LMFDB - Embedded newform 198.2.m.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(25,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 24]))

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

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

chi := DirichletCharacter("198.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.m (of order $15$, degree $8$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	198.49
Dual form			198.2.m.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 - 0.743145i) q^{2} +(-1.66291 + 0.484474i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.75609 + 1.95033i) q^{5} +(-0.752673 + 1.55996i) q^{6} +(1.40440 + 0.625278i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.53057 - 1.61128i) q^{9} +O(q^{10})$	\(q+(0.669131 - 0.743145i) q^{2} +(-1.66291 + 0.484474i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.75609 + 1.95033i) q^{5} +(-0.752673 + 1.55996i) q^{6} +(1.40440 + 0.625278i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.53057 - 1.61128i) q^{9} +2.62443 q^{10} +(3.23346 - 0.738058i) q^{11} +(0.655642 + 1.60316i) q^{12} +(1.58774 + 0.337484i) q^{13} +(1.40440 - 0.625278i) q^{14} +(-3.86511 - 2.39246i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.03227 + 3.17700i) q^{17} +(0.495870 - 2.95874i) q^{18} +(-3.99057 - 2.89932i) q^{19} +(1.75609 - 1.95033i) q^{20} +(-2.63832 - 0.359390i) q^{21} +(1.61512 - 2.89679i) q^{22} +(0.139293 - 0.241263i) q^{23} +(1.63009 + 0.585489i) q^{24} +(-0.197313 + 1.87731i) q^{25} +(1.31321 - 0.954099i) q^{26} +(-3.42750 + 3.90541i) q^{27} +(0.475053 - 1.46206i) q^{28} +(7.01122 + 3.12160i) q^{29} +(-4.36421 + 1.27147i) q^{30} +(-10.6635 - 2.26659i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.01940 + 2.79385i) q^{33} +(1.67025 + 2.89296i) q^{34} +(1.24675 + 3.83709i) q^{35} +(-1.86697 - 2.34828i) q^{36} +(-0.559637 + 0.406600i) q^{37} +(-4.82483 + 1.02555i) q^{38} +(-2.80378 + 0.208010i) q^{39} +(-0.274328 - 2.61006i) q^{40} +(-3.07428 + 1.36876i) q^{41} +(-2.03246 + 1.72018i) q^{42} +(-3.73048 - 6.46138i) q^{43} +(-1.07200 - 3.13860i) q^{44} +(7.58643 + 2.10591i) q^{45} +(-0.0860878 - 0.264951i) q^{46} +(-0.969749 + 9.22655i) q^{47} +(1.52585 - 0.819626i) q^{48} +(-3.10256 - 3.44574i) q^{49} +(1.26308 + 1.40280i) q^{50} +(0.177404 - 5.78319i) q^{51} +(0.169672 - 1.61432i) q^{52} +(-2.24432 - 6.90729i) q^{53} +(0.608840 + 5.16036i) q^{54} +(7.11770 + 5.01023i) q^{55} +(-0.768652 - 1.33134i) q^{56} +(8.04062 + 2.88799i) q^{57} +(7.01122 - 3.12160i) q^{58} +(-1.40689 - 13.3856i) q^{59} +(-1.97534 + 4.09402i) q^{60} +(4.72413 - 1.00415i) q^{61} +(-8.81966 + 6.40786i) q^{62} +(4.56142 - 0.680563i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.13000 + 3.68928i) q^{65} +(-1.28240 + 5.59959i) q^{66} +(-1.75990 + 3.04823i) q^{67} +(3.26750 + 0.694529i) q^{68} +(-0.114747 + 0.468683i) q^{69} +(3.68575 + 1.64100i) q^{70} +(-1.44023 + 4.43258i) q^{71} +(-2.99436 - 0.183881i) q^{72} +(-0.517949 + 0.376312i) q^{73} +(-0.0723075 + 0.687960i) q^{74} +(-0.581392 - 3.21740i) q^{75} +(-2.46631 + 4.27177i) q^{76} +(5.00255 + 0.985285i) q^{77} +(-1.72151 + 2.22280i) q^{78} +(8.84861 - 9.82737i) q^{79} +(-2.12321 - 1.54260i) q^{80} +(3.80757 - 8.15490i) q^{81} +(-1.03991 + 3.20051i) q^{82} +(8.66046 - 1.84084i) q^{83} +(-0.0816415 + 2.66144i) q^{84} +(-8.00897 + 3.56583i) q^{85} +(-7.29792 - 1.55122i) q^{86} +(-13.1714 - 1.79420i) q^{87} +(-3.04974 - 1.30348i) q^{88} -15.3382 q^{89} +(6.64131 - 4.22869i) q^{90} +(2.01880 + 1.46674i) q^{91} +(-0.254501 - 0.113311i) q^{92} +(18.8306 - 1.39703i) q^{93} +(6.20777 + 6.89443i) q^{94} +(-1.35315 - 12.8744i) q^{95} +(0.411891 - 1.68236i) q^{96} +(0.557588 - 0.619264i) q^{97} -4.63670 q^{98} +(6.99328 - 7.07771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 3 q^{3} + 7 q^{4} - q^{5} - 5 q^{6} - 14 q^{8} + 9 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 - q^5 - 5 * q^6 - 14 * q^8 + 9 * q^9	\( 56 q + 7 q^{2} + 3 q^{3} + 7 q^{4} - q^{5} - 5 q^{6} - 14 q^{8} + 9 q^{9} - 8 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} + 11 q^{15} + 7 q^{16} + 15 q^{18} - q^{20} + 2 q^{21} - 4 q^{22} - 14 q^{23} - 2 q^{24} + 22 q^{25} - 12 q^{26} - 48 q^{27} + 14 q^{29} + 2 q^{30} + 5 q^{31} - 28 q^{32} - 44 q^{33} - 20 q^{34} - 20 q^{35} - 9 q^{36} + 2 q^{37} + 5 q^{38} - 34 q^{39} - q^{40} - 14 q^{41} + 4 q^{42} + 6 q^{43} - 12 q^{44} + 8 q^{46} + 11 q^{47} + 35 q^{49} + 2 q^{50} - 69 q^{51} + 6 q^{52} - 50 q^{53} + 4 q^{54} + 6 q^{55} + 36 q^{57} + 14 q^{58} + 10 q^{59} + 12 q^{60} - 24 q^{61} - 10 q^{62} - 16 q^{63} - 14 q^{64} - 42 q^{65} - 6 q^{66} - 56 q^{67} + 70 q^{69} - 6 q^{71} + 9 q^{72} + 68 q^{73} - q^{74} - 92 q^{75} - 10 q^{76} + 10 q^{77} + 60 q^{78} - 12 q^{79} + 2 q^{80} - 67 q^{81} - 52 q^{82} - 25 q^{83} + 4 q^{84} - 7 q^{85} + 11 q^{86} + 86 q^{87} - 4 q^{88} + 104 q^{89} + 25 q^{90} - 158 q^{91} + 11 q^{92} + 95 q^{93} - 19 q^{94} + 68 q^{95} - 3 q^{96} + 32 q^{97} + 120 q^{98} + 155 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 - q^5 - 5 * q^6 - 14 * q^8 + 9 * q^9 - 8 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 + 11 * q^15 + 7 * q^16 + 15 * q^18 - q^20 + 2 * q^21 - 4 * q^22 - 14 * q^23 - 2 * q^24 + 22 * q^25 - 12 * q^26 - 48 * q^27 + 14 * q^29 + 2 * q^30 + 5 * q^31 - 28 * q^32 - 44 * q^33 - 20 * q^34 - 20 * q^35 - 9 * q^36 + 2 * q^37 + 5 * q^38 - 34 * q^39 - q^40 - 14 * q^41 + 4 * q^42 + 6 * q^43 - 12 * q^44 + 8 * q^46 + 11 * q^47 + 35 * q^49 + 2 * q^50 - 69 * q^51 + 6 * q^52 - 50 * q^53 + 4 * q^54 + 6 * q^55 + 36 * q^57 + 14 * q^58 + 10 * q^59 + 12 * q^60 - 24 * q^61 - 10 * q^62 - 16 * q^63 - 14 * q^64 - 42 * q^65 - 6 * q^66 - 56 * q^67 + 70 * q^69 - 6 * q^71 + 9 * q^72 + 68 * q^73 - q^74 - 92 * q^75 - 10 * q^76 + 10 * q^77 + 60 * q^78 - 12 * q^79 + 2 * q^80 - 67 * q^81 - 52 * q^82 - 25 * q^83 + 4 * q^84 - 7 * q^85 + 11 * q^86 + 86 * q^87 - 4 * q^88 + 104 * q^89 + 25 * q^90 - 158 * q^91 + 11 * q^92 + 95 * q^93 - 19 * q^94 + 68 * q^95 - 3 * q^96 + 32 * q^97 + 120 * q^98 + 155 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$3$	−1.66291	+	0.484474i	−0.960084	+	0.279711i
$3$	−1.66291	+	0.484474i	−0.960084	+	0.279711i
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	1.75609	+	1.95033i	0.785347	+	0.872216i	0.994399	−	0.105688i	$-0.0337046\pi$
$5$	1.75609	+	1.95033i	0.785347	+	0.872216i	−0.209053	+	0.977904i	$0.567038\pi$
$6$	−0.752673	+	1.55996i	−0.307277	+	0.636852i
$7$	1.40440	+	0.625278i	0.530812	+	0.236333i	0.654599	−	0.755976i	$-0.272837\pi$
$7$	1.40440	+	0.625278i	0.530812	+	0.236333i	−0.123787	+	0.992309i	$0.539504\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.53057	−	1.61128i	0.843523	−	0.537092i
$10$	2.62443			0.829919
$11$	3.23346	−	0.738058i	0.974925	−	0.222533i
$11$	3.23346	−	0.738058i	0.974925	−	0.222533i
$12$	0.655642	+	1.60316i	0.189267	+	0.462794i
$13$	1.58774	+	0.337484i	0.440360	+	0.0936014i	0.422756	−	0.906244i	$-0.361063\pi$
$13$	1.58774	+	0.337484i	0.440360	+	0.0936014i	0.0176040	+	0.999845i	$0.494396\pi$
$14$	1.40440	−	0.625278i	0.375341	−	0.167113i
$15$	−3.86511	−	2.39246i	−0.997967	−	0.617731i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−1.03227	+	3.17700i	−0.250362	+	0.770536i	0.744346	+	0.667795i	$0.232762\pi$
$17$	−1.03227	+	3.17700i	−0.250362	+	0.770536i	−0.994708	+	0.102742i	$0.967238\pi$
$18$	0.495870	−	2.95874i	0.116878	−	0.697381i
$19$	−3.99057	−	2.89932i	−0.915499	−	0.665149i	0.0269002	−	0.999638i	$-0.491436\pi$
$19$	−3.99057	−	2.89932i	−0.915499	−	0.665149i	−0.942400	+	0.334489i	$0.891436\pi$
$20$	1.75609	−	1.95033i	0.392673	−	0.436108i
$21$	−2.63832	−	0.359390i	−0.575729	−	0.0784254i
$22$	1.61512	−	2.89679i	0.344346	−	0.617597i
$23$	0.139293	−	0.241263i	0.0290446	−	0.0503067i	−0.851138	−	0.524942i	$-0.824087\pi$
$23$	0.139293	−	0.241263i	0.0290446	−	0.0503067i	0.880182	+	0.474636i	$0.157420\pi$
$24$	1.63009	+	0.585489i	0.332741	+	0.119512i
$25$	−0.197313	+	1.87731i	−0.0394626	+	0.375462i
$26$	1.31321	−	0.954099i	0.257541	−	0.187114i
$27$	−3.42750	+	3.90541i	−0.659623	+	0.751597i
$28$	0.475053	−	1.46206i	0.0897766	−	0.276304i
$29$	7.01122	+	3.12160i	1.30195	+	0.579666i	0.936337	−	0.351101i	$-0.114193\pi$
$29$	7.01122	+	3.12160i	1.30195	+	0.579666i	0.365613	+	0.930767i	$0.380859\pi$
$30$	−4.36421	+	1.27147i	−0.796792	+	0.232137i
$31$	−10.6635	−	2.26659i	−1.91522	−	0.407092i	−0.999991	−	0.00414980i	$-0.998679\pi$
$31$	−10.6635	−	2.26659i	−1.91522	−	0.407092i	−0.915225	−	0.402942i	$-0.867988\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−5.01940	+	2.79385i	−0.873765	+	0.486348i
$34$	1.67025	+	2.89296i	0.286445	+	0.496138i
$35$	1.24675	+	3.83709i	0.210738	+	0.648586i
$36$	−1.86697	−	2.34828i	−0.311161	−	0.391381i
$37$	−0.559637	+	0.406600i	−0.0920037	+	0.0668446i	−0.632836	−	0.774286i	$-0.718109\pi$
$37$	−0.559637	+	0.406600i	−0.0920037	+	0.0668446i	0.540832	+	0.841130i	$0.318109\pi$
$38$	−4.82483	+	1.02555i	−0.782690	+	0.166366i
$39$	−2.80378	+	0.208010i	−0.448964	+	0.0333083i
$40$	−0.274328	−	2.61006i	−0.0433751	−	0.412686i
$41$	−3.07428	+	1.36876i	−0.480121	+	0.213764i	−0.632503	−	0.774558i	$-0.717972\pi$
$41$	−3.07428	+	1.36876i	−0.480121	+	0.213764i	0.152382	+	0.988322i	$0.451306\pi$
$42$	−2.03246	+	1.72018i	−0.313616	+	0.265429i
$43$	−3.73048	−	6.46138i	−0.568893	−	0.985351i	−0.996676	−	0.0814699i	$-0.974039\pi$
$43$	−3.73048	−	6.46138i	−0.568893	−	0.985351i	0.427783	−	0.903882i	$-0.359295\pi$
$44$	−1.07200	−	3.13860i	−0.161611	−	0.473162i
$45$	7.58643	+	2.10591i	1.13092	+	0.313931i
$46$	−0.0860878	−	0.264951i	−0.0126930	−	0.0390649i
$47$	−0.969749	+	9.22655i	−0.141452	+	1.34583i	0.661571	+	0.749883i	$0.269890\pi$
$47$	−0.969749	+	9.22655i	−0.141452	+	1.34583i	−0.803023	+	0.595948i	$0.796777\pi$
$48$	1.52585	−	0.819626i	0.220237	−	0.118303i
$49$	−3.10256	−	3.44574i	−0.443222	−	0.492248i
$50$	1.26308	+	1.40280i	0.178627	+	0.198386i
$51$	0.177404	−	5.78319i	0.0248415	−	0.809809i
