LMFDB - Embedded newform 475.2.j.c.49.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(49,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.1387535264013605949997056.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 $ x^16 - 11x^14 + 82x^12 - 337x^10 + 1006x^8 - 1596x^6 + 1765x^4 - 414*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Root			$-1.19454 + 0.689667i$ of defining polynomial
Character	$\chi$	$=$	475.49
Dual form			475.2.j.c.349.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.950409 + 0.548719i) q^{2} +(0.328513 + 0.189667i) q^{3} +(-0.397815 - 0.689035i) q^{4} +(0.208148 + 0.360522i) q^{6} -1.89307i q^{7} -3.06803i q^{8} +(-1.42805 - 2.47346i) q^{9} +0.134400 q^{11} -0.301809i q^{12} +(3.04298 - 1.75687i) q^{13} +(1.03876 - 1.79919i) q^{14} +(0.887858 - 1.53781i) q^{16} +(-1.43867 - 0.830615i) q^{17} -3.13440i q^{18} +(-2.10596 + 3.81640i) q^{19} +(0.359052 - 0.621897i) q^{21} +(0.127735 + 0.0737478i) q^{22} +(4.65042 - 2.68492i) q^{23} +(0.581904 - 1.00789i) q^{24} +3.85611 q^{26} -2.22142i q^{27} +(-1.30439 + 0.753090i) q^{28} +(2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(-3.62633 + 2.09366i) q^{32} +(0.0441521 + 0.0254912i) q^{33} +(-0.911548 - 1.57885i) q^{34} +(-1.13620 + 1.96796i) q^{36} +1.69819i q^{37} +(-4.09566 + 2.47156i) q^{38} +1.33288 q^{39} +(-5.31637 + 9.20823i) q^{41} +(0.682493 - 0.394038i) q^{42} +(-7.36801 - 4.25392i) q^{43} +(-0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(9.62623 - 5.55771i) q^{47} +(0.583345 - 0.336794i) q^{48} +3.41630 q^{49} +(-0.315080 - 0.545735i) q^{51} +(-2.42109 - 1.39781i) q^{52} +(-0.229365 + 0.132424i) q^{53} +(1.21894 - 2.11126i) q^{54} -5.80799 q^{56} +(-1.41568 + 0.854305i) q^{57} +5.45492i q^{58} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(6.23917 + 3.60219i) q^{62} +(-4.68243 + 2.70340i) q^{63} -8.14676 q^{64} +(0.0279750 + 0.0484542i) q^{66} +(2.55784 - 1.47677i) q^{67} +1.32172i q^{68} +2.03696 q^{69} +(-0.664176 + 1.15039i) q^{71} +(-7.58865 + 4.38131i) q^{72} +(5.49266 + 3.17119i) q^{73} +(-0.931830 + 1.61398i) q^{74} +(3.46742 - 0.0671384i) q^{76} -0.254428i q^{77} +(1.26678 + 0.731376i) q^{78} +(-0.733639 + 1.27070i) q^{79} +(-3.86283 + 6.69062i) q^{81} +(-10.1055 + 5.83439i) q^{82} +7.44736i q^{83} -0.571345 q^{84} +(-4.66842 - 8.08593i) q^{86} +1.88551i q^{87} -0.412343i q^{88} +(4.86804 + 8.43169i) q^{89} +(-3.32587 - 5.76057i) q^{91} +(-3.70001 - 2.13620i) q^{92} +(2.15659 + 1.24511i) q^{93} +12.1985 q^{94} -1.58839 q^{96} +(15.1285 + 8.73447i) q^{97} +(3.24688 + 1.87459i) q^{98} +(-0.191930 - 0.332433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49}+ \cdots + 76 q^{99}+O(q^{100}) $ 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * 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 $

$2$	0.950409	+	0.548719i	0.672041	+	0.388003i	0.796850	−	0.604178i	$-0.206498\pi$
$2$	0.950409	+	0.548719i	0.672041	+	0.388003i	−0.124809	+	0.992181i	$0.539832\pi$
$3$	0.328513	+	0.189667i	0.189667	+	0.109504i	0.591827	−	0.806065i	$-0.298407\pi$
$3$	0.328513	+	0.189667i	0.189667	+	0.109504i	−0.402160	+	0.915570i	$0.631740\pi$
$4$	−0.397815	−	0.689035i	−0.198907	−	0.344518i
$5$		0			0
$5$		0			0
$6$	0.208148	+	0.360522i	0.0849759	+	0.147183i
$7$		−	1.89307i		−	0.715512i	−0.933815	−	0.357756i	$-0.883542\pi$
$7$		−	1.89307i		−	0.715512i	0.933815	−	0.357756i	$-0.116458\pi$
$8$		−	3.06803i		−	1.08471i
$9$	−1.42805	−	2.47346i	−0.476018	−	0.824487i
$10$		0			0
$11$	0.134400			0.0405231			0.0202615	−	0.999795i	$-0.493550\pi$
$11$	0.134400			0.0405231			0.0202615	+	0.999795i	$0.493550\pi$
$12$		−	0.301809i		−	0.0871248i
$13$	3.04298	−	1.75687i	0.843972	−	0.487267i	−0.0146407	−	0.999893i	$-0.504660\pi$
$13$	3.04298	−	1.75687i	0.843972	−	0.487267i	0.858612	+	0.512626i	$0.171327\pi$
$14$	1.03876	−	1.79919i	0.277621	−	0.480854i
$15$		0			0
$16$	0.887858	−	1.53781i	0.221964	−	0.384454i
$17$	−1.43867	−	0.830615i	−0.348928	−	0.201454i	0.315285	−	0.948997i	$-0.397900\pi$
$17$	−1.43867	−	0.830615i	−0.348928	−	0.201454i	−0.664213	+	0.747543i	$0.731233\pi$
$18$		−	3.13440i		−	0.738785i
$19$	−2.10596	+	3.81640i	−0.483141	+	0.875543i
$19$	−2.10596	+	3.81640i	−0.483141	+	0.875543i
$20$		0			0
$21$	0.359052	−	0.621897i	0.0783516	−	0.135709i
$22$	0.127735	+	0.0737478i	0.0272332	+	0.0157231i
$23$	4.65042	−	2.68492i	0.969679	−	0.559844i	0.0705407	−	0.997509i	$-0.477528\pi$
$23$	4.65042	−	2.68492i	0.969679	−	0.559844i	0.899138	+	0.437664i	$0.144194\pi$
$24$	0.581904	−	1.00789i	0.118781	−	0.205734i
$25$		0			0
$26$	3.85611			0.756245
$27$		−	2.22142i		−	0.427512i
$28$	−1.30439	+	0.753090i	−0.246507	+	0.142321i
$29$	2.48530	+	4.30466i	0.461508	+	0.799355i	0.999036	−	0.0438905i	$-0.0139753\pi$
$29$	2.48530	+	4.30466i	0.461508	+	0.799355i	−0.537528	+	0.843246i	$0.680642\pi$
$30$		0			0
$31$	6.56472			1.17906			0.589529	−	0.807747i	$-0.299313\pi$
$31$	6.56472			1.17906			0.589529	+	0.807747i	$0.299313\pi$
$32$	−3.62633	+	2.09366i	−0.641050	+	0.370111i
$33$	0.0441521	+	0.0254912i	0.00768589	+	0.00443745i
$34$	−0.911548	−	1.57885i	−0.156329	−	0.270770i
$35$		0			0
$36$	−1.13620	+	1.96796i	−0.189367	+	0.327993i
$37$			1.69819i			0.279181i	0.990209	+	0.139590i	$0.0445786\pi$
$37$			1.69819i			0.279181i	−0.990209	+	0.139590i	$0.955421\pi$
$38$	−4.09566	+	2.47156i	−0.664404	+	0.400940i
$39$	1.33288			0.213431
$40$		0			0
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	0.0675398	+	0.997717i	$0.478485\pi$
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	−0.897818	+	0.440367i	$0.854848\pi$
$42$	0.682493	−	0.394038i	0.105311	−	0.0608013i
$43$	−7.36801	−	4.25392i	−1.12361	−	0.648717i	−0.181290	−	0.983430i	$-0.558027\pi$
$43$	−7.36801	−	4.25392i	−1.12361	−	0.648717i	−0.942320	+	0.334713i	$0.891361\pi$
$44$	−0.0534662	−	0.0926063i	−0.00806034	−	0.0139609i
$45$		0			0
$46$	5.89307			0.868885
$47$	9.62623	−	5.55771i	1.40413	−	0.810675i	0.409316	−	0.912392i	$-0.365767\pi$
$47$	9.62623	−	5.55771i	1.40413	−	0.810675i	0.994813	+	0.101718i	$0.0324339\pi$
$48$	0.583345	−	0.336794i	0.0841986	−	0.0486121i
$49$	3.41630			0.488042
$50$		0			0
$51$	−0.315080	−	0.545735i	−0.0441201	−	0.0764182i
$52$	−2.42109	−	1.39781i	−0.335744	−	0.193842i
$53$	−0.229365	+	0.132424i	−0.0315057	+	0.0181898i	−0.515670	−	0.856787i	$-0.672457\pi$
$53$	−0.229365	+	0.132424i	−0.0315057	+	0.0181898i	0.484164	+	0.874977i	$0.339124\pi$
$54$	1.21894	−	2.11126i	0.165876	−	0.287306i
$55$		0			0
$56$	−5.80799			−0.776125
$57$	−1.41568	+	0.854305i	−0.187511	+	0.113155i
$58$			5.45492i			0.716266i
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	−0.998317	−	0.0579932i	$-0.981530\pi$
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	0.549382	+	0.835571i	$0.314863\pi$
$60$		0			0
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	−0.994568	−	0.104087i	$-0.966808\pi$
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	0.407142	−	0.913365i	$-0.366525\pi$
$62$	6.23917	+	3.60219i	0.792375	+	0.457478i
$63$	−4.68243	+	2.70340i	−0.589930	+	0.340596i
$64$	−8.14676			−1.01834
$65$		0			0
$66$	0.0279750	+	0.0484542i	0.00344349	+	0.00596430i
$67$	2.55784	−	1.47677i	0.312490	−	0.180416i	−0.335550	−	0.942022i	$-0.608922\pi$
$67$	2.55784	−	1.47677i	0.312490	−	0.180416i	0.648040	+	0.761606i	$0.275589\pi$
$68$			1.32172i			0.160282i
$69$	2.03696			0.245221
$70$		0			0
$71$	−0.664176	+	1.15039i	−0.0788232	+	0.136526i	−0.902742	−	0.430181i	$-0.858450\pi$
$71$	−0.664176	+	1.15039i	−0.0788232	+	0.136526i	0.823919	+	0.566707i	$0.191783\pi$
$72$	−7.58865	+	4.38131i	−0.894331	+	0.516342i
$73$	5.49266	+	3.17119i	0.642867	+	0.371159i	0.785718	−	0.618585i	$-0.212294\pi$
$73$	5.49266	+	3.17119i	0.642867	+	0.371159i	−0.142851	+	0.989744i	$0.545627\pi$
$74$	−0.931830	+	1.61398i	−0.108323	+	0.187621i
