LMFDB - Embedded newform 250.2.h.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(9,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.h (of order $50$, degree $20$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	250.229
Dual form			250.2.h.a.119.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 + 0.968583i) q^{2} +(-1.32984 + 0.253680i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.448945 + 2.19054i) q^{5} +(-0.576428 - 1.22497i) q^{6} +(0.268269 - 0.369241i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-1.08521 + 0.429667i) q^{9} +O(q^{10})$	\(q+(0.248690 + 0.968583i) q^{2} +(-1.32984 + 0.253680i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.448945 + 2.19054i) q^{5} +(-0.576428 - 1.22497i) q^{6} +(0.268269 - 0.369241i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-1.08521 + 0.429667i) q^{9} +(-2.01007 + 0.979605i) q^{10} +(-4.35568 + 1.11835i) q^{11} +(1.04313 - 0.862956i) q^{12} +(0.786419 + 1.98627i) q^{13} +(0.424356 + 0.168015i) q^{14} +(-1.15272 - 2.79917i) q^{15} +(0.535827 - 0.844328i) q^{16} +(2.21860 - 4.03561i) q^{17} +(-0.686050 - 0.944266i) q^{18} +(-1.16898 + 6.12799i) q^{19} +(-1.44871 - 1.70330i) q^{20} +(-0.263085 + 0.559085i) q^{21} +(-2.16643 - 3.94071i) q^{22} +(-8.88973 - 0.559294i) q^{23} +(1.09526 + 0.795754i) q^{24} +(-4.59690 + 1.96686i) q^{25} +(-1.72829 + 1.25568i) q^{26} +(4.76336 - 3.02292i) q^{27} +(-0.0572029 + 0.452808i) q^{28} +(3.83983 + 0.485083i) q^{29} +(2.42456 - 1.81263i) q^{30} +(6.79777 + 3.73711i) q^{31} +(0.951057 + 0.309017i) q^{32} +(5.50864 - 2.59217i) q^{33} +(4.46057 + 1.14528i) q^{34} +(0.929273 + 0.421884i) q^{35} +(0.743987 - 0.899325i) q^{36} +(5.58110 + 3.54187i) q^{37} +(-6.22618 + 0.391718i) q^{38} +(-1.54969 - 2.44191i) q^{39} +(1.28951 - 1.82679i) q^{40} +(0.295999 + 4.70476i) q^{41} +(-0.606947 - 0.115781i) q^{42} +(3.51997 - 1.14371i) q^{43} +(3.27814 - 3.07838i) q^{44} +(-1.42840 - 2.18430i) q^{45} +(-1.66906 - 8.74953i) q^{46} +(5.53019 - 5.88906i) q^{47} +(-0.498374 + 1.25875i) q^{48} +(2.09875 + 6.45928i) q^{49} +(-3.04827 - 3.96334i) q^{50} +(-1.92662 + 5.92952i) q^{51} +(-1.64604 - 1.36172i) q^{52} +(10.2518 + 4.82412i) q^{53} +(4.11255 + 3.86194i) q^{54} +(-4.40524 - 9.03919i) q^{55} +(-0.452808 + 0.0572029i) q^{56} -8.44578i q^{57} +(0.485083 + 3.83983i) q^{58} +(-6.25034 - 7.55536i) q^{59} +(2.35865 + 1.89760i) q^{60} +(-0.406709 + 6.46445i) q^{61} +(-1.92916 + 7.51359i) q^{62} +(-0.132479 + 0.515972i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-3.99793 + 2.61440i) q^{65} +(3.88068 + 4.69093i) q^{66} +(0.269193 + 2.13088i) q^{67} +4.60525i q^{68} +(11.9638 - 1.51138i) q^{69} +(-0.177529 + 1.00500i) q^{70} +(0.756542 + 0.710440i) q^{71} +(1.05609 + 0.496960i) q^{72} +(-4.93382 - 4.08161i) q^{73} +(-2.04263 + 6.28658i) q^{74} +(5.61417 - 3.78175i) q^{75} +(-1.92780 - 5.93316i) q^{76} +(-0.755554 + 1.90831i) q^{77} +(1.97981 - 2.10828i) q^{78} +(-0.665466 - 3.48850i) q^{79} +(2.09009 + 0.794691i) q^{80} +(-3.01514 + 2.83140i) q^{81} +(-4.48334 + 1.45673i) q^{82} +(-8.66762 - 1.65344i) q^{83} +(-0.0387977 - 0.616672i) q^{84} +(9.83618 + 3.04815i) q^{85} +(1.98315 + 3.12495i) q^{86} +(-5.22941 + 0.329006i) q^{87} +(3.79691 + 2.40959i) q^{88} +(-7.87843 + 9.52338i) q^{89} +(1.76045 - 1.92674i) q^{90} +(0.944383 + 0.242476i) q^{91} +(8.05957 - 3.79255i) q^{92} +(-9.98797 - 3.24529i) q^{93} +(7.07934 + 3.89190i) q^{94} +(-13.9484 + 0.190445i) q^{95} +(-1.34314 - 0.169678i) q^{96} +(0.557352 - 4.41189i) q^{97} +(-5.73442 + 3.63917i) q^{98} +(4.24633 - 3.08514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 10 q^{5}+O(q^{10}) $ 240 * q + 10 * q^5	$ 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) $ 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$3$	−1.32984	+	0.253680i	−0.767782	+	0.146462i	−0.556370	−	0.830935i	$-0.687806\pi$
$3$	−1.32984	+	0.253680i	−0.767782	+	0.146462i	−0.211412	+	0.977397i	$0.567806\pi$
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	0.448945	+	2.19054i	0.200774	+	0.979638i
$5$	0.448945	+	2.19054i	0.200774	+	0.979638i
$6$	−0.576428	−	1.22497i	−0.235326	−	0.500092i
$7$	0.268269	−	0.369241i	0.101396	−	0.139560i	−0.755304	−	0.655375i	$-0.772511\pi$
$7$	0.268269	−	0.369241i	0.101396	−	0.139560i	0.856700	+	0.515815i	$0.172511\pi$
$8$	−0.684547	−	0.728969i	−0.242024	−	0.257729i
$9$	−1.08521	+	0.429667i	−0.361738	+	0.143222i
$10$	−2.01007	+	0.979605i	−0.635639	+	0.309778i
$11$	−4.35568	+	1.11835i	−1.31329	+	0.337195i	−0.839459	−	0.543423i	$-0.817128\pi$
$11$	−4.35568	+	1.11835i	−1.31329	+	0.337195i	−0.473827	+	0.880618i	$0.657128\pi$
$12$	1.04313	−	0.862956i	0.301127	−	0.249114i
$13$	0.786419	+	1.98627i	0.218113	+	0.550891i	0.997096	−	0.0761540i	$-0.0242641\pi$
$13$	0.786419	+	1.98627i	0.218113	+	0.550891i	−0.778983	+	0.627045i	$0.784264\pi$
$14$	0.424356	+	0.168015i	0.113414	+	0.0449038i
$15$	−1.15272	−	2.79917i	−0.297631	−	0.722743i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	2.21860	−	4.03561i	0.538089	−	0.978780i	−0.457875	−	0.889017i	$-0.651389\pi$
$17$	2.21860	−	4.03561i	0.538089	−	0.978780i	0.995963	−	0.0897627i	$-0.0286109\pi$
$18$	−0.686050	−	0.944266i	−0.161703	−	0.222566i
$19$	−1.16898	+	6.12799i	−0.268182	+	1.40586i	0.552043	+	0.833816i	$0.313849\pi$
$19$	−1.16898	+	6.12799i	−0.268182	+	1.40586i	−0.820224	+	0.572042i	$0.806151\pi$
$20$	−1.44871	−	1.70330i	−0.323942	−	0.380870i
$21$	−0.263085	+	0.559085i	−0.0574099	+	0.122002i
$22$	−2.16643	−	3.94071i	−0.461884	−	0.840163i
$23$	−8.88973	−	0.559294i	−1.85364	−	0.116621i	−0.903526	−	0.428534i	$-0.859030\pi$
$23$	−8.88973	−	0.559294i	−1.85364	−	0.116621i	−0.950111	+	0.311913i	$0.899030\pi$
$24$	1.09526	+	0.795754i	0.223569	+	0.162433i
$25$	−4.59690	+	1.96686i	−0.919379	+	0.393372i
$26$	−1.72829	+	1.25568i	−0.338946	+	0.246258i
$27$	4.76336	−	3.02292i	0.916709	−	0.581761i
$28$	−0.0572029	+	0.452808i	−0.0108103	+	0.0855726i
$29$	3.83983	+	0.485083i	0.713038	+	0.0900777i	0.473480	−	0.880804i	$-0.342997\pi$
$29$	3.83983	+	0.485083i	0.713038	+	0.0900777i	0.239558	+	0.970882i	$0.422997\pi$
$30$	2.42456	−	1.81263i	0.442662	−	0.330939i
$31$	6.79777	+	3.73711i	1.22092	+	0.671204i	0.956085	−	0.293091i	$-0.0946837\pi$
$31$	6.79777	+	3.73711i	1.22092	+	0.671204i	0.264831	+	0.964295i	$0.414684\pi$
$32$	0.951057	+	0.309017i	0.168125	+	0.0546270i
$33$	5.50864	−	2.59217i	0.958932	−	0.451239i
$34$	4.46057	+	1.14528i	0.764981	+	0.196414i
$35$	0.929273	+	0.421884i	0.157076	+	0.0713115i
$36$	0.743987	−	0.899325i	0.123998	−	0.149888i
$37$	5.58110	+	3.54187i	0.917527	+	0.582280i	0.908594	−	0.417680i	$-0.137157\pi$
$37$	5.58110	+	3.54187i	0.917527	+	0.582280i	0.00893240	+	0.999960i	$0.497157\pi$
$38$	−6.22618	+	0.391718i	−1.01002	+	0.0635451i
$39$	−1.54969	−	2.44191i	−0.248148	−	0.391019i
$40$	1.28951	−	1.82679i	0.203889	−	0.288841i
$41$	0.295999	+	4.70476i	0.0462272	+	0.734761i	0.951062	+	0.308999i	$0.0999939\pi$
$41$	0.295999	+	4.70476i	0.0462272	+	0.734761i	−0.904835	+	0.425762i	$0.860006\pi$
$42$	−0.606947	−	0.115781i	−0.0936540	−	0.0178654i
$43$	3.51997	−	1.14371i	0.536790	−	0.174414i	−0.0280617	−	0.999606i	$-0.508933\pi$
$43$	3.51997	−	1.14371i	0.536790	−	0.174414i	0.564851	+	0.825193i	$0.308933\pi$
$44$	3.27814	−	3.07838i	0.494198	−	0.464083i
$45$	−1.42840	−	2.18430i	−0.212934	−	0.325617i
$46$	−1.66906	−	8.74953i	−0.246090	−	1.29005i
$47$	5.53019	−	5.88906i	0.806662	−	0.859007i	−0.185670	−	0.982612i	$-0.559446\pi$
$47$	5.53019	−	5.88906i	0.806662	−	0.859007i	0.992332	+	0.123605i	$0.0394455\pi$
$48$	−0.498374	+	1.25875i	−0.0719340	+	0.181685i
$49$	2.09875	+	6.45928i	0.299821	+	0.922755i
$50$	−3.04827	−	3.96334i	−0.431090	−	0.560501i
$51$	−1.92662	+	5.92952i	−0.269781	+	0.830299i
$52$	−1.64604	−	1.36172i	−0.228264	−	0.188836i
$53$	10.2518	+	4.82412i	1.40819	+	0.662643i	0.971515	−	0.236977i	$-0.0761565\pi$
$53$	10.2518	+	4.82412i	1.40819	+	0.662643i	0.436674	+	0.899620i	$0.356156\pi$
$54$	4.11255	+	3.86194i	0.559647	+	0.525543i
$55$	−4.40524	−	9.03919i	−0.594003	−	1.21884i
$56$	−0.452808	+	0.0572029i	−0.0605090	+	0.00764406i
$57$		−	8.44578i		−	1.11867i
$58$	0.485083	+	3.83983i	0.0636946	+	0.504194i
$59$	−6.25034	−	7.55536i	−0.813725	−	0.983624i	−0.999999	−	0.00112668i	$-0.999641\pi$
$59$	−6.25034	−	7.55536i	−0.813725	−	0.983624i	0.186274	−	0.982498i	$-0.440359\pi$
$60$	2.35865	+	1.89760i	0.304500	+	0.244980i
$61$	−0.406709	+	6.46445i	−0.0520737	+	0.827688i	0.882143	+	0.470982i	$0.156100\pi$
$61$	−0.406709	+	6.46445i	−0.0520737	+	0.827688i	−0.934217	+	0.356706i	$0.883900\pi$
$62$	−1.92916	+	7.51359i	−0.245004	+	0.954227i
$63$	−0.132479	+	0.515972i	−0.0166908	+	0.0650063i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−3.99793	+	2.61440i	−0.495882	+	0.324277i
$66$	3.88068	+	4.69093i	0.477678	+	0.577414i
$67$	0.269193	+	2.13088i	0.0328871	+	0.260328i	0.999983	+	0.00591429i	$0.00188259\pi$
$67$	0.269193	+	2.13088i	0.0328871	+	0.260328i	−0.967095	+	0.254414i	$0.918117\pi$
$68$			4.60525i			0.558469i
$69$	11.9638	−	1.51138i	1.44027	−	0.181948i
$70$	−0.177529	+	1.00500i	−0.0212188	+	0.120120i
$71$	0.756542	+	0.710440i	0.0897850	+	0.0843137i	0.728140	−	0.685428i	$-0.240385\pi$
$71$	0.756542	+	0.710440i	0.0897850	+	0.0843137i	−0.638355	+	0.769742i	$0.720385\pi$
$72$	1.05609	+	0.496960i	0.124462	+	0.0585673i
$73$	−4.93382	−	4.08161i	−0.577460	−	0.477716i	0.302249	−	0.953229i	$-0.402263\pi$
