LMFDB - Embedded newform 460.2.e.b.91.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (of order $2$, degree $1$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.10
Character	$\chi$	$=$	460.91
Dual form			460.2.e.b.91.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.265302 - 1.38911i) q^{2} -0.0612154i q^{3} +(-1.85923 + 0.737066i) q^{4} +1.00000i q^{5} +(-0.0850346 + 0.0162406i) q^{6} -0.810885 q^{7} +(1.51712 + 2.38712i) q^{8} +2.99625 q^{9} +O(q^{10})$	\(q+(-0.265302 - 1.38911i) q^{2} -0.0612154i q^{3} +(-1.85923 + 0.737066i) q^{4} +1.00000i q^{5} +(-0.0850346 + 0.0162406i) q^{6} -0.810885 q^{7} +(1.51712 + 2.38712i) q^{8} +2.99625 q^{9} +(1.38911 - 0.265302i) q^{10} -2.10140 q^{11} +(0.0451198 + 0.113813i) q^{12} +2.93504 q^{13} +(0.215130 + 1.12641i) q^{14} +0.0612154 q^{15} +(2.91347 - 2.74075i) q^{16} +4.65004i q^{17} +(-0.794913 - 4.16211i) q^{18} +6.20768 q^{19} +(-0.737066 - 1.85923i) q^{20} +0.0496387i q^{21} +(0.557507 + 2.91907i) q^{22} +(4.03517 - 2.59180i) q^{23} +(0.146129 - 0.0928711i) q^{24} -1.00000 q^{25} +(-0.778674 - 4.07709i) q^{26} -0.367063i q^{27} +(1.50762 - 0.597676i) q^{28} +5.24402 q^{29} +(-0.0162406 - 0.0850346i) q^{30} -2.58292i q^{31} +(-4.58014 - 3.31999i) q^{32} +0.128638i q^{33} +(6.45940 - 1.23367i) q^{34} -0.810885i q^{35} +(-5.57072 + 2.20844i) q^{36} +2.99380i q^{37} +(-1.64691 - 8.62312i) q^{38} -0.179670i q^{39} +(-2.38712 + 1.51712i) q^{40} +8.21934 q^{41} +(0.0689533 - 0.0131693i) q^{42} -10.1620 q^{43} +(3.90699 - 1.54887i) q^{44} +2.99625i q^{45} +(-4.67082 - 4.91766i) q^{46} -1.89447i q^{47} +(-0.167776 - 0.178349i) q^{48} -6.34247 q^{49} +(0.265302 + 1.38911i) q^{50} +0.284654 q^{51} +(-5.45692 + 2.16332i) q^{52} +8.12090i q^{53} +(-0.509889 + 0.0973827i) q^{54} -2.10140i q^{55} +(-1.23021 - 1.93568i) q^{56} -0.380006i q^{57} +(-1.39125 - 7.28450i) q^{58} +13.1005i q^{59} +(-0.113813 + 0.0451198i) q^{60} -13.7022i q^{61} +(-3.58795 + 0.685255i) q^{62} -2.42962 q^{63} +(-3.39669 + 7.24310i) q^{64} +2.93504i q^{65} +(0.178692 - 0.0341280i) q^{66} +1.42460 q^{67} +(-3.42739 - 8.64549i) q^{68} +(-0.158658 - 0.247014i) q^{69} +(-1.12641 + 0.215130i) q^{70} +2.26145i q^{71} +(4.54568 + 7.15242i) q^{72} -4.13040 q^{73} +(4.15870 - 0.794262i) q^{74} +0.0612154i q^{75} +(-11.5415 + 4.57547i) q^{76} +1.70400 q^{77} +(-0.249580 + 0.0476668i) q^{78} +14.9553 q^{79} +(2.74075 + 2.91347i) q^{80} +8.96629 q^{81} +(-2.18061 - 11.4175i) q^{82} -8.73564 q^{83} +(-0.0365870 - 0.0922896i) q^{84} -4.65004 q^{85} +(2.69601 + 14.1162i) q^{86} -0.321015i q^{87} +(-3.18808 - 5.01630i) q^{88} -5.82961i q^{89} +(4.16211 - 0.794913i) q^{90} -2.37998 q^{91} +(-5.59198 + 7.79293i) q^{92} -0.158114 q^{93} +(-2.63161 + 0.502606i) q^{94} +6.20768i q^{95} +(-0.203234 + 0.280375i) q^{96} -2.73446i q^{97} +(1.68267 + 8.81035i) q^{98} -6.29633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.265302	−	1.38911i	−0.187597	−	0.982246i
$2$	−0.265302	−	1.38911i	−0.187597	−	0.982246i
$3$		−	0.0612154i		−	0.0353427i	−0.999844	−	0.0176714i	$-0.994375\pi$
$3$		−	0.0612154i		−	0.0353427i	0.999844	−	0.0176714i	$-0.00562526\pi$
$4$	−1.85923	+	0.737066i	−0.929615	+	0.368533i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.0850346	+	0.0162406i	−0.0347152	+	0.00663019i
$7$	−0.810885			−0.306486			−0.153243	−	0.988189i	$-0.548972\pi$
$7$	−0.810885			−0.306486			−0.153243	+	0.988189i	$0.548972\pi$
$8$	1.51712	+	2.38712i	0.536383	+	0.843975i
$9$	2.99625			0.998751
$10$	1.38911	−	0.265302i	0.439274	−	0.0838960i
$11$	−2.10140			−0.633596			−0.316798	−	0.948493i	$-0.602608\pi$
$11$	−2.10140			−0.633596			−0.316798	+	0.948493i	$0.602608\pi$
$12$	0.0451198	+	0.113813i	0.0130250	+	0.0328551i
$13$	2.93504			0.814035			0.407017	−	0.913420i	$-0.366569\pi$
$13$	2.93504			0.814035			0.407017	+	0.913420i	$0.366569\pi$
$14$	0.215130	+	1.12641i	0.0574959	+	0.301044i
$15$	0.0612154			0.0158057
$16$	2.91347	−	2.74075i	0.728367	−	0.685187i
$17$			4.65004i			1.12780i	0.825843	+	0.563900i	$0.190700\pi$
$17$			4.65004i			1.12780i	−0.825843	+	0.563900i	$0.809300\pi$
$18$	−0.794913	−	4.16211i	−0.187363	−	0.981019i
$19$	6.20768			1.42414			0.712070	−	0.702109i	$-0.247758\pi$
$19$	6.20768			1.42414			0.712070	+	0.702109i	$0.247758\pi$
$20$	−0.737066	−	1.85923i	−0.164813	−	0.415736i
$21$			0.0496387i			0.0108320i
$22$	0.557507	+	2.91907i	0.118861	+	0.622348i
$23$	4.03517	−	2.59180i	0.841391	−	0.540427i
$23$	4.03517	−	2.59180i	0.841391	−	0.540427i
$24$	0.146129	−	0.0928711i	0.0298284	−	0.0189572i
$25$	−1.00000			−0.200000
$26$	−0.778674	−	4.07709i	−0.152711	−	0.799582i
$27$		−	0.367063i		−	0.0706413i
$28$	1.50762	−	0.597676i	0.284914	−	0.112950i
$29$	5.24402			0.973790			0.486895	−	0.873461i	$-0.338129\pi$
$29$	5.24402			0.973790			0.486895	+	0.873461i	$0.338129\pi$
$30$	−0.0162406	−	0.0850346i	−0.00296511	−	0.0155251i
$31$		−	2.58292i		−	0.463906i	−0.972727	−	0.231953i	$-0.925488\pi$
$31$		−	2.58292i		−	0.463906i	0.972727	−	0.231953i	$-0.0745116\pi$
$32$	−4.58014	−	3.31999i	−0.809662	−	0.586896i
$33$			0.128638i			0.0223930i
$34$	6.45940	−	1.23367i	1.10778	−	0.211572i
$35$		−	0.810885i		−	0.137065i
$36$	−5.57072	+	2.20844i	−0.928453	+	0.368073i
$37$			2.99380i			0.492178i	0.969247	+	0.246089i	$0.0791455\pi$
$37$			2.99380i			0.492178i	−0.969247	+	0.246089i	$0.920855\pi$
$38$	−1.64691	−	8.62312i	−0.267164	−	1.39886i
$39$		−	0.179670i		−	0.0287702i
$40$	−2.38712	+	1.51712i	−0.377437	+	0.239878i
$41$	8.21934			1.28365			0.641823	−	0.766853i	$-0.278178\pi$
$41$	8.21934			1.28365			0.641823	+	0.766853i	$0.278178\pi$
$42$	0.0689533	−	0.0131693i	0.0106397	−	0.00203206i
$43$	−10.1620			−1.54970			−0.774849	−	0.632147i	$-0.782174\pi$
$43$	−10.1620			−1.54970			−0.774849	+	0.632147i	$0.782174\pi$
$44$	3.90699	−	1.54887i	0.589001	−	0.233501i
$45$			2.99625i			0.446655i
$46$	−4.67082	−	4.91766i	−0.688675	−	0.725070i
$47$		−	1.89447i		−	0.276336i	−0.990409	−	0.138168i	$-0.955879\pi$
$47$		−	1.89447i		−	0.276336i	0.990409	−	0.138168i	$-0.0441214\pi$
$48$	−0.167776	−	0.178349i	−0.0242164	−	0.0257425i
$49$	−6.34247			−0.906066
$50$	0.265302	+	1.38911i	0.0375194	+	0.196449i
$51$	0.284654			0.0398595
$52$	−5.45692	+	2.16332i	−0.756738	+	0.299999i
$53$			8.12090i			1.11549i	0.830012	+	0.557745i	$0.188333\pi$
$53$			8.12090i			1.11549i	−0.830012	+	0.557745i	$0.811667\pi$
$54$	−0.509889	+	0.0973827i	−0.0693871	+	0.0132521i
$55$		−	2.10140i		−	0.283353i
$56$	−1.23021	−	1.93568i	−0.164394	−	0.258666i
$57$		−	0.380006i		−	0.0503330i
$58$	−1.39125	−	7.28450i	−0.182680	−	0.956501i
$59$			13.1005i			1.70554i	0.522284	+	0.852772i	$0.325080\pi$
$59$			13.1005i			1.70554i	−0.522284	+	0.852772i	$0.674920\pi$
$60$	−0.113813	+	0.0451198i	−0.0146933	+	0.00582494i
$61$		−	13.7022i		−	1.75439i	−0.480133	−	0.877196i	$-0.659412\pi$
$61$		−	13.7022i		−	1.75439i	0.480133	−	0.877196i	$-0.340588\pi$
$62$	−3.58795	+	0.685255i	−0.455670	+	0.0870275i
$63$	−2.42962			−0.306103
$64$	−3.39669	+	7.24310i	−0.424586	+	0.905387i
$65$			2.93504i			0.364047i
$66$	0.178692	−	0.0341280i	0.0219955	−	0.00420087i
$67$	1.42460			0.174042			0.0870211	−	0.996206i	$-0.472265\pi$
$67$	1.42460			0.174042			0.0870211	+	0.996206i	$0.472265\pi$
$68$	−3.42739	−	8.64549i	−0.415632	−	1.04842i
$69$	−0.158658	−	0.247014i	−0.0191002	−	0.0297370i
$70$	−1.12641	+	0.215130i	−0.134631	+	0.0257129i
$71$			2.26145i			0.268384i	0.990955	+	0.134192i	$0.0428439\pi$
$71$			2.26145i			0.268384i	−0.990955	+	0.134192i	$0.957156\pi$
$72$	4.54568	+	7.15242i	0.535713	+	0.842920i
$73$	−4.13040			−0.483426			−0.241713	−	0.970348i	$-0.577709\pi$
$73$	−4.13040			−0.483426			−0.241713	+	0.970348i	$0.577709\pi$
$74$	4.15870	−	0.794262i	0.483440	−	0.0923311i
$75$			0.0612154i			0.00706854i
$76$	−11.5415	+	4.57547i	−1.32390	+	0.524842i
$77$	1.70400			0.194188
