LMFDB - Embedded newform 405.3.s.a.118.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(37,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([28, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.29
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.271751 - 3.10613i) q^{2} +(-5.63494 - 0.993591i) q^{4} +(-0.0355463 - 4.99987i) q^{5} +(-6.87240 - 4.81211i) q^{7} +(-1.38954 + 5.18582i) q^{8} +(-15.5399 - 1.24831i) q^{10} +(-0.0997944 - 0.0363222i) q^{11} +(1.15037 + 13.1488i) q^{13} +(-16.8146 + 20.0388i) q^{14} +(-5.77697 - 2.10265i) q^{16} +(-2.77156 - 10.3436i) q^{17} +(23.9034 - 13.8006i) q^{19} +(-4.76753 + 28.2093i) q^{20} +(-0.139940 + 0.300103i) q^{22} +(-26.9117 + 18.8438i) q^{23} +(-24.9975 + 0.355454i) q^{25} +41.1545 q^{26} +(33.9443 + 33.9443i) q^{28} +(9.56923 + 11.4042i) q^{29} +(3.75387 - 21.2892i) q^{31} +(-17.1767 + 36.8356i) q^{32} +(-32.8817 + 5.79794i) q^{34} +(-23.8156 + 34.5322i) q^{35} +(9.55740 + 35.6687i) q^{37} +(-36.3707 - 77.9973i) q^{38} +(25.9778 + 6.76317i) q^{40} +(-42.1515 - 35.3693i) q^{41} +(22.1297 + 47.4572i) q^{43} +(0.526246 + 0.303828i) q^{44} +(51.2179 + 88.7119i) q^{46} +(30.4241 + 21.3032i) q^{47} +(7.31453 + 20.0965i) q^{49} +(-5.68900 + 77.7419i) q^{50} +(6.58228 - 75.2358i) q^{52} +(-24.3281 - 24.3281i) q^{53} +(-0.178059 + 0.500250i) q^{55} +(34.5042 - 28.9524i) q^{56} +(38.0232 - 26.6241i) q^{58} +(-1.23413 - 3.39074i) q^{59} +(-18.4286 - 104.514i) q^{61} +(-65.1069 - 17.4453i) q^{62} +(88.4518 + 51.0677i) q^{64} +(65.7016 - 6.21911i) q^{65} +(-62.2832 + 5.44908i) q^{67} +(5.34026 + 61.0394i) q^{68} +(100.789 + 83.3585i) q^{70} +(29.5576 - 51.1953i) q^{71} +(29.4612 - 109.951i) q^{73} +(113.389 - 19.9935i) q^{74} +(-148.406 + 54.0155i) q^{76} +(0.511041 + 0.729842i) q^{77} +(-64.0753 - 76.3619i) q^{79} +(-10.3076 + 28.9589i) q^{80} +(-121.316 + 121.316i) q^{82} +(-66.6928 - 5.83486i) q^{83} +(-51.6182 + 14.2251i) q^{85} +(153.422 - 55.8410i) q^{86} +(0.327028 - 0.467045i) q^{88} +(88.4162 - 51.0471i) q^{89} +(55.3678 - 95.8998i) q^{91} +(170.369 - 79.4442i) q^{92} +(74.4380 - 88.7118i) q^{94} +(-69.8511 - 119.023i) q^{95} +(-3.50866 + 1.63611i) q^{97} +(64.4100 - 17.2586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.271751	−	3.10613i	0.135875	−	1.55306i	−0.556084	−	0.831126i	$-0.687697\pi$
$2$	0.271751	−	3.10613i	0.135875	−	1.55306i	0.691959	−	0.721937i	$-0.256748\pi$
$3$		0			0
$3$		0			0
$4$	−5.63494	−	0.993591i	−1.40873	−	0.248398i
$5$	−0.0355463	−	4.99987i	−0.00710925	−	0.999975i
$5$	−0.0355463	−	4.99987i	−0.00710925	−	0.999975i
$6$		0			0
$7$	−6.87240	−	4.81211i	−0.981772	−	0.687444i	−0.0317070	−	0.999497i	$-0.510094\pi$
$7$	−6.87240	−	4.81211i	−0.981772	−	0.687444i	−0.950065	+	0.312053i	$0.898983\pi$
$8$	−1.38954	+	5.18582i	−0.173692	+	0.648228i
$9$		0			0
$10$	−15.5399	−	1.24831i	−1.55399	−	0.124831i
$11$	−0.0997944	−	0.0363222i	−0.00907222	−	0.00330202i	0.337480	−	0.941333i	$-0.390425\pi$
$11$	−0.0997944	−	0.0363222i	−0.00907222	−	0.00330202i	−0.346552	+	0.938031i	$0.612648\pi$
$12$		0			0
$13$	1.15037	+	13.1488i	0.0884903	+	1.01145i	0.902526	+	0.430634i	$0.141710\pi$
$13$	1.15037	+	13.1488i	0.0884903	+	1.01145i	−0.814036	+	0.580814i	$0.802734\pi$
$14$	−16.8146	+	20.0388i	−1.20104	+	1.43135i
$15$		0			0
$16$	−5.77697	−	2.10265i	−0.361061	−	0.131415i
$17$	−2.77156	−	10.3436i	−0.163033	−	0.608448i	−0.998283	−	0.0585771i	$-0.981344\pi$
$17$	−2.77156	−	10.3436i	−0.163033	−	0.608448i	0.835250	−	0.549871i	$-0.185323\pi$
$18$		0			0
$19$	23.9034	−	13.8006i	1.25807	−	0.726349i	0.285374	−	0.958416i	$-0.407882\pi$
$19$	23.9034	−	13.8006i	1.25807	−	0.726349i	0.972700	+	0.232067i	$0.0745488\pi$
$20$	−4.76753	+	28.2093i	−0.238377	+	1.41046i
$21$		0			0
$22$	−0.139940	+	0.300103i	−0.00636093	+	0.0136411i
$23$	−26.9117	+	18.8438i	−1.17007	+	0.819295i	−0.986508	−	0.163713i	$-0.947653\pi$
$23$	−26.9117	+	18.8438i	−1.17007	+	0.819295i	−0.183566	+	0.983007i	$0.558764\pi$
$24$		0			0
$25$	−24.9975	+	0.355454i	−0.999899	+	0.0142181i
$26$	41.1545			1.58287
$27$		0			0
$28$	33.9443	+	33.9443i	1.21230	+	1.21230i
$29$	9.56923	+	11.4042i	0.329974	+	0.393247i	0.905367	−	0.424629i	$-0.139596\pi$
$29$	9.56923	+	11.4042i	0.329974	+	0.393247i	−0.575394	+	0.817877i	$0.695151\pi$
$30$		0			0
$31$	3.75387	−	21.2892i	0.121092	−	0.686749i	−0.862460	−	0.506126i	$-0.831077\pi$
$31$	3.75387	−	21.2892i	0.121092	−	0.686749i	0.983552	−	0.180624i	$-0.0578116\pi$
$32$	−17.1767	+	36.8356i	−0.536772	+	1.15111i
$33$		0			0
$34$	−32.8817	+	5.79794i	−0.967110	+	0.170528i
$35$	−23.8156	+	34.5322i	−0.680447	+	0.986634i
$36$		0			0
$37$	9.55740	+	35.6687i	0.258308	+	0.964019i	0.966220	+	0.257718i	$0.0829706\pi$
$37$	9.55740	+	35.6687i	0.258308	+	0.964019i	−0.707912	+	0.706301i	$0.750363\pi$
$38$	−36.3707	−	77.9973i	−0.957125	−	2.05256i
$39$		0			0
$40$	25.9778	+	6.76317i	0.649446	+	0.169079i
$41$	−42.1515	−	35.3693i	−1.02808	−	0.862666i	−0.0374631	−	0.999298i	$-0.511928\pi$
$41$	−42.1515	−	35.3693i	−1.02808	−	0.862666i	−0.990622	+	0.136632i	$0.956372\pi$
$42$		0			0
$43$	22.1297	+	47.4572i	0.514643	+	1.10366i	0.976265	+	0.216579i	$0.0694899\pi$
$43$	22.1297	+	47.4572i	0.514643	+	1.10366i	−0.461622	+	0.887077i	$0.652732\pi$
$44$	0.526246	+	0.303828i	0.0119601	+	0.00690518i
$45$		0			0
$46$	51.2179	+	88.7119i	1.11343	+	1.92852i
$47$	30.4241	+	21.3032i	0.647320	+	0.453259i	0.850565	−	0.525869i	$-0.176260\pi$
$47$	30.4241	+	21.3032i	0.647320	+	0.453259i	−0.203245	+	0.979128i	$0.565149\pi$
$48$		0			0
$49$	7.31453	+	20.0965i	0.149276	+	0.410133i
$50$	−5.68900	+	77.7419i	−0.113780	+	1.55484i
$51$		0			0
$52$	6.58228	−	75.2358i	0.126582	−	1.44684i
$53$	−24.3281	−	24.3281i	−0.459020	−	0.459020i	0.439314	−	0.898334i	$-0.355222\pi$
$53$	−24.3281	−	24.3281i	−0.459020	−	0.459020i	−0.898334	+	0.439314i	$0.855222\pi$
$54$		0			0
$55$	−0.178059	+	0.500250i	−0.00323744	+	0.00909546i
$56$	34.5042	−	28.9524i	0.616146	−	0.517008i
$57$		0			0
$58$	38.0232	−	26.6241i	0.655573	−	0.459037i
$59$	−1.23413	−	3.39074i	−0.0209175	−	0.0574702i	0.928794	−	0.370595i	$-0.120846\pi$
$59$	−1.23413	−	3.39074i	−0.0209175	−	0.0574702i	−0.949712	+	0.313125i	$0.898624\pi$
$60$		0			0
$61$	−18.4286	−	104.514i	−0.302109	−	1.71334i	−0.636812	−	0.771019i	$-0.719747\pi$
$61$	−18.4286	−	104.514i	−0.302109	−	1.71334i	0.334703	−	0.942324i	$-0.391364\pi$
$62$	−65.1069	−	17.4453i	−1.05011	−	0.281376i
$63$		0			0
$64$	88.4518	+	51.0677i	1.38206	+	0.797933i
$65$	65.7016	−	6.21911i	1.01079	−	0.0956787i
$66$		0			0
$67$	−62.2832	+	5.44908i	−0.929600	+	0.0813295i	−0.541888	−	0.840451i	$-0.682290\pi$
$67$	−62.2832	+	5.44908i	−0.929600	+	0.0813295i	−0.387713	+	0.921780i	$0.626735\pi$
$68$	5.34026	+	61.0394i	0.0785332	+	0.897638i
$69$		0			0
$70$	100.789	+	83.3585i	1.43985	+	1.19084i
$71$	29.5576	−	51.1953i	0.416305	−	0.721061i	−0.579260	−	0.815143i	$-0.696658\pi$
$71$	29.5576	−	51.1953i	0.416305	−	0.721061i	0.995564	+	0.0940822i	$0.0299917\pi$
$72$		0			0
$73$	29.4612	−	109.951i	0.403578	−	1.50617i	−0.403086	−	0.915162i	$-0.632063\pi$
$73$	29.4612	−	109.951i	0.403578	−	1.50617i	0.806664	−	0.591010i	$-0.201271\pi$
$74$	113.389	−	19.9935i	1.53228	−	0.270182i
$75$		0			0
$76$	−148.406	+	54.0155i	−1.95272	+	0.710730i
$77$	0.511041	+	0.729842i	0.00663689	+	0.00947847i
$78$		0			0
$79$	−64.0753	−	76.3619i	−0.811079	−	0.966606i	0.188802	−	0.982015i	$-0.439540\pi$
$79$	−64.0753	−	76.3619i	−0.811079	−	0.966606i	−0.999881	+	0.0154087i	$0.995095\pi$
$80$	−10.3076	+	28.9589i	−0.128845	+	0.361986i
$81$		0			0
$82$	−121.316	+	121.316i	−1.47947	+	1.47947i
