LMFDB - Embedded newform 210.2.x.a.137.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(23,210)] 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("210.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.4
Character	$\chi$	$=$	210.137
Dual form			210.2.x.a.23.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.755113 - 1.55878i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36035 + 1.77467i) q^{5} +(0.325941 + 1.70111i) q^{6} +(2.62857 - 0.301012i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.85961 + 2.35411i) q^{9} +(-0.854674 - 2.06628i) q^{10} +(1.49091 + 0.860779i) q^{11} +(0.125444 - 1.72750i) q^{12} +(1.71166 - 1.71166i) q^{13} +(-2.61691 - 0.389569i) q^{14} +(1.73911 - 3.46056i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.641503 - 2.39412i) q^{17} +(2.40553 - 1.79260i) q^{18} +(3.74936 - 2.16470i) q^{19} +(0.290757 + 2.21708i) q^{20} +(-2.45408 - 3.87008i) q^{21} +(-1.21733 - 1.21733i) q^{22} +(1.97379 - 7.36627i) q^{23} +(-0.568280 + 1.63617i) q^{24} +(-1.29892 + 4.82833i) q^{25} +(-2.09634 + 1.21032i) q^{26} +(5.07377 + 1.12110i) q^{27} +(2.42692 + 1.05360i) q^{28} -3.49141 q^{29} +(-2.57551 + 2.89253i) q^{30} +(-2.74588 + 4.75601i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.215960 - 2.97400i) q^{33} +2.47858i q^{34} +(4.10996 + 4.25537i) q^{35} +(-2.78753 + 1.10892i) q^{36} +(-1.29513 + 4.83348i) q^{37} +(-4.18187 + 1.12053i) q^{38} +(-3.96059 - 1.37561i) q^{39} +(0.292973 - 2.21679i) q^{40} +5.76741i q^{41} +(1.36881 + 4.37337i) q^{42} +(-1.33337 + 1.33337i) q^{43} +(0.860779 + 1.49091i) q^{44} +(-6.70749 - 0.0977862i) q^{45} +(-3.81306 + 6.60442i) q^{46} +(5.84489 + 1.56613i) q^{47} +(0.972389 - 1.43334i) q^{48} +(6.81878 - 1.58246i) q^{49} +(2.50433 - 4.32763i) q^{50} +(-3.24751 + 2.80780i) q^{51} +(2.33817 - 0.626510i) q^{52} +(-13.1337 + 3.51917i) q^{53} +(-4.61072 - 2.39609i) q^{54} +(0.500556 + 3.81684i) q^{55} +(-2.07153 - 1.64583i) q^{56} +(-6.20549 - 4.20985i) q^{57} +(3.37245 + 0.903644i) q^{58} +(5.45213 - 9.44337i) q^{59} +(3.23640 - 2.12738i) q^{60} +(-4.22391 - 7.31603i) q^{61} +(3.88326 - 3.88326i) q^{62} +(-4.17950 + 6.74772i) q^{63} +1.00000i q^{64} +(5.36607 + 0.709185i) q^{65} +(-0.978328 + 2.81677i) q^{66} +(-13.2284 + 3.54455i) q^{67} +(0.641503 - 2.39412i) q^{68} +(-12.9729 + 2.48566i) q^{69} +(-2.86855 - 5.17411i) q^{70} +10.9125i q^{71} +(2.97955 - 0.349669i) q^{72} +(-0.849946 - 3.17204i) q^{73} +(2.50199 - 4.33358i) q^{74} +(8.50716 - 1.62120i) q^{75} +4.32939 q^{76} +(4.17808 + 1.81384i) q^{77} +(3.46961 + 2.35381i) q^{78} +(2.97847 - 1.71962i) q^{79} +(-0.856739 + 2.06543i) q^{80} +(-2.08371 - 8.75546i) q^{81} +(1.49272 - 5.57089i) q^{82} +(1.66979 + 1.66979i) q^{83} +(-0.190259 - 4.57862i) q^{84} +(3.37612 - 4.39529i) q^{85} +(1.63304 - 0.942836i) q^{86} +(2.63641 + 5.44236i) q^{87} +(-0.445572 - 1.66290i) q^{88} +(1.63686 + 2.83513i) q^{89} +(6.45363 + 1.83048i) q^{90} +(3.98398 - 5.01444i) q^{91} +(5.39249 - 5.39249i) q^{92} +(9.48704 + 0.688911i) q^{93} +(-5.24039 - 3.02554i) q^{94} +(8.94206 + 3.70916i) q^{95} +(-1.31023 + 1.13283i) q^{96} +(11.1959 + 11.1959i) q^{97} +(-6.99601 - 0.236290i) q^{98} +(-4.79889 + 1.90907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43}+ \cdots + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.755113	−	1.55878i	−0.435965	−	0.899964i
$3$	−0.755113	−	1.55878i	−0.435965	−	0.899964i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.36035	+	1.77467i	0.608365	+	0.793657i
$5$	1.36035	+	1.77467i	0.608365	+	0.793657i
$6$	0.325941	+	1.70111i	0.133065	+	0.694474i
$7$	2.62857	−	0.301012i	0.993507	−	0.113772i
$7$	2.62857	−	0.301012i	0.993507	−	0.113772i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.85961	+	2.35411i	−0.619869	+	0.784705i
$10$	−0.854674	−	2.06628i	−0.270272	−	0.653417i
$11$	1.49091	+	0.860779i	0.449527	+	0.259535i	0.707631	−	0.706583i	$-0.249764\pi$
$11$	1.49091	+	0.860779i	0.449527	+	0.259535i	−0.258103	+	0.966117i	$0.583097\pi$
$12$	0.125444	−	1.72750i	0.0362127	−	0.498687i
$13$	1.71166	−	1.71166i	0.474728	−	0.474728i	−0.428713	−	0.903441i	$-0.641033\pi$
$13$	1.71166	−	1.71166i	0.474728	−	0.474728i	0.903441	+	0.428713i	$0.141033\pi$
$14$	−2.61691	−	0.389569i	−0.699400	−	0.104117i
$15$	1.73911	−	3.46056i	0.449037	−	0.893513i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.641503	−	2.39412i	−0.155587	−	0.580660i	−0.999054	−	0.0434791i	$-0.986156\pi$
$17$	−0.641503	−	2.39412i	−0.155587	−	0.580660i	0.843467	−	0.537181i	$-0.180511\pi$
$18$	2.40553	−	1.79260i	0.566990	−	0.422519i
$19$	3.74936	−	2.16470i	0.860163	−	0.496615i	−0.00390374	−	0.999992i	$-0.501243\pi$
$19$	3.74936	−	2.16470i	0.860163	−	0.496615i	0.864067	+	0.503377i	$0.167909\pi$
$20$	0.290757	+	2.21708i	0.0650153	+	0.495755i
$21$	−2.45408	−	3.87008i	−0.535524	−	0.844520i
$22$	−1.21733	−	1.21733i	−0.259535	−	0.259535i
$23$	1.97379	−	7.36627i	0.411563	−	1.53597i	−0.380059	−	0.924962i	$-0.624096\pi$
$23$	1.97379	−	7.36627i	0.411563	−	1.53597i	0.791622	−	0.611012i	$-0.209237\pi$
$24$	−0.568280	+	1.63617i	−0.116000	+	0.333982i
$25$	−1.29892	+	4.82833i	−0.259784	+	0.965667i
$26$	−2.09634	+	1.21032i	−0.411126	+	0.237364i
$27$	5.07377	+	1.12110i	0.976447	+	0.215756i
$28$	2.42692	+	1.05360i	0.458644	+	0.199112i
$29$	−3.49141			−0.648339			−0.324170	−	0.945999i	$-0.605085\pi$
$29$	−3.49141			−0.648339			−0.324170	+	0.945999i	$0.605085\pi$
$30$	−2.57551	+	2.89253i	−0.470222	+	0.528101i
$31$	−2.74588	+	4.75601i	−0.493175	+	0.854204i	−0.999969	−	0.00786297i	$-0.997497\pi$
$31$	−2.74588	+	4.75601i	−0.493175	+	0.854204i	0.506794	+	0.862067i	$0.330830\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.215960	−	2.97400i	0.0375938	−	0.517706i
$34$			2.47858i			0.425073i
$35$	4.10996	+	4.25537i	0.694710	+	0.719289i
$36$	−2.78753	+	1.10892i	−0.464588	+	0.184820i
$37$	−1.29513	+	4.83348i	−0.212918	+	0.794619i	0.773972	+	0.633220i	$0.218267\pi$
$37$	−1.29513	+	4.83348i	−0.212918	+	0.794619i	−0.986889	+	0.161399i	$0.948399\pi$
$38$	−4.18187	+	1.12053i	−0.678389	+	0.181774i
$39$	−3.96059	−	1.37561i	−0.634203	−	0.220273i
$40$	0.292973	−	2.21679i	0.0463232	−	0.350506i
$41$			5.76741i			0.900718i	0.892848	+	0.450359i	$0.148704\pi$
$41$			5.76741i			0.900718i	−0.892848	+	0.450359i	$0.851296\pi$
$42$	1.36881	+	4.37337i	0.211212	+	0.674825i
$43$	−1.33337	+	1.33337i	−0.203337	+	0.203337i	−0.801428	−	0.598091i	$-0.795926\pi$
$43$	−1.33337	+	1.33337i	−0.203337	+	0.203337i	0.598091	+	0.801428i	$0.295926\pi$
$44$	0.860779	+	1.49091i	0.129767	+	0.224764i
$45$	−6.70749	−	0.0977862i	−0.999894	−	0.0145771i
$46$	−3.81306	+	6.60442i	−0.562206	+	0.973769i
$47$	5.84489	+	1.56613i	0.852565	+	0.228444i	0.658534	−	0.752551i	$-0.271177\pi$
$47$	5.84489	+	1.56613i	0.852565	+	0.228444i	0.194031	+	0.980995i	$0.437844\pi$
$48$	0.972389	−	1.43334i	0.140352	−	0.206885i
$49$	6.81878	−	1.58246i	0.974112	−	0.226066i
$50$	2.50433	−	4.32763i	0.354165	−	0.612019i
$51$	−3.24751	+	2.80780i	−0.454742	+	0.393170i
$52$	2.33817	−	0.626510i	0.324245	−	0.0868812i
$53$	−13.1337	+	3.51917i	−1.80406	+	0.483395i	−0.994600	−	0.103784i	$-0.966905\pi$
$53$	−13.1337	+	3.51917i	−1.80406	+	0.483395i	−0.809457	+	0.587180i	$0.800238\pi$
$54$	−4.61072	−	2.39609i	−0.627440	−	0.326067i
$55$	0.500556	+	3.81684i	0.0674949	+	0.514663i
$56$	−2.07153	−	1.64583i	−0.276820	−	0.219934i
$57$	−6.20549	−	4.20985i	−0.821937	−	0.557609i
$58$	3.37245	+	0.903644i	0.442824	+	0.118654i
$59$	5.45213	−	9.44337i	0.709807	−	1.22942i	−0.255121	−	0.966909i	$-0.582115\pi$
$59$	5.45213	−	9.44337i	0.709807	−	1.22942i	0.964928	−	0.262513i	$-0.0845513\pi$
$60$	3.23640	−	2.12738i	0.417817	−	0.274643i
$61$	−4.22391	−	7.31603i	−0.540817	−	0.936722i	−0.998857	−	0.0477908i	$-0.984782\pi$
$61$	−4.22391	−	7.31603i	−0.540817	−	0.936722i	0.458041	−	0.888931i	$-0.348551\pi$
$62$	3.88326	−	3.88326i	0.493175	−	0.493175i
$63$	−4.17950	+	6.74772i	−0.526567	+	0.850133i
$64$			1.00000i			0.125000i
$65$	5.36607	+	0.709185i	0.665579	+	0.0879636i
$66$	−0.978328	+	2.81677i	−0.120424	+	0.346720i
$67$	−13.2284	+	3.54455i	−1.61611	+	0.433035i	−0.949856	−	0.312689i	$-0.898770\pi$
$67$	−13.2284	+	3.54455i	−1.61611	+	0.433035i	−0.666255	+	0.745724i	$0.732104\pi$
$68$	0.641503	−	2.39412i	0.0777937	−	0.290330i
$69$	−12.9729	+	2.48566i	−1.56175	+	0.299239i
$70$	−2.86855	−	5.17411i	−0.342857	−	0.618425i
$71$			10.9125i			1.29507i	0.762034	+	0.647537i	$0.224201\pi$
$71$			10.9125i			1.29507i	−0.762034	+	0.647537i	$0.775799\pi$
$72$	2.97955	−	0.349669i	0.351144	−	0.0412089i
$73$	−0.849946	−	3.17204i	−0.0994786	−	0.371259i	0.898182	−	0.439624i	$-0.144888\pi$
$73$	−0.849946	−	3.17204i	−0.0994786	−	0.371259i	−0.997660	+	0.0683650i	$0.978222\pi$
$74$	2.50199	−	4.33358i	0.290851	−	0.503768i
$75$	8.50716	−	1.62120i	0.982322	−	0.187200i
$76$	4.32939			0.496615
$77$	4.17808	+	1.81384i	0.476136	+	0.206706i
$78$	3.46961	+	2.35381i	0.392856	+	0.266517i
$79$	2.97847	−	1.71962i	0.335104	−	0.193472i	−0.323001	−	0.946399i	$-0.604692\pi$
$79$	2.97847	−	1.71962i	0.335104	−	0.193472i	0.658105	+	0.752926i	$0.271358\pi$
$80$	−0.856739	+	2.06543i	−0.0957863	+	0.230922i
