LMFDB - Embedded newform 441.2.bb.f.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.f.298.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14923 - 0.783534i) q^{2} +(-0.0238713 + 0.0608230i) q^{4} +(3.53905 + 1.09165i) q^{5} +(-2.60134 + 0.482718i) q^{7} +(0.639241 + 2.80070i) q^{8} +O(q^{10})$	\(q+(1.14923 - 0.783534i) q^{2} +(-0.0238713 + 0.0608230i) q^{4} +(3.53905 + 1.09165i) q^{5} +(-2.60134 + 0.482718i) q^{7} +(0.639241 + 2.80070i) q^{8} +(4.92254 - 1.51840i) q^{10} +(-0.0190277 - 0.253907i) q^{11} +(3.89505 + 1.87576i) q^{13} +(-2.61132 + 2.59299i) q^{14} +(2.83328 + 2.62890i) q^{16} +(-6.47644 - 0.976167i) q^{17} +(2.20228 - 3.81445i) q^{19} +(-0.150879 + 0.189197i) q^{20} +(-0.220812 - 0.276890i) q^{22} +(1.41341 - 0.213037i) q^{23} +(7.20200 + 4.91024i) q^{25} +(5.94604 - 0.896221i) q^{26} +(0.0327370 - 0.169745i) q^{28} +(1.55920 - 1.95518i) q^{29} +(-1.02513 - 1.77557i) q^{31} +(-0.365341 - 0.0550663i) q^{32} +(-8.20780 + 3.95267i) q^{34} +(-9.73325 - 1.13140i) q^{35} +(-3.65832 - 9.32124i) q^{37} +(-0.457825 - 6.10925i) q^{38} +(-0.795083 + 10.6097i) q^{40} +(0.0761773 + 0.333754i) q^{41} +(1.72518 - 7.55849i) q^{43} +(0.0158976 + 0.00490377i) q^{44} +(1.45741 - 1.35228i) q^{46} +(2.26719 - 1.54575i) q^{47} +(6.53397 - 2.51143i) q^{49} +12.1241 q^{50} +(-0.207069 + 0.192132i) q^{52} +(-0.864149 + 2.20182i) q^{53} +(0.209839 - 0.919363i) q^{55} +(-3.01483 - 6.97700i) q^{56} +(0.259939 - 3.46864i) q^{58} +(-11.8919 + 3.66816i) q^{59} +(4.95104 + 12.6150i) q^{61} +(-2.56933 - 1.23733i) q^{62} +(-7.42759 + 3.57694i) q^{64} +(11.7371 + 10.8905i) q^{65} +(-2.84627 - 4.92989i) q^{67} +(0.213974 - 0.370615i) q^{68} +(-12.0723 + 6.32609i) q^{70} +(-7.60525 - 9.53668i) q^{71} +(4.41510 + 3.01017i) q^{73} +(-11.5078 - 7.84586i) q^{74} +(0.179435 + 0.225005i) q^{76} +(0.172063 + 0.651315i) q^{77} +(4.94546 - 8.56580i) q^{79} +(7.15729 + 12.3968i) q^{80} +(0.349053 + 0.323874i) q^{82} +(-7.97770 + 3.84186i) q^{83} +(-21.8548 - 10.5247i) q^{85} +(-3.93970 - 10.0382i) q^{86} +(0.698954 - 0.215599i) q^{88} +(-0.738465 + 9.85413i) q^{89} +(-11.0378 - 2.99928i) q^{91} +(-0.0207823 + 0.0910533i) q^{92} +(1.39439 - 3.55284i) q^{94} +(11.9580 - 11.0954i) q^{95} -11.9406 q^{97} +(5.54126 - 8.00580i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	1.14923	−	0.783534i	0.812630	−	0.554042i	−0.0841835	−	0.996450i	$-0.526828\pi$
$2$	1.14923	−	0.783534i	0.812630	−	0.554042i	0.896814	+	0.442408i	$0.145876\pi$
$3$		0			0
$3$		0			0
$4$	−0.0238713	+	0.0608230i	−0.0119356	+	0.0304115i
$5$	3.53905	+	1.09165i	1.58271	+	0.488202i	0.956569	−	0.291506i	$-0.0941562\pi$
$5$	3.53905	+	1.09165i	1.58271	+	0.488202i	0.626144	+	0.779708i	$0.284632\pi$
$6$		0			0
$7$	−2.60134	+	0.482718i	−0.983215	+	0.182450i
$7$	−2.60134	+	0.482718i	−0.983215	+	0.182450i
$8$	0.639241	+	2.80070i	0.226006	+	0.990196i
$9$		0			0
$10$	4.92254	−	1.51840i	1.55664	−	0.480161i
$11$	−0.0190277	−	0.253907i	−0.00573707	−	0.0765559i	0.993600	−	0.112953i	$-0.0360309\pi$
$11$	−0.0190277	−	0.253907i	−0.00573707	−	0.0765559i	−0.999337	+	0.0363971i	$0.988412\pi$
$12$		0			0
$13$	3.89505	+	1.87576i	1.08029	+	0.520242i	0.887410	−	0.460980i	$-0.152502\pi$
$13$	3.89505	+	1.87576i	1.08029	+	0.520242i	0.192883	+	0.981222i	$0.438216\pi$
$14$	−2.61132	+	2.59299i	−0.697905	+	0.693007i
$15$		0			0
$16$	2.83328	+	2.62890i	0.708321	+	0.657226i
$17$	−6.47644	−	0.976167i	−1.57077	−	0.236755i	−0.694828	−	0.719176i	$-0.744520\pi$
$17$	−6.47644	−	0.976167i	−1.57077	−	0.236755i	−0.875940	+	0.482420i	$0.839758\pi$
$18$		0			0
$19$	2.20228	−	3.81445i	0.505237	−	0.875096i	−0.494745	−	0.869038i	$-0.664739\pi$
$19$	2.20228	−	3.81445i	0.505237	−	0.875096i	0.999982	−	0.00605741i	$-0.00192814\pi$
$20$	−0.150879	+	0.189197i	−0.0337377	+	0.0423057i
$21$		0			0
$22$	−0.220812	−	0.276890i	−0.0470773	−	0.0590331i
$23$	1.41341	−	0.213037i	0.294716	−	0.0444213i	−1.99885e−5	−	1.00000i	$-0.500006\pi$
$23$	1.41341	−	0.213037i	0.294716	−	0.0444213i	0.294736	+	0.955579i	$0.404768\pi$
$24$		0			0
$25$	7.20200	+	4.91024i	1.44040	+	0.982048i
$26$	5.94604	−	0.896221i	1.16611	−	0.175763i
$27$		0			0
$28$	0.0327370	−	0.169745i	0.00618671	−	0.0320787i
$29$	1.55920	−	1.95518i	0.289537	−	0.363068i	−0.615696	−	0.787984i	$-0.711125\pi$
$29$	1.55920	−	1.95518i	0.289537	−	0.363068i	0.905233	+	0.424916i	$0.139696\pi$
$30$		0			0
$31$	−1.02513	−	1.77557i	−0.184119	−	0.318903i	0.759161	−	0.650903i	$-0.225610\pi$
$31$	−1.02513	−	1.77557i	−0.184119	−	0.318903i	−0.943279	+	0.332001i	$0.892276\pi$
$32$	−0.365341	−	0.0550663i	−0.0645838	−	0.00973444i
$33$		0			0
$34$	−8.20780	+	3.95267i	−1.40763	+	0.677877i
$35$	−9.73325	−	1.13140i	−1.64522	−	0.191241i
$36$		0			0
$37$	−3.65832	−	9.32124i	−0.601424	−	1.53240i	−0.829353	−	0.558725i	$-0.811291\pi$
$37$	−3.65832	−	9.32124i	−0.601424	−	1.53240i	0.227929	−	0.973678i	$-0.426804\pi$
$38$	−0.457825	−	6.10925i	−0.0742690	−	0.991051i
$39$		0			0
$40$	−0.795083	+	10.6097i	−0.125714	+	1.67753i
$41$	0.0761773	+	0.333754i	0.0118969	+	0.0521237i	0.980528	−	0.196380i	$-0.0629185\pi$
$41$	0.0761773	+	0.333754i	0.0118969	+	0.0521237i	−0.968631	+	0.248503i	$0.920061\pi$
$42$		0			0
$43$	1.72518	−	7.55849i	0.263087	−	1.15266i	−0.654796	−	0.755806i	$-0.727245\pi$
$43$	1.72518	−	7.55849i	0.263087	−	1.15266i	0.917882	−	0.396853i	$-0.129898\pi$
$44$	0.0158976	+	0.00490377i	0.00239666	+	0.000739271i
$45$		0			0
$46$	1.45741	−	1.35228i	0.214884	−	0.199383i
$47$	2.26719	−	1.54575i	0.330704	−	0.225470i	−0.386572	−	0.922259i	$-0.626341\pi$
$47$	2.26719	−	1.54575i	0.330704	−	0.225470i	0.717276	+	0.696789i	$0.245389\pi$
$48$		0			0
$49$	6.53397	−	2.51143i	0.933424	−	0.358776i
$50$	12.1241			1.71461
$51$		0			0
$52$	−0.207069	+	0.192132i	−0.0287153	+	0.0266439i
$53$	−0.864149	+	2.20182i	−0.118700	+	0.302443i	−0.977859	−	0.209267i	$-0.932892\pi$
$53$	−0.864149	+	2.20182i	−0.118700	+	0.302443i	0.859159	+	0.511709i	$0.170988\pi$
$54$		0			0
$55$	0.209839	−	0.919363i	0.0282946	−	0.123967i
$56$	−3.01483	−	6.97700i	−0.402874	−	0.932341i
$57$		0			0
$58$	0.259939	−	3.46864i	0.0341317	−	0.455455i
$59$	−11.8919	+	3.66816i	−1.54819	+	0.477554i	−0.946915	−	0.321485i	$-0.895818\pi$
$59$	−11.8919	+	3.66816i	−1.54819	+	0.477554i	−0.601278	+	0.799040i	$0.705342\pi$
$60$		0			0
$61$	4.95104	+	12.6150i	0.633915	+	1.61519i	0.779901	+	0.625903i	$0.215270\pi$
$61$	4.95104	+	12.6150i	0.633915	+	1.61519i	−0.145985	+	0.989287i	$0.546635\pi$
$62$	−2.56933	−	1.23733i	−0.326306	−	0.157141i
$63$		0			0
$64$	−7.42759	+	3.57694i	−0.928449	+	0.447117i
$65$	11.7371	+	10.8905i	1.45581	+	1.35079i
$66$		0			0
$67$	−2.84627	−	4.92989i	−0.347728	−	0.602282i	0.638118	−	0.769939i	$-0.279713\pi$
$67$	−2.84627	−	4.92989i	−0.347728	−	0.602282i	−0.985845	+	0.167657i	$0.946380\pi$
$68$	0.213974	−	0.370615i	0.0259482	−	0.0449436i
$69$		0			0
$70$	−12.0723	+	6.32609i	−1.44291	+	0.756112i
$71$	−7.60525	−	9.53668i	−0.902577	−	1.13180i	−0.990751	−	0.135690i	$-0.956675\pi$
$71$	−7.60525	−	9.53668i	−0.902577	−	1.13180i	0.0881745	−	0.996105i	$-0.471897\pi$
$72$		0			0
$73$	4.41510	+	3.01017i	0.516749	+	0.352313i	0.793443	−	0.608645i	$-0.208286\pi$
$73$	4.41510	+	3.01017i	0.516749	+	0.352313i	−0.276694	+	0.960958i	$0.589239\pi$
$74$	−11.5078	−	7.84586i	−1.33775	−	0.912063i
$75$		0			0
$76$	0.179435	+	0.225005i	0.0205827	+	0.0258098i
$77$	0.172063	+	0.651315i	0.0196084	+	0.0742242i
$78$		0			0
$79$	4.94546	−	8.56580i	0.556408	−	0.963727i	−0.441384	−	0.897318i	$-0.645512\pi$
$79$	4.94546	−	8.56580i	0.556408	−	0.963727i	0.997792	−	0.0664091i	$-0.0211543\pi$
$80$	7.15729	+	12.3968i	0.800209	+	1.38600i
$81$		0			0
