LMFDB - Embedded newform 220.3.w.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

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

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99886 - 0.0675795i) q^{2} +(-1.94413 + 0.990585i) q^{3} +(3.99087 + 0.270163i) q^{4} +(-3.70748 + 3.35479i) q^{5} +(3.95299 - 1.84865i) q^{6} +(-1.57918 + 3.09932i) q^{7} +(-7.95892 - 0.809719i) q^{8} +(-2.49168 + 3.42950i) q^{9} +(7.63743 - 6.45520i) q^{10} +(6.04402 - 9.19075i) q^{11} +(-8.02639 + 3.42806i) q^{12} +(0.557233 + 3.51823i) q^{13} +(3.36601 - 6.08838i) q^{14} +(3.88462 - 10.1947i) q^{15} +(15.8540 + 2.15637i) q^{16} +(-1.87144 + 11.8158i) q^{17} +(5.21227 - 6.68669i) q^{18} +(-3.77795 - 1.22753i) q^{19} +(-15.7024 + 12.3869i) q^{20} -7.58980i q^{21} +(-12.7022 + 17.9625i) q^{22} +(-27.4174 - 27.4174i) q^{23} +(16.2753 - 6.30978i) q^{24} +(2.49076 - 24.8756i) q^{25} +(-0.876069 - 7.07010i) q^{26} +(4.51893 - 28.5314i) q^{27} +(-7.13963 + 11.9423i) q^{28} +(-6.37004 - 19.6050i) q^{29} +(-8.45375 + 20.1153i) q^{30} +(33.6775 - 46.3530i) q^{31} +(-31.5442 - 5.38169i) q^{32} +(-2.64616 + 23.8551i) q^{33} +(4.53924 - 23.4916i) q^{34} +(-4.54279 - 16.7885i) q^{35} +(-10.8705 + 13.0135i) q^{36} +(-10.3741 + 20.3602i) q^{37} +(7.46863 + 2.70897i) q^{38} +(-4.56844 - 6.28792i) q^{39} +(32.2239 - 23.6985i) q^{40} +(-66.3703 - 21.5650i) q^{41} +(-0.512915 + 15.1709i) q^{42} +(-3.10057 + 3.10057i) q^{43} +(26.6039 - 35.0462i) q^{44} +(-2.26742 - 21.0738i) q^{45} +(52.9506 + 56.6563i) q^{46} +(-17.8070 - 34.9482i) q^{47} +(-32.9584 + 11.5125i) q^{48} +(21.6895 + 29.8530i) q^{49} +(-6.65975 + 49.5545i) q^{50} +(-8.06622 - 24.8253i) q^{51} +(1.27334 + 14.1913i) q^{52} +(30.8259 - 4.88234i) q^{53} +(-10.9608 + 56.7248i) q^{54} +(8.42498 + 54.3509i) q^{55} +(15.0782 - 23.3885i) q^{56} +(8.56081 - 1.35590i) q^{57} +(11.4079 + 39.6180i) q^{58} +(26.3599 + 81.1273i) q^{59} +(18.2572 - 39.6363i) q^{60} +(8.24903 + 11.3538i) q^{61} +(-70.4490 + 90.3772i) q^{62} +(-6.69431 - 13.1383i) q^{63} +(62.6887 + 12.8890i) q^{64} +(-13.8689 - 11.1744i) q^{65} +(6.90141 - 47.5042i) q^{66} +(-39.5762 + 39.5762i) q^{67} +(-10.6609 + 46.6497i) q^{68} +(80.4622 + 26.1438i) q^{69} +(7.94584 + 33.8648i) q^{70} +(-38.5603 - 53.0737i) q^{71} +(22.6080 - 25.2775i) q^{72} +(54.8494 - 107.648i) q^{73} +(22.1122 - 39.9962i) q^{74} +(19.7990 + 50.8288i) q^{75} +(-14.7457 - 5.91958i) q^{76} +(18.9405 + 33.2462i) q^{77} +(8.70672 + 12.8774i) q^{78} +(-32.9819 + 45.3957i) q^{79} +(-66.0126 + 45.1922i) q^{80} +(7.68780 + 23.6606i) q^{81} +(131.207 + 47.5907i) q^{82} +(-14.8404 + 93.6988i) q^{83} +(2.05049 - 30.2899i) q^{84} +(-32.7012 - 50.0851i) q^{85} +(6.40713 - 5.98806i) q^{86} +(31.8046 + 31.8046i) q^{87} +(-55.5458 + 68.2544i) q^{88} -6.98261i q^{89} +(3.10809 + 42.2768i) q^{90} +(-11.7841 - 3.82889i) q^{91} +(-102.012 - 116.826i) q^{92} +(-19.5568 + 123.477i) q^{93} +(33.2318 + 71.0598i) q^{94} +(18.1248 - 8.12320i) q^{95} +(66.6571 - 20.7845i) q^{96} +(7.72602 + 48.7802i) q^{97} +(-41.3368 - 61.1378i) q^{98} +(16.4599 + 43.6283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.99886	−	0.0675795i	−0.999429	−	0.0337897i
$2$	−1.99886	−	0.0675795i	−0.999429	−	0.0337897i
$3$	−1.94413	+	0.990585i	−0.648044	+	0.330195i	−0.746929	−	0.664904i	$-0.768472\pi$
$3$	−1.94413	+	0.990585i	−0.648044	+	0.330195i	0.0988849	+	0.995099i	$0.468472\pi$
$4$	3.99087	+	0.270163i	0.997717	+	0.0675409i
$5$	−3.70748	+	3.35479i	−0.741495	+	0.670958i
$5$	−3.70748	+	3.35479i	−0.741495	+	0.670958i
$6$	3.95299	−	1.84865i	0.658831	−	0.308109i
$7$	−1.57918	+	3.09932i	−0.225598	+	0.442760i	−0.975865	−	0.218374i	$-0.929925\pi$
$7$	−1.57918	+	3.09932i	−0.225598	+	0.442760i	0.750268	+	0.661134i	$0.229925\pi$
$8$	−7.95892	−	0.809719i	−0.994865	−	0.101215i
$9$	−2.49168	+	3.42950i	−0.276853	+	0.381055i
$10$	7.63743	−	6.45520i	0.763743	−	0.645520i
$11$	6.04402	−	9.19075i	0.549456	−	0.835523i
$11$	6.04402	−	9.19075i	0.549456	−	0.835523i
$12$	−8.02639	+	3.42806i	−0.668866	+	0.285671i
$13$	0.557233	+	3.51823i	0.0428641	+	0.270633i	0.999807	−	0.0196429i	$-0.00625292\pi$
$13$	0.557233	+	3.51823i	0.0428641	+	0.270633i	−0.956943	+	0.290276i	$0.906253\pi$
$14$	3.36601	−	6.08838i	0.240430	−	0.434884i
$15$	3.88462	−	10.1947i	0.258974	−	0.679648i
$16$	15.8540	+	2.15637i	0.990876	+	0.134773i
$17$	−1.87144	+	11.8158i	−0.110085	+	0.695047i	0.869488	+	0.493955i	$0.164449\pi$
$17$	−1.87144	+	11.8158i	−0.110085	+	0.695047i	−0.979572	+	0.201092i	$0.935551\pi$
$18$	5.21227	−	6.68669i	0.289571	−	0.371483i
$19$	−3.77795	−	1.22753i	−0.198840	−	0.0646069i	0.207904	−	0.978149i	$-0.433336\pi$
$19$	−3.77795	−	1.22753i	−0.198840	−	0.0646069i	−0.406744	+	0.913542i	$0.633336\pi$
$20$	−15.7024	+	12.3869i	−0.785119	+	0.619345i
$21$		−	7.58980i		−	0.361419i
$22$	−12.7022	+	17.9625i	−0.577375	+	0.816479i
$23$	−27.4174	−	27.4174i	−1.19206	−	1.19206i	−0.976488	−	0.215571i	$-0.930839\pi$
$23$	−27.4174	−	27.4174i	−1.19206	−	1.19206i	−0.215571	−	0.976488i	$-0.569161\pi$
$24$	16.2753	−	6.30978i	0.678137	−	0.262908i
$25$	2.49076	−	24.8756i	0.0996302	−	0.995025i
$26$	−0.876069	−	7.07010i	−0.0336950	−	0.271927i
$27$	4.51893	−	28.5314i	0.167368	−	1.05672i
$28$	−7.13963	+	11.9423i	−0.254987	+	0.426512i
$29$	−6.37004	−	19.6050i	−0.219656	−	0.676033i	−0.998790	−	0.0491753i	$-0.984341\pi$
$29$	−6.37004	−	19.6050i	−0.219656	−	0.676033i	0.779134	−	0.626858i	$-0.215659\pi$
$30$	−8.45375	+	20.1153i	−0.281792	+	0.670510i
$31$	33.6775	−	46.3530i	1.08637	−	1.49526i	0.234059	−	0.972222i	$-0.424799\pi$
$31$	33.6775	−	46.3530i	1.08637	−	1.49526i	0.852310	−	0.523037i	$-0.175201\pi$
$32$	−31.5442	−	5.38169i	−0.985757	−	0.168178i
$33$	−2.64616	+	23.8551i	−0.0801865	+	0.722883i
$34$	4.53924	−	23.4916i	0.133507	−	0.690930i
$35$	−4.54279	−	16.7885i	−0.129794	−	0.479671i
$36$	−10.8705	+	13.0135i	−0.301958	+	0.361486i
$37$	−10.3741	+	20.3602i	−0.280380	+	0.550277i	−0.987652	−	0.156665i	$-0.949926\pi$
$37$	−10.3741	+	20.3602i	−0.280380	+	0.550277i	0.707272	+	0.706942i	$0.249926\pi$
$38$	7.46863	+	2.70897i	0.196543	+	0.0712887i
$39$	−4.56844	−	6.28792i	−0.117139	−	0.161229i
$40$	32.2239	−	23.6985i	0.805598	−	0.592462i
$41$	−66.3703	−	21.5650i	−1.61879	−	0.525976i	−0.647132	−	0.762378i	$-0.724032\pi$
$41$	−66.3703	−	21.5650i	−1.61879	−	0.525976i	−0.971655	+	0.236402i	$0.924032\pi$
$42$	−0.512915	+	15.1709i	−0.0122123	+	0.361213i
$43$	−3.10057	+	3.10057i	−0.0721063	+	0.0721063i	−0.742240	−	0.670134i	$-0.766237\pi$
$43$	−3.10057	+	3.10057i	−0.0721063	+	0.0721063i	0.670134	+	0.742240i	$0.266237\pi$
$44$	26.6039	−	35.0462i	0.604633	−	0.796504i
$45$	−2.26742	−	21.0738i	−0.0503871	−	0.468308i
$46$	52.9506	+	56.6563i	1.15110	+	1.23166i
$47$	−17.8070	−	34.9482i	−0.378872	−	0.743578i	0.620296	−	0.784368i	$-0.287013\pi$
$47$	−17.8070	−	34.9482i	−0.378872	−	0.743578i	−0.999168	+	0.0407899i	$0.987013\pi$
$48$	−32.9584	+	11.5125i	−0.686633	+	0.239843i
$49$	21.6895	+	29.8530i	0.442643	+	0.609246i
$50$	−6.65975	+	49.5545i	−0.133195	+	0.991090i
$51$	−8.06622	−	24.8253i	−0.158161	−	0.486770i
$52$	1.27334	+	14.1913i	0.0244874	+	0.272910i
$53$	30.8259	−	4.88234i	0.581620	−	0.0921196i	0.141310	−	0.989965i	$-0.454868\pi$
$53$	30.8259	−	4.88234i	0.581620	−	0.0921196i	0.440310	+	0.897846i	$0.354868\pi$
