LMFDB - Embedded newform 441.2.bb.f.100.3

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			100.3
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.f.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12270 - 0.346307i) q^{2} +(-0.511951 - 0.349042i) q^{4} +(1.86885 - 0.281684i) q^{5} +(-0.330078 - 2.62508i) q^{7} +(1.91896 + 2.40631i) q^{8} +O(q^{10})$	\(q+(-1.12270 - 0.346307i) q^{2} +(-0.511951 - 0.349042i) q^{4} +(1.86885 - 0.281684i) q^{5} +(-0.330078 - 2.62508i) q^{7} +(1.91896 + 2.40631i) q^{8} +(-2.19571 - 0.330950i) q^{10} +(0.338113 - 0.313723i) q^{11} +(-0.629141 - 2.75645i) q^{13} +(-0.538505 + 3.06149i) q^{14} +(-0.868358 - 2.21254i) q^{16} +(0.364587 + 4.86507i) q^{17} +(1.59773 - 2.76734i) q^{19} +(-1.05508 - 0.508099i) q^{20} +(-0.488245 + 0.235126i) q^{22} +(0.505500 - 6.74543i) q^{23} +(-1.36461 + 0.420925i) q^{25} +(-0.248240 + 3.31254i) q^{26} +(-0.747280 + 1.45912i) q^{28} +(0.185825 + 0.0894884i) q^{29} +(-2.93559 - 5.08458i) q^{31} +(-0.251318 - 3.35361i) q^{32} +(1.27549 - 5.58828i) q^{34} +(-1.35631 - 4.81291i) q^{35} +(4.27026 - 2.91142i) q^{37} +(-2.75212 + 2.55359i) q^{38} +(4.26408 + 3.95648i) q^{40} +(-5.20798 - 6.53060i) q^{41} +(2.37588 - 2.97926i) q^{43} +(-0.282600 + 0.0425951i) q^{44} +(-2.90351 + 7.39803i) q^{46} +(1.25960 + 0.388534i) q^{47} +(-6.78210 + 1.73296i) q^{49} +1.67781 q^{50} +(-0.640027 + 1.63076i) q^{52} +(-7.08043 - 4.82735i) q^{53} +(0.543513 - 0.681543i) q^{55} +(5.68334 - 5.83171i) q^{56} +(-0.177635 - 0.164821i) q^{58} +(12.5882 + 1.89737i) q^{59} +(2.94076 - 2.00498i) q^{61} +(1.53495 + 6.72508i) q^{62} +(-1.93702 + 8.48663i) q^{64} +(-1.95222 - 4.97417i) q^{65} +(4.29205 + 7.43406i) q^{67} +(1.51147 - 2.61793i) q^{68} +(-0.144014 + 5.87315i) q^{70} +(-9.97902 + 4.80564i) q^{71} +(-5.05942 + 1.56063i) q^{73} +(-5.80247 + 1.78982i) q^{74} +(-1.78388 + 0.859070i) q^{76} +(-0.935153 - 0.784022i) q^{77} +(6.76956 - 11.7252i) q^{79} +(-2.24607 - 3.89031i) q^{80} +(3.58540 + 9.13546i) q^{82} +(-2.56563 + 11.2407i) q^{83} +(2.05177 + 8.98940i) q^{85} +(-3.69914 + 2.52203i) q^{86} +(1.40374 + 0.211580i) q^{88} +(7.41983 + 6.88460i) q^{89} +(-7.02823 + 2.56139i) q^{91} +(-2.61323 + 3.27689i) q^{92} +(-1.27960 - 0.872414i) q^{94} +(2.20640 - 5.62181i) q^{95} +8.20894 q^{97} +(8.21440 + 0.403088i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

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 $

$2$	−1.12270	−	0.346307i	−0.793869	−	0.244876i	−0.128812	−	0.991669i	$-0.541116\pi$
$2$	−1.12270	−	0.346307i	−0.793869	−	0.244876i	−0.665057	+	0.746793i	$0.731593\pi$
$3$		0			0
$3$		0			0
$4$	−0.511951	−	0.349042i	−0.255975	−	0.174521i
$5$	1.86885	−	0.281684i	0.835775	−	0.125973i	0.282809	−	0.959176i	$-0.408734\pi$
$5$	1.86885	−	0.281684i	0.835775	−	0.125973i	0.552967	+	0.833203i	$0.313496\pi$
$6$		0			0
$7$	−0.330078	−	2.62508i	−0.124758	−	0.992187i
$7$	−0.330078	−	2.62508i	−0.124758	−	0.992187i
$8$	1.91896	+	2.40631i	0.678456	+	0.850757i
$9$		0			0
$10$	−2.19571	−	0.330950i	−0.694344	−	0.104655i
$11$	0.338113	−	0.313723i	0.101945	−	0.0945912i	−0.627554	−	0.778573i	$-0.715944\pi$
$11$	0.338113	−	0.313723i	0.101945	−	0.0945912i	0.729499	+	0.683982i	$0.239753\pi$
$12$		0			0
$13$	−0.629141	−	2.75645i	−0.174492	−	0.764500i	−0.984112	−	0.177546i	$-0.943184\pi$
$13$	−0.629141	−	2.75645i	−0.174492	−	0.764500i	0.809620	−	0.586954i	$-0.199673\pi$
$14$	−0.538505	+	3.06149i	−0.143922	+	0.818217i
$15$		0			0
$16$	−0.868358	−	2.21254i	−0.217090	−	0.553135i
$17$	0.364587	+	4.86507i	0.0884253	+	1.17995i	0.848167	+	0.529729i	$0.177706\pi$
$17$	0.364587	+	4.86507i	0.0884253	+	1.17995i	−0.759742	+	0.650225i	$0.774675\pi$
$18$		0			0
$19$	1.59773	−	2.76734i	0.366544	−	0.634872i	−0.622479	−	0.782636i	$-0.713874\pi$
$19$	1.59773	−	2.76734i	0.366544	−	0.634872i	0.989023	+	0.147764i	$0.0472077\pi$
$20$	−1.05508	−	0.508099i	−0.235923	−	0.113614i
$21$		0			0
$22$	−0.488245	+	0.235126i	−0.104094	+	0.0501291i
$23$	0.505500	−	6.74543i	0.105404	−	1.40652i	−0.654293	−	0.756241i	$-0.727034\pi$
$23$	0.505500	−	6.74543i	0.105404	−	1.40652i	0.759697	−	0.650277i	$-0.225347\pi$
$24$		0			0
$25$	−1.36461	+	0.420925i	−0.272921	+	0.0841851i
$26$	−0.248240	+	3.31254i	−0.0486839	+	0.649642i
$27$		0			0
$28$	−0.747280	+	1.45912i	−0.141223	+	0.275748i
$29$	0.185825	+	0.0894884i	0.0345068	+	0.0166176i	0.451058	−	0.892495i	$-0.351047\pi$
$29$	0.185825	+	0.0894884i	0.0345068	+	0.0166176i	−0.416551	+	0.909112i	$0.636761\pi$
$30$		0			0
$31$	−2.93559	−	5.08458i	−0.527247	−	0.913218i	−0.999496	−	0.0317530i	$-0.989891\pi$
$31$	−2.93559	−	5.08458i	−0.527247	−	0.913218i	0.472249	−	0.881465i	$-0.343442\pi$
$32$	−0.251318	−	3.35361i	−0.0444272	−	0.592840i
$33$		0			0
$34$	1.27549	−	5.58828i	0.218744	−	0.958381i
$35$	−1.35631	−	4.81291i	−0.229258	−	0.813530i
$36$		0			0
$37$	4.27026	−	2.91142i	0.702027	−	0.478634i	−0.158944	−	0.987288i	$-0.550809\pi$
$37$	4.27026	−	2.91142i	0.702027	−	0.478634i	0.860971	+	0.508654i	$0.169857\pi$
$38$	−2.75212	+	2.55359i	−0.446452	+	0.414247i
$39$		0			0
$40$	4.26408	+	3.95648i	0.674210	+	0.625575i
$41$	−5.20798	−	6.53060i	−0.813349	−	1.01991i	−0.999302	−	0.0373493i	$-0.988109\pi$
$41$	−5.20798	−	6.53060i	−0.813349	−	1.01991i	0.185953	−	0.982559i	$-0.440463\pi$
$42$		0			0
$43$	2.37588	−	2.97926i	0.362318	−	0.454332i	−0.566943	−	0.823757i	$-0.691874\pi$
$43$	2.37588	−	2.97926i	0.362318	−	0.454332i	0.929261	+	0.369425i	$0.120445\pi$
$44$	−0.282600	+	0.0425951i	−0.0426036	+	0.00642146i
$45$		0			0
$46$	−2.90351	+	7.39803i	−0.428100	+	1.09078i
$47$	1.25960	+	0.388534i	0.183731	+	0.0566735i	0.385255	−	0.922810i	$-0.374113\pi$
$47$	1.25960	+	0.388534i	0.183731	+	0.0566735i	−0.201524	+	0.979483i	$0.564590\pi$
$48$		0			0
$49$	−6.78210	+	1.73296i	−0.968871	+	0.247566i
$50$	1.67781			0.237279
$51$		0			0
$52$	−0.640027	+	1.63076i	−0.0887557	+	0.226146i
$53$	−7.08043	−	4.82735i	−0.972572	−	0.663088i	−0.0308651	−	0.999524i	$-0.509826\pi$
$53$	−7.08043	−	4.82735i	−0.972572	−	0.663088i	−0.941707	+	0.336435i	$0.890779\pi$
$54$		0			0
$55$	0.543513	−	0.681543i	0.0732872	−	0.0918993i
$56$	5.68334	−	5.83171i	0.759468	−	0.779295i
$57$		0			0
$58$	−0.177635	−	0.164821i	−0.0233246	−	0.0216421i
$59$	12.5882	+	1.89737i	1.63885	+	0.247017i	0.902847	−	0.429963i	$-0.141473\pi$
$59$	12.5882	+	1.89737i	1.63885	+	0.247017i	0.736002	+	0.676980i	$0.236711\pi$
$60$		0			0
$61$	2.94076	−	2.00498i	0.376526	−	0.256711i	−0.360239	−	0.932860i	$-0.617305\pi$
$61$	2.94076	−	2.00498i	0.376526	−	0.256711i	0.736765	+	0.676149i	$0.236352\pi$
$62$	1.53495	+	6.72508i	0.194939	+	0.854086i
$63$		0			0
$64$	−1.93702	+	8.48663i	−0.242127	+	1.06083i
$65$	−1.95222	−	4.97417i	−0.242143	−	0.616969i
$66$		0			0
$67$	4.29205	+	7.43406i	0.524358	+	0.908214i	0.999598	+	0.0283582i	$0.00902791\pi$
$67$	4.29205	+	7.43406i	0.524358	+	0.908214i	−0.475240	+	0.879856i	$0.657639\pi$
$68$	1.51147	−	2.61793i	0.183292	−	0.317471i
$69$		0			0
$70$	−0.144014	+	5.87315i	−0.0172130	+	0.701976i
$71$	−9.97902	+	4.80564i	−1.18429	+	0.570325i	−0.919159	−	0.393887i	$-0.871130\pi$
$71$	−9.97902	+	4.80564i	−1.18429	+	0.570325i	−0.265133	+	0.964212i	$0.585416\pi$
$72$		0			0
$73$	−5.05942	+	1.56063i	−0.592161	+	0.182657i	−0.576330	−	0.817217i	$-0.695516\pi$
$73$	−5.05942	+	1.56063i	−0.592161	+	0.182657i	−0.0158311	+	0.999875i	$0.505039\pi$
$74$	−5.80247	+	1.78982i	−0.674523	+	0.208063i
$75$		0			0
$76$	−1.78388	+	0.859070i	−0.204625	+	0.0985421i
$77$	−0.935153	−	0.784022i	−0.106571	−	0.0893476i
$78$		0			0
$79$	6.76956	−	11.7252i	0.761636	−	1.31919i	−0.180372	−	0.983599i	$-0.557730\pi$
