LMFDB - Embedded newform 210.2.u.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			157.1
Root			$0.792206 + 1.03242i$ of defining polynomial
Character	$\chi$	$=$	210.157
Dual form			210.2.u.b.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619385 - 2.14857i) q^{5} +1.00000i q^{6} +(2.25331 - 1.38658i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q + 12 * q^5 - 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.258819	+	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	−0.764670	−	0.644422i	$-0.777098\pi$
$11$	0.582897	−	1.00961i	0.175750	−	0.304408i	0.940421	+	0.340013i	$0.110432\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	1.92501	+	1.92501i	0.533903	+	0.533903i	0.921731	−	0.387829i	$-0.126775\pi$
$13$	1.92501	+	1.92501i	0.533903	+	0.533903i	−0.387829	+	0.921731i	$0.626775\pi$
$14$	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	0.965242	−	0.261356i	$-0.0841698\pi$
$17$	−0.00560858	−	0.0209315i	−0.00136028	−	0.00507664i	−0.966603	+	0.256280i	$0.917503\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.989363	+	1.71363i	0.226976	+	0.393133i	0.956910	−	0.290384i	$-0.0937829\pi$
$19$	0.989363	+	1.71363i	0.226976	+	0.393133i	−0.729935	+	0.683517i	$0.760450\pi$
$20$	−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	−0.551434	−	0.834219i	$-0.685919\pi$
$23$	−6.93525	−	1.85829i	−1.44610	−	0.387481i	−0.894665	+	0.446738i	$0.852586\pi$
$24$	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	$0.174257\pi$
$29$			5.60604i			1.04102i	−0.853857	+	0.520508i	$0.825743\pi$
$30$	2.14857	−	0.619385i	0.392274	−	0.113084i
$31$	6.86850	+	3.96553i	1.23362	+	0.712231i	0.967783	−	0.251787i	$-0.0810183\pi$
$31$	6.86850	+	3.96553i	1.23362	+	0.712231i	0.265837	+	0.964018i	$0.414352\pi$
$32$	−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	−0.245054	−	0.969509i	$-0.578806\pi$
$37$	2.74894	−	10.2592i	0.451924	−	1.68660i	0.696978	−	0.717093i	$-0.254528\pi$
$38$	−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	$0.0622819\pi$
$41$			2.48977i			0.388837i	−0.980919	+	0.194418i	$0.937718\pi$
$42$	1.38658	+	2.25331i	0.213954	+	0.347693i
$43$	−7.87756	+	7.87756i	−1.20132	+	1.20132i	−0.227550	+	0.973766i	$0.573072\pi$
$43$	−7.87756	+	7.87756i	−1.20132	+	1.20132i	−0.973766	+	0.227550i	$0.926928\pi$
$44$	−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	−0.0408457	−	0.999165i	$-0.513005\pi$
$47$	−3.94750	−	1.05773i	−0.575802	−	0.154286i	−0.534956	+	0.844880i	$0.679672\pi$
$48$	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	0.894171	−	0.447725i	$-0.147766\pi$
$53$	−0.757613	−	2.82745i	−0.104066	−	0.388380i	−0.998238	+	0.0593446i	$0.981099\pi$
$54$	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	0.273815	+	0.961782i	$0.411714\pi$
$59$	−5.34623	+	9.25995i	−0.696020	+	1.20554i	−0.969835	+	0.243760i	$0.921619\pi$
$60$	0.0421887	+	2.23567i	0.00544654	+	0.288624i
$61$	−3.15795	+	1.82324i	−0.404334	+	0.233442i	−0.688352	−	0.725376i	$-0.741666\pi$
$61$	−3.15795	+	1.82324i	−0.404334	+	0.233442i	0.284018	+	0.958819i	$0.408332\pi$
$62$	−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	−0.977355	−	0.211608i	$-0.932130\pi$
$67$	−14.0621	+	3.76794i	−1.71796	+	0.460327i	−0.740610	+	0.671935i	$0.765463\pi$
$68$	−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	−0.0408122	−	0.999167i	$-0.512995\pi$
$73$	3.61776	−	0.969376i	0.423427	−	0.113457i	0.464239	+	0.885710i	$0.346328\pi$
$74$	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	−0.419489	−	0.907760i	$-0.637791\pi$
$79$	1.39464	−	0.805197i	0.156910	−	0.0905918i	0.576399	+	0.817169i	$0.304457\pi$
$80$	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	0.997358	+	0.0726405i	$0.0231426\pi$
$83$	9.74815	+	9.74815i	1.07000	+	1.07000i	0.0726405	+	0.997358i	$0.476857\pi$
