LMFDB - Embedded newform 325.2.m.d.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(49,325)]

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([3, 5]))

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

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

chi := DirichletCharacter("325.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (of order $6$, degree $2$, not 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 16 x^{18} + 172 x^{16} + 1018 x^{14} + 4330 x^{12} + 9943 x^{10} + 16225 x^{8} + 14698 x^{6} + \cdots + 729 $ x^20 + 16x^18 + 172x^16 + 1018x^14 + 4330x^12 + 9943x^10 + 16225x^8 + 14698x^6 + 9523x^4 + 3186*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.6
Root			$-0.333024 - 0.576815i$ of defining polynomial
Character	$\chi$	$=$	325.199
Dual form			325.2.m.d.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.333024 - 0.576815i) q^{2} +(2.15028 + 1.24146i) q^{3} +(0.778190 + 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.293872 - 0.509002i) q^{7} +2.36872 q^{8} +(1.58246 + 2.74090i) q^{9} +O(q^{10})$	\(q+(0.333024 - 0.576815i) q^{2} +(2.15028 + 1.24146i) q^{3} +(0.778190 + 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.293872 - 0.509002i) q^{7} +2.36872 q^{8} +(1.58246 + 2.74090i) q^{9} +(-2.58582 - 1.49292i) q^{11} +3.86437i q^{12} +(-3.04076 - 1.93746i) q^{13} -0.391466 q^{14} +(-0.767539 + 1.32942i) q^{16} +(5.69358 - 3.28719i) q^{17} +2.10798 q^{18} +(-5.19894 + 3.00161i) q^{19} -1.45932i q^{21} +(-1.72228 + 0.994358i) q^{22} +(0.580847 + 0.335352i) q^{23} +(5.09340 + 2.94068i) q^{24} +(-2.13020 + 1.10874i) q^{26} +0.409469i q^{27} +(0.457377 - 0.792200i) q^{28} +(-3.94620 + 6.83501i) q^{29} -4.53727i q^{31} +(2.87994 + 4.98820i) q^{32} +(-3.70681 - 6.42039i) q^{33} -4.37886i q^{34} +(-2.46290 + 4.26588i) q^{36} +(3.87363 - 6.70933i) q^{37} +3.99844i q^{38} +(-4.13319 - 7.94107i) q^{39} +(-0.629569 - 0.363482i) q^{41} +(-0.841760 - 0.485990i) q^{42} +(0.871843 - 0.503359i) q^{43} -4.64711i q^{44} +(0.386872 - 0.223361i) q^{46} -3.15624 q^{47} +(-3.30084 + 1.90574i) q^{48} +(3.32728 - 5.76302i) q^{49} +16.3237 q^{51} +(0.245144 - 5.60625i) q^{52} +4.94455i q^{53} +(0.236188 + 0.136363i) q^{54} +(-0.696101 - 1.20568i) q^{56} -14.9056 q^{57} +(2.62836 + 4.55245i) q^{58} +(12.3630 - 7.13776i) q^{59} +(4.03067 + 6.98133i) q^{61} +(-2.61716 - 1.51102i) q^{62} +(0.930080 - 1.61095i) q^{63} +0.766197 q^{64} -4.93783 q^{66} +(-0.318335 + 0.551372i) q^{67} +(8.86138 + 5.11612i) q^{68} +(0.832654 + 1.44220i) q^{69} +(-7.79982 + 4.50323i) q^{71} +(3.74840 + 6.49242i) q^{72} -16.8200 q^{73} +(-2.58003 - 4.46874i) q^{74} +(-8.09153 - 4.67165i) q^{76} +1.75491i q^{77} +(-5.95698 - 0.260480i) q^{78} -15.0859 q^{79} +(4.23903 - 7.34222i) q^{81} +(-0.419323 + 0.242096i) q^{82} +0.370576 q^{83} +(1.96697 - 1.13563i) q^{84} -0.670523i q^{86} +(-16.9708 + 9.79811i) q^{87} +(-6.12507 - 3.53631i) q^{88} +(8.00015 + 4.61889i) q^{89} +(-0.0925751 + 2.11712i) q^{91} +1.04387i q^{92} +(5.63284 - 9.75637i) q^{93} +(-1.05111 + 1.82057i) q^{94} +14.3013i q^{96} +(3.46123 + 5.99502i) q^{97} +(-2.21613 - 3.83845i) q^{98} -9.44994i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9}+O(q^{10}) $ 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9	$ 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9} - 18 q^{11} + 16 q^{14} - 24 q^{16} - 84 q^{24} - 34 q^{26} - 14 q^{29} - 6 q^{36} - 16 q^{39} + 24 q^{41} + 78 q^{46} + 2 q^{49} + 32 q^{51} + 18 q^{54} - 42 q^{56} + 96 q^{59} + 26 q^{61} + 68 q^{64} - 84 q^{66} - 40 q^{69} - 54 q^{71} + 52 q^{74} - 24 q^{76} - 8 q^{79} - 34 q^{81} + 180 q^{84} - 48 q^{89} + 26 q^{91} - 10 q^{94}+O(q^{100}) $ 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9 - 18 * q^11 + 16 * q^14 - 24 * q^16 - 84 * q^24 - 34 * q^26 - 14 * q^29 - 6 * q^36 - 16 * q^39 + 24 * q^41 + 78 * q^46 + 2 * q^49 + 32 * q^51 + 18 * q^54 - 42 * q^56 + 96 * q^59 + 26 * q^61 + 68 * q^64 - 84 * q^66 - 40 * q^69 - 54 * q^71 + 52 * q^74 - 24 * q^76 - 8 * q^79 - 34 * q^81 + 180 * q^84 - 48 * q^89 + 26 * q^91 - 10 * q^94

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 $

$2$	0.333024	−	0.576815i	0.235484	−	0.407869i	−0.723930	−	0.689874i	$-0.757666\pi$
$2$	0.333024	−	0.576815i	0.235484	−	0.407869i	0.959413	+	0.282004i	$0.0909993\pi$
$3$	2.15028	+	1.24146i	1.24146	+	0.716759i	0.969392	−	0.245519i	$-0.0789583\pi$
$3$	2.15028	+	1.24146i	1.24146	+	0.716759i	0.272070	+	0.962277i	$0.412292\pi$
$4$	0.778190	+	1.34786i	0.389095	+	0.673932i
$5$		0			0
$5$		0			0
$6$	1.43219	−	0.826874i	0.584688	−	0.337570i
$7$	−0.293872	−	0.509002i	−0.111073	−	0.192384i	0.805130	−	0.593098i	$-0.202095\pi$
$7$	−0.293872	−	0.509002i	−0.111073	−	0.192384i	−0.916203	+	0.400714i	$0.868762\pi$
$8$	2.36872			0.837469
$9$	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	$0.815290\pi$
$12$			3.86437i			1.11555i
$13$	−3.04076	−	1.93746i	−0.843356	−	0.537355i
$13$	−3.04076	−	1.93746i	−0.843356	−	0.537355i
$14$	−0.391466			−0.104624
$15$		0			0
$16$	−0.767539	+	1.32942i	−0.191885	+	0.332354i
$17$	5.69358	−	3.28719i	1.38090	−	0.797261i	0.388631	−	0.921393i	$-0.372948\pi$
$17$	5.69358	−	3.28719i	1.38090	−	0.797261i	0.992266	+	0.124132i	$0.0396148\pi$
$18$	2.10798			0.496857
$19$	−5.19894	+	3.00161i	−1.19272	+	0.688617i	−0.958922	−	0.283668i	$-0.908448\pi$
$19$	−5.19894	+	3.00161i	−1.19272	+	0.688617i	−0.233797	+	0.972285i	$0.575115\pi$
$20$		0			0
$21$		−	1.45932i		−	0.318451i
$22$	−1.72228	+	0.994358i	−0.367191	+	0.211998i
$23$	0.580847	+	0.335352i	0.121115	+	0.0699258i	0.559334	−	0.828943i	$-0.311057\pi$
$23$	0.580847	+	0.335352i	0.121115	+	0.0699258i	−0.438219	+	0.898868i	$0.644390\pi$
$24$	5.09340	+	2.94068i	1.03969	+	0.600263i
$25$		0			0
$26$	−2.13020	+	1.10874i	−0.417767	+	0.217441i
$27$			0.409469i			0.0788023i
$28$	0.457377	−	0.792200i	0.0864361	−	0.149712i
$29$	−3.94620	+	6.83501i	−0.732790	+	1.26923i	0.222896	+	0.974842i	$0.428449\pi$
$29$	−3.94620	+	6.83501i	−0.732790	+	1.26923i	−0.955686	+	0.294388i	$0.904884\pi$
$30$		0			0
$31$		−	4.53727i		−	0.814917i	−0.913224	−	0.407459i	$-0.866415\pi$
$31$		−	4.53727i		−	0.814917i	0.913224	−	0.407459i	$-0.133585\pi$
$32$	2.87994	+	4.98820i	0.509106	+	0.881797i
$33$	−3.70681	−	6.42039i	−0.645273	−	1.11765i
$34$		−	4.37886i		−	0.750967i
$35$		0			0
$36$	−2.46290	+	4.26588i	−0.410484	+	0.710979i
$37$	3.87363	−	6.70933i	0.636821	−	1.10301i	−0.349305	−	0.937009i	$-0.613582\pi$
$37$	3.87363	−	6.70933i	0.636821	−	1.10301i	0.986126	−	0.165998i	$-0.0530844\pi$
$38$			3.99844i			0.648632i
$39$	−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	$0.684746\pi$
$42$	−0.841760	−	0.485990i	−0.129886	−	0.0749899i
$43$	0.871843	−	0.503359i	0.132955	−	0.0767615i	−0.432047	−	0.901851i	$-0.642209\pi$
$43$	0.871843	−	0.503359i	0.132955	−	0.0767615i	0.565002	+	0.825089i	$0.308875\pi$
$44$		−	4.64711i		−	0.700578i
$45$		0			0
$46$	0.386872	−	0.223361i	0.0570412	−	0.0329327i
$47$	−3.15624			−0.460386			−0.230193	−	0.973145i	$-0.573936\pi$
$47$	−3.15624			−0.460386			−0.230193	+	0.973145i	$0.573936\pi$
$48$	−3.30084	+	1.90574i	−0.476436	+	0.275070i
$49$	3.32728	−	5.76302i	0.475325	−	0.823288i
$50$		0			0
$51$	16.3237			2.28577
$52$	0.245144	−	5.60625i	0.0339954	−	0.777447i
$53$			4.94455i			0.679186i	0.940573	+	0.339593i	$0.110289\pi$
$53$			4.94455i			0.679186i	−0.940573	+	0.339593i	$0.889711\pi$
$54$	0.236188	+	0.136363i	0.0321411	+	0.0185567i
