LMFDB - Embedded newform 230.2.l.a.107.1

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			107.1
Character	$\chi$	$=$	230.107
Dual form			230.2.l.a.43.1

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

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	−0.637689	−	0.770294i	$-0.720110\pi$
$3$	−2.81295	−	1.04918i	−1.62406	−	0.605742i	−0.986369	+	0.164551i	$0.947382\pi$
$4$	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	−0.571084	−	0.820892i	$-0.693477\pi$
$7$	−1.98312	+	0.431402i	−0.749550	+	0.163055i	−0.178466	+	0.983946i	$0.557113\pi$
$8$	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	−0.251658	−	0.967816i	$-0.580976\pi$
$11$	−0.731174	+	0.105127i	−0.220457	+	0.0316970i	0.0312010	+	0.999513i	$0.490067\pi$
$12$	−1.79918	+	2.40342i	−0.519378	+	0.693807i
$13$	−1.02603	+	4.71660i	−0.284570	+	1.30815i	0.583664	+	0.811995i	$0.301618\pi$
$13$	−1.02603	+	4.71660i	−0.284570	+	1.30815i	−0.868235	+	0.496154i	$0.834745\pi$
$14$	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	−0.936740	−	0.350026i	$-0.886173\pi$
$17$	−0.560082	+	1.02571i	−0.135840	+	0.248772i	0.800900	+	0.598798i	$0.204355\pi$
$18$	−5.99814	−	0.428996i	−1.41378	−	0.101115i
$19$	−4.62791	−	1.35888i	−1.06172	−	0.311748i	−0.296174	−	0.955134i	$-0.595711\pi$
$19$	−4.62791	−	1.35888i	−1.06172	−	0.311748i	−0.765542	+	0.643386i	$0.777529\pi$
$20$	−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	0.852712	+	0.522382i	$0.174957\pi$
$29$	2.24985	+	7.66227i	0.417786	+	1.42285i	−0.434925	+	0.900466i	$0.643225\pi$
$30$	−1.06281	−	6.62856i	−0.194042	−	1.21020i
$31$	−2.40496	+	5.26613i	−0.431944	+	0.945825i	0.561064	+	0.827773i	$0.310392\pi$
$31$	−2.40496	+	5.26613i	−0.431944	+	0.945825i	−0.993007	+	0.118052i	$0.962335\pi$
$32$	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	−0.687074	−	0.726587i	$-0.741105\pi$
$37$	−0.671522	−	9.38911i	−0.110398	−	1.54356i	0.576676	−	0.816973i	$-0.304349\pi$
$38$	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	0.991943	−	0.126688i	$-0.0404348\pi$
$41$	4.64467	+	5.36024i	0.725376	+	0.837128i	−0.266567	+	0.963816i	$0.585889\pi$
$42$	−5.34775	+	2.92009i	−0.825176	+	0.450580i
$43$	0.250080	−	0.670489i	0.0381368	−	0.102249i	−0.916486	−	0.400068i	$-0.868987\pi$
$43$	0.250080	−	0.670489i	0.0381368	−	0.102249i	0.954622	+	0.297819i	$0.0962593\pi$
$44$	−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	$0.817780\pi$
$48$	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	−0.993286	−	0.115683i	$-0.963094\pi$
$53$	−1.00333	−	4.61222i	−0.137818	−	0.633537i	0.855469	−	0.517855i	$-0.173269\pi$
$54$	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	−0.992331	−	0.123612i	$-0.960552\pi$
$59$	−5.31952	−	8.27734i	−0.692543	−	1.07762i	0.299788	−	0.954006i	$-0.403084\pi$
$60$	4.82317	+	4.66951i	0.622669	+	0.602831i
$61$	−10.6659	−	4.87095i	−1.36563	−	0.623662i	−0.408349	−	0.912826i	$-0.633895\pi$
$61$	−10.6659	−	4.87095i	−1.36563	−	0.623662i	−0.957280	+	0.289164i	$0.906623\pi$
$62$	−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	0.993830	−	0.110911i	$-0.0353768\pi$
$67$	4.97193	+	6.64172i	0.607418	+	0.811415i	−0.386413	+	0.922326i	$0.626286\pi$
$68$	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	0.619114	+	0.785301i	$0.287492\pi$
$71$	−1.65293	+	11.4964i	−0.196166	+	1.36437i	−0.815281	+	0.579066i	$0.803417\pi$
$72$	−2.10149	+	5.63431i	−0.247663	+	0.664010i
$73$	−10.7984	+	5.89636i	−1.26386	+	0.690117i	−0.964515	−	0.264029i	$-0.914948\pi$
$73$	−10.7984	+	5.89636i	−1.26386	+	0.690117i	−0.299340	+	0.954146i	$0.596767\pi$
$74$	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	−0.669146	−	0.743131i	$-0.733340\pi$
$79$	−2.40997	+	1.54880i	−0.271143	+	0.174253i	0.398003	+	0.917384i	$0.369703\pi$
$80$	−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	−0.497195	−	0.867639i	$-0.665637\pi$
