi$
$503$	−11.3085	−	34.8039i	−0.504219	−	1.55183i	0.297860	−	0.954610i	$-0.403727\pi$
$504$		0			0
$505$			5.68017i			0.252764i
$506$	−3.48503	+	8.34269i	−0.154928	+	0.370878i
$507$		0			0
$508$	−1.73959	+	3.90718i	−0.0771818	+	0.173353i
$509$	10.3681	+	9.33549i	0.459559	+	0.413788i	0.866121	−	0.499835i	$-0.166606\pi$
$509$	10.3681	+	9.33549i	0.459559	+	0.413788i	−0.406562	+	0.913623i	$0.633273\pi$
$510$		0			0
$511$	2.74595	−	1.22258i	0.121474	−	0.0540836i
$512$	17.4158	+	12.6533i	0.769677	+	0.559203i
$513$		0			0
$514$	9.33611	−	3.03349i	0.411798	−	0.133801i
$515$	3.71919	−	0.390903i	0.163887	−	0.0172252i
$516$		0			0
$517$	−0.501277	+	0.175820i	−0.0220461	+	0.00773255i
$518$	6.90769	−	3.98815i	0.303506	−	0.175229i
$519$		0			0
$520$	−3.33011	−	0.707836i	−0.146035	−	0.0310407i
$521$	6.74242	+	2.19075i	0.295391	+	0.0959783i	0.452963	−	0.891529i	$-0.350367\pi$
$521$	6.74242	+	2.19075i	0.295391	+	0.0959783i	−0.157573	+	0.987507i	$0.550367\pi$
$522$		0			0
$523$	7.47929	−	10.2944i	0.327047	−	0.450141i	−0.613556	−	0.789651i	$-0.710261\pi$
$523$	7.47929	−	10.2944i	0.327047	−	0.450141i	0.940602	+	0.339510i	$0.110261\pi$
$524$	−7.82493	−	8.69046i	−0.341834	−	0.379645i
$525$		0			0
$526$	−25.1008	−	11.1756i	−1.09445	−	0.487278i
$527$	9.89606	+	17.1405i	0.431079	+	0.746651i
$528$		0			0
$529$	−8.69973	+	15.0684i	−0.378249	+	0.655147i
$530$	8.49070	−	6.16886i	0.368813	−	0.267958i
$531$		0			0
$532$	1.25079	−	3.84955i	0.0542288	−	0.166899i
$533$	−1.72830	−	3.88182i	−0.0748609	−	0.168140i
$534$		0			0
$535$	−1.19918	−	5.64172i	−0.0518453	−	0.243913i
$536$	−13.6870	+	15.2010i	−0.591188	+	0.656581i
$537$		0			0
$538$	24.0009	+	13.8569i	1.03475	+	0.597414i
$539$	−18.7321	+	8.86584i	−0.806849	+	0.381879i
$540$		0			0
$541$	2.30481	+	3.17230i	0.0990915	+	0.136388i	0.855684	−	0.517499i	$-0.173137\pi$
$541$	2.30481	+	3.17230i	0.0990915	+	0.136388i	−0.756592	+	0.653887i	$0.773137\pi$
$542$	3.09409	−	14.5565i	0.132902	−	0.625257i
$543$		0			0
$544$	−1.18060	+	11.2327i	−0.0506178	+	0.481596i
$545$	1.65986	−	15.7925i	0.0711006	−	0.676477i
$546$		0			0
$547$	2.24588	−	10.5660i	0.0960269	−	0.451771i	−0.903695	−	0.428177i	$-0.859156\pi$
$547$	2.24588	−	10.5660i	0.0960269	−	0.451771i	0.999722	−	0.0235938i	$-0.00751083\pi$
$548$	−7.00292	−	9.63869i	−0.299150	−	0.411745i
$549$		0			0
$550$	−14.2305	+	6.73523i	−0.606789	+	0.287191i
$551$	21.7509	+	12.5579i	0.926618	+	0.534983i
$552$		0			0
$553$	−4.37791	+	4.86217i	−0.186168	+	0.206760i
$554$	1.59841	+	7.51993i	0.0679100	+	0.319491i
$555$		0			0
$556$	1.69160	+	3.79939i	0.0717397	+	0.161130i
$557$	−7.06108	+	21.7318i	−0.299188	+	0.920805i	0.682595	+	0.730797i	$0.260851\pi$
$557$	−7.06108	+	21.7318i	−0.299188	+	0.920805i	−0.981783	+	0.190008i	$0.939149\pi$
$558$		0			0
$559$	−3.65507	+	2.65556i	−0.154593	+	0.112318i
$560$	−0.894330	+	1.54903i	−0.0377924	+	0.0654583i
$561$		0			0
$562$	0.353491	+	0.612264i	0.0149111	+	0.0258268i
$563$	−9.90656	−	4.41068i	−0.417512	−	0.185888i	0.187219	−	0.982318i	$-0.440053\pi$
$563$	−9.90656	−	4.41068i	−0.417512	−	0.185888i	−0.604731	+	0.796430i	$0.706719\pi$
$564$		0			0
$565$	−5.02274	−	5.57832i	−0.211308	−	0.234682i
$566$	−12.8008	+	17.6188i	−0.538058	+	0.740574i
$567$		0			0
$568$	−32.5816	−	10.5864i	−1.36709	−	0.444195i
$569$	−16.4533	−	3.49726i	−0.689758	−	0.146613i	−0.150320	−	0.988637i	$-0.548030\pi$
$569$	−16.4533	−	3.49726i	−0.689758	−	0.146613i	−0.539439	+	0.842025i	$0.681364\pi$
$570$		0			0
$571$	14.1246	−	8.15487i	0.591098	−	0.341271i	−0.174434	−	0.984669i	$-0.555809\pi$
$571$	14.1246	−	8.15487i	0.591098	−	0.341271i	0.765532	+	0.643398i	$0.222476\pi$
$572$	2.48415	−	0.871301i	0.103867	−	0.0364309i
