LMFDB - Embedded newform 189.2.ba.a.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.204899 - 0.244189i) q^{2} +(1.66650 + 0.471978i) q^{3} +(0.329652 + 1.86955i) q^{4} +(-2.18935 + 1.83708i) q^{5} +(0.456717 - 0.310234i) q^{6} +(0.468007 - 2.60403i) q^{7} +(1.07619 + 0.621337i) q^{8} +(2.55447 + 1.57311i) q^{9} +O(q^{10})$	\(q+(0.204899 - 0.244189i) q^{2} +(1.66650 + 0.471978i) q^{3} +(0.329652 + 1.86955i) q^{4} +(-2.18935 + 1.83708i) q^{5} +(0.456717 - 0.310234i) q^{6} +(0.468007 - 2.60403i) q^{7} +(1.07619 + 0.621337i) q^{8} +(2.55447 + 1.57311i) q^{9} +0.911030i q^{10} +(-2.19030 + 2.61029i) q^{11} +(-0.333020 + 3.27120i) q^{12} +(1.17022 - 3.21516i) q^{13} +(-0.539981 - 0.647845i) q^{14} +(-4.51562 + 2.02818i) q^{15} +(-3.19557 + 1.16309i) q^{16} +4.66323 q^{17} +(0.907544 - 0.301446i) q^{18} -5.52060i q^{19} +(-4.15623 - 3.48749i) q^{20} +(2.00898 - 4.11874i) q^{21} +(0.188615 + 1.06969i) q^{22} +(0.470293 - 1.29212i) q^{23} +(1.50021 + 1.54340i) q^{24} +(0.550137 - 3.11998i) q^{25} +(-0.545329 - 0.944538i) q^{26} +(3.51457 + 3.82725i) q^{27} +(5.02264 + 0.0165384i) q^{28} +(-2.81504 - 7.73427i) q^{29} +(-0.429987 + 1.51824i) q^{30} +(2.17942 - 0.384290i) q^{31} +(-1.22079 + 3.35410i) q^{32} +(-4.88214 + 3.31629i) q^{33} +(0.955489 - 1.13871i) q^{34} +(3.75918 + 6.56089i) q^{35} +(-2.09891 + 5.29429i) q^{36} +(0.882419 - 1.52840i) q^{37} +(-1.34807 - 1.13116i) q^{38} +(3.46767 - 4.80576i) q^{39} +(-3.49759 + 0.616720i) q^{40} +(-4.96713 - 1.80789i) q^{41} +(-0.594112 - 1.33450i) q^{42} +(-1.57831 + 8.95103i) q^{43} +(-5.60210 - 3.23437i) q^{44} +(-8.48256 + 1.24869i) q^{45} +(-0.219159 - 0.379594i) q^{46} +(0.532155 - 3.01800i) q^{47} +(-5.87439 + 0.430058i) q^{48} +(-6.56194 - 2.43741i) q^{49} +(-0.649143 - 0.773618i) q^{50} +(7.77129 + 2.20094i) q^{51} +(6.39667 + 1.12790i) q^{52} +(-1.30996 - 0.756305i) q^{53} +(1.65470 - 0.0740197i) q^{54} -9.73859i q^{55} +(2.12164 - 2.51163i) q^{56} +(2.60560 - 9.20011i) q^{57} +(-2.46542 - 0.897340i) q^{58} +(-6.44995 - 2.34759i) q^{59} +(-5.28036 - 7.77358i) q^{60} +(9.69333 + 1.70919i) q^{61} +(0.352721 - 0.610930i) q^{62} +(5.29193 - 5.91570i) q^{63} +(-2.83176 - 4.90475i) q^{64} +(3.34449 + 9.18891i) q^{65} +(-0.190543 + 1.87167i) q^{66} +(-7.34743 + 6.16523i) q^{67} +(1.53724 + 8.71812i) q^{68} +(1.39360 - 1.93135i) q^{69} +(2.37235 + 0.426368i) q^{70} +(-9.64722 + 5.56983i) q^{71} +(1.77166 + 3.28015i) q^{72} +(-5.11937 + 2.95567i) q^{73} +(-0.192410 - 0.528643i) q^{74} +(2.38937 - 4.93981i) q^{75} +(10.3210 - 1.81988i) q^{76} +(5.77220 + 6.92523i) q^{77} +(-0.462992 - 1.83146i) q^{78} +(8.75642 + 7.34751i) q^{79} +(4.85952 - 8.41694i) q^{80} +(4.05066 + 8.03692i) q^{81} +(-1.45922 + 0.842484i) q^{82} +(-6.72578 + 2.44798i) q^{83} +(8.36244 + 2.39814i) q^{84} +(-10.2094 + 8.56673i) q^{85} +(1.86235 + 2.21946i) q^{86} +(-1.04087 - 14.2178i) q^{87} +(-3.97904 + 1.44825i) q^{88} +12.2586 q^{89} +(-1.43315 + 2.32720i) q^{90} +(-7.82471 - 4.55201i) q^{91} +(2.57071 + 0.453286i) q^{92} +(3.81339 + 0.388217i) q^{93} +(-0.627925 - 0.748331i) q^{94} +(10.1418 + 12.0865i) q^{95} +(-3.61752 + 5.01344i) q^{96} +(2.47531 + 0.436465i) q^{97} +(-1.93972 + 1.10293i) q^{98} +(-9.70132 + 3.22235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.204899	−	0.244189i	0.144885	−	0.172668i	−0.688721	−	0.725026i	$-0.741828\pi$
$2$	0.204899	−	0.244189i	0.144885	−	0.172668i	0.833607	+	0.552359i	$0.186272\pi$
$3$	1.66650	+	0.471978i	0.962157	+	0.272497i
$3$	1.66650	+	0.471978i	0.962157	+	0.272497i
$4$	0.329652	+	1.86955i	0.164826	+	0.934774i
$5$	−2.18935	+	1.83708i	−0.979106	+	0.821568i	−0.983954	−	0.178420i	$-0.942901\pi$
$5$	−2.18935	+	1.83708i	−0.979106	+	0.821568i	0.00484794	+	0.999988i	$0.498457\pi$
$6$	0.456717	−	0.310234i	0.186454	−	0.126652i
$7$	0.468007	−	2.60403i	0.176890	−	0.984231i
$7$	0.468007	−	2.60403i	0.176890	−	0.984231i
$8$	1.07619	+	0.621337i	0.380489	+	0.219676i
$9$	2.55447	+	1.57311i	0.851491	+	0.524369i
$10$			0.911030i			0.288093i
$11$	−2.19030	+	2.61029i	−0.660399	+	0.787033i	−0.987443	−	0.157976i	$-0.949503\pi$
$11$	−2.19030	+	2.61029i	−0.660399	+	0.787033i	0.327044	+	0.945009i	$0.393947\pi$
$12$	−0.333020	+	3.27120i	−0.0961347	+	0.944313i
$13$	1.17022	−	3.21516i	0.324562	−	0.891726i	−0.664900	−	0.746932i	$-0.731526\pi$
$13$	1.17022	−	3.21516i	0.324562	−	0.891726i	0.989462	−	0.144794i	$-0.0462518\pi$
$14$	−0.539981	−	0.647845i	−0.144316	−	0.173144i
$15$	−4.51562	+	2.02818i	−1.16593	+	0.523674i
$16$	−3.19557	+	1.16309i	−0.798893	+	0.290773i
$17$	4.66323			1.13100			0.565499	−	0.824749i	$-0.308683\pi$
$17$	4.66323			1.13100			0.565499	+	0.824749i	$0.308683\pi$
$18$	0.907544	−	0.301446i	0.213910	−	0.0710515i
$19$		−	5.52060i		−	1.26651i	−0.773942	−	0.633256i	$-0.781718\pi$
$19$		−	5.52060i		−	1.26651i	0.773942	−	0.633256i	$-0.218282\pi$
$20$	−4.15623	−	3.48749i	−0.929362	−	0.779827i
$21$	2.00898	−	4.11874i	0.438396	−	0.898782i
$22$	0.188615	+	1.06969i	0.0402129	+	0.228059i
$23$	0.470293	−	1.29212i	0.0980628	−	0.269425i	−0.880955	−	0.473200i	$-0.843099\pi$
$23$	0.470293	−	1.29212i	0.0980628	−	0.269425i	0.979018	+	0.203775i	$0.0653210\pi$
$24$	1.50021	+	1.54340i	0.306230	+	0.315045i
$25$	0.550137	−	3.11998i	0.110027	−	0.623997i
$26$	−0.545329	−	0.944538i	−0.106948	−	0.185239i
$27$	3.51457	+	3.82725i	0.676379	+	0.736554i
$28$	5.02264	+	0.0165384i	0.949189	+	0.00312546i
$29$	−2.81504	−	7.73427i	−0.522741	−	1.43622i	−0.867458	−	0.497511i	$-0.834247\pi$
$29$	−2.81504	−	7.73427i	−0.522741	−	1.43622i	0.344717	−	0.938707i	$-0.387975\pi$
$30$	−0.429987	+	1.51824i	−0.0785045	+	0.277191i
$31$	2.17942	−	0.384290i	0.391435	−	0.0690206i	0.0255331	−	0.999674i	$-0.491872\pi$
$31$	2.17942	−	0.384290i	0.391435	−	0.0690206i	0.365902	+	0.930653i	$0.380761\pi$
$32$	−1.22079	+	3.35410i	−0.215808	+	0.592927i
$33$	−4.88214	+	3.31629i	−0.849871	+	0.577292i
$34$	0.955489	−	1.13871i	0.163865	−	0.195287i
$35$	3.75918	+	6.56089i	0.635418	+	1.10899i
$36$	−2.09891	+	5.29429i	−0.349819	+	0.882381i
$37$	0.882419	−	1.52840i	0.145069	−	0.251267i	−0.784330	−	0.620344i	$-0.786993\pi$
$37$	0.882419	−	1.52840i	0.145069	−	0.251267i	0.929399	+	0.369077i	$0.120326\pi$
$38$	−1.34807	−	1.13116i	−0.218686	−	0.183499i
$39$	3.46767	−	4.80576i	0.555272	−	0.769538i
$40$	−3.49759	+	0.616720i	−0.553018	+	0.0975120i
$41$	−4.96713	−	1.80789i	−0.775735	−	0.282344i	−0.0763420	−	0.997082i	$-0.524324\pi$
$41$	−4.96713	−	1.80789i	−0.775735	−	0.282344i	−0.699393	+	0.714737i	$0.746546\pi$
$42$	−0.594112	−	1.33450i	−0.0916735	−	0.205917i
$43$	−1.57831	+	8.95103i	−0.240690	+	1.36502i	0.589603	+	0.807693i	$0.299284\pi$
$43$	−1.57831	+	8.95103i	−0.240690	+	1.36502i	−0.830293	+	0.557327i	$0.811827\pi$
$44$	−5.60210	−	3.23437i	−0.844548	−	0.487600i
$45$	−8.48256	+	1.24869i	−1.26451	+	0.186144i
$46$	−0.219159	−	0.379594i	−0.0323132	−	0.0559681i
$47$	0.532155	−	3.01800i	0.0776228	−	0.440221i	−0.921083	−	0.389366i	$-0.872694\pi$
$47$	0.532155	−	3.01800i	0.0776228	−	0.440221i	0.998706	−	0.0508551i	$-0.0161947\pi$
$48$	−5.87439	+	0.430058i	−0.847895	+	0.0620736i
$49$	−6.56194	−	2.43741i	−0.937420	−	0.348201i
$50$	−0.649143	−	0.773618i	−0.0918027	−	0.109406i
$51$	7.77129	+	2.20094i	1.08820	+	0.308194i
$52$	6.39667	+	1.12790i	0.887058	+	0.156412i
$53$	−1.30996	−	0.756305i	−0.179937	−	0.103886i	0.407326	−	0.913283i	$-0.366461\pi$
$53$	−1.30996	−	0.756305i	−0.179937	−	0.103886i	−0.587263	+	0.809396i	$0.699795\pi$
$54$	1.65470	−	0.0740197i	0.225176	−	0.0100728i
$55$		−	9.73859i		−	1.31315i
$56$	2.12164	−	2.51163i	0.283516	−	0.335631i
$57$	2.60560	−	9.20011i	0.345121	−	1.21858i
$58$	−2.46542	−	0.897340i	−0.323726	−	0.117827i
$59$	−6.44995	−	2.34759i	−0.839713	−	0.305630i	−0.113874	−	0.993495i	$-0.536326\pi$
$59$	−6.44995	−	2.34759i	−0.839713	−	0.305630i	−0.725839	+	0.687865i	$0.758548\pi$
$60$	−5.28036	−	7.77358i	−0.681691	−	1.00356i
$61$	9.69333	+	1.70919i	1.24110	+	0.218840i	0.755388	−	0.655277i	$-0.227448\pi$
$61$	9.69333	+	1.70919i	1.24110	+	0.218840i	0.485715	+	0.874117i	$0.338559\pi$
$62$	0.352721	−	0.610930i	0.0447956	−	0.0775882i
$63$	5.29193	−	5.91570i	0.666721	−	0.745308i
$64$	−2.83176	−	4.90475i	−0.353970	−	0.613094i
$65$	3.34449	+	9.18891i	0.414833	+	1.13974i
$66$	−0.190543	+	1.87167i	−0.0234542	+	0.230386i
$67$	−7.34743	+	6.16523i	−0.897632	+	0.753203i	−0.969726	−	0.244195i	$-0.921476\pi$
$67$	−7.34743	+	6.16523i	−0.897632	+	0.753203i	0.0720942	+	0.997398i	$0.477032\pi$
$68$	1.53724	+	8.71812i	0.186418	+	1.05723i
$69$	1.39360	−	1.93135i	0.167769	−	0.232508i
$70$	2.37235	+	0.426368i	0.283550	+	0.0509608i
$71$	−9.64722	+	5.56983i	−1.14491	+	0.661017i	−0.947643	−	0.319332i	$-0.896541\pi$
$71$	−9.64722	+	5.56983i	−1.14491	+	0.661017i	−0.197272	+	0.980349i	$0.563208\pi$
$72$	1.77166	+	3.28015i	0.208792	+	0.386569i
$73$	−5.11937	+	2.95567i	−0.599176	+	0.345935i	−0.768718	−	0.639588i	$-0.779105\pi$
$73$	−5.11937	+	2.95567i	−0.599176	+	0.345935i	0.169541	+	0.985523i	$0.445771\pi$
$74$	−0.192410	−	0.528643i	−0.0223673	−	0.0614535i
$75$	2.38937	−	4.93981i	0.275901	−	0.570401i
$76$	10.3210	−	1.81988i	1.18390	−	0.208754i
$77$	5.77220	+	6.92523i	0.657804	+	0.789203i
$78$	−0.462992	−	1.83146i	−0.0524235	−	0.207372i
