LMFDB - Embedded newform 230.2.l.a.227.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			227.12
Character	$\chi$	$=$	230.227
Dual form			230.2.l.a.153.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.599278 - 0.800541i) q^{2} +(1.04918 + 2.81295i) q^{3} +(-0.281733 - 0.959493i) q^{4} +(2.23578 - 0.0361909i) q^{5} +(2.88063 + 0.845830i) q^{6} +(0.431402 - 1.98312i) q^{7} +(-0.936950 - 0.349464i) q^{8} +(-4.54467 + 3.93798i) q^{9} +(1.31088 - 1.81152i) q^{10} +(-0.731174 - 0.105127i) q^{11} +(2.40342 - 1.79918i) q^{12} +(-4.71660 + 1.02603i) q^{13} +(-1.32904 - 1.53380i) q^{14} +(2.44753 + 6.25115i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(1.02571 - 0.560082i) q^{17} +(0.428996 + 5.99814i) q^{18} +(4.62791 - 1.35888i) q^{19} +(-0.664616 - 2.13501i) q^{20} +(6.03104 - 0.867133i) q^{21} +(-0.522335 + 0.522335i) q^{22} +(-3.60241 - 3.16585i) q^{23} -3.00224i q^{24} +(4.99738 - 0.161829i) q^{25} +(-2.00517 + 4.39071i) q^{26} +(-7.94049 - 4.33584i) q^{27} +(-2.02433 + 0.144783i) q^{28} +(-2.24985 + 7.66227i) q^{29} +(6.47105 + 1.78683i) q^{30} +(-2.40496 - 5.26613i) q^{31} +(-0.0713392 + 0.997452i) q^{32} +(-0.471413 - 2.16705i) q^{33} +(0.166319 - 1.15677i) q^{34} +(0.892747 - 4.44943i) q^{35} +(5.05885 + 3.25112i) q^{36} +(-9.38911 - 0.671522i) q^{37} +(1.68557 - 4.51918i) q^{38} +(-7.83472 - 12.1911i) q^{39} +(-2.10746 - 0.747414i) q^{40} +(4.64467 - 5.36024i) q^{41} +(2.92009 - 5.34775i) q^{42} +(0.670489 - 0.250080i) q^{43} +(0.105127 + 0.731174i) q^{44} +(-10.0183 + 8.96891i) q^{45} +(-4.69324 + 0.986658i) q^{46} +(-2.04894 - 2.04894i) q^{47} +(-2.40342 - 1.79918i) q^{48} +(2.62076 + 1.19686i) q^{49} +(2.86527 - 4.09759i) q^{50} +(2.65164 + 2.29766i) q^{51} +(2.31329 + 4.23648i) q^{52} +(4.61222 + 1.00333i) q^{53} +(-8.22958 + 3.75832i) q^{54} +(-1.63854 - 0.208578i) q^{55} +(-1.09723 + 1.70733i) q^{56} +(8.67795 + 11.5924i) q^{57} +(4.78568 + 6.39292i) q^{58} +(5.31952 - 8.27734i) q^{59} +(5.30839 - 4.10954i) q^{60} +(-10.6659 + 4.87095i) q^{61} +(-5.65700 - 1.23060i) q^{62} +(5.84892 + 10.7115i) q^{63} +(0.755750 + 0.654861i) q^{64} +(-10.5081 + 2.46468i) q^{65} +(-2.01732 - 0.921280i) q^{66} +(6.64172 + 4.97193i) q^{67} +(-0.826372 - 0.826372i) q^{68} +(5.12581 - 13.4550i) q^{69} +(-3.02695 - 3.38112i) q^{70} +(-1.65293 - 11.4964i) q^{71} +(5.63431 - 2.10149i) q^{72} +(-5.89636 + 10.7984i) q^{73} +(-6.16426 + 7.11394i) q^{74} +(5.69835 + 13.8876i) q^{75} +(-2.60767 - 4.05761i) q^{76} +(-0.523909 + 1.40466i) q^{77} +(-14.4546 - 1.03382i) q^{78} +(2.40997 + 1.54880i) q^{79} +(-1.86129 + 1.23920i) q^{80} +(1.29810 - 9.02851i) q^{81} +(-1.50764 - 6.93052i) q^{82} +(-0.564181 + 7.88828i) q^{83} +(-2.53115 - 5.54244i) q^{84} +(2.27300 - 1.28934i) q^{85} +(0.201610 - 0.686621i) q^{86} +(-23.9141 + 1.71037i) q^{87} +(0.648335 + 0.354018i) q^{88} +(4.10508 - 8.98888i) q^{89} +(1.17622 + 13.3950i) q^{90} +9.79622i q^{91} +(-2.02269 + 4.34841i) q^{92} +(12.2901 - 12.2901i) q^{93} +(-2.86814 + 0.412377i) q^{94} +(10.2978 - 3.20563i) q^{95} +(-2.88063 + 0.845830i) q^{96} +(0.204164 + 2.85459i) q^{97} +(2.52870 - 1.38077i) q^{98} +(3.73693 - 2.40158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.599278	−	0.800541i	0.423753	−	0.566068i
$2$	0.599278	−	0.800541i	0.423753	−	0.566068i
$3$	1.04918	+	2.81295i	0.605742	+	1.62406i	0.770294	+	0.637689i	$0.220110\pi$
$3$	1.04918	+	2.81295i	0.605742	+	1.62406i	−0.164551	+	0.986369i	$0.552618\pi$
$4$	−0.281733	−	0.959493i	−0.140866	−	0.479746i
$5$	2.23578	−	0.0361909i	0.999869	−	0.0161850i
$5$	2.23578	−	0.0361909i	0.999869	−	0.0161850i
$6$	2.88063	+	0.845830i	1.17601	+	0.345308i
$7$	0.431402	−	1.98312i	0.163055	−	0.749550i	−0.820892	−	0.571084i	$-0.806523\pi$
$7$	0.431402	−	1.98312i	0.163055	−	0.749550i	0.983946	−	0.178466i	$-0.0571133\pi$
$8$	−0.936950	−	0.349464i	−0.331262	−	0.123554i
$9$	−4.54467	+	3.93798i	−1.51489	+	1.31266i
$10$	1.31088	−	1.81152i	0.414536	−	0.572852i
$11$	−0.731174	−	0.105127i	−0.220457	−	0.0316970i	0.0312010	−	0.999513i	$-0.490067\pi$
$11$	−0.731174	−	0.105127i	−0.220457	−	0.0316970i	−0.251658	+	0.967816i	$0.580976\pi$
$12$	2.40342	−	1.79918i	0.693807	−	0.519378i
$13$	−4.71660	+	1.02603i	−1.30815	+	0.284570i	−0.811995	−	0.583664i	$-0.801618\pi$
$13$	−4.71660	+	1.02603i	−1.30815	+	0.284570i	−0.496154	+	0.868235i	$0.665255\pi$
$14$	−1.32904	−	1.53380i	−0.355201	−	0.409924i
$15$	2.44753	+	6.25115i	0.631948	+	1.61404i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	1.02571	−	0.560082i	0.248772	−	0.135840i	−0.350026	−	0.936740i	$-0.613827\pi$
$17$	1.02571	−	0.560082i	0.248772	−	0.135840i	0.598798	+	0.800900i	$0.295645\pi$
$18$	0.428996	+	5.99814i	0.101115	+	1.41378i
$19$	4.62791	−	1.35888i	1.06172	−	0.311748i	0.296174	−	0.955134i	$-0.404289\pi$
$19$	4.62791	−	1.35888i	1.06172	−	0.311748i	0.765542	+	0.643386i	$0.222471\pi$
$20$	−0.664616	−	2.13501i	−0.148613	−	0.477404i
$21$	6.03104	−	0.867133i	1.31608	−	0.189224i
$22$	−0.522335	+	0.522335i	−0.111362	+	0.111362i
$23$	−3.60241	−	3.16585i	−0.751155	−	0.660125i
$23$	−3.60241	−	3.16585i	−0.751155	−	0.660125i
$24$		−	3.00224i		−	0.612830i
$25$	4.99738	−	0.161829i	0.999476	−	0.0323659i
$26$	−2.00517	+	4.39071i	−0.393246	+	0.861089i
$27$	−7.94049	−	4.33584i	−1.52815	−	0.834432i
$28$	−2.02433	+	0.144783i	−0.382563	+	0.0273614i
$29$	−2.24985	+	7.66227i	−0.417786	+	1.42285i	0.434925	+	0.900466i	$0.356775\pi$
$29$	−2.24985	+	7.66227i	−0.417786	+	1.42285i	−0.852712	+	0.522382i	$0.825043\pi$
$30$	6.47105	+	1.78683i	1.18145	+	0.326229i
$31$	−2.40496	−	5.26613i	−0.431944	−	0.945825i	−0.993007	−	0.118052i	$-0.962335\pi$
$31$	−2.40496	−	5.26613i	−0.431944	−	0.945825i	0.561064	−	0.827773i	$-0.310392\pi$
$32$	−0.0713392	+	0.997452i	−0.0126111	+	0.176326i
$33$	−0.471413	−	2.16705i	−0.0820625	−	0.377235i
$34$	0.166319	−	1.15677i	0.0285234	−	0.198385i
$35$	0.892747	−	4.44943i	0.150902	−	0.752091i
$36$	5.05885	+	3.25112i	0.843141	+	0.541854i
$37$	−9.38911	−	0.671522i	−1.54356	−	0.110398i	−0.726587	−	0.687074i	$-0.758895\pi$
$37$	−9.38911	−	0.671522i	−1.54356	−	0.110398i	−0.816973	+	0.576676i	$0.804349\pi$
$38$	1.68557	−	4.51918i	0.273435	−	0.733108i
$39$	−7.83472	−	12.1911i	−1.25456	−	1.95213i
$40$	−2.10746	−	0.747414i	−0.333218	−	0.118177i
$41$	4.64467	−	5.36024i	0.725376	−	0.837128i	−0.266567	−	0.963816i	$-0.585889\pi$
$41$	4.64467	−	5.36024i	0.725376	−	0.837128i	0.991943	+	0.126688i	$0.0404348\pi$
$42$	2.92009	−	5.34775i	0.450580	−	0.825176i
$43$	0.670489	−	0.250080i	0.102249	−	0.0381368i	−0.297819	−	0.954622i	$-0.596259\pi$
$43$	0.670489	−	0.250080i	0.102249	−	0.0381368i	0.400068	+	0.916486i	$0.368987\pi$
$44$	0.105127	+	0.731174i	0.0158485	+	0.110229i
$45$	−10.0183	+	8.96891i	−1.49345	+	1.33701i
$46$	−4.69324	+	0.986658i	−0.691981	+	0.145475i
$47$	−2.04894	−	2.04894i	−0.298868	−	0.298868i	0.541702	−	0.840570i	$-0.317780\pi$
$47$	−2.04894	−	2.04894i	−0.298868	−	0.298868i	−0.840570	+	0.541702i	$0.817780\pi$
$48$	−2.40342	−	1.79918i	−0.346904	−	0.259689i
$49$	2.62076	+	1.19686i	0.374394	+	0.170980i
$50$	2.86527	−	4.09759i	0.405210	−	0.579487i
$51$	2.65164	+	2.29766i	0.371304	+	0.321736i
$52$	2.31329	+	4.23648i	0.320796	+	0.587493i
$53$	4.61222	+	1.00333i	0.633537	+	0.137818i	0.517855	−	0.855469i	$-0.326731\pi$
$53$	4.61222	+	1.00333i	0.633537	+	0.137818i	0.115683	+	0.993286i	$0.463094\pi$
$54$	−8.22958	+	3.75832i	−1.11990	+	0.511443i
$55$	−1.63854	−	0.208578i	−0.220941	−	0.0281247i
$56$	−1.09723	+	1.70733i	−0.146624	+	0.228151i
$57$	8.67795	+	11.5924i	1.14942	+	1.53545i
$58$	4.78568	+	6.39292i	0.628391	+	0.839432i
$59$	5.31952	−	8.27734i	0.692543	−	1.07762i	−0.299788	−	0.954006i	$-0.596916\pi$
$59$	5.31952	−	8.27734i	0.692543	−	1.07762i	0.992331	−	0.123612i	$-0.0394478\pi$
$60$	5.30839	−	4.10954i	0.685310	−	0.530539i
$61$	−10.6659	+	4.87095i	−1.36563	+	0.623662i	−0.957280	−	0.289164i	$-0.906623\pi$
$61$	−10.6659	+	4.87095i	−1.36563	+	0.623662i	−0.408349	+	0.912826i	$0.633895\pi$
$62$	−5.65700	−	1.23060i	−0.718439	−	0.156287i
$63$	5.84892	+	10.7115i	0.736894	+	1.34952i
$64$	0.755750	+	0.654861i	0.0944687	+	0.0818576i
$65$	−10.5081	+	2.46468i	−1.30337	+	0.305706i
$66$	−2.01732	−	0.921280i	−0.248315	−	0.113402i
$67$	6.64172	+	4.97193i	0.811415	+	0.607418i	0.922326	−	0.386413i	$-0.126286\pi$
$67$	6.64172	+	4.97193i	0.811415	+	0.607418i	−0.110911	+	0.993830i	$0.535377\pi$
$68$	−0.826372	−	0.826372i	−0.100212	−	0.100212i
$69$	5.12581	−	13.4550i	0.617075	−	1.61979i
$70$	−3.02695	−	3.38112i	−0.361789	−	0.404122i
$71$	−1.65293	−	11.4964i	−0.196166	−	1.36437i	−0.815281	−	0.579066i	$-0.803417\pi$
$71$	−1.65293	−	11.4964i	−0.196166	−	1.36437i	0.619114	−	0.785301i	$-0.287492\pi$
$72$	5.63431	−	2.10149i	0.664010	−	0.247663i
$73$	−5.89636	+	10.7984i	−0.690117	+	1.26386i	0.264029	+	0.964515i	$0.414948\pi$
$73$	−5.89636	+	10.7984i	−0.690117	+	1.26386i	−0.954146	+	0.299340i	$0.903233\pi$
$74$	−6.16426	+	7.11394i	−0.716581	+	0.826979i
$75$	5.69835	+	13.8876i	0.657989	+	1.60360i
$76$	−2.60767	−	4.05761i	−0.299120	−	0.465440i
$77$	−0.523909	+	1.40466i	−0.0597050	+	0.160075i
$78$	−14.4546	−	1.03382i	−1.63666	−	0.117057i
$79$	2.40997	+	1.54880i	0.271143	+	0.174253i	0.669146	−	0.743131i	$-0.266660\pi$
$79$	2.40997	+	1.54880i	0.271143	+	0.174253i	−0.398003	+	0.917384i	$0.630297\pi$
