LMFDB - Embedded newform 392.2.z.a.109.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.25
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.168780 + 1.40411i) q^{2} +(0.0286441 + 0.190041i) q^{3} +(-1.94303 - 0.473969i) q^{4} +(3.07037 + 1.20503i) q^{5} +(-0.271672 + 0.00814427i) q^{6} +(0.384038 - 2.61773i) q^{7} +(0.993446 - 2.64822i) q^{8} +(2.83142 - 0.873378i) q^{9} +O(q^{10})$	\(q+(-0.168780 + 1.40411i) q^{2} +(0.0286441 + 0.190041i) q^{3} +(-1.94303 - 0.473969i) q^{4} +(3.07037 + 1.20503i) q^{5} +(-0.271672 + 0.00814427i) q^{6} +(0.384038 - 2.61773i) q^{7} +(0.993446 - 2.64822i) q^{8} +(2.83142 - 0.873378i) q^{9} +(-2.21021 + 4.10774i) q^{10} +(0.799625 - 2.59232i) q^{11} +(0.0344173 - 0.382831i) q^{12} +(2.39344 - 0.546288i) q^{13} +(3.61075 + 0.981049i) q^{14} +(-0.141057 + 0.618013i) q^{15} +(3.55071 + 1.84187i) q^{16} +(-4.97960 + 3.39504i) q^{17} +(0.748429 + 4.12303i) q^{18} +(2.12167 - 1.22495i) q^{19} +(-5.39466 - 3.79667i) q^{20} +(0.508477 - 0.00199956i) q^{21} +(3.50493 + 1.56029i) q^{22} +(-4.24195 - 2.89212i) q^{23} +(0.531727 + 0.112940i) q^{24} +(4.30980 + 3.99891i) q^{25} +(0.363082 + 3.45285i) q^{26} +(0.497242 + 1.03253i) q^{27} +(-1.98692 + 4.90430i) q^{28} +(-2.12183 + 4.40602i) q^{29} +(-0.843948 - 0.302367i) q^{30} +(-2.86186 + 4.95689i) q^{31} +(-3.18546 + 4.67470i) q^{32} +(0.515551 + 0.0777069i) q^{33} +(-3.92653 - 7.56490i) q^{34} +(4.33358 - 7.57462i) q^{35} +(-5.91549 + 0.354992i) q^{36} +(3.51280 - 0.263248i) q^{37} +(1.36186 + 3.18579i) q^{38} +(0.172375 + 0.439205i) q^{39} +(6.24143 - 6.93388i) q^{40} +(-1.26219 - 1.58274i) q^{41} +(-0.0830129 + 0.714293i) q^{42} +(8.29503 + 6.61506i) q^{43} +(-2.78237 + 4.65795i) q^{44} +(9.74596 + 0.730359i) q^{45} +(4.77679 - 5.46802i) q^{46} +(-4.91600 + 4.56138i) q^{47} +(-0.248324 + 0.727539i) q^{48} +(-6.70503 - 2.01061i) q^{49} +(-6.34230 + 5.37648i) q^{50} +(-0.787832 - 0.849081i) q^{51} +(-4.90945 - 0.0729655i) q^{52} +(-11.7885 - 0.883424i) q^{53} +(-1.53371 + 0.523910i) q^{54} +(5.57897 - 6.99580i) q^{55} +(-6.55080 - 3.61759i) q^{56} +(0.293563 + 0.368116i) q^{57} +(-5.82840 - 3.72292i) q^{58} +(8.66453 - 3.40058i) q^{59} +(0.566997 - 1.13396i) q^{60} +(-2.16600 + 0.162320i) q^{61} +(-6.47697 - 4.85498i) q^{62} +(-1.19890 - 7.74731i) q^{63} +(-6.02613 - 5.26172i) q^{64} +(8.00705 + 1.20687i) q^{65} +(-0.196123 + 0.710774i) q^{66} +(-4.07561 - 2.35306i) q^{67} +(11.2846 - 4.23647i) q^{68} +(0.428114 - 0.888987i) q^{69} +(9.90415 + 7.36325i) q^{70} +(-7.32647 + 3.52824i) q^{71} +(0.499967 - 8.36588i) q^{72} +(1.71039 + 1.58701i) q^{73} +(-0.223261 + 4.97678i) q^{74} +(-0.636507 + 0.933584i) q^{75} +(-4.70304 + 1.37450i) q^{76} +(-6.47891 - 3.08875i) q^{77} +(-0.645783 + 0.167904i) q^{78} +(-4.47482 - 7.75061i) q^{79} +(8.68247 + 9.93392i) q^{80} +(7.16261 - 4.88339i) q^{81} +(2.43537 - 1.50512i) q^{82} +(-3.55762 - 0.812003i) q^{83} +(-0.988932 - 0.237117i) q^{84} +(-19.3803 + 4.42343i) q^{85} +(-10.6883 + 10.5306i) q^{86} +(-0.898102 - 0.277028i) q^{87} +(-6.07065 - 4.69291i) q^{88} +(14.8093 - 4.56807i) q^{89} +(-2.67042 + 13.5611i) q^{90} +(-0.510862 - 6.47519i) q^{91} +(6.87146 + 7.63001i) q^{92} +(-1.02399 - 0.401885i) q^{93} +(-5.57494 - 7.67245i) q^{94} +(7.99040 - 1.20436i) q^{95} +(-0.979629 - 0.471467i) q^{96} +8.27599 q^{97} +(3.95479 - 9.07522i) q^{98} -8.03833i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−0.168780	+	1.40411i	−0.119345	+	0.992853i
$2$	−0.168780	+	1.40411i	−0.119345	+	0.992853i
$3$	0.0286441	+	0.190041i	0.0165377	+	0.109720i	0.995577	−	0.0939526i	$-0.0299502\pi$
$3$	0.0286441	+	0.190041i	0.0165377	+	0.109720i	−0.979039	+	0.203673i	$0.934712\pi$
$4$	−1.94303	−	0.473969i	−0.971513	−	0.236984i
$5$	3.07037	+	1.20503i	1.37311	+	0.538906i	0.933272	−	0.359171i	$-0.116940\pi$
$5$	3.07037	+	1.20503i	1.37311	+	0.538906i	0.439838	+	0.898077i	$0.355036\pi$
$6$	−0.271672	+	0.00814427i	−0.110910	+	0.00332489i
$7$	0.384038	−	2.61773i	0.145153	−	0.989409i
$7$	0.384038	−	2.61773i	0.145153	−	0.989409i
$8$	0.993446	−	2.64822i	0.351236	−	0.936287i
$9$	2.83142	−	0.873378i	0.943808	−	0.291126i
$10$	−2.21021	+	4.10774i	−0.698929	+	1.29898i
$11$	0.799625	−	2.59232i	0.241096	−	0.781614i	−0.751455	−	0.659784i	$-0.770648\pi$
$11$	0.799625	−	2.59232i	0.241096	−	0.781614i	0.992551	−	0.121829i	$-0.0388761\pi$
$12$	0.0344173	−	0.382831i	0.00993542	−	0.110514i
$13$	2.39344	−	0.546288i	0.663822	−	0.151513i	0.122683	−	0.992446i	$-0.460850\pi$
$13$	2.39344	−	0.546288i	0.663822	−	0.151513i	0.541139	+	0.840933i	$0.317993\pi$
$14$	3.61075	+	0.981049i	0.965015	+	0.262196i
$15$	−0.141057	+	0.618013i	−0.0364209	+	0.159570i
$16$	3.55071	+	1.84187i	0.887677	+	0.460467i
$17$	−4.97960	+	3.39504i	−1.20773	+	0.823417i	−0.988346	−	0.152221i	$-0.951357\pi$
$17$	−4.97960	+	3.39504i	−1.20773	+	0.823417i	−0.219385	+	0.975638i	$0.570405\pi$
$18$	0.748429	+	4.12303i	0.176407	+	0.971807i
$19$	2.12167	−	1.22495i	0.486744	−	0.281022i	−0.236479	−	0.971637i	$-0.575993\pi$
$19$	2.12167	−	1.22495i	0.486744	−	0.281022i	0.723223	+	0.690615i	$0.242660\pi$
$20$	−5.39466	−	3.79667i	−1.20628	−	0.848960i
$21$	0.508477	−	0.00199956i	0.110959	−	0.000436339i
$22$	3.50493	+	1.56029i	0.747254	+	0.332655i
$23$	−4.24195	−	2.89212i	−0.884509	−	0.603048i	0.0335742	−	0.999436i	$-0.489311\pi$
$23$	−4.24195	−	2.89212i	−0.884509	−	0.603048i	−0.918083	+	0.396388i	$0.870263\pi$
$24$	0.531727	+	0.112940i	0.108538	+	0.0230537i
$25$	4.30980	+	3.99891i	0.861960	+	0.799782i
$26$	0.363082	+	3.45285i	0.0712062	+	0.677160i
$27$	0.497242	+	1.03253i	0.0956944	+	0.198711i
$28$	−1.98692	+	4.90430i	−0.375492	+	0.926826i
$29$	−2.12183	+	4.40602i	−0.394013	+	0.818177i	0.605733	+	0.795668i	$0.292880\pi$
$29$	−2.12183	+	4.40602i	−0.394013	+	0.818177i	−0.999747	+	0.0225095i	$0.992834\pi$
$30$	−0.843948	−	0.302367i	−0.154083	−	0.0552045i
$31$	−2.86186	+	4.95689i	−0.514005	+	0.890283i	0.485863	+	0.874035i	$0.338505\pi$
$31$	−2.86186	+	4.95689i	−0.514005	+	0.890283i	−0.999868	+	0.0162480i	$0.994828\pi$
$32$	−3.18546	+	4.67470i	−0.563116	+	0.826378i
$33$	0.515551	+	0.0777069i	0.0897460	+	0.0135270i
$34$	−3.92653	−	7.56490i	−0.673395	−	1.29737i
$35$	4.33358	−	7.57462i	0.732509	−	1.28034i
$36$	−5.91549	+	0.354992i	−0.985914	+	0.0591653i
$37$	3.51280	−	0.263248i	0.577501	−	0.0432777i	0.217222	−	0.976122i	$-0.430300\pi$
$37$	3.51280	−	0.263248i	0.577501	−	0.0432777i	0.360279	+	0.932845i	$0.382681\pi$
$38$	1.36186	+	3.18579i	0.220923	+	0.516804i
$39$	0.172375	+	0.439205i	0.0276021	+	0.0703290i
$40$	6.24143	−	6.93388i	0.986857	−	1.09634i
$41$	−1.26219	−	1.58274i	−0.197121	−	0.247183i	0.673440	−	0.739242i	$-0.264816\pi$
$41$	−1.26219	−	1.58274i	−0.197121	−	0.247183i	−0.870562	+	0.492059i	$0.836244\pi$
$42$	−0.0830129	+	0.714293i	−0.0128092	+	0.110218i
$43$	8.29503	+	6.61506i	1.26498	+	1.00879i	0.998995	+	0.0448107i	$0.0142685\pi$
$43$	8.29503	+	6.61506i	1.26498	+	1.00879i	0.265985	+	0.963977i	$0.414303\pi$
$44$	−2.78237	+	4.65795i	−0.419458	+	0.702212i
$45$	9.74596	+	0.730359i	1.45284	+	0.108875i
$46$	4.77679	−	5.46802i	0.704300	−	0.806216i
$47$	−4.91600	+	4.56138i	−0.717072	+	0.665345i	−0.951801	−	0.306715i	$-0.900770\pi$
$47$	−4.91600	+	4.56138i	−0.717072	+	0.665345i	0.234730	+	0.972061i	$0.424580\pi$
$48$	−0.248324	+	0.727539i	−0.0358425	+	0.105011i
$49$	−6.70503	−	2.01061i	−0.957861	−	0.287231i
$50$	−6.34230	+	5.37648i	−0.896937	+	0.760350i
$51$	−0.787832	−	0.849081i	−0.110319	−	0.118895i
$52$	−4.90945	−	0.0729655i	−0.680818	−	0.0101185i
$53$	−11.7885	−	0.883424i	−1.61927	−	0.121348i	−0.766009	−	0.642830i	$-0.777760\pi$
$53$	−11.7885	−	0.883424i	−1.61927	−	0.121348i	−0.853262	+	0.521483i	$0.825379\pi$
$54$	−1.53371	+	0.523910i	−0.208712	+	0.0712952i
$55$	5.57897	−	6.99580i	0.752268	−	0.943314i
$56$	−6.55080	−	3.61759i	−0.875388	−	0.483421i
$57$	0.293563	+	0.368116i	0.0388834	+	0.0487582i
$58$	−5.82840	−	3.72292i	−0.765306	−	0.488843i
$59$	8.66453	−	3.40058i	1.12803	−	0.442717i	0.273368	−	0.961910i	$-0.411862\pi$
$59$	8.66453	−	3.40058i	1.12803	−	0.442717i	0.854657	+	0.519192i	$0.173767\pi$
$60$	0.566997	−	1.13396i	0.0731990	−	0.146393i
$61$	−2.16600	+	0.162320i	−0.277328	+	0.0207829i	−0.212668	−	0.977124i	$-0.568215\pi$
$61$	−2.16600	+	0.162320i	−0.277328	+	0.0207829i	−0.0646601	+	0.997907i	$0.520596\pi$
$62$	−6.47697	−	4.85498i	−0.822576	−	0.616583i
$63$	−1.19890	−	7.74731i	−0.151047	−	0.976070i
$64$	−6.02613	−	5.26172i	−0.753266	−	0.657715i
$65$	8.00705	+	1.20687i	0.993152	+	0.149694i
$66$	−0.196123	+	0.710774i	−0.0241411	+	0.0874902i
$67$	−4.07561	−	2.35306i	−0.497915	−	0.287471i	0.229937	−	0.973206i	$-0.426148\pi$
$67$	−4.07561	−	2.35306i	−0.497915	−	0.287471i	−0.727852	+	0.685734i	$0.759481\pi$
$68$	11.2846	−	4.23647i	1.36846	−	0.513747i
$69$	0.428114	−	0.888987i	0.0515388	−	0.107022i
$70$	9.90415	+	7.36325i	1.18377	+	0.880077i
$71$	−7.32647	+	3.52824i	−0.869491	+	0.418725i	−0.814775	−	0.579777i	$-0.803140\pi$
$71$	−7.32647	+	3.52824i	−0.869491	+	0.418725i	−0.0547162	+	0.998502i	$0.517425\pi$
$72$	0.499967	−	8.36588i	0.0589217	−	0.985929i
$73$	1.71039	+	1.58701i	0.200186	+	0.185746i	0.773896	−	0.633313i	$-0.218306\pi$
$73$	1.71039	+	1.58701i	0.200186	+	0.185746i	−0.573709	+	0.819059i	$0.694496\pi$
$74$	−0.223261	+	4.97678i	−0.0259536	+	0.578539i
$75$	−0.636507	+	0.933584i	−0.0734975	+	0.107801i
$76$	−4.70304	+	1.37450i	−0.539476	+	0.157666i