$83$	−66.6928	−	5.83486i	−0.803527	−	0.0702995i	−0.322010	−	0.946736i	$-0.604359\pi$
$83$	−66.6928	−	5.83486i	−0.803527	−	0.0702995i	−0.481517	+	0.876437i	$0.659914\pi$
$84$		0			0
$85$	−51.6182	+	14.2251i	−0.607273	+	0.167355i
$86$	153.422	−	55.8410i	1.78397	−	0.649314i
$87$		0			0
$88$	0.327028	−	0.467045i	0.00371623	−	0.00530733i
$89$	88.4162	−	51.0471i	0.993440	−	0.573563i	0.0871392	−	0.996196i	$-0.472228\pi$
$89$	88.4162	−	51.0471i	0.993440	−	0.573563i	0.906301	+	0.422633i	$0.138894\pi$
$90$		0			0
$91$	55.3678	−	95.8998i	0.608437	−	1.05384i
$92$	170.369	−	79.4442i	1.85183	−	0.863524i
$93$		0			0
$94$	74.4380	−	88.7118i	0.791894	−	0.943742i
$95$	−69.8511	−	119.023i	−0.735275	−	1.25288i
$96$		0			0
$97$	−3.50866	+	1.63611i	−0.0361717	+	0.0168671i	−0.440620	−	0.897694i	$-0.645241\pi$
$97$	−3.50866	+	1.63611i	−0.0361717	+	0.0168671i	0.404448	+	0.914561i	$0.367464\pi$
$98$	64.4100	−	17.2586i	0.657245	−	0.176108i
$99$		0			0
$100$	141.212	+	22.8343i	1.41212	+	0.228343i
$101$	18.6472	+	105.754i	0.184626	+	1.04707i	0.926435	+	0.376455i	$0.122857\pi$
$101$	18.6472	+	105.754i	0.184626	+	1.04707i	−0.741809	+	0.670612i	$0.766032\pi$
$102$		0			0
$103$	12.8319	+	5.98363i	0.124582	+	0.0580935i	0.483910	−	0.875118i	$-0.339216\pi$
$103$	12.8319	+	5.98363i	0.124582	+	0.0580935i	−0.359328	+	0.933211i	$0.616994\pi$
$104$	−69.7860	−	12.3051i	−0.671019	−	0.118319i
$105$		0			0
$106$	−82.1772	+	68.9548i	−0.775256	+	0.650517i
$107$	−104.637	+	104.637i	−0.977914	+	0.977914i	−0.999761	−	0.0218471i	$-0.993045\pi$
$107$	−104.637	+	104.637i	−0.977914	+	0.977914i	0.0218471	+	0.999761i	$0.493045\pi$
$108$		0			0
$109$		−	87.0016i		−	0.798180i	−0.916912	−	0.399090i	$-0.869326\pi$
$109$		−	87.0016i		−	0.798180i	0.916912	−	0.399090i	$-0.130674\pi$
$110$	1.50545	+	0.689017i	0.0136859	+	0.00626379i
$111$		0			0
$112$	29.5835	+	42.2496i	0.264139	+	0.377229i
$113$	−31.1829	−	14.5408i	−0.275955	−	0.128680i	0.279714	−	0.960083i	$-0.409760\pi$
$113$	−31.1829	−	14.5408i	−0.275955	−	0.128680i	−0.555670	+	0.831403i	$0.687538\pi$
$114$		0			0
$115$	95.1731	+	133.885i	0.827592	+	1.16422i
$116$	−42.5909	−	73.7697i	−0.367163	−	0.635945i
$117$		0			0
$118$	−10.8675	+	2.91192i	−0.0920970	+	0.0246773i
$119$	−30.7273	+	84.4225i	−0.258212	+	0.709433i
$120$		0			0
$121$	−92.6827	−	77.7701i	−0.765973	−	0.642728i
$122$	−329.641	+	28.8399i	−2.70198	+	0.236392i
$123$		0			0
$124$	−42.3056	+	116.234i	−0.341174	+	0.937368i
$125$	2.66579	+	124.972i	0.0213263	+	0.999773i
$126$		0			0
$127$	−185.536	−	49.7142i	−1.46091	−	0.391450i	−0.561108	−	0.827743i	$-0.689625\pi$
$127$	−185.536	−	49.7142i	−1.46091	−	0.391450i	−0.899805	+	0.436292i	$0.856291\pi$
$128$	89.4107	−	127.692i	0.698521	−	0.997592i
$129$		0			0
$130$	−1.46289	−	205.767i	−0.0112530	−	1.58283i
$131$	−12.4544	+	70.6325i	−0.0950718	+	0.539179i	0.899653	+	0.436605i	$0.143819\pi$
$131$	−12.4544	+	70.6325i	−0.0950718	+	0.539179i	−0.994725	+	0.102575i	$0.967292\pi$
$132$		0			0
$133$	−230.684	−	20.1822i	−1.73447	−	0.151746i
$134$			194.940i			1.45478i
$135$		0			0
$136$	57.4913			0.422730
$137$	18.2824	−	208.969i	0.133448	−	1.52532i	−0.574176	−	0.818732i	$-0.694678\pi$
$137$	18.2824	−	208.969i	0.133448	−	1.52532i	0.707624	−	0.706589i	$-0.249767\pi$
$138$		0			0
$139$	−63.5413	−	11.2040i	−0.457131	−	0.0806046i	−0.0596592	−	0.998219i	$-0.519001\pi$
$139$	−63.5413	−	11.2040i	−0.457131	−	0.0806046i	−0.397472	+	0.917614i	$0.630113\pi$
$140$	168.510	−	170.924i	1.20365	−	1.22088i
$141$		0			0
$142$	−150.987	−	105.722i	−1.06329	−	0.744522i
$143$	0.362793	−	1.35396i	0.00253702	−	0.00946828i
$144$		0			0
$145$	56.6793	−	48.2503i	0.390891	−	0.332761i
$146$	−333.514	−	121.389i	−2.28434	−	0.831433i
$147$		0			0
$148$	−18.4152	−	210.487i	−0.124427	−	1.42221i
$149$	42.9391	−	51.1728i	0.288182	−	0.343441i	−0.602459	−	0.798150i	$-0.705812\pi$
$149$	42.9391	−	51.1728i	0.288182	−	0.343441i	0.890640	+	0.454709i	$0.150257\pi$
$150$		0			0
$151$	−8.90680	−	3.24181i	−0.0589854	−	0.0214689i	0.312359	−	0.949964i	$-0.398881\pi$
$151$	−8.90680	−	3.24181i	−0.0589854	−	0.0214689i	−0.371344	+	0.928495i	$0.621103\pi$
$152$	38.3530	+	143.135i	0.252322	+	0.941679i
$153$		0			0
$154$	2.40586	−	1.38902i	0.0156224	−	0.00901962i
$155$	−106.577	−	18.0121i	−0.687593	−	0.116207i
$156$		0			0
$157$	73.1084	−	156.781i	0.465658	−	0.998608i	−0.523537	−	0.852003i	$-0.675388\pi$
$157$	73.1084	−	156.781i	0.465658	−	0.998608i	0.989195	−	0.146605i	$-0.0468345\pi$
$158$	−254.602	+	178.274i	−1.61141	+	1.12832i
$159$		0			0
$160$	184.784	+	84.5721i	1.15490	+	0.528575i
$161$	275.626			1.71196
$162$		0			0
$163$	42.0886	+	42.0886i	0.258213	+	0.258213i	0.824327	−	0.566114i	$-0.191554\pi$
$163$	42.0886	+	42.0886i	0.258213	+	0.258213i	−0.566114	+	0.824327i	$0.691554\pi$
$164$	202.378	+	241.185i	1.23401	+	1.47064i
$165$		0			0
$166$	−36.2476	+	205.570i	−0.218359	+	1.23838i
$167$	104.004	−	223.036i	0.622776	−	1.33555i	−0.301370	−	0.953507i	$-0.597444\pi$
$167$	104.004	−	223.036i	0.622776	−	1.33555i	0.924146	−	0.382040i	$-0.124778\pi$
$168$		0			0
$169$	−5.13589	+	0.905596i	−0.0303899	+	0.00535856i
$170$	30.1578	+	164.198i	0.177399	+	0.965873i
$171$		0			0
$172$	−77.5461	−	289.406i	−0.450850	−	1.68259i
$173$	−3.86233	−	8.28278i	−0.0223256	−	0.0478774i	0.894829	−	0.446409i	$-0.147298\pi$
$173$	−3.86233	−	8.28278i	−0.0223256	−	0.0478774i	−0.917154	+	0.398532i	$0.869520\pi$
$174$		0			0
$175$	173.503	+	117.848i	0.991446	+	0.673415i
$176$	0.500137	+	0.419665i	0.00284169	+	0.00238446i
$177$		0			0
$178$	−134.532	−	288.504i	−0.755795	−	1.62081i
$179$	0.701250	+	0.404867i	0.00391760	+	0.00226183i	0.501958	−	0.864892i	$-0.332613\pi$
$179$	0.701250	+	0.404867i	0.00391760	+	0.00226183i	−0.498040	+	0.867154i	$0.665947\pi$
$180$		0			0
$181$	114.570	+	198.441i	0.632982	+	1.09636i	0.986939	+	0.161096i	$0.0515028\pi$
$181$	114.570	+	198.441i	0.632982	+	1.09636i	−0.353956	+	0.935262i	$0.615164\pi$
$182$	−282.830	−	198.040i	−1.55401	−	1.08813i
$183$		0			0
$184$	−60.3257	−	165.743i	−0.327857	−	0.900779i
$185$	177.999	−	49.0537i	0.962158	−	0.265155i
$186$		0			0
$187$	−0.0991162	+	1.13290i	−0.000530033	+	0.00605831i
$188$	−150.271	−	150.271i	−0.799314	−	0.799314i
$189$		0			0
$190$	−388.684	+	184.622i	−2.04570	+	0.971693i
$191$	−138.037	+	115.827i	−0.722708	+	0.606424i	−0.928133	−	0.372249i	$-0.878587\pi$
$191$	−138.037	+	115.827i	−0.722708	+	0.606424i	0.205425	+	0.978673i	$0.434142\pi$
$192$		0			0
$193$	230.730	−	161.559i	1.19549	−	0.837092i	0.205560	−	0.978644i	$-0.434098\pi$
$193$	230.730	−	161.559i	1.19549	−	0.837092i	0.989931	+	0.141553i	$0.0452095\pi$
$194$	4.12849	+	11.3429i	0.0212809	+	0.0584688i
$195$		0			0
$196$	−21.2492	−	120.510i	−0.108414	−	0.614848i
$197$	109.014	+	29.2102i	0.553370	+	0.148275i	0.524659	−	0.851313i	$-0.324193\pi$
$197$	109.014	+	29.2102i	0.553370	+	0.148275i	0.0287113	+	0.999588i	$0.490860\pi$
$198$		0			0
$199$	−170.998	−	98.7260i	−0.859289	−	0.496111i	0.00448527	−	0.999990i	$-0.498572\pi$
$199$	−170.998	−	98.7260i	−0.859289	−	0.496111i	−0.863774	+	0.503879i	$0.831906\pi$
$200$	32.8916	−	130.126i	0.164458	−	0.650632i
$201$		0			0
$202$	333.552	−	29.1820i	1.65125	−	0.144465i
$203$	−10.8855	−	124.422i	−0.0536233	−	0.612917i
$204$		0			0
$205$	−175.344	+	212.009i	−0.855335	+	1.03419i
$206$	22.0730	−	38.2315i	0.107150	−	0.185590i
$207$		0			0
$208$	21.0017	−	78.3793i	0.100970	−	0.376823i
$209$	−2.88670	+	0.509002i	−0.0138119	+	0.00243542i
$210$		0			0
$211$	338.142	−	123.074i	1.60257	−	0.583288i	0.622619	−	0.782525i	$-0.286069\pi$
$211$	338.142	−	123.074i	1.60257	−	0.583288i	0.979951	+	0.199237i	$0.0638464\pi$