$83$	−7.88828	+	0.564181i	−0.865851	+	0.0619269i	−0.368656	+	0.929566i	$0.620182\pi$
$84$	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	−0.992465	−	0.122526i	$-0.960900\pi$
$89$	−4.10508	−	8.98888i	−0.435138	−	0.952819i	0.557327	−	0.830293i	$-0.311827\pi$
$90$	−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	0.215502	−	0.976503i	$-0.430861\pi$
$97$	2.85459	+	0.204164i	0.289839	+	0.0207297i	0.0743375	+	0.997233i	$0.476316\pi$
$98$	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	0.117912	−	0.993024i	$-0.462380\pi$
$101$	10.8945	−	12.5730i	1.08405	−	1.25106i	0.966136	−	0.258034i	$-0.0830746\pi$
$102$	−0.745811	+	3.42844i	−0.0738463	+	0.339466i
$103$	−7.46278	+	9.96911i	−0.735330	+	0.982286i	0.264510	+	0.964383i	$0.414790\pi$
$103$	−7.46278	+	9.96911i	−0.735330	+	0.982286i	−0.999840	+	0.0179026i	$0.994301\pi$
$104$	−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	0.952404	−	0.304839i	$-0.0986028\pi$
$107$	0.341331	+	0.915143i	0.0329977	+	0.0884702i	−0.919406	+	0.393310i	$0.871330\pi$
$108$	−8.84039	+	1.92311i	−0.850667	+	0.185051i
$109$	−13.7799	+	4.04616i	−1.31988	+	0.387551i	−0.864449	−	0.502720i	$-0.832333\pi$
$109$	−13.7799	+	4.04616i	−1.31988	+	0.387551i	−0.455430	+	0.890272i	$0.650514\pi$
$110$	−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	−0.249244	−	0.968441i	$-0.580182\pi$
$113$	6.48171	−	4.85215i	0.609748	−	0.456451i	0.858992	+	0.511989i	$0.171091\pi$
$114$	−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	−0.412068	−	0.911153i	$-0.635193\pi$
$127$	6.51677	−	8.70539i	0.578270	−	0.772478i	0.990338	+	0.138675i	$0.0442843\pi$
$128$	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	0.553757	−	0.832678i	$-0.313194\pi$
$131$	0.301762	+	0.193931i	0.0263651	+	0.0169438i	−0.527392	+	0.849622i	$0.676830\pi$
$132$	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	−0.980507	−	0.196486i	$-0.937047\pi$
$137$	−9.17672	+	9.17672i	−0.784020	+	0.784020i	0.196486	+	0.980507i	$0.437047\pi$
$138$	12.1667	+	7.69946i	1.03570	+	0.655421i
$139$			5.70174i			0.483615i	0.970324	+	0.241808i	$0.0777403\pi$
$139$			5.70174i			0.483615i	−0.970324	+	0.241808i	$0.922260\pi$
$140$	4.44943	+	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	0.448511	+	0.893778i	$0.351955\pi$
$149$	3.29545	+	22.9204i	0.269974	+	1.87771i	−0.178536	+	0.983933i	$0.557136\pi$
$150$	−15.0034	+	0.485851i	−1.22502	+	0.0396696i
$151$	11.6029	−	7.45670i	0.944227	−	0.606818i	0.0246365	−	0.999696i	$-0.492157\pi$
$151$	11.6029	−	7.45670i	0.944227	−	0.606818i	0.919590	+	0.392879i	$0.128521\pi$
$152$	−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	0.0551403	−	0.998479i	$-0.482439\pi$
$157$	11.5893	−	6.32822i	0.924925	−	0.505047i	0.869785	+	0.493431i	$0.164258\pi$
$158$	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	0.864648	−	0.502378i	$-0.167541\pi$
$163$	1.77490	+	2.37099i	0.139021	+	0.185710i	−0.725627	+	0.688088i	$0.758450\pi$
$164$	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	0.597007	−	0.802236i	$-0.296357\pi$
$167$	3.16466	+	1.72803i	0.244889	+	0.133719i	−0.352118	+	0.935956i	$0.614538\pi$
$168$	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	0.730098	−	0.683343i	$-0.239474\pi$
$173$	3.68450	+	2.75819i	0.280128	+	0.209701i	−0.449970	+	0.893044i	$0.648565\pi$
$174$	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	−0.303925	−	0.952696i	$-0.598297\pi$
$179$	7.97153	−	6.90737i	0.595820	−	0.516281i	0.899746	+	0.436415i	$0.143752\pi$
$180$	−5.78312	−	12.1394i	−0.431048	−	0.904815i
$181$	−11.5280	+	5.26464i	−0.856867	+	0.391318i	−0.794886	−	0.606759i	$-0.792469\pi$
$181$	−11.5280	+	5.26464i	−0.856867	+	0.391318i	−0.0619812	+	0.998077i	$0.519742\pi$
$182$	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	−0.153411	−	0.988162i	$-0.549026\pi$
$191$	11.1831	−	17.4013i	0.809182	−	1.25911i	0.962593	−	0.270950i	$-0.0873378\pi$
$192$	2.81295	−	1.04918i	0.203007	−	0.0757178i
