LMFDB - Embedded newform 891.2.u.c.431.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			431.4
Character	$\chi$	$=$	891.431
Dual form			891.2.u.c.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57299 + 1.74698i) q^{2} +(-0.368594 + 3.50694i) q^{4} +(-1.67069 - 1.50430i) q^{5} +(-1.64772 - 3.70084i) q^{7} +(-2.90269 + 2.10893i) q^{8} +O(q^{10})$	\(q+(1.57299 + 1.74698i) q^{2} +(-0.368594 + 3.50694i) q^{4} +(-1.67069 - 1.50430i) q^{5} +(-1.64772 - 3.70084i) q^{7} +(-2.90269 + 2.10893i) q^{8} -5.28492i q^{10} +(1.64091 - 2.88226i) q^{11} +(-0.967343 - 4.55099i) q^{13} +(3.87346 - 8.69993i) q^{14} +(-1.35177 - 0.287327i) q^{16} +(-0.0235753 - 0.0725574i) q^{17} +(1.40822 + 1.93825i) q^{19} +(5.89128 - 5.30454i) q^{20} +(7.61640 - 1.66711i) q^{22} +(-2.79482 + 1.61359i) q^{23} +(0.00565702 + 0.0538229i) q^{25} +(6.42889 - 8.84860i) q^{26} +(13.5860 - 4.41435i) q^{28} +(-1.68021 + 0.748078i) q^{29} +(-1.63816 + 0.348201i) q^{31} +(1.96356 + 3.40098i) q^{32} +(0.0896728 - 0.155318i) q^{34} +(-2.81433 + 8.66162i) q^{35} +(-5.87906 - 4.27138i) q^{37} +(-1.17097 + 5.50899i) q^{38} +(8.02195 + 0.843141i) q^{40} +(7.71224 + 3.43371i) q^{41} +(-3.70733 - 2.14043i) q^{43} +(9.50306 + 6.81697i) q^{44} +(-7.21513 - 2.34434i) q^{46} +(6.18182 - 0.649735i) q^{47} +(-6.29732 + 6.99389i) q^{49} +(-0.0851293 + 0.0945457i) q^{50} +(16.3166 - 1.71494i) q^{52} +(1.16884 + 0.379779i) q^{53} +(-7.07723 + 2.34694i) q^{55} +(12.5876 + 7.26746i) q^{56} +(-3.94984 - 1.75858i) q^{58} +(0.577111 + 0.0606568i) q^{59} +(0.786366 - 3.69956i) q^{61} +(-3.18511 - 2.31412i) q^{62} +(-3.70690 + 11.4087i) q^{64} +(-5.22991 + 9.05847i) q^{65} +(-6.49920 - 11.2569i) q^{67} +(0.263144 - 0.0559330i) q^{68} +(-19.5586 + 8.70807i) q^{70} +(1.06563 - 0.346245i) q^{71} +(7.82153 - 10.7654i) q^{73} +(-1.78566 - 16.9895i) q^{74} +(-7.31639 + 4.22412i) q^{76} +(-13.3705 - 1.32361i) q^{77} +(-0.490373 + 0.441533i) q^{79} +(1.82616 + 2.51349i) q^{80} +(6.13265 + 18.8744i) q^{82} +(9.98801 + 2.12302i) q^{83} +(-0.0697608 + 0.156685i) q^{85} +(-2.09231 - 9.84353i) q^{86} +(1.31540 + 11.8269i) q^{88} +6.58983i q^{89} +(-15.2486 + 11.0787i) q^{91} +(-4.62860 - 10.3960i) q^{92} +(10.8590 + 9.77751i) q^{94} +(0.563001 - 5.35660i) q^{95} +(11.0036 + 12.2208i) q^{97} -22.1238 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4}+O(q^{10}) $ 32 * q + 4 * q^4	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.57299	+	1.74698i	1.11227	+	1.23530i	0.969380	+	0.245566i	$0.0789738\pi$
$2$	1.57299	+	1.74698i	1.11227	+	1.23530i	0.142893	+	0.989738i	$0.454359\pi$
$3$		0			0
$3$		0			0
$4$	−0.368594	+	3.50694i	−0.184297	+	1.75347i
$5$	−1.67069	−	1.50430i	−0.747156	−	0.672742i	0.204860	−	0.978791i	$-0.434326\pi$
$5$	−1.67069	−	1.50430i	−0.747156	−	0.672742i	−0.952016	+	0.306049i	$0.900993\pi$
$6$		0			0
$7$	−1.64772	−	3.70084i	−0.622780	−	1.39879i	−0.899110	−	0.437723i	$-0.855785\pi$
$7$	−1.64772	−	3.70084i	−0.622780	−	1.39879i	0.276330	−	0.961063i	$-0.410882\pi$
$8$	−2.90269	+	2.10893i	−1.02626	+	0.745618i
$9$		0			0
$10$		−	5.28492i		−	1.67124i
$11$	1.64091	−	2.88226i	0.494754	−	0.869033i
$11$	1.64091	−	2.88226i	0.494754	−	0.869033i
$12$		0			0
$13$	−0.967343	−	4.55099i	−0.268293	−	1.26222i	−0.881458	−	0.472263i	$-0.843437\pi$
$13$	−0.967343	−	4.55099i	−0.268293	−	1.26222i	0.613165	−	0.789955i	$-0.289896\pi$
$14$	3.87346	−	8.69993i	1.03523	−	2.32515i
$15$		0			0
$16$	−1.35177	−	0.287327i	−0.337942	−	0.0718317i
$17$	−0.0235753	−	0.0725574i	−0.00571786	−	0.0175978i	0.948157	−	0.317803i	$-0.102945\pi$
$17$	−0.0235753	−	0.0725574i	−0.00571786	−	0.0175978i	−0.953875	+	0.300205i	$0.902945\pi$
$18$		0			0
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	0.939401	−	0.342821i	$-0.111382\pi$
$19$	1.40822	+	1.93825i	0.323068	+	0.444665i	−0.616333	+	0.787486i	$0.711382\pi$
$20$	5.89128	−	5.30454i	1.31733	−	1.18613i
$21$		0			0
$22$	7.61640	−	1.66711i	1.62382	−	0.355430i
$23$	−2.79482	+	1.61359i	−0.582759	+	0.336456i	−0.762229	−	0.647307i	$-0.775895\pi$
$23$	−2.79482	+	1.61359i	−0.582759	+	0.336456i	0.179470	+	0.983763i	$0.442562\pi$
$24$		0			0
$25$	0.00565702	+	0.0538229i	0.00113140	+	0.0107646i
$26$	6.42889	−	8.84860i	1.26081	−	1.73535i
$27$		0			0
$28$	13.5860	−	4.41435i	2.56750	−	0.834233i
$29$	−1.68021	+	0.748078i	−0.312007	+	0.138915i	−0.556766	−	0.830669i	$-0.687958\pi$
$29$	−1.68021	+	0.748078i	−0.312007	+	0.138915i	0.244759	+	0.969584i	$0.421291\pi$
$30$		0			0
$31$	−1.63816	+	0.348201i	−0.294222	+	0.0625388i	−0.352658	−	0.935752i	$-0.614722\pi$
$31$	−1.63816	+	0.348201i	−0.294222	+	0.0625388i	0.0584358	+	0.998291i	$0.481389\pi$
$32$	1.96356	+	3.40098i	0.347111	+	0.601214i
$33$		0			0
$34$	0.0896728	−	0.155318i	0.0153788	−	0.0266368i
$35$	−2.81433	+	8.66162i	−0.475709	+	1.46408i
$36$		0			0
$37$	−5.87906	−	4.27138i	−0.966511	−	0.702211i	−0.0118571	−	0.999930i	$-0.503774\pi$
$37$	−5.87906	−	4.27138i	−0.966511	−	0.702211i	−0.954654	+	0.297718i	$0.903774\pi$
$38$	−1.17097	+	5.50899i	−0.189957	+	0.893676i
$39$		0			0
$40$	8.02195	+	0.843141i	1.26838	+	0.133312i
$41$	7.71224	+	3.43371i	1.20445	+	0.536256i	0.908072	−	0.418815i	$-0.137554\pi$
$41$	7.71224	+	3.43371i	1.20445	+	0.536256i	0.296378	+	0.955071i	$0.404221\pi$
$42$		0			0
$43$	−3.70733	−	2.14043i	−0.565363	−	0.326413i	0.189932	−	0.981797i	$-0.439173\pi$
$43$	−3.70733	−	2.14043i	−0.565363	−	0.326413i	−0.755295	+	0.655385i	$0.772507\pi$
$44$	9.50306	+	6.81697i	1.43264	+	1.02770i
$45$		0			0
$46$	−7.21513	−	2.34434i	−1.06381	−	0.345654i
$47$	6.18182	−	0.649735i	0.901711	−	0.0947736i	0.357685	−	0.933842i	$-0.383566\pi$
$47$	6.18182	−	0.649735i	0.901711	−	0.0947736i	0.544026	+	0.839069i	$0.316899\pi$
$48$		0			0
$49$	−6.29732	+	6.99389i	−0.899618	+	0.999127i
$50$	−0.0851293	+	0.0945457i	−0.0120391	+	0.0133708i
$51$		0			0
$52$	16.3166	−	1.71494i	2.26271	−	0.237820i
$53$	1.16884	+	0.379779i	0.160552	+	0.0521666i	0.388190	−	0.921579i	$-0.373100\pi$
$53$	1.16884	+	0.379779i	0.160552	+	0.0521666i	−0.227638	+	0.973746i	$0.573100\pi$
$54$		0			0
$55$	−7.07723	+	2.34694i	−0.954294	+	0.316461i
$56$	12.5876	+	7.26746i	1.68209	+	0.971156i
$57$		0			0
$58$	−3.94984	−	1.75858i	−0.518639	−	0.230913i
$59$	0.577111	+	0.0606568i	0.0751335	+	0.00789685i	0.142021	−	0.989864i	$-0.454640\pi$
$59$	0.577111	+	0.0606568i	0.0751335	+	0.00789685i	−0.0668871	+	0.997761i	$0.521307\pi$
$60$		0			0
$61$	0.786366	−	3.69956i	0.100684	−	0.473680i	−0.898699	−	0.438565i	$-0.855487\pi$
$61$	0.786366	−	3.69956i	0.100684	−	0.473680i	0.999383	−	0.0351153i	$-0.0111798\pi$
$62$	−3.18511	−	2.31412i	−0.404510	−	0.293893i
$63$		0			0
$64$	−3.70690	+	11.4087i	−0.463363	+	1.42608i
$65$	−5.22991	+	9.05847i	−0.648691	+	1.12357i
$66$		0			0
$67$	−6.49920	−	11.2569i	−0.794003	−	1.37525i	−0.923470	−	0.383670i	$-0.874660\pi$
$67$	−6.49920	−	11.2569i	−0.794003	−	1.37525i	0.129467	−	0.991584i	$-0.458673\pi$
$68$	0.263144	−	0.0559330i	0.0319109	−	0.00678287i
$69$		0			0
$70$	−19.5586	+	8.70807i	−2.33770	+	1.04081i
$71$	1.06563	−	0.346245i	0.126467	−	0.0410917i	−0.245100	−	0.969498i	$-0.578821\pi$
$71$	1.06563	−	0.346245i	0.126467	−	0.0410917i	0.371567	+	0.928406i	$0.378821\pi$
$72$		0			0
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	−0.0498335	−	0.998758i	$-0.515869\pi$
$73$	7.82153	−	10.7654i	0.915441	−	1.26000i	0.965274	−	0.261239i	$-0.0841309\pi$
$74$	−1.78566	−	16.9895i	−0.207579	−	1.97499i
$75$		0			0
$76$	−7.31639	+	4.22412i	−0.839247	+	0.484540i
$77$	−13.3705	−	1.32361i	−1.52371	−	0.150839i
$78$		0			0
$79$	−0.490373	+	0.441533i	−0.0551712	+	0.0496764i	−0.696255	−	0.717794i	$-0.745152\pi$
$79$	−0.490373	+	0.441533i	−0.0551712	+	0.0496764i	0.641084	+	0.767471i	$0.278485\pi$
$80$	1.82616	+	2.51349i	0.204171	+	0.281017i