$212$	112.915	+	161.259i	0.532617	+	0.760656i
$213$		0			0
$214$	296.580	+	353.450i	1.38589	+	1.65164i
$215$	236.493	−	112.332i	1.09997	−	0.522476i
$216$		0			0
$217$	−128.244	+	128.244i	−0.590987	+	0.590987i
$218$	−270.238	−	23.6428i	−1.23962	−	0.108453i
$219$		0			0
$220$	1.50040	−	2.64196i	0.00681998	−	0.0120089i
$221$	132.818	−	48.3418i	0.600987	−	0.218741i
$222$		0			0
$223$	−238.774	+	341.005i	−1.07074	+	1.52917i	−0.241395	+	0.970427i	$0.577605\pi$
$223$	−238.774	+	341.005i	−1.07074	+	1.52917i	−0.829341	+	0.558743i	$0.811284\pi$
$224$	295.302	−	170.493i	1.31831	−	0.761128i
$225$		0			0
$226$	−53.6397	+	92.9067i	−0.237344	+	0.411091i
$227$	−1.98656	+	0.926349i	−0.00875138	+	0.00408083i	−0.426989	−	0.904257i	$-0.640426\pi$
$227$	−1.98656	+	0.926349i	−0.00875138	+	0.00408083i	0.418238	+	0.908338i	$0.362648\pi$
$228$		0			0
$229$	−105.993	+	126.317i	−0.462850	+	0.551603i	−0.946098	−	0.323881i	$-0.895012\pi$
$229$	−105.993	+	126.317i	−0.462850	+	0.551603i	0.483248	+	0.875483i	$0.339457\pi$
$230$	441.728	−	259.236i	1.92056	−	1.12711i
$231$		0			0
$232$	−72.4368	+	33.7778i	−0.312227	+	0.145594i
$233$	349.671	−	93.6941i	1.50073	−	0.402120i	0.587388	−	0.809305i	$-0.300156\pi$
$233$	349.671	−	93.6941i	1.50073	−	0.402120i	0.913346	+	0.407185i	$0.133490\pi$
$234$		0			0
$235$	105.432	−	152.874i	0.448645	−	0.650526i
$236$	3.58523	+	20.3328i	0.0151916	+	0.0861561i
$237$		0			0
$238$	253.877	+	118.385i	1.06671	+	0.497415i
$239$	−186.473	−	32.8803i	−0.780223	−	0.137574i	−0.230668	−	0.973032i	$-0.574091\pi$
$239$	−186.473	−	32.8803i	−0.780223	−	0.137574i	−0.549554	+	0.835458i	$0.685202\pi$
$240$		0			0
$241$	−91.8704	+	77.0884i	−0.381205	+	0.319869i	−0.813175	−	0.582019i	$-0.802263\pi$
$241$	−91.8704	+	77.0884i	−0.381205	+	0.319869i	0.431970	+	0.901888i	$0.357819\pi$
$242$	−266.750	+	266.750i	−1.10227	+	1.10227i
$243$		0			0
$244$			607.240i			2.48869i
$245$	100.220	−	37.2861i	0.409061	−	0.152188i
$246$		0			0
$247$	208.960	+	298.426i	0.845992	+	1.20820i
$248$	105.186	+	49.0490i	0.424137	+	0.197778i
$249$		0			0
$250$	388.902	+	25.6808i	1.55561	+	0.102723i
$251$	−5.89620	−	10.2125i	−0.0234908	−	0.0406873i	0.854041	−	0.520206i	$-0.174145\pi$
$251$	−5.89620	−	10.2125i	−0.0234908	−	0.0406873i	−0.877532	+	0.479518i	$0.840811\pi$
$252$		0			0
$253$	3.37008	−	0.903011i	0.0133205	−	0.00356921i
$254$	−204.838	+	562.788i	−0.806449	+	2.21570i
$255$		0			0
$256$	−59.3682	−	49.8158i	−0.231907	−	0.194593i
$257$	−172.770	+	15.1154i	−0.672257	+	0.0588149i	−0.418173	−	0.908367i	$-0.637330\pi$
$257$	−172.770	+	15.1154i	−0.672257	+	0.0588149i	−0.254084	+	0.967182i	$0.581774\pi$
$258$		0			0
$259$	105.959	−	291.121i	0.409109	−	1.12402i
$260$	−376.404	−	30.2362i	−1.44771	−	0.116293i
$261$		0			0
$262$	216.009	+	57.8794i	0.824461	+	0.220914i
$263$	124.314	−	177.539i	0.472678	−	0.675054i	−0.510043	−	0.860149i	$-0.670370\pi$
$263$	124.314	−	177.539i	0.472678	−	0.675054i	0.982721	+	0.185095i	$0.0592593\pi$
$264$		0			0
$265$	−120.772	+	122.502i	−0.455745	+	0.462272i
$266$	−125.377	+	711.049i	−0.471342	+	2.67312i
$267$		0			0
$268$	356.376	+	31.1789i	1.32976	+	0.116339i
$269$		−	50.1821i		−	0.186551i	−0.995640	−	0.0932753i	$-0.970266\pi$
$269$		−	50.1821i		−	0.186551i	0.995640	−	0.0932753i	$-0.0297337\pi$
$270$		0			0
$271$	358.828			1.32409			0.662044	−	0.749465i	$-0.269689\pi$
$271$	358.828			1.32409			0.662044	+	0.749465i	$0.269689\pi$
$272$	−5.73771	+	65.5824i	−0.0210945	+	0.241112i
$273$		0			0
$274$	−644.115	−	113.575i	−2.35079	−	0.414507i
$275$	2.50752	+	0.872491i	0.00911825	+	0.00317269i
$276$		0			0
$277$	138.833	+	97.2121i	0.501203	+	0.350946i	0.796678	−	0.604404i	$-0.206589\pi$
$277$	138.833	+	97.2121i	0.501203	+	0.350946i	−0.295475	+	0.955351i	$0.595478\pi$
$278$	−52.0685	+	194.322i	−0.187297	+	0.699002i
$279$		0			0
$280$	−145.985	−	171.487i	−0.521375	−	0.612455i
$281$	486.132	+	176.938i	1.73001	+	0.629671i	0.998631	−	0.0523024i	$-0.0166560\pi$
$281$	486.132	+	176.938i	1.73001	+	0.629671i	0.731377	+	0.681974i	$0.238878\pi$
$282$		0			0
$283$	−0.596924	−	6.82287i	−0.00210927	−	0.0241091i	0.995067	−	0.0992039i	$-0.0316296\pi$
$283$	−0.596924	−	6.82287i	−0.00210927	−	0.0241091i	−0.997176	+	0.0750948i	$0.976074\pi$
$284$	−217.423	+	259.114i	−0.765572	+	0.912374i
$285$		0			0
$286$	−4.10699	−	1.49482i	−0.0143601	−	0.00522665i
$287$	119.481	+	445.909i	0.416310	+	1.55369i
$288$		0			0
$289$	150.973	−	87.1641i	0.522396	−	0.301606i
$290$	−134.469	−	189.165i	−0.463686	−	0.652293i
$291$		0			0
$292$	−275.258	+	590.292i	−0.942663	+	2.02155i
$293$	159.446	−	111.646i	0.544186	−	0.381043i	−0.268917	−	0.963163i	$-0.586666\pi$
$293$	159.446	−	111.646i	0.544186	−	0.381043i	0.813103	+	0.582120i	$0.197777\pi$
$294$		0			0
$295$	−16.9094	+	6.29102i	−0.0573201	+	0.0213255i
$296$	−198.252			−0.669770
$297$		0			0
$298$	−147.280	−	147.280i	−0.494229	−	0.494229i
$299$	−278.732	−	332.180i	−0.932215	−	1.11097i
$300$		0			0
$301$	76.2853	−	432.635i	0.253439	−	1.43733i
$302$	−12.4899	+	26.7847i	−0.0413573	+	0.0886910i
$303$		0			0
$304$	−167.107	+	29.4655i	−0.549695	+	0.0969260i
$305$	−521.901	+	95.8559i	−1.71115	+	0.314281i
$306$		0			0
$307$	−55.5523	−	207.324i	−0.180952	−	0.675322i	−0.995461	−	0.0951712i	$-0.969660\pi$
$307$	−55.5523	−	207.324i	−0.180952	−	0.675322i	0.814509	−	0.580151i	$-0.197007\pi$
$308$	−2.15452	−	4.62038i	−0.00699519	−	0.0150012i
$309$		0			0
$310$	−84.9102	+	326.146i	−0.273904	+	1.05209i
$311$	40.1648	+	33.7022i	0.129147	+	0.108367i	0.705073	−	0.709134i	$-0.250914\pi$
$311$	40.1648	+	33.7022i	0.129147	+	0.108367i	−0.575926	+	0.817502i	$0.695358\pi$
$312$		0			0
$313$	−28.6939	−	61.5344i	−0.0916739	−	0.196595i	0.855124	−	0.518423i	$-0.173481\pi$
$313$	−28.6939	−	61.5344i	−0.0916739	−	0.196595i	−0.946798	+	0.321827i	$0.895703\pi$
$314$	−467.115	−	269.689i	−1.48763	−	0.858883i
$315$		0			0
$316$	285.187	+	493.959i	0.902492	+	1.56316i
$317$	322.569	+	225.865i	1.01757	+	0.712509i	0.958309	−	0.285733i	$-0.0922371\pi$
$317$	322.569	+	225.865i	1.01757	+	0.712509i	0.0592596	+	0.998243i	$0.481126\pi$
$318$		0			0
$319$	−0.540731	−	1.48565i	−0.00169508	−	0.00465720i
$320$	252.188	−	444.063i	0.788087	−	1.38770i
$321$		0			0
$322$	74.9017	−	856.130i	0.232614	−	2.65879i
$323$	−208.998	−	208.998i	−0.647053	−	0.647053i
$324$		0			0
$325$	−33.4302	−	328.279i	−0.102862	−	1.01009i
$326$	142.170	−	119.295i	0.436105	−	0.365936i
$327$		0			0
$328$	241.990	−	169.443i	0.737774	−	0.516595i
$329$	−106.573	−	292.808i	−0.323931	−	0.889993i
$330$		0			0
$331$	53.2977	+	302.266i	0.161020	+	0.913191i	0.953073	+	0.302739i	$0.0979011\pi$
$331$	53.2977	+	302.266i	0.161020	+	0.913191i	−0.792053	+	0.610452i	$0.790988\pi$
$332$	370.012	+	99.1444i	1.11449	+	0.298628i
$333$		0			0
$334$	−664.516	−	383.659i	−1.98957	−	1.14868i
$335$	29.4586	+	311.215i	0.0879362	+	0.928999i
$336$		0			0
$337$	−268.651	+	23.5039i	−0.797184	+	0.0697446i	−0.478467	−	0.878105i	$-0.658807\pi$
$337$	−268.651	+	23.5039i	−0.797184	+	0.0697446i	−0.318717	+	0.947850i	$0.603252\pi$
$338$	1.41721	+	16.1988i	0.00419294	+	0.0479255i
$339$		0			0
$340$	304.999	−	28.8703i	0.897057	−	0.0849127i
$341$	−1.14789	+	1.98820i	−0.00336624	+	0.00583049i
$342$		0			0
$343$	−59.9605	+	223.776i	−0.174812	+	0.652407i
$344$	−276.855	+	48.8169i	−0.804810	+	0.141910i
$345$		0			0
$346$	−26.7770	+	9.74601i	−0.0773900	+	0.0281677i
$347$	99.2947	+	141.808i	0.286152	+	0.408667i	0.936334	−	0.351111i	$-0.114196\pi$
$347$	99.2947	+	141.808i	0.286152	+	0.408667i	−0.650182	+	0.759779i	$0.725307\pi$
$348$		0			0