$79$	6.76956	−	11.7252i	0.761636	−	1.31919i	0.942007	−	0.335593i	$-0.108937\pi$
$80$	−2.24607	−	3.89031i	−0.251118	−	0.434950i
$81$		0			0
$82$	3.58540	+	9.13546i	0.395942	+	1.00884i
$83$	−2.56563	+	11.2407i	−0.281614	+	1.23383i	0.614110	+	0.789221i	$0.289515\pi$
$83$	−2.56563	+	11.2407i	−0.281614	+	1.23383i	−0.895724	+	0.444611i	$0.853342\pi$
$84$		0			0
$85$	2.05177	+	8.98940i	0.222546	+	0.975037i
$86$	−3.69914	+	2.52203i	−0.398888	+	0.271957i
$87$		0			0
$88$	1.40374	+	0.211580i	0.149639	+	0.0225545i
$89$	7.41983	+	6.88460i	0.786500	+	0.729766i	0.967267	−	0.253760i	$-0.0816674\pi$
$89$	7.41983	+	6.88460i	0.786500	+	0.729766i	−0.180767	+	0.983526i	$0.557858\pi$
$90$		0			0
$91$	−7.02823	+	2.56139i	−0.736758	+	0.268506i
$92$	−2.61323	+	3.27689i	−0.272448	+	0.341639i
$93$		0			0
$94$	−1.27960	−	0.872414i	−0.131980	−	0.0899827i
$95$	2.20640	−	5.62181i	0.226371	−	0.576785i
$96$		0			0
$97$	8.20894			0.833491			0.416746	−	0.909023i	$-0.363171\pi$
$97$	8.20894			0.833491			0.416746	+	0.909023i	$0.363171\pi$
$98$	8.21440	+	0.403088i	0.829779	+	0.0407181i
$99$		0			0
$100$	0.845533	+	0.260812i	0.0845533	+	0.0260812i
$101$	−0.320036	+	0.815438i	−0.0318448	+	0.0811391i	−0.945912	−	0.324424i	$-0.894829\pi$
$101$	−0.320036	+	0.815438i	−0.0318448	+	0.0811391i	0.914067	+	0.405563i	$0.132925\pi$
$102$		0			0
$103$	14.2581	−	2.14906i	1.40489	−	0.211753i	0.597546	−	0.801834i	$-0.296142\pi$
$103$	14.2581	−	2.14906i	1.40489	−	0.211753i	0.807344	+	0.590081i	$0.200904\pi$
$104$	5.42555	−	6.80343i	0.532019	−	0.667131i
$105$		0			0
$106$	6.27745	+	7.87167i	0.609720	+	0.764564i
$107$	9.96153	+	9.24295i	0.963018	+	0.893550i	0.994371	−	0.105958i	$-0.0337911\pi$
$107$	9.96153	+	9.24295i	0.963018	+	0.893550i	−0.0313528	+	0.999508i	$0.509982\pi$
$108$		0			0
$109$	−8.25825	+	7.66254i	−0.790997	+	0.733938i	−0.968184	−	0.250239i	$-0.919491\pi$
$109$	−8.25825	+	7.66254i	−0.790997	+	0.733938i	0.177187	+	0.984177i	$0.443300\pi$
$110$	−0.846225	+	0.576946i	−0.0806844	+	0.0550097i
$111$		0			0
$112$	−5.52147	+	3.00982i	−0.521730	+	0.284402i
$113$	−2.45927	+	10.7748i	−0.231349	+	1.01361i	0.717173	+	0.696895i	$0.245436\pi$
$113$	−2.45927	+	10.7748i	−0.231349	+	1.01361i	−0.948522	+	0.316711i	$0.897421\pi$
$114$		0			0
$115$	−0.955375	−	12.7486i	−0.0890891	−	1.18881i
$116$	−0.0638979	−	0.110674i	−0.00593277	−	0.0102759i
$117$		0			0
$118$	−13.4757	−	6.48957i	−1.24054	−	0.597414i
$119$	12.6509	−	2.56293i	1.15970	−	0.234943i
$120$		0			0
$121$	−0.806133	+	10.7571i	−0.0732848	+	0.977918i
$122$	−3.99594	+	1.23258i	−0.361775	+	0.111593i
$123$		0			0
$124$	−0.271859	+	3.62770i	−0.0244136	+	0.325777i
$125$	−10.9457	+	5.27115i	−0.979009	+	0.471466i
$126$		0			0
$127$	14.8821	+	7.16682i	1.32057	+	0.635952i	0.955490	−	0.295024i	$-0.0953278\pi$
$127$	14.8821	+	7.16682i	1.32057	+	0.635952i	0.365079	+	0.930977i	$0.381042\pi$
$128$	1.75066	−	3.03223i	0.154738	−	0.268014i
$129$		0			0
$130$	0.469164	+	6.26056i	0.0411484	+	0.549088i
$131$	−2.76303	−	7.04008i	−0.241407	−	0.615095i	0.757898	−	0.652373i	$-0.226226\pi$
$131$	−2.76303	−	7.04008i	−0.241407	−	0.615095i	−0.999305	+	0.0372782i	$0.988131\pi$
$132$		0			0
$133$	−7.79187	−	3.28072i	−0.675641	−	0.284475i
$134$	−2.24422	−	9.83258i	−0.193871	−	0.849406i
$135$		0			0
$136$	−11.0072	+	10.2132i	−0.943861	+	0.875775i
$137$	10.9291	+	1.64730i	0.933738	+	0.140738i	0.598253	−	0.801307i	$-0.295862\pi$
$137$	10.9291	+	1.64730i	0.933738	+	0.140738i	0.335485	+	0.942046i	$0.391100\pi$
$138$		0			0
$139$	−4.81404	−	6.03662i	−0.408322	−	0.512019i	0.534567	−	0.845126i	$-0.320475\pi$
$139$	−4.81404	−	6.03662i	−0.408322	−	0.512019i	−0.942889	+	0.333106i	$0.891903\pi$
$140$	−0.985543	+	2.93738i	−0.0832936	+	0.248254i
$141$		0			0
$142$	12.8677	−	1.93949i	1.07983	−	0.162758i
$143$	−1.07748	−	0.734615i	−0.0901036	−	0.0614316i
$144$		0			0
$145$	0.372486	+	0.114897i	0.0309333	+	0.00954165i
$146$	6.22067			0.514826
$147$		0			0
$148$	−3.20237			−0.263233
$149$	6.14369	+	1.89508i	0.503311	+	0.155251i	0.536006	−	0.844214i	$-0.319933\pi$
$149$	6.14369	+	1.89508i	0.503311	+	0.155251i	−0.0326944	+	0.999465i	$0.510409\pi$
$150$		0			0
$151$	−0.368022	−	0.250913i	−0.0299492	−	0.0204190i	0.548253	−	0.836313i	$-0.315293\pi$
$151$	−0.368022	−	0.250913i	−0.0299492	−	0.0204190i	−0.578202	+	0.815894i	$0.696245\pi$
$152$	9.72505	−	1.46582i	0.788806	−	0.118893i
$153$		0			0
$154$	0.778384	+	1.20407i	0.0627240	+	0.0970268i
$155$	−6.91842	−	8.67542i	−0.555701	−	0.696827i
$156$		0			0
$157$	−3.85764	−	0.581446i	−0.307874	−	0.0464045i	−0.00671159	−	0.999977i	$-0.502136\pi$
$157$	−3.85764	−	0.581446i	−0.307874	−	0.0464045i	−0.301162	+	0.953573i	$0.597374\pi$
$158$	−11.6607	+	10.8196i	−0.927677	+	0.860759i
$159$		0			0
$160$	−1.41433	−	6.19660i	−0.111813	−	0.489884i
$161$	−17.8741	+	0.899542i	−1.40868	+	0.0708938i
$162$		0			0
$163$	0.711693	+	1.81336i	0.0557441	+	0.142034i	0.956033	−	0.293259i	$-0.0947400\pi$
$163$	0.711693	+	1.81336i	0.0557441	+	0.142034i	−0.900289	+	0.435293i	$0.856645\pi$
$164$	0.386775	+	5.16115i	0.0302020	+	0.403018i
$165$		0			0
$166$	6.77318	−	11.7315i	0.525701	−	0.910540i
$167$	−16.5627	−	7.97618i	−1.28166	−	0.617215i	−0.335844	−	0.941917i	$-0.609022\pi$
$167$	−16.5627	−	7.97618i	−1.28166	−	0.617215i	−0.945816	+	0.324702i	$0.894736\pi$
$168$		0			0
$169$	4.51042	−	2.17211i	0.346956	−	0.167085i
$170$	0.809568	−	10.8029i	0.0620911	−	0.828548i
$171$		0			0
$172$	−2.25622	+	0.695951i	−0.172035	+	0.0530658i
$173$	0.271524	−	3.62324i	0.0206436	−	0.275470i	−0.977324	−	0.211749i	$-0.932084\pi$
$173$	0.271524	−	3.62324i	0.0206436	−	0.275470i	0.997968	−	0.0637211i	$-0.0202968\pi$
$174$		0			0
$175$	1.55539	+	3.44326i	0.117576	+	0.260286i
$176$	−0.987730	−	0.475665i	−0.0744529	−	0.0358546i
$177$		0			0
$178$	−5.94606	−	10.2989i	−0.445676	−	0.771933i
$179$	1.31500	+	17.5474i	0.0982874	+	1.31155i	0.800390	+	0.599479i	$0.204626\pi$
$179$	1.31500	+	17.5474i	0.0982874	+	1.31155i	−0.702103	+	0.712075i	$0.747755\pi$
$180$		0			0
$181$	3.99993	−	17.5248i	0.297312	−	1.30261i	−0.576800	−	0.816885i	$-0.695699\pi$
$181$	3.99993	−	17.5248i	0.297312	−	1.30261i	0.874112	−	0.485724i	$-0.161444\pi$
$182$	8.77762	−	0.441746i	0.650640	−	0.0327444i
$183$		0			0
$184$	17.2016	−	11.7278i	1.26812	−	0.864588i
$185$	7.16039	−	6.64387i	0.526442	−	0.488467i
$186$		0			0
$187$	1.64956	+	1.53057i	0.120628	+	0.111926i
$188$	−0.509237	−	0.638563i	−0.0371399	−	0.0465720i
$189$		0			0
$190$	−4.42399	+	5.54751i	−0.320950	+	0.402459i
$191$	−7.81569	+	1.17803i	−0.565523	+	0.0852389i	−0.425580	−	0.904921i	$-0.639930\pi$
$191$	−7.81569	+	1.17803i	−0.565523	+	0.0852389i	−0.139943	+	0.990160i	$0.544692\pi$
$192$		0			0
$193$	−4.58487	+	11.6821i	−0.330026	+	0.840894i	0.665499	+	0.746399i	$0.268219\pi$
$193$	−4.58487	+	11.6821i	−0.330026	+	0.840894i	−0.995525	+	0.0944949i	$0.969876\pi$
$194$	−9.21617	−	2.84281i	−0.661683	−	0.204102i
$195$		0			0
$196$	4.07698	+	1.48004i	0.291213	+	0.105717i
$197$	25.9382			1.84802			0.924010	−	0.382368i	$-0.124891\pi$
$197$	25.9382			1.84802			0.924010	+	0.382368i	$0.124891\pi$
$198$		0			0
$199$	4.11848	−	10.4937i	0.291951	−	0.743879i	−0.707363	−	0.706850i	$-0.750115\pi$
$199$	4.11848	−	10.4937i	0.291951	−	0.743879i	0.999314	−	0.0370287i	$-0.0117893\pi$
$200$	−3.63151	−	2.47592i	−0.256786	−	0.175074i
$201$		0			0
$202$	0.641696	−	0.804662i	0.0451496	−	0.0566158i
$203$	0.173578	−	0.517343i	0.0121828	−	0.0363104i
$204$		0			0
$205$	−11.5725	−	10.7377i	−0.808258	−	0.749954i
$206$	−16.7518	−	2.52492i	−1.16715	−	0.175920i
$207$		0			0
$208$	−5.55243	+	3.78558i	−0.384992	+	0.262483i
$209$	−0.327968	−	1.43692i	−0.0226860	−	0.0993938i
$210$		0			0
