LMFDB - Embedded newform 475.2.j.c.349.5

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			349.5
Root			$-1.19454 - 0.689667i$ of defining polynomial
Character	$\chi$	$=$	475.349
Dual form			475.2.j.c.49.5

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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	−0.124809	−	0.992181i	$-0.539832\pi$
$2$	0.950409	−	0.548719i	0.672041	−	0.388003i	0.796850	+	0.604178i	$0.206498\pi$
$3$	0.328513	−	0.189667i	0.189667	−	0.109504i	−0.402160	−	0.915570i	$-0.631740\pi$
$3$	0.328513	−	0.189667i	0.189667	−	0.109504i	0.591827	+	0.806065i	$0.298407\pi$
$4$	−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	$0.116458\pi$
$7$			1.89307i			0.715512i	−0.933815	+	0.357756i	$0.883542\pi$
$8$			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	0.858612	−	0.512626i	$-0.171327\pi$
$13$	3.04298	+	1.75687i	0.843972	+	0.487267i	−0.0146407	+	0.999893i	$0.504660\pi$
$14$	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	−0.664213	−	0.747543i	$-0.731233\pi$
$17$	−1.43867	+	0.830615i	−0.348928	+	0.201454i	0.315285	+	0.948997i	$0.397900\pi$
$18$			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	0.899138	−	0.437664i	$-0.144194\pi$
$23$	4.65042	+	2.68492i	0.969679	+	0.559844i	0.0705407	+	0.997509i	$0.477528\pi$
$24$	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	−0.537528	−	0.843246i	$-0.680642\pi$
$29$	2.48530	−	4.30466i	0.461508	−	0.799355i	0.999036	+	0.0438905i	$0.0139753\pi$
$30$		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	$-0.955421\pi$
$37$		−	1.69819i		−	0.279181i	0.990209	−	0.139590i	$-0.0445786\pi$
$38$	−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	−0.897818	−	0.440367i	$-0.854848\pi$
$41$	−5.31637	−	9.20823i	−0.830278	−	1.43808i	0.0675398	−	0.997717i	$-0.478485\pi$
$42$	0.682493	+	0.394038i	0.105311	+	0.0608013i
$43$	−7.36801	+	4.25392i	−1.12361	+	0.648717i	−0.942320	−	0.334713i	$-0.891361\pi$
$43$	−7.36801	+	4.25392i	−1.12361	+	0.648717i	−0.181290	+	0.983430i	$0.558027\pi$
$44$	−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	0.994813	−	0.101718i	$-0.0324339\pi$
$47$	9.62623	+	5.55771i	1.40413	+	0.810675i	0.409316	+	0.912392i	$0.365767\pi$
$48$	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	0.484164	−	0.874977i	$-0.339124\pi$
$53$	−0.229365	−	0.132424i	−0.0315057	−	0.0181898i	−0.515670	+	0.856787i	$0.672457\pi$
$54$	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	0.549382	−	0.835571i	$-0.314863\pi$
$59$	−3.44833	−	5.97269i	−0.448935	−	0.777578i	−0.998317	+	0.0579932i	$0.981530\pi$
$60$		0			0
$61$	−4.58794	+	7.94655i	−0.587426	+	1.01745i	0.407142	+	0.913365i	$0.366525\pi$
$61$	−4.58794	+	7.94655i	−0.587426	+	1.01745i	−0.994568	+	0.104087i	$0.966808\pi$
$62$	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	0.648040	−	0.761606i	$-0.275589\pi$
$67$	2.55784	+	1.47677i	0.312490	+	0.180416i	−0.335550	+	0.942022i	$0.608922\pi$
$68$		−	1.32172i		−	0.160282i
$69$	2.03696			0.245221
$70$		0			0
$71$	−0.664176	−	1.15039i	−0.0788232	−	0.136526i	0.823919	−	0.566707i	$-0.191783\pi$
$71$	−0.664176	−	1.15039i	−0.0788232	−	0.136526i	−0.902742	+	0.430181i	$0.858450\pi$
$72$	−7.58865	−	4.38131i	−0.894331	−	0.516342i
$73$	5.49266	−	3.17119i	0.642867	−	0.371159i	−0.142851	−	0.989744i	$-0.545627\pi$
$73$	5.49266	−	3.17119i	0.642867	−	0.371159i	0.785718	+	0.618585i	$0.212294\pi$
