LMFDB - Embedded newform 475.2.e.h.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$1.62208 + 2.80952i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.h.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.155554 - 0.269427i) q^{2} +(-1.12208 + 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} -3.96928 q^{7} +1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +0.361495 q^{11} -4.27110 q^{12} +(1.25807 + 2.17905i) q^{13} +(-0.617436 + 1.06943i) q^{14} +(-1.71432 + 2.96929i) q^{16} +(0.00464089 - 0.00803826i) q^{17} -0.633487 q^{18} +(-3.45680 + 2.65529i) q^{19} +(4.45383 - 7.71427i) q^{21} +(0.0562320 - 0.0973967i) q^{22} +(-2.70404 - 4.68354i) q^{23} +(-1.36256 + 2.36002i) q^{24} +0.782793 q^{26} -2.16285 q^{27} +(-3.77719 - 6.54228i) q^{28} +(-4.72735 - 8.18801i) q^{29} +3.66745 q^{31} +(1.74766 + 3.02703i) q^{32} +(-0.405626 + 0.702564i) q^{33} +(-0.00144382 - 0.00250076i) q^{34} +(1.93769 - 3.35617i) q^{36} -0.0596692 q^{37} +(0.177689 + 1.34440i) q^{38} -5.64662 q^{39} +(-1.85906 + 3.21998i) q^{41} +(-1.38562 - 2.39997i) q^{42} +(-2.10671 + 3.64894i) q^{43} +(0.344001 + 0.595827i) q^{44} -1.68250 q^{46} +(6.45659 + 11.1831i) q^{47} +(-3.84720 - 6.66354i) q^{48} +8.75515 q^{49} +(0.0104149 + 0.0180391i) q^{51} +(-2.39438 + 4.14719i) q^{52} +(5.48564 + 9.50140i) q^{53} +(-0.336440 + 0.582731i) q^{54} -4.81997 q^{56} +(-1.28175 - 9.69770i) q^{57} -2.94143 q^{58} +(2.65944 - 4.60629i) q^{59} +(4.44875 + 7.70546i) q^{61} +(0.570486 - 0.988111i) q^{62} +(4.04118 + 6.99952i) q^{63} -5.76986 q^{64} +(0.126193 + 0.218573i) q^{66} +(-2.32498 - 4.02699i) q^{67} +0.0176652 q^{68} +12.1366 q^{69} +(-7.68968 + 13.3189i) q^{71} +(-1.23632 - 2.14136i) q^{72} +(4.83162 - 8.36861i) q^{73} +(-0.00928178 + 0.0160765i) q^{74} +(-7.66603 - 3.17081i) q^{76} -1.43487 q^{77} +(-0.878354 + 1.52135i) q^{78} +(-6.70596 + 11.6151i) q^{79} +(5.48123 - 9.49377i) q^{81} +(0.578367 + 1.00176i) q^{82} +15.5409 q^{83} +16.9532 q^{84} +(0.655415 + 1.13521i) q^{86} +21.2178 q^{87} +0.438971 q^{88} +(2.08578 + 3.61267i) q^{89} +(-4.99364 - 8.64923i) q^{91} +(5.14637 - 8.91377i) q^{92} +(-4.11516 + 7.12767i) q^{93} +4.01739 q^{94} -7.84403 q^{96} +(-1.87094 + 3.24056i) q^{97} +(1.36190 - 2.35888i) q^{98} +(-0.368044 - 0.637470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{6} - 4 q^{7} - 12 q^{8} - 7 q^{9} - 2 q^{11} - 14 q^{12} + 5 q^{13} + 6 q^{14} + 6 q^{16} - 3 q^{17} - 14 q^{18} - 6 q^{19} - 3 q^{21} + 9 q^{22} - 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 + q^6 - 4 * q^7 - 12 * q^8 - 7 * q^9 - 2 * q^11 - 14 * q^12 + 5 * q^13 + 6 * q^14 + 6 * q^16 - 3 * q^17 - 14 * q^18 - 6 * q^19 - 3 * q^21 + 9 * q^22 - 6 * q^23 - 11 * q^24 + 38 * q^26 - 36 * q^27 - 4 * q^28 - 3 * q^29 - 6 * q^31 - 6 * q^32 - 18 * q^33 + q^34 - 13 * q^36 + 12 * q^37 + 18 * q^38 + 16 * q^39 - 11 * q^41 - 11 * q^42 + 13 * q^43 - 21 * q^44 - 24 * q^46 - 6 * q^47 - 19 * q^48 + 8 * q^49 + 17 * q^51 - q^52 + 18 * q^53 - 18 * q^54 + 8 * q^56 + 20 * q^57 - 10 * q^58 - 4 * q^59 - 25 * q^61 - 21 * q^62 + 43 * q^63 - 44 * q^64 - 34 * q^66 + 6 * q^67 + 2 * q^68 + 26 * q^69 - 18 * q^71 + 13 * q^72 + q^73 + 6 * q^74 + 24 * q^76 + 22 * q^77 + 72 * q^78 - 3 * q^79 - 2 * q^81 + 31 * q^82 + 46 * q^83 + 74 * q^84 - 9 * q^86 - 22 * q^87 - 22 * q^88 - 12 * q^89 + 11 * q^91 + 28 * q^92 - 13 * q^93 + 16 * q^94 - 26 * q^96 + 3 * q^97 - 22 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.155554	−	0.269427i	0.109993	−	0.190514i	−0.805774	−	0.592223i	$-0.798250\pi$
$2$	0.155554	−	0.269427i	0.109993	−	0.190514i	0.915767	+	0.401709i	$0.131584\pi$
$3$	−1.12208	+	1.94349i	−0.647832	+	1.12208i	0.335808	+	0.941930i	$0.390991\pi$
$3$	−1.12208	+	1.94349i	−0.647832	+	1.12208i	−0.983640	+	0.180147i	$0.942343\pi$
$4$	0.951606	+	1.64823i	0.475803	+	0.824115i
$5$		0			0
$5$		0			0
$6$	0.349087	+	0.604636i	0.142514	+	0.246842i
$7$	−3.96928			−1.50025			−0.750123	−	0.661299i	$-0.770006\pi$
$7$	−3.96928			−1.50025			−0.750123	+	0.661299i	$0.770006\pi$
$8$	1.21432			0.429327
$9$	−1.01811	−	1.76343i	−0.339371	−	0.587809i
$10$		0			0
$11$	0.361495			0.108995			0.0544975	−	0.998514i	$-0.482644\pi$
$11$	0.361495			0.108995			0.0544975	+	0.998514i	$0.482644\pi$
$12$	−4.27110			−1.23296
$13$	1.25807	+	2.17905i	0.348927	+	0.604359i	0.986059	−	0.166396i	$-0.0532129\pi$
$13$	1.25807	+	2.17905i	0.348927	+	0.604359i	−0.637132	+	0.770754i	$0.719880\pi$
$14$	−0.617436	+	1.06943i	−0.165017	+	0.285817i
$15$		0			0
$16$	−1.71432	+	2.96929i	−0.428580	+	0.742322i
$17$	0.00464089	−	0.00803826i	0.00112558	−	0.00194956i	−0.865462	−	0.500974i	$-0.832975\pi$
$17$	0.00464089	−	0.00803826i	0.00112558	−	0.00194956i	0.866588	+	0.499025i	$0.166308\pi$
$18$	−0.633487			−0.149314
$19$	−3.45680	+	2.65529i	−0.793043	+	0.609165i
$19$	−3.45680	+	2.65529i	−0.793043	+	0.609165i
$20$		0			0
$21$	4.45383	−	7.71427i	0.971906	−	1.68339i
$22$	0.0562320	−	0.0973967i	0.0119887	−	0.0207650i
$23$	−2.70404	−	4.68354i	−0.563832	−	0.976586i	−0.997157	−	0.0753481i	$-0.975993\pi$
$23$	−2.70404	−	4.68354i	−0.563832	−	0.976586i	0.433325	−	0.901238i	$-0.357340\pi$
$24$	−1.36256	+	2.36002i	−0.278131	+	0.481738i
$25$		0			0
$26$	0.782793			0.153518
$27$	−2.16285			−0.416241
$28$	−3.77719	−	6.54228i	−0.713821	−	1.23637i
$29$	−4.72735	−	8.18801i	−0.877847	−	1.52047i	−0.853699	−	0.520766i	$-0.825646\pi$
$29$	−4.72735	−	8.18801i	−0.877847	−	1.52047i	−0.0241473	−	0.999708i	$-0.507687\pi$
$30$		0			0
$31$	3.66745			0.658693			0.329347	−	0.944209i	$-0.393172\pi$
$31$	3.66745			0.658693			0.329347	+	0.944209i	$0.393172\pi$
$32$	1.74766	+	3.02703i	0.308945	+	0.535109i
$33$	−0.405626	+	0.702564i	−0.0706103	+	0.122301i
$34$	−0.00144382	−	0.00250076i	−0.000247613	−	0.000428878i
$35$		0			0
$36$	1.93769	−	3.35617i	0.322948	−	0.559362i
$37$	−0.0596692			−0.00980956			−0.00490478	−	0.999988i	$-0.501561\pi$
$37$	−0.0596692			−0.00980956			−0.00490478	+	0.999988i	$0.501561\pi$
$38$	0.177689	+	1.34440i	0.0288250	+	0.218090i
$39$	−5.64662			−0.904183
$40$		0			0
$41$	−1.85906	+	3.21998i	−0.290336	+	0.502877i	−0.973889	−	0.227024i	$-0.927100\pi$
$41$	−1.85906	+	3.21998i	−0.290336	+	0.502877i	0.683553	+	0.729901i	$0.260434\pi$
$42$	−1.38562	−	2.39997i	−0.213806	−	0.370323i
$43$	−2.10671	+	3.64894i	−0.321271	+	0.556458i	−0.980751	−	0.195265i	$-0.937443\pi$
$43$	−2.10671	+	3.64894i	−0.321271	+	0.556458i	0.659480	+	0.751722i	$0.270777\pi$
$44$	0.344001	+	0.595827i	0.0518601	+	0.0898243i
$45$		0			0
$46$	−1.68250			−0.248071
$47$	6.45659	+	11.1831i	0.941790	+	1.63123i	0.762055	+	0.647513i	$0.224191\pi$
$47$	6.45659	+	11.1831i	0.941790	+	1.63123i	0.179735	+	0.983715i	$0.442476\pi$
$48$	−3.84720	−	6.66354i	−0.555295	−	0.961800i
$49$	8.75515			1.25074
$50$		0			0
$51$	0.0104149	+	0.0180391i	0.00145837	+	0.00252598i
$52$	−2.39438	+	4.14719i	−0.332041	+	0.575111i
$53$	5.48564	+	9.50140i	0.753510	+	1.30512i	0.946112	+	0.323841i	$0.104974\pi$
$53$	5.48564	+	9.50140i	0.753510	+	1.30512i	−0.192601	+	0.981277i	$0.561692\pi$
$54$	−0.336440	+	0.582731i	−0.0457837	+	0.0792997i
$55$		0			0
$56$	−4.81997			−0.644095
$57$	−1.28175	−	9.69770i	−0.169772	−	1.28449i
$58$	−2.94143			−0.386229
$59$	2.65944	−	4.60629i	0.346230	−	0.599688i	−0.639346	−	0.768919i	$-0.720795\pi$
$59$	2.65944	−	4.60629i	0.346230	−	0.599688i	0.985576	+	0.169231i	$0.0541283\pi$
$60$		0			0
$61$	4.44875	+	7.70546i	0.569604	+	0.986583i	0.996605	+	0.0823316i	$0.0262366\pi$
$61$	4.44875	+	7.70546i	0.569604	+	0.986583i	−0.427001	+	0.904251i	$0.640430\pi$
$62$	0.570486	−	0.988111i	0.0724518	−	0.125490i
$63$	4.04118	+	6.99952i	0.509140	+	0.881857i
$64$	−5.76986			−0.721232
$65$		0			0
$66$	0.126193	+	0.218573i	0.0155333	+	0.0269045i
$67$	−2.32498	−	4.02699i	−0.284042	−	0.491975i	0.688334	−	0.725393i	$-0.258342\pi$
$67$	−2.32498	−	4.02699i	−0.284042	−	0.491975i	−0.972376	+	0.233418i	$0.925009\pi$
