LMFDB - Embedded newform 175.2.x.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.77479 + 0.145421i) q^{2} +(0.835009 - 1.03115i) q^{3} +(5.68928 - 0.597968i) q^{4} +(0.745982 - 2.10796i) q^{5} +(-2.16703 + 2.98265i) q^{6} +(2.14677 - 1.54641i) q^{7} +(-10.2108 + 1.61724i) q^{8} +(0.257705 + 1.21240i) q^{9} +(-1.76340 + 5.95764i) q^{10} +(0.0303852 + 0.00645857i) q^{11} +(4.13401 - 6.36581i) q^{12} +(-2.44056 + 1.24353i) q^{13} +(-5.73196 + 4.60315i) q^{14} +(-1.55073 - 2.52939i) q^{15} +(16.9066 - 3.59360i) q^{16} +(1.52518 - 3.97323i) q^{17} +(-0.891386 - 3.32670i) q^{18} +(0.275868 - 2.62470i) q^{19} +(2.98361 - 12.4389i) q^{20} +(0.197993 - 3.50491i) q^{21} +(-0.0852518 - 0.0135026i) q^{22} +(0.103461 + 1.97415i) q^{23} +(-6.85853 + 11.8793i) q^{24} +(-3.88702 - 3.14500i) q^{25} +(6.59122 - 3.80544i) q^{26} +(5.01203 + 2.55376i) q^{27} +(11.2889 - 10.0817i) q^{28} +(0.472036 + 0.649701i) q^{29} +(4.67077 + 6.79302i) q^{30} +(-0.468898 - 1.05316i) q^{31} +(-26.4179 + 7.07866i) q^{32} +(0.0320317 - 0.0259387i) q^{33} +(-3.65427 + 11.2467i) q^{34} +(-1.65832 - 5.67891i) q^{35} +(2.19113 + 6.74362i) q^{36} +(-0.394204 - 0.255999i) q^{37} +(-0.383789 + 7.32313i) q^{38} +(-0.755627 + 3.55494i) q^{39} +(-4.20802 + 22.7305i) q^{40} +(-3.35339 - 1.08958i) q^{41} +(-0.0397023 + 9.75418i) q^{42} +(-6.90226 + 6.90226i) q^{43} +(0.176732 + 0.0185753i) q^{44} +(2.74795 + 0.361200i) q^{45} +(-0.574166 - 5.46282i) q^{46} +(3.24629 - 1.24613i) q^{47} +(10.4116 - 20.4339i) q^{48} +(2.21724 - 6.63957i) q^{49} +(11.2430 + 8.16148i) q^{50} +(-2.82346 - 4.89037i) q^{51} +(-13.1415 + 8.53417i) q^{52} +(8.21153 + 6.64957i) q^{53} +(-14.2787 - 6.35729i) q^{54} +(0.0362812 - 0.0592329i) q^{55} +(-19.4194 + 19.2620i) q^{56} +(-2.47611 - 2.47611i) q^{57} +(-1.40428 - 1.73414i) q^{58} +(-1.58584 - 1.76126i) q^{59} +(-10.3350 - 13.4631i) q^{60} +(0.651278 + 0.586413i) q^{61} +(1.45425 + 2.85412i) q^{62} +(2.42811 + 2.20424i) q^{63} +(39.3982 - 12.8013i) q^{64} +(0.800699 + 6.07227i) q^{65} +(-0.0851092 + 0.0766326i) q^{66} +(9.68701 + 3.71849i) q^{67} +(6.30132 - 23.5169i) q^{68} +(2.12204 + 1.54175i) q^{69} +(5.42733 + 15.5166i) q^{70} +(-2.26602 + 1.64636i) q^{71} +(-4.59213 - 11.9629i) q^{72} +(-3.90459 - 6.01254i) q^{73} +(1.13106 + 0.653020i) q^{74} +(-6.48867 + 1.38200i) q^{75} -15.0976i q^{76} +(0.0752176 - 0.0331229i) q^{77} +(1.57974 - 9.97412i) q^{78} +(-4.45946 + 10.0161i) q^{79} +(5.03681 - 38.3192i) q^{80} +(3.42140 - 1.52331i) q^{81} +(9.46340 + 2.53571i) q^{82} +(2.29277 + 14.4760i) q^{83} +(-0.969385 - 20.0588i) q^{84} +(-7.23767 - 6.17898i) q^{85} +(18.1486 - 20.1561i) q^{86} +(1.06409 + 0.0557668i) q^{87} +(-0.320703 - 0.0168074i) q^{88} +(-3.12526 + 3.47095i) q^{89} +(-7.67751 - 0.602646i) q^{90} +(-3.31632 + 6.44368i) q^{91} +(1.76910 + 11.1697i) q^{92} +(-1.47750 - 0.395896i) q^{93} +(-8.82657 + 3.92984i) q^{94} +(-5.32699 - 2.53950i) q^{95} +(-14.7600 + 33.1516i) q^{96} +(-0.0409086 + 0.258287i) q^{97} +(-5.18685 + 18.7459i) q^{98} +0.0385036i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−2.77479	+	0.145421i	−1.96207	+	0.102828i	−0.990818	−	0.135205i	$-0.956831\pi$
$2$	−2.77479	+	0.145421i	−1.96207	+	0.102828i	−0.971257	+	0.238033i	$0.923497\pi$
$3$	0.835009	−	1.03115i	0.482092	−	0.595335i	−0.476833	−	0.878994i	$-0.658215\pi$
$3$	0.835009	−	1.03115i	0.482092	−	0.595335i	0.958925	+	0.283660i	$0.0915485\pi$
$4$	5.68928	−	0.597968i	2.84464	−	0.298984i
$5$	0.745982	−	2.10796i	0.333613	−	0.942710i
$5$	0.745982	−	2.10796i	0.333613	−	0.942710i
$6$	−2.16703	+	2.98265i	−0.884684	+	1.21766i
$7$	2.14677	−	1.54641i	0.811403	−	0.584487i
$7$	2.14677	−	1.54641i	0.811403	−	0.584487i
$8$	−10.2108	+	1.61724i	−3.61008	+	0.571780i
$9$	0.257705	+	1.21240i	0.0859015	+	0.404135i
$10$	−1.76340	+	5.95764i	−0.557637	+	1.88397i
$11$	0.0303852	+	0.00645857i	0.00916148	+	0.00194733i	0.212490	−	0.977163i	$-0.431843\pi$
$11$	0.0303852	+	0.00645857i	0.00916148	+	0.00194733i	−0.203329	+	0.979111i	$0.565176\pi$
$12$	4.13401	−	6.36581i	1.19338	−	1.83765i
$13$	−2.44056	+	1.24353i	−0.676891	+	0.344893i	−0.758409	−	0.651779i	$-0.774023\pi$
$13$	−2.44056	+	1.24353i	−0.676891	+	0.344893i	0.0815185	+	0.996672i	$0.474023\pi$
$14$	−5.73196	+	4.60315i	−1.53193	+	1.23024i
$15$	−1.55073	−	2.52939i	−0.400396	−	0.653085i
$16$	16.9066	−	3.59360i	4.22664	−	0.898400i
$17$	1.52518	−	3.97323i	0.369911	−	0.963650i	−0.614680	−	0.788776i	$-0.710715\pi$
$17$	1.52518	−	3.97323i	0.369911	−	0.963650i	0.984591	−	0.174874i	$-0.0559518\pi$
$18$	−0.891386	−	3.32670i	−0.210102	−	0.784110i
$19$	0.275868	−	2.62470i	0.0632883	−	0.602148i	−0.916210	−	0.400698i	$-0.868768\pi$
$19$	0.275868	−	2.62470i	0.0632883	−	0.602148i	0.979499	−	0.201451i	$-0.0645656\pi$
$20$	2.98361	−	12.4389i	0.667155	−	2.78142i
$21$	0.197993	−	3.50491i	0.0432055	−	0.764833i
$22$	−0.0852518	−	0.0135026i	−0.0181758	−	0.00287876i
$23$	0.103461	+	1.97415i	0.0215731	+	0.411640i	0.987976	+	0.154608i	$0.0494113\pi$
$23$	0.103461	+	1.97415i	0.0215731	+	0.411640i	−0.966403	+	0.257032i	$0.917255\pi$
$24$	−6.85853	+	11.8793i	−1.39999	+	2.42486i
$25$	−3.88702	−	3.14500i	−0.777405	−	0.629001i
$26$	6.59122	−	3.80544i	1.29265	−	0.746309i
$27$	5.01203	+	2.55376i	0.964566	+	0.491471i
$28$	11.2889	−	10.0817i	2.13340	−	1.90525i
$29$	0.472036	+	0.649701i	0.0876548	+	0.120646i	0.850592	−	0.525826i	$-0.176244\pi$
$29$	0.472036	+	0.649701i	0.0876548	+	0.120646i	−0.762937	+	0.646472i	$0.776244\pi$
$30$	4.67077	+	6.79302i	0.852761	+	1.24023i
$31$	−0.468898	−	1.05316i	−0.0842166	−	0.189154i	0.866528	−	0.499128i	$-0.166346\pi$
$31$	−0.468898	−	1.05316i	−0.0842166	−	0.189154i	−0.950745	+	0.309974i	$0.899680\pi$
$32$	−26.4179	+	7.07866i	−4.67007	+	1.25134i
$33$	0.0320317	−	0.0259387i	0.00557600	−	0.00451535i
$34$	−3.65427	+	11.2467i	−0.626702	+	1.92879i
$35$	−1.65832	−	5.67891i	−0.280308	−	0.959910i
$36$	2.19113	+	6.74362i	0.365189	+	1.12394i
$37$	−0.394204	−	0.255999i	−0.0648068	−	0.0420860i	0.511829	−	0.859087i	$-0.328968\pi$
$37$	−0.394204	−	0.255999i	−0.0648068	−	0.0420860i	−0.576636	+	0.817001i	$0.695635\pi$
$38$	−0.383789	+	7.32313i	−0.0622588	+	1.18797i
$39$	−0.755627	+	3.55494i	−0.120997	+	0.569247i
$40$	−4.20802	+	22.7305i	−0.665347	+	3.59401i
$41$	−3.35339	−	1.08958i	−0.523711	−	0.170164i	0.0352178	−	0.999380i	$-0.488788\pi$
$41$	−3.35339	−	1.08958i	−0.523711	−	0.170164i	−0.558929	+	0.829216i	$0.688788\pi$
$42$	−0.0397023	+	9.75418i	−0.00612620	+	1.50510i
$43$	−6.90226	+	6.90226i	−1.05258	+	1.05258i	−0.0540463	+	0.998538i	$0.517212\pi$
$43$	−6.90226	+	6.90226i	−1.05258	+	1.05258i	−0.998538	+	0.0540463i	$0.982788\pi$
$44$	0.176732	+	0.0185753i	0.0266434	+	0.00280033i
$45$	2.74795	+	0.361200i	0.409640	+	0.0538445i
$46$	−0.574166	−	5.46282i	−0.0846561	−	0.805449i
$47$	3.24629	−	1.24613i	0.473520	−	0.181767i	−0.109892	−	0.993944i	$-0.535051\pi$
$47$	3.24629	−	1.24613i	0.473520	−	0.181767i	0.583412	+	0.812176i	$0.301717\pi$
$48$	10.4116	−	20.4339i	1.50278	−	2.94938i
$49$	2.21724	−	6.63957i	0.316749	−	0.948509i
$50$	11.2430	+	8.16148i	1.59000	+	1.15421i
$51$	−2.82346	−	4.89037i	−0.395363	−	0.684789i
$52$	−13.1415	+	8.53417i	−1.82239	+	1.18348i
$53$	8.21153	+	6.64957i	1.12794	+	0.913388i	0.996954	−	0.0779961i	$-0.0248522\pi$
$53$	8.21153	+	6.64957i	1.12794	+	0.913388i	0.130987	+	0.991384i	$0.458185\pi$
$54$	−14.2787	−	6.35729i	−1.94309	−	0.865118i
$55$	0.0362812	−	0.0592329i	0.00489216	−	0.00798696i
$56$	−19.4194	+	19.2620i	−2.59503	+	2.57399i
$57$	−2.47611	−	2.47611i	−0.327969	−	0.327969i
$58$	−1.40428	−	1.73414i	−0.184391	−	0.227704i
$59$	−1.58584	−	1.76126i	−0.206459	−	0.229296i	0.631018	−	0.775768i	$-0.282637\pi$
$59$	−1.58584	−	1.76126i	−0.206459	−	0.229296i	−0.837477	+	0.546472i	$0.815971\pi$
$60$	−10.3350	−	13.4631i	−1.33424	−	1.73808i
$61$	0.651278	+	0.586413i	0.0833875	+	0.0750825i	0.709770	−	0.704433i	$-0.248799\pi$
$61$	0.651278	+	0.586413i	0.0833875	+	0.0750825i	−0.626383	+	0.779516i	$0.715465\pi$
$62$	1.45425	+	2.85412i	0.184690	+	0.362474i
$63$	2.42811	+	2.20424i	0.305913	+	0.277708i
$64$	39.3982	−	12.8013i	4.92478	−	1.60016i
$65$	0.800699	+	6.07227i	0.0993145	+	0.753172i
$66$	−0.0851092	+	0.0766326i	−0.0104762	+	0.00943283i
$67$	9.68701	+	3.71849i	1.18346	+	0.454286i	0.868917	−	0.494958i	$-0.164817\pi$
$67$	9.68701	+	3.71849i	1.18346	+	0.454286i	0.314539	+	0.949244i	$0.398150\pi$
$68$	6.30132	−	23.5169i	0.764147	−	2.85184i
$69$	2.12204	+	1.54175i	0.255464	+	0.185605i
$70$	5.42733	+	15.5166i	0.648690	+	1.85459i
$71$	−2.26602	+	1.64636i	−0.268927	+	0.195387i	−0.714073	−	0.700071i	$-0.753152\pi$
$71$	−2.26602	+	1.64636i	−0.268927	+	0.195387i	0.445146	+	0.895458i	$0.353152\pi$
$72$	−4.59213	−	11.9629i	−0.541188	−	1.40984i
$73$	−3.90459	−	6.01254i	−0.456997	−	0.703714i	0.532793	−	0.846246i	$-0.321142\pi$
$73$	−3.90459	−	6.01254i	−0.456997	−	0.703714i	−0.989790	+	0.142531i	$0.954476\pi$
$74$	1.13106	+	0.653020i	0.131483	+	0.0759120i
$75$	−6.48867	+	1.38200i	−0.749247	+	0.159579i
$76$		−	15.0976i		−	1.73182i
$77$	0.0752176	−	0.0331229i	0.00857184	−	0.00377470i
$78$	1.57974	−	9.97412i	0.178871	−	1.12935i
$79$	−4.45946	+	10.0161i	−0.501729	+	1.12690i	0.468225	+	0.883610i	$0.344894\pi$
$79$	−4.45946	+	10.0161i	−0.501729	+	1.12690i	−0.969953	+	0.243292i	$0.921773\pi$
$80$	5.03681	−	38.3192i	0.563132	−	4.28422i
$81$	3.42140	−	1.52331i	0.380156	−	0.169256i
$82$	9.46340	+	2.53571i	1.04506	+	0.280022i
