LMFDB - Embedded newform 925.2.y.c.193.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.14
Character	$\chi$	$=$	925.193
Dual form			925.2.y.c.532.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.341622 - 0.197235i) q^{2} +(-0.203474 - 0.759377i) q^{3} +(-0.922196 + 1.59729i) q^{4} +(-0.219287 - 0.219287i) q^{6} +(-1.12467 - 4.19733i) q^{7} +1.51650i q^{8} +(2.06282 - 1.19097i) q^{9} +5.77783i q^{11} +(1.40059 + 0.375287i) q^{12} +(-2.98386 - 1.72273i) q^{13} +(-1.21207 - 1.21207i) q^{14} +(-1.54529 - 2.67651i) q^{16} +(-1.69018 - 2.92748i) q^{17} +(0.469804 - 0.813724i) q^{18} +(-1.49704 - 5.58703i) q^{19} +(-2.95852 + 1.70810i) q^{21} +(1.13959 + 1.97383i) q^{22} +4.62117i q^{23} +(1.15160 - 0.308569i) q^{24} -1.35914 q^{26} +(-2.99184 - 2.99184i) q^{27} +(7.74153 + 2.07434i) q^{28} +(-0.167787 - 0.167787i) q^{29} +(1.77197 - 1.77197i) q^{31} +(-3.68246 - 2.12607i) q^{32} +(4.38755 - 1.17564i) q^{33} +(-1.15481 - 0.666727i) q^{34} +4.39324i q^{36} +(-3.71107 - 4.81954i) q^{37} +(-1.61338 - 1.61338i) q^{38} +(-0.701064 + 2.61641i) q^{39} +(-5.73051 - 3.30851i) q^{41} +(-0.673796 + 1.16705i) q^{42} -10.1539i q^{43} +(-9.22887 - 5.32829i) q^{44} +(0.911458 + 1.57869i) q^{46} +(0.860410 - 0.860410i) q^{47} +(-1.71806 + 1.71806i) q^{48} +(-10.2905 + 5.94124i) q^{49} +(-1.87915 + 1.87915i) q^{51} +(5.50341 - 3.17740i) q^{52} +(-2.20800 + 8.24036i) q^{53} +(-1.61217 - 0.431980i) q^{54} +(6.36526 - 1.70557i) q^{56} +(-3.93805 + 2.27364i) q^{57} +(-0.0904134 - 0.0242262i) q^{58} +(-9.82324 - 2.63213i) q^{59} +(-2.37112 - 8.84912i) q^{61} +(0.255848 - 0.954838i) q^{62} +(-7.31891 - 7.31891i) q^{63} +4.50380 q^{64} +(1.26700 - 1.26700i) q^{66} +(4.03094 - 1.08009i) q^{67} +6.23472 q^{68} +(3.50921 - 0.940289i) q^{69} +(-3.66302 + 6.34453i) q^{71} +(1.80611 + 3.12827i) q^{72} +(4.73293 - 4.73293i) q^{73} +(-2.21837 - 0.914507i) q^{74} +(10.3047 + 2.76113i) q^{76} +(24.2515 - 6.49816i) q^{77} +(0.276549 + 1.03210i) q^{78} +(-0.0953001 - 0.355665i) q^{79} +(1.90975 - 3.30778i) q^{81} -2.61022 q^{82} +(-1.89576 + 7.07509i) q^{83} -6.30081i q^{84} +(-2.00271 - 3.46879i) q^{86} +(-0.0932734 + 0.161554i) q^{87} -8.76208 q^{88} +(3.18738 - 11.8955i) q^{89} +(-3.87502 + 14.4618i) q^{91} +(-7.38135 - 4.26162i) q^{92} +(-1.70614 - 0.985042i) q^{93} +(0.124231 - 0.463638i) q^{94} +(-0.865202 + 3.22898i) q^{96} -2.66709 q^{97} +(-2.34365 + 4.05931i) q^{98} +(6.88123 + 11.9186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 40 q^{4} - 32 q^{14} - 4 q^{16} - 24 q^{19} + 36 q^{21} + 52 q^{24} + 16 q^{26} + 12 q^{29} + 4 q^{31} - 60 q^{34} + 100 q^{39} - 48 q^{41} + 48 q^{44} + 24 q^{46} - 120 q^{49} - 84 q^{51} + 104 q^{54}+ \cdots - 24 q^{99}+O(q^{100}) $ 96 * q + 40 * q^4 - 32 * q^14 - 4 * q^16 - 24 * q^19 + 36 * q^21 + 52 * q^24 + 16 * q^26 + 12 * q^29 + 4 * q^31 - 60 * q^34 + 100 * q^39 - 48 * q^41 + 48 * q^44 + 24 * q^46 - 120 * q^49 - 84 * q^51 + 104 * q^54 - 68 * q^56 - 28 * q^59 + 68 * q^61 + 48 * q^64 + 4 * q^66 + 28 * q^69 + 48 * q^71 - 48 * q^74 - 152 * q^76 - 92 * q^79 - 16 * q^81 + 20 * q^86 - 8 * q^89 - 12 * q^91 + 56 * q^94 + 252 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.341622	−	0.197235i	0.241563	−	0.139466i	−0.374332	−	0.927295i	$-0.622128\pi$
$2$	0.341622	−	0.197235i	0.241563	−	0.139466i	0.615895	+	0.787828i	$0.288795\pi$
$3$	−0.203474	−	0.759377i	−0.117476	−	0.438427i	0.881984	−	0.471279i	$-0.156208\pi$
$3$	−0.203474	−	0.759377i	−0.117476	−	0.438427i	−0.999460	+	0.0328525i	$0.989541\pi$
$4$	−0.922196	+	1.59729i	−0.461098	+	0.798646i
$5$		0			0
$5$		0			0
$6$	−0.219287	−	0.219287i	−0.0895237	−	0.0895237i
$7$	−1.12467	−	4.19733i	−0.425086	−	1.58644i	−0.763735	−	0.645530i	$-0.776637\pi$
$7$	−1.12467	−	4.19733i	−0.425086	−	1.58644i	0.338649	−	0.940913i	$-0.390030\pi$
$8$			1.51650i			0.536164i
$9$	2.06282	−	1.19097i	0.687608	−	0.396991i
$10$		0			0
$11$			5.77783i			1.74208i	0.491212	+	0.871040i	$0.336554\pi$
$11$			5.77783i			1.74208i	−0.491212	+	0.871040i	$0.663446\pi$
$12$	1.40059	+	0.375287i	0.404315	+	0.108336i
$13$	−2.98386	−	1.72273i	−0.827574	−	0.477800i	0.0254471	−	0.999676i	$-0.491899\pi$
$13$	−2.98386	−	1.72273i	−0.827574	−	0.477800i	−0.853021	+	0.521876i	$0.825232\pi$
$14$	−1.21207	−	1.21207i	−0.323941	−	0.323941i
$15$		0			0
$16$	−1.54529	−	2.67651i	−0.386321	−	0.669128i
$17$	−1.69018	−	2.92748i	−0.409929	−	0.710018i	0.584952	−	0.811068i	$-0.301113\pi$
$17$	−1.69018	−	2.92748i	−0.409929	−	0.710018i	−0.994881	+	0.101049i	$0.967780\pi$
$18$	0.469804	−	0.813724i	0.110734	−	0.191797i
$19$	−1.49704	−	5.58703i	−0.343445	−	1.28175i	−0.894419	−	0.447230i	$-0.852410\pi$
$19$	−1.49704	−	5.58703i	−0.343445	−	1.28175i	0.550974	−	0.834522i	$-0.314256\pi$
$20$		0			0
$21$	−2.95852	+	1.70810i	−0.645601	+	0.372738i
$22$	1.13959	+	1.97383i	0.242962	+	0.420822i
$23$			4.62117i			0.963580i	0.876287	+	0.481790i	$0.160013\pi$
$23$			4.62117i			0.963580i	−0.876287	+	0.481790i	$0.839987\pi$
$24$	1.15160	−	0.308569i	0.235069	−	0.0629864i
$25$		0			0
$26$	−1.35914			−0.266548
$27$	−2.99184	−	2.99184i	−0.575779	−	0.575779i
$28$	7.74153	+	2.07434i	1.46301	+	0.392013i
$29$	−0.167787	−	0.167787i	−0.0311573	−	0.0311573i	0.691356	−	0.722514i	$-0.257013\pi$
$29$	−0.167787	−	0.167787i	−0.0311573	−	0.0311573i	−0.722514	+	0.691356i	$0.757013\pi$
$30$		0			0
$31$	1.77197	−	1.77197i	0.318255	−	0.318255i	−0.529842	−	0.848097i	$-0.677749\pi$
$31$	1.77197	−	1.77197i	0.318255	−	0.318255i	0.848097	+	0.529842i	$0.177749\pi$
$32$	−3.68246	−	2.12607i	−0.650974	−	0.375840i
$33$	4.38755	−	1.17564i	0.763774	−	0.204653i
$34$	−1.15481	−	0.666727i	−0.198048	−	0.114343i
$35$		0			0
$36$			4.39324i			0.732207i
$37$	−3.71107	−	4.81954i	−0.610096	−	0.792328i
$37$	−3.71107	−	4.81954i	−0.610096	−	0.792328i
$38$	−1.61338	−	1.61338i	−0.261725	−	0.261725i
$39$	−0.701064	+	2.61641i	−0.112260	+	0.418961i
$40$		0			0
$41$	−5.73051	−	3.30851i	−0.894955	−	0.516703i	−0.0193953	−	0.999812i	$-0.506174\pi$
$41$	−5.73051	−	3.30851i	−0.894955	−	0.516703i	−0.875560	+	0.483109i	$0.839507\pi$
$42$	−0.673796	+	1.16705i	−0.103969	+	0.180079i
$43$		−	10.1539i		−	1.54845i	−0.632908	−	0.774227i	$-0.718139\pi$
$43$		−	10.1539i		−	1.54845i	0.632908	−	0.774227i	$-0.281861\pi$
$44$	−9.22887	−	5.32829i	−1.39130	−	0.803270i
$45$		0			0
$46$	0.911458	+	1.57869i	0.134387	+	0.232765i
$47$	0.860410	−	0.860410i	0.125504	−	0.125504i	−0.641565	−	0.767069i	$-0.721715\pi$
$47$	0.860410	−	0.860410i	0.125504	−	0.125504i	0.767069	+	0.641565i	$0.221715\pi$
$48$	−1.71806	+	1.71806i	−0.247980	+	0.247980i
$49$	−10.2905	+	5.94124i	−1.47008	+	0.848749i
$50$		0			0
$51$	−1.87915	+	1.87915i	−0.263134	+	0.263134i
$52$	5.50341	−	3.17740i	0.763186	−	0.440626i
$53$	−2.20800	+	8.24036i	−0.303292	+	1.13190i	0.631114	+	0.775690i	$0.282598\pi$
$53$	−2.20800	+	8.24036i	−0.303292	+	1.13190i	−0.934406	+	0.356211i	$0.884069\pi$
$54$	−1.61217	−	0.431980i	−0.219389	−	0.0587851i
$55$		0			0
$56$	6.36526	−	1.70557i	0.850593	−	0.227916i
$57$	−3.93805	+	2.27364i	−0.521608	+	0.301150i
$58$	−0.0904134	−	0.0242262i	−0.0118719	−	0.00318106i
$59$	−9.82324	−	2.63213i	−1.27888	−	0.342674i	−0.445452	−	0.895306i	$-0.646957\pi$
$59$	−9.82324	−	2.63213i	−1.27888	−	0.342674i	−0.833425	+	0.552632i	$0.813624\pi$
$60$		0			0
$61$	−2.37112	−	8.84912i	−0.303590	−	1.13301i	−0.934152	−	0.356875i	$-0.883842\pi$
$61$	−2.37112	−	8.84912i	−0.303590	−	1.13301i	0.630562	−	0.776139i	$-0.282825\pi$
$62$	0.255848	−	0.954838i	0.0324927	−	0.121265i
$63$	−7.31891	−	7.31891i	−0.922096	−	0.922096i
$64$	4.50380			0.562974
$65$		0			0
$66$	1.26700	−	1.26700i	0.155957	−	0.155957i
$67$	4.03094	−	1.08009i	0.492458	−	0.131954i	−0.00403954	−	0.999992i	$-0.501286\pi$
$67$	4.03094	−	1.08009i	0.492458	−	0.131954i	0.496498	+	0.868038i	$0.334619\pi$
$68$	6.23472			0.756071
$69$	3.50921	−	0.940289i	0.422459	−	0.113198i
$70$		0			0
$71$	−3.66302	+	6.34453i	−0.434720	+	0.752957i	−0.997273	−	0.0738041i	$-0.976486\pi$
$71$	−3.66302	+	6.34453i	−0.434720	+	0.752957i	0.562553	+	0.826762i	$0.309819\pi$
$72$	1.80611	+	3.12827i	0.212852	+	0.368671i
$73$	4.73293	−	4.73293i	0.553947	−	0.553947i	−0.373630	−	0.927578i	$-0.621887\pi$