$81$		0			0
$82$	6.13265	+	18.8744i	0.677238	+	2.08432i
$83$	9.98801	+	2.12302i	1.09633	+	0.233031i	0.720359	−	0.693601i	$-0.243977\pi$
$83$	9.98801	+	2.12302i	1.09633	+	0.233031i	0.375967	+	0.926633i	$0.377310\pi$
$84$		0			0
$85$	−0.0697608	+	0.156685i	−0.00756662	+	0.0169949i
$86$	−2.09231	−	9.84353i	−0.225619	−	1.06146i
$87$		0			0
$88$	1.31540	+	11.8269i	0.140222	+	1.26075i
$89$			6.58983i			0.698520i	0.937026	+	0.349260i	$0.113567\pi$
$89$			6.58983i			0.698520i	−0.937026	+	0.349260i	$0.886433\pi$
$90$		0			0
$91$	−15.2486	+	11.0787i	−1.59849	+	1.16137i
$92$	−4.62860	−	10.3960i	−0.482565	−	1.08386i
$93$		0			0
$94$	10.8590	+	9.77751i	1.12002	+	1.00847i
$95$	0.563001	−	5.35660i	0.0577627	−	0.549576i
$96$		0			0
$97$	11.0036	+	12.2208i	1.11725	+	1.24083i	0.967708	+	0.252074i	$0.0811127\pi$
$97$	11.0036	+	12.2208i	1.11725	+	1.24083i	0.149540	+	0.988756i	$0.452221\pi$
$98$	−22.1238			−2.23485
$99$		0			0
$100$	−0.190839			−0.0190839
$101$	1.15217	+	1.27962i	0.114646	+	0.127327i	0.797736	−	0.603007i	$-0.206031\pi$
$101$	1.15217	+	1.27962i	0.114646	+	0.127327i	−0.683090	+	0.730334i	$0.739364\pi$
$102$		0			0
$103$	0.337717	−	3.21316i	0.0332762	−	0.316602i	−0.965204	−	0.261497i	$-0.915784\pi$
$103$	0.337717	−	3.21316i	0.0332762	−	0.316602i	0.998481	−	0.0551054i	$-0.0175495\pi$
$104$	12.4056	+	11.1701i	1.21647	+	1.09531i
$105$		0			0
$106$	1.17511	+	2.63933i	0.114136	+	0.256355i
$107$	11.9884	−	8.71006i	1.15896	−	0.842034i	0.169314	−	0.985562i	$-0.445845\pi$
$107$	11.9884	−	8.71006i	1.15896	−	0.842034i	0.989646	+	0.143529i	$0.0458449\pi$
$108$		0			0
$109$			14.9258i			1.42963i	0.699313	+	0.714815i	$0.253489\pi$
$109$			14.9258i			1.42963i	−0.699313	+	0.714815i	$0.746511\pi$
$110$	−15.2325	−	8.67210i	−1.45236	−	0.826852i
$111$		0			0
$112$	1.16398	+	5.47611i	0.109986	+	0.517444i
$113$	4.57438	−	10.2742i	0.430321	−	0.966518i	−0.560098	−	0.828426i	$-0.689237\pi$
$113$	4.57438	−	10.2742i	0.430321	−	0.966518i	0.990420	−	0.138091i	$-0.0440967\pi$
$114$		0			0
$115$	7.09659	+	1.50843i	0.661760	+	0.140662i
$116$	−2.00415	−	6.16813i	−0.186080	−	0.572697i
$117$		0			0
$118$	0.801825	+	1.10362i	0.0738139	+	0.101596i
$119$	−0.229678	+	0.206803i	−0.0210545	+	0.0189576i
$120$		0			0
$121$	−5.61480	−	9.45907i	−0.510436	−	0.859916i
$122$	7.70002	−	4.44561i	0.697127	−	0.402487i
$123$		0			0
$124$	−0.617305	−	5.87327i	−0.0554356	−	0.527435i
$125$	−6.53559	+	8.99547i	−0.584561	+	0.804580i
$126$		0			0
$127$	−5.76481	+	1.87310i	−0.511544	+	0.166211i	−0.553404	−	0.832913i	$-0.686672\pi$
$127$	−5.76481	+	1.87310i	−0.511544	+	0.166211i	0.0418604	+	0.999123i	$0.486672\pi$
$128$	−18.5865	+	8.27524i	−1.64283	+	0.731435i
$129$		0			0
$130$	−24.0516	+	5.11233i	−2.10947	+	0.448381i
$131$	3.57541	+	6.19280i	0.312385	+	0.541067i	0.978878	−	0.204444i	$-0.0655387\pi$
$131$	3.57541	+	6.19280i	0.312385	+	0.541067i	−0.666493	+	0.745511i	$0.732205\pi$
$132$		0			0
$133$	4.85280	−	8.40530i	0.420791	−	0.728832i
$134$	9.44251	−	29.0611i	0.815709	−	2.51049i
$135$		0			0
$136$	0.221450	+	0.160893i	0.0189892	+	0.0137964i
$137$	−2.20853	+	10.3903i	−0.188688	+	0.887706i	0.777302	+	0.629127i	$0.216587\pi$
$137$	−2.20853	+	10.3903i	−0.188688	+	0.887706i	−0.965990	+	0.258579i	$0.916746\pi$
$138$		0			0
$139$	0.0527856	+	0.00554799i	0.00447722	+	0.000470575i	0.106767	−	0.994284i	$-0.465950\pi$
$139$	0.0527856	+	0.00554799i	0.00447722	+	0.000470575i	−0.102290	+	0.994755i	$0.532617\pi$
$140$	−29.3384	−	13.0623i	−2.47955	−	1.10397i
$141$		0			0
$142$	2.28111	+	1.31700i	0.191427	+	0.110520i
$143$	−14.7044	−	4.67966i	−1.22965	−	0.391333i
$144$		0			0
$145$	3.93244	+	1.27773i	0.326572	+	0.106110i
$146$	31.1102	−	3.26981i	2.57470	−	0.270612i
$147$		0			0
$148$	17.1465	−	19.0431i	1.40943	−	1.56533i
$149$	−13.6469	+	15.1564i	−1.11800	+	1.24166i	−0.150545	+	0.988603i	$0.548103\pi$
$149$	−13.6469	+	15.1564i	−1.11800	+	1.24166i	−0.967451	+	0.253057i	$0.918564\pi$
$150$		0			0
$151$	−1.18266	+	0.124303i	−0.0962436	+	0.0101156i	−0.152528	−	0.988299i	$-0.548741\pi$
$151$	−1.18266	+	0.124303i	−0.0962436	+	0.0101156i	0.0562842	+	0.998415i	$0.482075\pi$
$152$	−8.17525	−	2.65630i	−0.663101	−	0.215454i
$153$		0			0
$154$	−18.7194	−	25.4401i	−1.50845	−	2.05003i
$155$	3.26066	+	1.88254i	0.261902	+	0.151209i
$156$		0			0
$157$	−1.58325	−	0.704910i	−0.126357	−	0.0562580i	0.342584	−	0.939487i	$-0.388698\pi$
$157$	−1.58325	−	0.704910i	−0.126357	−	0.0562580i	−0.468942	+	0.883229i	$0.655365\pi$
$158$	−1.54270	−	0.162145i	−0.122731	−	0.0128995i
$159$		0			0
$160$	1.83559	−	8.63576i	0.145116	−	0.682717i
$161$	10.5767	+	7.68443i	0.833561	+	0.605618i
$162$		0			0
$163$	−0.309821	+	0.953532i	−0.0242671	+	0.0746864i	−0.962457	−	0.271435i	$-0.912502\pi$
$163$	−0.309821	+	0.953532i	−0.0242671	+	0.0746864i	0.938190	+	0.346122i	$0.112502\pi$
$164$	−14.8845	+	25.7807i	−1.16228	+	2.01314i
$165$		0			0
$166$	12.0022	+	20.7884i	0.931550	+	1.61349i
$167$	13.2227	−	2.81058i	1.02321	−	0.217489i	0.334398	−	0.942432i	$-0.391467\pi$
$167$	13.2227	−	2.81058i	1.02321	−	0.217489i	0.688809	+	0.724943i	$0.258134\pi$
$168$		0			0
$169$	−7.89967	+	3.51716i	−0.607667	+	0.270551i
$170$	−0.383460	+	0.124594i	−0.0294100	+	0.00955590i
$171$		0			0
$172$	8.87286	−	12.2124i	0.676549	−	0.931190i
$173$	−0.786362	−	7.48173i	−0.0597860	−	0.568826i	−0.982879	−	0.184250i	$-0.941014\pi$
$173$	−0.786362	−	7.48173i	−0.0597860	−	0.568826i	0.923093	−	0.384576i	$-0.125652\pi$
$174$		0			0
$175$	0.189869	−	0.109621i	0.0143527	−	0.00828655i
$176$	−3.04628	+	3.42466i	−0.229622	+	0.258143i
$177$		0			0
$178$	−11.5123	+	10.3657i	−0.862885	+	0.776945i
$179$	7.34750	+	10.1130i	0.549178	+	0.755879i	0.989900	−	0.141765i	$-0.0452777\pi$
$179$	7.34750	+	10.1130i	0.549178	+	0.755879i	−0.440722	+	0.897643i	$0.645278\pi$
$180$		0			0
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	−0.913616	−	0.406578i	$-0.866722\pi$
$181$	−5.56261	−	17.1200i	−0.413466	−	1.27252i	0.500150	−	0.865939i	$-0.333278\pi$
$182$	−43.3403	−	9.21226i	−3.21259	−	0.682858i
$183$		0			0
$184$	4.70954	−	10.5778i	0.347192	−	0.779806i
$185$	3.39666	+	15.9800i	0.249727	+	1.17487i
$186$		0			0
$187$	−0.247814	−	0.0511104i	−0.0181220	−	0.00373756i
$188$			21.9187i			1.59859i
$189$		0			0
$190$	10.2435	−	7.44233i	0.743141	−	0.539924i
$191$	−8.80869	−	19.7846i	−0.637374	−	1.43157i	−0.886331	−	0.463051i	$-0.846755\pi$
$191$	−8.80869	−	19.7846i	−0.637374	−	1.43157i	0.248957	−	0.968514i	$-0.419912\pi$
$192$		0			0
$193$	3.85464	+	3.47073i	0.277463	+	0.249829i	0.796099	−	0.605166i	$-0.206893\pi$
$193$	3.85464	+	3.47073i	0.277463	+	0.249829i	−0.518636	+	0.854995i	$0.673560\pi$
$194$	−4.04087	+	38.4463i	−0.290117	+	2.76028i
$195$		0			0
$196$	−22.2060	−	24.6622i	−1.58614	−	1.76159i
$197$	−5.14679			−0.366693			−0.183347	−	0.983048i	$-0.558693\pi$
$197$	−5.14679			−0.366693			−0.183347	+	0.983048i	$0.558693\pi$
$198$		0			0
$199$	24.2595			1.71971			0.859855	−	0.510539i	$-0.170554\pi$
$199$	24.2595			1.71971			0.859855	+	0.510539i	$0.170554\pi$
$200$	−0.129929	−	0.144301i	−0.00918737	−	0.0102036i
$201$		0			0
$202$	−0.423114	+	4.02566i	−0.0297702	+	0.283244i
$203$	5.53703	+	4.98557i	0.388624	+	0.349918i
$204$		0			0
$205$	−7.71945	−	17.3382i	−0.539150	−	1.21095i
$206$	6.14457	−	4.46429i	0.428113	−	0.311042i
$207$		0			0
$208$			6.42982i			0.445828i
$209$	7.89730	−	0.878351i	0.546268	−	0.0607568i
$210$		0			0
$211$	3.89702	+	18.3340i	0.268282	+	1.26217i	0.881474	+	0.472233i	$0.156552\pi$
$211$	3.89702	+	18.3340i	0.268282	+	1.26217i	−0.613192	+	0.789934i	$0.710115\pi$
$212$	−1.76269	+	3.95906i	−0.121062	+	0.271909i
$213$		0			0
$214$	34.0739	+	7.24264i	2.32925	+	0.495097i
$215$	2.97397	+	9.15293i	0.202823	+	0.624225i
$216$		0			0
