LMFDB - Embedded newform 850.2.s.b.57.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(7,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 11]))

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

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

chi := DirichletCharacter("850.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.2
Character	$\chi$	$=$	850.57
Dual form			850.2.s.b.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 - 0.923880i) q^{2} +(0.828527 - 1.23998i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-1.46265 - 0.290940i) q^{6} +(0.683252 - 3.43494i) q^{7} +(0.923880 + 0.382683i) q^{8} +(0.296960 + 0.716925i) q^{9} +(0.279207 - 1.40367i) q^{11} +(0.290940 + 1.46265i) q^{12} -0.687320i q^{13} +(-3.43494 + 0.683252i) q^{14} -1.00000i q^{16} +(1.10961 - 3.97099i) q^{17} +(0.548711 - 0.548711i) q^{18} +(-0.0862003 + 0.208106i) q^{19} +(-3.69316 - 3.69316i) q^{21} +(-1.40367 + 0.279207i) q^{22} +(-0.536616 + 0.358556i) q^{23} +(1.23998 - 0.828527i) q^{24} +(-0.635001 + 0.263026i) q^{26} +(5.52298 + 1.09859i) q^{27} +(1.94574 + 2.91200i) q^{28} +(-3.16366 + 4.73475i) q^{29} +(-2.14661 - 10.7917i) q^{31} +(-0.923880 + 0.382683i) q^{32} +(-1.50919 - 1.50919i) q^{33} +(-4.09335 + 0.494483i) q^{34} +(-0.716925 - 0.296960i) q^{36} +(-0.351736 - 0.235023i) q^{37} +0.225252 q^{38} +(-0.852262 - 0.569463i) q^{39} +(-1.49783 - 2.24166i) q^{41} +(-1.99872 + 4.82535i) q^{42} +(-1.23847 + 2.98993i) q^{43} +(0.795115 + 1.18997i) q^{44} +(0.536616 + 0.358556i) q^{46} -4.97288 q^{47} +(-1.23998 - 0.828527i) q^{48} +(-4.86483 - 2.01508i) q^{49} +(-4.00460 - 4.66597i) q^{51} +(0.486008 + 0.486008i) q^{52} +(2.60552 - 1.07924i) q^{53} +(-1.09859 - 5.52298i) q^{54} +(1.94574 - 2.91200i) q^{56} +(0.186628 + 0.279308i) q^{57} +(5.58502 + 1.11093i) q^{58} +(2.73373 - 1.13235i) q^{59} +(-11.0227 + 7.36516i) q^{61} +(-9.14879 + 6.11303i) q^{62} +(2.66550 - 0.530200i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-0.816768 + 1.97185i) q^{66} +(5.28482 - 5.28482i) q^{67} +(2.02330 + 3.59253i) q^{68} +0.962466i q^{69} +(10.6099 - 2.11045i) q^{71} +0.775994i q^{72} +(-1.91332 - 9.61892i) q^{73} +(-0.0825290 + 0.414901i) q^{74} +(-0.0862003 - 0.208106i) q^{76} +(-4.63076 - 1.91812i) q^{77} +(-0.199969 + 1.00531i) q^{78} +(1.79628 + 0.357303i) q^{79} +(4.29203 - 4.29203i) q^{81} +(-1.49783 + 2.24166i) q^{82} +(0.978574 + 2.36249i) q^{83} +5.22292 q^{84} +3.23628 q^{86} +(3.24981 + 7.84575i) q^{87} +(0.795115 - 1.18997i) q^{88} +(-9.75720 + 9.75720i) q^{89} +(-2.36090 - 0.469613i) q^{91} +(0.125908 - 0.632982i) q^{92} +(-15.1601 - 6.27950i) q^{93} +(1.90304 + 4.59434i) q^{94} +(-0.290940 + 1.46265i) q^{96} +(1.72004 + 8.64723i) q^{97} +5.26566i q^{98} +(1.08924 - 0.216663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 16 q^{7} - 8 q^{9} - 16 q^{18} - 8 q^{22} - 32 q^{23} + 8 q^{27} - 16 q^{29} + 16 q^{31} + 8 q^{33} + 16 q^{34} + 48 q^{37} - 32 q^{39} + 48 q^{41} + 16 q^{42} - 8 q^{43} + 16 q^{44} + 32 q^{46}+ \cdots + 24 q^{99}+O(q^{100}) $ 24 * q + 8 * q^3 - 16 * q^7 - 8 * q^9 - 16 * q^18 - 8 * q^22 - 32 * q^23 + 8 * q^27 - 16 * q^29 + 16 * q^31 + 8 * q^33 + 16 * q^34 + 48 * q^37 - 32 * q^39 + 48 * q^41 + 16 * q^42 - 8 * q^43 + 16 * q^44 + 32 * q^46 - 16 * q^47 - 16 * q^49 + 64 * q^51 + 32 * q^53 - 48 * q^54 + 8 * q^59 + 16 * q^61 - 16 * q^62 + 64 * q^63 + 8 * q^66 + 48 * q^67 - 32 * q^71 - 8 * q^73 - 64 * q^77 - 16 * q^78 - 16 * q^79 - 56 * q^81 + 48 * q^82 - 48 * q^83 + 32 * q^84 - 16 * q^86 - 16 * q^87 + 16 * q^88 + 48 * q^89 - 48 * q^91 + 64 * q^93 - 32 * q^94 + 64 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.382683	−	0.923880i	−0.270598	−	0.653281i
$2$	−0.382683	−	0.923880i	−0.270598	−	0.653281i
$3$	0.828527	−	1.23998i	0.478351	−	0.715902i	−0.511300	−	0.859402i	$-0.670836\pi$
$3$	0.828527	−	1.23998i	0.478351	−	0.715902i	0.989650	+	0.143500i	$0.0458358\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−1.46265	−	0.290940i	−0.597126	−	0.118776i
$7$	0.683252	−	3.43494i	0.258245	−	1.29829i	−0.606101	−	0.795388i	$-0.707267\pi$
$7$	0.683252	−	3.43494i	0.258245	−	1.29829i	0.864346	−	0.502898i	$-0.167733\pi$
$8$	0.923880	+	0.382683i	0.326641	+	0.135299i
$9$	0.296960	+	0.716925i	0.0989867	+	0.238975i
$10$		0			0
$11$	0.279207	−	1.40367i	0.0841842	−	0.423222i	−0.915593	−	0.402107i	$-0.868278\pi$
$11$	0.279207	−	1.40367i	0.0841842	−	0.423222i	0.999777	−	0.0211159i	$-0.00672189\pi$
$12$	0.290940	+	1.46265i	0.0839872	+	0.422232i
$13$		−	0.687320i		−	0.190628i	−0.995447	−	0.0953141i	$-0.969614\pi$
$13$		−	0.687320i		−	0.190628i	0.995447	−	0.0953141i	$-0.0303855\pi$
$14$	−3.43494	+	0.683252i	−0.918027	+	0.182607i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	1.10961	−	3.97099i	0.269121	−	0.963106i
$17$	1.10961	−	3.97099i	0.269121	−	0.963106i
$18$	0.548711	−	0.548711i	0.129332	−	0.129332i
$19$	−0.0862003	+	0.208106i	−0.0197757	+	0.0477428i	−0.933459	−	0.358684i	$-0.883225\pi$
$19$	−0.0862003	+	0.208106i	−0.0197757	+	0.0477428i	0.913683	+	0.406427i	$0.133225\pi$
$20$		0			0
$21$	−3.69316	−	3.69316i	−0.805914	−	0.805914i
$22$	−1.40367	+	0.279207i	−0.299263	+	0.0595272i
$23$	−0.536616	+	0.358556i	−0.111892	+	0.0747640i	−0.610257	−	0.792203i	$-0.708934\pi$
$23$	−0.536616	+	0.358556i	−0.111892	+	0.0747640i	0.498365	+	0.866967i	$0.333934\pi$
$24$	1.23998	−	0.828527i	0.253110	−	0.169122i
$25$		0			0
$26$	−0.635001	+	0.263026i	−0.124534	+	0.0515836i
$27$	5.52298	+	1.09859i	1.06290	+	0.211423i
$28$	1.94574	+	2.91200i	0.367710	+	0.550317i
$29$	−3.16366	+	4.73475i	−0.587477	+	0.879222i	−0.999489	−	0.0319568i	$-0.989826\pi$
$29$	−3.16366	+	4.73475i	−0.587477	+	0.879222i	0.412012	+	0.911178i	$0.364826\pi$
$30$		0			0
$31$	−2.14661	−	10.7917i	−0.385542	−	1.93825i	−0.343548	−	0.939135i	$-0.611629\pi$
$31$	−2.14661	−	10.7917i	−0.385542	−	1.93825i	−0.0419943	−	0.999118i	$-0.513371\pi$
$32$	−0.923880	+	0.382683i	−0.163320	+	0.0676495i
$33$	−1.50919	−	1.50919i	−0.262716	−	0.262716i
$34$	−4.09335	+	0.494483i	−0.702003	+	0.0848032i
$35$		0			0
$36$	−0.716925	−	0.296960i	−0.119488	−	0.0494934i
$37$	−0.351736	−	0.235023i	−0.0578251	−	0.0386375i	0.526322	−	0.850286i	$-0.323571\pi$
$37$	−0.351736	−	0.235023i	−0.0578251	−	0.0386375i	−0.584147	+	0.811648i	$0.698571\pi$
$38$	0.225252			0.0365408
$39$	−0.852262	−	0.569463i	−0.136471	−	0.0911871i
$40$		0			0
$41$	−1.49783	−	2.24166i	−0.233922	−	0.350089i	0.695874	−	0.718164i	$-0.255017\pi$
$41$	−1.49783	−	2.24166i	−0.233922	−	0.350089i	−0.929796	+	0.368075i	$0.880017\pi$
$42$	−1.99872	+	4.82535i	−0.308410	+	0.744568i
$43$	−1.23847	+	2.98993i	−0.188865	+	0.455960i	−0.989742	−	0.142869i	$-0.954367\pi$
$43$	−1.23847	+	2.98993i	−0.188865	+	0.455960i	0.800877	+	0.598829i	$0.204367\pi$
$44$	0.795115	+	1.18997i	0.119868	+	0.179395i
$45$		0			0
$46$	0.536616	+	0.358556i	0.0791198	+	0.0528661i
$47$	−4.97288			−0.725369			−0.362685	−	0.931912i	$-0.618140\pi$
$47$	−4.97288			−0.725369			−0.362685	+	0.931912i	$0.618140\pi$
$48$	−1.23998	−	0.828527i	−0.178976	−	0.119588i
$49$	−4.86483	−	2.01508i	−0.694976	−	0.287869i
$50$		0			0
$51$	−4.00460	−	4.66597i	−0.560756	−	0.653367i
$52$	0.486008	+	0.486008i	0.0673973	+	0.0673973i
$53$	2.60552	−	1.07924i	0.357896	−	0.148245i	−0.196488	−	0.980506i	$-0.562954\pi$
$53$	2.60552	−	1.07924i	0.357896	−	0.148245i	0.554384	+	0.832261i	$0.312954\pi$
$54$	−1.09859	−	5.52298i	−0.149499	−	0.751582i
$55$		0			0
$56$	1.94574	−	2.91200i	0.260010	−	0.389133i
$57$	0.186628	+	0.279308i	0.0247195	+	0.0369953i
$58$	5.58502	+	1.11093i	0.733349	+	0.145872i
$59$	2.73373	−	1.13235i	0.355902	−	0.147419i	−0.197567	−	0.980289i	$-0.563304\pi$
$59$	2.73373	−	1.13235i	0.355902	−	0.147419i	0.553468	+	0.832870i	$0.313304\pi$
$60$		0			0
$61$	−11.0227	+	7.36516i	−1.41132	+	0.943012i	−0.411821	+	0.911265i	$0.635107\pi$
$61$	−11.0227	+	7.36516i	−1.41132	+	0.943012i	−0.999496	+	0.0317466i	$0.989893\pi$
$62$	−9.14879	+	6.11303i	−1.16190	+	0.776355i
$63$	2.66550	−	0.530200i	0.335821	−	0.0667989i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	−0.816768	+	1.97185i	−0.100537	+	0.242718i
$67$	5.28482	−	5.28482i	0.645644	−	0.645644i	−0.306293	−	0.951937i	$-0.599089\pi$
$67$	5.28482	−	5.28482i	0.645644	−	0.645644i	0.951937	+	0.306293i	$0.0990888\pi$
$68$	2.02330	+	3.59253i	0.245361	+	0.435658i
$69$			0.962466i			0.115867i
$70$		0			0
