LMFDB - Embedded newform 378.2.w.b.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.8
Character	$\chi$	$=$	378.121
Dual form			378.2.w.b.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(1.05262 - 1.37550i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.324117 + 0.117969i) q^{5} +(1.45959 - 0.932530i) q^{6} +(0.0472752 - 2.64533i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.783993 - 2.89575i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(1.05262 - 1.37550i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.324117 + 0.117969i) q^{5} +(1.45959 - 0.932530i) q^{6} +(0.0472752 - 2.64533i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.783993 - 2.89575i) q^{9} -0.344919 q^{10} +(0.821414 + 0.298970i) q^{11} +(1.69051 - 0.377084i) q^{12} +(0.0309187 - 0.175349i) q^{13} +(0.949180 - 2.46963i) q^{14} +(-0.178905 + 0.569999i) q^{15} +(0.173648 + 0.984808i) q^{16} +6.92584 q^{17} +(0.253692 - 2.98925i) q^{18} -3.35263 q^{19} +(-0.324117 - 0.117969i) q^{20} +(-3.58888 - 2.84955i) q^{21} +(0.669623 + 0.561880i) q^{22} +(-1.31015 + 7.43026i) q^{23} +(1.71753 + 0.223844i) q^{24} +(-3.73909 + 3.13747i) q^{25} +(0.0890268 - 0.154199i) q^{26} +(-4.80834 - 1.96973i) q^{27} +(1.73660 - 1.99605i) q^{28} +(-0.470725 - 2.66961i) q^{29} +(-0.363067 + 0.474435i) q^{30} +(5.72127 + 4.80071i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.27587 - 0.815153i) q^{33} +(6.50816 + 2.36878i) q^{34} +(0.296744 + 0.862974i) q^{35} +(1.26078 - 2.72221i) q^{36} +(-2.43522 - 4.21792i) q^{37} +(-3.15044 - 1.14667i) q^{38} +(-0.208646 - 0.227104i) q^{39} +(-0.264223 - 0.221709i) q^{40} +(0.625127 - 3.54527i) q^{41} +(-2.39785 - 3.90517i) q^{42} +(-6.79190 + 5.69908i) q^{43} +(0.437065 + 0.757020i) q^{44} +(0.595715 + 0.846075i) q^{45} +(-3.77244 + 6.53406i) q^{46} +(-1.30421 + 1.09436i) q^{47} +(1.53739 + 0.797773i) q^{48} +(-6.99553 - 0.250117i) q^{49} +(-4.58667 + 1.66941i) q^{50} +(7.29026 - 9.52648i) q^{51} +(0.136397 - 0.114451i) q^{52} +(5.57388 + 9.65424i) q^{53} +(-3.84467 - 3.49549i) q^{54} -0.301504 q^{55} +(2.31456 - 1.28172i) q^{56} +(-3.52904 + 4.61154i) q^{57} +(0.470725 - 2.66961i) q^{58} +(0.869906 - 4.93348i) q^{59} +(-0.503438 + 0.321647i) q^{60} +(0.132498 - 0.111179i) q^{61} +(3.73429 + 6.46798i) q^{62} +(-7.69727 + 1.93702i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0106644 + 0.0604810i) q^{65} +(1.47772 - 0.329620i) q^{66} +(-6.05460 + 2.20369i) q^{67} +(5.30550 + 4.45184i) q^{68} +(8.84122 + 9.62333i) q^{69} +(-0.0163061 + 0.912423i) q^{70} +(-4.67546 + 8.09814i) q^{71} +(2.11579 - 2.12683i) q^{72} +(5.90570 - 10.2290i) q^{73} +(-0.845743 - 4.79645i) q^{74} +(0.379753 + 8.44566i) q^{75} +(-2.56826 - 2.15503i) q^{76} +(0.829707 - 2.15878i) q^{77} +(-0.118389 - 0.284769i) q^{78} +(0.444522 + 0.161793i) q^{79} +(-0.172459 - 0.298708i) q^{80} +(-7.77071 + 4.54049i) q^{81} +(1.79998 - 3.11766i) q^{82} +(-0.240849 - 1.36592i) q^{83} +(-0.917591 - 4.48977i) q^{84} +(-2.24478 + 0.817035i) q^{85} +(-8.33150 + 3.03242i) q^{86} +(-4.16754 - 2.16260i) q^{87} +(0.151791 + 0.860851i) q^{88} +13.2090 q^{89} +(0.270414 + 0.998797i) q^{90} +(-0.462393 - 0.0900797i) q^{91} +(-5.77971 + 4.84976i) q^{92} +(12.6257 - 2.81628i) q^{93} +(-1.59985 + 0.582298i) q^{94} +(1.08665 - 0.395507i) q^{95} +(1.17182 + 1.27548i) q^{96} +(-3.52644 + 2.95904i) q^{97} +(-6.48810 - 2.62765i) q^{98} +(0.221760 - 2.61300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.05262	−	1.37550i	0.607729	−	0.794145i
$3$	1.05262	−	1.37550i	0.607729	−	0.794145i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.324117	+	0.117969i	−0.144950	+	0.0527574i	−0.413476	−	0.910515i	$-0.635686\pi$
$5$	−0.324117	+	0.117969i	−0.144950	+	0.0527574i	0.268527	+	0.963272i	$0.413463\pi$
$6$	1.45959	−	0.932530i	0.595873	−	0.380704i
$7$	0.0472752	−	2.64533i	0.0178683	−	0.999840i
$7$	0.0472752	−	2.64533i	0.0178683	−	0.999840i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.783993	−	2.89575i	−0.261331	−	0.965249i
$10$	−0.344919			−0.109073
$11$	0.821414	+	0.298970i	0.247666	+	0.0901430i	0.462870	−	0.886426i	$-0.346820\pi$
$11$	0.821414	+	0.298970i	0.247666	+	0.0901430i	−0.215205	+	0.976569i	$0.569042\pi$
$12$	1.69051	−	0.377084i	0.488007	−	0.108855i
$13$	0.0309187	−	0.175349i	0.00857530	−	0.0486329i	−0.980220	−	0.197912i	$-0.936584\pi$
$13$	0.0309187	−	0.175349i	0.00857530	−	0.0486329i	0.988795	+	0.149279i	$0.0476952\pi$
$14$	0.949180	−	2.46963i	0.253679	−	0.660036i
$15$	−0.178905	+	0.569999i	−0.0461932	+	0.147173i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	6.92584			1.67976			0.839881	−	0.542771i	$-0.182625\pi$
$17$	6.92584			1.67976			0.839881	+	0.542771i	$0.182625\pi$
$18$	0.253692	−	2.98925i	0.0597957	−	0.704574i
$19$	−3.35263			−0.769146			−0.384573	−	0.923095i	$-0.625651\pi$
$19$	−3.35263			−0.769146			−0.384573	+	0.923095i	$0.625651\pi$
$20$	−0.324117	−	0.117969i	−0.0724749	−	0.0263787i
$21$	−3.58888	−	2.84955i	−0.783159	−	0.621822i
$22$	0.669623	+	0.561880i	0.142764	+	0.119793i
$23$	−1.31015	+	7.43026i	−0.273186	+	1.54932i	0.471479	+	0.881877i	$0.343720\pi$
$23$	−1.31015	+	7.43026i	−0.273186	+	1.54932i	−0.744665	+	0.667438i	$0.767391\pi$
$24$	1.71753	+	0.223844i	0.350588	+	0.0456920i
$25$	−3.73909	+	3.13747i	−0.747817	+	0.627493i
$26$	0.0890268	−	0.154199i	0.0174596	−	0.0302409i
$27$	−4.80834	−	1.96973i	−0.925366	−	0.379075i
$28$	1.73660	−	1.99605i	0.328186	−	0.377218i
$29$	−0.470725	−	2.66961i	−0.0874114	−	0.495735i	−0.996810	−	0.0798093i	$-0.974569\pi$
$29$	−0.470725	−	2.66961i	−0.0874114	−	0.495735i	0.909399	−	0.415925i	$-0.136542\pi$
$30$	−0.363067	+	0.474435i	−0.0662867	+	0.0866196i
$31$	5.72127	+	4.80071i	1.02757	+	0.862234i	0.990560	−	0.137081i	$-0.0437721\pi$
$31$	5.72127	+	4.80071i	1.02757	+	0.862234i	0.0370102	+	0.999315i	$0.488217\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	1.27587	−	0.815153i	0.222100	−	0.141900i
$34$	6.50816	+	2.36878i	1.11614	+	0.406242i
$35$	0.296744	+	0.862974i	0.0501589	+	0.145869i
$36$	1.26078	−	2.72221i	0.210130	−	0.453702i
$37$	−2.43522	−	4.21792i	−0.400348	−	0.693422i	0.593420	−	0.804893i	$-0.297777\pi$
$37$	−2.43522	−	4.21792i	−0.400348	−	0.693422i	−0.993768	+	0.111470i	$0.964444\pi$
$38$	−3.15044	−	1.14667i	−0.511069	−	0.186014i
$39$	−0.208646	−	0.227104i	−0.0334101	−	0.0363657i
$40$	−0.264223	−	0.221709i	−0.0417773	−	0.0350553i
$41$	0.625127	−	3.54527i	0.0976285	−	0.553679i	−0.896282	−	0.443485i	$-0.853742\pi$
$41$	0.625127	−	3.54527i	0.0976285	−	0.553679i	0.993910	−	0.110193i	$-0.0351470\pi$
$42$	−2.39785	−	3.90517i	−0.369996	−	0.602581i
$43$	−6.79190	+	5.69908i	−1.03575	+	0.869101i	−0.991524	−	0.129920i	$-0.958528\pi$
$43$	−6.79190	+	5.69908i	−1.03575	+	0.869101i	−0.0442302	+	0.999021i	$0.514084\pi$
$44$	0.437065	+	0.757020i	0.0658901	+	0.114125i
$45$	0.595715	+	0.846075i	0.0888039	+	0.126125i
$46$	−3.77244	+	6.53406i	−0.556216	+	0.963394i
$47$	−1.30421	+	1.09436i	−0.190239	+	0.159629i	−0.732932	−	0.680301i	$-0.761849\pi$
$47$	−1.30421	+	1.09436i	−0.190239	+	0.159629i	0.542694	+	0.839931i	$0.317404\pi$
$48$	1.53739	+	0.797773i	0.221903	+	0.115149i
$49$	−6.99553	−	0.250117i	−0.999361	−	0.0357310i
$50$	−4.58667	+	1.66941i	−0.648653	+	0.236090i
$51$	7.29026	−	9.52648i	1.02084	−	1.33397i
$52$	0.136397	−	0.114451i	0.0189149	−	0.0158715i
$53$	5.57388	+	9.65424i	0.765631	+	1.32611i	0.939912	+	0.341416i	$0.110906\pi$
$53$	5.57388	+	9.65424i	0.765631	+	1.32611i	−0.174281	+	0.984696i	$0.555760\pi$
$54$	−3.84467	−	3.49549i	−0.523194	−	0.475676i
$55$	−0.301504			−0.0406548
$56$	2.31456	−	1.28172i	0.309296	−	0.171277i
$57$	−3.52904	+	4.61154i	−0.467432	+	0.610813i
$58$	0.470725	−	2.66961i	0.0618092	−	0.350537i
$59$	0.869906	−	4.93348i	0.113252	−	0.642285i	−0.874349	−	0.485298i	$-0.838711\pi$
$59$	0.869906	−	4.93348i	0.113252	−	0.642285i	0.987601	−	0.156986i	$-0.0501779\pi$
$60$	−0.503438	+	0.321647i	−0.0649936	+	0.0415244i
$61$	0.132498	−	0.111179i	0.0169646	−	0.0142350i	−0.634266	−	0.773115i	$-0.718698\pi$
$61$	0.132498	−	0.111179i	0.0169646	−	0.0142350i	0.651231	+	0.758880i	$0.274253\pi$
$62$	3.73429	+	6.46798i	0.474256	+	0.821435i
$63$	−7.69727	+	1.93702i	−0.969765	+	0.244042i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0106644	+	0.0604810i	0.00132276	+	0.00750174i
$66$	1.47772	−	0.329620i	0.181895	−	0.0405735i
$67$	−6.05460	+	2.20369i	−0.739687	+	0.269224i	−0.684259	−	0.729239i	$-0.739874\pi$
$67$	−6.05460	+	2.20369i	−0.739687	+	0.269224i	−0.0554276	+	0.998463i	$0.517652\pi$
$68$	5.30550	+	4.45184i	0.643386	+	0.539865i
$69$	8.84122	+	9.62333i	1.06436	+	1.15851i
$70$	−0.0163061	+	0.912423i	−0.00194895	+	0.109055i
$71$	−4.67546	+	8.09814i	−0.554876	+	0.961073i	0.443038	+	0.896503i	$0.353901\pi$
$71$	−4.67546	+	8.09814i	−0.554876	+	0.961073i	−0.997913	+	0.0645697i	$0.979433\pi$
$72$	2.11579	−	2.12683i	0.249349	−	0.250650i
$73$	5.90570	−	10.2290i	0.691210	−	1.19721i	−0.280232	−	0.959932i	$-0.590411\pi$
$73$	5.90570	−	10.2290i	0.691210	−	1.19721i	0.971442	−	0.237279i	$-0.0762554\pi$
$74$	−0.845743	−	4.79645i	−0.0983156	−	0.557576i
$75$	0.379753	+	8.44566i	0.0438501	+	0.975221i
$76$	−2.56826	−	2.15503i	−0.294600	−	0.247199i
$77$	0.829707	−	2.15878i	0.0945539	−	0.246015i
$78$	−0.118389	−	0.284769i	−0.0134049	−	0.0322437i