$217$	3.98787	+	5.48883i	0.270714	+	0.372606i
$218$	−26.0751	+	23.4781i	−1.76603	+	1.59014i
$219$		0			0
$220$	−5.62194	−	25.6845i	−0.379031	−	1.73165i
$221$	−0.307403	+	0.177479i	−0.0206781	+	0.0119385i
$222$		0			0
$223$	0.573715	+	5.45853i	0.0384188	+	0.365530i	0.996794	+	0.0800168i	$0.0254974\pi$
$223$	0.573715	+	5.45853i	0.0384188	+	0.365530i	−0.958375	+	0.285513i	$0.907836\pi$
$224$	9.35109	−	12.8707i	0.624796	−	0.859958i
$225$		0			0
$226$	25.1444	−	8.16990i	1.67258	−	0.543454i
$227$	12.5739	−	5.59824i	0.834557	−	0.371569i	0.0554511	−	0.998461i	$-0.482340\pi$
$227$	12.5739	−	5.59824i	0.834557	−	0.371569i	0.779105	+	0.626893i	$0.215674\pi$
$228$		0			0
$229$	20.6708	−	4.39372i	1.36597	−	0.290346i	0.534148	−	0.845391i	$-0.320632\pi$
$229$	20.6708	−	4.39372i	1.36597	−	0.290346i	0.831820	+	0.555045i	$0.187299\pi$
$230$	8.52768	+	14.7704i	0.562298	+	0.973929i
$231$		0			0
$232$	3.29949	−	5.71488i	0.216622	−	0.375200i
$233$	−4.62458	+	14.2330i	−0.302967	+	0.932435i	0.677462	+	0.735558i	$0.263080\pi$
$233$	−4.62458	+	14.2330i	−0.302967	+	0.932435i	−0.980428	+	0.196877i	$0.936920\pi$
$234$		0			0
$235$	−11.3053	−	8.21378i	−0.737477	−	0.535808i
$236$	−0.425440	+	2.00154i	−0.0276938	+	0.130289i
$237$		0			0
$238$	−0.722562	−	0.0759444i	−0.0468368	−	0.00492274i
$239$	−4.93771	−	2.19841i	−0.319394	−	0.142203i	0.240777	−	0.970581i	$-0.422598\pi$
$239$	−4.93771	−	2.19841i	−0.319394	−	0.142203i	−0.560171	+	0.828377i	$0.689265\pi$
$240$		0			0
$241$	−10.1404	−	5.85457i	−0.653202	−	0.377126i	0.136480	−	0.990643i	$-0.456421\pi$
$241$	−10.1404	−	5.85457i	−0.653202	−	0.377126i	−0.789682	+	0.613517i	$0.789754\pi$
$242$	7.69281	−	24.6880i	0.494513	−	1.58700i
$243$		0			0
$244$	12.6843	+	4.12137i	0.812028	+	0.263844i
$245$	21.0418	−	2.21158i	1.34431	−	0.141293i
$246$		0			0
$247$	7.45873	−	8.28376i	0.474587	−	0.527083i
$248$	4.02073	−	4.46548i	0.255317	−	0.283558i
$249$		0			0
$250$	−25.9954	+	2.73222i	−1.64409	+	0.172801i
$251$	21.4920	+	6.98319i	1.35657	+	0.440775i	0.894895	−	0.446276i	$-0.147250\pi$
$251$	21.4920	+	6.98319i	1.35657	+	0.440775i	0.461671	+	0.887051i	$0.347250\pi$
$252$		0			0
$253$	0.0647190	+	10.7031i	0.00406885	+	0.672900i
$254$	−12.3403	−	7.12466i	−0.774297	−	0.447041i
$255$		0			0
$256$	−21.7757	−	9.69518i	−1.36098	−	0.605949i
$257$	−27.3656	−	2.87624i	−1.70702	−	0.179415i	−0.799857	−	0.600191i	$-0.795091\pi$
$257$	−27.3656	−	2.87624i	−1.70702	−	0.179415i	−0.907165	+	0.420775i	$0.861758\pi$
$258$		0			0
$259$	−6.12067	+	28.7955i	−0.380320	+	1.78926i
$260$	−29.8398	−	21.6799i	−1.85059	−	1.34453i
$261$		0			0
$262$	−5.19462	+	15.9874i	−0.320925	+	0.987705i
$263$	−16.0193	+	27.7463i	−0.987793	+	1.71091i	−0.358993	+	0.933340i	$0.616880\pi$
$263$	−16.0193	+	27.7463i	−0.987793	+	1.71091i	−0.628800	+	0.777567i	$0.716453\pi$
$264$		0			0
$265$	−1.38147	−	2.39277i	−0.0848630	−	0.146987i
$266$	22.3173	−	4.74370i	1.36836	−	0.290855i
$267$		0			0
$268$	41.8729	−	18.6430i	2.55780	−	1.13880i
$269$	−25.7177	+	8.35619i	−1.56804	+	0.509486i	−0.958940	−	0.283610i	$-0.908468\pi$
$269$	−25.7177	+	8.35619i	−1.56804	+	0.509486i	−0.609097	+	0.793096i	$0.708468\pi$
$270$		0			0
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	−0.455997	−	0.889981i	$-0.650717\pi$
$271$	8.74690	−	12.0391i	0.531336	−	0.731322i	0.987333	+	0.158660i	$0.0507172\pi$
$272$	0.0110207	+	0.104855i	0.000668225	+	0.00635774i
$273$		0			0
$274$	−21.6257	+	12.4856i	−1.30646	+	0.754284i
$275$	0.164414	+	0.0720138i	0.00991454	+	0.00434260i
$276$		0			0
$277$	5.85587	−	5.27265i	0.351845	−	0.316803i	−0.474189	−	0.880423i	$-0.657259\pi$
$277$	5.85587	−	5.27265i	0.351845	−	0.316803i	0.826034	+	0.563621i	$0.190592\pi$
$278$	0.0733391	+	0.100943i	0.00439859	+	0.00605414i
$279$		0			0
$280$	−10.0976	−	31.0772i	−0.603447	−	1.85722i
$281$	−20.7658	−	4.41390i	−1.23878	−	0.263311i	−0.458475	−	0.888707i	$-0.651604\pi$
$281$	−20.7658	−	4.41390i	−1.23878	−	0.263311i	−0.780308	+	0.625396i	$0.784937\pi$
$282$		0			0
$283$	−1.74698	+	3.92378i	−0.103847	+	0.233244i	−0.957994	−	0.286787i	$-0.907413\pi$
$283$	−1.74698	+	3.92378i	−0.103847	+	0.233244i	0.854147	+	0.520031i	$0.174080\pi$
$284$	0.821474	+	3.86473i	0.0487455	+	0.229329i
$285$		0			0
$286$	−14.9547	−	33.0495i	−0.884289	−	1.95426i
$287$		−	34.1996i		−	2.01874i
$288$		0			0
$289$	13.7486	−	9.98893i	0.808740	−	0.587584i
$290$	3.95353	+	8.87977i	0.232159	+	0.521438i
$291$		0			0
$292$	34.8707	+	31.3977i	2.04065	+	1.83741i
$293$	1.99603	−	18.9909i	0.116609	−	1.10946i	−0.767133	−	0.641488i	$-0.778317\pi$
$293$	1.99603	−	18.9909i	0.116609	−	1.10946i	0.883742	−	0.467974i	$-0.155016\pi$
$294$		0			0
$295$	−0.872929	−	0.969486i	−0.0508239	−	0.0564456i
$296$	26.0731			1.51547
$297$		0			0
$298$	−47.9444			−2.77735
$299$	10.0470	+	11.1583i	0.581031	+	0.645300i
$300$		0			0
$301$	−1.81274	+	17.2471i	−0.104485	+	0.994105i
$302$	−2.07747	−	1.87056i	−0.119545	−	0.107639i
$303$		0			0
$304$	−1.34668	−	3.02468i	−0.0772371	−	0.173477i
$305$	−6.87902	+	4.99790i	−0.393891	+	0.286179i
$306$		0			0
$307$			1.86240i			0.106293i	0.998587	+	0.0531463i	$0.0169250\pi$
$307$			1.86240i			0.106293i	−0.998587	+	0.0531463i	$0.983075\pi$
$308$	9.57012	−	46.4018i	0.545308	−	2.64399i
$309$		0			0
$310$	1.84022	+	8.65753i	0.104517	+	0.491715i
$311$	3.64217	−	8.18044i	0.206528	−	0.463870i	−0.780348	−	0.625345i	$-0.784958\pi$
$311$	3.64217	−	8.18044i	0.206528	−	0.463870i	0.986877	+	0.161475i	$0.0516250\pi$
$312$		0			0
$313$	−16.7624	−	3.56295i	−0.947466	−	0.201390i	−0.291832	−	0.956469i	$-0.594265\pi$
$313$	−16.7624	−	3.56295i	−0.947466	−	0.201390i	−0.655633	+	0.755079i	$0.727598\pi$
$314$	−1.25898	−	3.87474i	−0.0710483	−	0.218664i
$315$		0			0
$316$	−1.36768	−	1.88245i	−0.0769381	−	0.105896i
$317$	20.2910	−	18.2701i	1.13965	−	1.02615i	0.140304	−	0.990108i	$-0.455192\pi$
$317$	20.2910	−	18.2701i	1.13965	−	1.02615i	0.999350	−	0.0360411i	$-0.0114747\pi$
$318$		0			0
$319$	−0.600930	+	6.07033i	−0.0336456	+	0.339873i
$320$	23.3551	−	13.4841i	1.30559	−	0.753783i
$321$		0			0
$322$	3.21250	+	30.5649i	0.179025	+	1.70331i
$323$	0.107435	−	0.147872i	0.00597785	−	0.00822781i
$324$		0			0
$325$	0.239475	−	0.0778102i	0.0132837	−	0.00431614i
$326$	−2.15315	+	0.958645i	−0.119252	+	0.0530944i
$327$		0			0
$328$	−29.6277	+	6.29756i	−1.63591	+	0.347724i
$329$	−12.5905	−	21.8073i	−0.694135	−	1.20228i
$330$		0			0
$331$	2.93609	−	5.08545i	0.161382	−	0.279522i	−0.773983	−	0.633207i	$-0.781738\pi$
$331$	2.93609	−	5.08545i	0.161382	−	0.279522i	0.935365	+	0.353685i	$0.115072\pi$
$332$	−11.1268	+	34.2448i	−0.610663	+	1.87943i
$333$		0			0
$334$	25.7093	+	18.6789i	1.40675	+	1.02206i
$335$	−6.07563	+	28.5836i	−0.331947	+	1.56169i
$336$		0			0
$337$	16.4800	+	1.73212i	0.897721	+	0.0943543i	0.542137	−	0.840290i	$-0.317615\pi$
$337$	16.4800	+	1.73212i	0.897721	+	0.0943543i	0.355584	+	0.934644i	$0.384282\pi$
$338$	−18.5705	−	8.26814i	−1.01010	−	0.449727i
$339$		0			0
$340$	−0.523772	−	0.302400i	−0.0284055	−	0.0163999i
$341$	−1.68447	+	5.29296i	−0.0912193	+	0.286630i
$342$		0			0
$343$	9.28988	+	3.01847i	0.501606	+	0.162982i
$344$	15.2752	−	1.60549i	0.823586	−	0.0865624i
$345$		0			0
$346$	11.8335	−	13.1425i	0.636174	−	0.706543i
$347$	1.68499	−	1.87137i	0.0904548	−	0.100460i	−0.696218	−	0.717830i	$-0.745135\pi$
$347$	1.68499	−	1.87137i	0.0904548	−	0.100460i	0.786673	+	0.617370i	$0.211802\pi$
$348$		0			0
$349$	−8.68163	+	0.912476i	−0.464717	+	0.0488437i	−0.333994	−	0.942575i	$-0.608397\pi$
$349$	−8.68163	+	0.912476i	−0.464717	+	0.0488437i	−0.130723	+	0.991419i	$0.541730\pi$
$350$	0.490168	+	0.159265i	0.0262006	+	0.00851308i
$351$		0			0
$352$	13.0245	−	0.0787558i	0.694210	−	0.00419770i
$353$	0.464623	+	0.268250i	0.0247294	+	0.0142775i	0.512314	−	0.858798i	$-0.328789\pi$