$71$	10.6099	−	2.11045i	1.25917	−	0.250464i	0.479995	−	0.877271i	$-0.340639\pi$
$71$	10.6099	−	2.11045i	1.25917	−	0.250464i	0.779174	+	0.626807i	$0.215639\pi$
$72$			0.775994i			0.0914518i
$73$	−1.91332	−	9.61892i	−0.223937	−	1.12581i	−0.915136	−	0.403145i	$-0.867917\pi$
$73$	−1.91332	−	9.61892i	−0.223937	−	1.12581i	0.691199	−	0.722665i	$-0.257083\pi$
$74$	−0.0825290	+	0.414901i	−0.00959380	+	0.0482313i
$75$		0			0
$76$	−0.0862003	−	0.208106i	−0.00988786	−	0.0238714i
$77$	−4.63076	−	1.91812i	−0.527724	−	0.218590i
$78$	−0.199969	+	1.00531i	−0.0226420	+	0.113829i
$79$	1.79628	+	0.357303i	0.202098	+	0.0401997i	0.295101	−	0.955466i	$-0.404647\pi$
$79$	1.79628	+	0.357303i	0.202098	+	0.0401997i	−0.0930034	+	0.995666i	$0.529647\pi$
$80$		0			0
$81$	4.29203	−	4.29203i	0.476892	−	0.476892i
$82$	−1.49783	+	2.24166i	−0.165408	+	0.247550i
$83$	0.978574	+	2.36249i	0.107412	+	0.259317i	0.968442	−	0.249238i	$-0.0801801\pi$
$83$	0.978574	+	2.36249i	0.107412	+	0.259317i	−0.861030	+	0.508554i	$0.830180\pi$
$84$	5.22292			0.569867
$85$		0			0
$86$	3.23628			0.348977
$87$	3.24981	+	7.84575i	0.348417	+	0.841152i
$88$	0.795115	−	1.18997i	0.0847596	−	0.126852i
$89$	−9.75720	+	9.75720i	−1.03426	+	1.03426i	−0.0348693	+	0.999392i	$0.511101\pi$
$89$	−9.75720	+	9.75720i	−1.03426	+	1.03426i	−0.999392	+	0.0348693i	$0.988899\pi$
$90$		0			0
$91$	−2.36090	−	0.469613i	−0.247490	−	0.0492288i
$92$	0.125908	−	0.632982i	0.0131268	−	0.0659929i
$93$	−15.1601	−	6.27950i	−1.57202	−	0.651154i
$94$	1.90304	+	4.59434i	0.196284	+	0.473870i
$95$		0			0
$96$	−0.290940	+	1.46265i	−0.0296940	+	0.149282i
$97$	1.72004	+	8.64723i	0.174644	+	0.877993i	0.964375	+	0.264540i	$0.0852200\pi$
$97$	1.72004	+	8.64723i	0.174644	+	0.877993i	−0.789731	+	0.613453i	$0.789780\pi$
$98$			5.26566i			0.531912i
$99$	1.08924	−	0.216663i	0.109473	−	0.0217755i
$100$		0			0
$101$			13.2302i			1.31645i	0.752820	+	0.658226i	$0.228693\pi$
$101$			13.2302i			1.31645i	−0.752820	+	0.658226i	$0.771307\pi$
$102$	−2.77830	+	5.48536i	−0.275093	+	0.543131i
$103$	−12.8336	+	12.8336i	−1.26454	+	1.26454i	−0.315665	+	0.948871i	$0.602227\pi$
$103$	−12.8336	+	12.8336i	−1.26454	+	1.26454i	−0.948871	+	0.315665i	$0.897773\pi$
$104$	0.263026	−	0.635001i	0.0257918	−	0.0622669i
$105$		0			0
$106$	−1.99418	−	1.99418i	−0.193692	−	0.193692i
$107$	14.2388	−	2.83228i	1.37652	−	0.273807i	0.549273	−	0.835643i	$-0.314905\pi$
$107$	14.2388	−	2.83228i	1.37652	−	0.273807i	0.827249	+	0.561836i	$0.189905\pi$
$108$	−4.68215	+	3.12852i	−0.450540	+	0.301042i
$109$	10.7548	−	7.18615i	1.03013	−	0.688308i	0.0789251	−	0.996881i	$-0.474851\pi$
$109$	10.7548	−	7.18615i	1.03013	−	0.688308i	0.951201	+	0.308572i	$0.0998512\pi$
$110$		0			0
$111$	−0.582846	+	0.241423i	−0.0553213	+	0.0229148i
$112$	−3.43494	−	0.683252i	−0.324571	−	0.0645613i
$113$	−1.67335	−	2.50435i	−0.157416	−	0.235589i	0.744376	−	0.667761i	$-0.232747\pi$
$113$	−1.67335	−	2.50435i	−0.157416	−	0.235589i	−0.901791	+	0.432172i	$0.857747\pi$
$114$	0.186628	−	0.279308i	0.0174793	−	0.0261596i
$115$		0			0
$116$	−1.11093	−	5.58502i	−0.103147	−	0.518556i
$117$	0.492757	−	0.204107i	0.0455554	−	0.0188697i
$118$	−2.09231	−	2.09231i	−0.192613	−	0.192613i
$119$	−12.8820	−	6.52464i	−1.18089	−	0.598113i
$120$		0			0
$121$	8.27034	+	3.42569i	0.751849	+	0.311426i
$122$	11.0227	+	7.36516i	0.997951	+	0.666810i
$123$	−4.02061			−0.362526
$124$	9.14879	+	6.11303i	0.821586	+	0.548966i
$125$		0			0
$126$	−1.50988	−	2.25970i	−0.134511	−	0.201310i
$127$	4.77400	−	11.5255i	0.423624	−	1.02272i	−0.557645	−	0.830079i	$-0.688295\pi$
$127$	4.77400	−	11.5255i	0.423624	−	1.02272i	0.981270	−	0.192640i	$-0.0617049\pi$
$128$	0.382683	−	0.923880i	0.0338248	−	0.0816602i
$129$	2.68135	+	4.01292i	0.236079	+	0.353318i
$130$		0			0
$131$	16.3126	+	10.8997i	1.42524	+	0.952314i	0.998858	+	0.0477705i	$0.0152116\pi$
$131$	16.3126	+	10.8997i	1.42524	+	0.952314i	0.426381	+	0.904544i	$0.359788\pi$
$132$	2.13432			0.185769
$133$	0.655936	+	0.438282i	0.0568768	+	0.0380039i
$134$	−6.90495	−	2.86013i	−0.596497	−	0.247077i
$135$		0			0
$136$	2.54478	−	3.24409i	0.218213	−	0.278178i
$137$	−5.01618	−	5.01618i	−0.428561	−	0.428561i	0.459577	−	0.888138i	$-0.348001\pi$
$137$	−5.01618	−	5.01618i	−0.428561	−	0.428561i	−0.888138	+	0.459577i	$0.848001\pi$
$138$	0.889203	−	0.368320i	0.0756940	−	0.0313535i
$139$	−2.05197	−	10.3159i	−0.174045	−	0.874986i	−0.964827	−	0.262887i	$-0.915325\pi$
$139$	−2.05197	−	10.3159i	−0.174045	−	0.874986i	0.790781	−	0.612099i	$-0.209675\pi$
$140$		0			0
$141$	−4.12017	+	6.16627i	−0.346981	+	0.519294i
$142$	−6.01005	−	8.99468i	−0.504352	−	0.754817i
$143$	−0.964770	−	0.191905i	−0.0806781	−	0.0160479i
$144$	0.716925	−	0.296960i	0.0597438	−	0.0247467i
$145$		0			0
$146$	−8.15453	+	5.44868i	−0.674874	+	0.450936i
$147$	−6.52931	+	4.36274i	−0.538528	+	0.359833i
$148$	0.414901	−	0.0825290i	0.0341047	−	0.00678384i
$149$	3.74622	+	3.74622i	0.306902	+	0.306902i	0.843707	−	0.536804i	$-0.180369\pi$
$149$	3.74622	+	3.74622i	0.306902	+	0.306902i	−0.536804	+	0.843707i	$0.680369\pi$
$150$		0			0
$151$	−4.01503	+	9.69314i	−0.326738	+	0.788816i	0.672092	+	0.740468i	$0.265396\pi$
$151$	−4.01503	+	9.69314i	−0.326738	+	0.788816i	−0.998831	+	0.0483488i	$0.984604\pi$
$152$	−0.159277	+	0.159277i	−0.0129191	+	0.0129191i
$153$	3.17641	−	0.383716i	0.256798	−	0.0310216i
$154$			5.01229i			0.403902i
$155$		0			0
$156$	1.00531	−	0.199969i	0.0804894	−	0.0160103i
$157$		−	15.0303i		−	1.19955i	−0.800170	−	0.599773i	$-0.795258\pi$
$157$		−	15.0303i		−	1.19955i	0.800170	−	0.599773i	$-0.204742\pi$
$158$	−0.357303	−	1.79628i	−0.0284255	−	0.142905i
$159$	0.820509	−	4.12498i	0.0650706	−	0.327132i
$160$		0			0
$161$	0.864973	+	2.08823i	0.0681694	+	0.164576i
$162$	−5.60781	−	2.32283i	−0.440591	−	0.182499i
$163$	2.92232	−	14.6915i	0.228894	−	1.15073i	−0.679842	−	0.733358i	$-0.737952\pi$
$163$	2.92232	−	14.6915i	0.228894	−	1.15073i	0.908736	−	0.417370i	$-0.137048\pi$
$164$	2.64422	+	0.525968i	0.206479	+	0.0410712i
$165$		0			0
$166$	1.80817	−	1.80817i	0.140341	−	0.140341i
$167$	4.23161	−	6.33305i	0.327452	−	0.490066i	−0.630818	−	0.775930i	$-0.717281\pi$
$167$	4.23161	−	6.33305i	0.327452	−	0.490066i	0.958270	+	0.285865i	$0.0922807\pi$
$168$	−1.99872	−	4.82535i	−0.154205	−	0.372284i
$169$	12.5276			0.963661
$170$		0			0
$171$	−0.174795			−0.0133669
$172$	−1.23847	−	2.98993i	−0.0944324	−	0.227980i
$173$	10.0963	−	15.1101i	0.767606	−	1.14880i	−0.217366	−	0.976090i	$-0.569747\pi$
$173$	10.0963	−	15.1101i	0.767606	−	1.14880i	0.984972	−	0.172713i	$-0.0552534\pi$
$174$	6.00487	−	6.00487i	0.455228	−	0.455228i
$175$		0			0
$176$	−1.40367	−	0.279207i	−0.105806	−	0.0210460i
$177$	0.860883	−	4.32795i	0.0647080	−	0.325309i
$178$	12.7484	+	5.28056i	0.955533	+	0.395795i
$179$	4.94606	+	11.9408i	0.369686	+	0.892501i	0.993802	+	0.111169i	$0.0354594\pi$
$179$	4.94606	+	11.9408i	0.369686	+	0.892501i	−0.624116	+	0.781332i	$0.714541\pi$
$180$		0			0
$181$	−1.11267	+	5.59375i	−0.0827039	+	0.415780i	0.917148	+	0.398548i	$0.130486\pi$
$181$	−1.11267	+	5.59375i	−0.0827039	+	0.415780i	−0.999852	+	0.0172328i	$0.994514\pi$
$182$	0.469613	+	2.36090i	0.0348100	+	0.175002i
$183$			19.7702i			1.46145i
$184$	−0.632982	+	0.125908i	−0.0466641	+	0.00928206i
$185$		0			0
$186$			16.4091i			1.20318i
$187$	−5.26415	−	2.66626i	−0.384953	−	0.194976i
$188$	3.51636	−	3.51636i	0.256457	−	0.256457i
$189$	7.54717	−	18.2205i	0.548976	−	1.32535i
$190$		0			0
$191$	15.3527	+	15.3527i	1.11088	+	1.11088i	0.993032	+	0.117849i	$0.0375997\pi$
$191$	15.3527	+	15.3527i	1.11088	+	1.11088i	0.117849	+	0.993032i	$0.462400\pi$
$192$	1.46265	−	0.290940i	0.105558	−	0.0209968i
$193$	−0.487981	+	0.326059i	−0.0351257	+	0.0234702i	−0.573009	−	0.819549i	$-0.694224\pi$
$193$	−0.487981	+	0.326059i	−0.0351257	+	0.0234702i	0.537883	+	0.843019i	$0.319224\pi$
$194$	7.33077	−	4.89826i	0.526318	−	0.351675i
$195$		0			0
$196$	4.86483	−	2.01508i	0.347488	−	0.143934i
$197$	17.4717	+	3.47533i	1.24481	+	0.247607i	0.773177	−	0.634190i	$-0.218666\pi$
$197$	17.4717	+	3.47533i	1.24481	+	0.247607i	0.471629	+	0.881797i	$0.343666\pi$
$198$	−0.617005	−	0.923413i	−0.0438486	−	0.0656241i
$199$	1.99127	−	2.98014i	0.141157	−	0.211256i	−0.754154	−	0.656697i	$-0.771953\pi$
$199$	1.99127	−	2.98014i	0.141157	−	0.211256i	0.895311	+	0.445441i	$0.146953\pi$
$200$		0			0
$201$	−2.17445	−	10.9317i	−0.153374	−	0.771062i
