LMFDB - Embedded newform 850.2.v.a.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (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			193.2
Character	$\chi$	$=$	850.193
Dual form			850.2.v.a.207.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{2} +(1.23998 + 0.828527i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.46265 - 0.290940i) q^{6} +(-3.43494 - 0.683252i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-0.296960 - 0.716925i) q^{9} +(0.279207 - 1.40367i) q^{11} +(1.46265 - 0.290940i) q^{12} +0.687320 q^{13} +(3.43494 - 0.683252i) q^{14} -1.00000i q^{16} +(-3.97099 - 1.10961i) q^{17} +(0.548711 + 0.548711i) q^{18} +(0.0862003 - 0.208106i) q^{19} +(-3.69316 - 3.69316i) q^{21} +(0.279207 + 1.40367i) q^{22} +(-0.358556 - 0.536616i) q^{23} +(-1.23998 + 0.828527i) q^{24} +(-0.635001 + 0.263026i) q^{26} +(1.09859 - 5.52298i) q^{27} +(-2.91200 + 1.94574i) q^{28} +(3.16366 - 4.73475i) q^{29} +(-2.14661 - 10.7917i) q^{31} +(0.382683 + 0.923880i) q^{32} +(1.50919 - 1.50919i) q^{33} +(4.09335 - 0.494483i) q^{34} +(-0.716925 - 0.296960i) q^{36} +(-0.235023 + 0.351736i) q^{37} +0.225252i q^{38} +(0.852262 + 0.569463i) q^{39} +(-1.49783 - 2.24166i) q^{41} +(4.82535 + 1.99872i) q^{42} +(-2.98993 - 1.23847i) q^{43} +(-0.795115 - 1.18997i) q^{44} +(0.536616 + 0.358556i) q^{46} +4.97288i q^{47} +(0.828527 - 1.23998i) q^{48} +(4.86483 + 2.01508i) q^{49} +(-4.00460 - 4.66597i) q^{51} +(0.486008 - 0.486008i) q^{52} +(1.07924 + 2.60552i) q^{53} +(1.09859 + 5.52298i) q^{54} +(1.94574 - 2.91200i) q^{56} +(0.279308 - 0.186628i) q^{57} +(-1.11093 + 5.58502i) q^{58} +(-2.73373 + 1.13235i) q^{59} +(-11.0227 + 7.36516i) q^{61} +(6.11303 + 9.14879i) q^{62} +(0.530200 + 2.66550i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-0.816768 + 1.97185i) q^{66} +(-5.28482 - 5.28482i) q^{67} +(-3.59253 + 2.02330i) q^{68} -0.962466i q^{69} +(10.6099 - 2.11045i) q^{71} +0.775994 q^{72} +(9.61892 - 1.91332i) q^{73} +(0.0825290 - 0.414901i) q^{74} +(-0.0862003 - 0.208106i) q^{76} +(-1.91812 + 4.63076i) q^{77} +(-1.00531 - 0.199969i) q^{78} +(-1.79628 - 0.357303i) q^{79} +(4.29203 - 4.29203i) q^{81} +(2.24166 + 1.49783i) q^{82} +(-2.36249 + 0.978574i) q^{83} -5.22292 q^{84} +3.23628 q^{86} +(7.84575 - 3.24981i) q^{87} +(1.18997 + 0.795115i) q^{88} +(9.75720 - 9.75720i) q^{89} +(-2.36090 - 0.469613i) q^{91} +(-0.632982 - 0.125908i) q^{92} +(6.27950 - 15.1601i) q^{93} +(-1.90304 - 4.59434i) q^{94} +(-0.290940 + 1.46265i) q^{96} +(8.64723 - 1.72004i) q^{97} -5.26566 q^{98} +(-1.08924 + 0.216663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Character values

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

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	1.23998	+	0.828527i	0.715902	+	0.478351i	0.859402	−	0.511300i	$-0.170836\pi$
$3$	1.23998	+	0.828527i	0.715902	+	0.478351i	−0.143500	+	0.989650i	$0.545836\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	−1.46265	−	0.290940i	−0.597126	−	0.118776i
$7$	−3.43494	−	0.683252i	−1.29829	−	0.258245i	−0.502898	−	0.864346i	$-0.667733\pi$
$7$	−3.43494	−	0.683252i	−1.29829	−	0.258245i	−0.795388	+	0.606101i	$0.792733\pi$
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	−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	$-0.00672189\pi$
$12$	1.46265	−	0.290940i	0.422232	−	0.0839872i
$13$	0.687320			0.190628			0.0953141	−	0.995447i	$-0.469614\pi$
$13$	0.687320			0.190628			0.0953141	+	0.995447i	$0.469614\pi$
$14$	3.43494	−	0.683252i	0.918027	−	0.182607i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−3.97099	−	1.10961i	−0.963106	−	0.269121i
$17$	−3.97099	−	1.10961i	−0.963106	−	0.269121i
$18$	0.548711	+	0.548711i	0.129332	+	0.129332i
$19$	0.0862003	−	0.208106i	0.0197757	−	0.0477428i	−0.913683	−	0.406427i	$-0.866775\pi$
$19$	0.0862003	−	0.208106i	0.0197757	−	0.0477428i	0.933459	+	0.358684i	$0.116775\pi$
$20$		0			0
$21$	−3.69316	−	3.69316i	−0.805914	−	0.805914i
$22$	0.279207	+	1.40367i	0.0595272	+	0.299263i
$23$	−0.358556	−	0.536616i	−0.0747640	−	0.111892i	0.792203	−	0.610257i	$-0.208934\pi$
$23$	−0.358556	−	0.536616i	−0.0747640	−	0.111892i	−0.866967	+	0.498365i	$0.833934\pi$
$24$	−1.23998	+	0.828527i	−0.253110	+	0.169122i
$25$		0			0
$26$	−0.635001	+	0.263026i	−0.124534	+	0.0515836i
$27$	1.09859	−	5.52298i	0.211423	−	1.06290i
$28$	−2.91200	+	1.94574i	−0.550317	+	0.367710i
$29$	3.16366	−	4.73475i	0.587477	−	0.879222i	−0.412012	−	0.911178i	$-0.635174\pi$
$29$	3.16366	−	4.73475i	0.587477	−	0.879222i	0.999489	+	0.0319568i	$0.0101739\pi$
$30$		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	$-0.513371\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	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
$37$	−0.235023	+	0.351736i	−0.0386375	+	0.0578251i	−0.850286	−	0.526322i	$-0.823571\pi$
$37$	−0.235023	+	0.351736i	−0.0386375	+	0.0578251i	0.811648	+	0.584147i	$0.198571\pi$
$38$			0.225252i			0.0365408i
$39$	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	$0.880017\pi$
$42$	4.82535	+	1.99872i	0.744568	+	0.308410i
$43$	−2.98993	−	1.23847i	−0.455960	−	0.188865i	0.142869	−	0.989742i	$-0.454367\pi$
$43$	−2.98993	−	1.23847i	−0.455960	−	0.188865i	−0.598829	+	0.800877i	$0.704367\pi$
$44$	−0.795115	−	1.18997i	−0.119868	−	0.179395i
$45$		0			0
$46$	0.536616	+	0.358556i	0.0791198	+	0.0528661i
$47$			4.97288i			0.725369i	0.931912	+	0.362685i	$0.118140\pi$
$47$			4.97288i			0.725369i	−0.931912	+	0.362685i	$0.881860\pi$
$48$	0.828527	−	1.23998i	0.119588	−	0.178976i
$49$	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
$53$	1.07924	+	2.60552i	0.148245	+	0.357896i	0.980506	−	0.196488i	$-0.0629537\pi$
$53$	1.07924	+	2.60552i	0.148245	+	0.357896i	−0.832261	+	0.554384i	$0.812954\pi$
$54$	1.09859	+	5.52298i	0.149499	+	0.751582i
$55$		0			0
$56$	1.94574	−	2.91200i	0.260010	−	0.389133i
$57$	0.279308	−	0.186628i	0.0369953	−	0.0247195i
$58$	−1.11093	+	5.58502i	−0.145872	+	0.733349i
$59$	−2.73373	+	1.13235i	−0.355902	+	0.147419i	−0.553468	−	0.832870i	$-0.686696\pi$
$59$	−2.73373	+	1.13235i	−0.355902	+	0.147419i	0.197567	+	0.980289i	$0.436696\pi$
$60$		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	$0.989893\pi$
$62$	6.11303	+	9.14879i	0.776355	+	1.16190i
$63$	0.530200	+	2.66550i	0.0667989	+	0.335821i
$64$	−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	$-0.400911\pi$
$67$	−5.28482	−	5.28482i	−0.645644	−	0.645644i	−0.951937	+	0.306293i	$0.900911\pi$
$68$	−3.59253	+	2.02330i	−0.435658	+	0.245361i
$69$		−	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	$0.215639\pi$
$72$	0.775994			0.0914518
$73$	9.61892	−	1.91332i	1.12581	−	0.223937i	0.403145	−	0.915136i	$-0.367917\pi$
$73$	9.61892	−	1.91332i	1.12581	−	0.223937i	0.722665	+	0.691199i	$0.242917\pi$
$74$	0.0825290	−	0.414901i	0.00959380	−	0.0482313i
$75$		0			0
$76$	−0.0862003	−	0.208106i	−0.00988786	−	0.0238714i
$77$	−1.91812	+	4.63076i	−0.218590	+	0.527724i
$78$	−1.00531	−	0.199969i	−0.113829	−	0.0226420i
$79$	−1.79628	−	0.357303i	−0.202098	−	0.0401997i	0.0930034	−	0.995666i	$-0.470353\pi$
