LMFDB - Embedded newform 210.2.u.b.103.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(73,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("210.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,12,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.1
Root			$0.792206 - 1.03242i$ of defining polynomial
Character	$\chi$	$=$	210.103
Dual form			210.2.u.b.157.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.619385 + 2.14857i) q^{5} -1.00000i q^{6} +(2.25331 + 1.38658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.23567 + 0.0421887i) q^{10} +(0.582897 + 1.00961i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(1.92501 - 1.92501i) q^{13} +(0.756134 - 2.53540i) q^{14} +(-1.15437 + 1.91505i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.00560858 + 0.0209315i) q^{17} +(0.258819 - 0.965926i) q^{18} +(0.989363 - 1.71363i) q^{19} +(-0.537883 - 2.17041i) q^{20} +(1.81766 + 1.92253i) q^{21} +(0.824341 - 0.824341i) q^{22} +(-6.93525 + 1.85829i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.23272 - 2.66159i) q^{25} +(-2.35765 - 1.36119i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.64471 - 0.0741591i) q^{28} -5.60604i q^{29} +(2.14857 + 0.619385i) q^{30} +(6.86850 - 3.96553i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.301730 + 1.12607i) q^{33} +0.0216699 q^{34} +(-4.37483 + 3.98257i) q^{35} -1.00000 q^{36} +(2.74894 + 10.2592i) q^{37} +(-1.91130 - 0.512132i) q^{38} +(2.35765 - 1.36119i) q^{39} +(-1.95724 + 1.08130i) q^{40} -2.48977i q^{41} +(1.38658 - 2.25331i) q^{42} +(-7.87756 - 7.87756i) q^{43} +(-1.00961 - 0.582897i) q^{44} +(-1.61069 + 1.55103i) q^{45} +(3.58995 + 6.21797i) q^{46} +(-3.94750 + 1.05773i) q^{47} +(0.707107 - 0.707107i) q^{48} +(3.15479 + 6.24878i) q^{49} +(-1.47539 + 4.77737i) q^{50} +(-0.0108349 + 0.0187667i) q^{51} +(-0.704604 + 2.62962i) q^{52} +(-0.757613 + 2.82745i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.53025 + 0.627061i) q^{55} +(0.612870 + 2.57379i) q^{56} +(1.39917 - 1.39917i) q^{57} +(-5.41502 + 1.45095i) q^{58} +(-5.34623 - 9.25995i) q^{59} +(0.0421887 - 2.23567i) q^{60} +(-3.15795 - 1.82324i) q^{61} +(-5.60811 - 5.60811i) q^{62} +(1.25813 + 2.32747i) q^{63} +1.00000i q^{64} +(2.94371 + 5.32835i) q^{65} +(1.00961 - 0.582897i) q^{66} +(-14.0621 - 3.76794i) q^{67} +(-0.00560858 - 0.0209315i) q^{68} -7.17989 q^{69} +(4.97916 + 3.19500i) q^{70} +7.51848 q^{71} +(0.258819 + 0.965926i) q^{72} +(3.61776 + 0.969376i) q^{73} +(9.19815 - 5.31055i) q^{74} +(-3.39963 - 3.66641i) q^{75} +1.97873i q^{76} +(-0.0864543 + 3.08319i) q^{77} +(-1.92501 - 1.92501i) q^{78} +(1.39464 + 0.805197i) q^{79} +(1.55103 + 1.61069i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.40493 + 0.644400i) q^{82} +(9.74815 - 9.74815i) q^{83} +(-2.53540 - 0.756134i) q^{84} +(-0.0414990 - 0.0250151i) q^{85} +(-5.57028 + 9.64800i) q^{86} +(1.45095 - 5.41502i) q^{87} +(-0.301730 + 1.12607i) q^{88} +(-1.80255 + 3.12211i) q^{89} +(1.91505 + 1.15437i) q^{90} +(7.00683 - 1.66846i) q^{91} +(5.07695 - 5.07695i) q^{92} +(7.66082 - 2.05271i) q^{93} +(2.04338 + 3.53923i) q^{94} +(3.06906 + 3.18711i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(0.265501 + 0.265501i) q^{97} +(5.21934 - 4.66460i) q^{98} +1.16579i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.619385	+	2.14857i	−0.276997	+	0.960871i
$5$	−0.619385	+	2.14857i	−0.276997	+	0.960871i
$6$		−	1.00000i		−	0.408248i
$7$	2.25331	+	1.38658i	0.851670	+	0.524078i
$7$	2.25331	+	1.38658i	0.851670	+	0.524078i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	2.23567	+	0.0421887i	0.706981	+	0.0133412i
$11$	0.582897	+	1.00961i	0.175750	+	0.304408i	0.940421	−	0.340013i	$-0.110432\pi$
$11$	0.582897	+	1.00961i	0.175750	+	0.304408i	−0.764670	+	0.644422i	$0.777098\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	−0.387829	−	0.921731i	$-0.626775\pi$
$13$	1.92501	−	1.92501i	0.533903	−	0.533903i	0.921731	+	0.387829i	$0.126775\pi$
$14$	0.756134	−	2.53540i	0.202085	−	0.677615i
$15$	−1.15437	+	1.91505i	−0.298057	+	0.494464i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.00560858	+	0.0209315i	−0.00136028	+	0.00507664i	−0.966603	−	0.256280i	$-0.917503\pi$
$17$	−0.00560858	+	0.0209315i	−0.00136028	+	0.00507664i	0.965242	+	0.261356i	$0.0841698\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	0.989363	−	1.71363i	0.226976	−	0.393133i	−0.729935	−	0.683517i	$-0.760450\pi$
$19$	0.989363	−	1.71363i	0.226976	−	0.393133i	0.956910	+	0.290384i	$0.0937829\pi$
$20$	−0.537883	−	2.17041i	−0.120274	−	0.485319i
$21$	1.81766	+	1.92253i	0.396645	+	0.419531i
$22$	0.824341	−	0.824341i	0.175750	−	0.175750i
$23$	−6.93525	+	1.85829i	−1.44610	+	0.387481i	−0.894665	−	0.446738i	$-0.852586\pi$
$23$	−6.93525	+	1.85829i	−1.44610	+	0.387481i	−0.551434	+	0.834219i	$0.685919\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.23272	−	2.66159i	−0.846545	−	0.532317i
$26$	−2.35765	−	1.36119i	−0.462373	−	0.266951i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.64471	−	0.0741591i	−0.499804	−	0.0140148i
$29$		−	5.60604i		−	1.04102i	−0.853857	−	0.520508i	$-0.825743\pi$
$29$		−	5.60604i		−	1.04102i	0.853857	−	0.520508i	$-0.174257\pi$
$30$	2.14857	+	0.619385i	0.392274	+	0.113084i
$31$	6.86850	−	3.96553i	1.23362	−	0.712231i	0.265837	−	0.964018i	$-0.414352\pi$
$31$	6.86850	−	3.96553i	1.23362	−	0.712231i	0.967783	+	0.251787i	$0.0810183\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.301730	+	1.12607i	0.0525244	+	0.196024i
$34$	0.0216699			0.00371636
$35$	−4.37483	+	3.98257i	−0.739482	+	0.673177i
$36$	−1.00000			−0.166667
$37$	2.74894	+	10.2592i	0.451924	+	1.68660i	0.696978	+	0.717093i	$0.254528\pi$
$37$	2.74894	+	10.2592i	0.451924	+	1.68660i	−0.245054	+	0.969509i	$0.578806\pi$
$38$	−1.91130	−	0.512132i	−0.310054	−	0.0830788i
$39$	2.35765	−	1.36119i	0.377526	−	0.217965i
$40$	−1.95724	+	1.08130i	−0.309467	+	0.170968i
$41$		−	2.48977i		−	0.388837i	−0.980919	−	0.194418i	$-0.937718\pi$
$41$		−	2.48977i		−	0.388837i	0.980919	−	0.194418i	$-0.0622819\pi$
$42$	1.38658	−	2.25331i	0.213954	−	0.347693i
$43$	−7.87756	−	7.87756i	−1.20132	−	1.20132i	−0.973766	−	0.227550i	$-0.926928\pi$
$43$	−7.87756	−	7.87756i	−1.20132	−	1.20132i	−0.227550	−	0.973766i	$-0.573072\pi$
$44$	−1.00961	−	0.582897i	−0.152204	−	0.0878751i
$45$	−1.61069	+	1.55103i	−0.240107	+	0.231213i
$46$	3.58995	+	6.21797i	0.529309	+	0.916790i
$47$	−3.94750	+	1.05773i	−0.575802	+	0.154286i	−0.534956	−	0.844880i	$-0.679672\pi$
$47$	−3.94750	+	1.05773i	−0.575802	+	0.154286i	−0.0408457	+	0.999165i	$0.513005\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	3.15479	+	6.24878i	0.450685	+	0.892683i
$50$	−1.47539	+	4.77737i	−0.208651	+	0.675622i
$51$	−0.0108349	+	0.0187667i	−0.00151720	+	0.00262786i
$52$	−0.704604	+	2.62962i	−0.0977110	+	0.364662i
$53$	−0.757613	+	2.82745i	−0.104066	+	0.388380i	−0.998238	−	0.0593446i	$-0.981099\pi$
$53$	−0.757613	+	2.82745i	−0.104066	+	0.388380i	0.894171	+	0.447725i	$0.147766\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.53025	+	0.627061i	−0.341179	+	0.0845529i
$56$	0.612870	+	2.57379i	0.0818981	+	0.343937i
$57$	1.39917	−	1.39917i	0.185325	−	0.185325i
$58$	−5.41502	+	1.45095i	−0.711027	+	0.190519i
$59$	−5.34623	−	9.25995i	−0.696020	−	1.20554i	−0.969835	−	0.243760i	$-0.921619\pi$
$59$	−5.34623	−	9.25995i	−0.696020	−	1.20554i	0.273815	−	0.961782i	$-0.411714\pi$
$60$	0.0421887	−	2.23567i	0.00544654	−	0.288624i
$61$	−3.15795	−	1.82324i	−0.404334	−	0.233442i	0.284018	−	0.958819i	$-0.408332\pi$
$61$	−3.15795	−	1.82324i	−0.404334	−	0.233442i	−0.688352	+	0.725376i	$0.741666\pi$
$62$	−5.60811	−	5.60811i	−0.712231	−	0.712231i
$63$	1.25813	+	2.32747i	0.158510	+	0.293233i
$64$			1.00000i			0.125000i
$65$	2.94371	+	5.32835i	0.365122	+	0.660901i
$66$	1.00961	−	0.582897i	0.124274	−	0.0717497i
$67$	−14.0621	−	3.76794i	−1.71796	−	0.460327i	−0.740610	−	0.671935i	$-0.765463\pi$
$67$	−14.0621	−	3.76794i	−1.71796	−	0.460327i	−0.977355	+	0.211608i	$0.932130\pi$
$68$	−0.00560858	−	0.0209315i	−0.000680140	−	0.00253832i
$69$	−7.17989			−0.864358
$70$	4.97916	+	3.19500i	0.595123	+	0.381875i
$71$	7.51848			0.892280			0.446140	−	0.894963i	$-0.352798\pi$
$71$	7.51848			0.892280			0.446140	+	0.894963i	$0.352798\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	3.61776	+	0.969376i	0.423427	+	0.113457i	0.464239	−	0.885710i	$-0.346328\pi$
$73$	3.61776	+	0.969376i	0.423427	+	0.113457i	−0.0408122	+	0.999167i	$0.512995\pi$
$74$	9.19815	−	5.31055i	1.06926	−	0.617339i
$75$	−3.39963	−	3.66641i	−0.392555	−	0.423360i
$76$			1.97873i			0.226976i
$77$	−0.0864543	+	3.08319i	−0.00985238	+	0.351362i
$78$	−1.92501	−	1.92501i	−0.217965	−	0.217965i
$79$	1.39464	+	0.805197i	0.156910	+	0.0905918i	0.576399	−	0.817169i	$-0.304457\pi$
$79$	1.39464	+	0.805197i	0.156910	+	0.0905918i	−0.419489	+	0.907760i	$0.637791\pi$
$80$	1.55103	+	1.61069i	0.173410	+	0.180081i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.40493	+	0.644400i	−0.265580	+	0.0711620i
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.0726405	−	0.997358i	$-0.476857\pi$
$83$	9.74815	−	9.74815i	1.07000	−	1.07000i	0.997358	−	0.0726405i	$-0.0231426\pi$
