LMFDB - Embedded newform 208.2.bj.a.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(29,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("208.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.bj (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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.1
Character	$\chi$	$=$	208.165
Dual form			208.2.bj.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41044 - 0.103276i) q^{2} +(-0.623697 - 2.32767i) q^{3} +(1.97867 + 0.291328i) q^{4} +(-2.33843 - 2.33843i) q^{5} +(0.639294 + 3.34744i) q^{6} +(-3.16277 + 1.82602i) q^{7} +(-2.76070 - 0.615248i) q^{8} +(-2.43097 + 1.40352i) q^{9} +O(q^{10})$	\(q+(-1.41044 - 0.103276i) q^{2} +(-0.623697 - 2.32767i) q^{3} +(1.97867 + 0.291328i) q^{4} +(-2.33843 - 2.33843i) q^{5} +(0.639294 + 3.34744i) q^{6} +(-3.16277 + 1.82602i) q^{7} +(-2.76070 - 0.615248i) q^{8} +(-2.43097 + 1.40352i) q^{9} +(3.05670 + 3.53971i) q^{10} +(3.60420 - 0.965741i) q^{11} +(-0.555974 - 4.78739i) q^{12} +(0.897619 + 3.49203i) q^{13} +(4.64947 - 2.24886i) q^{14} +(-3.98462 + 6.90156i) q^{15} +(3.83026 + 1.15288i) q^{16} +(1.39318 + 2.41306i) q^{17} +(3.57368 - 1.72852i) q^{18} +(-6.63086 - 1.77673i) q^{19} +(-3.94572 - 5.30822i) q^{20} +(6.22299 + 6.22299i) q^{21} +(-5.18323 + 0.989892i) q^{22} +(-5.70507 - 3.29383i) q^{23} +(0.289746 + 6.80973i) q^{24} +5.93649i q^{25} +(-0.905393 - 5.01799i) q^{26} +(-0.328797 - 0.328797i) q^{27} +(-6.79004 + 2.69169i) q^{28} +(-0.314295 - 1.17296i) q^{29} +(6.33282 - 9.32270i) q^{30} -4.09157 q^{31} +(-5.28327 - 2.02164i) q^{32} +(-4.49585 - 7.78705i) q^{33} +(-1.71579 - 3.54736i) q^{34} +(11.6659 + 3.12588i) q^{35} +(-5.21897 + 2.06889i) q^{36} +(3.69016 - 0.988774i) q^{37} +(9.16893 + 3.19078i) q^{38} +(7.56845 - 4.26733i) q^{39} +(5.01699 + 7.89441i) q^{40} +(-0.123461 - 0.0712802i) q^{41} +(-8.13445 - 9.41982i) q^{42} +(0.772184 - 2.88183i) q^{43} +(7.41286 - 0.860879i) q^{44} +(8.96668 + 2.40261i) q^{45} +(7.70648 + 5.23493i) q^{46} -7.34533 q^{47} +(0.294611 - 9.63462i) q^{48} +(3.16873 - 5.48840i) q^{49} +(0.613096 - 8.37305i) q^{50} +(4.74789 - 4.74789i) q^{51} +(0.758763 + 7.17107i) q^{52} +(-6.32639 - 6.32639i) q^{53} +(0.429791 + 0.497704i) q^{54} +(-10.6865 - 6.16984i) q^{55} +(9.85491 - 3.09522i) q^{56} +16.5426i q^{57} +(0.322154 + 1.68685i) q^{58} +(-0.387585 + 1.44649i) q^{59} +(-9.89485 + 12.4951i) q^{60} +(-2.41180 - 0.646240i) q^{61} +(5.77090 + 0.422560i) q^{62} +(5.12572 - 8.87801i) q^{63} +(7.24294 + 3.39703i) q^{64} +(6.06685 - 10.2649i) q^{65} +(5.53691 + 11.4475i) q^{66} +(-0.625756 - 2.33535i) q^{67} +(2.05365 + 5.18052i) q^{68} +(-4.10870 + 15.3339i) q^{69} +(-16.1312 - 5.61366i) q^{70} +(7.89833 - 4.56010i) q^{71} +(7.57469 - 2.37905i) q^{72} -10.8639i q^{73} +(-5.30685 + 1.01350i) q^{74} +(13.8182 - 3.70257i) q^{75} +(-12.6027 - 5.44732i) q^{76} +(-9.63576 + 9.63576i) q^{77} +(-11.1155 + 5.23716i) q^{78} +10.7847 q^{79} +(-6.26084 - 11.6527i) q^{80} +(-4.77082 + 8.26331i) q^{81} +(0.166772 + 0.113287i) q^{82} +(0.331076 - 0.331076i) q^{83} +(10.5003 + 14.1262i) q^{84} +(2.38492 - 8.90063i) q^{85} +(-1.38674 + 3.98489i) q^{86} +(-2.53425 + 1.46315i) q^{87} +(-10.5443 + 0.448647i) q^{88} +(-6.75424 - 3.89956i) q^{89} +(-12.3988 - 4.31478i) q^{90} +(-9.21549 - 9.40541i) q^{91} +(-10.3289 - 8.17944i) q^{92} +(2.55190 + 9.52382i) q^{93} +(10.3601 + 0.758594i) q^{94} +(11.3510 + 19.6606i) q^{95} +(-1.41055 + 13.5586i) q^{96} +(5.70247 + 9.87697i) q^{97} +(-5.03611 + 7.41379i) q^{98} +(-7.40625 + 7.40625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{8}+O(q^{10}) $ 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^8	$ 104 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{8} - 2 q^{10} - 2 q^{11} - 36 q^{12} - 4 q^{13} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{18} - 2 q^{19} - 10 q^{20} - 20 q^{21} + 18 q^{22} + 14 q^{24} - 40 q^{26} + 4 q^{27} - 16 q^{28} - 2 q^{29} - 2 q^{30} - 16 q^{31} - 2 q^{32} - 4 q^{33} + 20 q^{34} + 8 q^{35} - 24 q^{36} - 2 q^{37} + 12 q^{38} - 28 q^{40} + 14 q^{42} - 18 q^{43} - 24 q^{44} + 20 q^{45} + 32 q^{46} - 16 q^{47} - 48 q^{48} + 24 q^{49} + 64 q^{50} + 4 q^{51} - 42 q^{52} - 8 q^{53} - 26 q^{54} + 32 q^{56} + 34 q^{58} - 42 q^{59} + 56 q^{60} - 2 q^{61} + 18 q^{62} - 60 q^{63} - 44 q^{64} - 16 q^{65} - 24 q^{66} - 2 q^{67} + 32 q^{68} - 14 q^{69} - 112 q^{70} - 60 q^{72} + 6 q^{74} + 10 q^{75} + 46 q^{76} - 36 q^{77} - 116 q^{78} + 64 q^{79} + 30 q^{80} + 16 q^{81} + 68 q^{82} - 48 q^{83} + 88 q^{84} - 12 q^{85} - 48 q^{86} - 44 q^{88} + 220 q^{90} + 38 q^{91} - 72 q^{92} - 56 q^{93} - 2 q^{94} + 60 q^{95} + 168 q^{96} - 4 q^{97} + 38 q^{98} - 160 q^{99}+O(q^{100}) $ 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^8 - 2 * q^10 - 2 * q^11 - 36 * q^12 - 4 * q^13 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^18 - 2 * q^19 - 10 * q^20 - 20 * q^21 + 18 * q^22 + 14 * q^24 - 40 * q^26 + 4 * q^27 - 16 * q^28 - 2 * q^29 - 2 * q^30 - 16 * q^31 - 2 * q^32 - 4 * q^33 + 20 * q^34 + 8 * q^35 - 24 * q^36 - 2 * q^37 + 12 * q^38 - 28 * q^40 + 14 * q^42 - 18 * q^43 - 24 * q^44 + 20 * q^45 + 32 * q^46 - 16 * q^47 - 48 * q^48 + 24 * q^49 + 64 * q^50 + 4 * q^51 - 42 * q^52 - 8 * q^53 - 26 * q^54 + 32 * q^56 + 34 * q^58 - 42 * q^59 + 56 * q^60 - 2 * q^61 + 18 * q^62 - 60 * q^63 - 44 * q^64 - 16 * q^65 - 24 * q^66 - 2 * q^67 + 32 * q^68 - 14 * q^69 - 112 * q^70 - 60 * q^72 + 6 * q^74 + 10 * q^75 + 46 * q^76 - 36 * q^77 - 116 * q^78 + 64 * q^79 + 30 * q^80 + 16 * q^81 + 68 * q^82 - 48 * q^83 + 88 * q^84 - 12 * q^85 - 48 * q^86 - 44 * q^88 + 220 * q^90 + 38 * q^91 - 72 * q^92 - 56 * q^93 - 2 * q^94 + 60 * q^95 + 168 * q^96 - 4 * q^97 + 38 * q^98 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41044	−	0.103276i	−0.997330	−	0.0730270i
$2$	−1.41044	−	0.103276i	−0.997330	−	0.0730270i
$3$	−0.623697	−	2.32767i	−0.360092	−	1.34388i	−0.873954	−	0.486008i	$-0.838453\pi$
$3$	−0.623697	−	2.32767i	−0.360092	−	1.34388i	0.513863	−	0.857872i	$-0.328214\pi$
$4$	1.97867	+	0.291328i	0.989334	+	0.145664i
$5$	−2.33843	−	2.33843i	−1.04578	−	1.04578i	−0.998901	−	0.0468761i	$-0.985073\pi$
$5$	−2.33843	−	2.33843i	−1.04578	−	1.04578i	−0.0468761	−	0.998901i	$-0.514927\pi$
$6$	0.639294	+	3.34744i	0.260991	+	1.36659i
$7$	−3.16277	+	1.82602i	−1.19541	+	0.690172i	−0.959529	−	0.281609i	$-0.909132\pi$
$7$	−3.16277	+	1.82602i	−1.19541	+	0.690172i	−0.235884	+	0.971781i	$0.575799\pi$
$8$	−2.76070	−	0.615248i	−0.976055	−	0.217523i
$9$	−2.43097	+	1.40352i	−0.810323	+	0.467840i
$10$	3.05670	+	3.53971i	0.966615	+	1.11935i
$11$	3.60420	−	0.965741i	1.08671	−	0.291182i	0.329366	−	0.944202i	$-0.393165\pi$
$11$	3.60420	−	0.965741i	1.08671	−	0.291182i	0.757340	+	0.653020i	$0.226498\pi$
$12$	−0.555974	−	4.78739i	−0.160496	−	1.38200i
$13$	0.897619	+	3.49203i	0.248955	+	0.968515i
$13$	0.897619	+	3.49203i	0.248955	+	0.968515i
$14$	4.64947	−	2.24886i	1.24262	−	0.601032i
$15$	−3.98462	+	6.90156i	−1.02882	+	1.78197i
$16$	3.83026	+	1.15288i	0.957564	+	0.288221i
$17$	1.39318	+	2.41306i	0.337896	+	0.585254i	0.984037	−	0.177965i	$-0.0569513\pi$
$17$	1.39318	+	2.41306i	0.337896	+	0.585254i	−0.646140	+	0.763219i	$0.723618\pi$
$18$	3.57368	−	1.72852i	0.842324	−	0.407416i
$19$	−6.63086	−	1.77673i	−1.52122	−	0.407611i	−0.601080	−	0.799189i	$-0.705263\pi$
$19$	−6.63086	−	1.77673i	−1.52122	−	0.407611i	−0.920145	+	0.391578i	$0.871929\pi$
$20$	−3.94572	−	5.30822i	−0.882291	−	1.18695i
$21$	6.22299	+	6.22299i	1.35797	+	1.35797i
$22$	−5.18323	+	0.989892i	−1.10507	+	0.211046i
$23$	−5.70507	−	3.29383i	−1.18959	−	0.686810i	−0.231377	−	0.972864i	$-0.574323\pi$
$23$	−5.70507	−	3.29383i	−1.18959	−	0.686810i	−0.958213	+	0.286054i	$0.907656\pi$
$24$	0.289746	+	6.80973i	0.0591442	+	1.39003i
$25$			5.93649i			1.18730i
$26$	−0.905393	−	5.01799i	−0.177562	−	0.984110i
$27$	−0.328797	−	0.328797i	−0.0632770	−	0.0632770i
$28$	−6.79004	+	2.69169i	−1.28320	+	0.508682i
$29$	−0.314295	−	1.17296i	−0.0583631	−	0.217814i	0.930585	−	0.366076i	$-0.119299\pi$
$29$	−0.314295	−	1.17296i	−0.0583631	−	0.217814i	−0.988948	+	0.148262i	$0.952632\pi$
$30$	6.33282	−	9.32270i	1.15621	−	1.70208i
$31$	−4.09157			−0.734867			−0.367434	−	0.930050i	$-0.619764\pi$
$31$	−4.09157			−0.734867			−0.367434	+	0.930050i	$0.619764\pi$
$32$	−5.28327	−	2.02164i	−0.933959	−	0.357379i
$33$	−4.49585	−	7.78705i	−0.782627	−	1.35555i
$34$	−1.71579	−	3.54736i	−0.294255	−	0.608367i
$35$	11.6659	+	3.12588i	1.97190	+	0.528369i
$36$	−5.21897	+	2.06889i	−0.869828	+	0.344815i
$37$	3.69016	−	0.988774i	0.606658	−	0.162553i	0.0576027	−	0.998340i	$-0.481654\pi$
$37$	3.69016	−	0.988774i	0.606658	−	0.162553i	0.549055	+	0.835786i	$0.314988\pi$
$38$	9.16893	+	3.19078i	1.48740	+	0.517613i
$39$	7.56845	−	4.26733i	1.21192	−	0.683319i
$40$	5.01699	+	7.89441i	0.793255	+	1.24822i
$41$	−0.123461	−	0.0712802i	−0.0192814	−	0.0111321i	0.490328	−	0.871538i	$-0.336877\pi$
$41$	−0.123461	−	0.0712802i	−0.0192814	−	0.0111321i	−0.509610	+	0.860406i	$0.670210\pi$
$42$	−8.13445	−	9.41982i	−1.25517	−	1.45351i
$43$	0.772184	−	2.88183i	0.117757	−	0.439475i	−0.881721	−	0.471770i	$-0.843615\pi$
$43$	0.772184	−	2.88183i	0.117757	−	0.439475i	0.999478	+	0.0322955i	$0.0102818\pi$
$44$	7.41286	−	0.860879i	1.11753	−	0.129782i
$45$	8.96668	+	2.40261i	1.33667	+	0.358161i
$46$	7.70648	+	5.23493i	1.13626	+	0.771849i
$47$	−7.34533			−1.07143			−0.535713	−	0.844400i	$-0.679957\pi$
$47$	−7.34533			−1.07143			−0.535713	+	0.844400i	$0.679957\pi$
$48$	0.294611	−	9.63462i	0.0425234	−	1.39064i
$49$	3.16873	−	5.48840i	0.452675	−	0.784057i
$50$	0.613096	−	8.37305i	0.0867048	−	1.18413i
$51$	4.74789	−	4.74789i	0.664837	−	0.664837i
$52$	0.758763	+	7.17107i	0.105221	+	0.994449i