$79$	−1.79628	−	0.357303i	−0.202098	−	0.0401997i	−0.295101	+	0.955466i	$0.595353\pi$
$80$		0			0
$81$	4.29203	−	4.29203i	0.476892	−	0.476892i
$82$	2.24166	+	1.49783i	0.247550	+	0.165408i
$83$	−2.36249	+	0.978574i	−0.259317	+	0.107412i	−0.508554	−	0.861030i	$-0.669820\pi$
$83$	−2.36249	+	0.978574i	−0.259317	+	0.107412i	0.249238	+	0.968442i	$0.419820\pi$
$84$	−5.22292			−0.569867
$85$		0			0
$86$	3.23628			0.348977
$87$	7.84575	−	3.24981i	0.841152	−	0.348417i
$88$	1.18997	+	0.795115i	0.126852	+	0.0847596i
$89$	9.75720	−	9.75720i	1.03426	−	1.03426i	0.0348693	−	0.999392i	$-0.488899\pi$
$89$	9.75720	−	9.75720i	1.03426	−	1.03426i	0.999392	−	0.0348693i	$-0.0111015\pi$
$90$		0			0
$91$	−2.36090	−	0.469613i	−0.247490	−	0.0492288i
$92$	−0.632982	−	0.125908i	−0.0659929	−	0.0131268i
$93$	6.27950	−	15.1601i	0.651154	−	1.57202i
$94$	−1.90304	−	4.59434i	−0.196284	−	0.473870i
$95$		0			0
$96$	−0.290940	+	1.46265i	−0.0296940	+	0.149282i
$97$	8.64723	−	1.72004i	0.877993	−	0.174644i	0.264540	−	0.964375i	$-0.414780\pi$
$97$	8.64723	−	1.72004i	0.877993	−	0.174644i	0.613453	+	0.789731i	$0.289780\pi$
$98$	−5.26566			−0.531912
$99$	−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	$0.771307\pi$
$102$	5.48536	+	2.77830i	0.543131	+	0.275093i
$103$	−12.8336	−	12.8336i	−1.26454	−	1.26454i	−0.948871	−	0.315665i	$-0.897773\pi$
$103$	−12.8336	−	12.8336i	−1.26454	−	1.26454i	−0.315665	−	0.948871i	$-0.602227\pi$
$104$	−0.263026	+	0.635001i	−0.0257918	+	0.0622669i
$105$		0			0
$106$	−1.99418	−	1.99418i	−0.193692	−	0.193692i
$107$	−2.83228	−	14.2388i	−0.273807	−	1.37652i	−0.835643	−	0.549273i	$-0.814905\pi$
$107$	−2.83228	−	14.2388i	−0.273807	−	1.37652i	0.561836	−	0.827249i	$-0.310095\pi$
$108$	−3.12852	−	4.68215i	−0.301042	−	0.450540i
$109$	−10.7548	+	7.18615i	−1.03013	+	0.688308i	−0.951201	−	0.308572i	$-0.900149\pi$
$109$	−10.7548	+	7.18615i	−1.03013	+	0.688308i	−0.0789251	+	0.996881i	$0.525149\pi$
$110$		0			0
$111$	−0.582846	+	0.241423i	−0.0553213	+	0.0229148i
$112$	−0.683252	+	3.43494i	−0.0645613	+	0.324571i
$113$	2.50435	−	1.67335i	0.235589	−	0.157416i	−0.432172	−	0.901791i	$-0.642253\pi$
$113$	2.50435	−	1.67335i	0.235589	−	0.157416i	0.667761	+	0.744376i	$0.267253\pi$
$114$	−0.186628	+	0.279308i	−0.0174793	+	0.0261596i
$115$		0			0
$116$	−1.11093	−	5.58502i	−0.103147	−	0.518556i
$117$	−0.204107	−	0.492757i	−0.0188697	−	0.0455554i
$118$	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
$122$	7.36516	−	11.0227i	0.666810	−	0.997951i
$123$		−	4.02061i		−	0.362526i
$124$	−9.14879	−	6.11303i	−0.821586	−	0.548966i
$125$		0			0
$126$	−1.50988	−	2.25970i	−0.134511	−	0.201310i
$127$	−11.5255	−	4.77400i	−1.02272	−	0.423624i	−0.192640	−	0.981270i	$-0.561705\pi$
$127$	−11.5255	−	4.77400i	−1.02272	−	0.423624i	−0.830079	+	0.557645i	$0.811705\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	−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	$0.359788\pi$
$132$		−	2.13432i		−	0.185769i
$133$	−0.438282	+	0.655936i	−0.0380039	+	0.0568768i
$134$	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	−0.888138	−	0.459577i	$-0.848001\pi$
$137$	−5.01618	+	5.01618i	−0.428561	+	0.428561i	0.459577	+	0.888138i	$0.348001\pi$
$138$	0.368320	+	0.889203i	0.0313535	+	0.0756940i
$139$	2.05197	+	10.3159i	0.174045	+	0.874986i	0.964827	+	0.262887i	$0.0846745\pi$
$139$	2.05197	+	10.3159i	0.174045	+	0.874986i	−0.790781	+	0.612099i	$0.790325\pi$
$140$		0			0
$141$	−4.12017	+	6.16627i	−0.346981	+	0.519294i
$142$	−8.99468	+	6.01005i	−0.754817	+	0.504352i
$143$	0.191905	−	0.964770i	0.0160479	−	0.0806781i
$144$	−0.716925	+	0.296960i	−0.0597438	+	0.0247467i
$145$		0			0
$146$	−8.15453	+	5.44868i	−0.674874	+	0.450936i
$147$	4.36274	+	6.52931i	0.359833	+	0.538528i
$148$	0.0825290	+	0.414901i	0.00678384	+	0.0341047i
$149$	−3.74622	−	3.74622i	−0.306902	−	0.306902i	0.536804	−	0.843707i	$-0.319631\pi$
$149$	−3.74622	−	3.74622i	−0.306902	−	0.306902i	−0.843707	+	0.536804i	$0.819631\pi$
$150$		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
$153$	0.383716	+	3.17641i	0.0310216	+	0.256798i
$154$		−	5.01229i		−	0.403902i
$155$		0			0
$156$	1.00531	−	0.199969i	0.0804894	−	0.0160103i
$157$	−15.0303			−1.19955			−0.599773	−	0.800170i	$-0.704742\pi$
$157$	−15.0303			−1.19955			−0.599773	+	0.800170i	$0.704742\pi$
$158$	1.79628	−	0.357303i	0.142905	−	0.0284255i
$159$	−0.820509	+	4.12498i	−0.0650706	+	0.327132i
$160$		0			0
$161$	0.864973	+	2.08823i	0.0681694	+	0.164576i
$162$	−2.32283	+	5.60781i	−0.182499	+	0.440591i
$163$	14.6915	+	2.92232i	1.15073	+	0.228894i	0.733358	−	0.679842i	$-0.237952\pi$
$163$	14.6915	+	2.92232i	1.15073	+	0.228894i	0.417370	+	0.908736i	$0.362952\pi$
$164$	−2.64422	−	0.525968i	−0.206479	−	0.0410712i
$165$		0			0
$166$	1.80817	−	1.80817i	0.140341	−	0.140341i
$167$	−6.33305	−	4.23161i	−0.490066	−	0.327452i	0.285865	−	0.958270i	$-0.407719\pi$
$167$	−6.33305	−	4.23161i	−0.490066	−	0.327452i	−0.775930	+	0.630818i	$0.782719\pi$
$168$	4.82535	−	1.99872i	0.372284	−	0.154205i
$169$	−12.5276			−0.963661
$170$		0			0
$171$	−0.174795			−0.0133669
$172$	−2.98993	+	1.23847i	−0.227980	+	0.0944324i
$173$	15.1101	+	10.0963i	1.14880	+	0.767606i	0.976090	−	0.217366i	$-0.0697466\pi$
$173$	15.1101	+	10.0963i	1.14880	+	0.767606i	0.172713	+	0.984972i	$0.444747\pi$
$174$	−6.00487	+	6.00487i	−0.455228	+	0.455228i
$175$		0			0
$176$	−1.40367	−	0.279207i	−0.105806	−	0.0210460i
$177$	−4.32795	−	0.860883i	−0.325309	−	0.0647080i
$178$	−5.28056	+	12.7484i	−0.395795	+	0.955533i
$179$	−4.94606	−	11.9408i	−0.369686	−	0.892501i	−0.993802	−	0.111169i	$-0.964541\pi$
$179$	−4.94606	−	11.9408i	−0.369686	−	0.892501i	0.624116	−	0.781332i	$-0.285459\pi$
$180$		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	$0.994514\pi$
$182$	2.36090	−	0.469613i	0.175002	−	0.0348100i
$183$	−19.7702			−1.46145
$184$	0.632982	−	0.125908i	0.0466641	−	0.00928206i
$185$		0			0
$186$			16.4091i			1.20318i
$187$	−2.66626	+	5.26415i	−0.194976	+	0.384953i
$188$	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	$0.462400\pi$
$192$	−0.290940	−	1.46265i	−0.0209968	−	0.105558i
$193$	−0.326059	−	0.487981i	−0.0234702	−	0.0351257i	0.819549	−	0.573009i	$-0.194224\pi$
$193$	−0.326059	−	0.487981i	−0.0234702	−	0.0351257i	−0.843019	+	0.537883i	$0.819224\pi$
$194$	−7.33077	+	4.89826i	−0.526318	+	0.351675i
$195$		0			0
$196$	4.86483	−	2.01508i	0.347488	−	0.143934i
$197$	3.47533	−	17.4717i	0.247607	−	1.24481i	−0.634190	−	0.773177i	$-0.718666\pi$
$197$	3.47533	−	17.4717i	0.247607	−	1.24481i	0.881797	−	0.471629i	$-0.156334\pi$
$198$	0.923413	−	0.617005i	0.0656241	−	0.0438486i
$199$	−1.99127	+	2.98014i	−0.141157	+	0.211256i	−0.895311	−	0.445441i	$-0.853047\pi$
$199$	−1.99127	+	2.98014i	−0.141157	+	0.211256i	0.754154	+	0.656697i	$0.228047\pi$
$200$		0			0
$201$	−2.17445	−	10.9317i	−0.153374	−	0.771062i
$202$	−5.06297	−	12.2231i	−0.356230	−	0.860014i
$203$	−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
$207$	−0.278237	+	0.416411i	−0.0193388	+	0.0289426i
$208$		−	0.687320i		−	0.0476571i
