LMFDB - Embedded newform 475.2.e.e.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.3
Root			$0.689667 + 1.19454i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.e.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.548719 + 0.950409i) q^{2} +(-0.189667 - 0.328513i) q^{3} +(0.397815 - 0.689035i) q^{4} +(0.208148 - 0.360522i) q^{6} -1.89307 q^{7} +3.06803 q^{8} +(1.42805 - 2.47346i) q^{9} +0.134400 q^{11} -0.301809 q^{12} +(1.75687 - 3.04298i) q^{13} +(-1.03876 - 1.79919i) q^{14} +(0.887858 + 1.53781i) q^{16} +(-0.830615 - 1.43867i) q^{17} +3.13440 q^{18} +(2.10596 + 3.81640i) q^{19} +(0.359052 + 0.621897i) q^{21} +(0.0737478 + 0.127735i) q^{22} +(2.68492 - 4.65042i) q^{23} +(-0.581904 - 1.00789i) q^{24} +3.85611 q^{26} -2.22142 q^{27} +(-0.753090 + 1.30439i) q^{28} +(-2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(2.09366 - 3.62633i) q^{32} +(-0.0254912 - 0.0441521i) q^{33} +(0.911548 - 1.57885i) q^{34} +(-1.13620 - 1.96796i) q^{36} +1.69819 q^{37} +(-2.47156 + 4.09566i) q^{38} -1.33288 q^{39} +(-5.31637 - 9.20823i) q^{41} +(-0.394038 + 0.682493i) q^{42} +(4.25392 + 7.36801i) q^{43} +(0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(-5.55771 + 9.62623i) q^{47} +(0.336794 - 0.583345i) q^{48} -3.41630 q^{49} +(-0.315080 + 0.545735i) q^{51} +(-1.39781 - 2.42109i) q^{52} +(-0.132424 + 0.229365i) q^{53} +(-1.21894 - 2.11126i) q^{54} -5.80799 q^{56} +(0.854305 - 1.41568i) q^{57} -5.45492 q^{58} +(3.44833 + 5.97269i) q^{59} +(-4.58794 + 7.94655i) q^{61} +(3.60219 + 6.23917i) q^{62} +(-2.70340 + 4.68243i) q^{63} +8.14676 q^{64} +(0.0279750 - 0.0484542i) q^{66} +(-1.47677 + 2.55784i) q^{67} -1.32172 q^{68} -2.03696 q^{69} +(-0.664176 - 1.15039i) q^{71} +(4.38131 - 7.58865i) q^{72} +(-3.17119 - 5.49266i) q^{73} +(0.931830 + 1.61398i) q^{74} +(3.46742 + 0.0671384i) q^{76} -0.254428 q^{77} +(-0.731376 - 1.26678i) q^{78} +(0.733639 + 1.27070i) q^{79} +(-3.86283 - 6.69062i) q^{81} +(5.83439 - 10.1055i) q^{82} -7.44736 q^{83} +0.571345 q^{84} +(-4.66842 + 8.08593i) q^{86} +1.88551 q^{87} +0.412343 q^{88} +(-4.86804 + 8.43169i) q^{89} +(-3.32587 + 5.76057i) q^{91} +(-2.13620 - 3.70001i) q^{92} +(-1.24511 - 2.15659i) q^{93} -12.1985 q^{94} -1.58839 q^{96} +(8.73447 + 15.1285i) q^{97} +(-1.87459 - 3.24688i) q^{98} +(0.191930 - 0.332433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * 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 $

$2$	0.548719	+	0.950409i	0.388003	+	0.672041i	0.992181	−	0.124809i	$-0.0398317\pi$
$2$	0.548719	+	0.950409i	0.388003	+	0.672041i	−0.604178	+	0.796850i	$0.706498\pi$
$3$	−0.189667	−	0.328513i	−0.109504	−	0.189667i	0.806065	−	0.591827i	$-0.201593\pi$
$3$	−0.189667	−	0.328513i	−0.109504	−	0.189667i	−0.915570	+	0.402160i	$0.868260\pi$
$4$	0.397815	−	0.689035i	0.198907	−	0.344518i
$5$		0			0
$5$		0			0
$6$	0.208148	−	0.360522i	0.0849759	−	0.147183i
$7$	−1.89307			−0.715512			−0.357756	−	0.933815i	$-0.616458\pi$
$7$	−1.89307			−0.715512			−0.357756	+	0.933815i	$0.616458\pi$
$8$	3.06803			1.08471
$9$	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	$0.493550\pi$
$12$	−0.301809			−0.0871248
$13$	1.75687	−	3.04298i	0.487267	−	0.843972i	−0.512626	−	0.858612i	$-0.671327\pi$
$13$	1.75687	−	3.04298i	0.487267	−	0.843972i	0.999893	+	0.0146407i	$0.00466045\pi$
$14$	−1.03876	−	1.79919i	−0.277621	−	0.480854i
$15$		0			0
$16$	0.887858	+	1.53781i	0.221964	+	0.384454i
$17$	−0.830615	−	1.43867i	−0.201454	−	0.348928i	0.747543	−	0.664213i	$-0.231233\pi$
$17$	−0.830615	−	1.43867i	−0.201454	−	0.348928i	−0.948997	+	0.315285i	$0.897900\pi$
$18$	3.13440			0.738785
$19$	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
$22$	0.0737478	+	0.127735i	0.0157231	+	0.0272332i
$23$	2.68492	−	4.65042i	0.559844	−	0.969679i	−0.437664	−	0.899138i	$-0.644194\pi$
$23$	2.68492	−	4.65042i	0.559844	−	0.969679i	0.997509	−	0.0705407i	$-0.0224725\pi$
$24$	−0.581904	−	1.00789i	−0.118781	−	0.205734i
$25$		0			0
$26$	3.85611			0.756245
$27$	−2.22142			−0.427512
$28$	−0.753090	+	1.30439i	−0.142321	+	0.246507i
$29$	−2.48530	+	4.30466i	−0.461508	+	0.799355i	−0.999036	−	0.0438905i	$-0.986025\pi$
$29$	−2.48530	+	4.30466i	−0.461508	+	0.799355i	0.537528	+	0.843246i	$0.319358\pi$
$30$		0			0
$31$	6.56472			1.17906			0.589529	−	0.807747i	$-0.299313\pi$
$31$	6.56472			1.17906			0.589529	+	0.807747i	$0.299313\pi$
$32$	2.09366	−	3.62633i	0.370111	−	0.641050i
$33$	−0.0254912	−	0.0441521i	−0.00443745	−	0.00768589i
$34$	0.911548	−	1.57885i	0.156329	−	0.270770i
$35$		0			0
$36$	−1.13620	−	1.96796i	−0.189367	−	0.327993i
$37$	1.69819			0.279181			0.139590	−	0.990209i	$-0.455421\pi$
$37$	1.69819			0.279181			0.139590	+	0.990209i	$0.455421\pi$
$38$	−2.47156	+	4.09566i	−0.400940	+	0.664404i
$39$	−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	$-0.478485\pi$
$42$	−0.394038	+	0.682493i	−0.0608013	+	0.105311i
$43$	4.25392	+	7.36801i	0.648717	+	1.12361i	0.983430	+	0.181290i	$0.0580274\pi$
$43$	4.25392	+	7.36801i	0.648717	+	1.12361i	−0.334713	+	0.942320i	$0.608639\pi$
$44$	0.0534662	−	0.0926063i	0.00806034	−	0.0139609i
$45$		0			0
$46$	5.89307			0.868885
$47$	−5.55771	+	9.62623i	−0.810675	+	1.40413i	0.101718	+	0.994813i	$0.467566\pi$
$47$	−5.55771	+	9.62623i	−0.810675	+	1.40413i	−0.912392	+	0.409316i	$0.865767\pi$
$48$	0.336794	−	0.583345i	0.0486121	−	0.0841986i
$49$	−3.41630			−0.488042
$50$		0			0
$51$	−0.315080	+	0.545735i	−0.0441201	+	0.0764182i
$52$	−1.39781	−	2.42109i	−0.193842	−	0.335744i
$53$	−0.132424	+	0.229365i	−0.0181898	+	0.0315057i	−0.874977	−	0.484164i	$-0.839124\pi$
$53$	−0.132424	+	0.229365i	−0.0181898	+	0.0315057i	0.856787	+	0.515670i	$0.172457\pi$
$54$	−1.21894	−	2.11126i	−0.165876	−	0.287306i
$55$		0			0
$56$	−5.80799			−0.776125
$57$	0.854305	−	1.41568i	0.113155	−	0.187511i
$58$	−5.45492			−0.716266
$59$	3.44833	+	5.97269i	0.448935	+	0.777578i	0.998317	−	0.0579932i	$-0.0184702\pi$
$59$	3.44833	+	5.97269i	0.448935	+	0.777578i	−0.549382	+	0.835571i	$0.685137\pi$
$60$		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	$0.966808\pi$
$62$	3.60219	+	6.23917i	0.457478	+	0.792375i
$63$	−2.70340	+	4.68243i	−0.340596	+	0.589930i
$64$	8.14676			1.01834
$65$		0			0
$66$	0.0279750	−	0.0484542i	0.00344349	−	0.00596430i
$67$	−1.47677	+	2.55784i	−0.180416	+	0.312490i	−0.942022	−	0.335550i	$-0.891078\pi$
$67$	−1.47677	+	2.55784i	−0.180416	+	0.312490i	0.761606	+	0.648040i	$0.224411\pi$
$68$	−1.32172			−0.160282
$69$	−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	$0.858450\pi$
$72$	4.38131	−	7.58865i	0.516342	−	0.894331i
$73$	−3.17119	−	5.49266i	−0.371159	−	0.642867i	0.618585	−	0.785718i	$-0.287706\pi$
$73$	−3.17119	−	5.49266i	−0.371159	−	0.642867i	−0.989744	+	0.142851i	$0.954373\pi$
$74$	0.931830	+	1.61398i	0.108323	+	0.187621i
$75$		0			0
$76$	3.46742	+	0.0671384i	0.397740	+	0.00770130i
$77$	−0.254428			−0.0289948
$78$	−0.731376	−	1.26678i	−0.0828120	−	0.143435i
$79$	0.733639	+	1.27070i	0.0825408	+	0.142965i	0.904341	−	0.426811i	$-0.140363\pi$