$573$		0			0
$574$	−3.57827	+	0.376091i	−0.149354	+	0.0156977i
$575$	9.27503	−	3.01364i	0.386795	−	0.125677i
$576$		0			0
$577$	6.51886	+	4.73623i	0.271384	+	0.197172i	0.715150	−	0.698971i	$-0.246358\pi$
$577$	6.51886	+	4.73623i	0.271384	+	0.197172i	−0.443767	+	0.896142i	$0.646358\pi$
$578$	−7.66382	+	3.41215i	−0.318773	+	0.141927i
$579$		0			0
$580$	1.69789	+	1.52878i	0.0705009	+	0.0634793i
$581$	−5.08730	+	11.4263i	−0.211057	+	0.474042i
$582$		0			0
$583$	−12.4228	+	29.7385i	−0.514499	+	1.23164i
$584$		−	10.6773i		−	0.441830i
$585$		0			0
$586$	−0.748511	−	2.30368i	−0.0309207	−	0.0951642i
$587$	11.6957	−	10.5309i	0.482733	−	0.434655i	−0.391488	−	0.920183i	$-0.628039\pi$
$587$	11.6957	−	10.5309i	0.482733	−	0.434655i	0.874221	+	0.485528i	$0.161373\pi$
$588$		0			0
$589$	−43.8057	−	4.60417i	−1.80498	−	0.189711i
$590$	9.18672	−	1.95270i	0.378211	−	0.0803913i
$591$		0			0
$592$	−1.83762	−	17.4838i	−0.0755258	−	0.718580i
$593$	−22.2880			−0.915258			−0.457629	−	0.889143i	$-0.651301\pi$
$593$	−22.2880			−0.915258			−0.457629	+	0.889143i	$0.651301\pi$
$594$		0			0
$595$	−2.53351			−0.103864
$596$	−0.519352	−	4.94131i	−0.0212735	−	0.202404i
$597$		0			0
$598$	3.14445	−	0.668374i	0.128586	−	0.0273318i
$599$	28.4493	+	2.99015i	1.16241	+	0.122174i	0.666025	−	0.745930i	$-0.267994\pi$
$599$	28.4493	+	2.99015i	1.16241	+	0.122174i	0.496383	+	0.868104i	$0.334661\pi$
$600$		0			0
$601$	5.29836	−	4.77067i	0.216125	−	0.194600i	−0.553956	−	0.832546i	$-0.686882\pi$
$601$	5.29836	−	4.77067i	0.216125	−	0.194600i	0.770081	+	0.637946i	$0.220216\pi$
$602$	1.18215	+	3.63829i	0.0481809	+	0.148286i
$603$		0			0
$604$		−	9.07594i		−	0.369295i
$605$	−5.66898	+	8.61579i	−0.230477	+	0.350282i
$606$		0			0
$607$	−1.85819	+	4.17355i	−0.0754215	+	0.169399i	−0.947321	−	0.320285i	$-0.896221\pi$
$607$	−1.85819	+	4.17355i	−0.0754215	+	0.169399i	0.871900	+	0.489684i	$0.162888\pi$
$608$	−18.6795	−	16.8191i	−0.757555	−	0.682106i
$609$		0			0
$610$	13.3881	−	5.96078i	0.542070	−	0.241345i
$611$	0.152805	+	0.111019i	0.00618182	+	0.00449135i
$612$		0			0
$613$	−37.1400	+	12.0675i	−1.50007	+	0.487402i	−0.940038	−	0.341069i	$-0.889211\pi$
$613$	−37.1400	+	12.0675i	−1.50007	+	0.487402i	−0.560032	+	0.828471i	$0.689211\pi$
$614$	20.1753	−	2.12051i	0.814208	−	0.0855767i
$615$		0			0
$616$	−0.205171	−	8.85013i	−0.00826656	−	0.356582i
$617$	−27.0174	+	15.5985i	−1.08768	+	0.627972i	−0.932958	−	0.359986i	$-0.882782\pi$
$617$	−27.0174	+	15.5985i	−1.08768	+	0.627972i	−0.154722	+	0.987958i	$0.549448\pi$
$618$		0			0
$619$	−31.5210	−	6.69999i	−1.26693	−	0.269295i	−0.475046	−	0.879961i	$-0.657569\pi$
$619$	−31.5210	−	6.69999i	−1.26693	−	0.269295i	−0.791889	+	0.610665i	$0.790902\pi$
$620$	−3.81077	−	1.23819i	−0.153044	−	0.0497270i
$621$		0			0
$622$	7.45109	−	10.2556i	0.298762	−	0.411210i
$623$	5.38571	+	5.98144i	0.215774	+	0.239641i
$624$		0			0
$625$	11.4984	+	5.11940i	0.459935	+	0.204776i
$626$	2.24709	+	3.89207i	0.0898117	+	0.155558i
$627$		0			0
$628$	−0.986830	+	1.70924i	−0.0393788	+	0.0682061i
$629$	20.1453	−	14.6365i	0.803248	−	0.583594i
$630$		0			0
$631$	−0.555911	+	1.71092i	−0.0221305	+	0.0681105i	−0.961512	−	0.274764i	$-0.911400\pi$
$631$	−0.555911	+	1.71092i	−0.0221305	+	0.0681105i	0.939381	+	0.342874i	$0.111400\pi$
$632$	9.45297	+	21.2317i	0.376019	+	0.844552i
$633$		0			0
$634$	−5.17364	−	24.3400i	−0.205471	−	0.966667i
$635$	−3.98647	+	4.42743i	−0.158198	+	0.175697i
$636$		0			0
$637$	6.38142	+	3.68432i	0.252841	+	0.145978i
$638$	13.5922	+	2.56138i	0.538120	+	0.101406i
$639$		0			0
$640$	1.45023	+	1.99606i	0.0573252	+	0.0789014i
$641$	−1.60208	+	7.53719i	−0.0632783	+	0.297701i	−0.998395	−	0.0566398i	$-0.981961\pi$