$349$	193.473	+	230.572i	0.554364	+	0.660665i	0.968344	−	0.249621i	$-0.0803061\pi$
$349$	193.473	+	230.572i	0.554364	+	0.660665i	−0.413980	+	0.910286i	$0.635862\pi$
$350$	413.199	−	506.897i	1.18057	−	1.44828i
$351$		0			0
$352$	3.05209	−	3.05209i	0.00867071	−	0.00867071i
$353$	−407.959	−	35.6918i	−1.15569	−	0.101110i	−0.506851	−	0.862034i	$-0.669191\pi$
$353$	−407.959	−	35.6918i	−1.15569	−	0.101110i	−0.648841	+	0.760924i	$0.724746\pi$
$354$		0			0
$355$	−257.021	−	145.965i	−0.724002	−	0.411168i
$356$	−548.939	+	199.798i	−1.54196	+	0.561229i
$357$		0			0
$358$	1.44813	−	2.06815i	0.00404506	−	0.00577695i
$359$	−498.362	+	287.729i	−1.38819	+	0.801474i	−0.993112	−	0.117171i	$-0.962617\pi$
$359$	−498.362	+	287.729i	−1.38819	+	0.801474i	−0.395082	+	0.918646i	$0.629284\pi$
$360$		0			0
$361$	200.415	−	347.129i	0.555167	−	0.961577i
$362$	647.516	−	301.942i	1.78872	−	0.834093i
$363$		0			0
$364$	−407.279	+	485.376i	−1.11890	+	1.33345i
$365$	−550.786	−	143.394i	−1.50900	−	0.392860i
$366$		0			0
$367$	75.8768	−	35.3819i	0.206749	−	0.0964085i	−0.316486	−	0.948597i	$-0.602503\pi$
$367$	75.8768	−	35.3819i	0.206749	−	0.0964085i	0.523234	+	0.852189i	$0.324725\pi$
$368$	195.090	−	52.2742i	0.530136	−	0.142049i
$369$		0			0
$370$	−103.995	−	566.218i	−0.281069	−	1.53032i
$371$	50.1229	+	284.261i	0.135102	+	0.766203i
$372$		0			0
$373$	−396.530	−	184.905i	−1.06308	−	0.495724i	−0.189240	−	0.981931i	$-0.560603\pi$
$373$	−396.530	−	184.905i	−1.06308	−	0.495724i	−0.873844	+	0.486206i	$0.838380\pi$
$374$	3.49201	+	0.615735i	0.00933692	+	0.00164635i
$375$		0			0
$376$	−152.750	+	128.172i	−0.406249	+	0.340883i
$377$	−138.943	+	138.943i	−0.368550	+	0.368550i
$378$		0			0
$379$			218.630i			0.576860i	0.957501	+	0.288430i	$0.0931333\pi$
$379$			218.630i			0.576860i	−0.957501	+	0.288430i	$0.906867\pi$
$380$	275.346	+	740.093i	0.724595	+	1.94761i
$381$		0			0
$382$	322.261	+	460.237i	0.843616	+	1.20481i
$383$	444.131	+	207.102i	1.15961	+	0.540736i	0.904625	−	0.426209i	$-0.140151\pi$
$383$	444.131	+	207.102i	1.15961	+	0.540736i	0.254986	+	0.966945i	$0.417929\pi$
$384$		0			0
$385$	3.63095	−	2.58108i	0.00943104	−	0.00670411i
$386$	−439.121	−	760.579i	−1.13762	−	1.97041i
$387$		0			0
$388$	21.3967	−	5.73322i	0.0551461	−	0.0147764i
$389$	−84.6803	+	232.657i	−0.217687	+	0.598090i	−0.999683	−	0.0251937i	$-0.991980\pi$
$389$	−84.6803	+	232.657i	−0.217687	+	0.598090i	0.781996	+	0.623284i	$0.214202\pi$
$390$		0			0
$391$	269.500	+	226.138i	0.689259	+	0.578357i
$392$	−114.381	+	10.0070i	−0.291788	+	0.0255281i
$393$		0			0
$394$	120.355	−	330.673i	0.305470	−	0.839271i
$395$	−379.522	+	323.083i	−0.960816	+	0.817930i
$396$		0			0
$397$	379.584	+	101.709i	0.956130	+	0.256194i	0.702961	−	0.711228i	$-0.251861\pi$
$397$	379.584	+	101.709i	0.956130	+	0.256194i	0.253169	+	0.967422i	$0.418527\pi$
$398$	−353.124	+	504.314i	−0.887247	+	1.26712i
$399$		0			0
$400$	145.157	+	50.5074i	0.362893	+	0.126268i
$401$	97.2501	−	551.533i	0.242519	−	1.37539i	−0.583666	−	0.811994i	$-0.698382\pi$
$401$	97.2501	−	551.533i	0.242519	−	1.37539i	0.826185	−	0.563399i	$-0.190507\pi$
$402$		0			0
$403$	284.247	+	24.8684i	0.705327	+	0.0617081i
$404$		−	614.443i		−	1.52090i
$405$		0			0
$406$	−389.429			−0.959185
$407$	0.341790	−	3.90668i	0.000839780	−	0.00959873i
$408$		0			0
$409$	−232.405	−	40.9793i	−0.568228	−	0.100194i	−0.117849	−	0.993032i	$-0.537600\pi$
$409$	−232.405	−	40.9793i	−0.568228	−	0.100194i	−0.450379	+	0.892838i	$0.648711\pi$
$410$	610.878	+	602.253i	1.48995	+	1.46891i
$411$		0			0
$412$	−66.3619	−	46.4671i	−0.161072	−	0.112784i
$413$	−7.83519	+	29.2413i	−0.0189714	+	0.0708022i
$414$		0			0
$415$	−26.8029	+	333.663i	−0.0645853	+	0.804007i
$416$	−504.105	−	183.479i	−1.21179	−	0.441055i
$417$		0			0
$418$	0.796563	+	9.10476i	0.00190565	+	0.0217817i
$419$	330.898	−	394.349i	0.789734	−	0.941168i	−0.209596	−	0.977788i	$-0.567215\pi$
$419$	330.898	−	394.349i	0.789734	−	0.941168i	0.999329	+	0.0366202i	$0.0116592\pi$
$420$		0			0
$421$	264.298	+	96.1964i	0.627785	+	0.228495i	0.636267	−	0.771469i	$-0.280478\pi$
$421$	264.298	+	96.1964i	0.627785	+	0.228495i	−0.00848188	+	0.999964i	$0.502700\pi$
$422$	−290.392	−	1083.76i	−0.688133	−	2.56815i
$423$		0			0
$424$	159.966	−	92.3562i	0.377277	−	0.217821i
$425$	72.9587	+	257.579i	0.171668	+	0.606068i
$426$		0			0
$427$	−376.283	+	806.942i	−0.881225	+	1.88979i
$428$	693.588	−	485.656i	1.62053	−	1.13471i
$429$		0			0
$430$	−284.651	−	765.105i	−0.661980	−	1.77931i
$431$	−90.6464			−0.210316			−0.105158	−	0.994456i	$-0.533535\pi$
$431$	−90.6464			−0.210316			−0.105158	+	0.994456i	$0.533535\pi$
$432$		0			0
$433$	−227.619	−	227.619i	−0.525680	−	0.525680i	0.393601	−	0.919281i	$-0.371229\pi$
$433$	−227.619	−	227.619i	−0.525680	−	0.525680i	−0.919281	+	0.393601i	$0.871229\pi$
$434$	363.492	+	433.193i	0.837539	+	0.998140i
$435$		0			0
$436$	−86.4441	+	490.249i	−0.198266	+	1.12442i
$437$	−383.225	+	821.829i	−0.876946	+	1.88062i
$438$		0			0
$439$	277.715	−	48.9686i	0.632607	−	0.111546i	0.151856	−	0.988403i	$-0.451475\pi$
$439$	277.715	−	48.9686i	0.632607	−	0.111546i	0.480751	+	0.876857i	$0.340364\pi$
$440$	−2.34679	−	1.61850i	−0.00533361	−	0.00367841i
$441$		0			0
$442$	−114.062	−	425.687i	−0.258060	−	0.963092i
$443$	−82.3044	−	176.502i	−0.185789	−	0.398425i	0.791248	−	0.611495i	$-0.209432\pi$
$443$	−82.3044	−	176.502i	−0.185789	−	0.398425i	−0.977037	+	0.213070i	$0.931654\pi$
$444$		0			0
$445$	−258.372	−	440.255i	−0.580611	−	0.989337i
$446$	994.317	+	834.331i	2.22941	+	1.87070i
$447$		0			0
$448$	−362.133	−	776.597i	−0.808333	−	1.73348i
$449$	−330.750	−	190.959i	−0.736638	−	0.425298i	0.0842077	−	0.996448i	$-0.473164\pi$
$449$	−330.750	−	190.959i	−0.736638	−	0.425298i	−0.820846	+	0.571150i	$0.806497\pi$
$450$		0			0
$451$	2.92179	+	5.06069i	0.00647847	+	0.0112210i
$452$	161.266	+	112.920i	0.356784	+	0.249823i
$453$		0			0
$454$	2.33751	+	6.42225i	0.00514869	+	0.0141459i
$455$	−481.455	−	273.423i	−1.05814	−	0.600929i
$456$		0			0
$457$	10.3315	−	118.089i	0.0226072	−	0.258401i	−0.976477	−	0.215620i	$-0.930823\pi$
$457$	10.3315	−	118.089i	0.0226072	−	0.258401i	0.999084	−	0.0427810i	$-0.0136218\pi$
$458$	363.553	+	363.553i	0.793784	+	0.793784i
$459$		0			0
$460$	−403.267	−	848.998i	−0.876668	−	1.84565i
$461$	560.161	−	470.031i	1.21510	−	1.01959i	0.216033	−	0.976386i	$-0.430688\pi$
$461$	560.161	−	470.031i	1.21510	−	1.01959i	0.999066	−	0.0432029i	$-0.0137562\pi$
$462$		0			0
$463$	318.630	−	223.107i	0.688185	−	0.481872i	−0.176426	−	0.984314i	$-0.556454\pi$
$463$	318.630	−	223.107i	0.688185	−	0.481872i	0.864611	+	0.502442i	$0.167565\pi$
$464$	−31.3023	−	86.0023i	−0.0674618	−	0.185350i
$465$		0			0
$466$	−196.002	−	1111.58i	−0.420605	−	2.38537i
$467$	476.342	+	127.635i	1.02000	+	0.273309i	0.729804	−	0.683657i	$-0.239611\pi$
$467$	476.342	+	127.635i	1.02000	+	0.273309i	0.290200	+	0.956966i	$0.406278\pi$
$468$		0			0
$469$	454.257	+	262.265i	0.968565	+	0.559201i
$470$	−446.194	−	369.027i	−0.949348	−	0.785165i
$471$		0			0
$472$	19.2987	−	1.68841i	0.0408870	−	0.00357715i
$473$	−0.484666	−	5.53976i	−0.00102466	−	0.0117120i
$474$		0			0
$475$	−592.619	+	353.478i	−1.24762	+	0.744163i
$476$	257.028	−	445.185i	0.539974	−	0.935263i
$477$		0			0
$478$	−152.804	+	570.274i	−0.319675	+	1.19304i
$479$	71.8112	−	12.6622i	0.149919	−	0.0264347i	−0.0981850	−	0.995168i	$-0.531304\pi$
$479$	71.8112	−	12.6622i	0.149919	−	0.0264347i	0.248104	+	0.968733i	$0.420193\pi$
$480$		0			0
$481$	−458.007	+	166.701i	−0.952198	+	0.346572i
$482$	214.481	+	306.310i	0.444980	+	0.635498i
$483$		0			0