$77$	−6.47891	−	3.08875i	−0.738340	−	0.351996i
$78$	−0.645783	+	0.167904i	−0.0731205	+	0.0190114i
$79$	−4.47482	−	7.75061i	−0.503456	−	0.872012i	−0.999992	−	0.00399575i	$-0.998728\pi$
$79$	−4.47482	−	7.75061i	−0.503456	−	0.872012i	0.496536	−	0.868016i	$-0.334605\pi$
$80$	8.68247	+	9.93392i	0.970730	+	1.11065i
$81$	7.16261	−	4.88339i	0.795846	−	0.542599i
$82$	2.43537	−	1.50512i	0.268941	−	0.166213i
$83$	−3.55762	−	0.812003i	−0.390499	−	0.0891289i	0.0227631	−	0.999741i	$-0.492754\pi$
$83$	−3.55762	−	0.812003i	−0.390499	−	0.0891289i	−0.413262	+	0.910612i	$0.635611\pi$
$84$	−0.988932	−	0.237117i	−0.107901	−	0.0258716i
$85$	−19.3803	+	4.42343i	−2.10209	+	0.479789i
$86$	−10.6883	+	10.5306i	−1.15255	+	1.13555i
$87$	−0.898102	−	0.277028i	−0.0962867	−	0.0297005i
$88$	−6.07065	−	4.69291i	−0.647133	−	0.500266i
$89$	14.8093	−	4.56807i	1.56978	−	0.484214i	0.616771	−	0.787142i	$-0.288440\pi$
$89$	14.8093	−	4.56807i	1.56978	−	0.484214i	0.953013	+	0.302928i	$0.0979642\pi$
$90$	−2.67042	+	13.5611i	−0.281487	+	1.42946i
$91$	−0.510862	−	6.47519i	−0.0535529	−	0.678784i
$92$	6.87146	+	7.63001i	0.716399	+	0.795484i
$93$	−1.02399	−	0.401885i	−0.106183	−	0.0416736i
$94$	−5.57494	−	7.67245i	−0.575011	−	0.791352i
$95$	7.99040	−	1.20436i	0.819797	−	0.123565i
$96$	−0.979629	−	0.471467i	−0.0999830	−	0.0481189i
$97$	8.27599			0.840299			0.420150	−	0.907455i	$-0.361978\pi$
$97$	8.27599			0.840299			0.420150	+	0.907455i	$0.361978\pi$
$98$	3.95479	−	9.07522i	0.399494	−	0.916736i
$99$		−	8.03833i		−	0.807882i
$100$	−6.47870	−	9.81270i	−0.647870	−	0.981270i
$101$	2.04445	+	13.5641i	0.203431	+	1.34968i	0.824474	+	0.565899i	$0.191471\pi$
$101$	2.04445	+	13.5641i	0.203431	+	1.34968i	−0.621044	+	0.783776i	$0.713291\pi$
$102$	1.32517	−	0.962892i	0.131211	−	0.0953405i
$103$	1.00863	−	2.56994i	0.0993830	−	0.253224i	−0.872532	−	0.488558i	$-0.837523\pi$
$103$	1.00863	−	2.56994i	0.0993830	−	0.253224i	0.971915	+	0.235334i	$0.0756184\pi$
$104$	0.931066	−	6.88107i	0.0912985	−	0.674745i
$105$	1.56362	+	0.606591i	0.152594	+	0.0591972i
$106$	3.23007	−	16.4032i	0.313732	−	1.59322i
$107$	0.338042	+	1.09590i	0.0326797	+	0.105945i	0.970443	−	0.241329i	$-0.0775834\pi$
$107$	0.338042	+	1.09590i	0.0326797	+	0.105945i	−0.937764	+	0.347274i	$0.887107\pi$
$108$	−0.476766	−	2.24192i	−0.0458769	−	0.215729i
$109$	1.39320	−	4.51664i	0.133444	−	0.432616i	−0.864047	−	0.503412i	$-0.832078\pi$
$109$	1.39320	−	4.51664i	0.133444	−	0.432616i	0.997491	+	0.0707962i	$0.0225540\pi$
$110$	8.88123	+	9.01421i	0.846792	+	0.859471i
$111$	0.150649	+	0.660036i	0.0142990	+	0.0626478i
$112$	6.18512	−	8.58745i	0.584439	−	0.811438i
$113$	−0.957673	+	4.19584i	−0.0900903	+	0.394711i	−0.999789	−	0.0205583i	$-0.993456\pi$
$113$	−0.957673	+	4.19584i	−0.0900903	+	0.394711i	0.909698	+	0.415270i	$0.136313\pi$
$114$	−0.566422	+	0.350063i	−0.0530503	+	0.0327864i
$115$	−9.53927	−	13.9915i	−0.889542	−	1.30472i
$116$	6.21108	−	7.55534i	0.576685	−	0.701495i
$117$	6.29974	−	3.63715i	0.582411	−	0.336255i
$118$	3.31237	+	12.7399i	0.304929	+	1.17280i
$119$	6.97493	+	14.3391i	0.639391	+	1.31446i
$120$	1.49650	+	0.987513i	0.136611	+	0.0901472i
$121$	3.00791	+	2.05076i	0.273446	+	0.186432i
$122$	0.137663	−	3.06870i	0.0124635	−	0.277827i
$123$	0.264631	−	0.285205i	0.0238610	−	0.0257160i
$124$	7.91008	−	8.27493i	0.710346	−	0.743111i
$125$	1.25832	+	2.61292i	0.112547	+	0.233707i
$126$	11.0804	−	0.375789i	0.987120	−	0.0334779i
$127$	−15.0001	−	7.22368i	−1.33105	−	0.640998i	−0.373058	−	0.927808i	$-0.621691\pi$
$127$	−15.0001	−	7.22368i	−1.33105	−	0.640998i	−0.957988	+	0.286810i	$0.907405\pi$
$128$	8.40511	−	7.57326i	0.742913	−	0.669388i
$129$	−1.01953	+	1.76588i	−0.0897646	+	0.155477i
$130$	−3.04600	+	11.0390i	−0.267152	+	0.968188i
$131$	−2.74134	+	18.1876i	−0.239512	+	1.58906i	0.468896	+	0.883253i	$0.344652\pi$
$131$	−2.74134	+	18.1876i	−0.239512	+	1.58906i	−0.708408	+	0.705803i	$0.750586\pi$
$132$	−0.964900	−	0.395342i	−0.0839837	−	0.0344101i
$133$	−2.39178	−	6.02438i	−0.207393	−	0.522380i
$134$	3.99182	−	5.32544i	0.344841	−	0.460048i
$135$	0.282481	+	3.76945i	0.0243121	+	0.324423i
$136$	4.04383	+	16.5599i	0.346756	+	1.42000i
$137$	−8.50701	−	21.6755i	−0.726803	−	1.85186i	−0.459193	−	0.888337i	$-0.651861\pi$
$137$	−8.50701	−	21.6755i	−0.726803	−	1.85186i	−0.267610	−	0.963527i	$-0.586234\pi$
$138$	1.17598	+	0.751160i	0.100106	+	0.0639430i
$139$	−7.85277	+	6.26237i	−0.666063	+	0.531168i	−0.897128	−	0.441771i	$-0.854350\pi$
$139$	−7.85277	+	6.26237i	−0.666063	+	0.531168i	0.231065	+	0.972938i	$0.425779\pi$
$140$	−12.0104	+	12.6637i	−1.01506	+	1.07028i
$141$	−1.00766	−	0.803584i	−0.0848605	−	0.0676740i
$142$	−3.71746	−	10.8826i	−0.311963	−	0.913250i
$143$	0.497704	−	6.64140i	0.0416201	−	0.555381i
$144$	11.6622	+	2.11400i	0.971850	+	0.176166i
$145$	−11.8242	+	10.9712i	−0.981945	+	0.911112i
$146$	−2.51701	+	2.13372i	−0.208310	+	0.176588i
$147$	0.190040	−	1.33182i	0.0156742	−	0.109847i
$148$	−6.95024	−	1.15346i	−0.571306	−	0.0948139i
$149$	6.96226	+	7.50353i	0.570371	+	0.614713i	0.950690	−	0.310142i	$-0.100376\pi$
$149$	6.96226	+	7.50353i	0.570371	+	0.614713i	−0.380320	+	0.924855i	$0.624186\pi$
$150$	−1.20342	−	1.05129i	−0.0982590	−	0.0858377i
$151$	−1.10581	+	14.7560i	−0.0899897	+	1.20083i	0.751195	+	0.660081i	$0.229478\pi$
$151$	−1.10581	+	14.7560i	−0.0899897	+	1.20083i	−0.841184	+	0.540749i	$0.818141\pi$
$152$	−1.13616	−	6.83556i	−0.0921550	−	0.554437i
$153$	−11.1342	+	13.9619i	−0.900148	+	1.12875i
$154$	5.43044	−	8.57575i	0.437597	−	0.691054i
$155$	−14.7602	+	11.7708i	−1.18556	+	0.945456i
$156$	−0.126760	−	0.935087i	−0.0101489	−	0.0748669i
$157$	−0.0251994	+	0.00989005i	−0.00201113	+	0.000789312i	−0.366346	−	0.930479i	$-0.619391\pi$
$157$	−0.0251994	+	0.00989005i	−0.00201113	+	0.000789312i	0.364335	+	0.931268i	$0.381296\pi$
$158$	11.6379	−	4.97497i	0.925865	−	0.395788i
$159$	−0.169783	−	2.26560i	−0.0134647	−	0.179674i
$160$	−15.4137	+	10.5145i	−1.21856	+	0.831241i
$161$	−9.19985	+	9.99361i	−0.725050	+	0.787607i
$162$	5.64789	+	10.8813i	0.443740	+	0.854914i
$163$	−0.573343	+	3.80388i	−0.0449077	+	0.297943i	0.955091	+	0.296313i	$0.0957570\pi$
$163$	−0.573343	+	3.80388i	−0.0449077	+	0.297943i	−0.999999	+	0.00163022i	$0.999481\pi$
$164$	1.70231	+	3.67355i	0.132928	+	0.286856i
$165$	1.48929	+	0.859844i	0.115941	+	0.0669388i
$166$	1.74059	−	4.85822i	0.135096	−	0.377071i
$167$	−12.0130	−	5.78516i	−0.929594	−	0.447669i	−0.0931073	−	0.995656i	$-0.529680\pi$
$167$	−12.0130	−	5.78516i	−0.929594	−	0.447669i	−0.836487	+	0.547987i	$0.815394\pi$
$168$	0.499849	−	1.34854i	0.0385642	−	0.104042i
$169$	−6.28245	+	3.02547i	−0.483266	+	0.232728i
$170$	−2.93997	−	27.9586i	−0.225485	−	2.14433i
$171$	4.93750	−	5.32136i	0.377580	−	0.406934i
$172$	−12.9821	−	16.7848i	−0.989878	−	1.27983i
$173$	−9.83790	+	14.4296i	−0.747962	+	1.09706i	0.243908	+	0.969798i	$0.421571\pi$
$173$	−9.83790	+	14.4296i	−0.747962	+	1.09706i	−0.991869	+	0.127260i	$0.959382\pi$
$174$	0.540558	−	1.21427i	0.0409796	−	0.0920539i
$175$	12.1232	−	9.74617i	0.916428	−	0.736741i
$176$	7.61394	−	7.73176i	0.573923	−	0.582804i
$177$	0.894436	+	1.54921i	0.0672299	+	0.116446i
$178$	3.91454	+	21.5649i	0.293407	+	1.61635i
$179$	−12.4365	−	18.2410i	−0.929548	−	1.36340i	−0.931634	−	0.363399i	$-0.881616\pi$
$179$	−12.4365	−	18.2410i	−0.929548	−	1.36340i	0.00208590	−	0.999998i	$-0.499336\pi$
$180$	−18.5905	−	6.03839i	−1.38565	−	0.450075i
$181$	15.8757	+	3.62353i	1.18003	+	0.269335i	0.767161	−	0.641455i	$-0.221669\pi$
$181$	15.8757	+	3.62353i	1.18003	+	0.269335i	0.412871	+	0.910789i	$0.364526\pi$
$182$	9.17807	+	0.375575i	0.680324	+	0.0278395i
$183$	−0.0928906	−	0.406980i	−0.00686667	−	0.0300848i
$184$	−11.8731	+	8.36047i	−0.875297	+	0.616342i
$185$	11.1028	+	3.42477i	0.816295	+	0.251794i
$186$	0.737118	−	1.36996i	0.0540481	−	0.100450i
$187$	4.81920	+	15.6235i	0.352415	+	1.14250i
$188$	11.7139	−	6.53285i	0.854321	−	0.476457i
$189$	2.89386	−	0.905115i	0.210497	−	0.0658374i
$190$	0.342431	+	11.4226i	0.0248426	+	0.828685i
$191$	−1.08676	+	2.76901i	−0.0786350	+	0.200359i	−0.964785	−	0.263040i	$-0.915275\pi$
$191$	−1.08676	+	2.76901i	−0.0786350	+	0.200359i	0.886150	+	0.463399i	$0.153370\pi$
$192$	0.827330	−	1.29593i	0.0597074	−	0.0935257i
$193$	−7.96408	+	1.20039i	−0.573267	+	0.0864061i	−0.429277	−	0.903173i	$-0.641232\pi$
$193$	−7.96408	+	1.20039i	−0.573267	+	0.0864061i	−0.143990	+	0.989579i	$0.545993\pi$
$194$	−1.39682	+	11.6204i	−0.100286	+	0.834294i
$195$			1.55624i			0.111444i
$196$	12.0751	+	7.08465i	0.862506	+	0.506047i
$197$			2.38636i			0.170021i	0.996380	+	0.0850106i	$0.0270924\pi$
$197$			2.38636i			0.170021i	−0.996380	+	0.0850106i	$0.972908\pi$
$198$	11.2867	+	1.35671i	0.802108	+	0.0964169i
$199$	−4.67611	+	0.704810i	−0.331480	+	0.0499626i	−0.312674	−	0.949861i	$-0.601225\pi$
$199$	−4.67611	+	0.704810i	−0.331480	+	0.0499626i	−0.0188065	+	0.999823i	$0.505987\pi$
$200$	14.8715	−	7.44060i	1.05158	−	0.526130i
$201$	0.330435	−	0.841934i	0.0233071	−	0.0593855i
$202$	−19.3904	+	0.581293i	−1.36431	+	0.0408996i
$203$	10.7189	+	7.24645i	0.752320	+	0.508601i
$204$	1.12834	+	2.02320i	0.0789997	+	0.141652i
$205$	−1.96815	−	6.38058i	−0.137461	−	0.445639i
$206$	3.43823	+	1.84997i	0.239553	+	0.128894i
$207$	−14.5367	−	4.48397i	−1.01037	−	0.311658i
$208$	9.50461	+	2.46870i	0.659026	+	0.171174i
$209$	−1.47891	−	6.47954i	−0.102298	−	0.448199i
$210$	−1.11562	+	2.09311i	−0.0769854	+	0.144438i
