LMFDB - Embedded newform 322.2.o.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(5,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("322.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.o (of order $66$, degree $20$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	322.5
Dual form			322.2.o.b.129.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723734 - 0.690079i) q^{2} +(-0.290209 + 1.50575i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.209478 - 0.164735i) q^{5} +(0.829051 + 1.29003i) q^{6} +(0.478644 + 2.60210i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.602045 + 0.241023i) q^{9} +O(q^{10})$	\(q+(0.723734 - 0.690079i) q^{2} +(-0.290209 + 1.50575i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.209478 - 0.164735i) q^{5} +(0.829051 + 1.29003i) q^{6} +(0.478644 + 2.60210i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.602045 + 0.241023i) q^{9} +(-0.265286 + 0.0253318i) q^{10} +(-0.785235 + 0.823530i) q^{11} +(1.49023 + 0.361527i) q^{12} +(5.84432 + 2.66901i) q^{13} +(2.14206 + 1.55292i) q^{14} +(0.308842 - 0.267613i) q^{15} +(-0.995472 - 0.0950560i) q^{16} +(-1.19145 - 0.614236i) q^{17} +(0.602045 - 0.241023i) q^{18} +(2.52750 - 1.30302i) q^{19} +(-0.174516 + 0.201402i) q^{20} +(-4.05701 - 0.0344348i) q^{21} +1.13789i q^{22} +(-4.46895 + 1.74027i) q^{23} +(1.32802 - 0.766730i) q^{24} +(-1.16205 - 4.79004i) q^{25} +(6.07157 - 2.10139i) q^{26} +(-3.02479 + 4.70667i) q^{27} +(2.62192 - 0.354289i) q^{28} +(-1.57290 + 1.01084i) q^{29} +(0.0388453 - 0.406806i) q^{30} +(4.41703 + 1.52875i) q^{31} +(-0.786053 + 0.618159i) q^{32} +(-1.01215 - 1.42136i) q^{33} +(-1.28617 + 0.377652i) q^{34} +(0.328391 - 0.623930i) q^{35} +(0.269396 - 0.589895i) q^{36} +(3.12879 - 7.81534i) q^{37} +(0.930054 - 2.68721i) q^{38} +(-5.71494 + 8.02551i) q^{39} +(0.0126802 + 0.266191i) q^{40} +(10.7625 + 1.54741i) q^{41} +(-2.95996 + 2.77474i) q^{42} +(-8.41723 - 7.29357i) q^{43} +(0.785235 + 0.823530i) q^{44} +(-0.0864101 - 0.149667i) q^{45} +(-2.03341 + 4.34342i) q^{46} +(-9.16658 - 5.29233i) q^{47} +(0.432026 - 1.47134i) q^{48} +(-6.54180 + 2.49095i) q^{49} +(-4.14652 - 2.66481i) q^{50} +(1.27066 - 1.61577i) q^{51} +(2.94407 - 5.71071i) q^{52} +(-6.38608 - 4.54750i) q^{53} +(1.05883 + 5.49372i) q^{54} +(0.300153 - 0.0431555i) q^{55} +(1.65309 - 2.06574i) q^{56} +(1.22851 + 4.18393i) q^{57} +(-0.440801 + 1.81701i) q^{58} +(-0.672177 - 7.03936i) q^{59} +(-0.252615 - 0.321226i) q^{60} +(-0.832675 + 0.160485i) q^{61} +(4.25172 - 1.94169i) q^{62} +(-0.338998 + 1.68194i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.784575 - 1.52186i) q^{65} +(-1.71338 - 0.330227i) q^{66} +(-1.72326 + 0.418059i) q^{67} +(-0.670232 + 1.16088i) q^{68} +(-1.32347 - 7.23415i) q^{69} +(-0.192893 - 0.678175i) q^{70} +(7.08378 + 2.07998i) q^{71} +(-0.212103 - 0.612832i) q^{72} +(-0.626399 - 0.0298390i) q^{73} +(-3.12879 - 7.81534i) q^{74} +(7.54984 - 0.359643i) q^{75} +(-1.18128 - 2.58664i) q^{76} +(-2.51875 - 1.64908i) q^{77} +(1.40214 + 9.75210i) q^{78} +(9.57992 - 6.82183i) q^{79} +(0.192870 + 0.183901i) q^{80} +(-4.80122 - 4.57795i) q^{81} +(8.85699 - 6.30703i) q^{82} +(2.41023 + 16.7635i) q^{83} +(-0.227436 + 4.05078i) q^{84} +(0.148396 + 0.324943i) q^{85} +(-11.1250 + 0.529948i) q^{86} +(-1.06560 - 2.66175i) q^{87} +(1.13660 + 0.0541430i) q^{88} +(-3.48921 - 10.0814i) q^{89} +(-0.165820 - 0.0486891i) q^{90} +(-4.14768 + 16.4850i) q^{91} +(1.52565 + 4.54669i) q^{92} +(-3.58378 + 6.20729i) q^{93} +(-10.2863 + 2.49543i) q^{94} +(-0.744108 - 0.143415i) q^{95} +(-0.702672 - 1.36299i) q^{96} +(-0.122062 + 0.848961i) q^{97} +(-3.01557 + 6.31715i) q^{98} +(-0.671236 + 0.306543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 6 q^{3} + 8 q^{4} + 11 q^{7} - 16 q^{8} + 12 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 6 * q^3 + 8 * q^4 + 11 * q^7 - 16 * q^8 + 12 * q^9	$ 160 q + 8 q^{2} - 6 q^{3} + 8 q^{4} + 11 q^{7} - 16 q^{8} + 12 q^{9} - 27 q^{12} - 11 q^{14} + 8 q^{16} + 66 q^{17} + 12 q^{18} - 66 q^{21} - 18 q^{23} - 6 q^{24} - 2 q^{25} + 6 q^{26} - 22 q^{28} - 16 q^{29} - 22 q^{30} + 24 q^{31} + 8 q^{32} + 73 q^{35} + 20 q^{36} + 22 q^{37} - 33 q^{38} + 22 q^{42} - 110 q^{43} + 4 q^{46} - 162 q^{47} + 25 q^{49} + 4 q^{50} - 11 q^{51} + 60 q^{52} + 22 q^{53} - 54 q^{54} - 11 q^{56} - 44 q^{57} - 14 q^{58} - 36 q^{59} - 121 q^{63} - 16 q^{64} - 77 q^{65} + 32 q^{70} + 144 q^{71} - 32 q^{72} - 108 q^{73} - 22 q^{74} + 96 q^{75} - 17 q^{77} - 22 q^{78} - 44 q^{79} + 14 q^{81} - 27 q^{82} + 11 q^{84} - 2 q^{85} - 66 q^{86} - 108 q^{87} + 11 q^{88} + 198 q^{89} - 8 q^{92} - 50 q^{93} + 30 q^{94} - 28 q^{95} + 6 q^{96} - 45 q^{98} - 220 q^{99}+O(q^{100}) $ 160 * q + 8 * q^2 - 6 * q^3 + 8 * q^4 + 11 * q^7 - 16 * q^8 + 12 * q^9 - 27 * q^12 - 11 * q^14 + 8 * q^16 + 66 * q^17 + 12 * q^18 - 66 * q^21 - 18 * q^23 - 6 * q^24 - 2 * q^25 + 6 * q^26 - 22 * q^28 - 16 * q^29 - 22 * q^30 + 24 * q^31 + 8 * q^32 + 73 * q^35 + 20 * q^36 + 22 * q^37 - 33 * q^38 + 22 * q^42 - 110 * q^43 + 4 * q^46 - 162 * q^47 + 25 * q^49 + 4 * q^50 - 11 * q^51 + 60 * q^52 + 22 * q^53 - 54 * q^54 - 11 * q^56 - 44 * q^57 - 14 * q^58 - 36 * q^59 - 121 * q^63 - 16 * q^64 - 77 * q^65 + 32 * q^70 + 144 * q^71 - 32 * q^72 - 108 * q^73 - 22 * q^74 + 96 * q^75 - 17 * q^77 - 22 * q^78 - 44 * q^79 + 14 * q^81 - 27 * q^82 + 11 * q^84 - 2 * q^85 - 66 * q^86 - 108 * q^87 + 11 * q^88 + 198 * q^89 - 8 * q^92 - 50 * q^93 + 30 * q^94 - 28 * q^95 + 6 * q^96 - 45 * q^98 - 220 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	0.723734	−	0.690079i	0.511757	−	0.487960i
$2$	0.723734	−	0.690079i	0.511757	−	0.487960i
$3$	−0.290209	+	1.50575i	−0.167552	+	0.869345i	0.796703	+	0.604371i	$0.206575\pi$
$3$	−0.290209	+	1.50575i	−0.167552	+	0.869345i	−0.964256	+	0.264974i	$0.914637\pi$
$4$	0.0475819	−	0.998867i	0.0237910	−	0.499434i
$5$	−0.209478	−	0.164735i	−0.0936812	−	0.0736717i	0.570220	−	0.821492i	$-0.306858\pi$
$5$	−0.209478	−	0.164735i	−0.0936812	−	0.0736717i	−0.663901	+	0.747820i	$0.731100\pi$
$6$	0.829051	+	1.29003i	0.338459	+	0.526652i
$7$	0.478644	+	2.60210i	0.180910	+	0.983500i
$7$	0.478644	+	2.60210i	0.180910	+	0.983500i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.602045	+	0.241023i	0.200682	+	0.0803409i
$10$	−0.265286	+	0.0253318i	−0.0838909	+	0.00801061i
$11$	−0.785235	+	0.823530i	−0.236757	+	0.248304i	−0.831384	−	0.555698i	$-0.812451\pi$
$11$	−0.785235	+	0.823530i	−0.236757	+	0.248304i	0.594627	+	0.804002i	$0.297300\pi$
$12$	1.49023	+	0.361527i	0.430194	+	0.104364i
$13$	5.84432	+	2.66901i	1.62092	+	0.740251i	0.999080	−	0.0428903i	$-0.0136566\pi$
$13$	5.84432	+	2.66901i	1.62092	+	0.740251i	0.621844	+	0.783141i	$0.286384\pi$
$14$	2.14206	+	1.55292i	0.572490	+	0.415036i
$15$	0.308842	−	0.267613i	0.0797426	−	0.0690974i
$16$	−0.995472	−	0.0950560i	−0.248868	−	0.0237640i
$17$	−1.19145	−	0.614236i	−0.288969	−	0.148974i	0.307647	−	0.951501i	$-0.400458\pi$
$17$	−1.19145	−	0.614236i	−0.288969	−	0.148974i	−0.596617	+	0.802526i	$0.703489\pi$
$18$	0.602045	−	0.241023i	0.141903	−	0.0568096i
$19$	2.52750	−	1.30302i	0.579849	−	0.298933i	−0.143240	−	0.989688i	$-0.545752\pi$
$19$	2.52750	−	1.30302i	0.579849	−	0.298933i	0.723089	+	0.690755i	$0.242722\pi$
$20$	−0.174516	+	0.201402i	−0.0390229	+	0.0450348i
$21$	−4.05701	−	0.0344348i	−0.885312	−	0.00751428i
$22$			1.13789i			0.242599i
$23$	−4.46895	+	1.74027i	−0.931840	+	0.362870i
$23$	−4.46895	+	1.74027i	−0.931840	+	0.362870i
$24$	1.32802	−	0.766730i	0.271080	−	0.156508i
$25$	−1.16205	−	4.79004i	−0.232410	−	0.958008i
$26$	6.07157	−	2.10139i	1.19073	−	0.412116i
$27$	−3.02479	+	4.70667i	−0.582122	+	0.905799i
$28$	2.62192	−	0.354289i	0.495497	−	0.0669543i
$29$	−1.57290	+	1.01084i	−0.292080	+	0.187709i	−0.678472	−	0.734626i	$-0.737358\pi$
$29$	−1.57290	+	1.01084i	−0.292080	+	0.187709i	0.386392	+	0.922335i	$0.373721\pi$
$30$	0.0388453	−	0.406806i	0.00709214	−	0.0742723i
$31$	4.41703	+	1.52875i	0.793323	+	0.274572i	0.693522	−	0.720436i	$-0.256058\pi$
$31$	4.41703	+	1.52875i	0.793323	+	0.274572i	0.0998010	+	0.995007i	$0.468179\pi$
$32$	−0.786053	+	0.618159i	−0.138956	+	0.109276i
$33$	−1.01215	−	1.42136i	−0.176192	−	0.247427i
$34$	−1.28617	+	0.377652i	−0.220576	+	0.0647668i
$35$	0.328391	−	0.623930i	0.0555082	−	0.105463i
$36$	0.269396	−	0.589895i	0.0448993	−	0.0983158i
$37$	3.12879	−	7.81534i	0.514370	−	1.28483i	−0.413014	−	0.910725i	$-0.635524\pi$
$37$	3.12879	−	7.81534i	0.514370	−	1.28483i	0.927384	−	0.374110i	$-0.122052\pi$
$38$	0.930054	−	2.68721i	0.150875	−	0.435924i
$39$	−5.71494	+	8.02551i	−0.915123	+	1.28511i
$40$	0.0126802	+	0.266191i	0.00200492	+	0.0420885i
$41$	10.7625	+	1.54741i	1.68081	+	0.241665i	0.915594	−	0.402105i	$-0.131721\pi$
$41$	10.7625	+	1.54741i	1.68081	+	0.241665i	0.765220	+	0.643769i	$0.222630\pi$
$42$	−2.95996	+	2.77474i	−0.456731	+	0.428151i
$43$	−8.41723	−	7.29357i	−1.28361	−	1.11226i	−0.987586	−	0.157080i	$-0.949792\pi$
$43$	−8.41723	−	7.29357i	−1.28361	−	1.11226i	−0.296029	−	0.955179i	$-0.595662\pi$
$44$	0.785235	+	0.823530i	0.118379	+	0.124152i
$45$	−0.0864101	−	0.149667i	−0.0128813	−	0.0223110i
$46$	−2.03341	+	4.34342i	−0.299810	+	0.640402i
$47$	−9.16658	−	5.29233i	−1.33708	−	0.771965i	−0.350709	−	0.936484i	$-0.614059\pi$
$47$	−9.16658	−	5.29233i	−1.33708	−	0.771965i	−0.986374	+	0.164519i	$0.947393\pi$
$48$	0.432026	−	1.47134i	0.0623575	−	0.212370i
$49$	−6.54180	+	2.49095i	−0.934543	+	0.355851i
$50$	−4.14652	−	2.66481i	−0.586407	−	0.376861i
$51$	1.27066	−	1.61577i	0.177927	−	0.226253i
$52$	2.94407	−	5.71071i	0.408270	−	0.791933i
$53$	−6.38608	−	4.54750i	−0.877195	−	0.624648i	0.0501968	−	0.998739i	$-0.484015\pi$
$53$	−6.38608	−	4.54750i	−0.877195	−	0.624648i	−0.927392	+	0.374092i	$0.877955\pi$
$54$	1.05883	+	5.49372i	0.144088	+	0.747601i
$55$	0.300153	−	0.0431555i	0.0404727	−	0.00581909i
$56$	1.65309	−	2.06574i	0.220903	−	0.276047i
$57$	1.22851	+	4.18393i	0.162721	+	0.554175i