$75$		0			0
$76$	3.46742	−	0.0671384i	0.397740	−	0.00770130i
$77$		−	0.254428i		−	0.0289948i
$78$	1.26678	+	0.731376i	0.143435	+	0.0828120i
$79$	−0.733639	+	1.27070i	−0.0825408	+	0.142965i	−0.904341	−	0.426811i	$-0.859637\pi$
$79$	−0.733639	+	1.27070i	−0.0825408	+	0.142965i	0.821800	+	0.569776i	$0.192970\pi$
$80$		0			0
$81$	−3.86283	+	6.69062i	−0.429203	+	0.743402i
$82$	−10.1055	+	5.83439i	−1.11596	+	0.644301i
$83$			7.44736i			0.817454i	0.912657	+	0.408727i	$0.134027\pi$
$83$			7.44736i			0.817454i	−0.912657	+	0.408727i	$0.865973\pi$
$84$	−0.571345			−0.0623388
$85$		0			0
$86$	−4.66842	−	8.08593i	−0.503408	−	0.871929i
$87$			1.88551i			0.202148i
$88$		−	0.412343i		−	0.0439559i
$89$	4.86804	+	8.43169i	0.516011	+	0.893757i	0.999827	+	0.0185878i	$0.00591701\pi$
$89$	4.86804	+	8.43169i	0.516011	+	0.893757i	−0.483816	+	0.875170i	$0.660750\pi$
$90$		0			0
$91$	−3.32587	−	5.76057i	−0.348646	−	0.603872i
$92$	−3.70001	−	2.13620i	−0.385753	−	0.222714i
$93$	2.15659	+	1.24511i	0.223628	+	0.129112i
$94$	12.1985			1.25818
$95$		0			0
$96$	−1.58839			−0.162115
$97$	15.1285	+	8.73447i	1.53607	+	0.886851i	0.999063	+	0.0432737i	$0.0137788\pi$
$97$	15.1285	+	8.73447i	1.53607	+	0.886851i	0.537008	+	0.843577i	$0.319555\pi$
$98$	3.24688	+	1.87459i	0.327984	+	0.189362i
$99$	−0.191930	−	0.332433i	−0.0192897	−	0.0334108i
$100$		0			0
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	0.699955	−	0.714187i	$-0.253203\pi$
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	−0.968481	+	0.249086i	$0.919870\pi$
$102$		−	0.691562i		−	0.0684749i
$103$			2.14750i			0.211599i	0.994387	+	0.105800i	$0.0337402\pi$
$103$			2.14750i			0.211599i	−0.994387	+	0.105800i	$0.966260\pi$
$104$	−5.39012	−	9.33596i	−0.528545	−	0.915467i
$105$		0			0
$106$	−0.290654			−0.0282308
$107$			1.00093i			0.0967631i	0.998829	+	0.0483815i	$0.0154063\pi$
$107$			1.00093i			0.0967631i	−0.998829	+	0.0483815i	$0.984594\pi$
$108$	−1.53064	+	0.883713i	−0.147285	+	0.0850353i
$109$	8.13145	−	14.0841i	0.778852	−	1.34901i	−0.153752	−	0.988109i	$-0.549136\pi$
$109$	8.13145	−	14.0841i	0.778852	−	1.34901i	0.932604	−	0.360902i	$-0.117531\pi$
$110$		0			0
$111$	−0.322091	+	0.557877i	−0.0305715	+	0.0529514i
$112$	−2.91119	−	1.68077i	−0.275081	−	0.158818i
$113$			0.843010i			0.0793037i	0.999214	+	0.0396519i	$0.0126249\pi$
$113$			0.843010i			0.0793037i	−0.999214	+	0.0396519i	$0.987375\pi$
$114$	−1.81425	+	0.0351287i	−0.169920	+	0.00329010i
$115$		0			0
$116$	1.97737	−	3.42491i	0.183595	−	0.317995i
$117$	−8.69108	−	5.01780i	−0.803491	−	0.463896i
$118$	−6.55466	+	3.78433i	−0.603405	+	0.348376i
$119$	−1.57241	+	2.72349i	−0.144143	+	0.249662i
$120$		0			0
$121$	−10.9819			−0.998358
$122$		−	10.0700i		−	0.911692i
$123$	−3.49299	+	2.01668i	−0.314953	+	0.181838i
$124$	−2.61154	−	4.52332i	−0.234523	−	0.406206i
$125$		0			0
$126$	−5.93363			−0.528610
$127$	−16.2290	+	9.36984i	−1.44009	+	0.831439i	−0.997855	−	0.0654584i	$-0.979149\pi$
$127$	−16.2290	+	9.36984i	−1.44009	+	0.831439i	−0.442239	+	0.896897i	$0.645816\pi$
$128$	−0.490101	−	0.282960i	−0.0433193	−	0.0250104i
$129$	−1.61366	−	2.79493i	−0.142074	−	0.246080i
$130$		0			0
$131$	−1.44322	+	2.49973i	−0.126095	+	0.218402i	−0.922160	−	0.386808i	$-0.873578\pi$
$131$	−1.44322	+	2.49973i	−0.126095	+	0.218402i	0.796066	+	0.605210i	$0.206911\pi$
$132$		−	0.0405631i		−	0.00353057i
$133$	7.22471	+	3.98673i	0.626461	+	0.345693i
$134$	3.24133			0.280008
$135$		0			0
$136$	−2.54835	+	4.41387i	−0.218519	+	0.378487i
$137$	16.3086	−	9.41579i	1.39334	−	0.804445i	0.399656	−	0.916665i	$-0.369129\pi$
$137$	16.3086	−	9.41579i	1.39334	−	0.804445i	0.993683	+	0.112220i	$0.0357961\pi$
$138$	1.93595	+	1.11772i	0.164799	+	0.0951466i
$139$	−9.08974	−	15.7439i	−0.770982	−	1.33538i	−0.937025	−	0.349262i	$-0.886432\pi$
$139$	−9.08974	−	15.7439i	−0.770982	−	1.33538i	0.166043	−	0.986118i	$-0.446901\pi$
$140$		0			0
$141$	4.21645			0.355089
$142$	−1.26248	+	0.728892i	−0.105945	+	0.0611672i
$143$	0.408977	−	0.236123i	0.0342003	−	0.0197456i
$144$	−5.07163			−0.422636
$145$		0			0
$146$	3.48018	+	6.02785i	0.288022	+	0.498868i
$147$	1.12230	+	0.647958i	0.0925655	+	0.0534427i
$148$	1.17011	−	0.675565i	0.0961827	−	0.0555311i
$149$	−11.1272	+	19.2728i	−0.911573	+	1.57889i	−0.0997308	+	0.995014i	$0.531798\pi$
$149$	−11.1272	+	19.2728i	−0.911573	+	1.57889i	−0.811842	+	0.583877i	$0.801535\pi$
$150$		0			0
$151$	3.33482			0.271384			0.135692	−	0.990751i	$-0.456674\pi$
$151$	3.33482			0.271384			0.135692	+	0.990751i	$0.456674\pi$
$152$	11.7088	+	6.46116i	0.949712	+	0.524069i
$153$			4.74465i			0.383582i
$154$	0.139610	−	0.241811i	0.0112501	−	0.0194857i
$155$		0			0
$156$	−0.530238	−	0.918400i	−0.0424530	−	0.0735308i
$157$	6.28986	+	3.63145i	0.501986	+	0.289822i	0.729533	−	0.683945i	$-0.239737\pi$
$157$	6.28986	+	3.63145i	0.501986	+	0.289822i	−0.227548	+	0.973767i	$0.573071\pi$
$158$	−1.39451	+	0.805123i	−0.110942	+	0.0640522i
$159$	−0.100466			−0.00796744
$160$		0			0
$161$	−5.08273	−	8.80355i	−0.400576	−	0.693817i
$162$	−7.34254	+	4.23922i	−0.576884	+	0.333064i
$163$		−	19.7783i		−	1.54916i	−0.632478	−	0.774578i	$-0.717962\pi$
$163$		−	19.7783i		−	1.54916i	0.632478	−	0.774578i	$-0.282038\pi$
$164$	8.45972			0.660593
$165$		0			0
$166$	−4.08651	+	7.07805i	−0.317175	+	0.549363i
$167$	2.94726	−	1.70160i	0.228066	−	0.131674i	−0.381614	−	0.924322i	$-0.624632\pi$
$167$	2.94726	−	1.70160i	0.228066	−	0.131674i	0.609679	+	0.792648i	$0.291298\pi$
$168$	−1.90800	−	1.10158i	−0.147205	−	0.0849890i
$169$	−0.326838	+	0.566100i	−0.0251414	+	0.0435461i
$170$		0			0
$171$	12.4471	−	0.241010i	0.951857	−	0.0184305i
$172$			6.76909i			0.516138i
$173$	9.16750	+	5.29286i	0.696992	+	0.402409i	0.806226	−	0.591607i	$-0.201506\pi$
$173$	9.16750	+	5.29286i	0.696992	+	0.402409i	−0.109234	+	0.994016i	$0.534840\pi$
$174$	−1.03462	+	1.79201i	−0.0784341	+	0.135852i
$175$		0			0
$176$	0.119328	−	0.206682i	0.00899469	−	0.0155793i
$177$	−2.26564	+	1.30807i	−0.170296	+	0.0983205i
$178$			10.6847i			0.800855i
$179$	14.6024			1.09144			0.545718	−	0.837969i	$-0.316257\pi$
$179$	14.6024			1.09144			0.545718	+	0.837969i	$0.316257\pi$
$180$		0			0
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	0.949141	−	0.314851i	$-0.101955\pi$
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	−0.747240	+	0.664555i	$0.768621\pi$
$182$		−	7.29987i		−	0.541102i
$183$		−	3.48072i		−	0.257303i
$184$	−8.23742	−	14.2676i	−0.607270	−	1.05182i
$185$		0			0
$186$	1.36643	+	2.36673i	0.100192	+	0.173537i
$187$	−0.193357	−	0.111635i	−0.0141396	−	0.00816353i
$188$	−7.65891	−	4.42187i	−0.558583	−	0.322498i
$189$	−4.20530			−0.305890
$190$		0			0
$191$	20.4758			1.48157			0.740787	−	0.671740i	$-0.234453\pi$
$191$	20.4758			1.48157			0.740787	+	0.671740i	$0.234453\pi$
$192$	−2.67631	−	1.54517i	−0.193146	−	0.111513i
$193$	−9.54664	−	5.51176i	−0.687182	−	0.396745i	0.115373	−	0.993322i	$-0.463194\pi$
$193$	−9.54664	−	5.51176i	−0.687182	−	0.396745i	−0.802556	+	0.596577i	$0.796527\pi$
$194$	9.58554	+	16.6026i	0.688202	+	1.19200i
$195$		0			0
$196$	−1.35905	−	2.35395i	−0.0970752	−	0.168139i
$197$			19.8532i			1.41448i	0.706971	+	0.707242i	$0.250061\pi$
$197$			19.8532i			1.41448i	−0.706971	+	0.707242i	$0.749939\pi$
$198$		−	0.421263i		−	0.0299379i
$199$	10.5013	+	18.1888i	0.744417	+	1.28937i	0.950467	+	0.310826i	$0.100606\pi$
$199$	10.5013	+	18.1888i	0.744417	+	1.28937i	−0.206050	+	0.978542i	$0.566061\pi$
$200$		0			0
$201$	1.12038			0.0790254
$202$		−	5.92321i		−	0.416756i
$203$	8.14901	−	4.70483i	0.571948	−	0.330215i
$204$	−0.250687	+	0.434203i	−0.0175516	+	0.0304003i
$205$		0			0
$206$	−1.17837	+	2.04100i	−0.0821011	+	0.142203i
$207$	−13.2821	−	7.66842i	−0.923169	−	0.532992i
$208$		−	6.23939i		−	0.432624i
