LMFDB - Embedded newform 420.2.bh.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(101,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("420.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$-1.31611 - 1.12599i$ of defining polynomial
Character	$\chi$	$=$	420.101
Dual form			420.2.bh.b.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63319 + 0.576792i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.73439 - 1.99797i) q^{7} +(2.33462 - 1.88402i) q^{9} +O(q^{10})$	\(q+(-1.63319 + 0.576792i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.73439 - 1.99797i) q^{7} +(2.33462 - 1.88402i) q^{9} +(3.38064 + 1.95181i) q^{11} +6.06329i q^{13} +(-1.31611 - 1.12599i) q^{15} +(-1.53296 + 2.65516i) q^{17} +(-2.94930 + 1.70278i) q^{19} +(3.98500 + 2.26269i) q^{21} +(-2.48871 + 1.43686i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.72620 + 4.42356i) q^{27} +7.97997i q^{29} +(-5.63161 - 3.25141i) q^{31} +(-6.64702 - 1.23776i) q^{33} +(0.863098 - 2.50101i) q^{35} +(-0.0654987 - 0.113447i) q^{37} +(-3.49726 - 9.90252i) q^{39} +12.3654 q^{41} +4.43247 q^{43} +(2.79892 + 1.07983i) q^{45} +(5.02960 + 8.71153i) q^{47} +(-0.983778 + 6.93053i) q^{49} +(0.972138 - 5.22058i) q^{51} +(-4.64119 - 2.67959i) q^{53} +3.90363i q^{55} +(3.83462 - 4.48210i) q^{57} +(-1.28860 + 2.23193i) q^{59} +(7.44930 - 4.30086i) q^{61} +(-7.81337 - 1.39688i) q^{63} +(-5.25097 + 3.03165i) q^{65} +(7.99884 - 13.8544i) q^{67} +(3.23578 - 3.78214i) q^{69} +3.63245i q^{71} +(-6.72468 - 3.88250i) q^{73} +(0.317079 - 1.70278i) q^{75} +(-1.96368 - 10.1396i) q^{77} +(-1.22311 - 2.11848i) q^{79} +(1.90093 - 8.79696i) q^{81} -7.63648 q^{83} -3.06592 q^{85} +(-4.60278 - 13.0328i) q^{87} +(-4.11874 - 7.13387i) q^{89} +(12.1143 - 10.5161i) q^{91} +(11.0729 + 2.06191i) q^{93} +(-2.94930 - 1.70278i) q^{95} +5.74985i q^{97} +(11.5698 - 1.81245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−1.63319	+	0.576792i	−0.942923	+	0.333011i
$3$	−1.63319	+	0.576792i	−0.942923	+	0.333011i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.73439	−	1.99797i	−0.655538	−	0.755162i
$7$	−1.73439	−	1.99797i	−0.655538	−	0.755162i
$8$		0			0
$9$	2.33462	−	1.88402i	0.778208	−	0.628007i
$10$		0			0
$11$	3.38064	+	1.95181i	1.01930	+	0.588494i	0.913902	−	0.405936i	$-0.133054\pi$
$11$	3.38064	+	1.95181i	1.01930	+	0.588494i	0.105400	+	0.994430i	$0.466388\pi$
$12$		0			0
$13$			6.06329i			1.68166i	0.541303	+	0.840828i	$0.317931\pi$
$13$			6.06329i			1.68166i	−0.541303	+	0.840828i	$0.682069\pi$
$14$		0			0
$15$	−1.31611	−	1.12599i	−0.339819	−	0.290729i
$16$		0			0
$17$	−1.53296	+	2.65516i	−0.371797	+	0.643971i	−0.989842	−	0.142171i	$-0.954592\pi$
$17$	−1.53296	+	2.65516i	−0.371797	+	0.643971i	0.618045	+	0.786143i	$0.287925\pi$
$18$		0			0
$19$	−2.94930	+	1.70278i	−0.676616	+	0.390645i	−0.798579	−	0.601890i	$-0.794415\pi$
$19$	−2.94930	+	1.70278i	−0.676616	+	0.390645i	0.121963	+	0.992535i	$0.461081\pi$
$20$		0			0
$21$	3.98500	+	2.26269i	0.869599	+	0.493759i
$22$		0			0
$23$	−2.48871	+	1.43686i	−0.518933	+	0.299606i	−0.736498	−	0.676440i	$-0.763522\pi$
$23$	−2.48871	+	1.43686i	−0.518933	+	0.299606i	0.217565	+	0.976046i	$0.430189\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−2.72620	+	4.42356i	−0.524657	+	0.851314i
$28$		0			0
$29$			7.97997i			1.48184i	0.671591	+	0.740922i	$0.265611\pi$
$29$			7.97997i			1.48184i	−0.671591	+	0.740922i	$0.734389\pi$
$30$		0			0
$31$	−5.63161	−	3.25141i	−1.01147	−	0.583971i	−0.0998461	−	0.995003i	$-0.531835\pi$
$31$	−5.63161	−	3.25141i	−1.01147	−	0.583971i	−0.911621	+	0.411032i	$0.865168\pi$
$32$		0			0
$33$	−6.64702	−	1.23776i	−1.15710	−	0.215466i
$34$		0			0
$35$	0.863098	−	2.50101i	0.145890	−	0.422748i
$36$		0			0
$37$	−0.0654987	−	0.113447i	−0.0107679	−	0.0186506i	0.860591	−	0.509296i	$-0.170094\pi$
$37$	−0.0654987	−	0.113447i	−0.0107679	−	0.0186506i	−0.871359	+	0.490646i	$0.836761\pi$
$38$		0			0
$39$	−3.49726	−	9.90252i	−0.560009	−	1.58567i
$40$		0			0
$41$	12.3654			1.93116			0.965579	−	0.260108i	$-0.0837583\pi$
$41$	12.3654			1.93116			0.965579	+	0.260108i	$0.0837583\pi$
$42$		0			0
$43$	4.43247			0.675945			0.337972	−	0.941156i	$-0.390259\pi$
$43$	4.43247			0.675945			0.337972	+	0.941156i	$0.390259\pi$
$44$		0			0
$45$	2.79892	+	1.07983i	0.417239	+	0.160972i
$46$		0			0
$47$	5.02960	+	8.71153i	0.733643	+	1.27071i	0.955316	+	0.295586i	$0.0955148\pi$
$47$	5.02960	+	8.71153i	0.733643	+	1.27071i	−0.221674	+	0.975121i	$0.571152\pi$
$48$		0			0
$49$	−0.983778	+	6.93053i	−0.140540	+	0.990075i
$50$		0			0
$51$	0.972138	−	5.22058i	0.136127	−	0.731028i
$52$		0			0
$53$	−4.64119	−	2.67959i	−0.637516	−	0.368070i	0.146141	−	0.989264i	$-0.453315\pi$
$53$	−4.64119	−	2.67959i	−0.637516	−	0.368070i	−0.783657	+	0.621194i	$0.786648\pi$
$54$		0			0
$55$			3.90363i			0.526365i
$56$		0			0
$57$	3.83462	−	4.48210i	0.507908	−	0.593668i
$58$		0			0
$59$	−1.28860	+	2.23193i	−0.167762	+	0.290572i	−0.937633	−	0.347628i	$-0.886987\pi$
$59$	−1.28860	+	2.23193i	−0.167762	+	0.290572i	0.769871	+	0.638200i	$0.220321\pi$
$60$		0			0
$61$	7.44930	−	4.30086i	0.953785	−	0.550668i	0.0595306	−	0.998226i	$-0.481040\pi$
$61$	7.44930	−	4.30086i	0.953785	−	0.550668i	0.894255	+	0.447558i	$0.147706\pi$
$62$		0			0
$63$	−7.81337	−	1.39688i	−0.984392	−	0.175990i
$64$		0			0
$65$	−5.25097	+	3.03165i	−0.651302	+	0.376030i
$66$		0			0
$67$	7.99884	−	13.8544i	0.977213	−	1.69258i	0.304785	−	0.952421i	$-0.401415\pi$
$67$	7.99884	−	13.8544i	0.977213	−	1.69258i	0.672429	−	0.740162i	$-0.265251\pi$
$68$		0			0
$69$	3.23578	−	3.78214i	0.389542	−	0.455316i
$70$		0			0
$71$			3.63245i			0.431093i	0.976494	+	0.215547i	$0.0691533\pi$
$71$			3.63245i			0.431093i	−0.976494	+	0.215547i	$0.930847\pi$
$72$		0			0
$73$	−6.72468	−	3.88250i	−0.787064	−	0.454412i	0.0518638	−	0.998654i	$-0.483484\pi$
$73$	−6.72468	−	3.88250i	−0.787064	−	0.454412i	−0.838928	+	0.544242i	$0.816817\pi$
$74$		0			0
$75$	0.317079	−	1.70278i	0.0366131	−	0.196620i
$76$		0			0
$77$	−1.96368	−	10.1396i	−0.223783	−	1.15552i
$78$		0			0
$79$	−1.22311	−	2.11848i	−0.137610	−	0.238348i	0.788981	−	0.614417i	$-0.210609\pi$
$79$	−1.22311	−	2.11848i	−0.137610	−	0.238348i	−0.926591	+	0.376069i	$0.877275\pi$
$80$		0			0
$81$	1.90093	−	8.79696i	0.211214	−	0.977440i
$82$		0			0
$83$	−7.63648			−0.838213			−0.419106	−	0.907937i	$-0.637657\pi$
$83$	−7.63648			−0.838213			−0.419106	+	0.907937i	$0.637657\pi$
$84$		0			0
$85$	−3.06592			−0.332545
$86$		0			0
$87$	−4.60278	−	13.0328i	−0.493470	−	1.39726i
$88$		0			0
$89$	−4.11874	−	7.13387i	−0.436586	−	0.756189i	0.560838	−	0.827926i	$-0.310479\pi$