$52$	0.169672	−	1.61432i	0.0235292	−	0.223866i
$53$	−2.24432	−	6.90729i	−0.308280	−	0.948790i	−0.978433	−	0.206566i	$-0.933771\pi$
$53$	−2.24432	−	6.90729i	−0.308280	−	0.948790i	0.670152	−	0.742224i	$-0.266229\pi$
$54$	0.608840	+	5.16036i	0.0828527	+	0.702236i
$55$	7.11770	+	5.01023i	0.959751	+	0.675580i
$56$	−0.768652	−	1.33134i	−0.102715	−	0.177908i
$57$	8.04062	+	2.88799i	1.06501	+	0.382524i
$58$	7.01122	−	3.12160i	0.920618	−	0.409886i
$59$	−1.40689	−	13.3856i	−0.183161	−	1.74266i	−0.571016	−	0.820939i	$-0.693450\pi$
$59$	−1.40689	−	13.3856i	−0.183161	−	1.74266i	0.387855	−	0.921720i	$-0.373216\pi$
$60$	−1.97534	+	4.09402i	−0.255015	+	0.528535i
$61$	4.72413	−	1.00415i	0.604863	−	0.128568i	0.104707	−	0.994503i	$-0.466609\pi$
$61$	4.72413	−	1.00415i	0.604863	−	0.128568i	0.500156	+	0.865935i	$0.333276\pi$
$62$	−8.81966	+	6.40786i	−1.12010	+	0.813799i
$63$	4.56142	−	0.680563i	0.574685	−	0.0857429i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.13000	+	3.68928i	0.264195	+	0.457598i
$66$	−1.28240	+	5.59959i	−0.157852	+	0.689262i
$67$	−1.75990	+	3.04823i	−0.215006	+	0.372401i	−0.953274	−	0.302106i	$-0.902310\pi$
$67$	−1.75990	+	3.04823i	−0.215006	+	0.372401i	0.738269	+	0.674507i	$0.235644\pi$
$68$	3.26750	+	0.694529i	0.396243	+	0.0842240i
$69$	−0.114747	+	0.468683i	−0.0138139	+	0.0564228i
$70$	3.68575	+	1.64100i	0.440531	+	0.196137i
$71$	−1.44023	+	4.43258i	−0.170924	+	0.526051i	−0.999424	−	0.0339388i	$-0.989195\pi$
$71$	−1.44023	+	4.43258i	−0.170924	+	0.526051i	0.828500	+	0.559990i	$0.189195\pi$
$72$	−2.99436	−	0.183881i	−0.352889	−	0.0216706i
$73$	−0.517949	+	0.376312i	−0.0606214	+	0.0440440i	−0.617683	−	0.786427i	$-0.711929\pi$
$73$	−0.517949	+	0.376312i	−0.0606214	+	0.0440440i	0.557062	+	0.830471i	$0.311929\pi$
$74$	−0.0723075	+	0.687960i	−0.00840557	+	0.0799737i
$75$	−0.581392	−	3.21740i	−0.0671334	−	0.371513i
$76$	−2.46631	+	4.27177i	−0.282905	+	0.490006i
$77$	5.00255	+	0.985285i	0.570094	+	0.112284i
$78$	−1.72151	+	2.22280i	−0.194923	+	0.251682i
$79$	8.84861	−	9.82737i	0.995546	−	1.10567i	0.00114436	−	0.999999i	$-0.499636\pi$
$79$	8.84861	−	9.82737i	0.995546	−	1.10567i	0.994402	−	0.105666i	$-0.0336976\pi$
$80$	−2.12321	−	1.54260i	−0.237382	−	0.172468i
$81$	3.80757	−	8.15490i	0.423064	−	0.906100i
$82$	−1.03991	+	3.20051i	−0.114839	+	0.353437i
$83$	8.66046	−	1.84084i	0.950609	−	0.202058i	0.293589	−	0.955932i	$-0.405150\pi$
$83$	8.66046	−	1.84084i	0.950609	−	0.202058i	0.657020	+	0.753873i	$0.271817\pi$
$84$	−0.0816415	+	2.66144i	−0.00890782	+	0.290387i
$85$	−8.00897	+	3.56583i	−0.868695	+	0.386768i
$86$	−7.29792	−	1.55122i	−0.786955	−	0.167272i
$87$	−13.1714	−	1.79420i	−1.41212	−	0.192358i
$88$	−3.04974	−	1.30348i	−0.325104	−	0.138951i
$89$	−15.3382			−1.62585			−0.812923	−	0.582371i	$-0.802125\pi$
$89$	−15.3382			−1.62585			−0.812923	+	0.582371i	$0.802125\pi$
$90$	6.64131	−	4.22869i	0.700056	−	0.445743i
$91$	2.01880	+	1.46674i	0.211627	+	0.153756i
$92$	−0.254501	−	0.113311i	−0.0265336	−	0.0118135i
$93$	18.8306	−	1.39703i	1.95264	−	0.144865i
$94$	6.20777	+	6.89443i	0.640283	+	0.711106i
$95$	−1.35315	−	12.8744i	−0.138831	−	1.32089i
$96$	0.411891	−	1.68236i	0.0420384	−	0.171705i
$97$	0.557588	−	0.619264i	0.0566145	−	0.0628768i	−0.714172	−	0.699970i	$-0.753197\pi$
$97$	0.557588	−	0.619264i	0.0566145	−	0.0628768i	0.770787	+	0.637093i	$0.219863\pi$
$98$	−4.63670			−0.468377
$99$	6.99328	−	7.07771i	0.702852	−	0.711337i
$100$	1.88765			0.188765
$101$	−5.53017	+	6.14187i	−0.550272	+	0.611139i	−0.952551	−	0.304378i	$-0.901551\pi$
$101$	−5.53017	+	6.14187i	−0.550272	+	0.611139i	0.402279	+	0.915517i	$0.368218\pi$
$102$	−4.17904	−	4.00155i	−0.413787	−	0.396212i
$103$	0.695709	+	6.61923i	0.0685503	+	0.652212i	0.973811	+	0.227357i	$0.0730084\pi$
$103$	0.695709	+	6.61923i	0.0685503	+	0.652212i	−0.905261	+	0.424855i	$0.860325\pi$
$104$	−1.08614	−	1.20628i	−0.106505	−	0.118286i
$105$	−3.93220	−	5.77673i	−0.383743	−	0.563751i
$106$	−6.63486	−	2.95403i	−0.644435	−	0.286921i
$107$	11.2283	+	8.15787i	1.08549	+	0.788651i	0.978631	−	0.205623i	$-0.0659222\pi$
$107$	11.2283	+	8.15787i	1.08549	+	0.788651i	0.106854	+	0.994275i	$0.465922\pi$
$108$	4.24229	+	3.00050i	0.408214	+	0.288723i
$109$	−11.5586			−1.10712			−0.553559	−	0.832810i	$-0.686731\pi$
$109$	−11.5586			−1.10712			−0.553559	+	0.832810i	$0.686731\pi$
$110$	8.48600	−	1.93698i	0.809109	−	0.184684i
$111$	0.733641	−	0.947270i	0.0696342	−	0.0899109i
$112$	−1.50371	−	0.319623i	−0.142087	−	0.0302016i
$113$	2.44556	−	1.08883i	0.230059	−	0.102429i	−0.288470	−	0.957489i	$-0.593146\pi$
$113$	2.44556	−	1.08883i	0.230059	−	0.102429i	0.518529	+	0.855060i	$0.326480\pi$
$114$	7.52642	−	4.04290i	0.704914	−	0.378652i
$115$	0.715153	−	0.152011i	0.0666884	−	0.0141751i
$116$	2.37162	−	7.29910i	0.220200	−	0.677705i
$117$	4.56167	−	1.70426i	0.421726	−	0.157559i
$118$	−10.8888	−	7.91121i	−1.00240	−	0.728286i
$119$	−3.43623	+	3.81632i	−0.314998	+	0.349841i
$120$	1.72069	+	4.20740i	0.157077	+	0.384081i
$121$	9.91054	−	4.77296i	0.900958	−	0.433906i
$122$	2.41484	−	4.18262i	0.218629	−	0.378677i
$123$	4.44913	−	3.76553i	0.401165	−	0.339526i
$124$	−1.13954	+	10.8420i	−0.102334	+	0.973639i
$125$	6.60817	−	4.80112i	0.591053	−	0.429425i
$126$	2.54643	−	3.84518i	0.226854	−	0.342556i
$127$	−3.47110	+	10.6829i	−0.308010	+	0.947958i	0.670526	+	0.741886i	$0.266068\pi$
$127$	−3.47110	+	10.6829i	−0.308010	+	0.947958i	−0.978537	+	0.206073i	$0.933932\pi$
$128$	0.913545	+	0.406737i	0.0807468	+	0.0359508i
$129$	9.33384	+	8.93741i	0.821799	+	0.786895i
$130$	4.16692	+	0.885706i	0.365463	+	0.0776815i
$131$	2.10693	−	3.64931i	0.184083	−	0.318842i	−0.759184	−	0.650876i	$-0.774402\pi$
$131$	2.10693	−	3.64931i	0.184083	−	0.318842i	0.943267	+	0.332034i	$0.107735\pi$
$132$	3.30322	+	4.69987i	0.287508	+	0.409071i
$133$	−3.79146	−	6.56701i	−0.328762	−	0.569432i
$134$	1.08768	+	3.34752i	0.0939609	+	0.289182i
$135$	−13.6359	+	0.173476i	−1.17359	+	0.0149305i
$136$	2.70252	−	1.96350i	0.231739	−	0.168368i
$137$	−6.91945	+	1.47078i	−0.591169	+	0.125657i	−0.493776	−	0.869589i	$-0.664384\pi$
$137$	−6.91945	+	1.47078i	−0.591169	+	0.125657i	−0.0973929	+	0.995246i	$0.531050\pi$
$138$	0.271519	+	0.398884i	0.0231132	+	0.0339552i
$139$	1.84312	+	17.5361i	0.156331	+	1.48739i	0.738461	+	0.674296i	$0.235553\pi$
$139$	1.84312	+	17.5361i	0.156331	+	1.48739i	−0.582130	+	0.813095i	$0.697781\pi$
$140$	3.68575	−	1.64100i	0.311502	−	0.138690i
$141$	−2.85741	−	15.8128i	−0.240637	−	1.33168i
$142$	2.33035	+	4.03628i	0.195558	+	0.338717i
$143$	5.38298	−	0.0806010i	0.450147	−	0.00674019i
$144$	−2.14027	+	2.10220i	−0.178356	+	0.175183i
$145$	6.22417	+	19.1560i	0.516889	+	1.59082i
$146$	−0.0669213	+	0.636713i	−0.00553844	+	0.0526948i
$147$	6.82865	+	4.22686i	0.563218	+	0.348626i
$148$	0.462871	+	0.514070i	0.0380477	+	0.0422563i
$149$	5.85243	+	6.49978i	0.479449	+	0.532483i	0.933540	−	0.358473i	$-0.116702\pi$
$149$	5.85243	+	6.49978i	0.479449	+	0.532483i	−0.454091	+	0.890955i	$0.650036\pi$
$150$	−2.78002	−	1.72080i	−0.226988	−	0.140503i
$151$	−1.85419	+	17.6414i	−0.150892	+	1.43564i	0.612892	+	0.790167i	$0.290006\pi$
$151$	−1.85419	+	17.6414i	−0.150892	+	1.43564i	−0.763784	+	0.645472i	$0.776661\pi$
$152$	1.52426	+	4.69120i	0.123634	+	0.380506i
$153$	2.50680	+	9.70290i	0.202663	+	0.784433i
$154$	4.07957	−	3.05834i	0.328741	−	0.246448i
$155$	−14.3054	−	24.7777i	−1.14904	−	1.99019i
$156$	0.499945	+	2.76668i	0.0400277	+	0.221511i
$157$	11.8063	−	5.25651i	0.942247	−	0.419515i	0.122646	−	0.992450i	$-0.460862\pi$
$157$	11.8063	−	5.25651i	0.942247	−	0.419515i	0.819601	+	0.572935i	$0.194195\pi$
$158$	−1.38229	−	13.1516i	−0.109969	−	1.04628i
$159$	7.07851	+	10.3989i	0.561362	+	0.824689i
$160$	−2.56708	+	0.545650i	−0.202946	+	0.0431375i
$161$	0.346479	−	0.251732i	0.0273064	−	0.0198392i
$162$	−3.51251	−	8.28627i	−0.275969	−	0.651031i
$163$	0.199095	+	0.612751i	0.0155943	+	0.0479944i	0.958551	−	0.284921i	$-0.0919675\pi$
$163$	0.199095	+	0.612751i	0.0155943	+	0.0479944i	−0.942957	+	0.332916i	$0.891968\pi$
$164$	1.68261	+	2.91436i	0.131390	+	0.227573i
$165$	−14.2635	−	4.88325i	−1.11041	−	0.380161i
$166$	4.42697	−	7.66774i	0.343600	−	0.595132i
$167$	−15.9763	−	3.39586i	−1.23628	−	0.262780i	−0.457007	−	0.889463i	$-0.651079\pi$
$167$	−15.9763	−	3.39586i	−1.23628	−	0.262780i	−0.779274	+	0.626683i	$0.784412\pi$
$168$	1.92320	+	1.84152i	0.148378	+	0.142076i
$169$	−9.46907	−	4.21590i	−0.728390	−	0.324300i
$170$	−2.70913	+	8.33783i	−0.207780	+	0.639482i
$171$	−14.7700	−	0.907016i	−1.12949	−	0.0693613i
$172$	−6.03604	+	4.38544i	−0.460244	+	0.334387i
$173$	−0.250499	+	2.38334i	−0.0190451	+	0.181202i	−0.999909	−	0.0134930i	$-0.995705\pi$
$173$	−0.250499	+	2.38334i	−0.0190451	+	0.181202i	0.980864	+	0.194695i	$0.0623716\pi$
$174$	−10.1467	+	8.58770i	−0.769221	+	0.651032i
$175$	−1.45095	+	2.51311i	−0.109681	+	0.189973i
$176$	−3.00935	+	1.39420i	−0.226838	+	0.105092i
$177$	8.82451	+	21.5775i	0.663291	+	1.62187i
$178$	−10.2633	+	11.3985i	−0.769264	+	0.854354i
$179$	−17.3512	−	12.6064i	−1.29689	−	0.942245i	−0.296969	−	0.954887i	$-0.595976\pi$
$179$	−17.3512	−	12.6064i	−1.29689	−	0.942245i	−0.999920	+	0.0126417i	$0.995976\pi$
$180$	1.30138	−	7.76500i	0.0969989	−	0.578769i
$181$	7.56256	−	23.2752i	0.562120	−	1.73003i	−0.114236	−	0.993454i	$-0.536442\pi$
$181$	7.56256	−	23.2752i	0.562120	−	1.73003i	0.676356	−	0.736575i	$-0.263558\pi$
$182$	2.44084	−	0.518816i	0.180927	−	0.0384572i
$183$	−7.36935	+	3.95853i	−0.544758	+	0.292623i
$184$	−0.254501	+	0.113311i	−0.0187621	+	0.00835341i
$185$	−1.77578	−	0.377453i	−0.130558	−	0.0277509i
$186$	11.5619	−	14.9286i	0.847760	−	1.09462i
$187$	−0.992995	+	11.0346i	−0.0726150	+	0.806929i
$188$	9.27737			0.676622
$189$	−7.25554	+	3.34161i	−0.527763	+	0.243066i
$190$	−10.4730	−	7.60907i	−0.759790	−	0.552020i
$191$	−0.424318	−	0.188918i	−0.0307025	−	0.0136697i	0.391328	−	0.920251i	$-0.372016\pi$
$191$	−0.424318	−	0.188918i	−0.0307025	−	0.0136697i	−0.422030	+	0.906582i	$0.638682\pi$