$84$	−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	0.754535	−	0.656260i	$-0.227862\pi$
$89$	−1.80255	−	3.12211i	−0.191070	−	0.330943i	−0.945605	+	0.325317i	$0.894529\pi$
$90$	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	−0.693500	−	0.720457i	$-0.743932\pi$
$97$	0.265501	−	0.265501i	0.0269575	−	0.0269575i	0.720457	+	0.693500i	$0.243932\pi$
$98$	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	0.960371	−	0.278725i	$-0.0899119\pi$
$101$	12.0515	+	6.95796i	1.19917	+	0.692343i	0.238802	+	0.971068i	$0.423245\pi$
$102$	0.0209315	−	0.00560858i	0.00207253	−	0.000555332i
$103$	−3.10171	+	11.5757i	−0.305621	+	1.14059i	0.626789	+	0.779189i	$0.284369\pi$
$103$	−3.10171	+	11.5757i	−0.305621	+	1.14059i	−0.932410	+	0.361403i	$0.882298\pi$
$104$	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	−0.824133	−	0.566396i	$-0.808337\pi$
$107$	1.78730	−	6.67031i	0.172785	−	0.644843i	0.996918	−	0.0784469i	$-0.0249961\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	0.499969	+	0.288657i	0.0478883	+	0.0276483i	0.523753	−	0.851870i	$-0.324531\pi$
$109$	0.499969	+	0.288657i	0.0478883	+	0.0276483i	−0.475865	+	0.879519i	$0.657865\pi$
$110$	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	0.291728	−	0.956501i	$-0.405770\pi$
$113$	13.2689	−	13.2689i	1.24823	−	1.24823i	0.956501	−	0.291728i	$-0.0942301\pi$
$114$	−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	0.764912	−	0.644134i	$-0.222782\pi$
$127$	1.36110	+	1.36110i	0.120778	+	0.120778i	−0.644134	+	0.764912i	$0.722782\pi$
$128$	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	−0.979996	−	0.199019i	$-0.936225\pi$
$131$	−14.8522	+	8.57489i	−1.29764	+	0.749192i	−0.317643	+	0.948210i	$0.602891\pi$
$132$	−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	−0.655117	−	0.755527i	$-0.727381\pi$
$137$	−9.88699	+	2.64921i	−0.844702	+	0.226337i	−0.189585	+	0.981864i	$0.560714\pi$
$138$	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	−0.507812	−	0.861468i	$-0.669546\pi$
$149$	−0.191221	+	0.110402i	−0.0156655	+	0.00904446i	0.492147	+	0.870512i	$0.336212\pi$
$150$	−2.66159	−	4.23272i	−0.217318	−	0.345600i
$151$	3.18442	−	5.51559i	0.259145	−	0.448852i	−0.706868	−	0.707345i	$-0.749893\pi$
$151$	3.18442	−	5.51559i	0.259145	−	0.448852i	0.966013	+	0.258493i	$0.0832260\pi$
$152$	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	−0.937970	−	0.346715i	$-0.887297\pi$
$157$	−3.74673	−	13.9830i	−0.299022	−	1.11596i	0.638949	−	0.769249i	$-0.279370\pi$
$158$	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	−0.695671	−	0.718360i	$-0.744893\pi$
$163$	−21.1592	−	5.66960i	−1.65732	−	0.444078i	−0.961649	+	0.274283i	$0.911560\pi$
$164$	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	−0.112174	−	0.993689i	$-0.535781\pi$
$167$	11.3917	−	11.3917i	0.881515	−	0.881515i	0.993689	+	0.112174i	$0.0357814\pi$
$168$	−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	−0.783798	−	0.621016i	$-0.786720\pi$
$173$	2.70291	−	10.0874i	0.205499	−	0.766932i	0.989297	−	0.145916i	$-0.0466130\pi$
$174$	−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	0.450431	−	0.892811i	$-0.351270\pi$
$179$	−1.30513	−	0.753516i	−0.0975498	−	0.0563204i	−0.547981	+	0.836491i	$0.684603\pi$
$180$	0.619385	+	2.14857i	0.0461662	+	0.160145i
$181$		−	21.3457i		−	1.58662i	−0.608821	−	0.793308i	$-0.708357\pi$
$181$		−	21.3457i		−	1.58662i	0.608821	−	0.793308i	$-0.291643\pi$
$182$	−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	0.725418	−	0.688309i	$-0.241647\pi$
$191$	−3.22543	−	5.58661i	−0.233384	−	0.404233i	−0.958802	+	0.284076i	$0.908313\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−1.32996	−	4.96349i	−0.0957328	−	0.357280i	0.901397	−	0.432994i	$-0.142543\pi$