$211$	−2.87497	−	0.656192i	−0.197921	−	0.0451741i	0.122411	−	0.992479i	$-0.460937\pi$
$211$	−2.87497	−	0.656192i	−0.197921	−	0.0451741i	−0.320332	+	0.947305i	$0.603794\pi$
$212$	22.4866	+	7.30388i	1.54439	+	0.501633i
$213$	−0.880370	−	1.29127i	−0.0603220	−	0.0884761i
$214$	−1.59582	+	0.289680i	−0.109088	+	0.0198021i
$215$	17.4974	+	30.3064i	1.19332	+	2.06688i
$216$	3.22836	−	0.291040i	0.219662	−	0.0198028i
$217$	11.8767	+	9.39521i	0.806245	+	0.637788i
$218$	6.10670	+	2.71852i	0.413598	+	0.184121i
$219$	−0.252605	+	0.370503i	−0.0170695	+	0.0250363i
$220$	−14.1559	+	10.9488i	−0.954389	+	0.738166i
$221$	−10.0637	+	10.8461i	−0.676960	+	0.729589i
$222$	−0.952187	+	0.100126i	−0.0639066	+	0.00672005i
$223$	20.1962	−	9.72600i	1.35244	−	0.651301i	0.389503	−	0.921025i	$-0.372647\pi$
$223$	20.1962	−	9.72600i	1.35244	−	0.651301i	0.962938	+	0.269724i	$0.0869326\pi$
$224$	11.0138	+	10.1340i	0.735888	+	0.677103i
$225$	15.6954	+	7.55852i	1.04636	+	0.503902i
$226$	−5.72977	−	2.05285i	−0.381138	−	0.136553i
$227$	5.31592	+	3.06915i	0.352830	+	0.203706i	0.665931	−	0.746013i	$-0.268035\pi$
$227$	5.31592	+	3.06915i	0.352830	+	0.203706i	−0.313101	+	0.949720i	$0.601368\pi$
$228$	−0.395925	−	0.854400i	−0.0262208	−	0.0565840i
$229$	3.85557	−	25.5801i	0.254784	−	1.69038i	−0.385874	−	0.922552i	$-0.626100\pi$
$229$	3.85557	−	25.5801i	0.254784	−	1.69038i	0.640657	−	0.767827i	$-0.278662\pi$
$230$	21.2556	−	11.0327i	1.40156	−	0.727472i
$231$	0.401407	−	1.31973i	0.0264106	−	0.0868320i
$232$	9.56019	+	9.99621i	0.627657	+	0.656283i
$233$	1.65185	+	22.0424i	0.108216	+	1.44405i	0.741929	+	0.670478i	$0.233911\pi$
$233$	1.65185	+	22.0424i	0.108216	+	1.44405i	−0.633713	+	0.773569i	$0.718470\pi$
$234$	4.04368	+	9.45937i	0.264344	+	0.618379i
$235$	−20.5905	+	8.08118i	−1.34318	+	0.527158i
$236$	−18.4472	+	2.50070i	−1.20081	+	0.162781i
$237$	1.34476	−	1.07241i	0.0873514	−	0.0696604i
$238$	−21.3108	+	7.37340i	−1.38138	+	0.477947i
$239$	12.1161	−	15.1931i	0.783724	−	0.982759i	−0.216255	−	0.976337i	$-0.569384\pi$
$239$	12.1161	−	15.1931i	0.783724	−	0.982759i	0.999979	−	0.00642231i	$-0.00204430\pi$
$240$	−1.63915	+	1.93457i	−0.105807	+	0.124876i
$241$	1.82741	−	24.3851i	0.117714	−	1.57078i	−0.555617	−	0.831438i	$-0.687518\pi$
$241$	1.82741	−	24.3851i	0.117714	−	1.57078i	0.673331	−	0.739342i	$-0.264863\pi$
$242$	−3.38715	+	3.87730i	−0.217734	+	0.249242i
$243$	3.47170	+	3.74160i	0.222710	+	0.240024i
$244$	4.28554	+	0.711227i	0.274353	+	0.0455316i
$245$	−18.1641	−	14.2531i	−1.16046	−	0.910597i
$246$	0.355793	+	0.419707i	0.0226845	+	0.0267595i
$247$	4.40892	−	4.09088i	0.280533	−	0.260296i
$248$	10.2838	+	12.5032i	0.653023	+	0.793956i
$249$	0.0524092	−	0.699353i	0.00332130	−	0.0443197i
$250$	−3.88119	+	1.32580i	−0.245468	+	0.0838510i
$251$	18.9035	+	15.0750i	1.19318	+	0.951526i	0.999563	−	0.0295520i	$-0.00940807\pi$
$251$	18.9035	+	15.0750i	1.19318	+	0.951526i	0.193613	+	0.981078i	$0.437979\pi$
$252$	−1.34250	+	15.6215i	−0.0845694	+	0.984061i
$253$	−10.8893	+	8.68389i	−0.684602	+	0.545952i
$254$	12.6745	−	19.8426i	0.795271	−	1.24503i
$255$	−1.39577	−	3.55635i	−0.0874063	−	0.222707i
$256$	9.21504	+	13.0799i	0.575940	+	0.817492i
$257$	−0.531963	−	7.09855i	−0.0331829	−	0.442796i	−0.988907	−	0.148533i	$-0.952545\pi$
$257$	−0.531963	−	7.09855i	−0.0331829	−	0.442796i	0.955725	−	0.294263i	$-0.0950741\pi$
$258$	−2.30740	−	1.72957i	−0.143653	−	0.107678i
$259$	0.659936	−	9.29667i	0.0410064	−	0.577667i
$260$	−14.9859	−	6.14007i	−0.929385	−	0.380791i
$261$	−2.15967	+	14.3285i	−0.133680	+	0.886910i
$262$	−25.0746	−	6.91882i	−1.54911	−	0.427446i
$263$	−10.2569	+	17.7654i	−0.632466	+	1.09546i	0.354580	+	0.935026i	$0.384624\pi$
$263$	−10.2569	+	17.7654i	−0.632466	+	1.09546i	−0.987046	+	0.160438i	$0.948709\pi$
$264$	0.717957	−	1.28810i	0.0441872	−	0.0792768i
$265$	−35.1304	−	16.9179i	−2.15804	−	1.03926i
$266$	8.86255	−	2.34152i	0.543398	−	0.143568i
$267$	1.29232	+	2.68353i	0.0790887	+	0.164229i
$268$	6.80375	+	6.50376i	0.415605	+	0.397281i
$269$	14.2172	−	15.3225i	0.866840	−	0.934231i	−0.131530	−	0.991312i	$-0.541989\pi$
$269$	14.2172	−	15.3225i	0.866840	−	0.934231i	0.998370	+	0.0570813i	$0.0181794\pi$
$270$	−5.34039	−	0.239573i	−0.325006	−	0.0145799i
$271$	1.61819	+	1.10326i	0.0982980	+	0.0670185i	0.611472	−	0.791266i	$-0.290578\pi$
$271$	1.61819	+	1.10326i	0.0982980	+	0.0670185i	−0.513174	+	0.858285i	$0.671530\pi$
$272$	−23.9343	+	2.88301i	−1.45123	+	0.174808i
$273$	1.21592	−	0.282560i	0.0735907	−	0.0171013i
$274$	31.8705	−	8.28636i	1.92537	−	0.500597i
$275$	13.8127	−	7.97475i	0.832936	−	0.480896i
$276$	−1.25319	+	1.52441i	−0.0754331	+	0.0917589i
$277$	−3.12516	−	4.58377i	−0.187773	−	0.275412i	0.720796	−	0.693147i	$-0.243776\pi$
$277$	−3.12516	−	4.58377i	−0.187773	−	0.275412i	−0.908569	+	0.417735i	$0.862824\pi$
$278$	−7.46765	−	12.0831i	−0.447880	−	0.724695i
$279$	−3.77390	+	16.5345i	−0.225937	+	0.989896i
$280$	−15.7541	−	19.0013i	−0.941486	−	1.13554i
$281$	−3.89171	−	17.0507i	−0.232160	−	1.01716i	−0.947844	−	0.318735i	$-0.896742\pi$
$281$	−3.89171	−	17.0507i	−0.232160	−	1.01716i	0.715684	−	0.698424i	$-0.246115\pi$
$282$	1.29839	−	1.27924i	0.0773180	−	0.0761774i
$283$	−0.944613	+	3.06236i	−0.0561514	+	0.182038i	−0.979304	−	0.202396i	$-0.935127\pi$
$283$	−0.944613	+	3.06236i	−0.0561514	+	0.182038i	0.923152	+	0.384434i	$0.125603\pi$
$284$	15.9078	−	3.38295i	0.943954	−	0.200741i
$285$	0.457755	+	1.48401i	0.0271151	+	0.0879049i
$286$	9.24122	+	1.81976i	0.546445	+	0.107605i
$287$	−4.62792	+	2.69625i	−0.273177	+	0.159155i
$288$	−4.93662	+	16.0182i	−0.290893	+	0.943880i
$289$	7.05938	−	17.9870i	0.415258	−	1.05806i
$290$	−13.4091	−	18.4541i	−0.787409	−	1.08366i
$291$	0.237058	+	1.57278i	0.0138966	+	0.0921978i
$292$	−2.57115	−	3.89428i	−0.150465	−	0.227896i
$293$		−	10.2305i		−	0.597671i	−0.954305	−	0.298836i	$-0.903402\pi$
$293$		−	10.2305i		−	0.597671i	0.954305	−	0.298836i	$-0.0965982\pi$
$294$	1.83795	+	0.491621i	0.107191	+	0.0286719i
$295$	30.7011			1.78749
$296$	2.79264	−	9.56419i	0.162319	−	0.555907i
$297$	3.07427	−	0.463371i	0.178387	−	0.0268875i
$298$	−11.7108	+	8.50931i	−0.678391	+	0.492931i
$299$	−11.7328	−	4.60479i	−0.678526	−	0.266302i
$300$	1.67924	−	1.51229i	0.0969510	−	0.0873124i
$301$	20.5021	−	19.1737i	1.18172	−	1.10515i
$302$	−20.5324	−	4.04320i	−1.18151	−	0.232660i
$303$	−2.51917	+	0.777060i	−0.144722	+	0.0446409i
$304$	9.78961	−	0.441590i	0.561473	−	0.0253269i
$305$	−6.84603	−	2.11172i	−0.392002	−	0.120917i
$306$	−17.7247	−	17.9901i	−1.01325	−	1.02843i
$307$	13.0544	−	2.97958i	0.745052	−	0.170053i	0.166891	−	0.985975i	$-0.446627\pi$
$307$	13.0544	−	2.97958i	0.745052	−	0.170053i	0.578162	+	0.815922i	$0.303770\pi$
$308$	11.1247	+	9.07232i	0.633890	+	0.516944i
$309$	0.517285	+	0.118067i	0.0294273	+	0.00671659i
$310$	−14.0363	−	22.7115i	−0.797208	−	1.28993i
$311$	−8.88578	+	6.05822i	−0.503866	+	0.343530i	−0.788428	−	0.615128i	$-0.789104\pi$
$311$	−8.88578	+	6.05822i	−0.503866	+	0.343530i	0.284561	+	0.958658i	$0.408152\pi$
$312$	1.33436	−	0.0201612i	0.0755430	−	0.00114140i
$313$	−14.0410	−	24.3197i	−0.793642	−	1.37463i	−0.923698	−	0.383122i	$-0.874849\pi$
$313$	−14.0410	−	24.3197i	−0.793642	−	1.37463i	0.130055	−	0.991507i	$-0.458485\pi$
$314$	−0.00963353	−	0.0370519i	−0.000543652	−	0.00209096i
$315$	5.65470	−	25.2318i	0.318606	−	1.42165i
$316$	5.02114	+	17.1806i	0.282461	+	0.966483i
$317$	−10.4379	+	15.3096i	−0.586251	+	0.859872i	−0.998693	−	0.0511118i	$-0.983724\pi$
$317$	−10.4379	+	15.3096i	−0.586251	+	0.859872i	0.412442	+	0.910984i	$0.364676\pi$
$318$	3.20979	+	0.143993i	0.179996	+	0.00807474i
$319$	9.72514	+	9.02362i	0.544504	+	0.505225i
$320$	−12.1619	−	23.4171i	−0.679871	−	1.30906i
$321$	−0.198584	+	0.0956329i	−0.0110839	+	0.00533771i
$322$	−12.4793	−	14.6043i	−0.695447	−	0.813865i
$323$	−6.40633	+	13.3029i	−0.356458	+	0.740192i
$324$	−16.2317	+	6.09370i	−0.901763	+	0.338539i
$325$	12.4998	+	7.21678i	0.693365	+	0.400315i
$326$	−5.24428	−	1.44705i	−0.290454	−	0.0801447i
$327$	0.898254	+	0.135390i	0.0496736	+	0.00748708i
$328$	−5.44536	+	1.77020i	−0.300670	+	0.0977428i
$329$	10.0525	+	14.6205i	0.554214	+	0.806054i
$330$	−1.45867	+	1.94600i	−0.0802974	+	0.107124i
$331$	11.3319	−	0.849208i	0.622857	−	0.0466767i	0.240436	−	0.970665i	$-0.422709\pi$
$331$	11.3319	−	0.849208i	0.622857	−	0.0466767i	0.382421	+	0.923988i	$0.375090\pi$
$332$	6.52768	+	3.26394i	0.358253	+	0.179132i
$333$	9.71631	−	3.81337i	0.532451	−	0.208972i
$334$	10.1505	−	15.8911i	0.555412	−	0.869523i
$335$	−9.67812	−	12.1360i	−0.528772	−	0.663060i
$336$	1.80913	+	0.929447i	0.0986964	+	0.0507055i
$337$	−8.92254	+	11.1885i	−0.486042	+	0.609477i	−0.963017	−	0.269439i	$-0.913162\pi$
$337$	−8.92254	+	11.1885i	−0.486042	+	0.609477i	0.476976	+	0.878917i	$0.341733\pi$
$338$	−3.18773	−	9.33187i	−0.173390	−	0.507587i
$339$	−0.824813	−	0.0618112i	−0.0447977	−	0.00335712i
$340$	39.7531	+	0.590821i	2.15591	+	0.0320418i
$341$	10.5614	+	11.3825i	0.571933	+	0.616397i
$342$	6.63840	+	7.83091i	0.358964	+	0.423447i
$343$	−7.83823	+	16.7798i	−0.423225	+	0.906025i
$344$	25.7588	−	15.3953i	1.38882	−	0.830062i
$345$	2.38572	−	2.21363i	0.128443	−	0.119178i
$346$	−18.6002	−	16.2489i	−0.999952	−	0.873545i
$347$	−26.3917	−	1.97779i	−1.41678	−	0.106173i	−0.655795	−	0.754939i	$-0.727666\pi$
$347$	−26.3917	−	1.97779i	−1.41678	−	0.106173i	−0.760988	+	0.648766i	$0.775285\pi$