$79$	8.75642	+	7.34751i	0.985175	+	0.826660i	0.984862	−	0.173340i	$-0.0554560\pi$
$79$	8.75642	+	7.34751i	0.985175	+	0.826660i	0.000312673		1.00000i	$0.499900\pi$
$80$	4.85952	−	8.41694i	0.543311	−	0.941042i
$81$	4.05066	+	8.03692i	0.450074	+	0.892992i
$82$	−1.45922	+	0.842484i	−0.161144	+	0.0930367i
$83$	−6.72578	+	2.44798i	−0.738250	+	0.268701i	−0.683653	−	0.729807i	$-0.739610\pi$
$83$	−6.72578	+	2.44798i	−0.738250	+	0.268701i	−0.0545974	+	0.998508i	$0.517388\pi$
$84$	8.36244	+	2.39814i	0.912417	+	0.261658i
$85$	−10.2094	+	8.56673i	−1.10737	+	0.929192i
$86$	1.86235	+	2.21946i	0.200822	+	0.239331i
$87$	−1.04087	−	14.2178i	−0.111593	−	1.52431i
$88$	−3.97904	+	1.44825i	−0.424167	+	0.154384i
$89$	12.2586			1.29941			0.649703	−	0.760188i	$-0.274893\pi$
$89$	12.2586			1.29941			0.649703	+	0.760188i	$0.274893\pi$
$90$	−1.43315	+	2.32720i	−0.151067	+	0.245309i
$91$	−7.82471	−	4.55201i	−0.820252	−	0.477181i
$92$	2.57071	+	0.453286i	0.268015	+	0.0472583i
$93$	3.81339	+	0.388217i	0.395430	+	0.0402562i
$94$	−0.627925	−	0.748331i	−0.0647655	−	0.0771845i
$95$	10.1418	+	12.0865i	1.04053	+	1.24005i
$96$	−3.61752	+	5.01344i	−0.369212	+	0.511682i
$97$	2.47531	+	0.436465i	0.251330	+	0.0443163i	0.297894	−	0.954599i	$-0.403716\pi$
$97$	2.47531	+	0.436465i	0.251330	+	0.0443163i	−0.0465636	+	0.998915i	$0.514827\pi$
$98$	−1.93972	+	1.10293i	−0.195941	+	0.111413i
$99$	−9.70132	+	3.22235i	−0.975019	+	0.323858i
$100$	6.01431			0.601431
$101$	8.75323	−	3.18591i	0.870979	−	0.317010i	0.132415	−	0.991194i	$-0.457727\pi$
$101$	8.75323	−	3.18591i	0.870979	−	0.317010i	0.738563	+	0.674184i	$0.235505\pi$
$102$	2.12977	−	1.44669i	0.210879	−	0.143244i
$103$	−7.24467	−	8.63386i	−0.713838	−	0.850719i	0.280178	−	0.959948i	$-0.409606\pi$
$103$	−7.24467	−	8.63386i	−0.713838	−	0.850719i	−0.994017	+	0.109229i	$0.965162\pi$
$104$	3.25708	−	2.73301i	0.319383	−	0.267994i
$105$	3.16810	+	12.7080i	0.309174	+	1.24018i
$106$	−0.453090	+	0.164911i	−0.0440080	+	0.0160176i
$107$	5.79854	−	3.34779i	0.560566	−	0.323643i	−0.192807	−	0.981237i	$-0.561759\pi$
$107$	5.79854	−	3.34779i	0.560566	−	0.323643i	0.753373	+	0.657594i	$0.228426\pi$
$108$	−5.99664	+	7.83231i	−0.577027	+	0.753664i
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	0.127076	+	0.991893i	$0.459441\pi$
$109$	−8.30492	+	14.3845i	−0.795467	+	1.37779i	−0.922542	+	0.385896i	$0.873892\pi$
$110$	−2.37806	−	1.99543i	−0.226739	−	0.190256i
$111$	2.19193	−	2.13059i	0.208048	−	0.202227i
$112$	1.53318	+	8.86569i	0.144872	+	0.837729i
$113$	10.4246	−	1.83814i	0.980666	−	0.172918i	0.339739	−	0.940520i	$-0.389661\pi$
$113$	10.4246	−	1.83814i	0.980666	−	0.172918i	0.640927	+	0.767602i	$0.278550\pi$
$114$	−1.71268	−	2.52135i	−0.160407	−	0.236146i
$115$	1.34409	+	3.69286i	0.125337	+	0.344361i
$116$	13.5316	−	7.81247i	1.25638	−	0.725370i
$117$	8.04710	−	6.37216i	0.743955	−	0.589106i
$118$	−1.89484	+	1.09399i	−0.174434	+	0.100710i
$119$	2.18242	−	12.1432i	0.200062	−	1.11316i
$120$	−6.11983	−	0.623022i	−0.558662	−	0.0568739i
$121$	−0.106102	−	0.601736i	−0.00964566	−	0.0547033i
$122$	2.40352	−	2.01679i	0.217604	−	0.182592i
$123$	−7.42446	−	5.35723i	−0.669441	−	0.483045i
$124$	1.43690	+	3.94784i	0.129037	+	0.354527i
$125$	−2.61776	−	4.53409i	−0.234139	−	0.405541i
$126$	−0.360237	−	2.50435i	−0.0320925	−	0.223105i
$127$	8.48685	−	14.6997i	0.753086	−	1.30438i	−0.193234	−	0.981153i	$-0.561898\pi$
$127$	8.48685	−	14.6997i	0.753086	−	1.30438i	0.946320	−	0.323231i	$-0.104769\pi$
$128$	−8.80818	−	1.55312i	−0.778540	−	0.137278i
$129$	−6.85495	+	14.1720i	−0.603545	+	1.24778i
$130$	2.92911	+	1.06611i	0.256900	+	0.0935039i
$131$	−15.0308	−	5.47076i	−1.31325	−	0.477982i	−0.411958	−	0.911203i	$-0.635155\pi$
$131$	−15.0308	−	5.47076i	−1.31325	−	0.477982i	−0.901288	+	0.433221i	$0.857377\pi$
$132$	−7.80937	−	8.03417i	−0.679718	−	0.699285i
$133$	−14.3758	−	2.58368i	−1.24654	−	0.224033i
$134$			3.05741i			0.264120i
$135$	−14.7256	−	1.92263i	−1.26738	−	0.165474i
$136$	5.01850	+	2.89743i	0.430333	+	0.248453i
$137$	12.8335	+	2.26289i	1.09644	+	0.193332i	0.692475	−	0.721442i	$-0.256520\pi$
$137$	12.8335	+	2.26289i	1.09644	+	0.193332i	0.403965	+	0.914774i	$0.367632\pi$
$138$	−0.186069	−	0.736033i	−0.0158392	−	0.0626553i
$139$	2.63292	+	3.13779i	0.223321	+	0.266144i	0.866058	−	0.499943i	$-0.166646\pi$
$139$	2.63292	+	3.13779i	0.223321	+	0.266144i	−0.642737	+	0.766087i	$0.722201\pi$
$140$	−11.0267	+	9.19078i	−0.931925	+	0.776763i
$141$	2.31127	−	4.77835i	0.194644	−	0.402410i
$142$	−0.616615	+	3.49699i	−0.0517451	+	0.293461i
$143$	5.82938	+	10.0968i	0.487477	+	0.844335i
$144$	−9.99267	−	2.05589i	−0.832722	−	0.171324i
$145$	20.3716	+	11.7615i	1.69177	+	0.976743i
$146$	−0.327211	+	1.85570i	−0.0270802	+	0.153579i
$147$	−9.78510	−	7.15904i	−0.807061	−	0.590468i
$148$	3.14830	+	1.14589i	0.258789	+	0.0941913i
$149$	1.46897	−	0.259019i	0.120343	−	0.0212197i	−0.113152	−	0.993578i	$-0.536095\pi$
$149$	1.46897	−	0.259019i	0.120343	−	0.0212197i	0.233495	+	0.972358i	$0.424984\pi$
$150$	−0.716668	−	1.59562i	−0.0585157	−	0.130282i
$151$	−3.72109	−	3.12237i	−0.302818	−	0.254095i	0.478698	−	0.877980i	$-0.341109\pi$
$151$	−3.72109	−	3.12237i	−0.302818	−	0.254095i	−0.781516	+	0.623885i	$0.785553\pi$
$152$	3.43015	−	5.94120i	0.278222	−	0.481895i
$153$	11.9121	+	7.33576i	0.963035	+	0.593061i
$154$	2.87378	+	0.00946270i	0.231576	+	0.000762526i
$155$	−4.06553	+	4.84511i	−0.326551	+	0.389169i
$156$	10.1277	+	4.89875i	0.810867	+	0.392214i
$157$	−7.70444	+	21.1678i	−0.614882	+	1.68937i	0.104295	+	0.994546i	$0.466741\pi$
$157$	−7.70444	+	21.1678i	−0.614882	+	1.68937i	−0.719177	+	0.694827i	$0.755481\pi$
$158$	3.58836	−	0.632725i	0.285475	−	0.0503369i
$159$	−1.82609	−	1.87866i	−0.144818	−	0.148987i
$160$	−3.48902	−	9.58599i	−0.275831	−	0.757839i
$161$	−3.14462	−	1.82938i	−0.247830	−	0.144175i
$162$	2.79250	+	0.657629i	0.219400	+	0.0516682i
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	0.613635	−	0.789590i	$-0.289707\pi$
$163$	−4.81306	−	8.33646i	−0.376988	−	0.652962i	−0.990622	+	0.136628i	$0.956374\pi$
$164$	1.74251	−	9.88225i	0.136067	−	0.771674i
$165$	4.59640	−	16.2294i	0.357830	−	1.26346i
$166$	−0.780334	+	2.14395i	−0.0605657	+	0.166403i
$167$	−1.75065	−	9.92841i	−0.135469	−	0.768284i	−0.974532	−	0.224249i	$-0.928007\pi$
$167$	−1.75065	−	9.92841i	−0.135469	−	0.768284i	0.839063	−	0.544035i	$-0.183104\pi$
$168$	4.72116	−	3.18428i	0.364245	−	0.245672i
$169$	0.990731	+	0.831322i	0.0762101	+	0.0639479i
$170$			4.24834i			0.325833i
$171$	8.68450	−	14.1022i	0.664121	−	1.07842i
$172$	−17.2547			−1.31566
$173$	−11.6153	+	4.22763i	−0.883097	+	0.321421i	−0.743459	−	0.668782i	$-0.766816\pi$
$173$	−11.6153	+	4.22763i	−0.883097	+	0.321421i	−0.139638	+	0.990203i	$0.544594\pi$
$174$	−3.68511	−	2.65905i	−0.279368	−	0.201582i
$175$	−7.86706	−	2.89275i	−0.594694	−	0.218671i
$176$	3.96323	−	10.8889i	0.298740	−	0.820781i
$177$	−9.64086	−	6.95651i	−0.724652	−	0.522883i
$178$	2.51177	−	2.99341i	0.188265	−	0.224365i
$179$			15.7838i			1.17974i	0.807500	+	0.589868i	$0.200820\pi$
$179$			15.7838i			1.17974i	−0.807500	+	0.589868i	$0.799180\pi$
$180$	−5.13078	−	15.4469i	−0.382426	−	1.15134i
$181$	−11.3602	−	6.55879i	−0.844393	−	0.487511i	0.0143618	−	0.999897i	$-0.495428\pi$
$181$	−11.3602	−	6.55879i	−0.844393	−	0.487511i	−0.858755	+	0.512386i	$0.828762\pi$
$182$	−2.71482	+	0.978004i	−0.201236	+	0.0724945i
$183$	15.3473	+	7.42342i	1.13450	+	0.548755i
$184$	1.30896	−	1.09835i	0.0964981	−	0.0809715i
$185$	0.875863	+	4.96727i	0.0643947	+	0.365201i
$186$	0.876156	−	0.851641i	0.0642429	−	0.0624454i
$187$	−10.2138	+	12.1724i	−0.746910	+	0.890133i
$188$	5.81773			0.424301
$189$	11.6111	−	7.36086i	0.844584	−	0.535424i
$190$	5.02943			0.364874
$191$	−11.4242	+	13.6149i	−0.826629	+	0.985138i	0.173371	+	0.984857i	$0.444534\pi$
$191$	−11.4242	+	13.6149i	−0.826629	+	0.985138i	−1.00000		0.000281329i	$0.999910\pi$
$192$	−2.40420	−	9.51032i	−0.173508	−	0.686348i
$193$	−2.36579	−	13.4170i	−0.170293	−	0.965780i	−0.943438	−	0.331550i	$-0.892428\pi$
$193$	−2.36579	−	13.4170i	−0.170293	−	0.965780i	0.773144	−	0.634230i	$-0.218683\pi$
$194$	0.613769	−	0.515013i	0.0440660	−	0.0369758i
$195$	1.23664	+	16.8919i	0.0885575	+	1.20965i
$196$	2.39369	−	13.0714i	0.170978	−	0.933668i
$197$	7.98620	+	4.61083i	0.568993	+	0.328508i	0.756747	−	0.653708i	$-0.226787\pi$
$197$	7.98620	+	4.61083i	0.568993	+	0.328508i	−0.187754	+	0.982216i	$0.560121\pi$
$198$	−1.20093	+	3.02921i	−0.0853462	+	0.215277i
$199$		−	0.268183i		−	0.0190110i	−0.999955	−	0.00950548i	$-0.996974\pi$
$199$		−	0.268183i		−	0.0190110i	0.999955	−	0.00950548i	$-0.00302573\pi$
$200$	2.53061	−	3.01587i	0.178941	−	0.213254i
$201$	−15.1544	+	6.80655i	−1.06891	+	0.480097i
$202$	1.01556	−	2.79023i	0.0714546	−	0.196320i
$203$	−21.4577	+	3.71077i	−1.50604	+	0.260445i
$204$	−1.55295	+	15.2543i	−0.108728	+	1.06802i
$205$	14.1960	−	5.16692i	0.991492	−	0.360874i
$206$	−3.59272			−0.250316
$207$	3.23399	−	2.56086i	0.224778	−	0.177992i
$208$			11.6354i			0.806767i
$209$	14.4104	+	12.0917i	0.996787	+	0.836404i
$210$	3.75229	+	1.83024i	0.258933	+	0.126299i
$211$	−2.27165	−	12.8832i	−0.156387	−	0.886914i	−0.957507	−	0.288410i	$-0.906873\pi$
$211$	−2.27165	−	12.8832i	−0.156387	−	0.886914i	0.801120	−	0.598503i	$-0.204238\pi$