$209$	−0.283041	+	0.512924i	−0.0195784	+	0.0354797i
$210$		0			0
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	−0.556321	−	0.830967i	$-0.687788\pi$
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	0.997799	+	0.0663046i	$0.0211209\pi$
$212$	0.182489	+	0.105360i	0.0125334	+	0.00723617i
$213$	−0.436380	+	0.251944i	−0.0299003	+	0.0172629i
$214$	−0.549227	+	0.951289i	−0.0375444	+	0.0650288i
$215$		0			0
$216$	−6.81538			−0.463728
$217$		−	12.4275i		−	0.843630i
$218$	15.4564	−	8.92377i	1.04684	−	0.604394i
$219$	1.20294	+	2.08355i	0.0812870	+	0.140793i
$220$		0			0
$221$	−5.83712			−0.392647
$222$	−0.612236	+	0.353475i	−0.0410906	+	0.0237237i
$223$	−17.6621	−	10.1972i	−1.18274	−	0.682856i	−0.226095	−	0.974105i	$-0.572596\pi$
$223$	−17.6621	−	10.1972i	−1.18274	−	0.682856i	−0.956647	+	0.291249i	$0.905929\pi$
$224$	3.96344	+	6.86488i	0.264819	+	0.458679i
$225$		0			0
$226$	−0.462576	+	0.801205i	−0.0307701	+	0.0532954i
$227$		−	25.4172i		−	1.68700i	−0.537129	−	0.843500i	$-0.680491\pi$
$227$		−	25.4172i		−	1.68700i	0.537129	−	0.843500i	$-0.319509\pi$
$228$	1.15182	+	0.635598i	0.0762814	+	0.0420935i
$229$	−2.21553			−0.146406			−0.0732030	−	0.997317i	$-0.523322\pi$
$229$	−2.21553			−0.146406			−0.0732030	+	0.997317i	$0.523322\pi$
$230$		0			0
$231$	0.0482566	−	0.0835829i	0.00317505	−	0.00549935i
$232$	13.2068	−	7.62496i	0.867071	−	0.500603i
$233$	12.2609	+	7.07882i	0.803236	+	0.463749i	0.844602	−	0.535395i	$-0.179837\pi$
$233$	12.2609	+	7.07882i	0.803236	+	0.463749i	−0.0413652	+	0.999144i	$0.513171\pi$
$234$	−5.50672	−	9.53792i	−0.359986	−	0.623514i
$235$		0			0
$236$	5.48719			0.357186
$237$	−0.482019	+	0.278294i	−0.0313105	+	0.0180771i
$238$	−2.98887	+	1.72562i	−0.193739	+	0.111855i
$239$	−3.01476			−0.195008			−0.0975042	−	0.995235i	$-0.531086\pi$
$239$	−3.01476			−0.195008			−0.0975042	+	0.995235i	$0.531086\pi$
$240$		0			0
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	0.939781	+	0.341776i	$0.111028\pi$
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	−0.173904	+	0.984763i	$0.555638\pi$
$242$	−10.4373	−	6.02600i	−0.670937	−	0.387366i
$243$	−8.30939	+	4.79743i	−0.533048	+	0.307755i
$244$	−3.65030	+	6.32251i	−0.233687	+	0.404757i
$245$		0			0
$246$	−4.42636			−0.282215
$247$	0.296503	+	15.3131i	0.0188660	+	0.974352i
$248$		−	20.1407i		−	1.27894i
$249$	−1.41252	+	2.44655i	−0.0895147	+	0.155044i
$250$		0			0
$251$	−8.59495	−	14.8869i	−0.542509	−	0.939653i	−0.998759	−	0.0498012i	$-0.984141\pi$
$251$	−8.59495	−	14.8869i	−0.542509	−	0.939653i	0.456250	−	0.889851i	$-0.349192\pi$
$252$	3.72548	+	2.15090i	0.234683	+	0.135494i
$253$	0.625016	−	0.360853i	0.0392944	−	0.0226866i
$254$	−20.5656			−1.29040
$255$		0			0
$256$	7.83623	+	13.5727i	0.489764	+	0.848297i
$257$	16.9246	−	9.77143i	1.05573	−	0.609525i	0.131481	−	0.991319i	$-0.458027\pi$
$257$	16.9246	−	9.77143i	1.05573	−	0.609525i	0.924248	+	0.381794i	$0.124693\pi$
$258$		−	3.54178i		−	0.220501i
$259$	3.21479			0.199757
$260$		0			0
$261$	7.09827	−	12.2946i	0.439372	−	0.761014i
$262$	−2.74330	+	1.58384i	−0.169482	+	0.0978502i
$263$	−7.63280	−	4.40680i	−0.470659	−	0.271735i	0.245857	−	0.969306i	$-0.420931\pi$
$263$	−7.63280	−	4.40680i	−0.470659	−	0.271735i	−0.716515	+	0.697571i	$0.754264\pi$
$264$	0.0782078	−	0.135460i	0.00481336	−	0.00833698i
$265$		0			0
$266$	4.67883	+	7.75336i	0.286878	+	0.475389i
$267$			3.69322i			0.226022i
$268$	−2.03510	−	1.17496i	−0.124313	−	0.0717723i
$269$	0.144181	−	0.249729i	0.00879088	−	0.0152263i	−0.861596	−	0.507594i	$-0.830535\pi$
$269$	0.144181	−	0.249729i	0.00879088	−	0.0152263i	0.870387	+	0.492368i	$0.163868\pi$
$270$		0			0
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	−0.189761	−	0.981830i	$-0.560771\pi$
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	0.945171	−	0.326577i	$-0.105895\pi$
$272$	−2.55466	+	1.47494i	−0.154899	+	0.0894311i
$273$		−	2.52323i		−	0.152713i
$274$	20.6665			1.24851
$275$		0			0
$276$	−0.810333	−	1.40354i	−0.0487763	−	0.0844831i
$277$			4.40486i			0.264662i	0.991206	+	0.132331i	$0.0422463\pi$
$277$			4.40486i			0.264662i	−0.991206	+	0.132331i	$0.957754\pi$
$278$		−	19.9509i		−	1.19657i
$279$	−9.37476	−	16.2376i	−0.561252	−	0.972118i
$280$		0			0
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.676600	+	0.736350i	$0.263452\pi$
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.299398	+	0.954128i	$0.403214\pi$
$282$	4.00736	+	2.31365i	0.238635	+	0.137776i
$283$	1.15088	+	0.664463i	0.0684129	+	0.0394982i	0.533816	−	0.845600i	$-0.320757\pi$
$283$	1.15088	+	0.664463i	0.0684129	+	0.0394982i	−0.465403	+	0.885099i	$0.654091\pi$
$284$	1.05688			0.0627140
$285$		0			0
$286$	0.518260			0.0306454
$287$	17.4318	+	10.0643i	1.02897	+	0.594074i
$288$	10.3572	+	5.97972i	0.610302	+	0.352358i
$289$	−7.12016	−	12.3325i	−0.418833	−	0.725440i
$290$		0			0
$291$	3.31328	+	5.73877i	0.194228	+	0.336413i
$292$		−	5.04618i		−	0.295305i
$293$		−	7.72365i		−	0.451220i	−0.974218	−	0.225610i	$-0.927562\pi$
$293$		−	7.72365i		−	0.451220i	0.974218	−	0.225610i	$-0.0724375\pi$
$294$	0.711094	+	1.23165i	0.0414718	+	0.0718313i
$295$		0			0
$296$	5.21010			0.302831
$297$		−	0.298558i		−	0.0173241i
$298$	−21.1507	+	12.2114i	−1.22523	+	0.707386i
$299$	9.43409	−	16.3403i	0.545588	−	0.944986i
$300$		0			0
$301$	−8.05296	+	13.9481i	−0.464165	+	0.803957i
$302$	3.16944	+	1.82988i	0.182381	+	0.105298i
$303$		−	2.04738i		−	0.117619i
$304$	3.99912	+	6.62700i	0.229366	+	0.380085i
$305$		0			0
$306$	−2.60348	+	4.50936i	−0.148831	+	0.257783i
$307$	−7.88085	−	4.55001i	−0.449784	−	0.259683i	0.257955	−	0.966157i	$-0.416951\pi$
$307$	−7.88085	−	4.55001i	−0.449784	−	0.259683i	−0.707739	+	0.706474i	$0.750285\pi$
$308$	−0.175310	+	0.101215i	−0.00998921	+	0.00576727i
$309$	−0.407309	+	0.705480i	−0.0231710	+	0.0401333i
$310$		0			0
$311$	−12.4569			−0.706364			−0.353182	−	0.935555i	$-0.614900\pi$
$311$	−12.4569			−0.706364			−0.353182	+	0.935555i	$0.614900\pi$
$312$		−	4.08931i		−	0.231512i
$313$	1.77148	−	1.02277i	0.100130	−	0.0578101i	−0.449099	−	0.893482i	$-0.648255\pi$
$313$	1.77148	−	1.02277i	0.100130	−	0.0578101i	0.549229	+	0.835672i	$0.314922\pi$
$314$	3.98530	+	6.90274i	0.224903	+	0.389544i
$315$		0			0
$316$	1.16741			0.0656719
$317$	−20.4133	+	11.7856i	−1.14653	+	0.661947i	−0.948038	−	0.318157i	$-0.896936\pi$
$317$	−20.4133	+	11.7856i	−1.14653	+	0.661947i	−0.198487	+	0.980103i	$0.563603\pi$
$318$	−0.0954834	−	0.0551274i	−0.00535445	−	0.00309139i
$319$	0.334024	+	0.578546i	0.0187017	+	0.0323923i
$320$		0			0
$321$	−0.189842	+	0.328817i	−0.0105960	+	0.0183528i
$322$		−	11.1560i		−	0.621698i
$323$	6.19974	−	3.74129i	0.344963	−	0.208171i
$324$	6.14676			0.341487
$325$		0			0
$326$	10.8527	−	18.7975i	0.601077	−	1.04110i
$327$	5.34257	−	3.08454i	0.295445	−	0.170575i
$328$	28.2511	+	16.3108i	1.55991	+	0.900613i
$329$	−10.5211	−	18.2231i	−0.580048	−	1.00467i
$330$		0			0
$331$	−18.7175			−1.02881			−0.514403	−	0.857549i	$-0.671986\pi$
$331$	−18.7175			−1.02881			−0.514403	+	0.857549i	$0.671986\pi$
$332$	5.13150	−	2.96267i	0.281627	−	0.162598i
$333$	4.20041	−	2.42511i	0.230181	−	0.132895i
$334$	3.73480			0.204359
$335$		0			0
$336$	−0.637575	−	1.10431i	−0.0347826	−	0.0602451i
$337$	−28.3087	−	16.3440i	−1.54207	−	0.890316i	−0.998708	−	0.0508197i	$-0.983817\pi$
$337$	−28.3087	−	16.3440i	−1.54207	−	0.890316i	−0.543365	−	0.839497i	$-0.682850\pi$
$338$	−0.621259	+	0.358684i	−0.0337921	+	0.0195098i
$339$	−0.159891	+	0.276940i	−0.00868409	+	0.0150413i
$340$		0			0
$341$	0.882297			0.0477791
$342$	11.9621	+	6.60093i	0.646838	+	0.356937i
$343$		−	19.7188i		−	1.06471i
$344$	−13.0512	+	22.6053i	−0.703671	+	1.21879i
$345$		0			0
$346$	5.80859	+	10.0608i	0.312271	+	0.540870i
$347$	−2.22279	−	1.28333i	−0.119326	−	0.0688927i	0.439149	−	0.898414i	$-0.355280\pi$