$79$	0.444522	+	0.161793i	0.0500126	+	0.0182031i	0.366905	−	0.930258i	$-0.380417\pi$
$79$	0.444522	+	0.161793i	0.0500126	+	0.0182031i	−0.316893	+	0.948461i	$0.602640\pi$
$80$	−0.172459	−	0.298708i	−0.0192815	−	0.0333966i
$81$	−7.77071	+	4.54049i	−0.863412	+	0.504499i
$82$	1.79998	−	3.11766i	0.198775	−	0.344288i
$83$	−0.240849	−	1.36592i	−0.0264366	−	0.149929i	0.968732	−	0.248109i	$-0.0798091\pi$
$83$	−0.240849	−	1.36592i	−0.0264366	−	0.149929i	−0.995169	+	0.0981796i	$0.968698\pi$
$84$	−0.917591	−	4.48977i	−0.100117	−	0.489874i
$85$	−2.24478	+	0.817035i	−0.243481	+	0.0886198i
$86$	−8.33150	+	3.03242i	−0.898408	+	0.326994i
$87$	−4.16754	−	2.16260i	−0.446807	−	0.231855i
$88$	0.151791	+	0.860851i	0.0161810	+	0.0917670i
$89$	13.2090			1.40015			0.700076	−	0.714068i	$-0.253149\pi$
$89$	13.2090			1.40015			0.700076	+	0.714068i	$0.253149\pi$
$90$	0.270414	+	0.998797i	0.0285041	+	0.105282i
$91$	−0.462393	−	0.0900797i	−0.0484720	−	0.00944292i
$92$	−5.77971	+	4.84976i	−0.602577	+	0.505622i
$93$	12.6257	−	2.81628i	1.30922	−	0.292035i
$94$	−1.59985	+	0.582298i	−0.165012	+	0.0600595i
$95$	1.08665	−	0.395507i	0.111487	−	0.0405781i
$96$	1.17182	+	1.27548i	0.119598	+	0.130178i
$97$	−3.52644	+	2.95904i	−0.358056	+	0.300445i	−0.804015	−	0.594609i	$-0.797307\pi$
$97$	−3.52644	+	2.95904i	−0.358056	+	0.300445i	0.445959	+	0.895053i	$0.352863\pi$
$98$	−6.48810	−	2.62765i	−0.655397	−	0.265432i
$99$	0.221760	−	2.61300i	0.0222877	−	0.262616i
$100$	−4.88103			−0.488103
$101$	2.88068	+	16.3371i	0.286638	+	1.62560i	0.699376	+	0.714754i	$0.253462\pi$
$101$	2.88068	+	16.3371i	0.286638	+	1.62560i	−0.412738	+	0.910850i	$0.635427\pi$
$102$	10.1088	−	6.45855i	1.00093	−	0.639491i
$103$	−14.5889	+	5.30994i	−1.43749	+	0.523204i	−0.939068	−	0.343731i	$-0.888309\pi$
$103$	−14.5889	+	5.30994i	−1.43749	+	0.523204i	−0.498422	+	0.866935i	$0.666087\pi$
$104$	0.167316	−	0.0608979i	0.0164067	−	0.00597153i
$105$	1.49938	+	0.500210i	0.146324	+	0.0488155i
$106$	1.93579	+	10.9784i	0.188020	+	1.06632i
$107$	7.31071	−	12.6625i	0.706753	−	1.22413i	−0.259302	−	0.965796i	$-0.583493\pi$
$107$	7.31071	−	12.6625i	0.706753	−	1.22413i	0.966055	−	0.258336i	$-0.0831741\pi$
$108$	−2.41728	−	4.59965i	−0.232603	−	0.442601i
$109$	−2.18827	−	3.79020i	−0.209598	−	0.363035i	0.741990	−	0.670411i	$-0.233882\pi$
$109$	−2.18827	−	3.79020i	−0.209598	−	0.363035i	−0.951588	+	0.307376i	$0.900549\pi$
$110$	−0.283321	−	0.103120i	−0.0270136	−	0.00983215i
$111$	−8.36510	−	1.09022i	−0.793980	−	0.103479i
$112$	2.61335	−	0.412800i	0.246938	−	0.0390059i
$113$	−7.48470	−	6.28041i	−0.704101	−	0.590811i	0.218836	−	0.975762i	$-0.429774\pi$
$113$	−7.48470	−	6.28041i	−0.704101	−	0.590811i	−0.922937	+	0.384951i	$0.874218\pi$
$114$	−4.89345	+	3.12643i	−0.458313	+	0.292817i
$115$	−0.451897	−	2.56283i	−0.0421396	−	0.238985i
$116$	1.35540	−	2.34762i	0.125846	−	0.217971i
$117$	−0.532005	+	0.0479393i	−0.0491839	+	0.00443199i
$118$	2.50480	−	4.33843i	0.230585	−	0.399385i
$119$	0.327420	−	18.3211i	0.0300146	−	1.67949i
$120$	−0.583087	+	0.130063i	−0.0532283	+	0.0118731i
$121$	−7.84115	−	6.57951i	−0.712832	−	0.598137i
$122$	0.162533	−	0.0591570i	0.0147150	−	0.00535582i
$123$	−4.21850	−	4.59168i	−0.380369	−	0.414018i
$124$	1.29691	+	7.35512i	0.116466	+	0.660509i
$125$	1.70408	−	2.95155i	0.152417	−	0.263994i
$126$	−7.89557	−	0.812415i	−0.703393	−	0.0723757i
$127$	−4.76761	−	8.25775i	−0.423057	−	0.732757i	0.573180	−	0.819430i	$-0.305710\pi$
$127$	−4.76761	−	8.25775i	−0.423057	−	0.732757i	−0.996237	+	0.0866732i	$0.972376\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	0.689805	+	15.3412i	0.0607339	+	1.35072i
$130$	−0.0106644	+	0.0604810i	−0.000935332	+	0.00530453i
$131$	0.0746917	−	0.423598i	0.00652585	−	0.0370099i	−0.981371	−	0.192122i	$-0.938463\pi$
$131$	0.0746917	−	0.423598i	0.00652585	−	0.0370099i	0.987897	+	0.155113i	$0.0495740\pi$
$132$	1.50134	+	0.195669i	0.130675	+	0.0170308i
$133$	−0.158496	+	8.86881i	−0.0137434	+	0.769023i
$134$	−6.44317			−0.556605
$135$	1.79083	+	0.0711892i	0.154131	+	0.00612699i
$136$	3.46292	+	5.99795i	0.296943	+	0.514320i
$137$	2.08636	−	1.75067i	0.178250	−	0.149569i	−0.549297	−	0.835627i	$-0.685105\pi$
$137$	2.08636	−	1.75067i	0.178250	−	0.149569i	0.727547	+	0.686057i	$0.240660\pi$
$138$	5.01665	+	12.0668i	0.427046	+	1.02720i
$139$	2.29383	−	0.834887i	0.194560	−	0.0708142i	−0.242902	−	0.970051i	$-0.578099\pi$
$139$	2.29383	−	0.834887i	0.194560	−	0.0708142i	0.437463	+	0.899237i	$0.355877\pi$
$140$	−0.327390	+	0.851820i	−0.0276695	+	0.0719919i
$141$	0.132459	+	2.94589i	0.0111551	+	0.248088i
$142$	−7.16323	+	6.01066i	−0.601125	+	0.504404i
$143$	0.0778211	−	0.134790i	0.00650773	−	0.0112717i
$144$	2.71562	−	1.27492i	0.226301	−	0.106244i
$145$	0.467502	+	0.809737i	0.0388239	+	0.0672450i
$146$	9.04806	−	7.59222i	0.748823	−	0.628337i
$147$	−7.70765	+	9.35906i	−0.635716	+	0.771923i
$148$	0.845743	−	4.79645i	0.0695196	−	0.394265i
$149$	6.61534	+	5.55093i	0.541950	+	0.454750i	0.872204	−	0.489142i	$-0.162690\pi$
$149$	6.61534	+	5.55093i	0.541950	+	0.454750i	−0.330254	+	0.943892i	$0.607135\pi$
$150$	−2.53174	+	8.06621i	−0.206715	+	0.658603i
$151$	−0.259890	−	0.0945921i	−0.0211495	−	0.00769779i	0.331424	−	0.943482i	$-0.392471\pi$
$151$	−0.259890	−	0.0945921i	−0.0211495	−	0.00769779i	−0.352573	+	0.935784i	$0.614693\pi$
$152$	−1.67631	−	2.90346i	−0.135967	−	0.235502i
$153$	−5.42981	−	20.0555i	−0.438974	−	1.62139i
$154$	1.51802	−	1.74481i	0.122325	−	0.140601i
$155$	−2.42070	−	0.881062i	−0.194435	−	0.0707686i
$156$	−0.0138529	−	0.308087i	−0.00110912	−	0.0246667i
$157$	2.84896	−	16.1573i	0.227372	−	1.28949i	−0.630727	−	0.776005i	$-0.717243\pi$
$157$	2.84896	−	16.1573i	0.227372	−	1.28949i	0.858099	−	0.513485i	$-0.171646\pi$
$158$	0.362377	+	0.304071i	0.0288292	+	0.0241906i
$159$	19.1466	+	2.49536i	1.51842	+	0.197895i
$160$	−0.0598945	−	0.339678i	−0.00473507	−	0.0268539i
$161$	19.5935	+	3.81706i	1.54419	+	0.300826i
$162$	−8.85502	+	1.60893i	−0.695716	+	0.126409i
$163$	10.6016	−	18.3625i	0.830380	−	1.43826i	−0.0673579	−	0.997729i	$-0.521457\pi$
$163$	10.6016	−	18.3625i	0.830380	−	1.43826i	0.897737	−	0.440531i	$-0.145210\pi$
$164$	2.75773	−	2.31401i	0.215343	−	0.180694i
$165$	−0.317368	+	0.414718i	−0.0247071	+	0.0322858i
$166$	0.240849	−	1.36592i	0.0186935	−	0.106016i
$167$	−0.717784	−	0.602292i	−0.0555438	−	0.0466068i	0.614593	−	0.788844i	$-0.289320\pi$
$167$	−0.717784	−	0.602292i	−0.0555438	−	0.0466068i	−0.670137	+	0.742237i	$0.733765\pi$
$168$	0.673338	−	4.53284i	0.0519491	−	0.349716i
$169$	12.1862	+	4.43542i	0.937401	+	0.341186i
$170$	−2.38885			−0.183216
$171$	2.62844	+	9.70837i	0.201002	+	0.742418i
$172$	−8.86619			−0.676041
$173$	−2.14972	−	12.1917i	−0.163440	−	0.926915i	−0.950658	−	0.310240i	$-0.899590\pi$
$173$	−2.14972	−	12.1917i	−0.163440	−	0.926915i	0.787218	−	0.616675i	$-0.211521\pi$
$174$	−3.17656	−	3.45756i	−0.240814	−	0.262117i
$175$	8.12286	+	10.0394i	0.614031	+	0.758910i
$176$	−0.151791	+	0.860851i	−0.0114417	+	0.0648891i
$177$	−5.87032	−	6.38963i	−0.441240	−	0.480274i
$178$	12.4124	+	4.51775i	0.930349	+	0.338619i
$179$	8.49241			0.634752			0.317376	−	0.948300i	$-0.397198\pi$
$179$	8.49241			0.634752			0.317376	+	0.948300i	$0.397198\pi$
$180$	−0.0875030	+	1.03105i	−0.00652209	+	0.0768499i
$181$	2.84630	+	4.92994i	0.211564	+	0.366439i	0.952204	−	0.305462i	$-0.0988110\pi$
$181$	2.84630	+	4.92994i	0.211564	+	0.366439i	−0.740640	+	0.671902i	$0.765478\pi$
$182$	−0.403698	−	0.242795i	−0.0299241	−	0.0179972i
$183$	−0.0134569	−	0.299279i	−0.000994760	−	0.0221234i
$184$	−7.08987	+	2.58050i	−0.522672	+	0.190237i
$185$	1.28688	+	1.07982i	0.0946134	+	0.0793901i
$186$	12.8275	+	1.67180i	0.940557	+	0.122582i
$187$	5.68898	+	2.07062i	0.416020	+	0.151419i
$188$	−1.70253			−0.124169
$189$	−5.43791	+	12.6265i	−0.395550	+	0.918445i
$190$	1.15638			0.0838929
$191$	−15.3728	−	5.59525i	−1.11234	−	0.404858i	−0.280488	−	0.959858i	$-0.590496\pi$
$191$	−15.3728	−	5.59525i	−1.11234	−	0.404858i	−0.831851	+	0.554999i	$0.812718\pi$
$192$	0.664908	+	1.59934i	0.0479856	+	0.115423i
$193$	15.3852	+	12.9097i	1.10745	+	0.929261i	0.997903	−	0.0647210i	$-0.0206157\pi$
$193$	15.3852	+	12.9097i	1.10745	+	0.929261i	0.109546	+	0.993982i	$0.465060\pi$
$194$	−4.32582	+	1.57447i	−0.310576	+	0.113040i
$195$	0.0944171	+	0.0489944i	0.00676135	+	0.00350856i
$196$	−5.19812	−	4.68824i	−0.371294	−	0.334874i
$197$	4.50532	+	7.80344i	0.320991	+	0.555972i	0.980693	−	0.195555i	$-0.0626508\pi$
$197$	4.50532	+	7.80344i	0.320991	+	0.555972i	−0.659702	+	0.751527i	$0.729318\pi$
$198$	1.10208	−	2.37957i	0.0783217	−	0.169109i
$199$	21.0854			1.49470			0.747351	−	0.664429i	$-0.231325\pi$
$199$	21.0854			1.49470			0.747351	+	0.664429i	$0.231325\pi$
$200$	−4.58667	−	1.66941i	−0.324326	−	0.118045i
$201$	−3.34200	+	10.6477i	−0.235726	+	0.751034i
$202$	−2.88068	+	16.3371i	−0.202684	+	1.14948i
$203$	−7.08426	+	1.11902i	−0.497217	+	0.0785395i
$204$	11.7082	−	2.61162i	0.819735	−	0.182850i
$205$	0.215618	+	1.22283i	0.0150594	+	0.0854062i
$206$	−15.5252			−1.08169
$207$	22.5433	−	2.03139i	1.56687	−	0.141191i
$208$	0.178054			0.0123458
$209$	−2.75390	−	1.00234i	−0.190491	−	0.0693331i
$210$	1.23787	+	0.982861i	0.0854213	+	0.0678239i
$211$	−17.9188	−	15.0357i	−1.23358	−	1.03510i	−0.997998	−	0.0632469i	$-0.979854\pi$
