LMFDB - Embedded newform 891.2.u.c.512.1

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			512.1
Character	$\chi$	$=$	891.512
Dual form			891.2.u.c.134.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.29943 - 0.488759i) q^{2} +(3.22139 + 1.43426i) q^{4} +(-0.467414 - 2.19901i) q^{5} +(4.02888 - 0.423453i) q^{7} +(-2.90269 - 2.10893i) q^{8} +O(q^{10})$	\(q+(-2.29943 - 0.488759i) q^{2} +(3.22139 + 1.43426i) q^{4} +(-0.467414 - 2.19901i) q^{5} +(4.02888 - 0.423453i) q^{7} +(-2.90269 - 2.10893i) q^{8} +5.28492i q^{10} +(1.67565 - 2.86220i) q^{11} +(-3.45760 - 3.11324i) q^{13} +(-9.47109 - 0.995452i) q^{14} +(0.924716 + 1.02700i) q^{16} +(-0.0235753 + 0.0725574i) q^{17} +(1.40822 - 1.93825i) q^{19} +(1.64822 - 7.75427i) q^{20} +(-5.25196 + 5.76244i) q^{22} +(2.79482 - 1.61359i) q^{23} +(-0.0494405 + 0.0220123i) q^{25} +(6.42889 + 8.84860i) q^{26} +(13.5860 + 4.41435i) q^{28} +(0.192251 + 1.82914i) q^{29} +(1.12063 - 1.24459i) q^{31} +(1.96356 + 3.40098i) q^{32} +(0.0896728 - 0.155318i) q^{34} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(-4.18544 + 3.76859i) q^{38} +(-3.28079 + 7.36878i) q^{40} +(-0.882440 + 8.39585i) q^{41} +(3.70733 + 2.14043i) q^{43} +(9.50306 - 6.81697i) q^{44} +(-7.21513 + 2.34434i) q^{46} +(-2.52822 - 5.67848i) q^{47} +(9.20554 - 1.95670i) q^{49} +(0.124444 - 0.0264513i) q^{50} +(-6.67312 - 14.9881i) q^{52} +(1.16884 - 0.379779i) q^{53} +(-7.07723 - 2.34694i) q^{55} +(-12.5876 - 7.26746i) q^{56} +(0.451943 - 4.29995i) q^{58} +(-0.236025 + 0.530122i) q^{59} +(2.81073 - 2.53079i) q^{61} +(-3.18511 + 2.31412i) q^{62} +(-3.70690 - 11.4087i) q^{64} +(-5.22991 + 9.05847i) q^{65} +(-6.49920 - 11.2569i) q^{67} +(-0.180011 + 0.199923i) q^{68} +(2.23791 + 21.2923i) q^{70} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(15.6061 - 6.94830i) q^{74} +(7.31639 - 4.22412i) q^{76} +(5.53899 - 12.2410i) q^{77} +(-0.137193 + 0.645442i) q^{79} +(1.82616 - 2.51349i) q^{80} +(6.13265 - 18.8744i) q^{82} +(-6.83259 - 7.58836i) q^{83} +(0.170574 + 0.0179280i) q^{85} +(-7.47859 - 6.73376i) q^{86} +(-10.9001 + 4.77426i) q^{88} -6.58983i q^{89} +(-15.2486 - 11.0787i) q^{91} +(11.3175 - 1.18952i) q^{92} +(3.03806 + 14.2929i) q^{94} +(-4.92045 - 2.19073i) q^{95} +(-16.0853 - 3.41903i) q^{97} -22.1238 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.29943	−	0.488759i	−1.62594	−	0.345604i	−0.697356	−	0.716725i	$-0.745641\pi$
$2$	−2.29943	−	0.488759i	−1.62594	−	0.345604i	−0.928585	+	0.371120i	$0.878974\pi$
$3$		0			0
$3$		0			0
$4$	3.22139	+	1.43426i	1.61070	+	0.717129i
$5$	−0.467414	−	2.19901i	−0.209034	−	0.983427i	−0.950088	−	0.311982i	$-0.899007\pi$
$5$	−0.467414	−	2.19901i	−0.209034	−	0.983427i	0.741054	−	0.671445i	$-0.234326\pi$
$6$		0			0
$7$	4.02888	−	0.423453i	1.52277	−	0.160050i	0.694140	−	0.719840i	$-0.255785\pi$
$7$	4.02888	−	0.423453i	1.52277	−	0.160050i	0.828634	+	0.559790i	$0.189118\pi$
$8$	−2.90269	−	2.10893i	−1.02626	−	0.745618i
$9$		0			0
$10$			5.28492i			1.67124i
$11$	1.67565	−	2.86220i	0.505227	−	0.862986i
$11$	1.67565	−	2.86220i	0.505227	−	0.862986i
$12$		0			0
$13$	−3.45760	−	3.11324i	−0.958966	−	0.863457i	0.0317372	−	0.999496i	$-0.489896\pi$
$13$	−3.45760	−	3.11324i	−0.958966	−	0.863457i	−0.990703	+	0.136039i	$0.956563\pi$
$14$	−9.47109	−	0.995452i	−2.53126	−	0.266046i
$15$		0			0
$16$	0.924716	+	1.02700i	0.231179	+	0.256750i
$17$	−0.0235753	+	0.0725574i	−0.00571786	+	0.0175978i	−0.953875	−	0.300205i	$-0.902945\pi$
$17$	−0.0235753	+	0.0725574i	−0.00571786	+	0.0175978i	0.948157	+	0.317803i	$0.102945\pi$
$18$		0			0
$19$	1.40822	−	1.93825i	0.323068	−	0.444665i	−0.616333	−	0.787486i	$-0.711382\pi$
$19$	1.40822	−	1.93825i	0.323068	−	0.444665i	0.939401	+	0.342821i	$0.111382\pi$
$20$	1.64822	−	7.75427i	0.368553	−	1.73391i
$21$		0			0
$22$	−5.25196	+	5.76244i	−1.11972	+	1.22856i
$23$	2.79482	−	1.61359i	0.582759	−	0.336456i	−0.179470	−	0.983763i	$-0.557438\pi$
$23$	2.79482	−	1.61359i	0.582759	−	0.336456i	0.762229	+	0.647307i	$0.224105\pi$
$24$		0			0
$25$	−0.0494405	+	0.0220123i	−0.00988810	+	0.00440247i
$26$	6.42889	+	8.84860i	1.26081	+	1.73535i
$27$		0			0
$28$	13.5860	+	4.41435i	2.56750	+	0.834233i
$29$	0.192251	+	1.82914i	0.0357001	+	0.339664i	0.997764	+	0.0668387i	$0.0212913\pi$
$29$	0.192251	+	1.82914i	0.0357001	+	0.339664i	−0.962064	+	0.272825i	$0.912042\pi$
$30$		0			0
$31$	1.12063	−	1.24459i	0.201271	−	0.223534i	−0.634056	−	0.773287i	$-0.718611\pi$
$31$	1.12063	−	1.24459i	0.201271	−	0.223534i	0.835328	+	0.549752i	$0.185278\pi$
$32$	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	−0.954654	−	0.297718i	$-0.903774\pi$
$37$	−5.87906	+	4.27138i	−0.966511	+	0.702211i	−0.0118571	+	0.999930i	$0.503774\pi$
$38$	−4.18544	+	3.76859i	−0.678968	+	0.611346i
$39$		0			0
$40$	−3.28079	+	7.36878i	−0.518739	+	1.16511i
$41$	−0.882440	+	8.39585i	−0.137814	+	1.31121i	0.678926	+	0.734206i	$0.262446\pi$
$41$	−0.882440	+	8.39585i	−0.137814	+	1.31121i	−0.816740	+	0.577006i	$0.804221\pi$
$42$		0			0
$43$	3.70733	+	2.14043i	0.565363	+	0.326413i	0.755295	−	0.655385i	$-0.227493\pi$
$43$	3.70733	+	2.14043i	0.565363	+	0.326413i	−0.189932	+	0.981797i	$0.560827\pi$
$44$	9.50306	−	6.81697i	1.43264	−	1.02770i
$45$		0			0
$46$	−7.21513	+	2.34434i	−1.06381	+	0.345654i
$47$	−2.52822	−	5.67848i	−0.368779	−	0.828291i	−0.998668	−	0.0516056i	$-0.983566\pi$
$47$	−2.52822	−	5.67848i	−0.368779	−	0.828291i	0.629889	−	0.776686i	$-0.283101\pi$
$48$		0			0
$49$	9.20554	−	1.95670i	1.31508	−	0.279528i
$50$	0.124444	−	0.0264513i	0.0175990	−	0.00374078i
$51$		0			0
$52$	−6.67312	−	14.9881i	−0.925395	−	2.07847i
$53$	1.16884	−	0.379779i	0.160552	−	0.0521666i	−0.227638	−	0.973746i	$-0.573100\pi$
$53$	1.16884	−	0.379779i	0.160552	−	0.0521666i	0.388190	+	0.921579i	$0.373100\pi$
$54$		0			0
$55$	−7.07723	−	2.34694i	−0.954294	−	0.316461i
$56$	−12.5876	−	7.26746i	−1.68209	−	0.971156i
$57$		0			0
$58$	0.451943	−	4.29995i	0.0593430	−	0.564611i
$59$	−0.236025	+	0.530122i	−0.0307279	+	0.0690159i	−0.928257	−	0.371938i	$-0.878693\pi$
$59$	−0.236025	+	0.530122i	−0.0307279	+	0.0690159i	0.897530	+	0.440954i	$0.145360\pi$
$60$		0			0
$61$	2.81073	−	2.53079i	0.359877	−	0.324035i	−0.469281	−	0.883049i	$-0.655487\pi$
$61$	2.81073	−	2.53079i	0.359877	−	0.324035i	0.829158	+	0.559014i	$0.188820\pi$
$62$	−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	$-0.458673\pi$
$68$	−0.180011	+	0.199923i	−0.0218296	+	0.0242442i
$69$		0			0
$70$	2.23791	+	21.2923i	0.267482	+	2.54492i
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	0.371567	−	0.928406i	$-0.378821\pi$
$71$	1.06563	+	0.346245i	0.126467	+	0.0410917i	−0.245100	+	0.969498i	$0.578821\pi$
$72$		0			0
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	0.965274	+	0.261239i	$0.0841309\pi$
$73$	7.82153	+	10.7654i	0.915441	+	1.26000i	−0.0498335	+	0.998758i	$0.515869\pi$
$74$	15.6061	−	6.94830i	1.81418	−	0.807724i
$75$		0			0
$76$	7.31639	−	4.22412i	0.839247	−	0.484540i
$77$	5.53899	−	12.2410i	0.631226	−	1.39499i
$78$		0			0
