LMFDB - Embedded newform 225.2.m.c.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	225.109
Dual form			225.2.m.c.64.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.55211 - 2.13629i) q^{2} +(-1.53668 - 4.72941i) q^{4} +(0.398175 - 2.20033i) q^{5} +4.34551i q^{7} +(-7.46578 - 2.42578i) q^{8} +O(q^{10})$	\(q+(1.55211 - 2.13629i) q^{2} +(-1.53668 - 4.72941i) q^{4} +(0.398175 - 2.20033i) q^{5} +4.34551i q^{7} +(-7.46578 - 2.42578i) q^{8} +(-4.08254 - 4.26577i) q^{10} +(2.04985 + 1.48930i) q^{11} +(-1.30894 - 1.80161i) q^{13} +(9.28329 + 6.74470i) q^{14} +(-8.72373 + 6.33816i) q^{16} +(4.29265 + 1.39477i) q^{17} +(-0.267098 + 0.822042i) q^{19} +(-11.0181 + 1.49807i) q^{20} +(6.36317 - 2.06752i) q^{22} +(-0.209955 + 0.288979i) q^{23} +(-4.68291 - 1.75223i) q^{25} -5.88039 q^{26} +(20.5517 - 6.67765i) q^{28} +(-1.36199 - 4.19178i) q^{29} +(-0.140703 + 0.433039i) q^{31} +12.7740i q^{32} +(9.64230 - 7.00554i) q^{34} +(9.56156 + 1.73027i) q^{35} +(1.39668 + 1.92237i) q^{37} +(1.34156 + 1.84650i) q^{38} +(-8.31021 + 15.4613i) q^{40} +(2.24693 - 1.63249i) q^{41} +10.2326i q^{43} +(3.89356 - 11.9831i) q^{44} +(0.291470 + 0.897053i) q^{46} +(-7.53506 + 2.44829i) q^{47} -11.8834 q^{49} +(-11.0117 + 7.28442i) q^{50} +(-6.50911 + 8.95903i) q^{52} +(6.13570 - 1.99361i) q^{53} +(4.09315 - 3.91734i) q^{55} +(10.5412 - 32.4426i) q^{56} +(-11.0688 - 3.59648i) q^{58} +(-5.59575 + 4.06555i) q^{59} +(4.93738 + 3.58722i) q^{61} +(0.706713 + 0.972706i) q^{62} +(9.84157 + 7.15032i) q^{64} +(-4.48532 + 2.16275i) q^{65} +(10.4960 + 3.41036i) q^{67} -22.4450i q^{68} +(18.5370 - 17.7407i) q^{70} +(-2.27903 - 7.01412i) q^{71} +(-7.99599 + 11.0055i) q^{73} +6.27455 q^{74} +4.29822 q^{76} +(-6.47177 + 8.90762i) q^{77} +(-3.33214 - 10.2553i) q^{79} +(10.4725 + 21.7188i) q^{80} -7.33391i q^{82} +(-0.320491 - 0.104134i) q^{83} +(4.77818 - 8.88990i) q^{85} +(21.8599 + 15.8822i) q^{86} +(-11.6910 - 16.0913i) q^{88} +(-10.5700 - 7.67955i) q^{89} +(7.82890 - 5.68803i) q^{91} +(1.68933 + 0.548898i) q^{92} +(-6.46496 + 19.8971i) q^{94} +(1.70241 + 0.915020i) q^{95} +(-7.40730 + 2.40678i) q^{97} +(-18.4444 + 25.3865i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4}+O(q^{10}) $ 24 * q + 8 * q^4	$ 24 q + 8 q^{4} - 10 q^{10} - 24 q^{16} + 14 q^{19} + 70 q^{22} + 30 q^{28} - 18 q^{31} + 10 q^{34} - 20 q^{37} - 80 q^{40} - 72 q^{49} - 140 q^{52} - 10 q^{55} - 130 q^{58} - 12 q^{61} + 2 q^{64} + 80 q^{67} + 30 q^{70} - 20 q^{73} + 88 q^{76} + 36 q^{79} + 90 q^{85} + 180 q^{88} - 30 q^{91} + 50 q^{94} + 100 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 10 * q^10 - 24 * q^16 + 14 * q^19 + 70 * q^22 + 30 * q^28 - 18 * q^31 + 10 * q^34 - 20 * q^37 - 80 * q^40 - 72 * q^49 - 140 * q^52 - 10 * q^55 - 130 * q^58 - 12 * q^61 + 2 * q^64 + 80 * q^67 + 30 * q^70 - 20 * q^73 + 88 * q^76 + 36 * q^79 + 90 * q^85 + 180 * q^88 - 30 * q^91 + 50 * q^94 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.55211	−	2.13629i	1.09751	−	1.51059i	0.258858	−	0.965915i	$-0.416654\pi$
$2$	1.55211	−	2.13629i	1.09751	−	1.51059i	0.838648	−	0.544673i	$-0.183346\pi$
$3$		0			0
$3$		0			0
$4$	−1.53668	−	4.72941i	−0.768340	−	2.36471i
$5$	0.398175	−	2.20033i	0.178069	−	0.984018i
$5$	0.398175	−	2.20033i	0.178069	−	0.984018i
$6$		0			0
$7$			4.34551i			1.64245i	0.570606	+	0.821224i	$0.306708\pi$
$7$			4.34551i			1.64245i	−0.570606	+	0.821224i	$0.693292\pi$
$8$	−7.46578	−	2.42578i	−2.63955	−	0.857642i
$9$		0			0
$10$	−4.08254	−	4.26577i	−1.29101	−	1.34896i
$11$	2.04985	+	1.48930i	0.618052	+	0.449041i	0.852241	−	0.523150i	$-0.175243\pi$
$11$	2.04985	+	1.48930i	0.618052	+	0.449041i	−0.234189	+	0.972191i	$0.575243\pi$
$12$		0			0
$13$	−1.30894	−	1.80161i	−0.363036	−	0.499676i	0.587956	−	0.808893i	$-0.299933\pi$
$13$	−1.30894	−	1.80161i	−0.363036	−	0.499676i	−0.950991	+	0.309217i	$0.899933\pi$
$14$	9.28329	+	6.74470i	2.48106	+	1.80260i
$15$		0			0
$16$	−8.72373	+	6.33816i	−2.18093	+	1.58454i
$17$	4.29265	+	1.39477i	1.04112	+	0.338281i	0.779178	−	0.626802i	$-0.215637\pi$
$17$	4.29265	+	1.39477i	1.04112	+	0.338281i	0.261943	+	0.965083i	$0.415637\pi$
$18$		0			0
$19$	−0.267098	+	0.822042i	−0.0612764	+	0.188589i	−0.977009	−	0.213200i	$-0.931611\pi$
$19$	−0.267098	+	0.822042i	−0.0612764	+	0.188589i	0.915732	+	0.401789i	$0.131611\pi$
$20$	−11.0181	+	1.49807i	−2.46373	+	0.334978i
$21$		0			0
$22$	6.36317	−	2.06752i	1.35663	−	0.440797i
$23$	−0.209955	+	0.288979i	−0.0437787	+	0.0602562i	−0.830345	−	0.557249i	$-0.811857\pi$
$23$	−0.209955	+	0.288979i	−0.0437787	+	0.0602562i	0.786566	+	0.617506i	$0.211857\pi$
$24$		0			0
$25$	−4.68291	−	1.75223i	−0.936583	−	0.350447i
$26$	−5.88039			−1.15324
$27$		0			0
$28$	20.5517	−	6.67765i	3.88391	−	1.26196i
$29$	−1.36199	−	4.19178i	−0.252915	−	0.778393i	−0.994233	−	0.107239i	$-0.965799\pi$
$29$	−1.36199	−	4.19178i	−0.252915	−	0.778393i	0.741318	−	0.671154i	$-0.234201\pi$
$30$		0			0
$31$	−0.140703	+	0.433039i	−0.0252710	+	0.0777761i	−0.962897	−	0.269871i	$-0.913019\pi$
$31$	−0.140703	+	0.433039i	−0.0252710	+	0.0777761i	0.937626	+	0.347647i	$0.113019\pi$
$32$			12.7740i			2.25815i
$33$		0			0
$34$	9.64230	−	7.00554i	1.65364	−	1.20144i
$35$	9.56156	+	1.73027i	1.61620	+	0.292470i
$36$		0			0
$37$	1.39668	+	1.92237i	0.229613	+	0.316036i	0.908242	−	0.418446i	$-0.137425\pi$
$37$	1.39668	+	1.92237i	0.229613	+	0.316036i	−0.678628	+	0.734482i	$0.737425\pi$
$38$	1.34156	+	1.84650i	0.217630	+	0.299541i
$39$		0			0
$40$	−8.31021	+	15.4613i	−1.31396	+	2.44465i
$41$	2.24693	−	1.63249i	0.350911	−	0.254952i	−0.398340	−	0.917238i	$-0.630414\pi$
$41$	2.24693	−	1.63249i	0.350911	−	0.254952i	0.749251	+	0.662286i	$0.230414\pi$
$42$		0			0
$43$			10.2326i			1.56046i	0.625490	+	0.780232i	$0.284899\pi$
$43$			10.2326i			1.56046i	−0.625490	+	0.780232i	$0.715101\pi$
$44$	3.89356	−	11.9831i	0.586976	−	1.80653i
$45$		0			0
$46$	0.291470	+	0.897053i	0.0429749	+	0.132263i
$47$	−7.53506	+	2.44829i	−1.09910	+	0.357120i	−0.801757	−	0.597651i	$-0.796101\pi$
$47$	−7.53506	+	2.44829i	−1.09910	+	0.357120i	−0.297344	+	0.954770i	$0.596101\pi$
$48$		0			0
$49$	−11.8834			−1.69764
$50$	−11.0117	+	7.28442i	−1.55729	+	1.03017i
$51$		0			0
$52$	−6.50911	+	8.95903i	−0.902652	+	1.24239i
$53$	6.13570	−	1.99361i	0.842804	−	0.273844i	0.144375	−	0.989523i	$-0.453883\pi$
$53$	6.13570	−	1.99361i	0.842804	−	0.273844i	0.698429	+	0.715679i	$0.253883\pi$
$54$		0			0
$55$	4.09315	−	3.91734i	0.551921	−	0.528214i
$56$	10.5412	−	32.4426i	1.40863	−	4.33533i
$57$		0			0
$58$	−11.0688	−	3.59648i	−1.45341	−	0.472241i
$59$	−5.59575	+	4.06555i	−0.728504	+	0.529289i	−0.889090	−	0.457733i	$-0.848662\pi$
$59$	−5.59575	+	4.06555i	−0.728504	+	0.529289i	0.160586	+	0.987022i	$0.448662\pi$
$60$		0			0
$61$	4.93738	+	3.58722i	0.632167	+	0.459296i	0.857150	−	0.515066i	$-0.172233\pi$
$61$	4.93738	+	3.58722i	0.632167	+	0.459296i	−0.224983	+	0.974363i	$0.572233\pi$
$62$	0.706713	+	0.972706i	0.0897526	+	0.123534i
$63$		0			0
$64$	9.84157	+	7.15032i	1.23020	+	0.893790i
$65$	−4.48532	+	2.16275i	−0.556335	+	0.268257i
$66$		0			0
$67$	10.4960	+	3.41036i	1.28229	+	0.416641i	0.869386	−	0.494133i	$-0.164515\pi$
$67$	10.4960	+	3.41036i	1.28229	+	0.416641i	0.412904	+	0.910775i	$0.364515\pi$
$68$		−	22.4450i		−	2.72186i
$69$		0			0
$70$	18.5370	−	17.7407i	2.21559	−	2.12042i
$71$	−2.27903	−	7.01412i	−0.270471	−	0.832423i	−0.990382	−	0.138357i	$-0.955818\pi$
$71$	−2.27903	−	7.01412i	−0.270471	−	0.832423i	0.719912	−	0.694066i	$-0.244182\pi$
$72$		0			0