$347$	−2.22279	−	1.28333i	−0.119326	−	0.0688927i	−0.558475	+	0.829521i	$0.688613\pi$
$348$	1.29919	−	0.750085i	0.0696436	−	0.0402088i
$349$	−16.6195			−0.889619			−0.444810	−	0.895625i	$-0.646729\pi$
$349$	−16.6195			−0.889619			−0.444810	+	0.895625i	$0.646729\pi$
$350$		0			0
$351$	−3.90274	−	6.75974i	−0.208313	−	0.360808i
$352$	−0.487378	+	0.281388i	−0.0259773	+	0.0149980i
$353$			28.3629i			1.50961i	0.655951	+	0.754803i	$0.272268\pi$
$353$			28.3629i			1.50961i	−0.655951	+	0.754803i	$0.727732\pi$
$354$	−2.87105			−0.152595
$355$		0			0
$356$	3.87315	−	6.70850i	0.205277	−	0.355550i
$357$	−1.03311	+	0.596468i	−0.0546781	+	0.0315684i
$358$	13.8783	+	8.01262i	0.733489	+	0.423480i
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149224\pi$
$360$		0			0
$361$	−10.1298	−	16.0744i	−0.533150	−	0.846021i
$362$			5.96195i			0.313353i
$363$	−3.60771	−	2.08291i	−0.189355	−	0.109324i
$364$	−2.64616	+	4.58328i	−0.138696	+	0.240229i
$365$		0			0
$366$	1.90994	−	3.30811i	0.0998342	−	0.172918i
$367$	−22.3477	+	12.9024i	−1.16654	+	0.673501i	−0.952862	−	0.303404i	$-0.901877\pi$
$367$	−22.3477	+	12.9024i	−1.16654	+	0.673501i	−0.213676	+	0.976905i	$0.568544\pi$
$368$		−	9.53531i		−	0.497062i
$369$	30.3683			1.58091
$370$		0			0
$371$	0.250687	+	0.434203i	0.0130150	+	0.0225427i
$372$		−	1.98129i		−	0.102725i
$373$			27.0663i			1.40144i	0.713437	+	0.700719i	$0.247138\pi$
$373$			27.0663i			1.40144i	−0.713437	+	0.700719i	$0.752862\pi$
$374$	−0.122512	−	0.212197i	−0.00633495	−	0.0109724i
$375$		0			0
$376$	−17.0512	−	29.5336i	−0.879349	−	1.52308i
$377$	15.1254	+	8.73267i	0.778999	+	0.449755i
$378$	−3.99675	−	2.30753i	−0.205571	−	0.118686i
$379$	−12.4028			−0.637092			−0.318546	−	0.947907i	$-0.603194\pi$
$379$	−12.4028			−0.637092			−0.318546	+	0.947907i	$0.603194\pi$
$380$		0			0
$381$	−7.10859			−0.364184
$382$	19.4604	+	11.2354i	0.995678	+	0.574855i
$383$	4.64139	+	2.67971i	0.237164	+	0.136927i	0.613873	−	0.789405i	$-0.289611\pi$
$383$	4.64139	+	2.67971i	0.237164	+	0.136927i	−0.376709	+	0.926332i	$0.622944\pi$
$384$	−0.107336	−	0.185912i	−0.00547749	−	0.00948728i
$385$		0			0
$386$	−6.04881	−	10.4769i	−0.307877	−	0.533258i
$387$			24.2993i			1.23520i
$388$		−	13.8988i		−	0.705605i
$389$	4.28467	+	7.42126i	0.217241	+	0.376273i	0.953964	−	0.299923i	$-0.0969608\pi$
$389$	4.28467	+	7.42126i	0.217241	+	0.376273i	−0.736722	+	0.676195i	$0.763628\pi$
$390$		0			0
$391$	−8.92053			−0.451131
$392$		−	10.4813i		−	0.529386i
$393$	−0.948232	+	0.547462i	−0.0478320	+	0.0276158i
$394$	−10.8939	+	18.8687i	−0.548824	+	0.950592i
$395$		0			0
$396$	−0.152705	+	0.264493i	−0.00767373	+	0.0132913i
$397$	−9.21844	−	5.32227i	−0.462660	−	0.267117i	0.250502	−	0.968116i	$-0.419404\pi$
$397$	−9.21844	−	5.32227i	−0.462660	−	0.267117i	−0.713162	+	0.700999i	$0.752738\pi$
$398$			23.0490i			1.15534i
$399$	1.61726	+	2.67998i	0.0809641	+	0.134167i
$400$		0			0
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	−0.945603	−	0.325323i	$-0.894527\pi$
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	0.754539	+	0.656255i	$0.227860\pi$
$402$	1.06482	+	0.614773i	0.0531083	+	0.0306621i
$403$	19.9763	−	11.5333i	0.995091	−	0.574516i
$404$	−2.14713	+	3.71893i	−0.106824	+	0.185024i
$405$		0			0
$406$	10.3265			0.512497
$407$			0.228237i			0.0113133i
$408$	−1.67433	+	0.966676i	−0.0828918	+	0.0478576i
$409$	−8.84435	−	15.3189i	−0.437325	−	0.757469i	0.560157	−	0.828386i	$-0.310741\pi$
$409$	−8.84435	−	15.3189i	−0.437325	−	0.757469i	−0.997482	+	0.0709173i	$0.977407\pi$
$410$		0			0
$411$	7.14345			0.352361
$412$	1.47970	−	0.854305i	0.0728996	−	0.0420886i
$413$	11.3067	+	6.52793i	0.556367	+	0.321218i
$414$	−8.41561	−	14.5763i	−0.413605	−	0.716384i
$415$		0			0
$416$	−7.35657	+	12.7420i	−0.360685	+	0.624726i
$417$		−	6.89609i		−	0.337703i
$418$	−0.550456	+	0.332178i	−0.0269237	+	0.0162473i
$419$	−1.18732			−0.0580045			−0.0290023	−	0.999579i	$-0.509233\pi$
$419$	−1.18732			−0.0580045			−0.0290023	+	0.999579i	$0.509233\pi$
$420$		0			0
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	0.0975661	+	0.995229i	$0.468894\pi$
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	−0.910677	+	0.413120i	$0.864439\pi$
$422$	12.1896	−	7.03770i	0.593383	−	0.342590i
$423$	−27.4935	−	15.8734i	−1.33678	−	0.771791i
$424$	0.406280	+	0.703698i	0.0197307	+	0.0341746i
$425$		0			0
$426$	−0.552987			−0.0267923
$427$	−15.0434	+	8.68529i	−0.727999	+	0.420311i
$428$	0.689673	−	0.398183i	0.0333366	−	0.0192469i
$429$	0.179139			0.00864890
$430$		0			0
$431$	3.08799	+	5.34855i	0.148743	+	0.257631i	0.930763	−	0.365623i	$-0.119144\pi$
$431$	3.08799	+	5.34855i	0.148743	+	0.257631i	−0.782020	+	0.623253i	$0.785811\pi$
$432$	−3.41613	−	1.97230i	−0.164359	−	0.0948925i
$433$	−16.0693	+	9.27761i	−0.772241	+	0.445854i	−0.833673	−	0.552258i	$-0.813766\pi$
$433$	−16.0693	+	9.27761i	−0.772241	+	0.445854i	0.0614325	+	0.998111i	$0.480433\pi$
$434$	6.81918	−	11.8112i	0.327331	−	0.566954i
$435$		0			0
$436$	−12.9392			−0.619677
$437$	0.453129	+	23.4022i	0.0216761	+	1.11948i
$438$			2.64030i			0.126158i
$439$	−0.113656	+	0.196858i	−0.00542450	+	0.00939550i	−0.868725	−	0.495295i	$-0.835060\pi$
$439$	−0.113656	+	0.196858i	−0.00542450	+	0.00939550i	0.863300	+	0.504690i	$0.168393\pi$
$440$		0			0
$441$	−4.87865	−	8.45007i	−0.232317	−	0.402384i
$442$	−5.54765	−	3.20294i	−0.263875	−	0.152348i
$443$	−30.2959	+	17.4913i	−1.43940	+	0.831038i	−0.997808	−	0.0661770i	$-0.978920\pi$
$443$	−30.2959	+	17.4913i	−1.43940	+	0.831038i	−0.441593	+	0.897216i	$0.645586\pi$
$444$	0.512529			0.0243236
$445$		0			0
$446$	−11.1908	−	19.3831i	−0.529901	−	0.917815i
$447$	−7.31083	+	4.22091i	−0.345791	+	0.199642i
$448$			15.4224i			0.728638i
$449$	16.9509			0.799961			0.399980	−	0.916524i	$-0.369017\pi$
$449$	16.9509			0.799961			0.399980	+	0.916524i	$0.369017\pi$
$450$		0			0
$451$	−0.714520	+	1.23759i	−0.0336454	+	0.0582756i
$452$	0.580864	−	0.335362i	0.0273215	−	0.0157741i
$453$	1.09553	+	0.632505i	0.0514725	+	0.0297177i
$454$	13.9469	−	24.1568i	0.654561	−	1.13373i
$455$		0			0
$456$	2.62103	+	4.34335i	0.122741	+	0.203396i
$457$		−	1.60241i		−	0.0749578i	−0.999297	−	0.0374789i	$-0.988067\pi$
$457$		−	1.60241i		−	0.0749578i	0.999297	−	0.0374789i	$-0.0119327\pi$
$458$	−2.10566	−	1.21570i	−0.0983909	−	0.0568060i
$459$	−1.84514	+	3.19588i	−0.0861239	+	0.149171i
$460$		0			0
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	−0.746107	−	0.665826i	$-0.768079\pi$
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	0.949676	+	0.313234i	$0.101413\pi$
$462$	0.0917270	−	0.0529586i	0.00426753	−	0.00246386i
$463$			21.1886i			0.984718i	0.870392	+	0.492359i	$0.163865\pi$
$463$			21.1886i			0.984718i	−0.870392	+	0.492359i	$0.836135\pi$
$464$	8.82636			0.409753
$465$		0			0
$466$	7.76857	+	13.4556i	0.359872	+	0.623316i
$467$		−	20.4516i		−	0.946388i	−0.880958	−	0.473194i	$-0.843101\pi$
$467$		−	20.4516i		−	0.946388i	0.880958	−	0.473194i	$-0.156899\pi$
$468$			7.98461i			0.369089i
$469$	−2.79563	−	4.84217i	−0.129090	−	0.223591i
$470$		0			0
$471$	1.37753	+	2.38596i	0.0634734	+	0.109939i
$472$	18.3244	+	10.5796i	0.843449	+	0.486965i
$473$	−0.990259	−	0.571727i	−0.0455322	−	0.0262880i
$474$	−0.610821			−0.0280559
$475$		0			0
$476$	2.50211			0.114684
$477$	0.655090	+	0.378216i	0.0299945	+	0.0173173i
$478$	−2.86525	−	1.65425i	−0.131054	−	0.0756639i
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	0.999012	+	0.0444419i	$0.0141510\pi$
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	−0.461018	+	0.887391i	$0.652516\pi$
$480$		0			0
$481$	2.98350	+	5.16757i	0.136036	+	0.235621i
$482$			26.0962i			1.18865i
$483$		−	3.85611i		−	0.175459i
$484$	4.36877	+	7.56694i	0.198581	+	0.343952i
$485$		0			0
$486$	−10.5298			−0.477640