$193$	−1.32996	−	4.96349i	−0.0957328	−	0.357280i	−0.997130	+	0.0757145i	$0.975876\pi$
$194$	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	0.945738	+	0.324931i	$0.105341\pi$
$197$	17.8347	+	17.8347i	1.27067	+	1.27067i	0.324931	+	0.945738i	$0.394659\pi$
$198$	1.12607	+	0.301730i	0.0800264	+	0.0214430i
$199$	2.47098	−	4.27987i	0.175163	−	0.303392i	−0.765054	−	0.643966i	$-0.777288\pi$
$199$	2.47098	−	4.27987i	0.175163	−	0.303392i	0.940218	+	0.340574i	$0.110621\pi$
$200$	−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	0.601596	−	0.798801i	$-0.294532\pi$
$223$	−2.94490	−	2.94490i	−0.197205	−	0.197205i	−0.798801	+	0.601596i	$0.794532\pi$
$224$	−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	−0.922348	−	0.386360i	$-0.873732\pi$
$227$	−4.77234	−	17.8106i	−0.316751	−	1.18213i	0.605597	−	0.795772i	$-0.292935\pi$
$228$	−0.512132	−	1.91130i	−0.0339168	−	0.126579i
$229$	2.95505	+	5.11830i	0.195276	+	0.338227i	0.946991	−	0.321261i	$-0.104107\pi$
$229$	2.95505	+	5.11830i	0.195276	+	0.338227i	−0.751715	+	0.659488i	$0.770773\pi$
$230$	−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	0.0225196	−	0.999746i	$-0.492831\pi$
$233$	−6.98879	−	1.87264i	−0.457851	−	0.122681i	−0.480371	+	0.877066i	$0.659498\pi$
$234$	−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	$-0.956610\pi$
$239$		−	4.20172i		−	0.271787i	0.990723	−	0.135893i	$-0.0433904\pi$
$240$	1.08130	−	1.95724i	0.0697975	−	0.126339i
$241$	−18.9970	−	10.9679i	−1.22371	−	0.706507i	−0.258000	−	0.966145i	$-0.583064\pi$
$241$	−18.9970	−	10.9679i	−1.22371	−	0.706507i	−0.965706	+	0.259638i	$0.916397\pi$
$242$	−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	$0.158448\pi$
$251$			15.1293i			0.954952i	−0.878645	+	0.477476i	$0.841552\pi$
$252$	−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	0.873541	−	0.486751i	$-0.161818\pi$
$257$	22.2301	+	5.95653i	1.38667	+	0.371558i	0.513133	+	0.858309i	$0.328485\pi$
$258$	−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	−0.918163	−	0.396203i	$-0.870328\pi$
$263$	−5.20756	−	19.4349i	−0.321112	−	1.19841i	0.597051	−	0.802203i	$-0.296339\pi$
$264$	−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	−0.972021	−	0.234892i	$-0.924526\pi$
$269$	−4.63479	+	8.02770i	−0.282588	+	0.489457i	0.689433	+	0.724349i	$0.257860\pi$
$270$	1.55103	−	1.61069i	0.0943924	−	0.0980234i
$271$	22.7157	−	13.1149i	1.37988	−	0.796673i	0.387734	−	0.921771i	$-0.373258\pi$
$271$	22.7157	−	13.1149i	1.37988	−	0.796673i	0.992144	+	0.125098i	$0.0399244\pi$
$272$	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	−0.623193	−	0.782068i	$-0.714165\pi$
$277$	−12.8463	+	3.44216i	−0.771860	+	0.206819i	−0.148667	+	0.988887i	$0.547498\pi$
$278$	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	0.362313	−	0.932057i	$-0.381987\pi$
$283$	19.2133	−	5.14819i	1.14211	−	0.306028i	0.779800	+	0.626028i	$0.215321\pi$
$284$	−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	−0.999857	−	0.0169176i	$-0.994615\pi$
$293$	−17.4044	−	17.4044i	−1.01677	−	1.01677i	−0.0169176	−	0.999857i	$-0.505385\pi$
$294$	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	−0.690760	−	0.723084i	$-0.742724\pi$
$307$	0.566349	−	0.566349i	0.0323232	−	0.0323232i	0.723084	+	0.690760i	$0.242724\pi$
$308$	−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	0.791480	−	0.611196i	$-0.209311\pi$
$311$	11.6023	+	6.69862i	0.657909	+	0.379844i	−0.133571	+	0.991039i	$0.542644\pi$
$312$	2.62962	−	0.704604i	0.148873	−	0.0398903i
$313$	7.44312	−	27.7781i	0.420710	−	1.57011i	−0.352407	−	0.935847i	$-0.614637\pi$
$313$	7.44312	−	27.7781i	0.420710	−	1.57011i	0.773117	−	0.634263i	$-0.218697\pi$
$314$	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	0.0640314	+	0.997948i	$0.479604\pi$