$73$	−7.99599	+	11.0055i	−0.935860	+	1.28810i	0.0216690	+	0.999765i	$0.493102\pi$
$73$	−7.99599	+	11.0055i	−0.935860	+	1.28810i	−0.957529	+	0.288336i	$0.906898\pi$
$74$	6.27455			0.729402
$75$		0			0
$76$	4.29822			0.493039
$77$	−6.47177	+	8.90762i	−0.737526	+	1.01512i
$78$		0			0
$79$	−3.33214	−	10.2553i	−0.374895	−	1.15381i	−0.943549	−	0.331232i	$-0.892536\pi$
$79$	−3.33214	−	10.2553i	−0.374895	−	1.15381i	0.568654	−	0.822577i	$-0.307464\pi$
$80$	10.4725	+	21.7188i	1.17086	+	2.42823i
$81$		0			0
$82$		−	7.33391i		−	0.809894i
$83$	−0.320491	−	0.104134i	−0.0351784	−	0.0114302i	0.291375	−	0.956609i	$-0.405887\pi$
$83$	−0.320491	−	0.104134i	−0.0351784	−	0.0114302i	−0.326553	+	0.945179i	$0.605887\pi$
$84$		0			0
$85$	4.77818	−	8.88990i	0.518266	−	0.964245i
$86$	21.8599	+	15.8822i	2.35722	+	1.71262i
$87$		0			0
$88$	−11.6910	−	16.0913i	−1.24626	−	1.71533i
$89$	−10.5700	−	7.67955i	−1.12042	−	0.814031i	−0.136145	−	0.990689i	$-0.543471\pi$
$89$	−10.5700	−	7.67955i	−1.12042	−	0.814031i	−0.984272	+	0.176658i	$0.943471\pi$
$90$		0			0
$91$	7.82890	−	5.68803i	0.820691	−	0.596267i
$92$	1.68933	+	0.548898i	0.176125	+	0.0572265i
$93$		0			0
$94$	−6.46496	+	19.8971i	−0.666810	+	2.05223i
$95$	1.70241	+	0.915020i	0.174664	+	0.0938791i
$96$		0			0
$97$	−7.40730	+	2.40678i	−0.752098	+	0.244371i	−0.659884	−	0.751368i	$-0.729394\pi$
$97$	−7.40730	+	2.40678i	−0.752098	+	0.244371i	−0.0922142	+	0.995739i	$0.529394\pi$
$98$	−18.4444	+	25.3865i	−1.86317	+	2.56443i
$99$		0			0
$100$	−1.09090	+	24.8400i	−0.109090	+	2.48400i
$101$	−16.6461			−1.65635			−0.828176	−	0.560468i	$-0.810621\pi$
$101$	−16.6461			−1.65635			−0.828176	+	0.560468i	$0.810621\pi$
$102$		0			0
$103$	−1.71511	+	0.557272i	−0.168994	+	0.0549096i	−0.392292	−	0.919841i	$-0.628318\pi$
$103$	−1.71511	+	0.557272i	−0.168994	+	0.0549096i	0.223298	+	0.974750i	$0.428318\pi$
$104$	5.40199	+	16.6256i	0.529708	+	1.63028i
$105$		0			0
$106$	5.26434	−	16.2020i	0.511318	−	1.57368i
$107$		−	14.5670i		−	1.40824i	−0.710079	−	0.704122i	$-0.751341\pi$
$107$		−	14.5670i		−	1.40824i	0.710079	−	0.704122i	$-0.248659\pi$
$108$		0			0
$109$	−7.38454	+	5.36518i	−0.707310	+	0.513891i	−0.882305	−	0.470678i	$-0.844009\pi$
$109$	−7.38454	+	5.36518i	−0.707310	+	0.513891i	0.174995	+	0.984569i	$0.444009\pi$
$110$	−2.01557	−	14.8243i	−0.192177	−	1.41344i
$111$		0			0
$112$	−27.5425	−	37.9090i	−2.60252	−	3.58207i
$113$	1.28034	+	1.76224i	0.120444	+	0.165777i	0.864982	−	0.501803i	$-0.167330\pi$
$113$	1.28034	+	1.76224i	0.120444	+	0.165777i	−0.744537	+	0.667581i	$0.767330\pi$
$114$		0			0
$115$	0.552250	+	0.577035i	0.0514975	+	0.0538088i
$116$	−17.7317	+	12.8828i	−1.64635	+	1.19614i
$117$		0			0
$118$			18.2643i			1.68137i
$119$	−6.06098	+	18.6538i	−0.555609	+	1.70999i
$120$		0			0
$121$	−1.41533	−	4.35595i	−0.128667	−	0.395995i
$122$	15.3267	−	4.97995i	1.38761	−	0.450863i
$123$		0			0
$124$	2.26423			0.203334
$125$	−5.72012	+	9.60626i	−0.511623	+	0.859210i
$126$		0			0
$127$	3.63585	−	5.00432i	0.322630	−	0.444062i	−0.616638	−	0.787247i	$-0.711506\pi$
$127$	3.63585	−	5.00432i	0.322630	−	0.444062i	0.939268	+	0.343185i	$0.111506\pi$
$128$	6.25279	−	2.03166i	0.552674	−	0.179575i
$129$		0			0
$130$	−2.34142	+	12.9388i	−0.205356	+	1.13481i
$131$	1.95680	−	6.02240i	0.170966	−	0.526179i	−0.828460	−	0.560048i	$-0.810783\pi$
$131$	1.95680	−	6.02240i	0.170966	−	0.526179i	0.999426	+	0.0338684i	$0.0107827\pi$
$132$		0			0
$133$	−3.57219	−	1.16067i	−0.309748	−	0.100643i
$134$	23.5765	−	17.1293i	2.03670	−	1.47975i
$135$		0			0
$136$	−28.6646	−	20.8261i	−2.45797	−	1.78582i
$137$	10.4850	+	14.4313i	0.895791	+	1.23295i	0.971791	+	0.235843i	$0.0757849\pi$
$137$	10.4850	+	14.4313i	0.895791	+	1.23295i	−0.0760005	+	0.997108i	$0.524215\pi$
$138$		0			0
$139$	8.82690	+	6.41312i	0.748688	+	0.543954i	0.895420	−	0.445223i	$-0.146875\pi$
$139$	8.82690	+	6.41312i	0.748688	+	0.543954i	−0.146732	+	0.989176i	$0.546875\pi$
$140$	−6.50987	−	47.8794i	−0.550184	−	4.04655i
$141$		0			0
$142$	−18.5215	−	6.01801i	−1.55429	−	0.505020i
$143$		−	5.64243i		−	0.471843i
$144$		0			0
$145$	−9.76560	+	1.32777i	−0.810989	+	0.110265i
$146$	11.1004	+	34.1636i	0.918678	+	2.82740i
$147$		0			0
$148$	6.94542	−	9.55956i	0.570910	−	0.785791i
$149$	16.2808			1.33378			0.666889	−	0.745157i	$-0.267626\pi$
$149$	16.2808			1.33378			0.666889	+	0.745157i	$0.267626\pi$
$150$		0			0
$151$	19.1931			1.56191			0.780957	−	0.624585i	$-0.214732\pi$
$151$	19.1931			1.56191			0.780957	+	0.624585i	$0.214732\pi$
$152$	3.98818	−	5.48926i	0.323484	−	0.445238i
$153$		0			0
$154$	8.98442	+	27.6512i	0.723985	+	2.22820i
$155$	0.896805	+	0.482018i	0.0720331	+	0.0387166i
$156$		0			0
$157$			8.59302i			0.685798i	0.939372	+	0.342899i	$0.111409\pi$
$157$			8.59302i			0.685798i	−0.939372	+	0.342899i	$0.888591\pi$
$158$	−27.0801	−	8.79887i	−2.15438	−	0.700000i
$159$		0			0
$160$	28.1070	+	5.08629i	2.22206	+	0.402107i
$161$	−1.25576	−	0.912362i	−0.0989677	−	0.0719042i
$162$		0			0
$163$	−4.02645	−	5.54194i	−0.315376	−	0.434078i	0.621672	−	0.783277i	$-0.286454\pi$
$163$	−4.02645	−	5.54194i	−0.315376	−	0.434078i	−0.937048	+	0.349199i	$0.886454\pi$
$164$	−11.1735	−	8.11804i	−0.872506	−	0.633913i
$165$		0			0
$166$	−0.719897	+	0.523036i	−0.0558748	+	0.0405954i
$167$	−13.2230	−	4.29641i	−1.02323	−	0.332467i	−0.251118	−	0.967957i	$-0.580798\pi$
$167$	−13.2230	−	4.29641i	−1.02323	−	0.332467i	−0.772109	+	0.635490i	$0.780798\pi$
$168$		0			0
$169$	2.48477	−	7.64733i	0.191136	−	0.588256i
$170$	−11.5752	−	24.0057i	−0.887776	−	1.84115i
$171$		0			0
$172$	48.3944	−	15.7243i	3.69004	−	1.19897i
$173$	8.96086	−	12.3336i	0.681282	−	0.937704i	−0.318667	−	0.947867i	$-0.603235\pi$
$173$	8.96086	−	12.3336i	0.681282	−	0.937704i	0.999948	+	0.0101630i	$0.00323505\pi$
$174$		0			0
$175$	7.61435	−	20.3496i	0.575591	−	1.53829i
$176$	−27.3217			−2.05945
$177$		0			0
$178$	−32.8116	+	10.6611i	−2.45933	+	0.799085i
$179$	−2.11287	−	6.50273i	−0.157923	−	0.486037i	0.840522	−	0.541777i	$-0.182248\pi$
$179$	−2.11287	−	6.50273i	−0.157923	−	0.486037i	−0.998445	+	0.0557399i	$0.982248\pi$
$180$		0			0
$181$	3.97048	−	12.2199i	0.295123	−	0.908296i	−0.688057	−	0.725657i	$-0.741536\pi$
$181$	3.97048	−	12.2199i	0.295123	−	0.908296i	0.983180	−	0.182639i	$-0.0584640\pi$
$182$		−	25.5533i		−	1.89413i
$183$		0			0
$184$	2.26848	−	1.64815i	0.167234	−	0.121503i
$185$	4.78597	−	2.30773i	0.351872	−	0.169667i
$186$		0			0
$187$	6.72205	+	9.25211i	0.491565	+	0.676581i
$188$	23.1579	+	31.8742i	1.68897	+	2.32466i
$189$		0			0
$190$	4.59708	−	2.21664i	0.333507	−	0.160812i
$191$	0.141641	−	0.102908i	0.0102488	−	0.00744616i	−0.582649	−	0.812724i	$-0.697984\pi$
$191$	0.141641	−	0.102908i	0.0102488	−	0.00744616i	0.592898	+	0.805278i	$0.297984\pi$
$192$		0			0
$193$		−	10.0004i		−	0.719844i	−0.932982	−	0.359922i	$-0.882803\pi$
$193$		−	10.0004i		−	0.719844i	0.932982	−	0.359922i	$-0.117197\pi$
$194$	−6.35535	+	19.5598i	−0.456288	+	1.40431i
$195$		0			0
$196$	18.2610	+	56.2017i	1.30436	+	4.01441i
$197$	17.4544	−	5.67128i	1.24358	−	0.404062i	0.387961	−	0.921676i	$-0.373180\pi$
$197$	17.4544	−	5.67128i	1.24358	−	0.404062i	0.855614	+	0.517614i	$0.173180\pi$
$198$		0			0
$199$	−2.11923			−0.150228			−0.0751139	−	0.997175i	$-0.523932\pi$
$199$	−2.11923			−0.150228			−0.0751139	+	0.997175i	$0.523932\pi$
$200$	30.7111	+	24.4415i	2.17160	+	1.72828i
$201$		0			0
$202$	−25.8366	+	35.5611i	−1.81786	+	2.50207i
$203$	18.2154	−	5.91854i	1.27847	−	0.415400i
$204$		0			0
$205$	−2.69735	−	5.59401i	−0.188391	−	0.390702i