$84$	−2.53540	−	0.756134i	−0.276635	−	0.0825010i
$85$	−0.0414990	−	0.0250151i	−0.00450120	−	0.00271327i
$86$	−5.57028	+	9.64800i	−0.600658	+	1.04037i
$87$	1.45095	−	5.41502i	0.155558	−	0.580551i
$88$	−0.301730	+	1.12607i	−0.0321645	+	0.120040i
$89$	−1.80255	+	3.12211i	−0.191070	+	0.330943i	−0.945605	−	0.325317i	$-0.894529\pi$
$89$	−1.80255	+	3.12211i	−0.191070	+	0.330943i	0.754535	+	0.656260i	$0.227862\pi$
$90$	1.91505	+	1.15437i	0.201864	+	0.121681i
$91$	7.00683	−	1.66846i	0.734516	−	0.174903i
$92$	5.07695	−	5.07695i	0.529309	−	0.529309i
$93$	7.66082	−	2.05271i	0.794390	−	0.212856i
$94$	2.04338	+	3.53923i	0.210758	+	0.365044i
$95$	3.06906	+	3.18711i	0.314878	+	0.326991i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	0.720457	−	0.693500i	$-0.243932\pi$
$97$	0.265501	+	0.265501i	0.0269575	+	0.0269575i	−0.693500	+	0.720457i	$0.743932\pi$
$98$	5.21934	−	4.66460i	0.527233	−	0.471196i
$99$			1.16579i			0.117167i
$100$	4.99644	+	0.188640i	0.499644	+	0.0188640i
$101$	12.0515	−	6.95796i	1.19917	−	0.692343i	0.238802	−	0.971068i	$-0.423245\pi$
$101$	12.0515	−	6.95796i	1.19917	−	0.692343i	0.960371	+	0.278725i	$0.0899119\pi$
$102$	0.0209315	+	0.00560858i	0.00207253	+	0.000555332i
$103$	−3.10171	−	11.5757i	−0.305621	−	1.14059i	−0.932410	−	0.361403i	$-0.882298\pi$
$103$	−3.10171	−	11.5757i	−0.305621	−	1.14059i	0.626789	−	0.779189i	$-0.284369\pi$
$104$	2.72238			0.266951
$105$	−5.25653	+	2.71458i	−0.512985	+	0.264915i
$106$	2.92719			0.284314
$107$	1.78730	+	6.67031i	0.172785	+	0.644843i	0.996918	+	0.0784469i	$0.0249961\pi$
$107$	1.78730	+	6.67031i	0.172785	+	0.644843i	−0.824133	+	0.566396i	$0.808337\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	0.499969	−	0.288657i	0.0478883	−	0.0276483i	−0.475865	−	0.879519i	$-0.657865\pi$
$109$	0.499969	−	0.288657i	0.0478883	−	0.0276483i	0.523753	+	0.851870i	$0.324531\pi$
$110$	1.26057	+	2.28174i	0.120191	+	0.217556i
$111$			10.6211i			1.00811i
$112$	2.32747	−	1.25813i	0.219925	−	0.118882i
$113$	13.2689	+	13.2689i	1.24823	+	1.24823i	0.956501	+	0.291728i	$0.0942301\pi$
$113$	13.2689	+	13.2689i	1.24823	+	1.24823i	0.291728	+	0.956501i	$0.405770\pi$
$114$	−1.71363	−	0.989363i	−0.160496	−	0.0926624i
$115$	0.302911	−	16.0519i	0.0282466	−	1.49685i
$116$	2.80302	+	4.85498i	0.260254	+	0.450773i
$117$	2.62962	−	0.704604i	0.243108	−	0.0651406i
$118$	−7.56072	+	7.56072i	−0.696020	+	0.696020i
$119$	−0.0416611	+	0.0393884i	−0.00381906	+	0.00361073i
$120$	−2.17041	+	0.537883i	−0.198130	+	0.0491018i
$121$	4.82046	−	8.34928i	0.438224	−	0.759026i
$122$	−0.943781	+	3.52224i	−0.0854459	+	0.318888i
$123$	0.644400	−	2.40493i	0.0581036	−	0.216845i
$124$	−3.96553	+	6.86850i	−0.356115	+	0.616810i
$125$	8.34030	−	7.44577i	0.745979	−	0.665969i
$126$	1.92253	−	1.81766i	0.171273	−	0.161930i
$127$	1.36110	−	1.36110i	0.120778	−	0.120778i	−0.644134	−	0.764912i	$-0.722782\pi$
$127$	1.36110	−	1.36110i	0.120778	−	0.120778i	0.764912	+	0.644134i	$0.222782\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−5.57028	−	9.64800i	−0.490435	−	0.849459i
$130$	4.38491	−	4.22248i	0.384582	−	0.370336i
$131$	−14.8522	−	8.57489i	−1.29764	−	0.749192i	−0.317643	−	0.948210i	$-0.602891\pi$
$131$	−14.8522	−	8.57489i	−1.29764	−	0.749192i	−0.979996	+	0.199019i	$0.936225\pi$
$132$	−0.824341	−	0.824341i	−0.0717497	−	0.0717497i
$133$	4.60542	−	2.48950i	0.399341	−	0.215867i
$134$			14.5582i			1.25764i
$135$	−1.95724	+	1.08130i	−0.168453	+	0.0930634i
$136$	−0.0187667	+	0.0108349i	−0.00160923	+	0.000929089i
$137$	−9.88699	−	2.64921i	−0.844702	−	0.226337i	−0.189585	−	0.981864i	$-0.560714\pi$
$137$	−9.88699	−	2.64921i	−0.844702	−	0.226337i	−0.655117	+	0.755527i	$0.727381\pi$
$138$	1.85829	+	6.93525i	0.158188	+	0.590367i
$139$	−5.65119			−0.479327			−0.239664	−	0.970856i	$-0.577037\pi$
$139$	−5.65119			−0.479327			−0.239664	+	0.970856i	$0.577037\pi$
$140$	1.79743	−	5.63642i	0.151911	−	0.476365i
$141$	−4.08675			−0.344166
$142$	−1.94593	−	7.26230i	−0.163299	−	0.609439i
$143$	3.06559	+	0.821423i	0.256358	+	0.0686909i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	12.0450	+	3.47230i	1.00028	+	0.288359i
$146$		−	3.74538i		−	0.309970i
$147$	1.42999	+	6.85238i	0.117944	+	0.565175i
$148$	−7.51026	−	7.51026i	−0.617339	−	0.617339i
$149$	−0.191221	−	0.110402i	−0.0156655	−	0.00904446i	0.492147	−	0.870512i	$-0.336212\pi$
$149$	−0.191221	−	0.110402i	−0.0156655	−	0.00904446i	−0.507812	+	0.861468i	$0.669546\pi$
$150$	−2.66159	+	4.23272i	−0.217318	+	0.345600i
$151$	3.18442	+	5.51559i	0.259145	+	0.448852i	0.966013	−	0.258493i	$-0.0832260\pi$
$151$	3.18442	+	5.51559i	0.259145	+	0.448852i	−0.706868	+	0.707345i	$0.749893\pi$
$152$	1.91130	−	0.512132i	0.155027	−	0.0415394i
$153$	−0.0153229	+	0.0153229i	−0.00123879	+	0.00123879i
$154$	3.00051	−	0.714480i	0.241788	−	0.0575745i
$155$	4.26598	+	17.2137i	0.342652	+	1.38264i
$156$	−1.36119	+	2.35765i	−0.108982	+	0.188763i
$157$	−3.74673	+	13.9830i	−0.299022	+	1.11596i	0.638949	+	0.769249i	$0.279370\pi$
$157$	−3.74673	+	13.9830i	−0.299022	+	1.11596i	−0.937970	+	0.346715i	$0.887297\pi$
$158$	0.416801	−	1.55552i	0.0331589	−	0.123751i
$159$	−1.46360	+	2.53502i	−0.116071	+	0.201040i
$160$	1.15437	−	1.91505i	0.0912611	−	0.151398i
$161$	−18.2039	−	5.42896i	−1.43467	−	0.427862i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−21.1592	+	5.66960i	−1.65732	+	0.444078i	−0.961649	−	0.274283i	$-0.911560\pi$
$163$	−21.1592	+	5.66960i	−1.65732	+	0.444078i	−0.695671	+	0.718360i	$0.744893\pi$
$164$	1.24488	+	2.15620i	0.0972091	+	0.168371i
$165$	−2.60633	−	0.0491834i	−0.202903	−	0.00382892i
$166$	−11.9390	−	6.89298i	−0.926646	−	0.534999i
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	0.993689	−	0.112174i	$-0.0357814\pi$
$167$	11.3917	+	11.3917i	0.881515	+	0.881515i	−0.112174	+	0.993689i	$0.535781\pi$
$168$	−0.0741591	+	2.64471i	−0.00572150	+	0.204044i
$169$			5.58865i			0.429896i
$170$	−0.0134220	+	0.0465593i	−0.00102942	+	0.00357094i
$171$	1.71363	−	0.989363i	0.131044	−	0.0756585i
$172$	10.7609	+	2.88339i	0.820515	+	0.219856i
$173$	2.70291	+	10.0874i	0.205499	+	0.766932i	0.989297	+	0.145916i	$0.0466130\pi$
$173$	2.70291	+	10.0874i	0.205499	+	0.766932i	−0.783798	+	0.621016i	$0.786720\pi$
$174$	−5.60604			−0.424993
$175$	−5.84713	−	11.8664i	−0.442001	−	0.897014i
$176$	1.16579			0.0878751
$177$	−2.76741	−	10.3281i	−0.208012	−	0.776310i
$178$	3.48226	+	0.933068i	0.261006	+	0.0699364i
$179$	−1.30513	+	0.753516i	−0.0975498	+	0.0563204i	−0.547981	−	0.836491i	$-0.684603\pi$
$179$	−1.30513	+	0.753516i	−0.0975498	+	0.0563204i	0.450431	+	0.892811i	$0.351270\pi$
$180$	0.619385	−	2.14857i	0.0461662	−	0.160145i
$181$			21.3457i			1.58662i	0.608821	+	0.793308i	$0.291643\pi$
$181$			21.3457i			1.58662i	−0.608821	+	0.793308i	$0.708357\pi$
$182$	−3.42511	−	6.33625i	−0.253886	−	0.469674i
$183$	−2.57846	−	2.57846i	−0.190605	−	0.190605i
$184$	−6.21797	−	3.58995i	−0.458395	−	0.264654i
$185$	−23.7453	−	0.448091i	−1.74579	−	0.0329443i
$186$	−3.96553	−	6.86850i	−0.290767	−	0.503623i
$187$	−0.0244018	+	0.00653845i	−0.00178444	+	0.000478139i
$188$	2.88977	−	2.88977i	0.210758	−	0.210758i
$189$	0.612870	+	2.57379i	0.0445797	+	0.187216i
$190$	2.28419	−	3.78937i	0.165712	−	0.274909i
$191$	−3.22543	+	5.58661i	−0.233384	+	0.404233i	−0.958802	−	0.284076i	$-0.908313\pi$
$191$	−3.22543	+	5.58661i	−0.233384	+	0.404233i	0.725418	+	0.688309i	$0.241647\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	−1.32996	+	4.96349i	−0.0957328	+	0.357280i	−0.997130	−	0.0757145i	$-0.975876\pi$
$193$	−1.32996	+	4.96349i	−0.0957328	+	0.357280i	0.901397	+	0.432994i	$0.142543\pi$
$194$	0.187737	−	0.325171i	0.0134788	−	0.0233459i
$195$	1.46432	+	5.90868i	0.104862	+	0.423129i
$196$	−5.85652	−	3.83421i	−0.418323	−	0.273872i
$197$	17.8347	−	17.8347i	1.27067	−	1.27067i	0.324931	−	0.945738i	$-0.394659\pi$
$197$	17.8347	−	17.8347i	1.27067	−	1.27067i	0.945738	−	0.324931i	$-0.105341\pi$
$198$	1.12607	−	0.301730i	0.0800264	−	0.0214430i
$199$	2.47098	+	4.27987i	0.175163	+	0.303392i	0.940218	−	0.340574i	$-0.110621\pi$
$199$	2.47098	+	4.27987i	0.175163	+	0.303392i	−0.765054	+	0.643966i	$0.777288\pi$
$200$	−1.11096	−	4.87501i	−0.0785568	−	0.344716i
$201$	−12.6078	−	7.27910i	−0.889284	−	0.513428i
$202$	−9.84004	−	9.84004i	−0.692343	−	0.692343i
$203$	7.77323	−	12.6321i	0.545574	−	0.886603i
$204$		−	0.0216699i		−	0.00151720i
$205$	5.34945	+	1.54213i	0.373622	+	0.107707i
$206$	−10.3785	+	5.99204i	−0.723106	+	0.417485i
$207$	−6.93525	−	1.85829i	−0.482033	−	0.129160i
$208$	−0.704604	−	2.62962i	−0.0488555	−	0.182331i
$209$	2.30679			0.159564
$210$	3.98257	+	4.37483i	0.274823	+	0.301892i
$211$	−19.0455			−1.31115			−0.655574	−	0.755131i	$-0.727573\pi$
$211$	−19.0455			−1.31115			−0.655574	+	0.755131i	$0.727573\pi$
$212$	−0.757613	−	2.82745i	−0.0520331	−	0.194190i
$213$	7.26230	+	1.94593i	0.497604	+	0.133333i
$214$	5.98043	−	3.45281i	0.408814	−	0.236029i
$215$	21.8048	−	12.0463i	1.48707	−	0.821548i
$216$			1.00000i			0.0680414i
$217$	20.9754	+	0.588161i	1.42390	+	0.0399270i
$218$	−0.408223	−	0.408223i	−0.0276483	−	0.0276483i
$219$	3.24360	+	1.87269i	0.219182	+	0.126545i
$220$	1.87773	−	1.80818i	0.126597	−	0.121907i