$73$	4.73293	−	4.73293i	0.553947	−	0.553947i	0.927578	+	0.373630i	$0.121887\pi$
$74$	−2.21837	−	0.914507i	−0.257880	−	0.106309i
$75$		0			0
$76$	10.3047	+	2.76113i	1.18203	+	0.316723i
$77$	24.2515	−	6.49816i	2.76371	−	0.740534i
$78$	0.276549	+	1.03210i	0.0313131	+	0.116862i
$79$	−0.0953001	−	0.355665i	−0.0107221	−	0.0400154i	0.960358	−	0.278771i	$-0.0899271\pi$
$79$	−0.0953001	−	0.355665i	−0.0107221	−	0.0400154i	−0.971080	+	0.238756i	$0.923260\pi$
$80$		0			0
$81$	1.90975	−	3.30778i	0.212194	−	0.367531i
$82$	−2.61022			−0.288251
$83$	−1.89576	+	7.07509i	−0.208087	+	0.776592i	0.780399	+	0.625282i	$0.215016\pi$
$83$	−1.89576	+	7.07509i	−0.208087	+	0.776592i	−0.988486	+	0.151310i	$0.951651\pi$
$84$		−	6.30081i		−	0.687475i
$85$		0			0
$86$	−2.00271	−	3.46879i	−0.215957	−	0.374049i
$87$	−0.0932734	+	0.161554i	−0.00999996	+	0.0173204i
$88$	−8.76208			−0.934041
$89$	3.18738	−	11.8955i	0.337862	−	1.26092i	−0.562872	−	0.826544i	$-0.690303\pi$
$89$	3.18738	−	11.8955i	0.337862	−	1.26092i	0.900733	−	0.434373i	$-0.143030\pi$
$90$		0			0
$91$	−3.87502	+	14.4618i	−0.406212	+	1.51601i
$92$	−7.38135	−	4.26162i	−0.769559	−	0.444305i
$93$	−1.70614	−	0.985042i	−0.176919	−	0.102144i
$94$	0.124231	−	0.463638i	0.0128135	−	0.0478206i
$95$		0			0
$96$	−0.865202	+	3.22898i	−0.0883043	+	0.329556i
$97$	−2.66709			−0.270802			−0.135401	−	0.990791i	$-0.543232\pi$
$97$	−2.66709			−0.270802			−0.135401	+	0.990791i	$0.543232\pi$
$98$	−2.34365	+	4.05931i	−0.236744	+	0.410053i
$99$	6.88123	+	11.9186i	0.691590	+	1.19787i
$100$		0			0
$101$		−	1.29625i		−	0.128981i	−0.997918	−	0.0644906i	$-0.979458\pi$
$101$		−	1.29625i		−	0.128981i	0.997918	−	0.0644906i	$-0.0205423\pi$
$102$	−0.271324	+	1.01259i	−0.0268651	+	0.100262i
$103$	4.70046			0.463151			0.231575	−	0.972817i	$-0.425612\pi$
$103$	4.70046			0.463151			0.231575	+	0.972817i	$0.425612\pi$
$104$	2.61253	−	4.52503i	0.256179	−	0.443715i
$105$		0			0
$106$	0.870991	+	3.25058i	0.0845981	+	0.315724i
$107$	2.15296	+	8.03494i	0.208134	+	0.776767i	0.988471	+	0.151408i	$0.0483808\pi$
$107$	2.15296	+	8.03494i	0.208134	+	0.776767i	−0.780337	+	0.625359i	$0.784953\pi$
$108$	7.53790	−	2.01977i	0.725334	−	0.194353i
$109$	18.7148	+	5.01461i	1.79255	+	0.480312i	0.992775	−	0.119988i	$-0.0382857\pi$
$109$	18.7148	+	5.01461i	1.79255	+	0.480312i	0.799774	+	0.600301i	$0.204952\pi$
$110$		0			0
$111$	−2.90474	+	3.79875i	−0.275706	+	0.360562i
$112$	−9.49627	+	9.49627i	−0.897313	+	0.897313i
$113$	5.01412	+	8.68471i	0.471689	+	0.816989i	0.999475	−	0.0323882i	$-0.0103113\pi$
$113$	5.01412	+	8.68471i	0.471689	+	0.816989i	−0.527787	+	0.849377i	$0.676978\pi$
$114$	−0.896883	+	1.55345i	−0.0840008	+	0.145494i
$115$		0			0
$116$	0.422738	−	0.113272i	0.0392502	−	0.0105171i
$117$	−8.20691			−0.758729
$118$	−3.87498	+	1.03830i	−0.356721	+	0.0955831i
$119$	−10.3867	+	10.3867i	−0.952148	+	0.952148i
$120$		0			0
$121$	−22.3833			−2.03484
$122$	−2.55539	−	2.55539i	−0.231354	−	0.231354i
$123$	−1.34640	+	5.02482i	−0.121400	+	0.453072i
$124$	1.19625	+	4.46445i	0.107426	+	0.400920i
$125$		0			0
$126$	−3.94385	−	1.05675i	−0.351346	−	0.0941428i
$127$	−12.9571	−	3.47185i	−1.14976	−	0.308077i	−0.366890	−	0.930264i	$-0.619578\pi$
$127$	−12.9571	−	3.47185i	−1.14976	−	0.308077i	−0.782868	+	0.622187i	$0.786244\pi$
$128$	8.90352	−	5.14045i	0.786967	−	0.454356i
$129$	−7.71063	+	2.06606i	−0.678883	+	0.181906i
$130$		0			0
$131$	19.1655	+	5.13538i	1.67450	+	0.448680i	0.966318	−	0.257352i	$-0.0828499\pi$
$131$	19.1655	+	5.13538i	1.67450	+	0.448680i	0.708180	+	0.706032i	$0.249517\pi$
$132$	−2.16834	+	8.09236i	−0.188730	+	0.704350i
$133$	−21.7669	+	12.5671i	−1.88743	+	1.08971i
$134$	1.16403	−	1.16403i	0.100557	−	0.100557i
$135$		0			0
$136$	4.43953	−	2.56316i	0.380686	−	0.219789i
$137$	−10.9764	+	10.9764i	−0.937776	+	0.937776i	−0.998174	−	0.0603986i	$-0.980763\pi$
$137$	−10.9764	+	10.9764i	−0.937776	+	0.937776i	0.0603986	+	0.998174i	$0.480763\pi$
$138$	1.01336	−	1.01336i	0.0862632	−	0.0862632i
$139$	11.7586	+	20.3664i	0.997348	+	1.72746i	0.561703	+	0.827339i	$0.310146\pi$
$139$	11.7586	+	20.3664i	0.997348	+	1.72746i	0.435645	+	0.900118i	$0.356520\pi$
$140$		0			0
$141$	−0.828447	−	0.478304i	−0.0697678	−	0.0402805i
$142$			2.88991i			0.242516i
$143$	9.95365	−	17.2402i	0.832366	−	1.44170i
$144$	−6.37530	−	3.68078i	−0.531275	−	0.306732i
$145$		0			0
$146$	0.683370	−	2.55037i	0.0565561	−	0.211070i
$147$	6.60550	+	6.60550i	0.544813	+	0.544813i
$148$	11.1205	−	1.48309i	0.914103	−	0.121909i
$149$		−	16.1158i		−	1.32026i	−0.751151	−	0.660130i	$-0.770501\pi$
$149$		−	16.1158i		−	1.32026i	0.751151	−	0.660130i	$-0.229499\pi$
$150$		0			0
$151$	−6.45414	−	3.72630i	−0.525231	−	0.303242i	0.213841	−	0.976868i	$-0.431402\pi$
$151$	−6.45414	−	3.72630i	−0.525231	−	0.303242i	−0.739072	+	0.673626i	$0.764736\pi$
$152$	8.47273	−	2.27026i	0.687230	−	0.184143i
$153$	−6.97310	−	4.02592i	−0.563741	−	0.325476i
$154$	7.00316	−	7.00316i	0.564331	−	0.564331i
$155$		0			0
$156$	−3.53265	−	3.53265i	−0.282838	−	0.282838i
$157$	10.3540	+	2.77435i	0.826342	+	0.221418i	0.647117	−	0.762391i	$-0.275974\pi$
$157$	10.3540	+	2.77435i	0.826342	+	0.221418i	0.179225	+	0.983808i	$0.442641\pi$
$158$	−0.102706	−	0.102706i	−0.00817088	−	0.00817088i
$159$	6.70681			0.531885
$160$		0			0
$161$	19.3966	−	5.19730i	1.52866	−	0.409604i
$162$		−	1.50668i		−	0.118376i
$163$	0.408894	+	0.708225i	0.0320270	+	0.0554725i	0.881595	−	0.472007i	$-0.156470\pi$
$163$	0.408894	+	0.708225i	0.0320270	+	0.0554725i	−0.849568	+	0.527480i	$0.823137\pi$
$164$	10.5693	−	6.10220i	0.825325	−	0.476501i
$165$		0			0
$166$	0.747823	+	2.79091i	0.0580424	+	0.216617i
$167$	6.95452	−	12.0456i	0.538157	−	0.932115i	−0.460847	−	0.887480i	$-0.652454\pi$
$167$	6.95452	−	12.0456i	0.538157	−	0.932115i	0.999003	−	0.0446351i	$-0.0142125\pi$
$168$	−2.59033	−	4.48659i	−0.199849	−	0.346148i
$169$	−0.564381	−	0.977536i	−0.0434139	−	0.0751951i
$170$		0			0
$171$	−9.74213	−	9.74213i	−0.744999	−	0.744999i
$172$	16.2187	+	9.36388i	1.23667	+	0.713989i
$173$	−11.7392	−	3.14552i	−0.892517	−	0.239149i	−0.216717	−	0.976234i	$-0.569535\pi$
$173$	−11.7392	−	3.14552i	−0.892517	−	0.239149i	−0.675800	+	0.737085i	$0.736202\pi$
$174$			0.0735873i			0.00557864i
$175$		0			0
$176$	15.4644	−	8.92839i	1.16568	−	0.673003i
$177$			7.99511i			0.600950i
$178$	−1.25733	−	4.69241i	−0.0942408	−	0.351711i
$179$	15.2050	+	15.2050i	1.13648	+	1.13648i	0.989077	+	0.147400i	$0.0470905\pi$
$179$	15.2050	+	15.2050i	1.13648	+	1.13648i	0.147400	+	0.989077i	$0.452910\pi$
$180$		0			0
$181$	−3.79126	+	6.56665i	−0.281802	+	0.488095i	−0.971829	−	0.235689i	$-0.924265\pi$
$181$	−3.79126	+	6.56665i	−0.281802	+	0.488095i	0.690027	+	0.723784i	$0.257599\pi$
$182$	1.52858	+	5.70474i	0.113306	+	0.422864i
$183$	−6.23736	+	3.60114i	−0.461079	+	0.266204i
$184$	−7.00800			−0.516637
$185$		0			0
$186$	−0.777140			−0.0569827
$187$	16.9145	−	9.76558i	1.23691	−	0.714130i
$188$	0.580858	+	2.16779i	0.0423634	+	0.158103i
$189$	−9.19290	+	15.9226i	−0.668685	+	1.15820i
$190$		0			0
$191$	1.82684	+	1.82684i	0.132186	+	0.132186i	0.770104	−	0.637918i	$-0.220204\pi$
$191$	1.82684	+	1.82684i	0.132186	+	0.132186i	−0.637918	+	0.770104i	$0.720204\pi$
$192$	−0.916407	−	3.42008i	−0.0661360	−	0.246823i
$193$		−	0.203625i		−	0.0146573i	−0.999973	−	0.00732864i	$-0.997667\pi$
$193$		−	0.203625i		−	0.0146573i	0.999973	−	0.00732864i	$-0.00233280\pi$
$194$	−0.911137	+	0.526045i	−0.0654158	+	0.0377679i
$195$		0			0
$196$		−	21.9160i		−	1.56543i
$197$	1.43336	+	0.384069i	0.102123	+	0.0273638i	0.309519	−	0.950893i	$-0.399832\pi$
$197$	1.43336	+	0.384069i	0.102123	+	0.0273638i	−0.207396	+	0.978257i	$0.566499\pi$
$198$	4.70156	+	2.71445i	0.334125	+	0.192907i
$199$	8.49963	+	8.49963i	0.602523	+	0.602523i	0.940981	−	0.338458i	$-0.109905\pi$
$199$	8.49963	+	8.49963i	0.602523	+	0.602523i	−0.338458	+	0.940981i	$0.609905\pi$
$200$		0			0
$201$	−1.64039	−	2.84124i	−0.115704	−	0.200405i
$202$	−0.255665	−	0.442826i	−0.0179886	−	0.0311571i
$203$	−0.515553	+	0.892965i	−0.0361848	+	0.0626738i
$204$	−1.26861	−	4.73450i	−0.0888202	−	0.331481i
$205$		0			0
$206$	1.60578	−	0.927098i	0.111880	−	0.0645940i
$207$	5.50368	+	9.53266i	0.382532	+	0.662565i