$78$	−0.249580	+	0.0476668i	−0.0282594	+	0.00539720i
$79$	14.9553			1.68261			0.841304	−	0.540562i	$-0.181788\pi$
$79$	14.9553			1.68261			0.841304	+	0.540562i	$0.181788\pi$
$80$	2.74075	+	2.91347i	0.306425	+	0.325736i
$81$	8.96629			0.996254
$82$	−2.18061	−	11.4175i	−0.240808	−	1.26086i
$83$	−8.73564			−0.958861			−0.479431	−	0.877580i	$-0.659157\pi$
$83$	−8.73564			−0.958861			−0.479431	+	0.877580i	$0.659157\pi$
$84$	−0.0365870	−	0.0922896i	−0.00399197	−	0.0100696i
$85$	−4.65004			−0.504368
$86$	2.69601	+	14.1162i	0.290719	+	1.52218i
$87$		−	0.321015i		−	0.0344164i
$88$	−3.18808	−	5.01630i	−0.339850	−	0.534739i
$89$		−	5.82961i		−	0.617938i	−0.951072	−	0.308969i	$-0.900016\pi$
$89$		−	5.82961i		−	0.617938i	0.951072	−	0.308969i	$-0.0999839\pi$
$90$	4.16211	−	0.794913i	0.438725	−	0.0837912i
$91$	−2.37998			−0.249490
$92$	−5.59198	+	7.79293i	−0.583004	+	0.812469i
$93$	−0.158114			−0.0163957
$94$	−2.63161	+	0.502606i	−0.271430	+	0.0518399i
$95$			6.20768i			0.636895i
$96$	−0.203234	+	0.280375i	−0.0207425	+	0.0286157i
$97$		−	2.73446i		−	0.277643i	−0.990317	−	0.138821i	$-0.955669\pi$
$97$		−	2.73446i		−	0.277643i	0.990317	−	0.138821i	$-0.0443314\pi$
$98$	1.68267	+	8.81035i	0.169975	+	0.889980i
$99$	−6.29633			−0.632805
$100$	1.85923	−	0.737066i	0.185923	−	0.0737066i
$101$	−1.66981			−0.166152			−0.0830761	−	0.996543i	$-0.526474\pi$
$101$	−1.66981			−0.166152			−0.0830761	+	0.996543i	$0.526474\pi$
$102$	−0.0755194	−	0.395414i	−0.00747753	−	0.0391519i
$103$	3.01723			0.297297			0.148648	−	0.988890i	$-0.452508\pi$
$103$	3.01723			0.297297			0.148648	+	0.988890i	$0.452508\pi$
$104$	4.45281	+	7.00630i	0.436634	+	0.687024i
$105$	−0.0496387			−0.00484424
$106$	11.2808	−	2.15449i	1.09569	−	0.209263i
$107$	−12.4870			−1.20716			−0.603580	−	0.797302i	$-0.706260\pi$
$107$	−12.4870			−1.20716			−0.603580	+	0.797302i	$0.706260\pi$
$108$	0.270550	+	0.682454i	0.0260336	+	0.0656692i
$109$			11.3533i			1.08745i	0.839263	+	0.543726i	$0.182987\pi$
$109$			11.3533i			1.08745i	−0.839263	+	0.543726i	$0.817013\pi$
$110$	−2.91907	+	0.557507i	−0.278322	+	0.0531562i
$111$	0.183267			0.0173949
$112$	−2.36249	+	2.22243i	−0.223234	+	0.210000i
$113$			2.38506i			0.224367i	0.993687	+	0.112184i	$0.0357845\pi$
$113$			2.38506i			0.224367i	−0.993687	+	0.112184i	$0.964216\pi$
$114$	−0.527868	+	0.100816i	−0.0494394	+	0.00944232i
$115$	2.59180	+	4.03517i	0.241686	+	0.376281i
$116$	−9.74983	+	3.86519i	−0.905249	+	0.358874i
$117$	8.79413			0.813018
$118$	18.1980	−	3.47560i	1.67526	−	0.319955i
$119$		−	3.77065i		−	0.345655i
$120$	0.0928711	+	0.146129i	0.00847793	+	0.0133396i
$121$	−6.58411			−0.598556
$122$	−19.0338	+	3.63523i	−1.72324	+	0.329119i
$123$		−	0.503150i		−	0.0453675i
$124$	1.90378	+	4.80224i	0.170965	+	0.431254i
$125$		−	1.00000i		−	0.0894427i
$126$	0.644583	+	3.37500i	0.0574240	+	0.300668i
$127$			6.12439i			0.543452i	0.962375	+	0.271726i	$0.0875945\pi$
$127$			6.12439i			0.543452i	−0.962375	+	0.271726i	$0.912406\pi$
$128$	10.9626	+	2.79675i	0.968964	+	0.247200i
$129$			0.622073i			0.0547705i
$130$	4.07709	−	0.778674i	0.357584	−	0.0682942i
$131$			15.4796i			1.35245i	0.736693	+	0.676227i	$0.236386\pi$
$131$			15.4796i			1.35245i	−0.736693	+	0.676227i	$0.763614\pi$
$132$	−0.0948148	−	0.239168i	−0.00825257	−	0.0208169i
$133$	−5.03372			−0.436479
$134$	−0.377949	−	1.97892i	−0.0326498	−	0.170952i
$135$	0.367063			0.0315917
$136$	−11.1002	+	7.05467i	−0.951835	+	0.604933i
$137$		−	17.6295i		−	1.50619i	−0.657914	−	0.753093i	$-0.728561\pi$
$137$		−	17.6295i		−	1.50619i	0.657914	−	0.753093i	$-0.271439\pi$
$138$	−0.301037	+	0.285926i	−0.0256259	+	0.0243396i
$139$			2.39357i			0.203020i	0.994835	+	0.101510i	$0.0323674\pi$
$139$			2.39357i			0.203020i	−0.994835	+	0.101510i	$0.967633\pi$
$140$	0.597676	+	1.50762i	0.0505128	+	0.127417i
$141$	−0.115970			−0.00976647
$142$	3.14139	−	0.599967i	0.263619	−	0.0503481i
$143$	−6.16770			−0.515769
$144$	8.72948	−	8.21198i	0.727457	−	0.684332i
$145$			5.24402i			0.435492i
$146$	1.09580	+	5.73756i	0.0906894	+	0.474843i
$147$			0.388256i			0.0320228i
$148$	−2.20663	−	5.56616i	−0.181384	−	0.457536i
$149$			0.398304i			0.0326303i	0.999867	+	0.0163152i	$0.00519351\pi$
$149$			0.398304i			0.0326303i	−0.999867	+	0.0163152i	$0.994806\pi$
$150$	0.0850346	−	0.0162406i	0.00694305	−	0.00132604i
$151$		−	18.3711i		−	1.49502i	−0.664249	−	0.747511i	$-0.731249\pi$
$151$		−	18.3711i		−	1.49502i	0.664249	−	0.747511i	$-0.268751\pi$
$152$	9.41780	+	14.8185i	0.763884	+	1.20194i
$153$			13.9327i			1.12639i
$154$	−0.452074	−	2.36703i	−0.0364292	−	0.190741i
$155$	2.58292			0.207465
$156$	0.132429	+	0.334047i	0.0106028	+	0.0267452i
$157$		−	18.5760i		−	1.48252i	−0.671216	−	0.741261i	$-0.734228\pi$
$157$		−	18.5760i		−	1.48252i	0.671216	−	0.741261i	$-0.265772\pi$
$158$	−3.96769	−	20.7746i	−0.315652	−	1.65274i
$159$	0.497124			0.0394245
$160$	3.31999	−	4.58014i	0.262468	−	0.362092i
$161$	−3.27206	+	2.10165i	−0.257874	+	0.165633i
$162$	−2.37878	−	12.4551i	−0.186894	−	0.978567i
$163$		−	13.2878i		−	1.04078i	−0.853928	−	0.520392i	$-0.825786\pi$
$163$		−	13.2878i		−	1.04078i	0.853928	−	0.520392i	$-0.174214\pi$
$164$	−15.2816	+	6.05820i	−1.19330	+	0.473066i
$165$	−0.128638			−0.0100145
$166$	2.31759	+	12.1347i	0.179880	+	0.941838i
$167$			4.05918i			0.314109i	0.987590	+	0.157054i	$0.0501998\pi$
$167$			4.05918i			0.314109i	−0.987590	+	0.157054i	$0.949800\pi$
$168$	−0.118493	+	0.0753078i	−0.00914197	+	0.00581012i
$169$	−4.38552			−0.337348
$170$	1.23367	+	6.45940i	0.0946179	+	0.495413i
$171$	18.5998			1.42236
$172$	18.8936	−	7.49010i	1.44062	−	0.571115i
$173$	−18.4562			−1.40320			−0.701600	−	0.712571i	$-0.747531\pi$
$173$	−18.4562			−1.40320			−0.701600	+	0.712571i	$0.747531\pi$
$174$	−0.445923	+	0.0851659i	−0.0338053	+	0.00645641i
$175$	0.810885			0.0612972
$176$	−6.12236	+	5.75942i	−0.461491	+	0.434132i
$177$	0.801954			0.0602785
$178$	−8.09795	+	1.54661i	−0.606967	+	0.115923i
$179$			8.67585i			0.648464i	0.945978	+	0.324232i	$0.105106\pi$
$179$			8.67585i			0.648464i	−0.945978	+	0.324232i	$0.894894\pi$
$180$	−2.20844	−	5.57072i	−0.164607	−	0.415217i
$181$		−	21.9722i		−	1.63318i	−0.577218	−	0.816590i	$-0.695862\pi$
$181$		−	21.9722i		−	1.63318i	0.577218	−	0.816590i	$-0.304138\pi$
$182$	0.631415	+	3.30605i	0.0468036	+	0.245061i
$183$	−0.838787			−0.0620049
$184$	12.3088	+	5.70036i	0.907415	+	0.420236i
$185$	−2.99380			−0.220109
$186$	0.0419481	+	0.219638i	0.00307579	+	0.0161046i
$187$		−	9.77160i		−	0.714570i
$188$	1.39635	+	3.52225i	0.101839	+	0.256886i
$189$			0.297646i			0.0216506i
$190$	8.62312	−	1.64691i	0.625587	−	0.119480i
$191$	−12.6841			−0.917792			−0.458896	−	0.888490i	$-0.651755\pi$
$191$	−12.6841			−0.917792			−0.458896	+	0.888490i	$0.651755\pi$
$192$	0.443389	+	0.207930i	0.0319989	+	0.0150060i
$193$	−15.3963			−1.10825			−0.554126	−	0.832433i	$-0.686947\pi$
$193$	−15.3963			−1.10825			−0.554126	+	0.832433i	$0.686947\pi$
$194$	−3.79846	+	0.725460i	−0.272713	+	0.0520850i
$195$	0.179670			0.0128664
$196$	11.7921	−	4.67482i	0.842293	−	0.333915i
$197$	−9.62990			−0.686102			−0.343051	−	0.939317i	$-0.611460\pi$
$197$	−9.62990			−0.686102			−0.343051	+	0.939317i	$0.611460\pi$
$198$	1.67043	+	8.74627i	0.118712	+	0.621570i
$199$	2.04990			0.145313			0.0726567	−	0.997357i	$-0.476852\pi$
$199$	2.04990			0.145313			0.0726567	+	0.997357i	$0.476852\pi$
$200$	−1.51712	−	2.38712i	−0.107277	−	0.168795i
$201$		−	0.0872072i		−	0.00615112i
$202$	0.443004	+	2.31954i	0.0311697	+	0.163202i
$203$	−4.25230			−0.298453
$204$	−0.529237	+	0.209809i	−0.0370540	+	0.0146896i
$205$			8.21934i			0.574064i
$206$	−0.800479	−	4.19125i	−0.0557720	−	0.292019i
$207$	12.0904	−	7.76568i	0.840340	−	0.539752i
$208$	8.55115	−	8.04422i	0.592916	−	0.557766i
$209$	−13.0448			−0.902330
$210$	0.0131693	+	0.0689533i	0.000908765	+	0.00475823i