$73$	−4.93382	−	4.08161i	−0.577460	−	0.477716i	−0.879709	+	0.475513i	$0.842263\pi$
$74$	−2.04263	+	6.28658i	−0.237451	+	0.730800i
$75$	5.61417	−	3.78175i	0.648269	−	0.436679i
$76$	−1.92780	−	5.93316i	−0.221134	−	0.680580i
$77$	−0.755554	+	1.90831i	−0.0861034	+	0.217472i
$78$	1.97981	−	2.10828i	0.224169	−	0.238716i
$79$	−0.665466	−	3.48850i	−0.0748708	−	0.392486i	−0.999920	−	0.0126395i	$-0.995977\pi$
$79$	−0.665466	−	3.48850i	−0.0748708	−	0.392486i	0.925049	−	0.379847i	$-0.124023\pi$
$80$	2.09009	+	0.794691i	0.233679	+	0.0888492i
$81$	−3.01514	+	2.83140i	−0.335015	+	0.314600i
$82$	−4.48334	+	1.45673i	−0.495102	+	0.160869i
$83$	−8.66762	−	1.65344i	−0.951395	−	0.181488i	−0.311754	−	0.950163i	$-0.600917\pi$
$83$	−8.66762	−	1.65344i	−0.951395	−	0.181488i	−0.639640	+	0.768674i	$0.720917\pi$
$84$	−0.0387977	−	0.616672i	−0.00423318	−	0.0672845i
$85$	9.83618	+	3.04815i	1.06688	+	0.330618i
$86$	1.98315	+	3.12495i	0.213849	+	0.336972i
$87$	−5.22941	+	0.329006i	−0.560651	+	0.0352732i
$88$	3.79691	+	2.40959i	0.404752	+	0.256863i
$89$	−7.87843	+	9.52338i	−0.835111	+	1.00948i	0.164621	+	0.986357i	$0.447360\pi$
$89$	−7.87843	+	9.52338i	−0.835111	+	1.00948i	−0.999733	+	0.0231194i	$0.992640\pi$
$90$	1.76045	−	1.92674i	0.185568	−	0.203096i
$91$	0.944383	+	0.242476i	0.0989982	+	0.0254184i
$92$	8.05957	−	3.79255i	0.840268	−	0.395400i
$93$	−9.98797	−	3.24529i	−1.03570	−	0.336521i
$94$	7.07934	+	3.89190i	0.730179	+	0.401419i
$95$	−13.9484	+	0.190445i	−1.43108	+	0.0195392i
$96$	−1.34314	−	0.169678i	−0.137084	−	0.0173177i
$97$	0.557352	−	4.41189i	0.0565905	−	0.447960i	−0.938206	−	0.346077i	$-0.887513\pi$
$97$	0.557352	−	4.41189i	0.0565905	−	0.447960i	0.994796	−	0.101882i	$-0.0324865\pi$
$98$	−5.73442	+	3.63917i	−0.579263	+	0.367612i
$99$	4.24633	−	3.08514i	0.426772	−	0.310068i
$100$	3.08075	−	3.93814i	0.308075	−	0.393814i
$101$	−6.87631	−	4.99593i	−0.684218	−	0.497114i	0.190536	−	0.981680i	$-0.438977\pi$
$101$	−6.87631	−	4.99593i	−0.684218	−	0.497114i	−0.874754	+	0.484567i	$0.838977\pi$
$102$	−6.22237	−	0.391478i	−0.616106	−	0.0387621i
$103$	−2.45869	−	4.47234i	−0.242262	−	0.440673i	0.727023	−	0.686613i	$-0.240903\pi$
$103$	−2.45869	−	4.47234i	−0.242262	−	0.440673i	−0.969285	+	0.245940i	$0.920903\pi$
$104$	0.909586	−	1.93297i	0.0891922	−	0.189543i
$105$	−1.34281	−	0.325300i	−0.131045	−	0.0317460i
$106$	−2.12305	+	11.1294i	−0.206209	+	1.08098i
$107$	7.67869	+	10.5688i	0.742327	+	1.02173i	0.998481	+	0.0550894i	$0.0175444\pi$
$107$	7.67869	+	10.5688i	0.742327	+	1.02173i	−0.256155	+	0.966636i	$0.582456\pi$
$108$	−2.71786	+	4.94377i	−0.261526	+	0.475715i
$109$	7.14637	−	11.2609i	0.684498	−	1.07860i	−0.307403	−	0.951580i	$-0.599460\pi$
$109$	7.14637	−	11.2609i	0.684498	−	1.07860i	0.991901	−	0.127017i	$-0.0405402\pi$
$110$	7.65967	−	6.51480i	0.730321	−	0.621162i
$111$	−8.32046	−	3.29430i	−0.789743	−	0.312681i
$112$	−0.168015	−	0.424356i	−0.0158759	−	0.0400979i
$113$	0.596464	−	0.493438i	0.0561106	−	0.0464187i	−0.608946	−	0.793212i	$-0.708407\pi$
$113$	0.596464	−	0.493438i	0.0561106	−	0.0464187i	0.665057	+	0.746793i	$0.268407\pi$
$114$	8.18044	−	2.10038i	0.766169	−	0.196719i
$115$	−2.76584	−	19.7244i	−0.257916	−	1.83931i
$116$	−3.59856	+	1.42477i	−0.334118	+	0.132287i
$117$	−1.70687	−	1.81763i	−0.157800	−	0.168040i
$118$	5.76360	−	7.93292i	0.530582	−	0.730284i
$119$	−0.894931	−	1.90183i	−0.0820382	−	0.174340i
$120$	−1.25142	+	2.75646i	−0.114238	+	0.251629i
$121$	8.08185	−	4.44304i	0.734714	−	0.403912i
$122$	−6.36250	+	1.21371i	−0.576034	+	0.109884i
$123$	−1.58714	−	6.18149i	−0.143107	−	0.557366i
$124$	−7.75730			−0.696626
$125$	−6.37223	−	9.18666i	−0.569950	−	0.821680i
$126$	−0.532708			−0.0474574
$127$	3.69045	+	14.3733i	0.327474	+	1.27543i	0.892760	+	0.450532i	$0.148766\pi$
$127$	3.69045	+	14.3733i	0.327474	+	1.27543i	−0.565286	+	0.824895i	$0.691234\pi$
$128$	−0.982287	+	0.187381i	−0.0868227	+	0.0165623i
$129$	−4.39085	+	2.41389i	−0.386593	+	0.212531i
$130$	−3.52651	−	3.22215i	−0.309296	−	0.282602i
$131$	4.47338	+	9.50641i	0.390841	+	0.830579i	0.999315	+	0.0370054i	$0.0117819\pi$
$131$	4.47338	+	9.50641i	0.390841	+	0.830579i	−0.608474	+	0.793574i	$0.708218\pi$
$132$	−3.57847	+	4.92535i	−0.311466	+	0.428696i
$133$	1.94910	+	2.07559i	0.169009	+	0.179976i
$134$	−1.99699	+	0.790663i	−0.172513	+	0.0683029i
$135$	8.76030	+	9.07719i	0.753967	+	0.781240i
$136$	−4.46057	+	1.14528i	−0.382491	+	0.0982069i
$137$	−0.219877	+	0.181898i	−0.0187854	+	0.0155406i	−0.646769	−	0.762686i	$-0.723880\pi$
$137$	−0.219877	+	0.181898i	−0.0187854	+	0.0155406i	0.627984	+	0.778226i	$0.283880\pi$
$138$	4.43917	+	11.2121i	0.377887	+	0.954433i
$139$	−2.52598	−	1.00011i	−0.214251	−	0.0848280i	0.258548	−	0.965999i	$-0.416756\pi$
$139$	−2.52598	−	1.00011i	−0.214251	−	0.0848280i	−0.472798	+	0.881171i	$0.656756\pi$
$140$	−1.01757	+	0.0779807i	−0.0860006	+	0.00659057i
$141$	−5.86032	+	9.23439i	−0.493528	+	0.777676i
$142$	−0.499976	+	0.909453i	−0.0419571	+	0.0763196i
$143$	−5.64672	−	7.77205i	−0.472203	−	0.649931i
$144$	−0.218707	+	1.14650i	−0.0182256	+	0.0955419i
$145$	0.661280	+	8.62906i	0.0549163	+	0.716605i
$146$	2.72639	−	5.79387i	0.225637	−	0.479504i
$147$	−4.42959	−	8.05739i	−0.365346	−	0.664562i
$148$	−6.59706	−	0.415052i	−0.542275	−	0.0341171i
$149$	−13.2808	−	9.64908i	−1.08801	−	0.790483i	−0.108945	−	0.994048i	$-0.534747\pi$
$149$	−13.2808	−	9.64908i	−1.08801	−	0.790483i	−0.979062	+	0.203564i	$0.934747\pi$
$150$	5.05913	+	4.49731i	0.413076	+	0.367204i
$151$	3.94128	−	2.86351i	0.320737	−	0.233029i	−0.415753	−	0.909478i	$-0.636482\pi$
$151$	3.94128	−	2.86351i	0.320737	−	0.233029i	0.736490	+	0.676449i	$0.236482\pi$
$152$	5.26733	−	3.34275i	0.427237	−	0.271133i
$153$	−0.673684	+	5.33276i	−0.0544641	+	0.431128i
$154$	−2.03626	−	0.257239i	−0.164086	−	0.0207289i
$155$	−5.13444	+	16.5685i	−0.412408	+	1.33082i
$156$	2.53440	+	1.39330i	0.202915	+	0.111553i
$157$	−10.3362	−	3.35844i	−0.824920	−	0.268033i	−0.134016	−	0.990979i	$-0.542787\pi$
$157$	−10.3362	−	3.35844i	−0.824920	−	0.268033i	−0.690904	+	0.722946i	$0.742787\pi$
$158$	3.21340	−	1.51211i	0.255645	−	0.120297i
$159$	−14.8570	−	3.81462i	−1.17823	−	0.302519i
$160$	−0.249941	+	2.22206i	−0.0197596	+	0.175669i
$161$	−2.59135	+	3.13241i	−0.204227	+	0.246868i
$162$	−3.49228	−	2.21627i	−0.274379	−	0.174126i
$163$	12.0799	−	0.760005i	0.946173	−	0.0595282i	0.417799	−	0.908540i	$-0.362802\pi$
$163$	12.0799	−	0.760005i	0.946173	−	0.0595282i	0.528374	+	0.849011i	$0.322802\pi$
$164$	−2.52592	−	3.98022i	−0.197241	−	0.310803i
$165$	8.15132	+	10.9031i	0.634579	+	0.848808i
$166$	−0.554058	−	8.80650i	−0.0430032	−	0.683517i
$167$	−4.99057	−	0.952002i	−0.386182	−	0.0736681i	−0.00936560	−	0.999956i	$-0.502981\pi$
$167$	−4.99057	−	0.952002i	−0.386182	−	0.0736681i	−0.376816	+	0.926288i	$0.622981\pi$
$168$	0.587650	−	0.190939i	0.0453382	−	0.0147313i
$169$	6.14979	−	5.77504i	0.473061	−	0.444234i
$170$	−0.506226	+	10.2852i	−0.0388257	+	0.788839i
$171$	−1.36440	−	7.15245i	−0.104339	−	0.546962i
$172$	−2.53358	+	2.69799i	−0.193184	+	0.205720i
$173$	−0.479131	+	1.21015i	−0.0364276	+	0.0920057i	−0.946852	−	0.321671i	$-0.895756\pi$
$173$	−0.479131	+	1.21015i	−0.0364276	+	0.0920057i	0.910424	+	0.413677i	$0.135756\pi$
$174$	−1.61917	−	4.98330i	−0.122749	−	0.377783i
$175$	−0.506960	+	2.22501i	−0.0383226	+	0.168195i
$176$	−1.38964	+	4.27686i	−0.104748	+	0.322381i
$177$	10.2286	+	8.46182i	0.768828	+	0.636029i
$178$	−11.1835	−	5.26254i	−0.838237	−	0.394444i
$179$	12.2221	+	11.4773i	0.913521	+	0.857854i	0.990265	−	0.139197i	$-0.0444522\pi$
$179$	12.2221	+	11.4773i	0.913521	+	0.857854i	−0.0767432	+	0.997051i	$0.524452\pi$
$180$	2.30401	+	1.22598i	0.171731	+	0.0913793i
$181$	22.2555	−	2.81152i	1.65424	−	0.208979i	0.757906	−	0.652364i	$-0.226223\pi$
$181$	22.2555	−	2.81152i	1.65424	−	0.208979i	0.896331	+	0.443385i	$0.146223\pi$
$182$			0.975015i			0.0722729i
$183$	−1.09905	−	8.69985i	−0.0812439	−	0.643111i
$184$	5.67773	+	6.86320i	0.418568	+	0.505962i
$185$	−5.25299	+	13.8157i	−0.386208	+	1.01575i
$186$	0.659424	−	10.4812i	0.0483513	−	0.768522i
$187$	−5.15027	+	20.0590i	−0.376625	+	1.46686i
$188$	−2.00907	+	7.82481i	−0.146526	+	0.570683i
$189$	0.161677	−	2.56978i	0.0117603	−	0.186924i
$190$	−3.65329	−	13.4628i	−0.265037	−	0.976696i
$191$	4.91304	+	5.93884i	0.355495	+	0.429719i	0.917697	−	0.397280i	$-0.130046\pi$
$191$	4.91304	+	5.93884i	0.355495	+	0.429719i	−0.562203	+	0.827000i	$0.690046\pi$
$192$	−0.169678	−	1.34314i	−0.0122455	−	0.0969330i
$193$		−	2.38094i		−	0.171384i	−0.996322	−	0.0856919i	$-0.972690\pi$
$193$		−	2.38094i		−	0.171384i	0.996322	−	0.0856919i	$-0.0273101\pi$
$194$	4.41189	−	0.557352i	0.316755	−	0.0400155i
$195$	4.65338	−	4.49093i	0.333235	−	0.321602i
$196$	−4.95093	−	4.64923i	−0.353638	−	0.332088i
$197$	−9.96910	−	4.69110i	−0.710269	−	0.334227i	0.0364788	−	0.999334i	$-0.488386\pi$
$197$	−9.96910	−	4.69110i	−0.710269	−	0.334227i	−0.746748	+	0.665107i	$0.768386\pi$
$198$	4.04423	+	3.34568i	0.287411	+	0.237767i
$199$	−1.58532	+	4.87911i	−0.112380	+	0.345871i	−0.991392	−	0.130930i	$-0.958204\pi$
$199$	−1.58532	+	4.87911i	−0.112380	+	0.345871i	0.879011	+	0.476801i	$0.158204\pi$
$200$	4.58057	+	2.00458i	0.323895	+	0.141746i
$201$	−0.898544	−	2.76544i	−0.0633784	−	0.195059i
$202$	3.12891	−	7.90271i	0.220149	−	0.556033i
$203$	1.20922	−	1.28769i	0.0848706	−	0.0903780i
$204$	−1.16826	−	6.12424i	−0.0817946	−	0.428782i
$205$	−10.1731	+	2.76058i	−0.710518	+	0.192807i