$211$	−0.258403	+	1.13214i	−0.0177892	+	0.0779394i	−0.983043	−	0.183373i	$-0.941298\pi$
$211$	−0.258403	+	1.13214i	−0.0177892	+	0.0779394i	0.965254	+	0.261313i	$0.0841554\pi$
$212$	1.93988	+	4.94274i	0.133232	+	0.339469i
$213$		0			0
$214$	−7.98291	−	13.8268i	−0.545701	−	0.945181i
$215$	3.60095	−	6.23703i	0.245583	−	0.425362i
$216$		0			0
$217$	−12.3785	+	9.38446i	−0.840305	+	0.637059i
$218$	11.9251	−	5.74284i	0.807672	−	0.388954i
$219$		0			0
$220$	−0.516139	+	0.159208i	−0.0347981	+	0.0107338i
$221$	13.1809	−	4.06578i	0.886645	−	0.273494i
$222$		0			0
$223$	9.57727	−	4.61217i	0.641341	−	0.308854i	−0.0848012	−	0.996398i	$-0.527026\pi$
$223$	9.57727	−	4.61217i	0.641341	−	0.308854i	0.726143	+	0.687544i	$0.241311\pi$
$224$	−8.72054	+	1.76668i	−0.582666	+	0.118042i
$225$		0			0
$226$	6.49241	−	11.2452i	0.431869	−	0.748019i
$227$	−0.708160	−	1.22657i	−0.0470023	−	0.0814103i	0.841567	−	0.540153i	$-0.181633\pi$
$227$	−0.708160	−	1.22657i	−0.0470023	−	0.0814103i	−0.888569	+	0.458742i	$0.848300\pi$
$228$		0			0
$229$	−6.22270	−	15.8552i	−0.411208	−	1.04774i	−0.975075	−	0.221875i	$-0.928782\pi$
$229$	−6.22270	−	15.8552i	−0.411208	−	1.04774i	0.563867	−	0.825865i	$-0.309313\pi$
$230$	−3.34233	+	14.6437i	−0.220387	+	0.965576i
$231$		0			0
$232$	0.141254	+	0.618876i	0.00927381	+	0.0406312i
$233$	−5.12204	+	3.49215i	−0.335556	+	0.228778i	−0.719362	−	0.694636i	$-0.755566\pi$
$233$	−5.12204	+	3.49215i	−0.335556	+	0.228778i	0.383806	+	0.923414i	$0.374613\pi$
$234$		0			0
$235$	2.46344	+	0.371304i	0.160697	+	0.0242212i
$236$	−5.78229	−	5.36519i	−0.376395	−	0.349244i
$237$		0			0
$238$	−15.0907	−	1.50369i	−0.978184	−	0.0974696i
$239$	−10.7017	+	13.4195i	−0.692237	+	0.868038i	−0.996417	−	0.0845769i	$-0.973046\pi$
$239$	−10.7017	+	13.4195i	−0.692237	+	0.868038i	0.304180	+	0.952615i	$0.401618\pi$
$240$		0			0
$241$	−6.80813	−	4.64170i	−0.438550	−	0.298998i	0.323845	−	0.946110i	$-0.395024\pi$
$241$	−6.80813	−	4.64170i	−0.438550	−	0.298998i	−0.762395	+	0.647112i	$0.775977\pi$
$242$	4.63030	−	11.7978i	0.297647	−	0.758393i
$243$		0			0
$244$	−2.20535			−0.141183
$245$	−12.1866	+	5.14906i	−0.778572	+	0.328961i
$246$		0			0
$247$	−8.63323	−	2.66300i	−0.549319	−	0.169442i
$248$	6.60178	−	16.8211i	0.419213	−	1.06814i
$249$		0			0
$250$	14.1141	−	2.12736i	0.892655	−	0.134546i
$251$	17.4730	−	21.9105i	1.10289	−	1.38298i	0.186609	−	0.982434i	$-0.440250\pi$
$251$	17.4730	−	21.9105i	1.10289	−	1.38298i	0.916278	−	0.400543i	$-0.131178\pi$
$252$		0			0
$253$	−1.94528	−	2.43931i	−0.122299	−	0.153358i
$254$	−14.2262	−	13.1999i	−0.892629	−	0.828238i
$255$		0			0
$256$	9.74671	−	9.04363i	0.609170	−	0.565227i
$257$	−5.03920	+	3.43567i	−0.314337	+	0.214311i	−0.710203	−	0.703997i	$-0.751397\pi$
$257$	−5.03920	+	3.43567i	−0.314337	+	0.214311i	0.395866	+	0.918308i	$0.370444\pi$
$258$		0			0
$259$	−9.05223	−	10.2488i	−0.562478	−	0.636829i
$260$	−0.736755	+	3.22793i	−0.0456916	+	0.200188i
$261$		0			0
$262$	0.664022	+	8.86076i	0.0410234	+	0.547419i
$263$	1.02808	+	1.78068i	0.0633939	+	0.109801i	0.895980	−	0.444094i	$-0.146474\pi$
$263$	1.02808	+	1.78068i	0.0633939	+	0.109801i	−0.832587	+	0.553895i	$0.813141\pi$
$264$		0			0
$265$	−14.5921	−	7.02716i	−0.896383	−	0.431675i
$266$	7.61180	+	6.38165i	0.466709	+	0.391284i
$267$		0			0
$268$	0.397478	−	5.30398i	0.0242799	−	0.323992i
$269$	−19.8211	+	6.11401i	−1.20852	+	0.372778i	−0.832600	−	0.553875i	$-0.813148\pi$
$269$	−19.8211	+	6.11401i	−1.20852	+	0.372778i	−0.375917	+	0.926653i	$0.622672\pi$
$270$		0			0
$271$	−0.273784	+	3.65340i	−0.0166312	+	0.221928i	0.982695	+	0.185230i	$0.0593030\pi$
$271$	−0.273784	+	3.65340i	−0.0166312	+	0.221928i	−0.999326	+	0.0366981i	$0.988316\pi$
$272$	10.4476	−	5.03129i	0.633478	−	0.305067i
$273$		0			0
$274$	−11.6997	−	5.63426i	−0.706802	−	0.340378i
$275$	−0.329338	+	0.570430i	−0.0198598	+	0.0343982i
$276$		0			0
$277$	1.41810	+	18.9232i	0.0852052	+	1.13698i	0.861890	+	0.507095i	$0.169281\pi$
$277$	1.41810	+	18.9232i	0.0852052	+	1.13698i	−0.776685	+	0.629890i	$0.783100\pi$
$278$	3.31420	+	8.44445i	0.198773	+	0.506464i
$279$		0			0
$280$	8.97861	−	12.4995i	0.536575	−	0.746988i
$281$	−6.93882	−	30.4009i	−0.413935	−	1.81357i	−0.565056	−	0.825053i	$-0.691145\pi$
$281$	−6.93882	−	30.4009i	−0.413935	−	1.81357i	0.151120	−	0.988515i	$-0.451712\pi$
$282$		0			0
$283$	10.4000	−	9.64980i	0.618216	−	0.573621i	−0.307637	−	0.951504i	$-0.599538\pi$
$283$	10.4000	−	9.64980i	0.618216	−	0.573621i	0.925853	+	0.377883i	$0.123348\pi$
$284$	6.78614	+	1.02285i	0.402683	+	0.0606947i
$285$		0			0
$286$	0.955287	+	1.19789i	0.0564873	+	0.0708328i
$287$	−15.4243	+	15.8270i	−0.910468	+	0.934237i
$288$		0			0
$289$	−6.72589	+	1.01376i	−0.395640	+	0.0596332i
$290$	−0.378400	−	0.257989i	−0.0222204	−	0.0151496i
$291$		0			0
$292$	3.13490	+	0.966989i	0.183456	+	0.0565887i
$293$	24.5910			1.43662			0.718311	−	0.695722i	$-0.244916\pi$
$293$	24.5910			1.43662			0.718311	+	0.695722i	$0.244916\pi$
$294$		0			0
$295$	24.0600			1.40083
$296$	15.2002	+	4.68865i	0.883496	+	0.272523i
$297$		0			0
$298$	−6.24125	−	4.25521i	−0.361546	−	0.246498i
$299$	−18.9114	+	2.85044i	−1.09368	+	0.164845i
$300$		0			0
$301$	−8.60501	−	5.25348i	−0.495985	−	0.302806i
$302$	0.326285	+	0.409149i	0.0187756	+	0.0235439i
$303$		0			0
$304$	−7.51026	−	1.13199i	−0.430743	−	0.0649241i
$305$	4.93108	−	4.57537i	0.282353	−	0.261985i
$306$		0			0
$307$	6.81832	+	29.8730i	0.389142	+	1.70494i	0.667622	+	0.744500i	$0.267312\pi$
$307$	6.81832	+	29.8730i	0.389142	+	1.70494i	−0.278480	+	0.960442i	$0.589831\pi$
$308$	0.205096	+	0.727788i	0.0116864	+	0.0414696i
$309$		0			0
$310$	4.76295	+	12.1358i	0.270517	+	0.689267i
$311$	0.859504	+	11.4693i	0.0487380	+	0.650363i	0.967063	+	0.254536i	$0.0819229\pi$
$311$	0.859504	+	11.4693i	0.0487380	+	0.650363i	−0.918325	+	0.395827i	$0.870458\pi$
$312$		0			0
$313$	0.189155	−	0.327626i	0.0106917	−	0.0185185i	−0.860630	−	0.509231i	$-0.829930\pi$
$313$	0.189155	−	0.327626i	0.0106917	−	0.0185185i	0.871322	+	0.490712i	$0.163263\pi$
$314$	4.12962	+	1.98872i	0.233048	+	0.112230i
$315$		0			0
$316$	−7.55828	+	3.63988i	−0.425187	+	0.204759i
$317$	−2.55707	+	34.1217i	−0.143619	+	1.91647i	0.204239	+	0.978921i	$0.434528\pi$
$317$	−2.55707	+	34.1217i	−0.143619	+	1.91647i	−0.347858	+	0.937547i	$0.613091\pi$
$318$		0			0
$319$	0.0909044	−	0.0280403i	0.00508967	−	0.00156996i
$320$	−1.22945	+	16.4059i	−0.0687284	+	0.917116i
$321$		0			0
$322$	20.3788	+	5.18003i	1.13567	+	0.288672i
$323$	14.0458	+	6.76412i	0.781531	+	0.376366i
$324$		0			0
$325$	2.01879	+	3.49664i	0.111982	+	0.193959i
$326$	−0.171037	−	2.28233i	−0.00947286	−	0.126406i
$327$		0			0
$328$	5.72069	−	25.0640i	0.315872	−	1.38393i
$329$	0.604168	−	3.43479i	0.0333088	−	0.189366i
$330$		0			0
$331$	16.7758	−	11.4376i	0.922082	−	0.628665i	−0.00642492	−	0.999979i	$-0.502045\pi$
$331$	16.7758	−	11.4376i	0.922082	−	0.628665i	0.928507	+	0.371314i	$0.121093\pi$
$332$	5.23697	−	4.85920i	0.287416	−	0.266683i
$333$		0			0
$334$	15.8327	+	14.6906i	0.866329	+	0.803836i
$335$	10.1153	+	12.6841i	0.552656	+	0.693008i
$336$		0			0
$337$	−10.9153	+	13.6873i	−0.594592	+	0.745595i	−0.984524	−	0.175248i	$-0.943927\pi$
$337$	−10.9153	+	13.6873i	−0.594592	+	0.745595i	0.389932	+	0.920844i	$0.372499\pi$
$338$	−5.81607	+	0.876631i	−0.316352	+	0.0476824i
$339$		0			0
$340$	2.08727	−	5.31828i	0.113198	−	0.288424i
$341$	−2.58771	−	0.798204i	−0.140133	−	0.0432252i
$342$		0			0
$343$	6.78780	+	17.2315i	0.366507	+	0.930415i
$344$	11.7282			0.632344
$345$		0			0
$346$	−1.55959	+	3.97378i	−0.0838443	+	0.213632i
$347$	5.46000	+	3.72256i	0.293108	+	0.199838i	0.700942	−	0.713219i	$-0.252763\pi$