$80$	−1.86129	+	1.23920i	−0.208098	+	0.138546i
$81$	1.29810	−	9.02851i	0.144234	−	1.00317i
$82$	−1.50764	−	6.93052i	−0.166491	−	0.765348i
$83$	−0.564181	+	7.88828i	−0.0619269	+	0.865851i	0.867639	+	0.497195i	$0.165637\pi$
$83$	−0.564181	+	7.88828i	−0.0619269	+	0.865851i	−0.929566	+	0.368656i	$0.879818\pi$
$84$	−2.53115	−	5.54244i	−0.276171	−	0.604730i
$85$	2.27300	−	1.28934i	0.246541	−	0.139849i
$86$	0.201610	−	0.686621i	0.0217402	−	0.0740403i
$87$	−23.9141	+	1.71037i	−2.56386	+	0.183371i
$88$	0.648335	+	0.354018i	0.0691127	+	0.0377384i
$89$	4.10508	−	8.98888i	0.435138	−	0.952819i	−0.557327	−	0.830293i	$-0.688173\pi$
$89$	4.10508	−	8.98888i	0.435138	−	0.952819i	0.992465	−	0.122526i	$-0.0390995\pi$
$90$	1.17622	+	13.3950i	0.123984	+	1.41195i
$91$			9.79622i			1.02692i
$92$	−2.02269	+	4.34841i	−0.210880	+	0.453354i
$93$	12.2901	−	12.2901i	1.27443	−	1.27443i
$94$	−2.86814	+	0.412377i	−0.295826	+	0.0425334i
$95$	10.2978	−	3.20563i	1.05653	−	0.328891i
$96$	−2.88063	+	0.845830i	−0.294003	+	0.0863271i
$97$	0.204164	+	2.85459i	0.0207297	+	0.289839i	0.997233	+	0.0743375i	$0.0236842\pi$
$97$	0.204164	+	2.85459i	0.0207297	+	0.289839i	−0.976503	+	0.215502i	$0.930861\pi$
$98$	2.52870	−	1.38077i	0.255437	−	0.139479i
$99$	3.73693	−	2.40158i	0.375576	−	0.241368i
$100$	−1.56320	−	4.74936i	−0.156320	−	0.474936i
$101$	10.8945	+	12.5730i	1.08405	+	1.25106i	0.966136	+	0.258034i	$0.0830746\pi$
$101$	10.8945	+	12.5730i	1.08405	+	1.25106i	0.117912	+	0.993024i	$0.462380\pi$
$102$	3.42844	−	0.745811i	0.339466	−	0.0738463i
$103$	−9.96911	+	7.46278i	−0.982286	+	0.735330i	−0.964383	−	0.264510i	$-0.914790\pi$
$103$	−9.96911	+	7.46278i	−0.982286	+	0.735330i	−0.0179026	+	0.999840i	$0.505699\pi$
$104$	4.77778	+	0.686941i	0.468500	+	0.0673601i
$105$	13.4527	−	2.15698i	1.31285	−	0.210500i
$106$	3.56721	−	3.09100i	0.346478	−	0.300225i
$107$	0.915143	+	0.341331i	0.0884702	+	0.0329977i	0.393310	−	0.919406i	$-0.371330\pi$
$107$	0.915143	+	0.341331i	0.0884702	+	0.0329977i	−0.304839	+	0.952404i	$0.598603\pi$
$108$	−1.92311	+	8.84039i	−0.185051	+	0.850667i
$109$	13.7799	+	4.04616i	1.31988	+	0.387551i	0.864449	−	0.502720i	$-0.167667\pi$
$109$	13.7799	+	4.04616i	1.31988	+	0.387551i	0.455430	+	0.890272i	$0.349486\pi$
$110$	−1.14892	+	1.18673i	−0.109545	+	0.113150i
$111$	−7.96187	−	27.1156i	−0.755707	−	2.57370i
$112$	0.709239	+	1.90154i	0.0670167	+	0.179679i
$113$	4.85215	−	6.48171i	0.456451	−	0.609748i	−0.511989	−	0.858992i	$-0.671091\pi$
$113$	4.85215	−	6.48171i	0.456451	−	0.609748i	0.968441	+	0.249244i	$0.0801821\pi$
$114$	14.4807			1.35624
$115$	−8.16876	−	6.94775i	−0.761741	−	0.647881i
$116$	7.98575			0.741459
$117$	17.3949	−	23.2369i	1.60816	−	2.14825i
$118$	−3.43848	−	9.21892i	−0.316538	−	0.848671i
$119$	−0.668217	−	2.27574i	−0.0612553	−	0.208616i
$120$	−0.108654	−	6.71234i	−0.00991869	−	0.612750i
$121$	−10.0309	−	2.94533i	−0.911896	−	0.267757i
$122$	−2.49244	+	11.4575i	−0.225655	+	1.03732i
$123$	19.9512	+	7.44140i	1.79894	+	0.670968i
$124$	−4.37526	+	3.79118i	−0.392910	+	0.340458i
$125$	11.1672	−	0.542673i	0.998821	−	0.0485382i
$126$	12.0801	+	1.73686i	1.07618	+	0.154732i
$127$	−8.70539	+	6.51677i	−0.772478	+	0.578270i	−0.911153	−	0.412068i	$-0.864807\pi$
$127$	−8.70539	+	6.51677i	−0.772478	+	0.578270i	0.138675	+	0.990338i	$0.455716\pi$
$128$	0.977147	−	0.212565i	0.0863684	−	0.0187883i
$129$	1.40692	+	1.62368i	0.123873	+	0.142957i
$130$	−4.32421	+	9.88921i	−0.379258	+	0.867341i
$131$	0.301762	−	0.193931i	0.0263651	−	0.0169438i	−0.527392	−	0.849622i	$-0.676830\pi$
$131$	0.301762	−	0.193931i	0.0263651	−	0.0169438i	0.553757	+	0.832678i	$0.313194\pi$
$132$	−1.94646	+	1.06285i	−0.169418	+	0.0925090i
$133$	−0.698331	−	9.76394i	−0.0605530	−	0.846641i
$134$	7.96047	−	2.33740i	0.687680	−	0.201921i
$135$	−17.9101	−	9.40658i	−1.54145	−	0.809590i
$136$	−1.15677	+	0.166319i	−0.0991923	+	0.0142617i
$137$	9.17672	−	9.17672i	0.784020	−	0.784020i	−0.196486	−	0.980507i	$-0.562953\pi$
$137$	9.17672	−	9.17672i	0.784020	−	0.784020i	0.980507	+	0.196486i	$0.0629531\pi$
$138$	−7.69946	−	12.1667i	−0.655421	−	1.03570i
$139$			5.70174i			0.483615i	0.970324	+	0.241808i	$0.0777403\pi$
$139$			5.70174i			0.483615i	−0.970324	+	0.241808i	$0.922260\pi$
$140$	−4.52071	+	0.396965i	−0.382070	+	0.0335496i
$141$	3.61386	−	7.91326i	0.304342	−	0.666417i
$142$	−10.1939	−	5.56627i	−0.855451	−	0.467111i
$143$	3.55652	−	0.254367i	0.297411	−	0.0212712i
$144$	1.69419	−	5.76988i	0.141182	−	0.480823i
$145$	−4.75285	+	17.2125i	−0.394702	+	1.42942i
$146$	5.11099	+	11.1915i	0.422989	+	0.926216i
$147$	−0.617071	+	8.62778i	−0.0508952	+	0.711607i
$148$	2.00090	+	9.19797i	0.164473	+	0.756069i
$149$	−3.29545	+	22.9204i	−0.269974	+	1.87771i	0.178536	+	0.983933i	$0.442864\pi$
$149$	−3.29545	+	22.9204i	−0.269974	+	1.87771i	−0.448511	+	0.893778i	$0.648045\pi$
$150$	14.5325	+	3.76076i	1.18657	+	0.307065i
$151$	11.6029	+	7.45670i	0.944227	+	0.606818i	0.919590	−	0.392879i	$-0.128521\pi$
$151$	11.6029	+	7.45670i	0.944227	+	0.606818i	0.0246365	+	0.999696i	$0.492157\pi$
$152$	−4.81100	−	0.344090i	−0.390224	−	0.0279094i
$153$	−2.45594	+	6.58463i	−0.198551	+	0.532336i
$154$	0.810517	+	1.26119i	0.0653133	+	0.101630i
$155$	−5.56754	−	11.6868i	−0.447196	−	0.938710i
$156$	−9.48995	+	10.9520i	−0.759804	+	0.876860i
$157$	−6.32822	+	11.5893i	−0.505047	+	0.924925i	0.493431	+	0.869785i	$0.335742\pi$
$157$	−6.32822	+	11.5893i	−0.505047	+	0.924925i	−0.998479	+	0.0551403i	$0.982439\pi$
$158$	2.68412	−	1.00112i	0.213537	−	0.0796452i
$159$	2.01672	+	14.0266i	0.159937	+	1.11238i
$160$	−0.123400	+	2.23266i	−0.00975560	+	0.176507i
$161$	−7.83236	+	5.77828i	−0.617276	+	0.455392i
$162$	−6.44977	−	6.44977i	−0.506742	−	0.506742i
$163$	−2.37099	−	1.77490i	−0.185710	−	0.139021i	0.502378	−	0.864648i	$-0.332459\pi$
$163$	−2.37099	−	1.77490i	−0.185710	−	0.139021i	−0.688088	+	0.725627i	$0.741550\pi$
$164$	−6.45166	−	2.94638i	−0.503790	−	0.230073i
$165$	−1.13240	−	4.82798i	−0.0881574	−	0.375858i
$166$	5.97679	+	5.17892i	0.463889	+	0.401962i
$167$	1.72803	+	3.16466i	0.133719	+	0.244889i	0.935956	−	0.352118i	$-0.114538\pi$
$167$	1.72803	+	3.16466i	0.133719	+	0.244889i	−0.802236	+	0.597007i	$0.796357\pi$
$168$	−5.95382	−	1.29517i	−0.459347	−	0.0999248i
$169$	9.36834	−	4.27838i	0.720641	−	0.329106i
$170$	0.329986	−	2.59230i	0.0253088	−	0.198820i
$171$	−15.6811	+	24.4003i	−1.19916	+	1.86594i
$172$	−0.428848	−	0.572874i	−0.0326994	−	0.0436812i
$173$	−2.75819	−	3.68450i	−0.209701	−	0.280128i	0.683343	−	0.730098i	$-0.260526\pi$
$173$	−2.75819	−	3.68450i	−0.209701	−	0.280128i	−0.893044	+	0.449970i	$0.851435\pi$
$174$	−12.9620	+	20.1692i	−0.982643	+	1.52902i
$175$	1.83495	−	9.98023i	0.138709	−	0.754434i
$176$	0.671938	−	0.306864i	0.0506493	−	0.0231307i
$177$	28.8649	+	6.27917i	2.16962	+	0.471971i
$178$	−4.73588	−	8.67312i	−0.354969	−	0.650078i
$179$	−7.97153	−	6.90737i	−0.595820	−	0.516281i	0.303925	−	0.952696i	$-0.401703\pi$
$179$	−7.97153	−	6.90737i	−0.595820	−	0.516281i	−0.899746	+	0.436415i	$0.856248\pi$
$180$	11.4281	+	7.08570i	0.851801	+	0.528137i
$181$	−11.5280	−	5.26464i	−0.856867	−	0.391318i	−0.0619812	−	0.998077i	$-0.519742\pi$
$181$	−11.5280	−	5.26464i	−0.856867	−	0.391318i	−0.794886	+	0.606759i	$0.792469\pi$
$182$	7.84228	+	5.87066i	0.581309	+	0.435162i
$183$	−24.8922	−	24.8922i	−1.84008	−	1.84008i
$184$	2.26893	+	4.22516i	0.167268	+	0.311483i
$185$	−21.0162	−	1.16157i	−1.54514	−	0.0854005i
$186$	−2.47356	−	17.2040i	−0.181370	−	1.26146i
$187$	−0.808855	+	0.301687i	−0.0591493	+	0.0220616i
$188$	−1.38869	+	2.54319i	−0.101281	+	0.185481i
$189$	−12.0240	+	13.8765i	−0.874620	+	1.00937i
$190$	3.60500	−	10.1649i	0.261534	−	0.737437i
$191$	11.1831	+	17.4013i	0.809182	+	1.25911i	0.962593	+	0.270950i	$0.0873378\pi$
$191$	11.1831	+	17.4013i	0.809182	+	1.25911i	−0.153411	+	0.988162i	$0.549026\pi$
$192$	−1.04918	+	2.81295i	−0.0757178	+	0.203007i
$193$	−14.6147	−	1.04527i	−1.05199	−	0.0752399i	−0.465382	−	0.885110i	$-0.654083\pi$
$193$	−14.6147	−	1.04527i	−1.05199	−	0.0752399i	−0.586609	+	0.809870i	$0.699538\pi$
$194$	2.40757	+	1.54725i	0.172853	+	0.111086i
$195$	−17.9579	−	26.9729i	−1.28599	−	1.93157i
$196$	0.410026	−	2.85179i	0.0292876	−	0.203699i
$197$	−2.98566	−	13.7249i	−0.212720	−	0.977856i	−0.952389	−	0.304886i	$-0.901382\pi$
$197$	−2.98566	−	13.7249i	−0.212720	−	0.977856i	0.739669	−	0.672971i	$-0.234982\pi$
$198$	0.316896	−	4.43078i	0.0225208	−	0.314882i
$199$	−4.97953	−	10.9036i	−0.352989	−	0.772939i	−0.999946	−	0.0104118i	$-0.996686\pi$
$199$	−4.97953	−	10.9036i	−0.352989	−	0.772939i	0.646957	−	0.762527i	$-0.276042\pi$
$200$	−4.73885	−	1.59478i	−0.335087	−	0.112768i
$201$	−7.01746	+	23.8993i	−0.494973	+	1.68572i
$202$	16.5940	−	1.18683i	1.16755	−	0.0835050i
$203$	14.2246	+	7.76724i	0.998374	+	0.545153i
$204$	1.45753	−	3.19155i	0.102048	−	0.223453i
$205$	10.1904	−	12.1524i	0.711732	−	0.848759i
$206$			12.4530i			0.867639i
$207$	28.8389	+	0.201512i	2.00444	+	0.0140061i
$208$	3.41314	−	3.41314i	0.236659	−	0.236659i
$209$	−3.52666	+	0.507058i	−0.243944	+	0.0350739i
$210$	6.33513	−	12.0620i	0.437166	−	0.832361i
$211$	15.5890	−	4.57734i	1.07319	−	0.315117i	0.303039	−	0.952978i	$-0.401999\pi$
$211$	15.5890	−	4.57734i	1.07319	−	0.315117i	0.770152	+	0.637861i	$0.220181\pi$