$74$	−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	0.821800	−	0.569776i	$-0.192970\pi$
$79$	−0.733639	−	1.27070i	−0.0825408	−	0.142965i	−0.904341	+	0.426811i	$0.859637\pi$
$80$		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	$-0.865973\pi$
$83$		−	7.44736i		−	0.817454i	0.912657	−	0.408727i	$-0.134027\pi$
$84$	−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	−0.483816	−	0.875170i	$-0.660750\pi$
$89$	4.86804	−	8.43169i	0.516011	−	0.893757i	0.999827	−	0.0185878i	$-0.00591701\pi$
$90$		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	0.537008	−	0.843577i	$-0.319555\pi$
$97$	15.1285	−	8.73447i	1.53607	−	0.886851i	0.999063	−	0.0432737i	$-0.0137788\pi$
$98$	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	−0.968481	−	0.249086i	$-0.919870\pi$
$101$	−2.69865	+	4.67420i	−0.268526	+	0.465101i	0.699955	+	0.714187i	$0.253203\pi$
$102$			0.691562i			0.0684749i
$103$		−	2.14750i		−	0.211599i	−0.994387	−	0.105800i	$-0.966260\pi$
$103$		−	2.14750i		−	0.211599i	0.994387	−	0.105800i	$-0.0337402\pi$
$104$	−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	$-0.984594\pi$
$107$		−	1.00093i		−	0.0967631i	0.998829	−	0.0483815i	$-0.0154063\pi$
$108$	−1.53064	−	0.883713i	−0.147285	−	0.0850353i
$109$	8.13145	+	14.0841i	0.778852	+	1.34901i	0.932604	+	0.360902i	$0.117531\pi$
$109$	8.13145	+	14.0841i	0.778852	+	1.34901i	−0.153752	+	0.988109i	$0.549136\pi$
$110$		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	$-0.987375\pi$
$113$		−	0.843010i		−	0.0793037i	0.999214	−	0.0396519i	$-0.0126249\pi$
$114$	−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	−0.442239	−	0.896897i	$-0.645816\pi$
$127$	−16.2290	−	9.36984i	−1.44009	−	0.831439i	−0.997855	+	0.0654584i	$0.979149\pi$
$128$	−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	0.796066	−	0.605210i	$-0.206911\pi$
$131$	−1.44322	−	2.49973i	−0.126095	−	0.218402i	−0.922160	+	0.386808i	$0.873578\pi$
$132$			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	0.993683	−	0.112220i	$-0.0357961\pi$
$137$	16.3086	+	9.41579i	1.39334	+	0.804445i	0.399656	+	0.916665i	$0.369129\pi$
$138$	1.93595	−	1.11772i	0.164799	−	0.0951466i
$139$	−9.08974	+	15.7439i	−0.770982	+	1.33538i	0.166043	+	0.986118i	$0.446901\pi$
$139$	−9.08974	+	15.7439i	−0.770982	+	1.33538i	−0.937025	+	0.349262i	$0.886432\pi$
$140$		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	−0.811842	−	0.583877i	$-0.801535\pi$
$149$	−11.1272	−	19.2728i	−0.911573	−	1.57889i	−0.0997308	−	0.995014i	$-0.531798\pi$
$150$		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	−0.227548	−	0.973767i	$-0.573071\pi$
$157$	6.28986	−	3.63145i	0.501986	−	0.289822i	0.729533	+	0.683945i	$0.239737\pi$
$158$	−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	$0.282038\pi$
$163$			19.7783i			1.54916i	−0.632478	+	0.774578i	$0.717962\pi$
$164$	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	0.609679	−	0.792648i	$-0.291298\pi$
$167$	2.94726	+	1.70160i	0.228066	+	0.131674i	−0.381614	+	0.924322i	$0.624632\pi$
$168$	−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	−0.109234	−	0.994016i	$-0.534840\pi$
$173$	9.16750	−	5.29286i	0.696992	−	0.402409i	0.806226	+	0.591607i	$0.201506\pi$
$174$	−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	−0.747240	−	0.664555i	$-0.768621\pi$