$83$	2.29277	+	14.4760i	0.251664	+	1.58895i	0.712638	+	0.701532i	$0.247500\pi$
$83$	2.29277	+	14.4760i	0.251664	+	1.58895i	−0.460974	+	0.887414i	$0.652500\pi$
$84$	−0.969385	−	20.0588i	−0.105769	−	2.18859i
$85$	−7.23767	−	6.17898i	−0.785036	−	0.670205i
$86$	18.1486	−	20.1561i	1.95701	−	2.17349i
$87$	1.06409	+	0.0557668i	0.114083	+	0.00597882i
$88$	−0.320703	−	0.0168074i	−0.0341871	−	0.00179167i
$89$	−3.12526	+	3.47095i	−0.331277	+	0.367920i	−0.885654	−	0.464345i	$-0.846290\pi$
$89$	−3.12526	+	3.47095i	−0.331277	+	0.367920i	0.554378	+	0.832265i	$0.312956\pi$
$90$	−7.67751	−	0.602646i	−0.809281	−	0.0635245i
$91$	−3.31632	+	6.44368i	−0.347645	+	0.675481i
$92$	1.76910	+	11.1697i	0.184441	+	1.16452i
$93$	−1.47750	−	0.395896i	−0.153210	−	0.0410525i
$94$	−8.82657	+	3.92984i	−0.910391	+	0.405332i
$95$	−5.32699	−	2.53950i	−0.546538	−	0.260547i
$96$	−14.7600	+	33.1516i	−1.50644	+	3.38352i
$97$	−0.0409086	+	0.258287i	−0.00415364	+	0.0262251i	−0.989678	−	0.143308i	$-0.954226\pi$
$97$	−0.0409086	+	0.258287i	−0.00415364	+	0.0262251i	0.985524	+	0.169533i	$0.0542260\pi$
$98$	−5.18685	+	18.7459i	−0.523951	+	1.89362i
$99$			0.0385036i			0.00386975i
$100$	−23.9950	−	15.5685i	−2.39950	−	1.55685i
$101$	12.7732	+	7.37464i	1.27099	+	0.733804i	0.975174	−	0.221442i	$-0.0710764\pi$
$101$	12.7732	+	7.37464i	1.27099	+	0.733804i	0.295812	+	0.955246i	$0.404410\pi$
$102$	8.54567	+	13.1592i	0.846148	+	1.30295i
$103$	5.19355	+	13.5296i	0.511735	+	1.33312i	0.909529	+	0.415641i	$0.136443\pi$
$103$	5.19355	+	13.5296i	0.511735	+	1.33312i	−0.397794	+	0.917475i	$0.630224\pi$
$104$	22.9091	−	16.6445i	2.24642	−	1.63212i
$105$	−7.24052	−	3.03196i	−0.706602	−	0.295889i
$106$	−23.7523	−	17.2570i	−2.30703	−	1.67615i
$107$	−1.73705	+	6.48278i	−0.167927	+	0.626714i	0.829721	+	0.558178i	$0.188499\pi$
$107$	−1.73705	+	6.48278i	−0.167927	+	0.626714i	−0.997649	+	0.0685357i	$0.978167\pi$
$108$	30.0419	+	11.5320i	2.89079	+	1.10967i
$109$	1.76099	−	1.58560i	0.168672	−	0.151873i	−0.580472	−	0.814280i	$-0.697132\pi$
$109$	1.76099	−	1.58560i	0.168672	−	0.151873i	0.749144	+	0.662407i	$0.230465\pi$
$110$	−0.0920592	+	0.169635i	−0.00877750	+	0.0161741i
$111$	−0.593138	+	0.192722i	−0.0562982	+	0.0182924i
$112$	30.7373	−	33.8591i	2.90440	−	3.19938i
$113$	−2.10385	−	4.12905i	−0.197914	−	0.388428i	0.770625	−	0.637288i	$-0.219944\pi$
$113$	−2.10385	−	4.12905i	−0.197914	−	0.388428i	−0.968539	+	0.248860i	$0.919944\pi$
$114$	7.23077	+	6.51062i	0.677224	+	0.609775i
$115$	4.23863	+	1.25459i	0.395254	+	0.116991i
$116$	3.07404	+	3.41407i	0.285418	+	0.316989i
$117$	−2.13661	−	2.63849i	−0.197529	−	0.243928i
$118$	4.65651	+	4.65651i	0.428666	+	0.428666i
$119$	−2.87003	−	10.8882i	−0.263095	−	0.998117i
$120$	19.9248	+	23.3193i	1.81888	+	2.12875i
$121$	−10.0481	−	4.47371i	−0.913465	−	0.406701i
$122$	−1.89244	−	1.53247i	−0.171333	−	0.138743i
$123$	−3.92363	+	2.54803i	−0.353782	+	0.229749i
$124$	−3.29745	−	5.71136i	−0.296120	−	0.512895i
$125$	−9.52920	+	5.84759i	−0.852318	+	0.523024i
$126$	−7.05803	−	5.76321i	−0.628779	−	0.513427i
$127$	−1.59432	+	3.12902i	−0.141473	+	0.277656i	−0.950861	−	0.309618i	$-0.899799\pi$
$127$	−1.59432	+	3.12902i	−0.141473	+	0.277656i	0.809388	+	0.587274i	$0.199799\pi$
$128$	−56.3938	+	21.6475i	−4.98455	+	1.91339i
$129$	1.35382	+	12.8807i	0.119197	+	1.13408i
$130$	−3.10481	−	16.7329i	−0.272310	−	1.46757i
$131$	19.1151	+	2.00908i	1.67010	+	0.175534i	0.891821	−	0.452389i	$-0.149428\pi$
$131$	19.1151	+	2.00908i	1.67010	+	0.175534i	0.778275	+	0.627923i	$0.216095\pi$
$132$	0.166727	−	0.166727i	0.0145117	−	0.0145117i
$133$	−3.46664	−	6.06124i	−0.300596	−	0.525576i
$134$	−27.4202	−	8.90936i	−2.36874	−	0.769651i
$135$	9.12211	−	8.66012i	0.785106	−	0.745345i
$136$	−9.14772	+	43.0366i	−0.784410	+	3.69036i
$137$	0.868328	−	16.5687i	0.0741863	−	1.41556i	−0.667399	−	0.744700i	$-0.732592\pi$
$137$	0.868328	−	16.5687i	0.0741863	−	1.41556i	0.741585	−	0.670858i	$-0.234074\pi$
$138$	−6.11242	−	3.96945i	−0.520324	−	0.337902i
$139$	1.88349	+	5.79678i	0.159755	+	0.491677i	0.998612	−	0.0526764i	$-0.0167752\pi$
$139$	1.88349	+	5.79678i	0.159755	+	0.491677i	−0.838856	+	0.544353i	$0.816775\pi$
$140$	−12.8305	−	31.3173i	−1.08437	−	2.64679i
$141$	1.42573	−	4.38794i	0.120068	−	0.369532i
$142$	6.04831	−	4.89783i	0.507563	−	0.411017i
$143$	−0.0821884	+	0.0220223i	−0.00687294	+	0.00184160i
$144$	8.71380	+	19.5715i	0.726150	+	1.63096i
$145$	1.72168	−	0.510369i	0.142977	−	0.0423838i
$146$	11.7088	+	16.1157i	0.969024	+	1.33375i
$147$	−4.99497	−	7.83040i	−0.411978	−	0.645841i
$148$	−2.39582	−	1.22073i	−0.196935	−	0.100344i
$149$	2.64673	−	1.52809i	0.216829	−	0.125186i	−0.387652	−	0.921806i	$-0.626714\pi$
$149$	2.64673	−	1.52809i	0.216829	−	0.125186i	0.604481	+	0.796620i	$0.293381\pi$
$150$	17.8037	−	4.77834i	1.45367	−	0.390150i
$151$	−4.01875	+	6.96068i	−0.327041	+	0.566452i	−0.981923	−	0.189279i	$-0.939385\pi$
$151$	−4.01875	+	6.96068i	−0.327041	+	0.566452i	0.654882	+	0.755731i	$0.272718\pi$
$152$	1.42793	+	27.2466i	0.115821	+	2.20999i
$153$	5.21021	+	0.825217i	0.421221	+	0.0667148i
$154$	−0.203897	+	0.102847i	−0.0164305	+	0.00828767i
$155$	−2.56982	+	0.202780i	−0.206413	+	0.0162877i
$156$	−2.17323	+	20.6769i	−0.173998	+	1.65548i
$157$	−0.585981	−	2.18691i	−0.0467664	−	0.174534i	0.938592	−	0.345028i	$-0.112131\pi$
$157$	−0.585981	−	2.18691i	−0.0467664	−	0.174534i	−0.985359	+	0.170493i	$0.945464\pi$
$158$	10.9175	−	28.4411i	0.868552	−	2.26266i
$159$	13.7134	−	2.91487i	1.08754	−	0.231164i
$160$	−4.78572	+	60.9686i	−0.378345	+	4.81999i
$161$	3.27496	+	4.07806i	0.258103	+	0.321396i
$162$	−9.27216	+	4.72440i	−0.728490	+	0.371184i
$163$	5.17921	−	7.97528i	0.405667	−	0.624672i	−0.575507	−	0.817797i	$-0.695195\pi$
$163$	5.17921	−	7.97528i	0.405667	−	0.624672i	0.981174	+	0.193124i	$0.0618621\pi$
$164$	−19.7299	−	4.19372i	−1.54065	−	0.327475i
$165$	−0.0307829	−	0.0868714i	−0.00239644	−	0.00676293i
$166$	−8.46707	−	39.8344i	−0.657172	−	3.09175i
$167$	−12.3283	+	1.95260i	−0.953989	+	0.151097i	−0.613977	−	0.789324i	$-0.710431\pi$
$167$	−12.3283	+	1.95260i	−0.953989	+	0.151097i	−0.340012	+	0.940421i	$0.610431\pi$
$168$	3.64660	+	36.1082i	0.281341	+	2.78581i
$169$	−3.23122	+	4.44740i	−0.248556	+	0.342107i
$170$	20.9816	+	16.0929i	1.60921	+	1.23427i
$171$	3.25330	−	0.341935i	0.248786	−	0.0261484i
$172$	−35.1416	+	43.3962i	−2.67952	+	3.30893i
$173$	3.73313	−	0.195645i	0.283824	−	0.0148746i	0.0901073	−	0.995932i	$-0.471279\pi$
$173$	3.73313	−	0.195645i	0.283824	−	0.0148746i	0.193717	+	0.981057i	$0.437946\pi$
$174$	−2.96075			−0.224454
$175$	−13.2080	−	0.740676i	−0.998431	−	0.0559899i
$176$	0.536919			0.0404718
$177$	−3.14031	+	0.164577i	−0.236040	+	0.0123703i
$178$	8.16719	−	10.0856i	0.612157	−	0.755951i
$179$	−9.77886	+	1.02780i	−0.730906	+	0.0768214i	−0.462669	−	0.886531i	$-0.653108\pi$
$179$	−9.77886	+	1.02780i	−0.730906	+	0.0768214i	−0.268238	+	0.963353i	$0.586441\pi$
$180$	15.8498	+	0.411784i	1.18138	+	0.0306925i
$181$	7.66282	−	10.5470i	0.569573	−	0.783950i	−0.422931	−	0.906162i	$-0.638999\pi$
$181$	7.66282	−	10.5470i	0.569573	−	0.783950i	0.992504	+	0.122212i	$0.0389988\pi$
$182$	8.26507	−	18.3621i	0.612648	−	1.36109i
$183$	1.14850	−	0.181905i	0.0848997	−	0.0134468i
$184$	−4.24910	−	19.9905i	−0.313248	−	1.47372i
$185$	−0.833707	+	0.639998i	−0.0612953	+	0.0470536i
$186$	4.15734	+	0.883669i	0.304831	+	0.0647937i
$187$	0.0720043	−	0.110877i	0.00526548	−	0.00810812i
$188$	17.7239	−	9.03079i	1.29265	−	0.658638i
$189$	14.7088	−	2.26832i	1.06991	−	0.164996i
$190$	15.1506	+	6.27193i	1.09914	+	0.455014i
$191$	−10.0705	+	2.14056i	−0.728678	+	0.154885i	−0.557290	−	0.830318i	$-0.688159\pi$
$191$	−10.0705	+	2.14056i	−0.728678	+	0.154885i	−0.171389	+	0.985203i	$0.554825\pi$
$192$	19.6978	−	51.3146i	1.42157	−	3.70331i
$193$	−4.98675	−	18.6108i	−0.358954	−	1.33963i	−0.875435	−	0.483336i	$-0.839425\pi$
$193$	−4.98675	−	18.6108i	−0.358954	−	1.33963i	0.516481	−	0.856299i	$-0.327242\pi$
$194$	0.0759527	−	0.722642i	0.00545309	−	0.0518827i
$195$	6.93001	+	4.24476i	0.496268	+	0.303973i
$196$	8.64427	−	39.1002i	0.617448	−	2.79287i
$197$	17.7289	+	2.80798i	1.26313	+	0.200060i	0.751839	−	0.659347i	$-0.229167\pi$
$197$	17.7289	+	2.80798i	1.26313	+	0.200060i	0.511292	+	0.859407i	$0.329167\pi$
$198$	−0.00559922	−	0.106839i	−0.000397919	−	0.00759275i
$199$	3.48571	−	6.03743i	0.247096	−	0.427982i	−0.715623	−	0.698487i	$-0.753857\pi$
$199$	3.48571	−	6.03743i	0.247096	−	0.427982i	0.962719	+	0.270504i	$0.0871904\pi$
$200$	44.7760	+	25.8269i	3.16614	+	1.82624i
$201$	11.9231	−	6.88378i	0.840988	−	0.485544i
$202$	−36.5155	−	18.6056i	−2.56922	−	1.30909i
$203$	2.01806	+	0.664799i	0.141640	+	0.0466598i
$204$	−18.9877	−	26.1344i	−1.32941	−	1.82977i
$205$	−4.79836	+	6.25601i	−0.335132	+	0.436939i
$206$	−16.3785	−	36.7867i	−1.14114	−	2.56305i
$207$	−2.36681	+	0.634185i	−0.164505	+	0.0440789i
$208$	−36.7928	+	29.7942i	−2.55112	+	2.06586i
$209$	0.0253341	−	0.0779704i	0.00175240	−	0.00539333i
$210$	20.5318	+	7.36013i	1.41683	+	0.507897i
$211$	−4.64578	−	14.2982i	−0.319829	−	0.984332i	−0.973721	−	0.227744i	$-0.926865\pi$
$211$	−4.64578	−	14.2982i	−0.319829	−	0.984332i	0.653892	−	0.756588i	$-0.273135\pi$
$212$	50.6939	+	32.9210i	3.48167	+	2.26103i
$213$	−0.194502	+	3.71133i	−0.0133271	+	0.254296i
$214$	3.87724	−	18.2410i	0.265042	−	1.24693i
$215$	9.40075	+	19.6987i	0.641126	+	1.34344i
$216$	−55.3071	−	17.9704i	−3.76317	−	1.22273i