$347$	5.46000	+	3.72256i	0.293108	+	0.199838i	−0.407834	+	0.913056i	$0.633716\pi$
$348$		0			0
$349$	−16.8637	+	21.1464i	−0.902691	+	1.13194i	0.0880427	+	0.996117i	$0.471939\pi$
$349$	−16.8637	+	21.1464i	−0.902691	+	1.13194i	−0.990733	+	0.135822i	$0.956633\pi$
$350$	−0.553810	−	4.40440i	−0.0296024	−	0.235425i
$351$		0			0
$352$	−1.13708	−	1.05506i	−0.0606066	−	0.0562347i
$353$	33.9944	+	5.12383i	1.80934	+	0.272714i	0.964839	−	0.262841i	$-0.0846594\pi$
$353$	33.9944	+	5.12383i	1.80934	+	0.272714i	0.844500	+	0.535555i	$0.179897\pi$
$354$		0			0
$355$	−17.2956	+	11.7920i	−0.917956	+	0.625852i
$356$	−1.39557	−	6.11441i	−0.0739653	−	0.324063i
$357$		0			0
$358$	4.60044	−	20.1559i	0.243141	−	1.06527i
$359$	1.94817	+	4.96385i	0.102820	+	0.261982i	0.973021	−	0.230715i	$-0.0741064\pi$
$359$	1.94817	+	4.96385i	0.102820	+	0.261982i	−0.870201	+	0.492697i	$0.836011\pi$
$360$		0			0
$361$	4.39454	+	7.61157i	0.231292	+	0.400609i
$362$	−10.5597	+	18.2899i	−0.555005	+	0.961296i
$363$		0			0
$364$	4.49214	+	1.14184i	0.235452	+	0.0598488i
$365$	−9.01571	+	4.34173i	−0.471904	+	0.227257i
$366$		0			0
$367$	8.58414	−	2.64786i	0.448088	−	0.138217i	−0.0624948	−	0.998045i	$-0.519906\pi$
$367$	8.58414	−	2.64786i	0.448088	−	0.138217i	0.510583	+	0.859828i	$0.329429\pi$
$368$	−15.3635	+	4.73901i	−0.800877	+	0.247038i
$369$		0			0
$370$	−10.3398	+	4.97938i	−0.537540	+	0.258866i
$371$	−10.3351	+	20.1801i	−0.536572	+	1.04770i
$372$		0			0
$373$	−19.1103	+	33.1001i	−0.989496	+	1.71386i	−0.369555	+	0.929209i	$0.620490\pi$
$373$	−19.1103	+	33.1001i	−0.989496	+	1.71386i	−0.619941	+	0.784649i	$0.712843\pi$
$374$	−1.32191	−	2.28962i	−0.0683545	−	0.118394i
$375$		0			0
$376$	1.48219	+	3.77656i	0.0764381	+	0.194761i
$377$	0.129760	−	0.568516i	0.00668299	−	0.0292801i
$378$		0			0
$379$	−1.63574	−	7.16664i	−0.0840223	−	0.368126i	0.915384	−	0.402582i	$-0.131887\pi$
$379$	−1.63574	−	7.16664i	−0.0840223	−	0.368126i	−0.999406	+	0.0344563i	$0.989030\pi$
$380$	−3.09181	+	2.10796i	−0.158607	+	0.108136i
$381$		0			0
$382$	9.18263	+	1.38406i	0.469824	+	0.0708146i
$383$	−12.9293	−	11.9966i	−0.660655	−	0.612999i	0.276873	−	0.960906i	$-0.410702\pi$
$383$	−12.9293	−	11.9966i	−0.660655	−	0.612999i	−0.937529	+	0.347908i	$0.886892\pi$
$384$		0			0
$385$	−1.96851	−	1.20180i	−0.100324	−	0.0612495i
$386$	9.19302	−	11.5277i	0.467912	−	0.586744i
$387$		0			0
$388$	−4.20257	−	2.86527i	−0.213353	−	0.145462i
$389$	3.25289	−	8.28823i	0.164928	−	0.420230i	−0.824386	−	0.566027i	$-0.808480\pi$
$389$	3.25289	−	8.28823i	0.164928	−	0.420230i	0.989314	+	0.145798i	$0.0465748\pi$
$390$		0			0
$391$	33.0013			1.66895
$392$	−17.1846	−	12.9943i	−0.867956	−	0.656311i
$393$		0			0
$394$	−29.1208	−	8.98258i	−1.46709	−	0.452536i
$395$	9.34850	−	23.8196i	0.470374	−	1.19849i
$396$		0			0
$397$	6.70593	−	1.01076i	0.336561	−	0.0507284i	0.0214122	−	0.999771i	$-0.493184\pi$
$397$	6.70593	−	1.01076i	0.336561	−	0.0507284i	0.315149	+	0.949042i	$0.397946\pi$
$398$	−8.25786	+	10.3550i	−0.413929	+	0.519050i
$399$		0			0
$400$	2.11628	+	2.65373i	0.105814	+	0.132687i
$401$	7.68631	+	7.13186i	0.383836	+	0.356148i	0.848367	−	0.529409i	$-0.177586\pi$
$401$	7.68631	+	7.13186i	0.383836	+	0.356148i	−0.464530	+	0.885557i	$0.653777\pi$
$402$		0			0
$403$	−12.1685	+	11.2907i	−0.606155	+	0.562430i
$404$	0.448465	−	0.305758i	0.0223120	−	0.0152120i
$405$		0			0
$406$	−0.374035	+	0.520710i	−0.0185631	+	0.0258424i
$407$	0.530454	−	2.32407i	0.0262936	−	0.115200i
$408$		0			0
$409$	1.66505	+	22.2186i	0.0823315	+	1.09864i	0.873430	+	0.486949i	$0.161890\pi$
$409$	1.66505	+	22.2186i	0.0823315	+	1.09864i	−0.791099	+	0.611688i	$0.790491\pi$
$410$	9.27390	+	16.0629i	0.458005	+	0.793288i
$411$		0			0
$412$	−8.04955	−	3.87646i	−0.396573	−	0.190979i
$413$	0.825647	−	33.6714i	0.0406275	−	1.65686i
$414$		0			0
$415$	−1.62844	+	21.7300i	−0.0799368	+	1.06668i
$416$	−9.08593	+	2.80264i	−0.445474	+	0.137411i
$417$		0			0
$418$	−0.129406	+	1.72681i	−0.00632947	+	0.0844609i
$419$	20.3451	−	9.79768i	0.993923	−	0.478648i	0.135051	−	0.990839i	$-0.456880\pi$
$419$	20.3451	−	9.79768i	0.993923	−	0.478648i	0.858872	+	0.512191i	$0.171166\pi$
$420$		0			0
$421$	2.43236	+	1.17136i	0.118546	+	0.0570888i	0.492217	−	0.870473i	$-0.336187\pi$
$421$	2.43236	+	1.17136i	0.118546	+	0.0570888i	−0.373671	+	0.927561i	$0.621901\pi$
$422$	0.682175	−	1.18156i	0.0332078	−	0.0575175i
$423$		0			0
$424$	−1.97100	−	26.3012i	−0.0957203	−	1.27730i
$425$	−2.54535	−	6.48545i	−0.123468	−	0.314590i
$426$		0			0
$427$	−6.23392	−	7.05794i	−0.301680	−	0.341558i
$428$	−1.87364	−	8.20893i	−0.0905656	−	0.396794i
$429$		0			0
$430$	−6.20272	+	5.75528i	−0.299122	+	0.277544i
$431$	−14.4231	−	2.17394i	−0.694738	−	0.104715i	−0.207826	−	0.978166i	$-0.566639\pi$
$431$	−14.4231	−	2.17394i	−0.694738	−	0.104715i	−0.486912	+	0.873451i	$0.661877\pi$
$432$		0			0
$433$	16.8005	+	21.0672i	0.807383	+	1.01243i	0.999518	+	0.0310574i	$0.00988745\pi$
$433$	16.8005	+	21.0672i	0.807383	+	1.01243i	−0.192135	+	0.981369i	$0.561541\pi$
$434$	17.1472	−	6.24918i	0.823093	−	0.299970i
$435$		0			0
$436$	6.90237	−	1.04036i	0.330563	−	0.0498244i
$437$	−17.8593	−	12.1762i	−0.854324	−	0.582468i
$438$		0			0
$439$	−23.3375	−	7.19865i	−1.11384	−	0.343573i	−0.317398	−	0.948293i	$-0.602809\pi$
$439$	−23.3375	−	7.19865i	−1.11384	−	0.343573i	−0.796438	+	0.604720i	$0.793285\pi$
$440$	2.68298			0.127906
$441$		0			0
$442$	−16.2062			−0.770852
$443$	−20.6602	−	6.37282i	−0.981595	−	0.302782i	−0.237892	−	0.971292i	$-0.576456\pi$
$443$	−20.6602	−	6.37282i	−0.981595	−	0.302782i	−0.743703	+	0.668510i	$0.766933\pi$
$444$		0			0
$445$	15.8058	+	10.7762i	0.749268	+	0.510843i
$446$	−12.3496	+	1.86141i	−0.584772	+	0.0881402i
$447$		0			0
$448$	22.9175	+	2.28358i	1.08275	+	0.107889i
$449$	−7.22491	−	9.05975i	−0.340965	−	0.427556i	0.581554	−	0.813507i	$-0.302445\pi$
$449$	−7.22491	−	9.05975i	−0.340965	−	0.427556i	−0.922519	+	0.385951i	$0.873873\pi$
$450$		0			0
$451$	−3.80969	−	0.574218i	−0.179391	−	0.0270389i
$452$	5.01988	−	4.65777i	0.236115	−	0.219083i
$453$		0			0
$454$	0.370282	+	1.62231i	0.0173782	+	0.0761388i
$455$	−12.4132	+	6.76659i	−0.581940	+	0.317223i
$456$		0			0
$457$	15.3969	+	39.2306i	0.720235	+	1.83513i	0.516965	+	0.856007i	$0.327062\pi$
$457$	15.3969	+	39.2306i	0.720235	+	1.83513i	0.203270	+	0.979123i	$0.434843\pi$
$458$	1.49546	+	19.9556i	0.0698785	+	0.932463i
$459$		0			0
$460$	−3.96069	+	6.86012i	−0.184668	+	0.319855i
$461$	−15.3898	−	7.41132i	−0.716773	−	0.345179i	0.0396939	−	0.999212i	$-0.487362\pi$
$461$	−15.3898	−	7.41132i	−0.716773	−	0.345179i	−0.756467	+	0.654032i	$0.773076\pi$
$462$		0			0
$463$	8.07873	−	3.89051i	0.375451	−	0.180808i	−0.236636	−	0.971598i	$-0.576045\pi$
$463$	8.07873	−	3.89051i	0.375451	−	0.180808i	0.612086	+	0.790791i	$0.290330\pi$
$464$	0.0366344	−	0.488853i	0.00170071	−	0.0226944i
$465$		0			0
$466$	6.95987	−	2.14683i	0.322410	−	0.0994502i
$467$	1.78043	−	23.7582i	0.0823885	−	1.09940i	−0.790819	−	0.612050i	$-0.790345\pi$
$467$	1.78043	−	23.7582i	0.0823885	−	1.09940i	0.873208	−	0.487348i	$-0.162036\pi$
$468$		0			0
$469$	18.0983	−	13.7208i	0.835701	−	0.633568i
$470$	−2.63712	−	1.26997i	−0.121641	−	0.0585794i
$471$		0			0
$472$	19.5907	+	33.9321i	0.901736	+	1.56185i
$473$	−0.131346	−	1.75270i	−0.00603931	−	0.0805890i
$474$		0			0
$475$	−1.01542	+	4.44886i	−0.0465908	+	0.204128i
$476$	−7.37119	−	3.10359i	−0.337858	−	0.142253i
$477$		0			0
$478$	16.6621	−	11.3600i	0.762107	−	0.519596i
$479$	−5.23355	+	4.85602i	−0.239127	+	0.221877i	−0.790628	−	0.612297i	$-0.790246\pi$
$479$	−5.23355	+	4.85602i	−0.239127	+	0.221877i	0.551501	+	0.834174i	$0.314055\pi$