$82$	0.349053	+	0.323874i	0.0385465	+	0.0357659i
$83$	−7.97770	+	3.84186i	−0.875666	+	0.421699i	−0.817040	−	0.576581i	$-0.804386\pi$
$83$	−7.97770	+	3.84186i	−0.875666	+	0.421699i	−0.0586266	+	0.998280i	$0.518672\pi$
$84$		0			0
$85$	−21.8548	−	10.5247i	−2.37049	−	1.14157i
$86$	−3.93970	−	10.0382i	−0.424829	−	1.08245i
$87$		0			0
$88$	0.698954	−	0.215599i	0.0745088	−	0.0229829i
$89$	−0.738465	+	9.85413i	−0.0782771	+	1.04454i	0.810362	+	0.585929i	$0.199270\pi$
$89$	−0.738465	+	9.85413i	−0.0782771	+	1.04454i	−0.888640	+	0.458606i	$0.848349\pi$
$90$		0			0
$91$	−11.0378	−	2.99928i	−1.15708	−	0.314410i
$92$	−0.0207823	+	0.0910533i	−0.00216671	+	0.00949296i
$93$		0			0
$94$	1.39439	−	3.55284i	0.143820	−	0.366448i
$95$	11.9580	−	11.0954i	1.22687	−	1.13837i
$96$		0			0
$97$	−11.9406			−1.21238			−0.606192	−	0.795318i	$-0.707304\pi$
$97$	−11.9406			−1.21238			−0.606192	+	0.795318i	$0.707304\pi$
$98$	5.54126	−	8.00580i	0.559751	−	0.808708i
$99$		0			0
$100$	−0.470577	+	0.320834i	−0.0470577	+	0.0320834i
$101$	−2.00727	+	1.86248i	−0.199731	+	0.185323i	−0.773697	−	0.633556i	$-0.781595\pi$
$101$	−2.00727	+	1.86248i	−0.199731	+	0.185323i	0.573966	+	0.818879i	$0.305404\pi$
$102$		0			0
$103$	−7.99718	−	2.46680i	−0.787986	−	0.243061i	−0.125458	−	0.992099i	$-0.540040\pi$
$103$	−7.99718	−	2.46680i	−0.787986	−	0.243061i	−0.662528	+	0.749038i	$0.730516\pi$
$104$	−2.76356	+	12.1079i	−0.270989	+	1.18728i
$105$		0			0
$106$	0.732088	+	3.20749i	0.0711067	+	0.311539i
$107$	−1.38885	+	18.5329i	−0.134265	+	1.79164i	0.370958	+	0.928650i	$0.379029\pi$
$107$	−1.38885	+	18.5329i	−0.134265	+	1.79164i	−0.505223	+	0.862989i	$0.668590\pi$
$108$		0			0
$109$	0.522280	+	6.96934i	0.0500254	+	0.667542i	0.964700	+	0.263351i	$0.0848278\pi$
$109$	0.522280	+	6.96934i	0.0500254	+	0.667542i	−0.914675	+	0.404191i	$0.867553\pi$
$110$	−0.479198	−	1.22098i	−0.0456898	−	0.116416i
$111$		0			0
$112$	−8.63936	−	5.47100i	−0.816343	−	0.516961i
$113$	9.12193	−	4.39289i	0.858119	−	0.413248i	0.0475341	−	0.998870i	$-0.484864\pi$
$113$	9.12193	−	4.39289i	0.858119	−	0.413248i	0.810585	+	0.585621i	$0.199149\pi$
$114$		0			0
$115$	5.23469	+	0.789003i	0.488137	+	0.0735749i
$116$	0.0816998	+	0.141508i	0.00758563	+	0.0131387i
$117$		0			0
$118$	−10.7924	+	13.5333i	−0.993523	+	1.24584i
$119$	17.3187	−	0.586954i	1.58760	−	0.0538060i
$120$		0			0
$121$	10.8130	−	1.62980i	0.983003	−	0.148164i
$122$	15.5742	+	10.6183i	1.41002	+	0.961337i
$123$		0			0
$124$	0.132467	−	0.0199662i	0.0118959	−	0.00179302i
$125$	8.58221	+	10.7617i	0.767616	+	0.962560i
$126$		0			0
$127$	6.14310	−	7.70321i	0.545112	−	0.683549i	−0.430616	−	0.902535i	$-0.641704\pi$
$127$	6.14310	−	7.70321i	0.545112	−	0.683549i	0.975728	+	0.218986i	$0.0702750\pi$
$128$	−5.36391	+	9.29056i	−0.474107	+	0.821178i
$129$		0			0
$130$	22.0217	+	3.31924i	1.93143	+	0.291117i
$131$	−12.4778	−	11.5777i	−1.09019	−	1.01155i	−0.999878	−	0.0156329i	$-0.995024\pi$
$131$	−12.4778	−	11.5777i	−1.09019	−	1.01155i	−0.0903102	−	0.995914i	$-0.528786\pi$
$132$		0			0
$133$	−3.88757	+	10.9858i	−0.337095	+	0.952588i
$134$	−7.13377	−	3.43544i	−0.616264	−	0.296777i
$135$		0			0
$136$	−1.40606	−	18.7626i	−0.120569	−	1.60888i
$137$	2.25326	−	0.695039i	0.192509	−	0.0593812i	−0.197001	−	0.980403i	$-0.563120\pi$
$137$	2.25326	−	0.695039i	0.192509	−	0.0593812i	0.389511	+	0.921022i	$0.372644\pi$
$138$		0			0
$139$	3.03599	+	13.3015i	0.257509	+	1.12822i	0.923904	+	0.382624i	$0.124979\pi$
$139$	3.03599	+	13.3015i	0.257509	+	1.12822i	−0.666395	+	0.745599i	$0.732163\pi$
$140$	0.301160	−	0.564998i	0.0254527	−	0.0477510i
$141$		0			0
$142$	−16.2125	−	5.00090i	−1.36052	−	0.419666i
$143$	0.402155	−	1.02467i	0.0336299	−	0.0856875i
$144$		0			0
$145$	7.65248	−	5.21737i	0.635504	−	0.433279i
$146$	7.43255			0.615122
$147$		0			0
$148$	0.654275			0.0537811
$149$	14.3263	−	9.76752i	1.17366	−	0.800186i	0.190275	−	0.981731i	$-0.439062\pi$
$149$	14.3263	−	9.76752i	1.17366	−	0.800186i	0.983383	+	0.181544i	$0.0581096\pi$
$150$		0			0
$151$	−2.62155	+	6.67959i	−0.213338	+	0.543578i	−0.996982	−	0.0776332i	$-0.975264\pi$
$151$	−2.62155	+	6.67959i	−0.213338	+	0.543578i	0.783644	+	0.621211i	$0.213359\pi$
$152$	12.0909	+	3.72955i	0.980703	+	0.302507i
$153$		0			0
$154$	0.708068	+	0.613695i	0.0570577	+	0.0494529i
$155$	−1.68967	−	7.40294i	−0.135718	−	0.594618i
$156$		0			0
$157$	15.8693	−	4.89502i	1.26650	−	0.390665i	0.412513	−	0.910952i	$-0.364651\pi$
$157$	15.8693	−	4.89502i	1.26650	−	0.390665i	0.853992	+	0.520287i	$0.174175\pi$
$158$	−1.02810	−	13.7190i	−0.0817912	−	1.09143i
$159$		0			0
$160$	−1.23285	−	0.593708i	−0.0974652	−	0.0469368i
$161$	−3.57392	+	1.23646i	−0.281665	+	0.0974468i
$162$		0			0
$163$	−7.06736	−	6.55755i	−0.553558	−	0.513627i	0.353048	−	0.935605i	$-0.385145\pi$
$163$	−7.06736	−	6.55755i	−0.553558	−	0.513627i	−0.906606	+	0.421978i	$0.861336\pi$
$164$	−0.0221184	−	0.00333381i	−0.00172716	−	0.000260327i
$165$		0			0
$166$	−6.15801	+	10.6660i	−0.477954	+	0.827841i
$167$	−0.486670	+	0.610265i	−0.0376596	+	0.0472237i	−0.800305	−	0.599594i	$-0.795329\pi$
$167$	−0.486670	+	0.610265i	−0.0376596	+	0.0472237i	0.762645	+	0.646817i	$0.223900\pi$
$168$		0			0
$169$	3.54760	+	4.44854i	0.272892	+	0.342196i
$170$	−33.3628	+	5.02863i	−2.55881	+	0.385678i
$171$		0			0
$172$	0.418548	+	0.285361i	0.0319140	+	0.0217586i
$173$	−13.6185	+	2.05266i	−1.03540	+	0.156061i	−0.644682	−	0.764451i	$-0.723010\pi$
$173$	−13.6185	+	2.05266i	−1.03540	+	0.156061i	−0.390714	+	0.920512i	$0.627772\pi$
$174$		0			0
$175$	−21.1051	−	9.29668i	−1.59540	−	0.702763i
$176$	0.613586	−	0.769413i	0.0462508	−	0.0579967i
$177$		0			0
$178$	6.87237	+	11.9033i	0.515106	+	0.892190i
$179$	18.5724	+	2.79934i	1.38817	+	0.209232i	0.800239	−	0.599682i	$-0.204706\pi$
$179$	18.5724	+	2.79934i	1.38817	+	0.209232i	0.587927	+	0.808914i	$0.299944\pi$
$180$		0			0
$181$	12.0454	−	5.80075i	0.895326	−	0.431166i	0.0711274	−	0.997467i	$-0.477340\pi$
$181$	12.0454	−	5.80075i	0.895326	−	0.431166i	0.824198	+	0.566301i	$0.191626\pi$
$182$	−15.0351	+	5.20164i	−1.11447	+	0.385571i
$183$		0			0
$184$	1.50016	+	3.82235i	0.110593	+	0.281787i
$185$	−2.77142	−	36.9820i	−0.203759	−	2.71897i
$186$		0			0
$187$	−0.124624	+	1.66299i	−0.00911340	+	0.121610i
$188$	0.0398962	+	0.174797i	0.00290973	+	0.0127483i
$189$		0			0
$190$	5.04892	−	22.1208i	0.366287	−	1.60481i
$191$	4.79083	+	1.47778i	0.346652	+	0.106928i	0.463192	−	0.886258i	$-0.346704\pi$
$191$	4.79083	+	1.47778i	0.346652	+	0.106928i	−0.116540	+	0.993186i	$0.537180\pi$
$192$		0			0
$193$	5.85908	−	5.43643i	0.421746	−	0.391323i	−0.440550	−	0.897728i	$-0.645217\pi$
$193$	5.85908	−	5.43643i	0.421746	−	0.391323i	0.862296	+	0.506405i	$0.169026\pi$
$194$	−13.7225	+	9.35586i	−0.985220	+	0.671712i
$195$		0			0
$196$	−0.00322125	+	0.457367i	−0.000230089	+	0.0326691i
$197$	−22.0767			−1.57290			−0.786451	−	0.617653i	$-0.788084\pi$
$197$	−22.0767			−1.57290			−0.786451	+	0.617653i	$0.788084\pi$
$198$		0			0
$199$	10.9076	−	10.1208i	0.773218	−	0.717441i	−0.191279	−	0.981536i	$-0.561263\pi$
$199$	10.9076	−	10.1208i	0.773218	−	0.717441i	0.964497	+	0.264094i	$0.0850730\pi$
$200$	−9.14828	+	23.3094i	−0.646881	+	1.64823i
$201$		0			0
$202$	−0.847511	+	3.71319i	−0.0596306	+	0.261259i
$203$	−3.11222	+	5.83875i	−0.218435	+	0.409800i
$204$		0			0
$205$	−0.0947487	+	1.26433i	−0.00661754	+	0.0883049i
$206$	−11.1234	+	3.43113i	−0.775007	+	0.239058i
$207$		0			0
$208$	6.10460	+	15.5543i	0.423278	+	1.07849i
$209$	−1.01042	−	0.486593i	−0.0698923	−	0.0336584i
$210$		0			0
$211$	−6.01009	+	2.89431i	−0.413752	+	0.199252i	−0.629167	−	0.777270i	$-0.716604\pi$
$211$	−6.01009	+	2.89431i	−0.413752	+	0.199252i	0.215415	+	0.976523i	$0.430890\pi$