$317$	−8.73124	+	32.5854i	−0.490395	+	1.83018i	−0.554427	+	0.832232i	$0.687062\pi$
$318$	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	0.976258	−	0.216611i	$-0.0695004\pi$
$331$	5.46781	+	9.47053i	0.300538	+	0.520547i	−0.675720	+	0.737159i	$0.736167\pi$
$332$	−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	0.368866	−	0.929483i	$-0.379746\pi$
$337$	−10.2916	−	10.2916i	−0.560617	−	0.560617i	−0.929483	+	0.368866i	$0.879746\pi$
$338$	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	−0.191978	−	0.981399i	$-0.561490\pi$
$347$	2.46753	−	0.661173i	0.132464	−	0.0354936i	0.324442	+	0.945906i	$0.394824\pi$
$348$	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	−0.641678	−	0.766974i	$-0.721761\pi$
$353$	−15.2918	+	4.09742i	−0.813900	+	0.218084i	−0.172222	+	0.985058i	$0.555095\pi$
$354$	−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	−0.661636	−	0.749825i	$-0.730137\pi$
$359$	−6.50055	+	3.75309i	−0.343086	+	0.198081i	0.318550	+	0.947906i	$0.396804\pi$
$360$	−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	0.987453	−	0.157912i	$-0.0504761\pi$
$367$	1.02181	+	3.81343i	0.0533379	+	0.199060i	−0.934115	+	0.356971i	$0.883809\pi$
$368$	−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	0.121393	−	0.992605i	$-0.461264\pi$
$373$	−5.21031	−	1.39610i	−0.269780	−	0.0722872i	−0.391173	+	0.920317i	$0.627931\pi$
$374$	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	$-0.979761\pi$
$379$		−	2.47403i		−	0.127082i	0.997979	−	0.0635411i	$-0.0202394\pi$
$380$	−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	0.601524	+	0.798855i	$0.294561\pi$
$383$	−6.23980	+	23.2872i	−0.318839	+	1.18992i	−0.920362	+	0.391067i	$0.872106\pi$
$384$	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	0.351649	−	0.936132i	$-0.385621\pi$
$389$	−5.58638	−	3.22530i	−0.283241	−	0.163529i	−0.634890	+	0.772603i	$0.718954\pi$
$390$	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	0.682172	−	0.731192i	$-0.261036\pi$
$397$	18.0789	+	4.84423i	0.907354	+	0.243125i	0.225182	+	0.974317i	$0.427702\pi$
$398$	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	0.999327	−	0.0366779i	$-0.0116776\pi$
$401$	9.36968	+	16.2288i	0.467900	+	0.810426i	−0.531428	+	0.847104i	$0.678344\pi$
$402$	−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	0.418398	+	0.908264i	$0.362592\pi$
$409$	−11.6768	+	20.2248i	−0.577381	+	1.00005i	−0.995778	+	0.0917890i	$0.970741\pi$
$410$	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	−0.408334	−	0.912832i	$-0.633890\pi$
$431$	12.1733	−	21.0848i	0.586369	−	1.01562i	0.994703	−	0.102788i	$-0.0327764\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	18.0803	+	18.0803i	0.868885	+	0.868885i	0.992349	−	0.123464i	$-0.0394002\pi$
$433$	18.0803	+	18.0803i	0.868885	+	0.868885i	−0.123464	+	0.992349i	$0.539400\pi$
$434$	−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	0.992055	−	0.125808i	$-0.0401522\pi$
$439$	8.11012	+	14.0471i	0.387075	+	0.670433i	−0.604980	+	0.796241i	$0.706819\pi$
$440$	−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	−0.278444	−	0.960452i	$-0.589819\pi$
$443$	−21.0436	−	5.63860i	−0.999810	−	0.267898i	−0.721366	+	0.692554i	$0.756485\pi$
$444$	−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	$0.0770996\pi$
$449$			10.1648i			0.479708i	−0.970809	+	0.239854i	$0.922900\pi$
$450$	−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	0.546856	+	0.837226i	$0.315824\pi$
$457$	−7.38270	+	27.5526i	−0.345348	+	1.28886i	−0.892205	+	0.451631i	$0.850842\pi$
$458$	−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	$-0.844971\pi$
$461$		−	20.0972i		−	0.936022i	0.883723	−	0.468011i	$-0.155029\pi$
$462$	3.08319	−	0.0864543i	0.143443	−	0.00402222i
$463$	−7.34462	+	7.34462i	−0.341334	+	0.341334i	−0.856869	−	0.515535i	$-0.827593\pi$