$206$	3.72038	−	3.49367i	0.259211	−	0.243416i
$207$	9.88757	−	3.21267i	0.687233	−	0.223296i
$208$	2.09844	+	0.400300i	0.145501	+	0.0277558i
$209$	−1.76154	−	27.9989i	−0.121848	−	1.93672i
$210$	−0.0188626	−	1.38152i	−0.00130164	−	0.0953339i
$211$	−4.68014	−	7.37473i	−0.322194	−	0.507697i	0.644167	−	0.764885i	$-0.277204\pi$
$211$	−4.68014	−	7.37473i	−0.322194	−	0.507697i	−0.966361	+	0.257188i	$0.917204\pi$
$212$	−11.3077	+	0.711422i	−0.776618	+	0.0488607i
$213$	−1.18630	−	0.752851i	−0.0812841	−	0.0515845i
$214$	−8.32716	+	10.0658i	−0.569233	+	0.688084i
$215$	4.08560	+	7.19715i	0.278636	+	0.490842i
$216$	−5.46436	−	1.40301i	−0.371802	−	0.0954626i
$217$	3.20352	−	1.50746i	0.217469	−	0.102333i
$218$	12.6843	+	4.12139i	0.859091	+	0.279136i
$219$	7.59660	+	4.17627i	0.513331	+	0.282206i
$220$	8.21501	+	5.79886i	0.553856	+	0.390959i
$221$	9.76055	+	1.23304i	0.656565	+	0.0829435i
$222$	1.12159	−	8.87831i	0.0752763	−	0.595873i
$223$	−17.0416	+	10.8149i	−1.14119	+	0.724222i	−0.965546	−	0.260231i	$-0.916201\pi$
$223$	−17.0416	+	10.8149i	−1.14119	+	0.724222i	−0.175645	+	0.984454i	$0.556201\pi$
$224$	0.369241	−	0.268269i	0.0246709	−	0.0179245i
$225$	4.14352	−	4.10960i	0.276235	−	0.273973i
$226$	0.626270	+	0.455012i	0.0416589	+	0.0302669i
$227$	19.2248	+	1.20952i	1.27600	+	0.0802788i	0.686283	−	0.727335i	$-0.259241\pi$
$227$	19.2248	+	1.20952i	1.27600	+	0.0802788i	0.589712	+	0.807613i	$0.299241\pi$
$228$	4.06879	+	7.40110i	0.269462	+	0.490150i
$229$	−5.03354	+	10.6968i	−0.332626	+	0.706865i	−0.999258	−	0.0385216i	$-0.987735\pi$
$229$	−5.03354	+	10.6968i	−0.332626	+	0.706865i	0.666632	+	0.745387i	$0.267735\pi$
$230$	18.4168	−	7.58420i	1.21437	−	0.500087i
$231$	0.520664	−	2.72942i	0.0342572	−	0.179582i
$232$	−2.27493	−	3.13118i	−0.149357	−	0.205572i
$233$	11.2375	−	20.4410i	0.736196	−	1.33914i	−0.197227	−	0.980358i	$-0.563193\pi$
$233$	11.2375	−	20.4410i	0.736196	−	1.33914i	0.933423	−	0.358778i	$-0.116807\pi$
$234$	1.33604	−	2.10527i	0.0873398	−	0.137626i
$235$	15.3829	+	9.47022i	1.00347	+	0.617769i
$236$	9.11704	+	3.60969i	0.593469	+	0.234971i
$237$	1.76992	+	4.47032i	0.114969	+	0.290378i
$238$	1.61952	−	1.33978i	0.104978	−	0.0868451i
$239$	−17.3667	+	4.45901i	−1.12336	+	0.288429i	−0.764284	−	0.644880i	$-0.776907\pi$
$239$	−17.3667	+	4.45901i	−1.12336	+	0.288429i	−0.359074	+	0.933309i	$0.616907\pi$
$240$	−2.98108	−	0.526597i	−0.192428	−	0.0339917i
$241$	19.8056	−	7.84158i	1.27579	−	0.505120i	0.370071	−	0.929003i	$-0.379333\pi$
$241$	19.8056	−	7.84158i	1.27579	−	0.505120i	0.905717	+	0.423883i	$0.139333\pi$
$242$	6.31332	+	6.72301i	0.405836	+	0.432171i
$243$	−6.65677	+	9.16226i	−0.427032	+	0.587760i
$244$	−2.75787	−	5.86078i	−0.176555	−	0.375198i
$245$	−13.2071	+	7.49725i	−0.843769	+	0.478982i
$246$	5.59258	−	3.07455i	0.356570	−	0.196026i
$247$	−13.0911	+	2.49727i	−0.832969	+	0.158897i
$248$	−1.92916	−	7.51359i	−0.122502	−	0.477113i
$249$	11.9460			0.757045
$250$	7.31333	−	8.45667i	0.462536	−	0.534846i
$251$	0.706729			0.0446083			0.0223042	−	0.999751i	$-0.492900\pi$
$251$	0.706729			0.0446083			0.0223042	+	0.999751i	$0.492900\pi$
$252$	−0.132479	−	0.515972i	−0.00834539	−	0.0325032i
$253$	39.3463	−	7.50570i	2.47368	−	0.471880i
$254$	−13.0040	+	7.14901i	−0.815943	+	0.448569i
$255$	−13.8538	−	1.55830i	−0.867557	−	0.0975844i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	13.5616	−	18.6659i	0.845949	−	1.16435i	−0.138791	−	0.990322i	$-0.544322\pi$
$257$	13.5616	−	18.6659i	0.845949	−	1.16435i	0.984741	−	0.174028i	$-0.0556783\pi$
$258$	−3.43001	−	3.65259i	−0.213543	−	0.227400i
$259$	2.80504	−	1.11059i	0.174297	−	0.0690089i
$260$	2.24392	−	4.21704i	0.139162	−	0.261530i
$261$	−4.37546	+	1.12343i	−0.270834	+	0.0695384i
$262$	−8.09527	+	6.69699i	−0.500127	+	0.413741i
$263$	0.809197	+	2.04380i	0.0498972	+	0.126026i	0.952587	−	0.304265i	$-0.0984109\pi$
$263$	0.809197	+	2.04380i	0.0498972	+	0.126026i	−0.902690	+	0.430291i	$0.858411\pi$
$264$	−5.66054	−	2.24116i	−0.348382	−	0.137934i
$265$	−5.96492	+	24.6226i	−0.366422	+	1.51256i
$266$	−1.52565	+	2.40405i	−0.0935439	+	0.147402i
$267$	8.06114	−	14.6632i	0.493334	−	0.897370i
$268$	−1.26245	−	1.73762i	−0.0771167	−	0.106142i
$269$	−5.33423	+	27.9630i	−0.325234	+	1.70494i	0.325426	+	0.945567i	$0.394492\pi$
$269$	−5.33423	+	27.9630i	−0.325234	+	1.70494i	−0.650660	+	0.759369i	$0.725508\pi$
$270$	−6.61341	+	10.7425i	−0.402479	+	0.653767i
$271$	4.42258	−	9.39847i	0.268653	−	0.570916i	−0.724292	−	0.689493i	$-0.757833\pi$
$271$	4.42258	−	9.39847i	0.268653	−	0.570916i	0.992945	+	0.118577i	$0.0378333\pi$
$272$	−2.21860	−	4.03561i	−0.134522	−	0.244695i
$273$	−1.31739	−	0.0828830i	−0.0797319	−	0.00501631i
$274$	−0.230865	−	0.167733i	−0.0139471	−	0.0101331i
$275$	17.8230	−	13.7079i	1.07477	−	0.826620i
$276$	−9.75583	+	7.08802i	−0.587232	+	0.426649i
$277$	−9.13469	+	5.79705i	−0.548850	+	0.348311i	−0.781160	−	0.624331i	$-0.785372\pi$
$277$	−9.13469	+	5.79705i	−0.548850	+	0.348311i	0.232310	+	0.972642i	$0.425372\pi$
$278$	0.340501	−	2.69534i	0.0204219	−	0.161656i
$279$	−8.98275	−	1.13478i	−0.537783	−	0.0679378i
$280$	−0.328591	−	0.966211i	−0.0196371	−	0.0577421i
$281$	−15.2084	−	8.36091i	−0.907259	−	0.498770i	−0.0414480	−	0.999141i	$-0.513197\pi$
$281$	−15.2084	−	8.36091i	−0.907259	−	0.498770i	−0.865811	+	0.500371i	$0.833197\pi$
$282$	−10.4017	−	3.37971i	−0.619411	−	0.201259i
$283$	5.88741	−	2.77040i	0.349970	−	0.164683i	−0.242756	−	0.970087i	$-0.578052\pi$
$283$	5.88741	−	2.77040i	0.349970	−	0.164683i	0.592726	+	0.805404i	$0.298052\pi$
$284$	−1.00522	−	0.258097i	−0.0596488	−	0.0153152i
$285$	18.5008	−	3.79169i	1.09589	−	0.224600i
$286$	6.12359	−	7.40215i	0.362096	−	0.437698i
$287$	1.81660	+	1.15285i	0.107230	+	0.0680505i
$288$	−1.16487	+	0.0732877i	−0.0686409	+	0.00431852i
$289$	−2.25494	−	3.55321i	−0.132643	−	0.209012i
$290$	−8.19351	+	2.78646i	−0.481139	+	0.163627i
$291$	0.378022	+	6.00849i	0.0221601	+	0.352224i
$292$	6.28987	+	1.19986i	0.368087	+	0.0702163i
$293$	23.4027	−	7.60400i	1.36720	−	0.444230i	0.468759	−	0.883326i	$-0.344701\pi$
$293$	23.4027	−	7.60400i	1.36720	−	0.444230i	0.898440	+	0.439096i	$0.144701\pi$
$294$	6.70266	−	6.29422i	0.390907	−	0.367086i
$295$	13.7442	−	17.0835i	0.800220	−	0.994642i
$296$	−1.23861	−	6.49302i	−0.0719928	−	0.377399i
$297$	−17.3670	+	18.4940i	−1.00773	+	1.07313i
$298$	6.04313	−	15.2632i	0.350069	−	0.884174i
$299$	−5.88014	−	18.0972i	−0.340057	−	1.04659i
$300$	−3.09787	+	6.01862i	−0.178856	+	0.347485i
$301$	0.521995	−	1.60654i	0.0300873	−	0.0925992i
$302$	3.75370	+	3.10533i	0.216001	+	0.178692i
$303$	10.4117	+	4.89940i	0.598139	+	0.281463i
$304$	4.54767	+	4.27054i	0.260827	+	0.244932i
$305$	−14.3432	+	2.01127i	−0.821290	+	0.115165i
$306$	−5.33276	+	0.673684i	−0.304854	+	0.0385120i
$307$		−	10.9544i		−	0.625202i	−0.949885	−	0.312601i	$-0.898800\pi$
$307$		−	10.9544i		−	0.625202i	0.949885	−	0.312601i	$-0.101200\pi$
$308$	−0.257239	−	2.03626i	−0.0146576	−	0.116027i
$309$	4.40420	+	5.32376i	0.250546	+	0.302858i
$310$	−17.3249	−	0.852710i	−0.983987	−	0.0484307i
$311$	0.734542	−	11.6752i	0.0416521	−	0.662041i	−0.920706	−	0.390257i	$-0.872386\pi$
$311$	0.734542	−	11.6752i	0.0416521	−	0.662041i	0.962358	−	0.271784i	$-0.0876137\pi$
$312$	−0.719246	+	2.80128i	−0.0407193	+	0.158591i
$313$	−5.33027	+	20.7600i	−0.301285	+	1.17343i	0.620020	+	0.784586i	$0.287124\pi$
$313$	−5.33027	+	20.7600i	−0.301285	+	1.17343i	−0.921305	+	0.388841i	$0.872876\pi$
$314$	0.682417	−	10.8467i	0.0385110	−	0.612115i
$315$	−1.18973	−	0.0585571i	−0.0670337	−	0.00329932i
$316$	2.26375	+	2.73640i	0.127346	+	0.153935i
$317$	0.292021	+	2.31159i	0.0164015	+	0.129832i	0.998189	−	0.0601489i	$-0.0191575\pi$
$317$	0.292021	+	2.31159i	0.0164015	+	0.129832i	−0.981788	+	0.189980i	$0.939158\pi$
$318$		−	15.3389i		−	0.860161i
$319$	−17.2676	+	2.18140i	−0.966797	+	0.122135i
$320$	−2.21440	+	0.310514i	−0.123789	+	0.0173583i
$321$	−12.8925	−	12.1069i	−0.719590	−	0.675740i
$322$	−3.67844	−	1.73094i	−0.204992	−	0.0964617i
$323$	22.1367	+	18.3131i	1.23172	+	1.01897i
$324$	1.27815	−	3.93373i	0.0710081	−	0.218540i
$325$	−7.52180	−	7.58389i	−0.417234	−	0.420678i
$326$	3.74028	+	11.5114i	0.207155	+	0.637558i
$327$	−6.64685	+	16.7880i	−0.367572	+	0.928380i
$328$	3.22700	−	3.43641i	0.178181	−	0.189744i
$329$	−0.690900	−	3.62183i	−0.0380906	−	0.199678i
$330$	−8.53345	+	10.6067i	−0.469751	+	0.583881i
$331$	21.0429	−	19.7606i	1.15662	−	1.08614i	0.161560	−	0.986863i	$-0.448347\pi$
$331$	21.0429	−	19.7606i	1.15662	−	1.08614i	0.995060	−	0.0992759i	$-0.0316526\pi$
$332$	8.39204	−	2.72674i	0.460573	−	0.149649i
$333$	−7.57851	−	1.44568i	−0.415300	−	0.0792226i
$334$	−0.319011	−	5.07054i	−0.0174555	−	0.277447i
$335$	−4.54691	+	1.54632i	−0.248424	+	0.0844847i
$336$	0.331083	+	0.521703i	0.0180621	+	0.0284612i
$337$	−28.6481	+	1.80238i	−1.56056	+	0.0981821i	−0.819430	−	0.573179i	$-0.805710\pi$
$337$	−28.6481	+	1.80238i	−1.56056	+	0.0981821i	−0.741130	+	0.671361i	$0.765710\pi$
$338$	7.12299	+	4.52039i	0.387440	+	0.245877i
$339$	−0.668025	+	0.807503i	−0.0362821	+	0.0438576i
$340$	−10.0880	+	2.06750i	−0.547097	+	0.112126i
$341$	−33.7883	−	8.67536i	−1.82974	−	0.469797i
$342$	6.58843	−	3.10028i	0.356262	−	0.167644i
$343$	5.98654	+	1.94514i	0.323243	+	0.105028i
$344$	−3.24331	−	1.78302i	−0.174867	−	0.0961342i
$345$	8.68180	+	25.5286i	0.467413	+	1.37441i
$346$	−1.29128	−	0.163127i	−0.0694198	−	0.00876976i