$212$	0.982118	−	2.69835i	0.0674521	−	0.185323i
$213$	−18.7060	+	4.72886i	−1.28171	+	0.324016i
$214$	0.370621	−	2.10190i	0.0253351	−	0.143683i
$215$	−12.9883	−	22.4964i	−0.885795	−	1.53424i
$216$	1.40432	+	6.30256i	0.0955519	+	0.428835i
$217$	0.0192796	−	5.85512i	0.00130878	−	0.397471i
$218$	1.81088	+	4.97534i	0.122648	+	0.336973i
$219$	−9.92646	+	2.50940i	−0.670768	+	0.169570i
$220$	18.2068	−	3.21034i	1.22750	−	0.216441i
$221$	5.45702	−	14.9930i	0.367079	−	1.00854i
$222$	−0.0711445	−	0.971800i	−0.00477491	−	0.0652229i
$223$	−9.50475	+	11.3273i	−0.636485	+	0.758534i	−0.983811	−	0.179211i	$-0.942646\pi$
$223$	−9.50475	+	11.3273i	−0.636485	+	0.758534i	0.347325	+	0.937745i	$0.387090\pi$
$224$	8.16284	+	4.74872i	0.545403	+	0.317287i
$225$	6.31338	−	7.10449i	0.420892	−	0.473633i
$226$	1.68714	−	2.92221i	0.112227	−	0.194383i
$227$	−7.02467	−	5.89440i	−0.466244	−	0.391225i	0.379178	−	0.925324i	$-0.376207\pi$
$227$	−7.02467	−	5.89440i	−0.466244	−	0.391225i	−0.845422	+	0.534099i	$0.820651\pi$
$228$	18.0590	+	1.83847i	1.19598	+	0.121756i
$229$	12.5995	−	2.22163i	0.832599	−	0.146810i	0.258929	−	0.965896i	$-0.416630\pi$
$229$	12.5995	−	2.22163i	0.832599	−	0.146810i	0.573670	+	0.819087i	$0.305519\pi$
$230$	1.17716	+	0.428451i	0.0776196	+	0.0282512i
$231$	6.35085	+	14.2653i	0.417855	+	0.938586i
$232$	1.77607	−	10.0726i	0.116605	−	0.661299i
$233$	−14.7803	−	8.53340i	−0.968289	−	0.559042i	−0.0695746	−	0.997577i	$-0.522164\pi$
$233$	−14.7803	−	8.53340i	−0.968289	−	0.559042i	−0.898714	+	0.438535i	$0.855498\pi$
$234$	0.0928317	−	3.27066i	0.00606860	−	0.213810i
$235$	4.37924	+	7.58507i	0.285670	+	0.494796i
$236$	2.26270	−	12.8324i	0.147289	−	0.835317i
$237$	11.1248	+	16.3775i	0.722630	+	1.06383i
$238$	−2.51805	−	3.02105i	−0.163221	−	0.195825i
$239$	−4.33839	−	5.17029i	−0.280627	−	0.334438i	0.607257	−	0.794505i	$-0.292270\pi$
$239$	−4.33839	−	5.17029i	−0.280627	−	0.334438i	−0.887884	+	0.460067i	$0.847825\pi$
$240$	12.0710	−	11.7333i	0.779181	−	0.757379i
$241$	−2.76527	−	0.487591i	−0.178126	−	0.0314085i	0.0838734	−	0.996476i	$-0.473271\pi$
$241$	−2.76527	−	0.487591i	−0.178126	−	0.0314085i	−0.262000	+	0.965068i	$0.584382\pi$
$242$	−0.168677	−	0.0973859i	−0.0108430	−	0.00626021i
$243$	2.95719	+	15.3054i	0.189704	+	0.981841i
$244$			18.6856i			1.19622i
$245$	18.8441	−	6.71848i	1.20390	−	0.429228i
$246$	−2.82944	+	0.715280i	−0.180398	+	0.0456046i
$247$	−17.7496	−	6.46034i	−1.12938	−	0.411061i
$248$	2.58423	+	0.940584i	0.164099	+	0.0597272i
$249$	−12.3639	+	0.905152i	−0.783533	+	0.0573617i
$250$	−1.64355	−	0.289802i	−0.103947	−	0.0183287i
$251$	−11.4184	+	19.7772i	−0.720720	+	1.24832i	0.239992	+	0.970775i	$0.422855\pi$
$251$	−11.4184	+	19.7772i	−0.720720	+	1.24832i	−0.960712	+	0.277549i	$0.910478\pi$
$252$	12.8042	+	7.94340i	0.806587	+	0.500387i
$253$	2.34273	+	4.05772i	0.147286	+	0.255107i
$254$	−1.85055	−	5.08434i	−0.116114	−	0.319020i
$255$	−21.0574	+	9.45786i	−1.31866	+	0.592274i
$256$	6.49298	−	5.44825i	0.405811	−	0.340516i
$257$	2.17396	+	12.3291i	0.135608	+	0.769069i	0.974435	+	0.224671i	$0.0721307\pi$
$257$	2.17396	+	12.3291i	0.135608	+	0.769069i	−0.838827	+	0.544398i	$0.816758\pi$
$258$	2.05607	+	4.57773i	0.128006	+	0.284997i
$259$	−3.56701	−	3.01315i	−0.221643	−	0.187228i
$260$	−16.0766	+	9.28182i	−0.997027	+	0.575634i
$261$	4.97589	−	24.1854i	0.308000	−	1.49704i
$262$	−4.41569	+	2.54940i	−0.272802	+	0.157502i
$263$	4.35051	+	11.9529i	0.268264	+	0.737049i	0.998546	+	0.0539035i	$0.0171663\pi$
$263$	4.35051	+	11.9529i	0.268264	+	0.737049i	−0.730282	+	0.683146i	$0.760611\pi$
$264$	−7.31462	+	0.535497i	−0.450184	+	0.0329575i
$265$	4.25735	−	0.750685i	0.261527	−	0.0461142i
$266$	−3.57649	+	2.98102i	−0.219289	+	0.182778i
$267$	20.4290	+	5.78578i	1.25023	+	0.354084i
$268$	−13.9483	−	11.7040i	−0.852027	−	0.714936i
$269$	9.79421	−	16.9641i	0.597163	−	1.03432i	−0.396074	−	0.918218i	$-0.629628\pi$
$269$	9.79421	−	16.9641i	0.597163	−	1.03432i	0.993238	−	0.116099i	$-0.0370389\pi$
$270$	−3.48674	+	3.20188i	−0.212196	+	0.194860i
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.0788154	−	0.996889i	$-0.474886\pi$
$271$	16.1584	−	9.32907i	0.981555	−	0.566701i	0.902739	+	0.430188i	$0.141553\pi$
$272$	−14.9017	+	5.42376i	−0.903546	+	0.328864i
$273$	−10.8915	−	11.2790i	−0.659181	−	0.682639i
$274$	3.18214	−	2.67013i	0.192240	−	0.161309i
$275$	6.93911	+	8.26971i	0.418444	+	0.498682i
$276$	4.07016	+	1.96872i	0.244995	+	0.118503i
$277$	2.50916	−	0.913261i	0.150761	−	0.0548725i	−0.265537	−	0.964101i	$-0.585549\pi$
$277$	2.50916	−	0.913261i	0.150761	−	0.0548725i	0.416298	+	0.909228i	$0.363327\pi$
$278$	1.30570			0.0783104
$279$	6.17179	+	2.44680i	0.369496	+	0.146486i
$280$	−0.0309404	+	9.39647i	−0.00184904	+	0.561546i
$281$	17.0926	+	3.01388i	1.01966	+	0.179793i	0.658396	−	0.752672i	$-0.271235\pi$
$281$	17.0926	+	3.01388i	1.01966	+	0.179793i	0.361261	+	0.932465i	$0.382346\pi$
$282$	−0.693243	−	1.54346i	−0.0412820	−	0.0919120i
$283$	0.702594	+	0.837319i	0.0417649	+	0.0497734i	0.786523	−	0.617562i	$-0.211879\pi$
$283$	0.702594	+	0.837319i	0.0417649	+	0.0497734i	−0.744758	+	0.667335i	$0.767435\pi$
$284$	−13.5933	−	16.1998i	−0.806613	−	0.961284i
$285$	11.1968	+	24.9289i	0.663239	+	1.47666i
$286$	3.65995	+	0.645349i	0.216418	+	0.0381603i
$287$	−7.03244	+	12.0884i	−0.415112	+	0.713558i
$288$	−8.39485	+	6.64752i	−0.494671	+	0.391709i
$289$	4.74568			0.279158
$290$	7.04615	−	2.56459i	0.413764	−	0.150598i
$291$	3.91912	+	1.89567i	0.229743	+	0.111126i
$292$	−7.21337	−	8.59656i	−0.422130	−	0.503075i
$293$	−16.1311	+	13.5356i	−0.942391	+	0.790760i	−0.978000	−	0.208606i	$-0.933107\pi$
$293$	−16.1311	+	13.5356i	−0.942391	+	0.790760i	0.0356088	+	0.999366i	$0.488663\pi$
$294$	−3.75311	+	0.922532i	−0.218886	+	0.0538032i
$295$	18.4339	−	6.70940i	1.07326	−	0.390636i
$296$	1.89930	−	1.09656i	0.110394	−	0.0637362i
$297$	−17.6882	+	0.791244i	−1.02637	+	0.0459126i
$298$	0.237741	−	0.411779i	0.0137720	−	0.0238537i
$299$	−3.60402	−	3.02414i	−0.208426	−	0.174890i
$300$	10.0229	+	2.83863i	0.578671	+	0.163888i
$301$	22.5701	+	8.29911i	1.30092	+	0.478353i
$302$	−1.52489	+	0.268880i	−0.0877478	+	0.0154723i
$303$	16.0910	−	1.17800i	0.924402	−	0.0676746i
$304$	6.42097	+	17.6415i	0.368268	+	1.01181i
$305$	−24.3620	+	14.0654i	−1.39496	+	0.805383i
$306$	4.23208	−	1.40571i	0.241932	−	0.0803591i
$307$	19.7567	−	11.4065i	1.12757	−	0.651004i	0.184249	−	0.982880i	$-0.441015\pi$
$307$	19.7567	−	11.4065i	1.12757	−	0.651004i	0.943323	+	0.331876i	$0.107682\pi$
$308$	−11.0442	+	13.0743i	−0.629303	+	0.744979i
$309$	−7.99827	−	17.8077i	−0.455006	−	1.01304i
$310$	0.350100	+	1.98552i	0.0198843	+	0.112770i
$311$	17.2454	−	14.4706i	0.977895	−	0.820551i	−0.00587548	−	0.999983i	$-0.501870\pi$
$311$	17.2454	−	14.4706i	0.977895	−	0.820551i	0.983770	+	0.179431i	$0.0574258\pi$
$312$	6.71786	−	3.01731i	0.380324	−	0.170821i
$313$	0.482843	+	1.32660i	0.0272919	+	0.0749839i	0.952590	−	0.304256i	$-0.0984078\pi$
$313$	0.482843	+	1.32660i	0.0272919	+	0.0749839i	−0.925298	+	0.379240i	$0.876186\pi$
$314$	3.59031	+	6.21859i	0.202613	+	0.350935i
$315$	−0.718263	+	22.6732i	−0.0404695	+	1.27749i
$316$	−10.8500	+	18.7927i	−0.610358	+	1.05717i
$317$	6.75056	+	1.19031i	0.379149	+	0.0668542i	0.359975	−	0.932962i	$-0.382785\pi$
$317$	6.75056	+	1.19031i	0.379149	+	0.0668542i	0.0191741	+	0.999816i	$0.493896\pi$
$318$	−0.832911	+	0.0609766i	−0.0467073	+	0.00341940i
$319$	26.3545	+	9.59225i	1.47557	+	0.537063i
$320$	15.2101	+	5.53604i	0.850273	+	0.309474i
$321$	11.2434	−	2.84232i	0.627544	−	0.158643i
$322$	−1.09104	+	0.393043i	−0.0608014	+	0.0219034i
$323$		−	25.7438i		−	1.43242i
$324$	−13.6901	+	10.2223i	−0.760561	+	0.567905i
$325$	−9.38747	−	5.41986i	−0.520723	−	0.300640i
$326$	−3.02186	−	0.532836i	−0.167365	−	0.0295110i
$327$	−20.6294	+	20.0522i	−1.14081	+	1.10889i
$328$	−4.22225	−	5.03188i	−0.233135	−	0.277839i
$329$	−7.60992	−	2.79819i	−0.419548	−	0.154269i
$330$	−3.02124	−	4.44778i	−0.166314	−	0.244842i
$331$	0.516799	−	2.93091i	0.0284058	−	0.161098i	−0.967305	−	0.253615i	$-0.918380\pi$
$331$	0.516799	−	2.93091i	0.0284058	−	0.161098i	0.995711	+	0.0925176i	$0.0294914\pi$
$332$	−6.79379	−	11.7672i	−0.372858	−	0.645808i
$333$	4.65845	−	2.51610i	0.255281	−	0.137882i
$334$	−2.78311	−	1.60683i	−0.152285	−	0.0879219i
$335$	4.76007	−	26.9957i	0.260070	−	1.47493i
$336$	−1.62937	+	15.4983i	−0.0888893	+	0.845504i
$337$	23.6884	+	8.62186i	1.29039	+	0.469663i	0.893854	−	0.448357i	$-0.147991\pi$
$337$	23.6884	+	8.62186i	1.29039	+	0.469663i	0.396534	+	0.918020i	$0.370213\pi$
$338$	0.405999	−	0.0715886i	0.0220834	−	0.00389391i
$339$	18.2402	+	1.85693i	0.990674	+	0.100854i
$340$	−19.3815	−	16.2630i	−1.05111	−	0.881984i
$341$	−3.77046	+	6.53063i	−0.204182	+	0.353653i
$342$	−1.66416	−	5.01019i	−0.0899876	−	0.270920i
$343$	−9.41811	+	15.9468i	−0.508530	+	0.861044i
$344$	−7.26016	+	8.65232i	−0.391442	+	0.466502i
$345$	0.496984	+	6.78856i	0.0267567	+	0.365484i
$346$	−1.34763	+	3.70257i	−0.0724488	+	0.199051i
$347$	−2.26682	+	0.399701i	−0.121689	+	0.0214571i	−0.234161	−	0.972198i	$-0.575234\pi$
$347$	−2.26682	+	0.399701i	−0.121689	+	0.0214571i	0.112472	+	0.993655i	$0.464123\pi$
$348$	26.2378	−	6.63290i	1.40649	−	0.355561i
$349$	2.39148	+	6.57053i	0.128013	+	0.351712i	0.987097	−	0.160121i	$-0.0511886\pi$