$81$	−2.08371	−	8.75546i	−0.231524	−	0.972829i
$82$	1.49272	−	5.57089i	0.164843	−	0.615202i
$83$	1.66979	+	1.66979i	0.183283	+	0.183283i	0.792785	−	0.609502i	$-0.208630\pi$
$83$	1.66979	+	1.66979i	0.183283	+	0.183283i	−0.609502	+	0.792785i	$0.708630\pi$
$84$	−0.190259	−	4.57862i	−0.0207590	−	0.499569i
$85$	3.37612	−	4.39529i	0.366191	−	0.476736i
$86$	1.63304	−	0.942836i	0.176095	−	0.101669i
$87$	2.63641	+	5.44236i	0.282653	+	0.583482i
$88$	−0.445572	−	1.66290i	−0.0474981	−	0.177266i
$89$	1.63686	+	2.83513i	0.173507	+	0.300523i	0.939644	−	0.342155i	$-0.111157\pi$
$89$	1.63686	+	2.83513i	0.173507	+	0.300523i	−0.766136	+	0.642678i	$0.777823\pi$
$90$	6.45363	+	1.83048i	0.680272	+	0.192950i
$91$	3.98398	−	5.01444i	0.417635	−	0.525656i
$92$	5.39249	−	5.39249i	0.562206	−	0.562206i
$93$	9.48704	+	0.688911i	0.983760	+	0.0714367i
$94$	−5.24039	−	3.02554i	−0.540505	−	0.312060i
$95$	8.94206	+	3.70916i	0.917436	+	0.380552i
$96$	−1.31023	+	1.13283i	−0.133725	+	0.115619i
$97$	11.1959	+	11.1959i	1.13678	+	1.13678i	0.989025	+	0.147751i	$0.0472033\pi$
$97$	11.1959	+	11.1959i	1.13678	+	1.13678i	0.147751	+	0.989025i	$0.452797\pi$
$98$	−6.99601	−	0.236290i	−0.706704	−	0.0238689i
$99$	−4.79889	+	1.90907i	−0.482306	+	0.191869i
$100$	−3.53907	+	3.53200i	−0.353907	+	0.353200i
$101$	6.85108	+	3.95547i	0.681707	+	0.393584i	0.800498	−	0.599335i	$-0.204568\pi$
$101$	6.85108	+	3.95547i	0.681707	+	0.393584i	−0.118791	+	0.992919i	$0.537902\pi$
$102$	3.86357	−	1.87161i	0.382550	−	0.185317i
$103$	−13.3320	−	3.57231i	−1.31364	−	0.351990i	−0.467051	−	0.884230i	$-0.654684\pi$
$103$	−13.3320	−	3.57231i	−1.31364	−	0.351990i	−0.846593	+	0.532241i	$0.821350\pi$
$104$	−2.42065			−0.237364
$105$	3.52972	−	9.61983i	0.344465	−	0.938799i
$106$	13.5970			1.32066
$107$	−19.5649	−	5.24240i	−1.89141	−	0.506802i	−0.998386	−	0.0567934i	$-0.981912\pi$
$107$	−19.5649	−	5.24240i	−1.89141	−	0.506802i	−0.893024	−	0.450008i	$-0.851421\pi$
$108$	3.83346	+	3.50779i	0.368875	+	0.337537i
$109$	−6.61391	−	3.81854i	−0.633497	−	0.365750i	0.148608	−	0.988896i	$-0.452521\pi$
$109$	−6.61391	−	3.81854i	−0.633497	−	0.365750i	−0.782105	+	0.623146i	$0.785854\pi$
$110$	0.504371	−	3.81634i	0.0480899	−	0.363873i
$111$	8.51232	−	1.63100i	0.807953	−	0.154808i
$112$	1.57497	+	2.12590i	0.148821	+	0.200879i
$113$	−4.50613	−	4.50613i	−0.423901	−	0.423901i	0.462643	−	0.886545i	$-0.346901\pi$
$113$	−4.50613	−	4.50613i	−0.423901	−	0.423901i	−0.886545	+	0.462643i	$0.846901\pi$
$114$	4.90445	+	5.67251i	0.459344	+	0.531279i
$115$	15.7578	−	6.51785i	1.46942	−	0.607793i
$116$	−3.02365	−	1.74571i	−0.280739	−	0.162085i
$117$	0.846425	+	7.21244i	0.0782520	+	0.666791i
$118$	−7.71048	+	7.71048i	−0.709807	+	0.709807i
$119$	−2.40690	−	6.10003i	−0.220640	−	0.559188i
$120$	−3.67673	+	1.21725i	−0.335638	+	0.111119i
$121$	−4.01812	−	6.95958i	−0.365283	−	0.632690i
$122$	2.18646	+	8.15997i	0.197953	+	0.738769i
$123$	8.99014	−	4.35505i	0.810613	−	0.392681i
$124$	−4.75601	+	2.74588i	−0.427102	+	0.246588i
$125$	−10.3357	+	4.26304i	−0.924452	+	0.381298i
$126$	5.78353	−	5.43607i	0.515237	−	0.484283i
$127$	−3.77174	−	3.77174i	−0.334688	−	0.334688i	0.519676	−	0.854364i	$-0.326053\pi$
$127$	−3.77174	−	3.77174i	−0.334688	−	0.334688i	−0.854364	+	0.519676i	$0.826053\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	3.08528	+	1.07159i	0.271644	+	0.0943483i
$130$	−4.99968	−	2.07386i	−0.438501	−	0.181890i
$131$	−8.66142	+	5.00068i	−0.756752	+	0.436911i	−0.828128	−	0.560538i	$-0.810594\pi$
$131$	−8.66142	+	5.00068i	−0.756752	+	0.436911i	0.0713763	+	0.997449i	$0.477261\pi$
$132$	1.67402	−	2.46758i	0.145705	−	0.214775i
$133$	9.20388	−	6.81866i	0.798077	−	0.591253i
$134$	13.6951			1.18307
$135$	4.91249	+	10.5294i	0.422800	+	0.906223i
$136$	−1.23929	+	2.14651i	−0.106268	+	0.184062i
$137$	−0.641324	−	2.39345i	−0.0547920	−	0.204487i	0.933103	−	0.359608i	$-0.117090\pi$
$137$	−0.641324	−	2.39345i	−0.0547920	−	0.204487i	−0.987895	+	0.155122i	$0.950423\pi$
$138$	13.1742	+	0.956654i	1.12146	+	0.0814358i
$139$		−	3.57912i		−	0.303577i	−0.988413	−	0.151788i	$-0.951497\pi$
$139$		−	3.57912i		−	0.303577i	0.988413	−	0.151788i	$-0.0485033\pi$
$140$	1.43165	+	5.74024i	0.120996	+	0.485139i
$141$	−1.97229	−	10.2935i	−0.166097	−	0.866871i
$142$	2.82436	−	10.5407i	0.237015	−	0.884552i
$143$	4.02529	−	1.07857i	0.336612	−	0.0901948i
$144$	−2.96853	−	0.433411i	−0.247377	−	0.0361176i
$145$	−4.74953	−	6.19611i	−0.394427	−	0.514559i
$146$			3.28394i			0.271781i
$147$	−7.61567	−	9.43407i	−0.628130	−	0.778109i
$148$	−3.53835	+	3.53835i	−0.290851	+	0.290851i
$149$	6.70402	+	11.6117i	0.549215	+	0.951268i	0.998329	+	0.0577936i	$0.0184065\pi$
$149$	6.70402	+	11.6117i	0.549215	+	0.951268i	−0.449114	+	0.893475i	$0.648260\pi$
$150$	−8.63688	−	0.635855i	−0.705198	−	0.0519173i
$151$	−2.73907	+	4.74421i	−0.222903	+	0.386078i	−0.955688	−	0.294381i	$-0.904886\pi$
$151$	−2.73907	+	4.74421i	−0.222903	+	0.386078i	0.732786	+	0.680460i	$0.238220\pi$
$152$	−4.18187	−	1.12053i	−0.339195	−	0.0908869i
$153$	6.82899	+	2.94196i	0.552091	+	0.237843i
$154$	−3.56626	−	2.83340i	−0.287377	−	0.228322i
$155$	−12.1757	+	1.59677i	−0.977976	+	0.128256i
$156$	−2.74217	−	3.17161i	−0.219549	−	0.253932i
$157$	−10.6720	+	2.85955i	−0.851718	+	0.228217i	−0.658166	−	0.752873i	$-0.728667\pi$
$157$	−10.6720	+	2.85955i	−0.851718	+	0.228217i	−0.193552	+	0.981090i	$0.562001\pi$
$158$	−3.32205	+	0.890141i	−0.264288	+	0.0708158i
$159$	15.4031	+	17.8153i	1.22154	+	1.41284i
$160$	1.36212	−	1.77331i	0.107685	−	0.140193i
$161$	2.97091	−	19.9569i	0.234140	−	1.57283i
$162$	−0.253368	+	8.99643i	−0.0199065	+	0.706827i
$163$	−4.80653	−	1.28791i	−0.376476	−	0.100877i	0.0656186	−	0.997845i	$-0.479098\pi$
$163$	−4.80653	−	1.28791i	−0.376476	−	0.100877i	−0.442095	+	0.896968i	$0.645765\pi$
$164$	−2.88370	+	4.99472i	−0.225179	+	0.390022i
$165$	5.57165	−	3.66240i	0.433752	−	0.285118i
$166$	−1.18072	−	2.04507i	−0.0916417	−	0.158728i
$167$	12.6740	−	12.6740i	0.980742	−	0.980742i	−0.0190761	−	0.999818i	$-0.506072\pi$
$167$	12.6740	−	12.6740i	0.980742	−	0.980742i	0.999818	+	0.0190761i	$0.00607248\pi$
$168$	−1.00126	+	4.47185i	−0.0772488	+	0.345011i
$169$			7.14047i			0.549267i
$170$	−4.39866	+	3.37172i	−0.337362	+	0.258599i
$171$	−1.87640	+	12.8519i	−0.143492	+	0.982811i
$172$	−1.82142	+	0.488048i	−0.138882	+	0.0372133i
$173$	−1.99929	+	7.46147i	−0.152004	+	0.567285i	0.847340	+	0.531051i	$0.178203\pi$
$173$	−1.99929	+	7.46147i	−0.152004	+	0.567285i	−0.999343	+	0.0362338i	$0.988464\pi$
$174$	−1.13799	−	5.93926i	−0.0862710	−	0.450255i
$175$	−1.96093	+	13.0826i	−0.148232	+	0.988953i
$176$			1.72156i			0.129767i
$177$	−18.8371	−	1.36788i	−1.41589	−	0.102816i
$178$	−0.847304	−	3.16218i	−0.0635081	−	0.237015i
$179$	1.78392	−	3.08984i	0.133336	−	0.230945i	−0.791624	−	0.611008i	$-0.790764\pi$
$179$	1.78392	−	3.08984i	0.133336	−	0.230945i	0.924961	+	0.380063i	$0.124098\pi$
$180$	−5.75996	−	3.43843i	−0.429322	−	0.256286i
$181$	−22.4506			−1.66874			−0.834371	−	0.551203i	$-0.814169\pi$
$181$	−22.4506			−1.66874			−0.834371	+	0.551203i	$0.814169\pi$
$182$	−5.14606	+	3.81245i	−0.381452	+	0.282597i
$183$	−8.21457	+	12.1086i	−0.607239	+	0.895093i
$184$	−6.60442	+	3.81306i	−0.486884	+	0.281103i
$185$	−10.3397	+	4.27678i	−0.760187	+	0.314435i
$186$	−8.98547	−	3.12086i	−0.658847	−	0.228833i
$187$	1.10439	−	4.12162i	0.0807607	−	0.301403i
$188$	4.27876	+	4.27876i	0.312060	+	0.312060i
$189$	13.6742	+	1.41964i	0.994654	+	0.103263i
$190$	−7.67736	−	5.89715i	−0.556974	−	0.427824i
$191$	20.0377	−	11.5688i	1.44988	−	0.837088i	0.451406	−	0.892319i	$-0.350923\pi$
$191$	20.0377	−	11.5688i	1.44988	−	0.837088i	0.998474	+	0.0552306i	$0.0175894\pi$
$192$	1.55878	−	0.755113i	0.112495	−	0.0544956i
$193$	4.16280	+	15.5358i	0.299645	+	1.11829i	0.937458	+	0.348099i	$0.113173\pi$
$193$	4.16280	+	15.5358i	0.299645	+	1.11829i	−0.637813	+	0.770191i	$0.720161\pi$
$194$	−7.91672	−	13.7122i	−0.568388	−	0.984476i
$195$	−2.94652	−	8.90005i	−0.211005	−	0.637346i
$196$	6.69647	+	2.03894i	0.478319	+	0.145639i
$197$	−4.51365	+	4.51365i	−0.321584	+	0.321584i	−0.849375	−	0.527791i	$-0.823021\pi$
$197$	−4.51365	+	4.51365i	−0.321584	+	0.321584i	0.527791	+	0.849375i	$0.323021\pi$
$198$	5.12947	−	0.601976i	0.364536	−	0.0427805i
$199$	−1.87390	−	1.08190i	−0.132837	−	0.0766936i	0.432109	−	0.901821i	$-0.357770\pi$
$199$	−1.87390	−	1.08190i	−0.132837	−	0.0766936i	−0.564946	+	0.825128i	$0.691103\pi$
$200$	4.33262	−	2.49567i	0.306363	−	0.176471i
$201$	15.5141	+	17.9437i	1.09428	+	1.26565i
$202$	−5.59388	−	5.59388i	−0.393584	−	0.393584i
$203$	−9.17743	+	1.05096i	−0.644129	+	0.0737627i
$204$	−4.21633	+	0.807869i	−0.295202	+	0.0565622i
$205$	−10.2353	+	7.84567i	−0.714862	+	0.547965i
$206$	11.9532	+	6.90117i	0.832817	+	0.480827i
$207$	13.6706	+	18.3449i	0.950171	+	1.27506i
$208$	2.33817	+	0.626510i	0.162123	+	0.0434406i
$209$	7.45330			0.515556
$210$	−5.89924	+	8.37848i	−0.407086	+	0.578170i
$211$	8.92286			0.614275			0.307138	−	0.951665i	$-0.400629\pi$
$211$	8.92286			0.614275			0.307138	+	0.951665i	$0.400629\pi$
$212$	−13.1337	−	3.51917i	−0.902028	−	0.241698i
$213$	17.0102	−	8.24016i	1.16552	−	0.564607i