$202$	12.2231	−	5.06297i	0.860014	−	0.356230i
$203$	14.1020	+	14.1020i	0.989768	+	0.989768i
$204$	6.13102	+	0.467660i	0.429257	+	0.0327428i
$205$		0			0
$206$	16.7680	+	6.94551i	1.16828	+	0.483917i
$207$	−0.416411	−	0.278237i	−0.0289426	−	0.0193388i
$208$	−0.687320			−0.0476571
$209$	0.268044	+	0.179102i	0.0185410	+	0.0123887i
$210$		0			0
$211$	2.56243	+	3.83494i	0.176405	+	0.264008i	0.909127	−	0.416520i	$-0.136750\pi$
$211$	2.56243	+	3.83494i	0.176405	+	0.264008i	−0.732722	+	0.680528i	$0.761750\pi$
$212$	−1.07924	+	2.60552i	−0.0741227	+	0.178948i
$213$	6.17372	−	14.9047i	0.423016	−	1.02125i
$214$	−8.06566	−	12.0711i	−0.551357	−	0.825164i
$215$		0			0
$216$	4.68215	+	3.12852i	0.318580	+	0.212868i
$217$	−38.5357			−2.61597
$218$	−10.7548	−	7.18615i	−0.728409	−	0.486707i
$219$	−13.5125	−	5.59706i	−0.913090	−	0.378214i
$220$		0			0
$221$	−2.72934	−	0.762659i	−0.183595	−	0.0513020i
$222$	0.446091	+	0.446091i	0.0299397	+	0.0299397i
$223$	−9.20723	+	3.81376i	−0.616562	+	0.255388i	−0.669031	−	0.743234i	$-0.733291\pi$
$223$	−9.20723	+	3.81376i	−0.616562	+	0.255388i	0.0524694	+	0.998623i	$0.483291\pi$
$224$	0.683252	+	3.43494i	0.0456517	+	0.229507i
$225$		0			0
$226$	−1.67335	+	2.50435i	−0.111310	+	0.166587i
$227$	8.86159	+	13.2623i	0.588164	+	0.880250i	0.999512	−	0.0312282i	$-0.00994186\pi$
$227$	8.86159	+	13.2623i	0.588164	+	0.880250i	−0.411348	+	0.911478i	$0.634942\pi$
$228$	−0.329466	−	0.0655350i	−0.0218195	−	0.00434016i
$229$	26.3976	−	10.9342i	1.74440	−	0.722554i	0.746004	−	0.665941i	$-0.231970\pi$
$229$	26.3976	−	10.9342i	1.74440	−	0.722554i	0.998396	−	0.0566131i	$-0.0180302\pi$
$230$		0			0
$231$	−6.21514	+	4.15282i	−0.408926	+	0.273236i
$232$	−4.73475	+	3.16366i	−0.310852	+	0.207704i
$233$	23.3415	−	4.64291i	1.52915	−	0.304167i	0.642384	−	0.766383i	$-0.277945\pi$
$233$	23.3415	−	4.64291i	1.52915	−	0.304167i	0.886768	+	0.462215i	$0.152945\pi$
$234$	−0.377140	−	0.377140i	−0.0246544	−	0.0246544i
$235$		0			0
$236$	−1.13235	+	2.73373i	−0.0737096	+	0.177951i
$237$	1.93132	−	1.93132i	0.125453	−	0.125453i
$238$	−1.09827	+	14.3983i	−0.0711901	+	0.933301i
$239$			22.2129i			1.43683i	0.695614	+	0.718416i	$0.255132\pi$
$239$			22.2129i			1.43683i	−0.695614	+	0.718416i	$0.744868\pi$
$240$		0			0
$241$	−8.55756	+	1.70220i	−0.551241	+	0.109649i	−0.462849	−	0.886437i	$-0.653173\pi$
$241$	−8.55756	+	1.70220i	−0.551241	+	0.109649i	−0.0883919	+	0.996086i	$0.528173\pi$
$242$		−	8.95175i		−	0.575440i
$243$	1.52980	+	7.69083i	0.0981369	+	0.493367i
$244$	2.58630	−	13.0022i	0.165571	−	0.832381i
$245$		0			0
$246$	1.53862	+	3.71456i	0.0980989	+	0.236832i
$247$	0.143035	+	0.0592472i	0.00910113	+	0.00376981i
$248$	2.14661	−	10.7917i	0.136310	−	0.685276i
$249$	3.74021	+	0.743974i	0.237026	+	0.0471474i
$250$		0			0
$251$	−7.55862	+	7.55862i	−0.477096	+	0.477096i	−0.904202	−	0.427106i	$-0.859533\pi$
$251$	−7.55862	+	7.55862i	−0.477096	+	0.477096i	0.427106	+	0.904202i	$0.359533\pi$
$252$	−1.50988	+	2.25970i	−0.0951136	+	0.142348i
$253$	0.353466	+	0.853344i	0.0222222	+	0.0536493i
$254$	−12.4751			−0.782755
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	9.60595	+	23.1908i	0.599203	+	1.44660i	0.874395	+	0.485215i	$0.161259\pi$
$257$	9.60595	+	23.1908i	0.599203	+	1.44660i	−0.275192	+	0.961389i	$0.588741\pi$
$258$	2.68135	−	4.01292i	0.166933	−	0.249833i
$259$	−1.04761	+	1.04761i	−0.0650955	+	0.0650955i
$260$		0			0
$261$	−4.33395	−	0.862075i	−0.268264	−	0.0533611i
$262$	3.82748	−	19.2420i	0.236462	−	1.18878i
$263$	8.53235	+	3.53421i	0.526127	+	0.217929i	0.629906	−	0.776671i	$-0.283093\pi$
$263$	8.53235	+	3.53421i	0.526127	+	0.217929i	−0.103779	+	0.994600i	$0.533093\pi$
$264$	−0.816768	−	1.97185i	−0.0502686	−	0.121359i
$265$		0			0
$266$	0.153904	−	0.773729i	0.00943647	−	0.0474404i
$267$	4.01461	+	20.1828i	0.245690	+	1.23517i
$268$			7.47387i			0.456539i
$269$	−3.39522	+	0.675351i	−0.207010	+	0.0411768i	−0.297506	−	0.954720i	$-0.596155\pi$
$269$	−3.39522	+	0.675351i	−0.207010	+	0.0411768i	0.0904959	+	0.995897i	$0.471155\pi$
$270$		0			0
$271$		−	20.2345i		−	1.22916i	−0.788855	−	0.614579i	$-0.789326\pi$
$271$		−	20.2345i		−	1.22916i	0.788855	−	0.614579i	$-0.210674\pi$
$272$	−3.97099	−	1.10961i	−0.240777	−	0.0672802i
$273$	−2.53838	+	2.53838i	−0.153630	+	0.153630i
$274$	−2.71474	+	6.55395i	−0.164003	+	0.395939i
$275$		0			0
$276$	−0.680566	−	0.680566i	−0.0409653	−	0.0409653i
$277$	−19.6598	+	3.91058i	−1.18124	+	0.234964i	−0.746372	−	0.665529i	$-0.768206\pi$
$277$	−19.6598	+	3.91058i	−1.18124	+	0.234964i	−0.434871	+	0.900493i	$0.643206\pi$
$278$	−8.74542	+	5.84350i	−0.524515	+	0.350470i
$279$	7.09941	−	4.74367i	0.425031	−	0.283996i
$280$		0			0
$281$	20.1942	−	8.36471i	1.20468	−	0.498997i	0.312175	−	0.950025i	$-0.398942\pi$
$281$	20.1942	−	8.36471i	1.20468	−	0.498997i	0.892510	+	0.451028i	$0.148942\pi$
$282$	7.27361	+	1.44681i	0.433137	+	0.0861563i
$283$	11.1466	+	16.6821i	0.662600	+	0.991650i	0.998757	+	0.0498445i	$0.0158726\pi$
$283$	11.1466	+	16.6821i	0.662600	+	0.991650i	−0.336157	+	0.941806i	$0.609127\pi$
$284$	−6.01005	+	8.99468i	−0.356631	+	0.533736i
$285$		0			0
$286$	0.191905	+	0.964770i	0.0113476	+	0.0570481i
$287$	−8.72338	+	3.61334i	−0.514925	+	0.213289i
$288$	−0.548711	−	0.548711i	−0.0323331	−	0.0323331i
$289$	−14.5375	−	8.81252i	−0.855148	−	0.518384i
$290$		0			0
$291$	12.1475	+	5.03165i	0.712098	+	0.294961i
$292$	8.15453	+	5.44868i	0.477208	+	0.318860i
$293$	−15.9816			−0.933653			−0.466826	−	0.884349i	$-0.654603\pi$
$293$	−15.9816			−0.933653			−0.466826	+	0.884349i	$0.654603\pi$
$294$	6.52931	+	4.36274i	0.380797	+	0.254440i
$295$		0			0
$296$	−0.235023	−	0.351736i	−0.0136604	−	0.0204443i
$297$	3.08411	−	7.44570i	0.178958	−	0.432044i
$298$	2.02744	−	4.89467i	0.117446	−	0.283541i
$299$	0.246442	+	0.368827i	0.0142521	+	0.0213298i
$300$		0			0
$301$	9.42405	+	6.29695i	0.543193	+	0.362950i
$302$	10.4918			0.603734
$303$	16.4052	+	10.9616i	0.942451	+	0.629726i
$304$	0.208106	+	0.0862003i	0.0119357	+	0.00494393i
$305$		0			0
$306$	−1.57007	−	2.78778i	−0.0897548	−	0.159367i
$307$	1.37631	+	1.37631i	0.0785503	+	0.0785503i	0.745290	−	0.666740i	$-0.232311\pi$
$307$	1.37631	+	1.37631i	0.0785503	+	0.0785503i	−0.666740	+	0.745290i	$0.732311\pi$
$308$	4.63076	−	1.91812i	0.263862	−	0.109295i
$309$	5.28042	+	26.5465i	0.300392	+	1.51018i
$310$		0			0
$311$	−11.6826	+	17.4843i	−0.662461	+	0.991442i	0.336304	+	0.941753i	$0.390823\pi$
$311$	−11.6826	+	17.4843i	−0.662461	+	0.991442i	−0.998765	+	0.0496889i	$0.984177\pi$
$312$	−0.569463	−	0.852262i	−0.0322395	−	0.0482498i
$313$	−27.8535	−	5.54040i	−1.57437	−	0.313162i	−0.670813	−	0.741627i	$-0.734055\pi$
$313$	−27.8535	−	5.54040i	−1.57437	−	0.313162i	−0.903559	+	0.428465i	$0.859055\pi$
$314$	−13.8862	+	5.75183i	−0.783641	+	0.324595i
$315$		0			0
$316$	−1.52281	+	1.01751i	−0.0856650	+	0.0572395i
$317$	−22.9967	+	15.3659i	−1.29162	+	0.863035i	−0.995741	−	0.0921896i	$-0.970613\pi$
$317$	−22.9967	+	15.3659i	−1.29162	+	0.863035i	−0.295882	+	0.955225i	$0.595613\pi$
$318$	−4.12498	+	0.820509i	−0.231317	+	0.0460119i
$319$	5.76271	+	5.76271i	0.322650	+	0.322650i
$320$		0			0
$321$	8.28531	−	20.0025i	0.462441	−	1.11643i
$322$	1.59826	−	1.59826i	0.0890676	−	0.0890676i
$323$	0.730738	+	0.573218i	0.0406593	+	0.0318947i
$324$			6.06985i			0.337214i
$325$		0			0
$326$	−14.6915	+	2.92232i	−0.813688	+	0.161853i
$327$		−	19.2897i		−	1.06672i
$328$	−0.525968	−	2.64422i	−0.0290418	−	0.146003i
$329$	−3.39773	+	17.0816i	−0.187323	+	0.941737i
$330$		0			0
$331$	−13.1660	−	31.7855i	−0.723668	−	1.74709i	−0.662620	−	0.748955i	$-0.730556\pi$
$331$	−13.1660	−	31.7855i	−0.723668	−	1.74709i	−0.0610482	−	0.998135i	$-0.519444\pi$
$332$	−2.36249	−	0.978574i	−0.129658	−	0.0537062i
$333$	0.0640420	−	0.321961i	0.00350948	−	0.0176434i
$334$	−7.47034	−	1.48594i	−0.408759	−	0.0813072i
$335$		0			0
$336$	−3.69316	+	3.69316i	−0.201479	+	0.201479i
$337$	−7.29265	+	10.9142i	−0.397256	+	0.594536i	−0.975142	−	0.221582i	$-0.928878\pi$
$337$	−7.29265	+	10.9142i	−0.397256	+	0.594536i	0.577886	+	0.816118i	$0.303878\pi$
$338$	−4.79410	−	11.5740i	−0.260765	−	0.629542i
$339$	−4.49175			−0.243959
$340$		0			0
$341$	−15.7474			−0.852769
$342$	0.0668910	+	0.161489i	0.00361705	+	0.00873233i
$343$	3.37457	−	5.05041i	0.182210	−	0.272696i
$344$	−2.28839	+	2.28839i	−0.123382	+	0.123382i
$345$		0			0
$346$	−17.8236	−	3.54534i	−0.958205	−	0.190599i