$348$	1.61373	+	0.963945i	0.0865052	+	0.0516729i
$349$	−27.1499	−	21.6513i	−1.45330	−	1.15897i	−0.956731	−	0.290972i	$-0.906021\pi$
$349$	−27.1499	−	21.6513i	−1.45330	−	1.15897i	−0.496570	−	0.867997i	$-0.665407\pi$
$350$	11.6385	+	18.6672i	0.622104	+	0.997804i
$351$	1.75418	+	2.19968i	0.0936314	+	0.117410i
$352$	9.57114	+	11.9957i	0.510143	+	0.639375i
$353$	−1.92158	−	4.89611i	−0.102276	−	0.260594i	0.870572	−	0.492041i	$-0.163749\pi$
$353$	−1.92158	−	4.89611i	−0.102276	−	0.260594i	−0.972847	+	0.231447i	$0.925654\pi$
$354$	−2.32622	+	0.994408i	−0.123637	+	0.0528522i
$355$	−26.7466	+	2.00438i	−1.41956	+	0.106381i
$356$	−30.9400	+	1.85673i	−1.63982	+	0.0984064i
$357$	−2.52522	+	1.73625i	−0.133649	+	0.0918923i
$358$	27.7113	−	14.3835i	1.46459	−	0.760189i
$359$	7.65286	+	1.15348i	0.403903	+	0.0608785i	0.347852	−	0.937549i	$-0.386911\pi$
$359$	7.65286	+	1.15348i	0.403903	+	0.0608785i	0.0560504	+	0.998428i	$0.482149\pi$
$360$	11.6162	−	25.0839i	0.612229	−	1.32204i
$361$	−6.49902	+	11.2566i	−0.342054	+	0.592454i
$362$	−7.76731	+	21.6796i	−0.408241	+	1.13945i
$363$	−0.303569	+	0.630368i	−0.0159332	+	0.0330857i
$364$	−2.07642	+	12.8236i	−0.108834	+	0.672139i
$365$	3.33914	+	6.93379i	0.174778	+	0.362931i
$366$	0.587121	−	0.0617382i	0.0306893	−	0.00322711i
$367$	4.11769	+	3.82066i	0.214942	+	0.199437i	0.780294	−	0.625413i	$-0.215069\pi$
$367$	4.11769	+	3.82066i	0.214942	+	0.199437i	−0.565352	+	0.824849i	$0.691260\pi$
$368$	−9.73504	−	18.0822i	−0.507474	−	0.942599i
$369$	−4.95613	−	3.37904i	−0.258006	−	0.175906i
$370$	−6.68266	+	15.0115i	−0.347415	+	0.780411i
$371$	−6.83978	+	30.5198i	−0.355104	+	1.58451i
$372$	1.79915	+	1.26621i	0.0932818	+	0.0656500i
$373$	−9.58330	+	5.53292i	−0.496205	+	0.286484i	−0.727145	−	0.686484i	$-0.759153\pi$
$373$	−9.58330	+	5.53292i	−0.496205	+	0.286484i	0.230940	+	0.972968i	$0.425820\pi$
$374$	−22.7504	+	4.12975i	−1.17639	+	0.213544i
$375$	−0.460518	+	0.313976i	−0.0237811	+	0.0162137i
$376$	7.19575	+	17.5501i	0.371093	+	0.905078i
$377$	−2.67152	+	11.7047i	−0.137590	+	0.602822i
$378$	0.782453	+	4.21605i	0.0402450	+	0.216850i
$379$	12.3577	−	2.82056i	0.634772	−	0.144882i	0.106987	−	0.994260i	$-0.465880\pi$
$379$	12.3577	−	2.82056i	0.634772	−	0.144882i	0.527785	+	0.849378i	$0.323023\pi$
$380$	−16.0964	−	1.44710i	−0.825727	−	0.0742345i
$381$	0.943131	−	3.05756i	0.0483181	−	0.156643i
$382$	−3.70456	−	1.99328i	−0.189542	−	0.101985i
$383$	14.6489	−	4.51858i	0.748523	−	0.230889i	0.103054	−	0.994676i	$-0.467138\pi$
$383$	14.6489	−	4.51858i	0.748523	−	0.230889i	0.645468	+	0.763787i	$0.276662\pi$
$384$	1.67999	+	1.38039i	0.0857314	+	0.0704425i
$385$	−16.1706	−	17.2909i	−0.824130	−	0.881225i
$386$	−0.341304	−	11.3850i	−0.0173719	−	0.579482i
$387$	29.2642	+	11.4853i	1.48758	+	0.583833i
$388$	−16.0805	−	3.92256i	−0.816362	−	0.199138i
$389$	−3.54632	−	23.5283i	−0.179805	−	1.19293i	−0.878582	−	0.477591i	$-0.841510\pi$
$389$	−3.54632	−	23.5283i	−0.179805	−	1.19293i	0.698777	−	0.715340i	$-0.253728\pi$
$390$	−2.18512	−	0.262661i	−0.110648	−	0.0133004i
$391$	30.9421			1.56481
$392$	−11.9856	+	15.7590i	−0.605366	+	0.795947i
$393$	−3.53491			−0.178313
$394$	−3.35070	−	0.402769i	−0.168806	−	0.0202912i
$395$	−4.39961	−	29.1895i	−0.221369	−	1.46868i
$396$	−3.80992	+	15.6187i	−0.191456	+	0.784869i
$397$	32.4566	+	12.7383i	1.62895	+	0.639315i	0.991373	−	0.131073i	$-0.0418423\pi$
$397$	32.4566	+	12.7383i	1.62895	+	0.639315i	0.637575	+	0.770388i	$0.279938\pi$
$398$	−0.200396	−	6.68471i	−0.0100450	−	0.335074i
$399$	1.07637	−	0.627099i	0.0538859	−	0.0313942i
$400$	7.93737	+	22.1370i	0.396869	+	1.10685i
$401$	17.0946	−	5.27297i	0.853662	−	0.263320i	0.163115	−	0.986607i	$-0.447846\pi$
$401$	17.0946	−	5.27297i	0.853662	−	0.263320i	0.690547	+	0.723287i	$0.257370\pi$
$402$	1.12639	+	0.606067i	0.0561795	+	0.0302279i
$403$	−4.14181	+	13.4274i	−0.206318	+	0.668868i
$404$	2.45651	−	27.3244i	0.122216	−	1.35944i
$405$	27.8765	−	6.36263i	1.38519	−	0.316161i
$406$	−11.9839	+	13.8274i	−0.594752	+	0.686244i
$407$	2.12650	−	9.31680i	0.105407	−	0.461817i
$408$	−3.03122	+	1.24284i	−0.150068	+	0.0615296i
$409$	25.9991	−	17.7259i	1.28557	−	0.876488i	0.288849	−	0.957375i	$-0.406727\pi$
$409$	25.9991	−	17.7259i	1.28557	−	0.876488i	0.996723	+	0.0808864i	$0.0257751\pi$
$410$	9.29119	−	1.68658i	0.458859	−	0.0832941i
$411$	3.87556	−	2.23756i	0.191167	−	0.110371i
$412$	−3.17786	+	4.51540i	−0.156562	+	0.222458i
$413$	−5.57429	−	23.9873i	−0.274293	−	1.18034i
$414$	8.74947	−	19.6542i	0.430013	−	0.965953i
$415$	−9.94471	−	6.78019i	−0.488167	−	0.332826i
$416$	−5.07050	+	12.9288i	−0.248602	+	0.633887i
$417$	−1.41504	−	1.31297i	−0.0692950	−	0.0642963i
$418$	9.34757	−	0.982936i	0.457204	−	0.0480770i
$419$	12.8640	+	26.7124i	0.628449	+	1.30499i	0.935511	+	0.353298i	$0.114940\pi$
$419$	12.8640	+	26.7124i	0.628449	+	1.30499i	−0.307062	+	0.951690i	$0.599346\pi$
$420$	−2.75065	−	1.91973i	−0.134218	−	0.0936732i
$421$	15.0604	−	31.2733i	0.734000	−	1.52417i	−0.113597	−	0.993527i	$-0.536237\pi$
$421$	15.0604	−	31.2733i	0.734000	−	1.52417i	0.847597	−	0.530641i	$-0.178049\pi$
$422$	1.40660	−	3.92601i	0.0684722	−	0.191115i
$423$	−9.93546	+	17.2087i	−0.483078	+	0.836716i
$424$	−14.0507	+	30.3408i	−0.682362	+	1.47348i
$425$	−35.0375	−	5.28106i	−1.69957	−	0.256169i
$426$	1.96166	−	1.01819i	0.0950429	−	0.0493316i
$427$	−0.406918	+	5.73235i	−0.0196922	+	0.277408i
$428$	−0.137400	−	2.28959i	−0.00664146	−	0.110672i
$429$	1.27639	−	0.0956525i	0.0616249	−	0.00461815i
$430$	−45.5067	+	19.4531i	−2.19453	+	0.938114i
$431$	−9.58161	−	24.4135i	−0.461530	−	1.17596i	−0.952434	−	0.304745i	$-0.901429\pi$
$431$	−9.58161	−	24.4135i	−0.461530	−	1.17596i	0.490904	−	0.871214i	$-0.336667\pi$
$432$	−0.136230	+	4.58208i	−0.00655438	+	0.220456i
$433$	0.451955	+	0.566733i	0.0217195	+	0.0272355i	0.792573	−	0.609777i	$-0.208741\pi$
$433$	0.451955	+	0.566733i	0.0217195	+	0.0272355i	−0.770853	+	0.637013i	$0.780170\pi$
$434$	−15.1964	+	15.0905i	−0.729452	+	0.724366i
$435$	−2.42368	−	1.93282i	−0.116206	−	0.0926715i
$436$	−4.84777	+	8.11562i	−0.232166	+	0.388668i
$437$	−12.5427	−	0.939946i	−0.599999	−	0.0449637i
$438$	−0.477592	−	0.417218i	−0.0228202	−	0.0199354i
$439$	4.35053	−	4.03671i	0.207640	−	0.192661i	−0.569497	−	0.821994i	$-0.692862\pi$
$439$	4.35053	−	4.03671i	0.207640	−	0.192661i	0.777136	+	0.629332i	$0.216671\pi$
$440$	−12.9840	−	21.7243i	−0.618989	−	1.03566i
$441$	−20.7408	+	0.163127i	−0.987657	+	0.00776793i
$442$	−13.5306	−	15.9612i	−0.643583	−	0.759194i
$443$	−20.9356	−	22.5633i	−0.994682	−	1.07201i	−0.997403	−	0.0720162i	$-0.977057\pi$
$443$	−20.9356	−	22.5633i	−0.994682	−	1.07201i	0.00272127	−	0.999996i	$-0.499134\pi$
$444$	0.0201216	−	1.35387i	0.000954928	−	0.0642519i
$445$	50.9747	+	3.82003i	2.41643	+	0.181087i
$446$	10.2476	+	29.9992i	0.485239	+	1.42050i
$447$	−1.22655	+	1.53805i	−0.0580139	+	0.0727471i
$448$	−16.0880	+	13.7541i	−0.760088	+	0.649820i
$449$	18.1290	+	22.7330i	0.855559	+	1.07284i	0.996564	+	0.0828282i	$0.0263953\pi$
$449$	18.1290	+	22.7330i	0.855559	+	1.07284i	−0.141005	+	0.990009i	$0.545033\pi$
$450$	−13.2620	+	20.7623i	−0.625178	+	0.978746i
$451$	−5.11225	+	2.00641i	−0.240726	+	0.0944781i
$452$	3.84948	−	7.69872i	0.181064	−	0.362117i
$453$	−2.83593	+	0.212523i	−0.133244	+	0.00998522i
$454$	−5.20662	+	6.94610i	−0.244359	+	0.325997i
$455$	6.23426	−	20.4968i	0.292267	−	0.960905i
$456$	1.26649	−	0.411716i	0.0593089	−	0.0192804i
$457$	−24.0849	−	3.63021i	−1.12664	−	0.169814i	−0.440830	−	0.897591i	$-0.645316\pi$
$457$	−24.0849	−	3.63021i	−1.12664	−	0.169814i	−0.685814	+	0.727777i	$0.740554\pi$
$458$	35.2664	+	9.73103i	1.64789	+	0.454701i
$459$	−5.98156	−	3.45346i	−0.279195	−	0.161194i
$460$	11.9035	+	31.7073i	0.555004	+	1.47836i
$461$	3.54465	−	7.36054i	0.165091	−	0.342814i	−0.801968	−	0.597367i	$-0.796214\pi$
$461$	3.54465	−	7.36054i	0.165091	−	0.342814i	0.967059	+	0.254552i	$0.0819280\pi$
$462$	1.78530	+	0.786362i	0.0830594	+	0.0365849i
$463$	−6.18453	+	2.97831i	−0.287420	+	0.138414i	−0.572039	−	0.820227i	$-0.693847\pi$
$463$	−6.18453	+	2.97831i	−0.287420	+	0.138414i	0.284619	+	0.958641i	$0.408133\pi$
$464$	−15.6493	+	11.7364i	−0.726500	+	0.544847i
$465$	−2.65973	−	2.46787i	−0.123342	−	0.114445i
$466$	−31.2287	−	1.40094i	−1.44664	−	0.0648971i
$467$	−5.56337	+	8.15996i	−0.257442	+	0.377598i	−0.933100	−	0.359617i	$-0.882907\pi$
$467$	−5.56337	+	8.15996i	−0.257442	+	0.377598i	0.675658	+	0.737215i	$0.263860\pi$
$468$	−13.9645	+	4.08121i	−0.645507	+	0.188654i
$469$	−7.72485	+	9.76519i	−0.356701	+	0.450915i
$470$	−7.87158	−	30.2752i	−0.363089	−	1.39649i
$471$	−0.00260133	−	0.00450564i	−0.000119863	−	0.000207609i
$472$	−0.397735	−	26.3239i	−0.0183072	−	1.21165i
$473$	23.7813	−	16.2138i	1.09346	−	0.745511i
$474$	1.27881	+	2.06918i	0.0587376	+	0.0950407i
$475$	14.0424	+	3.20509i	0.644310	+	0.147060i
$476$	−6.75621	−	31.1671i	−0.309670	−	1.42854i
$477$	−34.1497	+	7.79445i	−1.56361	+	0.356883i
$478$	19.2878	+	19.5765i	0.882202	+	0.895410i
$479$	−32.3674	−	9.98402i	−1.47890	−	0.456181i	−0.552756	−	0.833343i	$-0.686424\pi$
$479$	−32.3674	−	9.98402i	−1.47890	−	0.456181i	−0.926147	+	0.377162i	$0.876900\pi$
$480$	−2.43969	−	2.62806i	−0.111356	−	0.119954i
$481$	8.26388	−	2.54907i	0.376801	−	0.116228i
$482$	33.9308	+	6.68157i	1.54550	+	0.304337i
$483$	−2.16272	−	1.46209i	−0.0984071	−	0.0665275i
$484$	−4.87245	−	5.41033i	−0.221475	−	0.245924i