$214$	17.5414	+	10.1275i	1.19911	+	0.692304i
$215$	−4.18014	−	0.552452i	−0.285083	−	0.0376769i
$216$	−2.79496	−	4.38044i	−0.190173	−	0.298051i
$217$	−5.78614	+	13.3281i	−0.392788	+	0.904767i
$218$	5.40023	+	5.40023i	0.365750	+	0.365750i
$219$	−4.30272	+	3.72013i	−0.290751	+	0.251383i
$220$	−1.47493	+	3.55576i	−0.0994395	+	0.239729i
$221$	−5.19595	−	2.99988i	−0.349517	−	0.201794i
$222$	−8.64440	−	0.627722i	−0.580174	−	0.0421299i
$223$	4.95541	−	4.95541i	0.331839	−	0.331839i	−0.521446	−	0.853284i	$-0.674607\pi$
$223$	4.95541	−	4.95541i	0.331839	−	0.331839i	0.853284	+	0.521446i	$0.174607\pi$
$224$	−0.971080	−	2.46110i	−0.0648830	−	0.164439i
$225$	−8.95096	−	12.0366i	−0.596731	−	0.802441i
$226$	3.18632	+	5.51886i	0.211951	+	0.367109i
$227$	−6.32181	−	23.5933i	−0.419593	−	1.56594i	−0.775454	−	0.631404i	$-0.782479\pi$
$227$	−6.32181	−	23.5933i	−0.419593	−	1.56594i	0.355862	−	0.934539i	$-0.384187\pi$
$228$	−3.26918	−	6.74858i	−0.216507	−	0.446936i
$229$	−1.56910	+	0.905917i	−0.103689	+	0.0598647i	−0.550948	−	0.834540i	$-0.685734\pi$
$229$	−1.56910	+	0.905917i	−0.103689	+	0.0598647i	0.447259	+	0.894405i	$0.352400\pi$
$230$	−16.9078	+	2.21735i	−1.11486	+	0.146208i
$231$	−0.327542	−	7.88237i	−0.0215507	−	0.518622i
$232$	2.46880	+	2.46880i	0.162085	+	0.162085i
$233$	−0.487986	+	1.82119i	−0.0319690	+	0.119310i	−0.980066	−	0.198670i	$-0.936338\pi$
$233$	−0.487986	+	1.82119i	−0.0319690	+	0.119310i	0.948097	+	0.317980i	$0.103004\pi$
$234$	1.04913	−	7.18576i	0.0685840	−	0.469748i
$235$	5.17170	+	12.5032i	0.337364	+	0.815622i
$236$	9.44337	−	5.45213i	0.614711	−	0.354904i
$237$	−4.92960	−	3.34428i	−0.320212	−	0.217234i
$238$	0.746081	+	6.51512i	0.0483613	+	0.422313i
$239$	7.33694			0.474587			0.237294	−	0.971438i	$-0.423740\pi$
$239$	7.33694			0.474587			0.237294	+	0.971438i	$0.423740\pi$
$240$	3.86649	−	0.224164i	0.249581	−	0.0144697i
$241$	7.03912	−	12.1921i	0.453430	−	0.785363i	−0.545167	−	0.838328i	$-0.683534\pi$
$241$	7.03912	−	12.1921i	0.453430	−	0.785363i	0.998596	+	0.0529643i	$0.0168669\pi$
$242$	2.07993	+	7.76241i	0.133703	+	0.498987i
$243$	−12.0744	+	9.85942i	−0.774575	+	0.632482i
$244$		−	8.44783i		−	0.540817i
$245$	12.0843	+	9.94841i	0.772035	+	0.635581i
$246$	−9.81098	+	1.87983i	−0.625525	+	0.119854i
$247$	2.71241	−	10.1228i	0.172586	−	0.644101i
$248$	5.30464	−	1.42137i	0.336845	−	0.0902573i
$249$	1.34196	−	3.86372i	0.0850433	−	0.244853i
$250$	11.0869	−	1.44271i	0.701195	−	0.0912447i
$251$		−	23.2410i		−	1.46696i	−0.679711	−	0.733480i	$-0.737895\pi$
$251$		−	23.2410i		−	1.46696i	0.679711	−	0.733480i	$-0.262105\pi$
$252$	−6.99341	+	3.75395i	−0.440544	+	0.236477i
$253$	9.28348	−	9.28348i	0.583647	−	0.583647i
$254$	2.66703	+	4.61942i	0.167344	+	0.289848i
$255$	−9.40066	−	1.94369i	−0.588692	−	0.121719i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.6104	+	3.91483i	0.911369	+	0.244201i	0.683892	−	0.729583i	$-0.260286\pi$
$257$	14.6104	+	3.91483i	0.911369	+	0.244201i	0.227477	+	0.973784i	$0.426952\pi$
$258$	−2.70281	−	1.83361i	−0.168269	−	0.114155i
$259$	−1.94940	+	13.0950i	−0.121130	+	0.813684i
$260$	4.29256	+	3.29721i	0.266213	+	0.204484i
$261$	6.49266	−	8.21919i	0.401886	−	0.508755i
$262$	9.66056	−	2.58854i	0.596832	−	0.159921i
$263$	−12.9229	+	3.46268i	−0.796859	+	0.213518i	−0.634205	−	0.773165i	$-0.718672\pi$
$263$	−12.9229	+	3.46268i	−0.796859	+	0.213518i	−0.162655	+	0.986683i	$0.552006\pi$
$264$	−2.25564	+	1.95023i	−0.138825	+	0.120028i
$265$	−24.1118	−	18.5208i	−1.48117	−	1.13772i
$266$	−10.6551	+	4.20419i	−0.653304	+	0.257775i
$267$	3.18334	−	4.69236i	0.194817	−	0.287168i
$268$	−13.2284	−	3.54455i	−0.808055	−	0.216518i
$269$	−1.71727	+	2.97440i	−0.104704	+	0.181352i	−0.913617	−	0.406576i	$-0.866723\pi$
$269$	−1.71727	+	2.97440i	−0.104704	+	0.181352i	0.808913	+	0.587928i	$0.200056\pi$
$270$	−2.01990	−	11.4420i	−0.122927	−	0.696340i
$271$	7.63352	+	13.2217i	0.463704	+	0.803158i	0.999142	−	0.0414162i	$-0.0131870\pi$
$271$	7.63352	+	13.2217i	0.463704	+	0.803158i	−0.535438	+	0.844574i	$0.679854\pi$
$272$	1.75262	−	1.75262i	0.106268	−	0.106268i
$273$	−10.8248	−	2.42369i	−0.655145	−	0.146689i
$274$			2.47789i			0.149695i
$275$	−6.09271	+	6.08054i	−0.367404	+	0.366670i
$276$	−12.4777	−	4.33378i	−0.751066	−	0.260863i
$277$	30.3945	−	8.14417i	1.82623	−	0.489336i	0.828704	−	0.559687i	$-0.189079\pi$
$277$	30.3945	−	8.14417i	1.82623	−	0.489336i	0.997522	+	0.0703507i	$0.0224118\pi$
$278$	−0.926344	+	3.45716i	−0.0555584	+	0.207347i
$279$	−6.08992	−	15.3084i	−0.364594	−	0.916492i
$280$	0.102821	−	5.91519i	0.00614474	−	0.353500i
$281$			6.72535i			0.401201i	0.979673	+	0.200600i	$0.0642893\pi$
$281$			6.72535i			0.401201i	−0.979673	+	0.200600i	$0.935711\pi$
$282$	−0.759073	+	10.4532i	−0.0452021	+	0.622482i
$283$	0.293117	+	1.09393i	0.0174240	+	0.0650272i	0.974090	−	0.226159i	$-0.0726168\pi$
$283$	0.293117	+	1.09393i	0.0174240	+	0.0650272i	−0.956666	+	0.291186i	$0.905950\pi$
$284$	−5.45624	+	9.45049i	−0.323768	+	0.560783i
$285$	−0.970492	−	16.7396i	−0.0574870	−	0.991566i
$286$	−4.16729			−0.246417
$287$	1.73606	+	15.1601i	0.102476	+	0.894870i
$288$	2.75520	+	1.18695i	0.162352	+	0.0699419i
$289$	9.40213	−	5.42832i	0.553067	−	0.319313i
$290$	2.98402	+	7.21425i	0.175228	+	0.423636i
$291$	8.99784	−	25.9062i	0.527463	−	1.51865i
$292$	0.849946	−	3.17204i	0.0497393	−	0.185630i
$293$	23.0536	+	23.0536i	1.34680	+	1.34680i	0.889110	+	0.457694i	$0.151324\pi$
$293$	23.0536	+	23.0536i	1.34680	+	1.34680i	0.457694	+	0.889110i	$0.348676\pi$
$294$	4.91446	+	11.0837i	0.286617	+	0.646414i
$295$	24.1757	−	3.17050i	1.40756	−	0.184593i
$296$	4.33358	−	2.50199i	0.251884	−	0.145425i
$297$	6.59953	+	6.03886i	0.382943	+	0.350410i
$298$	−3.47026	−	12.9512i	−0.201027	−	0.750242i
$299$	−9.23008	−	15.9870i	−0.533789	−	0.924550i
$300$	8.17801	+	2.84958i	0.472158	+	0.164520i
$301$	−3.10350	+	3.90623i	−0.178883	+	0.225151i
$302$	3.87363	−	3.87363i	0.222903	−	0.222903i
$303$	0.992382	−	13.6662i	0.0570109	−	0.785101i
$304$	3.74936	+	2.16470i	0.215041	+	0.124154i
$305$	7.23758	−	17.4484i	0.414423	−	0.999092i
$306$	−5.83486	−	4.60919i	−0.333557	−	0.263490i
$307$	−6.95926	−	6.95926i	−0.397186	−	0.397186i	0.480054	−	0.877239i	$-0.340617\pi$
$307$	−6.95926	−	6.95926i	−0.397186	−	0.397186i	−0.877239	+	0.480054i	$0.840617\pi$
$308$	2.71140	+	3.65987i	0.154497	+	0.208540i
$309$	4.49874	+	23.4792i	0.255924	+	1.33569i
$310$	12.1741	+	1.60894i	0.691442	+	0.0913817i
$311$	−7.67936	−	4.43368i	−0.435457	−	0.251411i	0.266212	−	0.963915i	$-0.414228\pi$
$311$	−7.67936	−	4.43368i	−0.435457	−	0.251411i	−0.701669	+	0.712503i	$0.747561\pi$
$312$	1.82786	+	3.77326i	0.103482	+	0.213619i
$313$	5.59536	+	1.49927i	0.316269	+	0.0847439i	0.413461	−	0.910522i	$-0.364320\pi$
$313$	5.59536	+	1.49927i	0.316269	+	0.0847439i	−0.0971927	+	0.995266i	$0.530986\pi$
$314$	11.0485			0.623501
$315$	−17.6606	+	1.76200i	−0.995060	+	0.0992772i
$316$	3.43924			0.193472
$317$	−4.10330	−	1.09948i	−0.230464	−	0.0617527i	0.141739	−	0.989904i	$-0.454731\pi$
$317$	−4.10330	−	1.09948i	−0.230464	−	0.0617527i	−0.372203	+	0.928151i	$0.621397\pi$
$318$	−10.2673	−	21.1948i	−0.575762	−	1.18855i
$319$	−5.20539	−	3.00534i	−0.291446	−	0.168267i
$320$	−1.77467	+	1.36035i	−0.0992072	+	0.0760456i
$321$	6.60195	+	34.4560i	0.368485	+	1.92315i
$322$	−8.03490	+	18.5080i	−0.447768	+	1.03141i
$323$	−7.58778	−	7.58778i	−0.422195	−	0.422195i
$324$	2.57318	−	8.62431i	0.142955	−	0.479128i
$325$	6.04114	+	10.4878i	0.335102	+	0.581756i
$326$	4.30942	+	2.48804i	0.238677	+	0.137800i
$327$	−0.958028	+	13.1931i	−0.0529791	+	0.729579i
$328$	4.07817	−	4.07817i	0.225179	−	0.225179i
$329$	15.8351	+	2.35731i	0.873020	+	0.129963i
$330$	−6.32970	+	2.09556i	−0.348438	+	0.115357i
$331$	−2.70453	−	4.68438i	−0.148654	−	0.257477i	0.782076	−	0.623183i	$-0.214161\pi$
$331$	−2.70453	−	4.68438i	−0.148654	−	0.257477i	−0.930730	+	0.365706i	$0.880828\pi$
$332$	0.611186	+	2.28098i	0.0335432	+	0.125185i
$333$	−8.97014	−	12.0373i	−0.491561	−	0.659638i
$334$	−15.5224	+	8.96186i	−0.849347	+	0.490371i
$335$	−24.2856	−	18.6543i	−1.32687	−	1.01919i
$336$	2.12454	−	4.06033i	0.115903	−	0.221509i
$337$	10.8084	+	10.8084i	0.588773	+	0.588773i	0.937299	−	0.348526i	$-0.113318\pi$
$337$	10.8084	+	10.8084i	0.588773	+	0.588773i	−0.348526	+	0.937299i	$0.613318\pi$
$338$	1.84809	−	6.89716i	0.100523	−	0.375156i
$339$	−3.62144	+	10.4267i	−0.196690	+	0.566302i
$340$	5.12145	−	2.11838i	0.277750	−	0.114885i
$341$	−8.18775	+	4.72720i	−0.443391	+	0.255992i
$342$	5.13879	−	11.9284i	0.277874	−	0.645012i
$343$	17.4473	−	6.21215i	0.942067	−	0.335425i
$344$	1.88567			0.101669
$345$	−22.0588	−	19.6412i	−1.18761	−	1.05745i
$346$	3.86234	−	6.68977i	0.207641	−	0.359644i
$347$	5.70057	+	21.2748i	0.306023	+	1.14209i	0.932061	+	0.362300i	$0.118009\pi$
$347$	5.70057	+	21.2748i	0.306023	+	1.14209i	−0.626039	+	0.779792i	$0.715325\pi$
$348$	−0.437978	+	6.03142i	−0.0234781	+	0.323318i
$349$		−	1.21120i		−	0.0648340i	−0.999474	−	0.0324170i	$-0.989680\pi$
$349$		−	1.21120i		−	0.0648340i	0.999474	−	0.0324170i	$-0.0103205\pi$
$350$	5.28014	−	12.1293i	0.282235	−	0.648339i
$351$	10.6035	−	6.76560i	0.565972	−	0.361121i