$347$	−4.18840	+	33.1546i	−0.224845	+	1.77983i	0.326143	+	0.945321i	$0.394251\pi$
$347$	−4.18840	+	33.1546i	−0.224845	+	1.77983i	−0.550988	+	0.834513i	$0.685749\pi$
$348$	4.42406	−	2.80760i	0.237155	−	0.150503i
$349$	−23.5715	+	17.1257i	−1.26175	+	0.916716i	−0.998842	−	0.0481046i	$-0.984682\pi$
$349$	−23.5715	+	17.1257i	−1.26175	+	0.916716i	−0.262909	+	0.964821i	$0.584682\pi$
$350$	−2.28118	+	0.0623040i	−0.121934	+	0.00333029i
$351$	9.75032	+	7.08402i	0.520434	+	0.378117i
$352$	−4.48808	−	0.282366i	−0.239216	−	0.0150502i
$353$	5.71943	+	10.4036i	0.304414	+	0.553728i	0.983628	−	0.180213i	$-0.0576788\pi$
$353$	5.71943	+	10.4036i	0.304414	+	0.553728i	−0.679213	+	0.733941i	$0.737679\pi$
$354$	−5.65223	+	12.0116i	−0.300413	+	0.638410i
$355$	−1.21660	+	1.97618i	−0.0645704	+	0.104885i
$356$	2.31599	−	12.1409i	0.122747	−	0.643464i
$357$	1.67257	+	2.30209i	0.0885218	+	0.121840i
$358$	−8.07721	+	14.6924i	−0.426894	+	0.776517i
$359$	−0.249640	+	0.393370i	−0.0131755	+	0.0207613i	−0.850852	−	0.525406i	$-0.823914\pi$
$359$	−0.249640	+	0.393370i	−0.0131755	+	0.0207613i	0.837676	+	0.546167i	$0.183914\pi$
$360$	−0.614481	+	2.53652i	−0.0323860	+	0.133686i
$361$	−18.5200	−	7.33260i	−0.974739	−	0.385926i
$362$	8.25791	+	20.8571i	0.434026	+	1.09622i
$363$	−9.62044	+	7.95872i	−0.504942	+	0.417725i
$364$	−0.944383	+	0.242476i	−0.0494991	+	0.0127092i
$365$	6.72590	−	12.6401i	0.352050	−	0.661614i
$366$	8.15321	−	3.22808i	0.426175	−	0.168735i
$367$	−7.99241	−	8.51105i	−0.417200	−	0.444273i	0.485698	−	0.874126i	$-0.338565\pi$
$367$	−7.99241	−	8.51105i	−0.417200	−	0.444273i	−0.902899	+	0.429853i	$0.858565\pi$
$368$	−5.23558	+	7.20616i	−0.272924	+	0.375647i
$369$	−2.34270	−	4.97849i	−0.121956	−	0.259170i
$370$	−14.6880	−	1.65214i	−0.763594	−	0.0858904i
$371$	4.53149	−	2.49121i	0.235263	−	0.129337i
$372$	10.3160	−	1.96787i	0.534857	−	0.102029i
$373$	−0.795290	−	3.09745i	−0.0411786	−	0.160380i	0.944669	−	0.328026i	$-0.106383\pi$
$373$	−0.795290	−	3.09745i	−0.0411786	−	0.160380i	−0.985847	+	0.167646i	$0.946383\pi$
$374$	−20.7096			−1.07087
$375$	10.8045	+	10.6003i	0.557942	+	0.547395i
$376$	−8.07862			−0.416623
$377$	2.05621	+	8.00841i	0.105900	+	0.412454i
$378$	2.52926	−	0.482481i	0.130091	−	0.0248162i
$379$	−14.9322	+	8.20904i	−0.767015	+	0.421670i	−0.816676	−	0.577096i	$-0.804186\pi$
$379$	−14.9322	+	8.20904i	−0.767015	+	0.421670i	0.0496614	+	0.998766i	$0.484186\pi$
$380$	12.1313	−	6.88658i	0.622324	−	0.353274i
$381$	−8.55392	−	18.1780i	−0.438231	−	0.931288i
$382$	−4.53044	+	6.23561i	−0.231797	+	0.319042i
$383$	0.115400	+	0.122889i	0.00589667	+	0.00627932i	0.731910	−	0.681401i	$-0.238629\pi$
$383$	0.115400	+	0.122889i	0.00589667	+	0.00627932i	−0.726014	+	0.687680i	$0.758629\pi$
$384$	1.25875	−	0.498374i	0.0642352	−	0.0254325i
$385$	−4.51943	−	0.798342i	−0.230331	−	0.0406873i
$386$	2.30614	−	0.592116i	0.117379	−	0.0301379i
$387$	−3.32850	+	2.75358i	−0.169197	+	0.139972i
$388$	1.63703	+	4.13468i	0.0831078	+	0.209906i
$389$	36.1245	+	14.3027i	1.83158	+	0.725175i	0.979399	+	0.201935i	$0.0647228\pi$
$389$	36.1245	+	14.3027i	1.83158	+	0.725175i	0.852185	+	0.523241i	$0.175277\pi$
$390$	5.50709	+	3.39034i	0.278862	+	0.171676i
$391$	−21.9798	+	34.6346i	−1.11157	+	1.75155i
$392$	3.27192	−	5.95161i	0.165257	−	0.300601i
$393$	−8.36046	−	11.5072i	−0.421729	−	0.580460i
$394$	2.06451	−	10.8225i	0.104008	−	0.545231i
$395$	7.34292	−	3.02387i	0.369462	−	0.152147i
$396$	−2.23481	+	4.74921i	−0.112303	+	0.238657i
$397$	−11.2899	−	20.5362i	−0.566623	−	1.03068i	−0.992068	−	0.125699i	$-0.959883\pi$
$397$	−11.2899	−	20.5362i	−0.566623	−	1.03068i	0.425445	−	0.904984i	$-0.360117\pi$
$398$	−5.12008	−	0.322128i	−0.256646	−	0.0161468i
$399$	−3.11853	−	2.26574i	−0.156122	−	0.113429i
$400$	−0.802465	+	4.93518i	−0.0401233	+	0.246759i
$401$	−15.1452	+	11.0036i	−0.756315	+	0.549495i	−0.897778	−	0.440449i	$-0.854819\pi$
$401$	−15.1452	+	11.0036i	−0.756315	+	0.549495i	0.141463	+	0.989944i	$0.454819\pi$
$402$	2.45509	−	1.55805i	0.122449	−	0.0777085i
$403$	−2.07700	+	16.4411i	−0.103463	+	0.818991i
$404$	8.43256	+	1.06528i	0.419536	+	0.0529997i
$405$	−7.55591	−	5.33362i	−0.375456	−	0.265030i
$406$	1.54795	+	0.850995i	0.0768237	+	0.0422342i
$407$	−28.2705	−	9.18564i	−1.40132	−	0.455315i
$408$	5.64130	−	2.65459i	0.279286	−	0.131422i
$409$	14.2064	+	3.64758i	0.702460	+	0.180361i	0.582993	−	0.812477i	$-0.301881\pi$
$409$	14.2064	+	3.64758i	0.702460	+	0.180361i	0.119467	+	0.992838i	$0.461881\pi$
$410$	−5.20379	−	9.16694i	−0.256997	−	0.452723i
$411$	0.246257	−	0.297674i	0.0121470	−	0.0146832i
$412$	4.30913	+	2.73466i	0.212296	+	0.134727i
$413$	−4.46652	+	0.281010i	−0.219783	+	0.0138276i
$414$	5.57067	+	8.77797i	0.273784	+	0.431414i
$415$	−0.269371	−	19.7290i	−0.0132229	−	0.968460i
$416$	0.134138	+	2.13207i	0.00657668	+	0.104533i
$417$	3.61285	+	0.689189i	0.176922	+	0.0337497i
$418$	26.6812	−	8.66924i	1.30502	−	0.424026i
$419$	26.9878	−	25.3432i	1.31844	−	1.23810i	0.367015	−	0.930215i	$-0.380380\pi$
$419$	26.9878	−	25.3432i	1.31844	−	1.23810i	0.951425	−	0.307882i	$-0.0996202\pi$
$420$	1.33342	−	0.361840i	0.0650645	−	0.0176560i
$421$	5.41993	+	28.4123i	0.264151	+	1.38473i	0.828868	+	0.559445i	$0.188986\pi$
$421$	5.41993	+	28.4123i	0.264151	+	1.38473i	−0.564716	+	0.825285i	$0.691014\pi$
$422$	5.97913	−	6.36713i	0.291060	−	0.309947i
$423$	−3.47111	+	8.76703i	−0.168771	+	0.426267i
$424$	−3.50119	−	10.7756i	−0.170033	−	0.523307i
$425$	−2.26117	+	22.9150i	−0.109683	+	1.11154i
$426$	0.434177	−	1.33626i	0.0210359	−	0.0647420i
$427$	2.27783	+	1.88439i	0.110232	+	0.0911919i
$428$	−11.8204	−	5.56228i	−0.571363	−	0.268863i
$429$	9.48084	+	8.90310i	0.457739	+	0.429846i
$430$	−5.95499	+	5.74710i	−0.287175	+	0.277150i
$431$	26.9563	−	3.40537i	1.29844	−	0.164031i	0.554447	−	0.832219i	$-0.312930\pi$
$431$	26.9563	−	3.40537i	1.29844	−	0.164031i	0.743992	+	0.668188i	$0.232930\pi$
$432$		−	5.64160i		−	0.271432i
$433$	−3.11552	−	24.6619i	−0.149722	−	1.18517i	−0.870557	−	0.492067i	$-0.836241\pi$
$433$	−3.11552	−	24.6619i	−0.149722	−	1.18517i	0.720835	−	0.693107i	$-0.243759\pi$
$434$	2.25679	+	2.72799i	0.108329	+	0.130948i
$435$	−3.06842	−	11.3075i	−0.147119	−	0.542153i
$436$	−0.837443	+	13.3108i	−0.0401062	+	0.637470i
$437$	13.8192	−	53.8224i	0.661064	−	2.57467i
$438$	−2.15586	+	8.39653i	−0.103011	+	0.401202i
$439$	−0.941378	+	14.9628i	−0.0449295	+	0.714134i	0.909501	+	0.415702i	$0.136464\pi$
$439$	−0.941378	+	14.9628i	−0.0449295	+	0.714134i	−0.954431	+	0.298433i	$0.903536\pi$
$440$	−3.57369	+	9.39904i	−0.170369	+	0.448081i
$441$	−5.05293	−	6.10794i	−0.240616	−	0.290854i
$442$	1.23304	+	9.76055i	0.0586499	+	0.464262i
$443$			23.3881i			1.11120i	0.831450	+	0.555600i	$0.187511\pi$
$443$			23.3881i			1.11120i	−0.831450	+	0.555600i	$0.812489\pi$
$444$	8.87831	−	1.12159i	0.421346	−	0.0532284i
$445$	−24.3983	−	12.9825i	−1.15659	−	0.615430i
$446$	−14.7132	−	13.8167i	−0.696693	−	0.654238i
$447$	20.1091	+	9.46263i	0.951129	+	0.447567i
$448$	0.351667	+	0.290925i	0.0166147	+	0.0137449i
$449$	7.01686	−	21.5957i	0.331146	−	1.01916i	−0.637443	−	0.770497i	$-0.720008\pi$
$449$	7.01686	−	21.5957i	0.331146	−	1.01916i	0.968589	−	0.248666i	$-0.0799920\pi$
$450$	5.01094	+	2.99133i	0.236218	+	0.141013i
$451$	−6.55084	−	20.1614i	−0.308467	−	0.949364i
$452$	−0.284970	+	0.719751i	−0.0134038	+	0.0338543i
$453$	−4.51485	+	4.80783i	−0.212126	+	0.225891i
$454$	3.60949	+	18.9216i	0.169402	+	0.888036i
$455$	−0.107177	+	2.17756i	−0.00502454	+	0.102086i
$456$	−6.15671	+	5.78154i	−0.288314	+	0.270745i
$457$	21.5309	−	6.99581i	1.00717	−	0.327250i	0.241445	−	0.970415i	$-0.422379\pi$
$457$	21.5309	−	6.99581i	1.00717	−	0.327250i	0.765728	+	0.643164i	$0.222379\pi$
$458$	−11.6125	−	2.21521i	−0.542618	−	0.103510i
$459$	−1.63136	−	25.9297i	−0.0761453	−	1.21030i
$460$	11.9260	+	15.9521i	0.556053	+	0.743772i
$461$	−16.5577	−	26.0907i	−0.771168	−	1.21517i	−0.971871	−	0.235515i	$-0.924322\pi$
$461$	−16.5577	−	26.0907i	−0.771168	−	1.21517i	0.200702	−	0.979652i	$-0.435678\pi$
$462$	2.77315	−	0.174472i	0.129019	−	0.00811716i
$463$	−21.7573	−	13.8076i	−1.01115	−	0.641693i	−0.0764252	−	0.997075i	$-0.524351\pi$
$463$	−21.7573	−	13.8076i	−1.01115	−	0.641693i	−0.934721	+	0.355382i	$0.884351\pi$
$464$	2.46705	−	2.98215i	0.114530	−	0.138443i
$465$	2.62487	−	23.3360i	0.121725	−	1.08218i
$466$	22.5935	+	5.80102i	1.04662	+	0.268727i
$467$	2.15339	−	1.01331i	0.0996469	−	0.0468903i	−0.375310	−	0.926899i	$-0.622464\pi$
$467$	2.15339	−	1.01331i	0.0996469	−	0.0468903i	0.474957	+	0.880009i	$0.342464\pi$
$468$	2.37139	+	0.770510i	0.109617	+	0.0356168i
$469$	0.859024	+	0.472252i	0.0396660	+	0.0218066i
$470$	−5.34712	+	17.2548i	−0.246644	+	0.795905i
$471$	14.5975	+	1.84409i	0.672616	+	0.0849712i
$472$	−1.22897	+	9.72830i	−0.0565680	+	0.447781i
$473$	−14.0528	+	8.91816i	−0.646147	+	0.410058i
$474$	−3.88971	+	2.82604i	−0.178660	+	0.129804i
$475$	−6.67924	−	30.4690i	−0.306464	−	1.39801i
$476$	1.70045	+	1.23545i	0.0779398	+	0.0566266i
$477$	−13.1981	−	0.830356i	−0.604301	−	0.0380194i
$478$	−8.63784	−	15.7122i	−0.395086	−	0.718658i
$479$	6.21446	−	13.2064i	0.283946	−	0.603415i	−0.711071	−	0.703120i	$-0.751790\pi$
$479$	6.21446	−	13.2064i	0.283946	−	0.603415i	0.995017	+	0.0997045i	$0.0317897\pi$
$480$	−0.231311	−	3.01838i	−0.0105578	−	0.137770i
$481$	−2.64602	+	13.8709i	−0.120648	+	0.632460i
$482$	12.5207	+	17.2332i	0.570300	+	0.784951i
$483$	2.65145	−	4.82297i	0.120645	−	0.219453i