$89$	−4.11874	−	7.13387i	−0.436586	−	0.756189i	−0.997424	+	0.0717367i	$0.977146\pi$
$90$		0			0
$91$	12.1143	−	10.5161i	1.26992	−	1.10239i
$92$		0			0
$93$	11.0729	+	2.06191i	1.14820	+	0.213810i
$94$		0			0
$95$	−2.94930	−	1.70278i	−0.302592	−	0.174702i
$96$		0			0
$97$			5.74985i			0.583809i	0.956447	+	0.291904i	$0.0942889\pi$
$97$			5.74985i			0.583809i	−0.956447	+	0.291904i	$0.905711\pi$
$98$		0			0
$99$	11.5698	−	1.81245i	1.16281	−	0.182158i
$100$		0			0
$101$	−4.54502	+	7.87220i	−0.452246	+	0.783313i	−0.998525	−	0.0542901i	$-0.982710\pi$
$101$	−4.54502	+	7.87220i	−0.452246	+	0.783313i	0.546279	+	0.837603i	$0.316044\pi$
$102$		0			0
$103$	−0.853234	+	0.492615i	−0.0840717	+	0.0485388i	−0.541446	−	0.840735i	$-0.682123\pi$
$103$	−0.853234	+	0.492615i	−0.0840717	+	0.0485388i	0.457375	+	0.889274i	$0.348790\pi$
$104$		0			0
$105$	0.0329582	+	4.58246i	0.00321640	+	0.447202i
$106$		0			0
$107$	−1.11849	+	0.645758i	−0.108128	+	0.0624278i	−0.553089	−	0.833122i	$-0.686551\pi$
$107$	−1.11849	+	0.645758i	−0.108128	+	0.0624278i	0.444961	+	0.895550i	$0.353218\pi$
$108$		0			0
$109$	3.68547	−	6.38342i	0.353004	−	0.611421i	−0.633770	−	0.773521i	$-0.718494\pi$
$109$	3.68547	−	6.38342i	0.353004	−	0.611421i	0.986774	+	0.162101i	$0.0518269\pi$
$110$		0			0
$111$	0.172407	+	0.147502i	0.0163642	+	0.0140002i
$112$		0			0
$113$		−	4.52778i		−	0.425938i	−0.977059	−	0.212969i	$-0.931687\pi$
$113$		−	4.52778i		−	0.425938i	0.977059	−	0.212969i	$-0.0683133\pi$
$114$		0			0
$115$	−2.48871	−	1.43686i	−0.232074	−	0.133988i
$116$		0			0
$117$	11.4234	+	14.1555i	1.05609	+	1.30868i
$118$		0			0
$119$	7.96368	−	1.54228i	0.730030	−	0.141381i
$120$		0			0
$121$	2.11916	+	3.67050i	0.192651	+	0.333681i
$122$		0			0
$123$	−20.1951	+	7.13229i	−1.82093	+	0.643097i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.700855			−0.0621908			−0.0310954	−	0.999516i	$-0.509900\pi$
$127$	−0.700855			−0.0621908			−0.0310954	+	0.999516i	$0.509900\pi$
$128$		0			0
$129$	−7.23906	+	2.55661i	−0.637364	+	0.225097i
$130$		0			0
$131$	−2.66028	−	4.60774i	−0.232430	−	0.402580i	0.726093	−	0.687597i	$-0.241334\pi$
$131$	−2.66028	−	4.60774i	−0.232430	−	0.402580i	−0.958523	+	0.285016i	$0.908001\pi$
$132$		0			0
$133$	8.51735	+	2.93933i	0.738548	+	0.254873i
$134$		0			0
$135$	−5.19401	−	0.149178i	−0.447029	−	0.0128392i
$136$		0			0
$137$	3.39919	+	1.96252i	0.290412	+	0.167670i	0.638128	−	0.769930i	$-0.279709\pi$
$137$	3.39919	+	1.96252i	0.290412	+	0.167670i	−0.347715	+	0.937600i	$0.613042\pi$
$138$		0			0
$139$			16.1726i			1.37174i	0.727724	+	0.685870i	$0.240578\pi$
$139$			16.1726i			1.37174i	−0.727724	+	0.685870i	$0.759422\pi$
$140$		0			0
$141$	−13.2390	−	11.3265i	−1.11493	−	0.953868i
$142$		0			0
$143$	−11.8344	+	20.4978i	−0.989645	+	1.71411i
$144$		0			0
$145$	−6.91086	+	3.98999i	−0.573915	+	0.331350i
$146$		0			0
$147$	−2.39077	−	11.8863i	−0.197188	−	0.980366i
$148$		0			0
$149$	17.4366	−	10.0670i	1.42846	−	0.824721i	0.431459	−	0.902132i	$-0.357999\pi$
$149$	17.4366	−	10.0670i	1.42846	−	0.824721i	0.996999	+	0.0774116i	$0.0246655\pi$
$150$		0			0
$151$	−2.38980	+	4.13926i	−0.194479	+	0.336848i	−0.946730	−	0.322029i	$-0.895635\pi$
$151$	−2.38980	+	4.13926i	−0.194479	+	0.336848i	0.752250	+	0.658877i	$0.228968\pi$
$152$		0			0
$153$	1.42350	+	9.08693i	0.115083	+	0.734635i
$154$		0			0
$155$		−	6.50282i		−	0.522319i
$156$		0			0
$157$	6.62784	+	3.82658i	0.528959	+	0.305395i	0.740592	−	0.671955i	$-0.234545\pi$
$157$	6.62784	+	3.82658i	0.528959	+	0.305395i	−0.211633	+	0.977349i	$0.567878\pi$
$158$		0			0
$159$	9.12551	+	1.69929i	0.723700	+	0.134762i
$160$		0			0
$161$	7.18721	+	2.48030i	0.566431	+	0.195475i
$162$		0			0
$163$	4.23749	+	7.33954i	0.331906	+	0.574877i	0.982885	−	0.184218i	$-0.0589751\pi$
$163$	4.23749	+	7.33954i	0.331906	+	0.574877i	−0.650980	+	0.759095i	$0.725642\pi$
$164$		0			0
$165$	−2.25158	−	6.37537i	−0.175285	−	0.496322i
$166$		0			0
$167$	20.5669			1.59152			0.795759	−	0.605614i	$-0.207072\pi$
$167$	20.5669			1.59152			0.795759	+	0.605614i	$0.207072\pi$
$168$		0			0
$169$	−23.7635			−1.82796
$170$		0			0
$171$	−3.67743	+	9.53190i	−0.281220	+	0.728922i
$172$		0			0
$173$	−8.30340	−	14.3819i	−0.631296	−	1.09344i	−0.987287	−	0.158948i	$-0.949190\pi$
$173$	−8.30340	−	14.3819i	−0.631296	−	1.09344i	0.355991	−	0.934489i	$-0.384143\pi$
$174$		0			0
$175$	2.59749	−	0.503041i	0.196352	−	0.0380263i
$176$		0			0
$177$	0.817179	−	4.38842i	0.0614229	−	0.329854i
$178$		0			0
$179$	0.336240	+	0.194128i	0.0251318	+	0.0145098i	0.512513	−	0.858679i	$-0.328715\pi$
$179$	0.336240	+	0.194128i	0.0251318	+	0.0145098i	−0.487381	+	0.873189i	$0.662048\pi$
$180$		0			0
$181$		−	20.6789i		−	1.53705i	−0.639820	−	0.768524i	$-0.720991\pi$
$181$		−	20.6789i		−	1.53705i	0.639820	−	0.768524i	$-0.279009\pi$
$182$		0			0
$183$	−9.68543	+	11.3208i	−0.715968	+	0.836859i
$184$		0			0
$185$	0.0654987	−	0.113447i	0.00481556	−	0.00834079i
$186$		0			0
$187$	−10.3648	+	5.98410i	−0.757947	+	0.437601i
$188$		0			0
$189$	13.5664	−	2.22531i	0.986812	−	0.161868i
$190$		0			0
$191$	−15.2933	+	8.82961i	−1.10659	+	0.638888i	−0.937943	−	0.346789i	$-0.887272\pi$
$191$	−15.2933	+	8.82961i	−1.10659	+	0.638888i	−0.168644	+	0.985677i	$0.553939\pi$
$192$		0			0
$193$	10.6903	−	18.5161i	0.769505	−	1.33282i	−0.168327	−	0.985731i	$-0.553837\pi$
$193$	10.6903	−	18.5161i	0.769505	−	1.33282i	0.937832	−	0.347090i	$-0.112830\pi$
$194$		0			0
$195$	6.82720	−	7.97997i	0.488906	−	0.571458i
$196$		0			0
$197$			22.5070i			1.60356i	0.597619	+	0.801780i	$0.296114\pi$
$197$			22.5070i			1.60356i	−0.597619	+	0.801780i	$0.703886\pi$
$198$		0			0
$199$	−8.48532	−	4.89900i	−0.601509	−	0.347281i	0.168126	−	0.985765i	$-0.446228\pi$
$199$	−8.48532	−	4.89900i	−0.601509	−	0.347281i	−0.769635	+	0.638484i	$0.779562\pi$
$200$		0			0
$201$	−5.07253	+	27.2405i	−0.357789	+	1.92140i
$202$		0			0
$203$	15.9438	−	13.8404i	1.11903	−	0.971405i
$204$		0			0
$205$	6.18272	+	10.7088i	0.431820	+	0.747935i
$206$		0			0
$207$	−3.10314	+	8.04332i	−0.215683	+	0.559049i
$208$		0			0
$209$	−13.2940			−0.919568
$210$		0			0
$211$	−1.96291			−0.135132			−0.0675660	−	0.997715i	$-0.521523\pi$
$211$	−1.96291			−0.135132			−0.0675660	+	0.997715i	$0.521523\pi$
$212$		0			0
$213$	−2.09517	−	5.93249i	−0.143559	−	0.406488i
$214$		0			0
$215$	2.21623	+	3.83863i	0.151146	+	0.261792i
$216$		0			0
$217$	3.27118	+	16.8910i	0.222062	+	1.14664i
$218$		0			0
$219$	13.2221	+	2.46212i	0.893465	+	0.166374i
$220$		0			0
$221$	−16.0990	−	9.29478i	−1.08294	−	0.625234i
$222$		0			0