$58$	−0.440801	+	1.81701i	−0.0578800	+	0.238585i
$59$	−0.672177	−	7.03936i	−0.0875100	−	0.916447i	−0.927495	−	0.373836i	$-0.878042\pi$
$59$	−0.672177	−	7.03936i	−0.0875100	−	0.916447i	0.839985	−	0.542610i	$-0.182564\pi$
$60$	−0.252615	−	0.321226i	−0.0326124	−	0.0414701i
$61$	−0.832675	+	0.160485i	−0.106613	+	0.0205480i	−0.242279	−	0.970207i	$-0.577895\pi$
$61$	−0.832675	+	0.160485i	−0.106613	+	0.0205480i	0.135666	+	0.990755i	$0.456683\pi$
$62$	4.25172	−	1.94169i	0.539968	−	0.246595i
$63$	−0.338998	+	1.68194i	−0.0427098	+	0.211905i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.784575	−	1.52186i	−0.0973145	−	0.188764i
$66$	−1.71338	−	0.330227i	−0.210902	−	0.0406481i
$67$	−1.72326	+	0.418059i	−0.210530	+	0.0510741i	−0.339637	−	0.940557i	$-0.610304\pi$
$67$	−1.72326	+	0.418059i	−0.210530	+	0.0510741i	0.129107	+	0.991631i	$0.458789\pi$
$68$	−0.670232	+	1.16088i	−0.0812776	+	0.140777i
$69$	−1.32347	−	7.23415i	−0.159328	−	0.870890i
$70$	−0.192893	−	0.678175i	−0.0230552	−	0.0810574i
$71$	7.08378	+	2.07998i	0.840689	+	0.246849i	0.673603	−	0.739094i	$-0.264746\pi$
$71$	7.08378	+	2.07998i	0.840689	+	0.246849i	0.167087	+	0.985942i	$0.446564\pi$
$72$	−0.212103	−	0.612832i	−0.0249966	−	0.0722229i
$73$	−0.626399	−	0.0298390i	−0.0733144	−	0.00349240i	0.0108927	−	0.999941i	$-0.496533\pi$
$73$	−0.626399	−	0.0298390i	−0.0733144	−	0.00349240i	−0.0842071	+	0.996448i	$0.526836\pi$
$74$	−3.12879	−	7.81534i	−0.363715	−	0.908515i
$75$	7.54984	−	0.359643i	0.871780	−	0.0415280i
$76$	−1.18128	−	2.58664i	−0.135502	−	0.296708i
$77$	−2.51875	−	1.64908i	−0.287038	−	0.187930i
$78$	1.40214	+	9.75210i	0.158761	+	1.10421i
$79$	9.57992	−	6.82183i	1.07782	−	0.767516i	0.103946	−	0.994583i	$-0.466853\pi$
$79$	9.57992	−	6.82183i	1.07782	−	0.767516i	0.973879	+	0.227067i	$0.0729137\pi$
$80$	0.192870	+	0.183901i	0.0215635	+	0.0205608i
$81$	−4.80122	−	4.57795i	−0.533469	−	0.508661i
$82$	8.85699	−	6.30703i	0.978091	−	0.696495i
$83$	2.41023	+	16.7635i	0.264558	+	1.84004i	0.497397	+	0.867523i	$0.334289\pi$
$83$	2.41023	+	16.7635i	0.264558	+	1.84004i	−0.232839	+	0.972515i	$0.574802\pi$
$84$	−0.227436	+	4.05078i	−0.0248153	+	0.441976i
$85$	0.148396	+	0.324943i	0.0160958	+	0.0352450i
$86$	−11.1250	+	0.529948i	−1.19964	+	0.0571457i
$87$	−1.06560	−	2.66175i	−0.114245	−	0.285369i
$88$	1.13660	+	0.0541430i	0.121162	+	0.00577167i
$89$	−3.48921	−	10.0814i	−0.369856	−	1.06863i	−0.964373	−	0.264546i	$-0.914778\pi$
$89$	−3.48921	−	10.0814i	−0.369856	−	1.06863i	0.594517	−	0.804083i	$-0.297343\pi$
$90$	−0.165820	−	0.0486891i	−0.0174789	−	0.00513228i
$91$	−4.14768	+	16.4850i	−0.434795	+	1.72810i
$92$	1.52565	+	4.54669i	0.159060	+	0.474025i
$93$	−3.58378	+	6.20729i	−0.371620	+	0.643666i
$94$	−10.2863	+	2.49543i	−1.06095	+	0.257384i
$95$	−0.744108	−	0.143415i	−0.0763439	−	0.0147141i
$96$	−0.702672	−	1.36299i	−0.0717162	−	0.139110i
$97$	−0.122062	+	0.848961i	−0.0123935	+	0.0861989i	−0.995079	−	0.0990804i	$-0.968410\pi$
$97$	−0.122062	+	0.848961i	−0.0123935	+	0.0861989i	0.982686	+	0.185279i	$0.0593190\pi$
$98$	−3.01557	+	6.31715i	−0.304618	+	0.638128i
$99$	−0.671236	+	0.306543i	−0.0674618	+	0.0308088i
$100$	−4.83991	+	0.932816i	−0.483991	+	0.0932816i
$101$	−5.57730	−	7.09211i	−0.554962	−	0.705691i	0.424929	−	0.905227i	$-0.360299\pi$
$101$	−5.57730	−	7.09211i	−0.554962	−	0.705691i	−0.979891	+	0.199536i	$0.936057\pi$
$102$	−0.195392	−	2.04624i	−0.0193467	−	0.202608i
$103$	−1.96524	+	8.10083i	−0.193641	+	0.798199i	0.789259	+	0.614060i	$0.210465\pi$
$103$	−1.96524	+	8.10083i	−0.193641	+	0.798199i	−0.982900	+	0.184139i	$0.941050\pi$
$104$	−1.81011	−	6.16468i	−0.177496	−	0.604496i
$105$	0.844180	+	0.675545i	0.0823835	+	0.0659264i
$106$	−7.75996	+	1.11571i	−0.753714	+	0.108368i
$107$	0.403852	+	2.09538i	0.0390418	+	0.202568i	0.996212	−	0.0869576i	$-0.0277145\pi$
$107$	0.403852	+	2.09538i	0.0390418	+	0.202568i	−0.957170	+	0.289526i	$0.906502\pi$
$108$	4.55741	+	3.24532i	0.438537	+	0.312281i
$109$	−0.611602	+	1.18634i	−0.0585808	+	0.113631i	−0.916308	−	0.400474i	$-0.868845\pi$
$109$	−0.611602	+	1.18634i	−0.0585808	+	0.113631i	0.857727	+	0.514105i	$0.171876\pi$
$110$	0.187450	−	0.238363i	0.0178727	−	0.0227270i
$111$	10.8599	+	6.97926i	1.03078	+	0.662442i
$112$	−0.229132	−	2.63581i	−0.0216509	−	0.249061i
$113$	2.47778	−	8.43856i	0.233090	−	0.793833i	−0.757002	−	0.653413i	$-0.773337\pi$
$113$	2.47778	−	8.43856i	0.233090	−	0.793833i	0.990092	−	0.140420i	$-0.0448452\pi$
$114$	3.77636	+	2.18028i	0.353689	+	0.204202i
$115$	1.22283	+	0.371645i	0.114029	+	0.0346561i
$116$	0.934855	+	1.61922i	0.0867991	+	0.150340i
$117$	2.87525	+	3.01548i	0.265817	+	0.278781i
$118$	−5.34419	−	4.63077i	−0.491973	−	0.426297i
$119$	1.02802	−	3.39427i	0.0942384	−	0.311152i
$120$	−0.404497	−	0.0581579i	−0.0369253	−	0.00530906i
$121$	0.461792	+	9.69421i	0.0419811	+	0.881292i
$122$	−0.491888	+	0.690760i	−0.0445334	+	0.0625384i
$123$	−5.45337	+	15.7565i	−0.491714	+	1.42071i
$124$	1.73719	−	4.33929i	0.156004	−	0.389680i
$125$	−1.09919	+	2.40689i	−0.0983145	+	0.215279i
$126$	0.915329	+	1.45122i	0.0815440	+	0.129285i
$127$	17.0517	−	5.00682i	1.51309	−	0.444283i	0.583264	−	0.812283i	$-0.301775\pi$
$127$	17.0517	−	5.00682i	1.51309	−	0.444283i	0.929826	+	0.367999i	$0.119957\pi$
$128$	0.580057	+	0.814576i	0.0512703	+	0.0719990i
$129$	13.4250	−	10.5576i	1.18201	−	0.929542i
$130$	−1.61803	−	0.560005i	−0.141911	−	0.0491157i
$131$	−0.238941	+	2.50231i	−0.0208764	+	0.218627i	0.979014	+	0.203795i	$0.0653276\pi$
$131$	−0.238941	+	2.50231i	−0.0208764	+	0.218627i	−0.999890	+	0.0148325i	$0.995278\pi$
$132$	−1.46791	+	0.943370i	−0.127765	+	0.0821098i
$133$	4.60035	+	5.95312i	0.398901	+	0.516201i
$134$	−0.958691	+	1.49175i	−0.0828183	+	0.128868i
$135$	1.40898	−	0.487653i	0.121266	−	0.0419705i
$136$	0.316026	+	1.30268i	0.0270990	+	0.111704i
$137$	−4.21381	+	2.43284i	−0.360010	+	0.207852i	−0.669085	−	0.743186i	$-0.733314\pi$
$137$	−4.21381	+	2.43284i	−0.360010	+	0.207852i	0.309075	+	0.951038i	$0.399981\pi$
$138$	−5.94998	−	4.32230i	−0.506496	−	0.367939i
$139$		−	6.03490i		−	0.511874i	−0.966693	−	0.255937i	$-0.917616\pi$
$139$		−	6.03490i		−	0.511874i	0.966693	−	0.255937i	$-0.0823839\pi$
$140$	−0.607598	−	0.357707i	−0.0513514	−	0.0302317i
$141$	10.6291	−	12.2667i	0.895135	−	1.03304i
$142$	6.56212	−	3.38301i	0.550681	−	0.283896i
$143$	−6.78718	+	2.71718i	−0.567572	+	0.227222i
$144$	−0.576409	−	0.297159i	−0.0480340	−	0.0247633i
$145$	0.496008	+	0.0473631i	0.0411912	+	0.00393329i
$146$	−0.473937	+	0.410669i	−0.0392233	+	0.0339872i
$147$	−1.85226	−	10.5732i	−0.152772	−	0.872063i
$148$	−7.65762	−	3.49712i	−0.629452	−	0.287461i
$149$	−8.32255	−	2.01903i	−0.681810	−	0.165405i	−0.120128	−	0.992758i	$-0.538330\pi$
$149$	−8.32255	−	2.01903i	−0.681810	−	0.165405i	−0.561682	+	0.827353i	$0.689846\pi$
$150$	5.21589	−	5.47027i	0.425876	−	0.446646i
$151$	17.4993	−	1.67098i	1.42407	−	0.135982i	0.645606	−	0.763671i	$-0.276605\pi$
$151$	17.4993	−	1.67098i	1.42407	−	0.135982i	0.778464	+	0.627689i	$0.215999\pi$
$152$	−2.63992	−	1.05686i	−0.214126	−	0.0857229i
$153$	−0.569263	−	0.656965i	−0.0460222	−	0.0531124i
$154$	−2.96090	+	0.544644i	−0.238596	+	0.0438887i
$155$	−0.673431	−	1.04788i	−0.0540913	−	0.0841677i
$156$	7.74449	+	6.09034i	0.620056	+	0.487617i
$157$	0.331889	−	6.96721i	0.0264876	−	0.556044i	−0.946152	−	0.323724i	$-0.895065\pi$
$157$	0.331889	−	6.96721i	0.0264876	−	0.556044i	0.972639	−	0.232320i	$-0.0746318\pi$
$158$	2.22571	−	11.5481i	0.177068	−	0.918717i
$159$	8.70070	−	8.29610i	0.690010	−	0.657923i
$160$	0.266493			0.0210681
$161$	−6.66737	−	10.7957i	−0.525462	−	0.850817i
$162$	−6.63395			−0.521213
$163$	−9.86776	+	9.40889i	−0.772902	+	0.736961i	−0.969916	−	0.243440i	$-0.921724\pi$
$163$	−9.86776	+	9.40889i	−0.772902	+	0.736961i	0.197014	+	0.980401i	$0.436876\pi$
$164$	2.05775	−	10.6766i	0.160684	−	0.833705i
$165$	−0.0221259	+	0.464480i	−0.00172250	+	0.0361597i
$166$	13.3125	+	10.4691i	1.03325	+	0.812560i
$167$	2.27897	+	3.54614i	0.176352	+	0.274409i	0.918165	−	0.396198i	$-0.129670\pi$
$167$	2.27897	+	3.54614i	0.176352	+	0.274409i	−0.741814	+	0.670606i	$0.766034\pi$
$168$	2.63075	+	3.08863i	0.202967	+	0.238293i
$169$	18.5193	+	21.3724i	1.42456	+	1.64403i
$170$	0.331635	+	0.132767i	0.0254353	+	0.0101827i
$171$	1.83573	−	0.175291i	0.140382	−	0.0134048i
$172$	−7.68581	+	8.06065i	−0.586038	+	0.614619i
$173$	5.00594	+	1.21443i	0.380595	+	0.0923313i	0.421492	−	0.906832i	$-0.361507\pi$
$173$	5.00594	+	1.21443i	0.380595	+	0.0923313i	−0.0408974	+	0.999163i	$0.513022\pi$
$174$	−2.60803	−	1.19105i	−0.197714	−	0.0902931i
$175$	11.9079	−	5.31649i	0.900155	−	0.401889i
$176$	0.859960	−	0.745160i	0.0648220	−	0.0561685i
$177$	10.7946	+	1.03076i	0.811370	+	0.0774765i
$178$	−9.48224	−	4.88844i	−0.710724	−	0.366404i
$179$	5.09759	−	2.04077i	0.381012	−	0.152534i	−0.173247	−	0.984878i	$-0.555426\pi$
$179$	5.09759	−	2.04077i	0.381012	−	0.152534i	0.554259	+	0.832344i	$0.313002\pi$
$180$	−0.153609	+	0.0791908i	−0.0114493	+	0.00590254i
$181$	12.5785	−	14.5163i	0.934950	−	1.07899i	−0.0617722	−	0.998090i	$-0.519675\pi$
$181$	12.5785	−	14.5163i	0.934950	−	1.07899i	0.996722	−	0.0808996i	$-0.0257793\pi$
$182$	8.37413	+	14.7930i	0.620732	+	1.09653i
$183$		−	1.30037i		−	0.0961263i
$184$	4.24174	+	2.23777i	0.312705	+	0.164971i
$185$	−1.94287	+	1.12172i	−0.142843	+	0.0824703i
$186$	1.68982	+	6.96551i	0.123903	+	0.510736i
$187$	1.44141	−	0.498877i	0.105406	−	0.0364815i
$188$	−5.72250	+	8.90438i	−0.417356	+	0.649418i
$189$	−13.6950	−	5.61798i	−0.996165	−	0.408648i
$190$	−0.637504	+	0.409699i	−0.0462494	+	0.0297227i
$191$	−1.08307	+	11.3424i	−0.0783681	+	0.820708i	0.867775	+	0.496958i	$0.165550\pi$
$191$	−1.08307	+	11.3424i	−0.0783681	+	0.820708i	−0.946143	+	0.323750i	$0.895056\pi$
$192$	−1.44912	−	0.501546i	−0.104581	−	0.0361960i
$193$	−5.43458	+	4.27380i	−0.391190	+	0.307635i	−0.794311	−	0.607512i	$-0.792168\pi$
$193$	−5.43458	+	4.27380i	−0.391190	+	0.307635i	0.403121	+	0.915147i	$0.367925\pi$
