LMFDB - Embedded newform 418.2.v.b.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	418.13
Dual form			418.2.v.b.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374607 - 0.927184i) q^{2} +(-0.582769 - 2.03236i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.69676 + 1.43389i) q^{5} +(-1.66606 + 1.30167i) q^{6} +(0.507726 + 1.14037i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.24671 + 0.779029i) q^{9} +O(q^{10})$	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.582769 - 2.03236i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.69676 + 1.43389i) q^{5} +(-1.66606 + 1.30167i) q^{6} +(0.507726 + 1.14037i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.24671 + 0.779029i) q^{9} +(2.33971 + 1.96325i) q^{10} +(-1.20183 + 3.09122i) q^{11} +(1.83100 + 1.05713i) q^{12} +(-0.0154167 - 0.441475i) q^{13} +(0.867136 - 0.897946i) q^{14} +(4.48577 + 4.64515i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-0.633903 + 1.01446i) q^{17} +(1.18933 + 0.864097i) q^{18} +(3.65165 + 2.38022i) q^{19} +(0.943822 - 2.90479i) q^{20} +(2.02175 - 1.69645i) q^{21} +(3.31634 - 0.0436757i) q^{22} +(-0.837859 + 4.75174i) q^{23} +(0.294248 - 2.09368i) q^{24} +(2.42052 - 3.58856i) q^{25} +(-0.403554 + 0.179674i) q^{26} +(-2.40379 - 2.16439i) q^{27} +(-1.15740 - 0.467618i) q^{28} +(1.45940 + 5.85335i) q^{29} +(2.62651 - 5.89924i) q^{30} +(0.935408 - 0.842245i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(6.98284 + 0.641075i) q^{33} +(1.17805 + 0.207722i) q^{34} +(-3.00439 - 2.34729i) q^{35} +(0.355647 - 1.42642i) q^{36} +(1.37335 - 1.89025i) q^{37} +(0.838972 - 4.27740i) q^{38} +(-0.888251 + 0.288610i) q^{39} +(-3.04683 + 0.213055i) q^{40} +(7.26672 - 2.08370i) q^{41} +(-2.33029 - 1.23903i) q^{42} +(-8.21055 + 1.44774i) q^{43} +(-1.28282 - 3.05849i) q^{44} +(2.24503 - 3.88850i) q^{45} +(4.71960 - 1.00318i) q^{46} +(-7.61805 - 0.532706i) q^{47} +(-2.05146 + 0.511485i) q^{48} +(3.64125 - 4.04402i) q^{49} +(-4.23400 - 0.899964i) q^{50} +(2.43116 + 0.697123i) q^{51} +(0.317764 + 0.306861i) q^{52} +(-5.85138 + 11.0048i) q^{53} +(-1.10631 + 3.03955i) q^{54} +(-1.19144 - 10.0596i) q^{55} +1.24829i q^{56} +(2.70939 - 8.80857i) q^{57} +(4.88043 - 3.54584i) q^{58} +(0.327971 + 4.69021i) q^{59} +(-6.45359 - 0.225364i) q^{60} +(1.81018 + 12.8801i) q^{61} +(-1.13133 - 0.551785i) q^{62} +(-1.52137 - 1.02618i) q^{63} +(0.669131 + 0.743145i) q^{64} +(0.674604 + 1.16845i) q^{65} +(-2.02142 - 6.71452i) q^{66} +(-6.00811 + 7.16019i) q^{67} +(-0.248709 - 1.17009i) q^{68} +(10.1455 - 1.06633i) q^{69} +(-1.05090 + 3.66493i) q^{70} +(1.04513 + 1.96561i) q^{71} +(-1.45578 + 0.204597i) q^{72} +(0.271266 - 0.182971i) q^{73} +(-2.26707 - 0.565245i) q^{74} +(-8.70383 - 2.82805i) q^{75} +(-4.28022 + 0.824460i) q^{76} +(-4.13533 + 0.198962i) q^{77} +(0.600339 + 0.715456i) q^{78} +(-3.16330 + 4.04884i) q^{79} +(1.33891 + 2.74516i) q^{80} +(-4.93128 + 10.1106i) q^{81} +(-4.65413 - 5.95702i) q^{82} +(-0.820449 + 3.85991i) q^{83} +(-0.275873 + 2.62475i) q^{84} +(0.254862 - 3.64470i) q^{85} +(4.41805 + 7.07036i) q^{86} +(11.0456 - 6.37718i) q^{87} +(-2.35523 + 2.33514i) q^{88} +(1.18754 + 3.26274i) q^{89} +(-4.44636 - 0.624895i) q^{90} +(0.495618 - 0.241729i) q^{91} +(-2.69813 - 4.00014i) q^{92} +(-2.25687 - 1.41025i) q^{93} +(2.35986 + 7.26289i) q^{94} +(-13.2606 - 1.18282i) q^{95} +(1.24273 + 1.71047i) q^{96} +(2.15274 - 0.869762i) q^{97} +(-5.11359 - 1.86119i) q^{98} +(-0.909821 - 4.79010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$3$	−0.582769	−	2.03236i	−0.336462	−	1.17338i	−0.929689	−	0.368346i	$-0.879924\pi$
$3$	−0.582769	−	2.03236i	−0.336462	−	1.17338i	0.593227	−	0.805035i	$-0.297854\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	−2.69676	+	1.43389i	−1.20603	+	0.641257i	−0.945944	−	0.324329i	$-0.894862\pi$
$5$	−2.69676	+	1.43389i	−1.20603	+	0.641257i	−0.260085	+	0.965586i	$0.583751\pi$
$6$	−1.66606	+	1.30167i	−0.680166	+	0.531404i
$7$	0.507726	+	1.14037i	0.191902	+	0.431020i	0.983713	−	0.179747i	$-0.0575279\pi$
$7$	0.507726	+	1.14037i	0.191902	+	0.431020i	−0.791810	+	0.610767i	$0.790861\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	−1.24671	+	0.779029i	−0.415569	+	0.259676i
$10$	2.33971	+	1.96325i	0.739881	+	0.620834i
$11$	−1.20183	+	3.09122i	−0.362364	+	0.932037i
$11$	−1.20183	+	3.09122i	−0.362364	+	0.932037i
$12$	1.83100	+	1.05713i	0.528565	+	0.305167i
$13$	−0.0154167	−	0.441475i	−0.00427581	−	0.122443i	−0.999652	−	0.0263877i	$-0.991600\pi$
$13$	−0.0154167	−	0.441475i	−0.00427581	−	0.122443i	0.995376	−	0.0960556i	$-0.0306227\pi$
$14$	0.867136	−	0.897946i	0.231752	−	0.239986i
$15$	4.48577	+	4.64515i	1.15822	+	1.19937i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	−0.633903	+	1.01446i	−0.153744	+	0.246042i	−0.915950	−	0.401293i	$-0.868561\pi$
$17$	−0.633903	+	1.01446i	−0.153744	+	0.246042i	0.762206	+	0.647335i	$0.224116\pi$
$18$	1.18933	+	0.864097i	0.280327	+	0.203670i
$19$	3.65165	+	2.38022i	0.837746	+	0.546060i
$19$	3.65165	+	2.38022i	0.837746	+	0.546060i
$20$	0.943822	−	2.90479i	0.211045	−	0.649530i
$21$	2.02175	−	1.69645i	0.441183	−	0.370196i
$22$	3.31634	−	0.0436757i	0.707045	−	0.00931169i
$23$	−0.837859	+	4.75174i	−0.174706	+	0.990806i	0.763777	+	0.645480i	$0.223343\pi$
$23$	−0.837859	+	4.75174i	−0.174706	+	0.990806i	−0.938483	+	0.345326i	$0.887768\pi$
$24$	0.294248	−	2.09368i	0.0600631	−	0.427371i
$25$	2.42052	−	3.58856i	0.484103	−	0.717712i
$26$	−0.403554	+	0.179674i	−0.0791434	+	0.0352369i
$27$	−2.40379	−	2.16439i	−0.462611	−	0.416536i
$28$	−1.15740	−	0.467618i	−0.218727	−	0.0883716i
$29$	1.45940	+	5.85335i	0.271005	+	1.08694i	0.939315	+	0.343057i	$0.111462\pi$
$29$	1.45940	+	5.85335i	0.271005	+	1.08694i	−0.668310	+	0.743883i	$0.732982\pi$
$30$	2.62651	−	5.89924i	0.479533	−	1.07705i
$31$	0.935408	−	0.842245i	0.168004	−	0.151272i	−0.580840	−	0.814018i	$-0.697276\pi$
$31$	0.935408	−	0.842245i	0.168004	−	0.151272i	0.748844	+	0.662746i	$0.230609\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	6.98284	+	0.641075i	1.21556	+	0.111597i
$34$	1.17805	+	0.207722i	0.202034	+	0.0356241i
$35$	−3.00439	−	2.34729i	−0.507834	−	0.396764i
$36$	0.355647	−	1.42642i	0.0592745	−	0.237737i
$37$	1.37335	−	1.89025i	0.225777	−	0.310755i	−0.681068	−	0.732220i	$-0.738484\pi$
$37$	1.37335	−	1.89025i	0.225777	−	0.310755i	0.906844	+	0.421465i	$0.138484\pi$
$38$	0.838972	−	4.27740i	0.136099	−	0.693885i
$39$	−0.888251	+	0.288610i	−0.142234	+	0.0462146i
$40$	−3.04683	+	0.213055i	−0.481747	+	0.0336870i
$41$	7.26672	−	2.08370i	1.13487	−	0.325419i	0.344946	−	0.938623i	$-0.387897\pi$
$41$	7.26672	−	2.08370i	1.13487	−	0.325419i	0.789925	+	0.613204i	$0.210119\pi$
$42$	−2.33029	−	1.23903i	−0.359571	−	0.191187i
$43$	−8.21055	+	1.44774i	−1.25210	+	0.220779i	−0.760093	−	0.649814i	$-0.774847\pi$
$43$	−8.21055	+	1.44774i	−1.25210	+	0.220779i	−0.492005	+	0.870593i	$0.663736\pi$
$44$	−1.28282	−	3.05849i	−0.193392	−	0.461085i
$45$	2.24503	−	3.88850i	0.334669	−	0.579664i
$46$	4.71960	−	1.00318i	0.695867	−	0.147911i
$47$	−7.61805	−	0.532706i	−1.11121	−	0.0777032i	−0.497668	−	0.867367i	$-0.665810\pi$
$47$	−7.61805	−	0.532706i	−1.11121	−	0.0777032i	−0.613539	+	0.789664i	$0.710255\pi$
$48$	−2.05146	+	0.511485i	−0.296102	+	0.0738266i
$49$	3.64125	−	4.04402i	0.520179	−	0.577717i
$50$	−4.23400	−	0.899964i	−0.598778	−	0.127274i
$51$	2.43116	+	0.697123i	0.340430	+	0.0976167i
$52$	0.317764	+	0.306861i	0.0440660	+	0.0425540i
$53$	−5.85138	+	11.0048i	−0.803749	+	1.51163i	0.0545664	+	0.998510i	$0.482622\pi$
$53$	−5.85138	+	11.0048i	−0.803749	+	1.51163i	−0.858316	+	0.513122i	$0.828489\pi$
$54$	−1.10631	+	3.03955i	−0.150549	+	0.413631i
$55$	−1.19144	−	10.0596i	−0.160653	−	1.35643i
$56$			1.24829i			0.166810i
$57$	2.70939	−	8.80857i	0.358868	−	1.16672i
$58$	4.88043	−	3.54584i	0.640832	−	0.465592i
$59$	0.327971	+	4.69021i	0.0426982	+	0.610613i	0.971045	+	0.238897i	$0.0767860\pi$
$59$	0.327971	+	4.69021i	0.0426982	+	0.610613i	−0.928347	+	0.371716i	$0.878770\pi$
$60$	−6.45359	−	0.225364i	−0.833155	−	0.0290944i
$61$	1.81018	+	12.8801i	0.231770	+	1.64913i	0.664269	+	0.747494i	$0.268743\pi$
$61$	1.81018	+	12.8801i	0.231770	+	1.64913i	−0.432499	+	0.901635i	$0.642368\pi$
$62$	−1.13133	−	0.551785i	−0.143679	−	0.0700767i
$63$	−1.52137	−	1.02618i	−0.191674	−	0.129286i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	0.674604	+	1.16845i	0.0836743	+	0.144928i
$66$	−2.02142	−	6.71452i	−0.248820	−	0.826501i
$67$	−6.00811	+	7.16019i	−0.734008	+	0.874757i	−0.995911	−	0.0903376i	$-0.971205\pi$
$67$	−6.00811	+	7.16019i	−0.734008	+	0.874757i	0.261903	+	0.965094i	$0.415650\pi$
$68$	−0.248709	−	1.17009i	−0.0301604	−	0.141894i
$69$	10.1455	−	1.06633i	1.22137	−	0.128372i
$70$	−1.05090	+	3.66493i	−0.125607	+	0.438043i
$71$	1.04513	+	1.96561i	0.124035	+	0.233275i	0.937227	−	0.348720i	$-0.113383\pi$
$71$	1.04513	+	1.96561i	0.124035	+	0.233275i	−0.813192	+	0.581995i	$0.802272\pi$
$72$	−1.45578	+	0.204597i	−0.171566	+	0.0241120i
$73$	0.271266	−	0.182971i	0.0317492	−	0.0214151i	−0.543216	−	0.839593i	$-0.682793\pi$
$73$	0.271266	−	0.182971i	0.0317492	−	0.0214151i	0.574965	+	0.818178i	$0.305016\pi$
$74$	−2.26707	−	0.565245i	−0.263542	−	0.0657084i
$75$	−8.70383	−	2.82805i	−1.00503	−	0.326555i
$76$	−4.28022	+	0.824460i	−0.490975	+	0.0945721i
$77$	−4.13533	+	0.198962i	−0.471265	+	0.0226738i
$78$	0.600339	+	0.715456i	0.0679750	+	0.0810095i