$347$	3.75756	−	18.8905i	0.201717	−	1.01410i	−0.738690	−	0.674045i	$-0.764555\pi$
$347$	3.75756	−	18.8905i	0.201717	−	1.01410i	0.940407	−	0.340052i	$-0.110445\pi$
$348$	−7.84575	−	3.24981i	−0.420576	−	0.174208i
$349$	−8.24203	−	19.8980i	−0.441186	−	1.06512i	−0.975533	−	0.219852i	$-0.929443\pi$
$349$	−8.24203	−	19.8980i	−0.441186	−	1.06512i	0.534347	−	0.845265i	$-0.320557\pi$
$350$		0			0
$351$	0.755082	−	3.79605i	0.0403033	−	0.202618i
$352$	0.279207	+	1.40367i	0.0148818	+	0.0748159i
$353$		−	7.84481i		−	0.417537i	−0.977965	−	0.208768i	$-0.933054\pi$
$353$		−	7.84481i		−	0.417537i	0.977965	−	0.208768i	$-0.0669455\pi$
$354$	−4.32795	+	0.860883i	−0.230028	+	0.0457554i
$355$		0			0
$356$		−	13.7988i		−	0.731333i
$357$	−18.7635	+	10.5675i	−0.993069	+	0.559293i
$358$	9.13913	−	9.13913i	0.483018	−	0.483018i
$359$	4.46689	−	10.7840i	0.235753	−	0.569159i	−0.761082	−	0.648656i	$-0.775331\pi$
$359$	4.46689	−	10.7840i	0.235753	−	0.569159i	0.996835	+	0.0794970i	$0.0253314\pi$
$360$		0			0
$361$	13.3992	+	13.3992i	0.705218	+	0.705218i
$362$	5.59375	−	1.11267i	0.294001	−	0.0584805i
$363$	11.1000	−	7.41677i	0.582598	−	0.389280i
$364$	2.00148	−	1.33734i	0.104906	−	0.0700959i
$365$		0			0
$366$	18.2653	−	7.56573i	0.954741	−	0.395467i
$367$	14.7935	+	2.94262i	0.772216	+	0.153603i	0.565445	−	0.824786i	$-0.308704\pi$
$367$	14.7935	+	2.94262i	0.772216	+	0.153603i	0.206771	+	0.978389i	$0.433704\pi$
$368$	0.358556	+	0.536616i	0.0186910	+	0.0279731i
$369$	1.16231	−	1.73952i	0.0605074	−	0.0905557i
$370$		0			0
$371$	−1.92691	−	9.68722i	−0.100040	−	0.502935i
$372$	15.1601	−	6.27950i	0.786012	−	0.325577i
$373$	0.0702693	+	0.0702693i	0.00363841	+	0.00363841i	0.708924	−	0.705285i	$-0.249181\pi$
$373$	0.0702693	+	0.0702693i	0.00363841	+	0.00363841i	−0.705285	+	0.708924i	$0.749181\pi$
$374$	−0.448801	+	5.88377i	−0.0232069	+	0.304243i
$375$		0			0
$376$	−4.59434	−	1.90304i	−0.236935	−	0.0981418i
$377$	3.25429	+	2.17445i	0.167604	+	0.111990i
$378$	−19.7217			−1.01438
$379$	11.0779	+	7.40200i	0.569032	+	0.380215i	0.806548	−	0.591168i	$-0.201333\pi$
$379$	11.0779	+	7.40200i	0.569032	+	0.380215i	−0.237516	+	0.971384i	$0.576333\pi$
$380$		0			0
$381$	−10.3359	−	15.4688i	−0.529526	−	0.792492i
$382$	8.30880	−	20.0592i	0.425115	−	1.02632i
$383$	−10.8760	+	26.2569i	−0.555736	+	1.34167i	0.357377	+	0.933960i	$0.383671\pi$
$383$	−10.8760	+	26.2569i	−0.555736	+	1.34167i	−0.913114	+	0.407705i	$0.866329\pi$
$384$	−0.828527	−	1.23998i	−0.0422806	−	0.0632774i
$385$		0			0
$386$	0.487981	+	0.326059i	0.0248376	+	0.0165959i
$387$	−2.51133			−0.127658
$388$	−7.33077	−	4.89826i	−0.372163	−	0.248672i
$389$	−28.5749	−	11.8361i	−1.44880	−	0.600115i	−0.486890	−	0.873463i	$-0.661869\pi$
$389$	−28.5749	−	11.8361i	−1.44880	−	0.600115i	−0.961915	+	0.273349i	$0.911869\pi$
$390$		0			0
$391$	0.828384	+	2.52876i	0.0418932	+	0.127885i
$392$	−3.72338	−	3.72338i	−0.188059	−	0.188059i
$393$	27.0309	−	11.1966i	1.36353	−	0.564792i
$394$	−3.47533	−	17.4717i	−0.175085	−	0.880211i
$395$		0			0
$396$	−0.617005	+	0.923413i	−0.0310057	+	0.0464033i
$397$	3.98598	+	5.96544i	0.200051	+	0.299397i	0.917908	−	0.396793i	$-0.129877\pi$
$397$	3.98598	+	5.96544i	0.200051	+	0.299397i	−0.717857	+	0.696190i	$0.754877\pi$
$398$	−3.51531	−	0.699239i	−0.176207	−	0.0350497i
$399$	1.08692	−	0.450218i	0.0544141	−	0.0225391i
$400$		0			0
$401$	6.19658	−	4.14042i	0.309442	−	0.206763i	−0.391146	−	0.920329i	$-0.627921\pi$
$401$	6.19658	−	4.14042i	0.309442	−	0.206763i	0.700588	+	0.713566i	$0.252921\pi$
$402$	−9.26744	+	6.19231i	−0.462218	+	0.308844i
$403$	−7.41737	+	1.47541i	−0.369486	+	0.0734953i
$404$	−9.35515	−	9.35515i	−0.465436	−	0.465436i
$405$		0			0
$406$	7.63196	−	18.4252i	0.378768	−	0.914426i
$407$	−0.428102	+	0.428102i	−0.0212202	+	0.0212202i
$408$	−1.91418	−	5.84329i	−0.0947659	−	0.289286i
$409$			18.1578i			0.897847i	0.893570	+	0.448924i	$0.148192\pi$
$409$			18.1578i			0.897847i	−0.893570	+	0.448924i	$0.851808\pi$
$410$		0			0
$411$	−10.3760	+	2.06391i	−0.511810	+	0.101805i
$412$		−	18.1495i		−	0.894162i
$413$	−2.02172	−	10.1639i	−0.0994825	−	0.500132i
$414$	−0.0977039	+	0.491190i	−0.00480188	+	0.0241407i
$415$		0			0
$416$	0.263026	+	0.635001i	0.0128959	+	0.0311335i
$417$	−14.4916	−	6.00263i	−0.709659	−	0.293950i
$418$	0.0628921	−	0.316180i	0.00307615	−	0.0154649i
$419$	−5.30674	−	1.05558i	−0.259251	−	0.0515683i	0.0637533	−	0.997966i	$-0.479693\pi$
$419$	−5.30674	−	1.05558i	−0.259251	−	0.0515683i	−0.323005	+	0.946397i	$0.604693\pi$
$420$		0			0
$421$	12.5830	−	12.5830i	0.613260	−	0.613260i	−0.330534	−	0.943794i	$-0.607229\pi$
$421$	12.5830	−	12.5830i	0.613260	−	0.613260i	0.943794	+	0.330534i	$0.107229\pi$
$422$	2.56243	−	3.83494i	0.124737	−	0.186682i
$423$	−1.47675	−	3.56518i	−0.0718019	−	0.173345i
$424$	2.82020			0.136961
$425$		0			0
$426$	−16.1327			−0.781632
$427$	17.7676	+	42.8947i	0.859833	+	2.07582i
$428$	−8.06566	+	12.0711i	−0.389868	+	0.583479i
$429$	−1.03730	+	1.03730i	−0.0500811	+	0.0500811i
$430$		0			0
$431$	−10.0155	−	1.99220i	−0.482429	−	0.0959611i	−0.0521163	−	0.998641i	$-0.516597\pi$
$431$	−10.0155	−	1.99220i	−0.482429	−	0.0959611i	−0.430313	+	0.902680i	$0.641597\pi$
$432$	1.09859	−	5.52298i	0.0528559	−	0.265724i
$433$	−32.2019	−	13.3385i	−1.54752	−	0.641006i	−0.564658	−	0.825325i	$-0.690992\pi$
$433$	−32.2019	−	13.3385i	−1.54752	−	0.641006i	−0.982867	+	0.184319i	$0.940992\pi$
$434$	14.7470	+	35.6023i	0.707877	+	1.70897i
$435$		0			0
$436$	−2.52344	+	12.6862i	−0.120851	+	0.607558i
$437$	−0.0283611	−	0.142581i	−0.00135669	−	0.00682056i
$438$			14.6258i			0.698849i
$439$	2.63978	−	0.525084i	0.125990	−	0.0250609i	−0.131693	−	0.991291i	$-0.542041\pi$
$439$	2.63978	−	0.525084i	0.125990	−	0.0250609i	0.257682	+	0.966230i	$0.417041\pi$
$440$		0			0
$441$		−	4.08612i		−	0.194577i
$442$	0.339868	+	2.81344i	0.0161659	+	0.133822i
$443$	−21.5344	+	21.5344i	−1.02313	+	1.02313i	−0.0234065	+	0.999726i	$0.507451\pi$
$443$	−21.5344	+	21.5344i	−1.02313	+	1.02313i	−0.999726	+	0.0234065i	$0.992549\pi$
$444$	0.241423	−	0.582846i	0.0114574	−	0.0276607i
$445$		0			0
$446$	7.04691	+	7.04691i	0.333681	+	0.333681i
$447$	7.74908	−	1.54139i	0.366519	−	0.0729052i
$448$	2.91200	−	1.94574i	0.137579	−	0.0919275i
$449$	−21.9479	+	14.6651i	−1.03578	+	0.692089i	−0.952532	−	0.304440i	$-0.901531\pi$
$449$	−21.9479	+	14.6651i	−1.03578	+	0.692089i	−0.0832522	+	0.996529i	$0.526531\pi$
$450$		0			0
$451$	−3.56476	+	1.47657i	−0.167858	+	0.0695291i
$452$	2.95408	+	0.587603i	0.138948	+	0.0276385i
$453$	8.69273	+	13.0096i	0.408420	+	0.611244i
$454$	8.86159	−	13.2623i	0.415895	−	0.622431i
$455$		0			0
$456$	0.0655350	+	0.329466i	0.00306896	+	0.0154287i
$457$	23.6859	−	9.81102i	1.10798	−	0.458940i	0.247738	−	0.968827i	$-0.420313\pi$
$457$	23.6859	−	9.81102i	1.10798	−	0.458940i	0.860241	+	0.509887i	$0.170313\pi$
$458$	−20.2038	−	20.2038i	−0.944063	−	0.944063i
$459$	10.4908	−	20.7127i	0.489671	−	0.966785i
$460$		0			0
$461$	−12.3509	−	5.11592i	−0.575240	−	0.238272i	0.0760463	−	0.997104i	$-0.475770\pi$
$461$	−12.3509	−	5.11592i	−0.575240	−	0.238272i	−0.651286	+	0.758832i	$0.725770\pi$
$462$	6.21514	+	4.15282i	0.289154	+	0.193207i
$463$	−32.8821			−1.52816			−0.764081	−	0.645121i	$-0.776807\pi$
$463$	−32.8821			−1.52816			−0.764081	+	0.645121i	$0.776807\pi$
$464$	4.73475	+	3.16366i	0.219805	+	0.146869i
$465$		0			0
$466$	−13.2219	−	19.7880i	−0.612492	−	0.916660i
$467$	−1.83229	+	4.42354i	−0.0847883	+	0.204697i	−0.960587	−	0.277979i	$-0.910335\pi$
$467$	−1.83229	+	4.42354i	−0.0847883	+	0.204697i	0.875799	+	0.482676i	$0.160335\pi$
$468$	−0.204107	+	0.492757i	−0.00943483	+	0.0227777i
$469$	−14.5422	−	21.7639i	−0.671496	−	1.00496i
$470$		0			0
$471$	−18.6372	−	12.4530i	−0.858758	−	0.573803i
$472$	2.95897			0.136198
$473$	3.85109	+	2.57321i	0.177073	+	0.118317i
$474$	−2.52339	−	1.04522i	−0.115903	−	0.0480086i
$475$		0			0
$476$	13.7225	−	4.49531i	0.628972	−	0.206042i
$477$	1.54747	+	1.54747i	0.0708540	+	0.0708540i
$478$	20.5220	−	8.50050i	0.938655	−	0.388804i
$479$	6.42297	+	32.2905i	0.293473	+	1.47539i	0.793070	+	0.609130i	$0.208481\pi$
$479$	6.42297	+	32.2905i	0.293473	+	1.47539i	−0.499597	+	0.866258i	$0.666519\pi$
$480$		0			0
$481$	−0.161536	+	0.241755i	−0.00736539	+	0.0110231i
$482$	4.84747	+	7.25475i	0.220796	+	0.330445i
$483$	3.30601	+	0.657607i	0.150429	+	0.0299222i
$484$	−8.27034	+	3.42569i	−0.375925	+	0.155713i
$485$		0			0