$487$		−	36.0392i		−	1.63309i	−0.577280	−	0.816546i	$-0.695886\pi$
$487$		−	36.0392i		−	1.63309i	0.577280	−	0.816546i	$-0.304114\pi$
$488$	−24.3803	+	14.0760i	−1.10364	+	0.637188i
$489$	3.75129	−	6.49742i	0.169639	−	0.293824i
$490$		0			0
$491$	−10.0297	+	17.3720i	−0.452635	+	0.783988i	−0.998549	−	0.0538541i	$-0.982849\pi$
$491$	−10.0297	+	17.3720i	−0.452635	+	0.783988i	0.545913	+	0.837842i	$0.316183\pi$
$492$	2.77913	+	1.60453i	0.125293	+	0.0723378i
$493$		−	8.25729i		−	0.371890i
$494$	−8.12081	+	14.7164i	−0.365373	+	0.662124i
$495$		0			0
$496$	5.82853	−	10.0953i	0.261709	−	0.453293i
$497$	2.17776	+	1.25733i	0.0976858	+	0.0563989i
$498$	−2.68494	+	1.55015i	−0.120315	+	0.0694640i
$499$	−18.4364	+	31.9328i	−0.825328	+	1.42951i	0.0763399	+	0.997082i	$0.475677\pi$
$499$	−18.4364	+	31.9328i	−0.825328	+	1.42951i	−0.901668	+	0.432429i	$0.857657\pi$
$500$		0			0
$501$	1.29095			0.0576753
$502$		−	18.8649i		−	0.841980i
$503$	−18.7483	+	10.8244i	−0.835947	+	0.482634i	−0.855884	−	0.517167i	$-0.826987\pi$
$503$	−18.7483	+	10.8244i	−0.835947	+	0.482634i	0.0199377	+	0.999801i	$0.493653\pi$
$504$	8.29412	+	14.3658i	0.369449	+	0.639905i
$505$		0			0
$506$	0.792028			0.0352099
$507$	−0.214741	+	0.123981i	−0.00953697	+	0.00550617i
$508$	12.9123	+	7.45492i	0.572891	+	0.330759i
$509$	−18.2279	−	31.5717i	−0.807938	−	1.39939i	−0.914289	−	0.405062i	$-0.867250\pi$
$509$	−18.2279	−	31.5717i	−0.807938	−	1.39939i	0.106351	−	0.994329i	$-0.466083\pi$
$510$		0			0
$511$	6.00327	−	10.3980i	0.265569	−	0.459979i
$512$			18.3314i			0.810141i
$513$	8.47783	+	4.67822i	0.374305	+	0.206549i
$514$	21.4471			0.945990
$515$		0			0
$516$	−1.28387	+	2.22373i	−0.0565193	+	0.0978943i
$517$	1.29376	−	0.746955i	0.0568997	−	0.0328511i
$518$	3.05537	+	1.76402i	0.134245	+	0.0775065i
$519$	2.00776	+	3.47754i	0.0881309	+	0.152647i
$520$		0			0
$521$	−22.6092			−0.990528			−0.495264	−	0.868742i	$-0.664929\pi$
$521$	−22.6092			−0.990528			−0.495264	+	0.868742i	$0.664929\pi$
$522$	13.4925	−	7.78991i	0.590552	−	0.340955i
$523$	0.461515	−	0.266456i	0.0201806	−	0.0116513i	−0.489876	−	0.871792i	$-0.662958\pi$
$523$	0.461515	−	0.266456i	0.0201806	−	0.0116513i	0.510056	+	0.860141i	$0.329625\pi$
$524$	2.29654			0.100325
$525$		0			0
$526$	−4.83619	−	8.37653i	−0.210868	−	0.365234i
$527$	−9.44444	−	5.45275i	−0.411406	−	0.237525i
$528$	0.0784015	−	0.0452651i	0.00341199	−	0.00196991i
$529$	2.91759	−	5.05341i	0.126852	−	0.219714i
$530$		0			0
$531$	19.6976			0.854804
$532$	−0.127098	−	6.56406i	−0.00551038	−	0.284588i
$533$			37.3606i			1.61827i
$534$	−2.02654	+	3.51007i	−0.0876971	+	0.151896i
$535$		0			0
$536$	−4.53078	−	7.84754i	−0.195700	−	0.338962i
$537$	4.79708	+	2.76959i	0.207009	+	0.119517i
$538$	0.274062	−	0.158230i	0.0118157	−	0.00682178i
$539$	0.459150			0.0197770
$540$		0			0
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	0.807057	−	0.590473i	$-0.201059\pi$
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	−0.914893	+	0.403696i	$0.867725\pi$
$542$	23.6378	−	13.6473i	1.01533	−	0.586202i
$543$			2.06077i			0.0884362i
$544$	6.95610			0.298240
$545$		0			0
$546$	1.38454	−	2.39810i	0.0592530	−	0.102629i
$547$	−19.5981	+	11.3149i	−0.837952	+	0.483792i	−0.856568	−	0.516035i	$-0.827408\pi$
$547$	−19.5981	+	11.3149i	−0.837952	+	0.483792i	0.0186154	+	0.999827i	$0.494074\pi$
$548$	−12.9756	−	7.49148i	−0.554291	−	0.320020i
$549$	−13.1037	+	22.6962i	−0.559250	+	0.968650i
$550$		0			0
$551$	−21.6622	+	0.419439i	−0.922843	+	0.0178687i
$552$		−	6.24946i		−	0.265995i
$553$	2.40552	+	1.38883i	0.102293	+	0.0590590i
$554$	−2.41703	+	4.18642i	−0.102690	+	0.177864i
$555$		0			0
$556$	−7.23207	+	12.5263i	−0.306708	+	0.531234i
$557$	−30.5321	+	17.6277i	−1.29369	+	0.746910i	−0.979306	−	0.202387i	$-0.935130\pi$
$557$	−30.5321	+	17.6277i	−1.29369	+	0.746910i	−0.314381	+	0.949297i	$0.601797\pi$
$558$		−	20.5764i		−	0.871070i
$559$	−29.8943			−1.26439
$560$		0			0
$561$	−0.0423468	−	0.0733467i	−0.00178788	−	0.00309670i
$562$			35.9097i			1.51476i
$563$		−	24.6295i		−	1.03801i	−0.854771	−	0.519005i	$-0.826302\pi$
$563$		−	24.6295i		−	1.03801i	0.854771	−	0.519005i	$-0.173698\pi$
$564$	−1.67737	−	2.90528i	−0.0706298	−	0.122334i
$565$		0			0
$566$	0.729207	+	1.26302i	0.0306509	+	0.0530888i
$567$	12.6658	+	7.31260i	0.531913	+	0.307100i
$568$	3.52942	+	2.03771i	0.148091	+	0.0855005i
$569$	20.0193			0.839252			0.419626	−	0.907697i	$-0.362161\pi$
$569$	20.0193			0.839252			0.419626	+	0.907697i	$0.362161\pi$
$570$		0			0
$571$	−16.6121			−0.695195			−0.347597	−	0.937644i	$-0.613002\pi$
$571$	−16.6121			−0.695195			−0.347597	+	0.937644i	$0.613002\pi$
$572$	−0.325394	−	0.187866i	−0.0136054	−	0.00785508i
$573$	6.72655	+	3.88357i	0.281006	+	0.162239i
$574$	11.0449	+	19.1303i	0.461005	+	0.798484i
$575$		0			0
$576$	11.6340	+	20.1507i	0.484750	+	0.839612i
$577$		−	12.4486i		−	0.518244i	−0.965845	−	0.259122i	$-0.916567\pi$
$577$		−	12.4486i		−	0.518244i	0.965845	−	0.259122i	$-0.0834331\pi$
$578$		−	15.6279i		−	0.650034i
$579$	−2.09080	−	3.62136i	−0.0868905	−	0.150499i
$580$		0			0
$581$	14.0984			0.584899
$582$			7.27224i			0.301444i
$583$	−0.0308266	+	0.0177977i	−0.00127671	+	0.000737107i
$584$	9.72930	−	16.8516i	0.402601	−	0.697326i
$585$		0			0
$586$	4.23811	−	7.34063i	0.175075	−	0.303238i
$587$	3.90702	+	2.25572i	0.161260	+	0.0931036i	0.578458	−	0.815712i	$-0.303655\pi$
$587$	3.90702	+	2.25572i	0.161260	+	0.0931036i	−0.417198	+	0.908816i	$0.636988\pi$
$588$		−	1.03107i		−	0.0425206i
$589$	−13.8250	+	25.0536i	−0.569651	+	1.03232i
$590$		0			0
$591$	−3.76550	+	6.52204i	−0.154892	+	0.268281i
$592$	2.61150	+	1.50775i	0.107332	+	0.0619682i
$593$	16.9812	−	9.80411i	0.697335	−	0.402606i	−0.109019	−	0.994040i	$-0.534771\pi$
$593$	16.9812	−	9.80411i	0.697335	−	0.402606i	0.806354	+	0.591433i	$0.201438\pi$
$594$	0.163825	−	0.283753i	0.00672181	−	0.0116425i
$595$		0			0
$596$	17.7062			0.725274
$597$			7.96699i			0.326067i
$598$	17.9325	−	10.3533i	0.733315	−	0.423379i
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	0.954852	−	0.297082i	$-0.0960134\pi$
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	−0.734706	+	0.678385i	$0.762680\pi$
$600$		0			0
$601$	15.0244			0.612860			0.306430	−	0.951893i	$-0.400866\pi$
$601$	15.0244			0.612860			0.306430	+	0.951893i	$0.400866\pi$
$602$	−15.3072	+	8.83763i	−0.623876	+	0.360195i
$603$	−7.30547	−	4.21782i	−0.297502	−	0.171763i
$604$	−1.32664	−	2.29781i	−0.0539802	−	0.0934964i
$605$		0			0
$606$	1.12344	−	1.94585i	0.0456365	−	0.0790448i
$607$		−	25.1901i		−	1.02243i	−0.859452	−	0.511217i	$-0.829195\pi$
$607$		−	25.1901i		−	1.02243i	0.859452	−	0.511217i	$-0.170805\pi$
$608$	−0.353343	−	18.2487i	−0.0143300	−	0.740082i
$609$	3.56940			0.144640
$610$		0			0
$611$	19.5283	−	33.8240i	0.790030	−	1.36837i
$612$	3.26923	−	1.88749i	0.132151	−	0.0762973i
$613$	−14.0600	−	8.11753i	−0.567877	−	0.327864i	0.188424	−	0.982088i	$-0.439662\pi$
$613$	−14.0600	−	8.11753i	−0.567877	−	0.327864i	−0.756301	+	0.654224i	$0.772995\pi$
$614$	−4.99336	−	8.64875i	−0.201516	−	0.349035i
$615$		0			0
$616$	−0.780593			−0.0314510
$617$	−5.64498	+	3.25913i	−0.227258	+	0.131208i	−0.609307	−	0.792935i	$-0.708552\pi$
$617$	−5.64498	+	3.25913i	−0.227258	+	0.131208i	0.382048	+	0.924142i	$0.375219\pi$
$618$	−0.774220	+	0.446996i	−0.0311437	+	0.0179808i
$619$	4.39112			0.176494			0.0882470	−	0.996099i	$-0.471874\pi$
$619$	4.39112			0.176494			0.0882470	+	0.996099i	$0.471874\pi$
$620$		0			0
$621$	−5.96433	−	10.3305i	−0.239340	−	0.414550i
$622$	−11.8391	−	6.83532i	−0.474705	−	0.274071i
$623$	15.9618	−	9.21553i	0.639494	−	0.369212i
$624$	1.18341	−	2.04972i	0.0473742	−	0.0820545i
$625$		0			0
$626$	2.24484			0.0897220
$627$	−0.190267	+	0.114819i	−0.00759855	+	0.00458541i
$628$		−	5.77858i		−	0.230590i
$629$	1.41054	−	2.44313i	0.0562420	−	0.0974140i