$54$	−10.9608	+	56.7248i	−0.202978	+	1.05046i
$55$	8.42498	+	54.3509i	0.153182	+	0.988198i
$56$	15.0782	−	23.3885i	0.269253	−	0.417653i
$57$	8.56081	−	1.35590i	0.150190	−	0.0237877i
$58$	11.4079	+	39.6180i	0.196688	+	0.683069i
$59$	26.3599	+	81.1273i	0.446777	+	1.37504i	0.880523	+	0.474004i	$0.157192\pi$
$59$	26.3599	+	81.1273i	0.446777	+	1.37504i	−0.433745	+	0.901036i	$0.642808\pi$
$60$	18.2572	−	39.6363i	0.304287	−	0.660605i
$61$	8.24903	+	11.3538i	0.135230	+	0.186128i	0.871261	−	0.490819i	$-0.163302\pi$
$61$	8.24903	+	11.3538i	0.135230	+	0.186128i	−0.736031	+	0.676947i	$0.763302\pi$
$62$	−70.4490	+	90.3772i	−1.13627	+	1.45770i
$63$	−6.69431	−	13.1383i	−0.106259	−	0.208545i
$64$	62.6887	+	12.8890i	0.979511	+	0.201390i
$65$	−13.8689	−	11.1744i	−0.213367	−	0.171913i
$66$	6.90141	−	47.5042i	0.104567	−	0.719761i
$67$	−39.5762	+	39.5762i	−0.590690	+	0.590690i	−0.937818	−	0.347128i	$-0.887157\pi$
$67$	−39.5762	+	39.5762i	−0.590690	+	0.590690i	0.347128	+	0.937818i	$0.387157\pi$
$68$	−10.6609	+	46.6497i	−0.156777	+	0.686024i
$69$	80.4622	+	26.1438i	1.16612	+	0.378895i
$70$	7.94584	+	33.8648i	0.113512	+	0.483783i
$71$	−38.5603	−	53.0737i	−0.543102	−	0.747516i	0.445954	−	0.895056i	$-0.352865\pi$
$71$	−38.5603	−	53.0737i	−0.543102	−	0.747516i	−0.989056	+	0.147540i	$0.952865\pi$
$72$	22.6080	−	25.2775i	0.314000	−	0.351077i
$73$	54.8494	−	107.648i	0.751362	−	1.47463i	−0.124578	−	0.992210i	$-0.539758\pi$
$73$	54.8494	−	107.648i	0.751362	−	1.47463i	0.875940	−	0.482421i	$-0.160242\pi$
$74$	22.1122	−	39.9962i	0.298814	−	0.540489i
$75$	19.7990	+	50.8288i	0.263987	+	0.677717i
$76$	−14.7457	−	5.91958i	−0.194022	−	0.0778892i
$77$	18.9405	+	33.2462i	0.245980	+	0.431769i
$78$	8.70672	+	12.8774i	0.111625	+	0.165095i
$79$	−32.9819	+	45.3957i	−0.417492	+	0.574629i	−0.965026	−	0.262155i	$-0.915567\pi$
$79$	−32.9819	+	45.3957i	−0.417492	+	0.574629i	0.547533	+	0.836784i	$0.315567\pi$
$80$	−66.0126	+	45.1922i	−0.825157	+	0.564903i
$81$	7.68780	+	23.6606i	0.0949111	+	0.292106i
$82$	131.207	+	47.5907i	1.60009	+	0.580374i
$83$	−14.8404	+	93.6988i	−0.178800	+	1.12890i	0.721108	+	0.692822i	$0.243633\pi$
$83$	−14.8404	+	93.6988i	−0.178800	+	1.12890i	−0.899909	+	0.436079i	$0.856367\pi$
$84$	2.05049	−	30.2899i	0.0244106	−	0.360594i
$85$	−32.7012	−	50.0851i	−0.384720	−	0.589236i
$86$	6.40713	−	5.98806i	0.0745015	−	0.0696286i
$87$	31.8046	+	31.8046i	0.365570	+	0.365570i
$88$	−55.5458	+	68.2544i	−0.631202	+	0.775619i
$89$		−	6.98261i		−	0.0784563i	−0.999230	−	0.0392281i	$-0.987510\pi$
$89$		−	6.98261i		−	0.0784563i	0.999230	−	0.0392281i	$-0.0124899\pi$
$90$	3.10809	+	42.2768i	0.0345344	+	0.469743i
$91$	−11.7841	−	3.82889i	−0.129496	−	0.0420757i
$92$	−102.012	−	116.826i	−1.10882	−	1.26985i
$93$	−19.5568	+	123.477i	−0.210288	+	1.32771i
$94$	33.2318	+	71.0598i	0.353530	+	0.755955i
$95$	18.1248	−	8.12320i	0.190787	−	0.0855073i
$96$	66.6571	−	20.7845i	0.694345	−	0.216505i
$97$	7.72602	+	48.7802i	0.0796497	+	0.502889i	0.994971	+	0.100164i	$0.0319368\pi$
$97$	7.72602	+	48.7802i	0.0796497	+	0.502889i	−0.915321	+	0.402725i	$0.868063\pi$
$98$	−41.3368	−	61.1378i	−0.421804	−	0.623855i
$99$	16.4599	+	43.6283i	0.166262	+	0.440690i
$100$	16.6608	−	98.6023i	0.166608	−	0.986023i
$101$	−4.59972	+	6.33098i	−0.0455418	+	0.0626830i	−0.831181	−	0.556003i	$-0.812334\pi$
$101$	−4.59972	+	6.33098i	−0.0455418	+	0.0626830i	0.785639	+	0.618685i	$0.212334\pi$
$102$	14.4456	+	50.1673i	0.141623	+	0.491836i
$103$	66.9723	−	131.440i	0.650216	−	1.27612i	−0.296801	−	0.954939i	$-0.595920\pi$
$103$	66.9723	−	131.440i	0.650216	−	1.27612i	0.947018	−	0.321182i	$-0.104080\pi$
$104$	−1.58619	−	28.4525i	−0.0152519	−	0.273582i
$105$	25.4622	+	28.1390i	0.242497	+	0.267991i
$106$	−61.9465	+	7.67591i	−0.584401	+	0.0724142i
$107$	−13.8933	+	7.07899i	−0.129844	+	0.0661588i	−0.517706	−	0.855559i	$-0.673214\pi$
$107$	−13.8933	+	7.07899i	−0.129844	+	0.0661588i	0.387862	+	0.921718i	$0.373214\pi$
$108$	25.7426	−	112.644i	0.238357	−	1.04300i
$109$	−180.398			−1.65503			−0.827515	−	0.561443i	$-0.810246\pi$
$109$	−180.398			−1.65503			−0.827515	+	0.561443i	$0.810246\pi$
$110$	−13.1673	−	109.209i	−0.119703	−	0.992810i
$111$		−	49.8594i		−	0.449184i
$112$	−31.7197	+	45.7314i	−0.283212	+	0.408316i
$113$	−26.7276	−	52.4558i	−0.236527	−	0.464211i	0.741980	−	0.670422i	$-0.233887\pi$
$113$	−26.7276	−	52.4558i	−0.236527	−	0.464211i	−0.978508	+	0.206211i	$0.933887\pi$
$114$	−17.2035	+	2.13171i	−0.150908	+	0.0186993i
$115$	193.629	+	9.66969i	1.68373	+	0.0840843i
$116$	−20.1254	−	79.9617i	−0.173495	−	0.689325i
$117$	−13.4542	−	6.85526i	−0.114993	−	0.0585920i
$118$	−47.2071	−	163.943i	−0.400060	−	1.38935i
$119$	−33.6656	−	24.4595i	−0.282904	−	0.205542i
$120$	−39.1722	+	77.9935i	−0.326435	+	0.649946i
$121$	−47.9397	−	111.098i	−0.396196	−	0.918166i
$122$	−15.7214	−	23.2521i	−0.128864	−	0.190591i
$123$	150.395	−	23.8202i	1.22272	−	0.193660i
$124$	146.925	−	175.890i	1.18488	−	1.41847i
$125$	74.2181	+	100.582i	0.593745	+	0.804654i
$126$	12.4931	+	26.7140i	0.0991515	+	0.212016i
$127$	−186.451	−	29.5310i	−1.46812	−	0.232528i	−0.629397	−	0.777084i	$-0.716698\pi$
$127$	−186.451	−	29.5310i	−1.46812	−	0.232528i	−0.838724	+	0.544556i	$0.816698\pi$
$128$	−124.435	−	29.9997i	−0.972147	−	0.234373i
$129$	2.95654	−	9.09929i	0.0229189	−	0.0705371i
$130$	26.9667	+	23.2732i	0.207436	+	0.179025i
$131$	−63.9787			−0.488387			−0.244193	−	0.969727i	$-0.578523\pi$
$131$	−63.9787			−0.488387			−0.244193	+	0.969727i	$0.578523\pi$
$132$	−17.0052	+	94.4878i	−0.128828	+	0.715816i
$133$	9.77059	−	9.77059i	0.0734631	−	0.0734631i
$134$	81.7818	−	76.4327i	0.610312	−	0.570393i
$135$	78.9630	+	120.940i	0.584911	+	0.895848i
$136$	24.4621	−	92.5256i	0.179868	−	0.680335i
$137$	−48.0255	−	7.60649i	−0.350551	−	0.0555218i	−0.0213240	−	0.999773i	$-0.506788\pi$
$137$	−48.0255	−	7.60649i	−0.350551	−	0.0555218i	−0.329227	+	0.944251i	$0.606788\pi$
$138$	−159.066	−	57.6952i	−1.15265	−	0.418081i
$139$	−115.416	+	37.5009i	−0.830330	+	0.269790i	−0.693184	−	0.720760i	$-0.743793\pi$
$139$	−115.416	+	37.5009i	−0.830330	+	0.269790i	−0.137145	+	0.990551i	$0.543793\pi$
$140$	−13.5940	−	68.2279i	−0.0971003	−	0.487342i
$141$	69.2382	+	50.3045i	0.491051	+	0.356770i
$142$	73.4898	+	108.693i	0.517534	+	0.765441i
$143$	35.7031	+	16.1429i	0.249672	+	0.112887i
$144$	−46.8984	+	48.9984i	−0.325683	+	0.340266i
$145$	89.3873	+	51.3148i	0.616464	+	0.353895i
$146$	−116.911	+	211.466i	−0.800760	+	1.44840i
$147$	−71.7392	−	36.5530i	−0.488022	−	0.248660i
$148$	−46.9021	+	78.4523i	−0.316906	+	0.530083i
$149$	−91.0686	+	66.1652i	−0.611199	+	0.444062i	−0.849836	−	0.527047i	$-0.823299\pi$
$149$	−91.0686	+	66.1652i	−0.611199	+	0.444062i	0.238637	+	0.971109i	$0.423299\pi$
$150$	−36.1405	−	102.938i	−0.240937	−	0.686250i
$151$	−23.3079	+	71.7345i	−0.154357	+	0.475063i	−0.998095	−	0.0616926i	$-0.980350\pi$
$151$	−23.3079	+	71.7345i	−0.154357	+	0.475063i	0.843738	+	0.536755i	$0.180350\pi$
$152$	29.0745	+	12.8289i	0.191279	+	0.0844006i
$153$	−35.8592	−	35.8592i	−0.234374	−	0.234374i
$154$	−35.6125	−	67.7345i	−0.231250	−	0.439834i
$155$	30.6464	+	284.834i	0.197719	+	1.83764i
$156$	−16.5333	−	26.3285i	−0.105982	−	0.168772i
$157$	157.719	−	80.3619i	1.00458	−	0.511860i	0.127314	−	0.991862i	$-0.459364\pi$
$157$	157.719	−	80.3619i	1.00458	−	0.511860i	0.877267	+	0.480003i	$0.159364\pi$