$223$		−	1.78864i		−	0.119776i	−0.998205	−	0.0598882i	$-0.980926\pi$
$223$		−	1.78864i		−	0.119776i	0.998205	−	0.0598882i	$-0.0190744\pi$
$224$		0			0
$225$	0.464299	+	2.96385i	0.0309532	+	0.197590i
$226$		0			0
$227$	13.7981	−	23.8990i	0.915813	−	1.58623i	0.110106	−	0.993920i	$-0.464881\pi$
$227$	13.7981	−	23.8990i	0.915813	−	1.58623i	0.805707	−	0.592315i	$-0.201786\pi$
$228$		0			0
$229$	−8.37613	+	4.83596i	−0.553510	+	0.319569i	−0.750537	−	0.660829i	$-0.770205\pi$
$229$	−8.37613	+	4.83596i	−0.553510	+	0.319569i	0.197026	+	0.980398i	$0.436872\pi$
$230$		0			0
$231$	9.05553	+	15.4273i	0.595810	+	1.01504i
$232$		0			0
$233$	−0.516767	+	0.298355i	−0.0338545	+	0.0195459i	−0.516832	−	0.856087i	$-0.672889\pi$
$233$	−0.516767	+	0.298355i	−0.0338545	+	0.0195459i	0.482977	+	0.875633i	$0.339555\pi$
$234$		0			0
$235$	−5.02960	+	8.71153i	−0.328095	+	0.568277i
$236$		0			0
$237$	3.21949	+	2.75441i	0.209128	+	0.178918i
$238$		0			0
$239$			8.90983i			0.576329i	0.957581	+	0.288165i	$0.0930450\pi$
$239$			8.90983i			0.576329i	−0.957581	+	0.288165i	$0.906955\pi$
$240$		0			0
$241$	1.82543	+	1.05391i	0.117586	+	0.0678886i	0.557640	−	0.830083i	$-0.311707\pi$
$241$	1.82543	+	1.05391i	0.117586	+	0.0678886i	−0.440053	+	0.897972i	$0.645040\pi$
$242$		0			0
$243$	1.96943	+	15.4635i	0.126339	+	0.991987i
$244$		0			0
$245$	−6.49390	+	2.61329i	−0.414880	+	0.166957i
$246$		0			0
$247$	−10.3245	−	17.8825i	−0.656930	−	1.13784i
$248$		0			0
$249$	12.4718	−	4.40466i	0.790370	−	0.279134i
$250$		0			0
$251$	29.8229			1.88241			0.941204	−	0.337840i	$-0.109696\pi$
$251$	29.8229			1.88241			0.941204	+	0.337840i	$0.109696\pi$
$252$		0			0
$253$	−11.2179			−0.705266
$254$		0			0
$255$	5.00723	−	1.76839i	0.313565	−	0.110741i
$256$		0			0
$257$	−6.78489	−	11.7518i	−0.423230	−	0.733055i	0.573024	−	0.819539i	$-0.305770\pi$
$257$	−6.78489	−	11.7518i	−0.423230	−	0.733055i	−0.996253	+	0.0864836i	$0.972437\pi$
$258$		0			0
$259$	−0.113064	+	0.327626i	−0.00702543	+	0.0203577i
$260$		0			0
$261$	15.0344	+	18.6302i	0.930608	+	1.15318i
$262$		0			0
$263$	10.5291	+	6.07897i	0.649252	+	0.374846i	0.788169	−	0.615458i	$-0.211029\pi$
$263$	10.5291	+	6.07897i	0.649252	+	0.374846i	−0.138918	+	0.990304i	$0.544362\pi$
$264$		0			0
$265$		−	5.35918i		−	0.329212i
$266$		0			0
$267$	10.8415	+	9.27532i	0.663486	+	0.567640i
$268$		0			0
$269$	−11.2201	+	19.4338i	−0.684101	+	1.18490i	0.289617	+	0.957143i	$0.406472\pi$
$269$	−11.2201	+	19.4338i	−0.684101	+	1.18490i	−0.973718	+	0.227756i	$0.926861\pi$
$270$		0			0
$271$	−7.19179	+	4.15218i	−0.436870	+	0.252227i	−0.702269	−	0.711912i	$-0.747830\pi$
$271$	−7.19179	+	4.15218i	−0.436870	+	0.252227i	0.265399	+	0.964139i	$0.414496\pi$
$272$		0			0
$273$	−13.7193	+	24.1622i	−0.830332	+	1.46237i
$274$		0			0
$275$	−3.38064	+	1.95181i	−0.203860	+	0.117699i
$276$		0			0
$277$	−3.02848	+	5.24547i	−0.181963	+	0.315170i	−0.942549	−	0.334068i	$-0.891579\pi$
$277$	−3.02848	+	5.24547i	−0.181963	+	0.315170i	0.760586	+	0.649238i	$0.224912\pi$
$278$		0			0
$279$	−19.2734	+	3.01925i	−1.15387	+	0.180758i
$280$		0			0
$281$		−	17.5771i		−	1.04856i	−0.851545	−	0.524282i	$-0.824334\pi$
$281$		−	17.5771i		−	1.04856i	0.851545	−	0.524282i	$-0.175666\pi$
$282$		0			0
$283$	7.10845	+	4.10407i	0.422554	+	0.243961i	0.696169	−	0.717878i	$-0.254886\pi$
$283$	7.10845	+	4.10407i	0.422554	+	0.243961i	−0.273616	+	0.961839i	$0.588220\pi$
$284$		0			0
$285$	5.79892	+	1.07983i	0.343498	+	0.0639637i
$286$		0			0
$287$	−21.4465	−	24.7058i	−1.26595	−	1.45834i
$288$		0			0
$289$	3.80008	+	6.58193i	0.223534	+	0.387172i
$290$		0			0
$291$	−3.31647	−	9.39060i	−0.194415	−	0.550487i
$292$		0			0
$293$	3.88610			0.227028			0.113514	−	0.993536i	$-0.463789\pi$
$293$	3.88610			0.227028			0.113514	+	0.993536i	$0.463789\pi$
$294$		0			0
$295$	−2.57721			−0.150051
$296$		0			0
$297$	−17.8503	+	9.63343i	−1.03578	+	0.558988i
$298$		0			0
$299$	−8.71210	−	15.0898i	−0.503834	−	0.872666i
$300$		0			0
$301$	−7.68763	−	8.85594i	−0.443108	−	0.510448i
$302$		0			0
$303$	2.88226	−	15.4783i	0.165581	−	0.889207i
$304$		0			0
$305$	7.44930	+	4.30086i	0.426546	+	0.246266i
$306$		0			0
$307$			0.119756i			0.00683482i	0.999994	+	0.00341741i	$0.00108780\pi$
$307$			0.119756i			0.00683482i	−0.999994	+	0.00341741i	$0.998912\pi$
$308$		0			0
$309$	1.10936	−	1.29667i	0.0631092	−	0.0737651i
$310$		0			0
$311$	6.57207	−	11.3832i	0.372668	−	0.645480i	−0.617307	−	0.786722i	$-0.711776\pi$
$311$	6.57207	−	11.3832i	0.372668	−	0.645480i	0.989975	+	0.141243i	$0.0451097\pi$
$312$		0			0
$313$	20.1517	−	11.6346i	1.13904	−	0.657625i	0.192847	−	0.981229i	$-0.438228\pi$
$313$	20.1517	−	11.6346i	1.13904	−	0.657625i	0.946192	+	0.323604i	$0.104895\pi$
$314$		0			0
$315$	−2.69695	−	7.46502i	−0.151956	−	0.420606i
$316$		0			0
$317$	−30.0933	+	17.3744i	−1.69021	+	0.975841i	−0.735861	+	0.677132i	$0.763223\pi$
$317$	−30.0933	+	17.3744i	−1.69021	+	0.975841i	−0.954344	+	0.298709i	$0.903444\pi$
$318$		0			0
$319$	−15.5754	+	26.9774i	−0.872056	+	1.51045i
$320$		0			0
$321$	1.45423	−	1.69978i	0.0811674	−	0.0948725i
$322$		0			0
$323$		−	10.4412i		−	0.580962i
$324$		0			0
$325$	−5.25097	−	3.03165i	−0.291271	−	0.168166i
$326$		0			0
$327$	−2.33717	+	12.5511i	−0.129246	+	0.694077i
$328$		0			0
$329$	8.68208	−	25.1582i	0.478659	−	1.38702i
$330$		0			0
$331$	12.8024	+	22.1744i	0.703684	+	1.21882i	0.967165	+	0.254151i	$0.0817961\pi$
$331$	12.8024	+	22.1744i	0.703684	+	1.21882i	−0.263481	+	0.964665i	$0.584871\pi$
$332$		0			0
$333$	−0.366651	−	0.141455i	−0.0200924	−	0.00775169i
$334$		0			0
$335$	15.9977			0.874046
$336$		0			0
$337$	26.5502			1.44628			0.723140	−	0.690702i	$-0.242698\pi$
$337$	26.5502			1.44628			0.723140	+	0.690702i	$0.242698\pi$
$338$		0			0
$339$	2.61159	+	7.39473i	0.141842	+	0.401627i
$340$		0			0
$341$	−12.6923	−	21.9837i	−0.687327	−	1.19048i
$342$		0			0
$343$	15.5532	−	10.0547i	0.839796	−	0.542902i
$344$		0			0
$345$	4.89331	+	0.911197i	0.263447	+	0.0490572i
$346$		0			0
$347$	16.6519	+	9.61397i	0.893920	+	0.516105i	0.875223	−	0.483720i	$-0.160715\pi$
$347$	16.6519	+	9.61397i	0.893920	+	0.516105i	0.0186975	+	0.999825i	$0.494048\pi$
$348$		0			0
$349$			1.40475i			0.0751943i	0.999293	+	0.0375972i	$0.0119704\pi$
$349$			1.40475i			0.0751943i	−0.999293	+	0.0375972i	$0.988030\pi$
$350$		0			0
$351$	−26.8213	−	16.5297i	−1.43162	−	0.882292i
$352$		0			0
$353$	9.43705	−	16.3454i	0.502283	−	0.869980i	−0.497713	−	0.867342i	$-0.665827\pi$
$353$	9.43705	−	16.3454i	0.502283	−	0.869980i	0.999997	−	0.00263867i	$-0.000839917\pi$
$354$		0			0