$192$	−0.974631	−	1.43182i	−0.0703379	−	0.103332i
$193$	−3.91527	−	4.34834i	−0.281827	−	0.313001i	0.585566	−	0.810625i	$-0.300872\pi$
$193$	−3.91527	−	4.34834i	−0.281827	−	0.313001i	−0.867393	+	0.497624i	$0.834206\pi$
$194$	−0.0871038	−	0.828737i	−0.00625369	−	0.0594999i
$195$	−5.32937	−	5.10302i	−0.381644	−	0.365435i
$196$	−3.10256	+	3.44574i	−0.221611	+	0.246124i
$197$	−17.5599			−1.25109			−0.625547	−	0.780186i	$-0.715124\pi$
$197$	−17.5599			−1.25109			−0.625547	+	0.780186i	$0.715124\pi$
$198$	−0.580342	−	9.93294i	−0.0412431	−	0.705903i
$199$	20.9697			1.48650			0.743252	−	0.669011i	$-0.233282\pi$
$199$	20.9697			1.48650			0.743252	+	0.669011i	$0.233282\pi$
$200$	1.26308	−	1.40280i	0.0893136	−	0.0991928i
$201$	1.44977	−	5.92157i	0.102259	−	0.417675i
$202$	0.863897	+	8.21943i	0.0607836	+	0.578317i
$203$	7.89467	+	8.76792i	0.554097	+	0.615387i
$204$	−5.77005	+	0.428076i	−0.403985	+	0.0299713i
$205$	−8.06823	−	3.59221i	−0.563510	−	0.250891i
$206$	5.38457	+	3.91212i	0.375161	+	0.272570i
$207$	−0.0362501	−	0.834972i	−0.00251956	−	0.0580345i
$208$	−1.62321			−0.112549
$209$	−15.0432	−	6.42956i	−1.04056	−	0.444742i
$210$	−6.92410	−	0.943196i	−0.477809	−	0.0650867i
$211$	−3.26410	−	0.693806i	−0.224710	−	0.0477636i	0.0941805	−	0.995555i	$-0.469977\pi$
$211$	−3.26410	−	0.693806i	−0.224710	−	0.0477636i	−0.318891	+	0.947792i	$0.603310\pi$
$212$	−6.63486	+	2.95403i	−0.455684	+	0.202884i
$213$	0.247515	−	8.06876i	0.0169595	−	0.552862i
$214$	13.5757	−	2.88561i	0.928017	−	0.197256i
$215$	6.05080	−	18.6224i	0.412661	−	1.27004i
$216$	5.06845	−	1.14491i	0.344864	−	0.0779012i
$217$	−13.5585	−	9.85083i	−0.920411	−	0.668718i
$218$	−7.73424	+	8.58975i	−0.523829	+	0.581771i
$219$	0.678992	−	0.876708i	0.0458820	−	0.0592424i
$220$	4.23878	−	7.60242i	0.285779	−	0.512555i
$221$	−2.71117	+	4.69588i	−0.182373	+	0.315879i
$222$	−0.213057	−	1.17905i	−0.0142995	−	0.0791326i
$223$	0.226508	−	2.15508i	0.0151681	−	0.144315i	−0.984317	−	0.176410i	$-0.943551\pi$
$223$	0.226508	−	2.15508i	0.0151681	−	0.144315i	0.999485	+	0.0320956i	$0.0102181\pi$
$224$	−1.24371	+	0.903605i	−0.0830985	+	0.0603746i
$225$	2.52555	+	5.06859i	0.168370	+	0.337906i
$226$	0.827239	−	2.54598i	0.0550271	−	0.169356i
$227$	24.7075	+	11.0005i	1.63989	+	0.730128i	0.999288	−	0.0377403i	$-0.0120160\pi$
$227$	24.7075	+	11.0005i	1.63989	+	0.730128i	0.640607	+	0.767869i	$0.278683\pi$
$228$	2.03170	−	8.29845i	0.134553	−	0.549578i
$229$	1.45899	+	0.310119i	0.0964130	+	0.0204932i	0.255866	−	0.966712i	$-0.417640\pi$
$229$	1.45899	+	0.310119i	0.0964130	+	0.0204932i	−0.159453	+	0.987206i	$0.550973\pi$
$230$	0.365565	−	0.633178i	0.0241047	−	0.0417505i
$231$	−8.79617	+	0.785161i	−0.578745	+	0.0516598i
$232$	−3.83737	−	6.64651i	−0.251935	−	0.436365i
$233$	8.88269	+	27.3381i	0.581924	+	1.79098i	0.611286	+	0.791409i	$0.290652\pi$
$233$	8.88269	+	27.3381i	0.581924	+	1.79098i	−0.0293622	+	0.999569i	$0.509348\pi$
$234$	1.78584	−	4.53035i	0.116744	−	0.296158i
$235$	−19.6978	+	14.3113i	−1.28494	+	0.933567i
$236$	−13.1652	+	2.79836i	−0.856984	+	0.182158i
$237$	−9.95337	+	20.6290i	−0.646541	+	1.34000i
$238$	0.536791	+	5.10723i	0.0347950	+	0.331052i
$239$	0.854980	−	0.380662i	0.0553041	−	0.0246229i	−0.378898	−	0.925438i	$-0.623697\pi$
$239$	0.854980	−	0.380662i	0.0553041	−	0.0246229i	0.434202	+	0.900815i	$0.357030\pi$
$240$	4.27807	+	1.53658i	0.276148	+	0.0991856i
$241$	4.19519	+	7.26629i	0.270236	+	0.468063i	0.968922	−	0.247366i	$-0.0795649\pi$
$241$	4.19519	+	7.26629i	0.270236	+	0.468063i	−0.698686	+	0.715428i	$0.746232\pi$
$242$	3.08444	−	10.5587i	0.198276	−	0.678739i
$243$	−2.38083	+	15.4056i	−0.152730	+	0.988268i
$244$	−1.49245	−	4.59329i	−0.0955444	−	0.294055i
$245$	1.27198	−	12.1020i	0.0812635	−	0.773171i
$246$	0.178716	−	5.82598i	0.0113945	−	0.371451i
$247$	−5.35751	−	5.95012i	−0.340890	−	0.378597i
$248$	7.29466	+	8.10155i	0.463212	+	0.514449i
$249$	−13.5098	+	7.25692i	−0.856147	+	0.459889i
$250$	0.853805	−	8.12341i	0.0539993	−	0.513769i
$251$	1.78259	+	5.48624i	0.112516	+	0.346289i	0.991421	−	0.130709i	$-0.0417252\pi$
$251$	1.78259	+	5.48624i	0.112516	+	0.346289i	−0.878905	+	0.476997i	$0.841725\pi$
$252$	−1.15363	−	4.46530i	−0.0726721	−	0.281287i
$253$	0.272333	−	0.882919i	0.0171214	−	0.0555087i
$254$	5.61636	+	9.72782i	0.352402	+	0.610378i
$255$	11.5907	−	9.80980i	0.725837	−	0.614314i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	2.92631	+	27.8420i	0.182539	+	1.73674i	0.576047	+	0.817417i	$0.304595\pi$
$257$	2.92631	+	27.8420i	0.182539	+	1.73674i	−0.393508	+	0.919321i	$0.628739\pi$
$258$	12.8873	−	0.956103i	0.802331	−	0.0595244i
$259$	−1.04019	+	0.221099i	−0.0646343	+	0.0137384i
$260$	3.44642	−	2.50397i	0.213738	−	0.155290i
$261$	22.7721	−	3.39760i	1.40956	−	0.210306i
$262$	−1.30216	−	4.00762i	−0.0804474	−	0.247592i
$263$	−0.664979	−	1.15178i	−0.0410043	−	0.0710216i	0.844795	−	0.535090i	$-0.179722\pi$
$263$	−0.664979	−	1.15178i	−0.0410043	−	0.0710216i	−0.885799	+	0.464069i	$0.846389\pi$
$264$	5.70297	+	0.690054i	0.350993	+	0.0424699i
$265$	9.53031	−	16.5070i	0.585442	−	1.01402i
$266$	−7.41722	−	1.57658i	−0.454779	−	0.0966663i
$267$	25.5061	−	7.43095i	1.56095	−	0.454767i
$268$	3.21549	+	1.43163i	0.196417	+	0.0874507i
$269$	4.12356	−	12.6910i	0.251418	−	0.773786i	−0.743096	−	0.669185i	$-0.766643\pi$
$269$	4.12356	−	12.6910i	0.251418	−	0.773786i	0.994514	−	0.104601i	$-0.0333565\pi$
$270$	−8.99525	+	10.2495i	−0.547433	+	0.623764i
$271$	24.8081	−	18.0241i	1.50698	−	1.09489i	0.539492	−	0.841991i	$-0.318616\pi$
$271$	24.8081	−	18.0241i	1.50698	−	1.09489i	0.967493	−	0.252898i	$-0.0813836\pi$
$272$	0.349177	−	3.32220i	0.0211720	−	0.201438i
$273$	−4.06768	−	1.46101i	−0.246187	−	0.0884244i
$274$	−3.53702	+	6.12630i	−0.213679	+	0.370103i
$275$	0.747559	+	6.21584i	0.0450795	+	0.374829i
$276$	0.478110	+	0.0651277i	0.0287788	+	0.00392023i
$277$	8.93091	−	9.91878i	0.536606	−	0.595962i	−0.412484	−	0.910965i	$-0.635339\pi$
$277$	8.93091	−	9.91878i	0.536606	−	0.595962i	0.949091	+	0.315003i	$0.102006\pi$
$278$	14.2651	+	10.3642i	0.855566	+	0.621605i
$279$	−30.6368	+	11.4460i	−1.83418	+	0.685257i
$280$	1.24675	−	3.83709i	0.0745073	−	0.229310i
$281$	20.4939	−	4.35612i	1.22257	−	0.259864i	0.448972	−	0.893546i	$-0.351790\pi$
$281$	20.4939	−	4.35612i	1.22257	−	0.259864i	0.773594	+	0.633682i	$0.218457\pi$
$282$	−13.6632	−	8.45735i	−0.813630	−	0.503628i
$283$	−20.3704	+	9.06951i	−1.21090	+	0.539126i	−0.910031	−	0.414540i	$-0.863942\pi$
$283$	−20.3704	+	9.06951i	−1.21090	+	0.539126i	−0.300866	+	0.953666i	$0.597276\pi$
$284$	4.55885	+	0.969013i	0.270518	+	0.0575003i
$285$	8.48749	+	20.7535i	0.502756	+	1.22933i
$286$	3.54202	−	4.05426i	0.209444	−	0.239734i
$287$	−5.17336			−0.305374
$288$	0.130122	+	2.99718i	0.00766750	+	0.176610i
$289$	4.72553	+	3.43330i	0.277972	+	0.201959i
$290$	18.4005	+	8.19242i	1.08051	+	0.481075i
$291$	−0.627204	+	1.29992i	−0.0367674	+	0.0762027i
$292$	0.428391	+	0.475777i	0.0250697	+	0.0278427i
$293$	−1.34171	−	12.7655i	−0.0783837	−	0.745771i	−0.961163	−	0.275982i	$-0.910997\pi$
$293$	−1.34171	−	12.7655i	−0.0783837	−	0.745771i	0.882779	−	0.469788i	$-0.155670\pi$
$294$	7.71043	−	2.24636i	0.449681	−	0.131010i
$295$	23.6358	−	26.2502i	1.37613	−	1.52835i
$296$	0.691749			0.0402071
$297$	−8.20027	+	15.1577i	−0.475828	+	0.879538i
$298$	8.74631			0.506660
$299$	0.302583	−	0.336053i	0.0174989	−	0.0194344i
$300$	−3.13900	+	0.914517i	−0.181230	+	0.0527997i
$301$	−1.19892	−	11.4069i	−0.0691044	−	0.657485i
$302$	11.8694	+	13.1824i	0.683010	+	0.758559i
$303$	6.22062	−	12.8926i	0.357365	−	0.740663i
$304$	4.50617	+	2.00628i	0.258446	+	0.115068i
$305$	10.2544	+	7.45027i	0.587166	+	0.426601i
$306$	8.88804	+	4.62959i	0.508095	+	0.264656i
$307$	22.9497			1.30981			0.654906	−	0.755711i	$-0.272708\pi$
$307$	22.9497			1.30981			0.654906	+	0.755711i	$0.272708\pi$
$308$	0.456978	−	5.07814i	0.0260388	−	0.289354i
$309$	−4.36375	−	10.6702i	−0.248245	−	0.607005i
$310$	−27.9856	−	5.94852i	−1.58947	−	0.337853i
$311$	−2.12846	+	0.947653i	−0.120694	+	0.0537365i	−0.466195	−	0.884682i	$-0.654376\pi$
$311$	−2.12846	+	0.947653i	−0.120694	+	0.0537365i	0.345501	+	0.938418i	$0.387709\pi$
$312$	2.39057	+	1.47974i	0.135339	+	0.0837735i
$313$	−20.4908	+	4.35546i	−1.15821	+	0.246185i	−0.746663	−	0.665203i	$-0.768345\pi$
$313$	−20.4908	+	4.35546i	−1.15821	+	0.246185i	−0.411548	+	0.911388i	$0.635012\pi$
$314$	3.99362	−	12.2911i	0.225373	−	0.693627i
$315$	9.33759	+	7.70117i	0.526113	+	0.433912i
$316$	−10.6985	−	7.77289i	−0.601836	−	0.437259i
$317$	−0.858654	+	0.953631i	−0.0482268	+	0.0535613i	−0.766776	−	0.641915i	$-0.778140\pi$
$317$	−0.858654	+	0.953631i	−0.0482268	+	0.0535613i	0.718549	+	0.695477i	$0.244807\pi$
$318$	12.4644	+	1.69788i	0.698966	+	0.0952126i
$319$	24.9744	+	4.91887i	1.39830	+	0.275404i
$320$	−1.31222	+	2.27283i	−0.0733551	+	0.127055i
$321$	−22.6241	−	8.12601i	−1.26275	−	0.453549i
$322$	0.0447665	−	0.425925i	0.00249474	−	0.0237359i
$323$	13.3305	−	9.68517i	0.741728	−	0.538897i
$324$	−8.50823	−	2.93429i	−0.472679	−	0.163016i
$325$	−0.946845	+	2.91409i	−0.0525215	+	0.161645i
$326$	0.588583	+	0.262054i	0.0325986	+	0.0145138i
$327$	19.2210	−	5.59986i	1.06293	−	0.309673i
$328$	3.29168	+	0.699667i	0.181752	+	0.0386327i
$329$	−7.13107	+	12.3514i	−0.393149	+	0.680953i
$330$	−13.1731	+	7.33229i	−0.725154	+	0.403629i
$331$	−2.41277	−	4.17905i	−0.132618	−	0.229701i	0.792067	−	0.610434i	$-0.209005\pi$
$331$	−2.41277	−	4.17905i	−0.132618	−	0.229701i	−0.924685	+	0.380733i	$0.875672\pi$
$332$	−2.73602	−	8.42060i	−0.150159	−	0.462140i
$333$	−0.761055	+	1.93066i	−0.0417056	+	0.105800i
$334$	−13.2138	+	9.60041i	−0.723029	+	0.525311i
$335$	−9.03560	+	1.92058i	−0.493668	+	0.104932i
$336$	2.65539	−	0.197002i	0.144863	−	0.0107473i
$337$	−0.713447	−	6.78800i	−0.0388640	−	0.369766i	−0.996618	−	0.0821766i	$-0.973813\pi$
$337$	−0.713447	−	6.78800i	−0.0388640	−	0.369766i	0.957754	−	0.287589i	$-0.0928538\pi$
$338$	−9.46907	+	4.21590i	−0.515049	+	0.229315i
$339$	−3.53925	+	2.99545i	−0.192226	+	0.162691i