$211$	−17.9188	−	15.0357i	−1.23358	−	1.03510i	−0.235587	−	0.971853i	$-0.575701\pi$
$212$	−1.93579	+	10.9784i	−0.132950	+	0.753999i
$213$	6.21751	+	14.9553i	0.426017	+	1.02472i
$214$	11.2007	−	9.39847i	0.765661	−	0.642466i
$215$	1.52906	−	2.64840i	0.104281	−	0.180620i
$216$	−0.698332	−	5.14901i	−0.0475155	−	0.350346i
$217$	12.9699	−	14.9077i	0.880457	−	1.01200i
$218$	−0.759978	−	4.31005i	−0.0514722	−	0.291914i
$219$	−7.85350	−	18.8905i	−0.530690	−	1.27650i
$220$	−0.230965	−	0.193803i	−0.0155717	−	0.0130662i
$221$	0.214138	−	1.21444i	0.0144045	−	0.0816918i
$222$	−7.48775	−	3.88550i	−0.502545	−	0.260778i
$223$	3.54993	+	1.29207i	0.237721	+	0.0865234i	0.458134	−	0.888883i	$-0.348518\pi$
$223$	3.54993	+	1.29207i	0.237721	+	0.0865234i	−0.220412	+	0.975407i	$0.570740\pi$
$224$	2.59693	+	0.505914i	0.173515	+	0.0338028i
$225$	12.0167	+	8.36770i	0.801115	+	0.557847i
$226$	−4.88529	−	8.46157i	−0.324965	−	0.562855i
$227$	−18.7403	−	6.82093i	−1.24384	−	0.452721i	−0.365524	−	0.930802i	$-0.619110\pi$
$227$	−18.7403	−	6.82093i	−1.24384	−	0.452721i	−0.878316	+	0.478081i	$0.841333\pi$
$228$	−5.66764	+	1.26422i	−0.375348	+	0.0837251i
$229$	−3.67926	−	3.08727i	−0.243133	−	0.204013i	0.513076	−	0.858343i	$-0.328506\pi$
$229$	−3.67926	−	3.08727i	−0.243133	−	0.204013i	−0.756208	+	0.654331i	$0.772950\pi$
$230$	0.451897	−	2.56283i	0.0297972	−	0.168988i
$231$	−2.09603	−	3.41363i	−0.137909	−	0.224600i
$232$	2.07659	−	1.74247i	0.136335	−	0.114398i
$233$	12.1202	+	20.9929i	0.794024	+	1.37529i	0.923457	+	0.383701i	$0.125351\pi$
$233$	12.1202	+	20.9929i	0.794024	+	1.37529i	−0.129433	+	0.991588i	$0.541316\pi$
$234$	−0.516318	−	0.136908i	−0.0337527	−	0.00894997i
$235$	0.293616	−	0.508559i	0.0191534	−	0.0331747i
$236$	3.83757	−	3.22010i	0.249804	−	0.209611i
$237$	0.690457	−	0.441133i	0.0448500	−	0.0286547i
$238$	6.57386	−	17.1042i	0.426120	−	1.10870i
$239$	−2.10441	+	0.765942i	−0.136123	+	0.0495447i	−0.409183	−	0.912452i	$-0.634186\pi$
$239$	−2.10441	+	0.765942i	−0.136123	+	0.0495447i	0.273060	+	0.961997i	$0.411964\pi$
$240$	−0.592406	−	0.0772080i	−0.0382397	−	0.00498375i
$241$	21.3949	−	17.9525i	1.37817	−	1.15642i	0.408283	−	0.912855i	$-0.366128\pi$
$241$	21.3949	−	17.9525i	1.37817	−	1.15642i	0.969885	−	0.243565i	$-0.0783168\pi$
$242$	−5.11795	−	8.86455i	−0.328994	−	0.569835i
$243$	−1.93414	+	15.4680i	−0.124075	+	0.992273i
$244$	0.172964			0.0110729
$245$	2.29688	−	0.744189i	0.146742	−	0.0475445i
$246$	−2.39365	−	5.75758i	−0.152613	−	0.367090i
$247$	−0.103659	+	0.587879i	−0.00659566	+	0.0374058i
$248$	−1.29691	+	7.35512i	−0.0823536	+	0.467051i
$249$	−2.13235	−	1.10651i	−0.135132	−	0.0701220i
$250$	2.61080	−	2.19072i	0.165121	−	0.138553i
$251$	−6.50629	−	11.2692i	−0.410673	−	0.711307i	0.584290	−	0.811545i	$-0.301373\pi$
$251$	−6.50629	−	11.2692i	−0.410673	−	0.711307i	−0.994963	+	0.100238i	$0.968040\pi$
$252$	−7.14154	−	3.46386i	−0.449875	−	0.218203i
$253$	−3.29761	+	5.71162i	−0.207319	+	0.359087i
$254$	−1.65577	−	9.39036i	−0.103893	−	0.589204i
$255$	−1.23907	+	3.94772i	−0.0775935	+	0.247216i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−5.22533	−	4.38457i	−0.325947	−	0.273502i	0.465099	−	0.885259i	$-0.346019\pi$
$257$	−5.22533	−	4.38457i	−0.325947	−	0.273502i	−0.791046	+	0.611757i	$0.790463\pi$
$258$	−4.59879	+	14.6519i	−0.286308	+	0.912190i
$259$	−11.2729	+	6.24255i	−0.700465	+	0.387893i
$260$	−0.0307070	+	0.0531861i	−0.00190437	+	0.00329846i
$261$	−7.36148	+	3.45606i	−0.455664	+	0.213925i
$262$	0.215066	−	0.372506i	0.0132868	−	0.0230135i
$263$	2.12278	+	12.0389i	0.130896	+	0.742351i	0.977630	+	0.210333i	$0.0674549\pi$
$263$	2.12278	+	12.0389i	0.130896	+	0.742351i	−0.846733	+	0.532018i	$0.821434\pi$
$264$	1.34388	+	0.697358i	0.0827099	+	0.0429194i
$265$	−2.94549	−	2.47156i	−0.180940	−	0.151827i
$266$	−3.18225	+	8.27974i	−0.195116	+	0.507664i
$267$	13.9040	−	18.1690i	0.850913	−	1.11192i
$268$	−6.05460	−	2.20369i	−0.369843	−	0.134612i
$269$	−12.8210	−	22.2066i	−0.781711	−	1.35396i	−0.930945	−	0.365161i	$-0.881014\pi$
$269$	−12.8210	−	22.2066i	−0.781711	−	1.35396i	0.149234	−	0.988802i	$-0.452319\pi$
$270$	1.65849	+	0.679398i	0.100932	+	0.0413468i
$271$	−8.25642	+	14.3005i	−0.501542	+	0.868696i	0.498457	+	0.866915i	$0.333900\pi$
$271$	−8.25642	+	14.3005i	−0.501542	+	0.868696i	−0.999998	+	0.00178119i	$0.999433\pi$
$272$	1.20266	+	6.82062i	0.0729219	+	0.413561i
$273$	−0.610627	+	0.541201i	−0.0369569	+	0.0327550i
$274$	2.55930	−	0.931510i	0.154613	−	0.0562746i
$275$	−4.00935	+	1.45928i	−0.241773	+	0.0879981i
$276$	0.587005	+	13.0549i	0.0353335	+	0.785814i
$277$	−4.06601	−	23.0595i	−0.244303	−	1.38551i	−0.822106	−	0.569335i	$-0.807201\pi$
$277$	−4.06601	−	23.0595i	−0.244303	−	1.38551i	0.577803	−	0.816177i	$-0.303910\pi$
$278$	2.44105			0.146404
$279$	9.41622	−	20.3311i	0.563734	−	1.21719i
$280$	−0.598985	+	0.688475i	−0.0357962	+	0.0411443i
$281$	−0.782905	+	0.656935i	−0.0467042	+	0.0391895i	−0.665841	−	0.746094i	$-0.731927\pi$
$281$	−0.782905	+	0.656935i	−0.0467042	+	0.0391895i	0.619137	+	0.785283i	$0.287483\pi$
$282$	−0.883081	+	2.81353i	−0.0525867	+	0.167543i
$283$	−9.35009	+	3.40315i	−0.555805	+	0.202297i	−0.604624	−	0.796511i	$-0.706677\pi$
$283$	−9.35009	+	3.40315i	−0.555805	+	0.202297i	0.0488187	+	0.998808i	$0.484454\pi$
$284$	−8.78700	+	3.19821i	−0.521412	+	0.189779i
$285$	0.599803	−	1.91100i	0.0355293	−	0.113198i
$286$	0.119229	−	0.100045i	0.00705015	−	0.00591578i
$287$	−9.34886	−	1.82127i	−0.551846	−	0.107506i
$288$	2.98789	−	0.269241i	0.176063	−	0.0158652i
$289$	30.9672			1.82160
$290$	0.162362	+	0.920799i	0.00953421	+	0.0540712i
$291$	0.358156	+	7.96535i	0.0209955	+	0.466937i
$292$	11.0991	−	4.03974i	0.649525	−	0.236408i
$293$	−5.48906	+	1.99786i	−0.320675	+	0.116716i	−0.497342	−	0.867555i	$-0.665691\pi$
$293$	−5.48906	+	1.99786i	−0.320675	+	0.116716i	0.176667	+	0.984271i	$0.443468\pi$
$294$	−10.4438	+	6.15847i	−0.609096	+	0.359169i
$295$	0.300047	+	1.70165i	0.0174694	+	0.0990739i
$296$	2.43522	−	4.21792i	0.141544	−	0.245162i
$297$	−3.36075	−	3.05552i	−0.195010	−	0.177299i
$298$	4.31786	+	7.47875i	0.250127	+	0.433232i
$299$	1.26238	+	0.459468i	0.0730051	+	0.0265717i
$300$	−5.13786	+	6.71385i	−0.296634	+	0.387624i
$301$	14.7548	+	18.2362i	0.850455	+	1.05112i
$302$	−0.211864	−	0.177775i	−0.0121914	−	0.0102298i
$303$	25.5039	+	13.2344i	1.46516	+	0.760295i
$304$	−0.582178	−	3.30170i	−0.0333902	−	0.189365i
$305$	−0.0298292	+	0.0516656i	−0.00170801	+	0.00295837i
$306$	1.75703	−	20.7031i	0.100443	−	1.18352i
$307$	5.06341	−	8.77008i	0.288984	−	0.500535i	−0.684584	−	0.728934i	$-0.740016\pi$
$307$	5.06341	−	8.77008i	0.288984	−	0.500535i	0.973567	+	0.228400i	$0.0733492\pi$
$308$	2.02323	−	1.12039i	0.115284	−	0.0638403i
$309$	−8.05275	+	25.6564i	−0.458105	+	1.45954i
$310$	−1.97337	−	1.65586i	−0.112080	−	0.0940463i
$311$	−25.4688	+	9.26990i	−1.44421	+	0.525648i	−0.940967	−	0.338500i	$-0.890081\pi$
$311$	−25.4688	+	9.26990i	−1.44421	+	0.525648i	−0.503239	+	0.864147i	$0.667858\pi$
$312$	0.0923544	−	0.294245i	0.00522854	−	0.0166583i
$313$	−5.42946	−	30.7920i	−0.306891	−	1.74047i	−0.614466	−	0.788943i	$-0.710629\pi$
$313$	−5.42946	−	30.7920i	−0.306891	−	1.74047i	0.307575	−	0.951524i	$-0.400483\pi$
$314$	8.20326	−	14.2085i	0.462937	−	0.801830i
$315$	2.26631	−	1.53586i	0.127692	−	0.0865360i
$316$	0.236525	+	0.409673i	0.0133056	+	0.0230459i
$317$	−13.9059	+	11.6685i	−0.781035	+	0.655366i	−0.943509	−	0.331346i	$-0.892497\pi$
$317$	−13.9059	+	11.6685i	−0.781035	+	0.655366i	0.162474	+	0.986713i	$0.448053\pi$
$318$	17.1384	+	8.89338i	0.961074	+	0.498716i
$319$	0.411475	−	2.33359i	0.0230382	−	0.130656i
$320$	0.0598945	−	0.339678i	0.00334820	−	0.0189886i
$321$	−9.72190	−	23.3847i	−0.542623	−	1.30520i
$322$	17.1064	+	10.2882i	0.953302	+	0.573341i
$323$	−23.2198			−1.29198
$324$	−8.87128	−	1.51670i	−0.492849	−	0.0842610i
$325$	0.434543	+	0.752650i	0.0241041	+	0.0417495i
$326$	16.2426	−	13.6291i	0.899592	−	0.754847i
$327$	−7.51682	−	0.979663i	−0.415681	−	0.0541755i
$328$	3.38286	−	1.23126i	0.186787	−	0.0679850i
$329$	2.83329	+	3.50180i	0.156204	+	0.193061i
$330$	−0.440071	+	0.281161i	−0.0242251	+	0.0154774i
$331$	−11.5333	+	9.67762i	−0.633930	+	0.531930i	−0.902147	−	0.431428i	$-0.858010\pi$
$331$	−11.5333	+	9.67762i	−0.633930	+	0.531930i	0.268218	+	0.963358i	$0.413565\pi$
$332$	0.693497	−	1.20117i	0.0380606	−	0.0659229i
$333$	−10.3048	+	10.3586i	−0.564702	+	0.567648i
$334$	−0.468500	−	0.811466i	−0.0256352	−	0.0444014i
$335$	1.70243	−	1.42851i	0.0930139	−	0.0780479i
$336$	2.18305	−	4.02918i	0.119095	−	0.219810i
$337$	−1.67610	+	9.50563i	−0.0913030	+	0.517805i	0.904515	+	0.426442i	$0.140233\pi$
$337$	−1.67610	+	9.50563i	−0.0913030	+	0.517805i	−0.995818	+	0.0913625i	$0.970878\pi$
$338$	9.93429	+	8.33586i	0.540354	+	0.453411i
$339$	−16.5172	+	3.68432i	−0.897092	+	0.200105i
$340$	−2.24478	−	0.817035i	−0.121741	−	0.0443099i
$341$	3.26426	+	5.65386i	0.176770	+	0.306174i
$342$	−0.850534	+	10.0219i	−0.0459916	+	0.541920i
$343$	−0.992356	+	18.4937i	−0.0535822	+	0.998563i
$344$	−8.33150	−	3.03242i	−0.449204	−	0.163497i
$345$	−4.00085	−	2.07610i	−0.215398	−	0.111773i
$346$	2.14972	−	12.1917i	0.115570	−	0.655428i
$347$	−20.6356	−	17.3153i	−1.10778	−	0.929536i	−0.109854	−	0.993948i	$-0.535038\pi$
$347$	−20.6356	−	17.3153i	−1.10778	−	0.929536i	−0.997923	+	0.0644121i	$0.979483\pi$