$181$	2.71630	−	4.70478i	0.201901	−	0.349703i	0.949141	+	0.314851i	$0.101955\pi$
$182$			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	−0.802556	−	0.596577i	$-0.796527\pi$
$193$	−9.54664	+	5.51176i	−0.687182	+	0.396745i	0.115373	+	0.993322i	$0.463194\pi$
$194$	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	$-0.749939\pi$
$197$		−	19.8532i		−	1.41448i	0.706971	−	0.707242i	$-0.250061\pi$
$198$			0.421263i			0.0299379i
$199$	10.5013	−	18.1888i	0.744417	−	1.28937i	−0.206050	−	0.978542i	$-0.566061\pi$
$199$	10.5013	−	18.1888i	0.744417	−	1.28937i	0.950467	−	0.310826i	$-0.100606\pi$
$200$		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	0.997799	−	0.0663046i	$-0.0211209\pi$
$211$	6.41284	+	11.1074i	0.441478	+	0.764663i	−0.556321	+	0.830967i	$0.687788\pi$
$212$	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	−0.956647	−	0.291249i	$-0.905929\pi$
$223$	−17.6621	+	10.1972i	−1.18274	+	0.682856i	−0.226095	+	0.974105i	$0.572596\pi$
$224$	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	$0.319509\pi$
$227$			25.4172i			1.68700i	−0.537129	+	0.843500i	$0.680491\pi$
$228$	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	−0.0413652	−	0.999144i	$-0.513171\pi$
$233$	12.2609	−	7.07882i	0.803236	−	0.463749i	0.844602	+	0.535395i	$0.179837\pi$
$234$	−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	−0.173904	−	0.984763i	$-0.555638\pi$
$241$	11.8896	−	20.5934i	0.765877	−	1.32654i	0.939781	−	0.341776i	$-0.111028\pi$
$242$	−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	0.456250	+	0.889851i	$0.349192\pi$
$251$	−8.59495	+	14.8869i	−0.542509	+	0.939653i	−0.998759	+	0.0498012i	$0.984141\pi$
$252$	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	0.924248	−	0.381794i	$-0.124693\pi$
$257$	16.9246	+	9.77143i	1.05573	+	0.609525i	0.131481	+	0.991319i	$0.458027\pi$
$258$			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	−0.716515	−	0.697571i	$-0.754264\pi$
$263$	−7.63280	+	4.40680i	−0.470659	+	0.271735i	0.245857	+	0.969306i	$0.420931\pi$
$264$	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	0.870387	−	0.492368i	$-0.163868\pi$
$269$	0.144181	+	0.249729i	0.00879088	+	0.0152263i	−0.861596	+	0.507594i	$0.830535\pi$
$270$		0			0
$271$	12.4356	+	21.5391i	0.755409	+	1.30841i	0.945171	+	0.326577i	$0.105895\pi$
$271$	12.4356	+	21.5391i	0.755409	+	1.30841i	−0.189761	+	0.981830i	$0.560771\pi$
$272$	−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	$-0.957754\pi$
$277$		−	4.40486i		−	0.264662i	0.991206	−	0.132331i	$-0.0422463\pi$
$278$			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	0.299398	−	0.954128i	$-0.403214\pi$
$281$	16.3607	−	28.3376i	0.975998	−	1.69048i	0.676600	−	0.736350i	$-0.263452\pi$
$282$	4.00736	−	2.31365i	0.238635	−	0.137776i
$283$	1.15088	−	0.664463i	0.0684129	−	0.0394982i	−0.465403	−	0.885099i	$-0.654091\pi$
$283$	1.15088	−	0.664463i	0.0684129	−	0.0394982i	0.533816	+	0.845600i	$0.320757\pi$
$284$	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	$0.0724375\pi$
$293$			7.72365i			0.451220i	−0.974218	+	0.225610i	$0.927562\pi$
$294$	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	−0.707739	−	0.706474i	$-0.750285\pi$
$307$	−7.88085	+	4.55001i	−0.449784	+	0.259683i	0.257955	+	0.966157i	$0.416951\pi$
$308$	−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	0.549229	−	0.835672i	$-0.314922\pi$