$463$	−7.34462	+	7.34462i	−0.341334	+	0.341334i	0.515535	+	0.856869i	$0.327593\pi$
$464$	−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	−0.310720	−	0.950502i	$-0.600570\pi$
$467$	−22.8001	−	6.10926i	−1.05506	−	0.282703i	−0.744342	+	0.667799i	$0.767237\pi$
$468$	−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	−0.430869	−	0.902414i	$-0.641793\pi$
$479$	12.3892	−	21.4588i	0.566079	−	0.980478i	0.996948	−	0.0780633i	$-0.0248736\pi$
$480$	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	−0.738228	−	0.674551i	$-0.764337\pi$
$487$	−22.9569	+	6.15129i	−1.04028	+	0.278741i	−0.302049	+	0.953292i	$0.597671\pi$
$488$	−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	−0.336307	−	0.941752i	$-0.609178\pi$
$499$	6.94992	−	4.01254i	0.311121	−	0.179626i	0.647428	+	0.762127i	$0.275845\pi$
$500$	−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	0.399819	−	0.916594i	$-0.369073\pi$
$503$	−11.5901	−	11.5901i	−0.516775	−	0.516775i	−0.916594	+	0.399819i	$0.869073\pi$
$504$	−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	0.640692	−	0.767798i	$-0.278648\pi$
$509$	−7.77422	−	13.4654i	−0.344586	−	0.596841i	−0.985279	+	0.170957i	$0.945314\pi$
$510$	−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	0.908661	−	0.417535i	$-0.137106\pi$
$521$	22.8573	+	13.1967i	1.00140	+	0.578156i	0.0927347	+	0.995691i	$0.470439\pi$
$522$	−5.41502	+	1.45095i	−0.237009	+	0.0635064i
$523$	−10.2125	+	38.1134i	−0.446559	+	1.66658i	0.265227	+	0.964186i	$0.414553\pi$
$523$	−10.2125	+	38.1134i	−0.446559	+	1.66658i	−0.711786	+	0.702396i	$0.752114\pi$
$524$	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	0.765215	−	0.643775i	$-0.222633\pi$
$541$	−4.06849	−	7.04683i	−0.174918	−	0.302967i	−0.940133	+	0.340808i	$0.889299\pi$
$542$	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	0.922155	−	0.386820i	$-0.126427\pi$
$547$	12.5204	+	12.5204i	0.535335	+	0.535335i	−0.386820	+	0.922155i	$0.626427\pi$
$548$	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	0.0882732	−	0.996096i	$-0.471865\pi$
$557$	15.6419	−	4.19123i	0.662768	−	0.177588i	0.574495	+	0.818508i	$0.305198\pi$
$558$	−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	−0.0761920	−	0.997093i	$-0.524276\pi$
$563$	8.45582	−	2.26573i	0.356370	−	0.0954892i	0.432562	+	0.901604i	$0.357610\pi$
$564$	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	0.508382	−	0.861132i	$-0.330244\pi$
$569$	35.9794	−	20.7727i	1.50833	−	0.870838i	0.999953	−	0.00970591i	$-0.00308954\pi$
$570$	3.18711	+	3.06906i	0.133494	+	0.128549i
$571$	−6.59259	+	11.4187i	−0.275891	+	0.477858i	−0.970360	−	0.241666i	$-0.922306\pi$
$571$	−6.59259	+	11.4187i	−0.275891	+	0.477858i	0.694468	+	0.719523i	$0.255640\pi$
$572$	−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	0.992692	+	0.120679i	$0.0385071\pi$
$577$	4.64406	+	17.3319i	0.193335	+	0.721535i	−0.799357	+	0.600857i	$0.794826\pi$
$578$	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	−0.847663	−	0.530535i	$-0.821991\pi$
$587$	−7.68342	+	7.68342i	−0.317129	+	0.317129i	0.530535	+	0.847663i	$0.321991\pi$
$588$	−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	−0.995025	−	0.0996223i	$-0.968237\pi$
$593$	−2.03328	+	7.58832i	−0.0834970	+	0.311615i	0.911528	+	0.411237i	$0.134903\pi$
$594$	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	0.857173	−	0.515029i	$-0.172219\pi$
$599$	20.5520	+	11.8657i	0.839731	+	0.484819i	−0.0174418	+	0.999848i	$0.505552\pi$
$600$	0.188640	+	4.99644i	0.00770120	+	0.203979i
$601$		−	14.4348i		−	0.588806i	−0.955681	−	0.294403i	$-0.904879\pi$
$601$		−	14.4348i		−	0.588806i	0.955681	−	0.294403i	$-0.0951208\pi$
$602$	−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	0.271881	−	0.962331i	$-0.412354\pi$