$158$	68.9940	−	88.5106i	0.436671	−	0.560194i
$159$	−55.0932	+	40.0276i	−0.346498	+	0.251746i
$160$	135.004	−	85.8718i	0.843774	−	0.536699i
$161$	128.272	−	41.6782i	0.796722	−	0.258871i
$162$	−13.7678	−	47.8137i	−0.0849867	−	0.295147i
$163$	−5.58571	−	35.2668i	−0.0342681	−	0.216361i	0.964612	−	0.263674i	$-0.0849342\pi$
$163$	−5.58571	−	35.2668i	−0.0342681	−	0.216361i	−0.998880	+	0.0473130i	$0.984934\pi$
$164$	−259.049	−	103.994i	−1.57957	−	0.634109i
$165$	−70.2184	−	97.3196i	−0.425566	−	0.589816i
$166$	35.9960	−	186.288i	0.216844	−	1.12221i
$167$	−22.2971	−	140.778i	−0.133515	−	0.842983i	−0.959995	−	0.280017i	$-0.909660\pi$
$167$	−22.2971	−	140.778i	−0.133515	−	0.842983i	0.826480	−	0.562967i	$-0.190340\pi$
$168$	−6.14561	+	60.4066i	−0.0365810	+	0.359563i
$169$	148.661	−	48.3029i	0.879652	−	0.285816i
$170$	61.9803	+	102.323i	0.364590	+	0.601899i
$171$	13.6233	−	9.89787i	0.0796681	−	0.0578823i
$172$	−13.2116	+	11.5363i	−0.0768117	+	0.0670715i
$173$	4.39809	−	2.24094i	0.0254225	−	0.0129534i	−0.441233	−	0.897393i	$-0.645459\pi$
$173$	4.39809	−	2.24094i	0.0254225	−	0.0129534i	0.466656	+	0.884439i	$0.345459\pi$
$174$	−61.4235	−	65.7221i	−0.353008	−	0.377713i
$175$	73.1642	+	47.0028i	0.418081	+	0.268587i
$176$	115.641	−	132.677i	0.657049	−	0.753848i
$177$	−131.611	−	131.611i	−0.743562	−	0.743562i
$178$	−0.471881	+	13.9572i	−0.00265102	+	0.0784115i
$179$	36.8391	−	113.379i	0.205805	−	0.633403i	−0.793874	−	0.608082i	$-0.791939\pi$
$179$	36.8391	−	113.379i	0.205805	−	0.633403i	0.999679	−	0.0253208i	$-0.00806073\pi$
$180$	−3.35559	−	84.7154i	−0.0186422	−	0.470641i
$181$	−213.562	+	155.162i	−1.17990	+	0.857248i	−0.992160	−	0.124971i	$-0.960116\pi$
$181$	−213.562	+	155.162i	−1.17990	+	0.857248i	−0.187740	+	0.982219i	$0.560116\pi$
$182$	23.2960	+	8.44976i	0.128000	+	0.0464273i
$183$	−27.2841	−	13.9020i	−0.149094	−	0.0759670i
$184$	196.012	+	240.413i	1.06528	+	1.30659i
$185$	−29.8428	−	110.288i	−0.161312	−	0.596151i
$186$	47.4358	−	245.491i	0.255031	−	1.31984i
$187$	97.2850	+	88.6148i	0.520241	+	0.473876i
$188$	−61.6236	−	144.284i	−0.327785	−	0.767469i
$189$	81.2917	+	59.0619i	0.430115	+	0.312497i
$190$	−36.7778	+	15.0123i	−0.193567	+	0.0790119i
$191$	−35.4160	+	11.5074i	−0.185424	+	0.0602480i	−0.400257	−	0.916403i	$-0.631079\pi$
$191$	−35.4160	+	11.5074i	−0.185424	+	0.0602480i	0.214833	+	0.976651i	$0.431079\pi$
$192$	−134.643	+	37.0406i	−0.701264	+	0.192920i
$193$	−224.593	−	35.5721i	−1.16370	−	0.184311i	−0.455440	−	0.890267i	$-0.650518\pi$
$193$	−224.593	−	35.5721i	−1.16370	−	0.184311i	−0.708256	+	0.705955i	$0.750518\pi$
$194$	−12.1467	−	98.0268i	−0.0626118	−	0.505293i
$195$	38.0320	+	7.98614i	0.195036	+	0.0409546i
$196$	78.4947	+	124.999i	0.400483	+	0.637751i
$197$	−23.5094	+	23.5094i	−0.119337	+	0.119337i	−0.764253	−	0.644916i	$-0.776892\pi$
$197$	−23.5094	+	23.5094i	−0.119337	+	0.119337i	0.644916	+	0.764253i	$0.276892\pi$
$198$	−29.9527	−	88.3192i	−0.151276	−	0.446056i
$199$	−250.493			−1.25876			−0.629379	−	0.777098i	$-0.716691\pi$
$199$	−250.493			−1.25876			−0.629379	+	0.777098i	$0.716691\pi$
$200$	−39.9660	+	195.966i	−0.199830	+	0.979831i
$201$	37.7378	−	116.145i	0.187750	−	0.577836i
$202$	9.62204	−	12.3439i	0.0476339	−	0.0611083i
$203$	70.8215	+	11.2170i	0.348875	+	0.0552563i
$204$	−25.4843	−	101.254i	−0.124923	−	0.496341i
$205$	318.412	−	142.707i	1.55323	−	0.696130i
$206$	−142.751	+	258.205i	−0.692965	+	1.25342i
$207$	162.343	−	25.7126i	0.784266	−	0.124216i
$208$	1.24777	+	56.9797i	0.00599889	+	0.273941i
$209$	−34.1159	+	27.3030i	−0.163234	+	0.130636i
$210$	−48.9937	−	57.9666i	−0.233303	−	0.276031i
$211$	−71.3005	−	51.8028i	−0.337917	−	0.245511i	0.405866	−	0.913933i	$-0.366970\pi$
$211$	−71.3005	−	51.8028i	−0.337917	−	0.245511i	−0.743782	+	0.668422i	$0.766970\pi$
$212$	124.341	−	11.1567i	0.586514	−	0.0526261i
$213$	127.540	+	64.9850i	0.598780	+	0.305094i
$214$	28.2491	−	13.2110i	0.132005	−	0.0617336i
$215$	1.09352	−	21.8970i	0.00508616	−	0.101847i
$216$	−59.0682	+	223.420i	−0.273464	+	1.03435i
$217$	90.4801	+	177.577i	0.416959	+	0.818328i
$218$	360.591	+	12.1912i	1.65409	+	0.0559230i
$219$			263.615i			1.20372i
$220$	18.9394	+	219.183i	0.0860880	+	0.996288i
$221$	−42.6135			−0.192821
$222$	−3.36947	+	99.6618i	−0.0151778	+	0.448927i
$223$	−84.0151	+	42.8079i	−0.376750	+	0.191963i	−0.632103	−	0.774884i	$-0.717808\pi$
$223$	−84.0151	+	42.8079i	−0.376750	+	0.191963i	0.255354	+	0.966848i	$0.417808\pi$
$224$	66.4937	−	89.2670i	0.296847	−	0.398513i
$225$	79.1047	+	70.5240i	0.351577	+	0.313440i
$226$	49.8797	+	106.658i	0.220707	+	0.471938i
$227$	137.275	−	269.416i	0.604734	−	1.18686i	−0.362265	−	0.932075i	$-0.617996\pi$
$227$	137.275	−	269.416i	0.604734	−	1.18686i	0.966999	−	0.254781i	$-0.0820035\pi$
$228$	34.5314	−	3.09839i	0.151453	−	0.0135894i
$229$	148.072	−	203.804i	0.646604	−	0.889973i	−0.352343	−	0.935871i	$-0.614615\pi$
$229$	148.072	−	203.804i	0.646604	−	0.889973i	0.998946	+	0.0458977i	$0.0146148\pi$
$230$	−386.383	−	32.4137i	−1.67993	−	0.140929i
$231$	−69.7560	−	45.8729i	−0.301974	−	0.198584i
$232$	34.8241	+	161.192i	0.150104	+	0.694794i
$233$	34.1396	+	215.549i	0.146522	+	0.925104i	0.945943	+	0.324333i	$0.105140\pi$
$233$	34.1396	+	215.549i	0.146522	+	0.925104i	−0.799421	+	0.600771i	$0.794860\pi$
$234$	26.4298	+	14.6119i	0.112948	+	0.0624441i
$235$	183.263	+	69.8308i	0.779842	+	0.297152i
$236$	83.2811	+	330.890i	0.352886	+	1.40208i
$237$	19.1529	−	120.927i	0.0808139	−	0.510239i
$238$	65.6398	+	51.1661i	0.275797	+	0.214984i
$239$	−129.224	−	41.9874i	−0.540686	−	0.175680i	0.0259265	−	0.999664i	$-0.491746\pi$
$239$	−129.224	−	41.9874i	−0.540686	−	0.175680i	−0.566613	+	0.823984i	$0.691746\pi$
$240$	83.5704	−	153.251i	0.348210	−	0.638545i
$241$			361.662i			1.50067i	0.661056	+	0.750337i	$0.270109\pi$
$241$			361.662i			1.50067i	−0.661056	+	0.750337i	$0.729891\pi$
$242$	88.3167	+	225.309i	0.364945	+	0.931029i
$243$	145.452	+	145.452i	0.598568	+	0.598568i
$244$	29.8534	+	47.5402i	0.122350	+	0.194837i
$245$	−180.564	−	37.9157i	−0.736996	−	0.154758i
$246$	−302.227	+	37.4495i	−1.22857	+	0.152234i
$247$	2.21354	−	13.9757i	0.00896169	−	0.0565819i
$248$	−305.569	+	341.651i	−1.23213	+	1.37762i
$249$	−63.9648	−	196.864i	−0.256887	−	0.790616i
$250$	−141.554	−	206.064i	−0.566216	−	0.824257i
$251$	−92.2195	+	126.929i	−0.367408	+	0.505694i	−0.952194	−	0.305494i	$-0.901179\pi$
$251$	−92.2195	+	126.929i	−0.367408	+	0.505694i	0.584786	+	0.811188i	$0.301179\pi$
$252$	−23.1666	−	54.2418i	−0.0919309	−	0.215245i
$253$	−417.697	+	86.2750i	−1.65098	+	0.341008i
$254$	370.694	+	71.6286i	1.45943	+	0.282002i
$255$	113.189	+	64.9786i	0.443878	+	0.254818i
$256$	246.700	+	68.3744i	0.963672	+	0.267087i
$257$	−76.3507	+	149.847i	−0.297084	+	0.583061i	−0.990506	−	0.137471i	$-0.956103\pi$
$257$	−76.3507	+	149.847i	−0.297084	+	0.583061i	0.693421	+	0.720532i	$0.256103\pi$
$258$	−6.52463	+	17.9884i	−0.0252893	+	0.0697224i
$259$	−46.7204	−	64.3051i	−0.180388	−	0.248282i
$260$	−52.3298	−	48.3422i	−0.201269	−	0.185932i
$261$	83.1073	+	27.0032i	0.318419	+	0.103460i
$262$	127.884	+	4.32365i	0.488108	+	0.0165025i
$263$	14.7959	−	14.7959i	0.0562583	−	0.0562583i	−0.678418	−	0.734676i	$-0.737334\pi$
$263$	14.7959	−	14.7959i	0.0562583	−	0.0562583i	0.734676	+	0.678418i	$0.237334\pi$