$349$	2.39148	+	6.57053i	0.128013	+	0.351712i	−0.859084	+	0.511834i	$0.828966\pi$
$350$	−2.31833	+	1.32833i	−0.123920	+	0.0710022i
$351$	16.4180	−	6.82117i	0.876331	−	0.364087i
$352$	−6.08129	−	10.5331i	−0.324134	−	0.561416i
$353$	−3.83541	+	21.7517i	−0.204138	+	1.15772i	0.694652	+	0.719346i	$0.255558\pi$
$353$	−3.83541	+	21.7517i	−0.204138	+	1.15772i	−0.898790	+	0.438379i	$0.855553\pi$
$354$	−3.67410	+	0.928811i	−0.195276	+	0.0493658i
$355$	10.8889	−	29.9170i	0.577923	−	1.58783i
$356$	4.04106	+	22.9180i	0.214176	+	1.21465i
$357$	9.36833	−	19.2066i	0.495825	−	1.01652i
$358$	3.85423	+	3.23408i	0.203702	+	0.170926i
$359$		−	32.6065i		−	1.72090i	−0.509532	−	0.860451i	$-0.670182\pi$
$359$		−	32.6065i		−	1.72090i	0.509532	−	0.860451i	$-0.329818\pi$
$360$	−9.90468	−	3.92670i	−0.522022	−	0.206955i
$361$	−11.4770			−0.604055
$362$	−3.92926	+	1.43014i	−0.206518	+	0.0751662i
$363$	0.107186	−	1.05287i	0.00562583	−	0.0552615i
$364$	5.93078	−	16.1292i	0.310857	−	0.845402i
$365$	5.77827	−	15.8757i	0.302449	−	0.830971i
$366$	4.95735	−	2.22658i	0.259125	−	0.116385i
$367$	2.73420	−	3.25850i	0.142724	−	0.170092i	−0.689947	−	0.723860i	$-0.742366\pi$
$367$	2.73420	−	3.25850i	0.142724	−	0.170092i	0.832671	+	0.553768i	$0.186811\pi$
$368$			4.67605i			0.243756i
$369$	−9.84439	−	12.4320i	−0.512479	−	0.647185i
$370$	1.39241	+	0.803911i	0.0723882	+	0.0417933i
$371$	−2.58251	+	3.05721i	−0.134077	+	0.158723i
$372$	0.531299	+	7.25728i	0.0275466	+	0.376273i
$373$	−18.6688	+	15.6650i	−0.966633	+	0.811101i	−0.982019	−	0.188780i	$-0.939547\pi$
$373$	−18.6688	+	15.6650i	−0.966633	+	0.811101i	0.0153863	+	0.999882i	$0.495102\pi$
$374$	0.879557	+	4.98821i	0.0454808	+	0.257934i
$375$	−2.22251	−	8.79160i	−0.114770	−	0.453996i
$376$	2.44789	−	2.91729i	0.126241	−	0.150448i
$377$	−28.1612			−1.45037
$378$	0.581662	−	4.34353i	0.0299175	−	0.223407i
$379$	−17.8518			−0.916987			−0.458493	−	0.888698i	$-0.651611\pi$
$379$	−17.8518			−0.916987			−0.458493	+	0.888698i	$0.651611\pi$
$380$	−19.2531	+	22.9449i	−0.987661	+	1.17705i
$381$	21.0813	−	20.4914i	1.08003	−	1.04981i
$382$	0.983789	+	5.57934i	0.0503350	+	0.285464i
$383$	20.9677	−	17.5940i	1.07140	−	0.899009i	0.0762189	−	0.997091i	$-0.475715\pi$
$383$	20.9677	−	17.5940i	1.07140	−	0.899009i	0.995178	+	0.0980821i	$0.0312708\pi$
$384$	−13.9458	−	6.74555i	−0.711670	−	0.344232i
$385$	−25.3596	−	4.55773i	−1.29244	−	0.232283i
$386$	−3.76104	−	2.17144i	−0.191432	−	0.110523i
$387$	−18.1127	+	20.3823i	−0.920720	+	1.03609i
$388$			4.77160i			0.242241i
$389$	10.4768	−	12.4858i	0.531197	−	0.633056i	−0.431993	−	0.901877i	$-0.642190\pi$
$389$	10.4768	−	12.4858i	0.531197	−	0.633056i	0.963190	+	0.268821i	$0.0866341\pi$
$390$	4.37819	+	3.15915i	0.221698	+	0.159970i
$391$	2.19308	−	6.02544i	0.110909	−	0.304720i
$392$	−5.54742	−	6.70028i	−0.280187	−	0.338415i
$393$	−22.4668	−	16.2112i	−1.13330	−	0.817749i
$394$	2.76228	−	1.00539i	0.139162	−	0.0506506i
$395$	−32.6688			−1.64375
$396$	−9.22239	−	17.0748i	−0.463443	−	0.858042i
$397$		−	4.55646i		−	0.228682i	−0.993442	−	0.114341i	$-0.963524\pi$
$397$		−	4.55646i		−	0.228682i	0.993442	−	0.114341i	$-0.0364757\pi$
$398$	−0.0654872	−	0.0549503i	−0.00328258	−	0.00275441i
$399$	−22.7379	−	11.0908i	−1.13832	−	0.555234i
$400$	1.87083	+	10.6100i	0.0935414	+	0.530499i
$401$	12.8930	−	35.4232i	0.643844	−	1.76895i	0.00454521	−	0.999990i	$-0.498553\pi$
$401$	12.8930	−	35.4232i	0.643844	−	1.76895i	0.639299	−	0.768958i	$-0.279225\pi$
$402$	−1.44303	+	5.09519i	−0.0719719	+	0.254125i
$403$	1.31485	−	7.45689i	0.0654974	−	0.371454i
$404$	8.84173	+	15.3143i	0.439893	+	0.761916i
$405$	−23.6328	−	10.1542i	−1.17432	−	0.504568i
$406$	−3.49053	+	6.00007i	−0.173232	+	0.297778i
$407$	2.05680	+	5.65101i	0.101952	+	0.280110i
$408$	6.99583	+	7.19721i	0.346345	+	0.356315i
$409$	−0.986288	+	0.173909i	−0.0487688	+	0.00859926i	−0.197979	−	0.980206i	$-0.563438\pi$
$409$	−0.986288	+	0.173909i	−0.0487688	+	0.00859926i	0.149211	+	0.988805i	$0.452327\pi$
$410$	1.64704	−	4.52520i	0.0813415	−	0.223484i
$411$	20.3190	+	9.82826i	1.00226	+	0.484792i
$412$	13.7532	−	16.3904i	0.677571	−	0.807498i
$413$	−9.13182	+	15.6972i	−0.449348	+	0.772408i
$414$	0.0373075	−	1.31442i	0.00183356	−	0.0646003i
$415$	10.2279	−	17.7153i	0.502069	−	0.869610i
$416$	9.35538	+	7.85009i	0.458685	+	0.384883i
$417$	2.90680	+	6.47183i	0.142347	+	0.316927i
$418$	5.90534	−	1.04127i	0.288840	−	0.0509302i
$419$	−2.20646	−	0.803084i	−0.107792	−	0.0392332i	0.287561	−	0.957762i	$-0.407156\pi$
$419$	−2.20646	−	0.803084i	−0.107792	−	0.0392332i	−0.395353	+	0.918529i	$0.629378\pi$
$420$	−22.7139	+	10.1121i	−1.10832	+	0.493421i
$421$	1.14047	−	6.46793i	0.0555831	−	0.315228i	−0.944322	−	0.329024i	$-0.893280\pi$
$421$	1.14047	−	6.46793i	0.0555831	−	0.315228i	0.999905	+	0.0137960i	$0.00439155\pi$
$422$	−3.61138	−	2.08503i	−0.175799	−	0.101498i
$423$	6.10702	−	6.87227i	0.296934	−	0.334141i
$424$	−0.939840	−	1.62785i	−0.0456426	−	0.0790554i
$425$	2.56542	−	14.5492i	0.124441	−	0.705740i
$426$	−2.67810	+	5.53673i	−0.129754	+	0.268255i
$427$	8.98734	−	24.4418i	0.434928	−	1.18282i
$428$	8.17035	+	9.73704i	0.394929	+	0.470658i
$429$	4.94922	+	19.5777i	0.238951	+	0.945219i
$430$	−8.15466	−	1.43789i	−0.393253	−	0.0693411i
$431$	13.3456	+	7.70506i	0.642833	+	0.371140i	0.785705	−	0.618602i	$-0.212300\pi$
$431$	13.3456	+	7.70506i	0.642833	+	0.371140i	−0.142872	+	0.989741i	$0.545634\pi$
$432$	−15.6825	−	8.14247i	−0.754524	−	0.391755i
$433$			9.87188i			0.474412i	0.971459	+	0.237206i	$0.0762317\pi$
$433$			9.87188i			0.474412i	−0.971459	+	0.237206i	$0.923768\pi$
$434$	−1.42580	−	1.20441i	−0.0684408	−	0.0578138i
$435$	28.3982	+	29.2156i	1.36159	+	1.40078i
$436$	−29.6303	−	10.7845i	−1.41903	−	0.516486i
$437$	−7.13327	−	2.59630i	−0.341231	−	0.124198i
$438$	−1.42115	+	2.93810i	−0.0679052	+	0.140388i
$439$	−34.7691	−	6.13074i	−1.65944	−	0.292604i	−0.736182	−	0.676784i	$-0.763373\pi$
$439$	−34.7691	−	6.13074i	−1.65944	−	0.292604i	−0.923258	+	0.384180i	$0.874484\pi$
$440$	6.05094	−	10.4805i	0.288467	−	0.499640i
$441$	−12.9280	−	16.5489i	−0.615619	−	0.788044i
$442$	−2.54299	−	4.40460i	−0.120958	−	0.209505i
$443$	1.52210	+	4.18193i	0.0723170	+	0.198689i	0.970585	−	0.240759i	$-0.0773963\pi$
$443$	1.52210	+	4.18193i	0.0723170	+	0.198689i	−0.898268	+	0.439448i	$0.855174\pi$
$444$	4.70582	+	3.39555i	0.223328	+	0.161146i
$445$	−26.8383	+	22.5200i	−1.27226	+	1.06755i
$446$	0.818494	+	4.64191i	0.0387568	+	0.219801i
$447$	2.57030	+	0.261666i	0.121571	+	0.0123764i
$448$	−14.0974	+	5.07853i	−0.666040	+	0.239938i
$449$	4.96216	−	2.86491i	0.234179	−	0.135203i	−0.378319	−	0.925675i	$-0.623498\pi$
$449$	4.96216	−	2.86491i	0.234179	−	0.135203i	0.612498	+	0.790472i	$0.290165\pi$
$450$	−0.441233	−	2.99736i	−0.0207999	−	0.141297i
$451$	15.5986	−	9.00585i	0.734509	−	0.424069i
$452$	6.87299	+	18.8834i	0.323278	+	0.888200i
$453$	−4.72753	−	6.95971i	−0.222119	−	0.326996i
$454$	−2.87869	+	0.507591i	−0.135104	+	0.0238224i
$455$	25.4934	−	4.40868i	1.19515	−	0.206682i
$456$	8.52048	−	8.28207i	0.399008	−	0.387844i
$457$	31.3062	+	26.2690i	1.46444	+	1.22881i	0.921115	+	0.389291i	$0.127280\pi$
$457$	31.3062	+	26.2690i	1.46444	+	1.22881i	0.543327	+	0.839521i	$0.317165\pi$
$458$	2.03913	−	3.53187i	0.0952821	−	0.165033i
$459$	16.3892	+	17.8473i	0.764983	+	0.833042i
$460$	−6.46090	+	3.73020i	−0.301241	+	0.173922i
$461$	25.5016	−	9.28183i	1.18773	−	0.432298i	0.328803	−	0.944399i	$-0.393355\pi$
$461$	25.5016	−	9.28183i	1.18773	−	0.432298i	0.858925	+	0.512101i	$0.171133\pi$
$462$	4.78470	+	1.37213i	0.222605	+	0.0638374i
$463$	−9.76642	+	8.19500i	−0.453884	+	0.380854i	−0.840875	−	0.541230i	$-0.817959\pi$
$463$	−9.76642	+	8.19500i	−0.453884	+	0.380854i	0.386991	+	0.922084i	$0.373515\pi$
$464$	17.9913	+	21.4412i	0.835227	+	0.995385i
$465$	−9.06202	+	6.15556i	−0.420241	+	0.285457i
$466$	−5.11222	+	1.86070i	−0.236819	+	0.0861951i
$467$	22.5443			1.04323			0.521613	−	0.853182i	$-0.325330\pi$
$467$	22.5443			1.04323			0.521613	+	0.853182i	$0.325330\pi$
$468$	14.5658	+	12.9438i	0.673304	+	0.598330i
$469$	12.6158	+	22.0183i	0.582543	+	1.01671i
$470$	2.74949	+	0.484810i	0.126825	+	0.0223626i
$471$	−22.8302	+	31.6399i	−1.05196	+	1.45789i
$472$	−5.48271	−	6.53404i	−0.252362	−	0.300754i
$473$	−19.9078	−	23.7252i	−0.915364	−	1.09089i
$474$	6.27865	+	0.639190i	0.288388	+	0.0293590i
$475$	−17.2242	−	3.03709i	−0.790300	−	0.139351i
$476$	23.4217	+	0.0771223i	1.07353	+	0.00353489i
$477$	−2.15650	−	3.99267i	−0.0987395	−	0.182812i
$478$	−2.15146			−0.0984053
$479$	−30.6612	+	11.1598i	−1.40095	+	0.509903i	−0.928460	−	0.371433i	$-0.878866\pi$
$479$	−30.6612	+	11.1598i	−1.40095	+	0.509903i	−0.472489	+	0.881337i	$0.656644\pi$
$480$	−1.29008	−	17.6218i	−0.0588837	−	0.804323i
$481$	−3.88141	−	4.62569i	−0.176977	−	0.210913i
$482$	−0.685664	+	0.575340i	−0.0312311	+	0.0262060i
$483$	−4.37709	−	4.53285i	−0.199164	−	0.206252i
$484$	1.09000	−	0.396726i	0.0495453	−	0.0180330i
$485$	−6.22115	+	3.59178i	−0.282488	+	0.163094i
$486$	4.34333	+	2.41394i	0.197017	+	0.109499i
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	−0.778223	−	0.627988i	$-0.783879\pi$
$487$	3.41485	−	5.91469i	0.154741	−	0.268020i	0.932965	+	0.359967i	$0.117212\pi$