$194$	0.497510	+	0.698655i	0.0357191	+	0.0501605i
$195$	2.51923	−	0.739714i	0.180406	−	0.0529720i
$196$	2.17686	+	6.65291i	0.155490	+	0.475208i
$197$	6.99675	−	15.3208i	0.498498	−	1.09156i	−0.478457	−	0.878111i	$-0.658804\pi$
$197$	6.99675	−	15.3208i	0.498498	−	1.09156i	0.976955	−	0.213447i	$-0.0684692\pi$
$198$	−0.274257	+	0.685062i	−0.0194906	+	0.0486852i
$199$	−1.39078	+	4.01840i	−0.0985898	+	0.284857i	−0.983501	−	0.180904i	$-0.942098\pi$
$199$	−1.39078	+	4.01840i	−0.0985898	+	0.284857i	0.884911	+	0.465760i	$0.154219\pi$
$200$	−2.85909	+	4.01503i	−0.202168	+	0.283905i
$201$	−0.129385	−	2.71613i	−0.00912612	−	0.191581i
$202$	−8.93059	−	1.28403i	−0.628354	−	0.0903437i
$203$	−3.38316	−	3.60900i	−0.237452	−	0.253302i
$204$	−1.55348	−	1.34610i	−0.108765	−	0.0942457i
$205$	−1.99958	−	2.09710i	−0.139657	−	0.146468i
$206$	4.16790	+	7.21902i	0.290392	+	0.502973i
$207$	−3.10995	−	0.0293980i	−0.216157	−	0.00204330i
$208$	−5.56415	−	3.21247i	−0.385805	−	0.222744i
$209$	−0.911607	+	3.10465i	−0.0630572	+	0.214753i
$210$	1.07714	−	0.0936361i	0.0743298	−	0.00646151i
$211$	−15.4926	−	9.95652i	−1.06656	−	0.685435i	−0.115144	−	0.993349i	$-0.536733\pi$
$211$	−15.4926	−	9.95652i	−1.06656	−	0.685435i	−0.951414	+	0.307914i	$0.900369\pi$
$212$	−4.84622	+	6.16246i	−0.332839	+	0.423240i
$213$	−5.18771	+	10.0628i	−0.355456	+	0.689489i
$214$	1.73826	+	1.23781i	0.118825	+	0.0846150i
$215$	0.561714	+	2.91445i	0.0383086	+	0.198764i
$216$	5.53788	−	0.796227i	0.376805	−	0.0541764i
$217$	−1.86377	+	12.2253i	−0.126521	+	0.829905i
$218$	0.376033	+	1.28065i	0.0254681	+	0.0867365i
$219$	0.226717	−	0.934539i	0.0153201	−	0.0631503i
$220$	−0.0288248	−	0.301867i	−0.00194337	−	0.0203519i
$221$	−5.32382	−	6.76979i	−0.358119	−	0.455386i
$222$	12.6759	−	2.44309i	0.850754	−	0.163969i
$223$	6.47601	−	2.95749i	0.433666	−	0.198048i	−0.186607	−	0.982435i	$-0.559749\pi$
$223$	6.47601	−	2.95749i	0.433666	−	0.198048i	0.620273	+	0.784386i	$0.287022\pi$
$224$	−1.98475	−	1.74951i	−0.132612	−	0.116894i
$225$	0.454900	−	3.16390i	0.0303267	−	0.210927i
$226$	−4.03002	−	7.81714i	−0.268073	−	0.519988i
$227$	−11.9102	−	2.29550i	−0.790507	−	0.152358i	−0.222011	−	0.975044i	$-0.571262\pi$
$227$	−11.9102	−	2.29550i	−0.790507	−	0.152358i	−0.568496	+	0.822686i	$0.692474\pi$
$228$	4.23765	−	1.02804i	0.280645	−	0.0680838i
$229$	−11.2802	+	19.5379i	−0.745417	+	1.29110i	0.204583	+	0.978849i	$0.434416\pi$
$229$	−11.2802	+	19.5379i	−0.745417	+	1.29110i	−0.950000	+	0.312251i	$0.898917\pi$
$230$	1.14147	−	0.574875i	0.0752660	−	0.0379061i
$231$	3.21406	−	3.31403i	0.211470	−	0.218047i
$232$	1.79397	+	0.526758i	0.117780	+	0.0345834i
$233$	9.26982	+	26.7834i	0.607286	+	1.75464i	0.654837	+	0.755770i	$0.272737\pi$
$233$	9.26982	+	26.7834i	0.607286	+	1.75464i	−0.0475512	+	0.998869i	$0.515142\pi$
$234$	4.16184	+	0.198253i	0.272068	+	0.0129602i
$235$	1.04836	+	2.61868i	0.0683876	+	0.170824i
$236$	−7.06337	+	0.336470i	−0.459786	+	0.0219023i
$237$	7.49178	+	16.4047i	0.486643	+	1.06560i
$238$	−1.59830	−	3.16596i	−0.103603	−	0.205219i
$239$	−0.304930	−	2.12084i	−0.0197243	−	0.137185i	0.977580	−	0.210565i	$-0.0675305\pi$
$239$	−0.304930	−	2.12084i	−0.0197243	−	0.137185i	−0.997304	+	0.0733800i	$0.976621\pi$
$240$	−0.332882	+	0.237044i	−0.0214874	+	0.0153011i
$241$	5.63588	+	5.37380i	0.363039	+	0.346157i	0.849541	−	0.527522i	$-0.176879\pi$
$241$	5.63588	+	5.37380i	0.363039	+	0.346157i	−0.486502	+	0.873679i	$0.661727\pi$
$242$	7.02399	+	6.69736i	0.451519	+	0.430522i
$243$	−5.38563	+	3.83509i	−0.345489	+	0.246021i
$244$	0.120683	+	0.839368i	0.00772593	+	0.0537350i
$245$	1.78071	+	0.555864i	0.113765	+	0.0355129i
$246$	6.92643	+	15.1668i	0.441613	+	0.966998i
$247$	18.2493	−	0.869322i	1.16118	−	0.0553136i
$248$	−1.73719	−	4.33929i	−0.110312	−	0.275545i
$249$	−25.9412	−	1.23573i	−1.64395	−	0.0783112i
$250$	0.865423	+	2.50048i	0.0547342	+	0.158144i
$251$	−29.1580	−	8.56155i	−1.84043	−	0.540400i	−0.840436	−	0.541911i	$-0.817701\pi$
$251$	−29.1580	−	8.56155i	−1.84043	−	0.540400i	−0.999999	+	0.00151075i	$0.999519\pi$
$252$	1.66391	+	0.418645i	0.104816	+	0.0263721i
$253$	2.07601	−	5.04683i	0.130518	−	0.317291i
$254$	8.88576	−	15.3906i	0.557542	−	0.965692i
$255$	−0.532348	+	0.129146i	−0.0333369	+	0.00808745i
$256$	0.981929	+	0.189251i	0.0613705	+	0.0118282i
$257$	0.632305	+	1.22650i	0.0394421	+	0.0765070i	0.907733	−	0.419548i	$-0.137812\pi$
$257$	0.632305	+	1.22650i	0.0394421	+	0.0765070i	−0.868291	+	0.496055i	$0.834781\pi$
$258$	2.43060	−	16.9052i	0.151323	−	1.05247i
$259$	21.8338	+	4.40065i	1.35669	+	0.273443i
$260$	−1.55747	+	0.711273i	−0.0965902	+	0.0441113i
$261$	−1.19059	+	0.229468i	−0.0736958	+	0.0142037i
$262$	1.55386	+	1.97589i	0.0959977	+	0.122071i
$263$	−2.32775	−	24.3773i	−0.143535	−	1.50317i	−0.724521	−	0.689253i	$-0.757939\pi$
$263$	−2.32775	−	24.3773i	−0.143535	−	1.50317i	0.580986	−	0.813913i	$-0.302667\pi$
$264$	−0.411378	+	1.69572i	−0.0253186	+	0.104365i
$265$	0.588607	+	2.00461i	0.0361578	+	0.123142i
$266$	7.43755	+	1.13387i	0.456026	+	0.0695221i
$267$	16.1927	−	2.32816i	0.990977	−	0.142481i
$268$	0.335590	+	1.74120i	0.0204994	+	0.106361i
$269$	−6.26921	−	4.46428i	−0.382240	−	0.272192i	0.372745	−	0.927934i	$-0.378417\pi$
$269$	−6.26921	−	4.46428i	−0.382240	−	0.272192i	−0.754985	+	0.655742i	$0.772356\pi$
$270$	0.683208	−	1.32524i	0.0415787	−	0.0806514i
$271$	−13.5856	+	17.2755i	−0.825266	+	1.04941i	0.172656	+	0.984982i	$0.444765\pi$
$271$	−13.5856	+	17.2755i	−0.825266	+	1.04941i	−0.997922	+	0.0644292i	$0.979477\pi$
$272$	1.12767	+	0.724709i	0.0683750	+	0.0439420i
$273$	−23.6186	−	11.0295i	−1.42946	−	0.667533i
$274$	−1.37082	+	4.66859i	−0.0828144	+	0.282040i
$275$	4.85723	+	2.80432i	0.292902	+	0.169107i
$276$	−7.28893	+	0.977760i	−0.438742	+	0.0588542i
$277$	0.829251	+	1.43631i	0.0498249	+	0.0862992i	0.889862	−	0.456229i	$-0.150800\pi$
$277$	0.829251	+	1.43631i	0.0498249	+	0.0862992i	−0.840037	+	0.542529i	$0.817467\pi$
$278$	−4.16456	−	4.36766i	−0.249774	−	0.261955i
$279$	2.29079	+	1.98498i	0.137146	+	0.118838i
$280$	−0.686585	+	0.160406i	−0.0410313	+	0.00958609i
$281$	−7.95973	−	1.14444i	−0.474838	−	0.0682714i	−0.0992586	−	0.995062i	$-0.531647\pi$
$281$	−7.95973	−	1.14444i	−0.474838	−	0.0682714i	−0.375579	+	0.926790i	$0.622556\pi$
$282$	−0.772309	−	16.2128i	−0.0459903	−	0.965456i
$283$	−17.3444	+	24.3568i	−1.03102	+	1.44786i	−0.142068	+	0.989857i	$0.545375\pi$
$283$	−17.3444	+	24.3568i	−1.03102	+	1.44786i	−0.888950	+	0.458005i	$0.848564\pi$
$284$	2.41469	−	6.97678i	0.143285	−	0.413996i
$285$	0.431894	−	1.07882i	0.0255832	−	0.0639037i
$286$	−3.03705	+	6.65020i	−0.179584	+	0.393235i
$287$	1.12488	+	28.7456i	0.0663997	+	1.69680i
$288$	−0.622230	+	0.182703i	−0.0366652	+	0.0107659i
$289$	−8.81870	−	12.3841i	−0.518747	−	0.728478i
$290$	0.391662	−	0.308007i	0.0229992	−	0.0180868i
$291$	−1.24290	−	0.430171i	−0.0728600	−	0.0252171i
$292$	−0.0596105	+	0.624269i	−0.00348844	+	0.0365326i
$293$	1.87505	−	1.20502i	0.109542	−	0.0703981i	−0.484723	−	0.874668i	$-0.661080\pi$
$293$	1.87505	−	1.20502i	0.109542	−	0.0703981i	0.594265	+	0.804270i	$0.297443\pi$
$294$	−8.63689	−	6.37398i	−0.503714	−	0.371738i
$295$	−1.01882	+	1.58532i	−0.0593182	+	0.0923009i
$296$	−7.95537	+	2.75338i	−0.462396	+	0.160037i
$297$	−1.50091	−	6.18685i	−0.0870918	−	0.358997i
$298$	−7.41660	+	4.28198i	−0.429632	+	0.248048i
$299$	−30.7628	−	1.75700i	−1.77906	−	0.101610i
$300$		−	7.55840i		−	0.436384i
$301$	14.9497	−	25.3934i	0.861687	−	1.46365i
$302$	11.5117	−	13.2852i	0.662424	−	0.764479i
$303$	12.2975	−	6.33981i	0.706474	−	0.364213i
$304$	−2.63992	+	1.05686i	−0.151410	+	0.0606153i
$305$	0.200864	+	0.103553i	0.0115014	+	0.00592941i
$306$	−0.865353	−	0.0826312i	−0.0494689	−	0.00472371i
$307$	6.07784	−	5.26648i	0.346881	−	0.300574i	−0.463942	−	0.885866i	$-0.653565\pi$
$307$	6.07784	−	5.26648i	0.346881	−	0.300574i	0.810823	+	0.585292i	$0.199020\pi$
$308$	−1.76706	+	2.43743i	−0.100687	+	0.138886i
$309$	−11.6275	−	5.31010i	−0.661465	−	0.302081i
$310$	−1.21050	−	0.293665i	−0.0687520	−	0.0166791i
$311$	5.21935	−	5.47389i	0.295962	−	0.310396i	−0.558917	−	0.829224i	$-0.688783\pi$
$311$	5.21935	−	5.47389i	0.295962	−	0.310396i	0.854879	+	0.518828i	$0.173631\pi$
$312$	9.80777	−	0.936528i	0.555255	−	0.0530205i
$313$	−1.20600	−	0.482810i	−0.0681672	−	0.0272900i	0.337328	−	0.941387i	$-0.390477\pi$
$313$	−1.20600	−	0.482810i	−0.0681672	−	0.0272900i	−0.405495	+	0.914097i	$0.632901\pi$
$314$	−4.56773	−	5.27144i	−0.257772	−	0.297484i
$315$	0.348087	−	0.296485i	0.0196125	−	0.0167050i
$316$	−6.35827	−	9.89366i	−0.357681	−	0.556562i
$317$	−8.71007	−	6.84967i	−0.489206	−	0.384716i	0.342865	−	0.939385i	$-0.388603\pi$
$317$	−8.71007	−	6.84967i	−0.489206	−	0.384716i	−0.832071	+	0.554669i	$0.812845\pi$
$318$	0.572028	−	12.0083i	0.0320777	−	0.673394i
$319$	0.402637	−	2.08908i	0.0225433	−	0.116966i
$320$	0.192870	−	0.183901i	0.0107818	−	0.0102804i
$321$	−3.27232			−0.182643
$322$	−12.2753	−	3.21217i	−0.684073	−	0.179007i
$323$	−3.81176			−0.212092
$324$	−4.80122	+	4.57795i	−0.266734	+	0.254331i
$325$	5.99328	−	31.0961i	0.332447	−	1.72490i
$326$	−0.648756	+	13.6191i	−0.0359313	+	0.754290i
$327$	−1.60884	−	1.26521i	−0.0889691	−	0.0699661i
$328$	−5.87846	−	9.14706i	−0.324584	−	0.505062i
$329$	9.38361	−	26.3855i	0.517335	−	1.45468i
$330$	0.304514	+	0.351428i	0.0167630	+	0.0193455i
$331$	−11.0161	−	4.41019i	−0.605501	−	0.242406i	0.0485939	−	0.998819i	$-0.484526\pi$
$331$	−11.0161	−	4.41019i	−0.605501	−	0.242406i	−0.654095	+	0.756413i	$0.726950\pi$
$332$	16.8592	−	1.60986i	0.925271	−	0.0883527i
$333$	3.76735	−	3.95108i	0.206449	−	0.216518i
$334$	4.09648	+	0.993796i	0.224150	+	0.0543781i
$335$	0.429854	+	0.196308i	0.0234855	+	0.0107254i
$336$	4.03537	+	0.419922i	0.220147	+	0.0229086i
$337$	−22.3324	+	19.3511i	−1.21652	+	1.05412i	−0.219610	+	0.975588i	$0.570478\pi$
$337$	−22.3324	+	19.3511i	−1.21652	+	1.05412i	−0.996911	+	0.0785337i	$0.974976\pi$