$206$	−1.47153	+	4.52892i	−0.102527	+	0.315545i
$207$		0			0
$208$	22.8377	+	7.42043i	1.58351	+	0.514514i
$209$	−1.77178	+	1.28727i	−0.122556	+	0.0890424i
$210$		0			0
$211$	−2.35973	−	1.71444i	−0.162450	−	0.118027i	0.503590	−	0.863943i	$-0.332012\pi$
$211$	−2.35973	−	1.71444i	−0.162450	−	0.118027i	−0.666040	+	0.745916i	$0.732012\pi$
$212$	−18.8572	−	25.9547i	−1.29512	−	1.78258i
$213$		0			0
$214$	−31.1194	−	22.6096i	−2.12728	−	1.54556i
$215$	22.5152	+	4.07439i	1.53552	+	0.277871i
$216$		0			0
$217$	−1.88177	−	0.611426i	−0.127743	−	0.0415063i
$218$			24.1029i			1.63245i
$219$		0			0
$220$	−24.8166	−	13.3385i	−1.67313	−	0.899282i
$221$	−3.10602	−	9.55935i	−0.208933	−	0.643031i
$222$		0			0
$223$	0.362852	−	0.499423i	0.0242984	−	0.0334438i	−0.796695	−	0.604382i	$-0.793420\pi$
$223$	0.362852	−	0.499423i	0.0242984	−	0.0334438i	0.820993	+	0.570938i	$0.193420\pi$
$224$	−55.5095			−3.70889
$225$		0			0
$226$	5.75189			0.382610
$227$	−10.1368	+	13.9521i	−0.672804	+	0.926036i	−0.999820	−	0.0189831i	$-0.993957\pi$
$227$	−10.1368	+	13.9521i	−0.672804	+	0.926036i	0.327015	+	0.945019i	$0.393957\pi$
$228$		0			0
$229$	−3.72924	−	11.4774i	−0.246435	−	0.758450i	−0.995397	−	0.0958366i	$-0.969447\pi$
$229$	−3.72924	−	11.4774i	−0.246435	−	0.758450i	0.748962	−	0.662613i	$-0.230553\pi$
$230$	2.08987	−	0.284147i	0.137802	−	0.0187361i
$231$		0			0
$232$			34.5988i			2.27152i
$233$	−2.66449	−	0.865745i	−0.174556	−	0.0567168i	0.220435	−	0.975402i	$-0.429252\pi$
$233$	−2.66449	−	0.865745i	−0.174556	−	0.0567168i	−0.394991	+	0.918685i	$0.629252\pi$
$234$		0			0
$235$	2.38677	+	17.5545i	0.155696	+	1.14513i
$236$	27.8265	+	20.2171i	1.81135	+	1.31602i
$237$		0			0
$238$	30.4426	+	41.9007i	1.97330	+	2.71602i
$239$	−10.3443	−	7.51560i	−0.669119	−	0.486143i	0.200611	−	0.979671i	$-0.435707\pi$
$239$	−10.3443	−	7.51560i	−0.669119	−	0.486143i	−0.869730	+	0.493528i	$0.835707\pi$
$240$		0			0
$241$	−2.60470	+	1.89242i	−0.167783	+	0.121902i	−0.668508	−	0.743705i	$-0.733067\pi$
$241$	−2.60470	+	1.89242i	−0.167783	+	0.121902i	0.500725	+	0.865606i	$0.333067\pi$
$242$	−11.5023	−	3.73734i	−0.739398	−	0.240245i
$243$		0			0
$244$	9.37826	−	28.8633i	0.600381	−	1.84778i
$245$	−4.73169	+	26.1475i	−0.302297	+	1.67050i
$246$		0			0
$247$	1.83061	−	0.594802i	0.116479	−	0.0378463i
$248$	2.10091	−	2.89166i	0.133408	−	0.183621i
$249$		0			0
$250$	11.6436	+	27.1298i	0.736404	+	1.71584i
$251$	18.8989			1.19289			0.596444	−	0.802655i	$-0.296580\pi$
$251$	18.8989			1.19289			0.596444	+	0.802655i	$0.296580\pi$
$252$		0			0
$253$	−0.860752	+	0.279675i	−0.0541150	+	0.0175830i
$254$	−5.04747	−	15.5345i	−0.316706	−	0.974721i
$255$		0			0
$256$	−2.15349	+	6.62777i	−0.134593	+	0.414235i
$257$			24.5521i			1.53152i	0.643128	+	0.765758i	$0.277636\pi$
$257$			24.5521i			1.53152i	−0.643128	+	0.765758i	$0.722364\pi$
$258$		0			0
$259$	−8.35367	+	6.06930i	−0.519072	+	0.377128i
$260$	17.1211	+	17.8895i	1.06180	+	1.10946i
$261$		0			0
$262$	−9.82846	−	13.5277i	−0.607204	−	0.835745i
$263$	4.84006	+	6.66177i	0.298451	+	0.410782i	0.931736	−	0.363136i	$-0.118294\pi$
$263$	4.84006	+	6.66177i	0.298451	+	0.410782i	−0.633285	+	0.773918i	$0.718294\pi$
$264$		0			0
$265$	−1.94352	−	14.2944i	−0.119389	−	0.878097i
$266$	−8.02397	+	5.82976i	−0.491981	+	0.357445i
$267$		0			0
$268$		−	54.8805i		−	3.35236i
$269$	−0.403113	+	1.24065i	−0.0245782	+	0.0756440i	−0.962593	−	0.270951i	$-0.912662\pi$
$269$	−0.403113	+	1.24065i	−0.0245782	+	0.0756440i	0.938015	+	0.346595i	$0.112662\pi$
$270$		0			0
$271$	−0.613602	−	1.88847i	−0.0372737	−	0.114717i	0.930688	−	0.365813i	$-0.119209\pi$
$271$	−0.613602	−	1.88847i	−0.0372737	−	0.114717i	−0.967962	+	0.251096i	$0.919209\pi$
$272$	−46.2882	+	15.0400i	−2.80663	+	0.911931i
$273$		0			0
$274$	47.1033			2.84562
$275$	−6.98965	−	10.5661i	−0.421492	−	0.637158i
$276$		0			0
$277$	8.08711	−	11.1310i	0.485908	−	0.668794i	−0.493719	−	0.869621i	$-0.664363\pi$
$277$	8.08711	−	11.1310i	0.485908	−	0.668794i	0.979627	+	0.200827i	$0.0643629\pi$
$278$	27.4006	−	8.90300i	1.64338	−	0.533967i
$279$		0			0
$280$	−67.1872	−	36.1121i	−4.01520	−	2.15811i
$281$	8.92325	−	27.4630i	0.532317	−	1.63830i	−0.217060	−	0.976158i	$-0.569647\pi$
$281$	8.92325	−	27.4630i	0.532317	−	1.63830i	0.749377	−	0.662144i	$-0.230353\pi$
$282$		0			0
$283$	30.1415	+	9.79358i	1.79173	+	0.582168i	0.999603	−	0.0281890i	$-0.00897404\pi$
$283$	30.1415	+	9.79358i	1.79173	+	0.582168i	0.792126	+	0.610357i	$0.208974\pi$
$284$	−29.6705	+	21.5569i	−1.76062	+	1.27917i
$285$		0			0
$286$	−12.0539	−	8.75766i	−0.712761	−	0.517851i
$287$	7.09400	+	9.76405i	0.418746	+	0.576354i
$288$		0			0
$289$	2.72821	+	1.98216i	0.160483	+	0.116598i
$290$	−12.3208	+	22.9230i	−0.723501	+	1.34609i
$291$		0			0
$292$	64.3370	+	20.9044i	3.76504	+	1.22334i
$293$		−	5.57990i		−	0.325981i	−0.986628	−	0.162991i	$-0.947886\pi$
$293$		−	5.57990i		−	0.325981i	0.986628	−	0.162991i	$-0.0521141\pi$
$294$		0			0
$295$	6.71746	+	13.9313i	0.391106	+	0.811111i
$296$	−5.76409	−	17.7400i	−0.335031	−	1.03112i
$297$		0			0
$298$	25.2696	−	34.7807i	1.46383	−	2.01479i
$299$	0.795445			0.0460018
$300$		0			0
$301$	−44.4661			−2.56298
$302$	29.7898	−	41.0021i	1.71421	−	2.35941i
$303$		0			0
$304$	−2.88015	−	8.86418i	−0.165188	−	0.508395i
$305$	9.85901	−	9.43553i	0.564525	−	0.540277i
$306$		0			0
$307$		−	18.1679i		−	1.03690i	−0.855109	−	0.518448i	$-0.826510\pi$
$307$		−	18.1679i		−	1.03690i	0.855109	−	0.518448i	$-0.173490\pi$
$308$	52.0729	+	16.9195i	2.96713	+	0.964078i
$309$		0			0
$310$	2.42167	−	1.16769i	0.137542	−	0.0663206i
$311$	−11.6023	−	8.42955i	−0.657905	−	0.477996i	0.208050	−	0.978118i	$-0.433288\pi$
$311$	−11.6023	−	8.42955i	−0.657905	−	0.477996i	−0.865955	+	0.500122i	$0.833288\pi$
$312$		0			0
$313$	5.33025	+	7.33646i	0.301284	+	0.414681i	0.932638	−	0.360813i	$-0.117501\pi$
$313$	5.33025	+	7.33646i	0.301284	+	0.414681i	−0.631355	+	0.775494i	$0.717501\pi$
$314$	18.3572	+	13.3373i	1.03596	+	0.752668i
$315$		0			0
$316$	−43.3810	+	31.5181i	−2.44037	+	1.77303i
$317$	−19.1636	−	6.22662i	−1.07633	−	0.349722i	−0.283382	−	0.959007i	$-0.591456\pi$
$317$	−19.1636	−	6.22662i	−1.07633	−	0.349722i	−0.792951	+	0.609285i	$0.791456\pi$
$318$		0			0
$319$	3.45094	−	10.6209i	0.193216	−	0.594657i
$320$	19.6517	−	18.8076i	1.09857	−	1.05138i
$321$		0			0
$322$	−3.89815	+	1.26659i	−0.217235	+	0.0705841i
$323$	−2.29311	+	3.15620i	−0.127592	+	0.175616i
$324$		0			0
$325$	2.97283	+	10.7303i	0.164903	+	0.595212i
$326$	−18.0887			−1.00184
$327$		0			0
$328$	−20.7351	+	6.73726i	−1.14491	+	0.372003i
$329$	−10.6391	−	32.7437i	−0.586550	−	1.80522i
$330$		0			0
$331$	−9.38756	+	28.8919i	−0.515987	+	1.58804i	0.265493	+	0.964113i	$0.414465\pi$
$331$	−9.38756	+	28.8919i	−0.515987	+	1.58804i	−0.781479	+	0.623931i	$0.785535\pi$
$332$			1.67575i			0.0919689i
$333$		0			0
$334$	−29.7020	+	21.5797i	−1.62522	+	1.18079i
$335$	11.6832	−	21.7367i	0.638319	−	1.18761i
$336$		0			0
$337$	−8.20597	−	11.2946i	−0.447008	−	0.615253i	0.524744	−	0.851260i	$-0.324161\pi$
$337$	−8.20597	−	11.2946i	−0.447008	−	0.615253i	−0.971751	+	0.236007i	$0.924161\pi$
$338$	−12.4803	−	17.1777i	−0.678840	−	0.934343i
$339$		0			0
$340$	−49.3865	−	8.93706i	−2.67836	−	0.484680i
$341$	−0.933344	+	0.678114i	−0.0505434	+	0.0367220i
$342$		0			0
$343$		−	21.2211i		−	1.14583i
$344$	24.8221	−	76.3947i	1.33832	−	4.11893i
$345$		0			0
$346$	−12.4399	−	38.2861i	−0.668773	−	2.05827i
$347$	11.8392	−	3.84680i	0.635563	−	0.206507i	0.0265251	−	0.999648i	$-0.491556\pi$