$55$		0			0
$56$	−0.696101	−	1.20568i	−0.0930204	−	0.161116i
$57$	−14.9056			−1.97429
$58$	2.62836	+	4.55245i	0.345120	+	0.597766i
$59$	12.3630	−	7.13776i	1.60952	−	0.929257i	0.620043	−	0.784568i	$-0.287115\pi$
$59$	12.3630	−	7.13776i	1.60952	−	0.929257i	0.989477	−	0.144689i	$-0.0462181\pi$
$60$		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	$0.660726\pi$
$62$	−2.61716	−	1.51102i	−0.332380	−	0.191900i
$63$	0.930080	−	1.61095i	0.117179	−	0.202960i
$64$	0.766197			0.0957747
$65$		0			0
$66$	−4.93783			−0.607805
$67$	−0.318335	+	0.551372i	−0.0388908	+	0.0673608i	−0.884816	−	0.465941i	$-0.845716\pi$
$67$	−0.318335	+	0.551372i	−0.0388908	+	0.0673608i	0.845925	+	0.533302i	$0.179049\pi$
$68$	8.86138	+	5.11612i	1.07460	+	0.620421i
$69$	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	$0.512809\pi$
$72$	3.74840	+	6.49242i	0.441753	+	0.765138i
$73$	−16.8200			−1.96864			−0.984318	−	0.176403i	$-0.943554\pi$
$73$	−16.8200			−1.96864			−0.984318	+	0.176403i	$0.943554\pi$
$74$	−2.58003	−	4.46874i	−0.299922	−	0.519480i
$75$		0			0
$76$	−8.09153	−	4.67165i	−0.928162	−	0.535875i
$77$			1.75491i			0.199991i
$78$	−5.95698	−	0.260480i	−0.674495	−	0.0294936i
$79$	−15.0859			−1.69729			−0.848646	−	0.528961i	$-0.822582\pi$
$79$	−15.0859			−1.69729			−0.848646	+	0.528961i	$0.822582\pi$
$80$		0			0
$81$	4.23903	−	7.34222i	0.471003	−	0.815802i
$82$	−0.419323	+	0.242096i	−0.0463065	+	0.0267351i
$83$	0.370576			0.0406760			0.0203380	−	0.999793i	$-0.493526\pi$
$83$	0.370576			0.0406760			0.0203380	+	0.999793i	$0.493526\pi$
$84$	1.96697	−	1.13563i	0.214614	−	0.123908i
$85$		0			0
$86$		−	0.670523i		−	0.0723043i
$87$	−16.9708	+	9.79811i	−1.81946	+	1.05047i
$88$	−6.12507	−	3.53631i	−0.652935	−	0.376972i
$89$	8.00015	+	4.61889i	0.848014	+	0.489601i	0.859980	−	0.510327i	$-0.170476\pi$
$89$	8.00015	+	4.61889i	0.848014	+	0.489601i	−0.0119665	+	0.999928i	$0.503809\pi$
$90$		0			0
$91$	−0.0925751	+	2.11712i	−0.00970451	+	0.221934i
$92$			1.04387i			0.108831i
$93$	5.63284	−	9.75637i	0.584099	−	1.01169i
$94$	−1.05111	+	1.82057i	−0.108413	+	0.187777i
$95$		0			0
$96$			14.3013i			1.45962i
$97$	3.46123	+	5.99502i	0.351434	+	0.608702i	0.986501	−	0.163755i	$-0.0523608\pi$
$97$	3.46123	+	5.99502i	0.351434	+	0.608702i	−0.635067	+	0.772457i	$0.719027\pi$
$98$	−2.21613	−	3.83845i	−0.223863	−	0.387742i
$99$		−	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	$0.924979\pi$
$102$	5.43618	−	9.41575i	0.538262	−	0.932298i
$103$		−	4.42075i		−	0.435590i	−0.975995	−	0.217795i	$-0.930114\pi$
$103$		−	4.42075i		−	0.435590i	0.975995	−	0.217795i	$-0.0698864\pi$
$104$	−7.20272	−	4.58930i	−0.706285	−	0.450018i
$105$		0			0
$106$	2.85209	+	1.64665i	0.277019	+	0.159937i
$107$	2.34408	+	1.35336i	0.226611	+	0.130834i	0.609008	−	0.793164i	$-0.291568\pi$
$107$	2.34408	+	1.35336i	0.226611	+	0.130834i	−0.382397	+	0.923998i	$0.624901\pi$
$108$	−0.551909	+	0.318645i	−0.0531074	+	0.0306616i
$109$			11.3266i			1.08489i	0.840091	+	0.542446i	$0.182502\pi$
$109$			11.3266i			1.08489i	−0.840091	+	0.542446i	$0.817498\pi$
$110$		0			0
$111$	16.6588	−	9.61794i	1.58118	−	0.912894i
$112$	0.902234			0.0852531
$113$	2.17293	−	1.25454i	0.204413	−	0.118018i	−0.394299	−	0.918982i	$-0.629013\pi$
$113$	2.17293	−	1.25454i	0.204413	−	0.118018i	0.598712	+	0.800964i	$0.295679\pi$
$114$	−4.96391	+	8.59774i	−0.464912	+	0.805252i
$115$		0			0
$116$	−12.2836			−1.14050
$117$	0.498503	−	11.4004i	0.0460866	−	1.05396i
$118$		−	9.50818i		−	0.875299i
$119$	−3.34637	−	1.93203i	−0.306761	−	0.177109i
$120$		0			0
$121$	−1.04237	−	1.80544i	−0.0947609	−	0.164131i
$122$	5.36924			0.486108
$123$	−0.902498	−	1.56317i	−0.0813755	−	0.140947i
$124$	6.11562	−	3.53085i	0.549199	−	0.317080i
$125$		0			0
$126$	−0.619478	−	1.07297i	−0.0551875	−	0.0955875i
$127$	−5.20546	−	3.00538i	−0.461910	−	0.266684i	0.250937	−	0.968003i	$-0.419261\pi$
$127$	−5.20546	−	3.00538i	−0.461910	−	0.266684i	−0.712847	+	0.701319i	$0.752595\pi$
$128$	−5.50471	+	9.53444i	−0.486553	+	0.842734i
$129$	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	$0.484473\pi$
$132$	5.76921	−	9.99256i	0.502145	−	0.869741i
$133$	3.05565	+	1.76418i	0.264958	+	0.152974i
$134$	0.212026	+	0.367240i	0.0183163	+	0.0317247i
$135$		0			0
$136$	13.4865	−	7.78644i	1.15646	−	0.667681i
$137$	9.84550	+	17.0529i	0.841158	+	1.45693i	0.888917	+	0.458069i	$0.151459\pi$
$137$	9.84550	+	17.0529i	0.841158	+	1.45693i	−0.0477593	+	0.998859i	$0.515208\pi$
$138$	1.10918			0.0944193
$139$	4.93518	+	8.54798i	0.418596	+	0.725030i	0.995799	−	0.0915711i	$-0.0291889\pi$
$139$	4.93518	+	8.54798i	0.418596	+	0.725030i	−0.577202	+	0.816601i	$0.695856\pi$
$140$		0			0
$141$	−6.78680	−	3.91836i	−0.571551	−	0.329985i
$142$			5.99873i			0.503402i
$143$	4.97038	+	9.54954i	0.415644	+	0.798573i
$144$	−4.85839			−0.404866
$145$		0			0
$146$	−5.60148	+	9.70204i	−0.463581	+	0.802946i
$147$	14.3091	−	8.26138i	1.18020	−	0.681387i
$148$	12.0577			0.991136
$149$	7.04577	−	4.06788i	0.577212	−	0.333254i	−0.182813	−	0.983148i	$-0.558520\pi$
$149$	7.04577	−	4.06788i	0.577212	−	0.333254i	0.760025	+	0.649894i	$0.225187\pi$
$150$		0			0
$151$		−	13.0169i		−	1.05930i	−0.848216	−	0.529650i	$-0.822323\pi$
$151$		−	13.0169i		−	1.05930i	0.848216	−	0.529650i	$-0.177677\pi$
$152$	−12.3148	+	7.10998i	−0.998866	+	0.576695i
$153$	18.0197	+	10.4037i	1.45681	+	0.841088i
$154$	1.01226	+	0.584428i	0.0815702	+	0.0470946i
$155$		0			0
$156$	7.48708	−	11.7506i	0.599446	−	0.940805i
$157$		−	12.3177i		−	0.983061i	−0.870860	−	0.491530i	$-0.836438\pi$
$157$		−	12.3177i		−	0.983061i	0.870860	−	0.491530i	$-0.163562\pi$
$158$	−5.02395	+	8.70174i	−0.399684	+	0.692274i
$159$	−6.13847	+	10.6321i	−0.486812	+	0.843184i
$160$		0			0
$161$		−	0.394203i		−	0.0310675i
$162$	−2.82340	−	4.89027i	−0.221827	−	0.384216i
$163$	1.06690	+	1.84793i	0.0835664	+	0.144741i	0.904779	−	0.425880i	$-0.140036\pi$
$163$	1.06690	+	1.84793i	0.0835664	+	0.144741i	−0.821213	+	0.570622i	$0.806702\pi$
$164$		−	1.13143i		−	0.0883500i
$165$		0			0
$166$	0.123411	−	0.213754i	0.00957852	−	0.0165905i
$167$	−0.0547430	+	0.0948176i	−0.00423614	+	0.00733720i	−0.868136	−	0.496327i	$-0.834682\pi$
$167$	−0.0547430	+	0.0948176i	−0.00423614	+	0.00733720i	0.863900	+	0.503664i	$0.168015\pi$
$168$		−	3.45673i		−	0.266693i
$169$	5.49249	+	11.7827i	0.422499	+	0.906363i
$170$		0			0
$171$	−16.4542	−	9.49984i	−1.25828	−	0.726471i
$172$	1.35692	+	0.783418i	0.103464	+	0.0597351i
$173$	7.10085	−	4.09968i	0.539868	−	0.311693i	−0.205158	−	0.978729i	$-0.565771\pi$
$173$	7.10085	−	4.09968i	0.539868	−	0.311693i	0.745025	+	0.667036i	$0.232437\pi$
$174$			13.0520i			0.989471i
$175$		0			0
$176$	3.96943	−	2.29175i	0.299207	−	0.172747i
$177$	35.4450			2.66421
$178$	5.32848	−	3.07640i	0.399387	−	0.230586i
$179$	0.0150584	−	0.0260820i	0.00112552	−	0.00194946i	−0.865462	−	0.500974i	$-0.832975\pi$
$179$	0.0150584	−	0.0260820i	0.00112552	−	0.00194946i	0.866588	+	0.499025i	$0.166308\pi$
$180$		0			0
$181$	11.4087			0.848004			0.424002	−	0.905661i	$-0.360625\pi$
$181$	11.4087			0.848004			0.424002	+	0.905661i	$0.360625\pi$
$182$	1.19036	+	0.758450i	0.0882350	+	0.0562201i
$183$			20.0157i			1.47960i
$184$	1.37586	+	0.794356i	0.101430	+	0.0585607i
$185$		0			0
$186$	−3.75175	−	6.49821i	−0.275091	−	0.476472i
$187$	−19.6301			−1.43549
$188$	−2.45616	−	4.25419i	−0.179134	−	0.310269i
$189$	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	$0.771495\pi$