$338$	28.1517	+	2.68816i	1.53125	+	0.146217i
$339$	11.9873	+	6.17987i	0.651059	+	0.335644i
$340$	0.331635	−	0.132767i	0.0179855	−	0.00720029i
$341$	−4.72738	+	2.43713i	−0.256002	+	0.131978i
$342$	1.20761	−	1.39366i	0.0653003	−	0.0753606i
$343$	−9.61289	−	15.8301i	−0.519047	−	0.854745i
$344$			11.1376i			0.600498i
$345$	−0.914480	+	1.73342i	−0.0492339	+	0.0933239i
$346$	4.46102	−	2.57557i	0.239826	−	0.138464i
$347$	−0.987668	−	4.07122i	−0.0530208	−	0.218555i	0.939138	−	0.343541i	$-0.111626\pi$
$347$	−0.987668	−	4.07122i	−0.0530208	−	0.218555i	−0.992158	+	0.124986i	$0.960111\pi$
$348$	−2.70944	+	0.937745i	−0.145241	+	0.0502684i
$349$	−5.01163	+	7.79825i	−0.268267	+	0.417431i	−0.949084	−	0.315022i	$-0.897988\pi$
$349$	−5.01163	+	7.79825i	−0.268267	+	0.417431i	0.680818	+	0.732453i	$0.261625\pi$
$350$	4.94938	−	12.0651i	0.264555	−	0.644909i
$351$	−30.2400	+	19.4341i	−1.61409	+	1.03731i
$352$	0.108163	−	1.13274i	0.00576513	−	0.0603752i
$353$	24.1466	+	8.35723i	1.28520	+	0.444811i	0.882409	−	0.470483i	$-0.155920\pi$
$353$	24.1466	+	8.35723i	1.28520	+	0.444811i	0.402787	+	0.915294i	$0.368042\pi$
$354$	8.52371	−	6.70312i	0.453030	−	0.356267i
$355$	−1.14125	−	1.60266i	−0.0605711	−	0.0850601i
$356$	−10.2360	+	3.00557i	−0.542508	+	0.159295i
$357$	4.81258	+	2.53299i	0.254709	+	0.134060i
$358$	2.28101	−	4.99471i	0.120555	−	0.263979i
$359$	10.7045	−	26.7385i	0.564960	−	1.41120i	−0.320840	−	0.947134i	$-0.603965\pi$
$359$	10.7045	−	26.7385i	0.564960	−	1.41120i	0.885800	−	0.464068i	$-0.153611\pi$
$360$	−0.0565240	+	0.163315i	−0.00297908	+	0.00860747i
$361$	−6.33067	+	8.89018i	−0.333193	+	0.467904i
$362$	−0.913946	−	19.1861i	−0.0480360	−	1.00840i
$363$	−14.7311	−	2.11801i	−0.773180	−	0.111167i
$364$	16.2690	+	4.92737i	0.852726	+	0.258264i
$365$	0.126301	+	0.109440i	0.00661089	+	0.00572837i
$366$	−0.897360	−	0.941124i	−0.0469058	−	0.0491934i
$367$	−2.15440	−	3.73153i	−0.112459	−	0.194784i	0.804302	−	0.594220i	$-0.202539\pi$
$367$	−2.15440	−	3.73153i	−0.112459	−	0.194784i	−0.916761	+	0.399436i	$0.869206\pi$
$368$	4.61413	−	1.30759i	0.240528	−	0.0681626i
$369$	6.10653	+	3.52560i	0.317893	+	0.183536i
$370$	−0.632049	+	2.15256i	−0.0328587	+	0.111906i
$371$	8.77638	−	18.7938i	0.455647	−	0.975726i
$372$	6.02973	+	3.87507i	0.312627	+	0.200913i
$373$	−19.2334	+	24.4573i	−0.995869	+	1.26635i	−0.0321350	+	0.999484i	$0.510231\pi$
$373$	−19.2334	+	24.4573i	−0.995869	+	1.26635i	−0.963734	+	0.266866i	$0.914012\pi$
$374$	0.698933	−	1.35574i	0.0361410	−	0.0701037i
$375$	−3.30518	−	2.35361i	−0.170679	−	0.121540i
$376$	2.00316	+	10.3934i	0.103305	+	0.535997i
$377$	−11.8905	+	1.70959i	−0.612391	+	0.0880486i
$378$	−13.7884	+	5.38471i	−0.709198	+	0.276960i
$379$	−7.38000	−	25.1340i	−0.379085	−	1.29105i	−0.899421	−	0.437084i	$-0.856011\pi$
$379$	−7.38000	−	25.1340i	−0.379085	−	1.29105i	0.520336	−	0.853962i	$-0.325807\pi$
$380$	−0.178659	+	0.736441i	−0.00916500	+	0.0377786i
$381$	2.59046	+	27.1285i	0.132713	+	1.38984i
$382$	7.04330	+	8.95629i	0.360367	+	0.458244i
$383$	−3.51186	+	0.676855i	−0.179447	+	0.0345857i	−0.278183	−	0.960528i	$-0.589732\pi$
$383$	−3.51186	+	0.676855i	−0.179447	+	0.0345857i	0.0987358	+	0.995114i	$0.468520\pi$
$384$	−1.39488	+	0.637023i	−0.0711824	+	0.0325079i
$385$	0.255961	+	0.760371i	0.0130450	+	0.0387521i
$386$	−0.983930	+	6.84339i	−0.0500807	+	0.348319i
$387$	−3.30964	−	6.41980i	−0.168238	−	0.326337i
$388$	0.842192	+	0.162319i	0.0427558	+	0.00824050i
$389$	26.6146	−	6.45663i	1.34941	−	0.327364i	0.505030	−	0.863102i	$-0.331482\pi$
$389$	26.6146	−	6.45663i	1.34941	−	0.327364i	0.844384	+	0.535738i	$0.179966\pi$
$390$	1.31279	−	2.27383i	0.0664759	−	0.115140i
$391$	6.39347	+	0.671545i	0.323332	+	0.0339615i
$392$	6.16651	+	3.31273i	0.311456	+	0.167318i
$393$	−3.69850	−	1.08598i	−0.186565	−	0.0547803i
$394$	−5.50874	−	15.9165i	−0.277526	−	0.801860i
$395$	−3.13057	−	0.149128i	−0.157516	−	0.00750342i
$396$	0.274257	+	0.685062i	0.0137820	+	0.0344256i
$397$	−12.3877	+	0.590097i	−0.621718	+	0.0296161i	−0.356078	−	0.934456i	$-0.615886\pi$
$397$	−12.3877	+	0.590097i	−0.621718	+	0.0296161i	−0.265640	+	0.964072i	$0.585583\pi$
$398$	1.76646	+	3.86800i	0.0885444	+	0.193885i
$399$	−10.2990	+	5.19932i	−0.515593	+	0.260292i
$400$	0.701467	+	4.87881i	0.0350734	+	0.243941i
$401$	−13.1411	+	9.35774i	−0.656235	+	0.467303i	−0.859035	−	0.511917i	$-0.828935\pi$
$401$	−13.1411	+	9.35774i	−0.656235	+	0.467303i	0.202799	+	0.979220i	$0.434996\pi$
$402$	−1.96798	−	1.87647i	−0.0981541	−	0.0935898i
$403$	21.7343	+	20.7236i	1.08266	+	1.03232i
$404$	−7.34945	+	5.23352i	−0.365649	+	0.260377i
$405$	0.251599	+	1.74991i	0.0125020	+	0.0869536i
$406$	−4.93901	−	0.277307i	−0.245119	−	0.0137625i
$407$	3.97934	+	8.71353i	0.197248	+	0.431914i
$408$	−2.05322	+	0.0978069i	−0.101650	+	0.00484216i
$409$	12.0035	+	29.9834i	0.593537	+	1.48258i	0.855654	+	0.517548i	$0.173155\pi$
$409$	12.0035	+	29.9834i	0.593537	+	1.48258i	−0.262118	+	0.965036i	$0.584421\pi$
$410$	−2.89433	−	0.137874i	−0.142941	−	0.00680911i
$411$	−2.44036	−	7.05097i	−0.120374	−	0.347799i
$412$	7.99815	+	2.34847i	0.394040	+	0.115701i
$413$	17.9954	−	5.11842i	0.885493	−	0.251861i
$414$	−2.27106	+	2.12484i	−0.111617	+	0.104430i
$415$	2.25665	−	3.90864i	0.110775	−	0.191867i
$416$	−6.24382	+	1.51473i	−0.306129	+	0.0742660i
$417$	9.08705	+	1.75139i	0.444995	+	0.0857657i
$418$	1.48269	+	2.87602i	0.0725208	+	0.140671i
$419$	−1.86863	+	12.9966i	−0.0912885	+	0.634926i	0.891886	+	0.452259i	$0.149382\pi$
$419$	−1.86863	+	12.9966i	−0.0912885	+	0.634926i	−0.983175	+	0.182666i	$0.941527\pi$
$420$	0.714947	−	0.811080i	0.0348859	−	0.0395767i
$421$	−13.5017	+	6.16601i	−0.658031	+	0.300513i	−0.716304	−	0.697788i	$-0.754168\pi$
$421$	−13.5017	+	6.16601i	−0.658031	+	0.300513i	0.0582732	+	0.998301i	$0.481441\pi$
$422$	−18.0833	+	3.48528i	−0.880283	+	0.169661i
$423$	−4.24313	−	5.39557i	−0.206308	−	0.262342i
$424$	0.745216	+	7.80426i	0.0361909	+	0.379008i
$425$	−1.55769	+	6.42088i	−0.0755590	+	0.311458i
$426$	3.18957	+	10.8627i	0.154535	+	0.526299i
$427$	−0.816152	−	2.08988i	−0.0394963	−	0.101137i
$428$	2.11223	−	0.303692i	0.102098	−	0.0146795i
$429$	−2.12168	−	11.0083i	−0.102436	−	0.531487i
$430$	2.41773	+	1.72166i	0.116593	+	0.0830258i
$431$	8.34013	−	16.1776i	0.401730	−	0.779248i	−0.598023	−	0.801479i	$-0.704047\pi$
$431$	8.34013	−	16.1776i	0.401730	−	0.779248i	0.999753	+	0.0222316i	$0.00707711\pi$
$432$	3.45849	−	4.39783i	0.166397	−	0.211591i
$433$	14.3861	+	9.24539i	0.691352	+	0.444305i	0.838566	−	0.544800i	$-0.183394\pi$
$433$	14.3861	+	9.24539i	0.691352	+	0.444305i	−0.147214	+	0.989105i	$0.547031\pi$
$434$	7.08753	+	10.1340i	0.340212	+	0.486447i
$435$	−0.215263	+	0.733119i	−0.0103211	+	0.0351504i
$436$	1.15590	+	0.667357i	0.0553574	+	0.0319606i
$437$	−9.02767	+	10.2216i	−0.431852	+	0.488967i
$438$	−0.480823	−	0.832811i	−0.0229746	−	0.0397932i
$439$	3.89545	+	4.08543i	0.185920	+	0.194987i	0.810097	−	0.586296i	$-0.199414\pi$
$439$	3.89545	+	4.08543i	0.185920	+	0.194987i	−0.624178	+	0.781283i	$0.714566\pi$
$440$	−0.229173	−	0.198580i	−0.0109254	−	0.00946692i
$441$	−4.53884	−	0.0770543i	−0.216135	−	0.00366925i
$442$	−8.52473	−	1.22567i	−0.405480	−	0.0582992i
$443$	0.732075	+	15.3681i	0.0347819	+	0.730163i	0.947150	+	0.320791i	$0.103949\pi$
$443$	0.732075	+	15.3681i	0.0347819	+	0.730163i	−0.912368	+	0.409371i	$0.865748\pi$
$444$	7.48809	−	10.5156i	0.355369	−	0.499046i
$445$	−0.929851	+	2.68663i	−0.0440792	+	0.127358i
$446$	2.64600	−	6.60940i	0.125292	−	0.312964i
$447$	5.45543	−	11.9457i	0.258033	−	0.565014i
$448$	−2.64373	+	0.103455i	−0.124904	+	0.00488780i
$449$	27.4896	−	8.07167i	1.29731	−	0.380926i	0.441058	−	0.897478i	$-0.354603\pi$
$449$	27.4896	−	8.07167i	1.29731	−	0.380926i	0.856255	+	0.516553i	$0.172785\pi$
$450$	−1.85412	−	2.60374i	−0.0874038	−	0.122742i
$451$	−9.72539	+	7.64813i	−0.457951	+	0.360136i
$452$	−8.31110	−	2.87650i	−0.390921	−	0.135299i
$453$	−2.56238	+	26.8344i	−0.120391	+	1.26079i
$454$	−10.2039	+	6.55764i	−0.478892	+	0.307765i
$455$	3.58450	−	2.76997i	0.168044	−	0.129858i
$456$	2.35750	−	3.66834i	0.110400	−	0.171786i
$457$	15.1847	−	5.25549i	0.710312	−	0.245841i	0.0520653	−	0.998644i	$-0.483420\pi$
$457$	15.1847	−	5.25549i	0.710312	−	0.245841i	0.658247	+	0.752802i	$0.271298\pi$
$458$	5.31882	+	21.9245i	0.248532	+	1.02446i
$459$	6.49490	−	3.74983i	0.303156	−	0.175027i
$460$	0.429409	−	1.20376i	0.0200213	−	0.0561255i
$461$			30.1769i			1.40548i	0.711448	+	0.702739i	$0.248040\pi$
$461$			30.1769i			1.40548i	−0.711448	+	0.702739i	$0.751960\pi$
$462$	0.0391830	−	4.61643i	0.00182296	−	0.214776i
$463$	−3.88957	+	4.48881i	−0.180764	+	0.208613i	−0.838899	−	0.544287i	$-0.816800\pi$
$463$	−3.88957	+	4.48881i	−0.180764	+	0.208613i	0.658135	+	0.752900i	$0.271346\pi$
$464$	1.66186	−	0.856751i	0.0771501	−	0.0397736i
$465$	1.77328	−	0.709914i	0.0822338	−	0.0329215i
$466$	25.1915	+	12.9871i	1.16698	+	0.601618i
$467$	5.95472	+	0.568607i	0.275551	+	0.0263120i	0.231917	−	0.972736i	$-0.425500\pi$
$467$	5.95472	+	0.568607i	0.275551	+	0.0263120i	0.0436345	+	0.999048i	$0.486106\pi$
$468$	3.14888	−	2.72852i	0.145557	−	0.126126i
$469$	−1.91266	−	4.28400i	−0.0883185	−	0.197817i
$470$	2.56583	+	1.17178i	0.118353	+	0.0540500i
$471$	10.3946	+	2.52169i	0.478956	+	0.116193i
$472$	−4.87981	+	5.11780i	−0.224612	+	0.235566i
$473$	12.6160	−	1.20468i	0.580083	−	0.0553912i
$474$	16.7426	+	6.70273i	0.769013	+	0.307866i
$475$	−9.17860	−	10.5927i	−0.421143	−	0.486025i
$476$	−3.34151	−	1.18836i	−0.153158	−	0.0544684i
$477$	−2.74866	−	4.27699i	−0.125852	−	0.195830i
$478$	−1.68423	−	1.32450i	−0.0770350	−	0.0605810i
$479$	−1.19381	+	25.0612i	−0.0545466	+	1.14507i	0.791223	+	0.611527i	$0.209445\pi$
$479$	−1.19381	+	25.0612i	−0.0545466	+	1.14507i	−0.845770	+	0.533548i	$0.820858\pi$
$480$	−0.0773387	+	0.401271i	−0.00353001	+	0.0183155i
$481$	39.1449	−	37.3246i	1.78485	−	1.70186i
$482$	7.78723			0.354698
$483$	18.1905	−	6.90639i	0.827695	−	0.314252i