$68$	0.0176652			0.00214222
$69$	12.1366			1.46107
$70$		0			0
$71$	−7.68968	+	13.3189i	−0.912597	+	1.58066i	−0.102215	+	0.994762i	$0.532593\pi$
$71$	−7.68968	+	13.3189i	−0.912597	+	1.58066i	−0.810382	+	0.585902i	$0.800740\pi$
$72$	−1.23632	−	2.14136i	−0.145701	−	0.252362i
$73$	4.83162	−	8.36861i	0.565498	−	0.979471i	−0.431505	−	0.902110i	$-0.642017\pi$
$73$	4.83162	−	8.36861i	0.565498	−	0.979471i	0.997003	−	0.0773609i	$-0.0246494\pi$
$74$	−0.00928178	+	0.0160765i	−0.00107898	+	0.00186886i
$75$		0			0
$76$	−7.66603	−	3.17081i	−0.879354	−	0.363716i
$77$	−1.43487			−0.163519
$78$	−0.878354	+	1.52135i	−0.0994540	+	0.172259i
$79$	−6.70596	+	11.6151i	−0.754480	+	1.30680i	0.191153	+	0.981560i	$0.438777\pi$
$79$	−6.70596	+	11.6151i	−0.754480	+	1.30680i	−0.945632	+	0.325237i	$0.894556\pi$
$80$		0			0
$81$	5.48123	−	9.49377i	0.609025	−	1.05486i
$82$	0.578367	+	1.00176i	0.0638700	+	0.110626i
$83$	15.5409			1.70583			0.852916	−	0.522048i	$-0.174832\pi$
$83$	15.5409			1.70583			0.852916	+	0.522048i	$0.174832\pi$
$84$	16.9532			1.84974
$85$		0			0
$86$	0.655415	+	1.13521i	0.0706753	+	0.122413i
$87$	21.2178			2.27479
$88$	0.438971			0.0467944
$89$	2.08578	+	3.61267i	0.221092	+	0.382942i	0.955140	−	0.296155i	$-0.0957046\pi$
$89$	2.08578	+	3.61267i	0.221092	+	0.382942i	−0.734048	+	0.679098i	$0.762371\pi$
$90$		0			0
$91$	−4.99364	−	8.64923i	−0.523475	−	0.906686i
$92$	5.14637	−	8.91377i	0.536546	−	0.929325i
$93$	−4.11516	+	7.12767i	−0.426722	+	0.739105i
$94$	4.01739			0.414362
$95$		0			0
$96$	−7.84403			−0.800578
$97$	−1.87094	+	3.24056i	−0.189965	+	0.329029i	−0.945238	−	0.326381i	$-0.894171\pi$
$97$	−1.87094	+	3.24056i	−0.189965	+	0.329029i	0.755273	+	0.655410i	$0.227504\pi$
$98$	1.36190	−	2.35888i	0.137572	−	0.238282i
$99$	−0.368044	−	0.637470i	−0.0369898	−	0.0640682i
$100$		0			0
$101$	8.61953	+	14.9295i	0.857675	+	1.48554i	0.874141	+	0.485672i	$0.161425\pi$
$101$	8.61953	+	14.9295i	0.857675	+	1.48554i	−0.0164664	+	0.999864i	$0.505242\pi$
$102$	0.00648030			0.000641645
$103$	−8.81660			−0.868725			−0.434362	−	0.900738i	$-0.643026\pi$
$103$	−8.81660			−0.868725			−0.434362	+	0.900738i	$0.643026\pi$
$104$	1.52770	+	2.64606i	0.149804	+	0.259467i
$105$		0			0
$106$	3.41325			0.331524
$107$	1.30581			0.126238			0.0631188	−	0.998006i	$-0.479895\pi$
$107$	1.30581			0.126238			0.0631188	+	0.998006i	$0.479895\pi$
$108$	−2.05818	−	3.56488i	−0.198049	−	0.343030i
$109$	3.04839	−	5.27997i	0.291983	−	0.505730i	−0.682295	−	0.731077i	$-0.739018\pi$
$109$	3.04839	−	5.27997i	0.291983	−	0.505730i	0.974279	+	0.225347i	$0.0723515\pi$
$110$		0			0
$111$	0.0669535	−	0.115967i	0.00635494	−	0.0110071i
$112$	6.80461	−	11.7859i	0.642975	−	1.11367i
$113$	11.2382			1.05720			0.528599	−	0.848872i	$-0.322718\pi$
$113$	11.2382			1.05720			0.528599	+	0.848872i	$0.322718\pi$
$114$	−2.81221	−	1.16318i	−0.263387	−	0.108942i
$115$		0			0
$116$	8.99715	−	15.5835i	0.835364	−	1.44689i
$117$	2.56172	−	4.43704i	0.236831	−	0.410204i
$118$	−0.827374	−	1.43305i	−0.0761659	−	0.131923i
$119$	−0.0184210	+	0.0319061i	−0.00168865	+	0.00292482i
$120$		0			0
$121$	−10.8693			−0.988120
$122$	2.76808			0.250610
$123$	−4.17201	−	7.22613i	−0.376178	−	0.651559i
$124$	3.48997	+	6.04480i	0.313408	+	0.542839i
$125$		0			0
$126$	2.51448			0.224008
$127$	5.92682	+	10.2656i	0.525921	+	0.910921i	0.999544	+	0.0301937i	$0.00961241\pi$
$127$	5.92682	+	10.2656i	0.525921	+	0.910921i	−0.473624	+	0.880727i	$0.657054\pi$
$128$	−4.39284	+	7.60862i	−0.388276	+	0.672514i
$129$	−4.72779	−	8.18878i	−0.416259	−	0.720982i
$130$		0			0
$131$	1.20298	−	2.08362i	0.105105	−	0.182047i	−0.808676	−	0.588254i	$-0.799816\pi$
$131$	1.20298	−	2.08362i	0.105105	−	0.182047i	0.913781	+	0.406207i	$0.133149\pi$
$132$	−1.54398			−0.134386
$133$	13.7210	−	10.5396i	1.18976	−	0.913897i
$134$	−1.44664			−0.124971
$135$		0			0
$136$	0.00563552	−	0.00976101i	0.000483242	−	0.000837000i
$137$	2.50867	+	4.34514i	0.214330	+	0.371230i	0.953065	−	0.302765i	$-0.0979099\pi$
$137$	2.50867	+	4.34514i	0.214330	+	0.371230i	−0.738735	+	0.673996i	$0.764577\pi$
$138$	1.88789	−	3.26993i	0.160708	−	0.278355i
$139$	−5.84248	−	10.1195i	−0.495553	−	0.858323i	0.504434	−	0.863450i	$-0.331701\pi$
$139$	−5.84248	−	10.1195i	−0.495553	−	0.858323i	−0.999987	+	0.00512757i	$0.998368\pi$
$140$		0			0
$141$	−28.9791			−2.44048
$142$	2.39232	+	4.14362i	0.200759	+	0.347725i
$143$	0.454787	+	0.787715i	0.0380312	+	0.0658720i
$144$	6.98149			0.581791
$145$		0			0
$146$	−1.50315	−	2.60354i	−0.124402	−	0.215470i
$147$	−9.82395	+	17.0156i	−0.810266	+	1.40342i
$148$	−0.0567816	−	0.0983486i	−0.00466742	−	0.00808420i
$149$	3.13033	−	5.42188i	0.256446	−	0.444178i	−0.708841	−	0.705368i	$-0.750782\pi$
$149$	3.13033	−	5.42188i	0.256446	−	0.444178i	0.965287	+	0.261190i	$0.0841150\pi$
$150$		0			0
$151$	−15.3436			−1.24864			−0.624322	−	0.781167i	$-0.714625\pi$
$151$	−15.3436			−1.24864			−0.624322	+	0.781167i	$0.714625\pi$
$152$	−4.19766	+	3.22437i	−0.340475	+	0.261531i
$153$	−0.0188998			−0.00152796
$154$	−0.223200	+	0.386594i	−0.0179860	+	0.0311527i
$155$		0			0
$156$	−5.37336	−	9.30693i	−0.430213	−	0.745151i
$157$	7.50595	−	13.0007i	0.599040	−	1.03757i	−0.393923	−	0.919143i	$-0.628882\pi$
$157$	7.50595	−	13.0007i	0.599040	−	1.03757i	0.992963	−	0.118424i	$-0.0377843\pi$
$158$	2.08628	+	3.61354i	0.165975	+	0.287478i
$159$	−24.6212			−1.95259
$160$		0			0
$161$	10.7331	+	18.5903i	0.845886	+	1.46512i
$162$	−1.70525	−	2.95359i	−0.133977	−	0.232056i
$163$	−11.8894			−0.931250			−0.465625	−	0.884982i	$-0.654170\pi$
$163$	−11.8894			−0.931250			−0.465625	+	0.884982i	$0.654170\pi$
$164$	−7.07636			−0.552571
$165$		0			0
$166$	2.41744	−	4.18714i	0.187630	−	0.324985i
$167$	−3.61678	−	6.26445i	−0.279875	−	0.484757i	0.691479	−	0.722397i	$-0.256960\pi$
$167$	−3.61678	−	6.26445i	−0.279875	−	0.484757i	−0.971353	+	0.237640i	$0.923626\pi$
$168$	5.40838	−	9.36758i	0.417265	−	0.722725i
$169$	3.33451	−	5.77553i	0.256500	−	0.444272i
$170$		0			0
$171$	8.20182	+	3.39242i	0.627209	+	0.259425i
$172$	−8.01905			−0.611447
$173$	1.72229	−	2.98309i	0.130943	−	0.226800i	−0.793097	−	0.609095i	$-0.791533\pi$
$173$	1.72229	−	2.98309i	0.130943	−	0.226800i	0.924040	+	0.382295i	$0.124866\pi$
$174$	3.30051	−	5.71665i	0.250211	−	0.433378i
$175$		0			0
$176$	−0.619718	+	1.07338i	−0.0467130	+	0.0809094i
$177$	5.96820	+	10.3372i	0.448597	+	0.776994i
$178$	1.29780			0.0972744
$179$	−5.87847			−0.439378			−0.219689	−	0.975570i	$-0.570504\pi$
$179$	−5.87847			−0.439378			−0.219689	+	0.975570i	$0.570504\pi$
$180$		0			0
$181$	−0.552356	−	0.956709i	−0.0410563	−	0.0711116i	0.844767	−	0.535134i	$-0.179739\pi$
$181$	−0.552356	−	0.956709i	−0.0410563	−	0.0711116i	−0.885823	+	0.464023i	$0.846406\pi$
$182$	−3.10712			−0.230315
$183$	−19.9674			−1.47603
$184$	−3.28357	−	5.68732i	−0.242068	−	0.419274i
$185$		0			0
$186$	1.28026	+	2.21747i	0.0938731	+	0.162593i
$187$	0.00167766	−	0.00290579i	0.000122683	−	0.000212493i
$188$	−12.2883	+	21.2839i	−0.896213	+	1.55229i
$189$	8.58495			0.624463
$190$		0			0
$191$	21.2415			1.53698			0.768491	−	0.639860i	$-0.221008\pi$
$191$	21.2415			1.53698			0.768491	+	0.639860i	$0.221008\pi$
$192$	6.47423	−	11.2137i	0.467237	−	0.809278i
$193$	−4.77026	+	8.26233i	−0.343371	+	0.594736i	−0.985056	−	0.172232i	$-0.944902\pi$
$193$	−4.77026	+	8.26233i	−0.343371	+	0.594736i	0.641686	+	0.766968i	$0.278235\pi$
$194$	0.582064	+	1.00816i	0.0417897	+	0.0723820i
$195$		0			0
$196$	8.33145	+	14.4305i	0.595104	+	1.03075i
$197$	2.05919			0.146711			0.0733556	−	0.997306i	$-0.476629\pi$
$197$	2.05919			0.146711			0.0733556	+	0.997306i	$0.476629\pi$
$198$	−0.229002			−0.0162745
$199$	9.95070	+	17.2351i	0.705386	+	1.22176i	0.966552	+	0.256471i	$0.0825598\pi$
$199$	9.95070	+	17.2351i	0.705386	+	1.22176i	−0.261166	+	0.965294i	$0.584107\pi$
$200$		0			0