$193$	1.04527	+	14.6147i	0.0752399	+	1.05199i	0.885110	+	0.465382i	$0.154083\pi$
$193$	1.04527	+	14.6147i	0.0752399	+	1.05199i	−0.809870	+	0.586609i	$0.800462\pi$
$194$	−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	−0.304886	−	0.952389i	$-0.598618\pi$
$197$	−13.7249	−	2.98566i	−0.977856	−	0.212720i	−0.672971	+	0.739669i	$0.734982\pi$
$198$	4.43078	−	0.316896i	0.314882	−	0.0225208i
$199$	4.97953	−	10.9036i	0.352989	−	0.772939i	−0.646957	−	0.762527i	$-0.723958\pi$
$199$	4.97953	−	10.9036i	0.352989	−	0.772939i	0.999946	−	0.0104118i	$-0.00331423\pi$
$200$	−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	0.770152	−	0.637861i	$-0.220181\pi$
$211$	15.5890	+	4.57734i	1.07319	+	0.315117i	0.303039	+	0.952978i	$0.401999\pi$
$212$	−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	−0.486481	−	0.873691i	$-0.661720\pi$
$223$	−8.45300	+	1.83884i	−0.566055	+	0.123138i	−0.0795739	+	0.996829i	$0.525356\pi$
$224$	−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	0.326128	−	0.945326i	$-0.394256\pi$
$227$	−0.699951	−	0.261068i	−0.0464574	−	0.0173277i	−0.372585	+	0.927998i	$0.621529\pi$
$228$	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	0.137771	−	0.990464i	$-0.456006\pi$
$233$	−6.20837	−	2.31560i	−0.406724	−	0.151700i	−0.544495	+	0.838764i	$0.683279\pi$
$234$	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	−0.00705924	−	0.999975i	$-0.502247\pi$
$239$	−15.4266	−	13.3672i	−0.997861	−	0.864651i	−0.990801	+	0.135324i	$0.956793\pi$
$240$	5.83921	−	3.31225i	0.376919	−	0.213805i
$241$	12.3815	−	1.78019i	0.797564	−	0.114672i	0.268528	−	0.963272i	$-0.413463\pi$
$241$	12.3815	−	1.78019i	0.797564	−	0.114672i	0.529036	+	0.848599i	$0.322554\pi$
$242$	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	0.183068	−	0.983100i	$-0.441397\pi$
$251$	1.29516	+	0.186216i	0.0817496	+	0.0117538i	−0.101319	+	0.994854i	$0.532306\pi$
$252$	−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	0.718439	−	0.695590i	$-0.244857\pi$
$257$	−4.09030	−	7.49083i	−0.255146	−	0.467265i	−0.973585	+	0.228325i	$0.926675\pi$
$258$	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	0.457302	−	0.889311i	$-0.348816\pi$
$263$	8.17100	+	1.77749i	0.503845	+	0.109605i	0.0465433	+	0.998916i	$0.485179\pi$
$264$	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	−0.561404	−	0.827542i	$-0.689738\pi$
$269$	6.96348	−	10.8354i	0.424571	−	0.660645i	0.985974	+	0.166897i	$0.0533748\pi$
$270$	10.6603	−	17.1934i	0.648766	−	1.04636i
$271$	5.61228	+	6.47691i	0.340922	+	0.393444i	0.900158	−	0.435564i	$-0.143451\pi$
$271$	5.61228	+	6.47691i	0.340922	+	0.393444i	−0.559236	+	0.829008i	$0.688906\pi$
$272$	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	0.471020	−	0.882122i	$-0.343886\pi$
$277$	−6.84211	−	6.84211i	−0.411102	−	0.411102i	−0.882122	+	0.471020i	$0.843886\pi$
$278$	−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	−0.858363	−	0.513042i	$-0.828518\pi$
$281$	−7.92391	+	6.86611i	−0.472701	+	0.409598i	0.385662	+	0.922640i	$0.373973\pi$
$282$	−7.63529	−	4.16918i	−0.454675	−	0.248271i
$283$	1.11411	+	5.12147i	0.0662268	+	0.304440i	0.998331	−	0.0577504i	$-0.0183927\pi$
$283$	1.11411	+	5.12147i	0.0662268	+	0.304440i	−0.932104	+	0.362190i	$0.882029\pi$
$284$	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	0.932835	−	0.360304i	$-0.117327\pi$
$293$	19.4119	+	10.5997i	1.13406	+	0.619242i	0.201222	+	0.979546i	$0.435509\pi$
$294$	−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	−0.183045	−	0.983105i	$-0.558595\pi$
$307$	5.64917	−	2.10703i	0.322415	−	0.120255i	0.505460	+	0.862850i	$0.331323\pi$
$308$	−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	0.984508	−	0.175339i	$-0.0561021\pi$
$311$	−0.167872	−	1.16758i	−0.00951916	−	0.0662072i	−0.994027	+	0.109132i	$0.965193\pi$
$312$	14.1604	+	3.08040i	0.801673	+	0.174393i