$79$	−0.137193	+	0.645442i	−0.0154354	+	0.0726179i	−0.985191	−	0.171459i	$-0.945152\pi$
$79$	−0.137193	+	0.645442i	−0.0154354	+	0.0726179i	0.969756	+	0.244077i	$0.0784851\pi$
$80$	1.82616	−	2.51349i	0.204171	−	0.281017i
$81$		0			0
$82$	6.13265	−	18.8744i	0.677238	−	2.08432i
$83$	−6.83259	−	7.58836i	−0.749974	−	0.832931i	0.240497	−	0.970650i	$-0.422690\pi$
$83$	−6.83259	−	7.58836i	−0.749974	−	0.832931i	−0.990471	+	0.137719i	$0.956023\pi$
$84$		0			0
$85$	0.170574	+	0.0179280i	0.0185013	+	0.00194457i
$86$	−7.47859	−	6.73376i	−0.806438	−	0.726120i
$87$		0			0
$88$	−10.9001	+	4.77426i	−1.16195	+	0.508937i
$89$		−	6.58983i		−	0.698520i	−0.937026	−	0.349260i	$-0.886433\pi$
$89$		−	6.58983i		−	0.698520i	0.937026	−	0.349260i	$-0.113567\pi$
$90$		0			0
$91$	−15.2486	−	11.0787i	−1.59849	−	1.16137i
$92$	11.3175	−	1.18952i	1.17993	−	0.124016i
$93$		0			0
$94$	3.03806	+	14.2929i	0.313352	+	1.47420i
$95$	−4.92045	−	2.19073i	−0.504828	−	0.224764i
$96$		0			0
$97$	−16.0853	−	3.41903i	−1.63321	−	0.347150i	−0.702157	−	0.712023i	$-0.747779\pi$
$97$	−16.0853	−	3.41903i	−1.63321	−	0.347150i	−0.931058	+	0.364872i	$0.881113\pi$
$98$	−22.1238			−2.23485
$99$		0			0
$100$	−0.190839			−0.0190839
$101$	−1.68427	−	0.358002i	−0.167591	−	0.0356226i	0.123352	−	0.992363i	$-0.460636\pi$
$101$	−1.68427	−	0.358002i	−0.167591	−	0.0356226i	−0.290943	+	0.956740i	$0.593969\pi$
$102$		0			0
$103$	−2.95154	−	1.31411i	−0.290824	−	0.129483i	0.256139	−	0.966640i	$-0.417549\pi$
$103$	−2.95154	−	1.31411i	−0.290824	−	0.129483i	−0.546963	+	0.837157i	$0.684216\pi$
$104$	3.47075	+	16.3286i	0.340335	+	1.60115i
$105$		0			0
$106$	−2.87328	+	0.301994i	−0.279078	+	0.0293323i
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.989646	−	0.143529i	$-0.0458449\pi$
$107$	11.9884	+	8.71006i	1.15896	+	0.842034i	0.169314	+	0.985562i	$0.445845\pi$
$108$		0			0
$109$		−	14.9258i		−	1.42963i	−0.699313	−	0.714815i	$-0.746511\pi$
$109$		−	14.9258i		−	1.42963i	0.699313	−	0.714815i	$-0.253489\pi$
$110$	15.1265	+	8.85567i	1.44226	+	0.844355i
$111$		0			0
$112$	4.16046	+	3.74609i	0.393126	+	0.353972i
$113$	−11.1849	−	1.17558i	−1.05219	−	0.110590i	−0.437389	−	0.899272i	$-0.644097\pi$
$113$	−11.1849	−	1.17558i	−1.05219	−	0.110590i	−0.614800	+	0.788683i	$0.710763\pi$
$114$		0			0
$115$	−4.85463	−	5.39161i	−0.452697	−	0.502771i
$116$	−2.00415	+	6.16813i	−0.186080	+	0.572697i
$117$		0			0
$118$	0.801825	−	1.10362i	0.0738139	−	0.101596i
$119$	−0.0642576	+	0.302308i	−0.00589048	+	0.0277125i
$120$		0			0
$121$	−5.38440	−	9.59209i	−0.489491	−	0.872009i
$122$	−7.70002	+	4.44561i	−0.697127	+	0.402487i
$123$		0			0
$124$	5.39505	−	2.40203i	0.484490	−	0.215709i
$125$	−6.53559	−	8.99547i	−0.584561	−	0.804580i
$126$		0			0
$127$	−5.76481	−	1.87310i	−0.511544	−	0.166211i	0.0418604	−	0.999123i	$-0.486672\pi$
$127$	−5.76481	−	1.87310i	−0.511544	−	0.166211i	−0.553404	+	0.832913i	$0.686672\pi$
$128$	2.12668	+	20.2340i	0.187974	+	1.78845i
$129$		0			0
$130$	16.4532	−	18.2731i	1.44304	−	1.60266i
$131$	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
$137$	−7.89402	+	7.10781i	−0.674432	+	0.607261i	−0.933491	−	0.358600i	$-0.883254\pi$
$137$	−7.89402	+	7.10781i	−0.674432	+	0.607261i	0.259059	+	0.965861i	$0.416587\pi$
$138$		0			0
$139$	−0.0215881	+	0.0484877i	−0.00183108	+	0.00411267i	−0.914459	−	0.404679i	$-0.867383\pi$
$139$	−0.0215881	+	0.0484877i	−0.00183108	+	0.00411267i	0.912628	+	0.408792i	$0.134050\pi$
$140$	3.35692	−	31.9390i	0.283712	−	2.69934i
$141$		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
$146$	−12.7234	−	28.5771i	−1.05299	−	2.36506i
$147$		0			0
$148$	−25.0650	+	5.32773i	−2.06033	+	0.437937i
$149$	19.9493	−	4.24035i	1.63431	−	0.347383i	0.702880	−	0.711309i	$-0.251897\pi$
$149$	19.9493	−	4.24035i	1.63431	−	0.347383i	0.931428	+	0.363926i	$0.118564\pi$
$150$		0			0
$151$	0.483681	+	1.08637i	0.0393614	+	0.0884072i	0.932156	−	0.362057i	$-0.117925\pi$
$151$	0.483681	+	1.08637i	0.0393614	+	0.0884072i	−0.892795	+	0.450464i	$0.851259\pi$
$152$	−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
$157$	0.181157	−	1.72359i	0.0144579	−	0.137558i	−0.984912	−	0.173057i	$-0.944635\pi$
$157$	0.181157	−	1.72359i	0.0144579	−	0.137558i	0.999370	+	0.0354993i	$0.0113022\pi$
$158$	0.630930	−	1.41709i	0.0501941	−	0.112738i
$159$		0			0
$160$	6.56100	−	5.90755i	0.518692	−	0.467033i
$161$	10.5767	−	7.68443i	0.833561	−	0.605618i
$162$		0			0
$163$	−0.309821	−	0.953532i	−0.0242671	−	0.0746864i	0.938190	−	0.346122i	$-0.112502\pi$
$163$	−0.309821	−	0.953532i	−0.0242671	−	0.0746864i	−0.962457	+	0.271435i	$0.912502\pi$
$164$	−14.8845	+	25.7807i	−1.16228	+	2.01314i
$165$		0			0
$166$	12.0022	+	20.7884i	0.931550	+	1.61349i
$167$	−9.04541	+	10.0459i	−0.699955	+	0.777379i	−0.983369	−	0.181619i	$-0.941866\pi$
$167$	−9.04541	+	10.0459i	−0.699955	+	0.777379i	0.283414	+	0.958998i	$0.408533\pi$
$168$		0			0
$169$	0.903886	+	8.59990i	0.0695297	+	0.661531i
$170$	−0.383460	−	0.124594i	−0.0294100	−	0.00955590i
$171$		0			0
$172$	8.87286	+	12.2124i	0.676549	+	0.931190i
$173$	6.87255	−	3.05986i	0.522510	−	0.232637i	−0.128494	−	0.991710i	$-0.541014\pi$
$173$	6.87255	−	3.05986i	0.522510	−	0.232637i	0.651005	+	0.759074i	$0.274348\pi$
$174$		0			0
$175$	−0.189869	+	0.109621i	−0.0143527	+	0.00828655i
$176$	4.48898	−	0.925829i	0.338370	−	0.0697870i
$177$		0			0
$178$	−3.22083	+	15.1528i	−0.241412	+	1.13575i
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	−0.440722	−	0.897643i	$-0.645278\pi$
$179$	7.34750	−	10.1130i	0.549178	−	0.755879i	0.989900	+	0.141765i	$0.0452777\pi$
$180$		0			0
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	0.500150	+	0.865939i	$0.333278\pi$
$181$	−5.56261	+	17.1200i	−0.413466	+	1.27252i	−0.913616	+	0.406578i	$0.866722\pi$
$182$	29.6482	+	32.9276i	2.19767	+	2.44076i
$183$		0			0
$184$	−11.5154	−	1.21032i	−0.848928	−	0.0892259i
$185$	12.1408	+	10.9316i	0.892607	+	0.803707i
$186$		0			0
$187$	0.168170	+	0.189058i	0.0122978	+	0.0138253i
$188$		−	21.9187i		−	1.59859i
$189$		0			0
$190$	10.2435	+	7.44233i	0.743141	+	0.539924i
$191$	21.5383	−	2.26377i	1.55846	−	0.163801i	0.714280	−	0.699861i	$-0.246755\pi$
$191$	21.5383	−	2.26377i	1.55846	−	0.163801i	0.844180	+	0.536060i	$0.180088\pi$
$192$		0			0
$193$	1.07842	+	5.07358i	0.0776266	+	0.365204i	0.999766	−	0.0216545i	$-0.00689339\pi$
$193$	1.07842	+	5.07358i	0.0776266	+	0.365204i	−0.922139	+	0.386859i	$0.873560\pi$
$194$	35.3159	+	15.7237i	2.53553	+	1.12889i
$195$		0			0
$196$	32.4611	+	6.89982i	2.31865	+	0.492844i
$197$	−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	$0.170554\pi$
$200$	0.189933	+	0.0403715i	0.0134303	+	0.00285469i
$201$		0			0
$202$	3.69788	+	1.64640i	0.260182	+	0.115840i
$203$	1.54911	+	7.28800i	0.108726	+	0.511517i
$204$		0			0
$205$	18.8750	−	1.98385i	1.31829	−	0.138558i
$206$	6.14457	+	4.46429i	0.428113	+	0.311042i
$207$		0			0
$208$		−	6.42982i		−	0.445828i
$209$	−3.18798	−	7.27844i	−0.220517	−	0.503460i
$210$		0			0
$211$	13.9292	+	12.5419i	0.958927	+	0.863422i	0.990699	−	0.136073i	$-0.0434483\pi$