$209$	−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	$0.761750\pi$
$212$	2.60552	+	1.07924i	0.178948	+	0.0741227i
$213$	14.9047	+	6.17372i	1.02125	+	0.423016i
$214$	8.06566	+	12.0711i	0.551357	+	0.825164i
$215$		0			0
$216$	4.68215	+	3.12852i	0.318580	+	0.212868i
$217$			38.5357i			2.61597i
$218$	7.18615	−	10.7548i	0.486707	−	0.728409i
$219$	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
$223$	−3.81376	−	9.20723i	−0.255388	−	0.616562i	0.743234	−	0.669031i	$-0.233291\pi$
$223$	−3.81376	−	9.20723i	−0.255388	−	0.616562i	−0.998623	+	0.0524694i	$0.983291\pi$
$224$	−0.683252	−	3.43494i	−0.0456517	−	0.229507i
$225$		0			0
$226$	−1.67335	+	2.50435i	−0.111310	+	0.166587i
$227$	13.2623	−	8.86159i	0.880250	−	0.588164i	−0.0312282	−	0.999512i	$-0.509942\pi$
$227$	13.2623	−	8.86159i	0.880250	−	0.588164i	0.911478	+	0.411348i	$0.134942\pi$
$228$	0.0655350	−	0.329466i	0.00434016	−	0.0218195i
$229$	−26.3976	+	10.9342i	−1.74440	+	0.722554i	−0.746004	+	0.665941i	$0.768030\pi$
$229$	−26.3976	+	10.9342i	−1.74440	+	0.722554i	−0.998396	+	0.0566131i	$0.981970\pi$
$230$		0			0
$231$	−6.21514	+	4.15282i	−0.408926	+	0.273236i
$232$	3.16366	+	4.73475i	0.207704	+	0.310852i
$233$	4.64291	+	23.3415i	0.304167	+	1.52915i	0.766383	+	0.642384i	$0.222055\pi$
$233$	4.64291	+	23.3415i	0.304167	+	1.52915i	−0.462215	+	0.886768i	$0.652945\pi$
$234$	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
$238$	−14.3983	−	1.09827i	−0.933301	−	0.0711901i
$239$		−	22.2129i		−	1.43683i	−0.695614	−	0.718416i	$-0.744868\pi$
$239$		−	22.2129i		−	1.43683i	0.695614	−	0.718416i	$-0.255132\pi$
$240$		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	$0.528173\pi$
$242$	−8.95175			−0.575440
$243$	−7.69083	+	1.52980i	−0.493367	+	0.0981369i
$244$	−2.58630	+	13.0022i	−0.165571	+	0.832381i
$245$		0			0
$246$	1.53862	+	3.71456i	0.0980989	+	0.236832i
$247$	0.0592472	−	0.143035i	0.00376981	−	0.00910113i
$248$	10.7917	+	2.14661i	0.685276	+	0.136310i
$249$	−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	$0.359533\pi$
$252$	2.25970	+	1.50988i	0.142348	+	0.0951136i
$253$	−0.853344	+	0.353466i	−0.0536493	+	0.0222222i
$254$	12.4751			0.782755
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	23.1908	−	9.60595i	1.44660	−	0.599203i	0.485215	−	0.874395i	$-0.338741\pi$
$257$	23.1908	−	9.60595i	1.44660	−	0.599203i	0.961389	+	0.275192i	$0.0887415\pi$
$258$	4.01292	+	2.68135i	0.249833	+	0.166933i
$259$	1.04761	−	1.04761i	0.0650955	−	0.0650955i
$260$		0			0
$261$	−4.33395	−	0.862075i	−0.268264	−	0.0533611i
$262$	−19.2420	−	3.82748i	−1.18878	−	0.236462i
$263$	−3.53421	+	8.53235i	−0.217929	+	0.526127i	−0.994600	−	0.103779i	$-0.966907\pi$
$263$	−3.53421	+	8.53235i	−0.217929	+	0.526127i	0.776671	+	0.629906i	$0.216907\pi$
$264$	0.816768	+	1.97185i	0.0502686	+	0.121359i
$265$		0			0
$266$	0.153904	−	0.773729i	0.00943647	−	0.0474404i
$267$	20.1828	−	4.01461i	1.23517	−	0.245690i
$268$	−7.47387			−0.456539
$269$	3.39522	−	0.675351i	0.207010	−	0.0411768i	−0.0904959	−	0.995897i	$-0.528845\pi$
$269$	3.39522	−	0.675351i	0.207010	−	0.0411768i	0.297506	+	0.954720i	$0.403845\pi$
$270$		0			0
$271$		−	20.2345i		−	1.22916i	−0.788855	−	0.614579i	$-0.789326\pi$
$271$		−	20.2345i		−	1.22916i	0.788855	−	0.614579i	$-0.210674\pi$
$272$	−1.10961	+	3.97099i	−0.0672802	+	0.240777i
$273$	−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
$277$	3.91058	+	19.6598i	0.234964	+	1.18124i	0.900493	+	0.434871i	$0.143206\pi$
$277$	3.91058	+	19.6598i	0.234964	+	1.18124i	−0.665529	+	0.746372i	$0.731794\pi$
$278$	−5.84350	−	8.74542i	−0.350470	−	0.524515i
$279$	−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	$0.148942\pi$
$282$	1.44681	−	7.27361i	0.0861563	−	0.433137i
$283$	−16.6821	+	11.1466i	−0.991650	+	0.662600i	−0.941806	−	0.336157i	$-0.890873\pi$
$283$	−16.6821	+	11.1466i	−0.991650	+	0.662600i	−0.0498445	+	0.998757i	$0.515873\pi$
$284$	6.01005	−	8.99468i	0.356631	−	0.533736i
$285$		0			0
$286$	0.191905	+	0.964770i	0.0113476	+	0.0570481i
$287$	3.61334	+	8.72338i	0.213289	+	0.514925i
$288$	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
$292$	5.44868	−	8.15453i	0.318860	−	0.477208i
$293$		−	15.9816i		−	0.933653i	−0.884349	−	0.466826i	$-0.845397\pi$
$293$		−	15.9816i		−	0.933653i	0.884349	−	0.466826i	$-0.154603\pi$
$294$	−6.52931	−	4.36274i	−0.380797	−	0.254440i
$295$		0			0
$296$	−0.235023	−	0.351736i	−0.0136604	−	0.0204443i
$297$	−7.44570	−	3.08411i	−0.432044	−	0.178958i
$298$	4.89467	+	2.02744i	0.283541	+	0.117446i
$299$	−0.246442	−	0.368827i	−0.0142521	−	0.0213298i
$300$		0			0
$301$	9.42405	+	6.29695i	0.543193	+	0.362950i
$302$		−	10.4918i		−	0.603734i
$303$	−10.9616	+	16.4052i	−0.629726	+	0.942451i
$304$	−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	−0.666740	−	0.745290i	$-0.732311\pi$
$307$	1.37631	−	1.37631i	0.0785503	−	0.0785503i	0.745290	+	0.666740i	$0.232311\pi$
$308$	1.91812	+	4.63076i	0.109295	+	0.263862i
$309$	−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	$0.984177\pi$
$312$	−0.852262	+	0.569463i	−0.0482498	+	0.0322395i
$313$	5.54040	−	27.8535i	0.313162	−	1.57437i	−0.428465	−	0.903559i	$-0.640945\pi$
$313$	5.54040	−	27.8535i	0.313162	−	1.57437i	0.741627	−	0.670813i	$-0.234055\pi$
$314$	13.8862	−	5.75183i	0.783641	−	0.324595i
$315$		0			0
$316$	−1.52281	+	1.01751i	−0.0856650	+	0.0572395i
$317$	15.3659	+	22.9967i	0.863035	+	1.29162i	0.955225	+	0.295882i	$0.0956134\pi$
$317$	15.3659	+	22.9967i	0.863035	+	1.29162i	−0.0921896	+	0.995741i	$0.529387\pi$
$318$	−0.820509	−	4.12498i	−0.0460119	−	0.231317i
$319$	−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
$323$	−0.573218	+	0.730738i	−0.0318947	+	0.0406593i
$324$		−	6.06985i		−	0.337214i
$325$		0			0
$326$	−14.6915	+	2.92232i	−0.813688	+	0.161853i
$327$	−19.2897			−1.06672
$328$	2.64422	−	0.525968i	0.146003	−	0.0290418i
$329$	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	$-0.519444\pi$
$332$	−0.978574	+	2.36249i	−0.0537062	+	0.129658i
$333$	0.321961	+	0.0640420i	0.0176434	+	0.00350948i
$334$	7.47034	+	1.48594i	0.408759	+	0.0813072i
$335$		0			0
$336$	−3.69316	+	3.69316i	−0.201479	+	0.201479i
$337$	10.9142	+	7.29265i	0.594536	+	0.397256i	0.816118	−	0.577886i	$-0.196122\pi$
$337$	10.9142	+	7.29265i	0.594536	+	0.397256i	−0.221582	+	0.975142i	$0.571122\pi$
$338$	11.5740	−	4.79410i	0.629542	−	0.260765i
$339$	4.49175			0.243959
$340$		0			0
$341$	−15.7474			−0.852769
$342$	0.161489	−	0.0668910i	0.00873233	−	0.00361705i
$343$	5.05041	+	3.37457i	0.272696	+	0.182210i
$344$	2.28839	−	2.28839i	0.123382	−	0.123382i
$345$		0			0
$346$	−17.8236	−	3.54534i	−0.958205	−	0.190599i
$347$	−18.8905	−	3.75756i	−1.01410	−	0.201717i	−0.340052	−	0.940407i	$-0.610445\pi$
$347$	−18.8905	−	3.75756i	−1.01410	−	0.201717i	−0.674045	+	0.738690i	$0.735445\pi$
$348$	3.24981	−	7.84575i	0.174208	−	0.420576i
$349$	8.24203	+	19.8980i	0.441186	+	1.06512i	0.975533	+	0.219852i	$0.0705575\pi$
$349$	8.24203	+	19.8980i	0.441186	+	1.06512i	−0.534347	+	0.845265i	$0.679443\pi$
$350$		0			0
$351$	0.755082	−	3.79605i	0.0403033	−	0.202618i
$352$	1.40367	−	0.279207i	0.0748159	−	0.0148818i