$313$	−6.16273	+	0.440767i	−0.348338	+	0.0249136i	−0.244412	−	0.969671i	$-0.578595\pi$
$313$	−6.16273	+	0.440767i	−0.348338	+	0.0249136i	−0.103926	+	0.994585i	$0.533140\pi$
$314$	−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	−0.995317	−	0.0966654i	$-0.969182\pi$
$317$	0.0645597	−	0.902663i	0.00362604	−	0.0506986i	0.998943	+	0.0459668i	$0.0146369\pi$
$318$	−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	−0.0712166	+	0.997461i	$0.522688\pi$
$331$	−19.0738	+	22.0123i	−1.04839	+	1.20991i	−0.977173	+	0.212445i	$0.931857\pi$
$332$	−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	0.961299	−	0.275509i	$-0.0888463\pi$
$337$	0.998243	+	2.67639i	0.0543778	+	0.145792i	−0.906921	+	0.421301i	$0.861574\pi$
$338$	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	−0.980803	−	0.195000i	$-0.937529\pi$
$347$	−19.9324	+	14.9212i	−1.07003	+	0.801012i	−0.0892235	+	0.996012i	$0.528439\pi$
$348$	−22.4635	−	8.37846i	−1.20417	−	0.449133i
$349$	2.59101	−	8.82418i	0.138694	−	0.472347i	−0.860626	−	0.509238i	$-0.829927\pi$
$349$	2.59101	−	8.82418i	0.138694	−	0.472347i	0.999319	+	0.0368909i	$0.0117454\pi$
$350$	−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	−0.998033	−	0.0626983i	$-0.980029\pi$
$353$	−5.35144	−	14.3478i	−0.284829	−	0.763655i	0.713204	−	0.700957i	$-0.247243\pi$
$354$	−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	−0.862645	−	0.505810i	$-0.831194\pi$
$359$	−4.53251	+	5.23080i	−0.239217	+	0.276071i	0.623428	+	0.781880i	$0.285739\pi$
$360$	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	−0.956104	−	0.293028i	$-0.905337\pi$
$367$	−12.7027	+	12.7027i	−0.663076	+	0.663076i	0.293028	+	0.956104i	$0.405337\pi$
$368$	−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	−0.593058	−	0.805160i	$-0.702079\pi$
$373$	2.09644	−	29.3121i	0.108550	−	1.51772i	0.701607	−	0.712564i	$-0.252466\pi$
$374$	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	−0.673433	−	0.739249i	$-0.735181\pi$
$379$	−4.58565	−	31.8939i	−0.235549	−	1.63828i	0.437883	−	0.899032i	$-0.355728\pi$
$380$	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	−0.267759	−	0.963486i	$-0.586283\pi$
$383$	3.14754	−	1.17397i	0.160832	−	0.0599871i	0.428591	+	0.903499i	$0.359010\pi$
$384$	−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	0.959441	+	0.281910i	$0.0909679\pi$
$389$	−0.799951	+	5.56378i	−0.0405591	+	0.282095i	−1.00000		0.000184902i	$0.999941\pi$
$390$	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	0.0124738	−	0.999922i	$-0.496029\pi$
$397$	−16.3776	−	8.94287i	−0.821970	−	0.448830i	−0.834444	+	0.551092i	$0.814211\pi$
$398$	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	0.628059	−	0.778166i	$-0.283850\pi$
$401$	−6.82233	−	10.6157i	−0.340691	−	0.530125i	−0.968750	+	0.248041i	$0.920213\pi$
$402$	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	−0.713430	−	0.700727i	$-0.752859\pi$
$409$	−2.45449	+	2.12683i	−0.121367	+	0.105165i	0.592063	+	0.805892i	$0.298314\pi$
$410$	−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	0.782612	−	0.622509i	$-0.213887\pi$
$419$	1.12709	+	1.30073i	0.0550617	+	0.0635446i	−0.727551	+	0.686054i	$0.759341\pi$
$420$	−11.5794	−	7.17949i	−0.565016	−	0.350323i
$421$	12.8613	−	20.0125i	0.626820	−	0.975351i	−0.372068	−	0.928206i	$-0.621351\pi$
$421$	12.8613	−	20.0125i	0.626820	−	0.975351i	0.998888	−	0.0471457i	$-0.0150125\pi$
$422$	−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	0.999567	+	0.0294185i	$0.00936554\pi$
$431$	3.62443	+	12.3437i	0.174583	+	0.594574i	−0.824985	+	0.565155i	$0.808816\pi$
$432$	−0.645416	+	9.02410i	−0.0310526	+	0.434172i
$433$	3.12697	+	5.72662i	0.150273	+	0.275204i	0.941962	−	0.335720i	$-0.108980\pi$
$433$	3.12697	+	5.72662i	0.150273	+	0.275204i	−0.791689	+	0.610924i	$0.790798\pi$
$434$	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	0.370579	−	0.928801i	$-0.379159\pi$