$355$	−3.14580	+	1.81623i	−0.166962	+	0.0963953i
$356$		0			0
$357$	−12.1166	+	7.11222i	−0.641281	+	0.376419i
$358$		0			0
$359$	−19.1592	+	11.0615i	−1.01118	+	0.583806i	−0.911537	−	0.411217i	$-0.865104\pi$
$359$	−19.1592	+	11.0615i	−1.01118	+	0.583806i	−0.0996440	+	0.995023i	$0.531770\pi$
$360$		0			0
$361$	−3.70108	+	6.41046i	−0.194794	+	0.337392i
$362$		0			0
$363$	−5.57811	−	4.77230i	−0.292775	−	0.250481i
$364$		0			0
$365$		−	7.76499i		−	0.406438i
$366$		0			0
$367$	−11.3631	−	6.56047i	−0.593147	−	0.342454i	0.173194	−	0.984888i	$-0.444591\pi$
$367$	−11.3631	−	6.56047i	−0.593147	−	0.342454i	−0.766341	+	0.642434i	$0.777925\pi$
$368$		0			0
$369$	28.8687	−	23.2968i	1.50284	−	1.21278i
$370$		0			0
$371$	2.69589	+	13.9204i	0.139964	+	0.722712i
$372$		0			0
$373$	−7.38003	−	12.7826i	−0.382123	−	0.661857i	0.609242	−	0.792984i	$-0.291474\pi$
$373$	−7.38003	−	12.7826i	−0.382123	−	0.661857i	−0.991366	+	0.131127i	$0.958140\pi$
$374$		0			0
$375$	1.63319	−	0.576792i	0.0843376	−	0.0297854i
$376$		0			0
$377$	−48.3849			−2.49195
$378$		0			0
$379$	29.9980			1.54089			0.770447	−	0.637505i	$-0.220033\pi$
$379$	29.9980			1.54089			0.770447	+	0.637505i	$0.220033\pi$
$380$		0			0
$381$	1.14463	−	0.404247i	0.0586411	−	0.0207102i
$382$		0			0
$383$	7.72052	+	13.3723i	0.394500	+	0.683294i	0.993037	−	0.117801i	$-0.0375844\pi$
$383$	7.72052	+	13.3723i	0.394500	+	0.683294i	−0.598537	+	0.801095i	$0.704251\pi$
$384$		0			0
$385$	7.79934	−	6.77042i	0.397491	−	0.345052i
$386$		0			0
$387$	10.3481	−	8.35086i	0.526025	−	0.424498i
$388$		0			0
$389$	7.53666	+	4.35129i	0.382124	+	0.220619i	0.678742	−	0.734377i	$-0.262525\pi$
$389$	7.53666	+	4.35129i	0.382124	+	0.220619i	−0.296618	+	0.954996i	$0.595859\pi$
$390$		0			0
$391$		−	8.81059i		−	0.445570i
$392$		0			0
$393$	7.00245	+	5.99089i	0.353227	+	0.302201i
$394$		0			0
$395$	1.22311	−	2.11848i	0.0615411	−	0.106592i
$396$		0			0
$397$	23.3904	−	13.5044i	1.17393	−	0.677768i	0.219327	−	0.975651i	$-0.429614\pi$
$397$	23.3904	−	13.5044i	1.17393	−	0.677768i	0.954602	+	0.297883i	$0.0962806\pi$
$398$		0			0
$399$	−15.6058	+	0.112241i	−0.781269	+	0.00561909i
$400$		0			0
$401$	−4.30215	+	2.48385i	−0.214839	+	0.124037i	−0.603558	−	0.797319i	$-0.706251\pi$
$401$	−4.30215	+	2.48385i	−0.214839	+	0.124037i	0.388719	+	0.921356i	$0.372918\pi$
$402$		0			0
$403$	19.7143	−	34.1461i	0.982037	−	1.70094i
$404$		0			0
$405$	8.56885	−	2.75223i	0.425790	−	0.136759i
$406$		0			0
$407$		−	0.511365i		−	0.0253474i
$408$		0			0
$409$	−7.00387	−	4.04369i	−0.346319	−	0.199947i	0.316744	−	0.948511i	$-0.397410\pi$
$409$	−7.00387	−	4.04369i	−0.346319	−	0.199947i	−0.663063	+	0.748564i	$0.730744\pi$
$410$		0			0
$411$	−6.68349	−	1.24455i	−0.329672	−	0.0613891i
$412$		0			0
$413$	6.69427	−	1.29644i	0.329403	−	0.0637937i
$414$		0			0
$415$	−3.81824	−	6.61339i	−0.187430	−	0.324638i
$416$		0			0
$417$	−9.32820	−	26.4129i	−0.456804	−	1.29345i
$418$		0			0
$419$	7.60294			0.371428			0.185714	−	0.982604i	$-0.440540\pi$
$419$	7.60294			0.371428			0.185714	+	0.982604i	$0.440540\pi$
$420$		0			0
$421$	−4.43892			−0.216340			−0.108170	−	0.994132i	$-0.534499\pi$
$421$	−4.43892			−0.216340			−0.108170	+	0.994132i	$0.534499\pi$
$422$		0			0
$423$	28.1549	+	10.8623i	1.36894	+	0.528141i
$424$		0			0
$425$	−1.53296	−	2.65516i	−0.0743594	−	0.128794i
$426$		0			0
$427$	−21.5130	−	7.42413i	−1.04109	−	0.359279i
$428$		0			0
$429$	7.50490	−	40.3029i	0.362340	−	1.94584i
$430$		0			0
$431$	−4.24065	−	2.44834i	−0.204265	−	0.117932i	0.394378	−	0.918948i	$-0.370960\pi$
$431$	−4.24065	−	2.44834i	−0.204265	−	0.117932i	−0.598643	+	0.801016i	$0.704293\pi$
$432$		0			0
$433$		−	18.6390i		−	0.895732i	−0.894101	−	0.447866i	$-0.852184\pi$
$433$		−	18.6390i		−	0.895732i	0.894101	−	0.447866i	$-0.147816\pi$
$434$		0			0
$435$	8.98536	−	10.5025i	0.430815	−	0.503558i
$436$		0			0
$437$	4.89331	−	8.47547i	0.234079	−	0.405437i
$438$		0			0
$439$	−2.87038	+	1.65722i	−0.136996	+	0.0790946i	−0.566932	−	0.823765i	$-0.691870\pi$
$439$	−2.87038	+	1.65722i	−0.136996	+	0.0790946i	0.429936	+	0.902860i	$0.358536\pi$
$440$		0			0
$441$	10.7605	+	18.0336i	0.512405	+	0.858744i
$442$		0			0
$443$	0.707683	−	0.408581i	0.0336231	−	0.0194123i	−0.483094	−	0.875568i	$-0.660487\pi$
$443$	0.707683	−	0.408581i	0.0336231	−	0.0194123i	0.516717	+	0.856156i	$0.327154\pi$
$444$		0			0
$445$	4.11874	−	7.13387i	0.195247	−	0.338178i
$446$		0			0
$447$	−22.6707	+	26.4986i	−1.07229	+	1.25334i
$448$		0			0
$449$		−	5.17892i		−	0.244408i	−0.992505	−	0.122204i	$-0.961004\pi$
$449$		−	5.17892i		−	0.244408i	0.992505	−	0.122204i	$-0.0389962\pi$
$450$		0			0
$451$	41.8032	+	24.1351i	1.96843	+	1.13648i
$452$		0			0
$453$	1.51551	−	8.13862i	0.0712051	−	0.382386i
$454$		0			0
$455$	15.1644	+	5.23322i	0.710917	+	0.245337i
$456$		0			0
$457$	−6.01889	−	10.4250i	−0.281552	−	0.487662i	0.690215	−	0.723604i	$-0.257516\pi$
$457$	−6.01889	−	10.4250i	−0.281552	−	0.487662i	−0.971767	+	0.235942i	$0.924183\pi$
$458$		0			0
$459$	−7.56611	−	14.0196i	−0.353156	−	0.654380i
$460$		0			0
$461$	−23.0451			−1.07332			−0.536658	−	0.843800i	$-0.680314\pi$
$461$	−23.0451			−1.07332			−0.536658	+	0.843800i	$0.680314\pi$
$462$		0			0
$463$	27.8549			1.29453			0.647263	−	0.762267i	$-0.275914\pi$
$463$	27.8549			1.29453			0.647263	+	0.762267i	$0.275914\pi$
$464$		0			0
$465$	3.75077	+	10.6203i	0.173938	+	0.492507i
$466$		0			0
$467$	1.10822	+	1.91950i	0.0512825	+	0.0888240i	0.890527	−	0.454930i	$-0.150336\pi$
$467$	1.10822	+	1.91950i	0.0512825	+	0.0888240i	−0.839245	+	0.543754i	$0.817002\pi$
$468$		0			0
$469$	−41.5538	+	8.04748i	−1.91878	+	0.371598i
$470$		0			0
$471$	−13.0317	−	2.42666i	−0.600467	−	0.111815i
$472$		0			0
$473$	14.9846	+	8.65135i	0.688992	+	0.397790i
$474$		0			0
$475$		−	3.40556i		−	0.156258i
$476$		0			0
$477$	−15.8838	+	2.48826i	−0.727271	+	0.113930i
$478$		0			0
$479$	3.53276	−	6.11892i	0.161416	−	0.279581i	−0.773961	−	0.633234i	$-0.781727\pi$
$479$	3.53276	−	6.11892i	0.161416	−	0.279581i	0.935377	+	0.353653i	$0.115061\pi$
$480$		0			0
$481$	0.687863	−	0.397138i	0.0313638	−	0.0181079i
$482$		0			0
$483$	−13.1687	+	0.0947128i	−0.599197	+	0.00430958i
$484$		0			0
$485$	−4.97952	+	2.87493i	−0.226108	+	0.130544i
$486$		0			0
$487$	−4.62036	+	8.00270i	−0.209368	+	0.362637i	−0.951516	−	0.307600i	$-0.900474\pi$
$487$	−4.62036	+	8.00270i	−0.209368	+	0.362637i	0.742147	+	0.670237i	$0.233807\pi$
$488$		0			0
$489$	−11.1540	−	9.54273i	−0.504402	−	0.431537i
$490$		0			0
$491$		−	14.0713i		−	0.635031i	−0.948253	−	0.317515i	$-0.897152\pi$