$313$	1.77148	+	1.02277i	0.100130	+	0.0578101i	−0.449099	+	0.893482i	$0.648255\pi$
$314$	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	−0.198487	−	0.980103i	$-0.563603\pi$
$317$	−20.4133	−	11.7856i	−1.14653	−	0.661947i	−0.948038	+	0.318157i	$0.896936\pi$
$318$	−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	−0.543365	+	0.839497i	$0.682850\pi$
$337$	−28.3087	+	16.3440i	−1.54207	+	0.890316i	−0.998708	+	0.0508197i	$0.983817\pi$
$338$	−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	−0.558475	−	0.829521i	$-0.688613\pi$
$347$	−2.22279	+	1.28333i	−0.119326	+	0.0688927i	0.439149	+	0.898414i	$0.355280\pi$
$348$	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	$-0.727732\pi$
$353$		−	28.3629i		−	1.50961i	0.655951	−	0.754803i	$-0.272268\pi$
$354$	−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	0.998901	−	0.0468628i	$-0.0149224\pi$
$359$	8.69427	+	15.0589i	0.458866	+	0.794780i	−0.540035	+	0.841643i	$0.681589\pi$
$360$		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	−0.213676	−	0.976905i	$-0.568544\pi$
$367$	−22.3477	−	12.9024i	−1.16654	−	0.673501i	−0.952862	+	0.303404i	$0.901877\pi$
$368$			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	$-0.752862\pi$
$373$		−	27.0663i		−	1.40144i	0.713437	−	0.700719i	$-0.247138\pi$
$374$	−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	−0.376709	−	0.926332i	$-0.622944\pi$
$383$	4.64139	−	2.67971i	0.237164	−	0.136927i	0.613873	+	0.789405i	$0.289611\pi$
$384$	−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	−0.736722	−	0.676195i	$-0.763628\pi$
$389$	4.28467	−	7.42126i	0.217241	−	0.376273i	0.953964	+	0.299923i	$0.0969608\pi$
$390$		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	−0.713162	−	0.700999i	$-0.752738\pi$
$397$	−9.21844	+	5.32227i	−0.462660	+	0.267117i	0.250502	+	0.968116i	$0.419404\pi$
$398$		−	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	0.754539	−	0.656255i	$-0.227860\pi$
$401$	−3.82604	−	6.62690i	−0.191063	−	0.330932i	−0.945603	+	0.325323i	$0.894527\pi$
$402$	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	−0.997482	−	0.0709173i	$-0.977407\pi$
$409$	−8.84435	+	15.3189i	−0.437325	+	0.757469i	0.560157	+	0.828386i	$0.310741\pi$
$410$		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	−0.910677	−	0.413120i	$-0.864439\pi$
$421$	−16.6836	−	28.8969i	−0.813111	−	1.40835i	0.0975661	−	0.995229i	$-0.468894\pi$
$422$	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	−0.782020	−	0.623253i	$-0.785811\pi$
$431$	3.08799	−	5.34855i	0.148743	−	0.257631i	0.930763	+	0.365623i	$0.119144\pi$
$432$	−3.41613	+	1.97230i	−0.164359	+	0.0948925i
$433$	−16.0693	−	9.27761i	−0.772241	−	0.445854i	0.0614325	−	0.998111i	$-0.480433\pi$
$433$	−16.0693	−	9.27761i	−0.772241	−	0.445854i	−0.833673	+	0.552258i	$0.813766\pi$
$434$	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	0.863300	−	0.504690i	$-0.168393\pi$
$439$	−0.113656	−	0.196858i	−0.00542450	−	0.00939550i	−0.868725	+	0.495295i	$0.835060\pi$
$440$		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	−0.441593	−	0.897216i	$-0.645586\pi$
$443$	−30.2959	−	17.4913i	−1.43940	−	0.831038i	−0.997808	+	0.0661770i	$0.978920\pi$
$444$	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	$0.0119327\pi$
$457$			1.60241i			0.0749578i	−0.999297	+	0.0374789i	$0.988067\pi$
