LMFDB - Embedded newform 230.2.l.a.43.1

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			43.1
Character	$\chi$	$=$	230.43
Dual form			230.2.l.a.107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.800541 - 0.599278i) q^{2} +(-2.81295 + 1.04918i) q^{3} +(0.281733 + 0.959493i) q^{4} +(0.282361 + 2.21817i) q^{5} +(2.88063 + 0.845830i) q^{6} +(-1.98312 - 0.431402i) q^{7} +(0.349464 - 0.936950i) q^{8} +(4.54467 - 3.93798i) q^{9} +(1.10326 - 1.94495i) q^{10} +(-0.731174 - 0.105127i) q^{11} +(-1.79918 - 2.40342i) q^{12} +(-1.02603 - 4.71660i) q^{13} +(1.32904 + 1.53380i) q^{14} +(-3.12152 - 5.94335i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-0.560082 - 1.02571i) q^{17} +(-5.99814 + 0.428996i) q^{18} +(-4.62791 + 1.35888i) q^{19} +(-2.04877 + 0.895854i) q^{20} +(6.03104 - 0.867133i) q^{21} +(0.522335 + 0.522335i) q^{22} +(3.16585 - 3.60241i) q^{23} +3.00224i q^{24} +(-4.84054 + 1.25265i) q^{25} +(-2.00517 + 4.39071i) q^{26} +(-4.33584 + 7.94049i) q^{27} +(-0.144783 - 2.02433i) q^{28} +(2.24985 - 7.66227i) q^{29} +(-1.06281 + 6.62856i) q^{30} +(-2.40496 - 5.26613i) q^{31} +(0.997452 + 0.0713392i) q^{32} +(2.16705 - 0.471413i) q^{33} +(-0.166319 + 1.15677i) q^{34} +(0.396965 - 4.52071i) q^{35} +(5.05885 + 3.25112i) q^{36} +(-0.671522 + 9.38911i) q^{37} +(4.51918 + 1.68557i) q^{38} +(7.83472 + 12.1911i) q^{39} +(2.17699 + 0.510612i) q^{40} +(4.64467 - 5.36024i) q^{41} +(-5.34775 - 2.92009i) q^{42} +(0.250080 + 0.670489i) 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} +(1.79918 - 2.40342i) q^{48} +(-2.62076 - 1.19686i) q^{49} +(4.62574 + 1.89803i) q^{50} +(2.65164 + 2.29766i) q^{51} +(4.23648 - 2.31329i) q^{52} +(-1.00333 + 4.61222i) q^{53} +(8.22958 - 3.75832i) q^{54} +(0.0267339 - 1.65155i) q^{55} +(-1.09723 + 1.70733i) q^{56} +(11.5924 - 8.67795i) q^{57} +(-6.39292 + 4.78568i) q^{58} +(-5.31952 + 8.27734i) q^{59} +(4.82317 - 4.66951i) q^{60} +(-10.6659 + 4.87095i) q^{61} +(-1.23060 + 5.65700i) q^{62} +(-10.7115 + 5.84892i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(10.1725 - 3.60770i) q^{65} +(-2.01732 - 0.921280i) q^{66} +(4.97193 - 6.64172i) 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} +(-2.10149 - 5.63431i) q^{72} +(-10.7984 - 5.89636i) q^{73} +(6.16426 - 7.11394i) q^{74} +(12.3020 - 8.60223i) q^{75} +(-2.60767 - 4.05761i) q^{76} +(1.40466 + 0.523909i) q^{77} +(1.03382 - 14.4546i) q^{78} +(-2.40997 - 1.54880i) q^{79} +(-1.43677 - 1.71339i) q^{80} +(1.29810 - 9.02851i) q^{81} +(-6.93052 + 1.50764i) q^{82} +(-7.88828 - 0.564181i) q^{83} +(2.53115 + 5.54244i) q^{84} +(2.11706 - 1.53198i) q^{85} +(0.201610 - 0.686621i) q^{86} +(1.71037 + 23.9141i) q^{87} +(-0.354018 + 0.648335i) q^{88} +(-4.10508 + 8.98888i) q^{89} +(-2.64523 - 13.1838i) q^{90} +9.79622i q^{91} +(4.34841 + 2.02269i) q^{92} +(12.2901 + 12.2901i) q^{93} +(2.86814 - 0.412377i) q^{94} +(-4.32096 - 9.88180i) q^{95} +(-2.88063 + 0.845830i) q^{96} +(2.85459 - 0.204164i) q^{97} +(1.38077 + 2.52870i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.800541	−	0.599278i	−0.566068	−	0.423753i
$2$	−0.800541	−	0.599278i	−0.566068	−	0.423753i
$3$	−2.81295	+	1.04918i	−1.62406	+	0.605742i	−0.986369	−	0.164551i	$-0.947382\pi$
$3$	−2.81295	+	1.04918i	−1.62406	+	0.605742i	−0.637689	+	0.770294i	$0.720110\pi$
$4$	0.281733	+	0.959493i	0.140866	+	0.479746i
$5$	0.282361	+	2.21817i	0.126276	+	0.991995i
$5$	0.282361	+	2.21817i	0.126276	+	0.991995i
$6$	2.88063	+	0.845830i	1.17601	+	0.345308i
$7$	−1.98312	−	0.431402i	−0.749550	−	0.163055i	−0.178466	−	0.983946i	$-0.557113\pi$
$7$	−1.98312	−	0.431402i	−0.749550	−	0.163055i	−0.571084	+	0.820892i	$0.693477\pi$
$8$	0.349464	−	0.936950i	0.123554	−	0.331262i
$9$	4.54467	−	3.93798i	1.51489	−	1.31266i
$10$	1.10326	−	1.94495i	0.348880	−	0.615047i
$11$	−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	$0.580976\pi$
$12$	−1.79918	−	2.40342i	−0.519378	−	0.693807i
$13$	−1.02603	−	4.71660i	−0.284570	−	1.30815i	−0.868235	−	0.496154i	$-0.834745\pi$
$13$	−1.02603	−	4.71660i	−0.284570	−	1.30815i	0.583664	−	0.811995i	$-0.301618\pi$
$14$	1.32904	+	1.53380i	0.355201	+	0.409924i
$15$	−3.12152	−	5.94335i	−0.805973	−	1.53457i
$16$	−0.841254	+	0.540641i	−0.210313	+	0.135160i
$17$	−0.560082	−	1.02571i	−0.135840	−	0.248772i	0.800900	−	0.598798i	$-0.204355\pi$
$17$	−0.560082	−	1.02571i	−0.135840	−	0.248772i	−0.936740	+	0.350026i	$0.886173\pi$
$18$	−5.99814	+	0.428996i	−1.41378	+	0.101115i
$19$	−4.62791	+	1.35888i	−1.06172	+	0.311748i	−0.765542	−	0.643386i	$-0.777529\pi$
$19$	−4.62791	+	1.35888i	−1.06172	+	0.311748i	−0.296174	+	0.955134i	$0.595711\pi$
$20$	−2.04877	+	0.895854i	−0.458118	+	0.200319i
$21$	6.03104	−	0.867133i	1.31608	−	0.189224i
$22$	0.522335	+	0.522335i	0.111362	+	0.111362i
$23$	3.16585	−	3.60241i	0.660125	−	0.751155i
$23$	3.16585	−	3.60241i	0.660125	−	0.751155i
$24$			3.00224i			0.612830i
$25$	−4.84054	+	1.25265i	−0.968109	+	0.250530i
$26$	−2.00517	+	4.39071i	−0.393246	+	0.861089i
$27$	−4.33584	+	7.94049i	−0.834432	+	1.52815i
$28$	−0.144783	−	2.02433i	−0.0273614	−	0.382563i
$29$	2.24985	−	7.66227i	0.417786	−	1.42285i	−0.434925	−	0.900466i	$-0.643225\pi$
$29$	2.24985	−	7.66227i	0.417786	−	1.42285i	0.852712	−	0.522382i	$-0.174957\pi$
$30$	−1.06281	+	6.62856i	−0.194042	+	1.21020i
$31$	−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	$-0.310392\pi$
$32$	0.997452	+	0.0713392i	0.176326	+	0.0126111i
$33$	2.16705	−	0.471413i	0.377235	−	0.0820625i
$34$	−0.166319	+	1.15677i	−0.0285234	+	0.198385i
$35$	0.396965	−	4.52071i	0.0670993	−	0.764140i
$36$	5.05885	+	3.25112i	0.843141	+	0.541854i
$37$	−0.671522	+	9.38911i	−0.110398	+	1.54356i	0.576676	+	0.816973i	$0.304349\pi$
$37$	−0.671522	+	9.38911i	−0.110398	+	1.54356i	−0.687074	+	0.726587i	$0.741105\pi$
$38$	4.51918	+	1.68557i	0.733108	+	0.273435i
$39$	7.83472	+	12.1911i	1.25456	+	1.95213i
$40$	2.17699	+	0.510612i	0.344212	+	0.0807348i
$41$	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	$0.0404348\pi$
$42$	−5.34775	−	2.92009i	−0.825176	−	0.450580i
$43$	0.250080	+	0.670489i	0.0381368	+	0.102249i	0.954622	−	0.297819i	$-0.0962593\pi$
$43$	0.250080	+	0.670489i	0.0381368	+	0.102249i	−0.916486	+	0.400068i	$0.868987\pi$
$44$	−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	−0.840570	−	0.541702i	$-0.817780\pi$
$47$	−2.04894	+	2.04894i	−0.298868	+	0.298868i	0.541702	+	0.840570i	$0.317780\pi$
$48$	1.79918	−	2.40342i	0.259689	−	0.346904i
$49$	−2.62076	−	1.19686i	−0.374394	−	0.170980i
$50$	4.62574	+	1.89803i	0.654179	+	0.268422i
$51$	2.65164	+	2.29766i	0.371304	+	0.321736i
$52$	4.23648	−	2.31329i	0.587493	−	0.320796i
$53$	−1.00333	+	4.61222i	−0.137818	+	0.633537i	0.855469	+	0.517855i	$0.173269\pi$
$53$	−1.00333	+	4.61222i	−0.137818	+	0.633537i	−0.993286	+	0.115683i	$0.963094\pi$
$54$	8.22958	−	3.75832i	1.11990	−	0.511443i
$55$	0.0267339	−	1.65155i	0.00360480	−	0.222695i
$56$	−1.09723	+	1.70733i	−0.146624	+	0.228151i
$57$	11.5924	−	8.67795i	1.53545	−	1.14942i
$58$	−6.39292	+	4.78568i	−0.839432	+	0.628391i
$59$	−5.31952	+	8.27734i	−0.692543	+	1.07762i	0.299788	+	0.954006i	$0.403084\pi$
$59$	−5.31952	+	8.27734i	−0.692543	+	1.07762i	−0.992331	+	0.123612i	$0.960552\pi$
$60$	4.82317	−	4.66951i	0.622669	−	0.602831i
$61$	−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	$0.633895\pi$
$62$	−1.23060	+	5.65700i	−0.156287	+	0.718439i
$63$	−10.7115	+	5.84892i	−1.34952	+	0.736894i
$64$	−0.755750	−	0.654861i	−0.0944687	−	0.0818576i
$65$	10.1725	−	3.60770i	1.26174	−	0.447480i
$66$	−2.01732	−	0.921280i	−0.248315	−	0.113402i
$67$	4.97193	−	6.64172i	0.607418	−	0.811415i	−0.386413	−	0.922326i	$-0.626286\pi$
$67$	4.97193	−	6.64172i	0.607418	−	0.811415i	0.993830	+	0.110911i	$0.0353768\pi$
$68$	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	$-0.287492\pi$
$72$	−2.10149	−	5.63431i	−0.247663	−	0.664010i
$73$	−10.7984	−	5.89636i	−1.26386	−	0.690117i	−0.299340	−	0.954146i	$-0.596767\pi$
$73$	−10.7984	−	5.89636i	−1.26386	−	0.690117i	−0.964515	+	0.264029i	$0.914948\pi$
$74$	6.16426	−	7.11394i	0.716581	−	0.826979i
$75$	12.3020	−	8.60223i	1.42051	−	0.993300i
$76$	−2.60767	−	4.05761i	−0.299120	−	0.465440i
$77$	1.40466	+	0.523909i	0.160075	+	0.0597050i
$78$	1.03382	−	14.4546i	0.117057	−	1.63666i
$79$	−2.40997	−	1.54880i	−0.271143	−	0.174253i	0.398003	−	0.917384i	$-0.369703\pi$
$79$	−2.40997	−	1.54880i	−0.271143	−	0.174253i	−0.669146	+	0.743131i	$0.733340\pi$
$80$	−1.43677	−	1.71339i	−0.160636	−	0.191562i
$81$	1.29810	−	9.02851i	0.144234	−	1.00317i