$486$	6.51997	−	4.35651i	0.295752	−	0.197615i
$487$	−25.2701	+	16.8849i	−1.14510	+	0.765130i	−0.975417	−	0.220369i	$-0.929274\pi$
$487$	−25.2701	+	16.8849i	−1.14510	+	0.765130i	−0.169681	+	0.985499i	$0.554274\pi$
$488$	−13.0022	+	2.58630i	−0.588582	+	0.117076i
$489$	−15.7959	−	15.7959i	−0.714318	−	0.714318i
$490$		0			0
$491$	6.24928	−	15.0871i	0.282026	−	0.680871i	−0.717857	−	0.696191i	$-0.754877\pi$
$491$	6.24928	−	15.0871i	0.282026	−	0.680871i	0.999883	+	0.0153199i	$0.00487666\pi$
$492$	2.84300	−	2.84300i	0.128172	−	0.128172i
$493$	15.2912	+	17.8166i	0.688682	+	0.802420i
$494$		−	0.154820i		−	0.00696570i
$495$		0			0
$496$	−10.7917	+	2.14661i	−0.484563	+	0.0963856i
$497$		−	37.8865i		−	1.69944i
$498$	−0.743974	−	3.74021i	−0.0333383	−	0.167603i
$499$	−4.87821	+	24.5244i	−0.218379	+	1.09786i	0.703592	+	0.710604i	$0.251578\pi$
$499$	−4.87821	+	24.5244i	−0.218379	+	1.09786i	−0.921971	+	0.387260i	$0.873422\pi$
$500$		0			0
$501$	−4.34684	−	10.4942i	−0.194203	−	0.468847i
$502$	9.87582	+	4.09070i	0.440779	+	0.182577i
$503$	0.843653	−	4.24133i	0.0376166	−	0.189111i	−0.957408	−	0.288737i	$-0.906765\pi$
$503$	0.843653	−	4.24133i	0.0376166	−	0.189111i	0.995025	+	0.0996258i	$0.0317646\pi$
$504$	2.66550	+	0.530200i	0.118731	+	0.0236170i
$505$		0			0
$506$	0.653121	−	0.653121i	0.0290348	−	0.0290348i
$507$	10.3795	−	15.5340i	0.460968	−	0.689887i
$508$	4.77400	+	11.5255i	0.211812	+	0.511360i
$509$	−14.6760			−0.650503			−0.325251	−	0.945628i	$-0.605449\pi$
$509$	−14.6760			−0.650503			−0.325251	+	0.945628i	$0.605449\pi$
$510$		0			0
$511$	−34.3477			−1.51945
$512$	0.382683	+	0.923880i	0.0169124	+	0.0408301i
$513$	−0.704705	+	1.05467i	−0.0311135	+	0.0465646i
$514$	17.7495	−	17.7495i	0.782896	−	0.782896i
$515$		0			0
$516$	−4.73356	−	0.941563i	−0.208383	−	0.0414500i
$517$	−1.38847	+	6.98029i	−0.0610646	+	0.306993i
$518$	1.36877	+	0.566964i	0.0601404	+	0.0249110i
$519$	−10.3712	−	25.0383i	−0.455246	−	1.09906i
$520$		0			0
$521$	−1.76990	+	8.89788i	−0.0775406	+	0.389823i	0.922452	+	0.386111i	$0.126182\pi$
$521$	−1.76990	+	8.89788i	−0.0775406	+	0.389823i	−0.999993	+	0.00371240i	$0.998818\pi$
$522$	0.862075	+	4.33395i	0.0377320	+	0.189692i
$523$		−	7.38904i		−	0.323100i	−0.986865	−	0.161550i	$-0.948351\pi$
$523$		−	7.38904i		−	0.323100i	0.986865	−	0.161550i	$-0.0516494\pi$
$524$	−19.2420	+	3.82748i	−0.840592	+	0.167204i
$525$		0			0
$526$		−	9.23535i		−	0.402680i
$527$	−45.2358	−	3.45048i	−1.97050	−	0.150305i
$528$	−1.50919	+	1.50919i	−0.0656791	+	0.0656791i
$529$	−8.64232	+	20.8644i	−0.375753	+	0.907149i
$530$		0			0
$531$	1.62362	+	1.62362i	0.0704591	+	0.0704591i
$532$	−0.773729	+	0.153904i	−0.0335454	+	0.00667259i
$533$	−1.54074	+	1.02949i	−0.0667368	+	0.0445921i
$534$	17.1102	−	11.4327i	0.740430	−	0.494739i
$535$		0			0
$536$	6.90495	−	2.86013i	0.298249	−	0.123539i
$537$	18.9043	+	3.76031i	0.815783	+	0.162269i
$538$	1.92324	+	2.87833i	0.0829166	+	0.124093i
$539$	−4.18681	+	6.26600i	−0.180338	+	0.269896i
$540$		0			0
$541$	−1.09529	−	5.50641i	−0.0470904	−	0.236739i	0.950071	−	0.312034i	$-0.101010\pi$
$541$	−1.09529	−	5.50641i	−0.0470904	−	0.236739i	−0.997161	+	0.0752947i	$0.976010\pi$
$542$	−18.6942	+	7.74341i	−0.802986	+	0.332608i
$543$	6.01426	+	6.01426i	0.258097	+	0.258097i
$544$	0.494483	+	4.09335i	0.0212008	+	0.175501i
$545$		0			0
$546$	3.31656	+	1.37376i	0.141936	+	0.0587916i
$547$	30.7977	+	20.5784i	1.31682	+	0.879868i	0.997696	−	0.0678469i	$-0.0216129\pi$
$547$	30.7977	+	20.5784i	1.31682	+	0.879868i	0.319119	+	0.947715i	$0.396613\pi$
$548$	7.09395			0.303038
$549$	−8.55358	−	5.71532i	−0.365058	−	0.243924i
$550$		0			0
$551$	−0.712622	−	1.06651i	−0.0303587	−	0.0454350i
$552$	−0.368320	+	0.889203i	−0.0156767	+	0.0378470i
$553$	2.45463	−	5.92600i	0.104381	−	0.251999i
$554$	11.1364	+	16.6668i	0.473140	+	0.708104i
$555$		0			0
$556$	8.74542	+	5.84350i	0.370888	+	0.247820i
$557$	−31.1211			−1.31864			−0.659321	−	0.751862i	$-0.729156\pi$
$557$	−31.1211			−1.31864			−0.659321	+	0.751862i	$0.729156\pi$
$558$	−7.09941	−	4.74367i	−0.300542	−	0.200816i
$559$	2.05504	+	0.851225i	0.0869189	+	0.0360030i
$560$		0			0
$561$	−7.66760	+	4.31836i	−0.323726	+	0.182321i
$562$	−15.4560	−	15.4560i	−0.651971	−	0.651971i
$563$	28.6912	−	11.8843i	1.20919	−	0.500863i	0.315233	−	0.949014i	$-0.397917\pi$
$563$	28.6912	−	11.8843i	1.20919	−	0.500863i	0.893958	+	0.448151i	$0.147917\pi$
$564$	−1.44681	−	7.27361i	−0.0609217	−	0.306274i
$565$		0			0
$566$	11.1466	−	16.6821i	0.468529	−	0.701203i
$567$	−11.8103	−	17.6754i	−0.495988	−	0.742298i
$568$	10.6099	+	2.11045i	0.445183	+	0.0885525i
$569$	−2.92191	+	1.21029i	−0.122493	+	0.0507381i	−0.443088	−	0.896478i	$-0.646117\pi$
$569$	−2.92191	+	1.21029i	−0.122493	+	0.0507381i	0.320595	+	0.947216i	$0.396117\pi$
$570$		0			0
$571$	−1.63933	+	1.09537i	−0.0686039	+	0.0458397i	−0.589399	−	0.807842i	$-0.700635\pi$
$571$	−1.63933	+	1.09537i	−0.0686039	+	0.0458397i	0.520795	+	0.853682i	$0.325635\pi$
$572$	0.817893	−	0.546498i	0.0341978	−	0.0228502i
$573$	31.7571	−	6.31688i	1.32667	−	0.263891i
$574$	6.67659	+	6.67659i	0.278675	+	0.278675i
$575$		0			0
$576$	−0.296960	+	0.716925i	−0.0123733	+	0.0298719i
$577$	−23.0553	+	23.0553i	−0.959807	+	0.959807i	−0.999223	−	0.0394163i	$-0.987450\pi$
$577$	−23.0553	+	23.0553i	−0.959807	+	0.959807i	0.0394163	+	0.999223i	$0.487450\pi$
$578$	−2.57844	+	16.8033i	−0.107249	+	0.698926i
$579$			0.875235i			0.0363735i
$580$		0			0
$581$	8.78362	−	1.74717i	0.364406	−	0.0724848i
$582$		−	13.1483i		−	0.545016i
$583$	−0.787420	−	3.95863i	−0.0326116	−	0.163950i
$584$	1.91332	−	9.61892i	0.0791739	−	0.398034i
$585$		0			0
$586$	6.11588	+	14.7650i	0.252645	+	0.609938i
$587$	28.4598	+	11.7884i	1.17466	+	0.486560i	0.882731	−	0.469879i	$-0.155703\pi$
$587$	28.4598	+	11.7884i	1.17466	+	0.486560i	0.291930	+	0.956440i	$0.405703\pi$
$588$	1.53199	−	7.70184i	0.0631783	−	0.317619i
$589$	2.43086	+	0.483529i	0.100162	+	0.0199235i
$590$		0			0
$591$	18.7851	−	18.7851i	0.772716	−	0.772716i
$592$	−0.235023	+	0.351736i	−0.00965937	+	0.0144563i
$593$	−2.88902	−	6.97472i	−0.118638	−	0.286417i	0.853394	−	0.521267i	$-0.174540\pi$
$593$	−2.88902	−	6.97472i	−0.118638	−	0.286417i	−0.972032	+	0.234849i	$0.924540\pi$
$594$	−8.05917			−0.330672
$595$		0			0
$596$	−5.29796			−0.217013
$597$	−2.04549	−	4.93825i	−0.0837164	−	0.202109i
$598$	0.246442	−	0.368827i	0.0100778	−	0.0150825i
$599$	0.148385	−	0.148385i	0.00606283	−	0.00606283i	−0.704069	−	0.710132i	$-0.748635\pi$
$599$	0.148385	−	0.148385i	0.00606283	−	0.00606283i	0.710132	+	0.704069i	$0.248635\pi$
$600$		0			0
$601$	−12.7537	−	2.53686i	−0.520233	−	0.103481i	−0.0720121	−	0.997404i	$-0.522942\pi$
$601$	−12.7537	−	2.53686i	−0.520233	−	0.103481i	−0.448220	+	0.893923i	$0.647942\pi$
$602$	2.21119	−	11.1164i	0.0901216	−	0.453072i
$603$	5.35821	+	2.21944i	0.218203	+	0.0903826i
$604$	−4.01503	−	9.69314i	−0.163369	−	0.394408i
$605$		0			0
$606$	3.84919	−	19.3512i	0.156363	−	0.786089i
$607$	−0.211963	−	1.06561i	−0.00860330	−	0.0432517i	0.976245	−	0.216669i	$-0.0695192\pi$
$607$	−0.211963	−	1.06561i	−0.00860330	−	0.0432517i	−0.984848	+	0.173417i	$0.944519\pi$
$608$		−	0.225252i		−	0.00913519i
$609$	29.1701	−	5.80230i	1.18203	−	0.235121i
$610$		0			0
$611$			3.41796i			0.138276i
$612$	−1.97474	+	2.51739i	−0.0798239	+	0.101760i
$613$	22.9407	−	22.9407i	0.926565	−	0.926565i	−0.0709174	−	0.997482i	$-0.522593\pi$
$613$	22.9407	−	22.9407i	0.926565	−	0.926565i	0.997482	+	0.0709174i	$0.0225927\pi$
$614$	0.744855	−	1.79824i	0.0300599	−	0.0725710i
$615$		0			0
$616$	−3.54423	−	3.54423i	−0.142801	−	0.142801i
$617$	2.04640	−	0.407054i	0.0823850	−	0.0163874i	−0.153726	−	0.988114i	$-0.549127\pi$
$617$	2.04640	−	0.407054i	0.0823850	−	0.0163874i	0.236111	+	0.971726i	$0.424127\pi$
$618$	22.5050	−	15.0374i	0.905284	−	0.604891i
$619$	−29.8012	+	19.9126i	−1.19781	+	0.800353i	−0.984286	−	0.176584i	$-0.943495\pi$
$619$	−29.8012	+	19.9126i	−1.19781	+	0.800353i	−0.213528	+	0.976937i	$0.568495\pi$
$620$		0			0
$621$	−3.35762	+	1.39077i	−0.134737	+	0.0558098i
$622$	20.6241	+	4.10239i	0.826951	+	0.164491i
$623$	26.8488	+	40.1820i	1.07567	+	1.60986i
$624$	−0.569463	+	0.852262i	−0.0227968	+	0.0341178i
$625$		0			0
$626$	5.54040	+	27.8535i	0.221439	+	1.11325i
$627$	0.444164	−	0.183979i	0.0177382	−	0.00734741i
$628$	10.6280	+	10.6280i	0.424104	+	0.424104i
$629$	−1.32356	+	1.13596i	−0.0527739	+	0.0452936i