$353$	0.464623	+	0.268250i	0.0247294	+	0.0142775i	−0.487584	+	0.873076i	$0.662122\pi$
$354$		0			0
$355$	−2.30120	−	1.02456i	−0.122135	−	0.0543779i
$356$	−23.1101	−	2.42897i	−1.22483	−	0.128735i
$357$		0			0
$358$	−6.10964	+	28.7436i	−0.322904	+	1.51915i
$359$	−12.7871	−	9.29040i	−0.674880	−	0.490329i	0.196775	−	0.980449i	$-0.436953\pi$
$359$	−12.7871	−	9.29040i	−0.674880	−	0.490329i	−0.871655	+	0.490120i	$0.836953\pi$
$360$		0			0
$361$	4.09760	−	12.6111i	0.215663	−	0.663742i
$362$	21.1584	−	36.6474i	1.11206	−	1.92614i
$363$		0			0
$364$	−33.2319	−	57.5594i	−1.74183	−	3.01693i
$365$	−29.2617	+	6.21977i	−1.53163	+	0.325558i
$366$		0			0
$367$	26.4318	−	11.7682i	1.37973	−	0.614296i	0.423229	−	0.906023i	$-0.360897\pi$
$367$	26.4318	−	11.7682i	1.37973	−	0.614296i	0.956502	+	0.291727i	$0.0942299\pi$
$368$	4.24157	−	1.37817i	0.221107	−	0.0718420i
$369$		0			0
$370$	−22.5739	+	31.0703i	−1.17356	+	1.61527i
$371$	−0.520419	−	4.95146i	−0.0270188	−	0.257067i
$372$		0			0
$373$	−5.72386	+	3.30467i	−0.296370	+	0.171109i	−0.640811	−	0.767699i	$-0.721402\pi$
$373$	−5.72386	+	3.30467i	−0.296370	+	0.171109i	0.344441	+	0.938808i	$0.388069\pi$
$374$	−0.300520	−	0.513323i	−0.0155395	−	0.0265433i
$375$		0			0
$376$	−16.5736	+	14.9230i	−0.854720	+	0.769594i
$377$	5.02984	+	6.92297i	0.259050	+	0.356551i
$378$		0			0
$379$	0.478524	+	1.47275i	0.0245801	+	0.0756498i	0.962594	−	0.270948i	$-0.0873370\pi$
$379$	0.478524	+	1.47275i	0.0245801	+	0.0756498i	−0.938014	+	0.346597i	$0.887337\pi$
$380$	18.5778	+	3.94882i	0.953019	+	0.202570i
$381$		0			0
$382$	20.7075	−	46.5097i	1.05949	−	2.37964i
$383$	2.80843	+	13.2126i	0.143504	+	0.675135i	0.989805	+	0.142429i	$0.0454913\pi$
$383$	2.80843	+	13.2126i	0.143504	+	0.675135i	−0.846301	+	0.532705i	$0.821175\pi$
$384$		0			0
$385$	20.3469	+	22.3246i	1.03698	+	1.13777i
$386$			12.1934i			0.620629i
$387$		0			0
$388$	−46.9133	+	34.0845i	−2.38166	+	1.73038i
$389$	−6.09270	−	13.6844i	−0.308912	−	0.693828i	0.690657	−	0.723182i	$-0.257321\pi$
$389$	−6.09270	−	13.6844i	−0.308912	−	0.693828i	−0.999569	+	0.0293547i	$0.990655\pi$
$390$		0			0
$391$	0.182966	+	0.164744i	0.00925301	+	0.00833145i
$392$	3.52957	−	33.5817i	0.178270	−	1.69613i
$393$		0			0
$394$	−8.09585	−	8.99135i	−0.407863	−	0.452978i
$395$	1.48346			0.0746409
$396$		0			0
$397$	−20.7132			−1.03956			−0.519782	−	0.854299i	$-0.673987\pi$
$397$	−20.7132			−1.03956			−0.519782	+	0.854299i	$0.673987\pi$
$398$	38.1600	+	42.3809i	1.91279	+	2.12436i
$399$		0			0
$400$	0.00781780	−	0.0743814i	0.000390890	−	0.00371907i
$401$	20.0982	+	18.0965i	1.00366	+	0.903695i	0.995355	−	0.0962701i	$-0.0306913\pi$
$401$	20.0982	+	18.0965i	1.00366	+	0.903695i	0.00830020	+	0.999966i	$0.497358\pi$
$402$		0			0
$403$	3.16932	+	7.11842i	0.157875	+	0.354594i
$404$	−4.91223	+	3.56894i	−0.244392	+	0.177561i
$405$		0			0
$406$			17.5154i			0.869273i
$407$	−21.9583	+	9.93597i	−1.08843	+	0.492508i
$408$		0			0
$409$	1.26941	+	5.97208i	0.0627681	+	0.295300i	0.998324	−	0.0578791i	$-0.0184338\pi$
$409$	1.26941	+	5.97208i	0.0627681	+	0.295300i	−0.935556	+	0.353180i	$0.885100\pi$
$410$	18.1469	−	40.7586i	0.896211	−	2.01292i
$411$		0			0
$412$	11.1439	+	2.36871i	0.549020	+	0.116698i
$413$	−0.726437	−	2.23574i	−0.0357456	−	0.110014i
$414$		0			0
$415$	−13.4932	−	18.5718i	−0.662357	−	0.911656i
$416$	13.5784	−	12.2260i	0.665736	−	0.599431i
$417$		0			0
$418$	13.9569	+	12.4148i	0.682652	+	0.607229i
$419$	30.8841	−	17.8309i	1.50879	−	0.871098i	0.508838	−	0.860862i	$-0.330075\pi$
$419$	30.8841	−	17.8309i	1.50879	−	0.871098i	0.999948	−	0.0102354i	$-0.00325810\pi$
$420$		0			0
$421$	−1.49556	−	14.2293i	−0.0728889	−	0.693492i	−0.968561	−	0.248777i	$-0.919972\pi$
$421$	−1.49556	−	14.2293i	−0.0728889	−	0.693492i	0.895672	−	0.444715i	$-0.146695\pi$
$422$	−25.8993	+	35.6473i	−1.26076	+	1.73528i
$423$		0			0
$424$	−4.19370	+	1.36262i	−0.203664	+	0.0661745i
$425$	0.00377188	−	0.00167935i	0.000182963	−	8.14605e-5i
$426$		0			0
$427$	−14.9872	+	3.18563i	−0.725282	+	0.154163i
$428$	26.1268	+	45.2530i	1.26289	+	2.18738i
$429$		0			0
$430$	−11.3120	+	19.5930i	−0.545513	+	0.944856i
$431$	−2.68944	+	8.27725i	−0.129546	+	0.398701i	−0.994702	−	0.102802i	$-0.967219\pi$
$431$	−2.68944	+	8.27725i	−0.129546	+	0.398701i	0.865156	+	0.501503i	$0.167219\pi$
$432$		0			0
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.983355	+	0.181693i	$0.0581576\pi$
$433$	30.3812	+	22.0733i	1.46003	+	1.06077i	0.476673	+	0.879080i	$0.341842\pi$
$434$	−3.31601	+	15.6006i	−0.159174	+	0.748853i
$435$		0			0
$436$	−52.3438	−	5.50156i	−2.50681	−	0.263477i
$437$	−7.06326	−	3.14476i	−0.337881	−	0.150434i
$438$		0			0
$439$	28.1171	+	16.2334i	1.34196	+	0.774779i	0.987094	−	0.160139i	$-0.0511942\pi$
$439$	28.1171	+	16.2334i	1.34196	+	0.774779i	0.354863	+	0.934918i	$0.384528\pi$
$440$	15.5935	−	21.7378i	0.743390	−	1.03631i
$441$		0			0
$442$	−0.793595	−	0.257855i	−0.0377474	−	0.0122649i
$443$	−18.7184	+	1.96738i	−0.889336	+	0.0934730i	−0.538166	−	0.842839i	$-0.680883\pi$
$443$	−18.7184	+	1.96738i	−0.889336	+	0.0934730i	−0.351170	+	0.936312i	$0.614216\pi$
$444$		0			0
$445$	9.91306	−	11.0096i	0.469924	−	0.521904i
$446$	−8.63351	+	9.58849i	−0.408809	+	0.454028i
$447$		0			0
$448$	48.3296	−	5.07965i	2.28336	−	0.239991i
$449$	6.86840	+	2.23168i	0.324140	+	0.105319i	0.466567	−	0.884486i	$-0.345491\pi$
$449$	6.86840	+	2.23168i	0.324140	+	0.105319i	−0.142427	+	0.989805i	$0.545491\pi$
$450$		0			0
$451$	22.5520	−	16.5942i	1.06193	−	0.781392i
$452$	34.3450	+	19.8291i	1.61545	+	0.932681i
$453$		0			0
$454$	29.5586	+	13.1603i	1.38725	+	0.617646i
$455$	42.1414	+	4.42924i	1.97562	+	0.207646i
$456$		0			0
$457$	−0.877843	+	4.12993i	−0.0410638	+	0.193190i	−0.993898	−	0.110301i	$-0.964819\pi$
$457$	−0.877843	+	4.12993i	−0.0410638	+	0.193190i	0.952835	+	0.303490i	$0.0981520\pi$
$458$	40.1908	+	29.2004i	1.87799	+	1.36444i
$459$		0			0
$460$	−7.90572	+	24.3313i	−0.368606	+	1.13445i
$461$	7.09611	−	12.2908i	0.330499	−	0.572441i	−0.652111	−	0.758123i	$-0.726116\pi$
$461$	7.09611	−	12.2908i	0.330499	−	0.572441i	0.982610	+	0.185683i	$0.0594497\pi$
$462$		0			0
$463$	20.1892	+	34.9687i	0.938271	+	1.62513i	0.768695	+	0.639616i	$0.220906\pi$
$463$	20.1892	+	34.9687i	0.938271	+	1.62513i	0.169576	+	0.985517i	$0.445760\pi$
$464$	2.48620	−	0.528457i	0.115419	−	0.0245330i
$465$		0			0
$466$	−32.1393	+	14.3093i	−1.48882	+	0.662867i
$467$	10.7476	−	3.49210i	0.497338	−	0.161595i	−0.0495980	−	0.998769i	$-0.515794\pi$
$467$	10.7476	−	3.49210i	0.497338	−	0.161595i	0.546936	+	0.837174i	$0.315794\pi$
$468$		0			0
$469$	−30.9513	+	42.6008i	−1.42920	+	1.96712i
$470$	−3.43380	−	32.6704i	−0.158389	−	1.50697i
$471$		0			0
$472$	−1.80309	+	1.04102i	−0.0829942	+	0.0479167i
$473$	−12.2527	+	7.17322i	−0.563379	+	0.329825i
$474$		0			0
$475$	−0.0963559	+	0.0867593i	−0.00442111	+	0.00398079i
$476$	−0.640587	−	0.881692i	−0.0293612	−	0.0404123i
$477$		0			0
$478$	−3.92639	−	12.0842i	−0.179589	−	0.552718i
$479$	22.3979	+	4.76083i	1.02339	+	0.217528i	0.688888	−	0.724868i	$-0.258099\pi$
$479$	22.3979	+	4.76083i	1.02339	+	0.217528i	0.334500	+	0.942396i	$0.391433\pi$
$480$		0			0
$481$	−13.7520	+	30.8874i	−0.627036	+	1.40835i
$482$	−5.72295	−	26.9243i	−0.260673	−	1.22637i
$483$		0			0
$484$	35.2420	−	16.2042i	1.60191	−	0.736554i
$485$		−	36.9698i		−	1.67871i
$486$		0			0
$487$	6.10169	−	4.43314i	0.276494	−	0.200885i	−0.440893	−	0.897560i	$-0.645338\pi$
$487$	6.10169	−	4.43314i	0.276494	−	0.200885i	0.717387	+	0.696675i	$0.245338\pi$
$488$	5.51953	+	12.3971i	0.249857	+	0.561189i
$489$		0			0
$490$	36.9621	+	33.2808i	1.66978	+	1.50347i
$491$	−3.99196	+	37.9810i	−0.180155	+	1.71406i	0.414477	+	0.910060i	$0.363964\pi$
$491$	−3.99196	+	37.9810i	−0.180155	+	1.71406i	−0.594632	+	0.803998i	$0.702702\pi$