$347$	11.8392	−	3.84680i	0.635563	−	0.206507i	0.609038	+	0.793141i	$0.291556\pi$
$348$		0			0
$349$	10.1110			0.541228			0.270614	−	0.962688i	$-0.412773\pi$
$349$	10.1110			0.541228			0.270614	+	0.962688i	$0.412773\pi$
$350$	−31.6545	−	47.8514i	−1.69201	−	2.55776i
$351$		0			0
$352$	−19.0243	+	26.1847i	−1.01400	+	1.39565i
$353$	−33.7047	+	10.9513i	−1.79392	+	0.582879i	−0.999694	−	0.0247458i	$-0.992122\pi$
$353$	−33.7047	+	10.9513i	−1.79392	+	0.582879i	−0.794224	+	0.607625i	$0.792122\pi$
$354$		0			0
$355$	−16.3408	+	2.22176i	−0.867282	+	0.117919i
$356$	−20.0771	+	61.7909i	−1.06408	+	3.27491i
$357$		0			0
$358$	−17.1712	−	5.57924i	−0.907523	−	0.294872i
$359$	−25.5295	+	18.5483i	−1.34740	+	0.978940i	−0.348259	+	0.937398i	$0.613227\pi$
$359$	−25.5295	+	18.5483i	−1.34740	+	0.978940i	−0.999137	+	0.0415420i	$0.986773\pi$
$360$		0			0
$361$	14.7669	+	10.7288i	0.777206	+	0.564673i
$362$	−19.9426	−	27.4487i	−1.04816	−	1.44267i
$363$		0			0
$364$	−38.9315	−	28.2854i	−2.04057	−	1.48256i
$365$	21.0320	+	21.9760i	1.10087	+	1.15027i
$366$		0			0
$367$	−12.3098	−	3.99968i	−0.642564	−	0.208782i	−0.0304317	−	0.999537i	$-0.509688\pi$
$367$	−12.3098	−	3.99968i	−0.642564	−	0.208782i	−0.612133	+	0.790755i	$0.709688\pi$
$368$		−	3.85170i		−	0.200784i
$369$		0			0
$370$	2.49837	−	13.8061i	0.129884	−	0.717745i
$371$	8.66326	+	26.6628i	0.449774	+	1.38426i
$372$		0			0
$373$	−4.81717	+	6.63027i	−0.249424	+	0.343302i	−0.915309	−	0.402752i	$-0.868054\pi$
$373$	−4.81717	+	6.63027i	−0.249424	+	0.343302i	0.665886	+	0.746054i	$0.268054\pi$
$374$	30.1986			1.56153
$375$		0			0
$376$	62.1941			3.20742
$377$	−5.76916	+	7.94057i	−0.297127	+	0.408960i
$378$		0			0
$379$	5.54799	+	17.0750i	0.284981	+	0.877081i	0.986404	+	0.164337i	$0.0525483\pi$
$379$	5.54799	+	17.0750i	0.284981	+	0.877081i	−0.701423	+	0.712745i	$0.747452\pi$
$380$	1.71144	−	9.45750i	0.0877952	−	0.485160i
$381$		0			0
$382$		−	0.462311i		−	0.0236539i
$383$	19.0998	+	6.20589i	0.975952	+	0.317106i	0.753216	−	0.657773i	$-0.228501\pi$
$383$	19.0998	+	6.20589i	0.975952	+	0.317106i	0.222736	+	0.974879i	$0.428501\pi$
$384$		0			0
$385$	17.0228	+	17.7868i	0.867564	+	0.906501i
$386$	−21.3638	−	15.5217i	−1.08739	−	0.790034i
$387$		0			0
$388$	22.7653	+	31.3337i	1.15573	+	1.59073i
$389$	15.4725	+	11.2414i	0.784486	+	0.569962i	0.906322	−	0.422588i	$-0.138878\pi$
$389$	15.4725	+	11.2414i	0.784486	+	0.569962i	−0.121836	+	0.992550i	$0.538878\pi$
$390$		0			0
$391$	−1.30432	+	0.947646i	−0.0659625	+	0.0479245i
$392$	88.7192	+	28.8266i	4.48100	+	1.45596i
$393$		0			0
$394$	14.9756	−	46.0902i	0.754461	−	2.32199i
$395$	−23.8918	+	3.24842i	−1.20213	+	0.163446i
$396$		0			0
$397$	−2.74253	+	0.891101i	−0.137643	+	0.0447231i	−0.377029	−	0.926202i	$-0.623054\pi$
$397$	−2.74253	+	0.891101i	−0.137643	+	0.0447231i	0.239385	+	0.970925i	$0.423054\pi$
$398$	−3.28927	+	4.52729i	−0.164876	+	0.226933i
$399$		0			0
$400$	51.9584	−	14.3950i	2.59792	−	0.719752i
$401$	5.50842			0.275077			0.137539	−	0.990496i	$-0.456081\pi$
$401$	5.50842			0.275077			0.137539	+	0.990496i	$0.456081\pi$
$402$		0			0
$403$	0.964338	−	0.313332i	0.0480371	−	0.0156082i
$404$	25.5798	+	78.7264i	1.27264	+	3.91679i
$405$		0			0
$406$	15.6285	−	48.0997i	0.775631	−	2.38715i
$407$			6.02064i			0.298432i
$408$		0			0
$409$	30.1238	−	21.8863i	1.48953	−	1.08221i	0.515201	−	0.857070i	$-0.327717\pi$
$409$	30.1238	−	21.8863i	1.48953	−	1.08221i	0.974327	−	0.225136i	$-0.0722826\pi$
$410$	−16.1370	−	2.92018i	−0.796951	−	0.144217i
$411$		0			0
$412$	5.27113	+	7.25509i	0.259690	+	0.357433i
$413$	−17.6669	−	24.3164i	−0.869330	−	1.19653i
$414$		0			0
$415$	−0.356740	+	0.663722i	−0.0175117	+	0.0325808i
$416$	23.0137	−	16.7204i	1.12834	−	0.819787i
$417$		0			0
$418$			5.78302i			0.282857i
$419$	−7.36168	+	22.6569i	−0.359642	+	1.10686i	0.593628	+	0.804740i	$0.297695\pi$
$419$	−7.36168	+	22.6569i	−0.359642	+	1.10686i	−0.953269	+	0.302123i	$0.902305\pi$
$420$		0			0
$421$	2.75855	+	8.48993i	0.134443	+	0.413774i	0.995503	−	0.0947300i	$-0.0301988\pi$
$421$	2.75855	+	8.48993i	0.134443	+	0.413774i	−0.861060	+	0.508504i	$0.830199\pi$
$422$	−7.32510	+	2.38007i	−0.356580	+	0.115860i
$423$		0			0
$424$	−50.6439			−2.45948
$425$	−17.6582	−	14.0533i	−0.856547	−	0.681686i
$426$		0			0
$427$	−15.5883	+	21.4554i	−0.754370	+	1.03830i
$428$	−68.8933	+	22.3848i	−3.33008	+	1.08201i
$429$		0			0
$430$	43.6502	−	41.7752i	2.10500	−	2.01458i
$431$	−8.04518	+	24.7605i	−0.387523	+	1.19267i	0.547111	+	0.837060i	$0.315728\pi$
$431$	−8.04518	+	24.7605i	−0.387523	+	1.19267i	−0.934634	+	0.355612i	$0.884272\pi$
$432$		0			0
$433$	−5.02408	−	1.63242i	−0.241442	−	0.0784492i	0.185797	−	0.982588i	$-0.440513\pi$
$433$	−5.02408	−	1.63242i	−0.241442	−	0.0784492i	−0.427238	+	0.904139i	$0.640513\pi$
$434$	−4.22690	+	3.07103i	−0.202898	+	0.147414i
$435$		0			0
$436$	36.7218	+	26.6800i	1.75866	+	1.27774i
$437$	−0.181474	−	0.249778i	−0.00868108	−	0.0119485i
$438$		0			0
$439$	13.8310	+	10.0488i	0.660118	+	0.479604i	0.866703	−	0.498825i	$-0.166235\pi$
$439$	13.8310	+	10.0488i	0.660118	+	0.479604i	−0.206584	+	0.978429i	$0.566235\pi$
$440$	−40.0612	+	19.3169i	−1.90984	+	0.920897i
$441$		0			0
$442$	−25.2425	−	8.20177i	−1.20066	−	0.390119i
$443$		−	7.99868i		−	0.380029i	−0.981781	−	0.190014i	$-0.939147\pi$
$443$		−	7.99868i		−	0.380029i	0.981781	−	0.190014i	$-0.0608534\pi$
$444$		0			0
$445$	−21.1063	+	20.1997i	−1.00053	+	0.957557i
$446$	−0.503729	−	1.55032i	−0.0238522	−	0.0734096i
$447$		0			0
$448$	−31.0718	+	42.7666i	−1.46800	+	2.02053i
$449$	22.6881			1.07072			0.535358	−	0.844625i	$-0.320177\pi$
$449$	22.6881			1.07072			0.535358	+	0.844625i	$0.320177\pi$
$450$		0			0
$451$	7.03713			0.331365
$452$	6.36688	−	8.76326i	0.299473	−	0.412189i
$453$		0			0
$454$	14.0724	+	43.3105i	0.660452	+	2.03266i
$455$	−9.39827	−	19.4910i	−0.440598	−	0.913752i
$456$		0			0
$457$			7.79373i			0.364575i	0.983245	+	0.182288i	$0.0583502\pi$
$457$			7.79373i			0.364575i	−0.983245	+	0.182288i	$0.941650\pi$
$458$	−30.3074	−	9.84746i	−1.41617	−	0.460142i
$459$		0			0
$460$	1.88041	−	3.49853i	0.0876744	−	0.163120i
$461$	−16.3338	−	11.8672i	−0.760741	−	0.552711i	0.138396	−	0.990377i	$-0.455805\pi$
$461$	−16.3338	−	11.8672i	−0.760741	−	0.552711i	−0.899138	+	0.437666i	$0.855805\pi$
$462$		0			0
$463$	−17.4472	−	24.0141i	−0.810842	−	1.11603i	−0.991193	−	0.132426i	$-0.957723\pi$
$463$	−17.4472	−	24.0141i	−0.810842	−	1.11603i	0.180350	−	0.983602i	$-0.442277\pi$
$464$	38.4498	+	27.9354i	1.78499	+	1.29687i
$465$		0			0
$466$	−5.98506	+	4.34840i	−0.277253	+	0.201436i
$467$	−31.4104	−	10.2059i	−1.45350	−	0.472271i	−0.527422	−	0.849604i	$-0.676841\pi$
$467$	−31.4104	−	10.2059i	−1.45350	−	0.472271i	−0.926078	+	0.377333i	$0.876841\pi$
$468$		0			0
$469$	−14.8197	+	45.6104i	−0.684311	+	2.10609i
$470$	41.2060	+	22.1476i	1.90069	+	1.02159i
$471$		0			0
$472$	51.6387	−	16.7784i	2.37687	−	0.772290i
$473$	−15.2395	+	20.9754i	−0.700712	+	0.964448i
$474$		0			0
$475$	2.69120	−	3.38153i	0.123481	−	0.155155i
$476$	97.5351			4.47051
$477$		0			0
$478$	−32.1111	+	10.4335i	−1.46873	+	0.477218i
$479$	−9.07522	−	27.9307i	−0.414657	−	1.27618i	−0.912557	−	0.408950i	$-0.865895\pi$
$479$	−9.07522	−	27.9307i	−0.414657	−	1.27618i	0.497899	−	0.867235i	$-0.334105\pi$
$480$		0			0
$481$	1.63517	−	5.03255i	0.0745575	−	0.229464i
$482$			8.50165i			0.387240i
$483$		0			0
$484$	−18.4262	+	13.3874i	−0.837553	+	0.608518i
$485$	2.34631	+	17.2568i	0.106540	+	0.783593i
$486$		0			0