$82$	−6.93052	+	1.50764i	−0.765348	+	0.166491i
$83$	−7.88828	−	0.564181i	−0.865851	−	0.0619269i	−0.368656	−	0.929566i	$-0.620182\pi$
$83$	−7.88828	−	0.564181i	−0.865851	−	0.0619269i	−0.497195	+	0.867639i	$0.665637\pi$
$84$	2.53115	+	5.54244i	0.276171	+	0.604730i
$85$	2.11706	−	1.53198i	0.229628	−	0.166166i
$86$	0.201610	−	0.686621i	0.0217402	−	0.0740403i
$87$	1.71037	+	23.9141i	0.183371	+	2.56386i
$88$	−0.354018	+	0.648335i	−0.0377384	+	0.0691127i
$89$	−4.10508	+	8.98888i	−0.435138	+	0.952819i	0.557327	+	0.830293i	$0.311827\pi$
$89$	−4.10508	+	8.98888i	−0.435138	+	0.952819i	−0.992465	+	0.122526i	$0.960900\pi$
$90$	−2.64523	−	13.1838i	−0.278832	−	1.38969i
$91$			9.79622i			1.02692i
$92$	4.34841	+	2.02269i	0.453354	+	0.210880i
$93$	12.2901	+	12.2901i	1.27443	+	1.27443i
$94$	2.86814	−	0.412377i	0.295826	−	0.0425334i
$95$	−4.32096	−	9.88180i	−0.443322	−	1.01385i
$96$	−2.88063	+	0.845830i	−0.294003	+	0.0863271i
$97$	2.85459	−	0.204164i	0.289839	−	0.0207297i	0.0743375	−	0.997233i	$-0.476316\pi$
$97$	2.85459	−	0.204164i	0.289839	−	0.0207297i	0.215502	+	0.976503i	$0.430861\pi$
$98$	1.38077	+	2.52870i	0.139479	+	0.255437i
$99$	−3.73693	+	2.40158i	−0.375576	+	0.241368i
$100$	−2.56565	−	4.29156i	−0.256565	−	0.429156i
$101$	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	$0.462380\pi$
$102$	−0.745811	−	3.42844i	−0.0738463	−	0.339466i
$103$	−7.46278	−	9.96911i	−0.735330	−	0.982286i	−0.999840	−	0.0179026i	$-0.994301\pi$
$103$	−7.46278	−	9.96911i	−0.735330	−	0.982286i	0.264510	−	0.964383i	$-0.414790\pi$
$104$	−4.77778	−	0.686941i	−0.468500	−	0.0673601i
$105$	3.62638	+	13.1330i	0.353899	+	1.28165i
$106$	3.56721	−	3.09100i	0.346478	−	0.300225i
$107$	0.341331	−	0.915143i	0.0329977	−	0.0884702i	−0.919406	−	0.393310i	$-0.871330\pi$
$107$	0.341331	−	0.915143i	0.0329977	−	0.0884702i	0.952404	+	0.304839i	$0.0986028\pi$
$108$	−8.84039	−	1.92311i	−0.850667	−	0.185051i
$109$	−13.7799	−	4.04616i	−1.31988	−	0.387551i	−0.455430	−	0.890272i	$-0.650514\pi$
$109$	−13.7799	−	4.04616i	−1.31988	−	0.387551i	−0.864449	+	0.502720i	$0.832333\pi$
$110$	−1.01114	+	1.30611i	−0.0964083	+	0.124533i
$111$	−7.96187	−	27.1156i	−0.755707	−	2.57370i
$112$	1.90154	−	0.709239i	0.179679	−	0.0670167i
$113$	6.48171	+	4.85215i	0.609748	+	0.456451i	0.858992	−	0.511989i	$-0.171091\pi$
$113$	6.48171	+	4.85215i	0.609748	+	0.456451i	−0.249244	+	0.968441i	$0.580182\pi$
$114$	−14.4807			−1.35624
$115$	8.88468	+	6.00521i	0.828500	+	0.559988i
$116$	7.98575			0.741459
$117$	−23.2369	−	17.3949i	−2.14825	−	1.60816i
$118$	9.21892	−	3.43848i	0.848671	−	0.316538i
$119$	0.668217	+	2.27574i	0.0612553	+	0.208616i
$120$	−6.65948	+	0.847718i	−0.607925	+	0.0773857i
$121$	−10.0309	−	2.94533i	−0.911896	−	0.267757i
$122$	11.4575	+	2.49244i	1.03732	+	0.225655i
$123$	−7.44140	+	19.9512i	−0.670968	+	1.79894i
$124$	4.37526	−	3.79118i	0.392910	−	0.340458i
$125$	−4.14537	−	10.3834i	−0.370773	−	0.928723i
$126$	12.0801	+	1.73686i	1.07618	+	0.154732i
$127$	6.51677	+	8.70539i	0.578270	+	0.772478i	0.990338	−	0.138675i	$-0.0442843\pi$
$127$	6.51677	+	8.70539i	0.578270	+	0.772478i	−0.412068	+	0.911153i	$0.635193\pi$
$128$	0.212565	+	0.977147i	0.0187883	+	0.0863684i
$129$	−1.40692	−	1.62368i	−0.123873	−	0.142957i
$130$	−10.3055	−	3.20804i	−0.903854	−	0.281364i
$131$	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	$0.313194\pi$
$132$	1.06285	+	1.94646i	0.0925090	+	0.169418i
$133$	9.76394	−	0.698331i	0.846641	−	0.0605530i
$134$	−7.96047	+	2.33740i	−0.687680	+	0.201921i
$135$	−18.8376	−	7.37553i	−1.62128	−	0.634784i
$136$	−1.15677	+	0.166319i	−0.0991923	+	0.0142617i
$137$	−9.17672	−	9.17672i	−0.784020	−	0.784020i	0.196486	−	0.980507i	$-0.437047\pi$
$137$	−9.17672	−	9.17672i	−0.784020	−	0.784020i	−0.980507	+	0.196486i	$0.937047\pi$
$138$	12.1667	−	7.69946i	1.03570	−	0.655421i
$139$		−	5.70174i		−	0.483615i	−0.970324	−	0.241808i	$-0.922260\pi$
$139$		−	5.70174i		−	0.483615i	0.970324	−	0.241808i	$-0.0777403\pi$
$140$	4.44943	−	0.892747i	0.376045	−	0.0754509i
$141$	3.61386	−	7.91326i	0.304342	−	0.666417i
$142$	−5.56627	+	10.1939i	−0.467111	+	0.855451i
$143$	0.254367	+	3.55652i	0.0212712	+	0.297411i
$144$	−1.69419	+	5.76988i	−0.141182	+	0.480823i
$145$	17.6315	+	2.82701i	1.46422	+	0.234770i
$146$	5.11099	+	11.1915i	0.422989	+	0.926216i
$147$	8.62778	+	0.617071i	0.711607	+	0.0508952i
$148$	−9.19797	+	2.00090i	−0.756069	+	0.164473i
$149$	3.29545	−	22.9204i	0.269974	−	1.87771i	−0.178536	−	0.983933i	$-0.557136\pi$
$149$	3.29545	−	22.9204i	0.269974	−	1.87771i	0.448511	−	0.893778i	$-0.351955\pi$
$150$	−15.0034	−	0.485851i	−1.22502	−	0.0396696i
$151$	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	$0.492157\pi$
$152$	−0.344090	+	4.81100i	−0.0279094	+	0.390224i
$153$	−6.58463	−	2.45594i	−0.532336	−	0.198551i
$154$	−0.810517	−	1.26119i	−0.0653133	−	0.101630i
$155$	11.0021	−	6.82156i	0.883710	−	0.547921i
$156$	−9.48995	+	10.9520i	−0.759804	+	0.876860i
$157$	11.5893	+	6.32822i	0.924925	+	0.505047i	0.869785	−	0.493431i	$-0.164258\pi$
$157$	11.5893	+	6.32822i	0.924925	+	0.505047i	0.0551403	+	0.998479i	$0.482439\pi$
$158$	1.00112	+	2.68412i	0.0796452	+	0.213537i
$159$	−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
$163$	1.77490	−	2.37099i	0.139021	−	0.185710i	−0.725627	−	0.688088i	$-0.758450\pi$
$163$	1.77490	−	2.37099i	0.139021	−	0.185710i	0.864648	+	0.502378i	$0.167541\pi$
$164$	6.45166	+	2.94638i	0.503790	+	0.230073i
$165$	1.65757	+	4.67378i	0.129041	+	0.363853i
$166$	5.97679	+	5.17892i	0.463889	+	0.401962i
$167$	3.16466	−	1.72803i	0.244889	−	0.133719i	−0.352118	−	0.935956i	$-0.614538\pi$
$167$	3.16466	−	1.72803i	0.244889	−	0.133719i	0.597007	+	0.802236i	$0.296357\pi$
$168$	1.29517	−	5.95382i	0.0999248	−	0.459347i
$169$	−9.36834	+	4.27838i	−0.720641	+	0.329106i
$170$	−2.61288	−	0.0422951i	−0.200398	−	0.00324388i
$171$	−15.6811	+	24.4003i	−1.19916	+	1.86594i
$172$	−0.572874	+	0.428848i	−0.0436812	+	0.0326994i
$173$	3.68450	−	2.75819i	0.280128	−	0.209701i	−0.449970	−	0.893044i	$-0.648565\pi$
$173$	3.68450	−	2.75819i	0.280128	−	0.209701i	0.730098	+	0.683343i	$0.239474\pi$
$174$	12.9620	−	20.1692i	0.982643	−	1.52902i
$175$	10.1398	−	0.395940i	0.766496	−	0.0299302i
$176$	0.671938	−	0.306864i	0.0506493	−	0.0231307i
$177$	6.27917	−	28.8649i	0.471971	−	2.16962i
$178$	8.67312	−	4.73588i	0.650078	−	0.354969i
$179$	7.97153	+	6.90737i	0.595820	+	0.516281i	0.899746	−	0.436415i	$-0.143752\pi$
$179$	7.97153	+	6.90737i	0.595820	+	0.516281i	−0.303925	+	0.952696i	$0.598297\pi$
$180$	−5.78312	+	12.1394i	−0.431048	+	0.904815i
$181$	−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	$0.792469\pi$
$182$	5.87066	−	7.84228i	0.435162	−	0.581309i
$183$	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
$187$	0.301687	+	0.808855i	0.0220616	+	0.0591493i
$188$	−2.54319	−	1.38869i	−0.185481	−	0.101281i
$189$	12.0240	−	13.8765i	0.874620	−	1.00937i
$190$	−2.46283	+	10.5002i	−0.178672	+	0.761768i
$191$	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	$0.549026\pi$
$192$	2.81295	+	1.04918i	0.203007	+	0.0757178i
$193$	1.04527	−	14.6147i	0.0752399	−	1.05199i	−0.809870	−	0.586609i	$-0.800462\pi$
$193$	1.04527	−	14.6147i	0.0752399	−	1.05199i	0.885110	−	0.465382i	$-0.154083\pi$
$194$	−2.40757	−	1.54725i	−0.172853	−	0.111086i
$195$	−24.8296	+	20.8210i	−1.77809	+	1.49102i
$196$	0.410026	−	2.85179i	0.0292876	−	0.203699i
$197$	−13.7249	+	2.98566i	−0.977856	+	0.212720i	−0.672971	−	0.739669i	$-0.734982\pi$
$197$	−13.7249	+	2.98566i	−0.977856	+	0.212720i	−0.304886	+	0.952389i	$0.598618\pi$
$198$	4.43078	+	0.316896i	0.314882	+	0.0225208i
$199$	4.97953	+	10.9036i	0.352989	+	0.772939i	0.999946	+	0.0104118i	$0.00331423\pi$
$199$	4.97953	+	10.9036i	0.352989	+	0.772939i	−0.646957	+	0.762527i	$0.723958\pi$
$200$	−0.517926	+	4.97310i	−0.0366229	+	0.351651i
$201$	−7.01746	+	23.8993i	−0.494973	+	1.68572i
$202$	−1.18683	−	16.5940i	−0.0835050	−	1.16755i
$203$	−7.76724	+	14.2246i	−0.545153	+	0.998374i
$204$	−1.45753	+	3.19155i	−0.102048	+	0.223453i
$205$	13.2014	+	8.78914i	0.922024	+	0.613860i
$206$			12.4530i			0.867639i
$207$	0.201512	−	28.8389i	0.0140061	−	2.00444i
$208$	3.41314	+	3.41314i	0.236659	+	0.236659i
$209$	3.52666	−	0.507058i	0.243944	−	0.0350739i
$210$	4.96726	−	12.6867i	0.342774	−	0.875468i
$211$	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	$0.220181\pi$
$212$	−4.70806	+	0.336727i	−0.323351	+	0.0231265i
$213$	16.7113	+	30.6045i	1.14504	+	2.09698i