$217$	−2.63524	−	1.53579i	−0.178892	−	0.104256i
$218$	−4.65579	+	4.65579i	−0.315330	+	0.315330i
$219$	−9.46019	−	0.994306i	−0.639260	−	0.0671890i
$220$	0.170995	−	0.358688i	0.0115285	−	0.0241827i
$221$	1.21853	+	11.5935i	0.0819672	+	0.779865i
$222$	1.61781	−	0.621019i	0.108580	−	0.0416800i
$223$	−10.7656	+	21.1287i	−0.720919	+	1.41488i	0.181222	+	0.983442i	$0.441995\pi$
$223$	−10.7656	+	21.1287i	−0.720919	+	1.41488i	−0.902141	+	0.431441i	$0.858005\pi$
$224$	−45.7667	+	56.0491i	−3.05792	+	3.74494i
$225$	2.81132	−	5.52313i	0.187421	−	0.368209i
$226$	6.43821	+	11.1513i	0.428263	+	0.741774i
$227$	23.1833	−	15.0554i	1.53873	−	0.999264i	0.552572	−	0.833465i	$-0.313647\pi$
$227$	23.1833	−	15.0554i	1.53873	−	0.999264i	0.986160	−	0.165798i	$-0.0530201\pi$
$228$	−15.5679	−	12.6067i	−1.03101	−	0.834897i
$229$	−10.7626	−	4.79182i	−0.711213	−	0.316653i	0.0190499	−	0.999819i	$-0.493936\pi$
$229$	−10.7626	−	4.79182i	−0.711213	−	0.316653i	−0.730263	+	0.683166i	$0.760603\pi$
$230$	−11.9438	−	2.86485i	−0.787548	−	0.188902i
$231$	0.0286527	−	0.105218i	0.00188521	−	0.00692287i
$232$	−5.87060	−	5.87060i	−0.385424	−	0.385424i
$233$	−12.3995	−	15.3121i	−0.812320	−	1.00313i	−0.999782	−	0.0208601i	$-0.993360\pi$
$233$	−12.3995	−	15.3121i	−0.812320	−	1.00313i	0.187462	−	0.982272i	$-0.439974\pi$
$234$	6.31233	+	7.01055i	0.412650	+	0.458294i
$235$	−0.205132	−	7.77265i	−0.0133814	−	0.507032i
$236$	−10.0755	−	9.07200i	−0.655858	−	0.590537i
$237$	6.60443	+	12.9619i	0.429004	+	0.841967i
$238$	9.54710	+	29.7950i	0.618846	+	1.93133i
$239$	1.79808	−	0.584231i	0.116308	−	0.0377908i	−0.250285	−	0.968172i	$-0.580524\pi$
$239$	1.79808	−	0.584231i	0.116308	−	0.0377908i	0.366593	+	0.930382i	$0.380524\pi$
$240$	−35.3070	−	37.1906i	−2.27906	−	2.40064i
$241$	−2.08314	+	1.87567i	−0.134187	+	0.120823i	−0.733491	−	0.679699i	$-0.762111\pi$
$241$	−2.08314	+	1.87567i	−0.134187	+	0.120823i	0.599304	+	0.800521i	$0.295444\pi$
$242$	28.5320	+	10.9524i	1.83411	+	0.704048i
$243$	−3.08153	+	11.5004i	−0.197680	+	0.737753i
$244$	4.05596	+	2.94683i	0.259656	+	0.188651i
$245$	−12.3419	−	9.62686i	−0.788498	−	0.615037i
$246$	10.5167	−	7.64084i	0.670522	−	0.487162i
$247$	2.59062	+	6.74881i	0.164837	+	0.429416i
$248$	6.49106	+	9.99536i	0.412183	+	0.634706i
$249$	16.8414	+	9.72338i	1.06728	+	0.616194i
$250$	25.5912	−	17.6116i	1.61853	−	1.11385i
$251$			11.2411i			0.709530i	0.934956	+	0.354765i	$0.115439\pi$
$251$			11.2411i			0.709530i	−0.934956	+	0.354765i	$0.884561\pi$
$252$	15.1322	+	11.0886i	0.953242	+	0.698516i
$253$	−0.00960654	+	0.0606533i	−0.000603958	+	0.00381324i
$254$	3.96887	−	8.91423i	0.249029	−	0.559329i
$255$	−12.4150	+	2.30362i	−0.777456	+	0.144258i
$256$	77.6444	−	34.5695i	4.85278	−	2.16060i
$257$	−23.8998	−	6.40393i	−1.49083	−	0.399466i	−0.580812	−	0.814038i	$-0.697265\pi$
$257$	−23.8998	−	6.40393i	−1.49083	−	0.399466i	−0.910017	+	0.414572i	$0.863931\pi$
$258$	−5.62968	−	35.5444i	−0.350489	−	2.21290i
$259$	−1.24215	+	0.0600294i	−0.0771832	+	0.00373005i
$260$	8.18642	+	34.0681i	0.507701	+	2.11281i
$261$	−0.666055	+	0.739729i	−0.0412278	+	0.0457881i
$262$	−53.3327	−	2.79505i	−3.29490	−	0.172679i
$263$	−20.7041	−	1.08505i	−1.27667	−	0.0669073i	−0.598085	−	0.801432i	$-0.704072\pi$
$263$	−20.7041	−	1.08505i	−1.27667	−	0.0669073i	−0.678581	+	0.734525i	$0.737405\pi$
$264$	−0.285121	+	0.316659i	−0.0175480	+	0.0194890i
$265$	20.1427	−	12.3492i	1.23736	−	0.758602i
$266$	10.5006	+	16.3146i	0.643835	+	1.00031i
$267$	0.969452	+	6.12088i	0.0593295	+	0.374592i
$268$	57.3357	+	15.3630i	3.50233	+	0.938447i
$269$	−7.72933	+	3.44132i	−0.471266	+	0.209821i	−0.628607	−	0.777723i	$-0.716374\pi$
$269$	−7.72933	+	3.44132i	−0.471266	+	0.209821i	0.157341	+	0.987544i	$0.449708\pi$
$270$	−24.0526	+	25.3566i	−1.46379	+	1.54315i
$271$	−6.93622	+	15.5790i	−0.421345	+	0.946357i	0.570780	+	0.821103i	$0.306641\pi$
$271$	−6.93622	+	15.5790i	−0.421345	+	0.946357i	−0.992125	+	0.125253i	$0.960026\pi$
$272$	11.5074	−	72.6546i	0.697736	−	4.40533i
$273$	3.87524	+	8.80015i	0.234540	+	0.532610i
$274$			46.1010i			2.78506i
$275$	−0.0977957	−	0.120666i	−0.00589730	−	0.00727645i
$276$	12.9948	+	7.50255i	0.782195	+	0.451601i
$277$	−1.52073	−	2.34172i	−0.0913718	−	0.140700i	0.790029	−	0.613070i	$-0.210066\pi$
$277$	−1.52073	−	2.34172i	−0.0913718	−	0.140700i	−0.881401	+	0.472369i	$0.843399\pi$
$278$	−6.06926	−	15.8110i	−0.364010	−	0.948279i
$279$	1.15602	−	0.839900i	0.0692093	−	0.0502835i
$280$	26.1170	+	55.3045i	1.56079	+	3.30508i
$281$	4.73304	+	3.43875i	0.282349	+	0.205139i	0.719941	−	0.694035i	$-0.244169\pi$
$281$	4.73304	+	3.43875i	0.282349	+	0.205139i	−0.437592	+	0.899174i	$0.644169\pi$
$282$	−3.31801	+	12.3830i	−0.197584	+	0.737395i
$283$	−15.2091	−	5.83822i	−0.904085	−	0.347046i	−0.138487	−	0.990364i	$-0.544224\pi$
$283$	−15.2091	−	5.83822i	−0.904085	−	0.347046i	−0.765599	+	0.643318i	$0.777557\pi$
$284$	−11.9075	+	10.7216i	−0.706583	+	0.636210i
$285$	−7.06669	+	3.37242i	−0.418594	+	0.199765i
$286$	0.224853	−	0.0730593i	0.0132959	−	0.00432009i
$287$	−8.88389	+	2.84663i	−0.524399	+	0.168031i
$288$	−15.3902	−	30.2050i	−0.906877	−	1.77985i
$289$	−0.826933	−	0.744574i	−0.0486431	−	0.0437985i
$290$	−4.70308	+	1.66653i	−0.276174	+	0.0978623i
$291$	0.232174	+	0.257855i	0.0136103	+	0.0151157i
$292$	−25.8096	−	31.8722i	−1.51039	−	1.86518i
$293$	−19.7336	−	19.7336i	−1.15285	−	1.15285i	−0.985979	−	0.166868i	$-0.946635\pi$
$293$	−19.7336	−	19.7336i	−1.15285	−	1.15285i	−0.166868	−	0.985979i	$-0.553365\pi$
$294$	14.9987	+	21.0014i	0.874743	+	1.22482i
$295$	−4.89567	+	2.02903i	−0.285037	+	0.118135i
$296$	4.43917	+	1.97645i	0.258022	+	0.114879i
$297$	0.135798	+	0.109967i	0.00787979	+	0.00638093i
$298$	−7.12191	+	4.62502i	−0.412561	+	0.267920i
$299$	−2.70742	−	4.68939i	−0.156574	−	0.271195i
$300$	−36.0895	+	11.7426i	−2.08363	+	0.677958i
$301$	−4.14385	+	25.4913i	−0.238848	+	1.46929i
$302$	10.1390	−	19.8989i	0.583432	−	1.14505i
$303$	18.2701	−	7.01325i	1.04959	−	0.402900i
$304$	−4.76817	−	45.3661i	−0.273473	−	2.60192i
$305$	1.72198	−	0.935416i	0.0986002	−	0.0535618i
$306$	−14.5773	−	1.53213i	−0.833327	−	0.0875862i
$307$	13.1692	−	13.1692i	0.751604	−	0.751604i	−0.223174	−	0.974779i	$-0.571642\pi$
$307$	13.1692	−	13.1692i	0.751604	−	0.751604i	0.974779	+	0.223174i	$0.0716419\pi$
$308$	0.408128	−	0.233423i	0.0232552	−	0.0133005i
$309$	18.2877	+	5.94205i	1.04035	+	0.338031i
$310$	7.10123	−	0.936379i	0.403323	−	0.0531827i
$311$	−2.28357	+	10.7434i	−0.129490	+	0.609200i	0.864767	+	0.502174i	$0.167466\pi$
$311$	−2.28357	+	10.7434i	−0.129490	+	0.609200i	−0.994256	+	0.107026i	$0.965867\pi$
$312$	1.96639	−	37.5210i	0.111325	−	2.12421i
$313$	15.8091	+	10.2665i	0.893582	+	0.580299i	0.907709	−	0.419601i	$-0.137830\pi$
$313$	15.8091	+	10.2665i	0.893582	+	0.580299i	−0.0141263	+	0.999900i	$0.504497\pi$
$314$	1.94400	+	5.98301i	0.109706	+	0.337641i
$315$	6.45778	−	3.47404i	0.363854	−	0.195740i
$316$	−19.3818	+	59.6511i	−1.09031	+	3.35564i
$317$	−10.3509	+	8.38196i	−0.581362	+	0.470778i	−0.874322	−	0.485347i	$-0.838693\pi$
$317$	−10.3509	+	8.38196i	−0.581362	+	0.470778i	0.292959	+	0.956125i	$0.405360\pi$
$318$	−37.6279	+	10.0824i	−2.11007	+	0.565392i
$319$	0.0101468	+	0.0227900i	0.000568109	+	0.00127599i
$320$	2.40576	−	92.5995i	0.134486	−	5.17647i
$321$	5.23426	+	7.20434i	0.292148	+	0.402107i
$322$	−9.68036	−	10.8395i	−0.539465	−	0.604063i
$323$	−10.0078	−	5.09923i	−0.556849	−	0.283729i
$324$	18.5544	−	10.7124i	1.03080	−	0.595134i
$325$	13.3974	+	2.84196i	0.743156	+	0.157643i
$326$	−13.2115	+	22.8829i	−0.731715	+	1.26737i
$327$	−0.164551	−	3.13983i	−0.00909972	−	0.173633i
$328$	36.0030	+	5.70232i	1.98793	+	0.314858i
$329$	5.04200	−	7.69525i	0.277975	−	0.424253i
$330$	0.0980490	+	0.236574i	0.00539742	+	0.0130229i
$331$	−0.637584	+	6.06621i	−0.0350448	+	0.333429i	0.962927	+	0.269764i	$0.0869456\pi$
$331$	−0.637584	+	6.06621i	−0.0350448	+	0.333429i	−0.997971	+	0.0636652i	$0.979721\pi$
$332$	21.7004	+	80.9870i	1.19096	+	4.44474i
$333$	0.208787	−	0.543908i	0.0114414	−	0.0298060i
$334$	33.9244	−	7.21086i	1.85626	−	0.394561i
$335$	15.0648	−	17.6459i	0.823077	−	0.964100i
$336$	−9.24786	−	59.9674i	−0.504512	−	3.27149i
$337$	5.99261	−	3.05339i	0.326438	−	0.166329i	−0.283089	−	0.959094i	$-0.591359\pi$
$337$	5.99261	−	3.05339i	0.326438	−	0.166329i	0.609527	+	0.792765i	$0.291359\pi$
$338$	8.31923	−	12.8105i	0.452506	−	0.696799i
$339$	−6.01440	−	1.27840i	−0.326657	−	0.0694332i
$340$	−44.8720	−	30.8261i	−2.43353	−	1.67178i
$341$	−0.00744564	−	0.0350290i	−0.000403204	−	0.00189693i
$342$	−8.97750	+	1.42190i	−0.485448	+	0.0768873i
$343$	−5.50757	−	17.6824i	−0.297381	−	0.954759i
$344$	59.3153	−	81.6405i	3.19807	−	4.40176i
$345$	4.83296	−	3.32306i	0.260198	−	0.178908i
$346$	−10.3302	+	1.08575i	−0.555355	+	0.0583702i
$347$	10.8871	−	13.4445i	0.584451	−	0.721737i	−0.396054	−	0.918227i	$-0.629621\pi$
$347$	10.8871	−	13.4445i	0.584451	−	0.721737i	0.980506	+	0.196490i	$0.0629542\pi$
$348$	6.08727	−	0.319020i	0.326312	−	0.0171013i
$349$	35.3960			1.89470			0.947351	−	0.320196i	$-0.103749\pi$
$349$	35.3960			1.89470			0.947351	+	0.320196i	$0.103749\pi$
$350$	36.7572	+	0.134505i	1.96475	+	0.00718962i
$351$	−15.4079			−0.822410
$352$	−0.848432	+	0.0444644i	−0.0452216	+	0.00236996i
$353$	15.2539	−	18.8369i	0.811881	−	1.00259i	−0.187911	−	0.982186i	$-0.560172\pi$
$353$	15.2539	−	18.8369i	0.811881	−	1.00259i	0.999792	−	0.0204032i	$-0.00649498\pi$