$492$		0			0
$493$	0.0938901	+	0.104276i	0.00422860	+	0.00469633i
$494$	26.2041			1.17898
$495$		0			0
$496$	2.31446			0.103922
$497$	−3.03726	−	3.37322i	−0.136240	−	0.151310i
$498$		0			0
$499$	0.842404	−	8.01494i	0.0377112	−	0.358798i	−0.959352	−	0.282213i	$-0.908932\pi$
$499$	0.842404	−	8.01494i	0.0377112	−	0.358798i	0.997063	−	0.0765852i	$-0.0244017\pi$
$500$	−29.1376	−	26.2356i	−1.30307	−	1.17329i
$501$		0			0
$502$	21.6073	+	48.5308i	0.964381	+	2.16603i
$503$	21.0846	−	15.3188i	0.940115	−	0.683033i	−0.00833362	−	0.999965i	$-0.502653\pi$
$503$	21.0846	−	15.3188i	0.940115	−	0.683033i	0.948448	+	0.316932i	$0.102653\pi$
$504$		0			0
$505$		−	3.87106i		−	0.172260i
$506$	−18.5964	+	16.9490i	−0.826711	+	0.753475i
$507$		0			0
$508$	−4.44397	−	20.9072i	−0.197169	−	0.927609i
$509$	−11.3737	+	25.5457i	−0.504130	+	1.13230i	0.464902	+	0.885362i	$0.346089\pi$
$509$	−11.3737	+	25.5457i	−0.504130	+	1.13230i	−0.969033	+	0.246933i	$0.920577\pi$
$510$		0			0
$511$	−52.7288	−	11.2078i	−2.33258	−	0.495806i
$512$	−4.74153	−	14.5929i	−0.209548	−	0.644922i
$513$		0			0
$514$	−38.0212	−	52.3316i	−1.67704	−	2.30825i
$515$	−5.39777	+	4.86018i	−0.237854	+	0.214165i
$516$		0			0
$517$	8.27113	−	18.8837i	0.363764	−	0.830506i
$518$	−59.9330	+	34.6024i	−2.63331	+	1.52034i
$519$		0			0
$520$	−3.92285	−	37.3234i	−0.172028	−	1.63674i
$521$	18.9804	−	26.1242i	0.831545	−	1.14452i	−0.156088	−	0.987743i	$-0.549888\pi$
$521$	18.9804	−	26.1242i	0.831545	−	1.14452i	0.987633	−	0.156781i	$-0.0501117\pi$
$522$		0			0
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.0750804	−	0.997177i	$-0.476079\pi$
$523$	16.5104	−	5.36454i	0.721948	−	0.234575i	0.646868	+	0.762602i	$0.276079\pi$
$524$	−23.0356	+	10.2561i	−1.00632	+	0.448041i
$525$		0			0
$526$	−73.6705	+	15.6591i	−3.21219	+	0.682771i
$527$	0.0638847	+	0.110652i	0.00278286	+	0.00482006i
$528$		0			0
$529$	−6.29267	+	10.8992i	−0.273594	+	0.473879i
$530$	2.00710	−	6.17722i	0.0871828	−	0.268321i
$531$		0			0
$532$	27.6881	+	20.1166i	1.20043	+	0.872166i
$533$	8.16641	−	38.4199i	0.353726	−	1.66415i
$534$		0			0
$535$	−33.1314	−	3.48225i	−1.43239	−	0.150551i
$536$	42.6052	+	18.9690i	1.84026	+	0.819338i
$537$		0			0
$538$	−55.0519	−	31.7842i	−2.37345	−	1.37031i
$539$	9.82480	+	29.6269i	0.423184	+	1.27612i
$540$		0			0
$541$	−9.58312	−	3.11375i	−0.412011	−	0.133870i	0.0956753	−	0.995413i	$-0.469499\pi$
$541$	−9.58312	−	3.11375i	−0.412011	−	0.133870i	−0.507686	+	0.861542i	$0.669499\pi$
$542$	34.7909	−	3.65667i	1.49440	−	0.157067i
$543$		0			0
$544$	0.200475	−	0.222650i	0.00859529	−	0.00954603i
$545$	22.4528	−	24.9364i	0.961773	−	1.06816i
$546$		0			0
$547$	−23.7290	+	2.49402i	−1.01458	+	0.106637i	−0.597197	−	0.802095i	$-0.703719\pi$
$547$	−23.7290	+	2.49402i	−1.01458	+	0.106637i	−0.417382	+	0.908731i	$0.637052\pi$
$548$	−35.6242	−	11.5750i	−1.52179	−	0.494460i
$549$		0			0
$550$	0.132815	+	0.400506i	0.00566325	+	0.0170776i
$551$	−3.81607	−	2.20321i	−0.162570	−	0.0938599i
$552$		0			0
$553$	2.44204	+	1.08727i	0.103846	+	0.0462353i
$554$	18.4225	+	1.93628i	0.782695	+	0.0822646i
$555$		0			0
$556$	−0.0389130	+	0.183071i	−0.00165028	+	0.00776394i
$557$	31.6776	+	23.0151i	1.34222	+	0.975181i	0.999359	+	0.0357950i	$0.0113963\pi$
$557$	31.6776	+	23.0151i	1.34222	+	0.975181i	0.342862	+	0.939386i	$0.388604\pi$
$558$		0			0
$559$	−6.15482	+	18.9426i	−0.260321	+	0.801185i
$560$	6.29304	−	10.8999i	0.265929	−	0.460603i
$561$		0			0
$562$	−24.9534	−	43.2205i	−1.05259	−	1.82315i
$563$	4.91096	−	1.04386i	0.206972	−	0.0439933i	−0.103259	−	0.994655i	$-0.532927\pi$
$563$	4.91096	−	1.04386i	0.206972	−	0.0439933i	0.310231	+	0.950661i	$0.399594\pi$
$564$		0			0
$565$	−23.0979	+	10.2838i	−0.971734	+	0.432644i
$566$	−9.60276	+	3.12012i	−0.403634	+	0.131149i
$567$		0			0
$568$	−2.36299	+	3.25238i	−0.0991489	+	0.136467i
$569$	−0.993979	−	9.45708i	−0.0416698	−	0.396461i	−0.995401	−	0.0957997i	$-0.969459\pi$
$569$	−0.993979	−	9.45708i	−0.0416698	−	0.396461i	0.953731	−	0.300662i	$-0.0972075\pi$
$570$		0			0
$571$	34.4930	−	19.9146i	1.44349	−	0.833398i	0.445408	−	0.895328i	$-0.353059\pi$
$571$	34.4930	−	19.9146i	1.44349	−	0.833398i	0.998081	+	0.0619297i	$0.0197254\pi$
$572$	21.8312	−	49.8427i	0.912810	−	2.08403i
$573$		0			0
$574$	59.7461	−	53.7956i	2.49375	−	2.24539i
$575$	−0.102658	−	0.141297i	−0.00428115	−	0.00589249i
$576$		0			0
$577$	−4.03506	−	12.4186i	−0.167982	−	0.516994i	0.831262	−	0.555881i	$-0.187619\pi$
$577$	−4.03506	−	12.4186i	−0.167982	−	0.516994i	−0.999244	+	0.0388866i	$0.987619\pi$
$578$	39.0769	+	8.30605i	1.62538	+	0.345486i
$579$		0			0
$580$	−5.93039	+	13.3199i	−0.246246	+	0.553078i
$581$	−8.60050	−	40.4622i	−0.356809	−	1.67865i
$582$		0			0
$583$	3.01258	−	2.74571i	0.124769	−	0.113716i
$584$			47.7437i			1.97565i
$585$		0			0
$586$	36.3166	−	26.3855i	1.50022	−	1.08998i
$587$	9.66059	+	21.6980i	0.398735	+	0.895574i	0.995642	+	0.0932631i	$0.0297298\pi$
$587$	9.66059	+	21.6980i	0.398735	+	0.895574i	−0.596906	+	0.802311i	$0.703604\pi$
$588$		0			0
$589$	−2.98179	−	2.68482i	−0.122863	−	0.110626i
$590$	0.320566	−	3.04999i	0.0131975	−	0.125566i
$591$		0			0
$592$	6.71983	+	7.46313i	0.276183	+	0.306733i
$593$	−37.1489			−1.52552			−0.762761	−	0.646680i	$-0.776157\pi$
$593$	−37.1489			−1.52552			−0.762761	+	0.646680i	$0.776157\pi$
$594$		0			0
$595$	0.694814			0.0284846
$596$	−48.1224	−	53.4453i	−1.97117	−	2.18921i
$597$		0			0
$598$	−3.68956	+	35.1038i	−0.150877	+	1.43550i
$599$	1.77298	+	1.59640i	0.0724422	+	0.0652272i	0.704556	−	0.709648i	$-0.251146\pi$
$599$	1.77298	+	1.59640i	0.0724422	+	0.0652272i	−0.632114	+	0.774875i	$0.717813\pi$
$600$		0			0
$601$	2.76331	+	6.20650i	0.112718	+	0.253168i	0.961092	−	0.276229i	$-0.0890848\pi$
$601$	2.76331	+	6.20650i	0.112718	+	0.253168i	−0.848374	+	0.529397i	$0.822418\pi$
$602$	−32.9818	+	23.9627i	−1.34424	+	0.976646i
$603$		0			0
$604$		−	4.19334i		−	0.170624i
$605$	−4.84866	+	24.2495i	−0.197126	+	0.985883i
$606$		0			0
$607$	8.41966	+	39.6114i	0.341744	+	1.60778i	0.728129	+	0.685440i	$0.240390\pi$
$607$	8.41966	+	39.6114i	0.341744	+	1.60778i	−0.386386	+	0.922337i	$0.626277\pi$
$608$	−3.82683	+	8.59520i	−0.155198	+	0.348581i
$609$		0			0
$610$	−19.5519	−	4.15588i	−0.791633	−	0.168267i
$611$	−8.93688	−	27.5049i	−0.361547	−	1.11273i
$612$		0			0
$613$	0.119072	+	0.163888i	0.00480926	+	0.00661938i	0.811415	−	0.584471i	$-0.198698\pi$
$613$	0.119072	+	0.163888i	0.00480926	+	0.00661938i	−0.806606	+	0.591090i	$0.798698\pi$
$614$	−3.25358	+	2.92953i	−0.131304	+	0.118226i
$615$		0			0
$616$	41.6019	−	24.3554i	1.67619	−	0.981309i
$617$	7.00117	−	4.04213i	0.281857	−	0.162730i	−0.352407	−	0.935847i	$-0.614637\pi$
$617$	7.00117	−	4.04213i	0.281857	−	0.162730i	0.634264	+	0.773117i	$0.281303\pi$
$618$		0			0
$619$	−2.19370	−	20.8716i	−0.0881722	−	0.838902i	−0.945826	−	0.324674i	$-0.894745\pi$
$619$	−2.19370	−	20.8716i	−0.0881722	−	0.838902i	0.857654	−	0.514228i	$-0.171921\pi$
$620$	−7.80381	+	10.7410i	−0.313409	+	0.431370i
$621$		0			0
$622$	20.0202	−	6.50496i	0.802737	−	0.260825i
$623$	24.3879	−	10.8582i	0.977081	−	0.435024i
$624$		0			0
$625$	24.7155	−	5.25344i	0.988620	−	0.210138i
$626$	−20.1427	−	34.8881i	−0.805062	−	1.39441i
$627$		0			0
$628$	3.05565	−	5.29255i	0.121934	−	0.211196i
$629$	−0.171320	+	0.527268i	−0.00683097	+	0.0210236i
$630$		0			0
$631$	19.6268	+	14.2597i	0.781332	+	0.567671i	0.905378	−	0.424606i	$-0.139587\pi$
$631$	19.6268	+	14.2597i	0.781332	+	0.567671i	−0.124047	+	0.992276i	$0.539587\pi$
$632$	0.492237	−	2.31579i	0.0195801	−	0.0921173i
$633$		0			0
$634$	63.8351	+	6.70933i	2.53521	+	0.266462i
$635$	12.4489	+	5.54261i	0.494020	+	0.219952i
$636$		0			0
$637$	37.9208	+	21.8936i	1.50248	+	0.867455i