$264$	40.3765	−	187.718i	0.152941	−	0.711055i
$265$	−97.9070	+	121.516i	−0.369460	+	0.458549i
$266$	−20.1903	+	18.8697i	−0.0759034	+	0.0709388i
$267$	6.91687	+	13.5751i	0.0259059	+	0.0508431i
$268$	−168.635	+	147.251i	−0.629237	+	0.549445i
$269$	51.4570	+	70.8245i	0.191290	+	0.263288i	0.893880	−	0.448307i	$-0.147973\pi$
$269$	51.4570	+	70.8245i	0.191290	+	0.263288i	−0.702589	+	0.711595i	$0.747973\pi$
$270$	−149.663	−	247.077i	−0.554307	−	0.915101i
$271$	−110.965	−	341.514i	−0.409464	−	1.26020i	−0.917110	−	0.398634i	$-0.869484\pi$
$271$	−110.965	−	341.514i	−0.409464	−	1.26020i	0.507647	−	0.861565i	$-0.330516\pi$
$272$	−55.1491	+	183.292i	−0.202754	+	0.673869i
$273$	26.7027	−	4.22929i	0.0978120	−	0.0154919i
$274$	95.4821	+	18.4498i	0.348475	+	0.0673352i
$275$	−213.571	−	173.241i	−0.776623	−	0.629966i
$276$	314.051	+	126.074i	1.13787	+	0.456790i
$277$	−220.021	+	34.8479i	−0.794301	+	0.125805i	−0.540381	−	0.841420i	$-0.681720\pi$
$277$	−220.021	+	34.8479i	−0.794301	+	0.125805i	−0.253920	+	0.967225i	$0.581720\pi$
$278$	233.234	−	67.1592i	0.838972	−	0.241580i
$279$	75.0544	+	230.994i	0.269012	+	0.827934i
$280$	22.5617	+	137.297i	0.0805777	+	0.490345i
$281$	211.184	+	290.669i	0.751543	+	1.03441i	0.997871	+	0.0652239i	$0.0207762\pi$
$281$	211.184	+	290.669i	0.751543	+	1.03441i	−0.246327	+	0.969187i	$0.579224\pi$
$282$	−134.998	−	105.231i	−0.478716	−	0.373158i
$283$	64.8838	+	127.342i	0.229271	+	0.449970i	0.976769	−	0.214294i	$-0.0687450\pi$
$283$	64.8838	+	127.342i	0.229271	+	0.449970i	−0.747498	+	0.664264i	$0.768745\pi$
$284$	−139.550	−	222.227i	−0.491374	−	0.782491i
$285$	−27.1902	+	33.7467i	−0.0954044	+	0.118409i
$286$	−70.2745	−	34.6801i	−0.245715	−	0.121259i
$287$	171.648	−	171.648i	0.598076	−	0.598076i
$288$	97.0545	−	94.7714i	0.336995	−	0.329067i
$289$	138.745	+	45.0809i	0.480085	+	0.155989i
$290$	−175.205	−	108.612i	−0.604154	−	0.374523i
$291$	−63.3413	−	87.1819i	−0.217668	−	0.299594i
$292$	247.979	−	414.791i	0.849244	−	1.42052i
$293$	244.018	−	478.913i	0.832827	−	1.63451i	0.0614722	−	0.998109i	$-0.480420\pi$
$293$	244.018	−	478.913i	0.832827	−	1.63451i	0.771355	−	0.636406i	$-0.219580\pi$
$294$	140.926	+	77.9123i	0.479341	+	0.265008i
$295$	−369.894	−	212.346i	−1.25388	−	0.719816i
$296$	99.0524	−	153.645i	0.334636	−	0.519072i
$297$	−234.912	−	213.977i	−0.790951	−	0.720460i
$298$	186.505	−	126.101i	0.625855	−	0.423156i
$299$	81.1827	−	111.738i	0.271514	−	0.373707i
$300$	65.2833	+	208.200i	0.217611	+	0.693999i
$301$	−4.71329	−	14.5060i	−0.0156588	−	0.0481928i
$302$	51.4370	−	141.812i	0.170321	−	0.469576i
$303$	2.67110	−	16.8647i	0.00881552	−	0.0556590i
$304$	−57.2487	−	27.6080i	−0.188318	−	0.0908157i
$305$	−68.6728	−	14.4202i	−0.225157	−	0.0472795i
$306$	69.2542	+	74.1009i	0.226321	+	0.242160i
$307$	−175.853	−	175.853i	−0.572811	−	0.572811i	0.360102	−	0.932913i	$-0.382742\pi$
$307$	−175.853	−	175.853i	−0.572811	−	0.572811i	−0.932913	+	0.360102i	$0.882742\pi$
$308$	66.6070	+	137.798i	0.216256	+	0.447397i
$309$			321.879i			1.04168i
$310$	−42.0089	−	571.413i	−0.135513	−	1.84327i
$311$	19.8837	+	6.46060i	0.0639347	+	0.0207736i	0.340810	−	0.940132i	$-0.389299\pi$
$311$	19.8837	+	6.46060i	0.0639347	+	0.0207736i	−0.276875	+	0.960906i	$0.589299\pi$
$312$	31.2684	+	53.7441i	0.100219	+	0.172257i
$313$	31.9632	−	201.807i	0.102119	−	0.644752i	−0.882537	−	0.470243i	$-0.844166\pi$
$313$	31.9632	−	201.807i	0.102119	−	0.644752i	0.984656	−	0.174509i	$-0.0558338\pi$
$314$	−320.689	+	149.974i	−1.02130	+	0.477623i
$315$	68.8953	+	26.2520i	0.218715	+	0.0833396i
$316$	−143.891	+	172.258i	−0.455350	+	0.545119i
$317$	−60.4218	−	381.488i	−0.190605	−	1.20343i	−0.878543	−	0.477664i	$-0.841484\pi$
$317$	−60.4218	−	381.488i	−0.190605	−	1.20343i	0.687938	−	0.725770i	$-0.258516\pi$
$318$	112.829	−	76.2862i	0.354807	−	0.239894i
$319$	−218.685	−	59.9473i	−0.685533	−	0.187923i
$320$	−275.657	+	162.522i	−0.861427	+	0.507881i
$321$	19.9981	−	27.5250i	0.0622993	−	0.0857476i
$322$	−259.215	+	74.6402i	−0.805014	+	0.231802i
$323$	21.5745	−	42.3423i	0.0667940	−	0.131091i
$324$	24.2887	+	96.5033i	0.0749653	+	0.297850i
$325$	88.9060	−	5.09846i	0.273557	−	0.0156876i
$326$	8.78173	+	70.8707i	0.0269378	+	0.217395i
$327$	350.718	−	178.700i	1.07253	−	0.546483i
$328$	510.774	+	225.375i	1.55724	+	0.687120i
$329$	136.436			0.414699
$330$	133.780	+	199.273i	0.405394	+	0.603859i
$331$		−	236.229i		−	0.713683i	−0.934165	−	0.356842i	$-0.883854\pi$
$331$		−	236.229i		−	0.713683i	0.934165	−	0.356842i	$-0.116146\pi$
$332$	−84.5402	+	369.930i	−0.254639	+	1.11425i
$333$	−43.9766	−	86.3090i	−0.132062	−	0.259186i
$334$	35.0550	+	282.902i	0.104955	+	0.847013i
$335$	13.9579	−	279.498i	0.0416655	−	0.834322i
$336$	16.3664	−	120.329i	0.0487097	−	0.358122i
$337$	302.087	+	153.921i	0.896400	+	0.456739i	0.840571	−	0.541702i	$-0.182220\pi$
$337$	302.087	+	153.921i	0.896400	+	0.456739i	0.0558293	+	0.998440i	$0.482220\pi$
$338$	−300.417	+	86.5042i	−0.888807	+	0.255930i
$339$	103.924	+	75.5051i	0.306560	+	0.222729i
$340$	−116.975	−	208.717i	−0.344044	−	0.613875i
$341$	−222.472	−	589.680i	−0.652410	−	1.72927i
$342$	−27.8998	+	18.8638i	−0.0815785	+	0.0551573i
$343$	−295.121	+	46.7426i	−0.860412	+	0.136276i
$344$	27.1878	−	22.1666i	0.0790342	−	0.0644377i
$345$	−386.018	+	173.007i	−1.11889	+	0.501468i
$346$	−8.94260	+	4.18210i	−0.0258457	+	0.0120870i
$347$	391.496	+	62.0068i	1.12823	+	0.178694i	0.692524	−	0.721395i	$-0.256499\pi$
$347$	391.496	+	62.0068i	1.12823	+	0.178694i	0.435706	+	0.900089i	$0.356499\pi$
$348$	118.335	+	135.520i	0.340044	+	0.389426i
$349$	−96.3407	+	296.506i	−0.276048	+	0.849588i	0.712892	+	0.701273i	$0.247385\pi$
$349$	−96.3407	+	296.506i	−0.276048	+	0.849588i	−0.988940	+	0.148314i	$0.952615\pi$
$350$	−143.068	−	98.8963i	−0.408767	−	0.282561i
$351$	102.898			0.293157
$352$	−240.116	+	257.388i	−0.682146	+	0.731216i
$353$	−121.881	+	121.881i	−0.345273	+	0.345273i	−0.858345	−	0.513072i	$-0.828507\pi$
$353$	−121.881	+	121.881i	−0.345273	+	0.345273i	0.513072	+	0.858345i	$0.328507\pi$
$354$	254.177	+	271.965i	0.718013	+	0.768263i
$355$	321.012	+	67.4077i	0.904260	+	0.189881i
$356$	1.88645	−	27.8667i	0.00529901	−	0.0782771i
$357$	89.6796	+	14.2038i	0.251203	+	0.0397867i
$358$	−81.2982	+	224.139i	−0.227090	+	0.626087i
$359$	−668.725	+	217.282i	−1.86274	+	0.605242i	−0.868826	+	0.495118i	$0.835125\pi$
$359$	−668.725	+	217.282i	−1.86274	+	0.605242i	−0.993918	+	0.110124i	$0.964875\pi$
$360$	0.982322	+	169.561i	0.00272867	+	0.471003i
$361$	−279.289	−	202.915i	−0.773654	−	0.562092i
$362$	437.366	−	295.714i	1.20819	−	0.816890i
$363$	203.253	+	168.501i	0.559926	+	0.464190i
$364$	−45.9943	−	18.4642i	−0.126358	−	0.0507258i
$365$	157.784	+	583.111i	0.432284	+	1.59756i
$366$	53.5976	+	29.6319i	0.146442	+	0.0809614i
$367$	−302.226	−	153.992i	−0.823504	−	0.419596i	−0.00914512	−	0.999958i	$-0.502911\pi$
$367$	−302.226	−	153.992i	−0.823504	−	0.419596i	−0.814359	+	0.580362i	$0.802911\pi$
$368$	−375.554	−	493.798i	−1.02053	−	1.34184i
$369$	239.330	−	173.884i	0.648592	−	0.471230i
$370$	52.1983	+	222.467i	0.141076	+	0.601261i
$371$	−33.5478	+	103.249i	−0.0904253	+	0.278300i
$372$	−111.407	+	487.496i	−0.299482	+	1.31047i
$373$	395.322	+	395.322i	1.05984	+	1.05984i	0.998092	+	0.0617522i	$0.0196688\pi$