$484$	−4.94173	+	7.78692i	−0.224624	+	0.353951i
$485$	9.91463	−	0.759798i	0.450200	−	0.0345006i
$486$	−10.5299	−	4.16908i	−0.477645	−	0.189113i
$487$	4.56972	+	11.5418i	0.207074	+	0.523008i	0.995781	−	0.0917603i	$-0.0292493\pi$
$487$	4.56972	+	11.5418i	0.207074	+	0.523008i	−0.788707	+	0.614769i	$0.789249\pi$
$488$	4.99079	−	4.12874i	0.225923	−	0.186899i
$489$	−15.8716	+	4.07512i	−0.717736	+	0.184283i
$490$	−10.5462	−	10.9277i	−0.476428	−	0.493661i
$491$	−3.45715	+	1.36878i	−0.156019	+	0.0617723i	−0.444836	−	0.895612i	$-0.646738\pi$
$491$	−3.45715	+	1.36878i	−0.156019	+	0.0617723i	0.288817	+	0.957384i	$0.406738\pi$
$492$	4.36877	+	4.65227i	0.196959	+	0.209740i
$493$	10.4766	−	14.4199i	0.471844	−	0.649438i
$494$	−5.67444	−	12.0588i	−0.255305	−	0.542551i
$495$	8.66447	+	7.91667i	0.389439	+	0.355828i
$496$	6.79777	−	3.73711i	0.305229	−	0.167801i
$497$	0.465280	−	0.0887570i	0.0208707	−	0.00398129i
$498$	2.97084	+	11.5707i	0.133127	+	0.518494i
$499$	24.7505			1.10798			0.553992	−	0.832522i	$-0.313104\pi$
$499$	24.7505			1.10798			0.553992	+	0.832522i	$0.313104\pi$
$500$	10.0097	+	4.98048i	0.447649	+	0.222734i
$501$	6.87815			0.307293
$502$	0.175756	+	0.684526i	0.00784439	+	0.0305519i
$503$	−3.38912	+	0.646509i	−0.151113	+	0.0288264i	−0.262383	−	0.964964i	$-0.584508\pi$
$503$	−3.38912	+	0.646509i	−0.151113	+	0.0288264i	0.111270	+	0.993790i	$0.464508\pi$
$504$	0.466815	−	0.256634i	0.0207936	−	0.0114314i
$505$	7.85668	−	17.3057i	0.349618	−	0.770094i
$506$	17.0549	+	36.2435i	0.758184	+	1.61122i
$507$	−6.71321	+	9.23994i	−0.298144	+	0.410360i
$508$	−10.1584	−	10.8176i	−0.450705	−	0.479952i
$509$	−31.2288	+	12.3644i	−1.38419	+	0.548041i	−0.937919	−	0.346855i	$-0.887249\pi$
$509$	−31.2288	+	12.3644i	−1.38419	+	0.548041i	−0.446274	+	0.894896i	$0.647249\pi$
$510$	−1.93595	−	13.8061i	−0.0857255	−	0.611343i
$511$	−2.83069	+	0.726797i	−0.125222	+	0.0321516i
$512$	0.770513	−	0.637424i	0.0340522	−	0.0281704i
$513$	12.9562	+	32.7236i	0.572029	+	1.44478i
$514$	21.4522	+	8.49351i	0.946214	+	0.374633i
$515$	8.69300	−	7.39368i	0.383059	−	0.325804i
$516$	2.68483	−	4.23062i	0.118193	−	0.186242i
$517$	−17.5017	+	31.8355i	−0.769725	+	1.40012i
$518$	1.77329	+	2.44072i	0.0779138	+	0.107239i
$519$	0.330176	−	1.73084i	0.0144931	−	0.0759756i
$520$	4.64259	+	1.12468i	0.203591	+	0.0493207i
$521$	4.63779	−	9.85581i	0.203185	−	0.431791i	−0.777100	−	0.629377i	$-0.783310\pi$
$521$	4.63779	−	9.85581i	0.203185	−	0.431791i	0.980286	+	0.197586i	$0.0633101\pi$
$522$	−2.17627	−	3.95861i	−0.0952526	−	0.173264i
$523$	20.1151	+	1.26553i	0.879572	+	0.0553380i	0.496151	−	0.868236i	$-0.334746\pi$
$523$	20.1151	+	1.26553i	0.879572	+	0.0553380i	0.383420	+	0.923574i	$0.374746\pi$
$524$	−8.49980	−	6.17547i	−0.371315	−	0.269776i
$525$	0.109734	−	3.08751i	0.00478920	−	0.134750i
$526$	−1.77835	+	1.29205i	−0.0775397	+	0.0563359i
$527$	30.1630	−	19.1420i	1.31392	−	0.833840i
$528$	0.763036	−	6.04006i	0.0332069	−	0.262860i
$529$	55.8958	+	7.06128i	2.43025	+	0.307012i
$530$	−25.3325	+	0.345878i	−1.10037	+	0.0150240i
$531$	10.0292	+	5.51362i	0.435232	+	0.239271i
$532$	−2.70793	−	0.879861i	−0.117404	−	0.0381468i
$533$	−9.11214	+	4.28785i	−0.394691	+	0.185727i
$534$	16.2072	+	4.16130i	0.701354	+	0.180077i
$535$	−19.7040	+	21.5653i	−0.851880	+	0.932347i
$536$	1.36907	−	1.65492i	0.0591348	−	0.0714817i
$537$	−19.1650	−	12.1625i	−0.827029	−	0.524848i
$538$	−28.4111	+	1.78747i	−1.22489	+	0.0770635i
$539$	−16.3652	−	25.7874i	−0.704899	−	1.11074i
$540$	−12.0497	−	3.73409i	−0.518536	−	0.160690i
$541$	0.252593	+	4.01485i	0.0108598	+	0.172612i	0.999718	+	0.0237507i	$0.00756080\pi$
$541$	0.252593	+	4.01485i	0.0108598	+	0.172612i	−0.988858	+	0.148861i	$0.952439\pi$
$542$	10.2030	+	1.94634i	0.438259	+	0.0836023i
$543$	−28.8830	+	9.38464i	−1.23949	+	0.402734i
$544$	3.35708	−	3.15251i	0.143934	−	0.135163i
$545$	27.8757	+	10.5989i	1.19406	+	0.454006i
$546$	−0.247342	−	1.29661i	−0.0105853	−	0.0554898i
$547$	−14.3441	+	15.2750i	−0.613311	+	0.653110i	−0.958389	−	0.285464i	$-0.907852\pi$
$547$	−14.3441	+	15.2750i	−0.613311	+	0.653110i	0.345078	+	0.938574i	$0.387852\pi$
$548$	0.105050	−	0.265326i	0.00448751	−	0.0113341i
$549$	−2.33619	−	7.19006i	−0.0997063	−	0.306864i
$550$	17.7097	+	13.8540i	0.755143	+	0.590736i
$551$	−7.46126	+	22.9634i	−0.317860	+	0.978274i
$552$	−9.29152	−	7.68661i	−0.395473	−	0.327164i
$553$	−1.46662	−	0.690139i	−0.0623670	−	0.0293477i
$554$	−7.88663	−	7.40604i	−0.335071	−	0.314653i
$555$	3.48086	−	19.7052i	0.147754	−	0.836440i
$556$	2.69534	−	0.340501i	0.114308	−	0.0144404i
$557$		−	42.6278i		−	1.80620i	−0.429433	−	0.903099i	$-0.641287\pi$
$557$		−	42.6278i		−	1.80620i	0.429433	−	0.903099i	$-0.358713\pi$
$558$	−1.13478	−	8.98275i	−0.0480393	−	0.380270i
$559$	5.03987	+	6.09216i	0.213164	+	0.257671i
$560$	0.854138	−	0.558554i	0.0360939	−	0.0236032i
$561$	1.76046	−	27.9817i	0.0743267	−	1.18139i
$562$	4.31605	−	16.8099i	0.182062	−	0.709083i
$563$	5.90235	−	22.9881i	0.248754	−	0.968835i	−0.714368	−	0.699770i	$-0.753286\pi$
$563$	5.90235	−	22.9881i	0.248754	−	0.968835i	0.963122	−	0.269064i	$-0.0867144\pi$
$564$	0.686738	−	10.9154i	0.0289169	−	0.459621i
$565$	1.34867	+	1.08505i	0.0567391	+	0.0456484i
$566$	4.14751	+	5.01347i	0.174333	+	0.210732i
$567$	0.236601	+	1.87289i	0.00993630	+	0.0786539i
$568$		−	1.03783i		−	0.0435462i
$569$	−14.8130	+	1.87132i	−0.620995	+	0.0784499i	−0.429535	−	0.903050i	$-0.641322\pi$
$569$	−14.8130	+	1.87132i	−0.620995	+	0.0784499i	−0.191460	+	0.981500i	$0.561322\pi$
$570$	8.27353	+	16.9766i	0.346540	+	0.711072i
$571$	30.1669	+	28.3286i	1.26244	+	1.18551i	0.973631	+	0.228128i	$0.0732605\pi$
$571$	30.1669	+	28.3286i	1.26244	+	1.18551i	0.288813	+	0.957386i	$0.406740\pi$
$572$	8.69248	+	4.09037i	0.363451	+	0.171027i
$573$	−8.04011	−	6.65136i	−0.335880	−	0.277864i
$574$	−0.664860	+	2.04623i	−0.0277507	+	0.0854079i
$575$	41.9652	−	14.9138i	1.75007	−	0.621950i
$576$	−0.360678	−	1.11005i	−0.0150282	−	0.0462521i
$577$	11.7646	−	29.7140i	0.489767	−	1.23701i	−0.449332	−	0.893365i	$-0.648338\pi$
$577$	11.7646	−	29.7140i	0.489767	−	1.23701i	0.939099	−	0.343646i	$-0.111662\pi$
$578$	2.88080	−	3.06774i	0.119825	−	0.127601i
$579$	0.603997	+	3.16627i	0.0251013	+	0.131585i
$580$	−4.73657	−	7.24313i	−0.196675	−	0.300755i
$581$	−2.93577	+	2.75687i	−0.121796	+	0.114374i
$582$	−5.72571	+	1.86040i	−0.237338	+	0.0771159i
$583$	−50.0484	−	9.54725i	−2.07279	−	0.395407i
$584$	0.402066	+	6.39065i	0.0166376	+	0.264447i
$585$	3.21529	−	4.55496i	0.132936	−	0.188325i
$586$	13.1851	+	20.7764i	0.544672	+	0.858266i
$587$	7.61262	−	0.478946i	0.314207	−	0.0197682i	0.0950956	−	0.995468i	$-0.469684\pi$
$587$	7.61262	−	0.478946i	0.314207	−	0.0197682i	0.219111	+	0.975700i	$0.429684\pi$
$588$	7.76335	+	4.92677i	0.320155	+	0.203177i
$589$	−30.8474	+	37.2881i	−1.27105	+	1.53643i
$590$	19.9649	+	9.06393i	0.821941	+	0.373156i
$591$	14.4473	+	3.70944i	0.594284	+	0.152586i
$592$	5.98100	−	2.81445i	0.245818	−	0.115673i
$593$	−11.2341	−	3.65017i	−0.461328	−	0.149895i	0.0691263	−	0.997608i	$-0.477979\pi$
$593$	−11.2341	−	3.65017i	−0.461328	−	0.149895i	−0.530455	+	0.847713i	$0.677979\pi$
$594$	−22.2319	−	12.2221i	−0.912187	−	0.501479i
$595$	3.76424	−	2.81420i	0.154319	−	0.115371i
$596$	16.2865	+	2.05747i	0.667123	+	0.0842772i
$597$	0.870484	−	6.89059i	0.0356265	−	0.282013i
$598$	16.0663	−	10.1960i	0.657001	−	0.416945i
$599$	−5.39896	+	3.92258i	−0.220596	+	0.160272i	−0.692595	−	0.721327i	$-0.743533\pi$
$599$	−5.39896	+	3.92258i	−0.220596	+	0.160272i	0.471999	+	0.881599i	$0.343533\pi$
$600$	−6.59994	−	1.50377i	−0.269442	−	0.0613913i
$601$	11.4563	+	8.32346i	0.467310	+	0.339521i	0.796392	−	0.604781i	$-0.206739\pi$
$601$	11.4563	+	8.32346i	0.467310	+	0.339521i	−0.329082	+	0.944301i	$0.606739\pi$
$602$	1.68588	+	0.106066i	0.0687113	+	0.00432295i
$603$	−1.20770	−	2.19680i	−0.0491813	−	0.0894605i
$604$	−2.07426	+	4.40804i	−0.0844006	+	0.179360i
$605$	13.3609	+	15.7089i	0.543199	+	0.638658i
$606$	−2.15618	+	11.3031i	−0.0875887	+	0.459156i
$607$	16.4781	+	22.6802i	0.668827	+	0.920561i	0.999733	−	0.0231023i	$-0.00735436\pi$
$607$	16.4781	+	22.6802i	0.668827	+	0.920561i	−0.330906	+	0.943664i	$0.607354\pi$
$608$	−3.00542	+	5.46683i	−0.121886	+	0.221709i
$609$	−1.28141	+	2.01917i	−0.0519252	+	0.0818210i
$610$	−5.51510	−	13.3924i	−0.223300	−	0.542243i
$611$	16.0463	+	6.35317i	0.649163	+	0.257022i
$612$	−1.97872	−	4.99768i	−0.0799851	−	0.202019i
$613$	19.3077	−	15.9727i	0.779830	−	0.645132i	−0.159867	−	0.987139i	$-0.551107\pi$
$613$	19.3077	−	15.9727i	0.779830	−	0.645132i	0.939698	+	0.342007i	$0.111107\pi$
$614$	10.6103	−	2.72425i	0.428195	−	0.109942i
$615$	12.8282	−	6.25182i	0.517284	−	0.252098i
$616$	1.90831	−	0.755554i	0.0768881	−	0.0304421i
$617$	−0.281551	−	0.299821i	−0.0113348	−	0.0120704i	0.723276	−	0.690559i	$-0.242635\pi$
$617$	−0.281551	−	0.299821i	−0.0113348	−	0.0120704i	−0.734611	+	0.678488i	$0.762635\pi$
$618$	−4.06123	+	5.58980i	−0.163367	+	0.224855i
$619$	11.0542	+	23.4915i	0.444308	+	0.944202i	0.994056	+	0.108871i	$0.0347237\pi$
$619$	11.0542	+	23.4915i	0.444308	+	0.944202i	−0.549748	+	0.835330i	$0.685276\pi$
$620$	−3.48260	−	16.9926i	−0.139865	−	0.682441i
$621$	−44.0357	+	24.2088i	−1.76709	+	0.971466i
$622$	11.4911	−	2.19204i	0.460751	−	0.0878929i
$623$	1.40288	+	5.46386i	0.0562053	+	0.218905i
$624$	−2.89214			−0.115778
$625$	17.2629	−	18.0829i	0.690517	−	0.723316i