$484$	444.990	+	530.318i	0.919400	+	1.09570i
$485$	8.30508	+	17.4847i	0.0171239	+	0.0360509i
$486$		0			0
$487$	−187.024	+	187.024i	−0.384032	+	0.384032i	−0.872553	−	0.488520i	$-0.837537\pi$
$487$	−187.024	+	187.024i	−0.384032	+	0.384032i	0.488520	+	0.872553i	$0.337537\pi$
$488$	567.598	+	49.6584i	1.16311	+	0.101759i
$489$		0			0
$490$	−88.5804	−	321.429i	−0.180776	−	0.655977i
$491$	−722.057	+	262.807i	−1.47058	+	0.535249i	−0.948259	−	0.317498i	$-0.897157\pi$
$491$	−722.057	+	262.807i	−1.47058	+	0.535249i	−0.522325	+	0.852747i	$0.674935\pi$
$492$		0			0
$493$	91.4386	−	130.588i	0.185474	−	0.264884i
$494$	983.734	−	567.959i	1.99136	−	1.14971i
$495$		0			0
$496$	−66.4497	+	115.094i	−0.133971	+	0.232045i
$497$	−449.489	+	209.600i	−0.904405	+	0.421731i
$498$		0			0
$499$	173.477	−	206.742i	0.347649	−	0.414312i	−0.563678	−	0.825995i	$-0.690614\pi$
$499$	173.477	−	206.742i	0.347649	−	0.414312i	0.911328	+	0.411682i	$0.135059\pi$
$500$	109.149	−	706.856i	0.218298	−	1.41371i
$501$		0			0
$502$	−33.3237	+	15.5391i	−0.0663818	+	0.0309543i
$503$	66.6029	−	17.8462i	0.132411	−	0.0354795i	−0.192005	−	0.981394i	$-0.561499\pi$
$503$	66.6029	−	17.8462i	0.132411	−	0.0354795i	0.324416	+	0.945914i	$0.394832\pi$
$504$		0			0
$505$	528.093	−	96.9930i	1.04573	−	0.192065i
$506$	−1.88904	−	10.7133i	−0.00373329	−	0.0211725i
$507$		0			0
$508$	996.088	+	464.483i	1.96080	+	0.914337i
$509$	622.428	+	109.751i	1.22284	+	0.215621i	0.747550	−	0.664206i	$-0.231230\pi$
$509$	622.428	+	109.751i	1.22284	+	0.215621i	0.475295	+	0.879826i	$0.342341\pi$
$510$		0			0
$511$	−731.563	+	613.854i	−1.43163	+	1.20128i
$512$	270.036	−	270.036i	0.527413	−	0.527413i
$513$		0			0
$514$			540.753i			1.05205i
$515$	29.4613	−	64.3707i	0.0572063	−	0.124992i
$516$		0			0
$517$	−2.26237	−	3.23100i	−0.00437596	−	0.00624952i
$518$	−875.463	−	408.235i	−1.69008	−	0.788099i
$519$		0			0
$520$	−59.0436	+	349.358i	−0.113545	+	0.671843i
$521$	−132.812	−	230.037i	−0.254917	−	0.441529i	0.709956	−	0.704246i	$-0.248715\pi$
$521$	−132.812	−	230.037i	−0.254917	−	0.441529i	−0.964873	+	0.262717i	$0.915381\pi$
$522$		0			0
$523$	−53.2090	+	14.2573i	−0.101738	+	0.0272606i	−0.309329	−	0.950955i	$-0.600104\pi$
$523$	−53.2090	+	14.2573i	−0.101738	+	0.0272606i	0.207591	+	0.978216i	$0.433438\pi$
$524$	140.360	−	385.635i	0.267862	−	0.735944i
$525$		0			0
$526$	−517.676	−	434.382i	−0.984176	−	0.825822i
$527$	−230.612	+	20.1759i	−0.437593	+	0.0382844i
$528$		0			0
$529$	188.223	−	517.139i	0.355809	−	0.977578i
$530$	347.686	+	408.424i	0.656012	+	0.770612i
$531$		0			0
$532$	1279.84	+	342.931i	2.40571	+	0.644607i
$533$	416.575	−	594.931i	0.781566	−	1.11619i
$534$		0			0
$535$	526.890	+	519.451i	0.984842	+	0.970937i
$536$	58.2869	−	330.561i	0.108744	−	0.616719i
$537$		0			0
$538$	−155.872	−	13.6370i	−0.289725	−	0.0253476i
$539$		−	2.27120i		−	0.00421373i
$540$		0			0
$541$	−57.5913			−0.106453			−0.0532267	−	0.998582i	$-0.516951\pi$
$541$	−57.5913			−0.106453			−0.0532267	+	0.998582i	$0.516951\pi$
$542$	97.5118	−	1114.56i	0.179911	−	2.05639i
$543$		0			0
$544$	428.619	+	75.5772i	0.787903	+	0.138929i
$545$	−434.997	+	3.09258i	−0.798160	+	0.00567446i
$546$		0			0
$547$	−202.802	−	142.004i	−0.370754	−	0.259605i	0.373319	−	0.927703i	$-0.378220\pi$
$547$	−202.802	−	142.004i	−0.370754	−	0.259605i	−0.744073	+	0.668098i	$0.767109\pi$
$548$	−310.650	+	1159.36i	−0.566879	+	2.11562i
$549$		0			0
$550$	3.39149	−	7.55157i	0.00616634	−	0.0137301i
$551$	386.122	+	140.537i	0.700766	+	0.255058i
$552$		0			0
$553$	72.8891	+	833.127i	0.131807	+	1.50656i
$554$	339.681	−	404.816i	0.613143	−	0.730715i
$555$		0			0
$556$	346.919	+	126.268i	0.623955	+	0.227101i
$557$	−138.066	−	515.268i	−0.247874	−	0.925077i	−0.971917	−	0.235323i	$-0.924385\pi$
$557$	−138.066	−	515.268i	−0.247874	−	0.925077i	0.724044	−	0.689754i	$-0.242281\pi$
$558$		0			0
$559$	−598.549	+	345.573i	−1.07075	+	0.618198i
$560$	210.191	−	149.416i	0.375342	−	0.266814i
$561$		0			0
$562$	681.697	−	1461.90i	1.21298	−	2.60125i
$563$	168.110	−	117.712i	0.298597	−	0.209080i	−0.414671	−	0.909972i	$-0.636103\pi$
$563$	168.110	−	117.712i	0.298597	−	0.209080i	0.713268	+	0.700892i	$0.247214\pi$
$564$		0			0
$565$	−71.5940	+	156.428i	−0.126715	+	0.276863i
$566$	−21.3549			−0.0377295
$567$		0			0
$568$	224.418	+	224.418i	0.395103	+	0.395103i
$569$	308.278	+	367.391i	0.541788	+	0.645678i	0.965588	−	0.260078i	$-0.0837483\pi$
$569$	308.278	+	367.391i	0.541788	+	0.645678i	−0.423799	+	0.905756i	$0.639304\pi$
$570$		0			0
$571$	141.141	−	800.451i	0.247182	−	1.40184i	−0.568187	−	0.822899i	$-0.692355\pi$
$571$	141.141	−	800.451i	0.247182	−	1.40184i	0.815370	−	0.578941i	$-0.196534\pi$
$572$	−3.38960	+	7.26903i	−0.00592588	+	0.0127081i
$573$		0			0
$574$	1417.52	−	249.947i	2.46955	−	0.435448i
$575$	666.026	−	480.613i	1.15831	−	0.835848i
$576$		0			0
$577$	−127.523	−	475.922i	−0.221010	−	0.824822i	−0.983964	−	0.178368i	$-0.942918\pi$
$577$	−127.523	−	475.922i	−0.221010	−	0.824822i	0.762953	−	0.646453i	$-0.223749\pi$
$578$	−229.716	−	492.627i	−0.397432	−	0.852295i
$579$		0			0
$580$	−367.325	+	215.572i	−0.633319	+	0.371675i
$581$	430.262	+	361.032i	0.740553	+	0.621398i
$582$		0			0
$583$	1.54416	+	3.31145i	0.00264864	+	0.00568002i
$584$	529.247	+	305.561i	0.906244	+	0.523220i
$585$		0			0
$586$	−303.456	−	525.600i	−0.517842	−	0.896929i
$587$	124.213	+	86.9750i	0.211607	+	0.148169i	0.674575	−	0.738206i	$-0.264327\pi$
$587$	124.213	+	86.9750i	0.211607	+	0.148169i	−0.462969	+	0.886375i	$0.653216\pi$
$588$		0			0
$589$	−204.075	−	560.691i	−0.346477	−	0.951937i
$590$	14.9456	+	54.2324i	0.0253314	+	0.0919193i
$591$		0			0
$592$	19.7858	−	226.153i	0.0334220	−	0.382015i
$593$	−295.509	−	295.509i	−0.498330	−	0.498330i	0.412588	−	0.910918i	$-0.364625\pi$
$593$	−295.509	−	295.509i	−0.498330	−	0.498330i	−0.910918	+	0.412588i	$0.864625\pi$
$594$		0			0
$595$	423.194	+	150.632i	0.711251	+	0.253162i
$596$	−292.804	+	245.691i	−0.491281	+	0.412234i
$597$		0			0
$598$	−1107.54	+	775.507i	−1.85207	+	1.29683i
$599$	89.8977	+	246.992i	0.150080	+	0.412340i	0.991836	−	0.127517i	$-0.0407006\pi$
$599$	89.8977	+	246.992i	0.150080	+	0.412340i	−0.841757	+	0.539857i	$0.818478\pi$
$600$		0			0
$601$	−118.138	−	669.994i	−0.196569	−	1.11480i	−0.910167	−	0.414242i	$-0.864047\pi$
$601$	−118.138	−	669.994i	−0.196569	−	1.11480i	0.713598	−	0.700556i	$-0.247065\pi$
$602$	−1323.09	−	354.521i	−2.19782	−	0.588905i
$603$		0			0
$604$	46.9682	+	27.1171i	0.0777619	+	0.0448959i
$605$	−385.546	+	466.166i	−0.637266	+	0.770523i
$606$		0			0
$607$	−214.256	+	18.7450i	−0.352976	+	0.0308814i	−0.262265	−	0.964996i	$-0.584469\pi$
$607$	−214.256	+	18.7450i	−0.352976	+	0.0308814i	−0.0907107	+	0.995877i	$0.528914\pi$
$608$	97.7726	+	1117.55i	0.160810	+	1.83807i
$609$		0			0
$610$	155.913	+	1647.14i	0.255595	+	2.70023i
$611$	−245.113	+	424.547i	−0.401166	+	0.694840i
$612$		0			0
$613$	59.8833	−	223.487i	0.0976888	−	0.364580i	−0.899725	−	0.436458i	$-0.856233\pi$
$613$	59.8833	−	223.487i	0.0976888	−	0.364580i	0.997413	+	0.0718784i	$0.0228994\pi$
$614$	−659.071	+	116.212i	−1.07340	+	0.189270i
$615$		0			0
$616$	−4.49494	+	1.63602i	−0.00729698	+	0.00265588i
$617$	−278.604	−	397.888i	−0.451546	−	0.644874i	0.527250	−	0.849710i	$-0.323223\pi$
$617$	−278.604	−	397.888i	−0.451546	−	0.644874i	−0.978796	+	0.204835i	$0.934334\pi$
$618$		0			0
$619$	−283.757	−	338.169i	−0.458412	−	0.546314i	0.486482	−	0.873691i	$-0.338280\pi$
$619$	−283.757	−	338.169i	−0.458412	−	0.546314i	−0.944894	+	0.327376i	$0.893836\pi$
$620$	582.657	+	207.391i	0.939770	+	0.334501i
$621$		0			0