$485$	25.4103	+	9.97282i	1.15382	+	0.452842i
$486$	−5.83956	+	4.24313i	−0.264888	+	0.192472i
$487$	7.49167	−	1.12919i	0.339480	−	0.0511683i	0.0229099	−	0.999738i	$-0.492707\pi$
$487$	7.49167	−	1.12919i	0.339480	−	0.0511683i	0.316570	+	0.948569i	$0.397469\pi$
$488$	−1.72195	+	5.89731i	−0.0779490	+	0.266959i
$489$	−0.739316			−0.0334330
$490$	23.0786	−	23.0986i	1.04258	−	1.04349i
$491$		−	32.7124i		−	1.47629i	−0.674641	−	0.738146i	$-0.735702\pi$
$491$		−	32.7124i		−	1.47629i	0.674641	−	0.738146i	$-0.264298\pi$
$492$	−0.649364	+	0.428733i	−0.0292756	+	0.0193288i
$493$	−4.39274	−	29.1439i	−0.197839	−	1.31258i
$494$	4.99989	+	6.88105i	0.224956	+	0.309593i
$495$	9.68643	−	24.6806i	0.435373	−	1.10931i
$496$	−19.2916	+	12.3293i	−0.866217	+	0.553601i
$497$	6.42234	+	20.5337i	0.288081	+	0.921062i
$498$	0.973119	+	0.191625i	0.0436065	+	0.00858690i
$499$	1.04344	+	3.38276i	0.0467110	+	0.151433i	0.975924	−	0.218112i	$-0.0699897\pi$
$499$	1.04344	+	3.38276i	0.0467110	+	0.151433i	−0.929213	+	0.369545i	$0.879514\pi$
$500$	−1.20650	−	5.67337i	−0.0539562	−	0.253721i
$501$	0.755316	−	2.44867i	0.0337450	−	0.109399i
$502$	−24.3574	+	23.9981i	−1.08713	+	1.07109i
$503$	9.30049	+	40.7481i	0.414688	+	1.81687i	0.561226	+	0.827663i	$0.310330\pi$
$503$	9.30049	+	40.7481i	0.414688	+	1.81687i	−0.146537	+	0.989205i	$0.546813\pi$
$504$	−21.7076	−	4.52160i	−0.966935	−	0.201408i
$505$	−10.0679	+	44.1103i	−0.448015	+	1.96288i
$506$	−10.3552	−	16.7553i	−0.460346	−	0.744866i
$507$	−0.754918	−	1.10726i	−0.0335271	−	0.0491752i
$508$	25.7219	+	21.1454i	1.14122	+	0.938175i
$509$	−24.3849	+	14.0786i	−1.08084	+	0.624025i	−0.931124	−	0.364703i	$-0.881170\pi$
$509$	−24.3849	+	14.0786i	−1.08084	+	0.624025i	−0.149719	+	0.988729i	$0.547837\pi$
$510$	5.22907	−	1.35956i	0.231547	−	0.0602025i
$511$	4.81123	−	3.86788i	0.212836	−	0.171105i
$512$	−19.9208	+	10.7313i	−0.880385	+	0.474260i
$513$	2.31978	+	1.58160i	0.102421	+	0.0698294i
$514$	10.0569	+	0.451158i	0.443591	+	0.0198997i
$515$	6.19371	−	6.67523i	0.272928	−	0.294146i
$516$	2.81795	−	2.94792i	0.124053	−	0.129775i
$517$	7.89359	+	16.3912i	0.347160	+	0.720885i
$518$	12.9421	+	2.49571i	0.568644	+	0.109655i
$519$	−3.02400	−	1.45628i	−0.132739	−	0.0639238i
$520$	11.1506	−	20.0055i	0.488987	−	0.877297i
$521$	−0.958545	+	1.66025i	−0.0419946	+	0.0727368i	−0.886259	−	0.463191i	$-0.846705\pi$
$521$	−0.958545	+	1.66025i	−0.0419946	+	0.0727368i	0.844264	+	0.535927i	$0.180038\pi$
$522$	−19.7542	−	5.45076i	−0.864617	−	0.238573i
$523$	−2.11633	+	14.0410i	−0.0925408	+	0.613968i	0.893701	+	0.448662i	$0.148099\pi$
$523$	−2.11633	+	14.0410i	−0.0925408	+	0.613968i	−0.986242	+	0.165306i	$0.947139\pi$
$524$	13.9468	−	34.0397i	0.609270	−	1.48703i
$525$	2.19943	+	2.02474i	0.0959910	+	0.0883667i
$526$	−23.2134	−	17.4002i	−1.01215	−	0.758684i
$527$	−2.57788	−	34.3994i	−0.112294	−	1.49846i
$528$	1.68745	+	1.22549i	0.0734367	+	0.0533327i
$529$	1.22700	+	3.12635i	0.0533480	+	0.135928i
$530$	29.6838	−	46.4714i	1.28938	−	2.01859i
$531$	21.5629	−	17.1959i	0.935752	−	0.746238i
$532$	1.79192	+	12.8392i	0.0776895	+	0.556648i
$533$	−3.88562	−	3.09868i	−0.168305	−	0.134219i
$534$	−3.98608	+	1.36163i	−0.172494	+	0.0589235i
$535$	−0.282686	+	3.77218i	−0.0122216	+	0.163086i
$536$	−10.2803	+	8.45548i	−0.444042	+	0.365221i
$537$	3.11031	−	2.88594i	0.134220	−	0.124538i
$538$	19.1149	+	22.5486i	0.824101	+	0.972140i
$539$	−10.5737	+	15.7738i	−0.455440	+	0.679427i
$540$	1.23773	−	7.45804i	0.0532636	−	0.320943i
$541$	5.44864	+	5.87224i	0.234255	+	0.252467i	0.839229	−	0.543778i	$-0.183007\pi$
$541$	5.44864	+	5.87224i	0.234255	+	0.252467i	−0.604973	+	0.796246i	$0.706816\pi$
$542$	−1.82222	+	2.08590i	−0.0782709	+	0.0895971i
$543$	−0.233874	+	3.12083i	−0.0100365	+	0.133928i
$544$	−0.00842079	−	34.0929i	−0.000361038	−	1.46172i
$545$	9.72032	−	12.1889i	0.416373	−	0.522115i
$546$	0.191523	+	1.75497i	0.00819642	+	0.0751057i
$547$	22.3487	−	17.8225i	0.955560	−	0.762034i	−0.0157437	−	0.999876i	$-0.505012\pi$
$547$	22.3487	−	17.8225i	0.955560	−	0.762034i	0.971304	+	0.237842i	$0.0764402\pi$
$548$	6.25584	+	46.1482i	0.267236	+	1.97135i
$549$	−5.99111	+	2.35134i	−0.255694	+	0.100353i
$550$	8.86610	+	20.7404i	0.378052	+	0.884375i
$551$	0.895321	+	11.9472i	0.0381420	+	0.508969i
$552$	−1.92893	−	2.01690i	−0.0821005	−	0.0858450i
$553$	−22.0075	+	8.73734i	−0.935855	+	0.371550i
$554$	6.96356	−	3.61441i	0.295853	−	0.153562i
$555$	−0.332816	+	2.20809i	−0.0141273	+	0.0937282i
$556$	18.2263	−	8.44599i	0.772968	−	0.358190i
$557$	23.9578	+	13.8320i	1.01512	+	0.586082i	0.912688	−	0.408657i	$-0.134003\pi$
$557$	23.9578	+	13.8320i	1.01512	+	0.586082i	0.102436	+	0.994740i	$0.467336\pi$
$558$	−22.5793	−	8.08964i	−0.955857	−	0.342462i
$559$	23.4674	+	11.3013i	0.992566	+	0.477995i
$560$	29.3387	−	18.9134i	1.23979	−	0.799236i
$561$	−2.83106	+	1.36337i	−0.119527	+	0.0575614i
$562$	24.5978	−	2.58656i	1.03760	−	0.109108i
$563$	9.65934	−	10.4103i	0.407092	−	0.438741i	−0.495912	−	0.868373i	$-0.665166\pi$
$563$	9.65934	−	10.4103i	0.407092	−	0.438741i	0.903004	+	0.429632i	$0.141357\pi$
$564$	1.57704	+	2.03899i	0.0664055	+	0.0858568i
$565$	−7.99652	+	11.7287i	−0.336416	+	0.493432i
$566$	−4.14045	−	1.84320i	−0.174036	−	0.0774755i
$567$	−10.0327	−	20.6252i	−0.421333	−	0.866177i
$568$	2.06511	+	22.9072i	0.0866500	+	0.961165i
$569$	9.48596	+	16.4302i	0.397672	+	0.688788i	0.993438	−	0.114370i	$-0.0364849\pi$
$569$	9.48596	+	16.4302i	0.397672	+	0.688788i	−0.595766	+	0.803158i	$0.703152\pi$
$570$	−2.16096	+	0.392267i	−0.0905127	+	0.0164302i
$571$	17.5719	+	25.7733i	0.735362	+	1.07858i	0.993651	+	0.112510i	$0.0358890\pi$
$571$	17.5719	+	25.7733i	0.735362	+	1.07858i	−0.258289	+	0.966068i	$0.583159\pi$
$572$	−4.11487	+	12.6685i	−0.172051	+	0.529697i
$573$	−0.557355	−	0.127213i	−0.0232838	−	0.00531439i
$574$	−3.00472	−	6.95316i	−0.125415	−	0.290219i
$575$	−6.71667	−	29.4276i	−0.280104	−	1.22722i
$576$	−21.6580	−	9.63507i	−0.902417	−	0.401461i
$577$	13.6861	+	4.22160i	0.569759	+	0.175748i	0.566231	−	0.824246i	$-0.308401\pi$
$577$	13.6861	+	4.22160i	0.569759	+	0.175748i	0.00352796	+	0.999994i	$0.498877\pi$
$578$	24.0642	+	12.9480i	1.00094	+	0.538564i
$579$	−0.456248	−	1.47912i	−0.0189610	−	0.0614701i
$580$	28.1747	−	15.7131i	1.16989	−	0.652452i
$581$	−3.49187	+	9.00105i	−0.144867	+	0.373426i
$582$	−2.24836	+	0.0674019i	−0.0931974	+	0.00279390i
$583$	−11.7165	+	29.8531i	−0.485246	+	1.23639i
$584$	5.90194	−	2.95289i	0.244224	−	0.122191i
$585$	23.7254	−	3.57603i	0.980924	−	0.147851i
$586$	14.3647	+	1.72670i	0.593400	+	0.0713292i
$587$		−	11.4370i		−	0.472055i	−0.971746	−	0.236027i	$-0.924155\pi$
$587$		−	11.4370i		−	0.472055i	0.971746	−	0.236027i	$-0.0758455\pi$
$588$	−1.00050	+	2.49769i	−0.0412597	+	0.103003i
$589$			14.0225i			0.577787i
$590$	−5.18171	+	43.1076i	−0.213328	+	1.77471i
$591$	−0.453507	+	0.0683551i	−0.0186548	+	0.00281175i
$592$	12.9578	+	5.53540i	0.532562	+	0.227504i
$593$	−12.2718	+	31.2679i	−0.503941	+	1.28402i	0.422083	+	0.906557i	$0.361299\pi$
$593$	−12.2718	+	31.2679i	−0.503941	+	1.28402i	−0.926024	+	0.377464i	$0.876796\pi$
$594$	0.131749	+	4.39480i	0.00540572	+	0.180321i
$595$	4.13658	+	52.4313i	0.169583	+	2.14947i
$596$	−9.97142	−	17.8795i	−0.408445	−	0.732371i
$597$	−0.267886	−	0.868464i	−0.0109638	−	0.0355438i
$598$	8.44587	−	15.6969i	0.345377	−	0.641894i
$599$	29.4394	+	9.08085i	1.20286	+	0.371033i	0.830481	−	0.557047i	$-0.188066\pi$
$599$	29.4394	+	9.08085i	1.20286	+	0.371033i	0.372380	+	0.928080i	$0.378542\pi$
$600$	1.84000	+	2.61307i	0.0751177	+	0.106678i
$601$	−3.11877	−	13.6642i	−0.127217	−	0.557375i	−0.997856	−	0.0654517i	$-0.979151\pi$
$601$	−3.11877	−	13.6642i	−0.127217	−	0.557375i	0.870639	−	0.491923i	$-0.163706\pi$
$602$	23.4616	+	32.0232i	0.956224	+	1.30517i
$603$	−13.5949	−	3.10294i	−0.553627	−	0.126362i
$604$	9.14252	−	28.1473i	0.372004	−	1.14530i
$605$	6.76416	+	9.92120i	0.275002	+	0.403354i
$606$	−0.665891	−	3.66833i	−0.0270500	−	0.149016i
$607$	11.2427	+	19.4730i	0.456329	+	0.790385i	0.998764	−	0.0497132i	$-0.0158307\pi$
$607$	11.2427	+	19.4730i	0.456329	+	0.790385i	−0.542435	+	0.840098i	$0.682497\pi$
$608$	−1.03225	+	13.8202i	−0.0418631	+	0.560482i
$609$	−1.07009	+	2.24460i	−0.0433622	+	0.0909558i
$610$	4.12055	−	9.25613i	0.166836	−	0.374770i
$611$	−9.27433	+	13.6029i	−0.375199	+	0.550316i
$612$	28.2516	−	21.8510i	1.14200	−	0.883274i
$613$	8.96579	−	9.66283i	0.362125	−	0.390278i	−0.525539	−	0.850769i	$-0.676136\pi$
$613$	8.96579	−	9.66283i	0.362125	−	0.390278i	0.887664	+	0.460492i	$0.152327\pi$
$614$	1.98033	+	18.8326i	0.0799195	+	0.760022i
$615$	1.15620	−	0.556794i	0.0466223	−	0.0224521i
$616$	−14.6161	+	14.0891i	−0.588901	+	0.567665i
$617$	20.4531	+	9.84967i	0.823409	+	0.396533i	0.797639	−	0.603135i	$-0.206082\pi$
$617$	20.4531	+	9.84967i	0.823409	+	0.396533i	0.0257699	+	0.999668i	$0.491796\pi$
$618$	−0.253086	+	0.706396i	−0.0101806	+	0.0284154i
$619$	26.4377	+	15.2638i	1.06262	+	0.613504i	0.926156	−	0.377141i	$-0.123093\pi$
$619$	26.4377	+	15.2638i	1.06262	+	0.613504i	0.136465	+	0.990645i	$0.456426\pi$
$620$	34.2584	−	15.8752i	1.37585	−	0.637563i
$621$	0.876930	−	5.81805i	0.0351900	−	0.233470i
$622$	−7.00665	−	13.4991i	−0.280941	−	0.541264i
$623$	−6.27064	−	40.5211i	−0.251228	−	1.62344i
$624$	−0.196903	+	1.87698i	−0.00788245	+	0.0751393i
$625$	−1.48194	−	19.7752i	−0.0592777	−	0.791007i
$626$	36.5172	−	15.6103i	1.45952	−	0.623915i