$353$	7.84481			0.417537			0.208768	−	0.977965i	$-0.433054\pi$
$353$	7.84481			0.417537			0.208768	+	0.977965i	$0.433054\pi$
$354$	4.32795	−	0.860883i	0.230028	−	0.0457554i
$355$		0			0
$356$		−	13.7988i		−	0.731333i
$357$	10.5675	+	18.7635i	0.559293	+	0.993069i
$358$	9.13913	+	9.13913i	0.483018	+	0.483018i
$359$	−4.46689	+	10.7840i	−0.235753	+	0.569159i	−0.996835	−	0.0794970i	$-0.974669\pi$
$359$	−4.46689	+	10.7840i	−0.235753	+	0.569159i	0.761082	+	0.648656i	$0.224669\pi$
$360$		0			0
$361$	13.3992	+	13.3992i	0.705218	+	0.705218i
$362$	−1.11267	−	5.59375i	−0.0584805	−	0.294001i
$363$	7.41677	+	11.1000i	0.389280	+	0.582598i
$364$	−2.00148	+	1.33734i	−0.104906	+	0.0700959i
$365$		0			0
$366$	18.2653	−	7.56573i	0.954741	−	0.395467i
$367$	2.94262	−	14.7935i	0.153603	−	0.772216i	−0.824786	−	0.565445i	$-0.808704\pi$
$367$	2.94262	−	14.7935i	0.153603	−	0.772216i	0.978389	−	0.206771i	$-0.0662956\pi$
$368$	−0.536616	+	0.358556i	−0.0279731	+	0.0186910i
$369$	−1.16231	+	1.73952i	−0.0605074	+	0.0905557i
$370$		0			0
$371$	−1.92691	−	9.68722i	−0.100040	−	0.502935i
$372$	−6.27950	−	15.1601i	−0.325577	−	0.786012i
$373$	−0.0702693	+	0.0702693i	−0.00363841	+	0.00363841i	−0.708924	−	0.705285i	$-0.750819\pi$
$373$	−0.0702693	+	0.0702693i	−0.00363841	+	0.00363841i	0.705285	+	0.708924i	$0.250819\pi$
$374$	0.448801	−	5.88377i	0.0232069	−	0.304243i
$375$		0			0
$376$	−4.59434	−	1.90304i	−0.236935	−	0.0981418i
$377$	2.17445	−	3.25429i	0.111990	−	0.167604i
$378$		−	19.7217i		−	1.01438i
$379$	−11.0779	−	7.40200i	−0.569032	−	0.380215i	0.237516	−	0.971384i	$-0.423667\pi$
$379$	−11.0779	−	7.40200i	−0.569032	−	0.380215i	−0.806548	+	0.591168i	$0.798667\pi$
$380$		0			0
$381$	−10.3359	−	15.4688i	−0.529526	−	0.792492i
$382$	−20.0592	−	8.30880i	−1.02632	−	0.425115i
$383$	−26.2569	−	10.8760i	−1.34167	−	0.555736i	−0.407705	−	0.913114i	$-0.633671\pi$
$383$	−26.2569	−	10.8760i	−1.34167	−	0.555736i	−0.933960	+	0.357377i	$0.883671\pi$
$384$	0.828527	+	1.23998i	0.0422806	+	0.0632774i
$385$		0			0
$386$	0.487981	+	0.326059i	0.0248376	+	0.0165959i
$387$			2.51133i			0.127658i
$388$	4.89826	−	7.33077i	0.248672	−	0.372163i
$389$	28.5749	+	11.8361i	1.44880	+	0.600115i	0.961915	−	0.273349i	$-0.0881313\pi$
$389$	28.5749	+	11.8361i	1.44880	+	0.600115i	0.486890	+	0.873463i	$0.338131\pi$
$390$		0			0
$391$	0.828384	+	2.52876i	0.0418932	+	0.127885i
$392$	−3.72338	+	3.72338i	−0.188059	+	0.188059i
$393$	11.1966	+	27.0309i	0.564792	+	1.36353i
$394$	3.47533	+	17.4717i	0.175085	+	0.880211i
$395$		0			0
$396$	−0.617005	+	0.923413i	−0.0310057	+	0.0464033i
$397$	5.96544	−	3.98598i	0.299397	−	0.200051i	−0.396793	−	0.917908i	$-0.629877\pi$
$397$	5.96544	−	3.98598i	0.299397	−	0.200051i	0.696190	+	0.717857i	$0.254877\pi$
$398$	0.699239	−	3.51531i	0.0350497	−	0.176207i
$399$	−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	$0.252921\pi$
$402$	6.19231	+	9.26744i	0.308844	+	0.462218i
$403$	−1.47541	−	7.41737i	−0.0734953	−	0.369486i
$404$	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
$408$	5.84329	−	1.91418i	0.289286	−	0.0947659i
$409$		−	18.1578i		−	0.897847i	−0.893570	−	0.448924i	$-0.851808\pi$
$409$		−	18.1578i		−	0.897847i	0.893570	−	0.448924i	$-0.148192\pi$
$410$		0			0
$411$	−10.3760	+	2.06391i	−0.511810	+	0.101805i
$412$	−18.1495			−0.894162
$413$	10.1639	−	2.02172i	0.500132	−	0.0994825i
$414$	0.0977039	−	0.491190i	0.00480188	−	0.0241407i
$415$		0			0
$416$	0.263026	+	0.635001i	0.0128959	+	0.0311335i
$417$	−6.00263	+	14.4916i	−0.293950	+	0.709659i
$418$	0.316180	+	0.0628921i	0.0154649	+	0.00307615i
$419$	5.30674	+	1.05558i	0.259251	+	0.0515683i	0.323005	−	0.946397i	$-0.395307\pi$
$419$	5.30674	+	1.05558i	0.259251	+	0.0515683i	−0.0637533	+	0.997966i	$0.520307\pi$
$420$		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	$0.107229\pi$
$422$	−3.83494	−	2.56243i	−0.186682	−	0.124737i
$423$	3.56518	−	1.47675i	0.173345	−	0.0718019i
$424$	−2.82020			−0.136961
$425$		0			0
$426$	−16.1327			−0.781632
$427$	42.8947	−	17.7676i	2.07582	−	0.859833i
$428$	−12.0711	−	8.06566i	−0.583479	−	0.389868i
$429$	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	$0.641597\pi$
$432$	−5.52298	−	1.09859i	−0.265724	−	0.0528559i
$433$	13.3385	−	32.2019i	0.641006	−	1.54752i	−0.184319	−	0.982867i	$-0.559008\pi$
$433$	13.3385	−	32.2019i	0.641006	−	1.54752i	0.825325	−	0.564658i	$-0.190992\pi$
$434$	−14.7470	−	35.6023i	−0.707877	−	1.70897i
$435$		0			0
$436$	−2.52344	+	12.6862i	−0.120851	+	0.607558i
$437$	−0.142581	+	0.0283611i	−0.00682056	+	0.00135669i
$438$	−14.6258			−0.698849
$439$	−2.63978	+	0.525084i	−0.125990	+	0.0250609i	−0.257682	−	0.966230i	$-0.582959\pi$
$439$	−2.63978	+	0.525084i	−0.125990	+	0.0250609i	0.131693	+	0.991291i	$0.457959\pi$
$440$		0			0
$441$		−	4.08612i		−	0.194577i
$442$	2.81344	−	0.339868i	0.133822	−	0.0161659i
$443$	−21.5344	−	21.5344i	−1.02313	−	1.02313i	−0.999726	−	0.0234065i	$-0.992549\pi$
$443$	−21.5344	−	21.5344i	−1.02313	−	1.02313i	−0.0234065	−	0.999726i	$-0.507451\pi$
$444$	−0.241423	+	0.582846i	−0.0114574	+	0.0276607i
$445$		0			0
$446$	7.04691	+	7.04691i	0.333681	+	0.333681i
$447$	−1.54139	−	7.74908i	−0.0729052	−	0.366519i
$448$	1.94574	+	2.91200i	0.0919275	+	0.137579i
$449$	21.9479	−	14.6651i	1.03578	−	0.692089i	0.0832522	−	0.996529i	$-0.473469\pi$
$449$	21.9479	−	14.6651i	1.03578	−	0.692089i	0.952532	+	0.304440i	$0.0984693\pi$
$450$		0			0
$451$	−3.56476	+	1.47657i	−0.167858	+	0.0695291i
$452$	0.587603	−	2.95408i	0.0276385	−	0.138948i
$453$	−13.0096	+	8.69273i	−0.611244	+	0.408420i
$454$	−8.86159	+	13.2623i	−0.415895	+	0.622431i
$455$		0			0
$456$	0.0655350	+	0.329466i	0.00306896	+	0.0154287i
$457$	−9.81102	−	23.6859i	−0.458940	−	1.10798i	−0.968827	−	0.247738i	$-0.920313\pi$
$457$	−9.81102	−	23.6859i	−0.458940	−	1.10798i	0.509887	−	0.860241i	$-0.329687\pi$
$458$	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	$0.725770\pi$
$462$	4.15282	−	6.21514i	0.193207	−	0.289154i
$463$		−	32.8821i		−	1.52816i	−0.645121	−	0.764081i	$-0.723193\pi$
$463$		−	32.8821i		−	1.52816i	0.645121	−	0.764081i	$-0.276807\pi$
$464$	−4.73475	−	3.16366i	−0.219805	−	0.146869i
$465$		0			0
$466$	−13.2219	−	19.7880i	−0.612492	−	0.916660i
$467$	4.42354	+	1.83229i	0.204697	+	0.0847883i	0.482676	−	0.875799i	$-0.339665\pi$
$467$	4.42354	+	1.83229i	0.204697	+	0.0847883i	−0.277979	+	0.960587i	$0.589665\pi$
$468$	−0.492757	−	0.204107i	−0.0227777	−	0.00943483i
$469$	14.5422	+	21.7639i	0.671496	+	1.00496i
$470$		0			0
$471$	−18.6372	−	12.4530i	−0.858758	−	0.573803i
$472$		−	2.95897i		−	0.136198i
$473$	−2.57321	+	3.85109i	−0.118317	+	0.177073i
$474$	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
$478$	8.50050	+	20.5220i	0.388804	+	0.938655i
$479$	−6.42297	−	32.2905i	−0.293473	−	1.47539i	−0.793070	−	0.609130i	$-0.791519\pi$
$479$	−6.42297	−	32.2905i	−0.293473	−	1.47539i	0.499597	−	0.866258i	$-0.333481\pi$
$480$		0			0
$481$	−0.161536	+	0.241755i	−0.00736539	+	0.0110231i
$482$	7.25475	−	4.84747i	0.330445	−	0.220796i
$483$	−0.657607	+	3.30601i	−0.0299222	+	0.150429i