$211$	13.9292	+	12.5419i	0.958927	+	0.863422i	−0.0317716	+	0.999495i	$0.510115\pi$
$212$	4.30999	+	0.452998i	0.296011	+	0.0311121i
$213$		0			0
$214$	−23.3093	−	25.8876i	−1.59339	−	1.76964i
$215$	2.97397	−	9.15293i	0.202823	−	0.624225i
$216$		0			0
$217$	3.98787	−	5.48883i	0.270714	−	0.372606i
$218$	−7.29511	+	34.3208i	−0.494087	+	2.32450i
$219$		0			0
$220$	−19.4324	−	17.7110i	−1.31013	−	1.19407i
$221$	0.307403	−	0.177479i	0.0206781	−	0.0119385i
$222$		0			0
$223$	−5.01408	+	2.23241i	−0.335768	+	0.149493i	−0.567693	−	0.823240i	$-0.692164\pi$
$223$	−5.01408	+	2.23241i	−0.335768	+	0.149493i	0.231926	+	0.972734i	$0.425497\pi$
$224$	9.35109	+	12.8707i	0.624796	+	0.859958i
$225$		0			0
$226$	25.1444	+	8.16990i	1.67258	+	0.543454i
$227$	−1.43871	−	13.6884i	−0.0954905	−	0.908531i	−0.932458	−	0.361279i	$-0.882340\pi$
$227$	−1.43871	−	13.6884i	−0.0954905	−	0.908531i	0.836967	−	0.547253i	$-0.184326\pi$
$228$		0			0
$229$	−14.1405	+	15.7046i	−0.934431	+	1.03779i	0.0647734	+	0.997900i	$0.479368\pi$
$229$	−14.1405	+	15.7046i	−0.934431	+	1.03779i	−0.999204	+	0.0398904i	$0.987299\pi$
$230$	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	−0.980428	−	0.196877i	$-0.936920\pi$
$233$	−4.62458	−	14.2330i	−0.302967	−	0.932435i	0.677462	−	0.735558i	$-0.263080\pi$
$234$		0			0
$235$	−11.3053	+	8.21378i	−0.737477	+	0.535808i
$236$	−1.52066	+	1.36921i	−0.0989866	+	0.0891280i
$237$		0			0
$238$	0.295511	−	0.663730i	0.0191552	−	0.0430232i
$239$	0.564976	−	5.37539i	0.0365453	−	0.347705i	−0.960936	−	0.276772i	$-0.910735\pi$
$239$	0.564976	−	5.37539i	0.0365453	−	0.347705i	0.997481	−	0.0709336i	$-0.0225978\pi$
$240$		0			0
$241$	10.1404	+	5.85457i	0.653202	+	0.377126i	0.789682	−	0.613517i	$-0.210246\pi$
$241$	10.1404	+	5.85457i	0.653202	+	0.377126i	−0.136480	+	0.990643i	$0.543579\pi$
$242$	7.69281	+	24.6880i	0.494513	+	1.58700i
$243$		0			0
$244$	12.6843	−	4.12137i	0.812028	−	0.263844i
$245$	−8.60560	−	19.3285i	−0.549792	−	1.23485i
$246$		0			0
$247$	−10.9033	+	2.31757i	−0.693761	+	0.147463i
$248$	−5.87758	+	1.24932i	−0.373227	+	0.0793318i
$249$		0			0
$250$	10.6315	+	23.8788i	0.672396	+	1.51023i
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.461671	−	0.887051i	$-0.347250\pi$
$251$	21.4920	−	6.98319i	1.35657	−	0.440775i	0.894895	+	0.446276i	$0.147250\pi$
$252$		0			0
$253$	0.0647190	−	10.7031i	0.00406885	−	0.672900i
$254$	12.3403	+	7.12466i	0.774297	+	0.447041i
$255$		0			0
$256$	2.49159	−	23.7059i	0.155725	−	1.48162i
$257$	11.1919	−	25.1375i	0.698133	−	1.56803i	−0.119852	−	0.992792i	$-0.538242\pi$
$257$	11.1919	−	25.1375i	0.698133	−	1.56803i	0.817985	−	0.575240i	$-0.195091\pi$
$258$		0			0
$259$	−21.8773	+	19.6984i	−1.35939	+	1.22400i
$260$	−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
$266$	−15.2668	+	16.9555i	−0.936069	+	1.03961i
$267$		0			0
$268$	−4.79113	−	45.5846i	−0.292665	−	2.78452i
$269$	−25.7177	−	8.35619i	−1.56804	−	0.509486i	−0.609097	−	0.793096i	$-0.708468\pi$
$269$	−25.7177	−	8.35619i	−1.56804	−	0.509486i	−0.958940	+	0.283610i	$0.908468\pi$
$270$		0			0
$271$	8.74690	+	12.0391i	0.531336	+	0.731322i	0.987333	−	0.158660i	$-0.0507172\pi$
$271$	8.74690	+	12.0391i	0.531336	+	0.731322i	−0.455997	+	0.889981i	$0.650717\pi$
$272$	−0.0963170	+	0.0428831i	−0.00584008	+	0.00260017i
$273$		0			0
$274$	21.6257	−	12.4856i	1.30646	−	0.754284i
$275$	−0.0198412	+	0.178394i	−0.00119647	+	0.0107575i
$276$		0			0
$277$	1.63831	−	7.70765i	0.0984366	−	0.463108i	−0.901127	−	0.433556i	$-0.857259\pi$
$277$	1.63831	−	7.70765i	0.0984366	−	0.463108i	0.999563	−	0.0295520i	$-0.00940805\pi$
$278$	0.0733391	−	0.100943i	0.00439859	−	0.00605414i
$279$		0			0
$280$	−10.0976	+	31.0772i	−0.603447	+	1.85722i
$281$	14.2054	+	15.7767i	0.847426	+	0.941161i	0.998881	−	0.0473027i	$-0.0150625\pi$
$281$	14.2054	+	15.7767i	0.847426	+	0.941161i	−0.151455	+	0.988464i	$0.548396\pi$
$282$		0			0
$283$	4.27158	+	0.448961i	0.253919	+	0.0266880i	0.230633	−	0.973041i	$-0.425920\pi$
$283$	4.27158	+	0.448961i	0.253919	+	0.0266880i	0.0232863	+	0.999729i	$0.492587\pi$
$284$	2.93622	+	2.64378i	0.174232	+	0.156880i
$285$		0			0
$286$	36.0990	−	3.57361i	2.13458	−	0.211312i
$287$			34.1996i			2.01874i
$288$		0			0
$289$	13.7486	+	9.98893i	0.808740	+	0.587584i
$290$	−9.66688	+	1.01603i	−0.567658	+	0.0596633i
$291$		0			0
$292$	9.75586	+	45.8977i	0.570919	+	2.68596i
$293$	−17.4446	−	7.76685i	−1.01913	−	0.453744i	−0.171978	−	0.985101i	$-0.555016\pi$
$293$	−17.4446	−	7.76685i	−1.01913	−	0.453744i	−0.847148	+	0.531356i	$0.821683\pi$
$294$		0			0
$295$	1.27606	+	0.271236i	0.0742953	+	0.0157920i
$296$	26.0731			1.51547
$297$		0			0
$298$	−47.9444			−2.77735
$299$	−14.6868	−	3.12178i	−0.849362	−	0.180537i
$300$		0			0
$301$	15.8428	+	7.05366i	0.913163	+	0.406566i
$302$	−0.581220	−	2.73442i	−0.0334454	−	0.157348i
$303$		0			0
$304$	3.29279	−	0.346086i	0.188854	−	0.0198494i
$305$	−6.87902	−	4.99790i	−0.393891	−	0.286179i
$306$		0			0
$307$		−	1.86240i		−	0.106293i	−0.998587	−	0.0531463i	$-0.983075\pi$
$307$		−	1.86240i		−	0.106293i	0.998587	−	0.0531463i	$-0.0169250\pi$
$308$	35.4001	−	31.4889i	2.01711	−	1.79424i
$309$		0			0
$310$	6.57754	+	5.92244i	0.373579	+	0.336372i
$311$	−8.90556	−	0.936012i	−0.504988	−	0.0530763i	−0.151390	−	0.988474i	$-0.548375\pi$
$311$	−8.90556	−	0.936012i	−0.504988	−	0.0530763i	−0.353597	+	0.935398i	$0.615042\pi$
$312$		0			0
$313$	11.4668	+	12.7352i	0.648142	+	0.719834i	0.974243	−	0.225501i	$-0.0724017\pi$
$313$	11.4668	+	12.7352i	0.648142	+	0.719834i	−0.326101	+	0.945335i	$0.605735\pi$
$314$	−1.25898	+	3.87474i	−0.0710483	+	0.218664i
$315$		0			0
$316$	−1.36768	+	1.88245i	−0.0769381	+	0.105896i
$317$	5.67686	−	26.7075i	0.318844	−	1.50004i	−0.468463	−	0.883483i	$-0.655192\pi$
$317$	5.67686	−	26.7075i	0.318844	−	1.50004i	0.787307	−	0.616561i	$-0.211475\pi$
$318$		0			0
$319$	5.55752	+	2.51474i	0.311162	+	0.140799i
$320$	−23.3551	+	13.4841i	−1.30559	+	0.753783i
$321$		0			0
$322$	−28.0762	+	12.5003i	−1.56463	+	0.696616i
$323$	0.107435	+	0.147872i	0.00597785	+	0.00822781i
$324$		0			0
$325$	0.239475	+	0.0778102i	0.0132837	+	0.00431614i
$326$	0.246365	+	2.34401i	0.0136449	+	0.129823i
$327$		0			0
$328$	20.2677	−	22.5095i	1.11910	−	1.24288i
$329$	−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
$335$	−21.7163	+	19.5534i	−1.18649	+	1.06832i
$336$		0			0
$337$	−6.73993	+	15.1381i	−0.367147	+	0.824627i	0.631634	+	0.775267i	$0.282385\pi$
$337$	−6.73993	+	15.1381i	−0.367147	+	0.824627i	−0.998781	+	0.0493597i	$0.984282\pi$
$338$	2.12485	−	20.2166i	0.115577	−	1.09964i
$339$		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
$344$	−6.24722	−	14.0315i	−0.336828	−	0.756527i
$345$		0			0
$346$	−17.2985	+	3.67690i	−0.929972	+	0.197672i
$347$	−2.46314	+	0.523557i	−0.132228	+	0.0281060i	−0.273550	−	0.961858i	$-0.588198\pi$
$347$	−2.46314	+	0.523557i	−0.132228	+	0.0281060i	0.141322	+	0.989964i	$0.454865\pi$
$348$		0			0
$349$	3.55059	+	7.97475i	0.190059	+	0.426879i	0.983291	−	0.182040i	$-0.0582701\pi$
$349$	3.55059	+	7.97475i	0.190059	+	0.426879i	−0.793232	+	0.608919i	$0.791603\pi$