$221$	0.0294968	+	0.0510900i	0.00198417	+	0.00343669i
$222$	10.2592	−	2.74894i	0.688553	−	0.184497i
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	−0.798801	−	0.601596i	$-0.794532\pi$
$223$	−2.94490	+	2.94490i	−0.197205	+	0.197205i	0.601596	+	0.798801i	$0.294532\pi$
$224$	−1.81766	−	1.92253i	−0.121447	−	0.128455i
$225$	−2.33485	−	4.42136i	−0.155657	−	0.294758i
$226$	9.38250	−	16.2510i	0.624115	−	1.08100i
$227$	−4.77234	+	17.8106i	−0.316751	+	1.18213i	0.605597	+	0.795772i	$0.292935\pi$
$227$	−4.77234	+	17.8106i	−0.316751	+	1.18213i	−0.922348	+	0.386360i	$0.873732\pi$
$228$	−0.512132	+	1.91130i	−0.0339168	+	0.126579i
$229$	2.95505	−	5.11830i	0.195276	−	0.338227i	−0.751715	−	0.659488i	$-0.770773\pi$
$229$	2.95505	−	5.11830i	0.195276	−	0.338227i	0.946991	+	0.321261i	$0.104107\pi$
$230$	−15.5833	+	3.86194i	−1.02753	+	0.254649i
$231$	−0.881497	+	2.95576i	−0.0579983	+	0.194475i
$232$	3.96407	−	3.96407i	0.260254	−	0.260254i
$233$	−6.98879	+	1.87264i	−0.457851	+	0.122681i	−0.480371	−	0.877066i	$-0.659498\pi$
$233$	−6.98879	+	1.87264i	−0.457851	+	0.122681i	0.0225196	+	0.999746i	$0.492831\pi$
$234$	−1.36119	−	2.35765i	−0.0889838	−	0.154124i
$235$	0.172415	−	9.13663i	0.0112471	−	0.596008i
$236$	9.25995	+	5.34623i	0.602771	+	0.348010i
$237$	1.13872	+	1.13872i	0.0739679	+	0.0739679i
$238$	0.0488289	+	0.0300470i	0.00316511	+	0.00194766i
$239$			4.20172i			0.271787i	0.990723	+	0.135893i	$0.0433904\pi$
$239$			4.20172i			0.271787i	−0.990723	+	0.135893i	$0.956610\pi$
$240$	1.08130	+	1.95724i	0.0697975	+	0.126339i
$241$	−18.9970	+	10.9679i	−1.22371	+	0.706507i	−0.965706	−	0.259638i	$-0.916397\pi$
$241$	−18.9970	+	10.9679i	−1.22371	+	0.706507i	−0.258000	+	0.966145i	$0.583064\pi$
$242$	−9.31242	−	2.49525i	−0.598625	−	0.160401i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	3.64649			0.233442
$245$	−15.3800	+	2.90790i	−0.982592	+	0.185779i
$246$	−2.48977			−0.158742
$247$	−1.39422	−	5.20329i	−0.0887120	−	0.331078i
$248$	7.66082	+	2.05271i	0.486463	+	0.130347i
$249$	11.9390	−	6.89298i	0.756603	−	0.436825i
$250$	−9.35068	−	6.12900i	−0.591389	−	0.387632i
$251$		−	15.1293i		−	0.954952i	−0.878645	−	0.477476i	$-0.841552\pi$
$251$		−	15.1293i		−	0.954952i	0.878645	−	0.477476i	$-0.158448\pi$
$252$	−2.25331	−	1.38658i	−0.141945	−	0.0873463i
$253$	−5.91868	−	5.91868i	−0.372105	−	0.372105i
$254$	−1.66700	−	0.962442i	−0.104597	−	0.0603890i
$255$	−0.0336106	−	0.0349035i	−0.00210477	−	0.00218574i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.2301	−	5.95653i	1.38667	−	0.371558i	0.513133	−	0.858309i	$-0.328485\pi$
$257$	22.2301	−	5.95653i	1.38667	−	0.371558i	0.873541	+	0.486751i	$0.161818\pi$
$258$	−7.87756	+	7.87756i	−0.490435	+	0.490435i
$259$	−8.03098	+	26.9288i	−0.499021	+	1.67327i
$260$	−5.21350	−	3.14264i	−0.323328	−	0.194898i
$261$	2.80302	−	4.85498i	0.173503	−	0.300516i
$262$	−4.43869	+	16.5654i	−0.274223	+	1.02342i
$263$	−5.20756	+	19.4349i	−0.321112	+	1.19841i	0.597051	+	0.802203i	$0.296339\pi$
$263$	−5.20756	+	19.4349i	−0.321112	+	1.19841i	−0.918163	+	0.396203i	$0.870328\pi$
$264$	−0.582897	+	1.00961i	−0.0358749	+	0.0621371i
$265$	−5.60573	−	3.37907i	−0.344357	−	0.207574i
$266$	−3.59664	−	3.80417i	−0.220524	−	0.233248i
$267$	−2.54919	+	2.54919i	−0.156008	+	0.156008i
$268$	14.0621	−	3.76794i	0.858982	−	0.230164i
$269$	−4.63479	−	8.02770i	−0.282588	−	0.489457i	0.689433	−	0.724349i	$-0.257860\pi$
$269$	−4.63479	−	8.02770i	−0.282588	−	0.489457i	−0.972021	+	0.234892i	$0.924526\pi$
$270$	1.55103	+	1.61069i	0.0943924	+	0.0980234i
$271$	22.7157	+	13.1149i	1.37988	+	0.796673i	0.992144	−	0.125098i	$-0.0399244\pi$
$271$	22.7157	+	13.1149i	1.37988	+	0.796673i	0.387734	+	0.921771i	$0.373258\pi$
$272$	0.0153229	+	0.0153229i	0.000929089	+	0.000929089i
$273$	7.19991	+	0.201889i	0.435758	+	0.0122189i
$274$			10.2358i			0.618365i
$275$	0.219916	−	5.82482i	0.0132614	−	0.351250i
$276$	6.21797	−	3.58995i	0.374278	−	0.216089i
$277$	−12.8463	−	3.44216i	−0.771860	−	0.206819i	−0.148667	−	0.988887i	$-0.547498\pi$
$277$	−12.8463	−	3.44216i	−0.771860	−	0.206819i	−0.623193	+	0.782068i	$0.714165\pi$
$278$	1.46263	+	5.45863i	0.0877230	+	0.327387i
$279$	7.93107			0.474821
$280$	−5.90957	−	0.277372i	−0.353165	−	0.0165762i
$281$	−13.5101			−0.805944			−0.402972	−	0.915212i	$-0.632023\pi$
$281$	−13.5101			−0.805944			−0.402972	+	0.915212i	$0.632023\pi$
$282$	1.05773	+	3.94750i	0.0629868	+	0.235070i
$283$	19.2133	+	5.14819i	1.14211	+	0.306028i	0.779800	−	0.626028i	$-0.215321\pi$
$283$	19.2133	+	5.14819i	1.14211	+	0.306028i	0.362313	+	0.932057i	$0.381987\pi$
$284$	−6.51120	+	3.75924i	−0.386369	+	0.223070i
$285$	2.13959	+	3.87285i	0.126739	+	0.229408i
$286$		−	3.17374i		−	0.187667i
$287$	3.45226	−	5.61022i	0.203781	−	0.331161i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	14.7220	+	8.49977i	0.866001	+	0.499986i
$290$	0.236512	−	12.5333i	0.0138885	−	0.735979i
$291$	0.187737	+	0.325171i	0.0110054	+	0.0190618i
$292$	−3.61776	+	0.969376i	−0.211713	+	0.0567284i
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.0169176	+	0.999857i	$0.505385\pi$
$293$	−17.4044	+	17.4044i	−1.01677	+	1.01677i	−0.999857	+	0.0169176i	$0.994615\pi$
$294$	6.24878	−	3.15479i	0.364436	−	0.183991i
$295$	23.2070	−	5.75129i	1.35117	−	0.334853i
$296$	−5.31055	+	9.19815i	−0.308670	+	0.534632i
$297$	−0.301730	+	1.12607i	−0.0175081	+	0.0653413i
$298$	−0.0571481	+	0.213280i	−0.00331050	+	0.0123550i
$299$	−9.77320	+	16.9277i	−0.565199	+	0.978953i
$300$	4.77737	+	1.47539i	0.275821	+	0.0851815i
$301$	−6.82771	−	28.6734i	−0.393542	−	1.65271i
$302$	4.50346	−	4.50346i	0.259145	−	0.259145i
$303$	13.4417	−	3.60170i	0.772208	−	0.206913i
$304$	−0.989363	−	1.71363i	−0.0567439	−	0.0982833i
$305$	5.87336	−	5.65580i	0.336308	−	0.323850i
$306$	0.0187667	+	0.0108349i	0.00107282	+	0.000619393i
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	0.723084	−	0.690760i	$-0.242724\pi$
$307$	0.566349	+	0.566349i	0.0323232	+	0.0323232i	−0.690760	+	0.723084i	$0.742724\pi$
$308$	−1.46672	−	2.71335i	−0.0835744	−	0.154607i
$309$		−	11.9841i		−	0.681751i
$310$	15.5230	−	8.57585i	0.881648	−	0.487076i
$311$	11.6023	−	6.69862i	0.657909	−	0.379844i	−0.133571	−	0.991039i	$-0.542644\pi$
$311$	11.6023	−	6.69862i	0.657909	−	0.379844i	0.791480	+	0.611196i	$0.209311\pi$
$312$	2.62962	+	0.704604i	0.148873	+	0.0398903i
$313$	7.44312	+	27.7781i	0.420710	+	1.57011i	0.773117	+	0.634263i	$0.218697\pi$
$313$	7.44312	+	27.7781i	0.420710	+	1.57011i	−0.352407	+	0.935847i	$0.614637\pi$
$314$	14.4763			0.816943
$315$	−5.78000	+	1.26159i	−0.325666	+	0.0710825i
$316$	−1.61039			−0.0905918
$317$	−8.73124	−	32.5854i	−0.490395	−	1.83018i	−0.554427	−	0.832232i	$-0.687062\pi$
$317$	−8.73124	−	32.5854i	−0.490395	−	1.83018i	0.0640314	−	0.997948i	$-0.479604\pi$
$318$	2.82745	+	0.757613i	0.158556	+	0.0424848i
$319$	5.65991	−	3.26775i	0.316894	−	0.182959i
$320$	−2.14857	−	0.619385i	−0.120109	−	0.0346247i
$321$			6.90561i			0.385434i
$322$	−0.532455	+	18.9888i	−0.0296725	+	1.05820i
$323$	0.0303199	+	0.0303199i	0.00168704	+	0.00168704i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−13.2716	+	3.02446i	−0.736178	+	0.167767i
$326$	10.9528	+	18.9709i	0.606621	+	1.05070i
$327$	0.557643	−	0.149420i	0.0308377	−	0.00826294i
$328$	1.76053	−	1.76053i	0.0972091	−	0.0972091i
$329$	−10.3616	−	3.09013i	−0.571251	−	0.170364i
$330$	0.627061	+	2.53025i	0.0345186	+	0.139286i
$331$	5.46781	−	9.47053i	0.300538	−	0.520547i	−0.675720	−	0.737159i	$-0.736167\pi$
$331$	5.46781	−	9.47053i	0.300538	−	0.520547i	0.976258	+	0.216611i	$0.0695004\pi$
$332$	−3.56807	+	13.3162i	−0.195823	+	0.730823i
$333$	−2.74894	+	10.2592i	−0.150641	+	0.562201i
$334$	8.05513	−	13.9519i	0.440757	−	0.763414i
$335$	16.8056	−	27.8797i	0.918187	−	1.52323i
$336$	2.57379	−	0.612870i	0.140412	−	0.0334348i
$337$	−10.2916	+	10.2916i	−0.560617	+	0.560617i	−0.929483	−	0.368866i	$-0.879746\pi$
$337$	−10.2916	+	10.2916i	−0.560617	+	0.560617i	0.368866	+	0.929483i	$0.379746\pi$
$338$	5.39822	−	1.44645i	0.293624	−	0.0786764i
$339$	9.38250	+	16.2510i	0.509587	+	0.882631i
$340$	0.0484467		0.000914225i	0.00262739		4.95808e-5i
$341$	8.00727	+	4.62300i	0.433618	+	0.250349i
$342$	−1.39917	−	1.39917i	−0.0756585	−	0.0756585i
$343$	−1.55571	+	18.4548i	−0.0840004	+	0.996466i
$344$		−	11.1406i		−	0.600658i
$345$	4.44712	−	15.4265i	0.239425	−	0.830536i
$346$	9.04413	−	5.22163i	0.486215	−	0.280717i
$347$	2.46753	+	0.661173i	0.132464	+	0.0354936i	0.324442	−	0.945906i	$-0.394824\pi$
$347$	2.46753	+	0.661173i	0.132464	+	0.0354936i	−0.191978	+	0.981399i	$0.561490\pi$
$348$	1.45095	+	5.41502i	0.0777791	+	0.290276i
$349$	18.6079			0.996058			0.498029	−	0.867160i	$-0.334057\pi$
$349$	18.6079			0.996058			0.498029	+	0.867160i	$0.334057\pi$
$350$	−9.94870	+	8.71914i	−0.531780	+	0.466058i
$351$	2.72238			0.145310
$352$	−0.301730	−	1.12607i	−0.0160823	−	0.0600198i
$353$	−15.2918	−	4.09742i	−0.813900	−	0.218084i	−0.172222	−	0.985058i	$-0.555095\pi$
$353$	−15.2918	−	4.09742i	−0.813900	−	0.218084i	−0.641678	+	0.766974i	$0.721761\pi$
$354$	−9.25995	+	5.34623i	−0.492161	+	0.284149i
$355$	−4.65684	+	16.1540i	−0.247159	+	0.857366i
$356$		−	3.60510i		−	0.191070i