$192$	1.64754	+	0.951205i	0.118901	+	0.0686473i
$193$	5.31227	−	9.20113i	0.382386	−	0.662312i	−0.609017	−	0.793157i	$-0.708436\pi$
$193$	5.31227	−	9.20113i	0.382386	−	0.662312i	0.991403	+	0.130846i	$0.0417692\pi$
$194$	4.61069			0.331028
$195$		0			0
$196$	10.3570			0.739787
$197$	2.82278	−	4.88920i	0.201115	−	0.348341i	−0.747773	−	0.663954i	$-0.768877\pi$
$197$	2.82278	−	4.88920i	0.201115	−	0.348341i	0.948888	+	0.315613i	$0.102210\pi$
$198$	−5.45086	−	3.14706i	−0.387376	−	0.223652i
$199$	−7.79679	−	13.5044i	−0.552700	−	0.957305i	−0.998079	−	0.0619621i	$-0.980264\pi$
$199$	−7.79679	−	13.5044i	−0.552700	−	0.957305i	0.445378	−	0.895342i	$-0.353069\pi$
$200$		0			0
$201$	−1.36901	+	0.790401i	−0.0965628	+	0.0557506i
$202$	4.60797	+	7.98123i	0.324215	+	0.561558i
$203$	4.63871			0.325574
$204$	12.7029	+	22.0021i	0.889383	+	1.54046i
$205$		0			0
$206$	−2.54996	−	1.47222i	−0.177664	−	0.102574i
$207$			2.12272i			0.147539i
$208$	4.90960	−	2.55536i	0.340419	−	0.177183i
$209$	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	$0.968594\pi$
$212$	−6.66458	+	3.84780i	−0.457725	+	0.264268i
$213$	−22.3623			−1.53224
$214$	1.56127	−	0.901400i	0.106726	−	0.0616184i
$215$		0			0
$216$			0.969917i			0.0659945i
$217$	−2.30948	+	1.33338i	−0.156777	+	0.0905155i
$218$	6.53335	+	3.77203i	0.442494	+	0.255474i
$219$	−36.1677	−	20.8814i	−2.44399	−	1.41104i
$220$		0			0
$221$	−23.6816	−	1.03553i	−1.59300	−	0.0696570i
$222$		−	12.8120i		−	0.859886i
$223$	−8.21470	+	14.2283i	−0.550097	+	0.952796i	0.448170	+	0.893948i	$0.352076\pi$
$223$	−8.21470	+	14.2283i	−0.550097	+	0.952796i	−0.998267	+	0.0588475i	$0.981257\pi$
$224$	1.69267	−	2.93179i	0.113096	−	0.195888i
$225$		0			0
$226$		−	1.67117i		−	0.111165i
$227$	8.62262	+	14.9348i	0.572304	+	0.991259i	0.996329	+	0.0856085i	$0.0272834\pi$
$227$	8.62262	+	14.9348i	0.572304	+	0.991259i	−0.424025	+	0.905650i	$0.639383\pi$
$228$	−11.5993	−	20.0907i	−0.768186	−	1.33054i
$229$			10.0809i			0.666162i	0.942898	+	0.333081i	$0.108088\pi$
$229$			10.0809i			0.666162i	−0.942898	+	0.333081i	$0.891912\pi$
$230$		0			0
$231$	−2.17866	+	3.77355i	−0.143345	+	0.248281i
$232$	−9.34744	+	16.1902i	−0.613689	+	1.06294i
$233$		−	19.7103i		−	1.29126i	−0.763648	−	0.645632i	$-0.776594\pi$
$233$		−	19.7103i		−	1.29126i	0.763648	−	0.645632i	$-0.223406\pi$
$234$	−6.40988	−	4.08414i	−0.419027	−	0.266989i
$235$		0			0
$236$	19.2415	+	11.1091i	1.25251	+	0.723138i
$237$	−32.4388	−	18.7285i	−2.10712	−	1.21655i
$238$	−2.22884	+	1.28682i	−0.144474	+	0.0834124i
$239$			11.2372i			0.726871i	0.931619	+	0.363435i	$0.118396\pi$
$239$			11.2372i			0.726871i	−0.931619	+	0.363435i	$0.881604\pi$
$240$		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	$0.294806\pi$
$242$	−1.38854			−0.0892586
$243$	19.2940	−	11.1394i	1.23771	−	0.714593i
$244$	−6.27326	+	10.8656i	−0.401604	+	0.695599i
$245$		0			0
$246$	−1.20221			−0.0766504
$247$	21.6243	+	0.945563i	1.37592	+	0.0601647i
$248$		−	10.7475i		−	0.682468i
$249$	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	$0.611020\pi$
$252$	2.89512			0.182375
$253$	−1.00131	−	1.73432i	−0.0629518	−	0.109036i
$254$	−3.46709	+	2.00172i	−0.217545	+	0.125599i
$255$		0			0
$256$	4.43260	+	7.67749i	0.277038	+	0.479843i
$257$	−12.4336	−	7.17856i	−0.775588	−	0.447786i	0.0592763	−	0.998242i	$-0.481121\pi$
$257$	−12.4336	−	7.17856i	−0.775588	−	0.447786i	−0.834864	+	0.550456i	$0.814454\pi$
$258$	0.832429	−	1.44181i	0.0518247	−	0.0897631i
$259$	−4.55341			−0.282935
$260$		0			0
$261$	−24.9787			−1.54615
$262$	0.371715	−	0.643829i	0.0229646	−	0.0397759i
$263$	−23.1590	−	13.3709i	−1.42805	−	0.824484i	−0.431081	−	0.902313i	$-0.641868\pi$
$263$	−23.1590	−	13.3709i	−1.42805	−	0.824484i	−0.996967	+	0.0778291i	$0.975201\pi$
$264$	−8.78040	−	15.2081i	−0.540396	−	0.935994i
$265$		0			0
$266$	2.03521	−	1.17503i	0.124787	−	0.0720456i
$267$	11.4683	+	19.8638i	0.701851	+	1.21564i
$268$	−0.990899			−0.0605288
$269$	0.215092	+	0.372550i	0.0131144	+	0.0227148i	0.872508	−	0.488600i	$-0.162492\pi$
$269$	0.215092	+	0.372550i	0.0131144	+	0.0227148i	−0.859394	+	0.511314i	$0.829159\pi$
$270$		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	$0.550375\pi$
$272$			10.0922i			0.611929i
$273$	−2.82739	+	4.43746i	−0.171121	+	0.268567i
$274$	13.1151			0.792315
$275$		0			0
$276$	−1.29593	+	2.24461i	−0.0780056	+	0.135110i
$277$	3.44320	−	1.98793i	0.206882	−	0.119443i	−0.392980	−	0.919547i	$-0.628556\pi$
$277$	3.44320	−	1.98793i	0.206882	−	0.119443i	0.599861	+	0.800104i	$0.295222\pi$
$278$	6.57413			0.394290
$279$	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	$-0.172882\pi$
$282$	−4.52033	+	2.60982i	−0.269182	+	0.155412i
$283$	7.80686	+	4.50729i	0.464070	+	0.267931i	0.713754	−	0.700397i	$-0.246994\pi$
$283$	7.80686	+	4.50729i	0.464070	+	0.267931i	−0.249684	+	0.968327i	$0.580327\pi$
$284$	−12.1395	−	7.00873i	−0.720346	−	0.415892i
$285$		0			0
$286$	7.16357	+	0.313241i	0.423591	+	0.0185223i
$287$			0.427269i			0.0252209i
$288$	−9.11476	+	15.7872i	−0.537092	+	0.930271i
$289$	13.1113	−	22.7094i	0.771250	−	1.33584i
$290$		0			0
$291$			17.1879i			1.00757i
$292$	−13.0892	−	22.6711i	−0.765986	−	1.32673i
$293$	13.5908	+	23.5400i	0.793984	+	1.37522i	0.923482	+	0.383641i	$0.125330\pi$
$293$	13.5908	+	23.5400i	0.793984	+	1.37522i	−0.129498	+	0.991580i	$0.541337\pi$
$294$		−	11.0050i		−	0.641822i
$295$		0			0
$296$	9.17555	−	15.8925i	0.533318	−	0.923734i
$297$	0.611305	−	1.05881i	0.0354715	−	0.0614385i
$298$		−	5.41881i		−	0.313903i
$299$	−1.11649	−	2.14510i	−0.0645681	−	0.124054i
$300$		0			0
$301$	−0.512421	−	0.295846i	−0.0295355	−	0.0170523i
$302$	−7.50833	−	4.33494i	−0.432056	−	0.249448i
$303$	−29.7528	+	17.1778i	−1.70925	+	0.986838i
$304$		−	9.21542i		−	0.528541i
$305$		0			0
$306$	12.0020	−	6.92935i	0.686108	−	0.396125i
$307$	−15.4630			−0.882522			−0.441261	−	0.897379i	$-0.645469\pi$
$307$	−15.4630			−0.882522			−0.441261	+	0.897379i	$0.645469\pi$
$308$	−2.36538	+	1.36566i	−0.134780	+	0.0778154i
$309$	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	$0.577481\pi$
$312$	−9.79038	−	18.8102i	−0.554271	−	1.06492i
$313$			4.81358i			0.272080i	0.990703	+	0.136040i	$0.0434375\pi$
$313$			4.81358i			0.272080i	−0.990703	+	0.136040i	$0.956562\pi$
$314$	−7.10504	−	4.10209i	−0.400960	−	0.231495i
$315$		0			0
$316$	−11.7397	−	20.3337i	−0.660408	−	1.14386i
$317$	−3.35387			−0.188372			−0.0941860	−	0.995555i	$-0.530025\pi$
$317$	−3.35387			−0.188372			−0.0941860	+	0.995555i	$0.530025\pi$
$318$	4.08852	+	7.08152i	0.229273	+	0.397112i
$319$	20.4083	−	11.7827i	1.14264	−	0.659706i
$320$		0			0
$321$	3.36028	+	5.82017i	0.187552	+	0.324850i
$322$	−0.227382	−	0.131279i	−0.0126715	−	0.00731589i
$323$	−19.7337	+	34.1798i	−1.09801	+	1.90182i
$324$	13.1951			0.733060
$325$		0			0
$326$	1.42122			0.0787141
$327$	−14.0616	+	24.3553i	−0.777606	+	1.34685i
$328$	−1.49127	−	0.860987i	−0.0823418	−	0.0475400i
$329$	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	$0.524509\pi$
$332$	0.288378	+	0.499486i	0.0158268	+	0.0274129i
$333$	24.5194			1.34366
$334$	0.0364614	+	0.0631531i	0.00199508	+	0.00345558i
$335$		0			0
$336$	1.94005	+	1.12009i	0.105838	+	0.0611059i
$337$			15.3344i			0.835316i	0.908604	+	0.417658i	$0.137149\pi$
$337$			15.3344i			0.835316i	−0.908604	+	0.417658i	$0.862851\pi$
$338$	8.62558	+	0.755785i	0.469170	+	0.0411093i
$339$	6.22988			0.338361
$340$		0			0
$341$	−6.77378	+	11.7325i	−0.366821	+	0.635352i