$350$	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	0.487584	−	0.873076i	$-0.337878\pi$
$353$	−0.464623	−	0.268250i	−0.0247294	−	0.0142775i	−0.512314	+	0.858798i	$0.671211\pi$
$354$		0			0
$355$	0.263304	−	2.50517i	0.0139748	−	0.132961i
$356$	9.45151	−	21.2284i	0.500929	−	1.12510i
$357$		0			0
$358$	−21.8379	+	19.6629i	−1.15417	+	1.03922i
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	−0.871655	−	0.490120i	$-0.836953\pi$
$359$	−12.7871	+	9.29040i	−0.674880	+	0.490329i	0.196775	+	0.980449i	$0.436953\pi$
$360$		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
$365$	20.0174	−	22.2315i	1.04776	−	1.16365i
$366$		0			0
$367$	−3.02435	−	28.7747i	−0.157870	−	1.50203i	−0.730894	−	0.682491i	$-0.760897\pi$
$367$	−3.02435	−	28.7747i	−0.157870	−	1.50203i	0.573024	−	0.819538i	$-0.305770\pi$
$368$	4.24157	+	1.37817i	0.221107	+	0.0718420i
$369$		0			0
$370$	−22.5739	−	31.0703i	−1.17356	−	1.61527i
$371$	4.54830	−	2.02503i	0.236136	−	0.105134i
$372$		0			0
$373$	5.72386	−	3.30467i	0.296370	−	0.171109i	−0.344441	−	0.938808i	$-0.611931\pi$
$373$	5.72386	−	3.30467i	0.296370	−	0.171109i	0.640811	+	0.767699i	$0.278598\pi$
$374$	−0.294291	−	0.516920i	−0.0152174	−	0.0267293i
$375$		0			0
$376$	−4.63685	+	21.8147i	−0.239127	+	1.12501i
$377$	5.02984	−	6.92297i	0.259050	−	0.356551i
$378$		0			0
$379$	0.478524	−	1.47275i	0.0245801	−	0.0756498i	−0.938014	−	0.346597i	$-0.887337\pi$
$379$	0.478524	−	1.47275i	0.0245801	−	0.0756498i	0.962594	+	0.270948i	$0.0873370\pi$
$380$	−12.7087	−	14.1144i	−0.651940	−	0.724053i
$381$		0			0
$382$	−50.6323	−	5.32167i	−2.59057	−	0.272280i
$383$	10.0383	+	9.03850i	0.512932	+	0.461846i	0.884487	−	0.466565i	$-0.154509\pi$
$383$	10.0383	+	9.03850i	0.512932	+	0.461846i	−0.371555	+	0.928411i	$0.621175\pi$
$384$		0			0
$385$	−29.5071	−	6.45866i	−1.50382	−	0.329164i
$386$		−	12.1934i		−	0.620629i
$387$		0			0
$388$	−46.9133	−	34.0845i	−2.38166	−	1.73038i
$389$	14.8974	−	1.56578i	0.755329	−	0.0793882i	0.280966	−	0.959718i	$-0.409345\pi$
$389$	14.8974	−	1.56578i	0.755329	−	0.0793882i	0.474363	+	0.880330i	$0.342679\pi$
$390$		0			0
$391$	0.0511890	+	0.240825i	0.00258874	+	0.0121791i
$392$	−30.8474	−	13.7341i	−1.55803	−	0.693678i
$393$		0			0
$394$	11.8347	+	2.51554i	0.596222	+	0.126731i
$395$	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	$0.673987\pi$
$398$	−55.7829	−	11.8570i	−2.79615	−	0.594339i
$399$		0			0
$400$	−0.0683251	−	0.0304203i	−0.00341626	−	0.00152101i
$401$	5.62292	+	26.4538i	0.280795	+	1.32104i	0.861845	+	0.507171i	$0.169309\pi$
$401$	5.62292	+	26.4538i	0.280795	+	1.32104i	−0.581050	+	0.813868i	$0.697358\pi$
$402$		0			0
$403$	−7.74939	+	0.814494i	−0.386025	+	0.0405728i
$404$	−4.91223	−	3.56894i	−0.244392	−	0.177561i
$405$		0			0
$406$		−	17.5154i		−	0.869273i
$407$	2.37432	+	23.9844i	0.117691	+	1.18886i
$408$		0			0
$409$	4.53727	+	4.08538i	0.224354	+	0.202009i	0.773640	−	0.633625i	$-0.218434\pi$
$409$	4.53727	+	4.08538i	0.224354	+	0.202009i	−0.549287	+	0.835634i	$0.685100\pi$
$410$	−44.3714	−	4.66362i	−2.19135	−	0.230320i
$411$		0			0
$412$	−7.62330	−	8.46653i	−0.375573	−	0.417116i
$413$	−0.726437	+	2.23574i	−0.0357456	+	0.110014i
$414$		0			0
$415$	−13.4932	+	18.5718i	−0.662357	+	0.911656i
$416$	3.79887	−	17.8723i	0.186255	−	0.876260i
$417$		0			0
$418$	3.77313	+	18.2944i	0.184550	+	0.894809i
$419$	−30.8841	+	17.8309i	−1.50879	+	0.871098i	−0.508838	+	0.860862i	$0.669925\pi$
$419$	−30.8841	+	17.8309i	−1.50879	+	0.871098i	−0.999948	+	0.0102354i	$0.996742\pi$
$420$		0			0
$421$	13.0707	−	5.81944i	0.637026	−	0.283622i	−0.0627012	−	0.998032i	$-0.519972\pi$
$421$	13.0707	−	5.81944i	0.637026	−	0.283622i	0.699727	+	0.714410i	$0.253305\pi$
$422$	−25.8993	−	35.6473i	−1.26076	−	1.73528i
$423$		0			0
$424$	−4.19370	−	1.36262i	−0.203664	−	0.0661745i
$425$	−0.000431581	−	0.00410622i	−2.09348e−5	−	0.000199181i
$426$		0			0
$427$	10.2524	−	11.3865i	0.496150	−	0.551031i
$428$	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	0.865156	−	0.501503i	$-0.167219\pi$
$431$	−2.68944	−	8.27725i	−0.129546	−	0.398701i	−0.994702	+	0.102802i	$0.967219\pi$
$432$		0			0
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.476673	−	0.879080i	$-0.341842\pi$
$433$	30.3812	−	22.0733i	1.46003	−	1.06077i	0.983355	−	0.181693i	$-0.0581576\pi$
$434$	−11.8525	+	10.6721i	−0.568939	+	0.512275i
$435$		0			0
$436$	21.4074	−	48.0818i	1.02523	−	2.30270i
$437$	0.808182	−	7.68934i	0.0386606	−	0.367831i
$438$		0			0
$439$	−28.1171	−	16.2334i	−1.34196	−	0.774779i	−0.354863	−	0.934918i	$-0.615472\pi$
$439$	−28.1171	−	16.2334i	−1.34196	−	0.774779i	−0.987094	+	0.160139i	$0.948806\pi$
$440$	15.5935	+	21.7378i	0.743390	+	1.03631i
$441$		0			0
$442$	−0.793595	+	0.257855i	−0.0377474	+	0.0122649i
$443$	7.65538	+	17.1943i	0.363718	+	0.816924i	0.999003	+	0.0446461i	$0.0142160\pi$
$443$	7.65538	+	17.1943i	0.363718	+	0.816924i	−0.635285	+	0.772278i	$0.719117\pi$
$444$		0			0
$445$	−14.4911	+	3.08018i	−0.686944	+	0.146014i
$446$	12.6206	−	2.68260i	0.597604	−	0.127025i
$447$		0			0
$448$	−19.7657	−	44.3945i	−0.933842	−	2.09744i
$449$	6.86840	−	2.23168i	0.324140	−	0.105319i	−0.142427	−	0.989805i	$-0.545491\pi$
$449$	6.86840	−	2.23168i	0.324140	−	0.105319i	0.466567	+	0.884486i	$0.345491\pi$
$450$		0			0
$451$	22.5520	+	16.5942i	1.06193	+	0.781392i
$452$	−34.3450	−	19.8291i	−1.61545	−	0.932681i
$453$		0			0
$454$	−3.38212	+	32.1787i	−0.158731	+	1.51022i
$455$	−17.2349	+	38.7101i	−0.807983	+	1.81476i
$456$		0			0
$457$	−3.13770	+	2.82520i	−0.146775	+	0.132157i	−0.739248	−	0.673434i	$-0.764819\pi$
$457$	−3.13770	+	2.82520i	−0.146775	+	0.132157i	0.592472	+	0.805591i	$0.298152\pi$
$458$	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	$0.445760\pi$
$464$	−1.70076	+	1.88888i	−0.0789556	+	0.0876891i
$465$		0			0
$466$	3.67740	+	34.9881i	0.170352	+	1.62079i
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	0.546936	−	0.837174i	$-0.315794\pi$
$467$	10.7476	+	3.49210i	0.497338	+	0.161595i	−0.0495980	+	0.998769i	$0.515794\pi$
$468$		0			0
$469$	−30.9513	−	42.6008i	−1.42920	−	1.96712i
$470$	30.0103	−	13.3614i	1.38427	−	0.616317i
$471$		0			0
$472$	1.80309	−	1.04102i	0.0829942	−	0.0479167i
$473$	12.3385	−	7.02453i	0.567326	−	0.322988i
$474$		0			0
$475$	−0.0269578	+	0.126826i	−0.00123691	+	0.00581919i
$476$	−0.640587	+	0.881692i	−0.0293612	+	0.0404123i
$477$		0			0
$478$	−3.92639	+	12.0842i	−0.179589	+	0.552718i
$479$	−15.3220	−	17.0168i	−0.700079	−	0.777516i	0.283310	−	0.959028i	$-0.408567\pi$
$479$	−15.3220	−	17.0168i	−0.700079	−	0.777516i	−0.983389	+	0.181512i	$0.941901\pi$
$480$		0			0
$481$	33.6253	+	3.53416i	1.53318	+	0.161144i
$482$	−20.4557	−	18.4184i	−0.931731	−	0.838935i
$483$		0			0
$484$	−3.58773	−	38.6225i	−0.163079	−	1.75557i
$485$			36.9698i			1.67871i
$486$		0			0
$487$	6.10169	+	4.43314i	0.276494	+	0.200885i	0.717387	−	0.696675i	$-0.245338\pi$
$487$	6.10169	+	4.43314i	0.276494	+	0.200885i	−0.440893	+	0.897560i	$0.645338\pi$
$488$	−13.4959	+	1.41848i	−0.610932	+	0.0642116i