$53$	−6.32639	−	6.32639i	−0.868997	−	0.868997i	0.123365	−	0.992361i	$-0.460631\pi$
$53$	−6.32639	−	6.32639i	−0.868997	−	0.868997i	−0.992361	+	0.123365i	$0.960631\pi$
$54$	0.429791	+	0.497704i	0.0584871	+	0.0677290i
$55$	−10.6865	−	6.16984i	−1.44096	−	0.831940i
$56$	9.85491	−	3.09522i	1.31692	−	0.413616i
$57$			16.5426i			2.19112i
$58$	0.322154	+	1.68685i	0.0423010	+	0.221495i
$59$	−0.387585	+	1.44649i	−0.0504593	+	0.188317i	−0.986555	−	0.163428i	$-0.947745\pi$
$59$	−0.387585	+	1.44649i	−0.0504593	+	0.188317i	0.936096	+	0.351745i	$0.114411\pi$
$60$	−9.89485	+	12.4951i	−1.27742	+	1.61311i
$61$	−2.41180	−	0.646240i	−0.308799	−	0.0827425i	0.101091	−	0.994877i	$-0.467767\pi$
$61$	−2.41180	−	0.646240i	−0.308799	−	0.0827425i	−0.409891	+	0.912135i	$0.634433\pi$
$62$	5.77090	+	0.422560i	0.732905	+	0.0536652i
$63$	5.12572	−	8.87801i	0.645781	−	1.11852i
$64$	7.24294	+	3.39703i	0.905367	+	0.424629i
$65$	6.06685	−	10.2649i	0.752500	−	1.27320i
$66$	5.53691	+	11.4475i	0.681546	+	1.40908i
$67$	−0.625756	−	2.33535i	−0.0764483	−	0.285309i	0.917110	−	0.398635i	$-0.130516\pi$
$67$	−0.625756	−	2.33535i	−0.0764483	−	0.285309i	−0.993558	+	0.113326i	$0.963849\pi$
$68$	2.05365	+	5.18052i	0.249042	+	0.628231i
$69$	−4.10870	+	15.3339i	−0.494629	+	1.84598i
$70$	−16.1312	−	5.61366i	−1.92805	−	0.670961i
$71$	7.89833	−	4.56010i	0.937359	−	0.541185i	0.0482279	−	0.998836i	$-0.484643\pi$
$71$	7.89833	−	4.56010i	0.937359	−	0.541185i	0.889132	+	0.457652i	$0.151309\pi$
$72$	7.57469	−	2.37905i	0.892686	−	0.280374i
$73$		−	10.8639i		−	1.27152i	−0.771885	−	0.635762i	$-0.780686\pi$
$73$		−	10.8639i		−	1.27152i	0.771885	−	0.635762i	$-0.219314\pi$
$74$	−5.30685	+	1.01350i	−0.616909	+	0.117817i
$75$	13.8182	−	3.70257i	1.59559	−	0.427536i
$76$	−12.6027	−	5.44732i	−1.44563	−	0.624851i
$77$	−9.63576	+	9.63576i	−1.09810	+	1.09810i
$78$	−11.1155	+	5.23716i	−1.25859	+	0.592992i
$79$	10.7847			1.21337			0.606686	−	0.794941i	$-0.292498\pi$
$79$	10.7847			1.21337			0.606686	+	0.794941i	$0.292498\pi$
$80$	−6.26084	−	11.6527i	−0.699984	−	1.30281i
$81$	−4.77082	+	8.26331i	−0.530091	+	0.918145i
$82$	0.166772	+	0.113287i	0.0184169	+	0.0125104i
$83$	0.331076	−	0.331076i	0.0363403	−	0.0363403i	−0.688703	−	0.725043i	$-0.741820\pi$
$83$	0.331076	−	0.331076i	0.0363403	−	0.0363403i	0.725043	+	0.688703i	$0.241820\pi$
$84$	10.5003	+	14.1262i	1.14568	+	1.54129i
$85$	2.38492	−	8.90063i	0.258681	−	0.965409i
$86$	−1.38674	+	3.98489i	−0.149536	+	0.429702i
$87$	−2.53425	+	1.46315i	−0.271700	+	0.156866i
$88$	−10.5443	+	0.448647i	−1.12402	+	0.0478260i
$89$	−6.75424	−	3.89956i	−0.715948	−	0.413353i	0.0973116	−	0.995254i	$-0.468976\pi$
$89$	−6.75424	−	3.89956i	−0.715948	−	0.413353i	−0.813259	+	0.581901i	$0.802309\pi$
$90$	−12.3988	−	4.31478i	−1.30695	−	0.454817i
$91$	−9.21549	−	9.40541i	−0.966046	−	0.985954i
$92$	−10.3289	−	8.17944i	−1.07686	−	0.852765i
$93$	2.55190	+	9.52382i	0.264620	+	0.987574i
$94$	10.3601	+	0.758594i	1.06857	+	0.0782430i
$95$	11.3510	+	19.6606i	1.16459	+	2.01713i
$96$	−1.41055	+	13.5586i	−0.143964	+	1.38382i
$97$	5.70247	+	9.87697i	0.578998	+	1.00285i	0.995595	+	0.0937630i	$0.0298896\pi$
$97$	5.70247	+	9.87697i	0.578998	+	1.00285i	−0.416596	+	0.909092i	$0.636777\pi$
$98$	−5.03611	+	7.41379i	−0.508724	+	0.748906i
$99$	−7.40625	+	7.40625i	−0.744356	+	0.744356i
$100$	−1.72947	+	11.7463i	−0.172947	+	1.17463i
$101$	−2.23780	+	0.599616i	−0.222669	+	0.0596640i	−0.368429	−	0.929656i	$-0.620104\pi$
$101$	−2.23780	+	0.599616i	−0.222669	+	0.0596640i	0.145759	+	0.989320i	$0.453437\pi$
$102$	−7.18694	+	6.20626i	−0.711613	+	0.614511i
$103$			8.68531i			0.855789i	0.903829	+	0.427895i	$0.140745\pi$
$103$			8.68531i			0.855789i	−0.903829	+	0.427895i	$0.859255\pi$
$104$	−0.329590	−	10.1927i	−0.0323189	−	0.999478i
$105$		−	29.1040i		−	2.84026i
$106$	8.26962	+	9.57634i	0.803216	+	0.930137i
$107$	−10.9540	+	2.93513i	−1.05897	+	0.283749i	−0.745953	−	0.665999i	$-0.768005\pi$
$107$	−10.9540	+	2.93513i	−1.05897	+	0.283749i	−0.313014	+	0.949748i	$0.601339\pi$
$108$	−0.554792	−	0.746368i	−0.0533849	−	0.0718193i
$109$	5.96844	−	5.96844i	0.571672	−	0.571672i	−0.360923	−	0.932596i	$-0.617538\pi$
$109$	5.96844	−	5.96844i	0.571672	−	0.571672i	0.932596	+	0.360923i	$0.117538\pi$
$110$	14.4354	+	9.80582i	1.37636	+	0.934948i
$111$	−4.60308	−	7.97277i	−0.436905	−	0.756741i
$112$	−14.2194	+	3.34784i	−1.34361	+	0.316341i
$113$	−4.70737	−	8.15341i	−0.442833	−	0.767008i	0.555066	−	0.831806i	$-0.312693\pi$
$113$	−4.70737	−	8.15341i	−0.442833	−	0.767008i	−0.997898	+	0.0647979i	$0.979360\pi$
$114$	1.70845	−	23.3323i	0.160011	−	2.18527i
$115$	5.63853	+	21.0433i	0.525796	+	1.96230i
$116$	−0.280168	−	2.41247i	−0.0260129	−	0.223992i
$117$	−7.08322	−	7.22919i	−0.654844	−	0.668339i
$118$	0.696052	−	2.00015i	0.0640768	−	0.184129i
$119$	−8.81262	−	5.08797i	−0.807852	−	0.466413i
$120$	15.2465	−	16.6016i	1.39181	−	1.51551i
$121$	2.53129	−	1.46144i	0.230117	−	0.132858i
$122$	3.33495	+	1.16056i	0.301932	+	0.105072i
$123$	−0.0889145	+	0.331833i	−0.00801715	+	0.0299204i
$124$	−8.09586	−	1.19199i	−0.727029	−	0.107044i
$125$	2.18992	−	2.18992i	0.195872	−	0.195872i
$126$	−8.14640	+	11.9925i	−0.725739	+	1.06838i
$127$	2.35499	−	4.07897i	0.208972	−	0.361950i	−0.742419	−	0.669936i	$-0.766322\pi$
$127$	2.35499	−	4.07897i	0.208972	−	0.361950i	0.951391	+	0.307986i	$0.0996549\pi$
$128$	−9.86488	−	5.53932i	−0.871941	−	0.489612i
$129$	−7.18956			−0.633005
$130$	−9.61702	+	13.8514i	−0.843469	+	1.21485i
$131$	−0.104732	+	0.104732i	−0.00915046	+	0.00915046i	−0.711667	−	0.702517i	$-0.752060\pi$
$131$	−0.104732	+	0.104732i	−0.00915046	+	0.00915046i	0.702517	+	0.711667i	$0.252060\pi$
$132$	−6.62722	−	16.7177i	−0.576825	−	1.45509i
$133$	24.2162	−	6.48872i	2.09981	−	0.562643i
$134$	0.641405	+	3.35850i	0.0554089	+	0.290130i
$135$			1.53774i			0.132347i
$136$	−2.36153	−	7.51890i	−0.202499	−	0.644740i
$137$	6.48097	−	3.74179i	0.553707	−	0.319683i	−0.196909	−	0.980422i	$-0.563090\pi$
$137$	6.48097	−	3.74179i	0.553707	−	0.319683i	0.750616	+	0.660739i	$0.229757\pi$
$138$	7.37868	−	21.2031i	0.628115	−	1.80493i
$139$	3.98009	−	14.8539i	0.337587	−	1.25989i	−0.563451	−	0.826150i	$-0.690527\pi$
$139$	3.98009	−	14.8539i	0.337587	−	1.25989i	0.901037	−	0.433741i	$-0.142807\pi$
$140$	22.1723	+	9.58368i	1.87391	+	0.809969i
$141$	4.58126	+	17.0975i	0.385812	+	1.43987i
$142$	−11.6111	+	5.61604i	−0.974378	+	0.471287i
$143$	6.60759	+	11.7191i	0.552555	+	0.980000i
$144$	−10.9293	+	2.57322i	−0.910777	+	0.214435i
$145$	−2.00794	+	3.47785i	−0.166750	+	0.288820i
$146$	−1.12198	+	15.3229i	−0.0928556	+	1.26813i
$147$	−14.7515	−	3.95265i	−1.21668	−	0.326009i
$148$	7.58965	−	0.881410i	0.623865	−	0.0724515i
$149$	−0.864092	+	3.22484i	−0.0707892	+	0.264189i	−0.992246	−	0.124293i	$-0.960334\pi$
$149$	−0.864092	+	3.22484i	−0.0707892	+	0.264189i	0.921456	+	0.388482i	$0.127000\pi$
$150$	−19.8721	+	3.79516i	−1.62255	+	0.309874i
$151$			20.8859i			1.69967i	0.527047	+	0.849836i	$0.323299\pi$
$151$			20.8859i			1.69967i	−0.527047	+	0.849836i	$0.676701\pi$
$152$	17.2127	+	8.98466i	1.39613	+	0.728752i
$153$	−6.77357	−	3.91072i	−0.547610	−	0.316163i
$154$	14.5858	−	12.5955i	1.17536	−	1.01497i
$155$	9.56784	+	9.56784i	0.768507	+	0.768507i
$156$	16.2186	−	6.23873i	1.29853	−	0.499498i
$157$	8.48001	−	8.48001i	0.676778	−	0.676778i	−0.282491	−	0.959270i	$-0.591161\pi$
$157$	8.48001	−	8.48001i	0.676778	−	0.676778i	0.959270	+	0.282491i	$0.0911609\pi$
$158$	−15.2111	−	1.11380i	−1.21013	−	0.0886089i
$159$	−10.7800	+	18.6715i	−0.854909	+	1.48075i
$160$	7.62709	+	17.0820i	0.602974	+	1.35045i
$161$	24.0584			1.89607
$162$	7.58235	−	11.1622i	0.595725	−	0.876983i
$163$	5.86275	+	1.57092i	0.459206	+	0.123044i	0.481004	−	0.876719i	$-0.340272\pi$
$163$	5.86275	+	1.57092i	0.459206	+	0.123044i	−0.0217979	+	0.999762i	$0.506939\pi$
$164$	−0.223522	−	0.177007i	−0.0174542	−	0.0138220i
$165$	−7.69622	+	28.7227i	−0.599150	+	2.23606i
$166$	−0.501154	+	0.432770i	−0.0388971	+	0.0335895i
$167$	−5.53339	−	3.19470i	−0.428186	−	0.247214i	0.270387	−	0.962752i	$-0.412848\pi$
$167$	−5.53339	−	3.19470i	−0.428186	−	0.247214i	−0.698574	+	0.715538i	$0.746182\pi$
$168$	−13.3511	−	21.0085i	−1.03006	−	1.62084i
$169$	−11.3886	+	6.26902i	−0.876043	+	0.482233i
$170$	−4.28300	+	12.3075i	−0.328491	+	0.943941i
$171$	18.6131	−	4.98737i	1.42338	−	0.381393i
$172$	2.36745	−	5.47723i	0.180517	−	0.417635i
$173$	−2.34286	−	0.627768i	−0.178125	−	0.0477283i	0.168654	−	0.985675i	$-0.446058\pi$
$173$	−2.34286	−	0.627768i	−0.178125	−	0.0477283i	−0.346779	+	0.937947i	$0.612725\pi$
$174$	3.72551	−	1.80195i	0.282430	−	0.136606i
$175$	−10.8402	−	18.7757i	−0.819440	−	1.41931i
$176$	14.9184	+	0.456179i	1.12452	+	0.0343858i
$177$	3.60868			0.271245
$178$	9.12370	+	6.19764i	0.683850	+	0.464533i
$179$	−4.93333	−	18.4114i	−0.368734	−	1.37614i	−0.862287	−	0.506419i	$-0.830969\pi$
$179$	−4.93333	−	18.4114i	−0.368734	−	1.37614i	0.493553	−	0.869716i	$-0.335698\pi$
$180$	17.0421	+	7.36622i	1.27025	+	0.549046i
$181$	−12.6523	−	12.6523i	−0.940441	−	0.940441i	0.0578822	−	0.998323i	$-0.481565\pi$
$181$	−12.6523	−	12.6523i	−0.940441	−	0.940441i	−0.998323	+	0.0578822i	$0.981565\pi$
$182$	12.0265	+	14.2175i	0.891465	+	1.05387i
$183$			6.01693i			0.444784i
$184$	13.7235	+	12.6033i	1.01171	+	0.929128i
$185$	−10.9413	−	6.31699i	−0.804423	−	0.464434i
$186$	−2.61571	−	13.6963i	−0.191794	−	1.00426i
$187$	7.35170	+	7.35170i	0.537609	+	0.537609i
$188$	−14.5340	−	2.13990i	−1.06000	−	0.156068i
$189$	1.64030	+	0.439517i	0.119314	+	0.0319701i
$190$	−13.9795	−	28.9023i	−1.01418	−	2.09679i
$191$	−6.30968	−	10.9287i	−0.456552	−	0.790772i	0.542224	−	0.840234i	$-0.317582\pi$
$191$	−6.30968	−	10.9287i	−0.456552	−	0.790772i	−0.998776	+	0.0494625i	$0.984249\pi$