$211$			4.14576i			0.285406i	0.989766	+	0.142703i	$0.0455793\pi$
$211$			4.14576i			0.285406i	−0.989766	+	0.142703i	$0.954421\pi$
$212$	−5.98564	−	15.0986i	−0.411095	−	1.03698i
$213$	0.138435			0.00948543
$214$	3.31282	+	17.3457i	0.226460	+	1.18573i
$215$		−	10.1620i		−	0.693046i
$216$	0.876223	−	0.556879i	0.0596195	−	0.0378908i
$217$			2.09445i			0.142181i
$218$	15.7710	−	3.01207i	1.06815	−	0.204003i
$219$			0.252844i			0.0170856i
$220$	1.54887	+	3.90699i	0.104425	+	0.263409i
$221$			13.6481i			0.918068i
$222$	−0.0486211	−	0.254577i	−0.00326323	−	0.0170861i
$223$		−	15.8065i		−	1.05848i	−0.848472	−	0.529240i	$-0.822477\pi$
$223$		−	15.8065i		−	1.05848i	0.848472	−	0.529240i	$-0.177523\pi$
$224$	3.71397	+	2.69213i	0.248150	+	0.179875i
$225$	−2.99625			−0.199750
$226$	3.31310	−	0.632761i	0.220384	−	0.0420907i
$227$	10.1465			0.673449			0.336725	−	0.941603i	$-0.390681\pi$
$227$	10.1465			0.673449			0.336725	+	0.941603i	$0.390681\pi$
$228$	0.280089	+	0.706517i	0.0185494	+	0.0467903i
$229$		−	12.6776i		−	0.837757i	−0.908042	−	0.418878i	$-0.862423\pi$
$229$		−	12.6776i		−	0.837757i	0.908042	−	0.418878i	$-0.137577\pi$
$230$	4.91766	−	4.67082i	0.324261	−	0.307985i
$231$		−	0.104311i		−	0.00686314i
$232$	7.95581	+	12.5181i	0.522324	+	0.821854i
$233$	13.5503			0.887710			0.443855	−	0.896099i	$-0.353611\pi$
$233$	13.5503			0.887710			0.443855	+	0.896099i	$0.353611\pi$
$234$	−2.33310	−	12.2160i	−0.152520	−	0.798583i
$235$	1.89447			0.123581
$236$	−9.65595	−	24.3569i	−0.628549	−	1.58550i
$237$		−	0.915497i		−	0.0594679i
$238$	−5.23783	+	1.00036i	−0.339518	+	0.0648438i
$239$		−	10.8030i		−	0.698785i	−0.936976	−	0.349392i	$-0.886388\pi$
$239$		−	10.8030i		−	0.698785i	0.936976	−	0.349392i	$-0.113612\pi$
$240$	0.178349	−	0.167776i	0.0115124	−	0.0108299i
$241$		−	23.5923i		−	1.51971i	−0.650090	−	0.759857i	$-0.725269\pi$
$241$		−	23.5923i		−	1.51971i	0.650090	−	0.759857i	$-0.274731\pi$
$242$	1.74678	+	9.14603i	0.112287	+	0.587929i
$243$		−	1.65006i		−	0.105852i
$244$	10.0995	+	25.4756i	0.646551	+	1.63091i
$245$		−	6.34247i		−	0.405205i
$246$	−0.698929	+	0.133487i	−0.0445621	+	0.00851082i
$247$	18.2198			1.15930
$248$	6.16574	−	3.91860i	0.391525	−	0.248831i
$249$			0.534756i			0.0338888i
$250$	−1.38911	+	0.265302i	−0.0878548	+	0.0167792i
$251$	−3.93647			−0.248468			−0.124234	−	0.992253i	$-0.539647\pi$
$251$	−3.93647			−0.248468			−0.124234	+	0.992253i	$0.539647\pi$
$252$	4.51722	−	1.79079i	0.284558	−	0.112809i
$253$	−8.47951	+	5.44641i	−0.533102	+	0.342413i
$254$	8.50743	−	1.62482i	0.533804	−	0.101950i
$255$			0.284654i			0.0178257i
$256$	0.976582	−	15.9702i	0.0610364	−	0.998136i
$257$	9.47781			0.591209			0.295605	−	0.955310i	$-0.404479\pi$
$257$	9.47781			0.591209			0.295605	+	0.955310i	$0.404479\pi$
$258$	0.864126	−	0.165038i	0.0537981	−	0.0102748i
$259$		−	2.42763i		−	0.150845i
$260$	−2.16332	−	5.45692i	−0.134163	−	0.338424i
$261$	15.7124			0.972573
$262$	21.5027	−	4.10676i	1.32844	−	0.253717i
$263$	24.4123			1.50532			0.752662	−	0.658407i	$-0.228769\pi$
$263$	24.4123			1.50532			0.752662	+	0.658407i	$0.228769\pi$
$264$	−0.307075	+	0.195160i	−0.0188991	+	0.0120112i
$265$	−8.12090			−0.498863
$266$	1.33546	+	6.99236i	0.0818821	+	0.428729i
$267$	−0.356862			−0.0218396
$268$	−2.64865	+	1.05002i	−0.161792	+	0.0641403i
$269$	−2.11000			−0.128649			−0.0643245	−	0.997929i	$-0.520489\pi$
$269$	−2.11000			−0.128649			−0.0643245	+	0.997929i	$0.520489\pi$
$270$	−0.0973827	−	0.509889i	−0.00592652	−	0.0310309i
$271$		−	25.7964i		−	1.56702i	−0.621379	−	0.783510i	$-0.713427\pi$
$271$		−	25.7964i		−	1.56702i	0.621379	−	0.783510i	$-0.286573\pi$
$272$	12.7446	+	13.5477i	0.772755	+	0.821452i
$273$			0.145692i			0.00881766i
$274$	−24.4892	+	4.67714i	−1.47944	+	0.282556i
$275$	2.10140			0.126719
$276$	0.477047	+	0.342315i	0.0287149	+	0.0206049i
$277$	−6.05641			−0.363894			−0.181947	−	0.983308i	$-0.558240\pi$
$277$	−6.05641			−0.363894			−0.181947	+	0.983308i	$0.558240\pi$
$278$	3.32492	−	0.635020i	0.199416	−	0.0380860i
$279$		−	7.73908i		−	0.463327i
$280$	1.93568	−	1.23021i	0.115679	−	0.0735192i
$281$		−	27.0312i		−	1.61255i	−0.591543	−	0.806274i	$-0.701481\pi$
$281$		−	27.0312i		−	1.61255i	0.591543	−	0.806274i	$-0.298519\pi$
$282$	0.0307672	+	0.161095i	0.00183216	+	0.00959308i
$283$	−21.0525			−1.25144			−0.625720	−	0.780048i	$-0.715195\pi$
$283$	−21.0525			−1.25144			−0.625720	+	0.780048i	$0.715195\pi$
$284$	−1.66684	−	4.20455i	−0.0989085	−	0.249494i
$285$	0.380006			0.0225096
$286$	1.63631	+	8.56759i	0.0967568	+	0.506612i
$287$	−6.66494			−0.393419
$288$	−13.7233	−	9.94752i	−0.808651	−	0.586163i
$289$	−4.62287			−0.271934
$290$	7.28450	−	1.39125i	0.427760	−	0.0816970i
$291$	−0.167391			−0.00981265
$292$	7.67935	−	3.04437i	0.449400	−	0.178159i
$293$			19.4086i			1.13386i	0.823766	+	0.566931i	$0.191869\pi$
$293$			19.4086i			1.13386i	−0.823766	+	0.566931i	$0.808131\pi$
$294$	0.539329	−	0.103005i	0.0314543	−	0.00600739i
$295$	−13.1005			−0.762742
$296$	−7.14656	+	4.54196i	−0.415385	+	0.263996i
$297$			0.771347i			0.0447581i
$298$	0.553286	−	0.105671i	0.0320510	−	0.00612136i
$299$	11.8434	−	7.60704i	0.684921	−	0.439926i
$300$	−0.0451198	−	0.113813i	−0.00260499	−	0.00657102i
$301$	8.24025			0.474960
$302$	−25.5195	+	4.87391i	−1.46848	+	0.280462i
$303$			0.102218i			0.00587227i
$304$	18.0859	−	17.0137i	1.03730	−	0.975803i
$305$	13.7022			0.784588
$306$	19.3540	−	3.69638i	1.10639	−	0.211308i
$307$			24.0934i			1.37508i	0.726144	+	0.687542i	$0.241310\pi$
$307$			24.0934i			1.37508i	−0.726144	+	0.687542i	$0.758690\pi$
$308$	−3.16812	+	1.25596i	−0.180520	+	0.0715648i
$309$		−	0.184701i		−	0.0105073i
$310$	−0.685255	−	3.58795i	−0.0389199	−	0.203782i
$311$			15.5862i			0.883811i	0.897062	+	0.441906i	$0.145697\pi$
$311$			15.5862i			0.883811i	−0.897062	+	0.441906i	$0.854303\pi$
$312$	0.428893	−	0.272581i	0.0242813	−	0.0154318i
$313$			26.8531i			1.51783i	0.651191	+	0.758914i	$0.274270\pi$
$313$			26.8531i			1.51783i	−0.651191	+	0.758914i	$0.725730\pi$
$314$	−25.8040	+	4.92825i	−1.45620	+	0.278117i
$315$		−	2.42962i		−	0.136893i
$316$	−27.8054	+	11.0231i	−1.56418	+	0.620097i
$317$	9.87979			0.554905			0.277452	−	0.960739i	$-0.410510\pi$
$317$	9.87979			0.554905			0.277452	+	0.960739i	$0.410510\pi$
$318$	−0.131888	−	0.690557i	−0.00739592	−	0.0387245i
$319$	−11.0198			−0.616990
$320$	−7.24310	−	3.39669i	−0.404902	−	0.189881i
$321$			0.764394i			0.0426643i
$322$	3.78750	+	3.98766i	0.211069	+	0.222224i
$323$			28.8660i			1.60615i
$324$	−16.6704	+	6.60875i	−0.926133	+	0.367153i
$325$	−2.93504			−0.162807
$326$	−18.4582	+	3.52530i	−1.02231	+	0.195248i
$327$	0.694999			0.0384335
$328$	12.4697	+	19.6206i	0.688526	+	1.08336i
$329$			1.53619i			0.0846931i
$330$	0.0341280	+	0.178692i	0.00187868	+	0.00983667i
$331$			16.4661i			0.905061i	0.891749	+	0.452531i	$0.149479\pi$
$331$			16.4661i			0.905061i	−0.891749	+	0.452531i	$0.850521\pi$
$332$	16.2416	−	6.43875i	0.891371	−	0.353372i
$333$			8.97018i			0.491563i
$334$	5.63863	−	1.07691i	0.308532	−	0.0589259i
$335$			1.42460i			0.0778340i
$336$	0.136047	+	0.144621i	0.00742198	+	0.00788970i
$337$			6.50726i			0.354473i	0.984168	+	0.177237i	$0.0567158\pi$
$337$			6.50726i			0.354473i	−0.984168	+	0.177237i	$0.943284\pi$
$338$	1.16349	+	6.09195i	0.0632855	+	0.331359i
$339$	0.146002			0.00792975
$340$	8.64549	−	3.42739i	0.468868	−	0.185876i
$341$			5.42775i			0.293929i
$342$	−4.93457	−	25.8371i	−0.266831	−	1.39711i
$343$	10.8192			0.584182
$344$	−15.4170	−	24.2580i	−0.831231	−	1.30791i
$345$	0.247014	−	0.158658i	0.0132988	−	0.00854185i
$346$	4.89648	+	25.6376i	0.263236	+	1.37829i
$347$			3.84426i			0.206371i	0.994662	+	0.103185i	$0.0329035\pi$
$347$			3.84426i			0.206371i	−0.994662	+	0.103185i	$0.967097\pi$
$348$	0.236609	+	0.596840i	0.0126836	+	0.0319940i