$79$	−3.16330	+	4.04884i	−0.355899	+	0.455530i	−0.932326	−	0.361618i	$-0.882224\pi$
$79$	−3.16330	+	4.04884i	−0.355899	+	0.455530i	0.576427	+	0.817149i	$0.304447\pi$
$80$	1.33891	+	2.74516i	0.149694	+	0.306919i
$81$	−4.93128	+	10.1106i	−0.547920	+	1.12340i
$82$	−4.65413	−	5.95702i	−0.513963	−	0.657842i
$83$	−0.820449	+	3.85991i	−0.0900559	+	0.423680i	0.909905	+	0.414817i	$0.136154\pi$
$83$	−0.820449	+	3.85991i	−0.0900559	+	0.423680i	−0.999961	+	0.00886269i	$0.997179\pi$
$84$	−0.275873	+	2.62475i	−0.0301002	+	0.286384i
$85$	0.254862	−	3.64470i	0.0276437	−	0.395323i
$86$	4.41805	+	7.07036i	0.476411	+	0.762416i
$87$	11.0456	−	6.37718i	1.18421	−	0.683705i
$88$	−2.35523	+	2.33514i	−0.251069	+	0.248927i
$89$	1.18754	+	3.26274i	0.125879	+	0.345850i	0.986584	−	0.163254i	$-0.0521991\pi$
$89$	1.18754	+	3.26274i	0.125879	+	0.345850i	−0.860705	+	0.509104i	$0.829977\pi$
$90$	−4.44636	−	0.624895i	−0.468688	−	0.0658697i
$91$	0.495618	−	0.241729i	0.0519549	−	0.0253401i
$92$	−2.69813	−	4.00014i	−0.281299	−	0.417043i
$93$	−2.25687	−	1.41025i	−0.234026	−	0.146236i
$94$	2.35986	+	7.26289i	0.243401	+	0.749110i
$95$	−13.2606	−	1.18282i	−1.36051	−	0.121354i
$96$	1.24273	+	1.71047i	0.126836	+	0.174574i
$97$	2.15274	−	0.869762i	0.218577	−	0.0883109i	−0.262707	−	0.964876i	$-0.584615\pi$
$97$	2.15274	−	0.869762i	0.218577	−	0.0883109i	0.481284	+	0.876565i	$0.340171\pi$
$98$	−5.11359	−	1.86119i	−0.516551	−	0.188009i
$99$	−0.909821	−	4.79010i	−0.0914405	−	0.481423i
$100$	0.751651	+	4.26283i	0.0751651	+	0.426283i
$101$	−14.0274	+	0.489847i	−1.39578	+	0.0487416i	−0.722869	−	0.690985i	$-0.757177\pi$
$101$	−14.0274	+	0.489847i	−1.39578	+	0.0487416i	−0.672907	+	0.739727i	$0.734955\pi$
$102$	−0.264366	−	2.51528i	−0.0261761	−	0.249049i
$103$	11.4022	+	1.19842i	1.12350	+	0.118084i	0.648005	−	0.761636i	$-0.275604\pi$
$103$	11.4022	+	1.19842i	1.12350	+	0.118084i	0.475491	+	0.879721i	$0.342270\pi$
$104$	0.165480	−	0.409578i	0.0162267	−	0.0401625i
$105$	−3.01966	+	7.47391i	−0.294688	+	0.729379i
$106$	12.3955	+	1.30282i	1.20396	+	0.126541i
$107$	−1.13246	−	10.7746i	−0.109479	−	1.04162i	−0.901987	−	0.431763i	$-0.857892\pi$
$107$	−1.13246	−	10.7746i	−0.109479	−	1.04162i	0.792508	−	0.609862i	$-0.208775\pi$
$108$	3.23265	−	0.112887i	0.311062	−	0.0108625i
$109$	−2.46110	−	13.9576i	−0.235730	−	1.33689i	−0.841070	−	0.540926i	$-0.818074\pi$
$109$	−2.46110	−	13.9576i	−0.235730	−	1.33689i	0.605339	−	0.795967i	$-0.293037\pi$
$110$	−8.88075	+	4.87306i	−0.846746	+	0.464628i
$111$	−4.64200	−	1.68955i	−0.440599	−	0.160365i
$112$	1.15740	−	0.467618i	0.109364	−	0.0441858i
$113$	−0.882708	−	1.21494i	−0.0830382	−	0.114292i	0.765477	−	0.643463i	$-0.222503\pi$
$113$	−0.882708	−	1.21494i	−0.0830382	−	0.114292i	−0.848515	+	0.529171i	$0.822503\pi$
$114$	−9.18212	+	0.787644i	−0.859984	+	0.0737696i
$115$	−4.55398	−	14.0157i	−0.424661	−	1.30697i
$116$	−5.11589	−	3.19676i	−0.474998	−	0.296812i
$117$	0.363142	+	0.538380i	0.0335725	+	0.0497733i
$118$	4.22583	−	2.06107i	0.389019	−	0.189737i
$119$	−1.47871	−	0.207819i	−0.135553	−	0.0190507i
$120$	2.20860	+	6.06809i	0.201617	+	0.553938i
$121$	−8.11123	−	7.43021i	−0.737384	−	0.675474i
$122$	11.2641	−	6.50334i	1.01981	−	0.588785i
$123$	−8.46963	−	13.5542i	−0.763681	−	1.22215i
$124$	−0.0878036	+	1.25565i	−0.00788499	+	0.112761i
$125$	0.214354	−	2.03944i	0.0191724	−	0.182413i
$126$	−0.381539	+	1.79500i	−0.0339902	+	0.159911i
$127$	−4.75079	−	6.08073i	−0.421564	−	0.539577i	0.529606	−	0.848244i	$-0.322340\pi$
$127$	−4.75079	−	6.08073i	−0.421564	−	0.539577i	−0.951170	+	0.308666i	$0.900117\pi$
$128$	0.438371	−	0.898794i	0.0387469	−	0.0794429i
$129$	7.72718	+	15.8431i	0.680340	+	1.39490i
$130$	0.830656	−	1.06319i	0.0728533	−	0.0932480i
$131$	−3.18861	−	3.80004i	−0.278590	−	0.332011i	0.608546	−	0.793519i	$-0.291753\pi$
$131$	−3.18861	−	3.80004i	−0.278590	−	0.332011i	−0.887136	+	0.461508i	$0.847309\pi$
$132$	−5.46836	+	4.38954i	−0.475960	+	0.382060i
$133$	−0.860300	+	5.37274i	−0.0745974	+	0.465875i
$134$	8.88949	+	2.88837i	0.767935	+	0.249517i
$135$	9.58597	+	2.39005i	0.825029	+	0.205703i
$136$	−0.991716	+	0.668921i	−0.0850389	+	0.0573595i
$137$	9.59155	−	1.34800i	0.819462	−	0.115168i	0.283029	−	0.959111i	$-0.408661\pi$
$137$	9.59155	−	1.34800i	0.819462	−	0.115168i	0.536432	+	0.843943i	$0.319772\pi$
$138$	−4.78926	−	9.00729i	−0.407689	−	0.766751i
$139$	5.99348	−	20.9017i	0.508360	−	1.77286i	−0.117658	−	0.993054i	$-0.537539\pi$
$139$	5.99348	−	20.9017i	0.508360	−	1.77286i	0.626018	−	0.779809i	$-0.284684\pi$
$140$	3.79174	−	0.398528i	0.320460	−	0.0336817i
$141$	3.35691	+	15.7930i	0.282703	+	1.33001i
$142$	1.43097	−	1.70536i	0.120084	−	0.143111i
$143$	1.38322	+	0.482920i	0.115671	+	0.0403838i
$144$	0.735045	+	1.27314i	0.0612538	+	0.106095i
$145$	−12.3288	−	13.6925i	−1.02385	−	1.13710i
$146$	−0.271266	−	0.182971i	−0.0224501	−	0.0151428i
$147$	−10.3409	−	5.04359i	−0.852903	−	0.415989i
$148$	0.325175	+	2.31374i	0.0267292	+	0.190188i
$149$	13.1618	+	0.459622i	1.07826	+	0.0376537i	0.568516	−	0.822672i	$-0.307518\pi$
$149$	13.1618	+	0.459622i	1.07826	+	0.0376537i	0.509744	+	0.860326i	$0.329740\pi$
$150$	0.638394	+	9.12946i	0.0521247	+	0.745417i
$151$	−9.39256	+	6.82409i	−0.764356	+	0.555337i	−0.900243	−	0.435387i	$-0.856611\pi$
$151$	−9.39256	+	6.82409i	−0.764356	+	0.555337i	0.135887	+	0.990724i	$0.456611\pi$
$152$	2.36782	+	3.65970i	0.192056	+	0.296841i
$153$		−	1.75856i		−	0.142171i
$154$	1.73360	+	3.75968i	0.139697	+	0.302964i
$155$	−1.31488	+	3.61261i	−0.105614	+	0.290172i
$156$	0.438469	−	0.824640i	0.0351056	−	0.0660240i
$157$	9.83691	+	9.49939i	0.785071	+	0.758134i	0.974651	−	0.223731i	$-0.0718238\pi$
$157$	9.83691	+	9.49939i	0.785071	+	0.758134i	−0.189580	+	0.981865i	$0.560713\pi$
$158$	4.93901	+	1.41624i	0.392927	+	0.112670i
$159$	25.7758	+	5.47881i	2.04415	+	0.434498i
$160$	2.04371	−	2.26977i	0.161569	−	0.179441i
$161$	−5.84415	+	1.45711i	−0.460583	+	0.114836i
$162$	11.2217	+	0.784698i	0.881660	+	0.0616517i
$163$	−13.3700	+	2.84188i	−1.04722	+	0.222593i	−0.699224	−	0.714903i	$-0.746471\pi$
$163$	−13.3700	+	2.84188i	−1.04722	+	0.222593i	−0.347996	+	0.937496i	$0.613138\pi$
$164$	−3.77978	+	6.54677i	−0.295151	+	0.511217i
$165$	−19.7503	+	8.28382i	−1.53756	+	0.644895i
$166$	3.88619	−	0.685240i	0.301627	−	0.0531849i
$167$	−5.90772	−	3.14119i	−0.457153	−	0.243072i	0.224891	−	0.974384i	$-0.427797\pi$
$167$	−5.90772	−	3.14119i	−0.457153	−	0.243072i	−0.682044	+	0.731312i	$0.738909\pi$
$168$	2.53697	−	0.727465i	0.195732	−	0.0561252i
$169$	12.7737	−	0.893222i	0.982590	−	0.0687094i
$170$	−3.47478	+	1.12902i	−0.266504	+	0.0865922i
$171$	−6.40680	−	0.122699i	−0.489940	−	0.00938304i
$172$	4.90049	−	6.74495i	0.373659	−	0.514298i
$173$	0.0219957	−	0.0882198i	0.00167230	−	0.00670723i	−0.969454	−	0.245274i	$-0.921122\pi$
$173$	0.0219957	−	0.0882198i	0.00167230	−	0.00670723i	0.971126	+	0.238567i	$0.0766776\pi$
$174$	−10.0506	−	7.85237i	−0.761932	−	0.595286i
$175$	5.32125	+	0.938280i	0.402249	+	0.0709273i
$176$	3.04739	+	1.30898i	0.229706	+	0.0986678i
$177$	9.34104	−	3.39986i	0.702116	−	0.255549i
$178$	2.58030	−	2.32331i	0.193402	−	0.174140i
$179$	−3.31641	+	7.44877i	−0.247880	+	0.556747i	−0.994040	−	0.109020i	$-0.965229\pi$
$179$	−3.31641	+	7.44877i	−0.247880	+	0.556747i	0.746160	+	0.665767i	$0.231896\pi$
$180$	1.08624	+	4.35668i	0.0809638	+	0.324728i
$181$	15.2985	+	6.18101i	1.13713	+	0.459431i	0.864472	−	0.502680i	$-0.167653\pi$
$181$	15.2985	+	6.18101i	1.13713	+	0.459431i	0.272658	+	0.962111i	$0.412097\pi$
$182$	−0.409789	−	0.368976i	−0.0303756	−	0.0273503i
$183$	25.1220	−	11.1851i	1.85707	−	0.826823i
$184$	−2.69813	+	4.00014i	−0.198909	+	0.294894i
$185$	−0.993172	+	7.06679i	−0.0730195	+	0.519561i
$186$	−0.462121	+	2.62082i	−0.0338844	+	0.192168i
$187$	−2.37406	−	3.17873i	−0.173609	−	0.232452i
$188$	5.85002	−	4.90875i	0.426656	−	0.358007i
$189$	1.24774	−	3.84013i	0.0907594	−	0.279329i
$190$	3.87083	+	12.7381i	0.280819	+	0.924121i
$191$	−13.9220	−	10.1149i	−1.00736	−	0.731891i	−0.0437071	−	0.999044i	$-0.513917\pi$
$191$	−13.9220	−	10.1149i	−1.00736	−	0.731891i	−0.963654	+	0.267154i	$0.913917\pi$
$192$	1.12039	−	1.79299i	0.0808569	−	0.129398i
$193$	0.642466	−	18.3978i	0.0462457	−	1.32430i	−0.725434	−	0.688292i	$-0.758361\pi$
$193$	0.642466	−	18.3978i	0.0462457	−	1.32430i	0.771679	−	0.636012i	$-0.219417\pi$
$194$	−1.61286	−	1.67016i	−0.115796	−	0.119911i
$195$	1.98157	−	2.05197i	0.141903	−	0.146945i
$196$	0.189915	+	5.43845i	0.0135654	+	0.388461i
$197$	6.14594	+	3.54836i	0.437880	+	0.252810i	0.702698	−	0.711488i	$-0.251978\pi$
$197$	6.14594	+	3.54836i	0.437880	+	0.252810i	−0.264818	+	0.964298i	$0.585312\pi$
$198$	−4.10048	+	2.63797i	−0.291408	+	0.187473i
$199$	17.1351	+	14.3780i	1.21467	+	1.01923i	0.999086	+	0.0427462i	$0.0136107\pi$
$199$	17.1351	+	14.3780i	1.21467	+	1.01923i	0.215586	+	0.976485i	$0.430834\pi$
$200$	3.67085	−	2.29380i	0.259568	−	0.162196i
$201$	18.0534	+	8.03789i	1.27339	+	0.566949i
$202$	5.70893	+	12.8225i	0.401679	+	0.902185i
$203$	−5.93402	+	4.63616i	−0.416486	+	0.325395i
$204$	−2.23309	+	1.18735i	−0.156348	+	0.0831315i
$205$	−16.6088	+	16.0389i	−1.16001	+	1.12021i
$206$	−3.16019	−	11.0209i	−0.220181	−	0.767863i
$207$	−2.65718	−	6.57674i	−0.184687	−	0.457115i
$208$	−0.441744			−0.0306295
$209$	−11.7464	+	8.42742i	−0.812517	+	0.582937i
$210$	8.06087			0.556253
$211$	0.135628	+	0.335692i	0.00933703	+	0.0231100i	0.931780	−	0.363023i	$-0.118255\pi$