$439$	9.73180	+	1.39922i	0.464474	+	0.0667812i	0.0938945	+	0.995582i	$0.470068\pi$
$440$	−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	−0.990531	−	0.137291i	$-0.956160\pi$
$443$	−7.14592	+	13.0868i	−0.339513	+	0.621771i	0.651018	+	0.759062i	$0.274342\pi$
$444$	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	−0.0661978	−	0.997807i	$-0.521087\pi$
$449$	3.20812	−	0.461258i	0.151400	−	0.0217681i	0.217598	+	0.976038i	$0.430178\pi$
$450$	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	0.227054	−	0.973882i	$-0.427091\pi$
$457$	−5.11152	−	1.90650i	−0.239107	−	0.0891823i	−0.466161	+	0.884700i	$0.654363\pi$
$458$	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	0.901716	−	0.432329i	$-0.142308\pi$
$463$	27.9742	+	10.4338i	1.30007	+	0.484902i	0.398356	+	0.917231i	$0.369581\pi$
$464$	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	−0.928438	−	0.371486i	$-0.878848\pi$
$467$	−34.9794	+	7.60931i	−1.61865	+	0.352117i	−0.690216	+	0.723603i	$0.742485\pi$
$468$	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	0.966005	−	0.258525i	$-0.0832363\pi$
$479$	35.8689	+	10.5321i	1.63889	+	0.481222i	0.672886	+	0.739746i	$0.265054\pi$
$480$	−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	0.919851	−	0.392269i	$-0.128310\pi$
$487$	2.04228	+	3.74016i	0.0925446	+	0.169483i	−0.827306	+	0.561751i	$0.810128\pi$
$488$	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	−0.794892	−	0.606751i	$-0.792473\pi$
$491$	4.08167	−	8.93760i	0.184203	−	0.403348i	0.979095	+	0.203402i	$0.0651999\pi$
$492$	−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	−0.795798	−	0.605562i	$-0.792948\pi$
$499$	1.91276	−	2.97631i	0.0856267	−	0.133238i	0.881425	+	0.472324i	$0.156585\pi$
$500$	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	−0.439977	−	0.898009i	$-0.645013\pi$
$503$	10.7789	−	28.8993i	0.480606	−	1.28856i	0.920583	−	0.390546i	$-0.127714\pi$
$504$	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	0.0157787	−	0.999876i	$-0.494977\pi$
$509$	17.6375	−	8.05476i	0.781767	−	0.357021i	0.765988	+	0.642854i	$0.222250\pi$
$510$	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	0.978800	−	0.204816i	$-0.0656597\pi$
$521$	33.4390	+	15.2711i	1.46499	+	0.669038i	0.486188	+	0.873854i	$0.338387\pi$
$522$	−10.2078	−	46.9246i	−0.446784	−	2.05383i
$523$	19.8005	+	10.8119i	0.865815	+	0.472771i	0.849803	−	0.527101i	$-0.176721\pi$
$523$	19.8005	+	10.8119i	0.865815	+	0.472771i	0.0160126	+	0.999872i	$0.494903\pi$
$524$	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	0.782620	+	0.622500i	$0.213883\pi$
$541$	4.81656	+	33.4999i	0.207080	+	1.44027i	−0.575540	+	0.817774i	$0.695208\pi$
$542$	−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	0.787613	+	0.616170i	$0.211317\pi$
$547$	−1.86340	+	26.0538i	−0.0796734	+	1.11398i	−0.867286	+	0.497810i	$0.834138\pi$
$548$	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	0.694839	−	0.719166i	$-0.255476\pi$
$557$	30.2151	+	2.16103i	1.28026	+	0.0915658i	0.585418	+	0.810731i	$0.300930\pi$
$558$	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	−0.999993	−	0.00385480i	$-0.998773\pi$
$563$	−16.9549	+	22.6491i	−0.714563	+	0.954545i	0.285429	+	0.958400i	$0.407864\pi$
$564$	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	0.584049	−	0.811718i	$-0.301468\pi$
$569$	36.1200	−	10.6058i	1.51423	−	0.444618i	0.930181	+	0.367100i	$0.119649\pi$
$570$	−4.08879	+	32.1206i	−0.171261	+	1.34538i
$571$	4.43010	−	15.0875i	0.185394	−	0.631394i	−0.813373	−	0.581743i	$-0.802371\pi$
$571$	4.43010	−	15.0875i	0.185394	−	0.631394i	0.998767	−	0.0496508i	$-0.0158108\pi$
$572$	−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	−0.386945	−	0.922103i	$-0.626470\pi$
$577$	9.33909	−	6.99115i	0.388791	−	0.291046i	0.775736	+	0.631057i	$0.217379\pi$
$578$	−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	−0.509757	−	0.860318i	$-0.670265\pi$