$201$	10.4352			0.736045
$202$	5.36320			0.377354
$203$	18.7641	+	32.5005i	1.31698	+	2.28108i
$204$	−0.0198217	+	0.0343322i	−0.00138780	+	0.00240374i
$205$		0			0
$206$	−1.37146	+	2.37543i	−0.0955539	+	0.165504i
$207$	−5.50605	+	9.53676i	−0.382697	+	0.662851i
$208$	−8.62696			−0.598172
$209$	−1.24962	+	0.959874i	−0.0864377	+	0.0663959i
$210$		0			0
$211$	10.7586	−	18.6345i	0.740655	−	1.28285i	−0.211542	−	0.977369i	$-0.567848\pi$
$211$	10.7586	−	18.6345i	0.740655	−	1.28285i	0.952197	−	0.305484i	$-0.0988182\pi$
$212$	−10.4403	+	18.0832i	−0.717045	+	1.24196i
$213$	−17.2568	−	29.8897i	−1.18242	−	2.04801i
$214$	0.203124	−	0.351822i	0.0138853	−	0.0240500i
$215$		0			0
$216$	−2.62639			−0.178703
$217$	−14.5571			−0.988201
$218$	−0.948379	−	1.64264i	−0.0642323	−	0.111254i
$219$	10.8429	+	18.7804i	0.732695	+	1.26906i
$220$		0			0
$221$	0.0233543			0.00157098
$222$	−0.0208297	−	0.0360782i	−0.00139800	−	0.00242141i
$223$	−2.76965	+	4.79718i	−0.185470	+	0.321243i	−0.943735	−	0.330704i	$-0.892714\pi$
$223$	−2.76965	+	4.79718i	−0.185470	+	0.321243i	0.758265	+	0.651946i	$0.226047\pi$
$224$	−6.93694	−	12.0151i	−0.463494	−	0.802794i
$225$		0			0
$226$	1.74814	−	3.02787i	0.116285	−	0.201411i
$227$	−16.2401			−1.07789			−0.538947	−	0.842340i	$-0.681178\pi$
$227$	−16.2401			−1.07789			−0.538947	+	0.842340i	$0.681178\pi$
$228$	14.7643	−	11.3410i	0.977791	−	0.751077i
$229$	10.5436			0.696739			0.348369	−	0.937357i	$-0.386736\pi$
$229$	10.5436			0.696739			0.348369	+	0.937357i	$0.386736\pi$
$230$		0			0
$231$	1.61004	−	2.78867i	0.105933	−	0.183481i
$232$	−5.74051	−	9.94286i	−0.376883	−	0.652781i
$233$	8.08922	−	14.0109i	0.529942	−	0.917887i	−0.469447	−	0.882960i	$-0.655547\pi$
$233$	8.08922	−	14.0109i	0.529942	−	0.917887i	0.999390	−	0.0349268i	$-0.0111198\pi$
$234$	−0.796972	−	1.38040i	−0.0520997	−	0.0902394i
$235$		0			0
$236$	10.1230			0.658949
$237$	−15.0492	−	26.0660i	−0.977552	−	1.69317i
$238$	0.00573091	+	0.00992622i	0.000371480	+	0.000643421i
$239$	−9.62683			−0.622708			−0.311354	−	0.950294i	$-0.600782\pi$
$239$	−9.62683			−0.622708			−0.311354	+	0.950294i	$0.600782\pi$
$240$		0			0
$241$	9.84997	+	17.0606i	0.634492	+	1.09897i	0.986622	+	0.163022i	$0.0521241\pi$
$241$	9.84997	+	17.0606i	0.634492	+	1.09897i	−0.352130	+	0.935951i	$0.614543\pi$
$242$	−1.69077	+	2.92849i	−0.108687	+	0.188251i
$243$	9.05645	+	15.6862i	0.580971	+	1.00627i
$244$	−8.46691	+	14.6651i	−0.542038	+	0.938838i
$245$		0			0
$246$	−2.59589			−0.165508
$247$	−10.1349	−	4.19197i	−0.644868	−	0.266729i
$248$	4.45346			0.282795
$249$	−17.4381	+	30.2036i	−1.10509	+	1.91408i
$250$		0			0
$251$	−4.60240	−	7.97158i	−0.290501	−	0.503162i	0.683428	−	0.730018i	$-0.260489\pi$
$251$	−4.60240	−	7.97158i	−0.290501	−	0.503162i	−0.973928	+	0.226856i	$0.927155\pi$
$252$	−7.69121	+	13.3216i	−0.484501	+	0.839180i
$253$	−0.977499	−	1.69308i	−0.0614548	−	0.106443i
$254$	3.68776			0.231391
$255$		0			0
$256$	−4.40321	−	7.62659i	−0.275201	−	0.476662i
$257$	0.229133	+	0.396869i	0.0142929	+	0.0247560i	0.873083	−	0.487571i	$-0.162117\pi$
$257$	0.229133	+	0.396869i	0.0142929	+	0.0247560i	−0.858790	+	0.512327i	$0.828784\pi$
$258$	−2.94171			−0.183143
$259$	0.236844			0.0147167
$260$		0			0
$261$	−9.62596	+	16.6727i	−0.595832	+	1.03201i
$262$	−0.374256	−	0.648230i	−0.0231216	−	0.0400478i
$263$	−5.87774	+	10.1806i	−0.362437	+	0.627760i	−0.988361	−	0.152124i	$-0.951389\pi$
$263$	−5.87774	+	10.1806i	−0.362437	+	0.627760i	0.625924	+	0.779884i	$0.284722\pi$
$264$	−0.492559	+	0.853137i	−0.0303149	+	0.0525070i
$265$		0			0
$266$	−0.705297	−	5.33628i	−0.0432445	−	0.327188i
$267$	−9.36161			−0.572921
$268$	4.42494	−	7.66421i	0.270296	−	0.468166i
$269$	−2.38296	+	4.12742i	−0.145292	+	0.251653i	−0.929482	−	0.368868i	$-0.879745\pi$
$269$	−2.38296	+	4.12742i	−0.145292	+	0.251653i	0.784190	+	0.620521i	$0.213079\pi$
$270$		0			0
$271$	7.75620	−	13.4341i	0.471155	−	0.816065i	−0.528300	−	0.849058i	$-0.677170\pi$
$271$	7.75620	−	13.4341i	0.471155	−	0.816065i	0.999456	+	0.0329925i	$0.0105038\pi$
$272$	0.0159119	+	0.0275603i	0.000964803	+	0.00167109i
$273$	22.4130			1.35650
$274$	1.56093			0.0942994
$275$		0			0
$276$	11.5492	+	20.0039i	0.695183	+	1.20409i
$277$	−4.90677			−0.294819			−0.147410	−	0.989076i	$-0.547094\pi$
$277$	−4.90677			−0.294819			−0.147410	+	0.989076i	$0.547094\pi$
$278$	−3.63528			−0.218030
$279$	−3.73388	−	6.46727i	−0.223542	−	0.387186i
$280$		0			0
$281$	−6.84266	−	11.8518i	−0.408199	−	0.707021i	0.586489	−	0.809957i	$-0.300510\pi$
$281$	−6.84266	−	11.8518i	−0.408199	−	0.707021i	−0.994688	+	0.102936i	$0.967176\pi$
$282$	−4.50782	+	7.80777i	−0.268437	+	0.464946i
$283$	8.43386	−	14.6079i	0.501341	−	0.868348i	−0.498658	−	0.866799i	$-0.666174\pi$
$283$	8.43386	−	14.6079i	0.501341	−	0.868348i	0.999999	−	0.00154919i	$-0.000493124\pi$
$284$	−29.2702			−1.73687
$285$		0			0
$286$	0.282976			0.0167327
$287$	7.37911	−	12.7810i	0.435575	−	0.754438i
$288$	3.55863	−	6.16373i	0.209694	−	0.363201i
$289$	8.49996	+	14.7224i	0.499997	+	0.866021i
$290$		0			0
$291$	−4.19868	−	7.27232i	−0.246131	−	0.426311i
$292$	18.3912			1.07626
$293$	−25.8794			−1.51189			−0.755944	−	0.654636i	$-0.772822\pi$
$293$	−25.8794			−1.51189			−0.755944	+	0.654636i	$0.772822\pi$
$294$	3.05631	+	5.29368i	0.178247	+	0.308734i
$295$		0			0
$296$	−0.0724575			−0.00421151
$297$	−0.781861			−0.0453681
$298$	−0.973869	−	1.68679i	−0.0564147	−	0.0977132i
$299$	6.80377	−	11.7845i	0.393472	−	0.681514i
$300$		0			0
$301$	8.36213	−	14.4836i	0.481985	−	0.834823i
$302$	−2.38676	+	4.13398i	−0.137342	+	0.237884i
$303$	−38.6871			−2.22252
$304$	−1.95827	−	14.8162i	−0.112314	−	0.849770i
$305$		0			0
$306$	−0.00293994	+	0.00509213i	−0.000168065	+	0.000291098i
$307$	−1.64721	+	2.85305i	−0.0940111	+	0.162832i	−0.909195	−	0.416370i	$-0.863302\pi$
$307$	−1.64721	+	2.85305i	−0.0940111	+	0.162832i	0.815184	+	0.579202i	$0.196636\pi$
$308$	−1.36543	−	2.36500i	−0.0778029	−	0.134759i
$309$	9.89290	−	17.1350i	0.562787	−	0.974776i
$310$		0			0
$311$	30.4253			1.72526			0.862629	−	0.505837i	$-0.168816\pi$
$311$	30.4253			1.72526			0.862629	+	0.505837i	$0.168816\pi$
$312$	−6.85680			−0.388190
$313$	4.37696	+	7.58112i	0.247401	+	0.428510i	0.962804	−	0.270201i	$-0.0870903\pi$
$313$	4.37696	+	7.58112i	0.247401	+	0.428510i	−0.715403	+	0.698712i	$0.753757\pi$
$314$	−2.33516	−	4.04461i	−0.131781	−	0.228251i
$315$		0			0
$316$	−25.5257			−1.43594
$317$	−4.18690	−	7.25192i	−0.235160	−	0.407308i	0.724159	−	0.689633i	$-0.242228\pi$
$317$	−4.18690	−	7.25192i	−0.235160	−	0.407308i	−0.959319	+	0.282324i	$0.908895\pi$
$318$	−3.82993	+	6.63363i	−0.214772	+	0.371996i
$319$	−1.70891	−	2.95993i	−0.0956808	−	0.165724i
$320$		0			0
$321$	−1.46522	+	2.53784i	−0.0817808	+	0.141648i
$322$	6.67830			0.372167
$323$	0.00530128	+	0.0401095i	0.000294971	+	0.00223175i
$324$	20.8639			1.15910
$325$		0			0
$326$	−1.84944	+	3.20333i	−0.102431	+	0.177416i
$327$	6.84107	+	11.8491i	0.378312	+	0.655255i
$328$	−2.25749	+	3.91009i	−0.124649	+	0.215898i
$329$	−25.6280	−	44.3889i	−1.41292	−	2.44724i
$330$		0			0
$331$	−17.8536			−0.981321			−0.490661	−	0.871351i	$-0.663245\pi$
$331$	−17.8536			−0.981321			−0.490661	+	0.871351i	$0.663245\pi$
$332$	14.7888	+	25.6149i	0.811640	+	1.40580i
$333$	0.0607501	+	0.105222i	0.00332908	+	0.00576614i
$334$	−2.25042			−0.123137
$335$		0			0
$336$	15.2706	+	26.4494i	0.833079	+	1.44293i
$337$	5.04723	−	8.74205i	0.274940	−	0.476210i	−0.695180	−	0.718836i	$-0.744675\pi$
$337$	5.04723	−	8.74205i	0.274940	−	0.476210i	0.970120	+	0.242626i	$0.0780087\pi$
$338$	−1.03739	−	1.79681i	−0.0564266	−	0.0977338i
$339$	−12.6101	+	21.8413i	−0.684886	+	1.18626i
$340$		0			0
$341$	1.32577			0.0717942
$342$	2.18983	−	1.68209i	0.118413	−	0.0909570i
$343$	−6.96666			−0.376164
$344$	−2.55823	+	4.43098i	−0.137930	+	0.238902i
$345$		0			0
