LMFDB - Embedded newform 225.2.w.a.212.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			212.28
Character	$\chi$	$=$	225.212
Dual form			225.2.w.a.173.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73930 + 2.14786i) q^{2} +(0.312495 - 1.70363i) q^{3} +(-1.17230 + 5.51525i) q^{4} +(2.23571 - 0.0402288i) q^{5} +(4.20267 - 2.29193i) q^{6} +(0.577528 - 2.15536i) q^{7} +(-8.95988 + 4.56529i) q^{8} +(-2.80469 - 1.06475i) q^{9} +O(q^{10})$	\(q+(1.73930 + 2.14786i) q^{2} +(0.312495 - 1.70363i) q^{3} +(-1.17230 + 5.51525i) q^{4} +(2.23571 - 0.0402288i) q^{5} +(4.20267 - 2.29193i) q^{6} +(0.577528 - 2.15536i) q^{7} +(-8.95988 + 4.56529i) q^{8} +(-2.80469 - 1.06475i) q^{9} +(3.97497 + 4.73201i) q^{10} +(-2.18323 - 0.229467i) q^{11} +(9.02960 + 3.72066i) q^{12} +(0.208873 + 0.169142i) q^{13} +(5.63391 - 2.50838i) q^{14} +(0.630113 - 3.82138i) q^{15} +(-15.0875 - 6.71741i) q^{16} +(1.40105 + 2.74972i) q^{17} +(-2.59127 - 7.87601i) q^{18} +(-5.85661 - 1.90293i) q^{19} +(-2.39905 + 12.3776i) q^{20} +(-3.49146 - 1.65743i) q^{21} +(-3.30444 - 5.08839i) q^{22} +(-0.181895 - 0.0698231i) q^{23} +(4.97763 + 16.6909i) q^{24} +(4.99676 - 0.179880i) q^{25} +0.742819i q^{26} +(-2.69039 + 4.44542i) q^{27} +(11.2103 + 5.71195i) q^{28} +(2.62137 - 2.91133i) q^{29} +(9.30374 - 5.29314i) q^{30} +(-0.246729 - 0.274020i) q^{31} +(-6.60842 - 24.6630i) q^{32} +(-1.07318 + 3.64771i) q^{33} +(-3.46916 + 7.79186i) q^{34} +(1.20447 - 4.84199i) q^{35} +(9.16032 - 14.2204i) q^{36} +(-4.48824 - 0.710867i) q^{37} +(-6.09919 - 15.8889i) q^{38} +(0.353427 - 0.302986i) q^{39} +(-19.8480 + 10.5671i) q^{40} +(10.9102 - 1.14671i) q^{41} +(-2.51277 - 10.3819i) q^{42} +(2.52213 + 0.675802i) q^{43} +(3.82498 - 11.7721i) q^{44} +(-6.31330 - 2.26764i) q^{45} +(-0.166401 - 0.512129i) q^{46} +(-0.0848923 - 1.61984i) q^{47} +(-16.1587 + 23.6044i) q^{48} +(1.75013 + 1.01044i) q^{49} +(9.07723 + 10.4195i) q^{50} +(5.12232 - 1.52760i) q^{51} +(-1.17772 + 0.953703i) q^{52} +(0.165221 - 0.324264i) q^{53} +(-14.2275 + 1.95335i) q^{54} +(-4.89030 - 0.425192i) q^{55} +(4.66527 + 21.9484i) q^{56} +(-5.07204 + 9.38282i) q^{57} +(10.8125 + 0.566658i) q^{58} +(-0.393886 - 3.74758i) q^{59} +(20.3372 + 7.95505i) q^{60} +(-0.925876 + 8.80912i) q^{61} +(0.159421 - 1.00654i) q^{62} +(-3.91471 + 5.43021i) q^{63} +(22.0636 - 30.3679i) q^{64} +(0.473784 + 0.369750i) q^{65} +(-9.70134 + 4.03943i) q^{66} +(-0.497315 + 9.48934i) q^{67} +(-16.8079 + 4.50365i) q^{68} +(-0.175794 + 0.288063i) q^{69} +(12.4949 - 5.83464i) q^{70} +(1.25086 - 0.406430i) q^{71} +(29.9906 - 3.26418i) q^{72} +(-15.0703 + 2.38690i) q^{73} +(-6.27956 - 10.8765i) q^{74} +(1.25502 - 8.56883i) q^{75} +(17.3608 - 30.0699i) q^{76} +(-1.75546 + 4.57313i) q^{77} +(1.26549 + 0.232128i) q^{78} +(-6.49052 - 5.84409i) q^{79} +(-34.0015 - 14.4112i) q^{80} +(6.73261 + 5.97260i) q^{81} +(21.4392 + 21.4392i) q^{82} +(9.70808 + 6.30450i) q^{83} +(13.2342 - 17.3133i) q^{84} +(3.24296 + 6.09121i) q^{85} +(2.93521 + 6.59260i) q^{86} +(-4.14065 - 5.37562i) q^{87} +(20.6091 - 7.91109i) q^{88} +(4.73767 + 3.44212i) q^{89} +(-6.11016 - 17.5042i) q^{90} +(0.485193 - 0.352513i) q^{91} +(0.598328 - 0.921345i) q^{92} +(-0.543930 + 0.334704i) q^{93} +(3.33154 - 2.99973i) q^{94} +(-13.1702 - 4.01878i) q^{95} +(-44.0816 + 3.55123i) q^{96} +(-3.49765 + 0.183304i) q^{97} +(0.873726 + 5.51649i) q^{98} +(5.87897 + 2.96818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	1.73930	+	2.14786i	1.22987	+	1.51877i	0.780144	+	0.625600i	$0.215146\pi$
$2$	1.73930	+	2.14786i	1.22987	+	1.51877i	0.449728	+	0.893166i	$0.351521\pi$
$3$	0.312495	−	1.70363i	0.180419	−	0.983590i
$3$	0.312495	−	1.70363i	0.180419	−	0.983590i
$4$	−1.17230	+	5.51525i	−0.586152	+	2.75763i
$5$	2.23571	−	0.0402288i	0.999838	−	0.0179909i
$5$	2.23571	−	0.0402288i	0.999838	−	0.0179909i
$6$	4.20267	−	2.29193i	1.71573	−	0.935675i
$7$	0.577528	−	2.15536i	0.218285	−	0.814650i	−0.766699	−	0.642006i	$-0.778102\pi$
$7$	0.577528	−	2.15536i	0.218285	−	0.814650i	0.984984	−	0.172644i	$-0.0552310\pi$
$8$	−8.95988	+	4.56529i	−3.16780	+	1.61407i
$9$	−2.80469	−	1.06475i	−0.934898	−	0.354917i
$10$	3.97497	+	4.73201i	1.25700	+	1.49639i
$11$	−2.18323	−	0.229467i	−0.658269	−	0.0691869i	−0.230496	−	0.973073i	$-0.574035\pi$
$11$	−2.18323	−	0.229467i	−0.658269	−	0.0691869i	−0.427773	+	0.903886i	$0.640702\pi$
$12$	9.02960	+	3.72066i	2.60662	+	1.07406i
$13$	0.208873	+	0.169142i	0.0579310	+	0.0469116i	0.657849	−	0.753150i	$-0.271467\pi$
$13$	0.208873	+	0.169142i	0.0579310	+	0.0469116i	−0.599918	+	0.800062i	$0.704800\pi$
$14$	5.63391	−	2.50838i	1.50573	−	0.670392i
$15$	0.630113	−	3.82138i	0.162694	−	0.986676i
$16$	−15.0875	−	6.71741i	−3.77189	−	1.67935i
$17$	1.40105	+	2.74972i	0.339805	+	0.666905i	0.996160	−	0.0875467i	$-0.0279027\pi$
$17$	1.40105	+	2.74972i	0.339805	+	0.666905i	−0.656355	+	0.754452i	$0.727903\pi$
$18$	−2.59127	−	7.87601i	−0.610769	−	1.85639i
$19$	−5.85661	−	1.90293i	−1.34360	−	0.436561i	−0.453064	−	0.891478i	$-0.649669\pi$
$19$	−5.85661	−	1.90293i	−1.34360	−	0.436561i	−0.890534	+	0.454917i	$0.849669\pi$
$20$	−2.39905	+	12.3776i	−0.536445	+	2.76773i
$21$	−3.49146	−	1.65743i	−0.761899	−	0.361681i
$22$	−3.30444	−	5.08839i	−0.704508	−	1.08485i
$23$	−0.181895	−	0.0698231i	−0.0379278	−	0.0145591i	0.339330	−	0.940667i	$-0.389800\pi$
$23$	−0.181895	−	0.0698231i	−0.0379278	−	0.0145591i	−0.377258	+	0.926108i	$0.623133\pi$
$24$	4.97763	+	16.6909i	1.01605	+	3.40702i
$25$	4.99676	−	0.179880i	0.999353	−	0.0359759i
$26$			0.742819i			0.145679i
$27$	−2.69039	+	4.44542i	−0.517766	+	0.855522i
$28$	11.2103	+	5.71195i	2.11855	+	1.07946i
$29$	2.62137	−	2.91133i	0.486777	−	0.540620i	−0.448852	−	0.893606i	$-0.648167\pi$
$29$	2.62137	−	2.91133i	0.486777	−	0.540620i	0.935629	+	0.352986i	$0.114834\pi$
$30$	9.30374	−	5.29314i	1.69862	−	0.966391i
$31$	−0.246729	−	0.274020i	−0.0443138	−	0.0492155i	0.720580	−	0.693371i	$-0.243875\pi$
$31$	−0.246729	−	0.274020i	−0.0443138	−	0.0492155i	−0.764894	+	0.644156i	$0.777209\pi$
$32$	−6.60842	−	24.6630i	−1.16822	−	4.35984i
$33$	−1.07318	+	3.64771i	−0.186816	+	0.634984i
$34$	−3.46916	+	7.79186i	−0.594956	+	1.33629i
$35$	1.20447	−	4.84199i	0.203593	−	0.818446i
$36$	9.16032	−	14.2204i	1.52672	−	2.37006i
$37$	−4.48824	−	0.710867i	−0.737862	−	0.116866i	−0.223819	−	0.974631i	$-0.571853\pi$
$37$	−4.48824	−	0.710867i	−0.737862	−	0.116866i	−0.514042	+	0.857765i	$0.671853\pi$
$38$	−6.09919	−	15.8889i	−0.989419	−	2.57752i
$39$	0.353427	−	0.302986i	0.0565937	−	0.0485166i
$40$	−19.8480	+	10.5671i	−3.13825	+	1.67080i
$41$	10.9102	−	1.14671i	1.70389	−	0.179086i	0.798019	−	0.602632i	$-0.205881\pi$
$41$	10.9102	−	1.14671i	1.70389	−	0.179086i	0.905875	+	0.423546i	$0.139215\pi$
$42$	−2.51277	−	10.3819i	−0.387729	−	1.60197i
$43$	2.52213	+	0.675802i	0.384621	+	0.103059i	0.445948	−	0.895059i	$-0.352867\pi$
$43$	2.52213	+	0.675802i	0.384621	+	0.103059i	−0.0613271	+	0.998118i	$0.519533\pi$
$44$	3.82498	−	11.7721i	0.576637	−	1.77471i
$45$	−6.31330	−	2.26764i	−0.941132	−	0.338040i
$46$	−0.166401	−	0.512129i	−0.0245345	−	0.0755093i
$47$	−0.0848923	−	1.61984i	−0.0123828	−	0.236278i	−0.997808	−	0.0661706i	$-0.978922\pi$
$47$	−0.0848923	−	1.61984i	−0.0123828	−	0.236278i	0.985426	−	0.170108i	$-0.0544115\pi$
$48$	−16.1587	+	23.6044i	−2.33231	+	3.40700i
$49$	1.75013	+	1.01044i	0.250019	+	0.144348i
$50$	9.07723	+	10.4195i	1.28371	+	1.47354i
$51$	5.12232	−	1.52760i	0.717269	−	0.213906i
$52$	−1.17772	+	0.953703i	−0.163321	+	0.132255i
$53$	0.165221	−	0.324264i	0.0226948	−	0.0445411i	−0.879381	−	0.476119i	$-0.842043\pi$
$53$	0.165221	−	0.324264i	0.0226948	−	0.0445411i	0.902076	+	0.431578i	$0.142043\pi$
$54$	−14.2275	+	1.95335i	−1.93612	+	0.265817i
$55$	−4.89030	−	0.425192i	−0.659407	−	0.0573328i
$56$	4.66527	+	21.9484i	0.623423	+	2.93297i
$57$	−5.07204	+	9.38282i	−0.671808	+	1.24278i
$58$	10.8125	+	0.566658i	1.41975	+	0.0744059i
$59$	−0.393886	−	3.74758i	−0.0512796	−	0.487893i	−0.989779	−	0.142611i	$-0.954450\pi$
$59$	−0.393886	−	3.74758i	−0.0512796	−	0.487893i	0.938499	−	0.345282i	$-0.112217\pi$
$60$	20.3372	+	7.95505i	2.62552	+	1.02699i
$61$	−0.925876	+	8.80912i	−0.118546	+	1.12789i	0.759896	+	0.650045i	$0.225250\pi$
$61$	−0.925876	+	8.80912i	−0.118546	+	1.12789i	−0.878442	+	0.477848i	$0.841417\pi$
$62$	0.159421	−	1.00654i	0.0202464	−	0.127831i
$63$	−3.91471	+	5.43021i	−0.493207	+	0.684142i
$64$	22.0636	−	30.3679i	2.75794	−	3.79598i
$65$	0.473784	+	0.369750i	0.0587656	+	0.0458618i
$66$	−9.70134	+	4.03943i	−1.19415	+	0.497220i
$67$	−0.497315	+	9.48934i	−0.0607567	+	1.15931i	0.782802	+	0.622271i	$0.213790\pi$
$67$	−0.497315	+	9.48934i	−0.0607567	+	1.15931i	−0.843559	+	0.537037i	$0.819544\pi$
$68$	−16.8079	+	4.50365i	−2.03825	+	0.546148i
$69$	−0.175794	+	0.288063i	−0.0211631	+	0.0346787i
$70$	12.4949	−	5.83464i	1.49342	−	0.697373i
$71$	1.25086	−	0.406430i	0.148450	−	0.0482343i	−0.233849	−	0.972273i	$-0.575132\pi$
$71$	1.25086	−	0.406430i	0.148450	−	0.0482343i	0.382299	+	0.924038i	$0.375132\pi$
$72$	29.9906	−	3.26418i	3.53443	−	0.384688i
$73$	−15.0703	+	2.38690i	−1.76385	+	0.279366i	−0.952354	−	0.304996i	$-0.901345\pi$
$73$	−15.0703	+	2.38690i	−1.76385	+	0.279366i	−0.811493	+	0.584362i	$0.801345\pi$
$74$	−6.27956	−	10.8765i	−0.729984	−	1.26437i
$75$	1.25502	−	8.56883i	0.144917	−	0.989444i
$76$	17.3608	−	30.0699i	1.99142	−	3.44925i
$77$	−1.75546	+	4.57313i	−0.200053	+	0.521157i