$192$	3.38977	−	18.9779i	0.244636	−	1.36961i
$193$	1.86581	−	3.23168i	0.134304	−	0.232621i	−0.791027	−	0.611781i	$-0.790454\pi$
$193$	1.86581	−	3.23168i	0.134304	−	0.232621i	0.925331	+	0.379160i	$0.123787\pi$
$194$	−7.02293	−	14.5198i	−0.504217	−	1.04246i
$195$	−27.6771	−	7.71944i	−1.98200	−	0.552800i
$196$	7.86878	−	9.93658i	0.562056	−	0.709755i
$197$	25.9395	−	6.95047i	1.84811	−	0.495201i	0.848682	−	0.528904i	$-0.177397\pi$
$197$	25.9395	−	6.95047i	1.84811	−	0.495201i	0.999432	+	0.0337033i	$0.0107301\pi$
$198$	11.2109	−	9.68117i	0.796727	−	0.688011i
$199$	0.729619	−	0.421246i	0.0517213	−	0.0298613i	−0.473916	−	0.880570i	$-0.657160\pi$
$199$	0.729619	−	0.421246i	0.0517213	−	0.0298613i	0.525638	+	0.850709i	$0.323827\pi$
$200$	3.65242	−	16.3889i	0.258265	−	1.15887i
$201$	−5.04565	+	2.91311i	−0.355893	+	0.205475i
$202$	3.21820	−	0.614611i	0.226432	−	0.0432439i
$203$	3.13590	+	3.13590i	0.220097	+	0.220097i
$204$	10.7777	−	8.01130i	0.754589	−	0.560903i
$205$	0.122021	+	0.455388i	0.00852231	+	0.0318057i
$206$	0.896982	−	12.2501i	0.0624957	−	0.853504i
$207$	18.4918			1.28527
$208$	−0.587794	+	14.4102i	−0.0407562	+	0.999169i
$209$	−25.6148			−1.77181
$210$	−3.00574	+	41.0494i	−0.207416	+	2.83268i
$211$	0.287056	+	1.07131i	0.0197617	+	0.0737518i	0.975103	−	0.221754i	$-0.0711784\pi$
$211$	0.287056	+	1.07131i	0.0197617	+	0.0737518i	−0.955341	+	0.295506i	$0.904512\pi$
$212$	−10.6748	−	14.3609i	−0.733146	−	0.986309i
$213$	−15.5406	−	15.5406i	−1.06482	−	1.06482i
$214$	15.7531	−	3.00852i	1.07686	−	0.205659i
$215$	−8.54465	+	4.93326i	−0.582740	+	0.336445i
$216$	0.705418	+	1.11000i	0.0479976	+	0.0755260i
$217$	12.9407	−	7.47130i	0.878470	−	0.507185i
$218$	−9.03450	+	7.80171i	−0.611894	+	0.528399i
$219$	−25.2876	+	6.77579i	−1.70878	+	0.457865i
$220$	−19.3475	−	15.3213i	−1.30441	−	1.03296i
$221$	−7.17594	+	7.03105i	−0.482706	+	0.472959i
$222$	5.66896	+	11.7205i	0.380476	+	0.786627i
$223$	6.94501	−	12.0291i	0.465072	−	0.805528i	−0.534133	−	0.845401i	$-0.679362\pi$
$223$	6.94501	−	12.0291i	0.465072	−	0.805528i	0.999205	+	0.0398723i	$0.0126951\pi$
$224$	20.4013	−	3.25340i	1.36312	−	0.217377i
$225$	−8.33199	−	14.4314i	−0.555466	−	0.962095i
$226$	5.79741	+	11.9860i	0.385638	+	0.797299i
$227$	11.7251	+	3.14174i	0.778224	+	0.208524i	0.626002	−	0.779822i	$-0.284690\pi$
$227$	11.7251	+	3.14174i	0.778224	+	0.208524i	0.152222	+	0.988346i	$0.451357\pi$
$228$	−4.81932	+	32.7323i	−0.319167	+	2.16775i
$229$	−7.51976	−	7.51976i	−0.496920	−	0.496920i	0.413558	−	0.910478i	$-0.364286\pi$
$229$	−7.51976	−	7.51976i	−0.496920	−	0.496920i	−0.910478	+	0.413558i	$0.864286\pi$
$230$	−5.77953	−	30.2626i	−0.381091	−	1.99545i
$231$	28.4387	+	16.4191i	1.87113	+	1.08030i
$232$	0.146010	+	3.43157i	0.00958600	+	0.225294i
$233$			8.49568i			0.556570i	0.960498	+	0.278285i	$0.0897660\pi$
$233$			8.49568i			0.556570i	−0.960498	+	0.278285i	$0.910234\pi$
$234$	9.24384	+	10.9278i	0.604289	+	0.714376i
$235$	17.1765	+	17.1765i	1.12047	+	1.12047i
$236$	−1.18830	+	2.74920i	−0.0773520	+	0.178958i
$237$	−6.72638	−	25.1032i	−0.436925	−	1.63063i
$238$	11.9042	+	8.08639i	0.771634	+	0.524163i
$239$	3.51330			0.227257			0.113628	−	0.993523i	$-0.463753\pi$
$239$	3.51330			0.227257			0.113628	+	0.993523i	$0.463753\pi$
$240$	−23.2188	+	21.8409i	−1.49877	+	1.40983i
$241$	−2.56875	−	4.44921i	−0.165468	−	0.286599i	0.771353	−	0.636407i	$-0.219580\pi$
$241$	−2.56875	−	4.44921i	−0.165468	−	0.286599i	−0.936821	+	0.349808i	$0.886247\pi$
$242$	−3.72116	+	1.79985i	−0.239205	+	0.115699i
$243$	20.8624	+	5.59005i	1.33832	+	0.358602i
$244$	−4.58388	−	1.98132i	−0.293453	−	0.126841i
$245$	−20.2441	+	5.42438i	−1.29335	+	0.346551i
$246$	0.159679	−	0.458848i	0.0101807	−	0.0292551i
$247$	0.252426	−	24.7500i	0.0160615	−	1.57481i
$248$	11.2956	+	2.51733i	0.717271	+	0.159851i
$249$	−0.977127	−	0.564144i	−0.0619229	−	0.0357512i
$250$	−3.31490	+	2.86257i	−0.209653	+	0.181045i
$251$	−2.42800	+	9.06141i	−0.153254	+	0.571951i	0.845995	+	0.533191i	$0.179007\pi$
$251$	−2.42800	+	9.06141i	−0.153254	+	0.571951i	−0.999249	+	0.0387600i	$0.987659\pi$
$252$	12.7285	−	16.0734i	0.801822	−	1.01253i
$253$	−23.7432	−	6.36197i	−1.49272	−	0.399973i
$254$	−3.74283	+	5.50992i	−0.234846	+	0.345723i
$255$	−22.2052			−1.39054
$256$	13.3417	+	8.83167i	0.833858	+	0.551980i
$257$	−2.52088	+	4.36629i	−0.157248	+	0.272362i	−0.933875	−	0.357599i	$-0.883596\pi$
$257$	−2.52088	+	4.36629i	−0.157248	+	0.272362i	0.776627	+	0.629960i	$0.216929\pi$
$258$	10.1404	+	0.742507i	0.631315	+	0.0462265i
$259$	−9.86557	+	9.86557i	−0.613017	+	0.613017i
$260$	14.9947	−	18.5433i	0.929933	−	1.15001i
$261$	2.41032	+	2.41032i	0.149195	+	0.149195i
$262$	0.158534	−	0.136901i	0.00979426	−	0.00845780i
$263$	15.3002	+	8.83358i	0.943451	+	0.544702i	0.891041	−	0.453924i	$-0.149976\pi$
$263$	15.3002	+	8.83358i	0.943451	+	0.544702i	0.0524109	+	0.998626i	$0.483309\pi$
$264$	7.62074	+	24.2638i	0.469024	+	1.49333i
$265$			29.5876i			1.81755i
$266$	−34.8256	+	6.65098i	−2.13530	+	0.407798i
$267$	−4.86429	+	18.1538i	−0.297690	+	1.11099i
$268$	−0.557810	−	4.80319i	−0.0340737	−	0.293402i
$269$	−21.6518	−	5.80158i	−1.32013	−	0.353729i	−0.471106	−	0.882077i	$-0.656145\pi$
$269$	−21.6518	−	5.80158i	−1.32013	−	0.353729i	−0.849028	+	0.528348i	$0.822812\pi$
$270$	0.158811	−	2.16888i	0.00966492	−	0.131994i
$271$	−3.22911	+	5.59299i	−0.196155	+	0.339750i	−0.947278	−	0.320412i	$-0.896179\pi$
$271$	−3.22911	+	5.59299i	−0.196155	+	0.339750i	0.751124	+	0.660161i	$0.229512\pi$
$272$	2.55427	+	10.8488i	0.154875	+	0.657807i
$273$	−16.1450	+	27.3167i	−0.977140	+	1.65328i
$274$	−9.52744	+	4.60824i	−0.575574	+	0.278394i
$275$	5.73311	+	21.3963i	0.345720	+	1.29024i
$276$	−12.5969	+	29.1437i	−0.758247	+	1.75424i
$277$	−8.02289	+	29.9418i	−0.482048	+	1.79903i	0.110950	+	0.993826i	$0.464611\pi$
$277$	−8.02289	+	29.9418i	−0.482048	+	1.79903i	−0.592999	+	0.805204i	$0.702056\pi$
$278$	−7.14772	+	20.5394i	−0.428691	+	1.23187i
$279$	9.94647	−	5.74260i	0.595480	−	0.343800i
$280$	−30.2829	−	15.8071i	−1.80975	−	0.944652i
$281$			32.1422i			1.91744i	0.284347	+	0.958721i	$0.408223\pi$
$281$			32.1422i			1.91744i	−0.284347	+	0.958721i	$0.591777\pi$
$282$	−4.69582	−	24.5881i	−0.279632	−	1.46420i
$283$	−6.23971	+	1.67193i	−0.370912	+	0.0993857i	−0.439460	−	0.898262i	$-0.644830\pi$
$283$	−6.23971	+	1.67193i	−0.370912	+	0.0993857i	0.0685476	+	0.997648i	$0.478164\pi$
$284$	16.9567	−	6.72193i	1.00619	−	0.398873i
$285$	38.6837	−	38.6837i	2.29142	−	2.29142i
$286$	−8.10930	−	17.2115i	−0.479513	−	1.01773i
$287$	0.520637			0.0307323
$288$	15.6809	−	2.50063i	0.924005	−	0.147351i
$289$	4.61809	−	7.99876i	0.271652	−	0.470515i
$290$	3.19125	−	4.69792i	0.187396	−	0.275871i
$291$	19.4337	−	19.4337i	1.13922	−	1.13922i
$292$	3.16496	−	21.4961i	0.185215	−	1.25796i
$293$	7.11431	−	26.5510i	0.415622	−	1.55112i	−0.367963	−	0.929840i	$-0.619945\pi$
$293$	7.11431	−	26.5510i	0.415622	−	1.55112i	0.783586	−	0.621284i	$-0.213389\pi$
$294$	20.3979	+	7.09844i	1.18963	+	0.413989i
$295$	4.28885	−	2.47617i	0.249706	−	0.144168i
$296$	−10.7958	+	0.459347i	−0.627491	+	0.0266990i
$297$	−1.50258	−	0.867515i	−0.0871886	−	0.0503384i
$298$	1.55180	−	4.45919i	0.0898931	−	0.258314i
$299$	6.38116	−	22.8789i	0.369032	−	1.32312i
$300$	28.4203	−	3.30054i	1.64084	−	0.190557i
$301$	2.82005	+	10.5246i	0.162545	+	0.606627i
$302$	2.15701	−	29.4583i	0.124122	−	1.69513i
$303$	2.79142	+	4.83487i	0.160363	+	0.277756i
$304$	−23.3495	−	14.4500i	−1.33919	−	0.828762i
$305$	4.12863	+	7.15100i	0.236405	+	0.409465i
$306$	9.14981	+	6.21537i	0.523060	+	0.355309i
$307$	19.3492	−	19.3492i	1.10432	−	1.10432i	0.110433	−	0.993884i	$-0.464776\pi$
$307$	19.3492	−	19.3492i	1.10432	−	1.10432i	0.993884	−	0.110433i	$-0.0352237\pi$
$308$	−21.8731	+	16.2588i	−1.24634	+	0.926432i
$309$	20.2165	−	5.41700i	1.15008	−	0.308163i
$310$	−12.5067	−	14.4830i	−0.710334	−	0.822577i
$311$			6.83310i			0.387469i	0.981054	+	0.193735i	$0.0620601\pi$
$311$			6.83310i			0.387469i	−0.981054	+	0.193735i	$0.937940\pi$
$312$	−23.5197	+	7.12434i	−1.33154	+	0.403336i
$313$			14.4698i			0.817879i	0.912562	+	0.408939i	$0.134101\pi$
$313$			14.4698i			0.817879i	−0.912562	+	0.408939i	$0.865899\pi$
$314$	−12.8363	+	11.0847i	−0.724395	+	0.625548i
$315$	−32.7467	+	8.77446i	−1.84507	+	0.494385i
$316$	21.3393	+	3.14188i	1.20043	+	0.176745i
$317$	9.83293	−	9.83293i	0.552272	−	0.552272i	−0.374824	−	0.927096i	$-0.622297\pi$
$317$	9.83293	−	9.83293i	0.552272	−	0.552272i	0.927096	+	0.374824i	$0.122297\pi$
$318$	17.1328	−	25.2217i	0.960761	−	1.41436i
$319$	−2.26556	−	3.92407i	−0.126847	−	0.219706i
$320$	−8.99337	−	24.8808i	−0.502745	−	1.39088i
$321$	13.6640	+	23.6667i	0.762650	+	1.32095i
$322$	−33.9329	−	2.48465i	−1.89101	−	0.138464i
$323$	−4.95063	−	18.4760i	−0.275460	−	1.02803i
$324$	−11.8472	+	14.9605i	−0.658178	+	0.831137i
$325$	−20.7304	+	5.32870i	−1.14992	+	0.295583i
$326$	−8.10680	−	2.82116i	−0.448994	−	0.156250i
$327$	−17.6150	−	10.1700i	−0.974114	−	0.562405i
$328$	0.296984	+	0.272742i	0.0163982	+	0.0150597i
$329$	23.2316	−	13.4127i	1.28080	−	0.739469i
$330$	13.8214	−	39.7167i	0.760842	−	2.18633i
$331$	2.10738	−	7.86485i	0.115832	−	0.432291i	−0.883516	−	0.468401i	$-0.844830\pi$
$331$	2.10738	−	7.86485i	0.115832	−	0.432291i	0.999348	+	0.0361104i	$0.0114968\pi$
$332$	0.751542	−	0.558638i	0.0412462	−	0.0306592i
$333$	−7.58289	+	7.58289i	−0.415540	+	0.415540i
$334$	7.47456	+	5.07739i	0.408990	+	0.277823i
$335$	−3.99777	+	6.92434i	−0.218422	+	0.378317i
$336$	16.6613	+	31.0100i	0.908946	+	1.69173i
$337$	11.9397			0.650399			0.325199	−	0.945646i	$-0.394569\pi$
$337$	11.9397			0.650399			0.325199	+	0.945646i	$0.394569\pi$
$338$	16.7103	−	7.66590i	0.908920	−	0.416970i
$339$	−16.0425	+	16.0425i	−0.871307	+	0.871307i