$346$	−0.535818	−	0.928063i	−0.0288057	−	0.0498930i
$347$	1.35145	−	2.34077i	0.0725494	−	0.125659i	−0.827469	−	0.561512i	$-0.810220\pi$
$347$	1.35145	−	2.34077i	0.0725494	−	0.125659i	0.900018	+	0.435853i	$0.143553\pi$
$348$	20.1910	+	34.9718i	1.08235	+	1.87469i
$349$	−11.2187			−0.600524			−0.300262	−	0.953857i	$-0.597074\pi$
$349$	−11.2187			−0.600524			−0.300262	+	0.953857i	$0.597074\pi$
$350$		0			0
$351$	−2.72102	−	4.71295i	−0.145238	−	0.251559i
$352$	0.631770	+	1.09426i	0.0336735	+	0.0583241i
$353$	−9.37058			−0.498746			−0.249373	−	0.968408i	$-0.580224\pi$
$353$	−9.37058			−0.498746			−0.249373	+	0.968408i	$0.580224\pi$
$354$	3.71351			0.197371
$355$		0			0
$356$	−3.96967	+	6.87568i	−0.210392	+	0.364410i
$357$	−0.0413395	−	0.0716021i	−0.00218792	−	0.00378959i
$358$	−0.914419	+	1.58382i	−0.0483286	+	0.0837075i
$359$	10.7443	−	18.6097i	0.567064	−	0.982184i	−0.429790	−	0.902929i	$-0.641413\pi$
$359$	10.7443	−	18.6097i	0.567064	−	0.982184i	0.996854	−	0.0792550i	$-0.0252541\pi$
$360$		0			0
$361$	4.89888	−	18.3576i	0.257836	−	0.966189i
$362$	−0.343685			−0.0180637
$363$	12.1962	−	21.1245i	0.640135	−	1.10875i
$364$	9.50395	−	16.4613i	0.498142	−	0.862808i
$365$		0			0
$366$	−3.10600	+	5.37975i	−0.162353	+	0.281204i
$367$	15.0567	+	26.0790i	0.785953	+	1.36131i	0.928428	+	0.371512i	$0.121161\pi$
$367$	15.0567	+	26.0790i	0.785953	+	1.36131i	−0.142475	+	0.989798i	$0.545506\pi$
$368$	18.5424			0.966588
$369$	7.57093			0.394127
$370$		0			0
$371$	−21.7740	−	37.7137i	−1.13045	−	1.95800i
$372$	−15.6640			−0.812143
$373$	−26.7206			−1.38354			−0.691769	−	0.722119i	$-0.743169\pi$
$373$	−26.7206			−1.38354			−0.691769	+	0.722119i	$0.743169\pi$
$374$	−0.000521933	0	0.000904015i	−2.69885e−5	0	4.67455e-5i
$375$		0			0
$376$	7.84036	+	13.5799i	0.404336	+	0.700330i
$377$	11.8947	−	20.6022i	0.612608	−	1.06107i
$378$	1.33542	−	2.31302i	0.0686867	−	0.118969i
$379$	22.9732			1.18005			0.590026	−	0.807384i	$-0.299117\pi$
$379$	22.9732			1.18005			0.590026	+	0.807384i	$0.299117\pi$
$380$		0			0
$381$	−26.6014			−1.36283
$382$	3.30420	−	5.72305i	0.169058	−	0.292816i
$383$	14.5442	−	25.1913i	0.743174	−	1.28722i	−0.207868	−	0.978157i	$-0.566653\pi$
$383$	14.5442	−	25.1913i	0.743174	−	1.28722i	0.951043	−	0.309059i	$-0.100014\pi$
$384$	−9.85821	−	17.0749i	−0.503075	−	0.871351i
$385$		0			0
$386$	1.48407	+	2.57048i	0.0755369	+	0.130834i
$387$	8.57951			0.436121
$388$	−7.12159			−0.361544
$389$	−1.81882	−	3.15029i	−0.0922178	−	0.159726i	0.816226	−	0.577732i	$-0.196062\pi$
$389$	−1.81882	−	3.15029i	−0.0922178	−	0.159726i	−0.908444	+	0.418006i	$0.862729\pi$
$390$		0			0
$391$	−0.0501967			−0.00253855
$392$	10.6315			0.536974
$393$	2.69967	+	4.67596i	0.136180	+	0.235871i
$394$	0.320315	−	0.554802i	0.0161372	−	0.0279505i
$395$		0			0
$396$	0.700465	−	1.21324i	0.0351997	−	0.0609676i
$397$	−6.96707	+	12.0673i	−0.349667	+	0.605641i	−0.986190	−	0.165616i	$-0.947039\pi$
$397$	−6.96707	+	12.0673i	−0.349667	+	0.605641i	0.636523	+	0.771258i	$0.280372\pi$
$398$	6.19148			0.310351
$399$	5.08761	+	38.4929i	0.254699	+	1.92705i
$400$		0			0
$401$	−13.2751	+	22.9931i	−0.662925	+	1.14822i	0.316918	+	0.948453i	$0.397352\pi$
$401$	−13.2751	+	22.9931i	−0.662925	+	1.14822i	−0.979843	+	0.199767i	$0.935981\pi$
$402$	1.62324	−	2.81154i	0.0809600	−	0.140227i
$403$	4.61392	+	7.99154i	0.229836	+	0.398087i
$404$	−16.4048	+	28.4139i	−0.816168	+	1.41365i
$405$		0			0
$406$	11.6753			0.579438
$407$	−0.0215701			−0.00106919
$408$	0.0126470	+	0.0219052i	0.000626119	+	0.00108447i
$409$	−7.49800	−	12.9869i	−0.370752	−	0.642162i	0.618929	−	0.785447i	$-0.287567\pi$
$409$	−7.49800	−	12.9869i	−0.370752	−	0.642162i	−0.989681	+	0.143285i	$0.954234\pi$
$410$		0			0
$411$	−11.2597			−0.555399
$412$	−8.38993	−	14.5318i	−0.413342	−	0.715929i
$413$	−10.5561	+	18.2836i	−0.519430	+	0.899679i
$414$	1.71298	+	2.96696i	0.0841881	+	0.145818i
$415$		0			0
$416$	−4.39736	+	7.61646i	−0.215598	+	0.373427i
$417$	26.2229			1.28414
$418$	0.0642337	+	0.485993i	0.00314177	+	0.0237707i
$419$	30.4528			1.48772			0.743859	−	0.668337i	$-0.232993\pi$
$419$	30.4528			1.48772			0.743859	+	0.668337i	$0.232993\pi$
$420$		0			0
$421$	0.444876	−	0.770547i	0.0216819	−	0.0375542i	−0.854981	−	0.518660i	$-0.826431\pi$
$421$	0.444876	−	0.770547i	0.0216819	−	0.0375542i	0.876663	+	0.481105i	$0.159765\pi$
$422$	−3.34710	−	5.79734i	−0.162934	−	0.282210i
$423$	13.1471	−	22.7714i	0.639233	−	1.10718i
$424$	6.66132	+	11.5377i	0.323502	+	0.560322i
$425$		0			0
$426$	−10.7375			−0.520232
$427$	−17.6583	−	30.5851i	−0.854545	−	1.48012i
$428$	1.24262	+	2.15228i	0.0600643	+	0.104034i
$429$	−2.04123			−0.0985513
$430$		0			0
$431$	−7.36739	−	12.7607i	−0.354875	−	0.614661i	0.632222	−	0.774787i	$-0.282143\pi$
$431$	−7.36739	−	12.7607i	−0.354875	−	0.614661i	−0.987097	+	0.160126i	$0.948810\pi$
$432$	3.70782	−	6.42213i	0.178393	−	0.308985i
$433$	0.742440	+	1.28594i	0.0356794	+	0.0617985i	0.883314	−	0.468782i	$-0.155307\pi$
$433$	0.742440	+	1.28594i	0.0356794	+	0.0617985i	−0.847634	+	0.530581i	$0.821974\pi$
$434$	−2.26442	+	3.92208i	−0.108695	+	0.188266i
$435$		0			0
$436$	11.6035			0.555706
$437$	21.7835	+	9.01003i	1.04205	+	0.431008i
$438$	6.74662			0.322366
$439$	7.34789	−	12.7269i	0.350696	−	0.607423i	−0.635676	−	0.771956i	$-0.719278\pi$
$439$	7.34789	−	12.7269i	0.350696	−	0.607423i	0.986372	+	0.164533i	$0.0526118\pi$
$440$		0			0
$441$	−8.91374	−	15.4391i	−0.424464	−	0.735193i
$442$	0.00363285	−	0.00629229i	0.000172797	−	0.000299294i
$443$	9.32539	+	16.1520i	0.443062	+	0.767407i	0.997915	−	0.0645421i	$-0.0205587\pi$
$443$	9.32539	+	16.1520i	0.443062	+	0.767407i	−0.554853	+	0.831949i	$0.687225\pi$
$444$	0.254853			0.0120948
$445$		0			0
$446$	0.861660	+	1.49244i	0.0408008	+	0.0706690i
$447$	7.02494	+	12.1675i	0.332268	+	0.575505i
$448$	22.9022			1.08203
$449$	5.17365			0.244160			0.122080	−	0.992520i	$-0.461044\pi$
$449$	5.17365			0.244160			0.122080	+	0.992520i	$0.461044\pi$
$450$		0			0
$451$	−0.672040	+	1.16401i	−0.0316451	+	0.0548110i
$452$	10.6943	+	18.5231i	0.503018	+	0.871252i
$453$	17.2167	−	29.8202i	0.808911	−	1.40107i
$454$	−2.52621	+	4.37553i	−0.118561	+	0.205354i
$455$		0			0
$456$	−1.55645	−	11.7761i	−0.0728875	−	0.551467i
$457$	20.2319			0.946409			0.473204	−	0.880953i	$-0.343097\pi$
$457$	20.2319			0.946409			0.473204	+	0.880953i	$0.343097\pi$
$458$	1.64009	−	2.84072i	0.0766365	−	0.132738i
$459$	−0.0100376	+	0.0173856i	−0.000468513	+	0.000811488i
$460$		0			0
$461$	−15.1012	+	26.1561i	−0.703334	+	1.21821i	0.263955	+	0.964535i	$0.414973\pi$
$461$	−15.1012	+	26.1561i	−0.703334	+	1.21821i	−0.967289	+	0.253675i	$0.918361\pi$
$462$	−0.500896	−	0.867577i	−0.0233038	−	0.0403633i
$463$	20.4060			0.948345			0.474173	−	0.880432i	$-0.342747\pi$
$463$	20.4060			0.948345			0.474173	+	0.880432i	$0.342747\pi$
$464$	32.4167			1.50491
$465$		0			0
$466$	−2.51662	−	4.35891i	−0.116580	−	0.201923i
$467$	−15.9143			−0.736425			−0.368212	−	0.929742i	$-0.620030\pi$
$467$	−15.9143			−0.736425			−0.368212	+	0.929742i	$0.620030\pi$
$468$	9.75101			0.450741
$469$	9.22850	+	15.9842i	0.426132	+	0.738083i
$470$		0			0
$471$	16.8445	+	29.1755i	0.776154	+	1.34434i
$472$	3.22941	−	5.59351i	0.148646	−	0.257462i
$473$	−0.761567	+	1.31907i	−0.0350169	+	0.0606511i
$474$	−9.36386			−0.430096
$475$		0			0
$476$	−0.0701180			−0.00321385
$477$	11.1700	−	19.3470i	0.511440	−	0.885839i
$478$	−1.49749	+	2.59373i	−0.0684936	+	0.118634i
$479$	18.6782	+	32.3515i	0.853428	+	1.47818i	0.878096	+	0.478484i	$0.158814\pi$
$479$	18.6782	+	32.3515i	0.853428	+	1.47818i	−0.0246685	+	0.999696i	$0.507853\pi$
$480$		0			0
$481$	−0.0750682	−	0.130022i	−0.00342282	−	0.00592849i
$482$	6.12881			0.279159
$483$	−48.1734			−2.19197
$484$	−10.3433	−	17.9151i	−0.470150	−	0.814325i
$485$		0			0
$486$	5.63506			0.255612
$487$	−39.0070			−1.76757			−0.883787	−	0.467889i	$-0.845015\pi$