$357$	−0.0504360	+	0.0272636i	−0.00266935	+	0.00144294i
$358$	1.06563	+	1.06563i	0.0563204	+	0.0563204i
$359$	−6.50055	−	3.75309i	−0.343086	−	0.198081i	0.318550	−	0.947906i	$-0.396804\pi$
$359$	−6.50055	−	3.75309i	−0.343086	−	0.198081i	−0.661636	+	0.749825i	$0.730137\pi$
$360$	−2.23567	−	0.0421887i	−0.117830	−	0.00222354i
$361$	7.54232	+	13.0637i	0.396964	+	0.687562i
$362$	20.6184	−	5.52468i	1.08368	−	0.290371i
$363$	6.81716	−	6.81716i	0.357808	−	0.357808i
$364$	−5.23386	+	4.94835i	−0.274329	+	0.259364i
$365$	−4.32356	+	7.17260i	−0.226306	+	0.375431i
$366$	−1.82324	+	3.15795i	−0.0953025	+	0.165069i
$367$	1.02181	−	3.81343i	0.0533379	−	0.199060i	−0.934115	−	0.356971i	$-0.883809\pi$
$367$	1.02181	−	3.81343i	0.0533379	−	0.199060i	0.987453	+	0.157912i	$0.0504761\pi$
$368$	−1.85829	+	6.93525i	−0.0968702	+	0.361525i
$369$	1.24488	−	2.15620i	0.0648061	−	0.112247i
$370$	5.71291	+	23.0522i	0.297000	+	1.19842i
$371$	−5.62762	+	5.32063i	−0.292172	+	0.276233i
$372$	−5.60811	+	5.60811i	−0.290767	+	0.290767i
$373$	−5.21031	+	1.39610i	−0.269780	+	0.0722872i	−0.391173	−	0.920317i	$-0.627931\pi$
$373$	−5.21031	+	1.39610i	−0.269780	+	0.0722872i	0.121393	+	0.992605i	$0.461264\pi$
$374$	0.0126313	+	0.0218781i	0.000653150	+	0.00113129i
$375$	9.98322	−	5.03343i	0.515531	−	0.259925i
$376$	−3.53923	−	2.04338i	−0.182522	−	0.105379i
$377$	−10.7917	−	10.7917i	−0.555801	−	0.555801i
$378$	2.32747	−	1.25813i	0.119712	−	0.0647113i
$379$			2.47403i			0.127082i	0.997979	+	0.0635411i	$0.0202394\pi$
$379$			2.47403i			0.127082i	−0.997979	+	0.0635411i	$0.979761\pi$
$380$	−4.25144	−	1.22559i	−0.218094	−	0.0628716i
$381$	1.66700	−	0.962442i	0.0854029	−	0.0493074i
$382$	6.23105	+	1.66960i	0.318808	+	0.0854244i
$383$	−6.23980	−	23.2872i	−0.318839	−	1.18992i	−0.920362	−	0.391067i	$-0.872106\pi$
$383$	−6.23980	−	23.2872i	−0.318839	−	1.18992i	0.601524	−	0.798855i	$-0.294561\pi$
$384$	1.00000			0.0510310
$385$	−6.57091	−	2.09544i	−0.334885	−	0.106793i
$386$	5.13858			0.261547
$387$	−2.88339	−	10.7609i	−0.146571	−	0.547010i
$388$	−0.362681	−	0.0971800i	−0.0184123	−	0.00493357i
$389$	−5.58638	+	3.22530i	−0.283241	+	0.163529i	−0.634890	−	0.772603i	$-0.718954\pi$
$389$	−5.58638	+	3.22530i	−0.283241	+	0.163529i	0.351649	+	0.936132i	$0.385621\pi$
$390$	5.32835	−	2.94371i	0.269812	−	0.149060i
$391$		−	0.155588i		−	0.00786840i
$392$	−2.18778	+	6.64933i	−0.110500	+	0.335842i
$393$	−12.1267	−	12.1267i	−0.611713	−	0.611713i
$394$	−21.8429	−	12.6110i	−1.10043	−	0.635334i
$395$	−2.59385	+	2.49776i	−0.130511	+	0.125676i
$396$	−0.582897	−	1.00961i	−0.0292917	−	0.0507347i
$397$	18.0789	−	4.84423i	0.907354	−	0.243125i	0.225182	−	0.974317i	$-0.427702\pi$
$397$	18.0789	−	4.84423i	0.907354	−	0.243125i	0.682172	+	0.731192i	$0.261036\pi$
$398$	3.49450	−	3.49450i	0.175163	−	0.175163i
$399$	5.09283	−	1.21270i	0.254960	−	0.0607110i
$400$	−4.42136	+	2.33485i	−0.221068	+	0.116743i
$401$	9.36968	−	16.2288i	0.467900	−	0.810426i	−0.531428	−	0.847104i	$-0.678344\pi$
$401$	9.36968	−	16.2288i	0.467900	−	0.810426i	0.999327	+	0.0366779i	$0.0116776\pi$
$402$	−3.76794	+	14.0621i	−0.187928	+	0.701356i
$403$	5.58826	−	20.8557i	0.278371	−	1.03889i
$404$	−6.95796	+	12.0515i	−0.346171	+	0.599587i
$405$	−2.17041	+	0.537883i	−0.107849	+	0.0267276i
$406$	−14.2136	−	4.23892i	−0.705408	−	0.210374i
$407$	−8.75542	+	8.75542i	−0.433990	+	0.433990i
$408$	−0.0209315	+	0.00560858i	−0.00103626	+	0.000277666i
$409$	−11.6768	−	20.2248i	−0.577381	−	1.00005i	−0.995778	−	0.0917890i	$-0.970741\pi$
$409$	−11.6768	−	20.2248i	−0.577381	−	1.00005i	0.418398	−	0.908264i	$-0.362592\pi$
$410$	0.105040	−	5.56630i	0.00518757	−	0.274900i
$411$	−8.86443	−	5.11788i	−0.437250	−	0.252446i
$412$	8.47403	+	8.47403i	0.417485	+	0.417485i
$413$	0.792944	−	28.2785i	0.0390182	−	1.39149i
$414$			7.17989i			0.352873i
$415$	14.9067	+	26.9825i	0.731743	+	1.32452i
$416$	−2.35765	+	1.36119i	−0.115593	+	0.0667378i
$417$	−5.45863	−	1.46263i	−0.267310	−	0.0716255i
$418$	−0.597041	−	2.22819i	−0.0292022	−	0.108984i
$419$	−8.27092			−0.404061			−0.202030	−	0.979379i	$-0.564754\pi$
$419$	−8.27092			−0.404061			−0.202030	+	0.979379i	$0.564754\pi$
$420$	3.19500	−	4.97916i	0.155900	−	0.242958i
$421$	−33.3728			−1.62649			−0.813246	−	0.581920i	$-0.802302\pi$
$421$	−33.3728			−1.62649			−0.813246	+	0.581920i	$0.802302\pi$
$422$	4.92934	+	18.3966i	0.239957	+	0.895530i
$423$	−3.94750	−	1.05773i	−0.191934	−	0.0514285i
$424$	−2.53502	+	1.46360i	−0.123112	+	0.0710785i
$425$	0.0794506	−	0.0736696i	0.00385392	−	0.00357350i
$426$		−	7.51848i		−	0.364272i
$427$	−4.58776	−	8.48708i	−0.222017	−	0.410719i
$428$	−4.88300	−	4.88300i	−0.236029	−	0.236029i
$429$	2.74854	+	1.58687i	0.132701	+	0.0766147i
$430$	−17.2793	−	17.9440i	−0.833281	−	0.865335i
$431$	12.1733	+	21.0848i	0.586369	+	1.01562i	0.994703	+	0.102788i	$0.0327764\pi$
$431$	12.1733	+	21.0848i	0.586369	+	1.01562i	−0.408334	+	0.912832i	$0.633890\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	−0.123464	−	0.992349i	$-0.539400\pi$
$433$	18.0803	−	18.0803i	0.868885	−	0.868885i	0.992349	+	0.123464i	$0.0394002\pi$
$434$	−4.86071	−	20.4129i	−0.233322	−	0.979850i
$435$	10.7359	+	6.47146i	0.514746	+	0.310283i
$436$	−0.288657	+	0.499969i	−0.0138242	+	0.0239442i
$437$	−3.67705	+	13.7230i	−0.175897	+	0.656458i
$438$	0.969376	−	3.61776i	0.0463186	−	0.172863i
$439$	8.11012	−	14.0471i	0.387075	−	0.670433i	−0.604980	−	0.796241i	$-0.706819\pi$
$439$	8.11012	−	14.0471i	0.387075	−	0.670433i	0.992055	+	0.125808i	$0.0401522\pi$
$440$	−2.23256	−	1.34576i	−0.106433	−	0.0641566i
$441$	−0.392259	+	6.98900i	−0.0186790	+	0.332810i
$442$	0.0417148	−	0.0417148i	0.00198417	−	0.00198417i
$443$	−21.0436	+	5.63860i	−0.999810	+	0.267898i	−0.721366	−	0.692554i	$-0.756485\pi$
$443$	−21.0436	+	5.63860i	−0.999810	+	0.267898i	−0.278444	+	0.960452i	$0.589819\pi$
$444$	−5.31055	−	9.19815i	−0.252028	−	0.436525i
$445$	−5.59160	−	5.80669i	−0.265067	−	0.275264i
$446$	3.60676	+	2.08236i	0.170785	+	0.0986027i
$447$	−0.156132	−	0.156132i	−0.00738477	−	0.00738477i
$448$	−1.38658	+	2.25331i	−0.0655097	+	0.106459i
$449$		−	10.1648i		−	0.479708i	−0.970809	−	0.239854i	$-0.922900\pi$
$449$		−	10.1648i		−	0.479708i	0.970809	−	0.239854i	$-0.0770996\pi$
$450$	−3.66641	+	3.39963i	−0.172836	+	0.160260i
$451$	2.51369	−	1.45128i	0.118365	−	0.0683381i
$452$	−18.1256	−	4.85674i	−0.852556	−	0.228442i
$453$	1.64838	+	6.15184i	0.0774476	+	0.289038i
$454$	18.4389			0.865381
$455$	−0.755113	+	16.0881i	−0.0354002	+	0.754222i
$456$	1.97873			0.0926624
$457$	−7.38270	−	27.5526i	−0.345348	−	1.28886i	−0.892205	−	0.451631i	$-0.850842\pi$
$457$	−7.38270	−	27.5526i	−0.345348	−	1.28886i	0.546856	−	0.837226i	$-0.315824\pi$
$458$	−5.70873	−	1.52965i	−0.266751	−	0.0714758i
$459$	−0.0187667	+	0.0108349i	−0.000875953	+	0.000505732i
$460$	7.76361	+	14.0528i	0.361980	+	0.655215i
$461$			20.0972i			0.936022i	0.883723	+	0.468011i	$0.155029\pi$
$461$			20.0972i			0.936022i	−0.883723	+	0.468011i	$0.844971\pi$
$462$	3.08319	+	0.0864543i	0.143443	+	0.00402222i
$463$	−7.34462	−	7.34462i	−0.341334	−	0.341334i	0.515535	−	0.856869i	$-0.327593\pi$
$463$	−7.34462	−	7.34462i	−0.341334	−	0.341334i	−0.856869	+	0.515535i	$0.827593\pi$
$464$	−4.85498	−	2.80302i	−0.225387	−	0.130127i
$465$	−0.334602	+	17.7312i	−0.0155168	+	0.822267i
$466$	3.61767	+	6.26598i	0.167585	+	0.290266i
$467$	−22.8001	+	6.10926i	−1.05506	+	0.282703i	−0.744342	−	0.667799i	$-0.767237\pi$
$467$	−22.8001	+	6.10926i	−1.05506	+	0.282703i	−0.310720	+	0.950502i	$0.600570\pi$
$468$	−1.92501	+	1.92501i	−0.0889838	+	0.0889838i
$469$	−26.4618	−	27.9886i	−1.22189	−	1.29239i
$470$	−8.86993	+	2.19819i	−0.409139	+	0.101395i
$471$	−7.23813	+	12.5368i	−0.333515	+	0.577666i
$472$	2.76741	−	10.3281i	0.127381	−	0.475391i
$473$	3.36144	−	12.5451i	0.154559	−	0.576822i
$474$	0.805197	−	1.39464i	0.0369839	−	0.0640581i
$475$	−8.74867	+	4.62004i	−0.401417	+	0.211982i
$476$	0.0163853	−	0.0549419i	0.000751021	−	0.00251826i
$477$	−2.06984	+	2.06984i	−0.0947714	+	0.0947714i
$478$	4.05855	−	1.08748i	0.185634	−	0.0497404i
$479$	12.3892	+	21.4588i	0.566079	+	0.980478i	0.996948	+	0.0780633i	$0.0248736\pi$
$479$	12.3892	+	21.4588i	0.566079	+	0.980478i	−0.430869	+	0.902414i	$0.641793\pi$
$480$	1.61069	−	1.55103i	0.0735176	−	0.0707943i
$481$	25.0409	+	14.4573i	1.14176	+	0.659198i
$482$	15.5110	+	15.5110i	0.706507	+	0.706507i
$483$	−16.1785	−	9.95550i	−0.736148	−	0.452991i
$484$			9.64092i			0.438224i
$485$	−0.734895	+	0.406000i	−0.0333699	+	0.0184355i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−22.9569	−	6.15129i	−1.04028	−	0.278741i	−0.302049	−	0.953292i	$-0.597671\pi$
$487$	−22.9569	−	6.15129i	−1.04028	−	0.278741i	−0.738228	+	0.674551i	$0.764337\pi$
$488$	−0.943781	−	3.52224i	−0.0427229	−	0.159444i
$489$	−21.9057			−0.990608
$490$	6.78945	+	14.1033i	0.306716	+	0.637123i
$491$	−0.386093			−0.0174242			−0.00871208	−	0.999962i	$-0.502773\pi$
$491$	−0.386093			−0.0174242			−0.00871208	+	0.999962i	$0.502773\pi$
$492$	0.644400	+	2.40493i	0.0290518	+	0.108423i
$493$	0.117343	+	0.0314419i	0.00528486	+	0.00141607i
$494$	−4.66514	+	2.69342i	−0.209895	+	0.121183i
$495$	−2.50479	−	0.722076i	−0.112582	−	0.0324549i