$373$	395.322	+	395.322i	1.05984	+	1.05984i	0.0617522	+	0.998092i	$0.480331\pi$
$374$	−188.470	−	183.703i	−0.503931	−	0.491184i
$375$	−243.924	−	122.025i	−0.650465	−	0.325399i
$376$	113.426	+	292.568i	0.301665	+	0.778107i
$377$	65.4252	−	33.3358i	0.173542	−	0.0884238i
$378$	−158.499	−	123.550i	−0.419310	−	0.326852i
$379$	−368.733	+	267.900i	−0.972910	+	0.706860i	−0.956113	−	0.292999i	$-0.905347\pi$
$379$	−368.733	+	267.900i	−0.972910	+	0.706860i	−0.0167970	+	0.999859i	$0.505347\pi$
$380$	74.5281	−	27.5219i	0.196127	−	0.0724262i
$381$	391.739	−	127.284i	1.02819	−	0.334078i
$382$	71.5693	−	20.6082i	0.187354	−	0.0539482i
$383$	−64.7246	−	408.655i	−0.168994	−	1.06698i	−0.915709	−	0.401841i	$-0.868370\pi$
$383$	−64.7246	−	408.655i	−0.168994	−	1.06698i	0.746716	−	0.665144i	$-0.231630\pi$
$384$	271.635	−	64.9398i	0.707382	−	0.169114i
$385$	−181.755	−	59.7183i	−0.472092	−	0.155112i
$386$	446.526	+	86.2815i	1.15680	+	0.223527i
$387$	−2.90778	−	18.3590i	−0.00751365	−	0.0474393i
$388$	17.6549	+	196.763i	0.0455023	+	0.507120i
$389$	−208.934	+	67.8868i	−0.537105	+	0.174516i	−0.564994	−	0.825095i	$-0.691122\pi$
$389$	−208.934	+	67.8868i	−0.537105	+	0.174516i	0.0278887	+	0.999611i	$0.491122\pi$
$390$	−75.4809	−	18.5333i	−0.193541	−	0.0475214i
$391$	375.268	−	272.648i	0.959764	−	0.697310i
$392$	−148.452	−	255.160i	−0.378705	−	0.650919i
$393$	124.383	−	63.3763i	0.316496	−	0.161263i
$394$	48.5807	−	45.4032i	0.123301	−	0.115237i
$395$	−30.0135	−	278.951i	−0.0759834	−	0.706205i
$396$	53.9025	+	178.562i	0.136118	+	0.450913i
$397$	−302.419	−	302.419i	−0.761762	−	0.761762i	0.214879	−	0.976641i	$-0.431064\pi$
$397$	−302.419	−	302.419i	−0.761762	−	0.761762i	−0.976641	+	0.214879i	$0.931064\pi$
$398$	500.700	+	16.9282i	1.25804	+	0.0425331i
$399$	−9.31672	+	28.6739i	−0.0233502	+	0.0718644i
$400$	93.1296	−	389.008i	0.232824	−	0.972519i
$401$	−84.2984	+	61.2463i	−0.210220	+	0.152734i	−0.687913	−	0.725793i	$-0.741473\pi$
$401$	−84.2984	+	61.2463i	−0.210220	+	0.152734i	0.477693	+	0.878527i	$0.341473\pi$
$402$	−83.2815	+	229.607i	−0.207168	+	0.571162i
$403$	181.847	+	92.6556i	0.451233	+	0.229915i
$404$	−20.0673	+	24.0234i	−0.0496715	+	0.0594639i
$405$	−107.879	−	61.9302i	−0.266367	−	0.152914i
$406$	−140.804	−	27.2073i	−0.346808	−	0.0670131i
$407$	124.425	+	218.403i	0.305712	+	0.536617i
$408$	44.0969	+	204.114i	0.108081	+	0.500279i
$409$	−405.406	−	294.545i	−0.991212	−	0.720158i	−0.0310261	−	0.999519i	$-0.509878\pi$
$409$	−405.406	−	294.545i	−0.991212	−	0.720158i	−0.960186	+	0.279361i	$0.909878\pi$
$410$	−646.105	+	263.732i	−1.57587	+	0.643249i
$411$	100.903	−	32.7853i	0.245506	−	0.0797696i
$412$	302.788	−	506.468i	0.734922	−	1.22929i
$413$	−293.067	−	46.4172i	−0.709605	−	0.112390i
$414$	−326.238	+	40.4248i	−0.788015	+	0.0976445i
$415$	−259.319	−	397.173i	−0.624866	−	0.957042i
$416$	1.35654	−	113.979i	0.00326092	−	0.273987i
$417$	187.236	−	187.236i	0.449007	−	0.449007i
$418$	70.0380	−	52.2693i	0.167555	−	0.125046i
$419$	704.010			1.68022			0.840108	−	0.542419i	$-0.182492\pi$
$419$	704.010			1.68022			0.840108	+	0.542419i	$0.182492\pi$
$420$	94.0141	+	119.178i	0.223843	+	0.283757i
$421$	74.0084	−	227.774i	0.175792	−	0.541032i	−0.823877	−	0.566769i	$-0.808193\pi$
$421$	74.0084	−	227.774i	0.175792	−	0.541032i	0.999669	+	0.0257370i	$0.00819325\pi$
$422$	139.019	+	108.365i	0.329428	+	0.256789i
$423$	164.224	+	26.0105i	0.388236	+	0.0614906i
$424$	−249.294	+	13.8978i	−0.587957	+	0.0327779i
$425$	289.264	+	75.9834i	0.680621	+	0.178785i
$426$	−250.543	−	138.515i	−0.588129	−	0.325152i
$427$	−48.2159	+	7.63664i	−0.112918	+	0.0178844i
$428$	−57.3588	+	24.4979i	−0.134016	+	0.0572380i
$429$	−85.4024	+	3.98308i	−0.199073	+	0.00928458i
$430$	−3.66559	+	43.6952i	−0.00852463	+	0.101617i
$431$	484.030	+	351.669i	1.12304	+	0.815936i	0.984667	−	0.174444i	$-0.0558128\pi$
$431$	484.030	+	351.669i	1.12304	+	0.815936i	0.138373	+	0.990380i	$0.455813\pi$
$432$	133.168	−	442.593i	0.308258	−	1.02452i
$433$	584.794	+	297.967i	1.35056	+	0.688146i	0.971459	−	0.237208i	$-0.0762323\pi$
$433$	584.794	+	297.967i	1.35056	+	0.688146i	0.379104	+	0.925354i	$0.376232\pi$
$434$	−168.856	−	361.066i	−0.389070	−	0.831950i
$435$	−224.612	−	11.2170i	−0.516350	−	0.0257862i
$436$	−719.945	−	48.7370i	−1.65125	−	0.111782i
$437$	69.9258	+	137.237i	0.160013	+	0.314044i
$438$	17.8150	−	526.929i	0.0406734	−	1.20303i
$439$		−	870.670i		−	1.98330i	−0.128945	−	0.991652i	$-0.541159\pi$
$439$		−	870.670i		−	1.98330i	0.128945	−	0.991652i	$-0.458841\pi$
$440$	−23.0448	−	439.396i	−0.0523745	−	0.998628i
$441$	−156.424			−0.354703
$442$	85.1783	+	2.87980i	0.192711	+	0.00651538i
$443$	−268.280	+	136.695i	−0.605598	+	0.308567i	−0.729769	−	0.683693i	$-0.760373\pi$
$443$	−268.280	+	136.695i	−0.605598	+	0.308567i	0.124172	+	0.992261i	$0.460373\pi$
$444$	13.4702	−	198.982i	0.0303383	−	0.448158i
$445$	23.4252	+	25.8879i	0.0526409	+	0.0581750i
$446$	170.827	−	79.8891i	0.383021	−	0.179124i
$447$	111.507	−	218.845i	0.249457	−	0.489586i
$448$	−138.944	+	173.938i	−0.310143	+	0.388255i
$449$	−62.6109	+	86.1766i	−0.139445	+	0.191930i	−0.873028	−	0.487670i	$-0.837847\pi$
$449$	−62.6109	+	86.1766i	−0.139445	+	0.191930i	0.733583	+	0.679600i	$0.237847\pi$
$450$	−153.353	−	146.313i	−0.340785	−	0.325141i
$451$	−599.342	+	479.653i	−1.32892	+	1.06353i
$452$	−92.4946	−	216.565i	−0.204634	−	0.479126i
$453$	−25.7454	−	162.550i	−0.0568330	−	0.358829i
$454$	−292.599	+	529.248i	−0.644492	+	1.16575i
$455$	56.5344	−	25.3377i	0.124251	−	0.0556872i
$456$	−69.2327	+	3.85964i	−0.151826	+	0.00846412i
$457$	−111.870	+	706.318i	−0.244792	+	1.54555i	0.492701	+	0.870198i	$0.336009\pi$
$457$	−111.870	+	706.318i	−0.244792	+	1.54555i	−0.737493	+	0.675355i	$0.763991\pi$
$458$	−309.748	+	397.368i	−0.676306	+	0.867617i
$459$	328.664	+	106.789i	0.716044	+	0.232657i
$460$	770.134	+	90.9019i	1.67420	+	0.197613i
$461$			67.6639i			0.146776i	0.997303	+	0.0733882i	$0.0233812\pi$
$461$			67.6639i			0.146776i	−0.997303	+	0.0733882i	$0.976619\pi$
$462$	136.332	+	96.4075i	0.295091	+	0.208674i
$463$	10.1650	+	10.1650i	0.0219545	+	0.0219545i	0.717999	−	0.696044i	$-0.245058\pi$
$463$	10.1650	+	10.1650i	0.0219545	+	0.0219545i	−0.696044	+	0.717999i	$0.745058\pi$
$464$	−58.7151	−	324.554i	−0.126541	−	0.699469i
$465$	−341.732	−	523.396i	−0.734908	−	1.12558i
$466$	−53.6736	−	433.159i	−0.115179	−	0.929527i
$467$	−59.7144	+	377.022i	−0.127868	+	0.807327i	0.837500	+	0.546437i	$0.184016\pi$
$467$	−59.7144	+	377.022i	−0.127868	+	0.807327i	−0.965368	+	0.260890i	$0.915984\pi$
$468$	−51.8419	−	30.9933i	−0.110773	−	0.0662249i
$469$	−60.1613	−	185.158i	−0.128276	−	0.394792i
$470$	−361.597	−	151.967i	−0.769356	−	0.323333i
$471$	−227.022	+	312.468i	−0.481999	+	0.663415i
$472$	−144.106	−	667.030i	−0.305309	−	1.41320i
$473$	9.75665	+	47.2365i	0.0206272	+	0.0998656i
$474$	−46.4561	+	240.421i	−0.0980086	+	0.507217i
$475$	−39.9455	+	90.9214i	−0.0840959	+	0.191413i
$476$	−127.747	−	106.710i	−0.268376	−	0.224180i
$477$	−60.0642	+	117.883i	−0.125921	+	0.247133i
$478$	255.463	+	92.6598i	0.534441	+	0.193849i
$479$	199.241	+	274.232i	0.415952	+	0.572509i	0.964658	−	0.263506i	$-0.0848790\pi$
$479$	199.241	+	274.232i	0.415952	+	0.572509i	−0.548705	+	0.836016i	$0.684879\pi$
$480$	−177.402	+	300.679i	−0.369588	+	0.626414i
