LMFDB - Embedded newform 325.2.n.e.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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.e.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576815 + 0.333024i) q^{2} +(1.24146 - 2.15028i) q^{3} +(-0.778190 - 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(0.509002 - 0.293872i) q^{7} -2.36872i q^{8} +(-1.58246 - 2.74090i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	0.689874	−	0.723930i	$-0.257666\pi$
$2$	0.576815	+	0.333024i	0.407869	+	0.235484i	−0.282004	+	0.959413i	$0.590999\pi$
$3$	1.24146	−	2.15028i	0.716759	−	1.24146i	−0.245519	−	0.969392i	$-0.578958\pi$
$3$	1.24146	−	2.15028i	0.716759	−	1.24146i	0.962277	−	0.272070i	$-0.0877084\pi$
$4$	−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	−0.400714	−	0.916203i	$-0.631238\pi$
$7$	0.509002	−	0.293872i	0.192384	−	0.111073i	0.593098	+	0.805130i	$0.297905\pi$
$8$		−	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	$0.127052\pi$
$17$	3.28719	+	5.69358i	0.797261	+	1.38090i	−0.124132	+	0.992266i	$0.539615\pi$
$18$		−	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	−0.828943	−	0.559334i	$-0.811057\pi$
$23$	0.335352	−	0.580847i	0.0699258	−	0.121115i	0.898868	+	0.438219i	$0.144390\pi$
$24$	−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	0.937009	−	0.349305i	$-0.113582\pi$
$37$	6.70933	+	3.87363i	1.10301	+	0.636821i	0.165998	+	0.986126i	$0.446916\pi$
$38$	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	0.825089	−	0.565002i	$-0.191125\pi$
$43$	−0.503359	−	0.871843i	−0.0767615	−	0.132955i	−0.901851	+	0.432047i	$0.857791\pi$
$44$			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	$-0.926064\pi$
$47$		−	3.15624i		−	0.460386i	0.973145	−	0.230193i	$-0.0739357\pi$
$48$	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	$-0.389711\pi$
$53$	4.94455			0.679186			0.339593	+	0.940573i	$0.389711\pi$
$54$	−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	0.465941	−	0.884816i	$-0.345716\pi$
$67$	−0.551372	−	0.318335i	−0.0673608	−	0.0388908i	−0.533302	+	0.845925i	$0.679049\pi$
$68$	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	$0.443554\pi$
$73$			16.8200i			1.96864i	−0.176403	+	0.984318i	$0.556446\pi$
$74$	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	$-0.993526\pi$
$83$		−	0.370576i		−	0.0406760i	0.999793	−	0.0203380i	$-0.00647423\pi$
$84$	−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	−0.772457	−	0.635067i	$-0.780973\pi$
$97$	−5.99502	+	3.46123i	−0.608702	+	0.351434i	0.163755	+	0.986501i	$0.447639\pi$
$98$	−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	$-0.569886\pi$
$103$	−4.42075			−0.435590			−0.217795	+	0.975995i	$0.569886\pi$
$104$	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	−0.923998	−	0.382397i	$-0.875099\pi$
$107$	−1.35336	+	2.34408i	−0.130834	+	0.226611i	0.793164	+	0.609008i	$0.208432\pi$
$108$	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	0.800964	−	0.598712i	$-0.204321\pi$
$113$	−1.25454	−	2.17293i	−0.118018	−	0.204413i	−0.918982	+	0.394299i	$0.870987\pi$
$114$	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	−0.701319	−	0.712847i	$-0.747405\pi$
$127$	3.00538	−	5.20546i	0.266684	−	0.461910i	0.968003	+	0.250937i	$0.0807387\pi$
$128$	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	−0.998859	−	0.0477593i	$-0.984792\pi$
$137$	−17.0529	+	9.84550i	−1.45693	+	0.841158i	−0.458069	+	0.888917i	$0.651459\pi$
$138$		−	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	$-0.336438\pi$
$157$	12.3177			0.983061			0.491530	+	0.870860i	$0.336438\pi$
$158$	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	−0.425880	−	0.904779i	$-0.640036\pi$
$163$	1.84793	−	1.06690i	0.144741	−	0.0835664i	0.570622	+	0.821213i	$0.306702\pi$
$164$			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	0.496327	−	0.868136i	$-0.334682\pi$
$167$	−0.0948176	−	0.0547430i	−0.00733720	−	0.00423614i	−0.503664	+	0.863900i	$0.668015\pi$
$168$	−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	0.667036	−	0.745025i	$-0.267563\pi$