$354$	8.68978	−	0.913332i	0.461856	−	0.0485431i
$355$	1.78006	+	6.00484i	0.0944755	+	0.318704i
$356$	−15.7050	+	21.6160i	−0.832361	+	1.14565i
$357$	−13.6238	−	6.13229i	−0.721049	−	0.324555i
$358$	26.9849	−	4.27398i	1.42619	−	0.225887i
$359$	−3.41066	−	16.0459i	−0.180008	−	0.846869i	−0.971750	−	0.236014i	$-0.924159\pi$
$359$	−3.41066	−	16.0459i	−0.180008	−	0.846869i	0.791742	−	0.610855i	$-0.209174\pi$
$360$	−28.6430	+	0.755934i	−1.50962	+	0.0398412i
$361$	11.7718	+	2.50218i	0.619570	+	0.131694i
$362$	−19.7290	+	30.3800i	−1.03693	+	1.59674i
$363$	−13.0033	+	6.62553i	−0.682498	+	0.347750i
$364$	−15.0144	+	38.6430i	−0.786968	+	2.02544i
$365$	−15.5870	+	3.74549i	−0.815859	+	0.196048i
$366$	−3.16040	+	0.671764i	−0.165197	+	0.0351137i
$367$	3.06282	−	7.97891i	0.159878	−	0.416496i	−0.830119	−	0.557586i	$-0.811728\pi$
$367$	3.06282	−	7.97891i	0.159878	−	0.416496i	0.989997	+	0.141091i	$0.0450609\pi$
$368$	8.84350	+	33.0044i	0.460999	+	1.72047i
$369$	0.456831	−	4.34645i	0.0237817	−	0.226267i
$370$	2.22029	−	1.89710i	0.115428	−	0.0986255i
$371$	27.9112	+	1.57671i	1.44908	+	0.0818586i
$372$	−8.64267	−	1.36886i	−0.448101	−	0.0709723i
$373$	1.26448	+	24.1276i	0.0654720	+	1.24928i	0.811893	+	0.583807i	$0.198437\pi$
$373$	1.26448	+	24.1276i	0.0654720	+	1.24928i	−0.746421	+	0.665474i	$0.768229\pi$
$374$	−0.183673	+	0.318131i	−0.00949752	+	0.0164502i
$375$	−1.92723	+	14.7088i	−0.0995217	+	0.759560i
$376$	−31.1321	+	17.9741i	−1.60551	+	0.926944i
$377$	−1.95996	−	0.998647i	−0.100943	−	0.0514329i
$378$	−40.4841	+	8.43308i	−2.08228	+	0.433751i
$379$	7.62907	+	10.5005i	0.391879	+	0.539375i	0.958683	−	0.284478i	$-0.0918202\pi$
$379$	7.62907	+	10.5005i	0.391879	+	0.539375i	−0.566804	+	0.823853i	$0.691820\pi$
$380$	−31.8253	−	11.2626i	−1.63260	−	0.577757i
$381$	1.89522	+	4.25674i	0.0970951	+	0.218079i
$382$	27.6324	−	7.40407i	1.41379	−	0.378825i
$383$	1.75517	−	1.42131i	0.0896853	−	0.0726257i	−0.583429	−	0.812164i	$-0.698289\pi$
$383$	1.75517	−	1.42131i	0.0896853	−	0.0726257i	0.673114	+	0.739538i	$0.264956\pi$
$384$	−24.7674	+	76.2263i	−1.26391	+	3.88991i
$385$	−0.0137108	−	0.183265i	−0.000698768	−	0.00934005i
$386$	16.5436	+	50.9159i	0.842046	+	2.59155i
$387$	−10.1471	−	6.58959i	−0.515805	−	0.334968i
$388$	−0.0782936	+	1.49393i	−0.00397475	+	0.0758428i
$389$	−5.74544	+	27.0302i	−0.291305	+	1.37048i	0.552356	+	0.833608i	$0.313729\pi$
$389$	−5.74544	+	27.0302i	−0.291305	+	1.37048i	−0.843662	+	0.536875i	$0.819605\pi$
$390$	−19.8466	−	10.7706i	−1.00497	−	0.545388i
$391$	8.00157	+	2.59987i	0.404657	+	0.131481i
$392$	−11.9021	+	71.3814i	−0.601149	+	3.60530i
$393$	18.0330	−	18.0330i	0.909642	−	0.909642i
$394$	−49.6023	−	5.21341i	−2.49893	−	0.262648i
$395$	17.7869	+	16.8722i	0.894958	+	0.848934i
$396$	0.0230239	+	0.219058i	0.00115699	+	0.0110081i
$397$	−33.2533	+	12.7648i	−1.66894	+	0.640645i	−0.995158	−	0.0982885i	$-0.968663\pi$
$397$	−33.2533	+	12.7648i	−1.66894	+	0.640645i	−0.673779	+	0.738933i	$0.735330\pi$
$398$	−8.79417	+	17.2595i	−0.440812	+	0.865142i
$399$	−9.14472	−	1.48656i	−0.457809	−	0.0744212i
$400$	−77.0181	−	39.2028i	−3.85091	−	1.96014i
$401$	−18.5807	−	32.1828i	−0.927877	−	1.60713i	−0.786867	−	0.617123i	$-0.788298\pi$
$401$	−18.5807	−	32.1828i	−0.927877	−	1.60713i	−0.141010	−	0.990008i	$-0.545035\pi$
$402$	−32.0830	+	20.8349i	−1.60015	+	1.03915i
$403$	2.45401	+	1.98722i	0.122243	+	0.0989906i
$404$	77.0804	+	34.3184i	3.83489	+	1.70741i
$405$	−0.658771	−	8.34855i	−0.0327346	−	0.414843i
$406$	−5.69636	−	1.55121i	−0.282706	−	0.0769854i
$407$	−0.0103246	−	0.0103246i	−0.000511771	−	0.000511771i
$408$	36.7388	+	45.3686i	1.81884	+	2.24608i
$409$	−11.8134	−	13.1201i	−0.584133	−	0.648746i	0.376549	−	0.926397i	$-0.377111\pi$
$409$	−11.8134	−	13.1201i	−0.584133	−	0.648746i	−0.960682	+	0.277651i	$0.910444\pi$
$410$	12.4047	−	18.0569i	0.612625	−	0.891767i
$411$	−16.3597	−	14.7304i	−0.806966	−	0.726596i
$412$	37.6378	+	73.8684i	1.85428	+	3.63924i
$413$	−6.12806	−	1.32865i	−0.301542	−	0.0653787i
$414$	6.47519	−	2.10392i	0.318238	−	0.103402i
$415$	32.2252	+	5.96574i	1.58187	+	0.292847i
$416$	55.6721	−	50.1274i	2.72955	−	2.45770i
$417$	7.55008	+	2.89820i	0.369729	+	0.141926i
$418$	−0.0589584	+	0.220036i	−0.00288375	+	0.0107623i
$419$	−19.8377	−	14.4129i	−0.969134	−	0.704117i	−0.0138799	−	0.999904i	$-0.504418\pi$
$419$	−19.8377	−	14.4129i	−0.969134	−	0.704117i	−0.955254	+	0.295787i	$0.904418\pi$
$420$	−43.0064	−	12.9201i	−2.09850	−	0.630435i
$421$	−14.7221	+	10.6962i	−0.717512	+	0.521303i	−0.885588	−	0.464471i	$-0.846244\pi$
$421$	−14.7221	+	10.6962i	−0.717512	+	0.521303i	0.168077	+	0.985774i	$0.446244\pi$
$422$	14.9703	+	38.9991i	0.728745	+	1.89844i
$423$	2.34740	+	3.61468i	0.114135	+	0.175752i
$424$	−94.6006	−	54.6177i	−4.59421	−	2.65247i
$425$	−18.4242	+	10.6473i	−0.893707	+	0.516472i
$426$		−	10.3264i		−	0.500318i
$427$	2.30498	+	0.251752i	0.111546	+	0.0121832i
$428$	−6.00611	+	37.9211i	−0.290316	+	1.83298i
$429$	−0.0459197	+	0.103137i	−0.00221703	+	0.00497952i
$430$	−28.9497	−	53.2927i	−1.39608	−	2.57000i
$431$	−10.1010	+	4.49727i	−0.486550	+	0.216626i	−0.635325	−	0.772245i	$-0.719134\pi$
$431$	−10.1010	+	4.49727i	−0.486550	+	0.216626i	0.148775	+	0.988871i	$0.452467\pi$
$432$	93.9134	+	25.1640i	4.51841	+	1.21070i
$433$	−6.01829	−	37.9980i	−0.289221	−	1.82607i	−0.521304	−	0.853371i	$-0.674554\pi$
$433$	−6.01829	−	37.9980i	−0.289221	−	1.82607i	0.232084	−	0.972696i	$-0.425446\pi$
$434$	7.53557	+	3.87828i	0.361719	+	0.186163i
$435$	0.911348	−	2.20147i	0.0436958	−	0.105552i
$436$	9.07061	−	10.0739i	0.434404	−	0.482454i
$437$	5.21011	+	0.273050i	0.249233	+	0.0130618i
$438$	26.3947	+	1.38329i	1.26119	+	0.0660959i
$439$	16.9119	−	18.7825i	0.807159	−	0.896441i	−0.189179	−	0.981943i	$-0.560583\pi$
$439$	16.9119	−	18.7825i	0.807159	−	0.896441i	0.996338	+	0.0855013i	$0.0272492\pi$
$440$	−0.274668	+	0.663493i	−0.0130943	+	0.0316308i
$441$	8.62124	+	0.977147i	0.410535	+	0.0465308i
$442$	−5.06711	−	31.9924i	−0.241018	−	1.52173i
$443$	−7.33193	−	1.96458i	−0.348351	−	0.0933402i	0.0804012	−	0.996763i	$-0.474380\pi$
$443$	−7.33193	−	1.96458i	−0.348351	−	0.0933402i	−0.428752	+	0.903422i	$0.641047\pi$
$444$	−3.25929	+	1.45113i	−0.154679	+	0.0688675i
$445$	4.98525	+	9.17719i	0.236324	+	0.435041i
$446$	26.7998	−	60.1934i	1.26901	−	2.85024i
$447$	0.634352	−	4.00514i	0.0300038	−	0.189437i
$448$	64.7829	−	88.4071i	3.06071	−	4.17684i
$449$			2.62419i			0.123843i	0.998081	+	0.0619217i	$0.0197229\pi$
$449$			2.62419i			0.123843i	−0.998081	+	0.0619217i	$0.980277\pi$
$450$	−6.99764	+	15.7344i	−0.329872	+	0.741725i
$451$	−0.0948562	−	0.0547652i	−0.00446660	−	0.00257879i
$452$	−14.4385	−	22.2333i	−0.679128	−	1.04577i
$453$	3.82181	+	9.95616i	0.179564	+	0.467781i
$454$	−62.1395	+	45.1470i	−2.91635	+	2.11885i
$455$	11.1091	+	11.7976i	0.520804	+	0.553078i
$456$	29.2876	+	21.2787i	1.37152	+	0.996467i
$457$	−7.30752	+	27.2720i	−0.341831	+	1.27573i	0.554440	+	0.832224i	$0.312933\pi$
$457$	−7.30752	+	27.2720i	−0.341831	+	1.27573i	−0.896271	+	0.443507i	$0.853734\pi$
$458$	30.5608	+	11.7312i	1.42801	+	0.548163i
$459$	17.7909	−	16.0190i	0.830409	−	0.747704i
$460$	24.8650	+	4.60316i	1.15933	+	0.214624i
$461$	−20.6080	+	6.69595i	−0.959811	+	0.311861i	−0.746696	−	0.665166i	$-0.768361\pi$
$461$	−20.6080	+	6.69595i	−0.959811	+	0.311861i	−0.213115	+	0.977027i	$0.568361\pi$
$462$	−0.0642044	+	0.296126i	−0.00298706	+	0.0137770i
$463$	−1.36603	−	2.68099i	−0.0634850	−	0.124596i	0.857083	−	0.515178i	$-0.172274\pi$
$463$	−1.36603	−	2.68099i	−0.0634850	−	0.124596i	−0.920568	+	0.390581i	$0.872274\pi$
$464$	10.3153	+	9.28791i	0.478874	+	0.431180i
$465$	−1.93672	+	2.81919i	−0.0898134	+	0.130737i
$466$	36.6328	+	40.6849i	1.69698	+	1.88469i
$467$	−20.0682	−	24.7822i	−0.928646	−	1.14678i	−0.988897	−	0.148600i	$-0.952523\pi$
$467$	−20.0682	−	24.7822i	−0.928646	−	1.14678i	0.0602510	−	0.998183i	$-0.480810\pi$
$468$	−13.7335	−	13.7335i	−0.634831	−	0.634831i
$469$	26.5461	−	6.99732i	1.22578	−	0.323106i
$470$	1.69951	+	21.5377i	0.0783923	+	0.993459i
$471$	−2.74433	−	1.22185i	−0.126452	−	0.0563001i
$472$	19.0412	+	15.4192i	0.876440	+	0.709727i
$473$	−0.254305	+	0.165148i	−0.0116930	+	0.00759350i
$474$	−20.2108	−	35.0062i	−0.928315	−	1.60789i
$475$	−9.32701	+	9.33468i	−0.427953	+	0.428304i
$476$	−22.8392	−	60.2297i	−1.04683	−	2.76062i
$477$	−5.94582	+	11.6693i	−0.272240	+	0.534302i
$478$	−4.90434	+	1.88260i	−0.224319	+	0.0861080i
$479$	0.454169	+	4.32113i	0.0207515	+	0.197437i	0.999986	−	0.00529349i	$-0.00168498\pi$
$479$	0.454169	+	4.32113i	0.0207515	+	0.197437i	−0.979234	+	0.202731i	$0.935018\pi$
$480$	58.8716	+	55.8441i	2.68711	+	2.54892i
$481$	1.28042	+	0.134578i	0.0583823	+	0.00613623i
$482$	5.50753	−	5.50753i	0.250861	−	0.250861i
$483$	6.93971	+	0.0282466i	0.315768	+	0.00128527i
$484$	−59.8417	−	19.4438i	−2.72008	−	0.883807i
$485$	0.513943	+	0.278911i	0.0233369	+	0.0126647i
$486$	6.87821	−	32.3594i	0.312002	−	1.46785i
$487$	0.745276	−	14.2207i	0.0337717	−	0.644402i	−0.928338	−	0.371738i	$-0.878762\pi$
$487$	0.745276	−	14.2207i	0.0337717	−	0.644402i	0.962109	−	0.272664i	$-0.0879048\pi$
$488$	−7.59846	−	4.93450i	−0.343966	−	0.223374i
$489$	−3.89903	−	12.0000i	−0.176320	−	0.542657i
$490$	35.6463	+	24.9178i	1.61033	+	1.12567i
$491$	6.63863	−	20.4316i	0.299597	−	0.922065i	−0.682041	−	0.731314i	$-0.738908\pi$