$488$	9.36984	+	7.86223i	0.424153	+	0.355906i
$489$	−4.08635	−	16.1644i	−0.184791	−	0.730980i
$490$	2.22055	−	5.97813i	0.100314	−	0.270064i
$491$	−2.93823	+	0.518089i	−0.132601	+	0.0233810i	−0.239554	−	0.970883i	$-0.577001\pi$
$491$	−2.93823	+	0.518089i	−0.132601	+	0.0233810i	0.106954	+	0.994264i	$0.465890\pi$
$492$	7.56811	−	15.6464i	0.341197	−	0.705394i
$493$	−13.1272	−	36.0667i	−0.591219	−	1.62436i
$494$	−5.21442	+	3.01055i	−0.234608	+	0.135451i
$495$	15.3199	−	24.8770i	0.688576	−	1.11814i
$496$	−6.51752	+	3.76289i	−0.292645	+	0.168959i
$497$	9.98903	+	27.7284i	0.448069	+	1.24379i
$498$	−2.31233	+	3.20460i	−0.103618	+	0.143602i
$499$	5.31326	+	30.1330i	0.237854	+	1.34894i	0.836518	+	0.547939i	$0.184587\pi$
$499$	5.31326	+	30.1330i	0.237854	+	1.34894i	−0.598664	+	0.801000i	$0.704302\pi$
$500$	7.61374	−	6.38869i	0.340497	−	0.285711i
$501$	1.76854	−	17.3720i	0.0790124	−	0.776124i
$502$	2.48976	+	6.84055i	0.111123	+	0.305309i
$503$	4.53519	+	7.85518i	0.202214	+	0.350245i	0.949242	−	0.314548i	$-0.101853\pi$
$503$	4.53519	+	7.85518i	0.202214	+	0.350245i	−0.747027	+	0.664793i	$0.768520\pi$
$504$	9.37074	−	3.07832i	0.417406	−	0.137119i
$505$	−13.3111	+	23.0555i	−0.592335	+	1.02595i
$506$	1.47087	+	0.259355i	0.0653883	+	0.0115297i
$507$	1.25869	+	1.85301i	0.0559005	+	0.0822949i
$508$	30.2794	+	11.0208i	1.34343	+	0.488969i
$509$	−7.01260	−	2.55238i	−0.310828	−	0.113132i	0.181896	−	0.983318i	$-0.441777\pi$
$509$	−7.01260	−	2.55238i	−0.310828	−	0.113132i	−0.492724	+	0.870186i	$0.663999\pi$
$510$	−2.00513	+	7.07988i	−0.0887884	+	0.313502i
$511$	5.30075	+	14.7143i	0.234491	+	0.650920i
$512$		−	20.5900i		−	0.909956i
$513$	21.1287	−	19.4025i	0.932855	−	0.856642i
$514$	3.45607	+	1.99536i	0.152441	+	0.0880117i
$515$	31.7222	+	5.59348i	1.39785	+	0.246478i
$516$	−28.7550	−	8.14383i	−1.26587	−	0.358512i
$517$	6.71229	+	7.99940i	0.295206	+	0.351813i
$518$	−1.46665	+	0.253634i	−0.0644410	+	0.0111440i
$519$	−21.3523	+	1.56318i	−0.937264	+	0.0686162i
$520$	−2.11011	+	11.9670i	−0.0925345	+	0.524789i
$521$	7.87991	+	13.6484i	0.345225	+	0.597947i	0.985395	−	0.170286i	$-0.0544692\pi$
$521$	7.87991	+	13.6484i	0.345225	+	0.597947i	−0.640170	+	0.768234i	$0.721136\pi$
$522$	−4.88624	−	6.17061i	−0.213865	−	0.270080i
$523$	4.87781	+	2.81620i	0.213292	+	0.123144i	0.602840	−	0.797862i	$-0.294036\pi$
$523$	4.87781	+	2.81620i	0.213292	+	0.123144i	−0.389549	+	0.921006i	$0.627369\pi$
$524$	5.27292	−	29.9042i	0.230348	−	1.30637i
$525$	−11.7452	−	8.53386i	−0.512602	−	0.372448i
$526$	3.81019	+	1.38679i	0.166132	+	0.0604671i
$527$	10.1631	−	1.79203i	0.442712	−	0.0780622i
$528$	11.7441	−	16.2758i	0.511095	−	0.708314i
$529$	16.1706	+	13.5688i	0.703071	+	0.589946i
$530$	0.689016	−	1.19341i	0.0299290	−	0.0518385i
$531$	−12.7832	−	16.1433i	−0.554744	−	0.700561i
$532$	0.0913019	−	27.7280i	0.00395844	−	1.20216i
$533$	−11.6253	+	13.8545i	−0.503548	+	0.600105i
$534$	5.59869	−	3.80303i	0.242279	−	0.164573i
$535$	−6.54487	+	17.9819i	−0.282959	+	0.777424i
$536$	−11.7379	+	2.06971i	−0.507000	+	0.0893977i
$537$	−7.44961	+	26.3038i	−0.321474	+	1.13509i
$538$	−2.13561	−	5.86755i	−0.0920729	−	0.252968i
$539$	20.7349	−	11.7899i	0.893117	−	0.507829i
$540$	−1.25986	−	28.1640i	−0.0542156	−	1.21198i
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	0.856262	−	0.516542i	$-0.172781\pi$
$541$	−0.446747	−	0.773788i	−0.0192071	−	0.0332677i	−0.875469	+	0.483274i	$0.839448\pi$
$542$	1.03279	−	5.85722i	0.0443620	−	0.251589i
$543$	−15.8361	−	16.2920i	−0.679594	−	0.699156i
$544$	−5.69283	+	15.6409i	−0.244078	+	0.670599i
$545$	−8.24321	−	46.7496i	−0.353100	−	2.00253i
$546$	−4.98586	+	0.348509i	−0.213375	+	0.0149148i
$547$	4.87449	+	4.09018i	0.208418	+	0.174884i	0.741021	−	0.671481i	$-0.234342\pi$
$547$	4.87449	+	4.09018i	0.208418	+	0.174884i	−0.532603	+	0.846365i	$0.678786\pi$
$548$			24.7388i			1.05679i
$549$	22.0726	+	19.6147i	0.942035	+	0.837137i
$550$	3.44118			0.146733
$551$	−42.6978	+	15.5407i	−1.81899	+	0.662058i
$552$	2.69979	−	1.21260i	0.114911	−	0.0516118i
$553$	23.2312	−	19.3633i	0.987891	−	0.823411i
$554$	0.291117	−	0.799836i	0.0123684	−	0.0339818i
$555$	−0.884813	+	8.69136i	−0.0375582	+	0.368928i
$556$	−4.99831	+	5.95675i	−0.211975	+	0.252622i
$557$			17.2809i			0.732217i	0.930572	+	0.366109i	$0.119310\pi$
$557$			17.2809i			0.732217i	−0.930572	+	0.366109i	$0.880690\pi$
$558$	1.86207	−	1.00574i	0.0788279	−	0.0425762i
$559$	26.9320	+	15.5492i	1.13910	+	0.657662i
$560$	−19.6437	−	16.5935i	−0.830096	−	0.701204i
$561$	−22.7665	+	15.4646i	−0.961203	+	0.652917i
$562$	4.23820	−	3.55627i	0.178778	−	0.150012i
$563$	−0.323777	−	1.83623i	−0.0136456	−	0.0773878i	0.977225	−	0.212208i	$-0.0680654\pi$
$563$	−0.323777	−	1.83623i	−0.0136456	−	0.0773878i	−0.990870	+	0.134820i	$0.956954\pi$
$564$	9.69526	+	2.74584i	0.408244	+	0.115621i
$565$	−19.4463	+	23.1752i	−0.818113	+	0.974989i
$566$	0.348424			0.0146454
$567$	22.8241	−	6.78671i	0.958523	−	0.285015i
$568$	−13.8429			−0.580837
$569$	16.5138	−	19.6804i	0.692296	−	0.825046i	−0.299336	−	0.954148i	$-0.596765\pi$
$569$	16.5138	−	19.6804i	0.692296	−	0.825046i	0.991631	+	0.129102i	$0.0412095\pi$
$570$	8.38157	+	2.37378i	0.351066	+	0.0994269i
$571$	−0.379935	−	2.15472i	−0.0158998	−	0.0901722i	0.975825	−	0.218552i	$-0.0701334\pi$
$571$	−0.379935	−	2.15472i	−0.0158998	−	0.0901722i	−0.991725	+	0.128380i	$0.959022\pi$
$572$	−16.9547	+	14.2267i	−0.708914	+	0.594849i
$573$	−25.4645	+	17.2973i	−1.06379	+	0.722603i
$574$	1.51092	+	4.19415i	0.0630648	+	0.175060i
$575$	−3.77267	−	2.17815i	−0.157331	−	0.0908351i
$576$	0.482052	−	16.9837i	0.0200855	−	0.707655i
$577$			14.2718i			0.594142i	0.954855	+	0.297071i	$0.0960098\pi$
$577$			14.2718i			0.594142i	−0.954855	+	0.297071i	$0.903990\pi$
$578$	0.972385	−	1.15884i	0.0404459	−	0.0482015i
$579$	2.38996	−	23.4762i	0.0993234	−	0.975636i
$580$	−15.2732	+	41.9629i	−0.634187	+	1.74241i
$581$	3.22691	+	18.6598i	0.133875	+	0.774139i
$582$	1.26592	−	0.568586i	0.0524742	−	0.0235686i
$583$	4.84337	−	1.76284i	0.200592	−	0.0730095i
$584$	−7.34586			−0.303974
$585$	−5.91174	+	28.7341i	−0.244420	+	1.18801i
$586$			6.71248i			0.277290i
$587$	20.9075	+	17.5435i	0.862947	+	0.724098i	0.962601	−	0.270924i	$-0.0873292\pi$
$587$	20.9075	+	17.5435i	0.862947	+	0.724098i	−0.0996541	+	0.995022i	$0.531774\pi$
$588$	10.1585	−	20.6537i	0.418929	−	0.851744i
$589$	−2.12151	−	12.0317i	−0.0874154	−	0.495757i
$590$	2.13873	−	5.87610i	0.0880500	−	0.241915i
$591$	11.1328	+	11.4533i	0.457943	+	0.471125i
$592$	−1.04217	+	5.91043i	−0.0428328	+	0.242917i
$593$	9.81715	+	17.0038i	0.403142	+	0.698262i	0.994103	−	0.108438i	$-0.0345848\pi$
$593$	9.81715	+	17.0038i	0.403142	+	0.698262i	−0.590961	+	0.806700i	$0.701251\pi$
$594$	−3.43107	+	4.48138i	−0.140779	+	0.183873i
$595$	17.5299	+	30.5949i	0.718657	+	1.25427i
$596$	0.968498	+	2.66093i	0.0396712	+	0.108996i
$597$	0.126576	−	0.446928i	0.00518043	−	0.0182915i
$598$	−1.47692	+	0.260421i	−0.0603958	+	0.0106494i
$599$	6.60034	−	18.1343i	0.269682	−	0.740946i	−0.728740	−	0.684791i	$-0.759894\pi$
$599$	6.60034	−	18.1343i	0.269682	−	0.740946i	0.998422	−	0.0561554i	$-0.0178842\pi$
$600$	5.64070	−	3.83156i	0.230281	−	0.156423i
$601$	13.5997	−	16.2075i	0.554743	−	0.661116i	−0.413683	−	0.910421i	$-0.635758\pi$
$601$	13.5997	−	16.2075i	0.554743	−	0.661116i	0.968425	+	0.249305i	$0.0802021\pi$
$602$	6.65113	−	3.81089i	0.271080	−	0.155320i
$603$	−28.4674	+	4.19060i	−1.15928	+	0.170654i
$604$	4.61075	−	7.98605i	0.187609	−	0.324948i
$605$	1.33773	+	1.12249i	0.0543866	+	0.0456357i
$606$	3.00936	−	4.17061i	0.122247	−	0.169419i
$607$	−14.7116	+	2.59404i	−0.597123	+	0.105289i	−0.464038	−	0.885816i	$-0.653600\pi$
$607$	−14.7116	+	2.59404i	−0.597123	+	0.105289i	−0.133086	+	0.991105i	$0.542489\pi$
$608$	18.5167	+	6.73951i	0.750949	+	0.273323i
$609$	−37.5108	−	3.94358i	−1.52001	−	0.159802i
$610$	−1.55713	+	8.83091i	−0.0630463	+	0.357553i
$611$	−9.08063	−	5.24270i	−0.367363	−	0.212097i
$612$	−9.78771	+	24.6885i	−0.395645	+	0.997972i
$613$	−2.79443	−	4.84009i	−0.112866	−	0.195490i	0.804059	−	0.594550i	$-0.202670\pi$
$613$	−2.79443	−	4.84009i	−0.112866	−	0.195490i	−0.916925	+	0.399060i	$0.869336\pi$
$614$	1.26277	−	7.16153i	0.0509613	−	0.289016i
$615$	26.0964	−	1.91049i	1.05231	−	0.0770385i
$616$	1.90907	+	11.0393i	0.0769187	+	0.444787i
$617$	4.78146	+	5.69832i	0.192494	+	0.229406i	0.853655	−	0.520838i	$-0.174381\pi$
$617$	4.78146	+	5.69832i	0.192494	+	0.229406i	−0.661161	+	0.750244i	$0.729936\pi$
$618$	−5.98728	−	1.69568i	−0.240844	−	0.0682104i
$619$	15.1027	+	2.66302i	0.607030	+	0.107036i	0.468710	−	0.883352i	$-0.344719\pi$
$619$	15.1027	+	2.66302i	0.607030	+	0.107036i	0.138320	+	0.990388i	$0.455830\pi$
$620$	−10.3984	−	6.00351i	−0.417609	−	0.241107i
$621$	6.59813	−	2.74131i	0.264774	−	0.110005i
$622$		−	7.17613i		−	0.287737i
$623$	5.73710	−	31.9217i	0.229852	−	1.27892i
$624$	−5.49164	+	19.3904i	−0.219841	+	0.776236i
$625$	28.9459	+	10.5355i	1.15784	+	0.421418i
$626$	0.422875	+	0.153914i	0.0169015	+	0.00615164i
$627$	18.3079	+	26.9523i	0.731148	+	1.07637i
$628$	−42.1140	−	7.42583i	−1.68053	−	0.296323i
$629$	4.11492	−	7.12725i	0.164073	−	0.284182i
$630$	5.38938	+	4.82111i	0.214718	+	0.192078i
$631$	−12.0123	−	20.8060i	−0.478203	−	0.828272i	0.521485	−	0.853261i	$-0.325378\pi$