$487$	−39.0070			−1.76757			−0.883787	+	0.467889i	$0.845015\pi$
$488$	5.40220	+	9.35689i	0.244546	+	0.423566i
$489$	13.3408	−	23.1070i	0.603293	−	1.04493i
$490$		0			0
$491$	10.2673	−	17.7835i	0.463357	−	0.802557i	−0.535769	−	0.844365i	$-0.679978\pi$
$491$	10.2673	−	17.7835i	0.463357	−	0.802557i	0.999126	+	0.0418074i	$0.0133116\pi$
$492$	7.94022	−	13.7529i	0.357973	−	0.620027i
$493$	−0.0877564			−0.00395235
$494$	−2.70595	+	2.07854i	−0.121747	+	0.0935180i
$495$		0			0
$496$	−6.28718	+	10.8897i	−0.282303	+	0.488963i
$497$	30.5225	−	52.8664i	1.36912	−	2.37138i
$498$	5.42512	+	9.39658i	0.243105	+	0.421071i
$499$	−0.368486	+	0.638237i	−0.0164957	+	0.0285714i	−0.874155	−	0.485646i	$-0.838584\pi$
$499$	−0.368486	+	0.638237i	−0.0164957	+	0.0285714i	0.857660	+	0.514218i	$0.171918\pi$
$500$		0			0
$501$	16.2332			0.725247
$502$	−2.86368			−0.127812
$503$	−4.99035	−	8.64354i	−0.222509	−	0.385397i	0.733060	−	0.680164i	$-0.238091\pi$
$503$	−4.99035	−	8.64354i	−0.222509	−	0.385397i	−0.955569	+	0.294767i	$0.904758\pi$
$504$	4.90728	+	8.49966i	0.218588	+	0.378605i
$505$		0			0
$506$	−0.608215			−0.0270385
$507$	7.48314	+	12.9612i	0.332338	+	0.575626i
$508$	−11.2800	+	19.5375i	−0.500469	+	0.866838i
$509$	15.2505	+	26.4147i	0.675968	+	1.17081i	0.976185	+	0.216940i	$0.0696075\pi$
$509$	15.2505	+	26.4147i	0.675968	+	1.17081i	−0.300217	+	0.953871i	$0.597059\pi$
$510$		0			0
$511$	−19.1780	+	33.2173i	−0.848386	+	1.46945i
$512$	−20.3111			−0.897633
$513$	7.47654	−	5.74300i	0.330097	−	0.253559i
$514$	0.142570			0.00628849
$515$		0			0
$516$	8.99799	−	15.5850i	0.396115	−	0.686090i
$517$	2.33402	+	4.04265i	0.102650	+	0.177796i
$518$	0.0368419	−	0.0638121i	0.00161874	−	0.00280374i
$519$	3.86508	+	6.69452i	0.169658	+	0.293857i
$520$		0			0
$521$	23.5752			1.03285			0.516424	−	0.856333i	$-0.327263\pi$
$521$	23.5752			1.03285			0.516424	+	0.856333i	$0.327263\pi$
$522$	2.99471	+	5.18699i	0.131075	+	0.227029i
$523$	−5.46896	−	9.47252i	−0.239141	−	0.414204i	0.721327	−	0.692595i	$-0.243532\pi$
$523$	−5.46896	−	9.47252i	−0.239141	−	0.414204i	−0.960468	+	0.278390i	$0.910199\pi$
$524$	4.57904			0.200036
$525$		0			0
$526$	1.82861	+	3.16725i	0.0797313	+	0.138099i
$527$	0.0170202	−	0.0294799i	0.000741413	−	0.00128416i
$528$	−1.39074	−	2.40884i	−0.0605244	−	0.104831i
$529$	−3.12370	+	5.41041i	−0.135813	+	0.235235i
$530$		0			0
$531$	−10.8305			−0.470002
$532$	30.4286	+	12.5858i	1.31925	+	0.545664i
$533$	−9.35532			−0.405224
$534$	−1.45623	+	2.52227i	−0.0630174	+	0.109149i
$535$		0			0
$536$	−2.82327	−	4.89005i	−0.121947	−	0.211218i
$537$	6.59610	−	11.4248i	0.284643	−	0.493016i
$538$	0.741359	+	1.28407i	0.0319623	+	0.0553603i
$539$	3.16494			0.136324
$540$		0			0
$541$	−14.7076	−	25.4743i	−0.632328	−	1.09522i	−0.987075	−	0.160261i	$-0.948766\pi$
$541$	−14.7076	−	25.4743i	−0.632328	−	1.09522i	0.354747	−	0.934962i	$-0.384567\pi$
$542$	−2.41301	−	4.17946i	−0.103648	−	0.179523i
$543$	2.47914			0.106390
$544$	0.0324428			0.00139097
$545$		0			0
$546$	3.48643	−	6.03867i	0.149205	−	0.258431i
$547$	16.3667	+	28.3480i	0.699790	+	1.21207i	0.968539	+	0.248861i	$0.0800563\pi$
$547$	16.3667	+	28.3480i	0.699790	+	1.21207i	−0.268750	+	0.963210i	$0.586610\pi$
$548$	−4.77453	+	8.26973i	−0.203958	+	0.353265i
$549$	9.05867	−	15.6901i	0.386614	−	0.669636i
$550$		0			0
$551$	38.0830	+	15.7518i	1.62239	+	0.671049i
$552$	14.7377			0.627278
$553$	26.6178	−	46.1034i	1.13190	−	1.96052i
$554$	−0.763267	+	1.32202i	−0.0324281	+	0.0561671i
$555$		0			0
$556$	11.1195	−	19.2595i	0.471571	−	0.816785i
$557$	4.74905	+	8.22560i	0.201224	+	0.348530i	0.948923	−	0.315508i	$-0.102175\pi$
$557$	4.74905	+	8.22560i	0.201224	+	0.348530i	−0.747699	+	0.664038i	$0.768841\pi$
$558$	−2.32328			−0.0983523
$559$	−10.6016			−0.448400
$560$		0			0
$561$	0.00376493	+	0.00652105i	0.000158955	+	0.000275319i
$562$	−4.25761			−0.179596
$563$	33.1253			1.39607			0.698033	−	0.716065i	$-0.254059\pi$
$563$	33.1253			1.39607			0.698033	+	0.716065i	$0.254059\pi$
$564$	−27.5767	−	47.7643i	−1.16119	−	2.01124i
$565$		0			0
$566$	−2.62384	−	4.54462i	−0.110288	−	0.191025i
$567$	−21.7565	+	37.6834i	−0.913687	+	1.58255i
$568$	−9.33773	+	16.1734i	−0.391802	+	0.678622i
$569$	26.5756			1.11411			0.557054	−	0.830476i	$-0.311932\pi$
$569$	26.5756			1.11411			0.557054	+	0.830476i	$0.311932\pi$
$570$		0			0
$571$	−6.14212			−0.257040			−0.128520	−	0.991707i	$-0.541023\pi$
$571$	−6.14212			−0.257040			−0.128520	+	0.991707i	$0.541023\pi$
$572$	−0.865557	+	1.49919i	−0.0361907	+	0.0626842i
$573$	−23.8346	+	41.2828i	−0.995706	+	1.72461i
$574$	−2.29570	−	3.97627i	−0.0958206	−	0.165966i
$575$		0			0
$576$	5.87438	+	10.1747i	0.244766	+	0.423947i
$577$	−11.1455			−0.463992			−0.231996	−	0.972717i	$-0.574526\pi$
$577$	−11.1455			−0.463992			−0.231996	+	0.972717i	$0.574526\pi$
$578$	5.28881			0.219985
$579$	−10.7052	−	18.5420i	−0.444893	−	0.770577i
$580$		0			0
$581$	−61.6860			−2.55917
$582$	−2.61248			−0.108291
$583$	1.98303	+	3.43471i	0.0821288	+	0.142251i
$584$	5.86713	−	10.1622i	0.242784	−	0.420513i
$585$		0			0
$586$	−4.02564	+	6.97261i	−0.166297	+	0.288036i
$587$	−10.8330	+	18.7633i	−0.447126	+	0.774445i	−0.998198	−	0.0600130i	$-0.980886\pi$
$587$	−10.8330	+	18.7633i	−0.447126	+	0.774445i	0.551072	+	0.834458i	$0.314219\pi$
$588$	−37.3941			−1.54211
$589$	−12.6776	+	9.73814i	−0.522372	+	0.401253i
$590$		0			0
$591$	−2.31057	+	4.00202i	−0.0950441	+	0.164621i
$592$	0.102292	−	0.177175i	0.00420418	−	0.00728185i
$593$	−12.1707	−	21.0803i	−0.499791	−	0.865664i	0.500209	−	0.865905i	$-0.333257\pi$
$593$	−12.1707	−	21.0803i	−0.499791	−	0.865664i	−1.00000		0.000240828i	$0.999923\pi$
$594$	−0.121621	+	0.210655i	−0.00499019	+	0.00864326i
$595$		0			0
$596$	11.9153			0.488072
$597$	−44.6618			−1.82789
$598$	−2.11671	−	3.66624i	−0.0865585	−	0.149924i
$599$	9.47682	+	16.4143i	0.387212	+	0.670672i	0.992073	−	0.125659i	$-0.0401046\pi$
$599$	9.47682	+	16.4143i	0.387212	+	0.670672i	−0.604861	+	0.796331i	$0.706771\pi$
$600$		0			0
$601$	4.40461			0.179668			0.0898339	−	0.995957i	$-0.471366\pi$
$601$	4.40461			0.179668			0.0898339	+	0.995957i	$0.471366\pi$
$602$	−2.60152	−	4.50597i	−0.106030	−	0.183650i
$603$	−4.73420	+	8.19987i	−0.192791	+	0.333925i
$604$	−14.6011	−	25.2898i	−0.594108	−	1.02903i
$605$		0			0
$606$	−6.01793	+	10.4234i	−0.244462	+	0.423420i
$607$	−17.3015			−0.702246			−0.351123	−	0.936329i	$-0.614200\pi$
$607$	−17.3015			−0.702246			−0.351123	+	0.936329i	$0.614200\pi$
$608$	−14.0789	−	5.82330i	−0.570977	−	0.236166i
$609$	−84.2193			−3.41274
$610$		0			0
$611$	−16.2457	+	28.1384i	−0.657231	+	1.13836i
$612$	−0.0179852	−	0.0311513i	−0.000727008	−	0.00125922i
$613$	1.85860	−	3.21918i	0.0750680	−	0.130022i	−0.826048	−	0.563600i	$-0.809416\pi$
$613$	1.85860	−	3.21918i	0.0750680	−	0.130022i	0.901116	+	0.433578i	$0.142749\pi$
$614$	0.512459	+	0.887606i	0.0206812	+	0.0358208i
$615$		0			0
$616$	−1.74240			−0.0702031
$617$	−9.04453	−	15.6656i	−0.364119	−	0.630673i	0.624515	−	0.781013i	$-0.285297\pi$
$617$	−9.04453	−	15.6656i	−0.364119	−	0.630673i	−0.988634	+	0.150340i	$0.951963\pi$
$618$	−3.07776	−	5.33083i	−0.123806	−	0.214438i
$619$	−40.6682			−1.63459			−0.817297	−	0.576216i	$-0.804529\pi$
$619$	−40.6682			−1.63459			−0.817297	+	0.576216i	$0.804529\pi$
$620$		0			0
$621$	5.84844	+	10.1298i	0.234690	+	0.406495i
$622$	4.73277	−	8.19739i	0.189767	−	0.328686i
$623$	−8.27902	−	14.3397i	−0.331692	−	0.574507i
$624$	9.68011	−	16.7664i	0.387515	−	0.671195i
$625$		0			0
$626$	2.72342			0.108850
$627$	−0.463346	−	3.50567i	−0.0185042	−	0.140003i
$628$	28.5708			1.14010
$629$	−0.000276918	0	0.000479637i	−1.10415e−5	0	1.91244e-5i
$630$		0			0
$631$	−8.14602	−	14.1093i	−0.324288	−	0.561683i	0.657080	−	0.753821i	$-0.271791\pi$
$631$	−8.14602	−	14.1093i	−0.324288	−	0.561683i	−0.981368	+	0.192138i	$0.938458\pi$