$641$	−1.60208	+	7.53719i	−0.0632783	+	0.297701i	0.935116	+	0.354341i	$0.115295\pi$
$642$		0			0
$643$	−2.21750	+	21.0981i	−0.0874496	+	0.832028i	0.859606	+	0.510958i	$0.170709\pi$
$643$	−2.21750	+	21.0981i	−0.0874496	+	0.832028i	−0.947056	+	0.321070i	$0.895958\pi$
$644$	−0.144330	+	1.37321i	−0.00568740	+	0.0541120i
$645$		0			0
$646$	−5.17928	+	24.3666i	−0.203776	+	0.958690i
$647$	29.4465	+	40.5296i	1.15766	+	1.59338i	0.719511	+	0.694482i	$0.244366\pi$
$647$	29.4465	+	40.5296i	1.15766	+	1.59338i	0.438150	+	0.898902i	$0.355634\pi$
$648$		0			0
$649$	−20.9803	+	19.7902i	−0.823548	+	0.776834i
$650$	4.84786	+	2.79891i	0.190149	+	0.109782i
$651$		0			0
$652$	9.91677	−	11.0137i	0.388371	−	0.431329i
$653$	3.66275	+	17.2319i	0.143334	+	0.674335i	0.989867	+	0.141998i	$0.0453527\pi$
$653$	3.66275	+	17.2319i	0.143334	+	0.674335i	−0.846533	+	0.532337i	$0.821314\pi$
$654$		0			0
$655$	−6.62563	−	14.8814i	−0.258885	−	0.581465i
$656$	−2.45053	+	7.54197i	−0.0956772	+	0.294464i
$657$		0			0
$658$	0.129387	−	0.0940050i	0.00504402	−	0.00366470i
$659$	−10.5664	+	18.3016i	−0.411609	+	0.712928i	−0.995066	−	0.0992163i	$-0.968366\pi$
$659$	−10.5664	+	18.3016i	−0.411609	+	0.712928i	0.583457	+	0.812144i	$0.301700\pi$
$660$		0			0
$661$	5.51647	+	9.55480i	0.214566	+	0.371639i	0.953138	−	0.302535i	$-0.0978331\pi$
$661$	5.51647	+	9.55480i	0.214566	+	0.371639i	−0.738572	+	0.674174i	$0.764500\pi$
$662$	−7.21061	−	3.21037i	−0.280248	−	0.124775i
$663$		0			0
$664$	29.7292	+	33.0177i	1.15372	+	1.28133i
$665$	3.31411	−	4.56147i	0.128515	−	0.176886i
$666$		0			0
$667$	−8.14837	−	2.64757i	−0.315506	−	0.102514i
$668$	0.424476	+	0.0902251i	0.0164235	+	0.00349091i
$669$		0			0
$670$	−6.21341	+	3.58731i	−0.240045	+	0.138590i
$671$	−25.6017	+	37.0122i	−0.988341	+	1.42884i
$672$		0			0
$673$	30.9325	−	3.25113i	1.19236	−	0.125322i	0.512515	−	0.858678i	$-0.328714\pi$
$673$	30.9325	−	3.25113i	1.19236	−	0.125322i	0.679844	+	0.733356i	$0.262047\pi$
$674$	−0.809780	+	0.263113i	−0.0311915	+	0.0101347i
$675$		0			0
$676$	6.32175	+	4.59302i	0.243144	+	0.176655i
$677$	19.5106	−	8.68666i	0.749852	−	0.333856i	0.00402196	−	0.999992i	$-0.498720\pi$
$677$	19.5106	−	8.68666i	0.749852	−	0.333856i	0.745830	+	0.666136i	$0.232053\pi$
$678$		0			0
$679$	7.84802	+	7.06639i	0.301179	+	0.271183i
$680$	−3.66046	+	8.22152i	−0.140372	+	0.315281i
$681$		0			0
$682$	−23.6037	+	5.59188i	−0.903832	+	0.214124i
$683$			17.2570i			0.660321i	0.943925	+	0.330161i	$0.107103\pi$
$683$			17.2570i			0.660321i	−0.943925	+	0.330161i	$0.892897\pi$
$684$		0			0
$685$	−5.12846	−	15.7838i	−0.195949	−	0.603068i
$686$	9.83106	−	8.85193i	0.375352	−	0.337968i
$687$		0			0
$688$	8.38543	+	0.881344i	0.319691	+	0.0336009i
$689$	11.2088	−	2.38250i	0.427020	−	0.0907659i
$690$		0			0
$691$	−2.19032	−	20.8395i	−0.0833236	−	0.792771i	−0.953776	−	0.300518i	$-0.902840\pi$
$691$	−2.19032	−	20.8395i	−0.0833236	−	0.792771i	0.870452	−	0.492253i	$-0.163826\pi$
$692$	9.08243			0.345262
$693$		0			0
$694$	−13.7130			−0.520539
$695$	0.605568	+	5.76159i	0.0229705	+	0.218550i
$696$		0			0
$697$	−10.9870	+	2.33535i	−0.416161	+	0.0884578i
$698$	11.6703	+	1.22660i	0.441728	+	0.0464275i
$699$		0			0
$700$	−1.78679	+	1.60883i	−0.0675344	+	0.0608082i
$701$	−15.1348	−	46.5802i	−0.571634	−	1.75931i	−0.647364	−	0.762181i	$-0.724128\pi$
$701$	−15.1348	−	46.5802i	−0.571634	−	1.75931i	0.0757293	−	0.997128i	$-0.475872\pi$
$702$		0			0
$703$			55.4168i			2.09008i
$704$	−26.2431	−	10.9626i	−0.989074	−	0.413170i
$705$		0			0
$706$	−14.7540	+	33.1380i	−0.555273	+	1.24716i
$707$	3.90261	+	3.51393i	0.146773	+	0.132155i
$708$		0			0