$484$	8.27034	−	3.42569i	0.375925	−	0.155713i
$485$		0			0
$486$	6.51997	−	4.35651i	0.295752	−	0.197615i
$487$	16.8849	+	25.2701i	0.765130	+	1.14510i	0.985499	+	0.169681i	$0.0542738\pi$
$487$	16.8849	+	25.2701i	0.765130	+	1.14510i	−0.220369	+	0.975417i	$0.570726\pi$
$488$	−2.58630	−	13.0022i	−0.117076	−	0.588582i
$489$	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
$493$	−17.8166	+	15.2912i	−0.802420	+	0.688682i
$494$			0.154820i			0.00696570i
$495$		0			0
$496$	−10.7917	+	2.14661i	−0.484563	+	0.0963856i
$497$	−37.8865			−1.69944
$498$	3.74021	−	0.743974i	0.167603	−	0.0333383i
$499$	4.87821	−	24.5244i	0.218379	−	1.09786i	−0.703592	−	0.710604i	$-0.748422\pi$
$499$	4.87821	−	24.5244i	0.218379	−	1.09786i	0.921971	−	0.387260i	$-0.126578\pi$
$500$		0			0
$501$	−4.34684	−	10.4942i	−0.194203	−	0.468847i
$502$	4.09070	−	9.87582i	0.182577	−	0.440779i
$503$	4.24133	+	0.843653i	0.189111	+	0.0376166i	0.288737	−	0.957408i	$-0.406765\pi$
$503$	4.24133	+	0.843653i	0.189111	+	0.0376166i	−0.0996258	+	0.995025i	$0.531765\pi$
$504$	−2.66550	−	0.530200i	−0.118731	−	0.0236170i
$505$		0			0
$506$	0.653121	−	0.653121i	0.0290348	−	0.0290348i
$507$	−15.5340	−	10.3795i	−0.689887	−	0.460968i
$508$	−11.5255	+	4.77400i	−0.511360	+	0.211812i
$509$	14.6760			0.650503			0.325251	−	0.945628i	$-0.394551\pi$
$509$	14.6760			0.650503			0.325251	+	0.945628i	$0.394551\pi$
$510$		0			0
$511$	−34.3477			−1.51945
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	−1.05467	−	0.704705i	−0.0465646	−	0.0311135i
$514$	−17.7495	+	17.7495i	−0.782896	+	0.782896i
$515$		0			0
$516$	−4.73356	−	0.941563i	−0.208383	−	0.0414500i
$517$	6.98029	+	1.38847i	0.306993	+	0.0610646i
$518$	−0.566964	+	1.36877i	−0.0249110	+	0.0601404i
$519$	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	$0.998818\pi$
$522$	4.33395	−	0.862075i	0.189692	−	0.0377320i
$523$	7.38904			0.323100			0.161550	−	0.986865i	$-0.448351\pi$
$523$	7.38904			0.323100			0.161550	+	0.986865i	$0.448351\pi$
$524$	19.2420	−	3.82748i	0.840592	−	0.167204i
$525$		0			0
$526$		−	9.23535i		−	0.402680i
$527$	−3.45048	+	45.2358i	−0.150305	+	1.97050i
$528$	−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
$532$	0.153904	+	0.773729i	0.00667259	+	0.0335454i
$533$	−1.02949	−	1.54074i	−0.0445921	−	0.0667368i
$534$	−17.1102	+	11.4327i	−0.740430	+	0.494739i
$535$		0			0
$536$	6.90495	−	2.86013i	0.298249	−	0.123539i
$537$	3.76031	−	18.9043i	0.162269	−	0.815783i
$538$	−2.87833	+	1.92324i	−0.124093	+	0.0829166i
$539$	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	$0.976010\pi$
$542$	7.74341	+	18.6942i	0.332608	+	0.802986i
$543$	−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
$547$	20.5784	−	30.7977i	0.879868	−	1.31682i	−0.0678469	−	0.997696i	$-0.521613\pi$
$547$	20.5784	−	30.7977i	0.879868	−	1.31682i	0.947715	−	0.319119i	$-0.103387\pi$
$548$			7.09395i			0.303038i
$549$	8.55358	+	5.71532i	0.365058	+	0.243924i
$550$		0			0
$551$	−0.712622	−	1.06651i	−0.0303587	−	0.0454350i
$552$	0.889203	+	0.368320i	0.0378470	+	0.0156767i
$553$	5.92600	+	2.45463i	0.251999	+	0.104381i
$554$	−11.1364	−	16.6668i	−0.473140	−	0.708104i
$555$		0			0
$556$	8.74542	+	5.84350i	0.370888	+	0.247820i
$557$			31.1211i			1.31864i	0.751862	+	0.659321i	$0.229156\pi$
$557$			31.1211i			1.31864i	−0.751862	+	0.659321i	$0.770844\pi$
$558$	4.74367	−	7.09941i	0.200816	−	0.300542i
$559$	−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
$563$	11.8843	+	28.6912i	0.500863	+	1.20919i	0.949014	+	0.315233i	$0.102083\pi$
$563$	11.8843	+	28.6912i	0.500863	+	1.20919i	−0.448151	+	0.893958i	$0.647917\pi$
$564$	1.44681	+	7.27361i	0.0609217	+	0.306274i
$565$		0			0
$566$	11.1466	−	16.6821i	0.468529	−	0.701203i
$567$	−17.6754	+	11.8103i	−0.742298	+	0.495988i
$568$	−2.11045	+	10.6099i	−0.0885525	+	0.445183i
$569$	2.92191	−	1.21029i	0.122493	−	0.0507381i	−0.320595	−	0.947216i	$-0.603883\pi$
$569$	2.92191	−	1.21029i	0.122493	−	0.0507381i	0.443088	+	0.896478i	$0.353883\pi$
$570$		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	$0.325635\pi$
$572$	−0.546498	−	0.817893i	−0.0228502	−	0.0341978i
$573$	6.31688	+	31.7571i	0.263891	+	1.32667i
$574$	−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	$-0.0125499\pi$
$577$	23.0553	+	23.0553i	0.959807	+	0.959807i	−0.0394163	+	0.999223i	$0.512550\pi$
$578$	−16.8033	−	2.57844i	−0.698926	−	0.107249i
$579$		−	0.875235i		−	0.0363735i
$580$		0			0
$581$	8.78362	−	1.74717i	0.364406	−	0.0724848i
$582$	−13.1483			−0.545016
$583$	3.95863	−	0.787420i	0.163950	−	0.0326116i
$584$	−1.91332	+	9.61892i	−0.0791739	+	0.398034i
$585$		0			0
$586$	6.11588	+	14.7650i	0.252645	+	0.609938i
$587$	11.7884	−	28.4598i	0.486560	−	1.17466i	−0.469879	−	0.882731i	$-0.655703\pi$
$587$	11.7884	−	28.4598i	0.486560	−	1.17466i	0.956440	−	0.291930i	$-0.0942975\pi$
$588$	7.70184	+	1.53199i	0.317619	+	0.0631783i
$589$	−2.43086	−	0.483529i	−0.100162	−	0.0199235i
$590$		0			0
$591$	18.7851	−	18.7851i	0.772716	−	0.772716i
$592$	0.351736	+	0.235023i	0.0144563	+	0.00965937i
$593$	6.97472	−	2.88902i	0.286417	−	0.118638i	−0.234849	−	0.972032i	$-0.575460\pi$
$593$	6.97472	−	2.88902i	0.286417	−	0.118638i	0.521267	+	0.853394i	$0.325460\pi$
$594$	8.05917			0.330672
$595$		0			0
$596$	−5.29796			−0.217013
$597$	−4.93825	+	2.04549i	−0.202109	+	0.0837164i
$598$	0.368827	+	0.246442i	0.0150825	+	0.0100778i
$599$	−0.148385	+	0.148385i	−0.00606283	+	0.00606283i	−0.710132	−	0.704069i	$-0.751365\pi$
$599$	−0.148385	+	0.148385i	−0.00606283	+	0.00606283i	0.704069	+	0.710132i	$0.251365\pi$
$600$		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	$0.647942\pi$
$602$	−11.1164	−	2.21119i	−0.453072	−	0.0901216i
$603$	−2.21944	+	5.35821i	−0.0903826	+	0.218203i
$604$	4.01503	+	9.69314i	0.163369	+	0.394408i
$605$		0			0
$606$	3.84919	−	19.3512i	0.156363	−	0.786089i
$607$	−1.06561	+	0.211963i	−0.0432517	+	0.00860330i	−0.216669	−	0.976245i	$-0.569519\pi$
$607$	−1.06561	+	0.211963i	−0.0432517	+	0.00860330i	0.173417	+	0.984848i	$0.444519\pi$
$608$	0.225252			0.00913519
$609$	−29.1701	+	5.80230i	−1.18203	+	0.235121i
$610$		0			0
$611$			3.41796i			0.138276i
$612$	2.51739	+	1.97474i	0.101760	+	0.0798239i
$613$	22.9407	+	22.9407i	0.926565	+	0.926565i	0.997482	−	0.0709174i	$-0.0225927\pi$
$613$	22.9407	+	22.9407i	0.926565	+	0.926565i	−0.0709174	+	0.997482i	$0.522593\pi$
$614$	−0.744855	+	1.79824i	−0.0300599	+	0.0725710i
$615$		0			0
$616$	−3.54423	−	3.54423i	−0.142801	−	0.142801i
$617$	−0.407054	−	2.04640i	−0.0163874	−	0.0823850i	0.971726	−	0.236111i	$-0.0758728\pi$
$617$	−0.407054	−	2.04640i	−0.0163874	−	0.0823850i	−0.988114	+	0.153726i	$0.950873\pi$
$618$	15.0374	+	22.5050i	0.604891	+	0.905284i
$619$	29.8012	−	19.9126i	1.19781	−	0.800353i	0.213528	−	0.976937i	$-0.431505\pi$
$619$	29.8012	−	19.9126i	1.19781	−	0.800353i	0.984286	+	0.176584i	$0.0565047\pi$
$620$		0			0
$621$	−3.35762	+	1.39077i	−0.134737	+	0.0558098i
$622$	4.10239	−	20.6241i	0.164491	−	0.826951i
$623$	−40.1820	+	26.8488i	−1.60986	+	1.07567i
$624$	0.569463	−	0.852262i	0.0227968	−	0.0341178i