$212$	−0.336727	−	4.70806i	−0.0231265	−	0.323351i
$213$	30.6045	−	16.7113i	2.09698	−	1.14504i
$214$	0.821674	−	0.528058i	0.0561685	−	0.0360973i
$215$	1.49001	−	0.583387i	0.101618	−	0.0397867i
$216$	5.92462	+	6.83738i	0.403119	+	0.465225i
$217$	−11.4809	+	2.49751i	−0.779373	+	0.169542i
$218$	11.4971	−	8.60664i	0.778684	−	0.582915i
$219$	−36.5616	−	5.25677i	−2.47061	−	0.355220i
$220$	0.261502	+	1.63094i	0.0176305	+	0.109958i
$221$	−4.26322	+	3.69410i	−0.286775	+	0.248492i
$222$	−26.4786	−	9.87599i	−1.77713	−	0.662833i
$223$	−1.83884	+	8.45300i	−0.123138	+	0.566055i	0.873691	+	0.486481i	$0.161720\pi$
$223$	−1.83884	+	8.45300i	−0.123138	+	0.566055i	−0.996829	+	0.0795739i	$0.974644\pi$
$224$	1.94729	+	0.571777i	0.130109	+	0.0382035i
$225$	−22.0742	+	20.4150i	−1.47161	+	1.36100i
$226$	−2.28109	−	7.76869i	−0.151736	−	0.516765i
$227$	−0.261068	−	0.699951i	−0.0173277	−	0.0464574i	0.927998	−	0.372585i	$-0.121529\pi$
$227$	−0.261068	−	0.699951i	−0.0173277	−	0.0464574i	−0.945326	+	0.326128i	$0.894256\pi$
$228$	8.67795	−	11.5924i	0.574712	−	0.767725i
$229$	17.9974			1.18930			0.594649	−	0.803985i	$-0.297291\pi$
$229$	17.9974			1.18930			0.594649	+	0.803985i	$0.297291\pi$
$230$	−10.4573	+	2.37580i	−0.689535	+	0.156655i
$231$	−4.50090			−0.296137
$232$	4.78568	−	6.39292i	0.314196	−	0.419716i
$233$	2.31560	+	6.20837i	0.151700	+	0.406724i	0.990464	−	0.137771i	$-0.0439939\pi$
$233$	2.31560	+	6.20837i	0.151700	+	0.406724i	−0.838764	+	0.544495i	$0.816721\pi$
$234$	−8.17769	−	27.8507i	−0.534592	−	1.82065i
$235$	−4.65512	−	4.50681i	−0.303666	−	0.293992i
$236$	−9.44073	−	2.77205i	−0.614539	−	0.180445i
$237$	−1.82820	+	8.40409i	−0.118754	+	0.545905i
$238$	−2.22227	−	0.828863i	−0.144048	−	0.0537272i
$239$	15.4266	−	13.3672i	0.997861	−	0.864651i	0.00705924	−	0.999975i	$-0.497753\pi$
$239$	15.4266	−	13.3672i	0.997861	−	0.864651i	0.990801	+	0.135324i	$0.0432075\pi$
$240$	−5.43862	−	3.93557i	−0.351061	−	0.254040i
$241$	12.3815	+	1.78019i	0.797564	+	0.114672i	0.529036	−	0.848599i	$-0.322554\pi$
$241$	12.3815	+	1.78019i	0.797564	+	0.114672i	0.268528	+	0.963272i	$0.413463\pi$
$242$	−8.36912	+	6.26505i	−0.537988	+	0.402733i
$243$	0.237505	−	0.0516660i	0.0152359	−	0.00331438i
$244$	7.67858	+	8.86155i	0.491571	+	0.567303i
$245$	5.90274	+	2.58106i	0.377112	+	0.164898i
$246$	17.9134	−	11.5123i	1.14212	−	0.733995i
$247$	−20.4338	+	11.1577i	−1.30017	+	0.709946i
$248$	0.413004	+	5.77455i	0.0262258	+	0.366684i
$249$	−22.7813	+	6.68918i	−1.44370	+	0.423910i
$250$	6.25780	−	9.26499i	0.395778	−	0.585969i
$251$	1.29516	−	0.186216i	0.0817496	−	0.0117538i	−0.101319	−	0.994854i	$-0.532306\pi$
$251$	1.29516	−	0.186216i	0.0817496	−	0.0117538i	0.183068	+	0.983100i	$0.441397\pi$
$252$	8.62977	−	8.62977i	0.543625	−	0.543625i
$253$	2.30118	+	2.69350i	0.144674	+	0.169339i
$254$			10.8744i			0.682319i
$255$	6.01162	+	5.04108i	0.376462	+	0.315685i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−7.49083	−	4.09030i	−0.467265	−	0.255146i	0.228325	−	0.973585i	$-0.426675\pi$
$257$	−7.49083	−	4.09030i	−0.467265	−	0.255146i	−0.695590	+	0.718439i	$0.744857\pi$
$258$	2.14296	−	0.153267i	0.133415	−	0.00954200i
$259$	−5.38219	+	18.3301i	−0.334433	+	1.13897i
$260$	5.32532	+	9.38809i	0.330262	+	0.582224i
$261$	−19.9491	−	43.6824i	−1.23482	−	2.70387i
$262$	0.0255897	−	0.357791i	0.00158094	−	0.0221044i
$263$	−1.77749	−	8.17100i	−0.109605	−	0.503845i	−0.998916	−	0.0465433i	$-0.985179\pi$
$263$	−1.77749	−	8.17100i	−0.109605	−	0.503845i	0.889311	−	0.457302i	$-0.151184\pi$
$264$	−0.315617	+	2.19516i	−0.0194249	+	0.135103i
$265$	10.3482	+	2.07629i	0.635685	+	0.127546i
$266$	−8.23493	−	5.29227i	−0.504916	−	0.324490i
$267$	29.5922	+	2.11648i	1.81101	+	0.129526i
$268$	2.89934	−	7.77344i	0.177106	−	0.474838i
$269$	−6.96348	−	10.8354i	−0.424571	−	0.660645i	0.561404	−	0.827542i	$-0.310262\pi$
$269$	−6.96348	−	10.8354i	−0.424571	−	0.660645i	−0.985974	+	0.166897i	$0.946625\pi$
$270$	−18.2635	+	8.70060i	−1.11148	+	0.529501i
$271$	5.61228	−	6.47691i	0.340922	−	0.393444i	−0.559236	−	0.829008i	$-0.688906\pi$
$271$	5.61228	−	6.47691i	0.340922	−	0.393444i	0.900158	+	0.435564i	$0.143451\pi$
$272$	−0.560082	+	1.02571i	−0.0339600	+	0.0621931i
$273$	−27.5563	+	10.2780i	−1.66778	+	0.622051i
$274$	−1.84694	−	12.8458i	−0.111578	−	0.776040i
$275$	−3.67097	−	0.407034i	−0.221368	−	0.0245451i
$276$	−14.3540	−	1.12748i	−0.864012	−	0.0678666i
$277$	−6.84211	−	6.84211i	−0.411102	−	0.411102i	0.471020	−	0.882122i	$-0.343886\pi$
$277$	−6.84211	−	6.84211i	−0.411102	−	0.411102i	−0.882122	+	0.471020i	$0.843886\pi$
$278$	4.56448	+	3.41693i	0.273759	+	0.204934i
$279$	31.6677	+	14.4621i	1.89589	+	0.865826i
$280$	−2.39137	+	3.85691i	−0.142912	+	0.230494i
$281$	−7.92391	−	6.86611i	−0.472701	−	0.409598i	0.385662	−	0.922640i	$-0.373973\pi$
$281$	−7.92391	−	6.86611i	−0.472701	−	0.409598i	−0.858363	+	0.513042i	$0.828518\pi$
$282$	−4.16918	−	7.63529i	−0.248271	−	0.454675i
$283$	−5.12147	−	1.11411i	−0.304440	−	0.0662268i	0.0577504	−	0.998331i	$-0.481607\pi$
$283$	−5.12147	−	1.11411i	−0.304440	−	0.0662268i	−0.362190	+	0.932104i	$0.617971\pi$
$284$	−10.5650	+	4.82487i	−0.626917	+	0.286303i
$285$	19.8215	+	25.6039i	1.17412	+	1.51664i
$286$	1.92771	−	2.99957i	0.113988	−	0.177369i
$287$	−8.62628	−	11.5234i	−0.509193	−	0.680203i
$288$	−3.60373	−	4.81403i	−0.212352	−	0.283669i
$289$	−8.45250	+	13.1523i	−0.497206	+	0.773667i
$290$	10.9311	+	14.1199i	0.641895	+	0.829152i
$291$	−7.81561	+	3.56927i	−0.458159	+	0.209234i
$292$	12.0222	+	2.61526i	0.703544	+	0.153047i
$293$	−10.5997	−	19.4119i	−0.619242	−	1.13406i	−0.979546	−	0.201222i	$-0.935509\pi$
$293$	−10.5997	−	19.4119i	−0.619242	−	1.13406i	0.360304	−	0.932835i	$-0.382673\pi$
$294$	6.53710	+	5.66443i	0.381251	+	0.330356i
$295$	11.5937	−	18.6988i	0.675011	−	1.08869i
$296$	8.56245	+	3.91034i	0.497682	+	0.227284i
$297$	5.35007	+	4.00501i	0.310442	+	0.232394i
$298$	16.3738	+	16.3738i	0.948510	+	0.948510i
$299$	20.2394	+	11.2358i	1.17048	+	0.649786i
$300$	11.7196	−	9.38012i	0.676634	−	0.541561i
$301$	−0.206688	−	1.43755i	−0.0119133	−	0.0828588i
$302$	12.9227	−	4.81993i	0.743619	−	0.277356i
$303$	−23.9369	+	43.8371i	−1.37514	+	2.51837i
$304$	−3.15858	+	3.64520i	−0.181157	+	0.209067i
$305$	−23.6703	+	11.2764i	−1.35536	+	0.645683i
$306$	3.79948	+	5.91211i	0.217202	+	0.337973i
$307$	−2.10703	+	5.64917i	−0.120255	+	0.322415i	−0.983105	−	0.183045i	$-0.941405\pi$
$307$	−2.10703	+	5.64917i	−0.120255	+	0.322415i	0.862850	+	0.505460i	$0.168677\pi$
$308$	1.49536	+	0.106950i	0.0852060	+	0.00609405i
$309$	−31.4518	−	20.2128i	−1.78923	−	1.14987i
$310$	−12.6923	−	2.54662i	−0.720875	−	0.144638i
$311$	−0.167872	+	1.16758i	−0.00951916	+	0.0662072i	−0.994027	−	0.109132i	$-0.965193\pi$
$311$	−0.167872	+	1.16758i	−0.00951916	+	0.0662072i	0.984508	+	0.175339i	$0.0561021\pi$
$312$	3.08040	+	14.1604i	0.174393	+	0.801673i
$313$	−0.440767	+	6.16273i	−0.0249136	+	0.348338i	0.969671	+	0.244412i	$0.0785950\pi$
$313$	−0.440767	+	6.16273i	−0.0249136	+	0.348338i	−0.994585	+	0.103926i	$0.966860\pi$
$314$	5.48533	+	12.0112i	0.309555	+	0.677831i
$315$	13.4645	+	23.7368i	0.758640	+	1.33742i
$316$	0.807091	−	2.74870i	0.0454024	−	0.154626i
$317$	−0.902663	+	0.0645597i	−0.0506986	+	0.00362604i	−0.0966654	−	0.995317i	$-0.530818\pi$
$317$	−0.902663	+	0.0645597i	−0.0506986	+	0.00362604i	0.0459668	+	0.998943i	$0.485363\pi$
$318$	12.4375	+	6.79137i	0.697458	+	0.380841i
$319$	2.45054	−	5.36593i	0.137204	−	0.300435i
$320$	1.71339	+	1.43677i	0.0957812	+	0.0803179i
$321$			2.93237i			0.163669i
$322$	−0.0680091	+	9.73292i	−0.00379000	+	0.542394i
$323$	3.98583	−	3.98583i	0.221778	−	0.221778i
$324$	−9.02851	+	1.29810i	−0.501584	+	0.0721168i
$325$	−23.4046	+	5.89076i	−1.29825	+	0.326761i
$326$	−2.84176	+	0.834416i	−0.157390	+	0.0462140i
$327$	3.07595	+	43.0074i	0.170101	+	2.37832i
$328$	−6.22503	+	3.39913i	−0.343720	+	0.187685i
$329$	−4.94721	+	3.17938i	−0.272748	+	0.175285i
$330$	−4.54362	−	1.98677i	−0.250118	−	0.109368i
$331$	−19.0738	−	22.0123i	−1.04839	−	1.20991i	−0.977173	−	0.212445i	$-0.931857\pi$
$331$	−19.0738	−	22.0123i	−1.04839	−	1.20991i	−0.0712166	−	0.997461i	$-0.522688\pi$
$332$	7.72770	−	1.68106i	0.424112	−	0.0922600i
$333$	45.3149	−	33.9223i	2.48324	−	1.85893i
$334$	3.56901	+	0.513146i	0.195288	+	0.0280781i
$335$	15.0293	+	10.8757i	0.821140	+	0.594205i
$336$	−4.60483	+	3.99011i	−0.251214	+	0.217678i
$337$	2.67639	+	0.998243i	0.145792	+	0.0543778i	0.421301	−	0.906921i	$-0.361574\pi$
$337$	2.67639	+	0.998243i	0.145792	+	0.0543778i	−0.275509	+	0.961299i	$0.588846\pi$
$338$	2.18922	−	10.0637i	0.119078	−	0.547392i
$339$	23.3235	+	6.84839i	1.26676	+	0.371954i
$340$	−1.87749	−	1.81767i	−0.101821	−	0.0985773i
$341$	1.20483	+	4.10328i	0.0652453	+	0.222205i
$342$	10.1361	+	27.1759i	0.548097	+	1.46951i
$343$	12.0178	−	16.0539i	0.648899	−	0.866827i
$344$	−0.715609			−0.0385830
$345$	10.9732	−	30.2678i	0.590778	−	1.62956i
$346$	−4.60252			−0.247433
$347$	14.9212	−	19.9324i	0.801012	−	1.07003i	−0.195000	−	0.980803i	$-0.562471\pi$
$347$	14.9212	−	19.9324i	0.801012	−	1.07003i	0.996012	−	0.0892235i	$-0.0284385\pi$
$348$	8.37846	+	22.4635i	0.449133	+	1.20417i
$349$	−2.59101	−	8.82418i	−0.138694	−	0.472347i	0.860626	−	0.509238i	$-0.170073\pi$