$208$			10.6485i			0.738338i
$209$	32.2809	−	8.64964i	2.23292	−	0.598308i
$210$		0			0
$211$	16.5588			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$211$	16.5588			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$212$	−11.1260	−	11.1260i	−0.764140	−	0.764140i
$213$	5.56322	+	1.49066i	0.381186	+	0.102138i
$214$	2.32027	+	2.32027i	0.158610	+	0.158610i
$215$		0			0
$216$	4.53712	−	4.53712i	0.308712	−	0.308712i
$217$	−9.43042	−	5.44466i	−0.640179	−	0.369607i
$218$	7.38243	−	1.97812i	0.500001	−	0.133975i
$219$	−4.55711	−	2.63105i	−0.307941	−	0.177790i
$220$		0			0
$221$			11.6469i			0.783457i
$222$	−0.243075	+	1.87065i	−0.0163141	+	0.125550i
$223$	2.31283	+	2.31283i	0.154879	+	0.154879i	0.780293	−	0.625414i	$-0.215070\pi$
$223$	2.31283	+	2.31283i	0.154879	+	0.154879i	−0.625414	+	0.780293i	$0.715070\pi$
$224$	−4.78226	+	17.8476i	−0.319528	+	1.19250i
$225$		0			0
$226$	3.42586	+	1.97792i	0.227885	+	0.131570i
$227$	−13.0815	+	22.6578i	−0.868249	+	1.50385i	−0.00446438	+	0.999990i	$0.501421\pi$
$227$	−13.0815	+	22.6578i	−0.868249	+	1.50385i	−0.863785	+	0.503861i	$0.831912\pi$
$228$		−	8.38695i		−	0.555440i
$229$	−17.7450	−	10.2451i	−1.17262	−	0.677013i	−0.218325	−	0.975876i	$-0.570059\pi$
$229$	−17.7450	−	10.2451i	−1.17262	−	0.677013i	−0.954296	+	0.298863i	$0.903393\pi$
$230$		0			0
$231$	−9.86911	−	17.0938i	−0.649339	−	1.12469i
$232$	0.254450	−	0.254450i	0.0167054	−	0.0167054i
$233$	16.5941	−	16.5941i	1.08712	−	1.08712i	0.0912937	−	0.995824i	$-0.470900\pi$
$233$	16.5941	−	16.5941i	1.08712	−	1.08712i	0.995824	−	0.0912937i	$-0.0291002\pi$
$234$	−2.80366	+	1.61869i	−0.183281	+	0.105817i
$235$		0			0
$236$	13.2632	−	13.2632i	0.863363	−	0.863363i
$237$	−0.250693	+	0.144737i	−0.0162842	+	0.00940171i
$238$	−1.49970	+	5.59695i	−0.0972110	+	0.362797i
$239$	5.57972	+	1.49508i	0.360922	+	0.0967087i	0.434723	−	0.900564i	$-0.356846\pi$
$239$	5.57972	+	1.49508i	0.360922	+	0.0967087i	−0.0738010	+	0.997273i	$0.523513\pi$
$240$		0			0
$241$	7.14060	−	1.91332i	0.459966	−	0.123248i	−0.0213926	−	0.999771i	$-0.506810\pi$
$241$	7.14060	−	1.91332i	0.459966	−	0.123248i	0.481359	+	0.876524i	$0.340143\pi$
$242$	−7.64662	+	4.41478i	−0.491543	+	0.283793i
$243$	−15.1612	−	4.06243i	−0.972592	−	0.260605i
$244$	16.3213	+	4.37327i	1.04486	+	0.279970i
$245$		0			0
$246$	0.531114	+	1.98214i	0.0338626	+	0.126377i
$247$	−5.15800	+	19.2499i	−0.328196	+	1.22484i
$248$	2.68719	+	2.68719i	0.170637	+	0.170637i
$249$	5.75840			0.364924
$250$		0			0
$251$	2.35462	−	2.35462i	0.148622	−	0.148622i	−0.628880	−	0.777502i	$-0.716486\pi$
$251$	2.35462	−	2.35462i	0.148622	−	0.148622i	0.777502	+	0.628880i	$0.216486\pi$
$252$	18.4399	−	4.94095i	1.16160	−	0.311251i
$253$	−26.7003			−1.67863
$254$	−5.11121	+	1.36954i	−0.320706	+	0.0859328i
$255$		0			0
$256$	−2.47604	+	4.28862i	−0.154752	+	0.268039i
$257$	−8.55026	−	14.8095i	−0.533351	−	0.923790i	−0.999241	−	0.0389480i	$-0.987599\pi$
$257$	−8.55026	−	14.8095i	−0.533351	−	0.923790i	0.465891	−	0.884842i	$-0.345734\pi$
$258$	−2.22662	+	2.22662i	−0.138623	+	0.138623i
$259$	−16.0555	+	20.9970i	−0.997640	+	1.30469i
$260$		0			0
$261$	−0.545946	−	0.146286i	−0.0337932	−	0.00905486i
$262$	7.56023	−	2.02576i	0.467073	−	0.125152i
$263$	−1.24249	−	4.63704i	−0.0766152	−	0.285932i	0.916980	−	0.398934i	$-0.130620\pi$
$263$	−1.24249	−	4.63704i	−0.0766152	−	0.285932i	−0.993595	+	0.113002i	$0.963953\pi$
$264$	1.78286	+	6.65372i	0.109727	+	0.409508i
$265$		0			0
$266$	−4.95737	+	8.58642i	−0.303956	+	0.526467i
$267$	−9.68170			−0.592510
$268$	−1.99211	+	7.43464i	−0.121687	+	0.454143i
$269$		−	16.9456i		−	1.03319i	−0.856229	−	0.516596i	$-0.827199\pi$
$269$		−	16.9456i		−	1.03319i	0.856229	−	0.516596i	$-0.172801\pi$
$270$		0			0
$271$	−2.31032	−	4.00159i	−0.140342	−	0.243079i	0.787284	−	0.616591i	$-0.211487\pi$
$271$	−2.31032	−	4.00159i	−0.140342	−	0.243079i	−0.927625	+	0.373512i	$0.878153\pi$
$272$	−5.22363	+	9.04758i	−0.316729	+	0.548590i
$273$	11.7704			0.712377
$274$	−1.58484	+	5.91470i	−0.0957437	+	0.357320i
$275$		0			0
$276$	−1.73426	+	6.47236i	−0.104390	+	0.389590i
$277$	−4.46888	−	2.58011i	−0.268509	−	0.155024i	0.359701	−	0.933068i	$-0.382879\pi$
$277$	−4.46888	−	2.58011i	−0.268509	−	0.155024i	−0.628210	+	0.778044i	$0.716212\pi$
$278$	8.03396	+	4.63841i	0.481845	+	0.278193i
$279$	1.54489	−	5.76562i	0.0924904	−	0.345179i
$280$		0			0
$281$	1.35544	−	5.05857i	0.0808588	−	0.301769i	−0.913639	−	0.406526i	$-0.866740\pi$
$281$	1.35544	−	5.05857i	0.0808588	−	0.301769i	0.994498	+	0.104757i	$0.0334066\pi$
$282$	−0.377354			−0.0224711
$283$	3.23918	−	5.61043i	0.192549	−	0.333506i	−0.753545	−	0.657396i	$-0.771658\pi$
$283$	3.23918	−	5.61043i	0.192549	−	0.333506i	0.946094	+	0.323891i	$0.104991\pi$
$284$	−6.75604	−	11.7018i	−0.400897	−	0.694375i
$285$		0			0
$286$		−	7.85285i		−	0.464349i
$287$	−7.44198	+	27.7738i	−0.439286	+	1.63944i
$288$	−10.1284			−0.596820
$289$	2.78657	−	4.82648i	0.163916	−	0.283911i
$290$		0			0
$291$	0.542685	+	2.02533i	0.0318128	+	0.118727i
$292$	3.19517	+	11.9246i	0.186983	+	0.697832i
$293$	2.20988	−	0.592137i	0.129103	−	0.0345930i	−0.193689	−	0.981063i	$-0.562045\pi$
$293$	2.20988	−	0.592137i	0.129103	−	0.0345930i	0.322792	+	0.946470i	$0.395379\pi$
$294$	3.55942	+	0.953744i	0.207590	+	0.0556235i
$295$		0			0
$296$	7.30884	−	5.62783i	0.424818	−	0.327111i
$297$	17.2863	−	17.2863i	1.00305	−	1.00305i
$298$	−3.17861	−	5.50552i	−0.184132	−	0.318926i
$299$	7.96104	−	13.7889i	0.460399	−	0.797434i
$300$		0			0
$301$	−42.6193	+	11.4198i	−2.45653	+	0.658226i
$302$	−2.93983			−0.169168
$303$	−0.984339	+	0.263753i	−0.0565488	+	0.0151522i
$304$	−12.6404	+	12.6404i	−0.724977	+	0.724977i
$305$		0			0
$306$	−3.17622			−0.181572
$307$	14.8585	+	14.8585i	0.848019	+	0.848019i	0.989886	−	0.141867i	$-0.0453105\pi$
$307$	14.8585	+	14.8585i	0.848019	+	0.848019i	−0.141867	+	0.989886i	$0.545311\pi$
$308$	−11.9852	+	44.7292i	−0.682918	+	2.54868i
$309$	−0.956424	−	3.56942i	−0.0544091	−	0.203057i
$310$		0			0
$311$	−30.1453	−	8.07740i	−1.70938	−	0.458027i	−0.734108	−	0.679033i	$-0.762400\pi$
$311$	−30.1453	−	8.07740i	−1.70938	−	0.458027i	−0.975273	+	0.221005i	$0.929066\pi$
$312$	−3.96778	−	1.06316i	−0.224632	−	0.0601898i
$313$	7.85507	−	4.53513i	0.443995	−	0.256340i	−0.261296	−	0.965259i	$-0.584150\pi$
$313$	7.85507	−	4.53513i	0.443995	−	0.256340i	0.705291	+	0.708918i	$0.250817\pi$
$314$	4.08436	−	1.09440i	0.230494	−	0.0617607i
$315$		0			0
$316$	0.655986	+	0.175771i	0.0369021	+	0.00988789i
$317$	0.179805	−	0.671041i	0.0100988	−	0.0376894i	−0.960693	−	0.277614i	$-0.910456\pi$
$317$	0.179805	−	0.671041i	0.0100988	−	0.0376894i	0.970791	+	0.239925i	$0.0771229\pi$
$318$	2.29119	−	1.32282i	0.128484	−	0.0741801i
$319$	0.969446	−	0.969446i	0.0542786	−	0.0542786i
$320$		0			0
$321$	5.66348	−	3.26981i	0.316105	−	0.182503i
$322$	5.60120	−	5.60120i	0.312143	−	0.312143i
$323$	−13.8257	+	13.8257i	−0.769280	+	0.769280i
$324$	3.52232	+	6.10084i	0.195685	+	0.338936i
$325$		0			0
$326$	0.279374	+	0.161297i	0.0154731	+	0.00893340i
$327$		−	15.2319i		−	0.842327i
$328$	5.01736	−	8.69032i	0.277037	−	0.479843i
$329$	−4.57911	−	2.64375i	−0.252454	−	0.145755i
$330$		0			0
$331$	1.69962	−	6.34308i	0.0934198	−	0.348647i	−0.903355	−	0.428893i	$-0.858904\pi$
$331$	1.69962	−	6.34308i	0.0934198	−	0.348647i	0.996775	+	0.0802455i	$0.0255704\pi$
$332$	−9.55270	−	9.55270i	−0.524273	−	0.524273i
$333$	−13.3952	−	5.52209i	−0.734054	−	0.302609i
$334$		−	5.48671i		−	0.300219i
$335$		0			0
$336$	9.14350	+	5.27900i	0.498819	+	0.287993i
$337$	−3.06404	+	0.821006i	−0.166909	+	0.0447230i	−0.341306	−	0.939952i	$-0.610869\pi$
$337$	−3.06404	+	0.821006i	−0.166909	+	0.0447230i	0.174397	+	0.984675i	$0.444202\pi$
$338$	−0.385610	−	0.222632i	−0.0209744	−	0.0121096i
$339$	5.57472	−	5.57472i	0.302777	−	0.302777i
$340$		0			0
$341$	10.2381	+	10.2381i	0.554426	+	0.554426i
$342$	−5.24962	−	1.40663i	−0.283867	−	0.0760619i
$343$	15.0022	+	15.0022i	0.810043	+	0.810043i
$344$	15.3984			0.830225
$345$		0			0
$346$	−4.63078	+	1.24082i	−0.248953	+	0.0667066i
$347$			19.9801i			1.07259i	0.844032	+	0.536293i	$0.180176\pi$
$347$			19.9801i			1.07259i	−0.844032	+	0.536293i	$0.819824\pi$