$491$		−	14.0713i		−	0.635031i	0.948253	−	0.317515i	$-0.102848\pi$
$492$		0			0
$493$	−21.1881	−	12.2330i	−0.954265	−	0.550945i
$494$		0			0
$495$	7.35452	+	9.11350i	0.330561	+	0.409622i
$496$		0			0
$497$	7.25754	−	6.30010i	0.325545	−	0.282598i
$498$		0			0
$499$	−6.50255	−	11.2627i	−0.291094	−	0.504190i	0.682975	−	0.730442i	$-0.260686\pi$
$499$	−6.50255	−	11.2627i	−0.291094	−	0.504190i	−0.974069	+	0.226252i	$0.927353\pi$
$500$		0			0
$501$	−33.5897	+	11.8628i	−1.50068	+	0.529993i
$502$		0			0
$503$	0.580122			0.0258664			0.0129332	−	0.999916i	$-0.495883\pi$
$503$	0.580122			0.0258664			0.0129332	+	0.999916i	$0.495883\pi$
$504$		0			0
$505$	−9.09003			−0.404501
$506$		0			0
$507$	38.8104	−	13.7066i	1.72363	−	0.608732i
$508$		0			0
$509$	−9.86251	−	17.0824i	−0.437148	−	0.757163i	0.560320	−	0.828276i	$-0.310678\pi$
$509$	−9.86251	−	17.0824i	−0.437148	−	0.757163i	−0.997468	+	0.0711133i	$0.977345\pi$
$510$		0			0
$511$	3.90611	+	20.1695i	0.172796	+	0.892245i
$512$		0			0
$513$	0.508034	−	17.6885i	0.0224302	−	0.780967i
$514$		0			0
$515$	−0.853234	−	0.492615i	−0.0375980	−	0.0217072i
$516$		0			0
$517$			39.2674i			1.72698i
$518$		0			0
$519$	21.8564	+	18.6991i	0.959390	+	0.820799i
$520$		0			0
$521$	−18.0051	+	31.1857i	−0.788818	+	1.36627i	0.137874	+	0.990450i	$0.455973\pi$
$521$	−18.0051	+	31.1857i	−0.788818	+	1.36627i	−0.926692	+	0.375822i	$0.877360\pi$
$522$		0			0
$523$	−18.5387	+	10.7033i	−0.810640	+	0.468023i	−0.847178	−	0.531309i	$-0.821700\pi$
$523$	−18.5387	+	10.7033i	−0.810640	+	0.468023i	0.0365378	+	0.999332i	$0.488367\pi$
$524$		0			0
$525$	−3.95205	+	2.31977i	−0.172481	+	0.101243i
$526$		0			0
$527$	17.2660	−	9.96855i	0.752121	−	0.434237i
$528$		0			0
$529$	−7.37087	+	12.7667i	−0.320472	+	0.555075i
$530$		0			0
$531$	1.19659	+	7.63846i	0.0519277	+	0.331481i
$532$		0			0
$533$			74.9754i			3.24754i
$534$		0			0
$535$	−1.11849	−	0.645758i	−0.0483564	−	0.0279186i
$536$		0			0
$537$	−0.661116	−	0.123108i	−0.0285293	−	0.00531251i
$538$		0			0
$539$	−16.8529	+	21.5095i	−0.725906	+	0.926479i
$540$		0			0
$541$	−2.32759	−	4.03151i	−0.100071	−	0.173328i	0.811643	−	0.584154i	$-0.198574\pi$
$541$	−2.32759	−	4.03151i	−0.100071	−	0.173328i	−0.911714	+	0.410826i	$0.865240\pi$
$542$		0			0
$543$	11.9274	+	33.7725i	0.511854	+	1.44932i
$544$		0			0
$545$	7.37094			0.315736
$546$		0			0
$547$	7.34057			0.313860			0.156930	−	0.987610i	$-0.449840\pi$
$547$	7.34057			0.313860			0.156930	+	0.987610i	$0.449840\pi$
$548$		0			0
$549$	9.28841	−	24.0755i	0.396420	−	1.02752i
$550$		0			0
$551$	−13.5881	−	23.5353i	−0.578874	−	1.00264i
$552$		0			0
$553$	−2.11132	+	6.11800i	−0.0897825	+	0.260164i
$554$		0			0
$555$	−0.0415365	+	0.223060i	−0.00176313	+	0.00946836i
$556$		0			0
$557$	27.9154	+	16.1169i	1.18281	+	0.682897i	0.956663	−	0.291196i	$-0.0940531\pi$
$557$	27.9154	+	16.1169i	1.18281	+	0.682897i	0.226149	+	0.974093i	$0.427386\pi$
$558$		0			0
$559$			26.8753i			1.13671i
$560$		0			0
$561$	13.4761	−	15.7515i	0.568960	−	0.665028i
$562$		0			0
$563$	11.4830	−	19.8892i	0.483952	−	0.838230i	−0.515878	−	0.856662i	$-0.672534\pi$
$563$	11.4830	−	19.8892i	0.483952	−	0.838230i	0.999830	+	0.0184324i	$0.00586756\pi$
$564$		0			0
$565$	3.92118	−	2.26389i	0.164965	−	0.0952426i
$566$		0			0
$567$	−20.8730	+	11.4594i	−0.876585	+	0.481248i
$568$		0			0
$569$	16.0347	−	9.25765i	0.672211	−	0.388101i	−0.124703	−	0.992194i	$-0.539798\pi$
$569$	16.0347	−	9.25765i	0.672211	−	0.388101i	0.796914	+	0.604093i	$0.206465\pi$
$570$		0			0
$571$	−21.9408	+	38.0025i	−0.918193	+	1.59036i	−0.116035	+	0.993245i	$0.537019\pi$
$571$	−21.9408	+	38.0025i	−0.918193	+	1.59036i	−0.802158	+	0.597112i	$0.796315\pi$
$572$		0			0
$573$	19.8841	−	23.2415i	0.830670	−	0.970928i
$574$		0			0
$575$		−	2.87372i		−	0.119842i
$576$		0			0
$577$	14.6663	+	8.46761i	0.610568	+	0.352511i	0.773188	−	0.634177i	$-0.218661\pi$
$577$	14.6663	+	8.46761i	0.610568	+	0.352511i	−0.162620	+	0.986689i	$0.551994\pi$
$578$		0			0
$579$	−6.77934	+	36.4065i	−0.281740	+	1.51300i
$580$		0			0
$581$	13.2446	+	15.2575i	0.549480	+	0.632987i
$582$		0			0
$583$	−10.4601	−	18.1175i	−0.433214	−	0.750349i
$584$		0			0
$585$	−6.54734	+	16.9707i	−0.270699	+	0.701651i
$586$		0			0
$587$	−15.3959			−0.635456			−0.317728	−	0.948182i	$-0.602920\pi$
$587$	−15.3959			−0.635456			−0.317728	+	0.948182i	$0.602920\pi$
$588$		0			0
$589$	22.1458			0.912500
$590$		0			0
$591$	−12.9819	−	36.7583i	−0.534003	−	1.51203i
$592$		0			0
$593$	−2.37500	−	4.11363i	−0.0975297	−	0.168926i	0.813132	−	0.582079i	$-0.197761\pi$
$593$	−2.37500	−	4.11363i	−0.0975297	−	0.168926i	−0.910662	+	0.413153i	$0.864427\pi$
$594$		0			0
$595$	5.31750	+	6.12561i	0.217996	+	0.251126i
$596$		0			0
$597$	16.6839	+	3.10674i	0.682825	+	0.127151i
$598$		0			0
$599$	19.2300	+	11.1024i	0.785716	+	0.453634i	0.838452	−	0.544975i	$-0.183461\pi$
$599$	19.2300	+	11.1024i	0.785716	+	0.453634i	−0.0527360	+	0.998608i	$0.516794\pi$
$600$		0			0
$601$		−	42.5924i		−	1.73738i	−0.495357	−	0.868689i	$-0.664963\pi$
$601$		−	42.5924i		−	1.73738i	0.495357	−	0.868689i	$-0.335037\pi$
$602$		0			0
$603$	−7.42770	−	47.4148i	−0.302479	−	1.93088i
$604$		0			0
$605$	−2.11916	+	3.67050i	−0.0861562	+	0.149227i
$606$		0			0
$607$	16.2862	−	9.40283i	0.661035	−	0.381649i	−0.131636	−	0.991298i	$-0.542023\pi$
$607$	16.2862	−	9.40283i	0.661035	−	0.381649i	0.792671	+	0.609649i	$0.208690\pi$
$608$		0			0
$609$	−18.0562	+	31.8002i	−0.731673	+	1.28861i
$610$		0			0
$611$	−52.8205	+	30.4960i	−2.13689	+	1.23373i
$612$		0			0
$613$	−7.74783	+	13.4196i	−0.312932	+	0.542014i	−0.978996	−	0.203881i	$-0.934645\pi$
$613$	−7.74783	+	13.4196i	−0.312932	+	0.542014i	0.666064	+	0.745895i	$0.267978\pi$
$614$		0			0
$615$	−16.2743	−	13.9234i	−0.656244	−	0.561444i
$616$		0			0
$617$			17.7219i			0.713459i	0.934208	+	0.356729i	$0.116108\pi$
$617$			17.7219i			0.713459i	−0.934208	+	0.356729i	$0.883892\pi$
$618$		0			0
$619$	5.96204	+	3.44219i	0.239635	+	0.138353i	0.615009	−	0.788520i	$-0.289152\pi$
$619$	5.96204	+	3.44219i	0.239635	+	0.138353i	−0.375374	+	0.926873i	$0.622486\pi$
$620$		0			0
$621$	0.428695	−	14.9261i	0.0172029	−	0.598965i
$622$		0			0
$623$	−7.10976	+	20.6021i	−0.284847	+	0.825404i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	21.7117	−	7.66789i	0.867082	−	0.306226i
$628$		0			0
$629$	0.401627			0.0160139
$630$		0			0
$631$	−49.6754			−1.97755			−0.988774	−	0.149421i	$-0.952259\pi$
$631$	−49.6754			−1.97755			−0.988774	+	0.149421i	$0.952259\pi$
$632$		0			0
$633$	3.20580	−	1.13219i	0.127419	−	0.0450004i
$634$		0			0
$635$	−0.350427	−	0.606958i	−0.0139063	−	0.0240864i