$630$		0			0
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	0.972124	+	0.234469i	$0.0753350\pi$
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	−0.283006	+	0.959118i	$0.591332\pi$
$632$	3.89855	+	2.25083i	0.155076	+	0.0895331i
$633$	4.21340	−	2.43261i	0.167468	−	0.0966875i
$634$	−25.8680			−1.02735
$635$		0			0
$636$	0.0399667	+	0.0692243i	0.00158478	+	0.00274492i
$637$	10.3957	−	6.00198i	0.411894	−	0.237807i
$638$			0.733141i			0.0290253i
$639$	3.79391			0.150085
$640$		0			0
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	−0.929889	−	0.367839i	$-0.880098\pi$
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	0.783503	+	0.621388i	$0.213431\pi$
$642$	−0.360856	+	0.208340i	−0.0142418	+	0.00822253i
$643$	14.3292	+	8.27294i	0.565087	+	0.326253i	0.755185	−	0.655512i	$-0.227547\pi$
$643$	14.3292	+	8.27294i	0.565087	+	0.326253i	−0.190098	+	0.981765i	$0.560880\pi$
$644$	−4.04397	+	7.00437i	−0.159355	+	0.276011i
$645$		0			0
$646$	7.94520	−	0.153840i	0.312600	−	0.00605276i
$647$		−	29.4822i		−	1.15907i	−0.814949	−	0.579533i	$-0.803235\pi$
$647$		−	29.4822i		−	1.15907i	0.814949	−	0.579533i	$-0.196765\pi$
$648$	20.5270	+	11.8513i	0.806377	+	0.465562i
$649$	−0.463456	+	0.802729i	−0.0181922	+	0.0315099i
$650$		0			0
$651$	2.35708	−	4.08258i	0.0923811	−	0.160009i
$652$	−13.6279	+	7.86810i	−0.533712	+	0.308138i
$653$			6.57421i			0.257269i	0.991692	+	0.128634i	$0.0410594\pi$
$653$			6.57421i			0.257269i	−0.991692	+	0.128634i	$0.958941\pi$
$654$	6.77017			0.264735
$655$		0			0
$656$	9.44037	+	16.3512i	0.368584	+	0.638407i
$657$		−	18.1145i		−	0.706713i
$658$		−	23.0925i		−	0.900241i
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	−0.999887	−	0.0150445i	$-0.995211\pi$
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	0.486915	−	0.873450i	$-0.338122\pi$
$660$		0			0
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	0.826880	−	0.562378i	$-0.190114\pi$
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	−0.900474	+	0.434910i	$0.856780\pi$
$662$	−17.7893	−	10.2706i	−0.691399	−	0.399180i
$663$	−1.91757	−	1.10711i	−0.0744721	−	0.0429965i
$664$	22.8487			0.886703
$665$		0			0
$666$	5.32281			0.206255
$667$	23.1153	+	13.3456i	0.895029	+	0.516745i
$668$	−2.34492	−	1.35384i	−0.0907278	−	0.0523817i
$669$	−3.86815	−	6.69983i	−0.149551	−	0.259031i
$670$		0			0
$671$	−0.616619	−	1.06802i	−0.0238043	−	0.0412303i
$672$			3.00694i			0.115995i
$673$		−	21.0431i		−	0.811150i	−0.914062	−	0.405575i	$-0.867071\pi$
$673$		−	21.0431i		−	0.811150i	0.914062	−	0.405575i	$-0.132929\pi$
$674$	−17.9366	−	31.0670i	−0.690891	−	1.19666i
$675$		0			0
$676$	0.520083			0.0200032
$677$			15.2744i			0.587043i	0.955952	+	0.293522i	$0.0948273\pi$
$677$			15.2744i			0.587043i	−0.955952	+	0.293522i	$0.905173\pi$
$678$	−0.303924	+	0.175471i	−0.0116721	+	0.00673891i
$679$	16.5349	−	28.6394i	0.634553	−	1.09908i
$680$		0			0
$681$	4.82081	−	8.34988i	0.184734	−	0.319968i
$682$	0.838544	+	0.484133i	0.0321095	+	0.0185384i
$683$		−	8.60225i		−	0.329156i	−0.986364	−	0.164578i	$-0.947374\pi$
$683$		−	8.60225i		−	0.329156i	0.986364	−	0.164578i	$-0.0526262\pi$
$684$	−5.11772	−	8.48064i	−0.195681	−	0.324265i
$685$		0			0
$686$	10.8201	−	18.7409i	0.413112	−	0.715530i
$687$	−0.727828	−	0.420212i	−0.0277684	−	0.0160321i
$688$	−13.0835	+	7.55375i	−0.498803	+	0.287984i
$689$	−0.465302	+	0.805926i	−0.0177266	+	0.0307033i
$690$		0			0
$691$	34.1079			1.29753			0.648763	−	0.760990i	$-0.275286\pi$
$691$	34.1079			1.29753			0.648763	+	0.760990i	$0.275286\pi$
$692$		−	8.42231i		−	0.320168i
$693$	−0.629318	+	0.363337i	−0.0239058	+	0.0138020i
$694$	−1.40837	−	2.43937i	−0.0534611	−	0.0925974i
$695$		0			0
$696$	5.78481			0.219273
$697$	15.2970	−	8.83172i	0.579414	−	0.334525i
$698$	−15.7953	−	9.11942i	−0.597861	−	0.345175i
$699$	2.68523	+	4.65096i	0.101565	+	0.175916i
$700$		0			0
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	−0.949372	−	0.314155i	$-0.898279\pi$
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	0.746752	+	0.665102i	$0.231612\pi$
$702$		−	8.56603i		−	0.323304i
$703$	−6.48098	−	3.57633i	−0.244435	−	0.134884i
$704$	−1.09492			−0.0412665
$705$		0			0
$706$	−15.5633	+	26.9564i	−0.585732	+	1.01452i
$707$	−8.84859	+	5.10873i	−0.332785	+	0.192134i
$708$	1.80261	+	1.04074i	0.0677463	+	0.0391134i
$709$	−14.4238	−	24.9828i	−0.541697	−	0.938247i	−0.998807	−	0.0488369i	$-0.984449\pi$
$709$	−14.4238	−	24.9828i	−0.541697	−	0.938247i	0.457109	−	0.889410i	$-0.348885\pi$
$710$		0			0
$711$	4.19070			0.157164
$712$	25.8687	−	14.9353i	0.969470	−	0.559724i
$713$	30.5287	−	17.6257i	1.14331	−	0.660089i
$714$	−1.30917			−0.0489946
$715$		0			0
$716$	−5.80905	−	10.0616i	−0.217095	−	0.376019i
$717$	−0.990386	−	0.571800i	−0.0369866	−	0.0213542i
$718$	16.5262	−	9.54143i	0.616754	−	0.356083i
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	−0.990173	−	0.139851i	$-0.955338\pi$
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	0.616200	+	0.787589i	$0.288671\pi$
$720$		0			0
$721$	4.06535			0.151402
$722$	−0.807171	−	20.8357i	−0.0300398	−	0.775424i
$723$			9.02026i			0.335467i
$724$	2.16117	−	3.74326i	0.0803193	−	0.139117i
$725$		0			0
$726$	−2.28587	−	3.95923i	−0.0848364	−	0.146941i
$727$	−0.675951	−	0.390261i	−0.0250697	−	0.0144740i	0.487413	−	0.873172i	$-0.337941\pi$
$727$	−0.675951	−	0.390261i	−0.0250697	−	0.0144740i	−0.512482	+	0.858698i	$0.671274\pi$
$728$	−17.6736	+	10.2039i	−0.655028	+	0.378180i
$729$	19.5373			0.723604
$730$		0			0
$731$	7.06674	+	12.2399i	0.261373	+	0.452711i
$732$	−2.39834	+	1.38468i	−0.0886452	+	0.0511794i
$733$		−	26.8391i		−	0.991326i	−0.868515	−	0.495663i	$-0.834925\pi$
$733$		−	26.8391i		−	0.991326i	0.868515	−	0.495663i	$-0.165075\pi$
$734$	−28.3192			−1.04528
$735$		0			0
$736$	−11.2426	+	19.4728i	−0.414409	+	0.717777i
$737$	0.343774	−	0.198478i	0.0126631	−	0.00731103i
$738$	28.8623	+	16.6636i	1.06243	+	0.613397i
$739$	10.3265	−	17.8861i	0.379867	−	0.657949i	−0.611175	−	0.791495i	$-0.709303\pi$
$739$	10.3265	−	17.8861i	0.379867	−	0.657949i	0.991043	+	0.133546i	$0.0426363\pi$
$740$		0			0
$741$	−2.80699	+	5.08680i	−0.103117	+	0.186868i
$742$			0.550227i			0.0201995i
$743$	−1.27580	−	0.736585i	−0.0468047	−	0.0270227i	0.476415	−	0.879220i	$-0.341936\pi$
$743$	−1.27580	−	0.736585i	−0.0468047	−	0.0270227i	−0.523220	+	0.852198i	$0.675269\pi$
$744$	3.82003	−	6.61649i	0.140049	−	0.242572i
$745$		0			0
$746$	−14.8518	+	25.7240i	−0.543762	+	0.941824i
$747$	18.4208	−	10.6352i	0.673980	−	0.389123i
$748$			0.177639i			0.00649514i
$749$	1.89482			0.0692352
$750$		0			0
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	0.688411	−	0.725321i	$-0.258308\pi$
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	−0.972352	+	0.233521i	$0.924975\pi$
$752$		−	19.7378i		−	0.719764i
$753$		−	6.52071i		−	0.237628i
$754$	9.58356	+	16.5992i	0.349013	+	0.604508i
$755$		0			0
$756$	1.67293	+	2.89760i	0.0608438	+	0.105385i
$757$	17.4726	+	10.0878i	0.635052	+	0.366647i	0.782706	−	0.622392i	$-0.213839\pi$
$757$	17.4726	+	10.0878i	0.635052	+	0.366647i	−0.147654	+	0.989039i	$0.547172\pi$
$758$	−11.7878	−	6.80568i	−0.428152	−	0.247193i
$759$	0.273767			0.00993713
$760$		0			0
$761$	−15.1076			−0.547649			−0.273825	−	0.961780i	$-0.588289\pi$
$761$	−15.1076			−0.547649			−0.273825	+	0.961780i	$0.588289\pi$
$762$	−6.75607	−	3.90062i	−0.244747	−	0.141305i
$763$	−26.6621	−	15.3934i	−0.965234	−	0.557278i
$764$	−8.14556	−	14.1085i	−0.294696	−	0.510428i
$765$		0			0
$766$	2.94082	+	5.09364i	0.106256	+	0.184041i
$767$			24.2331i			0.875005i
$768$			5.94509i			0.214525i
$769$	25.8290	+	44.7372i	0.931418	+	1.61326i	0.780900	+	0.624656i	$0.214761\pi$
$769$	25.8290	+	44.7372i	0.931418	+	1.61326i	0.150518	+	0.988607i	$0.451906\pi$
$770$		0			0