$211$	0.135628	+	0.335692i	0.00933703	+	0.0231100i	−0.922443	+	0.386132i	$0.873811\pi$
$212$	−3.43548	−	11.9809i	−0.235950	−	0.822854i
$213$	3.38575	−	3.26958i	0.231988	−	0.224028i
$214$	−9.56585	+	5.08625i	−0.653908	+	0.347689i
$215$	20.0660	−	15.6773i	1.36849	−	1.06918i
$216$	−1.31564	−	2.95498i	−0.0895180	−	0.201061i
$217$	1.43540	+	0.639083i	0.0974415	+	0.0433838i
$218$	−12.0193	+	7.51049i	−0.814050	+	0.508675i
$219$	−0.529947	−	0.444678i	−0.0358105	−	0.0300486i
$220$	7.84501	+	6.40861i	0.528911	+	0.432068i
$221$	0.457630	+	0.264213i	0.0307835	+	0.0177729i
$222$	0.172401	+	4.93691i	0.0115708	+	0.331343i
$223$	9.31050	−	9.64130i	0.623477	−	0.645629i	−0.331099	−	0.943596i	$-0.607420\pi$
$223$	9.31050	−	9.64130i	0.623477	−	0.645629i	0.954576	+	0.297967i	$0.0963084\pi$
$224$	−0.867136	−	0.897946i	−0.0579380	−	0.0599965i
$225$	−0.222080	+	6.35954i	−0.0148053	+	0.423969i
$226$	−0.795808	+	1.27356i	−0.0529363	+	0.0847159i
$227$	−11.1782	−	8.12140i	−0.741920	−	0.539036i	0.151392	−	0.988474i	$-0.451624\pi$
$227$	−11.1782	−	8.12140i	−0.741920	−	0.539036i	−0.893312	+	0.449437i	$0.851624\pi$
$228$	4.16997	+	8.21846i	0.276163	+	0.544281i
$229$	−4.66641	+	14.3617i	−0.308365	+	0.949051i	0.670035	+	0.742330i	$0.266279\pi$
$229$	−4.66641	+	14.3617i	−0.308365	+	0.949051i	−0.978400	+	0.206721i	$0.933721\pi$
$230$	−11.2892	+	9.47276i	−0.744387	+	0.624615i
$231$	2.81430	+	8.28852i	0.185168	+	0.545344i
$232$	−1.04754	+	5.94090i	−0.0687744	+	0.390039i
$233$	0.951496	−	6.77025i	0.0623346	−	0.443534i	−0.933949	−	0.357405i	$-0.883662\pi$
$233$	0.951496	−	6.77025i	0.0623346	−	0.443534i	0.996284	−	0.0861286i	$-0.0274496\pi$
$234$	0.363142	−	0.538380i	0.0237393	−	0.0351950i
$235$	21.3079	−	9.48690i	1.38998	−	0.618857i
$236$	−3.49402	−	3.14603i	−0.227441	−	0.204789i
$237$	10.0722	+	4.06942i	0.654257	+	0.264337i
$238$	0.361247	+	1.44888i	0.0234162	+	0.0939171i
$239$	4.42439	−	9.93735i	0.286190	−	0.642793i	−0.712048	−	0.702131i	$-0.752232\pi$
$239$	4.42439	−	9.93735i	0.286190	−	0.642793i	0.998238	+	0.0593374i	$0.0188988\pi$
$240$	4.79888	−	4.32093i	0.309766	−	0.278915i
$241$	−21.1061	+	7.68199i	−1.35956	+	0.494840i	−0.915919	−	0.401363i	$-0.868537\pi$
$241$	−21.1061	+	7.68199i	−1.35956	+	0.494840i	−0.443643	+	0.896203i	$0.646314\pi$
$242$	−3.85065	+	10.3040i	−0.247529	+	0.662366i
$243$	13.8657	+	2.44490i	0.889488	+	0.156841i
$244$	−10.2494	−	8.00772i	−0.656151	−	0.512641i
$245$	−4.02090	+	16.1269i	−0.256886	+	1.03031i
$246$	−9.39450	+	12.9304i	−0.598971	+	0.824413i
$247$	0.994513	−	1.64881i	0.0632794	−	0.104911i
$248$	1.19711	−	0.388965i	0.0760166	−	0.0246993i
$249$	8.32284	−	0.581989i	0.527438	−	0.0368821i
$250$	−1.97124	+	0.565244i	−0.124672	+	0.0357491i
$251$	−23.2892	−	12.3831i	−1.47000	−	0.781613i	−0.474858	−	0.880062i	$-0.657501\pi$
$251$	−23.2892	−	12.3831i	−1.47000	−	0.781613i	−0.995142	+	0.0984494i	$0.968612\pi$
$252$	1.80722	−	0.318662i	0.113844	−	0.0200738i
$253$	−13.6817	−	8.30077i	−0.860160	−	0.521865i
$254$	−3.85828	+	6.68273i	−0.242090	+	0.419312i
$255$	−7.55585	+	1.60605i	−0.473166	+	0.100575i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	19.3576	−	4.82639i	1.20749	−	0.301062i	0.414362	−	0.910112i	$-0.364005\pi$
$257$	19.3576	−	4.82639i	1.20749	−	0.301062i	0.793132	+	0.609050i	$0.208449\pi$
$258$	11.7948	−	13.0994i	0.734311	−	0.815535i
$259$	2.85287	+	0.606396i	0.177269	+	0.0376796i
$260$	−1.29694	−	0.371892i	−0.0804329	−	0.0230638i
$261$	−6.37938	−	6.16050i	−0.394874	−	0.381325i
$262$	−2.32886	+	4.37995i	−0.143877	+	0.270594i
$263$	−5.47636	+	15.0462i	−0.337687	+	0.927787i	0.648362	+	0.761332i	$0.275454\pi$
$263$	−5.47636	+	15.0462i	−0.337687	+	0.927787i	−0.986049	+	0.166455i	$0.946768\pi$
$264$	6.11839	+	3.42583i	0.376561	+	0.210845i
$265$		−	38.0677i		−	2.33848i
$266$	5.30379	−	1.21501i	0.325196	−	0.0744968i
$267$	5.93899	−	4.31493i	0.363460	−	0.264069i
$268$	−0.652011	−	9.32420i	−0.0398279	−	0.569566i
$269$	10.0529	+	0.351054i	0.612934	+	0.0214041i	0.339685	−	0.940539i	$-0.389679\pi$
$269$	10.0529	+	0.351054i	0.612934	+	0.0214041i	0.273249	+	0.961943i	$0.411902\pi$
$270$	−1.37495	−	9.78328i	−0.0836768	−	0.595392i
$271$	20.2806	+	9.89151i	1.23196	+	0.600866i	0.935211	−	0.354090i	$-0.115209\pi$
$271$	20.2806	+	9.89151i	1.23196	+	0.600866i	0.296747	+	0.954956i	$0.404098\pi$
$272$	0.991716	+	0.668921i	0.0601316	+	0.0405593i
$273$	−0.780111	−	0.866401i	−0.0472144	−	0.0524370i
$274$	−4.84291	−	8.38816i	−0.292571	−	0.506747i
$275$	8.18398	+	11.7952i	0.493512	+	0.711275i
$276$	−6.55732	+	7.81471i	−0.394704	+	0.470390i
$277$	−1.75268	−	8.24571i	−0.105308	−	0.495437i	−0.998914	−	0.0465844i	$-0.985166\pi$
$277$	−1.75268	−	8.24571i	−0.105308	−	0.495437i	0.893606	−	0.448852i	$-0.148167\pi$
$278$	−21.6250	+	2.27287i	−1.29698	+	0.136318i
$279$	−0.510047	+	1.77874i	−0.0305357	+	0.106491i
$280$	−1.78992	−	3.36635i	−0.106968	−	0.201178i
$281$	4.06022	−	0.570627i	0.242213	−	0.0340408i	−0.0170221	−	0.999855i	$-0.505419\pi$
$281$	4.06022	−	0.570627i	0.242213	−	0.0340408i	0.259235	+	0.965814i	$0.416530\pi$
$282$	13.3855	−	9.02866i	0.797097	−	0.537649i
$283$	11.9033	+	2.96783i	0.707579	+	0.176419i	0.579056	−	0.815287i	$-0.303421\pi$
$283$	11.9033	+	2.96783i	0.707579	+	0.176419i	0.128522	+	0.991707i	$0.458977\pi$
$284$	−2.11724	−	0.687932i	−0.125635	−	0.0408212i
$285$	5.32397	+	27.6396i	0.315365	+	1.63723i
$286$	−0.0704086	−	1.46341i	−0.00416335	−	0.0865331i
$287$	6.06569	+	7.22881i	0.358046	+	0.426703i
$288$	0.905078	−	1.15845i	0.0533322	−	0.0682621i
$289$	6.82502	+	13.9934i	0.401472	+	0.823139i
$290$	−8.07701	+	16.5603i	−0.474298	+	0.972455i
$291$	−3.02221	−	3.86826i	−0.177165	−	0.226761i
$292$	−0.0680298	+	0.320055i	−0.00398114	+	0.0187298i
$293$	0.385262	−	3.66553i	0.0225073	−	0.214142i	−0.977488	−	0.210992i	$-0.932331\pi$
$293$	0.385262	−	3.66553i	0.0225073	−	0.214142i	0.999995	−	0.00315023i	$-0.00100275\pi$
$294$	−0.802570	+	11.4773i	−0.0468068	+	0.669369i
$295$	−7.60973	−	12.1781i	−0.443055	−	0.709037i
$296$	2.02345	−	1.16824i	0.117611	−	0.0679025i
$297$	9.57953	−	4.82943i	0.555861	−	0.280232i
$298$	−4.50436	−	12.3756i	−0.260930	−	0.716901i
$299$	2.11069	+	0.296638i	0.122064	+	0.0171550i
$300$	8.22554	−	4.01186i	0.474902	−	0.231625i
$301$	−5.81968	−	8.62802i	−0.335440	−	0.497311i
$302$	9.84571	+	6.15228i	0.566557	+	0.354024i
$303$	9.17026	+	28.2232i	0.526818	+	1.62138i
$304$	2.50621	−	3.56636i	0.143741	−	0.204545i
$305$	−23.3503	−	32.1390i	−1.33704	−	1.84027i
$306$	−1.63051	+	0.658768i	−0.0932099	+	0.0376593i
$307$	22.2397	+	8.09459i	1.26929	+	0.461983i	0.886875	−	0.462009i	$-0.152871\pi$
$307$	22.2397	+	8.09459i	1.26929	+	0.461983i	0.382412	+	0.923992i	$0.375094\pi$
$308$	2.83650	−	3.01576i	0.161624	−	0.171839i
$309$	−4.20924	−	23.8718i	−0.239455	−	1.35802i
$310$	3.84212	−	0.134170i	0.218218	−	0.00762033i
$311$	2.24039	+	21.3159i	0.127041	+	1.20871i	0.853347	+	0.521343i	$0.174569\pi$
$311$	2.24039	+	21.3159i	0.127041	+	1.20871i	−0.726306	+	0.687371i	$0.758765\pi$
$312$	−0.928846	−	0.0976256i	−0.0525855	−	0.00552696i
$313$	−0.386828	+	0.957433i	−0.0218648	+	0.0541173i	−0.937721	−	0.347388i	$-0.887069\pi$
$313$	−0.386828	+	0.957433i	−0.0218648	+	0.0541173i	0.915857	+	0.401506i	$0.131513\pi$
$314$	5.12271	−	12.6792i	0.289091	−	0.715526i
$315$	5.57420	+	0.585872i	0.314070	+	0.0330101i
$316$	−0.537073	−	5.10991i	−0.0302127	−	0.287455i
$317$	20.0300	−	0.699461i	1.12499	−	0.0392857i	0.533650	−	0.845705i	$-0.320820\pi$
$317$	20.0300	−	0.699461i	1.12499	−	0.0392857i	0.591344	+	0.806420i	$0.298598\pi$
$318$	−4.57591	−	25.9513i	−0.256604	−	1.45528i
$319$	−19.8479	−	2.52338i	−1.11127	−	0.141282i
$320$	−2.87008	−	1.04462i	−0.160442	−	0.0583962i
$321$	−21.2380	+	8.58069i	−1.18539	+	0.478928i
$322$	3.54026	+	4.87276i	0.197291	+	0.271548i
$323$	−4.72942	+	2.19561i	−0.263152	+	0.122167i
$324$	−3.47616	−	10.6985i	−0.193120	−	0.594363i
$325$	−1.62158	−	1.01327i	−0.0899489	−	0.0562063i
$326$	7.64344	+	11.3319i	0.423331	+	0.627614i
$327$	−26.9325	+	13.1359i	−1.48937	+	0.726415i
$328$	7.48599	+	1.05209i	0.413345	+	0.0580918i
$329$	−3.26040	−	8.95788i	−0.179752	−	0.493864i
$330$	15.0792	+	15.2090i	0.830084	+	0.837227i
$331$	−27.6015	+	15.9357i	−1.51711	+	0.875906i	−0.517316	+	0.855794i	$0.673069\pi$
$331$	−27.6015	+	15.9357i	−1.51711	+	0.875906i	−0.999798	+	0.0201116i	$0.993598\pi$
$332$	−2.09114	−	3.34652i	−0.114766	−	0.183664i
$333$	−0.239602	+	3.42646i	−0.0131301	+	0.187769i
$334$	−0.699390	+	6.65425i	−0.0382689	+	0.364104i
$335$	5.93550	−	27.9243i	0.324291	−	1.52567i
$336$	−1.62486	−	2.07973i	−0.0886434	−	0.113458i
$337$	4.52756	−	9.28288i	0.246632	−	0.505671i	−0.739183	−	0.673504i	$-0.764788\pi$
$337$	4.52756	−	9.28288i	0.246632	−	0.505671i	0.985815	+	0.167834i	$0.0536771\pi$
$338$	−5.61328	−	11.5089i	−0.305322	−	0.626003i
$339$	−1.95478	+	2.50201i	−0.106169	+	0.135890i
$340$	2.34849	+	2.79882i	0.127365	+	0.151787i
$341$	1.47936	+	3.90378i	0.0801120	+	0.211402i
$342$	2.28626	+	5.98625i	0.123627	+	0.323699i
$343$	14.7708	+	4.79933i	0.797549	+	0.259139i
$344$	−8.08956	−	2.01695i	−0.436160	−	0.108747i
$345$	−25.8310	+	17.4232i	−1.39069	+	0.938035i
$346$	−0.0900357	+	0.0126537i	−0.00484035	+	0.000680267i
$347$	−14.0685	−	26.4590i	−0.755235	−	1.42039i	−0.902231	−	0.431254i	$-0.858071\pi$
$347$	−14.0685	−	26.4590i	−0.755235	−	1.42039i	0.146995	−	0.989137i	$-0.453040\pi$
$348$	−3.51558	+	12.2603i	−0.188455	+	0.657220i