$340$	4.38346	+	7.59237i	0.237726	+	0.411754i
$341$	−36.1528	+	0.541327i	−1.95778	+	0.0293145i
$342$	−10.5571	+	10.3694i	−0.570864	+	0.560710i
$343$	−5.52805	−	17.0136i	−0.298487	−	0.918647i
$344$	−0.779883	+	7.42009i	−0.0420485	+	0.400064i
$345$	−1.11559	+	0.599254i	−0.0600616	+	0.0322627i
$346$	1.60355	+	1.78092i	0.0862072	+	0.0957429i
$347$	7.14396	+	7.93417i	0.383508	+	0.425928i	0.903730	−	0.428102i	$-0.140818\pi$
$347$	7.14396	+	7.93417i	0.383508	+	0.425928i	−0.520223	+	0.854031i	$0.674151\pi$
$348$	−0.407582	+	13.2868i	−0.0218487	+	0.712246i
$349$	1.74387	−	16.5918i	0.0933472	−	0.888139i	−0.843201	−	0.537599i	$-0.819331\pi$
$349$	1.74387	−	16.5918i	0.0933472	−	0.888139i	0.936548	−	0.350540i	$-0.114002\pi$
$350$	0.896734	+	2.75986i	0.0479325	+	0.147521i
$351$	−6.76000	+	5.04405i	−0.360822	+	0.269231i
$352$	−0.977554	+	3.16929i	−0.0521038	+	0.168924i
$353$	−11.0976	−	19.2216i	−0.590667	−	1.02306i	−0.994143	−	0.108075i	$-0.965531\pi$
$353$	−11.0976	−	19.2216i	−0.590667	−	1.02306i	0.403476	−	0.914990i	$-0.367802\pi$
$354$	21.9400	+	7.88031i	1.16610	+	0.418834i
$355$	−11.1742	+	4.97507i	−0.593065	+	0.264049i
$356$	1.60328	+	15.2542i	0.0849736	+	0.808470i
$357$	3.86525	−	8.01097i	0.204571	−	0.423986i
$358$	−20.9786	+	4.45914i	−1.10875	+	0.235673i
$359$	1.51909	−	1.10369i	0.0801747	−	0.0582503i	−0.546976	−	0.837148i	$-0.684221\pi$
$359$	1.51909	−	1.10369i	0.0801747	−	0.0582503i	0.627151	+	0.778898i	$0.284221\pi$
$360$	−4.89973	−	6.16291i	−0.258238	−	0.324814i
$361$	1.64728	+	5.06979i	0.0866987	+	0.266831i
$362$	−12.2365	−	21.1942i	−0.643135	−	1.11394i
$363$	−14.1680	+	12.7384i	−0.743628	+	0.668594i
$364$	1.24768	−	2.16105i	0.0653964	−	0.113270i
$365$	−1.64350	−	0.349337i	−0.0860247	−	0.0182851i
$366$	−1.98930	+	8.12526i	−0.103982	+	0.424714i
$367$	16.1737	+	7.20098i	0.844258	+	0.375888i	0.782839	−	0.622224i	$-0.213771\pi$
$367$	16.1737	+	7.20098i	0.844258	+	0.375888i	0.0614191	+	0.998112i	$0.480437\pi$
$368$	−0.0860878	+	0.264951i	−0.00448764	+	0.0138115i
$369$	−5.57423	+	8.41724i	−0.290183	+	0.438184i
$370$	−1.46873	+	1.06709i	−0.0763556	+	0.0554756i
$371$	1.16707	−	11.1039i	0.0605911	−	0.576486i
$372$	−3.35770	−	18.5814i	−0.174089	−	0.963399i
$373$	12.4517	−	21.5670i	0.644725	−	1.11670i	−0.339640	−	0.940555i	$-0.610305\pi$
$373$	12.4517	−	21.5670i	0.644725	−	1.11670i	0.984365	−	0.176141i	$-0.0563613\pi$
$374$	7.53585	+	8.12152i	0.389670	+	0.419954i
$375$	−8.66281	+	11.1853i	−0.447346	+	0.577608i
$376$	6.20777	−	6.89443i	0.320141	−	0.355553i
$377$	10.0785	+	7.32246i	0.519069	+	0.377126i
$378$	−2.37161	+	7.62789i	−0.121982	+	0.392336i
$379$	0.218272	−	0.671771i	0.0112119	−	0.0345066i	−0.945294	−	0.326219i	$-0.894225\pi$
$379$	0.218272	−	0.671771i	0.0112119	−	0.0345066i	0.956506	+	0.291713i	$0.0942252\pi$
$380$	−12.6624	+	2.69148i	−0.649569	+	0.138070i
$381$	0.596535	−	19.4465i	0.0305614	−	0.996274i
$382$	−0.424318	+	0.188918i	−0.0217100	+	0.00966590i
$383$	14.6425	+	3.11236i	0.748196	+	0.159034i	0.566203	−	0.824266i	$-0.308412\pi$
$383$	14.6425	+	3.11236i	0.748196	+	0.159034i	0.181993	+	0.983300i	$0.441745\pi$
$384$	−1.71620	−	0.233780i	−0.0875795	−	0.0119300i
$385$	6.86329	+	11.4869i	0.349786	+	0.585427i
$386$	−5.85127			−0.297822
$387$	−19.8513	−	10.3401i	−1.00910	−	0.525619i
$388$	−0.674156	−	0.489803i	−0.0342251	−	0.0248660i
$389$	−1.35267	−	0.602248i	−0.0685832	−	0.0305352i	0.372158	−	0.928169i	$-0.378618\pi$
$389$	−1.35267	−	0.602248i	−0.0685832	−	0.0305352i	−0.440742	+	0.897634i	$0.645284\pi$
$390$	−7.35833	+	0.545909i	−0.372603	+	0.0276432i
$391$	0.622704	+	0.691582i	0.0314915	+	0.0349748i
$392$	0.484667	+	4.61130i	0.0244794	+	0.232906i
$393$	−1.73565	+	7.08925i	−0.0875520	+	0.357605i
$394$	−11.7499	+	13.0496i	−0.591951	+	0.657428i
$395$	34.7056			1.74623
$396$	−7.76993	−	6.21515i	−0.390454	−	0.312323i
$397$	28.1259			1.41160			0.705799	−	0.708413i	$-0.250588\pi$
$397$	28.1259			1.41160			0.705799	+	0.708413i	$0.250588\pi$
$398$	14.0315	−	15.5835i	0.703335	−	0.781133i
$399$	9.48643	+	9.08351i	0.474915	+	0.454744i
$400$	−0.197313	−	1.87731i	−0.00986566	−	0.0938655i
$401$	−9.05749	−	10.0594i	−0.452309	−	0.502340i	0.473258	−	0.880924i	$-0.343078\pi$
$401$	−9.05749	−	10.0594i	−0.452309	−	0.502340i	−0.925567	+	0.378584i	$0.876411\pi$
$402$	−3.43050	−	5.03969i	−0.171098	−	0.251357i
$403$	−16.1659	−	7.19752i	−0.805280	−	0.358534i
$404$	6.68629	+	4.85787i	0.332655	+	0.241688i
$405$	22.5912	−	6.89469i	1.12257	−	0.342600i
$406$	11.7984			0.585545
$407$	−1.50947	+	1.72777i	−0.0748216	+	0.0856424i
$408$	−3.54280	+	4.57442i	−0.175395	+	0.226468i
$409$	−21.0958	−	4.48405i	−1.04312	−	0.221722i	−0.345670	−	0.938356i	$-0.612348\pi$
$409$	−21.0958	−	4.48405i	−1.04312	−	0.221722i	−0.697449	+	0.716634i	$0.745682\pi$
$410$	−8.06823	+	3.59221i	−0.398462	+	0.177407i
$411$	10.7939	−	5.79807i	0.532424	−	0.285998i
$412$	6.51025	−	1.38380i	0.320737	−	0.0681748i
$413$	6.39391	−	19.6784i	0.314624	−	0.968312i
$414$	−0.644761	−	0.531766i	−0.0316883	−	0.0261349i
$415$	18.7988	+	13.6581i	0.922796	+	0.670451i
$416$	−1.08614	+	1.20628i	−0.0532524	+	0.0591428i
$417$	−11.5607	−	28.2681i	−0.566131	−	1.38429i
$418$	−14.8440	+	6.87707i	−0.726042	+	0.336369i
$419$	−1.45270	+	2.51616i	−0.0709692	+	0.122922i	−0.899326	−	0.437278i	$-0.855943\pi$
$419$	−1.45270	+	2.51616i	−0.0709692	+	0.122922i	0.828357	+	0.560200i	$0.189276\pi$
$420$	−5.33406	+	4.51449i	−0.260276	+	0.220285i
$421$	−3.14886	+	29.9594i	−0.153466	+	1.46013i	0.598602	+	0.801047i	$0.295723\pi$
$421$	−3.14886	+	29.9594i	−0.153466	+	1.46013i	−0.752068	+	0.659085i	$0.770944\pi$
$422$	−2.69971	+	1.96145i	−0.131420	+	0.0954821i
$423$	12.4125	+	24.9110i	0.603517	+	1.21121i
$424$	−2.24432	+	6.90729i	−0.108994	+	0.335448i
$425$	−5.76054	−	2.56476i	−0.279427	−	0.124409i
$426$	−5.83064	−	5.58300i	−0.282495	−	0.270497i
$427$	7.26243	+	1.54368i	0.351454	+	0.0747038i
$428$	6.93950	−	12.0196i	0.335433	−	0.580988i
$429$	−8.91238	+	2.74194i	−0.430294	+	0.132382i
$430$	−9.79040	−	16.9575i	−0.472135	−	0.817762i
$431$	1.90129	+	5.85158i	0.0915821	+	0.281861i	0.986348	−	0.164675i	$-0.0526575\pi$
$431$	1.90129	+	5.85158i	0.0915821	+	0.281861i	−0.894766	+	0.446536i	$0.852658\pi$
$432$	2.54062	−	4.53269i	0.122236	−	0.218079i
$433$	−29.5862	+	21.4957i	−1.42182	+	1.03302i	−0.430356	+	0.902659i	$0.641612\pi$
$433$	−29.5862	+	21.4957i	−1.42182	+	1.03302i	−0.991467	+	0.130356i	$0.958388\pi$
$434$	−16.3930	+	3.48444i	−0.786889	+	0.167259i
$435$	−19.6308	−	28.8394i	−0.941227	−	1.38274i
$436$	1.20821	+	11.4953i	0.0578626	+	0.550526i
$437$	−1.25536	+	0.558920i	−0.0600518	+	0.0267368i
$438$	−0.197187	−	1.09122i	−0.00942194	−	0.0521406i
$439$	−3.55521	−	6.15780i	−0.169681	−	0.293896i	0.768627	−	0.639697i	$-0.220940\pi$
$439$	−3.55521	−	6.15780i	−0.169681	−	0.293896i	−0.938308	+	0.345802i	$0.887607\pi$
$440$	−2.81340	−	8.23705i	−0.134124	−	0.392686i
$441$	−13.4033	−	3.72060i	−0.638251	−	0.177172i
$442$	1.67559	+	5.15694i	0.0796998	+	0.245291i
$443$	−1.13814	+	10.8287i	−0.0540746	+	0.514486i	0.933639	+	0.358214i	$0.116614\pi$
$443$	−1.13814	+	10.8287i	−0.0540746	+	0.514486i	−0.987714	+	0.156272i	$0.950052\pi$
$444$	−1.01877	−	0.630606i	−0.0483486	−	0.0299272i
$445$	−26.9352	−	29.9146i	−1.27685	−	1.41809i
$446$	−1.44997	−	1.61036i	−0.0686582	−	0.0762526i
$447$	−12.8811	−	7.97323i	−0.609253	−	0.377121i
$448$	−0.160692	+	1.52888i	−0.00759198	+	0.0722329i
$449$	1.10147	+	3.38997i	0.0519814	+	0.159982i	0.973677	−	0.227931i	$-0.0731960\pi$
$449$	1.10147	+	3.38997i	0.0519814	+	0.159982i	−0.921696	+	0.387913i	$0.873196\pi$
$450$	5.45662	+	1.51470i	0.257228	+	0.0714036i
$451$	−8.93033	+	6.69481i	−0.420513	+	0.315246i
$452$	−1.33850	−	2.31835i	−0.0629578	−	0.109046i
$453$	−5.46345	−	30.2345i	−0.256695	−	1.42054i
$454$	24.7075	−	11.0005i	1.15958	−	0.516279i
$455$	0.684549	+	6.51305i	0.0320922	+	0.305337i
$456$	−4.80748	−	7.06259i	−0.225131	−	0.330736i
$457$	13.6780	−	2.90736i	0.639831	−	0.136000i	0.123439	−	0.992352i	$-0.460608\pi$
$457$	13.6780	−	2.90736i	0.639831	−	0.136000i	0.516393	+	0.856352i	$0.327274\pi$
$458$	1.20672	−	0.876734i	0.0563863	−	0.0409671i
$459$	−8.86939	−	14.9206i	−0.413988	−	0.696435i
$460$	−0.225932	−	0.695346i	−0.0105341	−	0.0324207i
$461$	−0.332934	−	0.576659i	−0.0155063	−	0.0268577i	0.858168	−	0.513369i	$-0.171603\pi$
$461$	−0.332934	−	0.576659i	−0.0155063	−	0.0268577i	−0.873674	+	0.486511i	$0.838269\pi$
$462$	−5.30230	+	7.06220i	−0.246685	+	0.328563i
$463$	−14.8510	+	25.7227i	−0.690185	+	1.19544i	0.281592	+	0.959534i	$0.409137\pi$
$463$	−14.8510	+	25.7227i	−0.690185	+	1.19544i	−0.971777	+	0.235901i	$0.924196\pi$
$464$	−7.50702	−	1.59567i	−0.348505	−	0.0740770i
$465$	35.7928	+	34.2726i	1.65985	+	1.58935i
$466$	26.2598	+	11.6916i	1.21646	+	0.541605i
$467$	−1.21318	+	3.73379i	−0.0561394	+	0.172779i	−0.975194	−	0.221350i	$-0.928954\pi$
$467$	−1.21318	+	3.73379i	−0.0561394	+	0.172779i	0.919055	+	0.394129i	$0.128954\pi$
$468$	−2.17175	−	4.35853i	−0.100389	−	0.201473i
$469$	−4.37759	+	3.18050i	−0.202138	+	0.146862i
$470$	−2.54504	+	24.2145i	−0.117394	+	1.11693i
$471$	−17.0863	+	14.4610i	−0.787293	+	0.666327i
$472$	−6.72968	+	11.6561i	−0.309758	+	0.536517i
$473$	−16.8312	−	18.1393i	−0.773901	−	0.834047i
$474$	8.67023	+	21.2003i	0.398237	+	0.973762i
$475$	6.23031	−	6.91946i	0.285866	−	0.317487i
$476$	4.15459	+	3.01849i	0.190426	+	0.138352i
$477$	−16.8090	−	13.8632i	−0.769630	−	0.634751i
$478$	0.289207	−	0.890086i	0.0132280	−	0.0407116i
$479$	−1.03620	+	0.220251i	−0.0473453	+	0.0100635i	−0.231523	−	0.972829i	$-0.574371\pi$
$479$	−1.03620	+	0.220251i	−0.0473453	+	0.0100635i	0.184178	+	0.982893i	$0.441038\pi$
$480$	4.00449	−	2.15105i	0.182779	−	0.0981818i
$481$	−1.02578	+	0.456706i	−0.0467715	+	0.0208240i
$482$	8.20704	+	1.74446i	0.373820	+	0.0794579i
$483$	−0.454207	+	0.586468i	−0.0206672	+	0.0266852i
$484$	−5.78275	−	9.35734i	−0.262852	−	0.425334i
$485$	2.18695			0.0993041
$486$	9.85548	+	12.0776i	0.447054	+	0.547853i