$489$		0			0
$490$	10.3410	+	48.6505i	0.467158	+	2.19781i
$491$	34.8885	+	15.5333i	1.57449	+	0.701010i	0.993599	−	0.112967i	$-0.0360356\pi$
$491$	34.8885	+	15.5333i	1.57449	+	0.701010i	0.580896	+	0.813978i	$0.302702\pi$
$492$		0			0
$493$	−0.137250	−	0.0291735i	−0.00618144	−	0.00131391i
$494$	26.2041			1.17898
$495$		0			0
$496$	2.31446			0.103922
$497$	4.43992	+	0.943735i	0.199158	+	0.0423323i
$498$		0			0
$499$	−7.36234	−	3.27793i	−0.329584	−	0.146740i	0.235273	−	0.971929i	$-0.424402\pi$
$499$	−7.36234	−	3.27793i	−0.329584	−	0.146740i	−0.564856	+	0.825189i	$0.691068\pi$
$500$	−8.15190	−	38.3517i	−0.364564	−	1.71514i
$501$		0			0
$502$	−52.8325	+	5.55292i	−2.35803	+	0.247839i
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	0.948448	−	0.316932i	$-0.102653\pi$
$503$	21.0846	+	15.3188i	0.940115	+	0.683033i	−0.00833362	+	0.999965i	$0.502653\pi$
$504$		0			0
$505$			3.87106i			0.172260i
$506$	−5.38006	+	24.5795i	−0.239173	+	1.09269i
$507$		0			0
$508$	−15.8842	−	14.3022i	−0.704748	−	0.634558i
$509$	27.8101	+	2.92296i	1.23266	+	0.129558i	0.698367	−	0.715740i	$-0.253911\pi$
$509$	27.8101	+	2.92296i	1.23266	+	0.129558i	0.534295	+	0.845298i	$0.320577\pi$
$510$		0			0
$511$	36.0707	+	40.0605i	1.59567	+	1.77217i
$512$	−4.74153	+	14.5929i	−0.209548	+	0.644922i
$513$		0			0
$514$	−38.0212	+	52.3316i	−1.67704	+	2.30825i
$515$	−1.51015	+	7.10470i	−0.0665452	+	0.313070i
$516$		0			0
$517$	−20.4894	−	2.27886i	−0.901121	−	0.100224i
$518$	59.9330	−	34.6024i	2.63331	−	1.52034i
$519$		0			0
$520$	34.2844	−	15.2644i	1.50347	−	0.669389i
$521$	18.9804	+	26.1242i	0.831545	+	1.14452i	0.987633	+	0.156781i	$0.0501117\pi$
$521$	18.9804	+	26.1242i	0.831545	+	1.14452i	−0.156088	+	0.987743i	$0.549888\pi$
$522$		0			0
$523$	16.5104	+	5.36454i	0.721948	+	0.234575i	0.646868	−	0.762602i	$-0.276079\pi$
$523$	16.5104	+	5.36454i	0.721948	+	0.234575i	0.0750804	+	0.997177i	$0.476079\pi$
$524$	2.63575	+	25.0775i	0.115143	+	1.09552i
$525$		0			0
$526$	50.3965	−	55.9710i	2.19739	−	2.44045i
$527$	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
$533$	29.1894	−	26.2823i	1.26433	−	1.13841i
$534$		0			0
$535$	13.5500	−	30.4338i	0.585817	−	1.31577i
$536$	−4.87491	+	46.3817i	−0.210564	+	2.00338i
$537$		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	−0.507686	−	0.861542i	$-0.669499\pi$
$541$	−9.58312	+	3.11375i	−0.412011	+	0.133870i	0.0956753	+	0.995413i	$0.469499\pi$
$542$	−14.2287	−	31.9581i	−0.611174	−	1.37272i
$543$		0			0
$544$	−0.293058	+	0.0622914i	−0.0125648	+	0.00267072i
$545$	−32.8219	+	6.97652i	−1.40594	+	0.298841i
$546$		0			0
$547$	9.70462	+	21.7969i	0.414939	+	0.931969i	0.993233	+	0.116140i	$0.0370522\pi$
$547$	9.70462	+	21.7969i	0.414939	+	0.931969i	−0.578293	+	0.815829i	$0.696281\pi$
$548$	−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
$553$	−0.279420	+	2.65850i	−0.0118821	+	0.113051i
$554$	−7.53436	+	16.9225i	−0.320104	+	0.718966i
$555$		0			0
$556$	−0.139088	+	0.125235i	−0.00589863	+	0.00531115i
$557$	31.6776	−	23.0151i	1.34222	−	0.975181i	0.342862	−	0.939386i	$-0.388604\pi$
$557$	31.6776	−	23.0151i	1.34222	−	0.975181i	0.999359	−	0.0357950i	$-0.0113963\pi$
$558$		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
$563$	−3.35948	+	3.73108i	−0.141585	+	0.157246i	−0.809767	−	0.586752i	$-0.800406\pi$
$563$	−3.35948	+	3.73108i	−0.141585	+	0.157246i	0.668181	+	0.743998i	$0.267073\pi$
$564$		0			0
$565$	2.64287	+	25.1452i	0.111186	+	1.05787i
$566$	−9.60276	−	3.12012i	−0.403634	−	0.131149i
$567$		0			0
$568$	−2.36299	−	3.25238i	−0.0991489	−	0.136467i
$569$	8.68706	−	3.86773i	0.364181	−	0.162144i	−0.216485	−	0.976286i	$-0.569459\pi$
$569$	8.68706	−	3.86773i	0.364181	−	0.162144i	0.580665	+	0.814142i	$0.302792\pi$
$570$		0			0
$571$	−34.4930	+	19.9146i	−1.44349	+	0.833398i	−0.998081	−	0.0619297i	$-0.980275\pi$
$571$	−34.4930	+	19.9146i	−1.44349	+	0.833398i	−0.445408	+	0.895328i	$0.646941\pi$
$572$	−54.0807	−	6.01494i	−2.26123	−	0.251497i
$573$		0			0
$574$	16.7153	−	78.6395i	0.697685	−	3.28235i
$575$	−0.102658	+	0.141297i	−0.00428115	+	0.00589249i
$576$		0			0
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	−0.999244	−	0.0388866i	$-0.987619\pi$
$577$	−4.03506	+	12.4186i	−0.167982	+	0.516994i	0.831262	+	0.555881i	$0.187619\pi$
$578$	−26.7317	−	29.6886i	−1.11189	−	1.23488i
$579$		0			0
$580$	14.5005	+	1.52407i	0.602102	+	0.0632835i
$581$	−30.7410	−	27.6793i	−1.27535	−	1.14833i
$582$		0			0
$583$	0.871561	−	3.98183i	0.0360964	−	0.164911i
$584$		−	47.7437i		−	1.97565i
$585$		0			0
$586$	36.3166	+	26.3855i	1.50022	+	1.08998i
$587$	−23.6214	+	2.48270i	−0.974958	+	0.102472i	−0.578589	−	0.815619i	$-0.696396\pi$
$587$	−23.6214	+	2.48270i	−0.974958	+	0.102472i	−0.396369	+	0.918091i	$0.629730\pi$
$588$		0			0
$589$	−0.834224	−	3.92472i	−0.0343736	−	0.161715i
$590$	−2.80165	−	1.24737i	−0.115342	−	0.0513536i
$591$		0			0
$592$	−9.82317	−	2.08798i	−0.403730	−	0.0858154i
$593$	−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
$596$	70.3462	+	14.9525i	2.88149	+	0.612480i
$597$		0			0
$598$	32.2455	+	14.3566i	1.31862	+	0.587087i
$599$	0.496033	+	2.33365i	0.0202673	+	0.0953503i	0.987119	−	0.159989i	$-0.0511460\pi$
$599$	0.496033	+	2.33365i	0.0202673	+	0.0953503i	−0.966851	+	0.255340i	$0.917813\pi$
$600$		0			0
$601$	−6.75664	+	0.710152i	−0.275609	+	0.0289677i	−0.241325	−	0.970444i	$-0.577582\pi$
$601$	−6.75664	+	0.710152i	−0.275609	+	0.0289677i	−0.0342844	+	0.999412i	$0.510915\pi$
$602$	−32.9818	−	23.9627i	−1.34424	−	0.976646i
$603$		0			0
$604$			4.19334i			0.170624i
$605$	−18.5764	+	16.3238i	−0.755237	+	0.663658i
$606$		0			0
$607$	30.0946	+	27.0973i	1.22150	+	1.09985i	0.991960	+	0.126549i	$0.0403900\pi$
$607$	30.0946	+	27.0973i	1.22150	+	1.09985i	0.229544	+	0.973298i	$0.426277\pi$
$608$	9.35708	+	0.983468i	0.379480	+	0.0398849i
$609$		0			0
$610$	13.3750	+	14.8545i	0.541540	+	0.601441i
$611$	−8.93688	+	27.5049i	−0.361547	+	1.11273i
$612$		0			0
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	−0.806606	−	0.591090i	$-0.798698\pi$
$613$	0.119072	−	0.163888i	0.00480926	−	0.00661938i	0.811415	+	0.584471i	$0.198698\pi$
$614$	−0.910262	+	4.28245i	−0.0367352	+	0.172825i
$615$		0			0
$616$	−41.8934	+	23.8506i	−1.68793	+	0.960967i
$617$	−7.00117	+	4.04213i	−0.281857	+	0.162730i	−0.634264	−	0.773117i	$-0.718697\pi$
$617$	−7.00117	+	4.04213i	−0.281857	+	0.162730i	0.352407	+	0.935847i	$0.385363\pi$
$618$		0			0
$619$	19.1722	−	8.53602i	0.770597	−	0.343092i	0.0165075	−	0.999864i	$-0.494745\pi$
$619$	19.1722	−	8.53602i	0.770597	−	0.343092i	0.754089	+	0.656772i	$0.228079\pi$
$620$	−7.80381	−	10.7410i	−0.313409	−	0.431370i
$621$		0			0
$622$	20.0202	+	6.50496i	0.802737	+	0.260825i
$623$	−2.79048	−	26.5496i	−0.111798	−	1.06369i
$624$		0			0
$625$	−16.9074	+	18.7775i	−0.676295	+	0.751101i
$626$	−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	−0.124047	−	0.992276i	$-0.539587\pi$
$631$	19.6268	−	14.2597i	0.781332	−	0.567671i	0.905378	+	0.424606i	$0.139587\pi$
$632$	1.75942	−	1.58419i	0.0699859	−	0.0630156i