$79$	0.733639	+	1.27070i	0.0825408	+	0.142965i	−0.821800	+	0.569776i	$0.807030\pi$
$80$		0			0
$81$	−3.86283	−	6.69062i	−0.429203	−	0.743402i
$82$	5.83439	−	10.1055i	0.644301	−	1.11596i
$83$	−7.44736			−0.817454			−0.408727	−	0.912657i	$-0.634027\pi$
$83$	−7.44736			−0.817454			−0.408727	+	0.912657i	$0.634027\pi$
$84$	0.571345			0.0623388
$85$		0			0
$86$	−4.66842	+	8.08593i	−0.503408	+	0.871929i
$87$	1.88551			0.202148
$88$	0.412343			0.0439559
$89$	−4.86804	+	8.43169i	−0.516011	+	0.893757i	0.483816	+	0.875170i	$0.339250\pi$
$89$	−4.86804	+	8.43169i	−0.516011	+	0.893757i	−0.999827	+	0.0185878i	$0.994083\pi$
$90$		0			0
$91$	−3.32587	+	5.76057i	−0.348646	+	0.603872i
$92$	−2.13620	−	3.70001i	−0.222714	−	0.385753i
$93$	−1.24511	−	2.15659i	−0.129112	−	0.223628i
$94$	−12.1985			−1.25818
$95$		0			0
$96$	−1.58839			−0.162115
$97$	8.73447	+	15.1285i	0.886851	+	1.53607i	0.843577	+	0.537008i	$0.180445\pi$
$97$	8.73447	+	15.1285i	0.886851	+	1.53607i	0.0432737	+	0.999063i	$0.486221\pi$
$98$	−1.87459	−	3.24688i	−0.189362	−	0.327984i
$99$	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	$0.253203\pi$
$102$	−0.691562			−0.0684749
$103$	−2.14750			−0.211599			−0.105800	−	0.994387i	$-0.533740\pi$
$103$	−2.14750			−0.211599			−0.105800	+	0.994387i	$0.533740\pi$
$104$	5.39012	−	9.33596i	0.528545	−	0.915467i
$105$		0			0
$106$	−0.290654			−0.0282308
$107$	1.00093			0.0967631			0.0483815	−	0.998829i	$-0.484594\pi$
$107$	1.00093			0.0967631			0.0483815	+	0.998829i	$0.484594\pi$
$108$	−0.883713	+	1.53064i	−0.0850353	+	0.147285i
$109$	−8.13145	−	14.0841i	−0.778852	−	1.34901i	−0.932604	−	0.360902i	$-0.882469\pi$
$109$	−8.13145	−	14.0841i	−0.778852	−	1.34901i	0.153752	−	0.988109i	$-0.450864\pi$
$110$		0			0
$111$	−0.322091	−	0.557877i	−0.0305715	−	0.0529514i
$112$	−1.68077	−	2.91119i	−0.158818	−	0.275081i
$113$	−0.843010			−0.0793037			−0.0396519	−	0.999214i	$-0.512625\pi$
$113$	−0.843010			−0.0793037			−0.0396519	+	0.999214i	$0.512625\pi$
$114$	1.81425	+	0.0351287i	0.169920	+	0.00329010i
$115$		0			0
$116$	1.97737	+	3.42491i	0.183595	+	0.317995i
$117$	−5.01780	−	8.69108i	−0.463896	−	0.803491i
$118$	−3.78433	+	6.55466i	−0.348376	+	0.603405i
$119$	1.57241	+	2.72349i	0.144143	+	0.249662i
$120$		0			0
$121$	−10.9819			−0.998358
$122$	−10.0700			−0.911692
$123$	−2.01668	+	3.49299i	−0.181838	+	0.314953i
$124$	2.61154	−	4.52332i	0.234523	−	0.406206i
$125$		0			0
$126$	−5.93363			−0.528610
$127$	9.36984	−	16.2290i	0.831439	−	1.44009i	−0.0654584	−	0.997855i	$-0.520851\pi$
$127$	9.36984	−	16.2290i	0.831439	−	1.44009i	0.896897	−	0.442239i	$-0.145816\pi$
$128$	0.282960	+	0.490101i	0.0250104	+	0.0433193i
$129$	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	$0.873578\pi$
$132$	−0.0405631			−0.00353057
$133$	−3.98673	−	7.22471i	−0.345693	−	0.626461i
$134$	−3.24133			−0.280008
$135$		0			0
$136$	−2.54835	−	4.41387i	−0.218519	−	0.378487i
$137$	−9.41579	+	16.3086i	−0.804445	+	1.39334i	0.112220	+	0.993683i	$0.464204\pi$
$137$	−9.41579	+	16.3086i	−0.804445	+	1.39334i	−0.916665	+	0.399656i	$0.869129\pi$
$138$	−1.11772	−	1.93595i	−0.0951466	−	0.164799i
$139$	9.08974	−	15.7439i	0.770982	−	1.33538i	−0.166043	−	0.986118i	$-0.553099\pi$
$139$	9.08974	−	15.7439i	0.770982	−	1.33538i	0.937025	−	0.349262i	$-0.113568\pi$
$140$		0			0
$141$	4.21645			0.355089
$142$	0.728892	−	1.26248i	0.0611672	−	0.105945i
$143$	0.236123	−	0.408977i	0.0197456	−	0.0342003i
$144$	5.07163			0.422636
$145$		0			0
$146$	3.48018	−	6.02785i	0.288022	−	0.498868i
$147$	0.647958	+	1.12230i	0.0534427	+	0.0925655i
$148$	0.675565	−	1.17011i	0.0555311	−	0.0961827i
$149$	11.1272	+	19.2728i	0.911573	+	1.57889i	0.811842	+	0.583877i	$0.198465\pi$
$149$	11.1272	+	19.2728i	0.911573	+	1.57889i	0.0997308	+	0.995014i	$0.468202\pi$
$150$		0			0
$151$	3.33482			0.271384			0.135692	−	0.990751i	$-0.456674\pi$
$151$	3.33482			0.271384			0.135692	+	0.990751i	$0.456674\pi$
$152$	6.46116	+	11.7088i	0.524069	+	0.949712i
$153$	−4.74465			−0.383582
$154$	−0.139610	−	0.241811i	−0.0112501	−	0.0194857i
$155$		0			0
$156$	−0.530238	+	0.918400i	−0.0424530	+	0.0735308i
$157$	3.63145	+	6.28986i	0.289822	+	0.501986i	0.973767	−	0.227548i	$-0.0730707\pi$
$157$	3.63145	+	6.28986i	0.289822	+	0.501986i	−0.683945	+	0.729533i	$0.739737\pi$
$158$	−0.805123	+	1.39451i	−0.0640522	+	0.110942i
$159$	0.100466			0.00796744
$160$		0			0
$161$	−5.08273	+	8.80355i	−0.400576	+	0.693817i
$162$	4.23922	−	7.34254i	0.333064	−	0.576884i
$163$	19.7783			1.54916			0.774578	−	0.632478i	$-0.217962\pi$
$163$	19.7783			1.54916			0.774578	+	0.632478i	$0.217962\pi$
$164$	−8.45972			−0.660593
$165$		0			0
$166$	−4.08651	−	7.07805i	−0.317175	−	0.549363i
$167$	−1.70160	+	2.94726i	−0.131674	+	0.228066i	−0.924322	−	0.381614i	$-0.875368\pi$
$167$	−1.70160	+	2.94726i	−0.131674	+	0.228066i	0.792648	+	0.609679i	$0.208702\pi$
$168$	1.10158	+	1.90800i	0.0849890	+	0.147205i
$169$	0.326838	+	0.566100i	0.0251414	+	0.0435461i
$170$		0			0
$171$	12.4471	+	0.241010i	0.951857	+	0.0184305i
$172$	6.76909			0.516138
$173$	−5.29286	−	9.16750i	−0.402409	−	0.696992i	0.591607	−	0.806226i	$-0.298494\pi$
$173$	−5.29286	−	9.16750i	−0.402409	−	0.696992i	−0.994016	+	0.109234i	$0.965160\pi$
$174$	1.03462	+	1.79201i	0.0784341	+	0.135852i
$175$		0			0
$176$	0.119328	+	0.206682i	0.00899469	+	0.0155793i
$177$	1.30807	−	2.26564i	0.0983205	−	0.170296i
$178$	−10.6847			−0.800855
$179$	−14.6024			−1.09144			−0.545718	−	0.837969i	$-0.683743\pi$
$179$	−14.6024			−1.09144			−0.545718	+	0.837969i	$0.683743\pi$
$180$		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	$0.101955\pi$
$182$	−7.29987			−0.541102
$183$	3.48072			0.257303
$184$	8.23742	−	14.2676i	0.607270	−	1.05182i
$185$		0			0
$186$	1.36643	−	2.36673i	0.100192	−	0.173537i
$187$	−0.111635	−	0.193357i	−0.00816353	−	0.0141396i
$188$	4.42187	+	7.65891i	0.322498	+	0.558583i
$189$	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	$0.234453\pi$
$192$	−1.54517	−	2.67631i	−0.111513	−	0.193146i
$193$	5.51176	+	9.54664i	0.396745	+	0.687182i	0.993322	−	0.115373i	$-0.0368064\pi$
$193$	5.51176	+	9.54664i	0.396745	+	0.687182i	−0.596577	+	0.802556i	$0.703473\pi$
$194$	−9.58554	+	16.6026i	−0.688202	+	1.19200i
$195$		0			0
$196$	−1.35905	+	2.35395i	−0.0970752	+	0.168139i
$197$	19.8532			1.41448			0.707242	−	0.706971i	$-0.249939\pi$
$197$	19.8532			1.41448			0.707242	+	0.706971i	$0.249939\pi$
$198$	0.421263			0.0299379
$199$	−10.5013	+	18.1888i	−0.744417	+	1.28937i	0.206050	+	0.978542i	$0.433939\pi$
$199$	−10.5013	+	18.1888i	−0.744417	+	1.28937i	−0.950467	+	0.310826i	$0.899394\pi$
$200$		0			0
$201$	1.12038			0.0790254
$202$	−5.92321			−0.416756
$203$	4.70483	−	8.14901i	0.330215	−	0.571948i
$204$	0.250687	+	0.434203i	0.0175516	+	0.0304003i
$205$		0			0
$206$	−1.17837	−	2.04100i	−0.0821011	−	0.142203i
$207$	−7.66842	−	13.2821i	−0.532992	−	0.923169i
$208$	6.23939			0.432624
$209$	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	$0.687788\pi$