$342$	−10.9593	+	6.32735i	−0.592611	+	0.342144i
$343$	−8.02539			−0.433330
$344$	2.06515	−	1.19232i	0.111346	−	0.0642854i
$345$		0			0
$346$		−	5.46116i		−	0.293594i
$347$	13.0352	−	7.52585i	0.699764	−	0.404009i	−0.107495	−	0.994206i	$-0.534283\pi$
$347$	13.0352	−	7.52585i	0.699764	−	0.404009i	0.807260	+	0.590197i	$0.200950\pi$
$348$	−26.4130	−	15.2496i	−1.41589	−	0.817463i
$349$	−26.8768	−	15.5173i	−1.43868	−	0.830623i	−0.440923	−	0.897545i	$-0.645349\pi$
$349$	−26.8768	−	15.5173i	−1.43868	−	0.830623i	−0.997758	+	0.0669222i	$0.978682\pi$
$350$		0			0
$351$	0.793330	−	1.24510i	0.0423448	−	0.0664584i
$352$		−	17.1981i		−	0.916661i
$353$	14.2633	−	24.7048i	0.759161	−	1.31491i	−0.184118	−	0.982904i	$-0.558943\pi$
$353$	14.2633	−	24.7048i	0.759161	−	1.31491i	0.943279	−	0.332002i	$-0.107724\pi$
$354$	11.8040	−	20.4452i	0.627378	−	1.08665i
$355$		0			0
$356$			14.3775i			0.762005i
$357$	−4.79708	−	8.30879i	−0.253888	−	0.439748i
$358$	−0.0100296	−	0.0173718i	−0.000530083	−	0.000918131i
$359$			16.4735i			0.869437i	0.900566	+	0.434718i	$0.143152\pi$
$359$			16.4735i			0.869437i	−0.900566	+	0.434718i	$0.856848\pi$
$360$		0			0
$361$	8.51935	−	14.7559i	0.448387	−	0.776628i
$362$	3.79938	−	6.58072i	0.199691	−	0.345875i
$363$		−	5.17625i		−	0.271683i
$364$	−2.92563	+	1.52274i	−0.153345	+	0.0798134i
$365$		0			0
$366$	11.5453	+	6.66571i	0.603485	+	0.348422i
$367$	3.26441	+	1.88471i	0.170401	+	0.0983809i	0.582775	−	0.812634i	$-0.301967\pi$
$367$	3.26441	+	1.88471i	0.170401	+	0.0983809i	−0.412374	+	0.911015i	$0.635300\pi$
$368$	−0.891646	+	0.514792i	−0.0464803	+	0.0268354i
$369$		−	2.30078i		−	0.119774i
$370$		0			0
$371$	2.51678	−	1.45306i	0.130665	−	0.0754394i
$372$	17.5337			0.909080
$373$	11.4862	−	6.63155i	0.594732	−	0.343368i	−0.172235	−	0.985056i	$-0.555099\pi$
$373$	11.4862	−	6.63155i	0.594732	−	0.343368i	0.766966	+	0.641688i	$0.221765\pi$
$374$	−6.53729	+	11.3229i	−0.338035	+	0.585494i
$375$		0			0
$376$	−7.47626			−0.385559
$377$	25.2420	−	13.1381i	1.30003	−	0.676644i
$378$		−	0.160293i		−	0.00824459i
$379$	−19.0442	−	10.9952i	−0.978235	−	0.564784i	−0.0764985	−	0.997070i	$-0.524374\pi$
$379$	−19.0442	−	10.9952i	−0.978235	−	0.564784i	−0.901737	+	0.432285i	$0.857707\pi$
$380$		0			0
$381$	−7.46212	−	12.9248i	−0.382296	−	0.662156i
$382$	3.55404			0.181841
$383$	−11.3380	−	19.6380i	−0.579344	−	1.00345i	−0.995555	−	0.0941845i	$-0.969976\pi$
$383$	−11.3380	−	19.6380i	−0.579344	−	1.00345i	0.416211	−	0.909268i	$-0.363358\pi$
$384$	−23.6733	+	13.6678i	−1.20807	+	0.697481i
$385$		0			0
$386$	−3.53823	−	6.12839i	−0.180091	−	0.311927i
$387$	2.75931	+	1.59309i	0.140264	+	0.0809812i
$388$	−5.38698	+	9.33053i	−0.273483	+	0.473686i
$389$	18.3322			0.929480			0.464740	−	0.885447i	$-0.346148\pi$
$389$	18.3322			0.929480			0.464740	+	0.885447i	$0.346148\pi$
$390$		0			0
$391$	4.40947			0.222996
$392$	7.88139	−	13.6510i	0.398070	−	0.689478i
$393$	2.40009	+	1.38569i	0.121069	+	0.0698991i
$394$	−1.88011	−	3.25644i	−0.0947184	−	0.164057i
$395$		0			0
$396$	12.7372	−	7.35385i	0.640070	−	0.369545i
$397$	2.67834	+	4.63902i	0.134422	+	0.232826i	0.925377	−	0.379049i	$-0.123749\pi$
$397$	2.67834	+	4.63902i	0.134422	+	0.232826i	−0.790954	+	0.611875i	$0.790416\pi$
$398$	−10.3861			−0.520607
$399$	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	$0.574174\pi$
$402$			1.05289i			0.0525134i
$403$	−8.79078	+	13.7968i	−0.437900	+	0.687265i
$404$	−21.5352			−1.07142
$405$		0			0
$406$	1.54480	−	2.67568i	0.0766672	−	0.132792i
$407$	−20.0330	+	11.5661i	−0.992999	+	0.573308i
$408$	38.6663			1.91427
$409$	15.0683	−	8.69969i	0.745080	−	0.430172i	−0.0788336	−	0.996888i	$-0.525120\pi$
$409$	15.0683	−	8.69969i	0.745080	−	0.430172i	0.823913	+	0.566716i	$0.191786\pi$
$410$		0			0
$411$			48.8912i			2.41163i
$412$	5.95858	−	3.44019i	0.293558	−	0.169486i
$413$	−7.26626	−	4.19518i	−0.357549	−	0.206431i
$414$	1.22442	+	0.706918i	0.0601768	+	0.0347431i
$415$		0			0
$416$	0.907233	−	20.7477i	0.0444808	−	1.01724i
$417$			24.5073i			1.20013i
$418$	5.96935	−	10.3392i	0.291970	−	0.505708i
$419$	−11.2389	+	19.4664i	−0.549058	+	0.950996i	0.449282	+	0.893390i	$0.351680\pi$
$419$	−11.2389	+	19.4664i	−0.549058	+	0.950996i	−0.998339	+	0.0576056i	$0.981653\pi$
$420$		0			0
$421$		−	5.16889i		−	0.251916i	−0.992036	−	0.125958i	$-0.959799\pi$
$421$		−	5.16889i		−	0.251916i	0.992036	−	0.125958i	$-0.0402005\pi$
$422$	5.63926	+	9.76749i	0.274515	+	0.475474i
$423$	−4.99462	−	8.65094i	−0.242847	−	0.420623i
$424$			11.7122i			0.568797i
$425$		0			0
$426$	−7.44720	+	12.8989i	−0.360818	+	0.624955i
$427$	2.36900	−	4.10324i	0.114644	−	0.198569i
$428$			4.21267i			0.203627i
$429$	−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	$0.885241\pi$
$432$	−0.544355	−	0.314284i	−0.0261903	−	0.0151210i
$433$	16.3773	−	9.45546i	0.787045	−	0.454401i	−0.0518762	−	0.998654i	$-0.516520\pi$
$433$	16.3773	−	9.45546i	0.787045	−	0.454401i	0.838921	+	0.544253i	$0.183187\pi$
$434$			1.77619i			0.0852596i
$435$		0			0
$436$	−15.2667	+	8.81425i	−0.731144	+	0.422126i
$437$	−4.02639			−0.192608
$438$	−24.0894	+	13.9080i	−1.15104	+	0.664552i
$439$	−13.7455	+	23.8079i	−0.656037	+	1.13629i	0.325596	+	0.945509i	$0.394435\pi$
$439$	−13.7455	+	23.8079i	−0.656037	+	1.13629i	−0.981633	+	0.190780i	$0.938898\pi$
$440$		0			0
$441$	21.0611			1.00291
$442$	−8.48386	+	13.3151i	−0.403536	+	0.633333i
$443$		−	19.2846i		−	0.916240i	−0.888890	−	0.458120i	$-0.848523\pi$
$443$		−	19.2846i		−	0.916240i	0.888890	−	0.458120i	$-0.151477\pi$
$444$	25.9274	+	14.9692i	1.23046	+	0.710405i
$445$		0			0
$446$	5.47138	+	9.47672i	0.259078	+	0.448735i
$447$	20.2005			0.955450
$448$	−0.225164	−	0.389996i	−0.0106380	−	0.0184256i
$449$	−5.66090	+	3.26832i	−0.267154	+	0.154242i	−0.627594	−	0.778541i	$-0.715960\pi$
$449$	−5.66090	+	3.26832i	−0.267154	+	0.154242i	0.360439	+	0.932783i	$0.382627\pi$
$450$		0			0
$451$	1.08530	+	1.87979i	0.0511048	+	0.0885161i
$452$	3.38191	+	1.95255i	0.159072	+	0.0918401i
$453$	16.1600	−	27.9899i	0.759262	−	1.31508i
$454$	11.4862			0.539072
$455$		0			0
$456$	−35.3071			−1.65341
$457$	−7.20317	+	12.4763i	−0.336950	+	0.583614i	−0.983857	−	0.178954i	$-0.942729\pi$
$457$	−7.20317	+	12.4763i	−0.336950	+	0.583614i	0.646907	+	0.762569i	$0.276062\pi$
$458$	5.81478	+	3.35717i	0.271707	+	0.156870i
$459$	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	$0.233414\pi$
$462$	1.45109	+	2.51336i	0.0675108	+	0.116932i
$463$	−18.8671			−0.876827			−0.438413	−	0.898773i	$-0.644459\pi$
$463$	−18.8671			−0.876827			−0.438413	+	0.898773i	$0.644459\pi$
$464$	−6.05772	−	10.4923i	−0.281223	−	0.487092i
$465$		0			0
$466$	−11.3692	−	6.56400i	−0.526667	−	0.304072i
$467$		−	21.8870i		−	1.01281i	−0.862295	−	0.506406i	$-0.830974\pi$
$467$		−	21.8870i		−	1.01281i	0.862295	−	0.506406i	$-0.169026\pi$
$468$	15.7541	−	8.19974i	0.728233	−	0.379033i
$469$	0.374199			0.0172789
$470$		0			0
$471$	15.2920	−	26.4865i	0.704617	−	1.22043i
$472$	29.2844	−	16.9073i	1.34792	−	0.778224i
$473$	−3.00590			−0.138212
$474$	−21.6058	+	12.4741i	−0.992386	+	0.572954i
$475$		0			0
$476$		−	6.01394i		−	0.275648i
$477$	−13.5525	+	7.82453i	−0.620526	+	0.358261i
$478$	6.48175	+	3.74224i	0.296468	+	0.171166i
$479$	24.3402	+	14.0528i	1.11213	+	0.642089i	0.939381	−	0.342876i	$-0.111401\pi$
$479$	24.3402	+	14.0528i	1.11213	+	0.642089i	0.172751	+	0.984966i	$0.444734\pi$
$480$		0			0
$481$	−24.7779	+	12.8965i	−1.12977	+	0.588028i