$349$	7.73983			0.414304			0.207152	−	0.978309i	$-0.433581\pi$
$349$	7.73983			0.414304			0.207152	+	0.978309i	$0.433581\pi$
$350$	−0.215130	−	1.12641i	−0.0114992	−	0.0602089i
$351$		−	1.07735i		−	0.0575044i
$352$	9.62472	+	6.97663i	0.512999	+	0.371855i
$353$	−21.2558			−1.13133			−0.565667	−	0.824634i	$-0.691381\pi$
$353$	−21.2558			−1.13133			−0.565667	+	0.824634i	$0.691381\pi$
$354$	−0.212760	−	1.11400i	−0.0113081	−	0.0592084i
$355$	−2.26145			−0.120025
$356$	4.29681	+	10.8386i	0.227730	+	0.574444i
$357$	−0.230822			−0.0122164
$358$	12.0517	−	2.30172i	0.636951	−	0.121650i
$359$	−20.5153			−1.08275			−0.541377	−	0.840780i	$-0.682097\pi$
$359$	−20.5153			−1.08275			−0.541377	+	0.840780i	$0.682097\pi$
$360$	−7.15242	+	4.54568i	−0.376965	+	0.239578i
$361$	19.5353			1.02817
$362$	−30.5217	+	5.82927i	−1.60418	+	0.306380i
$363$			0.403049i			0.0211546i
$364$	4.42493	−	1.75420i	0.231930	−	0.0919453i
$365$		−	4.13040i		−	0.216195i
$366$	0.222532	+	1.16516i	0.0116319	+	0.0609041i
$367$	11.4965			0.600113			0.300057	−	0.953921i	$-0.402994\pi$
$367$	11.4965			0.600113			0.300057	+	0.953921i	$0.402994\pi$
$368$	4.65286	−	18.6105i	0.242547	−	0.970140i
$369$	24.6272			1.28204
$370$	0.794262	+	4.15870i	0.0412917	+	0.216201i
$371$		−	6.58511i		−	0.341882i
$372$	0.293971	−	0.116541i	0.0152417	−	0.00604236i
$373$		−	16.8099i		−	0.870386i	−0.900337	−	0.435193i	$-0.856680\pi$
$373$		−	16.8099i		−	0.870386i	0.900337	−	0.435193i	$-0.143320\pi$
$374$	−13.5738	+	2.59243i	−0.701884	+	0.134051i
$375$	−0.0612154			−0.00316115
$376$	4.52232	−	2.87413i	0.233221	−	0.148222i
$377$	15.3914			0.792698
$378$	0.413462	−	0.0789662i	0.0212662	−	0.00406158i
$379$	4.04643			0.207851			0.103926	−	0.994585i	$-0.466860\pi$
$379$	4.04643			0.207851			0.103926	+	0.994585i	$0.466860\pi$
$380$	−4.57547	−	11.5415i	−0.234717	−	0.592067i
$381$	0.374907			0.0192071
$382$	3.36513	+	17.6196i	0.172175	+	0.901498i
$383$	−11.0961			−0.566986			−0.283493	−	0.958974i	$-0.591493\pi$
$383$	−11.0961			−0.566986			−0.283493	+	0.958974i	$0.591493\pi$
$384$	0.171204	−	0.671079i	0.00873672	−	0.0342458i
$385$			1.70400i			0.0868437i
$386$	4.08468	+	21.3871i	0.207905	+	1.08858i
$387$	−30.4481			−1.54776
$388$	2.01548	+	5.08399i	0.102321	+	0.258101i
$389$			18.0429i			0.914809i	0.889259	+	0.457405i	$0.151221\pi$
$389$			18.0429i			0.914809i	−0.889259	+	0.457405i	$0.848779\pi$
$390$	−0.0476668	−	0.249580i	−0.00241370	−	0.0126380i
$391$	12.0520	+	18.7637i	0.609494	+	0.948921i
$392$	−9.62228	−	15.1402i	−0.485999	−	0.764697i
$393$	0.947587			0.0477994
$394$	2.55483	+	13.3769i	0.128711	+	0.673921i
$395$			14.9553i			0.752485i
$396$	11.7063	−	4.64081i	0.588265	−	0.233210i
$397$	−26.5667			−1.33334			−0.666672	−	0.745351i	$-0.732282\pi$
$397$	−26.5667			−1.33334			−0.666672	+	0.745351i	$0.732282\pi$
$398$	−0.543843	−	2.84753i	−0.0272604	−	0.142734i
$399$			0.308141i			0.0154263i
$400$	−2.91347	+	2.74075i	−0.145673	+	0.137037i
$401$			0.934463i			0.0466649i	0.999728	+	0.0233324i	$0.00742762\pi$
$401$			0.934463i			0.0466649i	−0.999728	+	0.0233324i	$0.992572\pi$
$402$	−0.121140	+	0.0231363i	−0.00604192	+	0.00115393i
$403$		−	7.58098i		−	0.377636i
$404$	3.10456	−	1.23076i	0.154458	−	0.0612326i
$405$			8.96629i			0.445538i
$406$	1.12814	+	5.90689i	0.0559889	+	0.293154i
$407$		−	6.29118i		−	0.311842i
$408$	0.431854	+	0.679503i	0.0213800	+	0.0336404i
$409$	−15.7550			−0.779037			−0.389518	−	0.921019i	$-0.627359\pi$
$409$	−15.7550			−0.779037			−0.389518	+	0.921019i	$0.627359\pi$
$410$	11.4175	−	2.18061i	0.563872	−	0.107693i
$411$	−1.07919			−0.0532327
$412$	−5.60973	+	2.22390i	−0.276371	+	0.109564i
$413$		−	10.6230i		−	0.522725i
$414$	−13.9950	−	14.7346i	−0.687815	−	0.724164i
$415$		−	8.73564i		−	0.428816i
$416$	−13.4429	−	9.74430i	−0.659093	−	0.477754i
$417$	0.146523			0.00717528
$418$	3.46082	+	18.1206i	0.169274	+	0.886310i
$419$	−24.9291			−1.21787			−0.608933	−	0.793222i	$-0.708402\pi$
$419$	−24.9291			−1.21787			−0.608933	+	0.793222i	$0.708402\pi$
$420$	0.0922896	−	0.0365870i	0.00450327	−	0.00178526i
$421$			16.2869i			0.793775i	0.917867	+	0.396888i	$0.129910\pi$
$421$			16.2869i			0.793775i	−0.917867	+	0.396888i	$0.870090\pi$
$422$	5.75889	−	1.09988i	0.280338	−	0.0535413i
$423$		−	5.67630i		−	0.275991i
$424$	−19.3856	+	12.3204i	−0.941446	+	0.598330i
$425$		−	4.65004i		−	0.225560i
$426$	−0.0367272	−	0.192301i	−0.00177944	−	0.00931703i
$427$			11.1109i			0.537696i
$428$	23.2161	−	9.20372i	1.12219	−	0.444879i
$429$			0.377558i			0.0182287i
$430$	−14.1162	+	2.69601i	−0.680741	+	0.130013i
$431$	24.5994			1.18491			0.592456	−	0.805603i	$-0.298158\pi$
$431$	24.5994			1.18491			0.592456	+	0.805603i	$0.298158\pi$
$432$	−1.00603	−	1.06943i	−0.0484025	−	0.0514528i
$433$		−	2.41636i		−	0.116123i	−0.998313	−	0.0580615i	$-0.981508\pi$
$433$		−	2.41636i		−	0.116123i	0.998313	−	0.0580615i	$-0.0184920\pi$
$434$	2.90942	−	0.555663i	0.139656	−	0.0266727i
$435$	0.321015			0.0153915
$436$	−8.36816	−	21.1085i	−0.400762	−	1.01091i
$437$	25.0490	−	16.0891i	1.19826	−	0.769644i
$438$	0.351227	−	0.0670800i	0.0167823	−	0.00320521i
$439$		−	20.2396i		−	0.965984i	−0.875625	−	0.482992i	$-0.839550\pi$
$439$		−	20.2396i		−	0.965984i	0.875625	−	0.482992i	$-0.160450\pi$
$440$	5.01630	−	3.18808i	0.239143	−	0.151986i
$441$	−19.0036			−0.904935
$442$	18.9586	−	3.62087i	0.901769	−	0.172227i
$443$			16.4810i			0.783035i	0.920171	+	0.391517i	$0.128050\pi$
$443$			16.4810i			0.783035i	−0.920171	+	0.391517i	$0.871950\pi$
$444$	−0.340735	+	0.135080i	−0.0161705	+	0.00641059i
$445$	5.82961			0.276350
$446$	−21.9569	+	4.19350i	−1.03969	+	0.198568i
$447$	0.0243823			0.00115324
$448$	2.75433	−	5.87332i	0.130130	−	0.277488i
$449$	28.5354			1.34667			0.673335	−	0.739337i	$-0.264861\pi$
$449$	28.5354			1.34667			0.673335	+	0.739337i	$0.264861\pi$
$450$	0.794913	+	4.16211i	0.0374726	+	0.196204i
$451$	−17.2721			−0.813313
$452$	−1.75794	−	4.43437i	−0.0826868	−	0.208575i
$453$	−1.12460			−0.0528382
$454$	−2.69190	−	14.0946i	−0.126337	−	0.661493i
$455$		−	2.37998i		−	0.111575i
$456$	0.907119	−	0.576514i	0.0424797	−	0.0269978i
$457$		−	4.16624i		−	0.194888i	−0.995241	−	0.0974442i	$-0.968933\pi$
$457$		−	4.16624i		−	0.194888i	0.995241	−	0.0974442i	$-0.0310667\pi$
$458$	−17.6105	+	3.36339i	−0.822883	+	0.157161i
$459$	1.70686			0.0796693
$460$	−7.79293	−	5.59198i	−0.363347	−	0.260727i
$461$	−15.8725			−0.739255			−0.369628	−	0.929180i	$-0.620515\pi$
$461$	−15.8725			−0.739255			−0.369628	+	0.929180i	$0.620515\pi$
$462$	−0.144899	+	0.0276739i	−0.00674130	+	0.00128751i
$463$			39.4302i			1.83248i	0.400632	+	0.916239i	$0.368791\pi$
$463$			39.4302i			1.83248i	−0.400632	+	0.916239i	$0.631209\pi$
$464$	15.2783	−	14.3725i	0.709276	−	0.667228i
$465$		−	0.158114i		−	0.00733238i
$466$	−3.59493	−	18.8228i	−0.166532	−	0.871949i
$467$	−11.3406			−0.524780			−0.262390	−	0.964962i	$-0.584511\pi$
$467$	−11.3406			−0.524780			−0.262390	+	0.964962i	$0.584511\pi$
$468$	−16.3503	+	6.48186i	−0.755793	+	0.299624i
$469$	−1.15518			−0.0533415
$470$	−0.502606	−	2.63161i	−0.0231835	−	0.121387i
$471$	−1.13713			−0.0523964
$472$	−31.2725	+	19.8751i	−1.43944	+	0.914825i
$473$	21.3545			0.981883
$474$	−1.27172	+	0.242884i	−0.0584122	+	0.0111560i
$475$	−6.20768			−0.284828
$476$	2.77922	+	7.01050i	0.127385	+	0.321326i
$477$			24.3323i			1.11410i
$478$	−15.0064	+	2.86605i	−0.686379	+	0.131090i
$479$	−23.3114			−1.06512			−0.532562	−	0.846391i	$-0.678771\pi$
$479$	−23.3114			−1.06512			−0.532562	+	0.846391i	$0.678771\pi$
$480$	−0.280375	−	0.203234i	−0.0127973	−	0.00927633i
$481$			8.78693i			0.400650i
$482$	−32.7722	+	6.25910i	−1.49273	+	0.285094i
$483$	0.128653	+	0.200300i	0.00585393	+	0.00911398i
$484$	12.2414	−	4.85292i	0.556426	−	0.220587i
$485$	2.73446			0.124166
$486$	−2.29211	+	0.437766i	−0.103972	+	0.0198575i