$484$	9.70520			0.441146
$485$	0.165423	−	0.157730i	0.00751147	−	0.00716217i
$486$	−1.25125	+	6.49210i	−0.0567578	+	0.294488i
$487$	0.532009	−	11.1682i	0.0241076	−	0.506081i	−0.954231	−	0.299070i	$-0.903323\pi$
$487$	0.532009	−	11.1682i	0.0241076	−	0.506081i	0.978339	−	0.207011i	$-0.0663735\pi$
$488$	0.666572	+	0.524198i	0.0301743	+	0.0237293i
$489$	−11.3037	−	17.5889i	−0.511171	−	0.795398i
$490$	1.67235	−	0.826531i	0.0755490	−	0.0373389i
$491$	−5.53716	−	6.39023i	−0.249889	−	0.288387i	0.616922	−	0.787024i	$-0.288379\pi$
$491$	−5.53716	−	6.39023i	−0.249889	−	0.288387i	−0.866811	+	0.498637i	$0.833834\pi$
$492$	15.4792	+	6.19692i	0.697854	+	0.279379i
$493$	2.49493	−	0.238237i	0.112366	−	0.0107297i
$494$	12.6077	−	13.2226i	0.567249	−	0.594914i
$495$	0.191107	+	0.0463621i	0.00858964	+	0.00208382i
$496$	−4.25172	−	1.94169i	−0.190908	−	0.0871846i
$497$	−2.02171	+	19.4282i	−0.0906861	+	0.871475i
$498$	−19.6273	+	17.0071i	−0.879518	+	0.762107i
$499$	−14.5857	−	1.39277i	−0.652946	−	0.0623488i	−0.236674	−	0.971589i	$-0.576057\pi$
$499$	−14.5857	−	1.39277i	−0.652946	−	0.0623488i	−0.416272	+	0.909240i	$0.636663\pi$
$500$	2.35186	+	1.21247i	0.105178	+	0.0542233i
$501$	−6.00097	+	2.40243i	−0.268104	+	0.107333i
$502$	−27.0108	+	13.9250i	−1.20555	+	0.621504i
$503$	−5.31434	+	6.13308i	−0.236955	+	0.273460i	−0.861755	−	0.507324i	$-0.830635\pi$
$503$	−5.31434	+	6.13308i	−0.236955	+	0.273460i	0.624801	+	0.780784i	$0.285180\pi$
$504$	1.49312	−	0.845241i	0.0665091	−	0.0376500i
$505$			2.40441i			0.106995i
$506$	−1.98023	−	5.08517i	−0.0880321	−	0.226063i
$507$	−37.5559	+	21.6829i	−1.66792	+	0.962973i
$508$	−4.18980	−	17.2706i	−0.185892	−	0.766258i
$509$	25.8141	−	8.93433i	1.14419	−	0.396007i	0.311771	−	0.950157i	$-0.399078\pi$
$509$	25.8141	−	8.93433i	1.14419	−	0.396007i	0.832417	+	0.554150i	$0.186957\pi$
$510$	−0.296157	+	0.460830i	−0.0131141	+	0.0204059i
$511$	−0.222178	−	1.64423i	−0.00982857	−	0.0727365i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−1.51230	+	15.8375i	−0.0667695	+	0.699242i
$514$	1.30400	+	0.451320i	0.0575171	+	0.0199069i
$515$	1.74616	−	1.37320i	0.0769452	−	0.0605104i
$516$	−9.90682	−	13.9122i	−0.436123	−	0.612450i
$517$	11.5563	−	3.39324i	0.508246	−	0.149234i
$518$	18.8387	−	11.8822i	0.827725	−	0.522073i
$519$	−3.28140	+	7.18525i	−0.144037	+	0.315398i
$520$	−0.636360	+	1.58955i	−0.0279062	+	0.0697064i
$521$	7.50997	−	21.6986i	0.329018	−	0.950635i	−0.652253	−	0.758001i	$-0.726176\pi$
$521$	7.50997	−	21.6986i	0.329018	−	0.950635i	0.981271	−	0.192633i	$-0.0617028\pi$
$522$	−0.703321	+	0.987677i	−0.0307835	+	0.0432294i
$523$	−0.496521	−	10.4233i	−0.0217113	−	0.455777i	−0.983380	−	0.181562i	$-0.941885\pi$
$523$	−0.496521	−	10.4233i	−0.0217113	−	0.455777i	0.961668	−	0.274216i	$-0.0884182\pi$
$524$	2.48810	+	0.357735i	0.108693	+	0.0156277i
$525$	4.54951	+	19.4733i	0.198557	+	0.849883i
$526$	−18.5069	−	16.0363i	−0.806939	−	0.699217i
$527$	−4.32367	−	4.53453i	−0.188342	−	0.197527i
$528$	0.872455	+	1.51114i	0.0379687	+	0.0657638i
$529$	16.9430	−	15.5543i	0.736650	−	0.676274i
$530$	1.80933	+	1.04462i	0.0785925	+	0.0453754i
$531$	1.29196	−	4.40002i	0.0560664	−	0.190945i
$532$	6.16527	−	4.31188i	0.267298	−	0.186944i
$533$	58.7692	+	37.7687i	2.54558	+	1.63594i
$534$	10.1126	−	12.8592i	0.437615	−	0.556472i
$535$	0.260585	−	0.505464i	0.0112661	−	0.0218531i
$536$	1.44445	+	1.02859i	0.0623906	+	0.0444281i
$537$	1.59351	+	8.26794i	0.0687652	+	0.356788i
$538$	−7.61795	+	1.09530i	−0.328433	+	0.0472215i
$539$	3.08547	−	7.34335i	0.132901	−	0.316301i
$540$	−0.420058	−	1.43059i	−0.0180764	−	0.0615627i
$541$	8.21270	−	33.8532i	0.353092	−	1.45546i	−0.467523	−	0.883981i	$-0.654853\pi$
$541$	8.21270	−	33.8532i	0.353092	−	1.45546i	0.820614	−	0.571482i	$-0.193631\pi$
$542$	2.08910	+	21.8780i	0.0897343	+	0.939740i
$543$	18.2076	+	23.1528i	0.781361	+	0.993581i
$544$	1.31624	−	0.253684i	0.0564333	−	0.0108766i
$545$	0.323549	−	0.147760i	0.0138593	−	0.00632934i
$546$	−24.7048	+	8.31628i	−1.05727	+	0.355904i
$547$	2.30334	−	16.0201i	0.0984837	−	0.684969i	−0.879440	−	0.476009i	$-0.842083\pi$
$547$	2.30334	−	16.0201i	0.0984837	−	0.684969i	0.977924	−	0.208960i	$-0.0670079\pi$
$548$	2.22959	+	4.32479i	0.0952432	+	0.184746i
$549$	−0.539988	−	0.104074i	−0.0230461	−	0.00444178i
$550$	5.45054	−	1.32229i	0.232412	−	0.0563825i
$551$	−2.65836	+	4.60442i	−0.113250	+	0.196155i
$552$	−4.60052	+	5.73758i	−0.195811	+	0.244207i
$553$	22.3364	+	21.6626i	0.949841	+	0.921189i
$554$	1.59132	+	0.467254i	0.0676088	+	0.0198517i
$555$	−1.12519	−	3.25101i	−0.0477615	−	0.137998i
$556$	−6.02807	−	0.287152i	−0.255647	−	0.0121780i
$557$	−12.6425	−	31.5794i	−0.535679	−	1.33806i	−0.911474	−	0.411358i	$-0.865055\pi$
$557$	−12.6425	−	31.5794i	−0.535679	−	1.33806i	0.375795	−	0.926703i	$-0.377370\pi$
$558$	3.02772	−	0.144228i	0.128173	−	0.00610566i
$559$	−29.7264	−	65.0917i	−1.25729	−	2.75308i
$560$	−0.386212	+	0.589889i	−0.0163205	+	0.0249274i
$561$	0.332873	+	2.31518i	0.0140539	+	0.0977471i
$562$	−6.55048	+	4.66458i	−0.276315	+	0.196763i
$563$	14.6573	+	13.9757i	0.617731	+	0.589006i	0.932947	−	0.360014i	$-0.117228\pi$
$563$	14.6573	+	13.9757i	0.617731	+	0.589006i	−0.315215	+	0.949020i	$0.602077\pi$
$564$	−11.7470	−	11.2008i	−0.494639	−	0.471638i
$565$	−1.90917	+	1.35951i	−0.0803192	+	0.0571951i
$566$	4.25539	+	29.5969i	0.178867	+	1.24405i
$567$	9.61419	−	14.6844i	0.403758	−	0.616688i
$568$	−3.06694	−	6.71566i	−0.128686	−	0.281783i
$569$	−20.0484	+	0.955023i	−0.840472	+	0.0400366i	−0.463402	−	0.886148i	$-0.653371\pi$
$569$	−20.0484	+	0.955023i	−0.840472	+	0.0400366i	−0.377070	+	0.926185i	$0.623068\pi$
$570$	−0.431894	−	1.07882i	−0.0180901	−	0.0451868i
$571$	19.3262	+	0.920622i	0.808778	+	0.0385269i	0.447897	−	0.894085i	$-0.352173\pi$
$571$	19.3262	+	0.920622i	0.808778	+	0.0385269i	0.360881	+	0.932612i	$0.382476\pi$
$572$	2.39115	+	6.90878i	0.0999791	+	0.288871i
$573$	−16.7645	−	4.92250i	−0.700347	−	0.205640i
$574$	20.6509	+	20.0279i	0.861950	+	0.835949i
$575$	13.5291	+	19.3842i	0.564202	+	0.808375i
$576$	−0.324249	+	0.561616i	−0.0135104	+	0.0234007i
$577$	−28.9872	+	7.03221i	−1.20675	+	0.292755i	−0.788189	−	0.615433i	$-0.788981\pi$
$577$	−28.9872	+	7.03221i	−1.20675	+	0.292755i	−0.418563	+	0.908188i	$0.637466\pi$
$578$	−14.9284	−	2.87722i	−0.620940	−	0.119676i
$579$	−4.85811	−	9.42341i	−0.201896	−	0.391624i
$580$	0.0709104	−	0.493193i	0.00294440	−	0.0204787i
$581$	−42.4667	+	14.2954i	−1.76182	+	0.593074i
$582$	−1.19638	+	0.546369i	−0.0495916	+	0.0226477i
$583$	8.75957	−	1.68827i	0.362785	−	0.0699210i
$584$	0.387653	+	0.492941i	0.0160412	+	0.0203980i
$585$	−0.105546	−	1.10533i	−0.00436380	−	0.0456998i
$586$	0.525477	−	2.16605i	0.0217073	−	0.0894786i
$587$	1.16070	+	3.95297i	0.0479071	+	0.163157i	0.979972	−	0.199134i	$-0.0638129\pi$
$587$	1.16070	+	3.95297i	0.0479071	+	0.163157i	−0.932065	+	0.362291i	$0.881995\pi$
$588$	−10.6494	+	1.34707i	−0.439172	+	0.0555522i
$589$	13.1561	−	1.89155i	0.542086	−	0.0779401i
$590$	0.356639	+	1.85042i	0.0146826	+	0.0761805i
$591$	21.0387	+	14.9816i	0.865416	+	0.616260i
$592$	−3.85752	+	7.48254i	−0.158543	+	0.307531i
$593$	−14.5422	+	18.4920i	−0.597178	+	0.759374i	−0.986860	−	0.161576i	$-0.948342\pi$
$593$	−14.5422	+	18.4920i	−0.597178	+	0.759374i	0.389682	+	0.920949i	$0.372585\pi$
$594$	−5.35568	−	3.44188i	−0.219746	−	0.141222i
$595$	−0.774502	+	0.541673i	−0.0317515	+	0.0222064i
$596$	−2.41274	+	8.21705i	−0.0988299	+	0.336584i
$597$	−5.64708	−	3.26034i	−0.231120	−	0.133437i
$598$	−23.4765	+	19.9571i	−0.960026	+	0.816108i
$599$	20.0745	+	34.7700i	0.820220	+	1.42066i	0.905518	+	0.424307i	$0.139482\pi$
$599$	20.0745	+	34.7700i	0.820220	+	1.42066i	−0.0852983	+	0.996355i	$0.527184\pi$
$600$	−5.21589	−	5.47027i	−0.212938	−	0.223323i
$601$	8.99328	+	7.79272i	0.366843	+	0.317872i	0.818703	−	0.574218i	$-0.194694\pi$
$601$	8.99328	+	7.79272i	0.366843	+	0.317872i	−0.451859	+	0.892089i	$0.649239\pi$
$602$	−6.70387	−	28.6946i	−0.273229	−	1.16950i
$603$	−1.13824	−	0.163655i	−0.0463529	−	0.00666454i
$604$	−0.836436	−	17.5590i	−0.0340341	−	0.714464i
$605$	1.50024	−	2.10679i	0.0609935	−	0.0856533i
$606$	4.52516	−	13.0746i	0.183822	−	0.531119i
$607$	10.3168	−	25.7702i	0.418747	−	1.04598i	−0.557665	−	0.830066i	$-0.688303\pi$
$607$	10.3168	−	25.7702i	0.418747	−	1.04598i	0.976412	−	0.215914i	$-0.0692731\pi$
$608$	−1.18128	+	2.58664i	−0.0479072	+	0.104902i
$609$	6.41608	−	4.04683i	0.259993	−	0.163986i
$610$	0.216832	−	0.0636675i	0.00877926	−	0.00257782i
$611$	−39.4472	−	55.3958i	−1.59586	−	2.24107i
$612$	−0.683307	+	0.537359i	−0.0276211	+	0.0217214i
$613$	9.30308	+	3.21983i	0.375748	+	0.130048i	0.508413	−	0.861113i	$-0.330232\pi$
$613$	9.30308	+	3.21983i	0.375748	+	0.130048i	−0.132665	+	0.991161i	$0.542354\pi$
$614$	0.764454	−	8.00573i	0.0308509	−	0.323085i
$615$	3.73800	−	2.40227i	0.150731	−	0.0968689i
$616$	0.403142	+	2.98346i	0.0162431	+	0.120207i
$617$	8.22131	−	12.7926i	0.330977	−	0.515011i	−0.635385	−	0.772196i	$-0.719159\pi$
$617$	8.22131	−	12.7926i	0.330977	−	0.515011i	0.966362	+	0.257185i	$0.0827949\pi$
$618$	−12.0796	+	4.18079i	−0.485913	+	0.168176i
$619$	0.839777	+	3.46161i	0.0337535	+	0.139134i	0.986195	−	0.165587i	$-0.0529519\pi$
$619$	0.839777	+	3.46161i	0.0337535	+	0.139134i	−0.952442	+	0.304721i	$0.901437\pi$
$620$	−1.07874	+	0.622808i	−0.0433230	+	0.0250126i
$621$	5.32678	−	26.2978i	0.213756	−	1.05529i
$622$		−	7.56340i		−	0.303265i
$623$	24.5627	−	13.9047i	0.984085	−	0.557079i
$624$	6.45194	−	7.44593i	0.258284	−	0.298076i
$625$	−21.2785	+	10.9698i	−0.851141	+	0.438793i
$626$	−1.20600	+	0.482810i	−0.0482015	+	0.0192970i
$627$	−4.41027	−	2.27365i	−0.176129	−	0.0908008i
$628$	−6.94353	−	0.663026i	−0.277077	−	0.0264576i
$629$	−8.52827	+	7.38979i	−0.340044	+	0.294650i
$630$	0.0473250	−	0.454784i	0.00188547	−	0.0181190i
$631$	4.57325	+	2.08853i	0.182058	+	0.0831431i	0.504359	−	0.863494i	$-0.331729\pi$
$631$	4.57325	+	2.08853i	0.182058	+	0.0831431i	−0.322301	+	0.946637i	$0.604456\pi$