$632$	−8.14318	+	14.1044i	−0.323918	+	0.561043i
$633$	24.1441	+	41.8187i	0.959640	+	1.66215i
$634$	−2.60515			−0.103464
$635$		0			0
$636$	−23.4297	−	40.5814i	−0.929048	−	1.60916i
$637$	11.0146	+	19.0779i	0.436415	+	0.755893i
$638$	−1.06331			−0.0420970
$639$	31.3159			1.23884
$640$		0			0
$641$	−5.03530	+	8.72139i	−0.198882	+	0.344474i	−0.948166	−	0.317775i	$-0.897064\pi$
$641$	−5.03530	+	8.72139i	−0.198882	+	0.344474i	0.749284	+	0.662249i	$0.230398\pi$
$642$	0.455842	+	0.789542i	0.0179907	+	0.0311607i
$643$	−2.14765	+	3.71984i	−0.0846950	+	0.146696i	−0.905261	−	0.424855i	$-0.860325\pi$
$643$	−2.14765	+	3.71984i	−0.0846950	+	0.146696i	0.820566	+	0.571552i	$0.193658\pi$
$644$	−20.4273	+	35.3812i	−0.804950	+	1.39421i
$645$		0			0
$646$	0.0116312	+	0.00481088i	0.000457625	+	0.000189282i
$647$	11.5451			0.453884			0.226942	−	0.973908i	$-0.427127\pi$
$647$	11.5451			0.453884			0.226942	+	0.973908i	$0.427127\pi$
$648$	6.65597	−	11.5285i	0.261471	−	0.452881i
$649$	0.961376	−	1.66515i	0.0377373	−	0.0653629i
$650$		0			0
$651$	16.3342	−	28.2917i	0.640188	−	1.10884i
$652$	−11.3140	−	19.5965i	−0.443092	−	0.767457i
$653$	−46.8302			−1.83261			−0.916304	−	0.400483i	$-0.868842\pi$
$653$	−46.8302			−1.83261			−0.916304	+	0.400483i	$0.868842\pi$
$654$	4.25662			0.166447
$655$		0			0
$656$	−6.37404	−	11.0402i	−0.248864	−	0.431046i
$657$	−19.6766			−0.767656
$658$	−15.9461			−0.621644
$659$	−22.0463	−	38.1854i	−0.858803	−	1.48749i	−0.873071	−	0.487593i	$-0.837875\pi$
$659$	−22.0463	−	38.1854i	−0.858803	−	1.48749i	0.0142676	−	0.999898i	$-0.495458\pi$
$660$		0			0
$661$	22.0688	+	38.2243i	0.858378	+	1.48675i	0.873475	+	0.486869i	$0.161861\pi$
$661$	22.0688	+	38.2243i	0.858378	+	1.48675i	−0.0150971	+	0.999886i	$0.504806\pi$
$662$	−2.77719	+	4.81024i	−0.107939	+	0.186955i
$663$	−0.0262053	+	0.0453890i	−0.00101773	+	0.00176276i
$664$	18.8716			0.732360
$665$		0			0
$666$	0.0377997			0.00146471
$667$	−25.5659	+	44.2815i	−0.989916	+	1.71458i
$668$	6.88350	−	11.9226i	0.266331	−	0.461298i
$669$	−6.21552	−	10.7656i	−0.240306	−	0.416222i
$670$		0			0
$671$	1.60820	+	2.78549i	0.0620839	+	0.107532i
$672$	31.1351			1.20106
$673$	−26.1730			−1.00889			−0.504447	−	0.863443i	$-0.668304\pi$
$673$	−26.1730			−1.00889			−0.504447	+	0.863443i	$0.668304\pi$
$674$	−1.57023	−	2.71972i	−0.0604831	−	0.104760i
$675$		0			0
$676$	12.6925			0.488175
$677$	19.7693			0.759796			0.379898	−	0.925028i	$-0.375959\pi$
$677$	19.7693			0.759796			0.379898	+	0.925028i	$0.375959\pi$
$678$	3.92310	+	6.79500i	0.150666	+	0.260960i
$679$	7.42627	−	12.8627i	0.284994	−	0.493624i
$680$		0			0
$681$	18.2227	−	31.5626i	0.698294	−	1.20948i
$682$	0.206228	−	0.357197i	0.00789688	−	0.0136778i
$683$	38.8945			1.48826			0.744128	−	0.668037i	$-0.232865\pi$
$683$	38.8945			1.48826			0.744128	+	0.668037i	$0.232865\pi$
$684$	2.21342	+	16.7467i	0.0846321	+	0.640327i
$685$		0			0
$686$	−1.08369	+	1.87701i	−0.0413755	+	0.0716645i
$687$	−11.8307	+	20.4914i	−0.451369	+	0.781795i
$688$	−7.22317	−	12.5109i	−0.275381	−	0.476973i
$689$	−13.8027	+	23.9069i	−0.525840	+	0.910781i
$690$		0			0
$691$	22.6319			0.860959			0.430479	−	0.902600i	$-0.358345\pi$
$691$	22.6319			0.860959			0.430479	+	0.902600i	$0.358345\pi$
$692$	6.55576			0.249213
$693$	1.46087	+	2.53029i	0.0554937	+	0.0961179i
$694$	−0.420445	−	0.728233i	−0.0159599	−	0.0276433i
$695$		0			0
$696$	25.7652			0.976627
$697$	0.0172554	+	0.0298872i	0.000653593	+	0.00113206i
$698$	−1.74511	+	3.02263i	−0.0660535	+	0.114408i
$699$	18.1535	+	31.4427i	0.686627	+	1.18927i
$700$		0			0
$701$	10.9167	−	18.9083i	0.412319	−	0.714158i	−0.582824	−	0.812599i	$-0.698052\pi$
$701$	10.9167	−	18.9083i	0.412319	−	0.714158i	0.995143	+	0.0984408i	$0.0313855\pi$
$702$	−1.69306			−0.0639006
$703$	0.206264	−	0.158439i	0.00777941	−	0.00597564i
$704$	−2.08578			−0.0786107
$705$		0			0
$706$	−1.45763	+	2.52469i	−0.0548586	+	0.0950179i
$707$	−34.2133	−	59.2591i	−1.28672	−	2.22867i
$708$	−11.3588	+	19.6739i	−0.426888	+	0.739392i
$709$	0.325939	+	0.564543i	0.0122409	+	0.0212019i	0.872081	−	0.489362i	$-0.162770\pi$
$709$	0.325939	+	0.564543i	0.0122409	+	0.0212019i	−0.859840	+	0.510563i	$0.829437\pi$
$710$		0			0
$711$	27.3098			1.02420
$712$	2.53280	+	4.38694i	0.0949206	+	0.164407i
$713$	−9.91694	−	17.1766i	−0.371392	−	0.643270i
$714$	−0.0257221			−0.000962625
$715$		0			0
$716$	−5.59399	−	9.68907i	−0.209057	−	0.362098i
$717$	10.8020	−	18.7097i	0.403410	−	0.698726i
$718$	−3.34264	−	5.78963i	−0.124746	−	0.216067i
$719$	2.31346	−	4.00704i	0.0862777	−	0.149437i	−0.819657	−	0.572854i	$-0.805836\pi$
$719$	2.31346	−	4.00704i	0.0862777	−	0.149437i	0.905935	+	0.423417i	$0.139169\pi$
$720$		0			0
$721$	34.9955			1.30330
$722$	−4.18399	−	4.17549i	−0.155712	−	0.155396i
$723$	−44.2097			−1.64418
$724$	1.05125	−	1.82082i	0.0390694	−	0.0676702i
$725$		0			0
$726$	−3.79434	−	6.57199i	−0.140821	−	0.243909i
$727$	7.91445	−	13.7082i	0.293531	−	0.508410i	−0.681111	−	0.732180i	$-0.738503\pi$
$727$	7.91445	−	13.7082i	0.293531	−	0.508410i	0.974642	+	0.223770i	$0.0718363\pi$
$728$	−6.06387	−	10.5029i	−0.224742	−	0.389265i
$729$	−7.76076			−0.287435
$730$		0			0
$731$	0.0195541	+	0.0338686i	0.000723233	+	0.00125268i
$732$	−19.0011	−	32.9108i	−0.702299	−	1.21642i
$733$	28.8257			1.06470			0.532350	−	0.846524i	$-0.321309\pi$
$733$	28.8257			1.06470			0.532350	+	0.846524i	$0.321309\pi$
$734$	9.36851			0.345798
$735$		0			0
$736$	9.45149	−	16.3705i	0.348386	−	0.603423i
$737$	−0.840470	−	1.45574i	−0.0309591	−	0.0536228i
$738$	1.17769	−	2.03981i	0.0433513	−	0.0750866i
$739$	−13.8458	+	23.9817i	−0.509327	+	0.882180i	0.490614	+	0.871377i	$0.336772\pi$
$739$	−13.8458	+	23.9817i	−0.509327	+	0.882180i	−0.999942	+	0.0108038i	$0.996561\pi$
$740$		0			0
$741$	19.5192	−	14.9934i	0.717056	−	0.550797i
$742$	−13.5481			−0.497367
$743$	22.4228	−	38.8374i	0.822611	−	1.42480i	−0.0811199	−	0.996704i	$-0.525850\pi$
$743$	22.4228	−	38.8374i	0.822611	−	1.42480i	0.903731	−	0.428100i	$-0.140817\pi$
$744$	−4.99712	+	8.65527i	−0.183203	+	0.317318i
$745$		0			0
$746$	−4.15649	+	7.19925i	−0.152180	+	0.263583i
$747$	−15.8224	−	27.4052i	−0.578911	−	1.00270i
$748$	0.00638588			0.000233491
$749$	−5.18313			−0.189387
$750$		0			0
$751$	12.3257	+	21.3488i	0.449772	+	0.779029i	0.998371	−	0.0570573i	$-0.0181718\pi$
$751$	12.3257	+	21.3488i	0.449772	+	0.779029i	−0.548599	+	0.836086i	$0.684838\pi$
$752$	−44.2746			−1.61453
$753$	20.6570			0.752782
$754$	−3.70053	−	6.40951i	−0.134765	−	0.233421i
$755$		0			0
$756$	8.16949	+	14.1500i	0.297122	+	0.514630i
$757$	−23.1313	+	40.0646i	−0.840721	+	1.45617i	0.0485649	+	0.998820i	$0.484535\pi$
$757$	−23.1313	+	40.0646i	−0.840721	+	1.45617i	−0.889286	+	0.457352i	$0.848798\pi$
$758$	3.57356	−	6.18960i	0.129798	−	0.224816i
$759$	4.38732			0.159250
$760$		0			0
$761$	−18.7036			−0.678004			−0.339002	−	0.940786i	$-0.610089\pi$
$761$	−18.7036			−0.678004			−0.339002	+	0.940786i	$0.610089\pi$
$762$	−4.13795	+	7.16715i	−0.149902	+	0.259638i
$763$	−12.0999	+	20.9577i	−0.438046	+	0.758719i
$764$	20.2136	+	35.0109i	0.731301	+	1.26665i
$765$		0			0
$766$	−4.52482	−	7.83721i	−0.163488	−	0.283170i
$767$	13.3831			0.483235
$768$	19.7630			0.713135
$769$	5.45393	+	9.44648i	0.196674	+	0.340649i	0.947448	−	0.319910i	$-0.103653\pi$
$769$	5.45393	+	9.44648i	0.196674	+	0.340649i	−0.750774	+	0.660559i	$0.770319\pi$
$770$		0			0
$771$	−1.02842			−0.0370376
$772$	−18.1576			−0.653508
$773$	−3.94152	−	6.82692i	−0.141767	−	0.245547i	0.786395	−	0.617724i	$-0.211945\pi$
$773$	−3.94152	−	6.82692i	−0.141767	−	0.245547i	−0.928162	+	0.372176i	$0.878612\pi$
$774$	1.33458	−	2.31155i	0.0479703	−	0.0830871i
$775$		0			0
$776$	−2.27192	+	3.93508i	−0.0815571	+	0.141261i
$777$	−0.265757	+	0.460304i	−0.00953397	+	0.0165133i
$778$	−1.13170			−0.0405733
$779$	−2.12360	−	16.0672i	−0.0760858	−	0.575665i