$214$	−0.821674	+	0.528058i	−0.0561685	+	0.0360973i
$215$	−1.41665	+	0.744039i	−0.0966144	+	0.0507430i
$216$	5.92462	+	6.83738i	0.403119	+	0.465225i
$217$	2.49751	+	11.4809i	0.169542	+	0.779373i
$218$	8.60664	+	11.4971i	0.582915	+	0.778684i
$219$	36.5616	+	5.25677i	2.47061	+	0.355220i
$220$	1.59218	−	0.439645i	0.107345	−	0.0296408i
$221$	−4.26322	+	3.69410i	−0.286775	+	0.248492i
$222$	−9.87599	+	26.4786i	−0.662833	+	1.77713i
$223$	−8.45300	−	1.83884i	−0.566055	−	0.123138i	−0.0795739	−	0.996829i	$-0.525356\pi$
$223$	−8.45300	−	1.83884i	−0.566055	−	0.123138i	−0.486481	+	0.873691i	$0.661720\pi$
$224$	−1.94729	−	0.571777i	−0.130109	−	0.0382035i
$225$	−17.0658	+	24.7549i	−1.13772	+	1.65032i
$226$	−2.28109	−	7.76869i	−0.151736	−	0.516765i
$227$	−0.699951	+	0.261068i	−0.0464574	+	0.0173277i	−0.372585	−	0.927998i	$-0.621529\pi$
$227$	−0.699951	+	0.261068i	−0.0464574	+	0.0173277i	0.326128	+	0.945326i	$0.394256\pi$
$228$	11.5924	+	8.67795i	0.767725	+	0.574712i
$229$	−17.9974			−1.18930			−0.594649	−	0.803985i	$-0.702709\pi$
$229$	−17.9974			−1.18930			−0.594649	+	0.803985i	$0.702709\pi$
$230$	−3.51376	−	10.1318i	−0.231691	−	0.668071i
$231$	−4.50090			−0.296137
$232$	−6.39292	−	4.78568i	−0.419716	−	0.314196i
$233$	−6.20837	+	2.31560i	−0.406724	+	0.151700i	−0.544495	−	0.838764i	$-0.683279\pi$
$233$	−6.20837	+	2.31560i	−0.406724	+	0.151700i	0.137771	+	0.990464i	$0.456006\pi$
$234$	8.17769	+	27.8507i	0.534592	+	1.82065i
$235$	−5.12343	−	3.96635i	−0.334216	−	0.258736i
$236$	−9.44073	−	2.77205i	−0.614539	−	0.180445i
$237$	8.40409	+	1.82820i	0.545905	+	0.118754i
$238$	0.828863	−	2.22227i	0.0537272	−	0.144048i
$239$	−15.4266	+	13.3672i	−0.997861	+	0.864651i	−0.990801	−	0.135324i	$-0.956793\pi$
$239$	−15.4266	+	13.3672i	−0.997861	+	0.864651i	−0.00705924	+	0.999975i	$0.502247\pi$
$240$	5.83921	+	3.31225i	0.376919	+	0.213805i
$241$	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	$0.413463\pi$
$242$	6.26505	+	8.36912i	0.402733	+	0.537988i
$243$	0.0516660	+	0.237505i	0.00331438	+	0.0152359i
$244$	−7.67858	−	8.86155i	−0.491571	−	0.567303i
$245$	1.91484	−	6.15123i	0.122334	−	0.392988i
$246$	17.9134	−	11.5123i	1.14212	−	0.733995i
$247$	11.1577	+	20.4338i	0.709946	+	1.30017i
$248$	−5.77455	+	0.413004i	−0.366684	+	0.0262258i
$249$	22.7813	−	6.68918i	1.44370	−	0.423910i
$250$	−2.90402	+	10.7966i	−0.183667	+	0.682837i
$251$	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
$253$	−2.69350	+	2.30118i	−0.169339	+	0.144674i
$254$		−	10.8744i		−	0.682319i
$255$	−4.34787	+	6.53055i	−0.272274	+	0.408959i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−4.09030	+	7.49083i	−0.255146	+	0.467265i	−0.973585	−	0.228325i	$-0.926675\pi$
$257$	−4.09030	+	7.49083i	−0.255146	+	0.467265i	0.718439	+	0.695590i	$0.244857\pi$
$258$	0.153267	+	2.14296i	0.00954200	+	0.133415i
$259$	5.38219	−	18.3301i	0.334433	−	1.13897i
$260$	6.32749	+	8.74403i	0.392414	+	0.542282i
$261$	−19.9491	−	43.6824i	−1.23482	−	2.70387i
$262$	−0.357791	−	0.0255897i	−0.0221044	−	0.00158094i
$263$	8.17100	−	1.77749i	0.503845	−	0.109605i	0.0465433	−	0.998916i	$-0.485179\pi$
$263$	8.17100	−	1.77749i	0.503845	−	0.109605i	0.457302	+	0.889311i	$0.348816\pi$
$264$	0.315617	−	2.19516i	0.0194249	−	0.135103i
$265$	−10.5140	−	0.923236i	−0.645869	−	0.0567139i
$266$	−8.23493	−	5.29227i	−0.504916	−	0.324490i
$267$	2.11648	−	29.5922i	0.129526	−	1.81101i
$268$	7.77344	+	2.89934i	0.474838	+	0.177106i
$269$	6.96348	+	10.8354i	0.424571	+	0.660645i	0.985974	−	0.166897i	$-0.0533748\pi$
$269$	6.96348	+	10.8354i	0.424571	+	0.660645i	−0.561404	+	0.827542i	$0.689738\pi$
$270$	10.6603	+	17.1934i	0.648766	+	1.04636i
$271$	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	$0.143451\pi$
$272$	1.02571	+	0.560082i	0.0621931	+	0.0339600i
$273$	−10.2780	−	27.5563i	−0.622051	−	1.66778i
$274$	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	−0.882122	−	0.471020i	$-0.843886\pi$
$277$	−6.84211	+	6.84211i	−0.411102	+	0.411102i	0.471020	+	0.882122i	$0.343886\pi$
$278$	−3.41693	+	4.56448i	−0.204934	+	0.273759i
$279$	−31.6677	−	14.4621i	−1.89589	−	0.865826i
$280$	−4.09695	−	1.95176i	−0.244840	−	0.116640i
$281$	−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	$0.828518\pi$
$282$	−7.63529	+	4.16918i	−0.454675	+	0.248271i
$283$	1.11411	−	5.12147i	0.0662268	−	0.304440i	−0.932104	−	0.362190i	$-0.882029\pi$
$283$	1.11411	−	5.12147i	0.0662268	−	0.304440i	0.998331	+	0.0577504i	$0.0183927\pi$
$284$	10.5650	−	4.82487i	0.626917	−	0.286303i
$285$	22.5224	+	23.2636i	1.33411	+	1.37801i
$286$	1.92771	−	2.99957i	0.113988	−	0.177369i
$287$	−11.5234	+	8.62628i	−0.680203	+	0.509193i
$288$	4.81403	−	3.60373i	0.283669	−	0.212352i
$289$	8.45250	−	13.1523i	0.497206	−	0.773667i
$290$	−12.4206	−	12.8293i	−0.729361	−	0.753362i
$291$	−7.81561	+	3.56927i	−0.458159	+	0.209234i
$292$	2.61526	−	12.0222i	0.153047	−	0.703544i
$293$	19.4119	−	10.5997i	1.13406	−	0.619242i	0.201222	−	0.979546i	$-0.435509\pi$
$293$	19.4119	−	10.5997i	1.13406	−	0.619242i	0.932835	+	0.360304i	$0.117327\pi$
$294$	−6.53710	−	5.66443i	−0.381251	−	0.330356i
$295$	−19.8626	−	9.46240i	−1.15644	−	0.550922i
$296$	8.56245	+	3.91034i	0.497682	+	0.227284i
$297$	4.00501	−	5.35007i	0.232394	−	0.310442i
$298$	−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
$302$	−4.81993	−	12.9227i	−0.277356	−	0.743619i
$303$	−43.8371	−	23.9369i	−2.51837	−	1.37514i
$304$	3.15858	−	3.64520i	0.181157	−	0.209067i
$305$	−13.8162	−	22.2834i	−0.791115	−	1.27594i
$306$	3.79948	+	5.91211i	0.217202	+	0.337973i
$307$	5.64917	+	2.10703i	0.322415	+	0.120255i	0.505460	−	0.862850i	$-0.331323\pi$
$307$	5.64917	+	2.10703i	0.322415	+	0.120255i	−0.183045	+	0.983105i	$0.558595\pi$
$308$	−0.106950	+	1.49536i	−0.00609405	+	0.0852060i
$309$	31.4518	+	20.2128i	1.78923	+	1.14987i
$310$	−12.8956	−	1.13237i	−0.732423	−	0.0643143i
$311$	−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	$0.0561021\pi$
$312$	14.1604	−	3.08040i	0.801673	−	0.174393i
$313$	−6.16273	−	0.440767i	−0.348338	−	0.0249136i	−0.103926	−	0.994585i	$-0.533140\pi$
$313$	−6.16273	−	0.440767i	−0.348338	−	0.0249136i	−0.244412	+	0.969671i	$0.578595\pi$
$314$	−5.48533	−	12.0112i	−0.309555	−	0.677831i
$315$	−15.9984	−	22.1084i	−0.901408	−	1.24567i
$316$	0.807091	−	2.74870i	0.0454024	−	0.154626i
$317$	0.0645597	+	0.902663i	0.00362604	+	0.0506986i	0.998943	−	0.0459668i	$-0.0146369\pi$
$317$	0.0645597	+	0.902663i	0.00362604	+	0.0506986i	−0.995317	+	0.0966654i	$0.969182\pi$
$318$	−6.79137	+	12.4375i	−0.380841	+	0.697458i
$319$	−2.45054	+	5.36593i	−0.137204	+	0.300435i
$320$	1.23920	−	1.86129i	0.0692732	−	0.104049i
$321$			2.93237i			0.163669i
$322$	9.73292	+	0.0680091i	0.542394	+	0.00379000i
$323$	3.98583	+	3.98583i	0.221778	+	0.221778i
$324$	9.02851	−	1.29810i	0.501584	−	0.0721168i
$325$	10.8748	+	21.5456i	0.603226	+	1.19514i
$326$	−2.84176	+	0.834416i	−0.157390	+	0.0462140i
$327$	43.0074	−	3.07595i	2.37832	−	0.170101i
$328$	−3.39913	−	6.22503i	−0.187685	−	0.343720i
$329$	4.94721	−	3.17938i	0.272748	−	0.175285i
$330$	1.47394	−	4.73490i	0.0811378	−	0.260647i
$331$	−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	$-0.522688\pi$
$332$	−1.68106	−	7.72770i	−0.0922600	−	0.424112i
$333$	33.9223	+	45.3149i	1.85893	+	2.48324i
$334$	−3.56901	−	0.513146i	−0.195288	−	0.0280781i
$335$	16.1363	+	9.15321i	0.881622	+	0.500093i
$336$	−4.60483	+	3.99011i	−0.251214	+	0.217678i
$337$	0.998243	−	2.67639i	0.0543778	−	0.145792i	−0.906921	−	0.421301i	$-0.861574\pi$
$337$	0.998243	−	2.67639i	0.0543778	−	0.145792i	0.961299	+	0.275509i	$0.0888463\pi$
$338$	10.0637	+	2.18922i	0.547392	+	0.119078i
$339$	−23.3235	−	6.84839i	−1.26676	−	0.371954i
$340$	2.06637	+	1.59970i	0.112065	+	0.0867557i
$341$	1.20483	+	4.10328i	0.0652453	+	0.222205i
$342$	27.1759	−	10.1361i	1.46951	−	0.548097i
$343$	16.0539	+	12.0178i	0.866827	+	0.648899i
$344$	0.715609			0.0385830
$345$	−31.2927	−	7.57076i	−1.68474	−	0.407596i
$346$	−4.60252			−0.247433
$347$	−19.9324	−	14.9212i	−1.07003	−	0.801012i	−0.0892235	−	0.996012i	$-0.528439\pi$
$347$	−19.9324	−	14.9212i	−1.07003	−	0.801012i	−0.980803	+	0.195000i	$0.937529\pi$
$348$	−22.4635	+	8.37846i	−1.20417	+	0.449133i
$349$	2.59101	+	8.82418i	0.138694	+	0.472347i	0.999319	−	0.0368909i	$-0.0117454\pi$
$349$	2.59101	+	8.82418i	0.138694	+	0.472347i	−0.860626	+	0.509238i	$0.829927\pi$
$350$	−8.35460	−	5.75958i	−0.446572	−	0.307863i
$351$	41.9008	+	12.3032i	2.23650	+	0.656696i
$352$	−0.721811	−	0.157020i	−0.0384727	−	0.00836922i