$340$	7.31196	−	16.9166i	0.396547	−	0.917432i
$341$	−14.7468	+	3.95140i	−0.798585	+	0.213980i
$342$	−26.7677	+	5.11209i	−1.44743	+	0.276430i
$343$		−	2.41965i		−	0.130649i
$344$	−3.90481	+	7.48079i	−0.210533	+	0.403337i
$345$	45.4651	−	26.2493i	2.44776	−	1.41321i
$346$	3.23963	+	1.12739i	0.174163	+	0.0606088i
$347$	−3.22684	+	12.0427i	−0.173226	+	0.646488i	0.823621	+	0.567141i	$0.191950\pi$
$347$	−3.22684	+	12.0427i	−0.173226	+	0.646488i	−0.996847	+	0.0793476i	$0.974716\pi$
$348$	−5.44069	+	2.15679i	−0.291652	+	0.115616i
$349$	−7.10822	−	26.5282i	−0.380494	−	1.42002i	−0.845148	−	0.534532i	$-0.820488\pi$
$349$	−7.10822	−	26.5282i	−0.380494	−	1.42002i	0.464654	−	0.885492i	$-0.346179\pi$
$350$	13.3503	+	27.6015i	0.713604	+	1.47536i
$351$	0.853035	−	1.44330i	0.0455316	−	0.0770378i
$352$	−20.9943	−	2.18412i	−1.11900	−	0.116414i
$353$	−17.4243	+	30.1797i	−0.927401	+	1.60631i	−0.139748	+	0.990187i	$0.544629\pi$
$353$	−17.4243	+	30.1797i	−0.927401	+	1.60631i	−0.787653	+	0.616119i	$0.788704\pi$
$354$	−5.08982	−	0.372689i	−0.270521	−	0.0198082i
$355$	−29.1332	−	7.80620i	−1.54623	−	0.414310i
$356$	−12.2283	−	9.68364i	−0.648101	−	0.513232i
$357$	−6.34670	+	23.6862i	−0.335903	+	1.25361i
$358$	5.05670	+	26.4777i	0.267255	+	1.39939i
$359$			4.13815i			0.218403i	0.994020	+	0.109202i	$0.0348294\pi$
$359$			4.13815i			0.218403i	−0.994020	+	0.109202i	$0.965171\pi$
$360$	−23.2761	−	12.1496i	−1.22676	−	0.640342i
$361$	24.3571	+	14.0626i	1.28195	+	0.740135i
$362$	16.5387	+	19.1520i	0.869253	+	1.00661i
$363$	−4.98051	−	4.98051i	−0.261409	−	0.261409i
$364$	−15.4943	−	21.2949i	−0.812124	−	1.11616i
$365$	−25.4045	+	25.4045i	−1.32973	+	1.32973i
$366$	0.621403	−	8.48650i	0.0324812	−	0.443597i
$367$	9.29156	−	16.0935i	0.485015	−	0.840071i	−0.514836	−	0.857288i	$-0.672147\pi$
$367$	9.29156	−	16.0935i	0.485015	−	0.840071i	0.999852	+	0.0172172i	$0.00548067\pi$
$368$	−18.0545	−	19.1935i	−0.941156	−	1.00053i
$369$	0.400173			0.0208322
$370$	14.7797	+	10.0397i	0.768359	+	0.521939i
$371$	31.5610	+	8.45675i	1.63857	+	0.439053i
$372$	2.27481	+	19.5879i	0.117943	+	1.01559i
$373$	4.18014	−	15.6005i	0.216439	−	0.807762i	−0.769216	−	0.638989i	$-0.779353\pi$
$373$	4.18014	−	15.6005i	0.216439	−	0.807762i	0.985655	−	0.168773i	$-0.0539805\pi$
$374$	−9.60986	−	11.1284i	−0.496914	−	0.575434i
$375$	−6.46324	−	3.73155i	−0.333760	−	0.192697i
$376$	20.2783	+	4.51920i	1.04577	+	0.233060i
$377$	3.81391	−	2.15040i	0.196426	−	0.110751i
$378$	−2.26815	−	0.789314i	−0.116661	−	0.0405979i
$379$	−23.1794	+	6.21090i	−1.19065	+	0.319033i	−0.799141	−	0.601143i	$-0.794712\pi$
$379$	−23.1794	+	6.21090i	−1.19065	+	0.319033i	−0.391505	+	0.920176i	$0.628045\pi$
$380$	16.7323	+	42.2086i	0.858346	+	2.16526i
$381$	−10.9633	−	2.93761i	−0.561667	−	0.150498i
$382$	7.77074	+	16.0659i	0.397585	+	0.822001i
$383$	2.67972	+	4.64141i	0.136927	+	0.237165i	0.926332	−	0.376708i	$-0.122944\pi$
$383$	2.67972	+	4.64141i	0.136927	+	0.237165i	−0.789405	+	0.613873i	$0.789611\pi$
$384$	−6.74102	+	26.4170i	−0.344001	+	1.34809i
$385$	45.0651			2.29673
$386$	−2.96536	+	4.36538i	−0.150933	+	0.222192i
$387$	2.16755	+	8.08942i	0.110183	+	0.411208i
$388$	8.40586	+	21.2045i	0.426743	+	1.07650i
$389$	11.0330	+	11.0330i	0.559397	+	0.559397i	0.929136	−	0.369738i	$-0.120553\pi$
$389$	11.0330	+	11.0330i	0.559397	+	0.559397i	−0.369738	+	0.929136i	$0.620553\pi$
$390$	38.2396	+	13.7462i	1.93634	+	0.696064i
$391$		−	18.3556i		−	0.928283i
$392$	−12.1246	+	13.2023i	−0.612387	+	0.666815i
$393$	0.309102	+	0.178460i	0.0155921	+	0.00900212i
$394$	−37.3039	+	7.12428i	−1.87934	+	0.358916i
$395$	−25.2192	−	25.2192i	−1.26892	−	1.26892i
$396$	−16.8122	+	12.4969i	−0.844843	+	0.627991i
$397$	−4.23444	−	1.13461i	−0.212520	−	0.0569447i	0.150988	−	0.988536i	$-0.451755\pi$
$397$	−4.23444	−	1.13461i	−0.212520	−	0.0569447i	−0.363508	+	0.931591i	$0.618421\pi$
$398$	−1.07259	+	0.518789i	−0.0537639	+	0.0260045i
$399$	−30.2072	−	52.3204i	−1.51225	−	2.61930i
$400$	−6.84408	+	22.7383i	−0.342204	+	1.13691i
$401$	9.11661	−	15.7904i	0.455262	−	0.788536i	−0.543441	−	0.839447i	$-0.682879\pi$
$401$	9.11661	−	15.7904i	0.455262	−	0.788536i	0.998703	+	0.0509106i	$0.0162123\pi$
$402$	7.41743	−	3.58766i	0.369948	−	0.178936i
$403$	−3.67267	−	14.2879i	−0.182949	−	0.711730i
$404$	−4.60254	+	0.534508i	−0.228985	+	0.0265928i
$405$	30.4794	−	8.16692i	1.51453	−	0.405818i
$406$	−4.09913	−	4.74686i	−0.203436	−	0.235583i
$407$	12.3451	−	7.12747i	0.611926	−	0.353296i
$408$	−16.0286	+	10.1864i	−0.793535	+	0.504300i
$409$	18.6321	−	10.7572i	0.921297	−	0.531911i	0.0372483	−	0.999306i	$-0.488141\pi$
$409$	18.6321	−	10.7572i	0.921297	−	0.531911i	0.884049	+	0.467395i	$0.154807\pi$
$410$	−0.125072	−	0.654898i	−0.00617688	−	0.0323431i
$411$	−12.7518	−	12.7518i	−0.629001	−	0.629001i
$412$	−2.53027	+	17.1853i	−0.124658	+	0.846661i
$413$	−1.41548	−	5.28264i	−0.0696512	−	0.259942i
$414$	−26.0815	−	1.90976i	−1.28184	−	0.0938594i
$415$	−1.54840			−0.0760077
$416$	2.31727	−	20.2640i	0.113614	−	0.993525i
$417$	−37.0573			−1.81470
$418$	36.1281	+	2.64539i	1.76708	+	0.129390i
$419$	3.23143	+	12.0599i	0.157866	+	0.589163i	0.998843	+	0.0480925i	$0.0153142\pi$
$419$	3.23143	+	12.0599i	0.157866	+	0.589163i	−0.840977	+	0.541071i	$0.818019\pi$
$420$	8.47881	−	57.5872i	0.413724	−	2.80997i
$421$	−26.0539	−	26.0539i	−1.26979	−	1.26979i	−0.946197	−	0.323592i	$-0.895109\pi$
$421$	−26.0539	−	26.0539i	−1.26979	−	1.26979i	−0.323592	−	0.946197i	$-0.604891\pi$
$422$	−0.294234	−	1.54066i	−0.0143231	−	0.0749980i
$423$	17.8563	−	10.3093i	0.868201	−	0.501256i
$424$	13.5730	+	21.3576i	0.659162	+	1.03722i
$425$	−14.3251	+	8.27061i	−0.694871	+	0.401184i
$426$	20.3140	+	23.5240i	0.984219	+	1.13974i
$427$	8.80801	−	2.36010i	0.426249	−	0.114213i
$428$	−22.5295	+	2.61642i	−1.08900	+	0.126470i
$429$	23.1570	−	22.6895i	1.11803	−	1.09546i
$430$	12.5612	−	6.07559i	0.605754	−	0.292991i
$431$	3.47069	−	6.01142i	0.167177	−	0.289560i	−0.770249	−	0.637743i	$-0.779868\pi$
$431$	3.47069	−	6.01142i	0.167177	−	0.289560i	0.937426	+	0.348184i	$0.113201\pi$
$432$	−0.880312	−	1.63844i	−0.0423540	−	0.0788295i
$433$	−6.31803	−	10.9431i	−0.303625	−	0.525894i	0.673329	−	0.739343i	$-0.264864\pi$
$433$	−6.31803	−	10.9431i	−0.303625	−	0.525894i	−0.976954	+	0.213449i	$0.931530\pi$
$434$	−19.0236	+	9.20135i	−0.913163	+	0.441679i
$435$	9.34762	+	2.50469i	0.448184	+	0.120091i
$436$	13.5483	−	10.0708i	0.648847	−	0.482303i
$437$	31.9773	+	31.9773i	1.52968	+	1.52968i
$438$	36.3663	−	6.94523i	1.73765	−	0.331856i
$439$	−0.128570	−	0.0742300i	−0.00613632	−	0.00354280i	0.496929	−	0.867791i	$-0.334461\pi$
$439$	−0.128570	−	0.0742300i	−0.00613632	−	0.00354280i	−0.503065	+	0.864249i	$0.667794\pi$
$440$	25.7062	+	23.6079i	1.22549	+	1.12546i
$441$			17.7895i			0.847119i
$442$	10.8474	−	9.17575i	0.515956	−	0.436446i
$443$	27.4219	+	27.4219i	1.30285	+	1.30285i	0.926461	+	0.376392i	$0.122835\pi$
$443$	27.4219	+	27.4219i	1.30285	+	1.30285i	0.376392	+	0.926461i	$0.377165\pi$
$444$	−6.78527	−	17.1165i	−0.322015	−	0.812311i
$445$	6.67546	+	24.9131i	0.316447	+	1.18100i
$446$	−11.0378	+	16.2490i	−0.522656	+	0.769415i
$447$	8.04528			0.380529
$448$	−29.1108	+	2.48176i	−1.37536	+	0.117252i
$449$	−4.95110	−	8.57556i	−0.233657	−	0.404706i	0.725225	−	0.688512i	$-0.241736\pi$
$449$	−4.95110	−	8.57556i	−0.233657	−	0.404706i	−0.958882	+	0.283807i	$0.908403\pi$
$450$	10.2613	+	21.2151i	0.483724	+	1.00009i
$451$	−0.513816	−	0.137676i	−0.0241946	−	0.00648293i
$452$	−6.93902	−	17.5043i	−0.326384	−	0.823332i
$453$	48.6155	−	13.0265i	2.28416	−	0.612038i
$454$	−16.2131	−	5.64215i	−0.760918	−	0.264799i
$455$	−0.444103	+	43.5436i	−0.0208199	+	2.04136i
$456$	10.1778	−	45.6692i	0.476620	−	2.13865i
$457$	−34.6636	−	20.0130i	−1.62149	−	0.936170i	−0.986521	−	0.163637i	$-0.947678\pi$
$457$	−34.6636	−	20.0130i	−1.62149	−	0.936170i	−0.634974	−	0.772534i	$-0.718989\pi$
$458$	9.82954	+	11.3828i	0.459304	+	0.531881i
$459$	0.335333	−	1.25148i	0.0156520	−	0.0584141i
$460$	5.02628	+	43.2803i	0.234352	+	2.01796i
$461$	8.15036	+	2.18388i	0.379600	+	0.101714i	0.443573	−	0.896238i	$-0.353711\pi$
$461$	8.15036	+	2.18388i	0.379600	+	0.101714i	−0.0639733	+	0.997952i	$0.520377\pi$
$462$	−38.4153	−	26.0951i	−1.78724	−	1.21405i
$463$	21.0993			0.980570			0.490285	−	0.871562i	$-0.336893\pi$
$463$	21.0993			0.980570			0.490285	+	0.871562i	$0.336893\pi$
$464$	0.148461	−	4.85510i	0.00689212	−	0.225392i
$465$	16.3033	−	28.2382i	0.756049	−	1.30951i
$466$	0.877398	−	11.9826i	0.0406447	−	0.555084i
$467$	−13.9906	+	13.9906i	−0.647408	+	0.647408i	−0.952366	−	0.304958i	$-0.901358\pi$
$467$	−13.9906	+	13.9906i	−0.647408	+	0.647408i	0.304958	+	0.952366i	$0.401358\pi$
$468$	−11.9093	−	16.3677i	−0.550506	−	0.756598i
$469$	6.24353	+	6.24353i	0.288300	+	0.288300i
$470$	−22.4525	−	26.0003i	−1.03566	−	1.19931i
$471$	−25.0276	−	14.4497i	−1.15321	−	0.665807i
$472$	1.95996	−	3.75486i	0.0902143	−	0.172831i
$473$		−	11.1324i		−	0.511869i
$474$	6.89459	+	36.1012i	0.316679	+	1.65818i
$475$	10.5476	−	39.3641i	0.483956	−	1.80615i
$476$	−15.9550	−	12.6348i	−0.731296	−	0.579114i
$477$	24.2585	+	6.50004i	1.11072	+	0.297616i
$478$	−4.95529	−	0.362839i	−0.226650	−	0.0165959i
$479$	−16.2487	+	28.1436i	−0.742423	+	1.28591i	0.208966	+	0.977923i	$0.432990\pi$
$479$	−16.2487	+	28.1436i	−0.742423	+	1.28591i	−0.951389	+	0.307991i	$0.900343\pi$
$480$	35.0043	−	28.4073i	1.59772	−	1.29661i
$481$	6.76518	+	11.9986i	0.308466	+	0.547089i
$482$	3.16357	+	6.54062i	0.144097	+	0.297917i
$483$	−15.0052	−	56.0000i	−0.682759	−	2.54809i
$484$	5.43435	−	2.15427i	0.247016	−	0.0979215i
$485$	9.76177	−	36.4314i	0.443259	−	1.65427i
$486$	−28.8477	−	10.0390i	−1.30856	−	0.455378i
$487$	23.9015	−	13.7995i	1.08308	−	0.625316i	0.151354	−	0.988480i	$-0.451637\pi$