$626$	−21.4334			−0.856652
$627$	9.44532	+	36.7871i	0.377210	+	1.46914i
$628$	10.6756	−	2.03649i	0.426005	−	0.0812647i
$629$	26.6758	−	14.6652i	1.06363	−	0.584738i
$630$	−0.239156	−	1.16692i	−0.00952822	−	0.0464910i
$631$	−13.6889	−	29.0905i	−0.544948	−	1.15807i	−0.967764	−	0.251858i	$-0.918958\pi$
$631$	−13.6889	−	29.0905i	−0.544948	−	1.15807i	0.422816	−	0.906216i	$-0.361042\pi$
$632$	−2.08746	+	2.87314i	−0.0830347	+	0.114288i
$633$	8.09466	+	8.61993i	0.321734	+	0.342612i
$634$	−2.16634	+	0.857715i	−0.0860363	+	0.0340642i
$635$	−29.8285	+	14.5369i	−1.18371	+	0.576879i
$636$	14.8570	−	3.81462i	0.589117	−	0.151260i
$637$	−11.1794	+	9.24838i	−0.442943	+	0.366434i
$638$	−6.40713	−	16.1826i	−0.253661	−	0.640674i
$639$	−1.12626	−	0.445919i	−0.0445542	−	0.0176403i
$640$	−0.851458	−	2.06761i	−0.0336569	−	0.0817295i
$641$	−5.21361	+	8.21534i	−0.205925	+	0.324487i	−0.931556	−	0.363598i	$-0.881548\pi$
$641$	−5.21361	+	8.21534i	−0.205925	+	0.324487i	0.725631	+	0.688085i	$0.241548\pi$
$642$	8.52028	−	15.4983i	0.336268	−	0.611670i
$643$	−3.41473	−	4.69997i	−0.134664	−	0.185349i	0.736360	−	0.676590i	$-0.236543\pi$
$643$	−3.41473	−	4.69997i	−0.134664	−	0.185349i	−0.871023	+	0.491242i	$0.836543\pi$
$644$	0.761771	−	3.99334i	0.0300180	−	0.157360i
$645$	−7.25896	−	8.53461i	−0.285821	−	0.336050i
$646$	−12.2326	+	25.9955i	−0.481284	+	1.02278i
$647$	−3.39487	−	6.17525i	−0.133466	−	0.242774i	0.801125	−	0.598496i	$-0.204235\pi$
$647$	−3.39487	−	6.17525i	−0.133466	−	0.242774i	−0.934592	+	0.355722i	$0.884235\pi$
$648$	4.12800	+	0.259712i	0.162163	+	0.0102025i
$649$	35.6740	+	25.9187i	1.40033	+	1.01740i
$650$	5.47503	−	9.17152i	0.214748	−	0.359737i
$651$	−3.87776	+	2.81735i	−0.151981	+	0.110421i
$652$	−10.2196	+	6.48555i	−0.400230	+	0.253994i
$653$	0.440901	−	3.49009i	0.0172538	−	0.136578i	−0.981135	−	0.193325i	$-0.938073\pi$
$653$	0.440901	−	3.49009i	0.0172538	−	0.136578i	0.998389	+	0.0567470i	$0.0180728\pi$
$654$	−17.9136	−	2.26302i	−0.700478	−	0.0884909i
$655$	−18.8158	+	14.0670i	−0.735196	+	0.549641i
$656$	4.13097	+	2.27102i	0.161287	+	0.0886684i
$657$	7.10798	+	2.30952i	0.277309	+	0.0901030i
$658$	3.33622	−	1.56991i	0.130059	−	0.0612013i
$659$	48.7077	+	12.5060i	1.89738	+	0.487165i	0.998833	+	0.0482917i	$0.0153777\pi$
$659$	48.7077	+	12.5060i	1.89738	+	0.487165i	0.898549	+	0.438873i	$0.144622\pi$
$660$	−12.3957	−	5.62756i	−0.482501	−	0.219053i
$661$	−3.32478	+	4.01897i	−0.129319	+	0.156320i	−0.831198	−	0.555976i	$-0.812345\pi$
$661$	−3.32478	+	4.01897i	−0.129319	+	0.156320i	0.701879	+	0.712296i	$0.252345\pi$
$662$	24.3729	+	15.4675i	0.947279	+	0.601162i
$663$	−13.2927	+	0.836309i	−0.516247	+	0.0324795i
$664$	4.72809	+	7.45028i	0.183485	+	0.289127i
$665$	−3.67160	+	5.20141i	−0.142379	+	0.201702i
$666$	−0.484439	−	7.69994i	−0.0187716	−	0.298367i
$667$	−33.8637	−	6.45985i	−1.31121	−	0.250127i
$668$	4.83190	−	1.56998i	0.186952	−	0.0607443i
$669$	19.9191	−	18.7052i	0.770115	−	0.723186i
$670$	−2.62851	−	4.01951i	−0.101548	−	0.155287i
$671$	−5.45801	−	28.6119i	−0.210704	−	1.10455i
$672$	−0.422976	+	0.450424i	−0.0163166	+	0.0173755i
$673$	−4.11165	+	10.3848i	−0.158493	+	0.400306i	−0.987224	−	0.159340i	$-0.949063\pi$
$673$	−4.11165	+	10.3848i	−0.158493	+	0.400306i	0.828731	+	0.559647i	$0.189063\pi$
$674$	−8.87025	−	27.2998i	−0.341669	−	1.05155i
$675$	−15.9510	+	23.2649i	−0.613955	+	0.895467i
$676$	−2.60696	+	8.02339i	−0.100268	+	0.308592i
$677$	−10.9201	−	9.03389i	−0.419693	−	0.347200i	0.403482	−	0.914987i	$-0.367800\pi$
$677$	−10.9201	−	9.03389i	−0.419693	−	0.347200i	−0.823176	+	0.567787i	$0.807800\pi$
$678$	−0.948265	−	0.446220i	−0.0364179	−	0.0171370i
$679$	−1.47953	−	1.38937i	−0.0567792	−	0.0533192i
$680$	−4.51132	−	9.25687i	−0.173001	−	0.354985i
$681$	−25.8727	+	3.26848i	−0.991444	+	0.125249i
$682$		−	34.8842i		−	1.33579i
$683$	5.58288	+	44.1931i	0.213623	+	1.69100i	0.625869	+	0.779929i	$0.284745\pi$
$683$	5.58288	+	44.1931i	0.213623	+	1.69100i	−0.412245	+	0.911073i	$0.635255\pi$
$684$	4.64136	+	5.61044i	0.177467	+	0.214520i
$685$	−0.497168	−	0.399987i	−0.0189958	−	0.0152827i
$686$	−0.395243	+	6.28220i	−0.0150904	+	0.239856i
$687$	3.98022	−	15.5019i	0.151855	−	0.591436i
$688$	0.920429	−	3.58483i	0.0350910	−	0.136671i
$689$	−1.51980	+	24.1565i	−0.0578998	+	0.920290i
$690$	−22.5675	+	14.7577i	−0.859129	+	0.561818i
$691$	24.3555	+	29.4407i	0.926527	+	1.11998i	0.992511	+	0.122158i	$0.0389813\pi$
$691$	24.3555	+	29.4407i	0.926527	+	1.11998i	−0.0659841	+	0.997821i	$0.521019\pi$
$692$	−0.163127	−	1.29128i	−0.00620115	−	0.0490872i
$693$		−	2.39556i		−	0.0909999i
$694$	−33.1546	+	4.18840i	−1.25853	+	0.158990i
$695$	1.05674	−	5.98225i	0.0400846	−	0.226920i
$696$	3.81961	+	3.58685i	0.144782	+	0.135959i
$697$	19.6433	+	9.24344i	0.744043	+	0.350120i
$698$	−22.4496	−	18.5719i	−0.849731	−	0.702958i
$699$	−9.75864	+	30.0340i	−0.369106	+	1.13599i
$700$	−0.627654	−	2.19402i	−0.0237231	−	0.0829262i
$701$	12.2872	+	37.8162i	0.464083	+	1.42830i	0.860133	+	0.510070i	$0.170381\pi$
$701$	12.2872	+	37.8162i	0.464083	+	1.42830i	−0.396050	+	0.918229i	$0.629619\pi$
$702$	−4.43666	+	11.2057i	−0.167451	+	0.422933i
$703$	−28.2287	+	30.0605i	−1.06467	+	1.13376i
$704$	−0.842646	−	4.41730i	−0.0317584	−	0.166483i
$705$	−22.8592	−	8.69152i	−0.860929	−	0.327341i
$706$	−8.65439	+	8.12701i	−0.325712	+	0.305864i
$707$	−3.68940	+	1.19876i	−0.138754	+	0.0450840i
$708$	−13.0399	−	2.48749i	−0.490069	−	0.0934857i
$709$	−0.238929	−	3.79767i	−0.00897318	−	0.142625i	−0.999962	−	0.00868228i	$-0.997236\pi$
$709$	−0.238929	−	3.79767i	−0.00897318	−	0.142625i	0.990989	−	0.133942i	$-0.0427637\pi$
$710$	−2.21665	−	0.686921i	−0.0831894	−	0.0257797i
$711$	2.22106	+	3.49984i	0.0832964	+	0.131254i
$712$	12.3354	−	0.776077i	0.462289	−	0.0290847i
$713$	−58.3402	−	37.0238i	−2.18486	−	1.38655i
$714$	−1.81382	+	2.19253i	−0.0678805	+	0.0820534i
$715$	14.4899	−	15.8586i	0.541891	−	0.593077i
$716$	−16.2395	−	4.16960i	−0.606900	−	0.155825i
$717$	21.9637	−	10.3353i	0.820250	−	0.385981i
$718$	−0.443095	−	0.143970i	−0.0165361	−	0.00537292i
$719$	15.3183	+	8.42130i	0.571276	+	0.314062i	0.741081	−	0.671416i	$-0.234314\pi$
$719$	15.3183	+	8.42130i	0.571276	+	0.314062i	−0.169805	+	0.985478i	$0.554314\pi$
$720$	−2.60964	+	0.0356309i	−0.0972557	+	0.00132788i
$721$	−2.31096	−	0.291942i	−0.0860646	−	0.0108725i
$722$	2.49649	−	19.7617i	0.0929096	−	0.735456i
$723$	−24.3489	+	15.4523i	−0.905547	+	0.574677i
$724$	−18.1482	+	13.1854i	−0.674471	+	0.490032i
$725$	−18.6054	+	5.32253i	−0.690987	+	0.197674i
$726$	−10.1012	−	7.33895i	−0.374890	−	0.272374i
$727$	−18.2456	−	1.14792i	−0.676692	−	0.0425739i	−0.279274	−	0.960211i	$-0.590094\pi$
$727$	−18.2456	−	1.14792i	−0.676692	−	0.0425739i	−0.397418	+	0.917638i	$0.630094\pi$
$728$	−0.469717	−	0.854412i	−0.0174089	−	0.0316666i
$729$	11.8114	−	25.1006i	0.437460	−	0.929650i
$730$	13.9157	+	3.37112i	0.515042	+	0.124771i
$731$	3.19383	−	16.7426i	0.118128	−	0.619249i
$732$	5.15429	+	7.09427i	0.190508	+	0.262212i
$733$	−1.88299	+	3.42515i	−0.0695498	+	0.126511i	−0.908796	−	0.417242i	$-0.862997\pi$
$733$	−1.88299	+	3.42515i	−0.0695498	+	0.126511i	0.839246	+	0.543752i	$0.182997\pi$
$734$	6.25603	−	9.85793i	0.230914	−	0.363863i
$735$	15.6614	−	13.3205i	0.577678	−	0.491334i
$736$	−8.28180	−	3.27900i	−0.305271	−	0.120865i
$737$	−3.55558	−	8.98037i	−0.130971	−	0.330796i
$738$	4.23948	−	3.50720i	0.156057	−	0.129102i
$739$	6.93978	−	1.78183i	0.255284	−	0.0655458i	−0.118879	−	0.992909i	$-0.537930\pi$
$739$	6.93978	−	1.78183i	0.255284	−	0.0655458i	0.374163	+	0.927363i	$0.377930\pi$
$740$	−2.05253	−	14.6374i	−0.0754526	−	0.538083i
$741$	16.7756	−	6.64192i	0.616266	−	0.243997i
$742$	3.53988	+	3.76959i	0.129953	+	0.138386i
$743$	15.2184	−	20.9463i	0.558307	−	0.768444i	−0.432803	−	0.901489i	$-0.642475\pi$
$743$	15.2184	−	20.9463i	0.558307	−	0.768444i	0.991110	+	0.133045i	$0.0424754\pi$
$744$	4.47152	+	9.50247i	0.163934	+	0.348377i
$745$	15.1743	−	33.4240i	0.555943	−	1.22456i
$746$	2.80236	−	1.54061i	0.102602	−	0.0564057i
$747$	10.1166	−	1.92985i	0.370149	−	0.0706096i
$748$	−5.15027	−	20.0590i	−0.188313	−	0.733429i
$749$	5.96239			0.217861
$750$	−7.58026	+	13.1012i	−0.276792	+	0.478390i
$751$	23.2806			0.849520			0.424760	−	0.905306i	$-0.360359\pi$
$751$	23.2806			0.849520			0.424760	+	0.905306i	$0.360359\pi$
$752$	−2.00907	−	7.82481i	−0.0732632	−	0.285342i
$753$	−0.939835	+	0.179283i	−0.0342495	+	0.00653344i
$754$	−7.24545	+	3.98322i	−0.263864	+	0.145060i
$755$	8.04204	+	7.34796i	0.292680	+	0.267420i
$756$	1.09632	+	2.32981i	0.0398729	+	0.0847342i
$757$	−1.49246	+	2.05419i	−0.0542444	+	0.0746610i	−0.835277	−	0.549829i	$-0.814693\pi$
$757$	−1.49246	+	2.05419i	−0.0542444	+	0.0746610i	0.781033	+	0.624490i	$0.214693\pi$
$758$	−11.6646	−	12.4216i	−0.423678	−	0.451171i
$759$	−50.4201	+	19.9627i	−1.83013	+	0.724602i
$760$	9.68716	+	10.0376i	0.351390	+	0.364101i
$761$	−20.9454	+	5.37787i	−0.759271	+	0.194948i	−0.608427	−	0.793610i	$-0.708199\pi$
$761$	−20.9454	+	5.37787i	−0.759271	+	0.194948i	−0.150844	+	0.988558i	$0.548199\pi$
$762$	15.4796	−	12.8059i	0.560768	−	0.463908i
$763$	−2.24082	−	5.65968i	−0.0811233	−	0.204894i
$764$	−7.16638	−	2.83737i	−0.259271	−	0.102653i
$765$	−11.9840	+	0.918386i	−0.433284	+	0.0332043i
$766$	−0.0903291	+	0.142336i	−0.00326372	+	0.00514280i
$767$	10.0916	−	18.3565i	0.364386	−	0.662816i
$768$	0.795754	+	1.09526i	0.0287143	+	0.0395219i