$212$	0.105360	+	0.182489i	0.00723617	+	0.0125334i
$213$	−0.251944	+	0.436380i	−0.0172629	+	0.0299003i
$214$	0.549227	+	0.951289i	0.0375444	+	0.0650288i
$215$		0			0
$216$	−6.81538			−0.463728
$217$	−12.4275			−0.843630
$218$	8.92377	−	15.4564i	0.604394	−	1.04684i
$219$	−1.20294	+	2.08355i	−0.0812870	+	0.140793i
$220$		0			0
$221$	−5.83712			−0.392647
$222$	0.353475	−	0.612236i	0.0237237	−	0.0410906i
$223$	10.1972	+	17.6621i	0.682856	+	1.18274i	0.974105	+	0.226095i	$0.0725959\pi$
$223$	10.1972	+	17.6621i	0.682856	+	1.18274i	−0.291249	+	0.956647i	$0.594071\pi$
$224$	−3.96344	+	6.86488i	−0.264819	+	0.458679i
$225$		0			0
$226$	−0.462576	−	0.801205i	−0.0307701	−	0.0532954i
$227$	−25.4172			−1.68700			−0.843500	−	0.537129i	$-0.819509\pi$
$227$	−25.4172			−1.68700			−0.843500	+	0.537129i	$0.819509\pi$
$228$	−0.635598	−	1.15182i	−0.0420935	−	0.0762814i
$229$	2.21553			0.146406			0.0732030	−	0.997317i	$-0.476678\pi$
$229$	2.21553			0.146406			0.0732030	+	0.997317i	$0.476678\pi$
$230$		0			0
$231$	0.0482566	+	0.0835829i	0.00317505	+	0.00549935i
$232$	−7.62496	+	13.2068i	−0.500603	+	0.867071i
$233$	−7.07882	−	12.2609i	−0.463749	−	0.803236i	0.535395	−	0.844602i	$-0.320163\pi$
$233$	−7.07882	−	12.2609i	−0.463749	−	0.803236i	−0.999144	+	0.0413652i	$0.986829\pi$
$234$	5.50672	−	9.53792i	0.359986	−	0.623514i
$235$		0			0
$236$	5.48719			0.357186
$237$	0.278294	−	0.482019i	0.0180771	−	0.0313105i
$238$	−1.72562	+	2.98887i	−0.111855	+	0.193739i
$239$	3.01476			0.195008			0.0975042	−	0.995235i	$-0.468914\pi$
$239$	3.01476			0.195008			0.0975042	+	0.995235i	$0.468914\pi$
$240$		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	$-0.111028\pi$
$242$	−6.02600	−	10.4373i	−0.387366	−	0.670937i
$243$	−4.79743	+	8.30939i	−0.307755	+	0.533048i
$244$	3.65030	+	6.32251i	0.233687	+	0.404757i
$245$		0			0
$246$	−4.42636			−0.282215
$247$	15.3131	+	0.296503i	0.974352	+	0.0188660i
$248$	20.1407			1.27894
$249$	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	$0.984141\pi$
$252$	2.15090	+	3.72548i	0.135494	+	0.234683i
$253$	0.360853	−	0.625016i	0.0226866	−	0.0392944i
$254$	20.5656			1.29040
$255$		0			0
$256$	7.83623	−	13.5727i	0.489764	−	0.848297i
$257$	−9.77143	+	16.9246i	−0.609525	+	1.05573i	0.381794	+	0.924248i	$0.375307\pi$
$257$	−9.77143	+	16.9246i	−0.609525	+	1.05573i	−0.991319	+	0.131481i	$0.958027\pi$
$258$	3.54178			0.220501
$259$	−3.21479			−0.199757
$260$		0			0
$261$	7.09827	+	12.2946i	0.439372	+	0.761014i
$262$	1.58384	−	2.74330i	0.0978502	−	0.169482i
$263$	4.40680	+	7.63280i	0.271735	+	0.470659i	0.969306	−	0.245857i	$-0.0790692\pi$
$263$	4.40680	+	7.63280i	0.271735	+	0.470659i	−0.697571	+	0.716515i	$0.745736\pi$
$264$	−0.0782078	−	0.135460i	−0.00481336	−	0.00833698i
$265$		0			0
$266$	4.67883	−	7.75336i	0.286878	−	0.475389i
$267$	3.69322			0.226022
$268$	1.17496	+	2.03510i	0.0717723	+	0.124313i
$269$	−0.144181	−	0.249729i	−0.00879088	−	0.0152263i	0.861596	−	0.507594i	$-0.169465\pi$
$269$	−0.144181	−	0.249729i	−0.00879088	−	0.0152263i	−0.870387	+	0.492368i	$0.836132\pi$
$270$		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	$0.560771\pi$
$272$	1.47494	−	2.55466i	0.0894311	−	0.154899i
$273$	2.52323			0.152713
$274$	−20.6665			−1.24851
$275$		0			0
$276$	−0.810333	+	1.40354i	−0.0487763	+	0.0844831i
$277$	4.40486			0.264662			0.132331	−	0.991206i	$-0.457754\pi$
$277$	4.40486			0.264662			0.132331	+	0.991206i	$0.457754\pi$
$278$	19.9509			1.19657
$279$	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	$-0.263452\pi$
$282$	2.31365	+	4.00736i	0.137776	+	0.238635i
$283$	−0.664463	−	1.15088i	−0.0394982	−	0.0684129i	0.845600	−	0.533816i	$-0.179243\pi$
$283$	−0.664463	−	1.15088i	−0.0394982	−	0.0684129i	−0.885099	+	0.465403i	$0.845909\pi$
$284$	−1.05688			−0.0627140
$285$		0			0
$286$	0.518260			0.0306454
$287$	10.0643	+	17.4318i	0.594074	+	1.02897i
$288$	−5.97972	−	10.3572i	−0.352358	−	0.610302i
$289$	7.12016	−	12.3325i	0.418833	−	0.725440i
$290$		0			0
$291$	3.31328	−	5.73877i	0.194228	−	0.336413i
$292$	−5.04618			−0.295305
$293$	7.72365			0.451220			0.225610	−	0.974218i	$-0.427562\pi$
$293$	7.72365			0.451220			0.225610	+	0.974218i	$0.427562\pi$
$294$	−0.711094	+	1.23165i	−0.0414718	+	0.0718313i
$295$		0			0
$296$	5.21010			0.302831
$297$	−0.298558			−0.0173241
$298$	−12.2114	+	21.1507i	−0.707386	+	1.22523i
$299$	−9.43409	−	16.3403i	−0.545588	−	0.944986i
$300$		0			0
$301$	−8.05296	−	13.9481i	−0.464165	−	0.803957i
$302$	1.82988	+	3.16944i	0.105298	+	0.182381i
$303$	2.04738			0.117619
$304$	−3.99912	+	6.62700i	−0.229366	+	0.380085i
$305$		0			0
$306$	−2.60348	−	4.50936i	−0.148831	−	0.257783i
$307$	−4.55001	−	7.88085i	−0.259683	−	0.449784i	0.706474	−	0.707739i	$-0.250285\pi$
$307$	−4.55001	−	7.88085i	−0.259683	−	0.449784i	−0.966157	+	0.257955i	$0.916951\pi$
$308$	−0.101215	+	0.175310i	−0.00576727	+	0.00998921i
$309$	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	$0.614900\pi$
$312$	−4.08931			−0.231512
$313$	1.02277	−	1.77148i	0.0578101	−	0.100130i	−0.835672	−	0.549229i	$-0.814922\pi$
$313$	1.02277	−	1.77148i	0.0578101	−	0.100130i	0.893482	+	0.449099i	$0.148255\pi$
$314$	−3.98530	+	6.90274i	−0.224903	+	0.389544i
$315$		0			0
$316$	1.16741			0.0656719
$317$	11.7856	−	20.4133i	0.661947	−	1.14653i	−0.318157	−	0.948038i	$-0.603064\pi$
$317$	11.7856	−	20.4133i	0.661947	−	1.14653i	0.980103	−	0.198487i	$-0.0636029\pi$
$318$	0.0551274	+	0.0954834i	0.00309139	+	0.00535445i
$319$	−0.334024	+	0.578546i	−0.0187017	+	0.0323923i
$320$		0			0
$321$	−0.189842	−	0.328817i	−0.0105960	−	0.0183528i
$322$	−11.1560			−0.621698
$323$	3.74129	−	6.19974i	0.208171	−	0.344963i
$324$	−6.14676			−0.341487
$325$		0			0
$326$	10.8527	+	18.7975i	0.601077	+	1.04110i
$327$	−3.08454	+	5.34257i	−0.170575	+	0.295445i
$328$	−16.3108	−	28.2511i	−0.900613	−	1.55991i
$329$	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	$0.671986\pi$
$332$	−2.96267	+	5.13150i	−0.162598	+	0.281627i
$333$	2.42511	−	4.20041i	0.132895	−	0.230181i
$334$	−3.73480			−0.204359
$335$		0			0
$336$	−0.637575	+	1.10431i	−0.0347826	+	0.0602451i
$337$	−16.3440	−	28.3087i	−0.890316	−	1.54207i	−0.839497	−	0.543365i	$-0.817150\pi$
$337$	−16.3440	−	28.3087i	−0.890316	−	1.54207i	−0.0508197	−	0.998708i	$-0.516183\pi$
$338$	−0.358684	+	0.621259i	−0.0195098	+	0.0337921i
$339$	0.159891	+	0.276940i	0.00868409	+	0.0150413i
$340$		0			0
$341$	0.882297			0.0477791
$342$	6.60093	+	11.9621i	0.356937	+	0.646838i
$343$	19.7188			1.06471
$344$	13.0512	+	22.6053i	0.703671	+	1.21879i
$345$		0			0
$346$	5.80859	−	10.0608i	0.312271	−	0.540870i
$347$	−1.28333	−	2.22279i	−0.0688927	−	0.119326i	0.829521	−	0.558475i	$-0.188613\pi$
$347$	−1.28333	−	2.22279i	−0.0688927	−	0.119326i	−0.898414	+	0.439149i	$0.855280\pi$
$348$	0.750085	−	1.29919i	0.0402088	−	0.0696436i
$349$	16.6195			0.889619			0.444810	−	0.895625i	$-0.353271\pi$
$349$	16.6195			0.889619			0.444810	+	0.895625i	$0.353271\pi$