$496$		−	7.93107i		−	0.356115i
$497$	16.9415	+	10.4250i	0.759928	+	0.467624i
$498$	−9.74815	−	9.74815i	−0.436825	−	0.436825i
$499$	6.94992	+	4.01254i	0.311121	+	0.179626i	0.647428	−	0.762127i	$-0.275845\pi$
$499$	6.94992	+	4.01254i	0.311121	+	0.179626i	−0.336307	+	0.941752i	$0.609178\pi$
$500$	−3.50003	+	10.6184i	−0.156526	+	0.474868i
$501$	8.05513	+	13.9519i	0.359877	+	0.623325i
$502$	−14.6138	+	3.91575i	−0.652244	+	0.174768i
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	−0.916594	−	0.399819i	$-0.869073\pi$
$503$	−11.5901	+	11.5901i	−0.516775	+	0.516775i	0.399819	+	0.916594i	$0.369073\pi$
$504$	−0.756134	+	2.53540i	−0.0336809	+	0.112936i
$505$	7.48513	+	30.2033i	0.333084	+	1.34403i
$506$	−4.18514	+	7.24888i	−0.186052	+	0.322252i
$507$	−1.44645	+	5.39822i	−0.0642390	+	0.239743i
$508$	−0.498197	+	1.85929i	−0.0221039	+	0.0824929i
$509$	−7.77422	+	13.4654i	−0.344586	+	0.596841i	−0.985279	−	0.170957i	$-0.945314\pi$
$509$	−7.77422	+	13.4654i	−0.344586	+	0.596841i	0.640692	+	0.767798i	$0.278648\pi$
$510$	−0.0250151	+	0.0414990i	−0.00110769	+	0.00183761i
$511$	6.80781	+	7.20062i	0.301160	+	0.318536i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.91130	−	0.512132i	0.0843861	−	0.0226112i
$514$	−11.5071	−	19.9309i	−0.507558	−	0.879116i
$515$	26.7925	+	0.505593i	1.18062	+	0.0222791i
$516$	9.64800	+	5.57028i	0.424730	+	0.245218i
$517$	−3.36888	−	3.36888i	−0.148163	−	0.148163i
$518$	28.0898	+	0.787652i	1.23419	+	0.0346074i
$519$			10.4433i			0.458408i
$520$	−1.68620	+	5.84923i	−0.0739448	+	0.256506i
$521$	22.8573	−	13.1967i	1.00140	−	0.578156i	0.0927347	−	0.995691i	$-0.470439\pi$
$521$	22.8573	−	13.1967i	1.00140	−	0.578156i	0.908661	+	0.417535i	$0.137106\pi$
$522$	−5.41502	−	1.45095i	−0.237009	−	0.0635064i
$523$	−10.2125	−	38.1134i	−0.446559	−	1.66658i	−0.711786	−	0.702396i	$-0.752114\pi$
$523$	−10.2125	−	38.1134i	−0.446559	−	1.66658i	0.265227	−	0.964186i	$-0.414553\pi$
$524$	17.1498			0.749192
$525$	−2.57665	−	12.9754i	−0.112454	−	0.566293i
$526$	20.1205			0.877294
$527$	0.0444820	+	0.166009i	0.00193767	+	0.00723147i
$528$	1.12607	+	0.301730i	0.0490060	+	0.0131311i
$529$	24.7258	−	14.2754i	1.07503	−	0.620671i
$530$	−1.81306	+	6.28928i	−0.0787543	+	0.273189i
$531$		−	10.6925i		−	0.464014i
$532$	−2.74366	+	4.45868i	−0.118953	+	0.193308i
$533$	−4.79284	−	4.79284i	−0.207601	−	0.207601i
$534$	3.12211	+	1.80255i	0.135107	+	0.0780040i
$535$	−15.4387	−	0.291339i	−0.667472	−	0.0125957i
$536$	−7.27910	−	12.6078i	−0.314409	−	0.544573i
$537$	−1.45568	+	0.390048i	−0.0628172	+	0.0168318i
$538$	−6.55459	+	6.55459i	−0.282588	+	0.282588i
$539$	−4.46990	+	6.82750i	−0.192532	+	0.294081i
$540$	1.15437	−	1.91505i	0.0496762	−	0.0824107i
$541$	−4.06849	+	7.04683i	−0.174918	+	0.302967i	−0.940133	−	0.340808i	$-0.889299\pi$
$541$	−4.06849	+	7.04683i	−0.174918	+	0.302967i	0.765215	+	0.643775i	$0.222633\pi$
$542$	6.78877	−	25.3360i	0.291603	−	1.08828i
$543$	−5.52468	+	20.6184i	−0.237087	+	0.884820i
$544$	0.0108349	−	0.0187667i	0.000464544	−	0.000804615i
$545$	0.310527	+	1.25301i	0.0133015	+	0.0536730i
$546$	−1.66846	−	7.00683i	−0.0714037	−	0.299865i
$547$	12.5204	−	12.5204i	0.535335	−	0.535335i	−0.386820	−	0.922155i	$-0.626427\pi$
$547$	12.5204	−	12.5204i	0.535335	−	0.535335i	0.922155	+	0.386820i	$0.126427\pi$
$548$	9.88699	−	2.64921i	0.422351	−	0.113169i
$549$	−1.82324	−	3.15795i	−0.0778142	−	0.134778i
$550$	−5.68327	+	1.29515i	−0.242335	+	0.0552255i
$551$	−9.60667	−	5.54641i	−0.409258	−	0.236285i
$552$	−5.07695	−	5.07695i	−0.216089	−	0.216089i
$553$	2.02609	+	3.74814i	0.0861581	+	0.159387i
$554$			13.2995i			0.565040i
$555$	−22.8202	−	6.57856i	−0.968664	−	0.279244i
$556$	4.89407	−	2.82559i	0.207555	−	0.119832i
$557$	15.6419	+	4.19123i	0.662768	+	0.177588i	0.574495	−	0.818508i	$-0.305198\pi$
$557$	15.6419	+	4.19123i	0.662768	+	0.177588i	0.0882732	+	0.996096i	$0.471865\pi$
$558$	−2.05271	−	7.66082i	−0.0868982	−	0.324308i
$559$	−30.3288			−1.28277
$560$	1.26159	+	5.78000i	0.0533119	+	0.244250i
$561$	−0.0252626			−0.00106659
$562$	3.49667	+	13.0497i	0.147498	+	0.550470i
$563$	8.45582	+	2.26573i	0.356370	+	0.0954892i	0.432562	−	0.901604i	$-0.357610\pi$
$563$	8.45582	+	2.26573i	0.356370	+	0.0954892i	−0.0761920	+	0.997093i	$0.524276\pi$
$564$	3.53923	−	2.04338i	0.149028	−	0.0860416i
$565$	−36.7276	+	20.2906i	−1.54514	+	0.853630i
$566$		−	19.8911i		−	0.836085i
$567$	−0.0741591	+	2.64471i	−0.00311439	+	0.111067i
$568$	5.31637	+	5.31637i	0.223070	+	0.223070i
$569$	35.9794	+	20.7727i	1.50833	+	0.870838i	0.999953	+	0.00970591i	$0.00308954\pi$
$569$	35.9794	+	20.7727i	1.50833	+	0.870838i	0.508382	+	0.861132i	$0.330244\pi$
$570$	3.18711	−	3.06906i	0.133494	−	0.128549i
$571$	−6.59259	−	11.4187i	−0.275891	−	0.477858i	0.694468	−	0.719523i	$-0.255640\pi$
$571$	−6.59259	−	11.4187i	−0.275891	−	0.477858i	−0.970360	+	0.241666i	$0.922306\pi$
$572$	−3.06559	+	0.821423i	−0.128179	+	0.0343454i
$573$	−4.56144	+	4.56144i	−0.190557	+	0.190557i
$574$	−6.31256	−	1.88260i	−0.263481	−	0.0785782i
$575$	34.3010	+	10.5931i	1.43045	+	0.441764i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.64406	−	17.3319i	0.193335	−	0.721535i	−0.799357	−	0.600857i	$-0.794826\pi$
$577$	4.64406	−	17.3319i	0.193335	−	0.721535i	0.992692	−	0.120679i	$-0.0385071\pi$
$578$	4.39980	−	16.4203i	0.183008	−	0.682994i
$579$	−2.56929	+	4.45014i	−0.106776	+	0.184942i
$580$	−12.1674	+	3.01539i	−0.505225	+	0.125207i
$581$	35.4822	−	8.44900i	1.47205	−	0.350524i
$582$	0.265501	−	0.265501i	0.0110054	−	0.0110054i
$583$	−3.29623	+	0.883222i	−0.136516	+	0.0365793i
$584$	1.87269	+	3.24360i	0.0774925	+	0.134221i
$585$	−0.114854	+	6.08634i	−0.00474862	+	0.251639i
$586$	21.3159	+	12.3068i	0.880553	+	0.508387i
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	0.530535	−	0.847663i	$-0.321991\pi$
$587$	−7.68342	−	7.68342i	−0.317129	−	0.317129i	−0.847663	+	0.530535i	$0.821991\pi$
$588$	−4.66460	−	5.21934i	−0.192365	−	0.215242i
$589$		−	15.6934i		−	0.646636i
$590$	−11.5618	−	20.9277i	−0.475990	−	0.861582i
$591$	21.8429	−	12.6110i	0.898499	−	0.518748i
$592$	10.2592	+	2.74894i	0.421651	+	0.112981i
$593$	−2.03328	−	7.58832i	−0.0834970	−	0.311615i	0.911528	−	0.411237i	$-0.134903\pi$
$593$	−2.03328	−	7.58832i	−0.0834970	−	0.311615i	−0.995025	+	0.0996223i	$0.968237\pi$
$594$	1.16579			0.0478331
$595$	−0.0588246	−	0.113908i	−0.00241157	−	0.00466979i
$596$	0.220803			0.00904446
$597$	1.27908	+	4.77357i	0.0523491	+	0.195369i
$598$	18.8804	+	5.05898i	0.772076	+	0.206877i
$599$	20.5520	−	11.8657i	0.839731	−	0.484819i	−0.0174418	−	0.999848i	$-0.505552\pi$
$599$	20.5520	−	11.8657i	0.839731	−	0.484819i	0.857173	+	0.515029i	$0.172219\pi$
$600$	0.188640	−	4.99644i	0.00770120	−	0.203979i
$601$			14.4348i			0.588806i	0.955681	+	0.294403i	$0.0951208\pi$
$601$			14.4348i			0.588806i	−0.955681	+	0.294403i	$0.904879\pi$
$602$	−25.9293	+	14.0163i	−1.05680	+	0.571261i
$603$	−10.2942	−	10.2942i	−0.419213	−	0.419213i
$604$	−5.51559	−	3.18442i	−0.224426	−	0.129572i
$605$	14.9533	+	15.5285i	0.607939	+	0.631325i
$606$	−6.95796	−	12.0515i	−0.282648	−	0.489560i
$607$	0.644795	−	0.172772i	0.0261714	−	0.00701261i	−0.245710	−	0.969343i	$-0.579021\pi$
$607$	0.644795	−	0.172772i	0.0261714	−	0.00701261i	0.271881	+	0.962331i	$0.412354\pi$
$608$	−1.39917	+	1.39917i	−0.0567439	+	0.0567439i
$609$	10.7778	−	10.1899i	0.436738	−	0.412914i
$610$	−6.98322	−	4.20940i	−0.282742	−	0.170434i
$611$	−5.56284	+	9.63513i	−0.225049	+	0.389796i
$612$	0.00560858	−	0.0209315i	0.000226713	−	0.000846106i
$613$	−3.82018	+	14.2571i	−0.154296	+	0.575839i	0.844869	+	0.534973i	$0.179678\pi$
$613$	−3.82018	+	14.2571i	−0.154296	+	0.575839i	−0.999165	+	0.0408659i	$0.986988\pi$
$614$	0.400469	−	0.693633i	0.0161616	−	0.0279927i
$615$	4.76804	+	2.87412i	0.192266	+	0.115896i
$616$	−2.24128	+	2.11901i	−0.0903037	+	0.0853775i
$617$	−4.88322	+	4.88322i	−0.196591	+	0.196591i	−0.798537	−	0.601946i	$-0.794392\pi$
$617$	−4.88322	+	4.88322i	−0.196591	+	0.196591i	0.601946	+	0.798537i	$0.294392\pi$
$618$	−11.5757	+	3.10171i	−0.465644	+	0.124769i
$619$	13.8975	+	24.0712i	0.558589	+	0.967504i	0.997615	+	0.0690295i	$0.0219903\pi$
$619$	13.8975	+	24.0712i	0.558589	+	0.967504i	−0.439026	+	0.898474i	$0.644676\pi$
$620$	−12.3013	−	12.7745i	−0.494032	−	0.513036i
$621$	−6.21797	−	3.58995i	−0.249519	−	0.144060i
$622$	−9.47327	−	9.47327i	−0.379844	−	0.379844i
$623$	−8.39075	+	4.53569i	−0.336168	+	0.181719i
$624$		−	2.72238i		−	0.108982i
$625$	10.8319	+	22.5315i	0.433276	+	0.901261i
$626$	24.9051	−	14.3790i	0.995410	−	0.574700i
$627$	2.22819	+	0.597041i	0.0889852	+	0.0238435i
$628$	−3.74673	−	13.9830i	−0.149511	−	0.557982i
$629$	−0.230158			−0.00917701
$630$	2.71458	+	5.25653i	0.108151	+	0.209425i
$631$	6.30112			0.250844			0.125422	−	0.992104i	$-0.459972\pi$
$631$	6.30112			0.250844			0.125422	+	0.992104i	$0.459972\pi$
$632$	0.416801	+	1.55552i	0.0165794	+	0.0618753i
$633$	−18.3966	−	4.92934i	−0.731197	−	0.195924i
$634$	−29.2153	+	16.8675i	−1.16029	+	0.669893i
$635$	2.08137	+	3.76746i	0.0825968	+	0.149507i
$636$		−	2.92719i		−	0.116071i
$637$	18.1020	+	5.95597i	0.717228	+	0.235984i