$212$	−0.113293	−	0.105120i	−0.00778098	−	0.00721969i
$213$		0			0
$214$	12.9250	+	22.3868i	0.883535	+	1.53033i
$215$	14.3567	−	24.8666i	0.979121	−	1.69589i
$216$		0			0
$217$	3.52381	+	4.12403i	0.239212	+	0.279957i
$218$	6.06093	+	7.60017i	0.410498	+	0.514749i
$219$		0			0
$220$	0.0509093	+	0.0347094i	0.00343231	+	0.00234011i
$221$	−23.3950	−	15.9505i	−1.57372	−	1.07294i
$222$		0			0
$223$	4.87172	+	6.10895i	0.326235	+	0.409085i	0.917718	−	0.397232i	$-0.130029\pi$
$223$	4.87172	+	6.10895i	0.326235	+	0.409085i	−0.591484	+	0.806317i	$0.701458\pi$
$224$	0.976959	−	0.0331105i	0.0652758	−	0.00221229i
$225$		0			0
$226$	7.04124	−	12.1958i	0.468376	−	0.811252i
$227$	10.9186	+	18.9115i	0.724690	+	1.25520i	0.959102	+	0.283062i	$0.0913502\pi$
$227$	10.9186	+	18.9115i	0.724690	+	1.25520i	−0.234412	+	0.972137i	$0.575316\pi$
$228$		0			0
$229$	6.57547	+	6.10114i	0.434519	+	0.403175i	0.866873	−	0.498529i	$-0.166126\pi$
$229$	6.57547	+	6.10114i	0.434519	+	0.403175i	−0.432354	+	0.901704i	$0.642317\pi$
$230$	6.63409	−	3.19481i	0.437439	−	0.210659i
$231$		0			0
$232$	6.47258	+	3.11703i	0.424945	+	0.204643i
$233$	−8.86833	−	22.5961i	−0.580984	−	1.48032i	−0.855016	−	0.518601i	$-0.826453\pi$
$233$	−8.86833	−	22.5961i	−0.580984	−	1.48032i	0.274033	−	0.961720i	$-0.411642\pi$
$234$		0			0
$235$	9.71114	−	2.99549i	0.633485	−	0.195404i
$236$	0.0607659	−	0.810865i	0.00395553	−	0.0527828i
$237$		0			0
$238$	19.4433	−	14.2443i	1.26032	−	0.923321i
$239$	−4.46611	+	19.5673i	−0.288889	+	1.26570i	0.597163	+	0.802120i	$0.296294\pi$
$239$	−4.46611	+	19.5673i	−0.288889	+	1.26570i	−0.886052	+	0.463585i	$0.846563\pi$
$240$		0			0
$241$	−1.71823	+	4.37799i	−0.110681	+	0.282011i	−0.975473	−	0.220120i	$-0.929355\pi$
$241$	−1.71823	+	4.37799i	−0.110681	+	0.282011i	0.864792	+	0.502131i	$0.167450\pi$
$242$	11.1497	−	10.3454i	0.716729	−	0.665027i
$243$		0			0
$244$	−0.885473			−0.0566866
$245$	25.8657	−	1.75526i	1.65250	−	0.112140i
$246$		0			0
$247$	15.7330	−	10.7266i	1.00106	−	0.682515i
$248$	4.31755	−	4.00610i	0.274164	−	0.254387i
$249$		0			0
$250$	18.2951	+	5.64330i	1.15709	+	0.356914i
$251$	3.23619	−	14.1787i	0.204267	−	0.894951i	−0.764037	−	0.645173i	$-0.776785\pi$
$251$	3.23619	−	14.1787i	0.204267	−	0.894951i	0.968303	−	0.249778i	$-0.0803576\pi$
$252$		0			0
$253$	−0.0809856	−	0.354821i	−0.00509152	−	0.0223074i
$254$	1.02413	−	13.6661i	0.0642598	−	0.857487i
$255$		0			0
$256$	−0.117062	−	1.56208i	−0.00731636	−	0.0976301i
$257$	3.02570	+	7.70936i	0.188738	+	0.480897i	0.993652	−	0.112494i	$-0.0358840\pi$
$257$	3.02570	+	7.70936i	0.188738	+	0.480897i	−0.804914	+	0.593391i	$0.797789\pi$
$258$		0			0
$259$	14.0161	+	22.4818i	0.870916	+	1.39695i
$260$	−0.942571	+	0.453918i	−0.0584558	+	0.0281508i
$261$		0			0
$262$	−23.4114	−	3.52870i	−1.44636	−	0.218004i
$263$	9.10478	+	15.7699i	0.561425	+	0.972416i	0.997372	+	0.0724443i	$0.0230799\pi$
$263$	9.10478	+	15.7699i	0.561425	+	0.972416i	−0.435948	+	0.899972i	$0.643587\pi$
$264$		0			0
$265$	−5.46189	+	6.84899i	−0.335521	+	0.420730i
$266$	4.14001	+	15.6713i	0.253840	+	0.960866i
$267$		0			0
$268$	0.367795	−	0.0554362i	0.0224667	−	0.00338631i
$269$	−3.88750	−	2.65045i	−0.237025	−	0.161601i	0.438983	−	0.898496i	$-0.355339\pi$
$269$	−3.88750	−	2.65045i	−0.237025	−	0.161601i	−0.676008	+	0.736895i	$0.736291\pi$
$270$		0			0
$271$	−4.04568	+	0.609788i	−0.245758	+	0.0370420i	−0.270766	−	0.962645i	$-0.587277\pi$
$271$	−4.04568	+	0.609788i	−0.245758	+	0.0370420i	0.0250082	+	0.999687i	$0.492039\pi$
$272$	−15.7834	−	19.7917i	−0.957006	−	1.20005i
$273$		0			0
$274$	2.04493	−	2.56427i	0.123539	−	0.154913i
$275$	1.10971	−	1.92207i	0.0669179	−	0.115905i
$276$		0			0
$277$	−27.4153	−	4.13219i	−1.64723	−	0.248279i	−0.741133	−	0.671358i	$-0.765711\pi$
$277$	−27.4153	−	4.13219i	−1.64723	−	0.248279i	−0.906093	+	0.423079i	$0.860949\pi$
$278$	13.9113	+	12.9078i	0.834342	+	0.774157i
$279$		0			0
$280$	−3.05319	−	27.9831i	−0.182463	−	1.67231i
$281$	6.25972	+	3.01452i	0.373423	+	0.179831i	0.611176	−	0.791494i	$-0.290697\pi$
$281$	6.25972	+	3.01452i	0.373423	+	0.179831i	−0.237753	+	0.971326i	$0.576411\pi$
$282$		0			0
$283$	−0.0634573	−	0.846779i	−0.00377215	−	0.0503358i	0.995000	−	0.0998742i	$-0.0318440\pi$
$283$	−0.0634573	−	0.846779i	−0.00377215	−	0.0503358i	−0.998772	+	0.0495384i	$0.984225\pi$
$284$	0.761597	−	0.234921i	0.0451925	−	0.0139400i
$285$		0			0
$286$	−0.340697	−	1.49269i	−0.0201458	−	0.0882646i
$287$	−0.359273	−	0.831438i	−0.0212072	−	0.0490782i
$288$		0			0
$289$	24.7467	+	7.63334i	1.45569	+	0.449020i
$290$	4.70650	−	11.9920i	0.276375	−	0.704192i
$291$		0			0
$292$	−0.288482	+	0.196683i	−0.0168821	+	0.0115100i
$293$	−6.40082			−0.373940			−0.186970	−	0.982366i	$-0.559867\pi$
$293$	−6.40082			−0.373940			−0.186970	+	0.982366i	$0.559867\pi$
$294$		0			0
$295$	−46.0904			−2.68349
$296$	23.7674	−	16.2044i	1.38145	−	0.941860i
$297$		0			0
$298$	8.81110	−	22.4503i	0.510413	−	1.30051i
$299$	5.90491	+	1.82142i	0.341490	+	0.105336i
$300$		0			0
$301$	−0.839151	+	20.4950i	−0.0483679	+	1.18131i
$302$	2.22092	+	9.73048i	0.127799	+	0.559926i
$303$		0			0
$304$	16.2675	−	5.01786i	0.933005	−	0.287794i
$305$	3.75074	+	50.0501i	0.214767	+	2.86586i
$306$		0			0
$307$	0.0571051	+	0.0275004i	0.00325916	+	0.00156953i	0.435513	−	0.900183i	$-0.356567\pi$
$307$	0.0571051	+	0.0275004i	0.00325916	+	0.00156953i	−0.432253	+	0.901752i	$0.642281\pi$
$308$	−0.0437223	−	0.00508230i	−0.00249131	−	0.000289591i
$309$		0			0
$310$	−7.74228	−	7.18378i	−0.439732	−	0.408011i
$311$	13.3838	+	2.01728i	0.758924	+	0.114389i	0.517093	−	0.855929i	$-0.327014\pi$
$311$	13.3838	+	2.01728i	0.758924	+	0.114389i	0.241831	+	0.970318i	$0.422252\pi$
$312$		0			0
$313$	−1.91602	+	3.31864i	−0.108300	+	0.187581i	−0.915082	−	0.403269i	$-0.867874\pi$
$313$	−1.91602	+	3.31864i	−0.108300	+	0.187581i	0.806782	+	0.590849i	$0.201207\pi$
$314$	14.4021	−	18.0596i	0.812755	−	1.01916i
$315$		0			0
$316$	0.402943	+	0.505275i	0.0226673	+	0.0284239i
$317$	3.70792	−	0.558880i	0.208258	−	0.0313898i	−0.0440847	−	0.999028i	$-0.514037\pi$
$317$	3.70792	−	0.558880i	0.208258	−	0.0313898i	0.252342	+	0.967638i	$0.418799\pi$
$318$		0			0
$319$	−0.526102	−	0.358691i	−0.0294561	−	0.0200828i
$320$	−30.1914	+	4.55062i	−1.68775	+	0.254388i
$321$		0			0
$322$	−3.13846	+	4.22127i	−0.174900	+	0.235242i
$323$	−17.9865	+	22.5543i	−1.00079	+	1.25496i
$324$		0			0
$325$	18.8417	+	32.6348i	1.04515	+	1.81026i
$326$	−13.2601	−	1.99864i	−0.734409	−	0.110694i
$327$		0			0
$328$	−0.886050	+	0.426699i	−0.0489239	+	0.0235605i
$329$	−5.15159	+	5.11543i	−0.284016	+	0.282023i
$330$		0			0
$331$	−1.75879	−	4.48132i	−0.0966717	−	0.246316i	0.874355	−	0.485287i	$-0.161285\pi$
$331$	−1.75879	−	4.48132i	−0.0966717	−	0.246316i	−0.971027	+	0.238972i	$0.923190\pi$
$332$	−0.0432355	−	0.576938i	−0.00237286	−	0.0316636i
$333$		0			0
$334$	−0.0811340	+	1.08266i	−0.00443946	+	0.0592404i
$335$	−4.69138	−	20.5543i	−0.256318	−	1.12300i
$336$		0			0
$337$	−2.44348	+	10.7056i	−0.133105	+	0.583172i	0.863750	+	0.503921i	$0.168110\pi$
$337$	−2.44348	+	10.7056i	−0.133105	+	0.583172i	−0.996855	+	0.0792504i	$0.974747\pi$
$338$	7.56259	+	2.33275i	0.411351	+	0.126885i
$339$		0			0
$340$	1.16185	−	1.07804i	0.0630101	−	0.0584649i
$341$	−0.431325	+	0.294073i	−0.0233576	+	0.0159249i
$342$		0			0
$343$	−15.7848	+	9.68716i	−0.852297	+	0.523057i
$344$	22.2718			1.20082
$345$		0			0
$346$	−14.0425	+	13.0295i	−0.754930	+	0.700473i
$347$	−13.5776	+	34.5952i	−0.728884	+	1.85717i	−0.299170	+	0.954200i	$0.596710\pi$
$347$	−13.5776	+	34.5952i	−0.728884	+	1.85717i	−0.429714	+	0.902965i	$0.641385\pi$