$173$	−4.09968	−	7.10085i	−0.311693	−	0.539868i	−0.978729	+	0.205158i	$0.934229\pi$
$174$		−	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	0.130846	−	0.991403i	$-0.458231\pi$
$193$	−9.20113	−	5.31227i	−0.662312	−	0.382386i	−0.793157	+	0.609017i	$0.791564\pi$
$194$	−4.61069			−0.331028
$195$		0			0
$196$	10.3570			0.739787
$197$	4.88920	+	2.82278i	0.348341	+	0.201115i	0.663954	−	0.747773i	$-0.268877\pi$
$197$	4.88920	+	2.82278i	0.348341	+	0.201115i	−0.315613	+	0.948888i	$0.602210\pi$
$198$	−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	0.893948	−	0.448170i	$-0.147924\pi$
$223$	14.2283	+	8.21470i	0.952796	+	0.550097i	0.0588475	+	0.998267i	$0.481257\pi$
$224$	−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	−0.905650	−	0.424025i	$-0.860617\pi$
$227$	−14.9348	+	8.62262i	−0.991259	+	0.572304i	−0.0856085	+	0.996329i	$0.527283\pi$
$228$	−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	$-0.723406\pi$
$233$	−19.7103			−1.29126			−0.645632	+	0.763648i	$0.723406\pi$
$234$	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	−0.550456	−	0.834864i	$-0.685546\pi$
$257$	7.17856	−	12.4336i	0.447786	−	0.775588i	0.998242	+	0.0592763i	$0.0188793\pi$
$258$	−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	$0.475201\pi$
$263$	−13.3709	+	23.1590i	−0.824484	+	1.42805i	−0.902313	+	0.431081i	$0.858132\pi$
$264$	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	0.919547	−	0.392980i	$-0.128556\pi$
$277$	1.98793	+	3.44320i	0.119443	+	0.206882i	−0.800104	+	0.599861i	$0.795222\pi$
$278$		−	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	−0.700397	−	0.713754i	$-0.746994\pi$
$283$	4.50729	−	7.80686i	0.267931	−	0.464070i	0.968327	+	0.249684i	$0.0803268\pi$
$284$	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	0.383641	−	0.923482i	$-0.374670\pi$
$293$	23.5400	−	13.5908i	1.37522	−	0.793984i	0.991580	+	0.129498i	$0.0413366\pi$
$294$			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	$-0.854531\pi$
$307$		−	15.4630i		−	0.882522i	0.897379	−	0.441261i	$-0.145469\pi$
$308$	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	$-0.456562\pi$
$313$	4.81358			0.272080			0.136040	+	0.990703i	$0.456562\pi$
$314$	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	$-0.969975\pi$
$317$		−	3.35387i		−	0.188372i	0.995555	−	0.0941860i	$-0.0300248\pi$
$318$	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	$-0.637149\pi$
$337$	−15.3344			−0.835316			−0.417658	+	0.908604i	$0.637149\pi$
$338$	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	0.994206	−	0.107495i	$-0.0342831\pi$
$347$	7.52585	+	13.0352i	0.404009	+	0.699764i	−0.590197	+	0.807260i	$0.700950\pi$
$348$	−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	−0.332002	−	0.943279i	$-0.607724\pi$
$353$	−24.7048	−	14.2633i	−1.31491	−	0.759161i	−0.982904	+	0.184118i	$0.941057\pi$
$354$	−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	−0.911015	−	0.412374i	$-0.864700\pi$
$367$	−1.88471	+	3.26441i	−0.0983809	+	0.170401i	0.812634	+	0.582775i	$0.198033\pi$
$368$	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	0.641688	−	0.766966i	$-0.278235\pi$
$373$	−6.63155	−	11.4862i	−0.343368	−	0.594732i	−0.985056	+	0.172235i	$0.944901\pi$
$374$	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	−0.909268	−	0.416211i	$-0.863358\pi$
$383$	−19.6380	+	11.3380i	−1.00345	+	0.579344i	−0.0941845	+	0.995555i	$0.530024\pi$
$384$	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	−0.611875	−	0.790954i	$-0.709584\pi$
$397$	−4.63902	+	2.67834i	−0.232826	+	0.134422i	0.379049	+	0.925377i	$0.376251\pi$
$398$			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	0.544253	−	0.838921i	$-0.316813\pi$
$433$	−9.45546	−	16.3773i	−0.454401	−	0.787045i	−0.998654	+	0.0518762i	$0.983480\pi$
$434$		−	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	$-0.651477\pi$
$443$	−19.2846			−0.916240			−0.458120	+	0.888890i	$0.651477\pi$
$444$	−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	0.178954	−	0.983857i	$-0.442729\pi$