$349$	−17.6015	+	1.84999i	−0.942187	+	0.0990279i	−0.563151	−	0.826354i	$-0.690411\pi$
$349$	−17.6015	+	1.84999i	−0.942187	+	0.0990279i	−0.379036	+	0.925382i	$0.623744\pi$
$350$	−1.12342	−	5.28526i	−0.0600492	−	0.282509i
$351$	−0.918465	+	1.09458i	−0.0490240	+	0.0584246i
$352$	0.0720894	−	3.31584i	0.00384238	−	0.176735i
$353$	−8.57376	−	14.8502i	−0.456335	−	0.790396i	0.542428	−	0.840102i	$-0.317505\pi$
$353$	−8.57376	−	14.8502i	−0.456335	−	0.790396i	−0.998764	+	0.0497058i	$0.984172\pi$
$354$	−6.65151	−	7.38725i	−0.353524	−	0.392628i
$355$	−5.63696	−	3.80218i	−0.299179	−	0.201799i
$356$	−3.12074	−	1.52208i	−0.165399	−	0.0806703i
$357$	0.439382	+	3.12637i	0.0232546	+	0.165465i
$358$	8.14873	+	0.284560i	0.430674	+	0.0150395i
$359$	1.18806	+	16.9901i	0.0627036	+	0.896703i	0.922483	+	0.386037i	$0.126156\pi$
$359$	1.18806	+	16.9901i	0.0627036	+	0.896703i	−0.859780	+	0.510665i	$0.829399\pi$
$360$	3.63253	−	2.63919i	0.191451	−	0.139098i
$361$	7.66908	+	17.3835i	0.403636	+	0.914920i
$362$		−	16.5000i		−	0.867221i
$363$	−10.3739	+	20.8150i	−0.544486	+	1.09250i
$364$	−0.188599	+	0.518171i	−0.00988526	+	0.0271595i
$365$	−0.469178	+	0.882396i	−0.0245579	+	0.0461867i
$366$	−19.7815	−	19.1028i	−1.03399	−	0.998517i
$367$	26.3131	+	7.54517i	1.37353	+	0.393855i	0.879629	−	0.475661i	$-0.157791\pi$
$367$	26.3131	+	7.54517i	1.37353	+	0.393855i	0.493906	+	0.869515i	$0.335569\pi$
$368$	4.71960	+	1.00318i	0.246026	+	0.0522945i
$369$	−7.43621	+	8.25875i	−0.387114	+	0.429933i
$370$	6.92426	−	1.72641i	0.359975	−	0.0897519i
$371$	−15.5205	−	1.08530i	−0.805785	−	0.0563460i
$372$	2.60310	−	0.553305i	0.134964	−	0.0286875i
$373$	−4.55589	+	7.89103i	−0.235895	+	0.408582i	−0.959532	−	0.281598i	$-0.909135\pi$
$373$	−4.55589	+	7.89103i	−0.235895	+	0.408582i	0.723638	+	0.690180i	$0.242469\pi$
$374$	−2.05793	+	3.39197i	−0.106413	+	0.175394i
$375$	−4.26980	+	0.752880i	−0.220491	+	0.0388786i
$376$	−6.74277	−	3.58519i	−0.347732	−	0.184892i
$377$	2.56161	−	0.734530i	0.131930	−	0.0378302i
$378$	−4.02792	+	0.281660i	−0.207174	+	0.0144870i
$379$	−18.5421	+	6.02470i	−0.952446	+	0.309468i	−0.743709	−	0.668504i	$-0.766935\pi$
$379$	−18.5421	+	6.02470i	−0.952446	+	0.309468i	−0.208737	+	0.977972i	$0.566935\pi$
$380$	10.3605	−	8.36076i	0.531485	−	0.428898i
$381$	−9.58960	+	13.1989i	−0.491290	+	0.676203i
$382$	−4.16312	+	16.6974i	−0.213004	+	0.854312i
$383$	−20.6607	−	16.1419i	−1.05571	−	0.824813i	−0.0707354	−	0.997495i	$-0.522535\pi$
$383$	−20.6607	−	16.1419i	−1.05571	−	0.824813i	−0.984978	+	0.172682i	$0.944757\pi$
$384$	−2.08214	−	0.367137i	−0.106254	−	0.0187354i
$385$	10.8667	−	6.46618i	0.553819	−	0.329547i
$386$	−17.2988	+	6.29626i	−0.880487	+	0.320471i
$387$	9.10832	−	8.20117i	0.463002	−	0.416889i
$388$	−0.944362	+	2.12107i	−0.0479427	+	0.107681i
$389$	4.66092	+	18.6939i	0.236318	+	0.947821i	0.964848	+	0.262807i	$0.0846482\pi$
$389$	4.66092	+	18.6939i	0.236318	+	0.947821i	−0.728530	+	0.685014i	$0.759796\pi$
$390$	−2.64486	−	1.06859i	−0.133928	−	0.0541103i
$391$	−4.28931	−	3.86211i	−0.216920	−	0.195315i
$392$	4.97130	−	2.21337i	0.251089	−	0.111792i
$393$	−5.86481	+	8.69494i	−0.295840	+	0.438602i
$394$	0.987673	−	7.02766i	0.0497582	−	0.354048i
$395$	2.72506	−	15.4546i	0.137113	−	0.777606i
$396$	3.98195	+	2.81369i	0.200101	+	0.141393i
$397$	10.7075	−	8.98467i	0.537395	−	0.450928i	−0.333251	−	0.942838i	$-0.608146\pi$
$397$	10.7075	−	8.98467i	0.537395	−	0.450928i	0.870646	+	0.491910i	$0.163701\pi$
$398$	6.91216	−	21.2735i	0.346475	−	1.06634i
$399$	11.4207	−	1.38263i	0.571749	−	0.0692179i
$400$	−3.50190	−	2.54428i	−0.175095	−	0.127214i
$401$	−14.2106	+	22.7418i	−0.709645	+	1.13567i	0.275058	+	0.961428i	$0.411303\pi$
$401$	−14.2106	+	22.7418i	−0.709645	+	1.13567i	−0.984703	+	0.174241i	$0.944253\pi$
$402$	0.689680	−	19.7499i	0.0343981	−	0.985034i
$403$	−0.386251	−	0.399975i	−0.0192406	−	0.0199242i
$404$	9.75018	−	10.0966i	0.485089	−	0.502325i
$405$	−1.19907	−	34.3369i	−0.0595823	−	1.70622i
$406$	6.52150	+	3.76519i	0.323656	+	0.186863i
$407$	4.19264	+	6.51706i	0.207822	+	0.323039i
$408$	1.93743	+	1.62569i	0.0959169	+	0.0804838i
$409$	18.6153	−	11.6322i	0.920469	−	0.575173i	0.0151407	−	0.999885i	$-0.495180\pi$
$409$	18.6153	−	11.6322i	0.920469	−	0.575173i	0.905328	+	0.424712i	$0.139625\pi$
$410$	21.0928	+	9.39113i	1.04170	+	0.463795i
$411$	−8.32928	−	18.7079i	−0.410853	−	0.922791i
$412$	−9.03458	+	7.05858i	−0.445102	+	0.347751i
$413$	−5.18206	+	2.75535i	−0.254992	+	0.135582i
$414$	−5.10245	+	4.92738i	−0.250772	+	0.242168i
$415$	−3.32214	−	11.5857i	−0.163078	−	0.568719i
$416$	0.165480	+	0.409578i	0.00811334	+	0.0200812i
$417$	−45.9726			−2.25129
$418$	12.2141	+	7.73413i	0.597409	+	0.378289i
$419$	28.8431			1.40908			0.704538	−	0.709667i	$-0.251154\pi$
$419$	28.8431			1.40908			0.704538	+	0.709667i	$0.251154\pi$
$420$	−3.01966	−	7.47391i	−0.147344	−	0.364690i
$421$	−3.24875	−	11.3297i	−0.158334	−	0.552178i	−0.999927	−	0.0120653i	$-0.996159\pi$
$421$	−3.24875	−	11.3297i	−0.158334	−	0.552178i	0.841593	−	0.540113i	$-0.181618\pi$
$422$	0.260441	−	0.251505i	0.0126781	−	0.0122431i
$423$	9.91248	−	5.27056i	0.481961	−	0.256263i
$424$	−9.82158	+	7.67346i	−0.476978	+	0.372656i
$425$	2.10607	+	4.73031i	0.102159	+	0.229454i
$426$	−4.29983	−	1.91441i	−0.208327	−	0.0927534i
$427$	−13.7690	+	8.60384i	−0.666330	+	0.416369i
$428$	8.29932	+	6.96396i	0.401163	+	0.336616i
$429$	0.175367	−	3.09263i	0.00846680	−	0.149314i
$430$	−22.0526	−	12.7321i	−1.06347	−	0.613995i
$431$	0.219799	+	6.29423i	0.0105874	+	0.303182i	0.993121	+	0.117095i	$0.0373584\pi$
$431$	0.219799	+	6.29423i	0.0105874	+	0.303182i	−0.982533	+	0.186087i	$0.940419\pi$
$432$	−2.24696	+	2.32679i	−0.108107	+	0.111948i
$433$	−1.06243	−	1.10018i	−0.0510574	−	0.0528714i	0.693325	−	0.720625i	$-0.256145\pi$
$433$	−1.06243	−	1.10018i	−0.0510574	−	0.0528714i	−0.744383	+	0.667753i	$0.767256\pi$
$434$	0.0548356	−	1.57029i	0.00263220	−	0.0753762i
$435$	−20.6432	+	33.0360i	−0.989764	+	1.58395i
$436$	11.4661	+	8.33062i	0.549127	+	0.398964i
$437$	−14.3698	+	15.3574i	−0.687399	+	0.734643i
$438$	−0.213777	+	0.657938i	−0.0102147	+	0.0314375i
$439$	−23.6126	+	19.8133i	−1.12697	+	0.945637i	−0.998935	−	0.0461334i	$-0.985310\pi$
$439$	−23.6126	+	19.8133i	−1.12697	+	0.945637i	−0.128031	+	0.991770i	$0.540866\pi$
$440$	3.00316	−	9.67447i	0.143170	−	0.461212i
$441$	−1.38917	+	7.87835i	−0.0661508	+	0.375160i
$442$	0.0735427	−	0.523283i	0.00349807	−	0.0248901i
$443$	−13.8472	+	20.5293i	−0.657898	+	0.975374i	0.341472	+	0.939892i	$0.389074\pi$
$443$	−13.8472	+	20.5293i	−0.657898	+	0.975374i	−0.999370	+	0.0354822i	$0.988703\pi$
$444$	4.51284	−	2.00924i	0.214170	−	0.0953545i
$445$	−7.88094	−	7.09603i	−0.373593	−	0.336384i
$446$	−12.4270	−	5.02085i	−0.588437	−	0.237744i
$447$	−6.73619	−	27.0174i	−0.318611	−	1.27788i
$448$	−0.507726	+	1.14037i	−0.0239878	+	0.0538775i
$449$	24.9361	−	22.4526i	1.17681	−	1.05960i	0.179690	−	0.983723i	$-0.442490\pi$
$449$	24.9361	−	22.4526i	1.17681	−	1.05960i	0.997117	−	0.0758789i	$-0.0241762\pi$
$450$	5.97965	−	2.17642i	0.281884	−	0.102597i
$451$	−2.29217	+	24.9672i	−0.107934	+	1.17566i
$452$	1.47894	+	0.260777i	0.0695634	+	0.0122659i
$453$	19.3427	+	15.1122i	0.908798	+	0.710031i
$454$	−3.34262	+	13.4065i	−0.156877	+	0.629200i
$455$	−0.989951	+	1.36255i	−0.0464096	+	0.0638774i
$456$	6.05792	−	6.94502i	0.283688	−	0.325230i
$457$	−24.7539	+	8.04303i	−1.15794	+	0.376237i	−0.824128	−	0.566403i	$-0.808335\pi$
$457$	−24.7539	+	8.04303i	−1.15794	+	0.376237i	−0.333810	+	0.942640i	$0.608335\pi$
$458$	15.0640	−	1.05338i	0.703897	−	0.0492212i
$459$	3.71945	−	1.06654i	0.173609	−	0.0497816i
$460$	13.0120	+	6.91860i	0.606687	+	0.322581i
$461$	8.43314	−	1.48699i	0.392771	−	0.0692561i	0.0262249	−	0.999656i	$-0.491651\pi$
$461$	8.43314	−	1.48699i	0.392771	−	0.0692561i	0.366546	+	0.930400i	$0.380540\pi$
$462$	6.63072	−	5.71431i	0.308489	−	0.265854i
$463$	−11.2519	+	19.4889i	−0.522922	+	0.905728i	0.476722	+	0.879054i	$0.341825\pi$
$463$	−11.2519	+	19.4889i	−0.522922	+	0.905728i	−0.999644	+	0.0266737i	$0.991509\pi$
$464$	5.90072	−	1.25424i	0.273934	−	0.0582265i
$465$	8.10839	+	0.566994i	0.376018	+	0.0262937i
$466$	−6.63370	+	1.65397i	−0.307300	+	0.0766186i
$467$	−8.89608	+	9.88009i	−0.411661	+	0.457196i	−0.912942	−	0.408088i	$-0.866196\pi$
$467$	−8.89608	+	9.88009i	−0.411661	+	0.457196i	0.501281	+	0.865284i	$0.332862\pi$
$468$	−0.635213	−	0.135019i	−0.0293627	−	0.00624124i
$469$	−11.2158	−	3.21606i	−0.517895	−	0.148504i
$470$	−16.7782	−	16.2025i	−0.773921	−	0.747366i
$471$	13.5735	−	25.5281i	0.625434	−	1.17627i
$472$	−1.60806	+	4.41812i	−0.0740171	+	0.203360i
$473$	5.39238	−	27.1205i	0.247942	−	1.24700i
$474$		−	10.8632i		−	0.498962i
$475$	17.3804	−	7.34280i	0.797470	−	0.336911i
$476$	1.20806	−	0.877704i	0.0553711	−	0.0402295i
$477$	−1.27814	−	18.2782i	−0.0585219	−	0.836902i
$478$	−10.8712	−	0.379629i	−0.497235	−	0.0173638i
$479$	−4.81316	−	34.2474i	−0.219919	−	1.56480i	−0.716984	−	0.697090i	$-0.754478\pi$
$479$	−4.81316	−	34.2474i	−0.219919	−	1.56480i	0.497065	−	0.867713i	$-0.334411\pi$
$480$	−5.80398	−	2.83079i	−0.264914	−	0.129207i
$481$	−0.855671	−	0.577157i	−0.0390152	−	0.0263161i
$482$	15.0291	+	16.6915i	0.684556	+	0.760277i
$483$	6.36715	+	11.0282i	0.289715	+	0.501802i
$484$	10.9962	−	0.289687i	0.499827	−	0.0131676i
$485$	−4.55827	+	5.43234i	−0.206981	+	0.246670i
$486$	−2.92732	−	13.7720i	−0.132786	−	0.624709i