$769$	−3.36279	+	17.6284i	−0.121265	+	0.635696i	0.868809	+	0.495148i	$0.164886\pi$
$769$	−3.36279	+	17.6284i	−0.121265	+	0.635696i	−0.990074	+	0.140547i	$0.955114\pi$
$770$	−0.350676	−	4.57598i	−0.0126375	−	0.164907i
$771$	−13.2996	+	28.2630i	−0.478972	+	1.01787i
$772$	1.14703	+	2.08643i	0.0412824	+	0.0750924i
$773$	−21.2963	−	1.33985i	−0.765975	−	0.0481910i	−0.325004	−	0.945713i	$-0.605366\pi$
$773$	−21.2963	−	1.33985i	−0.765975	−	0.0481910i	−0.440970	+	0.897522i	$0.645366\pi$
$774$	−3.49483	−	2.53915i	−0.125619	−	0.0912677i
$775$	−38.5990	−	3.80883i	−1.38652	−	0.136817i
$776$	−3.59766	+	2.61386i	−0.129149	+	0.0938320i
$777$	−3.44851	+	2.18849i	−0.123715	+	0.0785117i
$778$	−4.86956	+	38.5465i	−0.174582	+	1.38196i
$779$	−29.1768	−	3.68588i	−1.04537	−	0.132060i
$780$	−1.91427	+	6.17721i	−0.0685417	+	0.221180i
$781$	−4.08977	−	2.24837i	−0.146344	−	0.0804530i
$782$	−39.0127	−	12.6760i	−1.39509	−	0.453292i
$783$	19.7569	−	9.29687i	0.706052	−	0.332243i
$784$	6.57832	+	1.68903i	0.234940	+	0.0603223i
$785$	2.71639	−	24.1496i	0.0969523	−	0.861937i
$786$	9.06650	−	10.9595i	0.323391	−	0.390913i
$787$	−18.4060	−	11.6808i	−0.656103	−	0.416375i	0.165678	−	0.986180i	$-0.447019\pi$
$787$	−18.4060	−	11.6808i	−0.656103	−	0.416375i	−0.821780	+	0.569805i	$0.807019\pi$
$788$	10.9959	−	0.691806i	0.391714	−	0.0246446i
$789$	−1.59457	−	2.51264i	−0.0567682	−	0.0894524i
$790$	4.75498	+	6.36022i	0.169175	+	0.226287i
$791$	−0.0221845	−	0.352613i	−0.000788791	−	0.0125375i
$792$	−5.15578	−	0.983517i	−0.183203	−	0.0349478i
$793$	−13.1600	+	4.27593i	−0.467324	+	0.151843i
$794$	17.0834	−	16.0423i	0.606266	−	0.569321i
$795$	1.68610	−	34.2573i	0.0598000	−	1.21498i
$796$	−0.961304	−	5.03933i	−0.0340725	−	0.178614i
$797$	−37.1117	+	39.5200i	−1.31456	+	1.39987i	−0.453599	+	0.891206i	$0.649860\pi$
$797$	−37.1117	+	39.5200i	−1.31456	+	1.39987i	−0.860966	+	0.508663i	$0.830140\pi$
$798$	1.41901	−	3.58402i	0.0502326	−	0.126873i
$799$	−11.4967	−	35.3832i	−0.406723	−	1.25177i
$800$	−4.97970	+	0.450076i	−0.176059	+	0.0159126i
$801$	4.45790	−	13.7200i	0.157512	−	0.484772i
$802$	−14.4244	−	11.9329i	−0.509342	−	0.421365i
$803$	26.0548	+	12.2604i	0.919453	+	0.432662i
$804$	2.11966	+	1.99049i	0.0747546	+	0.0701992i
$805$	−8.02503	−	4.27018i	−0.282845	−	0.150504i
$806$	−16.4411	+	2.07700i	−0.579114	+	0.0731591i
$807$		−	38.5395i		−	1.35665i
$808$	1.06528	+	8.43256i	0.0374764	+	0.296657i
$809$	28.2744	+	34.1779i	0.994074	+	1.20163i	0.979440	+	0.201737i	$0.0646585\pi$
$809$	28.2744	+	34.1779i	0.994074	+	1.20163i	0.0146346	+	0.999893i	$0.495341\pi$
$810$	3.28697	−	8.64495i	0.115493	−	0.303753i
$811$	1.17998	−	18.7552i	0.0414347	−	0.658585i	−0.921421	−	0.388567i	$-0.872970\pi$
$811$	1.17998	−	18.7552i	0.0414347	−	0.658585i	0.962855	−	0.270018i	$-0.0870297\pi$
$812$	−0.439299	+	1.71096i	−0.0154164	+	0.0600428i
$813$	−3.49711	+	13.6204i	−0.122649	+	0.477687i
$814$	1.86647	−	29.6667i	0.0654198	−	1.03982i
$815$	7.08804	+	26.1203i	0.248283	+	0.914955i
$816$	3.97413	+	4.80390i	0.139122	+	0.168170i
$817$	2.89386	+	22.9073i	0.101243	+	0.801425i
$818$			14.6672i			0.512826i
$819$	−1.12904	+	0.142631i	−0.0394519	+	0.00498393i
$820$	7.58481	−	7.32002i	0.264873	−	0.255626i
$821$	20.5581	+	19.3054i	0.717483	+	0.673761i	0.954658	−	0.297706i	$-0.0962214\pi$
$821$	20.5581	+	19.3054i	0.717483	+	0.673761i	−0.237175	+	0.971467i	$0.576221\pi$
$822$	0.349564	+	0.164492i	0.0121924	+	0.00573732i
$823$	15.3799	+	12.7233i	0.536109	+	0.443508i	0.865662	−	0.500629i	$-0.166898\pi$
$823$	15.3799	+	12.7233i	0.536109	+	0.443508i	−0.329553	+	0.944137i	$0.606898\pi$
$824$	−1.57711	+	4.85383i	−0.0549411	+	0.169091i
$825$	−20.2242	+	22.7507i	−0.704117	+	0.792077i
$826$	−1.38296	−	4.25631i	−0.0481193	−	0.148096i
$827$	−8.63139	+	21.8004i	−0.300143	+	0.758074i	0.698937	+	0.715183i	$0.253657\pi$
$827$	−8.63139	+	21.8004i	−0.300143	+	0.758074i	−0.999080	+	0.0428909i	$0.986343\pi$
$828$	−7.11683	+	7.57865i	−0.247327	+	0.263376i
$829$	−6.60751	−	34.6378i	−0.229488	−	1.20302i	−0.891322	−	0.453370i	$-0.850222\pi$
$829$	−6.60751	−	34.6378i	−0.229488	−	1.20302i	0.661834	−	0.749650i	$-0.269778\pi$
$830$	19.0422	−	5.16732i	0.660965	−	0.179360i
$831$	10.6771	−	10.0264i	0.370383	−	0.347813i
$832$	−2.03173	+	0.660148i	−0.0704375	+	0.0228865i
$833$	30.7234	+	5.86081i	1.06450	+	0.203065i
$834$	0.230944	+	3.67074i	0.00799692	+	0.127107i
$835$	−0.155096	−	11.3594i	−0.00536733	−	0.393109i
$836$	15.0322	+	23.6870i	0.519900	+	0.819231i
$837$	43.6772	−	2.74794i	1.50971	−	0.0949826i
$838$	31.2586	+	19.8373i	1.07981	+	0.685269i
$839$	18.1627	−	21.9550i	0.627047	−	0.757969i	−0.357343	−	0.933973i	$-0.616317\pi$
$839$	18.1627	−	21.9550i	0.627047	−	0.757969i	0.984389	+	0.176004i	$0.0563172\pi$
$840$	0.682081	+	1.20155i	0.0235340	+	0.0414573i
$841$	−13.5799	−	3.48673i	−0.468273	−	0.120232i
$842$	−26.1718	+	12.3155i	−0.901939	+	0.424420i
$843$	22.3458	+	7.26058i	0.769629	+	0.250068i
$844$	7.65404	+	4.20785i	0.263463	+	0.144840i
$845$	15.4113	+	10.8787i	0.530166	+	0.374237i
$846$	−9.35482	−	1.18179i	−0.321625	−	0.0406307i
$847$	0.527561	−	4.17608i	0.0181272	−	0.143492i
$848$	9.56631	−	6.07096i	0.328508	−	0.208478i
$849$	−7.12650	+	5.17771i	−0.244581	+	0.177698i
$850$	−22.7574	+	3.50858i	−0.780571	+	0.120343i
$851$	−47.6335	−	34.6077i	−1.63285	−	1.18634i
$852$	1.40225	+	0.0882223i	0.0480404	+	0.00302245i
$853$	−17.3116	−	31.4897i	−0.592739	−	1.07819i	−0.987232	−	0.159289i	$-0.949080\pi$
$853$	−17.3116	−	31.4897i	−0.592739	−	1.07819i	0.394493	−	0.918899i	$-0.370920\pi$
$854$	−1.25871	+	2.67490i	−0.0430722	+	0.0915331i
$855$	15.0552	−	6.19983i	0.514876	−	0.212030i
$856$	2.44791	−	12.8324i	0.0836677	−	0.438601i
$857$	22.8844	+	31.4977i	0.781717	+	1.07594i	0.995090	+	0.0989708i	$0.0315551\pi$
$857$	22.8844	+	31.4977i	0.781717	+	1.07594i	−0.213373	+	0.976971i	$0.568445\pi$
$858$	−6.26561	+	11.3971i	−0.213904	+	0.389090i
$859$	12.8589	−	20.2623i	0.438739	−	0.691342i	−0.550956	−	0.834535i	$-0.685737\pi$
$859$	12.8589	−	20.2623i	0.438739	−	0.691342i	0.989695	+	0.143192i	$0.0457367\pi$
$860$	−7.04749	−	4.33866i	−0.240318	−	0.147947i
$861$	−2.70824	−	1.07227i	−0.0922964	−	0.0365427i
$862$	10.0021	+	25.2625i	0.340674	+	0.860445i
$863$	12.5228	−	10.3598i	0.426282	−	0.352651i	−0.399410	−	0.916772i	$-0.630785\pi$
$863$	12.5228	−	10.3598i	0.426282	−	0.352651i	0.825692	+	0.564121i	$0.190785\pi$
$864$	5.46436	−	1.40301i	0.185901	−	0.0477313i
$865$	−2.86597	−	0.506264i	−0.0974460	−	0.0172135i
$866$	23.1123	−	9.15080i	0.785387	−	0.310957i
$867$	3.90008	+	4.15316i	0.132454	+	0.141049i
$868$	−2.08104	+	2.86431i	−0.0706352	+	0.0972210i
$869$	6.79991	+	14.4505i	0.230671	+	0.490201i
$870$	10.1892	−	5.78408i	0.345445	−	0.196099i
$871$	−4.02080	+	2.21045i	−0.136239	+	0.0748983i
$872$	−13.1009	+	2.49912i	−0.443651	+	0.0846309i
$873$	1.29080	+	5.02732i	0.0436869	+	0.170149i
$874$	55.5682			1.87962
$875$	−5.10156	−	0.111608i	−0.172464	−	0.00377305i
$876$	−8.66888			−0.292894
$877$	2.05016	+	7.98484i	0.0692289	+	0.269629i	0.993770	−	0.111455i	$-0.0355510\pi$
$877$	2.05016	+	7.98484i	0.0692289	+	0.269629i	−0.924541	+	0.381084i	$0.875551\pi$
$878$	−14.7268	+	2.80929i	−0.497006	+	0.0948089i
$879$	−29.1928	+	16.0489i	−0.984649	+	0.541315i
$880$	−9.99249	−	1.12397i	−0.336847	−	0.0378891i
$881$	−2.19288	−	4.66010i	−0.0738799	−	0.157003i	0.864475	−	0.502675i	$-0.167651\pi$
$881$	−2.19288	−	4.66010i	−0.0738799	−	0.157003i	−0.938355	+	0.345672i	$0.887651\pi$
$882$	4.65944	−	6.41317i	0.156891	−	0.215943i
$883$	−4.20389	−	4.47669i	−0.141472	−	0.150653i	0.654330	−	0.756209i	$-0.272951\pi$
$883$	−4.20389	−	4.47669i	−0.141472	−	0.150653i	−0.795802	+	0.605556i	$0.792951\pi$
$884$	−9.14726	+	3.62166i	−0.307656	+	0.121809i
$885$	−13.9439	+	26.2050i	−0.468717	+	0.880871i
$886$	−22.6533	+	5.81637i	−0.761052	+	0.195405i
$887$	25.2745	−	20.9089i	0.848634	−	0.702051i	−0.107745	−	0.994179i	$-0.534363\pi$
$887$	25.2745	−	20.9089i	0.848634	−	0.702051i	0.956379	+	0.292127i	$0.0943631\pi$
$888$	3.29430	+	8.32046i	0.110550	+	0.279216i
$889$	6.29725	+	2.49326i	0.211203	+	0.0836212i
$890$	6.50702	−	26.8604i	0.218116	−	0.900362i
$891$	9.96647	−	15.7046i	0.333889	−	0.526125i
$892$	9.72355	−	17.6871i	0.325568	−	0.592207i
$893$	29.6234	+	40.7732i	0.991310	+	1.36442i
$894$	−4.16441	+	21.8306i	−0.139279	+	0.730125i
$895$	−19.6544	+	31.9256i	−0.656974	+	1.06715i
$896$	−0.194329	+	0.412969i	−0.00649206	+	0.0137963i
$897$	12.4105	+	22.5747i	0.414376	+	0.753747i
$898$	22.6622	+	1.42579i	0.756248	+	0.0475791i
$899$	24.2895	+	17.6473i	0.810100	+	0.588572i
$900$	−1.65118	+	5.59742i	−0.0550394	+	0.186581i
$901$	42.2128	−	30.6694i	1.40631	−	1.02175i
$902$	17.8989	−	11.3590i	0.595967	−	0.378212i
$903$	−0.286623	+	2.26885i	−0.00953821	+	0.0755027i
$904$	−0.768008	−	0.0970220i	−0.0255436	−	0.00322690i
$905$	16.1502	+	47.4892i	0.536852	+	1.57860i
$906$	−5.77958	−	3.17735i	−0.192014	−	0.105560i
$907$	−16.4911	−	5.35827i	−0.547577	−	0.177918i	0.0221471	−	0.999755i	$-0.492950\pi$
$907$	−16.4911	−	5.35827i	−0.547577	−	0.177918i	−0.569724	+	0.821836i	$0.692950\pi$
$908$	−17.4295	+	8.20171i	−0.578419	+	0.272183i
$909$	9.60885	+	2.46713i	0.318705	+	0.0818296i
$910$	−2.13580	+	0.437728i	−0.0708012	+	0.0145105i
$911$	−7.28864	+	8.81046i	−0.241484	+	0.291903i	−0.877306	−	0.479932i	$-0.840661\pi$
$911$	−7.28864	+	8.81046i	−0.241484	+	0.291903i	0.635822	+	0.771836i	$0.280661\pi$
$912$	−7.13101	−	4.52548i	−0.236131	−	0.149854i