$638$	−4.62129	−	4.62129i	−0.182959	−	0.182959i
$639$	6.51120	+	3.75924i	0.257579	+	0.148713i
$640$	−0.0421887	+	2.23567i	−0.00166766	+	0.0883726i
$641$	−2.63684	−	4.56715i	−0.104149	−	0.180391i	0.809241	−	0.587477i	$-0.199879\pi$
$641$	−2.63684	−	4.56715i	−0.104149	−	0.180391i	−0.913390	+	0.407085i	$0.866545\pi$
$642$	6.67031	−	1.78730i	0.263256	−	0.0705393i
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	−0.593714	−	0.804677i	$-0.702339\pi$
$643$	5.34948	−	5.34948i	0.210963	−	0.210963i	0.804677	+	0.593714i	$0.202339\pi$
$644$	18.4795	−	4.40034i	0.728196	−	0.173398i
$645$	24.1796	−	5.99231i	0.952070	−	0.235947i
$646$	0.0214394	−	0.0371341i	0.000843522	−	0.00146102i
$647$	−5.73506	+	21.4035i	−0.225469	+	0.841460i	0.756748	+	0.653707i	$0.226787\pi$
$647$	−5.73506	+	21.4035i	−0.225469	+	0.841460i	−0.982216	+	0.187753i	$0.939880\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	6.23261	−	10.7952i	0.244651	−	0.423749i
$650$	6.35636	+	12.0366i	0.249317	+	0.472116i
$651$	20.1084	+	5.99695i	0.788112	+	0.235039i
$652$	15.4896	−	15.4896i	0.606621	−	0.606621i
$653$	42.8267	−	11.4754i	1.67594	−	0.449066i	0.709235	−	0.704972i	$-0.249041\pi$
$653$	42.8267	−	11.4754i	1.67594	−	0.449066i	0.966702	+	0.255907i	$0.0823739\pi$
$654$	−0.288657	−	0.499969i	−0.0112874	−	0.0195503i
$655$	27.6230	−	26.5998i	1.07932	−	1.03934i
$656$	−2.15620	−	1.24488i	−0.0841856	−	0.0486046i
$657$	2.64838	+	2.64838i	0.103323	+	0.103323i
$658$	−0.303070	+	10.8083i	−0.0118149	+	0.421351i
$659$		−	38.6387i		−	1.50515i	−0.658507	−	0.752575i	$-0.728812\pi$
$659$		−	38.6387i		−	1.50515i	0.658507	−	0.752575i	$-0.271188\pi$
$660$	2.28174	−	1.26057i	0.0888167	−	0.0490677i
$661$	−24.7737	+	14.3031i	−0.963587	+	0.556327i	−0.897275	−	0.441472i	$-0.854457\pi$
$661$	−24.7737	+	14.3031i	−0.963587	+	0.556327i	−0.0663118	+	0.997799i	$0.521123\pi$
$662$	−10.5630	−	2.83035i	−0.410543	−	0.110005i
$663$	0.0152687	+	0.0569835i	0.000592987	+	0.00221306i
$664$	13.7860			0.534999
$665$	2.49634	+	11.4370i	0.0968039	+	0.443509i
$666$	10.6211			0.411560
$667$	10.4177	+	38.8793i	0.403374	+	1.50541i
$668$	−15.5613	−	4.16964i	−0.602086	−	0.161328i
$669$	−3.60676	+	2.08236i	−0.139445	+	0.0805088i
$670$	−31.2794	−	9.01714i	−1.20843	−	0.348362i
$671$		−	4.25106i		−	0.164110i
$672$	−1.25813	−	2.32747i	−0.0485335	−	0.0897840i
$673$	36.6126	+	36.6126i	1.41131	+	1.41131i	0.750932	+	0.660379i	$0.229604\pi$
$673$	36.6126	+	36.6126i	1.41131	+	1.41131i	0.660379	+	0.750932i	$0.270396\pi$
$674$	12.6045	+	7.27723i	0.485509	+	0.280309i
$675$	−1.11096	−	4.87501i	−0.0427609	−	0.187639i
$676$	−2.79432	−	4.83991i	−0.107474	−	0.186150i
$677$	−25.9359	+	6.94951i	−0.996798	+	0.267091i	−0.720104	−	0.693867i	$-0.755906\pi$
$677$	−25.9359	+	6.94951i	−0.996798	+	0.267091i	−0.276695	+	0.960958i	$0.589239\pi$
$678$	13.2689	−	13.2689i	0.509587	−	0.509587i
$679$	0.230117	+	0.966393i	0.00883108	+	0.0370868i
$680$	−0.0116559	−	0.0470326i	−0.000446982	−	0.00180362i
$681$	−9.21945	+	15.9686i	−0.353290	+	0.611917i
$682$	2.39304	−	8.93095i	0.0916342	−	0.341984i
$683$	−0.514460	+	1.91999i	−0.0196853	+	0.0734664i	−0.975070	−	0.221899i	$-0.928775\pi$
$683$	−0.514460	+	1.91999i	−0.0196853	+	0.0734664i	0.955384	+	0.295365i	$0.0954413\pi$
$684$	−0.989363	+	1.71363i	−0.0378293	+	0.0655222i
$685$	11.8159	−	19.6020i	0.451461	−	0.748955i
$686$	18.2286	−	3.27375i	0.695972	−	0.124993i
$687$	4.17908	−	4.17908i	0.159442	−	0.159442i
$688$	−10.7609	+	2.88339i	−0.410257	+	0.109928i
$689$	3.98446	+	6.90130i	0.151796	+	0.262918i
$690$	−16.0519	−	0.302911i	−0.611084	−	0.0115316i
$691$	−8.33571	−	4.81262i	−0.317105	−	0.183081i	0.332996	−	0.942928i	$-0.391940\pi$
$691$	−8.33571	−	4.81262i	−0.317105	−	0.183081i	−0.650102	+	0.759847i	$0.725274\pi$
$692$	−7.38450	−	7.38450i	−0.280717	−	0.280717i
$693$	−1.61647	+	2.62690i	−0.0614045	+	0.0997875i
$694$		−	2.55458i		−	0.0969703i
$695$	3.50026	−	12.1420i	0.132772	−	0.460572i
$696$	4.85498	−	2.80302i	0.184027	−	0.106248i
$697$	0.0521146	+	0.0139641i	0.00197398	+	0.000528927i
$698$	−4.81608	−	17.9739i	−0.182291	−	0.680320i
$699$	−7.23533			−0.273665
$700$	10.9970	+	7.35303i	0.415646	+	0.277918i
$701$	−12.4958			−0.471959			−0.235980	−	0.971758i	$-0.575830\pi$
$701$	−12.4958			−0.471959			−0.235980	+	0.971758i	$0.575830\pi$
$702$	−0.704604	−	2.62962i	−0.0265936	−	0.0992485i
$703$	20.3002	+	5.43941i	0.765635	+	0.205151i
$704$	−1.00961	+	0.582897i	−0.0380510	+	0.0219688i
$705$	2.53127	−	8.78068i	0.0953332	−	0.330699i
$706$			15.8312i			0.595816i
$707$	36.8036	+	1.03199i	1.38414	+	0.0388121i
$708$	7.56072	+	7.56072i	0.284149	+	0.284149i
$709$	−39.6174	−	22.8731i	−1.48786	−	0.859018i	−0.487958	−	0.872867i	$-0.662258\pi$
$709$	−39.6174	−	22.8731i	−1.48786	−	0.859018i	−0.999904	+	0.0138494i	$0.995591\pi$
$710$	16.8089	+	0.317195i	0.630825	+	0.0119041i
$711$	0.805197	+	1.39464i	0.0301973	+	0.0523032i
$712$	−3.48226	+	0.933068i	−0.130503	+	0.0349682i
$713$	−40.2656	+	40.2656i	−1.50796	+	1.50796i
$714$	0.0393884	+	0.0416611i	0.00147407	+	0.00155913i
$715$	−3.66367	+	6.07787i	−0.137014	+	0.227300i
$716$	0.753516	−	1.30513i	0.0281602	−	0.0487749i
$717$	−1.08748	+	4.05855i	−0.0406129	+	0.151569i
$718$	−1.94274	+	7.25042i	−0.0725025	+	0.270583i
$719$	8.05439	−	13.9506i	0.300378	−	0.520270i	−0.675844	−	0.737045i	$-0.736221\pi$
$719$	8.05439	−	13.9506i	0.300378	−	0.520270i	0.976222	+	0.216775i	$0.0695539\pi$
$720$	0.537883	+	2.17041i	0.0200457	+	0.0808864i
$721$	9.06157	−	30.3845i	0.337471	−	1.13158i
$722$	10.6665	−	10.6665i	0.396964	−	0.396964i
$723$	−21.1884	+	5.67742i	−0.788006	+	0.211146i
$724$	−10.6729	−	18.4859i	−0.396654	−	0.687025i
$725$	−14.9210	+	23.7288i	−0.554151	+	0.881267i
$726$	−8.34928	−	4.82046i	−0.309871	−	0.178904i
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	0.00843633	−	0.999964i	$-0.497315\pi$
$727$	−26.7345	−	26.7345i	−0.991528	−	0.991528i	−0.999964	+	0.00843633i	$0.997315\pi$
$728$	6.13436	+	3.77480i	0.227355	+	0.139903i
$729$			1.00000i			0.0370370i
$730$	8.04722	+	2.31983i	0.297841	+	0.0858609i
$731$	0.209071	−	0.120707i	0.00773278	−	0.00446452i
$732$	3.52224	+	0.943781i	0.130186	+	0.0348831i
$733$	−2.63030	−	9.81640i	−0.0971523	−	0.362577i	0.900185	−	0.435508i	$-0.143431\pi$
$733$	−2.63030	−	9.81640i	−0.0971523	−	0.362577i	−0.997337	+	0.0729311i	$0.976765\pi$
$734$	−3.94796			−0.145722
$735$	−15.6086	−	1.17182i	−0.575730	−	0.0432232i
$736$	7.17989			0.264654
$737$	−4.39265	−	16.3936i	−0.161805	−	0.603865i
$738$	−2.40493	−	0.644400i	−0.0885268	−	0.0237207i
$739$	−1.51357	+	0.873858i	−0.0556775	+	0.0321454i	−0.527580	−	0.849505i	$-0.676901\pi$
$739$	−1.51357	+	0.873858i	−0.0556775	+	0.0321454i	0.471903	+	0.881651i	$0.343567\pi$
$740$	20.7881	−	11.4846i	0.764185	−	0.422182i
$741$		−	5.38685i		−	0.197891i
$742$	6.59587	+	4.05879i	0.242142	+	0.149003i
$743$	4.26452	+	4.26452i	0.156450	+	0.156450i	0.780992	−	0.624542i	$-0.214714\pi$
$743$	4.26452	+	4.26452i	0.156450	+	0.156450i	−0.624542	+	0.780992i	$0.714714\pi$
$744$	6.86850	+	3.96553i	0.251812	+	0.145383i
$745$	0.355646	−	0.342472i	0.0130299	−	0.0125472i
$746$	2.69706	+	4.67144i	0.0987462	+	0.171033i
$747$	13.3162	−	3.56807i	0.487215	−	0.130549i
$748$	0.0178634	−	0.0178634i	0.000653150	−	0.000653150i
$749$	−5.22157	+	17.5085i	−0.190792	+	0.639747i
$750$	−7.44577	−	8.34030i	−0.271881	−	0.304545i
$751$	−7.54354	+	13.0658i	−0.275268	+	0.476778i	−0.970203	−	0.242295i	$-0.922100\pi$
$751$	−7.54354	+	13.0658i	−0.275268	+	0.476778i	0.694935	+	0.719073i	$0.255433\pi$
$752$	−1.05773	+	3.94750i	−0.0385714	+	0.143950i
$753$	3.91575	−	14.6138i	0.142698	−	0.532555i
$754$	−7.63089	+	13.2171i	−0.277901	+	0.481338i
$755$	−13.8230	+	3.42569i	−0.503071	+	0.124674i
$756$	−1.81766	−	1.92253i	−0.0661075	−	0.0699218i
$757$	−7.26095	+	7.26095i	−0.263904	+	0.263904i	−0.826638	−	0.562734i	$-0.809749\pi$
$757$	−7.26095	+	7.26095i	−0.263904	+	0.263904i	0.562734	+	0.826638i	$0.309749\pi$
$758$	2.38973	−	0.640325i	0.0867987	−	0.0232576i
$759$	−4.18514	−	7.24888i	−0.151911	−	0.263118i
$760$	−0.0834800	+	4.42378i	−0.00302814	+	0.160467i
$761$	−10.7048	−	6.18041i	−0.388048	−	0.224040i	0.293266	−	0.956031i	$-0.405258\pi$
$761$	−10.7048	−	6.18041i	−0.388048	−	0.224040i	−0.681314	+	0.731991i	$0.738591\pi$
$762$	−1.36110	−	1.36110i	−0.0493074	−	0.0493074i
$763$	1.52683	+	0.0428131i	0.0552750	+	0.00154994i
$764$		−	6.45086i		−	0.233384i
$765$	−0.0234316	−	0.0424132i	−0.000847172	−	0.00153345i
$766$	−20.8788	+	12.0544i	−0.754380	+	0.435542i
$767$	−28.1171	−	7.53395i	−1.01525	−	0.272035i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	−17.1708			−0.619196			−0.309598	−	0.950867i	$-0.600195\pi$
$769$	−17.1708			−0.619196			−0.309598	+	0.950867i	$0.600195\pi$
$770$	−0.323359	+	6.88935i	−0.0116531	+	0.248275i
$771$	23.0143			0.828839
$772$	−1.32996	−	4.96349i	−0.0478664	−	0.178640i
$773$	−1.22292	−	0.327680i	−0.0439853	−	0.0117858i	0.236759	−	0.971568i	$-0.423915\pi$
$773$	−1.22292	−	0.327680i	−0.0439853	−	0.0117858i	−0.280745	+	0.959783i	$0.590581\pi$
$774$	−9.64800	+	5.57028i	−0.346790	+	0.200219i
$775$	−39.6271	−	1.49612i	−1.42345	−	0.0537421i
$776$			0.375475i			0.0134788i