$352$	0.445572	−	1.66290i	0.0237491	−	0.0886328i
$353$	−12.9424	+	3.46790i	−0.688854	+	0.184578i	−0.586233	−	0.810143i	$-0.699390\pi$
$353$	−12.9424	+	3.46790i	−0.688854	+	0.184578i	−0.102621	+	0.994721i	$0.532723\pi$
$354$	17.8413	+	6.19668i	0.948252	+	0.329350i
$355$	−19.3661	+	14.8447i	−1.02784	+	0.787877i
$356$			3.27373i			0.173507i
$357$	−7.69114	+	8.35804i	−0.407058	+	0.442354i
$358$	−2.52284	+	2.52284i	−0.133336	+	0.133336i
$359$	6.11095	+	10.5845i	0.322523	+	0.558627i	0.981008	−	0.193967i	$-0.0621355\pi$
$359$	6.11095	+	10.5845i	0.322523	+	0.558627i	−0.658485	+	0.752594i	$0.728802\pi$
$360$	4.67377	+	4.81206i	0.246329	+	0.253618i
$361$	−0.128177	+	0.222010i	−0.00674618	+	0.0116847i
$362$	21.6857	+	5.81065i	1.13977	+	0.305401i
$363$	−7.81435	+	11.5186i	−0.410147	+	0.604572i
$364$	5.95745	−	2.35064i	0.312255	−	0.123207i
$365$	4.47311	−	5.82345i	0.234133	−	0.304813i
$366$	11.0686	−	9.56992i	0.578565	−	0.500228i
$367$	15.3979	−	4.12585i	0.803762	−	0.215368i	0.166527	−	0.986037i	$-0.446745\pi$
$367$	15.3979	−	4.12585i	0.803762	−	0.215368i	0.637235	+	0.770669i	$0.280078\pi$
$368$	7.36627	−	1.97379i	0.383994	−	0.102891i
$369$	−13.5771	−	10.7251i	−0.706798	−	0.558328i
$370$	11.0943	−	1.45495i	0.576763	−	0.0756391i
$371$	−33.4636	+	13.2038i	−1.73735	+	0.685507i
$372$	7.87156	+	5.34013i	0.408121	+	0.276873i
$373$	21.0213	+	5.63264i	1.08844	+	0.291647i	0.758050	−	0.652196i	$-0.226152\pi$
$373$	21.0213	+	5.63264i	1.08844	+	0.291647i	0.330392	+	0.943844i	$0.392819\pi$
$374$	−2.13351	+	3.69535i	−0.110321	+	0.191082i
$375$	14.4498	+	12.8920i	0.746183	+	0.665741i
$376$	−3.02554	−	5.24039i	−0.156030	−	0.270252i
$377$	−5.97610	+	5.97610i	−0.307785	+	0.307785i
$378$	−12.8409	−	4.91041i	−0.660463	−	0.252564i
$379$		−	20.0870i		−	1.03180i	−0.856649	−	0.515900i	$-0.827457\pi$
$379$		−	20.0870i		−	1.03180i	0.856649	−	0.515900i	$-0.172543\pi$
$380$	5.88947	+	7.68325i	0.302123	+	0.394143i
$381$	−3.03124	+	8.72742i	−0.155295	+	0.447119i
$382$	−22.3492	+	5.98845i	−1.14348	+	0.306396i
$383$	−0.0948076	+	0.353827i	−0.00484444	+	0.0180797i	−0.968306	−	0.249768i	$-0.919646\pi$
$383$	−0.0948076	+	0.353827i	−0.00484444	+	0.0180797i	0.963461	+	0.267848i	$0.0863124\pi$
$384$	−1.70111	+	0.325941i	−0.0868092	+	0.0166331i
$385$	2.46466	+	9.88216i	0.125611	+	0.503642i
$386$		−	16.0838i		−	0.818645i
$387$	−0.659361	−	5.61846i	−0.0335172	−	0.285602i
$388$	4.09800	+	15.2939i	0.208044	+	0.776432i
$389$	6.65686	−	11.5300i	0.337516	−	0.584595i	−0.646449	−	0.762958i	$-0.723747\pi$
$389$	6.65686	−	11.5300i	0.337516	−	0.584595i	0.983965	+	0.178362i	$0.0570798\pi$
$390$	0.542621	+	9.35941i	0.0274767	+	0.473932i
$391$	−18.9020			−0.955913
$392$	−5.94058	−	3.70264i	−0.300045	−	0.187011i
$393$	14.3353	+	9.72520i	0.723121	+	0.490572i
$394$	5.52807	−	3.19163i	0.278500	−	0.160792i
$395$	7.10351	+	2.94653i	0.357416	+	0.148256i
$396$	−5.11049	−	0.746142i	−0.256812	−	0.0374950i
$397$	2.27942	−	8.50692i	0.114401	−	0.426950i	−0.884840	−	0.465894i	$-0.845733\pi$
$397$	2.27942	−	8.50692i	0.114401	−	0.426950i	0.999241	+	0.0389441i	$0.0123994\pi$
$398$	1.53003	+	1.53003i	0.0766936	+	0.0766936i
$399$	−17.5788	−	9.19798i	−0.880040	−	0.460475i
$400$	−4.83092	+	1.28927i	−0.241546	+	0.0644634i
$401$	15.4318	−	8.90955i	0.770627	−	0.444922i	−0.0624713	−	0.998047i	$-0.519898\pi$
$401$	15.4318	−	8.90955i	0.770627	−	0.444922i	0.833098	+	0.553125i	$0.186565\pi$
$402$	−10.3413	−	21.3477i	−0.515779	−	1.06472i
$403$	3.44064	+	12.8407i	0.171391	+	0.639638i
$404$	3.95547	+	6.85108i	0.196792	+	0.340854i
$405$	12.7035	−	15.6084i	0.631242	−	0.775586i
$406$	9.13673	+	1.36015i	0.453448	+	0.0675030i
$407$	−6.09148	+	6.09148i	−0.301944	+	0.301944i
$408$	4.28175	+	0.310924i	0.211978	+	0.0153930i
$409$	−11.3497	−	6.55276i	−0.561208	−	0.324013i	0.192423	−	0.981312i	$-0.438366\pi$
$409$	−11.3497	−	6.55276i	−0.561208	−	0.324013i	−0.753630	+	0.657299i	$0.771699\pi$
$410$	11.9171	−	4.92925i	0.588544	−	0.243438i
$411$	−3.24660	+	2.80701i	−0.160143	+	0.138460i
$412$	−9.75972	−	9.75972i	−0.480827	−	0.480827i
$413$	11.4888	−	26.4637i	0.565325	−	1.30220i
$414$	−8.45676	−	21.2580i	−0.415627	−	1.04477i
$415$	−0.691839	+	5.23482i	−0.0339611	+	0.256967i
$416$	−2.09634	−	1.21032i	−0.102782	−	0.0593410i
$417$	−5.57907	+	2.70264i	−0.273208	+	0.132349i
$418$	−7.19934	−	1.92906i	−0.352131	−	0.0943533i
$419$	−12.5812			−0.614634			−0.307317	−	0.951607i	$-0.599431\pi$
$419$	−12.5812			−0.614634			−0.307317	+	0.951607i	$0.599431\pi$
$420$	7.86674	−	6.56616i	0.383858	−	0.320396i
$421$	−6.71657			−0.327346			−0.163673	−	0.986515i	$-0.552334\pi$
$421$	−6.71657			−0.327346			−0.163673	+	0.986515i	$0.552334\pi$
$422$	−8.61882	−	2.30941i	−0.419558	−	0.112420i
$423$	−14.5561	+	10.8471i	−0.707740	+	0.527406i
$424$	11.7754	+	6.79852i	0.571863	+	0.330165i
$425$	12.3929	+	0.0123874i	0.601143	+	0.000600876i
$426$	−18.5633	+	3.55682i	−0.899395	+	0.172329i
$427$	−13.3051	−	17.9593i	−0.643878	−	0.869110i
$428$	−14.3225	−	14.3225i	−0.692304	−	0.692304i
$429$	−4.72081	−	5.46011i	−0.227923	−	0.263616i
$430$	3.89472	+	1.61553i	0.187820	+	0.0779077i
$431$	16.1423	+	9.31978i	0.777549	+	0.448918i	0.835561	−	0.549398i	$-0.185143\pi$
$431$	16.1423	+	9.31978i	0.777549	+	0.448918i	−0.0580119	+	0.998316i	$0.518476\pi$
$432$	1.56598	+	4.95456i	0.0753433	+	0.238377i
$433$	−2.13742	+	2.13742i	−0.102718	+	0.102718i	−0.756598	−	0.653880i	$-0.773140\pi$
$433$	−2.13742	+	2.13742i	−0.102718	+	0.102718i	0.653880	+	0.756598i	$0.273140\pi$
$434$	9.03853	−	11.3763i	0.433863	−	0.546082i
$435$	−6.07197	+	12.0822i	−0.291128	+	0.579299i
$436$	−3.81854	−	6.61391i	−0.182875	−	0.316749i
$437$	−8.54530	−	31.8915i	−0.408777	−	1.52558i
$438$	5.11895	−	2.47974i	0.244593	−	0.118487i
$439$	12.7163	−	7.34175i	0.606915	−	0.350403i	−0.164842	−	0.986320i	$-0.552711\pi$
$439$	12.7163	−	7.34175i	0.606915	−	0.350403i	0.771757	+	0.635917i	$0.219378\pi$
$440$	2.34497	−	3.05286i	0.111792	−	0.145539i
$441$	−8.95497	+	18.9950i	−0.426427	+	0.904522i
$442$	4.24247	+	4.24247i	0.201794	+	0.201794i
$443$	1.88373	−	7.03018i	0.0894987	−	0.334014i	−0.906629	−	0.421928i	$-0.861353\pi$
$443$	1.88373	−	7.03018i	0.0894987	−	0.334014i	0.996128	+	0.0879143i	$0.0280202\pi$
$444$	8.18738	+	2.84367i	0.388556	+	0.134955i
$445$	−2.80473	+	6.76166i	−0.132957	+	0.320533i
$446$	−6.06911	+	3.50400i	−0.287381	+	0.165919i
$447$	13.0378	−	19.2183i	0.616669	−	0.908993i
$448$	0.301012	+	2.62857i	0.0142215	+	0.124188i
$449$	−32.4071			−1.52939			−0.764694	−	0.644394i	$-0.777110\pi$
$449$	−32.4071			−1.52939			−0.764694	+	0.644394i	$0.777110\pi$
$450$	5.53066	+	13.9432i	0.260718	+	0.657287i
$451$	−4.96447	+	8.59871i	−0.233768	+	0.404897i
$452$	−1.64936	−	6.15549i	−0.0775793	−	0.289530i
$453$	9.46350	+	0.687202i	0.444634	+	0.0322876i
$454$			24.4256i			1.14635i
$455$	14.3186	+	0.248894i	0.671265	+	0.0116683i
$456$	1.41112	+	7.36476i	0.0660820	+	0.344886i
$457$	2.47225	−	9.22656i	0.115647	−	0.431601i	−0.883687	−	0.468077i	$-0.844947\pi$
$457$	2.47225	−	9.22656i	0.115647	−	0.431601i	0.999334	+	0.0364769i	$0.0116135\pi$
$458$	1.75010	−	0.468937i	0.0817767	−	0.0219120i
$459$	−0.570782	−	12.8664i	−0.0266418	−	0.600553i
$460$	16.9055	+	2.23425i	0.788225	+	0.104173i
$461$			20.6157i			0.960170i	0.877222	+	0.480085i	$0.159394\pi$
$461$			20.6157i			0.960170i	−0.877222	+	0.480085i	$0.840606\pi$
$462$	−1.72373	+	7.69856i	−0.0801950	+	0.358169i
$463$	−21.4096	+	21.4096i	−0.994986	+	0.994986i	−0.999987	−	0.00500119i	$-0.998408\pi$
$463$	−21.4096	+	21.4096i	−0.994986	+	0.994986i	0.00500119	+	0.999987i	$0.498408\pi$
$464$	−1.74571	−	3.02365i	−0.0810424	−	0.140370i
$465$	11.6831	+	17.7735i	0.541789	+	0.824228i
$466$	0.942716	−	1.63283i	0.0436705	−	0.0756395i
$467$	−25.7099	−	6.88896i	−1.18971	−	0.318783i	−0.390942	−	0.920416i	$-0.627851\pi$
$467$	−25.7099	−	6.88896i	−1.18971	−	0.318783i	−0.798773	+	0.601632i	$0.794517\pi$
$468$	−2.87320	+	6.66937i	−0.132814	+	0.308292i
$469$	−33.7049	+	13.2990i	−1.55635	+	0.614091i
$470$	−1.75940	−	13.4157i	−0.0811549	−	0.618822i
$471$	12.5160	+	14.4760i	0.576706	+	0.667020i
$472$	−10.5327	+	2.82223i	−0.484807	+	0.129904i
$473$	−3.13568	+	0.840203i	−0.144179	+	0.0386326i
$474$	3.89606	+	4.50620i	0.178952	+	0.206977i
$475$	5.58174	+	20.9150i	0.256108	+	0.959644i
$476$	0.965579	−	6.48623i	0.0442572	−	0.297296i
$477$	16.1391	−	37.4626i	0.738957	−	1.71529i
$478$	−7.08694	−	1.89894i	−0.324149	−	0.0868555i
$479$	−15.6629	+	27.1290i	−0.715657	+	1.23955i	0.247049	+	0.969003i	$0.420539\pi$
$479$	−15.6629	+	27.1290i	−0.715657	+	1.23955i	−0.962706	+	0.270551i	$0.912794\pi$
$480$	−3.79276	−	0.784196i	−0.173115	−	0.0357935i
$481$	6.05644	+	10.4901i	0.276150	+	0.478306i
$482$	−9.95482	+	9.95482i	−0.453430	+	0.453430i
$483$	−33.3519	+	10.4387i	−1.51756	+	0.474979i
$484$		−	8.03624i		−	0.365283i
$485$	−4.63878	+	35.0995i	−0.210636	+	1.59378i
$486$	14.2148	−	6.39838i	0.644797	−	0.290236i
$487$	3.80941	−	1.02073i	0.172621	−	0.0462536i	−0.171473	−	0.985189i	$-0.554853\pi$
$487$	3.80941	−	1.02073i	0.172621	−	0.0462536i	0.344094	+	0.938935i	$0.388186\pi$
$488$	−2.18646	+	8.15997i	−0.0989763	+	0.369385i