$348$		0			0
$349$	1.83713	−	8.04901i	0.0983395	−	0.430853i	−0.901659	−	0.432447i	$-0.857650\pi$
$349$	1.83713	−	8.04901i	0.0983395	−	0.430853i	0.999999	+	0.00159382i	$0.000507328\pi$
$350$	−31.5390	+	5.85253i	−1.68583	+	0.312831i
$351$		0			0
$352$	−0.00703013	+	0.0938105i	−0.000374707	+	0.00500012i
$353$	−28.5196	+	8.79714i	−1.51795	+	0.468224i	−0.938060	−	0.346473i	$-0.887379\pi$
$353$	−28.5196	+	8.79714i	−1.51795	+	0.468224i	−0.579886	+	0.814697i	$0.696903\pi$
$354$		0			0
$355$	−16.5046	−	42.0531i	−0.875975	−	2.23195i
$356$	−0.581730	−	0.280146i	−0.0308316	−	0.0148477i
$357$		0			0
$358$	23.5374	−	11.3350i	1.24399	−	0.599073i
$359$	−4.59799	−	4.26631i	−0.242673	−	0.225167i	0.549454	−	0.835524i	$-0.314836\pi$
$359$	−4.59799	−	4.26631i	−0.242673	−	0.225167i	−0.792127	+	0.610357i	$0.791026\pi$
$360$		0			0
$361$	−0.200036	−	0.346473i	−0.0105282	−	0.0182354i
$362$	9.29786	−	16.1044i	0.488685	−	0.846427i
$363$		0			0
$364$	0.445912	−	0.599758i	0.0233722	−	0.0314358i
$365$	12.3392	+	15.4729i	0.645865	+	0.809889i
$366$		0			0
$367$	−6.77152	−	4.61674i	−0.353470	−	0.240992i	0.373547	−	0.927611i	$-0.378142\pi$
$367$	−6.77152	−	4.61674i	−0.353470	−	0.240992i	−0.727017	+	0.686619i	$0.759094\pi$
$368$	4.56464	+	3.11212i	0.237948	+	0.162230i
$369$		0			0
$370$	−32.1616	−	40.3294i	−1.67200	−	2.09663i
$371$	1.18509	−	6.14482i	0.0615268	−	0.319023i
$372$		0			0
$373$	−8.27066	+	14.3252i	−0.428238	+	0.741730i	−0.996717	−	0.0809677i	$-0.974199\pi$
$373$	−8.27066	+	14.3252i	−0.428238	+	0.741730i	0.568478	+	0.822698i	$0.307532\pi$
$374$	1.15979	+	2.00881i	0.0599711	+	0.103873i
$375$		0			0
$376$	5.77845	+	5.36162i	0.298001	+	0.276504i
$377$	9.74062	−	4.69084i	0.501668	−	0.241590i
$378$		0			0
$379$	14.8945	+	7.17280i	0.765078	+	0.368442i	0.775372	−	0.631505i	$-0.217562\pi$
$379$	14.8945	+	7.17280i	0.765078	+	0.368442i	−0.0102940	+	0.999947i	$0.503277\pi$
$380$	0.389404	+	0.992186i	0.0199760	+	0.0508981i
$381$		0			0
$382$	6.66366	−	2.05547i	0.340943	−	0.105167i
$383$	−1.35955	+	18.1419i	−0.0694696	+	0.927007i	0.848203	+	0.529671i	$0.177685\pi$
$383$	−1.35955	+	18.1419i	−0.0694696	+	0.927007i	−0.917673	+	0.397337i	$0.869935\pi$
$384$		0			0
$385$	−0.102069	+	2.49287i	−0.00520190	+	0.127048i
$386$	2.47382	−	10.8385i	0.125914	−	0.551665i
$387$		0			0
$388$	0.285037	−	0.726264i	0.0144706	−	0.0368705i
$389$	−6.74716	+	6.26045i	−0.342095	+	0.317417i	−0.832445	−	0.554108i	$-0.813059\pi$
$389$	−6.74716	+	6.26045i	−0.342095	+	0.317417i	0.490350	+	0.871526i	$0.336869\pi$
$390$		0			0
$391$	−9.36182			−0.473448
$392$	11.2105	+	16.6943i	0.566218	+	0.843187i
$393$		0			0
$394$	−25.3713	+	17.2979i	−1.27819	+	0.871453i
$395$	26.8531	−	24.9161i	1.35113	−	1.25366i
$396$		0			0
$397$	−7.30668	−	2.25381i	−0.366712	−	0.113116i	0.105922	−	0.994374i	$-0.466221\pi$
$397$	−7.30668	−	2.25381i	−0.366712	−	0.113116i	−0.472634	+	0.881259i	$0.656697\pi$
$398$	4.60540	−	20.1776i	0.230848	−	1.01141i
$399$		0			0
$400$	7.49676	+	32.8454i	0.374838	+	1.64227i
$401$	0.699947	−	9.34015i	0.0349537	−	0.466425i	−0.952073	−	0.305870i	$-0.901053\pi$
$401$	0.699947	−	9.34015i	0.0349537	−	0.466425i	0.987027	−	0.160555i	$-0.0513283\pi$
$402$		0			0
$403$	−0.662380	−	8.83885i	−0.0329955	−	0.440294i
$404$	−0.0653654	−	0.166548i	−0.00325205	−	0.00828608i
$405$		0			0
$406$	0.998188	+	9.14861i	0.0495392	+	0.454038i
$407$	−2.29712	+	1.10624i	−0.113864	+	0.0548340i
$408$		0			0
$409$	−19.7849	−	2.98210i	−0.978301	−	0.147455i	−0.359621	−	0.933098i	$-0.617094\pi$
$409$	−19.7849	−	2.98210i	−0.978301	−	0.147455i	−0.618680	+	0.785643i	$0.712332\pi$
$410$	0.881760	+	1.52725i	0.0435470	+	0.0754256i
$411$		0			0
$412$	0.340941	−	0.427527i	0.0167970	−	0.0210627i
$413$	29.1642	−	15.2826i	1.43508	−	0.752007i
$414$		0			0
$415$	−32.4275	+	4.88766i	−1.59180	+	0.239926i
$416$	−1.31973	−	0.899778i	−0.0647052	−	0.0441152i
$417$		0			0
$418$	−1.54247	+	0.232490i	−0.0754448	+	0.0113715i
$419$	5.29343	+	6.63775i	0.258601	+	0.324275i	0.894135	−	0.447798i	$-0.147791\pi$
$419$	5.29343	+	6.63775i	0.258601	+	0.324275i	−0.635534	+	0.772073i	$0.719220\pi$
$420$		0			0
$421$	21.9546	−	27.5302i	1.07000	−	1.34174i	0.133510	−	0.991048i	$-0.457375\pi$
$421$	21.9546	−	27.5302i	1.07000	−	1.34174i	0.936491	−	0.350691i	$-0.114053\pi$
$422$	−4.63920	+	8.03534i	−0.225833	+	0.391154i
$423$		0			0
$424$	−6.71902	−	1.01273i	−0.326304	−	0.0491825i
$425$	−41.8501	−	38.8312i	−2.03003	−	1.88359i
$426$		0			0
$427$	−18.9689	−	30.4261i	−0.917967	−	1.47242i
$428$	−1.09407	−	0.526877i	−0.0528839	−	0.0254676i
$429$		0			0
$430$	−2.98458	−	39.8265i	−0.143929	−	1.92060i
$431$	22.6248	−	6.97882i	1.08980	−	0.336158i	0.302762	−	0.953066i	$-0.402091\pi$
$431$	22.6248	−	6.97882i	1.08980	−	0.336158i	0.787035	+	0.616908i	$0.211615\pi$
$432$		0			0
$433$	7.40402	+	32.4391i	0.355815	+	1.55893i	0.763503	+	0.645805i	$0.223478\pi$
$433$	7.40402	+	32.4391i	0.355815	+	1.55893i	−0.407688	+	0.913121i	$0.633665\pi$
$434$	7.28100	+	1.97844i	0.349499	+	0.0949683i
$435$		0			0
$436$	−0.436364	−	0.134600i	−0.0208981	−	0.00644619i
$437$	2.30010	−	5.86055i	0.110028	−	0.280348i
$438$		0			0
$439$	−27.5109	+	18.7566i	−1.31302	+	0.895205i	−0.998538	−	0.0540565i	$-0.982785\pi$
$439$	−27.5109	+	18.7566i	−1.31302	+	0.895205i	−0.314487	+	0.949262i	$0.601833\pi$
$440$	2.70900			0.129146
$441$		0			0
$442$	−39.3841			−1.87331
$443$	−6.18711	+	4.21830i	−0.293959	+	0.200418i	−0.701315	−	0.712852i	$-0.747403\pi$
$443$	−6.18711	+	4.21830i	−0.293959	+	0.200418i	0.407356	+	0.913269i	$0.366451\pi$
$444$		0			0
$445$	−13.3708	+	34.0681i	−0.633835	+	1.61498i
$446$	10.3853	+	3.20344i	0.491758	+	0.151687i
$447$		0			0
$448$	17.5951	−	12.8903i	0.831288	−	0.609008i
$449$	−2.61274	−	11.4472i	−0.123303	−	0.540226i	−0.998414	−	0.0563030i	$-0.982069\pi$
$449$	−2.61274	−	11.4472i	−0.123303	−	0.540226i	0.875111	−	0.483923i	$-0.160788\pi$
$450$		0			0
$451$	0.0832932	−	0.0256925i	0.00392212	−	0.00120981i
$452$	0.0494367	+	0.659687i	0.00232531	+	0.0310291i
$453$		0			0
$454$	27.3657	+	13.1786i	1.28434	+	0.618504i
$455$	−35.7893	−	22.6641i	−1.67783	−	1.06251i
$456$		0			0
$457$	14.3149	+	13.2823i	0.669624	+	0.621320i	0.939895	−	0.341464i	$-0.110923\pi$
$457$	14.3149	+	13.2823i	0.669624	+	0.621320i	−0.270271	+	0.962784i	$0.587113\pi$
$458$	12.3372	+	1.85953i	0.576479	+	0.0868903i
$459$		0			0
$460$	−0.172948	+	0.299555i	−0.00806376	+	0.0139668i
$461$	−16.2728	+	20.4055i	−0.757902	+	0.950379i	−0.999802	−	0.0199226i	$-0.993658\pi$
$461$	−16.2728	+	20.4055i	−0.757902	+	0.950379i	0.241900	+	0.970301i	$0.422229\pi$
$462$		0			0
$463$	16.8609	+	21.1429i	0.783592	+	0.982593i	0.999980	+	0.00628602i	$0.00200091\pi$
$463$	16.8609	+	21.1429i	0.783592	+	0.982593i	−0.216388	+	0.976307i	$0.569428\pi$
$464$	9.55764	−	1.44058i	0.443702	−	0.0668774i
$465$		0			0
$466$	−27.8966	−	19.0196i	−1.29229	−	0.881065i
$467$	16.3656	−	2.46671i	0.757308	−	0.114146i	0.240972	−	0.970532i	$-0.422534\pi$
$467$	16.3656	−	2.46671i	0.757308	−	0.114146i	0.516336	+	0.856386i	$0.327296\pi$
$468$		0			0
$469$	9.78388	+	11.4504i	0.451778	+	0.528730i
$470$	8.81329	−	11.0515i	0.406527	−	0.509768i
$471$		0			0
$472$	−17.8752	−	30.9608i	−0.822773	−	1.42509i
$473$	−1.95198	−	0.294214i	−0.0897522	−	0.0135280i
$474$		0			0
$475$	34.5907	−	16.6580i	1.58713	−	0.764321i
$476$	−0.377718	+	1.06738i	−0.0173127	+	0.0489235i
$477$		0			0
$478$	10.1990	+	25.9868i	0.466494	+	1.18861i
$479$	1.60020	+	21.3532i	0.0731151	+	0.975653i	0.906294	+	0.422649i	$0.138900\pi$
$479$	1.60020	+	21.3532i	0.0731151	+	0.975653i	−0.833178	+	0.553004i	$0.813481\pi$
$480$		0			0
$481$	3.23506	−	43.1688i	0.147506	−	1.96833i