$491$	6.63863	−	20.4316i	0.299597	−	0.922065i	0.981638	−	0.190751i	$-0.0610924\pi$
$492$	−20.7990	+	16.8427i	−0.937691	+	0.759327i
$493$	3.30135	−	0.884595i	0.148685	−	0.0398402i
$494$	−8.16986	−	18.3498i	−0.367579	−	0.825597i
$495$	0.0811641	+	0.0287230i	0.00364806	+	0.00129100i
$496$	−11.7121	−	16.1203i	−0.525889	−	0.723824i
$497$	−2.31868	+	7.03854i	−0.104007	+	0.315722i
$498$	−48.1453	−	24.5313i	−2.15744	−	1.09927i
$499$	−4.04729	+	2.33670i	−0.181182	+	0.104605i	−0.587848	−	0.808972i	$-0.700025\pi$
$499$	−4.04729	+	2.33670i	−0.181182	+	0.104605i	0.406666	+	0.913577i	$0.366691\pi$
$500$	−50.7177	+	38.9667i	−2.26816	+	1.74265i
$501$	−8.28078	+	14.3427i	−0.369958	+	0.640786i
$502$	−1.63468	−	31.1916i	−0.0729595	−	1.39215i
$503$	4.28002	+	0.677889i	0.190837	+	0.0302256i	0.251121	−	0.967956i	$-0.419201\pi$
$503$	4.28002	+	0.677889i	0.190837	+	0.0302256i	−0.0602844	+	0.998181i	$0.519201\pi$
$504$	−28.3578	−	18.5803i	−1.26316	−	0.827632i
$505$	25.0741	−	21.4242i	1.11578	−	0.953364i
$506$	0.0178359	−	0.169697i	0.000792903	−	0.00754396i
$507$	1.88783	+	7.04549i	0.0838416	+	0.312901i
$508$	−7.19946	+	18.7552i	−0.319424	+	0.832129i
$509$	−21.5543	+	4.58150i	−0.955376	+	0.203071i	−0.659120	−	0.752037i	$-0.729071\pi$
$509$	−21.5543	+	4.58150i	−0.955376	+	0.203071i	−0.296255	+	0.955109i	$0.595738\pi$
$510$	34.1140	−	8.19746i	1.51059	−	0.362990i
$511$	−17.6801	−	6.86945i	−0.782121	−	0.303886i
$512$	−102.776	+	52.3670i	−4.54210	+	2.31432i
$513$	8.08551	−	12.4506i	0.356984	−	0.549707i
$514$	67.2482	+	14.2941i	2.96619	+	0.630484i
$515$	32.3943	−	0.854936i	1.42746	−	0.0376730i
$516$	15.4045	+	72.4725i	0.678145	+	3.19042i
$517$	0.106687	−	0.0168976i	0.00469211	−	0.000743157i
$518$	3.43797	−	0.347203i	0.151056	−	0.0152552i
$519$	2.91545	−	4.01278i	0.127974	−	0.176141i
$520$	−17.9961	−	60.7081i	−0.789182	−	2.66222i
$521$	−32.4060	+	3.40601i	−1.41973	+	0.149220i	−0.783076	−	0.621926i	$-0.786350\pi$
$521$	−32.4060	+	3.40601i	−1.41973	+	0.149220i	−0.636658	+	0.771146i	$0.719684\pi$
$522$	1.74059	−	2.14945i	0.0761837	−	0.0940790i
$523$	28.0540	−	1.47025i	1.22671	−	0.0642894i	0.572056	−	0.820214i	$-0.306146\pi$
$523$	28.0540	−	1.47025i	1.22671	−	0.0642894i	0.654658	+	0.755925i	$0.272813\pi$
$524$	109.953			4.80331
$525$	−11.7925	+	13.0010i	−0.514669	+	0.567408i
$526$	57.6072			2.51180
$527$	−4.89962	+	0.256778i	−0.213431	+	0.0111854i
$528$	0.448332	−	0.553644i	0.0195111	−	0.0240943i
$529$	18.9874	−	1.99566i	0.825540	−	0.0867678i
$530$	−54.0960	+	37.1955i	−2.34978	+	1.61567i
$531$	1.72668	−	2.37657i	0.0749314	−	0.103134i
$532$	−23.3471	−	32.4112i	−1.01223	−	1.40520i
$533$	9.53908	−	1.51084i	0.413183	−	0.0654418i
$534$	−3.58013	−	16.8432i	−0.154927	−	0.728876i
$535$	12.3696	+	8.49768i	0.534787	+	0.367387i
$536$	−104.926	−	22.3028i	−4.53212	−	0.963332i
$537$	−7.10562	+	10.9417i	−0.306630	+	0.472169i
$538$	20.9468	−	10.6730i	0.903083	−	0.460144i
$539$	0.110253	−	0.187424i	0.00474895	−	0.00807294i
$540$	46.7198	−	54.7246i	2.01050	−	2.35497i
$541$	5.40569	−	1.14901i	0.232409	−	0.0494000i	−0.0902350	−	0.995921i	$-0.528762\pi$
$541$	5.40569	−	1.14901i	0.232409	−	0.0494000i	0.322644	+	0.946521i	$0.395428\pi$
$542$	16.9811	−	44.2372i	0.729399	−	1.90015i
$543$	−4.47698	−	16.7083i	−0.192126	−	0.717023i
$544$	−12.1669	+	115.761i	−0.521653	+	4.96320i
$545$	−2.02872	−	4.89492i	−0.0869009	−	0.209675i
$546$	−12.0327	−	23.8551i	−0.514952	−	1.02090i
$547$	15.7780	+	2.49899i	0.674619	+	0.106849i	0.484339	−	0.874881i	$-0.339060\pi$
$547$	15.7780	+	2.49899i	0.674619	+	0.106849i	0.190280	+	0.981730i	$0.439060\pi$
$548$	−4.96738	−	94.7832i	−0.212196	−	4.04894i
$549$	−0.543133	+	0.940733i	−0.0231803	+	0.0401495i
$550$	0.288910	+	0.320602i	0.0123192	+	0.0136705i
$551$	1.83549	−	1.05972i	0.0781946	−	0.0451457i
$552$	−24.1612	−	12.3107i	−1.02837	−	0.523980i
$553$	5.91557	+	28.3984i	0.251556	+	1.20762i
$554$	4.56025	+	6.27664i	0.193746	+	0.266669i
$555$	−0.0362186	+	1.39408i	−0.00153739	+	0.0591754i
$556$	14.1820	+	31.8533i	0.601450	+	1.35088i
$557$	−20.7131	+	5.55006i	−0.877642	+	0.235163i	−0.669389	−	0.742912i	$-0.733444\pi$
$557$	−20.7131	+	5.55006i	−0.877642	+	0.235163i	−0.208252	+	0.978075i	$0.566778\pi$
$558$	−3.08558	+	2.49866i	−0.130623	+	0.105777i
$559$	8.26224	−	25.4286i	0.349456	−	1.07551i
$560$	−48.4443	−	90.0514i	−2.04714	−	3.80537i
$561$	−0.0542065	−	0.166830i	−0.00228860	−	0.00704359i
$562$	−13.6333	−	8.85354i	−0.575084	−	0.373464i
$563$	0.819018	−	15.6278i	0.0345175	−	0.658633i	−0.925509	−	0.378725i	$-0.876363\pi$
$563$	0.819018	−	15.6278i	0.0345175	−	0.658633i	0.960027	−	0.279908i	$-0.0903040\pi$
$564$	5.48753	−	25.8168i	0.231067	−	1.08708i
$565$	−10.2733	+	1.35466i	−0.432202	+	0.0569908i
$566$	43.0510	+	13.9881i	1.80957	+	0.587965i
$567$	4.98931	−	8.56107i	0.209531	−	0.359531i
$568$	20.4754	−	20.4754i	0.859128	−	0.859128i
$569$	−22.1158	−	2.32446i	−0.927142	−	0.0974466i	−0.371093	−	0.928596i	$-0.621017\pi$
$569$	−22.1158	−	2.32446i	−0.927142	−	0.0974466i	−0.556050	+	0.831149i	$0.687684\pi$
$570$	19.1182	−	10.3854i	0.800772	−	0.434997i
$571$	−2.15410	−	20.4949i	−0.0901462	−	0.857684i	−0.942385	−	0.334531i	$-0.891422\pi$
$571$	−2.15410	−	20.4949i	−0.0901462	−	0.857684i	0.852239	−	0.523153i	$-0.175244\pi$
$572$	−0.454425	+	0.174437i	−0.0190004	+	0.00729359i
$573$	−6.20175	+	12.1716i	−0.259082	+	0.508477i
$574$	24.2370	−	9.19070i	1.01163	−	0.383612i
$575$	5.80657	−	7.99897i	0.242151	−	0.333580i
$576$	25.6734	+	44.4677i	1.06973	+	1.85282i
$577$	−11.4883	+	7.46057i	−0.478263	+	0.310588i	−0.761162	−	0.648562i	$-0.775371\pi$
$577$	−11.4883	+	7.46057i	−0.478263	+	0.310588i	0.282899	+	0.959150i	$0.408704\pi$
$578$	2.40284	+	1.94579i	0.0999452	+	0.0809340i
$579$	−23.3545	−	10.3981i	−0.970580	−	0.432130i
$580$	9.48992	−	3.93314i	0.394048	−	0.163315i
$581$	27.3078	+	27.5310i	1.13292	+	1.14218i
$582$	−0.681731	−	0.681731i	−0.0282587	−	0.0282587i
$583$	0.206562	+	0.255083i	0.00855493	+	0.0105645i
$584$	49.5928	+	55.0784i	2.05217	+	2.27916i
$585$	−7.15571	+	2.53562i	−0.295852	+	0.104835i
$586$	57.6262	+	51.8869i	2.38052	+	2.14343i
$587$	−1.68807	−	3.31302i	−0.0696741	−	0.136743i	0.853542	−	0.521023i	$-0.174450\pi$
$587$	−1.68807	−	3.31302i	−0.0696741	−	0.136743i	−0.923216	+	0.384280i	$0.874450\pi$
$588$	−33.1001	−	41.5626i	−1.36503	−	1.71401i
$589$	−2.89359	+	0.940186i	−0.119228	+	0.0387397i
$590$	13.2894	−	6.34208i	0.547116	−	0.261099i
$591$	17.6992	−	15.9364i	0.728048	−	0.655538i
$592$	−7.58460	−	2.91146i	−0.311725	−	0.119660i
$593$	−0.804417	+	3.00212i	−0.0330334	+	0.123282i	−0.980474	−	0.196650i	$-0.936994\pi$
$593$	−0.804417	+	3.00212i	−0.0330334	+	0.123282i	0.947440	+	0.319933i	$0.103660\pi$
$594$	−0.392803	−	0.285388i	−0.0161169	−	0.0117096i
$595$	−25.0928	−	2.07246i	−1.02871	−	0.0849625i
$596$	14.1442	−	10.2764i	0.579371	−	0.420938i
$597$	−3.31490	−	8.63560i	−0.135670	−	0.353432i
$598$	8.19447	+	12.6184i	0.335097	+	0.516004i
$599$	3.72331	+	2.14965i	0.152130	+	0.0878325i	0.574133	−	0.818762i	$-0.305339\pi$
$599$	3.72331	+	2.14965i	0.152130	+	0.0878325i	−0.422002	+	0.906595i	$0.638673\pi$
$600$	64.0198	−	24.6051i	2.61360	−	1.00450i
$601$		−	24.6722i		−	1.00640i	−0.864169	−	0.503201i	$-0.832156\pi$
$601$		−	24.6722i		−	1.00640i	0.864169	−	0.503201i	$-0.167844\pi$
$602$	7.79136	−	71.3356i	0.317552	−	2.90742i
$603$	−2.01193	+	12.7028i	−0.0819323	+	0.517300i
$604$	−18.7016	+	42.0044i	−0.760955	+	1.70913i
$605$	−16.9261	+	17.8438i	−0.688145	+	0.725452i
$606$	−49.6760	+	22.1172i	−2.01795	+	0.898448i
$607$	21.6785	+	5.80874i	0.879904	+	0.235769i	0.670366	−	0.742031i	$-0.266137\pi$
$607$	21.6785	+	5.80874i	0.879904	+	0.235769i	0.209538	+	0.977800i	$0.432804\pi$
$608$	11.2915	+	71.2920i	0.457932	+	2.89127i
$609$	2.37060	−	1.52580i	0.0960616	−	0.0618287i
$610$	−4.64210	+	2.84600i	−0.187953	+	0.115231i
$611$	−6.37317	+	7.07813i	−0.257831	+	0.286350i
$612$	30.1358	+	1.57935i	1.21817	+	0.0638415i
$613$	−49.2257	−	2.57981i	−1.98821	−	0.104198i	−0.989127	−	0.147065i	$-0.953017\pi$
$613$	−49.2257	−	2.57981i	−1.98821	−	0.104198i	−0.999081	+	0.0428675i	$0.986351\pi$
$614$	−34.6266	+	38.4568i	−1.39742	+	1.55199i
$615$	2.44421	+	10.1717i	0.0985600	+	0.410161i
$616$	−0.714468	+	0.459857i	−0.0287867	+	0.0185282i
$617$	4.28721	+	27.0684i	0.172597	+	1.08973i	0.910100	+	0.414389i	$0.136005\pi$
$617$	4.28721	+	27.0684i	0.172597	+	1.08973i	−0.737503	+	0.675344i	$0.763995\pi$
$618$	−51.6088	−	13.8285i	−2.07601	−	0.556265i
$619$	−12.2712	+	5.46350i	−0.493222	+	0.219597i	−0.638247	−	0.769831i	$-0.720340\pi$
$619$	−12.2712	+	5.46350i	−0.493222	+	0.219597i	0.145025	+	0.989428i	$0.453674\pi$
$620$	−14.4992	+	2.69034i	−0.582301	+	0.108047i
$621$	−4.52296	+	10.1587i	−0.181500	+	0.407656i
$622$	4.77413	−	30.1427i	0.191425	−	1.20861i
$623$	−1.34170	+	12.2843i	−0.0537541	+	0.492158i
$624$			62.8173i			2.51471i
$625$	5.21789	+	24.4494i	0.208716	+	0.977976i
$626$	−45.3599	−	26.1886i	−1.81295	−	1.04671i
$627$	−0.0592450	−	0.0912293i	−0.00236602	−	0.00364335i
$628$	−4.64151	−	12.0916i	−0.185217	−	0.482506i
$629$	−1.61838	+	1.17582i	−0.0645290	+	0.0468830i
$630$	−17.4138	+	10.5788i	−0.693782	+	0.421471i
$631$	−5.43708	−	3.95027i	−0.216447	−	0.157258i	0.474279	−	0.880375i	$-0.342709\pi$
$631$	−5.43708	−	3.95027i	−0.216447	−	0.157258i	−0.690726	+	0.723117i	$0.742709\pi$
$632$	29.3364	−	109.485i	1.16694	−	4.35508i
$633$	−18.6229	−	7.14866i	−0.740194	−	0.284134i
$634$	27.5026	−	24.7634i	1.09227	−	0.983482i