$78$	1.26549	+	0.232128i	0.143288	+	0.0262833i
$79$	−6.49052	−	5.84409i	−0.730240	−	0.657511i	0.217680	−	0.976020i	$-0.430151\pi$
$79$	−6.49052	−	5.84409i	−0.730240	−	0.657511i	−0.947920	+	0.318509i	$0.896818\pi$
$80$	−34.0015	−	14.4112i	−3.80149	−	1.61122i
$81$	6.73261	+	5.97260i	0.748068	+	0.663623i
$82$	21.4392	+	21.4392i	2.36756	+	2.36756i
$83$	9.70808	+	6.30450i	1.06560	+	0.692009i	0.953410	−	0.301678i	$-0.0975467\pi$
$83$	9.70808	+	6.30450i	1.06560	+	0.692009i	0.112190	+	0.993687i	$0.464213\pi$
$84$	13.2342	−	17.3133i	1.44397	−	1.88903i
$85$	3.24296	+	6.09121i	0.351748	+	0.660684i
$86$	2.93521	+	6.59260i	0.316512	+	0.710898i
$87$	−4.14065	−	5.37562i	−0.443925	−	0.576327i
$88$	20.6091	−	7.91109i	2.19694	−	0.843325i
$89$	4.73767	+	3.44212i	0.502192	+	0.364864i	0.809854	−	0.586632i	$-0.199546\pi$
$89$	4.73767	+	3.44212i	0.502192	+	0.364864i	−0.307661	+	0.951496i	$0.599546\pi$
$90$	−6.11016	−	17.5042i	−0.644068	−	1.84510i
$91$	0.485193	−	0.352513i	0.0508620	−	0.0369534i
$92$	0.598328	−	0.921345i	0.0623801	−	0.0960569i
$93$	−0.543930	+	0.334704i	−0.0564029	+	0.0347072i
$94$	3.33154	−	2.99973i	0.343622	−	0.309398i
$95$	−13.1702	−	4.01878i	−1.35123	−	0.412318i
$96$	−44.0816	+	3.55123i	−4.49906	+	0.362446i
$97$	−3.49765	+	0.183304i	−0.355133	+	0.0186117i	−0.229068	−	0.973410i	$-0.573568\pi$
$97$	−3.49765	+	0.183304i	−0.355133	+	0.0186117i	−0.126065	+	0.992022i	$0.540235\pi$
$98$	0.873726	+	5.51649i	0.0882596	+	0.557249i
$99$	5.87897	+	2.96818i	0.590859	+	0.298314i
$100$	−4.86564	+	27.7693i	−0.486564	+	2.77693i
$101$	−1.90784	+	1.10149i	−0.189837	+	0.109602i	−0.591906	−	0.806007i	$-0.701624\pi$
$101$	−1.90784	+	1.10149i	−0.189837	+	0.109602i	0.402069	+	0.915609i	$0.368291\pi$
$102$	12.1903	+	8.34507i	1.20702	+	0.826285i
$103$	−2.17831	+	1.41461i	−0.214635	+	0.139386i	−0.647479	−	0.762083i	$-0.724177\pi$
$103$	−2.17831	+	1.41461i	−0.214635	+	0.139386i	0.432844	+	0.901469i	$0.357510\pi$
$104$	−2.64366	−	0.561928i	−0.259232	−	0.0551016i
$105$	−7.87255	−	3.56507i	−0.768283	−	0.347916i
$106$	0.983842	−	0.209122i	0.0955591	−	0.0203117i
$107$	−4.76766	+	4.76766i	−0.460907	+	0.460907i	−0.898953	−	0.438046i	$-0.855671\pi$
$107$	−4.76766	+	4.76766i	−0.460907	+	0.460907i	0.438046	+	0.898953i	$0.355671\pi$
$108$	−21.3637	−	20.0496i	−2.05572	−	1.92927i
$109$	2.94139	+	4.04848i	0.281734	+	0.387774i	0.926307	−	0.376769i	$-0.122965\pi$
$109$	2.94139	+	4.04848i	0.281734	+	0.387774i	−0.644573	+	0.764543i	$0.722965\pi$
$110$	−7.59245	−	11.2432i	−0.723912	−	1.07200i
$111$	−2.61361	+	7.42414i	−0.248072	+	0.704668i
$112$	−23.1919	+	28.6396i	−2.19143	+	2.70619i
$113$	−5.46927	+	6.75398i	−0.514505	+	0.635361i	−0.966502	−	0.256658i	$-0.917378\pi$
$113$	−5.46927	+	6.75398i	−0.514505	+	0.635361i	0.451997	+	0.892020i	$0.350712\pi$
$114$	−28.9748	+	5.42553i	−2.71374	+	0.508147i
$115$	−0.409473	−	0.148786i	−0.0381836	−	0.0138744i
$116$	12.9837	+	17.8705i	1.20550	+	1.65923i
$117$	−0.405731	−	0.696790i	−0.0375098	−	0.0644183i
$118$	7.36418	−	7.36418i	0.677927	−	0.677927i
$119$	6.73579	−	1.43174i	0.617469	−	0.131247i
$120$	11.8000	+	37.1158i	1.07719	+	3.38819i
$121$	−6.04578	−	1.28507i	−0.549616	−	0.116824i
$122$	−20.5311	+	13.3331i	−1.85880	+	1.20712i
$123$	1.45583	−	18.9453i	0.131268	−	1.70824i
$124$	1.80053	−	1.03954i	0.161692	−	0.0933532i
$125$	11.1641	−	0.603172i	0.998544	−	0.0539493i
$126$	−18.4722	+	1.03652i	−1.64563	+	0.0923403i
$127$	−2.31090	−	14.5905i	−0.205060	−	1.29470i	−0.848498	−	0.529198i	$-0.822493\pi$
$127$	−2.31090	−	14.5905i	−0.205060	−	1.29470i	0.643439	−	0.765497i	$-0.277507\pi$
$128$	52.6051	−	2.75692i	4.64968	−	0.243679i
$129$	1.93947	−	4.08558i	0.170761	−	0.359715i
$130$	0.0298828	+	1.66073i	0.00262089	+	0.145655i
$131$	2.47543	−	2.22889i	0.216279	−	0.194739i	−0.553869	−	0.832604i	$-0.686849\pi$
$131$	2.47543	−	2.22889i	0.216279	−	0.194739i	0.770148	+	0.637865i	$0.220182\pi$
$132$	−18.8599	−	10.1951i	−1.64155	−	0.887366i
$133$	−7.48385	+	11.5241i	−0.648932	+	0.999268i
$134$	−21.2467	+	15.4367i	−1.83544	+	1.33352i
$135$	−5.83610	+	10.0469i	−0.502291	+	0.864699i
$136$	−25.1065	−	18.2410i	−2.15287	−	1.56415i
$137$	16.7526	−	6.43074i	1.43127	−	0.549415i	0.485499	−	0.874237i	$-0.338638\pi$
$137$	16.7526	−	6.43074i	1.43127	−	0.549415i	0.945775	+	0.324822i	$0.105304\pi$
$138$	−0.924476	+	0.123447i	−0.0786967	+	0.0105085i
$139$	−4.59807	−	10.3274i	−0.390003	−	0.875962i	−0.996711	−	0.0810370i	$-0.974177\pi$
$139$	−4.59807	−	10.3274i	−0.390003	−	0.875962i	0.606708	−	0.794925i	$-0.292490\pi$
$140$	25.2928	+	12.3193i	2.13763	+	1.04117i
$141$	−2.78613	−	0.361568i	−0.234635	−	0.0304495i
$142$	3.04858	+	1.97977i	0.255831	+	0.166139i
$143$	−0.417206	−	0.417206i	−0.0348885	−	0.0348885i
$144$	35.1636	+	34.9047i	2.93030	+	2.90873i
$145$	5.74350	−	6.61433i	0.476972	−	0.549290i
$146$	−31.3386	−	28.2174i	−2.59360	−	2.33529i
$147$	2.26832	−	2.66581i	0.187088	−	0.219872i
$148$	9.18219	−	23.9204i	0.754771	−	1.96625i
$149$	6.18746	−	10.7170i	0.506897	−	0.877971i	−0.493071	−	0.869989i	$-0.664126\pi$
$149$	6.18746	−	10.7170i	0.506897	−	0.877971i	0.999968	−	0.00798219i	$-0.00254084\pi$
$150$	20.5875	−	12.2082i	1.68096	−	0.996794i
$151$	6.05748	+	10.4919i	0.492950	+	0.853815i	0.999967	−	0.00812103i	$-0.00258503\pi$
$151$	6.05748	+	10.4919i	0.492950	+	0.853815i	−0.507017	+	0.861936i	$0.669252\pi$
$152$	61.1619	−	9.68710i	4.96089	−	0.785727i
$153$	−1.00175	−	9.20390i	−0.0809870	−	0.744091i
$154$	−12.8757	+	4.18357i	−1.03755	+	0.337122i
$155$	−0.562637	−	0.602703i	−0.0451921	−	0.0484103i
$156$	1.25672	+	2.30443i	0.100618	+	0.184502i
$157$	5.73140	−	1.53572i	0.457415	−	0.122564i	−0.0227517	−	0.999741i	$-0.507243\pi$
$157$	5.73140	−	1.53572i	0.457415	−	0.122564i	0.480167	+	0.877177i	$0.340576\pi$
$158$	1.26331	−	24.1053i	0.100503	−	1.91772i
$159$	−0.500794	−	0.382805i	−0.0397156	−	0.0303584i
$160$	−15.7667	−	54.8733i	−1.24646	−	4.33812i
$161$	−0.255544	+	0.351726i	−0.0201397	+	0.0277199i
$162$	−1.11827	+	24.8488i	−0.0878595	+	1.95231i
$163$	−2.06743	+	13.0532i	−0.161933	+	1.02241i	0.764136	+	0.645055i	$0.223165\pi$
$163$	−2.06743	+	13.0532i	−0.161933	+	1.02241i	−0.926070	+	0.377352i	$0.876835\pi$
$164$	−6.46570	+	61.5170i	−0.504887	+	4.80367i
$165$	−2.25256	+	8.19837i	−0.175362	+	0.638242i
$166$	3.34410	+	31.8170i	0.259553	+	2.46948i
$167$	16.6739	+	0.873843i	1.29027	+	0.0676200i	0.685082	−	0.728466i	$-0.259766\pi$
$167$	16.6739	+	0.873843i	1.29027	+	0.0676200i	0.605184	+	0.796086i	$0.293100\pi$
$168$	38.8497	−	1.08912i	2.99732	−	0.0840273i
$169$	−2.68783	−	12.6453i	−0.206756	−	0.972712i
$170$	−7.44256	+	17.5599i	−0.570818	+	1.34678i
$171$	14.3998	+	11.5730i	1.10118	+	0.885006i
$172$	−6.68392	+	13.1179i	−0.509644	+	1.00023i
$173$	−17.7763	+	14.3949i	−1.35151	+	1.09443i	−0.364945	+	0.931029i	$0.618912\pi$
$173$	−17.7763	+	14.3949i	−1.35151	+	1.09443i	−0.986560	+	0.163398i	$0.947754\pi$
$174$	4.34422	−	18.2434i	0.329335	−	1.38303i
$175$	2.49806	−	10.8737i	0.188836	−	0.821976i
$176$	31.3982	+	18.1277i	2.36673	+	1.36643i
$177$	−6.50756	−	0.500065i	−0.489138	−	0.0375872i
$178$	0.847053	+	16.1627i	0.0634893	+	1.21145i
$179$	−3.58231	−	11.0252i	−0.267754	−	0.824063i	−0.991046	−	0.133521i	$-0.957372\pi$
$179$	−3.58231	−	11.0252i	−0.267754	−	0.824063i	0.723292	−	0.690543i	$-0.242628\pi$
$180$	19.9077	−	32.1611i	1.48383	−	2.39715i
$181$	−2.81066	+	8.65032i	−0.208915	+	0.642973i	0.790615	+	0.612313i	$0.209761\pi$
$181$	−2.81066	+	8.65032i	−0.208915	+	0.642973i	−0.999530	+	0.0306599i	$0.990239\pi$
$182$	1.60105	+	0.428999i	0.118677	+	0.0317995i
$183$	14.7181	+	4.33016i	1.08800	+	0.320095i
$184$	1.94852	−	0.204798i	0.143647	−	0.0150979i
$185$	−10.0630	−	1.40873i	−0.739845	−	0.103572i
$186$	−1.66495	−	0.586133i	−0.122080	−	0.0429774i
$187$	−2.42785	−	6.32478i	−0.177542	−	0.462513i
$188$	9.03335	+	1.43074i	0.658825	+	0.104348i
$189$	8.02772	+	8.36613i	0.583931	+	0.608546i
$190$	−14.2752	−	35.2776i	−1.03563	−	2.55931i
$191$	4.52167	−	10.1558i	0.327177	−	0.734851i	−0.672811	−	0.739814i	$-0.734913\pi$
$191$	4.52167	−	10.1558i	0.327177	−	0.734851i	0.999988	+	0.00496354i	$0.00157995\pi$
$192$	−44.8408	−	47.0779i	−3.23611	−	3.39755i
$193$	−3.81601	−	14.2415i	−0.274683	−	1.02513i	−0.956054	−	0.293191i	$-0.905283\pi$
$193$	−3.81601	−	14.2415i	−0.274683	−	1.02513i	0.681371	−	0.731938i	$-0.261384\pi$
$194$	−6.47719	−	7.19364i	−0.465035	−	0.516474i
$195$	0.777971	−	0.691606i	0.0557116	−	0.0495269i
$196$	−7.62450	+	8.46787i	−0.544607	+	0.604848i
$197$	−2.90497	−	1.48016i	−0.206971	−	0.105457i	0.347433	−	0.937705i	$-0.387054\pi$
$197$	−2.90497	−	1.48016i	−0.206971	−	0.105457i	−0.554403	+	0.832248i	$0.687054\pi$
$198$	3.85006	+	17.7898i	0.273612	+	1.26426i
$199$		−	9.72169i		−	0.689152i	−0.938758	−	0.344576i	$-0.888023\pi$
$199$		−	9.72169i		−	0.689152i	0.938758	−	0.344576i	$-0.111977\pi$
$200$	−43.9492	+	24.4234i	−3.10768	+	1.72699i
$201$	16.0109	+	3.81262i	1.12932	+	0.268921i
$202$	−5.68415	−	2.18194i	−0.399936	−	0.153521i
$203$	−4.76105	−	7.33138i	−0.334160	−	0.514562i
$204$	2.42017	+	30.0417i	0.169446	+	2.10334i
$205$	24.3460	−	3.00262i	1.70040	−	0.209712i
$206$	−6.82711	−	2.21826i	−0.475667	−	0.154554i
$207$	0.435816	+	0.389506i	0.0302913	+	0.0270725i
$208$	−2.01519	−	3.95503i	−0.139728	−	0.274232i
$209$	12.3497	+	5.49843i	0.854245	+	0.380334i
$210$	−6.03547	−	23.1099i	−0.416487	−	1.59473i