$487$	23.9015	−	13.7995i	1.08308	−	0.625316i	0.931725	+	0.363163i	$0.118303\pi$
$488$	6.26066	+	3.26793i	0.283407	+	0.147932i
$489$		−	14.6263i		−	0.661425i
$490$	29.1132	−	5.56003i	1.31520	−	0.251176i
$491$	−40.2542	+	10.7861i	−1.81664	+	0.486768i	−0.996364	−	0.0851933i	$-0.972849\pi$
$491$	−40.2542	+	10.7861i	−1.81664	+	0.486768i	−0.820280	+	0.571962i	$0.806183\pi$
$492$	−0.272605	+	0.630685i	−0.0122900	+	0.0284335i
$493$	2.39257	−	2.39257i	0.107756	−	0.107756i
$494$	−2.91211	+	34.8823i	−0.131022	+	1.56943i
$495$	34.6380			1.55686
$496$	−15.6718	−	4.71710i	−0.703683	−	0.211804i
$497$	−16.6537	+	28.8451i	−0.747021	+	1.29388i
$498$	1.31991	+	0.896604i	0.0591468	+	0.0401778i
$499$	−23.5197	+	23.5197i	−1.05288	+	1.05288i	−0.0543635	+	0.998521i	$0.517313\pi$
$499$	−23.5197	+	23.5197i	−1.05288	+	1.05288i	−0.998521	+	0.0543635i	$0.982687\pi$
$500$	4.97110	−	3.69513i	0.222314	−	0.165251i
$501$	−3.98505	+	14.8724i	−0.178039	+	0.664451i
$502$	4.36036	−	12.5298i	0.194613	−	0.559233i
$503$	−0.355066	+	0.204998i	−0.0158316	+	0.00914039i	−0.507895	−	0.861419i	$-0.669576\pi$
$503$	−0.355066	+	0.204998i	−0.0158316	+	0.00914039i	0.492063	+	0.870559i	$0.336243\pi$
$504$	−19.6128	+	21.3559i	−0.873622	+	0.951270i
$505$	6.63509	+	3.83077i	0.295258	+	0.170467i
$506$	32.8312	+	11.4253i	1.45953	+	0.507915i
$507$	21.6952	+	22.5988i	0.963519	+	1.00365i
$508$	5.84807	−	7.38485i	0.259466	−	0.327650i
$509$	3.52551	+	13.1574i	0.156265	+	0.583190i	0.998994	+	0.0448510i	$0.0142813\pi$
$509$	3.52551	+	13.1574i	0.156265	+	0.583190i	−0.842728	+	0.538339i	$0.819052\pi$
$510$	31.3190	+	2.29326i	1.38683	+	0.101547i
$511$	19.8378	+	34.3600i	0.877571	+	1.52000i
$512$	−17.9056	−	13.8344i	−0.791322	−	0.611400i
$513$	1.59602	+	2.76439i	0.0704661	+	0.122051i
$514$	4.00647	−	5.89803i	0.176718	−	0.260151i
$515$	20.3100	−	20.3100i	0.894964	−	0.894964i
$516$	−14.2257	−	2.09452i	−0.626254	−	0.0922061i
$517$	−26.4740	+	7.09369i	−1.16433	+	0.311980i
$518$	14.9337	−	12.8959i	0.656147	−	0.566613i
$519$			5.84495i			0.256565i
$520$	−23.0642	+	24.6056i	−1.01143	+	1.07903i
$521$		−	36.1745i		−	1.58483i	−0.609979	−	0.792417i	$-0.708822\pi$
$521$		−	36.1745i		−	1.58483i	0.609979	−	0.792417i	$-0.291178\pi$
$522$	−3.15068	−	3.64853i	−0.137901	−	0.159692i
$523$	−31.8439	+	8.53256i	−1.39244	+	0.373103i	−0.875623	−	0.482994i	$-0.839549\pi$
$523$	−31.8439	+	8.53256i	−1.39244	+	0.373103i	−0.516815	+	0.856097i	$0.672882\pi$
$524$	−0.237741	+	0.176718i	−0.0103858	+	0.00771997i
$525$	−36.9427	+	36.9427i	−1.61231	+	1.61231i
$526$	−20.6677	−	14.0394i	−0.901154	−	0.612145i
$527$	−5.70030	−	9.87321i	−0.248309	−	0.430084i
$528$	−8.24271	−	35.0096i	−0.358718	−	1.52360i
$529$	10.1986	+	17.6645i	0.443416	+	0.768020i
$530$	3.05568	−	41.7315i	0.132730	−	1.81270i
$531$	−1.08797	−	4.06035i	−0.0472138	−	0.176204i
$532$	49.8062	−	5.78416i	2.15937	−	0.250775i
$533$	0.138092	−	0.495112i	0.00598142	−	0.0214457i
$534$	8.73562	−	25.1024i	0.378027	−	1.08629i
$535$	32.4788	+	18.7516i	1.40418	+	0.810704i
$536$	0.290703	+	6.83221i	0.0125565	+	0.295107i
$537$	−39.7788	+	22.9663i	−1.71658	+	0.991070i
$538$	29.9393	+	10.4189i	1.29078	+	0.449190i
$539$	6.12034	−	22.8414i	0.263622	−	0.983850i
$540$	−0.447985	+	3.04267i	−0.0192782	+	0.130936i
$541$	−13.1581	+	13.1581i	−0.565709	+	0.565709i	−0.930923	−	0.365214i	$-0.880996\pi$
$541$	−13.1581	+	13.1581i	−0.565709	+	0.565709i	0.365214	+	0.930923i	$0.380996\pi$
$542$	5.13208	−	7.55507i	0.220442	−	0.324518i
$543$	−21.5592	+	37.3417i	−0.925195	+	1.60249i
$544$	−2.48221	−	15.5654i	−0.106424	−	0.667360i
$545$	−27.9135			−1.19568
$546$	25.5927	−	36.8612i	1.09526	−	1.57751i
$547$	−10.3233	+	10.3233i	−0.441392	+	0.441392i	−0.892480	−	0.451087i	$-0.851036\pi$
$547$	−10.3233	+	10.3233i	−0.441392	+	0.441392i	0.451087	+	0.892480i	$0.351036\pi$
$548$	13.9138	−	5.51567i	0.594367	−	0.235618i
$549$	6.77002	−	1.81402i	0.288937	−	0.0774205i
$550$	−5.87648	−	30.7702i	−0.250574	−	1.31205i
$551$			8.33619i			0.355133i
$552$	20.7770	−	39.8044i	0.884329	−	1.69419i
$553$	−34.1095	+	19.6931i	−1.45048	+	0.837436i
$554$	14.4080	−	41.4025i	0.612139	−	1.75902i
$555$	−7.87977	+	29.4077i	−0.334478	+	1.24829i
$556$	12.2026	−	28.2314i	0.517507	−	1.19728i
$557$	−7.24872	−	27.0526i	−0.307138	−	1.14626i	−0.931089	−	0.364792i	$-0.881140\pi$
$557$	−7.24872	−	27.0526i	−0.307138	−	1.14626i	0.623951	−	0.781464i	$-0.285527\pi$
$558$	−14.6220	+	7.07235i	−0.618997	+	0.299396i
$559$	10.7566	+	0.109707i	0.454954	+	0.00464010i
$560$	41.0797	+	25.4224i	1.73593	+	1.07429i
$561$	12.5271	−	21.6975i	0.528894	−	0.916071i
$562$	3.31951	−	45.3346i	0.140025	−	1.91232i
$563$	19.4048	+	5.19950i	0.817815	+	0.219133i	0.643391	−	0.765538i	$-0.277527\pi$
$563$	19.4048	+	5.19950i	0.817815	+	0.219133i	0.174424	+	0.984671i	$0.444194\pi$
$564$	4.08381	+	35.1649i	0.171960	+	1.48071i
$565$	−8.05831	+	30.0740i	−0.339016	+	1.26522i
$566$	8.97339	−	1.71374i	0.377180	−	0.0720337i
$567$		−	34.8465i		−	1.46342i
$568$	−24.6105	+	7.72965i	−1.03263	+	0.324329i
$569$	−2.23116	−	1.28816i	−0.0935352	−	0.0540026i	0.452503	−	0.891763i	$-0.350531\pi$
$569$	−2.23116	−	1.28816i	−0.0935352	−	0.0540026i	−0.546038	+	0.837760i	$0.683865\pi$
$570$	−58.5560	+	50.5658i	−2.45264	+	2.11797i
$571$	−24.9092	−	24.9092i	−1.04242	−	1.04242i	−0.999060	−	0.0433595i	$-0.986194\pi$
$571$	−24.9092	−	24.9092i	−1.04242	−	1.04242i	−0.0433595	−	0.999060i	$-0.513806\pi$
$572$	9.66013	+	25.1132i	0.403910	+	1.05003i
$573$	−21.5030	+	21.5030i	−0.898302	+	0.898302i
$574$	−0.734326	−	0.0537692i	−0.0306502	−	0.00224428i
$575$	19.5538	−	33.8681i	0.815448	−	1.41240i
$576$	−22.3752	+	1.90753i	−0.932299	+	0.0794804i
$577$	11.3178			0.471166			0.235583	−	0.971854i	$-0.424300\pi$
$577$	11.3178			0.471166			0.235583	+	0.971854i	$0.424300\pi$
$578$	−7.33960	+	10.8048i	−0.305287	+	0.449421i
$579$	−8.68597	−	2.32740i	−0.360977	−	0.0967234i
$580$	−4.98624	+	6.29654i	−0.207042	+	0.261450i
$581$	−0.442563	+	1.65167i	−0.0183606	+	0.0685228i
$582$	−29.4171	+	25.4030i	−1.21938	+	1.05299i
$583$	−28.9112	−	16.6919i	−1.19738	−	0.691308i
$584$	−6.68400	+	29.9920i	−0.276586	+	1.24108i
$585$	−0.341347	+	33.4685i	−0.0141130	+	1.38375i
$586$	−12.7764	+	36.7137i	−0.527787	+	1.51663i
$587$	43.9722	−	11.7823i	1.81493	−	0.486309i	0.818789	−	0.574094i	$-0.194646\pi$
$587$	43.9722	−	11.7823i	1.81493	−	0.486309i	0.996139	+	0.0877856i	$0.0279790\pi$
$588$	−28.0368	−	12.1185i	−1.15622	−	0.499759i
$589$	27.1306	+	7.26963i	1.11790	+	0.299540i
$590$	−6.30488	+	3.04954i	−0.259568	+	0.125548i
$591$	−32.3568	−	56.0436i	−1.33098	−	2.30533i
$592$	15.2742	+	0.467059i	0.627765	+	0.0191960i
$593$	−43.9585			−1.80516			−0.902580	−	0.430522i	$-0.858329\pi$
$593$	−43.9585			−1.80516			−0.902580	+	0.430522i	$0.858329\pi$
$594$	2.02970	+	1.37876i	0.0832797	+	0.0565711i
$595$	8.70983	+	32.5055i	0.357068	+	1.33260i
$596$	−2.64924	+	6.12915i	−0.108517	+	0.251060i
$597$	−1.43558	−	1.43558i	−0.0587545	−	0.0587545i
$598$	−11.3631	+	31.6102i	−0.464670	+	1.29264i
$599$		−	19.5769i		−	0.799891i	−0.916539	−	0.399946i	$-0.869029\pi$
$599$		−	19.5769i		−	0.799891i	0.916539	−	0.399946i	$-0.130971\pi$
$600$	−40.4259	+	1.72008i	−1.65038	+	0.0702218i
$601$	37.8441	+	21.8493i	1.54369	+	0.891252i	0.998601	+	0.0528759i	$0.0168388\pi$
$601$	37.8441	+	21.8493i	1.54369	+	0.891252i	0.545092	+	0.838376i	$0.316495\pi$
$602$	−2.89057	−	15.1355i	−0.117811	−	0.616877i
$603$	4.79891	+	4.79891i	0.195427	+	0.195427i
$604$	−6.08465	+	41.3263i	−0.247581	+	1.68154i
$605$	−9.33672	−	2.50177i	−0.379592	−	0.101711i
$606$	−3.43779	−	7.10757i	−0.139651	−	0.288725i
$607$	10.8339	+	18.7648i	0.439734	+	0.761641i	0.997669	−	0.0682435i	$-0.0217395\pi$
$607$	10.8339	+	18.7648i	0.439734	+	0.761641i	−0.557935	+	0.829885i	$0.688406\pi$
$608$	31.4407	+	22.7922i	1.27509	+	0.924346i
$609$	5.34349	−	9.25520i	0.216529	−	0.375039i
$610$	−5.08466	−	10.5124i	−0.205872	−	0.425636i
$611$	−6.59330	−	25.6501i	−0.266737	−	1.03769i
$612$	−12.2633	−	9.71135i	−0.495716	−	0.392558i
$613$	−22.2681	+	5.96673i	−0.899402	+	0.240994i	−0.678759	−	0.734361i	$-0.737482\pi$
$613$	−22.2681	+	5.96673i	−0.899402	+	0.240994i	−0.220642	+	0.975355i	$0.570815\pi$
$614$	−29.2891	+	25.2925i	−1.18201	+	1.02072i
$615$	0.983889	−	0.568048i	0.0396742	−	0.0229059i
$616$	32.5298	−	20.6731i	1.31066	−	0.832942i
$617$	9.87594	−	5.70188i	0.397590	−	0.229549i	−0.287853	−	0.957674i	$-0.592942\pi$
$617$	9.87594	−	5.70188i	0.397590	−	0.229549i	0.685444	+	0.728126i	$0.259608\pi$
$618$	−29.0736	+	5.55247i	−1.16951	+	0.223353i
$619$	30.6367	+	30.6367i	1.23139	+	1.23139i	0.963429	+	0.267964i	$0.0863507\pi$
$619$	30.6367	+	30.6367i	1.23139	+	1.23139i	0.267964	+	0.963429i	$0.413649\pi$
$620$	16.1442	+	21.7190i	0.648367	+	0.872254i
$621$	0.792811	+	2.95881i	0.0318144	+	0.118733i
$622$	0.705693	−	9.63766i	0.0282957	−	0.386435i
$623$	28.4828			1.14114
$624$	33.9088	−	7.61942i	1.35744	−	0.305021i
$625$	19.4405			0.777621
$626$	1.49437	−	20.4087i	0.0597272	−	0.815695i
$627$	15.9759	+	59.6228i	0.638015	+	2.38110i
$628$	19.2496	−	14.3087i	0.768142	−	0.570978i
$629$	7.52703	+	7.52703i	0.300123	+	0.300123i
$630$	47.0934	−	8.99389i	1.87625	−	0.358325i
$631$	−25.5498	+	14.7512i	−1.01712	+	0.587236i	−0.913269	−	0.407356i	$-0.866451\pi$
$631$	−25.5498	+	14.7512i	−1.01712	+	0.587236i	−0.103854	+	0.994593i	$0.533117\pi$
$632$	−29.7733	−	6.63526i	−1.18432	−	0.263937i
$633$	2.31461	−	1.33634i	0.0919975	−	0.0531148i
$634$	−14.8842	+	12.8532i	−0.591128	+	0.510467i
$635$	−15.0454	+	4.03139i	−0.597057	+	0.159981i
$636$	−26.7696	+	33.8042i	−1.06148	+	1.34042i
$637$	22.0100	+	6.13881i	0.872066	+	0.243228i
$638$	2.79017	+	5.76863i	0.110464	+	0.228382i
$639$	−12.8004	+	22.1709i	−0.506376	+	0.877069i