$487$	−25.2392	−	18.3373i	−1.14370	−	0.830943i	−0.156065	−	0.987747i	$-0.549881\pi$
$487$	−25.2392	−	18.3373i	−1.14370	−	0.830943i	−0.987630	+	0.156803i	$0.949881\pi$
$488$	−4.41213	−	1.96440i	−0.199728	−	0.0889244i
$489$	−0.627939	−	0.922496i	−0.0283964	−	0.0417167i
$490$	−8.14245	−	9.04311i	−0.367838	−	0.408526i
$491$	3.38417	+	32.1983i	0.152726	+	1.45309i	0.755486	+	0.655165i	$0.227401\pi$
$491$	3.38417	+	32.1983i	0.152726	+	1.45309i	−0.602760	+	0.797923i	$0.705932\pi$
$492$	−4.20996	−	4.03115i	−0.189800	−	0.181738i
$493$	−17.1548	+	19.0523i	−0.772613	+	0.858073i
$494$	−8.00667			−0.360237
$495$	26.0847	+	1.21016i	1.17242	+	0.0543925i
$496$	10.9017			0.489501
$497$	−4.79426	+	5.32456i	−0.215052	+	0.238839i
$498$	−3.64686	+	14.8955i	−0.163420	+	0.667485i
$499$	0.0916132	+	0.871641i	0.00410117	+	0.0390200i	0.996381	−	0.0849983i	$-0.0270885\pi$
$499$	0.0916132	+	0.871641i	0.00410117	+	0.0390200i	−0.992280	+	0.124018i	$0.960422\pi$
$500$	−5.46556	−	6.07012i	−0.244427	−	0.271464i
$501$	28.2124	−	2.09306i	1.26044	−	0.0935109i
$502$	5.26986	+	2.34629i	0.235205	+	0.104720i
$503$	3.77153	+	2.74018i	0.168164	+	0.122179i	0.668684	−	0.743546i	$-0.266858\pi$
$503$	3.77153	+	2.74018i	0.168164	+	0.122179i	−0.500520	+	0.865725i	$0.666858\pi$
$504$	−4.09029	−	2.13055i	−0.182196	−	0.0949022i
$505$	−21.6902			−0.965200
$506$	−0.473911	−	0.793171i	−0.0210679	−	0.0352608i
$507$	17.7887	+	2.42317i	0.790026	+	0.107617i
$508$	10.9873	+	2.33541i	0.487481	+	0.103617i
$509$	4.58408	−	2.04096i	0.203186	−	0.0904641i	−0.302621	−	0.953111i	$-0.597862\pi$
$509$	4.58408	−	2.04096i	0.203186	−	0.0904641i	0.505807	+	0.862647i	$0.331195\pi$
$510$	0.465584	−	15.1776i	0.0206164	−	0.672075i
$511$	−0.962706	+	0.204629i	−0.0425876	+	0.00905228i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	25.0007	−	5.64740i	1.10381	−	0.249339i
$514$	22.6487	+	16.4553i	0.998993	+	0.725811i
$515$	−11.6880	+	12.9808i	−0.515034	+	0.572004i
$516$	7.91279	−	10.2169i	0.348341	−	0.449775i
$517$	3.67408	+	30.5494i	0.161586	+	1.34356i
$518$	−0.531714	+	0.920956i	−0.0233622	+	0.0404645i
$519$	−0.738106	−	4.08464i	−0.0323993	−	0.179296i
$520$	0.445292	−	4.23667i	0.0195274	−	0.185790i
$521$	6.06420	−	4.40590i	0.265677	−	0.193026i	−0.446969	−	0.894550i	$-0.647497\pi$
$521$	6.06420	−	4.40590i	0.265677	−	0.193026i	0.712646	+	0.701524i	$0.247497\pi$
$522$	12.7126	−	19.1964i	0.556416	−	0.840205i
$523$	−11.2787	+	34.7121i	−0.493181	+	1.51786i	0.326591	+	0.945166i	$0.394100\pi$
$523$	−11.2787	+	34.7121i	−0.493181	+	1.51786i	−0.819772	+	0.572690i	$0.805900\pi$
$524$	−3.84956	−	1.71393i	−0.168169	−	0.0748735i
$525$	1.19526	−	4.88204i	0.0521655	−	0.213070i
$526$	−1.30089	−	0.276514i	−0.0567217	−	0.0120566i
$527$	18.2086	−	31.5382i	0.793177	−	1.37382i
$528$	4.32884	−	3.77639i	0.188389	−	0.164346i
$529$	11.4612	+	19.8514i	0.498313	+	0.863103i
$530$	−5.89006	−	18.1277i	−0.255848	−	0.787418i
$531$	−25.1282	−	31.6064i	−1.09047	−	1.37160i
$532$	−6.13472	+	4.45713i	−0.265974	+	0.193241i
$533$	−5.34308	+	1.13571i	−0.231435	+	0.0491930i
$534$	11.5446	−	23.9270i	0.499586	−	1.03542i
$535$	3.80740	+	36.2250i	0.164608	+	1.56614i
$536$	3.21549	−	1.43163i	0.138888	−	0.0618370i
$537$	34.9610	+	12.5571i	1.50868	+	0.541881i
$538$	−6.67207	−	11.5564i	−0.287653	−	0.498230i
$539$	−12.5751	−	8.85179i	−0.541650	−	0.381274i
$540$	1.59786	+	13.5430i	0.0687610	+	0.582799i
$541$	2.27475	+	7.00097i	0.0977992	+	0.300995i	0.987973	−	0.154626i	$-0.0494172\pi$
$541$	2.27475	+	7.00097i	0.0977992	+	0.300995i	−0.890174	+	0.455621i	$0.849417\pi$
$542$	3.20531	−	30.4965i	0.137680	−	1.30994i
$543$	−1.29968	+	42.3685i	−0.0557748	+	1.81820i
$544$	−2.23523	−	2.48247i	−0.0958347	−	0.106435i
$545$	−20.2980	−	22.5432i	−0.869471	−	0.965645i
$546$	−3.80755	+	2.04527i	−0.162948	+	0.0875294i
$547$	−0.575699	+	5.47741i	−0.0246151	+	0.234197i	0.975296	+	0.220900i	$0.0708994\pi$
$547$	−0.575699	+	5.47741i	−0.0246151	+	0.234197i	−0.999912	+	0.0132972i	$0.995767\pi$
$548$	2.18600	+	6.72781i	0.0933812	+	0.287398i
$549$	10.3368	−	10.1529i	0.441164	−	0.433317i
$550$	5.11948	+	3.60366i	0.218295	+	0.153661i
$551$	−18.9283	−	32.7847i	−0.806371	−	1.39667i
$552$	0.368317	−	0.311726i	0.0156766	−	0.0132679i
$553$	18.5718	−	8.26870i	0.789753	−	0.351621i
$554$	−1.39515	−	13.2739i	−0.0592740	−	0.563955i
$555$	3.13583	−	0.232645i	0.133109	−	0.00987524i
$556$	17.2474	−	3.66604i	0.731451	−	0.155475i
$557$	−1.83217	+	1.33115i	−0.0776314	+	0.0564025i	−0.625924	−	0.779884i	$-0.715278\pi$
$557$	−1.83217	+	1.33115i	−0.0776314	+	0.0564025i	0.548293	+	0.836287i	$0.315278\pi$
$558$	−11.9939	+	30.4265i	−0.507744	+	1.28806i
$559$	−3.74242	−	11.5180i	−0.158287	−	0.487158i
$560$	−2.01728	−	3.49402i	−0.0852455	−	0.147649i
$561$	−3.69470	−	18.8307i	−0.155990	−	0.795031i
$562$	10.4759	−	18.1448i	0.441899	−	0.765391i
$563$	9.73652	+	2.06956i	0.410345	+	0.0872216i	0.408459	−	0.912777i	$-0.366066\pi$
$563$	9.73652	+	2.06956i	0.410345	+	0.0872216i	0.00188627	+	0.999998i	$0.499400\pi$
$564$	−15.4275	+	4.49464i	−0.649614	+	0.189259i
$565$	6.41822	+	2.85757i	0.270016	+	0.120219i
$566$	−6.89053	+	21.2069i	−0.289631	+	0.891392i
$567$	10.4464	−	9.07193i	0.438708	−	0.380985i
$568$	3.77058	−	2.73949i	0.158210	−	0.114946i
$569$	−2.37130	+	22.5614i	−0.0994102	+	0.945825i	0.825182	+	0.564867i	$0.191072\pi$
$569$	−2.37130	+	22.5614i	−0.0994102	+	0.945825i	−0.924592	+	0.380958i	$0.875594\pi$
$570$	21.1021	+	7.57935i	0.883869	+	0.317464i
$571$	17.4825	−	30.2806i	0.731621	−	1.26720i	−0.224569	−	0.974458i	$-0.572098\pi$
$571$	17.4825	−	30.2806i	0.731621	−	1.26720i	0.956190	−	0.292746i	$-0.0945691\pi$
$572$	−0.642834	−	5.34506i	−0.0268782	−	0.223488i
$573$	0.797130	+	0.108584i	0.0333006	+	0.00453618i
$574$	−3.46165	+	3.84455i	−0.144487	+	0.160469i
$575$	0.425440	+	0.309100i	0.0177421	+	0.0128904i
$576$	2.31440	+	1.90880i	0.0964335	+	0.0795335i
$577$	−2.76556	+	8.51151i	−0.115132	+	0.354339i	−0.991974	−	0.126438i	$-0.959645\pi$
$577$	−2.76556	+	8.51151i	−0.115132	+	0.354339i	0.876843	+	0.480777i	$0.159645\pi$
$578$	5.71343	−	1.21443i	0.237647	−	0.0505135i
$579$	8.61741	+	5.33408i	0.358127	+	0.221677i
$580$	18.4005	−	8.19242i	0.764038	−	0.340172i
$581$	13.3138	+	2.82993i	0.552348	+	0.117405i
$582$	0.546348	+	1.33592i	0.0226468	+	0.0553757i
$583$	−12.3549	−	20.6780i	−0.511687	−	0.856397i
$584$	0.640220			0.0264925
$585$	11.3346	+	5.90394i	0.468627	+	0.244098i
$586$	−10.3844	−	7.54473i	−0.428977	−	0.311670i
$587$	8.69968	+	3.87335i	0.359074	+	0.159870i	0.578342	−	0.815795i	$-0.303700\pi$
$587$	8.69968	+	3.87335i	0.359074	+	0.159870i	−0.219267	+	0.975665i	$0.570367\pi$
$588$	3.48992	−	7.23307i	0.143922	−	0.298287i
$589$	35.9818	+	39.9618i	1.48260	+	1.64660i
$590$	−3.69228	−	35.1297i	−0.152009	−	1.44627i
$591$	29.2007	−	8.50733i	1.20116	−	0.349945i
$592$	0.462871	−	0.514070i	0.0190239	−	0.0211281i
$593$	13.5703			0.557266			0.278633	−	0.960398i	$-0.410119\pi$
$593$	13.5703			0.557266			0.278633	+	0.960398i	$0.410119\pi$
$594$	5.77731	+	16.2365i	0.237046	+	0.666190i
$595$	−13.4774			−0.552520
$596$	5.85243	−	6.49978i	0.239725	−	0.266241i
$597$	−34.8709	+	10.1593i	−1.42717	+	0.415792i
$598$	−0.0472682	−	0.449727i	−0.00193294	−	0.0183907i
$599$	−5.34569	−	5.93699i	−0.218419	−	0.242579i	0.623971	−	0.781448i	$-0.285518\pi$
$599$	−5.34569	−	5.93699i	−0.218419	−	0.242579i	−0.842390	+	0.538869i	$0.818852\pi$
$600$	−1.42078	+	2.94466i	−0.0580033	+	0.120215i
$601$	−14.4283	−	6.42392i	−0.588545	−	0.262037i	0.0907846	−	0.995871i	$-0.471063\pi$
$601$	−14.4283	−	6.42392i	−0.588545	−	0.262037i	−0.679329	+	0.733834i	$0.737729\pi$
$602$	−9.27923	−	6.74176i	−0.378193	−	0.274774i
$603$	0.458002	+	10.5494i	0.0186513	+	0.429607i
$604$	17.7386			0.721774
$605$	26.7127	+	10.9471i	1.08602	+	0.445064i
$606$	−5.41869	−	13.2497i	−0.220119	−	0.538231i
$607$	−13.0809	−	2.78042i	−0.530936	−	0.112854i	−0.0653596	−	0.997862i	$-0.520819\pi$
$607$	−13.0809	−	2.78042i	−0.530936	−	0.112854i	−0.465576	+	0.885008i	$0.654153\pi$
$608$	4.50617	−	2.00628i	0.182749	−	0.0813652i
$609$	−17.3760	−	10.7555i	−0.704111	−	0.435836i
$610$	12.3982	−	2.63531i	0.501987	−	0.106701i
$611$	−4.65353	+	14.3221i	−0.188262	+	0.579409i
$612$	9.38772	−	3.50729i	0.379476	−	0.141774i
$613$	−31.7821	−	23.0911i	−1.28367	−	0.932639i	−0.284010	−	0.958821i	$-0.591665\pi$
$613$	−31.7821	−	23.0911i	−1.28367	−	0.932639i	−0.999657	+	0.0261821i	$0.991665\pi$
$614$	15.3564	−	17.0550i	0.619733	−	0.688283i
$615$	15.1571	+	2.06469i	0.611194	+	0.0832563i
$616$	−3.46802	−	3.73754i	−0.139730	−	0.150590i
$617$	−15.0834	+	26.1251i	−0.607233	+	1.05176i	0.384461	+	0.923141i	$0.374387\pi$
$617$	−15.0834	+	26.1251i	−0.607233	+	1.05176i	−0.991694	+	0.128617i	$0.958946\pi$
$618$	−10.8494	−	3.89684i	−0.436427	−	0.156754i
$619$	0.0700929	−	0.666889i	0.00281727	−	0.0268045i	−0.993023	−	0.117921i	$-0.962377\pi$
$619$	0.0700929	−	0.666889i	0.00281727	−	0.0268045i	0.995840	+	0.0911167i	$0.0290436\pi$
$620$	−23.1466	+	16.8170i	−0.929591	+	0.675387i
$621$	0.464803	+	1.37092i	0.0186519	+	0.0550133i
$622$	−0.719976	+	2.21586i	−0.0288684	+	0.0888479i
$623$	−21.5409	−	9.59064i	−0.863019	−	0.384241i
$624$	2.69926	−	0.786403i	0.108057	−	0.0314813i
$625$	30.2003	+	6.41928i	1.20801	+	0.256771i
$626$	−10.4743	+	18.1420i	−0.418638	+	0.725102i
$627$	28.1305	+	3.40377i	1.12343	+	0.135933i
$628$	−6.46181	−	11.1922i	−0.257854	−	0.446617i
$629$	−0.714072	−	2.19769i	−0.0284719	−	0.0876276i
$630$	11.9711	−	1.78609i	0.476942	−	0.0711596i
$631$	6.56487	−	4.76966i	0.261343	−	0.189877i	−0.449396	−	0.893333i	$-0.648361\pi$
$631$	6.56487	−	4.76966i	0.261343	−	0.189877i	0.710739	+	0.703456i	$0.248361\pi$
$632$	−12.9351	+	2.74943i	−0.514529	+	0.109367i
$633$	5.76405	−	0.427631i	0.229101	−	0.0169968i
$634$	0.134135	+	1.27621i	0.00532718	+	0.0506847i
$635$	−26.9309	+	11.9904i	−1.06872	+	0.475825i
$636$	9.60206	−	8.12672i	0.380746	−	0.322245i
$637$	−3.76317	−	6.51800i	−0.149102	−	0.258252i
$638$	20.3666	−	15.2682i	0.806321	−	0.604475i