$481$	−77.4128	−	25.1529i	−0.160941	−	0.0522930i
$482$	24.4409	−	722.912i	0.0507074	−	1.49982i
$483$	−208.092	+	208.092i	−0.430833	+	0.430833i
$484$	−161.306	−	456.329i	−0.333277	−	0.942829i
$485$	−192.291	−	154.932i	−0.396477	−	0.319448i
$486$	−280.908	−	300.568i	−0.578001	−	0.618452i
$487$	−347.474	−	681.957i	−0.713500	−	1.40032i	−0.907810	−	0.419382i	$-0.862247\pi$
$487$	−347.474	−	681.957i	−0.713500	−	1.40032i	0.194310	−	0.980940i	$-0.437753\pi$
$488$	−56.4600	−	97.0435i	−0.115697	−	0.198860i
$489$	45.7941	+	63.0301i	0.0936484	+	0.128896i
$490$	358.360	+	87.9905i	0.731346	+	0.179572i
$491$	245.327	+	755.039i	0.499648	+	1.53776i	0.809586	+	0.587001i	$0.199692\pi$
$491$	245.327	+	755.039i	0.499648	+	1.53776i	−0.309939	+	0.950757i	$0.600308\pi$
$492$	606.640	−	54.4319i	1.23301	−	0.110634i
$493$	243.569	−	38.5776i	0.494055	−	0.0782507i
$494$	−5.36902	+	27.7859i	−0.0108685	+	0.0562468i
$495$	−207.389	−	106.531i	−0.418967	−	0.215215i
$496$	633.878	−	662.261i	1.27798	−	1.33520i
$497$	225.386	−	35.6976i	0.453493	−	0.0718263i
$498$	114.553	+	397.825i	0.230025	+	0.798845i
$499$	−45.2225	−	139.180i	−0.0906262	−	0.278919i	0.895463	−	0.445136i	$-0.146845\pi$
$499$	−45.2225	−	139.180i	−0.0906262	−	0.278919i	−0.986089	+	0.166217i	$0.946845\pi$
$500$	269.021	+	421.459i	0.538042	+	0.842918i
$501$	182.801	+	251.604i	0.364873	+	0.502204i
$502$	192.911	−	247.481i	0.384286	−	0.492991i
$503$	254.510	+	499.503i	0.505983	+	0.993048i	0.992827	+	0.119559i	$0.0381481\pi$
$503$	254.510	+	499.503i	0.505983	+	0.993048i	−0.486844	+	0.873489i	$0.661852\pi$
$504$	42.6411	+	109.987i	0.0846053	+	0.218229i
$505$	−4.18574	−	38.9031i	−0.00828859	−	0.0770358i
$506$	840.748	−	144.224i	1.66156	−	0.285027i
$507$	−241.169	+	241.169i	−0.475678	+	0.475678i
$508$	−736.124	−	168.227i	−1.44906	−	0.331155i
$509$	−159.906	−	51.9565i	−0.314157	−	0.102076i	0.147695	−	0.989033i	$-0.452815\pi$
$509$	−159.906	−	51.9565i	−0.314157	−	0.102076i	−0.461851	+	0.886957i	$0.652815\pi$
$510$	−221.857	−	137.532i	−0.435015	−	0.269671i
$511$	247.019	+	339.992i	0.483402	+	0.665346i
$512$	−488.498	−	153.342i	−0.954097	−	0.299497i
$513$	−52.0955	+	102.243i	−0.101551	+	0.199304i
$514$	162.741	−	294.363i	0.316616	−	0.572690i
$515$	192.657	+	711.990i	0.374092	+	1.38251i
$516$	14.2574	−	35.5153i	0.0276307	−	0.0688281i
$517$	−428.826	−	47.5679i	−0.829450	−	0.0920076i
$518$	89.0417	+	131.694i	0.171895	+	0.254236i
$519$	−6.33063	+	8.71336i	−0.0121977	+	0.0167887i
$520$	101.333	+	100.166i	0.194871	+	0.192626i
$521$	289.060	+	889.635i	0.554818	+	1.70755i	0.696424	+	0.717630i	$0.254773\pi$
$521$	289.060	+	889.635i	0.554818	+	1.70755i	−0.141607	+	0.989923i	$0.545227\pi$
$522$	−164.295	−	59.5919i	−0.314741	−	0.114161i
$523$	−97.1674	+	613.491i	−0.185789	+	1.17302i	0.701796	+	0.712378i	$0.252382\pi$
$523$	−97.1674	+	613.491i	−0.185789	+	1.17302i	−0.887585	+	0.460645i	$0.847618\pi$
$524$	−255.330	−	17.2847i	−0.487272	−	0.0329861i
$525$	−188.801	−	18.9043i	−0.359621	−	0.0360083i
$526$	−30.5749	+	28.5751i	−0.0581271	+	0.0543252i
$527$	484.673	+	484.673i	0.919682	+	0.919682i
$528$	−93.3928	+	372.494i	−0.176880	+	0.705481i
$529$			974.424i			1.84201i
$530$	203.914	−	236.276i	0.384744	−	0.445803i
$531$	−343.906	−	111.742i	−0.647658	−	0.210437i
$532$	41.6328	−	36.3535i	0.0782571	−	0.0683336i
$533$	38.8870	−	245.523i	0.0729586	−	0.460643i
$534$	−12.9084	−	27.6022i	−0.0241731	−	0.0516894i
$535$	27.7606	−	72.8543i	0.0518889	−	0.136176i
$536$	347.029	−	282.938i	0.647443	−	0.527870i
$537$	40.6915	+	256.916i	0.0757756	+	0.478428i
$538$	−98.0690	−	145.046i	−0.182284	−	0.269601i
$539$	405.464	−	18.9104i	0.752251	−	0.0350843i
$540$	282.457	+	503.986i	0.523069	+	0.933308i
$541$	406.346	−	559.287i	0.751102	−	1.03380i	−0.246801	−	0.969066i	$-0.579379\pi$
$541$	406.346	−	559.287i	0.751102	−	1.03380i	0.997902	−	0.0647367i	$-0.0206207\pi$
$542$	198.723	+	690.137i	0.366648	+	1.27332i
$543$	261.492	−	513.206i	0.481569	−	0.945132i
$544$	122.622	−	362.648i	0.225408	−	0.666633i
$545$	668.822	−	605.199i	1.22720	−	1.11046i
$546$	−53.6607	+	6.64919i	−0.0982796	+	0.0121780i
$547$	−890.035	+	453.495i	−1.62712	+	0.829059i	−0.628431	+	0.777865i	$0.716303\pi$
$547$	−890.035	+	453.495i	−1.62712	+	0.829059i	−0.998689	+	0.0511942i	$0.983697\pi$
$548$	−189.608	−	43.3312i	−0.346001	−	0.0790716i
$549$	−59.4918			−0.108364
$550$	415.191	+	360.716i	0.754893	+	0.655848i
$551$			81.8860i			0.148613i
$552$	−619.223	−	273.228i	−1.12178	−	0.494978i
$553$	−88.6114	−	173.910i	−0.160238	−	0.314484i
$554$	442.146	−	54.7872i	0.798098	−	0.0988938i
$555$	167.268	+	184.852i	0.301383	+	0.333068i
$556$	−470.740	+	118.480i	−0.846655	+	0.213093i
$557$	737.242	+	375.643i	1.32359	+	0.674405i	0.965774	−	0.259386i	$-0.0835202\pi$
$557$	737.242	+	375.643i	1.32359	+	0.674405i	0.357820	+	0.933791i	$0.383520\pi$
$558$	−134.413	−	466.795i	−0.240883	−	0.836551i
$559$	−12.6363	−	9.18078i	−0.0226051	−	0.0164236i
$560$	−35.8193	−	275.961i	−0.0639630	−	0.492788i
$561$	−276.915	−	75.9098i	−0.493610	−	0.135312i
$562$	−402.483	−	595.278i	−0.716162	−	1.05921i
$563$	−462.401	+	73.2371i	−0.821316	+	0.130084i	−0.552930	−	0.833228i	$-0.686490\pi$
$563$	−462.401	+	73.2371i	−0.821316	+	0.130084i	−0.268386	+	0.963311i	$0.586490\pi$
$564$	262.730	+	219.464i	0.465833	+	0.389121i
$565$	275.070	+	104.813i	0.486850	+	0.185510i
$566$	−121.088	−	258.923i	−0.213936	−	0.457461i
$567$	−85.4723	−	13.5375i	−0.150745	−	0.0238756i
$568$	263.923	+	453.632i	0.464654	+	0.798648i
$569$	314.641	−	968.366i	0.552972	−	1.70187i	−0.148266	−	0.988947i	$-0.547369\pi$
$569$	314.641	−	968.366i	0.552972	−	1.70187i	0.701239	−	0.712927i	$-0.252631\pi$
$570$	56.6300	−	65.6173i	0.0993509	−	0.115118i
$571$	626.329			1.09690			0.548449	−	0.836184i	$-0.315219\pi$
$571$	626.329			1.09690			0.548449	+	0.836184i	$0.315219\pi$
$572$	138.125	+	74.0697i	0.241477	+	0.129492i
$573$	57.4544	−	57.4544i	0.100269	−	0.100269i
$574$	−354.699	+	331.500i	−0.617943	+	0.577525i
$575$	−750.314	+	613.734i	−1.30489	+	1.06736i
$576$	−200.403	+	182.876i	−0.347921	+	0.317493i
$577$	−233.889	−	37.0444i	−0.405353	−	0.0642017i	−0.0495713	−	0.998771i	$-0.515785\pi$
$577$	−233.889	−	37.0444i	−0.405353	−	0.0642017i	−0.355782	+	0.934569i	$0.615785\pi$
$578$	−274.284	−	99.4865i	−0.474540	−	0.172122i
$579$	471.876	−	153.322i	0.814985	−	0.264805i
$580$	342.869	+	228.940i	0.591154	+	0.394723i
$581$	−266.967	−	193.963i	−0.459496	−	0.333843i
$582$	120.719	+	178.545i	0.207420	+	0.306778i
$583$	141.440	−	312.822i	0.242607	−	0.536573i
$584$	−523.707	+	812.349i	−0.896758	+	1.39101i
$585$	72.8791	−	19.7203i	0.124580	−	0.0337100i
$586$	−520.122	+	940.788i	−0.887581	+	1.60544i
$587$	815.832	+	415.687i	1.38983	+	0.708155i	0.979058	−	0.203581i	$-0.0652581\pi$
$587$	815.832	+	415.687i	1.38983	+	0.708155i	0.410775	+	0.911737i	$0.365258\pi$
$588$	−276.426	−	165.259i	−0.470113	−	0.281053i
$589$	−184.132	+	133.779i	−0.312617	+	0.227130i
$590$	725.015	+	449.446i	1.22884	+	0.761773i
$591$	22.4173	−	68.9934i	0.0379312	−	0.116740i
$592$	−208.375	+	300.421i	−0.351985	+	0.507469i
$593$	259.129	+	259.129i	0.436979	+	0.436979i	0.890994	−	0.454015i	$-0.150009\pi$
$593$	259.129	+	259.129i	0.436979	+	0.436979i	−0.454015	+	0.890994i	$0.650009\pi$
$594$	455.096	+	443.584i	0.766155	+	0.746775i
$595$	206.871	−	22.2581i	0.347682	−	0.0374085i