$489$	1.62191	+	8.46485i	0.0733452	+	0.382794i
$490$	−9.09765	−	12.7371i	−0.410990	−	0.575402i
$491$			17.7217i			0.799771i	0.916565	+	0.399886i	$0.130950\pi$
$491$			17.7217i			0.799771i	−0.916565	+	0.399886i	$0.869050\pi$
$492$	9.96321	+	0.723489i	0.449176	+	0.0326174i
$493$	2.23975	+	8.35887i	0.100873	+	0.376465i
$494$	−5.23997	+	9.07589i	−0.235757	+	0.408343i
$495$	−9.91612	−	5.91946i	−0.445696	−	0.266060i
$496$	−5.49176			−0.246588
$497$	3.28479	+	28.6843i	0.147343	+	1.28666i
$498$	−2.29624	+	3.38474i	−0.102897	+	0.151674i
$499$	14.7187	−	8.49786i	0.658901	−	0.380417i	−0.132957	−	0.991122i	$-0.542447\pi$
$499$	14.7187	−	8.49786i	0.658901	−	0.380417i	0.791858	+	0.610705i	$0.209114\pi$
$500$	−11.0825	−	1.47595i	−0.495624	−	0.0660063i
$501$	−29.3263	−	10.1857i	−1.31020	−	0.455063i
$502$	−6.01522	+	22.4491i	−0.268472	+	1.00195i
$503$	−13.9310	−	13.9310i	−0.621153	−	0.621153i	0.324673	−	0.945826i	$-0.394746\pi$
$503$	−13.9310	−	13.9310i	−0.621153	−	0.621153i	−0.945826	+	0.324673i	$0.894746\pi$
$504$	7.72671	−	1.81601i	0.344175	−	0.0808915i
$505$	2.30016	+	17.5392i	0.102356	+	0.780485i
$506$	−11.3699	+	6.56441i	−0.505453	+	0.291824i
$507$	11.1304	−	5.39186i	0.494320	−	0.239461i
$508$	−1.38055	−	5.15230i	−0.0612522	−	0.228596i
$509$	−8.58091	−	14.8626i	−0.380342	−	0.658772i	0.610769	−	0.791809i	$-0.290860\pi$
$509$	−8.58091	−	14.8626i	−0.380342	−	0.658772i	−0.991111	+	0.133037i	$0.957527\pi$
$510$	8.57727	+	4.31053i	0.379808	+	0.190874i
$511$	−3.18897	−	8.08209i	−0.141072	−	0.357531i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	21.4503	−	6.77975i	0.947052	−	0.299333i
$514$	−13.0993	−	7.56288i	−0.577785	−	0.333584i
$515$	−11.7965	−	28.5196i	−0.519815	−	1.25672i
$516$	2.13614	+	2.47067i	0.0940383	+	0.108765i
$517$	7.36613	+	7.36613i	0.323962	+	0.323962i
$518$	5.27221	−	12.1443i	0.231648	−	0.533588i
$519$	13.1405	−	2.51779i	0.576804	−	0.110519i
$520$	−3.29292	−	4.29585i	−0.144404	−	0.188386i
$521$	−0.555645	−	0.320802i	−0.0243433	−	0.0140546i	0.487779	−	0.872967i	$-0.337807\pi$
$521$	−0.555645	−	0.320802i	−0.0243433	−	0.0140546i	−0.512122	+	0.858913i	$0.671141\pi$
$522$	−8.39871	+	6.25870i	−0.367602	+	0.273936i
$523$	−11.0142	−	2.95123i	−0.481615	−	0.129048i	0.00983936	−	0.999952i	$-0.496868\pi$
$523$	−11.0142	−	2.95123i	−0.481615	−	0.129048i	−0.491455	+	0.870903i	$0.663535\pi$
$524$	−10.0014			−0.436911
$525$	21.8737	−	6.82220i	0.954645	−	0.297745i
$526$	13.3788			0.583341
$527$	13.1480	+	3.52299i	0.572734	+	0.153464i
$528$	2.68354	−	1.29997i	0.116786	−	0.0565740i
$529$	−30.4476	−	17.5789i	−1.32381	−	0.764300i
$530$	18.4967	+	24.1303i	0.803444	+	1.04815i
$531$	12.0919	+	30.3959i	0.524746	+	1.31907i
$532$	11.3801	−	1.30320i	0.493391	−	0.0565008i
$533$	9.87182	+	9.87182i	0.427596	+	0.427596i
$534$	−4.28934	+	3.70857i	−0.185618	+	0.160485i
$535$	−17.3115	−	41.8528i	−0.748440	−	1.80945i
$536$	11.8603	+	6.84754i	0.512286	+	0.295769i
$537$	−6.16344	−	0.447565i	−0.265972	−	0.0193138i
$538$	2.42859	−	2.42859i	0.104704	−	0.104704i
$539$	11.5284	+	3.51015i	0.496562	+	0.151193i
$540$	−1.01034	+	11.5749i	−0.0434782	+	0.498106i
$541$	7.98850	+	13.8365i	0.343452	+	0.594877i	0.985071	−	0.172147i	$-0.0550703\pi$
$541$	7.98850	+	13.8365i	0.343452	+	0.594877i	−0.641619	+	0.767023i	$0.721737\pi$
$542$	−3.95140	−	14.7468i	−0.169727	−	0.633431i
$543$	16.9528	+	34.9957i	0.727513	+	1.50181i
$544$	−2.14651	+	1.23929i	−0.0920310	+	0.0531341i
$545$	−2.22054	−	16.9320i	−0.0951174	−	0.725289i
$546$	9.82864	+	5.14277i	0.420627	+	0.220090i
$547$	−9.35884	−	9.35884i	−0.400155	−	0.400155i	0.478132	−	0.878288i	$-0.341314\pi$
$547$	−9.35884	−	9.35884i	−0.400155	−	0.400155i	−0.878288	+	0.478132i	$0.841314\pi$
$548$	0.641324	−	2.39345i	0.0273960	−	0.102243i
$549$	25.0776	+	3.66138i	1.07029	+	0.156264i
$550$	7.45887	−	4.29644i	0.318047	−	0.183201i
$551$	−13.0906	+	7.55785i	−0.557677	+	0.321975i
$552$	10.9308	+	7.41556i	0.465247	+	0.315627i
$553$	7.31150	−	5.41670i	0.310916	−	0.230342i
$554$	−31.4667			−1.33689
$555$	14.4742	+	12.8878i	0.614395	+	0.547058i
$556$	1.78956	−	3.09961i	0.0758942	−	0.131453i
$557$	5.02971	+	18.7711i	0.213116	+	0.795358i	0.986821	+	0.161813i	$0.0517342\pi$
$557$	5.02971	+	18.7711i	0.213116	+	0.795358i	−0.773706	+	0.633545i	$0.781599\pi$
$558$	1.92030	+	16.3630i	0.0812928	+	0.692701i
$559$			4.56455i			0.193060i
$560$	−1.63028	+	5.68702i	−0.0688919	+	0.240320i
$561$	−7.25865	+	1.39079i	−0.306461	+	0.0587194i
$562$	1.74065	−	6.49619i	0.0734249	−	0.274025i
$563$	30.5854	−	8.19533i	1.28902	−	0.345392i	0.451732	−	0.892154i	$-0.350806\pi$
$563$	30.5854	−	8.19533i	1.28902	−	0.345392i	0.837288	+	0.546761i	$0.184140\pi$
$564$	3.43871	−	9.90060i	0.144796	−	0.416890i
$565$	1.86701	−	14.1268i	0.0785458	−	0.594319i
$566$		−	1.13252i		−	0.0476032i
$567$	−8.11269	−	22.3871i	−0.340701	−	0.940172i
$568$	7.71629	−	7.71629i	0.323768	−	0.323768i
$569$	−2.76033	−	4.78104i	−0.115719	−	0.200432i	0.802348	−	0.596857i	$-0.203584\pi$
$569$	−2.76033	−	4.78104i	−0.115719	−	0.200432i	−0.918067	+	0.396425i	$0.870251\pi$
$570$	−3.39509	+	16.4204i	−0.142205	+	0.687773i
$571$	10.0033	−	17.3262i	0.418623	−	0.725077i	−0.577178	−	0.816618i	$-0.695846\pi$
$571$	10.0033	−	17.3262i	0.418623	−	0.725077i	0.995801	+	0.0915415i	$0.0291794\pi$
$572$	4.02529	+	1.07857i	0.168306	+	0.0450974i
$573$	−33.1640	−	22.4987i	−1.38545	−	0.939898i
$574$	2.24681	−	15.0928i	0.0937799	−	0.629962i
$575$	33.0030	+	19.0983i	1.37632	+	0.796455i
$576$	−2.35411	−	1.85961i	−0.0980881	−	0.0774837i
$577$	−7.38948	+	1.98001i	−0.307628	+	0.0824287i	−0.409331	−	0.912386i	$-0.634238\pi$
$577$	−7.38948	+	1.98001i	−0.307628	+	0.0824287i	0.101702	+	0.994815i	$0.467571\pi$
$578$	−10.4867	+	2.80991i	−0.436190	+	0.116877i
$579$	21.0735	−	18.2202i	0.875786	−	0.757205i
$580$	−1.01515	−	7.74076i	−0.0421520	−	0.321417i
$581$	4.89179	+	3.88654i	0.202946	+	0.161241i
$582$	−15.3963	+	22.6947i	−0.638196	+	0.940725i
$583$	−22.6105	−	6.05846i	−0.936430	−	0.250916i
$584$	−1.64197	+	2.84397i	−0.0679452	+	0.117684i
$585$	−11.6483	+	11.3135i	−0.481598	+	0.467757i
$586$	−16.3013	−	28.2347i	−0.673402	−	1.16637i
$587$	16.6172	−	16.6172i	0.685865	−	0.685865i	−0.275450	−	0.961315i	$-0.588827\pi$
$587$	16.6172	−	16.6172i	0.685865	−	0.685865i	0.961315	+	0.275450i	$0.0888269\pi$
$588$	−1.87833	−	11.9780i	−0.0774610	−	0.493963i
$589$			23.7760i			0.979673i
$590$	−24.1725	−	3.19466i	−0.995166	−	0.131522i
$591$	10.4441	+	3.62748i	0.429613	+	0.149215i
$592$	−4.83348	+	1.29513i	−0.198655	+	0.0532294i
$593$	11.0056	−	41.0736i	0.451948	−	1.68669i	−0.244961	−	0.969533i	$-0.578775\pi$
$593$	11.0056	−	41.0736i	0.451948	−	1.68669i	0.696909	−	0.717159i	$-0.254558\pi$
$594$	−4.81168	−	7.54118i	−0.197426	−	0.309418i
$595$	7.55133	−	12.5696i	0.309575	−	0.515303i
$596$			13.4080i			0.549215i
$597$	−0.271435	+	3.73795i	−0.0111091	+	0.152984i
$598$	4.77784	+	17.8311i	0.195380	+	0.729170i
$599$	−2.61599	+	4.53103i	−0.106887	+	0.185133i	−0.914507	−	0.404569i	$-0.867422\pi$
$599$	−2.61599	+	4.53103i	−0.106887	+	0.185133i	0.807621	+	0.589702i	$0.200755\pi$
$600$	−7.16183	−	4.86911i	−0.292380	−	0.198780i
$601$	35.0786			1.43089			0.715443	−	0.698671i	$-0.246225\pi$
$601$	35.0786			1.43089			0.715443	+	0.698671i	$0.246225\pi$
$602$	4.00876	−	2.96988i	0.163385	−	0.121043i
$603$	16.2554	−	37.7327i	0.661972	−	1.53660i
$604$	−4.74421	+	2.73907i	−0.193039	+	0.111451i
$605$	6.88495	−	16.5983i	0.279913	−	0.674816i
$606$	−4.49563	+	12.9437i	−0.182623	+	0.525800i
$607$	−3.76707	+	14.0589i	−0.152900	+	0.570632i	0.846376	+	0.532587i	$0.178780\pi$
$607$	−3.76707	+	14.0589i	−0.152900	+	0.570632i	−0.999276	+	0.0380457i	$0.987887\pi$
$608$	−3.06134	−	3.06134i	−0.124154	−	0.124154i
$609$	8.56821	+	13.5120i	0.347201	+	0.547535i
$610$	−11.5069	+	14.9806i	−0.465902	+	0.606548i
$611$	12.6851	−	7.32376i	0.513185	−	0.296288i
$612$	4.44310	+	5.96230i	0.179602	+	0.241012i
$613$	−7.43363	−	27.7427i	−0.300241	−	1.12052i	−0.936965	−	0.349424i	$-0.886377\pi$
$613$	−7.43363	−	27.7427i	−0.300241	−	1.12052i	0.636723	−	0.771092i	$-0.280289\pi$
$614$	4.92094	+	8.52331i	0.198593	+	0.343973i
$615$	19.9585	+	10.0302i	0.804803	+	0.404456i
$616$	−1.67177	−	4.23692i	−0.0673575	−	0.170711i
$617$	24.1611	−	24.1611i	0.972689	−	0.972689i	−0.0269478	−	0.999637i	$-0.508579\pi$
$617$	24.1611	−	24.1611i	0.972689	−	0.972689i	0.999637	+	0.0269478i	$0.00857878\pi$
$618$	1.73142	−	23.8436i	0.0696481	−	0.959129i
$619$	−1.28110	−	0.739645i	−0.0514919	−	0.0297288i	0.474033	−	0.880507i	$-0.342798\pi$
$619$	−1.28110	−	0.739645i	−0.0514919	−	0.0297288i	−0.525525	+	0.850778i	$0.676131\pi$
$620$	−11.3429	−	4.70501i	−0.455540	−	0.188958i
$621$	18.2729	−	35.1619i	0.733266	−	1.41100i
$622$	6.27017	+	6.27017i	0.251411	+	0.251411i
$623$	5.15603	+	6.95964i	0.206572	+	0.278832i
$624$	−0.788987	−	4.11778i	−0.0315848	−	0.164843i
$625$	−21.6256	−	12.5433i	−0.865024	−	0.501730i
$626$	−5.01667	−	2.89637i	−0.200506	−	0.115762i
$627$	−5.62809	−	11.6181i	−0.224764	−	0.463982i
$628$	−10.6720	−	2.85955i	−0.425859	−	0.114109i
$629$	12.4028			0.494531
$630$	17.5148	+	2.86893i	0.697807	+	0.114301i
$631$	−46.0928			−1.83492			−0.917462	−	0.397824i	$-0.869765\pi$