$631$	−12.0123	−	20.8060i	−0.478203	−	0.828272i	−0.999688	+	0.0249886i	$0.992045\pi$
$632$	4.85827	+	13.3480i	0.193252	+	0.530954i
$633$	2.29486	−	22.5420i	0.0912126	−	0.895965i
$634$	1.67384	−	1.40452i	0.0664767	−	0.0557806i
$635$	8.42380	+	47.7737i	0.334288	+	1.89584i
$636$	2.91026	−	4.03327i	0.115399	−	0.159929i
$637$	−15.5156	+	18.2454i	−0.614750	+	0.722909i
$638$	7.74232	−	4.47003i	0.306521	−	0.176970i
$639$	−33.4055	−	0.948154i	−1.32150	−	0.0375084i
$640$	22.1374	−	12.7810i	0.875056	−	0.505214i
$641$	−15.3856	−	42.2717i	−0.607696	−	1.66963i	−0.735248	−	0.677798i	$-0.762934\pi$
$641$	−15.3856	−	42.2717i	−0.607696	−	1.66963i	0.127552	−	0.991832i	$-0.459288\pi$
$642$	1.60969	−	3.32790i	0.0635295	−	0.131342i
$643$	5.46038	−	0.962813i	0.215337	−	0.0379696i	−0.0649390	−	0.997889i	$-0.520685\pi$
$643$	5.46038	−	0.962813i	0.215337	−	0.0379696i	0.280276	+	0.959920i	$0.409574\pi$
$644$	2.38348	−	6.48206i	0.0939222	−	0.255429i
$645$	−11.0273	−	43.6206i	−0.434198	−	1.71756i
$646$	−6.28635	−	5.27488i	−0.247333	−	0.207537i
$647$	−17.8595	+	30.9335i	−0.702127	+	1.21612i	0.265591	+	0.964086i	$0.414433\pi$
$647$	−17.8595	+	30.9335i	−0.702127	+	1.21612i	−0.967718	+	0.252035i	$0.918900\pi$
$648$	−0.634367	+	11.1661i	−0.0249203	+	0.438644i
$649$	20.2552	−	11.6943i	0.795086	−	0.459043i
$650$	−3.24695	+	1.18179i	−0.127356	+	0.0463538i
$651$	2.79562	−	9.74848i	0.109569	−	0.382073i
$652$	13.9988	−	11.7464i	0.548235	−	0.460023i
$653$	17.1210	+	20.4041i	0.669998	+	0.798473i	0.988784	−	0.149354i	$-0.0477195\pi$
$653$	17.1210	+	20.4041i	0.669998	+	0.798473i	−0.318786	+	0.947827i	$0.603275\pi$
$654$	0.669579	+	9.14612i	0.0261826	+	0.357642i
$655$	42.9578	−	15.6354i	1.67850	−	0.610925i
$656$	17.9755			0.701827
$657$	−17.7269	−	0.503145i	−0.691591	−	0.0196295i
$658$	−2.24255	+	1.28491i	−0.0874237	+	0.0500910i
$659$	27.7440	+	4.89202i	1.08075	+	0.190566i	0.685549	−	0.728027i	$-0.259562\pi$
$659$	27.7440	+	4.89202i	1.08075	+	0.190566i	0.395205	+	0.918593i	$0.370673\pi$
$660$	31.8568	+	3.24315i	1.24003	+	0.126239i
$661$	−21.3442	−	25.4370i	−0.830193	−	0.989386i	−0.999992	−	0.00390705i	$-0.998756\pi$
$661$	−21.3442	−	25.4370i	−0.830193	−	0.989386i	0.169799	−	0.985479i	$-0.445688\pi$
$662$	−0.609805	−	0.726737i	−0.0237007	−	0.0282454i
$663$	16.1705	−	22.4104i	0.628011	−	0.870346i
$664$	−8.75922	−	1.54449i	−0.339924	−	0.0599377i
$665$	36.2201	−	20.7530i	1.40455	−	0.804765i
$666$	0.340106	−	1.65309i	0.0131788	−	0.0640558i
$667$	−11.3175			−0.438215
$668$	17.9845	−	6.54584i	0.695843	−	0.253266i
$669$	−21.1860	+	14.3910i	−0.819097	+	0.556388i
$670$	−5.61671	−	6.69373i	−0.216992	−	0.258602i
$671$	−25.6927	+	21.5588i	−0.991857	+	0.832267i
$672$	11.3621	+	11.7664i	0.438303	+	0.453901i
$673$	2.51415	−	0.915077i	0.0969135	−	0.0352736i	−0.293108	−	0.956079i	$-0.594690\pi$
$673$	2.51415	−	0.915077i	0.0969135	−	0.0352736i	0.390022	+	0.920806i	$0.372467\pi$
$674$	6.95908	−	4.01783i	0.268054	−	0.154761i
$675$	13.8744	−	8.85988i	0.534028	−	0.341017i
$676$	−1.22760	+	2.12627i	−0.0472154	+	0.0817795i
$677$	−30.4165	−	25.5225i	−1.16900	−	0.980909i	−0.169013	−	0.985614i	$-0.554058\pi$
$677$	−30.4165	−	25.5225i	−1.16900	−	0.980909i	−0.999989	+	0.00470491i	$0.998502\pi$
$678$	4.19084	−	4.07358i	0.160948	−	0.156445i
$679$	2.29503	−	6.24152i	0.0880752	−	0.239528i
$680$	−16.3101	+	2.87591i	−0.625463	+	0.110286i
$681$	−8.92461	−	13.1385i	−0.341992	−	0.503470i
$682$	0.822144	+	2.25882i	0.0314815	+	0.0864947i
$683$	−16.9924	+	9.81058i	−0.650197	+	0.375392i	−0.788532	−	0.614994i	$-0.789158\pi$
$683$	−16.9924	+	9.81058i	−0.650197	+	0.375392i	0.138335	+	0.990386i	$0.455825\pi$
$684$	29.2276	+	11.5873i	1.11755	+	0.443050i
$685$	−32.2541	+	18.6219i	−1.23237	+	0.711507i
$686$	1.96426	+	5.56727i	0.0749958	+	0.212559i
$687$	22.0457	+	2.24433i	0.841096	+	0.0856267i
$688$	−5.36728	−	30.4394i	−0.204626	−	1.16049i
$689$	−3.96459	+	3.32668i	−0.151039	+	0.126737i
$690$	1.75952	+	1.26961i	0.0669838	+	0.0483332i
$691$	1.90749	+	5.24080i	0.0725645	+	0.199369i	0.970673	−	0.240406i	$-0.0772804\pi$
$691$	1.90749	+	5.24080i	0.0725645	+	0.199369i	−0.898108	+	0.439775i	$0.855058\pi$
$692$	−11.7328	−	20.3218i	−0.446013	−	0.772517i
$693$	3.85081	+	26.7706i	0.146280	+	1.01693i
$694$	−0.366866	+	0.635430i	−0.0139260	+	0.0241206i
$695$	−11.5288	−	2.03283i	−0.437311	−	0.0771097i
$696$	7.71389	−	15.9478i	0.292394	−	0.604499i
$697$	−23.1628	−	8.43059i	−0.877355	−	0.319331i
$698$	2.09446	+	0.762322i	0.0792765	+	0.0288543i
$699$	−20.6038	−	21.1969i	−0.779308	−	0.801741i
$700$	2.81474	−	15.6614i	0.106387	−	0.591947i
$701$			46.9342i			1.77268i	0.463033	+	0.886341i	$0.346761\pi$
$701$			46.9342i			1.77268i	−0.463033	+	0.886341i	$0.653239\pi$
$702$	1.69839	−	5.40675i	0.0641014	−	0.204065i
$703$	−8.43766	−	4.87149i	−0.318232	−	0.183732i
$704$	19.0052	+	3.35113i	0.716286	+	0.126301i
$705$	3.71804	+	14.7075i	0.140029	+	0.553915i
$706$	4.52564	+	5.39345i	0.170325	+	0.202985i
$707$	−4.19964	−	24.2847i	−0.157944	−	0.913320i
$708$	9.82740	−	20.3173i	0.369336	−	0.763570i
$709$	−3.01382	+	17.0922i	−0.113186	+	0.641911i	0.874446	+	0.485123i	$0.161225\pi$
$709$	−3.01382	+	17.0922i	−0.113186	+	0.641911i	−0.987632	+	0.156788i	$0.949886\pi$
$710$	−5.07428	−	8.78891i	−0.190434	−	0.329842i
$711$	10.8096	+	32.5438i	0.405392	+	1.22049i
$712$	13.1925	+	7.61670i	0.494410	+	0.285448i
$713$	0.528416	−	2.99680i	0.0197893	−	0.112231i
$714$	−2.77048	−	6.22305i	−0.103683	−	0.232892i
$715$	−31.3111	−	11.3963i	−1.17097	−	0.426198i
$716$	−29.5086	+	5.20315i	−1.10279	+	0.194451i
$717$	−4.78967	−	10.6639i	−0.178874	−	0.398252i
$718$	−7.96213	−	6.68102i	−0.297144	−	0.249334i
$719$	13.3361	−	23.0988i	0.497353	−	0.861441i	−0.502642	−	0.864495i	$-0.667639\pi$
$719$	13.3361	−	23.0988i	0.497353	−	0.861441i	0.999995	+	0.00305366i	$0.000972012\pi$
$720$	25.6543	−	13.8563i	0.956078	−	0.516393i
$721$	−25.8734	+	14.8246i	−0.963575	+	0.552098i
$722$	−2.35163	+	2.80257i	−0.0875187	+	0.104301i
$723$	−4.37820	−	2.11772i	−0.162827	−	0.0787588i
$724$	8.51707	−	23.4005i	0.316534	−	0.869671i
$725$	−25.6795	+	4.52798i	−0.953711	+	0.168165i
$726$	−0.235138	−	0.241906i	−0.00872677	−	0.00897798i
$727$	−11.6117	−	31.9029i	−0.430654	−	1.18321i	−0.945412	−	0.325878i	$-0.894340\pi$
$727$	−11.6117	−	31.9029i	−0.430654	−	1.18321i	0.514758	−	0.857336i	$-0.327882\pi$
$728$	−5.59251	−	9.76059i	−0.207272	−	0.361752i
$729$	−2.29564	+	26.9022i	−0.0850239	+	0.996379i
$730$	−2.69270	−	4.66390i	−0.0996614	−	0.172619i
$731$	−7.36001	+	41.7407i	−0.272220	+	1.54384i
$732$	−8.81919	+	31.1396i	−0.325967	+	1.15095i
$733$	5.22487	−	14.3552i	0.192985	−	0.530222i	−0.805027	−	0.593238i	$-0.797849\pi$
$733$	5.22487	−	14.3552i	0.192985	−	0.530222i	0.998013	+	0.0630153i	$0.0200717\pi$
$734$	−0.235454	−	1.33532i	−0.00869076	−	0.0492877i
$735$	34.5747	−	2.30238i	1.27531	−	0.0849245i
$736$	3.75977	+	3.15482i	0.138587	+	0.116288i
$737$		−	32.6826i		−	1.20388i
$738$	−5.05287	−	0.143416i	−0.185999	−	0.00527923i
$739$	−31.0643			−1.14272			−0.571359	−	0.820701i	$-0.693583\pi$
$739$	−31.0643			−1.14272			−0.571359	+	0.820701i	$0.693583\pi$
$740$	−8.99781	+	3.27494i	−0.330766	+	0.120389i
$741$	−26.5307	−	19.1436i	−0.974629	−	0.703259i
$742$	0.217385	+	1.25704i	0.00798044	+	0.0461474i
$743$	−10.8218	+	29.7328i	−0.397015	+	1.09079i	0.566716	+	0.823913i	$0.308214\pi$
$743$	−10.8218	+	29.7328i	−0.397015	+	1.09079i	−0.963731	+	0.266876i	$0.914008\pi$
$744$	3.86270	+	2.78719i	0.141614	+	0.102183i
$745$	−2.74025	+	3.26571i	−0.100395	+	0.119646i
$746$			7.76844i			0.284423i
$747$	−21.0318	−	4.32707i	−0.769512	−	0.158319i
$748$	−26.1239	−	15.0826i	−0.955183	−	0.551475i
$749$	−6.00399	−	16.6664i	−0.219381	−	0.608976i
$750$	−2.60220	−	1.25868i	−0.0950189	−	0.0459603i
$751$	−16.1329	+	13.5371i	−0.588698	+	0.493976i	−0.887790	−	0.460248i	$-0.847760\pi$
$751$	−16.1329	+	13.5371i	−0.588698	+	0.493976i	0.299093	+	0.954224i	$0.403316\pi$
$752$	1.80968	+	10.2632i	0.0659921	+	0.374260i
$753$	−28.3631	+	27.5695i	−1.03361	+	1.00469i
$754$	−5.77019	+	6.87664i	−0.210138	+	0.250433i
$755$	13.8828			0.505247
$756$	17.5891	+	19.2810i	0.639709	+	0.701243i
$757$	−13.1053			−0.476322			−0.238161	−	0.971226i	$-0.576545\pi$
$757$	−13.1053			−0.476322			−0.238161	+	0.971226i	$0.576545\pi$
$758$	−3.65782	+	4.35922i	−0.132858	+	0.158334i
$759$	1.98901	+	7.86793i	0.0721964	+	0.285588i
$760$	3.40467	+	19.3088i	0.123500	+	0.700405i
$761$	−7.76470	+	6.51536i	−0.281470	+	0.236182i	−0.772582	−	0.634915i	$-0.781035\pi$
$761$	−7.76470	+	6.51536i	−0.281470	+	0.236182i	0.491112	+	0.871097i	$0.336591\pi$
$762$	−0.684248	−	9.34649i	−0.0247877	−	0.338588i
$763$	33.5710	+	28.3583i	1.21535	+	1.02664i
$764$	−29.2197	−	16.8700i	−1.05713	−	0.610335i
$765$	−39.5561	+	5.82294i	−1.43015	+	0.210529i
$766$		−	8.72505i		−	0.315249i
$767$	−15.0958	+	17.9904i	−0.545077	+	0.649597i
$768$	13.3920	−	6.01499i	0.483243	−	0.217047i
$769$	7.15123	−	19.6478i	0.257880	−	0.708519i	−0.741418	−	0.671044i	$-0.765846\pi$
$769$	7.15123	−	19.6478i	0.257880	−	0.708519i	0.999298	−	0.0374752i	$-0.0119315\pi$
$770$	−6.30909	+	5.25865i	−0.227364	+	0.189509i
$771$	−2.19617	+	21.5726i	−0.0790931	+	0.776917i
$772$	24.3039	−	8.84590i	0.874717	−	0.318371i