$487$	16.4441	−	1.72835i	0.745154	−	0.0783188i	0.275661	−	0.961255i	$-0.411103\pi$
$487$	16.4441	−	1.72835i	0.745154	−	0.0783188i	0.469493	+	0.882936i	$0.344437\pi$
$488$	−3.58513	+	12.5028i	−0.162291	+	0.565976i
$489$	13.5673	+	25.5165i	0.613536	+	1.15389i
$490$	16.4589	−	2.31315i	0.743537	−	0.104497i
$491$	8.09500	−	5.46015i	0.365322	−	0.246413i	−0.362790	−	0.931871i	$-0.618176\pi$
$491$	8.09500	−	5.46015i	0.365322	−	0.246413i	0.728112	+	0.685458i	$0.240398\pi$
$492$	15.5081	+	3.86661i	0.699160	+	0.174320i
$493$	−6.86309	−	2.22995i	−0.309098	−	0.100432i
$494$	−1.90130	−	0.304442i	−0.0855435	−	0.0136975i
$495$	9.32207	+	11.6132i	0.418996	+	0.521973i
$496$	−0.809087	−	0.964232i	−0.0363291	−	0.0432953i
$497$	−1.71089	+	2.18983i	−0.0767437	+	0.0982275i
$498$	−3.65740	−	7.49878i	−0.163892	−	0.336028i
$499$	2.16232	−	4.43341i	0.0967986	−	0.198467i	−0.844900	−	0.534924i	$-0.820340\pi$
$499$	2.16232	−	4.43341i	0.0967986	−	0.198467i	0.941699	+	0.336458i	$0.109229\pi$
$500$	1.26252	+	1.61596i	0.0564618	+	0.0722678i
$501$	−2.94118	+	13.8372i	−0.131402	+	0.618199i
$502$	−2.75711	+	26.2321i	−0.123056	+	1.17080i
$503$	2.50160	−	35.7746i	0.111541	−	1.59511i	−0.543430	−	0.839455i	$-0.682875\pi$
$503$	2.50160	−	35.7746i	0.111541	−	1.59511i	0.654971	−	0.755654i	$-0.272681\pi$
$504$	−0.972456	−	1.55625i	−0.0433166	−	0.0693211i
$505$	37.1261	−	21.4348i	1.65209	−	0.953835i
$506$	−2.57109	+	15.7950i	−0.114299	+	0.702171i
$507$	−9.25944	−	25.4401i	−0.411226	−	1.12983i
$508$	7.64146	+	1.07394i	0.339035	+	0.0476482i
$509$	22.1461	−	10.8014i	0.981611	−	0.478763i	0.123565	−	0.992337i	$-0.460567\pi$
$509$	22.1461	−	10.8014i	0.981611	−	0.478763i	0.858046	+	0.513573i	$0.171678\pi$
$510$	4.31957	+	6.40403i	0.191274	+	0.283575i
$511$	0.346383	+	0.216444i	0.0153231	+	0.00957493i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−3.62609	−	13.6251i	−0.160096	−	0.601565i
$514$	−11.7264	−	16.1401i	−0.517231	−	0.711907i
$515$	−32.4675	+	13.1177i	−1.43069	+	0.578037i
$516$	−16.5640	−	6.02880i	−0.729189	−	0.265403i
$517$	10.8023	−	22.9088i	0.475084	−	1.00753i
$518$	−0.506463	−	2.87229i	−0.0222527	−	0.126201i
$519$	−0.192112	+	0.00670872i	−0.00843280	+	0.000294480i
$520$	0.141031	+	1.34182i	0.00618460	+	0.0588426i
$521$	26.4149	+	2.77632i	1.15726	+	0.121633i	0.663645	−	0.748048i	$-0.269009\pi$
$521$	26.4149	+	2.77632i	1.15726	+	0.121633i	0.493614	+	0.869681i	$0.335675\pi$
$522$	−3.32216	+	8.22262i	−0.145407	+	0.359894i
$523$	−1.24454	+	3.08034i	−0.0544198	+	0.134694i	−0.951945	−	0.306270i	$-0.900919\pi$
$523$	−1.24454	+	3.08034i	−0.0544198	+	0.134694i	0.897525	+	0.440964i	$0.145363\pi$
$524$	4.93342	+	0.518524i	0.215518	+	0.0226518i
$525$	−1.19414	−	11.3615i	−0.0521165	−	0.495855i
$526$	16.0020	−	0.558804i	0.697722	−	0.0243650i
$527$	0.261463	+	1.48283i	0.0113895	+	0.0645932i
$528$	0.884382	−	6.95621i	0.0384878	−	0.302730i
$529$	−0.264066	−	0.0961123i	−0.0114811	−	0.00417880i
$530$	−35.2958	+	14.2604i	−1.53315	+	0.619433i
$531$	−4.06269	−	5.59182i	−0.176306	−	0.242664i
$532$	−3.11337	−	4.46244i	−0.134982	−	0.193471i
$533$	−1.03193	−	3.17595i	−0.0446978	−	0.137566i
$534$	−6.22552	−	3.89014i	−0.269405	−	0.168343i
$535$	18.5037	+	27.4329i	0.799984	+	1.18603i
$536$	−8.40100	+	4.09744i	−0.362868	+	0.176982i
$537$	17.0713	+	2.39921i	0.736679	+	0.103533i
$538$	−3.44038	−	9.45237i	−0.148325	−	0.407520i
$539$	8.12479	+	16.1161i	0.349959	+	0.694170i
$540$	−8.55584	+	4.93971i	−0.368185	+	0.212571i
$541$	−1.48358	−	2.37422i	−0.0637840	−	0.102076i	0.814619	−	0.579997i	$-0.196946\pi$
$541$	−1.48358	−	2.37422i	−0.0637840	−	0.102076i	−0.878403	+	0.477921i	$0.841391\pi$
$542$	1.57400	−	22.5093i	0.0676091	−	0.966856i
$543$	3.64650	−	34.6942i	0.156486	−	1.48887i
$544$	0.248709	−	1.17009i	0.0106633	−	0.0501670i
$545$	26.6507	+	34.1113i	1.14159	+	1.46117i
$546$	−0.511078	+	1.04787i	−0.0218721	+	0.0448445i
$547$	15.9447	+	32.6916i	0.681748	+	1.39779i	0.906008	+	0.423261i	$0.139115\pi$
$547$	15.9447	+	32.6916i	0.681748	+	1.39779i	−0.224260	+	0.974529i	$0.571996\pi$
$548$	−5.96318	+	7.63252i	−0.254735	+	0.326045i
$549$	−12.2907	−	14.6475i	−0.524556	−	0.625142i
$550$	7.87051	−	12.0066i	0.335600	−	0.511963i
$551$	−8.60304	+	24.8481i	−0.366502	+	1.05856i
$552$	9.70209	+	3.15240i	0.412948	+	0.134175i
$553$	−6.22327	−	1.55164i	−0.264640	−	0.0659823i
$554$	−6.98872	+	4.71395i	−0.296922	+	0.200277i
$555$	14.9410	−	2.09982i	0.634211	−	0.0891325i
$556$	10.2082	+	19.1989i	0.432925	+	0.814214i
$557$	0.280229	−	0.977274i	0.0118737	−	0.0414084i	−0.955102	−	0.296278i	$-0.904255\pi$
$557$	0.280229	−	0.977274i	0.0118737	−	0.0414084i	0.966976	+	0.254869i	$0.0820324\pi$
$558$	1.84029	−	0.193422i	0.0779057	−	0.00818821i
$559$	0.765722	+	3.60244i	0.0323866	+	0.152367i
$560$	−2.45071	+	2.92064i	−0.103561	+	0.123420i
$561$	−5.07678	+	6.67741i	−0.214342	+	0.281920i
$562$	−2.05006	−	3.55081i	−0.0864766	−	0.149782i
$563$	24.7591	+	27.4978i	1.04347	+	1.15889i	0.987038	+	0.160487i	$0.0513066\pi$
$563$	24.7591	+	27.4978i	1.04347	+	1.15889i	0.0564347	+	0.998406i	$0.482027\pi$
$564$	−13.3855	−	9.02866i	−0.563633	−	0.380175i
$565$	4.12256	+	2.01070i	0.173437	+	0.0845910i
$566$	−1.70734	−	12.1483i	−0.0717647	−	0.510632i
$567$	−14.0336	−	0.490064i	−0.589356	−	0.0205808i
$568$	0.155291	+	2.22077i	0.00651588	+	0.0931815i
$569$	21.1718	−	15.3822i	0.887568	−	0.644856i	−0.0476749	−	0.998863i	$-0.515181\pi$
$569$	21.1718	−	15.3822i	0.887568	−	0.644856i	0.935243	+	0.354007i	$0.115181\pi$
$570$	23.6326	−	15.2903i	0.989861	−	0.640439i
$571$			30.7982i			1.28886i	0.764661	+	0.644432i	$0.222906\pi$
$571$			30.7982i			1.28886i	−0.764661	+	0.644432i	$0.777094\pi$
$572$	−1.33047	+	0.613484i	−0.0556298	+	0.0256510i
$573$	−12.4438	+	34.1891i	−0.519848	+	1.42827i
$574$	4.43019	−	8.33197i	0.184912	−	0.347770i
$575$	15.0238	+	14.5084i	0.626538	+	0.605041i
$576$	−1.41314	−	0.405212i	−0.0588809	−	0.0168838i
$577$	−26.4520	−	5.62255i	−1.10121	−	0.234070i	−0.378762	−	0.925494i	$-0.623650\pi$
$577$	−26.4520	−	5.62255i	−1.10121	−	0.234070i	−0.722449	+	0.691424i	$0.756984\pi$
$578$	10.4177	−	11.5701i	0.433320	−	0.481251i
$579$	−37.7653	+	9.41595i	−1.56947	+	0.391314i
$580$	18.3802	+	1.28527i	0.763195	+	0.0533678i
$581$	−4.81829	+	1.02416i	−0.199896	+	0.0424893i
$582$	−2.45444	+	4.25122i	−0.101740	+	0.176219i
$583$	−26.9860	−	31.3138i	−1.11765	−	1.29689i
$584$	0.322234	−	0.0568186i	0.0133342	−	0.00235117i
$585$	−1.75129	−	0.931177i	−0.0724069	−	0.0384994i
$586$	−3.54294	+	1.01592i	−0.146357	+	0.0419673i
$587$	9.10198	−	0.636473i	0.375679	−	0.0262700i	0.119331	−	0.992855i	$-0.461925\pi$
$587$	9.10198	−	0.636473i	0.375679	−	0.0262700i	0.256348	+	0.966585i	$0.417481\pi$
$588$	10.9422	−	3.55533i	0.451249	−	0.146620i
$589$	5.42051	−	0.849105i	0.223348	−	0.0349868i
$590$	−8.44069	+	11.6176i	−0.347498	+	0.478290i
$591$	3.62987	−	14.5586i	0.149313	−	0.598861i
$592$	−1.84117	−	1.43848i	−0.0756716	−	0.0591211i
$593$	−10.5944	−	1.86808i	−0.435060	−	0.0767128i	−0.0481710	−	0.998839i	$-0.515339\pi$
$593$	−10.5944	−	1.86808i	−0.435060	−	0.0767128i	−0.386889	+	0.922126i	$0.626450\pi$
$594$	−8.06633	−	7.07285i	−0.330965	−	0.290202i
$595$	4.28571	−	1.55987i	0.175697	−	0.0639485i
$596$	−9.78712	+	8.81236i	−0.400896	+	0.360968i
$597$	19.2355	−	43.2036i	0.787256	−	1.76821i
$598$	−0.515641	−	2.06812i	−0.0210861	−	0.0845718i
$599$	23.8385	+	9.63139i	0.974016	+	0.393528i	0.805777	−	0.592218i	$-0.201748\pi$
$599$	23.8385	+	9.63139i	0.974016	+	0.393528i	0.168238	+	0.985746i	$0.446192\pi$
$600$	−6.80108	−	6.12372i	−0.277653	−	0.250000i
$601$	40.8605	−	18.1923i	1.66674	−	0.742079i	0.666741	−	0.745289i	$-0.267689\pi$
$601$	40.8605	−	18.1923i	1.66674	−	0.742079i	0.999995	+	0.00321038i	$0.00102190\pi$
$602$	−5.81968	+	8.62802i	−0.237192	+	0.351652i
$603$	1.91236	−	13.6072i	0.0778774	−	0.554126i
$604$	2.01603	−	11.4335i	0.0820310	−	0.465221i
$605$	32.5282	+	8.40687i	1.32246	+	0.341788i
$606$	22.7328	−	19.0751i	0.923458	−	0.774873i
$607$	−10.6717	+	32.8441i	−0.433151	+	1.33310i	0.461819	+	0.886974i	$0.347197\pi$
$607$	−10.6717	+	32.8441i	−0.433151	+	1.33310i	−0.894970	+	0.446127i	$0.852803\pi$
$608$	−4.24551	−	0.987740i	−0.172178	−	0.0400581i
$609$	12.8805	+	9.35822i	0.521944	+	0.379214i
$610$	−21.0516	+	33.6895i	−0.852353	+	1.36405i
$611$	−0.117732	+	3.37140i	−0.00476292	+	0.136392i
$612$	1.22160	+	1.26500i	0.0493802	+	0.0511347i
$613$	−23.4173	+	24.2493i	−0.945814	+	0.979419i	−0.999817	−	0.0191219i	$-0.993913\pi$
$613$	−23.4173	+	24.2493i	−0.945814	+	0.979419i	0.0540033	+	0.998541i	$0.482802\pi$
$614$	−0.825966	−	23.6526i	−0.0333333	−	0.954541i
$615$	42.2760	+	24.4080i	1.70473	+	0.984227i
$616$	−3.85874	−	1.50023i	−0.155473	−	0.0604460i
$617$	22.6070	+	18.9696i	0.910125	+	0.763686i	0.972143	−	0.234389i	$-0.0753090\pi$
$617$	22.6070	+	18.9696i	0.910125	+	0.763686i	−0.0620175	+	0.998075i	$0.519753\pi$
$618$	−20.5567	+	12.8453i	−0.826913	+	0.516713i
$619$	−18.8809	−	8.40630i	−0.758886	−	0.337878i	−0.00945059	−	0.999955i	$-0.503008\pi$
$619$	−18.8809	−	8.40630i	−0.758886	−	0.337878i	−0.749435	+	0.662078i	$0.769675\pi$
$620$	−1.56368	−	3.51209i	−0.0627991	−	0.141049i
$621$	12.2986	−	9.60875i	0.493527	−	0.385586i
$622$	18.9245	−	10.0623i	0.758803	−	0.403463i
$623$	−3.11779	+	3.01082i	−0.124912	+	0.120626i
$624$	0.257435	+	0.897782i	0.0103056	+	0.0359400i
$625$	10.4539	+	25.8742i	0.418155	+	1.03497i
$626$	1.03262			0.0412720
$627$	23.9730	+	18.9617i	0.957388	+	0.757257i
