LMFDB - Embedded newform 325.2.n.f.251.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(101,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 $ x^10 + 16x^8 + 84x^6 + 163x^4 + 118x^2 + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.3
Root			$-0.666048i$ of defining polynomial
Character	$\chi$	$=$	325.251
Dual form			325.2.n.f.101.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.576815 - 0.333024i) q^{2} +(-1.24146 + 2.15028i) q^{3} +(-0.778190 - 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.509002 + 0.293872i) q^{7} +2.36872i q^{8} +(-1.58246 - 2.74090i) q^{9} +(-2.58582 - 1.49292i) q^{11} +3.86437 q^{12} +(1.93746 - 3.04076i) q^{13} +0.391466 q^{14} +(-0.767539 + 1.32942i) q^{16} +(-3.28719 - 5.69358i) q^{17} +2.10798i q^{18} +(5.19894 - 3.00161i) q^{19} -1.45932i q^{21} +(0.994358 + 1.72228i) q^{22} +(-0.335352 + 0.580847i) q^{23} +(-5.09340 - 2.94068i) q^{24} +(-2.13020 + 1.10874i) q^{26} +0.409469 q^{27} +(0.792200 + 0.457377i) q^{28} +(3.94620 - 6.83501i) q^{29} -4.53727i q^{31} +(4.98820 - 2.87994i) q^{32} +(6.42039 - 3.70681i) q^{33} +4.37886i q^{34} +(-2.46290 + 4.26588i) q^{36} +(-6.70933 - 3.87363i) q^{37} -3.99844 q^{38} +(4.13319 + 7.94107i) q^{39} +(-0.629569 - 0.363482i) q^{41} +(-0.485990 + 0.841760i) q^{42} +(0.503359 + 0.871843i) q^{43} +4.64711i q^{44} +(0.386872 - 0.223361i) q^{46} +3.15624i q^{47} +(-1.90574 - 3.30084i) q^{48} +(-3.32728 + 5.76302i) q^{49} +16.3237 q^{51} +(-5.60625 - 0.245144i) q^{52} -4.94455 q^{53} +(-0.236188 - 0.136363i) q^{54} +(-0.696101 - 1.20568i) q^{56} +14.9056i q^{57} +(-4.55245 + 2.62836i) q^{58} +(-12.3630 + 7.13776i) q^{59} +(4.03067 + 6.98133i) q^{61} +(-1.51102 + 2.61716i) q^{62} +(1.61095 + 0.930080i) q^{63} -0.766197 q^{64} -4.93783 q^{66} +(0.551372 + 0.318335i) q^{67} +(-5.11612 + 8.86138i) q^{68} +(-0.832654 - 1.44220i) q^{69} +(-7.79982 + 4.50323i) q^{71} +(6.49242 - 3.74840i) q^{72} -16.8200i q^{73} +(2.58003 + 4.46874i) q^{74} +(-8.09153 - 4.67165i) q^{76} +1.75491 q^{77} +(0.260480 - 5.95698i) q^{78} +15.0859 q^{79} +(4.23903 - 7.34222i) q^{81} +(0.242096 + 0.419323i) q^{82} +0.370576i q^{83} +(-1.96697 + 1.13563i) q^{84} -0.670523i q^{86} +(9.79811 + 16.9708i) q^{87} +(3.53631 - 6.12507i) q^{88} +(-8.00015 - 4.61889i) q^{89} +(-0.0925751 + 2.11712i) q^{91} +1.04387 q^{92} +(9.75637 + 5.63284i) q^{93} +(1.05111 - 1.82057i) q^{94} +14.3013i q^{96} +(5.99502 - 3.46123i) q^{97} +(3.83845 - 2.21613i) q^{98} +9.44994i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9} - 9 q^{11} + 28 q^{12} - 8 q^{13} - 8 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{22} - 13 q^{23} + 42 q^{24} - 17 q^{26} - 30 q^{27} - 33 q^{28} + 7 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) $ 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9 - 9 * q^11 + 28 * q^12 - 8 * q^13 - 8 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^22 - 13 * q^23 + 42 * q^24 - 17 * q^26 - 30 * q^27 - 33 * q^28 + 7 * q^29 - 3 * q^32 + 6 * q^33 - 3 * q^36 - 3 * q^37 + 62 * q^38 + 8 * q^39 + 12 * q^41 - 32 * q^42 - 4 * q^43 + 39 * q^46 + 26 * q^48 - q^49 + 16 * q^51 - 61 * q^52 - 24 * q^53 - 9 * q^54 - 21 * q^56 - 18 * q^58 - 48 * q^59 + 13 * q^61 - 17 * q^62 - 34 * q^64 - 42 * q^66 - 6 * q^67 + 13 * q^68 + 20 * q^69 - 27 * q^71 + 141 * q^72 - 26 * q^74 - 12 * q^76 + 48 * q^77 - 56 * q^78 + 4 * q^79 - 17 * q^81 + q^82 - 90 * q^84 + 49 * q^87 + 6 * q^88 + 24 * q^89 + 13 * q^91 - 34 * q^92 + 63 * q^93 + 5 * q^94 + 15 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.576815	−	0.333024i	−0.407869	−	0.235484i	0.282004	−	0.959413i	$-0.409001\pi$
$2$	−0.576815	−	0.333024i	−0.407869	−	0.235484i	−0.689874	+	0.723930i	$0.742334\pi$
$3$	−1.24146	+	2.15028i	−0.716759	+	1.24146i	0.245519	+	0.969392i	$0.421042\pi$
$3$	−1.24146	+	2.15028i	−0.716759	+	1.24146i	−0.962277	+	0.272070i	$0.912292\pi$
$4$	−0.778190	−	1.34786i	−0.389095	−	0.673932i
$5$		0			0
$5$		0			0
$6$	1.43219	−	0.826874i	0.584688	−	0.337570i
$7$	−0.509002	+	0.293872i	−0.192384	+	0.111073i	−0.593098	−	0.805130i	$-0.702095\pi$
$7$	−0.509002	+	0.293872i	−0.192384	+	0.111073i	0.400714	+	0.916203i	$0.368762\pi$
$8$			2.36872i			0.837469i
$9$	−1.58246	−	2.74090i	−0.527486	−	0.913632i
$10$		0			0
$11$	−2.58582	−	1.49292i	−0.779653	−	0.450133i	0.0566544	−	0.998394i	$-0.481957\pi$
$11$	−2.58582	−	1.49292i	−0.779653	−	0.450133i	−0.836307	+	0.548261i	$0.815290\pi$
$12$	3.86437			1.11555
$13$	1.93746	−	3.04076i	0.537355	−	0.843356i
$13$	1.93746	−	3.04076i	0.537355	−	0.843356i
$14$	0.391466			0.104624
$15$		0			0
$16$	−0.767539	+	1.32942i	−0.191885	+	0.332354i
$17$	−3.28719	−	5.69358i	−0.797261	−	1.38090i	−0.921393	−	0.388631i	$-0.872948\pi$
$17$	−3.28719	−	5.69358i	−0.797261	−	1.38090i	0.124132	−	0.992266i	$-0.460385\pi$
$18$			2.10798i			0.496857i
$19$	5.19894	−	3.00161i	1.19272	−	0.688617i	0.233797	−	0.972285i	$-0.424885\pi$
$19$	5.19894	−	3.00161i	1.19272	−	0.688617i	0.958922	+	0.283668i	$0.0915515\pi$
$20$		0			0
$21$		−	1.45932i		−	0.318451i
$22$	0.994358	+	1.72228i	0.211998	+	0.367191i
$23$	−0.335352	+	0.580847i	−0.0699258	+	0.121115i	−0.898868	−	0.438219i	$-0.855610\pi$
$23$	−0.335352	+	0.580847i	−0.0699258	+	0.121115i	0.828943	+	0.559334i	$0.188943\pi$
$24$	−5.09340	−	2.94068i	−1.03969	−	0.600263i
$25$		0			0
$26$	−2.13020	+	1.10874i	−0.417767	+	0.217441i
$27$	0.409469			0.0788023
$28$	0.792200	+	0.457377i	0.149712	+	0.0864361i
$29$	3.94620	−	6.83501i	0.732790	−	1.26923i	−0.222896	−	0.974842i	$-0.571551\pi$
$29$	3.94620	−	6.83501i	0.732790	−	1.26923i	0.955686	−	0.294388i	$-0.0951157\pi$
$30$		0			0
$31$		−	4.53727i		−	0.814917i	−0.913224	−	0.407459i	$-0.866415\pi$
$31$		−	4.53727i		−	0.814917i	0.913224	−	0.407459i	$-0.133585\pi$
$32$	4.98820	−	2.87994i	0.881797	−	0.509106i
$33$	6.42039	−	3.70681i	1.11765	−	0.645273i
$34$			4.37886i			0.750967i
$35$		0			0
$36$	−2.46290	+	4.26588i	−0.410484	+	0.710979i
$37$	−6.70933	−	3.87363i	−1.10301	−	0.636821i	−0.165998	−	0.986126i	$-0.553084\pi$
$37$	−6.70933	−	3.87363i	−1.10301	−	0.636821i	−0.937009	+	0.349305i	$0.886418\pi$
$38$	−3.99844			−0.648632
$39$	4.13319	+	7.94107i	0.661841	+	1.27159i
$40$		0			0
$41$	−0.629569	−	0.363482i	−0.0983222	−	0.0567663i	0.450033	−	0.893012i	$-0.351412\pi$
$41$	−0.629569	−	0.363482i	−0.0983222	−	0.0567663i	−0.548355	+	0.836246i	$0.684746\pi$
$42$	−0.485990	+	0.841760i	−0.0749899	+	0.129886i
$43$	0.503359	+	0.871843i	0.0767615	+	0.132955i	0.901851	−	0.432047i	$-0.142209\pi$
$43$	0.503359	+	0.871843i	0.0767615	+	0.132955i	−0.825089	+	0.565002i	$0.808875\pi$
$44$			4.64711i			0.700578i
$45$		0			0
$46$	0.386872	−	0.223361i	0.0570412	−	0.0329327i
$47$			3.15624i			0.460386i	0.973145	+	0.230193i	$0.0739357\pi$
$47$			3.15624i			0.460386i	−0.973145	+	0.230193i	$0.926064\pi$
$48$	−1.90574	−	3.30084i	−0.275070	−	0.476436i
$49$	−3.32728	+	5.76302i	−0.475325	+	0.823288i
$50$		0			0
$51$	16.3237			2.28577
$52$	−5.60625	−	0.245144i	−0.777447	−	0.0339954i
$53$	−4.94455			−0.679186			−0.339593	−	0.940573i	$-0.610289\pi$
$53$	−4.94455			−0.679186			−0.339593	+	0.940573i	$0.610289\pi$
$54$	−0.236188	−	0.136363i	−0.0321411	−	0.0185567i
$55$		0			0
$56$	−0.696101	−	1.20568i	−0.0930204	−	0.161116i
$57$			14.9056i			1.97429i
$58$	−4.55245	+	2.62836i	−0.597766	+	0.345120i
$59$	−12.3630	+	7.13776i	−1.60952	+	0.929257i	−0.620043	+	0.784568i	$0.712885\pi$
$59$	−12.3630	+	7.13776i	−1.60952	+	0.929257i	−0.989477	+	0.144689i	$0.953782\pi$
$60$		0			0
$61$	4.03067	+	6.98133i	0.516075	+	0.893867i	0.999826	+	0.0186618i	$0.00594058\pi$
$61$	4.03067	+	6.98133i	0.516075	+	0.893867i	−0.483751	+	0.875205i	$0.660726\pi$
$62$	−1.51102	+	2.61716i	−0.191900	+	0.332380i
$63$	1.61095	+	0.930080i	0.202960	+	0.117179i
$64$	−0.766197			−0.0957747
$65$		0			0
$66$	−4.93783			−0.607805
$67$	0.551372	+	0.318335i	0.0673608	+	0.0388908i	0.533302	−	0.845925i	$-0.320951\pi$