$773$	21.1888			0.762108			0.381054	−	0.924553i	$-0.375561\pi$
$773$	21.1888			0.762108			0.381054	+	0.924553i	$0.375561\pi$
$774$	1.26587	+	8.59923i	0.0455007	+	0.309093i
$775$		−	7.01116i		−	0.251848i
$776$	2.39271	+	2.00772i	0.0858932	+	0.0720730i
$777$	−4.52229	−	6.70497i	−0.162236	−	0.240539i
$778$	−0.902204	−	5.11665i	−0.0323456	−	0.183441i
$779$	−9.98062	+	27.4215i	−0.357593	+	0.982478i
$780$	−31.1725	+	7.88039i	−1.11615	+	0.282163i
$781$	6.59139	−	37.3816i	0.235858	−	1.33762i
$782$	−1.02199	−	1.77013i	−0.0365462	−	0.0632998i
$783$	19.7073	−	37.9565i	0.704282	−	1.35645i
$784$	23.8041	+	0.156764i	0.850145	+	0.00559873i
$785$	−22.0192	−	60.4974i	−0.785900	−	2.15924i
$786$	−8.56202	+	2.16447i	−0.305397	+	0.0772042i
$787$	−21.4804	+	3.78757i	−0.765693	+	0.135012i	−0.542836	−	0.839839i	$-0.682650\pi$
$787$	−21.4804	+	3.78757i	−0.765693	+	0.135012i	−0.222857	+	0.974851i	$0.571538\pi$
$788$	−5.98751	+	16.4505i	−0.213296	+	0.586027i
$789$	1.60862	+	21.9730i	0.0572684	+	0.782258i
$790$	−6.69381	+	7.97737i	−0.238155	+	0.283822i
$791$	0.0922183	−	28.0063i	0.00327891	−	0.995789i
$792$	−12.4426	−	2.55994i	−0.442128	−	0.0909634i
$793$	16.8387	−	29.1655i	0.597960	−	1.03570i
$794$	−1.11264	−	0.933613i	−0.0394860	−	0.0331327i
$795$	7.44920	+	0.758356i	0.264196	+	0.0268961i
$796$	0.501380	−	0.0884069i	0.0177710	−	0.00313350i
$797$	14.4170	+	5.24735i	0.510676	+	0.185871i	0.584490	−	0.811401i	$-0.301295\pi$
$797$	14.4170	+	5.24735i	0.510676	+	0.185871i	−0.0738137	+	0.997272i	$0.523517\pi$
$798$	−7.36722	+	3.27985i	−0.260797	+	0.116106i
$799$	2.48156	−	14.0736i	0.0877913	−	0.497889i
$800$	9.79314	+	5.65407i	0.346240	+	0.199902i
$801$	31.3142	+	19.2841i	1.10643	+	0.681369i
$802$	−6.00818	−	10.4065i	−0.212156	−	0.367466i
$803$	3.49777	−	19.8368i	0.123434	−	0.700026i
$804$	−17.7208	−	26.0881i	−0.624966	−	0.920055i
$805$	10.2454	−	1.77177i	0.361102	−	0.0624467i
$806$	−1.55148	−	1.84898i	−0.0546485	−	0.0651275i
$807$	24.3288	−	23.6480i	0.856413	−	0.832450i
$808$	11.3996	+	2.01006i	0.401038	+	0.0707137i
$809$	−11.6471	−	6.72444i	−0.409489	−	0.236419i	0.281081	−	0.959684i	$-0.409307\pi$
$809$	−11.6471	−	6.72444i	−0.409489	−	0.236419i	−0.690570	+	0.723265i	$0.742640\pi$
$810$	−7.32188	+	3.69028i	−0.257265	+	0.129663i
$811$		−	3.07886i		−	0.108113i	−0.998538	−	0.0540566i	$-0.982785\pi$
$811$		−	3.07886i		−	0.108113i	0.998538	−	0.0540566i	$-0.0172152\pi$
$812$	−14.0110	−	38.8930i	−0.491691	−	1.36488i
$813$	31.3312	−	7.92051i	1.09883	−	0.277784i
$814$	1.80135	+	0.655637i	0.0631373	+	0.0229801i
$815$	25.8522	+	9.40944i	0.905564	+	0.329598i
$816$	−27.3936	+	2.00546i	−0.958968	+	0.0702051i
$817$	49.4151	+	8.71321i	1.72881	+	0.304837i
$818$	−0.159623	+	0.276474i	−0.00558107	+	0.00966670i
$819$	−12.8272	−	23.9371i	−0.448218	−	0.836430i
$820$	14.3395	+	24.8368i	0.500759	+	0.867340i
$821$	−1.54402	−	4.24217i	−0.0538868	−	0.148053i	0.909829	−	0.414984i	$-0.136213\pi$
$821$	−1.54402	−	4.24217i	−0.0538868	−	0.148053i	−0.963716	+	0.266931i	$0.913990\pi$
$822$	6.56330	−	2.94789i	0.228921	−	0.102819i
$823$	23.4546	−	19.6807i	0.817575	−	0.686027i	−0.134828	−	0.990869i	$-0.543048\pi$
$823$	23.4546	−	19.6807i	0.817575	−	0.686027i	0.952403	+	0.304842i	$0.0986036\pi$
$824$	−2.43208	−	13.7930i	−0.0847256	−	0.480503i
$825$	7.66093	+	17.0566i	0.266719	+	0.593835i
$826$	1.96198	+	5.44622i	0.0682660	+	0.189498i
$827$	12.8966	−	7.44587i	0.448459	−	0.258918i	−0.258720	−	0.965952i	$-0.583301\pi$
$827$	12.8966	−	7.44587i	0.448459	−	0.258918i	0.707179	+	0.707034i	$0.249967\pi$
$828$	5.85374	+	5.20191i	0.203432	+	0.180779i
$829$	21.8853	−	12.6355i	0.760107	−	0.438848i	−0.0692275	−	0.997601i	$-0.522053\pi$
$829$	21.8853	−	12.6355i	0.760107	−	0.438848i	0.829334	+	0.558753i	$0.188720\pi$
$830$	−2.23019	−	6.12739i	−0.0774109	−	0.212685i
$831$	4.61257	−	0.337682i	0.160008	−	0.0117141i
$832$	−19.0834	+	3.36491i	−0.661597	+	0.116657i
$833$	−30.5998	−	11.3662i	−1.06022	−	0.393815i
$834$	2.17595	+	0.616260i	0.0753469	+	0.0213394i
$835$	22.0721	+	18.5207i	0.763836	+	0.640934i
$836$	−17.8557	+	30.9270i	−0.617552	+	1.06963i
$837$	9.13048	+	6.99056i	0.315596	+	0.241629i
$838$	−0.648204	+	0.374241i	−0.0223918	+	0.0129279i
$839$	−16.6975	+	6.07738i	−0.576460	+	0.209814i	−0.613764	−	0.789490i	$-0.710345\pi$
$839$	−16.6975	+	6.07738i	−0.576460	+	0.209814i	0.0373037	+	0.999304i	$0.488123\pi$
$840$	−4.48649	+	15.6446i	−0.154799	+	0.539792i
$841$	−29.6792	+	24.9038i	−1.02342	+	0.858751i
$842$	−1.34572	−	1.60376i	−0.0463764	−	0.0552692i
$843$	27.0623	+	13.0900i	0.932077	+	0.450842i
$844$	23.3368	−	8.49391i	0.803287	−	0.292373i
$845$	−3.69626			−0.127155
$846$	−0.426810	−	2.89939i	−0.0146740	−	0.0996829i
$847$	−1.61659	−	0.00532307i	−0.0555468	−	0.000182903i
$848$	5.06571	+	0.893222i	0.173957	+	0.0306734i
$849$	0.775679	+	1.72700i	0.0266212	+	0.0592706i
$850$	−3.02710	−	3.60756i	−0.103829	−	0.123738i
$851$	−1.55987	−	1.85898i	−0.0534717	−	0.0637251i
$852$	−15.0073	−	33.4128i	−0.514141	−	1.14470i
$853$	13.7587	+	2.42603i	0.471089	+	0.0830656i	0.404152	−	0.914692i	$-0.367567\pi$
$853$	13.7587	+	2.42603i	0.471089	+	0.0830656i	0.0669361	+	0.997757i	$0.478678\pi$
$854$	−4.12692	−	7.20270i	−0.141220	−	0.246471i
$855$	6.89353	+	46.8288i	0.235754	+	1.60151i
$856$	8.32042			0.284386
$857$	20.0805	−	7.30871i	0.685937	−	0.249661i	0.0245424	−	0.999699i	$-0.492187\pi$
$857$	20.0805	−	7.30871i	0.685937	−	0.249661i	0.661395	+	0.750038i	$0.269965\pi$
$858$	5.79474	+	2.80290i	0.197829	+	0.0956893i
$859$	7.97036	+	9.49870i	0.271945	+	0.324092i	0.884682	−	0.466196i	$-0.154376\pi$
$859$	7.97036	+	9.49870i	0.271945	+	0.324092i	−0.612737	+	0.790287i	$0.709931\pi$
$860$	37.7765	−	31.6982i	1.28817	−	1.08090i
$861$	−17.4251	+	16.8263i	−0.593845	+	0.573438i
$862$	4.61598	−	1.68008i	0.157221	−	0.0572237i
$863$	9.03144	−	5.21430i	0.307434	−	0.177497i	−0.338344	−	0.941023i	$-0.609867\pi$
$863$	9.03144	−	5.21430i	0.307434	−	0.177497i	0.645778	+	0.763526i	$0.276533\pi$
$864$	−17.1275	+	7.11593i	−0.582690	+	0.242089i
$865$	17.6635	−	30.5941i	0.600577	−	1.04023i
$866$	2.41060	+	2.02274i	0.0819156	+	0.0687354i
$867$	7.90870	+	2.23986i	0.268594	+	0.0760696i
$868$	10.9528	−	1.89411i	0.371762	−	0.0642901i
$869$	−38.3583	+	6.76360i	−1.30122	+	0.229440i
$870$	12.9529	−	0.948268i	0.439144	−	0.0321493i
$871$	11.2241	+	30.8379i	0.380313	+	1.04490i
$872$	−17.8753	+	10.3203i	−0.605333	+	0.349489i
$873$	5.63652	+	5.00887i	0.190767	+	0.169525i
$874$	−2.09559	+	1.20989i	−0.0708843	+	0.0409250i
$875$	−13.0320	+	4.69473i	−0.440563	+	0.158711i
$876$	−7.96372	−	17.7308i	−0.269069	−	0.599067i
$877$	7.13778	+	40.4804i	0.241026	+	1.36693i	0.829544	+	0.558441i	$0.188600\pi$
$877$	7.13778	+	40.4804i	0.241026	+	1.36693i	−0.588518	+	0.808484i	$0.700289\pi$
$878$	−8.62121	+	7.23405i	−0.290952	+	0.244137i
$879$	−33.2711	+	14.9436i	−1.12221	+	0.504036i
$880$	11.3269	+	31.1203i	0.381829	+	1.04907i
$881$	14.4200	+	24.9761i	0.485821	+	0.841467i	0.999867	−	0.0162958i	$-0.00518736\pi$
$881$	14.4200	+	24.9761i	0.485821	+	0.841467i	−0.514046	+	0.857762i	$0.671854\pi$
$882$	−6.68999	−	0.233985i	−0.225264	−	0.00787867i
$883$	24.3484	−	42.1726i	0.819388	−	1.41922i	−0.0867455	−	0.996231i	$-0.527647\pi$
$883$	24.3484	−	42.1726i	0.819388	−	1.41922i	0.906134	−	0.422991i	$-0.139020\pi$
$884$	29.8291	+	5.25967i	1.00326	+	0.176902i
$885$	33.8869	−	2.48083i	1.13910	−	0.0833921i
$886$	1.33306	+	0.485193i	0.0447849	+	0.0163004i
$887$	−7.47224	−	2.71967i	−0.250893	−	0.0913177i	0.213512	−	0.976940i	$-0.431510\pi$
$887$	−7.47224	−	2.71967i	−0.250893	−	0.0913177i	−0.464405	+	0.885623i	$0.653732\pi$
$888$	3.68274	−	0.930994i	0.123585	−	0.0312421i
$889$	−34.3064	−	28.9796i	−1.15060	−	0.971943i
$890$			11.1679i			0.374350i
$891$	−29.8509	−	7.02982i	−1.00004	−	0.235508i
$892$	−24.3102	−	14.0355i	−0.813967	−	0.469944i
$893$	−16.6612	−	2.93782i	−0.557545	−	0.0983103i
$894$	0.590547	−	0.574024i	0.0197509	−	0.0191982i
$895$	−28.9961	−	34.5562i	−0.969233	−	1.15509i
$896$	−8.16665	+	22.2099i	−0.272829	+	0.741980i
$897$	−4.57880	−	6.74076i	−0.152882	−	0.225067i
$898$	0.317163	−	1.79872i	0.0105839	−	0.0600241i
$899$	−9.10736	−	15.7744i	−0.303748	−	0.526106i
$900$	15.3634	+	9.46116i	0.512113	+	0.315372i
$901$	−6.10863	−	3.52682i	−0.203508	−	0.117495i
$902$	0.997004	−	5.65429i	0.0331966	−	0.188267i
$903$	33.6962	+	24.4831i	1.12134	+	0.814746i
$904$	12.3609	+	4.49902i	0.411119	+	0.149635i
$905$	36.9204	−	6.51005i	1.22727	−	0.216402i
$906$	−2.66815	−	0.271628i	−0.0886433	−	0.00902422i
$907$	33.1849	+	27.8455i	1.10189	+	0.924593i	0.997551	−	0.0699485i	$-0.0222835\pi$
$907$	33.1849	+	27.8455i	1.10189	+	0.924593i	0.104337	+	0.994542i	$0.466728\pi$
$908$	8.70416	−	15.0761i	0.288858	−	0.500316i
$909$	27.3717	+	5.63144i	0.907861	+	0.186783i
$910$	4.14702	−	7.12854i	0.137472	−	0.236309i
$911$	−32.8056	+	39.0962i	−1.08690	+	1.29531i	−0.134346	+	0.990934i	$0.542893\pi$
$911$	−32.8056	+	39.0962i	−1.08690	+	1.29531i	−0.952551	+	0.304379i	$0.901551\pi$
$912$	2.37418	+	32.4301i	0.0786170	+	1.07387i
$913$	8.34149	−	22.9181i	0.276063	−	0.758477i
$914$	12.8292	−	2.26213i	0.424352	−	0.0748247i
$915$	−47.2379	+	11.9417i	−1.56164	+	0.394781i
$916$	8.30690	+	22.8230i	0.274468	+	0.754094i
$917$	−21.2805	+	36.5802i	−0.702745	+	1.20799i