$638$	−11.5500	+	8.49876i	−0.457270	+	0.336469i
$639$		0			0
$640$	43.5007	+	14.1342i	1.71952	+	0.558705i
$641$	−16.0507	+	1.68700i	−0.633965	+	0.0666324i	−0.416059	−	0.909338i	$-0.636589\pi$
$641$	−16.0507	+	1.68700i	−0.633965	+	0.0666324i	−0.217905	+	0.975970i	$0.569922\pi$
$642$		0			0
$643$	8.42032	−	9.35171i	0.332065	−	0.368796i	−0.553871	−	0.832602i	$-0.686850\pi$
$643$	8.42032	−	9.35171i	0.332065	−	0.368796i	0.885936	+	0.463807i	$0.153517\pi$
$644$	−30.8473	+	34.2594i	−1.21555	+	1.35001i
$645$		0			0
$646$	0.427324	−	0.0449136i	0.0168128	−	0.00176710i
$647$	−28.7701	−	9.34797i	−1.13107	−	0.367507i	−0.317087	−	0.948396i	$-0.602705\pi$
$647$	−28.7701	−	9.34797i	−1.13107	−	0.367507i	−0.813982	+	0.580890i	$0.802705\pi$
$648$		0			0
$649$	1.12182	−	1.56385i	0.0440352	−	0.0613865i
$650$	0.512626	+	0.295965i	0.0201068	+	0.0116087i
$651$		0			0
$652$	−3.22978	−	1.43799i	−0.126488	−	0.0563161i
$653$	−19.4852	−	2.04798i	−0.762516	−	0.0801436i	−0.284715	−	0.958612i	$-0.591899\pi$
$653$	−19.4852	−	2.04798i	−0.762516	−	0.0801436i	−0.477800	+	0.878468i	$0.658566\pi$
$654$		0			0
$655$	3.34240	−	15.7247i	0.130598	−	0.614416i
$656$	−9.43855	−	6.85751i	−0.368514	−	0.267741i
$657$		0			0
$658$	18.2924	−	56.2981i	0.713111	−	2.19473i
$659$	0.674716	−	1.16864i	0.0262832	−	0.0455238i	−0.852585	−	0.522589i	$-0.824966\pi$
$659$	0.674716	−	1.16864i	0.0262832	−	0.0455238i	0.878868	+	0.477065i	$0.158300\pi$
$660$		0			0
$661$	−14.3929	−	24.9293i	−0.559821	−	0.969638i	−0.997511	−	0.0705120i	$-0.977537\pi$
$661$	−14.3929	−	24.9293i	−0.559821	−	0.969638i	0.437690	−	0.899126i	$-0.355797\pi$
$662$	13.5026	−	2.87007i	0.524795	−	0.111549i
$663$		0			0
$664$	−33.4694	+	14.9015i	−1.29886	+	0.578291i
$665$	−20.7516	+	6.74260i	−0.804712	+	0.261467i
$666$		0			0
$667$	3.48879	−	4.80191i	0.135086	−	0.185931i
$668$	4.98271	+	47.4073i	0.192787	+	1.83424i
$669$		0			0
$670$	−59.4920	+	34.3477i	−2.29838	+	1.32697i
$671$	−9.37273	−	8.33718i	−0.361830	−	0.321853i
$672$		0			0
$673$	−16.1641	+	14.5542i	−0.623080	+	0.561023i	−0.919034	−	0.394179i	$-0.871029\pi$
$673$	−16.1641	+	14.5542i	−0.623080	+	0.561023i	0.295954	+	0.955202i	$0.404362\pi$
$674$	22.8969	+	31.5149i	0.881955	+	1.21391i
$675$		0			0
$676$	−9.42270	−	29.0001i	−0.362411	−	1.11539i
$677$	−18.4922	−	3.93065i	−0.710714	−	0.151067i	−0.161651	−	0.986848i	$-0.551682\pi$
$677$	−18.4922	−	3.93065i	−0.710714	−	0.151067i	−0.549063	+	0.835781i	$0.685015\pi$
$678$		0			0
$679$	27.0962	−	60.8590i	1.03986	−	2.33555i
$680$	−0.127944	−	0.601929i	−0.00490643	−	0.0230829i
$681$		0			0
$682$	−11.8964	+	5.38304i	−0.455536	+	0.206127i
$683$		−	33.7466i		−	1.29128i	−0.763642	−	0.645640i	$-0.776591\pi$
$683$		−	33.7466i		−	1.29128i	0.763642	−	0.645640i	$-0.223409\pi$
$684$		0			0
$685$	19.3199	−	14.0367i	0.738176	−	0.536316i
$686$	9.33969	+	20.9773i	0.356591	+	0.800917i
$687$		0			0
$688$	4.39645	+	3.95858i	0.167613	+	0.150919i
$689$	0.597702	−	5.68675i	0.0227706	−	0.216648i
$690$		0			0
$691$	−18.4231	−	20.4609i	−0.700849	−	0.778371i	0.282662	−	0.959219i	$-0.408782\pi$
$691$	−18.4231	−	20.4609i	−0.700849	−	0.778371i	−0.983511	+	0.180848i	$0.942116\pi$
$692$	26.5278			1.00844
$693$		0			0
$694$	5.91971			0.224709
$695$	−0.0798427	−	0.0886743i	−0.00302861	−	0.00336361i
$696$		0			0
$697$	0.0673225	−	0.640531i	0.00255002	−	0.0242618i
$698$	−15.2502	−	13.7314i	−0.577229	−	0.519739i
$699$		0			0
$700$	0.314449	+	0.706264i	0.0118851	+	0.0266943i
$701$	8.43699	−	6.12983i	0.318661	−	0.231521i	−0.416943	−	0.908933i	$-0.636899\pi$
$701$	8.43699	−	6.12983i	0.318661	−	0.231521i	0.735604	+	0.677412i	$0.236899\pi$
$702$		0			0
$703$		−	17.4101i		−	0.656636i
$704$	26.8000	+	29.4049i	1.01006	+	1.10824i
$705$		0			0
$706$	0.262219	+	1.23364i	0.00986875	+	0.0464288i
$707$	2.83720	−	6.37246i	0.106704	−	0.239661i
$708$		0			0
$709$	19.6086	+	4.16794i	0.736417	+	0.156530i	0.560827	−	0.827933i	$-0.310483\pi$
$709$	19.6086	+	4.16794i	0.736417	+	0.156530i	0.175590	+	0.984463i	$0.443817\pi$
$710$	−1.82988	−	5.63178i	−0.0686740	−	0.211357i
$711$		0			0
$712$	−13.8975	−	19.1282i	−0.520829	−	0.716860i
$713$	4.01650	−	3.61647i	0.150419	−	0.135438i
$714$		0			0
$715$	17.5270	+	29.9381i	0.655473	+	1.11962i
$716$	−38.1738	+	22.0397i	−1.42662	+	0.823660i
$717$		0			0
$718$	−3.88388	−	36.9527i	−0.144945	−	1.37906i
$719$	6.01752	−	8.28241i	0.224416	−	0.308882i	−0.681931	−	0.731417i	$-0.738860\pi$
$719$	6.01752	−	8.28241i	0.224416	−	0.308882i	0.906347	+	0.422535i	$0.138860\pi$
$720$		0			0
$721$	−12.4479	+	4.04456i	−0.463583	+	0.150627i
$722$	28.4769	−	12.6787i	1.05980	−	0.471853i
$723$		0			0
$724$	62.0890	−	13.1974i	2.30752	−	0.490478i
$725$	−0.0497687	−	0.0862019i	−0.00184836	−	0.00320146i
$726$		0			0
$727$	7.22282	−	12.5103i	0.267880	−	0.463981i	−0.700434	−	0.713717i	$-0.747010\pi$
$727$	7.22282	−	12.5103i	0.267880	−	0.463981i	0.968314	+	0.249736i	$0.0803437\pi$
$728$	20.8976	−	64.3163i	0.774517	−	2.38372i
$729$		0			0
$730$	−56.8943	−	41.3361i	−2.10575	−	1.52992i
$731$	−0.0679024	+	0.319456i	−0.00251146	+	0.0118155i
$732$		0			0
$733$	−7.26913	−	0.764016i	−0.268491	−	0.0282196i	−0.0306739	−	0.999529i	$-0.509765\pi$
$733$	−7.26913	−	0.764016i	−0.268491	−	0.0282196i	−0.237817	+	0.971310i	$0.576432\pi$
$734$	62.1359	+	27.6647i	2.29348	+	1.02112i
$735$		0			0
$736$	−10.9756	−	6.33674i	−0.404565	−	0.233575i
$737$	−43.1100	+	0.260675i	−1.58798	+	0.00960207i
$738$		0			0
$739$	−12.4909	−	4.05854i	−0.459485	−	0.149296i	0.0701229	−	0.997538i	$-0.477661\pi$
$739$	−12.4909	−	4.05854i	−0.459485	−	0.149296i	−0.529608	+	0.848243i	$0.677661\pi$
$740$	−57.2929	+	6.02173i	−2.10613	+	0.221363i
$741$		0			0
$742$	7.83150	−	8.69776i	0.287503	−	0.319305i
$743$	23.6688	−	26.2868i	0.868323	−	0.964370i	−0.131313	−	0.991341i	$-0.541919\pi$
$743$	23.6688	−	26.2868i	0.868323	−	0.964370i	0.999636	+	0.0269705i	$0.00858600\pi$
$744$		0			0
$745$	45.5995	−	4.79270i	1.67063	−	0.175591i
$746$	−14.7768	−	4.80127i	−0.541017	−	0.175787i
$747$		0			0
$748$	0.270584	−	0.850230i	0.00989352	−	0.0310875i
$749$	−51.9880	−	30.0153i	−1.89960	−	1.09674i
$750$		0			0
$751$	−21.0742	−	9.38284i	−0.769009	−	0.342385i	−0.0155493	−	0.999879i	$-0.504950\pi$
$751$	−21.0742	−	9.38284i	−0.769009	−	0.342385i	−0.753460	+	0.657494i	$0.771616\pi$
$752$	−8.54306	−	0.897912i	−0.311533	−	0.0327435i
$753$		0			0
$754$	−4.18244	+	19.6768i	−0.152315	+	0.716588i
$755$	2.16285	+	1.57140i	0.0787141	+	0.0571892i
$756$		0			0
$757$	3.02640	−	9.31430i	0.109996	−	0.338534i	−0.880874	−	0.473350i	$-0.843044\pi$
$757$	3.02640	−	9.31430i	0.109996	−	0.338534i	0.990871	+	0.134816i	$0.0430445\pi$
$758$	−1.82015	+	3.15259i	−0.0661108	+	0.114507i
$759$		0			0
$760$	9.66246	+	16.7359i	0.350494	+	0.607074i
$761$	−47.3669	+	10.0682i	−1.71705	+	0.364970i	−0.958157	−	0.286244i	$-0.907593\pi$
$761$	−47.3669	+	10.0682i	−1.71705	+	0.364970i	−0.758894	+	0.651215i	$0.774260\pi$
$762$		0			0
$763$	55.2379	−	24.5935i	1.99975	−	0.890345i
$764$	72.6303	−	23.5990i	2.62767	−	0.853783i
$765$		0			0
$766$	−18.6646	+	25.6897i	−0.674381	+	0.928205i
$767$	−0.282216	−	2.68510i	−0.0101902	−	0.0969535i
$768$		0			0
$769$	−28.9445	+	16.7111i	−1.04377	+	0.602619i	−0.920898	−	0.389804i	$-0.872543\pi$
$769$	−28.9445	+	16.7111i	−1.04377	+	0.602619i	−0.122869	+	0.992423i	$0.539209\pi$
$770$	−6.99517	+	70.6622i	−0.252089	+	2.54649i
$771$		0			0
$772$	−13.5924	+	12.2387i	−0.489203	+	0.440480i
$773$	−3.82924	−	5.27050i	−0.137728	−	0.189567i	0.734581	−	0.678521i	$-0.237379\pi$
$773$	−3.82924	−	5.27050i	−0.137728	−	0.189567i	−0.872310	+	0.488954i	$0.837379\pi$
$774$		0			0
$775$	−0.0280083	−	0.0862007i	−0.00100609	−	0.00309642i
$776$	−57.7127	−	12.2672i	−2.07177	−	0.440368i
$777$		0			0
$778$	14.3227	−	32.1693i	0.513494	−	1.15333i