$67$	0.551372	+	0.318335i	0.0673608	+	0.0388908i	−0.465941	+	0.884816i	$0.654284\pi$
$68$	−5.11612	+	8.86138i	−0.620421	+	1.07460i
$69$	−0.832654	−	1.44220i	−0.100240	−	0.173620i
$70$		0			0
$71$	−7.79982	+	4.50323i	−0.925668	+	0.534435i	−0.885439	−	0.464756i	$-0.846142\pi$
$71$	−7.79982	+	4.50323i	−0.925668	+	0.534435i	−0.0402292	+	0.999190i	$0.512809\pi$
$72$	6.49242	−	3.74840i	0.765138	−	0.441753i
$73$		−	16.8200i		−	1.96864i	−0.176403	−	0.984318i	$-0.556446\pi$
$73$		−	16.8200i		−	1.96864i	0.176403	−	0.984318i	$-0.443554\pi$
$74$	2.58003	+	4.46874i	0.299922	+	0.519480i
$75$		0			0
$76$	−8.09153	−	4.67165i	−0.928162	−	0.535875i
$77$	1.75491			0.199991
$78$	0.260480	−	5.95698i	0.0294936	−	0.674495i
$79$	15.0859			1.69729			0.848646	−	0.528961i	$-0.177418\pi$
$79$	15.0859			1.69729			0.848646	+	0.528961i	$0.177418\pi$
$80$		0			0
$81$	4.23903	−	7.34222i	0.471003	−	0.815802i
$82$	0.242096	+	0.419323i	0.0267351	+	0.0463065i
$83$			0.370576i			0.0406760i	0.999793	+	0.0203380i	$0.00647423\pi$
$83$			0.370576i			0.0406760i	−0.999793	+	0.0203380i	$0.993526\pi$
$84$	−1.96697	+	1.13563i	−0.214614	+	0.123908i
$85$		0			0
$86$		−	0.670523i		−	0.0723043i
$87$	9.79811	+	16.9708i	1.05047	+	1.81946i
$88$	3.53631	−	6.12507i	0.376972	−	0.652935i
$89$	−8.00015	−	4.61889i	−0.848014	−	0.489601i	0.0119665	−	0.999928i	$-0.496191\pi$
$89$	−8.00015	−	4.61889i	−0.848014	−	0.489601i	−0.859980	+	0.510327i	$0.829524\pi$
$90$		0			0
$91$	−0.0925751	+	2.11712i	−0.00970451	+	0.221934i
$92$	1.04387			0.108831
$93$	9.75637	+	5.63284i	1.01169	+	0.584099i
$94$	1.05111	−	1.82057i	0.108413	−	0.187777i
$95$		0			0
$96$			14.3013i			1.45962i
$97$	5.99502	−	3.46123i	0.608702	−	0.351434i	−0.163755	−	0.986501i	$-0.552361\pi$
$97$	5.99502	−	3.46123i	0.608702	−	0.351434i	0.772457	+	0.635067i	$0.219027\pi$
$98$	3.83845	−	2.21613i	0.387742	−	0.223863i
$99$			9.44994i			0.949754i
$100$		0			0
$101$	−6.91837	+	11.9830i	−0.688403	+	1.19235i	0.283951	+	0.958839i	$0.408355\pi$
$101$	−6.91837	+	11.9830i	−0.688403	+	1.19235i	−0.972354	+	0.233511i	$0.924979\pi$
$102$	−9.41575	−	5.43618i	−0.932298	−	0.538262i
$103$	4.42075			0.435590			0.217795	−	0.975995i	$-0.430114\pi$
$103$	4.42075			0.435590			0.217795	+	0.975995i	$0.430114\pi$
$104$	7.20272	+	4.58930i	0.706285	+	0.450018i
$105$		0			0
$106$	2.85209	+	1.64665i	0.277019	+	0.159937i
$107$	1.35336	−	2.34408i	0.130834	−	0.226611i	−0.793164	−	0.609008i	$-0.791568\pi$
$107$	1.35336	−	2.34408i	0.130834	−	0.226611i	0.923998	+	0.382397i	$0.124901\pi$
$108$	−0.318645	−	0.551909i	−0.0306616	−	0.0531074i
$109$		−	11.3266i		−	1.08489i	−0.840091	−	0.542446i	$-0.817498\pi$
$109$		−	11.3266i		−	1.08489i	0.840091	−	0.542446i	$-0.182502\pi$
$110$		0			0
$111$	16.6588	−	9.61794i	1.58118	−	0.912894i
$112$		−	0.902234i		−	0.0852531i
$113$	1.25454	+	2.17293i	0.118018	+	0.204413i	0.918982	−	0.394299i	$-0.129013\pi$
$113$	1.25454	+	2.17293i	0.118018	+	0.204413i	−0.800964	+	0.598712i	$0.795679\pi$
$114$	4.96391	−	8.59774i	0.464912	−	0.805252i
$115$		0			0
$116$	−12.2836			−1.14050
$117$	−11.4004	−	0.498503i	−1.05396	−	0.0460866i
$118$	9.50818			0.875299
$119$	3.34637	+	1.93203i	0.306761	+	0.177109i
$120$		0			0
$121$	−1.04237	−	1.80544i	−0.0947609	−	0.164131i
$122$		−	5.36924i		−	0.486108i
$123$	1.56317	−	0.902498i	0.140947	−	0.0813755i
$124$	−6.11562	+	3.53085i	−0.549199	+	0.317080i
$125$		0			0
$126$	−0.619478	−	1.07297i	−0.0551875	−	0.0955875i
$127$	−3.00538	+	5.20546i	−0.266684	+	0.461910i	−0.968003	−	0.250937i	$-0.919261\pi$
$127$	−3.00538	+	5.20546i	−0.266684	+	0.461910i	0.701319	+	0.712847i	$0.252595\pi$
$128$	−9.53444	−	5.50471i	−0.842734	−	0.486553i
$129$	−2.49961			−0.220078
$130$		0			0
$131$	1.11618			0.0975211			0.0487605	−	0.998810i	$-0.484473\pi$
$131$	1.11618			0.0975211			0.0487605	+	0.998810i	$0.484473\pi$
$132$	−9.99256	−	5.76921i	−0.869741	−	0.502145i
$133$	−1.76418	+	3.05565i	−0.152974	+	0.264958i
$134$	−0.212026	−	0.367240i	−0.0183163	−	0.0317247i
$135$		0			0
$136$	13.4865	−	7.78644i	1.15646	−	0.667681i
$137$	17.0529	−	9.84550i	1.45693	−	0.841158i	0.458069	−	0.888917i	$-0.348541\pi$
$137$	17.0529	−	9.84550i	1.45693	−	0.841158i	0.998859	+	0.0477593i	$0.0152080\pi$
$138$			1.10918i			0.0944193i
$139$	−4.93518	−	8.54798i	−0.418596	−	0.725030i	0.577202	−	0.816601i	$-0.304144\pi$
$139$	−4.93518	−	8.54798i	−0.418596	−	0.725030i	−0.995799	+	0.0915711i	$0.970811\pi$
$140$		0			0
$141$	−6.78680	−	3.91836i	−0.571551	−	0.329985i
$142$	5.99873			0.503402
$143$	−9.54954	+	4.97038i	−0.798573	+	0.415644i
$144$	4.85839			0.404866
$145$		0			0
$146$	−5.60148	+	9.70204i	−0.463581	+	0.802946i
$147$	−8.26138	−	14.3091i	−0.681387	−	1.18020i
$148$			12.0577i			0.991136i
$149$	−7.04577	+	4.06788i	−0.577212	+	0.333254i	−0.760025	−	0.649894i	$-0.774813\pi$
$149$	−7.04577	+	4.06788i	−0.577212	+	0.333254i	0.182813	+	0.983148i	$0.441480\pi$
$150$		0			0
$151$		−	13.0169i		−	1.05930i	−0.848216	−	0.529650i	$-0.822323\pi$
$151$		−	13.0169i		−	1.05930i	0.848216	−	0.529650i	$-0.177677\pi$
$152$	7.10998	+	12.3148i	0.576695	+	0.998866i
$153$	−10.4037	+	18.0197i	−0.841088	+	1.45681i
$154$	−1.01226	−	0.584428i	−0.0815702	−	0.0470946i
$155$		0			0
$156$	7.48708	−	11.7506i	0.599446	−	0.940805i
$157$	−12.3177			−0.983061			−0.491530	−	0.870860i	$-0.663562\pi$
$157$	−12.3177			−0.983061			−0.491530	+	0.870860i	$0.663562\pi$
$158$	−8.70174	−	5.02395i	−0.692274	−	0.399684i
$159$	6.13847	−	10.6321i	0.486812	−	0.843184i
$160$		0			0
$161$		−	0.394203i		−	0.0310675i
$162$	−4.89027	+	2.82340i	−0.384216	+	0.221827i
$163$	−1.84793	+	1.06690i	−0.144741	+	0.0835664i	−0.570622	−	0.821213i	$-0.693298\pi$
$163$	−1.84793	+	1.06690i	−0.144741	+	0.0835664i	0.425880	+	0.904779i	$0.359964\pi$
$164$			1.13143i			0.0883500i
$165$		0			0
$166$	0.123411	−	0.213754i	0.00957852	−	0.0165905i
$167$	0.0948176	+	0.0547430i	0.00733720	+	0.00423614i	0.503664	−	0.863900i	$-0.331985\pi$
$167$	0.0948176	+	0.0547430i	0.00733720	+	0.00423614i	−0.496327	+	0.868136i	$0.665318\pi$
$168$	3.45673			0.266693
$169$	−5.49249	−	11.7827i	−0.422499	−	0.906363i
$170$		0			0
$171$	−16.4542	−	9.49984i	−1.25828	−	0.726471i
$172$	0.783418	−	1.35692i	0.0597351	−	0.103464i
$173$	4.09968	+	7.10085i	0.311693	+	0.539868i	0.978729	−	0.205158i	$-0.0657707\pi$
$173$	4.09968	+	7.10085i	0.311693	+	0.539868i	−0.667036	+	0.745025i	$0.732437\pi$
$174$		−	13.0520i		−	0.989471i
$175$		0			0
$176$	3.96943	−	2.29175i	0.299207	−	0.172747i
$177$		−	35.4450i		−	2.66421i
$178$	3.07640	+	5.32848i	0.230586	+	0.399387i
$179$	−0.0150584	+	0.0260820i	−0.00112552	+	0.00194946i	−0.866588	−	0.499025i	$-0.833692\pi$
$179$	−0.0150584	+	0.0260820i	−0.00112552	+	0.00194946i	0.865462	+	0.500974i	$0.167025\pi$
$180$		0			0
$181$	11.4087			0.848004			0.424002	−	0.905661i	$-0.360625\pi$
$181$	11.4087			0.848004			0.424002	+	0.905661i	$0.360625\pi$
$182$	0.758450	−	1.19036i	0.0562201	−	0.0882350i
$183$	−20.0157			−1.47960
$184$	−1.37586	−	0.794356i	−0.101430	−	0.0585607i
$185$		0			0
$186$	−3.75175	−	6.49821i	−0.275091	−	0.476472i
$187$			19.6301i			1.43549i
$188$	4.25419	−	2.45616i	0.310269	−	0.179134i
$189$	−0.208420	+	0.120332i	−0.0151603	+	0.00875283i
$190$		0			0
$191$	2.66801	+	4.62112i	0.193050	+	0.334373i	0.946260	−	0.323408i	$-0.104829\pi$
$191$	2.66801	+	4.62112i	0.193050	+	0.334373i	−0.753209	+	0.657781i	$0.771495\pi$
$192$	0.951205	−	1.64754i	0.0686473	−	0.118901i
$193$	9.20113	+	5.31227i	0.662312	+	0.382386i	0.793157	−	0.609017i	$-0.208436\pi$
$193$	9.20113	+	5.31227i	0.662312	+	0.382386i	−0.130846	+	0.991403i	$0.541769\pi$
$194$	−4.61069			−0.331028
$195$		0			0
$196$	10.3570			0.739787
$197$	−4.88920	−	2.82278i	−0.348341	−	0.201115i	0.315613	−	0.948888i	$-0.397790\pi$
$197$	−4.88920	−	2.82278i	−0.348341	−	0.201115i	−0.663954	+	0.747773i	$0.731123\pi$
$198$	3.14706	−	5.45086i	0.223652	−	0.387376i
$199$	7.79679	+	13.5044i	0.552700	+	0.957305i	0.998079	+	0.0619621i	$0.0197358\pi$