$627$	1.18902	−	0.466654i	0.0474847	−	0.0186364i
$628$	0.0536508	−	0.00727289i	0.00214090	−	0.000290220i
$629$	−16.5986	+	13.2370i	−0.661830	+	0.527792i
$630$	34.4737	+	12.1984i	1.37347	+	0.485996i
$631$	−30.4982	+	38.2435i	−1.21411	+	1.52245i	−0.428743	+	0.903427i	$0.641043\pi$
$631$	−30.4982	+	38.2435i	−1.21411	+	1.52245i	−0.785372	+	0.619024i	$0.787528\pi$
$632$	−24.9708	+	4.15049i	−0.993286	+	0.165098i
$633$	0.0423527	−	0.565158i	0.00168337	−	0.0224630i
$634$	−19.7346	−	17.2399i	−0.783760	−	0.684682i
$635$	−37.3512	−	40.2550i	−1.48224	−	1.59747i
$636$	−0.743929	+	4.48259i	−0.0294987	+	0.177746i
$637$	−17.1465	−	1.14942i	−0.679369	−	0.0455416i
$638$	−14.3115	+	12.1321i	−0.566598	+	0.480316i
$639$	−17.6628	+	16.3887i	−0.698731	+	0.648328i
$640$	34.9328	−	13.1243i	1.38084	−	0.518782i
$641$	0.964557	−	12.8711i	0.0380977	−	0.508379i	−0.945214	−	0.326451i	$-0.894147\pi$
$641$	0.964557	−	12.8711i	0.0380977	−	0.508379i	0.983312	−	0.181928i	$-0.0582337\pi$
$642$	−0.100762	−	0.294974i	−0.00397675	−	0.0116417i
$643$	−28.6305	−	22.8320i	−1.12908	−	0.900408i	−0.133196	−	0.991090i	$-0.542524\pi$
$643$	−28.6305	−	22.8320i	−1.12908	−	0.900408i	−0.995880	+	0.0906819i	$0.971095\pi$
$644$	22.6122	−	15.0574i	0.891046	−	0.593345i
$645$	−5.25827	+	4.19333i	−0.207044	+	0.165112i
$646$	−17.5974	−	11.2404i	−0.692360	−	0.442248i
$647$	10.9755	+	27.9651i	0.431491	+	1.09942i	0.966974	+	0.254875i	$0.0820343\pi$
$647$	10.9755	+	27.9651i	0.431491	+	1.09942i	−0.535483	+	0.844546i	$0.679870\pi$
$648$	−5.81661	−	23.8196i	−0.228498	−	0.935720i
$649$	−1.88701	−	25.1804i	−0.0740716	−	0.988417i
$650$	−12.2428	+	16.3330i	−0.480203	+	0.640634i
$651$	−1.44528	+	2.52618i	−0.0566449	+	0.0990089i
$652$	2.91694	−	7.11929i	0.114236	−	0.278813i
$653$	−4.38565	+	29.0969i	−0.171624	+	1.13865i	0.722678	+	0.691185i	$0.242911\pi$
$653$	−4.38565	+	29.0969i	−0.171624	+	1.13865i	−0.894302	+	0.447464i	$0.852327\pi$
$654$	−0.341709	+	1.23839i	−0.0133619	+	0.0484250i
$655$	−30.3335	+	52.5392i	−1.18523	+	2.05288i
$656$	−1.56648	−	7.94464i	−0.0611608	−	0.310186i
$657$	6.22891	+	2.99969i	0.243013	+	0.117029i
$658$	−22.2254	+	11.6472i	−0.866436	+	0.454054i
$659$	2.28247	+	4.73961i	0.0889126	+	0.184629i	0.940683	−	0.339286i	$-0.110185\pi$
$659$	2.28247	+	4.73961i	0.0889126	+	0.184629i	−0.851771	+	0.523915i	$0.824471\pi$
$660$	−2.48620	−	2.37658i	−0.0967751	−	0.0925082i
$661$	−13.1948	+	14.2206i	−0.513217	+	0.553116i	−0.935490	−	0.353353i	$-0.885042\pi$
$661$	−13.1948	+	14.2206i	−0.513217	+	0.553116i	0.422274	+	0.906468i	$0.361232\pi$
$662$	−0.720214	+	16.0545i	−0.0279919	+	0.623976i
$663$	−2.34947	−	1.60184i	−0.0912460	−	0.0622105i
$664$	−5.68466	+	8.61467i	−0.220608	+	0.334314i
$665$	−0.0840726	−	21.3792i	−0.00326020	−	0.829051i
$666$	3.71446	+	14.2864i	0.143933	+	0.553585i
$667$	21.7434	−	12.5536i	0.841908	−	0.486076i
$668$	20.5996	+	16.9345i	0.797023	+	0.655216i
$669$	2.42684	+	3.55952i	0.0938271	+	0.137619i
$670$	18.6737	−	11.5408i	0.721427	−	0.445860i
$671$	−1.31121	+	5.74477i	−0.0506185	+	0.221774i
$672$	−1.61039	+	2.38335i	−0.0621220	+	0.0919395i
$673$	−2.11007	−	9.24484i	−0.0813374	−	0.356362i	0.917838	−	0.396954i	$-0.129933\pi$
$673$	−2.11007	−	9.24484i	−0.0813374	−	0.356362i	−0.999176	+	0.0405918i	$0.987076\pi$
$674$	−14.2039	−	14.4166i	−0.547114	−	0.555306i
$675$	−1.98600	+	6.43845i	−0.0764411	+	0.247816i
$676$	13.6410	−	2.90088i	0.524652	−	0.111572i
$677$	−5.71126	−	18.5154i	−0.219501	−	0.711606i	−0.996612	−	0.0822424i	$-0.973792\pi$
$677$	−5.71126	−	18.5154i	−0.219501	−	0.711606i	0.777111	−	0.629364i	$-0.216684\pi$
$678$	0.226001	−	1.14769i	0.00867952	−	0.0440769i
$679$	3.17829	−	21.6643i	0.121972	−	0.831400i
$680$	−7.53908	+	55.7178i	−0.289111	+	2.13668i
$681$	−0.430994	+	1.09816i	−0.0165157	+	0.0420814i
$682$	−17.7648	+	12.9082i	−0.680249	+	0.494281i
$683$	−3.06134	−	20.3106i	−0.117139	−	0.777165i	−0.967849	−	0.251531i	$-0.919066\pi$
$683$	−3.06134	−	20.3106i	−0.117139	−	0.777165i	0.850711	−	0.525635i	$-0.176172\pi$
$684$	−12.1159	+	7.99932i	−0.463261	+	0.305862i
$685$		−	76.8030i		−	2.93449i
$686$	−22.2377	−	13.8378i	−0.849039	−	0.528330i
$687$	4.97170			0.189682
$688$	17.2691	+	38.7665i	0.658380	+	1.47796i
$689$	−28.6976	+	4.32547i	−1.09329	+	0.164787i
$690$	2.70551	+	3.72342i	0.102997	+	0.141748i
$691$	7.71014	+	3.02601i	0.293308	+	0.115115i	0.507432	−	0.861692i	$-0.330595\pi$
$691$	7.71014	+	3.02601i	0.293308	+	0.115115i	−0.214125	+	0.976806i	$0.568690\pi$
$692$	25.9545	−	23.3741i	0.986641	−	0.888552i
$693$	−21.0422	−	3.08702i	−0.799326	−	0.117266i
$694$	7.23141	−	36.7230i	0.274501	−	1.39399i
$695$	−31.6572	+	9.76496i	−1.20083	+	0.370406i
$696$	−1.62585	+	2.10316i	−0.0616276	+	0.0797201i
$697$	11.6587	+	3.59623i	0.441604	+	0.136217i
$698$	34.9831	−	34.4670i	1.32413	−	1.30460i
$699$	−4.14165	+	0.945304i	−0.156652	+	0.0357547i
$700$	−28.1751	+	13.1910i	−1.06492	+	0.498575i
$701$	23.9176	+	5.45904i	0.903356	+	0.206185i	0.648877	−	0.760893i	$-0.275239\pi$
$701$	23.9176	+	5.45904i	0.903356	+	0.206185i	0.254479	+	0.967078i	$0.418096\pi$
$702$	−3.38465	+	2.09180i	−0.127745	+	0.0789498i
$703$	7.13053	−	4.86152i	0.268933	−	0.183356i
$704$	−18.4587	+	11.4143i	−0.695689	+	0.430191i
$705$	−2.12555	−	3.68156i	−0.0800529	−	0.138656i
$706$	7.19898	−	1.87174i	0.270937	−	0.0704439i
$707$	36.2922	−	0.142717i	1.36491	−	0.00536743i
$708$	−1.00364	−	3.43409i	−0.0377190	−	0.129061i
$709$	−8.98561	+	13.1795i	−0.337462	+	0.494965i	−0.957035	−	0.289974i	$-0.906353\pi$
$709$	−8.98561	+	13.1795i	−0.337462	+	0.494965i	0.619573	+	0.784939i	$0.287306\pi$
$710$	1.69992	−	37.8933i	0.0637967	−	1.42211i
$711$	−19.4393	−	18.0371i	−0.729032	−	0.676442i
$712$	2.61500	−	43.7565i	0.0980014	−	1.63984i
$713$	26.4758	−	12.7501i	0.991525	−	0.477493i
$714$	−2.01168	−	3.83873i	−0.0752851	−	0.143661i
$715$	9.53122	−	19.7918i	0.356447	−	0.740171i
$716$	15.5188	+	41.3373i	0.579965	+	1.54485i
$717$	3.23436	+	1.86736i	0.120790	+	0.0697379i
$718$	−2.91126	+	10.5507i	−0.108647	+	0.393750i
$719$	−9.48810	−	1.43010i	−0.353846	−	0.0533338i	−0.0302860	−	0.999541i	$-0.509642\pi$
$719$	−9.48810	−	1.43010i	−0.353846	−	0.0533338i	−0.323560	+	0.946208i	$0.604880\pi$
$720$	33.2598	+	20.5441i	1.23952	+	0.765632i
$721$	−6.34006	−	3.62727i	−0.236116	−	0.135086i
$722$	−14.7086	−	11.0252i	−0.547397	−	0.410315i
$723$	4.68651	−	0.351205i	0.174293	−	0.0130615i
$724$	−29.1295	−	14.5652i	−1.08259	−	0.541311i
$725$	−26.7639	+	10.5041i	−0.993988	+	0.390111i
$726$	−0.833867	−	0.532637i	−0.0309477	−	0.0197680i
$727$	11.6045	+	14.5516i	0.430388	+	0.539690i	0.948982	−	0.315331i	$-0.102116\pi$
$727$	11.6045	+	14.5516i	0.430388	+	0.539690i	−0.518593	+	0.855021i	$0.673544\pi$
$728$	−17.6552	−	5.07987i	−0.654346	−	0.188273i
$729$	15.6034	−	19.5660i	0.577903	−	0.724667i
$730$	−10.2994	+	3.51822i	−0.381196	+	0.130215i
$731$	−63.7643	−	4.77848i	−2.35841	−	0.176738i
$732$	−0.0124070	+	0.834801i	−0.000458577	+	0.0308551i
$733$	−5.48843	−	5.91512i	−0.202720	−	0.218480i	0.623507	−	0.781818i	$-0.285707\pi$
$733$	−5.48843	−	5.91512i	−0.202720	−	0.218480i	−0.826227	+	0.563338i	$0.809517\pi$
$734$	−6.05959	+	5.13682i	−0.223664	+	0.189604i
$735$	2.18838	−	3.86018i	0.0807196	−	0.142385i
$736$	27.0324	−	10.6171i	0.996426	−	0.391353i
$737$	−9.35883	+	8.68372i	−0.344737	+	0.319869i
$738$	5.58102	−	6.38863i	0.205440	−	0.235169i
$739$	14.7620	+	1.10626i	0.543027	+	0.0406943i	0.343420	−	0.939182i	$-0.388414\pi$
$739$	14.7620	+	1.10626i	0.543027	+	0.0406943i	0.199607	+	0.979876i	$0.436034\pi$
$740$	−19.9498	−	11.9168i	−0.733371	−	0.438070i
$741$	0.903724	+	0.720696i	0.0331991	+	0.0264754i
$742$	−41.6986	−	14.7549i	−1.53080	−	0.541669i
$743$	−26.1401	−	32.7787i	−0.958989	−	1.20253i	−0.979233	−	0.202739i	$-0.935016\pi$
$743$	−26.1401	−	32.7787i	−0.958989	−	1.20253i	0.0202441	−	0.999795i	$-0.493556\pi$
$744$	−2.08156	+	2.31249i	−0.0763136	+	0.0847800i
$745$	12.3347	+	31.4283i	0.451909	+	1.15145i
$746$	−6.15134	−	14.3898i	−0.225217	−	0.526849i
$747$	−10.7823	+	0.808022i	−0.394504	+	0.0295640i
$748$	−1.95880	−	32.6410i	−0.0716209	−	1.19347i
$749$	2.99860	−	0.464033i	0.109567	−	0.0169554i
$750$	−0.363130	−	0.699609i	−0.0132596	−	0.0255461i
$751$	11.7477	+	1.77068i	0.428679	+	0.0646130i	0.359838	−	0.933015i	$-0.382832\pi$
$751$	11.7477	+	1.77068i	0.428679	+	0.0646130i	0.0688407	+	0.997628i	$0.478070\pi$
$752$	−25.8567	+	7.14150i	−0.942897	+	0.260424i
$753$	−2.32340	+	4.02424i	−0.0846693	+	0.146652i
$754$	−15.9837	−	5.72661i	−0.582093	−	0.208551i
$755$	−21.1767	+	43.9739i	−0.770700	+	1.60038i
$756$	−6.05184	+	0.387064i	−0.220103	+	0.0140774i
$757$	−5.05915	−	10.5054i	−0.183878	−	0.381826i	0.788571	−	0.614944i	$-0.210821\pi$
$757$	−5.05915	−	10.5054i	−0.183878	−	0.381826i	−0.972448	+	0.233118i	$0.925107\pi$
$758$	1.87464	+	17.8276i	0.0680901	+	0.647526i
$759$	−1.96221	−	1.82066i	−0.0712237	−	0.0660859i
$760$	4.74862	−	22.3568i	0.172251	−	0.810966i
$761$	−7.91905	−	5.39912i	−0.287066	−	0.195718i	0.411222	−	0.911535i	$-0.365102\pi$
$761$	−7.91905	−	5.39912i	−0.287066	−	0.195718i	−0.698288	+	0.715817i	$0.746054\pi$
$762$	4.13395	+	1.84031i	0.149757	+	0.0666673i
$763$	−11.2883	−	5.38158i	−0.408664	−	0.194826i
$764$	3.42402	−	4.86518i	0.123877	−	0.176016i
$765$	−51.0106	+	29.4510i	−1.84429	+	1.06480i
$766$	3.87213	+	21.3312i	0.139906	+	0.770728i
$767$	18.8804	−	12.8724i	0.681730	−	0.464796i
$768$	−2.22176	+	2.12590i	−0.0801707	+	0.0767117i