$587$	11.1286	−	14.8661i	0.459328	−	0.613590i	0.969085	+	0.246728i	$0.0793556\pi$
$588$	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	−0.208052	−	0.978118i	$-0.566712\pi$
$593$	−13.4710	−	0.963465i	−0.553188	−	0.0395648i	−0.345135	+	0.938553i	$0.612167\pi$
$594$	−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	$-0.691993\pi$
$599$		−	40.3117i		−	1.64709i	0.567251	−	0.823545i	$-0.308007\pi$
$600$	−3.76076	+	14.5325i	−0.153532	+	0.593286i
$601$	−3.92524	−	8.59507i	−0.160114	−	0.350600i	0.812524	−	0.582928i	$-0.198093\pi$
$601$	−3.92524	−	8.59507i	−0.160114	−	0.350600i	−0.972638	+	0.232328i	$0.925366\pi$
$602$	−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	0.582570	−	0.812781i	$-0.302047\pi$
$607$	31.4097	−	2.24647i	1.27488	−	0.0911812i	0.692311	+	0.721600i	$0.256593\pi$
$608$	−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	−0.593234	−	0.805030i	$-0.702149\pi$
$613$	−12.7357	+	4.75016i	−0.514389	+	0.191857i	0.0788458	+	0.996887i	$0.474877\pi$
$614$	−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	−0.566456	−	0.824092i	$-0.691686\pi$
$617$	−4.45710	+	2.43376i	−0.179436	+	0.0979795i	0.387021	+	0.922071i	$0.373504\pi$
$618$	−13.0654	+	35.0296i	−0.525566	+	1.40910i
$619$	−3.11471	+	21.6633i	−0.125191	+	0.870722i	0.826341	+	0.563171i	$0.190419\pi$
$619$	−3.11471	+	21.6633i	−0.125191	+	0.870722i	−0.951532	+	0.307551i	$0.900491\pi$
$620$	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	−0.827003	−	0.562198i	$-0.809956\pi$
$631$	−24.9903	−	38.8856i	−0.994847	−	1.54801i	−0.167844	−	0.985814i	$-0.553680\pi$
$632$	−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	−0.695810	−	0.718226i	$-0.744955\pi$
$641$	−15.4103	+	7.03765i	−0.608670	+	0.277970i	0.0871400	+	0.996196i	$0.472227\pi$
$642$	1.75730	+	2.34748i	0.0693552	+	0.0926477i
$643$	−8.22121	−	8.22121i	−0.324213	−	0.324213i	0.526168	−	0.850381i	$-0.323628\pi$
$643$	−8.22121	−	8.22121i	−0.324213	−	0.324213i	−0.850381	+	0.526168i	$0.823628\pi$
$644$	−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	−0.995612	−	0.0935742i	$-0.970171\pi$
$647$	−4.62686	+	12.4051i	−0.181901	+	0.487694i	0.813712	+	0.581269i	$0.197443\pi$
$648$	−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	−0.946953	−	0.321373i	$-0.895856\pi$
$653$	−1.41504	−	19.7848i	−0.0553747	−	0.774240i	0.891578	−	0.452867i	$-0.149599\pi$
$654$	−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	0.519620	+	0.854398i	$0.326074\pi$
$659$	−11.9722	+	26.2154i	−0.466369	+	1.02121i	−0.985989	+	0.166809i	$0.946654\pi$
$660$	−4.01747	−	2.90718i	−0.156380	−	0.113162i
$661$	4.76418	+	16.2253i	0.185305	+	0.631091i	0.998775	+	0.0494839i	$0.0157576\pi$
$661$	4.76418	+	16.2253i	0.185305	+	0.631091i	−0.813470	+	0.581607i	$0.802424\pi$
$662$	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	0.0765328	+	0.997067i	$0.475615\pi$
$673$	−20.8480	+	38.1802i	−0.803630	+	1.47174i	−0.880163	+	0.474672i	$0.842567\pi$
$674$	−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	0.612063	+	0.790809i	$0.290340\pi$
$677$	−7.10853	+	32.6774i	−0.273203	+	1.25589i	−0.885266	+	0.465085i	$0.846024\pi$
$678$	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	−0.430885	−	0.902407i	$-0.641799\pi$
$683$	−11.7071	+	2.54672i	−0.447959	+	0.0974476i	−0.0170739	+	0.999854i	$0.505435\pi$
$684$	−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	−0.0367989	−	0.999323i	$-0.511716\pi$
$701$	5.54507	−	0.797261i	0.209435	−	0.0301121i	0.246233	+	0.969211i	$0.420807\pi$
$702$	−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	−0.0710014	−	0.997476i	$-0.522619\pi$
$709$	−17.8403	−	5.23840i	−0.670008	−	0.196732i	−0.599007	+	0.800744i	$0.704438\pi$
$710$	−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	0.997196	−	0.0748351i	$-0.0238430\pi$
$719$	3.15985	+	10.7615i	0.117842	+	0.401334i	−0.879353	+	0.476170i	$0.842025\pi$