$607$	0.644795	+	0.172772i	0.0261714	+	0.00701261i	−0.245710	+	0.969343i	$0.579021\pi$
$608$	−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	−0.999165	−	0.0408659i	$-0.986988\pi$
$613$	−3.82018	−	14.2571i	−0.154296	−	0.575839i	0.844869	−	0.534973i	$-0.179678\pi$
$614$	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	0.601946	−	0.798537i	$-0.294392\pi$
$617$	−4.88322	−	4.88322i	−0.196591	−	0.196591i	−0.798537	+	0.601946i	$0.794392\pi$
$618$	−11.5757	−	3.10171i	−0.465644	−	0.124769i
$619$	13.8975	−	24.0712i	0.558589	−	0.967504i	−0.439026	−	0.898474i	$-0.644676\pi$
$619$	13.8975	−	24.0712i	0.558589	−	0.967504i	0.997615	−	0.0690295i	$-0.0219903\pi$
$620$	−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	−0.913390	−	0.407085i	$-0.866545\pi$
$641$	−2.63684	+	4.56715i	−0.104149	+	0.180391i	0.809241	+	0.587477i	$0.199879\pi$
$642$	6.67031	+	1.78730i	0.263256	+	0.0705393i
$643$	5.34948	+	5.34948i	0.210963	+	0.210963i	0.804677	−	0.593714i	$-0.202339\pi$
$643$	5.34948	+	5.34948i	0.210963	+	0.210963i	−0.593714	+	0.804677i	$0.702339\pi$
$644$	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	−0.982216	−	0.187753i	$-0.939880\pi$
$647$	−5.73506	−	21.4035i	−0.225469	−	0.841460i	0.756748	−	0.653707i	$-0.226787\pi$
$648$	−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	0.966702	−	0.255907i	$-0.0823739\pi$
$653$	42.8267	+	11.4754i	1.67594	+	0.449066i	0.709235	+	0.704972i	$0.249041\pi$
$654$	−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	$0.271188\pi$
$659$			38.6387i			1.50515i	−0.658507	+	0.752575i	$0.728812\pi$
$660$	2.28174	+	1.26057i	0.0888167	+	0.0490677i
$661$	−24.7737	−	14.3031i	−0.963587	−	0.556327i	−0.0663118	−	0.997799i	$-0.521123\pi$
$661$	−24.7737	−	14.3031i	−0.963587	−	0.556327i	−0.897275	+	0.441472i	$0.854457\pi$
$662$	−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	0.660379	−	0.750932i	$-0.270396\pi$
$673$	36.6126	−	36.6126i	1.41131	−	1.41131i	0.750932	−	0.660379i	$-0.229604\pi$
$674$	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	−0.276695	−	0.960958i	$-0.589239\pi$
$677$	−25.9359	−	6.94951i	−0.996798	−	0.267091i	−0.720104	+	0.693867i	$0.755906\pi$
$678$	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	0.955384	−	0.295365i	$-0.0954413\pi$
$683$	−0.514460	−	1.91999i	−0.0196853	−	0.0734664i	−0.975070	+	0.221899i	$0.928775\pi$
$684$	−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	−0.650102	−	0.759847i	$-0.725274\pi$
$691$	−8.33571	+	4.81262i	−0.317105	+	0.183081i	0.332996	+	0.942928i	$0.391940\pi$
$692$	−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	−0.999904	−	0.0138494i	$-0.995591\pi$
$709$	−39.6174	+	22.8731i	−1.48786	+	0.859018i	−0.487958	+	0.872867i	$0.662258\pi$
$710$	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	0.976222	−	0.216775i	$-0.0695539\pi$
$719$	8.05439	+	13.9506i	0.300378	+	0.520270i	−0.675844	+	0.737045i	$0.736221\pi$
$720$	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	−0.999964	−	0.00843633i	$-0.997315\pi$
$727$	−26.7345	+	26.7345i	−0.991528	+	0.991528i	0.00843633	+	0.999964i	$0.497315\pi$
$728$	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	−0.997337	−	0.0729311i	$-0.976765\pi$
$733$	−2.63030	+	9.81640i	−0.0971523	+	0.362577i	0.900185	+	0.435508i	$0.143431\pi$
$734$	−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	0.471903	−	0.881651i	$-0.343567\pi$
$739$	−1.51357	−	0.873858i	−0.0556775	−	0.0321454i	−0.527580	+	0.849505i	$0.676901\pi$
$740$	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	−0.624542	−	0.780992i	$-0.714714\pi$
$743$	4.26452	−	4.26452i	0.156450	−	0.156450i	0.780992	+	0.624542i	$0.214714\pi$
$744$	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	0.694935	−	0.719073i	$-0.255433\pi$
$751$	−7.54354	−	13.0658i	−0.275268	−	0.476778i	−0.970203	+	0.242295i	$0.922100\pi$