$630$		0			0
$631$	26.5925	+	11.0150i	1.05863	+	0.438499i	0.842965	−	0.537969i	$-0.180808\pi$
$631$	26.5925	+	11.0150i	1.05863	+	0.438499i	0.215664	+	0.976468i	$0.430808\pi$
$632$	1.52281	+	1.01751i	0.0605743	+	0.0404745i
$633$	6.87829			0.273387
$634$	22.9967	+	15.3659i	0.913315	+	0.610258i
$635$		0			0
$636$	2.33661	+	3.49699i	0.0926527	+	0.138665i
$637$	−1.38500	+	3.34370i	−0.0548759	+	0.132482i
$638$	3.11876	−	7.52935i	0.123473	−	0.298090i
$639$	4.66377	+	6.97982i	0.184496	+	0.276117i
$640$		0			0
$641$	17.5118	+	11.7010i	0.691676	+	0.462163i	0.851070	−	0.525052i	$-0.175954\pi$
$641$	17.5118	+	11.7010i	0.691676	+	0.462163i	−0.159394	+	0.987215i	$0.550954\pi$
$642$	−21.6505			−0.854479
$643$	15.0254	+	10.0396i	0.592542	+	0.395924i	0.815375	−	0.578933i	$-0.196531\pi$
$643$	15.0254	+	10.0396i	0.592542	+	0.395924i	−0.222833	+	0.974857i	$0.571531\pi$
$644$	−2.08823	−	0.864973i	−0.0822878	−	0.0340847i
$645$		0			0
$646$	0.249943	−	0.894475i	0.00983387	−	0.0351926i
$647$	−30.4615	−	30.4615i	−1.19756	−	1.19756i	−0.974894	−	0.222671i	$-0.928523\pi$
$647$	−30.4615	−	30.4615i	−1.19756	−	1.19756i	−0.222671	−	0.974894i	$-0.571477\pi$
$648$	5.60781	−	2.32283i	0.220296	−	0.0912494i
$649$	−0.826166	−	4.15342i	−0.0324299	−	0.163036i
$650$		0			0
$651$	−31.9279	+	47.7834i	−1.25135	+	1.87278i
$652$	8.32208	+	12.4549i	0.325918	+	0.487770i
$653$	−41.2569	−	8.20651i	−1.61451	−	0.321145i	−0.696454	−	0.717602i	$-0.745240\pi$
$653$	−41.2569	−	8.20651i	−1.61451	−	0.321145i	−0.918054	+	0.396456i	$0.870240\pi$
$654$	−17.8213	+	7.38184i	−0.696870	+	0.288653i
$655$		0			0
$656$	−2.24166	+	1.49783i	−0.0875222	+	0.0584805i
$657$	6.32787	−	4.22815i	0.246874	−	0.164956i
$658$	17.0816	−	3.39773i	0.665909	−	0.132457i
$659$	13.4187	+	13.4187i	0.522718	+	0.522718i	0.918391	−	0.395673i	$-0.129489\pi$
$659$	13.4187	+	13.4187i	0.522718	+	0.522718i	−0.395673	+	0.918391i	$0.629489\pi$
$660$		0			0
$661$	9.49648	−	22.9265i	0.369370	−	0.891738i	−0.624484	−	0.781038i	$-0.714691\pi$
$661$	9.49648	−	22.9265i	0.369370	−	0.891738i	0.993854	−	0.110701i	$-0.0353094\pi$
$662$	−24.3276	+	24.3276i	−0.945518	+	0.945518i
$663$	−3.20701	+	2.75244i	−0.124550	+	0.106896i
$664$			2.55714i			0.0992362i
$665$		0			0
$666$	−0.321961	+	0.0640420i	−0.0124757	+	0.00248158i
$667$		−	3.67509i		−	0.142300i
$668$	1.48594	+	7.47034i	0.0574929	+	0.289036i
$669$	−2.89946	+	14.5766i	−0.112100	+	0.563563i
$670$		0			0
$671$	7.26062	+	17.5287i	0.280293	+	0.676688i
$672$	4.82535	+	1.99872i	0.186142	+	0.0771025i
$673$	1.65702	−	8.33039i	0.0638733	−	0.321113i	−0.935618	−	0.353015i	$-0.885156\pi$
$673$	1.65702	−	8.33039i	0.0638733	−	0.321113i	0.999491	+	0.0319020i	$0.0101565\pi$
$674$	12.8742	+	2.56084i	0.495896	+	0.0986398i
$675$		0			0
$676$	−8.85834	+	8.85834i	−0.340706	+	0.340706i
$677$	3.03110	−	4.53636i	0.116495	−	0.174347i	−0.768640	−	0.639682i	$-0.779066\pi$
$677$	3.03110	−	4.53636i	0.116495	−	0.174347i	0.885135	+	0.465335i	$0.154066\pi$
$678$	1.71892	+	4.14984i	0.0660147	+	0.159374i
$679$	30.8779			1.18499
$680$		0			0
$681$	23.7871			0.911522
$682$	6.02626	+	14.5487i	0.230758	+	0.557098i
$683$	20.3551	−	30.4635i	0.778866	−	1.16565i	−0.203571	−	0.979060i	$-0.565255\pi$
$683$	20.3551	−	30.4635i	0.778866	−	1.16565i	0.982437	−	0.186595i	$-0.0597451\pi$
$684$	0.123598	−	0.123598i	0.00472590	−	0.00472590i
$685$		0			0
$686$	−5.95736	−	1.18499i	−0.227453	−	0.0452432i
$687$	8.31289	−	41.7917i	0.317157	−	1.59445i
$688$	2.98993	+	1.23847i	0.113990	+	0.0472162i
$689$	−0.741785	−	1.79083i	−0.0282598	−	0.0682251i
$690$		0			0
$691$	−1.37635	+	6.91939i	−0.0523589	+	0.263226i	−0.998094	−	0.0617127i	$-0.980344\pi$
$691$	−1.37635	+	6.91939i	−0.0523589	+	0.263226i	0.945735	+	0.324939i	$0.105344\pi$
$692$	3.54534	+	17.8236i	0.134774	+	0.677553i
$693$		−	3.88951i		−	0.147750i
$694$	−18.8905	+	3.75756i	−0.717075	+	0.142635i
$695$		0			0
$696$			8.49217i			0.321895i
$697$	−10.5636	+	3.46050i	−0.400126	+	0.131076i
$698$	−15.2293	+	15.2293i	−0.576437	+	0.576437i
$699$	13.5820	−	32.7897i	0.513717	−	1.24022i
$700$		0			0
$701$	16.7123	+	16.7123i	0.631215	+	0.631215i	0.948373	−	0.317158i	$-0.102728\pi$
$701$	16.7123	+	16.7123i	0.631215	+	0.631215i	−0.317158	+	0.948373i	$0.602728\pi$
$702$	−3.79605	+	0.755082i	−0.143273	+	0.0284987i
$703$	0.0792294	−	0.0529394i	0.00298819	−	0.00199665i
$704$	1.18997	−	0.795115i	0.0448488	−	0.0299670i
$705$		0			0
$706$	−7.24766	+	3.00208i	−0.272769	+	0.112985i
$707$	45.4449	+	9.03956i	1.70913	+	0.339967i
$708$	2.45159	+	3.66906i	0.0921363	+	0.137892i
$709$	14.4329	−	21.6003i	0.542038	−	0.811217i	−0.454807	−	0.890590i	$-0.650292\pi$
$709$	14.4329	−	21.6003i	0.542038	−	0.811217i	0.996845	+	0.0793729i	$0.0252918\pi$
$710$		0			0
$711$	0.277265	+	1.39390i	0.0103982	+	0.0522755i
$712$	−12.7484	+	5.28056i	−0.477766	+	0.197897i
$713$	5.02134	+	5.02134i	0.188051	+	0.188051i
$714$	16.9436	+	13.2912i	0.634098	+	0.497410i
$715$		0			0
$716$	−11.9408	−	4.94606i	−0.446250	−	0.184843i
$717$	27.5435	+	18.4040i	1.02863	+	0.687309i
$718$	−11.6725			−0.435615
$719$	−31.3017	−	20.9151i	−1.16735	−	0.780002i	−0.188004	−	0.982168i	$-0.560202\pi$
$719$	−31.3017	−	20.9151i	−1.16735	−	0.780002i	−0.979351	+	0.202167i	$0.935202\pi$
$720$		0			0
$721$	35.3142	+	52.8514i	1.31517	+	1.96829i
$722$	7.25157	−	17.5068i	0.269875	−	0.651537i
$723$	−4.97948	+	12.0215i	−0.185189	+	0.447085i
$724$	−3.16861	−	4.74216i	−0.117760	−	0.176241i
$725$		0			0
$726$	−11.1000	−	7.41677i	−0.411959	−	0.275262i
$727$	−11.7248			−0.434847			−0.217424	−	0.976077i	$-0.569765\pi$
$727$	−11.7248			−0.434847			−0.217424	+	0.976077i	$0.569765\pi$
$728$	−2.00148	−	1.33734i	−0.0741797	−	0.0495653i
$729$	27.6274	+	11.4436i	1.02324	+	0.423838i
$730$		0			0
$731$	10.4988	+	8.23562i	0.388311	+	0.304605i
$732$	−13.9796	−	13.9796i	−0.516702	−	0.516702i
$733$	−36.6816	+	15.1940i	−1.35486	+	0.561203i	−0.937642	−	0.347601i	$-0.886996\pi$
$733$	−36.6816	+	15.1940i	−1.35486	+	0.561203i	−0.417222	+	0.908805i	$0.636996\pi$
$734$	−2.94262	−	14.7935i	−0.108614	−	0.546039i
$735$		0			0
$736$	0.358556	−	0.536616i	0.0132165	−	0.0197799i
$737$	−5.94259	−	8.89371i	−0.218898	−	0.327604i
$738$	−2.05190	−	0.408149i	−0.0755315	−	0.0150242i
$739$	41.6307	−	17.2440i	1.53141	−	0.634332i	0.551574	−	0.834126i	$-0.314027\pi$
$739$	41.6307	−	17.2440i	1.53141	−	0.634332i	0.979838	+	0.199795i	$0.0640275\pi$
$740$		0			0
$741$	0.191974	−	0.128273i	0.00705234	−	0.00471223i
$742$	−8.21243	+	5.48737i	−0.301488	+	0.201448i
$743$	−25.3180	+	5.03606i	−0.928826	+	0.184755i	−0.636246	−	0.771486i	$-0.719514\pi$
$743$	−25.3180	+	5.03606i	−0.928826	+	0.184755i	−0.292580	+	0.956241i	$0.594514\pi$
$744$	−11.6030	−	11.6030i	−0.425387	−	0.425387i
$745$		0			0
$746$	0.0380295	−	0.0918113i	0.00139236	−	0.00336145i
$747$	−1.40313	+	1.40313i	−0.0513378	+	0.0513378i
$748$	5.60765	−	1.83698i	0.205036	−	0.0671668i
$749$		−	50.8448i		−	1.85783i
$750$		0			0
$751$	19.7948	−	3.93743i	0.722322	−	0.143679i	0.179779	−	0.983707i	$-0.442462\pi$
$751$	19.7948	−	3.93743i	0.722322	−	0.143679i	0.542543	+	0.840028i	$0.317462\pi$
$752$			4.97288i			0.181342i
$753$	3.11001	+	15.6351i	0.113335	+	0.569773i
$754$	0.763564	−	3.83870i	0.0278074	−	0.139797i
$755$		0			0
$756$	7.54717	+	18.2205i	0.274488	+	0.662673i
$757$	10.7444	+	4.45049i	0.390513	+	0.161756i	0.569296	−	0.822133i	$-0.307216\pi$
$757$	10.7444	+	4.45049i	0.390513	+	0.161756i	−0.178783	+	0.983889i	$0.557216\pi$
$758$	2.59924	−	13.0672i	0.0944086	−	0.474624i
$759$	1.35098	+	0.268728i	0.0490376	+	0.00975419i
$760$		0			0
$761$	−27.7743	+	27.7743i	−1.00682	+	1.00682i	−0.00684140	+	0.999977i	$0.502178\pi$
$761$	−27.7743	+	27.7743i	−1.00682	+	1.00682i	−0.999977	+	0.00684140i	$0.997822\pi$
$762$	−10.3359	+	15.4688i	−0.374431	+	0.560376i
$763$	−17.3357	−	41.8522i	−0.627596	−	1.51515i
$764$	−21.7120			−0.785511
$765$		0			0
$766$	28.4203			1.02687
$767$	−0.778286	−	1.87895i	−0.0281023	−	0.0678449i
$768$	−0.828527	+	1.23998i	−0.0298969	+	0.0447439i
$769$	4.24272	−	4.24272i	0.152997	−	0.152997i	−0.626458	−	0.779455i	$-0.715496\pi$
$769$	4.24272	−	4.24272i	0.152997	−	0.152997i	0.779455	+	0.626458i	$0.215496\pi$
$770$		0			0
$771$	36.7149	+	7.30305i	1.32226	+	0.263013i
$772$	0.114497	−	0.575613i	0.00412082	−	0.0207168i
$773$	9.40030	+	3.89373i	0.338105	+	0.140048i	0.545275	−	0.838257i	$-0.316425\pi$