$349$	−2.59101	−	8.82418i	−0.138694	−	0.472347i	−0.999319	+	0.0368909i	$0.988255\pi$
$350$	−6.88994	−	7.44988i	−0.368283	−	0.398213i
$351$	41.9008	+	12.3032i	2.23650	+	0.656696i
$352$	0.157020	−	0.721811i	0.00836922	−	0.0384727i
$353$	14.3478	+	5.35144i	0.763655	+	0.284829i	0.700957	−	0.713204i	$-0.252757\pi$
$353$	14.3478	+	5.35144i	0.763655	+	0.284829i	0.0626983	+	0.998033i	$0.480029\pi$
$354$	22.3248	−	19.3446i	1.18655	−	1.02815i
$355$	−4.11164	−	25.6434i	−0.218223	−	1.36101i
$356$	−9.78130	−	1.40634i	−0.518408	−	0.0745358i
$357$	5.70046	−	4.26731i	0.301700	−	0.225850i
$358$	−10.3068	+	2.24211i	−0.544731	+	0.118499i
$359$	4.53251	+	5.23080i	0.239217	+	0.276071i	0.862645	−	0.505810i	$-0.168806\pi$
$359$	4.53251	+	5.23080i	0.239217	+	0.276071i	−0.623428	+	0.781880i	$0.714261\pi$
$360$	12.5210	−	4.90237i	0.659915	−	0.258378i
$361$	3.58722	−	2.30536i	0.188801	−	0.121335i
$362$	−11.1230	+	6.07363i	−0.584613	+	0.319223i
$363$	−2.23908	−	31.3065i	−0.117521	−	1.64316i
$364$	9.39941	−	2.75991i	0.492663	−	0.144659i
$365$	−12.7921	+	24.3562i	−0.669571	+	1.27486i
$366$	−34.8445	+	5.00989i	−1.82135	+	0.261871i
$367$	12.7027	−	12.7027i	0.663076	−	0.663076i	−0.293028	−	0.956104i	$-0.594663\pi$
$367$	12.7027	−	12.7027i	0.663076	−	0.663076i	0.956104	+	0.293028i	$0.0946628\pi$
$368$	4.74213	+	0.715670i	0.247201	+	0.0373069i
$369$			42.6511i			2.22033i
$370$	−13.5244	+	16.1283i	−0.703103	+	0.838468i
$371$	3.97944	−	8.71376i	0.206602	−	0.452396i
$372$	−15.2548	−	8.32977i	−0.790926	−	0.431878i
$373$	29.3121	−	2.09644i	1.51772	−	0.108550i	0.712564	−	0.701607i	$-0.247534\pi$
$373$	29.3121	−	2.09644i	1.51772	−	0.108550i	0.805160	+	0.593058i	$0.202079\pi$
$374$	−0.243216	+	0.828316i	−0.0125764	+	0.0428312i
$375$	13.2428	+	30.8433i	0.683857	+	1.59274i
$376$	1.20372	+	2.63578i	0.0620772	+	0.135930i
$377$	2.74988	−	38.4483i	0.141626	−	1.98019i
$378$	3.90296	+	17.9416i	0.200746	+	0.922816i
$379$	4.58565	−	31.8939i	0.235549	−	1.63828i	−0.437883	−	0.899032i	$-0.644272\pi$
$379$	4.58565	−	31.8939i	0.235549	−	1.63828i	0.673433	−	0.739249i	$-0.264819\pi$
$380$	−5.97701	−	8.97753i	−0.306614	−	0.460538i
$381$	−27.4648	−	17.6506i	−1.40707	−	0.904267i
$382$	20.6322	+	1.47565i	1.05564	+	0.0755007i
$383$	1.17397	−	3.14754i	0.0599871	−	0.160832i	−0.903499	−	0.428591i	$-0.859010\pi$
$383$	1.17397	−	3.14754i	0.0599871	−	0.160832i	0.963486	+	0.267759i	$0.0862830\pi$
$384$	1.62314	+	2.52565i	0.0828303	+	0.128886i
$385$	−1.12051	+	3.15945i	−0.0571064	+	0.161021i
$386$	−9.59506	+	11.0733i	−0.488376	+	0.563616i
$387$	−2.06235	+	3.77690i	−0.104835	+	0.191991i
$388$	2.68144	−	1.00012i	0.136129	−	0.0507736i
$389$	0.799951	+	5.56378i	0.0405591	+	0.282095i	1.00000		0.000184902i	$5.88560e-5\pi$
$389$	0.799951	+	5.56378i	0.0405591	+	0.282095i	−0.959441	+	0.281910i	$0.909032\pi$
$390$	−32.3547	−	1.78825i	−1.63834	−	0.0905517i
$391$	−5.46818	−	1.22961i	−0.276538	−	0.0621840i
$392$	−2.03726	−	2.03726i	−0.102897	−	0.102897i
$393$	0.862119	+	0.645374i	0.0434881	+	0.0325548i
$394$	−12.7766	−	5.83486i	−0.643674	−	0.293956i
$395$	5.44421	+	3.37554i	0.273928	+	0.169842i
$396$	−3.35712	−	2.90896i	−0.168701	−	0.146181i
$397$	−8.94287	−	16.3776i	−0.448830	−	0.821970i	0.551092	−	0.834444i	$-0.314211\pi$
$397$	−8.94287	−	16.3776i	−0.448830	−	0.821970i	−0.999922	+	0.0124738i	$0.996029\pi$
$398$	−11.7129	−	2.54799i	−0.587116	−	0.127719i
$399$	26.7328	−	12.2085i	1.33831	−	0.611188i
$400$	−4.11657	+	2.83793i	−0.205829	+	0.141896i
$401$	−6.82233	+	10.6157i	−0.340691	+	0.530125i	−0.968750	−	0.248041i	$-0.920213\pi$
$401$	−6.82233	+	10.6157i	−0.340691	+	0.530125i	0.628059	+	0.778166i	$0.283850\pi$
$402$	14.9269	+	19.9401i	0.744488	+	0.994520i
$403$	16.7465	+	22.3707i	0.834201	+	1.11436i
$404$	8.99433	−	13.9955i	0.447485	−	0.696300i
$405$	2.57552	−	20.2327i	0.127978	−	1.00537i
$406$	14.7425	−	6.73268i	0.731658	−	0.334137i
$407$	6.79448	+	1.47805i	0.336790	+	0.0732641i
$408$	−1.68150	−	3.07944i	−0.0832468	−	0.152455i
$409$	2.45449	+	2.12683i	0.121367	+	0.105165i	0.713430	−	0.700727i	$-0.247141\pi$
$409$	2.45449	+	2.12683i	0.121367	+	0.105165i	−0.592063	+	0.805892i	$0.701686\pi$
$410$	−3.62157	−	15.4405i	−0.178857	−	0.762553i
$411$	35.4417	+	16.1857i	1.74821	+	0.798380i
$412$	9.96911	+	7.46278i	0.491143	+	0.367665i
$413$	−14.1201	−	14.1201i	−0.694806	−	0.694806i
$414$	17.4438	−	22.9659i	0.857316	−	1.12871i
$415$	−0.975898	+	17.6568i	−0.0479049	+	0.866740i
$416$	−0.686941	−	4.77778i	−0.0336800	−	0.234250i
$417$	−16.0387	+	5.98213i	−0.785419	+	0.292946i
$418$	−1.70753	+	3.12711i	−0.0835180	+	0.152952i
$419$	−1.12709	+	1.30073i	−0.0550617	+	0.0635446i	−0.782612	−	0.622509i	$-0.786113\pi$
$419$	−1.12709	+	1.30073i	−0.0550617	+	0.0635446i	0.727551	+	0.686054i	$0.240659\pi$
$420$	−5.85967	−	12.3001i	−0.285922	−	0.600181i
$421$	12.8613	+	20.0125i	0.626820	+	0.975351i	0.998888	+	0.0471457i	$0.0150125\pi$
$421$	12.8613	+	20.0125i	0.626820	+	0.975351i	−0.372068	+	0.928206i	$0.621351\pi$
$422$	5.67779	−	15.2227i	0.276390	−	0.741031i
$423$	17.3804	+	1.24307i	0.845065	+	0.0604403i
$424$	−3.97079	−	2.55187i	−0.192839	−	0.123930i
$425$	5.03525	−	2.96493i	0.244245	−	0.143820i
$426$	4.96249	−	34.5149i	0.240433	−	1.67225i
$427$	5.05841	+	23.2531i	0.244794	+	1.12530i
$428$	0.0696788	−	0.974237i	0.00336805	−	0.0470915i
$429$	4.44694	+	9.73743i	0.214700	+	0.470128i
$430$	0.425906	−	1.54243i	0.0205390	−	0.0743825i
$431$	3.62443	−	12.3437i	0.174583	−	0.594574i	−0.824985	−	0.565155i	$-0.808816\pi$
$431$	3.62443	−	12.3437i	0.174583	−	0.594574i	0.999567	−	0.0294185i	$-0.00936554\pi$
$432$	9.02410	−	0.645416i	0.434172	−	0.0310526i
$433$	−5.72662	−	3.12697i	−0.275204	−	0.150273i	0.335720	−	0.941962i	$-0.391020\pi$
$433$	−5.72662	−	3.12697i	−0.275204	−	0.150273i	−0.610924	+	0.791689i	$0.709202\pi$
$434$	−4.88088	+	10.6876i	−0.234290	+	0.513023i
$435$	−53.4046	+	4.68947i	−2.56056	+	0.224843i
$436$		−	14.3617i		−	0.687800i
$437$	−20.9737	−	9.75604i	−1.00331	−	0.466695i
$438$	−26.1188	+	26.1188i	−1.24801	+	1.24801i
$439$	−9.73180	+	1.39922i	−0.464474	+	0.0667812i	−0.370579	−	0.928801i	$-0.620841\pi$
$439$	−9.73180	+	1.39922i	−0.464474	+	0.0667812i	−0.0938945	+	0.995582i	$0.529932\pi$
$440$	1.46234	+	0.768040i	0.0697145	+	0.0366149i
$441$	−16.6237	+	4.88116i	−0.791604	+	0.232436i
$442$	0.402428	+	5.62667i	0.0191415	+	0.267634i
$443$	−13.0868	+	7.14592i	−0.621771	+	0.339513i	−0.759062	−	0.651018i	$-0.774342\pi$
$443$	−13.0868	+	7.14592i	−0.621771	+	0.339513i	0.137291	+	0.990531i	$0.456160\pi$
$444$	−23.7742	+	15.2787i	−1.12827	+	0.725096i
$445$	8.85272	−	20.2457i	0.419659	−	0.959737i
$446$	5.66500	+	6.53776i	0.268245	+	0.309572i
$447$	−67.9314	+	14.7776i	−3.21305	+	0.698955i
$448$	1.62470	−	1.21624i	0.0767599	−	0.0574617i
$449$	−3.20812	−	0.461258i	−0.151400	−	0.0217681i	0.0661978	−	0.997807i	$-0.478913\pi$
$449$	−3.20812	−	0.461258i	−0.151400	−	0.0217681i	−0.217598	+	0.976038i	$0.569822\pi$
$450$	3.11453	+	29.9056i	0.146820	+	1.40976i
$451$	−3.95957	+	3.43098i	−0.186449	+	0.161559i
$452$	−7.58616	−	2.82949i	−0.356823	−	0.133088i
$453$	−8.80189	+	40.4617i	−0.413549	+	1.90105i
$454$	−0.716792	−	0.210469i	−0.0336407	−	0.00987780i
$455$	0.354534	+	21.9022i	0.0166208	+	1.02679i
$456$	−4.07968	−	13.8941i	−0.191049	−	0.650652i
$457$	−1.90650	−	5.11152i	−0.0891823	−	0.239107i	0.884700	−	0.466161i	$-0.154363\pi$
$457$	−1.90650	−	5.11152i	−0.0891823	−	0.239107i	−0.973882	+	0.227054i	$0.927091\pi$
$458$	10.7854	−	14.4076i	0.503969	−	0.673224i
$459$	−10.5731			−0.493510
$460$	−4.36492	+	9.79528i	−0.203515	+	0.456707i
$461$	−5.15179			−0.239943			−0.119971	−	0.992777i	$-0.538280\pi$
$461$	−5.15179			−0.239943			−0.119971	+	0.992777i	$0.538280\pi$
$462$	−2.69729	+	3.60316i	−0.125489	+	0.167634i
$463$	−10.4338	−	27.9742i	−0.484902	−	1.30007i	−0.917231	−	0.398356i	$-0.869581\pi$
$463$	−10.4338	−	27.9742i	−0.484902	−	1.30007i	0.432329	−	0.901716i	$-0.357692\pi$
$464$	−2.24985	−	7.66227i	−0.104447	−	0.355712i
$465$	27.0332	−	27.9228i	1.25363	−	1.29489i
$466$	6.35775	+	1.86680i	0.294517	+	0.0864780i
$467$	7.60931	−	34.9794i	0.352117	−	1.61865i	−0.371486	−	0.928438i	$-0.621152\pi$
$467$	7.60931	−	34.9794i	0.352117	−	1.61865i	0.723603	−	0.690216i	$-0.242485\pi$
$468$	−27.1963	−	10.1437i	−1.25715	−	0.468893i
$469$	12.7252	−	11.0264i	0.587595	−	0.509154i
$470$	−6.39760	+	1.02578i	−0.295099	+	0.0473158i
$471$	−39.2395	−	5.64179i	−1.80806	−	0.259960i
$472$	−7.87676	+	5.89647i	−0.362557	+	0.271407i
$473$	−0.516534	+	0.112365i	−0.0237503	+	0.00516655i
$474$	5.63223	+	6.49993i	0.258697	+	0.298552i
$475$	22.9075	−	7.53976i	1.05107	−	0.345948i
$476$	−1.99530	+	1.28230i	−0.0914542	+	0.0587741i
$477$	−24.9121	+	13.6030i	−1.14065	+	0.622841i
$478$	−1.45619	−	20.3602i	−0.0666047	−	0.931256i
$479$	−35.8689	+	10.5321i	−1.63889	+	0.481222i	−0.966005	−	0.258525i	$-0.916764\pi$
$479$	−35.8689	+	10.5321i	−1.63889	+	0.481222i	−0.672886	+	0.739746i	$0.734946\pi$
$480$	−6.40983	+	1.99534i	−0.292567	+	0.0910743i
$481$	44.9737	−	6.46624i	2.05062	−	0.294835i
$482$	8.84509	−	8.84509i	0.402883	−	0.402883i
$483$	−24.4715	−	15.9696i	−1.11349	−	0.726642i
$484$			10.4543i			0.475197i
$485$	0.559775	+	6.37482i	0.0254181	+	0.289466i
$486$	0.100971	−	0.221095i	0.00458012	−	0.0100291i