$639$	3.49751	+	13.5376i	0.138359	+	0.535538i
$640$	0.810995	+	2.49598i	0.0320574	+	0.0986625i
$641$	3.01265	−	28.6635i	0.118993	−	1.13214i	−0.758207	−	0.652014i	$-0.773924\pi$
$641$	3.01265	−	28.6635i	0.118993	−	1.13214i	0.877200	−	0.480126i	$-0.159409\pi$
$642$	−21.1773	+	11.3756i	−0.835799	+	0.448959i
$643$	−8.02806	−	8.91606i	−0.316596	−	0.351615i	0.563752	−	0.825944i	$-0.309357\pi$
$643$	−8.02806	−	8.91606i	−0.316596	−	0.351615i	−0.880348	+	0.474329i	$0.842691\pi$
$644$	−0.286569	−	0.318268i	−0.0112924	−	0.0125415i
$645$	−1.03988	+	33.8990i	−0.0409451	+	1.33477i
$646$	1.72236	−	16.3871i	0.0677652	−	0.644743i
$647$	−6.31337	−	19.4306i	−0.248204	−	0.763894i	−0.995093	−	0.0989449i	$-0.968453\pi$
$647$	−6.31337	−	19.4306i	−0.248204	−	0.763894i	0.746889	−	0.664949i	$-0.231547\pi$
$648$	−7.87372	+	4.35942i	−0.309309	+	0.171254i
$649$	−14.4285	−	42.2435i	−0.566367	−	1.65820i
$650$	1.53203	+	2.65355i	0.0600911	+	0.104081i
$651$	27.3191	+	9.81235i	1.07072	+	0.384576i
$652$	0.588583	−	0.262054i	0.0230507	−	0.0102628i
$653$	2.13471	+	20.3104i	0.0835377	+	0.794808i	0.953440	+	0.301584i	$0.0975153\pi$
$653$	2.13471	+	20.3104i	0.0835377	+	0.794808i	−0.869902	+	0.493225i	$0.835818\pi$
$654$	8.69988	−	18.0311i	0.340192	−	0.705070i
$655$	10.8173	−	2.29930i	0.422668	−	0.0898409i
$656$	2.72252	−	1.97802i	0.106296	−	0.0772288i
$657$	−0.704364	+	1.78684i	−0.0274798	+	0.0697114i
$658$	4.40724	+	13.5641i	0.171812	+	0.528784i
$659$	19.1171	+	33.1118i	0.744697	+	1.28985i	0.950336	+	0.311225i	$0.100739\pi$
$659$	19.1171	+	33.1118i	0.744697	+	1.28985i	−0.205639	+	0.978628i	$0.565927\pi$
$660$	−3.36556	+	14.6958i	−0.131004	+	0.572032i
$661$	−23.1608	+	40.1157i	−0.900851	+	1.56032i	−0.0744599	+	0.997224i	$0.523723\pi$
$661$	−23.1608	+	40.1157i	−0.900851	+	1.56032i	−0.826391	+	0.563096i	$0.809610\pi$
$662$	−4.72010	−	1.00329i	−0.183452	−	0.0389939i
$663$	2.23341	−	9.12233i	0.0867384	−	0.354282i
$664$	−8.08848	−	3.60122i	−0.313894	−	0.139755i
$665$	6.14971	−	18.9269i	0.238476	−	0.733953i
$666$	0.925515	+	1.85744i	0.0358630	+	0.0719743i
$667$	1.72974	−	1.25673i	0.0669757	−	0.0486607i
$668$	−1.70728	+	16.2437i	−0.0660568	+	0.628489i
$669$	0.667416	+	3.69345i	0.0258038	+	0.142797i
$670$	−4.61873	+	7.99988i	−0.178437	+	0.309062i
$671$	14.5342	−	6.73355i	0.561086	−	0.259946i
$672$	1.63040	−	2.10516i	0.0628941	−	0.0812083i
$673$	18.7968	−	20.8760i	0.724564	−	0.804710i	−0.262518	−	0.964927i	$-0.584553\pi$
$673$	18.7968	−	20.8760i	0.724564	−	0.804710i	0.987082	+	0.160217i	$0.0512195\pi$
$674$	−5.52186	−	4.01186i	−0.212694	−	0.154531i
$675$	−6.65538	−	7.20507i	−0.256166	−	0.277323i
$676$	−3.20302	+	9.85788i	−0.123193	+	0.379149i
$677$	−38.9483	+	8.27873i	−1.49691	+	0.318177i	−0.882312	−	0.470666i	$-0.844014\pi$
$677$	−38.9483	+	8.27873i	−1.49691	+	0.318177i	−0.614595	+	0.788843i	$0.710680\pi$
$678$	−0.142167	+	4.63452i	−0.00545991	+	0.177988i
$679$	1.17029	−	0.521045i	0.0449115	−	0.0199959i
$680$	8.57534	+	1.82274i	0.328849	+	0.0698990i
$681$	−46.4159	−	6.32274i	−1.77866	−	0.242288i
$682$	−23.7887	+	27.2290i	−0.910915	+	1.04265i
$683$	18.6693			0.714359			0.357180	−	0.934036i	$-0.383738\pi$
$683$	18.6693			0.714359			0.357180	+	0.934036i	$0.383738\pi$
$684$	0.641840	+	14.7839i	0.0245414	+	0.565277i
$685$	−15.0197	−	10.9124i	−0.573872	−	0.416943i
$686$	−16.3425	−	7.27617i	−0.623961	−	0.277805i
$687$	−2.57643	+	0.191143i	−0.0982968	+	0.00729257i
$688$	4.99236	+	5.54457i	0.190332	+	0.211385i
$689$	−1.23228	−	11.7244i	−0.0469463	−	0.446664i
$690$	−0.301146	+	1.23003i	−0.0114644	+	0.0468263i
$691$	−18.7815	+	20.8589i	−0.714480	+	0.793511i	−0.985611	−	0.169032i	$-0.945936\pi$
$691$	−18.7815	+	20.8589i	−0.714480	+	0.793511i	0.271130	+	0.962543i	$0.412603\pi$
$692$	2.39646			0.0910999
$693$	14.2469	−	5.56717i	0.541194	−	0.211479i
$694$	10.6765			0.405273
$695$	−30.9645	+	34.3896i	−1.17455	+	1.30447i
$696$	9.60127	+	9.19348i	0.363935	+	0.348478i
$697$	−1.17506	−	11.1799i	−0.0445084	−	0.423469i
$698$	−11.1632	−	12.3980i	−0.422535	−	0.469272i
$699$	−28.0157	−	41.1575i	−1.05965	−	1.55672i
$700$	2.65101	+	1.18031i	0.100199	+	0.0446114i
$701$	25.1214	+	18.2518i	0.948823	+	0.689360i	0.950528	−	0.310638i	$-0.100543\pi$
$701$	25.1214	+	18.2518i	0.948823	+	0.689360i	−0.00170538	+	0.999999i	$0.500543\pi$
$702$	−0.774861	+	8.39878i	−0.0292453	+	0.316992i
$703$	3.41213			0.128691
$704$	1.70113	+	2.84713i	0.0641137	+	0.107305i
$705$	25.8223	−	33.3416i	0.972526	−	1.25572i
$706$	−21.7102	−	4.61465i	−0.817075	−	0.173675i
$707$	−11.6069	+	5.16774i	−0.436524	+	0.194353i
$708$	20.5369	−	11.0316i	0.771825	−	0.414594i
$709$	14.3388	−	3.04780i	0.538504	−	0.114463i	0.0693726	−	0.997591i	$-0.477900\pi$
$709$	14.3388	−	3.04780i	0.538504	−	0.114463i	0.469132	+	0.883128i	$0.344567\pi$
$710$	−3.77980	+	11.6330i	−0.141853	+	0.436579i
$711$	6.55740	−	39.1264i	0.245922	−	1.46736i
$712$	12.4089	+	9.01557i	0.465042	+	0.337873i
$713$	−2.03219	+	2.25698i	−0.0761062	+	0.0845245i
$714$	−3.36696	−	8.23282i	−0.126005	−	0.308106i
$715$	9.61018	+	10.3571i	0.359401	+	0.387332i
$716$	−10.7236	+	18.5739i	−0.400761	+	0.694138i
$717$	−1.23734	+	1.04722i	−0.0462092	+	0.0391093i
$718$	0.196273	−	1.86742i	0.00732486	−	0.0696914i
$719$	1.78723	−	1.29850i	0.0666525	−	0.0484258i	−0.553960	−	0.832543i	$-0.686884\pi$
$719$	1.78723	−	1.29850i	0.0666525	−	0.0484258i	0.620613	+	0.784117i	$0.286884\pi$
$720$	−7.85850	−	0.482584i	−0.292869	−	0.0179849i
$721$	−3.16181	+	9.73104i	−0.117752	+	0.362403i
$722$	4.86983	+	2.16819i	0.181236	+	0.0806916i
$723$	−10.4966	−	10.0508i	−0.390372	−	0.373792i
$724$	−23.9382	−	5.08821i	−0.889654	−	0.189102i
$725$	−7.24361	+	12.5463i	−0.269021	+	0.465958i
$726$	−0.0137511	+	19.0526i	−0.000510353	+	0.707107i
$727$	10.0913	+	17.4786i	0.374264	+	0.648245i	0.990217	−	0.139539i	$-0.0445620\pi$
$727$	10.0913	+	17.4786i	0.374264	+	0.648245i	−0.615952	+	0.787783i	$0.711229\pi$
$728$	−0.771111	−	2.37324i	−0.0285793	−	0.0879580i
$729$	−3.50447	−	26.7716i	−0.129795	−	0.991541i
$730$	−1.35932	+	0.987606i	−0.0503108	+	0.0365529i
$731$	24.3787	−	5.18185i	0.901678	−	0.191658i
$732$	4.70715	+	6.91520i	0.173981	+	0.255593i
$733$	−1.25576	−	11.9477i	−0.0463825	−	0.441300i	−0.992927	−	0.118727i	$-0.962119\pi$
$733$	−1.25576	−	11.9477i	−0.0463825	−	0.441300i	0.946544	−	0.322573i	$-0.104548\pi$
$734$	16.1737	−	7.20098i	0.596981	−	0.265793i
$735$	3.74793	+	20.7409i	0.138245	+	0.765040i
$736$	0.139293	+	0.241263i	0.00513441	+	0.00889306i
$737$	−3.44079	+	11.1552i	−0.126743	+	0.410909i
$738$	2.52535	+	9.77469i	0.0929593	+	0.359811i
$739$	1.00381	+	3.08940i	0.0369256	+	0.113645i	0.967820	−	0.251642i	$-0.0809706\pi$
$739$	1.00381	+	3.08940i	0.0369256	+	0.113645i	−0.930895	+	0.365288i	$0.880971\pi$
$740$	−0.189766	+	1.80550i	−0.00697594	+	0.0663717i
$741$	11.7918	+	7.29897i	0.433181	+	0.268134i
$742$	−7.47089	−	8.29726i	−0.274265	−	0.304602i
$743$	−31.3706	−	34.8406i	−1.15088	−	1.27818i	−0.954687	−	0.297613i	$-0.903810\pi$
$743$	−31.3706	−	34.8406i	−1.15088	−	1.27818i	−0.196190	−	0.980566i	$-0.562857\pi$
$744$	−16.0554	−	9.93811i	−0.588619	−	0.364349i
$745$	−2.39936	+	22.8284i	−0.0879057	+	0.836367i
$746$	−7.69558	−	23.6845i	−0.281755	−	0.867153i
$747$	18.9498	−	18.6128i	0.693337	−	0.681006i
$748$	11.0779	−	0.165873i	0.405049	−	0.00606493i
$749$	10.6681	+	18.4777i	0.389805	+	0.675162i
$750$	2.51577	+	13.9222i	0.0918631	+	0.508366i
$751$	4.09035	−	1.82114i	0.149259	−	0.0664543i	−0.330748	−	0.943719i	$-0.607301\pi$
$751$	4.09035	−	1.82114i	0.149259	−	0.0664543i	0.480007	+	0.877265i	$0.340634\pi$
$752$	−0.969749	−	9.22655i	−0.0353631	−	0.336458i
$753$	−5.62223	−	8.25954i	−0.204886	−	0.300994i
$754$	12.1855	−	2.59010i	0.443769	−	0.0943260i
$755$	−37.6628	+	27.3636i	−1.37069	+	0.995864i
$756$	4.08171	+	6.86650i	0.148450	+	0.249732i
$757$	−0.910430	−	2.80202i	−0.0330901	−	0.101841i	0.933147	−	0.359494i	$-0.117051\pi$
$757$	−0.910430	−	2.80202i	−0.0330901	−	0.101841i	−0.966237	+	0.257653i	$0.917051\pi$
$758$	−0.353171	−	0.611710i	−0.0128277	−	0.0222183i
$759$	−0.0251148	+	1.60016i	−0.000911611	+	0.0580820i
$760$	−6.47266	+	11.2110i	−0.234788	+	0.406665i
$761$	30.6877	+	6.52288i	1.11243	+	0.236454i	0.727240	−	0.686383i	$-0.240803\pi$
$761$	30.6877	+	6.52288i	1.11243	+	0.236454i	0.385190	+	0.922837i	$0.374136\pi$
$762$	−14.0524	−	13.4556i	−0.509065	−	0.487443i
$763$	−16.2329	−	7.22736i	−0.587671	−	0.261648i
$764$	−0.143530	+	0.441740i	−0.00519274	+	0.0159816i
$765$	−14.5217	+	21.9282i	−0.525035	+	0.792817i
$766$	12.1107	−	8.79892i	0.437576	−	0.317918i
$767$	2.28367	−	21.7277i	0.0824586	−	0.784541i
$768$	−1.32209	+	1.11896i	−0.0477070	+	0.0403769i
$769$	−4.86661	+	8.42922i	−0.175495	+	0.303966i	−0.940332	−	0.340257i	$-0.889486\pi$
$769$	−4.86661	+	8.42922i	−0.175495	+	0.303966i	0.764838	+	0.644223i	$0.222819\pi$
$770$	13.1289	+	2.58582i	0.473132	+	0.0931863i
$771$	−18.3549	−	44.8812i	−0.661037	−	1.61636i
$772$	−3.91527	+	4.34834i	−0.140913	+	0.156500i
$773$	18.4444	+	13.4006i	0.663397	+	0.481986i	0.867809	−	0.496899i	$-0.165528\pi$
$773$	18.4444	+	13.4006i	0.663397	+	0.481986i	−0.204411	+	0.978885i	$0.565528\pi$
$774$	−20.9673	+	7.83350i	−0.753656	+	0.281569i
$775$	6.35914	−	19.5714i	0.228427	−	0.703026i
$776$	−0.815093	+	0.173253i	−0.0292601	+	0.00621943i
$777$	1.62263	−	0.871614i	0.0582116	−	0.0312690i
$778$	−1.35267	+	0.602248i	−0.0484956	+	0.0215916i
$779$	16.2366	+	3.45119i	0.581736	+	0.123652i
$780$	−4.51799	+	5.83359i	−0.161770	+	0.208876i
$781$	−1.38544	+	15.3956i	−0.0495748	+	0.550896i
$782$	0.930616			0.0332788
$783$	−36.2221	+	16.6824i	−1.29447	+	0.596181i
$784$	3.75117	+	2.72538i	0.133970	+	0.0973351i
$785$	30.9849	+	13.7954i	1.10590	+	0.492378i
$786$	4.10696	+	6.03347i	0.146490	+	0.215207i
$787$	−25.9533	−	28.8240i	−0.925135	−	1.02747i	−0.999543	−	0.0302384i	$-0.990373\pi$
$787$	−25.9533	−	28.8240i	−0.925135	−	1.02747i	0.0744079	−	0.997228i	$-0.476293\pi$
$788$	1.83551	+	17.4637i	0.0653875	+	0.622120i
$789$	1.66381	+	1.59314i	0.0592332	+	0.0567174i