$632$	−11.4291	−	2.77267i	−0.454625	−	0.110291i
$633$	19.4881	−	20.4386i	0.774584	−	0.812360i
$634$	−11.0306	+	1.05329i	−0.438081	+	0.0418316i
$635$	−4.39674	−	1.76019i	−0.174479	−	0.0698510i
$636$	−7.87271	−	9.08559i	−0.312173	−	0.360267i
$637$	−44.8808	−	2.90221i	−1.77824	−	0.114990i
$638$	−1.15023	−	1.78979i	−0.0455379	−	0.0708584i
$639$	3.76343	+	2.95959i	0.148879	+	0.117080i
$640$	0.0126802	−	0.266191i	0.000501231	−	0.0105221i
$641$	−7.96383	+	41.3203i	−0.314552	+	1.63205i	0.388879	+	0.921289i	$0.372863\pi$
$641$	−7.96383	+	41.3203i	−0.314552	+	1.63205i	−0.703431	+	0.710764i	$0.748350\pi$
$642$	−2.36829	+	2.25816i	−0.0934690	+	0.0891225i
$643$	17.0270			0.671478			0.335739	−	0.941955i	$-0.391014\pi$
$643$	17.0270			0.671478			0.335739	+	0.941955i	$0.391014\pi$
$644$	−11.1007	+	6.14614i	−0.437428	+	0.242192i
$645$	−4.55145			−0.179213
$646$	−2.75870	+	2.63041i	−0.108540	+	0.103492i
$647$	−1.56538	+	8.12196i	−0.0615415	+	0.319307i	−0.999633	−	0.0270793i	$-0.991379\pi$
$647$	−1.56538	+	8.12196i	−0.0615415	+	0.319307i	0.938092	+	0.346387i	$0.112591\pi$
$648$	−0.315656	+	6.62644i	−0.0124001	+	0.260311i
$649$	6.32494	+	4.97399i	0.248276	+	0.195246i
$650$	−17.1212	−	26.6411i	−0.671549	−	1.04495i
$651$	−17.8673	−	6.35425i	−0.700275	−	0.249043i
$652$	8.92870	+	10.3043i	0.349675	+	0.403546i
$653$	11.0932	+	4.44106i	0.434111	+	0.173792i	0.578417	−	0.815741i	$-0.303671\pi$
$653$	11.0932	+	4.44106i	0.434111	+	0.173792i	−0.144306	+	0.989533i	$0.546095\pi$
$654$	−2.03746	+	0.194554i	−0.0796712	+	0.00760768i
$655$	0.462270	−	0.484815i	0.0180624	−	0.0189433i
$656$	−10.5666	−	2.56344i	−0.412558	−	0.100085i
$657$	−0.369928	−	0.168941i	−0.0144323	−	0.00659100i
$658$	−11.4168	−	25.5715i	−0.445074	−	0.996880i
$659$	−23.5901	+	20.4410i	−0.918941	+	0.796267i	−0.979405	−	0.201904i	$-0.935287\pi$
$659$	−23.5901	+	20.4410i	−0.918941	+	0.796267i	0.0604647	+	0.998170i	$0.480742\pi$
$660$	0.462901	+	0.0442017i	0.0180184	+	0.00172055i
$661$	29.3618	+	15.1371i	1.14204	+	0.588764i	0.922178	−	0.386766i	$-0.126408\pi$
$661$	29.3618	+	15.1371i	1.14204	+	0.588764i	0.219865	+	0.975530i	$0.429438\pi$
$662$	−11.0161	+	4.41019i	−0.428154	+	0.171407i
$663$	11.7386	−	6.05169i	0.455891	−	0.235028i
$664$	11.0907	−	12.7993i	0.430402	−	0.496710i
$665$	0.0170169	−	2.00488i	0.000659887	−	0.0777461i
$666$		−	5.45930i		−	0.211544i
$667$	5.27007	−	7.25466i	0.204058	−	0.280902i
$668$	3.65056	−	2.10765i	0.141244	−	0.0815475i
$669$	2.57385	+	10.6095i	0.0995106	+	0.410188i
$670$	0.446568	−	0.154559i	0.0172524	−	0.00597113i
$671$	0.521681	−	0.811751i	0.0201393	−	0.0313373i
$672$	3.21031	−	2.48081i	0.123840	−	0.0956993i
$673$	−4.56352	+	2.93280i	−0.175911	+	0.113051i	−0.625633	−	0.780117i	$-0.715159\pi$
$673$	−4.56352	+	2.93280i	−0.175911	+	0.113051i	0.449722	+	0.893168i	$0.351523\pi$
$674$	−2.80890	+	29.4161i	−0.108195	+	1.13307i
$675$	26.0601	+	9.01949i	1.00305	+	0.347160i
$676$	22.2294	−	17.4814i	0.854976	−	0.672361i
$677$	19.3685	+	27.1993i	0.744393	+	1.04535i	0.996971	+	0.0777775i	$0.0247824\pi$
$677$	19.3685	+	27.1993i	0.744393	+	1.04535i	−0.252577	+	0.967577i	$0.581278\pi$
$678$	12.9402	−	3.79958i	0.496965	−	0.145922i
$679$	−2.26750	+	0.0887326i	−0.0870187	+	0.00340525i
$680$	0.148396	−	0.324943i	0.00569074	−	0.0124610i
$681$	6.91289	−	17.2676i	0.264903	−	0.661695i
$682$	−1.73955	+	5.02610i	−0.0666108	+	0.192459i
$683$	−25.8359	+	36.2814i	−0.988582	+	1.38827i	−0.0680152	+	0.997684i	$0.521667\pi$
$683$	−25.8359	+	36.2814i	−0.988582	+	1.38827i	−0.920567	+	0.390585i	$0.872273\pi$
$684$	−0.0877447	−	1.84199i	−0.00335500	−	0.0704302i
$685$	1.28347	+	0.184536i	0.0490390	+	0.00705074i
$686$	−17.8812	−	4.82313i	−0.682707	−	0.184148i
$687$	−26.1455	−	22.6552i	−0.997514	−	0.864351i
$688$	7.68581	+	8.06065i	0.293019	+	0.307309i
$689$	−25.1849	−	43.6216i	−0.959470	−	1.66185i
$690$	0.534353	+	1.88560i	0.0203425	+	0.0717834i
$691$	−41.6188	−	24.0286i	−1.58325	−	0.914091i	−0.994381	−	0.105865i	$-0.966239\pi$
$691$	−41.6188	−	24.0286i	−1.58325	−	0.914091i	−0.588872	−	0.808226i	$-0.700428\pi$
$692$	1.45125	−	4.94249i	0.0551681	−	0.187885i
$693$	−1.11894	−	1.59990i	−0.0425049	−	0.0607750i
$694$	−3.52428	−	2.26491i	−0.133780	−	0.0859750i
$695$	−0.994160	+	1.26418i	−0.0377106	+	0.0479530i
$696$	−1.31379	+	2.54840i	−0.0497992	+	0.0965970i
$697$	−11.8725	−	8.45435i	−0.449702	−	0.320231i
$698$	1.75432	+	9.10228i	0.0664020	+	0.344526i
$699$	−43.0193	+	6.18524i	−1.62714	+	0.233947i
$700$	−4.74387	−	12.1474i	−0.179301	−	0.459129i
$701$	2.95015	+	10.0473i	0.111426	+	0.379481i	0.996258	−	0.0864287i	$-0.0275455\pi$
$701$	2.95015	+	10.0473i	0.111426	+	0.379481i	−0.884832	+	0.465909i	$0.845727\pi$
$702$	−8.47468	+	34.9331i	−0.319856	+	1.31847i
$703$	−2.27551	−	23.8302i	−0.0858223	−	0.898772i
$704$	−0.703397	−	0.894443i	−0.0265103	−	0.0337106i
$705$	−4.24732	+	0.818604i	−0.159963	+	0.0308304i
$706$	23.2429	−	10.6147i	0.874758	−	0.399489i
$707$	15.7848	−	17.9072i	0.593649	−	0.673471i
$708$	1.54322	−	10.7333i	0.0579976	−	0.403382i
$709$	12.3306	+	23.9180i	0.463085	+	0.898260i	0.998557	+	0.0537068i	$0.0171036\pi$
$709$	12.3306	+	23.9180i	0.463085	+	0.898260i	−0.535472	+	0.844553i	$0.679866\pi$
$710$	−1.93192	−	0.372347i	−0.0725036	−	0.0139739i
$711$	7.41176	−	1.79807i	0.277963	−	0.0674330i
$712$	−5.33408	+	9.23890i	−0.199903	+	0.346242i
$713$	−22.3999	+	0.854911i	−0.838883	+	0.0320167i
$714$	5.23099	−	1.48785i	0.195765	−	0.0556814i
$715$	1.86938	+	0.548898i	0.0699107	+	0.0205276i
$716$	−1.79590	−	5.18892i	−0.0671160	−	0.193919i
$717$	3.28194	+	0.156338i	0.122566	+	0.00583855i
$718$	−10.7045	−	26.7385i	−0.399487	−	0.997870i
$719$	13.4050	−	0.638561i	0.499923	−	0.0238143i	0.203894	−	0.978993i	$-0.434640\pi$
$719$	13.4050	−	0.638561i	0.499923	−	0.0238143i	0.296030	+	0.955179i	$0.404337\pi$
$720$	0.0717921	+	0.157203i	0.00267554	+	0.00585861i
$721$	−22.0198	−	1.23633i	−0.820060	−	0.0460433i
$722$	1.55321	+	10.8028i	0.0578044	+	0.402038i
$723$	−9.72718	+	6.92669i	−0.361758	+	0.257606i
$724$	−13.9014	−	13.2549i	−0.516641	−	0.492616i
$725$	6.66976	+	6.35961i	0.247709	+	0.236190i
$726$	−12.1230	+	8.63273i	−0.449925	+	0.320390i
$727$	−4.40805	−	30.6587i	−0.163485	−	1.13707i	−0.892000	−	0.452036i	$-0.850698\pi$
$727$	−4.40805	−	30.6587i	−0.163485	−	1.13707i	0.728514	−	0.685031i	$-0.240211\pi$
$728$	15.1747	−	7.66077i	0.562411	−	0.283927i
$729$	−12.4793	−	27.3258i	−0.462195	−	1.01207i
$730$	0.166931	−	0.00795189i	0.00617839	−	0.000294313i
$731$	5.54875	+	13.8601i	0.205228	+	0.512634i
$732$	−1.29890	−	0.0618742i	−0.0480087	−	0.00228694i
$733$	14.4296	+	41.6915i	0.532968	+	1.53991i	0.814385	+	0.580325i	$0.197075\pi$
$733$	14.4296	+	41.6915i	0.532968	+	1.53991i	−0.281417	+	0.959586i	$0.590804\pi$
$734$	−4.13427	−	1.21393i	−0.152599	−	0.0448070i
$735$	−1.35377	+	2.51998i	−0.0499346	+	0.0929509i
$736$	2.43707	−	4.13046i	0.0898315	−	0.152251i
$737$	1.00888	−	1.74744i	0.0371627	−	0.0643676i
$738$	6.85245	−	1.66239i	0.252242	−	0.0611933i
$739$	−4.84341	−	0.933491i	−0.178168	−	0.0343390i	0.0993869	−	0.995049i	$-0.468312\pi$
$739$	−4.84341	−	0.933491i	−0.178168	−	0.0343390i	−0.277555	+	0.960710i	$0.589524\pi$
$740$	1.02800	+	1.99405i	0.0377901	+	0.0733026i
$741$	−3.98714	+	27.7312i	−0.146471	+	1.01873i
$742$	−6.61745	−	19.6581i	−0.242934	−	0.721672i
$743$	16.8035	−	7.67389i	0.616460	−	0.281528i	−0.0826091	−	0.996582i	$-0.526325\pi$
$743$	16.8035	−	7.67389i	0.616460	−	0.281528i	0.699069	+	0.715054i	$0.253598\pi$
$744$	7.03803	−	1.35647i	0.258027	−	0.0497306i
$745$	1.41078	+	1.79396i	0.0516871	+	0.0657255i
$746$	2.95758	+	30.9731i	0.108285	+	1.13401i
$747$	−2.58932	+	10.6733i	−0.0947384	+	0.390517i
$748$	−0.429727	−	1.46352i	−0.0157124	−	0.0535114i
$749$	−5.25908	+	2.05380i	−0.192163	+	0.0750443i
$750$	−4.01624	+	0.577448i	−0.146652	+	0.0210854i
$751$	3.97882	+	20.6441i	0.145189	+	0.753313i	0.979410	+	0.201882i	$0.0647058\pi$
$751$	3.97882	+	20.6441i	0.145189	+	0.753313i	−0.834221	+	0.551431i	$0.814082\pi$
$752$	8.62200	+	6.13970i	0.314412	+	0.223892i
$753$	21.3535	−	41.4199i	0.778163	−	1.50943i
$754$	−7.42579	+	9.44267i	−0.270431	+	0.343882i
$755$	−3.94097	−	2.53271i	−0.143427	−	0.0921747i
$756$	−6.26325	+	13.4122i	−0.227792	+	0.487796i
$757$	−10.7159	+	36.4949i	−0.389475	+	1.32643i	0.498639	+	0.866809i	$0.333833\pi$
$757$	−10.7159	+	36.4949i	−0.389475	+	1.32643i	−0.888115	+	0.459622i	$0.847985\pi$
$758$	−22.6856	−	13.0975i	−0.823977	−	0.475724i
$759$	6.99678	+	4.59058i	0.253967	+	0.166628i
$760$	0.378901	+	0.656276i	0.0137442	+	0.0238056i
$761$	−21.0006	−	22.0248i	−0.761271	−	0.798398i	0.223046	−	0.974808i	$-0.428400\pi$
$761$	−21.0006	−	22.0248i	−0.761271	−	0.798398i	−0.984317	+	0.176410i	$0.943552\pi$
$762$	20.5956	+	17.8462i	0.746101	+	0.646501i
$763$	−3.37971	−	1.02361i	−0.122354	−	0.0370572i
$764$	11.2780	+	1.62154i	0.408025	+	0.0586651i
$765$	0.0110228	+	0.231397i	0.000398530	+	0.00836617i
$766$	−2.07457	+	2.91332i	−0.0749571	+	0.105263i
$767$	14.8597	−	42.9343i	0.536553	−	1.55027i
$768$	−0.569930	+	1.42362i	−0.0205656	+	0.0513703i
$769$	17.2313	−	37.7312i	0.621376	−	1.36062i	−0.293139	−	0.956070i	$-0.594700\pi$
$769$	17.2313	−	37.7312i	0.621376	−	1.36062i	0.914514	−	0.404553i	$-0.132573\pi$
$770$	0.709964	+	0.373673i	0.0255853	+	0.0134662i
$771$	−2.03030	+	0.596151i	−0.0731196	+	0.0214698i
$772$	4.01037	+	5.63178i	0.144337	+	0.202692i
$773$	−18.7521	+	14.7468i	−0.674466	+	0.530406i	−0.895613	−	0.444834i	$-0.853263\pi$
$773$	−18.7521	+	14.7468i	−0.674466	+	0.530406i	0.221147	+	0.975241i	$0.429020\pi$
$774$	−6.82547	−	2.36232i	−0.245336	−	0.0849117i
$775$	2.18996	−	22.9343i	0.0786655	−	0.823823i
$776$	0.721536	−	0.463703i	0.0259016	−	0.0166460i
$777$	−12.9627	+	31.5992i	−0.465033	+	1.13361i
$778$	14.8063	−	23.0391i	0.530832	−	0.825991i
$779$	29.2184	−	10.1126i	1.04686	−	0.362321i
$780$	−0.619006	−	2.55158i	−0.0221640	−	0.0913612i
$781$	−7.27535	+	4.20043i	−0.260333	+	0.150303i