$348$	−1.80243	−	4.33549i	−0.0966204	−	0.232407i
$349$	4.71314	+	26.7296i	0.252289	+	1.43080i	0.802937	+	0.596063i	$0.203269\pi$
$349$	4.71314	+	26.7296i	0.252289	+	1.43080i	−0.550649	+	0.834737i	$0.685620\pi$
$350$	4.19931	+	12.2122i	0.224462	+	0.652768i
$351$	−0.494058	+	0.782234i	−0.0263708	+	0.0417526i
$352$	−0.437065	+	0.757020i	−0.0232957	+	0.0403493i
$353$	−5.09416	+	4.27451i	−0.271135	+	0.227509i	−0.768209	−	0.640199i	$-0.778852\pi$
$353$	−5.09416	+	4.27451i	−0.271135	+	0.227509i	0.497075	+	0.867708i	$0.334408\pi$
$354$	−3.33092	−	8.01205i	−0.177036	−	0.425836i
$355$	0.560069	−	3.17631i	0.0297254	−	0.168581i
$356$	10.1187	+	8.49059i	0.536289	+	0.450000i
$357$	−24.8560	−	19.7355i	−1.31552	−	1.04451i
$358$	7.98025	+	2.90457i	0.421769	+	0.153512i
$359$	2.32368			0.122639			0.0613196	−	0.998118i	$-0.480469\pi$
$359$	2.32368			0.122639			0.0613196	+	0.998118i	$0.480469\pi$
$360$	−0.434865	+	0.938942i	−0.0229194	+	0.0494866i
$361$	−7.75988			−0.408415
$362$	0.988510	+	5.60612i	0.0519549	+	0.294651i
$363$	−17.3038	+	3.85979i	−0.908216	+	0.202586i
$364$	−0.296311	−	0.366226i	−0.0155309	−	0.0191954i
$365$	−0.707438	+	4.01208i	−0.0370290	+	0.210002i
$366$	0.0897142	−	0.285833i	0.00468944	−	0.0149407i
$367$	16.2100	+	5.89997i	0.846157	+	0.307976i	0.728472	−	0.685075i	$-0.240231\pi$
$367$	16.2100	+	5.89997i	0.846157	+	0.307976i	0.117684	+	0.993051i	$0.462453\pi$
$368$	−7.54488			−0.393304
$369$	−10.7563	+	0.969258i	−0.559951	+	0.0504576i
$370$	0.839952	+	1.45484i	0.0436670	+	0.0756335i
$371$	25.8021	−	14.2883i	1.33958	−	0.741813i
$372$	11.4821	+	5.95824i	0.595319	+	0.308920i
$373$	−9.27459	+	3.37567i	−0.480220	+	0.174786i	−0.570776	−	0.821106i	$-0.693358\pi$
$373$	−9.27459	+	3.37567i	−0.480220	+	0.174786i	0.0905564	+	0.995891i	$0.471135\pi$
$374$	4.63770	+	3.89149i	0.239810	+	0.201224i
$375$	−2.26611	−	5.45080i	−0.117021	−	0.281478i
$376$	−1.59985	−	0.582298i	−0.0825060	−	0.0300297i
$377$	−0.482667			−0.0248586
$378$	−9.42849	+	10.0052i	−0.484949	+	0.514611i
$379$	3.71099			0.190621			0.0953104	−	0.995448i	$-0.469616\pi$
$379$	3.71099			0.190621			0.0953104	+	0.995448i	$0.469616\pi$
$380$	1.08665	+	0.395507i	0.0557437	+	0.0202891i
$381$	−16.3770	−	2.13440i	−0.839019	−	0.109349i
$382$	−12.5320	−	10.5156i	−0.641195	−	0.538027i
$383$	8.71676	−	3.17264i	0.445406	−	0.162114i	−0.109573	−	0.993979i	$-0.534948\pi$
$383$	8.71676	−	3.17264i	0.445406	−	0.162114i	0.554979	+	0.831864i	$0.312726\pi$
$384$	0.0778017	+	1.73030i	0.00397030	+	0.0882991i
$385$	−0.0142537	+	0.797577i	−0.000726433	+	0.0406483i
$386$	10.0420	+	17.3932i	0.511123	+	0.885290i
$387$	21.8279	+	15.1996i	1.10957	+	0.772638i
$388$	−4.60344			−0.233704
$389$	1.90376	+	0.692912i	0.0965244	+	0.0351320i	0.389831	−	0.920886i	$-0.372533\pi$
$389$	1.90376	+	0.692912i	0.0965244	+	0.0351320i	−0.293307	+	0.956018i	$0.594756\pi$
$390$	0.0719659	+	0.0783322i	0.00364414	+	0.00396651i
$391$	−9.07392	+	51.4607i	−0.458888	+	2.60248i
$392$	−3.28116	−	6.18337i	−0.165723	−	0.312307i
$393$	−0.504036	−	0.548625i	−0.0254253	−	0.0276745i
$394$	1.56468	+	8.87375i	0.0788275	+	0.447053i
$395$	−0.163164			−0.00820966
$396$	1.84948	−	1.85913i	0.0929399	−	0.0934248i
$397$	−17.3648			−0.871516			−0.435758	−	0.900064i	$-0.643520\pi$
$397$	−17.3648			−0.871516			−0.435758	+	0.900064i	$0.643520\pi$
$398$	19.8138	+	7.21162i	0.993175	+	0.361486i
$399$	12.0322	+	9.55347i	0.602363	+	0.478272i
$400$	−3.73909	−	3.13747i	−0.186954	−	0.156873i
$401$	−2.98995	+	16.9568i	−0.149311	+	0.846784i	0.814493	+	0.580173i	$0.197015\pi$
$401$	−2.98995	+	16.9568i	−0.149311	+	0.846784i	−0.963804	+	0.266611i	$0.914096\pi$
$402$	−6.78219	+	8.86257i	−0.338265	+	0.442025i
$403$	1.01869	−	0.854784i	0.0507447	−	0.0425798i
$404$	−8.29457	+	14.3666i	−0.412670	+	0.714766i
$405$	1.98298	−	2.38836i	0.0985353	−	0.118678i
$406$	−7.03975	−	1.37143i	−0.349377	−	0.0680628i
$407$	−0.739290	−	4.19272i	−0.0366452	−	0.207825i
$408$	11.8953	+	1.55031i	0.588905	+	0.0767517i
$409$	−12.4541	−	10.4503i	−0.615818	−	0.516733i	0.280668	−	0.959805i	$-0.409444\pi$
$409$	−12.4541	−	10.4503i	−0.615818	−	0.516733i	−0.896486	+	0.443072i	$0.853888\pi$
$410$	−0.215618	+	1.22283i	−0.0106486	+	0.0603913i
$411$	−0.211897	−	4.71257i	−0.0104521	−	0.232454i
$412$	−14.5889	−	5.30994i	−0.718745	−	0.261602i
$413$	−13.0096	−	2.53442i	−0.640159	−	0.124711i
$414$	21.8785	+	5.80138i	1.07527	+	0.285122i
$415$	0.239200	+	0.414306i	0.0117419	+	0.0203375i
$416$	0.167316	+	0.0608979i	0.00820333	+	0.00298577i
$417$	1.26614	−	4.03398i	0.0620033	−	0.197545i
$418$	−2.24500	−	1.88378i	−0.109806	−	0.0921385i
$419$	3.14062	−	17.8113i	0.153429	−	0.870141i	−0.806778	−	0.590854i	$-0.798791\pi$
$419$	3.14062	−	17.8113i	0.153429	−	0.870141i	0.960208	−	0.279287i	$-0.0900980\pi$
$420$	0.827061	+	1.34696i	0.0403565	+	0.0657252i
$421$	11.5132	−	9.66070i	0.561118	−	0.470834i	−0.317567	−	0.948236i	$-0.602866\pi$
$421$	11.5132	−	9.66070i	0.561118	−	0.470834i	0.878685	+	0.477402i	$0.158421\pi$
$422$	−11.6957	−	20.2575i	−0.569338	−	0.986122i
$423$	4.19149	+	2.91869i	0.203797	+	0.141912i
$424$	−5.57388	+	9.65424i	−0.270691	+	0.468851i
$425$	−25.8963	+	21.7296i	−1.25616	+	1.05404i
$426$	0.727518	+	16.1799i	0.0352484	+	0.783920i
$427$	−0.287841	−	0.355756i	−0.0139296	−	0.0172162i
$428$	13.7396	−	5.00082i	0.664130	−	0.241724i
$429$	−0.103488	−	0.248925i	−0.00499643	−	0.0120182i
$430$	2.34265	−	1.96572i	0.112973	−	0.0947953i
$431$	14.4158	+	24.9690i	0.694387	+	1.20271i	0.970387	+	0.241556i	$0.0776576\pi$
$431$	14.4158	+	24.9690i	0.694387	+	1.20271i	−0.276000	+	0.961158i	$0.589009\pi$
$432$	1.10485	−	5.07733i	0.0531571	−	0.244283i
$433$	−8.60887			−0.413716			−0.206858	−	0.978371i	$-0.566324\pi$
$433$	−8.60887			−0.413716			−0.206858	+	0.978371i	$0.566324\pi$
$434$	17.2865	−	9.57266i	0.829778	−	0.459502i
$435$	1.60589	+	0.209295i	0.0769967	+	0.0100349i
$436$	0.759978	−	4.31005i	0.0363964	−	0.206414i
$437$	4.39246	−	24.9109i	0.210120	−	1.19165i
$438$	−0.918947	−	20.4373i	−0.0439090	−	0.976532i
$439$	−18.8911	+	15.8516i	−0.901625	+	0.756553i	−0.970507	−	0.241071i	$-0.922501\pi$
$439$	−18.8911	+	15.8516i	−0.901625	+	0.756553i	0.0688821	+	0.997625i	$0.478057\pi$
$440$	−0.150752	−	0.261110i	−0.00718682	−	0.0124479i
$441$	4.76017	+	20.4534i	0.226675	+	0.973970i
$442$	0.616585	−	1.06796i	0.0293280	−	0.0507975i
$443$	1.64737	+	9.34269i	0.0782689	+	0.443885i	0.998607	+	0.0527615i	$0.0168023\pi$
$443$	1.64737	+	9.34269i	0.0782689	+	0.443885i	−0.920338	+	0.391123i	$0.872087\pi$
$444$	−5.70726	−	6.21214i	−0.270855	−	0.294815i
$445$	−4.28127	+	1.55825i	−0.202952	+	0.0738684i
$446$	2.89393	+	2.42830i	0.137032	+	0.114983i
$447$	14.5987	−	3.25639i	0.690496	−	0.154022i
$448$	2.26728	+	1.36361i	0.107119	+	0.0644243i
$449$	−9.94850	+	17.2313i	−0.469499	+	0.813196i	−0.999392	−	0.0348687i	$-0.988899\pi$
$449$	−9.94850	+	17.2313i	−0.469499	+	0.813196i	0.529893	+	0.848064i	$0.322232\pi$
$450$	8.43011	+	11.9730i	0.397399	+	0.564414i
$451$	1.57342	−	2.72524i	0.0740895	−	0.128327i
$452$	−1.69664	−	9.62214i	−0.0798034	−	0.452587i
$453$	−0.403676	+	0.257908i	−0.0189663	+	0.0121176i
$454$	−15.2773	−	12.8191i	−0.716998	−	0.601632i
$455$	0.160496	−	0.0253517i	0.00752418	−	0.00118850i
$456$	−5.75823	−	0.750466i	−0.269654	−	0.0351438i
$457$	−25.8542	−	9.41015i	−1.20941	−	0.440188i	−0.342909	−	0.939369i	$-0.611412\pi$
$457$	−25.8542	−	9.41015i	−1.20941	−	0.440188i	−0.866498	+	0.499180i	$0.833634\pi$
$458$	−2.40147	−	4.15947i	−0.112213	−	0.194359i
$459$	−33.3018	−	13.6421i	−1.55439	−	0.636756i
$460$	1.30118	−	2.25372i	0.0606680	−	0.105080i
$461$	1.54638	+	8.76995i	0.0720220	+	0.408457i	0.999410	+	0.0343554i	$0.0109378\pi$
$461$	1.54638	+	8.76995i	0.0720220	+	0.408457i	−0.927388	+	0.374102i	$0.877951\pi$
$462$	−0.802095	−	3.92465i	−0.0373168	−	0.182591i
$463$	37.9447	−	13.8107i	1.76344	−	0.641840i	0.763448	−	0.645869i	$-0.223505\pi$
$463$	37.9447	−	13.8107i	1.76344	−	0.641840i	0.999992	+	0.00402929i	$0.00128257\pi$
$464$	2.54731	−	0.927147i	0.118256	−	0.0430417i
$465$	−3.75997	+	2.40225i	−0.174364	+	0.111401i
$466$	4.20932	+	23.8722i	0.194993	+	1.10586i
$467$	−23.0727			−1.06768			−0.533840	−	0.845586i	$-0.679251\pi$
$467$	−23.0727			−1.06768			−0.533840	+	0.845586i	$0.679251\pi$
$468$	−0.438355	−	0.305243i	−0.0202629	−	0.0141099i
$469$	5.54326	+	16.1206i	0.255964	+	0.744379i
$470$	0.449846	−	0.377466i	0.0207499	−	0.0174112i
$471$	−19.2254	−	20.9262i	−0.885861	−	0.964227i
$472$	4.70748	−	1.71338i	0.216679	−	0.0788647i
$473$	−7.28282	+	2.65073i	−0.334864	+	0.121881i
$474$	0.799694	−	0.178379i	0.0367312	−	0.00819324i
$475$	12.5358	−	10.5188i	0.575181	−	0.482634i
$476$	12.0274	−	13.8243i	0.551275	−	0.633637i
$477$	23.5864	−	23.7094i	1.07995	−	1.08558i
$478$	−2.23946			−0.102431
$479$	−0.767672	−	4.35368i	−0.0350758	−	0.198925i	0.962234	−	0.272223i	$-0.0877587\pi$
$479$	−0.767672	−	4.35368i	−0.0350758	−	0.198925i	−0.997310	+	0.0732979i	$0.976648\pi$
$480$	−0.530273	−	0.275167i	−0.0242036	−	0.0125596i
$481$	−0.814901	+	0.296600i	−0.0371563	+	0.0135238i
$482$	26.2448	−	9.55231i	1.19542	−	0.435096i
$483$	25.8749	−	22.9330i	1.17735	−	1.04349i
$484$	−1.77744	−	10.0804i	−0.0807929	−	0.458200i
$485$	0.793907	−	1.37509i	0.0360494	−	0.0624395i
$486$	−7.10787	+	13.8737i	−0.322420	+	0.629322i