$631$	−46.0928			−1.83492			−0.917462	+	0.397824i	$0.869765\pi$
$632$	−3.32205	−	0.890141i	−0.132144	−	0.0354079i
$633$	−6.73777	−	13.9088i	−0.267802	−	0.552825i
$634$	3.67892	+	2.12403i	0.146109	+	0.0843558i
$635$	1.56273	−	11.8245i	0.0620152	−	0.469240i
$636$	4.43183	+	23.1300i	0.175733	+	0.917164i
$637$	8.96278	−	14.3800i	0.355118	−	0.569758i
$638$	4.25019	+	4.25019i	0.168267	+	0.168267i
$639$	−25.6892	−	20.2929i	−1.01625	−	0.802777i
$640$	2.06628	−	0.854674i	0.0816771	−	0.0337839i
$641$	−8.05187	−	4.64875i	−0.318030	−	0.183614i	0.332484	−	0.943109i	$-0.392113\pi$
$641$	−8.05187	−	4.64875i	−0.318030	−	0.183614i	−0.650514	+	0.759494i	$0.725446\pi$
$642$	2.54088	−	34.9907i	0.100281	−	1.38097i
$643$	18.9401	−	18.9401i	0.746924	−	0.746924i	−0.226976	−	0.973900i	$-0.572884\pi$
$643$	18.9401	−	18.9401i	0.746924	−	0.746924i	0.973900	+	0.226976i	$0.0728840\pi$
$644$	12.5513	−	15.7977i	0.494592	−	0.622518i
$645$	2.29533	+	6.93310i	0.0903785	+	0.272991i
$646$	5.36537	+	9.29310i	0.211098	+	0.365632i
$647$	8.89500	+	33.1966i	0.349698	+	1.30509i	0.887026	+	0.461719i	$0.152767\pi$
$647$	8.89500	+	33.1966i	0.349698	+	1.30509i	−0.537328	+	0.843373i	$0.680566\pi$
$648$	−4.71764	+	7.66446i	−0.185326	+	0.301088i
$649$	16.2573	−	9.38617i	0.638156	−	0.368439i
$650$	−3.12086	−	11.6940i	−0.122410	−	0.458675i
$651$	25.1447	−	1.04486i	0.985500	−	0.0409512i
$652$	−3.51862	−	3.51862i	−0.137800	−	0.137800i
$653$	−6.94497	+	25.9190i	−0.271778	+	1.01429i	0.686193	+	0.727420i	$0.259281\pi$
$653$	−6.94497	+	25.9190i	−0.271778	+	1.01429i	−0.957970	+	0.286868i	$0.907386\pi$
$654$	4.34000	−	12.4956i	0.169708	−	0.488616i
$655$	−20.6571	−	8.56854i	−0.807139	−	0.334801i
$656$	−4.99472	+	2.88370i	−0.195011	+	0.112590i
$657$	9.04791	+	3.89788i	0.352993	+	0.152071i
$658$	−14.6855	−	6.37543i	−0.572499	−	0.248540i
$659$	−5.40014			−0.210360			−0.105180	−	0.994453i	$-0.533542\pi$
$659$	−5.40014			−0.210360			−0.105180	+	0.994453i	$0.533542\pi$
$660$	6.65639	−	0.385911i	0.259100	−	0.0150216i
$661$	12.2794	−	21.2685i	0.477613	−	0.827250i	−0.522057	−	0.852910i	$-0.674835\pi$
$661$	12.2794	−	21.2685i	0.477613	−	0.827250i	0.999671	+	0.0256598i	$0.00816868\pi$
$662$	1.39997	+	5.22475i	0.0544113	+	0.203066i
$663$	−0.752636	+	10.3646i	−0.0292300	+	0.402528i
$664$		−	2.36144i		−	0.0916417i
$665$	24.6213	+	7.05813i	0.954775	+	0.273702i
$666$	5.54902	+	13.9487i	0.215020	+	0.540503i
$667$	−6.89131	+	25.7187i	−0.266832	+	0.995832i
$668$	17.3130	−	4.63900i	0.669859	−	0.179488i
$669$	−11.4663	−	3.98251i	−0.443313	−	0.153973i
$670$	18.6300	+	24.3043i	0.719741	+	0.938956i
$671$		−	14.5434i		−	0.561443i
$672$	−3.10304	+	3.37211i	−0.119702	+	0.130082i
$673$	18.8221	−	18.8221i	0.725540	−	0.725540i	−0.244188	−	0.969728i	$-0.578521\pi$
$673$	18.8221	−	18.8221i	0.725540	−	0.725540i	0.969728	+	0.244188i	$0.0785214\pi$
$674$	−7.64272	−	13.2376i	−0.294386	−	0.509892i
$675$	−12.0035	+	23.0416i	−0.462014	+	0.886872i
$676$	−3.57023	+	6.18383i	−0.137317	+	0.237840i
$677$	27.4373	+	7.35179i	1.05450	+	0.282552i	0.744110	−	0.668057i	$-0.232874\pi$
$677$	27.4373	+	7.35179i	1.05450	+	0.282552i	0.310389	+	0.950609i	$0.399541\pi$
$678$	6.19668	−	9.13414i	0.237982	−	0.350795i
$679$	32.7994	+	26.0592i	1.25873	+	1.00006i
$680$	−5.49522	+	0.720665i	−0.210732	+	0.0276362i
$681$	−32.0032	+	27.6699i	−1.22636	+	1.06031i
$682$	9.13224	−	2.44698i	0.349692	−	0.0936996i
$683$	2.45890	−	0.658859i	0.0940871	−	0.0252106i	−0.211468	−	0.977385i	$-0.567825\pi$
$683$	2.45890	−	0.658859i	0.0940871	−	0.0252106i	0.305555	+	0.952174i	$0.401158\pi$
$684$	−8.05098	+	10.1919i	−0.307837	+	0.389697i
$685$	3.37517	−	4.39406i	0.128959	−	0.167889i
$686$	−18.4606	+	1.48478i	−0.704831	+	0.0566891i
$687$	2.59697	+	1.76181i	0.0990807	+	0.0672172i
$688$	−1.82142	−	0.488048i	−0.0694410	−	0.0186067i
$689$	−16.4568	+	28.5040i	−0.626955	+	1.08592i
$690$	16.2236	+	24.6812i	0.617624	+	0.939596i
$691$	−2.47893	−	4.29362i	−0.0943028	−	0.163337i	0.815015	−	0.579440i	$-0.196729\pi$
$691$	−2.47893	−	4.29362i	−0.0943028	−	0.163337i	−0.909317	+	0.416103i	$0.863396\pi$
$692$	−5.46217	+	5.46217i	−0.207641	+	0.207641i
$693$	−12.0396	+	6.46265i	−0.457346	+	0.245496i
$694$		−	22.0253i		−	0.836070i
$695$	6.35176	−	4.86884i	0.240936	−	0.184686i
$696$	1.98410	−	5.71255i	0.0752072	−	0.216534i
$697$	13.8079	−	3.69981i	0.523011	−	0.140140i
$698$	−0.313481	+	1.16993i	−0.0118654	+	0.0442824i
$699$	3.20732	−	0.614539i	0.121312	−	0.0232440i
$700$	−8.23952	+	10.3494i	−0.311424	+	0.391171i
$701$		−	7.09309i		−	0.267902i	−0.990988	−	0.133951i	$-0.957233\pi$
$701$		−	7.09309i		−	0.267902i	0.990988	−	0.133951i	$-0.0427665\pi$
$702$	−11.9932	+	3.79069i	−0.452656	+	0.143070i
$703$	5.60712	+	20.9260i	0.211476	+	0.789241i
$704$	−0.860779	+	1.49091i	−0.0324418	+	0.0561909i
$705$	15.5846	−	17.5029i	0.586951	−	0.659198i
$706$	13.3989			0.504276
$707$	19.1992	+	8.33498i	0.722060	+	0.313469i
$708$	−15.6295	−	10.6032i	−0.587393	−	0.398492i
$709$	−24.9741	+	14.4188i	−0.937921	+	0.541509i	−0.889308	−	0.457309i	$-0.848814\pi$
$709$	−24.9741	+	14.4188i	−0.937921	+	0.541509i	−0.0486133	+	0.998818i	$0.515480\pi$
$710$	22.5483	−	9.32661i	0.846223	−	0.350022i
$711$	−1.49060	+	10.2095i	−0.0559020	+	0.382885i
$712$	0.847304	−	3.16218i	0.0317540	−	0.118508i
$713$	29.6143	+	29.6143i	1.10906	+	1.10906i
$714$	9.59229	−	6.08263i	0.358982	−	0.227637i
$715$	7.38989	+	5.67634i	0.276366	+	0.212283i
$716$	3.08984	−	1.78392i	0.115473	−	0.0666681i
$717$	−5.54022	−	11.4367i	−0.206903	−	0.427111i
$718$	−3.16326	−	11.8054i	−0.118052	−	0.440575i
$719$	−7.22895	−	12.5209i	−0.269594	−	0.466951i	0.699163	−	0.714962i	$-0.253556\pi$
$719$	−7.22895	−	12.5209i	−0.269594	−	0.466951i	−0.968757	+	0.248012i	$0.920223\pi$
$720$	−3.26906	−	5.85775i	−0.121831	−	0.218305i
$721$	−36.1195	−	5.37697i	−1.34516	−	0.200249i
$722$	0.181270	−	0.181270i	0.00674618	−	0.00674618i
$723$	−24.3202	−	1.76604i	−0.904478	−	0.0656796i
$724$	−19.4428	−	11.2253i	−0.722587	−	0.417186i
$725$	4.53507	−	16.8577i	0.168428	−	0.626079i
$726$	10.5293	−	9.10366i	0.390780	−	0.337868i
$727$	16.0036	+	16.0036i	0.593541	+	0.593541i	0.938586	−	0.345045i	$-0.112136\pi$
$727$	16.0036	+	16.0036i	0.593541	+	0.593541i	−0.345045	+	0.938586i	$0.612136\pi$
$728$	−6.36285	+	0.728643i	−0.235823	+	0.0270053i
$729$	24.4863	+	11.3764i	0.906898	+	0.421349i
$730$	−5.82791	+	4.46729i	−0.215701	+	0.165342i
$731$	4.04762	+	2.33689i	0.149707	+	0.0864332i
$732$	−13.1683	+	6.37907i	−0.486715	+	0.235777i
$733$	11.5274	+	3.08877i	0.425775	+	0.114086i	0.465342	−	0.885131i	$-0.345931\pi$
$733$	11.5274	+	3.08877i	0.425775	+	0.114086i	−0.0395671	+	0.999217i	$0.512598\pi$
$734$	−15.9411			−0.588395
$735$	6.38243	−	26.3489i	0.235420	−	0.971894i
$736$	−7.62613			−0.281103
$737$	−22.7735	−	6.10215i	−0.838873	−	0.224775i
$738$	10.3386	+	13.8737i	0.380571	+	0.510698i
$739$	29.8148	+	17.2136i	1.09675	+	0.633211i	0.935366	−	0.353680i	$-0.115070\pi$
$739$	29.8148	+	17.2136i	1.09675	+	0.633211i	0.161387	+	0.986891i	$0.448403\pi$
$740$	−11.0928	−	1.46604i	−0.407779	−	0.0538925i
$741$	−17.8275	+	3.41583i	−0.654909	+	0.125484i
$742$	35.7408	−	4.09287i	1.31209	−	0.150254i
$743$	33.6273	+	33.6273i	1.23367	+	1.23367i	0.962545	+	0.271121i	$0.0873943\pi$
$743$	33.6273	+	33.6273i	1.23367	+	1.23367i	0.271121	+	0.962545i	$0.412606\pi$
$744$	−6.22121	−	7.19548i	−0.228081	−	0.263799i
$745$	−11.4872	+	27.6934i	−0.420858	+	1.01461i
$746$	−18.8472	−	10.8814i	−0.690045	−	0.398398i
$747$	−7.03604	+	0.825723i	−0.257435	+	0.0302116i
$748$	3.01724	−	3.01724i	0.110321	−	0.110321i
$749$	−53.0058	−	7.89076i	−1.93679	−	0.288322i
$750$	−10.6207	−	16.1926i	−0.387813	−	0.591271i
$751$	18.5581	+	32.1436i	0.677196	+	1.17294i	0.975822	+	0.218567i	$0.0701383\pi$
$751$	18.5581	+	32.1436i	0.677196	+	1.17294i	−0.298626	+	0.954370i	$0.596528\pi$
$752$	1.56613	+	5.84489i	0.0571110	+	0.213141i
$753$	−36.2277	+	17.5496i	−1.32021	+	0.639543i
$754$	7.31919	−	4.22574i	0.266549	−	0.153892i
$755$	−12.1455	+	1.59281i	−0.442020	+	0.0579683i
$756$	11.1324	+	8.06656i	0.404882	+	0.293378i
$757$	−8.10894	−	8.10894i	−0.294724	−	0.294724i	0.544219	−	0.838943i	$-0.316826\pi$
$757$	−8.10894	−	8.10894i	−0.294724	−	0.294724i	−0.838943	+	0.544219i	$0.816826\pi$
$758$	−5.19890	+	19.4026i	−0.188833	+	0.704733i
$759$	−21.4810	−	7.46085i	−0.779711	−	0.270812i
$760$	−3.70022	−	8.94576i	−0.134221	−	0.324497i
$761$	−25.8264	+	14.9109i	−0.936205	+	0.540518i	−0.888769	−	0.458356i	$-0.848438\pi$
$761$	−25.8264	+	14.9109i	−0.936205	+	0.540518i	−0.0474360	+	0.998874i	$0.515105\pi$
$762$	5.18677	−	7.64550i	0.187897	−	0.276967i
$763$	−18.5346	−	8.04645i	−0.670996	−	0.291301i
$764$	23.1376			0.837088
$765$	4.06877	+	16.1213i	0.147107	+	0.582867i
$766$	0.183154	−	0.317232i	0.00661763	−	0.0114621i
$767$	−6.83163	−	25.4960i	−0.246676	−	0.920606i
$768$	1.72750	+	0.125444i	0.0623359	+	0.00452658i
$769$		−	11.1146i		−	0.400803i	−0.979714	−	0.200401i	$-0.935775\pi$
$769$		−	11.1146i		−	0.400803i	0.979714	−	0.200401i	$-0.0642246\pi$
$770$	0.177013	−	10.1833i	0.00637909	−	0.366982i
$771$	−4.93010	−	25.7305i	−0.177553	−	0.926662i