$790$	23.2226	−	25.7913i	0.826222	−	0.917613i
$791$	4.11537			0.146326
$792$	−9.81786	+	1.61544i	−0.348862	+	0.0574021i
$793$	7.83958			0.278392
$794$	18.8199	−	20.9016i	0.667893	−	0.741770i
$795$	−7.85090	+	32.0669i	−0.278443	+	1.13730i
$796$	−2.19193	−	20.8549i	−0.0776910	−	0.739181i
$797$	−12.8456	−	14.2665i	−0.455013	−	0.505344i	0.471365	−	0.881938i	$-0.343762\pi$
$797$	−12.8456	−	14.2665i	−0.455013	−	0.505344i	−0.926378	+	0.376595i	$0.877095\pi$
$798$	13.0980	−	0.971733i	0.463665	−	0.0343990i
$799$	−28.3117	−	12.6052i	−1.00160	−	0.445940i
$800$	−1.52714	−	1.10953i	−0.0539926	−	0.0392279i
$801$	−38.8144	+	24.7141i	−1.37144	+	0.873229i
$802$	−13.5362			−0.477980
$803$	−1.39703	+	1.59907i	−0.0493001	+	0.0564299i
$804$	−6.04068	−	0.822856i	−0.213038	−	0.0290199i
$805$	1.09941	+	0.233686i	0.0387491	+	0.00823637i
$806$	−16.1659	+	7.19752i	−0.569419	+	0.253522i
$807$	−0.708666	+	23.1019i	−0.0249462	+	0.813224i
$808$	8.08410	−	1.71833i	0.284398	−	0.0604506i
$809$	−11.0368	+	33.9678i	−0.388034	+	1.19425i	0.546221	+	0.837641i	$0.316066\pi$
$809$	−11.0368	+	33.9678i	−0.388034	+	1.19425i	−0.934255	+	0.356605i	$0.883934\pi$
$810$	9.99272	−	21.4020i	0.351108	−	0.751989i
$811$	39.5687	+	28.7483i	1.38944	+	1.00949i	0.995926	+	0.0901733i	$0.0287421\pi$
$811$	39.5687	+	28.7483i	1.38944	+	1.00949i	0.393518	+	0.919317i	$0.371258\pi$
$812$	7.89467	−	8.76792i	0.277049	−	0.307694i
$813$	−32.5215	+	41.9915i	−1.14058	+	1.47271i
$814$	0.273951	+	2.27786i	0.00960197	+	0.0798389i
$815$	−0.845441	+	1.46435i	−0.0296145	+	0.0512938i
$816$	1.02887	+	5.69370i	0.0360175	+	0.199319i
$817$	−3.84686	+	36.6004i	−0.134585	+	1.28049i
$818$	−17.4481	+	12.6768i	−0.610059	+	0.443234i
$819$	7.47203	+	0.458852i	0.261094	+	0.0160336i
$820$	−2.72917	+	8.39952i	−0.0953068	+	0.293324i
$821$	16.6396	+	7.40844i	0.580727	+	0.258556i	0.676008	−	0.736894i	$-0.263708\pi$
$821$	16.6396	+	7.40844i	0.580727	+	0.258556i	−0.0952811	+	0.995450i	$0.530375\pi$
$822$	2.91373	−	11.9011i	0.101628	−	0.415099i
$823$	−46.1127	−	9.80156i	−1.60739	−	0.341661i	−0.685185	−	0.728369i	$-0.740279\pi$
$823$	−46.1127	−	9.80156i	−1.60739	−	0.341661i	−0.922202	+	0.386708i	$0.873612\pi$
$824$	3.32785	−	5.76400i	0.115931	−	0.200798i
$825$	−4.25454	−	9.97423i	−0.148124	−	0.347258i
$826$	−10.3456	−	17.9190i	−0.359968	−	0.623483i
$827$	1.35976	+	4.18490i	0.0472833	+	0.145523i	0.971911	−	0.235350i	$-0.0756235\pi$
$827$	1.35976	+	4.18490i	0.0472833	+	0.145523i	−0.924627	+	0.380873i	$0.875624\pi$
$828$	−0.826608	+	0.123330i	−0.0287266	+	0.00428601i
$829$	30.4125	−	22.0960i	1.05627	−	0.767425i	0.0828749	−	0.996560i	$-0.473590\pi$
$829$	30.4125	−	22.0960i	1.05627	−	0.767425i	0.973395	+	0.229135i	$0.0735898\pi$
$830$	22.7288	−	4.83116i	0.788928	−	0.167692i
$831$	−10.0460	+	20.8209i	−0.348490	+	0.722268i
$832$	0.169672	+	1.61432i	0.00588231	+	0.0559664i
$833$	14.1498	−	6.29989i	0.490261	−	0.218278i
$834$	−28.7429	−	10.3237i	−0.995285	−	0.357482i
$835$	−21.4327	−	37.1225i	−0.741709	−	1.28468i
$836$	−4.82190	+	15.6329i	−0.166769	+	0.540674i
$837$	45.4010	−	33.8765i	1.56929	−	1.17094i
$838$	0.897820	+	2.76321i	0.0310147	+	0.0954534i
$839$	0.738999	−	7.03111i	0.0255131	−	0.242741i	−0.974332	−	0.225118i	$-0.927723\pi$
$839$	0.738999	−	7.03111i	0.0255131	−	0.242741i	0.999845	−	0.0176233i	$-0.00560995\pi$
$840$	−0.214263	+	6.98476i	−0.00739277	+	0.240997i
$841$	20.0080	+	22.2212i	0.689932	+	0.766247i
$842$	20.1572	+	22.3868i	0.694662	+	0.771501i
$843$	−31.9692	+	17.1726i	−1.10108	+	0.591457i
$844$	−0.348814	+	3.31874i	−0.0120067	+	0.114236i
$845$	−8.40611	−	25.8713i	−0.289179	−	0.890001i
$846$	26.8180	+	7.44440i	0.922023	+	0.255944i
$847$	16.9028	−	0.506294i	0.580786	−	0.0173965i
$848$	3.63138	+	6.28973i	0.124702	+	0.215990i
$849$	29.4804	−	24.9508i	1.01176	−	0.856308i
$850$	−5.76054	+	2.56476i	−0.197585	+	0.0879704i
$851$	0.0201439	+	0.191656i	0.000690522	+	0.00656988i
$852$	−8.05043	+	0.597256i	−0.275803	+	0.0204617i
$853$	7.87201	−	1.67325i	0.269532	−	0.0572909i	−0.0711626	−	0.997465i	$-0.522671\pi$
$853$	7.87201	−	1.67325i	0.269532	−	0.0572909i	0.340695	+	0.940174i	$0.389338\pi$
$854$	6.00669	−	4.36411i	0.205545	−	0.149337i
$855$	−24.1685	−	30.3993i	−0.826545	−	1.03963i
$856$	−4.28885	−	13.1997i	−0.146590	−	0.451157i
$857$	4.57921	+	7.93143i	0.156423	+	0.270933i	0.933576	−	0.358379i	$-0.116670\pi$
$857$	4.57921	+	7.93143i	0.156423	+	0.270933i	−0.777153	+	0.629311i	$0.783337\pi$
$858$	−3.92589	+	8.45791i	−0.134028	+	0.288748i
$859$	19.8702	−	34.4162i	0.677963	−	1.17427i	−0.297631	−	0.954681i	$-0.596196\pi$
$859$	19.8702	−	34.4162i	0.677963	−	1.17427i	0.975593	−	0.219585i	$-0.0704702\pi$
$860$	−19.1529	−	4.07108i	−0.653109	−	0.138823i
$861$	8.60285	−	2.50636i	0.293184	−	0.0854164i
$862$	5.62079	+	2.50254i	0.191445	+	0.0852367i
$863$	0.799304	−	2.46000i	0.0272086	−	0.0837395i	−0.936530	−	0.350587i	$-0.885982\pi$
$863$	0.799304	−	2.46000i	0.0272086	−	0.0837395i	0.963739	+	0.266848i	$0.0859820\pi$
$864$	−1.66843	−	4.92101i	−0.0567613	−	0.167416i
$865$	−5.08820	+	3.69679i	−0.173004	+	0.125695i
$866$	−3.82267	+	36.3703i	−0.129900	+	1.23591i
$867$	−9.52149	−	3.41989i	−0.323367	−	0.116145i
$868$	−8.37962	+	14.5139i	−0.284423	+	0.492635i
$869$	21.3585	−	38.3072i	0.724536	−	1.29948i
$870$	−34.5674	−	4.70875i	−1.17195	−	0.159641i
$871$	−3.82299	+	4.24586i	−0.129537	+	0.143865i
$872$	9.35114	+	6.79400i	0.316670	+	0.230074i
$873$	0.413209	−	2.46552i	0.0139850	−	0.0834452i
$874$	−0.424638	+	1.30690i	−0.0143636	+	0.0442066i
$875$	12.2825	−	2.61073i	0.415225	−	0.0882589i
$876$	−0.942879	−	0.583631i	−0.0318569	−	0.0197191i
$877$	26.8398	−	11.9499i	0.906317	−	0.403518i	0.0999899	−	0.994988i	$-0.468119\pi$
$877$	26.8398	−	11.9499i	0.906317	−	0.403518i	0.806327	+	0.591470i	$0.201452\pi$
$878$	−6.95504	−	1.47834i	−0.234721	−	0.0498915i
$879$	8.41572	+	20.5780i	0.283855	+	0.694078i
$880$	−8.00385	−	3.42089i	−0.269810	−	0.115318i
$881$	−23.7518			−0.800218			−0.400109	−	0.916468i	$-0.631028\pi$
$881$	−23.7518			−0.800218			−0.400109	+	0.916468i	$0.631028\pi$
$882$	−11.7335	+	7.47100i	−0.395087	+	0.251562i
$883$	−26.7756	−	19.4536i	−0.901070	−	0.654665i	0.0376708	−	0.999290i	$-0.488006\pi$
$883$	−26.7756	−	19.4536i	−0.901070	−	0.654665i	−0.938741	+	0.344625i	$0.888006\pi$
$884$	4.95355	+	2.20546i	0.166606	+	0.0741777i
$885$	−26.5868	+	55.1028i	−0.893705	+	1.85226i
$886$	7.28571	+	8.09160i	0.244768	+	0.271843i
$887$	0.699145	+	6.65193i	0.0234750	+	0.223350i	0.999970	+	0.00780752i	$0.00248524\pi$
$887$	0.699145	+	6.65193i	0.0234750	+	0.223350i	−0.976495	+	0.215542i	$0.930848\pi$
$888$	−1.15032	+	0.335134i	−0.0386022	+	0.0112464i
$889$	−11.5546	+	12.8327i	−0.387529	+	0.430395i
$890$	−40.2541			−1.34932
$891$	6.29285	−	29.1788i	0.210818	−	0.977525i
$892$	−2.16695			−0.0725549
$893$	30.6206	−	34.0076i	1.02468	−	1.13802i
$894$	−14.5444	+	4.23736i	−0.486437	+	0.141719i
$895$	−5.88358	−	55.9786i	−0.196667	−	1.87116i
$896$	1.02866	+	1.14244i	0.0343650	+	0.0381662i
$897$	−0.340362	+	0.705421i	−0.0113643	+	0.0235533i
$898$	3.25626	+	1.44978i	0.108663	+	0.0483798i
$899$	−67.6886	−	49.1786i	−2.25754	−	1.64020i
$900$	4.77683	−	3.04153i	0.159228	−	0.101384i
$901$	24.2612			0.808259
$902$	−1.00034	+	11.1162i	−0.0333078	+	0.370130i
$903$	7.52006	+	18.3879i	0.250252	+	0.611911i
$904$	−2.61850	−	0.556580i	−0.0870901	−	0.0185116i
$905$	58.6748	−	26.1237i	1.95042	−	0.868382i
$906$	−26.1244	−	16.1707i	−0.867924	−	0.537235i
$907$	−21.1186	+	4.48889i	−0.701230	+	0.149051i	−0.544711	−	0.838624i	$-0.683361\pi$
$907$	−21.1186	+	4.48889i	−0.701230	+	0.149051i	−0.156519	+	0.987675i	$0.550027\pi$
$908$	8.35759	−	25.7220i	0.277356	−	0.853615i
$909$	−4.09822	+	24.4531i	−0.135929	+	0.811057i
$910$	5.29819	+	3.84936i	0.175633	+	0.127605i
$911$	1.98887	−	2.20886i	0.0658942	−	0.0731829i	−0.709296	−	0.704910i	$-0.750987\pi$
$911$	1.98887	−	2.20886i	0.0658942	−	0.0731829i	0.775191	+	0.631728i	$0.217654\pi$
$912$	−8.46536	−	1.15314i	−0.280316	−	0.0381844i
$913$	26.6446	−	12.3442i	0.881808	−	0.408533i
$914$	6.99180	−	12.1102i	0.231268	−	0.400568i
$915$	−20.6617	−	7.42117i	−0.683054	−	0.245336i
$916$	0.155913	−	1.48342i	0.00515152	−	0.0490135i
$917$	5.24080	−	3.80767i	0.173067	−	0.125740i
$918$	−17.0230	−	3.39260i	−0.561841	−	0.111973i
$919$	11.7515	−	36.1673i	0.387646	−	1.19305i	−0.546897	−	0.837200i	$-0.684191\pi$
$919$	11.7515	−	36.1673i	0.387646	−	1.19305i	0.934543	−	0.355851i	$-0.115809\pi$
$920$	−0.667921	−	0.297378i	−0.0220207	−	0.00980425i
$921$	−38.1635	+	11.1185i	−1.25753	+	0.366369i
$922$	−0.651318	−	0.138442i	−0.0214500	−	0.00455934i
$923$	−3.78264	+	6.55173i	−0.124507	+	0.215653i
$924$	1.70031	+	8.66591i	0.0559361	+	0.285087i
$925$	−0.652891	−	1.13084i	−0.0214669	−	0.0371818i
$926$	9.17843	+	28.2483i	0.301622	+	0.928297i
$927$	12.4260	+	15.6295i	0.408122	+	0.513339i
$928$	−6.20899	+	4.51109i	−0.203820	+	0.148084i
$929$	55.6410	−	11.8269i	1.82552	−	0.388027i	0.838022	−	0.545636i	$-0.183712\pi$
$929$	55.6410	−	11.8269i	1.82552	−	0.388027i	0.987502	+	0.157609i	$0.0503787\pi$
$930$	49.4195	−	3.66640i	1.62053	−	0.120226i
$931$	2.39067	+	22.7458i	0.0783512	+	0.745462i
$932$	26.2598	−	11.6916i	0.860170	−	0.382972i
$933$	3.08034	−	2.60705i	0.100846	−	0.0853510i
$934$	1.96297	+	3.39997i	0.0642304	+	0.111250i
$935$	−23.2649	+	17.4410i	−0.760844	+	0.570383i
$936$	−4.69221	−	1.30251i	−0.153370	−	0.0425737i
$937$	−8.40861	−	25.8790i	−0.274697	−	0.845431i	−0.989299	−	0.145900i	$-0.953392\pi$
$937$	−8.40861	−	25.8790i	−0.274697	−	0.845431i	0.714602	−	0.699531i	$-0.246608\pi$
$938$	−0.565603	+	5.38135i	−0.0184676	+	0.175707i
$939$	31.9644	−	17.1700i	1.04312	−	0.560323i
$940$	16.2919	+	18.0940i	0.531383	+	0.590160i
$941$	13.9698	+	15.5151i	0.455403	+	0.505777i	0.926495	−	0.376308i	$-0.122806\pi$
$941$	13.9698	+	15.5151i	0.455403	+	0.505777i	−0.471091	+	0.882084i	$0.656140\pi$
$942$	−0.686334	+	22.3739i	−0.0223620	+	0.728980i
$943$	−0.0979956	+	0.932366i	−0.00319118	+	0.0303620i