$777$	−14.7270	+	23.9326i	−0.528329	+	0.858578i
$778$	4.56126	+	4.56126i	0.163529	+	0.163529i
$779$	−4.26654	−	2.46329i	−0.152865	−	0.0882564i
$780$	−4.22248	−	4.38491i	−0.151189	−	0.157005i
$781$	4.38251	+	7.59072i	0.156818	+	0.271617i
$782$	−0.150286	+	0.0402690i	−0.00537422	+	0.00144002i
$783$	3.96407	−	3.96407i	0.141664	−	0.141664i
$784$	6.98900	+	0.392259i	0.249607	+	0.0140092i
$785$	−27.7228	−	16.7110i	−0.989469	−	0.596441i
$786$	−8.57489	+	14.8522i	−0.305856	+	0.529759i
$787$	3.96605	−	14.8015i	0.141375	−	0.527617i	−0.858515	−	0.512788i	$-0.828613\pi$
$787$	3.96605	−	14.8015i	0.141375	−	0.527617i	0.999890	−	0.0148294i	$-0.00472053\pi$
$788$	−6.52795	+	24.3626i	−0.232549	+	0.867883i
$789$	−10.0602	+	17.4248i	−0.358154	+	0.620341i
$790$	3.08399	+	1.85899i	0.109723	+	0.0661400i
$791$	11.5005	+	48.2971i	0.408911	+	1.71725i
$792$	−0.824341	+	0.824341i	−0.0292917	+	0.0292917i
$793$	−9.58887	+	2.56933i	−0.340511	+	0.0912396i
$794$	−9.35833	−	16.2091i	−0.332115	−	0.575240i
$795$	−4.54015	−	4.71480i	−0.161023	−	0.167217i
$796$	−4.27987	−	2.47098i	−0.151696	−	0.0875817i
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.933570	+	0.358396i	$0.116676\pi$
$797$	36.4737	+	36.4737i	1.29197	+	1.29197i	0.358396	+	0.933570i	$0.383324\pi$
$798$	−2.48950	−	4.60542i	−0.0881273	−	0.163030i
$799$		−	0.0885594i		−	0.00313301i
$800$	3.39963	+	3.66641i	0.120195	+	0.129627i
$801$	−3.12211	+	1.80255i	−0.110314	+	0.0636900i
$802$	−18.1008	−	4.85010i	−0.639163	−	0.171263i
$803$	1.13009	+	4.21757i	0.0398801	+	0.148835i
$804$	14.5582			0.513428
$805$	22.9398	−	35.7498i	0.808520	−	1.26002i
$806$	−21.5914			−0.760524
$807$	−2.39915	−	8.95373i	−0.0844539	−	0.315186i
$808$	13.4417	+	3.60170i	0.472879	+	0.126708i
$809$	12.0158	−	6.93731i	0.422452	−	0.243903i	−0.273674	−	0.961823i	$-0.588239\pi$
$809$	12.0158	−	6.93731i	0.422452	−	0.243903i	0.696126	+	0.717920i	$0.254906\pi$
$810$	1.08130	+	1.95724i	0.0379930	+	0.0687705i
$811$		−	18.4047i		−	0.646275i	−0.946352	−	0.323137i	$-0.895262\pi$
$811$		−	18.4047i		−	0.646275i	0.946352	−	0.323137i	$-0.104738\pi$
$812$	−0.415739	+	14.8264i	−0.0145896	+	0.520304i
$813$	18.5473	+	18.5473i	0.650481	+	0.650481i
$814$	10.7232	+	6.19102i	0.375846	+	0.216995i
$815$	0.924172	−	48.9738i	0.0323723	−	1.71548i
$816$	0.0108349	+	0.0187667i	0.000379299	+	0.000656965i
$817$	−21.2930	+	5.70544i	−0.744947	+	0.199608i
$818$	−16.5135	+	16.5135i	−0.577381	+	0.577381i
$819$	6.90233	+	2.05848i	0.241187	+	0.0719292i
$820$	−5.40382	+	1.33920i	−0.188710	+	0.0467670i
$821$	−16.4402	+	28.4753i	−0.573768	+	0.993796i	0.422406	+	0.906407i	$0.361186\pi$
$821$	−16.4402	+	28.4753i	−0.573768	+	0.993796i	−0.996174	+	0.0873891i	$0.972148\pi$
$822$	−2.64921	+	9.88699i	−0.0924018	+	0.344848i
$823$	−6.31918	+	23.5835i	−0.220273	+	0.822069i	0.763971	+	0.645251i	$0.223247\pi$
$823$	−6.31918	+	23.5835i	−0.220273	+	0.822069i	−0.984244	+	0.176818i	$0.943420\pi$
$824$	5.99204	−	10.3785i	0.208743	−	0.361553i
$825$	1.72000	−	5.56943i	0.0598826	−	0.193903i
$826$	−27.5202	+	6.55309i	−0.957549	+	0.228011i
$827$	1.94367	−	1.94367i	0.0675881	−	0.0675881i	−0.672505	−	0.740093i	$-0.734782\pi$
$827$	1.94367	−	1.94367i	0.0675881	−	0.0675881i	0.740093	+	0.672505i	$0.234782\pi$
$828$	6.93525	−	1.85829i	0.241016	−	0.0645802i
$829$	8.99161	+	15.5739i	0.312291	+	0.540905i	0.978858	−	0.204541i	$-0.0655701\pi$
$829$	8.99161	+	15.5739i	0.312291	+	0.540905i	−0.666567	+	0.745446i	$0.732237\pi$
$830$	22.2049	−	21.3824i	0.770744	−	0.742194i
$831$	−11.5177	−	6.64974i	−0.399544	−	0.230677i
$832$	1.92501	+	1.92501i	0.0667378	+	0.0667378i
$833$	−0.148490	+	0.0309878i	−0.00514489	+	0.00107366i
$834$			5.65119i			0.195685i
$835$	−31.5317	+	17.4200i	−1.09120	+	0.602844i
$836$	−1.99774	+	1.15339i	−0.0690932	+	0.0398910i
$837$	7.66082	+	2.05271i	0.264797	+	0.0709521i
$838$	2.14067	+	7.98909i	0.0739483	+	0.275979i
$839$	4.25819			0.147009			0.0735045	−	0.997295i	$-0.476582\pi$
$839$	4.25819			0.147009			0.0735045	+	0.997295i	$0.476582\pi$
$840$	−5.63642	−	1.79743i	−0.194475	−	0.0620173i
$841$	−2.42773			−0.0837148
$842$	8.63752	+	32.2357i	0.297669	+	1.11091i
$843$	−13.0497	−	3.49667i	−0.449457	−	0.120432i
$844$	16.4939	−	9.52276i	0.567743	−	0.327787i
$845$	−12.0076	−	3.46153i	−0.413074	−	0.119080i
$846$			4.08675i			0.140505i
$847$	22.4389	−	12.1296i	0.771011	−	0.416776i
$848$	2.06984	+	2.06984i	0.0710785	+	0.0710785i
$849$	17.2262	+	9.94554i	0.591201	+	0.341330i
$850$	−0.0917227	−	0.0576763i	−0.00314606	−	0.00197828i
$851$	−38.1292	−	66.0417i	−1.30705	−	2.26388i
$852$	−7.26230	+	1.94593i	−0.248802	+	0.0666664i
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.295436	−	0.955362i	$-0.404535\pi$
$853$	36.5310	−	36.5310i	1.25080	−	1.25080i	0.955362	−	0.295436i	$-0.0954650\pi$
$854$	−7.01049	+	6.62806i	−0.239894	+	0.226807i
$855$	1.06432	+	4.29465i	0.0363991	+	0.146874i
$856$	−3.45281	+	5.98043i	−0.118014	+	0.204407i
$857$	−0.820966	+	3.06389i	−0.0280437	+	0.104660i	−0.978529	−	0.206109i	$-0.933920\pi$
$857$	−0.820966	+	3.06389i	−0.0280437	+	0.104660i	0.950485	+	0.310769i	$0.100587\pi$
$858$	0.821423	−	3.06559i	0.0280429	−	0.104658i
$859$	14.9376	−	25.8726i	0.509663	−	0.882763i	−0.490274	−	0.871568i	$-0.663103\pi$
$859$	14.9376	−	25.8726i	0.509663	−	0.882763i	0.999937	−	0.0111943i	$-0.00356334\pi$
$860$	−12.8603	+	21.3347i	−0.438534	+	0.727509i
$861$	4.78666	−	4.52554i	0.163129	−	0.154230i
$862$	17.2157	−	17.2157i	0.586369	−	0.586369i
$863$	−31.2103	+	8.36277i	−1.06241	+	0.284672i	−0.747371	−	0.664407i	$-0.768684\pi$
$863$	−31.2103	+	8.36277i	−1.06241	+	0.284672i	−0.315039	+	0.949079i	$0.602018\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−23.3477	−	0.440588i	−0.793845	−	0.0149804i
$866$	−22.1438	−	12.7847i	−0.752477	−	0.434443i
$867$	12.0205	+	12.0205i	0.408237	+	0.408237i
$868$	−18.4593	+	9.97833i	−0.626549	+	0.338687i
$869$			1.87739i			0.0636861i
$870$	3.47230	−	12.0450i	0.117722	−	0.408363i
$871$	−34.3232	+	19.8165i	−1.16300	+	0.671456i
$872$	0.557643	+	0.149420i	0.0188842	+	0.00506000i
$873$	0.0971800	+	0.362681i	0.00328905	+	0.0122749i
$874$	14.2070			0.480561
$875$	29.1174	−	5.21311i	0.984348	−	0.176235i
$876$	−3.74538			−0.126545
$877$	1.05466	+	3.93603i	0.0356132	+	0.132910i	0.981444	−	0.191751i	$-0.0614165\pi$
$877$	1.05466	+	3.93603i	0.0356132	+	0.132910i	−0.945830	+	0.324661i	$0.894750\pi$
$878$	−15.6675	−	4.19811i	−0.528754	−	0.141679i
$879$	−21.3159	+	12.3068i	−0.718968	+	0.415096i
$880$	−0.722076	+	2.50479i	−0.0243412	+	0.0844366i
$881$		−	19.0783i		−	0.642764i	−0.946950	−	0.321382i	$-0.895853\pi$
$881$		−	19.0783i		−	0.642764i	0.946950	−	0.321382i	$-0.104147\pi$
$882$	6.85238	−	1.42999i	0.230732	−	0.0481504i
$883$	6.02976	+	6.02976i	0.202918	+	0.202918i	0.801249	−	0.598331i	$-0.204169\pi$
$883$	6.02976	+	6.02976i	0.202918	+	0.202918i	−0.598331	+	0.801249i	$0.704169\pi$
$884$	−0.0510900	−	0.0294968i	−0.00171834	−	0.000992086i
$885$	23.9048	+	0.451102i	0.803552	+	0.0151636i
$886$	10.8929	+	18.8671i	0.365956	+	0.633854i
$887$	−42.0695	+	11.2725i	−1.41256	+	0.378494i	−0.882837	−	0.469679i	$-0.844370\pi$
$887$	−42.0695	+	11.2725i	−1.41256	+	0.378494i	−0.529720	+	0.848173i	$0.677703\pi$
$888$	−7.51026	+	7.51026i	−0.252028	+	0.252028i
$889$	4.95424	−	1.17970i	0.166160	−	0.0395660i
$890$	−4.16162	+	6.90395i	−0.139498	+	0.231421i
$891$	−0.582897	+	1.00961i	−0.0195278	+	0.0338231i
$892$	1.07791	−	4.02281i	0.0360911	−	0.134694i
$893$	−2.09296	+	7.81102i	−0.0700381	+	0.261386i
$894$	−0.110402	+	0.191221i	−0.00369239	+	0.00639540i
$895$	−0.810606	−	3.27088i	−0.0270956	−	0.109333i
$896$	2.53540	+	0.756134i	0.0847018	+	0.0252607i
$897$	−13.8214	+	13.8214i	−0.461483	+	0.461483i
$898$	−9.81847	+	2.63085i	−0.327647	+	0.0877926i
$899$	−22.2310	−	38.5051i	−0.741444	−	1.28422i
$900$	4.23272	+	2.66159i	0.141091	+	0.0887196i
$901$	−0.0549337	−	0.0317160i	−0.00183011	−	0.00105661i
$902$	−2.05242	−	2.05242i	−0.0683381	−	0.0683381i
$903$	0.826173	−	29.4636i	0.0274933	−	0.980486i
$904$			18.7650i			0.624115i
$905$	−45.8628	−	13.2212i	−1.52453	−	0.439488i
$906$	5.51559	−	3.18442i	0.183243	−	0.105795i
$907$	55.1066	+	14.7658i	1.82979	+	0.490290i	0.997907	−	0.0646668i	$-0.0205985\pi$
$907$	55.1066	+	14.7658i	1.82979	+	0.490290i	0.831879	+	0.554957i	$0.187265\pi$
$908$	−4.77234	−	17.8106i	−0.158376	−	0.591066i
$909$	13.9159			0.461562
$910$	15.7354	−	3.43452i	0.521622	−	0.113853i
$911$	−32.4993			−1.07675			−0.538375	−	0.842705i	$-0.680962\pi$
$911$	−32.4993			−1.07675			−0.538375	+	0.842705i	$0.680962\pi$
$912$	−0.512132	−	1.91130i	−0.0169584	−	0.0632896i
$913$	15.5240	+	4.15964i	0.513769	+	0.137664i
$914$	−24.7030	+	14.2623i	−0.817103	+	0.471755i
$915$	7.13706	−	3.94294i	0.235944	−	0.130350i
$916$			5.91011i			0.195276i
$917$	−21.5767	−	39.9156i	−0.712525	−	1.31813i
$918$	0.0153229	+	0.0153229i	0.000505732	+	0.000505732i
$919$	1.92544	+	1.11165i	0.0635143	+	0.0366700i	0.531421	−	0.847108i	$-0.321658\pi$
$919$	1.92544	+	1.11165i	0.0635143	+	0.0366700i	−0.467907	+	0.883778i	$0.654992\pi$
$920$	11.5646	−	11.1362i	0.381273	−	0.367150i
$921$	0.400469	+	0.693633i	0.0131959	+	0.0228560i
$922$	19.4125	−	5.20155i	0.639315	−	0.171304i