$487$	−12.7540	−	17.5544i	−0.577940	−	0.795466i	0.415528	−	0.909581i	$-0.363597\pi$
$487$	−12.7540	−	17.5544i	−0.577940	−	0.795466i	−0.993468	+	0.114115i	$0.963597\pi$
$488$	−28.1596	−	38.7584i	−1.27473	−	1.75451i
$489$		0			0
$490$	48.5147	+	50.6921i	2.19167	+	2.29004i
$491$	−22.5391	+	16.3756i	−1.01717	+	0.739020i	−0.965702	−	0.259655i	$-0.916391\pi$
$491$	−22.5391	+	16.3756i	−1.01717	+	0.739020i	−0.0514718	+	0.998674i	$0.516391\pi$
$492$		0			0
$493$		−	19.8935i		−	0.895958i
$494$	1.57064	−	4.83392i	0.0706663	−	0.217489i
$495$		0			0
$496$	−1.51722	−	4.66951i	−0.0681250	−	0.209667i
$497$	30.4799	−	9.90353i	1.36721	−	0.444234i
$498$		0			0
$499$	9.83737			0.440381			0.220191	−	0.975457i	$-0.429332\pi$
$499$	9.83737			0.440381			0.220191	+	0.975457i	$0.429332\pi$
$500$	54.2220	+	12.2910i	2.42488	+	0.549672i
$501$		0			0
$502$	29.3331	−	40.3736i	1.30920	−	1.80196i
$503$	25.2703	−	8.21082i	1.12675	−	0.366102i	0.314408	−	0.949288i	$-0.398194\pi$
$503$	25.2703	−	8.21082i	1.12675	−	0.366102i	0.812339	+	0.583186i	$0.198194\pi$
$504$		0			0
$505$	−6.62808	+	36.6270i	−0.294946	+	1.62988i
$506$	−0.738512	+	2.27291i	−0.0328309	+	0.101043i
$507$		0			0
$508$	−29.2546	−	9.50541i	−1.29796	−	0.421734i
$509$	10.2254	−	7.42915i	0.453231	−	0.329291i	−0.337639	−	0.941276i	$-0.609628\pi$
$509$	10.2254	−	7.42915i	0.453231	−	0.329291i	0.790870	+	0.611984i	$0.209628\pi$
$510$		0			0
$511$	−47.8247	−	34.7467i	−2.11564	−	1.53710i
$512$	18.5453	+	25.5254i	0.819593	+	1.12807i
$513$		0			0
$514$	52.4505	+	38.1075i	2.31349	+	1.68085i
$515$	0.543269	+	3.99569i	0.0239393	+	0.176071i
$516$		0			0
$517$	−19.0919	−	6.20335i	−0.839663	−	0.272823i
$518$			27.2661i			1.19800i
$519$		0			0
$520$	38.7328	−	5.26626i	1.69854	−	0.230941i
$521$	−7.43316	−	22.8769i	−0.325653	−	1.00226i	−0.971145	−	0.238489i	$-0.923348\pi$
$521$	−7.43316	−	22.8769i	−0.325653	−	1.00226i	0.645493	−	0.763767i	$-0.276652\pi$
$522$		0			0
$523$	−2.53935	+	3.49512i	−0.111038	+	0.152831i	−0.860919	−	0.508742i	$-0.830111\pi$
$523$	−2.53935	+	3.49512i	−0.111038	+	0.152831i	0.749881	+	0.661573i	$0.230111\pi$
$524$	−31.4894			−1.37562
$525$		0			0
$526$	21.7438			0.948075
$527$	−1.20798	+	1.66264i	−0.0526203	+	0.0724257i
$528$		0			0
$529$	7.06796	+	21.7530i	0.307303	+	0.945781i
$530$	−33.5536	−	18.0345i	−1.45747	−	0.783369i
$531$		0			0
$532$			18.6779i			0.809791i
$533$	−5.88221	−	1.91125i	−0.254787	−	0.0827852i
$534$		0			0
$535$	−32.0522	−	5.80021i	−1.38574	−	0.250765i
$536$	−70.0880	−	50.9219i	−3.02734	−	2.19949i
$537$		0			0
$538$	2.02473	+	2.78680i	0.0872921	+	0.120147i
$539$	−24.3592	−	17.6980i	−1.04923	−	0.762308i
$540$		0			0
$541$	−6.35517	+	4.61730i	−0.273230	+	0.198513i	−0.715959	−	0.698142i	$-0.754010\pi$
$541$	−6.35517	+	4.61730i	−0.273230	+	0.198513i	0.442729	+	0.896655i	$0.354010\pi$
$542$	−4.98671	−	1.62028i	−0.214198	−	0.0695970i
$543$		0			0
$544$	−17.8168	+	54.8344i	−0.763887	+	2.35100i
$545$	8.86483	+	18.3847i	0.379728	+	0.787514i
$546$		0			0
$547$	−15.9585	+	5.18523i	−0.682336	+	0.221704i	−0.629618	−	0.776905i	$-0.716788\pi$
$547$	−15.9585	+	5.18523i	−0.682336	+	0.221704i	−0.0527180	+	0.998609i	$0.516788\pi$
$548$	52.1396	−	71.7640i	2.22729	−	3.06561i
$549$		0			0
$550$	−33.4209	−	1.46775i	−1.42507	−	0.0625852i
$551$	3.80960			0.162294
$552$		0			0
$553$	44.5644	−	14.4798i	1.89507	−	0.615746i
$554$	−11.2269	−	34.5529i	−0.476986	−	1.46801i
$555$		0			0
$556$	16.7662	−	51.6009i	0.711044	−	2.18837i
$557$		−	32.4327i		−	1.37422i	−0.726554	−	0.687109i	$-0.758879\pi$
$557$		−	32.4327i		−	1.37422i	0.726554	−	0.687109i	$-0.241121\pi$
$558$		0			0
$559$	18.4352	−	13.3940i	0.779726	−	0.566504i
$560$	−94.3792	+	45.5082i	−3.98825	+	1.92307i
$561$		0			0
$562$	−44.8191	−	61.6882i	−1.89058	−	2.60216i
$563$	15.9941	+	22.0140i	0.674072	+	0.927780i	0.999844	−	0.0176683i	$-0.00562428\pi$
$563$	15.9941	+	22.0140i	0.674072	+	0.927780i	−0.325772	+	0.945448i	$0.605624\pi$
$564$		0			0
$565$	4.38731	−	2.11549i	0.184575	−	0.0889995i
$566$	67.7049	−	49.1905i	2.84585	−	2.06763i
$567$		0			0
$568$			57.8943i			2.42919i
$569$	−14.2708	+	43.9211i	−0.598264	+	1.84127i	−0.0605069	+	0.998168i	$0.519272\pi$
$569$	−14.2708	+	43.9211i	−0.598264	+	1.84127i	−0.537757	+	0.843100i	$0.680728\pi$
$570$		0			0
$571$	2.01162	+	6.19112i	0.0841835	+	0.259090i	0.984284	−	0.176592i	$-0.0565072\pi$
$571$	2.01162	+	6.19112i	0.0841835	+	0.259090i	−0.900101	+	0.435682i	$0.856507\pi$
$572$	−26.6854	+	8.67060i	−1.11577	+	0.362536i
$573$		0			0
$574$	31.8696			1.33021
$575$	1.48956	−	0.985371i	0.0621190	−	0.0410928i
$576$		0			0
$577$	17.2410	−	23.7302i	0.717753	−	0.987902i	−0.281843	−	0.959461i	$-0.590946\pi$
$577$	17.2410	−	23.7302i	0.717753	−	0.987902i	0.999595	−	0.0284414i	$-0.00905439\pi$
$578$	8.46895	−	2.75173i	0.352262	−	0.114457i
$579$		0			0
$580$	21.2862	+	44.1452i	0.883860	+	1.83303i
$581$	0.452514	−	1.39269i	0.0187734	−	0.0577787i
$582$		0			0
$583$	15.5463	+	5.05131i	0.643864	+	0.209204i
$584$	86.3934	−	62.7684i	3.57498	−	2.59738i
$585$		0			0
$586$	−11.9203	−	8.66062i	−0.492424	−	0.357767i
$587$	1.94077	+	2.67125i	0.0801043	+	0.110254i	0.847189	−	0.531292i	$-0.178293\pi$
$587$	1.94077	+	2.67125i	0.0801043	+	0.110254i	−0.767084	+	0.641546i	$0.778293\pi$
$588$		0			0
$589$	−0.318395	−	0.231327i	−0.0131192	−	0.00953168i
$590$	40.1876	+	7.27241i	1.65450	+	0.299400i
$591$		0			0
$592$	−24.3686	−	7.91783i	−1.00154	−	0.325421i
$593$			21.5576i			0.885263i	0.896704	+	0.442631i	$0.145955\pi$
$593$			21.5576i			0.885263i	−0.896704	+	0.442631i	$0.854045\pi$
$594$		0			0
$595$	38.6311	+	20.7636i	1.58372	+	0.851225i
$596$	−25.0184	−	76.9987i	−1.02479	−	3.15399i
$597$		0			0
$598$	1.23462	−	1.69931i	0.0504873	−	0.0694898i
$599$	32.2761			1.31877			0.659383	−	0.751807i	$-0.270818\pi$
$599$	32.2761			1.31877			0.659383	+	0.751807i	$0.270818\pi$
$600$		0			0
$601$	−7.60616			−0.310262			−0.155131	−	0.987894i	$-0.549580\pi$
$601$	−7.60616			−0.310262			−0.155131	+	0.987894i	$0.549580\pi$
$602$	−69.0162	+	94.9926i	−2.81289	+	3.87161i
$603$		0			0
$604$	−29.4936	−	90.7721i	−1.20008	−	3.69346i
$605$	−10.1481	+	1.37977i	−0.412578	+	0.0560957i
$606$		0			0
$607$		−	31.1356i		−	1.26375i	−0.775069	−	0.631877i	$-0.782285\pi$
$607$		−	31.1356i		−	1.26375i	0.775069	−	0.631877i	$-0.217715\pi$
$608$	−10.5008	−	3.41190i	−0.425862	−	0.138371i
$609$		0			0
$610$	−4.85482	−	35.7067i	−0.196566	−	1.44572i
$611$	14.2738	+	10.3705i	0.577457	+	0.419547i
$612$		0			0
$613$	−13.0280	−	17.9315i	−0.526196	−	0.724246i	0.460349	−	0.887738i	$-0.347724\pi$
$613$	−13.0280	−	17.9315i	−0.526196	−	0.724246i	−0.986545	+	0.163492i	$0.947724\pi$
$614$	−38.8120	−	28.1986i	−1.56632	−	1.13800i
$615$		0			0
$616$	69.9247	−	50.8033i	2.81735	−	2.04692i
$617$	11.3889	+	3.70046i	0.458498	+	0.148975i	0.529154	−	0.848526i	$-0.322509\pi$
$617$	11.3889	+	3.70046i	0.458498	+	0.148975i	−0.0706562	+	0.997501i	$0.522509\pi$
$618$		0			0
$619$	−9.85294	+	30.3242i	−0.396023	+	1.21883i	0.532139	+	0.846657i	$0.321389\pi$
$619$	−9.85294	+	30.3242i	−0.396023	+	1.21883i	−0.928162	+	0.372177i	$0.878611\pi$
$620$	0.901562	−	4.98207i	0.0362076	−	0.200085i
$621$		0			0
$622$	−36.0160	+	11.7023i	−1.44411	+	0.469220i
$623$	33.3716	−	45.9320i	1.33700	−	1.84023i
$624$		0			0
$625$	18.8593	+	16.4111i	0.754374	+	0.656445i
$626$	23.9460			0.957074
$627$		0			0
$628$	40.6399	−	13.2047i	1.62171	−	0.526926i
$629$	3.31422	+	10.2001i	0.132147	+	0.406705i
$630$		0			0
$631$	−2.47332	+	7.61208i	−0.0984611	+	0.303032i	−0.988140	−	0.153554i	$-0.950928\pi$