$622$	115.598	−	115.598i	0.185849	−	0.185849i
$623$	−853.275	−	74.6519i	−1.36962	−	0.119827i
$624$		0			0
$625$	624.747	−	17.7709i	0.999596	−	0.0284334i
$626$	−198.931	+	72.4050i	−0.317781	+	0.115663i
$627$		0			0
$628$	−567.738	+	810.813i	−0.904041	+	1.29110i
$629$	342.454	−	197.716i	0.544442	−	0.314334i
$630$		0			0
$631$	−90.3423	+	156.477i	−0.143173	+	0.247983i	−0.928690	−	0.370857i	$-0.879064\pi$
$631$	−90.3423	+	156.477i	−0.143173	+	0.247983i	0.785517	+	0.618840i	$0.212397\pi$
$632$	485.034	−	226.175i	0.767459	−	0.357872i
$633$		0			0
$634$	789.225	−	940.562i	1.24483	−	1.48354i
$635$	−241.970	+	929.423i	−0.381055	+	1.46366i
$636$		0			0
$637$	−255.831	+	119.296i	−0.401619	+	0.187278i
$638$	−4.76155	+	1.27585i	−0.00746325	+	0.00199977i
$639$		0			0
$640$	−641.621	−	442.503i	−1.00253	−	0.691411i
$641$	−204.816	−	1161.57i	−0.319525	−	1.81212i	−0.545642	−	0.838018i	$-0.683714\pi$
$641$	−204.816	−	1161.57i	−0.319525	−	1.81212i	0.226116	−	0.974100i	$-0.427397\pi$
$642$		0			0
$643$	−1103.31	−	514.484i	−1.71588	−	0.800130i	−0.994156	−	0.107955i	$-0.965570\pi$
$643$	−1103.31	−	514.484i	−1.71588	−	0.800130i	−0.721729	−	0.692176i	$-0.756652\pi$
$644$	−1553.14	−	273.860i	−2.41170	−	0.425248i
$645$		0			0
$646$	−705.970	+	592.379i	−1.09283	+	0.916996i
$647$	−806.671	+	806.671i	−1.24679	+	1.24679i	−0.289656	+	0.957131i	$0.593541\pi$
$647$	−806.671	+	806.671i	−1.24679	+	1.24679i	−0.957131	+	0.289656i	$0.906459\pi$
$648$		0			0
$649$			0.383203i			0.000590452i
$650$	−1028.76	+	14.6285i	−1.58271	+	0.0225054i
$651$		0			0
$652$	−195.348	−	278.986i	−0.299613	−	0.427892i
$653$	17.7512	+	8.27751i	0.0271840	+	0.0126761i	0.436163	−	0.899868i	$-0.356337\pi$
$653$	17.7512	+	8.27751i	0.0271840	+	0.0126761i	−0.408979	+	0.912544i	$0.634115\pi$
$654$		0			0
$655$	353.596	+	59.7598i	0.539841	+	0.0912363i
$656$	169.139	+	292.957i	0.257834	+	0.446581i
$657$		0			0
$658$	−938.459	+	251.459i	−1.42623	+	0.382157i
$659$	−249.462	+	685.391i	−0.378546	+	1.04005i	0.593413	+	0.804898i	$0.297780\pi$
$659$	−249.462	+	685.391i	−0.378546	+	1.04005i	−0.971959	+	0.235149i	$0.924442\pi$
$660$		0			0
$661$	63.2227	+	53.0501i	0.0956470	+	0.0802574i	0.689357	−	0.724422i	$-0.257893\pi$
$661$	63.2227	+	53.0501i	0.0956470	+	0.0802574i	−0.593710	+	0.804679i	$0.702337\pi$
$662$	953.361	−	83.4083i	1.44012	−	0.125994i
$663$		0			0
$664$	122.931	−	337.749i	0.185136	−	0.508658i
$665$	−92.7086	+	1154.11i	−0.139411	+	1.73550i
$666$		0			0
$667$	−472.422	−	126.585i	−0.708279	−	0.189783i
$668$	−807.661	+	1153.46i	−1.20907	+	1.72674i
$669$		0			0
$670$	974.677	−	6.92940i	1.45474	−	0.0103424i
$671$	−1.95710	+	11.0993i	−0.00291669	+	0.0165414i
$672$		0			0
$673$	714.542	+	62.5143i	1.06173	+	0.0928890i	0.604613	−	0.796519i	$-0.293328\pi$
$673$	714.542	+	62.5143i	1.06173	+	0.0928890i	0.457113	+	0.889408i	$0.348883\pi$
$674$			840.851i			1.24755i
$675$		0			0
$676$	29.8402			0.0441423
$677$	−28.8457	+	329.707i	−0.0426081	+	0.487012i	0.944671	+	0.328018i	$0.106381\pi$
$677$	−28.8457	+	329.707i	−0.0426081	+	0.487012i	−0.987279	+	0.158994i	$0.949175\pi$
$678$		0			0
$679$	31.9860	+	5.64000i	0.0471076	+	0.00830634i
$680$	−2.04360	−	287.449i	−0.00300530	−	0.422719i
$681$		0			0
$682$	5.86365	+	4.10577i	0.00859773	+	0.00602019i
$683$	−70.0105	+	261.283i	−0.102504	+	0.382551i	−0.998050	−	0.0624180i	$-0.980119\pi$
$683$	−70.0105	+	261.283i	−0.102504	+	0.382551i	0.895546	+	0.444969i	$0.146785\pi$
$684$		0			0
$685$	−1045.47	−	83.9817i	−1.52623	−	0.122601i
$686$	678.781	+	247.056i	0.989477	+	0.360140i
$687$		0			0
$688$	−28.0567	−	320.690i	−0.0407801	−	0.466119i
$689$	291.899	−	347.872i	0.423656	−	0.504894i
$690$		0			0
$691$	842.590	+	306.678i	1.21938	+	0.443817i	0.869947	−	0.493145i	$-0.164153\pi$
$691$	842.590	+	306.678i	1.21938	+	0.443817i	0.349430	+	0.936962i	$0.386375\pi$
$692$	13.5343	+	50.5105i	0.0195582	+	0.0729921i
$693$		0			0
$694$	467.455	−	269.886i	0.673567	−	0.388884i
$695$	−53.7601	+	318.097i	−0.0773527	+	0.457693i
$696$		0			0
$697$	−249.021	+	534.027i	−0.357275	+	0.766179i
$698$	768.762	−	538.293i	1.10138	−	0.771193i
$699$		0			0
$700$	−860.587	−	836.455i	−1.22941	−	1.19494i
$701$	−948.002			−1.35236			−0.676179	−	0.736738i	$-0.736365\pi$
$701$	−948.002			−1.35236			−0.676179	+	0.736738i	$0.736365\pi$
$702$		0			0
$703$	720.705	+	720.705i	1.02519	+	1.02519i
$704$	−6.97211	−	8.30903i	−0.00990356	−	0.0118026i
$705$		0			0
$706$	−221.727	+	1257.47i	−0.314060	+	1.78112i
$707$	380.747	−	816.515i	0.538539	−	1.15490i
$708$		0			0
$709$	−350.604	+	61.8209i	−0.494505	+	0.0871945i	−0.415339	−	0.909667i	$-0.636337\pi$
$709$	−350.604	+	61.8209i	−0.494505	+	0.0871945i	−0.0791661	+	0.996861i	$0.525226\pi$
$710$	−523.230	+	758.673i	−0.736944	+	1.06855i
$711$		0			0
$712$	141.864	+	529.442i	0.199247	+	0.743599i
$713$	300.147	+	643.666i	0.420963	+	0.902758i
$714$		0			0
$715$	−6.78254	−	1.76579i	−0.00948607	−	0.00246964i
$716$	−3.54923	−	2.97815i	−0.00495702	−	0.00415943i
$717$		0			0
$718$	758.293	+	1626.16i	1.05612	+	2.26485i
$719$	223.764	+	129.190i	0.311215	+	0.179680i	0.647470	−	0.762091i	$-0.275827\pi$
$719$	223.764	+	129.190i	0.311215	+	0.179680i	−0.336255	+	0.941771i	$0.609160\pi$
$720$		0			0
$721$	−59.3923	−	102.871i	−0.0823749	−	0.142678i
$722$	−1023.76	−	716.848i	−1.41796	−	0.992864i
$723$		0			0
$724$	−448.425	−	1232.04i	−0.619371	−	1.70171i
$725$	−243.260	−	281.674i	−0.335531	−	0.388516i
$726$		0			0
$727$	−43.2271	+	494.088i	−0.0594596	+	0.679626i	0.906716	+	0.421741i	$0.138581\pi$
$727$	−43.2271	+	494.088i	−0.0594596	+	0.679626i	−0.966176	+	0.257885i	$0.916975\pi$
$728$	420.383	+	420.383i	0.577450	+	0.577450i
$729$		0			0
$730$	−595.076	+	1671.84i	−0.815172	+	2.29020i
$731$	429.545	−	360.431i	0.587613	−	0.493066i
$732$		0			0
$733$	−757.994	+	530.753i	−1.03410	+	0.724084i	−0.961926	−	0.273309i	$-0.911882\pi$
$733$	−757.994	+	530.753i	−1.03410	+	0.724084i	−0.0721722	+	0.997392i	$0.522993\pi$
$734$	−89.2811	−	245.298i	−0.121636	−	0.334193i
$735$		0			0
$736$	−231.867	−	1314.98i	−0.315037	−	1.78666i
$737$	6.41344	+	1.71848i	0.00870209	+	0.00233172i
$738$		0			0
$739$	−162.414	−	93.7697i	−0.219775	−	0.126887i	0.386071	−	0.922469i	$-0.373832\pi$
$739$	−162.414	−	93.7697i	−0.219775	−	0.126887i	−0.605846	+	0.795582i	$0.707165\pi$
$740$	−1051.75	+	99.5558i	−1.42129	+	0.134535i
$741$		0			0
$742$	896.572	−	78.4399i	1.20832	−	0.105714i
$743$	110.170	+	1259.24i	0.148277	+	1.69481i	0.597882	+	0.801584i	$0.296009\pi$
$743$	110.170	+	1259.24i	0.148277	+	1.69481i	−0.449606	+	0.893227i	$0.648435\pi$
$744$		0			0
$745$	−257.384	−	212.871i	−0.345482	−	0.285733i
$746$	−682.096	+	1181.43i	−0.914338	+	1.58368i
$747$		0			0
$748$	1.68416	−	6.28536i	0.00225155	−	0.00840289i
$749$	1222.63	−	215.583i	1.63235	−	0.287827i
$750$		0			0
$751$	9.41271	−	3.42595i	0.0125336	−	0.00456185i	−0.335746	−	0.941953i	$-0.608988\pi$
$751$	9.41271	−	3.42595i	0.0125336	−	0.00456185i	0.348279	+	0.937391i	$0.386766\pi$
$752$	−130.966	−	187.039i	−0.174157	−	0.248722i
$753$		0			0
$754$	393.817	+	469.333i	0.522304	+	0.622458i
$755$	−15.8920	+	44.6481i	−0.0210491	+	0.0591366i
$756$		0			0
$757$	50.7114	−	50.7114i	0.0669900	−	0.0669900i	−0.672818	−	0.739808i	$-0.734916\pi$
$757$	50.7114	−	50.7114i	0.0669900	−	0.0669900i	0.739808	+	0.672818i	$0.234916\pi$
$758$	679.092	+	59.4129i	0.895900	+	0.0783811i
$759$		0			0
$760$	714.295	−	196.848i	0.939862	−	0.259010i
$761$	−249.620	+	90.8541i	−0.328015	+	0.119388i	−0.500778	−	0.865576i	$-0.666953\pi$
$761$	−249.620	+	90.8541i	−0.328015	+	0.119388i	0.172763	+	0.984963i	$0.444731\pi$