$350$		0			0
$351$	−3.90274	+	6.75974i	−0.208313	+	0.360808i
$352$	0.281388	−	0.487378i	0.0149980	−	0.0259773i
$353$	−28.3629			−1.50961			−0.754803	−	0.655951i	$-0.772268\pi$
$353$	−28.3629			−1.50961			−0.754803	+	0.655951i	$0.772268\pi$
$354$	2.87105			0.152595
$355$		0			0
$356$	3.87315	+	6.70850i	0.205277	+	0.355550i
$357$	0.596468	−	1.03311i	0.0315684	−	0.0546781i
$358$	−8.01262	−	13.8783i	−0.423480	−	0.733489i
$359$	−8.69427	−	15.0589i	−0.458866	−	0.794780i	0.540035	−	0.841643i	$-0.318411\pi$
$359$	−8.69427	−	15.0589i	−0.458866	−	0.794780i	−0.998901	+	0.0468628i	$0.985078\pi$
$360$		0			0
$361$	−10.1298	+	16.0744i	−0.533150	+	0.846021i
$362$	5.96195			0.313353
$363$	2.08291	+	3.60771i	0.109324	+	0.189355i
$364$	2.64616	+	4.58328i	0.138696	+	0.240229i
$365$		0			0
$366$	1.90994	+	3.30811i	0.0998342	+	0.172918i
$367$	12.9024	−	22.3477i	0.673501	−	1.16654i	−0.303404	−	0.952862i	$-0.598123\pi$
$367$	12.9024	−	22.3477i	0.673501	−	1.16654i	0.976905	−	0.213676i	$-0.0685436\pi$
$368$	9.53531			0.497062
$369$	−30.3683			−1.58091
$370$		0			0
$371$	0.250687	−	0.434203i	0.0130150	−	0.0225427i
$372$	−1.98129			−0.102725
$373$	−27.0663			−1.40144			−0.700719	−	0.713437i	$-0.747138\pi$
$373$	−27.0663			−1.40144			−0.700719	+	0.713437i	$0.747138\pi$
$374$	0.122512	−	0.212197i	0.00633495	−	0.0109724i
$375$		0			0
$376$	−17.0512	+	29.5336i	−0.879349	+	1.52308i
$377$	8.73267	+	15.1254i	0.449755	+	0.778999i
$378$	2.30753	+	3.99675i	0.118686	+	0.205571i
$379$	12.4028			0.637092			0.318546	−	0.947907i	$-0.396806\pi$
$379$	12.4028			0.637092			0.318546	+	0.947907i	$0.396806\pi$
$380$		0			0
$381$	−7.10859			−0.364184
$382$	11.2354	+	19.4604i	0.574855	+	0.995678i
$383$	−2.67971	−	4.64139i	−0.136927	−	0.237164i	0.789405	−	0.613873i	$-0.210389\pi$
$383$	−2.67971	−	4.64139i	−0.136927	−	0.237164i	−0.926332	+	0.376709i	$0.877056\pi$
$384$	0.107336	−	0.185912i	0.00547749	−	0.00948728i
$385$		0			0
$386$	−6.04881	+	10.4769i	−0.307877	+	0.533258i
$387$	24.2993			1.23520
$388$	13.8988			0.705605
$389$	−4.28467	+	7.42126i	−0.217241	+	0.376273i	−0.953964	−	0.299923i	$-0.903039\pi$
$389$	−4.28467	+	7.42126i	−0.217241	+	0.376273i	0.736722	+	0.676195i	$0.236372\pi$
$390$		0			0
$391$	−8.92053			−0.451131
$392$	−10.4813			−0.529386
$393$	−0.547462	+	0.948232i	−0.0276158	+	0.0478320i
$394$	10.8939	+	18.8687i	0.548824	+	0.950592i
$395$		0			0
$396$	−0.152705	−	0.264493i	−0.00767373	−	0.0132913i
$397$	−5.32227	−	9.21844i	−0.267117	−	0.462660i	0.700999	−	0.713162i	$-0.252738\pi$
$397$	−5.32227	−	9.21844i	−0.267117	−	0.462660i	−0.968116	+	0.250502i	$0.919404\pi$
$398$	−23.0490			−1.15534
$399$	−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	$0.894527\pi$
$402$	0.614773	+	1.06482i	0.0306621	+	0.0531083i
$403$	11.5333	−	19.9763i	0.574516	−	0.995091i
$404$	2.14713	+	3.71893i	0.106824	+	0.185024i
$405$		0			0
$406$	10.3265			0.512497
$407$	0.228237			0.0113133
$408$	−0.966676	+	1.67433i	−0.0478576	+	0.0828918i
$409$	8.84435	−	15.3189i	0.437325	−	0.757469i	−0.560157	−	0.828386i	$-0.689259\pi$
$409$	8.84435	−	15.3189i	0.437325	−	0.757469i	0.997482	+	0.0709173i	$0.0225927\pi$
$410$		0			0
$411$	7.14345			0.352361
$412$	−0.854305	+	1.47970i	−0.0420886	+	0.0728996i
$413$	−6.52793	−	11.3067i	−0.321218	−	0.556367i
$414$	8.41561	−	14.5763i	0.413605	−	0.716384i
$415$		0			0
$416$	−7.35657	−	12.7420i	−0.360685	−	0.624726i
$417$	−6.89609			−0.337703
$418$	−0.332178	+	0.550456i	−0.0162473	+	0.0269237i
$419$	1.18732			0.0580045			0.0290023	−	0.999579i	$-0.490767\pi$
$419$	1.18732			0.0580045			0.0290023	+	0.999579i	$0.490767\pi$
$420$		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	$-0.468894\pi$
$422$	−7.03770	+	12.1896i	−0.342590	+	0.593383i
$423$	15.8734	+	27.4935i	0.771791	+	1.33678i
$424$	−0.406280	+	0.703698i	−0.0197307	+	0.0341746i
$425$		0			0
$426$	−0.552987			−0.0267923
$427$	8.68529	−	15.0434i	0.420311	−	0.727999i
$428$	0.398183	−	0.689673i	0.0192469	−	0.0333366i
$429$	−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	$0.119144\pi$
$432$	−1.97230	−	3.41613i	−0.0948925	−	0.164359i
$433$	−9.27761	+	16.0693i	−0.445854	+	0.772241i	−0.998111	−	0.0614325i	$-0.980433\pi$
$433$	−9.27761	+	16.0693i	−0.445854	+	0.772241i	0.552258	+	0.833673i	$0.313766\pi$
$434$	−6.81918	−	11.8112i	−0.327331	−	0.566954i
$435$		0			0
$436$	−12.9392			−0.619677
$437$	23.4022	+	0.453129i	1.11948	+	0.0216761i
$438$	−2.64030			−0.126158
$439$	0.113656	+	0.196858i	0.00542450	+	0.00939550i	0.868725	−	0.495295i	$-0.164940\pi$
$439$	0.113656	+	0.196858i	0.00542450	+	0.00939550i	−0.863300	+	0.504690i	$0.831607\pi$
$440$		0			0
$441$	−4.87865	+	8.45007i	−0.232317	+	0.402384i
$442$	−3.20294	−	5.54765i	−0.152348	−	0.263875i
$443$	−17.4913	+	30.2959i	−0.831038	+	1.43940i	0.0661770	+	0.997808i	$0.478920\pi$
$443$	−17.4913	+	30.2959i	−0.831038	+	1.43940i	−0.897216	+	0.441593i	$0.854414\pi$
$444$	−0.512529			−0.0243236
$445$		0			0
$446$	−11.1908	+	19.3831i	−0.529901	+	0.917815i
$447$	4.22091	−	7.31083i	0.199642	−	0.345791i
$448$	−15.4224			−0.728638
$449$	−16.9509			−0.799961			−0.399980	−	0.916524i	$-0.630983\pi$
$449$	−16.9509			−0.799961			−0.399980	+	0.916524i	$0.630983\pi$
$450$		0			0
$451$	−0.714520	−	1.23759i	−0.0336454	−	0.0582756i
$452$	−0.335362	+	0.580864i	−0.0157741	+	0.0273215i
$453$	−0.632505	−	1.09553i	−0.0297177	−	0.0514725i
$454$	−13.9469	−	24.1568i	−0.654561	−	1.13373i
$455$		0			0
$456$	2.62103	−	4.34335i	0.122741	−	0.203396i
$457$	−1.60241			−0.0749578			−0.0374789	−	0.999297i	$-0.511933\pi$
$457$	−1.60241			−0.0749578			−0.0374789	+	0.999297i	$0.511933\pi$
$458$	1.21570	+	2.10566i	0.0568060	+	0.0983909i
$459$	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	$0.768079\pi$
$462$	−0.0529586	+	0.0917270i	−0.00246386	+	0.00426753i
$463$	−21.1886			−0.984718			−0.492359	−	0.870392i	$-0.663865\pi$
$463$	−21.1886			−0.984718			−0.492359	+	0.870392i	$0.663865\pi$
$464$	−8.82636			−0.409753
$465$		0			0
$466$	7.76857	−	13.4556i	0.359872	−	0.623316i
$467$	−20.4516			−0.946388			−0.473194	−	0.880958i	$-0.656899\pi$
$467$	−20.4516			−0.946388			−0.473194	+	0.880958i	$0.656899\pi$
$468$	−7.98461			−0.369089
$469$	2.79563	−	4.84217i	0.129090	−	0.223591i
$470$		0			0
$471$	1.37753	−	2.38596i	0.0634734	−	0.109939i
$472$	10.5796	+	18.3244i	0.486965	+	0.843449i
$473$	0.571727	+	0.990259i	0.0262880	+	0.0455322i
$474$	0.610821			0.0280559
$475$		0			0
$476$	2.50211			0.114684
$477$	0.378216	+	0.655090i	0.0173173	+	0.0299945i
$478$	1.65425	+	2.86525i	0.0756639	+	0.131054i
$479$	−11.7746	+	20.3942i	−0.537994	+	0.931833i	0.461018	+	0.887391i	$0.347484\pi$
$479$	−11.7746	+	20.3942i	−0.537994	+	0.931833i	−0.999012	+	0.0444419i	$0.985849\pi$
$480$		0			0
$481$	2.98350	−	5.16757i	0.136036	−	0.235621i
$482$	26.0962			1.18865
$483$	3.85611			0.175459
$484$	−4.36877	+	7.56694i	−0.198581	+	0.343952i
$485$		0			0
$486$	−10.5298			−0.477640
$487$	−36.0392			−1.63309			−0.816546	−	0.577280i	$-0.804114\pi$