$633$		0			0
$634$	−26.1071	+	58.6374i	−1.03684	+	2.32879i
$635$	−1.42441	+	13.5524i	−0.0565261	+	0.537810i
$636$		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
$641$	6.56437	+	14.7438i	0.259277	+	0.582346i	0.995539	−	0.0943509i	$-0.0300776\pi$
$641$	6.56437	+	14.7438i	0.259277	+	0.582346i	−0.736262	+	0.676697i	$0.763411\pi$
$642$		0			0
$643$	−12.3090	+	2.61635i	−0.485419	+	0.103179i	−0.444119	−	0.895968i	$-0.646483\pi$
$643$	−12.3090	+	2.61635i	−0.485419	+	0.103179i	−0.0412999	+	0.999147i	$0.513150\pi$
$644$	45.0932	−	9.58485i	1.77692	−	0.377696i
$645$		0			0
$646$	−0.174766	−	0.392530i	−0.00687607	−	0.0154439i
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.813982	−	0.580890i	$-0.802705\pi$
$647$	−28.7701	+	9.34797i	−1.13107	+	0.367507i	−0.317087	+	0.948396i	$0.602705\pi$
$648$		0			0
$649$	1.12182	+	1.56385i	0.0440352	+	0.0613865i
$650$	−0.512626	−	0.295965i	−0.0201068	−	0.0116087i
$651$		0			0
$652$	0.369553	−	3.51607i	0.0144728	−	0.137700i
$653$	7.96901	−	17.8987i	0.311851	−	0.700430i	−0.687825	−	0.725877i	$-0.741434\pi$
$653$	7.96901	−	17.8987i	0.311851	−	0.700430i	0.999676	+	0.0254470i	$0.00810090\pi$
$654$		0			0
$655$	11.9468	−	10.7570i	0.466801	−	0.420310i
$656$	−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	$-0.355797\pi$
$662$	−9.23687	+	10.2586i	−0.359001	+	0.398711i
$663$		0			0
$664$	3.82959	+	36.4361i	0.148617	+	1.41399i
$665$	−20.7516	−	6.74260i	−0.804712	−	0.261467i
$666$		0			0
$667$	3.48879	+	4.80191i	0.135086	+	0.185931i
$668$	−43.5473	+	19.3885i	−1.68490	+	0.750164i
$669$		0			0
$670$	59.4920	−	34.3477i	2.29838	−	1.32697i
$671$	−2.53384	−	12.2856i	−0.0978179	−	0.474281i
$672$		0			0
$673$	−4.52227	+	21.2756i	−0.174321	+	0.820114i	0.800886	+	0.598817i	$0.204362\pi$
$673$	−4.52227	+	21.2756i	−0.174321	+	0.820114i	−0.975206	+	0.221297i	$0.928971\pi$
$674$	22.8969	−	31.5149i	0.881955	−	1.21391i
$675$		0			0
$676$	−9.42270	+	29.0001i	−0.362411	+	1.11539i
$677$	12.6502	+	14.0494i	0.486185	+	0.539963i	0.935461	−	0.353430i	$-0.114985\pi$
$677$	12.6502	+	14.0494i	0.486185	+	0.539963i	−0.449276	+	0.893393i	$0.648318\pi$
$678$		0			0
$679$	−66.2536	−	6.96353i	−2.54258	−	0.267236i
$680$	−0.457314	−	0.411767i	−0.0175372	−	0.0157905i
$681$		0			0
$682$	1.28634	+	12.9941i	0.0492567	+	0.497569i
$683$			33.7466i			1.29128i	0.763642	+	0.645640i	$0.223409\pi$
$683$			33.7466i			1.29128i	−0.763642	+	0.645640i	$0.776591\pi$
$684$		0			0
$685$	19.3199	+	14.0367i	0.738176	+	0.536316i
$686$	−22.8367	+	2.40024i	−0.871910	+	0.0916414i
$687$		0			0
$688$	1.23001	+	5.78672i	0.0468936	+	0.220617i
$689$	−5.22372	−	2.32575i	−0.199008	−	0.0886041i
$690$		0			0
$691$	26.9313	+	5.72442i	1.02451	+	0.217767i	0.689377	−	0.724403i	$-0.257884\pi$
$691$	26.9313	+	5.72442i	1.02451	+	0.217767i	0.335136	+	0.942170i	$0.391218\pi$
$692$	26.5278			1.00844
$693$		0			0
$694$	5.91971			0.224709
$695$	0.116716	+	0.0248087i	0.00442727	+	0.000941046i
$696$		0			0
$697$	−0.588377	−	0.261963i	−0.0222864	−	0.00992254i
$698$	−4.26659	−	20.0727i	−0.161493	−	0.759765i
$699$		0			0
$700$	−0.768867	+	0.0808112i	−0.0290604	+	0.00305437i
$701$	8.43699	+	6.12983i	0.318661	+	0.231521i	0.735604	−	0.677412i	$-0.236899\pi$
$701$	8.43699	+	6.12983i	0.318661	+	0.231521i	−0.416943	+	0.908933i	$0.636899\pi$
$702$		0			0
$703$			17.4101i			0.656636i
$704$	−38.8654	−	8.50704i	−1.46479	−	0.320621i
$705$		0			0
$706$	0.937258	+	0.843911i	0.0352742	+	0.0317610i
$707$	−6.93732	−	0.729141i	−0.260905	−	0.0274222i
$708$		0			0
$709$	−13.4139	−	14.8976i	−0.503768	−	0.559491i	0.436598	−	0.899657i	$-0.356183\pi$
$709$	−13.4139	−	14.8976i	−0.503768	−	0.559491i	−0.940365	+	0.340166i	$0.889517\pi$
$710$	−1.82988	+	5.63178i	−0.0686740	+	0.211357i
$711$		0			0
$712$	−13.8975	+	19.1282i	−0.520829	+	0.716860i
$713$	1.12371	−	5.28663i	0.0420832	−	0.197986i
$714$		0			0
$715$	17.1637	+	30.1479i	0.641885	+	1.12747i
$716$	38.1738	−	22.0397i	1.42662	−	0.823660i
$717$		0			0
$718$	33.9439	−	15.1128i	1.26677	−	0.564004i
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	0.906347	−	0.422535i	$-0.138860\pi$
$719$	6.01752	+	8.28241i	0.224416	+	0.308882i	−0.681931	+	0.731417i	$0.738860\pi$
$720$		0			0
$721$	−12.4479	−	4.04456i	−0.463583	−	0.150627i
$722$	−3.25834	−	31.0011i	−0.121263	−	1.15374i
$723$		0			0
$724$	−42.4738	+	47.1719i	−1.57853	+	1.75313i
$725$	−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
$731$	−0.242706	+	0.218533i	−0.00897679	+	0.00808274i
$732$		0			0
$733$	2.97291	−	6.67726i	0.109807	−	0.246630i	−0.850281	−	0.526329i	$-0.823568\pi$
$733$	2.97291	−	6.67726i	0.109807	−	0.246630i	0.960088	+	0.279699i	$0.0902347\pi$
$734$	−7.10963	+	67.6436i	−0.262421	+	2.49677i
$735$		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	−0.529608	−	0.848243i	$-0.677661\pi$
$739$	−12.4909	+	4.05854i	−0.459485	+	0.149296i	0.0701229	+	0.997538i	$0.477661\pi$
$740$	23.4315	+	52.6280i	0.861358	+	1.93464i
$741$		0			0
$742$	−11.4482	+	2.43340i	−0.420278	+	0.0893328i
$743$	−34.5995	+	7.35434i	−1.26933	+	0.269805i	−0.792870	−	0.609391i	$-0.791414\pi$
$743$	−34.5995	+	7.35434i	−1.26933	+	0.269805i	−0.476461	+	0.879196i	$0.658081\pi$
$744$		0			0
$745$	−18.6491	−	41.8866i	−0.683251	−	1.53461i
$746$	−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
$751$	2.41132	−	22.9422i	0.0879905	−	0.837174i	−0.858146	−	0.513406i	$-0.828384\pi$
$751$	2.41132	−	22.9422i	0.0879905	−	0.837174i	0.946137	−	0.323768i	$-0.104950\pi$
$752$	3.49392	−	7.84746i	0.127410	−	0.286168i
$753$		0			0
$754$	−14.9494	+	13.4605i	−0.544425	+	0.490203i
$755$	2.16285	−	1.57140i	0.0787141	−	0.0571892i
$756$		0			0
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	0.990871	−	0.134816i	$-0.0430445\pi$
$757$	3.02640	+	9.31430i	0.109996	+	0.338534i	−0.880874	+	0.473350i	$0.843044\pi$
$758$	−1.82015	+	3.15259i	−0.0661108	+	0.114507i
$759$		0			0
$760$	9.66246	+	16.7359i	0.350494	+	0.607074i
$761$	32.4027	−	35.9869i	1.17460	−	1.30452i	0.231183	−	0.972910i	$-0.425740\pi$
$761$	32.4027	−	35.9869i	1.17460	−	1.30452i	0.943415	−	0.331614i	$-0.107593\pi$
$762$		0			0
$763$	−6.32036	−	60.1342i	−0.228812	−	2.17701i
$764$	72.6303	+	23.5990i	2.62767	+	0.853783i
$765$		0			0
$766$	−18.6646	−	25.6897i	−0.674381	−	0.928205i
$767$	2.46648	−	1.09815i	0.0890593	−	0.0396518i
$768$		0			0
$769$	28.9445	−	16.7111i	1.04377	−	0.602619i	0.122869	−	0.992423i	$-0.460791\pi$
$769$	28.9445	−	16.7111i	1.04377	−	0.602619i	0.920898	+	0.389804i	$0.127457\pi$
$770$	64.6928	+	29.2731i	2.33137	+	1.05493i
$771$		0			0
$772$	−3.80279	+	17.8907i	−0.136866	+	0.643902i
$773$	−3.82924	+	5.27050i	−0.137728	+	0.189567i	−0.872310	−	0.488954i	$-0.837379\pi$
$773$	−3.82924	+	5.27050i	−0.137728	+	0.189567i	0.734581	+	0.678521i	$0.237379\pi$
$774$		0			0
$775$	−0.0280083	+	0.0862007i	−0.00100609	+	0.00309642i
$776$	39.4801	+	43.8471i	1.41725	+	1.57402i
$777$		0			0
$778$	−35.0208	−	3.68084i	−1.25556	−	0.131964i
$779$	15.0306	+	13.5336i	0.538527	+	0.484892i
$780$		0			0
$781$	2.77665	−	2.46987i	0.0993563	−	0.0883788i