$487$	3.74016	+	2.04228i	0.169483	+	0.0925446i	0.561751	−	0.827306i	$-0.310128\pi$
$487$	3.74016	+	2.04228i	0.169483	+	0.0925446i	−0.392269	+	0.919851i	$0.628310\pi$
$488$	11.6956	−	0.836488i	0.529437	−	0.0378661i
$489$	2.50512	−	8.53165i	0.113285	−	0.385815i
$490$	5.60363	−	3.17861i	0.253146	−	0.143595i
$491$	4.08167	+	8.93760i	0.184203	+	0.403348i	0.979095	−	0.203402i	$-0.0651999\pi$
$491$	4.08167	+	8.93760i	0.184203	+	0.403348i	−0.794892	+	0.606751i	$0.792473\pi$
$492$	1.51908	−	21.2395i	0.0684853	−	0.957550i
$493$	1.98380	+	9.11940i	0.0893461	+	0.410717i
$494$	−3.31331	+	23.0446i	−0.149073	+	1.03683i
$495$	8.26803	−	5.50464i	0.371620	−	0.247415i
$496$	4.87027	+	3.12993i	0.218681	+	0.140538i
$497$	−23.5118	−	1.68159i	−1.05465	−	0.0754298i
$498$	−8.29734	+	22.2460i	−0.371812	+	0.996868i
$499$	−1.91276	−	2.97631i	−0.0856267	−	0.133238i	0.795798	−	0.605562i	$-0.207052\pi$
$499$	−1.91276	−	2.97631i	−0.0856267	−	0.133238i	−0.881425	+	0.472324i	$0.843415\pi$
$500$	−3.66684	−	10.5619i	−0.163986	−	0.472344i
$501$	−7.08901	+	8.18116i	−0.316714	+	0.365507i
$502$	0.627086	−	1.14842i	0.0279882	−	0.0512566i
$503$	28.8993	−	10.7789i	1.28856	−	0.480606i	0.390546	−	0.920583i	$-0.372286\pi$
$503$	28.8993	−	10.7789i	1.28856	−	0.480606i	0.898009	+	0.439977i	$0.145013\pi$
$504$	−1.73686	−	12.0801i	−0.0773658	−	0.538091i
$505$	24.8128	+	27.7161i	1.10415	+	1.23335i
$506$	3.53530	−	0.228033i	0.157163	−	0.0101373i
$507$	21.8639	+	21.8639i	0.971010	+	0.971010i
$508$	8.70539	+	6.51677i	0.386239	+	0.289135i
$509$	−17.6375	−	8.05476i	−0.781767	−	0.357021i	−0.0157787	−	0.999876i	$-0.505023\pi$
$509$	−17.6375	−	8.05476i	−0.781767	−	0.357021i	−0.765988	+	0.642854i	$0.777750\pi$
$510$	7.63822	−	1.79154i	0.338226	−	0.0793309i
$511$	18.8708	+	16.3517i	0.834796	+	0.723354i
$512$	−0.479249	−	0.877679i	−0.0211800	−	0.0387883i
$513$	−42.6398	−	9.27572i	−1.88259	−	0.409533i
$514$	−7.76354	+	3.54549i	−0.342435	+	0.156385i
$515$	−22.0186	+	17.0459i	−0.970256	+	0.751132i
$516$	1.16153	−	1.80737i	0.0511335	−	0.0795652i
$517$	1.28273	+	1.71353i	0.0564144	+	0.0753609i
$518$	11.4485	+	15.2935i	0.503020	+	0.671956i
$519$	7.47051	−	11.6243i	0.327919	−	0.510252i
$520$	10.7069	+	1.36293i	0.469528	+	0.0597686i
$521$	33.4390	−	15.2711i	1.46499	−	0.669038i	0.486188	−	0.873854i	$-0.338387\pi$
$521$	33.4390	−	15.2711i	1.46499	−	0.669038i	0.978800	+	0.204816i	$0.0656597\pi$
$522$	−46.9246	−	10.2078i	−2.05383	−	0.446784i
$523$	−10.8119	−	19.8005i	−0.472771	−	0.865815i	−0.999872	−	0.0160126i	$-0.994903\pi$
$523$	−10.8119	−	19.8005i	−0.472771	−	0.865815i	0.527101	−	0.849803i	$-0.323279\pi$
$524$	−0.271091	−	0.234902i	−0.0118427	−	0.0102617i
$525$	29.9991	−	5.30939i	1.30927	−	0.231721i
$526$	−7.60643	−	3.47374i	−0.331656	−	0.151462i
$527$	−5.41627	−	4.05457i	−0.235936	−	0.176620i
$528$	1.56818	+	1.56818i	0.0682461	+	0.0682461i
$529$	2.95478	+	22.8094i	0.128469	+	0.991714i
$530$	7.86360	−	7.03988i	0.341573	−	0.305793i
$531$	8.42052	+	58.5660i	0.365419	+	2.54155i
$532$	−9.17169	+	3.42086i	−0.397643	+	0.148313i
$533$	−16.4073	+	30.0477i	−0.710677	+	1.30151i
$534$	19.4283	−	22.4214i	0.840744	−	0.970270i
$535$	2.05841	+	0.730019i	0.0889927	+	0.0315615i
$536$	−4.48545	−	6.97949i	−0.193742	−	0.301468i
$537$	11.0666	−	29.6706i	0.477557	−	1.28038i
$538$	−12.8472	−	0.918852i	−0.553883	−	0.0396145i
$539$	−1.79041	−	1.15062i	−0.0771183	−	0.0495609i
$540$	−3.97970	+	19.8347i	−0.171259	+	0.853551i
$541$	4.81656	−	33.4999i	0.207080	−	1.44027i	−0.575540	−	0.817774i	$-0.695208\pi$
$541$	4.81656	−	33.4999i	0.207080	−	1.44027i	0.782620	−	0.622500i	$-0.213883\pi$
$542$	−1.82172	−	8.37433i	−0.0782497	−	0.359708i
$543$	2.71432	−	37.9511i	0.116483	−	1.62864i
$544$	0.485482	+	1.06306i	0.0208149	+	0.0455782i
$545$	30.9553	+	8.54759i	1.32598	+	0.366138i
$546$	−8.28594	+	28.2193i	−0.354605	+	1.20767i
$547$	26.0538	−	1.86340i	1.11398	−	0.0796734i	0.497810	−	0.867286i	$-0.334138\pi$
$547$	26.0538	−	1.86340i	1.11398	−	0.0796734i	0.616170	+	0.787613i	$0.288683\pi$
$548$	−11.3904	−	6.21962i	−0.486573	−	0.265689i
$549$	29.2913	−	64.1390i	1.25012	−	2.73739i
$550$	−2.52578	+	2.69483i	−0.107699	+	0.114908i
$551$			38.5176i			1.64091i
$552$	−9.50465	+	10.8153i	−0.404545	+	0.460331i
$553$	4.11112	−	4.11112i	0.174823	−	0.174823i
$554$	−9.57771	+	1.37707i	−0.406918	+	0.0585060i
$555$	−18.7823	−	60.3363i	−0.797264	−	2.56114i
$556$	5.47078	−	1.60637i	0.232013	−	0.0681251i
$557$	2.16103	+	30.2151i	0.0915658	+	1.28026i	0.810731	+	0.585418i	$0.199070\pi$
$557$	2.16103	+	30.2151i	0.0915658	+	1.28026i	−0.719166	+	0.694839i	$0.755476\pi$
$558$	30.5553	−	16.6844i	1.29351	−	0.706309i
$559$	−2.90584	+	1.86747i	−0.122904	+	0.0789855i
$560$	1.65452	+	4.22575i	0.0699161	+	0.178571i
$561$	−1.69726	−	1.95875i	−0.0716585	−	0.0826983i
$562$	−10.2452	+	2.22871i	−0.432169	+	0.0940126i
$563$	−22.6491	+	16.9549i	−0.954545	+	0.714563i	−0.958400	−	0.285429i	$-0.907864\pi$
$563$	−22.6491	+	16.9549i	−0.954545	+	0.714563i	0.00385480	+	0.999993i	$0.498773\pi$
$564$	−8.61086	−	1.23805i	−0.362583	−	0.0521315i
$565$	10.6137	−	14.6672i	0.446523	−	0.617056i
$566$	−3.96107	+	3.43229i	−0.166496	+	0.144270i
$567$	−17.3446	−	6.46921i	−0.728406	−	0.271681i
$568$	−2.46886	+	11.3491i	−0.103591	+	0.476200i
$569$	−36.1200	−	10.6058i	−1.51423	−	0.444618i	−0.584049	−	0.811718i	$-0.698532\pi$
$569$	−36.1200	−	10.6058i	−1.51423	−	0.444618i	−0.930181	+	0.367100i	$0.880351\pi$
$570$	32.3756	−	0.524069i	1.35606	−	0.0219508i
$571$	4.43010	+	15.0875i	0.185394	+	0.631394i	0.998767	+	0.0496508i	$0.0158108\pi$
$571$	4.43010	+	15.0875i	0.185394	+	0.631394i	−0.813373	+	0.581743i	$0.802371\pi$
$572$	−1.24605	−	3.34079i	−0.0521000	−	0.139685i
$573$	−37.2159	+	49.7146i	−1.55472	+	2.07686i
$574$	−14.3945			−0.600813
$575$	−18.5150	−	15.2380i	−0.772127	−	0.635468i
$576$	−6.01346			−0.250561
$577$	−6.99115	+	9.33909i	−0.291046	+	0.388791i	−0.922103	−	0.386945i	$-0.873530\pi$
$577$	−6.99115	+	9.33909i	−0.291046	+	0.388791i	0.631057	+	0.775736i	$0.282621\pi$
$578$	5.46360	+	14.6485i	0.227256	+	0.609296i
$579$	−12.3931	−	42.2072i	−0.515042	−	1.75407i
$580$	17.8543	−	0.289011i	0.741361	−	0.0120005i
$581$	15.4000	+	4.52186i	0.638901	+	0.187598i
$582$	−1.82637	+	8.39570i	−0.0757056	+	0.348013i
$583$	−3.26686	−	1.21848i	−0.135299	−	0.0504641i
$584$	9.29824	−	8.05697i	0.384764	−	0.333400i
$585$	38.0501	−	52.5819i	1.57318	−	2.17399i
$586$	−21.8922	−	3.14763i	−0.904360	−	0.130027i
$587$	−14.8661	+	11.1286i	−0.613590	+	0.459328i	−0.860318	−	0.509757i	$-0.829735\pi$
$587$	−14.8661	+	11.1286i	−0.613590	+	0.459328i	0.246728	+	0.969085i	$0.420644\pi$
$588$	8.45214	−	1.83865i	0.348560	−	0.0758247i
$589$	−18.2860	−	21.1032i	−0.753461	−	0.869540i
$590$	−8.02131	−	20.4870i	−0.330232	−	0.843436i
$591$	35.4749	−	22.7983i	1.45924	−	0.937798i
$592$	8.26167	−	4.51122i	0.339553	−	0.185410i
$593$	0.963465	+	13.4710i	0.0395648	+	0.553188i	0.978118	+	0.208052i	$0.0667125\pi$
$593$	0.963465	+	13.4710i	0.0395648	+	0.553188i	−0.938553	+	0.345135i	$0.887833\pi$
$594$	6.41235	−	1.88284i	0.263102	−	0.0772537i
$595$	−1.57634	−	5.06385i	−0.0646238	−	0.207598i
$596$	22.9204	−	3.29545i	0.938855	−	0.134987i
$597$	25.4470	−	25.4470i	1.04148	−	1.04148i
$598$	21.1238	−	9.46909i	0.863816	−	0.387220i
$599$		−	40.3117i		−	1.64709i	−0.567251	−	0.823545i	$-0.691993\pi$
$599$		−	40.3117i		−	1.64709i	0.567251	−	0.823545i	$-0.308007\pi$
$600$	−0.485851	−	15.0034i	−0.0198348	−	0.612509i
$601$	−3.92524	+	8.59507i	−0.160114	+	0.350600i	−0.972638	−	0.232328i	$-0.925366\pi$
$601$	−3.92524	+	8.59507i	−0.160114	+	0.350600i	0.812524	+	0.582928i	$0.198093\pi$
$602$	−1.27468	−	0.696027i	−0.0519520	−	0.0283680i
$603$	−49.7638	+	3.55918i	−2.02654	+	0.144941i
$604$	3.88575	−	13.2337i	0.158109	−	0.538470i
$605$	−22.5333	−	6.22206i	−0.916111	−	0.252963i
$606$	20.7486	+	45.4330i	0.842853	+	1.84559i
$607$	−2.24647	+	31.4097i	−0.0911812	+	1.27488i	0.721600	+	0.692311i	$0.243407\pi$
$607$	−2.24647	+	31.4097i	−0.0911812	+	1.27488i	−0.812781	+	0.582570i	$0.802047\pi$
$608$	1.02526	+	4.71306i	0.0415800	+	0.191140i
$609$	−6.92471	+	48.1624i	−0.280603	+	1.95164i
$610$	−5.15787	+	25.7067i	−0.208836	+	1.04083i
$611$	11.7663	+	7.56174i	0.476013	+	0.305915i
$612$	7.00983	+	0.501353i	0.283355	+	0.0202660i
$613$	−4.75016	+	12.7357i	−0.191857	+	0.514389i	−0.996887	−	0.0788458i	$-0.974877\pi$
$613$	−4.75016	+	12.7357i	−0.191857	+	0.514389i	0.805030	+	0.593234i	$0.202149\pi$
$614$	3.25970	+	5.07219i	0.131551	+	0.204697i
$615$	44.8756	+	15.9152i	1.80956	+	0.641764i
$616$	0.981753	−	1.13300i	0.0395560	−	0.0456500i
$617$	2.43376	−	4.45710i	0.0979795	−	0.179436i	−0.824092	−	0.566456i	$-0.808314\pi$
$617$	2.43376	−	4.45710i	0.0979795	−	0.179436i	0.922071	+	0.387021i	$0.126496\pi$
$618$	−35.0296	+	13.0654i	−1.40910	+	0.525566i
$619$	3.11471	+	21.6633i	0.125191	+	0.870722i	0.951532	+	0.307551i	$0.0995095\pi$
$619$	3.11471	+	21.6633i	0.125191	+	0.870722i	−0.826341	+	0.563171i	$0.809581\pi$
$620$	−9.64489	+	8.63458i	−0.387348	+	0.346773i
$621$	14.8783	+	40.7579i	0.597047	+	1.63556i
$622$	0.834091	+	0.834091i	0.0334440	+	0.0334440i
$623$	−16.0551	−	12.0187i	−0.643234	−	0.481519i
$624$	13.1820	+	6.02001i	0.527701	+	0.240993i
$625$	24.9476	−	1.61745i	0.997905	−	0.0646978i