$458$	−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	0.949676	−	0.313234i	$-0.101413\pi$
$461$	4.37081	+	7.57046i	0.203569	+	0.352592i	−0.746107	+	0.665826i	$0.768079\pi$
$462$	0.0917270	+	0.0529586i	0.00426753	+	0.00246386i
$463$		−	21.1886i		−	0.984718i	−0.870392	−	0.492359i	$-0.836135\pi$
$463$		−	21.1886i		−	0.984718i	0.870392	−	0.492359i	$-0.163865\pi$
$464$	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	$0.156899\pi$
$467$			20.4516i			0.946388i	−0.880958	+	0.473194i	$0.843101\pi$
$468$		−	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	−0.461018	−	0.887391i	$-0.652516\pi$
$479$	11.7746	−	20.3942i	0.537994	−	0.931833i	0.999012	−	0.0444419i	$-0.0141510\pi$
$480$		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	$0.304114\pi$
$487$			36.0392i			1.63309i	−0.577280	+	0.816546i	$0.695886\pi$
$488$	−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	0.545913	−	0.837842i	$-0.316183\pi$
$491$	−10.0297	−	17.3720i	−0.452635	−	0.783988i	−0.998549	+	0.0538541i	$0.982849\pi$
$492$	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	−0.901668	−	0.432429i	$-0.857657\pi$
$499$	−18.4364	−	31.9328i	−0.825328	−	1.42951i	0.0763399	−	0.997082i	$-0.475677\pi$
$500$		0			0
$501$	1.29095			0.0576753
$502$			18.8649i			0.841980i
$503$	−18.7483	−	10.8244i	−0.835947	−	0.482634i	0.0199377	−	0.999801i	$-0.493653\pi$
$503$	−18.7483	−	10.8244i	−0.835947	−	0.482634i	−0.855884	+	0.517167i	$0.826987\pi$
$504$	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	0.106351	+	0.994329i	$0.466083\pi$
$509$	−18.2279	+	31.5717i	−0.807938	+	1.39939i	−0.914289	+	0.405062i	$0.867250\pi$
$510$		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	0.510056	−	0.860141i	$-0.329625\pi$
$523$	0.461515	+	0.266456i	0.0201806	+	0.0116513i	−0.489876	+	0.871792i	$0.662958\pi$
$524$	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	−0.914893	−	0.403696i	$-0.867725\pi$
$541$	−2.50820	+	4.34433i	−0.107836	+	0.186777i	0.807057	+	0.590473i	$0.201059\pi$
$542$	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	0.0186154	−	0.999827i	$-0.494074\pi$
$547$	−19.5981	−	11.3149i	−0.837952	−	0.483792i	−0.856568	+	0.516035i	$0.827408\pi$
$548$	−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	−0.314381	−	0.949297i	$-0.601797\pi$
$557$	−30.5321	−	17.6277i	−1.29369	−	0.746910i	−0.979306	+	0.202387i	$0.935130\pi$
$558$			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	$0.173698\pi$
$563$			24.6295i			1.03801i	−0.854771	+	0.519005i	$0.826302\pi$
$564$	−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	$0.0834331\pi$
$577$			12.4486i			0.518244i	−0.965845	+	0.259122i	$0.916567\pi$
$578$			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	−0.417198	−	0.908816i	$-0.636988\pi$
$587$	3.90702	−	2.25572i	0.161260	−	0.0931036i	0.578458	+	0.815712i	$0.303655\pi$
$588$			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	0.806354	−	0.591433i	$-0.201438\pi$
$593$	16.9812	+	9.80411i	0.697335	+	0.402606i	−0.109019	+	0.994040i	$0.534771\pi$
$594$	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	−0.734706	−	0.678385i	$-0.762680\pi$
$599$	5.38795	−	9.33221i	0.220146	−	0.381304i	0.954852	+	0.297082i	$0.0960134\pi$
$600$		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	$0.170805\pi$
$607$			25.1901i			1.02243i	−0.859452	+	0.511217i	$0.829195\pi$