$628$	−13.6749			−0.545688
$629$	1.04701	+	2.59144i	0.0417469	+	0.103327i
$630$	−1.54492	−	5.38778i	−0.0615511	−	0.214654i
$631$	−11.0852	+	10.7048i	−0.441294	+	0.426153i	−0.881819	−	0.471588i	$-0.843681\pi$
$631$	−11.0852	+	10.7048i	−0.441294	+	0.426153i	0.440525	+	0.897740i	$0.354792\pi$
$632$	−4.53663	+	2.41217i	−0.180458	+	0.0959510i
$633$	0.603205	−	0.471275i	0.0239752	−	0.0187315i
$634$	−8.15188	−	18.3094i	−0.323753	−	0.727160i
$635$	21.5309	+	9.58616i	0.854427	+	0.380415i
$636$	−22.3474	+	13.9642i	−0.886134	+	0.553718i
$637$	−1.84147	−	1.54518i	−0.0729618	−	0.0612222i
$638$	5.09553	+	19.3479i	0.201734	+	0.765993i
$639$	−2.83425	−	1.63635i	−0.112121	−	0.0647331i
$640$	0.106593	+	3.05241i	0.00421344	+	0.120657i
$641$	−31.8086	+	32.9388i	−1.25637	+	1.30100i	−0.321106	+	0.947043i	$0.604054\pi$
$641$	−31.8086	+	32.9388i	−1.25637	+	1.30100i	−0.935260	+	0.353961i	$0.884834\pi$
$642$	15.9118	+	16.4771i	0.627987	+	0.650300i
$643$	1.35736	−	38.8698i	0.0535292	−	1.53288i	−0.614605	−	0.788835i	$-0.710684\pi$
$643$	1.35736	−	38.8698i	0.0535292	−	1.53288i	0.668134	−	0.744041i	$-0.267093\pi$
$644$	3.19173	−	5.10784i	0.125772	−	0.201277i
$645$	−43.5557	−	31.6450i	−1.71500	−	1.24602i
$646$	3.80741	+	3.56256i	0.149800	+	0.140167i
$647$	−9.11823	+	28.0630i	−0.358475	+	1.10327i	0.595493	+	0.803361i	$0.296957\pi$
$647$	−9.11823	+	28.0630i	−0.358475	+	1.10327i	−0.953967	+	0.299910i	$0.903043\pi$
$648$	−8.61731	+	7.23079i	−0.338520	+	0.284052i
$649$	−14.8926	−	4.62299i	−0.584586	−	0.181468i
$650$	−0.332038	+	1.88308i	−0.0130236	+	0.0738605i
$651$	0.462335	−	3.28969i	0.0181204	−	0.128933i
$652$	7.64344	−	11.3319i	0.299340	−	0.443790i
$653$	25.3965	−	11.3072i	0.993841	−	0.442487i	0.155620	−	0.987817i	$-0.450263\pi$
$653$	25.3965	−	11.3072i	0.993841	−	0.442487i	0.838221	+	0.545331i	$0.183596\pi$
$654$	22.2685	+	20.0506i	0.870766	+	0.784041i
$655$	14.0478	+	5.67567i	0.548892	+	0.221767i
$656$	−1.82882	−	7.33501i	−0.0714036	−	0.286384i
$657$	−0.195649	+	0.439435i	−0.00763300	+	0.0171440i
$658$	−7.08423	+	6.37867i	−0.276172	+	0.248667i
$659$	20.0636	−	7.30254i	0.781566	−	0.284467i	0.0797402	−	0.996816i	$-0.474591\pi$
$659$	20.0636	−	7.30254i	0.781566	−	0.284467i	0.701825	+	0.712349i	$0.252369\pi$
$660$	8.45275	−	19.6786i	0.329023	−	0.765988i
$661$	−20.2804	−	3.57599i	−0.788817	−	0.139090i	−0.235295	−	0.971924i	$-0.575606\pi$
$661$	−20.2804	−	3.57599i	−0.788817	−	0.139090i	−0.553522	+	0.832834i	$0.686717\pi$
$662$	25.1150	+	19.6220i	0.976123	+	0.762631i
$663$	0.270282	−	1.08404i	0.0104969	−	0.0421007i
$664$	−2.31948	+	3.19249i	−0.0900134	+	0.123893i
$665$	−5.38391	−	15.7226i	−0.208779	−	0.609695i
$666$	3.26672	−	1.06142i	0.126583	−	0.0411292i
$667$	−29.0364	+	2.03042i	−1.12429	+	0.0786182i
$668$	6.43171	−	1.84426i	0.248850	−	0.0713567i
$669$	−25.0204	−	13.3036i	−0.967345	−	0.514347i
$670$	−28.1145	+	4.95734i	−1.08616	+	0.191519i
$671$	−41.9907	−	9.88399i	−1.62103	−	0.381567i
$672$	−1.31961	+	2.28562i	−0.0509049	+	0.0881699i
$673$	−25.1240	+	5.34028i	−0.968460	+	0.205853i	−0.664878	−	0.746952i	$-0.731516\pi$
$673$	−25.1240	+	5.34028i	−0.968460	+	0.205853i	−0.303583	+	0.952805i	$0.598183\pi$
$674$	−10.3030	−	0.720456i	−0.396857	−	0.0277509i
$675$	−13.5855	+	3.38723i	−0.522904	+	0.130375i
$676$	−8.56812	+	9.51587i	−0.329543	+	0.365995i
$677$	32.6042	+	6.93024i	1.25308	+	0.266351i	0.786202	−	0.617970i	$-0.212045\pi$
$677$	32.6042	+	6.93024i	1.25308	+	0.266351i	0.466880	+	0.884321i	$0.345378\pi$
$678$	3.05210	+	0.875175i	0.117215	+	0.0336109i
$679$	2.08485	+	2.01332i	0.0800093	+	0.0772640i
$680$	1.71526	−	3.22594i	0.0657773	−	0.123709i
$681$	−9.99131	+	27.4509i	−0.382868	+	1.05192i
$682$	3.06534	−	2.83402i	0.117378	−	0.108520i
$683$		−	2.11181i		−	0.0808060i	−0.999183	−	0.0404030i	$-0.987136\pi$
$683$		−	2.11181i		−	0.0808060i	0.999183	−	0.0404030i	$-0.0128642\pi$
$684$	4.69390	−	4.36228i	0.179476	−	0.166796i
$685$	−23.9332	+	17.3885i	−0.914442	+	0.664381i
$686$	−1.08338	−	15.4931i	−0.0413638	−	0.591530i
$687$	31.9076	+	1.11424i	1.21735	+	0.0425108i
$688$	1.16032	+	8.25608i	0.0442366	+	0.314760i
$689$	4.94858	+	2.41358i	0.188526	+	0.0919502i
$690$	25.8310	+	17.4232i	0.983369	+	0.663291i
$691$	−29.9998	−	33.3182i	−1.14125	−	1.26748i	−0.958742	−	0.284277i	$-0.908246\pi$
$691$	−29.9998	−	33.3182i	−1.14125	−	1.26748i	−0.182504	−	0.983205i	$-0.558420\pi$
$692$	0.0454603	+	0.0787395i	0.00172814	+	0.00299323i
$693$	5.00055	−	3.46959i	0.189955	−	0.131799i
$694$	−19.2622	+	22.9558i	−0.731182	+	0.871389i
$695$	13.8079	+	64.9611i	0.523764	+	2.46411i
$696$	12.6845	−	1.33319i	0.480804	−	0.0505346i
$697$	−2.49257	+	8.69263i	−0.0944129	+	0.329257i
$698$	8.30892	+	15.6268i	0.314497	+	0.591484i
$699$	−14.3141	+	2.01171i	−0.541407	+	0.0760898i
$700$	−4.47957	+	3.02151i	−0.169312	+	0.114202i
$701$	20.5441	+	5.12223i	0.775942	+	0.193464i	0.609712	−	0.792623i	$-0.291285\pi$
$701$	20.5441	+	5.12223i	0.775942	+	0.193464i	0.166230	+	0.986087i	$0.446841\pi$
$702$	1.35894	+	0.441547i	0.0512900	+	0.0166651i
$703$	9.51419	−	3.63366i	0.358835	−	0.137046i
$704$	−3.10140	+	1.17530i	−0.116888	+	0.0442956i
$705$	−31.6984	−	37.7766i	−1.19383	−	1.42275i
$706$	−10.5571	+	13.5124i	−0.397321	+	0.508547i
$707$	−7.68067	−	15.7477i	−0.288861	−	0.592254i
$708$	−4.35764	+	8.93449i	−0.163770	+	0.335779i
$709$	−23.2954	−	29.8167i	−0.874877	−	1.11979i	−0.991945	−	0.126667i	$-0.959572\pi$
$709$	−23.2954	−	29.8167i	−0.874877	−	1.11979i	0.117069	−	0.993124i	$-0.462650\pi$
$710$	−1.41368	+	6.65082i	−0.0530543	+	0.249601i
$711$	0.789546	−	7.51202i	0.0296103	−	0.281723i
$712$	−0.242204	+	3.46368i	−0.00907698	+	0.129807i
$713$	3.21839	+	5.15050i	0.120530	+	0.192888i
$714$	2.73412	−	1.57855i	0.102322	−	0.0590756i
$715$	−4.42268	+	0.681074i	−0.165399	+	0.0254707i
$716$	−2.78873	−	7.66197i	−0.104220	−	0.286341i
$717$	−22.7746	−	3.20076i	−0.850534	−	0.119535i
$718$	15.3079	−	7.46615i	0.571285	−	0.278634i
$719$	−22.0379	−	32.6726i	−0.821876	−	1.21848i	−0.973192	−	0.229996i	$-0.926129\pi$
$719$	−22.0379	−	32.6726i	−0.821876	−	1.21848i	0.151316	−	0.988485i	$-0.451649\pi$
$720$	−3.80779	−	2.37937i	−0.141908	−	0.0886738i
$721$	4.42256	+	13.6112i	0.164705	+	0.506909i
$722$	13.2448	−	13.6226i	0.492920	−	0.506981i
$723$	27.9125	+	38.4183i	1.03808	+	1.42879i
$724$	−15.2985	+	6.18101i	−0.568565	+	0.229715i
$725$	24.5376	+	8.93096i	0.911304	+	0.331688i
$726$	23.1854	+	1.82104i	0.860492	+	0.0675852i
$727$	5.65789	+	32.0875i	0.209839	+	1.19006i	0.889640	+	0.456662i	$0.150955\pi$
$727$	5.65789	+	32.0875i	0.209839	+	1.19006i	−0.679801	+	0.733397i	$0.737934\pi$
$728$	0.551090	−	0.0192445i	0.0204248	−	0.000713248i
$729$	0.415950	+	3.95750i	0.0154056	+	0.146574i
$730$	0.993900	+	0.104463i	0.0367859	+	0.00386635i
$731$	3.73602	−	9.24698i	0.138182	−	0.342012i
$732$	−10.3015	+	25.4971i	−0.380754	+	0.942400i
$733$	14.9077	+	1.56687i	0.550630	+	0.0578735i	0.375758	−	0.926718i	$-0.377382\pi$
$733$	14.9077	+	1.56687i	0.550630	+	0.0578735i	0.174872	+	0.984591i	$0.444049\pi$
$734$	−2.86131	−	27.2236i	−0.105613	−	1.00484i
$735$	35.1189	−	1.22638i	1.29538	−	0.0452357i
$736$	−0.837859	−	4.75174i	−0.0308839	−	0.175151i
$737$	−14.9130	−	27.1777i	−0.549327	−	1.00110i
$738$	10.4430	+	3.80095i	0.384413	+	0.139915i
$739$	43.9091	−	17.7404i	1.61522	−	0.652592i	0.623598	−	0.781745i	$-0.285670\pi$
$739$	43.9091	−	17.7404i	1.61522	−	0.652592i	0.991625	+	0.129153i	$0.0412258\pi$
$740$	−4.19458	−	5.77334i	−0.154196	−	0.212232i
$741$	−3.93054	−	1.06033i	−0.144392	−	0.0389522i
$742$	4.80781	+	14.7969i	0.176500	+	0.543212i
$743$	2.84311	+	1.77657i	0.104303	+	0.0651760i	0.581068	−	0.813855i	$-0.302635\pi$
$743$	2.84311	+	1.77657i	0.104303	+	0.0651760i	−0.476765	+	0.879031i	$0.658191\pi$
$744$	−1.48815	−	2.20628i	−0.0545583	−	0.0808860i
$745$	−36.1534	+	17.6332i	−1.32456	+	0.646031i
$746$	9.02310	+	1.26811i	0.330359	+	0.0464289i
$747$	−1.98412	−	5.45133i	−0.0725952	−	0.199454i
$748$	3.91589	+	0.637425i	0.143179	+	0.0233066i
$749$	11.7121	−	6.76200i	0.427952	−	0.247078i
$750$	2.29755	+	3.67685i	0.0838947	+	0.134260i
$751$	2.91675	−	41.7114i	0.106434	−	1.52207i	−0.591732	−	0.806135i	$-0.701556\pi$
$751$	2.91675	−	41.7114i	0.106434	−	1.52207i	0.698166	−	0.715936i	$-0.254000\pi$
$752$	−0.798248	+	7.59482i	−0.0291091	+	0.276955i
$753$	−11.5946	+	54.5484i	−0.422531	+	1.98785i
$754$	−1.64064	−	2.09992i	−0.0597486	−	0.0764747i
$755$	15.5445	−	31.8709i	0.565722	−	1.15990i
$756$	1.77004	+	3.62911i	0.0643756	+	0.131989i
$757$	25.3058	−	32.3899i	0.919755	−	1.17723i	−0.0640423	−	0.997947i	$-0.520399\pi$
$757$	25.3058	−	32.3899i	0.919755	−	1.17723i	0.983797	−	0.179285i	$-0.0573785\pi$
$758$	12.5320	+	14.9351i	0.455183	+	0.542466i
$759$	−8.89686	+	32.6435i	−0.322935	+	1.18488i
$760$	−11.6331	−	6.47414i	−0.421976	−	0.234842i
$761$	40.1326	+	13.0399i	1.45480	+	0.472695i	0.926479	−	0.376347i	$-0.122820\pi$
$761$	40.1326	+	13.0399i	1.45480	+	0.472695i	0.528326	+	0.849042i	$0.322820\pi$
$762$	15.8302	+	3.94691i	0.573467	+	0.142981i
$763$	14.6673	−	9.89319i	0.530990	−	0.358158i
$764$	17.0411	−	2.39497i	0.616524	−	0.0866469i
$765$	2.52159	+	4.74242i	0.0911683	+	0.171463i
$766$	−7.22689	+	25.2031i	−0.261118	+	0.910627i
$767$	2.06556	−	0.217099i	0.0745829	−	0.00783898i
$768$	0.439579	+	2.06806i	0.0158619	+	0.0746246i
$769$	10.6760	−	12.7232i	0.384987	−	0.458810i	−0.538394	−	0.842693i	$-0.680969\pi$
$769$	10.6760	−	12.7232i	0.384987	−	0.458810i	0.923382	+	0.383883i	$0.125413\pi$