$348$	−0.172033	−	0.297970i	−0.00922193	−	0.0159728i
$349$	−15.1964	+	8.77364i	−0.813444	+	0.469642i	−0.848150	−	0.529756i	$-0.822284\pi$
$349$	−15.1964	+	8.77364i	−0.813444	+	0.469642i	0.0347066	+	0.999398i	$0.488950\pi$
$350$		0			0
$351$	3.77309	+	14.0814i	0.201393	+	0.751608i
$352$	12.2841	−	21.2766i	0.654743	−	1.13405i
$353$	−3.62804	−	6.28395i	−0.193101	−	0.334461i	0.753175	−	0.657820i	$-0.228521\pi$
$353$	−3.62804	−	6.28395i	−0.193101	−	0.334461i	−0.946276	+	0.323359i	$0.895188\pi$
$354$	1.57692	+	2.73130i	0.0838123	+	0.145167i
$355$		0			0
$356$	16.0611	+	16.0611i	0.851238	+	0.851238i
$357$	10.0009	+	5.77400i	0.529302	+	0.305592i
$358$	8.19334	+	2.19540i	0.433031	+	0.116030i
$359$		−	0.829565i		−	0.0437828i	−0.999760	−	0.0218914i	$-0.993031\pi$
$359$		−	0.829565i		−	0.0437828i	0.999760	−	0.0218914i	$-0.00696880\pi$
$360$		0			0
$361$	−12.5193	+	7.22802i	−0.658910	+	0.380422i
$362$			2.99108i			0.157208i
$363$	4.55443	+	16.9974i	0.239045	+	0.892130i
$364$	−19.5261	−	19.5261i	−1.02345	−	1.02345i
$365$		0			0
$366$	−1.42055	+	2.46046i	−0.0742531	+	0.128610i
$367$	−7.88403	−	29.4236i	−0.411543	−	1.53590i	−0.791660	−	0.610961i	$-0.790783\pi$
$367$	−7.88403	−	29.4236i	−0.411543	−	1.53590i	0.380117	−	0.924938i	$-0.375884\pi$
$368$	12.3686	−	7.14102i	0.644758	−	0.372251i
$369$	−15.7614			−0.820505
$370$		0			0
$371$	37.0708			1.92462
$372$	3.14680	−	1.81680i	0.163154	−	0.0941969i
$373$	−8.00235	−	29.8652i	−0.414346	−	1.54636i	−0.786143	−	0.618045i	$-0.787925\pi$
$373$	−8.00235	−	29.8652i	−0.414346	−	1.54636i	0.371797	−	0.928314i	$-0.378742\pi$
$374$	3.85224	−	6.67227i	0.199194	−	0.345015i
$375$		0			0
$376$	1.30481	+	1.30481i	0.0672906	+	0.0672906i
$377$	0.211601	+	0.789707i	0.0108980	+	0.0406720i
$378$			7.25266i			0.373037i
$379$	−1.36807	+	0.789853i	−0.0702728	+	0.0405720i	−0.534725	−	0.845026i	$-0.679585\pi$
$379$	−1.36807	+	0.789853i	−0.0702728	+	0.0405720i	0.464452	+	0.885598i	$0.346251\pi$
$380$		0			0
$381$			10.5458i			0.540276i
$382$	0.984406	+	0.263771i	0.0503666	+	0.0134957i
$383$	−13.5287	−	7.81083i	−0.691287	−	0.399115i	0.112807	−	0.993617i	$-0.464016\pi$
$383$	−13.5287	−	7.81083i	−0.691287	−	0.399115i	−0.804094	+	0.594502i	$0.797349\pi$
$384$	−5.71518	−	5.71518i	−0.291651	−	0.291651i
$385$		0			0
$386$	−0.0401622	−	0.0695629i	−0.00204420	−	0.00354066i
$387$	−12.0930	−	20.9457i	−0.614722	−	1.06473i
$388$	2.45958	−	4.26012i	0.124866	−	0.216275i
$389$	4.56576	+	17.0396i	0.231493	+	0.863944i	0.979698	+	0.200477i	$0.0642492\pi$
$389$	4.56576	+	17.0396i	0.231493	+	0.863944i	−0.748205	+	0.663467i	$0.769084\pi$
$390$		0			0
$391$	13.5284	−	7.81061i	0.684159	−	0.395000i
$392$	−9.00990	−	15.6056i	−0.455069	−	0.788202i
$393$		−	15.5988i		−	0.786853i
$394$	0.565420	−	0.151504i	0.0284855	−	0.00763266i
$395$		0			0
$396$	−25.3834			−1.27556
$397$	−0.529825	−	0.529825i	−0.0265912	−	0.0265912i	0.693686	−	0.720277i	$-0.255985\pi$
$397$	−0.529825	−	0.529825i	−0.0265912	−	0.0265912i	−0.720277	+	0.693686i	$0.755985\pi$
$398$	4.58009	+	1.22723i	0.229579	+	0.0615155i
$399$	13.9722	+	13.9722i	0.699486	+	0.699486i
$400$		0			0
$401$	−9.51076	+	9.51076i	−0.474945	+	0.474945i	−0.903511	−	0.428566i	$-0.859019\pi$
$401$	−9.51076	+	9.51076i	−0.474945	+	0.474945i	0.428566	+	0.903511i	$0.359019\pi$
$402$	−1.12078	−	0.647085i	−0.0558996	−	0.0322737i
$403$	−8.33994	+	2.23468i	−0.415442	+	0.111317i
$404$	2.07048	+	1.19539i	0.103010	+	0.0594730i
$405$		0			0
$406$			0.406742i			0.0201862i
$407$	27.8465	−	21.4419i	1.38030	−	1.06284i
$408$	−2.84974	−	2.84974i	−0.141083	−	0.141083i
$409$	2.01758	−	7.52971i	0.0997630	−	0.372320i	−0.897936	−	0.440127i	$-0.854933\pi$
$409$	2.01758	−	7.52971i	0.0997630	−	0.372320i	0.997698	+	0.0678066i	$0.0216001\pi$
$410$		0			0
$411$	10.5686	+	6.10180i	0.521312	+	0.300980i
$412$	−4.33475	+	7.50801i	−0.213558	+	0.369893i
$413$			44.1917i			2.17453i
$414$	3.76035	+	2.17104i	0.184811	+	0.106701i
$415$		0			0
$416$	7.32530	+	12.6878i	0.359153	+	0.622071i
$417$	13.0732	−	13.0732i	0.640199	−	0.640199i
$418$	9.32184	−	9.32184i	0.455946	−	0.455946i
$419$	−0.856708	+	0.494620i	−0.0418529	+	0.0241638i	−0.520780	−	0.853691i	$-0.674359\pi$
$419$	−0.856708	+	0.494620i	−0.0418529	+	0.0241638i	0.478928	+	0.877854i	$0.341026\pi$
$420$		0			0
$421$	−1.41804	+	1.41804i	−0.0691112	+	0.0691112i	−0.740818	−	0.671706i	$-0.765562\pi$
$421$	−1.41804	+	1.41804i	−0.0691112	+	0.0691112i	0.671706	+	0.740818i	$0.265562\pi$
$422$	5.65684	−	3.26598i	0.275370	−	0.158985i
$423$	0.750150	−	2.79960i	0.0364736	−	0.136121i
$424$	−12.4965	−	3.34843i	−0.606884	−	0.162614i
$425$		0			0
$426$	2.19453	−	0.588022i	0.106325	−	0.0284898i
$427$	−34.4760	+	19.9047i	−1.66841	+	0.963257i
$428$	−14.8196	−	3.97090i	−0.716332	−	0.191941i
$429$	−15.1172	−	4.05063i	−0.729863	−	0.195566i
$430$		0			0
$431$	3.09674	+	11.5572i	0.149165	+	0.556691i	0.999535	+	0.0305051i	$0.00971159\pi$
$431$	3.09674	+	11.5572i	0.149165	+	0.556691i	−0.850370	+	0.526186i	$0.823622\pi$
$432$	−3.38445	+	12.6309i	−0.162834	+	0.607706i
$433$	−15.8328	−	15.8328i	−0.760878	−	0.760878i	0.215603	−	0.976481i	$-0.430828\pi$
$433$	−15.8328	−	15.8328i	−0.760878	−	0.760878i	−0.976481	+	0.215603i	$0.930828\pi$
$434$	−4.29552			−0.206191
$435$		0			0
$436$	−25.2685	+	25.2685i	−1.21014	+	1.21014i
$437$	25.8186	−	6.91807i	1.23507	−	0.330936i
$438$	−2.07574			−0.0991828
$439$	−12.1958	+	3.26786i	−0.582075	+	0.155967i	−0.537829	−	0.843054i	$-0.680755\pi$
$439$	−12.1958	+	3.26786i	−0.582075	+	0.155967i	−0.0442463	+	0.999021i	$0.514089\pi$
$440$		0			0
$441$	−14.1517	+	24.5115i	−0.673891	+	1.16721i
$442$	2.29719	+	3.97884i	0.109266	+	0.189254i
$443$	13.4157	−	13.4157i	0.637399	−	0.637399i	−0.312514	−	0.949913i	$-0.601171\pi$
$443$	13.4157	−	13.4157i	0.637399	−	0.637399i	0.949913	+	0.312514i	$0.101171\pi$
$444$	−3.38897	−	8.14291i	−0.160833	−	0.386446i
$445$		0			0
$446$	1.24629	+	0.333942i	0.0590134	+	0.0158126i
$447$	−12.2380	+	3.27916i	−0.578837	+	0.155099i
$448$	−5.06529	−	18.9039i	−0.239313	−	0.893126i
$449$	−5.77147	−	21.5394i	−0.272373	−	1.01651i	−0.957582	−	0.288162i	$-0.906956\pi$
$449$	−5.77147	−	21.5394i	−0.272373	−	1.01651i	0.685209	−	0.728347i	$-0.259711\pi$
$450$		0			0
$451$	19.1160	−	33.1099i	0.900138	−	1.55908i
$452$	−18.4960			−0.869979
$453$	−1.51641	+	5.65934i	−0.0712474	+	0.265899i
$454$			10.3205i			0.484367i
$455$		0			0
$456$	−3.44797	−	5.97206i	−0.161466	−	0.279667i
$457$	12.3379	−	21.3699i	0.577143	−	0.999640i	−0.418663	−	0.908142i	$-0.637501\pi$
$457$	12.3379	−	21.3699i	0.577143	−	0.999640i	0.995805	−	0.0914984i	$-0.0291657\pi$
$458$	−8.08276			−0.377683
$459$	−3.70180	+	13.8153i	−0.172785	+	0.644843i
$460$		0			0
$461$	0.355974	−	1.32851i	0.0165793	−	0.0618750i	−0.957141	−	0.289624i	$-0.906470\pi$
$461$	0.355974	−	1.32851i	0.0165793	−	0.0618750i	0.973720	+	0.227749i	$0.0731365\pi$
$462$	−6.74300	−	3.89307i	−0.313713	−	0.181122i
$463$	21.9872	+	12.6943i	1.02183	+	0.589954i	0.914634	−	0.404284i	$-0.132479\pi$
$463$	21.9872	+	12.6943i	1.02183	+	0.589954i	0.107197	+	0.994238i	$0.465812\pi$
$464$	−0.189806	+	0.708364i	−0.00881150	+	0.0328850i
$465$		0			0
$466$	2.39597	−	8.94187i	0.110991	−	0.414224i
$467$	−39.2385			−1.81574			−0.907870	−	0.419252i	$-0.862292\pi$
$467$	−39.2385			−1.81574			−0.907870	+	0.419252i	$0.862292\pi$
$468$	7.56838	−	13.1088i	0.349849	−	0.605956i
$469$	−9.06697	−	15.7045i	−0.418674	−	0.725165i
$470$		0			0
$471$		−	8.42712i		−	0.388301i
$472$	3.99163	−	14.8970i	0.183729	−	0.685688i
$473$	58.6674			2.69753
$474$	−0.0570947	+	0.0988909i	−0.00262245	+	0.00454221i
$475$		0			0
$476$	−7.01201	−	26.1692i	−0.321395	−	1.19946i
$477$	5.25933	+	19.6281i	0.240808	+	0.898708i
$478$	2.20104	−	0.589766i	0.100673	−	0.0269753i
$479$	−28.2573	−	7.57152i	−1.29111	−	0.345952i	−0.453028	−	0.891496i	$-0.649656\pi$
$479$	−28.2573	−	7.57152i	−1.29111	−	0.345952i	−0.838082	+	0.545545i	$0.816323\pi$
$480$		0			0
$481$	2.77052	+	20.7740i	0.126325	+	0.947214i
$482$	2.06201	−	2.06201i	0.0939220	−	0.0939220i
$483$	−7.89341	−	13.6718i	−0.359163	−	0.622088i
$484$	20.6418	−	35.7526i	0.938263	−	1.62512i
$485$		0			0
$486$	−5.98066	+	1.60251i	−0.271288	+	0.0726914i