$487$	−36.0392			−1.63309			−0.816546	+	0.577280i	$0.804114\pi$
$488$	−14.0760	+	24.3803i	−0.637188	+	1.10364i
$489$	−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	$0.982849\pi$
$492$	1.60453	+	2.77913i	0.0723378	+	0.125293i
$493$	8.25729			0.371890
$494$	8.12081	+	14.7164i	0.365373	+	0.662124i
$495$		0			0
$496$	5.82853	+	10.0953i	0.261709	+	0.453293i
$497$	1.25733	+	2.17776i	0.0563989	+	0.0976858i
$498$	−1.55015	+	2.68494i	−0.0694640	+	0.120315i
$499$	18.4364	+	31.9328i	0.825328	+	1.42951i	0.901668	+	0.432429i	$0.142343\pi$
$499$	18.4364	+	31.9328i	0.825328	+	1.42951i	−0.0763399	+	0.997082i	$0.524323\pi$
$500$		0			0
$501$	1.29095			0.0576753
$502$	−18.8649			−0.841980
$503$	−10.8244	+	18.7483i	−0.482634	+	0.835947i	−0.999801	−	0.0199377i	$-0.993653\pi$
$503$	−10.8244	+	18.7483i	−0.482634	+	0.835947i	0.517167	+	0.855884i	$0.326987\pi$
$504$	−8.29412	+	14.3658i	−0.369449	+	0.639905i
$505$		0			0
$506$	0.792028			0.0352099
$507$	0.123981	−	0.214741i	0.00550617	−	0.00953697i
$508$	−7.45492	−	12.9123i	−0.330759	−	0.572891i
$509$	18.2279	−	31.5717i	0.807938	−	1.39939i	−0.106351	−	0.994329i	$-0.533917\pi$
$509$	18.2279	−	31.5717i	0.807938	−	1.39939i	0.914289	−	0.405062i	$-0.132750\pi$
$510$		0			0
$511$	6.00327	+	10.3980i	0.265569	+	0.459979i
$512$	18.3314			0.810141
$513$	−4.67822	−	8.47783i	−0.206549	−	0.374305i
$514$	−21.4471			−0.945990
$515$		0			0
$516$	−1.28387	−	2.22373i	−0.0565193	−	0.0978943i
$517$	−0.746955	+	1.29376i	−0.0328511	+	0.0568997i
$518$	−1.76402	−	3.05537i	−0.0775065	−	0.134245i
$519$	−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	$0.664929\pi$
$522$	−7.78991	+	13.4925i	−0.340955	+	0.590552i
$523$	0.266456	−	0.461515i	0.0116513	−	0.0201806i	−0.860141	−	0.510056i	$-0.829625\pi$
$523$	0.266456	−	0.461515i	0.0116513	−	0.0201806i	0.871792	+	0.489876i	$0.162958\pi$
$524$	−2.29654			−0.100325
$525$		0			0
$526$	−4.83619	+	8.37653i	−0.210868	+	0.365234i
$527$	−5.45275	−	9.44444i	−0.237525	−	0.411406i
$528$	0.0452651	−	0.0784015i	0.00196991	−	0.00341199i
$529$	−2.91759	−	5.05341i	−0.126852	−	0.219714i
$530$		0			0
$531$	19.6976			0.854804
$532$	−6.56406	−	0.127098i	−0.284588	−	0.00551038i
$533$	−37.3606			−1.61827
$534$	2.02654	+	3.51007i	0.0876971	+	0.151896i
$535$		0			0
$536$	−4.53078	+	7.84754i	−0.195700	+	0.338962i
$537$	2.76959	+	4.79708i	0.119517	+	0.207009i
$538$	0.158230	−	0.274062i	0.00682178	−	0.0118157i
$539$	−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	$0.201059\pi$
$542$	−13.6473	+	23.6378i	−0.586202	+	1.01533i
$543$	−2.06077			−0.0884362
$544$	−6.95610			−0.298240
$545$		0			0
$546$	1.38454	+	2.39810i	0.0592530	+	0.102629i
$547$	11.3149	−	19.5981i	0.483792	−	0.837952i	−0.516035	−	0.856568i	$-0.672592\pi$
$547$	11.3149	−	19.5981i	0.483792	−	0.837952i	0.999827	+	0.0186154i	$0.00592582\pi$
$548$	7.49148	+	12.9756i	0.320020	+	0.554291i
$549$	13.1037	+	22.6962i	0.559250	+	0.968650i
$550$		0			0
$551$	−21.6622	−	0.419439i	−0.922843	−	0.0178687i
$552$	−6.24946			−0.265995
$553$	−1.38883	−	2.40552i	−0.0590590	−	0.102293i
$554$	2.41703	+	4.18642i	0.102690	+	0.177864i
$555$		0			0
$556$	−7.23207	−	12.5263i	−0.306708	−	0.531234i
$557$	17.6277	−	30.5321i	0.746910	−	1.29369i	−0.202387	−	0.979306i	$-0.564870\pi$
$557$	17.6277	−	30.5321i	0.746910	−	1.29369i	0.949297	−	0.314381i	$-0.101797\pi$
$558$	20.5764			0.871070
$559$	29.8943			1.26439
$560$		0			0
$561$	−0.0423468	+	0.0733467i	−0.00178788	+	0.00309670i
$562$	35.9097			1.51476
$563$	24.6295			1.03801			0.519005	−	0.854771i	$-0.326302\pi$
$563$	24.6295			1.03801			0.519005	+	0.854771i	$0.326302\pi$
$564$	1.67737	−	2.90528i	0.0706298	−	0.122334i
$565$		0			0
$566$	0.729207	−	1.26302i	0.0306509	−	0.0530888i
$567$	7.31260	+	12.6658i	0.307100	+	0.531913i
$568$	−2.03771	−	3.52942i	−0.0855005	−	0.148091i
$569$	−20.0193			−0.839252			−0.419626	−	0.907697i	$-0.637839\pi$
$569$	−20.0193			−0.839252			−0.419626	+	0.907697i	$0.637839\pi$
$570$		0			0
$571$	−16.6121			−0.695195			−0.347597	−	0.937644i	$-0.613002\pi$
$571$	−16.6121			−0.695195			−0.347597	+	0.937644i	$0.613002\pi$
$572$	−0.187866	−	0.325394i	−0.00785508	−	0.0136054i
$573$	−3.88357	−	6.72655i	−0.162239	−	0.281006i
$574$	−11.0449	+	19.1303i	−0.461005	+	0.798484i
$575$		0			0
$576$	11.6340	−	20.1507i	0.484750	−	0.839612i
$577$	−12.4486			−0.518244			−0.259122	−	0.965845i	$-0.583433\pi$
$577$	−12.4486			−0.518244			−0.259122	+	0.965845i	$0.583433\pi$
$578$	15.6279			0.650034
$579$	2.09080	−	3.62136i	0.0868905	−	0.150499i
$580$		0			0
$581$	14.0984			0.584899
$582$	7.27224			0.301444
$583$	−0.0177977	+	0.0308266i	−0.000737107	+	0.00127671i
$584$	−9.72930	−	16.8516i	−0.402601	−	0.697326i
$585$		0			0
$586$	4.23811	+	7.34063i	0.175075	+	0.303238i
$587$	2.25572	+	3.90702i	0.0931036	+	0.161260i	0.908816	−	0.417198i	$-0.136988\pi$
$587$	2.25572	+	3.90702i	0.0931036	+	0.161260i	−0.815712	+	0.578458i	$0.803655\pi$
$588$	1.03107			0.0425206
$589$	13.8250	+	25.0536i	0.569651	+	1.03232i
$590$		0			0
$591$	−3.76550	−	6.52204i	−0.154892	−	0.268281i
$592$	1.50775	+	2.61150i	0.0619682	+	0.107332i
$593$	9.80411	−	16.9812i	0.402606	−	0.697335i	−0.591433	−	0.806354i	$-0.701438\pi$
$593$	9.80411	−	16.9812i	0.402606	−	0.697335i	0.994040	+	0.109019i	$0.0347710\pi$
$594$	−0.163825	−	0.283753i	−0.00672181	−	0.0116425i
$595$		0			0
$596$	17.7062			0.725274
$597$	7.96699			0.326067
$598$	10.3533	−	17.9325i	0.423379	−	0.733315i
$599$	−5.38795	+	9.33221i	−0.220146	+	0.381304i	−0.954852	−	0.297082i	$-0.903987\pi$
$599$	−5.38795	+	9.33221i	−0.220146	+	0.381304i	0.734706	+	0.678385i	$0.237320\pi$
$600$		0			0
$601$	15.0244			0.612860			0.306430	−	0.951893i	$-0.400866\pi$
$601$	15.0244			0.612860			0.306430	+	0.951893i	$0.400866\pi$
$602$	8.83763	−	15.3072i	0.360195	−	0.623876i
$603$	4.21782	+	7.30547i	0.171763	+	0.297502i
$604$	1.32664	−	2.29781i	0.0539802	−	0.0934964i
$605$		0			0
$606$	1.12344	+	1.94585i	0.0456365	+	0.0790448i
$607$	−25.1901			−1.02243			−0.511217	−	0.859452i	$-0.670805\pi$
$607$	−25.1901			−1.02243			−0.511217	+	0.859452i	$0.670805\pi$
$608$	18.2487	+	0.353343i	0.740082	+	0.0143300i
$609$	−3.56940			−0.144640
$610$		0			0
$611$	19.5283	+	33.8240i	0.790030	+	1.36837i
$612$	−1.88749	+	3.26923i	−0.0762973	+	0.132151i
$613$	8.11753	+	14.0600i	0.327864	+	0.567877i	0.982088	−	0.188424i	$-0.0603379\pi$
$613$	8.11753	+	14.0600i	0.327864	+	0.567877i	−0.654224	+	0.756301i	$0.727005\pi$
$614$	4.99336	−	8.64875i	0.201516	−	0.349035i
$615$		0			0
$616$	−0.780593			−0.0314510
$617$	3.25913	−	5.64498i	0.131208	−	0.227258i	−0.792935	−	0.609307i	$-0.791448\pi$
$617$	3.25913	−	5.64498i	0.131208	−	0.227258i	0.924142	+	0.382048i	$0.124781\pi$
$618$	−0.446996	+	0.774220i	−0.0179808	+	0.0311437i
$619$	−4.39112			−0.176494			−0.0882470	−	0.996099i	$-0.528126\pi$
$619$	−4.39112			−0.176494			−0.0882470	+	0.996099i	$0.528126\pi$
$620$		0			0
$621$	−5.96433	+	10.3305i	−0.239340	+	0.414550i