$211$	13.3805	−	5.95739i	0.921152	−	0.410123i	0.109315	−	0.994007i	$-0.465134\pi$
$211$	13.3805	−	5.95739i	0.921152	−	0.410123i	0.811837	+	0.583884i	$0.198468\pi$
$212$	1.59471	+	1.29137i	0.109525	+	0.0886916i
$213$	−0.301516	−	2.25801i	−0.0206596	−	0.154716i
$214$	−18.5327	−	1.94786i	−1.26687	−	0.133153i
$215$	5.66593	+	1.40943i	0.386413	+	0.0961225i
$216$	3.81098	−	52.1129i	0.259304	−	3.54583i
$217$	−0.733105	+	0.373536i	−0.0497664	+	0.0253573i
$218$	−3.57959	+	13.3592i	−0.242441	+	0.904801i
$219$	−0.643010	+	26.4201i	−0.0434506	+	1.78530i
$220$	8.07795	−	26.4728i	0.544615	−	1.78479i
$221$	−0.172451	+	0.811320i	−0.0116003	+	0.0545753i
$222$	−20.4919	+	7.29917i	−1.37532	+	0.489888i
$223$	16.6634	+	20.5776i	1.11586	+	1.37798i	0.917447	+	0.397857i	$0.130246\pi$
$223$	16.6634	+	20.5776i	1.11586	+	1.37798i	0.198415	+	0.980118i	$0.436421\pi$
$224$	−56.9742			−3.80675
$225$	−14.2059	−	4.81580i	−0.947061	−	0.321054i
$226$	−24.0193			−1.59774
$227$	0.0331461	+	0.0409320i	0.00219998	+	0.00271675i	0.778245	−	0.627961i	$-0.216110\pi$
$227$	0.0331461	+	0.0409320i	0.00219998	+	0.00271675i	−0.776045	+	0.630678i	$0.782777\pi$
$228$	−45.8027	−	38.9731i	−3.03335	−	2.58106i
$229$	4.17492	−	19.6415i	0.275887	−	1.29794i	−0.593909	−	0.804532i	$-0.702416\pi$
$229$	4.17492	−	19.6415i	0.275887	−	1.29794i	0.869796	−	0.493412i	$-0.164251\pi$
$230$	−0.392626	−	1.13828i	−0.0258890	−	0.0750557i
$231$	7.24234	+	4.41973i	0.476511	+	0.290797i
$232$	−10.1961	+	38.0525i	−0.669409	+	2.49827i
$233$	−25.5665	+	13.0268i	−1.67492	+	0.853414i	−0.682449	+	0.730933i	$0.739085\pi$
$233$	−25.5665	+	13.0268i	−1.67492	+	0.853414i	−0.992471	+	0.122482i	$0.960915\pi$
$234$	0.790918	−	2.08338i	0.0517039	−	0.136195i
$235$	−0.254959	−	3.61807i	−0.0166317	−	0.236017i
$236$	21.1306	+	2.22091i	1.37548	+	0.144569i
$237$	−11.9844	+	9.23117i	−0.778471	+	0.599629i
$238$	14.7907	+	11.9773i	0.958741	+	0.776374i
$239$	6.25481	−	2.78482i	0.404590	−	0.180135i	−0.194344	−	0.980933i	$-0.562258\pi$
$239$	6.25481	−	2.78482i	0.404590	−	0.180135i	0.598934	+	0.800798i	$0.295591\pi$
$240$	−35.1766	+	53.4225i	−2.27064	+	3.44841i
$241$	2.28983	+	1.01950i	0.147501	+	0.0656715i	0.479159	−	0.877728i	$-0.340942\pi$
$241$	2.28983	+	1.01950i	0.147501	+	0.0656715i	−0.331659	+	0.943399i	$0.607608\pi$
$242$	−7.75528	−	15.2206i	−0.498528	−	0.978417i
$243$	12.2790	−	9.60345i	0.787698	−	0.616061i
$244$	−47.4991	−	15.4334i	−3.04082	−	0.988023i
$245$	3.95342	+	2.18864i	0.252575	+	0.139827i
$246$	43.2240	−	29.8247i	2.75586	−	1.90156i
$247$	−0.901423	−	1.38807i	−0.0573562	−	0.0883208i
$248$	3.46164	+	1.32880i	0.219815	+	0.0843789i
$249$	13.7743	−	14.5688i	0.872908	−	0.923262i
$250$	20.7132	+	22.9297i	1.31002	+	1.45020i
$251$		−	18.5465i		−	1.17064i	−0.810801	−	0.585322i	$-0.800968\pi$
$251$		−	18.5465i		−	1.17064i	0.810801	−	0.585322i	$-0.199032\pi$
$252$	−25.3597	−	27.9565i	−1.59751	−	1.76109i
$253$	0.381098	+	0.194179i	0.0239594	+	0.0122079i
$254$	27.3189	−	30.3407i	1.71414	−	1.90375i
$255$	11.3906	−	3.62132i	0.713304	−	0.226776i
$256$	47.1836	+	52.4027i	2.94897	+	3.27517i
$257$	3.97862	+	14.8484i	0.248179	+	0.926218i	0.971759	+	0.235977i	$0.0758289\pi$
$257$	3.97862	+	14.8484i	0.248179	+	0.926218i	−0.723579	+	0.690241i	$0.757504\pi$
$258$	12.1486	−	2.94036i	0.756337	−	0.183059i
$259$	−4.12426	+	9.26323i	−0.256269	+	0.575589i
$260$	−2.59468	+	2.17958i	−0.160915	+	0.135172i
$261$	−10.4520	+	5.37428i	−0.646962	+	0.332659i
$262$	9.09285	+	1.44017i	0.561758	+	0.0889738i
$263$	4.99040	+	13.0004i	0.307722	+	0.801642i	0.997018	+	0.0771631i	$0.0245862\pi$
$263$	4.99040	+	13.0004i	0.307722	+	0.801642i	−0.689297	+	0.724479i	$0.742080\pi$
$264$	−7.03730	−	37.5824i	−0.433116	−	2.31304i
$265$	0.356340	−	0.731605i	0.0218898	−	0.0449422i
$266$	−37.7688	+	3.96967i	−2.31576	+	0.243396i
$267$	7.34459	−	6.99558i	0.449482	−	0.428123i
$268$	−51.7531	−	13.8672i	−3.16132	−	0.847074i
$269$	−2.55993	+	7.87865i	−0.156082	+	0.480370i	−0.998269	−	0.0588155i	$-0.981268\pi$
$269$	−2.55993	+	7.87865i	−0.156082	+	0.480370i	0.842187	+	0.539185i	$0.181268\pi$
$270$	−31.7300	+	4.93946i	−1.93103	+	0.300606i
$271$	2.81683	+	8.66932i	0.171110	+	0.526623i	0.999434	−	0.0336257i	$-0.0107054\pi$
$271$	2.81683	+	8.66932i	0.171110	+	0.526623i	−0.828324	+	0.560249i	$0.810705\pi$
$272$	−2.66745	−	50.8980i	−0.161738	−	3.08614i
$273$	−0.448931	−	0.936746i	−0.0271705	−	0.0566945i
$274$	42.9502	+	24.7973i	2.59472	+	1.49806i
$275$	−10.9504	−	0.753873i	−0.660332	−	0.0454602i
$276$	−1.38265	−	1.30724i	−0.0832260	−	0.0786869i
$277$	17.3453	−	14.0459i	1.04218	−	0.843938i	0.0541983	−	0.998530i	$-0.482740\pi$
$277$	17.3453	−	14.0459i	1.04218	−	0.843938i	0.987978	+	0.154592i	$0.0494064\pi$
$278$	14.1844	−	27.8385i	0.850726	−	1.66964i
$279$	0.400235	+	1.03125i	0.0239615	+	0.0617392i
$280$	11.3131	+	48.8824i	0.676089	+	2.92128i
$281$	−3.81218	−	17.9349i	−0.227416	−	1.06991i	−0.932608	−	0.360890i	$-0.882473\pi$
$281$	−3.81218	−	17.9349i	−0.227416	−	1.06991i	0.705193	−	0.709016i	$-0.250860\pi$
$282$	−4.06933	−	6.61310i	−0.242325	−	0.393804i
$283$	−17.7677	−	0.931166i	−1.05618	−	0.0553521i	−0.483671	−	0.875250i	$-0.660697\pi$
$283$	−17.7677	−	0.931166i	−1.05618	−	0.0553521i	−0.572510	+	0.819898i	$0.694030\pi$
$284$	0.775173	+	7.37528i	0.0459981	+	0.437642i
$285$	−10.9621	+	21.1813i	−0.649341	+	1.25467i
$286$	0.170453	−	1.62175i	0.0100791	−	0.0958959i
$287$	3.82939	−	24.1778i	0.226041	−	1.42717i
$288$	−7.72534	+	76.2084i	−0.455220	+	4.49062i
$289$	4.39433	−	6.04828i	0.258490	−	0.355781i
$290$	24.1963	+	0.831908i	1.42086	+	0.0488513i
$291$	−0.780719	+	6.01598i	−0.0457665	+	0.352663i
$292$	4.50260	−	85.9148i	0.263495	−	5.02778i
$293$	4.79047	−	1.28360i	0.279862	−	0.0749888i	−0.116158	−	0.993231i	$-0.537058\pi$
$293$	4.79047	−	1.28360i	0.279862	−	0.0749888i	0.396020	+	0.918242i	$0.370391\pi$
$294$	9.67107	+	0.235374i	0.564029	+	0.0137273i
$295$	−1.03137	−	8.36263i	−0.0600489	−	0.486891i
$296$	43.4594	−	14.1208i	2.52603	−	0.820756i
$297$	6.89383	−	9.08803i	0.400021	−	0.527341i
$298$	33.7805	−	5.35030i	1.95685	−	0.309935i
$299$	−0.0261830	−	0.0453504i	−0.00151420	−	0.00262268i
$300$	45.7880	+	16.9670i	2.64357	+	0.979591i
$301$	2.91320	−	5.04581i	0.167914	−	0.290835i
$302$	−11.9992	+	31.2591i	−0.690479	+	1.79876i
$303$	1.28034	+	3.59446i	0.0735536	+	0.206496i
$304$	75.5791	+	68.0517i	4.33476	+	3.90303i
$305$	−1.71561	+	19.7319i	−0.0982353	+	1.12984i
$306$	18.0263	−	18.1600i	1.03050	−	1.03814i
$307$	−21.5414	−	21.5414i	−1.22943	−	1.22943i	−0.964178	−	0.265255i	$-0.914544\pi$
$307$	−21.5414	−	21.5414i	−1.22943	−	1.22943i	−0.265255	−	0.964178i	$-0.585456\pi$
$308$	−23.1640	−	15.0429i	−1.31989	−	0.857149i
$309$	1.72926	+	4.15308i	0.0983739	+	0.236260i
$310$	0.315926	−	2.25675i	0.0179434	−	0.128175i
$311$	−9.17567	−	20.6089i	−0.520304	−	1.16862i	−0.962395	−	0.271653i	$-0.912430\pi$
$311$	−9.17567	−	20.6089i	−0.520304	−	1.16862i	0.442091	−	0.896970i	$-0.354237\pi$
$312$	−1.78345	+	4.32822i	−0.100968	+	0.245037i
$313$	12.9678	−	4.97789i	0.732985	−	0.281367i	0.0368932	−	0.999319i	$-0.488254\pi$
$313$	12.9678	−	4.97789i	0.732985	−	0.281367i	0.696092	+	0.717953i	$0.254921\pi$
$314$	13.2671	+	9.63915i	0.748708	+	0.543969i
$315$	−8.53370	+	12.2978i	−0.480819	+	0.692904i
$316$	39.8405	−	28.9458i	2.24120	−	1.62833i
$317$	−15.3271	+	23.6016i	−0.860854	+	1.32560i	0.0834460	+	0.996512i	$0.473407\pi$
$317$	−15.3271	+	23.6016i	−0.860854	+	1.32560i	−0.944300	+	0.329086i	$0.893259\pi$
$318$	−0.0488200	−	1.74145i	−0.00273769	−	0.0976556i
$319$	−6.39112	+	5.75459i	−0.357834	+	0.322195i
$320$	48.1060	−	68.7812i	2.68920	−	3.84499i
$321$	6.63245	+	9.61219i	0.370187	+	0.536500i
$322$	−1.19992	+	0.0628854i	−0.0668692	+	0.00350446i
$323$	−2.97290	−	18.7701i	−0.165416	−	1.04440i
$324$	−40.8331	+	30.1303i	−2.26850	+	1.67391i
$325$	1.07412	+	0.807592i	0.0595812	+	0.0447971i
$326$	−31.6324	+	18.2629i	−1.75195	+	1.01149i
$327$	7.81627	−	3.74591i	0.432241	−	0.207149i
$328$	−92.5194	+	60.0828i	−5.10853	+	3.31752i
$329$	−3.54037	−	0.752529i	−0.195187	−	0.0414883i
$330$	−21.5268	+	9.42126i	−1.18501	+	0.518623i
$331$	−23.4866	+	4.99224i	−1.29094	+	0.274398i	−0.801688	−	0.597743i	$-0.796064\pi$
$331$	−23.4866	+	4.99224i	−1.29094	+	0.274398i	−0.489254	+	0.872141i	$0.662731\pi$
$332$	−46.1517	+	46.1517i	−2.53291	+	2.53291i
$333$	11.8312	+	6.77262i	0.648348	+	0.371137i
$334$	27.1241	+	37.3331i	1.48416	+	2.04278i
$335$	−0.730106	+	21.2354i	−0.0398899	+	1.16021i
$336$	41.5439	+	48.4601i	2.26641	+	2.64372i
$337$	9.56542	−	11.8123i	0.521062	−	0.643458i	−0.446892	−	0.894588i	$-0.647469\pi$
$337$	9.56542	−	11.8123i	0.521062	−	0.643458i	0.967953	+	0.251131i	$0.0808024\pi$
$338$	22.4853	−	27.7670i	1.22304	−	1.51033i
$339$	9.79715	+	11.4282i	0.532108	+	0.620694i
$340$	−37.3963	+	10.7450i	−2.02810	+	0.582730i
$341$	0.475788	+	0.654866i	0.0257654	+	0.0354630i
$342$	0.188592	+	51.0577i	0.0101979	+	2.76088i
$343$	14.2335	−	14.2335i	0.768534	−	0.768534i
$344$	−25.6832	+	5.45914i	−1.38475	+	0.294337i
$345$	−0.381435	+	0.651095i	−0.0205358	+	0.0350538i
$346$	−61.8366	−	13.1438i	−3.32436	−	0.706614i
$347$	6.54517	−	4.25048i	0.351363	−	0.228178i	−0.356874	−	0.934153i	$-0.616157\pi$
$347$	6.54517	−	4.25048i	0.351363	−	0.228178i	0.708237	+	0.705975i	$0.249491\pi$
$348$	34.5020	−	16.5349i	1.84950	−	0.886363i
$349$	−13.7550	+	7.94143i	−0.736286	+	0.425095i	−0.820717	−	0.571334i	$-0.806426\pi$