$772$	−4.16280	+	15.5358i	−0.149822	+	0.559145i
$773$	−3.31800	+	0.889057i	−0.119340	+	0.0319771i	−0.317995	−	0.948092i	$-0.603009\pi$
$773$	−3.31800	+	0.889057i	−0.119340	+	0.0319771i	0.198655	+	0.980070i	$0.436343\pi$
$774$	−0.817271	+	5.59767i	−0.0293762	+	0.201204i
$775$	−19.3969	−	19.4357i	−0.696757	−	0.698152i
$776$		−	15.8334i		−	0.568388i
$777$	21.8843	−	6.84952i	0.785094	−	0.245725i
$778$	−9.41423	+	9.41423i	−0.337516	+	0.337516i
$779$	12.4847	+	21.6241i	0.447310	+	0.774764i
$780$	1.89826	−	9.18094i	0.0679687	−	0.328730i
$781$	−9.39324	+	16.2696i	−0.336117	+	0.582171i
$782$	18.2579	+	4.89219i	0.652901	+	0.174944i
$783$	−17.7146	−	3.91423i	−0.633069	−	0.139883i
$784$	4.77984	+	5.11401i	0.170709	+	0.182643i
$785$	−19.5924	−	15.0493i	−0.699281	−	0.537133i
$786$	−11.3298	−	13.1041i	−0.404120	−	0.467407i
$787$	−49.6552	+	13.3051i	−1.77002	+	0.474275i	−0.988706	−	0.149868i	$-0.952115\pi$
$787$	−49.6552	+	13.3051i	−1.77002	+	0.474275i	−0.781311	+	0.624142i	$0.785449\pi$
$788$	−6.16576	+	1.65211i	−0.219646	+	0.0588540i
$789$	15.1558	+	17.5293i	0.539561	+	0.624058i
$790$	−6.09884	−	4.68465i	−0.216987	−	0.166672i
$791$	−13.2011	−	10.4883i	−0.469377	−	0.372921i
$792$	4.74324	+	2.04341i	0.168544	+	0.0726094i
$793$	−19.7524	−	5.29264i	−0.701429	−	0.187947i
$794$	−4.40351	+	7.62710i	−0.156275	+	0.270676i
$795$	−10.6627	+	51.5703i	−0.378169	+	1.82901i
$796$	−1.08190	−	1.87390i	−0.0383468	−	0.0664186i
$797$	−27.0994	+	27.0994i	−0.959910	+	0.959910i	−0.999227	−	0.0393164i	$-0.987482\pi$
$797$	−27.0994	+	27.0994i	−0.959910	+	0.959910i	0.0393164	+	0.999227i	$0.487482\pi$
$798$	14.5992	+	13.4343i	0.516806	+	0.475569i
$799$		−	14.9981i		−	0.530594i
$800$	5.00000	+	0.00499778i	0.176777	+	0.000176698i
$801$	−9.71816	−	1.41887i	−0.343374	−	0.0501333i
$802$	−17.2119	+	4.61192i	−0.607774	+	0.162853i
$803$	1.46323	−	5.46085i	0.0516363	−	0.192709i
$804$	4.46378	+	23.2968i	0.157425	+	0.821614i
$805$	39.4584	−	21.8759i	1.39073	−	0.771024i
$806$		−	13.2936i		−	0.468248i
$807$	5.93318	+	0.430844i	0.208858	+	0.0151664i
$808$	−2.04750	−	7.64138i	−0.0720309	−	0.268823i
$809$	0.674354	−	1.16802i	0.0237090	−	0.0410653i	−0.853927	−	0.520392i	$-0.825786\pi$
$809$	0.674354	−	1.16802i	0.0237090	−	0.0410653i	0.877636	+	0.479327i	$0.159119\pi$
$810$	−16.3104	+	11.7886i	−0.573089	+	0.414210i
$811$	24.7652			0.869624			0.434812	−	0.900521i	$-0.356815\pi$
$811$	24.7652			0.869624			0.434812	+	0.900521i	$0.356815\pi$
$812$	−8.47337	−	3.67856i	−0.297357	−	0.129092i
$813$	14.8455	−	21.8828i	0.520655	−	0.767465i
$814$	7.46051	−	4.30733i	0.261491	−	0.150972i
$815$	−4.25293	−	10.2820i	−0.148974	−	0.360163i
$816$	−4.05538	−	1.40853i	−0.141967	−	0.0493083i
$817$	−2.11295	+	7.88564i	−0.0739228	+	0.275884i
$818$	9.26701	+	9.26701i	0.324013	+	0.324013i
$819$	4.39592	+	18.7036i	0.153606	+	0.653558i
$820$	−12.7868	+	1.67692i	−0.446535	+	0.0585605i
$821$	−15.4089	+	8.89631i	−0.537773	+	0.310483i	−0.744176	−	0.667984i	$-0.767158\pi$
$821$	−15.4089	+	8.89631i	−0.537773	+	0.310483i	0.206403	+	0.978467i	$0.433824\pi$
$822$	3.86249	−	1.87108i	0.134720	−	0.0652616i
$823$	−0.521507	−	1.94629i	−0.0181786	−	0.0678434i	0.956241	−	0.292581i	$-0.0945141\pi$
$823$	−0.521507	−	1.94629i	−0.0181786	−	0.0678434i	−0.974419	+	0.224738i	$0.927847\pi$
$824$	6.90117	+	11.9532i	0.240414	+	0.416408i
$825$	14.0789	+	4.90571i	0.490165	+	0.170795i
$826$	−17.9466	+	22.5885i	−0.624442	+	0.785954i
$827$	−4.04681	+	4.04681i	−0.140721	+	0.140721i	−0.773958	−	0.633237i	$-0.781726\pi$
$827$	−4.04681	+	4.04681i	−0.140721	+	0.140721i	0.633237	+	0.773958i	$0.281726\pi$
$828$	2.66662	+	22.7224i	0.0926714	+	0.789660i
$829$	26.8242	+	15.4870i	0.931643	+	0.537884i	0.887331	−	0.461134i	$-0.152557\pi$
$829$	26.8242	+	15.4870i	0.931643	+	0.537884i	0.0443119	+	0.999018i	$0.485890\pi$
$830$	2.02314	−	4.87739i	0.0702241	−	0.169297i
$831$	−35.6463	−	41.2286i	−1.23656	−	1.43020i
$832$	1.71166	+	1.71166i	0.0593410	+	0.0593410i
$833$	−8.16288	−	15.3099i	−0.282827	−	0.530455i
$834$	6.08846	−	1.16658i	0.210826	−	0.0403954i
$835$	39.7331	+	5.25117i	1.37502	+	0.181724i
$836$	6.45475	+	3.72665i	0.223242	+	0.128889i
$837$	−19.2639	+	21.0525i	−0.665859	+	0.727680i
$838$	12.1525	+	3.25627i	0.419803	+	0.112486i
$839$	29.6641			1.02412			0.512060	−	0.858950i	$-0.328883\pi$
$839$	29.6641			1.02412			0.512060	+	0.858950i	$0.328883\pi$
$840$	−9.29813	+	4.30636i	−0.320816	+	0.148583i
$841$	−16.8100			−0.579656
$842$	6.48771	+	1.73838i	0.223581	+	0.0599084i
$843$	10.4834	−	5.07840i	0.361066	−	0.174909i
$844$	7.72742	+	4.46143i	0.265989	+	0.153569i
$845$	−12.6720	+	9.71350i	−0.435930	+	0.334155i
$846$	16.8675	−	6.71015i	0.579918	−	0.230700i
$847$	−12.6568	−	17.0843i	−0.434894	−	0.587022i
$848$	−9.61456	−	9.61456i	−0.330165	−	0.330165i
$849$	1.48386	−	1.28294i	0.0509259	−	0.0440305i
$850$	−11.9674	−	3.21948i	−0.410479	−	0.110427i
$851$	33.0484	+	19.0805i	1.13289	+	0.654072i
$852$	18.8513	+	1.36891i	0.645836	+	0.0468981i
$853$	−27.7032	+	27.7032i	−0.948539	+	0.948539i	−0.998739	−	0.0502004i	$-0.984014\pi$
$853$	−27.7032	+	27.7032i	−0.948539	+	0.948539i	0.0502004	+	0.998739i	$0.484014\pi$
$854$	8.20351	+	20.7909i	0.280718	+	0.711451i
$855$	−25.3605	+	14.1530i	−0.867311	+	0.484024i
$856$	10.1275	+	17.5414i	0.346152	+	0.599553i
$857$	6.03643	+	22.5283i	0.206200	+	0.769551i	0.989080	+	0.147378i	$0.0470833\pi$
$857$	6.03643	+	22.5283i	0.206200	+	0.769551i	−0.782880	+	0.622173i	$0.786250\pi$
$858$	3.14677	+	6.49589i	0.107429	+	0.221766i
$859$	26.1491	−	15.0972i	0.892195	−	0.515109i	0.0175351	−	0.999846i	$-0.494418\pi$
$859$	26.1491	−	15.0972i	0.892195	−	0.515109i	0.874660	+	0.484737i	$0.161085\pi$
$860$	−3.34389	−	2.56851i	−0.114026	−	0.0875854i
$861$	22.3203	−	14.1537i	0.760674	−	0.482357i
$862$	−13.1802	−	13.1802i	−0.448918	−	0.448918i
$863$	3.44152	−	12.8439i	0.117151	−	0.437212i	−0.882288	−	0.470710i	$-0.843998\pi$
$863$	3.44152	−	12.8439i	0.117151	−	0.437212i	0.999439	+	0.0334974i	$0.0106645\pi$
$864$	−0.230286	−	5.19105i	−0.00783449	−	0.176603i
$865$	−15.9614	+	6.60208i	−0.542703	+	0.224477i
$866$	2.61779	−	1.51138i	0.0889561	−	0.0513589i
$867$	−15.5613	−	10.5569i	−0.528488	−	0.358531i
$868$	−11.6750	+	8.64936i	−0.396274	+	0.293579i
$869$	5.92085			0.200851
$870$	8.99218	−	10.0990i	0.304864	−	0.342389i
$871$	−16.5755	+	28.7096i	−0.561639	+	0.972787i
$872$	1.97662	+	7.37685i	0.0669369	+	0.249812i
$873$	−47.1766	+	5.53646i	−1.59669	+	0.187381i
$874$			33.0165i			1.11680i
$875$	−25.8849	+	14.3169i	−0.875069	+	0.483999i
$876$	−5.58633	+	1.07037i	−0.188745	+	0.0361644i
$877$	6.58233	−	24.5656i	0.222269	−	0.829521i	−0.761211	−	0.648505i	$-0.775395\pi$
$877$	6.58233	−	24.5656i	0.222269	−	0.829521i	0.983480	−	0.181016i	$-0.0579386\pi$
$878$	−14.1832	+	3.80037i	−0.478659	+	0.128256i
$879$	18.5275	−	53.3436i	0.624916	−	1.79923i
$880$	−3.05520	+	2.34191i	−0.102991	+	0.0789459i
$881$		−	42.8833i		−	1.44478i	−0.691488	−	0.722388i	$-0.743045\pi$
$881$		−	42.8833i		−	1.44478i	0.691488	−	0.722388i	$-0.256955\pi$
$882$	13.5661	−	16.0300i	0.456794	−	0.539758i
$883$	2.85947	−	2.85947i	0.0962290	−	0.0962290i	−0.657353	−	0.753582i	$-0.728324\pi$
$883$	2.85947	−	2.85947i	0.0962290	−	0.0962290i	0.753582	+	0.657353i	$0.228324\pi$
$884$	−2.99988	−	5.19595i	−0.100897	−	0.174759i
$885$	−23.1975	−	35.2905i	−0.779775	−	1.18628i
$886$	−3.63909	+	6.30308i	−0.122258	+	0.211756i
$887$	−19.4438	−	5.20994i	−0.652858	−	0.174933i	−0.0828372	−	0.996563i	$-0.526398\pi$
$887$	−19.4438	−	5.20994i	−0.652858	−	0.174933i	−0.570021	+	0.821630i	$0.693065\pi$
$888$	−7.17241	−	4.86582i	−0.240690	−	0.163286i
$889$	−11.0496	−	8.77896i	−0.370593	−	0.294437i
$890$	4.45921	−	5.80534i	0.149473	−	0.194596i
$891$	4.42988	−	14.8473i	0.148407	−	0.497402i
$892$	6.76921	−	1.81381i	0.226650	−	0.0607307i
$893$	25.3048	−	6.78041i	0.846794	−	0.226898i
$894$	−17.5676	+	15.1890i	−0.587550	+	0.507996i
$895$	7.91019	−	1.03737i	0.264409	−	0.0346756i
$896$	0.389569	−	2.61691i	0.0130146	−	0.0874249i
$897$	−17.9505	+	26.4597i	−0.599348	+	0.883462i
$898$	31.3029	+	8.38758i	1.04459	+	0.279897i
$899$	9.58701	−	16.6052i	0.319745	−	0.553814i
$900$	−1.73345	−	14.8995i	−0.0577818	−	0.496650i
$901$	16.8507	+	29.1862i	0.561377	+	0.972333i
$902$	7.02082	−	7.02082i	0.233768	−	0.233768i
$903$	8.43245	+	1.88805i	0.280614	+	0.0628303i
$904$			6.37263i			0.211951i
$905$	−30.5406	−	39.8425i	−1.01520	−	1.32441i
$906$	−8.96318	−	3.11312i	−0.297782	−	0.103427i
$907$	−13.6878	+	3.66762i	−0.454494	+	0.121781i	−0.478802	−	0.877923i	$-0.658929\pi$
$907$	−13.6878	+	3.66762i	−0.454494	+	0.121781i	0.0243072	+	0.999705i	$0.492262\pi$
$908$	6.32181	−	23.5933i	0.209796	−	0.782971i
$909$	−22.0519	+	8.77259i	−0.731417	+	0.290969i
$910$	−13.7663	−	3.94633i	−0.456347	−	0.130820i
$911$			8.31142i			0.275370i	0.990476	+	0.137685i	$0.0439661\pi$
$911$			8.31142i			0.275370i	−0.990476	+	0.137685i	$0.956034\pi$
$912$	0.543098	−	7.47904i	0.0179838	−	0.247656i
$913$	1.05219	+	3.92683i	0.0348225	+	0.129959i
$914$	−4.77602	+	8.27231i	−0.157977	+	0.273624i
$915$	−32.6634	+	1.89370i	−1.07982	+	0.0626036i
$916$	−1.81183			−0.0598647
$917$	−21.2619	+	15.7518i	−0.702130	+	0.520171i