$626$	4.66938	+	4.04604i	0.186626	+	0.161712i
$627$	−5.12642	−	9.38834i	−0.204730	−	0.374934i
$628$	12.9027	+	2.80681i	0.514874	+	0.112004i
$629$	−10.0066	+	4.56988i	−0.398991	+	0.182213i
$630$	27.0713	+	3.44604i	1.07855	+	0.137293i
$631$	−24.9903	+	38.8856i	−0.994847	+	1.54801i	−0.167844	+	0.985814i	$0.553680\pi$
$631$	−24.9903	+	38.8856i	−0.994847	+	1.54801i	−0.827003	+	0.562198i	$0.809956\pi$
$632$	−1.71677	−	2.29334i	−0.0682896	−	0.0912243i
$633$	29.2314	+	39.0486i	1.16185	+	1.55204i
$634$	−0.489263	+	0.761308i	−0.0194311	+	0.0302354i
$635$	−19.2274	+	14.8851i	−0.763018	+	0.590697i
$636$	12.8903	−	5.88679i	0.511132	−	0.233426i
$637$	−13.5891	−	2.95612i	−0.538419	−	0.117126i
$638$	−2.82710	−	5.17744i	−0.111926	−	0.204977i
$639$	52.7844	+	45.7380i	2.08812	+	1.80937i
$640$	2.17699	−	0.510612i	0.0860530	−	0.0201837i
$641$	−15.4103	−	7.03765i	−0.608670	−	0.277970i	0.0871400	−	0.996196i	$-0.472227\pi$
$641$	−15.4103	−	7.03765i	−0.608670	−	0.277970i	−0.695810	+	0.718226i	$0.744955\pi$
$642$	2.34748	+	1.75730i	0.0926477	+	0.0693552i
$643$	8.22121	+	8.22121i	0.324213	+	0.324213i	0.850381	−	0.526168i	$-0.176372\pi$
$643$	8.22121	+	8.22121i	0.324213	+	0.324213i	−0.526168	+	0.850381i	$0.676372\pi$
$644$	7.75084	+	5.88716i	0.305426	+	0.231987i
$645$	3.20433	+	3.57926i	0.126170	+	0.140933i
$646$	−0.802203	−	5.57944i	−0.0315623	−	0.219520i
$647$	12.4051	−	4.62686i	0.487694	−	0.181901i	−0.0935742	−	0.995612i	$-0.529829\pi$
$647$	12.4051	−	4.62686i	0.487694	−	0.181901i	0.581269	+	0.813712i	$0.302557\pi$
$648$	−4.37140	+	8.00562i	−0.171725	+	0.314490i
$649$	−4.75967	+	5.49295i	−0.186833	+	0.215617i
$650$	−9.31005	+	22.2665i	−0.365170	+	0.873366i
$651$	−19.0709	−	29.6748i	−0.747446	−	1.16305i
$652$	−1.03502	+	2.77499i	−0.0405344	+	0.108677i
$653$	19.7848	+	1.41504i	0.774240	+	0.0553747i	0.452867	−	0.891578i	$-0.350401\pi$
$653$	19.7848	+	1.41504i	0.774240	+	0.0553747i	0.321373	+	0.946953i	$0.395856\pi$
$654$	36.2726	+	23.3110i	1.41837	+	0.911531i
$655$	0.667653	−	0.444506i	0.0260874	−	0.0173683i
$656$	−1.00938	+	7.02042i	−0.0394098	+	0.274101i
$657$	−15.7268	−	72.2949i	−0.613560	−	2.82049i
$658$	−0.419529	+	5.86578i	−0.0163549	+	0.228672i
$659$	11.9722	+	26.2154i	0.466369	+	1.02121i	0.985989	+	0.166809i	$0.0533463\pi$
$659$	11.9722	+	26.2154i	0.466369	+	1.02121i	−0.519620	+	0.854398i	$0.673926\pi$
$660$	−4.31338	+	2.44673i	−0.167898	+	0.0952389i
$661$	4.76418	−	16.2253i	0.185305	−	0.631091i	−0.813470	−	0.581607i	$-0.802424\pi$
$661$	4.76418	−	16.2253i	0.185305	−	0.631091i	0.998775	−	0.0494839i	$-0.0157576\pi$
$662$	−29.0523	+	2.07786i	−1.12915	+	0.0807582i
$663$	−14.8642	−	8.11646i	−0.577277	−	0.315217i
$664$	3.28528	−	7.19376i	0.127494	−	0.279172i
$665$	−1.91468	−	21.8047i	−0.0742480	−	0.845550i
$666$		−	56.6053i		−	2.19341i
$667$	32.3625	−	20.4800i	1.25308	−	0.792989i
$668$	2.54962	−	2.54962i	0.0986479	−	0.0986479i
$669$	−25.7071	+	3.69613i	−0.993895	+	0.142901i
$670$	17.7132	−	5.51401i	0.684321	−	0.213025i
$671$	8.31070	−	2.44024i	0.320831	−	0.0942044i
$672$	0.434674	+	6.07754i	0.0167679	+	0.234446i
$673$	−38.1802	+	20.8480i	−1.47174	+	0.803630i	−0.997067	−	0.0765328i	$-0.975615\pi$
$673$	−38.1802	+	20.8480i	−1.47174	+	0.803630i	−0.474672	+	0.880163i	$0.657433\pi$
$674$	2.40304	−	1.54434i	0.0925616	−	0.0594857i
$675$	−40.3833	−	20.3828i	−1.55435	−	0.784535i
$676$	−6.74444	−	7.78349i	−0.259401	−	0.299365i
$677$	32.6774	−	7.10853i	1.25589	−	0.273203i	0.465085	−	0.885266i	$-0.346024\pi$
$677$	32.6774	−	7.10853i	1.25589	−	0.273203i	0.790809	+	0.612063i	$0.209660\pi$
$678$	19.4597	−	14.5673i	0.747344	−	0.559455i
$679$	5.74907	+	0.826592i	0.220629	+	0.0317217i
$680$	−2.58026	+	0.413716i	−0.0989485	+	0.0158653i
$681$	1.69502	−	1.46874i	0.0649533	−	0.0562824i
$682$	4.00688	+	1.49449i	0.153431	+	0.0572269i
$683$	−2.54672	+	11.7071i	−0.0974476	+	0.447959i	0.902407	+	0.430885i	$0.141799\pi$
$683$	−2.54672	+	11.7071i	−0.0974476	+	0.447959i	−0.999854	+	0.0170739i	$0.994565\pi$
$684$	27.8298	+	8.17156i	1.06410	+	0.312447i
$685$	20.1850	−	20.8492i	0.771228	−	0.796607i
$686$	−5.64980	−	19.2414i	−0.215710	−	0.734642i
$687$	18.8824	+	50.6257i	0.720409	+	1.93149i
$688$	−0.428848	+	0.572874i	−0.0163497	+	0.0218406i
$689$	−22.7834			−0.867980
$690$	−17.6546	−	26.9233i	−0.672098	−	1.02495i
$691$	−41.3245			−1.57206			−0.786028	−	0.618191i	$-0.787866\pi$
$691$	−41.3245			−1.57206			−0.786028	+	0.618191i	$0.787866\pi$
$692$	−2.75819	+	3.68450i	−0.104850	+	0.140064i
$693$	−3.15051	−	8.44684i	−0.119678	−	0.320869i
$694$	−7.01476	−	23.8901i	−0.266277	−	0.906855i
$695$	0.206351	+	12.7478i	0.00782734	+	0.483552i
$696$	23.0040	+	6.75459i	0.871965	+	0.256032i
$697$	1.76193	−	8.09947i	0.0667379	−	0.306789i
$698$	−8.61685	−	3.21392i	−0.326153	−	0.121649i
$699$	−15.0344	+	13.0274i	−0.568652	+	0.492740i
$700$	−10.0929	+	1.05113i	−0.381477	+	0.0397291i
$701$	5.54507	+	0.797261i	0.209435	+	0.0301121i	0.246233	−	0.969211i	$-0.420807\pi$
$701$	5.54507	+	0.797261i	0.209435	+	0.0301121i	−0.0367989	+	0.999323i	$0.511716\pi$
$702$	34.9594	−	26.1703i	1.31946	−	0.987735i
$703$	−44.3645	+	9.65091i	−1.67324	+	0.363991i
$704$	−0.483741	−	0.558267i	−0.0182317	−	0.0210405i
$705$	7.79340	−	17.8231i	0.293516	−	0.671255i
$706$	12.8824	−	8.27898i	0.484834	−	0.311584i
$707$	29.6337	−	16.1812i	1.11449	−	0.608557i
$708$	−2.10736	−	29.4647i	−0.0791993	−	1.10735i
$709$	17.8403	−	5.23840i	0.670008	−	0.196732i	0.0710014	−	0.997476i	$-0.477381\pi$
$709$	17.8403	−	5.23840i	0.670008	−	0.196732i	0.599007	+	0.800744i	$0.295562\pi$
$710$	−22.9926	−	12.0760i	−0.862899	−	0.453205i
$711$	−17.0517	+	2.45166i	−0.639487	+	0.0919444i
$712$	−6.98755	+	6.98755i	−0.261869	+	0.261869i
$713$	−8.00812	+	26.5845i	−0.299906	+	0.995599i
$714$		−	7.12076i		−	0.266488i
$715$	7.94236	−	0.697421i	0.297028	−	0.0260821i
$716$	−4.38173	+	9.59466i	−0.163753	+	0.358569i
$717$	53.7864	+	29.3696i	2.00869	+	1.09683i
$718$	6.90370	−	0.493763i	0.257644	−	0.0184271i
$719$	−3.15985	+	10.7615i	−0.117842	+	0.401334i	−0.997196	−	0.0748351i	$-0.976157\pi$
$719$	−3.15985	+	10.7615i	−0.117842	+	0.401334i	0.879353	+	0.476170i	$0.157975\pi$
$720$	3.57901	−	12.9615i	0.133382	−	0.483045i
$721$	10.4989	+	22.9894i	0.391000	+	0.856171i
$722$	0.304200	−	4.25327i	0.0113211	−	0.158290i
$723$	7.98280	+	36.6963i	0.296884	+	1.36475i
$724$	−1.80359	+	12.5442i	−0.0670298	+	0.466202i
$725$	−10.0034	+	38.6554i	−0.371515	+	1.43563i
$726$	−26.4040	−	16.9688i	−0.979943	−	0.629771i
$727$	−20.0235	−	1.43211i	−0.742630	−	0.0531139i	−0.305103	−	0.952319i	$-0.598691\pi$
$727$	−20.0235	−	1.43211i	−0.742630	−	0.0531139i	−0.437527	+	0.899205i	$0.644145\pi$
$728$	3.42343	−	9.17857i	0.126881	−	0.340180i
$729$	−14.3996	−	22.4062i	−0.533319	−	0.829860i
$730$	11.8321	+	24.8367i	0.437924	+	0.919249i
$731$	0.547665	−	0.632039i	0.0202561	−	0.0233768i
$732$	−16.8709	+	30.8968i	−0.623567	+	1.14198i
$733$	14.3121	−	5.33813i	0.528629	−	0.197168i	−0.0709560	−	0.997479i	$-0.522605\pi$
$733$	14.3121	−	5.33813i	0.528629	−	0.197168i	0.599585	+	0.800311i	$0.295332\pi$
$734$	−2.55659	−	17.7815i	−0.0943656	−	0.656327i
$735$	−1.06738	+	19.3121i	−0.0393711	+	0.712338i
$736$	3.41478	−	3.36739i	0.125870	−	0.124124i
$737$	−4.33357	−	4.33357i	−0.159629	−	0.159629i
$738$	34.1440	+	25.5599i	1.25686	+	0.940872i
$739$	30.4248	+	13.8945i	1.11919	+	0.511119i	0.887101	−	0.461575i	$-0.152716\pi$
$739$	30.4248	+	13.8945i	1.11919	+	0.511119i	0.232092	+	0.972694i	$0.425443\pi$
$740$	4.80644	+	20.4922i	0.176688	+	0.753308i
$741$	−52.8246	−	45.7728i	−1.94056	−	1.68150i
$742$	−4.59094	−	8.40767i	−0.168539	−	0.308655i
$743$	27.9116	+	6.07179i	1.02398	+	0.222752i	0.693039	−	0.720900i	$-0.256271\pi$
$743$	27.9116	+	6.07179i	1.02398	+	0.222752i	0.330938	+	0.943653i	$0.392635\pi$
$744$	−15.8102	+	7.22028i	−0.579630	+	0.264708i
$745$	−6.53838	+	51.3641i	−0.239548	+	1.88183i
$746$	15.8878	−	24.7219i	0.581694	−	0.905133i
$747$	−28.4999	−	38.0714i	−1.04276	−	1.39296i
$748$	0.517348	+	0.691096i	0.0189161	+	0.0252690i
$749$	1.07169	−	1.66759i	0.0391589	−	0.0609324i
$750$	32.6275	+	7.88227i	1.19139	+	0.287820i
$751$	11.1266	−	5.08134i	0.406015	−	0.185421i	−0.201930	−	0.979400i	$-0.564721\pi$
$751$	11.1266	−	5.08134i	0.406015	−	0.185421i	0.607945	+	0.793979i	$0.291994\pi$
$752$	2.83142	+	0.615937i	0.103251	+	0.0224609i
$753$	1.88266	+	3.44784i	0.0686081	+	0.125646i
$754$	−29.1315	−	25.2426i	−1.06091	−	0.919281i
$755$	26.2112	+	16.2516i	0.953925	+	0.591456i
$756$	16.7019	+	7.62752i	0.607444	+	0.277410i
$757$	24.9495	+	18.6770i	0.906806	+	0.678827i	0.947298	−	0.320353i	$-0.103802\pi$
$757$	24.9495	+	18.6770i	0.906806	+	0.678827i	−0.0404918	+	0.999180i	$0.512892\pi$
$758$	−22.7843	−	22.7843i	−0.827564	−	0.827564i
$759$	−5.16234	+	9.29905i	−0.187381	+	0.337534i
$760$	−10.7688	−	0.595193i	−0.390624	−	0.0215899i
$761$	−2.24265	−	15.5980i	−0.0812961	−	0.565427i	−0.989236	−	0.146327i	$-0.953255\pi$
$761$	−2.24265	−	15.5980i	−0.0812961	−	0.565427i	0.907940	−	0.419100i	$-0.137654\pi$
$762$	−30.5891	+	11.4091i	−1.10813	+	0.413309i
$763$	13.9687	−	25.5818i	0.505701	−	0.926123i
$764$	13.5458	−	15.6326i	0.490068	−	0.565569i
$765$	−5.25263	+	14.8106i	−0.189909	+	0.535480i
$766$	−1.81620	−	2.82606i	−0.0656220	−	0.102110i
$767$	−16.5972	+	44.4989i	−0.599291	+	1.60676i