$199$	7.79679	+	13.5044i	0.552700	+	0.957305i	−0.445378	+	0.895342i	$0.646931\pi$
$200$		0			0
$201$	−1.36901	+	0.790401i	−0.0965628	+	0.0557506i
$202$	7.98123	−	4.60797i	0.561558	−	0.324215i
$203$			4.63871i			0.325574i
$204$	−12.7029	−	22.0021i	−0.889383	−	1.54046i
$205$		0			0
$206$	−2.54996	−	1.47222i	−0.177664	−	0.102574i
$207$	2.12272			0.147539
$208$	2.55536	+	4.90960i	0.177183	+	0.340419i
$209$	−17.9247			−1.23988
$210$		0			0
$211$	−8.46675	+	14.6648i	−0.582875	+	1.00957i	0.412262	+	0.911066i	$0.364739\pi$
$211$	−8.46675	+	14.6648i	−0.582875	+	1.00957i	−0.995137	+	0.0985037i	$0.968594\pi$
$212$	3.84780	+	6.66458i	0.264268	+	0.457725i
$213$		−	22.3623i		−	1.53224i
$214$	−1.56127	+	0.901400i	−0.106726	+	0.0616184i
$215$		0			0
$216$			0.969917i			0.0659945i
$217$	1.33338	+	2.30948i	0.0905155	+	0.156777i
$218$	−3.77203	+	6.53335i	−0.255474	+	0.442494i
$219$	36.1677	+	20.8814i	2.44399	+	1.41104i
$220$		0			0
$221$	−23.6816	−	1.03553i	−1.59300	−	0.0696570i
$222$	−12.8120			−0.859886
$223$	−14.2283	−	8.21470i	−0.952796	−	0.550097i	−0.0588475	−	0.998267i	$-0.518743\pi$
$223$	−14.2283	−	8.21470i	−0.952796	−	0.550097i	−0.893948	+	0.448170i	$0.852076\pi$
$224$	−1.69267	+	2.93179i	−0.113096	+	0.195888i
$225$		0			0
$226$		−	1.67117i		−	0.111165i
$227$	14.9348	−	8.62262i	0.991259	−	0.572304i	0.0856085	−	0.996329i	$-0.472717\pi$
$227$	14.9348	−	8.62262i	0.991259	−	0.572304i	0.905650	+	0.424025i	$0.139383\pi$
$228$	20.0907	−	11.5993i	1.33054	−	0.768186i
$229$		−	10.0809i		−	0.666162i	−0.942898	−	0.333081i	$-0.891912\pi$
$229$		−	10.0809i		−	0.666162i	0.942898	−	0.333081i	$-0.108088\pi$
$230$		0			0
$231$	−2.17866	+	3.77355i	−0.143345	+	0.248281i
$232$	16.1902	+	9.34744i	1.06294	+	0.613689i
$233$	19.7103			1.29126			0.645632	−	0.763648i	$-0.276594\pi$
$233$	19.7103			1.29126			0.645632	+	0.763648i	$0.276594\pi$
$234$	6.40988	+	4.08414i	0.419027	+	0.266989i
$235$		0			0
$236$	19.2415	+	11.1091i	1.25251	+	0.723138i
$237$	−18.7285	+	32.4388i	−1.21655	+	2.10712i
$238$	−1.28682	−	2.22884i	−0.0834124	−	0.144474i
$239$		−	11.2372i		−	0.726871i	−0.931619	−	0.363435i	$-0.881604\pi$
$239$		−	11.2372i		−	0.726871i	0.931619	−	0.363435i	$-0.118396\pi$
$240$		0			0
$241$	3.24657	−	1.87441i	0.209130	−	0.120741i	−0.391777	−	0.920060i	$-0.628140\pi$
$241$	3.24657	−	1.87441i	0.209130	−	0.120741i	0.600907	+	0.799319i	$0.294806\pi$
$242$			1.38854i			0.0892586i
$243$	11.1394	+	19.2940i	0.714593	+	1.23771i
$244$	6.27326	−	10.8656i	0.401604	−	0.695599i
$245$		0			0
$246$	−1.20221			−0.0766504
$247$	0.945563	−	21.6243i	0.0601647	−	1.37592i
$248$	10.7475			0.682468
$249$	−0.796840	−	0.460056i	−0.0504977	−	0.0291549i
$250$		0			0
$251$	10.1871	+	17.6446i	0.643007	+	1.11372i	0.984758	+	0.173930i	$0.0556466\pi$
$251$	10.1871	+	17.6446i	0.643007	+	1.11372i	−0.341751	+	0.939790i	$0.611020\pi$
$252$		−	2.89512i		−	0.182375i
$253$	1.73432	−	1.00131i	0.109036	−	0.0629518i
$254$	3.46709	−	2.00172i	0.217545	−	0.125599i
$255$		0			0
$256$	4.43260	+	7.67749i	0.277038	+	0.479843i
$257$	−7.17856	+	12.4336i	−0.447786	+	0.775588i	−0.998242	−	0.0592763i	$-0.981121\pi$
$257$	−7.17856	+	12.4336i	−0.447786	+	0.775588i	0.550456	+	0.834864i	$0.314454\pi$
$258$	1.44181	+	0.832429i	0.0897631	+	0.0518247i
$259$	4.55341			0.282935
$260$		0			0
$261$	−24.9787			−1.54615
$262$	−0.643829	−	0.371715i	−0.0397759	−	0.0229646i
$263$	13.3709	−	23.1590i	0.824484	−	1.42805i	−0.0778291	−	0.996967i	$-0.524799\pi$
$263$	13.3709	−	23.1590i	0.824484	−	1.42805i	0.902313	−	0.431081i	$-0.141868\pi$
$264$	8.78040	+	15.2081i	0.540396	+	0.935994i
$265$		0			0
$266$	2.03521	−	1.17503i	0.124787	−	0.0720456i
$267$	19.8638	−	11.4683i	1.21564	−	0.701851i
$268$		−	0.990899i		−	0.0605288i
$269$	−0.215092	−	0.372550i	−0.0131144	−	0.0227148i	0.859394	−	0.511314i	$-0.170841\pi$
$269$	−0.215092	−	0.372550i	−0.0131144	−	0.0227148i	−0.872508	+	0.488600i	$0.837508\pi$
$270$		0			0
$271$	10.1868	+	5.88137i	0.618806	+	0.357268i	0.776404	−	0.630235i	$-0.217042\pi$
$271$	10.1868	+	5.88137i	0.618806	+	0.357268i	−0.157598	+	0.987503i	$0.550375\pi$
$272$	10.0922			0.611929
$273$	−4.43746	−	2.82739i	−0.268567	−	0.171121i
$274$	−13.1151			−0.792315
$275$		0			0
$276$	−1.29593	+	2.24461i	−0.0780056	+	0.135110i
$277$	−1.98793	−	3.44320i	−0.119443	−	0.206882i	0.800104	−	0.599861i	$-0.204778\pi$
$277$	−1.98793	−	3.44320i	−0.119443	−	0.206882i	−0.919547	+	0.392980i	$0.871444\pi$
$278$			6.57413i			0.394290i
$279$	−12.4362	+	7.18003i	−0.744534	+	0.429857i
$280$		0			0
$281$		−	17.3267i		−	1.03363i	−0.856098	−	0.516814i	$-0.827118\pi$
$281$		−	17.3267i		−	1.03363i	0.856098	−	0.516814i	$-0.172882\pi$
$282$	2.60982	+	4.52033i	0.155412	+	0.269182i
$283$	−4.50729	+	7.80686i	−0.267931	+	0.464070i	−0.968327	−	0.249684i	$-0.919673\pi$
$283$	−4.50729	+	7.80686i	−0.267931	+	0.464070i	0.700397	+	0.713754i	$0.253006\pi$
$284$	12.1395	+	7.00873i	0.720346	+	0.415892i
$285$		0			0
$286$	7.16357	+	0.313241i	0.423591	+	0.0185223i
$287$	0.427269			0.0252209
$288$	−15.7872	−	9.11476i	−0.930271	−	0.537092i
$289$	−13.1113	+	22.7094i	−0.771250	+	1.33584i
$290$		0			0
$291$			17.1879i			1.00757i
$292$	−22.6711	+	13.0892i	−1.32673	+	0.765986i
$293$	−23.5400	+	13.5908i	−1.37522	+	0.793984i	−0.991580	−	0.129498i	$-0.958663\pi$
$293$	−23.5400	+	13.5908i	−1.37522	+	0.793984i	−0.383641	+	0.923482i	$0.625330\pi$
$294$			11.0050i			0.641822i
$295$		0			0
$296$	9.17555	−	15.8925i	0.533318	−	0.923734i
$297$	−1.05881	−	0.611305i	−0.0614385	−	0.0354715i
$298$	5.41881			0.313903
$299$	1.11649	+	2.14510i	0.0645681	+	0.124054i
$300$		0			0
$301$	−0.512421	−	0.295846i	−0.0295355	−	0.0170523i
$302$	−4.33494	+	7.50833i	−0.249448	+	0.432056i
$303$	−17.1778	−	29.7528i	−0.986838	−	1.70925i
$304$			9.21542i			0.528541i
$305$		0			0
$306$	12.0020	−	6.92935i	0.686108	−	0.396125i
$307$			15.4630i			0.882522i	0.897379	+	0.441261i	$0.145469\pi$
$307$			15.4630i			0.882522i	−0.897379	+	0.441261i	$0.854531\pi$
$308$	−1.36566	−	2.36538i	−0.0778154	−	0.134780i
$309$	−5.48820	+	9.50584i	−0.312213	+	0.540768i
$310$		0			0
$311$	−8.50072			−0.482032			−0.241016	−	0.970521i	$-0.577481\pi$
$311$	−8.50072			−0.482032			−0.241016	+	0.970521i	$0.577481\pi$
$312$	−18.8102	+	9.79038i	−1.06492	+	0.554271i
$313$	−4.81358			−0.272080			−0.136040	−	0.990703i	$-0.543438\pi$
$313$	−4.81358			−0.272080			−0.136040	+	0.990703i	$0.543438\pi$
$314$	7.10504	+	4.10209i	0.400960	+	0.231495i
$315$		0			0
$316$	−11.7397	−	20.3337i	−0.660408	−	1.14386i
$317$			3.35387i			0.188372i	0.995555	+	0.0941860i	$0.0300248\pi$
$317$			3.35387i			0.188372i	−0.995555	+	0.0941860i	$0.969975\pi$
$318$	−7.08152	+	4.08852i	−0.397112	+	0.229273i
$319$	−20.4083	+	11.7827i	−1.14264	+	0.659706i
$320$		0			0
$321$	3.36028	+	5.82017i	0.187552	+	0.324850i
$322$	−0.131279	+	0.227382i	−0.00731589	+	0.0126715i
$323$	−34.1798	−	19.7337i	−1.90182	−	1.09801i
$324$	−13.1951			−0.733060
$325$		0			0
$326$	1.42122			0.0787141
$327$	24.3553	+	14.0616i	1.34685	+	0.777606i
$328$	0.860987	−	1.49127i	0.0475400	−	0.0823418i
$329$	−0.927533	−	1.60653i	−0.0511365	−	0.0885711i
$330$		0			0
$331$	−17.8085	+	10.2817i	−0.978842	+	0.565135i	−0.901920	−	0.431902i	$-0.857843\pi$
$331$	−17.8085	+	10.2817i	−0.978842	+	0.565135i	−0.0769218	+	0.997037i	$0.524509\pi$
$332$	0.499486	−	0.288378i	0.0274129	−	0.0158268i
$333$			24.5194i			1.34366i
$334$	−0.0364614	−	0.0631531i	−0.00199508	−	0.00345558i
$335$		0			0
$336$	1.94005	+	1.12009i	0.105838	+	0.0611059i
$337$	15.3344			0.835316			0.417658	−	0.908604i	$-0.362851\pi$
$337$	15.3344			0.835316			0.417658	+	0.908604i	$0.362851\pi$
$338$	−0.755785	+	8.62558i	−0.0411093	+	0.469170i
$339$	−6.22988			−0.338361
$340$		0			0
$341$	−6.77378	+	11.7325i	−0.366821	+	0.635352i
$342$	6.32735	+	10.9593i	0.342144	+	0.592611i
$343$		−	8.02539i		−	0.433330i
$344$	−2.06515	+	1.19232i	−0.111346	+	0.0642854i
$345$		0			0