$773$	9.40030	+	3.89373i	0.338105	+	0.140048i	−0.207170	+	0.978305i	$0.566425\pi$
$774$	0.961046	+	2.32017i	0.0345441	+	0.0833968i
$775$		0			0
$776$	−1.72004	+	8.64723i	−0.0617459	+	0.310417i
$777$	0.431042	+	2.16700i	0.0154636	+	0.0777405i
$778$			30.9292i			1.10887i
$779$	0.595617	−	0.118476i	0.0213402	−	0.00424483i
$780$		0			0
$781$		−	15.4821i		−	0.553994i
$782$	2.01926	−	1.73304i	0.0722085	−	0.0619734i
$783$	−22.6744	+	22.6744i	−0.810316	+	0.810316i
$784$	−2.01508	+	4.86483i	−0.0719672	+	0.173744i
$785$		0			0
$786$	−20.6885	−	20.6885i	−0.737936	−	0.737936i
$787$	38.7801	−	7.71384i	1.38236	−	0.274969i	0.552768	−	0.833336i	$-0.313572\pi$
$787$	38.7801	−	7.71384i	1.38236	−	0.274969i	0.829594	+	0.558367i	$0.188572\pi$
$788$	−14.8118	+	9.89692i	−0.527648	+	0.352563i
$789$	11.4516	−	7.65174i	0.407689	−	0.272409i
$790$		0			0
$791$	−9.74560	+	4.03676i	−0.346514	+	0.143531i
$792$	1.08924	+	0.216663i	0.0387045	+	0.00769880i
$793$	5.06222	+	7.57614i	0.179765	+	0.269037i
$794$	3.98598	−	5.96544i	0.141457	−	0.211706i
$795$		0			0
$796$	0.699239	+	3.51531i	0.0247839	+	0.124597i
$797$	40.1553	−	16.6329i	1.42237	−	0.589166i	0.466917	−	0.884301i	$-0.345365\pi$
$797$	40.1553	−	16.6329i	1.42237	−	0.589166i	0.955455	+	0.295135i	$0.0953647\pi$
$798$	−0.831894	−	0.831894i	−0.0294487	−	0.0294487i
$799$	−5.51797	+	19.7473i	−0.195212	+	0.698608i
$800$		0			0
$801$	−9.89268	−	4.09768i	−0.349541	−	0.144785i
$802$	−6.19658	−	4.14042i	−0.218809	−	0.146203i
$803$	−14.0360			−0.495320
$804$	9.26744	+	6.19231i	0.326837	+	0.218386i
$805$		0			0
$806$	4.20160	+	6.28815i	0.147995	+	0.221490i
$807$	−1.97561	+	4.76954i	−0.0695447	+	0.167896i
$808$	−5.06297	+	12.2231i	−0.178115	+	0.430007i
$809$	25.9551	+	38.8446i	0.912534	+	1.36570i	0.930667	+	0.365868i	$0.119228\pi$
$809$	25.9551	+	38.8446i	0.912534	+	1.36570i	−0.0181324	+	0.999836i	$0.505772\pi$
$810$		0			0
$811$	−12.7865	−	8.54365i	−0.448994	−	0.300008i	0.310440	−	0.950593i	$-0.399524\pi$
$811$	−12.7865	−	8.54365i	−0.448994	−	0.300008i	−0.759433	+	0.650585i	$0.774524\pi$
$812$	−19.9433			−0.699872
$813$	−25.0904	−	16.7648i	−0.879957	−	0.587969i
$814$	0.559342	+	0.231687i	0.0196049	+	0.00812062i
$815$		0			0
$816$	−4.66597	+	4.00460i	−0.163342	+	0.140189i
$817$	−0.515466	−	0.515466i	−0.0180339	−	0.0180339i
$818$	16.7757	−	6.94870i	0.586547	−	0.242956i
$819$	−0.364417	−	1.83205i	−0.0127338	−	0.0640169i
$820$		0			0
$821$	8.91045	−	13.3354i	0.310977	−	0.465410i	−0.642753	−	0.766073i	$-0.722208\pi$
$821$	8.91045	−	13.3354i	0.310977	−	0.465410i	0.953730	+	0.300663i	$0.0972080\pi$
$822$	5.87753	+	8.79634i	0.205002	+	0.306808i
$823$	−13.7681	−	2.73864i	−0.479925	−	0.0954631i	−0.0508015	−	0.998709i	$-0.516178\pi$
$823$	−13.7681	−	2.73864i	−0.479925	−	0.0954631i	−0.429124	+	0.903246i	$0.641178\pi$
$824$	−16.7680	+	6.94551i	−0.584139	+	0.241958i
$825$		0			0
$826$	−8.61653	+	5.75738i	−0.299807	+	0.200325i
$827$	−27.5862	+	18.4325i	−0.959267	+	0.640962i	−0.933451	−	0.358705i	$-0.883218\pi$
$827$	−27.5862	+	18.4325i	−0.959267	+	0.640962i	−0.0258161	+	0.999667i	$0.508218\pi$
$828$	0.491190	−	0.0977039i	0.0170700	−	0.00339544i
$829$	19.3397	+	19.3397i	0.671696	+	0.671696i	0.958107	−	0.286411i	$-0.0924622\pi$
$829$	19.3397	+	19.3397i	0.671696	+	0.671696i	−0.286411	+	0.958107i	$0.592462\pi$
$830$		0			0
$831$	−11.4397	+	27.6178i	−0.396837	+	0.958050i
$832$	0.486008	−	0.486008i	0.0168493	−	0.0168493i
$833$	−13.3999	+	17.0822i	−0.464281	+	0.591865i
$834$			15.6856i			0.543149i
$835$		0			0
$836$	−0.316180	+	0.0628921i	−0.0109353	+	0.00217517i
$837$		−	61.9607i		−	2.14168i
$838$	1.05558	+	5.30674i	0.0364643	+	0.183318i
$839$	2.67790	−	13.4627i	0.0924512	−	0.464784i	−0.906630	−	0.421927i	$-0.861354\pi$
$839$	2.67790	−	13.4627i	0.0924512	−	0.464784i	0.999081	−	0.0428571i	$-0.0136460\pi$
$840$		0			0
$841$	−1.31132	−	3.16579i	−0.0452178	−	0.109165i
$842$	−16.4405	−	6.80990i	−0.566579	−	0.234685i
$843$	6.35938	−	31.9708i	0.219029	−	1.10113i
$844$	−4.52362	−	0.899804i	−0.155709	−	0.0309725i
$845$		0			0
$846$	−2.72867	+	2.72867i	−0.0938138	+	0.0938138i
$847$	17.4178	−	26.0675i	0.598482	−	0.895691i
$848$	−1.07924	−	2.60552i	−0.0370614	−	0.0894741i
$849$	29.9208			1.02688
$850$		0			0
$851$	0.273016			0.00935887
$852$	6.17372	+	14.9047i	0.211508	+	0.510626i
$853$	16.4654	−	24.6422i	0.563765	−	0.843734i	−0.434616	−	0.900616i	$-0.643116\pi$
$853$	16.4654	−	24.6422i	0.563765	−	0.843734i	0.998381	+	0.0568820i	$0.0181159\pi$
$854$	32.8302	−	32.8302i	1.12343	−	1.12343i
$855$		0			0
$856$	14.2388	+	2.83228i	0.486674	+	0.0968055i
$857$	0.560290	−	2.81677i	0.0191391	−	0.0962190i	−0.970035	−	0.242965i	$-0.921880\pi$
$857$	0.560290	−	2.81677i	0.0191391	−	0.0962190i	0.989174	+	0.146746i	$0.0468800\pi$
$858$	1.35529	+	0.561381i	0.0462689	+	0.0191652i
$859$	−14.7311	−	35.5640i	−0.502618	−	1.21343i	−0.948053	−	0.318112i	$-0.896951\pi$
$859$	−14.7311	−	35.5640i	−0.502618	−	1.21343i	0.445435	−	0.895314i	$-0.353049\pi$
$860$		0			0
$861$	−2.74709	+	13.8106i	−0.0936206	+	0.470663i
$862$	1.99220	+	10.0155i	0.0678547	+	0.341129i
$863$		−	12.3538i		−	0.420530i	−0.977644	−	0.210265i	$-0.932567\pi$
$863$		−	12.3538i		−	0.420530i	0.977644	−	0.210265i	$-0.0674326\pi$
$864$	−5.52298	+	1.09859i	−0.187895	+	0.0373747i
$865$		0			0
$866$			34.8551i			1.18442i
$867$	−22.9721	+	10.7248i	−0.780173	+	0.364233i
$868$	27.2488	−	27.2488i	0.924885	−	0.924885i
$869$	1.00307	−	2.42163i	0.0340268	−	0.0821480i
$870$		0			0
$871$	−3.63236	−	3.63236i	−0.123078	−	0.123078i
$872$	12.6862	−	2.52344i	0.429609	−	0.0854545i
$873$	−5.68863	+	3.80102i	−0.192531	+	0.128645i
$874$	−0.120874	+	0.0807655i	−0.00408863	+	0.00273193i
$875$		0			0
$876$	13.5125	−	5.59706i	0.456545	−	0.189107i
$877$	−4.23953	−	0.843295i	−0.143159	−	0.0284760i	0.122991	−	0.992408i	$-0.460751\pi$
$877$	−4.23953	−	0.843295i	−0.143159	−	0.0284760i	−0.266149	+	0.963932i	$0.585751\pi$
$878$	−1.49531	−	2.23789i	−0.0504644	−	0.0755253i
$879$	−13.2412	+	19.8168i	−0.446613	+	0.668404i
$880$		0			0
$881$	−5.73703	−	28.8420i	−0.193285	−	0.971711i	−0.948631	−	0.316385i	$-0.897531\pi$
$881$	−5.73703	−	28.8420i	−0.193285	−	0.971711i	0.755346	−	0.655327i	$-0.227469\pi$
$882$	−3.77508	+	1.56369i	−0.127114	+	0.0526522i
$883$	−34.6701	−	34.6701i	−1.16674	−	1.16674i	−0.982969	−	0.183773i	$-0.941169\pi$
$883$	−34.6701	−	34.6701i	−1.16674	−	1.16674i	−0.183773	−	0.982969i	$-0.558831\pi$
$884$	2.46922	−	1.39065i	0.0830487	−	0.0467727i
$885$		0			0
$886$	28.1361	+	11.6544i	0.945251	+	0.391536i
$887$	−7.35669	−	4.91559i	−0.247014	−	0.165049i	0.425900	−	0.904770i	$-0.359957\pi$
$887$	−7.35669	−	4.91559i	−0.247014	−	0.165049i	−0.672914	+	0.739721i	$0.734957\pi$
$888$	−0.630868			−0.0211706
$889$	−36.3274	−	24.2732i	−1.21838	−	0.814097i
$890$		0			0
$891$	−4.82623	−	7.22296i	−0.161685	−	0.241978i
$892$	3.81376	−	9.20723i	0.127694	−	0.308281i
$893$	0.428664	−	1.03489i	0.0143447	−	0.0346312i
$894$	−4.38950	−	6.56936i	−0.146807	−	0.219712i
$895$		0			0
$896$	−2.91200	−	1.94574i	−0.0972832	−	0.0650026i
$897$	0.661522			0.0220876
$898$	21.9479	+	14.6651i	0.732410	+	0.489380i
$899$	57.8873	+	23.9777i	1.93065	+	0.799702i
$900$		0			0
$901$	−1.39454	−	11.5441i	−0.0464589	−	0.384588i
$902$	2.72835	+	2.72835i	0.0908441	+	0.0908441i
$903$	15.6162	−	6.46843i	0.519674	−	0.215256i
$904$	−0.587603	−	2.95408i	−0.0195434	−	0.0982512i
$905$		0			0
$906$	8.69273	−	13.0096i	0.288796	−	0.432214i
$907$	−5.07974	−	7.60237i	−0.168670	−	0.252433i	0.737499	−	0.675348i	$-0.236007\pi$
$907$	−5.07974	−	7.60237i	−0.168670	−	0.252433i	−0.906169	+	0.422916i	$0.861007\pi$
$908$	−15.6440	−	3.11178i	−0.519163	−	0.103268i
$909$	−9.48505	+	3.92884i	−0.314599	+	0.130311i
$910$		0			0
$911$	25.4797	−	17.0250i	0.844181	−	0.564064i	−0.0565701	−	0.998399i	$-0.518016\pi$
$911$	25.4797	−	17.0250i	0.844181	−	0.564064i	0.900752	+	0.434335i	$0.143016\pi$
$912$	0.279308	−	0.186628i	0.00924882	−	0.00617986i
$913$	3.58938	−	0.713971i	0.118791	−	0.0236290i
$914$	−18.1284	−	18.1284i	−0.599634	−	0.599634i
$915$		0			0
$916$	−10.9342	+	26.3976i	−0.361277	+	0.872200i
$917$	48.5856	−	48.5856i	1.60444	−	1.60444i
$918$	−23.1507	−	1.76588i	−0.764087	−	0.0582828i
$919$		−	43.0164i		−	1.41898i	−0.704716	−	0.709490i	$-0.748926\pi$
$919$		−	43.0164i		−	1.41898i	0.704716	−	0.709490i	$-0.251074\pi$
$920$		0			0
$921$	2.84691	−	0.566286i	0.0938089	−	0.0186597i