$482$	1.45565	+	6.37762i	0.0663030	+	0.290492i
$483$		0			0
$484$	−0.158991	+	0.696587i	−0.00722688	+	0.0316630i
$485$	−42.2584	−	13.0350i	−1.91886	−	0.591889i
$486$		0			0
$487$	−25.9216	+	24.0517i	−1.17462	+	1.08989i	−0.180282	+	0.983615i	$0.557701\pi$
$487$	−25.9216	+	24.0517i	−1.17462	+	1.08989i	−0.994337	+	0.106272i	$0.966109\pi$
$488$	−32.1660	+	21.9304i	−1.45609	+	0.992743i
$489$		0			0
$490$	28.3504	−	22.2838i	1.28074	−	1.00668i
$491$	−40.7900			−1.84083			−0.920413	−	0.390948i	$-0.872147\pi$
$491$	−40.7900			−1.84083			−0.920413	+	0.390948i	$0.872147\pi$
$492$		0			0
$493$	−12.0067	+	11.1406i	−0.540753	+	0.501746i
$494$	9.67623	−	24.6546i	0.435354	−	1.10926i
$495$		0			0
$496$	1.76333	−	7.72567i	0.0791760	−	0.346893i
$497$	24.3874	+	21.1370i	1.09392	+	0.948123i
$498$		0			0
$499$	2.86987	−	38.2957i	0.128473	−	1.71435i	−0.445337	−	0.895363i	$-0.646916\pi$
$499$	2.86987	−	38.2957i	0.128473	−	1.71435i	0.573810	−	0.818988i	$-0.305465\pi$
$500$	−0.859431	+	0.265099i	−0.0384349	+	0.0118556i
$501$		0			0
$502$	−7.39034	−	18.8303i	−0.329847	−	0.840436i
$503$	−1.87450	−	0.902713i	−0.0835799	−	0.0402500i	0.391627	−	0.920124i	$-0.371912\pi$
$503$	−1.87450	−	0.902713i	−0.0835799	−	0.0402500i	−0.475207	+	0.879874i	$0.657627\pi$
$504$		0			0
$505$	−9.13703	+	4.40016i	−0.406592	+	0.195805i
$506$	−0.371086	−	0.344317i	−0.0164968	−	0.0153068i
$507$		0			0
$508$	0.321889	+	0.557527i	0.0142815	+	0.0247363i
$509$	1.13925	−	1.97324i	0.0504964	−	0.0874624i	−0.839672	−	0.543093i	$-0.817253\pi$
$509$	1.13925	−	1.97324i	0.0504964	−	0.0874624i	0.890169	+	0.455631i	$0.150586\pi$
$510$		0			0
$511$	−12.9383	−	5.69922i	−0.572355	−	0.252119i
$512$	−14.7358	−	18.4782i	−0.651238	−	0.816627i
$513$		0			0
$514$	9.51778	+	6.48911i	0.419811	+	0.286222i
$515$	−25.6096	−	17.4603i	−1.12849	−	0.769393i
$516$		0			0
$517$	−0.435616	−	0.546245i	−0.0191584	−	0.0240238i
$518$	33.7230	+	14.8548i	1.48170	+	0.652681i
$519$		0			0
$520$	−22.9980	+	39.8338i	−1.00853	+	1.74683i
$521$	1.90874	+	3.30603i	0.0836233	+	0.144840i	0.904804	−	0.425829i	$-0.140017\pi$
$521$	1.90874	+	3.30603i	0.0836233	+	0.144840i	−0.821180	+	0.570669i	$0.806684\pi$
$522$		0			0
$523$	−4.01701	−	3.72724i	−0.175651	−	0.162981i	0.587448	−	0.809262i	$-0.300133\pi$
$523$	−4.01701	−	3.72724i	−0.175651	−	0.162981i	−0.763099	+	0.646281i	$0.776323\pi$
$524$	1.00205	−	0.482562i	0.0437748	−	0.0210808i
$525$		0			0
$526$	22.8198	+	10.9894i	0.994990	+	0.479162i
$527$	4.90593	+	12.5001i	0.213706	+	0.544513i
$528$		0			0
$529$	−20.0258	+	6.17715i	−0.870688	+	0.268572i
$530$	−0.910566	+	12.1507i	−0.0395524	+	0.527791i
$531$		0			0
$532$	−0.575387	−	0.498698i	−0.0249462	−	0.0216213i
$533$	−0.329328	+	1.44288i	−0.0142648	+	0.0624981i
$534$		0			0
$535$	−25.1466	+	64.0726i	−1.08718	+	2.77010i
$536$	11.9877	−	11.1229i	0.517789	−	0.480438i
$537$		0			0
$538$	−6.54436			−0.282147
$539$	−0.761997	−	1.61123i	−0.0328215	−	0.0694008i
$540$		0			0
$541$	6.36486	−	4.33949i	0.273647	−	0.186569i	−0.418719	−	0.908116i	$-0.637521\pi$
$541$	6.36486	−	4.33949i	0.273647	−	0.186569i	0.692366	+	0.721547i	$0.256568\pi$
$542$	−4.17164	+	3.87072i	−0.179187	+	0.166261i
$543$		0			0
$544$	2.31236	+	0.713268i	0.0991415	+	0.0305811i
$545$	−5.75973	+	25.2350i	−0.246720	+	1.08095i
$546$		0			0
$547$	−3.92940	−	17.2158i	−0.168009	−	0.736096i	−0.986792	−	0.161993i	$-0.948208\pi$
$547$	−3.92940	−	17.2158i	−0.168009	−	0.736096i	0.818783	−	0.574103i	$-0.194649\pi$
$548$	−0.0115138	+	0.153642i	−0.000491847	+	0.00656324i
$549$		0			0
$550$	−0.230694	−	3.07840i	−0.00983683	−	0.131263i
$551$	−4.02415	−	10.2534i	−0.171434	−	0.436808i
$552$		0			0
$553$	−8.72998	+	24.6698i	−0.371237	+	1.04907i
$554$	−34.7443	+	16.7320i	−1.47614	+	0.710873i
$555$		0			0
$556$	−0.881514	−	0.132867i	−0.0373845	−	0.00563481i
$557$	−22.0376	−	38.1702i	−0.933763	−	1.61733i	−0.776825	−	0.629717i	$-0.783171\pi$
$557$	−22.0376	−	38.1702i	−0.933763	−	1.61733i	−0.156938	−	0.987608i	$-0.550162\pi$
$558$		0			0
$559$	20.8975	−	26.2047i	0.883872	−	1.10834i
$560$	−24.6027	−	28.7933i	−1.03965	−	1.21674i
$561$		0			0
$562$	9.55585	−	1.44031i	0.403089	−	0.0607559i
$563$	−18.2281	−	12.4277i	−0.768224	−	0.523766i	0.114633	−	0.993408i	$-0.463431\pi$
$563$	−18.2281	−	12.4277i	−0.768224	−	0.523766i	−0.882857	+	0.469642i	$0.844383\pi$
$564$		0			0
$565$	37.0785	−	5.58869i	1.55990	−	0.235118i
$566$	−0.736407	−	0.923425i	−0.0309535	−	0.0388144i
$567$		0			0
$568$	21.8478	−	27.3962i	0.916712	−	1.14952i
$569$	7.89484	−	13.6743i	0.330969	−	0.573255i	−0.651733	−	0.758448i	$-0.725958\pi$
$569$	7.89484	−	13.6743i	0.330969	−	0.573255i	0.982702	+	0.185193i	$0.0592911\pi$
$570$		0			0
$571$	20.6319	+	3.10976i	0.863418	+	0.130139i	0.565797	−	0.824545i	$-0.308569\pi$
$571$	20.6319	+	3.10976i	0.863418	+	0.130139i	0.297621	+	0.954684i	$0.403807\pi$
$572$	0.0527238	+	0.0489205i	0.00220449	+	0.00204547i
$573$		0			0
$574$	−1.06435	−	0.674013i	−0.0444250	−	0.0281328i
$575$	11.2254	+	5.40588i	0.468133	+	0.225441i
$576$		0			0
$577$	−1.27649	−	17.0336i	−0.0531409	−	0.709116i	−0.958613	−	0.284711i	$-0.908102\pi$
$577$	−1.27649	−	17.0336i	−0.0531409	−	0.709116i	0.905472	−	0.424405i	$-0.139517\pi$
$578$	34.4207	−	10.6174i	1.43171	−	0.441624i
$579$		0			0
$580$	0.134662	+	0.589993i	0.00559153	+	0.0244981i
$581$	18.8982	−	13.8450i	0.784029	−	0.574386i
$582$		0			0
$583$	0.575500	+	0.177518i	0.0238348	+	0.00735205i
$584$	−5.60825	+	14.2896i	−0.232071	+	0.591308i
$585$		0			0
$586$	−7.35604	+	5.01526i	−0.303875	+	0.207179i
$587$	−14.0400			−0.579493			−0.289747	−	0.957103i	$-0.593571\pi$
$587$	−14.0400			−0.579493			−0.289747	+	0.957103i	$0.593571\pi$
$588$		0			0
$589$	−9.03046			−0.372094
$590$	−52.9686	+	36.1134i	−2.18068	+	1.48676i
$591$		0			0
$592$	14.1396	−	36.0271i	0.581133	−	1.48070i
$593$	26.0192	+	8.02586i	1.06848	+	0.329583i	0.778626	−	0.627488i	$-0.215917\pi$
$593$	26.0192	+	8.02586i	1.06848	+	0.329583i	0.289855	+	0.957071i	$0.406393\pi$
$594$		0			0
$595$	61.9324	+	16.8287i	2.53898	+	0.689910i
$596$	0.252103	+	1.10453i	0.0103265	+	0.0452435i
$597$		0			0
$598$	8.21326	−	2.53345i	0.335865	−	0.103601i
$599$	0.727581	+	9.70890i	0.0297282	+	0.396695i	0.992143	+	0.125111i	$0.0399285\pi$
$599$	0.727581	+	9.70890i	0.0297282	+	0.396695i	−0.962415	+	0.271584i	$0.912452\pi$
$600$		0			0
$601$	−1.12159	−	0.540130i	−0.0457507	−	0.0220324i	0.410869	−	0.911695i	$-0.365226\pi$
$601$	−1.12159	−	0.540130i	−0.0457507	−	0.0220324i	−0.456619	+	0.889662i	$0.650940\pi$
$602$	15.0941	+	24.2110i	0.615191	+	0.986767i
$603$		0			0
$604$	−0.343693	−	0.318901i	−0.0139847	−	0.0129759i
$605$	40.0471	+	6.03613i	1.62815	+	0.245403i
$606$		0			0
$607$	3.65698	−	6.33407i	0.148432	−	0.257092i	−0.782216	−	0.623007i	$-0.785911\pi$
$607$	3.65698	−	6.33407i	0.148432	−	0.257092i	0.930648	+	0.365915i	$0.119244\pi$
$608$	−1.01463	+	1.27231i	−0.0411487	+	0.0515988i
$609$		0			0
$610$	43.5264	+	54.5804i	1.76233	+	2.20990i
$611$	11.7303	−	1.76806i	0.474556	−	0.0715279i
$612$		0			0
$613$	−6.96625	−	4.74951i	−0.281364	−	0.191831i	0.414412	−	0.910089i	$-0.363987\pi$
$613$	−6.96625	−	4.74951i	−0.281364	−	0.191831i	−0.695776	+	0.718258i	$0.744940\pi$
$614$	0.0871746	−	0.0131395i	0.00351808	−	0.000530265i
$615$		0			0
$616$	−1.71415	+	0.898245i	−0.0690649	+	0.0361913i
$617$	22.7489	−	28.5262i	0.915837	−	1.14842i	−0.0726863	−	0.997355i	$-0.523157\pi$
$617$	22.7489	−	28.5262i	0.915837	−	1.14842i	0.988523	−	0.151068i	$-0.0482714\pi$
$618$		0			0
$619$	22.0733	+	38.2321i	0.887202	+	1.53668i	0.843169	+	0.537649i	$0.180687\pi$
$619$	22.0733	+	38.2321i	0.887202	+	1.53668i	0.0440332	+	0.999030i	$0.485979\pi$