$353$	−5.35144	+	14.3478i	−0.284829	+	0.763655i	0.713204	+	0.700957i	$0.247243\pi$
$353$	−5.35144	+	14.3478i	−0.284829	+	0.763655i	−0.998033	+	0.0626983i	$0.980029\pi$
$354$	−22.3248	+	19.3446i	−1.18655	+	1.02815i
$355$	25.0341	−	6.91260i	1.32867	−	0.366883i
$356$	−9.78130	−	1.40634i	−0.518408	−	0.0745358i
$357$	−4.26731	−	5.70046i	−0.225850	−	0.301700i
$358$	−2.24211	−	10.3068i	−0.118499	−	0.544731i
$359$	−4.53251	−	5.23080i	−0.239217	−	0.276071i	0.623428	−	0.781880i	$-0.285739\pi$
$359$	−4.53251	−	5.23080i	−0.239217	−	0.276071i	−0.862645	+	0.505810i	$0.831194\pi$
$360$	11.9045	−	6.25237i	0.627421	−	0.329529i
$361$	3.58722	−	2.30536i	0.188801	−	0.121335i
$362$	6.07363	+	11.1230i	0.319223	+	0.584613i
$363$	31.3065	−	2.23908i	1.64316	−	0.117521i
$364$	−9.39941	+	2.75991i	−0.492663	+	0.144659i
$365$	10.0301	−	25.6175i	0.524998	−	1.34088i
$366$	−34.8445	+	5.00989i	−1.82135	+	0.261871i
$367$	−12.7027	−	12.7027i	−0.663076	−	0.663076i	0.293028	−	0.956104i	$-0.405337\pi$
$367$	−12.7027	−	12.7027i	−0.663076	−	0.663076i	−0.956104	+	0.293028i	$0.905337\pi$
$368$	−0.715670	+	4.74213i	−0.0373069	+	0.247201i
$369$		−	42.6511i		−	2.22033i
$370$	17.5205	+	11.6647i	0.910846	+	0.606418i
$371$	3.97944	−	8.71376i	0.206602	−	0.452396i
$372$	−8.32977	+	15.2548i	−0.431878	+	0.790926i
$373$	2.09644	+	29.3121i	0.108550	+	1.51772i	0.701607	+	0.712564i	$0.252466\pi$
$373$	2.09644	+	29.3121i	0.108550	+	1.51772i	−0.593058	+	0.805160i	$0.702079\pi$
$374$	0.243216	−	0.828316i	0.0125764	−	0.0428312i
$375$	22.5548	+	24.8589i	1.16472	+	1.28371i
$376$	1.20372	+	2.63578i	0.0620772	+	0.135930i
$377$	−38.4483	−	2.74988i	−1.98019	−	0.141626i
$378$	−17.9416	+	3.90296i	−0.922816	+	0.200746i
$379$	−4.58565	+	31.8939i	−0.235549	+	1.63828i	0.437883	+	0.899032i	$0.355728\pi$
$379$	−4.58565	+	31.8939i	−0.235549	+	1.63828i	−0.673433	+	0.739249i	$0.735181\pi$
$380$	8.26416	−	6.92996i	0.423942	−	0.355499i
$381$	−27.4648	−	17.6506i	−1.40707	−	0.904267i
$382$	1.47565	−	20.6322i	0.0755007	−	1.05564i
$383$	3.14754	+	1.17397i	0.160832	+	0.0599871i	0.428591	−	0.903499i	$-0.359010\pi$
$383$	3.14754	+	1.17397i	0.160832	+	0.0599871i	−0.267759	+	0.963486i	$0.586283\pi$
$384$	−1.62314	−	2.52565i	−0.0828303	−	0.128886i
$385$	−0.765499	+	3.26369i	−0.0390134	+	0.166333i
$386$	−9.59506	+	11.0733i	−0.488376	+	0.563616i
$387$	3.77690	+	2.06235i	0.191991	+	0.104835i
$388$	1.00012	+	2.68144i	0.0507736	+	0.136129i
$389$	−0.799951	−	5.56378i	−0.0405591	−	0.282095i	−1.00000		0.000184902i	$-0.999941\pi$
$389$	−0.799951	−	5.56378i	−0.0405591	−	0.282095i	0.959441	−	0.281910i	$-0.0909679\pi$
$390$	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
$393$	−0.645374	+	0.862119i	−0.0325548	+	0.0434881i
$394$	12.7766	+	5.83486i	0.643674	+	0.293956i
$395$	2.75501	−	5.78305i	0.138619	−	0.290977i
$396$	−3.35712	−	2.90896i	−0.168701	−	0.146181i
$397$	−16.3776	+	8.94287i	−0.821970	+	0.448830i	−0.834444	−	0.551092i	$-0.814211\pi$
$397$	−16.3776	+	8.94287i	−0.821970	+	0.448830i	0.0124738	+	0.999922i	$0.496029\pi$
$398$	2.54799	−	11.7129i	0.127719	−	0.587116i
$399$	−26.7328	+	12.2085i	−1.33831	+	0.611188i
$400$	3.39489	−	3.67079i	0.169745	−	0.183540i
$401$	−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	$0.283850\pi$
$402$	19.9401	−	14.9269i	0.994520	−	0.744488i
$403$	−22.3707	+	16.7465i	−1.11436	+	0.834201i
$404$	−8.99433	+	13.9955i	−0.447485	+	0.696300i
$405$	20.3933	+	0.330110i	1.01335	+	0.0164033i
$406$	14.7425	−	6.73268i	0.731658	−	0.334137i
$407$	1.47805	−	6.79448i	0.0732641	−	0.336790i
$408$	3.07944	−	1.68150i	0.152455	−	0.0832468i
$409$	−2.45449	−	2.12683i	−0.121367	−	0.105165i	0.592063	−	0.805892i	$-0.298314\pi$
$409$	−2.45449	−	2.12683i	−0.121367	−	0.105165i	−0.713430	+	0.700727i	$0.752859\pi$
$410$	−5.30112	−	14.9474i	−0.261803	−	0.738198i
$411$	35.4417	+	16.1857i	1.74821	+	0.798380i
$412$	7.46278	−	9.96911i	0.367665	−	0.491143i
$413$	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
$417$	5.98213	+	16.0387i	0.292946	+	0.785419i
$418$	−3.12711	−	1.70753i	−0.152952	−	0.0835180i
$419$	1.12709	−	1.30073i	0.0550617	−	0.0635446i	−0.727551	−	0.686054i	$-0.759341\pi$
$419$	1.12709	−	1.30073i	0.0550617	−	0.0635446i	0.782612	+	0.622509i	$0.213887\pi$
$420$	−11.5794	+	7.17949i	−0.565016	+	0.350323i
$421$	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	$0.621351\pi$
$422$	−15.2227	−	5.67779i	−0.741031	−	0.276390i
$423$	−1.24307	+	17.3804i	−0.0604403	+	0.845065i
$424$	3.97079	+	2.55187i	0.192839	+	0.123930i
$425$	3.99596	+	4.26343i	0.193833	+	0.206807i
$426$	4.96249	−	34.5149i	0.240433	−	1.67225i
$427$	23.2531	−	5.05841i	1.12530	−	0.244794i
$428$	0.974237	+	0.0696788i	0.0470915	+	0.00336805i
$429$	−4.44694	−	9.73743i	−0.214700	−	0.470128i
$430$	1.57997	+	0.253330i	0.0761929	+	0.0122167i
$431$	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	$-0.00936554\pi$
$432$	−0.645416	−	9.02410i	−0.0310526	−	0.434172i
$433$	3.12697	−	5.72662i	0.150273	−	0.275204i	−0.791689	−	0.610924i	$-0.790798\pi$
$433$	3.12697	−	5.72662i	0.150273	−	0.275204i	0.941962	+	0.335720i	$0.108980\pi$
$434$	4.88088	−	10.6876i	0.234290	−	0.513023i
$435$	−52.5625	+	10.5463i	−2.52018	+	0.505657i
$436$		−	14.3617i		−	0.687800i
$437$	−9.75604	+	20.9737i	−0.466695	+	1.00331i
$438$	−26.1188	−	26.1188i	−1.24801	−	1.24801i
$439$	9.73180	−	1.39922i	0.464474	−	0.0667812i	0.0938945	−	0.995582i	$-0.470068\pi$
$439$	9.73180	−	1.39922i	0.464474	−	0.0667812i	0.370579	+	0.928801i	$0.379159\pi$
$440$	−1.53808	−	0.602206i	−0.0733250	−	0.0287090i
$441$	−16.6237	+	4.88116i	−0.791604	+	0.232436i
$442$	5.62667	−	0.402428i	0.267634	−	0.0191415i
$443$	−7.14592	−	13.0868i	−0.339513	−	0.621771i	0.651018	−	0.759062i	$-0.274342\pi$
$443$	−7.14592	−	13.0868i	−0.339513	−	0.621771i	−0.990531	+	0.137291i	$0.956160\pi$
$444$	23.7742	−	15.2787i	1.12827	−	0.725096i
$445$	−21.0980	−	6.56765i	−1.00014	−	0.311337i
$446$	5.66500	+	6.53776i	0.268245	+	0.309572i
$447$	14.7776	+	67.9314i	0.698955	+	3.21305i
$448$	1.21624	+	1.62470i	0.0574617	+	0.0767599i
$449$	3.20812	+	0.461258i	0.151400	+	0.0217681i	0.217598	−	0.976038i	$-0.430178\pi$
$449$	3.20812	+	0.461258i	0.151400	+	0.0217681i	−0.0661978	+	0.997807i	$0.521087\pi$
$450$	28.4969	−	9.59015i	1.34336	−	0.452084i
$451$	−3.95957	+	3.43098i	−0.186449	+	0.161559i
$452$	−2.82949	+	7.58616i	−0.133088	+	0.356823i
$453$	−40.4617	−	8.80189i	−1.90105	−	0.413549i
$454$	0.716792	+	0.210469i	0.0336407	+	0.00987780i
$455$	−21.7297	+	2.76608i	−1.01870	+	0.129676i
$456$	−4.07968	−	13.8941i	−0.191049	−	0.650652i
$457$	−5.11152	+	1.90650i	−0.239107	+	0.0891823i	−0.466161	−	0.884700i	$-0.654363\pi$
$457$	−5.11152	+	1.90650i	−0.239107	+	0.0891823i	0.227054	+	0.973882i	$0.427091\pi$
$458$	14.4076	+	10.7854i	0.673224	+	0.503969i
$459$	10.5731			0.493510
$460$	−3.25885	+	10.2166i	−0.151945	+	0.476354i
$461$	−5.15179			−0.239943			−0.119971	−	0.992777i	$-0.538280\pi$
$461$	−5.15179			−0.239943			−0.119971	+	0.992777i	$0.538280\pi$
$462$	3.60316	+	2.69729i	0.167634	+	0.125489i
$463$	27.9742	−	10.4338i	1.30007	−	0.484902i	0.398356	−	0.917231i	$-0.369581\pi$
$463$	27.9742	−	10.4338i	1.30007	−	0.484902i	0.901716	+	0.432329i	$0.142308\pi$
$464$	2.24985	+	7.66227i	0.104447	+	0.355712i
$465$	−23.7913	+	30.7319i	−1.10330	+	1.42516i
$466$	6.35775	+	1.86680i	0.294517	+	0.0864780i
$467$	−34.9794	−	7.60931i	−1.61865	−	0.352117i	−0.690216	−	0.723603i	$-0.742485\pi$
$467$	−34.9794	−	7.60931i	−1.61865	−	0.352117i	−0.928438	+	0.371486i	$0.878848\pi$
$468$	10.1437	−	27.1963i	0.468893	−	1.25715i
$469$	−12.7252	+	11.0264i	−0.587595	+	0.509154i
$470$	1.72457	+	6.24558i	0.0795486	+	0.288087i
$471$	−39.2395	−	5.64179i	−1.80806	−	0.259960i
$472$	5.89647	+	7.87676i	0.271407	+	0.362557i
$473$	−0.112365	−	0.516534i	−0.00516655	−	0.0237503i
$474$	−5.63223	−	6.49993i	−0.258697	−	0.298552i
$475$	20.6994	−	12.3749i	0.949754	−	0.567798i
$476$	−1.99530	+	1.28230i	−0.0914542	+	0.0587741i
$477$	13.6030	+	24.9121i	0.622841	+	1.14065i
$478$	20.3602	−	1.45619i	0.931256	−	0.0666047i
$479$	35.8689	−	10.5321i	1.63889	−	0.481222i	0.672886	−	0.739746i	$-0.265054\pi$
$479$	35.8689	−	10.5321i	1.63889	−	0.481222i	0.966005	+	0.258525i	$0.0832363\pi$
$480$	−2.68957	−	6.15090i	−0.122762	−	0.280749i
$481$	44.9737	−	6.46624i	2.05062	−	0.294835i
$482$	−8.84509	−	8.84509i	−0.402883	−	0.402883i
$483$	15.9696	−	24.4715i	0.726642	−	1.11349i
$484$		−	10.4543i		−	0.475197i
$485$	1.25890	+	6.27431i	0.0571635	+	0.284902i
$486$	0.100971	−	0.221095i	0.00458012	−	0.0100291i