$622$	−6.83532	−	11.8391i	−0.274071	−	0.474705i
$623$	9.21553	−	15.9618i	0.369212	−	0.639494i
$624$	−1.18341	−	2.04972i	−0.0473742	−	0.0820545i
$625$		0			0
$626$	2.24484			0.0897220
$627$	0.114819	−	0.190267i	0.00458541	−	0.00759855i
$628$	5.77858			0.230590
$629$	−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	$-0.0753350\pi$
$632$	2.25083	+	3.89855i	0.0895331	+	0.155076i
$633$	2.43261	−	4.21340i	0.0966875	−	0.167468i
$634$	25.8680			1.02735
$635$		0			0
$636$	0.0399667	−	0.0692243i	0.00158478	−	0.00274492i
$637$	−6.00198	+	10.3957i	−0.237807	+	0.411894i
$638$	−0.733141			−0.0290253
$639$	−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	$0.880098\pi$
$642$	0.208340	−	0.360856i	0.00822253	−	0.0142418i
$643$	−8.27294	−	14.3292i	−0.326253	−	0.565087i	0.655512	−	0.755185i	$-0.272453\pi$
$643$	−8.27294	−	14.3292i	−0.326253	−	0.565087i	−0.981765	+	0.190098i	$0.939120\pi$
$644$	4.04397	+	7.00437i	0.159355	+	0.276011i
$645$		0			0
$646$	7.94520	+	0.153840i	0.312600	+	0.00605276i
$647$	−29.4822			−1.15907			−0.579533	−	0.814949i	$-0.696765\pi$
$647$	−29.4822			−1.15907			−0.579533	+	0.814949i	$0.696765\pi$
$648$	−11.8513	−	20.5270i	−0.465562	−	0.806377i
$649$	0.463456	+	0.802729i	0.0181922	+	0.0315099i
$650$		0			0
$651$	2.35708	+	4.08258i	0.0923811	+	0.160009i
$652$	7.86810	−	13.6279i	0.308138	−	0.533712i
$653$	−6.57421			−0.257269			−0.128634	−	0.991692i	$-0.541059\pi$
$653$	−6.57421			−0.257269			−0.128634	+	0.991692i	$0.541059\pi$
$654$	−6.77017			−0.264735
$655$		0			0
$656$	9.44037	−	16.3512i	0.368584	−	0.638407i
$657$	−18.1145			−0.706713
$658$	23.0925			0.900241
$659$	13.1685	−	22.8085i	0.512972	−	0.888494i	−0.486915	−	0.873450i	$-0.661878\pi$
$659$	13.1685	−	22.8085i	0.512972	−	0.888494i	0.999887	−	0.0150445i	$-0.00478898\pi$
$660$		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	$0.190114\pi$
$662$	−10.2706	−	17.7893i	−0.399180	−	0.691399i
$663$	1.10711	+	1.91757i	0.0429965	+	0.0744721i
$664$	−22.8487			−0.886703
$665$		0			0
$666$	5.32281			0.206255
$667$	13.3456	+	23.1153i	0.516745	+	0.895029i
$668$	1.35384	+	2.34492i	0.0523817	+	0.0907278i
$669$	3.86815	−	6.69983i	0.149551	−	0.259031i
$670$		0			0
$671$	−0.616619	+	1.06802i	−0.0238043	+	0.0412303i
$672$	3.00694			0.115995
$673$	21.0431			0.811150			0.405575	−	0.914062i	$-0.367071\pi$
$673$	21.0431			0.811150			0.405575	+	0.914062i	$0.367071\pi$
$674$	17.9366	−	31.0670i	0.690891	−	1.19666i
$675$		0			0
$676$	0.520083			0.0200032
$677$	15.2744			0.587043			0.293522	−	0.955952i	$-0.405173\pi$
$677$	15.2744			0.587043			0.293522	+	0.955952i	$0.405173\pi$
$678$	−0.175471	+	0.303924i	−0.00673891	+	0.0116721i
$679$	−16.5349	−	28.6394i	−0.634553	−	1.09908i
$680$		0			0
$681$	4.82081	+	8.34988i	0.184734	+	0.319968i
$682$	0.484133	+	0.838544i	0.0185384	+	0.0321095i
$683$	8.60225			0.329156			0.164578	−	0.986364i	$-0.447374\pi$
$683$	8.60225			0.329156			0.164578	+	0.986364i	$0.447374\pi$
$684$	5.11772	−	8.48064i	0.195681	−	0.324265i
$685$		0			0
$686$	10.8201	+	18.7409i	0.413112	+	0.715530i
$687$	−0.420212	−	0.727828i	−0.0160321	−	0.0277684i
$688$	−7.55375	+	13.0835i	−0.287984	+	0.498803i
$689$	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	$0.275286\pi$
$692$	−8.42231			−0.320168
$693$	−0.363337	+	0.629318i	−0.0138020	+	0.0239058i
$694$	1.40837	−	2.43937i	0.0534611	−	0.0925974i
$695$		0			0
$696$	5.78481			0.219273
$697$	−8.83172	+	15.2970i	−0.334525	+	0.579414i
$698$	9.11942	+	15.7953i	0.345175	+	0.597861i
$699$	−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	$0.898279\pi$
$702$	−8.56603			−0.323304
$703$	3.57633	+	6.48098i	0.134884	+	0.244435i
$704$	1.09492			0.0412665
$705$		0			0
$706$	−15.5633	−	26.9564i	−0.585732	−	1.01452i
$707$	5.10873	−	8.84859i	0.192134	−	0.332785i
$708$	−1.04074	−	1.80261i	−0.0391134	−	0.0677463i
$709$	14.4238	−	24.9828i	0.541697	−	0.938247i	−0.457109	−	0.889410i	$-0.651115\pi$
$709$	14.4238	−	24.9828i	0.541697	−	0.938247i	0.998807	−	0.0488369i	$-0.0155514\pi$
$710$		0			0
$711$	4.19070			0.157164
$712$	−14.9353	+	25.8687i	−0.559724	+	0.969470i
$713$	17.6257	−	30.5287i	0.660089	−	1.14331i
$714$	1.30917			0.0489946
$715$		0			0
$716$	−5.80905	+	10.0616i	−0.217095	+	0.376019i
$717$	−0.571800	−	0.990386i	−0.0213542	−	0.0369866i
$718$	9.54143	−	16.5262i	0.356083	−	0.616754i
$719$	10.0278	+	17.3686i	0.373972	+	0.647739i	0.990173	−	0.139851i	$-0.0446622\pi$
$719$	10.0278	+	17.3686i	0.373972	+	0.647739i	−0.616200	+	0.787589i	$0.711329\pi$
$720$		0			0
$721$	4.06535			0.151402
$722$	−20.8357	−	0.807171i	−0.775424	−	0.0300398i
$723$	−9.02026			−0.335467
$724$	−2.16117	−	3.74326i	−0.0803193	−	0.139117i
$725$		0			0
$726$	−2.28587	+	3.95923i	−0.0848364	+	0.146941i
$727$	−0.390261	−	0.675951i	−0.0144740	−	0.0250697i	0.858698	−	0.512482i	$-0.171274\pi$
$727$	−0.390261	−	0.675951i	−0.0144740	−	0.0250697i	−0.873172	+	0.487413i	$0.837941\pi$
$728$	−10.2039	+	17.6736i	−0.378180	+	0.655028i
$729$	−19.5373			−0.723604
$730$		0			0
$731$	7.06674	−	12.2399i	0.261373	−	0.452711i
$732$	1.38468	−	2.39834i	0.0511794	−	0.0886452i
$733$	26.8391			0.991326			0.495663	−	0.868515i	$-0.334925\pi$
$733$	26.8391			0.991326			0.495663	+	0.868515i	$0.334925\pi$
$734$	28.3192			1.04528
$735$		0			0
$736$	−11.2426	−	19.4728i	−0.414409	−	0.717777i
$737$	−0.198478	+	0.343774i	−0.00731103	+	0.0126631i
$738$	−16.6636	−	28.8623i	−0.613397	−	1.06243i
$739$	−10.3265	−	17.8861i	−0.379867	−	0.657949i	0.611175	−	0.791495i	$-0.290697\pi$
$739$	−10.3265	−	17.8861i	−0.379867	−	0.657949i	−0.991043	+	0.133546i	$0.957364\pi$
$740$		0			0
$741$	−2.80699	−	5.08680i	−0.103117	−	0.186868i
$742$	0.550227			0.0201995
$743$	0.736585	+	1.27580i	0.0270227	+	0.0468047i	0.879220	−	0.476415i	$-0.158064\pi$
$743$	0.736585	+	1.27580i	0.0270227	+	0.0468047i	−0.852198	+	0.523220i	$0.824731\pi$
$744$	−3.82003	−	6.61649i	−0.140049	−	0.242572i
$745$		0			0
$746$	−14.8518	−	25.7240i	−0.543762	−	0.941824i
$747$	−10.6352	+	18.4208i	−0.389123	+	0.673980i
$748$	−0.177639			−0.00649514
$749$	−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	$0.258308\pi$
$752$	−19.7378			−0.719764
$753$	6.52071			0.237628
$754$	−9.58356	+	16.5992i	−0.349013	+	0.604508i
$755$		0			0
$756$	1.67293	−	2.89760i	0.0608438	−	0.105385i
$757$	10.0878	+	17.4726i	0.366647	+	0.635052i	0.989039	−	0.147654i	$-0.0471722\pi$
$757$	10.0878	+	17.4726i	0.366647	+	0.635052i	−0.622392	+	0.782706i	$0.713839\pi$
$758$	6.80568	+	11.7878i	0.247193	+	0.428152i
$759$	−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	$0.588289\pi$
$762$	−3.90062	−	6.75607i	−0.141305	−	0.244747i
$763$	15.3934	+	26.6621i	0.557278	+	0.965234i
$764$	8.14556	−	14.1085i	0.294696	−	0.510428i
$765$		0			0
$766$	2.94082	−	5.09364i	0.106256	−	0.184041i
$767$	24.2331			0.875005
$768$	−5.94509			−0.214525
$769$	−25.8290	+	44.7372i	−0.931418	+	1.61326i	−0.150518	+	0.988607i	$0.548094\pi$
$769$	−25.8290	+	44.7372i	−0.931418	+	1.61326i	−0.780900	+	0.624656i	$0.785239\pi$