$709$	37.9596	−	16.9007i	1.42560	−	0.634719i	0.458404	−	0.888744i	$-0.348421\pi$
$709$	37.9596	−	16.9007i	1.42560	−	0.634719i	0.967198	+	0.254025i	$0.0817546\pi$
$710$	−9.72133	−	7.06296i	−0.364835	−	0.265068i
$711$		0			0
$712$	27.1917	−	8.83513i	1.01905	−	0.331111i
$713$	14.9434	−	1.57062i	0.559635	−	0.0588200i
$714$		0			0
$715$	3.66606	−	0.0849893i	0.137103	−	0.00317842i
$716$	−0.651774	+	0.376302i	−0.0243579	+	0.0140631i
$717$		0			0
$718$	31.2700	+	6.64664i	1.16699	+	0.248050i
$719$	27.4285	+	8.91207i	1.02291	+	0.332364i	0.771984	−	0.635642i	$-0.219264\pi$
$719$	27.4285	+	8.91207i	1.02291	+	0.332364i	0.250927	+	0.968006i	$0.419264\pi$
$720$		0			0
$721$	2.03223	−	2.79713i	0.0756843	−	0.104170i
$722$	−22.4510	−	24.9343i	−0.835539	−	0.927960i
$723$		0			0
$724$	−14.2812	−	6.35839i	−0.530756	−	0.236308i
$725$	−7.45956	−	12.9203i	−0.277041	−	0.479849i
$726$		0			0
$727$	−9.19217	+	15.9213i	−0.340919	+	0.590489i	−0.984604	−	0.174802i	$-0.944071\pi$
$727$	−9.19217	+	15.9213i	−0.340919	+	0.590489i	0.643685	+	0.765291i	$0.277405\pi$
$728$	−2.54643	+	1.85009i	−0.0943770	+	0.0685689i
$729$		0			0
$730$	1.15730	−	3.56181i	0.0428336	−	0.131828i
$731$	4.85757	+	10.9103i	0.179664	+	0.403532i
$732$		0			0
$733$	6.56061	+	30.8652i	0.242322	+	1.14003i	0.916053	+	0.401057i	$0.131357\pi$
$733$	6.56061	+	30.8652i	0.242322	+	1.14003i	−0.673732	+	0.738976i	$0.735310\pi$
$734$	−13.0155	+	14.4551i	−0.480409	+	0.533549i
$735$		0			0
$736$	7.42577	+	4.28727i	0.273718	+	0.158031i
$737$	10.5710	−	19.3307i	0.389386	−	0.712055i
$738$		0			0
$739$	−26.9990	−	37.1609i	−0.993173	−	1.36698i	−0.929422	−	0.369019i	$-0.879694\pi$
$739$	−26.9990	−	37.1609i	−0.993173	−	1.36698i	−0.0637507	−	0.997966i	$-0.520306\pi$
$740$	−1.04812	+	4.93100i	−0.0385296	+	0.181267i
$741$		0			0
$742$	1.01424	−	9.64986i	0.0372340	−	0.354257i
$743$	−2.27001	+	21.5977i	−0.0832787	+	0.792344i	0.870568	+	0.492049i	$0.163752\pi$
$743$	−2.27001	+	21.5977i	−0.0832787	+	0.792344i	−0.953846	+	0.300295i	$0.902915\pi$
$744$		0			0
$745$	1.43897	−	6.76981i	0.0527197	−	0.248027i
$746$	−4.06871	−	5.60010i	−0.148966	−	0.205034i
$747$		0			0
$748$	−0.887605	−	6.90204i	−0.0324541	−	0.252364i
$749$	−4.61805	−	2.66623i	−0.168740	−	0.0974220i
$750$		0			0
$751$	11.3807	−	12.6396i	0.415288	−	0.461224i	−0.498813	−	0.866709i	$-0.666231\pi$
$751$	11.3807	−	12.6396i	0.415288	−	0.461224i	0.914102	+	0.405485i	$0.132897\pi$
$752$	−0.0732877	−	0.344791i	−0.00267253	−	0.0125733i
$753$		0			0
$754$	−2.00027	−	4.49267i	−0.0728454	−	0.163613i
$755$	3.90677	−	12.0238i	0.142182	−	0.437591i
$756$		0			0
$757$	−18.8951	+	13.7281i	−0.686756	+	0.498957i	−0.875592	−	0.483051i	$-0.839528\pi$
$757$	−18.8951	+	13.7281i	−0.686756	+	0.498957i	0.188836	+	0.982009i	$0.439528\pi$
$758$	−4.90028	+	8.48753i	−0.177986	+	0.308281i
$759$		0			0
$760$	−10.0142	−	17.3451i	−0.363253	−	0.629173i
$761$	−18.5426	−	8.25571i	−0.672170	−	0.299269i	0.0421271	−	0.999112i	$-0.486587\pi$
$761$	−18.5426	−	8.25571i	−0.672170	−	0.299269i	−0.714297	+	0.699843i	$0.753253\pi$
$762$		0			0
$763$	−9.82355	−	10.9102i	−0.355636	−	0.394974i
$764$	1.18346	−	1.62889i	0.0428159	−	0.0589310i
$765$		0			0
$766$	−11.0916	−	3.60388i	−0.400755	−	0.130213i
$767$	10.0306	+	2.13208i	0.362185	+	0.0769848i
$768$		0			0
$769$	−20.3619	+	11.7559i	−0.734268	+	0.423930i	−0.819981	−	0.572390i	$-0.806016\pi$
$769$	−20.3619	+	11.7559i	−0.734268	+	0.423930i	0.0857137	+	0.996320i	$0.472683\pi$
$770$	0.890813	−	2.97452i	0.0321027	−	0.107194i
$771$		0			0
$772$	−6.62038	+	0.695830i	−0.238273	+	0.0250435i
$773$	−12.8627	+	4.17933i	−0.462638	+	0.150320i	−0.531056	−	0.847337i	$-0.678205\pi$
$773$	−12.8627	+	4.17933i	−0.462638	+	0.150320i	0.0684183	+	0.997657i	$0.478205\pi$