$346$		−	5.46116i		−	0.293594i
$347$	−7.52585	−	13.0352i	−0.404009	−	0.699764i	0.590197	−	0.807260i	$-0.299050\pi$
$347$	−7.52585	−	13.0352i	−0.404009	−	0.699764i	−0.994206	+	0.107495i	$0.965717\pi$
$348$	15.2496	−	26.4130i	0.817463	−	1.41589i
$349$	26.8768	+	15.5173i	1.43868	+	0.830623i	0.997758	−	0.0669222i	$-0.0213179\pi$
$349$	26.8768	+	15.5173i	1.43868	+	0.830623i	0.440923	+	0.897545i	$0.354651\pi$
$350$		0			0
$351$	0.793330	−	1.24510i	0.0423448	−	0.0664584i
$352$	−17.1981			−0.916661
$353$	24.7048	+	14.2633i	1.31491	+	0.759161i	0.982904	−	0.184118i	$-0.0589427\pi$
$353$	24.7048	+	14.2633i	1.31491	+	0.759161i	0.332002	+	0.943279i	$0.392276\pi$
$354$	−11.8040	+	20.4452i	−0.627378	+	1.08665i
$355$		0			0
$356$			14.3775i			0.762005i
$357$	−8.30879	+	4.79708i	−0.439748	+	0.253888i
$358$	0.0173718	−	0.0100296i	0.000918131	−	0.000530083i
$359$		−	16.4735i		−	0.869437i	−0.900566	−	0.434718i	$-0.856848\pi$
$359$		−	16.4735i		−	0.869437i	0.900566	−	0.434718i	$-0.143152\pi$
$360$		0			0
$361$	8.51935	−	14.7559i	0.448387	−	0.776628i
$362$	−6.58072	−	3.79938i	−0.345875	−	0.199691i
$363$	5.17625			0.271683
$364$	2.92563	−	1.52274i	0.153345	−	0.0798134i
$365$		0			0
$366$	11.5453	+	6.66571i	0.603485	+	0.348422i
$367$	1.88471	−	3.26441i	0.0983809	−	0.170401i	−0.812634	−	0.582775i	$-0.801967\pi$
$367$	1.88471	−	3.26441i	0.0983809	−	0.170401i	0.911015	+	0.412374i	$0.135300\pi$
$368$	−0.514792	−	0.891646i	−0.0268354	−	0.0464803i
$369$			2.30078i			0.119774i
$370$		0			0
$371$	2.51678	−	1.45306i	0.130665	−	0.0754394i
$372$		−	17.5337i		−	0.909080i
$373$	6.63155	+	11.4862i	0.343368	+	0.594732i	0.985056	−	0.172235i	$-0.0550987\pi$
$373$	6.63155	+	11.4862i	0.343368	+	0.594732i	−0.641688	+	0.766966i	$0.721765\pi$
$374$	6.53729	−	11.3229i	0.338035	−	0.585494i
$375$		0			0
$376$	−7.47626			−0.385559
$377$	−13.1381	−	25.2420i	−0.676644	−	1.30003i
$378$	0.160293			0.00824459
$379$	19.0442	+	10.9952i	0.978235	+	0.564784i	0.901737	−	0.432285i	$-0.142293\pi$
$379$	19.0442	+	10.9952i	0.978235	+	0.564784i	0.0764985	+	0.997070i	$0.475626\pi$
$380$		0			0
$381$	−7.46212	−	12.9248i	−0.382296	−	0.662156i
$382$		−	3.55404i		−	0.181841i
$383$	19.6380	−	11.3380i	1.00345	−	0.579344i	0.0941845	−	0.995555i	$-0.469976\pi$
$383$	19.6380	−	11.3380i	1.00345	−	0.579344i	0.909268	+	0.416211i	$0.136642\pi$
$384$	23.6733	−	13.6678i	1.20807	−	0.697481i
$385$		0			0
$386$	−3.53823	−	6.12839i	−0.180091	−	0.311927i
$387$	1.59309	−	2.75931i	0.0809812	−	0.140264i
$388$	−9.33053	−	5.38698i	−0.473686	−	0.273483i
$389$	−18.3322			−0.929480			−0.464740	−	0.885447i	$-0.653852\pi$
$389$	−18.3322			−0.929480			−0.464740	+	0.885447i	$0.653852\pi$
$390$		0			0
$391$	4.40947			0.222996
$392$	−13.6510	−	7.88139i	−0.689478	−	0.398070i
$393$	−1.38569	+	2.40009i	−0.0698991	+	0.121069i
$394$	1.88011	+	3.25644i	0.0947184	+	0.164057i
$395$		0			0
$396$	12.7372	−	7.35385i	0.640070	−	0.369545i
$397$	4.63902	−	2.67834i	0.232826	−	0.134422i	−0.379049	−	0.925377i	$-0.623749\pi$
$397$	4.63902	−	2.67834i	0.232826	−	0.134422i	0.611875	+	0.790954i	$0.290416\pi$
$398$		−	10.3861i		−	0.520607i
$399$	−4.38033	−	7.58695i	−0.219291	−	0.379822i
$400$		0			0
$401$	9.93714	+	5.73721i	0.496237	+	0.286503i	0.727158	−	0.686470i	$-0.240841\pi$
$401$	9.93714	+	5.73721i	0.496237	+	0.286503i	−0.230921	+	0.972972i	$0.574174\pi$
$402$	1.05289			0.0525134
$403$	−13.7968	−	8.79078i	−0.687265	−	0.437900i
$404$	21.5352			1.07142
$405$		0			0
$406$	1.54480	−	2.67568i	0.0766672	−	0.132792i
$407$	11.5661	+	20.0330i	0.573308	+	0.992999i
$408$			38.6663i			1.91427i
$409$	−15.0683	+	8.69969i	−0.745080	+	0.430172i	−0.823913	−	0.566716i	$-0.808214\pi$
$409$	−15.0683	+	8.69969i	−0.745080	+	0.430172i	0.0788336	+	0.996888i	$0.474880\pi$
$410$		0			0
$411$			48.8912i			2.41163i
$412$	−3.44019	−	5.95858i	−0.169486	−	0.293558i
$413$	4.19518	−	7.26626i	0.206431	−	0.357549i
$414$	−1.22442	−	0.706918i	−0.0601768	−	0.0347431i
$415$		0			0
$416$	0.907233	−	20.7477i	0.0444808	−	1.01724i
$417$	24.5073			1.20013
$418$	10.3392	+	5.96935i	0.505708	+	0.291970i
$419$	11.2389	−	19.4664i	0.549058	−	0.950996i	−0.449282	−	0.893390i	$-0.648320\pi$
$419$	11.2389	−	19.4664i	0.549058	−	0.950996i	0.998339	−	0.0576056i	$-0.0183466\pi$
$420$		0			0
$421$		−	5.16889i		−	0.251916i	−0.992036	−	0.125958i	$-0.959799\pi$
$421$		−	5.16889i		−	0.251916i	0.992036	−	0.125958i	$-0.0402005\pi$
$422$	9.76749	−	5.63926i	0.475474	−	0.274515i
$423$	8.65094	−	4.99462i	0.420623	−	0.242847i
$424$		−	11.7122i		−	0.568797i
$425$		0			0
$426$	−7.44720	+	12.8989i	−0.360818	+	0.624955i
$427$	−4.10324	−	2.36900i	−0.198569	−	0.114644i
$428$	−4.21267			−0.203627
$429$	1.16771	−	26.7047i	0.0563777	−	1.28931i
$430$		0			0
$431$	−22.7964	−	13.1615i	−1.09806	−	0.633968i	−0.162352	−	0.986733i	$-0.551908\pi$
$431$	−22.7964	−	13.1615i	−1.09806	−	0.633968i	−0.935712	+	0.352765i	$0.885241\pi$
$432$	−0.314284	+	0.544355i	−0.0151210	+	0.0261903i
$433$	9.45546	+	16.3773i	0.454401	+	0.787045i	0.998654	−	0.0518762i	$-0.0165201\pi$
$433$	9.45546	+	16.3773i	0.454401	+	0.787045i	−0.544253	+	0.838921i	$0.683187\pi$
$434$		−	1.77619i		−	0.0852596i
$435$		0			0
$436$	−15.2667	+	8.81425i	−0.731144	+	0.422126i
$437$			4.02639i			0.192608i
$438$	−13.9080	−	24.0894i	−0.664552	−	1.15104i
$439$	13.7455	−	23.8079i	0.656037	−	1.13629i	−0.325596	−	0.945509i	$-0.605565\pi$
$439$	13.7455	−	23.8079i	0.656037	−	1.13629i	0.981633	−	0.190780i	$-0.0611018\pi$
$440$		0			0
$441$	21.0611			1.00291
$442$	13.3151	+	8.48386i	0.633333	+	0.403536i
$443$	19.2846			0.916240			0.458120	−	0.888890i	$-0.348523\pi$
$443$	19.2846			0.916240			0.458120	+	0.888890i	$0.348523\pi$
$444$	−25.9274	−	14.9692i	−1.23046	−	0.710405i
$445$		0			0
$446$	5.47138	+	9.47672i	0.259078	+	0.448735i
$447$		−	20.2005i		−	0.955450i
$448$	0.389996	−	0.225164i	0.0184256	−	0.0106380i
$449$	5.66090	−	3.26832i	0.267154	−	0.154242i	−0.360439	−	0.932783i	$-0.617373\pi$
$449$	5.66090	−	3.26832i	0.267154	−	0.154242i	0.627594	+	0.778541i	$0.284040\pi$
$450$		0			0
$451$	1.08530	+	1.87979i	0.0511048	+	0.0885161i
$452$	1.95255	−	3.38191i	0.0918401	−	0.159072i
$453$	27.9899	+	16.1600i	1.31508	+	0.759262i
$454$	−11.4862			−0.539072
$455$		0			0
$456$	−35.3071			−1.65341
$457$	12.4763	+	7.20317i	0.583614	+	0.336950i	0.762569	−	0.646907i	$-0.223938\pi$
$457$	12.4763	+	7.20317i	0.583614	+	0.336950i	−0.178954	+	0.983857i	$0.557271\pi$
$458$	−3.35717	+	5.81478i	−0.156870	+	0.271707i
$459$	−1.34600	−	2.33135i	−0.0628260	−	0.108818i
$460$		0			0
$461$	11.4829	−	6.62968i	0.534814	−	0.308775i	−0.208161	−	0.978095i	$-0.566748\pi$
$461$	11.4829	−	6.62968i	0.534814	−	0.308775i	0.742975	+	0.669320i	$0.233414\pi$
$462$	2.51336	−	1.45109i	0.116932	−	0.0675108i
$463$		−	18.8671i		−	0.876827i	−0.898773	−	0.438413i	$-0.855541\pi$
$463$		−	18.8671i		−	0.876827i	0.898773	−	0.438413i	$-0.144459\pi$
$464$	6.05772	+	10.4923i	0.281223	+	0.487092i
$465$		0			0
$466$	−11.3692	−	6.56400i	−0.526667	−	0.304072i
$467$	−21.8870			−1.01281			−0.506406	−	0.862295i	$-0.669026\pi$
$467$	−21.8870			−1.01281			−0.506406	+	0.862295i	$0.669026\pi$
$468$	8.19974	+	15.7541i	0.379033	+	0.728233i
$469$	−0.374199			−0.0172789
$470$		0			0
$471$	15.2920	−	26.4865i	0.704617	−	1.22043i
$472$	−16.9073	−	29.2844i	−0.778224	−	1.34792i
$473$		−	3.00590i		−	0.138212i
$474$	21.6058	−	12.4741i	0.992386	−	0.572954i
$475$		0			0
$476$		−	6.01394i		−	0.275648i
$477$	7.82453	+	13.5525i	0.358261	+	0.620526i
$478$	−3.74224	+	6.48175i	−0.171166	+	0.296468i
$479$	−24.3402	−	14.0528i	−1.11213	−	0.642089i	−0.172751	−	0.984966i	$-0.555266\pi$
$479$	−24.3402	−	14.0528i	−1.11213	−	0.642089i	−0.939381	+	0.342876i	$0.888599\pi$
$480$		0			0
$481$	−24.7779	+	12.8965i	−1.12977	+	0.588028i
$482$	−2.49689			−0.113730
$483$	0.847645	+	0.489388i	0.0385692	+	0.0222679i
$484$	−1.62232	+	2.80995i	−0.0737420	+	0.127725i
$485$		0			0
$486$		−	14.8387i		−	0.673099i