$635$	5.40653	+	5.69495i	0.214552	+	0.225997i
$636$	76.2764	−	24.7837i	3.02456	−	0.982738i
$637$	2.84518	+	18.9615i	0.112730	+	0.751282i
$638$	−0.0314693	−	0.0617619i	−0.00124588	−	0.00244518i
$639$	−2.58002	−	2.32306i	−0.102064	−	0.0918987i
$640$	3.56351	+	135.025i	0.140860	+	5.33732i
$641$	5.70525	+	6.33632i	0.225344	+	0.250270i	0.845206	−	0.534441i	$-0.179478\pi$
$641$	5.70525	+	6.33632i	0.225344	+	0.250270i	−0.619862	+	0.784711i	$0.712811\pi$
$642$	−15.5716	−	19.2294i	−0.614564	−	0.758923i
$643$	20.6442	+	20.6442i	0.814129	+	0.814129i	0.985250	−	0.171121i	$-0.0547389\pi$
$643$	20.6442	+	20.6442i	0.814129	+	0.814129i	−0.171121	+	0.985250i	$0.554739\pi$
$644$	21.0707	+	21.2429i	0.830302	+	0.837089i
$645$	28.1620	+	6.75498i	1.10888	+	0.265977i
$646$	28.5111	+	12.6940i	1.12176	+	0.499438i
$647$	13.4357	+	10.8801i	0.528214	+	0.427739i	0.855972	−	0.517023i	$-0.172960\pi$
$647$	13.4357	+	10.8801i	0.528214	+	0.427739i	−0.327758	+	0.944762i	$0.606293\pi$
$648$	−32.4718	+	21.0875i	−1.27561	+	0.828394i
$649$	−0.0368109	−	0.0637584i	−0.00144495	−	0.00250274i
$650$	−37.5884	−	5.93758i	−1.47434	−	0.232891i
$651$	−3.78407	+	1.43493i	−0.148310	+	0.0562392i
$652$	24.6970	−	48.4706i	0.967210	−	1.89826i
$653$	29.6865	−	11.3956i	1.16172	−	0.445943i	0.300305	−	0.953843i	$-0.402911\pi$
$653$	29.6865	−	11.3956i	1.16172	−	0.445943i	0.861416	+	0.507900i	$0.169578\pi$
$654$	0.913192	+	8.68845i	0.0357087	+	0.339745i
$655$	18.4946	−	38.7953i	0.722644	−	1.51586i
$656$	−60.6098	−	6.37035i	−2.36641	−	0.248720i
$657$	6.28340	−	6.28340i	0.245139	−	0.245139i
$658$	−12.8715	+	22.0859i	−0.501782	+	0.861000i
$659$	−11.8279	−	3.84312i	−0.460750	−	0.149707i	0.0694392	−	0.997586i	$-0.477879\pi$
$659$	−11.8279	−	3.84312i	−0.460750	−	0.149707i	−0.530189	+	0.847880i	$0.677879\pi$
$660$	−0.227079	−	0.475829i	−0.00883903	−	0.0185216i
$661$	9.79486	−	46.0812i	0.380976	−	1.79235i	−0.201485	−	0.979492i	$-0.564577\pi$
$661$	9.79486	−	46.0812i	0.380976	−	1.79235i	0.582461	−	0.812859i	$-0.302090\pi$
$662$	0.887012	−	16.9252i	0.0344747	−	0.657816i
$663$	12.9722	+	8.42421i	0.503797	+	0.327169i
$664$	−46.8222	−	144.104i	−1.81705	−	5.59232i
$665$	−15.3629	+	2.78598i	−0.595749	+	0.108036i
$666$	−0.500244	+	1.53959i	−0.0193841	+	0.0596580i
$667$	−1.23377	+	0.999090i	−0.0477719	+	0.0386849i
$668$	−68.9714	+	18.4808i	−2.66858	+	0.715044i
$669$	12.7975	+	28.7436i	0.494779	+	1.11129i
$670$	−39.2356	+	51.1545i	−1.51580	+	1.97627i
$671$	0.0160018	+	0.0220246i	0.000617743	+	0.000850250i
$672$	19.5795	+	93.9938i	0.755295	+	3.62589i
$673$	32.2488	+	16.4316i	1.24310	+	0.633391i	0.946836	−	0.321716i	$-0.104259\pi$
$673$	32.2488	+	16.4316i	1.24310	+	0.633391i	0.296263	+	0.955106i	$0.404259\pi$
$674$	−16.1842	+	9.34397i	−0.623393	+	0.359916i
$675$	−11.4503	−	25.6894i	−0.440722	−	0.988784i
$676$	−15.7239	+	27.2347i	−0.604767	+	1.04749i
$677$	1.99722	+	38.1092i	0.0767594	+	1.46466i	0.717317	+	0.696747i	$0.245370\pi$
$677$	1.99722	+	38.1092i	0.0767594	+	1.46466i	−0.640557	+	0.767910i	$0.721297\pi$
$678$	16.8746	+	2.67268i	0.648066	+	0.102644i
$679$	0.311596	+	0.617744i	0.0119580	+	0.0237069i
$680$	83.8956	+	51.3876i	3.21725	+	1.97062i
$681$	3.83388	−	36.4769i	0.146914	−	1.39780i
$682$	0.0257540	+	0.0961154i	0.000986173	+	0.00368045i
$683$	−10.3500	+	26.9627i	−0.396033	+	1.03170i	0.580104	+	0.814543i	$0.303012\pi$
$683$	−10.3500	+	26.9627i	−0.396033	+	1.03170i	−0.976136	+	0.217158i	$0.930321\pi$
$684$	18.3045	−	3.89073i	0.699888	−	0.148766i
$685$	−34.2784	−	14.1903i	−1.30971	−	0.542185i
$686$	17.8538	+	48.2640i	0.681660	+	1.84273i
$687$	−13.9280	+	7.09665i	−0.531385	+	0.270754i
$688$	−91.8895	+	141.497i	−3.50326	+	5.39454i
$689$	−28.3097	−	6.01741i	−1.07851	−	0.229245i
$690$	−12.9272	+	9.92363i	−0.492131	+	0.377786i
$691$	−5.59023	−	26.3000i	−0.212662	−	1.00050i	−0.946881	−	0.321585i	$-0.895785\pi$
$691$	−5.59023	−	26.3000i	−0.212662	−	1.00050i	0.734219	−	0.678913i	$-0.237549\pi$
$692$	21.1218	−	3.34537i	0.802931	−	0.127172i
$693$	0.0595422	+	0.0826583i	0.00226182	+	0.00313993i
$694$	−28.2544	+	38.8889i	−1.07252	+	1.47620i
$695$	13.6245	+	0.353967i	0.516805	+	0.0134267i
$696$	−10.9555	+	1.15147i	−0.415266	+	0.0436462i
$697$	−9.44368	+	11.6620i	−0.357705	+	0.441729i
$698$	−98.2165	+	5.14731i	−3.71755	+	0.194828i
$699$	−26.1428			−0.988813
$700$	−75.5870	+	3.68404i	−2.85692	+	0.139244i
$701$	7.94356			0.300024			0.150012	−	0.988684i	$-0.452069\pi$
$701$	7.94356			0.300024			0.150012	+	0.988684i	$0.452069\pi$
$702$	42.7536	−	2.24062i	1.61363	−	0.0845668i
$703$	−0.780671	+	0.964048i	−0.0294436	+	0.0363598i
$704$	1.27980	−	0.134512i	0.0482343	−	0.00506963i
$705$	−8.18606	−	6.27871i	−0.308305	−	0.236470i
$706$	−39.5870	+	54.4868i	−1.48988	+	2.05064i
$707$	38.8254	−	3.92101i	1.46018	−	0.147465i
$708$	−17.7677	+	2.81413i	−0.667751	+	0.105761i
$709$	10.2251	+	48.1053i	0.384012	+	1.80663i	0.567229	+	0.823560i	$0.308015\pi$
$709$	10.2251	+	48.1053i	0.384012	+	1.80663i	−0.183217	+	0.983072i	$0.558651\pi$
$710$	−5.81251	−	16.4033i	−0.218140	−	0.615605i
$711$	−13.2928	−	2.82547i	−0.498519	−	0.105964i
$712$	26.2982	−	40.4956i	0.985565	−	1.51764i
$713$	2.03059	−	1.03464i	0.0760463	−	0.0387475i
$714$	38.6951	+	15.0346i	1.44813	+	0.562657i
$715$	−0.0148888	+	0.189678i	−0.000556810	+	0.00709357i
$716$	−55.0201	+	11.6949i	−2.05620	+	0.437059i
$717$	0.898981	−	2.34193i	0.0335731	−	0.0874608i
$718$	11.7973	+	44.0280i	0.440270	+	1.64311i
$719$	2.52199	−	23.9951i	0.0940544	−	0.894868i	−0.841160	−	0.540786i	$-0.818127\pi$
$719$	2.52199	−	23.9951i	0.0940544	−	0.894868i	0.935214	−	0.354082i	$-0.115207\pi$
$720$	47.7564	−	3.76838i	1.77978	−	0.140439i
$721$	32.0717	+	21.0137i	1.19441	+	0.782591i
$722$	−33.0283	−	5.23116i	−1.22919	−	0.194684i
$723$	0.194655	+	3.71423i	0.00723928	+	0.138134i
$724$	37.2892	−	64.5868i	1.38584	−	2.40035i
$725$	0.208500	−	4.00996i	0.00774351	−	0.148926i
$726$	35.1181	−	20.2754i	1.30335	−	0.752491i
$727$	−8.05183	−	4.10261i	−0.298626	−	0.152158i	0.298258	−	0.954485i	$-0.403595\pi$
$727$	−8.05183	−	4.10261i	−0.298626	−	0.152158i	−0.596884	+	0.802328i	$0.703595\pi$
$728$	23.4415	−	71.1587i	0.868800	−	2.63732i
$729$	15.8897	+	21.8703i	0.588506	+	0.810009i
$730$	42.7059	−	12.6596i	1.58062	−	0.468553i
$731$	16.8971	+	37.9515i	0.624961	+	1.40369i
$732$	6.42538	−	1.72168i	0.237489	−	0.0636350i
$733$	13.3389	−	10.8017i	0.492685	−	0.398968i	−0.350525	−	0.936553i	$-0.613997\pi$
$733$	13.3389	−	10.8017i	0.492685	−	0.398968i	0.843209	+	0.537585i	$0.180663\pi$
$734$	−7.33839	+	22.5852i	−0.270865	+	0.833636i
$735$	−20.2324	+	4.68788i	−0.746282	+	0.172915i
$736$	−16.7076	−	51.4207i	−0.615850	−	1.89539i
$737$	0.270325	+	0.175551i	0.00995757	+	0.00646652i
$738$	−0.635546	+	12.1269i	−0.0233948	+	0.446399i
$739$	−8.49369	+	39.9597i	−0.312445	+	1.46994i	0.489217	+	0.872162i	$0.337283\pi$
$739$	−8.49369	+	39.9597i	−0.312445	+	1.46994i	−0.801662	+	0.597777i	$0.796051\pi$
$740$	−4.36050	+	4.13966i	−0.160295	+	0.152177i
$741$	9.12222	+	2.96399i	0.335113	+	0.108885i
$742$	−77.6771	−	0.316168i	−2.85162	−	0.0116069i
$743$	16.4859	−	16.4859i	0.604808	−	0.604808i	−0.336777	−	0.941584i	$-0.609337\pi$
$743$	16.4859	−	16.4859i	0.604808	−	0.604808i	0.941584	+	0.336777i	$0.109337\pi$
$744$	15.7268	+	1.65295i	0.576573	+	0.0606002i
$745$	−1.24675	−	6.71914i	−0.0456773	−	0.246170i
$746$	−7.01731	−	66.7653i	−0.256922	−	2.44445i
$747$	−16.9599	+	6.51029i	−0.620530	+	0.238199i
$748$	0.343352	−	0.673867i	0.0125542	−	0.0246390i
$749$	6.29596	+	16.6032i	0.230050	+	0.606669i
$750$	3.20869	−	41.0942i	0.117165	−	1.50055i
$751$	−8.88707	−	15.3929i	−0.324294	−	0.561693i	0.657075	−	0.753825i	$-0.271793\pi$
$751$	−8.88707	−	15.3929i	−0.324294	−	0.561693i	−0.981369	+	0.192132i	$0.938460\pi$
$752$	50.4055	−	32.7337i	1.83810	−	1.19368i
$753$	11.5912	+	9.38638i	0.422408	+	0.342059i
$754$	5.58369	+	2.48602i	0.203346	+	0.0905355i
$755$	11.6750	+	13.6639i	0.424895	+	0.497281i
$756$	82.3263	−	21.7005i	2.99418	−	0.789240i
$757$	−0.545391	−	0.545391i	−0.0198226	−	0.0198226i	0.697126	−	0.716949i	$-0.254462\pi$
$757$	−0.545391	−	0.545391i	−0.0198226	−	0.0198226i	−0.716949	+	0.697126i	$0.754462\pi$
$758$	−22.6961	−	28.0273i	−0.824359	−	1.01800i
$759$	0.0545211	+	0.0605518i	0.00197899	+	0.00219789i
$760$	58.5000	+	17.3154i	2.12202	+	0.628096i
$761$	12.6470	+	11.3874i	0.458454	+	0.412794i	0.865730	−	0.500511i	$-0.166855\pi$
$761$	12.6470	+	11.3874i	0.458454	+	0.412794i	−0.407276	+	0.913305i	$0.633521\pi$
$762$	−5.87786	−	11.5360i	−0.212933	−	0.417904i
$763$	1.32845	−	6.12712i	0.0480930	−	0.221817i
$764$	−56.0141	+	18.2001i	−2.02652	+	0.658457i
$765$	5.62625	−	10.3673i	0.203417	−	0.374832i
$766$	−4.66356	+	4.19909i	−0.168501	+	0.151719i
$767$	6.06052	+	2.32642i	0.218833	+	0.0840020i
$768$	29.1874	−	108.929i	1.05321	−	3.93063i
$769$	−5.73647	−	4.16779i	−0.206863	−	0.150294i	0.479530	−	0.877525i	$-0.340807\pi$
$769$	−5.73647	−	4.16779i	−0.206863	−	0.150294i	−0.686393	+	0.727231i	$0.740807\pi$
$770$	0.0646952	+	0.506529i	0.00233145	+	0.0182540i
$771$	−26.5599	+	19.2969i	−0.956533	+	0.694962i
$772$	−39.4997	−	102.900i	−1.42162	−	3.70346i
$773$	−0.963937	−	1.48433i	−0.0346704	−	0.0533877i	0.820910	−	0.571057i	$-0.193466\pi$
$773$	−0.963937	−	1.48433i	−0.0346704	−	0.0533877i	−0.855581	+	0.517669i	$0.826800\pi$
$774$	29.1143	+	16.8091i	1.04649	+	0.604192i
$775$	−1.48958	+	5.56836i	−0.0535074	+	0.200021i