$769$	−6.85068	+	30.0148i	−0.247042	+	1.08236i	0.687409	+	0.726270i	$0.258748\pi$
$769$	−6.85068	+	30.0148i	−0.247042	+	1.08236i	−0.934451	+	0.356091i	$0.884109\pi$
$770$	27.0075	−	19.7869i	0.973283	−	0.713070i
$771$	1.33378	−	0.304426i	0.0480349	−	0.0109636i
$772$	16.0434	+	1.44233i	0.577414	+	0.0519107i
$773$	−9.80332	+	31.7816i	−0.352601	+	1.14310i	0.589498	+	0.807770i	$0.299326\pi$
$773$	−9.80332	+	31.7816i	−0.352601	+	1.14310i	−0.942099	+	0.335335i	$0.891151\pi$
$774$	−21.0658	+	39.1515i	−0.757196	+	1.40727i
$775$	−32.1562	+	9.91887i	−1.15508	+	0.356296i
$776$	8.22174	−	21.9166i	0.295143	−	0.786761i
$777$	1.78565	−	0.140880i	0.0640599	−	0.00505403i
$778$	33.6347	−	1.00831i	1.20586	−	0.0361497i
$779$	−4.61673	−	1.81193i	−0.165411	−	0.0649192i
$780$	0.737608	−	3.02381i	0.0264106	−	0.108270i
$781$	3.28790	+	21.8138i	0.117650	+	0.780559i
$782$	−5.22239	+	43.4460i	−0.186752	+	1.55362i
$783$	−5.60443			−0.200286
$784$	−20.1043	−	19.4889i	−0.718011	−	0.696032i
$785$	−0.0892894			−0.00318687
$786$	0.596621	−	4.96339i	0.0212808	−	0.177038i
$787$	0.612336	+	4.06258i	0.0218274	+	0.144815i	0.997090	−	0.0762344i	$-0.0242897\pi$
$787$	0.612336	+	4.06258i	0.0218274	+	0.144815i	−0.975263	+	0.221050i	$0.929052\pi$
$788$	1.13106	−	4.63676i	0.0402924	−	0.165178i
$789$	−3.66996	−	1.44035i	−0.130654	−	0.0512779i
$790$	41.7278	−	1.25093i	1.48461	−	0.0445060i
$791$	10.6158	+	4.11829i	0.377454	+	0.146430i
$792$	−21.2873	−	7.98564i	−0.756410	−	0.283757i
$793$	−5.09554	+	1.57176i	−0.180948	+	0.0558150i
$794$	−23.3639	+	43.4225i	−0.829153	+	1.54101i
$795$	2.20882	−	7.16081i	0.0783387	−	0.253968i
$796$	9.41986	+	0.846865i	0.333878	+	0.0300163i
$797$	−20.3483	+	4.64437i	−0.720774	+	0.164512i	−0.567147	−	0.823617i	$-0.691953\pi$
$797$	−20.3483	+	4.64437i	−0.720774	+	0.164512i	−0.153628	+	0.988129i	$0.549096\pi$
$798$	0.698844	+	1.61718i	0.0247388	+	0.0572475i
$799$	8.99367	−	39.4038i	0.318173	−	1.39401i
$800$	−32.4224	+	7.40863i	−1.14631	+	0.261935i
$801$	37.9418	−	25.8683i	1.34061	−	0.914011i
$802$	4.51860	+	24.8925i	0.159557	+	0.878986i
$803$	5.48172	−	3.16487i	0.193446	−	0.111686i
$804$	−1.04109	+	1.47929i	−0.0367166	+	0.0521704i
$805$	−40.2895	+	19.5980i	−1.42002	+	0.690738i
$806$	−18.1545	−	8.08182i	−0.639464	−	0.284670i
$807$	3.31915	+	2.26296i	0.116840	+	0.0796598i
$808$	37.9517	+	8.06100i	1.33514	+	0.283585i
$809$	18.5141	+	17.1786i	0.650921	+	0.603966i	0.934920	−	0.354858i	$-0.115471\pi$
$809$	18.5141	+	17.1786i	0.650921	+	0.603966i	−0.283999	+	0.958824i	$0.591661\pi$
$810$	4.22882	+	40.2154i	0.148586	+	1.41303i
$811$	10.9652	+	22.7696i	0.385042	+	0.799547i	0.999940	+	0.0109409i	$0.00348267\pi$
$811$	10.9652	+	22.7696i	0.385042	+	0.799547i	−0.614899	+	0.788606i	$0.710803\pi$
$812$	−17.3925	−	19.1605i	−0.610359	−	0.672401i
$813$	−0.163314	+	0.339124i	−0.00572766	+	0.0118936i
$814$	12.7229	+	4.55832i	0.445936	+	0.159769i
$815$	−6.34416	+	10.9884i	−0.222226	+	0.384907i
$816$	−1.23347	−	4.46592i	−0.0431799	−	0.156339i
$817$	25.7024	+	3.87401i	0.899213	+	0.135535i
$818$	20.5009	+	39.4972i	0.716797	+	1.38099i
$819$	−7.10176	−	17.8878i	−0.248155	−	0.625051i
$820$	0.799969	+	13.3305i	0.0279361	+	0.465520i
$821$	46.7985	−	3.50706i	1.63328	−	0.122397i	0.773751	−	0.633489i	$-0.218378\pi$
$821$	46.7985	−	3.50706i	1.63328	−	0.122397i	0.859526	+	0.511092i	$0.170759\pi$
$822$	2.48765	+	5.81935i	0.0867668	+	0.202973i
$823$	−3.17454	−	8.08859i	−0.110657	−	0.281951i	0.864808	−	0.502102i	$-0.167440\pi$
$823$	−3.17454	−	8.08859i	−0.110657	−	0.281951i	−0.975466	+	0.220152i	$0.929345\pi$
$824$	−5.80375	−	5.22416i	−0.202183	−	0.181992i
$825$	1.91118	+	2.39655i	0.0665388	+	0.0834370i
$826$	34.6216	−	3.77832i	1.20464	−	0.131464i
$827$	32.2246	+	25.6982i	1.12056	+	0.893615i	0.995138	−	0.0984886i	$-0.0314008\pi$
$827$	32.2246	+	25.6982i	1.12056	+	0.893615i	0.125420	+	0.992104i	$0.459972\pi$
$828$	26.1199	+	15.6024i	0.907729	+	0.542221i
$829$	−24.7186	−	1.85240i	−0.858511	−	0.0643365i	−0.361804	−	0.932254i	$-0.617839\pi$
$829$	−24.7186	−	1.85240i	−0.858511	−	0.0643365i	−0.496708	+	0.867918i	$0.665458\pi$
$830$	11.1986	−	12.8191i	0.388708	−	0.444956i
$831$	0.781587	−	0.725207i	0.0271129	−	0.0251571i
$832$	−17.2976	−	9.30164i	−0.599687	−	0.322476i
$833$	40.2145	−	12.7518i	1.39335	−	0.441822i
$834$	2.08238	−	1.76527i	0.0721068	−	0.0611262i
$835$	−29.9130	−	32.2386i	−1.03518	−	1.11566i
$836$	−0.197532	+	13.2909i	−0.00683180	+	0.459674i
$837$	−6.54120	−	0.490195i	−0.226097	−	0.0169436i
$838$	−39.6783	+	13.5539i	−1.37066	+	0.468213i
$839$	16.9408	−	21.2431i	0.584860	−	0.733392i	−0.398073	−	0.917354i	$-0.630321\pi$
$839$	16.9408	−	21.2431i	0.584860	−	0.733392i	0.982933	+	0.183962i	$0.0588924\pi$
$840$	3.15976	−	3.53819i	0.109022	−	0.122079i
$841$	3.17034	+	3.97548i	0.109322	+	0.137086i
$842$	41.3691	+	26.4247i	1.42567	+	0.910656i
$843$	3.12886	−	1.22799i	0.107764	−	0.0422941i
$844$	5.27512	+	2.63764i	0.181577	+	0.0907914i
$845$	−22.9352	+	1.71876i	−0.788996	+	0.0591271i
$846$	−22.4860	−	16.8549i	−0.773083	−	0.579484i
$847$	6.52348	−	7.08632i	0.224149	−	0.243489i
$848$	−40.2303	−	24.8496i	−1.38151	−	0.853338i
$849$	−0.609032	−	0.0917967i	−0.0209019	−	0.00315046i
$850$	13.3288	−	48.3051i	0.457174	−	1.65685i
$851$	−15.6625	−	9.04274i	−0.536903	−	0.309981i
$852$	1.09856	+	2.92623i	0.0376362	+	0.100251i
$853$	−6.94130	+	14.4138i	−0.237665	+	0.493517i	−0.985352	−	0.170535i	$-0.945450\pi$
$853$	−6.94130	+	14.4138i	−0.237665	+	0.493517i	0.747686	+	0.664052i	$0.231165\pi$
$854$	−7.98015	−	1.53886i	−0.273075	−	0.0526587i
$855$	21.5723	−	10.3887i	0.737758	−	0.355286i
$856$	3.23802	+	0.193513i	0.110673	+	0.00661413i
$857$	6.84053	+	6.34709i	0.233668	+	0.216812i	0.788312	−	0.615275i	$-0.210955\pi$
$857$	6.84053	+	6.34709i	0.233668	+	0.216812i	−0.554644	+	0.832088i	$0.687146\pi$
$858$	−0.0811230	+	1.80834i	−0.00276949	+	0.0617356i
$859$	16.1121	−	23.6321i	0.549739	−	0.806319i	−0.446333	−	0.894867i	$-0.647270\pi$
$859$	16.1121	−	23.6321i	0.549739	−	0.806319i	0.996072	+	0.0885483i	$0.0282228\pi$
$860$	−19.6337	−	67.1795i	−0.669503	−	2.29080i
$861$	−0.644961	−	0.802263i	−0.0219802	−	0.0273410i
$862$	35.8964	−	9.33309i	1.22264	−	0.317886i
$863$	−6.97180	−	12.0755i	−0.237323	−	0.411055i	0.722622	−	0.691243i	$-0.242937\pi$
$863$	−6.97180	−	12.0755i	−0.237323	−	0.411055i	−0.959945	+	0.280188i	$0.909603\pi$
$864$	−6.41074	−	0.964644i	−0.218098	−	0.0328178i
$865$	−47.5940	+	32.4491i	−1.61825	+	1.10330i
$866$	−0.872034	+	0.538939i	−0.0296329	+	0.0183139i
$867$	3.62048	+	0.826351i	0.122958	+	0.0280643i
$868$	−18.6238	−	23.8843i	−0.632132	−	0.810688i
$869$	−23.6702	+	5.40258i	−0.802958	+	0.183270i
$870$	3.12295	−	3.07688i	0.105878	−	0.104316i
$871$	−11.0402	−	3.40545i	−0.374083	−	0.115389i
$872$	−10.5770	−	8.17653i	−0.358182	−	0.276892i
$873$	23.4328	−	7.22807i	0.793081	−	0.244633i
$874$	3.43674	−	17.4526i	0.116249	−	0.590344i
$875$	7.32316	−	2.29047i	0.247568	−	0.0774321i
$876$	0.666425	−	0.600171i	0.0225164	−	0.0202779i
$877$	−38.0978	−	14.9523i	−1.28647	−	0.504902i	−0.379147	−	0.925336i	$-0.623783\pi$
$877$	−38.0978	−	14.9523i	−1.28647	−	0.504902i	−0.907323	+	0.420434i	$0.861878\pi$
$878$	4.93368	+	6.78992i	0.166504	+	0.229149i
$879$	1.94421	−	0.293043i	0.0655766	−	0.00988409i
$880$	32.6946	−	14.5643i	1.10214	−	0.490963i
$881$	−29.9935			−1.01051			−0.505254	−	0.862971i	$-0.668601\pi$
$881$	−29.9935			−1.01051			−0.505254	+	0.862971i	$0.668601\pi$
$882$	3.27158	−	29.1498i	0.110160	−	0.981526i
$883$		−	22.0162i		−	0.740904i	−0.928852	−	0.370452i	$-0.879203\pi$
$883$		−	22.0162i		−	0.740904i	0.928852	−	0.370452i	$-0.120797\pi$
$884$	24.6948	−	16.3044i	0.830577	−	0.548377i
$885$	0.879404	+	5.83446i	0.0295608	+	0.196123i
$886$	35.2147	−	25.5876i	1.18306	−	0.859634i
$887$	5.27791	−	13.4479i	0.177215	−	0.451536i	−0.814473	−	0.580201i	$-0.802974\pi$
$887$	5.27791	−	13.4479i	0.177215	−	0.451536i	0.991688	+	0.128665i	$0.0410692\pi$
$888$	1.89758	+	0.256759i	0.0636787	+	0.00861625i
$889$	−24.6703	+	36.4921i	−0.827414	+	1.22391i
$890$	−13.9672	+	70.9292i	−0.468182	+	2.37755i
$891$	−6.93190	−	22.4727i	−0.232227	−	0.752862i
$892$	−43.8517	+	9.32549i	−1.46826	+	0.312240i
$893$	−4.84267	+	15.6996i	−0.162054	+	0.525366i
$894$	−1.95256	−	1.98180i	−0.0653035	−	0.0662813i
$895$	−16.2037	−	70.9929i	−0.541629	−	2.37303i
$896$	−16.5969	−	24.9107i	−0.554462	−	0.832209i
$897$	0.539023	−	2.36161i	0.0179975	−	0.0788520i
$898$	−34.9794	+	21.6181i	−1.16728	+	0.721406i
$899$	−15.7678	−	23.1271i	−0.525885	−	0.771331i
$900$	−26.9141	−	22.1256i	−0.897138	−	0.737519i
$901$	61.7011	−	35.6232i	2.05556	−	1.18678i
$902$	−1.95437	−	7.51678i	−0.0650734	−	0.250281i
$903$	4.23106	+	3.34702i	0.140801	+	0.111382i
$904$	10.1601	+	6.70446i	0.337920	+	0.222987i
$905$	44.3778	+	30.2563i	1.47517	+	1.00575i
$906$	0.180241	−	4.01781i	0.00598812	−	0.133483i
$907$	6.70491	−	7.22617i	0.222633	−	0.239941i	−0.611852	−	0.790973i	$-0.709575\pi$
$907$	6.70491	−	7.22617i	0.222633	−	0.239941i	0.834485	+	0.551031i	$0.185766\pi$
$908$	−8.87429	−	8.48301i	−0.294504	−	0.281519i
$909$	17.6353	+	36.6200i	0.584925	+	1.21461i
$910$	27.7275	+	12.2130i	0.919157	+	0.404857i
$911$	2.11294	+	1.01754i	0.0700048	+	0.0337125i	0.468559	−	0.883432i	$-0.344773\pi$
$911$	2.11294	+	1.01754i	0.0700048	+	0.0337125i	−0.398554	+	0.917145i	$0.630488\pi$
$912$	0.364335	+	1.84778i	0.0120643	+	0.0611861i