$487$	−7.81853			−0.354292			−0.177146	−	0.984185i	$-0.556686\pi$
$487$	−7.81853			−0.354292			−0.177146	+	0.984185i	$0.556686\pi$
$488$	13.4197	−	3.59580i	0.607481	−	0.162774i
$489$	0.454610	−	0.454610i	0.0205582	−	0.0205582i
$490$		0			0
$491$	−9.60909			−0.433652			−0.216826	−	0.976210i	$-0.569570\pi$
$491$	−9.60909			−0.433652			−0.216826	+	0.976210i	$0.569570\pi$
$492$	−6.78445	−	6.78445i	−0.305867	−	0.305867i
$493$	−0.207603	+	0.774785i	−0.00934997	+	0.0348946i
$494$	2.03468	+	7.59353i	0.0915446	+	0.341649i
$495$		0			0
$496$	−7.48089	−	2.00450i	−0.335902	−	0.0900047i
$497$	30.7498	+	8.23938i	1.37932	+	0.369587i
$498$	1.96719	−	1.13576i	0.0881521	−	0.0508946i
$499$	26.2172	−	7.02487i	1.17364	−	0.314476i	0.381240	−	0.924476i	$-0.375497\pi$
$499$	26.2172	−	7.02487i	1.17364	−	0.314476i	0.792402	+	0.610000i	$0.208830\pi$
$500$		0			0
$501$	−10.5622	−	2.83013i	−0.471884	−	0.126441i
$502$	0.339974	−	1.26880i	0.0151738	−	0.0566294i
$503$	22.3667	−	12.9134i	0.997282	−	0.575781i	0.0898393	−	0.995956i	$-0.471365\pi$
$503$	22.3667	−	12.9134i	0.997282	−	0.575781i	0.907443	+	0.420175i	$0.138031\pi$
$504$	11.0991	−	11.0991i	0.494394	−	0.494394i
$505$		0			0
$506$	−9.12140	+	5.26624i	−0.405496	+	0.234113i
$507$	−0.627482	+	0.627482i	−0.0278674	+	0.0278674i
$508$	17.4946	−	17.4946i	0.776196	−	0.776196i
$509$	−8.09090	−	14.0138i	−0.358623	−	0.621153i	0.629108	−	0.777318i	$-0.283420\pi$
$509$	−8.09090	−	14.0138i	−0.358623	−	0.621153i	−0.987731	+	0.156165i	$0.950087\pi$
$510$		0			0
$511$	−25.1887	−	14.5427i	−1.11428	−	0.643330i
$512$			22.5152i			0.995043i
$513$	−12.2366	+	21.1944i	−0.540258	+	0.935755i
$514$	−5.84191	−	3.37283i	−0.257676	−	0.148769i
$515$		0			0
$516$	3.81062	−	14.2214i	0.167753	−	0.626064i
$517$	4.97130	+	4.97130i	0.218638	+	0.218638i
$518$	−1.34356	+	10.3397i	−0.0590325	+	0.454302i
$519$			9.55454i			0.419398i
$520$		0			0
$521$	12.3847	+	7.15032i	0.542584	+	0.313261i	0.746126	−	0.665805i	$-0.231912\pi$
$521$	12.3847	+	7.15032i	0.542584	+	0.313261i	−0.203541	+	0.979066i	$0.565245\pi$
$522$	−0.215360	+	0.0577055i	−0.00942604	+	0.00252570i
$523$	35.5320	+	20.5144i	1.55371	+	0.897032i	0.997835	+	0.0657628i	$0.0209481\pi$
$523$	35.5320	+	20.5144i	1.55371	+	0.897032i	0.555870	+	0.831269i	$0.312385\pi$
$524$	−25.8771	+	25.8771i	−1.13044	+	1.13044i
$525$		0			0
$526$	−1.33905	−	1.33905i	−0.0583853	−	0.0583853i
$527$	−8.18235	−	2.19245i	−0.356429	−	0.0955048i
$528$	−9.92663	−	9.92663i	−0.432001	−	0.432001i
$529$	1.64482			0.0715140
$530$		0			0
$531$	−23.3984	+	6.26959i	−1.01540	+	0.272077i
$532$		−	46.3575i		−	2.00985i
$533$	11.3994	+	19.7443i	0.493761	+	0.855220i
$534$	−3.30748	+	1.90957i	−0.143129	+	0.0826353i
$535$		0			0
$536$	1.63795	+	6.11293i	0.0707488	+	0.264038i
$537$	8.45251	−	14.6402i	0.364753	−	0.631770i
$538$	−3.34227	−	5.78899i	−0.144096	−	0.249581i
$539$	−34.3275	−	59.4569i	−1.47859	−	2.56099i
$540$		0			0
$541$	−3.12762	−	3.12762i	−0.134467	−	0.134467i	0.636670	−	0.771137i	$-0.280311\pi$
$541$	−3.12762	−	3.12762i	−0.134467	−	0.134467i	−0.771137	+	0.636670i	$0.780311\pi$
$542$	−1.57851	−	0.911352i	−0.0678028	−	0.0391459i
$543$	5.75799	+	1.54285i	0.247099	+	0.0662100i
$544$			14.3738i			0.616271i
$545$		0			0
$546$	4.02102	−	2.32154i	0.172084	−	0.0993527i
$547$		−	34.0616i		−	1.45637i	−0.685381	−	0.728185i	$-0.740364\pi$
$547$		−	34.0616i		−	1.45637i	0.685381	−	0.728185i	$-0.259636\pi$
$548$	−7.41010	−	27.6549i	−0.316544	−	1.18136i
$549$	−15.4303	−	15.4303i	−0.658547	−	0.658547i
$550$		0			0
$551$	−0.686248	+	1.18862i	−0.0292352	+	0.0506368i
$552$	1.42595	+	5.32172i	0.0606924	+	0.226507i
$553$	−1.38566	+	0.800013i	−0.0589244	+	0.0340200i
$554$	−2.03556			−0.0864825
$555$		0			0
$556$	−43.3748			−1.83950
$557$	−4.09297	+	2.36308i	−0.173425	+	0.100127i	−0.584200	−	0.811610i	$-0.698592\pi$
$557$	−4.09297	+	2.36308i	−0.173425	+	0.100127i	0.410775	+	0.911737i	$0.365258\pi$
$558$	−0.609416	−	2.27437i	−0.0257986	−	0.0962818i
$559$	−17.4924	+	30.2978i	−0.739852	+	1.28146i
$560$		0			0
$561$	−10.8574	−	10.8574i	−0.458401	−	0.458401i
$562$	−0.534682	−	1.99546i	−0.0225542	−	0.0841734i
$563$			38.0878i			1.60521i	0.596512	+	0.802604i	$0.296553\pi$
$563$			38.0878i			1.60521i	−0.596512	+	0.802604i	$0.703447\pi$
$564$	1.52798	−	0.882181i	0.0643396	−	0.0371465i
$565$		0			0
$566$		−	2.55553i		−	0.107417i
$567$	−16.0317	−	4.29568i	−0.673268	−	0.180401i
$568$	−9.62149	−	5.55497i	−0.403709	−	0.233081i
$569$	21.1738	+	21.1738i	0.887650	+	0.887650i	0.994297	−	0.106647i	$-0.0340115\pi$
$569$	21.1738	+	21.1738i	0.887650	+	0.887650i	−0.106647	+	0.994297i	$0.534011\pi$
$570$		0			0
$571$	4.88390	+	8.45916i	0.204385	+	0.354005i	0.949937	−	0.312443i	$-0.101147\pi$
$571$	4.88390	+	8.45916i	0.204385	+	0.354005i	−0.745552	+	0.666448i	$0.767814\pi$
$572$	18.3584	+	31.7978i	0.767605	+	1.32953i
$573$	1.01555	−	1.75898i	0.0424250	−	0.0734823i
$574$	2.93564	+	10.9560i	0.122531	+	0.457293i
$575$		0			0
$576$	9.29054	−	5.36390i	0.387106	−	0.223496i
$577$	−4.42586	−	7.66581i	−0.184251	−	0.319132i	0.759073	−	0.651006i	$-0.225653\pi$
$577$	−4.42586	−	7.66581i	−0.184251	−	0.319132i	−0.943324	+	0.331874i	$0.892319\pi$
$578$		−	2.19844i		−	0.0914432i
$579$	−0.154629	+	0.0414326i	−0.00642614	+	0.00172188i
$580$		0			0
$581$	31.8286			1.32047
$582$	0.584860	+	0.584860i	0.0242432	+	0.0242432i
$583$	−47.6114	−	12.7574i	−1.97186	−	0.528359i
$584$	7.17749	+	7.17749i	0.297007	+	0.297007i
$585$		0			0
$586$	0.638154	−	0.638154i	0.0263619	−	0.0263619i
$587$	5.63963	+	3.25604i	0.232773	+	0.134391i	0.611850	−	0.790973i	$-0.290425\pi$
$587$	5.63963	+	3.25604i	0.232773	+	0.134391i	−0.379078	+	0.925365i	$0.623759\pi$
$588$	−16.6425	+	4.45934i	−0.686324	+	0.183900i
$589$	−12.5527	−	7.24733i	−0.517227	−	0.298621i
$590$		0			0
$591$		−	1.16661i		−	0.0479880i
$592$	−7.16491	+	17.3803i	−0.294476	+	0.714325i
$593$	16.1646	+	16.1646i	0.663800	+	0.663800i	0.956274	−	0.292473i	$-0.0944783\pi$
$593$	16.1646	+	16.1646i	0.663800	+	0.663800i	−0.292473	+	0.956274i	$0.594478\pi$
$594$	2.49591	−	9.31486i	0.102408	−	0.382193i
$595$		0			0
$596$	25.7417	+	14.8620i	1.05442	+	0.608769i
$597$	4.72497	−	8.18388i	0.193380	−	0.334944i
$598$		−	6.28079i		−	0.256841i
$599$	−16.9500	−	9.78611i	−0.692560	−	0.399850i	0.112010	−	0.993707i	$-0.464271\pi$
$599$	−16.9500	−	9.78611i	−0.692560	−	0.399850i	−0.804570	+	0.593857i	$0.797604\pi$
$600$		0			0
$601$	4.89362	+	8.47600i	0.199615	+	0.345743i	0.948404	−	0.317066i	$-0.102698\pi$
$601$	4.89362	+	8.47600i	0.199615	+	0.345743i	−0.748789	+	0.662809i	$0.769364\pi$
$602$	−12.3073	+	12.3073i	−0.501607	+	0.501607i
$603$	7.02877	−	7.02877i	0.286234	−	0.286234i
$604$	11.9040	−	6.87277i	0.484366	−	0.279649i
$605$		0			0
$606$	−0.284250	+	0.284250i	−0.0115469	+	0.0115469i
$607$	−24.8156	+	14.3273i	−1.00723	+	0.581527i	−0.910381	−	0.413771i	$-0.864211\pi$
$607$	−24.8156	+	14.3273i	−1.00723	+	0.581527i	−0.0968538	+	0.995299i	$0.530878\pi$
$608$	−6.36563	+	23.7568i	−0.258160	+	0.963467i
$609$	0.782999	+	0.209804i	0.0317287	+	0.00850168i
$610$		0			0
$611$	−4.04960	+	1.08509i	−0.163829	+	0.0438979i
$612$	12.8611	−	7.42538i	0.519880	−	0.300153i
$613$	−28.6239	−	7.66975i	−1.15611	−	0.309778i	−0.370698	−	0.928754i	$-0.620881\pi$
$613$	−28.6239	−	7.66975i	−1.15611	−	0.309778i	−0.785410	+	0.618975i	$0.787548\pi$
$614$	8.00660	+	2.14536i	0.323120	+	0.0865798i
$615$		0			0
$616$	9.85446	+	36.7774i	0.397048	+	1.48180i
$617$	0.474109	−	1.76940i	0.0190869	−	0.0712333i	−0.955726	−	0.294260i	$-0.904927\pi$
$617$	0.474109	−	1.76940i	0.0190869	−	0.0712333i	0.974812	+	0.223026i	$0.0715936\pi$
$618$	−1.03075	−	1.03075i	−0.0414629	−	0.0414629i
$619$	11.0737			0.445089			0.222544	−	0.974923i	$-0.428564\pi$
$619$	11.0737			0.445089			0.222544	+	0.974923i	$0.428564\pi$
$620$		0			0
$621$	13.8258	−	13.8258i	0.554809	−	0.554809i
$622$	−11.8914	+	3.18630i	−0.476803	+	0.127759i
$623$	−53.5140			−2.14399
$624$	8.08619	−	2.16669i	0.323707	−	0.0867370i
$625$		0			0
$626$	1.78897	−	3.09860i	0.0715018	−	0.123845i
$627$	−13.1367	−	22.7534i	−0.524628	−	0.908683i
$628$	−13.9799	+	13.9799i	−0.557859	+	0.557859i
$629$	−7.83674	+	19.0100i	−0.312471	+	0.757977i
$630$		0			0