$596$	−381.318	+	239.453i	−0.639796	+	0.401767i
$597$	486.991	−	248.134i	0.815731	−	0.415636i
$598$	−169.824	+	217.863i	−0.283987	+	0.364319i
$599$	157.968	−	114.770i	0.263719	−	0.191603i	−0.448066	−	0.894001i	$-0.647887\pi$
$599$	157.968	−	114.770i	0.263719	−	0.191603i	0.711785	+	0.702397i	$0.247887\pi$
$600$	−116.422	−	420.574i	−0.194037	−	0.700956i
$601$	−81.2154	+	26.3885i	−0.135134	+	0.0439076i	−0.375803	−	0.926700i	$-0.622633\pi$
$601$	−81.2154	+	26.3885i	−0.135134	+	0.0439076i	0.240669	+	0.970607i	$0.422633\pi$
$602$	8.44090	+	29.3140i	0.0140214	+	0.0486944i
$603$	−37.1154	−	234.338i	−0.0615513	−	0.388620i
$604$	−112.399	+	279.986i	−0.186091	+	0.463552i
$605$	550.446	+	251.066i	0.909828	+	0.414985i
$606$	−6.47886	+	33.5296i	−0.0106912	+	0.0553293i
$607$	85.5908	+	540.399i	0.141006	+	0.890278i	0.952194	+	0.305493i	$0.0988212\pi$
$607$	85.5908	+	540.399i	0.141006	+	0.890278i	−0.811188	+	0.584785i	$0.801179\pi$
$608$	112.566	+	59.0533i	0.185142	+	0.0971271i
$609$	−148.798	+	48.3473i	−0.244331	+	0.0793881i
$610$	136.293	+	33.4649i	0.223431	+	0.0548604i
$611$	113.033	−	82.1233i	0.184997	−	0.134408i
$612$	−133.422	−	152.797i	−0.218009	−	0.249669i
$613$	−472.612	+	240.808i	−0.770982	+	0.392835i	−0.794792	−	0.606882i	$-0.792420\pi$
$613$	−472.612	+	240.808i	−0.770982	+	0.392835i	0.0238104	+	0.999716i	$0.492420\pi$
$614$	339.621	+	363.389i	0.553129	+	0.591840i
$615$	−477.672	+	592.855i	−0.776703	+	0.963992i
$616$	−123.826	−	279.940i	−0.201015	−	0.454449i
$617$	−607.931	−	607.931i	−0.985301	−	0.985301i	0.0145927	−	0.999894i	$-0.495355\pi$
$617$	−607.931	−	607.931i	−0.985301	−	0.985301i	−0.999894	+	0.0145927i	$0.995355\pi$
$618$	21.7524	−	643.391i	0.0351981	−	1.04109i
$619$	152.133	−	468.218i	0.245773	−	0.756411i	−0.749736	−	0.661738i	$-0.769819\pi$
$619$	152.133	−	468.218i	0.245773	−	0.756411i	0.995508	−	0.0946734i	$-0.0301807\pi$
$620$	45.3541	+	1145.01i	0.0731517	+	1.84679i
$621$	−906.153	+	658.359i	−1.45918	+	1.06016i
$622$	−39.3080	−	14.2575i	−0.0631962	−	0.0229221i
$623$	21.6414	+	11.0268i	0.0347373	+	0.0176995i
$624$	−58.8690	−	109.540i	−0.0943414	−	0.175545i
$625$	−612.592	−	123.918i	−0.980148	−	0.198269i
$626$	−77.5279	+	401.224i	−0.123846	+	0.640934i
$627$	39.2800	−	86.8753i	0.0626475	−	0.138557i
$628$	651.147	−	278.104i	1.03686	−	0.442840i
$629$	−221.158	−	160.681i	−0.351603	−	0.255454i
$630$	−135.938	−	57.1299i	−0.215774	−	0.0906824i
$631$	−1126.54	+	366.036i	−1.78533	+	0.580089i	−0.999275	−	0.0380658i	$-0.987880\pi$
$631$	−1126.54	+	366.036i	−1.78533	+	0.580089i	−0.786056	+	0.618155i	$0.787880\pi$
$632$	299.258	−	334.594i	0.473509	−	0.529422i
$633$	189.933	+	30.0824i	0.300051	+	0.0475235i
$634$	94.9939	+	766.625i	0.149833	+	1.20919i
$635$	790.334	−	516.020i	1.24462	−	0.812630i
$636$	−230.684	+	144.860i	−0.362710	+	0.227768i
$637$	−92.9437	+	92.9437i	−0.145909	+	0.145909i
$638$	433.069	+	134.605i	0.678791	+	0.210979i
$639$	278.096			0.435205
$640$	561.982	−	306.230i	0.878096	−	0.478484i
$641$	314.274	−	967.234i	0.490286	−	1.50895i	−0.333890	−	0.942612i	$-0.608361\pi$
$641$	314.274	−	967.234i	0.490286	−	1.50895i	0.824176	−	0.566334i	$-0.191639\pi$
$642$	−41.8334	+	53.6671i	−0.0651611	+	0.0835936i
$643$	106.617	+	16.8864i	0.165811	+	0.0262619i	0.238788	−	0.971072i	$-0.423250\pi$
$643$	106.617	+	16.8864i	0.165811	+	0.0262619i	−0.0729767	+	0.997334i	$0.523250\pi$
$644$	523.177	−	131.678i	0.812387	−	0.204468i
$645$	19.5649	+	43.6540i	0.0303332	+	0.0676806i
$646$	−45.9857	+	83.1782i	−0.0711854	+	0.128759i
$647$	−245.112	+	38.8219i	−0.378843	+	0.0600029i	−0.342952	−	0.939353i	$-0.611427\pi$
$647$	−245.112	+	38.8219i	−0.378843	+	0.0600029i	−0.0358910	+	0.999356i	$0.511427\pi$
$648$	−42.0281	−	194.538i	−0.0648582	−	0.300213i
$649$	904.940	+	248.068i	1.39436	+	0.382231i
$650$	−178.055	+	4.18287i	−0.273931	+	0.00643519i
$651$	−351.810	−	255.605i	−0.540415	−	0.392635i
$652$	−12.7640	−	142.254i	−0.0195767	−	0.218181i
$653$	544.207	+	277.287i	0.833395	+	0.424636i	0.817981	−	0.575245i	$-0.195093\pi$
$653$	544.207	+	277.287i	0.833395	+	0.424636i	0.0154138	+	0.999881i	$0.495093\pi$
$654$	−713.112	+	333.494i	−1.09039	+	0.509930i
$655$	237.199	−	214.635i	0.362137	−	0.327687i
$656$	−1005.73	−	485.011i	−1.53313	−	0.739346i
$657$	232.512	+	456.330i	0.353899	+	0.694566i
$658$	−272.716	−	9.22028i	−0.414463	−	0.0140126i
$659$		−	269.497i		−	0.408949i	−0.978872	−	0.204474i	$-0.934451\pi$
$659$		−	269.497i		−	0.408949i	0.978872	−	0.204474i	$-0.0655485\pi$
$660$	−253.940	−	407.360i	−0.384758	−	0.617212i
$661$	761.720			1.15237			0.576187	−	0.817318i	$-0.304540\pi$
$661$	761.720			1.15237			0.576187	+	0.817318i	$0.304540\pi$
$662$	−15.9642	+	472.189i	−0.0241152	+	0.713276i
$663$	82.8463	−	42.2123i	0.124957	−	0.0636686i
$664$	193.983	−	733.724i	0.292144	−	1.10501i
$665$	−3.44594	+	69.0025i	−0.00518187	+	0.103763i
$666$	82.0703	+	175.491i	0.123229	+	0.263500i
$667$	−362.867	+	712.166i	−0.544028	+	1.06772i
$668$	−50.9515	−	567.851i	−0.0762747	−	0.850076i
$669$	120.932	−	166.448i	0.180765	−	0.248802i
$670$	−46.7882	+	557.733i	−0.0698332	+	0.832438i
$671$	154.207	−	7.19208i	0.229817	−	0.0107185i
$672$	−40.8460	+	239.414i	−0.0607827	+	0.356271i
$673$	−151.222	−	954.776i	−0.224698	−	1.41869i	−0.799634	−	0.600488i	$-0.794973\pi$
$673$	−151.222	−	954.776i	−0.224698	−	1.41869i	0.574936	−	0.818198i	$-0.305027\pi$
$674$	−593.427	−	328.081i	−0.880455	−	0.486767i
$675$	−698.480	−	183.476i	−1.03479	−	0.271816i
$676$	606.336	−	152.608i	0.896947	−	0.225751i
$677$	20.3733	−	128.632i	0.0300935	−	0.190003i	−0.968062	−	0.250711i	$-0.919336\pi$
$677$	20.3733	−	128.632i	0.0300935	−	0.190003i	0.998156	+	0.0607076i	$0.0193357\pi$
$678$	−202.627	−	157.947i	−0.298859	−	0.232960i
$679$	−163.386	−	53.0874i	−0.240628	−	0.0781847i
$680$	219.711	+	425.102i	0.323105	+	0.625149i
$681$			659.763i			0.968815i
$682$	404.840	+	1193.72i	0.593606	+	1.75032i
$683$	−700.152	−	700.152i	−1.02511	−	1.02511i	−0.999676	−	0.0254362i	$-0.991903\pi$
$683$	−700.152	−	700.152i	−1.02511	−	1.02511i	−0.0254362	−	0.999676i	$-0.508097\pi$
$684$	57.0426	−	35.8206i	0.0833956	−	0.0523693i
$685$	203.572	−	132.915i	0.297185	−	0.194036i
$686$	593.065	−	73.4878i	0.864526	−	0.107125i
$687$	−85.9869	+	542.900i	−0.125163	+	0.790247i
$688$	−55.8425	+	42.4705i	−0.0811664	+	0.0617304i
$689$	34.3544	+	105.732i	0.0498612	+	0.153457i
$690$	783.288	−	319.729i	1.13520	−	0.463375i
$691$	357.515	−	492.078i	0.517388	−	0.712124i	−0.467755	−	0.883858i	$-0.654937\pi$
$691$	357.515	−	492.078i	0.517388	−	0.712124i	0.985143	+	0.171734i	$0.0549371\pi$
$692$	18.1576	−	7.75508i	0.0262393	−	0.0112068i
$693$	−161.211	−	17.8825i	−0.232628	−	0.0258045i
$694$	−778.354	−	150.400i	−1.12155	−	0.216714i
$695$	302.094	−	526.230i	0.434667	−	0.757165i
$696$	−227.377	−	278.883i	−0.326691	−	0.400693i
$697$	379.016	−	743.860i	0.543781	−	1.06723i
$698$	212.609	−	586.163i	0.304598	−	0.839775i
$699$	−279.892	−	385.238i	−0.400417	−	0.551127i
$700$	279.290	+	207.348i	0.398986	+	0.296212i
$701$	−421.132	−	136.834i	−0.600759	−	0.195198i	−0.00718020	−	0.999974i	$-0.502286\pi$
$701$	−421.132	−	136.834i	−0.600759	−	0.195198i	−0.593579	+	0.804776i	$0.702286\pi$
$702$	−205.679	−	6.95380i	−0.292990	−	0.00990569i
$703$	64.1855	−	64.1855i	0.0913023	−	0.0913023i