$913$	−4.94973	+	8.57319i	−0.163812	+	0.283731i
$914$	9.16224	−	33.2050i	0.303060	−	1.09833i
$915$	0.205215	−	1.36151i	0.00678421	−	0.0450103i
$916$	−19.6156	+	47.8753i	−0.648119	+	1.58185i
$917$	46.5574	+	14.1608i	1.53746	+	0.467631i
$918$	5.85858	−	7.81587i	0.193362	−	0.257962i
$919$	−2.60820	−	34.8040i	−0.0860365	−	1.14808i	−0.858429	−	0.512932i	$-0.828559\pi$
$919$	−2.60820	−	34.8040i	−0.0860365	−	1.14808i	0.772393	−	0.635145i	$-0.219060\pi$
$920$	−46.5294	+	11.3623i	−1.53403	+	0.374602i
$921$	0.940172	+	2.39552i	0.0309797	+	0.0789350i
$922$	9.73671	+	6.21937i	0.320662	+	0.204824i
$923$	−15.6080	+	12.4470i	−0.513745	+	0.409698i
$924$	−1.40546	+	2.37402i	−0.0462361	+	0.0780996i
$925$	16.1922	+	12.9128i	0.532396	+	0.424571i
$926$	−3.13805	−	9.18642i	−0.103123	−	0.301884i
$927$	0.611320	−	8.15750i	0.0200784	−	0.267927i
$928$	−13.8378	−	23.9541i	−0.454248	−	0.786333i
$929$	21.3379	−	19.7986i	0.700072	−	0.649572i	−0.247583	−	0.968867i	$-0.579636\pi$
$929$	21.3379	−	19.7986i	0.700072	−	0.649572i	0.947656	+	0.319294i	$0.103446\pi$
$930$	3.91406	−	3.31802i	0.128347	−	0.108802i
$931$	−16.6887	+	3.94744i	−0.546951	+	0.129372i
$932$	7.23783	−	43.6119i	0.237083	−	1.42856i
$933$	−1.40584	−	1.51513i	−0.0460250	−	0.0496031i
$934$	−10.5185	−	9.18879i	−0.344175	−	0.300667i
$935$	−4.03004	+	53.7771i	−0.131796	+	1.75870i
$936$	−3.37354	−	20.2964i	−0.110268	−	0.663409i
$937$	−3.32272	+	4.16655i	−0.108548	+	0.136115i	−0.833138	−	0.553065i	$-0.813458\pi$
$937$	−3.32272	+	4.16655i	−0.108548	+	0.136115i	0.724589	+	0.689181i	$0.242029\pi$
$938$	−12.4076	−	12.4947i	−0.405121	−	0.407966i
$939$	4.21954	−	3.36497i	0.137700	−	0.109812i
$940$	43.8382	−	5.94269i	1.42984	−	0.193829i
$941$	19.6791	−	7.72346i	0.641519	−	0.251778i	−0.0222069	−	0.999753i	$-0.507069\pi$
$941$	19.6791	−	7.72346i	0.641519	−	0.251778i	0.663726	+	0.747976i	$0.268974\pi$
$942$	0.00676544	−	0.00289208i	0.000220430	−	9.42292e-5i
$943$	0.776699	+	10.3643i	0.0252928	+	0.337509i
$944$	37.0286	+	3.88447i	1.20518	+	0.126429i
$945$	9.97590	+	0.708152i	0.324516	+	0.0230362i
$946$	18.7521	+	36.1280i	0.609683	+	1.17462i
$947$	4.18515	−	27.7666i	0.135999	−	0.902295i	−0.811917	−	0.583773i	$-0.801576\pi$
$947$	4.18515	−	27.7666i	0.135999	−	0.902295i	0.947916	−	0.318521i	$-0.103186\pi$
$948$	−3.12119	+	1.44635i	−0.101371	+	0.0469751i
$949$	4.96070	+	2.86406i	0.161031	+	0.0929713i
$950$	−6.87036	+	19.1761i	−0.222904	+	0.622154i
$951$	−3.20843	−	1.54510i	−0.104041	−	0.0501033i
$952$	44.9023	−	4.22606i	1.45529	−	0.136967i
$953$	−18.9007	+	9.10210i	−0.612254	+	0.294846i	−0.714197	−	0.699944i	$-0.753208\pi$
$953$	−18.9007	+	9.10210i	−0.612254	+	0.294846i	0.101944	+	0.994790i	$0.467494\pi$
$954$	−5.18046	−	49.2654i	−0.167724	−	1.59502i
$955$	−6.67349	+	7.19231i	−0.215949	+	0.232738i
$956$	−30.7429	+	23.7779i	−0.994297	+	0.769033i
$957$	−1.43629	+	2.10665i	−0.0464286	+	0.0680983i
$958$	19.4816	−	43.7621i	0.629421	−	1.41389i
$959$	−60.0077	+	13.9449i	−1.93775	+	0.450303i
$960$	4.10184	−	2.98202i	0.132386	−	0.0962443i
$961$	−0.880484	−	1.52504i	−0.0284027	−	0.0491949i
$962$	2.18439	+	12.0336i	0.0704276	+	0.387979i
$963$	1.91428	+	2.80773i	0.0616867	+	0.0904778i
$964$	−15.1085	+	46.5147i	−0.486611	+	1.49814i
$965$	−25.8992	−	5.91132i	−0.833724	−	0.190292i
$966$	2.41795	−	2.78991i	0.0777964	−	0.0897640i
$967$	2.26588	+	9.92748i	0.0728658	+	0.319246i	0.998205	−	0.0598951i	$-0.0190766\pi$
$967$	2.26588	+	9.92748i	0.0728658	+	0.319246i	−0.925339	+	0.379141i	$0.876219\pi$
$968$	8.41905	−	5.92828i	0.270598	−	0.190542i
$969$	−2.71160	−	0.836417i	−0.0871090	−	0.0268696i
$970$	−18.2916	+	33.9956i	−0.587309	+	1.09153i
$971$	16.8167	+	54.5183i	0.539672	+	1.74957i	0.654370	+	0.756174i	$0.272934\pi$
$971$	16.8167	+	54.5183i	0.539672	+	1.74957i	−0.114698	+	0.993400i	$0.536590\pi$
$972$	−4.97220	−	8.91551i	−0.159483	−	0.285965i
$973$	13.3774	+	22.9614i	0.428861	+	0.736109i
$974$	0.321058	+	10.7097i	0.0102874	+	0.343160i
$975$	−1.01344	+	2.58220i	−0.0324560	+	0.0826965i
$976$	−7.98982	−	3.41314i	−0.255748	−	0.109252i
$977$	−35.5120	+	5.35257i	−1.13613	+	0.171244i	−0.690058	−	0.723754i	$-0.742415\pi$
$977$	−35.5120	+	5.35257i	−1.13613	+	0.171244i	−0.446070	+	0.894998i	$0.647177\pi$
$978$	0.124781	−	1.03808i	0.00399007	−	0.0331941i
$979$		−	42.0432i		−	1.34371i
$980$	28.5377	+	36.3033i	0.911604	+	1.15967i
$981$		−	14.0053i		−	0.447155i
$982$	45.9317	+	5.52119i	1.46574	+	0.176188i
$983$	11.5992	−	1.74830i	0.369957	−	0.0557621i	0.0385673	−	0.999256i	$-0.487721\pi$
$983$	11.5992	−	1.74830i	0.369957	−	0.0557621i	0.331390	+	0.943494i	$0.392483\pi$
$984$	−0.492388	−	0.984137i	−0.0156967	−	0.0313731i
$985$	−2.87564	+	7.32701i	−0.0916255	+	0.233458i
$986$	41.6625	−	1.24897i	1.32681	−	0.0397754i
$987$	−2.49055	+	2.32918i	−0.0792750	+	0.0741387i
$988$	−10.5056	+	5.85900i	−0.334228	+	0.186400i
$989$	−16.0556	−	52.0510i	−0.510539	−	1.65513i
$990$	33.0193	+	17.7664i	1.04942	+	0.564652i
$991$	4.72670	+	1.45799i	0.150149	+	0.0463147i	0.368918	−	0.929462i	$-0.379728\pi$
$991$	4.72670	+	1.45799i	0.150149	+	0.0463147i	−0.218770	+	0.975776i	$0.570204\pi$
$992$	−14.0556	−	29.1683i	−0.446266	−	0.926095i
$993$	0.485976	+	2.12920i	0.0154220	+	0.0675681i
$994$	−29.9154	+	5.55198i	−0.948860	+	0.176098i
$995$	−15.2067	−	3.47083i	−0.482084	−	0.110033i
$996$	−0.433304	+	1.33402i	−0.0137298	+	0.0422701i
$997$	9.86881	+	14.4749i	0.312548	+	0.458424i	0.950083	−	0.311997i	$-0.100998\pi$
$997$	9.86881	+	14.4749i	0.312548	+	0.458424i	−0.637535	+	0.770422i	$0.720046\pi$
$998$	−4.92587	+	0.894165i	−0.155926	+	0.0283043i
$999$	2.01853	+	3.49619i	0.0638634	+	0.110615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.25	yes	648
8.5	even	2	inner	392.2.z.a.109.2	✓	648
49.9	even	21	inner	392.2.z.a.205.2	yes	648
392.205	even	42	inner	392.2.z.a.205.25	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.2	✓	648	8.5	even	2	inner
392.2.z.a.109.25	yes	648	1.1	even	1	trivial
392.2.z.a.205.2	yes	648	49.9	even	21	inner
392.2.z.a.205.25	yes	648	392.205	even	42	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.168780 + 1.40411i) q^{2} +(0.0286441 + 0.190041i) q^{3} +(-1.94303 - 0.473969i) q^{4} +(3.07037 + 1.20503i) q^{5} +(-0.271672 + 0.00814427i) q^{6} +(0.384038 - 2.61773i) q^{7} +(0.993446 - 2.64822i) q^{8} +(2.83142 - 0.873378i) q^{9} +O(q^{10})\)	\(q+(-0.168780 + 1.40411i) q^{2} +(0.0286441 + 0.190041i) q^{3} +(-1.94303 - 0.473969i) q^{4} +(3.07037 + 1.20503i) q^{5} +(-0.271672 + 0.00814427i) q^{6} +(0.384038 - 2.61773i) q^{7} +(0.993446 - 2.64822i) q^{8} +(2.83142 - 0.873378i) q^{9} +(-2.21021 + 4.10774i) q^{10} +(0.799625 - 2.59232i) q^{11} +(0.0344173 - 0.382831i) q^{12} +(2.39344 - 0.546288i) q^{13} +(3.61075 + 0.981049i) q^{14} +(-0.141057 + 0.618013i) q^{15} +(3.55071 + 1.84187i) q^{16} +(-4.97960 + 3.39504i) q^{17} +(0.748429 + 4.12303i) q^{18} +(2.12167 - 1.22495i) q^{19} +(-5.39466 - 3.79667i) q^{20} +(0.508477 - 0.00199956i) q^{21} +(3.50493 + 1.56029i) q^{22} +(-4.24195 - 2.89212i) q^{23} +(0.531727 + 0.112940i) q^{24} +(4.30980 + 3.99891i) q^{25} +(0.363082 + 3.45285i) q^{26} +(0.497242 + 1.03253i) q^{27} +(-1.98692 + 4.90430i) q^{28} +(-2.12183 + 4.40602i) q^{29} +(-0.843948 - 0.302367i) q^{30} +(-2.86186 + 4.95689i) q^{31} +(-3.18546 + 4.67470i) q^{32} +(0.515551 + 0.0777069i) q^{33} +(-3.92653 - 7.56490i) q^{34} +(4.33358 - 7.57462i) q^{35} +(-5.91549 + 0.354992i) q^{36} +(3.51280 - 0.263248i) q^{37} +(1.36186 + 3.18579i) q^{38} +(0.172375 + 0.439205i) q^{39} +(6.24143 - 6.93388i) q^{40} +(-1.26219 - 1.58274i) q^{41} +(-0.0830129 + 0.714293i) q^{42} +(8.29503 + 6.61506i) q^{43} +(-2.78237 + 4.65795i) q^{44} +(9.74596 + 0.730359i) q^{45} +(4.77679 - 5.46802i) q^{46} +(-4.91600 + 4.56138i) q^{47} +(-0.248324 + 0.727539i) q^{48} +(-6.70503 - 2.01061i) q^{49} +(-6.34230 + 5.37648i) q^{50} +(-0.787832 - 0.849081i) q^{51} +(-4.90945 - 0.0729655i) q^{52} +(-11.7885 - 0.883424i) q^{53} +(-1.53371 + 0.523910i) q^{54} +(5.57897 - 6.99580i) q^{55} +(-6.55080 - 3.61759i) q^{56} +(0.293563 + 0.368116i) q^{57} +(-5.82840 - 3.72292i) q^{58} +(8.66453 - 3.40058i) q^{59} +(0.566997 - 1.13396i) q^{60} +(-2.16600 + 0.162320i) q^{61} +(-6.47697 - 4.85498i) q^{62} +(-1.19890 - 7.74731i) q^{63} +(-6.02613 - 5.26172i) q^{64} +(8.00705 + 1.20687i) q^{65} +(-0.196123 + 0.710774i) q^{66} +(-4.07561 - 2.35306i) q^{67} +(11.2846 - 4.23647i) q^{68} +(0.428114 - 0.888987i) q^{69} +(9.90415 + 7.36325i) q^{70} +(-7.32647 + 3.52824i) q^{71} +(0.499967 - 8.36588i) q^{72} +(1.71039 + 1.58701i) q^{73} +(-0.223261 + 4.97678i) q^{74} +(-0.636507 + 0.933584i) q^{75} +(-4.70304 + 1.37450i) q^{76} +(-6.47891 - 3.08875i) q^{77} +(-0.645783 + 0.167904i) q^{78} +(-4.47482 - 7.75061i) q^{79} +(8.68247 + 9.93392i) q^{80} +(7.16261 - 4.88339i) q^{81} +(2.43537 - 1.50512i) q^{82} +(-3.55762 - 0.812003i) q^{83} +(-0.988932 - 0.237117i) q^{84} +(-19.3803 + 4.42343i) q^{85} +(-10.6883 + 10.5306i) q^{86} +(-0.898102 - 0.277028i) q^{87} +(-6.07065 - 4.69291i) q^{88} +(14.8093 - 4.56807i) q^{89} +(-2.67042 + 13.5611i) q^{90} +(-0.510862 - 6.47519i) q^{91} +(6.87146 + 7.63001i) q^{92} +(-1.02399 - 0.401885i) q^{93} +(-5.57494 - 7.67245i) q^{94} +(7.99040 - 1.20436i) q^{95} +(-0.979629 - 0.471467i) q^{96} +8.27599 q^{97} +(3.95479 - 9.07522i) q^{98} -8.03833i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

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