$349$	−13.7550	+	7.94143i	−0.736286	+	0.425095i	0.0844312	+	0.996429i	$0.473093\pi$
$350$	27.7001	−	13.5472i	1.48063	−	0.724128i
$351$	−1.31386	+	0.473471i	−0.0701286	+	0.0252720i
$352$	8.76839	+	55.3614i	0.467357	+	2.95077i
$353$	−1.58347	+	0.0829864i	−0.0842799	+	0.00441692i	−0.0944293	−	0.995532i	$-0.530103\pi$
$353$	−1.58347	+	0.0829864i	−0.0842799	+	0.00441692i	0.0101494	+	0.999948i	$0.496769\pi$
$354$	−10.2445	−	14.8471i	−0.544491	−	0.789114i
$355$	2.78021	−	0.958978i	0.147558	−	0.0508973i
$356$	−24.5382	+	22.0943i	−1.30052	+	1.17099i
$357$	−0.334242	−	11.9227i	−0.0176900	−	0.631016i
$358$	17.4499	−	26.8705i	0.922255	−	1.42015i
$359$	−25.4590	+	18.4970i	−1.34367	+	0.976236i	−0.344374	+	0.938833i	$0.611909\pi$
$359$	−25.4590	+	18.4970i	−1.34367	+	0.976236i	−0.999300	+	0.0374035i	$0.988091\pi$
$360$	66.9189	−	8.50425i	3.52694	−	0.448213i
$361$	15.3074	+	11.1215i	0.805652	+	0.585340i
$362$	−23.4682	+	9.00862i	−1.23346	+	0.473482i
$363$	−4.07856	+	9.89817i	−0.214069	+	0.519519i
$364$	1.37541	+	3.08921i	0.0720909	+	0.161919i
$365$	−33.5968	+	5.94268i	−1.75854	+	0.311054i
$366$	16.2987	+	39.1439i	0.851947	+	2.04609i
$367$	3.05972	+	1.98701i	0.159716	+	0.103721i	0.622022	−	0.782999i	$-0.286311\pi$
$367$	3.05972	+	1.98701i	0.159716	+	0.103721i	−0.462306	+	0.886720i	$0.652978\pi$
$368$	2.27532	+	2.27532i	0.118609	+	0.118609i
$369$	−31.8209	−	8.40052i	−1.65653	−	0.437314i
$370$	−14.4768	−	24.0641i	−0.752613	−	1.25103i
$371$	−0.603487	−	0.543382i	−0.0313315	−	0.0282110i
$372$	−1.20833	−	3.39229i	−0.0626488	−	0.175882i
$373$	3.30965	−	8.62193i	0.171367	−	0.446427i	−0.820820	−	0.571187i	$-0.806483\pi$
$373$	3.30965	−	8.62193i	0.171367	−	0.446427i	0.992187	+	0.124761i	$0.0398163\pi$
$374$	9.36195	−	16.2154i	0.484095	−	0.838477i
$375$	2.46114	−	19.2079i	0.127093	−	0.991891i
$376$	8.15567	+	14.1260i	0.420596	+	0.728495i
$377$	1.03996	−	0.164714i	0.0535608	−	0.00848320i
$378$	−4.00663	+	31.7936i	−0.206079	+	1.63529i
$379$	−10.6025	+	3.44497i	−0.544615	+	0.176956i	−0.568387	−	0.822761i	$-0.692432\pi$
$379$	−10.6025	+	3.44497i	−0.544615	+	0.176956i	0.0237722	+	0.999717i	$0.492432\pi$
$380$	37.6041	−	67.9258i	1.92905	−	3.48452i
$381$	−25.5789	−	0.622536i	−1.31045	−	0.0318935i
$382$	29.6779	−	7.95216i	1.51845	−	0.406868i
$383$	0.502991	−	9.59763i	0.0257016	−	0.490416i	−0.955206	−	0.295942i	$-0.904367\pi$
$383$	0.502991	−	9.59763i	0.0257016	−	0.490416i	0.980908	−	0.194474i	$-0.0623001\pi$
$384$	11.7421	−	90.4810i	0.599211	−	4.61734i
$385$	−3.74072	+	10.2948i	−0.190645	+	0.524672i
$386$	23.9516	−	32.9666i	1.21911	−	1.67796i
$387$	−6.35424	−	4.58086i	−0.323004	−	0.232858i
$388$	3.08934	−	19.5053i	0.156838	−	0.990233i
$389$	0.575883	−	5.47916i	0.0291984	−	0.277804i	−0.970175	−	0.242406i	$-0.922063\pi$
$389$	0.575883	−	5.47916i	0.0291984	−	0.277804i	0.999373	−	0.0353983i	$-0.0112700\pi$
$390$	2.83860	+	0.468060i	0.143738	+	0.0237011i
$391$	−0.0628510	−	0.597987i	−0.00317851	−	0.0302415i
$392$	−20.2939	−	1.06356i	−1.02500	−	0.0537178i
$393$	−3.02363	−	4.91373i	−0.152522	−	0.247865i
$394$	−1.87346	−	8.81391i	−0.0943833	−	0.444039i
$395$	−14.7460	−	12.8046i	−0.741951	−	0.644267i
$396$	−23.2622	+	28.9444i	−1.16897	+	1.45451i
$397$	−13.8752	+	27.2316i	−0.696376	+	1.36672i	0.223576	+	0.974686i	$0.428227\pi$
$397$	−13.8752	+	27.2316i	−0.696376	+	1.36672i	−0.919953	+	0.392029i	$0.871773\pi$
$398$	20.8808	−	16.9090i	1.04666	−	0.847569i
$399$	17.2941	+	16.3509i	0.865790	+	0.818570i
$400$	−76.5972	−	30.8513i	−3.82986	−	1.54257i
$401$	14.5258	+	8.38650i	0.725386	+	0.418802i	0.816732	−	0.577017i	$-0.195784\pi$
$401$	14.5258	+	8.38650i	0.725386	+	0.418802i	−0.0913459	+	0.995819i	$0.529117\pi$
$402$	19.6588	+	41.0204i	0.980492	+	2.04591i
$403$	−0.00518668	−	0.0989677i	−0.000258367	−	0.00492993i
$404$	−3.83844	−	11.8135i	−0.190969	−	0.587743i
$405$	15.2924	+	13.0821i	0.759886	+	0.650057i
$406$	7.46586	−	22.9776i	0.370524	−	1.14036i
$407$	9.63574	+	2.58189i	0.477626	+	0.127980i
$408$	−38.9215	+	37.0720i	−1.92690	+	1.83534i
$409$	−18.4938	+	1.94378i	−0.914460	+	0.0961136i	−0.550056	−	0.835128i	$-0.685394\pi$
$409$	−18.4938	+	1.94378i	−0.914460	+	0.0961136i	−0.364403	+	0.931241i	$0.618727\pi$
$410$	48.7942	+	47.0692i	2.40977	+	2.32458i
$411$	−5.72046	−	30.5498i	−0.282169	−	1.50691i
$412$	−5.24829	−	13.6723i	−0.258565	−	0.673584i
$413$	−8.30486	−	1.31536i	−0.408656	−	0.0647247i
$414$	−0.0785869	+	1.61354i	−0.00386234	+	0.0793012i
$415$	21.9580	+	13.7045i	1.07788	+	0.672726i
$416$	2.79123	−	6.26920i	0.136851	−	0.307373i
$417$	−19.0310	+	4.60612i	−0.931951	+	0.225563i
$418$	9.66996	+	36.0888i	0.472973	+	1.76516i
$419$	−1.30254	−	1.44662i	−0.0636335	−	0.0706721i	0.710488	−	0.703710i	$-0.248474\pi$
$419$	−1.30254	−	1.44662i	−0.0636335	−	0.0706721i	−0.774121	+	0.633038i	$0.781808\pi$
$420$	28.8913	−	39.2398i	1.40975	−	1.91470i
$421$	9.66090	−	10.7295i	0.470843	−	0.522925i	−0.460209	−	0.887811i	$-0.652225\pi$
$421$	9.66090	−	10.7295i	0.470843	−	0.522925i	0.931052	+	0.364886i	$0.118892\pi$
$422$	36.0684	+	18.3777i	1.75578	+	0.894615i
$423$	−1.48663	+	4.63355i	−0.0722825	+	0.225291i
$424$			3.65965i			0.177728i
$425$	7.49535	+	13.4877i	0.363578	+	0.654249i
$426$	4.32546	−	4.57498i	0.209569	−	0.221658i
$427$	18.4521	+	7.08311i	0.892961	+	0.342776i
$428$	−20.7057	−	31.8840i	−1.00085	−	1.54117i
$429$	−0.841139	+	0.580389i	−0.0406106	+	0.0280214i
$430$	6.82749	+	14.6210i	0.329251	+	0.705089i
$431$	31.4149	+	10.2073i	1.51320	+	0.491669i	0.943836	−	0.330415i	$-0.107189\pi$
$431$	31.4149	+	10.2073i	1.51320	+	0.491669i	0.569366	+	0.822084i	$0.307189\pi$
$432$	70.4531	−	48.9980i	3.38968	−	2.35742i
$433$	−0.918095	−	1.80186i	−0.0441208	−	0.0865920i	0.867894	−	0.496750i	$-0.165473\pi$
$433$	−0.918095	−	1.80186i	−0.0441208	−	0.0865920i	−0.912014	+	0.410158i	$0.865473\pi$
$434$	−2.07739	−	0.924915i	−0.0997181	−	0.0443973i
$435$	−9.47354	−	11.8517i	−0.454221	−	0.568247i
$436$	−25.7766	+	11.4765i	−1.23447	+	0.549623i
$437$	0.932421	+	0.755060i	0.0446038	+	0.0361194i
$438$	−57.8650	+	44.5714i	−2.76490	+	2.12970i
$439$	23.6081	+	2.48131i	1.12675	+	0.118426i	0.649515	−	0.760349i	$-0.274972\pi$
$439$	23.6081	+	2.48131i	1.12675	+	0.118426i	0.477236	+	0.878775i	$0.341639\pi$
$440$	45.7576	−	18.5159i	2.18141	−	0.882713i
$441$	−3.83271	−	4.69742i	−0.182510	−	0.223687i
$442$	−2.04255	+	1.04073i	−0.0971540	+	0.0495025i
$443$	−2.44649	+	9.13043i	−0.116236	+	0.433800i	−0.999376	−	0.0353094i	$-0.988758\pi$
$443$	−2.44649	+	9.13043i	−0.116236	+	0.433800i	0.883140	+	0.469109i	$0.155425\pi$
$444$	−37.8821	−	23.1180i	−1.79780	−	1.09713i
$445$	10.7305	+	7.50498i	0.508675	+	0.355770i
$446$	−15.2150	+	71.5812i	−0.720453	+	3.38947i
$447$	−16.3242	−	13.8901i	−0.772109	−	0.656981i
$448$	−52.7115	−	65.0932i	−2.49038	−	3.07537i
$449$	−11.0470			−0.521342			−0.260671	−	0.965428i	$-0.583944\pi$
$449$	−11.0470			−0.521342			−0.260671	+	0.965428i	$0.583944\pi$
$450$	−14.3647	−	38.8884i	−0.677159	−	1.83322i
$451$	−24.0827			−1.13401
$452$	−30.8383	−	38.0821i	−1.45051	−	1.79123i
$453$	19.7672	−	7.04103i	0.928742	−	0.330816i
$454$	−0.0302651	+	0.142386i	−0.00142041	+	0.00668251i
$455$	1.07057	−	0.807635i	0.0501890	−	0.0378625i
$456$	2.60961	−	107.224i	0.122206	−	5.02124i
$457$	4.49594	−	16.7791i	0.210311	−	0.784893i	−0.777453	−	0.628941i	$-0.783489\pi$
$457$	4.49594	−	16.7791i	0.210311	−	0.784893i	0.987765	−	0.155952i	$-0.0498445\pi$
$458$	49.4485	−	25.1953i	2.31058	−	1.17730i
$459$	−15.9931	−	1.16956i	−0.746492	−	0.0545904i
$460$	1.30062	−	2.08393i	0.0606418	−	0.0971636i
$461$	−40.0980	−	4.21447i	−1.86755	−	0.196287i	−0.897802	−	0.440399i	$-0.854837\pi$
$461$	−40.0980	−	4.21447i	−1.86755	−	0.196287i	−0.969747	+	0.244112i	$0.921504\pi$
$462$	3.10365	+	23.2428i	0.144395	+	1.08135i
$463$	0.312044	+	0.252688i	0.0145019	+	0.0117434i	0.636544	−	0.771240i	$-0.280363\pi$
$463$	0.312044	+	0.252688i	0.0145019	+	0.0117434i	−0.622042	+	0.782984i	$0.713697\pi$
$464$	−59.1067	+	26.3160i	−2.74396	+	1.22169i
$465$	−1.20260	+	0.770181i	−0.0557694	+	0.0357163i
$466$	−72.4477	−	32.2558i	−3.35607	−	1.49422i
$467$	5.59964	+	10.9899i	0.259121	+	0.508553i	0.983514	−	0.180834i	$-0.0578798\pi$
$467$	5.59964	+	10.9899i	0.259121	+	0.508553i	−0.724393	+	0.689387i	$0.757880\pi$
$468$	4.31861	−	1.42086i	0.199628	−	0.0656792i
$469$	20.1658	+	6.55225i	0.931168	+	0.302555i
$470$	7.32766	−	6.84054i	0.338000	−	0.315530i
$471$	−0.825265	−	10.2441i	−0.0380262	−	0.472022i
$472$	20.6379	+	31.7796i	0.949938	+	1.46278i
$473$	−5.35132	−	2.05418i	−0.246054	−	0.0944512i
$474$	−40.6718	−	9.68502i	−1.86812	−	0.444847i
$475$	−29.6064	−	8.45499i	−1.35843	−	0.387942i
$476$			38.8280i			1.77968i
$477$	−0.808654	+	0.733542i	−0.0370257	+	0.0335866i
$478$	16.8604	+	8.59081i	0.771177	+	0.392934i
$479$	3.29374	−	3.65806i	0.150495	−	0.167141i	−0.663184	−	0.748457i	$-0.730795\pi$
$479$	3.29374	−	3.65806i	0.150495	−	0.167141i	0.813678	+	0.581316i	$0.197462\pi$
$480$	−98.4107	+	9.71285i	−4.49181	+	0.443329i
$481$	−0.817235	−	0.907631i	−0.0372627	−	0.0413844i
$482$	1.79296	+	6.69144i	0.0816673	+	0.304787i
$483$	0.519353	+	0.545264i	0.0236314	+	0.0248104i
$484$	14.1750	−	31.8375i	0.644317	−	1.44716i
$485$	−7.81235	+	0.550521i	−0.354741	+	0.0249979i
$486$	41.9837	+	9.67026i	1.90442	+	0.438652i
$487$	15.4228	+	2.44273i	0.698872	+	0.110690i	0.495753	−	0.868464i	$-0.334892\pi$