$487$	−15.8678	+	9.16127i	−0.719038	+	0.415137i	−0.814398	−	0.580306i	$-0.802933\pi$
$487$	−15.8678	+	9.16127i	−0.719038	+	0.415137i	0.0953608	+	0.995443i	$0.469600\pi$
$488$	−16.5368	+	9.54753i	−0.748586	+	0.432196i
$489$		−	5.29809i		−	0.239588i
$490$		0			0
$491$	10.8603	−	18.8106i	0.490118	−	0.848908i	−0.509818	−	0.860282i	$-0.670287\pi$
$491$	10.8603	−	18.8106i	0.490118	−	0.848908i	0.999935	+	0.0113739i	$0.00362052\pi$
$492$	−2.43289	−	1.40463i	−0.109683	−	0.0633256i
$493$	−51.8876			−2.33690
$494$	−7.74681	+	12.1583i	−0.348546	+	0.547028i
$495$		0			0
$496$	6.03192	+	3.48253i	0.270841	+	0.156370i
$497$	2.64675	−	4.58430i	0.118723	−	0.205634i
$498$	0.306419	+	0.530734i	0.0137310	+	0.0237828i
$499$		−	14.7418i		−	0.659933i	−0.943993	−	0.329966i	$-0.892963\pi$
$499$		−	14.7418i		−	0.659933i	0.943993	−	0.329966i	$-0.107037\pi$
$500$		0			0
$501$	−0.235425	+	0.135923i	−0.0105180	+	0.00607257i
$502$		−	13.5703i		−	0.605670i
$503$	18.5694	+	32.1631i	0.827969	+	1.43408i	0.899629	+	0.436655i	$0.143837\pi$
$503$	18.5694	+	32.1631i	0.827969	+	1.43408i	−0.0716604	+	0.997429i	$0.522830\pi$
$504$	−2.20310	+	3.81588i	−0.0981338	+	0.169973i
$505$		0			0
$506$	−1.33384			−0.0592964
$507$	32.1548	+	2.81745i	1.42805	+	0.125127i
$508$	9.35501			0.415062
$509$	−11.0110	−	6.35722i	−0.488055	−	0.281779i	0.235712	−	0.971823i	$-0.424258\pi$
$509$	−11.0110	−	6.35722i	−0.488055	−	0.281779i	−0.723767	+	0.690044i	$0.757591\pi$
$510$		0			0
$511$	4.94294	+	8.56142i	0.218663	+	0.378735i
$512$			16.1142i			0.712154i
$513$	2.12881	−	1.22907i	0.0939891	−	0.0542646i
$514$	8.28139	−	4.78126i	0.365276	−	0.210892i
$515$		0			0
$516$	1.94517	+	3.36913i	0.0856312	+	0.148318i
$517$	4.71203	−	8.16147i	0.207235	−	0.358941i
$518$	−2.62647	−	1.51640i	−0.115401	−	0.0666266i
$519$	−20.3584			−0.893634
$520$		0			0
$521$	34.3347			1.50423			0.752116	−	0.659031i	$-0.229033\pi$
$521$	34.3347			1.50423			0.752116	+	0.659031i	$0.229033\pi$
$522$	14.4081	+	8.31852i	0.630626	+	0.364092i
$523$	−11.9219	+	20.6494i	−0.521309	+	0.902934i	0.478384	+	0.878151i	$0.341223\pi$
$523$	−11.9219	+	20.6494i	−0.521309	+	0.902934i	−0.999693	+	0.0247827i	$0.992111\pi$
$524$	−0.868600	−	1.50446i	−0.0379450	−	0.0657226i
$525$		0			0
$526$	−15.4250	+	8.90565i	−0.672564	+	0.388305i
$527$	−25.8333	+	14.9149i	−1.12532	+	0.649702i
$528$			11.3805i			0.495272i
$529$	11.2751	+	19.5290i	0.490221	+	0.849087i
$530$		0			0
$531$	39.1277	+	22.5904i	1.69800	+	0.980339i
$532$	5.49147			0.238085
$533$	−2.32503	+	1.21014i	−0.100708	+	0.0524169i
$534$	−15.2769			−0.661098
$535$		0			0
$536$	−0.754046	+	1.30605i	−0.0325698	+	0.0564126i
$537$	−0.0373890	−	0.0647596i	−0.00161345	−	0.00279458i
$538$			0.286523i			0.0123529i
$539$	17.2075	−	9.93473i	0.741178	−	0.427919i
$540$		0			0
$541$		−	16.3426i		−	0.702624i	−0.936258	−	0.351312i	$-0.885736\pi$
$541$		−	16.3426i		−	0.702624i	0.936258	−	0.351312i	$-0.114264\pi$
$542$	−3.91728	−	6.78492i	−0.168261	−	0.291437i
$543$	−14.1635	+	24.5319i	−0.607814	+	1.05277i
$544$	−32.7943	−	18.9338i	−1.40605	−	0.811781i
$545$		0			0
$546$	1.61801	+	3.10866i	0.0692442	+	0.133038i
$547$	3.13542			0.134061			0.0670305	−	0.997751i	$-0.478648\pi$
$547$	3.13542			0.134061			0.0670305	+	0.997751i	$0.478648\pi$
$548$	−26.5408	−	15.3233i	−1.13377	−	0.654580i
$549$	12.7567	−	22.0953i	0.544444	−	0.943004i
$550$		0			0
$551$		−	47.3798i		−	2.01845i
$552$	3.41617	−	1.97233i	0.145402	−	0.0839477i
$553$	−7.67873	+	4.43331i	−0.326533	+	0.188524i
$554$			2.64812i			0.112508i
$555$		0			0
$556$	−7.68101	+	13.3039i	−0.325747	+	0.564211i
$557$	−20.4120	−	11.7849i	−0.864883	−	0.499341i	0.000761144	−	1.00000i	$-0.499758\pi$
$557$	−20.4120	−	11.7849i	−0.864883	−	0.499341i	−0.865645	+	0.500659i	$0.833091\pi$
$558$	9.56449			0.404897
$559$	3.62631	+	0.158567i	0.153377	+	0.00670668i
$560$		0			0
$561$	−42.2101	−	24.3700i	−1.78211	−	1.02890i
$562$	−5.77022	+	9.99432i	−0.243402	+	0.421585i
$563$	−7.30716	−	12.6564i	−0.307960	−	0.533402i	0.669956	−	0.742401i	$-0.266313\pi$
$563$	−7.30716	−	12.6564i	−0.307960	−	0.533402i	−0.977916	+	0.208999i	$0.932980\pi$
$564$			12.1969i			0.513583i
$565$		0			0
$566$	5.19974	−	3.00207i	0.218561	−	0.126187i
$567$			4.98293i			0.209263i
$568$	−10.6669	−	18.4756i	−0.447573	−	0.775218i
$569$	−8.80300	+	15.2472i	−0.369041	+	0.639198i	−0.989416	−	0.145108i	$-0.953647\pi$
$569$	−8.80300	+	15.2472i	−0.369041	+	0.639198i	0.620375	+	0.784305i	$0.286980\pi$
$570$		0			0
$571$	−3.82424			−0.160039			−0.0800197	−	0.996793i	$-0.525498\pi$
$571$	−3.82424			−0.160039			−0.0800197	+	0.996793i	$0.525498\pi$
$572$	14.1308	+	9.00359i	0.590836	+	0.376459i
$573$	−13.2489			−0.553482
$574$	−0.246455	−	0.142291i	−0.0102868	−	0.00593910i
$575$		0			0
$576$	1.21247	+	2.10007i	0.0505198	+	0.0875028i
$577$		−	6.37523i		−	0.265405i	−0.991156	−	0.132702i	$-0.957635\pi$
$577$		−	6.37523i		−	0.265405i	0.991156	−	0.132702i	$-0.0423654\pi$
$578$	15.1255	−	8.73273i	0.629139	−	0.363234i
$579$	−22.8457	+	13.1900i	−0.949435	+	0.548156i
$580$		0			0
$581$	−0.108902	−	0.188624i	−0.00451801	−	0.00782543i
$582$	5.72399	−	9.91424i	0.237267	−	0.410959i
$583$	12.7857	+	7.38182i	0.529529	+	0.305724i
$584$	39.8419			1.64867
$585$		0			0
$586$	18.1043			0.747881
$587$	−40.9293	−	23.6306i	−1.68933	−	0.975338i	−0.955026	−	0.296522i	$-0.904173\pi$
$587$	−40.9293	−	23.6306i	−1.68933	−	0.975338i	−0.734308	−	0.678816i	$-0.762493\pi$
$588$	−12.8578	+	22.2704i	−0.530249	+	0.918418i
$589$	−13.6191	−	23.5890i	−0.561166	−	0.971967i
$590$		0			0
$591$	12.1395	−	7.00875i	0.499353	−	0.288301i
$592$	10.2993	−	5.94633i	0.423301	−	0.244393i
$593$			6.35373i			0.260916i	0.991454	+	0.130458i	$0.0416448\pi$
$593$			6.35373i			0.260916i	−0.991454	+	0.130458i	$0.958355\pi$
$594$	0.407159	+	0.705219i	0.0167059	+	0.0289355i
$595$		0			0
$596$	10.9659	+	6.33117i	0.449181	+	0.259335i
$597$	−38.7177			−1.58461
$598$	0.0703627	−	1.60914i	0.00287735	−	0.0658026i
$599$	43.2542			1.76732			0.883658	−	0.468132i	$-0.155073\pi$
$599$	43.2542			1.76732			0.883658	+	0.468132i	$0.155073\pi$
$600$		0			0
$601$	2.89558	−	5.01529i	0.118113	−	0.204578i	−0.800907	−	0.598789i	$-0.795649\pi$
$601$	2.89558	−	5.01529i	0.118113	−	0.204578i	0.919020	+	0.394211i	$0.128982\pi$
$602$	0.197048	+	0.341297i	0.00803107	+	0.0139102i
$603$		−	2.01500i		−	0.0820573i
$604$	−17.5450	+	10.1296i	−0.713896	+	0.412168i
$605$		0			0
$606$			22.8825i			0.929537i
$607$	−11.6175	−	20.1221i	−0.471540	−	0.816731i	0.527930	−	0.849288i	$-0.322968\pi$
$607$	−11.6175	−	20.1221i	−0.471540	−	0.816731i	−0.999470	+	0.0325569i	$0.989635\pi$
$608$	17.2889	−	29.9453i	0.701158	−	1.21444i
$609$	−9.97450	−	5.75878i	−0.404187	−	0.233358i
$610$		0			0
$611$	9.59739	+	6.11510i	0.388269	+	0.247391i
$612$	32.3842			1.30905
$613$	20.1997	+	11.6623i	0.815857	+	0.471035i	0.848986	−	0.528416i	$-0.177214\pi$
$613$	20.1997	+	11.6623i	0.815857	+	0.471035i	−0.0331286	+	0.999451i	$0.510547\pi$
$614$	5.14956	−	8.91930i	0.207819	−	0.359954i
$615$		0			0
$616$			4.15690i			0.167486i
$617$	15.8269	−	9.13768i	0.637168	−	0.367869i	−0.146355	−	0.989232i	$-0.546754\pi$
$617$	15.8269	−	9.13768i	0.637168	−	0.367869i	0.783523	+	0.621363i	$0.213421\pi$
$618$	6.33135	−	3.65540i	0.254684	−	0.147042i
$619$			45.4589i			1.82715i	0.406675	+	0.913573i	$0.366688\pi$
$619$			45.4589i			1.82715i	−0.406675	+	0.913573i	$0.633312\pi$
$620$		0			0
$621$	−0.137316	+	0.237839i	−0.00551032	+	0.00954415i
$622$	4.90334	+	2.83095i	0.196606	+	0.113511i
$623$	5.42945			0.217526
$624$	−13.7294	−	0.600344i	−0.549615	−	0.0240330i
$625$		0			0
$626$	2.77654	+	1.60304i	0.110973	+	0.0640703i
$627$	22.2528	−	38.5430i	0.888692	−	1.53926i
$628$	9.58552	+	16.6026i	0.382504	+	0.662516i
$629$			50.9335i			2.03085i
$630$		0			0
$631$	−33.5920	+	19.3944i	−1.33728	+	0.772077i	−0.986403	−	0.164346i	$-0.947449\pi$
$631$	−33.5920	+	19.3944i	−1.33728	+	0.772077i	−0.350874	+	0.936423i	$0.614115\pi$