$770$		0			0
$771$	7.41327			0.266982
$772$	8.77063			0.315662
$773$	15.0779	−	26.1157i	0.542314	−	0.939316i	−0.456457	−	0.889746i	$-0.650882\pi$
$773$	15.0779	−	26.1157i	0.542314	−	0.939316i	0.998771	−	0.0495699i	$-0.0157851\pi$
$774$	13.3335	+	23.0943i	0.479262	+	0.830107i
$775$		0			0
$776$	26.7976	+	46.4148i	0.961978	+	1.66620i
$777$	0.609739	+	1.05610i	0.0218743	+	0.0378874i
$778$	−9.40431			−0.337161
$779$	23.9462	−	39.6816i	0.857962	−	1.42174i
$780$		0			0
$781$	−0.0892652	−	0.154612i	−0.00319416	−	0.00553244i
$782$	−4.89487	−	8.47816i	−0.175040	−	0.303178i
$783$	5.52088	−	9.56245i	0.197300	−	0.341734i
$784$	−3.03318	−	5.25363i	−0.108328	−	0.187630i
$785$		0			0
$786$	−1.20161			−0.0428601
$787$	−43.0969			−1.53624			−0.768119	−	0.640307i	$-0.778807\pi$
$787$	−43.0969			−1.53624			−0.768119	+	0.640307i	$0.778807\pi$
$788$	7.89791	−	13.6796i	0.281351	−	0.487315i
$789$	1.67165	−	2.89538i	0.0595123	−	0.103078i
$790$		0			0
$791$	1.59588			0.0567428
$792$	0.588848	−	1.01991i	0.0209238	−	0.0362411i
$793$	16.1208	+	27.9221i	0.572467	+	0.991542i
$794$	5.84086	−	10.1167i	0.207284	−	0.359027i
$795$		0			0
$796$	8.35514	+	14.4715i	0.296140	+	0.512929i
$797$	50.5062			1.78902			0.894510	−	0.447048i	$-0.147525\pi$
$797$	50.5062			1.78902			0.894510	+	0.447048i	$0.147525\pi$
$798$	−3.43450	−	0.0665010i	−0.121580	−	0.00235411i
$799$	18.4652			0.653253
$800$		0			0
$801$	13.9036	+	24.0818i	0.491261	+	0.850889i
$802$	4.19885	−	7.27261i	0.148266	−	0.256805i
$803$	−0.426207	−	0.738212i	−0.0150405	−	0.0260509i
$804$	0.445703	−	0.771981i	0.0157187	−	0.0272257i
$805$		0			0
$806$	25.3142			0.891656
$807$	−0.0546928	+	0.0947307i	−0.00192528	+	0.00333468i
$808$	−8.27955	+	14.3406i	−0.291274	+	0.504501i
$809$	−30.0872			−1.05781			−0.528905	−	0.848681i	$-0.677397\pi$
$809$	−30.0872			−1.05781			−0.528905	+	0.848681i	$0.677397\pi$
$810$		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	$0.298685\pi$
$812$	−3.74330	−	6.48359i	−0.131364	−	0.227529i
$813$	4.71725	−	8.17051i	0.165441	−	0.286552i
$814$	0.125238	+	0.216918i	0.00438958	+	0.00760298i
$815$		0			0
$816$	−1.11899			−0.0391723
$817$	−19.1607	+	31.7514i	−0.670347	+	1.11084i
$818$	19.4123			0.678734
$819$	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	$-0.0646941\pi$
$822$	3.91975	+	6.78921i	0.136717	+	0.236801i
$823$	26.8966	−	46.5862i	0.937556	−	1.62389i	0.167544	−	0.985865i	$-0.446416\pi$
$823$	26.8966	−	46.5862i	0.937556	−	1.62389i	0.770012	−	0.638030i	$-0.220250\pi$
$824$	−6.58858			−0.229524
$825$		0			0
$826$	7.16400	−	12.4084i	0.249267	−	0.431744i
$827$	16.2046	−	28.0672i	0.563490	−	0.975993i	−0.433699	−	0.901058i	$-0.642792\pi$
$827$	16.2046	−	28.0672i	0.563490	−	0.975993i	0.997188	−	0.0749347i	$-0.0238748\pi$
$828$	−12.2024			−0.424064
$829$	−18.5305			−0.643592			−0.321796	−	0.946809i	$-0.604287\pi$
$829$	−18.5305			−0.643592			−0.321796	+	0.946809i	$0.604287\pi$
$830$		0			0
$831$	−0.835456	−	1.44705i	−0.0289817	−	0.0501977i
$832$	14.3128	−	24.7904i	0.496206	−	0.859454i
$833$	2.83763	+	4.91491i	0.0983179	+	0.170292i
$834$	−3.78402	−	6.55411i	−0.131030	−	0.226950i
$835$		0			0
$836$	0.466021	+	0.00902339i	0.0161177	+	0.000312081i
$837$	−14.5830			−0.504062
$838$	0.651507	+	1.12844i	0.0225059	+	0.0389814i
$839$	−0.413304	−	0.715864i	−0.0142688	−	0.0247144i	0.858803	−	0.512306i	$-0.171209\pi$
$839$	−0.413304	−	0.715864i	−0.0142688	−	0.0247144i	−0.873072	+	0.487592i	$0.837875\pi$
$840$		0			0
$841$	2.14661	+	3.71803i	0.0740209	+	0.128208i
$842$	18.3093	−	31.7126i	0.630979	−	1.09289i
$843$	−12.4123			−0.427504
$844$	10.2045			0.351253
$845$		0			0
$846$	−17.4201	+	30.1725i	−0.598914	+	1.03735i
$847$	20.7895			0.714337
$848$	−0.470294			−0.0161500
$849$	−0.252053	+	0.436569i	−0.00865044	+	0.0149830i
$850$		0			0
$851$	4.55951	−	7.89730i	0.156298	−	0.270716i
$852$	0.200454	+	0.347197i	0.00686745	+	0.0118948i
$853$	−3.67469	−	6.36475i	−0.125819	−	0.217925i	0.796234	−	0.604989i	$-0.206823\pi$
$853$	−3.67469	−	6.36475i	−0.125819	−	0.217925i	−0.922053	+	0.387064i	$0.873489\pi$
$854$	19.0631			0.652327
$855$		0			0
$856$	3.07087			0.104960
$857$	−22.6748	−	39.2739i	−0.774556	−	1.34157i	−0.935044	−	0.354532i	$-0.884640\pi$
$857$	−22.6748	−	39.2739i	−0.774556	−	1.34157i	0.160488	−	0.987038i	$-0.448693\pi$
$858$	−0.0982968	−	0.170255i	−0.00335580	−	0.00581241i
$859$	−14.8143	+	25.6590i	−0.505456	+	0.875475i	0.494524	+	0.869164i	$0.335342\pi$
$859$	−14.8143	+	25.6590i	−0.505456	+	0.875475i	−0.999980	+	0.00631148i	$0.997991\pi$
$860$		0			0
$861$	3.81771	−	6.61247i	0.130107	−	0.225352i
$862$	6.77775			0.230851
$863$	−41.0807			−1.39840			−0.699201	−	0.714925i	$-0.746461\pi$
$863$	−41.0807			−1.39840			−0.699201	+	0.714925i	$0.746461\pi$
$864$	−4.65090	+	8.05559i	−0.158227	+	0.274057i
$865$		0			0
$866$	−20.3632			−0.691970
$867$	−5.40183			−0.183456
$868$	−4.94382	+	8.56295i	−0.167804	+	0.290645i
$869$	0.0986010	+	0.170782i	0.00334481	+	0.00579338i
$870$		0			0
$871$	5.18898	+	8.98758i	0.175822	+	0.304533i
$872$	−24.9475	−	43.2104i	−0.844831	−	1.46329i
$873$	49.8931			1.68863
$874$	12.4106	+	22.4903i	0.419794	+	0.760746i
$875$		0			0
$876$	0.957093	+	1.65773i	0.0323372	+	0.0560096i
$877$	27.3154	+	47.3116i	0.922374	+	1.59760i	0.795731	+	0.605650i	$0.207087\pi$
$877$	27.3154	+	47.3116i	0.922374	+	1.59760i	0.126643	+	0.991948i	$0.459580\pi$
$878$	−0.124730	+	0.216039i	−0.00420944	+	0.00729097i
$879$	−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	$0.583978\pi$
$882$	−10.7080			−0.360558
$883$	−22.6747	+	39.2738i	−0.763066	+	1.32167i	0.178197	+	0.983995i	$0.442973\pi$
$883$	−22.6747	+	39.2738i	−0.763066	+	1.32167i	−0.941263	+	0.337674i	$0.890360\pi$
$884$	−2.32209	+	4.02198i	−0.0781004	+	0.135274i
$885$		0			0
$886$	−38.3913			−1.28978
$887$	−15.5700	+	26.9680i	−0.522788	+	0.905496i	0.476860	+	0.878979i	$0.341775\pi$
$887$	−15.5700	+	26.9680i	−0.522788	+	0.905496i	−0.999648	+	0.0265165i	$0.991559\pi$
$888$	−0.988184	−	1.71158i	−0.0331613	−	0.0574370i
$889$	−17.7377	+	30.7227i	−0.594905	+	1.03041i
$890$		0			0
$891$	−0.519164	−	0.899218i	−0.0173926	−	0.0301249i
$892$	16.2264			0.543301
$893$	−48.4419	−	0.937963i	−1.62105	−	0.0313877i
$894$	9.26438			0.309847
$895$		0			0
$896$	−0.535663	−	0.927795i	−0.0178952	−	0.0309955i
$897$	−3.57867	+	6.19844i	−0.119488	+	0.206960i
$898$	−9.30127	−	16.1103i	−0.310387	−	0.537606i
$899$	−16.3153	+	28.2589i	−0.544145	+	0.942486i
$900$		0			0
$901$	0.439972			0.0146576
$902$	0.784142	−	1.35817i	0.0261091	−	0.0452222i
$903$	−3.05476	+	5.29100i	−0.101656	+	0.176073i
$904$	−2.58638			−0.0860218
$905$		0			0
$906$	0.694135	−	1.20228i	0.0230611	−	0.0399430i
$907$	21.7707	+	37.7080i	0.722886	+	1.25207i	0.959838	+	0.280554i	$0.0905181\pi$
$907$	21.7707	+	37.7080i	0.722886	+	1.25207i	−0.236952	+	0.971521i	$0.576149\pi$
$908$	−10.1113	+	17.5134i	−0.335557	+	0.581201i
$909$	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	$0.469751\pi$