$782$		−	0.578780i		−	0.0206971i
$783$		0			0
$784$	10.5220	+	7.64471i	0.375787	+	0.273025i
$785$	−3.87487	+	0.407266i	−0.138300	+	0.0145359i
$786$		0			0
$787$	−6.02818	−	28.3604i	−0.214881	−	1.01094i	−0.944862	−	0.327470i	$-0.893804\pi$
$787$	−6.02818	−	28.3604i	−0.214881	−	1.01094i	0.729980	−	0.683468i	$-0.239529\pi$
$788$	−16.5798	−	7.38182i	−0.590632	−	0.262966i
$789$		0			0
$790$	−3.41111	−	0.725053i	−0.121362	−	0.0257962i
$791$	−45.5606			−1.61995
$792$		0			0
$793$	−17.5974			−0.624901
$794$	47.6285	+	10.1237i	1.69027	+	0.359278i
$795$		0			0
$796$	78.1494	+	34.7943i	2.76993	+	1.23325i
$797$	−5.62407	−	26.4592i	−0.199215	−	0.937232i	−0.958194	−	0.286118i	$-0.907635\pi$
$797$	−5.62407	−	26.4592i	−0.199215	−	0.937232i	0.758980	−	0.651114i	$-0.225698\pi$
$798$		0			0
$799$	0.471619	−	0.0495692i	0.0166847	−	0.00175363i
$800$	−0.171943	−	0.124924i	−0.00607910	−	0.00441672i
$801$		0			0
$802$		−	63.5768i		−	2.24498i
$803$	43.9189	−	4.34774i	1.54987	−	0.153428i
$804$		0			0
$805$	−21.8418	−	19.6665i	−0.769823	−	0.693152i
$806$	18.2173	+	1.91471i	0.641676	+	0.0674428i
$807$		0			0
$808$	4.13391	+	4.59117i	0.145430	+	0.161517i
$809$	12.9385	−	39.8205i	0.454892	−	1.40001i	−0.416370	−	0.909195i	$-0.636698\pi$
$809$	12.9385	−	39.8205i	0.454892	−	1.40001i	0.871262	−	0.490818i	$-0.163302\pi$
$810$		0			0
$811$	−7.51871	+	10.3486i	−0.264018	+	0.363389i	−0.920359	−	0.391075i	$-0.872103\pi$
$811$	−7.51871	+	10.3486i	−0.264018	+	0.363389i	0.656341	+	0.754464i	$0.272103\pi$
$812$	−5.46256	+	25.6993i	−0.191698	+	0.901870i
$813$		0			0
$814$	6.26299	−	56.3108i	0.219518	−	1.97369i
$815$	−1.95201	+	1.12699i	−0.0683760	+	0.0394769i
$816$		0			0
$817$	9.36944	−	4.17154i	0.327795	−	0.145944i
$818$	−8.43637	−	11.6117i	−0.294971	−	0.405992i
$819$		0			0
$820$	63.6493	+	20.6809i	2.22273	+	0.722208i
$821$	1.23995	+	11.7973i	0.0432746	+	0.411730i	0.994619	+	0.103601i	$0.0330364\pi$
$821$	1.23995	+	11.7973i	0.0432746	+	0.411730i	−0.951344	+	0.308130i	$0.900297\pi$
$822$		0			0
$823$	17.5821	−	19.5269i	0.612875	−	0.680666i	−0.354197	−	0.935171i	$-0.615246\pi$
$823$	17.5821	−	19.5269i	0.612875	−	0.680666i	0.967072	+	0.254505i	$0.0819124\pi$
$824$	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	0.988359	+	0.152138i	$0.0486159\pi$
$827$	7.99992	+	24.6212i	0.278184	+	0.856163i	−0.710175	+	0.704025i	$0.751384\pi$
$828$		0			0
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	−0.803998	−	0.594632i	$-0.797298\pi$
$829$	−14.0195	+	10.1858i	−0.486918	+	0.353766i	0.317080	+	0.948399i	$0.397298\pi$
$830$	40.1039	−	36.1097i	1.39203	−	1.25339i
$831$		0			0
$832$	−22.7009	+	50.9871i	−0.787013	+	1.76766i
$833$	−0.0750507	+	0.714060i	−0.00260035	+	0.0247407i
$834$		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
$839$	12.6296	+	28.3664i	0.436021	+	0.979318i	0.989243	+	0.146284i	$0.0467315\pi$
$839$	12.6296	+	28.3664i	0.436021	+	0.979318i	−0.553222	+	0.833034i	$0.686602\pi$
$840$		0			0
$841$	25.0575	−	5.32613i	0.864051	−	0.183660i
$842$	−32.8994	+	6.99298i	−1.13379	+	0.240994i
$843$		0			0
$844$	26.8832	+	60.3806i	0.925357	+	2.07839i
$845$	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
$850$	−0.00101456	+	0.00965290i	−3.47992e−5	+	0.000331092i
$851$	−9.53862	+	21.4241i	−0.326980	+	0.734409i
$852$		0			0
$853$	−0.237337	+	0.213699i	−0.00812626	+	0.00731692i	−0.673184	−	0.739475i	$-0.735074\pi$
$853$	−0.237337	+	0.213699i	−0.00812626	+	0.00731692i	0.665057	+	0.746792i	$0.268407\pi$
$854$	−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	$0.786565\pi$
$860$	22.7080	−	25.2198i	0.774336	−	0.859987i
$861$		0			0
$862$	2.13860	+	20.3474i	0.0728410	+	0.693036i
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.994712	−	0.102700i	$-0.0327482\pi$
$863$	51.0889	+	16.5998i	1.73909	+	0.565063i	0.744374	+	0.667763i	$0.232748\pi$
$864$		0			0
$865$	−9.94098	−	13.6826i	−0.338004	−	0.465222i
$866$	−80.6480	+	35.9068i	−2.74053	+	1.22016i
$867$		0			0
$868$	20.7189	−	11.9620i	0.703245	−	0.406018i
$869$	1.61750	+	1.47421i	0.0548698	+	0.0500091i
$870$		0			0
$871$	−12.5739	+	59.1556i	−0.426050	+	2.00441i
$872$	−31.4774	+	43.3249i	−1.06596	+	1.46717i
$873$		0			0
$874$	−5.61659	+	17.2861i	−0.189984	+	0.584710i
$875$	−30.1403	−	33.4742i	−1.01893	−	1.13163i
$876$		0			0
$877$	43.7743	+	4.60087i	1.47815	+	0.155360i	0.809020	−	0.587782i	$-0.199999\pi$
$877$	43.7743	+	4.60087i	1.47815	+	0.155360i	0.669134	+	0.743142i	$0.266665\pi$
$878$	56.7191	+	51.0701i	1.91418	+	1.72353i
$879$		0			0
$880$	−4.13412	−	9.43857i	−0.139361	−	0.318174i
$881$			7.44194i			0.250725i	0.992111	+	0.125363i	$0.0400095\pi$
$881$			7.44194i			0.250725i	−0.992111	+	0.125363i	$0.959991\pi$
$882$		0			0
$883$	7.59369	+	5.51714i	0.255548	+	0.185667i	0.708182	−	0.706030i	$-0.249516\pi$
$883$	7.59369	+	5.51714i	0.255548	+	0.185667i	−0.452634	+	0.891696i	$0.649516\pi$
$884$	1.24482	−	0.130835i	0.0418677	−	0.00440047i
$885$		0			0
$886$	−9.19915	−	43.2786i	−0.309052	−	1.45397i
$887$	22.0938	+	9.83681i	0.741838	+	0.330288i	0.742621	−	0.669712i	$-0.233582\pi$
$887$	22.0938	+	9.83681i	0.741838	+	0.330288i	−0.000782633		1.00000i	$0.500249\pi$
$888$		0			0
$889$	−24.0189	−	5.10537i	−0.805568	−	0.171229i
$890$	34.8267			1.16739
$891$		0			0
$892$	−19.3542			−0.648026
$893$	−14.5666	−	3.09623i	−0.487453	−	0.103611i
$894$		0			0
$895$	−25.6728	−	11.4303i	−0.858148	−	0.382072i
$896$	17.1363	+	80.6199i	0.572483	+	2.69332i
$897$		0			0
$898$	−16.8842	+	1.77460i	−0.563431	+	0.0592190i
$899$	2.49197	+	1.81052i	0.0831119	+	0.0603843i
$900$		0			0
$901$			0.0937613i			0.00312364i
$902$	−43.7461	−	49.1797i	−1.45658	−	1.63751i
$903$		0			0
$904$	29.9871	+	27.0005i	0.997357	+	0.898024i
$905$	40.2470	+	4.23013i	1.33786	+	0.140614i
$906$		0			0
$907$	−23.9778	−	26.6300i	−0.796168	−	0.884234i	0.199241	−	0.979951i	$-0.436152\pi$
$907$	−23.9778	−	26.6300i	−0.796168	−	0.884234i	−0.995409	+	0.0957163i	$0.969486\pi$
$908$	14.9980	−	46.1592i	0.497728	−	1.53185i
$909$		0			0
$910$	58.5502	−	80.5875i	1.94092	−	2.67145i
$911$	−1.82117	+	8.56791i	−0.0603379	+	0.283868i	−0.997964	−	0.0637775i	$-0.979685\pi$
$911$	−1.82117	+	8.56791i	−0.0603379	+	0.283868i	0.937626	+	0.347645i	$0.113019\pi$
$912$		0			0
$913$	−33.1684	+	6.84082i	−1.09772	+	0.226398i
$914$	8.59575	−	4.96276i	0.284322	−	0.164154i
$915$		0			0
$916$	−68.0766	+	30.3097i	−2.24931	+	1.00146i
$917$	17.0273	+	23.4360i	0.562290	+	0.773926i
$918$		0			0
$919$	−39.4876	−	12.8303i	−1.30258	−	0.423233i	−0.426100	−	0.904676i	$-0.640113\pi$
$919$	−39.4876	−	12.8303i	−1.30258	−	0.423233i	−0.876477	+	0.481443i	$0.840113\pi$
$920$	2.72096	+	25.8882i	0.0897075	+	0.853510i
$921$		0			0
$922$	−22.3242	+	24.7936i	−0.735209	+	0.816533i
$923$	−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
$929$	−40.2699	+	36.2591i	−1.32121	+	1.18962i	−0.354118	+	0.935201i	$0.615219\pi$
$929$	−40.2699	+	36.2591i	−1.32121	+	1.18962i	−0.967093	+	0.254423i	$0.918114\pi$
$930$		0			0
$931$	9.17087	−	20.5981i	0.300563	−	0.675076i