$482$		−	2.49689i		−	0.113730i
$483$	0.489388	−	0.847645i	0.0222679	−	0.0385692i
$484$	1.62232	−	2.80995i	0.0737420	−	0.127725i
$485$		0			0
$486$		−	14.8387i		−	0.673099i
$487$	−9.16127	−	15.8678i	−0.415137	−	0.719038i	0.580306	−	0.814398i	$-0.302933\pi$
$487$	−9.16127	−	15.8678i	−0.415137	−	0.719038i	−0.995443	+	0.0953608i	$0.969600\pi$
$488$	9.54753	+	16.5368i	0.432196	+	0.748586i
$489$			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	$0.00362052\pi$
$492$	1.40463	−	2.43289i	0.0633256	−	0.109683i
$493$			51.8876i			2.33690i
$494$	7.74681	−	12.1583i	0.348546	−	0.547028i
$495$		0			0
$496$	6.03192	+	3.48253i	0.270841	+	0.156370i
$497$	4.58430	+	2.64675i	0.205634	+	0.118723i
$498$	0.530734	−	0.306419i	0.0237828	−	0.0137310i
$499$			14.7418i			0.659933i	0.943993	+	0.329966i	$0.107037\pi$
$499$			14.7418i			0.659933i	−0.943993	+	0.329966i	$0.892963\pi$
$500$		0			0
$501$	−0.235425	+	0.135923i	−0.0105180	+	0.00607257i
$502$	13.5703			0.605670
$503$	32.1631	−	18.5694i	1.43408	−	0.827969i	0.436655	−	0.899629i	$-0.356163\pi$
$503$	32.1631	−	18.5694i	1.43408	−	0.827969i	0.997429	+	0.0716604i	$0.0228298\pi$
$504$	2.20310	−	3.81588i	0.0981338	−	0.169973i
$505$		0			0
$506$	−1.33384			−0.0592964
$507$	−2.81745	+	32.1548i	−0.125127	+	1.42805i
$508$		−	9.35501i		−	0.415062i
$509$	11.0110	+	6.35722i	0.488055	+	0.281779i	0.723767	−	0.690044i	$-0.242409\pi$
$509$	11.0110	+	6.35722i	0.488055	+	0.281779i	−0.235712	+	0.971823i	$0.575742\pi$
$510$		0			0
$511$	4.94294	+	8.56142i	0.218663	+	0.378735i
$512$	−16.1142			−0.712154
$513$	−1.22907	−	2.12881i	−0.0542646	−	0.0939891i
$514$	−8.28139	+	4.78126i	−0.365276	+	0.210892i
$515$		0			0
$516$	1.94517	+	3.36913i	0.0856312	+	0.148318i
$517$	8.16147	+	4.71203i	0.358941	+	0.207235i
$518$	−1.51640	+	2.62647i	−0.0666266	+	0.115401i
$519$	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	$0.229033\pi$
$522$	−8.31852	+	14.4081i	−0.364092	+	0.630626i
$523$	20.6494	+	11.9219i	0.902934	+	0.521309i	0.878151	−	0.478384i	$-0.158777\pi$
$523$	20.6494	+	11.9219i	0.902934	+	0.521309i	0.0247827	+	0.999693i	$0.492111\pi$
$524$	0.868600	+	1.50446i	0.0379450	+	0.0657226i
$525$		0			0
$526$	−15.4250	+	8.90565i	−0.672564	+	0.388305i
$527$	−14.9149	−	25.8333i	−0.649702	−	1.12532i
$528$	11.3805			0.495272
$529$	−11.2751	−	19.5290i	−0.490221	−	0.849087i
$530$		0			0
$531$	39.1277	+	22.5904i	1.69800	+	0.980339i
$532$			5.49147i			0.238085i
$533$	1.21014	+	2.32503i	0.0524169	+	0.100708i
$534$	15.2769			0.661098
$535$		0			0
$536$	−0.754046	+	1.30605i	−0.0325698	+	0.0564126i
$537$	0.0647596	−	0.0373890i	0.00279458	−	0.00161345i
$538$	0.286523			0.0123529
$539$	−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	$-0.114264\pi$
$542$	6.78492	−	3.91728i	0.291437	−	0.168261i
$543$	24.5319	+	14.1635i	1.05277	+	0.607814i
$544$	32.7943	+	18.9338i	1.40605	+	0.811781i
$545$		0			0
$546$	1.61801	+	3.10866i	0.0692442	+	0.133038i
$547$			3.13542i			0.134061i	0.997751	+	0.0670305i	$0.0213525\pi$
$547$			3.13542i			0.134061i	−0.997751	+	0.0670305i	$0.978648\pi$
$548$	−15.3233	+	26.5408i	−0.654580	+	1.13377i
$549$	−12.7567	+	22.0953i	−0.544444	+	0.943004i
$550$		0			0
$551$		−	47.3798i		−	2.01845i
$552$	1.97233	+	3.41617i	0.0839477	+	0.145402i
$553$	4.43331	+	7.67873i	0.188524	+	0.326533i
$554$		−	2.64812i		−	0.112508i
$555$		0			0
$556$	−7.68101	+	13.3039i	−0.325747	+	0.564211i
$557$	11.7849	−	20.4120i	0.499341	−	0.864883i	−0.500659	−	0.865645i	$-0.666909\pi$
$557$	11.7849	−	20.4120i	0.499341	−	0.864883i	1.00000		0.000761144i	$0.000242280\pi$
$558$		−	9.56449i		−	0.404897i
$559$	−3.62631	−	0.158567i	−0.153377	−	0.00670668i
$560$		0			0
$561$	−42.2101	−	24.3700i	−1.78211	−	1.02890i
$562$	−9.99432	−	5.77022i	−0.421585	−	0.243402i
$563$	−12.6564	+	7.30716i	−0.533402	+	0.307960i	−0.742401	−	0.669956i	$-0.766313\pi$
$563$	−12.6564	+	7.30716i	−0.533402	+	0.307960i	0.208999	+	0.977916i	$0.432980\pi$
$564$		−	12.1969i		−	0.513583i
$565$		0			0
$566$	5.19974	−	3.00207i	0.218561	−	0.126187i
$567$	−4.98293			−0.209263
$568$	−18.4756	+	10.6669i	−0.775218	+	0.447573i
$569$	8.80300	−	15.2472i	0.369041	−	0.639198i	−0.620375	−	0.784305i	$-0.713020\pi$
$569$	8.80300	−	15.2472i	0.369041	−	0.639198i	0.989416	+	0.145108i	$0.0463529\pi$
$570$		0			0
$571$	−3.82424			−0.160039			−0.0800197	−	0.996793i	$-0.525498\pi$
$571$	−3.82424			−0.160039			−0.0800197	+	0.996793i	$0.525498\pi$
$572$	−9.00359	+	14.1308i	−0.376459	+	0.590836i
$573$			13.2489i			0.553482i
$574$	0.246455	+	0.142291i	0.0102868	+	0.00593910i
$575$		0			0
$576$	1.21247	+	2.10007i	0.0505198	+	0.0875028i
$577$	6.37523			0.265405			0.132702	−	0.991156i	$-0.457635\pi$
$577$	6.37523			0.265405			0.132702	+	0.991156i	$0.457635\pi$
$578$	−8.73273	−	15.1255i	−0.363234	−	0.629139i
$579$	22.8457	−	13.1900i	0.949435	−	0.548156i
$580$		0			0
$581$	−0.108902	−	0.188624i	−0.00451801	−	0.00782543i
$582$	9.91424	+	5.72399i	0.410959	+	0.237267i
$583$	7.38182	−	12.7857i	0.305724	−	0.529529i
$584$	−39.8419			−1.64867
$585$		0			0
$586$	18.1043			0.747881
$587$	23.6306	−	40.9293i	0.975338	−	1.68933i	0.296522	−	0.955026i	$-0.404173\pi$
$587$	23.6306	−	40.9293i	0.975338	−	1.68933i	0.678816	−	0.734308i	$-0.262493\pi$
$588$	22.2704	+	12.8578i	0.918418	+	0.530249i
$589$	13.6191	+	23.5890i	0.561166	+	0.971967i
$590$		0			0
$591$	12.1395	−	7.00875i	0.499353	−	0.288301i
$592$	5.94633	+	10.2993i	0.244393	+	0.423301i
$593$	6.35373			0.260916			0.130458	−	0.991454i	$-0.458355\pi$
$593$	6.35373			0.260916			0.130458	+	0.991454i	$0.458355\pi$
$594$	−0.407159	−	0.705219i	−0.0167059	−	0.0289355i
$595$		0			0
$596$	10.9659	+	6.33117i	0.449181	+	0.259335i
$597$		−	38.7177i		−	1.58461i
$598$	−1.60914	−	0.0703627i	−0.0658026	−	0.00287735i
$599$	−43.2542			−1.76732			−0.883658	−	0.468132i	$-0.844927\pi$
$599$	−43.2542			−1.76732			−0.883658	+	0.468132i	$0.844927\pi$
$600$		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	$0.128982\pi$
$602$	−0.341297	+	0.197048i	−0.0139102	+	0.00803107i
$603$	−2.01500			−0.0820573
$604$	17.5450	−	10.1296i	0.713896	−	0.412168i
$605$		0			0
$606$			22.8825i			0.929537i
$607$	20.1221	−	11.6175i	0.816731	−	0.471540i	−0.0325569	−	0.999470i	$-0.510365\pi$
$607$	20.1221	−	11.6175i	0.816731	−	0.471540i	0.849288	+	0.527930i	$0.177032\pi$
$608$	−29.9453	−	17.2889i	−1.21444	−	0.701158i
$609$	9.97450	+	5.75878i	0.404187	+	0.233358i
$610$		0			0
$611$	9.59739	+	6.11510i	0.388269	+	0.247391i
$612$			32.3842i			1.30905i
$613$	11.6623	−	20.1997i	0.471035	−	0.815857i	−0.528416	−	0.848986i	$-0.677214\pi$
$613$	11.6623	−	20.1997i	0.471035	−	0.815857i	0.999451	+	0.0331286i	$0.0105471\pi$
$614$	−5.14956	+	8.91930i	−0.207819	+	0.359954i
$615$		0			0
$616$			4.15690i			0.167486i
$617$	9.13768	+	15.8269i	0.367869	+	0.637168i	0.989232	−	0.146355i	$-0.0467540\pi$
$617$	9.13768	+	15.8269i	0.367869	+	0.637168i	−0.621363	+	0.783523i	$0.713421\pi$
$618$	−3.65540	−	6.33135i	−0.147042	−	0.254684i
$619$		−	45.4589i		−	1.82715i	−0.406675	−	0.913573i	$-0.633312\pi$
$619$		−	45.4589i		−	1.82715i	0.406675	−	0.913573i	$-0.366688\pi$
$620$		0			0
$621$	−0.137316	+	0.237839i	−0.00551032	+	0.00954415i
$622$	−2.83095	+	4.90334i	−0.113511	+	0.196606i
$623$		−	5.42945i		−	0.217526i
$624$	13.7294	+	0.600344i	0.549615	+	0.0240330i
$625$		0			0
$626$	2.77654	+	1.60304i	0.110973	+	0.0640703i
$627$	38.5430	+	22.2528i	1.53926	+	0.888692i
$628$	16.6026	−	9.58552i	0.662516	−	0.382504i