$480$		0			0
$481$	−10.7118	−	9.93906i	−0.488414	−	0.453182i
$482$	6.03603	+	7.56894i	0.274934	+	0.344756i
$483$		0			0
$484$	4.16738	−	5.22573i	0.189426	−	0.237533i
$485$	15.3413	−	2.31233i	0.696612	−	0.104997i
$486$		0			0
$487$	2.60548	−	6.63864i	0.118065	−	0.300826i	−0.859609	−	0.510953i	$-0.829293\pi$
$487$	2.60548	−	6.63864i	0.118065	−	0.300826i	0.977674	+	0.210127i	$0.0673879\pi$
$488$	10.4678	+	3.22889i	0.473856	+	0.146165i
$489$		0			0
$490$	15.4650	−	1.56055i	0.698639	−	0.0704985i
$491$	8.73786			0.394334			0.197167	−	0.980370i	$-0.436826\pi$
$491$	8.73786			0.394334			0.197167	+	0.980370i	$0.436826\pi$
$492$		0			0
$493$	−0.367619	+	0.936677i	−0.0165567	+	0.0421858i
$494$	8.77031	+	5.97949i	0.394595	+	0.269030i
$495$		0			0
$496$	−8.70071	+	10.9103i	−0.390673	+	0.489889i
$497$	15.9091	+	24.6095i	0.713618	+	1.10389i
$498$		0			0
$499$	−14.1781	−	13.1554i	−0.634699	−	0.588914i	0.295782	−	0.955256i	$-0.404420\pi$
$499$	−14.1781	−	13.1554i	−0.634699	−	0.588914i	−0.930481	+	0.366341i	$0.880610\pi$
$500$	7.44349	+	1.12193i	0.332883	+	0.0501740i
$501$		0			0
$502$	−27.2047	+	18.5479i	−1.21421	+	0.827832i
$503$	−5.99362	−	26.2598i	−0.267242	−	1.17086i	−0.913206	−	0.407497i	$-0.866402\pi$
$503$	−5.99362	−	26.2598i	−0.267242	−	1.17086i	0.645964	−	0.763368i	$-0.276456\pi$
$504$		0			0
$505$	−0.368403	+	1.61408i	−0.0163937	+	0.0718257i
$506$	1.33922	+	3.41227i	0.0595355	+	0.151694i
$507$		0			0
$508$	−5.11736	−	8.86352i	−0.227046	−	0.393255i
$509$	7.77307	−	13.4633i	0.344535	−	0.596752i	−0.640734	−	0.767763i	$-0.721370\pi$
$509$	7.77307	−	13.4633i	0.344535	−	0.596752i	0.985269	+	0.171011i	$0.0547032\pi$
$510$		0			0
$511$	5.76678	+	12.7663i	0.255107	+	0.564746i
$512$	−20.3837	+	9.81625i	−0.900839	+	0.433821i
$513$		0			0
$514$	6.84730	−	2.11211i	0.302022	−	0.0931613i
$515$	26.0409	−	8.03254i	1.14750	−	0.353956i
$516$		0			0
$517$	0.547779	−	0.263796i	0.0240913	−	0.0116017i
$518$	6.61371	+	14.6412i	0.290590	+	0.643296i
$519$		0			0
$520$	8.22313	−	14.2429i	0.360608	−	0.624591i
$521$	−21.7512	−	37.6742i	−0.952938	−	1.65054i	−0.739017	−	0.673687i	$-0.764710\pi$
$521$	−21.7512	−	37.6742i	−0.952938	−	1.65054i	−0.213921	−	0.976851i	$-0.568624\pi$
$522$		0			0
$523$	−12.9699	−	33.0468i	−0.567134	−	1.44503i	−0.870504	−	0.492162i	$-0.836207\pi$
$523$	−12.9699	−	33.0468i	−0.567134	−	1.44503i	0.303369	−	0.952873i	$-0.401888\pi$
$524$	−1.04275	+	4.56859i	−0.0455528	+	0.199580i
$525$		0			0
$526$	−0.537559	−	2.35520i	−0.0234387	−	0.102692i
$527$	23.6666	−	16.1356i	1.03093	−	0.702878i
$528$		0			0
$529$	−22.5021	−	3.39165i	−0.978354	−	0.147463i
$530$	13.9489	+	12.9427i	0.605903	+	0.562196i
$531$		0			0
$532$	2.84395	+	4.39926i	0.123301	+	0.190732i
$533$	−14.7247	+	18.4642i	−0.637797	+	0.799772i
$534$		0			0
$535$	21.2202	+	14.4677i	0.917430	+	0.625493i
$536$	−9.65231	+	24.5937i	−0.416916	+	1.06229i
$537$		0			0
$538$	24.3705			1.05069
$539$	−1.74945	+	2.71364i	−0.0753540	+	0.116885i
$540$		0			0
$541$	−43.6608	−	13.4676i	−1.87712	−	0.579016i	−0.993931	−	0.110005i	$-0.964913\pi$
$541$	−43.6608	−	13.4676i	−1.87712	−	0.579016i	−0.883193	−	0.469010i	$-0.844611\pi$
$542$	1.57258	−	4.00686i	0.0675479	−	0.172109i
$543$		0			0
$544$	16.2239	−	2.44536i	0.695595	−	0.104844i
$545$	−13.2750	+	16.6464i	−0.568640	+	0.713051i
$546$		0			0
$547$	−9.14037	−	11.4617i	−0.390814	−	0.490065i	0.547035	−	0.837110i	$-0.315757\pi$
$547$	−9.14037	−	11.4617i	−0.390814	−	0.490065i	−0.937849	+	0.347045i	$0.887185\pi$
$548$	−5.02020	−	4.65806i	−0.214452	−	0.198983i
$549$		0			0
$550$	0.567291	−	0.526369i	0.0241894	−	0.0224445i
$551$	0.544542	−	0.371263i	0.0231983	−	0.0158163i
$552$		0			0
$553$	−33.0142	−	13.9004i	−1.40390	−	0.591105i
$554$	4.96114	−	21.7362i	0.210779	−	0.923482i
$555$		0			0
$556$	0.357519	+	4.77076i	0.0151622	+	0.202325i
$557$	−8.53694	−	14.7864i	−0.361722	−	0.626521i	0.626522	−	0.779403i	$-0.284478\pi$
$557$	−8.53694	−	14.7864i	−0.361722	−	0.626521i	−0.988244	+	0.152883i	$0.951144\pi$
$558$		0			0
$559$	−9.70692	−	4.67461i	−0.410559	−	0.197715i
$560$	−9.47099	+	7.18022i	−0.400222	+	0.303420i
$561$		0			0
$562$	−2.73785	+	36.5341i	−0.115489	+	1.54110i
$563$	−27.2023	+	8.39080i	−1.14644	+	0.353630i	−0.809053	−	0.587736i	$-0.800019\pi$
$563$	−27.2023	+	8.39080i	−1.14644	+	0.353630i	−0.337387	+	0.941366i	$0.609543\pi$
$564$		0			0
$565$	−1.56093	+	20.8292i	−0.0656689	+	0.876291i
$566$	−15.0179	+	7.23223i	−0.631249	+	0.303993i
$567$		0			0
$568$	−30.7132	−	14.7907i	−1.28870	−	0.620604i
$569$	−12.7518	+	22.0868i	−0.534585	+	0.925929i	0.464598	+	0.885522i	$0.346199\pi$
$569$	−12.7518	+	22.0868i	−0.534585	+	0.925929i	−0.999183	+	0.0404072i	$0.987134\pi$
$570$		0			0
$571$	−0.786127	−	10.4901i	−0.0328984	−	0.438998i	−0.989196	−	0.146602i	$-0.953166\pi$
$571$	−0.786127	−	10.4901i	−0.0328984	−	0.438998i	0.956297	−	0.292396i	$-0.0944527\pi$
$572$	0.295206	+	0.752174i	0.0123432	+	0.0314500i
$573$		0			0
$574$	22.7979	−	12.4274i	0.951564	−	0.518709i
$575$	2.14951	+	9.41763i	0.0896409	+	0.392743i
$576$		0			0
$577$	20.6514	−	19.1617i	0.859727	−	0.797711i	−0.121089	−	0.992642i	$-0.538639\pi$
$577$	20.6514	−	19.1617i	0.859727	−	0.797711i	0.980817	+	0.194931i	$0.0624483\pi$
$578$	7.90223	+	1.19107i	0.328689	+	0.0495419i
$579$		0			0
$580$	−0.150591	−	0.188835i	−0.00625294	−	0.00784094i
$581$	30.3547	+	3.02465i	1.25933	+	0.125484i
$582$		0			0
$583$	−3.90844	+	0.589103i	−0.161871	+	0.0243981i
$584$	−13.4642	−	9.17973i	−0.557152	−	0.379860i
$585$		0			0
$586$	−27.6083	−	8.51604i	−1.14049	−	0.351794i
$587$	−20.5942			−0.850013			−0.425006	−	0.905190i	$-0.639728\pi$
$587$	−20.5942			−0.850013			−0.425006	+	0.905190i	$0.639728\pi$
$588$		0			0
$589$	−18.7611			−0.773036
$590$	−27.0121	−	8.33214i	−1.11207	−	0.343029i
$591$		0			0
$592$	−10.1498	−	6.91998i	−0.417152	−	0.284410i
$593$	26.7622	−	4.03376i	1.09899	−	0.165647i	0.425586	−	0.904918i	$-0.360068\pi$
$593$	26.7622	−	4.03376i	1.09899	−	0.165647i	0.673408	+	0.739271i	$0.264830\pi$
$594$		0			0
$595$	22.9206	−	8.35327i	0.939655	−	0.342451i
$596$	−2.48381	−	3.11460i	−0.101741	−	0.127579i
$597$		0			0
$598$	22.2190	+	3.34897i	0.908602	+	0.136950i
$599$	−13.4449	+	12.4751i	−0.549345	+	0.509717i	−0.905293	−	0.424788i	$-0.860349\pi$
$599$	−13.4449	+	12.4751i	−0.549345	+	0.509717i	0.355948	+	0.934506i	$0.384158\pi$
$600$		0			0
$601$	8.17057	+	35.7976i	0.333285	+	1.46022i	0.812728	+	0.582643i	$0.197981\pi$
$601$	8.17057	+	35.7976i	0.333285	+	1.46022i	−0.479444	+	0.877573i	$0.659162\pi$
$602$	7.84153	+	8.87806i	0.319597	+	0.361843i
$603$		0			0
$604$	0.100830	+	0.256911i	0.00410271	+	0.0104535i
$605$	1.52356	+	20.3305i	0.0619415	+	0.826551i
$606$		0			0
$607$	13.4670	−	23.3255i	0.546607	−	0.946751i	−0.451897	−	0.892070i	$-0.649252\pi$
$607$	13.4670	−	23.3255i	0.546607	−	0.946751i	0.998504	−	0.0546810i	$-0.0174142\pi$
$608$	−9.68213	−	4.66267i	−0.392662	−	0.189096i
$609$		0			0
$610$	−7.12061	+	3.42910i	−0.288305	+	0.138840i
$611$	0.278510	−	3.71645i	0.0112673	−	0.150352i
$612$		0			0
$613$	32.6293	−	10.0648i	1.31789	−	0.406514i	0.445479	−	0.895292i	$-0.353033\pi$
$613$	32.6293	−	10.0648i	1.31789	−	0.406514i	0.872408	+	0.488778i	$0.162557\pi$
$614$	2.69031	−	35.8996i	0.108572	−	1.44879i
$615$		0			0
$616$	0.0920698	−	3.75477i	0.00370960	−	0.151284i
$617$	24.9646	+	12.0223i	1.00504	+	0.484000i	0.862645	−	0.505810i	$-0.168806\pi$
$617$	24.9646	+	12.0223i	1.00504	+	0.484000i	0.142392	+	0.989810i	$0.454521\pi$
$618$		0			0
$619$	−12.6376	−	21.8890i	−0.507948	−	0.879792i	−0.999958	−	0.00920228i	$-0.997071\pi$
$619$	−12.6376	−	21.8890i	−0.507948	−	0.879792i	0.492009	−	0.870590i	$-0.336263\pi$