$640$	10.1150	+	36.0216i	0.399831	+	1.42388i
$641$	−4.47481	−	7.75060i	−0.176744	−	0.306130i	0.764019	−	0.645194i	$-0.223223\pi$
$641$	−4.47481	−	7.75060i	−0.176744	−	0.306130i	−0.940764	+	0.339063i	$0.889890\pi$
$642$	−16.8280	−	34.7916i	−0.664149	−	1.37312i
$643$	−27.0746	−	7.25463i	−1.06772	−	0.286095i	−0.318164	−	0.948036i	$-0.603066\pi$
$643$	−27.0746	−	7.25463i	−1.06772	−	0.286095i	−0.749556	+	0.661941i	$0.769733\pi$
$644$	47.6036	+	7.00889i	1.87585	+	0.276189i
$645$	16.8123	+	16.8123i	0.661982	+	0.661982i
$646$	5.07443	+	26.5705i	0.199651	+	1.04540i
$647$	12.1204	+	6.99773i	0.476503	+	0.275109i	0.718958	−	0.695054i	$-0.244619\pi$
$647$	12.1204	+	6.99773i	0.476503	+	0.275109i	−0.242455	+	0.970163i	$0.577953\pi$
$648$	18.2548	−	19.8773i	0.717116	−	0.780853i
$649$			5.58773i			0.219338i
$650$	29.7893	−	5.37486i	1.16843	−	0.210819i
$651$	−25.4618	−	25.4618i	−0.997926	−	0.997926i
$652$	11.1428	+	4.81631i	0.436385	+	0.188621i
$653$	−8.83272	−	32.9642i	−0.345651	−	1.28999i	−0.891850	−	0.452332i	$-0.850592\pi$
$653$	−8.83272	−	32.9642i	−0.345651	−	1.28999i	0.546198	−	0.837656i	$-0.316074\pi$
$654$	23.7946	+	16.1634i	0.930442	+	0.632040i
$655$	0.489816			0.0191387
$656$	−0.390709	−	0.415357i	−0.0152546	−	0.0162170i
$657$	15.2477	+	26.4098i	0.594870	+	1.03035i
$658$	−34.1519	+	16.5186i	−1.33138	+	0.643962i
$659$	−19.8239	−	5.31180i	−0.772230	−	0.206918i	−0.148874	−	0.988856i	$-0.547565\pi$
$659$	−19.8239	−	5.31180i	−0.772230	−	0.206918i	−0.623356	+	0.781938i	$0.714231\pi$
$660$	−23.5960	+	54.5905i	−0.918472	+	2.12493i
$661$	−5.23300	+	1.40218i	−0.203540	+	0.0545384i	−0.359148	−	0.933280i	$-0.616933\pi$
$661$	−5.23300	+	1.40218i	−0.203540	+	0.0545384i	0.155609	+	0.987819i	$0.450266\pi$
$662$	−3.78457	+	10.8752i	−0.147092	+	0.422678i
$663$	20.8416	+	12.3180i	0.809419	+	0.478391i
$664$	−1.11770	+	0.710308i	−0.0433750	+	0.0275653i
$665$	−71.8013	−	41.4545i	−2.78434	−	1.60754i
$666$	11.4783	−	9.91206i	0.444776	−	0.384085i
$667$	−2.07047	+	7.72708i	−0.0801687	+	0.299194i
$668$	−10.0180	−	7.93329i	−0.387609	−	0.306948i
$669$	−32.3313	−	8.66316i	−1.25000	−	0.334937i
$670$	6.35372	−	9.35348i	0.245466	−	0.361356i
$671$	−9.31670			−0.359667
$672$	−20.2971	−	45.4584i	−0.782977	−	1.75360i
$673$	−20.3005	+	35.1615i	−0.782527	+	1.35538i	0.147938	+	0.988997i	$0.452736\pi$
$673$	−20.3005	+	35.1615i	−0.782527	+	1.35538i	−0.930465	+	0.366380i	$0.880597\pi$
$674$	−16.8402	−	1.23308i	−0.648662	−	0.0474966i
$675$	1.95190	−	1.95190i	0.0751286	−	0.0751286i
$676$	−24.3605	+	9.08651i	−0.936943	+	0.349481i
$677$	−0.547336	−	0.547336i	−0.0210358	−	0.0210358i	0.696511	−	0.717546i	$-0.254735\pi$
$677$	−0.547336	−	0.547336i	−0.0210358	−	0.0210358i	−0.717546	+	0.696511i	$0.754735\pi$
$678$	24.2837	−	20.9701i	0.932610	−	0.805352i
$679$	−36.0712	−	20.8257i	−1.38428	−	0.799217i
$680$	−12.0601	+	23.1047i	−0.462485	+	0.886023i
$681$		−	29.2517i		−	1.12093i
$682$	21.2075	−	4.05021i	0.812079	−	0.155091i
$683$	−3.52328	+	13.1491i	−0.134815	+	0.503135i	0.865184	+	0.501455i	$0.167202\pi$
$683$	−3.52328	+	13.1491i	−0.134815	+	0.503135i	−0.999999	+	0.00168044i	$0.999465\pi$
$684$	38.2821	−	4.44583i	1.46375	−	0.169990i
$685$	−23.9052	−	6.40538i	−0.913371	−	0.244737i
$686$	−0.249891	+	3.41276i	−0.00954088	+	0.130300i
$687$	−12.8135	+	22.1936i	−0.488864	+	0.846737i
$688$	6.28008	−	10.1479i	0.239426	−	0.386885i
$689$	16.4133	−	27.7706i	0.625296	−	1.05798i
$690$	−66.8365	+	32.3275i	−2.54442	+	1.23069i
$691$	6.56734	+	24.5096i	0.249833	+	0.932391i	0.970892	+	0.239517i	$0.0769891\pi$
$691$	6.56734	+	24.5096i	0.249833	+	0.932391i	−0.721059	+	0.692874i	$0.756344\pi$
$692$	−4.45286	−	1.92469i	−0.169272	−	0.0731656i
$693$	9.90025	−	36.9482i	0.376079	−	1.40355i
$694$	5.79498	−	16.6523i	0.219975	−	0.632112i
$695$	−44.0419	+	25.4276i	−1.67061	+	0.964524i
$696$	7.89650	−	2.48012i	0.299316	−	0.0940089i
$697$		−	0.397225i		−	0.0150460i
$698$	7.28598	+	38.1505i	0.275778	+	1.44402i
$699$	19.7751	−	5.29873i	0.747964	−	0.200416i
$700$	−15.9792	−	40.3090i	−0.603957	−	1.52354i
$701$	−17.3322	+	17.3322i	−0.654629	+	0.654629i	−0.954104	−	0.299475i	$-0.903189\pi$
$701$	−17.3322	+	17.3322i	−0.654629	+	0.654629i	0.299475	+	0.954104i	$0.403189\pi$
$702$	−1.35221	+	1.94759i	−0.0510359	+	0.0735071i
$703$	−26.2257			−0.989121
$704$	29.3856	+	5.24877i	1.10751	+	0.197820i
$705$	29.2683	−	50.6942i	1.10231	−	1.90925i
$706$	27.6927	−	40.7671i	1.04223	−	1.53429i
$707$	5.98272	−	5.98272i	0.225003	−	0.225003i
$708$	7.14038	+	1.05131i	0.268352	+	0.0395106i
$709$	−2.81472	+	10.5047i	−0.105709	+	0.394511i	−0.998425	−	0.0561091i	$-0.982131\pi$
$709$	−2.81472	+	10.5047i	−0.105709	+	0.394511i	0.892716	+	0.450620i	$0.148797\pi$
$710$	40.2843	+	14.0189i	1.51184	+	0.526120i
$711$	−26.2172	+	15.1365i	−0.983223	+	0.567664i
$712$	16.2472	+	14.9211i	0.608891	+	0.559190i
$713$	23.3427	+	13.4769i	0.874191	+	0.504714i
$714$	11.3978	−	32.7525i	0.426553	−	1.22573i
$715$	11.9529	−	42.8556i	0.447013	−	1.60271i
$716$	−4.39765	−	37.8673i	−0.164348	−	1.41517i
$717$	−2.19124	−	8.17780i	−0.0818332	−	0.305406i
$718$	0.427371	−	5.83661i	0.0159493	−	0.217820i
$719$	−8.88267	−	15.3852i	−0.331268	−	0.573772i	0.651493	−	0.758655i	$-0.274143\pi$
$719$	−8.88267	−	15.3852i	−0.331268	−	0.573772i	−0.982761	+	0.184882i	$0.940810\pi$
$720$	31.5747	+	19.5402i	1.17672	+	0.728219i
$721$	−15.8596	−	27.4696i	−0.590642	−	1.02302i
$722$	−32.9018	−	22.3499i	−1.22448	−	0.831776i
$723$	−8.75416	+	8.75416i	−0.325571	+	0.325571i
$724$	−21.3488	−	28.7208i	−0.793422	−	1.06740i
$725$	6.96329	−	1.86581i	0.258610	−	0.0692944i
$726$	6.51034	+	7.53907i	0.241621	+	0.279801i
$727$		−	5.81246i		−	0.215572i	−0.994174	−	0.107786i	$-0.965624\pi$
$727$		−	5.81246i		−	0.215572i	0.994174	−	0.107786i	$-0.0343762\pi$
$728$	19.6546	+	31.6353i	0.728446	+	1.17248i
$729$		−	23.4222i		−	0.867490i
$730$	38.4551	−	33.2078i	1.42329	−	1.22907i
$731$	8.02983	−	2.15159i	0.296994	−	0.0795793i
$732$	−1.75290	+	11.9055i	−0.0647890	+	0.440040i
$733$	10.6617	−	10.6617i	0.393797	−	0.393797i	−0.482241	−	0.876038i	$-0.660177\pi$
$733$	10.6617	−	10.6617i	0.393797	−	0.393797i	0.876038	+	0.482241i	$0.160177\pi$
$734$	−14.7672	+	21.7392i	−0.545068	+	0.802409i
$735$	25.2523	+	43.7383i	0.931446	+	1.61331i
$736$	23.4825	+	28.9358i	0.865577	+	1.06659i
$737$	−4.51070	−	7.81275i	−0.166154	−	0.287787i
$738$	−0.564419	−	0.0413282i	−0.0207765	−	0.00152131i
$739$	1.81200	+	6.76247i	0.0666554	+	0.248761i	0.991212	−	0.132284i	$-0.0422309\pi$
$739$	1.81200	+	6.76247i	0.0666554	+	0.248761i	−0.924556	+	0.381045i	$0.875564\pi$
$740$	−19.8090	−	15.6867i	−0.728192	−	0.576656i
$741$	−57.7673	+	14.8489i	−2.12213	+	0.545490i
$742$	−43.6415	−	15.1872i	−1.60213	−	0.557540i
$743$	26.4580	+	15.2755i	0.970649	+	0.560404i	0.899434	−	0.437057i	$-0.143979\pi$
$743$	26.4580	+	15.2755i	0.970649	+	0.560404i	0.0712146	+	0.997461i	$0.477312\pi$
$744$	−1.18552	−	27.8625i	−0.0434631	−	1.02149i
$745$	9.56166	−	5.52043i	0.350312	−	0.202253i
$746$	−7.50697	+	21.5718i	−0.274850	+	0.789800i
$747$	−0.340164	+	1.26951i	−0.0124459	+	0.0464489i
$748$	12.4048	+	16.6883i	0.453565	+	0.610186i
$749$	29.2855	−	29.2855i	1.07007	−	1.07007i
$750$	8.73062	+	5.93062i	0.318797	+	0.216556i
$751$	14.1774	−	24.5560i	0.517341	−	0.896061i	−0.482456	−	0.875920i	$-0.660255\pi$
$751$	14.1774	−	24.5560i	0.517341	−	0.896061i	0.999797	−	0.0201407i	$-0.00641142\pi$
$752$	−28.1345	−	8.46831i	−1.02596	−	0.308807i
$753$	22.6063			0.823820
$754$	−5.60137	+	2.63912i	−0.203990	+	0.0961112i
$755$	48.8402	−	48.8402i	1.77748	−	1.77748i
$756$	3.11756	+	1.34752i	0.113385	+	0.0490089i
$757$	−12.6239	+	3.38255i	−0.458822	+	0.122941i	−0.480824	−	0.876817i	$-0.659663\pi$
$757$	−12.6239	+	3.38255i	−0.458822	+	0.122941i	0.0220023	+	0.999758i	$0.492996\pi$
$758$	33.3345	−	6.36622i	1.21076	−	0.231232i
$759$			59.2342i			2.15007i
$760$	−19.2407	−	61.2606i	−0.697933	−	2.22216i
$761$	−23.2880	+	13.4453i	−0.844189	+	0.487393i	−0.858686	−	0.512502i	$-0.828719\pi$
$761$	−23.2880	+	13.4453i	−0.844189	+	0.487393i	0.0144972	+	0.999895i	$0.495385\pi$
$762$	15.1597	+	5.27555i	0.549177	+	0.191113i
$763$	−7.97826	+	29.7753i	−0.288832	+	1.07794i
$764$	−9.30093	−	23.4624i	−0.336496	−	0.848840i
$765$	6.69456	+	24.9844i	0.242042	+	0.903314i
$766$	−3.30023	−	6.82317i	−0.119242	−	0.246531i
$767$	−5.39908	−	0.0550655i	−0.194950	−	0.00198830i
$768$	12.2360	−	36.5634i	0.441529	−	1.31937i
$769$	0.556208	−	0.963381i	0.0200574	−	0.0347404i	−0.855822	−	0.517270i	$-0.826948\pi$
$769$	0.556208	−	0.963381i	0.0200574	−	0.0347404i	0.875880	+	0.482529i	$0.160282\pi$
$770$	−63.5615	−	4.65413i	−2.29060	−	0.167723i
$771$	11.7355	+	3.14453i	0.422645	+	0.113247i
$772$	4.63329	−	5.85085i	0.166756	−	0.210577i
$773$	−11.3874	+	42.4985i	−0.409578	+	1.52857i	0.385875	+	0.922551i	$0.373900\pi$
$773$	−11.3874	+	42.4985i	−0.409578	+	1.52857i	−0.795453	+	0.606015i	$0.792767\pi$
$774$	−2.22176	−	11.6335i	−0.0798594	−	0.418156i
$775$		−	24.2896i		−	0.872507i
$776$	−9.66603	−	30.7758i	−0.346990	−	1.10479i
$777$	29.1169	+	16.8107i	1.04456	+	0.603079i
$778$	−14.4220	−	16.7009i	−0.517053	−	0.598755i
$779$	0.692007	+	0.692007i	0.0247937	+	0.0247937i
$780$	−52.5149	−	23.3373i	−1.88034	−	0.835610i
$781$	24.0633	−	24.0633i	0.861051	−	0.861051i
$782$	−1.89569	+	25.8894i	−0.0677897	+	0.925804i
$783$	−0.282328	+	0.489006i	−0.0100896	+	0.0174757i
$784$	18.4645	−	17.3688i	0.659447	−	0.620314i
$785$	−39.6598			−1.41552
$786$	−0.417538	−	0.283630i	−0.0148931	−	0.0101167i
$787$	−11.2513	−	3.01478i	−0.401067	−	0.107465i	0.0526467	−	0.998613i	$-0.483234\pi$
$787$	−11.2513	−	3.01478i	−0.401067	−	0.107465i	−0.453713	+	0.891148i	$0.649901\pi$
$788$	53.3506	−	6.19577i	1.90053	−	0.220715i
$789$	11.0190	−	41.1233i	0.392285	−	1.46403i