$918$	7.71625	−	0.345170i	0.254674	−	0.0113923i
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	0.983980	+	0.178279i	$0.0570529\pi$
$919$	19.5951	+	33.9398i	0.646384	+	1.11957i	−0.337596	+	0.941291i	$0.609614\pi$
$920$	−0.848017	+	4.80935i	−0.0279583	+	0.158559i
$921$	38.3082	−	9.68428i	1.26230	−	0.319108i
$922$	2.95873	−	8.12904i	0.0974406	−	0.267716i
$923$	6.61849	+	37.5353i	0.217850	+	1.23549i
$924$	−24.5760	+	16.5758i	−0.808493	+	0.545303i
$925$	−4.28312	−	3.59396i	−0.140828	−	0.118169i
$926$			4.06400i			0.133551i
$927$	−4.92431	−	33.4516i	−0.161736	−	1.09869i
$928$	29.3781			0.964384
$929$	−28.7454	+	10.4625i	−0.943107	+	0.343263i	−0.767392	−	0.641178i	$-0.778446\pi$
$929$	−28.7454	+	10.4625i	−0.943107	+	0.343263i	−0.175715	+	0.984441i	$0.556224\pi$
$930$	−0.353677	+	3.47411i	−0.0115975	+	0.113921i
$931$	−13.4560	+	36.2259i	−0.441001	+	1.18725i
$932$	11.0813	−	30.4455i	0.362979	−	0.997275i
$933$	35.5693	−	15.9758i	1.16449	−	0.523026i
$934$	4.61930	−	5.50507i	0.151148	−	0.180131i
$935$		−	45.4133i		−	1.48517i
$936$	12.6194	−	1.85767i	0.412479	−	0.0607199i
$937$	4.39414	+	2.53696i	0.143550	+	0.0828787i	0.570055	−	0.821607i	$-0.306922\pi$
$937$	4.39414	+	2.53696i	0.143550	+	0.0828787i	−0.426505	+	0.904485i	$0.640255\pi$
$938$	7.96158	+	1.43089i	0.259955	+	0.0467202i
$939$	0.178533	+	2.43868i	0.00582621	+	0.0795832i
$940$	−12.7370	+	10.6876i	−0.415436	+	0.348592i
$941$	−2.52700	−	14.3313i	−0.0823778	−	0.467188i	−0.997892	−	0.0649013i	$-0.979327\pi$
$941$	−2.52700	−	14.3313i	−0.0823778	−	0.467188i	0.915514	−	0.402286i	$-0.131784\pi$
$942$	3.04822	+	12.0579i	0.0993163	+	0.392866i
$943$	−4.67201	+	5.56788i	−0.152142	+	0.181315i
$944$	23.3417			0.759709
$945$	−11.8983	+	37.4460i	−0.387051	+	1.21812i
$946$	−9.87254			−0.320984
$947$	−35.0139	+	41.7280i	−1.13780	+	1.35598i	−0.212310	+	0.977202i	$0.568099\pi$
$947$	−35.0139	+	41.7280i	−1.13780	+	1.35598i	−0.925489	+	0.378774i	$0.876346\pi$
$948$	−26.9512	+	26.1971i	−0.875335	+	0.850843i
$949$	3.51215	+	19.9184i	0.114009	+	0.646578i
$950$	−4.27084	+	3.58366i	−0.138564	+	0.116269i
$951$	10.6880	+	5.16977i	0.346583	+	0.167641i
$952$	9.89370	−	11.7123i	0.320657	−	0.379598i
$953$	19.6055	+	11.3192i	0.635084	+	0.366666i	0.782718	−	0.622376i	$-0.213833\pi$
$953$	19.6055	+	11.3192i	0.635084	+	0.366666i	−0.147634	+	0.989042i	$0.547166\pi$
$954$	−1.41683	−	0.291498i	−0.0458715	−	0.00943760i
$955$		−	50.7950i		−	1.64369i
$956$	8.23594	−	9.81521i	0.266369	−	0.317447i
$957$	39.3925	+	28.4243i	1.27338	+	0.918826i
$958$	−3.55736	+	9.77376i	−0.114933	+	0.315776i
$959$	11.8988	−	32.3598i	0.384232	−	1.04495i
$960$	22.7349	+	16.4047i	0.733765	+	0.529459i
$961$	−24.5283	+	8.92757i	−0.791235	+	0.287986i
$962$	−1.92484			−0.0620592
$963$	20.0787	+	0.569896i	0.647025	+	0.0183646i
$964$		−	5.33053i		−	0.171685i
$965$	29.8277	+	25.0284i	0.960189	+	0.805694i
$966$	−2.00373	+	0.140060i	−0.0644690	+	0.00450635i
$967$	5.14316	+	29.1683i	0.165393	+	0.937990i	0.948658	+	0.316303i	$0.102441\pi$
$967$	5.14316	+	29.1683i	0.165393	+	0.937990i	−0.783265	+	0.621687i	$0.786447\pi$
$968$	0.259695	−	0.713505i	0.00834690	−	0.0229329i
$969$	12.1505	−	42.9022i	0.390331	−	1.37822i
$970$	−0.397633	+	2.25509i	−0.0127672	+	0.0724065i
$971$	−7.12855	−	12.3470i	−0.228766	−	0.396234i	0.728677	−	0.684858i	$-0.240136\pi$
$971$	−7.12855	−	12.3470i	−0.228766	−	0.396234i	−0.957443	+	0.288623i	$0.906802\pi$
$972$	−27.6393	+	10.5741i	−0.886531	+	0.339163i
$973$	9.40313	−	5.38769i	0.301450	−	0.172722i
$974$	−0.744603	−	2.04578i	−0.0238586	−	0.0655510i
$975$	−13.0862	−	13.4629i	−0.419094	−	0.431158i
$976$	−32.9637	+	5.81238i	−1.05514	+	0.186050i
$977$	6.86194	−	18.8530i	0.219533	−	0.603162i	−0.780217	−	0.625508i	$-0.784892\pi$
$977$	6.86194	−	18.8530i	0.219533	−	0.603162i	0.999750	+	0.0223468i	$0.00711380\pi$
$978$	−4.78446	−	2.31423i	−0.152990	−	0.0740008i
$979$	−26.8499	+	31.9985i	−0.858126	+	1.02268i
$980$	18.7725	+	33.0152i	0.599666	+	1.05463i
$981$	−43.8431	+	23.6804i	−1.39980	+	0.756056i
$982$	−0.475528	+	0.823639i	−0.0151747	+	0.0262834i
$983$	−12.8242	−	10.7608i	−0.409029	−	0.343216i	0.414942	−	0.909848i	$-0.363802\pi$
$983$	−12.8242	−	10.7608i	−0.409029	−	0.343216i	−0.823971	+	0.566632i	$0.808246\pi$
$984$	−4.66146	−	10.3785i	−0.148602	−	0.330853i
$985$	−25.9551	+	4.57658i	−0.826997	+	0.145822i
$986$	−11.4968	−	4.18450i	−0.366133	−	0.133262i
$987$	−11.3613	−	8.25492i	−0.361633	−	0.262757i
$988$	6.22671	−	35.3134i	0.198098	−	1.12347i
$989$	10.8235	+	6.24897i	0.344168	+	0.198706i
$990$	−2.93566	−	8.83820i	−0.0933013	−	0.280896i
$991$	−11.0601	−	19.1566i	−0.351335	−	0.608531i	0.635148	−	0.772390i	$-0.280939\pi$
$991$	−11.0601	−	19.1566i	−0.351335	−	0.608531i	−0.986484	+	0.163859i	$0.947606\pi$
$992$	−1.37167	+	7.77913i	−0.0435506	+	0.246988i
$993$	2.24457	−	4.64046i	0.0712294	−	0.147261i
$994$	8.81770	+	3.24230i	0.279680	+	0.102840i
$995$	0.492673	+	0.587145i	0.0156188	+	0.0186138i
$996$	−5.76802	−	22.8166i	−0.182767	−	0.722971i
$997$	−43.9525	−	7.75001i	−1.39199	−	0.245445i	−0.573141	−	0.819457i	$-0.694275\pi$
$997$	−43.9525	−	7.75001i	−1.39199	−	0.245445i	−0.818847	+	0.574011i	$0.805387\pi$
$998$	8.44683	+	4.87678i	0.267380	+	0.154372i
$999$	8.95087	−	1.99441i	0.283193	−	0.0631003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.13	✓	132
3.2	odd	2		567.2.ba.a.143.10		132
7.5	odd	6		189.2.bd.a.47.10	yes	132
21.5	even	6		567.2.bd.a.467.13		132
27.4	even	9		567.2.bd.a.17.13		132
27.23	odd	18		189.2.bd.a.185.10	yes	132
189.131	even	18	inner	189.2.ba.a.131.13	yes	132
189.166	odd	18		567.2.ba.a.341.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.13	✓	132	1.1	even	1	trivial
189.2.ba.a.131.13	yes	132	189.131	even	18	inner
189.2.bd.a.47.10	yes	132	7.5	odd	6
189.2.bd.a.185.10	yes	132	27.23	odd	18
567.2.ba.a.143.10		132	3.2	odd	2
567.2.ba.a.341.10		132	189.166	odd	18
567.2.bd.a.17.13		132	27.4	even	9
567.2.bd.a.467.13		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.204899 - 0.244189i) q^{2} +(1.66650 + 0.471978i) q^{3} +(0.329652 + 1.86955i) q^{4} +(-2.18935 + 1.83708i) q^{5} +(0.456717 - 0.310234i) q^{6} +(0.468007 - 2.60403i) q^{7} +(1.07619 + 0.621337i) q^{8} +(2.55447 + 1.57311i) q^{9} +O(q^{10})\)	\(q+(0.204899 - 0.244189i) q^{2} +(1.66650 + 0.471978i) q^{3} +(0.329652 + 1.86955i) q^{4} +(-2.18935 + 1.83708i) q^{5} +(0.456717 - 0.310234i) q^{6} +(0.468007 - 2.60403i) q^{7} +(1.07619 + 0.621337i) q^{8} +(2.55447 + 1.57311i) q^{9} +0.911030i q^{10} +(-2.19030 + 2.61029i) q^{11} +(-0.333020 + 3.27120i) q^{12} +(1.17022 - 3.21516i) q^{13} +(-0.539981 - 0.647845i) q^{14} +(-4.51562 + 2.02818i) q^{15} +(-3.19557 + 1.16309i) q^{16} +4.66323 q^{17} +(0.907544 - 0.301446i) q^{18} -5.52060i q^{19} +(-4.15623 - 3.48749i) q^{20} +(2.00898 - 4.11874i) q^{21} +(0.188615 + 1.06969i) q^{22} +(0.470293 - 1.29212i) q^{23} +(1.50021 + 1.54340i) q^{24} +(0.550137 - 3.11998i) q^{25} +(-0.545329 - 0.944538i) q^{26} +(3.51457 + 3.82725i) q^{27} +(5.02264 + 0.0165384i) q^{28} +(-2.81504 - 7.73427i) q^{29} +(-0.429987 + 1.51824i) q^{30} +(2.17942 - 0.384290i) q^{31} +(-1.22079 + 3.35410i) q^{32} +(-4.88214 + 3.31629i) q^{33} +(0.955489 - 1.13871i) q^{34} +(3.75918 + 6.56089i) q^{35} +(-2.09891 + 5.29429i) q^{36} +(0.882419 - 1.52840i) q^{37} +(-1.34807 - 1.13116i) q^{38} +(3.46767 - 4.80576i) q^{39} +(-3.49759 + 0.616720i) q^{40} +(-4.96713 - 1.80789i) q^{41} +(-0.594112 - 1.33450i) q^{42} +(-1.57831 + 8.95103i) q^{43} +(-5.60210 - 3.23437i) q^{44} +(-8.48256 + 1.24869i) q^{45} +(-0.219159 - 0.379594i) q^{46} +(0.532155 - 3.01800i) q^{47} +(-5.87439 + 0.430058i) q^{48} +(-6.56194 - 2.43741i) q^{49} +(-0.649143 - 0.773618i) q^{50} +(7.77129 + 2.20094i) q^{51} +(6.39667 + 1.12790i) q^{52} +(-1.30996 - 0.756305i) q^{53} +(1.65470 - 0.0740197i) q^{54} -9.73859i q^{55} +(2.12164 - 2.51163i) q^{56} +(2.60560 - 9.20011i) q^{57} +(-2.46542 - 0.897340i) q^{58} +(-6.44995 - 2.34759i) q^{59} +(-5.28036 - 7.77358i) q^{60} +(9.69333 + 1.70919i) q^{61} +(0.352721 - 0.610930i) q^{62} +(5.29193 - 5.91570i) q^{63} +(-2.83176 - 4.90475i) q^{64} +(3.34449 + 9.18891i) q^{65} +(-0.190543 + 1.87167i) q^{66} +(-7.34743 + 6.16523i) q^{67} +(1.53724 + 8.71812i) q^{68} +(1.39360 - 1.93135i) q^{69} +(2.37235 + 0.426368i) q^{70} +(-9.64722 + 5.56983i) q^{71} +(1.77166 + 3.28015i) q^{72} +(-5.11937 + 2.95567i) q^{73} +(-0.192410 - 0.528643i) q^{74} +(2.38937 - 4.93981i) q^{75} +(10.3210 - 1.81988i) q^{76} +(5.77220 + 6.92523i) q^{77} +(-0.462992 - 1.83146i) q^{78} +(8.75642 + 7.34751i) q^{79} +(4.85952 - 8.41694i) q^{80} +(4.05066 + 8.03692i) q^{81} +(-1.45922 + 0.842484i) q^{82} +(-6.72578 + 2.44798i) q^{83} +(8.36244 + 2.39814i) q^{84} +(-10.2094 + 8.56673i) q^{85} +(1.86235 + 2.21946i) q^{86} +(-1.04087 - 14.2178i) q^{87} +(-3.97904 + 1.44825i) q^{88} +12.2586 q^{89} +(-1.43315 + 2.32720i) q^{90} +(-7.82471 - 4.55201i) q^{91} +(2.57071 + 0.453286i) q^{92} +(3.81339 + 0.388217i) q^{93} +(-0.627925 - 0.748331i) q^{94} +(10.1418 + 12.0865i) q^{95} +(-3.61752 + 5.01344i) q^{96} +(2.47531 + 0.436465i) q^{97} +(-1.93972 + 1.10293i) q^{98} +(-9.70132 + 3.22235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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