$774$		0			0
$775$	21.1676	+	15.3792i	0.760362	+	0.552436i
$776$	34.2701	−	15.2580i	1.23022	−	0.547731i
$777$		0			0
$778$	−7.98841	−	7.19279i	−0.286398	−	0.257874i
$779$	10.1674	−	22.8364i	0.364286	−	0.818200i
$780$		0			0
$781$	36.7775	+	3.00554i	1.31600	+	0.107547i
$782$		−	8.49784i		−	0.303882i
$783$		0			0
$784$	−4.24954	−	13.0787i	−0.151769	−	0.467098i
$785$	−2.04310	+	1.83962i	−0.0729215	+	0.0656588i
$786$		0			0
$787$	46.0880	+	4.84404i	1.64286	+	0.172671i	0.880356	−	0.474313i	$-0.157303\pi$
$787$	46.0880	+	4.84404i	1.64286	+	0.172671i	0.762503	+	0.646984i	$0.223970\pi$
$788$	3.25613	−	0.692112i	0.115995	−	0.0246555i
$789$		0			0
$790$	0.852102	+	8.10721i	0.0303164	+	0.288442i
$791$	−6.93985			−0.246753
$792$		0			0
$793$	16.0014			0.568226
$794$	−1.24415	−	11.8373i	−0.0441533	−	0.420090i
$795$		0			0
$796$	−5.03572	+	1.07038i	−0.178486	+	0.0379384i
$797$	48.4746	+	5.09489i	1.71706	+	0.180470i	0.911291	−	0.411762i	$-0.135087\pi$
$797$	48.4746	+	5.09489i	1.71706	+	0.180470i	0.805767	+	0.592232i	$0.201753\pi$
$798$		0			0
$799$	0.371040	−	0.334086i	0.0131265	−	0.0118191i
$800$	4.61394	+	14.2003i	0.163127	+	0.502055i
$801$		0			0
$802$		−	17.0865i		−	0.603345i
$803$	2.65121	+	11.1909i	0.0935590	+	0.394919i
$804$		0			0
$805$	−0.782311	+	1.75710i	−0.0275728	+	0.0619296i
$806$	6.40942	+	5.77107i	0.225762	+	0.203277i
$807$		0			0
$808$	17.0416	−	7.58741i	0.599521	−	0.266924i
$809$	−4.11235	−	2.98780i	−0.144583	−	0.105045i	0.513143	−	0.858303i	$-0.328481\pi$
$809$	−4.11235	−	2.98780i	−0.144583	−	0.105045i	−0.657725	+	0.753258i	$0.728481\pi$
$810$		0			0
$811$	5.95516	−	1.93495i	0.209114	−	0.0679453i	−0.202587	−	0.979264i	$-0.564935\pi$
$811$	5.95516	−	1.93495i	0.209114	−	0.0679453i	0.411701	+	0.911319i	$0.364935\pi$
$812$	2.10073	−	0.220796i	0.0737212	−	0.00774841i
$813$		0			0
$814$	10.1009	+	28.7984i	0.354036	+	1.00938i
$815$	17.8786	−	10.3222i	0.626261	−	0.361572i
$816$		0			0
$817$	−25.9977	−	5.52598i	−0.909544	−	0.193330i
$818$	−9.57054	−	3.10966i	−0.334626	−	0.108727i
$819$		0			0
$820$	1.33661	−	1.83969i	0.0466766	−	0.0642448i
$821$	−23.0033	−	25.5477i	−0.802820	−	0.891621i	0.193163	−	0.981167i	$-0.438125\pi$
$821$	−23.0033	−	25.5477i	−0.802820	−	0.891621i	−0.995983	+	0.0895452i	$0.971459\pi$
$822$		0			0
$823$	9.65088	+	4.29685i	0.336408	+	0.149779i	0.567987	−	0.823038i	$-0.307722\pi$
$823$	9.65088	+	4.29685i	0.336408	+	0.149779i	−0.231579	+	0.972816i	$0.574389\pi$
$824$	−6.14077	−	10.6361i	−0.213924	−	0.370527i
$825$		0			0
$826$	4.34157	−	7.51982i	0.151063	−	0.261648i
$827$	−22.4299	+	16.2963i	−0.779965	+	0.566678i	−0.904969	−	0.425479i	$-0.860106\pi$
$827$	−22.4299	+	16.2963i	−0.779965	+	0.566678i	0.125004	+	0.992156i	$0.460106\pi$
$828$		0			0
$829$	7.49749	−	23.0749i	0.260399	−	0.801425i	−0.732319	−	0.680962i	$-0.761562\pi$
$829$	7.49749	−	23.0749i	0.260399	−	0.801425i	0.992718	−	0.120463i	$-0.0384379\pi$
$830$	6.33853	+	14.2366i	0.220014	+	0.494158i
$831$		0			0
$832$	2.10246	+	9.89132i	0.0728898	+	0.342920i
$833$	13.0336	−	14.4753i	0.451589	−	0.501540i
$834$		0			0
$835$	0.523508	+	0.302248i	0.0181168	+	0.0104597i
$836$	13.5879	+	7.43051i	0.469947	+	0.256990i
$837$		0			0
$838$	−23.8144	−	32.7778i	−0.822656	−	1.13229i
$839$	−4.51778	+	21.2545i	−0.155971	+	0.733786i	0.828746	+	0.559625i	$0.189055\pi$
$839$	−4.51778	+	21.2545i	−0.155971	+	0.733786i	−0.984717	+	0.174161i	$0.944279\pi$
$840$		0			0
$841$	1.66129	−	15.8061i	0.0572857	−	0.545037i
$842$	0.192099	−	1.82770i	0.00662015	−	0.0629866i
$843$		0			0
$844$	3.28936	−	15.4752i	0.113224	−	0.532679i
$845$	6.39798	+	8.80607i	0.220097	+	0.302938i
$846$		0			0