$944$	4.15917	+	12.8006i	0.135369	+	0.416624i
$945$	−19.2586	−	8.28257i	−0.626483	−	0.269432i
$946$	−24.7424	+	0.370476i	−0.804446	+	0.0120452i
$947$	13.8847	+	24.0490i	0.451192	+	0.781488i	0.998460	−	0.0554693i	$-0.0176655\pi$
$947$	13.8847	+	24.0490i	0.451192	+	0.781488i	−0.547268	+	0.836957i	$0.684332\pi$
$948$	21.5564	+	7.74253i	0.700119	+	0.251466i
$949$	−0.949368	+	0.422686i	−0.0308178	+	0.0137210i
$950$	−0.973270	−	9.26005i	−0.0315771	−	0.300436i
$951$	0.965858	−	2.00180i	0.0313201	−	0.0649129i
$952$	5.02314	−	1.06770i	0.162801	−	0.0346044i
$953$	45.7990	−	33.2749i	1.48357	−	1.07788i	0.507192	−	0.861833i	$-0.330683\pi$
$953$	45.7990	−	33.2749i	1.48357	−	1.07788i	0.976383	−	0.216047i	$-0.0693165\pi$
$954$	−21.5497	+	3.21522i	−0.697699	+	0.104097i
$955$	−0.376685	−	1.15932i	−0.0121893	−	0.0375147i
$956$	−0.467946	−	0.810506i	−0.0151345	−	0.0262136i
$957$	−43.9134	+	3.91979i	−1.41952	+	0.126709i
$958$	−0.529676	+	0.917425i	−0.0171130	+	0.0296407i
$959$	−10.6373	−	2.26103i	−0.343496	−	0.0730124i
$960$	1.08098	−	4.41525i	0.0348885	−	0.142502i
$961$	80.2524	+	35.7307i	2.58879	+	1.15260i
$962$	−0.346981	+	1.06790i	−0.0111871	+	0.0344304i
$963$	41.5587	+	2.55209i	1.33921	+	0.0822400i
$964$	6.78796	−	4.93174i	0.218626	−	0.158841i
$965$	1.60517	−	15.2722i	0.0516722	−	0.491628i
$966$	0.131907	+	0.729966i	0.00424403	+	0.0234863i
$967$	4.31343	−	7.47108i	0.138711	−	0.240254i	−0.788298	−	0.615293i	$-0.789038\pi$
$967$	4.31343	−	7.47108i	0.138711	−	0.240254i	0.927009	+	0.375040i	$0.122371\pi$
$968$	−10.8233	−	1.96386i	−0.347873	−	0.0631209i
$969$	−17.4753	+	22.5639i	−0.561386	+	0.724856i
$970$	1.46335	−	1.62522i	0.0469854	−	0.0521826i
$971$	−18.0447	−	13.1102i	−0.579082	−	0.420727i	0.259311	−	0.965794i	$-0.416504\pi$
$971$	−18.0447	−	13.1102i	−0.579082	−	0.420727i	−0.838393	+	0.545066i	$0.816504\pi$
$972$	15.5700	+	0.757470i	0.499409	+	0.0242959i
$973$	−8.37646	+	25.7801i	−0.268537	+	0.826472i
$974$	−30.5156	+	6.48629i	−0.977782	+	0.207834i
$975$	0.162723	−	5.30460i	0.00521129	−	0.169883i
$976$	−4.41213	+	1.96440i	−0.141229	+	0.0628791i
$977$	−6.85348	−	1.45675i	−0.219262	−	0.0466056i	0.0969706	−	0.995287i	$-0.469085\pi$
$977$	−6.85348	−	1.45675i	−0.219262	−	0.0466056i	−0.316233	+	0.948682i	$0.602418\pi$
$978$	−1.10572	−	0.150620i	−0.0353571	−	0.00481631i
$979$	−49.5955	+	11.3205i	−1.58508	+	0.361804i
$980$	−12.1687			−0.388715
$981$	−29.2500	+	18.6242i	−0.933879	+	0.594624i
$982$	26.1924	+	19.0299i	0.835834	+	0.607269i
$983$	−1.18792	−	0.528894i	−0.0378886	−	0.0168691i	0.387705	−	0.921784i	$-0.373268\pi$
$983$	−1.18792	−	0.528894i	−0.0378886	−	0.0168691i	−0.425594	+	0.904914i	$0.639935\pi$
$984$	−5.81275	+	0.431244i	−0.185304	+	0.0137475i
$985$	−30.8368	−	34.2478i	−0.982543	−	1.09122i
$986$	2.67984	+	25.4970i	0.0853435	+	0.811989i
$987$	5.87444	−	23.9941i	0.186986	−	0.763741i
$988$	−5.35751	+	5.95012i	−0.170445	+	0.189298i
$989$	−2.07852			−0.0660931
$990$	18.3534	−	18.5750i	0.583310	−	0.590352i
$991$	−5.89868			−0.187378			−0.0936889	−	0.995602i	$-0.529866\pi$
$991$	−5.89868			−0.187378			−0.0936889	+	0.995602i	$0.529866\pi$
$992$	7.29466	−	8.10155i	0.231606	−	0.257224i
$993$	6.03687	+	5.78047i	0.191574	+	0.183438i
$994$	0.748936	+	7.12565i	0.0237548	+	0.226012i
$995$	36.8247	+	40.8980i	1.16742	+	1.29655i
$996$	8.62932	+	12.6772i	0.273431	+	0.401693i
$997$	−7.27950	−	3.24104i	−0.230544	−	0.102645i	0.288214	−	0.957566i	$-0.406939\pi$
$997$	−7.27950	−	3.24104i	−0.230544	−	0.102645i	−0.518758	+	0.854921i	$0.673605\pi$
$998$	0.709057	+	0.515160i	0.0224448	+	0.0163071i
$999$	0.330216	−	3.57923i	0.0104476	−	0.113242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.m.b.49.1	yes	56
3.2	odd	2		594.2.n.b.577.2		56
9.2	odd	6		594.2.n.b.181.6		56
9.7	even	3	inner	198.2.m.b.115.4	yes	56
11.9	even	5	inner	198.2.m.b.31.4	✓	56
33.20	odd	10		594.2.n.b.361.6		56
99.20	odd	30		594.2.n.b.559.2		56
99.97	even	15	inner	198.2.m.b.97.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.m.b.31.4	✓	56	11.9	even	5	inner
198.2.m.b.49.1	yes	56	1.1	even	1	trivial
198.2.m.b.97.1	yes	56	99.97	even	15	inner
198.2.m.b.115.4	yes	56	9.7	even	3	inner
594.2.n.b.181.6		56	9.2	odd	6
594.2.n.b.361.6		56	33.20	odd	10
594.2.n.b.559.2		56	99.20	odd	30
594.2.n.b.577.2		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 - 0.743145i) q^{2} +(-1.66291 + 0.484474i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.75609 + 1.95033i) q^{5} +(-0.752673 + 1.55996i) q^{6} +(1.40440 + 0.625278i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.53057 - 1.61128i) q^{9} +O(q^{10})\)	\(q+(0.669131 - 0.743145i) q^{2} +(-1.66291 + 0.484474i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.75609 + 1.95033i) q^{5} +(-0.752673 + 1.55996i) q^{6} +(1.40440 + 0.625278i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.53057 - 1.61128i) q^{9} +2.62443 q^{10} +(3.23346 - 0.738058i) q^{11} +(0.655642 + 1.60316i) q^{12} +(1.58774 + 0.337484i) q^{13} +(1.40440 - 0.625278i) q^{14} +(-3.86511 - 2.39246i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.03227 + 3.17700i) q^{17} +(0.495870 - 2.95874i) q^{18} +(-3.99057 - 2.89932i) q^{19} +(1.75609 - 1.95033i) q^{20} +(-2.63832 - 0.359390i) q^{21} +(1.61512 - 2.89679i) q^{22} +(0.139293 - 0.241263i) q^{23} +(1.63009 + 0.585489i) q^{24} +(-0.197313 + 1.87731i) q^{25} +(1.31321 - 0.954099i) q^{26} +(-3.42750 + 3.90541i) q^{27} +(0.475053 - 1.46206i) q^{28} +(7.01122 + 3.12160i) q^{29} +(-4.36421 + 1.27147i) q^{30} +(-10.6635 - 2.26659i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.01940 + 2.79385i) q^{33} +(1.67025 + 2.89296i) q^{34} +(1.24675 + 3.83709i) q^{35} +(-1.86697 - 2.34828i) q^{36} +(-0.559637 + 0.406600i) q^{37} +(-4.82483 + 1.02555i) q^{38} +(-2.80378 + 0.208010i) q^{39} +(-0.274328 - 2.61006i) q^{40} +(-3.07428 + 1.36876i) q^{41} +(-2.03246 + 1.72018i) q^{42} +(-3.73048 - 6.46138i) q^{43} +(-1.07200 - 3.13860i) q^{44} +(7.58643 + 2.10591i) q^{45} +(-0.0860878 - 0.264951i) q^{46} +(-0.969749 + 9.22655i) q^{47} +(1.52585 - 0.819626i) q^{48} +(-3.10256 - 3.44574i) q^{49} +(1.26308 + 1.40280i) q^{50} +(0.177404 - 5.78319i) q^{51} +(0.169672 - 1.61432i) q^{52} +(-2.24432 - 6.90729i) q^{53} +(0.608840 + 5.16036i) q^{54} +(7.11770 + 5.01023i) q^{55} +(-0.768652 - 1.33134i) q^{56} +(8.04062 + 2.88799i) q^{57} +(7.01122 - 3.12160i) q^{58} +(-1.40689 - 13.3856i) q^{59} +(-1.97534 + 4.09402i) q^{60} +(4.72413 - 1.00415i) q^{61} +(-8.81966 + 6.40786i) q^{62} +(4.56142 - 0.680563i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.13000 + 3.68928i) q^{65} +(-1.28240 + 5.59959i) q^{66} +(-1.75990 + 3.04823i) q^{67} +(3.26750 + 0.694529i) q^{68} +(-0.114747 + 0.468683i) q^{69} +(3.68575 + 1.64100i) q^{70} +(-1.44023 + 4.43258i) q^{71} +(-2.99436 - 0.183881i) q^{72} +(-0.517949 + 0.376312i) q^{73} +(-0.0723075 + 0.687960i) q^{74} +(-0.581392 - 3.21740i) q^{75} +(-2.46631 + 4.27177i) q^{76} +(5.00255 + 0.985285i) q^{77} +(-1.72151 + 2.22280i) q^{78} +(8.84861 - 9.82737i) q^{79} +(-2.12321 - 1.54260i) q^{80} +(3.80757 - 8.15490i) q^{81} +(-1.03991 + 3.20051i) q^{82} +(8.66046 - 1.84084i) q^{83} +(-0.0816415 + 2.66144i) q^{84} +(-8.00897 + 3.56583i) q^{85} +(-7.29792 - 1.55122i) q^{86} +(-13.1714 - 1.79420i) q^{87} +(-3.04974 - 1.30348i) q^{88} -15.3382 q^{89} +(6.64131 - 4.22869i) q^{90} +(2.01880 + 1.46674i) q^{91} +(-0.254501 - 0.113311i) q^{92} +(18.8306 - 1.39703i) q^{93} +(6.20777 + 6.89443i) q^{94} +(-1.35315 - 12.8744i) q^{95} +(0.411891 - 1.68236i) q^{96} +(0.557588 - 0.619264i) q^{97} -4.63670 q^{98} +(6.99328 - 7.07771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 3 q^{3} + 7 q^{4} - q^{5} - 5 q^{6} - 14 q^{8} + 9 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 - q^5 - 5 * q^6 - 14 * q^8 + 9 * q^9	\( 56 q + 7 q^{2} + 3 q^{3} + 7 q^{4} - q^{5} - 5 q^{6} - 14 q^{8} + 9 q^{9} - 8 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} + 11 q^{15} + 7 q^{16} + 15 q^{18} - q^{20} + 2 q^{21} - 4 q^{22} - 14 q^{23} - 2 q^{24} + 22 q^{25} - 12 q^{26} - 48 q^{27} + 14 q^{29} + 2 q^{30} + 5 q^{31} - 28 q^{32} - 44 q^{33} - 20 q^{34} - 20 q^{35} - 9 q^{36} + 2 q^{37} + 5 q^{38} - 34 q^{39} - q^{40} - 14 q^{41} + 4 q^{42} + 6 q^{43} - 12 q^{44} + 8 q^{46} + 11 q^{47} + 35 q^{49} + 2 q^{50} - 69 q^{51} + 6 q^{52} - 50 q^{53} + 4 q^{54} + 6 q^{55} + 36 q^{57} + 14 q^{58} + 10 q^{59} + 12 q^{60} - 24 q^{61} - 10 q^{62} - 16 q^{63} - 14 q^{64} - 42 q^{65} - 6 q^{66} - 56 q^{67} + 70 q^{69} - 6 q^{71} + 9 q^{72} + 68 q^{73} - q^{74} - 92 q^{75} - 10 q^{76} + 10 q^{77} + 60 q^{78} - 12 q^{79} + 2 q^{80} - 67 q^{81} - 52 q^{82} - 25 q^{83} + 4 q^{84} - 7 q^{85} + 11 q^{86} + 86 q^{87} - 4 q^{88} + 104 q^{89} + 25 q^{90} - 158 q^{91} + 11 q^{92} + 95 q^{93} - 19 q^{94} + 68 q^{95} - 3 q^{96} + 32 q^{97} + 120 q^{98} + 155 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 - q^5 - 5 * q^6 - 14 * q^8 + 9 * q^9 - 8 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 + 11 * q^15 + 7 * q^16 + 15 * q^18 - q^20 + 2 * q^21 - 4 * q^22 - 14 * q^23 - 2 * q^24 + 22 * q^25 - 12 * q^26 - 48 * q^27 + 14 * q^29 + 2 * q^30 + 5 * q^31 - 28 * q^32 - 44 * q^33 - 20 * q^34 - 20 * q^35 - 9 * q^36 + 2 * q^37 + 5 * q^38 - 34 * q^39 - q^40 - 14 * q^41 + 4 * q^42 + 6 * q^43 - 12 * q^44 + 8 * q^46 + 11 * q^47 + 35 * q^49 + 2 * q^50 - 69 * q^51 + 6 * q^52 - 50 * q^53 + 4 * q^54 + 6 * q^55 + 36 * q^57 + 14 * q^58 + 10 * q^59 + 12 * q^60 - 24 * q^61 - 10 * q^62 - 16 * q^63 - 14 * q^64 - 42 * q^65 - 6 * q^66 - 56 * q^67 + 70 * q^69 - 6 * q^71 + 9 * q^72 + 68 * q^73 - q^74 - 92 * q^75 - 10 * q^76 + 10 * q^77 + 60 * q^78 - 12 * q^79 + 2 * q^80 - 67 * q^81 - 52 * q^82 - 25 * q^83 + 4 * q^84 - 7 * q^85 + 11 * q^86 + 86 * q^87 - 4 * q^88 + 104 * q^89 + 25 * q^90 - 158 * q^91 + 11 * q^92 + 95 * q^93 - 19 * q^94 + 68 * q^95 - 3 * q^96 + 32 * q^97 + 120 * q^98 + 155 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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