$768$	2.99459	+	0.214178i	0.108058	+	0.00772847i
$769$	3.48307	+	2.23843i	0.125603	+	0.0807199i	0.601934	−	0.798546i	$-0.294397\pi$
$769$	3.48307	+	2.23843i	0.125603	+	0.0807199i	−0.476331	+	0.879266i	$0.658034\pi$
$770$	1.85778	+	2.79040i	0.0669497	+	0.100559i
$771$	3.64662	−	25.3628i	0.131330	−	0.913418i
$772$	3.11452	+	14.3172i	0.112094	+	0.515288i
$773$	0.208991	−	2.92208i	0.00751689	−	0.105100i	−0.992308	−	0.123790i	$-0.960495\pi$
$773$	0.208991	−	2.92208i	0.00751689	−	0.105100i	0.999825	+	0.0186902i	$0.00594961\pi$
$774$	1.78765	+	3.91441i	0.0642557	+	0.140700i
$775$	−12.8707	−	25.9277i	−0.462330	−	0.931349i
$776$	0.806284	−	2.74595i	0.0289439	−	0.0985739i
$777$	−57.2084	+	4.09163i	−2.05234	+	0.146786i
$778$	4.93343	+	2.69386i	0.176872	+	0.0965794i
$779$	14.2112	−	31.1182i	0.509170	−	1.11493i
$780$	−20.8210	+	24.8296i	−0.745512	+	0.889043i
$781$			8.57960i			0.307002i
$782$	−4.26131	+	3.64063i	−0.152384	+	0.130189i
$783$	51.0873	−	51.0873i	1.82571	−	1.82571i
$784$	−2.85179	+	0.410026i	−0.101850	+	0.0146438i
$785$	−13.7291	+	26.1400i	−0.490011	+	0.932978i
$786$	1.03330	−	0.303403i	0.0368565	−	0.0108220i
$787$	−1.75403	−	24.5245i	−0.0625243	−	0.874204i	−0.927840	−	0.372977i	$-0.878337\pi$
$787$	−1.75403	−	24.5245i	−0.0625243	−	0.874204i	0.865316	−	0.501226i	$-0.167118\pi$
$788$	−12.3278	+	6.73146i	−0.439158	+	0.239798i
$789$	21.1197	−	13.5728i	0.751882	−	0.483205i
$790$	5.96485	−	2.33543i	0.212220	−	0.0830908i
$791$	−10.7608	−	12.4186i	−0.382610	−	0.441555i
$792$	−4.34058	+	0.944236i	−0.154236	+	0.0335520i
$793$	45.3090	−	33.9179i	1.60897	−	1.20446i
$794$	−18.4702	−	2.65562i	−0.655484	−	0.0942444i
$795$	5.01658	+	31.2874i	0.177920	+	1.10965i
$796$	−9.05907	+	7.84973i	−0.321090	+	0.278226i
$797$	−14.7442	−	5.49929i	−0.522266	−	0.194795i	0.0744845	−	0.997222i	$-0.476269\pi$
$797$	−14.7442	−	5.49929i	−0.522266	−	0.194795i	−0.596750	+	0.802427i	$0.703542\pi$
$798$	6.24700	−	28.7170i	0.221141	−	1.01657i
$799$	−3.24920	−	0.954051i	−0.114948	−	0.0337519i
$800$	−0.195092	+	4.99619i	−0.00689755	+	0.176642i
$801$	16.7418	+	57.0172i	0.591541	+	2.01460i
$802$	4.40988	+	11.8233i	0.155718	+	0.417496i
$803$	5.44647	−	7.27563i	0.192202	−	0.256751i
$804$	24.9082			0.878445
$805$	−17.3023	+	13.2024i	−0.609825	+	0.465323i
$806$	27.9444			0.984300
$807$	23.1735	−	30.9561i	0.815745	−	1.08971i
$808$	−5.81384	−	15.5875i	−0.204530	−	0.548366i
$809$	4.90048	+	16.6895i	0.172292	+	0.586772i	0.999684	+	0.0251471i	$0.00800540\pi$
$809$	4.90048	+	16.6895i	0.172292	+	0.586772i	−0.827392	+	0.561625i	$0.810176\pi$
$810$	−14.6537	−	14.1868i	−0.514877	−	0.498474i
$811$	−51.4576	−	15.1093i	−1.80692	−	0.530560i	−0.808593	−	0.588368i	$-0.799771\pi$
$811$	−51.4576	−	15.1093i	−1.80692	−	0.530560i	−0.998328	+	0.0578085i	$0.981589\pi$
$812$	3.44507	−	15.8367i	0.120898	−	0.555760i
$813$	24.1075	+	8.99164i	0.845487	+	0.315350i
$814$	5.25502	−	4.55350i	0.184188	−	0.159600i
$815$	−5.36523	−	3.88246i	−0.187936	−	0.135997i
$816$	−3.47291	−	0.499329i	−0.121576	−	0.0174800i
$817$	2.76314	−	2.06846i	0.0966700	−	0.0723662i
$818$	3.17353	−	0.690360i	0.110960	−	0.0241379i
$819$	−38.5773	−	44.5206i	−1.34800	−	1.55568i
$820$	−14.5311	−	6.35394i	−0.507448	−	0.221889i
$821$	14.5242	−	9.33412i	0.506897	−	0.325763i	−0.262073	−	0.965048i	$-0.584406\pi$
$821$	14.5242	−	9.33412i	0.506897	−	0.325763i	0.768970	+	0.639285i	$0.220770\pi$
$822$	34.1967	−	18.6728i	1.19275	−	0.651289i
$823$	1.58335	+	22.1381i	0.0551922	+	0.771687i	0.947398	+	0.320058i	$0.103702\pi$
$823$	1.58335	+	22.1381i	0.0551922	+	0.771687i	−0.892206	+	0.451629i	$0.850843\pi$
$824$	11.9485	−	3.50840i	0.416247	−	0.122221i
$825$	−2.70652	−	10.7533i	−0.0942291	−	0.374382i
$826$	−19.7656	+	2.84187i	−0.687734	+	0.0988812i
$827$	15.4974	−	15.4974i	0.538899	−	0.538899i	−0.384307	−	0.923206i	$-0.625559\pi$
$827$	15.4974	−	15.4974i	0.538899	−	0.538899i	0.923206	+	0.384307i	$0.125559\pi$
$828$	−7.93149	−	27.7274i	−0.275638	−	0.963595i
$829$			20.2475i			0.703226i	0.936145	+	0.351613i	$0.114367\pi$
$829$			20.2475i			0.703226i	−0.936145	+	0.351613i	$0.885633\pi$
$830$	13.5502	+	11.3626i	0.470334	+	0.394401i
$831$	12.0679	−	26.4251i	0.418632	−	0.916676i
$832$	−4.23648	−	2.31329i	−0.146873	−	0.0801989i
$833$	3.35849	−	0.240204i	0.116365	−	0.00832257i
$834$	−4.82270	+	16.4246i	−0.166996	+	0.568738i
$835$	3.97803	+	7.01292i	0.137665	+	0.242692i
$836$	1.48009	+	3.24095i	0.0511901	+	0.112091i
$837$	−3.73651	+	52.2432i	−0.129153	+	1.80579i
$838$	0.365848	+	1.68177i	0.0126380	+	0.0580959i
$839$	−2.98596	+	20.7678i	−0.103087	+	0.716983i	0.871078	+	0.491145i	$0.163421\pi$
$839$	−2.98596	+	20.7678i	−0.103087	+	0.716983i	−0.974165	+	0.225839i	$0.927488\pi$
$840$	−13.3583	−	2.68024i	−0.460904	−	0.0924771i
$841$	−29.2523	−	18.7993i	−1.00870	−	0.648252i
$842$	23.7283	+	1.69708i	0.817732	+	0.0584854i
$843$	11.0004	−	29.4933i	0.378875	−	1.01580i
$844$	−8.78386	−	13.6679i	−0.302353	−	0.470470i
$845$	20.7907	−	9.90453i	0.715220	−	0.340726i
$846$	11.4108	−	13.1688i	0.392313	−	0.452753i
$847$	−10.1683	+	18.6218i	−0.349386	+	0.639853i
$848$	−4.42249	+	1.64950i	−0.151869	+	0.0566441i
$849$	−2.23940	−	15.5753i	−0.0768559	−	0.534544i
$850$	0.643958	−	5.80774i	0.0220876	−	0.199204i
$851$	31.6975	+	32.1436i	1.08658	+	1.10187i
$852$	−24.6567	−	24.6567i	−0.844723	−	0.844723i
$853$	16.3267	+	12.2220i	0.559015	+	0.418473i	0.841071	−	0.540925i	$-0.181926\pi$
$853$	16.3267	+	12.2220i	0.559015	+	0.418473i	−0.282056	+	0.959398i	$0.591017\pi$
$854$	21.6465	+	9.88561i	0.740727	+	0.338279i
$855$	−34.1764	+	55.1211i	−1.16881	+	1.88510i
$856$	−0.738160	−	0.639619i	−0.0252298	−	0.0218617i
$857$	14.4934	+	26.5428i	0.495087	+	0.906683i	0.999076	+	0.0429737i	$0.0136832\pi$
$857$	14.4934	+	26.5428i	0.495087	+	0.906683i	−0.503990	+	0.863710i	$0.668135\pi$
$858$	10.4602	+	2.27547i	0.357104	+	0.0776832i
$859$	−25.4185	+	11.6082i	−0.867269	+	0.396068i	−0.798808	−	0.601586i	$-0.794536\pi$
$859$	−25.4185	+	11.6082i	−0.867269	+	0.396068i	−0.0684602	+	0.997654i	$0.521809\pi$
$860$	−0.979541	−	1.26530i	−0.0334021	−	0.0431463i
$861$	23.3642	−	36.3554i	0.796249	−	1.23899i
$862$	−7.70958	−	10.2988i	−0.262589	−	0.350778i
$863$	19.1924	+	25.6381i	0.653318	+	0.872730i	0.997816	−	0.0660567i	$-0.0210418\pi$
$863$	19.1924	+	25.6381i	0.653318	+	0.872730i	−0.344498	+	0.938787i	$0.611951\pi$
$864$	4.89126	−	7.61095i	0.166404	−	0.258930i
$865$	−6.30003	−	8.13790i	−0.214207	−	0.276697i
$866$	−5.93511	+	2.71047i	−0.201683	+	0.0921056i
$867$	−45.8650	−	9.97733i	−1.55766	−	0.338848i
$868$	5.63089	+	10.3122i	0.191125	+	0.350019i
$869$	−1.59929	−	1.38579i	−0.0542522	−	0.0470098i
$870$	−28.2501	+	45.5629i	−0.957767	+	1.54473i
$871$	−36.4277	−	16.6360i	−1.23430	−	0.563688i
$872$	−11.4971	−	8.60664i	−0.389342	−	0.291458i
$873$	−12.1692	−	12.1692i	−0.411864	−	0.411864i
$874$	−20.3792	+	10.9437i	−0.689335	+	0.370176i
$875$	3.74135	−	22.3800i	0.126481	−	0.756581i
$876$	5.25677	+	36.5616i	0.177610	+	1.23530i
$877$	−17.5307	+	6.53861i	−0.591969	+	0.220793i	−0.627553	−	0.778574i	$-0.715944\pi$
$877$	−17.5307	+	6.53861i	−0.591969	+	0.220793i	0.0355841	+	0.999367i	$0.488671\pi$
$878$	−4.71192	+	8.62923i	−0.159020	+	0.291222i
$879$	43.4838	−	50.1830i	1.46667	−	1.69263i
$880$	1.49120	−	0.710397i	0.0502683	−	0.0239475i
$881$	−15.0806	−	23.4659i	−0.508079	−	0.790587i	0.488558	−	0.872532i	$-0.337523\pi$
$881$	−15.0806	−	23.4659i	−0.508079	−	0.790587i	−0.996637	+	0.0819450i	$0.973887\pi$
$882$	−6.05464	+	16.2331i	−0.203870	+	0.546598i
$883$	−24.2115	−	1.73164i	−0.814783	−	0.0582745i	−0.342274	−	0.939600i	$-0.611197\pi$
$883$	−24.2115	−	1.73164i	−0.814783	−	0.0582745i	−0.472509	+	0.881326i	$0.656652\pi$
$884$	4.74555	+	3.04978i	0.159610	+	0.102575i
$885$	64.7626	+	12.9942i	2.17697	+	0.436794i
$886$	−2.12201	+	14.7589i	−0.0712903	+	0.495835i
$887$	2.45610	+	11.2905i	0.0824678	+	0.379098i	0.999820	−	0.0189786i	$-0.00604143\pi$
$887$	2.45610	+	11.2905i	0.0824678	+	0.379098i	−0.917352	+	0.398077i	$0.869678\pi$
$888$	−2.01607	+	28.1884i	−0.0676550	+	0.945940i
$889$	9.16803	+	20.0752i	0.307486	+	0.673300i
$890$	−10.9023	−	19.2197i	−0.365444	−	0.644247i
$891$	−1.89828	+	6.46494i	−0.0635947	+	0.216584i
$892$	8.62865	−	0.617133i	0.288909	−	0.0206632i
$893$	−12.2666	−	6.69805i	−0.410485	−	0.224142i
$894$	−28.8797	+	63.2378i	−0.965882	+	2.11499i
$895$	−18.0725	−	15.1548i	−0.604098	−	0.506570i
$896$		−	2.02950i		−	0.0678009i
$897$	−10.3712	+	68.7208i	−0.346283	+	2.29452i
$898$	−2.29181	+	2.29181i	−0.0764787	+	0.0764787i
$899$	45.7613	−	6.57949i	1.52623	−	0.219438i
$900$	25.8071	+	15.4284i	0.860237	+	0.514281i
$901$	5.29277	−	1.55410i	0.176328	−	0.0517745i
$902$	0.373764	+	5.22591i	0.0124450	+	0.174004i
$903$	3.82690	−	2.08964i	0.127351	−	0.0695390i
$904$	−6.81134	+	4.37738i	−0.226542	+	0.145590i
$905$	−25.9645	−	11.3534i	−0.863088	−	0.377398i
$906$	27.1164	+	31.2940i	0.900883	+	1.03967i
$907$	46.6617	−	10.1506i	1.54938	−	0.337046i	0.645135	−	0.764068i	$-0.276801\pi$
$907$	46.6617	−	10.1506i	1.54938	−	0.337046i	0.904241	+	0.427022i	$0.140437\pi$
$908$	−0.598047	+	0.447692i	−0.0198469	+	0.0148572i
$909$	−99.0243	−	14.2375i	−3.28443	−	0.472229i
$910$	17.7460	+	12.8417i	0.588275	+	0.425697i
$911$	25.8606	−	22.4083i	0.856799	−	0.742420i	−0.111087	−	0.993811i	$-0.535433\pi$