$913$	39.6025	−	2.49158i	1.31065	−	0.0824591i
$914$	12.1305	+	19.1147i	0.401243	+	0.632258i
$915$	18.5639	−	6.31325i	0.613704	−	0.208710i
$916$	−0.742306	−	11.7986i	−0.0245265	−	0.389837i
$917$	4.71022	+	0.898523i	0.155545	+	0.0296719i
$918$	24.7094	−	8.02856i	0.815531	−	0.264982i
$919$	−11.3809	+	10.6873i	−0.375420	+	0.352542i	−0.849173	−	0.528115i	$-0.822899\pi$
$919$	−11.3809	+	10.6873i	−0.375420	+	0.352542i	0.473753	+	0.880658i	$0.342899\pi$
$920$	−12.4851	+	15.5185i	−0.411621	+	0.511629i
$921$	2.77892	+	14.5676i	0.0915685	+	0.480019i
$922$	21.1533	−	22.5260i	0.696648	−	0.741854i
$923$	−0.816165	+	2.06140i	−0.0268644	+	0.0678517i
$924$	0.858645	+	2.64264i	0.0282473	+	0.0869364i
$925$	−32.6221	−	5.30438i	−1.07261	−	0.174407i
$926$	7.96298	−	24.5075i	0.261680	−	0.805368i
$927$	4.58982	+	3.79703i	0.150749	+	0.124711i
$928$	3.50200	+	1.64791i	0.114959	+	0.0540954i
$929$	26.7304	+	25.1015i	0.876996	+	0.823554i	0.985348	−	0.170559i	$-0.0545573\pi$
$929$	26.7304	+	25.1015i	0.876996	+	0.823554i	−0.108352	+	0.994113i	$0.534557\pi$
$930$	23.2556	−	3.26101i	0.762581	−	0.106933i
$931$	−42.0358	+	5.31036i	−1.37767	+	0.174040i
$932$			23.3263i			0.764080i
$933$	1.98495	+	15.7125i	0.0649843	+	0.514404i
$934$	1.51700	+	1.83374i	0.0496377	+	0.0600017i
$935$	−46.2521	−	2.27648i	−1.51261	−	0.0744487i
$936$	−0.156563	+	2.48850i	−0.00511743	+	0.0813392i
$937$	−2.58656	+	10.0740i	−0.0844993	+	0.329103i	−0.996753	−	0.0805233i	$-0.974341\pi$
$937$	−2.58656	+	10.0740i	−0.0844993	+	0.329103i	0.912253	+	0.409626i	$0.134341\pi$
$938$	−0.243785	+	0.949480i	−0.00795986	+	0.0310016i
$939$	1.82199	−	28.9597i	0.0594584	−	0.945063i
$940$	−18.0425	−	0.888031i	−0.588481	−	0.0289644i
$941$	−7.19487	−	8.69711i	−0.234546	−	0.283518i	0.640088	−	0.768302i	$-0.278898\pi$
$941$	−7.19487	−	8.69711i	−0.234546	−	0.283518i	−0.874634	+	0.484784i	$0.838898\pi$
$942$	1.84409	+	14.5975i	0.0600837	+	0.475611i
$943$		−	41.9896i		−	1.36737i
$944$	−9.72830	+	1.22897i	−0.316629	+	0.0399996i
$945$	5.70179	−	0.799532i	0.185479	−	0.0260088i
$946$	−12.1328	−	11.3934i	−0.394470	−	0.370432i
$947$	−36.6708	−	17.2560i	−1.19164	−	0.560744i	−0.275384	−	0.961334i	$-0.588805\pi$
$947$	−36.6708	−	17.2560i	−1.19164	−	0.560744i	−0.916257	+	0.400590i	$0.868805\pi$
$948$	−3.70459	−	3.06470i	−0.120319	−	0.0995369i
$949$	4.22712	−	13.0097i	0.137218	−	0.422314i
$950$	27.8507	−	14.0467i	0.903595	−	0.455736i
$951$	−0.974744	−	2.99995i	−0.0316082	−	0.0972802i
$952$	−0.773749	+	1.95427i	−0.0250773	+	0.0633381i
$953$	25.0182	−	26.6417i	0.810418	−	0.863008i	−0.182328	−	0.983238i	$-0.558363\pi$
$953$	25.0182	−	26.6417i	0.810418	−	0.863008i	0.992746	+	0.120230i	$0.0383632\pi$
$954$	−2.47797	−	12.9900i	−0.0802273	−	0.420566i
$955$	−10.8036	+	13.4284i	−0.349595	+	0.434533i
$956$	13.0704	−	12.2739i	0.422727	−	0.396967i
$957$	22.4097	−	7.28134i	0.724402	−	0.235372i
$958$	14.3370	+	2.73492i	0.463206	+	0.0883613i
$959$	0.00817799	+	0.129985i	0.000264081	+	0.00419745i
$960$	2.86603	−	0.974684i	0.0925006	−	0.0314578i
$961$	15.6331	+	24.6338i	0.504294	+	0.794640i
$962$	−14.0932	+	0.886669i	−0.454383	+	0.0285874i
$963$	−12.8741	−	8.17014i	−0.414862	−	0.263279i
$964$	−13.5780	+	16.4130i	−0.437319	+	0.528628i
$965$	5.21554	−	1.06891i	0.167894	−	0.0344095i
$966$	5.33084	+	1.36873i	0.171517	+	0.0440381i
$967$	23.9289	−	11.2601i	0.769503	−	0.362101i	−0.000616846	−	1.00000i	$-0.500196\pi$
$967$	23.9289	−	11.2601i	0.769503	−	0.362101i	0.770120	+	0.637899i	$0.220196\pi$
$968$	−8.77124	−	2.84995i	−0.281918	−	0.0916008i
$969$	−34.0839	−	18.7378i	−1.09493	−	0.601944i
$970$	3.20160	+	9.41419i	0.102797	+	0.302271i
$971$	−57.7041	−	7.28972i	−1.85181	−	0.233938i	−0.880888	−	0.473325i	$-0.843054\pi$
$971$	−57.7041	−	7.28972i	−1.85181	−	0.233938i	−0.970924	+	0.239387i	$0.923054\pi$
$972$	1.41942	−	11.2359i	0.0455280	−	0.360391i
$973$	−1.04692	+	0.664398i	−0.0335628	+	0.0212996i
$974$	−10.0427	+	7.29648i	−0.321790	+	0.233794i
$975$	11.9267	+	8.17721i	0.381959	+	0.261880i
$976$	5.24019	+	3.80722i	0.167734	+	0.121866i
$977$	−4.06179	−	0.255546i	−0.129948	−	0.00817565i	−0.00231684	−	0.999997i	$-0.500737\pi$
$977$	−4.06179	−	0.255546i	−0.129948	−	0.00817565i	−0.127631	+	0.991822i	$0.540737\pi$
$978$	−7.89419	−	14.3595i	−0.252428	−	0.459165i
$979$	23.6654	−	50.2916i	0.756350	−	1.60733i
$980$	7.96162	−	12.9324i	0.254325	−	0.413112i
$981$	−2.91692	+	15.2910i	−0.0931300	+	0.488205i
$982$	−2.18554	−	3.00814i	−0.0697434	−	0.0959935i
$983$	3.32146	−	6.04172i	0.105938	−	0.192701i	−0.818025	−	0.575183i	$-0.804931\pi$
$983$	3.32146	−	6.04172i	0.105938	−	0.192701i	0.923963	+	0.382482i	$0.124931\pi$
$984$	−3.41964	+	5.38849i	−0.109014	+	0.171779i
$985$	5.80045	−	23.9437i	0.184818	−	0.762911i
$986$	16.5723	+	6.56142i	0.527768	+	0.208958i
$987$	1.83757	+	4.64117i	0.0584905	+	0.147730i
$988$	10.2688	−	8.49507i	0.326693	−	0.270264i
$989$	−31.9312	+	8.19854i	−1.01535	+	0.260698i
$990$	−5.51319	+	10.3611i	−0.175221	+	0.329296i
$991$	31.0266	−	12.2843i	0.985591	−	0.390223i	0.180630	−	0.983551i	$-0.442186\pi$
$991$	31.0266	−	12.2843i	0.985591	−	0.390223i	0.804961	+	0.593328i	$0.202186\pi$
$992$	5.31024	+	5.65483i	0.168600	+	0.179541i
$993$	−22.9707	+	31.6165i	−0.728954	+	1.00332i
$994$	0.201679	+	0.428590i	0.00639687	+	0.0135940i
$995$	−11.3996	−	1.28225i	−0.361391	−	0.0406500i
$996$	−10.4683	+	5.75502i	−0.331702	+	0.182355i
$997$	28.7690	−	5.48799i	0.911124	−	0.173806i	0.289551	−	0.957162i	$-0.406494\pi$
$997$	28.7690	−	5.48799i	0.911124	−	0.173806i	0.621573	+	0.783356i	$0.286494\pi$
$998$	6.15519	+	23.9729i	0.194839	+	0.758849i
$999$	37.2916			1.17985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.229.8	yes	240
125.119	even	50	inner	250.2.h.a.119.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.119.8	✓	240	125.119	even	50	inner
250.2.h.a.229.8	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 + 0.968583i) q^{2} +(-1.32984 + 0.253680i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.448945 + 2.19054i) q^{5} +(-0.576428 - 1.22497i) q^{6} +(0.268269 - 0.369241i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-1.08521 + 0.429667i) q^{9} +O(q^{10})\)	\(q+(0.248690 + 0.968583i) q^{2} +(-1.32984 + 0.253680i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.448945 + 2.19054i) q^{5} +(-0.576428 - 1.22497i) q^{6} +(0.268269 - 0.369241i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(-1.08521 + 0.429667i) q^{9} +(-2.01007 + 0.979605i) q^{10} +(-4.35568 + 1.11835i) q^{11} +(1.04313 - 0.862956i) q^{12} +(0.786419 + 1.98627i) q^{13} +(0.424356 + 0.168015i) q^{14} +(-1.15272 - 2.79917i) q^{15} +(0.535827 - 0.844328i) q^{16} +(2.21860 - 4.03561i) q^{17} +(-0.686050 - 0.944266i) q^{18} +(-1.16898 + 6.12799i) q^{19} +(-1.44871 - 1.70330i) q^{20} +(-0.263085 + 0.559085i) q^{21} +(-2.16643 - 3.94071i) q^{22} +(-8.88973 - 0.559294i) q^{23} +(1.09526 + 0.795754i) q^{24} +(-4.59690 + 1.96686i) q^{25} +(-1.72829 + 1.25568i) q^{26} +(4.76336 - 3.02292i) q^{27} +(-0.0572029 + 0.452808i) q^{28} +(3.83983 + 0.485083i) q^{29} +(2.42456 - 1.81263i) q^{30} +(6.79777 + 3.73711i) q^{31} +(0.951057 + 0.309017i) q^{32} +(5.50864 - 2.59217i) q^{33} +(4.46057 + 1.14528i) q^{34} +(0.929273 + 0.421884i) q^{35} +(0.743987 - 0.899325i) q^{36} +(5.58110 + 3.54187i) q^{37} +(-6.22618 + 0.391718i) q^{38} +(-1.54969 - 2.44191i) q^{39} +(1.28951 - 1.82679i) q^{40} +(0.295999 + 4.70476i) q^{41} +(-0.606947 - 0.115781i) q^{42} +(3.51997 - 1.14371i) q^{43} +(3.27814 - 3.07838i) q^{44} +(-1.42840 - 2.18430i) q^{45} +(-1.66906 - 8.74953i) q^{46} +(5.53019 - 5.88906i) q^{47} +(-0.498374 + 1.25875i) q^{48} +(2.09875 + 6.45928i) q^{49} +(-3.04827 - 3.96334i) q^{50} +(-1.92662 + 5.92952i) q^{51} +(-1.64604 - 1.36172i) q^{52} +(10.2518 + 4.82412i) q^{53} +(4.11255 + 3.86194i) q^{54} +(-4.40524 - 9.03919i) q^{55} +(-0.452808 + 0.0572029i) q^{56} -8.44578i q^{57} +(0.485083 + 3.83983i) q^{58} +(-6.25034 - 7.55536i) q^{59} +(2.35865 + 1.89760i) q^{60} +(-0.406709 + 6.46445i) q^{61} +(-1.92916 + 7.51359i) q^{62} +(-0.132479 + 0.515972i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-3.99793 + 2.61440i) q^{65} +(3.88068 + 4.69093i) q^{66} +(0.269193 + 2.13088i) q^{67} +4.60525i q^{68} +(11.9638 - 1.51138i) q^{69} +(-0.177529 + 1.00500i) q^{70} +(0.756542 + 0.710440i) q^{71} +(1.05609 + 0.496960i) q^{72} +(-4.93382 - 4.08161i) q^{73} +(-2.04263 + 6.28658i) q^{74} +(5.61417 - 3.78175i) q^{75} +(-1.92780 - 5.93316i) q^{76} +(-0.755554 + 1.90831i) q^{77} +(1.97981 - 2.10828i) q^{78} +(-0.665466 - 3.48850i) q^{79} +(2.09009 + 0.794691i) q^{80} +(-3.01514 + 2.83140i) q^{81} +(-4.48334 + 1.45673i) q^{82} +(-8.66762 - 1.65344i) q^{83} +(-0.0387977 - 0.616672i) q^{84} +(9.83618 + 3.04815i) q^{85} +(1.98315 + 3.12495i) q^{86} +(-5.22941 + 0.329006i) q^{87} +(3.79691 + 2.40959i) q^{88} +(-7.87843 + 9.52338i) q^{89} +(1.76045 - 1.92674i) q^{90} +(0.944383 + 0.242476i) q^{91} +(8.05957 - 3.79255i) q^{92} +(-9.98797 - 3.24529i) q^{93} +(7.07934 + 3.89190i) q^{94} +(-13.9484 + 0.190445i) q^{95} +(-1.34314 - 0.169678i) q^{96} +(0.557352 - 4.41189i) q^{97} +(-5.73442 + 3.63917i) q^{98} +(4.24633 - 3.08514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 10 q^{5}+O(q^{10}) \) 240 * q + 10 * q^5	\( 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) \) 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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