$631$	−2.47332	+	7.61208i	−0.0984611	+	0.303032i	0.889679	+	0.456586i	$0.150928\pi$
$632$			84.6467i			3.36706i
$633$		0			0
$634$	−43.0458	+	31.2746i	−1.70957	+	1.24207i
$635$	−9.56346	−	9.99267i	−0.379514	−	0.396547i
$636$		0			0
$637$	15.5548	+	21.4093i	0.616302	+	0.848267i
$638$	−17.3332	−	23.8570i	−0.686226	−	0.944509i
$639$		0			0
$640$	−1.98061	−	14.5672i	−0.0782904	−	0.575818i
$641$	39.1299	−	28.4296i	1.54554	−	1.12290i	0.598800	−	0.800899i	$-0.295645\pi$
$641$	39.1299	−	28.4296i	1.54554	−	1.12290i	0.946739	−	0.322001i	$-0.104355\pi$
$642$		0			0
$643$			34.0606i			1.34322i	0.740906	+	0.671609i	$0.234396\pi$
$643$			34.0606i			1.34322i	−0.740906	+	0.671609i	$0.765604\pi$
$644$	−2.38524	+	7.34101i	−0.0939916	+	0.289276i
$645$		0			0
$646$	3.18341	+	9.79754i	0.125250	+	0.385479i
$647$	−8.30394	+	2.69811i	−0.326462	+	0.106074i	−0.467662	−	0.883907i	$-0.654904\pi$
$647$	−8.30394	+	2.69811i	−0.326462	+	0.106074i	0.141201	+	0.989981i	$0.454904\pi$
$648$		0			0
$649$	−17.5252			−0.687926
$650$	27.5373	+	10.3038i	1.08010	+	0.404149i
$651$		0			0
$652$	−20.0227	+	27.5589i	−0.784151	+	1.07929i
$653$	−8.06946	+	2.62193i	−0.315782	+	0.102604i	−0.462620	−	0.886557i	$-0.653091\pi$
$653$	−8.06946	+	2.62193i	−0.315782	+	0.102604i	0.146838	+	0.989161i	$0.453091\pi$
$654$		0			0
$655$	−12.4721	−	6.70357i	−0.487326	−	0.261930i
$656$	−9.25462	+	28.4828i	−0.361332	+	1.11207i
$657$		0			0
$658$	−86.4631	−	28.0936i	−3.37068	−	1.09520i
$659$	21.7447	−	15.7984i	0.847052	−	0.615419i	−0.0772796	−	0.997009i	$-0.524623\pi$
$659$	21.7447	−	15.7984i	0.847052	−	0.615419i	0.924332	+	0.381590i	$0.124623\pi$
$660$		0			0
$661$	23.7544	+	17.2586i	0.923938	+	0.671280i	0.944501	−	0.328509i	$-0.106546\pi$
$661$	23.7544	+	17.2586i	0.923938	+	0.671280i	−0.0205634	+	0.999789i	$0.506546\pi$
$662$	47.1512	+	64.8980i	1.83258	+	2.52233i
$663$		0			0
$664$	2.14011	+	1.55488i	0.0830523	+	0.0603410i
$665$	−3.97623	+	7.39785i	−0.154191	+	0.286876i
$666$		0			0
$667$	1.49729	+	0.486499i	0.0579753	+	0.0188373i
$668$			69.1392i			2.67508i
$669$		0			0
$670$	−28.3026	−	58.6965i	−1.09342	−	2.26764i
$671$	4.77843	+	14.7065i	0.184469	+	0.567738i
$672$		0			0
$673$	−14.8360	+	20.4200i	−0.571887	+	0.787135i	−0.992777	−	0.119977i	$-0.961718\pi$
$673$	−14.8360	+	20.4200i	−0.571887	+	0.787135i	0.420890	+	0.907112i	$0.361718\pi$
$674$	−36.8651			−1.41999
$675$		0			0
$676$	−39.9857			−1.53791
$677$	0.0353259	−	0.0486219i	0.00135768	−	0.00186869i	−0.808338	−	0.588719i	$-0.799632\pi$
$677$	0.0353259	−	0.0486219i	0.00135768	−	0.00186869i	0.809695	+	0.586851i	$0.199632\pi$
$678$		0			0
$679$	−10.4587	−	32.1885i	−0.401367	−	1.23528i
$680$	−57.2378	+	54.7792i	−2.19497	+	2.10069i
$681$		0			0
$682$			3.04641i			0.116653i
$683$	30.4911	+	9.90715i	1.16671	+	0.379087i	0.827413	−	0.561593i	$-0.189811\pi$
$683$	30.4911	+	9.90715i	1.16671	+	0.379087i	0.339295	+	0.940680i	$0.389811\pi$
$684$		0			0
$685$	35.9285	−	17.3242i	1.37276	−	0.661924i
$686$	−45.3344	−	32.9374i	−1.73088	−	1.25756i
$687$		0			0
$688$	−64.8562	−	89.2668i	−2.47262	−	3.40327i
$689$	−11.6230	−	8.44460i	−0.442801	−	0.321714i
$690$		0			0
$691$	−30.6635	+	22.2783i	−1.16649	+	0.847508i	−0.990585	−	0.136899i	$-0.956286\pi$
$691$	−30.6635	+	22.2783i	−1.16649	+	0.847508i	−0.175909	+	0.984406i	$0.556286\pi$
$692$	−72.1005	−	23.4269i	−2.74085	−	0.890556i
$693$		0			0
$694$	10.1579	−	31.2627i	0.385588	−	1.18672i
$695$	17.6256	−	16.8686i	0.668578	−	0.639861i
$696$		0			0
$697$	11.9222	−	3.87377i	0.451587	−	0.146729i
$698$	15.6933	−	21.6000i	0.594002	−	0.817573i
$699$		0			0
$700$	−107.943	−	4.74054i	−4.07985	−	0.179175i
$701$	−12.6083			−0.476209			−0.238104	−	0.971240i	$-0.576526\pi$
$701$	−12.6083			−0.476209			−0.238104	+	0.971240i	$0.576526\pi$
$702$		0			0
$703$	−1.95332	+	0.634672i	−0.0736708	+	0.0239371i
$704$	9.52473	+	29.3141i	0.358977	+	1.10482i
$705$		0			0
$706$	−28.9181	+	89.0007i	−1.08835	+	3.34959i
$707$		−	72.3359i		−	2.72047i
$708$		0			0
$709$	34.6432	−	25.1697i	1.30105	−	0.945269i	0.301086	−	0.953597i	$-0.402651\pi$
$709$	34.6432	−	25.1697i	1.30105	−	0.945269i	0.999965	+	0.00832796i	$0.00265090\pi$
$710$	−20.6164	+	38.3573i	−0.773721	+	1.43952i
$711$		0			0
$712$	60.2844	+	82.9743i	2.25925	+	3.10960i
$713$	−0.0955977	−	0.131579i	−0.00358016	−	0.00492767i
$714$		0			0
$715$	−12.4152	−	2.24667i	−0.464302	−	0.0840209i
$716$	−27.5073	+	19.9852i	−1.02800	+	0.746883i
$717$		0			0
$718$			83.3275i			3.10975i
$719$	−8.68714	+	26.7363i	−0.323976	+	0.997095i	0.647925	+	0.761704i	$0.275637\pi$
$719$	−8.68714	+	26.7363i	−0.323976	+	0.997095i	−0.971901	+	0.235391i	$0.924363\pi$
$720$		0			0
$721$	−2.42163	−	7.45301i	−0.0901862	−	0.277565i
$722$	45.8397	−	14.8942i	1.70598	−	0.554306i
$723$		0			0
$724$	−63.8942			−2.37461
$725$	−0.966892	+	22.0162i	−0.0359095	+	0.817663i
$726$		0			0
$727$	−6.43602	+	8.85842i	−0.238699	+	0.328540i	−0.911513	−	0.411271i	$-0.865085\pi$
$727$	−6.43602	+	8.85842i	−0.238699	+	0.328540i	0.672815	+	0.739811i	$0.265085\pi$
$728$	−72.2467	+	23.4744i	−2.67764	+	0.870019i
$729$		0			0
$730$	79.5911	−	10.8215i	2.94580	−	0.400522i
$731$	−14.2722	+	43.9252i	−0.527875	+	1.62463i
$732$		0			0
$733$	27.8180	+	9.03862i	1.02748	+	0.333849i	0.773794	−	0.633437i	$-0.218357\pi$
$733$	27.8180	+	9.03862i	1.02748	+	0.333849i	0.253688	+	0.967286i	$0.418357\pi$
$734$	−27.6506	+	20.0893i	−1.02060	+	0.741511i
$735$		0			0
$736$	−3.69141	−	2.68197i	−0.136067	−	0.0988587i
$737$	16.4361	+	22.6224i	0.605433	+	0.833307i
$738$		0			0
$739$	−9.13635	−	6.63794i	−0.336086	−	0.244181i	0.406923	−	0.913463i	$-0.366602\pi$
$739$	−9.13635	−	6.63794i	−0.336086	−	0.244181i	−0.743009	+	0.669282i	$0.766602\pi$
$740$	−18.2687	−	19.0886i	−0.671570	−	0.701711i
$741$		0			0
$742$	70.4058	+	22.8762i	2.58468	+	0.839813i
$743$			4.14745i			0.152155i	0.997102	+	0.0760777i	$0.0242397\pi$
$743$			4.14745i			0.152155i	−0.997102	+	0.0760777i	$0.975760\pi$
$744$		0			0
$745$	6.48262	−	35.8232i	0.237505	−	1.31246i
$746$	6.68743	+	20.5818i	0.244844	+	0.753553i
$747$		0			0
$748$	33.4274	−	46.0089i	1.22223	−	1.68225i
$749$	63.3010			2.31297
$750$		0			0
$751$	−3.25169			−0.118656			−0.0593279	−	0.998239i	$-0.518896\pi$
$751$	−3.25169			−0.118656			−0.0593279	+	0.998239i	$0.518896\pi$
$752$	50.2162	−	69.1166i	1.83119	−	2.52042i
$753$		0			0
$754$	8.00903	+	24.6493i	0.291672	+	0.897673i
$755$	7.64222	−	42.2312i	0.278129	−	1.53695i
$756$		0			0
$757$		−	28.7514i		−	1.04499i	−0.852643	−	0.522494i	$-0.825002\pi$
$757$		−	28.7514i		−	1.04499i	0.852643	−	0.522494i	$-0.174998\pi$
$758$	45.0882	+	14.6501i	1.63768	+	0.532114i
$759$		0			0
$760$	−10.4902	−	10.9610i	−0.380520	−	0.397598i
$761$	11.8402	+	8.60242i	0.429207	+	0.311837i	0.781332	−	0.624116i	$-0.214541\pi$
$761$	11.8402	+	8.60242i	0.429207	+	0.311837i	−0.352124	+	0.935953i	$0.614541\pi$
$762$		0			0
$763$	−23.3144	−	32.0896i	−0.844039	−	1.16172i
$764$	−0.704350	−	0.511740i	−0.0254825	−	0.0185141i
$765$		0			0
$766$	42.9025	−	31.1705i	1.55013	−	1.12624i
$767$	14.6490	+	4.75976i	0.528946	+	0.171865i
$768$		0			0
$769$	3.45265	−	10.6262i	0.124506	−	0.383189i	−0.869305	−	0.494276i	$-0.835433\pi$
$769$	3.45265	−	10.6262i	0.124506	−	0.383189i	0.993811	+	0.111087i	$0.0354333\pi$
$770$	64.4192	−	8.75868i	2.32151	−	0.315641i
$771$		0			0
$772$	−47.2960	+	15.3674i	−1.70222	+	0.553085i
$773$	−27.3294	+	37.6156i	−0.982969	+	1.35294i	−0.0477539	+	0.998859i	$0.515206\pi$