$771$	7.41327			0.266982
$772$			8.77063i			0.315662i
$773$	26.1157	−	15.0779i	0.939316	−	0.542314i	0.0495699	−	0.998771i	$-0.484215\pi$
$773$	26.1157	−	15.0779i	0.939316	−	0.542314i	0.889746	+	0.456457i	$0.150882\pi$
$774$	−13.3335	+	23.0943i	−0.479262	+	0.830107i
$775$		0			0
$776$	26.7976	−	46.4148i	0.961978	−	1.66620i
$777$	1.05610	+	0.609739i	0.0378874	+	0.0218743i
$778$			9.40431i			0.337161i
$779$	−23.9462	−	39.6816i	−0.857962	−	1.42174i
$780$		0			0
$781$	−0.0892652	+	0.154612i	−0.00319416	+	0.00553244i
$782$	−8.47816	−	4.89487i	−0.303178	−	0.175040i
$783$	9.56245	−	5.52088i	0.341734	−	0.197300i
$784$	3.03318	−	5.25363i	0.108328	−	0.187630i
$785$		0			0
$786$	−1.20161			−0.0428601
$787$		−	43.0969i		−	1.53624i	−0.640307	−	0.768119i	$-0.721193\pi$
$787$		−	43.0969i		−	1.53624i	0.640307	−	0.768119i	$-0.278807\pi$
$788$	13.6796	−	7.89791i	0.487315	−	0.281351i
$789$	−1.67165	−	2.89538i	−0.0595123	−	0.103078i
$790$		0			0
$791$	1.59588			0.0567428
$792$	−1.01991	+	0.588848i	−0.0362411	+	0.0209238i
$793$	−27.9221	−	16.1208i	−0.991542	−	0.572467i
$794$	−5.84086	−	10.1167i	−0.207284	−	0.359027i
$795$		0			0
$796$	8.35514	−	14.4715i	0.296140	−	0.512929i
$797$			50.5062i			1.78902i	0.447048	+	0.894510i	$0.352475\pi$
$797$			50.5062i			1.78902i	−0.447048	+	0.894510i	$0.647525\pi$
$798$	0.0665010	+	3.43450i	0.00235411	+	0.121580i
$799$	−18.4652			−0.653253
$800$		0			0
$801$	13.9036	−	24.0818i	0.491261	−	0.850889i
$802$	−7.27261	+	4.19885i	−0.256805	+	0.148266i
$803$	0.738212	+	0.426207i	0.0260509	+	0.0150405i
$804$	−0.445703	−	0.771981i	−0.0157187	−	0.0272257i
$805$		0			0
$806$	25.3142			0.891656
$807$	0.0947307	−	0.0546928i	0.00333468	−	0.00192528i
$808$	−14.3406	+	8.27955i	−0.504501	+	0.291274i
$809$	30.0872			1.05781			0.528905	−	0.848681i	$-0.322603\pi$
$809$	30.0872			1.05781			0.528905	+	0.848681i	$0.322603\pi$
$810$		0			0
$811$	−11.4755	−	19.8761i	−0.402958	−	0.697944i	0.591123	−	0.806581i	$-0.298685\pi$
$811$	−11.4755	−	19.8761i	−0.402958	−	0.697944i	−0.994081	+	0.108637i	$0.965351\pi$
$812$	−6.48359	−	3.74330i	−0.227529	−	0.131364i
$813$	8.17051	−	4.71725i	0.286552	−	0.165441i
$814$	−0.125238	+	0.216918i	−0.00438958	+	0.00760298i
$815$		0			0
$816$	−1.11899			−0.0391723
$817$	31.7514	−	19.1607i	1.11084	−	0.670347i
$818$		−	19.4123i		−	0.678734i
$819$	−9.49903	+	16.4528i	−0.331923	+	0.574907i
$820$		0			0
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	0.979417	+	0.201846i	$0.0646941\pi$
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	−0.314905	+	0.949123i	$0.601973\pi$
$822$	6.78921	+	3.91975i	0.236801	+	0.136717i
$823$	46.5862	−	26.8966i	1.62389	−	0.937556i	0.638030	−	0.770012i	$-0.279750\pi$
$823$	46.5862	−	26.8966i	1.62389	−	0.937556i	0.985865	−	0.167544i	$-0.0535836\pi$
$824$	6.58858			0.229524
$825$		0			0
$826$	7.16400	+	12.4084i	0.249267	+	0.431744i
$827$	−28.0672	+	16.2046i	−0.975993	+	0.563490i	−0.901058	−	0.433699i	$-0.857208\pi$
$827$	−28.0672	+	16.2046i	−0.975993	+	0.563490i	−0.0749347	+	0.997188i	$0.523875\pi$
$828$			12.2024i			0.424064i
$829$	18.5305			0.643592			0.321796	−	0.946809i	$-0.395713\pi$
$829$	18.5305			0.643592			0.321796	+	0.946809i	$0.395713\pi$
$830$		0			0
$831$	−0.835456	+	1.44705i	−0.0289817	+	0.0501977i
$832$	−24.7904	+	14.3128i	−0.859454	+	0.496206i
$833$	−4.91491	−	2.83763i	−0.170292	−	0.0983179i
$834$	3.78402	−	6.55411i	0.131030	−	0.226950i
$835$		0			0
$836$	0.466021	−	0.00902339i	0.0161177	−	0.000312081i
$837$		−	14.5830i		−	0.504062i
$838$	−1.12844	−	0.651507i	−0.0389814	−	0.0225059i
$839$	0.413304	−	0.715864i	0.0142688	−	0.0247144i	−0.858803	−	0.512306i	$-0.828791\pi$
$839$	0.413304	−	0.715864i	0.0142688	−	0.0247144i	0.873072	+	0.487592i	$0.162125\pi$
$840$		0			0
$841$	2.14661	−	3.71803i	0.0740209	−	0.128208i
$842$	−31.7126	+	18.3093i	−1.09289	+	0.630979i
$843$			12.4123i			0.427504i
$844$	−10.2045			−0.351253
$845$		0			0
$846$	−17.4201	−	30.1725i	−0.598914	−	1.03735i
$847$			20.7895i			0.714337i
$848$			0.470294i			0.0161500i
$849$	0.252053	+	0.436569i	0.00865044	+	0.0149830i
$850$		0			0
$851$	4.55951	+	7.89730i	0.156298	+	0.270716i
$852$	0.347197	+	0.200454i	0.0118948	+	0.00686745i
$853$	6.36475	+	3.67469i	0.217925	+	0.125819i	0.604989	−	0.796234i	$-0.293177\pi$
$853$	6.36475	+	3.67469i	0.217925	+	0.125819i	−0.387064	+	0.922053i	$0.626511\pi$
$854$	−19.0631			−0.652327
$855$		0			0
$856$	3.07087			0.104960
$857$	−39.2739	−	22.6748i	−1.34157	−	0.774556i	−0.354532	−	0.935044i	$-0.615360\pi$
$857$	−39.2739	−	22.6748i	−1.34157	−	0.774556i	−0.987038	+	0.160488i	$0.948693\pi$
$858$	0.170255	+	0.0982968i	0.00581241	+	0.00335580i
$859$	14.8143	+	25.6590i	0.505456	+	0.875475i	0.999980	+	0.00631148i	$0.00200902\pi$
$859$	14.8143	+	25.6590i	0.505456	+	0.875475i	−0.494524	+	0.869164i	$0.664658\pi$
$860$		0			0
$861$	3.81771	+	6.61247i	0.130107	+	0.225352i
$862$			6.77775i			0.230851i
$863$			41.0807i			1.39840i	0.714925	+	0.699201i	$0.246461\pi$
$863$			41.0807i			1.39840i	−0.714925	+	0.699201i	$0.753539\pi$
$864$	4.65090	+	8.05559i	0.158227	+	0.274057i
$865$		0			0
$866$	−20.3632			−0.691970
$867$		−	5.40183i		−	0.183456i
$868$	−8.56295	+	4.94382i	−0.290645	+	0.167804i
$869$	−0.0986010	+	0.170782i	−0.00334481	+	0.00579338i
$870$		0			0
$871$	5.18898	−	8.98758i	0.175822	−	0.304533i
$872$	−43.2104	−	24.9475i	−1.46329	−	0.844831i
$873$		−	49.8931i		−	1.68863i
$874$	−12.4106	+	22.4903i	−0.419794	+	0.760746i
$875$		0			0
$876$	0.957093	−	1.65773i	0.0323372	−	0.0560096i
$877$	47.3116	+	27.3154i	1.59760	+	0.922374i	0.991948	+	0.126643i	$0.0404204\pi$
$877$	47.3116	+	27.3154i	1.59760	+	0.922374i	0.605650	+	0.795731i	$0.292913\pi$
$878$	−0.216039	+	0.124730i	−0.00729097	+	0.00420944i
$879$	1.46492	−	2.53732i	0.0494105	−	0.0855815i
$880$		0			0
$881$	−15.4805			−0.521552			−0.260776	−	0.965399i	$-0.583978\pi$
$881$	−15.4805			−0.521552			−0.260776	+	0.965399i	$0.583978\pi$
$882$		−	10.7080i		−	0.360558i
$883$	−39.2738	+	22.6747i	−1.32167	+	0.763066i	−0.983995	−	0.178197i	$-0.942973\pi$
$883$	−39.2738	+	22.6747i	−1.32167	+	0.763066i	−0.337674	+	0.941263i	$0.609640\pi$
$884$	2.32209	+	4.02198i	0.0781004	+	0.135274i
$885$		0			0
$886$	−38.3913			−1.28978
$887$	26.9680	−	15.5700i	0.905496	−	0.522788i	0.0265165	−	0.999648i	$-0.491559\pi$
$887$	26.9680	−	15.5700i	0.905496	−	0.522788i	0.878979	+	0.476860i	$0.158225\pi$
$888$	1.71158	+	0.988184i	0.0574370	+	0.0331613i
$889$	17.7377	+	30.7227i	0.594905	+	1.03041i
$890$		0			0
$891$	−0.519164	+	0.899218i	−0.0173926	+	0.0301249i
$892$			16.2264i			0.543301i
$893$	0.937963	+	48.4419i	0.0313877	+	1.62105i
$894$	−9.26438			−0.309847
$895$		0			0
$896$	−0.535663	+	0.927795i	−0.0178952	+	0.0309955i
$897$	6.19844	−	3.57867i	0.206960	−	0.119488i
$898$	16.1103	+	9.30127i	0.537606	+	0.310387i
$899$	16.3153	+	28.2589i	0.544145	+	0.942486i
$900$		0			0
$901$	0.439972			0.0146576
$902$	−1.35817	+	0.784142i	−0.0452222	+	0.0261091i
$903$	−5.29100	+	3.05476i	−0.176073	+	0.101656i
$904$	2.58638			0.0860218
$905$		0			0
$906$	0.694135	+	1.20228i	0.0230611	+	0.0399430i
$907$	37.7080	+	21.7707i	1.25207	+	0.722886i	0.971521	−	0.236952i	$-0.0761486\pi$
$907$	37.7080	+	21.7707i	1.25207	+	0.722886i	0.280554	+	0.959838i	$0.409482\pi$
$908$	−17.5134	+	10.1113i	−0.581201	+	0.335557i
$909$	−7.70764	+	13.3500i	−0.255646	+	0.442792i
$910$		0			0
$911$	5.72789			0.189774			0.0948868	−	0.995488i	$-0.469751\pi$
$911$	5.72789			0.189774			0.0948868	+	0.995488i	$0.469751\pi$
$912$	0.0568401	+	2.93556i	0.00188217	+	0.0972060i
$913$			1.00093i			0.0331258i
$914$	0.879275	−	1.52295i	0.0290838	−	0.0503747i
$915$		0			0
$916$	0.881369	+	1.52658i	0.0291212	+	0.0504395i
$917$	4.73216	+	2.73211i	0.156270	+	0.0902223i
$918$	−3.50728	+	2.02493i	−0.115758	+	0.0668327i