$608$	−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	−0.756301	−	0.654224i	$-0.772995\pi$
$613$	−14.0600	+	8.11753i	−0.567877	+	0.327864i	0.188424	+	0.982088i	$0.439662\pi$
$614$	−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	0.382048	−	0.924142i	$-0.375219\pi$
$617$	−5.64498	−	3.25913i	−0.227258	−	0.131208i	−0.609307	+	0.792935i	$0.708552\pi$
$618$	−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	−0.283006	−	0.959118i	$-0.591332\pi$
$631$	17.3104	−	29.9826i	0.689118	−	1.19359i	0.972124	−	0.234469i	$-0.0753350\pi$
$632$	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	0.783503	−	0.621388i	$-0.213431\pi$
$641$	−3.70621	−	6.41934i	−0.146386	−	0.253549i	−0.929889	+	0.367839i	$0.880098\pi$
$642$	−0.360856	−	0.208340i	−0.0142418	−	0.00822253i
$643$	14.3292	−	8.27294i	0.565087	−	0.326253i	−0.190098	−	0.981765i	$-0.560880\pi$
$643$	14.3292	−	8.27294i	0.565087	−	0.326253i	0.755185	+	0.655512i	$0.227547\pi$
$644$	−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	$0.196765\pi$
$647$			29.4822i			1.15907i	−0.814949	+	0.579533i	$0.803235\pi$
$648$	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	$-0.958941\pi$
$653$		−	6.57421i		−	0.257269i	0.991692	−	0.128634i	$-0.0410594\pi$
$654$	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	0.486915	+	0.873450i	$0.338122\pi$
$659$	−13.1685	+	22.8085i	−0.512972	+	0.888494i	−0.999887	+	0.0150445i	$0.995211\pi$
$660$		0			0
$661$	−1.89210	+	3.27721i	−0.0735941	+	0.127469i	−0.900474	−	0.434910i	$-0.856780\pi$
$661$	−1.89210	+	3.27721i	−0.0735941	+	0.127469i	0.826880	+	0.562378i	$0.190114\pi$
$662$	−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	$0.132929\pi$
$673$			21.0431i			0.811150i	−0.914062	+	0.405575i	$0.867071\pi$
$674$	−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	$-0.905173\pi$
$677$		−	15.2744i		−	0.587043i	0.955952	−	0.293522i	$-0.0948273\pi$
$678$	−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	$0.0526262\pi$
$683$			8.60225i			0.329156i	−0.986364	+	0.164578i	$0.947374\pi$
$684$	−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	0.746752	−	0.665102i	$-0.231612\pi$
$701$	−5.36463	−	9.29181i	−0.202619	−	0.350947i	−0.949372	+	0.314155i	$0.898279\pi$
$702$			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	0.457109	+	0.889410i	$0.348885\pi$
$709$	−14.4238	+	24.9828i	−0.541697	+	0.938247i	−0.998807	+	0.0488369i	$0.984449\pi$
$710$		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	0.616200	−	0.787589i	$-0.288671\pi$
$719$	−10.0278	−	17.3686i	−0.373972	−	0.647739i	−0.990173	+	0.139851i	$0.955338\pi$
$720$		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	−0.512482	−	0.858698i	$-0.671274\pi$
$727$	−0.675951	+	0.390261i	−0.0250697	+	0.0144740i	0.487413	+	0.873172i	$0.337941\pi$
$728$	−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	$0.165075\pi$
$733$			26.8391i			0.991326i	−0.868515	+	0.495663i	$0.834925\pi$
$734$	−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	0.991043	−	0.133546i	$-0.0426363\pi$
$739$	10.3265	+	17.8861i	0.379867	+	0.657949i	−0.611175	+	0.791495i	$0.709303\pi$
$740$		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	−0.523220	−	0.852198i	$-0.675269\pi$
$743$	−1.27580	+	0.736585i	−0.0468047	+	0.0270227i	0.476415	+	0.879220i	$0.341936\pi$
$744$	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	−0.972352	−	0.233521i	$-0.924975\pi$