$487$	15.4228	+	2.44273i	0.698872	+	0.110690i	0.203119	+	0.979154i	$0.434892\pi$
$488$	−31.9205	−	83.1556i	−1.44497	−	3.76428i
$489$	21.5918	+	7.60120i	0.976413	+	0.343738i
$490$	2.17532	+	12.2981i	0.0982707	+	0.555571i
$491$	−25.8615	+	2.71815i	−1.16711	+	0.122668i	−0.668198	−	0.743983i	$-0.732934\pi$
$491$	−25.8615	+	2.71815i	−1.16711	+	0.122668i	−0.498913	+	0.866652i	$0.666267\pi$
$492$	102.782	+	30.2389i	4.63375	+	1.36328i
$493$	11.6780	+	3.12912i	0.525952	+	0.140928i
$494$	1.41353	−	4.35040i	0.0635978	−	0.195734i
$495$	13.2631	+	6.39948i	0.596130	+	0.287635i
$496$	1.88183	+	5.79167i	0.0844965	+	0.260054i
$497$	−0.153596	−	2.93079i	−0.00688972	−	0.131464i
$498$	55.2494	+	4.24557i	2.47578	+	0.190248i
$499$	1.71608	+	0.990782i	0.0768225	+	0.0443535i	0.537919	−	0.842996i	$-0.319211\pi$
$499$	1.71608	+	0.990782i	0.0768225	+	0.0443535i	−0.461097	+	0.887350i	$0.652544\pi$
$500$	−9.76101	+	62.2797i	−0.436526	+	2.78523i
$501$	6.69922	−	28.1331i	0.299299	−	1.25689i
$502$	39.8352	−	32.2579i	1.77793	−	1.43974i
$503$	−9.23640	+	18.1275i	−0.411831	+	0.808263i	−1.00000		0.000474569i	$-0.999849\pi$
$503$	−9.23640	+	18.1275i	−0.411831	+	0.808263i	0.588169	+	0.808738i	$0.299849\pi$
$504$	10.2849	−	66.5258i	0.458126	−	2.96330i
$505$	−4.22106	+	2.53936i	−0.187835	+	0.113000i
$506$	0.245775	+	1.15628i	0.0109260	+	0.0514029i
$507$	−22.3827	+	0.627481i	−0.994053	+	0.0278674i
$508$	83.1792	+	4.35924i	3.69048	+	0.193410i
$509$	2.52870	+	24.0589i	0.112083	+	1.06639i	0.895550	+	0.444961i	$0.146783\pi$
$509$	2.52870	+	24.0589i	0.112083	+	1.06639i	−0.783467	+	0.621433i	$0.786551\pi$
$510$	27.5897	+	18.1667i	1.22169	+	0.804436i
$511$	−3.55888	+	33.8605i	−0.157436	+	1.49790i
$512$	−14.0060	+	88.4302i	−0.618983	+	3.90810i
$513$	24.2159	−	20.9155i	1.06916	−	0.923441i
$514$	−24.9723	+	34.3714i	−1.10148	+	1.51606i
$515$	−4.81314	+	3.25028i	−0.212092	+	0.143224i
$516$	20.2594	+	15.4862i	0.891869	+	0.681742i
$517$	−0.186360	+	3.55597i	−0.00819612	+	0.156391i
$518$	−27.0694	+	7.25323i	−1.18936	+	0.318689i
$519$	18.9686	+	34.7825i	0.832630	+	1.52678i
$520$	−5.93306	−	1.14995i	−0.260182	−	0.0504288i
$521$	−16.8365	+	5.47052i	−0.737622	+	0.239668i	−0.653647	−	0.756800i	$-0.726762\pi$
$521$	−16.8365	+	5.47052i	−0.737622	+	0.239668i	−0.0839755	+	0.996468i	$0.526762\pi$
$522$	−29.7223	−	13.1019i	−1.30091	−	0.573455i
$523$	−15.0649	+	2.38604i	−0.658741	+	0.104334i	−0.476850	−	0.878985i	$-0.658222\pi$
$523$	−15.0649	+	2.38604i	−0.658741	+	0.104334i	−0.181890	+	0.983319i	$0.558222\pi$
$524$	9.39092	+	16.2656i	0.410244	+	0.710564i
$525$	−17.7441	−	7.65376i	−0.774418	−	0.334037i
$526$	−19.2433	+	33.3304i	−0.839048	+	1.45327i
$527$	0.407799	−	1.06235i	0.0177640	−	0.0462768i
$528$	40.6947	−	47.8260i	1.77101	−	2.08136i
$529$	−17.0641	−	15.3646i	−0.741918	−	0.668026i
$530$	2.19117	−	0.507114i	0.0951782	−	0.0220276i
$531$	−2.88551	+	10.9302i	−0.125220	+	0.474330i
$532$	−54.7851	−	54.7851i	−2.37523	−	2.37523i
$533$	2.47282	+	1.60587i	0.107110	+	0.0695577i
$534$	27.8000	+	3.60772i	1.20302	+	0.156121i
$535$	−10.4673	+	10.8509i	−0.452541	+	0.469125i
$536$	−38.8657	−	87.2938i	−1.67874	−	3.77052i
$537$	−19.9023	+	2.65759i	−0.858849	+	0.114684i
$538$	−21.3747	+	8.20498i	−0.921529	+	0.353742i
$539$	−3.58908	−	2.60762i	−0.154592	−	0.112318i
$540$	−48.5695	−	43.9655i	−2.09010	−	1.89198i
$541$	−0.0690279	+	0.0501517i	−0.00296774	+	0.00215619i	−0.589268	−	0.807938i	$-0.700584\pi$
$541$	−0.0690279	+	0.0501517i	−0.00296774	+	0.00215619i	0.586300	+	0.810094i	$0.300584\pi$
$542$	−13.7211	+	21.1287i	−0.589374	+	0.907556i
$543$	13.8586	+	7.49150i	0.594730	+	0.321491i
$544$	58.5576	−	52.7255i	2.51063	−	2.26059i
$545$	6.73895	+	8.93288i	0.288665	+	0.382643i
$546$	1.23117	−	2.59352i	0.0526893	−	0.110993i
$547$	−36.4136	+	1.90836i	−1.55693	+	0.0815955i	−0.811248	−	0.584702i	$-0.801212\pi$
$547$	−36.4136	+	1.90836i	−1.55693	+	0.0815955i	−0.745686	+	0.666297i	$0.767878\pi$
$548$	15.8280	+	99.9338i	0.676137	+	4.26896i
$549$	11.9763	−	23.7211i	0.511137	−	1.01239i
$550$	−17.4268	−	24.8311i	−0.743081	−	1.05880i
$551$	−20.8924	+	12.0622i	−0.890046	+	0.513868i
$552$	0.260005	−	3.38356i	0.0110665	−	0.144014i
$553$	−16.3446	+	10.6143i	−0.695042	+	0.451366i
$554$	60.3373	+	12.8251i	2.56349	+	0.544886i
$555$	−5.54459	+	16.7033i	−0.235355	+	0.709017i
$556$	62.3488	−	13.2526i	2.64418	−	0.562037i
$557$	3.17812	−	3.17812i	0.134661	−	0.134661i	−0.636563	−	0.771225i	$-0.719645\pi$
$557$	3.17812	−	3.17812i	0.134661	−	0.134661i	0.771225	+	0.636563i	$0.219645\pi$
$558$	−1.51884	+	2.65330i	−0.0642978	+	0.112323i
$559$	0.412498	+	0.567755i	0.0174468	+	0.0240135i
$560$	−50.6982	+	64.9628i	−2.14239	+	2.74518i
$561$	−11.5338	+	2.15970i	−0.486955	+	0.0911824i
$562$	31.8911	−	39.3822i	1.34524	−	1.66124i
$563$	21.5021	−	26.5529i	0.906206	−	1.11907i	−0.0862263	−	0.996276i	$-0.527481\pi$
$563$	21.5021	−	26.5529i	0.906206	−	1.11907i	0.992432	−	0.122795i	$-0.0391859\pi$
$564$	5.26033	−	14.9424i	0.221500	−	0.629187i
$565$	−11.9560	+	15.3199i	−0.502991	+	0.644515i
$566$	−28.9034	−	39.7821i	−1.21490	−	1.67217i
$567$	16.7614	−	11.0619i	0.703912	−	0.464555i
$568$	−9.35211	+	9.35211i	−0.392406	+	0.392406i
$569$	40.9128	−	8.69629i	1.71515	−	0.364567i	0.757577	−	0.652745i	$-0.226383\pi$
$569$	40.9128	−	8.69629i	1.71515	−	0.364567i	0.957577	+	0.288178i	$0.0930495\pi$
$570$	−64.5608	+	13.2955i	−2.70416	+	0.556887i
$571$	10.0838	+	2.14337i	0.421992	+	0.0896972i	0.414013	−	0.910271i	$-0.364127\pi$
$571$	10.0838	+	2.14337i	0.421992	+	0.0896972i	0.00797906	+	0.999968i	$0.497460\pi$
$572$	2.79009	−	1.81191i	0.116660	−	0.0757596i
$573$	−15.8888	−	10.8769i	−0.663763	−	0.454389i
$574$	58.5909	−	33.8275i	2.44554	−	1.41193i
$575$	−0.921448	−	0.316170i	−0.0384270	−	0.0131852i
$576$	−94.2157	+	61.6804i	−3.92566	+	2.57002i
$577$	−3.91285	−	24.7048i	−0.162894	−	1.02847i	−0.924708	−	0.380677i	$-0.875691\pi$
$577$	−3.91285	−	24.7048i	−0.162894	−	1.02847i	0.761814	−	0.647796i	$-0.224309\pi$
$578$	20.6339	−	1.08138i	0.858258	−	0.0449794i
$579$	−25.4548	+	2.05064i	−1.05786	+	0.0852218i
$580$	29.7466	+	39.4308i	1.23516	+	1.63728i
$581$	19.1952	−	17.2834i	0.796350	−	0.717037i
$582$	−14.2794	+	8.78673i	−0.591899	+	0.364222i
$583$	−0.435123	+	0.670031i	−0.0180210	+	0.0277498i
$584$	124.131	−	90.1867i	5.13659	−	3.73195i
$585$	−0.935126	−	1.54150i	−0.0386627	−	0.0637330i
$586$	11.0891	+	8.05668i	0.458085	+	0.332818i
$587$	4.66340	−	1.79011i	0.192479	−	0.0738859i	−0.260219	−	0.965550i	$-0.583795\pi$
$587$	4.66340	−	1.79011i	0.192479	−	0.0738859i	0.452698	+	0.891664i	$0.350461\pi$
$588$	12.0435	+	15.6355i	0.496664	+	0.644796i
$589$	0.923553	+	2.07434i	0.0380544	+	0.0854715i
$590$	16.1679	−	16.7604i	0.665621	−	0.690014i
$591$	−3.42943	+	4.48645i	−0.141068	+	0.184548i
$592$	62.9413	+	40.8745i	2.58687	+	1.67993i
$593$	12.1478	+	12.1478i	0.498849	+	0.498849i	0.911079	−	0.412231i	$-0.135250\pi$
$593$	12.1478	+	12.1478i	0.498849	+	0.498849i	−0.412231	+	0.911079i	$0.635250\pi$
$594$	31.5103	−	0.999855i	1.29288	−	0.0410246i
$595$	15.0017	−	3.47192i	0.615008	−	0.142335i
$596$	51.8534	+	46.6890i	2.12400	+	1.91246i
$597$	−16.5621	−	3.03798i	−0.677843	−	0.124336i
$598$	0.0518659	−	0.135115i	0.00212096	−	0.00552528i
$599$	7.84305	−	13.5846i	0.320458	−	0.555050i	−0.660124	−	0.751156i	$-0.729496\pi$
$599$	7.84305	−	13.5846i	0.320458	−	0.555050i	0.980583	+	0.196106i	$0.0628297\pi$
$600$	27.8744	+	82.5053i	1.13797	+	3.36826i
$601$	−14.9665	−	25.9227i	−0.610496	−	1.05741i	−0.991157	−	0.132696i	$-0.957637\pi$
$601$	−14.9665	−	25.9227i	−0.610496	−	1.05741i	0.380661	−	0.924715i	$-0.375697\pi$
$602$	15.9046	−	2.51904i	0.648223	−	0.102669i
$603$	11.4986	−	26.0852i	0.468259	−	1.06227i
$604$	−64.9664	+	21.1089i	−2.64345	+	0.858908i
$605$	−13.5683	−	2.62982i	−0.551629	−	0.106918i
$606$	−5.49349	+	9.00184i	−0.223158	+	0.365675i
$607$	−46.0941	+	12.3509i	−1.87090	+	0.501306i	−0.870950	+	0.491371i	$0.836496\pi$
$607$	−46.0941	+	12.3509i	−1.87090	+	0.501306i	−0.999951	+	0.00993502i	$0.996838\pi$
$608$	−8.22890	+	157.017i	−0.333726	+	6.36787i
$609$	−13.9777	+	5.82004i	−0.566407	+	0.235840i
$610$	−45.3652	+	30.6348i	−1.83678	+	1.24037i
$611$	0.256252	−	0.352700i	0.0103668	−	0.0142687i
$612$	51.9362	+	5.26483i	2.09940	+	0.212818i
$613$	2.87702	−	18.1648i	0.116202	−	0.733669i	−0.858938	−	0.512079i	$-0.828875\pi$
$613$	2.87702	−	18.1648i	0.116202	−	0.733669i	0.975140	−	0.221590i	$-0.0711245\pi$
$614$	8.80090	−	83.7349i	0.355175	−	3.37927i
$615$	2.49266	−	42.4148i	0.100514	−	1.71033i
$616$	−5.14894	−	48.9889i	−0.207457	−	1.97382i
$617$	44.6347	+	2.33921i	1.79693	+	0.0941729i	0.921308	−	0.388833i	$-0.127122\pi$
$617$	44.6347	+	2.33921i	1.79693	+	0.0941729i	0.875617	+	0.483005i	$0.160455\pi$
$618$	−5.91253	+	10.9377i	−0.237837	+	0.439977i
$619$	3.97436	+	18.6979i	0.159743	+	0.751532i	0.982962	+	0.183808i	$0.0588425\pi$
$619$	3.97436	+	18.6979i	0.159743	+	0.751532i	−0.823219	+	0.567724i	$0.807824\pi$
$620$	3.98364	−	2.39653i	0.159987	−	0.0962471i
$621$	0.799763	−	0.620750i	0.0320934	−	0.0249098i
$622$	28.3057	−	55.5531i	1.13496	−	2.22748i
$623$	10.1552	−	8.22348i	0.406858	−	0.329467i
$624$	−7.36763	+	2.19720i	−0.294941	+	0.0879584i
$625$	24.9353	−	1.79763i	0.997411	−	0.0719053i
$626$	33.2468	+	19.1950i	1.32881	+	0.767188i
$627$	13.2265	−	19.3210i	0.528215	−	0.771607i
$628$	1.75097	+	33.4104i	0.0698712	+	1.33322i
$629$	−4.33357	−	13.3374i	−0.172791	−	0.531796i