$847$	2.41255	+	9.22492i	0.0828963	+	0.316972i
$848$	−18.5207	−	10.6929i	−0.636003	−	0.367196i
$849$		0			0
$850$	9.90144	−	10.9967i	0.339617	−	0.377182i
$851$	−3.93042	−	18.4912i	−0.134733	−	0.633869i
$852$		0			0
$853$	−16.6944	−	37.4962i	−0.571604	−	1.28384i	−0.935803	−	0.352523i	$-0.885324\pi$
$853$	−16.6944	−	37.4962i	−0.571604	−	1.28384i	0.364199	−	0.931321i	$-0.381343\pi$
$854$	4.18690	−	12.8860i	0.143273	−	0.440948i
$855$		0			0
$856$	−15.3244	+	11.1338i	−0.523778	+	0.380547i
$857$	−3.74660	+	6.48930i	−0.127981	+	0.221670i	−0.922894	−	0.385053i	$-0.874183\pi$
$857$	−3.74660	+	6.48930i	−0.127981	+	0.221670i	0.794913	+	0.606723i	$0.207516\pi$
$858$		0			0
$859$	−0.815011	−	1.41164i	−0.0278078	−	0.0481646i	0.851787	−	0.523889i	$-0.175519\pi$
$859$	−0.815011	−	1.41164i	−0.0278078	−	0.0481646i	−0.879594	+	0.475724i	$0.842186\pi$
$860$	−2.20877	−	0.983407i	−0.0753184	−	0.0335339i
$861$		0			0
$862$	−22.7381	−	25.2532i	−0.774463	−	0.860129i
$863$	−11.2828	+	15.5294i	−0.384070	+	0.528626i	−0.956657	−	0.291217i	$-0.905940\pi$
$863$	−11.2828	+	15.5294i	−0.384070	+	0.528626i	0.572587	+	0.819844i	$0.305940\pi$
$864$		0			0
$865$	12.0324	+	3.90957i	0.409114	+	0.132929i
$866$	−12.9146	−	2.74508i	−0.438855	−	0.0932814i
$867$		0			0
$868$	−3.20817	+	1.85224i	−0.108892	+	0.0628690i
$869$	−15.1796	−	19.9058i	−0.514932	−	0.675259i
$870$		0			0
$871$	−7.79079	+	0.818845i	−0.263981	+	0.0277455i
$872$	−49.5978	+	16.1153i	−1.67959	+	0.545733i
$873$		0			0
$874$	15.3000	+	11.1161i	0.517529	+	0.376007i
$875$	−6.77204	+	3.01511i	−0.228937	+	0.101929i
$876$		0			0
$877$	41.7575	+	37.5986i	1.41005	+	1.26962i	0.916579	+	0.399854i	$0.130939\pi$
$877$	41.7575	+	37.5986i	1.41005	+	1.26962i	0.493472	+	0.869762i	$0.335728\pi$
$878$	1.42330	−	3.19679i	0.0480342	−	0.107887i
$879$		0			0
$880$	−5.19060	−	4.46020i	−0.174975	−	0.150353i
$881$		−	16.2929i		−	0.548922i	−0.961598	−	0.274461i	$-0.911501\pi$
$881$		−	16.2929i		−	0.548922i	0.961598	−	0.274461i	$-0.0884994\pi$
$882$		0			0
$883$	−9.20073	−	28.3169i	−0.309629	−	0.952941i	−0.977909	−	0.209031i	$-0.932969\pi$
$883$	−9.20073	−	28.3169i	−0.309629	−	0.952941i	0.668280	−	0.743910i	$-0.267031\pi$
$884$	−1.83874	+	1.65561i	−0.0618436	+	0.0556842i
$885$		0			0
$886$	−18.9621	−	1.99299i	−0.637043	−	0.0669559i
$887$	1.10473	−	0.234817i	0.0370931	−	0.00788437i	−0.189328	−	0.981914i	$-0.560631\pi$
$887$	1.10473	−	0.234817i	0.0370931	−	0.00788437i	0.226421	+	0.974030i	$0.427298\pi$
$888$		0			0
$889$	0.575749	+	5.47789i	0.0193100	+	0.183722i
$890$	10.0284			0.336154
$891$		0			0
$892$	14.0668			0.470992
$893$	0.116147	+	1.10506i	0.00388670	+	0.0369794i
$894$		0			0
$895$	−1.02545	+	0.217966i	−0.0342771	+	0.00728581i
$896$	2.26857	+	0.238436i	0.0757876	+	0.00796559i
$897$		0			0
$898$	0.222485	−	0.200326i	0.00742441	−	0.00668497i
$899$	−7.10316	−	21.8613i	−0.236904	−	0.729114i
$900$		0			0
$901$		−	30.2916i		−	1.00916i
$902$	1.12128	−	13.7206i	0.0373346	−	0.456846i
$903$		0			0
$904$	−10.0268	+	22.5205i	−0.333486	+	0.749022i
$905$	−16.1827	−	14.5710i	−0.537932	−	0.484356i
$906$		0			0
$907$	24.3607	−	10.8461i	0.808882	−	0.360138i	0.0397359	−	0.999210i	$-0.487348\pi$
$907$	24.3607	−	10.8461i	0.808882	−	0.360138i	0.769146	+	0.639073i	$0.220682\pi$
$908$	−6.46774	−	4.69909i	−0.214639	−	0.155945i
$909$		0			0
$910$	−1.04998	+	0.341161i	−0.0348066	+	0.0113094i
$911$	−3.89697	+	0.409588i	−0.129112	+	0.0135703i	−0.168864	−	0.985639i	$-0.554010\pi$
$911$	−3.89697	+	0.409588i	−0.129112	+	0.0135703i	0.0397518	+	0.999210i	$0.487343\pi$
$912$		0			0
$913$	−39.3577	−	27.2241i	−1.30255	−	0.900986i
$914$	−5.42679	+	3.13316i	−0.179502	+	0.103636i
$915$		0			0