$629$		−	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	$0.614115\pi$
$632$	−35.7342			−1.42143
$633$	−36.4117	+	21.0223i	−1.44723	+	0.835561i
$634$	−1.11692	+	1.93456i	−0.0443585	+	0.0768312i
$635$		0			0
$636$	−19.1076			−0.757665
$637$	−21.2831	+	11.0775i	−0.843267	+	0.438906i
$638$		−	15.6957i		−	0.621400i
$639$	−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	$0.697965\pi$
$642$	4.47621			0.176662
$643$	−0.719272	−	1.24581i	−0.0283653	−	0.0491301i	0.851494	−	0.524364i	$-0.175697\pi$
$643$	−0.719272	−	1.24581i	−0.0283653	−	0.0491301i	−0.879860	+	0.475234i	$0.842364\pi$
$644$	0.531332	−	0.306765i	0.0209374	−	0.0120882i
$645$		0			0
$646$	13.1436	+	22.7654i	0.517129	+	0.895694i
$647$	−41.6923	−	24.0711i	−1.63909	−	0.946331i	−0.981146	−	0.193268i	$-0.938091\pi$
$647$	−41.6923	−	24.0711i	−1.63909	−	0.946331i	−0.657948	−	0.753063i	$-0.728575\pi$
$648$	10.0411	−	17.3917i	0.394451	−	0.683209i
$649$	−42.6244			−1.67316
$650$		0			0
$651$	−6.62134			−0.259511
$652$	−1.66051	+	2.87609i	−0.0650305	+	0.112636i
$653$	−32.5257	−	18.7787i	−1.27283	−	0.734869i	−0.297311	−	0.954781i	$-0.596090\pi$
$653$	−32.5257	−	18.7787i	−1.27283	−	0.734869i	−0.975520	+	0.219911i	$0.929423\pi$
$654$	9.36567	+	16.2218i	0.366227	+	0.634323i
$655$		0			0
$656$	0.966438	−	0.557973i	0.0377331	−	0.0217852i
$657$	−26.6170	−	46.1020i	−1.03843	−	1.79861i
$658$	1.23556			0.0481672
$659$	−6.65871	−	11.5332i	−0.259387	−	0.449271i	0.706691	−	0.707522i	$-0.250187\pi$
$659$	−6.65871	−	11.5332i	−0.259387	−	0.449271i	−0.966078	+	0.258251i	$0.916854\pi$
$660$		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	$0.926078\pi$
$662$			13.6962i			0.532320i
$663$	−49.6365	−	31.6265i	−1.92772	−	1.22827i
$664$	0.877790			0.0340649
$665$		0			0
$666$	8.16556	−	14.1432i	0.316409	−	0.548036i
$667$	−4.58427	+	2.64673i	−0.177504	+	0.102482i
$668$	−0.170402			−0.00659304
$669$	−35.3277	+	20.3965i	−1.36585	+	0.788573i
$670$		0			0
$671$		−	24.0699i		−	0.929208i
$672$	7.27940	−	4.20276i	0.280809	−	0.162125i
$673$	−41.0691	−	23.7113i	−1.58310	−	0.914002i	−0.994404	−	0.105647i	$-0.966309\pi$
$673$	−41.0691	−	23.7113i	−1.58310	−	0.914002i	−0.588695	−	0.808356i	$-0.700358\pi$
$674$	8.84509	+	5.10671i	0.340700	+	0.196703i
$675$		0			0
$676$	−11.6073	+	16.5723i	−0.446435	+	0.637397i
$677$		−	5.91735i		−	0.227422i	−0.993514	−	0.113711i	$-0.963726\pi$
$677$		−	5.91735i		−	0.227422i	0.993514	−	0.113711i	$-0.0362738\pi$
$678$	2.07470	−	3.59348i	0.0796783	−	0.138007i
$679$	2.03432	−	3.52354i	0.0780699	−	0.135221i
$680$		0			0
$681$			42.8186i			1.64081i
$682$	4.51166	+	7.81443i	0.172761	+	0.299230i
$683$	−7.50043	−	12.9911i	−0.286996	−	0.497092i	0.686095	−	0.727512i	$-0.259323\pi$
$683$	−7.50043	−	12.9911i	−0.286996	−	0.497092i	−0.973091	+	0.230420i	$0.925990\pi$
$684$		−	29.5707i		−	1.13067i
$685$		0			0
$686$	−2.67265	+	4.62916i	−0.102042	+	0.176742i
$687$	−12.5150	+	21.6766i	−0.477477	+	0.827014i
$688$			1.54539i			0.0589175i
$689$	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	$0.453431\pi$
$692$	11.0516	+	6.38066i	0.420120	+	0.242556i
$693$	−4.81003	+	2.77707i	−0.182718	+	0.105492i
$694$		−	10.0252i		−	0.380550i
$695$		0			0
$696$	−40.1991	+	23.2090i	−1.52374	+	0.879734i
$697$	−4.77934			−0.181030
$698$	−17.9012	+	10.3353i	−0.677571	+	0.391196i
$699$	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	$0.547255\pi$
$702$	−0.453993	−	0.872252i	−0.0171349	−	0.0329210i
$703$			46.5086i			1.75410i
$704$	−1.98125	−	1.14387i	−0.0746710	−	0.0431113i
$705$		0			0
$706$	−9.50007	−	16.4546i	−0.357540	−	0.619277i
$707$	8.13246			0.305853
$708$	27.5830	+	47.7751i	1.03663	+	1.79550i
$709$	−27.3294	+	15.7786i	−1.02638	+	0.592580i	−0.915945	−	0.401304i	$-0.868557\pi$
$709$	−27.3294	+	15.7786i	−1.02638	+	0.592580i	−0.110433	+	0.993884i	$0.535224\pi$
$710$		0			0
$711$	−23.8727	−	41.3488i	−0.895297	−	1.55070i
$712$	18.9501	+	10.9408i	0.710185	+	0.410026i
$713$	1.52158	−	2.63546i	0.0569837	−	0.0986987i
$714$	−6.39017			−0.239146
$715$		0			0
$716$	0.0468733			0.00175174
$717$	−13.9505	+	24.1630i	−0.520991	+	0.902383i
$718$	9.50214	+	5.48606i	0.354617	+	0.204738i
$719$	8.91325	+	15.4382i	0.332408	+	0.575748i	0.982984	−	0.183694i	$-0.0588055\pi$
$719$	8.91325	+	15.4382i	0.332408	+	0.575748i	−0.650575	+	0.759442i	$0.725472\pi$
$720$		0			0
$721$	−2.25017	+	1.29914i	−0.0838007	+	0.0483824i
$722$	−5.67429	−	9.82816i	−0.211175	−	0.365766i
$723$	9.30803			0.346169
$724$	8.87816	+	15.3774i	0.329954	+	0.571498i
$725$		0			0
$726$	−2.98574	−	1.72382i	−0.110811	−	0.0639768i
$727$			4.62813i			0.171648i	0.996310	+	0.0858240i	$0.0273523\pi$
$727$			4.62813i			0.171648i	−0.996310	+	0.0858240i	$0.972648\pi$
$728$	−0.219285	+	5.01486i	−0.00812722	+	0.185863i
$729$	29.8824			1.10675
$730$		0			0
$731$	3.30928	−	5.73183i	0.122398	−	0.211999i
$732$	−26.9785	+	15.5760i	−0.997152	+	0.575706i
$733$	−9.92820			−0.366706			−0.183353	−	0.983047i	$-0.558695\pi$
$733$	−9.92820			−0.366706			−0.183353	+	0.983047i	$0.558695\pi$
$734$	2.17425	−	1.25531i	0.0802531	−	0.0463342i
$735$		0			0
$736$			3.86318i			0.142399i
$737$	1.64631	−	0.950497i	0.0606426	−	0.0350120i
$738$	−1.32712	−	0.766214i	−0.0488520	−	0.0282047i
$739$	24.7225	+	14.2735i	0.909432	+	0.525061i	0.880248	−	0.474513i	$-0.157376\pi$
$739$	24.7225	+	14.2735i	0.909432	+	0.525061i	0.0291834	+	0.999574i	$0.490709\pi$
$740$		0			0
$741$	45.3243	+	28.8789i	1.66503	+	1.06089i
$742$		−	1.93562i		−	0.0710589i
$743$	11.5568	−	20.0170i	0.423979	−	0.734354i	−0.572345	−	0.820013i	$-0.693966\pi$
$743$	11.5568	−	20.0170i	0.423979	−	0.734354i	0.996325	+	0.0856590i	$0.0272996\pi$
$744$	13.3426	−	23.1101i	0.489165	−	0.847258i
$745$		0			0
$746$		−	8.83386i		−	0.323430i
$747$	0.586420	+	1.01571i	0.0214560	+	0.0371629i
$748$	−15.2759	−	26.4587i	−0.558543	−	0.967425i
$749$		−	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	$0.0110646\pi$
$752$	2.42254	−	4.19597i	0.0883410	−	0.153011i
$753$			50.5878i			1.84352i
$754$	0.827980	−	18.9353i	0.0301533	−	0.689581i
$755$		0			0
$756$	0.324381	+	0.187282i	0.0117976	+	0.00681137i
$757$	12.2811	+	7.09047i	0.446363	+	0.257708i	0.706293	−	0.707920i	$-0.250366\pi$
$757$	12.2811	+	7.09047i	0.446363	+	0.257708i	−0.259930	+	0.965627i	$0.583700\pi$
$758$	−12.6844	+	7.32332i	−0.460717	+	0.265995i
$759$		−	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	$0.187722\pi$
$762$	−9.94026			−0.360098
$763$	5.76526	−	3.32857i	0.208716	−	0.120502i
$764$	−4.15243	+	7.19222i	−0.150230	+	0.260206i
$765$		0			0
$766$	−15.1033			−0.545704
$767$	−51.4220	−	2.24852i	−1.85674	−	0.0811895i
$768$			22.0116i			0.794276i
$769$	10.2768	+	5.93333i	0.370592	+	0.213961i	0.673717	−	0.738989i	$-0.264697\pi$
$769$	10.2768	+	5.93333i	0.370592	+	0.213961i	−0.303125	+	0.952951i	$0.598030\pi$
$770$		0			0
$771$	−17.8238	−	30.8717i	−0.641909	−	1.11182i
$772$	16.5358			0.595137
$773$	0.879642	+	1.52359i	0.0316385	+	0.0547995i	0.881411	−	0.472350i	$-0.156594\pi$
$773$	0.879642	+	1.52359i	0.0316385	+	0.0547995i	−0.849773	+	0.527149i	$0.823261\pi$
$774$	1.83783	−	1.06107i	0.0660595	−	0.0381395i
$775$		0			0
$776$	8.19867	+	14.2005i	0.294315	+	0.509769i
$777$	−9.79109	−	5.65289i	−0.351253	−	0.202796i
$778$	6.10507	−	10.5743i	0.218877	−	0.379107i
$779$	4.36413			0.156361
$780$		0			0
$781$	26.8919			0.962266
$782$	1.46846	−	2.54345i	0.0525120	−	0.0909534i
$783$	−2.79873	−	1.61585i	−0.100018	−	0.0577456i