$630$	−41.2567	+	3.06046i	−1.64371	+	0.121932i
$631$	−14.3412	+	44.1375i	−0.570912	+	1.75709i	0.0787822	+	0.996892i	$0.474897\pi$
$631$	−14.3412	+	44.1375i	−0.570912	+	1.75709i	−0.649694	+	0.760195i	$0.725103\pi$
$632$	84.8342	+	22.7313i	3.37452	+	0.904201i
$633$	−5.96782	−	24.6571i	−0.237200	−	0.980030i
$634$	−77.3513	+	8.12995i	−3.07201	+	0.322882i
$635$	−5.75346	−	32.5270i	−0.228319	−	1.29080i
$636$	2.69835	−	2.31324i	0.106997	−	0.0917260i
$637$	0.194648	+	0.507074i	0.00771222	+	0.0200910i
$638$	−23.4761	−	3.71825i	−0.929429	−	0.147207i
$639$	−3.94103	−	0.191947i	−0.155905	−	0.00759329i
$640$	117.499	−	8.27989i	4.64454	−	0.327292i
$641$	15.4600	−	34.7237i	0.610633	−	1.37150i	−0.298264	−	0.954483i	$-0.596408\pi$
$641$	15.4600	−	34.7237i	0.610633	−	1.37150i	0.908897	−	0.417020i	$-0.136926\pi$
$642$	−9.10980	+	30.9641i	−0.359535	+	1.22205i
$643$	9.98866	+	37.2782i	0.393914	+	1.47011i	0.823621	+	0.567140i	$0.191950\pi$
$643$	9.98866	+	37.2782i	0.393914	+	1.47011i	−0.429707	+	0.902969i	$0.641383\pi$
$644$	−1.64028	−	1.82172i	−0.0646361	−	0.0717857i
$645$	4.17172	−	9.21218i	0.164261	−	0.362729i
$646$	35.1448	−	39.0323i	1.38276	−	1.53571i
$647$	3.90836	+	1.99141i	0.153654	+	0.0782904i	0.529127	−	0.848543i	$-0.322520\pi$
$647$	3.90836	+	1.99141i	0.153654	+	0.0782904i	−0.375473	+	0.926833i	$0.622520\pi$
$648$	−87.5900	−	22.7775i	−3.44086	−	0.894786i
$649$			8.27221i			0.324713i
$650$	0.133618	+	3.71169i	0.00524093	+	0.145585i
$651$	0.407274	+	1.36567i	0.0159623	+	0.0535247i
$652$	−69.5682	−	26.7047i	−2.72450	−	1.04584i
$653$	7.33630	+	11.2969i	0.287092	+	0.442082i	0.952563	−	0.304341i	$-0.0984362\pi$
$653$	7.33630	+	11.2969i	0.287092	+	0.442082i	−0.665472	+	0.746423i	$0.731769\pi$
$654$	21.6405	+	10.2730i	0.846212	+	0.401706i
$655$	5.44467	−	5.08272i	0.212741	−	0.198598i
$656$	−172.312	−	55.9875i	−6.72764	−	2.18594i
$657$	44.8091	+	9.35161i	1.74817	+	0.364841i
$658$	−4.54145	−	8.91310i	−0.177044	−	0.347469i
$659$	−10.3040	−	4.58763i	−0.401387	−	0.178709i	0.196107	−	0.980583i	$-0.437170\pi$
$659$	−10.3040	−	4.58763i	−0.401387	−	0.178709i	−0.597494	+	0.801874i	$0.703837\pi$
$660$	−42.5754	−	22.0344i	−1.65725	−	0.857689i
$661$	12.1765	−	5.42134i	0.473612	−	0.210865i	−0.156028	−	0.987753i	$-0.549869\pi$
$661$	12.1765	−	5.42134i	0.473612	−	0.210865i	0.629640	+	0.776887i	$0.283202\pi$
$662$	−51.5730	−	41.7630i	−2.00444	−	1.62316i
$663$	1.32830	+	0.547327i	0.0515868	+	0.0212564i
$664$	−115.765	−	12.1674i	−4.49256	−	0.472187i
$665$	−16.2681	+	26.0656i	−0.630849	+	1.01078i
$666$	6.03145	+	37.1914i	0.233714	+	1.44114i
$667$	−0.680094	+	0.346525i	−0.0263333	+	0.0134175i
$668$	−24.3663	+	90.9364i	−0.942762	+	3.51844i
$669$	40.2637	−	21.9578i	1.55669	−	0.848938i
$670$	−46.8805	+	35.3666i	−1.81115	+	1.36633i
$671$	4.04281	−	19.0199i	0.156071	−	0.734255i
$672$	−17.8042	+	97.0628i	−0.686811	+	3.74428i
$673$	−2.06833	−	2.55418i	−0.0797284	−	0.0984564i	0.735721	−	0.677285i	$-0.236843\pi$
$673$	−2.06833	−	2.55418i	−0.0797284	−	0.0984564i	−0.815449	+	0.578828i	$0.803510\pi$
$674$	42.0083			1.61810
$675$	−12.6436	+	22.6967i	−0.486653	+	0.873595i
$676$	72.8928			2.80357
$677$	−5.57514	−	6.88473i	−0.214270	−	0.264602i	0.658667	−	0.752435i	$-0.271121\pi$
$677$	−5.57514	−	6.88473i	−0.214270	−	0.264602i	−0.872937	+	0.487833i	$0.837787\pi$
$678$	−7.50592	+	40.9199i	−0.288263	+	1.57152i
$679$	−1.62490	+	7.64457i	−0.0623581	+	0.293372i
$680$	−56.8647	−	39.7714i	−2.18066	−	1.52517i
$681$	0.0800908	−	0.0436775i	0.00306909	−	0.00167373i
$682$	−0.579020	+	2.16093i	−0.0221718	+	0.0827464i
$683$	−0.432407	+	0.220322i	−0.0165456	+	0.00843040i	−0.462244	−	0.886753i	$-0.652955\pi$
$683$	−0.432407	+	0.220322i	−0.0165456	+	0.00843040i	0.445698	+	0.895183i	$0.352955\pi$
$684$	−80.7088	+	65.8517i	−3.08598	+	2.51790i
$685$	37.1953	−	15.0512i	1.42116	−	0.575076i
$686$	55.3277	+	5.81518i	2.11242	+	0.222024i
$687$	−32.1571	−	13.2504i	−1.22687	−	0.505533i
$688$	−33.5131	−	27.1384i	−1.27767	−	1.03464i
$689$	0.0893569	−	0.0397842i	0.00340423	−	0.00151566i
$690$	−2.06189	+	0.313182i	−0.0784949	+	0.0119226i
$691$	15.0739	+	6.71135i	0.573439	+	0.255312i	0.672904	−	0.739729i	$-0.265047\pi$
$691$	15.0739	+	6.71135i	0.573439	+	0.255312i	−0.0994652	+	0.995041i	$0.531713\pi$
$692$	−58.5526	−	114.916i	−2.22583	−	4.36845i
$693$	9.79278	−	10.9571i	0.371997	−	0.416226i
$694$	20.5135	+	6.66523i	0.778680	+	0.253009i
$695$	−10.6954	−	22.9041i	−0.405700	−	0.868804i
$696$	61.6410	+	29.2616i	2.33650	+	1.10916i
$697$	18.4390	+	28.3935i	0.698426	+	1.07548i
$698$	−40.9811	−	15.7312i	−1.55116	−	0.595434i
$699$	14.2034	+	47.6267i	0.537222	+	1.80141i
$700$	57.0428	+	26.5247i	2.15602	+	1.00254i
$701$		−	2.68231i		−	0.101310i	−0.998716	−	0.0506548i	$-0.983869\pi$
$701$		−	2.68231i		−	0.101310i	0.998716	−	0.0506548i	$-0.0161308\pi$
$702$	−3.30215	−	1.99848i	−0.124631	−	0.0754276i
$703$	24.9331	+	12.7041i	0.940370	+	0.479143i
$704$	−55.1383	+	61.2373i	−2.07810	+	2.30797i
$705$	−6.24352	−	0.696277i	−0.235145	−	0.0262233i
$706$	−2.93238	−	3.25674i	−0.110362	−	0.122569i
$707$	1.27228	+	4.74823i	0.0478491	+	0.178575i
$708$	10.3868	−	35.3046i	0.390361	−	1.32683i
$709$	1.65751	−	3.72283i	0.0622491	−	0.139814i	−0.879742	−	0.475451i	$-0.842285\pi$
$709$	1.65751	−	3.72283i	0.0622491	−	0.139814i	0.941991	+	0.335637i	$0.108952\pi$
$710$	6.89537	+	4.30355i	0.258779	+	0.161509i
$711$	11.9814	+	23.3017i	0.449338	+	0.873881i
$712$	−58.1633	−	9.21216i	−2.17976	−	0.345240i
$713$	0.0257459	+	0.0670704i	0.000964192	+	0.00251180i
$714$	25.0269	−	21.4551i	0.936609	−	0.802936i
$715$	−0.949534	−	0.915967i	−0.0355106	−	0.0342552i
$716$	65.0064	−	6.83245i	2.42940	−	0.255341i
$717$	−2.78970	−	11.5261i	−0.104183	−	0.430451i
$718$	−84.0099	−	22.5104i	−3.13522	−	0.840080i
$719$	−16.2764	+	50.0935i	−0.607006	+	1.86817i	−0.124641	+	0.992202i	$0.539778\pi$
$719$	−16.2764	+	50.0935i	−0.607006	+	1.86817i	−0.482365	+	0.875970i	$0.660222\pi$
$720$	80.0196	+	76.6222i	2.98215	+	2.85554i
$721$	1.79096	+	5.51201i	0.0666989	+	0.205278i
$722$	2.73682	+	52.2217i	0.101854	+	1.94349i
$723$	2.45240	−	3.58242i	0.0912058	−	0.133232i
$724$	−44.4138	−	25.6423i	−1.65062	−	0.952988i
$725$	12.5747	−	15.0188i	0.467012	−	0.557783i
$726$	−28.3537	+	8.45574i	−1.05231	+	0.313822i
$727$	8.66739	−	7.01872i	0.321456	−	0.260310i	−0.454986	−	0.890498i	$-0.650356\pi$
$727$	8.66739	−	7.01872i	0.321456	−	0.260310i	0.776442	+	0.630189i	$0.217022\pi$
$728$	−2.73795	+	5.37352i	−0.101475	+	0.199156i
$729$	−12.5236	−	23.9199i	−0.463836	−	0.885921i
$730$	−71.1989	−	61.8250i	−2.63519	−	2.28825i
$731$	1.67537	+	7.88199i	0.0619657	+	0.291526i
$732$	−41.1360	+	76.0980i	−1.52043	+	2.81266i
$733$	−4.26723	−	0.223636i	−0.157614	−	0.00826018i	−0.0266341	−	0.999645i	$-0.508479\pi$
$733$	−4.26723	−	0.223636i	−0.157614	−	0.00826018i	−0.130980	+	0.991385i	$0.541812\pi$
$734$	1.05397	+	10.0278i	0.0389027	+	0.370135i
$735$	4.96405	−	6.05122i	0.183102	−	0.223203i
$736$	−0.520003	+	4.94750i	−0.0191676	+	0.182367i
$737$	3.26324	−	20.6033i	0.120203	−	0.758933i
$738$	−37.3029	−	82.9577i	−1.37314	−	3.05372i
$739$	7.44133	−	10.2421i	0.273734	−	0.376762i	−0.649912	−	0.760010i	$-0.725194\pi$
$739$	7.44133	−	10.2421i	0.273734	−	0.376762i	0.923646	+	0.383247i	$0.125194\pi$
$740$	19.5664	−	53.8484i	0.719274	−	1.97951i
$741$	−2.64644	+	1.10192i	−0.0972196	+	0.0404802i
$742$	0.117462	−	2.24131i	0.00431217	−	0.0822810i
$743$	15.7373	−	4.21679i	0.577344	−	0.154699i	0.0416814	−	0.999131i	$-0.486729\pi$
$743$	15.7373	−	4.21679i	0.577344	−	0.154699i	0.535663	+	0.844432i	$0.320062\pi$
$744$	3.34553	−	5.48211i	0.122653	−	0.200984i
$745$	13.4022	−	24.2090i	0.491019	−	0.886949i
$746$	24.2752	−	7.88748i	0.888777	−	0.288781i
$747$	−20.5155	−	28.0189i	−0.750622	−	1.02516i
$748$	37.7289	−	5.97567i	1.37951	−	0.218492i
$749$	7.52258	+	13.0295i	0.274869	+	0.476087i
$750$	45.5365	−	28.1221i	1.66276	−	1.02688i
$751$	−13.7164	+	23.7576i	−0.500520	+	0.866927i	0.499479	+	0.866326i	$0.333525\pi$
$751$	−13.7164	+	23.7576i	−0.500520	+	0.866927i	−1.00000		0.000600951i	$0.999809\pi$
$752$	−9.60032	+	25.0097i	−0.350088	+	0.912009i
$753$	−31.5963	−	5.79569i	−1.15143	−	0.211207i
$754$	2.16259	+	1.94721i	0.0787570	+	0.0709131i
$755$	13.9648	+	23.2130i	0.508232	+	0.844808i
$756$	−55.5522	+	34.4673i	−2.02041	+	1.25356i
$757$	30.0759	+	30.0759i	1.09313	+	1.09313i	0.995193	+	0.0979360i	$0.0312241\pi$
$757$	30.0759	+	30.0759i	1.09313	+	1.09313i	0.0979360	+	0.995193i	$0.468776\pi$
$758$	−25.8403	−	16.7809i	−0.938561	−	0.609509i
$759$	0.449900	−	0.588568i	0.0163303	−	0.0213637i
$760$	136.350	−	24.1180i	4.94595	−	0.874851i
$761$	9.50427	+	21.3469i	0.344529	+	0.773826i	0.999830	+	0.0184572i	$0.00587546\pi$
$761$	9.50427	+	21.3469i	0.344529	+	0.773826i	−0.655300	+	0.755369i	$0.727458\pi$
$762$	−43.1523	−	56.0226i	−1.56324	−	2.02948i
$763$	10.4247	−	4.00166i	0.377399	−	0.144870i
$764$	50.7113	+	36.8439i	1.83467	+	1.33296i
$765$	−2.60989	−	20.5369i	−0.0943608	−	0.742514i
$766$	21.4892	−	15.6128i	0.776437	−	0.564114i
$767$	0.551601	−	0.849391i	0.0199172	−	0.0306697i
$768$	104.019	−	64.0076i	3.75347	−	2.30968i
$769$	31.8036	−	28.6361i	1.14687	−	1.03265i	0.147821	−	0.989014i	$-0.452774\pi$
$769$	31.8036	−	28.6361i	1.14687	−	1.03265i	0.999048	−	0.0436311i	$-0.0138926\pi$
$770$	−28.6180	+	9.87122i	−1.03132	+	0.355734i
$771$	26.5394	−	2.13802i	0.955795	−	0.0769991i