$916$	6.45273	+	1.37157i	0.213204	+	0.0453180i
$917$	−14.3232	−	4.65390i	−0.472994	−	0.153685i
$918$		0			0
$919$	−7.16542	+	9.86236i	−0.236365	+	0.325329i	−0.910678	−	0.413117i	$-0.864440\pi$
$919$	−7.16542	+	9.86236i	−0.236365	+	0.325329i	0.674313	+	0.738446i	$0.264440\pi$
$920$	4.57168	+	5.07736i	0.150724	+	0.167396i
$921$		0			0
$922$	30.8997	+	13.7574i	1.01763	+	0.453077i
$923$	−6.56003	−	11.3623i	−0.215926	−	0.373995i
$924$		0			0
$925$	16.4592	−	28.5082i	0.541175	−	0.937343i
$926$	−18.9950	+	13.8007i	−0.624216	+	0.453519i
$927$		0			0
$928$	4.05348	−	12.4753i	0.133062	−	0.409522i
$929$	1.91994	+	4.31226i	0.0629912	+	0.141481i	0.942298	−	0.334775i	$-0.108660\pi$
$929$	1.91994	+	4.31226i	0.0629912	+	0.141481i	−0.879307	+	0.476256i	$0.841994\pi$
$930$		0			0
$931$	9.01277	+	42.4017i	0.295382	+	1.38966i
$932$	7.02682	−	7.80407i	0.230171	−	0.255631i
$933$		0			0
$934$	0.498520	+	0.287821i	0.0163121	+	0.00941778i
$935$	1.79511	−	9.52591i	0.0587064	−	0.311530i
$936$		0			0
$937$	−17.0091	−	23.4110i	−0.555662	−	0.764803i	0.435105	−	0.900380i	$-0.356711\pi$
$937$	−17.0091	−	23.4110i	−0.555662	−	0.764803i	−0.990767	+	0.135577i	$0.956711\pi$
$938$	−1.37911	+	6.48820i	−0.0450295	+	0.211847i
$939$		0			0
$940$	−0.0105656	+	0.100525i	−0.000344613	+	0.00327877i
$941$	5.95507	−	56.6587i	0.194130	−	1.84702i	−0.271992	−	0.962299i	$-0.587683\pi$
$941$	5.95507	−	56.6587i	0.194130	−	1.84702i	0.466122	−	0.884720i	$-0.345651\pi$
$942$		0			0
$943$	−1.77295	+	8.34105i	−0.0577350	+	0.271622i
$944$	−11.2490	−	15.4830i	−0.366125	−	0.503928i
$945$		0			0
$946$	−14.5174	+	1.86695i	−0.472002	+	0.0606997i
$947$	−0.812966	−	0.469366i	−0.0264179	−	0.0152524i	0.486733	−	0.873551i	$-0.338188\pi$
$947$	−0.812966	−	0.469366i	−0.0264179	−	0.0152524i	−0.513151	+	0.858298i	$0.671522\pi$
$948$		0			0
$949$	2.73617	−	3.03882i	0.0888197	−	0.0986443i
$950$	6.84685	+	32.2119i	0.222141	+	1.04509i
$951$		0			0
$952$	3.38420	+	7.60103i	0.109682	+	0.246351i
$953$	3.50554	−	10.7889i	0.113556	−	0.349488i	−0.878087	−	0.478500i	$-0.841181\pi$
$953$	3.50554	−	10.7889i	0.113556	−	0.349488i	0.991643	+	0.129012i	$0.0411806\pi$
$954$		0			0
$955$	2.26900	−	1.64853i	0.0734232	−	0.0533451i
$956$	−10.0876	+	17.4722i	−0.326256	+	0.565092i
$957$		0			0
$958$	6.18978	+	10.7210i	0.199983	+	0.346380i
$959$	−14.0170	−	6.24078i	−0.452633	−	0.201525i
$960$		0			0
$961$	6.23130	+	6.92056i	0.201010	+	0.223244i
$962$	6.37807	−	8.77866i	0.205637	−	0.283035i
$963$		0			0
$964$	1.21485	+	0.394730i	0.0391278	+	0.0127134i
$965$	−9.07021	−	1.92793i	−0.291980	−	0.0620623i
$966$		0			0
$967$	−14.9869	+	8.65272i	−0.481948	+	0.278253i	−0.721228	−	0.692698i	$-0.756422\pi$
$967$	−14.9869	+	8.65272i	−0.481948	+	0.278253i	0.239280	+	0.970951i	$0.423089\pi$
$968$	33.4215	+	5.49929i	1.07421	+	0.176754i
$969$		0			0
$970$	13.0858	−	1.37538i	0.420161	−	0.0441607i
$971$	23.6890	−	7.69701i	0.760215	−	0.247009i	0.0968441	−	0.995300i	$-0.469125\pi$
$971$	23.6890	−	7.69701i	0.760215	−	0.247009i	0.663371	+	0.748291i	$0.269125\pi$
$972$		0			0
$973$	4.33318	+	3.14824i	0.138915	+	0.100928i
$974$	32.1213	−	14.3013i	1.02923	−	0.458244i
$975$		0			0
$976$	−22.1924	−	19.9821i	−0.710360	−	0.639611i
$977$	−3.04616	+	6.84178i	−0.0974552	+	0.218888i	−0.955694	−	0.294363i	$-0.904892\pi$
$977$	−3.04616	+	6.84178i	−0.0974552	+	0.218888i	0.858238	+	0.513251i	$0.171559\pi$
$978$		0			0
$979$	−26.3060	+	16.0119i	−0.840743	+	0.511743i
$980$			3.94338i			0.125967i
$981$		0			0
$982$	8.92466	+	27.4673i	0.284797	+	0.876516i
$983$	−3.96119	+	3.56667i	−0.126342	+	0.113759i	−0.729880	−	0.683575i	$-0.760424\pi$
$983$	−3.96119	+	3.56667i	−0.126342	+	0.113759i	0.603538	+	0.797335i	$0.293757\pi$