$487$		−	31.8314i		−	1.44242i	−0.692718	−	0.721209i	$-0.743587\pi$
$487$		−	31.8314i		−	1.44242i	0.692718	−	0.721209i	$-0.256413\pi$
$488$	32.7089	−	20.7879i	1.48066	−	0.941026i
$489$	−0.813420			−0.0367841
$490$	−8.81035	+	1.68267i	−0.398011	+	0.0760153i
$491$		−	27.6085i		−	1.24595i	−0.782241	−	0.622976i	$-0.785923\pi$
$491$		−	27.6085i		−	1.24595i	0.782241	−	0.622976i	$-0.214077\pi$
$492$	0.370855	+	0.935472i	0.0167194	+	0.0421743i
$493$			24.3849i			1.09824i
$494$	−4.83376	−	25.3092i	−0.217481	−	1.13872i
$495$		−	6.29633i		−	0.282999i
$496$	−7.07914	−	7.52525i	−0.317863	−	0.337894i
$497$		−	1.83377i		−	0.0822560i
$498$	0.742832	−	0.141872i	0.0332871	−	0.00635743i
$499$			36.7032i			1.64306i	0.570165	+	0.821530i	$0.306879\pi$
$499$			36.7032i			1.64306i	−0.570165	+	0.821530i	$0.693121\pi$
$500$	0.737066	+	1.85923i	0.0329626	+	0.0831473i
$501$	0.248484			0.0111015
$502$	1.04436	+	5.46818i	0.0466119	+	0.244057i
$503$	43.1029			1.92186			0.960932	−	0.276783i	$-0.0892683\pi$
$503$	43.1029			1.92186			0.960932	+	0.276783i	$0.0892683\pi$
$504$	−3.68602	−	5.79979i	−0.164188	−	0.258343i
$505$		−	1.66981i		−	0.0743056i
$506$	9.81527	+	10.3340i	0.436342	+	0.459402i
$507$			0.268461i			0.0119228i
$508$	−4.51408	−	11.3867i	−0.200280	−	0.505201i
$509$	6.26173			0.277546			0.138773	−	0.990324i	$-0.455684\pi$
$509$	6.26173			0.277546			0.138773	+	0.990324i	$0.455684\pi$
$510$	0.395414	−	0.0755194i	0.0175092	−	0.00334405i
$511$	3.34928			0.148163
$512$	−22.4433	+	2.88035i	−0.991865	+	0.127295i
$513$		−	2.27861i		−	0.100603i
$514$	−2.51448	−	13.1657i	−0.110909	−	0.580713i
$515$			3.01723i			0.132955i
$516$	−0.458509	−	1.15658i	−0.0201847	−	0.0509155i
$517$			3.98103i			0.175086i
$518$	−3.37223	+	0.644056i	−0.148167	+	0.0282982i
$519$			1.12980i			0.0495929i
$520$	−7.00630	+	4.45281i	−0.307247	+	0.195269i
$521$			28.1514i			1.23334i	0.787223	+	0.616668i	$0.211518\pi$
$521$			28.1514i			1.23334i	−0.787223	+	0.616668i	$0.788482\pi$
$522$	−4.16854	−	21.8262i	−0.182452	−	0.955306i
$523$	27.1711			1.18811			0.594054	−	0.804425i	$-0.297526\pi$
$523$	27.1711			1.18811			0.594054	+	0.804425i	$0.297526\pi$
$524$	−11.4095	−	28.7800i	−0.498424	−	1.25726i
$525$		−	0.0496387i		−	0.00216641i
$526$	−6.47663	−	33.9112i	−0.282395	−	1.47860i
$527$	12.0107			0.523194
$528$	0.352565	+	0.374783i	0.0153434	+	0.0163103i
$529$	9.56516	−	20.9167i	0.415877	−	0.909421i
$530$	2.15449	+	11.2808i	0.0935852	+	0.490006i
$531$			39.2525i			1.70341i
$532$	9.35883	−	3.71018i	0.405757	−	0.160857i
$533$	24.1241			1.04493
$534$	0.0946763	+	0.495719i	0.00409704	+	0.0214519i
$535$		−	12.4870i		−	0.539859i
$536$	2.16129	+	3.40068i	0.0933533	+	0.146887i
$537$	0.531096			0.0229185
$538$	0.559788	+	2.93101i	0.0241342	+	0.126365i
$539$	13.3281			0.574080
$540$	−0.682454	+	0.270550i	−0.0293681	+	0.0116426i
$541$	22.7074			0.976269			0.488134	−	0.872769i	$-0.337678\pi$
$541$	22.7074			0.976269			0.488134	+	0.872769i	$0.337678\pi$
$542$	−35.8339	+	6.84385i	−1.53920	+	0.293969i
$543$	−1.34504			−0.0577210
$544$	15.4381	−	21.2978i	0.661902	−	0.913137i
$545$	−11.3533			−0.486324
$546$	0.202381	−	0.0386523i	0.00866111	−	0.00165417i
$547$			35.1637i			1.50349i	0.659454	+	0.751745i	$0.270787\pi$
$547$			35.1637i			1.50349i	−0.659454	+	0.751745i	$0.729213\pi$
$548$	12.9941	+	32.7772i	0.555079	+	1.40017i
$549$		−	41.0553i		−	1.75220i
$550$	−0.557507	−	2.91907i	−0.0237722	−	0.124470i
$551$	32.5532			1.38681
$552$	0.348950	−	0.753486i	0.0148523	−	0.0320705i
$553$	−12.1271			−0.515696
$554$	1.60678	+	8.41299i	0.0682655	+	0.357434i
$555$			0.183267i			0.00777923i
$556$	−1.76422	−	4.45020i	−0.0748196	−	0.188730i
$557$		−	16.2425i		−	0.688219i	−0.938930	−	0.344109i	$-0.888181\pi$
$557$		−	16.2425i		−	0.688219i	0.938930	−	0.344109i	$-0.111819\pi$
$558$	−10.7504	+	2.05320i	−0.455101	+	0.0869188i
$559$	−29.8260			−1.26151
$560$	−2.22243	−	2.36249i	−0.0939150	−	0.0998333i
$561$	−0.598172			−0.0252549
$562$	−37.5492	+	7.17145i	−1.58392	+	0.302509i
$563$	−30.7320			−1.29520			−0.647599	−	0.761981i	$-0.724227\pi$
$563$	−30.7320			−1.29520			−0.647599	+	0.761981i	$0.724227\pi$
$564$	0.215616	−	0.0854779i	0.00907906	−	0.00359927i
$565$	−2.38506			−0.100340
$566$	5.58528	+	29.2441i	0.234767	+	1.22922i
$567$	−7.27063			−0.305338
$568$	−5.39835	+	3.43089i	−0.226510	+	0.143957i
$569$			27.0381i			1.13350i	0.823891	+	0.566748i	$0.191799\pi$
$569$			27.0381i			1.13350i	−0.823891	+	0.566748i	$0.808201\pi$
$570$	−0.100816	−	0.527868i	−0.00422273	−	0.0221100i
$571$	−35.8888			−1.50190			−0.750949	−	0.660360i	$-0.770404\pi$
$571$	−35.8888			−1.50190			−0.750949	+	0.660360i	$0.770404\pi$
$572$	11.4672	−	4.54601i	0.479467	−	0.190078i
$573$			0.776464i			0.0324373i
$574$	1.76823	+	9.25831i	0.0738043	+	0.386434i
$575$	−4.03517	+	2.59180i	−0.168278	+	0.108085i
$576$	−10.1773	+	21.7022i	−0.424056	+	0.904257i
$577$	13.0988			0.545309			0.272654	−	0.962112i	$-0.412098\pi$
$577$	13.0988			0.545309			0.272654	+	0.962112i	$0.412098\pi$
$578$	1.22646	+	6.42166i	0.0510140	+	0.267106i
$579$			0.942492i			0.0391686i
$580$	−3.86519	−	9.74983i	−0.160493	−	0.404840i
$581$	7.08360			0.293877
$582$	0.0444093	+	0.232524i	0.00184082	+	0.00963843i
$583$		−	17.0653i		−	0.706771i
$584$	−6.26631	−	9.85975i	−0.259302	−	0.407999i
$585$			8.79413i			0.363593i
$586$	26.9606	−	5.14914i	1.11373	−	0.212709i
$587$		−	22.9195i		−	0.945990i	−0.881065	−	0.472995i	$-0.843173\pi$
$587$		−	22.9195i		−	0.945990i	0.881065	−	0.472995i	$-0.156827\pi$
$588$	−0.286171	−	0.721858i	−0.0118015	−	0.0297689i
$589$		−	16.0339i		−	0.660667i
$590$	3.47560	+	18.1980i	0.143088	+	0.749201i
$591$			0.589498i			0.0242487i
$592$	8.20526	+	8.72234i	0.337234	+	0.358486i
$593$	−17.0185			−0.698866			−0.349433	−	0.936961i	$-0.613626\pi$
$593$	−17.0185			−0.698866			−0.349433	+	0.936961i	$0.613626\pi$
$594$	1.07148	−	0.204640i	0.0439634	−	0.00839648i
$595$	3.77065			0.154582
$596$	−0.293576	−	0.740538i	−0.0120254	−	0.0303336i
$597$		−	0.125485i		−	0.00513577i
$598$	−13.7091	−	14.4336i	−0.560605	−	0.590232i
$599$		−	47.0562i		−	1.92266i	−0.275391	−	0.961332i	$-0.588807\pi$
$599$		−	47.0562i		−	1.92266i	0.275391	−	0.961332i	$-0.411193\pi$
$600$	−0.146129	+	0.0928711i	−0.00596567	+	0.00379145i
$601$	−17.1272			−0.698633			−0.349316	−	0.937005i	$-0.613586\pi$
$601$	−17.1272			−0.698633			−0.349316	+	0.937005i	$0.613586\pi$
$602$	−2.18616	−	11.4466i	−0.0891012	−	0.466528i
$603$	4.26845			0.173825
$604$	13.5407	+	34.1562i	0.550965	+	1.38979i
$605$		−	6.58411i		−	0.267682i
$606$	0.141992	−	0.0271187i	0.00576802	−	0.00110162i
$607$		−	4.02268i		−	0.163276i	−0.996662	−	0.0816379i	$-0.973985\pi$
$607$		−	4.02268i		−	0.163276i	0.996662	−	0.0816379i	$-0.0260151\pi$
$608$	−28.4321	−	20.6094i	−1.15307	−	0.835822i
$609$			0.260306i			0.0105481i
$610$	−3.63523	−	19.0338i	−0.147186	−	0.770658i
$611$		−	5.56034i		−	0.224947i
$612$	−10.2693	−	25.9041i	−0.415113	−	1.04711i
$613$		−	11.6582i		−	0.470870i	−0.971890	−	0.235435i	$-0.924348\pi$
$613$		−	11.6582i		−	0.470870i	0.971890	−	0.235435i	$-0.0756515\pi$
$614$	33.4683	−	6.39204i	1.35067	−	0.257962i
$615$	0.503150			0.0202890
$616$	2.58517	+	4.06764i	0.104159	+	0.163890i
$617$			20.3418i			0.818928i	0.912326	+	0.409464i	$0.134284\pi$
$617$			20.3418i			0.818928i	−0.912326	+	0.409464i	$0.865716\pi$
$618$	−0.256569	+	0.0490016i	−0.0103207	+	0.00197113i
$619$	27.1446			1.09103			0.545516	−	0.838100i	$-0.316334\pi$
$619$	27.1446			1.09103			0.545516	+	0.838100i	$0.316334\pi$
$620$	−4.80224	+	1.90378i	−0.192863	+	0.0764578i
$621$	−0.951353	−	1.48116i	−0.0381765	−	0.0594369i
$622$	21.6508	−	4.13505i	0.868120	−	0.165800i
$623$			4.72715i			0.189389i
$624$	−0.492430	−	0.523462i	−0.0197130	−	0.0209553i
$625$	1.00000			0.0400000
$626$	37.3018	−	7.12420i	1.49088	−	0.284740i