$457$	−12.4763	−	7.20317i	−0.583614	−	0.336950i	−0.762569	+	0.646907i	$0.776062\pi$
$458$	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	$0.144459\pi$
$463$			18.8671i			0.876827i	−0.898773	+	0.438413i	$0.855541\pi$
$464$	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	$-0.330974\pi$
$467$	21.8870			1.01281			0.506406	+	0.862295i	$0.330974\pi$
$468$	−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	−0.0953608	−	0.995443i	$-0.530400\pi$
$487$	15.8678	−	9.16127i	0.719038	−	0.415137i	0.814398	+	0.580306i	$0.197067\pi$
$488$	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	$-0.856163\pi$
$503$	−18.5694	−	32.1631i	−0.827969	−	1.43408i	0.0716604	−	0.997429i	$-0.477170\pi$
$504$	−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	$-0.658777\pi$
$523$	11.9219	−	20.6494i	0.521309	−	0.902934i	0.999693	−	0.0247827i	$-0.00788940\pi$
$524$	−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	$-0.521352\pi$
$547$	−3.13542			−0.134061			−0.0670305	+	0.997751i	$0.521352\pi$
$548$	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	0.865645	−	0.500659i	$-0.166909\pi$
$557$	20.4120	+	11.7849i	0.864883	+	0.499341i	−0.000761144		1.00000i	$0.500242\pi$
$558$	−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	0.977916	−	0.208999i	$-0.0670204\pi$
$563$	7.30716	+	12.6564i	0.307960	+	0.533402i	−0.669956	+	0.742401i	$0.733687\pi$
$564$			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	$0.0423654\pi$
$577$			6.37523i			0.265405i	−0.991156	+	0.132702i	$0.957635\pi$
$578$	−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	$0.0958267\pi$
$587$	40.9293	+	23.6306i	1.68933	+	0.975338i	0.734308	+	0.678816i	$0.237507\pi$
$588$	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	$-0.958355\pi$
$593$		−	6.35373i		−	0.260916i	0.991454	−	0.130458i	$-0.0416448\pi$
$594$	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	0.999470	−	0.0325569i	$-0.0103650\pi$
$607$	11.6175	+	20.1221i	0.471540	+	0.816731i	−0.527930	+	0.849288i	$0.677032\pi$
$608$	−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	0.0331286	−	0.999451i	$-0.489453\pi$
$613$	−20.1997	−	11.6623i	−0.815857	−	0.471035i	−0.848986	+	0.528416i	$0.822786\pi$
$614$	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	−0.783523	−	0.621363i	$-0.786579\pi$
$617$	−15.8269	+	9.13768i	−0.637168	+	0.367869i	0.146355	+	0.989232i	$0.453246\pi$
$618$	−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	−0.524364	−	0.851494i	$-0.675697\pi$
$643$	−1.24581	+	0.719272i	−0.0491301	+	0.0283653i	0.475234	+	0.879860i	$0.342364\pi$
$644$	−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	$-0.438091\pi$
$647$	24.0711	−	41.6923i	0.946331	−	1.63909i	0.753063	−	0.657948i	$-0.228575\pi$
$648$	−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	$0.429423\pi$
$653$	−18.7787	+	32.5257i	−0.734869	+	1.27283i	−0.954781	+	0.297311i	$0.903910\pi$
$654$	−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	$0.533691\pi$
$673$	−23.7113	+	41.0691i	−0.914002	+	1.58310i	−0.808356	+	0.588695i	$0.799642\pi$
$674$	−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	$-0.463726\pi$
$677$	5.91735			0.227422			0.113711	+	0.993514i	$0.463726\pi$
$678$	−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	−0.727512	−	0.686095i	$-0.759323\pi$
$683$	−12.9911	+	7.50043i	−0.497092	+	0.286996i	0.230420	+	0.973091i	$0.425990\pi$
$684$			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	$-0.527352\pi$
$727$	−4.62813			−0.171648			−0.0858240	+	0.996310i	$0.527352\pi$
$728$	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	$0.0586952\pi$
$733$			9.92820i			0.366706i	−0.983047	+	0.183353i	$0.941305\pi$
$734$	−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	0.0856590	−	0.996325i	$-0.472700\pi$
$743$	−20.0170	−	11.5568i	−0.734354	−	0.423979i	−0.820013	+	0.572345i	$0.806034\pi$
$744$	−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	−0.965627	−	0.259930i	$-0.916300\pi$
$757$	−7.09047	+	12.2811i	−0.257708	+	0.446363i	0.707920	+	0.706293i	$0.249634\pi$
$758$	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	−0.472350	−	0.881411i	$-0.656594\pi$