$487$	11.4644	+	19.8569i	0.519502	+	0.899803i	0.999743	+	0.0226668i	$0.00721568\pi$
$487$	11.4644	+	19.8569i	0.519502	+	0.899803i	−0.480242	+	0.877136i	$0.659451\pi$
$488$	0.162533	+	0.0591570i	0.00735750	+	0.00267791i
$489$	−14.0981	−	33.9111i	−0.637540	−	1.53351i
$490$	2.41289	+	0.0862699i	0.109003	+	0.00389728i
$491$	18.2266	+	15.2939i	0.822554	+	0.690205i	0.953569	−	0.301175i	$-0.0973790\pi$
$491$	18.2266	+	15.2939i	0.822554	+	0.690205i	−0.131014	+	0.991380i	$0.541823\pi$
$492$	−0.280083	−	6.22903i	−0.0126271	−	0.280826i
$493$	−3.26016	−	18.4893i	−0.146830	−	0.832716i
$494$	−0.298474	+	0.516972i	−0.0134290	+	0.0232597i
$495$	0.236377	+	0.873079i	0.0106244	+	0.0392420i
$496$	−3.73429	+	6.46798i	−0.167675	+	0.290421i
$497$	21.2012	+	12.7510i	0.951005	+	0.571960i
$498$	−1.62530	−	1.76908i	−0.0728315	−	0.0792744i
$499$	−8.74284	−	7.33611i	−0.391383	−	0.328409i	0.425769	−	0.904832i	$-0.360004\pi$
$499$	−8.74284	−	7.33611i	−0.391383	−	0.328409i	−0.817152	+	0.576423i	$0.804448\pi$
$500$	3.20261	−	1.16566i	0.143225	−	0.0521297i
$501$	−1.58400	+	0.353327i	−0.0707681	+	0.0157855i
$502$	−2.25961	−	12.8149i	−0.100851	−	0.571956i
$503$	−6.01608	+	10.4202i	−0.268244	+	0.464612i	−0.968408	−	0.249370i	$-0.919777\pi$
$503$	−6.01608	+	10.4202i	−0.268244	+	0.464612i	0.700165	+	0.713981i	$0.253110\pi$
$504$	−5.52614	−	5.69752i	−0.246154	−	0.253788i
$505$	−2.86095	−	4.95531i	−0.127311	−	0.220509i
$506$	−5.05223	+	4.23932i	−0.224599	+	0.188461i
$507$	18.9283	−	12.0933i	0.840637	−	0.537083i
$508$	1.65577	−	9.39036i	0.0734631	−	0.416630i
$509$	5.78457	−	32.8059i	0.256396	−	1.45410i	−0.536066	−	0.844176i	$-0.680090\pi$
$509$	5.78457	−	32.8059i	0.256396	−	1.45410i	0.792462	−	0.609921i	$-0.208799\pi$
$510$	−2.51454	+	3.28586i	−0.111346	+	0.145500i
$511$	−26.7798	−	16.1061i	−1.18467	−	0.712492i
$512$	−1.00000			−0.0441942
$513$	16.1206	+	6.60379i	0.711741	+	0.291564i
$514$	−3.41059	−	5.90732i	−0.150435	−	0.260561i
$515$	4.10212	−	3.44209i	0.180761	−	0.151676i
$516$	−9.33271	+	12.1954i	−0.410850	+	0.536874i
$517$	−1.39848	+	0.509005i	−0.0615051	+	0.0223860i
$518$	−12.7282	+	2.01052i	−0.559243	+	0.0883370i
$519$	−19.0325	−	9.87622i	−0.835432	−	0.433518i
$520$	−0.0470458	+	0.0394762i	−0.00206310	+	0.00173114i
$521$	10.2487	−	17.7513i	0.449003	−	0.777697i	−0.549318	−	0.835613i	$-0.685112\pi$
$521$	10.2487	−	17.7513i	0.449003	−	0.777697i	0.998321	+	0.0579167i	$0.0184458\pi$
$522$	−8.09957	+	0.729857i	−0.354509	+	0.0319450i
$523$	−4.11749	−	7.13170i	−0.180045	−	0.311848i	0.761850	−	0.647753i	$-0.224291\pi$
$523$	−4.11749	−	7.13170i	−0.180045	−	0.311848i	−0.941896	+	0.335905i	$0.890958\pi$
$524$	0.329501	−	0.276484i	0.0143943	−	0.0120783i
$525$	22.3595	−	0.605301i	0.975849	−	0.0264175i
$526$	−2.12278	+	12.0389i	−0.0925578	+	0.524921i
$527$	39.6246	+	33.2490i	1.72607	+	1.44835i
$528$	1.02432	+	1.11494i	0.0445779	+	0.0485213i
$529$	−31.8793	−	11.6031i	−1.38606	−	0.504483i
$530$	−1.92253	−	3.32993i	−0.0835095	−	0.144643i
$531$	−14.9681	+	1.34879i	−0.649561	+	0.0585324i
$532$	−5.82217	+	6.69202i	−0.252423	+	0.290136i
$533$	−0.602330	−	0.219230i	−0.0260898	−	0.00949592i
$534$	19.2797	−	12.3178i	0.834313	−	0.533043i
$535$	−0.875742	+	4.96658i	−0.0378616	+	0.214724i
$536$	−4.93575	−	4.14159i	−0.213192	−	0.178889i
$537$	8.93926	−	11.6813i	0.385757	−	0.504085i
$538$	−4.45269	−	25.2525i	−0.191969	−	1.08871i
$539$	−5.67145	−	2.29691i	−0.244287	−	0.0989347i
$540$	1.32610	+	1.20566i	0.0570662	+	0.0518834i
$541$	−15.8713	+	27.4898i	−0.682358	+	1.18188i	0.291901	+	0.956449i	$0.405712\pi$
$541$	−15.8713	+	27.4898i	−0.682358	+	1.18188i	−0.974259	+	0.225431i	$0.927621\pi$
$542$	−12.6496	+	10.6142i	−0.543345	+	0.455921i
$543$	9.77719	+	1.27426i	0.419579	+	0.0546835i
$544$	−1.20266	+	6.82062i	−0.0515636	+	0.292432i
$545$	1.15638	+	0.970320i	0.0495340	+	0.0415640i
$546$	−0.758904	+	0.299716i	−0.0324781	+	0.0128267i
$547$	9.28683	+	3.38013i	0.397076	+	0.144524i	0.532837	−	0.846218i	$-0.321126\pi$
$547$	9.28683	+	3.38013i	0.397076	+	0.144524i	−0.135761	+	0.990742i	$0.543348\pi$
$548$	2.72355			0.116344
$549$	−0.425823	−	0.296517i	−0.0181737	−	0.0126550i
$550$	−4.26666			−0.181931
$551$	1.57817	+	8.95022i	0.0672321	+	0.381292i
$552$	−3.91344	+	12.4684i	−0.166567	+	0.530690i
$553$	0.449010	−	1.16826i	0.0190938	−	0.0496794i
$554$	4.06601	−	23.0595i	0.172748	−	0.979705i
$555$	2.83989	−	0.633465i	0.120547	−	0.0268891i
$556$	2.29383	+	0.834887i	0.0972802	+	0.0354071i
$557$	35.8802			1.52029			0.760147	−	0.649751i	$-0.225127\pi$
$557$	35.8802			1.52029			0.760147	+	0.649751i	$0.225127\pi$
$558$	15.8020	−	15.8844i	0.668952	−	0.672441i
$559$	0.789329	+	1.36716i	0.0333851	+	0.0578246i
$560$	−0.798335	+	0.442090i	−0.0337358	+	0.0186817i
$561$	8.83646	−	5.64562i	0.373075	−	0.238358i
$562$	−0.960375	+	0.349548i	−0.0405110	+	0.0147448i
$563$	−22.6450	−	19.0014i	−0.954373	−	0.800814i	0.0256557	−	0.999671i	$-0.491833\pi$
$563$	−22.6450	−	19.0014i	−0.954373	−	0.800814i	−0.980029	+	0.198857i	$0.936277\pi$
$564$	−1.79211	+	2.34182i	−0.0754614	+	0.0986085i
$565$	3.16681	+	1.15263i	0.133229	+	0.0484913i
$566$	−9.95016			−0.418236
$567$	11.6437	+	20.7707i	0.488991	+	0.872289i
$568$	−9.35093			−0.392356
$569$	26.7769	+	9.74600i	1.12255	+	0.408574i	0.835581	−	0.549367i	$-0.185131\pi$
$569$	26.7769	+	9.74600i	1.12255	+	0.408574i	0.286966	+	0.957941i	$0.407353\pi$
$570$	1.21723	−	1.59060i	0.0509842	−	0.0666231i
$571$	33.9081	+	28.4523i	1.41901	+	1.19069i	0.951868	+	0.306509i	$0.0991609\pi$
$571$	33.9081	+	28.4523i	1.41901	+	1.19069i	0.467142	+	0.884182i	$0.345284\pi$
$572$	0.146256	−	0.0532328i	0.00611526	−	0.00222577i
$573$	−23.8780	+	15.2556i	−0.997516	+	0.637314i
$574$	−8.16214	−	4.90893i	−0.340681	−	0.204895i
$575$	−18.4134	−	31.8929i	−0.767892	−	1.33003i
$576$	2.89979	+	0.768916i	0.120824	+	0.0320382i
$577$	5.80082			0.241491			0.120746	−	0.992683i	$-0.461471\pi$
$577$	5.80082			0.241491			0.120746	+	0.992683i	$0.461471\pi$
$578$	29.0997	+	10.5914i	1.21039	+	0.440545i
$579$	33.9520	−	7.57332i	1.41100	−	0.314737i
$580$	−0.162362	+	0.920799i	−0.00674170	+	0.0382341i
$581$	−3.62470	+	0.572550i	−0.150378	+	0.0237534i
$582$	−2.38775	+	7.60748i	−0.0989756	+	0.315340i
$583$	1.69213	+	9.59655i	0.0700809	+	0.397449i
$584$	11.8114			0.488759
$585$	0.166777	−	0.0782982i	0.00689537	−	0.00323723i
$586$	−5.84134			−0.241304
$587$	25.5478	+	9.29864i	1.05447	+	0.383796i	0.810348	−	0.585949i	$-0.199278\pi$
$587$	25.5478	+	9.29864i	1.05447	+	0.383796i	0.244122	+	0.969744i	$0.421500\pi$
$588$	−11.9203	+	2.21508i	−0.491585	+	0.0913482i
$589$	−19.1813	−	16.0950i	−0.790351	−	0.663183i
$590$	−0.300047	+	1.70165i	−0.0123527	+	0.0700558i
$591$	15.4760	+	2.01698i	0.636598	+	0.0829674i
$592$	3.73097	−	3.13066i	0.153342	−	0.128669i
$593$	6.64686	−	11.5127i	0.272954	−	0.472770i	−0.696663	−	0.717398i	$-0.745333\pi$
$593$	6.64686	−	11.5127i	0.272954	−	0.472770i	0.969617	+	0.244629i	$0.0786661\pi$
$594$	−2.11302	−	4.02069i	−0.0866983	−	0.164971i
$595$	2.05520	+	5.97682i	0.0842551	+	0.245026i
$596$	1.49958	+	8.50452i	0.0614250	+	0.348359i
$597$	22.1948	−	29.0029i	0.908374	−	1.18701i
$598$	1.02910	+	0.863516i	0.0420830	+	0.0353118i
$599$	−3.95210	+	22.4135i	−0.161478	+	0.915790i	0.791143	+	0.611631i	$0.209486\pi$
$599$	−3.95210	+	22.4135i	−0.161478	+	0.915790i	−0.952621	+	0.304159i	$0.901625\pi$
$600$	−7.12428	+	4.55171i	−0.290848	+	0.185823i
$601$	28.4675	+	10.3613i	1.16121	+	0.422647i	0.849531	−	0.527539i	$-0.176885\pi$
$601$	28.4675	+	10.3613i	1.16121	+	0.422647i	0.311683	+	0.950186i	$0.399107\pi$
$602$	7.62787	+	22.1829i	0.310889	+	0.904108i
$603$	11.1281	+	15.8049i	0.453171	+	0.643626i
$604$	−0.138284	−	0.239516i	−0.00562671	−	0.00974575i
$605$	3.31763	+	1.20752i	0.134881	+	0.0490926i
$606$	19.4394	+	21.1591i	0.789673	+	0.859530i
$607$	4.40384	+	3.69526i	0.178746	+	0.149986i	0.727771	−	0.685820i	$-0.240556\pi$
$607$	4.40384	+	3.69526i	0.178746	+	0.149986i	−0.549025	+	0.835806i	$0.685001\pi$
$608$	0.582178	−	3.30170i	0.0236104	−	0.133901i
$609$	−5.91781	+	10.9223i	−0.239802	+	0.442593i
$610$	−0.0457009	+	0.0383476i	−0.00185038	+	0.00155265i
$611$	0.151570	+	0.262528i	0.00613189	+	0.0106207i
$612$	8.73194	−	18.8536i	0.352968	−	0.762112i
$613$	3.46186	−	5.99611i	0.139823	−	0.242181i	−0.787606	−	0.616179i	$-0.788680\pi$
$613$	3.46186	−	5.99611i	0.139823	−	0.242181i	0.927430	+	0.373998i	$0.122013\pi$
$614$	7.75759	−	6.50939i	0.313071	−	0.262698i
$615$	1.90896	+	0.990590i	0.0769769	+	0.0399445i
$616$	2.28441	−	0.360841i	0.0920415	−	0.0145387i
$617$	45.8449	−	16.6862i	1.84565	−	0.671761i	0.858310	−	0.513132i	$-0.171515\pi$
$617$	45.8449	−	16.6862i	1.84565	−	0.671761i	0.987338	−	0.158629i	$-0.0507073\pi$
$618$	−16.3421	+	21.3549i	−0.657376	+	0.859020i
$619$	−27.1910	+	22.8160i	−1.09290	+	0.917051i	−0.996927	−	0.0783331i	$-0.975040\pi$
$619$	−27.1910	+	22.8160i	−1.09290	+	0.917051i	−0.0959716	+	0.995384i	$0.530596\pi$
$620$	−1.28803	−	2.23093i	−0.0517284	−	0.0895962i
$621$	20.9353	−	33.1466i	0.840104	−	1.33013i
$622$	−27.1034			−1.08675
$623$	0.624458	−	34.9422i	0.0250184	−	1.39993i
$624$	0.187422	−	0.244913i	0.00750290	−	0.00980435i
$625$	4.03378	−	22.8767i	0.161351	−	0.915068i
$626$	5.42946	−	30.7920i	0.217005	−	1.23070i
$627$	−4.27751	+	2.73291i	−0.170827	+	0.109142i