$751$	−7.78121	+	13.4775i	−0.283940	+	0.491799i	0.688411	+	0.725321i	$0.258308\pi$
$752$			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	−0.147654	−	0.989039i	$-0.547172\pi$
$757$	17.4726	−	10.0878i	0.635052	−	0.366647i	0.782706	+	0.622392i	$0.213839\pi$
$758$	−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	0.150518	−	0.988607i	$-0.451906\pi$
$769$	25.8290	−	44.7372i	0.931418	−	1.61326i	0.780900	−	0.624656i	$-0.214761\pi$
$770$		0			0
$771$	7.41327			0.266982
$772$		−	8.77063i		−	0.315662i
$773$	26.1157	+	15.0779i	0.939316	+	0.542314i	0.889746	−	0.456457i	$-0.150882\pi$
$773$	26.1157	+	15.0779i	0.939316	+	0.542314i	0.0495699	+	0.998771i	$0.484215\pi$
$774$	−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	$0.278807\pi$
$787$			43.0969i			1.53624i	−0.640307	+	0.768119i	$0.721193\pi$
$788$	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	$-0.647525\pi$
$797$		−	50.5062i		−	1.78902i	0.447048	−	0.894510i	$-0.352475\pi$
$798$	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	−0.994081	−	0.108637i	$-0.965351\pi$
$811$	−11.4755	+	19.8761i	−0.402958	+	0.697944i	0.591123	+	0.806581i	$0.298685\pi$
$812$	−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	−0.314905	−	0.949123i	$-0.601973\pi$
$821$	19.0403	−	32.9788i	0.664513	−	1.15097i	0.979417	−	0.201846i	$-0.0646941\pi$
$822$	6.78921	−	3.91975i	0.236801	−	0.136717i
$823$	46.5862	+	26.8966i	1.62389	+	0.937556i	0.985865	+	0.167544i	$0.0535836\pi$
$823$	46.5862	+	26.8966i	1.62389	+	0.937556i	0.638030	+	0.770012i	$0.279750\pi$
$824$	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	−0.0749347	−	0.997188i	$-0.523875\pi$
$827$	−28.0672	−	16.2046i	−0.975993	−	0.563490i	−0.901058	+	0.433699i	$0.857208\pi$
$828$		−	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	0.873072	−	0.487592i	$-0.162125\pi$
$839$	0.413304	+	0.715864i	0.0142688	+	0.0247144i	−0.858803	+	0.512306i	$0.828791\pi$
$840$		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	−0.387064	−	0.922053i	$-0.626511\pi$
$853$	6.36475	−	3.67469i	0.217925	−	0.125819i	0.604989	+	0.796234i	$0.293177\pi$
$854$	−19.0631			−0.652327
$855$		0			0
$856$	3.07087			0.104960
$857$	−39.2739	+	22.6748i	−1.34157	+	0.774556i	−0.987038	−	0.160488i	$-0.948693\pi$
$857$	−39.2739	+	22.6748i	−1.34157	+	0.774556i	−0.354532	+	0.935044i	$0.615360\pi$
$858$	0.170255	−	0.0982968i	0.00581241	−	0.00335580i
$859$	14.8143	−	25.6590i	0.505456	−	0.875475i	−0.494524	−	0.869164i	$-0.664658\pi$
$859$	14.8143	−	25.6590i	0.505456	−	0.875475i	0.999980	−	0.00631148i	$-0.00200902\pi$
$860$		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	$-0.753539\pi$
$863$		−	41.0807i		−	1.39840i	0.714925	−	0.699201i	$-0.246461\pi$
$864$	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	0.605650	−	0.795731i	$-0.292913\pi$
$877$	47.3116	−	27.3154i	1.59760	−	0.922374i	0.991948	−	0.126643i	$-0.0404204\pi$
$878$	−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	−0.337674	−	0.941263i	$-0.609640\pi$
$883$	−39.2738	−	22.6747i	−1.32167	−	0.763066i	−0.983995	+	0.178197i	$0.942973\pi$
$884$	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	0.878979	−	0.476860i	$-0.158225\pi$
$887$	26.9680	+	15.5700i	0.905496	+	0.522788i	0.0265165	+	0.999648i	$0.491559\pi$
$888$	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	0.280554	−	0.959838i	$-0.409482\pi$