$627$			0.798544i			0.0318908i
$628$	13.6917	+	34.5370i	0.546359	+	1.37818i
$629$	−13.9213			−0.555078
$630$	−3.37500	+	0.644583i	−0.134463	+	0.0256808i
$631$	−1.23029			−0.0489770			−0.0244885	−	0.999700i	$-0.507796\pi$
$631$	−1.23029			−0.0489770			−0.0244885	+	0.999700i	$0.507796\pi$
$632$	22.6891	+	35.7002i	0.902523	+	1.42008i
$633$	0.253784			0.0100870
$634$	−2.62113	−	13.7241i	−0.104098	−	0.545053i
$635$	−6.12439			−0.243039
$636$	−0.924267	+	0.366413i	−0.0366496	+	0.0145292i
$637$	−18.6154			−0.737569
$638$	2.92358	+	15.3077i	0.115745	+	0.606036i
$639$			6.77587i			0.268049i
$640$	−2.79675	+	10.9626i	−0.110551	+	0.433334i
$641$			24.7595i			0.977943i	0.872300	+	0.488971i	$0.162628\pi$
$641$			24.7595i			0.977943i	−0.872300	+	0.488971i	$0.837372\pi$
$642$	1.06182	−	0.202796i	0.0419069	−	0.00800371i
$643$	24.5967			0.969999			0.485000	−	0.874514i	$-0.338820\pi$
$643$	24.5967			0.969999			0.485000	+	0.874514i	$0.338820\pi$
$644$	4.53445	−	6.31917i	0.178682	−	0.249010i
$645$	−0.622073			−0.0244941
$646$	40.0979	−	7.65821i	1.57763	−	0.301308i
$647$		−	15.0168i		−	0.590372i	−0.955440	−	0.295186i	$-0.904618\pi$
$647$		−	15.0168i		−	0.590372i	0.955440	−	0.295186i	$-0.0953817\pi$
$648$	13.6029	+	21.4036i	0.534374	+	0.840813i
$649$		−	27.5295i		−	1.08063i
$650$	0.778674	+	4.07709i	0.0305421	+	0.159916i
$651$	0.128213			0.00502505
$652$	9.79402	+	24.7051i	0.383563	+	0.967528i
$653$	37.5839			1.47077			0.735385	−	0.677650i	$-0.237001\pi$
$653$	37.5839			1.47077			0.735385	+	0.677650i	$0.237001\pi$
$654$	−0.184385	−	0.965427i	−0.00721002	−	0.0377512i
$655$	−15.4796			−0.604836
$656$	23.9468	−	22.5272i	0.934965	−	0.879538i
$657$	−12.3757			−0.482822
$658$	2.13394	−	0.407556i	0.0831895	−	0.0158882i
$659$	−11.1544			−0.434512			−0.217256	−	0.976115i	$-0.569711\pi$
$659$	−11.1544			−0.434512			−0.217256	+	0.976115i	$0.569711\pi$
$660$	0.239168	−	0.0948148i	0.00930959	−	0.00369066i
$661$		−	10.2362i		−	0.398141i	−0.979985	−	0.199070i	$-0.936208\pi$
$661$		−	10.2362i		−	0.398141i	0.979985	−	0.199070i	$-0.0637922\pi$
$662$	22.8732	−	4.36851i	0.888993	−	0.169787i
$663$	0.835472			0.0324470
$664$	−13.2530	−	20.8530i	−0.514317	−	0.809255i
$665$		−	5.03372i		−	0.195199i
$666$	12.4605	−	2.37981i	0.482836	−	0.0922158i
$667$	21.1605	−	13.5914i	0.819338	−	0.526263i
$668$	−2.99188	−	7.54694i	−0.115759	−	0.292000i
$669$	−0.967600			−0.0374096
$670$	1.97892	−	0.377949i	0.0764522	−	0.0146014i
$671$			28.7939i			1.11158i
$672$	0.164800	−	0.227352i	0.00635728	−	0.00877029i
$673$	30.8981			1.19103			0.595517	−	0.803343i	$-0.296947\pi$
$673$	30.8981			1.19103			0.595517	+	0.803343i	$0.296947\pi$
$674$	9.03927	−	1.72639i	0.348180	−	0.0664981i
$675$			0.367063i			0.0141283i
$676$	8.15369	−	3.23242i	0.313603	−	0.124324i
$677$			9.44975i			0.363184i	0.983374	+	0.181592i	$0.0581249\pi$
$677$			9.44975i			0.363184i	−0.983374	+	0.181592i	$0.941875\pi$
$678$	−0.0387347	−	0.202812i	−0.00148760	−	0.00778897i
$679$			2.21734i			0.0850936i
$680$	−7.05467	−	11.1002i	−0.270534	−	0.425674i
$681$		−	0.621124i		−	0.0238015i
$682$	7.53972	−	1.44000i	0.288711	−	0.0551403i
$683$		−	44.7124i		−	1.71087i	−0.517908	−	0.855436i	$-0.673289\pi$
$683$		−	44.7124i		−	1.71087i	0.517908	−	0.855436i	$-0.326711\pi$
$684$	−34.5813	+	13.7093i	−1.32225	+	0.524187i
$685$	17.6295			0.673587
$686$	−2.87036	−	15.0290i	−0.109591	−	0.573811i
$687$	−0.776061			−0.0296086
$688$	−29.6068	+	27.8516i	−1.12875	+	1.06183i
$689$			23.8352i			0.908048i
$690$	−0.285926	−	0.301037i	−0.0108850	−	0.0114603i
$691$			8.99904i			0.342339i	0.985242	+	0.171170i	$0.0547546\pi$
$691$			8.99904i			0.342339i	−0.985242	+	0.171170i	$0.945245\pi$
$692$	34.3143	−	13.6035i	1.30444	−	0.517126i
$693$	5.10560			0.193946
$694$	5.34008	−	1.01989i	0.202707	−	0.0387146i
$695$	−2.39357			−0.0907933
$696$	0.766300	−	0.487018i	0.0290465	−	0.0184604i
$697$			38.2203i			1.44770i
$698$	−2.05340	−	10.7514i	−0.0777222	−	0.406948i
$699$		−	0.829487i		−	0.0313741i
$700$	−1.50762	+	0.597676i	−0.0569827	+	0.0225900i
$701$			21.2257i			0.801685i	0.916147	+	0.400842i	$0.131283\pi$
$701$			21.2257i			0.801685i	−0.916147	+	0.400842i	$0.868717\pi$
$702$	−1.49655	+	0.285822i	−0.0564835	+	0.0107877i
$703$			18.5846i			0.700930i
$704$	7.13781	−	15.2207i	0.269016	−	0.573650i
$705$		−	0.115970i		−	0.00436770i
$706$	5.63922	+	29.5266i	0.212235	+	1.11125i
$707$	1.35402			0.0509233
$708$	−1.49102	+	0.591093i	−0.0560358	+	0.0222146i
$709$			22.2321i			0.834944i	0.908690	+	0.417472i	$0.137084\pi$
$709$			22.2321i			0.834944i	−0.908690	+	0.417472i	$0.862916\pi$
$710$	0.599967	+	3.14139i	0.0225164	+	0.117894i
$711$	44.8100			1.68051
$712$	13.9160	−	8.84422i	0.521524	−	0.331451i
$713$	−6.69441	−	10.4225i	−0.250708	−	0.390326i
$714$	0.0612376	+	0.320636i	0.00229176	+	0.0119995i
$715$		−	6.16770i		−	0.230659i
$716$	−6.39468	−	16.1304i	−0.238980	−	0.602821i
$717$	−0.661307			−0.0246970
$718$	5.44275	+	28.4979i	0.203122	+	1.06353i
$719$			3.06420i			0.114275i	0.998366	+	0.0571377i	$0.0181974\pi$
$719$			3.06420i			0.114275i	−0.998366	+	0.0571377i	$0.981803\pi$
$720$	8.21198	+	8.72948i	0.306042	+	0.325329i
$721$	−2.44663			−0.0911172
$722$	−5.18276	−	27.1366i	−0.192882	−	1.00992i
$723$	−1.44421			−0.0537108
$724$	16.1950	+	40.8513i	0.601881	+	1.51823i
$725$	−5.24402			−0.194758
$726$	0.559877	−	0.106930i	0.0207790	−	0.00396854i
$727$	−32.1935			−1.19399			−0.596995	−	0.802245i	$-0.703639\pi$
$727$	−32.1935			−1.19399			−0.596995	+	0.802245i	$0.703639\pi$
$728$	−3.61072	−	5.68131i	−0.133822	−	0.210563i
$729$	26.7979			0.992513
$730$	−5.73756	+	1.09580i	−0.212356	+	0.0405575i
$731$		−	47.2539i		−	1.74775i
$732$	1.55950	−	0.618242i	0.0576407	−	0.0228509i
$733$		−	32.2471i		−	1.19107i	−0.803328	−	0.595536i	$-0.796940\pi$
$733$		−	32.2471i		−	1.19107i	0.803328	−	0.595536i	$-0.203060\pi$
$734$	−3.05005	−	15.9699i	−0.112579	−	0.589459i
$735$	−0.388256			−0.0143211
$736$	−27.0864	−	1.52590i	−0.998417	−	0.0562456i
$737$	−2.99365			−0.110273
$738$	−6.53366	−	34.2098i	−0.240507	−	1.25928i
$739$		−	9.69792i		−	0.356744i	−0.983963	−	0.178372i	$-0.942917\pi$
$739$		−	9.69792i		−	0.356744i	0.983963	−	0.178372i	$-0.0570830\pi$
$740$	5.56616	−	2.20663i	0.204616	−	0.0811173i
$741$		−	1.11533i		−	0.0409728i
$742$	−9.14742	+	1.74705i	−0.335812	+	0.0641361i
$743$	11.0808			0.406514			0.203257	−	0.979125i	$-0.434847\pi$
$743$	11.0808			0.406514			0.203257	+	0.979125i	$0.434847\pi$
$744$	−0.239879	−	0.377438i	−0.00879438	−	0.0138376i
$745$	−0.398304			−0.0145927
$746$	−23.3508	+	4.45972i	−0.854933	+	0.163282i
$747$	−26.1742			−0.957664
$748$	7.20232	+	18.1676i	0.263343	+	0.664275i
$749$	10.1255			0.369978
$750$	0.0162406	+	0.0850346i	0.000593022	+	0.00310503i
$751$	−12.5716			−0.458743			−0.229372	−	0.973339i	$-0.573667\pi$
$751$	−12.5716			−0.458743			−0.229372	+	0.973339i	$0.573667\pi$
$752$	−5.19226	−	5.51946i	−0.189342	−	0.201274i
$753$			0.240973i			0.00878153i
$754$	−4.08338	−	21.3803i	−0.148708	−	0.778625i
$755$	18.3711			0.668594
$756$	−0.219385	−	0.553392i	−0.00797894	−	0.0201267i
$757$			53.8727i			1.95804i	0.203772	+	0.979018i	$0.434680\pi$
$757$			53.8727i			1.95804i	−0.203772	+	0.979018i	$0.565320\pi$
$758$	−1.07353	−	5.62092i	−0.0389923	−	0.204161i
$759$	0.333404	+	0.519076i	0.0121018	+	0.0188413i
$760$	−14.8185	+	9.41780i	−0.537523	+	0.341620i
$761$	−19.8277			−0.718754			−0.359377	−	0.933192i	$-0.617011\pi$
$761$	−19.8277			−0.718754			−0.359377	+	0.933192i	$0.617011\pi$
$762$	−0.0994638	−	0.520786i	−0.00360319	−	0.0188661i
$763$		−	9.20626i		−	0.333289i
$764$	23.5827	−	9.34905i	0.853193	−	0.338237i
$765$	−13.9327			−0.503738
$766$	2.94383	+	15.4137i	0.106365	+	0.556919i
$767$			38.4506i			1.38837i
$768$	−0.977620	−	0.0597819i	−0.0352768	−	0.00215719i
$769$		−	24.6347i		−	0.888350i	−0.895940	−	0.444175i	$-0.853497\pi$