$628$	12.5681	−	10.5459i	0.501523	−	0.420827i
$629$	−16.8659	−	29.2126i	−0.672489	−	1.16478i
$630$	2.65493	−	0.668115i	0.105775	−	0.0266183i
$631$	10.1540	−	17.5873i	0.404226	−	0.700140i	−0.590005	−	0.807400i	$-0.700874\pi$
$631$	10.1540	−	17.5873i	0.404226	−	0.700140i	0.994231	+	0.107259i	$0.0342075\pi$
$632$	0.0821443	+	0.465863i	0.00326752	+	0.0185311i
$633$	−39.5433	+	8.82051i	−1.57170	+	0.350584i
$634$	−17.0582	+	6.20866i	−0.677466	+	0.246577i
$635$	2.51943	+	2.11405i	0.0999803	+	0.0838935i
$636$	13.0631	+	14.2187i	0.517987	+	0.563809i
$637$	−0.260150	+	1.21892i	−0.0103075	+	0.0482955i
$638$	1.18480	−	2.05213i	0.0469065	−	0.0812444i
$639$	27.1157	+	7.19008i	1.07268	+	0.284435i
$640$	0.172459	−	0.298708i	0.00681705	−	0.0118075i
$641$	−1.73860	−	9.86012i	−0.0686708	−	0.389451i	−0.999700	−	0.0245058i	$-0.992199\pi$
$641$	−1.73860	−	9.86012i	−0.0686708	−	0.389451i	0.931029	−	0.364945i	$-0.118912\pi$
$642$	−1.13757	−	25.2995i	−0.0448964	−	0.998491i
$643$	34.3845	+	28.8520i	1.35599	+	1.13781i	0.977198	+	0.212331i	$0.0681054\pi$
$643$	34.3845	+	28.8520i	1.35599	+	1.13781i	0.378794	+	0.925481i	$0.376339\pi$
$644$	12.5560	+	15.5185i	0.494774	+	0.611515i
$645$	−2.03336	−	4.89097i	−0.0800637	−	0.192582i
$646$	−21.8194	−	7.94163i	−0.858474	−	0.312459i
$647$	−3.03773	−	5.26150i	−0.119425	−	0.206851i	0.800115	−	0.599847i	$-0.204772\pi$
$647$	−3.03773	−	5.26150i	−0.119425	−	0.206851i	−0.919540	+	0.392996i	$0.871439\pi$
$648$	−7.81754	−	4.45939i	−0.307102	−	0.175181i
$649$	2.18952	−	3.79236i	0.0859461	−	0.148863i
$650$	0.150915	+	0.855882i	0.00591938	+	0.0335704i
$651$	−6.85311	−	33.5322i	−0.268594	−	1.31423i
$652$	19.9244	−	7.25191i	0.780302	−	0.284007i
$653$	−35.4955	+	12.9193i	−1.38905	+	0.505572i	−0.924908	−	0.380190i	$-0.875859\pi$
$653$	−35.4955	+	12.9193i	−1.38905	+	0.505572i	−0.464139	+	0.885762i	$0.653636\pi$
$654$	−6.72844	−	3.49149i	−0.263103	−	0.136528i
$655$	0.0257626	+	0.146107i	0.00100663	+	0.00570886i
$656$	3.59996			0.140555
$657$	−34.2506	−	9.08198i	−1.33624	−	0.354322i
$658$	1.46474	+	4.25966i	0.0571014	+	0.166059i
$659$	−5.02289	+	4.21470i	−0.195664	+	0.164181i	−0.735356	−	0.677681i	$-0.762985\pi$
$659$	−5.02289	+	4.21470i	−0.195664	+	0.164181i	0.539692	+	0.841862i	$0.318541\pi$
$660$	−0.509694	+	0.113692i	−0.0198398	+	0.00442546i
$661$	−29.0420	+	10.5704i	−1.12960	+	0.411142i	−0.838148	−	0.545443i	$-0.816362\pi$
$661$	−29.0420	+	10.5704i	−1.12960	+	0.411142i	−0.291455	+	0.956585i	$0.594139\pi$
$662$	−14.1477	+	5.14935i	−0.549867	+	0.200135i
$663$	−1.44505	−	1.57288i	−0.0561211	−	0.0610857i
$664$	1.06250	−	0.891542i	0.0412330	−	0.0345986i
$665$	−0.994874	−	2.89323i	−0.0385796	−	0.112195i
$666$	−13.2262	+	6.20944i	−0.512506	+	0.240611i
$667$	20.4526			0.791929
$668$	−0.162708	−	0.922765i	−0.00629538	−	0.0357029i
$669$	5.51396	−	3.52287i	0.213182	−	0.136202i
$670$	2.08834	−	0.760095i	0.0806797	−	0.0293650i
$671$	0.142075	−	0.0517110i	0.00548473	−	0.00199628i
$672$	3.42946	−	3.03954i	0.132294	−	0.117253i
$673$	−6.01881	−	34.1344i	−0.232008	−	1.31578i	−0.848824	−	0.528676i	$-0.822689\pi$
$673$	−6.01881	−	34.1344i	−0.232008	−	1.31578i	0.616815	−	0.787108i	$-0.288423\pi$
$674$	−4.82614	+	8.35911i	−0.185896	+	0.321981i
$675$	24.1588	−	7.72101i	0.929872	−	0.297182i
$676$	6.48415	+	11.2309i	0.249390	+	0.431957i
$677$	33.7765	+	12.2936i	1.29814	+	0.472483i	0.896389	−	0.443268i	$-0.146181\pi$
$677$	33.7765	+	12.2936i	1.29814	+	0.472483i	0.401746	+	0.915751i	$0.368403\pi$
$678$	−16.7812	−	2.18709i	−0.644479	−	0.0839945i
$679$	7.66091	+	9.46849i	0.293999	+	0.363367i
$680$	−1.82996	−	1.53552i	−0.0701759	−	0.0588846i
$681$	−29.1086	+	18.5975i	−1.11544	+	0.712657i
$682$	1.13367	+	6.42934i	0.0434103	+	0.246192i
$683$	−17.9003	+	31.0043i	−0.684937	+	1.18635i	0.288519	+	0.957474i	$0.406837\pi$
$683$	−17.9003	+	31.0043i	−0.684937	+	1.18635i	−0.973457	+	0.228872i	$0.926496\pi$
$684$	−4.22692	+	9.12657i	−0.161620	+	0.348963i
$685$	−0.469702	+	0.813547i	−0.0179464	+	0.0310841i
$686$	−7.25771	+	17.0389i	−0.277101	+	0.650550i
$687$	−8.11939	+	1.81111i	−0.309774	+	0.0690981i
$688$	−6.79190	−	5.69908i	−0.258939	−	0.217275i
$689$	1.86519	−	0.678875i	0.0710582	−	0.0258631i
$690$	−3.04950	−	3.31927i	−0.116092	−	0.126362i
$691$	0.709614	+	4.02442i	0.0269950	+	0.153096i	0.995326	−	0.0965747i	$-0.0307887\pi$
$691$	0.709614	+	4.02442i	0.0269950	+	0.153096i	−0.968331	+	0.249671i	$0.919678\pi$
$692$	6.18987	−	10.7212i	0.235304	−	0.407558i
$693$	−6.90176	−	0.710157i	−0.262176	−	0.0269766i
$694$	−13.4689	−	23.3289i	−0.511274	−	0.885552i
$695$	−0.644981	+	0.541203i	−0.0244655	+	0.0205290i
$696$	−0.210905	−	4.69050i	−0.00799432	−	0.177793i
$697$	4.32953	−	24.5540i	0.163993	−	0.930048i
$698$	−4.71314	+	26.7296i	−0.178395	+	1.01173i
$699$	41.6337	+	5.42609i	1.57473	+	0.205234i
$700$	−0.230752	+	12.9119i	−0.00872159	+	0.488025i
$701$	35.0169			1.32257			0.661285	−	0.750135i	$-0.270011\pi$
$701$	35.0169			1.32257			0.661285	+	0.750135i	$0.270011\pi$
$702$	−0.731802	+	0.566082i	−0.0276201	+	0.0213654i
$703$	8.16439	+	14.1411i	0.307926	+	0.533343i
$704$	−0.669623	+	0.561880i	−0.0252374	+	0.0211767i
$705$	−0.390456	−	0.939187i	−0.0147054	−	0.0353718i
$706$	−6.24891	+	2.27442i	−0.235181	+	0.0855989i
$707$	43.3532	−	6.84799i	1.63047	−	0.257545i
$708$	−0.389755	−	8.66811i	−0.0146479	−	0.325767i
$709$	−11.9094	+	9.99314i	−0.447265	+	0.375300i	−0.838420	−	0.545025i	$-0.816520\pi$
$709$	−11.9094	+	9.99314i	−0.447265	+	0.375300i	0.391155	+	0.920325i	$0.372076\pi$
$710$	1.61265	−	2.79320i	0.0605218	−	0.104827i
$711$	0.120009	−	1.41407i	0.00450068	−	0.0530317i
$712$	6.60450	+	11.4393i	0.247514	+	0.428707i
$713$	−43.1663	+	36.2208i	−1.61659	+	1.35648i
$714$	−16.6071	−	27.0466i	−0.621504	−	1.01219i
$715$	−0.00932211	+	0.0528683i	−0.000348627	+	0.00197716i
$716$	6.50556	+	5.45881i	0.243124	+	0.204005i
$717$	−1.16158	+	3.70085i	−0.0433802	+	0.138211i
$718$	2.18355	+	0.794746i	0.0814892	+	0.0296596i
$719$	7.59799	+	13.1601i	0.283357	+	0.490789i	0.972210	−	0.234112i	$-0.0752184\pi$
$719$	7.59799	+	13.1601i	0.283357	+	0.490789i	−0.688852	+	0.724902i	$0.741885\pi$
$720$	−0.729777	+	0.733584i	−0.0271972	+	0.0273391i
$721$	13.3568	+	38.8435i	0.497434	+	1.44661i
$722$	−7.29190	−	2.65403i	−0.271376	−	0.0987729i
$723$	−2.17293	−	48.3258i	−0.0808122	−	1.79725i
$724$	−0.988510	+	5.60612i	−0.0367377	+	0.208350i
$725$	10.1359	+	8.50503i	0.376438	+	0.315869i
$726$	−17.5804	−	2.29125i	−0.652470	−	0.0850361i
$727$	−2.20445	−	12.5021i	−0.0817585	−	0.463676i	−0.998009	−	0.0630700i	$-0.979911\pi$
$727$	−2.20445	−	12.5021i	−0.0817585	−	0.463676i	0.916251	−	0.400606i	$-0.131200\pi$
$728$	−0.153185	−	0.445484i	−0.00567742	−	0.0165107i
$729$	19.2403	+	18.9423i	0.712604	+	0.701567i
$730$	−2.03699	+	3.52816i	−0.0753922	+	0.130583i
$731$	−47.0396	+	39.4709i	−1.73982	+	1.45988i
$732$	0.182064	−	0.237911i	0.00672929	−	0.00879345i
$733$	4.28481	−	24.3004i	0.158263	−	0.897554i	−0.797479	−	0.603347i	$-0.793833\pi$
$733$	4.28481	−	24.3004i	0.158263	−	0.897554i	0.955742	−	0.294207i	$-0.0950555\pi$
$734$	13.2145	+	11.0883i	0.487757	+	0.409277i
$735$	1.39410	−	3.94270i	0.0514223	−	0.145429i
$736$	−7.08987	−	2.58050i	−0.261336	−	0.0951185i
$737$	−5.63217			−0.207464
$738$	−10.4391	−	2.76807i	−0.384270	−	0.101894i
$739$	−50.2708			−1.84924			−0.924621	−	0.380888i	$-0.875618\pi$
$739$	−50.2708			−1.84924			−0.924621	+	0.380888i	$0.875618\pi$
$740$	0.291712	+	1.65438i	0.0107236	+	0.0608163i
$741$	0.699513	+	0.761394i	0.0256973	+	0.0279705i
$742$	29.1330	−	4.60179i	1.06951	−	0.168937i
$743$	3.50903	−	19.9007i	0.128734	−	0.730086i	−0.850286	−	0.526321i	$-0.823571\pi$
$743$	3.50903	−	19.9007i	0.128734	−	0.730086i	0.979020	−	0.203765i	$-0.0653178\pi$
$744$	8.75181	+	9.52602i	0.320857	+	0.349241i
$745$	−2.79898	−	1.01875i	−0.102547	−	0.0373240i
$746$	−9.86981			−0.361360
$747$	−3.76654	+	1.76831i	−0.137811	+	0.0646991i
$748$	3.02704	+	5.24299i	0.110680	+	0.191703i
$749$	−33.1509	−	19.9379i	−1.21131	−	0.728513i
$750$	−0.265160	−	5.89713i	−0.00968227	−	0.215333i
$751$	14.0341	−	5.10801i	0.512113	−	0.186394i	−0.0730210	−	0.997330i	$-0.523264\pi$
$751$	14.0341	−	5.10801i	0.512113	−	0.186394i	0.585134	+	0.810936i	$0.301042\pi$
$752$	−1.30421	−	1.09436i	−0.0475597	−	0.0399073i
$753$	−22.3494	−	2.91279i	−0.814458	−	0.106148i
$754$	−0.453559	−	0.165082i	−0.0165176	−	0.00601193i
$755$	0.0953937			0.00347173
$756$	−12.2819	+	6.17706i	−0.446687	+	0.224658i
$757$	−39.1056			−1.42132			−0.710658	−	0.703538i	$-0.751603\pi$
$757$	−39.1056			−1.42132			−0.710658	+	0.703538i	$0.751603\pi$
$758$	3.48719	+	1.26923i	0.126660	+	0.0461006i
$759$	4.38521	+	10.5480i	0.159173	+	0.382868i
$760$	0.885842	+	0.743309i	0.0321329	+	0.0269627i
$761$	0.664821	−	0.241975i	0.0240998	−	0.00877159i	−0.329942	−	0.944001i	$-0.607029\pi$
$761$	0.664821	−	0.241975i	0.0240998	−	0.00877159i	0.354042	+	0.935230i	$0.384807\pi$
$762$	−14.6593	−	7.60694i	−0.531051	−	0.275571i
$763$	−10.1298	+	5.60951i	−0.366722	+	0.203078i
$764$	−8.17971	−	14.1677i	−0.295932	−	0.512568i
$765$	4.12582	+	5.85978i	0.149169	+	0.211861i
$766$	9.27618			0.335162
$767$	−0.838183	−	0.305074i	−0.0302650	−	0.0110156i
$768$	−0.518689	+	1.65256i	−0.0187166	+	0.0596317i
$769$	−6.43977	+	36.5218i	−0.232224	+	1.31701i	0.616157	+	0.787623i	$0.288689\pi$