$632$			35.7342i			1.42143i
$633$	−21.0223	−	36.4117i	−0.835561	−	1.44723i
$634$	1.11692	−	1.93456i	0.0443585	−	0.0768312i
$635$		0			0
$636$	−19.1076			−0.757665
$637$	11.0775	+	21.2831i	0.438906	+	0.843267i
$638$	15.6957			0.621400
$639$	24.6858	+	14.2523i	0.976553	+	0.563813i
$640$		0			0
$641$	10.4454	+	18.0920i	0.412569	+	0.714591i	0.995170	−	0.0981679i	$-0.0312982\pi$
$641$	10.4454	+	18.0920i	0.412569	+	0.714591i	−0.582601	+	0.812758i	$0.697965\pi$
$642$		−	4.47621i		−	0.176662i
$643$	1.24581	−	0.719272i	0.0491301	−	0.0283653i	−0.475234	−	0.879860i	$-0.657636\pi$
$643$	1.24581	−	0.719272i	0.0491301	−	0.0283653i	0.524364	+	0.851494i	$0.324303\pi$
$644$	−0.531332	+	0.306765i	−0.0209374	+	0.0120882i
$645$		0			0
$646$	13.1436	+	22.7654i	0.517129	+	0.895694i
$647$	−24.0711	+	41.6923i	−0.946331	+	1.63909i	−0.193268	+	0.981146i	$0.561909\pi$
$647$	−24.0711	+	41.6923i	−0.946331	+	1.63909i	−0.753063	+	0.657948i	$0.771425\pi$
$648$	17.3917	+	10.0411i	0.683209	+	0.394451i
$649$	42.6244			1.67316
$650$		0			0
$651$	−6.62134			−0.259511
$652$	2.87609	+	1.66051i	0.112636	+	0.0650305i
$653$	18.7787	−	32.5257i	0.734869	−	1.27283i	−0.219911	−	0.975520i	$-0.570577\pi$
$653$	18.7787	−	32.5257i	0.734869	−	1.27283i	0.954781	−	0.297311i	$-0.0960898\pi$
$654$	−9.36567	−	16.2218i	−0.366227	−	0.634323i
$655$		0			0
$656$	0.966438	−	0.557973i	0.0377331	−	0.0217852i
$657$	−46.1020	+	26.6170i	−1.79861	+	1.03843i
$658$			1.23556i			0.0481672i
$659$	6.65871	+	11.5332i	0.259387	+	0.449271i	0.966078	−	0.258251i	$-0.0831463\pi$
$659$	6.65871	+	11.5332i	0.259387	+	0.449271i	−0.706691	+	0.707522i	$0.749813\pi$
$660$		0			0
$661$	−32.4052	−	18.7091i	−1.26041	−	0.727701i	−0.287260	−	0.957853i	$-0.592744\pi$
$661$	−32.4052	−	18.7091i	−1.26041	−	0.727701i	−0.973155	+	0.230152i	$0.926078\pi$
$662$	13.6962			0.532320
$663$	31.6265	−	49.6365i	1.22827	−	1.92772i
$664$	−0.877790			−0.0340649
$665$		0			0
$666$	8.16556	−	14.1432i	0.316409	−	0.548036i
$667$	2.64673	+	4.58427i	0.102482	+	0.177504i
$668$		−	0.170402i		−	0.00659304i
$669$	35.3277	−	20.3965i	1.36585	−	0.788573i
$670$		0			0
$671$		−	24.0699i		−	0.929208i
$672$	−4.20276	−	7.27940i	−0.162125	−	0.280809i
$673$	23.7113	−	41.0691i	0.914002	−	1.58310i	0.105647	−	0.994404i	$-0.466309\pi$
$673$	23.7113	−	41.0691i	0.914002	−	1.58310i	0.808356	−	0.588695i	$-0.200358\pi$
$674$	−8.84509	−	5.10671i	−0.340700	−	0.196703i
$675$		0			0
$676$	−11.6073	+	16.5723i	−0.446435	+	0.637397i
$677$	−5.91735			−0.227422			−0.113711	−	0.993514i	$-0.536274\pi$
$677$	−5.91735			−0.227422			−0.113711	+	0.993514i	$0.536274\pi$
$678$	3.59348	+	2.07470i	0.138007	+	0.0796783i
$679$	−2.03432	+	3.52354i	−0.0780699	+	0.135221i
$680$		0			0
$681$			42.8186i			1.64081i
$682$	7.81443	−	4.51166i	0.299230	−	0.172761i
$683$	12.9911	−	7.50043i	0.497092	−	0.286996i	−0.230420	−	0.973091i	$-0.574010\pi$
$683$	12.9911	−	7.50043i	0.497092	−	0.286996i	0.727512	+	0.686095i	$0.240677\pi$
$684$			29.5707i			1.13067i
$685$		0			0
$686$	−2.67265	+	4.62916i	−0.102042	+	0.176742i
$687$	21.6766	+	12.5150i	0.827014	+	0.477477i
$688$	−1.54539			−0.0589175
$689$	−9.57987	+	15.0352i	−0.364964	+	0.572795i
$690$		0			0
$691$	28.2700	+	16.3217i	1.07544	+	0.620907i	0.929663	−	0.368410i	$-0.120098\pi$
$691$	28.2700	+	16.3217i	1.07544	+	0.620907i	0.145779	+	0.989317i	$0.453431\pi$
$692$	6.38066	−	11.0516i	0.242556	−	0.420120i
$693$	−2.77707	−	4.81003i	−0.105492	−	0.182718i
$694$			10.0252i			0.380550i
$695$		0			0
$696$	−40.1991	+	23.2090i	−1.52374	+	0.879734i
$697$			4.77934i			0.181030i
$698$	−10.3353	−	17.9012i	−0.391196	−	0.677571i
$699$	−24.4696	+	42.3826i	−0.925525	+	1.60306i
$700$		0			0
$701$	−7.83225			−0.295820			−0.147910	−	0.989001i	$-0.547255\pi$
$701$	−7.83225			−0.295820			−0.147910	+	0.989001i	$0.547255\pi$
$702$	−0.872252	+	0.453993i	−0.0329210	+	0.0171349i
$703$	−46.5086			−1.75410
$704$	1.98125	+	1.14387i	0.0746710	+	0.0431113i
$705$		0			0
$706$	−9.50007	−	16.4546i	−0.357540	−	0.619277i
$707$		−	8.13246i		−	0.305853i
$708$	−47.7751	+	27.5830i	−1.79550	+	1.03663i
$709$	27.3294	−	15.7786i	1.02638	−	0.592580i	0.110433	−	0.993884i	$-0.464776\pi$
$709$	27.3294	−	15.7786i	1.02638	−	0.592580i	0.915945	+	0.401304i	$0.131443\pi$
$710$		0			0
$711$	−23.8727	−	41.3488i	−0.895297	−	1.55070i
$712$	10.9408	−	18.9501i	0.410026	−	0.710185i
$713$	2.63546	+	1.52158i	0.0986987	+	0.0569837i
$714$	6.39017			0.239146
$715$		0			0
$716$	0.0468733			0.00175174
$717$	24.1630	+	13.9505i	0.902383	+	0.520991i
$718$	−5.48606	+	9.50214i	−0.204738	+	0.354617i
$719$	−8.91325	−	15.4382i	−0.332408	−	0.575748i	0.650575	−	0.759442i	$-0.274528\pi$
$719$	−8.91325	−	15.4382i	−0.332408	−	0.575748i	−0.982984	+	0.183694i	$0.941195\pi$
$720$		0			0
$721$	−2.25017	+	1.29914i	−0.0838007	+	0.0483824i
$722$	−9.82816	+	5.67429i	−0.365766	+	0.211175i
$723$			9.30803i			0.346169i
$724$	−8.87816	−	15.3774i	−0.329954	−	0.571498i
$725$		0			0
$726$	−2.98574	−	1.72382i	−0.110811	−	0.0639768i
$727$	4.62813			0.171648			0.0858240	−	0.996310i	$-0.472648\pi$
$727$	4.62813			0.171648			0.0858240	+	0.996310i	$0.472648\pi$
$728$	−5.01486	−	0.219285i	−0.185863	−	0.00812722i
$729$	−29.8824			−1.10675
$730$		0			0
$731$	3.30928	−	5.73183i	0.122398	−	0.211999i
$732$	15.5760	+	26.9785i	0.575706	+	0.997152i
$733$		−	9.92820i		−	0.366706i	−0.983047	−	0.183353i	$-0.941305\pi$
$733$		−	9.92820i		−	0.366706i	0.983047	−	0.183353i	$-0.0586952\pi$
$734$	−2.17425	+	1.25531i	−0.0802531	+	0.0463342i
$735$		0			0
$736$			3.86318i			0.142399i
$737$	−0.950497	−	1.64631i	−0.0350120	−	0.0606426i
$738$	0.766214	−	1.32712i	0.0282047	−	0.0488520i
$739$	−24.7225	−	14.2735i	−0.909432	−	0.525061i	−0.0291834	−	0.999574i	$-0.509291\pi$
$739$	−24.7225	−	14.2735i	−0.909432	−	0.525061i	−0.880248	+	0.474513i	$0.842624\pi$
$740$		0			0
$741$	45.3243	+	28.8789i	1.66503	+	1.06089i
$742$	−1.93562			−0.0710589
$743$	20.0170	+	11.5568i	0.734354	+	0.423979i	0.820013	−	0.572345i	$-0.193966\pi$
$743$	20.0170	+	11.5568i	0.734354	+	0.423979i	−0.0856590	+	0.996325i	$0.527300\pi$
$744$	−13.3426	+	23.1101i	−0.489165	+	0.847258i
$745$		0			0
$746$		−	8.83386i		−	0.323430i
$747$	1.01571	−	0.586420i	0.0371629	−	0.0214560i
$748$	26.4587	−	15.2759i	0.967425	−	0.558543i
$749$			1.59085i			0.0581285i
$750$		0			0
$751$	12.8691	−	22.2900i	0.469601	−	0.813372i	−0.529795	−	0.848126i	$-0.677731\pi$
$751$	12.8691	−	22.2900i	0.469601	−	0.813372i	0.999396	+	0.0347534i	$0.0110646\pi$
$752$	−4.19597	−	2.42254i	−0.153011	−	0.0883410i
$753$	−50.5878			−1.84352
$754$	−0.827980	+	18.9353i	−0.0301533	+	0.689581i
$755$		0			0
$756$	0.324381	+	0.187282i	0.0117976	+	0.00681137i
$757$	7.09047	−	12.2811i	0.257708	−	0.446363i	−0.707920	−	0.706293i	$-0.750366\pi$
$757$	7.09047	−	12.2811i	0.257708	−	0.446363i	0.965627	+	0.259930i	$0.0836996\pi$
$758$	−7.32332	−	12.6844i	−0.265995	−	0.460717i
$759$			4.97235i			0.180485i
$760$		0			0
$761$	21.1030	−	12.1838i	0.764983	−	0.441663i	−0.0660987	−	0.997813i	$-0.521055\pi$
$761$	21.1030	−	12.1838i	0.764983	−	0.441663i	0.831082	+	0.556150i	$0.187722\pi$
$762$			9.94026i			0.360098i
$763$	3.32857	+	5.76526i	0.120502	+	0.208716i
$764$	4.15243	−	7.19222i	0.150230	−	0.260206i
$765$		0			0
$766$	−15.1033			−0.545704
$767$	−2.24852	+	51.4220i	−0.0811895	+	1.85674i
$768$	−22.0116			−0.794276
$769$	−10.2768	−	5.93333i	−0.370592	−	0.213961i	0.303125	−	0.952951i	$-0.401970\pi$
$769$	−10.2768	−	5.93333i	−0.370592	−	0.213961i	−0.673717	+	0.738989i	$0.735303\pi$
$770$		0			0
$771$	−17.8238	−	30.8717i	−0.641909	−	1.11182i
$772$		−	16.5358i		−	0.595137i
$773$	−1.52359	+	0.879642i	−0.0547995	+	0.0316385i	−0.527149	−	0.849773i	$-0.676739\pi$
$773$	−1.52359	+	0.879642i	−0.0547995	+	0.0316385i	0.472350	+	0.881411i	$0.343406\pi$
$774$	−1.83783	+	1.06107i	−0.0660595	+	0.0381395i
$775$		0			0
$776$	8.19867	+	14.2005i	0.294315	+	0.509769i