$720$	−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	−0.952319	−	0.305103i	$-0.901309\pi$
$727$	−1.43211	−	20.0235i	−0.0531139	−	0.742630i	0.899205	−	0.437527i	$-0.144145\pi$
$728$	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	−0.800311	−	0.599585i	$-0.795332\pi$
$733$	5.33813	−	14.3121i	0.197168	−	0.528629i	0.997479	+	0.0709560i	$0.0226050\pi$
$734$	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	−0.887101	−	0.461575i	$-0.847284\pi$
$739$	−30.4248	+	13.8945i	−1.11919	+	0.511119i	−0.232092	+	0.972694i	$0.574557\pi$
$740$	−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	−0.943653	−	0.330938i	$-0.892635\pi$
$743$	−6.07179	−	27.9116i	−0.222752	−	1.02398i	0.720900	−	0.693039i	$-0.243729\pi$
$744$	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	0.607945	−	0.793979i	$-0.291994\pi$
$751$	11.1266	+	5.08134i	0.406015	+	0.185421i	−0.201930	+	0.979400i	$0.564721\pi$
$752$	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	0.999180	−	0.0404918i	$-0.0128925\pi$
$757$	18.6770	+	24.9495i	0.678827	+	0.906806i	−0.320353	+	0.947298i	$0.603802\pi$
$758$	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	0.907940	+	0.419100i	$0.137654\pi$
$761$	−2.24265	+	15.5980i	−0.0812961	+	0.565427i	−0.989236	+	0.146327i	$0.953255\pi$
$762$	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	−0.601934	−	0.798546i	$-0.705603\pi$
$769$	−3.48307	+	2.23843i	−0.125603	+	0.0807199i	0.476331	+	0.879266i	$0.341966\pi$
$770$	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	−0.0186902	−	0.999825i	$-0.505950\pi$
$773$	2.92208	−	0.208991i	0.105100	−	0.00751689i	0.123790	+	0.992308i	$0.460495\pi$
$774$	−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	−0.372977	−	0.927840i	$-0.621663\pi$
$787$	−24.5245	−	1.75403i	−0.874204	−	0.0625243i	−0.501226	+	0.865316i	$0.667118\pi$
$788$	−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	0.802427	−	0.596750i	$-0.203542\pi$
$797$	−5.49929	−	14.7442i	−0.194795	−	0.522266i	−0.997222	+	0.0744845i	$0.976269\pi$
$798$	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	0.827392	+	0.561625i	$0.189824\pi$
$809$	−4.90048	+	16.6895i	−0.172292	+	0.586772i	−0.999684	+	0.0251471i	$0.991995\pi$
$810$	−16.1278	+	12.4855i	−0.566674	+	0.438696i
$811$	−51.4576	+	15.1093i	−1.80692	+	0.530560i	−0.998328	−	0.0578085i	$-0.981589\pi$
$811$	−51.4576	+	15.1093i	−1.80692	+	0.530560i	−0.808593	+	0.588368i	$0.799771\pi$
$812$	−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	0.768970	−	0.639285i	$-0.220770\pi$
$821$	14.5242	+	9.33412i	0.506897	+	0.325763i	−0.262073	+	0.965048i	$0.584406\pi$
$822$	−18.6728	+	34.1967i	−0.651289	+	1.19275i
$823$	−22.1381	−	1.58335i	−0.771687	−	0.0551922i	−0.320058	−	0.947398i	$-0.603702\pi$
$823$	−22.1381	−	1.58335i	−0.771687	−	0.0551922i	−0.451629	+	0.892206i	$0.649157\pi$
$824$	−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	−0.923206	−	0.384307i	$-0.874441\pi$
$827$	−15.4974	+	15.4974i	−0.538899	+	0.538899i	0.384307	+	0.923206i	$0.374441\pi$
$828$	27.7274	+	7.93149i	0.963595	+	0.275638i
$829$			20.2475i			0.703226i	0.936145	+	0.351613i	$0.114367\pi$
$829$			20.2475i			0.703226i	−0.936145	+	0.351613i	$0.885633\pi$
$830$	−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	0.974165	+	0.225839i	$0.0725123\pi$
$839$	2.98596	+	20.7678i	0.103087	+	0.716983i	−0.871078	+	0.491145i	$0.836579\pi$
$840$	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	0.540925	−	0.841071i	$-0.318074\pi$
$853$	−12.2220	−	16.3267i	−0.418473	−	0.559015i	−0.959398	+	0.282056i	$0.908983\pi$
$854$	−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	0.863710	−	0.503990i	$-0.168135\pi$
$857$	26.5428	+	14.4934i	0.906683	+	0.495087i	0.0429737	+	0.999076i	$0.486317\pi$
$858$	−2.27547	−	10.4602i	−0.0776832	−	0.357104i
$859$	25.4185	+	11.6082i	0.867269	+	0.396068i	0.798808	−	0.601586i	$-0.205464\pi$
$859$	25.4185	+	11.6082i	0.867269	+	0.396068i	0.0684602	+	0.997654i	$0.478191\pi$