$984$		0			0
$985$	4.61165	+	0.484703i	0.146939	+	0.0154439i
$986$	−12.7159	+	2.70285i	−0.404957	+	0.0860762i
$987$		0			0
$988$	−0.575581	−	5.47628i	−0.0183117	−	0.174224i
$989$	9.06669			0.288304
$990$		0			0
$991$	−23.5423			−0.747846			−0.373923	−	0.927460i	$-0.621988\pi$
$991$	−23.5423			−0.747846			−0.373923	+	0.927460i	$0.621988\pi$
$992$	2.40464	+	22.8786i	0.0763475	+	0.726398i
$993$		0			0
$994$	−10.8666	+	2.30976i	−0.344667	+	0.0732612i
$995$	−7.13207	−	0.749611i	−0.226102	−	0.0237643i
$996$		0			0
$997$	10.5563	−	9.50498i	0.334323	−	0.301026i	−0.484821	−	0.874613i	$-0.661115\pi$
$997$	10.5563	−	9.50498i	0.334323	−	0.301026i	0.819144	+	0.573588i	$0.194449\pi$
$998$	1.76924	+	5.44517i	0.0560044	+	0.172364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.8.3		80
3.2	odd	2		99.2.p.a.74.8	yes	80
9.2	odd	6		891.2.k.a.404.14		80
9.4	even	3		99.2.p.a.41.8	yes	80
9.5	odd	6	inner	297.2.t.a.206.3		80
9.7	even	3		891.2.k.a.404.7		80
11.7	odd	10	inner	297.2.t.a.62.3		80
33.29	even	10		99.2.p.a.29.8	✓	80
99.7	odd	30		891.2.k.a.161.14		80
99.29	even	30		891.2.k.a.161.7		80
99.40	odd	30		99.2.p.a.95.8	yes	80
99.95	even	30	inner	297.2.t.a.260.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.8	✓	80	33.29	even	10
99.2.p.a.41.8	yes	80	9.4	even	3
99.2.p.a.74.8	yes	80	3.2	odd	2
99.2.p.a.95.8	yes	80	99.40	odd	30
297.2.t.a.8.3		80	1.1	even	1	trivial
297.2.t.a.62.3		80	11.7	odd	10	inner
297.2.t.a.206.3		80	9.5	odd	6	inner
297.2.t.a.260.3		80	99.95	even	30	inner
891.2.k.a.161.7		80	99.29	even	30
891.2.k.a.161.14		80	99.7	odd	30
891.2.k.a.404.7		80	9.7	even	3
891.2.k.a.404.14		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.120408 - 1.14561i) q^{2} +(0.658378 - 0.139943i) q^{4} +(0.932459 + 0.0980053i) q^{5} +(0.644183 - 0.580025i) q^{7} +(-0.951517 - 2.92847i) q^{8} -1.08003i q^{10} +(1.72444 + 2.83308i) q^{11} +(0.479642 - 1.07729i) q^{13} +(-0.742046 - 0.668141i) q^{14} +(-2.01051 + 0.895139i) q^{16} +(-2.52191 - 1.83228i) q^{17} +(6.59786 - 2.14377i) q^{19} +(0.627625 - 0.0659661i) q^{20} +(3.03796 - 2.31665i) q^{22} +(-2.04949 + 1.18327i) q^{23} +(-4.03086 - 0.856787i) q^{25} +(-1.29191 - 0.419767i) q^{26} +(0.342946 - 0.472024i) q^{28} +(2.42248 + 2.69044i) q^{29} +(-5.80030 - 2.58246i) q^{31} +(-1.81162 - 3.13781i) q^{32} +(-1.79541 + 3.10974i) q^{34} +(0.657520 - 0.477716i) q^{35} +(-2.46847 + 7.59716i) q^{37} +(-3.25036 - 7.30042i) q^{38} +(-0.600245 - 2.82393i) q^{40} +(2.41108 - 2.67778i) q^{41} +(-3.31791 - 1.91560i) q^{43} +(1.53180 + 1.62391i) q^{44} +(1.60234 + 2.20543i) q^{46} +(-0.0333008 + 0.156668i) q^{47} +(-0.653156 + 6.21437i) q^{49} +(-0.496192 + 4.72095i) q^{50} +(0.165027 - 0.776389i) q^{52} +(5.71174 + 7.86153i) q^{53} +(1.33031 + 2.81073i) q^{55} +(-2.31154 - 1.33457i) q^{56} +(2.79050 - 3.09916i) q^{58} +(1.80800 + 8.50597i) q^{59} +(5.51908 + 12.3961i) q^{61} +(-2.26008 + 6.95581i) q^{62} +(-6.93750 + 5.04039i) q^{64} +(0.552827 - 0.957525i) q^{65} +(-3.32149 - 5.75299i) q^{67} +(-1.91678 - 0.853407i) q^{68} +(-0.626445 - 0.695738i) q^{70} +(6.53958 - 9.00097i) q^{71} +(3.29787 + 1.07154i) q^{73} +(9.00058 + 1.91313i) q^{74} +(4.04388 - 2.33473i) q^{76} +(2.75411 + 0.824803i) q^{77} +(-7.50645 + 0.788960i) q^{79} +(-1.96245 + 0.637639i) q^{80} +(-3.35800 - 2.43973i) q^{82} +(-13.1816 + 5.86883i) q^{83} +(-2.17201 - 1.95568i) q^{85} +(-1.79502 + 4.03167i) q^{86} +(6.65574 - 7.74568i) q^{88} +9.28531i q^{89} +(-0.315880 - 0.972179i) q^{91} +(-1.18375 + 1.06585i) q^{92} +(0.183489 + 0.0192855i) q^{94} +(6.36233 - 1.35236i) q^{95} +(1.27346 + 12.1162i) q^{97} +7.19787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more