$919$	−7.93860			−0.261870			−0.130935	−	0.991391i	$-0.541798\pi$
$919$	−7.93860			−0.261870			−0.130935	+	0.991391i	$0.541798\pi$
$920$		0			0
$921$	−1.72597	−	2.98947i	−0.0568728	−	0.0985065i
$922$	8.30812	−	4.79669i	0.273613	−	0.157971i
$923$			4.66747i			0.153632i
$924$	−0.0767887			−0.00252616
$925$		0			0
$926$	−11.6266	+	20.1378i	−0.382073	+	0.661771i
$927$	5.31174	−	3.06674i	0.174461	−	0.100725i
$928$	−18.0250	−	10.4067i	−0.591700	−	0.341618i
$929$	−14.4784	+	25.0772i	−0.475019	+	0.822758i	−0.999591	−	0.0286089i	$-0.990892\pi$
$929$	−14.4784	+	25.0772i	−0.475019	+	0.822758i	0.524571	+	0.851366i	$0.324226\pi$
$930$		0			0
$931$	−7.19459	+	13.0380i	−0.235793	+	0.427302i
$932$		−	11.2642i		−	0.368972i
$933$	−4.09224	−	2.36265i	−0.133974	−	0.0773498i
$934$	11.2222	−	19.4374i	0.367201	−	0.636011i
$935$		0			0
$936$	−15.3948	+	26.6645i	−0.503193	+	0.871556i
$937$	12.7146	−	7.34080i	0.415369	−	0.239813i	−0.277725	−	0.960661i	$-0.589580\pi$
$937$	12.7146	−	7.34080i	0.415369	−	0.239813i	0.693094	+	0.720847i	$0.256247\pi$
$938$		−	6.13606i		−	0.200349i
$939$	0.775939			0.0253218
$940$		0			0
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	0.867284	−	0.497814i	$-0.165864\pi$
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	−0.864761	+	0.502183i	$0.832530\pi$
$942$			3.02352i			0.0985114i
$943$			57.0961i			1.85931i
$944$	6.12326	+	10.6058i	0.199295	+	0.345189i
$945$		0			0
$946$	−0.627435	−	1.08675i	−0.0203997	−	0.0353332i
$947$	−6.51084	−	3.75904i	−0.211574	−	0.122152i	0.390469	−	0.920616i	$-0.372313\pi$
$947$	−6.51084	−	3.75904i	−0.211574	−	0.122152i	−0.602043	+	0.798464i	$0.705646\pi$
$948$	0.383509	+	0.221419i	0.0124558	+	0.00719135i
$949$	22.2854			0.723415
$950$		0			0
$951$	−8.94137			−0.289944
$952$	8.35576	+	4.82420i	0.270812	+	0.156353i
$953$	−19.6365	−	11.3372i	−0.636090	−	0.367247i	0.147017	−	0.989134i	$-0.453033\pi$
$953$	−19.6365	−	11.3372i	−0.636090	−	0.367247i	−0.783107	+	0.621887i	$0.786366\pi$
$954$	0.415069	+	0.718920i	0.0134384	+	0.0232759i
$955$		0			0
$956$	1.19931	+	2.07727i	0.0387886	+	0.0671838i
$957$			0.253413i			0.00819167i
$958$			25.8437i			0.834973i
$959$	−17.8247	−	30.8733i	−0.575590	−	0.996952i
$960$		0			0
$961$	12.0955			0.390177
$962$			6.54840i			0.211129i
$963$	2.47575	−	1.42937i	0.0797799	−	0.0460609i
$964$	9.45972	−	16.3847i	0.304677	−	0.527716i
$965$		0			0
$966$	2.11592	−	3.66488i	0.0680786	−	0.117916i
$967$	24.9714	+	14.4172i	0.803025	+	0.463627i	0.844528	−	0.535512i	$-0.179881\pi$
$967$	24.9714	+	14.4172i	0.803025	+	0.463627i	−0.0415030	+	0.999138i	$0.513215\pi$
$968$			33.6929i			1.08293i
$969$	2.74629	−	0.0531755i	0.0882236	−	0.00170824i
$970$		0			0
$971$	−13.1831	+	22.8338i	−0.423065	+	0.732770i	−0.996238	−	0.0866647i	$-0.972379\pi$
$971$	−13.1831	+	22.8338i	−0.423065	+	0.732770i	0.573173	+	0.819435i	$0.305712\pi$
$972$	6.61120	+	3.81698i	0.212054	+	0.122430i
$973$	−29.8043	+	17.2075i	−0.955481	+	0.551647i
$974$	19.7754	−	34.2520i	0.633645	−	1.09750i
$975$		0			0
$976$	−16.2938			−0.521551
$977$		−	4.59218i		−	0.146917i	−0.997298	−	0.0734585i	$-0.976596\pi$
$977$		−	4.59218i		−	0.146917i	0.997298	−	0.0734585i	$-0.0234036\pi$
$978$	7.13052	−	4.11681i	0.228009	−	0.131641i
$979$	0.654264	+	1.13322i	0.0209104	+	0.0362178i
$980$		0			0
$981$	−46.4486			−1.48299
$982$	−19.0647	+	11.0070i	−0.608379	+	0.351248i
$983$	−5.98833	−	3.45737i	−0.190998	−	0.110273i	0.401452	−	0.915880i	$-0.368506\pi$
$983$	−5.98833	−	3.45737i	−0.190998	−	0.110273i	−0.592450	+	0.805607i	$0.701839\pi$
$984$	6.18724	+	10.7166i	0.197242	+	0.341633i
$985$		0			0
$986$	4.53094	−	7.84781i	0.144294	−	0.249925i
$987$		−	7.98203i		−	0.254071i
$988$	10.4333	−	6.29609i	0.331929	−	0.200305i
$989$	−45.6857			−1.45272
$990$		0			0
$991$	19.0035	−	32.9150i	0.603666	−	1.04558i	−0.388594	−	0.921409i	$-0.627039\pi$
$991$	19.0035	−	32.9150i	0.603666	−	1.04558i	0.992261	−	0.124172i	$-0.0396274\pi$
$992$	−23.8058	+	13.7443i	−0.755835	+	0.436382i
$993$	−6.14893	−	3.55009i	−0.195130	−	0.112659i
$994$	1.37984	+	2.38996i	0.0437659	+	0.0758048i
$995$		0			0
$996$	2.24768			0.0712205
$997$	−14.0526	+	8.11326i	−0.445050	+	0.256950i	−0.705737	−	0.708474i	$-0.749384\pi$
$997$	−14.0526	+	8.11326i	−0.445050	+	0.256950i	0.260688	+	0.965423i	$0.416051\pi$
$998$	−35.0443	+	20.2329i	−1.10931	+	0.640460i
$999$	3.77239			0.119353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.c.49.5		16
5.2	odd	4		95.2.e.c.11.2	✓	8
5.3	odd	4		475.2.e.e.201.3		8
5.4	even	2	inner	475.2.j.c.49.4		16
15.2	even	4		855.2.k.h.676.3		8
19.7	even	3	inner	475.2.j.c.349.4		16
20.7	even	4		1520.2.q.o.961.2		8
95.7	odd	12		95.2.e.c.26.2	yes	8
95.8	even	12		9025.2.a.bp.1.3		4
95.27	even	12		1805.2.a.i.1.2		4
95.64	even	6	inner	475.2.j.c.349.5		16
95.68	odd	12		9025.2.a.bg.1.2		4
95.83	odd	12		475.2.e.e.26.3		8
95.87	odd	12		1805.2.a.o.1.3		4
285.197	even	12		855.2.k.h.406.3		8
380.7	even	12		1520.2.q.o.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	5.2	odd	4
95.2.e.c.26.2	yes	8	95.7	odd	12
475.2.e.e.26.3		8	95.83	odd	12
475.2.e.e.201.3		8	5.3	odd	4
475.2.j.c.49.4		16	5.4	even	2	inner
475.2.j.c.49.5		16	1.1	even	1	trivial
475.2.j.c.349.4		16	19.7	even	3	inner
475.2.j.c.349.5		16	95.64	even	6	inner
855.2.k.h.406.3		8	285.197	even	12
855.2.k.h.676.3		8	15.2	even	4
1520.2.q.o.881.2		8	380.7	even	12
1520.2.q.o.961.2		8	20.7	even	4
1805.2.a.i.1.2		4	95.27	even	12
1805.2.a.o.1.3		4	95.87	odd	12
9025.2.a.bg.1.2		4	95.68	odd	12
9025.2.a.bp.1.3		4	95.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.950409 + 0.548719i) q^{2} +(0.328513 + 0.189667i) q^{3} +(-0.397815 - 0.689035i) q^{4} +(0.208148 + 0.360522i) q^{6} -1.89307i q^{7} -3.06803i q^{8} +(-1.42805 - 2.47346i) q^{9} +0.134400 q^{11} -0.301809i q^{12} +(3.04298 - 1.75687i) q^{13} +(1.03876 - 1.79919i) q^{14} +(0.887858 - 1.53781i) q^{16} +(-1.43867 - 0.830615i) q^{17} -3.13440i q^{18} +(-2.10596 + 3.81640i) q^{19} +(0.359052 - 0.621897i) q^{21} +(0.127735 + 0.0737478i) q^{22} +(4.65042 - 2.68492i) q^{23} +(0.581904 - 1.00789i) q^{24} +3.85611 q^{26} -2.22142i q^{27} +(-1.30439 + 0.753090i) q^{28} +(2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(-3.62633 + 2.09366i) q^{32} +(0.0441521 + 0.0254912i) q^{33} +(-0.911548 - 1.57885i) q^{34} +(-1.13620 + 1.96796i) q^{36} +1.69819i q^{37} +(-4.09566 + 2.47156i) q^{38} +1.33288 q^{39} +(-5.31637 + 9.20823i) q^{41} +(0.682493 - 0.394038i) q^{42} +(-7.36801 - 4.25392i) q^{43} +(-0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(9.62623 - 5.55771i) q^{47} +(0.583345 - 0.336794i) q^{48} +3.41630 q^{49} +(-0.315080 - 0.545735i) q^{51} +(-2.42109 - 1.39781i) q^{52} +(-0.229365 + 0.132424i) q^{53} +(1.21894 - 2.11126i) q^{54} -5.80799 q^{56} +(-1.41568 + 0.854305i) q^{57} +5.45492i q^{58} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(6.23917 + 3.60219i) q^{62} +(-4.68243 + 2.70340i) q^{63} -8.14676 q^{64} +(0.0279750 + 0.0484542i) q^{66} +(2.55784 - 1.47677i) q^{67} +1.32172i q^{68} +2.03696 q^{69} +(-0.664176 + 1.15039i) q^{71} +(-7.58865 + 4.38131i) q^{72} +(5.49266 + 3.17119i) q^{73} +(-0.931830 + 1.61398i) q^{74} +(3.46742 - 0.0671384i) q^{76} -0.254428i q^{77} +(1.26678 + 0.731376i) q^{78} +(-0.733639 + 1.27070i) q^{79} +(-3.86283 + 6.69062i) q^{81} +(-10.1055 + 5.83439i) q^{82} +7.44736i q^{83} -0.571345 q^{84} +(-4.66842 - 8.08593i) q^{86} +1.88551i q^{87} -0.412343i q^{88} +(4.86804 + 8.43169i) q^{89} +(-3.32587 - 5.76057i) q^{91} +(-3.70001 - 2.13620i) q^{92} +(2.15659 + 1.24511i) q^{93} +12.1985 q^{94} -1.58839 q^{96} +(15.1285 + 8.73447i) q^{97} +(3.24688 + 1.87459i) q^{98} +(-0.191930 - 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49}+ \cdots + 76 q^{99}+O(q^{100}) \) 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more