$918$	−2.77874	+	12.5757i	−0.0917121	+	0.415061i
$919$	−8.31275	+	4.79937i	−0.274212	+	0.158316i	−0.630800	−	0.775945i	$-0.717273\pi$
$919$	−8.31275	+	4.79937i	−0.274212	+	0.158316i	0.356588	+	0.934262i	$0.383940\pi$
$920$	−15.7512	−	6.53360i	−0.519303	−	0.215406i
$921$	−5.59294	+	16.1030i	−0.184294	+	0.530612i
$922$	5.33574	−	19.9133i	0.175723	−	0.655808i
$923$	18.6784	+	18.6784i	0.614808	+	0.614808i
$924$	3.65753	−	6.99010i	0.120324	−	0.229958i
$925$	−21.6554	−	12.5316i	−0.712025	−	0.412037i
$926$	26.2212	−	15.1388i	0.861683	−	0.497493i
$927$	33.2020	−	24.7420i	1.09050	−	0.812635i
$928$	0.903644	+	3.37245i	0.0296636	+	0.110706i
$929$	1.09625	+	1.89876i	0.0359667	+	0.0622962i	0.883448	−	0.468528i	$-0.155216\pi$
$929$	1.09625	+	1.89876i	0.0359667	+	0.0622962i	−0.847482	+	0.530825i	$0.821882\pi$
$930$	−6.68483	−	20.1917i	−0.219204	−	0.662112i
$931$	22.1406	−	20.6938i	0.725627	−	0.678213i
$932$	−1.33320	+	1.33320i	−0.0436705	+	0.0436705i
$933$	−1.11236	+	15.3184i	−0.0364170	+	0.501502i
$934$	23.0509	+	13.3084i	0.754249	+	0.435466i
$935$	8.81688	−	3.64691i	0.288343	−	0.119267i
$936$	4.50146	−	5.69848i	0.147135	−	0.186261i
$937$	26.2254	+	26.2254i	0.856748	+	0.856748i	0.990954	−	0.134206i	$-0.0428482\pi$
$937$	26.2254	+	26.2254i	0.856748	+	0.856748i	−0.134206	+	0.990954i	$0.542848\pi$
$938$	35.9985	−	4.12238i	1.17539	−	0.134601i
$939$	−1.88809	−	9.85408i	−0.0616155	−	0.321576i
$940$	−1.77280	+	13.4140i	−0.0578225	+	0.437516i
$941$	−17.9055	−	10.3377i	−0.583702	−	0.337000i	0.178902	−	0.983867i	$-0.442746\pi$
$941$	−17.9055	−	10.3377i	−0.583702	−	0.337000i	−0.762603	+	0.646867i	$0.776079\pi$
$942$	−8.34284	−	17.2221i	−0.271824	−	0.561128i
$943$	42.4843	+	11.3836i	1.38348	+	0.370702i
$944$	10.9043			0.354904
$945$	16.0823	+	26.1985i	0.523157	+	0.852236i
$946$	3.24630			0.105546
$947$	19.7344	+	5.28781i	0.641281	+	0.171831i	0.564783	−	0.825239i	$-0.308960\pi$
$947$	19.7344	+	5.28781i	0.641281	+	0.171831i	0.0764972	+	0.997070i	$0.475626\pi$
$948$	−2.59702	−	5.36103i	−0.0843471	−	0.174118i
$949$	−6.88426	−	3.97463i	−0.223472	−	0.129022i
$950$	0.0216373	−	21.6470i	0.000702008	−	0.702320i
$951$	1.38461	+	7.22639i	0.0448991	+	0.234332i
$952$	−2.61144	+	6.01530i	−0.0846371	+	0.194957i
$953$	−23.8399	−	23.8399i	−0.772251	−	0.772251i	0.206249	−	0.978500i	$-0.433874\pi$
$953$	−23.8399	−	23.8399i	−0.772251	−	0.772251i	−0.978500	+	0.206249i	$0.933874\pi$
$954$	−25.2852	+	32.0090i	−0.818637	+	1.03633i
$955$	47.7890	+	19.8229i	1.54642	+	0.641453i
$956$	6.35398	+	3.66847i	0.205502	+	0.118647i
$957$	−0.754005	+	10.3834i	−0.0243735	+	0.335649i
$958$	22.1507	−	22.1507i	0.715657	−	0.715657i
$959$	−2.40623	−	6.09832i	−0.0777011	−	0.196925i
$960$	3.46056	+	1.73911i	0.111689	+	0.0561297i
$961$	0.420261	+	0.727914i	0.0135568	+	0.0234811i
$962$	−3.13505	−	11.7002i	−0.101078	−	0.377228i
$963$	48.7243	−	36.3092i	1.57012	−	1.17005i
$964$	12.1921	−	7.03912i	0.392682	−	0.226715i
$965$	−21.9081	+	28.5216i	−0.705246	+	0.918144i
$966$	34.9172	−	1.45094i	1.12344	−	0.0466832i
$967$	27.2454	+	27.2454i	0.876152	+	0.876152i	0.993134	−	0.116982i	$-0.0373219\pi$
$967$	27.2454	+	27.2454i	0.876152	+	0.876152i	−0.116982	+	0.993134i	$0.537322\pi$
$968$	−2.07993	+	7.76241i	−0.0668515	+	0.249493i
$969$	−6.09807	+	17.5573i	−0.195898	+	0.564023i
$970$	13.5651	−	32.7029i	0.435550	−	1.05003i
$971$	19.3176	−	11.1530i	0.619933	−	0.357918i	−0.156910	−	0.987613i	$-0.550153\pi$
$971$	19.3176	−	11.1530i	0.619933	−	0.357918i	0.776843	+	0.629695i	$0.216820\pi$
$972$	−15.3865	+	2.50130i	−0.493521	+	0.0802291i
$973$	−1.07736	−	9.40797i	−0.0345385	−	0.301606i
$974$	−3.94379			−0.126367
$975$	11.7864	−	17.3363i	0.377466	−	0.555205i
$976$	4.22391	−	7.31603i	0.135204	−	0.234181i
$977$	−12.4818	−	46.5829i	−0.399330	−	1.49032i	−0.814279	−	0.580474i	$-0.802867\pi$
$977$	−12.4818	−	46.5829i	−0.399330	−	1.49032i	0.414949	−	0.909845i	$-0.363799\pi$
$978$	0.624222	−	8.59620i	0.0199604	−	0.274876i
$979$			5.63592i			0.180125i
$980$	5.49106	+	14.6577i	0.175406	+	0.468223i
$981$	21.2886	−	8.46891i	0.679691	−	0.270391i
$982$	4.58672	−	17.1179i	0.146368	−	0.546254i
$983$	−12.3214	+	3.30152i	−0.392993	+	0.105302i	−0.449904	−	0.893077i	$-0.648542\pi$
$983$	−12.3214	+	3.30152i	−0.392993	+	0.105302i	0.0569107	+	0.998379i	$0.481875\pi$
$984$	−9.43647	−	3.27751i	−0.300824	−	0.104483i
$985$	−14.1504	−	1.87013i	−0.450868	−	0.0595871i
$986$		−	8.65374i		−	0.275591i
$987$	−8.28278	−	26.4636i	−0.263644	−	0.842345i
$988$	7.41043	−	7.41043i	0.235757	−	0.235757i
$989$	7.19019	+	12.4538i	0.228635	+	0.396007i
$990$	8.04616	+	8.28424i	0.255724	+	0.263290i
$991$	20.9965	−	36.3671i	0.666977	−	1.15524i	−0.311768	−	0.950158i	$-0.600921\pi$
$991$	20.9965	−	36.3671i	0.666977	−	1.15524i	0.978745	−	0.205080i	$-0.0657456\pi$
$992$	5.30464	+	1.42137i	0.168422	+	0.0451286i
$993$	−5.25971	+	7.75301i	−0.166912	+	0.246034i
$994$	4.25117	−	28.5570i	0.134839	−	0.905774i
$995$	−0.629139	−	4.79731i	−0.0199450	−	0.152085i
$996$	3.09403	−	2.67510i	0.0980382	−	0.0847638i
$997$	−36.8933	+	9.88552i	−1.16842	+	0.313078i	−0.790325	−	0.612688i	$-0.790088\pi$
$997$	−36.8933	+	9.88552i	−1.16842	+	0.313078i	−0.378097	+	0.925766i	$0.623421\pi$
$998$	−16.4166	+	4.39882i	−0.519659	+	0.139242i
$999$	−11.9900	+	23.0720i	−0.379347	+	0.729966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.137.4	yes	64
3.2	odd	2	inner	210.2.x.a.137.11	yes	64
5.3	odd	4	inner	210.2.x.a.53.8	yes	64
7.2	even	3	inner	210.2.x.a.107.16	yes	64
15.8	even	4	inner	210.2.x.a.53.16	yes	64
21.2	odd	6	inner	210.2.x.a.107.8	yes	64
35.23	odd	12	inner	210.2.x.a.23.11	yes	64
105.23	even	12	inner	210.2.x.a.23.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.4	✓	64	105.23	even	12	inner
210.2.x.a.23.11	yes	64	35.23	odd	12	inner
210.2.x.a.53.8	yes	64	5.3	odd	4	inner
210.2.x.a.53.16	yes	64	15.8	even	4	inner
210.2.x.a.107.8	yes	64	21.2	odd	6	inner
210.2.x.a.107.16	yes	64	7.2	even	3	inner
210.2.x.a.137.4	yes	64	1.1	even	1	trivial
210.2.x.a.137.11	yes	64	3.2	odd	2	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.755113 - 1.55878i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.36035 + 1.77467i) q^{5} +(0.325941 + 1.70111i) q^{6} +(2.62857 - 0.301012i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.85961 + 2.35411i) q^{9} +(-0.854674 - 2.06628i) q^{10} +(1.49091 + 0.860779i) q^{11} +(0.125444 - 1.72750i) q^{12} +(1.71166 - 1.71166i) q^{13} +(-2.61691 - 0.389569i) q^{14} +(1.73911 - 3.46056i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.641503 - 2.39412i) q^{17} +(2.40553 - 1.79260i) q^{18} +(3.74936 - 2.16470i) q^{19} +(0.290757 + 2.21708i) q^{20} +(-2.45408 - 3.87008i) q^{21} +(-1.21733 - 1.21733i) q^{22} +(1.97379 - 7.36627i) q^{23} +(-0.568280 + 1.63617i) q^{24} +(-1.29892 + 4.82833i) q^{25} +(-2.09634 + 1.21032i) q^{26} +(5.07377 + 1.12110i) q^{27} +(2.42692 + 1.05360i) q^{28} -3.49141 q^{29} +(-2.57551 + 2.89253i) q^{30} +(-2.74588 + 4.75601i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.215960 - 2.97400i) q^{33} +2.47858i q^{34} +(4.10996 + 4.25537i) q^{35} +(-2.78753 + 1.10892i) q^{36} +(-1.29513 + 4.83348i) q^{37} +(-4.18187 + 1.12053i) q^{38} +(-3.96059 - 1.37561i) q^{39} +(0.292973 - 2.21679i) q^{40} +5.76741i q^{41} +(1.36881 + 4.37337i) q^{42} +(-1.33337 + 1.33337i) q^{43} +(0.860779 + 1.49091i) q^{44} +(-6.70749 - 0.0977862i) q^{45} +(-3.81306 + 6.60442i) q^{46} +(5.84489 + 1.56613i) q^{47} +(0.972389 - 1.43334i) q^{48} +(6.81878 - 1.58246i) q^{49} +(2.50433 - 4.32763i) q^{50} +(-3.24751 + 2.80780i) q^{51} +(2.33817 - 0.626510i) q^{52} +(-13.1337 + 3.51917i) q^{53} +(-4.61072 - 2.39609i) q^{54} +(0.500556 + 3.81684i) q^{55} +(-2.07153 - 1.64583i) q^{56} +(-6.20549 - 4.20985i) q^{57} +(3.37245 + 0.903644i) q^{58} +(5.45213 - 9.44337i) q^{59} +(3.23640 - 2.12738i) q^{60} +(-4.22391 - 7.31603i) q^{61} +(3.88326 - 3.88326i) q^{62} +(-4.17950 + 6.74772i) q^{63} +1.00000i q^{64} +(5.36607 + 0.709185i) q^{65} +(-0.978328 + 2.81677i) q^{66} +(-13.2284 + 3.54455i) q^{67} +(0.641503 - 2.39412i) q^{68} +(-12.9729 + 2.48566i) q^{69} +(-2.86855 - 5.17411i) q^{70} +10.9125i q^{71} +(2.97955 - 0.349669i) q^{72} +(-0.849946 - 3.17204i) q^{73} +(2.50199 - 4.33358i) q^{74} +(8.50716 - 1.62120i) q^{75} +4.32939 q^{76} +(4.17808 + 1.81384i) q^{77} +(3.46961 + 2.35381i) q^{78} +(2.97847 - 1.71962i) q^{79} +(-0.856739 + 2.06543i) q^{80} +(-2.08371 - 8.75546i) q^{81} +(1.49272 - 5.57089i) q^{82} +(1.66979 + 1.66979i) q^{83} +(-0.190259 - 4.57862i) q^{84} +(3.37612 - 4.39529i) q^{85} +(1.63304 - 0.942836i) q^{86} +(2.63641 + 5.44236i) q^{87} +(-0.445572 - 1.66290i) q^{88} +(1.63686 + 2.83513i) q^{89} +(6.45363 + 1.83048i) q^{90} +(3.98398 - 5.01444i) q^{91} +(5.39249 - 5.39249i) q^{92} +(9.48704 + 0.688911i) q^{93} +(-5.24039 - 3.02554i) q^{94} +(8.94206 + 3.70916i) q^{95} +(-1.31023 + 1.13283i) q^{96} +(11.1959 + 11.1959i) q^{97} +(-6.99601 - 0.236290i) q^{98} +(-4.79889 + 1.90907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43}+ \cdots + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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