$777$	−5.65289	+	9.79109i	−0.202796	+	0.351253i
$778$	10.5743	+	6.10507i	0.379107	+	0.218877i
$779$	−4.36413			−0.156361
$780$		0			0
$781$	26.8919			0.962266
$782$	−2.54345	−	1.46846i	−0.0909534	−	0.0525120i
$783$	1.61585	−	2.79873i	0.0577456	−	0.100018i
$784$	−5.10763	−	8.84668i	−0.182415	−	0.315953i
$785$		0			0
$786$	1.59858	−	0.922939i	0.0570194	−	0.0329202i
$787$	−27.0347	+	15.6085i	−0.963684	+	0.556383i	−0.897305	−	0.441411i	$-0.854478\pi$
$787$	−27.0347	+	15.6085i	−0.963684	+	0.556383i	−0.0663793	+	0.997794i	$0.521145\pi$
$788$			8.78664i			0.313011i
$789$	33.1989	+	57.5022i	1.18191	+	2.04713i
$790$		0			0
$791$	−1.27713	−	0.737351i	−0.0454095	−	0.0262172i
$792$	−22.3843			−0.795390
$793$	29.0378	+	1.26974i	1.03116	+	0.0450896i
$794$	−3.56781			−0.126617
$795$		0			0
$796$	12.1348	−	21.0180i	0.430106	−	0.744965i
$797$	−1.95382	−	3.38411i	−0.0692077	−	0.119871i	0.829345	−	0.558737i	$-0.188714\pi$
$797$	−1.95382	−	3.38411i	−0.0692077	−	0.119871i	−0.898553	+	0.438866i	$0.855380\pi$
$798$			5.83502i			0.206557i
$799$	17.9703	−	10.3752i	0.635745	−	0.367048i
$800$		0			0
$801$			29.2368i			1.03303i
$802$	−3.82126	−	6.61861i	−0.134933	−	0.233711i
$803$	−25.1110	+	43.4935i	−0.886148	+	1.53485i
$804$	2.13071	+	1.23016i	0.0751442	+	0.0433845i
$805$		0			0
$806$	5.03063	+	9.66530i	0.177196	+	0.340446i
$807$	1.06811			0.0375994
$808$	−28.3843	−	16.3877i	−0.998556	−	0.576517i
$809$	10.0804	−	17.4597i	0.354407	−	0.613851i	−0.632609	−	0.774471i	$-0.718016\pi$
$809$	10.0804	−	17.4597i	0.354407	−	0.613851i	0.987016	+	0.160620i	$0.0513493\pi$
$810$		0			0
$811$			34.1631i			1.19963i	0.800139	+	0.599815i	$0.204759\pi$
$811$			34.1631i			1.19963i	−0.800139	+	0.599815i	$0.795241\pi$
$812$	6.25235	−	3.60980i	0.219415	−	0.126679i
$813$	−25.2931	+	14.6030i	−0.887069	+	0.512150i
$814$		−	15.4071i		−	0.540019i
$815$		0			0
$816$	−12.5291	+	21.7010i	−0.438605	+	0.759687i
$817$	5.23387	+	3.02178i	0.183110	+	0.105719i
$818$	11.5888			0.405194
$819$	5.94930	−	3.09651i	0.207885	−	0.108201i
$820$		0			0
$821$	44.8414	+	25.8892i	1.56497	+	0.903538i	0.996741	+	0.0806706i	$0.0257062\pi$
$821$	44.8414	+	25.8892i	1.56497	+	0.903538i	0.568233	+	0.822868i	$0.307627\pi$
$822$	16.2820	−	28.2012i	0.567899	−	0.983629i
$823$	14.0554	+	24.3447i	0.489941	+	0.848602i	0.999933	−	0.0115767i	$-0.00368507\pi$
$823$	14.0554	+	24.3447i	0.489941	+	0.848602i	−0.509992	+	0.860179i	$0.670352\pi$
$824$			10.4715i			0.364793i
$825$		0			0
$826$	−4.83968	+	2.79419i	−0.168394	+	0.0972223i
$827$			49.5177i			1.72190i	0.508691	+	0.860949i	$0.330130\pi$
$827$			49.5177i			1.72190i	−0.508691	+	0.860949i	$0.669870\pi$
$828$	−1.65188	−	2.86114i	−0.0574068	−	0.0994316i
$829$	−10.8664	+	18.8212i	−0.377406	+	0.653687i	−0.990684	−	0.136180i	$-0.956517\pi$
$829$	−10.8664	+	18.8212i	−0.377406	+	0.653687i	0.613278	+	0.789867i	$0.289851\pi$
$830$		0			0
$831$	9.87177			0.342448
$832$	−1.48448	+	2.32982i	−0.0514650	+	0.0807721i
$833$	43.7496			1.51583
$834$	−14.1362	−	8.16154i	−0.489496	−	0.282611i
$835$		0			0
$836$	13.9488	+	24.1600i	0.482430	+	0.835593i
$837$		−	1.85787i		−	0.0642174i
$838$	−12.9656	+	7.48567i	−0.447888	+	0.258588i
$839$	−31.2115	+	18.0199i	−1.07754	+	0.622118i	−0.930232	−	0.366973i	$-0.880394\pi$
$839$	−31.2115	+	18.0199i	−1.07754	+	0.622118i	−0.147308	+	0.989091i	$0.547061\pi$
$840$		0			0
$841$	−16.6449	−	28.8299i	−0.573963	−	0.994134i
$842$	−1.72137	+	2.98149i	−0.0593222	+	0.102749i
$843$	37.2573	+	21.5105i	1.28321	+	0.740861i
$844$	26.3550			0.907175
$845$		0			0
$846$	−6.65332			−0.228746
$847$	1.06114	+	0.612647i	0.0364611	+	0.0210508i
$848$	3.79513	−	6.57337i	0.130325	−	0.225730i
$849$	−11.1913	−	19.3838i	−0.384083	−	0.665252i
$850$		0			0
$851$	4.49998	−	2.59806i	0.154257	−	0.0890605i
$852$	−30.1414	+	17.4022i	−1.03263	+	0.596188i
$853$		−	38.4465i		−	1.31638i	−0.752851	−	0.658191i	$-0.771322\pi$
$853$		−	38.4465i		−	1.31638i	0.752851	−	0.658191i	$-0.228678\pi$
$854$	1.57787	+	2.73295i	0.0539936	+	0.0935197i
$855$		0			0
$856$	5.55247	+	3.20572i	0.189780	+	0.109569i
$857$	2.31635			0.0791251			0.0395625	−	0.999217i	$-0.487404\pi$
$857$	2.31635			0.0791251			0.0395625	+	0.999217i	$0.487404\pi$
$858$	−9.56685	+	15.0148i	−0.326607	+	0.512596i
$859$	−1.38239			−0.0471667			−0.0235833	−	0.999722i	$-0.507508\pi$
$859$	−1.38239			−0.0471667			−0.0235833	+	0.999722i	$0.507508\pi$
$860$		0			0
$861$	−0.530438	+	0.918746i	−0.0180773	+	0.0313108i
$862$	8.76620	+	15.1835i	0.298578	+	0.517152i
$863$		−	10.5783i		−	0.360091i	−0.983658	−	0.180046i	$-0.942375\pi$
$863$		−	10.5783i		−	0.360091i	0.983658	−	0.180046i	$-0.0576245\pi$
$864$	2.04251	−	1.17925i	0.0694877	−	0.0401187i
$865$		0			0
$866$		−	12.5956i		−	0.428015i
$867$	−32.5543	−	56.3856i	−1.10560	−	1.91496i
$868$	2.07524	−	3.59442i	0.0704382	−	0.122003i
$869$	−39.0093	−	22.5220i	−1.32330	−	0.764007i
$870$		0			0
$871$	2.03624	−	1.05983i	0.0689954	−	0.0359110i
$872$	26.8296			0.908563
$873$	−18.9737	−	10.9545i	−0.642163	−	0.370753i
$874$	1.34088	−	2.32248i	0.0453561	−	0.0785591i
$875$		0			0
$876$		−	64.9989i		−	2.19611i
$877$	16.2742	−	9.39590i	0.549540	−	0.317277i	−0.199397	−	0.979919i	$-0.563898\pi$
$877$	16.2742	−	9.39590i	0.549540	−	0.317277i	0.748936	+	0.662642i	$0.230565\pi$
$878$	−15.8572	+	9.15516i	−0.535155	+	0.308972i
$879$		−	67.4900i		−	2.27638i
$880$		0			0
$881$	19.8767	−	34.4275i	0.669663	−	1.15989i	−0.308335	−	0.951278i	$-0.599772\pi$
$881$	19.8767	−	34.4275i	0.669663	−	1.15989i	0.977998	−	0.208613i	$-0.0668948\pi$
$882$	−12.1483	−	7.01385i	−0.409056	−	0.236169i
$883$	−17.2515			−0.580560			−0.290280	−	0.956942i	$-0.593748\pi$
$883$	−17.2515			−0.580560			−0.290280	+	0.956942i	$0.593748\pi$
$884$	17.0331	+	32.7255i	0.572884	+	1.10068i
$885$		0			0
$886$	−11.1237	−	6.42224i	−0.373706	−	0.215760i
$887$	18.2982	−	31.6934i	0.614394	−	1.06416i	−0.376097	−	0.926580i	$-0.622734\pi$
$887$	18.2982	−	31.6934i	0.614394	−	1.06416i	0.990491	−	0.137581i	$-0.0439327\pi$
$888$	22.7822	+	39.4599i	0.764521	+	1.32419i
$889$		−	3.53279i		−	0.118486i
$890$		0			0
$891$	−21.9227	+	12.6571i	−0.734438	+	0.424028i
$892$			25.5704i			0.856160i
$893$	9.47382	+	16.4091i	0.317029	+	0.549111i
$894$	−6.72724	+	11.6519i	−0.224993	+	0.389699i
$895$		0			0
$896$	6.47073			0.216172
$897$	−5.99862	−	0.262301i	−0.200288	−	0.00875799i
$898$	−4.35372			−0.145286
$899$	−31.0123	−	17.9049i	−1.03432	−	0.597163i
$900$		0			0
$901$	16.2537	+	28.1522i	0.541488	+	0.937885i
$902$		−	1.44572i		−	0.0481373i
$903$	1.27230	−	0.734564i	0.0423396	−	0.0244448i
$904$	−5.14707	+	2.97166i	−0.171189	+	0.0988361i
$905$		0			0
$906$	−10.7633	−	18.6426i	−0.357587	−	0.619360i
$907$	19.6178	−	33.9791i	0.651400	−	1.12826i	−0.331384	−	0.943496i	$-0.607515\pi$
$907$	19.6178	−	33.9791i	0.651400	−	1.12826i	0.982783	−	0.184762i	$-0.0591513\pi$
$908$	−23.2443	−	13.4201i	−0.771388	−	0.445361i
$909$	43.7921			1.45249
$910$		0			0
$911$	−7.66019			−0.253793			−0.126897	−	0.991916i	$-0.540502\pi$
$911$	−7.66019			−0.253793			−0.126897	+	0.991916i	$0.540502\pi$
$912$	−19.8157	−	11.4406i	−0.656163	−	0.378836i
$913$	0.553241	−	0.958241i	0.0183096	−	0.0317131i
$914$	−4.79766	−	8.30978i	−0.158692	−	0.274863i
$915$		0			0
$916$	−13.5876	+	7.84482i	−0.448948	+	0.259200i
$917$	−0.568137	+	0.328014i	−0.0187615	+	0.0108320i
$918$			1.79301i			0.0591780i
$919$	−6.62625	−	11.4770i	−0.218580	−	0.378592i	0.735794	−	0.677205i	$-0.236809\pi$
$919$	−6.62625	−	11.4770i	−0.218580	−	0.378592i	−0.954374	+	0.298614i	$0.903476\pi$
$920$		0			0
$921$	−33.2498	−	19.1968i	−1.09562	−	0.632555i
$922$	−8.83137			−0.290846
$923$	−1.41860	+	32.4422i	−0.0466938	+	1.06785i
$924$	6.78164			0.223100
$925$		0			0
$926$	−6.28319	+	10.8828i	−0.206478	+	0.357631i
$927$	−6.99565	−	12.1168i	−0.229767	−	0.397969i
$928$		−	45.4592i		−	1.49227i
$929$	39.4042	−	22.7500i	1.29281	−	0.746405i	0.313659	−	0.949536i	$-0.398445\pi$