$762$		0			0
$763$	−418.661	+	597.910i	−0.548704	+	0.783631i
$764$	892.915	−	515.525i	1.16874	−	0.674771i
$765$		0			0
$766$	763.977	−	1323.25i	0.997359	−	1.72748i
$767$	43.1646	−	20.1280i	0.0562772	−	0.0262425i
$768$		0			0
$769$	222.398	−	265.044i	0.289205	−	0.344661i	−0.601807	−	0.798642i	$-0.705552\pi$
$769$	222.398	−	265.044i	0.289205	−	0.344661i	0.891011	+	0.453981i	$0.149997\pi$
$770$	−7.03045	−	11.9796i	−0.00913046	−	0.0155579i
$771$		0			0
$772$	−1460.67	+	681.122i	−1.89206	+	0.882282i
$773$	116.008	−	31.0841i	0.150075	−	0.0402124i	−0.183000	−	0.983113i	$-0.558581\pi$
$773$	116.008	−	31.0841i	0.150075	−	0.0402124i	0.333074	+	0.942901i	$0.391914\pi$
$774$		0			0
$775$	−86.2698	+	533.511i	−0.111316	+	0.688402i
$776$	−3.60918	−	20.4687i	−0.00465101	−	0.0263772i
$777$		0			0
$778$	699.650	+	326.252i	0.899293	+	0.419347i
$779$	−1495.68	−	263.729i	−1.92000	−	0.338548i
$780$		0			0
$781$	−4.80921	+	4.03541i	−0.00615776	+	0.00516697i
$782$	775.648	−	775.648i	0.991878	−	0.991878i
$783$		0			0
$784$		−	131.477i		−	0.167700i
$785$	−786.486	−	359.960i	−1.00189	−	0.458547i
$786$		0			0
$787$	248.426	+	354.789i	0.315662	+	0.450812i	0.945360	−	0.326028i	$-0.105710\pi$
$787$	248.426	+	354.789i	0.315662	+	0.450812i	−0.629698	+	0.776840i	$0.716821\pi$
$788$	−585.263	−	272.913i	−0.742720	−	0.346336i
$789$		0			0
$790$	900.399	+	1266.64i	1.13975	+	1.60334i
$791$	144.330	+	249.986i	0.182465	+	0.316038i
$792$		0			0
$793$	1353.04	−	362.545i	1.70622	−	0.457181i
$794$	419.073	−	1151.39i	0.527800	−	1.45012i
$795$		0			0
$796$	865.472	+	726.217i	1.08728	+	0.912333i
$797$	1097.56	−	96.0243i	1.37712	−	0.120482i	0.625574	−	0.780165i	$-0.284865\pi$
$797$	1097.56	−	96.0243i	1.37712	−	0.120482i	0.751544	+	0.659683i	$0.229309\pi$
$798$		0			0
$799$	136.029	−	373.738i	0.170250	−	0.467757i
$800$	416.281	−	926.902i	0.520351	−	1.15863i
$801$		0			0
$802$	−1686.70	−	451.950i	−2.10312	−	0.563529i
$803$	−6.93370	+	9.90236i	−0.00863475	+	0.0123317i
$804$		0			0
$805$	−9.79748	−	1378.10i	−0.0121708	−	1.71192i
$806$	154.489	−	876.148i	0.191673	−	1.08703i
$807$		0			0
$808$	−574.331	−	50.2474i	−0.710806	−	0.0621874i
$809$		−	95.9737i		−	0.118632i	−0.998239	−	0.0593162i	$-0.981108\pi$
$809$		−	95.9737i		−	0.118632i	0.998239	−	0.0593162i	$-0.0188920\pi$
$810$		0			0
$811$	574.147			0.707949			0.353975	−	0.935255i	$-0.384830\pi$
$811$	574.147			0.707949			0.353975	+	0.935255i	$0.384830\pi$
$812$	−62.2855	+	711.927i	−0.0767063	+	0.876757i
$813$		0			0
$814$	−12.0418	−	2.12329i	−0.0147933	−	0.00260846i
$815$	208.942	−	211.934i	0.256370	−	0.260042i
$816$		0			0
$817$	1183.91	+	828.985i	1.44910	+	1.01467i
$818$	−190.443	+	710.743i	−0.232816	+	0.868879i
$819$		0			0
$820$	1198.70	−	1020.44i	1.46183	−	1.24444i
$821$	−113.306	−	41.2401i	−0.138010	−	0.0502316i	0.272092	−	0.962271i	$-0.412285\pi$
$821$	−113.306	−	41.2401i	−0.138010	−	0.0502316i	−0.410102	+	0.912040i	$0.634507\pi$
$822$		0			0
$823$	−57.8337	−	661.043i	−0.0702719	−	0.803211i	−0.946792	−	0.321846i	$-0.895697\pi$
$823$	−57.8337	−	661.043i	−0.0702719	−	0.803211i	0.876520	−	0.481365i	$-0.159859\pi$
$824$	−48.8605	+	58.2296i	−0.0592967	+	0.0706670i
$825$		0			0
$826$	88.6980	+	32.2834i	0.107383	+	0.0390840i
$827$	−130.092	−	485.512i	−0.157306	−	0.587076i	−0.998897	−	0.0469594i	$-0.985047\pi$
$827$	−130.092	−	485.512i	−0.157306	−	0.587076i	0.841590	−	0.540116i	$-0.181620\pi$
$828$		0			0
$829$	−1003.54	+	579.396i	−1.21055	+	0.698910i	−0.962879	−	0.269935i	$-0.912998\pi$
$829$	−1003.54	+	579.396i	−1.21055	+	0.698910i	−0.247669	+	0.968845i	$0.579665\pi$
$830$	1029.11	+	173.926i	1.23990	+	0.209550i
$831$		0			0
$832$	−569.728	+	1221.79i	−0.684769	+	1.46849i
$833$	187.598	−	131.357i	0.225208	−	0.157692i
$834$		0			0
$835$	−1118.85	−	512.077i	−1.33994	−	0.613266i
$836$	16.7721			0.0200623
$837$		0			0
$838$	−1134.98	−	1134.98i	−1.35439	−	1.35439i
$839$	−362.266	−	431.732i	−0.431783	−	0.514579i	0.505653	−	0.862737i	$-0.331252\pi$
$839$	−362.266	−	431.732i	−0.431783	−	0.514579i	−0.937436	+	0.348158i	$0.886807\pi$
$840$		0			0
$841$	107.553	−	609.965i	0.127887	−	0.725285i
$842$	370.621	−	794.800i	0.440168	−	0.943943i
$843$		0			0
$844$	−2027.70	+	357.537i	−2.40248	+	0.423623i
$845$	4.71043	+	25.6466i	0.00557447	+	0.0303510i
$846$		0			0
$847$	262.715	+	980.466i	0.310171	+	1.15758i
$848$	89.3892	+	191.696i	0.105412	+	0.226056i
$849$		0			0
$850$	819.899	−	156.622i	0.964587	−	0.184261i
$851$	−929.339	−	779.808i	−1.09206	−	0.916343i
$852$		0			0
$853$	−0.0740019	−	0.158698i	−8.67549e−5	−	0.000186046i	0.906264	−	0.422711i	$-0.138922\pi$
$853$	−0.0740019	−	0.158698i	−8.67549e−5	−	0.000186046i	−0.906351	+	0.422525i	$0.861144\pi$
$854$	2404.21	+	1388.07i	2.81523	+	1.62537i
$855$		0			0
$856$	−397.231	−	688.024i	−0.464055	−	0.803767i
$857$	786.659	+	550.825i	0.917922	+	0.642736i	0.934053	−	0.357134i	$-0.116246\pi$
$857$	786.659	+	550.825i	0.917922	+	0.642736i	−0.0161313	+	0.999870i	$0.505135\pi$
$858$		0			0
$859$	−277.643	−	762.818i	−0.323217	−	0.888031i	−0.989783	−	0.142585i	$-0.954459\pi$
$859$	−277.643	−	762.818i	−0.323217	−	0.888031i	0.666566	−	0.745446i	$-0.267764\pi$
$860$	−1444.24	+	398.008i	−1.67935	+	0.462800i
$861$		0			0
$862$	−24.6332	+	281.559i	−0.0285768	+	0.326635i
$863$	359.023	+	359.023i	0.416018	+	0.416018i	0.883829	−	0.467811i	$-0.154957\pi$
$863$	359.023	+	359.023i	0.416018	+	0.416018i	−0.467811	+	0.883829i	$0.654957\pi$
$864$		0			0
$865$	−41.2756	+	19.6056i	−0.0477174	+	0.0226654i
$866$	−768.870	+	645.159i	−0.887841	+	0.744987i
$867$		0			0
$868$	850.070	−	595.225i	0.979343	−	0.685743i
$869$	3.62072	+	9.94784i	0.00416654	+	0.0114475i
$870$		0			0
$871$	−143.298	−	812.683i	−0.164521	−	0.933046i
$872$	451.175	+	120.892i	0.517402	+	0.138638i
$873$		0			0
$874$	2448.56	+	1413.68i	2.80156	+	1.61748i
$875$	583.056	−	871.683i	0.666350	−	0.996209i
$876$		0			0
$877$	−619.123	+	54.1662i	−0.705955	+	0.0617631i	−0.434479	−	0.900682i	$-0.643067\pi$
$877$	−619.123	+	54.1662i	−0.705955	+	0.0617631i	−0.271476	+	0.962445i	$0.587512\pi$
$878$	−76.6334	−	875.924i	−0.0872818	−	0.997635i
$879$		0			0
$880$	2.08049	−	2.51554i	0.00236420	−	0.00285857i
$881$	211.398	−	366.153i	0.239953	−	0.415611i	−0.720748	−	0.693198i	$-0.756201\pi$
$881$	211.398	−	366.153i	0.239953	−	0.415611i	0.960701	+	0.277587i	$0.0895347\pi$
$882$		0			0
$883$	130.466	−	486.907i	0.147754	−	0.551424i	−0.851864	−	0.523763i	$-0.824528\pi$
$883$	130.466	−	486.907i	0.147754	−	0.551424i	0.999617	−	0.0276605i	$-0.00880573\pi$
$884$	−796.453	+	140.436i	−0.900965	+	0.158865i
$885$		0			0
$886$	−570.605	+	207.683i	−0.644023	+	0.234405i
$887$	815.794	+	1165.07i	0.919722	+	1.31350i	0.949442	+	0.313942i	$0.101650\pi$
$887$	815.794	+	1165.07i	0.919722	+	1.31350i	−0.0297198	+	0.999558i	$0.509462\pi$
$888$		0			0
$889$	1035.85	+	1234.47i	1.16518	+	1.38861i
$890$	−1437.70	+	682.896i	−1.61539	+	0.767299i
$891$		0			0
$892$	1684.30	−	1684.30i	1.88822	−	1.88822i
$893$	1021.24	+	89.3465i	1.14360	+	0.100052i
$894$		0			0
$895$	1.99936	−	3.52055i	0.00223392	−	0.00393358i
$896$	−1228.93	+	447.295i	−1.37158	+	0.499213i
$897$		0			0
$898$	−683.024	+	975.459i	−0.760606	+	1.08626i
$899$	278.708	−	160.912i	0.310020	−	0.178990i
$900$		0			0
$901$	−184.213	+	319.067i	−0.204454	+	0.354125i
$902$	16.5131	−	7.70020i	0.0183073	−	0.00853681i
$903$		0			0
$904$	118.736	−	141.504i	0.131345	−	0.156531i
$905$	988.106	−	579.888i	1.09183	−	0.640761i
$906$		0			0
$907$	−636.372	+	296.745i	−0.701623	+	0.327172i	−0.740486	−	0.672072i	$-0.765404\pi$
$907$	−636.372	+	296.745i	−0.701623	+	0.327172i	0.0388622	+	0.999245i	$0.487627\pi$