$773$	−27.3294	+	37.6156i	−0.982969	+	1.35294i	−0.935215	+	0.354081i	$0.884794\pi$
$774$		0			0
$775$	1.41769	−	1.78134i	0.0509248	−	0.0639876i
$776$	61.1396			2.19478
$777$		0			0
$778$	48.0300	−	15.6059i	1.72196	−	0.559498i
$779$	0.741825	+	2.28310i	0.0265787	+	0.0818007i
$780$		0			0
$781$	5.77448	−	17.7720i	0.206627	−	0.635933i
$782$			4.25727i			0.152240i
$783$		0			0
$784$	103.668	−	75.3192i	3.70243	−	2.68997i
$785$	18.9075	+	3.42153i	0.674838	+	0.122120i
$786$		0			0
$787$	1.66356	+	2.28969i	0.0592995	+	0.0816188i	0.837637	−	0.546228i	$-0.183937\pi$
$787$	1.66356	+	2.28969i	0.0592995	+	0.0816188i	−0.778337	+	0.627846i	$0.783937\pi$
$788$	−53.6437	−	73.8342i	−1.91098	−	2.63023i
$789$		0			0
$790$	−30.1431	+	56.0818i	−1.07244	+	1.99530i
$791$	−7.65782	+	5.56373i	−0.272281	+	0.197824i
$792$		0			0
$793$		−	13.5907i		−	0.482619i
$794$	−2.35305	+	7.24193i	−0.0835065	+	0.257007i
$795$		0			0
$796$	3.25657	+	10.0227i	0.115426	+	0.355245i
$797$	−1.65389	+	0.537382i	−0.0585838	+	0.0190350i	−0.338162	−	0.941088i	$-0.609805\pi$
$797$	−1.65389	+	0.537382i	−0.0585838	+	0.0190350i	0.279578	+	0.960123i	$0.409805\pi$
$798$		0			0
$799$	−35.7602			−1.26510
$800$	22.3830	−	59.8195i	0.791360	−	2.11494i
$801$		0			0
$802$	8.54966	−	11.7676i	0.301899	−	0.415528i
$803$	−32.7811	+	10.6512i	−1.15682	+	0.375874i
$804$		0			0
$805$	−2.50751	+	2.39981i	−0.0883782	+	0.0845820i
$806$	0.827387	−	2.54644i	0.0291435	−	0.0896944i
$807$		0			0
$808$	124.276	+	40.3799i	4.37203	+	1.42056i
$809$	17.4093	−	12.6486i	0.612077	−	0.444700i	−0.238068	−	0.971249i	$-0.576514\pi$
$809$	17.4093	−	12.6486i	0.612077	−	0.444700i	0.850145	+	0.526548i	$0.176514\pi$
$810$		0			0
$811$	6.39495	+	4.64620i	0.224557	+	0.163150i	0.694376	−	0.719613i	$-0.255681\pi$
$811$	6.39495	+	4.64620i	0.224557	+	0.163150i	−0.469819	+	0.882763i	$0.655681\pi$
$812$	−55.9824	−	77.0532i	−1.96460	−	2.70404i
$813$		0			0
$814$	12.8619	+	9.34469i	0.450808	+	0.327531i
$815$	−13.7973	+	6.65287i	−0.483299	+	0.233040i
$816$		0			0
$817$	−8.41166	−	2.73312i	−0.294287	−	0.0956196i
$818$		−	98.3233i		−	3.43779i
$819$		0			0
$820$	−22.3114	+	21.3531i	−0.779148	+	0.745681i
$821$	−8.01641	−	24.6720i	−0.279775	−	0.861058i	−0.987916	−	0.154988i	$-0.950466\pi$
$821$	−8.01641	−	24.6720i	−0.279775	−	0.861058i	0.708142	−	0.706070i	$-0.249534\pi$
$822$		0			0
$823$	−1.56186	+	2.14972i	−0.0544432	+	0.0749346i	−0.835371	−	0.549687i	$-0.814747\pi$
$823$	−1.56186	+	2.14972i	−0.0544432	+	0.0749346i	0.780927	+	0.624622i	$0.214747\pi$
$824$	14.1564			0.493162
$825$		0			0
$826$	−79.3678			−2.76156
$827$	−1.79020	+	2.46399i	−0.0622512	+	0.0856815i	−0.839008	−	0.544120i	$-0.816864\pi$
$827$	−1.79020	+	2.46399i	−0.0622512	+	0.0856815i	0.776756	+	0.629801i	$0.216864\pi$
$828$		0			0
$829$	−7.33415	−	22.5722i	−0.254725	−	0.783964i	−0.993884	−	0.110432i	$-0.964776\pi$
$829$	−7.33415	−	22.5722i	−0.254725	−	0.783964i	0.739158	−	0.673532i	$-0.235224\pi$
$830$	0.864206	+	1.79227i	0.0299970	+	0.0622106i
$831$		0			0
$832$		−	27.0900i		−	0.939177i
$833$	−51.0115	−	16.5746i	−1.76744	−	0.574277i
$834$		0			0
$835$	−14.7186	+	27.3843i	−0.509358	+	0.947671i
$836$	8.81069	+	6.40134i	0.304724	+	0.221395i
$837$		0			0
$838$	36.9757	+	50.8927i	1.27731	+	1.75806i
$839$	4.77364	+	3.46825i	0.164804	+	0.119737i	0.667131	−	0.744941i	$-0.267522\pi$
$839$	4.77364	+	3.46825i	0.164804	+	0.119737i	−0.502326	+	0.864678i	$0.667522\pi$
$840$		0			0
$841$	7.74553	−	5.62746i	0.267087	−	0.194050i
$842$	22.4186	+	7.28423i	0.772594	+	0.251031i
$843$		0			0
$844$	−4.48216	+	13.7947i	−0.154282	+	0.474832i
$845$	−15.8373	−	8.51229i	−0.544819	−	0.292832i
$846$		0			0
$847$	18.9288	−	6.15034i	0.650402	−	0.211328i
$848$	−40.8904	+	56.2808i	−1.40418	+	1.93269i
$849$		0			0
$850$	−57.4294	+	15.9108i	−1.96981	+	0.545735i
$851$	−0.848765			−0.0290953
$852$		0			0
$853$	42.2811	−	13.7380i	1.44768	−	0.470378i	0.523395	−	0.852090i	$-0.324665\pi$
$853$	42.2811	−	13.7380i	1.44768	−	0.470378i	0.924281	+	0.381712i	$0.124665\pi$
$854$	21.6404	+	66.6023i	0.740520	+	2.27909i
$855$		0			0
$856$	−35.3363	+	108.754i	−1.20777	+	3.71713i
$857$		−	17.1872i		−	0.587103i	−0.955943	−	0.293551i	$-0.905163\pi$
$857$		−	17.1872i		−	0.587103i	0.955943	−	0.293551i	$-0.0948372\pi$
$858$		0			0
$859$	24.3810	−	17.7138i	0.831868	−	0.604387i	−0.0882193	−	0.996101i	$-0.528118\pi$
$859$	24.3810	−	17.7138i	0.831868	−	0.604387i	0.920087	+	0.391714i	$0.128118\pi$
$860$	−15.3292	−	112.745i	−0.522721	−	3.84456i
$861$		0			0
$862$	40.4088	+	55.6179i	1.37633	+	1.89435i
$863$	−8.27520	−	11.3898i	−0.281691	−	0.387714i	0.644602	−	0.764518i	$-0.277023\pi$
$863$	−8.27520	−	11.3898i	−0.281691	−	0.387714i	−0.926293	+	0.376804i	$0.877023\pi$
$864$		0			0
$865$	−23.5699	−	24.6278i	−0.801402	−	0.837370i
$866$	−11.2853	+	8.19921i	−0.383488	+	0.278621i
$867$		0			0
$868$			9.83925i			0.333966i
$869$	8.44281	−	25.9843i	0.286403	−	0.881457i
$870$		0			0
$871$	−7.59455	−	23.3736i	−0.257331	−	0.791985i
$872$	68.1461	−	22.1420i	2.30772	−	0.749823i
$873$		0			0
$874$	−0.815266			−0.0275768
$875$	−41.7441	−	24.8568i	−1.41121	−	0.840314i
$876$		0			0
$877$	−22.3728	+	30.7935i	−0.755475	+	1.03982i	0.242102	+	0.970251i	$0.422163\pi$
$877$	−22.3728	+	30.7935i	−0.755475	+	1.03982i	−0.997577	+	0.0695710i	$0.977837\pi$
$878$	42.9345	−	13.9503i	1.44897	−	0.470799i
$879$		0			0
$880$	−10.8788	+	60.1168i	−0.366725	+	2.02654i
$881$	−8.94103	+	27.5176i	−0.301231	+	0.927093i	0.679826	+	0.733373i	$0.262055\pi$
$881$	−8.94103	+	27.5176i	−0.301231	+	0.927093i	−0.981057	+	0.193720i	$0.937945\pi$
$882$		0			0
$883$	−13.0493	−	4.23997i	−0.439144	−	0.142686i	0.0810968	−	0.996706i	$-0.474158\pi$
$883$	−13.0493	−	4.23997i	−0.439144	−	0.142686i	−0.520240	+	0.854020i	$0.674158\pi$
$884$	−40.4371	+	29.3793i	−1.36005	+	0.988133i
$885$		0			0
$886$	−17.0875	−	12.4148i	−0.574067	−	0.417084i
$887$	−8.80375	−	12.1173i	−0.295601	−	0.406860i	0.635222	−	0.772329i	$-0.280908\pi$
$887$	−8.80375	−	12.1173i	−0.295601	−	0.406860i	−0.930823	+	0.365469i	$0.880908\pi$
$888$		0			0
$889$	21.7463	+	15.7996i	0.729348	+	0.529902i
$890$	10.3933	+	76.4413i	0.348383	+	2.56232i
$891$		0			0
$892$	−2.91956	−	0.948624i	−0.0977542	−	0.0317623i
$893$		−	6.84806i		−	0.229162i
$894$		0			0
$895$	−15.1495	+	2.05978i	−0.506390	+	0.0688508i
$896$	8.82858	+	27.1716i	0.294942	+	0.907738i
$897$		0			0
$898$	35.2144	−	48.4684i	1.17512	−	1.61741i
$899$	2.00684			0.0669318
$900$		0			0
$901$	29.1191			0.970097
$902$	10.9224	−	15.0334i	0.363676	−	0.500557i
$903$		0			0
$904$	−5.28395	−	16.2623i	−0.175741	−	0.540877i
$905$	−25.3068	−	13.6020i	−0.841227	−	0.452146i
$906$		0			0
$907$			19.4807i			0.646848i	0.946254	+	0.323424i	$0.104834\pi$
$907$			19.4807i			0.646848i	−0.946254	+	0.323424i	$0.895166\pi$
$908$	81.5624	+	26.5012i	2.70674	+	0.879475i
$909$		0			0
$910$	−56.2257	−	10.1747i	−1.86386	−	0.337287i
$911$	31.4257	+	22.8321i	1.04118	+	0.756461i	0.970515	−	0.241039i	$-0.0774882\pi$
$911$	31.4257	+	22.8321i	1.04118	+	0.756461i	0.0706638	+	0.997500i	$0.477488\pi$
$912$		0			0
$913$	−0.501870	−	0.690765i	−0.0166095	−	0.0228610i
$914$	16.6497	+	12.0967i	0.550723	+	0.400124i
$915$		0			0
$916$	−48.5508	+	35.2742i	−1.60416	+	1.16549i
$917$	26.1704	+	8.50328i	0.864222	+	0.280803i
$918$		0			0
$919$	−9.74095	+	29.9796i	−0.321324	+	0.988934i	0.651748	+	0.758435i	$0.274036\pi$
$919$	−9.74095	+	29.9796i	−0.321324	+	0.988934i	−0.973073	+	0.230499i	$0.925964\pi$
$920$	−2.72321	−	5.64765i	−0.0897817	−	0.186198i
$921$		0			0