$631$	28.3582	+	7.59857i	1.12892	+	0.302494i	0.774490	−	0.632587i	$-0.218007\pi$
$631$	28.3582	+	7.59857i	1.12892	+	0.302494i	0.354434	+	0.935081i	$0.384673\pi$
$632$	0.539366	−	0.144523i	0.0214548	−	0.00574881i
$633$	−3.36929	−	12.5743i	−0.133917	−	0.499786i
$634$	−0.0709278	−	0.264706i	−0.00281690	−	0.0105128i
$635$		0			0
$636$	−6.18500	+	10.7127i	−0.245251	+	0.424788i
$637$	40.9407			1.62213
$638$	0.139975	−	0.522393i	0.00554165	−	0.0206817i
$639$			17.4502i			0.690320i
$640$		0			0
$641$	−19.4157	−	33.6290i	−0.766874	−	1.32826i	−0.939250	−	0.343233i	$-0.888478\pi$
$641$	−19.4157	−	33.6290i	−0.766874	−	1.32826i	0.172376	−	0.985031i	$-0.444856\pi$
$642$	1.28984	−	2.23408i	0.0509061	−	0.0881720i
$643$	13.2557			0.522755			0.261377	−	0.965237i	$-0.415823\pi$
$643$	13.2557			0.522755			0.261377	+	0.965237i	$0.415823\pi$
$644$	−9.58585	+	35.7749i	−0.377736	+	1.40973i
$645$		0			0
$646$	−1.99624	+	7.45005i	−0.0785408	+	0.293118i
$647$	3.39006	+	1.95725i	0.133277	+	0.0769476i	0.565156	−	0.824984i	$-0.308816\pi$
$647$	3.39006	+	1.95725i	0.133277	+	0.0769476i	−0.431879	+	0.901932i	$0.642149\pi$
$648$	5.01625	+	2.89613i	0.197057	+	0.113771i
$649$	15.2080	−	56.7570i	0.596966	−	2.22791i
$650$		0			0
$651$	−2.21570	+	8.26909i	−0.0868400	+	0.324091i
$652$	−1.50832			−0.0590704
$653$	3.88818	−	6.73452i	0.152156	−	0.263542i	−0.779864	−	0.625949i	$-0.784712\pi$
$653$	3.88818	−	6.73452i	0.152156	−	0.263542i	0.932020	+	0.362407i	$0.118045\pi$
$654$	−3.00427	−	5.20355i	−0.117476	−	0.203475i
$655$		0			0
$656$			20.4504i			0.798453i
$657$	4.12641	−	15.4000i	0.160987	−	0.600811i
$658$	−2.08576			−0.0813115
$659$	−22.8781	+	39.6261i	−0.891205	+	1.54361i	−0.0527730	+	0.998607i	$0.516806\pi$
$659$	−22.8781	+	39.6261i	−0.891205	+	1.54361i	−0.838432	+	0.545006i	$0.816527\pi$
$660$		0			0
$661$	4.24598	+	15.8462i	0.165150	+	0.616347i	0.998021	+	0.0628802i	$0.0200286\pi$
$661$	4.24598	+	15.8462i	0.165150	+	0.616347i	−0.832871	+	0.553466i	$0.813305\pi$
$662$	−0.670452	−	2.50216i	−0.0260579	−	0.0972493i
$663$	8.84441	−	2.36985i	0.343488	−	0.0920374i
$664$	−10.7294	−	2.87493i	−0.416380	−	0.111569i
$665$		0			0
$666$	−5.66525	+	0.755544i	−0.219524	+	0.0292768i
$667$	0.775373	−	0.775373i	0.0300226	−	0.0300226i
$668$	12.8269	+	22.2168i	0.496286	+	0.859593i
$669$	1.28571	−	2.22692i	0.0497084	−	0.0860976i
$670$		0			0
$671$	51.1287	−	13.6999i	1.97380	−	0.528879i
$672$	14.5262			0.560359
$673$	17.4142	−	4.66612i	0.671268	−	0.179866i	0.0929423	−	0.995671i	$-0.470373\pi$
$673$	17.4142	−	4.66612i	0.671268	−	0.179866i	0.578326	+	0.815806i	$0.303706\pi$
$674$	−0.884810	+	0.884810i	−0.0340816	+	0.0340816i
$675$		0			0
$676$	2.08188			0.0800723
$677$	−26.3649	−	26.3649i	−1.01329	−	1.01329i	−0.999911	−	0.0133766i	$-0.995742\pi$
$677$	−26.3649	−	26.3649i	−1.01329	−	1.01329i	−0.0133766	−	0.999911i	$-0.504258\pi$
$678$	0.804914	−	3.00398i	0.0309125	−	0.115367i
$679$	2.99961	+	11.1947i	0.115114	+	0.429612i
$680$		0			0
$681$	19.8676	+	5.32350i	0.761327	+	0.203997i
$682$	5.51689	+	1.47825i	0.211253	+	0.0566049i
$683$	−10.0445	+	5.79920i	−0.384342	+	0.221900i	−0.679706	−	0.733485i	$-0.737893\pi$
$683$	−10.0445	+	5.79920i	−0.384342	+	0.221900i	0.295364	+	0.955385i	$0.404559\pi$
$684$	24.5452	−	6.57686i	0.938508	−	0.251472i
$685$		0			0
$686$	8.08405	+	2.16611i	0.308650	+	0.0827026i
$687$	−4.16922	+	15.5597i	−0.159066	+	0.593641i
$688$	−27.1770	+	15.6907i	−1.03611	+	0.598201i
$689$	20.7843	−	20.7843i	0.791819	−	0.791819i
$690$		0			0
$691$	7.30966	−	4.22023i	0.278073	−	0.160545i	−0.354478	−	0.935064i	$-0.615341\pi$
$691$	7.30966	−	4.22023i	0.278073	−	0.160545i	0.632551	+	0.774519i	$0.282008\pi$
$692$	15.8502	−	15.8502i	0.602534	−	0.602534i
$693$	42.2874	−	42.2874i	1.60636	−	1.60636i
$694$	3.94077	+	6.82562i	0.149590	+	0.259097i
$695$		0			0
$696$	−0.244997	−	0.141449i	−0.00928659	−	0.00536162i
$697$			22.3679i			0.847246i
$698$	−3.46094	+	5.99453i	−0.130999	+	0.226896i
$699$	−15.9777	−	9.22472i	−0.604332	−	0.348911i
$700$		0			0
$701$	10.1537	−	37.8942i	0.383501	−	1.43124i	−0.457016	−	0.889458i	$-0.651082\pi$
$701$	10.1537	−	37.8942i	0.383501	−	1.43124i	0.840517	−	0.541786i	$-0.182252\pi$
$702$	4.06631	+	4.06631i	0.153473	+	0.153473i
$703$	−21.3713	+	27.9489i	−0.806034	+	1.05411i
$704$			26.0222i			0.980747i
$705$		0			0
$706$	−2.47884	−	1.43116i	−0.0932922	−	0.0538623i
$707$	−5.44077	+	1.45785i	−0.204621	+	0.0548281i
$708$	−12.7705	−	7.37307i	−0.479946	−	0.277097i
$709$	1.71394	−	1.71394i	0.0643685	−	0.0643685i	−0.674190	−	0.738558i	$-0.735507\pi$
$709$	1.71394	−	1.71394i	0.0643685	−	0.0643685i	0.738558	+	0.674190i	$0.235507\pi$
$710$		0			0
$711$	−0.620175	−	0.620175i	−0.0232584	−	0.0232584i
$712$	18.0395	+	4.83367i	0.676058	+	0.181149i
$713$	8.18856	+	8.18856i	0.306664	+	0.306664i
$714$	4.55535			0.170480
$715$		0			0
$716$	−38.3089	+	10.2648i	−1.43167	+	0.383615i
$717$		−	4.54132i		−	0.169599i
$718$	−0.163620	−	0.283398i	−0.00610623	−	0.0105763i
$719$	19.3847	−	11.1918i	0.722927	−	0.417382i	−0.0929019	−	0.995675i	$-0.529614\pi$
$719$	19.3847	−	11.1918i	0.722927	−	0.417382i	0.815829	+	0.578293i	$0.196281\pi$
$720$		0			0
$721$	−5.28648	−	19.7294i	−0.196879	−	0.734762i
$722$	−2.85124	+	4.93849i	−0.106112	+	0.183792i
$723$	−2.90586	−	5.03310i	−0.108070	−	0.187183i
$724$	−6.99257	−	12.1115i	−0.259877	−	0.450120i
$725$		0			0
$726$	4.90837	+	4.90837i	0.182167	+	0.182167i
$727$	−35.8755	−	20.7127i	−1.33055	−	0.768193i	−0.345166	−	0.938542i	$-0.612177\pi$
$727$	−35.8755	−	20.7127i	−1.33055	−	0.768193i	−0.985384	+	0.170348i	$0.945511\pi$
$728$	−21.9313	−	5.87647i	−0.812827	−	0.217796i
$729$			0.881195i			0.0326369i
$730$		0			0
$731$	−29.7253	+	17.1619i	−1.09943	+	0.634757i
$732$		−	13.2838i		−	0.490985i
$733$	12.6786	+	47.3172i	0.468295	+	1.74770i	0.645727	+	0.763568i	$0.276554\pi$
$733$	12.6786	+	47.3172i	0.468295	+	1.74770i	−0.177432	+	0.984133i	$0.556779\pi$
$734$	−8.49673	−	8.49673i	−0.313620	−	0.313620i
$735$		0			0
$736$	9.82493	−	17.0173i	0.362152	−	0.627265i
$737$	6.24056	+	23.2901i	0.229874	+	0.857902i
$738$	−5.38443	+	3.10870i	−0.198204	+	0.114433i
$739$	43.1882			1.58870			0.794352	−	0.607458i	$-0.207811\pi$
$739$	43.1882			1.58870			0.794352	+	0.607458i	$0.207811\pi$
$740$		0			0
$741$	15.6675			0.575559
$742$	12.6642	−	7.31168i	0.464917	−	0.268420i
$743$	−9.07127	−	33.8544i	−0.332793	−	1.24200i	−0.906243	−	0.422758i	$-0.861062\pi$
$743$	−9.07127	−	33.8544i	−0.332793	−	1.24200i	0.573450	−	0.819240i	$-0.305605\pi$
$744$	1.49382	−	2.58737i	0.0547660	−	0.0948574i
$745$		0			0
$746$	−8.62424	−	8.62424i	−0.315756	−	0.315756i
$747$	4.51560	+	16.8525i	0.165217	+	0.616599i
$748$			36.0231i			1.31714i
$749$	31.3039	−	18.0733i	1.14382	−	0.660386i
$750$		0			0
$751$			34.8532i			1.27181i	0.771767	+	0.635906i	$0.219373\pi$
$751$			34.8532i			1.27181i	−0.771767	+	0.635906i	$0.780627\pi$
$752$	−3.63248	−	0.973319i	−0.132463	−	0.0354933i
$753$	−2.26714	−	1.30894i	−0.0826193	−	0.0477003i
$754$	0.228046	+	0.228046i	0.00830494	+	0.00830494i
$755$		0			0
$756$	−16.9553	−	29.3675i	−0.616659	−	1.06808i
$757$	22.0224	+	38.1439i	0.800418	+	1.38636i	0.919341	+	0.393461i	$0.128722\pi$
$757$	22.0224	+	38.1439i	0.800418	+	1.38636i	−0.118924	+	0.992903i	$0.537944\pi$
$758$	−0.311574	+	0.539662i	−0.0113169	+	0.0196014i
$759$	5.43283	+	20.2756i	0.197199	+	0.735957i
$760$		0			0
$761$	−9.18539	+	5.30319i	−0.332970	+	0.192240i	−0.657159	−	0.753752i	$-0.728242\pi$
$761$	−9.18539	+	5.30319i	−0.332970	+	0.192240i	0.324189	+	0.945992i	$0.394909\pi$
$762$	2.08000	+	3.60267i	0.0753505	+	0.130511i
$763$		−	84.1919i		−	3.04795i
$764$	−4.60270	+	1.23329i	−0.166520	+	0.0446189i
$765$		0			0
$766$	−6.16229			−0.222652
$767$	24.7767	+	24.7767i	0.894636	+	0.894636i
$768$	3.76049	+	1.00762i	0.135695	+	0.0363594i
$769$	12.9050	+	12.9050i	0.465365	+	0.465365i	0.900409	−	0.435044i	$-0.143267\pi$
$769$	12.9050	+	12.9050i	0.465365	+	0.465365i	−0.435044	+	0.900409i	$0.643267\pi$
$770$		0			0
$771$	−9.50622	+	9.50622i	−0.342358	+	0.342358i
$772$	0.325249	+	0.187783i	0.0117060	+	0.00675845i
$773$	−21.4087	+	5.73645i	−0.770018	+	0.206326i	−0.622379	−	0.782716i	$-0.713834\pi$