$636$		0			0
$637$	−42.0218	−	5.96493i	−1.66496	−	0.236339i
$638$		0			0
$639$	6.84362	+	8.48041i	0.270729	+	0.335480i
$640$		0			0
$641$	23.3007	+	13.4527i	0.920324	+	0.531349i	0.883738	−	0.467981i	$-0.155019\pi$
$641$	23.3007	+	13.4527i	0.920324	+	0.531349i	0.0365856	+	0.999331i	$0.488352\pi$
$642$		0			0
$643$			13.9638i			0.550679i	0.961347	+	0.275339i	$0.0887902\pi$
$643$			13.9638i			0.550679i	−0.961347	+	0.275339i	$0.911210\pi$
$644$		0			0
$645$	−5.83362	−	4.99091i	−0.229699	−	0.196517i
$646$		0			0
$647$	−15.3377	+	26.5656i	−0.602985	+	1.04440i	0.389381	+	0.921077i	$0.372689\pi$
$647$	−15.3377	+	26.5656i	−0.602985	+	1.04440i	−0.992366	+	0.123324i	$0.960644\pi$
$648$		0			0
$649$	−8.71262	+	5.03023i	−0.342000	+	0.197454i
$650$		0			0
$651$	−15.0851	−	25.6994i	−0.591230	−	1.00724i
$652$		0			0
$653$	11.3602	−	6.55879i	0.444557	−	0.256665i	−0.260971	−	0.965347i	$-0.584043\pi$
$653$	11.3602	−	6.55879i	0.444557	−	0.256665i	0.705529	+	0.708681i	$0.250710\pi$
$654$		0			0
$655$	2.66028	−	4.60774i	0.103946	−	0.180039i
$656$		0			0
$657$	−23.0143	+	3.60527i	−0.897873	+	0.140655i
$658$		0			0
$659$			37.1306i			1.44640i	0.690638	+	0.723201i	$0.257330\pi$
$659$			37.1306i			1.44640i	−0.690638	+	0.723201i	$0.742670\pi$
$660$		0			0
$661$	4.41297	+	2.54783i	0.171645	+	0.0990992i	0.583361	−	0.812213i	$-0.301737\pi$
$661$	4.41297	+	2.54783i	0.171645	+	0.0990992i	−0.411716	+	0.911312i	$0.635071\pi$
$662$		0			0
$663$	31.6539	+	5.89436i	1.22934	+	0.228918i
$664$		0			0
$665$	1.71314	+	8.84591i	0.0664326	+	0.343030i
$666$		0			0
$667$	−11.4661	−	19.8599i	−0.443969	−	0.768977i
$668$		0			0
$669$	1.03168	+	2.92120i	0.0398869	+	0.112940i
$670$		0			0
$671$	33.5779			1.29626
$672$		0			0
$673$	29.0339			1.11918			0.559588	−	0.828771i	$-0.310960\pi$
$673$	29.0339			1.11918			0.559588	+	0.828771i	$0.310960\pi$
$674$		0			0
$675$	−2.46781	−	4.57273i	−0.0949862	−	0.176005i
$676$		0			0
$677$	12.4783	+	21.6131i	0.479581	+	0.830658i	0.999726	−	0.0234197i	$-0.00745540\pi$
$677$	12.4783	+	21.6131i	0.479581	+	0.830658i	−0.520145	+	0.854078i	$0.674122\pi$
$678$		0			0
$679$	11.4880	−	9.97249i	0.440870	−	0.382709i
$680$		0			0
$681$	−8.75019	+	46.9903i	−0.335308	+	1.80067i
$682$		0			0
$683$	29.3107	+	16.9226i	1.12154	+	0.647524i	0.941795	−	0.336189i	$-0.109138\pi$
$683$	29.3107	+	16.9226i	1.12154	+	0.647524i	0.179749	+	0.983712i	$0.442471\pi$
$684$		0			0
$685$			3.92505i			0.149968i
$686$		0			0
$687$	10.8905	−	12.7293i	0.415498	−	0.485654i
$688$		0			0
$689$	16.2472	−	28.1409i	0.618967	−	1.07208i
$690$		0			0
$691$	9.82503	−	5.67249i	0.373762	−	0.215792i	−0.301339	−	0.953517i	$-0.597434\pi$
$691$	9.82503	−	5.67249i	0.373762	−	0.215792i	0.675101	+	0.737726i	$0.264100\pi$
$692$		0			0
$693$	−23.6878	−	19.9726i	−0.899823	−	0.758696i
$694$		0			0
$695$	−14.0059	+	8.08629i	−0.531273	+	0.306730i
$696$		0			0
$697$	−18.9557	+	32.8323i	−0.717999	+	1.24361i
$698$		0			0
$699$	0.671890	−	0.785338i	0.0254132	−	0.0297042i
$700$		0			0
$701$		−	23.1947i		−	0.876052i	−0.898962	−	0.438026i	$-0.855678\pi$
$701$		−	23.1947i		−	0.876052i	0.898962	−	0.438026i	$-0.144322\pi$
$702$		0			0
$703$	0.386351	+	0.223060i	0.0145715	+	0.00841285i
$704$		0			0
$705$	3.18956	−	17.1286i	0.120126	−	0.645101i
$706$		0			0
$707$	23.6113	−	4.57266i	0.887993	−	0.171972i
$708$		0			0
$709$	7.29490	+	12.6351i	0.273966	+	0.474522i	0.969874	−	0.243609i	$-0.0783312\pi$
$709$	7.29490	+	12.6351i	0.273966	+	0.474522i	−0.695908	+	0.718131i	$0.744998\pi$
$710$		0			0
$711$	−6.84675	−	2.64150i	−0.256773	−	0.0990639i
$712$		0			0
$713$	18.6873			0.699844
$714$		0			0
$715$	−23.6689			−0.885165
$716$		0			0
$717$	−5.13912	−	14.5515i	−0.191924	−	0.543434i
$718$		0			0
$719$	9.35171	+	16.1976i	0.348760	+	0.604070i	0.986029	−	0.166571i	$-0.0532696\pi$
$719$	9.35171	+	16.1976i	0.348760	+	0.604070i	−0.637270	+	0.770641i	$0.719936\pi$
$720$		0			0
$721$	2.46407	+	0.850351i	0.0917668	+	0.0316687i
$722$		0			0
$723$	−3.58917	−	0.668348i	−0.133483	−	0.0248561i
$724$		0			0
$725$	−6.91086	−	3.98999i	−0.256663	−	0.148184i
$726$		0			0
$727$		−	23.0483i		−	0.854815i	−0.904059	−	0.427407i	$-0.859427\pi$
$727$		−	23.0483i		−	0.854815i	0.904059	−	0.427407i	$-0.140573\pi$
$728$		0			0
$729$	−12.1357	−	24.1190i	−0.449470	−	0.893295i
$730$		0			0
$731$	−6.79479	+	11.7689i	−0.251314	+	0.435289i
$732$		0			0
$733$	15.4109	−	8.89746i	0.569213	−	0.328635i	−0.187622	−	0.982241i	$-0.560078\pi$
$733$	15.4109	−	8.89746i	0.569213	−	0.328635i	0.756835	+	0.653606i	$0.226745\pi$
$734$		0			0
$735$	9.09846	−	8.01362i	0.335602	−	0.295587i
$736$		0			0
$737$	54.0824	−	31.2245i	1.99215	−	1.15017i
$738$		0			0
$739$	6.97258	−	12.0769i	0.256491	−	0.444255i	−0.708809	−	0.705401i	$-0.750767\pi$
$739$	6.97258	−	12.0769i	0.256491	−	0.444255i	0.965299	+	0.261146i	$0.0841004\pi$
$740$		0			0
$741$	27.1763	+	23.2504i	0.998345	+	0.854127i
$742$		0			0
$743$		−	30.8975i		−	1.13352i	−0.823883	−	0.566760i	$-0.808197\pi$
$743$		−	30.8975i		−	1.13352i	0.823883	−	0.566760i	$-0.191803\pi$
$744$		0			0
$745$	17.4366	+	10.0670i	0.638826	+	0.368826i
$746$		0			0
$747$	−17.8283	+	14.3873i	−0.652304	+	0.526404i
$748$		0			0
$749$	3.23010	+	1.11471i	0.118025	+	0.0407305i
$750$		0			0
$751$	−11.7085	−	20.2797i	−0.427249	−	0.740017i	0.569378	−	0.822076i	$-0.307184\pi$
$751$	−11.7085	−	20.2797i	−0.427249	−	0.740017i	−0.996628	+	0.0820583i	$0.973851\pi$
$752$		0			0
$753$	−48.7065	+	17.2016i	−1.77497	+	0.626862i
$754$		0			0
$755$	−4.77961			−0.173948
$756$		0			0
$757$	25.7901			0.937357			0.468679	−	0.883369i	$-0.344730\pi$
$757$	25.7901			0.937357			0.468679	+	0.883369i	$0.344730\pi$
$758$		0			0
$759$	18.3210	−	6.47041i	0.665011	−	0.234861i
$760$		0			0
$761$	9.03119	+	15.6425i	0.327380	+	0.567039i	0.981991	−	0.188927i	$-0.0605008\pi$
$761$	9.03119	+	15.6425i	0.327380	+	0.567039i	−0.654611	+	0.755966i	$0.727168\pi$
$762$		0			0
$763$	−19.1459	+	3.70788i	−0.693129	+	0.134234i
$764$		0			0
$765$	−7.15776	+	5.77625i	−0.258789	+	0.208841i
$766$		0			0
$767$	−13.5328	−	7.81318i	−0.488642	−	0.282118i
$768$		0			0
$769$		−	46.2208i		−	1.66677i	−0.552696	−	0.833383i	$-0.686401\pi$
$769$		−	46.2208i		−	1.66677i	0.552696	−	0.833383i	$-0.313599\pi$
$770$		0			0
$771$	17.8593	+	15.2794i	0.643188	+	0.550275i
$772$		0			0
$773$	−2.03651	+	3.52734i	−0.0732482	+	0.126870i	−0.900323	−	0.435222i	$-0.856670\pi$
$773$	−2.03651	+	3.52734i	−0.0732482	+	0.126870i	0.827075	+	0.562092i	$0.190003\pi$
$774$		0			0
$775$	5.63161	−	3.25141i	0.202293	−	0.116794i
$776$		0			0