$620$	0.490604	+	0.0739466i	0.0197031	+	0.00296977i
$621$		0			0
$622$	16.9617	−	8.16831i	0.680101	−	0.327519i
$623$	−2.83577	−	25.9904i	−0.113613	−	1.04128i
$624$		0			0
$625$	2.70213	+	6.88491i	0.108085	+	0.275396i
$626$	0.398316	+	5.31515i	0.0159199	+	0.212436i
$627$		0			0
$628$	−0.0810897	+	1.08207i	−0.00323583	+	0.0431792i
$629$	14.5938	+	63.9396i	0.581893	+	2.54944i
$630$		0			0
$631$	−1.60711	+	7.04123i	−0.0639782	+	0.280307i	−0.996790	−	0.0800562i	$-0.974490\pi$
$631$	−1.60711	+	7.04123i	−0.0639782	+	0.280307i	0.932812	+	0.360363i	$0.117347\pi$
$632$	27.1516	+	8.37515i	1.08003	+	0.333145i
$633$		0			0
$634$	3.82337	−	3.54757i	0.151845	−	0.140892i
$635$	30.1500	−	20.5559i	1.19647	−	0.815737i
$636$		0			0
$637$	30.1610	+	2.47398i	1.19502	+	0.0980228i
$638$	−0.885660			−0.0350636
$639$		0			0
$640$	−29.1252	+	27.0243i	−1.15128	+	1.06823i
$641$	2.05755	−	5.24255i	0.0812683	−	0.207068i	−0.884464	−	0.466608i	$-0.845476\pi$
$641$	2.05755	−	5.24255i	0.0812683	−	0.207068i	0.965732	+	0.259540i	$0.0835710\pi$
$642$		0			0
$643$	7.69166	−	33.6994i	0.303329	−	1.32897i	−0.561737	−	0.827316i	$-0.689867\pi$
$643$	7.69166	−	33.6994i	0.303329	−	1.32897i	0.865066	−	0.501657i	$-0.167276\pi$
$644$	0.0101088	−	0.246893i	0.000398344	−	0.00972894i
$645$		0			0
$646$	−2.99857	+	40.0131i	−0.117977	+	1.57430i
$647$	24.4985	−	7.55678i	0.963134	−	0.297088i	0.226979	−	0.973900i	$-0.427115\pi$
$647$	24.4985	−	7.55678i	0.963134	−	0.297088i	0.736156	+	0.676812i	$0.236639\pi$
$648$		0			0
$649$	1.15765	+	2.94964i	0.0454417	+	0.115784i
$650$	47.2240	+	22.7419i	1.85228	+	0.892010i
$651$		0			0
$652$	0.567557	−	0.273321i	0.0222272	−	0.0107041i
$653$	0.150065	+	0.139240i	0.00587251	+	0.00544889i	0.683104	−	0.730322i	$-0.260630\pi$
$653$	0.150065	+	0.139240i	0.00587251	+	0.00544889i	−0.677231	+	0.735770i	$0.736820\pi$
$654$		0			0
$655$	−31.5207	−	54.5954i	−1.23162	−	2.13322i
$656$	−0.661576	+	1.14588i	−0.0258302	+	0.0447392i
$657$		0			0
$658$	−1.91226	+	9.91526i	−0.0745476	+	0.386537i
$659$	14.6544	+	18.3760i	0.570853	+	0.715827i	0.980522	−	0.196407i	$-0.0629274\pi$
$659$	14.6544	+	18.3760i	0.570853	+	0.715827i	−0.409670	+	0.912234i	$0.634356\pi$
$660$		0			0
$661$	−11.0006	−	7.50009i	−0.427874	−	0.291720i	0.330172	−	0.943921i	$-0.392893\pi$
$661$	−11.0006	−	7.50009i	−0.427874	−	0.291720i	−0.758046	+	0.652201i	$0.773846\pi$
$662$	−5.53252	−	3.77201i	−0.215028	−	0.146603i
$663$		0			0
$664$	−15.8596	−	19.8873i	−0.615470	−	0.771775i
$665$	−25.7510	+	34.6354i	−0.998580	+	1.34310i
$666$		0			0
$667$	1.78727	−	3.09564i	0.0692032	−	0.119864i
$668$	−0.0255007	−	0.0441685i	−0.000986652	−	0.00170893i
$669$		0			0
$670$	−21.4965	−	19.9458i	−0.830481	−	0.770574i
$671$	3.10884	−	1.49714i	0.120016	−	0.0577964i
$672$		0			0
$673$	−19.9438	−	9.60441i	−0.768776	−	0.370223i	0.00802616	−	0.999968i	$-0.497445\pi$
$673$	−19.9438	−	9.60441i	−0.768776	−	0.370223i	−0.776802	+	0.629745i	$0.783159\pi$
$674$	5.58007	+	14.2178i	0.214936	+	0.547649i
$675$		0			0
$676$	−0.355260	+	0.109583i	−0.0136638	+	0.00421473i
$677$	−2.91252	+	38.8648i	−0.111937	+	1.49370i	0.604814	+	0.796367i	$0.293248\pi$
$677$	−2.91252	+	38.8648i	−0.111937	+	1.49370i	−0.716751	+	0.697329i	$0.754371\pi$
$678$		0			0
$679$	31.0616	−	5.76395i	1.19203	−	0.221200i
$680$	15.5061	−	67.9367i	0.594632	−	2.60525i
$681$		0			0
$682$	−0.265277	+	0.675916i	−0.0101580	+	0.0258822i
$683$	26.2062	−	24.3158i	1.00275	−	0.930418i	0.00517484	−	0.999987i	$-0.498353\pi$
$683$	26.2062	−	24.3158i	1.00275	−	0.930418i	0.997577	+	0.0695687i	$0.0221623\pi$
$684$		0			0
$685$	8.73315			0.333676
$686$	−10.5502	+	23.5007i	−0.402807	+	0.897261i
$687$		0			0
$688$	24.7584	−	16.8800i	0.943907	−	0.643545i
$689$	−7.49598	+	6.95525i	−0.285574	+	0.264974i
$690$		0			0
$691$	22.1559	+	6.83420i	0.842851	+	0.259985i	0.685968	−	0.727632i	$-0.259379\pi$
$691$	22.1559	+	6.83420i	0.842851	+	0.259985i	0.156883	+	0.987617i	$0.449855\pi$
$692$	0.200242	−	0.877319i	0.00761207	−	0.0333507i
$693$		0			0
$694$	11.5026	+	50.3964i	0.436634	+	1.91302i
$695$	−3.77614	+	50.3891i	−0.143237	+	1.91137i
$696$		0			0
$697$	−0.167558	−	2.23590i	−0.00634670	−	0.0846909i
$698$	−4.19537	−	10.6896i	−0.158797	−	0.404609i
$699$		0			0
$700$	1.06926	−	1.06175i	0.0404142	−	0.0401305i
$701$	−1.07696	+	0.518635i	−0.0406761	+	0.0195886i	−0.454111	−	0.890945i	$-0.650043\pi$
$701$	−1.07696	+	0.518635i	−0.0406761	+	0.0195886i	0.413435	+	0.910534i	$0.364329\pi$
$702$		0			0
$703$	−43.6121	−	6.57346i	−1.64486	−	0.247923i
$704$	1.04954	+	1.81786i	0.0395561	+	0.0685131i
$705$		0			0
$706$	−25.8828	+	32.4560i	−0.974113	+	1.22150i
$707$	4.32255	−	5.81389i	0.162566	−	0.218654i
$708$		0			0
$709$	4.48605	−	0.676163i	0.168477	−	0.0253939i	−0.0642619	−	0.997933i	$-0.520469\pi$
$709$	4.48605	−	0.676163i	0.168477	−	0.0253939i	0.232739	+	0.972539i	$0.425231\pi$
$710$	−51.9177	−	35.3969i	−1.94844	−	1.32842i
$711$		0			0
$712$	−28.0705	+	4.23095i	−1.05199	+	0.158561i
$713$	−1.82719	−	2.29122i	−0.0684288	−	0.0858070i
$714$		0			0
$715$	2.54183	−	3.18736i	0.0950592	−	0.119201i
$716$	−0.613611	+	1.06281i	−0.0229317	+	0.0397189i
$717$		0			0
$718$	−8.62696	−	1.30030i	−0.321955	−	0.0485269i
$719$	−27.5855	−	25.5956i	−1.02877	−	0.954556i	−0.0297799	−	0.999556i	$-0.509481\pi$
$719$	−27.5855	−	25.5956i	−1.02877	−	0.954556i	−0.998987	+	0.0450004i	$0.985671\pi$
$720$		0			0
$721$	21.9942	+	2.55662i	0.819106	+	0.0952133i
$722$	−0.501362	−	0.241443i	−0.0186588	−	0.00898558i
$723$		0			0
$724$	0.0652805	+	0.871108i	0.00242613	+	0.0323745i
$725$	20.8298	−	6.42514i	0.773599	−	0.238624i
$726$		0			0
$727$	−4.56155	−	19.9854i	−0.169178	−	0.741219i	−0.986328	−	0.164793i	$-0.947304\pi$
$727$	−4.56155	−	19.9854i	−0.169178	−	0.741219i	0.817150	−	0.576425i	$-0.195553\pi$
$728$	1.34424	−	32.8309i	0.0498207	−	1.21679i
$729$		0			0
$730$	26.3042	+	8.11377i	0.973562	+	0.300304i
$731$	−18.5513	+	47.2681i	−0.686146	+	1.74827i
$732$		0			0
$733$	21.0488	−	14.3508i	0.777455	−	0.530060i	−0.108353	−	0.994113i	$-0.534558\pi$
$733$	21.0488	−	14.3508i	0.777455	−	0.530060i	0.885808	+	0.464053i	$0.153605\pi$
$734$	−11.3994			−0.420760
$735$		0			0
$736$	−0.528107			−0.0194663
$737$	−1.19758	+	0.816494i	−0.0441133	+	0.0300760i
$738$		0			0
$739$	−2.65188	+	6.75688i	−0.0975510	+	0.248556i	−0.971316	−	0.237793i	$-0.923576\pi$
$739$	−2.65188	+	6.75688i	−0.0975510	+	0.248556i	0.873765	+	0.486348i	$0.161671\pi$
$740$	2.31551	+	0.714241i	0.0851200	+	0.0262560i
$741$		0			0
$742$	−3.45273	−	7.99038i	−0.126754	−	0.293336i
$743$	1.78147	+	7.80515i	0.0653560	+	0.286343i	0.997036	−	0.0769368i	$-0.0245140\pi$
$743$	1.78147	+	7.80515i	0.0653560	+	0.286343i	−0.931680	+	0.363280i	$0.881657\pi$
$744$		0			0
$745$	61.3644	−	18.9284i	2.24822	−	0.693483i
$746$	1.71936	+	22.9433i	0.0629504	+	0.840014i
$747$		0			0
$748$	−0.0981732	−	0.0472777i	−0.00358957	−	0.00172864i
$749$	−5.33329	−	48.8807i	−0.194874	−	1.78606i
$750$		0			0
$751$	10.0216	+	9.29869i	0.365694	+	0.339314i	0.841521	−	0.540225i	$-0.181661\pi$
$751$	10.0216	+	9.29869i	0.365694	+	0.339314i	−0.475827	+	0.879539i	$0.657851\pi$
$752$	10.4872	+	1.58069i	0.382429	+	0.0576420i
$753$		0			0
$754$	7.51881	−	13.0230i	0.273819	−	0.474269i
$755$	−16.5696	+	20.7776i	−0.603029	+	0.756175i
$756$		0			0
$757$	9.69548	+	12.1577i	0.352388	+	0.441881i	0.926158	−	0.377136i	$-0.123091\pi$
$757$	9.69548	+	12.1577i	0.352388	+	0.441881i	−0.573770	+	0.819017i	$0.694520\pi$
$758$	22.7373	−	3.42710i	0.825858	−	0.124478i
$759$		0			0
$760$	38.7190	+	26.3982i	1.40449	+	0.957563i
$761$	25.0869	−	3.78125i	0.909401	−	0.137070i	0.322350	−	0.946620i	$-0.395527\pi$
$761$	25.0869	−	3.78125i	0.909401	−	0.137070i	0.587050	+	0.809550i	$0.300289\pi$