$923$	14.4732	−	14.4732i	0.476391	−	0.476391i
$924$	−0.714480	−	3.00051i	−0.0235047	−	0.0987095i
$925$	15.6702	−	50.7409i	0.515234	−	1.66835i
$926$	−5.19343	+	8.99529i	−0.170667	+	0.295604i
$927$	3.10171	−	11.5757i	0.101874	−	0.380197i
$928$	−1.45095	+	5.41502i	−0.0476298	+	0.177757i
$929$	0.358305	−	0.620603i	0.0117556	−	0.0203613i	−0.860088	−	0.510146i	$-0.829591\pi$
$929$	0.358305	−	0.620603i	0.0117556	−	0.0203613i	0.871843	+	0.489785i	$0.162925\pi$
$930$	17.2137	−	4.26598i	0.564458	−	0.139887i
$931$	13.8293	+	0.776173i	0.453238	+	0.0254380i
$932$	5.11615	−	5.11615i	0.167585	−	0.167585i
$933$	12.9407	−	3.46746i	0.423661	−	0.113520i
$934$	11.8022	+	20.4420i	0.386179	+	0.668882i
$935$	0.00106580	−	0.0564789i	3.48554e−5	−	0.00184706i
$936$	2.35765	+	1.36119i	0.0770622	+	0.0444919i
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	0.490435	−	0.871478i	$-0.336838\pi$
$937$	−11.6639	−	11.6639i	−0.381042	−	0.381042i	−0.871478	+	0.490435i	$0.836838\pi$
$938$	−20.1861	+	32.8041i	−0.659100	+	1.07109i
$939$			28.7580i			0.938481i
$940$	4.41900	+	7.99876i	0.144132	+	0.260891i
$941$	26.7812	−	15.4621i	0.873041	−	0.504051i	0.00468360	−	0.999989i	$-0.498509\pi$
$941$	26.7812	−	15.4621i	0.873041	−	0.504051i	0.868358	+	0.495938i	$0.165176\pi$
$942$	13.9830	+	3.74673i	0.455591	+	0.122075i
$943$	4.62672	+	17.2672i	0.150667	+	0.562296i
$944$	−10.6925			−0.348010
$945$	−5.90957	−	0.277372i	−0.192238	−	0.00902292i
$946$	−12.9876			−0.422263
$947$	−4.22786	−	15.7786i	−0.137387	−	0.512735i	−0.999977	−	0.00683099i	$-0.997826\pi$
$947$	−4.22786	−	15.7786i	−0.137387	−	0.512735i	0.862590	−	0.505904i	$-0.168841\pi$
$948$	−1.55552	−	0.416801i	−0.0505210	−	0.0135371i
$949$	8.83030	−	5.09817i	0.286644	−	0.165494i
$950$	6.72693	+	7.25481i	0.218251	+	0.235377i
$951$		−	33.7349i		−	1.09393i
$952$	−0.0573106	−	0.00160702i	−0.00185745	−	5.20838e-5i
$953$	−8.22927	−	8.22927i	−0.266572	−	0.266572i	0.561145	−	0.827717i	$-0.310361\pi$
$953$	−8.22927	−	8.22927i	−0.266572	−	0.266572i	−0.827717	+	0.561145i	$0.810361\pi$
$954$	2.53502	+	1.46360i	0.0820744	+	0.0473857i
$955$	−10.0054	−	10.3903i	−0.323768	−	0.336223i
$956$	−2.10086	−	3.63880i	−0.0679467	−	0.117687i
$957$	6.31281	−	1.69151i	0.204064	−	0.0546788i
$958$	17.5210	−	17.5210i	0.566079	−	0.566079i
$959$	−18.6051	−	19.6786i	−0.600789	−	0.635454i
$960$	−1.91505	−	1.15437i	−0.0618081	−	0.0372572i
$961$	15.9509	−	27.6278i	0.514545	−	0.891219i
$962$	7.48367	−	27.9294i	0.241283	−	0.900481i
$963$	−1.78730	+	6.67031i	−0.0575951	+	0.214948i
$964$	10.9679	−	18.9970i	0.353254	−	0.611853i
$965$	−9.84065	−	5.93183i	−0.316782	−	0.190952i
$966$	−5.42896	+	18.2039i	−0.174674	+	0.585701i
$967$	1.15164	−	1.15164i	0.0370342	−	0.0370342i	−0.688347	−	0.725381i	$-0.741663\pi$
$967$	1.15164	−	1.15164i	0.0370342	−	0.0370342i	0.725381	+	0.688347i	$0.241663\pi$
$968$	9.31242	−	2.49525i	0.299312	−	0.0802005i
$969$	0.0214394	+	0.0371341i	0.000688733	+	0.00119292i
$970$	0.582371	+	0.604773i	0.0186988	+	0.0194181i
$971$	12.4747	+	7.20230i	0.400334	+	0.231133i	0.686628	−	0.727009i	$-0.259090\pi$
$971$	12.4747	+	7.20230i	0.400334	+	0.231133i	−0.286294	+	0.958142i	$0.592424\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−12.7339	−	7.83582i	−0.408229	−	0.251205i
$974$			23.7668i			0.761536i
$975$	−13.6022	−	0.513550i	−0.435619	−	0.0164468i
$976$	−3.15795	+	1.82324i	−0.101084	+	0.0583606i
$977$	35.9426	+	9.63078i	1.14990	+	0.308116i	0.782927	−	0.622114i	$-0.213726\pi$
$977$	35.9426	+	9.63078i	1.14990	+	0.308116i	0.366977	+	0.930230i	$0.380393\pi$
$978$	5.66960	+	21.1592i	0.181294	+	0.676598i
$979$	−4.20281			−0.134322
$980$	11.8655	−	10.2083i	0.379030	−	0.326093i
$981$	0.577314			0.0184322
$982$	0.0999283	+	0.372938i	0.00318884	+	0.0119009i
$983$	27.3293	+	7.32286i	0.871669	+	0.233563i	0.666809	−	0.745228i	$-0.267659\pi$
$983$	27.3293	+	7.32286i	0.871669	+	0.233563i	0.204860	+	0.978791i	$0.434326\pi$
$984$	2.15620	−	1.24488i	0.0687372	−	0.0396855i
$985$	27.2726	+	49.3656i	0.868976	+	1.57292i
$986$		−	0.121482i		−	0.00386879i
$987$	−9.20871	−	5.66660i	−0.293116	−	0.180370i
$988$	3.80907	+	3.80907i	0.121183	+	0.121183i
$989$	69.2716	+	39.9940i	2.20271	+	1.27174i
$990$	−0.0491834	+	2.60633i	−0.00156315	+	0.0828347i
$991$	−18.6725	−	32.3417i	−0.593151	−	1.02737i	−0.993805	−	0.111139i	$-0.964550\pi$
$991$	−18.6725	−	32.3417i	−0.593151	−	1.02737i	0.400654	−	0.916230i	$-0.368783\pi$
$992$	−7.66082	+	2.05271i	−0.243231	+	0.0651736i
$993$	7.73266	−	7.73266i	0.245388	−	0.245388i
$994$	5.68498	−	19.0624i	0.180317	−	0.604622i
$995$	−10.7261	+	2.65820i	−0.340040	+	0.0842706i
$996$	−6.89298	+	11.9390i	−0.218413	+	0.378302i
$997$	9.59160	−	35.7963i	0.303769	−	1.13368i	−0.630231	−	0.776408i	$-0.717040\pi$
$997$	9.59160	−	35.7963i	0.303769	−	1.13368i	0.934000	−	0.357274i	$-0.116294\pi$
$998$	2.07704	−	7.75163i	0.0657476	−	0.245373i
$999$	−5.31055	+	9.19815i	−0.168018	+	0.291017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.103.1	yes	16
3.2	odd	2		630.2.bv.b.523.4		16
5.2	odd	4		210.2.u.a.187.4	yes	16
5.3	odd	4		1050.2.bc.h.607.2		16
5.4	even	2		1050.2.bc.g.943.3		16
7.2	even	3		1470.2.m.e.1273.4		16
7.3	odd	6		210.2.u.a.73.4	✓	16
7.5	odd	6		1470.2.m.d.1273.1		16
15.2	even	4		630.2.bv.a.397.1		16
21.17	even	6		630.2.bv.a.73.1		16
35.2	odd	12		1470.2.m.d.97.1		16
35.3	even	12		1050.2.bc.g.157.3		16
35.12	even	12		1470.2.m.e.97.4		16
35.17	even	12	inner	210.2.u.b.157.1	yes	16
35.24	odd	6		1050.2.bc.h.493.2		16
105.17	odd	12		630.2.bv.b.577.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.4	✓	16	7.3	odd	6
210.2.u.a.187.4	yes	16	5.2	odd	4
210.2.u.b.103.1	yes	16	1.1	even	1	trivial
210.2.u.b.157.1	yes	16	35.17	even	12	inner
630.2.bv.a.73.1		16	21.17	even	6
630.2.bv.a.397.1		16	15.2	even	4
630.2.bv.b.523.4		16	3.2	odd	2
630.2.bv.b.577.4		16	105.17	odd	12
1050.2.bc.g.157.3		16	35.3	even	12
1050.2.bc.g.943.3		16	5.4	even	2
1050.2.bc.h.493.2		16	35.24	odd	6
1050.2.bc.h.607.2		16	5.3	odd	4
1470.2.m.d.97.1		16	35.2	odd	12
1470.2.m.d.1273.1		16	7.5	odd	6
1470.2.m.e.97.4		16	35.12	even	12
1470.2.m.e.1273.4		16	7.2	even	3

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.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.619385 + 2.14857i) q^{5} -1.00000i q^{6} +(2.25331 + 1.38658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.23567 + 0.0421887i) q^{10} +(0.582897 + 1.00961i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(1.92501 - 1.92501i) q^{13} +(0.756134 - 2.53540i) q^{14} +(-1.15437 + 1.91505i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.00560858 + 0.0209315i) q^{17} +(0.258819 - 0.965926i) q^{18} +(0.989363 - 1.71363i) q^{19} +(-0.537883 - 2.17041i) q^{20} +(1.81766 + 1.92253i) q^{21} +(0.824341 - 0.824341i) q^{22} +(-6.93525 + 1.85829i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.23272 - 2.66159i) q^{25} +(-2.35765 - 1.36119i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.64471 - 0.0741591i) q^{28} -5.60604i q^{29} +(2.14857 + 0.619385i) q^{30} +(6.86850 - 3.96553i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.301730 + 1.12607i) q^{33} +0.0216699 q^{34} +(-4.37483 + 3.98257i) q^{35} -1.00000 q^{36} +(2.74894 + 10.2592i) q^{37} +(-1.91130 - 0.512132i) q^{38} +(2.35765 - 1.36119i) q^{39} +(-1.95724 + 1.08130i) q^{40} -2.48977i q^{41} +(1.38658 - 2.25331i) q^{42} +(-7.87756 - 7.87756i) q^{43} +(-1.00961 - 0.582897i) q^{44} +(-1.61069 + 1.55103i) q^{45} +(3.58995 + 6.21797i) q^{46} +(-3.94750 + 1.05773i) q^{47} +(0.707107 - 0.707107i) q^{48} +(3.15479 + 6.24878i) q^{49} +(-1.47539 + 4.77737i) q^{50} +(-0.0108349 + 0.0187667i) q^{51} +(-0.704604 + 2.62962i) q^{52} +(-0.757613 + 2.82745i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.53025 + 0.627061i) q^{55} +(0.612870 + 2.57379i) q^{56} +(1.39917 - 1.39917i) q^{57} +(-5.41502 + 1.45095i) q^{58} +(-5.34623 - 9.25995i) q^{59} +(0.0421887 - 2.23567i) q^{60} +(-3.15795 - 1.82324i) q^{61} +(-5.60811 - 5.60811i) q^{62} +(1.25813 + 2.32747i) q^{63} +1.00000i q^{64} +(2.94371 + 5.32835i) q^{65} +(1.00961 - 0.582897i) q^{66} +(-14.0621 - 3.76794i) q^{67} +(-0.00560858 - 0.0209315i) q^{68} -7.17989 q^{69} +(4.97916 + 3.19500i) q^{70} +7.51848 q^{71} +(0.258819 + 0.965926i) q^{72} +(3.61776 + 0.969376i) q^{73} +(9.19815 - 5.31055i) q^{74} +(-3.39963 - 3.66641i) q^{75} +1.97873i q^{76} +(-0.0864543 + 3.08319i) q^{77} +(-1.92501 - 1.92501i) q^{78} +(1.39464 + 0.805197i) q^{79} +(1.55103 + 1.61069i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.40493 + 0.644400i) q^{82} +(9.74815 - 9.74815i) q^{83} +(-2.53540 - 0.756134i) q^{84} +(-0.0414990 - 0.0250151i) q^{85} +(-5.57028 + 9.64800i) q^{86} +(1.45095 - 5.41502i) q^{87} +(-0.301730 + 1.12607i) q^{88} +(-1.80255 + 3.12211i) q^{89} +(1.91505 + 1.15437i) q^{90} +(7.00683 - 1.66846i) q^{91} +(5.07695 - 5.07695i) q^{92} +(7.66082 - 2.05271i) q^{93} +(2.04338 + 3.53923i) q^{94} +(3.06906 + 3.18711i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(0.265501 + 0.265501i) q^{97} +(5.21934 - 4.66460i) q^{98} +1.16579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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