$773$	−21.4087	+	5.73645i	−0.770018	+	0.206326i	−0.147638	+	0.989041i	$0.547167\pi$
$774$	−8.26247	−	4.77034i	−0.296988	−	0.171466i
$775$		0			0
$776$		−	4.04465i		−	0.145194i
$777$	19.2115	+	7.91982i	0.689209	+	0.284122i
$778$	4.92058	+	4.92058i	0.176411	+	0.176411i
$779$	−9.90595	+	36.9695i	−0.354918	+	1.32457i
$780$		0			0
$781$	−36.6576	−	21.1643i	−1.31171	−	0.757318i
$782$	3.08106	−	5.33655i	0.110178	−	0.190835i
$783$			1.00398i			0.0358795i
$784$	31.8036	+	18.3618i	1.13584	+	0.655779i
$785$		0			0
$786$	−3.07663	−	5.32888i	−0.109740	−	0.190075i
$787$	−3.33777	+	3.33777i	−0.118979	+	0.118979i	−0.764089	−	0.645111i	$-0.776811\pi$
$787$	−3.33777	+	3.33777i	−0.118979	+	0.118979i	0.645111	+	0.764089i	$0.276811\pi$
$788$	−1.93531	+	1.93531i	−0.0689427	+	0.0689427i
$789$	−3.26844	+	1.88704i	−0.116360	+	0.0671803i
$790$		0			0
$791$	30.8134	−	30.8134i	1.09560	−	1.09560i
$792$	−18.0746	+	10.4354i	−0.642254	+	0.370806i
$793$	−8.16960	+	30.4894i	−0.290111	+	1.08271i
$794$	−0.285500	−	0.0764995i	−0.0101320	−	0.00271487i
$795$		0			0
$796$	−21.4147	+	5.73806i	−0.759024	+	0.203380i
$797$	10.6120	−	6.12687i	0.375898	−	0.217025i	−0.300134	−	0.953897i	$-0.597031\pi$
$797$	10.6120	−	6.12687i	0.375898	−	0.217025i	0.676032	+	0.736872i	$0.263698\pi$
$798$	7.52903	+	2.01740i	0.266525	+	0.0714151i
$799$	−3.97308	−	1.06458i	−0.140558	−	0.0376623i
$800$		0			0
$801$	−7.59216	−	28.3343i	−0.268256	−	1.00114i
$802$	−1.37322	+	5.12494i	−0.0484902	+	0.180968i
$803$	27.3460	+	27.3460i	0.965021	+	0.965021i
$804$	6.05104			0.213404
$805$		0			0
$806$	−2.40835	+	2.40835i	−0.0848304	+	0.0848304i
$807$	−12.8681	+	3.44800i	−0.452979	+	0.121375i
$808$	1.96576			0.0691551
$809$	42.3807	−	11.3559i	1.49003	−	0.399252i	0.580281	−	0.814416i	$-0.302943\pi$
$809$	42.3807	−	11.3559i	1.49003	−	0.399252i	0.909746	+	0.415164i	$0.136276\pi$
$810$		0			0
$811$	18.9420	−	32.8086i	0.665145	−	1.15206i	−0.314101	−	0.949390i	$-0.601703\pi$
$811$	18.9420	−	32.8086i	0.665145	−	1.15206i	0.979246	−	0.202675i	$-0.0649636\pi$
$812$	−0.950883	−	1.64698i	−0.0333695	−	0.0577976i
$813$	−2.56862	+	2.56862i	−0.0900855	+	0.0900855i
$814$	5.28386	−	12.8173i	0.185199	−	0.449247i
$815$		0			0
$816$	7.93340	+	2.12575i	0.277725	+	0.0744161i
$817$	−56.7301	+	15.2008i	−1.98474	+	0.531808i
$818$	−0.795877	−	2.97025i	−0.0278272	−	0.103852i
$819$	9.23008	+	34.4471i	0.322525	+	1.20368i
$820$		0			0
$821$	11.3331	−	19.6295i	0.395527	−	0.685073i	−0.597641	−	0.801764i	$-0.703895\pi$
$821$	11.3331	−	19.6295i	0.395527	−	0.685073i	0.993168	+	0.116691i	$0.0372286\pi$
$822$	4.81396			0.167906
$823$	10.6862	−	39.8815i	0.372498	−	1.39018i	−0.484469	−	0.874809i	$-0.660987\pi$
$823$	10.6862	−	39.8815i	0.372498	−	1.39018i	0.856966	−	0.515372i	$-0.172346\pi$
$824$			7.12826i			0.248325i
$825$		0			0
$826$	8.71616	+	15.0968i	0.303274	+	0.525286i
$827$	9.61442	−	16.6527i	0.334326	−	0.579070i	−0.649029	−	0.760764i	$-0.724825\pi$
$827$	9.61442	−	16.6527i	0.334326	−	0.579070i	0.983355	+	0.181694i	$0.0581580\pi$
$828$	−20.3019			−0.705540
$829$	0.555337	−	2.07254i	0.0192876	−	0.0719824i	−0.955611	−	0.294631i	$-0.904803\pi$
$829$	0.555337	−	2.07254i	0.0192876	−	0.0719824i	0.974899	+	0.222648i	$0.0714701\pi$
$830$		0			0
$831$	−1.04997	+	3.91855i	−0.0364232	+	0.135933i
$832$	−13.4387	−	7.75884i	−0.465903	−	0.268989i
$833$	34.7857	+	20.0836i	1.20525	+	0.695854i
$834$	1.88760	−	7.04460i	0.0653621	−	0.243935i
$835$		0			0
$836$	−15.9533	+	59.5386i	−0.551758	+	2.05919i
$837$	−10.6029			−0.366489
$838$	−0.195113	+	0.337946i	−0.00674008	+	0.0116742i
$839$	−27.2967	−	47.2793i	−0.942387	−	1.63226i	−0.760901	−	0.648868i	$-0.775243\pi$
$839$	−27.2967	−	47.2793i	−0.942387	−	1.63226i	−0.181486	−	0.983393i	$-0.558091\pi$
$840$		0			0
$841$		−	28.9437i		−	0.998058i
$842$	−0.204746	+	0.764123i	−0.00705602	+	0.0263334i
$843$	−4.11716			−0.141803
$844$	−15.2704	+	26.4492i	−0.525630	+	0.910418i
$845$		0			0
$846$	−0.295912	−	1.10436i	−0.0101737	−	0.0379687i
$847$	25.1739	+	93.9501i	0.864984	+	3.22816i
$848$	25.4674	−	6.82397i	0.874555	−	0.234336i
$849$	−4.91952	−	1.31818i	−0.168838	−	0.0452399i
$850$		0			0
$851$	22.2719	−	17.1495i	0.763471	−	0.587876i
$852$	−7.51140	+	7.51140i	−0.257336	+	0.257336i
$853$	8.38257	+	14.5190i	0.287014	+	0.497122i	0.973096	−	0.230402i	$-0.0740041\pi$
$853$	8.38257	+	14.5190i	0.287014	+	0.497122i	−0.686082	+	0.727524i	$0.740671\pi$
$854$	−7.85183	+	13.5998i	−0.268684	+	0.465375i
$855$		0			0
$856$	−12.1850	+	3.26496i	−0.416475	+	0.111594i
$857$	−44.1787			−1.50912			−0.754558	−	0.656234i	$-0.772148\pi$
$857$	−44.1787			−1.50912			−0.754558	+	0.656234i	$0.772148\pi$
$858$	−5.96328	+	1.59785i	−0.203583	+	0.0545499i
$859$	−4.03671	+	4.03671i	−0.137731	+	0.137731i	−0.772611	−	0.634880i	$-0.781050\pi$
$859$	−4.03671	+	4.03671i	−0.137731	+	0.137731i	0.634880	+	0.772611i	$0.281050\pi$
$860$		0			0
$861$	22.6051			0.770379
$862$	3.33740	+	3.33740i	0.113672	+	0.113672i
$863$	4.35564	−	16.2555i	0.148268	−	0.553343i	−0.851320	−	0.524646i	$-0.824198\pi$
$863$	4.35564	−	16.2555i	0.148268	−	0.553343i	0.999588	−	0.0286969i	$-0.00913575\pi$
$864$	4.65647	+	17.3782i	0.158416	+	0.591218i
$865$		0			0
$866$	−8.53164	−	2.28605i	−0.289917	−	0.0776830i
$867$	−4.23212	−	1.13399i	−0.143730	−	0.0385124i
$868$	17.3934	−	10.0421i	0.590371	−	0.340851i
$869$	2.05497	−	0.550628i	0.0697101	−	0.0186788i
$870$		0			0
$871$	−13.8885	−	3.72141i	−0.470593	−	0.126095i
$872$	−7.60466	+	28.3810i	−0.257526	+	0.961101i
$873$	−5.50175	+	3.17643i	−0.186206	+	0.107506i
$874$	7.45570	−	7.45570i	0.252193	−	0.252193i
$875$		0			0
$876$	8.40510	−	4.85268i	0.283982	−	0.163957i
$877$	7.16854	−	7.16854i	0.242064	−	0.242064i	−0.575639	−	0.817704i	$-0.695247\pi$
$877$	7.16854	−	7.16854i	0.242064	−	0.242064i	0.817704	+	0.575639i	$0.195247\pi$
$878$	−3.52182	+	3.52182i	−0.118856	+	0.118856i
$879$	−0.899310	−	1.55765i	−0.0303330	−	0.0525383i
$880$		0			0
$881$	−14.4069	−	8.31783i	−0.485381	−	0.280235i	0.237275	−	0.971442i	$-0.423746\pi$
$881$	−14.4069	−	8.31783i	−0.485381	−	0.280235i	−0.722656	+	0.691208i	$0.757079\pi$
$882$			11.1649i			0.375941i
$883$	−13.8328	+	23.9592i	−0.465512	+	0.806290i	−0.999224	−	0.0393756i	$-0.987463\pi$
$883$	−13.8328	+	23.9592i	−0.465512	+	0.806290i	0.533713	+	0.845666i	$0.320796\pi$
$884$	−18.6035	−	10.7408i	−0.625705	−	0.361251i
$885$		0			0
$886$	1.93704	−	7.22914i	0.0650762	−	0.242868i
$887$	22.4653	+	22.4653i	0.754310	+	0.754310i	0.975280	−	0.220971i	$-0.0709225\pi$
$887$	22.4653	+	22.4653i	0.754310	+	0.754310i	−0.220971	+	0.975280i	$0.570923\pi$
$888$	−5.76081	−	4.40504i	−0.193320	−	0.147824i
$889$			58.2900i			1.95499i
$890$		0			0
$891$	19.1118	+	11.0342i	0.640269	+	0.369659i
$892$	−5.82716	+	1.56138i	−0.195108	+	0.0522789i
$893$	−6.09521	−	3.51907i	−0.203968	−	0.117761i
$894$	−3.53400	+	3.53400i	−0.118195	+	0.118195i
$895$		0			0
$896$	−31.5897	−	31.5897i	−1.05534	−	1.05534i
$897$	−12.0909	−	3.23974i	−0.403702	−	0.108172i
$898$	−6.22000	−	6.22000i	−0.207564	−	0.207564i
$899$	−0.594628			−0.0198319
$900$		0			0
$901$	27.8554	−	7.46384i	0.927999	−	0.248656i
$902$		−	15.0814i		−	0.502156i
$903$	17.3439	+	30.0405i	0.577168	+	0.999684i
$904$	−13.1704	+	7.60392i	−0.438040	+	0.252902i
$905$		0			0
$906$	0.598181	+	2.23244i	0.0198732	+	0.0741680i
$907$	−24.4127	+	42.2840i	−0.810610	+	1.40402i	0.101828	+	0.994802i	$0.467531\pi$
$907$	−24.4127	+	42.2840i	−0.810610	+	1.40402i	−0.912438	+	0.409215i	$0.865803\pi$
$908$	−24.1274	−	41.7899i	−0.800696	−	1.38685i
$909$	−1.54379	−	2.67393i	−0.0512044	−	0.0886885i
$910$		0			0
$911$	2.44702	+	2.44702i	0.0810734	+	0.0810734i	0.746481	−	0.665407i	$-0.231742\pi$
$911$	2.44702	+	2.44702i	0.0810734	+	0.0810734i	−0.665407	+	0.746481i	$0.731742\pi$
$912$	12.1708	+	7.02683i	0.403016	+	0.232682i
$913$	−40.8786	−	10.9534i	−1.35289	−	0.362504i
$914$		−	9.73388i		−	0.321968i
$915$		0			0
$916$	32.7287	−	18.8959i	1.08139	−	0.624339i
$917$		−	86.2196i		−	2.84722i
$918$	1.46025	+	5.44973i	0.0481955	+	0.179868i
$919$	−38.8681	−	38.8681i	−1.28214	−	1.28214i	−0.939448	−	0.342691i	$-0.888662\pi$
$919$	−38.8681	−	38.8681i	−1.28214	−	1.28214i	−0.342691	−	0.939448i	$-0.611338\pi$
$920$		0			0