$907$	37.7080	−	21.7707i	1.25207	−	0.722886i	0.971521	+	0.236952i	$0.0761486\pi$
$908$	−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	0.524571	−	0.851366i	$-0.324226\pi$
$929$	−14.4784	−	25.0772i	−0.475019	−	0.822758i	−0.999591	+	0.0286089i	$0.990892\pi$
$930$		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	0.693094	−	0.720847i	$-0.256247\pi$
$937$	12.7146	+	7.34080i	0.415369	+	0.239813i	−0.277725	+	0.960661i	$0.589580\pi$
$938$			6.13606i			0.200349i
$939$	0.775939			0.0253218
$940$		0			0
$941$	0.0773773	−	0.134021i	0.00252243	−	0.00436897i	−0.864761	−	0.502183i	$-0.832530\pi$
$941$	0.0773773	−	0.134021i	0.00252243	−	0.00436897i	0.867284	+	0.497814i	$0.165864\pi$
$942$		−	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	−0.602043	−	0.798464i	$-0.705646\pi$
$947$	−6.51084	+	3.75904i	−0.211574	+	0.122152i	0.390469	+	0.920616i	$0.372313\pi$
$948$	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	−0.783107	−	0.621887i	$-0.786366\pi$
$953$	−19.6365	+	11.3372i	−0.636090	+	0.367247i	0.147017	+	0.989134i	$0.453033\pi$
$954$	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	−0.0415030	−	0.999138i	$-0.513215\pi$
$967$	24.9714	−	14.4172i	0.803025	−	0.463627i	0.844528	+	0.535512i	$0.179881\pi$
$968$		−	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	0.573173	−	0.819435i	$-0.305712\pi$
$971$	−13.1831	−	22.8338i	−0.423065	−	0.732770i	−0.996238	+	0.0866647i	$0.972379\pi$
$972$	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	$0.0234036\pi$
$977$			4.59218i			0.146917i	−0.997298	+	0.0734585i	$0.976596\pi$
$978$	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	−0.592450	−	0.805607i	$-0.701839\pi$
$983$	−5.98833	+	3.45737i	−0.190998	+	0.110273i	0.401452	+	0.915880i	$0.368506\pi$
$984$	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	0.992261	+	0.124172i	$0.0396274\pi$
$991$	19.0035	+	32.9150i	0.603666	+	1.04558i	−0.388594	+	0.921409i	$0.627039\pi$
$992$	−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	0.260688	−	0.965423i	$-0.416051\pi$
$997$	−14.0526	−	8.11326i	−0.445050	−	0.256950i	−0.705737	+	0.708474i	$0.749384\pi$
$998$	−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.349.5		16
5.2	odd	4		475.2.e.e.26.3		8
5.3	odd	4		95.2.e.c.26.2	yes	8
5.4	even	2	inner	475.2.j.c.349.4		16
15.8	even	4		855.2.k.h.406.3		8
19.11	even	3	inner	475.2.j.c.49.4		16
20.3	even	4		1520.2.q.o.881.2		8
95.7	odd	12		9025.2.a.bg.1.2		4
95.12	even	12		9025.2.a.bp.1.3		4
95.49	even	6	inner	475.2.j.c.49.5		16
95.68	odd	12		95.2.e.c.11.2	✓	8
95.83	odd	12		1805.2.a.o.1.3		4
95.87	odd	12		475.2.e.e.201.3		8
95.88	even	12		1805.2.a.i.1.2		4
285.68	even	12		855.2.k.h.676.3		8
380.163	even	12		1520.2.q.o.961.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	95.68	odd	12
95.2.e.c.26.2	yes	8	5.3	odd	4
475.2.e.e.26.3		8	5.2	odd	4
475.2.e.e.201.3		8	95.87	odd	12
475.2.j.c.49.4		16	19.11	even	3	inner
475.2.j.c.49.5		16	95.49	even	6	inner
475.2.j.c.349.4		16	5.4	even	2	inner
475.2.j.c.349.5		16	1.1	even	1	trivial
855.2.k.h.406.3		8	15.8	even	4
855.2.k.h.676.3		8	285.68	even	12
1520.2.q.o.881.2		8	20.3	even	4
1520.2.q.o.961.2		8	380.163	even	12
1805.2.a.i.1.2		4	95.88	even	12
1805.2.a.o.1.3		4	95.83	odd	12
9025.2.a.bg.1.2		4	95.7	odd	12
9025.2.a.bp.1.3		4	95.12	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