$780$		0			0
$781$	−2.77978	+	4.81472i	−0.0994684	+	0.172284i
$782$	−0.00780829	+	0.0135244i	−0.000279224	+	0.000483630i
$783$	10.2246	+	17.7094i	0.365396	+	0.632884i
$784$	−15.0091	+	25.9966i	−0.536040	+	0.928449i
$785$		0			0
$786$	1.67978			0.0599156
$787$	35.5229			1.26625			0.633127	−	0.774048i	$-0.281771\pi$
$787$	35.5229			1.26625			0.633127	+	0.774048i	$0.281771\pi$
$788$	1.95954	+	3.39402i	0.0698056	+	0.120907i
$789$	−13.1906	−	22.8467i	−0.469596	−	0.813365i
$790$		0			0
$791$	−44.6074			−1.58605
$792$	−0.446923	−	0.774092i	−0.0158807	−	0.0275062i
$793$	−11.1937	+	19.3881i	−0.397500	+	0.688490i
$794$	2.16751	+	3.75424i	0.0769221	+	0.133233i
$795$		0			0
$796$	−18.9383	+	32.8021i	−0.671250	+	1.16264i
$797$	−26.0958			−0.924359			−0.462180	−	0.886786i	$-0.652932\pi$
$797$	−26.0958			−0.924359			−0.462180	+	0.886786i	$0.652932\pi$
$798$	11.1624	+	4.61697i	0.395145	+	0.163439i
$799$	0.119857			0.00424024
$800$		0			0
$801$	4.24712	−	7.35622i	0.150064	−	0.259919i
$802$	4.12998	+	7.15333i	0.145835	+	0.252593i
$803$	1.74661	−	3.02521i	0.0616364	−	0.106757i
$804$	9.93024	+	17.1997i	0.350213	+	0.606586i
$805$		0			0
$806$	2.87085			0.101121
$807$	−5.34774	−	9.26256i	−0.188249	−	0.326058i
$808$	10.4669	+	18.1291i	0.368223	+	0.637781i
$809$	9.65732			0.339533			0.169767	−	0.985484i	$-0.445699\pi$
$809$	9.65732			0.339533			0.169767	+	0.985484i	$0.445699\pi$
$810$		0			0
$811$	−3.70765	−	6.42183i	−0.130193	−	0.225501i	0.793558	−	0.608495i	$-0.208226\pi$
$811$	−3.70765	−	6.42183i	−0.130193	−	0.225501i	−0.923751	+	0.382994i	$0.874893\pi$
$812$	−35.7121	+	61.8553i	−1.25325	+	2.17069i
$813$	17.4061	+	30.1483i	0.610459	+	1.05735i
$814$	−0.00335532	+	0.00581158i	−0.000117604	+	0.000203696i
$815$		0			0
$816$	−0.0714177			−0.00250012
$817$	−2.40650	−	18.2076i	−0.0841927	−	0.637002i
$818$	−4.66538			−0.163121
$819$	−10.1682	+	17.6118i	−0.355305	+	0.615407i
$820$		0			0
$821$	−13.4155	−	23.2363i	−0.468203	−	0.810951i	0.531137	−	0.847286i	$-0.321765\pi$
$821$	−13.4155	−	23.2363i	−0.468203	−	0.810951i	−0.999340	+	0.0363349i	$0.988432\pi$
$822$	−1.75149	+	3.03366i	−0.0610901	+	0.105811i
$823$	18.3038	+	31.7031i	0.638031	+	1.10510i	0.985864	+	0.167546i	$0.0535841\pi$
$823$	18.3038	+	31.7031i	0.638031	+	1.10510i	−0.347833	+	0.937556i	$0.613083\pi$
$824$	−10.7062			−0.372967
$825$		0			0
$826$	3.28407	+	5.68818i	0.114268	+	0.197917i
$827$	10.2533	+	17.7593i	0.356544	+	0.617552i	0.987381	−	0.158363i	$-0.0506217\pi$
$827$	10.2533	+	17.7593i	0.356544	+	0.617552i	−0.630837	+	0.775915i	$0.717288\pi$
$828$	−20.9584			−0.728353
$829$	−19.9749			−0.693758			−0.346879	−	0.937910i	$-0.612759\pi$
$829$	−19.9749			−0.693758			−0.346879	+	0.937910i	$0.612759\pi$
$830$		0			0
$831$	5.50577	−	9.53628i	0.190993	−	0.330810i
$832$	−7.25890	−	12.5728i	−0.251657	−	0.435883i
$833$	0.0406317	−	0.0703761i	0.00140780	−	0.00243839i
$834$	4.07907	−	7.06515i	0.141247	−	0.244646i
$835$		0			0
$836$	−2.77124	−	1.14623i	−0.0958452	−	0.0396432i
$837$	−7.93215			−0.274175
$838$	4.73706	−	8.20482i	0.163639	−	0.283431i
$839$	−9.96670	+	17.2628i	−0.344089	+	0.595979i	−0.985188	−	0.171479i	$-0.945145\pi$
$839$	−9.96670	+	17.2628i	−0.344089	+	0.595979i	0.641099	+	0.767458i	$0.278479\pi$
$840$		0			0
$841$	−30.1956	+	52.3004i	−1.04123	+	1.80346i
$842$	−0.138404	−	0.239723i	−0.00476973	−	0.00826141i
$843$	30.7120			1.05778
$844$	40.9520			1.40962
$845$		0			0
$846$	−4.09016	−	7.08437i	−0.140623	−	0.243566i
$847$	43.1433			1.48242
$848$	−37.6165			−1.29176
$849$	18.9269	+	32.7823i	0.649569	+	1.12509i
$850$		0			0
$851$	0.161348	+	0.279463i	0.00553094	+	0.00957987i
$852$	32.8434	−	56.8864i	1.12520	−	1.94890i
$853$	0.802795	−	1.39048i	0.0274872	−	0.0476092i	−0.851955	−	0.523616i	$-0.824583\pi$
$853$	0.802795	−	1.39048i	0.0274872	−	0.0476092i	0.879442	+	0.476006i	$0.157916\pi$
$854$	−10.9873			−0.375977
$855$		0			0
$856$	1.58567			0.0541972
$857$	−8.79122	+	15.2268i	−0.300302	+	0.520139i	−0.976204	−	0.216853i	$-0.930421\pi$
$857$	−8.79122	+	15.2268i	−0.300302	+	0.520139i	0.675902	+	0.736991i	$0.263754\pi$
$858$	−0.317521	+	0.549962i	−0.0108400	+	0.0187754i
$859$	−6.97697	−	12.0845i	−0.238051	−	0.412317i	0.722104	−	0.691785i	$-0.243175\pi$
$859$	−6.97697	−	12.0845i	−0.238051	−	0.412317i	−0.960155	+	0.279468i	$0.909842\pi$
$860$		0			0
$861$	16.5599	+	28.6825i	0.564358	+	0.977498i
$862$	−4.58411			−0.156135
$863$	−19.9200			−0.678085			−0.339042	−	0.940771i	$-0.610103\pi$
$863$	−19.9200			−0.678085			−0.339042	+	0.940771i	$0.610103\pi$
$864$	−3.77992	−	6.54702i	−0.128596	−	0.222734i
$865$		0			0
$866$	0.461958			0.0156980
$867$	−38.1504			−1.29566
$868$	−13.8526	−	23.9935i	−0.470189	−	0.814392i
$869$	−2.42417	+	4.19879i	−0.0822345	+	0.142434i
$870$		0			0
$871$	5.85000	−	10.1325i	0.198220	−	0.343326i
$872$	3.70173	−	6.41158i	0.125356	−	0.217123i
$873$	7.61932			0.257875
$874$	5.81605	−	4.46752i	0.196731	−	0.151116i
$875$		0			0
$876$	−20.6363	+	35.7432i	−0.697237	+	1.20765i
$877$	5.07142	−	8.78395i	0.171250	−	0.296613i	−0.767607	−	0.640920i	$-0.778553\pi$
$877$	5.07142	−	8.78395i	0.171250	−	0.296613i	0.938857	+	0.344307i	$0.111886\pi$
$878$	−2.28599	−	3.95944i	−0.0771483	−	0.133625i
$879$	29.0386	−	50.2964i	0.979449	−	1.69646i
$880$		0			0
$881$	21.4114			0.721370			0.360685	−	0.932688i	$-0.382543\pi$
$881$	21.4114			0.721370			0.360685	+	0.932688i	$0.382543\pi$
$882$	−5.54627			−0.186753
$883$	11.1287	+	19.2755i	0.374512	+	0.648673i	0.990254	−	0.139275i	$-0.0444771\pi$
$883$	11.1287	+	19.2755i	0.374512	+	0.648673i	−0.615742	+	0.787948i	$0.711144\pi$
$884$	0.0222241	+	0.0384933i	0.000747477	+	0.00129467i
$885$		0			0
$886$	5.80240			0.194935
$887$	15.1467	+	26.2349i	0.508577	+	0.880881i	0.999951	+	0.00993225i	$0.00316158\pi$
$887$	15.1467	+	26.2349i	0.508577	+	0.880881i	−0.491374	+	0.870949i	$0.663505\pi$
$888$	0.0813029	−	0.140821i	0.00272835	−	0.00472564i
$889$	−23.5252	−	40.7468i	−0.789010	−	1.36660i
$890$		0			0
$891$	1.98144	−	3.43195i	0.0663807	−	0.114975i
$892$	−10.5425			−0.352988
$893$	−52.0135	−	21.5137i	−1.74057	−	0.719929i
$894$	4.37102			0.146189
$895$		0			0
$896$	17.4364	−	30.2007i	0.582509	−	1.00894i
$897$	15.2687	+	26.4462i	0.509807	+	0.883012i
$898$	0.804782	−	1.39392i	0.0268559	−	0.0465158i
$899$	−17.3373	−	30.0291i	−0.578232	−	1.00153i
$900$		0			0
$901$	0.101833			0.00339255
$902$	0.209077	+	0.362132i	0.00696150	+	0.0120577i
$903$	18.7659	+	32.5035i	0.624490	+	1.08165i
$904$	13.6467			0.453883
$905$		0			0
$906$	−5.35625	−	9.27729i	−0.177949	−	0.308217i
$907$	19.8755	−	34.4254i	0.659956	−	1.14308i	−0.320670	−	0.947191i	$-0.603908\pi$
$907$	19.8755	−	34.4254i	0.659956	−	1.14308i	0.980626	−	0.195887i	$-0.0627586\pi$
$908$	−15.4542	−	26.7674i	−0.512865	−	0.888308i
$909$	17.5513	−	30.3998i	0.582141	−	1.00830i
$910$		0			0
$911$	25.5927			0.847924			0.423962	−	0.905680i	$-0.360639\pi$
$911$	25.5927			0.847924			0.423962	+	0.905680i	$0.360639\pi$
$912$	30.9926	+	12.8191i	1.02627	+	0.424482i
$913$	5.61795			0.185927
$914$	3.14715	−	5.45103i	0.104099	−	0.180304i
$915$		0			0
$916$	10.0333	+	17.3782i	0.331510	+	0.574193i
$917$	−4.77495	+	8.27046i	−0.157683	+	0.273115i
$918$	0.00312276	+	0.00540878i	0.000103067	+	0.000178516i
$919$	37.3594			1.23237			0.616186	−	0.787601i	$-0.288677\pi$
$919$	37.3594			1.23237			0.616186	+	0.787601i	$0.288677\pi$
$920$		0			0
$921$	−3.69659	−	6.40268i	−0.121807	−	0.210975i
$922$	4.69811	+	8.13736i	0.154724	+	0.267990i
$923$	−38.6967			−1.27372
$924$	6.12849			0.201613
$925$		0			0
$926$	3.17423	−	5.49792i	0.104312	−	0.180673i
$927$	8.97630	+	15.5474i	0.294820	+	0.510644i
$928$	16.5236	−	28.6197i	0.542413	−	0.939487i
$929$	−1.05742	+	1.83151i	−0.0346929	+	0.0600898i	−0.882851	−	0.469654i	$-0.844379\pi$
$929$	−1.05742	+	1.83151i	−0.0346929	+	0.0600898i	0.848158	+	0.529744i	$0.177712\pi$