$487$	2.04228	−	3.74016i	0.0925446	−	0.169483i	−0.827306	−	0.561751i	$-0.810128\pi$
$487$	2.04228	−	3.74016i	0.0925446	−	0.169483i	0.919851	+	0.392269i	$0.128310\pi$
$488$	0.836488	+	11.6956i	0.0378661	+	0.529437i
$489$	−2.50512	+	8.53165i	−0.113285	+	0.385815i
$490$	−5.21920	+	3.77679i	−0.235779	+	0.170618i
$491$	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	$0.792473\pi$
$492$	−21.2395	−	1.51908i	−0.957550	−	0.0684853i
$493$	−9.11940	+	1.98380i	−0.410717	+	0.0893461i
$494$	3.31331	−	23.0446i	0.149073	−	1.03683i
$495$	−6.38228	−	7.61103i	−0.286862	−	0.342091i
$496$	4.87027	+	3.12993i	0.218681	+	0.140538i
$497$	−1.68159	+	23.5118i	−0.0754298	+	1.05465i
$498$	−22.2460	−	8.29734i	−0.996868	−	0.371812i
$499$	1.91276	+	2.97631i	0.0856267	+	0.133238i	0.881425	−	0.472324i	$-0.156585\pi$
$499$	1.91276	+	2.97631i	0.0856267	+	0.133238i	−0.795798	+	0.605562i	$0.792948\pi$
$500$	8.79495	−	6.90281i	0.393322	−	0.308703i
$501$	−7.08901	+	8.18116i	−0.316714	+	0.365507i
$502$	−1.14842	−	0.627086i	−0.0512566	−	0.0279882i
$503$	10.7789	+	28.8993i	0.480606	+	1.28856i	0.920583	+	0.390546i	$0.127714\pi$
$503$	10.7789	+	28.8993i	0.480606	+	1.28856i	−0.439977	+	0.898009i	$0.645013\pi$
$504$	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
$508$	−6.51677	+	8.70539i	−0.289135	+	0.386239i
$509$	17.6375	+	8.05476i	0.781767	+	0.357021i	0.765988	−	0.642854i	$-0.222250\pi$
$509$	17.6375	+	8.05476i	0.781767	+	0.357021i	0.0157787	+	0.999876i	$0.494977\pi$
$510$	7.39427	−	2.62239i	0.327424	−	0.116122i
$511$	18.8708	+	16.3517i	0.834796	+	0.723354i
$512$	−0.877679	+	0.479249i	−0.0387883	+	0.0211800i
$513$	9.27572	−	42.6398i	0.409533	−	1.88259i
$514$	7.76354	−	3.54549i	0.342435	−	0.156385i
$515$	20.0060	−	19.3686i	0.881568	−	0.853483i
$516$	1.16153	−	1.80737i	0.0511335	−	0.0795652i
$517$	1.71353	−	1.28273i	0.0753609	−	0.0564144i
$518$	−15.2935	+	11.4485i	−0.671956	+	0.503020i
$519$	−7.47051	+	11.6243i	−0.327919	+	0.510252i
$520$	0.174690	−	10.7919i	0.00766066	−	0.473255i
$521$	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	$0.0656597\pi$
$522$	−10.2078	+	46.9246i	−0.446784	+	2.05383i
$523$	19.8005	−	10.8119i	0.865815	−	0.472771i	0.0160126	−	0.999872i	$-0.494903\pi$
$523$	19.8005	−	10.8119i	0.865815	−	0.472771i	0.849803	+	0.527101i	$0.176721\pi$
$524$	0.271091	+	0.234902i	0.0118427	+	0.0102617i
$525$	−28.1073	+	11.7522i	−1.22670	+	0.512907i
$526$	−7.60643	−	3.47374i	−0.331656	−	0.151462i
$527$	−4.05457	+	5.41627i	−0.176620	+	0.235936i
$528$	−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
$532$	3.42086	+	9.17169i	0.148313	+	0.397643i
$533$	−30.0477	−	16.4073i	−1.30151	−	0.710677i
$534$	−19.4283	+	22.4214i	−0.840744	+	0.970270i
$535$	2.12632	+	0.498728i	0.0919288	+	0.0215619i
$536$	−4.48545	−	6.97949i	−0.193742	−	0.301468i
$537$	−29.6706	−	11.0666i	−1.28038	−	0.477557i
$538$	0.918852	−	12.8472i	0.0396145	−	0.553883i
$539$	1.79041	+	1.15062i	0.0771183	+	0.0495609i
$540$	1.76960	−	20.1525i	0.0761513	−	0.867225i
$541$	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	$-0.213883\pi$
$542$	−8.37433	+	1.82172i	−0.359708	+	0.0782497i
$543$	37.9511	+	2.71432i	1.62864	+	0.116483i
$544$	−0.485482	−	1.06306i	−0.0208149	−	0.0455782i
$545$	5.08413	−	31.7087i	0.217780	−	1.35825i
$546$	−8.28594	+	28.2193i	−0.354605	+	1.20767i
$547$	−1.86340	−	26.0538i	−0.0796734	−	1.11398i	−0.867286	−	0.497810i	$-0.834138\pi$
$547$	−1.86340	−	26.0538i	−0.0796734	−	1.11398i	0.787613	−	0.616170i	$-0.211317\pi$
$548$	6.21962	−	11.3904i	0.265689	−	0.486573i
$549$	−29.2913	+	64.1390i	−1.25012	+	2.73739i
$550$	−3.18269	−	1.87408i	−0.135710	−	0.0799111i
$551$			38.5176i			1.64091i
$552$	10.8153	+	9.50465i	0.460331	+	0.404545i
$553$	4.11112	+	4.11112i	0.174823	+	0.174823i
$554$	9.57771	−	1.37707i	0.406918	−	0.0585060i
$555$	57.8990	−	25.3172i	2.45767	−	1.07465i
$556$	5.47078	−	1.60637i	0.232013	−	0.0681251i
$557$	30.2151	−	2.16103i	1.28026	−	0.0915658i	0.585418	−	0.810731i	$-0.300930\pi$
$557$	30.2151	−	2.16103i	1.28026	−	0.0915658i	0.694839	+	0.719166i	$0.255476\pi$
$558$	16.6844	+	30.5553i	0.706309	+	1.29351i
$559$	2.90584	−	1.86747i	0.122904	−	0.0789855i
$560$	2.11013	+	4.01768i	0.0891694	+	0.169778i
$561$	−1.69726	−	1.95875i	−0.0716585	−	0.0826983i
$562$	2.22871	+	10.2452i	0.0940126	+	0.432169i
$563$	−16.9549	−	22.6491i	−0.714563	−	0.954545i	0.285429	−	0.958400i	$-0.407864\pi$
$563$	−16.9549	−	22.6491i	−0.714563	−	0.954545i	−0.999993	+	0.00385480i	$0.998773\pi$
$564$	8.61086	+	1.23805i	0.362583	+	0.0521315i
$565$	−8.93269	+	15.7476i	−0.375801	+	0.662506i
$566$	−3.96107	+	3.43229i	−0.166496	+	0.144270i
$567$	−6.46921	+	17.3446i	−0.271681	+	0.728406i
$568$	−11.3491	−	2.46886i	−0.476200	−	0.103591i
$569$	36.1200	+	10.6058i	1.51423	+	0.444618i	0.930181	−	0.367100i	$-0.119649\pi$
$569$	36.1200	+	10.6058i	1.51423	+	0.444618i	0.584049	+	0.811718i	$0.301468\pi$
$570$	−4.08879	−	32.1206i	−0.171261	−	1.34538i
$571$	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	$0.802371\pi$
$572$	−3.34079	+	1.24605i	−0.139685	+	0.0521000i
$573$	−49.7146	−	37.2159i	−2.07686	−	1.55472i
$574$	14.3945			0.600813
$575$	−10.8119	+	21.4034i	−0.450886	+	0.892581i
$576$	−6.01346			−0.250561
$577$	9.33909	+	6.99115i	0.388791	+	0.291046i	0.775736	−	0.631057i	$-0.217379\pi$
$577$	9.33909	+	6.99115i	0.388791	+	0.291046i	−0.386945	+	0.922103i	$0.626470\pi$
$578$	−14.6485	+	5.46360i	−0.609296	+	0.227256i
$579$	12.3931	+	42.2072i	0.515042	+	1.75407i
$580$	2.25487	+	17.7137i	0.0936283	+	0.735523i
$581$	15.4000	+	4.52186i	0.638901	+	0.187598i
$582$	8.39570	+	1.82637i	0.348013	+	0.0757056i
$583$	1.21848	−	3.26686i	0.0504641	−	0.135299i
$584$	−9.29824	+	8.05697i	−0.384764	+	0.333400i
$585$	32.0236	−	56.4549i	1.32401	−	2.33412i
$586$	−21.8922	−	3.14763i	−0.904360	−	0.130027i
$587$	11.1286	+	14.8661i	0.459328	+	0.613590i	0.969085	−	0.246728i	$-0.0793556\pi$
$587$	11.1286	+	14.8661i	0.459328	+	0.613590i	−0.509757	+	0.860318i	$0.670265\pi$
$588$	1.83865	+	8.45214i	0.0758247	+	0.348560i
$589$	18.2860	+	21.1032i	0.753461	+	0.869540i
$590$	10.2302	+	19.4782i	0.421171	+	0.801906i
$591$	35.4749	−	22.7983i	1.45924	−	0.937798i
$592$	−4.51122	−	8.26167i	−0.185410	−	0.339553i
$593$	−13.4710	+	0.963465i	−0.553188	+	0.0395648i	−0.345135	−	0.938553i	$-0.612167\pi$
$593$	−13.4710	+	0.963465i	−0.553188	+	0.0395648i	−0.208052	+	0.978118i	$0.566712\pi$
$594$	−6.41235	+	1.88284i	−0.263102	+	0.0772537i
$595$	−4.85929	+	2.12480i	−0.199211	+	0.0871082i
$596$	22.9204	−	3.29545i	0.938855	−	0.134987i
$597$	−25.4470	−	25.4470i	−1.04148	−	1.04148i
$598$	9.46909	+	21.1238i	0.387220	+	0.863816i
$599$			40.3117i			1.64709i	0.567251	+	0.823545i	$0.308007\pi$
$599$			40.3117i			1.64709i	−0.567251	+	0.823545i	$0.691993\pi$
$600$	−3.76076	−	14.5325i	−0.153532	−	0.593286i
$601$	−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	$0.198093\pi$
$602$	−0.696027	+	1.27468i	−0.0283680	+	0.0519520i
$603$	−3.55918	−	49.7638i	−0.144941	−	2.02654i
$604$	−3.88575	+	13.2337i	−0.158109	+	0.538470i
$605$	3.70090	−	23.0818i	0.150463	−	0.938408i
$606$	20.7486	+	45.4330i	0.842853	+	1.84559i
$607$	31.4097	+	2.24647i	1.27488	+	0.0911812i	0.692311	−	0.721600i	$-0.256593\pi$
$607$	31.4097	+	2.24647i	1.27488	+	0.0911812i	0.582570	+	0.812781i	$0.302047\pi$
$608$	−4.71306	+	1.02526i	−0.191140	+	0.0415800i
$609$	6.92471	−	48.1624i	0.280603	−	1.95164i
$610$	−2.29348	+	26.1185i	−0.0928601	+	1.05751i
$611$	11.7663	+	7.56174i	0.476013	+	0.305915i
$612$	0.501353	−	7.00983i	0.0202660	−	0.283355i
$613$	−12.7357	−	4.75016i	−0.514389	−	0.191857i	0.0788458	−	0.996887i	$-0.474877\pi$
$613$	−12.7357	−	4.75016i	−0.514389	−	0.191857i	−0.593234	+	0.805030i	$0.702149\pi$
$614$	−3.25970	−	5.07219i	−0.131551	−	0.204697i
$615$	−46.3562	−	10.8728i	−1.86926	−	0.438435i
$616$	0.981753	−	1.13300i	0.0395560	−	0.0456500i
$617$	−4.45710	−	2.43376i	−0.179436	−	0.0979795i	0.387021	−	0.922071i	$-0.373504\pi$
$617$	−4.45710	−	2.43376i	−0.179436	−	0.0979795i	−0.566456	+	0.824092i	$0.691686\pi$
$618$	−13.0654	−	35.0296i	−0.525566	−	1.40910i
$619$	−3.11471	−	21.6633i	−0.125191	−	0.870722i	−0.951532	−	0.307551i	$-0.900491\pi$
$619$	−3.11471	−	21.6633i	−0.125191	−	0.870722i	0.826341	−	0.563171i	$-0.190419\pi$
$620$	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
$623$	12.0187	−	16.0551i	0.481519	−	0.643234i
$624$	−13.1820	−	6.02001i	−0.527701	−	0.240993i
$625$	21.8617	−	12.1270i	0.874469	−	0.485081i
$626$	4.66938	+	4.04604i	0.186626	+	0.161712i