$625$		0			0
$626$	5.54040	+	27.8535i	0.221439	+	1.11325i
$627$	−0.183979	−	0.444164i	−0.00734741	−	0.0177382i
$628$	−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	$0.430808\pi$
$632$	1.01751	−	1.52281i	0.0404745	−	0.0605743i
$633$			6.87829i			0.273387i
$634$	−22.9967	−	15.3659i	−0.913315	−	0.610258i
$635$		0			0
$636$	2.33661	+	3.49699i	0.0926527	+	0.138665i
$637$	3.34370	+	1.38500i	0.132482	+	0.0548759i
$638$	7.52935	+	3.11876i	0.298090	+	0.123473i
$639$	−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	$0.550954\pi$
$642$			21.6505i			0.854479i
$643$	−10.0396	+	15.0254i	−0.395924	+	0.592542i	−0.974857	−	0.222833i	$-0.928469\pi$
$643$	−10.0396	+	15.0254i	−0.395924	+	0.592542i	0.578933	+	0.815375i	$0.303469\pi$
$644$	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	−0.222671	+	0.974894i	$0.571477\pi$
$647$	−30.4615	+	30.4615i	−1.19756	+	1.19756i	−0.974894	+	0.222671i	$0.928523\pi$
$648$	2.32283	+	5.60781i	0.0912494	+	0.220296i
$649$	0.826166	+	4.15342i	0.0324299	+	0.163036i
$650$		0			0
$651$	−31.9279	+	47.7834i	−1.25135	+	1.87278i
$652$	12.4549	−	8.32208i	0.487770	−	0.325918i
$653$	8.20651	−	41.2569i	0.321145	−	1.61451i	−0.396456	−	0.918054i	$-0.629760\pi$
$653$	8.20651	−	41.2569i	0.321145	−	1.61451i	0.717602	−	0.696454i	$-0.245240\pi$
$654$	17.8213	−	7.38184i	0.696870	−	0.288653i
$655$		0			0
$656$	−2.24166	+	1.49783i	−0.0875222	+	0.0584805i
$657$	−4.22815	−	6.32787i	−0.164956	−	0.246874i
$658$	3.39773	+	17.0816i	0.132457	+	0.665909i
$659$	−13.4187	−	13.4187i	−0.522718	−	0.522718i	0.395673	−	0.918391i	$-0.370511\pi$
$659$	−13.4187	−	13.4187i	−0.522718	−	0.522718i	−0.918391	+	0.395673i	$0.870511\pi$
$660$		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
$663$	−2.75244	−	3.20701i	−0.106896	−	0.124550i
$664$		−	2.55714i		−	0.0992362i
$665$		0			0
$666$	−0.321961	+	0.0640420i	−0.0124757	+	0.00248158i
$667$	−3.67509			−0.142300
$668$	−7.47034	+	1.48594i	−0.289036	+	0.0574929i
$669$	2.89946	−	14.5766i	0.112100	−	0.563563i
$670$		0			0
$671$	7.26062	+	17.5287i	0.280293	+	0.676688i
$672$	1.99872	−	4.82535i	0.0771025	−	0.186142i
$673$	8.33039	+	1.65702i	0.321113	+	0.0638733i	0.353015	−	0.935618i	$-0.385156\pi$
$673$	8.33039	+	1.65702i	0.321113	+	0.0638733i	−0.0319020	+	0.999491i	$0.510156\pi$
$674$	−12.8742	−	2.56084i	−0.495896	−	0.0986398i
$675$		0			0
$676$	−8.85834	+	8.85834i	−0.340706	+	0.340706i
$677$	−4.53636	−	3.03110i	−0.174347	−	0.116495i	0.465335	−	0.885135i	$-0.345934\pi$
$677$	−4.53636	−	3.03110i	−0.174347	−	0.116495i	−0.639682	+	0.768640i	$0.720934\pi$
$678$	−4.14984	+	1.71892i	−0.159374	+	0.0660147i
$679$	−30.8779			−1.18499
$680$		0			0
$681$	23.7871			0.911522
$682$	14.5487	−	6.02626i	0.557098	−	0.230758i
$683$	30.4635	+	20.3551i	1.16565	+	0.778866i	0.979060	−	0.203571i	$-0.0652549\pi$
$683$	30.4635	+	20.3551i	1.16565	+	0.778866i	0.186595	+	0.982437i	$0.440255\pi$
$684$	−0.123598	+	0.123598i	−0.00472590	+	0.00472590i
$685$		0			0
$686$	−5.95736	−	1.18499i	−0.227453	−	0.0452432i
$687$	−41.7917	−	8.31289i	−1.59445	−	0.317157i
$688$	−1.23847	+	2.98993i	−0.0472162	+	0.113990i
$689$	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	$0.105344\pi$
$692$	17.8236	−	3.54534i	0.677553	−	0.134774i
$693$	3.88951			0.147750
$694$	18.8905	−	3.75756i	0.717075	−	0.142635i
$695$		0			0
$696$			8.49217i			0.321895i
$697$	3.46050	+	10.5636i	0.131076	+	0.400126i
$698$	−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	$0.602728\pi$
$702$	0.755082	+	3.79605i	0.0284987	+	0.143273i
$703$	0.0529394	+	0.0792294i	0.00199665	+	0.00298819i
$704$	−1.18997	+	0.795115i	−0.0448488	+	0.0299670i
$705$		0			0
$706$	−7.24766	+	3.00208i	−0.272769	+	0.112985i
$707$	9.03956	−	45.4449i	0.339967	−	1.70913i
$708$	−3.66906	+	2.45159i	−0.137892	+	0.0921363i
$709$	−14.4329	+	21.6003i	−0.542038	+	0.811217i	−0.996845	−	0.0793729i	$-0.974708\pi$
$709$	−14.4329	+	21.6003i	−0.542038	+	0.811217i	0.454807	+	0.890590i	$0.349708\pi$
$710$		0			0
$711$	0.277265	+	1.39390i	0.0103982	+	0.0522755i
$712$	5.28056	+	12.7484i	0.197897	+	0.477766i
$713$	−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
$717$	18.4040	−	27.5435i	0.687309	−	1.02863i
$718$		−	11.6725i		−	0.435615i
$719$	31.3017	+	20.9151i	1.16735	+	0.780002i	0.979351	−	0.202167i	$-0.0647983\pi$
$719$	31.3017	+	20.9151i	1.16735	+	0.780002i	0.188004	+	0.982168i	$0.439798\pi$
$720$		0			0
$721$	35.3142	+	52.8514i	1.31517	+	1.96829i
$722$	−17.5068	−	7.25157i	−0.651537	−	0.269875i
$723$	−12.0215	−	4.97948i	−0.447085	−	0.185189i
$724$	3.16861	+	4.74216i	0.117760	+	0.176241i
$725$		0			0
$726$	−11.1000	−	7.41677i	−0.411959	−	0.275262i
$727$			11.7248i			0.434847i	0.976077	+	0.217424i	$0.0697653\pi$
$727$			11.7248i			0.434847i	−0.976077	+	0.217424i	$0.930235\pi$
$728$	1.33734	−	2.00148i	0.0495653	−	0.0741797i
$729$	−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
$733$	−15.1940	−	36.6816i	−0.561203	−	1.35486i	−0.908805	−	0.417222i	$-0.863004\pi$
$733$	−15.1940	−	36.6816i	−0.561203	−	1.35486i	0.347601	−	0.937642i	$-0.386996\pi$
$734$	2.94262	+	14.7935i	0.108614	+	0.546039i
$735$		0			0
$736$	0.358556	−	0.536616i	0.0132165	−	0.0197799i
$737$	−8.89371	+	5.94259i	−0.327604	+	0.218898i
$738$	0.408149	−	2.05190i	0.0150242	−	0.0755315i
$739$	−41.6307	+	17.2440i	−1.53141	+	0.634332i	−0.979838	−	0.199795i	$-0.935973\pi$
$739$	−41.6307	+	17.2440i	−1.53141	+	0.634332i	−0.551574	+	0.834126i	$0.685973\pi$
$740$		0			0
$741$	0.191974	−	0.128273i	0.00705234	−	0.00471223i
$742$	5.48737	+	8.21243i	0.201448	+	0.301488i
$743$	−5.03606	−	25.3180i	−0.184755	−	0.928826i	−0.956241	−	0.292580i	$-0.905486\pi$
$743$	−5.03606	−	25.3180i	−0.184755	−	0.928826i	0.771486	−	0.636246i	$-0.219514\pi$
$744$	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
$748$	1.83698	+	5.60765i	0.0671668	+	0.205036i
$749$			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	$0.317462\pi$
$752$	4.97288			0.181342
$753$	−15.6351	+	3.11001i	−0.569773	+	0.113335i
$754$	−0.763564	+	3.83870i	−0.0278074	+	0.139797i
$755$		0			0
$756$	7.54717	+	18.2205i	0.274488	+	0.662673i
$757$	4.45049	−	10.7444i	0.161756	−	0.390513i	−0.822133	−	0.569296i	$-0.807216\pi$
$757$	4.45049	−	10.7444i	0.161756	−	0.390513i	0.983889	+	0.178783i	$0.0572160\pi$
$758$	13.0672	+	2.59924i	0.474624	+	0.0944086i
$759$	−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	$0.997822\pi$
$762$	15.4688	+	10.3359i	0.560376	+	0.374431i
$763$	41.8522	−	17.3357i	1.51515	−	0.627596i
$764$	21.7120			0.785511
$765$		0			0
$766$	28.4203			1.02687
$767$	−1.87895	+	0.778286i	−0.0678449	+	0.0281023i
$768$	−1.23998	−	0.828527i	−0.0447439	−	0.0298969i
$769$	−4.24272	+	4.24272i	−0.152997	+	0.152997i	−0.779455	−	0.626458i	$-0.784504\pi$
$769$	−4.24272	+	4.24272i	−0.152997	+	0.152997i	0.626458	+	0.779455i	$0.284504\pi$
$770$		0			0
$771$	36.7149	+	7.30305i	1.32226	+	0.263013i
$772$	−0.575613	−	0.114497i	−0.0207168	−	0.00412082i
$773$	−3.89373	+	9.40030i	−0.140048	+	0.338105i	−0.978305	−	0.207170i	$-0.933575\pi$