$752$	−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	0.562734	−	0.826638i	$-0.309749\pi$
$757$	−7.26095	−	7.26095i	−0.263904	−	0.263904i	−0.826638	+	0.562734i	$0.809749\pi$
$758$	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	−0.681314	−	0.731991i	$-0.738591\pi$
$761$	−10.7048	+	6.18041i	−0.388048	+	0.224040i	0.293266	+	0.956031i	$0.405258\pi$
$762$	−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	−0.280745	−	0.959783i	$-0.590581\pi$
$773$	−1.22292	+	0.327680i	−0.0439853	+	0.0117858i	0.236759	+	0.971568i	$0.423915\pi$
$774$	−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	0.999890	+	0.0148294i	$0.00472053\pi$
$787$	3.96605	+	14.8015i	0.141375	+	0.527617i	−0.858515	+	0.512788i	$0.828613\pi$
$788$	−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	0.358396	−	0.933570i	$-0.383324\pi$
$797$	36.4737	−	36.4737i	1.29197	−	1.29197i	0.933570	−	0.358396i	$-0.116676\pi$
$798$	−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	0.696126	−	0.717920i	$-0.254906\pi$
$809$	12.0158	+	6.93731i	0.422452	+	0.243903i	−0.273674	+	0.961823i	$0.588239\pi$
$810$	1.08130	−	1.95724i	0.0379930	−	0.0687705i
$811$			18.4047i			0.646275i	0.946352	+	0.323137i	$0.104738\pi$
$811$			18.4047i			0.646275i	−0.946352	+	0.323137i	$0.895262\pi$
$812$	−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	−0.996174	−	0.0873891i	$-0.972148\pi$
$821$	−16.4402	−	28.4753i	−0.573768	−	0.993796i	0.422406	−	0.906407i	$-0.361186\pi$
$822$	−2.64921	−	9.88699i	−0.0924018	−	0.344848i
$823$	−6.31918	−	23.5835i	−0.220273	−	0.822069i	−0.984244	−	0.176818i	$-0.943420\pi$
$823$	−6.31918	−	23.5835i	−0.220273	−	0.822069i	0.763971	−	0.645251i	$-0.223247\pi$
$824$	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	0.740093	−	0.672505i	$-0.234782\pi$
$827$	1.94367	+	1.94367i	0.0675881	+	0.0675881i	−0.672505	+	0.740093i	$0.734782\pi$
$828$	6.93525	+	1.85829i	0.241016	+	0.0645802i
$829$	8.99161	−	15.5739i	0.312291	−	0.540905i	−0.666567	−	0.745446i	$-0.732237\pi$
$829$	8.99161	−	15.5739i	0.312291	−	0.540905i	0.978858	+	0.204541i	$0.0655701\pi$
$830$	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	0.955362	+	0.295436i	$0.0954650\pi$
$853$	36.5310	+	36.5310i	1.25080	+	1.25080i	0.295436	+	0.955362i	$0.404535\pi$
$854$	−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	0.950485	−	0.310769i	$-0.100587\pi$
$857$	−0.820966	−	3.06389i	−0.0280437	−	0.104660i	−0.978529	+	0.206109i	$0.933920\pi$
$858$	0.821423	+	3.06559i	0.0280429	+	0.104658i
$859$	14.9376	+	25.8726i	0.509663	+	0.882763i	0.999937	+	0.0111943i	$0.00356334\pi$
$859$	14.9376	+	25.8726i	0.509663	+	0.882763i	−0.490274	+	0.871568i	$0.663103\pi$
$860$	−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	−0.315039	−	0.949079i	$-0.602018\pi$
$863$	−31.2103	−	8.36277i	−1.06241	−	0.284672i	−0.747371	+	0.664407i	$0.768684\pi$
$864$	−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	−0.945830	−	0.324661i	$-0.894750\pi$
$877$	1.05466	−	3.93603i	0.0356132	−	0.132910i	0.981444	+	0.191751i	$0.0614165\pi$
$878$	−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	$0.104147\pi$
$881$			19.0783i			0.642764i	−0.946950	+	0.321382i	$0.895853\pi$
$882$	6.85238	+	1.42999i	0.230732	+	0.0481504i
$883$	6.02976	−	6.02976i	0.202918	−	0.202918i	−0.598331	−	0.801249i	$-0.704169\pi$
$883$	6.02976	−	6.02976i	0.202918	−	0.202918i	0.801249	+	0.598331i	$0.204169\pi$
$884$	−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	−0.529720	−	0.848173i	$-0.677703\pi$
$887$	−42.0695	−	11.2725i	−1.41256	−	0.378494i	−0.882837	+	0.469679i	$0.844370\pi$
$888$	−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	0.831879	−	0.554957i	$-0.187265\pi$
$907$	55.1066	−	14.7658i	1.82979	−	0.490290i	0.997907	+	0.0646668i	$0.0205985\pi$