$772$	83.0193	−	4.35085i	2.98793	−	0.156591i
$773$	2.07484	+	13.1001i	0.0746270	+	0.471176i	0.996494	+	0.0836689i	$0.0266638\pi$
$773$	2.07484	+	13.1001i	0.0746270	+	0.471176i	−0.921867	+	0.387507i	$0.873336\pi$
$774$	−1.21290	−	21.6155i	−0.0435966	−	0.776953i
$775$	−1.28214	−	1.32483i	−0.0460557	−	0.0475894i
$776$	30.5017	−	17.6102i	1.09495	−	0.632169i
$777$	14.4923	+	9.92091i	0.519908	+	0.355911i
$778$	12.7701	−	8.29300i	0.457830	−	0.297318i
$779$	−66.0791	−	14.0456i	−2.36753	−	0.503234i
$780$	2.90236	+	5.10148i	0.103921	+	0.182662i
$781$	−2.82418	+	0.600299i	−0.101057	+	0.0214804i
$782$	1.17508	−	1.17508i	0.0420206	−	0.0420206i
$783$	5.88956	+	19.4857i	0.210476	+	0.696363i
$784$	−19.6176	−	27.0014i	−0.700630	−	0.964334i
$785$	12.7519	−	3.66399i	0.455136	−	0.130774i
$786$	5.29498	−	15.0408i	0.188866	−	0.536487i
$787$	−22.3930	+	27.6531i	−0.798226	+	0.985727i	0.201755	+	0.979436i	$0.435336\pi$
$787$	−22.3930	+	27.6531i	−0.798226	+	0.985727i	−0.999980	+	0.00629053i	$0.997998\pi$
$788$	11.5690	−	14.2865i	0.412127	−	0.508934i
$789$	23.7074	−	4.43921i	0.844006	−	0.158040i
$790$	1.85465	−	53.9433i	0.0659857	−	1.91922i
$791$	11.3986	+	15.6889i	0.405288	+	0.557832i
$792$	−66.2255	+	0.244617i	−2.35322	+	0.00869209i
$793$	−1.68339	+	1.68339i	−0.0597788	+	0.0597788i
$794$	−82.6228	+	17.5620i	−2.93217	+	0.623253i
$795$	−1.13503	−	0.835694i	−0.0402553	−	0.0296390i
$796$	53.6176	+	11.3968i	1.90042	+	0.403948i
$797$	36.2761	−	23.5580i	1.28497	−	0.834467i	0.292415	−	0.956292i	$-0.405541\pi$
$797$	36.2761	−	23.5580i	1.28497	−	0.834467i	0.992552	+	0.121825i	$0.0388745\pi$
$798$	−5.03976	+	65.5845i	−0.178406	+	2.32167i
$799$	4.33517	−	2.50291i	0.153367	−	0.0885467i
$800$	−37.4571	−	122.046i	−1.32431	−	4.31499i
$801$	−9.62272	−	14.6985i	−0.340002	−	0.519347i
$802$	7.25181	+	45.7861i	0.256070	+	1.61676i
$803$	33.4497	−	1.75302i	1.18041	−	0.0618629i
$804$	−39.7972	+	83.8346i	−1.40354	+	2.95662i
$805$	−0.557171	+	0.796635i	−0.0196377	+	0.0280777i
$806$	0.203547	−	0.183275i	0.00716965	−	0.00645559i
$807$	12.6223	+	6.82320i	0.444326	+	0.240188i
$808$	12.0654	−	18.5791i	0.424459	−	0.653609i
$809$	17.8268	−	12.9519i	0.626756	−	0.455365i	−0.228519	−	0.973540i	$-0.573388\pi$
$809$	17.8268	−	12.9519i	0.626756	−	0.455365i	0.855275	+	0.518175i	$0.173388\pi$
$810$	−1.50048	+	55.5997i	−0.0527215	+	1.95357i
$811$	−16.8937	−	12.2740i	−0.593218	−	0.430998i	0.250247	−	0.968182i	$-0.419488\pi$
$811$	−16.8937	−	12.2740i	−0.593218	−	0.430998i	−0.843465	+	0.537184i	$0.819488\pi$
$812$	46.0158	−	17.6638i	1.61484	−	0.619878i
$813$	15.6495	−	2.08971i	0.548853	−	0.0732893i
$814$	11.2139	+	25.1869i	0.393048	+	0.882800i
$815$	−4.09704	+	29.2663i	−0.143513	+	1.02516i
$816$	−87.5448	−	11.3610i	−3.06468	−	0.397716i
$817$	−13.4851	−	8.75733i	−0.471784	−	0.306380i
$818$	−36.3413	−	36.3413i	−1.27064	−	1.27064i
$819$	−1.73616	+	0.472082i	−0.0606662	+	0.0164959i
$820$	−11.9807	+	137.794i	−0.418382	+	4.81198i
$821$	−34.2891	−	30.8740i	−1.19670	−	1.07751i	−0.995184	−	0.0980242i	$-0.968748\pi$
$821$	−34.2891	−	30.8740i	−1.19670	−	1.07751i	−0.201512	−	0.979486i	$-0.564586\pi$
$822$	55.6671	−	65.4221i	1.94161	−	2.28186i
$823$	−0.267940	+	0.698007i	−0.00933979	+	0.0243310i	−0.938171	−	0.346172i	$-0.887481\pi$
$823$	−0.267940	+	0.698007i	−0.00933979	+	0.0243310i	0.928831	+	0.370503i	$0.120815\pi$
$824$	13.0593	−	22.6193i	0.454941	−	0.787981i
$825$	−4.70626	+	18.4198i	−0.163851	+	0.641294i
$826$	−11.6195	−	20.1255i	−0.404292	−	0.700255i
$827$	−32.5103	+	5.14912i	−1.13049	+	0.179052i	−0.693530	−	0.720428i	$-0.743946\pi$
$827$	−32.5103	+	5.14912i	−1.13049	+	0.179052i	−0.436962	+	0.899480i	$0.643946\pi$
$828$	−2.65913	+	1.94702i	−0.0924112	+	0.0676636i
$829$	32.1096	−	10.4331i	1.11521	−	0.362355i	0.307275	−	0.951621i	$-0.400583\pi$
$829$	32.1096	−	10.4331i	1.11521	−	0.362355i	0.807939	+	0.589266i	$0.200583\pi$
$830$	8.75639	+	70.9990i	0.303939	+	2.46441i
$831$	−18.5087	−	33.9392i	−0.642060	−	1.17734i
$832$	9.74498	−	2.61116i	0.337846	−	0.0905256i
$833$	−0.326398	+	6.22805i	−0.0113090	+	0.215789i
$834$	−42.9939	−	32.8644i	−1.48876	−	1.13800i
$835$	37.3131	+	1.28288i	1.29127	+	0.0443960i
$836$	−44.8028	+	61.6657i	−1.54954	+	2.13275i
$837$	1.88193	−	0.359592i	0.0650491	−	0.0124293i
$838$	0.841622	−	5.31380i	0.0290734	−	0.183562i
$839$	−1.73542	+	16.5114i	−0.0599132	+	0.570036i	0.922849	+	0.385162i	$0.125854\pi$
$839$	−1.73542	+	16.5114i	−0.0599132	+	0.570036i	−0.982762	+	0.184874i	$0.940812\pi$
$840$	86.8128	−	3.99783i	2.99532	−	0.137938i
$841$	1.42708	+	13.5778i	0.0492097	+	0.468199i
$842$	39.8487	+	2.08838i	1.37328	+	0.0719704i
$843$	−31.7457	+	0.889962i	−1.09338	+	0.0306519i
$844$	17.1705	+	80.7807i	0.591032	+	2.78059i
$845$	−6.51791	−	28.1630i	−0.224223	−	0.968835i
$846$	−12.5379	+	4.86606i	−0.431062	+	0.167299i
$847$	−6.26139	+	12.2887i	−0.215144	+	0.422244i
$848$	−4.67099	+	3.78249i	−0.160402	+	0.129891i
$849$	−7.13868	+	29.9786i	−0.244999	+	1.02886i
$850$	−15.9330	+	39.5581i	−0.546496	+	1.35683i
$851$	0.766755	+	0.442686i	0.0262840	+	0.0151751i
$852$	12.8070	+	0.984135i	0.438759	+	0.0337159i
$853$	−0.464024	−	8.85410i	−0.0158879	−	0.303158i	−0.995003	−	0.0998497i	$-0.968164\pi$
$853$	−0.464024	−	8.85410i	−0.0158879	−	0.303158i	0.979115	−	0.203309i	$-0.0651695\pi$
$854$	16.8803	+	51.9522i	0.577632	+	1.77777i
$855$	32.6594	+	25.2944i	1.11693	+	0.865052i
$856$	20.9519	−	64.4834i	0.716123	−	2.20400i
$857$	−7.61666	−	2.04088i	−0.260180	−	0.0697151i	0.126371	−	0.991983i	$-0.459667\pi$
$857$	−7.61666	−	2.04088i	−0.260180	−	0.0697151i	−0.386551	+	0.922268i	$0.626334\pi$
$858$	−2.70959	−	0.797176i	−0.0925038	−	0.0272151i
$859$	2.57716	−	0.270870i	0.0879315	−	0.00924198i	−0.0604605	−	0.998171i	$-0.519257\pi$
$859$	2.57716	−	0.270870i	0.0879315	−	0.00924198i	0.148392	+	0.988929i	$0.452590\pi$
$860$	−14.4156	+	29.5967i	−0.491567	+	1.00924i
$861$	−39.9933	−	14.0793i	−1.36297	−	0.479821i
$862$	32.7161	+	85.2283i	1.11431	+	2.90289i
$863$	−39.1295	−	6.19750i	−1.33198	−	0.210965i	−0.550470	−	0.834855i	$-0.685552\pi$
$863$	−39.1295	−	6.19750i	−1.33198	−	0.210965i	−0.781513	+	0.623889i	$0.785552\pi$
$864$	127.417	+	36.9759i	4.33480	+	1.25794i
$865$	−39.1634	+	32.8980i	−1.33160	+	1.11857i
$866$	2.27330	−	5.10592i	0.0772499	−	0.173506i
$867$	−8.93080	−	9.37636i	−0.303306	−	0.318438i
$868$	−1.20072	−	4.48116i	−0.0407552	−	0.152100i
$869$	12.8293	+	14.2484i	0.435204	+	0.483343i
$870$	8.97850	−	40.9616i	0.304400	−	1.38873i
$871$	−1.70892	+	1.89795i	−0.0579047	+	0.0643097i
$872$	−44.8370	−	22.8456i	−1.51837	−	0.773649i
$873$	10.0050	+	3.21002i	0.338619	+	0.108643i
$874$			3.31599i			0.112165i
$875$	5.14750	−	24.4109i	0.174017	−	0.825240i
$876$	−144.960	−	34.5187i	−4.89773	−	1.16628i
$877$	33.2612	+	12.7678i	1.12315	+	0.431137i	0.847858	−	0.530223i	$-0.177892\pi$
$877$	33.2612	+	12.7678i	1.12315	+	0.431137i	0.275293	+	0.961360i	$0.411225\pi$
$878$	35.7320	+	55.0225i	1.20590	+	1.85692i
$879$	−0.689781	−	8.56229i	−0.0232657	−	0.288799i
$880$	70.9264	+	39.2652i	2.39093	+	1.32363i
$881$	26.8281	+	8.71699i	0.903862	+	0.293683i	0.723830	−	0.689978i	$-0.242380\pi$
$881$	26.8281	+	8.71699i	0.903862	+	0.293683i	0.180032	+	0.983661i	$0.442380\pi$
$882$	3.42316	−	16.4024i	0.115264	−	0.552296i
$883$	1.81169	+	3.55565i	0.0609684	+	0.119657i	0.919480	−	0.393137i	$-0.128610\pi$
$883$	1.81169	+	3.55565i	0.0609684	+	0.119657i	−0.858511	+	0.512794i	$0.828610\pi$
$884$	−4.27247	−	1.90223i	−0.143699	−	0.0639788i
$885$	−14.5691	−	0.856207i	−0.489735	−	0.0287811i
$886$	−23.8661	+	10.6259i	−0.801796	+	0.356983i
$887$	9.18533	+	7.43813i	0.308413	+	0.249748i	0.771013	−	0.636819i	$-0.219750\pi$
$887$	9.18533	+	7.43813i	0.308413	+	0.249748i	−0.462600	+	0.886567i	$0.653083\pi$
$888$	−10.4757	−	78.4513i	−0.351543	−	2.63265i
$889$	−32.7824	−	3.44557i	−1.09949	−	0.115561i
$890$	2.54397	+	36.1011i	0.0852741	+	1.21011i
$891$	−13.3283	−	14.5845i	−0.446516	−	0.488599i
$892$	−133.025	+	67.7796i	−4.45401	+	2.26943i
$893$	−2.58526	+	9.64832i	−0.0865124	+	0.322869i
$894$	1.44132	−	59.2213i	0.0482050	−	1.98066i
$895$	−8.45253	−	24.5050i	−0.282537	−	0.819113i
$896$	24.4387	−	114.975i	0.816441	−	3.84105i
$897$	−0.0854422	+	0.0304344i	−0.00285283	+	0.00101617i
$898$	−19.2141	−	23.7275i	−0.641184	−	0.791797i
$899$	−1.44453			−0.0481778
$900$	43.2140	−	72.7036i	1.44047	−	2.42345i
$901$	1.12312			0.0374165
$902$	−41.8871	−	51.7263i	−1.39469	−	1.72230i
$903$	−7.68581	−	6.53979i	−0.255768	−	0.217631i
$904$	18.1701	−	85.4837i	0.604329	−	2.84314i
$905$	−5.93582	+	19.4526i	−0.197313	+	0.646628i
$906$	49.5042	+	30.2106i	1.64467	+	1.00368i
$907$	−12.8244	+	47.8611i	−0.425826	+	1.58920i	0.336287	+	0.941759i	$0.390829\pi$
$907$	−12.8244	+	47.8611i	−0.425826	+	1.58920i	−0.762113	+	0.647444i	$0.775838\pi$
$908$	−0.264607	+	0.134824i	−0.00878131	+	0.00447430i
$909$	6.52372	−	1.05797i	0.216378	−	0.0350907i
$910$	3.59672	+	0.894707i	0.119230	+	0.0296592i
$911$	55.0061	+	5.78137i	1.82243	+	0.191545i	0.953094	−	0.302673i	$-0.0978791\pi$
$911$	55.0061	+	5.78137i	1.82243	+	0.191545i	0.869338	+	0.494219i	$0.164546\pi$
$912$	139.553	−	107.493i	4.62106	−	3.55944i
$913$	−19.7483	−	15.9919i	−0.653574	−	0.529254i
$914$	43.8589	−	19.5272i	1.45072	−	0.645904i
$915$	33.0796	+	9.08887i	1.09358	+	0.300469i
$916$	103.433	+	46.0515i	3.41753	+	1.52158i
$917$	−3.37443	−	6.62269i	−0.111434	−	0.218701i
$918$	−25.3047	−	36.3850i	−0.835180	−	1.20089i