$773$	−3.89373	+	9.40030i	−0.140048	+	0.338105i	0.838257	+	0.545275i	$0.183575\pi$
$774$	−0.961046	−	2.32017i	−0.0345441	−	0.0833968i
$775$		0			0
$776$	−1.72004	+	8.64723i	−0.0617459	+	0.310417i
$777$	2.16700	−	0.431042i	0.0777405	−	0.0154636i
$778$	−30.9292			−1.10887
$779$	−0.595617	+	0.118476i	−0.0213402	+	0.00424483i
$780$		0			0
$781$		−	15.4821i		−	0.553994i
$782$	−1.73304	−	2.01926i	−0.0619734	−	0.0722085i
$783$	−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
$787$	−7.71384	−	38.7801i	−0.274969	−	1.38236i	−0.833336	−	0.552768i	$-0.813572\pi$
$787$	−7.71384	−	38.7801i	−0.274969	−	1.38236i	0.558367	−	0.829594i	$-0.311428\pi$
$788$	−9.89692	−	14.8118i	−0.352563	−	0.527648i
$789$	−11.4516	+	7.65174i	−0.407689	+	0.272409i
$790$		0			0
$791$	−9.74560	+	4.03676i	−0.346514	+	0.143531i
$792$	0.216663	−	1.08924i	0.00769880	−	0.0387045i
$793$	−7.57614	+	5.06222i	−0.269037	+	0.179765i
$794$	−3.98598	+	5.96544i	−0.141457	+	0.211706i
$795$		0			0
$796$	0.699239	+	3.51531i	0.0247839	+	0.124597i
$797$	−16.6329	−	40.1553i	−0.589166	−	1.42237i	−0.884301	−	0.466917i	$-0.845365\pi$
$797$	−16.6329	−	40.1553i	−0.589166	−	1.42237i	0.295135	−	0.955455i	$-0.404635\pi$
$798$	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
$802$	−4.14042	+	6.19658i	−0.146203	+	0.218809i
$803$		−	14.0360i		−	0.495320i
$804$	−9.26744	−	6.19231i	−0.326837	−	0.218386i
$805$		0			0
$806$	4.20160	+	6.28815i	0.147995	+	0.221490i
$807$	4.76954	+	1.97561i	0.167896	+	0.0695447i
$808$	−12.2231	−	5.06297i	−0.430007	−	0.178115i
$809$	−25.9551	−	38.8446i	−0.912534	−	1.36570i	−0.930667	−	0.365868i	$-0.880772\pi$
$809$	−25.9551	−	38.8446i	−0.912534	−	1.36570i	0.0181324	−	0.999836i	$-0.494228\pi$
$810$		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	$0.774524\pi$
$812$			19.9433i			0.699872i
$813$	16.7648	−	25.0904i	0.587969	−	0.879957i
$814$	−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
$818$	6.94870	+	16.7757i	0.242956	+	0.586547i
$819$	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	$0.0972080\pi$
$822$	8.79634	−	5.87753i	0.306808	−	0.205002i
$823$	2.73864	−	13.7681i	0.0954631	−	0.479925i	−0.903246	−	0.429124i	$-0.858822\pi$
$823$	2.73864	−	13.7681i	0.0954631	−	0.479925i	0.998709	−	0.0508015i	$-0.0161776\pi$
$824$	16.7680	−	6.94551i	0.584139	−	0.241958i
$825$		0			0
$826$	−8.61653	+	5.75738i	−0.299807	+	0.200325i
$827$	18.4325	+	27.5862i	0.640962	+	0.959267i	0.999667	+	0.0258161i	$0.00821843\pi$
$827$	18.4325	+	27.5862i	0.640962	+	0.959267i	−0.358705	+	0.933451i	$0.616782\pi$
$828$	0.0977039	+	0.491190i	0.00339544	+	0.0170700i
$829$	−19.3397	−	19.3397i	−0.671696	−	0.671696i	0.286411	−	0.958107i	$-0.407538\pi$
$829$	−19.3397	−	19.3397i	−0.671696	−	0.671696i	−0.958107	+	0.286411i	$0.907538\pi$
$830$		0			0
$831$	−11.4397	+	27.6178i	−0.396837	+	0.958050i
$832$	−0.486008	−	0.486008i	−0.0168493	−	0.0168493i
$833$	−17.0822	−	13.3999i	−0.591865	−	0.464281i
$834$		−	15.6856i		−	0.543149i
$835$		0			0
$836$	−0.316180	+	0.0628921i	−0.0109353	+	0.00217517i
$837$	−61.9607			−2.14168
$838$	−5.30674	+	1.05558i	−0.183318	+	0.0364643i
$839$	−2.67790	+	13.4627i	−0.0924512	+	0.464784i	0.906630	+	0.421927i	$0.138646\pi$
$839$	−2.67790	+	13.4627i	−0.0924512	+	0.464784i	−0.999081	+	0.0428571i	$0.986354\pi$
$840$		0			0
$841$	−1.31132	−	3.16579i	−0.0452178	−	0.109165i
$842$	−6.80990	+	16.4405i	−0.234685	+	0.566579i
$843$	31.9708	+	6.35938i	1.10113	+	0.219029i
$844$	4.52362	+	0.899804i	0.155709	+	0.0309725i
$845$		0			0
$846$	−2.72867	+	2.72867i	−0.0938138	+	0.0938138i
$847$	−26.0675	−	17.4178i	−0.895691	−	0.598482i
$848$	2.60552	−	1.07924i	0.0894741	−	0.0370614i
$849$	−29.9208			−1.02688
$850$		0			0
$851$	0.273016			0.00935887
$852$	14.9047	−	6.17372i	0.510626	−	0.211508i
$853$	24.6422	+	16.4654i	0.843734	+	0.563765i	0.900616	−	0.434616i	$-0.143116\pi$
$853$	24.6422	+	16.4654i	0.843734	+	0.563765i	−0.0568820	+	0.998381i	$0.518116\pi$
$854$	−32.8302	+	32.8302i	−1.12343	+	1.12343i
$855$		0			0
$856$	14.2388	+	2.83228i	0.486674	+	0.0968055i
$857$	−2.81677	−	0.560290i	−0.0962190	−	0.0191391i	0.146746	−	0.989174i	$-0.453120\pi$
$857$	−2.81677	−	0.560290i	−0.0962190	−	0.0191391i	−0.242965	+	0.970035i	$0.578120\pi$
$858$	−0.561381	+	1.35529i	−0.0191652	+	0.0462689i
$859$	14.7311	+	35.5640i	0.502618	+	1.21343i	0.948053	+	0.318112i	$0.103049\pi$
$859$	14.7311	+	35.5640i	0.502618	+	1.21343i	−0.445435	+	0.895314i	$0.646951\pi$
$860$		0			0
$861$	−2.74709	+	13.8106i	−0.0936206	+	0.470663i
$862$	10.0155	−	1.99220i	0.341129	−	0.0678547i
$863$	12.3538			0.420530			0.210265	−	0.977644i	$-0.432567\pi$
$863$	12.3538			0.420530			0.210265	+	0.977644i	$0.432567\pi$
$864$	5.52298	−	1.09859i	0.187895	−	0.0373747i
$865$		0			0
$866$			34.8551i			1.18442i
$867$	10.7248	+	22.9721i	0.364233	+	0.780173i
$868$	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
$872$	−2.52344	−	12.6862i	−0.0854545	−	0.429609i
$873$	−3.80102	−	5.68863i	−0.128645	−	0.192531i
$874$	0.120874	−	0.0807655i	0.00408863	−	0.00273193i
$875$		0			0
$876$	13.5125	−	5.59706i	0.456545	−	0.189107i
$877$	−0.843295	+	4.23953i	−0.0284760	+	0.143159i	−0.992408	−	0.122991i	$-0.960751\pi$
$877$	−0.843295	+	4.23953i	−0.0284760	+	0.143159i	0.963932	+	0.266149i	$0.0857515\pi$
$878$	2.23789	−	1.49531i	0.0755253	−	0.0504644i
$879$	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	$-0.227469\pi$
$882$	1.56369	+	3.77508i	0.0526522	+	0.127114i
$883$	34.6701	−	34.6701i	1.16674	−	1.16674i	0.183773	−	0.982969i	$-0.441169\pi$
$883$	34.6701	−	34.6701i	1.16674	−	1.16674i	0.982969	−	0.183773i	$-0.0588310\pi$
$884$	−2.46922	+	1.39065i	−0.0830487	+	0.0467727i
$885$		0			0
$886$	28.1361	+	11.6544i	0.945251	+	0.391536i
$887$	−4.91559	+	7.35669i	−0.165049	+	0.247014i	−0.904770	−	0.425900i	$-0.859957\pi$
$887$	−4.91559	+	7.35669i	−0.165049	+	0.247014i	0.739721	+	0.672914i	$0.234957\pi$
$888$		−	0.630868i		−	0.0211706i
$889$	36.3274	+	24.2732i	1.21838	+	0.814097i
$890$		0			0
$891$	−4.82623	−	7.22296i	−0.161685	−	0.241978i
$892$	−9.20723	−	3.81376i	−0.308281	−	0.127694i
$893$	1.03489	+	0.428664i	0.0346312	+	0.0143447i
$894$	4.38950	+	6.56936i	0.146807	+	0.219712i
$895$		0			0
$896$	−2.91200	−	1.94574i	−0.0972832	−	0.0650026i
$897$		−	0.661522i		−	0.0220876i
$898$	−14.6651	+	21.9479i	−0.489380	+	0.732410i
$899$	−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
$903$	6.46843	+	15.6162i	0.215256	+	0.519674i
$904$	0.587603	+	2.95408i	0.0195434	+	0.0982512i
$905$		0			0
$906$	8.69273	−	13.0096i	0.288796	−	0.432214i
$907$	−7.60237	+	5.07974i	−0.252433	+	0.168670i	−0.675348	−	0.737499i	$-0.736007\pi$
$907$	−7.60237	+	5.07974i	−0.252433	+	0.168670i	0.422916	+	0.906169i	$0.361007\pi$
$908$	3.11178	−	15.6440i	0.103268	−	0.519163i
$909$	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	$0.143016\pi$
$912$	−0.186628	−	0.279308i	−0.00617986	−	0.00924882i
$913$	0.713971	+	3.58938i	0.0236290	+	0.118791i
$914$	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
$918$	1.76588	−	23.1507i	0.0582828	−	0.764087i
$919$			43.0164i			1.41898i	0.704716	+	0.709490i	$0.251074\pi$