$776$		−	2.70349i		−	0.0970495i
$777$	−0.975303	+	1.33096i	−0.0349888	+	0.0477481i
$778$	12.0117	−	75.8386i	0.430639	−	2.71894i
$779$	−3.78492	+	8.50107i	−0.135609	+	0.304582i
$780$	41.9650	+	20.0057i	1.50259	+	0.716319i
$781$	−0.0794865	+	0.0353897i	−0.00284425	+	0.00126634i
$782$	−22.5808	−	6.05050i	−0.807487	−	0.216365i
$783$	0.706678	+	4.46179i	0.0252546	+	0.159451i
$784$	13.6260	−	120.220i	0.486642	−	4.29358i
$785$	−5.04706	−	0.396169i	−0.180137	−	0.0141399i
$786$	−47.4154	+	52.6601i	−1.69125	+	1.87832i
$787$	−17.4691	−	0.915517i	−0.622706	−	0.0326346i	−0.261626	−	0.965169i	$-0.584259\pi$
$787$	−17.4691	−	0.915517i	−0.622706	−	0.0326346i	−0.361080	+	0.932535i	$0.617592\pi$
$788$	102.544	+	5.37409i	3.65297	+	0.191444i
$789$	−18.4069	+	20.4430i	−0.655304	+	0.727788i
$790$	−51.8086	−	44.2303i	−1.84327	−	1.57364i
$791$	−10.9017	−	5.61069i	−0.387619	−	0.199493i
$792$	−0.0622694	−	0.393154i	−0.00221265	−	0.0139701i
$793$	−2.31871	−	0.621295i	−0.0823397	−	0.0220628i
$794$	90.4148	−	40.2553i	3.20870	−	1.42861i
$795$	4.08550	−	31.0818i	0.144898	−	1.10236i
$796$	16.2210	−	36.4330i	0.574939	−	1.29133i
$797$	6.49832	−	41.0288i	0.230182	−	1.45331i	−0.553861	−	0.832609i	$-0.686846\pi$
$797$	6.49832	−	41.0288i	0.230182	−	1.45331i	0.784044	−	0.620706i	$-0.213154\pi$
$798$	25.5909	+	2.79507i	0.905907	+	0.0989443i
$799$		−	14.7988i		−	0.523545i
$800$	124.949	+	55.5696i	4.41763	+	1.96468i
$801$	−5.01359	−	2.89460i	−0.177146	−	0.102276i
$802$	56.2377	+	86.5985i	1.98582	+	3.05790i
$803$	−0.0798092	−	0.207910i	−0.00281641	−	0.00733699i
$804$	63.7174	−	46.2934i	2.24714	−	1.63264i
$805$	11.0395	−	3.86133i	0.389090	−	0.136094i
$806$	−7.09837	−	5.15726i	−0.250029	−	0.181657i
$807$	−2.90554	+	10.8436i	−0.102280	+	0.381714i
$808$	−142.352	−	54.6439i	−5.00793	−	1.92237i
$809$	−24.7545	+	22.2890i	−0.870322	+	0.783641i	−0.977574	−	0.210591i	$-0.932461\pi$
$809$	−24.7545	+	22.2890i	−0.870322	+	0.783641i	0.107253	+	0.994232i	$0.465795\pi$
$810$	3.04201	+	23.0697i	0.106885	+	0.810586i
$811$	−30.7233	+	9.98261i	−1.07884	+	0.350537i	−0.793925	−	0.608016i	$-0.791966\pi$
$811$	−30.7233	+	9.98261i	−1.07884	+	0.350537i	−0.284916	+	0.958552i	$0.591966\pi$
$812$	11.8788	+	2.57550i	0.416865	+	0.0903823i
$813$	10.2725	+	20.1609i	0.360272	+	0.707073i
$814$	0.0301500	+	0.0271472i	0.00105676	+	0.000951508i
$815$	−12.9480	−	16.8670i	−0.453549	−	0.590825i
$816$	−65.3090	−	72.5330i	−2.28627	−	2.53916i
$817$	16.2123	+	20.0205i	0.567196	+	0.700429i
$818$	34.6876	+	34.6876i	1.21282	+	1.21282i
$819$	−8.66698	−	2.36016i	−0.302849	−	0.0824707i
$820$	−23.5584	+	38.4615i	−0.822694	+	1.34313i
$821$	19.6844	+	8.76406i	0.686991	+	0.305868i	0.720385	−	0.693574i	$-0.243965\pi$
$821$	19.6844	+	8.76406i	0.686991	+	0.305868i	−0.0333945	+	0.999442i	$0.510632\pi$
$822$	47.5370	+	38.4947i	1.65804	+	1.34266i
$823$	−23.6833	+	15.3801i	−0.825546	+	0.536116i	−0.886879	−	0.462001i	$-0.847132\pi$
$823$	−23.6833	+	15.3801i	−0.825546	+	0.536116i	0.0613330	+	0.998117i	$0.480465\pi$
$824$	−74.9111	−	129.750i	−2.60965	−	4.52005i
$825$	−0.206085		8.46979e-5i	−0.00717497		2.94880e-6i
$826$	17.1973	+	2.79559i	0.598371	+	0.0972709i
$827$	−14.2955	+	28.0565i	−0.497103	+	0.975619i	0.497059	+	0.867717i	$0.334413\pi$
$827$	−14.2955	+	28.0565i	−0.497103	+	0.975619i	−0.994161	+	0.107902i	$0.965587\pi$
$828$	−13.0862	+	5.02334i	−0.454778	+	0.174573i
$829$	−3.14082	−	29.8829i	−0.109085	−	1.03787i	−0.902940	−	0.429767i	$-0.858596\pi$
$829$	−3.14082	−	29.8829i	−0.109085	−	1.03787i	0.793855	−	0.608107i	$-0.208071\pi$
$830$	−90.2858	−	11.8675i	−3.13387	−	0.411926i
$831$	−3.68449	−	0.387255i	−0.127813	−	0.0134337i
$832$	−80.2351	+	80.2351i	−2.78165	+	2.78165i
$833$	−22.9988	−	18.9362i	−0.796863	−	0.656099i
$834$	−21.3714	−	6.94398i	−0.740030	−	0.240450i
$835$	−5.08064	+	27.4441i	−0.175823	+	0.949743i
$836$	0.0975092	−	0.458745i	0.00337243	−	0.0158660i
$837$	0.339389	−	6.47594i	0.0117310	−	0.223841i
$838$	57.1414	+	37.1080i	1.97392	+	1.28188i
$839$	13.0052	+	40.0259i	0.448990	+	1.38185i	0.878048	+	0.478572i	$0.158845\pi$
$839$	13.0052	+	40.0259i	0.448990	+	1.38185i	−0.429058	+	0.903277i	$0.641155\pi$
$840$	78.8352	+	19.2492i	2.72007	+	0.664160i
$841$	8.76220	−	26.9673i	0.302145	−	0.929906i
$842$	39.2953	−	31.8207i	1.35421	−	1.09661i
$843$	7.49799	−	2.00908i	0.258245	−	0.0691964i
$844$	−34.9810	−	78.5687i	−1.20410	−	2.70445i
$845$	6.96452	+	10.1290i	0.239587	+	0.348447i
$846$	−7.03921	−	9.68864i	−0.242013	−	0.333102i
$847$	−28.4892	+	5.93447i	−0.978900	+	0.203911i
$848$	162.725	+	82.9124i	5.58799	+	2.84722i
$849$	−18.7198	+	10.8079i	−0.642461	+	0.370925i
$850$	49.5751	−	32.2234i	1.70041	−	1.10525i
$851$	0.464598	−	0.804706i	0.0159262	−	0.0275850i
$852$	1.11267	+	21.2311i	0.0381196	+	0.727365i
$853$	−12.7092	−	2.01294i	−0.435154	−	0.0689216i	−0.0649853	−	0.997886i	$-0.520700\pi$
$853$	−12.7092	−	2.01294i	−0.435154	−	0.0689216i	−0.370168	+	0.928965i	$0.620700\pi$
$854$	−6.43244	−	0.363369i	−0.220114	−	0.0124342i
$855$	1.70611	−	7.11291i	0.0583478	−	0.243256i
$856$	7.25260	−	69.0038i	0.247889	−	2.35850i
$857$	3.02647	+	11.2950i	0.103382	+	0.385828i	0.998157	−	0.0606906i	$-0.0193303\pi$
$857$	3.02647	+	11.2950i	0.103382	+	0.385828i	−0.894774	+	0.446519i	$0.852664\pi$
$858$	0.112419	−	0.292863i	0.00383794	−	0.00999816i
$859$	4.08883	−	0.869107i	0.139509	−	0.0296535i	−0.137628	−	0.990484i	$-0.543948\pi$
$859$	4.08883	−	0.869107i	0.139509	−	0.0296535i	0.277137	+	0.960830i	$0.410614\pi$
$860$	65.2627	+	106.450i	2.22544	+	3.62991i
$861$	−4.48283	+	11.5376i	−0.152774	+	0.393200i
$862$	27.3743	−	13.9479i	0.932373	−	0.475068i
$863$	17.8835	−	27.5381i	0.608760	−	0.937409i	−0.391094	−	0.920351i	$-0.627903\pi$
$863$	17.8835	−	27.5381i	0.608760	−	0.937409i	0.999855	−	0.0170580i	$-0.00543000\pi$
$864$	−150.485	−	31.9865i	−5.11959	−	1.08820i
$865$	2.37243	−	8.01524i	0.0806651	−	0.272526i
$866$	22.2252	+	104.561i	0.755243	+	3.55314i
$867$	−1.45826	+	0.230966i	−0.0495252	+	0.00784403i
$868$	−15.9110	−	7.16176i	−0.540053	−	0.243086i
$869$	−0.200191	+	0.275540i	−0.00679103	+	0.00934705i
$870$	−2.20866	+	6.24115i	−0.0748807	+	0.211595i
$871$	−28.2658	+	2.97086i	−0.957751	+	0.100664i
$872$	−15.4169	+	19.0382i	−0.522081	+	0.644716i
$873$	−0.323691	+	0.0169639i	−0.0109553	+	0.000574142i
$874$	−14.4967			−0.490358
$875$	−11.4142	+	27.2895i	−0.385872	+	0.922552i
$876$	−54.4163			−1.83856
$877$	39.2447	−	2.05673i	1.32520	−	0.0694508i	0.623444	−	0.781868i	$-0.285733\pi$
$877$	39.2447	−	2.05673i	1.32520	−	0.0694508i	0.701757	+	0.712417i	$0.252399\pi$
$878$	−44.1956	+	54.5770i	−1.49153	+	1.84188i
$879$	−36.8260	+	3.87056i	−1.24211	+	0.130551i
$880$	0.400532	−	1.13181i	0.0135019	−	0.0381532i
$881$	21.0874	−	29.0243i	0.710453	−	0.977854i	−0.289335	−	0.957228i	$-0.593434\pi$
$881$	21.0874	−	29.0243i	0.710453	−	0.977854i	0.999787	−	0.0206263i	$-0.00656601\pi$
$882$	−24.0642	−	1.45768i	−0.810285	−	0.0490825i
$883$	−37.2287	+	5.89645i	−1.25285	+	0.198431i	−0.747370	−	0.664408i	$-0.768684\pi$
$883$	−37.2287	+	5.89645i	−1.25285	+	0.198431i	−0.505477	+	0.862840i	$0.668684\pi$
$884$	13.8651	+	65.2303i	0.466334	+	2.19393i
$885$	−1.99569	+	6.74243i	−0.0670845	+	0.226644i
$886$	20.6303	+	4.38510i	0.693088	+	0.147320i
$887$	23.3500	−	35.9558i	0.784016	−	1.20728i	−0.190219	−	0.981742i	$-0.560920\pi$
$887$	23.3500	−	35.9558i	0.784016	−	1.20728i	0.974235	−	0.225537i	$-0.0724136\pi$
$888$	5.74476	−	2.92710i	0.192781	−	0.0982271i
$889$	1.41612	+	9.18275i	0.0474950	+	0.307980i
$890$	−15.1676	−	24.7398i	−0.508419	−	0.829282i
$891$	0.113798	−	0.0241886i	0.00381239	−	0.000810348i
$892$	−48.6144	+	126.645i	−1.62773	+	4.24038i
$893$	−2.37519	−	8.86432i	−0.0794826	−	0.296633i
$894$	−1.17777	+	11.2057i	−0.0393904	+	0.374774i
$895$	−5.12829	+	21.3802i	−0.171420	+	0.714661i
$896$	−87.5885	+	133.680i	−2.92613	+	4.46594i
$897$	−7.09619	−	1.12393i	−0.236935	−	0.0375268i
$898$	−0.381612	−	7.28159i	−0.0127346	−	0.242990i
$899$	0.462905	−	0.801774i	0.0154387	−	0.0267407i
$900$	12.6917	−	33.1037i	0.423057	−	1.10346i
$901$	38.9443	−	22.4845i	1.29742	−	0.749068i
$902$	0.271170	+	0.138168i	0.00902898	+	0.00460050i
$903$	22.8252	+	25.5584i	0.759574	+	0.850529i
$904$	28.1598	+	38.7586i	0.936580	+	1.28909i
$905$	−16.5163	−	24.0208i	−0.549020	−	0.798478i
$906$	−12.0526	−	27.0705i	−0.400420	−	0.899358i
$907$	36.2880	−	9.72335i	1.20492	−	0.322858i	0.400156	−	0.916447i	$-0.368956\pi$
$907$	36.2880	−	9.72335i	1.20492	−	0.322858i	0.804769	+	0.593589i	$0.202289\pi$
$908$	122.894	−	99.5175i	4.07838	−	3.30260i
$909$	−5.64932	+	17.3868i	−0.187376	+	0.576685i
$910$	−32.5411	−	31.1203i	−1.07873	−	1.03163i
$911$	−3.26942	−	10.0623i	−0.108321	−	0.333377i	0.882175	−	0.470922i	$-0.156079\pi$
$911$	−3.26942	−	10.0623i	−0.108321	−	0.333377i	−0.990496	+	0.137545i	$0.956079\pi$
$912$	−50.7607	−	32.9644i	−1.68085	−	1.09156i
$913$	−0.0238279	+	0.454664i	−0.000788589	+	0.0150472i
$914$	16.3109	−	76.7369i	0.539517	−	2.53823i
$915$	0.473313	−	2.55670i	0.0156472	−	0.0845218i
$916$	−64.0969	−	20.8263i	−2.11782	−	0.688122i
$917$	44.1426	−	25.2468i	1.45772	−	0.833721i
$918$	−47.0366	+	47.0366i	−1.55244	+	1.55244i
$919$	23.3442	+	2.45357i	0.770054	+	0.0809359i	0.481404	−	0.876499i	$-0.340127\pi$
$919$	23.3442	+	2.45357i	0.770054	+	0.0809359i	0.288650	+	0.957435i	$0.406794\pi$
$920$	−45.3089	−	5.95556i	−1.49379	−	0.196349i
$921$	−2.58302	−	24.5758i	−0.0851133	−	0.809799i