$930$		0			0
$931$	−30.2648	+	23.2474i	−0.991887	+	0.761904i
$932$	30.7910			1.00859
$933$	−34.1395	+	59.1313i	−1.11768	+	1.93587i
$934$	−2.47553	+	4.28774i	−0.0810017	+	0.140299i
$935$		0			0
$936$	3.11075	−	5.38798i	0.101678	−	0.176112i
$937$	22.3198	+	38.6590i	0.729156	+	1.26294i	0.957240	+	0.289294i	$0.0934207\pi$
$937$	22.3198	+	38.6590i	0.729156	+	1.26294i	−0.228084	+	0.973642i	$0.573246\pi$
$938$	5.74212			0.187487
$939$	−19.6452			−0.641096
$940$		0			0
$941$	−8.90021	−	15.4156i	−0.290139	−	0.502535i	0.683704	−	0.729760i	$-0.260368\pi$
$941$	−8.90021	−	15.4156i	−0.290139	−	0.502535i	−0.973842	+	0.227225i	$0.927035\pi$
$942$	10.4809			0.341487
$943$	20.1079			0.654803
$944$	9.11827	+	15.7933i	0.296774	+	0.514028i
$945$		0			0
$946$	0.236930	+	0.410374i	0.00770324	+	0.0133424i
$947$	29.4788	−	51.0587i	0.957932	−	1.65919i	0.230419	−	0.973091i	$-0.425990\pi$
$947$	29.4788	−	51.0587i	0.957932	−	1.65919i	0.727512	−	0.686095i	$-0.240676\pi$
$948$	28.6419	−	49.6091i	0.930244	−	1.61123i
$949$	24.3141			0.789269
$950$		0			0
$951$	18.7921			0.609375
$952$	−0.0223689	+	0.0387442i	−0.000724982	+	0.00125571i
$953$	19.3641	−	33.5396i	0.627265	−	1.08645i	−0.360833	−	0.932630i	$-0.617508\pi$
$953$	19.3641	−	33.5396i	0.627265	−	1.08645i	0.988098	−	0.153824i	$-0.0491590\pi$
$954$	−3.47508	−	6.01901i	−0.112510	−	0.194873i
$955$		0			0
$956$	−9.16095	−	15.8672i	−0.296286	−	0.513183i
$957$	7.67013			0.247940
$958$	11.6219			0.375485
$959$	−9.95760	−	17.2471i	−0.321548	−	0.556937i
$960$		0			0
$961$	−17.5498			−0.566123
$962$	−0.0467086			−0.00150595
$963$	−1.32947	−	2.30270i	−0.0428415	−	0.0742036i
$964$	−18.7466	+	32.4700i	−0.603787	+	1.04579i
$965$		0			0
$966$	−7.49357	+	12.9792i	−0.241102	+	0.417600i
$967$	−3.39611	+	5.88224i	−0.109212	+	0.189160i	−0.915451	−	0.402429i	$-0.868166\pi$
$967$	−3.39611	+	5.88224i	−0.109212	+	0.189160i	0.806239	+	0.591589i	$0.201499\pi$
$968$	−13.1988			−0.424227
$969$	−0.0839011	−	0.0347030i	−0.00269529	−	0.00111482i
$970$		0			0
$971$	20.1819	−	34.9560i	0.647667	−	1.12179i	−0.336011	−	0.941858i	$-0.609078\pi$
$971$	20.1819	−	34.9560i	0.647667	−	1.12179i	0.983679	−	0.179935i	$-0.0575887\pi$
$972$	−17.2363	+	29.8542i	−0.552856	+	0.957574i
$973$	23.1904	+	40.1670i	0.743451	+	1.28769i
$974$	−6.06769	+	10.5095i	−0.194421	+	0.336747i
$975$		0			0
$976$	−30.5063			−0.976483
$977$	29.7383			0.951412			0.475706	−	0.879604i	$-0.342193\pi$
$977$	29.7383			0.951412			0.475706	+	0.879604i	$0.342193\pi$
$978$	−4.15044	−	7.18877i	−0.132716	−	0.229871i
$979$	0.753998	+	1.30596i	0.0240979	+	0.0417388i
$980$		0			0
$981$	−12.4145			−0.396363
$982$	−3.19424	−	5.53258i	−0.101932	−	0.176552i
$983$	1.76233	−	3.05245i	0.0562097	−	0.0973580i	−0.836551	−	0.547888i	$-0.815432\pi$
$983$	1.76233	−	3.05245i	0.0562097	−	0.0973580i	0.892761	+	0.450530i	$0.148765\pi$
$984$	−5.06615	−	8.77484i	−0.161503	−	0.279732i
$985$		0			0
$986$	−0.0136509	+	0.0236440i	−0.000434732	+	0.000752977i
$987$	115.026			3.66132
$988$	−2.73510	−	20.6937i	−0.0870150	−	0.658356i
$989$	22.7866			0.724571
$990$		0			0
$991$	8.39292	−	14.5370i	0.266610	−	0.461782i	−0.701374	−	0.712793i	$-0.747430\pi$
$991$	8.39292	−	14.5370i	0.266610	−	0.461782i	0.967984	+	0.251011i	$0.0807631\pi$
$992$	6.40945	+	11.1015i	0.203500	+	0.352473i
$993$	20.0331	−	34.6983i	0.635731	−	1.10112i
$994$	−9.49577	−	16.4472i	−0.301188	−	0.521672i
$995$		0			0
$996$	−66.3767			−2.10322
$997$	−8.62648	−	14.9415i	−0.273203	−	0.473202i	0.696477	−	0.717579i	$-0.254750\pi$
$997$	−8.62648	−	14.9415i	−0.273203	−	0.473202i	−0.969680	+	0.244377i	$0.921416\pi$
$998$	0.114639	+	0.198560i	0.00362883	+	0.00628532i
$999$	0.129056			0.00408314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.h.201.3	yes	12
5.2	odd	4		475.2.j.d.49.8		24
5.3	odd	4		475.2.j.d.49.5		24
5.4	even	2		475.2.e.f.201.4	yes	12
19.7	even	3	inner	475.2.e.h.26.3	yes	12
19.8	odd	6		9025.2.a.by.1.3		6
19.11	even	3		9025.2.a.br.1.4		6
95.7	odd	12		475.2.j.d.349.5		24
95.49	even	6		9025.2.a.bz.1.3		6
95.64	even	6		475.2.e.f.26.4	✓	12
95.83	odd	12		475.2.j.d.349.8		24
95.84	odd	6		9025.2.a.bs.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.4	✓	12	95.64	even	6
475.2.e.f.201.4	yes	12	5.4	even	2
475.2.e.h.26.3	yes	12	19.7	even	3	inner
475.2.e.h.201.3	yes	12	1.1	even	1	trivial
475.2.j.d.49.5		24	5.3	odd	4
475.2.j.d.49.8		24	5.2	odd	4
475.2.j.d.349.5		24	95.7	odd	12
475.2.j.d.349.8		24	95.83	odd	12
9025.2.a.br.1.4		6	19.11	even	3
9025.2.a.bs.1.4		6	95.84	odd	6
9025.2.a.by.1.3		6	19.8	odd	6
9025.2.a.bz.1.3		6	95.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.155554 - 0.269427i) q^{2} +(-1.12208 + 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} -3.96928 q^{7} +1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +0.361495 q^{11} -4.27110 q^{12} +(1.25807 + 2.17905i) q^{13} +(-0.617436 + 1.06943i) q^{14} +(-1.71432 + 2.96929i) q^{16} +(0.00464089 - 0.00803826i) q^{17} -0.633487 q^{18} +(-3.45680 + 2.65529i) q^{19} +(4.45383 - 7.71427i) q^{21} +(0.0562320 - 0.0973967i) q^{22} +(-2.70404 - 4.68354i) q^{23} +(-1.36256 + 2.36002i) q^{24} +0.782793 q^{26} -2.16285 q^{27} +(-3.77719 - 6.54228i) q^{28} +(-4.72735 - 8.18801i) q^{29} +3.66745 q^{31} +(1.74766 + 3.02703i) q^{32} +(-0.405626 + 0.702564i) q^{33} +(-0.00144382 - 0.00250076i) q^{34} +(1.93769 - 3.35617i) q^{36} -0.0596692 q^{37} +(0.177689 + 1.34440i) q^{38} -5.64662 q^{39} +(-1.85906 + 3.21998i) q^{41} +(-1.38562 - 2.39997i) q^{42} +(-2.10671 + 3.64894i) q^{43} +(0.344001 + 0.595827i) q^{44} -1.68250 q^{46} +(6.45659 + 11.1831i) q^{47} +(-3.84720 - 6.66354i) q^{48} +8.75515 q^{49} +(0.0104149 + 0.0180391i) q^{51} +(-2.39438 + 4.14719i) q^{52} +(5.48564 + 9.50140i) q^{53} +(-0.336440 + 0.582731i) q^{54} -4.81997 q^{56} +(-1.28175 - 9.69770i) q^{57} -2.94143 q^{58} +(2.65944 - 4.60629i) q^{59} +(4.44875 + 7.70546i) q^{61} +(0.570486 - 0.988111i) q^{62} +(4.04118 + 6.99952i) q^{63} -5.76986 q^{64} +(0.126193 + 0.218573i) q^{66} +(-2.32498 - 4.02699i) q^{67} +0.0176652 q^{68} +12.1366 q^{69} +(-7.68968 + 13.3189i) q^{71} +(-1.23632 - 2.14136i) q^{72} +(4.83162 - 8.36861i) q^{73} +(-0.00928178 + 0.0160765i) q^{74} +(-7.66603 - 3.17081i) q^{76} -1.43487 q^{77} +(-0.878354 + 1.52135i) q^{78} +(-6.70596 + 11.6151i) q^{79} +(5.48123 - 9.49377i) q^{81} +(0.578367 + 1.00176i) q^{82} +15.5409 q^{83} +16.9532 q^{84} +(0.655415 + 1.13521i) q^{86} +21.2178 q^{87} +0.438971 q^{88} +(2.08578 + 3.61267i) q^{89} +(-4.99364 - 8.64923i) q^{91} +(5.14637 - 8.91377i) q^{92} +(-4.11516 + 7.12767i) q^{93} +4.01739 q^{94} -7.84403 q^{96} +(-1.87094 + 3.24056i) q^{97} +(1.36190 - 2.35888i) q^{98} +(-0.368044 - 0.637470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{6} - 4 q^{7} - 12 q^{8} - 7 q^{9} - 2 q^{11} - 14 q^{12} + 5 q^{13} + 6 q^{14} + 6 q^{16} - 3 q^{17} - 14 q^{18} - 6 q^{19} - 3 q^{21} + 9 q^{22} - 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 + q^6 - 4 * q^7 - 12 * q^8 - 7 * q^9 - 2 * q^11 - 14 * q^12 + 5 * q^13 + 6 * q^14 + 6 * q^16 - 3 * q^17 - 14 * q^18 - 6 * q^19 - 3 * q^21 + 9 * q^22 - 6 * q^23 - 11 * q^24 + 38 * q^26 - 36 * q^27 - 4 * q^28 - 3 * q^29 - 6 * q^31 - 6 * q^32 - 18 * q^33 + q^34 - 13 * q^36 + 12 * q^37 + 18 * q^38 + 16 * q^39 - 11 * q^41 - 11 * q^42 + 13 * q^43 - 21 * q^44 - 24 * q^46 - 6 * q^47 - 19 * q^48 + 8 * q^49 + 17 * q^51 - q^52 + 18 * q^53 - 18 * q^54 + 8 * q^56 + 20 * q^57 - 10 * q^58 - 4 * q^59 - 25 * q^61 - 21 * q^62 + 43 * q^63 - 44 * q^64 - 34 * q^66 + 6 * q^67 + 2 * q^68 + 26 * q^69 - 18 * q^71 + 13 * q^72 + q^73 + 6 * q^74 + 24 * q^76 + 22 * q^77 + 72 * q^78 - 3 * q^79 - 2 * q^81 + 31 * q^82 + 46 * q^83 + 74 * q^84 - 9 * q^86 - 22 * q^87 - 22 * q^88 - 12 * q^89 + 11 * q^91 + 28 * q^92 - 13 * q^93 + 16 * q^94 - 26 * q^96 + 3 * q^97 - 22 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more