$790$	32.9656	+	38.1747i	1.17286	+	1.35819i
$791$	29.7767	+	17.1916i	1.05874	+	0.611261i
$792$	25.0031	−	15.8898i	0.888447	−	0.564618i
$793$	0.0918133	−	9.00216i	0.00326039	−	0.319676i
$794$	5.85523	+	2.03762i	0.207794	+	0.0723124i
$795$	68.8702	−	18.4537i	2.44257	−	0.654486i
$796$	1.56639	−	0.620947i	0.0555194	−	0.0220089i
$797$	9.96647	+	2.67051i	0.353030	+	0.0945942i	0.430976	−	0.902363i	$-0.358169\pi$
$797$	9.96647	+	2.67051i	0.353030	+	0.0945942i	−0.0779455	+	0.996958i	$0.524836\pi$
$798$	37.2019	+	76.9143i	1.31693	+	2.72274i
$799$	−10.2334	−	17.7247i	−0.362031	−	0.627056i
$800$	12.0015	−	31.3641i	0.424316	−	1.10889i
$801$	21.8925			0.773532
$802$	−14.4892	+	21.3299i	−0.511631	+	0.753185i
$803$	−10.4917	−	39.1557i	−0.370245	−	1.38177i
$804$	−10.8323	+	4.29413i	−0.382027	+	0.151442i
$805$	−56.2589	−	56.2589i	−1.98287	−	1.98287i
$806$	3.70448	+	20.5315i	0.130485	+	0.723190i
$807$			54.0166i			1.90148i
$808$	6.54680	−	0.278559i	0.230316	−	0.00979968i
$809$	26.6642	+	15.3946i	0.937463	+	0.541245i	0.889164	−	0.457588i	$-0.151287\pi$
$809$	26.6642	+	15.3946i	0.937463	+	0.541245i	0.0482991	+	0.998833i	$0.484620\pi$
$810$	−43.8327	+	8.37115i	−1.54012	+	0.294132i
$811$	34.8062	+	34.8062i	1.22221	+	1.22221i	0.966844	+	0.255369i	$0.0821970\pi$
$811$	34.8062	+	34.8062i	1.22221	+	1.22221i	0.255369	+	0.966844i	$0.417803\pi$
$812$	5.29133	+	7.11849i	0.185689	+	0.249810i
$813$	15.0326	+	4.02798i	0.527217	+	0.141267i
$814$	−18.1481	+	8.77790i	−0.636092	+	0.307665i
$815$	−10.0361	−	17.3831i	−0.351550	−	0.608903i
$816$	23.6594	−	12.7119i	0.828244	−	0.445004i
$817$	−10.2405	+	17.7371i	−0.358270	+	0.620541i
$818$	−27.3903	+	13.2482i	−0.957681	+	0.463211i
$819$	35.6032	+	9.93012i	1.24408	+	0.346986i
$820$	0.108772	+	0.936610i	0.00379847	+	0.0327078i
$821$	−13.2634	+	3.55391i	−0.462894	+	0.124032i	−0.482727	−	0.875771i	$-0.660354\pi$
$821$	−13.2634	+	3.55391i	−0.462894	+	0.124032i	0.0198321	+	0.999803i	$0.493687\pi$
$822$	16.6687	+	19.3026i	0.581387	+	0.673255i
$823$	−24.3305	+	14.0472i	−0.848107	+	0.489655i	−0.860012	−	0.510274i	$-0.829544\pi$
$823$	−24.3305	+	14.0472i	−0.848107	+	0.489655i	0.0119046	+	0.999929i	$0.496211\pi$
$824$	5.34362	−	23.9775i	0.186154	−	0.835297i
$825$	46.2277	−	26.6896i	1.60944	−	0.929212i
$826$	1.45088	+	7.59702i	0.0504825	+	0.264334i
$827$	−8.95549	−	8.95549i	−0.311413	−	0.311413i	0.534044	−	0.845457i	$-0.320672\pi$
$827$	−8.95549	−	8.95549i	−0.311413	−	0.311413i	−0.845457	+	0.534044i	$0.820672\pi$
$828$	36.5892	+	5.38718i	1.27156	+	0.187218i
$829$	4.06744	+	15.1799i	0.141268	+	0.527220i	0.999893	+	0.0146157i	$0.00465249\pi$
$829$	4.06744	+	15.1799i	0.141268	+	0.527220i	−0.858625	+	0.512604i	$0.828681\pi$
$830$	2.18392	+	0.159912i	0.0758048	+	0.00555062i
$831$	74.6985			2.59126
$832$	−5.36115	+	28.3418i	−0.185864	+	0.982575i
$833$	17.6585			0.611829
$834$	52.2670	+	3.82712i	1.80986	+	0.132522i
$835$	5.46885	+	20.4100i	0.189257	+	0.706318i
$836$	−50.6832	−	7.46231i	−1.75291	−	0.258089i
$837$	1.34529	+	1.34529i	0.0465002	+	0.0465002i
$838$	−3.31224	−	17.3434i	−0.114420	−	0.599119i
$839$	39.9019	−	23.0374i	1.37757	−	0.795338i	0.385700	−	0.922624i	$-0.373960\pi$
$839$	39.9019	−	23.0374i	1.37757	−	0.795338i	0.991866	+	0.127286i	$0.0406265\pi$
$840$	−17.9062	+	80.3475i	−0.617823	+	2.77225i
$841$	23.8377	−	13.7627i	0.821989	−	0.474575i
$842$	34.0566	+	39.4381i	1.17367	+	1.35913i
$843$	74.8164	−	20.0470i	2.57681	−	0.690455i
$844$	0.255886	+	2.20339i	0.00880797	+	0.0758437i
$845$	41.2910	+	11.9717i	1.42045	+	0.411838i
$846$	−26.2499	+	12.6965i	−0.902489	+	0.436516i
$847$	−5.33726	+	9.24440i	−0.183390	+	0.317641i
$848$	−16.9381	−	31.5253i	−0.581657	−	1.08258i
$849$	7.78338	+	13.4812i	0.267125	+	0.462674i
$850$	21.0588	−	10.1857i	0.722313	−	0.349368i
$851$	−24.3095	−	6.51370i	−0.833318	−	0.223287i
$852$	−26.2222	−	35.2771i	−0.898359	−	1.20857i
$853$	−37.7165	−	37.7165i	−1.29139	−	1.29139i	−0.933929	−	0.357458i	$-0.883644\pi$
$853$	−37.7165	−	37.7165i	−1.29139	−	1.29139i	−0.357458	−	0.933929i	$-0.616356\pi$
$854$	−12.6669	+	2.41912i	−0.433452	+	0.0827805i
$855$	−55.1880	−	31.8628i	−1.88739	−	1.08969i
$856$	32.0467	−	1.36355i	1.09533	−	0.0466052i
$857$		−	9.46712i		−	0.323391i	−0.986841	−	0.161695i	$-0.948304\pi$
$857$		−	9.46712i		−	0.323391i	0.986841	−	0.161695i	$-0.0516962\pi$
$858$	−35.0048	+	29.6105i	−1.19505	+	1.01089i
$859$	−8.81388	−	8.81388i	−0.300726	−	0.300726i	0.540572	−	0.841298i	$-0.318208\pi$
$859$	−8.81388	−	8.81388i	−0.300726	−	0.300726i	−0.841298	+	0.540572i	$0.818208\pi$
$860$	−18.3442	+	7.27198i	−0.625533	+	0.247972i
$861$	−0.324720	−	1.21187i	−0.0110664	−	0.0413005i
$862$	−5.51603	+	8.12029i	−0.187877	+	0.276578i
$863$	−36.6455			−1.24743			−0.623714	−	0.781653i	$-0.714377\pi$
$863$	−36.6455			−1.24743			−0.623714	+	0.781653i	$0.714377\pi$
$864$	1.07241	+	2.40183i	0.0364843	+	0.0817120i
$865$	4.01062	+	6.94661i	0.136365	+	0.236192i
$866$	7.78102	+	16.0871i	0.264410	+	0.546663i
$867$	−21.4987	−	5.76057i	−0.730136	−	0.195639i
$868$	27.7819	−	11.0132i	0.942979	−	0.373814i
$869$	38.8701	−	10.4152i	1.31858	−	0.353312i
$870$	−12.9256	−	4.49809i	−0.438218	−	0.152500i
$871$	7.59344	−	4.28142i	0.257294	−	0.145070i
$872$	−20.1491	+	12.8050i	−0.682336	+	0.433632i
$873$	−27.7251	−	16.0071i	−0.938351	−	0.541757i
$874$	−41.7995	−	48.4045i	−1.41389	−	1.63731i
$875$	−2.92735	+	10.9250i	−0.0989626	+	0.369333i
$876$	−52.0097	+	6.04005i	−1.75725	+	0.204075i
$877$	40.6721	+	10.8981i	1.37340	+	0.368001i	0.868719	−	0.495305i	$-0.164944\pi$
$877$	40.6721	+	10.8981i	1.37340	+	0.368001i	0.504681	+	0.863306i	$0.331610\pi$
$878$	0.173674	+	0.117975i	0.00586121	+	0.00398146i
$879$	−66.2390			−2.23419
$880$	−33.8188	−	35.9523i	−1.14003	−	1.21195i
$881$	2.72997	−	4.72845i	0.0919750	−	0.159305i	−0.816367	−	0.577533i	$-0.804015\pi$
$881$	2.72997	−	4.72845i	0.0919750	−	0.159305i	0.908342	+	0.418228i	$0.137349\pi$
$882$	1.83722	−	25.0910i	0.0618625	−	0.844857i
$883$	−17.0761	+	17.0761i	−0.574657	+	0.574657i	−0.933426	−	0.358769i	$-0.883197\pi$
$883$	−17.0761	+	17.0761i	−0.574657	+	0.574657i	0.358769	+	0.933426i	$0.383197\pi$
$884$	−16.2472	+	11.8216i	−0.546451	+	0.397602i
$885$	−8.43864	−	8.43864i	−0.283662	−	0.283662i
$886$	−35.8448	−	41.5089i	−1.20423	−	1.39452i
$887$	−5.61724	−	3.24312i	−0.188609	−	0.108893i	0.402722	−	0.915322i	$-0.368064\pi$
$887$	−5.61724	−	3.24312i	−0.188609	−	0.108893i	−0.591331	+	0.806429i	$0.701397\pi$
$888$	7.80249	+	24.8425i	0.261834	+	0.833658i
$889$			17.2011i			0.576907i
$890$	−6.84239	−	35.8278i	−0.229357	−	1.20095i
$891$	−9.21476	+	34.3900i	−0.308706	+	1.15211i
$892$	17.2463	−	21.7783i	0.577448	−	0.729192i
$893$	48.7059	+	13.0507i	1.62988	+	0.436725i
$894$	−11.3474	−	0.830883i	−0.379513	−	0.0277889i
$895$	−31.5176	+	54.5900i	−1.05352	+	1.82474i
$896$	41.3153	−	0.493923i	1.38025	−	0.0165008i
$897$	−57.2344	−	0.583736i	−1.91100	−	0.0194904i
$898$	6.09757	+	12.6066i	0.203479	+	0.420688i
$899$	1.28596	+	4.79926i	0.0428891	+	0.160064i
$900$	−12.2820	−	30.9823i	−0.409399	−	1.03274i
$901$	6.45216	−	24.0798i	0.214953	−	0.802214i
$902$	0.710486	+	0.247249i	0.0236566	+	0.00823248i
$903$	22.7389	−	13.1283i	0.756703	−	0.436883i
$904$	7.97928	+	25.4053i	0.265387	+	0.844969i
$905$			59.1732i			1.96698i
$906$	−69.9145	+	13.3522i	−2.32275	+	0.443598i
$907$	40.4610	−	10.8415i	1.34349	−	0.359986i	0.485760	−	0.874092i	$-0.338543\pi$
$907$	40.4610	−	10.8415i	1.34349	−	0.359986i	0.857727	+	0.514106i	$0.171876\pi$
$908$	22.2849	+	9.63231i	0.739549	+	0.319660i
$909$	4.59844	−	4.59844i	0.152521	−	0.152521i
$910$	5.12338	−	61.3697i	0.169838	−	2.03439i
$911$	−27.7840			−0.920525			−0.460263	−	0.887783i	$-0.652245\pi$
$911$	−27.7840			−0.920525			−0.460263	+	0.887783i	$0.652245\pi$
$912$	−19.0717	+	63.3624i	−0.631527	+	2.09814i
$913$	0.873529	−	1.51300i	0.0289096	−	0.0500729i
$914$	46.8240	+	31.8070i	1.54880	+	1.05208i
$915$	14.0702	−	14.0702i	0.465145	−	0.465145i
$916$	−12.6884	−	17.0698i	−0.419236	−	0.564003i
$917$	0.139999	−	0.522485i	0.00462319	−	0.0172540i
$918$	−0.602215	+	1.73050i	−0.0198760	+	0.0571152i
$919$	32.2776	−	18.6355i	1.06474	−	0.614729i	0.138001	−	0.990432i	$-0.455932\pi$
$919$	32.2776	−	18.6355i	1.06474	−	0.614729i	0.926740	+	0.375703i	$0.122599\pi$
$920$	−2.61945	−	61.5633i	−0.0863607	−	2.02968i
$921$	−57.1065	−	32.9705i	−1.88172	−	1.08641i
$922$	−11.2700	−	3.92196i	−0.371159	−	0.129163i
$923$	23.0137	+	23.4880i	0.757506	+	0.773116i
$924$	51.4873	+	40.7729i	1.69381	+	1.34133i
$925$	5.86985	+	21.9066i	0.192999	+	0.720284i
$926$	−29.7593	−	2.17905i	−0.977952	−	0.0716081i
$927$	−12.1900	−	21.1137i	−0.400373	−	0.693466i
$928$	−0.710809	+	6.83248i	−0.0233334	+	0.224287i
$929$	−2.54306	−	4.40470i	−0.0834350	−	0.144514i	0.821288	−	0.570513i	$-0.193256\pi$
$929$	−2.54306	−	4.40470i	−0.0834350	−	0.144514i	−0.904723	+	0.426000i	$0.859922\pi$
$930$	−25.9111	+	38.1445i	−0.849660	+	1.25081i
$931$	−30.7628	+	30.7628i	−1.00821	+	1.00821i
$932$	−2.47503	+	16.8101i	−0.0810723	+	0.550634i
$933$	15.9052	−	4.26178i	0.520712	−	0.139524i
$934$	21.1778	−	18.2880i	0.692957	−	0.598401i
$935$		−	34.3828i		−	1.12444i
$936$	15.1069	+	24.3156i	0.493785	+	0.794780i
$937$		−	8.61858i		−	0.281557i	−0.990041	−	0.140778i	$-0.955040\pi$
$937$		−	8.61858i		−	0.281557i	0.990041	−	0.140778i	$-0.0449605\pi$
$938$	−8.16131	−	9.45092i	−0.266476	−	0.308583i
$939$	33.6808	−	9.02474i	1.09913	−	0.294511i
$940$	28.9826	+	38.9906i	0.945310	+	1.27173i
$941$	26.1193	−	26.1193i	0.851464	−	0.851464i	−0.138850	−	0.990313i	$-0.544340\pi$
$941$	26.1193	−	26.1193i	0.851464	−	0.851464i	0.990313	+	0.138850i	$0.0443405\pi$
$942$	33.8076	+	22.9651i	1.10151	+	0.748245i
$943$	0.469569	+	0.813318i	0.0152913	+	0.0264853i
$944$	−3.15218	+	5.09358i	−0.102595	+	0.165782i