$779$	4.20515	+	19.7837i	0.150665	+	0.708824i
$780$		0			0
$781$	0.750645	−	3.63958i	0.0268602	−	0.130234i
$782$			0.578780i			0.0206971i
$783$		0			0
$784$	10.5220	−	7.64471i	0.375787	−	0.273025i
$785$	1.58473	+	3.55937i	0.0565616	+	0.127039i
$786$		0			0
$787$	−21.5467	−	19.4007i	−0.768057	−	0.691562i	0.188834	−	0.982009i	$-0.439529\pi$
$787$	−21.5467	−	19.4007i	−0.768057	−	0.691562i	−0.956891	+	0.290447i	$0.906196\pi$
$788$	1.89707	−	18.0495i	0.0675805	−	0.642985i
$789$		0			0
$790$	2.33347	+	2.59158i	0.0830211	+	0.0922042i
$791$	−45.5606			−1.61995
$792$		0			0
$793$	−17.5974			−0.624901
$794$	−32.5816	−	36.1856i	−1.15628	−	1.28418i
$795$		0			0
$796$	−8.94190	+	85.0765i	−0.316937	+	3.01546i
$797$	−20.1023	−	18.1002i	−0.712059	−	0.641141i	0.231312	−	0.972880i	$-0.425698\pi$
$797$	−20.1023	−	18.1002i	−0.712059	−	0.641141i	−0.943371	+	0.331738i	$0.892365\pi$
$798$		0			0
$799$	−0.192881	−	0.433219i	−0.00682366	−	0.0153262i
$800$	−0.171943	+	0.124924i	−0.00607910	+	0.00441672i
$801$		0			0
$802$			63.5768i			2.24498i
$803$	−18.1942	−	40.2088i	−0.642060	−	1.41894i
$804$		0			0
$805$	−6.11075	−	28.7488i	−0.215376	−	1.01326i
$806$	−7.45044	+	16.7340i	−0.262431	+	0.589429i
$807$		0			0
$808$	−6.04302	−	1.28448i	−0.212593	−	0.0451880i
$809$	12.9385	+	39.8205i	0.454892	+	1.40001i	0.871262	+	0.490818i	$0.163302\pi$
$809$	12.9385	+	39.8205i	0.454892	+	1.40001i	−0.416370	+	0.909195i	$0.636698\pi$
$810$		0			0
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	0.656341	−	0.754464i	$-0.272103\pi$
$811$	−7.51871	−	10.3486i	−0.264018	−	0.363389i	−0.920359	+	0.391075i	$0.872103\pi$
$812$	−19.5250	+	17.5804i	−0.685193	+	0.616951i
$813$		0			0
$814$	−51.8981	−	22.7315i	−1.81903	−	0.796739i
$815$	1.95201	−	1.12699i	0.0683760	−	0.0394769i
$816$		0			0
$817$	−1.07206	−	10.1999i	−0.0375065	−	0.356851i
$818$	−8.43637	+	11.6117i	−0.294971	+	0.405992i
$819$		0			0
$820$	63.6493	−	20.6809i	2.22273	−	0.722208i
$821$	−10.8368	+	4.82484i	−0.378206	+	0.168388i	−0.587030	−	0.809565i	$-0.699703\pi$
$821$	−10.8368	+	4.82484i	−0.378206	+	0.168388i	0.208824	+	0.977953i	$0.433036\pi$
$822$		0			0
$823$	−25.7019	+	5.46311i	−0.895912	+	0.190432i	−0.632783	−	0.774329i	$-0.718088\pi$
$823$	−25.7019	+	5.46311i	−0.895912	+	0.190432i	−0.263128	+	0.964761i	$0.584754\pi$
$824$	5.79604	+	10.0390i	0.201914	+	0.349726i
$825$		0			0
$826$	2.76313	−	4.78588i	0.0961415	−	0.166522i
$827$	7.99992	−	24.6212i	0.278184	−	0.856163i	−0.710175	−	0.704025i	$-0.751384\pi$
$827$	7.99992	−	24.6212i	0.278184	−	0.856163i	0.988359	−	0.152138i	$-0.0486159\pi$
$828$		0			0
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	0.317080	−	0.948399i	$-0.397298\pi$
$829$	−14.0195	−	10.1858i	−0.486918	−	0.353766i	−0.803998	+	0.594632i	$0.797298\pi$
$830$	11.2200	−	52.7858i	0.389451	−	1.83222i
$831$		0			0
$832$	55.5066	+	5.83398i	1.92435	+	0.202257i
$833$	0.655920	+	0.292034i	0.0227263	+	0.0101184i
$834$		0			0
$835$	−26.3191	−	15.1953i	−0.910809	−	0.525856i
$836$	0.169424	+	28.0191i	0.00585965	+	0.969061i
$837$		0			0
$838$	79.7307	+	25.9061i	2.75425	+	0.894911i
$839$	−30.8808	+	3.24571i	−1.06612	+	0.112054i	−0.621307	−	0.783567i	$-0.713398\pi$
$839$	−30.8808	+	3.24571i	−1.06612	+	0.112054i	−0.444818	+	0.895621i	$0.646731\pi$
$840$		0			0
$841$	−17.1413	+	19.0373i	−0.591079	+	0.656460i
$842$	22.5058	−	24.9952i	0.775601	−	0.861392i
$843$		0			0
$844$	−65.7327	+	6.90879i	−2.26261	+	0.237810i
$845$	18.4888	+	6.00737i	0.636033	+	0.206660i
$846$		0			0
$847$	−25.7549	+	36.3654i	−0.884949	+	1.24953i
$848$	−1.47088	−	0.849211i	−0.0505101	−	0.0291620i
$849$		0			0
$850$	0.00886694	+	0.00394782i	0.000304134	+	0.000135409i
$851$	23.3231	+	2.45136i	0.799507	+	0.0840315i
$852$		0			0
$853$	−0.0664004	+	0.312389i	−0.00227351	+	0.0106960i	−0.979270	−	0.202561i	$-0.935074\pi$
$853$	−0.0664004	+	0.312389i	−0.00227351	+	0.0106960i	0.976996	+	0.213257i	$0.0684070\pi$
$854$	−29.1400	−	21.1714i	−0.997150	−	0.724472i
$855$		0			0
$856$	−16.4296	+	50.5652i	−0.561553	+	1.72828i
$857$	−6.62378	+	11.4727i	−0.226264	+	0.391901i	−0.956698	−	0.291083i	$-0.905985\pi$
$857$	−6.62378	+	11.4727i	−0.226264	+	0.391901i	0.730434	+	0.682983i	$0.239318\pi$
$858$		0			0
$859$	4.29076	+	7.43181i	0.146399	+	0.253570i	0.929894	−	0.367828i	$-0.119898\pi$
$859$	4.29076	+	7.43181i	0.146399	+	0.253570i	−0.783495	+	0.621398i	$0.786565\pi$
$860$	−33.1949	+	7.05580i	−1.13194	+	0.240601i
$861$		0			0
$862$	−18.6907	+	8.32163i	−0.636607	+	0.283436i
$863$	51.0889	−	16.5998i	1.73909	−	0.565063i	0.744374	−	0.667763i	$-0.232748\pi$
$863$	51.0889	−	16.5998i	1.73909	−	0.565063i	0.994712	+	0.102700i	$0.0327482\pi$
$864$		0			0
$865$	−9.94098	+	13.6826i	−0.338004	+	0.465222i
$866$	9.22779	+	87.7966i	0.313573	+	2.98345i
$867$		0			0
$868$	−20.7189	+	11.9620i	−0.703245	+	0.406018i
$869$	0.467953	+	2.13790i	0.0158742	+	0.0725232i
$870$		0			0
$871$	−44.9433	+	40.4671i	−1.52284	+	1.37118i
$872$	−31.4774	−	43.3249i	−1.06596	−	1.46717i
$873$		0			0
$874$	−5.61659	−	17.2861i	−0.189984	−	0.584710i
$875$	44.0596	+	9.36517i	1.48949	+	0.316600i
$876$		0			0
$877$	−17.9027	+	40.2101i	−0.604531	+	1.35780i	0.309013	+	0.951058i	$0.400001\pi$
$877$	−17.9027	+	40.2101i	−0.604531	+	1.35780i	−0.913544	+	0.406741i	$0.866665\pi$
$878$	15.8685	+	74.6552i	0.535535	+	2.51949i
$879$		0			0
$880$	10.2411	−	1.13903i	0.345228	−	0.0383968i
$881$		−	7.44194i		−	0.250725i	−0.992111	−	0.125363i	$-0.959991\pi$
$881$		−	7.44194i		−	0.250725i	0.992111	−	0.125363i	$-0.0400095\pi$
$882$		0			0
$883$	7.59369	−	5.51714i	0.255548	−	0.185667i	−0.452634	−	0.891696i	$-0.649516\pi$
$883$	7.59369	−	5.51714i	0.255548	−	0.185667i	0.708182	+	0.706030i	$0.249516\pi$
$884$	−0.509101	−	1.14346i	−0.0171229	−	0.0384587i
$885$		0			0
$886$	−32.8808	−	29.6060i	−1.10465	−	0.994633i
$887$	−2.52799	+	24.0522i	−0.0848816	+	0.807595i	0.866416	+	0.499322i	$0.166418\pi$
$887$	−2.52799	+	24.0522i	−0.0848816	+	0.807595i	−0.951298	+	0.308273i	$0.900249\pi$
$888$		0			0
$889$	16.4308	+	18.2483i	0.551072	+	0.612028i
$890$	34.8267			1.16739
$891$		0			0
$892$	−19.3542			−0.648026
$893$	9.96472	+	11.0669i	0.333457	+	0.370341i
$894$		0			0
$895$	2.93750	−	27.9485i	0.0981899	−	0.934214i
$896$	61.2507	+	55.1504i	2.04624	+	1.84244i
$897$		0			0
$898$	6.90523	+	15.5094i	0.230431	+	0.517555i
$899$	2.49197	−	1.81052i	0.0831119	−	0.0603843i
$900$		0			0
$901$		−	0.0937613i		−	0.00312364i
$902$	64.4639	+	13.2953i	2.14641	+	0.442686i
$903$		0			0
$904$	8.38958	+	39.4699i	0.279033	+	1.31275i
$905$	−16.4601	+	36.9700i	−0.547152	+	1.22892i
$906$		0			0
$907$	35.0511	+	7.45035i	1.16385	+	0.247385i	0.749042	−	0.662523i	$-0.230514\pi$
$907$	35.0511	+	7.45035i	1.16385	+	0.247385i	0.414812	+	0.909907i	$0.363848\pi$
$908$	14.9980	+	46.1592i	0.497728	+	1.53185i
$909$		0			0
$910$	58.5502	+	80.5875i	1.94092	+	2.67145i
$911$	−6.50944	+	5.86113i	−0.215668	+	0.194188i	−0.769883	−	0.638186i	$-0.779685\pi$
$911$	−6.50944	+	5.86113i	−0.215668	+	0.194188i	0.554215	+	0.832374i	$0.313019\pi$
$912$		0			0
$913$	22.5085	−	25.3043i	0.744924	−	0.837450i
$914$	−8.59575	+	4.96276i	−0.284322	+	0.164154i
$915$		0			0
$916$	7.78937	+	74.1109i	0.257368	+	2.44869i
$917$	17.0273	−	23.4360i	0.562290	−	0.773926i
$918$		0			0
$919$	−39.4876	+	12.8303i	−1.30258	+	0.423233i	−0.876477	−	0.481443i	$-0.840113\pi$
$919$	−39.4876	+	12.8303i	−1.30258	+	0.423233i	−0.426100	+	0.904676i	$0.640113\pi$
$920$	−23.7803	+	10.5877i	−0.784015	+	0.349066i
$921$		0			0
$922$	32.6340	−	6.93657i	1.07474	−	0.228444i
$923$	−2.60659	−	4.51474i	−0.0857969	−	0.148605i
$924$		0			0
$925$	0.196640	−	0.340591i	0.00646550	−	0.0111986i
$926$	−29.3323	+	90.2756i	−0.963920	+	2.96664i
$927$		0			0
$928$	−5.84339	−	4.24547i	−0.191819	−	0.139364i