$919$	−20.9743	−	6.81495i	−0.691877	−	0.224805i	−0.0580894	−	0.998311i	$-0.518501\pi$
$919$	−20.9743	−	6.81495i	−0.691877	−	0.224805i	−0.633788	+	0.773507i	$0.718501\pi$
$920$	4.34809	−	0.536255i	0.143352	−	0.0176798i
$921$	−43.4301	+	29.9670i	−1.43107	+	0.987445i
$922$	−60.6904	−	93.4550i	−1.99873	−	3.07778i
$923$	0.330016	+	0.126681i	0.0108626	+	0.00416977i
$924$	−32.8662	+	34.7621i	−1.08122	+	1.14359i
$925$	−22.5545	−	2.74469i	−0.741588	−	0.0902449i
$926$			1.10973i			0.0364679i
$927$	7.61569	−	1.64819i	0.250132	−	0.0541336i
$928$	−89.1252	−	45.4115i	−2.92568	−	1.49071i
$929$	−21.0919	+	23.4249i	−0.692001	+	0.768545i	−0.982081	−	0.188457i	$-0.939651\pi$
$929$	−21.0919	+	23.4249i	−0.692001	+	0.768545i	0.290080	+	0.957002i	$0.406318\pi$
$930$	−3.74593	−	1.24344i	−0.122834	−	0.0407741i
$931$	−8.32703	−	9.24811i	−0.272907	−	0.303094i
$932$	−41.8744	−	156.277i	−1.37164	−	5.11903i
$933$	−37.9772	+	9.19174i	−1.24332	+	0.300924i
$934$	−13.8653	+	31.1420i	−0.453687	+	1.01900i
$935$	−5.68241	−	14.0427i	−0.185835	−	0.459244i
$936$	6.81635	+	4.39088i	0.222799	+	0.143520i
$937$	37.8209	+	5.99024i	1.23556	+	0.195693i	0.739834	−	0.672789i	$-0.234904\pi$
$937$	37.8209	+	5.99024i	1.23556	+	0.195693i	0.495721	+	0.868482i	$0.334904\pi$
$938$	21.0010	+	54.7095i	0.685708	+	1.78633i
$939$	−4.42807	−	23.6479i	−0.144505	−	0.771721i
$940$	20.2535	+	2.83532i	0.660596	+	0.0924779i
$941$	−35.1239	+	3.69167i	−1.14501	+	0.120345i	−0.657975	−	0.753039i	$-0.728587\pi$
$941$	−35.1239	+	3.69167i	−1.14501	+	0.120345i	−0.487031	+	0.873384i	$0.661920\pi$
$942$	20.5674	−	19.5901i	0.670123	−	0.638280i
$943$	−2.06459	−	0.553205i	−0.0672323	−	0.0180148i
$944$	−19.2312	+	59.1876i	−0.625923	+	1.92639i
$945$	18.2842	+	18.3813i	0.594784	+	0.597942i
$946$	−4.89547	−	15.0667i	−0.159165	−	0.489861i
$947$	0.896495	+	17.1061i	0.0291322	+	0.555875i	0.973739	+	0.227669i	$0.0731105\pi$
$947$	0.896495	+	17.1061i	0.0291322	+	0.555875i	−0.944606	+	0.328206i	$0.893556\pi$
$948$	−36.8629	−	76.9188i	−1.19725	−	2.49821i
$949$	−3.55151	−	2.05047i	−0.115287	−	0.0665609i
$950$	−33.3343	−	78.2961i	−1.08151	−	2.54026i
$951$	35.4187	+	33.4870i	1.14853	+	1.08589i
$952$	−53.8156	+	43.5790i	−1.74417	+	1.41240i
$953$	9.56971	−	18.7816i	0.309993	−	0.608396i	−0.682473	−	0.730910i	$-0.739096\pi$
$953$	9.56971	−	18.7816i	0.309993	−	0.608396i	0.992467	+	0.122514i	$0.0390957\pi$
$954$	−2.98204	−	0.461024i	−0.0965470	−	0.0149262i
$955$	9.70057	−	22.8874i	0.313903	−	0.740618i
$956$	8.02646	+	37.7615i	0.259594	+	1.22130i
$957$	7.80648	+	12.6864i	0.252348	+	0.410092i
$958$	13.5858	+	0.712002i	0.438937	+	0.0230037i
$959$	−4.18545	−	39.8219i	−0.135155	−	1.28592i
$960$	−102.145	−	103.448i	−3.29671	−	3.33878i
$961$	3.22617	−	30.6950i	0.104070	−	0.990160i
$962$	0.528046	−	3.33395i	0.0170249	−	0.107491i
$963$	18.4482	−	8.29545i	0.594485	−	0.267317i
$964$	−8.30715	+	11.4338i	−0.267555	+	0.368258i
$965$	−9.10440	−	31.6864i	−0.293081	−	1.02002i
$966$	−0.267838	+	2.06388i	−0.00861753	+	0.0664041i
$967$	−1.60218	+	30.5714i	−0.0515226	+	0.983110i	0.843511	+	0.537111i	$0.180485\pi$
$967$	−1.60218	+	30.5714i	−0.0515226	+	0.983110i	−0.895034	+	0.445998i	$0.852849\pi$
$968$	60.0362	−	16.0866i	1.92964	−	0.517044i
$969$	−32.9063	−	0.800871i	−1.05710	−	0.0257277i
$970$	−14.7705	−	15.8223i	−0.474251	−	0.508024i
$971$	8.91233	−	2.89579i	0.286010	−	0.0929303i	−0.162499	−	0.986709i	$-0.551955\pi$
$971$	8.91233	−	2.89579i	0.286010	−	0.0929303i	0.448509	+	0.893778i	$0.351955\pi$
$972$	38.5707	+	78.9799i	1.23716	+	2.53328i
$973$	−24.9149	+	3.94613i	−0.798735	+	0.126507i
$974$	21.5782	+	37.3746i	0.691411	+	1.19756i
$975$	1.71149	−	1.57752i	0.0548116	−	0.0505212i
$976$	73.1437	−	126.689i	2.34127	−	4.05520i
$977$	−17.4179	+	45.3752i	−0.557248	+	1.45168i	0.308512	+	0.951221i	$0.400169\pi$
$977$	−17.4179	+	45.3752i	−0.557248	+	1.45168i	−0.865760	+	0.500460i	$0.833164\pi$
$978$	21.2283	+	59.5968i	0.678806	+	1.90570i
$979$	−9.55359	−	8.60209i	−0.305334	−	0.274924i
$980$	−16.7055	+	19.2384i	−0.533637	+	0.614548i
$981$	−3.93908	−	14.4866i	−0.125765	−	0.462521i
$982$	−50.8191	−	50.8191i	−1.62170	−	1.62170i
$983$	17.0656	+	11.0825i	0.544307	+	0.353477i	0.787319	−	0.616546i	$-0.211469\pi$
$983$	17.0656	+	11.0825i	0.544307	+	0.353477i	−0.243011	+	0.970023i	$0.578135\pi$
$984$	73.4469	+	176.394i	2.34140	+	5.62324i
$985$	−6.55421	−	3.19233i	−0.208835	−	0.101716i
$986$	13.5907	+	30.5252i	0.432816	+	0.972121i
$987$	−2.38838	+	5.79631i	−0.0760230	+	0.184499i
$988$	8.71230	−	3.34434i	0.277175	−	0.106398i
$989$	−0.411577	−	0.299028i	−0.0130874	−	0.00950854i
$990$	9.32327	+	39.6178i	0.296313	+	1.25914i
$991$	30.5820	−	22.2191i	0.971468	−	0.705813i	0.0156825	−	0.999877i	$-0.495008\pi$
$991$	30.5820	−	22.2191i	0.971468	−	0.705813i	0.955786	+	0.294064i	$0.0950079\pi$
$992$	−5.12766	+	7.89591i	−0.162803	+	0.250695i
$993$	1.16545	+	41.5725i	0.0369844	+	1.31926i
$994$	6.02776	−	5.42742i	0.191189	−	0.172147i
$995$	−0.391092	−	21.7348i	−0.0123985	−	0.689041i
$996$	64.2032	+	93.0476i	2.03435	+	2.94832i
$997$	−49.3077	+	2.58411i	−1.56159	+	0.0818395i	−0.813424	−	0.581672i	$-0.802399\pi$
$997$	−49.3077	+	2.58411i	−1.56159	+	0.0818395i	−0.748166	+	0.663511i	$0.769065\pi$
$998$	0.856729	+	5.40918i	0.0271193	+	0.171224i
$999$	15.2352	−	18.0396i	0.482021	−	0.570748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.212.28	yes	448
3.2	odd	2		675.2.bd.a.287.1		448
9.2	odd	6	inner	225.2.w.a.137.1	yes	448
9.7	even	3		675.2.bd.a.62.28		448
25.23	odd	20	inner	225.2.w.a.23.1	✓	448
75.23	even	20		675.2.bd.a.98.28		448
225.173	even	60	inner	225.2.w.a.173.28	yes	448
225.223	odd	60		675.2.bd.a.548.1		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.23.1	✓	448	25.23	odd	20	inner
225.2.w.a.137.1	yes	448	9.2	odd	6	inner
225.2.w.a.173.28	yes	448	225.173	even	60	inner
225.2.w.a.212.28	yes	448	1.1	even	1	trivial
675.2.bd.a.62.28		448	9.7	even	3
675.2.bd.a.98.28		448	75.23	even	20
675.2.bd.a.287.1		448	3.2	odd	2
675.2.bd.a.548.1		448	225.223	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73930 + 2.14786i) q^{2} +(0.312495 - 1.70363i) q^{3} +(-1.17230 + 5.51525i) q^{4} +(2.23571 - 0.0402288i) q^{5} +(4.20267 - 2.29193i) q^{6} +(0.577528 - 2.15536i) q^{7} +(-8.95988 + 4.56529i) q^{8} +(-2.80469 - 1.06475i) q^{9} +O(q^{10})\)	\(q+(1.73930 + 2.14786i) q^{2} +(0.312495 - 1.70363i) q^{3} +(-1.17230 + 5.51525i) q^{4} +(2.23571 - 0.0402288i) q^{5} +(4.20267 - 2.29193i) q^{6} +(0.577528 - 2.15536i) q^{7} +(-8.95988 + 4.56529i) q^{8} +(-2.80469 - 1.06475i) q^{9} +(3.97497 + 4.73201i) q^{10} +(-2.18323 - 0.229467i) q^{11} +(9.02960 + 3.72066i) q^{12} +(0.208873 + 0.169142i) q^{13} +(5.63391 - 2.50838i) q^{14} +(0.630113 - 3.82138i) q^{15} +(-15.0875 - 6.71741i) q^{16} +(1.40105 + 2.74972i) q^{17} +(-2.59127 - 7.87601i) q^{18} +(-5.85661 - 1.90293i) q^{19} +(-2.39905 + 12.3776i) q^{20} +(-3.49146 - 1.65743i) q^{21} +(-3.30444 - 5.08839i) q^{22} +(-0.181895 - 0.0698231i) q^{23} +(4.97763 + 16.6909i) q^{24} +(4.99676 - 0.179880i) q^{25} +0.742819i q^{26} +(-2.69039 + 4.44542i) q^{27} +(11.2103 + 5.71195i) q^{28} +(2.62137 - 2.91133i) q^{29} +(9.30374 - 5.29314i) q^{30} +(-0.246729 - 0.274020i) q^{31} +(-6.60842 - 24.6630i) q^{32} +(-1.07318 + 3.64771i) q^{33} +(-3.46916 + 7.79186i) q^{34} +(1.20447 - 4.84199i) q^{35} +(9.16032 - 14.2204i) q^{36} +(-4.48824 - 0.710867i) q^{37} +(-6.09919 - 15.8889i) q^{38} +(0.353427 - 0.302986i) q^{39} +(-19.8480 + 10.5671i) q^{40} +(10.9102 - 1.14671i) q^{41} +(-2.51277 - 10.3819i) q^{42} +(2.52213 + 0.675802i) q^{43} +(3.82498 - 11.7721i) q^{44} +(-6.31330 - 2.26764i) q^{45} +(-0.166401 - 0.512129i) q^{46} +(-0.0848923 - 1.61984i) q^{47} +(-16.1587 + 23.6044i) q^{48} +(1.75013 + 1.01044i) q^{49} +(9.07723 + 10.4195i) q^{50} +(5.12232 - 1.52760i) q^{51} +(-1.17772 + 0.953703i) q^{52} +(0.165221 - 0.324264i) q^{53} +(-14.2275 + 1.95335i) q^{54} +(-4.89030 - 0.425192i) q^{55} +(4.66527 + 21.9484i) q^{56} +(-5.07204 + 9.38282i) q^{57} +(10.8125 + 0.566658i) q^{58} +(-0.393886 - 3.74758i) q^{59} +(20.3372 + 7.95505i) q^{60} +(-0.925876 + 8.80912i) q^{61} +(0.159421 - 1.00654i) q^{62} +(-3.91471 + 5.43021i) q^{63} +(22.0636 - 30.3679i) q^{64} +(0.473784 + 0.369750i) q^{65} +(-9.70134 + 4.03943i) q^{66} +(-0.497315 + 9.48934i) q^{67} +(-16.8079 + 4.50365i) q^{68} +(-0.175794 + 0.288063i) q^{69} +(12.4949 - 5.83464i) q^{70} +(1.25086 - 0.406430i) q^{71} +(29.9906 - 3.26418i) q^{72} +(-15.0703 + 2.38690i) q^{73} +(-6.27956 - 10.8765i) q^{74} +(1.25502 - 8.56883i) q^{75} +(17.3608 - 30.0699i) q^{76} +(-1.75546 + 4.57313i) q^{77} +(1.26549 + 0.232128i) q^{78} +(-6.49052 - 5.84409i) q^{79} +(-34.0015 - 14.4112i) q^{80} +(6.73261 + 5.97260i) q^{81} +(21.4392 + 21.4392i) q^{82} +(9.70808 + 6.30450i) q^{83} +(13.2342 - 17.3133i) q^{84} +(3.24296 + 6.09121i) q^{85} +(2.93521 + 6.59260i) q^{86} +(-4.14065 - 5.37562i) q^{87} +(20.6091 - 7.91109i) q^{88} +(4.73767 + 3.44212i) q^{89} +(-6.11016 - 17.5042i) q^{90} +(0.485193 - 0.352513i) q^{91} +(0.598328 - 0.921345i) q^{92} +(-0.543930 + 0.334704i) q^{93} +(3.33154 - 2.99973i) q^{94} +(-13.1702 - 4.01878i) q^{95} +(-44.0816 + 3.55123i) q^{96} +(-3.49765 + 0.183304i) q^{97} +(0.873726 + 5.51649i) q^{98} +(5.87897 + 2.96818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

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