$620$	0.513802	+	6.85621i	0.0206348	+	0.275352i
$621$		0			0
$622$	3.00693	−	13.1742i	0.120567	−	0.528238i
$623$	15.6235	−	21.7501i	0.625942	−	0.871400i
$624$		0			0
$625$	−13.0714	+	8.91196i	−0.522858	+	0.356478i
$626$	−0.325823	+	0.302320i	−0.0130225	+	0.0120831i
$627$		0			0
$628$	1.77198	+	1.64415i	0.0707095	+	0.0656088i
$629$	15.7211	+	19.7137i	0.626843	+	0.786036i
$630$		0			0
$631$	28.2465	−	35.4200i	1.12447	−	1.41005i	0.224298	−	0.974521i	$-0.427991\pi$
$631$	28.2465	−	35.4200i	1.12447	−	1.41005i	0.900177	−	0.435525i	$-0.143437\pi$
$632$	41.2050	−	6.21066i	1.63905	−	0.247047i
$633$		0			0
$634$	14.6874	−	37.4230i	0.583312	−	1.48626i
$635$	29.8311	+	9.20168i	1.18381	+	0.365157i
$636$		0			0
$637$	9.04372	+	17.6042i	0.358325	+	0.697504i
$638$	−0.111769			−0.00442498
$639$		0			0
$640$	2.41759	−	6.15992i	0.0955636	−	0.243492i
$641$	−5.64023	−	3.84545i	−0.222776	−	0.151886i	0.446790	−	0.894639i	$-0.352567\pi$
$641$	−5.64023	−	3.84545i	−0.222776	−	0.151886i	−0.669565	+	0.742753i	$0.733520\pi$
$642$		0			0
$643$	−22.6543	+	28.4076i	−0.893399	+	1.12029i	0.0987356	+	0.995114i	$0.468520\pi$
$643$	−22.6543	+	28.4076i	−0.893399	+	1.12029i	−0.992135	+	0.125174i	$0.960051\pi$
$644$	9.46466	+	5.77831i	0.372960	+	0.227697i
$645$		0			0
$646$	−13.4268	−	12.4582i	−0.528270	−	0.490163i
$647$	46.1665	+	6.95848i	1.81499	+	0.273566i	0.966691	−	0.255946i	$-0.0823871\pi$
$647$	46.1665	+	6.95848i	1.81499	+	0.273566i	0.848302	+	0.529513i	$0.177625\pi$
$648$		0			0
$649$	4.85150	−	3.30770i	0.190438	−	0.129838i
$650$	−1.05558	−	4.62480i	−0.0414033	−	0.181400i
$651$		0			0
$652$	0.268589	−	1.17676i	0.0105187	−	0.0460857i
$653$	−2.76687	−	7.04988i	−0.108276	−	0.275883i	0.866459	−	0.499249i	$-0.166391\pi$
$653$	−2.76687	−	7.04988i	−0.108276	−	0.275883i	−0.974735	+	0.223366i	$0.928295\pi$
$654$		0			0
$655$	−7.14677	−	12.3786i	−0.279247	−	0.483670i
$656$	−9.92682	+	17.1938i	−0.387577	+	0.671304i
$657$		0			0
$658$	−1.86779	+	3.64701i	−0.0728141	+	0.142175i
$659$	7.99176	−	3.84863i	0.311315	−	0.149921i	−0.271702	−	0.962381i	$-0.587587\pi$
$659$	7.99176	−	3.84863i	0.311315	−	0.149921i	0.583017	+	0.812460i	$0.301872\pi$
$660$		0			0
$661$	11.2561	−	3.47206i	0.437813	−	0.135047i	−0.0680100	−	0.997685i	$-0.521665\pi$
$661$	11.2561	−	3.47206i	0.437813	−	0.135047i	0.505823	+	0.862637i	$0.331189\pi$
$662$	−22.7951	+	7.03136i	−0.885957	+	0.273282i
$663$		0			0
$664$	−31.9720	+	15.3969i	−1.24075	+	0.597516i
$665$	−15.4860	−	3.93633i	−0.600520	−	0.152644i
$666$		0			0
$667$	0.697572	−	1.20823i	0.0270101	−	0.0467829i
$668$	5.69527	+	9.86450i	0.220357	+	0.381669i
$669$		0			0
$670$	−6.96380	−	17.7435i	−0.269035	−	0.685490i
$671$	0.365303	−	1.60050i	0.0141024	−	0.0617865i
$672$		0			0
$673$	−7.56588	−	33.1483i	−0.291643	−	1.27777i	−0.882238	−	0.470804i	$-0.843964\pi$
$673$	−7.56588	−	33.1483i	−0.291643	−	1.27777i	0.590595	−	0.806968i	$-0.298893\pi$
$674$	16.9946	−	11.5867i	0.654607	−	0.446303i
$675$		0			0
$676$	−3.06727	−	0.462317i	−0.117972	−	0.0177814i
$677$	−28.5525	−	26.4929i	−1.09736	−	1.01820i	−0.999736	−	0.0229813i	$-0.992684\pi$
$677$	−28.5525	−	26.4929i	−1.09736	−	1.01820i	−0.0976274	−	0.995223i	$-0.531125\pi$
$678$		0			0
$679$	−2.70959	−	21.5491i	−0.103985	−	0.826979i
$680$	−17.6940	+	22.1875i	−0.678532	+	0.850853i
$681$		0			0
$682$	2.62880	+	1.79229i	0.100662	+	0.0686302i
$683$	−11.6956	+	29.8000i	−0.447521	+	1.14027i	0.512089	+	0.858932i	$0.328872\pi$
$683$	−11.6956	+	29.8000i	−0.447521	+	1.14027i	−0.959610	+	0.281333i	$0.909224\pi$
$684$		0			0
$685$	20.8889			0.798125
$686$	−1.65326	−	21.6965i	−0.0631216	−	0.828376i
$687$		0			0
$688$	−8.65484	−	2.66967i	−0.329963	−	0.101780i
$689$	−8.85175	+	22.5539i	−0.337225	+	0.859235i
$690$		0			0
$691$	−26.7009	+	4.02452i	−1.01575	+	0.153100i	−0.635757	−	0.771889i	$-0.719312\pi$
$691$	−26.7009	+	4.02452i	−1.01575	+	0.153100i	−0.379994	+	0.924989i	$0.624074\pi$
$692$	−1.40367	+	1.76015i	−0.0533595	+	0.0669108i
$693$		0			0
$694$	−4.84079	−	6.07016i	−0.183754	−	0.230420i
$695$	−10.6971	−	9.92550i	−0.405766	−	0.376496i
$696$		0			0
$697$	29.8731	−	27.7182i	1.13152	−	1.04990i
$698$	26.2560	−	17.9010i	0.993803	−	0.677563i
$699$		0			0
$700$	0.405561	−	2.30568i	0.0153288	−	0.0871465i
$701$	−6.04342	+	26.4780i	−0.228257	+	1.00006i	0.722803	+	0.691054i	$0.242853\pi$
$701$	−6.04342	+	26.4780i	−0.228257	+	1.00006i	−0.951060	+	0.309005i	$0.900004\pi$
$702$		0			0
$703$	−1.23418	−	16.4689i	−0.0465478	−	0.621138i
$704$	2.00752	+	3.47713i	0.0756614	+	0.131049i
$705$		0			0
$706$	−36.3911	−	17.5250i	−1.36960	−	0.659563i
$707$	2.24623	+	0.570961i	0.0844781	+	0.0214732i
$708$		0			0
$709$	−1.72771	+	23.0547i	−0.0648854	+	0.865836i	0.865888	+	0.500239i	$0.166754\pi$
$709$	−1.72771	+	23.0547i	−0.0648854	+	0.865836i	−0.930773	+	0.365597i	$0.880865\pi$
$710$	23.5014	−	7.24923i	0.881993	−	0.272059i
$711$		0			0
$712$	−2.32805	+	31.0657i	−0.0872474	+	1.16424i
$713$	−35.7816	+	17.2315i	−1.34003	+	0.645326i
$714$		0			0
$715$	−2.22058	−	1.06938i	−0.0830451	−	0.0399924i
$716$	5.45157	−	9.44240i	0.203735	−	0.352879i
$717$		0			0
$718$	−0.468191	−	6.24758i	−0.0174728	−	0.233158i
$719$	16.2030	+	41.2847i	0.604271	+	1.53966i	0.825480	+	0.564431i	$0.190905\pi$
$719$	16.2030	+	41.2847i	0.604271	+	1.53966i	−0.221209	+	0.975226i	$0.571000\pi$
$720$		0			0
$721$	−10.3477	−	36.7192i	−0.385370	−	1.36750i
$722$	−2.29781	−	10.0674i	−0.0855157	−	0.374669i
$723$		0			0
$724$	−8.16467	+	7.57570i	−0.303437	+	0.281549i
$725$	−0.291246	−	0.0438982i	−0.0108166	−	0.00163034i
$726$		0			0
$727$	27.9016	+	34.9875i	1.03481	+	1.29761i	0.953651	+	0.300914i	$0.0972917\pi$
$727$	27.9016	+	34.9875i	1.03481	+	1.29761i	0.0811621	+	0.996701i	$0.474137\pi$
$728$	−19.6504	−	11.9968i	−0.728292	−	0.444633i
$729$		0			0
$730$	11.6255	−	1.75226i	0.430279	−	0.0648542i
$731$	15.3605	+	10.4726i	0.568129	+	0.387344i
$732$		0			0
$733$	−36.4228	−	11.2349i	−1.34531	−	0.414972i	−0.463297	−	0.886203i	$-0.653334\pi$
$733$	−36.4228	−	11.2349i	−1.34531	−	0.414972i	−0.882010	+	0.471231i	$0.843810\pi$
$734$	−10.5544			−0.389569
$735$		0			0
$736$	−22.7486			−0.838523
$737$	3.78344	+	1.16704i	0.139365	+	0.0429883i
$738$		0			0
$739$	−18.7005	−	12.7498i	−0.687910	−	0.469009i	0.168234	−	0.985747i	$-0.446194\pi$
$739$	−18.7005	−	12.7498i	−0.687910	−	0.469009i	−0.856143	+	0.516738i	$0.827146\pi$
$740$	−5.98476	+	0.902057i	−0.220004	+	0.0331603i
$741$		0			0
$742$	18.5917	−	19.0771i	0.682524	−	0.700342i
$743$	−14.3016	−	17.9337i	−0.524676	−	0.657923i	0.446919	−	0.894575i	$-0.352521\pi$
$743$	−14.3016	−	17.9337i	−0.524676	−	0.657923i	−0.971594	+	0.236652i	$0.923950\pi$
$744$		0			0
$745$	12.0155	+	1.81104i	0.440212	+	0.0663514i
$746$	32.9180	−	30.5434i	1.20521	−	1.11827i
$747$		0			0
$748$	−0.310261	−	1.35934i	−0.0113443	−	0.0497024i
$749$	20.9754	−	29.2007i	0.766425	−	1.06697i
$750$		0			0
$751$	10.2482	+	26.1121i	0.373964	+	0.952844i	0.986699	+	0.162556i	$0.0519738\pi$
$751$	10.2482	+	26.1121i	0.373964	+	0.952844i	−0.612736	+	0.790288i	$0.709931\pi$
$752$	−0.234134	−	3.12430i	−0.00853797	−	0.113931i
$753$		0			0
$754$	−0.342563	+	0.593336i	−0.0124754	+	0.0216080i
$755$	−0.758457	−	0.365253i	−0.0276031	−	0.0132929i
$756$		0			0
$757$	9.02616	−	4.34677i	0.328061	−	0.157986i	−0.262602	−	0.964904i	$-0.584581\pi$
$757$	9.02616	−	4.34677i	0.328061	−	0.157986i	0.590663	+	0.806918i	$0.298866\pi$
$758$	−0.645415	+	8.61246i	−0.0234425	+	0.312819i
$759$		0			0
$760$	17.7618	−	5.47878i	0.644287	−	0.198736i
$761$	−3.86586	+	51.5863i	−0.140137	+	1.87000i	0.276616	+	0.960981i	$0.410787\pi$
$761$	−3.86586	+	51.5863i	−0.140137	+	1.87000i	−0.416753	+	0.909020i	$0.636832\pi$