$769$	−6.43977	+	36.5218i	−0.232224	+	1.31701i	−0.848381	+	0.529386i	$0.822422\pi$
$770$	−0.286181	+	0.744602i	−0.0103133	+	0.0268336i
$771$	−11.5313	+	2.57216i	−0.415288	+	0.0926340i
$772$	3.48754	+	19.7788i	0.125519	+	0.711855i
$773$	−3.28679			−0.118218			−0.0591089	−	0.998252i	$-0.518826\pi$
$773$	−3.28679			−0.118218			−0.0591089	+	0.998252i	$0.518826\pi$
$774$	15.3129	+	21.7485i	0.550413	+	0.781734i
$775$	−36.4544			−1.30948
$776$	−4.32582	−	1.57447i	−0.155288	−	0.0565202i
$777$	−3.27945	+	22.0769i	−0.117650	+	0.792005i
$778$	1.55196	+	1.30225i	0.0556404	+	0.0466879i
$779$	−2.09582	+	11.8860i	−0.0750905	+	0.425860i
$780$	0.0408347	+	0.0982220i	0.00146212	+	0.00351691i
$781$	−6.26160	+	5.25410i	−0.224058	+	0.188007i
$782$	−26.1273	+	45.2538i	−0.934310	+	1.61827i
$783$	−2.99502	+	13.7636i	−0.107033	+	0.491871i
$784$	−0.968444	−	6.93268i	−0.0345873	−	0.247596i
$785$	0.982660	+	5.57294i	0.0350726	+	0.198907i
$786$	−0.285999	−	0.687929i	−0.0102012	−	0.0245376i
$787$	7.12539	+	5.97891i	0.253993	+	0.213125i	0.760889	−	0.648882i	$-0.224763\pi$
$787$	7.12539	+	5.97891i	0.253993	+	0.213125i	−0.506897	+	0.862007i	$0.669207\pi$
$788$	−1.56468	+	8.87375i	−0.0557394	+	0.316114i
$789$	18.7940	+	9.75248i	0.669083	+	0.347197i
$790$	−0.153324	−	0.0558053i	−0.00545502	−	0.00198546i
$791$	−16.9676	+	19.5026i	−0.603298	+	0.693432i
$792$	2.37380	−	1.11445i	0.0843494	−	0.0396003i
$793$	−0.0153984	−	0.0266708i	−0.000546813	−	0.000947108i
$794$	−16.3176	−	5.93912i	−0.579090	−	0.210772i
$795$	−6.50011	+	1.44991i	−0.230535	+	0.0514231i
$796$	16.1523	+	13.5534i	0.572504	+	0.480388i
$797$	5.26438	−	29.8558i	0.186474	−	1.05755i	−0.737573	−	0.675267i	$-0.764028\pi$
$797$	5.26438	−	29.8558i	0.186474	−	1.05755i	0.924047	−	0.382279i	$-0.124861\pi$
$798$	8.03909	+	13.0926i	0.284581	+	0.463472i
$799$	−9.03275	+	7.57938i	−0.319556	+	0.268139i
$800$	−2.44052	−	4.22710i	−0.0862853	−	0.149450i
$801$	−10.3558	−	38.2500i	−0.365903	−	1.35150i
$802$	−8.60921	+	14.9116i	−0.304002	+	0.526547i
$803$	7.90919	−	6.63660i	0.279109	−	0.234200i
$804$	−9.40435	+	6.00845i	−0.331666	+	0.211902i
$805$	−6.80090	+	1.07426i	−0.239700	+	0.0378626i
$806$	1.24961	−	0.454821i	0.0440157	−	0.0160204i
$807$	−44.0408	−	5.73981i	−1.55031	−	0.202051i
$808$	−12.7080	+	10.6633i	−0.447067	+	0.375134i
$809$	−0.598540	−	1.03670i	−0.0210435	−	0.0364485i	0.855312	−	0.518114i	$-0.173366\pi$
$809$	−0.598540	−	1.03670i	−0.0210435	−	0.0364485i	−0.876355	+	0.481665i	$0.840032\pi$
$810$	2.68026	−	1.56610i	0.0941748	−	0.0550271i
$811$	−47.3836			−1.66386			−0.831932	−	0.554878i	$-0.812765\pi$
$811$	−47.3836			−1.66386			−0.831932	+	0.554878i	$0.812765\pi$
$812$	−6.14614	−	3.69646i	−0.215687	−	0.129720i
$813$	10.9795	+	26.4097i	0.385069	+	0.926228i
$814$	0.739290	−	4.19272i	0.0259121	−	0.146955i
$815$	−1.26995	+	7.20225i	−0.0444845	+	0.252284i
$816$	10.6477	+	5.52525i	0.372744	+	0.193422i
$817$	22.7707	−	19.1069i	0.796646	−	0.668466i
$818$	−8.12887	−	14.0796i	−0.284219	−	0.492282i
$819$	0.101665	+	1.40960i	0.00355245	+	0.0492552i
$820$	−0.620847	+	1.07534i	−0.0216809	+	0.0375525i
$821$	−1.93306	−	10.9629i	−0.0674642	−	0.382609i	−0.999780	−	0.0209639i	$-0.993326\pi$
$821$	−1.93306	−	10.9629i	−0.0674642	−	0.382609i	0.932316	−	0.361645i	$-0.117785\pi$
$822$	1.41268	−	4.50084i	0.0492727	−	0.156985i
$823$	25.1804	−	9.16491i	0.877733	−	0.319469i	0.136438	−	0.990649i	$-0.456434\pi$
$823$	25.1804	−	9.16491i	0.877733	−	0.319469i	0.741294	+	0.671180i	$0.234212\pi$
$824$	−11.8930	−	9.97942i	−0.414312	−	0.347649i
$825$	−2.21307	+	7.05092i	−0.0770491	+	0.245482i
$826$	−11.3582	−	6.83111i	−0.395201	−	0.237685i
$827$	6.01479	−	10.4179i	0.209155	−	0.362267i	−0.742294	−	0.670075i	$-0.766262\pi$
$827$	6.01479	−	10.4179i	0.209155	−	0.362267i	0.951449	+	0.307808i	$0.0995954\pi$
$828$	18.5749	+	12.9344i	0.645523	+	0.449502i
$829$	17.6088	−	30.4994i	0.611580	−	1.05929i	−0.379394	−	0.925235i	$-0.623868\pi$
$829$	17.6088	−	30.4994i	0.611580	−	1.05929i	0.990974	−	0.134053i	$-0.0427992\pi$
$830$	0.0830733	+	0.471132i	0.00288352	+	0.0163532i
$831$	−35.9983	−	18.6800i	−1.24877	−	0.648004i
$832$	0.136397	+	0.114451i	0.00472871	+	0.00396786i
$833$	−48.4499	−	1.73227i	−1.67869	−	0.0600195i
$834$	2.56949	−	3.35766i	0.0889741	−	0.116266i
$835$	0.303698	+	0.110537i	0.0105099	+	0.00382529i
$836$	−1.46532	−	2.53801i	−0.0506791	−	0.0877788i
$837$	−18.0537	−	34.3528i	−0.624027	−	1.18741i
$838$	9.04305	−	15.6630i	0.312387	−	0.541070i
$839$	9.00886	+	51.0918i	0.311021	+	1.76389i	0.593715	+	0.804675i	$0.297661\pi$
$839$	9.00886	+	51.0918i	0.311021	+	1.76389i	−0.282695	+	0.959210i	$0.591228\pi$
$840$	0.316494	+	1.54860i	0.0109201	+	0.0534319i
$841$	20.3458	−	7.40528i	0.701581	−	0.255354i
$842$	14.1230	−	5.14035i	0.486711	−	0.177148i
$843$	0.0795141	+	1.76839i	0.00273861	+	0.0609065i
$844$	−4.06187	−	23.0360i	−0.139815	−	0.792933i
$845$	−4.47301			−0.153876
$846$	2.94046	+	4.17625i	0.101095	+	0.143582i
$847$	−17.7757	+	20.4314i	−0.610779	+	0.702030i
$848$	−8.53968	+	7.16564i	−0.293254	+	0.246069i
$849$	−5.16103	+	16.4433i	−0.177126	+	0.564331i
$850$	−31.7665	+	11.5621i	−1.08958	+	0.396576i
$851$	34.5308	−	12.5682i	1.18370	−	0.430831i
$852$	−4.85022	+	15.4530i	−0.166166	+	0.529411i
$853$	26.1780	−	21.9659i	0.896317	−	0.752100i	−0.0731497	−	0.997321i	$-0.523305\pi$
$853$	26.1780	−	21.9659i	0.896317	−	0.752100i	0.969467	+	0.245221i	$0.0788607\pi$
$854$	−0.148806	−	0.432749i	−0.00509204	−	0.0148084i
$855$	−1.99721	−	2.83658i	−0.0683031	−	0.0970089i
$856$	14.6214			0.499750
$857$	−2.00925	−	11.3950i	−0.0686347	−	0.389247i	−0.999702	−	0.0244000i	$-0.992232\pi$
$857$	−2.00925	−	11.3950i	−0.0686347	−	0.389247i	0.931068	−	0.364847i	$-0.118879\pi$
$858$	−0.0121092	−	0.269308i	−0.000413402	−	0.00919402i
$859$	47.4257	−	17.2615i	1.61814	−	0.588956i	0.635117	−	0.772416i	$-0.280952\pi$
$859$	47.4257	−	17.2615i	1.61814	−	0.588956i	0.983027	+	0.183460i	$0.0587297\pi$
$860$	2.87369	−	1.04594i	0.0979919	−	0.0356661i
$861$	−12.3459	+	10.9422i	−0.420748	+	0.372911i
$862$	5.00657	+	28.3937i	0.170524	+	0.967092i
$863$	1.06132	−	1.83825i	0.0361276	−	0.0625748i	−0.847396	−	0.530961i	$-0.821831\pi$
$863$	1.06132	−	1.83825i	0.0361276	−	0.0625748i	0.883524	+	0.468386i	$0.155164\pi$
$864$	2.77477	−	4.39325i	0.0943995	−	0.149461i
$865$	2.13500	+	3.69793i	0.0725922	+	0.125733i
$866$	−8.08969	−	2.94441i	−0.274899	−	0.100055i
$867$	32.5966	−	42.5954i	1.10704	−	1.44661i
$868$	19.5180	−	3.08303i	0.662485	−	0.104645i
$869$	0.316765	+	0.265798i	0.0107455	+	0.00901657i
$870$	1.43746	+	0.745921i	0.0487345	+	0.0252891i
$871$	0.199214	+	1.12980i	0.00675012	+	0.0382818i
$872$	2.18827	−	3.79020i	0.0741042	−	0.128352i
$873$	11.3333	+	7.89182i	0.383575	+	0.267098i
$874$	12.6476	−	21.9063i	0.427811	−	0.740991i
$875$	−7.72725	−	4.64737i	−0.261229	−	0.157110i
$876$	6.12644	−	19.5191i	0.206993	−	0.659489i
$877$	−5.26052	−	4.41410i	−0.177635	−	0.149054i	0.549635	−	0.835405i	$-0.314767\pi$
$877$	−5.26052	−	4.41410i	−0.177635	−	0.149054i	−0.727270	+	0.686351i	$0.759211\pi$
$878$	−23.1734	+	8.43444i	−0.782065	+	0.284648i
$879$	−3.02984	+	9.65318i	−0.102194	+	0.325594i
$880$	−0.0523556	−	0.296923i	−0.00176491	−	0.0100093i
$881$	−27.2296	+	47.1630i	−0.917388	+	1.58896i	−0.114022	+	0.993478i	$0.536373\pi$
$881$	−27.2296	+	47.1630i	−0.917388	+	1.58896i	−0.803367	+	0.595485i	$0.796960\pi$
$882$	−2.52237	+	20.8480i	−0.0849326	+	0.701987i
$883$	−6.18561	−	10.7138i	−0.208162	−	0.360548i	0.742973	−	0.669321i	$-0.233415\pi$
$883$	−6.18561	−	10.7138i	−0.208162	−	0.360548i	−0.951136	+	0.308773i	$0.900082\pi$
$884$	0.944663	−	0.792667i	0.0317725	−	0.0266603i
$885$	2.65645	+	1.37847i	0.0892957	+	0.0463368i
$886$	−1.64737	+	9.34269i	−0.0553444	+	0.313874i
$887$	5.90919	−	33.5127i	0.198411	−	1.12525i	−0.709065	−	0.705143i	$-0.750883\pi$
$887$	5.90919	−	33.5127i	0.198411	−	1.12525i	0.907477	−	0.420103i	$-0.138006\pi$
$888$	−3.23839	−	7.78950i	−0.108673	−	0.261399i
$889$	−22.0698	+	12.2215i	−0.740199	+	0.409896i
$890$	−4.55603			−0.152719
$891$	−7.74044	+	1.40641i	−0.259315	+	0.0471166i
$892$	1.88888	+	3.27164i	0.0632444	+	0.109543i
$893$	4.37254	−	3.66899i	0.146321	−	0.122778i
$894$	14.8321	+	1.93305i	0.496058	+	0.0646510i
$895$	−2.75254	+	1.00184i	−0.0920072	+	0.0334879i
$896$	1.66417	+	2.05683i	0.0555960	+	0.0687138i
$897$	1.96080	−	1.25275i	0.0654691	−	0.0418282i
$898$	−15.2420	+	12.7895i	−0.508632	+	0.426793i
$899$	10.1229	−	17.5334i	0.337618	−	0.584771i
$900$	3.82669	+	14.1342i	0.127556	+	0.471141i
$901$	38.6038	+	66.8637i	1.28608	+	2.22755i
$902$	2.41062	−	2.02275i	0.0802648	−	0.0673502i
$903$	40.6151	−	1.09950i	1.35159	−	0.0365892i
$904$	1.69664	−	9.62214i	0.0564295	−	0.320028i
$905$	−1.50412	−	1.26210i	−0.0499985	−	0.0419537i
$906$	−0.467541	+	0.104290i	−0.0155330	+	0.00346479i
$907$	−15.1153	−	5.50151i	−0.501895	−	0.182675i	0.0786514	−	0.996902i	$-0.474939\pi$
$907$	−15.1153	−	5.50151i	−0.501895	−	0.182675i	−0.580546	+	0.814228i	$0.697161\pi$
$908$	−9.97153	−	17.2712i	−0.330917	−	0.573165i
$909$	45.0498	−	21.1499i	1.49421	−	0.701498i
$910$	0.159488	+	0.0310702i	0.00528697	+	0.00102997i
$911$	3.71447	+	1.35196i	0.123066	+	0.0447923i	0.402819	−	0.915280i	$-0.368030\pi$
$911$	3.71447	+	1.35196i	0.123066	+	0.0447923i	−0.279753	+	0.960072i	$0.590253\pi$