$770$	−10.0661	−	7.65317i	−0.362757	−	0.275801i
$771$	−21.0900	−	36.5289i	−0.759536	−	1.31556i
$772$	12.3180	+	13.6806i	0.443336	+	0.492375i
$773$	24.0913	+	16.2498i	0.866504	+	0.584465i	0.910009	−	0.414589i	$-0.136075\pi$
$773$	24.0913	+	16.2498i	0.866504	+	0.584465i	−0.0435046	+	0.999053i	$0.513852\pi$
$774$	−11.0160	−	5.37288i	−0.395963	−	0.193124i
$775$	−0.758279	−	5.39544i	−0.0272382	−	0.193810i
$776$	2.32039	+	0.0810297i	0.0832970	+	0.00290880i
$777$	−0.430150	−	6.15143i	−0.0154316	−	0.220681i
$778$	15.5867	−	11.3244i	0.558811	−	0.406000i
$779$	31.4952	+	9.68747i	1.12843	+	0.347090i
$780$			2.85258i			0.102139i
$781$	−7.33220	+	0.868412i	−0.262367	+	0.0310742i
$782$	−1.97408	+	5.42375i	−0.0705931	+	0.193953i
$783$	9.16081	−	17.2290i	0.327381	−	0.615713i
$784$	−3.91448	−	3.78017i	−0.139803	−	0.135006i
$785$	−40.1489	−	11.5125i	−1.43298	−	0.410900i
$786$	10.2588	+	2.18058i	0.365919	+	0.0777786i
$787$	−9.62881	+	10.6939i	−0.343230	+	0.381196i	−0.889902	−	0.456151i	$-0.849228\pi$
$787$	−9.62881	+	10.6939i	−0.343230	+	0.381196i	0.546672	+	0.837347i	$0.315894\pi$
$788$	−6.88592	+	1.71685i	−0.245301	+	0.0611603i
$789$	33.7706	+	2.36147i	1.20227	+	0.0840706i
$790$	−15.3501	+	3.26276i	−0.546132	+	0.116084i
$791$	0.937313	−	1.62347i	0.0333270	−	0.0577241i
$792$	1.11715	−	4.74603i	0.0396960	−	0.168643i
$793$	5.65834	−	0.997718i	0.200934	−	0.0354300i
$794$	−12.3415	−	6.56212i	−0.437985	−	0.232881i
$795$	−77.3672	+	22.1847i	−2.74393	+	0.786810i
$796$	−22.3137	+	1.56033i	−0.790890	+	0.0553044i
$797$	−7.12738	+	2.31583i	−0.252465	+	0.0820308i	−0.432515	−	0.901627i	$-0.642374\pi$
$797$	−7.12738	+	2.31583i	−0.252465	+	0.0820308i	0.180050	+	0.983657i	$0.442374\pi$
$798$	−5.56021	−	10.0711i	−0.196829	−	0.356514i
$799$	5.36952	−	7.39050i	0.189960	−	0.261457i
$800$	−1.04718	+	4.20001i	−0.0370234	+	0.148493i
$801$	−4.02229	−	3.14255i	−0.142121	−	0.111037i
$802$	26.4092	+	4.65665i	0.932541	+	0.164432i
$803$	0.239588	+	1.05844i	0.00845489	+	0.0373515i
$804$	−18.5701	+	6.75897i	−0.654917	+	0.238370i
$805$	13.6709	−	12.3094i	0.481837	−	0.433848i
$806$	−0.226158	+	0.507959i	−0.00796608	+	0.0178921i
$807$	−5.14503	−	20.6356i	−0.181114	−	0.726407i
$808$	−13.0139	−	5.25795i	−0.457827	−	0.184974i
$809$	−2.59574	−	2.33721i	−0.0912613	−	0.0821720i	0.622237	−	0.782829i	$-0.286224\pi$
$809$	−2.59574	−	2.33721i	−0.0912613	−	0.0821720i	−0.713499	+	0.700657i	$0.752891\pi$
$810$	−31.3875	+	13.9746i	−1.10284	+	0.491017i
$811$	11.4449	−	16.9677i	0.401883	−	0.595817i	−0.572721	−	0.819750i	$-0.694112\pi$
$811$	11.4449	−	16.9677i	0.401883	−	0.595817i	0.974604	+	0.223934i	$0.0718899\pi$
$812$	1.04803	−	7.45709i	0.0367785	−	0.261693i
$813$	8.28417	−	46.9819i	0.290538	−	1.64773i
$814$	4.47192	−	6.32869i	0.156741	−	0.221820i
$815$	31.9808	−	26.8351i	1.12024	−	0.939992i
$816$	0.781544	−	2.40535i	0.0273595	−	0.0842040i
$817$	−33.4280	−	14.2563i	−1.16950	−	0.498765i
$818$	−17.7586	−	12.9024i	−0.620914	−	0.451120i
$819$	−0.429577	+	0.687467i	−0.0150106	+	0.0240220i
$820$	0.805794	−	23.0749i	0.0281395	−	0.805811i
$821$	−23.8430	−	24.6901i	−0.832125	−	0.861690i	0.159978	−	0.987121i	$-0.448858\pi$
$821$	−23.8430	−	24.6901i	−0.832125	−	0.861690i	−0.992102	+	0.125430i	$0.959969\pi$
$822$	−14.2254	+	14.7309i	−0.496169	+	0.513798i
$823$	−0.370726	−	10.6162i	−0.0129227	−	0.370057i	−0.988575	−	0.150732i	$-0.951837\pi$
$823$	−0.370726	−	10.6162i	−0.0129227	−	0.370057i	0.975652	−	0.219325i	$-0.0703854\pi$
$824$	9.92902	+	5.73252i	0.345894	+	0.199702i
$825$	19.2026	−	23.5066i	0.668549	−	0.818395i
$826$	4.49595	+	3.77255i	0.156434	+	0.131264i
$827$	−11.9323	+	7.45614i	−0.414928	+	0.259276i	−0.721281	−	0.692642i	$-0.756447\pi$
$827$	−11.9323	+	7.45614i	−0.414928	+	0.259276i	0.306354	+	0.951918i	$0.400891\pi$
$828$	6.48000	+	2.88508i	0.225196	+	0.100264i
$829$	−20.4585	−	45.9506i	−0.710554	−	1.59593i	−0.800044	−	0.599942i	$-0.795190\pi$
$829$	−20.4585	−	45.9506i	−0.710554	−	1.59593i	0.0894899	−	0.995988i	$-0.471476\pi$
$830$	−9.49757	+	7.42032i	−0.329665	+	0.257563i
$831$	−15.7368	+	8.36741i	−0.545904	+	0.290262i
$832$	0.317764	−	0.306861i	0.0110165	−	0.0106385i
$833$	1.79428	+	6.25741i	0.0621683	+	0.216806i
$834$	17.2216	+	42.6250i	0.596337	+	1.47598i
$835$	20.4358			0.707212
$836$	2.59549	−	14.2219i	0.0897671	−	0.491876i
$837$	−4.07147			−0.140731
$838$	−10.8048	−	26.7428i	−0.373246	−	0.923815i
$839$	1.10280	+	3.84591i	0.0380728	+	0.132775i	0.978003	−	0.208591i	$-0.0668879\pi$
$839$	1.10280	+	3.84591i	0.0380728	+	0.132775i	−0.939930	+	0.341367i	$0.889110\pi$
$840$	−5.79851	+	5.59955i	−0.200068	+	0.193203i
$841$	−6.52639	+	3.47014i	−0.225048	+	0.119660i
$842$	−9.28775	+	7.25639i	−0.320077	+	0.250072i
$843$	−3.52589	−	7.91927i	−0.121438	−	0.272754i
$844$	−0.330754	−	0.147261i	−0.0113850	−	0.00506893i
$845$	−33.1668	+	20.7249i	−1.14097	+	0.712958i
$846$	−8.60006	−	7.21630i	−0.295676	−	0.248102i
$847$	4.35492	−	13.0223i	0.149637	−	0.447452i
$848$	10.7939	+	6.23188i	0.370665	+	0.214004i
$849$	−0.905193	−	25.9213i	−0.0310661	−	0.889618i
$850$	3.59692	−	3.72472i	0.123373	−	0.127757i
$851$	7.83130	+	8.10954i	0.268453	+	0.277992i
$852$	−0.164263	+	4.70388i	−0.00562756	+	0.161152i
$853$	−1.72956	+	2.76788i	−0.0592191	+	0.0947704i	−0.876333	−	0.481706i	$-0.840017\pi$
$853$	−1.72956	+	2.76788i	−0.0592191	+	0.0947704i	0.817114	+	0.576477i	$0.195573\pi$
$854$	13.1353	+	9.54336i	0.449481	+	0.326567i
$855$	17.4536	−	8.85579i	0.596899	−	0.302861i
$856$	3.34789	−	10.3037i	0.114429	−	0.352175i
$857$	30.7277	−	25.7836i	1.04964	−	0.880751i	0.0565827	−	0.998398i	$-0.481980\pi$
$857$	30.7277	−	25.7836i	1.04964	−	0.880751i	0.993055	+	0.117647i	$0.0375351\pi$
$858$	−2.93313	+	0.995923i	−0.100136	+	0.0340003i
$859$	−1.75601	+	9.95881i	−0.0599142	+	0.339790i	−0.999999	−	0.00114959i	$-0.999634\pi$
$859$	−1.75601	+	9.95881i	−0.0599142	+	0.339790i	0.940085	+	0.340940i	$0.110745\pi$
$860$	−3.54392	+	25.2163i	−0.120847	+	0.859869i
$861$	11.1566	−	16.5404i	0.380217	−	0.563694i
$862$	5.75357	−	2.56165i	0.195967	−	0.0872503i
$863$	−29.7199	−	26.7599i	−1.01168	−	0.910919i	−0.0156425	−	0.999878i	$-0.504979\pi$
$863$	−29.7199	−	26.7599i	−1.01168	−	0.910919i	−0.996035	+	0.0889589i	$0.971646\pi$
$864$	2.99909	+	1.21171i	0.102031	+	0.0412233i
$865$	0.0671808	+	0.269447i	0.00228422	+	0.00916149i
$866$	−0.622077	+	1.39721i	−0.0211390	+	0.0474791i
$867$	24.4621	−	22.0258i	0.830776	−	0.748034i
$868$	−1.47649	+	0.537397i	−0.0501152	+	0.0182405i
$869$	−8.71410	−	14.6445i	−0.295606	−	0.496779i
$870$	38.3635	+	6.76452i	1.30064	+	0.229339i
$871$	3.25367	+	2.54205i	0.110246	+	0.0861340i
$872$	3.42873	−	13.7519i	0.116112	−	0.465698i
$873$	−2.00626	+	2.76138i	−0.0679017	+	0.0934587i
$874$	19.6221	+	7.57043i	0.663728	+	0.256074i
$875$	2.43456	−	0.791035i	0.0823030	−	0.0267419i
$876$	0.690112	−	0.0482573i	0.0233167	−	0.00163046i
$877$	−1.30528	+	0.374282i	−0.0440761	+	0.0126386i	−0.297603	−	0.954690i	$-0.596187\pi$
$877$	−1.30528	+	0.374282i	−0.0440761	+	0.0126386i	0.253527	+	0.967328i	$0.418409\pi$
$878$	27.2160	+	14.4710i	0.918495	+	0.488372i
$879$	−7.67417	+	1.35316i	−0.258843	+	0.0456411i
$880$	−10.0950	+	0.839636i	−0.340303	+	0.0283041i
$881$	5.19193	−	8.99268i	0.174920	−	0.302971i	−0.765213	−	0.643777i	$-0.777366\pi$
$881$	5.19193	−	8.99268i	0.174920	−	0.302971i	0.940134	+	0.340806i	$0.110700\pi$
$882$	7.82507	−	1.66327i	0.263484	−	0.0560052i
$883$	−22.1096	−	1.54606i	−0.744048	−	0.0520289i	−0.307300	−	0.951613i	$-0.599425\pi$
$883$	−22.1096	−	1.54606i	−0.744048	−	0.0520289i	−0.436748	+	0.899584i	$0.643870\pi$
$884$	−0.512729	+	0.127838i	−0.0172450	+	0.00429965i
$885$	−20.3155	+	22.5627i	−0.682899	+	0.758437i
$886$	24.2216	+	5.14847i	0.813741	+	0.172966i
$887$	−38.7326	−	11.1064i	−1.30051	−	0.372917i	−0.447257	−	0.894406i	$-0.647599\pi$
$887$	−38.7326	−	11.1064i	−1.30051	−	0.372917i	−0.853258	+	0.521489i	$0.825377\pi$
$888$	−3.55348	−	3.43155i	−0.119247	−	0.115155i
$889$	4.52219	−	8.50500i	0.151669	−	0.285249i
$890$	−3.62707	+	9.96531i	−0.121580	+	0.334038i
$891$	−25.3276	−	27.3949i	−0.848506	−	0.917763i
$892$			13.4030i			0.448765i
$893$	−26.5505	−	20.0779i	−0.888479	−	0.671882i
$894$	−22.5267	+	16.3666i	−0.753405	+	0.547381i
$895$	−1.73719	−	24.8429i	−0.0580678	−	0.830408i
$896$	1.24753	+	0.0435648i	0.0416771	+	0.00145540i
$897$	−0.627170	−	4.46255i	−0.0209406	−	0.149000i
$898$	−30.1589	−	14.7095i	−1.00642	−	0.490861i
$899$	6.29510	+	4.24610i	0.209953	+	0.141615i
$900$	−4.25796	−	4.72894i	−0.141932	−	0.157631i
$901$	−7.45474	−	12.9120i	−0.248353	−	0.430160i
$902$	24.0079	−	7.22762i	0.799375	−	0.240654i
$903$	−14.1437	+	16.8558i	−0.470673	+	0.560926i
$904$	−0.312232	−	1.46894i	−0.0103847	−	0.0488561i
$905$	−50.1194	+	5.26777i	−1.66603	+	0.175106i
$906$	6.76585	−	23.5953i	0.224780	−	0.783903i
$907$	21.7721	+	40.9474i	0.722931	+	1.35964i	0.924887	+	0.380241i	$0.124159\pi$
$907$	21.7721	+	40.9474i	0.722931	+	1.35964i	−0.201956	+	0.979395i	$0.564730\pi$
$908$	13.6825	−	1.92295i	0.454069	−	0.0638153i
$909$	17.1064	−	11.5384i	0.567384	−	0.382706i
$910$	1.63418	+	0.407446i	0.0541725	+	0.0135067i
$911$	56.1871	+	18.2563i	1.86156	+	0.604858i	0.994249	+	0.107098i	$0.0341558\pi$
$911$	56.1871	+	18.2563i	1.86156	+	0.604858i	0.867314	+	0.497761i	$0.165844\pi$
$912$	−8.70865	−	3.01516i	−0.288372	−	0.0998418i
$913$	−10.9458	−	7.17512i	−0.362252	−	0.237462i
$914$	16.7303	+	19.9384i	0.553391	+	0.659505i