$762$		0			0
$763$	22.8406	+	19.1493i	0.826887	+	0.693253i
$764$	4.41243	+	2.12491i	0.159636	+	0.0768767i
$765$		0			0
$766$	10.3612	+	17.9461i	0.374365	+	0.648419i
$767$	−2.68977	−	35.8925i	−0.0971220	−	1.29600i
$768$		0			0
$769$	9.96848	−	43.6748i	0.359473	−	1.57495i	−0.395038	−	0.918665i	$-0.629268\pi$
$769$	9.96848	−	43.6748i	0.359473	−	1.57495i	0.754510	−	0.656288i	$-0.227874\pi$
$770$	1.79385	+	2.03097i	0.0646459	+	0.0731911i
$771$		0			0
$772$	6.42477	−	4.38033i	0.231232	−	0.157652i
$773$	−18.3934	+	17.0666i	−0.661566	+	0.613844i	−0.937771	−	0.347255i	$-0.887114\pi$
$773$	−18.3934	+	17.0666i	−0.661566	+	0.613844i	0.276204	+	0.961099i	$0.410923\pi$
$774$		0			0
$775$	6.14615	+	5.70280i	0.220776	+	0.204850i
$776$	15.7527	+	19.7532i	0.565488	+	0.709099i
$777$		0			0
$778$	−6.52229	+	8.17869i	−0.233835	+	0.293220i
$779$	−26.3933	+	3.97815i	−0.945639	+	0.142532i
$780$		0			0
$781$	−1.86640	+	4.75550i	−0.0667849	+	0.170165i
$782$	−37.0506	−	11.4286i	−1.32492	−	0.408685i
$783$		0			0
$784$	9.72355	+	13.5008i	0.347270	+	0.482173i
$785$	−7.37315			−0.263159
$786$		0			0
$787$	−5.07070	+	12.9199i	−0.180751	+	0.460546i	−0.992318	−	0.123713i	$-0.960520\pi$
$787$	−5.07070	+	12.9199i	−0.180751	+	0.460546i	0.811567	+	0.584259i	$0.198615\pi$
$788$	−13.2791	−	9.05353i	−0.473048	−	0.322519i
$789$		0			0
$790$	−18.7444	+	23.5048i	−0.666898	+	0.836263i
$791$	29.0964	+	2.89927i	1.03455	+	0.103086i
$792$		0			0
$793$	−7.37677	−	6.84464i	−0.261957	−	0.243060i
$794$	−7.87878	−	1.18753i	−0.279607	−	0.0421440i
$795$		0			0
$796$	−5.77120	+	3.93474i	−0.204555	+	0.139463i
$797$	−5.72798	−	25.0959i	−0.202895	−	0.888943i	−0.969163	−	0.246421i	$-0.920745\pi$
$797$	−5.72798	−	25.0959i	−0.202895	−	0.888943i	0.766268	−	0.642522i	$-0.222112\pi$
$798$		0			0
$799$	−1.43101	+	6.26968i	−0.0506256	+	0.221805i
$800$	1.75457	+	4.47057i	0.0620334	+	0.158059i
$801$		0			0
$802$	−6.15961	−	10.6688i	−0.217503	−	0.376727i
$803$	−1.22105	+	2.11493i	−0.0430901	+	0.0746342i
$804$		0			0
$805$	−33.1507	+	6.71597i	−1.16841	+	0.236707i
$806$	17.5716	−	8.46204i	0.618933	−	0.298063i
$807$		0			0
$808$	−2.57633	+	0.794693i	−0.0906350	+	0.0279572i
$809$	−22.8520	+	7.04890i	−0.803432	+	0.247826i	−0.669160	−	0.743118i	$-0.733346\pi$
$809$	−22.8520	+	7.04890i	−0.803432	+	0.247826i	−0.134272	+	0.990944i	$0.542870\pi$
$810$		0			0
$811$	−2.19768	+	1.05834i	−0.0771708	+	0.0371635i	−0.472071	−	0.881560i	$-0.656493\pi$
$811$	−2.19768	+	1.05834i	−0.0771708	+	0.0371635i	0.394900	+	0.918724i	$0.370779\pi$
$812$	−0.269438	+	0.204268i	−0.00945541	+	0.00716841i
$813$		0			0
$814$	−1.40038	+	2.42553i	−0.0490834	+	0.0850149i
$815$	1.84084	+	3.18843i	0.0644819	+	0.111686i
$816$		0			0
$817$	−4.44862	−	11.3349i	−0.155638	−	0.396558i
$818$	5.82509	−	25.5214i	0.203670	−	0.892335i
$819$		0			0
$820$	2.17664	+	9.53647i	0.0760115	+	0.333028i
$821$	3.93048	−	2.67976i	0.137175	−	0.0935241i	−0.492788	−	0.870149i	$-0.664022\pi$
$821$	3.93048	−	2.67976i	0.137175	−	0.0935241i	0.629963	+	0.776625i	$0.283070\pi$
$822$		0			0
$823$	21.3531	+	3.21846i	0.744323	+	0.112189i	0.510245	−	0.860029i	$-0.329555\pi$
$823$	21.3531	+	3.21846i	0.744323	+	0.112189i	0.234078	+	0.972218i	$0.424793\pi$
$824$	32.5320	+	30.1853i	1.13331	+	1.05156i
$825$		0			0
$826$	−12.5876	+	37.5170i	−0.437979	+	1.30538i
$827$	−33.4720	+	41.9726i	−1.16394	+	1.45953i	−0.301425	+	0.953490i	$0.597462\pi$
$827$	−33.4720	+	41.9726i	−1.16394	+	1.45953i	−0.862511	+	0.506039i	$0.831109\pi$
$828$		0			0
$829$	35.7913	+	24.4021i	1.24308	+	0.847519i	0.992698	−	0.120627i	$-0.0384905\pi$
$829$	35.7913	+	24.4021i	1.24308	+	0.847519i	0.250385	+	0.968146i	$0.419443\pi$
$830$	9.35349	−	23.8323i	0.324664	−	0.827231i
$831$		0			0
$832$	24.6116			0.853254
$833$	−10.9037	−	32.3636i	−0.377790	−	1.12133i
$834$		0			0
$835$	−33.2000	−	10.2408i	−1.14893	−	0.354399i
$836$	−0.333642	+	0.850107i	−0.0115393	+	0.0294016i
$837$		0			0
$838$	−26.2344	+	3.95421i	−0.906254	+	0.136596i
$839$	6.81690	−	8.54812i	0.235345	−	0.295114i	−0.650108	−	0.759842i	$-0.725276\pi$
$839$	6.81690	−	8.54812i	0.235345	−	0.295114i	0.885454	+	0.464728i	$0.153848\pi$
$840$		0			0
$841$	−18.0547	−	22.6399i	−0.622575	−	0.780685i
$842$	−2.32516	−	2.15743i	−0.0801304	−	0.0743501i
$843$		0			0
$844$	0.527452	−	0.489404i	0.0181557	−	0.0168460i
$845$	7.81746	−	5.32985i	0.268929	−	0.183353i
$846$		0			0
$847$	28.5043	−	1.43452i	0.979420	−	0.0492907i
$848$	−4.53237	+	19.8576i	−0.155642	+	0.681913i
$849$		0			0
$850$	0.611709	+	8.16269i	0.0209814	+	0.279978i
$851$	−17.4801	−	30.2765i	−0.599211	−	1.03786i
$852$		0			0
$853$	7.50527	+	3.61435i	0.256976	+	0.123753i	0.557937	−	0.829883i	$-0.311593\pi$
$853$	7.50527	+	3.61435i	0.256976	+	0.123753i	−0.300961	+	0.953636i	$0.597307\pi$
$854$	4.55460	+	10.0828i	0.155855	+	0.345026i
$855$		0			0
$856$	−3.12554	+	41.7074i	−0.106829	+	1.42553i
$857$	3.94038	−	1.21545i	0.134601	−	0.0415189i	−0.226723	−	0.973959i	$-0.572801\pi$
$857$	3.94038	−	1.21545i	0.134601	−	0.0415189i	0.361324	+	0.932440i	$0.382325\pi$
$858$		0			0
$859$	0.852965	−	11.3820i	0.0291028	−	0.388350i	−0.963565	−	0.267475i	$-0.913811\pi$
$859$	0.852965	−	11.3820i	0.0291028	−	0.388350i	0.992668	−	0.120875i	$-0.0385701\pi$
$860$	−4.02050	+	1.93617i	−0.137098	+	0.0660228i
$861$		0			0
$862$	15.4400	+	7.43552i	0.525889	+	0.253255i
$863$	4.18010	−	7.24014i	0.142292	−	0.246457i	−0.786067	−	0.618141i	$-0.787886\pi$
$863$	4.18010	−	7.24014i	0.142292	−	0.246457i	0.928359	+	0.371684i	$0.121219\pi$
$864$		0			0
$865$	−0.513170	−	6.84778i	−0.0174483	−	0.232831i
$866$	−11.5662	−	29.4703i	−0.393037	−	1.00144i
$867$		0			0
$868$	9.61274	−	0.483775i	0.326278	−	0.0164204i
$869$	−1.38960	−	6.08823i	−0.0471389	−	0.206529i
$870$		0			0
$871$	17.7913	−	16.5079i	0.602834	−	0.559348i
$872$	−34.2857	−	5.16774i	−1.16106	−	0.175002i
$873$		0			0
$874$	15.8339	+	19.8551i	0.535589	+	0.671607i
$875$	17.4501	+	26.9933i	0.589922	+	0.912541i
$876$		0			0
$877$	−14.2871	+	2.15344i	−0.482442	+	0.0727164i	−0.385761	−	0.922599i	$-0.626061\pi$
$877$	−14.2871	+	2.15344i	−0.482442	+	0.0727164i	−0.0966814	+	0.995315i	$0.530823\pi$
$878$	23.7080	+	16.1639i	0.800107	+	0.545504i
$879$		0			0
$880$	−1.97991	−	0.610720i	−0.0667426	−	0.0205874i
$881$	17.9972			0.606340			0.303170	−	0.952936i	$-0.401955\pi$
$881$	17.9972			0.606340			0.303170	+	0.952936i	$0.401955\pi$
$882$		0			0
$883$	42.6816			1.43635			0.718175	−	0.695863i	$-0.244978\pi$
$883$	42.6816			1.43635			0.718175	+	0.695863i	$0.244978\pi$
$884$	−8.16712	−	2.51922i	−0.274690	−	0.0847306i
$885$		0			0
$886$	20.9882	+	14.3095i	0.705114	+	0.480738i
$887$	−8.56875	+	1.29153i	−0.287710	+	0.0433654i	−0.291312	−	0.956628i	$-0.594092\pi$
$887$	−8.56875	+	1.29153i	−0.287710	+	0.0433654i	0.00360141	+	0.999994i	$0.498854\pi$
$888$		0			0
$889$	13.9012	−	41.4322i	0.466232	−	1.38959i
$890$	−14.0133	−	17.5722i	−0.469728	−	0.589020i
$891$		0			0
$892$	−6.51293	−	0.981667i	−0.218069	−	0.0328686i
$893$	3.08770	−	2.86496i	0.103326	−	0.0958724i
$894$		0			0
$895$	7.40035	+	32.4231i	0.247367	+	1.08378i
$896$	−8.53770	−	3.59475i	−0.285225	−	0.120092i
$897$		0			0
$898$	4.97395	+	12.6734i	0.165983	+	0.422918i
$899$	−0.0904928	−	1.20754i	−0.00301810	−	0.0402738i
$900$		0			0
$901$	20.9040	−	36.2068i	0.696413	−	1.20622i
$902$	4.07828	+	1.96400i	0.135792	+	0.0653939i
$903$		0			0
$904$	−30.6467	+	14.7587i	−1.01929	+	0.490866i
$905$	2.53880	−	33.8780i	0.0843927	−	1.12614i
$906$		0			0
$907$	−54.4868	+	16.8070i	−1.80920	+	0.558066i	−0.999583	−	0.0288861i	$-0.990804\pi$
$907$	−54.4868	+	16.8070i	−1.80920	+	0.558066i	−0.809622	+	0.586952i	$0.800328\pi$