$769$		−	24.6347i		−	0.888350i	0.895940	−	0.444175i	$-0.146503\pi$
$770$	2.36703	−	0.452074i	0.0853018	−	0.0162916i
$771$		−	0.580188i		−	0.0208949i
$772$	28.6253	−	11.3481i	1.03025	−	0.408427i
$773$		−	14.1357i		−	0.508428i	−0.967148	−	0.254214i	$-0.918183\pi$
$773$		−	14.1357i		−	0.508428i	0.967148	−	0.254214i	$-0.0818167\pi$
$774$	8.07794	+	42.2956i	0.290356	+	1.52028i
$775$			2.58292i			0.0927812i
$776$	6.52749	−	4.14851i	0.234323	−	0.148923i
$777$	−0.148608			−0.00533129
$778$	25.0634	−	4.78681i	0.898568	−	0.171616i
$779$	51.0231			1.82809
$780$	−0.334047	+	0.132429i	−0.0119608	+	0.00474170i
$781$		−	4.75221i		−	0.170047i
$782$	22.8673	−	21.7195i	0.817734	−	0.776688i
$783$		−	1.92488i		−	0.0687898i
$784$	−18.4786	+	17.3831i	−0.659949	+	0.620825i
$785$	18.5760			0.663004
$786$	−0.251397	−	1.31630i	−0.00896703	−	0.0469508i
$787$	−11.4575			−0.408417			−0.204209	−	0.978927i	$-0.565462\pi$
$787$	−11.4575			−0.408417			−0.204209	+	0.978927i	$0.565462\pi$
$788$	17.9042	−	7.09787i	0.637810	−	0.252851i
$789$		−	1.49441i		−	0.0532023i
$790$	20.7746	−	3.96769i	0.739126	−	0.141164i
$791$		−	1.93401i		−	0.0687654i
$792$	−9.55229	−	15.0301i	−0.339426	−	0.534071i
$793$		−	40.2166i		−	1.42813i
$794$	7.04821	+	36.9040i	0.250132	+	1.30967i
$795$			0.497124i			0.0176312i
$796$	−3.81123	+	1.51091i	−0.135086	+	0.0535528i
$797$		−	13.6750i		−	0.484393i	−0.970227	−	0.242197i	$-0.922132\pi$
$797$		−	13.6750i		−	0.484393i	0.970227	−	0.242197i	$-0.0778679\pi$
$798$	0.428040	−	0.0817505i	0.0151525	−	0.00289394i
$799$	8.80934			0.311652
$800$	4.58014	+	3.31999i	0.161932	+	0.117379i
$801$		−	17.4670i		−	0.617166i
$802$	1.29807	−	0.247915i	0.0458364	−	0.00875420i
$803$	8.67962			0.306297
$804$	0.0642775	+	0.162138i	0.00226689	+	0.00571818i
$805$	−2.10165	−	3.27206i	−0.0740735	−	0.115325i
$806$	−10.5308	+	2.01125i	−0.370931	+	0.0708434i
$807$			0.129164i			0.00454680i
$808$	−2.53330	−	3.98604i	−0.0891213	−	0.140228i
$809$	−22.1172			−0.777598			−0.388799	−	0.921323i	$-0.627110\pi$
$809$	−22.1172			−0.777598			−0.388799	+	0.921323i	$0.627110\pi$
$810$	12.4551	−	2.37878i	0.437628	−	0.0835817i
$811$		−	52.1933i		−	1.83276i	−0.400314	−	0.916378i	$-0.631099\pi$
$811$		−	52.1933i		−	1.83276i	0.400314	−	0.916378i	$-0.368901\pi$
$812$	7.90600	−	3.13422i	0.277446	−	0.109990i
$813$	−1.57914			−0.0553828
$814$	−8.73911	+	1.66906i	−0.306306	+	0.0585007i
$815$	13.2878			0.465453
$816$	0.829330	−	0.780165i	0.0290324	−	0.0273112i
$817$	−63.0827			−2.20699
$818$	4.17985	+	21.8854i	0.146145	+	0.765206i
$819$	−7.13103			−0.249178
$820$	−6.05820	−	15.2816i	−0.211561	−	0.533658i
$821$	−30.4424			−1.06245			−0.531223	−	0.847232i	$-0.678267\pi$
$821$	−30.4424			−1.06245			−0.531223	+	0.847232i	$0.678267\pi$
$822$	0.286313	+	1.49911i	0.00998630	+	0.0522876i
$823$			13.7812i			0.480383i	0.970726	+	0.240191i	$0.0772102\pi$
$823$			13.7812i			0.480383i	−0.970726	+	0.240191i	$0.922790\pi$
$824$	4.57751	+	7.20250i	0.159465	+	0.250911i
$825$		−	0.128638i		−	0.00447860i
$826$	−14.7565	+	2.81831i	−0.513444	+	0.0980617i
$827$	16.4113			0.570677			0.285339	−	0.958427i	$-0.407894\pi$
$827$	16.4113			0.570677			0.285339	+	0.958427i	$0.407894\pi$
$828$	−16.7550	+	23.3496i	−0.582276	+	0.811455i
$829$	14.8055			0.514215			0.257108	−	0.966383i	$-0.417231\pi$
$829$	14.8055			0.514215			0.257108	+	0.966383i	$0.417231\pi$
$830$	−12.1347	+	2.31759i	−0.421203	+	0.0804446i
$831$			0.370745i			0.0128610i
$832$	−9.96943	+	21.2588i	−0.345628	+	0.737017i
$833$		−	29.4927i		−	1.02186i
$834$	−0.0388730	−	0.203536i	−0.00134606	−	0.00704789i
$835$	−4.05918			−0.140474
$836$	24.2533	−	9.61490i	0.838819	−	0.332538i
$837$	−0.948094			−0.0327709
$838$	6.61375	+	34.6291i	0.228468	+	1.19624i
$839$	−52.1192			−1.79936			−0.899678	−	0.436554i	$-0.856199\pi$
$839$	−52.1192			−1.79936			−0.899678	+	0.436554i	$0.856199\pi$
$840$	−0.0753078	−	0.118493i	−0.00259837	−	0.00408841i
$841$	−1.50027			−0.0517336
$842$	22.6242	−	4.32095i	0.779683	−	0.148910i
$843$	−1.65473			−0.0569918
$844$	−3.05570	−	7.70791i	−0.105181	−	0.265317i
$845$		−	4.38552i		−	0.150867i
$846$	−7.88498	+	1.50594i	−0.271091	+	0.0517751i
$847$	5.33896			0.183449
$848$	22.2573	+	23.6600i	0.764320	+	0.812486i
$849$			1.28874i			0.0442293i
$850$	−6.45940	+	1.23367i	−0.221556	+	0.0423144i
$851$	7.75932	+	12.0805i	0.265986	+	0.414114i
$852$	−0.257383	+	0.102036i	−0.00881780	+	0.00349570i
$853$	−55.0356			−1.88438			−0.942192	−	0.335074i	$-0.891239\pi$
$853$	−55.0356			−1.88438			−0.942192	+	0.335074i	$0.891239\pi$
$854$	15.4343	−	2.94776i	0.528150	−	0.100870i
$855$			18.5998i			0.636099i
$856$	−18.9442	−	29.8079i	−0.647501	−	1.01881i
$857$	−12.5217			−0.427735			−0.213867	−	0.976863i	$-0.568606\pi$
$857$	−12.5217			−0.427735			−0.213867	+	0.976863i	$0.568606\pi$
$858$	0.524469	−	0.100167i	0.0179051	−	0.00341965i
$859$			19.8656i			0.677806i	0.940821	+	0.338903i	$0.110056\pi$
$859$			19.8656i			0.677806i	−0.940821	+	0.338903i	$0.889944\pi$
$860$	7.49010	+	18.8936i	0.255410	+	0.644265i
$861$			0.407997i			0.0139045i
$862$	−6.52628	−	34.1712i	−0.222286	−	1.16388i
$863$			14.6491i			0.498663i	0.968418	+	0.249331i	$0.0802108\pi$
$863$			14.6491i			0.498663i	−0.968418	+	0.249331i	$0.919789\pi$
$864$	−1.21864	+	1.68120i	−0.0414591	+	0.0571956i
$865$		−	18.4562i		−	0.627530i
$866$	−3.35658	+	0.641067i	−0.114061	+	0.0217843i
$867$			0.282991i			0.00961088i
$868$	−1.54375	−	3.89407i	−0.0523983	−	0.132173i
$869$	−31.4272			−1.06609
$870$	−0.0851659	−	0.445923i	−0.00288740	−	0.0151182i
$871$	4.18125			0.141676
$872$	−27.1018	+	17.2244i	−0.917783	+	0.583291i
$873$		−	8.19314i		−	0.277296i
$874$	−28.9950	−	30.5273i	−0.980769	−	1.03260i
$875$			0.810885i			0.0274129i
$876$	−0.186363	−	0.470094i	−0.00629661	−	0.0158830i
$877$	−34.0401			−1.14945			−0.574726	−	0.818346i	$-0.694891\pi$
$877$	−34.0401			−1.14945			−0.574726	+	0.818346i	$0.694891\pi$
$878$	−28.1150	+	5.36962i	−0.948834	+	0.181216i
$879$	1.18810			0.0400737
$880$	−5.75942	−	6.12236i	−0.194150	−	0.206385i
$881$			3.90153i			0.131446i	0.997838	+	0.0657230i	$0.0209354\pi$
$881$			3.90153i			0.131446i	−0.997838	+	0.0657230i	$0.979065\pi$
$882$	5.04171	+	26.3980i	0.169763	+	0.888869i
$883$			34.1418i			1.14896i	0.818518	+	0.574481i	$0.194796\pi$
$883$			34.1418i			1.14896i	−0.818518	+	0.574481i	$0.805204\pi$
$884$	−10.0595	−	25.3749i	−0.338339	−	0.853450i
$885$			0.801954i			0.0269574i
$886$	22.8938	−	4.37244i	0.769133	−	0.146895i
$887$		−	21.0867i		−	0.708023i	−0.935241	−	0.354012i	$-0.884817\pi$
$887$		−	21.0867i		−	0.708023i	0.935241	−	0.354012i	$-0.115183\pi$
$888$	0.278038	+	0.437479i	0.00933033	+	0.0146809i
$889$		−	4.96618i		−	0.166560i
$890$	−1.54661	−	8.09795i	−0.0518425	−	0.271444i
$891$	−18.8418			−0.631223
$892$	11.6504	+	29.3879i	0.390085	+	0.983979i
$893$		−	11.7602i		−	0.393541i
$894$	−0.00646869	−	0.0338696i	−0.000216345	−	0.00113277i
$895$	−8.67585			−0.290002
$896$	−8.88940	−	2.26784i	−0.296974	−	0.0757633i
$897$	−0.465668	−	0.724998i	−0.0155482	−	0.0242070i
$898$	−7.57052	−	39.6388i	−0.252632	−	1.32276i
$899$		−	13.5449i		−	0.451747i
$900$	5.57072	−	2.20844i	0.185691	−	0.0736145i
$901$	−37.7625			−1.25805
$902$	4.58234	+	23.9928i	0.152575	+	0.798874i
$903$		−	0.504430i		−	0.0167864i
$904$	−5.69342	+	3.61842i	−0.189360	+	0.120347i
$905$	21.9722			0.730380
$906$	0.298358	+	1.56218i	0.00991229	+	0.0519001i
$907$	40.0954			1.33135			0.665673	−	0.746243i	$-0.268145\pi$
$907$	40.0954			1.33135			0.665673	+	0.746243i	$0.268145\pi$
$908$	−18.8647	+	7.47867i	−0.626048	+	0.248188i
$909$	−5.00317			−0.165945
$910$	−3.30605	+	0.631415i	−0.109594	+	0.0209312i
$911$	−43.9481			−1.45607			−0.728033	−	0.685542i	$-0.759565\pi$
$911$	−43.9481			−1.45607			−0.728033	+	0.685542i	$0.759565\pi$
$912$	−1.04150	−	1.10713i	−0.0344875	−	0.0366609i