$922$	−50.7037	+	16.4746i	−1.66984	+	0.542563i
$923$	−9.65357	+	13.2870i	−0.317751	+	0.437347i
$924$		0			0
$925$	−3.17210	−	11.4496i	−0.104298	−	0.376461i
$926$	−78.3812			−2.57577
$927$		0			0
$928$	53.5457	−	17.3981i	1.75772	−	0.571119i
$929$	−7.00292	−	21.5528i	−0.229758	−	0.707124i	−0.997774	−	0.0666920i	$-0.978755\pi$
$929$	−7.00292	−	21.5528i	−0.229758	−	0.707124i	0.768015	−	0.640432i	$-0.221245\pi$
$930$		0			0
$931$	3.17404	−	9.76869i	0.104025	−	0.320156i
$932$			13.9318i			0.456352i
$933$		0			0
$934$	−70.5551	+	51.2613i	−2.30863	+	1.67732i
$935$	23.0343	−	11.1068i	0.753301	−	0.363230i
$936$		0			0
$937$	4.69990	+	6.46885i	0.153539	+	0.211328i	0.878856	−	0.477086i	$-0.158307\pi$
$937$	4.69990	+	6.46885i	0.153539	+	0.211328i	−0.725318	+	0.688414i	$0.758307\pi$
$938$	74.4355	+	102.452i	2.43041	+	3.34517i
$939$		0			0
$940$	79.3546	−	38.2636i	2.58826	−	1.24802i
$941$	−10.9522	+	7.95726i	−0.357033	+	0.259399i	−0.751813	−	0.659376i	$-0.770821\pi$
$941$	−10.9522	+	7.95726i	−0.357033	+	0.259399i	0.394781	+	0.918775i	$0.370821\pi$
$942$		0			0
$943$			0.992064i			0.0323061i
$944$	23.0477	−	70.9335i	0.750138	−	2.30869i
$945$		0			0
$946$	21.1562	+	65.1121i	0.687847	+	2.11698i
$947$	−33.9208	+	11.0215i	−1.10228	+	0.358152i	−0.802979	−	0.596007i	$-0.796753\pi$
$947$	−33.9208	+	11.0215i	−1.10228	+	0.358152i	−0.299299	+	0.954159i	$0.596753\pi$
$948$		0			0
$949$	30.2940			0.983384
$950$	−3.04691	−	10.9977i	−0.0988547	−	0.356813i
$951$		0			0
$952$	90.4998	−	124.562i	2.93312	−	4.03709i
$953$	−27.4175	+	8.90850i	−0.888141	+	0.288574i	−0.717334	−	0.696730i	$-0.754638\pi$
$953$	−27.4175	+	8.90850i	−0.888141	+	0.288574i	−0.170807	+	0.985304i	$0.554638\pi$
$954$		0			0
$955$	−0.170034	−	0.352632i	−0.00550216	−	0.0114109i
$956$	−19.6484	+	60.4716i	−0.635476	+	1.95579i
$957$		0			0
$958$	−73.7539	−	23.9641i	−2.38288	−	0.774244i
$959$	−62.7114	+	45.5625i	−2.02506	+	1.47129i
$960$		0			0
$961$	24.9118	+	18.0995i	0.803606	+	0.583854i
$962$	−8.21304	−	11.3043i	−0.264799	−	0.364464i
$963$		0			0
$964$	12.9526	+	9.41064i	0.417176	+	0.303096i
$965$	−22.0042	−	3.98191i	−0.708340	−	0.128182i
$966$		0			0
$967$	30.8235	+	10.0151i	0.991215	+	0.322065i	0.759350	−	0.650682i	$-0.225517\pi$
$967$	30.8235	+	10.0151i	0.991215	+	0.322065i	0.231866	+	0.972748i	$0.425517\pi$
$968$			35.9538i			1.15560i
$969$		0			0
$970$	40.5074	+	21.7721i	1.30061	+	0.699060i
$971$	13.3069	+	40.9546i	0.427040	+	1.31429i	0.901027	+	0.433763i	$0.142814\pi$
$971$	13.3069	+	40.9546i	0.427040	+	1.31429i	−0.473987	+	0.880532i	$0.657186\pi$
$972$		0			0
$973$	−27.8683	+	38.3574i	−0.893415	+	1.22968i
$974$	−57.2970			−1.83591
$975$		0			0
$976$	−65.8087			−2.10649
$977$	−6.66257	+	9.17025i	−0.213155	+	0.293382i	−0.902184	−	0.431351i	$-0.858037\pi$
$977$	−6.66257	+	9.17025i	−0.213155	+	0.293382i	0.689030	+	0.724733i	$0.258037\pi$
$978$		0			0
$979$	−10.2297	−	31.4838i	−0.326943	−	1.00623i
$980$	130.933	−	17.8022i	4.18252	−	0.568671i
$981$		0			0
$982$			73.5668i			2.34761i
$983$	−21.6685	−	7.04052i	−0.691117	−	0.224558i	−0.0576611	−	0.998336i	$-0.518364\pi$
$983$	−21.6685	−	7.04052i	−0.691117	−	0.224558i	−0.633456	+	0.773779i	$0.718364\pi$
$984$		0			0
$985$	−5.52878	−	40.6636i	−0.176162	−	1.29565i
$986$	−42.4984	−	30.8769i	−1.35342	−	0.983320i
$987$		0			0
$988$	−5.62613	−	7.74370i	−0.178991	−	0.246360i
$989$	−2.95702	−	2.14840i	−0.0940276	−	0.0683151i
$990$		0			0
$991$	40.9066	−	29.7204i	1.29944	−	0.944099i	0.299491	−	0.954099i	$-0.403183\pi$
$991$	40.9066	−	29.7204i	1.29944	−	0.944099i	0.999950	+	0.00999973i	$0.00318307\pi$
$992$	−5.53164	−	1.79734i	−0.175630	−	0.0570656i
$993$		0			0
$994$	26.1513	−	80.4854i	0.829469	−	2.55284i
$995$	−0.843823	+	4.66300i	−0.0267510	+	0.147827i
$996$		0			0
$997$	57.3525	−	18.6350i	1.81637	−	0.590176i	0.816455	−	0.577409i	$-0.195936\pi$
$997$	57.3525	−	18.6350i	1.81637	−	0.590176i	0.999919	−	0.0127664i	$-0.00406377\pi$
$998$	15.2687	−	21.0155i	0.483321	−	0.665235i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.c.109.6	yes	24
3.2	odd	2	inner	225.2.m.c.109.1	yes	24
25.8	odd	20		5625.2.a.bf.1.24		24
25.14	even	10	inner	225.2.m.c.64.6	yes	24
25.17	odd	20		5625.2.a.bf.1.1		24
75.8	even	20		5625.2.a.bf.1.2		24
75.14	odd	10	inner	225.2.m.c.64.1	✓	24
75.17	even	20		5625.2.a.bf.1.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.m.c.64.1	✓	24	75.14	odd	10	inner
225.2.m.c.64.6	yes	24	25.14	even	10	inner
225.2.m.c.109.1	yes	24	3.2	odd	2	inner
225.2.m.c.109.6	yes	24	1.1	even	1	trivial
5625.2.a.bf.1.1		24	25.17	odd	20
5625.2.a.bf.1.2		24	75.8	even	20
5625.2.a.bf.1.23		24	75.17	even	20
5625.2.a.bf.1.24		24	25.8	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.55211 - 2.13629i) q^{2} +(-1.53668 - 4.72941i) q^{4} +(0.398175 - 2.20033i) q^{5} +4.34551i q^{7} +(-7.46578 - 2.42578i) q^{8} +O(q^{10})\)	\(q+(1.55211 - 2.13629i) q^{2} +(-1.53668 - 4.72941i) q^{4} +(0.398175 - 2.20033i) q^{5} +4.34551i q^{7} +(-7.46578 - 2.42578i) q^{8} +(-4.08254 - 4.26577i) q^{10} +(2.04985 + 1.48930i) q^{11} +(-1.30894 - 1.80161i) q^{13} +(9.28329 + 6.74470i) q^{14} +(-8.72373 + 6.33816i) q^{16} +(4.29265 + 1.39477i) q^{17} +(-0.267098 + 0.822042i) q^{19} +(-11.0181 + 1.49807i) q^{20} +(6.36317 - 2.06752i) q^{22} +(-0.209955 + 0.288979i) q^{23} +(-4.68291 - 1.75223i) q^{25} -5.88039 q^{26} +(20.5517 - 6.67765i) q^{28} +(-1.36199 - 4.19178i) q^{29} +(-0.140703 + 0.433039i) q^{31} +12.7740i q^{32} +(9.64230 - 7.00554i) q^{34} +(9.56156 + 1.73027i) q^{35} +(1.39668 + 1.92237i) q^{37} +(1.34156 + 1.84650i) q^{38} +(-8.31021 + 15.4613i) q^{40} +(2.24693 - 1.63249i) q^{41} +10.2326i q^{43} +(3.89356 - 11.9831i) q^{44} +(0.291470 + 0.897053i) q^{46} +(-7.53506 + 2.44829i) q^{47} -11.8834 q^{49} +(-11.0117 + 7.28442i) q^{50} +(-6.50911 + 8.95903i) q^{52} +(6.13570 - 1.99361i) q^{53} +(4.09315 - 3.91734i) q^{55} +(10.5412 - 32.4426i) q^{56} +(-11.0688 - 3.59648i) q^{58} +(-5.59575 + 4.06555i) q^{59} +(4.93738 + 3.58722i) q^{61} +(0.706713 + 0.972706i) q^{62} +(9.84157 + 7.15032i) q^{64} +(-4.48532 + 2.16275i) q^{65} +(10.4960 + 3.41036i) q^{67} -22.4450i q^{68} +(18.5370 - 17.7407i) q^{70} +(-2.27903 - 7.01412i) q^{71} +(-7.99599 + 11.0055i) q^{73} +6.27455 q^{74} +4.29822 q^{76} +(-6.47177 + 8.90762i) q^{77} +(-3.33214 - 10.2553i) q^{79} +(10.4725 + 21.7188i) q^{80} -7.33391i q^{82} +(-0.320491 - 0.104134i) q^{83} +(4.77818 - 8.88990i) q^{85} +(21.8599 + 15.8822i) q^{86} +(-11.6910 - 16.0913i) q^{88} +(-10.5700 - 7.67955i) q^{89} +(7.82890 - 5.68803i) q^{91} +(1.68933 + 0.548898i) q^{92} +(-6.46496 + 19.8971i) q^{94} +(1.70241 + 0.915020i) q^{95} +(-7.40730 + 2.40678i) q^{97} +(-18.4444 + 25.3865i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4}+O(q^{10}) \) 24 * q + 8 * q^4	\( 24 q + 8 q^{4} - 10 q^{10} - 24 q^{16} + 14 q^{19} + 70 q^{22} + 30 q^{28} - 18 q^{31} + 10 q^{34} - 20 q^{37} - 80 q^{40} - 72 q^{49} - 140 q^{52} - 10 q^{55} - 130 q^{58} - 12 q^{61} + 2 q^{64} + 80 q^{67} + 30 q^{70} - 20 q^{73} + 88 q^{76} + 36 q^{79} + 90 q^{85} + 180 q^{88} - 30 q^{91} + 50 q^{94} + 100 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 10 * q^10 - 24 * q^16 + 14 * q^19 + 70 * q^22 + 30 * q^28 - 18 * q^31 + 10 * q^34 - 20 * q^37 - 80 * q^40 - 72 * q^49 - 140 * q^52 - 10 * q^55 - 130 * q^58 - 12 * q^61 + 2 * q^64 + 80 * q^67 + 30 * q^70 - 20 * q^73 + 88 * q^76 + 36 * q^79 + 90 * q^85 + 180 * q^88 - 30 * q^91 + 50 * q^94 + 100 * q^97

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