$945$	−2.80794	−	4.86350i	−0.0913424	−	0.158210i
$946$	−1.14971	+	15.7016i	−0.0373802	+	0.510502i
$947$	−0.844658	−	3.15231i	−0.0274477	−	0.102436i	0.950843	−	0.309673i	$-0.100220\pi$
$947$	−0.844658	−	3.15231i	−0.0274477	−	0.102436i	−0.978291	+	0.207237i	$0.933553\pi$
$948$	−5.99601	−	51.6305i	−0.194741	−	1.67688i
$949$	37.9371	−	9.75165i	1.23149	−	0.316552i
$950$	−18.9420	+	54.4312i	−0.614561	+	1.76598i
$951$	−29.0206	−	16.7550i	−0.941056	−	0.543319i
$952$	21.1986	+	19.4683i	0.687052	+	0.630972i
$953$	−26.3291	+	15.2011i	−0.852883	+	0.492412i	−0.861623	−	0.507550i	$-0.830551\pi$
$953$	−26.3291	+	15.2011i	−0.852883	+	0.492412i	0.00873957	+	0.999962i	$0.497218\pi$
$954$	−33.5438	−	11.6732i	−1.08602	−	0.377934i
$955$	−10.8012	+	40.3107i	−0.349519	+	1.30442i
$956$	6.95166	+	1.02352i	0.224833	+	0.0331031i
$957$	−7.72090	+	7.72090i	−0.249581	+	0.249581i
$958$	25.8244	−	38.0167i	0.834347	−	1.22826i
$959$	−13.6652	+	23.6688i	−0.441272	+	0.764306i
$960$	−52.3051	+	36.4517i	−1.68814	+	1.17647i
$961$	−14.2591			−0.459970
$962$	−8.30270	−	17.6219i	−0.267690	−	0.568154i
$963$	22.5094	−	22.5094i	0.725356	−	0.725356i
$964$	−3.78653	−	9.55186i	−0.121956	−	0.307645i
$965$	−11.9201	+	3.19398i	−0.383722	+	0.102818i
$966$	15.3804	+	80.5342i	0.494856	+	2.59115i
$967$		−	15.2093i		−	0.489098i	−0.969637	−	0.244549i	$-0.921360\pi$
$967$		−	15.2093i		−	0.489098i	0.969637	−	0.244549i	$-0.0786399\pi$
$968$	−7.88729	+	2.47723i	−0.253507	+	0.0796212i
$969$	−39.9183	+	23.0469i	−1.28236	+	0.740372i
$970$	−17.5308	+	50.3761i	−0.562881	+	1.61748i
$971$	11.3040	−	42.1871i	0.362763	−	1.35385i	−0.507666	−	0.861554i	$-0.669492\pi$
$971$	11.3040	−	42.1871i	0.362763	−	1.35385i	0.870428	−	0.492295i	$-0.163842\pi$
$972$	39.6511	+	17.1386i	1.27181	+	0.549722i
$973$	14.5355	+	54.2471i	0.465986	+	1.73908i
$974$	−35.1367	+	16.9949i	−1.12585	+	0.544553i
$975$	25.3330	+	44.9300i	0.811304	+	1.43891i
$976$	−8.49277	−	5.25579i	−0.271847	−	0.168234i
$977$	22.9985	−	39.8345i	0.735786	−	1.27442i	−0.218591	−	0.975817i	$-0.570146\pi$
$977$	22.9985	−	39.8345i	0.735786	−	1.27442i	0.954377	−	0.298603i	$-0.0965206\pi$
$978$	−1.51054	+	20.6295i	−0.0483019	+	0.659659i
$979$	−28.1096	−	7.53194i	−0.898386	−	0.240722i
$980$	−41.6366	+	4.83539i	−1.33003	+	0.154461i
$981$	−6.13226	+	22.8859i	−0.195788	+	0.730691i
$982$	57.8899	−	11.0558i	1.84734	−	0.352805i
$983$		−	35.1499i		−	1.12111i	−0.828118	−	0.560553i	$-0.810588\pi$
$983$		−	35.1499i		−	1.12111i	0.828118	−	0.560553i	$-0.189412\pi$
$984$	0.449626	−	0.861388i	0.0143336	−	0.0274601i
$985$	−76.9109	−	44.4045i	−2.45058	−	1.41485i
$986$	−3.62166	+	3.12747i	−0.115337	+	0.0995990i
$987$	−45.7099	−	45.7099i	−1.45496	−	1.45496i
$988$	7.70984	−	48.8985i	0.245283	−	1.55567i
$989$	−13.8976	+	13.8976i	−0.441918	+	0.441918i
$990$	−48.8547	−	3.57726i	−1.55270	−	0.113693i
$991$	11.4614	−	19.8518i	0.364085	−	0.630613i	−0.624544	−	0.780990i	$-0.714715\pi$
$991$	11.4614	−	19.8518i	0.364085	−	0.630613i	0.988629	+	0.150376i	$0.0480485\pi$
$992$	21.6169	+	8.27169i	0.686336	+	0.262626i
$993$	−19.6211			−0.622658
$994$	26.4680	−	38.9643i	0.839515	−	1.23587i
$995$	−2.69121	−	0.721109i	−0.0853172	−	0.0228607i
$996$	−1.76906	−	1.40092i	−0.0560548	−	0.0443898i
$997$	−3.17660	+	11.8552i	−0.100604	+	0.375459i	−0.997809	−	0.0661544i	$-0.978927\pi$
$997$	−3.17660	+	11.8552i	−0.100604	+	0.375459i	0.897205	+	0.441613i	$0.145594\pi$
$998$	35.6020	−	30.7440i	1.12696	−	0.973184i
$999$	−1.53842	−	0.888206i	−0.0486734	−	0.0281016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.bj.a.165.1	yes	104
4.3	odd	2		832.2.br.a.113.23		104
13.3	even	3	inner	208.2.bj.a.133.18	yes	104
16.3	odd	4		832.2.br.a.529.4		104
16.13	even	4	inner	208.2.bj.a.61.18	yes	104
52.3	odd	6		832.2.br.a.497.4		104
208.3	odd	12		832.2.br.a.81.23		104
208.29	even	12	inner	208.2.bj.a.29.1	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.bj.a.29.1	✓	104	208.29	even	12	inner
208.2.bj.a.61.18	yes	104	16.13	even	4	inner
208.2.bj.a.133.18	yes	104	13.3	even	3	inner
208.2.bj.a.165.1	yes	104	1.1	even	1	trivial
832.2.br.a.81.23		104	208.3	odd	12
832.2.br.a.113.23		104	4.3	odd	2
832.2.br.a.497.4		104	52.3	odd	6
832.2.br.a.529.4		104	16.3	odd	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.bj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41044 - 0.103276i) q^{2} +(-0.623697 - 2.32767i) q^{3} +(1.97867 + 0.291328i) q^{4} +(-2.33843 - 2.33843i) q^{5} +(0.639294 + 3.34744i) q^{6} +(-3.16277 + 1.82602i) q^{7} +(-2.76070 - 0.615248i) q^{8} +(-2.43097 + 1.40352i) q^{9} +O(q^{10})\)	\(q+(-1.41044 - 0.103276i) q^{2} +(-0.623697 - 2.32767i) q^{3} +(1.97867 + 0.291328i) q^{4} +(-2.33843 - 2.33843i) q^{5} +(0.639294 + 3.34744i) q^{6} +(-3.16277 + 1.82602i) q^{7} +(-2.76070 - 0.615248i) q^{8} +(-2.43097 + 1.40352i) q^{9} +(3.05670 + 3.53971i) q^{10} +(3.60420 - 0.965741i) q^{11} +(-0.555974 - 4.78739i) q^{12} +(0.897619 + 3.49203i) q^{13} +(4.64947 - 2.24886i) q^{14} +(-3.98462 + 6.90156i) q^{15} +(3.83026 + 1.15288i) q^{16} +(1.39318 + 2.41306i) q^{17} +(3.57368 - 1.72852i) q^{18} +(-6.63086 - 1.77673i) q^{19} +(-3.94572 - 5.30822i) q^{20} +(6.22299 + 6.22299i) q^{21} +(-5.18323 + 0.989892i) q^{22} +(-5.70507 - 3.29383i) q^{23} +(0.289746 + 6.80973i) q^{24} +5.93649i q^{25} +(-0.905393 - 5.01799i) q^{26} +(-0.328797 - 0.328797i) q^{27} +(-6.79004 + 2.69169i) q^{28} +(-0.314295 - 1.17296i) q^{29} +(6.33282 - 9.32270i) q^{30} -4.09157 q^{31} +(-5.28327 - 2.02164i) q^{32} +(-4.49585 - 7.78705i) q^{33} +(-1.71579 - 3.54736i) q^{34} +(11.6659 + 3.12588i) q^{35} +(-5.21897 + 2.06889i) q^{36} +(3.69016 - 0.988774i) q^{37} +(9.16893 + 3.19078i) q^{38} +(7.56845 - 4.26733i) q^{39} +(5.01699 + 7.89441i) q^{40} +(-0.123461 - 0.0712802i) q^{41} +(-8.13445 - 9.41982i) q^{42} +(0.772184 - 2.88183i) q^{43} +(7.41286 - 0.860879i) q^{44} +(8.96668 + 2.40261i) q^{45} +(7.70648 + 5.23493i) q^{46} -7.34533 q^{47} +(0.294611 - 9.63462i) q^{48} +(3.16873 - 5.48840i) q^{49} +(0.613096 - 8.37305i) q^{50} +(4.74789 - 4.74789i) q^{51} +(0.758763 + 7.17107i) q^{52} +(-6.32639 - 6.32639i) q^{53} +(0.429791 + 0.497704i) q^{54} +(-10.6865 - 6.16984i) q^{55} +(9.85491 - 3.09522i) q^{56} +16.5426i q^{57} +(0.322154 + 1.68685i) q^{58} +(-0.387585 + 1.44649i) q^{59} +(-9.89485 + 12.4951i) q^{60} +(-2.41180 - 0.646240i) q^{61} +(5.77090 + 0.422560i) q^{62} +(5.12572 - 8.87801i) q^{63} +(7.24294 + 3.39703i) q^{64} +(6.06685 - 10.2649i) q^{65} +(5.53691 + 11.4475i) q^{66} +(-0.625756 - 2.33535i) q^{67} +(2.05365 + 5.18052i) q^{68} +(-4.10870 + 15.3339i) q^{69} +(-16.1312 - 5.61366i) q^{70} +(7.89833 - 4.56010i) q^{71} +(7.57469 - 2.37905i) q^{72} -10.8639i q^{73} +(-5.30685 + 1.01350i) q^{74} +(13.8182 - 3.70257i) q^{75} +(-12.6027 - 5.44732i) q^{76} +(-9.63576 + 9.63576i) q^{77} +(-11.1155 + 5.23716i) q^{78} +10.7847 q^{79} +(-6.26084 - 11.6527i) q^{80} +(-4.77082 + 8.26331i) q^{81} +(0.166772 + 0.113287i) q^{82} +(0.331076 - 0.331076i) q^{83} +(10.5003 + 14.1262i) q^{84} +(2.38492 - 8.90063i) q^{85} +(-1.38674 + 3.98489i) q^{86} +(-2.53425 + 1.46315i) q^{87} +(-10.5443 + 0.448647i) q^{88} +(-6.75424 - 3.89956i) q^{89} +(-12.3988 - 4.31478i) q^{90} +(-9.21549 - 9.40541i) q^{91} +(-10.3289 - 8.17944i) q^{92} +(2.55190 + 9.52382i) q^{93} +(10.3601 + 0.758594i) q^{94} +(11.3510 + 19.6606i) q^{95} +(-1.41055 + 13.5586i) q^{96} +(5.70247 + 9.87697i) q^{97} +(-5.03611 + 7.41379i) q^{98} +(-7.40625 + 7.40625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{8}+O(q^{10}) \) 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^8	\( 104 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{8} - 2 q^{10} - 2 q^{11} - 36 q^{12} - 4 q^{13} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{18} - 2 q^{19} - 10 q^{20} - 20 q^{21} + 18 q^{22} + 14 q^{24} - 40 q^{26} + 4 q^{27} - 16 q^{28} - 2 q^{29} - 2 q^{30} - 16 q^{31} - 2 q^{32} - 4 q^{33} + 20 q^{34} + 8 q^{35} - 24 q^{36} - 2 q^{37} + 12 q^{38} - 28 q^{40} + 14 q^{42} - 18 q^{43} - 24 q^{44} + 20 q^{45} + 32 q^{46} - 16 q^{47} - 48 q^{48} + 24 q^{49} + 64 q^{50} + 4 q^{51} - 42 q^{52} - 8 q^{53} - 26 q^{54} + 32 q^{56} + 34 q^{58} - 42 q^{59} + 56 q^{60} - 2 q^{61} + 18 q^{62} - 60 q^{63} - 44 q^{64} - 16 q^{65} - 24 q^{66} - 2 q^{67} + 32 q^{68} - 14 q^{69} - 112 q^{70} - 60 q^{72} + 6 q^{74} + 10 q^{75} + 46 q^{76} - 36 q^{77} - 116 q^{78} + 64 q^{79} + 30 q^{80} + 16 q^{81} + 68 q^{82} - 48 q^{83} + 88 q^{84} - 12 q^{85} - 48 q^{86} - 44 q^{88} + 220 q^{90} + 38 q^{91} - 72 q^{92} - 56 q^{93} - 2 q^{94} + 60 q^{95} + 168 q^{96} - 4 q^{97} + 38 q^{98} - 160 q^{99}+O(q^{100}) \) 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^8 - 2 * q^10 - 2 * q^11 - 36 * q^12 - 4 * q^13 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^18 - 2 * q^19 - 10 * q^20 - 20 * q^21 + 18 * q^22 + 14 * q^24 - 40 * q^26 + 4 * q^27 - 16 * q^28 - 2 * q^29 - 2 * q^30 - 16 * q^31 - 2 * q^32 - 4 * q^33 + 20 * q^34 + 8 * q^35 - 24 * q^36 - 2 * q^37 + 12 * q^38 - 28 * q^40 + 14 * q^42 - 18 * q^43 - 24 * q^44 + 20 * q^45 + 32 * q^46 - 16 * q^47 - 48 * q^48 + 24 * q^49 + 64 * q^50 + 4 * q^51 - 42 * q^52 - 8 * q^53 - 26 * q^54 + 32 * q^56 + 34 * q^58 - 42 * q^59 + 56 * q^60 - 2 * q^61 + 18 * q^62 - 60 * q^63 - 44 * q^64 - 16 * q^65 - 24 * q^66 - 2 * q^67 + 32 * q^68 - 14 * q^69 - 112 * q^70 - 60 * q^72 + 6 * q^74 + 10 * q^75 + 46 * q^76 - 36 * q^77 - 116 * q^78 + 64 * q^79 + 30 * q^80 + 16 * q^81 + 68 * q^82 - 48 * q^83 + 88 * q^84 - 12 * q^85 - 48 * q^86 - 44 * q^88 + 220 * q^90 + 38 * q^91 - 72 * q^92 - 56 * q^93 - 2 * q^94 + 60 * q^95 + 168 * q^96 - 4 * q^97 + 38 * q^98 - 160 * q^99

Introduction

L-functions

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