$777$	−0.00431744	−	0.600290i	−0.000154887	−	0.0215353i
$778$		0			0
$779$	−36.4694	+	21.0556i	−1.30665	+	0.754397i
$780$		0			0
$781$	−7.08988	+	12.2800i	−0.253696	+	0.439414i
$782$		0			0
$783$	−35.2998	−	21.7550i	−1.26151	−	0.777459i
$784$		0			0
$785$			7.65317i			0.273153i
$786$		0			0
$787$	10.0876	+	5.82407i	0.359584	+	0.207606i	0.668898	−	0.743354i	$-0.266766\pi$
$787$	10.0876	+	5.82407i	0.359584	+	0.207606i	−0.309314	+	0.950960i	$0.600100\pi$
$788$		0			0
$789$	−20.7023	−	3.85503i	−0.737022	−	0.137243i
$790$		0			0
$791$	−9.04638	+	7.85295i	−0.321652	+	0.279219i
$792$		0			0
$793$	26.0774	+	45.1673i	0.926034	+	1.60394i
$794$		0			0
$795$	3.09113	+	8.75257i	0.109631	+	0.310422i
$796$		0			0
$797$	−36.7250			−1.30087			−0.650433	−	0.759564i	$-0.725412\pi$
$797$	−36.7250			−1.30087			−0.650433	+	0.759564i	$0.725412\pi$
$798$		0			0
$799$	−30.8407			−1.09106
$800$		0			0
$801$	−23.0561	−	8.89511i	−0.814647	−	0.314293i
$802$		0			0
$803$	−15.1558	−	26.2507i	−0.534837	−	0.926366i
$804$		0			0
$805$	1.44560	+	7.46446i	0.0509506	+	0.263088i
$806$		0			0
$807$	7.11532	−	38.2107i	0.250471	−	1.34508i
$808$		0			0
$809$	34.1224	+	19.7006i	1.19968	+	0.692635i	0.960484	−	0.278336i	$-0.0897829\pi$
$809$	34.1224	+	19.7006i	1.19968	+	0.692635i	0.239196	+	0.970971i	$0.423116\pi$
$810$		0			0
$811$		−	50.4733i		−	1.77236i	−0.463345	−	0.886178i	$-0.653351\pi$
$811$		−	50.4733i		−	1.77236i	0.463345	−	0.886178i	$-0.346649\pi$
$812$		0			0
$813$	9.35062	−	10.9295i	0.327941	−	0.383313i
$814$		0			0
$815$	−4.23749	+	7.33954i	−0.148433	+	0.257093i
$816$		0			0
$817$	−13.0727	+	7.54752i	−0.457355	+	0.264054i
$818$		0			0
$819$	8.46970	−	47.3748i	0.295955	−	1.65541i
$820$		0			0
$821$	−23.6817	+	13.6726i	−0.826498	+	0.477179i	−0.852652	−	0.522479i	$-0.825007\pi$
$821$	−23.6817	+	13.6726i	−0.826498	+	0.477179i	0.0261543	+	0.999658i	$0.491674\pi$
$822$		0			0
$823$	12.0437	−	20.8603i	0.419817	−	0.727144i	−0.576104	−	0.817377i	$-0.695428\pi$
$823$	12.0437	−	20.8603i	0.419817	−	0.727144i	0.995921	+	0.0902322i	$0.0287609\pi$
$824$		0			0
$825$	4.39544	−	5.13761i	0.153030	−	0.178869i
$826$		0			0
$827$			21.4026i			0.744242i	0.928184	+	0.372121i	$0.121369\pi$
$827$			21.4026i			0.744242i	−0.928184	+	0.372121i	$0.878631\pi$
$828$		0			0
$829$	27.3957	+	15.8169i	0.951494	+	0.549345i	0.893545	−	0.448974i	$-0.148211\pi$
$829$	27.3957	+	15.8169i	0.951494	+	0.549345i	0.0579490	+	0.998320i	$0.481544\pi$
$830$		0			0
$831$	1.92053	−	10.3137i	0.0666225	−	0.357777i
$832$		0			0
$833$	−16.8936	−	13.2363i	−0.585328	−	0.458610i
$834$		0			0
$835$	10.2835	+	17.8115i	0.355874	+	0.616392i
$836$		0			0
$837$	29.7357	−	16.0478i	1.02782	−	0.554691i
$838$		0			0
$839$	−40.4562			−1.39670			−0.698351	−	0.715755i	$-0.746083\pi$
$839$	−40.4562			−1.39670			−0.698351	+	0.715755i	$0.746083\pi$
$840$		0			0
$841$	−34.6799			−1.19586
$842$		0			0
$843$	10.1383	+	28.7068i	0.349183	+	0.988716i
$844$		0			0
$845$	−11.8818	−	20.5798i	−0.408745	−	0.707968i
$846$		0			0
$847$	3.65809	−	10.6001i	0.125693	−	0.364224i
$848$		0			0
$849$	−13.9766	−	2.60263i	−0.479677	−	0.0893220i
$850$		0			0
$851$	0.326015	+	0.188225i	0.0111756	+	0.00645226i
$852$		0			0
$853$			45.7681i			1.56707i	0.621347	+	0.783536i	$0.286586\pi$
$853$			45.7681i			1.56707i	−0.621347	+	0.783536i	$0.713414\pi$
$854$		0			0
$855$	−10.0936	+	1.58120i	−0.345193	+	0.0540758i
$856$		0			0
$857$	2.95930	−	5.12566i	0.101088	−	0.175089i	−0.811045	−	0.584983i	$-0.801101\pi$
$857$	2.95930	−	5.12566i	0.101088	−	0.175089i	0.912133	+	0.409894i	$0.134434\pi$
$858$		0			0
$859$	18.8859	−	10.9038i	0.644377	−	0.372031i	−0.141921	−	0.989878i	$-0.545328\pi$
$859$	18.8859	−	10.9038i	0.644377	−	0.372031i	0.786299	+	0.617847i	$0.211995\pi$
$860$		0			0
$861$	49.2764	+	27.9791i	1.67933	+	0.953526i
$862$		0			0
$863$	−32.8100	+	18.9429i	−1.11687	+	0.644823i	−0.940599	−	0.339519i	$-0.889736\pi$
$863$	−32.8100	+	18.9429i	−1.11687	+	0.644823i	−0.176267	+	0.984342i	$0.556402\pi$
$864$		0			0
$865$	8.30340	−	14.3819i	0.282324	−	0.489000i
$866$		0			0
$867$	−10.0027	−	8.55769i	−0.339708	−	0.290634i
$868$		0			0
$869$		−	9.54910i		−	0.323931i
$870$		0			0
$871$	84.0032	+	48.4993i	2.84634	+	1.64334i
$872$		0			0
$873$	10.8328	+	13.4237i	0.366636	+	0.454325i
$874$		0			0
$875$	1.73439	+	1.99797i	0.0586331	+	0.0675438i
$876$		0			0
$877$	26.8427	+	46.4929i	0.906412	+	1.56995i	0.819010	+	0.573779i	$0.194523\pi$
$877$	26.8427	+	46.4929i	0.906412	+	1.56995i	0.0874025	+	0.996173i	$0.472143\pi$
$878$		0			0
$879$	−6.34674	+	2.24147i	−0.214070	+	0.0756029i
$880$		0			0
$881$	−1.12570			−0.0379259			−0.0189630	−	0.999820i	$-0.506036\pi$
$881$	−1.12570			−0.0379259			−0.0189630	+	0.999820i	$0.506036\pi$
$882$		0			0
$883$	−48.0889			−1.61832			−0.809161	−	0.587587i	$-0.800078\pi$
$883$	−48.0889			−1.61832			−0.809161	+	0.587587i	$0.800078\pi$
$884$		0			0
$885$	4.20907	−	1.48651i	0.141486	−	0.0499685i
$886$		0			0
$887$	−25.9434	−	44.9352i	−0.871093	−	1.50878i	−0.860867	−	0.508829i	$-0.830078\pi$
$887$	−25.9434	−	44.9352i	−0.871093	−	1.50878i	−0.0102253	−	0.999948i	$-0.503255\pi$
$888$		0			0
$889$	1.21556	+	1.40029i	0.0407684	+	0.0469641i
$890$		0			0
$891$	23.5964	−	26.0291i	0.790509	−	0.872008i
$892$		0			0
$893$	−29.6676	−	17.1286i	−0.992789	−	0.573187i
$894$		0			0
$895$			0.388257i			0.0129780i
$896$		0			0
$897$	22.9322	+	19.6195i	0.765684	+	0.655075i
$898$		0			0
$899$	25.9462	−	44.9401i	0.865353	−	1.49884i
$900$		0			0
$901$	14.2295	−	8.21540i	0.474053	−	0.273695i
$902$		0			0
$903$	17.6634	+	10.0293i	0.587801	+	0.333754i
$904$		0			0
$905$	17.9084	−	10.3394i	0.595296	−	0.343695i
$906$		0			0
$907$	3.57234	−	6.18747i	0.118618	−	0.205452i	−0.800602	−	0.599196i	$-0.795487\pi$
$907$	3.57234	−	6.18747i	0.118618	−	0.205452i	0.919220	+	0.393744i	$0.128820\pi$
$908$		0			0
$909$	4.22049	+	26.9415i	0.139985	+	0.893594i
$910$		0			0
$911$		−	38.4884i		−	1.27518i	−0.770377	−	0.637589i	$-0.779932\pi$
$911$		−	38.4884i		−	1.27518i	0.770377	−	0.637589i	$-0.220068\pi$
$912$		0			0
$913$	−25.8162	−	14.9050i	−0.854392	−	0.493283i
$914$		0			0
$915$	−14.6468	−	2.72742i	−0.484209	−	0.0901659i
$916$		0			0
$917$	−4.59217	+	13.3068i	−0.151647	+	0.439429i
$918$		0			0
$919$	−27.0403	−	46.8351i	−0.891976	−	1.54495i	−0.837503	−	0.546433i	$-0.815985\pi$
$919$	−27.0403	−	46.8351i	−0.891976	−	1.54495i	−0.0544730	−	0.998515i	$-0.517348\pi$
$920$		0			0
$921$	−0.0690741	−	0.195584i	−0.00227607	−	0.00644471i
$922$		0			0
$923$	−22.0246			−0.724950
$924$		0			0
$925$	0.130997			0.00430717
$926$		0			0