$704$	497.351	−	498.255i	0.706464	−	0.707748i
$705$	−425.460	+	45.7770i	−0.603490	+	0.0649319i
$706$	251.860	−	235.387i	0.356743	−	0.333409i
$707$	−12.3579	−	24.2538i	−0.0174794	−	0.0343052i
$708$	−489.684	−	560.796i	−0.691644	−	0.792085i
$709$	−168.577	−	232.026i	−0.237767	−	0.327259i	0.673413	−	0.739267i	$-0.264828\pi$
$709$	−168.577	−	232.026i	−0.237767	−	0.327259i	−0.911180	+	0.412008i	$0.864828\pi$
$710$	−637.103	−	156.432i	−0.897328	−	0.220327i
$711$	−73.5042	−	226.223i	−0.103381	−	0.318176i
$712$	−5.65395	+	55.5740i	−0.00794094	+	0.0780534i
$713$	−2194.23	+	347.531i	−3.07745	+	0.487421i
$714$	−178.297	−	34.4520i	−0.249715	−	0.0482521i
$715$	−186.524	+	59.9271i	−0.260873	+	0.0838142i
$716$	177.651	−	442.528i	0.248116	−	0.618056i
$717$	292.821	−	46.3782i	0.408397	−	0.0646837i
$718$	1351.37	−	389.124i	1.88213	−	0.541955i
$719$	15.9495	+	49.0876i	0.0221829	+	0.0682721i	0.961535	−	0.274682i	$-0.0885725\pi$
$719$	15.9495	+	49.0876i	0.0221829	+	0.0682721i	−0.939352	+	0.342954i	$0.888573\pi$
$720$	9.49531	−	338.995i	0.0131879	−	0.470826i
$721$	301.615	+	415.137i	0.418328	+	0.575780i
$722$	544.546	+	424.473i	0.754219	+	0.587913i
$723$	−358.257	−	703.119i	−0.495515	−	0.972503i
$724$	−894.217	+	561.534i	−1.23511	+	0.775599i
$725$	−503.552	+	109.627i	−0.694554	+	0.151210i
$726$	−394.887	−	350.545i	−0.543921	−	0.482845i
$727$	−74.3118	+	74.3118i	−0.102217	+	0.102217i	−0.756366	−	0.654149i	$-0.773027\pi$
$727$	−74.3118	+	74.3118i	−0.102217	+	0.102217i	0.654149	+	0.756366i	$0.273027\pi$
$728$	90.6883	+	40.0156i	0.124572	+	0.0549665i
$729$	−639.806	−	207.886i	−0.877649	−	0.285165i
$730$	−275.981	−	1176.22i	−0.378056	−	1.61126i
$731$	−30.8332	−	42.4382i	−0.0421794	−	0.0580550i
$732$	−105.132	−	62.8520i	−0.143622	−	0.0858634i
$733$	114.982	−	225.665i	0.156865	−	0.307865i	−0.799176	−	0.601097i	$-0.794731\pi$
$733$	114.982	−	225.665i	0.156865	−	0.307865i	0.956041	+	0.293232i	$0.0947307\pi$
$734$	593.700	+	328.232i	0.808855	+	0.447182i
$735$	388.599	−	105.151i	0.528706	−	0.143062i
$736$	717.308	+	1012.41i	0.974603	+	1.37556i
$737$	124.536	+	602.934i	0.168976	+	0.818093i
$738$	−490.138	+	331.395i	−0.664144	+	0.449045i
$739$	313.964	−	432.134i	0.424849	−	0.584755i	−0.541912	−	0.840435i	$-0.682299\pi$
$739$	313.964	−	432.134i	0.424849	−	0.584755i	0.966761	+	0.255680i	$0.0822994\pi$
$740$	−89.3028	−	448.207i	−0.120679	−	0.605685i
$741$	9.54073	+	29.3633i	0.0128755	+	0.0396266i
$742$	74.0348	−	204.114i	0.0997773	−	0.275086i
$743$	98.4216	−	621.410i	0.132465	−	0.836352i	−0.828562	−	0.559898i	$-0.810840\pi$
$743$	98.4216	−	621.410i	0.132465	−	0.836352i	0.961027	−	0.276455i	$-0.0891595\pi$
$744$	255.632	−	966.906i	0.343592	−	1.29960i
$745$	115.664	−	550.822i	0.155254	−	0.739359i
$746$	−763.476	−	816.908i	−1.02343	−	1.09505i
$747$	−284.362	−	284.362i	−0.380672	−	0.380672i
$748$	364.311	+	379.933i	0.487047	+	0.507931i
$749$		−	54.2389i		−	0.0724150i
$750$	479.324	+	260.395i	0.639098	+	0.347193i
$751$	788.214	+	256.106i	1.04955	+	0.341020i	0.782493	−	0.622660i	$-0.213948\pi$
$751$	788.214	+	256.106i	1.04955	+	0.341020i	0.267060	+	0.963680i	$0.413948\pi$
$752$	−206.951	−	592.468i	−0.275201	−	0.787856i
$753$	53.5527	−	338.118i	0.0711191	−	0.449028i
$754$	−133.028	+	62.2121i	−0.176430	+	0.0825094i
$755$	−154.241	−	344.147i	−0.204292	−	0.455824i
$756$	308.468	+	257.670i	0.408027	+	0.340834i
$757$	174.782	+	1103.53i	0.230887	+	1.45777i	0.781971	+	0.623315i	$0.214215\pi$
$757$	174.782	+	1103.53i	0.230887	+	1.45777i	−0.551083	+	0.834450i	$0.685785\pi$
$758$	755.149	−	510.575i	0.996239	−	0.673582i
$759$	726.596	−	581.494i	0.957307	−	0.766132i
$760$	−150.831	+	49.9759i	−0.198462	+	0.0657577i
$761$	406.881	−	560.023i	0.534666	−	0.735905i	−0.453167	−	0.891426i	$-0.649706\pi$
$761$	406.881	−	560.023i	0.534666	−	0.735905i	0.987833	+	0.155521i	$0.0497057\pi$
$762$	−791.632	+	227.949i	−1.03889	+	0.299145i
$763$	284.882	−	559.112i	0.373371	−	0.732782i
$764$	−144.450	+	36.3562i	−0.189070	+	0.0475867i
$765$	253.247	+	12.6470i	0.331042	+	0.0165320i
$766$	101.759	+	821.218i	0.132844	+	1.07209i
$767$	−270.736	+	137.947i	−0.352980	+	0.179853i
$768$	−547.348	+	111.449i	−0.712693	+	0.145115i
$769$	−539.723			−0.701850			−0.350925	−	0.936404i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99886 - 0.0675795i) q^{2} +(-1.94413 + 0.990585i) q^{3} +(3.99087 + 0.270163i) q^{4} +(-3.70748 + 3.35479i) q^{5} +(3.95299 - 1.84865i) q^{6} +(-1.57918 + 3.09932i) q^{7} +(-7.95892 - 0.809719i) q^{8} +(-2.49168 + 3.42950i) q^{9} +(7.63743 - 6.45520i) q^{10} +(6.04402 - 9.19075i) q^{11} +(-8.02639 + 3.42806i) q^{12} +(0.557233 + 3.51823i) q^{13} +(3.36601 - 6.08838i) q^{14} +(3.88462 - 10.1947i) q^{15} +(15.8540 + 2.15637i) q^{16} +(-1.87144 + 11.8158i) q^{17} +(5.21227 - 6.68669i) q^{18} +(-3.77795 - 1.22753i) q^{19} +(-15.7024 + 12.3869i) q^{20} -7.58980i q^{21} +(-12.7022 + 17.9625i) q^{22} +(-27.4174 - 27.4174i) q^{23} +(16.2753 - 6.30978i) q^{24} +(2.49076 - 24.8756i) q^{25} +(-0.876069 - 7.07010i) q^{26} +(4.51893 - 28.5314i) q^{27} +(-7.13963 + 11.9423i) q^{28} +(-6.37004 - 19.6050i) q^{29} +(-8.45375 + 20.1153i) q^{30} +(33.6775 - 46.3530i) q^{31} +(-31.5442 - 5.38169i) q^{32} +(-2.64616 + 23.8551i) q^{33} +(4.53924 - 23.4916i) q^{34} +(-4.54279 - 16.7885i) q^{35} +(-10.8705 + 13.0135i) q^{36} +(-10.3741 + 20.3602i) q^{37} +(7.46863 + 2.70897i) q^{38} +(-4.56844 - 6.28792i) q^{39} +(32.2239 - 23.6985i) q^{40} +(-66.3703 - 21.5650i) q^{41} +(-0.512915 + 15.1709i) q^{42} +(-3.10057 + 3.10057i) q^{43} +(26.6039 - 35.0462i) q^{44} +(-2.26742 - 21.0738i) q^{45} +(52.9506 + 56.6563i) q^{46} +(-17.8070 - 34.9482i) q^{47} +(-32.9584 + 11.5125i) q^{48} +(21.6895 + 29.8530i) q^{49} +(-6.65975 + 49.5545i) q^{50} +(-8.06622 - 24.8253i) q^{51} +(1.27334 + 14.1913i) q^{52} +(30.8259 - 4.88234i) q^{53} +(-10.9608 + 56.7248i) q^{54} +(8.42498 + 54.3509i) q^{55} +(15.0782 - 23.3885i) q^{56} +(8.56081 - 1.35590i) q^{57} +(11.4079 + 39.6180i) q^{58} +(26.3599 + 81.1273i) q^{59} +(18.2572 - 39.6363i) q^{60} +(8.24903 + 11.3538i) q^{61} +(-70.4490 + 90.3772i) q^{62} +(-6.69431 - 13.1383i) q^{63} +(62.6887 + 12.8890i) q^{64} +(-13.8689 - 11.1744i) q^{65} +(6.90141 - 47.5042i) q^{66} +(-39.5762 + 39.5762i) q^{67} +(-10.6609 + 46.6497i) q^{68} +(80.4622 + 26.1438i) q^{69} +(7.94584 + 33.8648i) q^{70} +(-38.5603 - 53.0737i) q^{71} +(22.6080 - 25.2775i) q^{72} +(54.8494 - 107.648i) q^{73} +(22.1122 - 39.9962i) q^{74} +(19.7990 + 50.8288i) q^{75} +(-14.7457 - 5.91958i) q^{76} +(18.9405 + 33.2462i) q^{77} +(8.70672 + 12.8774i) q^{78} +(-32.9819 + 45.3957i) q^{79} +(-66.0126 + 45.1922i) q^{80} +(7.68780 + 23.6606i) q^{81} +(131.207 + 47.5907i) q^{82} +(-14.8404 + 93.6988i) q^{83} +(2.05049 - 30.2899i) q^{84} +(-32.7012 - 50.0851i) q^{85} +(6.40713 - 5.98806i) q^{86} +(31.8046 + 31.8046i) q^{87} +(-55.5458 + 68.2544i) q^{88} -6.98261i q^{89} +(3.10809 + 42.2768i) q^{90} +(-11.7841 - 3.82889i) q^{91} +(-102.012 - 116.826i) q^{92} +(-19.5568 + 123.477i) q^{93} +(33.2318 + 71.0598i) q^{94} +(18.1248 - 8.12320i) q^{95} +(66.6571 - 20.7845i) q^{96} +(7.72602 + 48.7802i) q^{97} +(-41.3368 - 61.1378i) q^{98} +(16.4599 + 43.6283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

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