$627$	−9.38834	+	5.12642i	−0.374934	+	0.204730i
$628$	−2.80681	+	12.9027i	−0.112004	+	0.514874i
$629$	10.0066	−	4.56988i	0.398991	−	0.182213i
$630$	−0.441686	+	27.2862i	−0.0175972	+	1.08711i
$631$	−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	$0.809956\pi$
$632$	−2.29334	+	1.71677i	−0.0912243	+	0.0682896i
$633$	−39.0486	+	29.2314i	−1.55204	+	1.16185i
$634$	0.489263	−	0.761308i	0.0194311	−	0.0302354i
$635$	−17.4699	+	16.9134i	−0.693273	+	0.671186i
$636$	12.8903	−	5.88679i	0.511132	−	0.233426i
$637$	−2.95612	+	13.5891i	−0.117126	+	0.538419i
$638$	5.17744	−	2.82710i	0.204977	−	0.111926i
$639$	−52.7844	−	45.7380i	−2.08812	−	1.80937i
$640$	−2.10746	+	0.747414i	−0.0833045	+	0.0295441i
$641$	−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	$0.744955\pi$
$642$	1.75730	−	2.34748i	0.0693552	−	0.0926477i
$643$	−8.22121	+	8.22121i	−0.324213	+	0.324213i	−0.850381	−	0.526168i	$-0.823628\pi$
$643$	−8.22121	+	8.22121i	−0.324213	+	0.324213i	0.526168	+	0.850381i	$0.323628\pi$
$644$	−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
$647$	−4.62686	−	12.4051i	−0.181901	−	0.487694i	0.813712	−	0.581269i	$-0.197443\pi$
$647$	−4.62686	−	12.4051i	−0.181901	−	0.487694i	−0.995612	+	0.0935742i	$0.970171\pi$
$648$	−8.00562	−	4.37140i	−0.314490	−	0.171725i
$649$	4.75967	−	5.49295i	0.186833	−	0.215617i
$650$	4.20609	−	23.7652i	0.164976	−	0.932148i
$651$	−19.0709	−	29.6748i	−0.747446	−	1.16305i
$652$	2.77499	+	1.03502i	0.108677	+	0.0405344i
$653$	−1.41504	+	19.7848i	−0.0553747	+	0.774240i	0.891578	+	0.452867i	$0.149599\pi$
$653$	−1.41504	+	19.7848i	−0.0553747	+	0.774240i	−0.946953	+	0.321373i	$0.895856\pi$
$654$	−36.2726	−	23.3110i	−1.41837	−	0.911531i
$655$	0.515377	+	0.614600i	0.0201374	+	0.0240144i
$656$	−1.00938	+	7.02042i	−0.0394098	+	0.274101i
$657$	−72.2949	+	15.7268i	−2.82049	+	0.613560i
$658$	−5.86578	−	0.419529i	−0.228672	−	0.0163549i
$659$	−11.9722	−	26.2154i	−0.466369	−	1.02121i	−0.985989	−	0.166809i	$-0.946654\pi$
$659$	−11.9722	−	26.2154i	−0.466369	−	1.02121i	0.519620	−	0.854398i	$-0.326074\pi$
$660$	−4.01747	+	2.90718i	−0.156380	+	0.113162i
$661$	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	$-0.0157576\pi$
$662$	2.07786	+	29.0523i	0.0807582	+	1.12915i
$663$	8.11646	−	14.8642i	0.315217	−	0.577277i
$664$	−3.28528	+	7.19376i	−0.127494	+	0.279172i
$665$	4.30598	+	21.4609i	0.166979	+	0.832217i
$666$		−	56.6053i		−	2.19341i
$667$	−20.4800	−	32.3625i	−0.792989	−	1.25308i
$668$	2.54962	+	2.54962i	0.0986479	+	0.0986479i
$669$	25.7071	−	3.69613i	0.993895	−	0.142901i
$670$	−7.43249	−	16.9977i	−0.287142	−	0.656677i
$671$	8.31070	−	2.44024i	0.320831	−	0.0942044i
$672$	6.07754	−	0.434674i	0.234446	−	0.0167679i
$673$	−20.8480	−	38.1802i	−0.803630	−	1.47174i	−0.880163	−	0.474672i	$-0.842567\pi$
$673$	−20.8480	−	38.1802i	−0.803630	−	1.47174i	0.0765328	−	0.997067i	$-0.475615\pi$
$674$	−2.40304	+	1.54434i	−0.0925616	+	0.0594857i
$675$	11.0411	−	43.8676i	0.424974	−	1.68846i
$676$	−6.74444	−	7.78349i	−0.259401	−	0.299365i
$677$	−7.10853	−	32.6774i	−0.273203	−	1.25589i	−0.885266	−	0.465085i	$-0.846024\pi$
$677$	−7.10853	−	32.6774i	−0.273203	−	1.25589i	0.612063	−	0.790809i	$-0.290340\pi$
$678$	14.5673	+	19.4597i	0.559455	+	0.747344i
$679$	−5.74907	−	0.826592i	−0.220629	−	0.0317217i
$680$	−0.695550	−	2.51895i	−0.0266731	−	0.0965974i
$681$	1.69502	−	1.46874i	0.0649533	−	0.0562824i
$682$	1.49449	−	4.00688i	0.0572269	−	0.153431i
$683$	−11.7071	−	2.54672i	−0.447959	−	0.0974476i	−0.0170739	−	0.999854i	$-0.505435\pi$
$683$	−11.7071	−	2.54672i	−0.447959	−	0.0974476i	−0.430885	+	0.902407i	$0.641799\pi$
$684$	−27.8298	−	8.17156i	−1.06410	−	0.312447i
$685$	17.7644	−	22.9467i	0.678742	−	0.876747i
$686$	−5.64980	−	19.2414i	−0.215710	−	0.734642i
$687$	50.6257	−	18.8824i	1.93149	−	0.720409i
$688$	−0.572874	−	0.428848i	−0.0218406	−	0.0163497i
$689$	22.7834			0.867980
$690$	20.5141	+	24.8137i	0.780958	+	0.944642i
$691$	−41.3245			−1.57206			−0.786028	−	0.618191i	$-0.787866\pi$
$691$	−41.3245			−1.57206			−0.786028	+	0.618191i	$0.787866\pi$
$692$	3.68450	+	2.75819i	0.140064	+	0.104850i
$693$	8.44684	−	3.15051i	0.320869	−	0.119678i
$694$	7.01476	+	23.8901i	0.266277	+	0.906855i
$695$	12.6474	−	1.60995i	0.479744	−	0.0610689i
$696$	23.0040	+	6.75459i	0.871965	+	0.256032i
$697$	−8.09947	−	1.76193i	−0.306789	−	0.0667379i
$698$	3.21392	−	8.61685i	0.121649	−	0.326153i
$699$	15.0344	−	13.0274i	0.568652	−	0.492740i
$700$	3.23661	+	9.61750i	0.122332	+	0.363508i
$701$	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	$0.511716\pi$
$702$	−26.1703	−	34.9594i	−0.987735	−	1.31946i
$703$	−9.65091	−	44.3645i	−0.363991	−	1.67324i
$704$	0.483741	+	0.558267i	0.0182317	+	0.0210405i
$705$	18.5734	+	5.78176i	0.699513	+	0.217754i
$706$	12.8824	−	8.27898i	0.484834	−	0.311584i
$707$	−16.1812	−	29.6337i	−0.608557	−	1.11449i
$708$	29.4647	−	2.10736i	1.10735	−	0.0791993i
$709$	−17.8403	+	5.23840i	−0.670008	+	0.196732i	−0.599007	−	0.800744i	$-0.704438\pi$
$709$	−17.8403	+	5.23840i	−0.670008	+	0.196732i	−0.0710014	+	0.997476i	$0.522619\pi$
$710$	−24.1834	−	9.46858i	−0.907588	−	0.355349i
$711$	−17.0517	+	2.45166i	−0.639487	+	0.0919444i
$712$	6.98755	+	6.98755i	0.261869	+	0.261869i
$713$	−26.5845	−	8.00812i	−0.995599	−	0.299906i
$714$			7.12076i			0.266488i
$715$	−7.81713	+	1.56845i	−0.292344	+	0.0586568i
$716$	−4.38173	+	9.59466i	−0.163753	+	0.358569i
$717$	29.3696	−	53.7864i	1.09683	−	2.00869i
$718$	0.493763	+	6.90370i	0.0184271	+	0.257644i
$719$	3.15985	−	10.7615i	0.117842	−	0.401334i	−0.879353	−	0.476170i	$-0.842025\pi$
$719$	3.15985	−	10.7615i	0.117842	−	0.401334i	0.997196	+	0.0748351i	$0.0238430\pi$
$720$	−13.2769	−	2.12880i	−0.494802	−	0.0793359i
$721$	10.4989	+	22.9894i	0.391000	+	0.856171i
$722$	−4.25327	−	0.304200i	−0.158290	−	0.0113211i
$723$	−36.6963	+	7.98280i	−1.36475	+	0.296884i
$724$	1.80359	−	12.5442i	0.0670298	−	0.466202i
$725$	−1.29233	+	39.9078i	−0.0479959	+	1.48214i
$726$	−26.4040	−	16.9688i	−0.979943	−	0.629771i
$727$	−1.43211	+	20.0235i	−0.0531139	+	0.742630i	0.899205	+	0.437527i	$0.144145\pi$
$727$	−1.43211	+	20.0235i	−0.0531139	+	0.742630i	−0.952319	+	0.305103i	$0.901309\pi$
$728$	9.17857	+	3.42343i	0.340180	+	0.126881i
$729$	14.3996	+	22.4062i	0.533319	+	0.829860i
$730$	−23.3815	+	14.4971i	−0.865389	+	0.536562i
$731$	0.547665	−	0.632039i	0.0202561	−	0.0233768i
$732$	30.8968	+	16.8709i	1.14198	+	0.623567i
$733$	5.33813	+	14.3121i	0.197168	+	0.528629i	0.997479	−	0.0709560i	$-0.0226050\pi$
$733$	5.33813	+	14.3121i	0.197168	+	0.528629i	−0.800311	+	0.599585i	$0.795332\pi$
$734$	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
$738$	−25.5599	+	34.1440i	−0.940872	+	1.25686i
$739$	−30.4248	−	13.8945i	−1.11919	−	0.511119i	−0.232092	−	0.972694i	$-0.574557\pi$
$739$	−30.4248	−	13.8945i	−1.11919	−	0.511119i	−0.887101	+	0.461575i	$0.847284\pi$
$740$	−7.03548	−	19.8377i	−0.258629	−	0.729248i
$741$	−52.8246	−	45.7728i	−1.94056	−	1.68150i
$742$	−8.40767	+	4.59094i	−0.308655	+	0.168539i
$743$	−6.07179	+	27.9116i	−0.222752	+	1.02398i	0.720900	+	0.693039i	$0.243729\pi$
$743$	−6.07179	+	27.9116i	−0.222752	+	1.02398i	−0.943653	+	0.330938i	$0.892635\pi$
$744$	15.8102	−	7.22028i	0.579630	−	0.264708i
$745$	51.7718	+	0.838039i	1.89677	+	0.0307034i
$746$	15.8878	−	24.7219i	0.581694	−	0.905133i
$747$	−38.0714	+	28.4999i	−1.39296	+	1.04276i
$748$	−0.691096	+	0.517348i	−0.0252690	+	0.0189161i
$749$	−1.07169	+	1.66759i	−0.0391589	+	0.0609324i
$750$	−3.15867	−	33.4171i	−0.115338	−	1.22022i
$751$	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	$0.291994\pi$
$752$	0.615937	−	2.83142i	0.0224609	−	0.103251i
$753$	−3.44784	+	1.88266i	−0.125646	+	0.0686081i
$754$	29.1315	+	25.2426i	1.06091	+	0.919281i
$755$	−13.2640	+	27.8426i	−0.482727	+	1.01329i
$756$	16.7019	+	7.62752i	0.607444	+	0.277410i
$757$	18.6770	−	24.9495i	0.678827	−	0.906806i	−0.320353	−	0.947298i	$-0.603802\pi$
$757$	18.6770	−	24.9495i	0.678827	−	0.906806i	0.999180	+	0.0404918i	$0.0128925\pi$
$758$	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	$-0.137654\pi$
$762$	11.4091	+	30.5891i	0.413309	+	1.10813i
$763$	25.5818	+	13.9687i	0.926123	+	0.505701i
$764$	−13.5458	+	15.6326i	−0.490068	+	0.565569i
$765$	3.58844	−	15.2993i	0.129740	−	0.553147i
$766$	−1.81620	−	2.82606i	−0.0656220	−	0.102110i
$767$	44.4989	+	16.5972i	1.60676	+	0.599291i
$768$	−0.214178	+	2.99459i	−0.00772847	+	0.108058i
$769$	−3.48307	−	2.23843i	−0.125603	−	0.0807199i	0.476331	−	0.879266i	$-0.341966\pi$