$908$	12.1146	−	3.24609i	0.0133420	−	0.00357499i
$909$		0			0
$910$	−980.122	+	1421.16i	−1.07706	+	1.56171i
$911$	−37.4638	−	212.468i	−0.0411238	−	0.233224i	0.957317	−	0.289039i	$-0.0933356\pi$
$911$	−37.4638	−	212.468i	−0.0411238	−	0.233224i	−0.998441	+	0.0558143i	$0.982225\pi$
$912$		0			0
$913$	6.44363	+	3.00471i	0.00705765	+	0.00329103i
$914$	−363.993	−	64.1818i	−0.398242	−	0.0702207i
$915$		0			0
$916$	722.769	−	606.475i	0.789049	−	0.662091i
$917$	425.483	−	425.483i	0.463994	−	0.463994i
$918$		0			0
$919$		−	443.470i		−	0.482557i	−0.970456	−	0.241279i	$-0.922433\pi$
$919$		−	443.470i		−	0.482557i	0.970456	−	0.241279i	$-0.0775668\pi$
$920$	−826.552	+	307.512i	−0.898426	+	0.334252i
$921$		0			0
$922$	−1307.75	−	1867.66i	−1.41838	−	2.02566i
$923$	707.161	+	329.755i	0.766155	+	0.357264i
$924$		0			0
$925$	−251.589	−	888.230i	−0.271989	−	0.960249i
$926$	−606.410	−	1050.33i	−0.654871	−	1.13427i
$927$		0			0
$928$	−584.447	+	156.602i	−0.629792	+	0.168752i
$929$	−27.4836	+	75.5106i	−0.0295841	+	0.0812816i	−0.953605	−	0.301059i	$-0.902660\pi$
$929$	−27.4836	+	75.5106i	−0.0295841	+	0.0812816i	0.924021	+	0.382341i	$0.124882\pi$
$930$		0			0
$931$	452.187	+	379.430i	0.485700	+	0.407551i
$932$	−2063.47	+	180.530i	−2.21402	+	0.193702i
$933$		0			0
$934$	525.898	−	1444.89i	0.563060	−	1.54699i
$935$	5.66790	+	0.455298i	0.00606192	+	0.000486950i
$936$		0			0
$937$	1562.85	+	418.765i	1.66793	+	0.446921i	0.964552	−	0.263892i	$-0.0850062\pi$
$937$	1562.85	+	418.765i	1.66793	+	0.446921i	0.703381	+	0.710813i	$0.251673\pi$
$938$	938.074	−	1339.71i	1.00008	−	1.42826i
$939$		0			0
$940$	−745.994	+	756.678i	−0.793611	+	0.804976i
$941$	151.665	−	860.133i	0.161174	−	0.914063i	−0.791748	−	0.610848i	$-0.790829\pi$
$941$	151.665	−	860.133i	0.161174	−	0.914063i	0.952922	−	0.303215i	$-0.0980601\pi$
$942$		0			0
$943$	1800.86	+	157.555i	1.90971	+	0.167078i
$944$			22.1832i			0.0234991i
$945$		0			0
$946$	−17.3389			−0.0183286
$947$	74.8506	−	855.546i	0.0790397	−	0.903428i	−0.848376	−	0.529395i	$-0.822419\pi$
$947$	74.8506	−	855.546i	0.0790397	−	0.903428i	0.927415	−	0.374033i	$-0.122025\pi$
$948$		0			0
$949$	1479.61	+	260.896i	1.55913	+	0.274916i
$950$	936.901	+	1936.81i	0.986212	+	2.03874i
$951$		0			0
$952$	−395.103	−	276.654i	−0.415024	−	0.290603i
$953$	134.463	−	501.824i	0.141095	−	0.526573i	−0.858804	−	0.512305i	$-0.828792\pi$
$953$	134.463	−	501.824i	0.141095	−	0.526573i	0.999898	−	0.0142675i	$-0.00454163\pi$
$954$		0			0
$955$	584.027	+	686.051i	0.611546	+	0.718378i
$956$	1018.09	+	370.556i	1.06495	+	0.387611i
$957$		0			0
$958$	−19.8158	−	226.495i	−0.0206845	−	0.236425i
$959$	−1131.22	+	1348.14i	−1.17959	+	1.40578i
$960$		0			0
$961$	463.905	+	168.848i	0.482731	+	0.175700i
$962$	393.330	+	1467.93i	0.408867	+	1.52591i
$963$		0			0
$964$	594.278	−	343.107i	0.616471	−	0.355920i
$965$	−815.975	−	1147.88i	−0.845570	−	1.18951i
$966$		0			0
$967$	210.575	−	451.579i	0.217761	−	0.466989i	−0.766833	−	0.641847i	$-0.778169\pi$
$967$	210.575	−	451.579i	0.217761	−	0.466989i	0.984594	+	0.174857i	$0.0559464\pi$
$968$	532.088	−	372.572i	0.549677	−	0.384888i
$969$		0			0
$970$	56.5665	−	21.0451i	0.0583160	−	0.0216960i
$971$	331.692			0.341598			0.170799	−	0.985306i	$-0.445365\pi$
$971$	331.692			0.341598			0.170799	+	0.985306i	$0.445365\pi$
$972$		0			0
$973$	382.766	+	382.766i	0.393388	+	0.393388i
$974$	530.095	+	631.743i	0.544246	+	0.648607i
$975$		0			0
$976$	−113.294	+	642.523i	−0.116080	+	0.658323i
$977$	612.766	−	1314.08i	0.627192	−	1.34502i	−0.293962	−	0.955817i	$-0.594974\pi$
$977$	612.766	−	1314.08i	0.627192	−	1.34502i	0.921153	−	0.389200i	$-0.127248\pi$
$978$		0			0
$979$	−10.6776	+	1.88275i	−0.0109066	+	0.00192313i
$980$	−601.781	+	110.527i	−0.614062	+	0.112783i
$981$		0			0
$982$	620.092	+	2314.22i	0.631459	+	2.35664i
$983$	−593.979	−	1273.79i	−0.604251	−	1.29582i	−0.935850	−	0.352400i	$-0.885366\pi$
$983$	−593.979	−	1273.79i	−0.604251	−	1.29582i	0.331599	−	0.943420i	$-0.392412\pi$
$984$		0			0
$985$	142.172	−	546.094i	0.144337	−	0.554410i
$986$	−380.774	−	319.507i	−0.386180	−	0.324044i
$987$		0			0
$988$	−880.963	−	1889.23i	−0.891663	−	1.91218i
$989$	−1489.82	−	860.148i	−1.50639	−	0.869715i
$990$		0			0
$991$	556.051	+	963.109i	0.561101	+	0.971855i	0.997401	+	0.0720540i	$0.0229554\pi$
$991$	556.051	+	963.109i	0.561101	+	0.971855i	−0.436300	+	0.899801i	$0.643711\pi$
$992$	719.722	+	503.955i	0.725526	+	0.508019i
$993$		0			0
$994$	528.896	+	1453.13i	0.532088	+	1.46190i
$995$	−487.539	+	858.480i	−0.489989	+	0.862794i
$996$		0			0
$997$	−11.5767	+	132.322i	−0.0116115	+	0.132721i	−0.999788	−	0.0206019i	$-0.993442\pi$
$997$	−11.5767	+	132.322i	−0.0116115	+	0.132721i	0.988176	+	0.153322i	$0.0489973\pi$
$998$	−595.024	−	595.024i	−0.596216	−	0.596216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.29		408
3.2	odd	2		135.3.r.a.103.6	yes	408
5.2	odd	4	inner	405.3.s.a.37.29		408
15.2	even	4		135.3.r.a.22.6	✓	408
27.11	odd	18		135.3.r.a.43.6	yes	408
27.16	even	9	inner	405.3.s.a.208.29		408
135.92	even	36		135.3.r.a.97.6	yes	408
135.97	odd	36	inner	405.3.s.a.127.29		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.6	✓	408	15.2	even	4
135.3.r.a.43.6	yes	408	27.11	odd	18
135.3.r.a.97.6	yes	408	135.92	even	36
135.3.r.a.103.6	yes	408	3.2	odd	2
405.3.s.a.37.29		408	5.2	odd	4	inner
405.3.s.a.118.29		408	1.1	even	1	trivial
405.3.s.a.127.29		408	135.97	odd	36	inner
405.3.s.a.208.29		408	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.271751 - 3.10613i) q^{2} +(-5.63494 - 0.993591i) q^{4} +(-0.0355463 - 4.99987i) q^{5} +(-6.87240 - 4.81211i) q^{7} +(-1.38954 + 5.18582i) q^{8} +(-15.5399 - 1.24831i) q^{10} +(-0.0997944 - 0.0363222i) q^{11} +(1.15037 + 13.1488i) q^{13} +(-16.8146 + 20.0388i) q^{14} +(-5.77697 - 2.10265i) q^{16} +(-2.77156 - 10.3436i) q^{17} +(23.9034 - 13.8006i) q^{19} +(-4.76753 + 28.2093i) q^{20} +(-0.139940 + 0.300103i) q^{22} +(-26.9117 + 18.8438i) q^{23} +(-24.9975 + 0.355454i) q^{25} +41.1545 q^{26} +(33.9443 + 33.9443i) q^{28} +(9.56923 + 11.4042i) q^{29} +(3.75387 - 21.2892i) q^{31} +(-17.1767 + 36.8356i) q^{32} +(-32.8817 + 5.79794i) q^{34} +(-23.8156 + 34.5322i) q^{35} +(9.55740 + 35.6687i) q^{37} +(-36.3707 - 77.9973i) q^{38} +(25.9778 + 6.76317i) q^{40} +(-42.1515 - 35.3693i) q^{41} +(22.1297 + 47.4572i) q^{43} +(0.526246 + 0.303828i) q^{44} +(51.2179 + 88.7119i) q^{46} +(30.4241 + 21.3032i) q^{47} +(7.31453 + 20.0965i) q^{49} +(-5.68900 + 77.7419i) q^{50} +(6.58228 - 75.2358i) q^{52} +(-24.3281 - 24.3281i) q^{53} +(-0.178059 + 0.500250i) q^{55} +(34.5042 - 28.9524i) q^{56} +(38.0232 - 26.6241i) q^{58} +(-1.23413 - 3.39074i) q^{59} +(-18.4286 - 104.514i) q^{61} +(-65.1069 - 17.4453i) q^{62} +(88.4518 + 51.0677i) q^{64} +(65.7016 - 6.21911i) q^{65} +(-62.2832 + 5.44908i) q^{67} +(5.34026 + 61.0394i) q^{68} +(100.789 + 83.3585i) q^{70} +(29.5576 - 51.1953i) q^{71} +(29.4612 - 109.951i) q^{73} +(113.389 - 19.9935i) q^{74} +(-148.406 + 54.0155i) q^{76} +(0.511041 + 0.729842i) q^{77} +(-64.0753 - 76.3619i) q^{79} +(-10.3076 + 28.9589i) q^{80} +(-121.316 + 121.316i) q^{82} +(-66.6928 - 5.83486i) q^{83} +(-51.6182 + 14.2251i) q^{85} +(153.422 - 55.8410i) q^{86} +(0.327028 - 0.467045i) q^{88} +(88.4162 - 51.0471i) q^{89} +(55.3678 - 95.8998i) q^{91} +(170.369 - 79.4442i) q^{92} +(74.4380 - 88.7118i) q^{94} +(-69.8511 - 119.023i) q^{95} +(-3.50866 + 1.63611i) q^{97} +(64.4100 - 17.2586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Introduction

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