$782$	5.09059	−	3.92598i	0.182039	−	0.140393i
$783$		−	10.4607i		−	0.373835i
$784$	6.74896	−	1.85784i	0.241034	−	0.0663513i
$785$	−1.21727	+	1.40480i	−0.0434461	+	0.0501395i
$786$	−3.42614	+	1.76630i	−0.122206	+	0.0630018i
$787$	−8.85441	+	3.54477i	−0.315625	+	0.126357i	−0.524066	−	0.851678i	$-0.675585\pi$
$787$	−8.85441	+	3.54477i	−0.315625	+	0.126357i	0.208440	+	0.978035i	$0.433161\pi$
$788$	−14.9705	−	7.71782i	−0.533301	−	0.274936i
$789$	37.3816	+	3.56951i	1.33082	+	0.127078i
$790$	−2.36861	+	2.05241i	−0.0842714	+	0.0730216i
$791$	23.1439	+	2.40837i	0.822903	+	0.0856317i
$792$	0.671236	+	0.306543i	0.0238513	+	0.0108925i
$793$	−5.29476	−	1.28449i	−0.188022	−	0.0456137i
$794$	−8.55815	+	8.97553i	−0.303717	+	0.318530i
$795$	−3.18926	+	0.304537i	−0.113111	+	0.0108008i
$796$	3.94767	+	1.58041i	0.139921	+	0.0560161i
$797$	−4.81114	−	5.55235i	−0.170419	−	0.196674i	0.664115	−	0.747631i	$-0.268809\pi$
$797$	−4.81114	−	5.55235i	−0.170419	−	0.196674i	−0.834534	+	0.550956i	$0.814263\pi$
$798$	−3.86577	+	10.8700i	−0.136847	+	0.384795i
$799$	7.67080	+	11.9360i	0.271373	+	0.422265i
$800$	3.87444	+	3.04689i	0.136982	+	0.107724i
$801$	0.329185	−	6.91045i	0.0116312	−	0.244169i
$802$	−3.05309	+	15.8409i	−0.107808	+	0.559362i
$803$	0.516443	−	0.492428i	0.0182249	−	0.0173774i
$804$	−2.71921			−0.0958991
$805$	−0.381757	+	3.35980i	−0.0134552	+	0.118417i
$806$	30.0308			1.05779
$807$	8.54147	−	8.14428i	0.300674	−	0.286692i
$808$	−1.70751	+	8.85938i	−0.0600698	+	0.311672i
$809$	1.15111	−	24.1648i	0.0404709	−	0.849588i	−0.883803	−	0.467859i	$-0.845026\pi$
$809$	1.15111	−	24.1648i	0.0404709	−	0.849588i	0.924274	−	0.381729i	$-0.124671\pi$
$810$	1.38966	+	1.09284i	0.0488278	+	0.0383986i
$811$	−16.9244	−	26.3349i	−0.594296	−	0.924743i	−0.999943	−	0.0107130i	$-0.996590\pi$
$811$	−16.9244	−	26.3349i	−0.594296	−	0.924743i	0.405646	−	0.914030i	$-0.367046\pi$
$812$	−3.76589	+	3.20761i	−0.132157	+	0.112565i
$813$	−22.0699	−	25.4700i	−0.774025	−	0.893272i
$814$	8.89301	+	3.56022i	0.311700	+	0.124786i
$815$	3.61705	−	0.345386i	0.126700	−	0.0120983i
$816$	−1.41849	+	1.48767i	−0.0496571	+	0.0520789i
$817$	−30.7782	−	7.46671i	−1.07679	−	0.261227i
$818$	29.3783	+	13.4166i	1.02719	+	0.469101i
$819$	−6.47034	+	8.92503i	−0.226092	+	0.311866i
$820$	−2.18987	+	1.89753i	−0.0764736	+	0.0662647i
$821$	34.1259	+	3.25863i	1.19100	+	0.113727i	0.671673	−	0.740848i	$-0.265576\pi$
$821$	34.1259	+	3.25863i	1.19100	+	0.113727i	0.519328	+	0.854575i	$0.326182\pi$
$822$	−6.63190	−	3.41898i	−0.231314	−	0.119251i
$823$	31.9261	−	12.7813i	1.11287	−	0.445528i	0.258932	−	0.965896i	$-0.416629\pi$
$823$	31.9261	−	12.7813i	1.11287	−	0.445528i	0.853942	+	0.520368i	$0.174205\pi$
$824$	7.40916	−	3.81969i	0.258110	−	0.133065i
$825$	−5.63222	+	6.49992i	−0.196089	+	0.226298i
$826$	9.49174	−	16.1226i	0.330260	−	0.560977i
$827$			43.0132i			1.49572i	0.663858	+	0.747858i	$0.268918\pi$
$827$			43.0132i			1.49572i	−0.663858	+	0.747858i	$0.731082\pi$
$828$	−0.177342	+	3.10503i	−0.00616306	+	0.107907i
$829$	31.8307	−	18.3774i	1.10552	−	0.638275i	0.167858	−	0.985811i	$-0.446315\pi$
$829$	31.8307	−	18.3774i	1.10552	−	0.638275i	0.937666	+	0.347536i	$0.112982\pi$
$830$	−1.06405	−	4.38608i	−0.0369338	−	0.152243i
$831$	−2.40337	+	0.831815i	−0.0833720	+	0.0288553i
$832$	−3.47358	+	5.40500i	−0.120425	+	0.187385i
$833$	9.32427	+	1.05036i	0.323067	+	0.0363927i
$834$	7.78520	−	5.00324i	0.269579	−	0.173248i
$835$	0.106781	−	1.11826i	0.00369531	−	0.0386991i
$836$	3.05776	+	1.05830i	0.105755	+	0.0366021i
$837$	−20.5559	+	16.1654i	−0.710517	+	0.558757i
$838$	7.61629	+	10.6956i	0.263101	+	0.369473i
$839$	29.9067	−	8.78140i	1.03249	−	0.303168i	0.278769	−	0.960358i	$-0.410073\pi$
$839$	29.9067	−	8.78140i	1.03249	−	0.303168i	0.753725	+	0.657190i	$0.228255\pi$
$840$	−0.0422776	−	1.08038i	−0.00145872	−	0.0372765i
$841$	−10.5948	+	23.1994i	−0.365339	+	0.799980i
$842$	−5.51659	+	13.7798i	−0.190114	+	0.474882i
$843$	4.03322	−	11.6532i	0.138912	−	0.401359i
$844$	−10.6824	+	15.0014i	−0.367704	+	0.516368i
$845$	−0.358594	−	7.52782i	−0.0123360	−	0.258965i
$846$	−6.79427	−	0.976868i	−0.233592	−	0.0335854i
$847$	−25.0042	+	5.84170i	−0.859155	+	0.200723i
$848$	5.92489	+	5.13395i	0.203462	+	0.176300i
$849$	−31.6417	−	33.1849i	−1.08594	−	1.13890i
$850$	3.30356	+	5.72193i	0.113311	+	0.196261i
$851$	−0.381625	+	40.3713i	−0.0130819	+	1.38391i
$852$	9.80452	+	5.66064i	0.335897	+	0.193930i
$853$	−2.45737	+	8.36905i	−0.0841389	+	0.286551i	−0.990805	−	0.135298i	$-0.956801\pi$
$853$	−2.45737	+	8.36905i	−0.0841389	+	0.286551i	0.906666	+	0.421849i	$0.138619\pi$
$854$	−2.03286	−	0.949311i	−0.0695631	−	0.0324847i
$855$	−0.413420	−	0.265689i	−0.0141387	−	0.00908638i
$856$	1.31912	−	1.67739i	0.0450865	−	0.0573322i
$857$	−7.25955	+	14.0816i	−0.247981	+	0.481017i	−0.979668	−	0.200624i	$-0.935703\pi$
$857$	−7.25955	+	14.0816i	−0.247981	+	0.481017i	0.731687	+	0.681641i	$0.238733\pi$
$858$	−9.13215	−	6.50298i	−0.311767	−	0.222008i
$859$	−2.80447	−	14.5510i	−0.0956873	−	0.496473i	−0.997877	−	0.0651327i	$-0.979253\pi$
$859$	−2.80447	−	14.5510i	−0.0956873	−	0.496473i	0.902189	−	0.431340i	$-0.141959\pi$
$860$	2.93788	−	0.422403i	0.100181	−	0.0144038i
$861$	−43.6101	−	6.64845i	−1.48623	−	0.226579i
$862$	−5.12778	−	17.4636i	−0.174653	−	0.594814i
$863$	−6.82569	+	28.1359i	−0.232349	+	0.957757i	0.729457	+	0.684027i	$0.239773\pi$
$863$	−6.82569	+	28.1359i	−0.232349	+	0.957757i	−0.961806	+	0.273730i	$0.911742\pi$
$864$	−0.531822	−	5.56950i	−0.0180930	−	0.189478i
$865$	−0.848574	−	1.07905i	−0.0288524	−	0.0366888i
$866$	16.7918	−	3.23635i	0.570607	−	0.109976i
$867$	21.2067	−	9.68475i	0.720216	−	0.328911i
$868$	12.1227	+	2.44336i	0.411473	+	0.0829330i
$869$	−1.90450	+	13.2461i	−0.0646057	+	0.449343i
$870$	0.350117	+	0.679132i	0.0118701	+	0.0230247i
$871$	−11.1871	−	2.15614i	−0.379061	−	0.0730580i
$872$	1.29709	−	0.314671i	0.0439251	−	0.0106561i
$873$	−0.278106	+	0.481693i	−0.00941245	+	0.0163028i
$874$	0.520107	+	13.6276i	0.0175929	+	0.460959i
$875$	−6.78908	−	1.70815i	−0.229513	−	0.0577461i
$876$	−0.922693	−	0.270927i	−0.0311749	−	0.00915378i
$877$	9.50566	+	27.4648i	0.320983	+	0.927421i	0.983899	+	0.178726i	$0.0571977\pi$
$877$	9.50566	+	27.4648i	0.320983	+	0.927421i	−0.662915	+	0.748694i	$0.730681\pi$
$878$	5.63854	+	0.268597i	0.190291	+	0.00906470i
$879$	1.27030	+	3.17306i	0.0428462	+	0.107025i
$880$	−0.302896	+	0.0144287i	−0.0102106	+	0.000486392i
$881$	21.0824	+	46.1640i	0.710284	+	1.55531i	0.827039	+	0.562145i	$0.190024\pi$
$881$	21.0824	+	46.1640i	0.710284	+	1.55531i	−0.116754	+	0.993161i	$0.537249\pi$
$882$	−3.33808	+	3.07639i	−0.112399	+	0.103587i
$883$	−6.79617	−	47.2684i	−0.228709	−	1.59071i	−0.703556	−	0.710640i	$-0.748405\pi$
$883$	−6.79617	−	47.2684i	−0.228709	−	1.59071i	0.474846	−	0.880069i	$-0.342504\pi$
$884$	−7.01544	+	4.99567i	−0.235955	+	0.168023i
$885$	−2.09142	−	1.99417i	−0.0703024	−	0.0670332i
$886$	11.1351	+	10.6173i	0.374090	+	0.356694i
$887$	−25.4458	+	18.1199i	−0.854386	+	0.608406i	−0.921082	−	0.389368i	$-0.872694\pi$
$887$	−25.4458	+	18.1199i	−0.854386	+	0.608406i	0.0666961	+	0.997773i	$0.478754\pi$
$888$	−1.83718	−	12.7778i	−0.0616516	−	0.428796i
$889$	21.1899	+	41.9736i	0.710686	+	1.40775i
$890$	1.18102	+	2.58608i	0.0395879	+	0.0866854i
$891$	7.54016	−	0.359182i	0.252605	−	0.0120331i
$892$	−2.64600	−	6.60940i	−0.0885948	−	0.221299i
$893$	−30.0645	−	1.43215i	−1.00607	−	0.0479251i
$894$	−4.29521	−	12.4102i	−0.143653	−	0.415059i
$895$	−1.40402	−	0.412256i	−0.0469311	−	0.0137802i
$896$	−1.84196	+	1.89926i	−0.0615357	+	0.0634497i
$897$	11.5732	−	45.8111i	0.386419	−	1.52959i
$898$	14.3251	−	24.8117i	0.478033	−	0.827978i
$899$	−8.49288	+	2.06035i	−0.283253	+	0.0687165i
$900$	−3.13867	−	0.604930i	−0.104622	−	0.0201643i
$901$	4.81546	+	9.34069i	0.160426	+	0.311183i
$902$	−1.76078	+	12.2465i	−0.0586276	+	0.407764i
$903$	33.8976	+	29.8799i	1.12804	+	0.994341i
$904$	−8.00004	+	3.65350i	−0.266077	+	0.121513i
$905$	−5.02625	+	0.968731i	−0.167078	+	0.0322017i
$906$	16.6634	+	21.1892i	0.553604	+	0.703965i
$907$	1.81200	+	18.9761i	0.0601663	+	0.630090i	0.974388	+	0.224875i	$0.0721974\pi$
$907$	1.81200	+	18.9761i	0.0601663	+	0.630090i	−0.914221	+	0.405215i	$0.867197\pi$
$908$	−2.85961	+	11.7875i	−0.0948995	+	0.391181i
$909$	−1.64843	−	5.61402i	−0.0546748	−	0.186205i
$910$	0.682728	−	4.47831i	0.0226322	−	0.148455i
$911$	21.4746	−	3.08758i	0.711485	−	0.102296i	0.222937	−	0.974833i	$-0.428436\pi$
$911$	21.4746	−	3.08758i	0.711485	−	0.102296i	0.488548	+	0.872537i	$0.337527\pi$
$912$	−0.825242	−	4.28176i	−0.0273265	−	0.141783i
$913$	−15.6979	−	11.1784i	−0.519524	−	0.369952i
$914$	7.36301	−	14.2822i	0.243547	−	0.472415i
$915$	−0.214217	+	0.272399i	−0.00708179	+	0.00900523i
$916$	18.9790	+	12.1971i	0.627085	+	0.403003i
$917$	−6.62560	+	0.575965i	−0.218797	+	0.0190201i
$918$	2.11290	−	7.19588i	0.0697361	−	0.237499i
$919$	−28.9967	−	16.7413i	−0.956513	−	0.552243i	−0.0614149	−	0.998112i	$-0.519561\pi$
$919$	−28.9967	−	16.7413i	−0.956513	−	0.552243i	−0.895098	+	0.445869i	$0.852895\pi$
$920$	−0.519911	−	1.16753i	−0.0171409	−	0.0384922i
$921$	6.16615	+	10.6801i	0.203182	+	0.351921i
$922$	20.8244	+	21.8400i	0.685816	+	0.719263i
$923$	35.8484	+	31.0628i	1.17996	+	1.02244i
$924$	−3.15735	−	3.36811i	−0.103869	−	0.110803i
$925$	−41.0716	−	5.90521i	−1.35043	−	0.194162i
$926$	0.282615	+	5.93282i	0.00928730	+	0.194964i
$927$	−3.13565	+	4.40340i	−0.102988	+	0.144627i
$928$	0.611522	−	1.76688i	0.0200742	−	0.0580006i
$929$	6.92846	−	17.3065i	0.227315	−	0.567806i	−0.770235	−	0.637760i	$-0.779861\pi$
$929$	6.92846	−	17.3065i	0.227315	−	0.567806i	0.997550	+	0.0699540i	$0.0222853\pi$
$930$	0.793486	−	1.73749i	0.0260194	−	0.0569746i
$931$	−13.2887	+	14.8200i	−0.435518	+	0.485705i
$932$	27.1941	−	7.98492i	0.890773	−	0.261555i
$933$	6.72761	+	9.44760i	0.220252	+	0.309301i
$934$	4.70201	−	3.69771i	0.153855	−	0.120993i
$935$	−0.384126	−	0.132947i	−0.0125623	−	0.00434784i