$769$	−3.48307	−	2.23843i	−0.125603	−	0.0807199i	−0.601934	+	0.798546i	$0.705603\pi$
$770$	2.56867	−	2.15398i	0.0925685	−	0.0776239i
$771$	3.64662	−	25.3628i	0.131330	−	0.913418i
$772$	14.3172	−	3.11452i	0.515288	−	0.112094i
$773$	2.92208	+	0.208991i	0.105100	+	0.00751689i	0.123790	−	0.992308i	$-0.460495\pi$
$773$	2.92208	+	0.208991i	0.105100	+	0.00751689i	−0.0186902	+	0.999825i	$0.505950\pi$
$774$	−1.78765	−	3.91441i	−0.0642557	−	0.140700i
$775$	18.2379	+	22.4784i	0.655126	+	0.807447i
$776$	0.806284	−	2.74595i	0.0289439	−	0.0985739i
$777$	4.09163	+	57.2084i	0.146786	+	2.05234i
$778$	−2.69386	+	4.93343i	−0.0965794	+	0.176872i
$779$	−14.2112	+	31.1182i	−0.509170	+	1.11493i
$780$	−26.9729	−	17.9579i	−0.965786	−	0.642995i
$781$			8.57960i			0.307002i
$782$	3.64063	+	4.26131i	0.130189	+	0.152384i
$783$	51.0873	+	51.0873i	1.82571	+	1.82571i
$784$	2.85179	−	0.410026i	0.101850	−	0.0146438i
$785$	−10.7647	+	27.4938i	−0.384209	+	0.981297i
$786$	1.03330	−	0.303403i	0.0368565	−	0.0108220i
$787$	−24.5245	+	1.75403i	−0.874204	+	0.0625243i	−0.501226	−	0.865316i	$-0.667118\pi$
$787$	−24.5245	+	1.75403i	−0.874204	+	0.0625243i	−0.372977	+	0.927840i	$0.621663\pi$
$788$	−6.73146	−	12.3278i	−0.239798	−	0.439158i
$789$	−21.1197	+	13.5728i	−0.751882	+	0.483205i
$790$	−5.67115	+	2.97855i	−0.201770	+	0.105972i
$791$	−10.7608	−	12.4186i	−0.382610	−	0.441555i
$792$	0.944236	+	4.34058i	0.0335520	+	0.154236i
$793$	33.9179	+	45.3090i	1.20446	+	1.60897i
$794$	18.4702	+	2.65562i	0.655484	+	0.0942444i
$795$	30.5440	−	8.43401i	1.08328	−	0.299123i
$796$	−9.05907	+	7.84973i	−0.321090	+	0.278226i
$797$	−5.49929	+	14.7442i	−0.194795	+	0.522266i	−0.997222	−	0.0744845i	$-0.976269\pi$
$797$	−5.49929	+	14.7442i	−0.194795	+	0.522266i	0.802427	+	0.596750i	$0.203542\pi$
$798$	28.7170	+	6.24700i	1.01657	+	0.221141i
$799$	3.24920	+	0.954051i	0.114948	+	0.0337519i
$800$	−4.91757	+	0.904139i	−0.173862	+	0.0319661i
$801$	16.7418	+	57.0172i	0.591541	+	2.01460i
$802$	11.8233	−	4.40988i	0.417496	−	0.155718i
$803$	7.27563	+	5.44647i	0.256751	+	0.192202i
$804$	−24.9082			−0.878445
$805$	−15.0287	−	15.7419i	−0.529694	−	0.554830i
$806$	27.9444			0.984300
$807$	−30.9561	−	23.1735i	−1.08971	−	0.815745i
$808$	15.5875	−	5.81384i	0.548366	−	0.204530i
$809$	−4.90048	−	16.6895i	−0.172292	−	0.586772i	−0.999684	−	0.0251471i	$-0.991995\pi$
$809$	−4.90048	−	16.6895i	−0.172292	−	0.586772i	0.827392	−	0.561625i	$-0.189824\pi$
$810$	−16.1278	−	12.4855i	−0.566674	−	0.438696i
$811$	−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	$0.981589\pi$
$812$	−15.8367	−	3.44507i	−0.555760	−	0.120898i
$813$	−8.99164	+	24.1075i	−0.315350	+	0.845487i
$814$	−5.25502	+	4.55350i	−0.184188	+	0.159600i
$815$	5.76041	+	3.26755i	0.201778	+	0.114457i
$816$	−3.47291	−	0.499329i	−0.121576	−	0.0174800i
$817$	−2.06846	−	2.76314i	−0.0723662	−	0.0966700i
$818$	0.690360	+	3.17353i	0.0241379	+	0.110960i
$819$	38.5773	+	44.5206i	1.34800	+	1.55568i
$820$	−4.71386	+	15.1428i	−0.164615	+	0.528810i
$821$	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	$0.220770\pi$
$822$	−18.6728	−	34.1967i	−0.651289	−	1.19275i
$823$	−22.1381	+	1.58335i	−0.771687	+	0.0551922i	−0.451629	−	0.892206i	$-0.649157\pi$
$823$	−22.1381	+	1.58335i	−0.771687	+	0.0551922i	−0.320058	+	0.947398i	$0.603702\pi$
$824$	−11.9485	+	3.50840i	−0.416247	+	0.122221i
$825$	−9.89920	+	4.99646i	−0.344646	+	0.173954i
$826$	−19.7656	+	2.84187i	−0.687734	+	0.0988812i
$827$	−15.4974	−	15.4974i	−0.538899	−	0.538899i	0.384307	−	0.923206i	$-0.374441\pi$
$827$	−15.4974	−	15.4974i	−0.538899	−	0.538899i	−0.923206	+	0.384307i	$0.874441\pi$
$828$	27.7274	−	7.93149i	0.963595	−	0.275638i
$829$		−	20.2475i		−	0.703226i	−0.936145	−	0.351613i	$-0.885633\pi$
$829$		−	20.2475i		−	0.703226i	0.936145	−	0.351613i	$-0.114367\pi$
$830$	−9.80010	+	14.7199i	−0.340166	+	0.510934i
$831$	12.0679	−	26.4251i	0.418632	−	0.916676i
$832$	−2.31329	+	4.23648i	−0.0801989	+	0.146873i
$833$	0.240204	+	3.35849i	0.00832257	+	0.116365i
$834$	4.82270	−	16.4246i	0.166996	−	0.568738i
$835$	4.72665	+	6.53181i	0.163572	+	0.226043i
$836$	1.48009	+	3.24095i	0.0511901	+	0.112091i
$837$	52.2432	+	3.73651i	1.80579	+	0.129153i
$838$	−1.68177	+	0.365848i	−0.0580959	+	0.0126380i
$839$	2.98596	−	20.7678i	0.103087	−	0.716983i	−0.871078	−	0.491145i	$-0.836579\pi$
$839$	2.98596	−	20.7678i	0.103087	−	0.716983i	0.974165	−	0.225839i	$-0.0725123\pi$
$840$	13.5723	+	1.19178i	0.468288	+	0.0411205i
$841$	−29.2523	−	18.7993i	−1.00870	−	0.648252i
$842$	1.69708	−	23.7283i	0.0584854	−	0.817732i
$843$	29.4933	+	11.0004i	1.01580	+	0.378875i
$844$	8.78386	+	13.6679i	0.302353	+	0.470470i
$845$	−12.1354	−	19.5725i	−0.417471	−	0.673314i
$846$	11.4108	−	13.1688i	0.392313	−	0.452753i
$847$	18.6218	+	10.1683i	0.639853	+	0.349386i
$848$	−1.64950	−	4.42249i	−0.0566441	−	0.151869i
$849$	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
$853$	−12.2220	+	16.3267i	−0.418473	+	0.559015i	−0.959398	−	0.282056i	$-0.908983\pi$
$853$	−12.2220	+	16.3267i	−0.418473	+	0.559015i	0.540925	+	0.841071i	$0.318074\pi$
$854$	−21.6465	−	9.88561i	−0.740727	−	0.338279i
$855$	−58.5517	−	27.8937i	−2.00243	−	0.953943i
$856$	−0.738160	−	0.639619i	−0.0252298	−	0.0218617i
$857$	26.5428	−	14.4934i	0.906683	−	0.495087i	0.0429737	−	0.999076i	$-0.486317\pi$
$857$	26.5428	−	14.4934i	0.906683	−	0.495087i	0.863710	+	0.503990i	$0.168135\pi$
$858$	−2.27547	+	10.4602i	−0.0776832	+	0.357104i
$859$	25.4185	−	11.6082i	0.867269	−	0.396068i	0.0684602	−	0.997654i	$-0.478191\pi$
$859$	25.4185	−	11.6082i	0.867269	−	0.396068i	0.798808	+	0.601586i	$0.205464\pi$
$860$	−1.11302	−	1.14964i	−0.0379535	−	0.0392024i
$861$	23.3642	−	36.3554i	0.796249	−	1.23899i
$862$	−10.2988	+	7.70958i	−0.350778	+	0.262589i
$863$	−25.6381	+	19.1924i	−0.872730	+	0.653318i	−0.938787	−	0.344498i	$-0.888049\pi$
$863$	−25.6381	+	19.1924i	−0.872730	+	0.653318i	0.0660567	+	0.997816i	$0.478958\pi$
$864$	−4.89126	+	7.61095i	−0.166404	+	0.258930i
$865$	7.15848	+	7.39405i	0.243396	+	0.251405i
$866$	−5.93511	+	2.71047i	−0.201683	+	0.0921056i
$867$	−9.97733	+	45.8650i	−0.338848	+	1.55766i
$868$	−10.3122	+	5.63089i	−0.350019	+	0.191125i
$869$	1.59929	+	1.38579i	0.0542522	+	0.0470098i
$870$	48.3986	+	23.0568i	1.64087	+	0.781699i
$871$	−36.4277	−	16.6360i	−1.23430	−	0.563688i
$872$	−8.60664	+	11.4971i	−0.291458	+	0.389342i
$873$	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
$877$	6.53861	+	17.5307i	0.220793	+	0.591969i	0.999367	−	0.0355841i	$-0.0113291\pi$
$877$	6.53861	+	17.5307i	0.220793	+	0.591969i	−0.778574	+	0.627553i	$0.784056\pi$
$878$	−8.62923	−	4.71192i	−0.291222	−	0.159020i
$879$	−43.4838	+	50.1830i	−1.46667	+	1.69263i
$880$	0.870406	+	1.40383i	0.0293414	+	0.0473230i
$881$	−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	$0.973887\pi$
$882$	16.2331	+	6.05464i	0.546598	+	0.203870i
$883$	1.73164	−	24.2115i	0.0582745	−	0.814783i	−0.881326	−	0.472509i	$-0.843348\pi$
$883$	1.73164	−	24.2115i	0.0582745	−	0.814783i	0.939600	−	0.342274i	$-0.111197\pi$
$884$	−4.74555	−	3.04978i	−0.159610	−	0.102575i
$885$	65.8001	+	5.77793i	2.21185	+	0.194223i
$886$	−2.12201	+	14.7589i	−0.0712903	+	0.495835i
$887$	11.2905	−	2.45610i	0.379098	−	0.0824678i	−0.0189786	−	0.999820i	$-0.506041\pi$
$887$	11.2905	−	2.45610i	0.379098	−	0.0824678i	0.398077	+	0.917352i	$0.369678\pi$
$888$	−28.1884	−	2.01607i	−0.945940	−	0.0676550i
$889$	−9.16803	−	20.0752i	−0.307486	−	0.673300i
$890$	12.9539	+	17.9012i	0.434217	+	0.600050i
$891$	−1.89828	+	6.46494i	−0.0635947	+	0.216584i
$892$	−0.617133	−	8.62865i	−0.0206632	−	0.288909i
$893$	6.69805	−	12.2666i	0.224142	−	0.410485i
$894$	28.8797	−	63.2378i	0.965882	−	2.11499i
$895$	−13.0709	+	19.6326i	−0.436911	+	0.656245i
$896$		−	2.02950i		−	0.0678009i
$897$	68.7208	+	10.3712i	2.29452	+	0.346283i
$898$	−2.29181	−	2.29181i	−0.0764787	−	0.0764787i
$899$	−45.7613	+	6.57949i	−1.52623	+	0.219438i
$900$	−28.5601	−	9.40024i	−0.952003	−	0.313341i
$901$	5.29277	−	1.55410i	0.176328	−	0.0517745i
$902$	5.22591	−	0.373764i	0.174004	−	0.0124450i
$903$	2.08964	+	3.82690i	0.0695390	+	0.127351i
$904$	6.81134	−	4.37738i	0.226542	−	0.145590i
$905$	8.42282	−	27.0575i	0.279984	−	0.899422i
$906$	27.1164	+	31.2940i	0.900883	+	1.03967i
$907$	−10.1506	−	46.6617i	−0.337046	−	1.54938i	−0.764068	−	0.645135i	$-0.776801\pi$
$907$	−10.1506	−	46.6617i	−0.337046	−	1.54938i	0.427022	−	0.904241i	$-0.359563\pi$
$908$	−0.447692	−	0.598047i	−0.0148572	−	0.0198469i