$932$	5.51618	−	52.4830i	0.180689	−	1.71914i
$933$		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	−0.566520	−	0.824048i	$-0.691710\pi$
$937$	−16.5444	+	5.37559i	−0.540480	+	0.175613i	0.0260393	+	0.999661i	$0.491710\pi$
$938$	50.3487	+	113.085i	1.64394	+	3.69236i
$939$		0			0
$940$	−48.1995	+	10.2451i	−1.57209	+	0.334159i
$941$	21.0404	−	4.47227i	0.685896	−	0.145792i	0.148234	−	0.988952i	$-0.452641\pi$
$941$	21.0404	−	4.47227i	0.685896	−	0.145792i	0.537662	+	0.843161i	$0.319308\pi$
$942$		0			0
$943$	11.0812	+	24.8888i	0.360853	+	0.810489i
$944$	−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	0.973161	−	0.230126i	$-0.0739137\pi$
$947$	38.7882	+	22.3944i	1.26045	+	0.727719i	0.287286	+	0.957845i	$0.407247\pi$
$948$		0			0
$949$	6.47156	−	61.5728i	0.210076	−	1.99874i
$950$	0.123975	−	0.278452i	0.00402228	−	0.00903418i
$951$		0			0
$952$	0.824065	−	0.741992i	0.0267081	−	0.0240481i
$953$	8.11741	−	5.89765i	0.262949	−	0.191043i	−0.448497	−	0.893784i	$-0.648041\pi$
$953$	8.11741	−	5.89765i	0.262949	−	0.191043i	0.711446	+	0.702741i	$0.248041\pi$
$954$		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
$959$	−28.7943	+	31.9793i	−0.929815	+	1.03266i
$960$		0			0
$961$	2.94720	+	28.0407i	0.0950710	+	0.904540i
$962$	−75.5916	−	24.5612i	−2.43717	−	0.791884i
$963$		0			0
$964$	24.2693	+	33.4039i	0.781662	+	1.07587i
$965$	10.6528	−	4.74292i	0.342925	−	0.152680i
$966$		0			0
$967$	3.74268	−	2.16084i	0.120356	−	0.0694878i	−0.438613	−	0.898676i	$-0.644530\pi$
$967$	3.74268	−	2.16084i	0.120356	−	0.0694878i	0.558970	+	0.829188i	$0.311197\pi$
$968$	−4.59980	+	39.1981i	−0.147843	+	1.25988i
$969$		0			0
$970$	18.0693	−	85.0095i	0.580171	−	2.72949i
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.225947	+	0.974140i	$0.572548\pi$
$971$	−33.7344	+	46.4314i	−1.08259	+	1.49005i	−0.856640	+	0.515914i	$0.827452\pi$
$972$		0			0
$973$	−0.0664437	+	0.204493i	−0.00213009	+	0.00655574i
$974$	−11.8637	−	13.1759i	−0.380136	−	0.422184i
$975$		0			0
$976$	5.19826	+	0.546359i	0.166392	+	0.0174885i
$977$	2.56397	+	2.30861i	0.0820288	+	0.0738591i	0.709125	−	0.705083i	$-0.249090\pi$
$977$	2.56397	+	2.30861i	0.0820288	+	0.0738591i	−0.627096	+	0.778942i	$0.715757\pi$
$978$		0			0
$979$	−18.8614	−	11.0422i	−0.602813	−	0.352912i
$980$		−	74.6073i		−	2.38324i
$981$		0			0
$982$	−72.6315	−	52.7699i	−2.31776	−	1.68395i
$983$	1.02901	−	0.108153i	0.0328203	−	0.00344955i	−0.0881041	−	0.996111i	$-0.528081\pi$
$983$	1.02901	−	0.108153i	0.0328203	−	0.00344955i	0.120924	+	0.992662i	$0.461414\pi$
$984$		0			0
$985$	2.40568	+	11.3178i	0.0766513	+	0.360616i
$986$	0.301338	+	0.134165i	0.00959657	+	0.00427267i
$987$		0			0
$988$	−38.4478	−	8.17234i	−1.22319	−	0.259997i
$989$	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	$0.450307\pi$
$992$	6.43324	+	1.36743i	0.204255	+	0.0434158i
$993$		0			0
$994$	−9.74803	−	4.34010i	−0.309189	−	0.137660i
$995$	−11.3392	−	53.3468i	−0.359477	−	1.69121i
$996$		0			0
$997$	11.5510	−	1.21406i	0.365823	−	0.0384496i	0.0801664	−	0.996781i	$-0.474455\pi$
$997$	11.5510	−	1.21406i	0.365823	−	0.0384496i	0.285657	+	0.958332i	$0.407788\pi$
$998$	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.512.1		32
3.2	odd	2	inner	891.2.u.c.512.4		32
9.2	odd	6		99.2.j.a.17.1	✓	16
9.4	even	3	inner	891.2.u.c.215.4		32
9.5	odd	6	inner	891.2.u.c.215.1		32
9.7	even	3		99.2.j.a.17.4	yes	16
11.2	odd	10	inner	891.2.u.c.431.1		32
33.2	even	10	inner	891.2.u.c.431.4		32
36.7	odd	6		1584.2.cd.c.17.4		16
36.11	even	6		1584.2.cd.c.17.1		16
99.2	even	30		99.2.j.a.35.4	yes	16
99.13	odd	30	inner	891.2.u.c.134.4		32
99.25	even	15		1089.2.d.g.1088.14		16
99.47	odd	30		1089.2.d.g.1088.3		16
99.52	odd	30		1089.2.d.g.1088.4		16
99.68	even	30	inner	891.2.u.c.134.1		32
99.74	even	30		1089.2.d.g.1088.13		16
99.79	odd	30		99.2.j.a.35.1	yes	16
396.79	even	30		1584.2.cd.c.1025.1		16
396.299	odd	30		1584.2.cd.c.1025.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.1	✓	16	9.2	odd	6
99.2.j.a.17.4	yes	16	9.7	even	3
99.2.j.a.35.1	yes	16	99.79	odd	30
99.2.j.a.35.4	yes	16	99.2	even	30
891.2.u.c.134.1		32	99.68	even	30	inner
891.2.u.c.134.4		32	99.13	odd	30	inner
891.2.u.c.215.1		32	9.5	odd	6	inner
891.2.u.c.215.4		32	9.4	even	3	inner
891.2.u.c.431.1		32	11.2	odd	10	inner
891.2.u.c.431.4		32	33.2	even	10	inner
891.2.u.c.512.1		32	1.1	even	1	trivial
891.2.u.c.512.4		32	3.2	odd	2	inner
1089.2.d.g.1088.3		16	99.47	odd	30
1089.2.d.g.1088.4		16	99.52	odd	30
1089.2.d.g.1088.13		16	99.74	even	30
1089.2.d.g.1088.14		16	99.25	even	15
1584.2.cd.c.17.1		16	36.11	even	6
1584.2.cd.c.17.4		16	36.7	odd	6
1584.2.cd.c.1025.1		16	396.79	even	30
1584.2.cd.c.1025.4		16	396.299	odd	30

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)

\(f(q)\)	\(=\)	\(q+(-2.29943 - 0.488759i) q^{2} +(3.22139 + 1.43426i) q^{4} +(-0.467414 - 2.19901i) q^{5} +(4.02888 - 0.423453i) q^{7} +(-2.90269 - 2.10893i) q^{8} +O(q^{10})\)	\(q+(-2.29943 - 0.488759i) q^{2} +(3.22139 + 1.43426i) q^{4} +(-0.467414 - 2.19901i) q^{5} +(4.02888 - 0.423453i) q^{7} +(-2.90269 - 2.10893i) q^{8} +5.28492i q^{10} +(1.67565 - 2.86220i) q^{11} +(-3.45760 - 3.11324i) q^{13} +(-9.47109 - 0.995452i) q^{14} +(0.924716 + 1.02700i) q^{16} +(-0.0235753 + 0.0725574i) q^{17} +(1.40822 - 1.93825i) q^{19} +(1.64822 - 7.75427i) q^{20} +(-5.25196 + 5.76244i) q^{22} +(2.79482 - 1.61359i) q^{23} +(-0.0494405 + 0.0220123i) q^{25} +(6.42889 + 8.84860i) q^{26} +(13.5860 + 4.41435i) q^{28} +(0.192251 + 1.82914i) q^{29} +(1.12063 - 1.24459i) q^{31} +(1.96356 + 3.40098i) q^{32} +(0.0896728 - 0.155318i) q^{34} +(-2.81433 - 8.66162i) q^{35} +(-5.87906 + 4.27138i) q^{37} +(-4.18544 + 3.76859i) q^{38} +(-3.28079 + 7.36878i) q^{40} +(-0.882440 + 8.39585i) q^{41} +(3.70733 + 2.14043i) q^{43} +(9.50306 - 6.81697i) q^{44} +(-7.21513 + 2.34434i) q^{46} +(-2.52822 - 5.67848i) q^{47} +(9.20554 - 1.95670i) q^{49} +(0.124444 - 0.0264513i) q^{50} +(-6.67312 - 14.9881i) q^{52} +(1.16884 - 0.379779i) q^{53} +(-7.07723 - 2.34694i) q^{55} +(-12.5876 - 7.26746i) q^{56} +(0.451943 - 4.29995i) q^{58} +(-0.236025 + 0.530122i) q^{59} +(2.81073 - 2.53079i) q^{61} +(-3.18511 + 2.31412i) q^{62} +(-3.70690 - 11.4087i) q^{64} +(-5.22991 + 9.05847i) q^{65} +(-6.49920 - 11.2569i) q^{67} +(-0.180011 + 0.199923i) q^{68} +(2.23791 + 21.2923i) q^{70} +(1.06563 + 0.346245i) q^{71} +(7.82153 + 10.7654i) q^{73} +(15.6061 - 6.94830i) q^{74} +(7.31639 - 4.22412i) q^{76} +(5.53899 - 12.2410i) q^{77} +(-0.137193 + 0.645442i) q^{79} +(1.82616 - 2.51349i) q^{80} +(6.13265 - 18.8744i) q^{82} +(-6.83259 - 7.58836i) q^{83} +(0.170574 + 0.0179280i) q^{85} +(-7.47859 - 6.73376i) q^{86} +(-10.9001 + 4.77426i) q^{88} -6.58983i q^{89} +(-15.2486 - 11.0787i) q^{91} +(11.3175 - 1.18952i) q^{92} +(3.03806 + 14.2929i) q^{94} +(-4.92045 - 2.19073i) q^{95} +(-16.0853 - 3.41903i) q^{97} -22.1238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4}+O(q^{10}) \) 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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