$762$		0			0
$763$	−4.72286	−	17.8775i	−0.170979	−	0.647210i
$764$	−0.204246	+	0.256116i	−0.00738936	+	0.00926597i
$765$		0			0
$766$	12.6523	+	21.9145i	0.457148	+	0.791803i
$767$	−53.2001	−	8.01863i	−1.92095	−	0.289536i
$768$		0			0
$769$	21.1193	−	10.1705i	0.761580	−	0.366757i	−0.0124370	−	0.999923i	$-0.503959\pi$
$769$	21.1193	−	10.1705i	0.761580	−	0.366757i	0.774017	+	0.633165i	$0.218245\pi$
$770$	1.83595	+	2.94486i	0.0661629	+	0.106125i
$771$		0			0
$772$	0.190796	+	0.486141i	0.00686691	+	0.0174966i
$773$	0.951072	+	12.6912i	0.0342077	+	0.456470i	0.987838	+	0.155488i	$0.0496952\pi$
$773$	0.951072	+	12.6912i	0.0342077	+	0.456470i	−0.953630	+	0.300981i	$0.902686\pi$
$774$		0			0
$775$	1.33552	−	17.8213i	0.0479734	−	0.640160i
$776$	−7.63292	−	33.4420i	−0.274006	−	1.20050i
$777$		0			0
$778$	−2.84878	+	12.4813i	−0.102134	+	0.447478i
$779$	1.44085	+	0.444445i	0.0516240	+	0.0159239i
$780$		0			0
$781$	−2.27672	+	2.11249i	−0.0814675	+	0.0755908i
$782$	−10.7589	+	7.33530i	−0.384738	+	0.262310i
$783$		0			0
$784$	25.1149	+	10.0616i	0.896960	+	0.359342i
$785$	61.5058			2.19524
$786$		0			0
$787$	−27.4605	+	25.4797i	−0.978863	+	0.908252i	−0.995795	−	0.0916047i	$-0.970800\pi$
$787$	−27.4605	+	25.4797i	−0.978863	+	0.908252i	0.0169327	+	0.999857i	$0.494610\pi$
$788$	0.527000	−	1.34277i	0.0187736	−	0.0478343i
$789$		0			0
$790$	11.3379	−	49.6747i	0.403385	−	1.76735i
$791$	−21.6087	+	15.8307i	−0.768318	+	0.562876i
$792$		0			0
$793$	−4.37821	+	58.4232i	−0.155475	+	2.07467i
$794$	−10.1630	+	3.13487i	−0.360672	+	0.111253i
$795$		0			0
$796$	0.355197	+	0.905028i	0.0125896	+	0.0320779i
$797$	−30.7931	−	14.8292i	−1.09075	−	0.525276i	−0.200010	−	0.979794i	$-0.564097\pi$
$797$	−30.7931	−	14.8292i	−1.09075	−	0.525276i	−0.890738	+	0.454517i	$0.849812\pi$
$798$		0			0
$799$	−16.1923	+	7.79778i	−0.572841	+	0.275866i
$800$	−2.36080	−	2.19050i	−0.0834668	−	0.0774458i
$801$		0			0
$802$	−6.51392	−	11.2824i	−0.230014	−	0.398397i
$803$	0.680294	−	1.17830i	0.0240070	−	0.0415814i
$804$		0			0
$805$	−13.9981	+	0.474415i	−0.493368	+	0.0167209i
$806$	−7.68676	−	9.63890i	−0.270755	−	0.339516i
$807$		0			0
$808$	−6.49937	−	4.43120i	−0.228647	−	0.155889i
$809$	−0.422579	−	0.288109i	−0.0148571	−	0.0101294i	0.555869	−	0.831270i	$-0.312386\pi$
$809$	−0.422579	−	0.288109i	−0.0148571	−	0.0101294i	−0.570726	+	0.821141i	$0.693338\pi$
$810$		0			0
$811$	21.9875	+	27.5715i	0.772086	+	0.968165i	0.999985	−	0.00551971i	$-0.00175699\pi$
$811$	21.9875	+	27.5715i	0.772086	+	0.968165i	−0.227899	+	0.973685i	$0.573186\pi$
$812$	−0.280838	−	0.328673i	−0.00985547	−	0.0115342i
$813$		0			0
$814$	−1.77315	+	3.07119i	−0.0621490	+	0.107645i
$815$	−17.8532	−	30.9226i	−0.625370	−	1.08317i
$816$		0			0
$817$	−25.0322	−	23.2265i	−0.875765	−	0.812592i
$818$	−25.0740	+	12.0750i	−0.876694	+	0.422193i
$819$		0			0
$820$	−0.0746389	−	0.0359442i	−0.00260650	−	0.00125523i
$821$	14.2680	+	36.3544i	0.497958	+	1.26878i	0.930211	+	0.367025i	$0.119624\pi$
$821$	14.2680	+	36.3544i	0.497958	+	1.26878i	−0.432253	+	0.901752i	$0.642281\pi$
$822$		0			0
$823$	−16.7014	+	5.15169i	−0.582173	+	0.179577i	−0.571833	−	0.820370i	$-0.693768\pi$
$823$	−16.7014	+	5.15169i	−0.582173	+	0.179577i	−0.0103399	+	0.999947i	$0.503291\pi$
$824$	1.79665	−	23.9746i	0.0625891	−	0.835194i
$825$		0			0
$826$	21.5420	−	40.4144i	0.749543	−	1.40620i
$827$	2.54323	−	11.1426i	0.0884368	−	0.387467i	−0.911267	−	0.411817i	$-0.864894\pi$
$827$	2.54323	−	11.1426i	0.0884368	−	0.387467i	0.999703	+	0.0243498i	$0.00775156\pi$
$828$		0			0
$829$	9.50352	−	24.2146i	0.330071	−	0.841007i	−0.665448	−	0.746444i	$-0.731759\pi$
$829$	9.50352	−	24.2146i	0.330071	−	0.841007i	0.995519	−	0.0945629i	$-0.0301453\pi$
$830$	−33.4371	+	31.0251i	−1.16062	+	1.07690i
$831$		0			0
$832$	−35.6403			−1.23561
$833$	−44.7684	+	9.88690i	−1.55113	+	0.342561i
$834$		0			0
$835$	−2.38855	+	1.62848i	−0.0826591	+	0.0563560i
$836$	0.0537162	−	0.0498413i	0.00185781	−	0.00172380i
$837$		0			0
$838$	11.2843	+	3.48074i	0.389809	+	0.120240i
$839$	3.60624	−	15.8000i	0.124501	−	0.545476i	−0.873751	−	0.486374i	$-0.838319\pi$
$839$	3.60624	−	15.8000i	0.124501	−	0.545476i	0.998252	−	0.0591017i	$-0.0188236\pi$
$840$		0			0
$841$	5.06150	+	22.1759i	0.174534	+	0.764685i
$842$	3.66011	−	48.8407i	0.126136	−	1.68316i
$843$		0			0
$844$	−0.0325720	−	0.434643i	−0.00112117	−	0.0149610i
$845$	7.69886	+	19.6164i	0.264849	+	0.674824i
$846$		0			0
$847$	−27.3417	+	9.45932i	−0.939471	+	0.325026i
$848$	−8.23674	+	3.96660i	−0.282851	+	0.136214i
$849$		0			0
$850$	−78.5211	−	11.8351i	−2.69325	−	0.405942i
$851$	−7.15647	−	12.3954i	−0.245321	−	0.424908i
$852$		0			0
$853$	−3.45114	+	4.32760i	−0.118165	+	0.148174i	−0.837396	−	0.546597i	$-0.815923\pi$
$853$	−3.45114	+	4.32760i	−0.118165	+	0.148174i	0.719231	+	0.694771i	$0.244494\pi$
$854$	−45.6395	−	20.1039i	−1.56175	−	0.687942i
$855$		0			0
$856$	−52.7927	+	7.95723i	−1.80442	+	0.271972i
$857$	−27.8478	−	18.9863i	−0.951263	−	0.648560i	−0.0150101	−	0.999887i	$-0.504778\pi$
$857$	−27.8478	−	18.9863i	−0.951263	−	0.648560i	−0.936253	+	0.351327i	$0.885730\pi$
$858$		0			0
$859$	−32.7097	+	4.93019i	−1.11604	+	0.168216i	−0.681063	−	0.732225i	$-0.738482\pi$
$859$	−32.7097	+	4.93019i	−1.11604	+	0.168216i	−0.434978	+	0.900441i	$0.643244\pi$
$860$	1.16975	+	1.46682i	0.0398881	+	0.0500181i
$861$		0			0
$862$	20.5330	−	25.7476i	0.699357	−	0.876965i
$863$	25.1810	−	43.6147i	0.857170	−	1.48466i	−0.0174464	−	0.999848i	$-0.505554\pi$
$863$	25.1810	−	43.6147i	0.857170	−	1.48466i	0.874617	−	0.484815i	$-0.161113\pi$
$864$		0			0
$865$	−50.4374	−	7.60222i	−1.71492	−	0.258483i
$866$	33.9261	+	31.4788i	1.15286	+	1.06969i
$867$		0			0
$868$	−0.334954	+	0.115883i	−0.0113691	+	0.00393333i
$869$	−2.26902	−	1.09270i	−0.0769712	−	0.0370674i
$870$		0			0
$871$	−1.83910	−	24.5411i	−0.0623156	−	0.831544i
$872$	−19.1852	+	5.91784i	−0.649692	+	0.200403i
$873$		0			0
$874$	−1.94859	−	8.53733i	−0.0659121	−	0.288780i
$875$	−27.5202	−	23.8522i	−0.930351	−	0.806352i
$876$		0			0
$877$	−50.6184	−	15.6137i	−1.70926	−	0.527238i	−0.722777	−	0.691081i	$-0.757135\pi$
$877$	−50.6184	−	15.6137i	−1.70926	−	0.527238i	−0.986486	+	0.163843i	$0.947611\pi$
$878$	−16.9200	+	43.1115i	−0.571022	+	1.45494i
$879$		0			0
$880$	3.01145	−	2.05317i	0.101516	−	0.0692124i
$881$	10.3461			0.348567			0.174284	−	0.984695i	$-0.444239\pi$
$881$	10.3461			0.348567			0.174284	+	0.984695i	$0.444239\pi$
$882$		0			0
$883$	7.57414			0.254890			0.127445	−	0.991846i	$-0.459322\pi$
$883$	7.57414			0.254890			0.127445	+	0.991846i	$0.459322\pi$
$884$	1.52863	−	1.04220i	0.0514132	−	0.0350529i
$885$		0			0
$886$	−3.80525	+	9.69562i	−0.127840	+	0.325731i
$887$	56.5459	+	17.4421i	1.89862	+	0.585648i	0.982998	+	0.183618i	$0.0587810\pi$
$887$	56.5459	+	17.4421i	1.89862	+	0.585648i	0.915627	+	0.402030i	$0.131695\pi$
$888$		0			0
$889$	−12.2618	+	23.0041i	−0.411249	+	0.771532i
$890$	11.3274	+	49.6286i	0.379696	+	1.66356i
$891$		0			0
$892$	−0.487859	+	0.150485i	−0.0163347	+	0.00503859i
$893$	−0.903192	−	12.0523i	−0.0302242	−	0.403314i
$894$		0			0
$895$	62.6728	+	30.1816i	2.09492	+	1.00886i
$896$	9.46864	−	26.7572i	0.316325	−	0.893895i
$897$		0			0
$898$	−11.9719	−	11.1083i	−0.399507	−	0.370689i
$899$	−5.06995	−	0.764172i	−0.169092	−	0.0254866i
$900$		0			0
$901$	7.74595	−	13.4164i	0.258055	−	0.446964i
$902$	0.0755923	−	0.0947897i	0.00251695	−	0.00315615i
$903$		0			0
$904$	18.1343	+	22.7397i	0.603137	+	0.756310i
$905$	48.9616	−	7.37978i	1.62754	−	0.245312i
$906$		0			0
$907$	−11.5681	−	7.88701i	−0.384113	−	0.261884i	0.355834	−	0.934549i	$-0.384197\pi$