$908$	−0.0655813	+	0.875121i	−0.00217639	+	0.0290419i
$909$		0			0
$910$	16.2796	−	3.29807i	0.539664	−	0.109330i
$911$	−1.29283	−	0.622596i	−0.0428335	−	0.0206275i	0.412344	−	0.911028i	$-0.364710\pi$
$911$	−1.29283	−	0.622596i	−0.0428335	−	0.0206275i	−0.455178	+	0.890401i	$0.650424\pi$
$912$		0			0
$913$	2.65901	+	4.60554i	0.0880004	+	0.152421i
$914$	−3.70024	−	49.3762i	−0.122393	−	1.63322i
$915$		0			0
$916$	−2.34841	+	10.2891i	−0.0775937	+	0.339960i
$917$	−17.5688	+	9.57695i	−0.580172	+	0.316259i
$918$		0			0
$919$	42.1941	−	28.7674i	1.39185	−	0.948950i	0.392277	−	0.919847i	$-0.371687\pi$
$919$	42.1941	−	28.7674i	1.39185	−	0.948950i	0.999576	−	0.0291024i	$-0.00926488\pi$
$920$	28.8437	−	26.7630i	0.950947	−	0.882350i
$921$		0			0
$922$	14.7115	+	13.6503i	0.484497	+	0.449548i
$923$	19.5247	+	24.4832i	0.642663	+	0.805874i
$924$		0			0
$925$	−4.60174	+	5.77040i	−0.151304	+	0.189730i
$926$	−10.4173	+	1.57016i	−0.342334	+	0.0515985i
$927$		0			0
$928$	0.253408	−	0.645673i	0.00831853	−	0.0211953i
$929$	34.4208	+	10.6174i	1.12931	+	0.348346i	0.802446	−	0.596725i	$-0.203532\pi$
$929$	34.4208	+	10.6174i	1.12931	+	0.348346i	0.326864	+	0.945071i	$0.394008\pi$
$930$		0			0
$931$	−6.04023	+	21.5372i	−0.197960	+	0.705853i
$932$	3.84114			0.125821
$933$		0			0
$934$	−10.2265	+	26.0568i	−0.334622	+	0.852603i
$935$	3.51392	+	2.39575i	0.114917	+	0.0783493i
$936$		0			0
$937$	−1.64758	+	2.06599i	−0.0538239	+	0.0674931i	−0.808015	−	0.589162i	$-0.799458\pi$
$937$	−1.64758	+	2.06599i	−0.0538239	+	0.0674931i	0.754191	+	0.656655i	$0.228029\pi$
$938$	−25.0706	+	9.13679i	−0.818583	+	0.298327i
$939$		0			0
$940$	−1.13156	−	1.04993i	−0.0369074	−	0.0342451i
$941$	−4.17378	−	0.629096i	−0.136061	−	0.0205079i	0.0806585	−	0.996742i	$-0.474298\pi$
$941$	−4.17378	−	0.629096i	−0.136061	−	0.0205079i	−0.216720	+	0.976234i	$0.569536\pi$
$942$		0			0
$943$	−46.6843	+	31.8288i	−1.52025	+	1.03649i
$944$	−6.73309	−	29.4996i	−0.219143	−	0.960130i
$945$		0			0
$946$	−0.459508	+	2.01324i	−0.0149399	+	0.0654560i
$947$	−7.39838	−	18.8508i	−0.240415	−	0.612568i	0.758835	−	0.651283i	$-0.225769\pi$
$947$	−7.39838	−	18.8508i	−0.240415	−	0.612568i	−0.999250	+	0.0387149i	$0.987674\pi$
$948$		0			0
$949$	7.48487	+	12.9642i	0.242969	+	0.420835i
$950$	2.68069	−	4.64309i	0.0869730	−	0.150642i
$951$		0			0
$952$	30.4437	+	25.5237i	0.986687	+	0.827227i
$953$	12.2707	−	5.90927i	0.397488	−	0.191420i	−0.224452	−	0.974485i	$-0.572059\pi$
$953$	12.2707	−	5.90927i	0.397488	−	0.191420i	0.621940	+	0.783065i	$0.286345\pi$
$954$		0			0
$955$	−14.2745	+	4.40311i	−0.461913	+	0.142481i
$956$	10.1627	−	3.13479i	0.328687	−	0.101386i
$957$		0			0
$958$	7.55738	−	3.63944i	0.244168	−	0.117585i
$959$	0.716829	−	29.2336i	0.0231476	−	0.944002i
$960$		0			0
$961$	−1.73533	+	3.00568i	−0.0559784	+	0.0969574i
$962$	8.58412	+	14.8681i	0.276763	+	0.479368i
$963$		0			0
$964$	1.86528	+	4.75265i	0.0600765	+	0.153072i
$965$	−5.27779	+	23.1235i	−0.169898	+	0.744373i
$966$		0			0
$967$	1.80529	+	7.90950i	0.0580543	+	0.254352i	0.995625	−	0.0934434i	$-0.0297874\pi$
$967$	1.80529	+	7.90950i	0.0580543	+	0.254352i	−0.937570	+	0.347796i	$0.886930\pi$
$968$	−27.4318	+	18.7027i	−0.881691	+	0.601127i
$969$		0			0
$970$	−18.0244	−	2.71675i	−0.578729	−	0.0872294i
$971$	−2.85981	−	2.65352i	−0.0917757	−	0.0851554i	0.632951	−	0.774192i	$-0.281843\pi$
$971$	−2.85981	−	2.65352i	−0.0917757	−	0.0851554i	−0.724727	+	0.689037i	$0.758034\pi$
$972$		0			0
$973$	−14.2576	+	14.6298i	−0.457078	+	0.469010i
$974$	−5.22418	+	6.55091i	−0.167393	+	0.209905i
$975$		0			0
$976$	−6.98974	−	4.76552i	−0.223736	−	0.152541i
$977$	0.311633	−	0.794028i	0.00997003	−	0.0254032i	−0.925802	−	0.378009i	$-0.876609\pi$
$977$	0.311633	−	0.794028i	0.00997003	−	0.0254032i	0.935772	+	0.352605i	$0.114704\pi$
$978$		0			0
$979$	4.66860			0.149209
$980$	8.03617	+	1.61756i	0.256706	+	0.0516712i
$981$		0			0
$982$	−9.80999	−	3.02598i	−0.313049	−	0.0965630i
$983$	−5.88419	+	14.9927i	−0.187676	+	0.478192i	−0.993482	−	0.113988i	$-0.963637\pi$
$983$	−5.88419	+	14.9927i	−0.187676	+	0.478192i	0.805806	+	0.592180i	$0.201733\pi$
$984$		0			0
$985$	48.4746	−	7.30638i	1.54453	−	0.232800i
$986$	0.737103	−	0.924298i	0.0234741	−	0.0294356i
$987$		0			0
$988$	3.49029	+	4.37668i	0.111041	+	0.139241i
$989$	−18.8954	−	17.5323i	−0.600837	−	0.557495i
$990$		0			0
$991$	−8.78612	+	8.15233i	−0.279100	+	0.258967i	−0.807284	−	0.590163i	$-0.799064\pi$
$991$	−8.78612	+	8.15233i	−0.279100	+	0.258967i	0.528184	+	0.849130i	$0.322873\pi$
$992$	−16.3139	+	11.1227i	−0.517968	+	0.353145i
$993$		0			0
$994$	−9.33865	−	33.1385i	−0.296204	−	1.05109i
$995$	4.74091	−	20.7713i	0.150297	−	0.658494i
$996$		0			0
$997$	0.355057	+	4.73791i	0.0112448	+	0.150051i	1.00000		0.000507191i	$0.000161444\pi$
$997$	0.355057	+	4.73791i	0.0112448	+	0.150051i	−0.988755	+	0.149544i	$0.952220\pi$
$998$	11.3620	+	19.6795i	0.359656	+	0.622943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.100.3	✓	72
3.2	odd	2	inner	441.2.bb.f.100.4	yes	72
49.25	even	21	inner	441.2.bb.f.172.3	yes	72
147.74	odd	42	inner	441.2.bb.f.172.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.100.3	✓	72	1.1	even	1	trivial
441.2.bb.f.100.4	yes	72	3.2	odd	2	inner
441.2.bb.f.172.3	yes	72	49.25	even	21	inner
441.2.bb.f.172.4	yes	72	147.74	odd	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12270 - 0.346307i) q^{2} +(-0.511951 - 0.349042i) q^{4} +(1.86885 - 0.281684i) q^{5} +(-0.330078 - 2.62508i) q^{7} +(1.91896 + 2.40631i) q^{8} +O(q^{10})\)	\(q+(-1.12270 - 0.346307i) q^{2} +(-0.511951 - 0.349042i) q^{4} +(1.86885 - 0.281684i) q^{5} +(-0.330078 - 2.62508i) q^{7} +(1.91896 + 2.40631i) q^{8} +(-2.19571 - 0.330950i) q^{10} +(0.338113 - 0.313723i) q^{11} +(-0.629141 - 2.75645i) q^{13} +(-0.538505 + 3.06149i) q^{14} +(-0.868358 - 2.21254i) q^{16} +(0.364587 + 4.86507i) q^{17} +(1.59773 - 2.76734i) q^{19} +(-1.05508 - 0.508099i) q^{20} +(-0.488245 + 0.235126i) q^{22} +(0.505500 - 6.74543i) q^{23} +(-1.36461 + 0.420925i) q^{25} +(-0.248240 + 3.31254i) q^{26} +(-0.747280 + 1.45912i) q^{28} +(0.185825 + 0.0894884i) q^{29} +(-2.93559 - 5.08458i) q^{31} +(-0.251318 - 3.35361i) q^{32} +(1.27549 - 5.58828i) q^{34} +(-1.35631 - 4.81291i) q^{35} +(4.27026 - 2.91142i) q^{37} +(-2.75212 + 2.55359i) q^{38} +(4.26408 + 3.95648i) q^{40} +(-5.20798 - 6.53060i) q^{41} +(2.37588 - 2.97926i) q^{43} +(-0.282600 + 0.0425951i) q^{44} +(-2.90351 + 7.39803i) q^{46} +(1.25960 + 0.388534i) q^{47} +(-6.78210 + 1.73296i) q^{49} +1.67781 q^{50} +(-0.640027 + 1.63076i) q^{52} +(-7.08043 - 4.82735i) q^{53} +(0.543513 - 0.681543i) q^{55} +(5.68334 - 5.83171i) q^{56} +(-0.177635 - 0.164821i) q^{58} +(12.5882 + 1.89737i) q^{59} +(2.94076 - 2.00498i) q^{61} +(1.53495 + 6.72508i) q^{62} +(-1.93702 + 8.48663i) q^{64} +(-1.95222 - 4.97417i) q^{65} +(4.29205 + 7.43406i) q^{67} +(1.51147 - 2.61793i) q^{68} +(-0.144014 + 5.87315i) q^{70} +(-9.97902 + 4.80564i) q^{71} +(-5.05942 + 1.56063i) q^{73} +(-5.80247 + 1.78982i) q^{74} +(-1.78388 + 0.859070i) q^{76} +(-0.935153 - 0.784022i) q^{77} +(6.76956 - 11.7252i) q^{79} +(-2.24607 - 3.89031i) q^{80} +(3.58540 + 9.13546i) q^{82} +(-2.56563 + 11.2407i) q^{83} +(2.05177 + 8.98940i) q^{85} +(-3.69914 + 2.52203i) q^{86} +(1.40374 + 0.211580i) q^{88} +(7.41983 + 6.88460i) q^{89} +(-7.02823 + 2.56139i) q^{91} +(-2.61323 + 3.27689i) q^{92} +(-1.27960 - 0.872414i) q^{94} +(2.20640 - 5.62181i) q^{95} +8.20894 q^{97} +(8.21440 + 0.403088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 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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