$919$			43.0164i			1.41898i	−0.704716	+	0.709490i	$0.748926\pi$
$920$		0			0
$921$	2.84691	−	0.566286i	0.0938089	−	0.0186597i
$922$	13.3685			0.440270
$923$	7.29243	−	1.45055i	0.240033	−	0.0477456i
$924$	−1.45828	+	7.33126i	−0.0479738	+	0.241181i
$925$		0			0
$926$	12.5834	+	30.3791i	0.413517	+	0.998319i
$927$	−5.38968	+	13.0118i	−0.177020	+	0.427365i
$928$	5.58502	+	1.11093i	0.183337	+	0.0364681i
$929$	−41.3633	−	8.22767i	−1.35709	−	0.269941i	−0.537677	−	0.843151i	$-0.680698\pi$
$929$	−41.3633	−	8.22767i	−1.35709	−	0.269941i	−0.819408	+	0.573210i	$0.805698\pi$
$930$		0			0
$931$	0.838701	−	0.838701i	0.0274873	−	0.0274873i
$932$	19.7880	+	13.2219i	0.648176	+	0.433098i
$933$	−28.9724	+	12.0008i	−0.948514	+	0.392887i
$934$	−4.78801			−0.156668
$935$		0			0
$936$	0.533356			0.0174333
$937$	39.8003	−	16.4858i	1.30022	−	0.538569i	0.378205	−	0.925722i	$-0.376542\pi$
$937$	39.8003	−	16.4858i	1.30022	−	0.538569i	0.922015	+	0.387153i	$0.126542\pi$
$938$	−21.7639	−	14.5422i	−0.710617	−	0.474819i
$939$	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	$0.471569\pi$
$942$	21.9841	+	4.37291i	0.716280	+	0.142477i
$943$	−0.665857	+	1.60752i	−0.0216833	+	0.0523481i
$944$	1.13235	+	2.73373i	0.0368548	+	0.0889754i
$945$		0			0
$946$	0.903593	−	4.54267i	0.0293783	−	0.147695i
$947$	8.23276	−	1.63760i	0.267529	−	0.0532148i	−0.0595030	−	0.998228i	$-0.518952\pi$
$947$	8.23276	−	1.63760i	0.267529	−	0.0532148i	0.327032	+	0.945013i	$0.393952\pi$
$948$	−2.73129			−0.0887083
$949$	6.61128	−	1.31506i	0.214611	−	0.0426888i
$950$		0			0
$951$			41.2465i			1.33751i
$952$	−10.9577	+	9.40452i	−0.355141	+	0.304802i
$953$	17.1743	+	17.1743i	0.556330	+	0.556330i	0.928261	−	0.371930i	$-0.121304\pi$
$953$	17.1743	+	17.1743i	0.556330	+	0.556330i	−0.371930	+	0.928261i	$0.621304\pi$
$954$	−0.837487	+	2.02187i	−0.0271146	+	0.0654605i
$955$		0			0
$956$	−15.7069	−	15.7069i	−0.507997	−	0.507997i
$957$	−2.37108	−	11.9202i	−0.0766460	−	0.385326i
$958$	18.2911	+	27.3745i	0.590958	+	0.884431i
$959$	20.6576	−	13.8030i	0.667068	−	0.445721i
$960$		0			0
$961$	−83.2134	+	34.4681i	−2.68430	+	1.11187i
$962$	0.0567238	−	0.285170i	0.00182885	−	0.00919424i
$963$	−9.36712	+	6.25891i	−0.301851	+	0.201690i
$964$	−4.84747	+	7.25475i	−0.156126	+	0.233660i
$965$		0			0
$966$	−0.657607	−	3.30601i	−0.0211582	−	0.106369i
$967$	0.445933	+	1.07658i	0.0143402	+	0.0346204i	0.930887	−	0.365306i	$-0.119036\pi$
$967$	0.445933	+	1.07658i	0.0143402	+	0.0346204i	−0.916547	+	0.399926i	$0.869036\pi$
$968$	−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	$0.724827\pi$
$972$	−4.35651	+	6.51997i	−0.139735	+	0.209128i
$973$		−	36.8366i		−	1.18093i
$974$	−25.2701	−	16.8849i	−0.809706	−	0.541029i
$975$		0			0
$976$	7.36516	+	11.0227i	0.235753	+	0.352829i
$977$	−23.2223	−	9.61901i	−0.742949	−	0.307739i	−0.0210877	−	0.999778i	$-0.506713\pi$
$977$	−23.2223	−	9.61901i	−0.742949	−	0.307739i	−0.721861	+	0.692038i	$0.756713\pi$
$978$	−20.6384	−	8.54871i	−0.659943	−	0.273357i
$979$	−10.9716	−	16.4202i	−0.350654	−	0.524791i
$980$		0			0
$981$	8.34569	+	5.57641i	0.266457	+	0.178041i
$982$			16.3302i			0.521116i
$983$	19.1109	−	28.6015i	0.609543	−	0.912245i	−0.390422	−	0.920636i	$-0.627671\pi$
$983$	19.1109	−	28.6015i	0.609543	−	0.912245i	0.999965	+	0.00839065i	$0.00267086\pi$
$984$	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
$988$	−0.0592472	−	0.143035i	−0.00188490	−	0.00455056i
$989$	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	$0.0268608\pi$
$992$	9.14879	−	6.11303i	0.290474	−	0.194089i
$993$	10.0096	−	50.3218i	0.317646	−	1.59691i
$994$	35.0026	−	14.4985i	1.11021	−	0.459866i
$995$		0			0
$996$	−3.17080	+	2.11866i	−0.100471	+	0.0671323i
$997$	30.7399	+	46.0056i	0.973543	+	1.45701i	0.887548	+	0.460715i	$0.152407\pi$
$997$	30.7399	+	46.0056i	0.973543	+	1.45701i	0.0859950	+	0.996296i	$0.472593\pi$
$998$	4.87821	+	24.5244i	0.154417	+	0.776307i
$999$	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.v.a.193.2	yes	24
5.2	odd	4		850.2.s.b.57.2	yes	24
5.3	odd	4		850.2.s.a.57.2	✓	24
5.4	even	2		850.2.v.b.193.2	yes	24
17.3	odd	16		850.2.s.b.343.2	yes	24
85.3	even	16		850.2.v.b.207.2	yes	24
85.37	even	16	inner	850.2.v.a.207.2	yes	24
85.54	odd	16		850.2.s.a.343.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.s.a.57.2	✓	24	5.3	odd	4
850.2.s.a.343.2	yes	24	85.54	odd	16
850.2.s.b.57.2	yes	24	5.2	odd	4
850.2.s.b.343.2	yes	24	17.3	odd	16
850.2.v.a.193.2	yes	24	1.1	even	1	trivial
850.2.v.a.207.2	yes	24	85.37	even	16	inner
850.2.v.b.193.2	yes	24	5.4	even	2
850.2.v.b.207.2	yes	24	85.3	even	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.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(1.23998 + 0.828527i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.46265 - 0.290940i) q^{6} +(-3.43494 - 0.683252i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-0.296960 - 0.716925i) q^{9} +(0.279207 - 1.40367i) q^{11} +(1.46265 - 0.290940i) q^{12} +0.687320 q^{13} +(3.43494 - 0.683252i) q^{14} -1.00000i q^{16} +(-3.97099 - 1.10961i) q^{17} +(0.548711 + 0.548711i) q^{18} +(0.0862003 - 0.208106i) q^{19} +(-3.69316 - 3.69316i) q^{21} +(0.279207 + 1.40367i) q^{22} +(-0.358556 - 0.536616i) q^{23} +(-1.23998 + 0.828527i) q^{24} +(-0.635001 + 0.263026i) q^{26} +(1.09859 - 5.52298i) q^{27} +(-2.91200 + 1.94574i) q^{28} +(3.16366 - 4.73475i) q^{29} +(-2.14661 - 10.7917i) q^{31} +(0.382683 + 0.923880i) q^{32} +(1.50919 - 1.50919i) q^{33} +(4.09335 - 0.494483i) q^{34} +(-0.716925 - 0.296960i) q^{36} +(-0.235023 + 0.351736i) q^{37} +0.225252i q^{38} +(0.852262 + 0.569463i) q^{39} +(-1.49783 - 2.24166i) q^{41} +(4.82535 + 1.99872i) q^{42} +(-2.98993 - 1.23847i) q^{43} +(-0.795115 - 1.18997i) q^{44} +(0.536616 + 0.358556i) q^{46} +4.97288i q^{47} +(0.828527 - 1.23998i) q^{48} +(4.86483 + 2.01508i) q^{49} +(-4.00460 - 4.66597i) q^{51} +(0.486008 - 0.486008i) q^{52} +(1.07924 + 2.60552i) q^{53} +(1.09859 + 5.52298i) q^{54} +(1.94574 - 2.91200i) q^{56} +(0.279308 - 0.186628i) q^{57} +(-1.11093 + 5.58502i) q^{58} +(-2.73373 + 1.13235i) q^{59} +(-11.0227 + 7.36516i) q^{61} +(6.11303 + 9.14879i) q^{62} +(0.530200 + 2.66550i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-0.816768 + 1.97185i) q^{66} +(-5.28482 - 5.28482i) q^{67} +(-3.59253 + 2.02330i) q^{68} -0.962466i q^{69} +(10.6099 - 2.11045i) q^{71} +0.775994 q^{72} +(9.61892 - 1.91332i) q^{73} +(0.0825290 - 0.414901i) q^{74} +(-0.0862003 - 0.208106i) q^{76} +(-1.91812 + 4.63076i) q^{77} +(-1.00531 - 0.199969i) q^{78} +(-1.79628 - 0.357303i) q^{79} +(4.29203 - 4.29203i) q^{81} +(2.24166 + 1.49783i) q^{82} +(-2.36249 + 0.978574i) q^{83} -5.22292 q^{84} +3.23628 q^{86} +(7.84575 - 3.24981i) q^{87} +(1.18997 + 0.795115i) q^{88} +(9.75720 - 9.75720i) q^{89} +(-2.36090 - 0.469613i) q^{91} +(-0.632982 - 0.125908i) q^{92} +(6.27950 - 15.1601i) q^{93} +(-1.90304 - 4.59434i) q^{94} +(-0.290940 + 1.46265i) q^{96} +(8.64723 - 1.72004i) q^{97} -5.26566 q^{98} +(-1.08924 + 0.216663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more