$936$	0.396057	−	4.14769i	0.0129455	−	0.135572i
$937$	−40.3794	+	25.9503i	−1.31914	+	0.847759i	−0.995156	−	0.0983042i	$-0.968658\pi$
$937$	−40.3794	+	25.9503i	−1.31914	+	0.847759i	−0.323982	+	0.946063i	$0.605022\pi$
$938$	−4.34055	−	1.78059i	−0.141724	−	0.0581382i
$939$	1.07698	−	1.67582i	0.0351460	−	0.0546883i
$940$	2.66560	−	0.922572i	0.0869422	−	0.0300910i
$941$	−6.76978	−	27.9054i	−0.220689	−	0.909691i	−0.969142	−	0.246503i	$-0.920718\pi$
$941$	−6.76978	−	27.9054i	−0.220689	−	0.909691i	0.748453	−	0.663188i	$-0.230797\pi$
$942$	9.26306	−	5.34803i	0.301807	−	0.174248i
$943$	−50.7897	+	11.8143i	−1.65394	+	0.384725i
$944$			7.07138i			0.230154i
$945$	1.94332	+	3.43289i	0.0632161	+	0.111672i
$946$	8.29928	−	9.57788i	0.269833	−	0.311404i
$947$	1.99326	−	1.02760i	0.0647722	−	0.0333924i	−0.425536	−	0.904941i	$-0.639914\pi$
$947$	1.99326	−	1.02760i	0.0647722	−	0.0333924i	0.490308	+	0.871549i	$0.336884\pi$
$948$	16.7426	−	6.70273i	0.543774	−	0.217694i
$949$	−3.58124	−	1.84626i	−0.116252	−	0.0599320i
$950$	−13.9526	−	1.33232i	−0.452683	−	0.0432260i
$951$	12.8416	−	11.1273i	0.416418	−	0.360829i
$952$	−3.23843	+	1.44585i	−0.104958	+	0.0468603i
$953$	38.1063	+	17.4026i	1.23438	+	0.563724i	0.922353	−	0.386348i	$-0.126264\pi$
$953$	38.1063	+	17.4026i	1.23438	+	0.563724i	0.312030	+	0.950072i	$0.398991\pi$
$954$	−4.94076	−	1.19861i	−0.159963	−	0.0388066i
$955$	2.09537	−	2.19756i	0.0678046	−	0.0711114i
$956$	−2.13294	+	0.203671i	−0.0689843	+	0.00658720i
$957$	3.02878	+	1.21254i	0.0979065	+	0.0391959i
$958$	16.4302	+	18.9615i	0.530836	+	0.612617i
$959$	−8.34740	−	9.80026i	−0.269552	−	0.316467i
$960$	0.220936	+	0.343784i	0.00713069	+	0.0110956i
$961$	−7.19454	−	5.65785i	−0.232082	−	0.182511i
$962$	2.57358	−	54.0262i	0.0829757	−	1.74187i
$963$	−0.261897	+	1.35885i	−0.00843953	+	0.0437884i
$964$	5.63588	−	5.37380i	0.181519	−	0.173078i
$965$	1.84247			0.0593111
$966$	8.39912	−	17.5513i	0.270237	−	0.564702i
$967$	−3.70831			−0.119251			−0.0596255	−	0.998221i	$-0.518991\pi$
$967$	−3.70831			−0.119251			−0.0596255	+	0.998221i	$0.518991\pi$
$968$	7.02399	−	6.69736i	0.225759	−	0.215261i
$969$	1.10621	−	5.73955i	0.0355365	−	0.184381i
$970$	0.0108757	−	0.228310i	0.000349199	−	0.00733058i
$971$	39.2715	+	30.8835i	1.26028	+	0.991098i	0.999671	+	0.0256548i	$0.00816709\pi$
$971$	39.2715	+	30.8835i	1.26028	+	0.991098i	0.260613	+	0.965443i	$0.416075\pi$
$972$	3.57449	+	5.56201i	0.114652	+	0.178402i
$973$	15.7034	−	2.88857i	0.503428	−	0.0926033i
$974$	−7.32194	−	8.44996i	−0.234610	−	0.270754i
$975$	45.0836	+	18.0487i	1.44383	+	0.578022i
$976$	0.844159	−	0.0806074i	0.0270209	−	0.00258018i
$977$	22.0742	−	23.1508i	0.706217	−	0.740659i	−0.268701	−	0.963224i	$-0.586594\pi$
$977$	22.0742	−	23.1508i	0.706217	−	0.740659i	0.974918	+	0.222564i	$0.0714428\pi$
$978$	−20.3186	−	4.92924i	−0.649718	−	0.157620i
$979$	11.0422	+	5.04281i	0.352911	+	0.161169i
$980$	0.639964	−	1.75224i	0.0204429	−	0.0559733i
$981$	−0.654147	+	0.566822i	−0.0208853	+	0.0180972i
$982$	−8.41719	−	0.803744i	−0.268603	−	0.0256485i
$983$	−32.1487	−	16.5738i	−1.02539	−	0.528623i	−0.138378	−	0.990379i	$-0.544189\pi$
$983$	−32.1487	−	16.5738i	−1.02539	−	0.528623i	−0.887007	+	0.461757i	$0.847219\pi$
$984$	15.4792	−	6.19692i	0.493458	−	0.197551i
$985$	−3.98953	+	2.05674i	−0.127117	+	0.0655333i
$986$	1.64126	−	1.89412i	0.0522685	−	0.0603210i
$987$	37.0067	+	21.7867i	1.17793	+	0.693477i
$988$		−	18.2700i		−	0.581246i
$989$	50.3089	+	17.9463i	1.59973	+	0.570661i
$990$	0.170304	−	0.0983253i	0.00541263	−	0.00312498i
$991$	4.18636	+	17.2564i	0.132984	+	0.548168i	0.998852	+	0.0478956i	$0.0152515\pi$
$991$	4.18636	+	17.2564i	0.132984	+	0.548168i	−0.865868	+	0.500272i	$0.833233\pi$
$992$	−4.41703	+	1.52875i	−0.140241	+	0.0485379i
$993$	9.83762	−	15.3076i	0.312187	−	0.485773i
$994$	11.9438	+	15.4560i	0.378835	+	0.490235i
$995$	0.953308	−	0.612654i	0.0302219	−	0.0194224i
$996$	−2.46866	+	25.8530i	−0.0782225	+	0.819183i
$997$	23.8056	+	8.23918i	0.753929	+	0.260937i	0.676884	−	0.736090i	$-0.263330\pi$
$997$	23.8056	+	8.23918i	0.753929	+	0.260937i	0.0770458	+	0.997028i	$0.475451\pi$
$998$	−11.5173	+	9.05730i	−0.364573	+	0.286704i
$999$	27.3203	+	38.3660i	0.864376	+	1.21385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.o.b.5.2	✓	160
7.3	odd	6	inner	322.2.o.b.143.2	yes	160
23.14	odd	22	inner	322.2.o.b.313.2	yes	160
161.129	even	66	inner	322.2.o.b.129.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.o.b.5.2	✓	160	1.1	even	1	trivial
322.2.o.b.129.2	yes	160	161.129	even	66	inner
322.2.o.b.143.2	yes	160	7.3	odd	6	inner
322.2.o.b.313.2	yes	160	23.14	odd	22	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723734 - 0.690079i) q^{2} +(-0.290209 + 1.50575i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.209478 - 0.164735i) q^{5} +(0.829051 + 1.29003i) q^{6} +(0.478644 + 2.60210i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.602045 + 0.241023i) q^{9} +O(q^{10})\)	\(q+(0.723734 - 0.690079i) q^{2} +(-0.290209 + 1.50575i) q^{3} +(0.0475819 - 0.998867i) q^{4} +(-0.209478 - 0.164735i) q^{5} +(0.829051 + 1.29003i) q^{6} +(0.478644 + 2.60210i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.602045 + 0.241023i) q^{9} +(-0.265286 + 0.0253318i) q^{10} +(-0.785235 + 0.823530i) q^{11} +(1.49023 + 0.361527i) q^{12} +(5.84432 + 2.66901i) q^{13} +(2.14206 + 1.55292i) q^{14} +(0.308842 - 0.267613i) q^{15} +(-0.995472 - 0.0950560i) q^{16} +(-1.19145 - 0.614236i) q^{17} +(0.602045 - 0.241023i) q^{18} +(2.52750 - 1.30302i) q^{19} +(-0.174516 + 0.201402i) q^{20} +(-4.05701 - 0.0344348i) q^{21} +1.13789i q^{22} +(-4.46895 + 1.74027i) q^{23} +(1.32802 - 0.766730i) q^{24} +(-1.16205 - 4.79004i) q^{25} +(6.07157 - 2.10139i) q^{26} +(-3.02479 + 4.70667i) q^{27} +(2.62192 - 0.354289i) q^{28} +(-1.57290 + 1.01084i) q^{29} +(0.0388453 - 0.406806i) q^{30} +(4.41703 + 1.52875i) q^{31} +(-0.786053 + 0.618159i) q^{32} +(-1.01215 - 1.42136i) q^{33} +(-1.28617 + 0.377652i) q^{34} +(0.328391 - 0.623930i) q^{35} +(0.269396 - 0.589895i) q^{36} +(3.12879 - 7.81534i) q^{37} +(0.930054 - 2.68721i) q^{38} +(-5.71494 + 8.02551i) q^{39} +(0.0126802 + 0.266191i) q^{40} +(10.7625 + 1.54741i) q^{41} +(-2.95996 + 2.77474i) q^{42} +(-8.41723 - 7.29357i) q^{43} +(0.785235 + 0.823530i) q^{44} +(-0.0864101 - 0.149667i) q^{45} +(-2.03341 + 4.34342i) q^{46} +(-9.16658 - 5.29233i) q^{47} +(0.432026 - 1.47134i) q^{48} +(-6.54180 + 2.49095i) q^{49} +(-4.14652 - 2.66481i) q^{50} +(1.27066 - 1.61577i) q^{51} +(2.94407 - 5.71071i) q^{52} +(-6.38608 - 4.54750i) q^{53} +(1.05883 + 5.49372i) q^{54} +(0.300153 - 0.0431555i) q^{55} +(1.65309 - 2.06574i) q^{56} +(1.22851 + 4.18393i) q^{57} +(-0.440801 + 1.81701i) q^{58} +(-0.672177 - 7.03936i) q^{59} +(-0.252615 - 0.321226i) q^{60} +(-0.832675 + 0.160485i) q^{61} +(4.25172 - 1.94169i) q^{62} +(-0.338998 + 1.68194i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.784575 - 1.52186i) q^{65} +(-1.71338 - 0.330227i) q^{66} +(-1.72326 + 0.418059i) q^{67} +(-0.670232 + 1.16088i) q^{68} +(-1.32347 - 7.23415i) q^{69} +(-0.192893 - 0.678175i) q^{70} +(7.08378 + 2.07998i) q^{71} +(-0.212103 - 0.612832i) q^{72} +(-0.626399 - 0.0298390i) q^{73} +(-3.12879 - 7.81534i) q^{74} +(7.54984 - 0.359643i) q^{75} +(-1.18128 - 2.58664i) q^{76} +(-2.51875 - 1.64908i) q^{77} +(1.40214 + 9.75210i) q^{78} +(9.57992 - 6.82183i) q^{79} +(0.192870 + 0.183901i) q^{80} +(-4.80122 - 4.57795i) q^{81} +(8.85699 - 6.30703i) q^{82} +(2.41023 + 16.7635i) q^{83} +(-0.227436 + 4.05078i) q^{84} +(0.148396 + 0.324943i) q^{85} +(-11.1250 + 0.529948i) q^{86} +(-1.06560 - 2.66175i) q^{87} +(1.13660 + 0.0541430i) q^{88} +(-3.48921 - 10.0814i) q^{89} +(-0.165820 - 0.0486891i) q^{90} +(-4.14768 + 16.4850i) q^{91} +(1.52565 + 4.54669i) q^{92} +(-3.58378 + 6.20729i) q^{93} +(-10.2863 + 2.49543i) q^{94} +(-0.744108 - 0.143415i) q^{95} +(-0.702672 - 1.36299i) q^{96} +(-0.122062 + 0.848961i) q^{97} +(-3.01557 + 6.31715i) q^{98} +(-0.671236 + 0.306543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 6 q^{3} + 8 q^{4} + 11 q^{7} - 16 q^{8} + 12 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 6 * q^3 + 8 * q^4 + 11 * q^7 - 16 * q^8 + 12 * q^9	\( 160 q + 8 q^{2} - 6 q^{3} + 8 q^{4} + 11 q^{7} - 16 q^{8} + 12 q^{9} - 27 q^{12} - 11 q^{14} + 8 q^{16} + 66 q^{17} + 12 q^{18} - 66 q^{21} - 18 q^{23} - 6 q^{24} - 2 q^{25} + 6 q^{26} - 22 q^{28} - 16 q^{29} - 22 q^{30} + 24 q^{31} + 8 q^{32} + 73 q^{35} + 20 q^{36} + 22 q^{37} - 33 q^{38} + 22 q^{42} - 110 q^{43} + 4 q^{46} - 162 q^{47} + 25 q^{49} + 4 q^{50} - 11 q^{51} + 60 q^{52} + 22 q^{53} - 54 q^{54} - 11 q^{56} - 44 q^{57} - 14 q^{58} - 36 q^{59} - 121 q^{63} - 16 q^{64} - 77 q^{65} + 32 q^{70} + 144 q^{71} - 32 q^{72} - 108 q^{73} - 22 q^{74} + 96 q^{75} - 17 q^{77} - 22 q^{78} - 44 q^{79} + 14 q^{81} - 27 q^{82} + 11 q^{84} - 2 q^{85} - 66 q^{86} - 108 q^{87} + 11 q^{88} + 198 q^{89} - 8 q^{92} - 50 q^{93} + 30 q^{94} - 28 q^{95} + 6 q^{96} - 45 q^{98} - 220 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 6 * q^3 + 8 * q^4 + 11 * q^7 - 16 * q^8 + 12 * q^9 - 27 * q^12 - 11 * q^14 + 8 * q^16 + 66 * q^17 + 12 * q^18 - 66 * q^21 - 18 * q^23 - 6 * q^24 - 2 * q^25 + 6 * q^26 - 22 * q^28 - 16 * q^29 - 22 * q^30 + 24 * q^31 + 8 * q^32 + 73 * q^35 + 20 * q^36 + 22 * q^37 - 33 * q^38 + 22 * q^42 - 110 * q^43 + 4 * q^46 - 162 * q^47 + 25 * q^49 + 4 * q^50 - 11 * q^51 + 60 * q^52 + 22 * q^53 - 54 * q^54 - 11 * q^56 - 44 * q^57 - 14 * q^58 - 36 * q^59 - 121 * q^63 - 16 * q^64 - 77 * q^65 + 32 * q^70 + 144 * q^71 - 32 * q^72 - 108 * q^73 - 22 * q^74 + 96 * q^75 - 17 * q^77 - 22 * q^78 - 44 * q^79 + 14 * q^81 - 27 * q^82 + 11 * q^84 - 2 * q^85 - 66 * q^86 - 108 * q^87 + 11 * q^88 + 198 * q^89 - 8 * q^92 - 50 * q^93 + 30 * q^94 - 28 * q^95 + 6 * q^96 - 45 * q^98 - 220 * q^99

Introduction

L-functions

Modular forms

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