$773$	1.52359	−	0.879642i	0.0547995	−	0.0316385i	0.527149	+	0.849773i	$0.323261\pi$
$774$	−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	0.0663793	−	0.997794i	$-0.478855\pi$
$787$	27.0347	−	15.6085i	0.963684	−	0.556383i	0.897305	+	0.441411i	$0.145522\pi$
$788$		−	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	0.898553	−	0.438866i	$-0.144620\pi$
$797$	1.95382	+	3.38411i	0.0692077	+	0.119871i	−0.829345	+	0.558737i	$0.811286\pi$
$798$		−	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	0.509992	−	0.860179i	$-0.329648\pi$
$823$	−14.0554	−	24.3447i	−0.489941	−	0.848602i	−0.999933	+	0.0115767i	$0.996315\pi$
$824$			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	$-0.669870\pi$
$827$		−	49.5177i		−	1.72190i	0.508691	−	0.860949i	$-0.330130\pi$
$828$	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	$0.228678\pi$
$853$			38.4465i			1.31638i	−0.752851	+	0.658191i	$0.771322\pi$
$854$	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	$-0.512596\pi$
$857$	−2.31635			−0.0791251			−0.0395625	+	0.999217i	$0.512596\pi$
$858$	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	$0.0576245\pi$
$863$			10.5783i			0.360091i	−0.983658	+	0.180046i	$0.942375\pi$
$864$	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	−0.748936	−	0.662642i	$-0.769435\pi$
$877$	−16.2742	+	9.39590i	−0.549540	+	0.317277i	0.199397	+	0.979919i	$0.436102\pi$
$878$	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	$-0.406252\pi$
$883$	17.2515			0.580560			0.290280	+	0.956942i	$0.406252\pi$
$884$	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	$0.377266\pi$
$887$	−18.2982	+	31.6934i	−0.614394	+	1.06416i	−0.990491	+	0.137581i	$0.956067\pi$
$888$	−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	$0.392485\pi$
$907$	−19.6178	+	33.9791i	−0.651400	+	1.12826i	−0.982783	+	0.184762i	$0.940849\pi$
$908$	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	$-0.588536\pi$
$937$	−16.8095			−0.549141			−0.274570	+	0.961567i	$0.588536\pi$
$938$	−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	0.00604474	−	0.999982i	$-0.498076\pi$
$947$	−26.3710	−	15.2253i	−0.856942	−	0.494756i	−0.862987	+	0.505226i	$0.831409\pi$
$948$	−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	0.902685	−	0.430301i	$-0.141593\pi$
$953$	2.42924	+	4.20756i	0.0786907	+	0.136296i	−0.823995	+	0.566598i	$0.808259\pi$
$954$		−	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	$0.140467\pi$
$967$			26.5631i			0.854211i	−0.904202	+	0.427106i	$0.859533\pi$
$968$	−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	−0.286479	−	0.958086i	$-0.592485\pi$
$977$	−39.3665	−	22.7283i	−1.25945	−	0.727141i	−0.972967	+	0.230945i	$0.925818\pi$
$978$	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	$-0.952515\pi$
$983$		−	9.31963i		−	0.297250i	0.988894	−	0.148625i	$-0.0474847\pi$
$984$	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	$-0.828366\pi$
$997$	−27.5880	−	47.7839i	−0.873722	−	1.51333i	−0.0156032	−	0.999878i	$-0.504967\pi$
$998$	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.e.251.3	yes	10
5.2	odd	4		325.2.m.d.199.5		20
5.3	odd	4		325.2.m.d.199.6		20
5.4	even	2		325.2.n.f.251.3	yes	10
13.6	odd	12		4225.2.a.bv.1.5		10
13.7	odd	12		4225.2.a.bv.1.6		10
13.10	even	6	inner	325.2.n.e.101.3	✓	10
65.19	odd	12		4225.2.a.bu.1.6		10
65.23	odd	12		325.2.m.d.49.5		20
65.49	even	6		325.2.n.f.101.3	yes	10
65.59	odd	12		4225.2.a.bu.1.5		10
65.62	odd	12		325.2.m.d.49.6		20

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

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

\(f(q)\)	\(=\)	\(q+(0.576815 + 0.333024i) q^{2} +(1.24146 - 2.15028i) q^{3} +(-0.778190 - 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(0.509002 - 0.293872i) q^{7} -2.36872i q^{8} +(-1.58246 - 2.74090i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

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Representations

Groups

Database

Properties

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