$915$	−51.7100	+	66.1858i	−1.70948	+	2.18804i
$916$	−6.61977	−	13.5725i	−0.218723	−	0.448449i
$917$	2.71451	−	5.56558i	0.0896412	−	0.183792i
$918$	−2.38220	−	3.04908i	−0.0786245	−	0.100635i
$919$	−0.135158	+	0.635869i	−0.00445845	+	0.0209754i	−0.980321	−	0.197412i	$-0.936746\pi$
$919$	−0.135158	+	0.635869i	−0.00445845	+	0.0209754i	0.975862	+	0.218387i	$0.0700796\pi$
$920$	1.54044	−	14.6563i	0.0507866	−	0.483203i
$921$	3.49049	−	49.9163i	0.115015	−	1.64480i
$922$	−4.53783	−	7.26204i	−0.149445	−	0.239163i
$923$	0.851657	−	0.491704i	0.0280326	−	0.0161846i
$924$	−7.78213	−	4.00728i	−0.256013	−	0.131830i
$925$	−3.45907	−	9.50371i	−0.113733	−	0.312480i
$926$	22.2849	+	3.13194i	0.732327	+	0.102922i
$927$	−15.1489	+	7.38859i	−0.497554	+	0.242673i
$928$	−3.37336	−	5.00121i	−0.110736	−	0.164173i
$929$	−14.7258	−	9.20169i	−0.483137	−	0.301898i	0.266397	−	0.963863i	$-0.414167\pi$
$929$	−14.7258	−	9.20169i	−0.483137	−	0.301898i	−0.749534	+	0.661966i	$0.769722\pi$
$930$	−2.51175	−	7.73037i	−0.0823635	−	0.253489i
$931$	22.9223	−	6.10036i	0.751246	−	0.199931i
$932$	4.01856	+	5.53107i	0.131632	+	0.181176i
$933$	42.0159	−	16.9755i	1.37554	−	0.555753i
$934$	12.4932	+	4.54715i	0.408790	+	0.148787i
$935$	10.9603	+	5.16813i	0.358439	+	0.169016i
$936$	0.112768	+	0.639538i	0.00368593	+	0.0209040i
$937$	−48.6683	+	1.69953i	−1.58992	+	0.0555213i	−0.816111	−	0.577895i	$-0.803874\pi$
$937$	−48.6683	+	1.69953i	−1.58992	+	0.0555213i	−0.773811	+	0.633416i	$0.781652\pi$
$938$	1.21961	+	11.6038i	0.0398217	+	0.378878i
$939$	2.17128	+	0.228210i	0.0708569	+	0.00744736i
$940$	−8.73749	+	21.6260i	−0.284985	+	0.705364i
$941$	−5.68545	+	14.0720i	−0.185340	+	0.458734i	−0.991036	−	0.133596i	$-0.957347\pi$
$941$	−5.68545	+	14.0720i	−0.185340	+	0.458734i	0.805695	+	0.592330i	$0.201792\pi$
$942$	−28.7539	−	3.02216i	−0.936853	−	0.0984673i
$943$	3.81270	+	36.2754i	0.124158	+	1.18129i
$944$	4.69880	−	0.164086i	0.152933	−	0.00534053i
$945$	2.14150	+	12.1451i	0.0696630	+	0.395079i
$946$	−27.1657	+	5.15980i	−0.883234	+	0.167760i
$947$	16.2344	+	5.90884i	0.527547	+	0.192011i	0.592043	−	0.805907i	$-0.298322\pi$
$947$	16.2344	+	5.90884i	0.527547	+	0.192011i	−0.0644958	+	0.997918i	$0.520544\pi$
$948$	−10.0722	+	4.06942i	−0.327129	+	0.132169i
$949$	−0.0849592	−	0.116936i	−0.00275789	−	0.00379591i
$950$	−13.3190	−	13.3642i	−0.432124	−	0.433592i
$951$	−13.0944	−	40.3004i	−0.424614	−	1.30683i
$952$	−1.26634	−	0.791296i	−0.0410423	−	0.0256460i
$953$	−26.0529	−	38.6249i	−0.843935	−	1.25118i	−0.965969	−	0.258659i	$-0.916719\pi$
$953$	−26.0529	−	38.6249i	−0.843935	−	1.25118i	0.122034	−	0.992526i	$-0.461058\pi$
$954$	−16.4685	+	8.03221i	−0.533187	+	0.260052i
$955$	52.0481	+	7.31488i	1.68424	+	0.236704i
$956$	3.72042	+	10.2218i	0.120327	+	0.330596i
$957$	6.43834	+	41.8086i	0.208122	+	1.35148i
$958$	−29.9506	+	17.2920i	−0.967660	+	0.558678i
$959$	6.40711	+	10.2535i	0.206896	+	0.331103i
$960$	−0.450454	+	6.44179i	−0.0145383	+	0.207908i
$961$	−3.07477	+	29.2545i	−0.0991862	+	0.943693i
$962$	−0.214591	+	1.00957i	−0.00691869	+	0.0325499i
$963$	9.80561	+	12.5506i	0.315981	+	0.404438i
$964$	9.84609	−	20.1875i	0.317121	−	0.650195i
$965$	24.6480	+	50.5358i	0.793446	+	1.62680i
$966$	7.84002	−	10.0348i	0.252248	−	0.322863i
$967$	−14.7980	−	17.6356i	−0.475872	−	0.567122i	0.473694	−	0.880690i	$-0.342920\pi$
$967$	−14.7980	−	17.6356i	−0.475872	−	0.567122i	−0.949566	+	0.313567i	$0.898476\pi$
$968$	−4.38784	−	10.0870i	−0.141030	−	0.324207i
$969$	7.21842	+	8.33234i	0.231889	+	0.267673i
$970$	6.74434	+	2.19137i	0.216548	+	0.0703606i
$971$	2.10428	+	0.524655i	0.0675294	+	0.0168370i	0.275540	−	0.961290i	$-0.411143\pi$
$971$	2.10428	+	0.524655i	0.0675294	+	0.0168370i	−0.208011	+	0.978127i	$0.566699\pi$
$972$	−11.6726	+	7.87324i	−0.374397	+	0.252534i
$973$	26.8788	−	3.77757i	0.861694	−	0.121103i
$974$	−7.76257	−	14.5993i	−0.248729	−	0.467791i
$975$	−1.11433	+	3.88613i	−0.0356871	+	0.124456i
$976$	12.9354	−	1.35957i	0.414053	−	0.0435187i
$977$	4.60268	+	21.6539i	0.147253	+	0.692771i	0.988389	+	0.151947i	$0.0485542\pi$
$977$	4.60268	+	21.6539i	0.147253	+	0.692771i	−0.841136	+	0.540824i	$0.818112\pi$
$978$	18.5760	−	22.1381i	0.593996	−	0.707897i
$979$	−11.5131	−	0.250304i	−0.367959	−	0.00799976i
$980$	−8.31032	−	14.3939i	−0.265464	−	0.459796i
$981$	13.9416	+	15.4838i	0.445122	+	0.494358i
$982$	−8.09500	−	5.46015i	−0.258322	−	0.174240i
$983$	53.0563	+	25.8773i	1.69223	+	0.825358i	0.993987	+	0.109501i	$0.0349252\pi$
$983$	53.0563	+	25.8773i	1.69223	+	0.825358i	0.698247	+	0.715857i	$0.253964\pi$
$984$	−2.22439	−	15.8273i	−0.0709108	−	0.504557i
$985$	−21.6621	−	0.756458i	−0.690213	−	0.0241028i
$986$	0.503383	+	7.19871i	0.0160310	+	0.229253i
$987$	−16.3055	+	11.8467i	−0.519011	+	0.377084i
$988$	0.429965	+	1.87690i	0.0136790	+	0.0597121i
$989$		−	40.2274i		−	1.27916i
$990$	7.27544	−	12.9936i	0.231229	−	0.412965i
$991$	−0.00485796	+	0.0133471i	−0.000154318	+	0.000423985i	−0.939770	−	0.341808i	$-0.888961\pi$
$991$	−0.00485796	+	0.0133471i	−0.000154318	+	0.000423985i	0.939615	+	0.342232i	$0.111183\pi$
$992$	−0.590931	+	1.11138i	−0.0187621	+	0.0352864i
$993$	48.4723	+	46.8092i	1.53822	+	1.48544i
$994$	2.67129	+	0.765979i	0.0847281	+	0.0242954i
$995$	−66.8258	−	14.2043i	−2.11852	−	0.450305i
$996$	−5.58266	+	6.20018i	−0.176893	+	0.196460i
$997$	−36.1854	+	9.02205i	−1.14600	+	0.285731i	−0.768235	−	0.640168i	$-0.778865\pi$
$997$	−36.1854	+	9.02205i	−1.14600	+	0.285731i	−0.377770	+	0.925899i	$0.623309\pi$
$998$	−4.92060	−	0.344082i	−0.155759	−	0.0108917i
$999$	−7.39247	+	1.57132i	−0.233887	+	0.0497143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.13.2	yes	240
11.6	odd	10		418.2.v.a.127.9	yes	240
19.3	odd	18		418.2.v.a.79.9	✓	240
209.193	even	90	inner	418.2.v.b.193.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.79.9	✓	240	19.3	odd	18
418.2.v.a.127.9	yes	240	11.6	odd	10
418.2.v.b.13.2	yes	240	1.1	even	1	trivial
418.2.v.b.193.2	yes	240	209.193	even	90	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.582769 - 2.03236i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.69676 + 1.43389i) q^{5} +(-1.66606 + 1.30167i) q^{6} +(0.507726 + 1.14037i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.24671 + 0.779029i) q^{9} +O(q^{10})\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.582769 - 2.03236i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.69676 + 1.43389i) q^{5} +(-1.66606 + 1.30167i) q^{6} +(0.507726 + 1.14037i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-1.24671 + 0.779029i) q^{9} +(2.33971 + 1.96325i) q^{10} +(-1.20183 + 3.09122i) q^{11} +(1.83100 + 1.05713i) q^{12} +(-0.0154167 - 0.441475i) q^{13} +(0.867136 - 0.897946i) q^{14} +(4.48577 + 4.64515i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-0.633903 + 1.01446i) q^{17} +(1.18933 + 0.864097i) q^{18} +(3.65165 + 2.38022i) q^{19} +(0.943822 - 2.90479i) q^{20} +(2.02175 - 1.69645i) q^{21} +(3.31634 - 0.0436757i) q^{22} +(-0.837859 + 4.75174i) q^{23} +(0.294248 - 2.09368i) q^{24} +(2.42052 - 3.58856i) q^{25} +(-0.403554 + 0.179674i) q^{26} +(-2.40379 - 2.16439i) q^{27} +(-1.15740 - 0.467618i) q^{28} +(1.45940 + 5.85335i) q^{29} +(2.62651 - 5.89924i) q^{30} +(0.935408 - 0.842245i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(6.98284 + 0.641075i) q^{33} +(1.17805 + 0.207722i) q^{34} +(-3.00439 - 2.34729i) q^{35} +(0.355647 - 1.42642i) q^{36} +(1.37335 - 1.89025i) q^{37} +(0.838972 - 4.27740i) q^{38} +(-0.888251 + 0.288610i) q^{39} +(-3.04683 + 0.213055i) q^{40} +(7.26672 - 2.08370i) q^{41} +(-2.33029 - 1.23903i) q^{42} +(-8.21055 + 1.44774i) q^{43} +(-1.28282 - 3.05849i) q^{44} +(2.24503 - 3.88850i) q^{45} +(4.71960 - 1.00318i) q^{46} +(-7.61805 - 0.532706i) q^{47} +(-2.05146 + 0.511485i) q^{48} +(3.64125 - 4.04402i) q^{49} +(-4.23400 - 0.899964i) q^{50} +(2.43116 + 0.697123i) q^{51} +(0.317764 + 0.306861i) q^{52} +(-5.85138 + 11.0048i) q^{53} +(-1.10631 + 3.03955i) q^{54} +(-1.19144 - 10.0596i) q^{55} +1.24829i q^{56} +(2.70939 - 8.80857i) q^{57} +(4.88043 - 3.54584i) q^{58} +(0.327971 + 4.69021i) q^{59} +(-6.45359 - 0.225364i) q^{60} +(1.81018 + 12.8801i) q^{61} +(-1.13133 - 0.551785i) q^{62} +(-1.52137 - 1.02618i) q^{63} +(0.669131 + 0.743145i) q^{64} +(0.674604 + 1.16845i) q^{65} +(-2.02142 - 6.71452i) q^{66} +(-6.00811 + 7.16019i) q^{67} +(-0.248709 - 1.17009i) q^{68} +(10.1455 - 1.06633i) q^{69} +(-1.05090 + 3.66493i) q^{70} +(1.04513 + 1.96561i) q^{71} +(-1.45578 + 0.204597i) q^{72} +(0.271266 - 0.182971i) q^{73} +(-2.26707 - 0.565245i) q^{74} +(-8.70383 - 2.82805i) q^{75} +(-4.28022 + 0.824460i) q^{76} +(-4.13533 + 0.198962i) q^{77} +(0.600339 + 0.715456i) q^{78} +(-3.16330 + 4.04884i) q^{79} +(1.33891 + 2.74516i) q^{80} +(-4.93128 + 10.1106i) q^{81} +(-4.65413 - 5.95702i) q^{82} +(-0.820449 + 3.85991i) q^{83} +(-0.275873 + 2.62475i) q^{84} +(0.254862 - 3.64470i) q^{85} +(4.41805 + 7.07036i) q^{86} +(11.0456 - 6.37718i) q^{87} +(-2.35523 + 2.33514i) q^{88} +(1.18754 + 3.26274i) q^{89} +(-4.44636 - 0.624895i) q^{90} +(0.495618 - 0.241729i) q^{91} +(-2.69813 - 4.00014i) q^{92} +(-2.25687 - 1.41025i) q^{93} +(2.35986 + 7.26289i) q^{94} +(-13.2606 - 1.18282i) q^{95} +(1.24273 + 1.71047i) q^{96} +(2.15274 - 0.869762i) q^{97} +(-5.11359 - 1.86119i) q^{98} +(-0.909821 - 4.79010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

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