$912$	−5.15429	−	2.67464i	−0.170676	−	0.0885661i
$913$	0.210533	−	1.19399i	0.00696764	−	0.0395155i
$914$	−21.0765	−	17.6853i	−0.697149	−	0.584978i
$915$	0.0396673	+	0.0954141i	0.00131136	+	0.00315429i
$916$	−0.834022	−	4.72997i	−0.0275568	−	0.156283i
$917$	−1.11702	−	0.217610i	−0.0368874	−	0.00718611i
$918$	−26.6276	−	24.2092i	−0.878841	−	0.799023i
$919$	16.7643	−	29.0365i	0.553002	−	0.957827i	−0.445054	−	0.895504i	$-0.646816\pi$
$919$	16.7643	−	29.0365i	0.553002	−	0.957827i	0.998056	−	0.0623234i	$-0.0198510\pi$
$920$	1.99353	−	1.67277i	0.0657248	−	0.0551496i
$921$	−6.73340	−	16.1962i	−0.221873	−	0.533685i
$922$	−1.54638	+	8.76995i	−0.0509273	+	0.288823i
$923$	1.27544	+	1.07022i	0.0419816	+	0.0352267i
$924$	0.588585	−	3.96229i	0.0193630	−	0.130350i
$925$	22.3391	+	8.13076i	0.734505	+	0.267338i
$926$	40.3799			1.32697
$927$	26.8139	+	38.0829i	0.880682	+	1.25081i
$928$	2.71080			0.0889862
$929$	9.07403	+	51.4614i	0.297709	+	1.68839i	0.655982	+	0.754777i	$0.272255\pi$
$929$	9.07403	+	51.4614i	0.297709	+	1.68839i	−0.358272	+	0.933617i	$0.616634\pi$
$930$	−4.35483	+	0.971388i	−0.142801	+	0.0318531i
$931$	23.4534	+	0.838549i	0.768655	+	0.0274823i
$932$	−4.20932	+	23.8722i	−0.137881	+	0.781961i
$933$	−14.0582	+	44.7900i	−0.460245	+	1.46636i
$934$	−21.6813	−	7.89134i	−0.709433	−	0.258213i
$935$	−2.08817			−0.0682904
$936$	−0.307519	−	0.436760i	−0.0100516	−	0.0142760i
$937$	2.60312	+	4.50873i	0.0850401	+	0.147294i	0.905408	−	0.424542i	$-0.139565\pi$
$937$	2.60312	+	4.50873i	0.0850401	+	0.147294i	−0.820368	+	0.571836i	$0.806232\pi$
$938$	−0.304602	+	17.0443i	−0.00994561	+	0.556516i
$939$	−48.0695	−	24.9440i	−1.56869	−	0.814016i
$940$	0.551818	−	0.200845i	0.0179983	−	0.00655086i
$941$	38.7667	+	32.5291i	1.26376	+	1.06042i	0.995271	+	0.0971365i	$0.0309684\pi$
$941$	38.7667	+	32.5291i	1.26376	+	1.06042i	0.268488	+	0.963283i	$0.413476\pi$
$942$	−10.9088	−	26.2396i	−0.355429	−	0.854934i
$943$	25.5233	+	9.28971i	0.831152	+	0.302515i
$944$	5.00959			0.163048
$945$	0.272981	−	4.73398i	0.00888007	−	0.153996i
$946$	−7.75021			−0.251981
$947$	−49.7279	−	18.0995i	−1.61594	−	0.588154i	−0.633338	−	0.773875i	$-0.718316\pi$
$947$	−49.7279	−	18.0995i	−1.61594	−	0.588154i	−0.982602	+	0.185721i	$0.940538\pi$
$948$	0.812476	+	0.105890i	0.0263880	+	0.00343913i
$949$	−1.61104	−	1.35182i	−0.0522966	−	0.0438820i
$950$	15.3774	−	5.59692i	0.498909	−	0.181588i
$951$	1.41233	+	31.4100i	0.0457979	+	1.01854i
$952$	16.0303	−	8.87700i	0.519544	−	0.287705i
$953$	12.1486	+	21.0420i	0.393531	+	0.681616i	0.992913	−	0.118848i	$-0.0379200\pi$
$953$	12.1486	+	21.0420i	0.393531	+	0.681616i	−0.599381	+	0.800464i	$0.704587\pi$
$954$	30.2730	−	14.2125i	0.980125	−	0.460148i
$955$	5.64267			0.182592
$956$	−2.10441	−	0.765942i	−0.0680614	−	0.0247723i
$957$	−2.77673	−	3.02236i	−0.0897588	−	0.0976991i
$958$	0.767672	−	4.35368i	0.0248023	−	0.140661i
$959$	−4.53245	−	5.60188i	−0.146361	−	0.180894i
$960$	−0.404181	−	0.439936i	−0.0130449	−	0.0141989i
$961$	4.30296	+	24.4033i	0.138805	+	0.787203i
$962$	−0.867199			−0.0279596
$963$	−42.3990	−	11.2426i	−1.36629	−	0.362289i
$964$	27.9291			0.899535
$965$	−6.50955	−	2.36928i	−0.209550	−	0.0762699i
$966$	32.1579	−	12.7002i	1.03467	−	0.408623i
$967$	11.7983	+	9.89991i	0.379406	+	0.318360i	0.812469	−	0.583004i	$-0.198123\pi$
$967$	11.7983	+	9.89991i	0.379406	+	0.318360i	−0.433063	+	0.901364i	$0.642567\pi$
$968$	1.77744	−	10.0804i	0.0571292	−	0.323996i
$969$	−24.4415	+	31.9388i	−0.785175	+	1.02602i
$970$	1.21634	−	1.02063i	0.0390542	−	0.0327703i
$971$	5.50393	−	9.53309i	0.176630	−	0.305932i	−0.764094	−	0.645104i	$-0.776814\pi$
$971$	5.50393	−	9.53309i	0.176630	−	0.305932i	0.940724	+	0.339173i	$0.110147\pi$
$972$	−11.4243	+	10.6059i	−0.366434	+	0.340185i
$973$	−2.10011	−	6.10741i	−0.0673264	−	0.195795i
$974$	3.98154	+	22.5805i	0.127577	+	0.723525i
$975$	1.49268	+	0.194540i	0.0478039	+	0.00623025i
$976$	0.132498	+	0.111179i	0.00424115	+	0.00355875i
$977$	7.14576	−	40.5256i	0.228613	−	1.29653i	−0.627043	−	0.778985i	$-0.715735\pi$
$977$	7.14576	−	40.5256i	0.228613	−	1.29653i	0.855656	−	0.517545i	$-0.173154\pi$
$978$	−1.64964	−	36.6879i	−0.0527497	−	1.17315i
$979$	10.8501	+	3.94910i	0.346770	+	0.126214i
$980$	2.23787	+	0.906324i	0.0714860	+	0.0289514i
$981$	−9.25986	+	9.30817i	−0.295645	+	0.297187i
$982$	11.8966	+	20.6054i	0.379634	+	0.657546i
$983$	35.2805	+	12.8410i	1.12527	+	0.409566i	0.836574	−	0.547855i	$-0.184555\pi$
$983$	35.2805	+	12.8410i	1.12527	+	0.409566i	0.288698	+	0.957420i	$0.406778\pi$
$984$	1.86726	−	5.94917i	0.0595261	−	0.189652i
$985$	−2.38082	−	1.99774i	−0.0758591	−	0.0636534i
$986$	3.26016	−	18.4893i	0.103825	−	0.588819i
$987$	7.79910	−	0.211132i	0.248248	−	0.00672039i
$988$	−0.457289	+	0.383711i	−0.0145483	+	0.0122075i
$989$	−33.4472	−	57.9322i	−1.06356	−	1.84214i
$990$	−0.0764890	+	0.901272i	−0.00243098	+	0.0286443i
$991$	28.3910	−	49.1747i	0.901870	−	1.56208i	0.0768054	−	0.997046i	$-0.475528\pi$
$991$	28.3910	−	49.1747i	0.901870	−	1.56208i	0.825065	−	0.565038i	$-0.191139\pi$
$992$	−5.72127	+	4.80071i	−0.181650	+	0.152423i
$993$	1.17136	+	26.0509i	0.0371720	+	0.826701i
$994$	15.5615	+	19.2332i	0.493582	+	0.610042i
$995$	−6.83414	+	2.48742i	−0.216657	+	0.0788566i
$996$	−0.922223	−	2.21828i	−0.0292218	−	0.0702888i
$997$	25.4564	−	21.3604i	0.806212	−	0.676492i	−0.143489	−	0.989652i	$-0.545832\pi$
$997$	25.4564	−	21.3604i	0.806212	−	0.676492i	0.949700	+	0.313160i	$0.101388\pi$
$998$	−5.70648	−	9.88391i	−0.180635	−	0.312870i
$999$	3.40118	+	25.0780i	0.107609	+	0.793431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.121.8	yes	72
7.4	even	3		378.2.v.a.67.1	✓	72
27.25	even	9		378.2.v.a.79.1	yes	72
189.25	even	9	inner	378.2.w.b.25.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.1	✓	72	7.4	even	3
378.2.v.a.79.1	yes	72	27.25	even	9
378.2.w.b.25.8	yes	72	189.25	even	9	inner
378.2.w.b.121.8	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.05262 - 1.37550i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.324117 + 0.117969i) q^{5} +(1.45959 - 0.932530i) q^{6} +(0.0472752 - 2.64533i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.783993 - 2.89575i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.05262 - 1.37550i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.324117 + 0.117969i) q^{5} +(1.45959 - 0.932530i) q^{6} +(0.0472752 - 2.64533i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.783993 - 2.89575i) q^{9} -0.344919 q^{10} +(0.821414 + 0.298970i) q^{11} +(1.69051 - 0.377084i) q^{12} +(0.0309187 - 0.175349i) q^{13} +(0.949180 - 2.46963i) q^{14} +(-0.178905 + 0.569999i) q^{15} +(0.173648 + 0.984808i) q^{16} +6.92584 q^{17} +(0.253692 - 2.98925i) q^{18} -3.35263 q^{19} +(-0.324117 - 0.117969i) q^{20} +(-3.58888 - 2.84955i) q^{21} +(0.669623 + 0.561880i) q^{22} +(-1.31015 + 7.43026i) q^{23} +(1.71753 + 0.223844i) q^{24} +(-3.73909 + 3.13747i) q^{25} +(0.0890268 - 0.154199i) q^{26} +(-4.80834 - 1.96973i) q^{27} +(1.73660 - 1.99605i) q^{28} +(-0.470725 - 2.66961i) q^{29} +(-0.363067 + 0.474435i) q^{30} +(5.72127 + 4.80071i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.27587 - 0.815153i) q^{33} +(6.50816 + 2.36878i) q^{34} +(0.296744 + 0.862974i) q^{35} +(1.26078 - 2.72221i) q^{36} +(-2.43522 - 4.21792i) q^{37} +(-3.15044 - 1.14667i) q^{38} +(-0.208646 - 0.227104i) q^{39} +(-0.264223 - 0.221709i) q^{40} +(0.625127 - 3.54527i) q^{41} +(-2.39785 - 3.90517i) q^{42} +(-6.79190 + 5.69908i) q^{43} +(0.437065 + 0.757020i) q^{44} +(0.595715 + 0.846075i) q^{45} +(-3.77244 + 6.53406i) q^{46} +(-1.30421 + 1.09436i) q^{47} +(1.53739 + 0.797773i) q^{48} +(-6.99553 - 0.250117i) q^{49} +(-4.58667 + 1.66941i) q^{50} +(7.29026 - 9.52648i) q^{51} +(0.136397 - 0.114451i) q^{52} +(5.57388 + 9.65424i) q^{53} +(-3.84467 - 3.49549i) q^{54} -0.301504 q^{55} +(2.31456 - 1.28172i) q^{56} +(-3.52904 + 4.61154i) q^{57} +(0.470725 - 2.66961i) q^{58} +(0.869906 - 4.93348i) q^{59} +(-0.503438 + 0.321647i) q^{60} +(0.132498 - 0.111179i) q^{61} +(3.73429 + 6.46798i) q^{62} +(-7.69727 + 1.93702i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0106644 + 0.0604810i) q^{65} +(1.47772 - 0.329620i) q^{66} +(-6.05460 + 2.20369i) q^{67} +(5.30550 + 4.45184i) q^{68} +(8.84122 + 9.62333i) q^{69} +(-0.0163061 + 0.912423i) q^{70} +(-4.67546 + 8.09814i) q^{71} +(2.11579 - 2.12683i) q^{72} +(5.90570 - 10.2290i) q^{73} +(-0.845743 - 4.79645i) q^{74} +(0.379753 + 8.44566i) q^{75} +(-2.56826 - 2.15503i) q^{76} +(0.829707 - 2.15878i) q^{77} +(-0.118389 - 0.284769i) q^{78} +(0.444522 + 0.161793i) q^{79} +(-0.172459 - 0.298708i) q^{80} +(-7.77071 + 4.54049i) q^{81} +(1.79998 - 3.11766i) q^{82} +(-0.240849 - 1.36592i) q^{83} +(-0.917591 - 4.48977i) q^{84} +(-2.24478 + 0.817035i) q^{85} +(-8.33150 + 3.03242i) q^{86} +(-4.16754 - 2.16260i) q^{87} +(0.151791 + 0.860851i) q^{88} +13.2090 q^{89} +(0.270414 + 0.998797i) q^{90} +(-0.462393 - 0.0900797i) q^{91} +(-5.77971 + 4.84976i) q^{92} +(12.6257 - 2.81628i) q^{93} +(-1.59985 + 0.582298i) q^{94} +(1.08665 - 0.395507i) q^{95} +(1.17182 + 1.27548i) q^{96} +(-3.52644 + 2.95904i) q^{97} +(-6.48810 - 2.62765i) q^{98} +(0.221760 - 2.61300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

L-functions

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