$784$	5.10763	+	8.84668i	0.182415	+	0.315953i
$785$		0			0
$786$	1.59858	−	0.922939i	0.0570194	−	0.0329202i
$787$	−15.6085	−	27.0347i	−0.556383	−	0.963684i	−0.997794	−	0.0663793i	$-0.978855\pi$
$787$	−15.6085	−	27.0347i	−0.556383	−	0.963684i	0.441411	−	0.897305i	$-0.354478\pi$
$788$	8.78664			0.313011
$789$	−33.1989	−	57.5022i	−1.18191	−	2.04713i
$790$		0			0
$791$	−1.27713	−	0.737351i	−0.0454095	−	0.0262172i
$792$		−	22.3843i		−	0.795390i
$793$	1.26974	−	29.0378i	0.0450896	−	1.03116i
$794$	3.56781			0.126617
$795$		0			0
$796$	12.1348	−	21.0180i	0.430106	−	0.744965i
$797$	3.38411	−	1.95382i	0.119871	−	0.0692077i	−0.438866	−	0.898553i	$-0.644620\pi$
$797$	3.38411	−	1.95382i	0.119871	−	0.0692077i	0.558737	+	0.829345i	$0.311286\pi$
$798$	5.83502			0.206557
$799$	−17.9703	+	10.3752i	−0.635745	+	0.367048i
$800$		0			0
$801$			29.2368i			1.03303i
$802$	6.61861	−	3.82126i	0.233711	−	0.134933i
$803$	43.4935	+	25.1110i	1.53485	+	0.886148i
$804$	−2.13071	−	1.23016i	−0.0751442	−	0.0433845i
$805$		0			0
$806$	5.03063	+	9.66530i	0.177196	+	0.340446i
$807$			1.06811i			0.0375994i
$808$	−16.3877	+	28.3843i	−0.576517	+	0.998556i
$809$	−10.0804	+	17.4597i	−0.354407	+	0.613851i	−0.987016	−	0.160620i	$-0.948651\pi$
$809$	−10.0804	+	17.4597i	−0.354407	+	0.613851i	0.632609	+	0.774471i	$0.281984\pi$
$810$		0			0
$811$			34.1631i			1.19963i	0.800139	+	0.599815i	$0.204759\pi$
$811$			34.1631i			1.19963i	−0.800139	+	0.599815i	$0.795241\pi$
$812$	3.60980	+	6.25235i	0.126679	+	0.219415i
$813$	14.6030	+	25.2931i	0.512150	+	0.887069i
$814$			15.4071i			0.540019i
$815$		0			0
$816$	−12.5291	+	21.7010i	−0.438605	+	0.759687i
$817$	−3.02178	+	5.23387i	−0.105719	+	0.183110i
$818$		−	11.5888i		−	0.405194i
$819$	−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	$0.307627\pi$
$822$	28.2012	+	16.2820i	0.983629	+	0.567899i
$823$	24.3447	−	14.0554i	0.848602	−	0.489941i	−0.0115767	−	0.999933i	$-0.503685\pi$
$823$	24.3447	−	14.0554i	0.848602	−	0.489941i	0.860179	+	0.509992i	$0.170352\pi$
$824$		−	10.4715i		−	0.364793i
$825$		0			0
$826$	−4.83968	+	2.79419i	−0.168394	+	0.0972223i
$827$	−49.5177			−1.72190			−0.860949	−	0.508691i	$-0.830130\pi$
$827$	−49.5177			−1.72190			−0.860949	+	0.508691i	$0.830130\pi$
$828$	−2.86114	+	1.65188i	−0.0994316	+	0.0574068i
$829$	10.8664	−	18.8212i	0.377406	−	0.653687i	−0.613278	−	0.789867i	$-0.710149\pi$
$829$	10.8664	−	18.8212i	0.377406	−	0.653687i	0.990684	+	0.136180i	$0.0434827\pi$
$830$		0			0
$831$	9.87177			0.342448
$832$	−2.32982	−	1.48448i	−0.0807721	−	0.0514650i
$833$		−	43.7496i		−	1.51583i
$834$	14.1362	+	8.16154i	0.489496	+	0.282611i
$835$		0			0
$836$	13.9488	+	24.1600i	0.482430	+	0.835593i
$837$	1.85787			0.0642174
$838$	7.48567	+	12.9656i	0.258588	+	0.447888i
$839$	31.2115	−	18.0199i	1.07754	−	0.622118i	0.147308	−	0.989091i	$-0.452939\pi$
$839$	31.2115	−	18.0199i	1.07754	−	0.622118i	0.930232	+	0.366973i	$0.119606\pi$
$840$		0			0
$841$	−16.6449	−	28.8299i	−0.573963	−	0.994134i
$842$	−2.98149	−	1.72137i	−0.102749	−	0.0593222i
$843$	21.5105	−	37.2573i	0.740861	−	1.28321i
$844$	−26.3550			−0.907175
$845$		0			0
$846$	−6.65332			−0.228746
$847$	−0.612647	+	1.06114i	−0.0210508	+	0.0364611i
$848$	−6.57337	−	3.79513i	−0.225730	−	0.130325i
$849$	11.1913	+	19.3838i	0.384083	+	0.665252i
$850$		0			0
$851$	4.49998	−	2.59806i	0.154257	−	0.0890605i
$852$	−17.4022	−	30.1414i	−0.596188	−	1.03263i
$853$	−38.4465			−1.31638			−0.658191	−	0.752851i	$-0.728678\pi$
$853$	−38.4465			−1.31638			−0.658191	+	0.752851i	$0.728678\pi$
$854$	−1.57787	−	2.73295i	−0.0539936	−	0.0935197i
$855$		0			0
$856$	5.55247	+	3.20572i	0.189780	+	0.109569i
$857$			2.31635i			0.0791251i	0.999217	+	0.0395625i	$0.0125964\pi$
$857$			2.31635i			0.0791251i	−0.999217	+	0.0395625i	$0.987404\pi$
$858$	15.0148	+	9.56685i	0.512596	+	0.326607i
$859$	1.38239			0.0471667			0.0235833	−	0.999722i	$-0.492492\pi$
$859$	1.38239			0.0471667			0.0235833	+	0.999722i	$0.492492\pi$
$860$		0			0
$861$	−0.530438	+	0.918746i	−0.0180773	+	0.0313108i
$862$	−15.1835	+	8.76620i	−0.517152	+	0.298578i
$863$	−10.5783			−0.360091			−0.180046	−	0.983658i	$-0.557625\pi$
$863$	−10.5783			−0.360091			−0.180046	+	0.983658i	$0.557625\pi$
$864$	−2.04251	+	1.17925i	−0.0694877	+	0.0401187i
$865$		0			0
$866$		−	12.5956i		−	0.428015i
$867$	56.3856	−	32.5543i	1.91496	−	1.10560i
$868$	−3.59442	−	2.07524i	−0.122003	−	0.0704382i
$869$	39.0093	+	22.5220i	1.32330	+	0.764007i
$870$		0			0
$871$	2.03624	−	1.05983i	0.0689954	−	0.0359110i
$872$			26.8296i			0.908563i
$873$	−10.9545	+	18.9737i	−0.370753	+	0.642163i
$874$	−1.34088	+	2.32248i	−0.0453561	+	0.0785591i
$875$		0			0
$876$		−	64.9989i		−	2.19611i
$877$	9.39590	+	16.2742i	0.317277	+	0.549540i	0.979919	−	0.199397i	$-0.0638982\pi$
$877$	9.39590	+	16.2742i	0.317277	+	0.549540i	−0.662642	+	0.748936i	$0.730565\pi$
$878$	9.15516	+	15.8572i	0.308972	+	0.535155i
$879$			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	$-0.0668948\pi$
$882$	7.01385	−	12.1483i	0.236169	−	0.409056i
$883$			17.2515i			0.580560i	0.956942	+	0.290280i	$0.0937484\pi$
$883$			17.2515i			0.580560i	−0.956942	+	0.290280i	$0.906252\pi$
$884$	−17.0331	−	32.7255i	−0.572884	−	1.10068i
$885$		0			0
$886$	−11.1237	−	6.42224i	−0.373706	−	0.215760i
$887$	31.6934	+	18.2982i	1.06416	+	0.614394i	0.926580	−	0.376097i	$-0.122734\pi$
$887$	31.6934	+	18.2982i	1.06416	+	0.614394i	0.137581	+	0.990491i	$0.456067\pi$
$888$	39.4599	−	22.7822i	1.32419	−	0.764521i
$889$			3.53279i			0.118486i
$890$		0			0
$891$	−21.9227	+	12.6571i	−0.734438	+	0.424028i
$892$	−25.5704			−0.856160
$893$	16.4091	−	9.47382i	0.549111	−	0.317029i
$894$	6.72724	−	11.6519i	0.224993	−	0.389699i
$895$		0			0
$896$	6.47073			0.216172
$897$	0.262301	−	5.99862i	0.00875799	−	0.200288i
$898$			4.35372i			0.145286i
$899$	31.0123	+	17.9049i	1.03432	+	0.597163i
$900$		0			0
$901$	16.2537	+	28.1522i	0.541488	+	0.937885i
$902$	1.44572			0.0481373
$903$	−0.734564	−	1.27230i	−0.0244448	−	0.0423396i
$904$	5.14707	−	2.97166i	0.171189	−	0.0988361i
$905$		0			0
$906$	−10.7633	−	18.6426i	−0.357587	−	0.619360i
$907$	33.9791	+	19.6178i	1.12826	+	0.651400i	0.943496	−	0.331384i	$-0.107515\pi$
$907$	33.9791	+	19.6178i	1.12826	+	0.651400i	0.184762	+	0.982783i	$0.440849\pi$
$908$	−13.4201	+	23.2443i	−0.445361	+	0.771388i
$909$	−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	$0.540502\pi$
$912$	11.4406	−	19.8157i	0.378836	−	0.656163i
$913$	−0.958241	−	0.553241i	−0.0317131	−	0.0183096i
$914$	4.79766	+	8.30978i	0.158692	+	0.274863i
$915$		0			0
$916$	−13.5876	+	7.84482i	−0.448948	+	0.259200i
$917$	−0.328014	−	0.568137i	−0.0108320	−	0.0187615i
$918$	1.79301			0.0591780
$919$	6.62625	+	11.4770i	0.218580	+	0.378592i	0.954374	−	0.298614i	$-0.0965242\pi$
$919$	6.62625	+	11.4770i	0.218580	+	0.378592i	−0.735794	+	0.677205i	$0.763191\pi$
$920$		0			0
$921$	−33.2498	−	19.1968i	−1.09562	−	0.632555i
$922$		−	8.83137i		−	0.290846i
$923$	32.4422	+	1.41860i	1.06785	+	0.0466938i
$924$	−6.78164			−0.223100
$925$		0			0
$926$	−6.28319	+	10.8828i	−0.206478	+	0.357631i
$927$	12.1168	−	6.99565i	0.397969	−	0.229767i
$928$	−45.4592			−1.49227
$929$	−39.4042	+	22.7500i	−1.29281	+	0.746405i	−0.979152	−	0.203131i	$-0.934888\pi$
$929$	−39.4042	+	22.7500i	−1.29281	+	0.746405i	−0.313659	+	0.949536i	$0.601555\pi$
$930$		0			0
$931$			39.9488i			1.30927i
$932$	26.5668	−	15.3384i	0.870225	−	0.502425i