$909$	99.0243	+	14.2375i	3.28443	+	0.472229i
$910$	19.0531	+	10.8078i	0.631606	+	0.358273i
$911$	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	$0.0808878\pi$
$912$	−5.06048	+	13.5677i	−0.167569	+	0.449271i
$913$	5.70839	+	1.24178i	0.188920	+	0.0410971i
$914$	5.23451	+	1.53699i	0.173142	+	0.0508391i
$915$	62.2436	+	48.1864i	2.05771	+	1.59299i
$916$	−5.07044	−	17.2683i	−0.167532	−	0.570562i
$917$	−0.682093	+	0.254407i	−0.0225247	+	0.00840127i
$918$	−8.46420	−	6.33622i	−0.279360	−	0.209127i
$919$	20.4703			0.675254			0.337627	−	0.941280i	$-0.390376\pi$
$919$	20.4703			0.675254			0.337627	+	0.941280i	$0.390376\pi$
$920$	8.73145	−	6.22589i	0.287867	−	0.205262i
$921$	−18.1015			−0.596464
$922$	4.12422	+	3.08735i	0.135824	+	0.101677i
$923$	−52.5277	+	19.5918i	−1.72897	+	0.644873i
$924$	−1.26805	−	4.31858i	−0.0417158	−	0.142071i
$925$	−8.51074	−	46.2896i	−0.279831	−	1.52199i
$926$	−28.6473	−	8.41160i	−0.941408	−	0.276422i
$927$	−73.1741	−	15.9180i	−2.40335	−	0.522817i
$928$	2.79073	−	7.48225i	0.0916104	−	0.245617i
$929$	40.4724	−	35.0695i	1.32785	−	1.15059i	0.351075	−	0.936347i	$-0.385816\pi$
$929$	40.4724	−	35.0695i	1.32785	−	1.15059i	0.976780	−	0.214245i	$-0.0687292\pi$
$930$	37.4629	−	10.3445i	1.22846	−	0.339210i
$931$	13.7550	+	1.97767i	0.450803	+	0.0648156i
$932$	−3.97091	−	5.30451i	−0.130071	−	0.173755i
$933$	−0.752778	−	3.46046i	−0.0246448	−	0.113291i
$934$	23.4424	+	27.0540i	0.767058	+	0.885232i
$935$	−1.70899	+	0.897583i	−0.0558900	+	0.0293541i
$936$	−24.4186	+	15.6929i	−0.798147	+	0.512938i
$937$	−1.51676	−	2.77774i	−0.0495504	−	0.0907448i	0.851730	−	0.523981i	$-0.175554\pi$
$937$	−1.51676	−	2.77774i	−0.0495504	−	0.0907448i	−0.901281	+	0.433236i	$0.857372\pi$
$938$	16.7949	−	1.20120i	0.548374	−	0.0392205i
$939$	17.7979	−	5.22594i	0.580813	−	0.170542i
$940$	2.36225	−	6.03334i	0.0770480	−	0.196786i
$941$	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
$943$	−4.60546	−	33.7017i	−0.149974	−	1.09748i
$944$		−	9.83929i		−	0.320242i
$945$	34.1755	+	22.7532i	1.11173	+	0.740160i
$946$	−0.219594	+	0.480845i	−0.00713963	+	0.0156336i
$947$	15.8176	−	28.9678i	0.514004	−	0.941328i	−0.483805	−	0.875176i	$-0.660746\pi$
$947$	15.8176	−	28.9678i	0.514004	−	0.941328i	0.997810	−	0.0661527i	$-0.0210724\pi$
$948$	0.613563	+	8.57873i	0.0199276	+	0.278624i
$949$	−16.7313	+	56.9815i	−0.543120	+	1.84970i
$950$	−23.9867	−	2.49811i	−0.778232	−	0.0810493i
$951$	−1.12866	−	2.47141i	−0.0365992	−	0.0801410i
$952$	2.36577	+	0.169203i	0.0766750	+	0.00548391i
$953$	0.666170	−	0.144916i	0.0215794	−	0.00469430i	−0.201763	−	0.979434i	$-0.564667\pi$
$953$	0.666170	−	0.144916i	0.0215794	−	0.00469430i	0.223342	+	0.974740i	$0.428303\pi$
$954$	4.03948	−	28.0952i	0.130783	−	0.909615i
$955$	−35.4413	+	29.7195i	−1.14685	+	0.961701i
$956$	−17.1719	−	11.0357i	−0.555378	−	0.356920i
$957$	1.26344	−	17.6652i	0.0408411	−	0.571033i
$958$	−35.0261	−	13.0641i	−1.13164	−	0.422081i
$959$	14.2397	+	22.1574i	0.459824	+	0.715500i
$960$	−1.53298	+	6.53585i	−0.0494768	+	0.210944i
$961$	−1.64762	+	1.90145i	−0.0531489	+	0.0613371i
$962$	−39.8783	−	21.7752i	−1.28573	−	0.702061i
$963$	−2.05258	−	5.50318i	−0.0661434	−	0.177337i
$964$	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	−0.149486	+	0.988764i	$0.547762\pi$
$967$	−35.3957	+	35.3957i	−1.13825	+	1.13825i	−0.988764	+	0.149486i	$0.952238\pi$
$968$	−6.26505	+	8.36912i	−0.201366	+	0.268994i
$969$	−15.3938	−	7.03011i	−0.494520	−	0.225840i
$970$	2.75225	−	5.77727i	0.0883695	−	0.185497i
$971$	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	$0.662957\pi$
$972$	−0.213328	+	0.116486i	−0.00684250	+	0.00373629i
$973$	−2.45974	+	11.3072i	−0.0788557	+	0.362494i
$974$	−3.87632	+	1.77026i	−0.124205	+	0.0567227i
$975$	−53.1955	−	49.1972i	−1.70362	−	1.57557i
$976$	6.33929	−	9.86413i	0.202916	−	0.315743i
$977$	−1.66425	+	1.24584i	−0.0532440	+	0.0398579i	−0.625568	−	0.780169i	$-0.715133\pi$
$977$	−1.66425	+	1.24584i	−0.0532440	+	0.0398579i	0.572324	+	0.820027i	$0.306042\pi$
$978$	7.11828	−	5.32868i	0.227617	−	0.170392i
$979$	3.94650	−	6.14088i	0.126131	−	0.196263i
$980$	6.44153	+	0.104270i	0.205767	+	0.00333079i
$981$	−78.5590	+	35.8767i	−2.50820	+	1.14545i
$982$	2.08856	−	9.60097i	0.0666487	−	0.306379i
$983$	10.6685	−	5.82544i	0.340272	−	0.185803i	−0.300022	−	0.953932i	$-0.596994\pi$
$983$	10.6685	−	5.82544i	0.340272	−	0.185803i	0.640294	+	0.768130i	$0.278812\pi$
$984$	16.0927	+	13.9444i	0.513017	+	0.444532i
$985$	−10.4981	−	29.6010i	−0.334497	−	0.943167i
$986$	8.48931	+	3.87694i	0.270355	+	0.123467i
$987$	−10.5805	+	14.1339i	−0.336782	+	0.449888i
$988$	−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	$0.988414\pi$
$992$	−2.02315	−	5.42428i	−0.0642352	−	0.172221i
$993$	76.7484	+	41.9078i	2.43554	+	1.32990i
$994$	15.4363	−	17.8144i	0.489608	−	0.565038i
$995$	−22.7801	+	14.1242i	−0.722177	+	0.447767i
$996$	12.8364	+	19.9739i	0.406738	+	0.632897i
$997$	8.98232	+	3.35023i	0.284473	+	0.106103i	0.487650	−	0.873039i	$-0.337854\pi$
$997$	8.98232	+	3.35023i	0.284473	+	0.106103i	−0.203177	+	0.979142i	$0.565127\pi$
$998$	0.252394	−	3.52893i	0.00798939	−	0.111706i
$999$	−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.43.1	✓	240
5.2	odd	4	inner	230.2.l.a.227.12	yes	240
23.15	odd	22	inner	230.2.l.a.153.12	yes	240
115.107	even	44	inner	230.2.l.a.107.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.1	✓	240	1.1	even	1	trivial
230.2.l.a.107.1	yes	240	115.107	even	44	inner
230.2.l.a.153.12	yes	240	23.15	odd	22	inner
230.2.l.a.227.12	yes	240	5.2	odd	4	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.800541 - 0.599278i) q^{2} +(-2.81295 + 1.04918i) q^{3} +(0.281733 + 0.959493i) q^{4} +(0.282361 + 2.21817i) q^{5} +(2.88063 + 0.845830i) q^{6} +(-1.98312 - 0.431402i) q^{7} +(0.349464 - 0.936950i) q^{8} +(4.54467 - 3.93798i) q^{9} +(1.10326 - 1.94495i) q^{10} +(-0.731174 - 0.105127i) q^{11} +(-1.79918 - 2.40342i) q^{12} +(-1.02603 - 4.71660i) q^{13} +(1.32904 + 1.53380i) q^{14} +(-3.12152 - 5.94335i) q^{15} +(-0.841254 + 0.540641i) q^{16} +(-0.560082 - 1.02571i) q^{17} +(-5.99814 + 0.428996i) q^{18} +(-4.62791 + 1.35888i) q^{19} +(-2.04877 + 0.895854i) q^{20} +(6.03104 - 0.867133i) q^{21} +(0.522335 + 0.522335i) q^{22} +(3.16585 - 3.60241i) q^{23} +3.00224i q^{24} +(-4.84054 + 1.25265i) q^{25} +(-2.00517 + 4.39071i) q^{26} +(-4.33584 + 7.94049i) q^{27} +(-0.144783 - 2.02433i) q^{28} +(2.24985 - 7.66227i) q^{29} +(-1.06281 + 6.62856i) q^{30} +(-2.40496 - 5.26613i) q^{31} +(0.997452 + 0.0713392i) q^{32} +(2.16705 - 0.471413i) q^{33} +(-0.166319 + 1.15677i) q^{34} +(0.396965 - 4.52071i) q^{35} +(5.05885 + 3.25112i) q^{36} +(-0.671522 + 9.38911i) q^{37} +(4.51918 + 1.68557i) q^{38} +(7.83472 + 12.1911i) q^{39} +(2.17699 + 0.510612i) q^{40} +(4.64467 - 5.36024i) q^{41} +(-5.34775 - 2.92009i) q^{42} +(0.250080 + 0.670489i) 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} +(1.79918 - 2.40342i) q^{48} +(-2.62076 - 1.19686i) q^{49} +(4.62574 + 1.89803i) q^{50} +(2.65164 + 2.29766i) q^{51} +(4.23648 - 2.31329i) q^{52} +(-1.00333 + 4.61222i) q^{53} +(8.22958 - 3.75832i) q^{54} +(0.0267339 - 1.65155i) q^{55} +(-1.09723 + 1.70733i) q^{56} +(11.5924 - 8.67795i) q^{57} +(-6.39292 + 4.78568i) q^{58} +(-5.31952 + 8.27734i) q^{59} +(4.82317 - 4.66951i) q^{60} +(-10.6659 + 4.87095i) q^{61} +(-1.23060 + 5.65700i) q^{62} +(-10.7115 + 5.84892i) q^{63} +(-0.755750 - 0.654861i) q^{64} +(10.1725 - 3.60770i) q^{65} +(-2.01732 - 0.921280i) q^{66} +(4.97193 - 6.64172i) 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} +(-2.10149 - 5.63431i) q^{72} +(-10.7984 - 5.89636i) q^{73} +(6.16426 - 7.11394i) q^{74} +(12.3020 - 8.60223i) q^{75} +(-2.60767 - 4.05761i) q^{76} +(1.40466 + 0.523909i) q^{77} +(1.03382 - 14.4546i) q^{78} +(-2.40997 - 1.54880i) q^{79} +(-1.43677 - 1.71339i) q^{80} +(1.29810 - 9.02851i) q^{81} +(-6.93052 + 1.50764i) q^{82} +(-7.88828 - 0.564181i) q^{83} +(2.53115 + 5.54244i) q^{84} +(2.11706 - 1.53198i) q^{85} +(0.201610 - 0.686621i) q^{86} +(1.71037 + 23.9141i) q^{87} +(-0.354018 + 0.648335i) q^{88} +(-4.10508 + 8.98888i) q^{89} +(-2.64523 - 13.1838i) q^{90} +9.79622i q^{91} +(4.34841 + 2.02269i) q^{92} +(12.2901 + 12.2901i) q^{93} +(2.86814 - 0.412377i) q^{94} +(-4.32096 - 9.88180i) q^{95} +(-2.88063 + 0.845830i) q^{96} +(2.85459 - 0.204164i) q^{97} +(1.38077 + 2.52870i) 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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