$907$	−11.5681	−	7.88701i	−0.384113	−	0.261884i	−0.739947	+	0.672665i	$0.765149\pi$
$908$	−1.41089	+	0.212658i	−0.0468222	+	0.00705730i
$909$		0			0
$910$	−58.8883	+	1.99581i	−1.95213	+	0.0661604i
$911$	4.36063	−	5.46806i	0.144474	−	0.181165i	−0.704329	−	0.709873i	$-0.748752\pi$
$911$	4.36063	−	5.46806i	0.144474	−	0.181165i	0.848803	+	0.528709i	$0.177324\pi$
$912$		0			0
$913$	1.12727	+	1.95249i	0.0373073	+	0.0646181i
$914$	26.8583	+	4.04824i	0.888394	+	0.133904i
$915$		0			0
$916$	−0.528055	+	0.254298i	−0.0174474	+	0.00840224i
$917$	38.0477	+	24.0943i	1.25645	+	0.795663i
$918$		0			0
$919$	−1.23553	−	3.14807i	−0.0407562	−	0.103845i	0.909046	−	0.416695i	$-0.136812\pi$
$919$	−1.23553	−	3.14807i	−0.0407562	−	0.103845i	−0.949803	+	0.312850i	$0.898716\pi$
$920$	1.13647	+	15.1652i	0.0374683	+	0.499980i
$921$		0			0
$922$	−2.71289	+	36.2010i	−0.0893442	+	1.19222i
$923$	−11.7343	−	51.4115i	−0.386240	−	1.69223i
$924$		0			0
$925$	19.4223	−	85.0948i	0.638602	−	2.79790i
$926$	35.9432	+	11.0870i	1.18117	+	0.364342i
$927$		0			0
$928$	−0.677306	+	0.628448i	−0.0222336	+	0.0206298i
$929$	9.16982	−	6.25188i	0.300852	−	0.205117i	−0.403479	−	0.914989i	$-0.632199\pi$
$929$	9.16982	−	6.25188i	0.300852	−	0.205117i	0.704331	+	0.709871i	$0.251247\pi$
$930$		0			0
$931$	4.80986	−	30.4544i	0.157637	−	0.998102i
$932$	1.58606			0.0519532
$933$		0			0
$934$	16.8751	−	15.6578i	0.552170	−	0.512339i
$935$	−2.25646	+	5.74936i	−0.0737941	+	0.188024i
$936$		0			0
$937$	7.44595	−	32.6228i	0.243249	−	1.06574i	−0.694791	−	0.719212i	$-0.744503\pi$
$937$	7.44595	−	32.6228i	0.243249	−	1.06574i	0.938039	−	0.346529i	$-0.112640\pi$
$938$	20.2157	+	5.49316i	0.660067	+	0.179358i
$939$		0			0
$940$	−0.0496226	+	0.662167i	−0.00161851	+	0.0215975i
$941$	−8.65842	+	2.67077i	−0.282256	+	0.0870645i	−0.432651	−	0.901561i	$-0.642422\pi$
$941$	−8.65842	+	2.67077i	−0.282256	+	0.0870645i	0.150395	+	0.988626i	$0.451946\pi$
$942$		0			0
$943$	0.178772	+	0.455503i	0.00582161	+	0.0148332i
$944$	−43.3364	−	20.8697i	−1.41048	−	0.679251i
$945$		0			0
$946$	−2.47381	+	1.19132i	−0.0804304	+	0.0387332i
$947$	−20.5998	−	19.1138i	−0.669404	−	0.621116i	0.270433	−	0.962739i	$-0.412833\pi$
$947$	−20.5998	−	19.1138i	−0.669404	−	0.621116i	−0.939837	+	0.341623i	$0.889023\pi$
$948$		0			0
$949$	11.5507	+	20.0064i	0.374952	+	0.649436i
$950$	26.7006	−	46.2468i	0.866283	−	1.50045i
$951$		0			0
$952$	12.7147	+	48.1291i	0.412085	+	1.55987i
$953$	6.84398	+	8.58208i	0.221698	+	0.278001i	0.880225	−	0.474556i	$-0.157392\pi$
$953$	6.84398	+	8.58208i	0.221698	+	0.278001i	−0.658527	+	0.752557i	$0.728820\pi$
$954$		0			0
$955$	15.3418	+	10.4598i	0.496448	+	0.338473i
$956$	−1.08353	−	0.738740i	−0.0350439	−	0.0238925i
$957$		0			0
$958$	18.5700	+	23.2860i	0.599968	+	0.752336i
$959$	−5.52599	+	2.89572i	−0.178444	+	0.0935078i
$960$		0			0
$961$	13.3982	−	23.2064i	0.432201	−	0.748594i
$962$	−30.1064	−	52.1458i	−0.970669	−	1.68125i
$963$		0			0
$964$	−0.225266	−	0.209016i	−0.00725533	−	0.00673196i
$965$	26.6703	−	12.8437i	0.858547	−	0.413454i
$966$		0			0
$967$	−6.70494	−	3.22893i	−0.215616	−	0.103835i	0.322958	−	0.946413i	$-0.395323\pi$
$967$	−6.70494	−	3.22893i	−0.215616	−	0.103835i	−0.538575	+	0.842578i	$0.681037\pi$
$968$	11.4767	+	29.2422i	0.368876	+	0.939880i
$969$		0			0
$970$	−58.7781	+	18.1306i	−1.88725	+	0.582140i
$971$	−2.02111	+	26.9699i	−0.0648606	+	0.865504i	0.865980	+	0.500079i	$0.166696\pi$
$971$	−2.02111	+	26.9699i	−0.0648606	+	0.865504i	−0.930841	+	0.365425i	$0.880924\pi$
$972$		0			0
$973$	−14.3186	−	33.1364i	−0.459032	−	1.06230i
$974$	−10.9446	+	47.9514i	−0.350688	+	1.53646i
$975$		0			0
$976$	−19.1360	+	48.7578i	−0.612529	+	1.56070i
$977$	−19.3816	+	17.9835i	−0.620074	+	0.575344i	−0.926381	−	0.376588i	$-0.877097\pi$
$977$	−19.3816	+	17.9835i	−0.620074	+	0.575344i	0.306307	+	0.951933i	$0.400907\pi$
$978$		0			0
$979$	2.51609			0.0804144
$980$	−0.510686	+	1.61513i	−0.0163133	+	0.0515934i
$981$		0			0
$982$	−46.8772	+	31.9603i	−1.49591	+	1.01989i
$983$	−12.7833	+	11.8612i	−0.407725	+	0.378314i	−0.857204	−	0.514977i	$-0.827800\pi$
$983$	−12.7833	+	11.8612i	−0.407725	+	0.378314i	0.449478	+	0.893291i	$0.351610\pi$
$984$		0			0
$985$	−78.1307	−	24.1001i	−2.48945	−	0.767894i
$986$	−5.06946	+	22.2107i	−0.161444	+	0.707334i
$987$		0			0
$988$	0.276856	+	1.21298i	0.00880795	+	0.0385902i
$989$	0.828140	−	11.0508i	0.0263333	−	0.351394i
$990$		0			0
$991$	−0.263245	−	3.51276i	−0.00836226	−	0.111587i	0.991461	−	0.130406i	$-0.0416282\pi$
$991$	−0.263245	−	3.51276i	−0.00836226	−	0.111587i	−0.999823	+	0.0188197i	$0.994009\pi$
$992$	0.276747	+	0.705140i	0.00878673	+	0.0223882i
$993$		0			0
$994$	44.5883	+	5.18297i	1.41426	+	0.164394i
$995$	49.6509	−	23.9106i	1.57404	−	0.758017i
$996$		0			0
$997$	4.57823	+	0.690057i	0.144994	+	0.0218543i	0.221138	−	0.975243i	$-0.429023\pi$
$997$	4.57823	+	0.690057i	0.144994	+	0.0218543i	−0.0761442	+	0.997097i	$0.524261\pi$
$998$	−26.7078	−	46.2593i	−0.845421	−	1.46431i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.37.5	yes	72
3.2	odd	2	inner	441.2.bb.f.37.2	✓	72
49.4	even	21	inner	441.2.bb.f.298.5	yes	72
147.53	odd	42	inner	441.2.bb.f.298.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.37.2	✓	72	3.2	odd	2	inner
441.2.bb.f.37.5	yes	72	1.1	even	1	trivial
441.2.bb.f.298.2	yes	72	147.53	odd	42	inner
441.2.bb.f.298.5	yes	72	49.4	even	21	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14923 - 0.783534i) q^{2} +(-0.0238713 + 0.0608230i) q^{4} +(3.53905 + 1.09165i) q^{5} +(-2.60134 + 0.482718i) q^{7} +(0.639241 + 2.80070i) q^{8} +O(q^{10})\)	\(q+(1.14923 - 0.783534i) q^{2} +(-0.0238713 + 0.0608230i) q^{4} +(3.53905 + 1.09165i) q^{5} +(-2.60134 + 0.482718i) q^{7} +(0.639241 + 2.80070i) q^{8} +(4.92254 - 1.51840i) q^{10} +(-0.0190277 - 0.253907i) q^{11} +(3.89505 + 1.87576i) q^{13} +(-2.61132 + 2.59299i) q^{14} +(2.83328 + 2.62890i) q^{16} +(-6.47644 - 0.976167i) q^{17} +(2.20228 - 3.81445i) q^{19} +(-0.150879 + 0.189197i) q^{20} +(-0.220812 - 0.276890i) q^{22} +(1.41341 - 0.213037i) q^{23} +(7.20200 + 4.91024i) q^{25} +(5.94604 - 0.896221i) q^{26} +(0.0327370 - 0.169745i) q^{28} +(1.55920 - 1.95518i) q^{29} +(-1.02513 - 1.77557i) q^{31} +(-0.365341 - 0.0550663i) q^{32} +(-8.20780 + 3.95267i) q^{34} +(-9.73325 - 1.13140i) q^{35} +(-3.65832 - 9.32124i) q^{37} +(-0.457825 - 6.10925i) q^{38} +(-0.795083 + 10.6097i) q^{40} +(0.0761773 + 0.333754i) q^{41} +(1.72518 - 7.55849i) q^{43} +(0.0158976 + 0.00490377i) q^{44} +(1.45741 - 1.35228i) q^{46} +(2.26719 - 1.54575i) q^{47} +(6.53397 - 2.51143i) q^{49} +12.1241 q^{50} +(-0.207069 + 0.192132i) q^{52} +(-0.864149 + 2.20182i) q^{53} +(0.209839 - 0.919363i) q^{55} +(-3.01483 - 6.97700i) q^{56} +(0.259939 - 3.46864i) q^{58} +(-11.8919 + 3.66816i) q^{59} +(4.95104 + 12.6150i) q^{61} +(-2.56933 - 1.23733i) q^{62} +(-7.42759 + 3.57694i) q^{64} +(11.7371 + 10.8905i) q^{65} +(-2.84627 - 4.92989i) q^{67} +(0.213974 - 0.370615i) q^{68} +(-12.0723 + 6.32609i) q^{70} +(-7.60525 - 9.53668i) q^{71} +(4.41510 + 3.01017i) q^{73} +(-11.5078 - 7.84586i) q^{74} +(0.179435 + 0.225005i) q^{76} +(0.172063 + 0.651315i) q^{77} +(4.94546 - 8.56580i) q^{79} +(7.15729 + 12.3968i) q^{80} +(0.349053 + 0.323874i) q^{82} +(-7.97770 + 3.84186i) q^{83} +(-21.8548 - 10.5247i) q^{85} +(-3.93970 - 10.0382i) q^{86} +(0.698954 - 0.215599i) q^{88} +(-0.738465 + 9.85413i) q^{89} +(-11.0378 - 2.99928i) q^{91} +(-0.0207823 + 0.0910533i) q^{92} +(1.39439 - 3.55284i) q^{94} +(11.9580 - 11.0954i) q^{95} -11.9406 q^{97} +(5.54126 - 8.00580i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

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