$933$	−18.2789	−	10.5533i	−0.598424	−	0.345500i
$934$	−12.6248	−	7.28891i	−0.413095	−	0.238500i
$935$		0			0
$936$	1.18081	−	27.0043i	0.0385961	−	0.882662i
$937$			16.8095i			0.549141i	0.961567	+	0.274570i	$0.0885357\pi$
$937$			16.8095i			0.549141i	−0.961567	+	0.274570i	$0.911464\pi$
$938$	0.124617	−	0.215843i	0.00406889	−	0.00704753i
$939$	−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	$-0.0462822\pi$
$942$	−10.1852	−	17.6413i	−0.331851	−	0.574784i
$943$	−0.243789	−	0.422255i	−0.00793886	−	0.0137505i
$944$			21.9140i			0.713241i
$945$		0			0
$946$	−1.00104	+	1.73385i	−0.0325465	+	0.0563723i
$947$	−15.2253	+	26.3710i	−0.494756	+	0.856942i	−0.999982	−	0.00604474i	$-0.998076\pi$
$947$	−15.2253	+	26.3710i	−0.494756	+	0.856942i	0.505226	+	0.862987i	$0.331409\pi$
$948$		−	58.2974i		−	1.89341i
$949$	51.1457	+	32.5882i	1.66026	+	1.05786i
$950$		0			0
$951$	−7.21174	−	4.16370i	−0.233857	−	0.135017i
$952$	−7.92662	−	4.57643i	−0.256903	−	0.148323i
$953$	−4.20756	+	2.42924i	−0.136296	+	0.0786907i	−0.566598	−	0.823995i	$-0.691741\pi$
$953$	−4.20756	+	2.42924i	−0.136296	+	0.0786907i	0.430301	+	0.902685i	$0.358407\pi$
$954$			10.4230i			0.337458i
$955$		0			0
$956$	−15.1462	+	8.74464i	−0.489862	+	0.282822i
$957$	58.5112			1.89140
$958$	16.2117	−	9.35985i	0.523777	−	0.302403i
$959$	5.78663	−	10.0227i	0.186860	−	0.323651i
$960$		0			0
$961$	10.4132			0.335910
$962$	−0.812755	+	18.5871i	−0.0262043	+	0.599271i
$963$			8.56651i			0.276052i
$964$	5.05290	+	2.91729i	0.162743	+	0.0939597i
$965$		0			0
$966$	−0.325956	−	0.564572i	−0.0104875	−	0.0181648i
$967$	26.5631			0.854211			0.427106	−	0.904202i	$-0.359533\pi$
$967$	26.5631			0.854211			0.427106	+	0.904202i	$0.359533\pi$
$968$	−2.46908	−	4.27658i	−0.0793593	−	0.137454i
$969$	−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	$-0.410532\pi$
$972$	30.0288	+	17.3371i	0.963174	+	0.556089i
$973$	2.90062	−	5.02403i	0.0929897	−	0.161063i
$974$	−12.2037			−0.391031
$975$		0			0
$976$	−12.3748			−0.396107
$977$	−22.7283	+	39.3665i	−0.727141	+	1.25945i	0.230945	+	0.972967i	$0.425818\pi$
$977$	−22.7283	+	39.3665i	−0.727141	+	1.25945i	−0.958086	+	0.286479i	$0.907515\pi$
$978$	3.05601	+	1.76439i	0.0977205	+	0.0564190i
$979$	−13.7913	−	23.8872i	−0.440771	−	0.763438i
$980$		0			0
$981$	−31.0450	+	17.9239i	−0.991192	+	0.572265i
$982$	−7.23347	−	12.5287i	−0.230829	−	0.399808i
$983$	9.31963			0.297250			0.148625	−	0.988894i	$-0.452515\pi$
$983$	9.31963			0.297250			0.148625	+	0.988894i	$0.452515\pi$
$984$	−2.13777	−	3.70272i	−0.0681495	−	0.118038i
$985$		0			0
$986$	29.9295	+	17.2798i	0.953150	+	0.550302i
$987$			4.60599i			0.146610i
$988$	15.5533	+	29.8824i	0.494816	+	0.950686i
$989$	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	$0.146258\pi$
$992$	22.6328	−	13.0670i	0.718592	−	0.414879i
$993$	−51.0575			−1.62026
$994$	3.05336	−	1.76286i	0.0968468	−	0.0559145i
$995$		0			0
$996$			1.43204i			0.0453760i
$997$	−47.7839	+	27.5880i	−1.51333	+	0.873722i	−0.513452	+	0.858118i	$0.671634\pi$
$997$	−47.7839	+	27.5880i	−1.51333	+	0.873722i	−0.999878	+	0.0156032i	$0.995033\pi$
$998$	8.50327	+	4.90937i	0.269166	+	0.155403i
$999$	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.m.d.199.6		20
5.2	odd	4		325.2.n.e.251.3	yes	10
5.3	odd	4		325.2.n.f.251.3	yes	10
5.4	even	2	inner	325.2.m.d.199.5		20
13.10	even	6	inner	325.2.m.d.49.5		20
65.7	even	12		4225.2.a.bv.1.6		10
65.23	odd	12		325.2.n.f.101.3	yes	10
65.32	even	12		4225.2.a.bv.1.5		10
65.33	even	12		4225.2.a.bu.1.5		10
65.49	even	6	inner	325.2.m.d.49.6		20
65.58	even	12		4225.2.a.bu.1.6		10
65.62	odd	12		325.2.n.e.101.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.5		20	13.10	even	6	inner
325.2.m.d.49.6		20	65.49	even	6	inner
325.2.m.d.199.5		20	5.4	even	2	inner
325.2.m.d.199.6		20	1.1	even	1	trivial
325.2.n.e.101.3	✓	10	65.62	odd	12
325.2.n.e.251.3	yes	10	5.2	odd	4
325.2.n.f.101.3	yes	10	65.23	odd	12
325.2.n.f.251.3	yes	10	5.3	odd	4
4225.2.a.bu.1.5		10	65.33	even	12
4225.2.a.bu.1.6		10	65.58	even	12
4225.2.a.bv.1.5		10	65.32	even	12
4225.2.a.bv.1.6		10	65.7	even	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.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.333024 - 0.576815i) q^{2} +(2.15028 + 1.24146i) q^{3} +(0.778190 + 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.293872 - 0.509002i) q^{7} +2.36872 q^{8} +(1.58246 + 2.74090i) q^{9} +O(q^{10})\)	\(q+(0.333024 - 0.576815i) q^{2} +(2.15028 + 1.24146i) q^{3} +(0.778190 + 1.34786i) q^{4} +(1.43219 - 0.826874i) q^{6} +(-0.293872 - 0.509002i) q^{7} +2.36872 q^{8} +(1.58246 + 2.74090i) q^{9} +(-2.58582 - 1.49292i) q^{11} +3.86437i q^{12} +(-3.04076 - 1.93746i) q^{13} -0.391466 q^{14} +(-0.767539 + 1.32942i) q^{16} +(5.69358 - 3.28719i) q^{17} +2.10798 q^{18} +(-5.19894 + 3.00161i) q^{19} -1.45932i q^{21} +(-1.72228 + 0.994358i) q^{22} +(0.580847 + 0.335352i) q^{23} +(5.09340 + 2.94068i) q^{24} +(-2.13020 + 1.10874i) q^{26} +0.409469i q^{27} +(0.457377 - 0.792200i) q^{28} +(-3.94620 + 6.83501i) q^{29} -4.53727i q^{31} +(2.87994 + 4.98820i) q^{32} +(-3.70681 - 6.42039i) q^{33} -4.37886i q^{34} +(-2.46290 + 4.26588i) q^{36} +(3.87363 - 6.70933i) q^{37} +3.99844i q^{38} +(-4.13319 - 7.94107i) q^{39} +(-0.629569 - 0.363482i) q^{41} +(-0.841760 - 0.485990i) q^{42} +(0.871843 - 0.503359i) q^{43} -4.64711i q^{44} +(0.386872 - 0.223361i) q^{46} -3.15624 q^{47} +(-3.30084 + 1.90574i) q^{48} +(3.32728 - 5.76302i) q^{49} +16.3237 q^{51} +(0.245144 - 5.60625i) q^{52} +4.94455i q^{53} +(0.236188 + 0.136363i) q^{54} +(-0.696101 - 1.20568i) q^{56} -14.9056 q^{57} +(2.62836 + 4.55245i) q^{58} +(12.3630 - 7.13776i) q^{59} +(4.03067 + 6.98133i) q^{61} +(-2.61716 - 1.51102i) q^{62} +(0.930080 - 1.61095i) q^{63} +0.766197 q^{64} -4.93783 q^{66} +(-0.318335 + 0.551372i) q^{67} +(8.86138 + 5.11612i) q^{68} +(0.832654 + 1.44220i) q^{69} +(-7.79982 + 4.50323i) q^{71} +(3.74840 + 6.49242i) q^{72} -16.8200 q^{73} +(-2.58003 - 4.46874i) q^{74} +(-8.09153 - 4.67165i) q^{76} +1.75491i q^{77} +(-5.95698 - 0.260480i) q^{78} -15.0859 q^{79} +(4.23903 - 7.34222i) q^{81} +(-0.419323 + 0.242096i) q^{82} +0.370576 q^{83} +(1.96697 - 1.13563i) q^{84} -0.670523i q^{86} +(-16.9708 + 9.79811i) q^{87} +(-6.12507 - 3.53631i) q^{88} +(8.00015 + 4.61889i) q^{89} +(-0.0925751 + 2.11712i) q^{91} +1.04387i q^{92} +(5.63284 - 9.75637i) q^{93} +(-1.05111 + 1.82057i) q^{94} +14.3013i q^{96} +(3.46123 + 5.99502i) q^{97} +(-2.21613 - 3.83845i) q^{98} -9.44994i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9}+O(q^{10}) \) 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9	\( 20 q - 12 q^{4} + 18 q^{6} + 16 q^{9} - 18 q^{11} + 16 q^{14} - 24 q^{16} - 84 q^{24} - 34 q^{26} - 14 q^{29} - 6 q^{36} - 16 q^{39} + 24 q^{41} + 78 q^{46} + 2 q^{49} + 32 q^{51} + 18 q^{54} - 42 q^{56} + 96 q^{59} + 26 q^{61} + 68 q^{64} - 84 q^{66} - 40 q^{69} - 54 q^{71} + 52 q^{74} - 24 q^{76} - 8 q^{79} - 34 q^{81} + 180 q^{84} - 48 q^{89} + 26 q^{91} - 10 q^{94}+O(q^{100}) \) 20 * q - 12 * q^4 + 18 * q^6 + 16 * q^9 - 18 * q^11 + 16 * q^14 - 24 * q^16 - 84 * q^24 - 34 * q^26 - 14 * q^29 - 6 * q^36 - 16 * q^39 + 24 * q^41 + 78 * q^46 + 2 * q^49 + 32 * q^51 + 18 * q^54 - 42 * q^56 + 96 * q^59 + 26 * q^61 + 68 * q^64 - 84 * q^66 - 40 * q^69 - 54 * q^71 + 52 * q^74 - 24 * q^76 - 8 * q^79 - 34 * q^81 + 180 * q^84 - 48 * q^89 + 26 * q^91 - 10 * q^94

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