$911$	25.8606	−	22.4083i	0.856799	−	0.742420i	0.967886	+	0.251391i	$0.0808878\pi$
$912$	−13.5677	−	5.06048i	−0.449271	−	0.167569i
$913$	1.24178	−	5.70839i	0.0410971	−	0.188920i
$914$	−5.23451	−	1.53699i	−0.173142	−	0.0508391i
$915$	−56.5542	−	54.7524i	−1.86962	−	1.81006i
$916$	−5.07044	−	17.2683i	−0.167532	−	0.570562i
$917$	−0.254407	−	0.682093i	−0.00840127	−	0.0225247i
$918$	−6.33622	+	8.46420i	−0.209127	+	0.279360i
$919$	−20.4703			−0.675254			−0.337627	−	0.941280i	$-0.609624\pi$
$919$	−20.4703			−0.675254			−0.337627	+	0.941280i	$0.609624\pi$
$920$	5.22573	+	9.36439i	0.172287	+	0.308735i
$921$	−18.1015			−0.596464
$922$	−3.08735	+	4.12422i	−0.101677	+	0.135824i
$923$	19.5918	+	52.5277i	0.644873	+	1.72897i
$924$	1.26805	+	4.31858i	0.0417158	+	0.142071i
$925$	−47.0296	−	1.83642i	−1.54632	−	0.0603811i
$926$	−28.6473	−	8.41160i	−0.941408	−	0.276422i
$927$	15.9180	−	73.1741i	0.522817	−	2.40335i
$928$	−7.48225	−	2.79073i	−0.245617	−	0.0916104i
$929$	−40.4724	+	35.0695i	−1.32785	+	1.15059i	−0.351075	+	0.936347i	$0.614184\pi$
$929$	−40.4724	+	35.0695i	−1.32785	+	1.15059i	−0.976780	+	0.214245i	$0.931271\pi$
$930$	−6.15294	−	38.3747i	−0.201763	−	1.25836i
$931$	13.7550	+	1.97767i	0.450803	+	0.0648156i
$932$	5.30451	−	3.97091i	0.173755	−	0.130071i
$933$	−3.46046	+	0.752778i	−0.113291	+	0.0246448i
$934$	−23.4424	−	27.0540i	−0.767058	−	0.885232i
$935$	−1.79750	+	0.703778i	−0.0587845	+	0.0230160i
$936$	−24.4186	+	15.6929i	−0.798147	+	0.512938i
$937$	2.77774	−	1.51676i	0.0907448	−	0.0495504i	−0.433236	−	0.901281i	$-0.642628\pi$
$937$	2.77774	−	1.51676i	0.0907448	−	0.0495504i	0.523981	+	0.851730i	$0.324446\pi$
$938$	−1.20120	−	16.7949i	−0.0392205	−	0.548374i
$939$	−17.7979	+	5.22594i	−0.580813	+	0.170542i
$940$	−3.01276	+	5.73627i	−0.0982652	+	0.187096i
$941$	32.0886	−	4.61364i	1.04606	−	0.150400i	0.402205	−	0.915550i	$-0.368244\pi$
$941$	32.0886	−	4.61364i	1.04606	−	0.150400i	0.643853	+	0.765149i	$0.277335\pi$
$942$	−28.0318	+	28.0318i	−0.913327	+	0.913327i
$943$	−33.7017	+	4.60546i	−1.09748	+	0.149974i
$944$			9.83929i			0.320242i
$945$	−26.3808	+	31.4598i	−0.858169	+	1.02339i
$946$	−0.219594	+	0.480845i	−0.00713963	+	0.0156336i
$947$	28.9678	+	15.8176i	0.941328	+	0.514004i	0.875176	−	0.483805i	$-0.160746\pi$
$947$	28.9678	+	15.8176i	0.941328	+	0.514004i	0.0661527	+	0.997810i	$0.478928\pi$
$948$	8.57873	−	0.613563i	0.278624	−	0.0199276i
$949$	16.7313	−	56.9815i	0.543120	−	1.84970i
$950$	7.69208	−	22.8568i	0.249564	−	0.741574i
$951$	−1.12866	−	2.47141i	−0.0365992	−	0.0801410i
$952$	−0.169203	+	2.36577i	−0.00548391	+	0.0766750i
$953$	−0.144916	−	0.666170i	−0.00469430	−	0.0215794i	0.974740	−	0.223342i	$-0.0716967\pi$
$953$	−0.144916	−	0.666170i	−0.00469430	−	0.0215794i	−0.979434	+	0.201763i	$0.935333\pi$
$954$	−4.03948	+	28.0952i	−0.130783	+	0.909615i
$955$	25.6327	+	38.5006i	0.829455	+	1.24585i
$956$	−17.1719	−	11.0357i	−0.555378	−	0.356920i
$957$	17.6652	+	1.26344i	0.571033	+	0.0408411i
$958$	−13.0641	+	35.0261i	−0.422081	+	1.13164i
$959$	−14.2397	−	22.1574i	−0.459824	−	0.715500i
$960$	−2.24392	+	6.32710i	−0.0724222	+	0.204206i
$961$	−1.64762	+	1.90145i	−0.0531489	+	0.0613371i
$962$	21.7752	−	39.8783i	0.702061	−	1.28573i
$963$	−5.50318	+	2.05258i	−0.177337	+	0.0661434i
$964$	−1.78019	−	12.3815i	−0.0573362	−	0.398782i
$965$	−32.7131	−	1.80806i	−1.05307	−	0.0582035i
$966$	−27.4496	+	10.0202i	−0.883175	+	0.322396i
$967$	−35.3957	−	35.3957i	−1.13825	−	1.13825i	−0.988764	−	0.149486i	$-0.952238\pi$
$967$	−35.3957	−	35.3957i	−1.13825	−	1.13825i	−0.149486	−	0.988764i	$-0.547762\pi$
$968$	8.36912	+	6.26505i	0.268994	+	0.201366i
$969$	15.3938	+	7.03011i	0.494520	+	0.225840i
$970$	5.43877	+	3.37217i	0.174628	+	0.108274i
$971$	9.45202	+	8.19022i	0.303330	+	0.262837i	0.793204	−	0.608957i	$-0.208412\pi$
$971$	9.45202	+	8.19022i	0.303330	+	0.262837i	−0.489874	+	0.871793i	$0.662957\pi$
$972$	−0.116486	−	0.213328i	−0.00373629	−	0.00684250i
$973$	11.3072	+	2.45974i	0.362494	+	0.0788557i
$974$	3.87632	−	1.77026i	0.124205	−	0.0567227i
$975$	−41.1260	−	59.6555i	−1.31709	−	1.91051i
$976$	6.33929	−	9.86413i	0.202916	−	0.315743i
$977$	−1.24584	−	1.66425i	−0.0398579	−	0.0532440i	0.780169	−	0.625568i	$-0.215133\pi$
$977$	−1.24584	−	1.66425i	−0.0398579	−	0.0532440i	−0.820027	+	0.572324i	$0.806042\pi$
$978$	−5.32868	−	7.11828i	−0.170392	−	0.227617i
$979$	−3.94650	+	6.14088i	−0.126131	+	0.196263i
$980$	0.813517	−	6.39081i	0.0259868	−	0.204147i
$981$	−78.5590	+	35.8767i	−2.50820	+	1.14545i
$982$	9.60097	+	2.08856i	0.306379	+	0.0666487i
$983$	−5.82544	−	10.6685i	−0.185803	−	0.340272i	0.768130	−	0.640294i	$-0.221188\pi$
$983$	−5.82544	−	10.6685i	−0.185803	−	0.340272i	−0.953932	+	0.300022i	$0.903006\pi$
$984$	−16.0927	−	13.9444i	−0.513017	−	0.444532i
$985$	−7.17198	−	30.5777i	−0.228518	−	0.974285i
$986$	8.48931	+	3.87694i	0.270355	+	0.123467i
$987$	−14.1339	−	10.5805i	−0.449888	−	0.336782i
$988$	16.4626	+	16.4626i	0.523744	+	0.523744i
$989$	−3.20709	−	1.22178i	−0.101980	−	0.0388503i
$990$	0.548154	−	9.91770i	0.0174215	−	0.315205i
$991$	−0.951575	−	6.61835i	−0.0302278	−	0.210239i	0.969110	−	0.246629i	$-0.0793231\pi$
$991$	−0.951575	−	6.61835i	−0.0302278	−	0.210239i	−0.999338	+	0.0363906i	$0.988414\pi$
$992$	5.42428	−	2.02315i	0.172221	−	0.0642352i
$993$	41.9078	−	76.7484i	1.32990	−	2.43554i
$994$	−15.4363	+	17.8144i	−0.489608	+	0.565038i
$995$	−11.5277	−	24.1979i	−0.365453	−	0.767124i
$996$	12.8364	+	19.9739i	0.406738	+	0.632897i
$997$	−3.35023	+	8.98232i	−0.106103	+	0.284473i	−0.979142	−	0.203177i	$-0.934873\pi$
$997$	−3.35023	+	8.98232i	−0.106103	+	0.284473i	0.873039	+	0.487650i	$0.162146\pi$
$998$	−3.52893	−	0.252394i	−0.111706	−	0.00798939i
$999$	71.6425	+	46.0419i	2.26667	+	1.45670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.227.12	yes	240
5.3	odd	4	inner	230.2.l.a.43.1	✓	240
23.15	odd	22	inner	230.2.l.a.107.1	yes	240
115.38	even	44	inner	230.2.l.a.153.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.1	✓	240	5.3	odd	4	inner
230.2.l.a.107.1	yes	240	23.15	odd	22	inner
230.2.l.a.153.12	yes	240	115.38	even	44	inner
230.2.l.a.227.12	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599278 - 0.800541i) q^{2} +(1.04918 + 2.81295i) q^{3} +(-0.281733 - 0.959493i) q^{4} +(2.23578 - 0.0361909i) q^{5} +(2.88063 + 0.845830i) q^{6} +(0.431402 - 1.98312i) q^{7} +(-0.936950 - 0.349464i) q^{8} +(-4.54467 + 3.93798i) q^{9} +(1.31088 - 1.81152i) q^{10} +(-0.731174 - 0.105127i) q^{11} +(2.40342 - 1.79918i) q^{12} +(-4.71660 + 1.02603i) q^{13} +(-1.32904 - 1.53380i) q^{14} +(2.44753 + 6.25115i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(1.02571 - 0.560082i) q^{17} +(0.428996 + 5.99814i) q^{18} +(4.62791 - 1.35888i) q^{19} +(-0.664616 - 2.13501i) q^{20} +(6.03104 - 0.867133i) q^{21} +(-0.522335 + 0.522335i) q^{22} +(-3.60241 - 3.16585i) q^{23} -3.00224i q^{24} +(4.99738 - 0.161829i) q^{25} +(-2.00517 + 4.39071i) q^{26} +(-7.94049 - 4.33584i) q^{27} +(-2.02433 + 0.144783i) q^{28} +(-2.24985 + 7.66227i) q^{29} +(6.47105 + 1.78683i) q^{30} +(-2.40496 - 5.26613i) q^{31} +(-0.0713392 + 0.997452i) q^{32} +(-0.471413 - 2.16705i) q^{33} +(0.166319 - 1.15677i) q^{34} +(0.892747 - 4.44943i) q^{35} +(5.05885 + 3.25112i) q^{36} +(-9.38911 - 0.671522i) q^{37} +(1.68557 - 4.51918i) q^{38} +(-7.83472 - 12.1911i) q^{39} +(-2.10746 - 0.747414i) q^{40} +(4.64467 - 5.36024i) q^{41} +(2.92009 - 5.34775i) q^{42} +(0.670489 - 0.250080i) q^{43} +(0.105127 + 0.731174i) q^{44} +(-10.0183 + 8.96891i) q^{45} +(-4.69324 + 0.986658i) q^{46} +(-2.04894 - 2.04894i) q^{47} +(-2.40342 - 1.79918i) q^{48} +(2.62076 + 1.19686i) q^{49} +(2.86527 - 4.09759i) q^{50} +(2.65164 + 2.29766i) q^{51} +(2.31329 + 4.23648i) q^{52} +(4.61222 + 1.00333i) q^{53} +(-8.22958 + 3.75832i) q^{54} +(-1.63854 - 0.208578i) q^{55} +(-1.09723 + 1.70733i) q^{56} +(8.67795 + 11.5924i) q^{57} +(4.78568 + 6.39292i) q^{58} +(5.31952 - 8.27734i) q^{59} +(5.30839 - 4.10954i) q^{60} +(-10.6659 + 4.87095i) q^{61} +(-5.65700 - 1.23060i) q^{62} +(5.84892 + 10.7115i) q^{63} +(0.755750 + 0.654861i) q^{64} +(-10.5081 + 2.46468i) q^{65} +(-2.01732 - 0.921280i) q^{66} +(6.64172 + 4.97193i) q^{67} +(-0.826372 - 0.826372i) q^{68} +(5.12581 - 13.4550i) q^{69} +(-3.02695 - 3.38112i) q^{70} +(-1.65293 - 11.4964i) q^{71} +(5.63431 - 2.10149i) q^{72} +(-5.89636 + 10.7984i) q^{73} +(-6.16426 + 7.11394i) q^{74} +(5.69835 + 13.8876i) q^{75} +(-2.60767 - 4.05761i) q^{76} +(-0.523909 + 1.40466i) q^{77} +(-14.4546 - 1.03382i) q^{78} +(2.40997 + 1.54880i) q^{79} +(-1.86129 + 1.23920i) q^{80} +(1.29810 - 9.02851i) q^{81} +(-1.50764 - 6.93052i) q^{82} +(-0.564181 + 7.88828i) q^{83} +(-2.53115 - 5.54244i) q^{84} +(2.27300 - 1.28934i) q^{85} +(0.201610 - 0.686621i) q^{86} +(-23.9141 + 1.71037i) q^{87} +(0.648335 + 0.354018i) q^{88} +(4.10508 - 8.98888i) q^{89} +(1.17622 + 13.3950i) q^{90} +9.79622i q^{91} +(-2.02269 + 4.34841i) q^{92} +(12.2901 - 12.2901i) q^{93} +(-2.86814 + 0.412377i) q^{94} +(10.2978 - 3.20563i) q^{95} +(-2.88063 + 0.845830i) q^{96} +(0.204164 + 2.85459i) q^{97} +(2.52870 - 1.38077i) q^{98} +(3.73693 - 2.40158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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