$860$	−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	0.0660567	−	0.997816i	$-0.478958\pi$
$863$	−25.6381	−	19.1924i	−0.872730	−	0.653318i	−0.938787	+	0.344498i	$0.888049\pi$
$864$	−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	−0.778574	−	0.627553i	$-0.784056\pi$
$877$	6.53861	−	17.5307i	0.220793	−	0.591969i	0.999367	+	0.0355841i	$0.0113291\pi$
$878$	−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	−0.996637	−	0.0819450i	$-0.973887\pi$
$881$	−15.0806	+	23.4659i	−0.508079	+	0.790587i	0.488558	+	0.872532i	$0.337523\pi$
$882$	16.2331	−	6.05464i	0.546598	−	0.203870i
$883$	1.73164	+	24.2115i	0.0582745	+	0.814783i	0.939600	+	0.342274i	$0.111197\pi$
$883$	1.73164	+	24.2115i	0.0582745	+	0.814783i	−0.881326	+	0.472509i	$0.843348\pi$
$884$	−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	0.398077	−	0.917352i	$-0.369678\pi$
$887$	11.2905	+	2.45610i	0.379098	+	0.0824678i	−0.0189786	+	0.999820i	$0.506041\pi$
$888$	−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	0.427022	+	0.904241i	$0.359563\pi$
$907$	−10.1506	+	46.6617i	−0.337046	+	1.54938i	−0.764068	+	0.645135i	$0.776801\pi$
$908$	−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	0.967886	−	0.251391i	$-0.0808878\pi$
$911$	25.8606	+	22.4083i	0.856799	+	0.742420i	−0.111087	+	0.993811i	$0.535433\pi$
$912$	−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	0.976780	+	0.214245i	$0.0687292\pi$
$929$	40.4724	+	35.0695i	1.32785	+	1.15059i	0.351075	+	0.936347i	$0.385816\pi$
$930$	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	−0.901281	−	0.433236i	$-0.857372\pi$
$937$	−1.51676	+	2.77774i	−0.0495504	+	0.0907448i	0.851730	+	0.523981i	$0.175554\pi$
$938$	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	0.643853	−	0.765149i	$-0.277335\pi$
$941$	32.0886	+	4.61364i	1.04606	+	0.150400i	0.402205	+	0.915550i	$0.368244\pi$
$942$	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	0.997810	+	0.0661527i	$0.0210724\pi$
$947$	15.8176	+	28.9678i	0.514004	+	0.941328i	−0.483805	+	0.875176i	$0.660746\pi$
$948$	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	0.223342	−	0.974740i	$-0.428303\pi$
$953$	0.666170	+	0.144916i	0.0215794	+	0.00469430i	−0.201763	+	0.979434i	$0.564667\pi$
$954$	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	−0.988764	−	0.149486i	$-0.952238\pi$
$967$	−35.3957	−	35.3957i	−1.13825	−	1.13825i	−0.149486	−	0.988764i	$-0.547762\pi$
$968$	−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	−0.489874	−	0.871793i	$-0.662957\pi$
$971$	9.45202	−	8.19022i	0.303330	−	0.262837i	0.793204	+	0.608957i	$0.208412\pi$
$972$	−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	0.572324	−	0.820027i	$-0.306042\pi$
$977$	−1.66425	−	1.24584i	−0.0532440	−	0.0398579i	−0.625568	+	0.780169i	$0.715133\pi$
$978$	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	0.640294	−	0.768130i	$-0.278812\pi$
$983$	10.6685	+	5.82544i	0.340272	+	0.185803i	−0.300022	+	0.953932i	$0.596994\pi$
$984$	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	−0.999338	−	0.0363906i	$-0.988414\pi$
$991$	−0.951575	+	6.61835i	−0.0302278	+	0.210239i	0.969110	+	0.246629i	$0.0793231\pi$
$992$	−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	−0.203177	−	0.979142i	$-0.565127\pi$
$997$	8.98232	−	3.35023i	0.284473	−	0.106103i	0.487650	+	0.873039i	$0.337854\pi$
$998$	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.107.1	yes	240
5.3	odd	4	inner	230.2.l.a.153.12	yes	240
23.20	odd	22	inner	230.2.l.a.227.12	yes	240
115.43	even	44	inner	230.2.l.a.43.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.43.1	✓	240	115.43	even	44	inner
230.2.l.a.107.1	yes	240	1.1	even	1	trivial
230.2.l.a.153.12	yes	240	5.3	odd	4	inner
230.2.l.a.227.12	yes	240	23.20	odd	22	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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