$927$	−1.06388	+	2.75758i	−0.0349425	+	0.0905709i
$928$		0			0
$929$	18.8140	+	32.5869i	0.617269	+	1.06914i	0.989982	+	0.141194i	$0.0450942\pi$
$929$	18.8140	+	32.5869i	0.617269	+	1.06914i	−0.372713	+	0.927947i	$0.621573\pi$
$930$		0			0
$931$	−8.89970	−	22.1154i	−0.291676	−	0.724802i
$932$		0			0
$933$	−4.16773	+	22.3816i	−0.136445	+	0.732740i
$934$		0			0
$935$	−10.3648	−	5.98410i	−0.338964	−	0.195701i
$936$		0			0
$937$		−	3.05652i		−	0.0998522i	−0.998753	−	0.0499261i	$-0.984101\pi$
$937$		−	3.05652i		−	0.0998522i	0.998753	−	0.0499261i	$-0.0158986\pi$
$938$		0			0
$939$	−26.2008	+	30.6248i	−0.855030	+	0.999402i
$940$		0			0
$941$	27.3577	−	47.3849i	0.891835	−	1.54470i	0.0541612	−	0.998532i	$-0.482752\pi$
$941$	27.3577	−	47.3849i	0.891835	−	1.54470i	0.837674	−	0.546171i	$-0.183915\pi$
$942$		0			0
$943$	−30.7741	+	17.7674i	−1.00214	+	0.578587i
$944$		0			0
$945$	8.71039	+	10.6362i	0.283349	+	0.345996i
$946$		0			0
$947$	−6.20664	+	3.58341i	−0.201689	+	0.116445i	−0.597443	−	0.801911i	$-0.703817\pi$
$947$	−6.20664	+	3.58341i	−0.201689	+	0.116445i	0.395754	+	0.918356i	$0.370483\pi$
$948$		0			0
$949$	23.5407	−	40.7737i	0.764164	−	1.32357i
$950$		0			0
$951$	39.1266	−	45.7332i	1.26877	−	1.48300i
$952$		0			0
$953$			0.140553i			0.00455295i	0.999997	+	0.00227648i	$0.000724625\pi$
$953$			0.140553i			0.00455295i	−0.999997	+	0.00227648i	$0.999275\pi$
$954$		0			0
$955$	−15.2933	−	8.82961i	−0.494881	−	0.285720i
$956$		0			0
$957$	9.87729	−	53.0431i	0.319287	−	1.71464i
$958$		0			0
$959$	−1.97446	−	10.1953i	−0.0637586	−	0.329222i
$960$		0			0
$961$	5.64335	+	9.77457i	0.182043	+	0.315309i
$962$		0			0
$963$	−1.39462	+	3.61485i	−0.0449410	+	0.116487i
$964$		0			0
$965$	21.3806			0.688266
$966$		0			0
$967$	21.4958			0.691258			0.345629	−	0.938371i	$-0.387666\pi$
$967$	21.4958			0.691258			0.345629	+	0.938371i	$0.387666\pi$
$968$		0			0
$969$	6.02238	+	17.0524i	0.193467	+	0.547802i
$970$		0			0
$971$	7.37642	+	12.7763i	0.236721	+	0.410012i	0.959771	−	0.280783i	$-0.0905940\pi$
$971$	7.37642	+	12.7763i	0.236721	+	0.410012i	−0.723051	+	0.690795i	$0.757261\pi$
$972$		0			0
$973$	32.3123	−	28.0496i	1.03589	−	0.899228i
$974$		0			0
$975$	10.3245	+	1.92254i	0.330647	+	0.0615707i
$976$		0			0
$977$	−1.07585	−	0.621141i	−0.0344194	−	0.0198720i	0.482692	−	0.875790i	$-0.339659\pi$
$977$	−1.07585	−	0.621141i	−0.0344194	−	0.0198720i	−0.517111	+	0.855918i	$0.672993\pi$
$978$		0			0
$979$		−	32.1561i		−	1.02771i
$980$		0			0
$981$	−3.42232	−	21.8464i	−0.109266	−	0.697501i
$982$		0			0
$983$	−6.04373	+	10.4680i	−0.192765	+	0.333879i	−0.946166	−	0.323683i	$-0.895079\pi$
$983$	−6.04373	+	10.4680i	−0.192765	+	0.333879i	0.753401	+	0.657562i	$0.228412\pi$
$984$		0			0
$985$	−19.4917	+	11.2535i	−0.621056	+	0.358567i
$986$		0			0
$987$	0.331534	+	46.0959i	0.0105528	+	1.46725i
$988$		0			0
$989$	−11.0311	+	6.36883i	−0.350770	+	0.202517i
$990$		0			0
$991$	−4.50767	+	7.80752i	−0.143191	+	0.248014i	−0.928697	−	0.370841i	$-0.879070\pi$
$991$	−4.50767	+	7.80752i	−0.143191	+	0.248014i	0.785506	+	0.618854i	$0.212403\pi$
$992$		0			0
$993$	−33.6988	−	28.8307i	−1.06940	−	0.914915i
$994$		0			0
$995$		−	9.79801i		−	0.310618i
$996$		0			0
$997$	−37.2746	−	21.5205i	−1.18050	−	0.681562i	−0.224370	−	0.974504i	$-0.572032\pi$
$997$	−37.2746	−	21.5205i	−1.18050	−	0.681562i	−0.956130	+	0.292942i	$0.905366\pi$
$998$		0			0
$999$	0.680401	+	0.0195419i	0.0215270	+	0.000618278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bh.b.101.1	yes	10
3.2	odd	2		420.2.bh.a.101.3	✓	10
5.2	odd	4		2100.2.bo.g.1949.7		20
5.3	odd	4		2100.2.bo.g.1949.4		20
5.4	even	2		2100.2.bi.j.101.5		10
7.3	odd	6		2940.2.d.b.881.1		10
7.4	even	3		2940.2.d.a.881.10		10
7.5	odd	6		420.2.bh.a.341.3	yes	10
15.2	even	4		2100.2.bo.h.1949.1		20
15.8	even	4		2100.2.bo.h.1949.10		20
15.14	odd	2		2100.2.bi.k.101.3		10
21.5	even	6	inner	420.2.bh.b.341.1	yes	10
21.11	odd	6		2940.2.d.b.881.2		10
21.17	even	6		2940.2.d.a.881.9		10
35.12	even	12		2100.2.bo.h.1349.10		20
35.19	odd	6		2100.2.bi.k.1601.3		10
35.33	even	12		2100.2.bo.h.1349.1		20
105.47	odd	12		2100.2.bo.g.1349.4		20
105.68	odd	12		2100.2.bo.g.1349.7		20
105.89	even	6		2100.2.bi.j.1601.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.3	✓	10	3.2	odd	2
420.2.bh.a.341.3	yes	10	7.5	odd	6
420.2.bh.b.101.1	yes	10	1.1	even	1	trivial
420.2.bh.b.341.1	yes	10	21.5	even	6	inner
2100.2.bi.j.101.5		10	5.4	even	2
2100.2.bi.j.1601.5		10	105.89	even	6
2100.2.bi.k.101.3		10	15.14	odd	2
2100.2.bi.k.1601.3		10	35.19	odd	6
2100.2.bo.g.1349.4		20	105.47	odd	12
2100.2.bo.g.1349.7		20	105.68	odd	12
2100.2.bo.g.1949.4		20	5.3	odd	4
2100.2.bo.g.1949.7		20	5.2	odd	4
2100.2.bo.h.1349.1		20	35.33	even	12
2100.2.bo.h.1349.10		20	35.12	even	12
2100.2.bo.h.1949.1		20	15.2	even	4
2100.2.bo.h.1949.10		20	15.8	even	4
2940.2.d.a.881.9		10	21.17	even	6
2940.2.d.a.881.10		10	7.4	even	3
2940.2.d.b.881.1		10	7.3	odd	6
2940.2.d.b.881.2		10	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63319 + 0.576792i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.73439 - 1.99797i) q^{7} +(2.33462 - 1.88402i) q^{9} +O(q^{10})\)	\(q+(-1.63319 + 0.576792i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.73439 - 1.99797i) q^{7} +(2.33462 - 1.88402i) q^{9} +(3.38064 + 1.95181i) q^{11} +6.06329i q^{13} +(-1.31611 - 1.12599i) q^{15} +(-1.53296 + 2.65516i) q^{17} +(-2.94930 + 1.70278i) q^{19} +(3.98500 + 2.26269i) q^{21} +(-2.48871 + 1.43686i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.72620 + 4.42356i) q^{27} +7.97997i q^{29} +(-5.63161 - 3.25141i) q^{31} +(-6.64702 - 1.23776i) q^{33} +(0.863098 - 2.50101i) q^{35} +(-0.0654987 - 0.113447i) q^{37} +(-3.49726 - 9.90252i) q^{39} +12.3654 q^{41} +4.43247 q^{43} +(2.79892 + 1.07983i) q^{45} +(5.02960 + 8.71153i) q^{47} +(-0.983778 + 6.93053i) q^{49} +(0.972138 - 5.22058i) q^{51} +(-4.64119 - 2.67959i) q^{53} +3.90363i q^{55} +(3.83462 - 4.48210i) q^{57} +(-1.28860 + 2.23193i) q^{59} +(7.44930 - 4.30086i) q^{61} +(-7.81337 - 1.39688i) q^{63} +(-5.25097 + 3.03165i) q^{65} +(7.99884 - 13.8544i) q^{67} +(3.23578 - 3.78214i) q^{69} +3.63245i q^{71} +(-6.72468 - 3.88250i) q^{73} +(0.317079 - 1.70278i) q^{75} +(-1.96368 - 10.1396i) q^{77} +(-1.22311 - 2.11848i) q^{79} +(1.90093 - 8.79696i) q^{81} -7.63648 q^{83} -3.06592 q^{85} +(-4.60278 - 13.0328i) q^{87} +(-4.11874 - 7.13387i) q^{89} +(12.1143 - 10.5161i) q^{91} +(11.0729 + 2.06191i) q^{93} +(-2.94930 - 1.70278i) q^{95} +5.74985i q^{97} +(11.5698 - 1.81245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more