$908$	−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	−0.467907	−	0.883778i	$-0.654992\pi$
$919$	1.92544	−	1.11165i	0.0635143	−	0.0366700i	0.531421	+	0.847108i	$0.321658\pi$
$920$	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	0.871843	−	0.489785i	$-0.162925\pi$
$929$	0.358305	+	0.620603i	0.0117556	+	0.0203613i	−0.860088	+	0.510146i	$0.829591\pi$
$930$	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	−0.871478	−	0.490435i	$-0.836838\pi$
$937$	−11.6639	+	11.6639i	−0.381042	+	0.381042i	0.490435	+	0.871478i	$0.336838\pi$
$938$	−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	0.868358	−	0.495938i	$-0.165176\pi$
$941$	26.7812	+	15.4621i	0.873041	+	0.504051i	0.00468360	+	0.999989i	$0.498509\pi$
$942$	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	0.862590	+	0.505904i	$0.168841\pi$
$947$	−4.22786	+	15.7786i	−0.137387	+	0.512735i	−0.999977	+	0.00683099i	$0.997826\pi$
$948$	−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	−0.827717	−	0.561145i	$-0.810361\pi$
$953$	−8.22927	+	8.22927i	−0.266572	+	0.266572i	0.561145	+	0.827717i	$0.310361\pi$
$954$	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	0.725381	−	0.688347i	$-0.241663\pi$
$967$	1.15164	+	1.15164i	0.0370342	+	0.0370342i	−0.688347	+	0.725381i	$0.741663\pi$
$968$	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	−0.286294	−	0.958142i	$-0.592424\pi$
$971$	12.4747	−	7.20230i	0.400334	−	0.231133i	0.686628	+	0.727009i	$0.259090\pi$
$972$	−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	0.366977	−	0.930230i	$-0.380393\pi$
$977$	35.9426	−	9.63078i	1.14990	−	0.308116i	0.782927	+	0.622114i	$0.213726\pi$
$978$	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	0.204860	−	0.978791i	$-0.434326\pi$
$983$	27.3293	−	7.32286i	0.871669	−	0.233563i	0.666809	+	0.745228i	$0.267659\pi$
$984$	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	0.400654	+	0.916230i	$0.368783\pi$
$991$	−18.6725	+	32.3417i	−0.593151	+	1.02737i	−0.993805	+	0.111139i	$0.964550\pi$
$992$	−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	0.934000	+	0.357274i	$0.116294\pi$
$997$	9.59160	+	35.7963i	0.303769	+	1.13368i	−0.630231	+	0.776408i	$0.717040\pi$
$998$	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.157.1	yes	16
3.2	odd	2		630.2.bv.b.577.4		16
5.2	odd	4		1050.2.bc.h.493.2		16
5.3	odd	4		210.2.u.a.73.4	✓	16
5.4	even	2		1050.2.bc.g.157.3		16
7.3	odd	6		1470.2.m.d.97.1		16
7.4	even	3		1470.2.m.e.97.4		16
7.5	odd	6		210.2.u.a.187.4	yes	16
15.8	even	4		630.2.bv.a.73.1		16
21.5	even	6		630.2.bv.a.397.1		16
35.3	even	12		1470.2.m.e.1273.4		16
35.12	even	12		1050.2.bc.g.943.3		16
35.18	odd	12		1470.2.m.d.1273.1		16
35.19	odd	6		1050.2.bc.h.607.2		16
35.33	even	12	inner	210.2.u.b.103.1	yes	16
105.68	odd	12		630.2.bv.b.523.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.4	✓	16	5.3	odd	4
210.2.u.a.187.4	yes	16	7.5	odd	6
210.2.u.b.103.1	yes	16	35.33	even	12	inner
210.2.u.b.157.1	yes	16	1.1	even	1	trivial
630.2.bv.a.73.1		16	15.8	even	4
630.2.bv.a.397.1		16	21.5	even	6
630.2.bv.b.523.4		16	105.68	odd	12
630.2.bv.b.577.4		16	3.2	odd	2
1050.2.bc.g.157.3		16	5.4	even	2
1050.2.bc.g.943.3		16	35.12	even	12
1050.2.bc.h.493.2		16	5.2	odd	4
1050.2.bc.h.607.2		16	35.19	odd	6
1470.2.m.d.97.1		16	7.3	odd	6
1470.2.m.d.1273.1		16	35.18	odd	12
1470.2.m.e.97.4		16	7.4	even	3
1470.2.m.e.1273.4		16	35.3	even	12

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.619385 - 2.14857i) q^{5} +1.00000i q^{6} +(2.25331 - 1.38658i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 4 * q^7	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) \) 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

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