$912$	2.93556	+	0.0568401i	0.0972060	+	0.00188217i
$913$	−1.00093			−0.0331258
$914$	−0.879275	−	1.52295i	−0.0290838	−	0.0503747i
$915$		0			0
$916$	0.881369	−	1.52658i	0.0291212	−	0.0504395i
$917$	2.73211	+	4.73216i	0.0902223	+	0.156270i
$918$	−2.02493	+	3.50728i	−0.0668327	+	0.115758i
$919$	7.93860			0.261870			0.130935	−	0.991391i	$-0.458202\pi$
$919$	7.93860			0.261870			0.130935	+	0.991391i	$0.458202\pi$
$920$		0			0
$921$	−1.72597	+	2.98947i	−0.0568728	+	0.0985065i
$922$	−4.79669	+	8.30812i	−0.157971	+	0.273613i
$923$	−4.66747			−0.153632
$924$	0.0767887			0.00252616
$925$		0			0
$926$	−11.6266	−	20.1378i	−0.382073	−	0.661771i
$927$	−3.06674	+	5.31174i	−0.100725	+	0.174461i
$928$	10.4067	+	18.0250i	0.341618	+	0.591700i
$929$	14.4784	+	25.0772i	0.475019	+	0.822758i	0.999591	−	0.0286089i	$-0.00910773\pi$
$929$	14.4784	+	25.0772i	0.475019	+	0.822758i	−0.524571	+	0.851366i	$0.675774\pi$
$930$		0			0
$931$	−7.19459	−	13.0380i	−0.235793	−	0.427302i
$932$	−11.2642			−0.368972
$933$	2.36265	+	4.09224i	0.0773498	+	0.133974i
$934$	−11.2222	−	19.4374i	−0.367201	−	0.636011i
$935$		0			0
$936$	−15.3948	−	26.6645i	−0.503193	−	0.871556i
$937$	−7.34080	+	12.7146i	−0.239813	+	0.415369i	−0.960661	−	0.277725i	$-0.910420\pi$
$937$	−7.34080	+	12.7146i	−0.239813	+	0.415369i	0.720847	+	0.693094i	$0.243753\pi$
$938$	6.13606			0.200349
$939$	−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	$0.165864\pi$
$942$	3.02352			0.0985114
$943$	−57.0961			−1.85931
$944$	−6.12326	+	10.6058i	−0.199295	+	0.345189i
$945$		0			0
$946$	−0.627435	+	1.08675i	−0.0203997	+	0.0353332i
$947$	−3.75904	−	6.51084i	−0.122152	−	0.211574i	0.798464	−	0.602043i	$-0.205646\pi$
$947$	−3.75904	−	6.51084i	−0.122152	−	0.211574i	−0.920616	+	0.390469i	$0.872313\pi$
$948$	−0.221419	−	0.383509i	−0.00719135	−	0.0124558i
$949$	−22.2854			−0.723415
$950$		0			0
$951$	−8.94137			−0.289944
$952$	4.82420	+	8.35576i	0.156353	+	0.270812i
$953$	11.3372	+	19.6365i	0.367247	+	0.636090i	0.989134	−	0.147017i	$-0.0469671\pi$
$953$	11.3372	+	19.6365i	0.367247	+	0.636090i	−0.621887	+	0.783107i	$0.713634\pi$
$954$	−0.415069	+	0.718920i	−0.0134384	+	0.0232759i
$955$		0			0
$956$	1.19931	−	2.07727i	0.0387886	−	0.0671838i
$957$	0.253413			0.00819167
$958$	−25.8437			−0.834973
$959$	17.8247	−	30.8733i	0.575590	−	0.996952i
$960$		0			0
$961$	12.0955			0.390177
$962$	6.54840			0.211129
$963$	1.42937	−	2.47575i	0.0460609	−	0.0797799i
$964$	−9.45972	−	16.3847i	−0.304677	−	0.527716i
$965$		0			0
$966$	2.11592	+	3.66488i	0.0680786	+	0.117916i
$967$	14.4172	+	24.9714i	0.463627	+	0.803025i	0.999138	−	0.0415030i	$-0.0132146\pi$
$967$	14.4172	+	24.9714i	0.463627	+	0.803025i	−0.535512	+	0.844528i	$0.679881\pi$
$968$	−33.6929			−1.08293
$969$	−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	$0.972379\pi$
$972$	3.81698	+	6.61120i	0.122430	+	0.212054i
$973$	−17.2075	+	29.8043i	−0.551647	+	0.955481i
$974$	−19.7754	−	34.2520i	−0.633645	−	1.09750i
$975$		0			0
$976$	−16.2938			−0.521551
$977$	−4.59218			−0.146917			−0.0734585	−	0.997298i	$-0.523404\pi$
$977$	−4.59218			−0.146917			−0.0734585	+	0.997298i	$0.523404\pi$
$978$	4.11681	−	7.13052i	0.131641	−	0.228009i
$979$	−0.654264	+	1.13322i	−0.0209104	+	0.0362178i
$980$		0			0
$981$	−46.4486			−1.48299
$982$	11.0070	−	19.0647i	0.351248	−	0.608379i
$983$	3.45737	+	5.98833i	0.110273	+	0.190998i	0.915880	−	0.401452i	$-0.131494\pi$
$983$	3.45737	+	5.98833i	0.110273	+	0.190998i	−0.805607	+	0.592450i	$0.798161\pi$
$984$	−6.18724	+	10.7166i	−0.197242	+	0.341633i
$985$		0			0
$986$	4.53094	+	7.84781i	0.144294	+	0.249925i
$987$	−7.98203			−0.254071
$988$	6.29609	−	10.4333i	0.200305	−	0.331929i
$989$	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	$0.627039\pi$
$992$	13.7443	−	23.8058i	0.436382	−	0.755835i
$993$	3.55009	+	6.14893i	0.112659	+	0.195130i
$994$	−1.37984	+	2.38996i	−0.0437659	+	0.0758048i
$995$		0			0
$996$	2.24768			0.0712205
$997$	8.11326	−	14.0526i	0.256950	−	0.445050i	−0.708474	−	0.705737i	$-0.750616\pi$
$997$	8.11326	−	14.0526i	0.256950	−	0.445050i	0.965423	+	0.260688i	$0.0839493\pi$
$998$	−20.2329	+	35.0443i	−0.640460	+	1.10931i
$999$	−3.77239			−0.119353

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	95.49	even	6
95.2.e.c.26.2	yes	8	5.4	even	2
475.2.e.e.26.3		8	1.1	even	1	trivial
475.2.e.e.201.3		8	19.11	even	3	inner
475.2.j.c.49.4		16	95.68	odd	12
475.2.j.c.49.5		16	95.87	odd	12
475.2.j.c.349.4		16	5.2	odd	4
475.2.j.c.349.5		16	5.3	odd	4
855.2.k.h.406.3		8	15.14	odd	2
855.2.k.h.676.3		8	285.239	odd	6
1520.2.q.o.881.2		8	20.19	odd	2
1520.2.q.o.961.2		8	380.239	odd	6
1805.2.a.i.1.2		4	95.69	odd	6
1805.2.a.o.1.3		4	95.64	even	6
9025.2.a.bg.1.2		4	19.7	even	3
9025.2.a.bp.1.3		4	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.548719 + 0.950409i) q^{2} +(-0.189667 - 0.328513i) q^{3} +(0.397815 - 0.689035i) q^{4} +(0.208148 - 0.360522i) q^{6} -1.89307 q^{7} +3.06803 q^{8} +(1.42805 - 2.47346i) q^{9} +0.134400 q^{11} -0.301809 q^{12} +(1.75687 - 3.04298i) q^{13} +(-1.03876 - 1.79919i) q^{14} +(0.887858 + 1.53781i) q^{16} +(-0.830615 - 1.43867i) q^{17} +3.13440 q^{18} +(2.10596 + 3.81640i) q^{19} +(0.359052 + 0.621897i) q^{21} +(0.0737478 + 0.127735i) q^{22} +(2.68492 - 4.65042i) q^{23} +(-0.581904 - 1.00789i) q^{24} +3.85611 q^{26} -2.22142 q^{27} +(-0.753090 + 1.30439i) q^{28} +(-2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(2.09366 - 3.62633i) q^{32} +(-0.0254912 - 0.0441521i) q^{33} +(0.911548 - 1.57885i) q^{34} +(-1.13620 - 1.96796i) q^{36} +1.69819 q^{37} +(-2.47156 + 4.09566i) q^{38} -1.33288 q^{39} +(-5.31637 - 9.20823i) q^{41} +(-0.394038 + 0.682493i) q^{42} +(4.25392 + 7.36801i) q^{43} +(0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(-5.55771 + 9.62623i) q^{47} +(0.336794 - 0.583345i) q^{48} -3.41630 q^{49} +(-0.315080 + 0.545735i) q^{51} +(-1.39781 - 2.42109i) q^{52} +(-0.132424 + 0.229365i) q^{53} +(-1.21894 - 2.11126i) q^{54} -5.80799 q^{56} +(0.854305 - 1.41568i) q^{57} -5.45492 q^{58} +(3.44833 + 5.97269i) q^{59} +(-4.58794 + 7.94655i) q^{61} +(3.60219 + 6.23917i) q^{62} +(-2.70340 + 4.68243i) q^{63} +8.14676 q^{64} +(0.0279750 - 0.0484542i) q^{66} +(-1.47677 + 2.55784i) q^{67} -1.32172 q^{68} -2.03696 q^{69} +(-0.664176 - 1.15039i) q^{71} +(4.38131 - 7.58865i) q^{72} +(-3.17119 - 5.49266i) q^{73} +(0.931830 + 1.61398i) q^{74} +(3.46742 + 0.0671384i) q^{76} -0.254428 q^{77} +(-0.731376 - 1.26678i) q^{78} +(0.733639 + 1.27070i) q^{79} +(-3.86283 - 6.69062i) q^{81} +(5.83439 - 10.1055i) q^{82} -7.44736 q^{83} +0.571345 q^{84} +(-4.66842 + 8.08593i) q^{86} +1.88551 q^{87} +0.412343 q^{88} +(-4.86804 + 8.43169i) q^{89} +(-3.32587 + 5.76057i) q^{91} +(-2.13620 - 3.70001i) q^{92} +(-1.24511 - 2.15659i) q^{93} -12.1985 q^{94} -1.58839 q^{96} +(8.73447 + 15.1285i) q^{97} +(-1.87459 - 3.24688i) q^{98} +(0.191930 - 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

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