$913$	18.3571			0.607531
$914$	−5.78734	+	1.10531i	−0.191428	+	0.0365605i
$915$		−	0.838787i		−	0.0277295i
$916$	9.34420	+	23.5705i	0.308741	+	0.778791i
$917$		−	12.5521i		−	0.414508i
$918$	−0.452833	−	2.37101i	−0.0149457	−	0.0782548i
$919$	29.9313			0.987342			0.493671	−	0.869649i	$-0.335655\pi$
$919$	29.9313			0.987342			0.493671	+	0.869649i	$0.335655\pi$
$920$	−5.70036	+	12.3088i	−0.187935	+	0.405808i
$921$	1.47489			0.0485992
$922$	4.21101	+	22.0486i	0.138682	+	0.726131i
$923$			6.63744i			0.218474i
$924$	0.0768839	+	0.193938i	0.00252929	+	0.00638008i
$925$		−	2.99380i		−	0.0984355i
$926$	54.7728	−	10.4609i	1.79994	−	0.343768i
$927$	9.04039			0.296925
$928$	−24.0183	−	17.4101i	−0.788441	−	0.571514i
$929$	−29.9571			−0.982862			−0.491431	−	0.870917i	$-0.663526\pi$
$929$	−29.9571			−0.982862			−0.491431	+	0.870917i	$0.663526\pi$
$930$	−0.219638	+	0.0419481i	−0.00720220	+	0.00137553i
$931$	−39.3720			−1.29037
$932$	−25.1931	+	9.98747i	−0.825228	+	0.327150i
$933$	0.954114			0.0312363
$934$	3.00869	+	15.7533i	0.0984472	+	0.515463i
$935$	9.77160			0.319566
$936$	13.3418	+	20.9927i	0.436089	+	0.686166i
$937$		−	38.2177i		−	1.24852i	−0.781218	−	0.624259i	$-0.785401\pi$
$937$		−	38.2177i		−	1.24852i	0.781218	−	0.624259i	$-0.214599\pi$
$938$	0.306473	+	1.60467i	0.0100067	+	0.0523944i
$939$	1.64382			0.0536442
$940$	−3.52225	+	1.39635i	−0.114883	+	0.0455438i
$941$		−	1.41138i		−	0.0460096i	−0.999735	−	0.0230048i	$-0.992677\pi$
$941$		−	1.41138i		−	0.0460096i	0.999735	−	0.0230048i	$-0.00732330\pi$
$942$	0.301684	+	1.57960i	0.00982941	+	0.0514661i
$943$	33.1664	−	21.3029i	1.08005	−	0.693717i
$944$	35.9053	+	38.1680i	1.16862	+	1.24226i
$945$	−0.297646			−0.00968242
$946$	−5.66541	−	29.6637i	−0.184198	−	0.964450i
$947$		−	40.9764i		−	1.33155i	−0.746150	−	0.665777i	$-0.768100\pi$
$947$		−	40.9764i		−	1.33155i	0.746150	−	0.665777i	$-0.231900\pi$
$948$	0.674782	+	1.70212i	0.0219159	+	0.0552823i
$949$	−12.1229			−0.393526
$950$	1.64691	+	8.62312i	0.0534329	+	0.279771i
$951$		−	0.604795i		−	0.0196118i
$952$	9.00099	−	5.72053i	0.291724	−	0.185403i
$953$		−	33.8456i		−	1.09637i	−0.836358	−	0.548184i	$-0.815319\pi$
$953$		−	33.8456i		−	1.09637i	0.836358	−	0.548184i	$-0.184681\pi$
$954$	33.8001	−	6.45541i	1.09432	−	0.209001i
$955$		−	12.6841i		−	0.410449i
$956$	7.96249	+	20.0852i	0.257525	+	0.649601i
$957$			0.674581i			0.0218061i
$958$	6.18456	+	32.3819i	0.199814	+	1.04621i
$959$			14.2955i			0.461625i
$960$	−0.207930	+	0.443389i	−0.00671090	+	0.0143103i
$961$	24.3285			0.784791
$962$	12.2060	−	2.33119i	0.393536	−	0.0751607i
$963$	−37.4141			−1.20565
$964$	17.3891	+	43.8635i	0.560065	+	1.41275i
$965$		−	15.3963i		−	0.495625i
$966$	0.244106	−	0.231853i	0.00785399	−	0.00745976i
$967$		−	13.1812i		−	0.423879i	−0.977283	−	0.211940i	$-0.932022\pi$
$967$		−	13.1812i		−	0.423879i	0.977283	−	0.211940i	$-0.0679780\pi$
$968$	−9.98889	−	15.7171i	−0.321055	−	0.505166i
$969$	1.76704			0.0567655
$970$	−0.725460	−	3.79846i	−0.0232931	−	0.121961i
$971$	−43.9189			−1.40942			−0.704712	−	0.709494i	$-0.748924\pi$
$971$	−43.9189			−1.40942			−0.704712	+	0.709494i	$0.748924\pi$
$972$	1.21621	+	3.06785i	0.0390098	+	0.0984012i
$973$		−	1.94091i		−	0.0622228i
$974$	−44.2171	+	8.44494i	−1.41681	+	0.270593i
$975$			0.179670i			0.00575404i
$976$	−37.5544	−	39.9210i	−1.20209	−	1.27784i
$977$		−	40.2462i		−	1.28759i	−0.765198	−	0.643795i	$-0.777359\pi$
$977$		−	40.2462i		−	1.28759i	0.765198	−	0.643795i	$-0.222641\pi$
$978$	0.215802	+	1.12993i	0.00690060	+	0.0361311i
$979$			12.2504i			0.391523i
$980$	4.67482	+	11.7921i	0.149332	+	0.376685i
$981$			34.0175i			1.08609i
$982$	−38.3511	+	7.32459i	−1.22383	+	0.233737i
$983$	−0.484037			−0.0154384			−0.00771919	−	0.999970i	$-0.502457\pi$
$983$	−0.484037			−0.0154384			−0.00771919	+	0.999970i	$0.502457\pi$
$984$	1.20108	−	0.763340i	0.0382890	−	0.0243344i
$985$		−	9.62990i		−	0.306834i
$986$	33.8732	−	6.46937i	1.07874	−	0.206027i
$987$	0.0940387			0.00299329
$988$	−33.8748	+	13.4292i	−1.07770	+	0.427240i
$989$	−41.0056	+	26.3380i	−1.30390	+	0.837499i
$990$	−8.74627	+	1.67043i	−0.277975	+	0.0530898i
$991$			16.2271i			0.515471i	0.966215	+	0.257736i	$0.0829764\pi$
$991$			16.2271i			0.515471i	−0.966215	+	0.257736i	$0.917024\pi$
$992$	−8.57526	+	11.8301i	−0.272265	+	0.375607i
$993$	1.00798			0.0319873
$994$	−2.54731	+	0.486505i	−0.0807956	+	0.0154310i
$995$			2.04990i			0.0649862i
$996$	−0.394150	−	0.994233i	−0.0124891	−	0.0315035i
$997$	36.2944			1.14946			0.574728	−	0.818345i	$-0.305108\pi$
$997$	36.2944			1.14946			0.574728	+	0.818345i	$0.305108\pi$
$998$	50.9846	−	9.73744i	1.61389	−	0.308233i
$999$	1.09891			0.0347681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.b.91.10	yes	32
4.3	odd	2	inner	460.2.e.b.91.12	yes	32
23.22	odd	2	inner	460.2.e.b.91.9	✓	32
92.91	even	2	inner	460.2.e.b.91.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.b.91.9	✓	32	23.22	odd	2	inner
460.2.e.b.91.10	yes	32	1.1	even	1	trivial
460.2.e.b.91.11	yes	32	92.91	even	2	inner
460.2.e.b.91.12	yes	32	4.3	odd	2	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.265302 - 1.38911i) q^{2} -0.0612154i q^{3} +(-1.85923 + 0.737066i) q^{4} +1.00000i q^{5} +(-0.0850346 + 0.0162406i) q^{6} -0.810885 q^{7} +(1.51712 + 2.38712i) q^{8} +2.99625 q^{9} +O(q^{10})\)	\(q+(-0.265302 - 1.38911i) q^{2} -0.0612154i q^{3} +(-1.85923 + 0.737066i) q^{4} +1.00000i q^{5} +(-0.0850346 + 0.0162406i) q^{6} -0.810885 q^{7} +(1.51712 + 2.38712i) q^{8} +2.99625 q^{9} +(1.38911 - 0.265302i) q^{10} -2.10140 q^{11} +(0.0451198 + 0.113813i) q^{12} +2.93504 q^{13} +(0.215130 + 1.12641i) q^{14} +0.0612154 q^{15} +(2.91347 - 2.74075i) q^{16} +4.65004i q^{17} +(-0.794913 - 4.16211i) q^{18} +6.20768 q^{19} +(-0.737066 - 1.85923i) q^{20} +0.0496387i q^{21} +(0.557507 + 2.91907i) q^{22} +(4.03517 - 2.59180i) q^{23} +(0.146129 - 0.0928711i) q^{24} -1.00000 q^{25} +(-0.778674 - 4.07709i) q^{26} -0.367063i q^{27} +(1.50762 - 0.597676i) q^{28} +5.24402 q^{29} +(-0.0162406 - 0.0850346i) q^{30} -2.58292i q^{31} +(-4.58014 - 3.31999i) q^{32} +0.128638i q^{33} +(6.45940 - 1.23367i) q^{34} -0.810885i q^{35} +(-5.57072 + 2.20844i) q^{36} +2.99380i q^{37} +(-1.64691 - 8.62312i) q^{38} -0.179670i q^{39} +(-2.38712 + 1.51712i) q^{40} +8.21934 q^{41} +(0.0689533 - 0.0131693i) q^{42} -10.1620 q^{43} +(3.90699 - 1.54887i) q^{44} +2.99625i q^{45} +(-4.67082 - 4.91766i) q^{46} -1.89447i q^{47} +(-0.167776 - 0.178349i) q^{48} -6.34247 q^{49} +(0.265302 + 1.38911i) q^{50} +0.284654 q^{51} +(-5.45692 + 2.16332i) q^{52} +8.12090i q^{53} +(-0.509889 + 0.0973827i) q^{54} -2.10140i q^{55} +(-1.23021 - 1.93568i) q^{56} -0.380006i q^{57} +(-1.39125 - 7.28450i) q^{58} +13.1005i q^{59} +(-0.113813 + 0.0451198i) q^{60} -13.7022i q^{61} +(-3.58795 + 0.685255i) q^{62} -2.42962 q^{63} +(-3.39669 + 7.24310i) q^{64} +2.93504i q^{65} +(0.178692 - 0.0341280i) q^{66} +1.42460 q^{67} +(-3.42739 - 8.64549i) q^{68} +(-0.158658 - 0.247014i) q^{69} +(-1.12641 + 0.215130i) q^{70} +2.26145i q^{71} +(4.54568 + 7.15242i) q^{72} -4.13040 q^{73} +(4.15870 - 0.794262i) q^{74} +0.0612154i q^{75} +(-11.5415 + 4.57547i) q^{76} +1.70400 q^{77} +(-0.249580 + 0.0476668i) q^{78} +14.9553 q^{79} +(2.74075 + 2.91347i) q^{80} +8.96629 q^{81} +(-2.18061 - 11.4175i) q^{82} -8.73564 q^{83} +(-0.0365870 - 0.0922896i) q^{84} -4.65004 q^{85} +(2.69601 + 14.1162i) q^{86} -0.321015i q^{87} +(-3.18808 - 5.01630i) q^{88} -5.82961i q^{89} +(4.16211 - 0.794913i) q^{90} -2.37998 q^{91} +(-5.59198 + 7.79293i) q^{92} -0.158114 q^{93} +(-2.63161 + 0.502606i) q^{94} +6.20768i q^{95} +(-0.203234 + 0.280375i) q^{96} -2.73446i q^{97} +(1.68267 + 8.81035i) q^{98} -6.29633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

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