$929$	39.4042	−	22.7500i	1.29281	−	0.746405i	0.979152	+	0.203131i	$0.0651117\pi$
$930$		0			0
$931$			39.9488i			1.30927i
$932$	−15.3384	−	26.5668i	−0.502425	−	0.870225i
$933$	10.5533	−	18.2789i	0.345500	−	0.598424i
$934$	12.6248	+	7.28891i	0.413095	+	0.238500i
$935$		0			0
$936$	1.18081	−	27.0043i	0.0385961	−	0.882662i
$937$	16.8095			0.549141			0.274570	−	0.961567i	$-0.411464\pi$
$937$	16.8095			0.549141			0.274570	+	0.961567i	$0.411464\pi$
$938$	0.215843	+	0.124617i	0.00704753	+	0.00406889i
$939$	5.97588	−	10.3505i	0.195015	−	0.337777i
$940$		0			0
$941$		−	8.88910i		−	0.289776i	−0.989448	−	0.144888i	$-0.953718\pi$
$941$		−	8.88910i		−	0.289776i	0.989448	−	0.144888i	$-0.0462822\pi$
$942$	−17.6413	+	10.1852i	−0.574784	+	0.331851i
$943$	0.422255	−	0.243789i	0.0137505	−	0.00793886i
$944$		−	21.9140i		−	0.713241i
$945$		0			0
$946$	−1.00104	+	1.73385i	−0.0325465	+	0.0563723i
$947$	26.3710	+	15.2253i	0.856942	+	0.494756i	0.862987	−	0.505226i	$-0.168591\pi$
$947$	26.3710	+	15.2253i	0.856942	+	0.494756i	−0.00604474	+	0.999982i	$0.501924\pi$
$948$	58.2974			1.89341
$949$	−51.1457	−	32.5882i	−1.66026	−	1.05786i
$950$		0			0
$951$	−7.21174	−	4.16370i	−0.233857	−	0.135017i
$952$	−4.57643	+	7.92662i	−0.148323	+	0.256903i
$953$	−2.42924	−	4.20756i	−0.0786907	−	0.136296i	0.823995	−	0.566598i	$-0.191741\pi$
$953$	−2.42924	−	4.20756i	−0.0786907	−	0.136296i	−0.902685	+	0.430301i	$0.858407\pi$
$954$		−	10.4230i		−	0.337458i
$955$		0			0
$956$	−15.1462	+	8.74464i	−0.489862	+	0.282822i
$957$		−	58.5112i		−	1.89140i
$958$	9.35985	+	16.2117i	0.302403	+	0.523777i
$959$	−5.78663	+	10.0227i	−0.186860	+	0.323651i
$960$		0			0
$961$	10.4132			0.335910
$962$	18.5871	+	0.812755i	0.599271	+	0.0262043i
$963$	−8.56651			−0.276052
$964$	−5.05290	−	2.91729i	−0.162743	−	0.0939597i
$965$		0			0
$966$	−0.325956	−	0.564572i	−0.0104875	−	0.0181648i
$967$		−	26.5631i		−	0.854211i	−0.904202	−	0.427106i	$-0.859533\pi$
$967$		−	26.5631i		−	0.854211i	0.904202	−	0.427106i	$-0.140467\pi$
$968$	4.27658	−	2.46908i	0.137454	−	0.0793593i
$969$	84.8660	−	48.9974i	2.72629	−	1.57402i
$970$		0			0
$971$	−21.6053	−	37.4216i	−0.693349	−	1.20091i	−0.970734	−	0.240156i	$-0.922801\pi$
$971$	−21.6053	−	37.4216i	−0.693349	−	1.20091i	0.277386	−	0.960759i	$-0.410532\pi$
$972$	17.3371	−	30.0288i	0.556089	−	0.963174i
$973$	5.02403	+	2.90062i	0.161063	+	0.0929897i
$974$	12.2037			0.391031
$975$		0			0
$976$	−12.3748			−0.396107
$977$	39.3665	+	22.7283i	1.25945	+	0.727141i	0.972967	−	0.230945i	$-0.0741817\pi$
$977$	39.3665	+	22.7283i	1.25945	+	0.727141i	0.286479	+	0.958086i	$0.407515\pi$
$978$	−1.76439	+	3.05601i	−0.0564190	+	0.0977205i
$979$	13.7913	+	23.8872i	0.440771	+	0.763438i
$980$		0			0
$981$	−31.0450	+	17.9239i	−0.991192	+	0.572265i
$982$	−12.5287	+	7.23347i	−0.399808	+	0.230829i
$983$			9.31963i			0.297250i	0.988894	+	0.148625i	$0.0474847\pi$
$983$			9.31963i			0.297250i	−0.988894	+	0.148625i	$0.952515\pi$
$984$	2.13777	+	3.70272i	0.0681495	+	0.118038i
$985$		0			0
$986$	29.9295	+	17.2798i	0.953150	+	0.550302i
$987$	4.60599			0.146610
$988$	−29.8824	+	15.5533i	−0.950686	+	0.494816i
$989$	−0.675210			−0.0214704
$990$		0			0
$991$	2.01694	−	3.49344i	0.0640702	−	0.110973i	−0.832211	−	0.554459i	$-0.812925\pi$
$991$	2.01694	−	3.49344i	0.0640702	−	0.110973i	0.896281	+	0.443486i	$0.146258\pi$
$992$	−13.0670	−	22.6328i	−0.414879	−	0.718592i
$993$		−	51.0575i		−	1.62026i
$994$	−3.05336	+	1.76286i	−0.0968468	+	0.0559145i
$995$		0			0
$996$			1.43204i			0.0453760i
$997$	27.5880	+	47.7839i	0.873722	+	1.51333i	0.858118	+	0.513452i	$0.171634\pi$
$997$	27.5880	+	47.7839i	0.873722	+	1.51333i	0.0156032	+	0.999878i	$0.495033\pi$
$998$	−4.90937	+	8.50327i	−0.155403	+	0.269166i
$999$	−2.74726	−	1.58613i	−0.0869195	−	0.0501830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.f.251.3	yes	10
5.2	odd	4		325.2.m.d.199.6		20
5.3	odd	4		325.2.m.d.199.5		20
5.4	even	2		325.2.n.e.251.3	yes	10
13.6	odd	12		4225.2.a.bu.1.6		10
13.7	odd	12		4225.2.a.bu.1.5		10
13.10	even	6	inner	325.2.n.f.101.3	yes	10
65.19	odd	12		4225.2.a.bv.1.5		10
65.23	odd	12		325.2.m.d.49.6		20
65.49	even	6		325.2.n.e.101.3	✓	10
65.59	odd	12		4225.2.a.bv.1.6		10
65.62	odd	12		325.2.m.d.49.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.5		20	65.62	odd	12
325.2.m.d.49.6		20	65.23	odd	12
325.2.m.d.199.5		20	5.3	odd	4
325.2.m.d.199.6		20	5.2	odd	4
325.2.n.e.101.3	✓	10	65.49	even	6
325.2.n.e.251.3	yes	10	5.4	even	2
325.2.n.f.101.3	yes	10	13.10	even	6	inner
325.2.n.f.251.3	yes	10	1.1	even	1	trivial
4225.2.a.bu.1.5		10	13.7	odd	12
4225.2.a.bu.1.6		10	13.6	odd	12
4225.2.a.bv.1.5		10	65.19	odd	12
4225.2.a.bv.1.6		10	65.59	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576815 - 0.333024i) q^{2} +(-1.24146 + 2.15028i) q^{3} +(-0.778190 - 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.509002 + 0.293872i) q^{7} +2.36872i q^{8} +(-1.58246 - 2.74090i) q^{9} +(-2.58582 - 1.49292i) q^{11} +3.86437 q^{12} +(1.93746 - 3.04076i) q^{13} +0.391466 q^{14} +(-0.767539 + 1.32942i) q^{16} +(-3.28719 - 5.69358i) q^{17} +2.10798i q^{18} +(5.19894 - 3.00161i) q^{19} -1.45932i q^{21} +(0.994358 + 1.72228i) q^{22} +(-0.335352 + 0.580847i) q^{23} +(-5.09340 - 2.94068i) q^{24} +(-2.13020 + 1.10874i) q^{26} +0.409469 q^{27} +(0.792200 + 0.457377i) q^{28} +(3.94620 - 6.83501i) q^{29} -4.53727i q^{31} +(4.98820 - 2.87994i) q^{32} +(6.42039 - 3.70681i) q^{33} +4.37886i q^{34} +(-2.46290 + 4.26588i) q^{36} +(-6.70933 - 3.87363i) q^{37} -3.99844 q^{38} +(4.13319 + 7.94107i) q^{39} +(-0.629569 - 0.363482i) q^{41} +(-0.485990 + 0.841760i) q^{42} +(0.503359 + 0.871843i) q^{43} +4.64711i q^{44} +(0.386872 - 0.223361i) q^{46} +3.15624i q^{47} +(-1.90574 - 3.30084i) q^{48} +(-3.32728 + 5.76302i) q^{49} +16.3237 q^{51} +(-5.60625 - 0.245144i) q^{52} -4.94455 q^{53} +(-0.236188 - 0.136363i) q^{54} +(-0.696101 - 1.20568i) q^{56} +14.9056i q^{57} +(-4.55245 + 2.62836i) q^{58} +(-12.3630 + 7.13776i) q^{59} +(4.03067 + 6.98133i) q^{61} +(-1.51102 + 2.61716i) q^{62} +(1.61095 + 0.930080i) q^{63} -0.766197 q^{64} -4.93783 q^{66} +(0.551372 + 0.318335i) q^{67} +(-5.11612 + 8.86138i) q^{68} +(-0.832654 - 1.44220i) q^{69} +(-7.79982 + 4.50323i) q^{71} +(6.49242 - 3.74840i) q^{72} -16.8200i q^{73} +(2.58003 + 4.46874i) q^{74} +(-8.09153 - 4.67165i) q^{76} +1.75491 q^{77} +(0.260480 - 5.95698i) q^{78} +15.0859 q^{79} +(4.23903 - 7.34222i) q^{81} +(0.242096 + 0.419323i) q^{82} +0.370576i q^{83} +(-1.96697 + 1.13563i) q^{84} -0.670523i q^{86} +(9.79811 + 16.9708i) q^{87} +(3.53631 - 6.12507i) q^{88} +(-8.00015 - 4.61889i) q^{89} +(-0.0925751 + 2.11712i) q^{91} +1.04387 q^{92} +(9.75637 + 5.63284i) q^{93} +(1.05111 - 1.82057i) q^{94} +14.3013i q^{96} +(5.99502 - 3.46123i) q^{97} +(3.83845 - 2.21613i) q^{98} +9.44994i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} + 6 q^{4} + 9 q^{6} + 6 q^{7} - 8 q^{9} - 9 q^{11} + 28 q^{12} - 8 q^{13} - 8 q^{14} - 12 q^{16} - 8 q^{17} + 12 q^{22} - 13 q^{23} + 42 q^{24} - 17 q^{26} - 30 q^{27} - 33 q^{28} + 7 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) \) 10 * q + 3 * q^3 + 6 * q^4 + 9 * q^6 + 6 * q^7 - 8 * q^9 - 9 * q^11 + 28 * q^12 - 8 * q^13 - 8 * q^14 - 12 * q^16 - 8 * q^17 + 12 * q^22 - 13 * q^23 + 42 * q^24 - 17 * q^26 - 30 * q^27 - 33 * q^28 + 7 * q^29 - 3 * q^32 + 6 * q^33 - 3 * q^36 - 3 * q^37 + 62 * q^38 + 8 * q^39 + 12 * q^41 - 32 * q^42 - 4 * q^43 + 39 * q^46 + 26 * q^48 - q^49 + 16 * q^51 - 61 * q^52 - 24 * q^53 - 9 * q^54 - 21 * q^56 - 18 * q^58 - 48 * q^59 + 13 * q^61 - 17 * q^62 - 34 * q^64 - 42 * q^66 - 6 * q^67 + 13 * q^68 + 20 * q^69 - 27 * q^71 + 141 * q^72 - 26 * q^74 - 12 * q^76 + 48 * q^77 - 56 * q^78 + 4 * q^79 - 17 * q^81 + q^82 - 90 * q^84 + 49 * q^87 + 6 * q^88 + 24 * q^89 + 13 * q^91 - 34 * q^92 + 63 * q^93 + 5 * q^94 + 15 * q^97 + 45 * q^98

Introduction

L-functions

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