$929$	−11.2664	+	53.0043i	−0.369639	+	1.73901i	0.263210	+	0.964739i	$0.415219\pi$
$929$	−11.2664	+	53.0043i	−0.369639	+	1.73901i	−0.632849	+	0.774276i	$0.718114\pi$
$930$		0			0
$931$	−22.4239	−	2.35685i	−0.734915	−	0.0772426i
$932$	−48.2097	−	21.4643i	−1.57916	−	0.703088i
$933$		0			0
$934$	23.0065	+	13.2828i	0.752795	+	0.434626i
$935$	0.337136	+	0.458176i	0.0110255	+	0.0149839i
$936$		0			0
$937$	−16.5444	−	5.37559i	−0.540480	−	0.175613i	0.0260393	−	0.999661i	$-0.491710\pi$
$937$	−16.5444	−	5.37559i	−0.540480	−	0.175613i	−0.566520	+	0.824048i	$0.691710\pi$
$938$	−123.109	+	12.9393i	−4.01965	+	0.422482i
$939$		0			0
$940$	32.9723	−	36.6194i	1.07544	−	1.19439i
$941$	−14.3933	+	15.9854i	−0.469207	+	0.521108i	−0.930575	−	0.366101i	$-0.880692\pi$
$941$	−14.3933	+	15.9854i	−0.469207	+	0.521108i	0.461368	+	0.887209i	$0.347359\pi$
$942$		0			0
$943$	−27.0949	+	2.84779i	−0.882331	+	0.0927367i
$944$	−0.762692	−	0.247814i	−0.0248235	−	0.00806564i
$945$		0			0
$946$	−31.8049	−	10.1218i	−1.03407	−	0.329089i
$947$	−38.7882	−	22.3944i	−1.26045	−	0.727719i	−0.287286	−	0.957845i	$-0.592753\pi$
$947$	−38.7882	−	22.3944i	−1.26045	−	0.727719i	−0.973161	+	0.230126i	$0.926086\pi$
$948$		0			0
$949$	−56.5594	−	25.1819i	−1.83600	−	0.817438i
$950$	−0.303134	−	0.0318607i	−0.00983497	−	0.00103370i
$951$		0			0
$952$	0.230551	−	1.08466i	0.00747220	−	0.0351540i
$953$	8.11741	+	5.89765i	0.262949	+	0.191043i	0.711446	−	0.702741i	$-0.248041\pi$
$953$	8.11741	+	5.89765i	0.262949	+	0.191043i	−0.448497	+	0.893784i	$0.648041\pi$
$954$		0			0
$955$	−15.0454	+	46.3049i	−0.486857	+	1.49839i
$956$	9.52970	−	16.5059i	0.308213	−	0.533840i
$957$		0			0
$958$	26.9147	+	46.6176i	0.869574	+	1.50615i
$959$	42.0920	−	8.94693i	1.35922	−	0.288911i
$960$		0			0
$961$	−25.7576	+	11.4680i	−0.830890	+	0.369936i
$962$	−75.5916	+	24.5612i	−2.43717	+	0.791884i
$963$		0			0
$964$	24.2693	−	33.4039i	0.781662	−	1.07587i
$965$	−1.21890	−	11.5970i	−0.0392377	−	0.373322i
$966$		0			0
$967$	−3.74268	+	2.16084i	−0.120356	+	0.0694878i	−0.558970	−	0.829188i	$-0.688803\pi$
$967$	−3.74268	+	2.16084i	−0.120356	+	0.0694878i	0.438613	+	0.898676i	$0.355470\pi$
$968$	36.2465	+	15.6155i	1.16501	+	0.501902i
$969$		0			0
$970$	64.5857	−	58.1532i	2.07372	−	1.86719i
$971$	−33.7344	−	46.4314i	−1.08259	−	1.49005i	−0.856640	−	0.515914i	$-0.827452\pi$
$971$	−33.7344	−	46.4314i	−1.08259	−	1.49005i	−0.225947	−	0.974140i	$-0.572548\pi$
$972$		0			0
$973$	−0.0664437	−	0.204493i	−0.00213009	−	0.00655574i
$974$	17.3425	+	3.68627i	0.555690	+	0.118116i
$975$		0			0
$976$	−2.12597	+	4.77500i	−0.0680506	+	0.152844i
$977$	0.717330	+	3.37477i	0.0229494	+	0.107969i	0.988131	−	0.153611i	$-0.0490901\pi$
$977$	0.717330	+	3.37477i	0.0229494	+	0.107969i	−0.965182	+	0.261579i	$0.915757\pi$
$978$		0			0
$979$	18.9936	+	10.8133i	0.607037	+	0.345596i
$980$			74.6073i			2.38324i
$981$		0			0
$982$	−72.6315	+	52.7699i	−2.31776	+	1.68395i
$983$	−0.420841	−	0.945223i	−0.0134227	−	0.0301479i	0.906710	−	0.421755i	$-0.138586\pi$
$983$	−0.420841	−	0.945223i	−0.0134227	−	0.0301479i	−0.920132	+	0.391607i	$0.871919\pi$
$984$		0			0
$985$	8.59869	+	7.74230i	0.273977	+	0.246690i
$986$	−0.0344793	+	0.328049i	−0.00109805	+	0.0104472i
$987$		0			0
$988$	26.3014	+	29.2106i	0.836758	+	0.929314i
$989$	13.8151			0.439294
$990$		0			0
$991$	9.78910			0.310961			0.155481	−	0.987839i	$-0.450307\pi$
$991$	9.78910			0.310961			0.155481	+	0.987839i	$0.450307\pi$
$992$	−4.40085	−	4.88763i	−0.139727	−	0.155183i
$993$		0			0
$994$	1.11538	−	10.6121i	0.0353776	−	0.336595i
$995$	−40.5301	−	36.4935i	−1.28489	−	1.15692i
$996$		0			0
$997$	−4.72409	−	10.6105i	−0.149613	−	0.336037i	0.823155	−	0.567817i	$-0.192212\pi$
$997$	−4.72409	−	10.6105i	−0.149613	−	0.336037i	−0.972768	+	0.231780i	$0.925545\pi$
$998$	15.3271	−	11.1358i	0.485170	−	0.352496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.431.4		32
3.2	odd	2	inner	891.2.u.c.431.1		32
9.2	odd	6		99.2.j.a.35.1	yes	16
9.4	even	3	inner	891.2.u.c.134.1		32
9.5	odd	6	inner	891.2.u.c.134.4		32
9.7	even	3		99.2.j.a.35.4	yes	16
11.6	odd	10	inner	891.2.u.c.512.4		32
33.17	even	10	inner	891.2.u.c.512.1		32
36.7	odd	6		1584.2.cd.c.1025.4		16
36.11	even	6		1584.2.cd.c.1025.1		16
99.7	odd	30		1089.2.d.g.1088.3		16
99.29	even	30		1089.2.d.g.1088.14		16
99.50	even	30	inner	891.2.u.c.215.4		32
99.61	odd	30		99.2.j.a.17.1	✓	16
99.70	even	15		1089.2.d.g.1088.13		16
99.83	even	30		99.2.j.a.17.4	yes	16
99.92	odd	30		1089.2.d.g.1088.4		16
99.94	odd	30	inner	891.2.u.c.215.1		32
396.83	odd	30		1584.2.cd.c.17.4		16
396.259	even	30		1584.2.cd.c.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	99.61	odd	30
99.2.j.a.17.4	yes	16	99.83	even	30
99.2.j.a.35.1	yes	16	9.2	odd	6
99.2.j.a.35.4	yes	16	9.7	even	3
891.2.u.c.134.1		32	9.4	even	3	inner
891.2.u.c.134.4		32	9.5	odd	6	inner
891.2.u.c.215.1		32	99.94	odd	30	inner
891.2.u.c.215.4		32	99.50	even	30	inner
891.2.u.c.431.1		32	3.2	odd	2	inner
891.2.u.c.431.4		32	1.1	even	1	trivial
891.2.u.c.512.1		32	33.17	even	10	inner
891.2.u.c.512.4		32	11.6	odd	10	inner
1089.2.d.g.1088.3		16	99.7	odd	30
1089.2.d.g.1088.4		16	99.92	odd	30
1089.2.d.g.1088.13		16	99.70	even	15
1089.2.d.g.1088.14		16	99.29	even	30
1584.2.cd.c.17.1		16	396.259	even	30
1584.2.cd.c.17.4		16	396.83	odd	30
1584.2.cd.c.1025.1		16	36.11	even	6
1584.2.cd.c.1025.4		16	36.7	odd	6

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57299 + 1.74698i) q^{2} +(-0.368594 + 3.50694i) q^{4} +(-1.67069 - 1.50430i) q^{5} +(-1.64772 - 3.70084i) q^{7} +(-2.90269 + 2.10893i) q^{8} +O(q^{10})\)	\(q+(1.57299 + 1.74698i) q^{2} +(-0.368594 + 3.50694i) q^{4} +(-1.67069 - 1.50430i) q^{5} +(-1.64772 - 3.70084i) q^{7} +(-2.90269 + 2.10893i) q^{8} -5.28492i q^{10} +(1.64091 - 2.88226i) q^{11} +(-0.967343 - 4.55099i) q^{13} +(3.87346 - 8.69993i) q^{14} +(-1.35177 - 0.287327i) q^{16} +(-0.0235753 - 0.0725574i) q^{17} +(1.40822 + 1.93825i) q^{19} +(5.89128 - 5.30454i) q^{20} +(7.61640 - 1.66711i) q^{22} +(-2.79482 + 1.61359i) q^{23} +(0.00565702 + 0.0538229i) q^{25} +(6.42889 - 8.84860i) q^{26} +(13.5860 - 4.41435i) q^{28} +(-1.68021 + 0.748078i) q^{29} +(-1.63816 + 0.348201i) q^{31} +(1.96356 + 3.40098i) q^{32} +(0.0896728 - 0.155318i) q^{34} +(-2.81433 + 8.66162i) q^{35} +(-5.87906 - 4.27138i) q^{37} +(-1.17097 + 5.50899i) q^{38} +(8.02195 + 0.843141i) q^{40} +(7.71224 + 3.43371i) q^{41} +(-3.70733 - 2.14043i) q^{43} +(9.50306 + 6.81697i) q^{44} +(-7.21513 - 2.34434i) q^{46} +(6.18182 - 0.649735i) q^{47} +(-6.29732 + 6.99389i) q^{49} +(-0.0851293 + 0.0945457i) q^{50} +(16.3166 - 1.71494i) q^{52} +(1.16884 + 0.379779i) q^{53} +(-7.07723 + 2.34694i) q^{55} +(12.5876 + 7.26746i) q^{56} +(-3.94984 - 1.75858i) q^{58} +(0.577111 + 0.0606568i) q^{59} +(0.786366 - 3.69956i) q^{61} +(-3.18511 - 2.31412i) q^{62} +(-3.70690 + 11.4087i) q^{64} +(-5.22991 + 9.05847i) q^{65} +(-6.49920 - 11.2569i) q^{67} +(0.263144 - 0.0559330i) q^{68} +(-19.5586 + 8.70807i) q^{70} +(1.06563 - 0.346245i) q^{71} +(7.82153 - 10.7654i) q^{73} +(-1.78566 - 16.9895i) q^{74} +(-7.31639 + 4.22412i) q^{76} +(-13.3705 - 1.32361i) q^{77} +(-0.490373 + 0.441533i) q^{79} +(1.82616 + 2.51349i) q^{80} +(6.13265 + 18.8744i) q^{82} +(9.98801 + 2.12302i) q^{83} +(-0.0697608 + 0.156685i) q^{85} +(-2.09231 - 9.84353i) q^{86} +(1.31540 + 11.8269i) q^{88} +6.58983i q^{89} +(-15.2486 + 11.0787i) q^{91} +(-4.62860 - 10.3960i) q^{92} +(10.8590 + 9.77751i) q^{94} +(0.563001 - 5.35660i) q^{95} +(11.0036 + 12.2208i) q^{97} -22.1238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4}+O(q^{10}) \) 32 * q + 4 * q^4	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Introduction

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