$922$			13.3685i			0.440270i
$923$	−1.45055	−	7.29243i	−0.0477456	−	0.240033i
$924$	1.45828	−	7.33126i	0.0479738	−	0.241181i
$925$		0			0
$926$	12.5834	+	30.3791i	0.413517	+	0.998319i
$927$	−13.0118	−	5.38968i	−0.427365	−	0.177020i
$928$	1.11093	−	5.58502i	0.0364681	−	0.183337i
$929$	41.3633	+	8.22767i	1.35709	+	0.269941i	0.819408	−	0.573210i	$-0.194302\pi$
$929$	41.3633	+	8.22767i	1.35709	+	0.269941i	0.537677	+	0.843151i	$0.319302\pi$
$930$		0			0
$931$	0.838701	−	0.838701i	0.0274873	−	0.0274873i
$932$	−13.2219	+	19.7880i	−0.433098	+	0.648176i
$933$	12.0008	+	28.9724i	0.392887	+	0.948514i
$934$	4.78801			0.156668
$935$		0			0
$936$	0.533356			0.0174333
$937$	16.4858	+	39.8003i	0.538569	+	1.30022i	0.925722	+	0.378205i	$0.123458\pi$
$937$	16.4858	+	39.8003i	0.538569	+	1.30022i	−0.387153	+	0.922015i	$0.626542\pi$
$938$	−14.5422	+	21.7639i	−0.474819	+	0.710617i
$939$	−29.9474	+	29.9474i	−0.977295	+	0.977295i
$940$		0			0
$941$	16.9565	+	3.37287i	0.552768	+	0.109952i	0.463568	−	0.886061i	$-0.346569\pi$
$941$	16.9565	+	3.37287i	0.552768	+	0.109952i	0.0891997	+	0.996014i	$0.471569\pi$
$942$	−4.37291	+	21.9841i	−0.142477	+	0.716280i
$943$	1.60752	+	0.665857i	0.0523481	+	0.0216833i
$944$	−1.13235	−	2.73373i	−0.0368548	−	0.0889754i
$945$		0			0
$946$	0.903593	−	4.54267i	0.0293783	−	0.147695i
$947$	1.63760	+	8.23276i	0.0532148	+	0.267529i	0.998228	−	0.0595030i	$-0.0189516\pi$
$947$	1.63760	+	8.23276i	0.0532148	+	0.267529i	−0.945013	+	0.327032i	$0.893952\pi$
$948$			2.73129i			0.0887083i
$949$	−6.61128	+	1.31506i	−0.214611	+	0.0426888i
$950$		0			0
$951$			41.2465i			1.33751i
$952$	−9.40452	−	10.9577i	−0.304802	−	0.355141i
$953$	17.1743	−	17.1743i	0.556330	−	0.556330i	−0.371930	−	0.928261i	$-0.621304\pi$
$953$	17.1743	−	17.1743i	0.556330	−	0.556330i	0.928261	+	0.371930i	$0.121304\pi$
$954$	0.837487	−	2.02187i	0.0271146	−	0.0654605i
$955$		0			0
$956$	−15.7069	−	15.7069i	−0.507997	−	0.507997i
$957$	11.9202	−	2.37108i	0.385326	−	0.0766460i
$958$	27.3745	−	18.2911i	0.884431	−	0.590958i
$959$	−20.6576	+	13.8030i	−0.667068	+	0.445721i
$960$		0			0
$961$	−83.2134	+	34.4681i	−2.68430	+	1.11187i
$962$	0.285170	+	0.0567238i	0.00919424	+	0.00182885i
$963$	6.25891	+	9.36712i	0.201690	+	0.301851i
$964$	4.84747	−	7.25475i	0.156126	−	0.233660i
$965$		0			0
$966$	−0.657607	−	3.30601i	−0.0211582	−	0.106369i
$967$	−1.07658	+	0.445933i	−0.0346204	+	0.0143402i	−0.399926	−	0.916547i	$-0.630964\pi$
$967$	−1.07658	+	0.445933i	−0.0346204	+	0.0143402i	0.365306	+	0.930887i	$0.380964\pi$
$968$	6.32985	+	6.32985i	0.203449	+	0.203449i
$969$	1.31621	−	0.431173i	0.0422829	−	0.0138513i
$970$		0			0
$971$	−17.7627	−	7.35756i	−0.570033	−	0.236115i	0.0790013	−	0.996875i	$-0.474827\pi$
$971$	−17.7627	−	7.35756i	−0.570033	−	0.236115i	−0.649034	+	0.760759i	$0.724827\pi$
$972$	−6.51997	−	4.35651i	−0.209128	−	0.139735i
$973$	−36.8366			−1.18093
$974$	25.2701	+	16.8849i	0.809706	+	0.541029i
$975$		0			0
$976$	7.36516	+	11.0227i	0.235753	+	0.352829i
$977$	9.61901	−	23.2223i	0.307739	−	0.742949i	−0.692038	−	0.721861i	$-0.743287\pi$
$977$	9.61901	−	23.2223i	0.307739	−	0.742949i	0.999778	−	0.0210877i	$-0.00671293\pi$
$978$	−8.54871	+	20.6384i	−0.273357	+	0.659943i
$979$	10.9716	+	16.4202i	0.350654	+	0.524791i
$980$		0			0
$981$	8.34569	+	5.57641i	0.266457	+	0.178041i
$982$	−16.3302			−0.521116
$983$	−28.6015	−	19.1109i	−0.912245	−	0.609543i	0.00839065	−	0.999965i	$-0.497329\pi$
$983$	−28.6015	−	19.1109i	−0.912245	−	0.609543i	−0.920636	+	0.390422i	$0.872329\pi$
$984$	−3.71456	−	1.53862i	−0.118416	−	0.0490494i
$985$		0			0
$986$	10.6087	−	20.9454i	0.337850	−	0.667036i
$987$	18.3657	+	18.3657i	0.584585	+	0.584585i
$988$	−0.143035	+	0.0592472i	−0.00455056	+	0.00188490i
$989$	−0.407473	−	2.04851i	−0.0129569	−	0.0651387i
$990$		0			0
$991$	16.9127	−	25.3117i	0.537250	−	0.804052i	−0.459191	−	0.888337i	$-0.651861\pi$
$991$	16.9127	−	25.3117i	0.537250	−	0.804052i	0.996442	+	0.0842855i	$0.0268608\pi$
$992$	6.11303	+	9.14879i	0.194089	+	0.290474i
$993$	−50.3218	−	10.0096i	−1.59691	−	0.317646i
$994$	−35.0026	+	14.4985i	−1.11021	+	0.459866i
$995$		0			0
$996$	−3.17080	+	2.11866i	−0.100471	+	0.0671323i
$997$	−46.0056	+	30.7399i	−1.45701	+	0.973543i	−0.460715	+	0.887548i	$0.652407\pi$
$997$	−46.0056	+	30.7399i	−1.45701	+	0.973543i	−0.996296	+	0.0859950i	$0.972593\pi$
$998$	24.5244	−	4.87821i	0.776307	−	0.154417i
$999$	−1.68444	−	1.68444i	−0.0532933	−	0.0532933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.s.b.57.2	yes	24
5.2	odd	4		850.2.v.b.193.2	yes	24
5.3	odd	4		850.2.v.a.193.2	yes	24
5.4	even	2		850.2.s.a.57.2	✓	24
17.3	odd	16		850.2.v.a.207.2	yes	24
85.3	even	16	inner	850.2.s.b.343.2	yes	24
85.37	even	16		850.2.s.a.343.2	yes	24
85.54	odd	16		850.2.v.b.207.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.s.a.57.2	✓	24	5.4	even	2
850.2.s.a.343.2	yes	24	85.37	even	16
850.2.s.b.57.2	yes	24	1.1	even	1	trivial
850.2.s.b.343.2	yes	24	85.3	even	16	inner
850.2.v.a.193.2	yes	24	5.3	odd	4
850.2.v.a.207.2	yes	24	17.3	odd	16
850.2.v.b.193.2	yes	24	5.2	odd	4
850.2.v.b.207.2	yes	24	85.54	odd	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{2} +(0.828527 - 1.23998i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-1.46265 - 0.290940i) q^{6} +(0.683252 - 3.43494i) q^{7} +(0.923880 + 0.382683i) q^{8} +(0.296960 + 0.716925i) q^{9} +(0.279207 - 1.40367i) q^{11} +(0.290940 + 1.46265i) q^{12} -0.687320i q^{13} +(-3.43494 + 0.683252i) q^{14} -1.00000i q^{16} +(1.10961 - 3.97099i) q^{17} +(0.548711 - 0.548711i) q^{18} +(-0.0862003 + 0.208106i) q^{19} +(-3.69316 - 3.69316i) q^{21} +(-1.40367 + 0.279207i) q^{22} +(-0.536616 + 0.358556i) q^{23} +(1.23998 - 0.828527i) q^{24} +(-0.635001 + 0.263026i) q^{26} +(5.52298 + 1.09859i) q^{27} +(1.94574 + 2.91200i) q^{28} +(-3.16366 + 4.73475i) q^{29} +(-2.14661 - 10.7917i) q^{31} +(-0.923880 + 0.382683i) q^{32} +(-1.50919 - 1.50919i) q^{33} +(-4.09335 + 0.494483i) q^{34} +(-0.716925 - 0.296960i) q^{36} +(-0.351736 - 0.235023i) q^{37} +0.225252 q^{38} +(-0.852262 - 0.569463i) q^{39} +(-1.49783 - 2.24166i) q^{41} +(-1.99872 + 4.82535i) q^{42} +(-1.23847 + 2.98993i) q^{43} +(0.795115 + 1.18997i) q^{44} +(0.536616 + 0.358556i) q^{46} -4.97288 q^{47} +(-1.23998 - 0.828527i) q^{48} +(-4.86483 - 2.01508i) q^{49} +(-4.00460 - 4.66597i) q^{51} +(0.486008 + 0.486008i) q^{52} +(2.60552 - 1.07924i) q^{53} +(-1.09859 - 5.52298i) q^{54} +(1.94574 - 2.91200i) q^{56} +(0.186628 + 0.279308i) q^{57} +(5.58502 + 1.11093i) q^{58} +(2.73373 - 1.13235i) q^{59} +(-11.0227 + 7.36516i) q^{61} +(-9.14879 + 6.11303i) q^{62} +(2.66550 - 0.530200i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-0.816768 + 1.97185i) q^{66} +(5.28482 - 5.28482i) q^{67} +(2.02330 + 3.59253i) q^{68} +0.962466i q^{69} +(10.6099 - 2.11045i) q^{71} +0.775994i q^{72} +(-1.91332 - 9.61892i) q^{73} +(-0.0825290 + 0.414901i) q^{74} +(-0.0862003 - 0.208106i) q^{76} +(-4.63076 - 1.91812i) q^{77} +(-0.199969 + 1.00531i) q^{78} +(1.79628 + 0.357303i) q^{79} +(4.29203 - 4.29203i) q^{81} +(-1.49783 + 2.24166i) q^{82} +(0.978574 + 2.36249i) q^{83} +5.22292 q^{84} +3.23628 q^{86} +(3.24981 + 7.84575i) q^{87} +(0.795115 - 1.18997i) q^{88} +(-9.75720 + 9.75720i) q^{89} +(-2.36090 - 0.469613i) q^{91} +(0.125908 - 0.632982i) q^{92} +(-15.1601 - 6.27950i) q^{93} +(1.90304 + 4.59434i) q^{94} +(-0.290940 + 1.46265i) q^{96} +(1.72004 + 8.64723i) q^{97} +5.26566i q^{98} +(1.08924 - 0.216663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 16 q^{7} - 8 q^{9} - 16 q^{18} - 8 q^{22} - 32 q^{23} + 8 q^{27} - 16 q^{29} + 16 q^{31} + 8 q^{33} + 16 q^{34} + 48 q^{37} - 32 q^{39} + 48 q^{41} + 16 q^{42} - 8 q^{43} + 16 q^{44} + 32 q^{46}+ \cdots + 24 q^{99}+O(q^{100}) \) 24 * q + 8 * q^3 - 16 * q^7 - 8 * q^9 - 16 * q^18 - 8 * q^22 - 32 * q^23 + 8 * q^27 - 16 * q^29 + 16 * q^31 + 8 * q^33 + 16 * q^34 + 48 * q^37 - 32 * q^39 + 48 * q^41 + 16 * q^42 - 8 * q^43 + 16 * q^44 + 32 * q^46 - 16 * q^47 - 16 * q^49 + 64 * q^51 + 32 * q^53 - 48 * q^54 + 8 * q^59 + 16 * q^61 - 16 * q^62 + 64 * q^63 + 8 * q^66 + 48 * q^67 - 32 * q^71 - 8 * q^73 - 64 * q^77 - 16 * q^78 - 16 * q^79 - 56 * q^81 + 48 * q^82 - 48 * q^83 + 32 * q^84 - 16 * q^86 - 16 * q^87 + 16 * q^88 + 48 * q^89 - 48 * q^91 + 64 * q^93 - 32 * q^94 + 64 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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