$921$	8.25987	−	14.3065i	0.272172	−	0.471416i
$922$	−0.140421	−	0.524059i	−0.00462453	−	0.0172590i
$923$	21.8599	−	12.6208i	0.719526	−	0.415419i
$924$	36.4050			1.19764
$925$		0			0
$926$	10.0151			0.329115
$927$	9.69623	−	5.59812i	0.318466	−	0.183866i
$928$	0.261143	+	0.974598i	0.00857243	+	0.0319927i
$929$	22.8627	−	39.5994i	0.750102	−	1.29921i	−0.197671	−	0.980268i	$-0.563338\pi$
$929$	22.8627	−	39.5994i	0.750102	−	1.29921i	0.947773	−	0.318946i	$-0.103329\pi$
$930$		0			0
$931$	48.5992	+	48.5992i	1.59278	+	1.59278i
$932$	11.2026	+	41.8087i	0.366954	+	1.36949i
$933$			24.5352i			0.803245i
$934$	−13.4047	+	7.73921i	−0.438616	+	0.253235i
$935$		0			0
$936$		−	12.4458i		−	0.406803i
$937$	42.7066	+	11.4432i	1.39516	+	0.373833i	0.876605	−	0.481210i	$-0.159803\pi$
$937$	42.7066	+	11.4432i	1.39516	+	0.373833i	0.518557	+	0.855043i	$0.326469\pi$
$938$	−6.19495	−	3.57666i	−0.202272	−	0.116782i
$939$	−5.04218	−	5.04218i	−0.164545	−	0.164545i
$940$		0			0
$941$	14.5236	+	25.1556i	0.473455	+	0.820048i	0.999538	−	0.0303851i	$-0.00967337\pi$
$941$	14.5236	+	25.1556i	0.473455	+	0.820048i	−0.526083	+	0.850433i	$0.676340\pi$
$942$	−1.66213	−	2.87889i	−0.0541550	−	0.0937993i
$943$	15.2892	−	26.4816i	0.497884	−	0.862361i
$944$	8.13478	+	30.3594i	0.264765	+	0.988115i
$945$		0			0
$946$	20.0421	−	11.5713i	0.651624	−	0.376215i
$947$	8.75476	+	15.1637i	0.284491	+	0.492754i	0.972486	−	0.232963i	$-0.0748419\pi$
$947$	8.75476	+	15.1637i	0.284491	+	0.492754i	−0.687994	+	0.725716i	$0.741509\pi$
$948$		−	0.533906i		−	0.0173404i
$949$	−22.2760	+	5.96883i	−0.723109	+	0.193756i
$950$		0			0
$951$	−0.546159			−0.0177104
$952$	−15.7515	−	15.7515i	−0.510507	−	0.510507i
$953$	15.3542	+	4.11414i	0.497371	+	0.133270i	0.498780	−	0.866729i	$-0.333782\pi$
$953$	15.3542	+	4.11414i	0.497371	+	0.133270i	−0.00140872	+	0.999999i	$0.500448\pi$
$954$	5.66806	+	5.66806i	0.183510	+	0.183510i
$955$		0			0
$956$	−7.53367	+	7.53367i	−0.243656	+	0.243656i
$957$	−0.933433	−	0.538918i	−0.0301736	−	0.0174207i
$958$	−11.1467	+	2.98675i	−0.360133	+	0.0964974i
$959$	58.4164	+	33.7267i	1.88636	+	1.08909i
$960$		0			0
$961$			24.7203i			0.797428i
$962$	5.04384	+	6.55041i	0.162620	+	0.211194i
$963$	14.0106	+	14.0106i	0.451484	+	0.451484i
$964$	−3.52891	+	13.1701i	−0.113659	+	0.424179i
$965$		0			0
$966$	−5.39312	−	3.11372i	−0.173521	−	0.100182i
$967$	9.69545	−	16.7930i	0.311785	−	0.540027i	−0.666964	−	0.745090i	$-0.732407\pi$
$967$	9.69545	−	16.7930i	0.311785	−	0.540027i	0.978749	+	0.205063i	$0.0657399\pi$
$968$		−	33.9443i		−	1.09101i
$969$	13.3120	+	7.68572i	0.427645	+	0.246901i
$970$		0			0
$971$	19.8289	+	34.3447i	0.636341	+	1.10217i	0.986229	+	0.165384i	$0.0528862\pi$
$971$	19.8289	+	34.3447i	0.636341	+	1.10217i	−0.349888	+	0.936791i	$0.613780\pi$
$972$	20.4705	−	20.4705i	0.656592	−	0.656592i
$973$	72.2601	−	72.2601i	2.31655	−	2.31655i
$974$	−2.67098	+	1.54209i	−0.0855838	+	0.0494118i
$975$		0			0
$976$	−20.0207	+	20.0207i	−0.640848	+	0.640848i
$977$	35.2979	−	20.3792i	1.12928	−	0.651989i	0.185525	−	0.982639i	$-0.440601\pi$
$977$	35.2979	−	20.3792i	1.12928	−	0.651989i	0.943753	+	0.330650i	$0.107268\pi$
$978$	0.0656395	−	0.244970i	0.00209892	−	0.00783328i
$979$	68.7300	+	18.4161i	2.19662	+	0.588582i
$980$		0			0
$981$	44.5775	−	11.9445i	1.42325	−	0.381359i
$982$	−3.28268	+	1.89525i	−0.104754	+	0.0604800i
$983$	−16.3804	−	4.38912i	−0.522454	−	0.139991i	−0.0120523	−	0.999927i	$-0.503836\pi$
$983$	−16.3804	−	4.38912i	−0.522454	−	0.139991i	−0.510401	+	0.859936i	$0.670503\pi$
$984$	−7.62014	−	2.04181i	−0.242921	−	0.0650905i
$985$		0			0
$986$	0.0818933	+	0.305630i	0.00260802	+	0.00973325i
$987$	−1.07587	+	4.01520i	−0.0342453	+	0.127805i
$988$	−25.9910	−	25.9910i	−0.826885	−	0.826885i
$989$	46.9228			1.49206
$990$		0			0
$991$	−16.5526	+	16.5526i	−0.525811	+	0.525811i	−0.919321	−	0.393509i	$-0.871261\pi$
$991$	−16.5526	+	16.5526i	−0.525811	+	0.525811i	0.393509	+	0.919321i	$0.371261\pi$
$992$	−10.2925	+	2.75788i	−0.326788	+	0.0875627i
$993$	−5.16262			−0.163831
$994$	12.1299	−	3.25020i	0.384737	−	0.103090i
$995$		0			0
$996$	−5.31037	+	9.19784i	−0.168266	+	0.291445i
$997$	−5.42200	−	9.39119i	−0.171717	−	0.297422i	0.767304	−	0.641284i	$-0.221598\pi$
$997$	−5.42200	−	9.39119i	−0.171717	−	0.297422i	−0.939020	+	0.343862i	$0.888265\pi$
$998$	7.57080	−	7.57080i	0.239650	−	0.239650i
$999$	−3.31638	+	25.5222i	−0.104926	+	0.807486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.c.193.14	yes	96
5.2	odd	4		925.2.t.c.82.14	yes	96
5.3	odd	4		925.2.t.c.82.11	✓	96
5.4	even	2	inner	925.2.y.c.193.11	yes	96
37.14	odd	12		925.2.t.c.643.14	yes	96
185.14	odd	12		925.2.t.c.643.11	yes	96
185.88	even	12	inner	925.2.y.c.532.11	yes	96
185.162	even	12	inner	925.2.y.c.532.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.c.82.11	✓	96	5.3	odd	4
925.2.t.c.82.14	yes	96	5.2	odd	4
925.2.t.c.643.11	yes	96	185.14	odd	12
925.2.t.c.643.14	yes	96	37.14	odd	12
925.2.y.c.193.11	yes	96	5.4	even	2	inner
925.2.y.c.193.14	yes	96	1.1	even	1	trivial
925.2.y.c.532.11	yes	96	185.88	even	12	inner
925.2.y.c.532.14	yes	96	185.162	even	12	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.341622 - 0.197235i) q^{2} +(-0.203474 - 0.759377i) q^{3} +(-0.922196 + 1.59729i) q^{4} +(-0.219287 - 0.219287i) q^{6} +(-1.12467 - 4.19733i) q^{7} +1.51650i q^{8} +(2.06282 - 1.19097i) q^{9} +5.77783i q^{11} +(1.40059 + 0.375287i) q^{12} +(-2.98386 - 1.72273i) q^{13} +(-1.21207 - 1.21207i) q^{14} +(-1.54529 - 2.67651i) q^{16} +(-1.69018 - 2.92748i) q^{17} +(0.469804 - 0.813724i) q^{18} +(-1.49704 - 5.58703i) q^{19} +(-2.95852 + 1.70810i) q^{21} +(1.13959 + 1.97383i) q^{22} +4.62117i q^{23} +(1.15160 - 0.308569i) q^{24} -1.35914 q^{26} +(-2.99184 - 2.99184i) q^{27} +(7.74153 + 2.07434i) q^{28} +(-0.167787 - 0.167787i) q^{29} +(1.77197 - 1.77197i) q^{31} +(-3.68246 - 2.12607i) q^{32} +(4.38755 - 1.17564i) q^{33} +(-1.15481 - 0.666727i) q^{34} +4.39324i q^{36} +(-3.71107 - 4.81954i) q^{37} +(-1.61338 - 1.61338i) q^{38} +(-0.701064 + 2.61641i) q^{39} +(-5.73051 - 3.30851i) q^{41} +(-0.673796 + 1.16705i) q^{42} -10.1539i q^{43} +(-9.22887 - 5.32829i) q^{44} +(0.911458 + 1.57869i) q^{46} +(0.860410 - 0.860410i) q^{47} +(-1.71806 + 1.71806i) q^{48} +(-10.2905 + 5.94124i) q^{49} +(-1.87915 + 1.87915i) q^{51} +(5.50341 - 3.17740i) q^{52} +(-2.20800 + 8.24036i) q^{53} +(-1.61217 - 0.431980i) q^{54} +(6.36526 - 1.70557i) q^{56} +(-3.93805 + 2.27364i) q^{57} +(-0.0904134 - 0.0242262i) q^{58} +(-9.82324 - 2.63213i) q^{59} +(-2.37112 - 8.84912i) q^{61} +(0.255848 - 0.954838i) q^{62} +(-7.31891 - 7.31891i) q^{63} +4.50380 q^{64} +(1.26700 - 1.26700i) q^{66} +(4.03094 - 1.08009i) q^{67} +6.23472 q^{68} +(3.50921 - 0.940289i) q^{69} +(-3.66302 + 6.34453i) q^{71} +(1.80611 + 3.12827i) q^{72} +(4.73293 - 4.73293i) q^{73} +(-2.21837 - 0.914507i) q^{74} +(10.3047 + 2.76113i) q^{76} +(24.2515 - 6.49816i) q^{77} +(0.276549 + 1.03210i) q^{78} +(-0.0953001 - 0.355665i) q^{79} +(1.90975 - 3.30778i) q^{81} -2.61022 q^{82} +(-1.89576 + 7.07509i) q^{83} -6.30081i q^{84} +(-2.00271 - 3.46879i) q^{86} +(-0.0932734 + 0.161554i) q^{87} -8.76208 q^{88} +(3.18738 - 11.8955i) q^{89} +(-3.87502 + 14.4618i) q^{91} +(-7.38135 - 4.26162i) q^{92} +(-1.70614 - 0.985042i) q^{93} +(0.124231 - 0.463638i) q^{94} +(-0.865202 + 3.22898i) q^{96} -2.66709 q^{97} +(-2.34365 + 4.05931i) q^{98} +(6.88123 + 11.9186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 40 q^{4} - 32 q^{14} - 4 q^{16} - 24 q^{19} + 36 q^{21} + 52 q^{24} + 16 q^{26} + 12 q^{29} + 4 q^{31} - 60 q^{34} + 100 q^{39} - 48 q^{41} + 48 q^{44} + 24 q^{46} - 120 q^{49} - 84 q^{51} + 104 q^{54}+ \cdots - 24 q^{99}+O(q^{100}) \) 96 * q + 40 * q^4 - 32 * q^14 - 4 * q^16 - 24 * q^19 + 36 * q^21 + 52 * q^24 + 16 * q^26 + 12 * q^29 + 4 * q^31 - 60 * q^34 + 100 * q^39 - 48 * q^41 + 48 * q^44 + 24 * q^46 - 120 * q^49 - 84 * q^51 + 104 * q^54 - 68 * q^56 - 28 * q^59 + 68 * q^61 + 48 * q^64 + 4 * q^66 + 28 * q^69 + 48 * q^71 - 48 * q^74 - 152 * q^76 - 92 * q^79 - 16 * q^81 + 20 * q^86 - 8 * q^89 - 12 * q^91 + 56 * q^94 + 252 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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