$922$	56.2092	−	21.5767i	1.85115	−	0.710591i
$923$	3.48306	−	6.83590i	0.114646	−	0.225006i
$924$	0.100096	−	0.615751i	0.00329292	−	0.0202567i
$925$	0.727162	+	2.23485i	0.0239090	+	0.0734814i
$926$	4.18033	+	7.24055i	0.137374	+	0.237939i
$927$	−15.0650	+	9.78333i	−0.494800	+	0.321327i
$928$	−17.0692	−	13.8224i	−0.560324	−	0.453742i
$929$	−34.1723	−	15.2145i	−1.12116	−	0.499171i	−0.239421	−	0.970916i	$-0.576958\pi$
$929$	−34.1723	−	15.2145i	−1.12116	−	0.499171i	−0.881735	+	0.471745i	$0.843624\pi$
$930$	4.96404	−	8.10431i	0.162777	−	0.265751i
$931$	−16.8152	−	7.65124i	−0.551097	−	0.250759i
$932$	−79.7006	−	79.7006i	−2.61068	−	2.61068i
$933$	9.17122	+	11.3255i	0.300252	+	0.370781i
$934$	59.2890	+	65.8471i	1.94000	+	2.15458i
$935$	−0.180011	−	0.234495i	−0.00588698	−	0.00766880i
$936$	26.0836	+	23.4858i	0.852569	+	0.767657i
$937$	25.4630	+	49.9739i	0.831840	+	1.63258i	0.773083	+	0.634305i	$0.218714\pi$
$937$	25.4630	+	49.9739i	0.831840	+	1.63258i	0.0587564	+	0.998272i	$0.481286\pi$
$938$	−72.6423	+	23.2765i	−2.37186	+	0.760004i
$939$	23.7871	−	7.72889i	0.776262	−	0.252223i
$940$	−5.81485	−	44.0982i	−0.189660	−	1.43832i
$941$	−6.04233	+	5.44054i	−0.196974	+	0.177357i	−0.761716	−	0.647912i	$-0.775643\pi$
$941$	−6.04233	+	5.44054i	−0.196974	+	0.177357i	0.564741	+	0.825268i	$0.308976\pi$
$942$	7.79263	+	2.99131i	0.253898	+	0.0974622i
$943$	1.80406	−	6.73283i	0.0587482	−	0.219251i
$944$	−33.1404	−	24.0779i	−1.07863	−	0.783669i
$945$	6.19098	−	32.6978i	0.201393	−	1.06366i
$946$	0.681628	−	0.495232i	0.0221617	−	0.0161014i
$947$	5.93955	+	15.4730i	0.193009	+	0.502806i	0.995598	−	0.0937264i	$-0.0298779\pi$
$947$	5.93955	+	15.4730i	0.193009	+	0.502806i	−0.802589	+	0.596533i	$0.796545\pi$
$948$	45.3253	+	69.7948i	1.47210	+	2.26683i
$949$	17.0062	+	9.81851i	0.552043	+	0.318722i
$950$	24.5231	−	27.2581i	0.795633	−	0.884371i
$951$			17.6723i			0.573064i
$952$	46.9142	+	106.536i	1.52050	+	3.45285i
$953$	6.39977	−	40.4065i	0.207309	−	1.30890i	−0.636093	−	0.771613i	$-0.719450\pi$
$953$	6.39977	−	40.4065i	0.207309	−	1.30890i	0.843402	−	0.537284i	$-0.180550\pi$
$954$	14.8014	−	33.2446i	0.479215	−	1.07633i
$955$	−3.00022	+	22.8251i	−0.0970847	+	0.738604i
$956$	9.88043	−	4.39905i	0.319556	−	0.142275i
$957$	0.0319725	+	0.00856701i	0.00103352	+	0.000276932i
$958$	−1.88861	−	11.9242i	−0.0610181	−	0.385253i
$959$	−23.7579	−	36.9120i	−0.767181	−	1.19195i
$960$	−93.4751	−	79.8021i	−3.01690	−	2.57560i
$961$	19.8538	−	22.0498i	0.640444	−	0.711285i
$962$	−3.57248	−	0.187226i	−0.115181	−	0.00603640i
$963$	−8.30740	−	0.435372i	−0.267702	−	0.0140297i
$964$	−10.7300	+	11.9169i	−0.345590	+	0.383817i
$965$	−42.9509	−	3.37143i	−1.38264	−	0.108530i
$966$	−19.2604	+	0.930799i	−0.619692	+	0.0299480i
$967$	5.35578	+	33.8150i	0.172230	+	1.08742i	0.910681	+	0.413111i	$0.135558\pi$
$967$	5.35578	+	33.8150i	0.172230	+	1.08742i	−0.738451	+	0.674307i	$0.764442\pi$
$968$	109.835	+	29.4301i	3.53022	+	0.945921i
$969$	−13.6147	+	6.06165i	−0.437367	+	0.194728i
$970$	−1.46664	−	0.699183i	−0.0470911	−	0.0224494i
$971$	3.19175	−	7.16879i	0.102428	−	0.230057i	−0.855061	−	0.518528i	$-0.826480\pi$
$971$	3.19175	−	7.16879i	0.102428	−	0.230057i	0.957489	+	0.288471i	$0.0931468\pi$
$972$	−10.6548	+	67.2719i	−0.341754	+	2.15775i
$973$	13.0076	+	9.53171i	0.417005	+	0.305573i
$974$			39.5679i			1.26784i
$975$	14.1175	−	11.4417i	0.452120	−	0.366428i
$976$	13.1182	+	7.57380i	0.419903	+	0.242431i
$977$	−20.2105	−	31.1214i	−0.646591	−	0.995662i	−0.998227	−	0.0595256i	$-0.981041\pi$
$977$	−20.2105	−	31.1214i	−0.646591	−	0.995662i	0.351636	−	0.936137i	$-0.385625\pi$
$978$	12.5640	+	32.7304i	0.401753	+	1.04660i
$979$	−0.117379	+	0.0852808i	−0.00375145	+	0.00272559i
$980$	−75.9734	−	47.3898i	−2.42688	−	1.51381i
$981$	2.37620	+	1.72641i	0.0758663	+	0.0551201i
$982$	−15.4496	+	57.6588i	−0.493018	+	1.83997i
$983$	44.4214	+	17.0518i	1.41682	+	0.543867i	0.941820	−	0.336117i	$-0.109114\pi$
$983$	44.4214	+	17.0518i	1.41682	+	0.543867i	0.475003	+	0.879984i	$0.342447\pi$
$984$	35.9428	−	32.3630i	1.14581	−	1.03170i
$985$	19.1445	−	35.2771i	0.609996	−	1.12402i
$986$	−9.03193	+	2.93465i	−0.287635	+	0.0934584i
$987$	−3.72484	−	11.6247i	−0.118563	−	0.370017i
$988$	18.7744	+	36.8468i	0.597292	+	1.17225i
$989$	−14.3402	−	12.9120i	−0.455993	−	0.410578i
$990$	−0.229391	−	0.0678973i	−0.00729051	−	0.00215792i
$991$	−34.1027	−	37.8749i	−1.08331	−	1.20314i	−0.977980	−	0.208699i	$-0.933077\pi$
$991$	−34.1027	−	37.8749i	−1.08331	−	1.20314i	−0.105329	−	0.994437i	$-0.533589\pi$
$992$	19.8423	+	24.5032i	0.629994	+	0.777977i
$993$	5.72278	+	5.72278i	0.181607	+	0.181607i
$994$	5.41029	−	19.8677i	0.171604	−	0.630164i
$995$	−10.1264	−	11.8516i	−0.321029	−	0.375720i
$996$	101.630	+	45.2485i	3.22026	+	1.43375i
$997$	−10.7279	−	8.68731i	−0.339757	−	0.275130i	0.444223	−	0.895916i	$-0.353480\pi$
$997$	−10.7279	−	8.68731i	−0.339757	−	0.275130i	−0.783979	+	0.620787i	$0.786813\pi$
$998$	10.8906	−	7.07243i	0.344735	−	0.223874i
$999$	−1.32200	−	2.28978i	−0.0418264	−	0.0724454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.17.1	yes	288
5.2	odd	4		875.2.bb.a.143.1		288
5.3	odd	4		875.2.bb.b.143.18		288
5.4	even	2		875.2.bb.c.857.18		288
7.5	odd	6	inner	175.2.x.a.117.18	yes	288
25.3	odd	20	inner	175.2.x.a.3.18	✓	288
25.4	even	10		875.2.bb.a.507.1		288
25.21	even	5		875.2.bb.b.507.18		288
25.22	odd	20		875.2.bb.c.493.1		288
35.12	even	12		875.2.bb.a.768.1		288
35.19	odd	6		875.2.bb.c.607.1		288
35.33	even	12		875.2.bb.b.768.18		288
175.47	even	60		875.2.bb.c.243.18		288
175.54	odd	30		875.2.bb.a.257.1		288
175.96	odd	30		875.2.bb.b.257.18		288
175.103	even	60	inner	175.2.x.a.103.1	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.18	✓	288	25.3	odd	20	inner
175.2.x.a.17.1	yes	288	1.1	even	1	trivial
175.2.x.a.103.1	yes	288	175.103	even	60	inner
175.2.x.a.117.18	yes	288	7.5	odd	6	inner
875.2.bb.a.143.1		288	5.2	odd	4
875.2.bb.a.257.1		288	175.54	odd	30
875.2.bb.a.507.1		288	25.4	even	10
875.2.bb.a.768.1		288	35.12	even	12
875.2.bb.b.143.18		288	5.3	odd	4
875.2.bb.b.257.18		288	175.96	odd	30
875.2.bb.b.507.18		288	25.21	even	5
875.2.bb.b.768.18		288	35.33	even	12
875.2.bb.c.243.18		288	175.47	even	60
875.2.bb.c.493.1		288	25.22	odd	20
875.2.bb.c.607.1		288	35.19	odd	6
875.2.bb.c.857.18		288	5.4	even	2

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77479 + 0.145421i) q^{2} +(0.835009 - 1.03115i) q^{3} +(5.68928 - 0.597968i) q^{4} +(0.745982 - 2.10796i) q^{5} +(-2.16703 + 2.98265i) q^{6} +(2.14677 - 1.54641i) q^{7} +(-10.2108 + 1.61724i) q^{8} +(0.257705 + 1.21240i) q^{9} +(-1.76340 + 5.95764i) q^{10} +(0.0303852 + 0.00645857i) q^{11} +(4.13401 - 6.36581i) q^{12} +(-2.44056 + 1.24353i) q^{13} +(-5.73196 + 4.60315i) q^{14} +(-1.55073 - 2.52939i) q^{15} +(16.9066 - 3.59360i) q^{16} +(1.52518 - 3.97323i) q^{17} +(-0.891386 - 3.32670i) q^{18} +(0.275868 - 2.62470i) q^{19} +(2.98361 - 12.4389i) q^{20} +(0.197993 - 3.50491i) q^{21} +(-0.0852518 - 0.0135026i) q^{22} +(0.103461 + 1.97415i) q^{23} +(-6.85853 + 11.8793i) q^{24} +(-3.88702 - 3.14500i) q^{25} +(6.59122 - 3.80544i) q^{26} +(5.01203 + 2.55376i) q^{27} +(11.2889 - 10.0817i) q^{28} +(0.472036 + 0.649701i) q^{29} +(4.67077 + 6.79302i) q^{30} +(-0.468898 - 1.05316i) q^{31} +(-26.4179 + 7.07866i) q^{32} +(0.0320317 - 0.0259387i) q^{33} +(-3.65427 + 11.2467i) q^{34} +(-1.65832 - 5.67891i) q^{35} +(2.19113 + 6.74362i) q^{36} +(-0.394204 - 0.255999i) q^{37} +(-0.383789 + 7.32313i) q^{38} +(-0.755627 + 3.55494i) q^{39} +(-4.20802 + 22.7305i) q^{40} +(-3.35339 - 1.08958i) q^{41} +(-0.0397023 + 9.75418i) q^{42} +(-6.90226 + 6.90226i) q^{43} +(0.176732 + 0.0185753i) q^{44} +(2.74795 + 0.361200i) q^{45} +(-0.574166 - 5.46282i) q^{46} +(3.24629 - 1.24613i) q^{47} +(10.4116 - 20.4339i) q^{48} +(2.21724 - 6.63957i) q^{49} +(11.2430 + 8.16148i) q^{50} +(-2.82346 - 4.89037i) q^{51} +(-13.1415 + 8.53417i) q^{52} +(8.21153 + 6.64957i) q^{53} +(-14.2787 - 6.35729i) q^{54} +(0.0362812 - 0.0592329i) q^{55} +(-19.4194 + 19.2620i) q^{56} +(-2.47611 - 2.47611i) q^{57} +(-1.40428 - 1.73414i) q^{58} +(-1.58584 - 1.76126i) q^{59} +(-10.3350 - 13.4631i) q^{60} +(0.651278 + 0.586413i) q^{61} +(1.45425 + 2.85412i) q^{62} +(2.42811 + 2.20424i) q^{63} +(39.3982 - 12.8013i) q^{64} +(0.800699 + 6.07227i) q^{65} +(-0.0851092 + 0.0766326i) q^{66} +(9.68701 + 3.71849i) q^{67} +(6.30132 - 23.5169i) q^{68} +(2.12204 + 1.54175i) q^{69} +(5.42733 + 15.5166i) q^{70} +(-2.26602 + 1.64636i) q^{71} +(-4.59213 - 11.9629i) q^{72} +(-3.90459 - 6.01254i) q^{73} +(1.13106 + 0.653020i) q^{74} +(-6.48867 + 1.38200i) q^{75} -15.0976i q^{76} +(0.0752176 - 0.0331229i) q^{77} +(1.57974 - 9.97412i) q^{78} +(-4.45946 + 10.0161i) q^{79} +(5.03681 - 38.3192i) q^{80} +(3.42140 - 1.52331i) q^{81} +(9.46340 + 2.53571i) q^{82} +(2.29277 + 14.4760i) q^{83} +(-0.969385 - 20.0588i) q^{84} +(-7.23767 - 6.17898i) q^{85} +(18.1486 - 20.1561i) q^{86} +(1.06409 + 0.0557668i) q^{87} +(-0.320703 - 0.0168074i) q^{88} +(-3.12526 + 3.47095i) q^{89} +(-7.67751 - 0.602646i) q^{90} +(-3.31632 + 6.44368i) q^{91} +(1.76910 + 11.1697i) q^{92} +(-1.47750 - 0.395896i) q^{93} +(-8.82657 + 3.92984i) q^{94} +(-5.32699 - 2.53950i) q^{95} +(-14.7600 + 33.1516i) q^{96} +(-0.0409086 + 0.258287i) q^{97} +(-5.18685 + 18.7459i) q^{98} +0.0385036i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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