LMFDB - Embedded newform 468.2.bp.d.179.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(179,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("468.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.bp (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.18
Character	$\chi$	$=$	468.179
Dual form			468.2.bp.d.251.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36583 - 0.366771i) q^{2} +(1.73096 - 1.00189i) q^{4} +3.86412 q^{5} +(0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +O(q^{10})$	\(q+(1.36583 - 0.366771i) q^{2} +(1.73096 - 1.00189i) q^{4} +3.86412 q^{5} +(0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +(5.27771 - 1.41724i) q^{10} +(-4.31382 + 2.49059i) q^{11} +(-3.19318 + 1.67439i) q^{13} +(0.329088 - 1.23086i) q^{14} +(1.99244 - 3.46846i) q^{16} +(-2.93265 - 1.69317i) q^{17} +(-3.89294 + 6.74276i) q^{19} +(6.68863 - 3.87142i) q^{20} +(-4.97845 + 4.98389i) q^{22} +(-3.15217 - 5.45971i) q^{23} +9.93140 q^{25} +(-3.74721 + 3.45809i) q^{26} +(-0.00196606 - 1.80184i) q^{28} +(1.80867 - 1.04424i) q^{29} +4.02376 q^{31} +(1.44919 - 5.46808i) q^{32} +(-4.62650 - 1.23696i) q^{34} +(1.74063 - 3.01486i) q^{35} +(-3.49810 + 2.01963i) q^{37} +(-2.84402 + 10.6373i) q^{38} +(7.71557 - 7.74087i) q^{40} +(2.26815 + 3.92854i) q^{41} +(3.69023 + 2.13055i) q^{43} +(-4.97176 + 8.63307i) q^{44} +(-6.30777 - 6.30089i) q^{46} -9.87089i q^{47} +(3.09417 + 5.35926i) q^{49} +(13.5646 - 3.64254i) q^{50} +(-3.84971 + 6.09752i) q^{52} -5.39166i q^{53} +(-16.6691 + 9.62392i) q^{55} +(-0.663546 - 2.46027i) q^{56} +(2.08734 - 2.08961i) q^{58} +(-8.43231 - 4.86840i) q^{59} +(1.64463 - 2.84858i) q^{61} +(5.49575 - 1.47580i) q^{62} +(-0.0261874 - 7.99996i) q^{64} +(-12.3388 + 6.47005i) q^{65} +(1.48167 + 2.56634i) q^{67} +(-6.77267 + 0.00738995i) q^{68} +(1.27163 - 4.75618i) q^{70} +(8.54844 + 4.93545i) q^{71} +2.37988i q^{73} +(-4.03706 + 4.04146i) q^{74} +(0.0169910 + 15.5717i) q^{76} +4.48763i q^{77} -3.68370i q^{79} +(7.69900 - 13.4025i) q^{80} +(4.53876 + 4.53382i) q^{82} +1.75782i q^{83} +(-11.3321 - 6.54260i) q^{85} +(5.82163 + 1.55650i) q^{86} +(-3.62419 + 13.6148i) q^{88} +(0.982423 + 1.70161i) q^{89} +(-0.132006 + 3.24563i) q^{91} +(-10.9263 - 6.29242i) q^{92} +(-3.62035 - 13.4819i) q^{94} +(-15.0428 + 26.0548i) q^{95} +(-7.46572 - 4.31034i) q^{97} +(6.19172 + 6.18497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{4}+O(q^{10}) $ 40 * q + 12 * q^4	$ 40 q + 12 q^{4} + 16 q^{10} - 44 q^{13} - 24 q^{25} - 48 q^{37} + 40 q^{40} - 48 q^{46} - 24 q^{49} + 28 q^{52} - 72 q^{58} - 4 q^{61} + 60 q^{76} - 64 q^{82} - 24 q^{85} - 4 q^{88} - 24 q^{94} + 84 q^{97}+O(q^{100}) $ 40 * q + 12 * q^4 + 16 * q^10 - 44 * q^13 - 24 * q^25 - 48 * q^37 + 40 * q^40 - 48 * q^46 - 24 * q^49 + 28 * q^52 - 72 * q^58 - 4 * q^61 + 60 * q^76 - 64 * q^82 - 24 * q^85 - 4 * q^88 - 24 * q^94 + 84 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.36583	−	0.366771i	0.965784	−	0.259346i
$2$	1.36583	−	0.366771i	0.965784	−	0.259346i
$3$		0			0
$3$		0			0
$4$	1.73096	−	1.00189i	0.865479	−	0.500945i
$5$	3.86412			1.72809			0.864043	−	0.503419i	$-0.167925\pi$
$5$	3.86412			1.72809			0.864043	+	0.503419i	$0.167925\pi$
$6$		0			0
$7$	0.450459	−	0.780219i	0.170258	−	0.294895i	−0.768252	−	0.640147i	$-0.778873\pi$
$7$	0.450459	−	0.780219i	0.170258	−	0.294895i	0.938510	+	0.345252i	$0.112207\pi$
$8$	1.99672	−	2.00327i	0.705949	−	0.708263i
$9$		0			0
$10$	5.27771	−	1.41724i	1.66896	−	0.448172i
$11$	−4.31382	+	2.49059i	−1.30067	+	0.750940i	−0.980518	−	0.196428i	$-0.937066\pi$
$11$	−4.31382	+	2.49059i	−1.30067	+	0.750940i	−0.320148	+	0.947368i	$0.603733\pi$
$12$		0			0
$13$	−3.19318	+	1.67439i	−0.885629	+	0.464393i
$13$	−3.19318	+	1.67439i	−0.885629	+	0.464393i
$14$	0.329088	−	1.23086i	0.0879524	−	0.328961i
$15$		0			0
$16$	1.99244	−	3.46846i	0.498109	−	0.867114i
$17$	−2.93265	−	1.69317i	−0.711273	−	0.410654i	0.100259	−	0.994961i	$-0.468033\pi$
$17$	−2.93265	−	1.69317i	−0.711273	−	0.410654i	−0.811532	+	0.584308i	$0.801366\pi$
$18$		0			0
$19$	−3.89294	+	6.74276i	−0.893101	+	1.54690i	−0.0569627	+	0.998376i	$0.518142\pi$
$19$	−3.89294	+	6.74276i	−0.893101	+	1.54690i	−0.836138	+	0.548519i	$0.815192\pi$
$20$	6.68863	−	3.87142i	1.49562	−	0.865675i
$21$		0			0
$22$	−4.97845	+	4.98389i	−1.06141	+	1.06257i
$23$	−3.15217	−	5.45971i	−0.657272	−	1.13843i	−0.981319	−	0.192388i	$-0.938377\pi$
$23$	−3.15217	−	5.45971i	−0.657272	−	1.13843i	0.324047	−	0.946041i	$-0.394957\pi$
$24$		0			0
$25$	9.93140			1.98628
$26$	−3.74721	+	3.45809i	−0.734888	+	0.678188i
$27$		0			0
$28$	−0.00196606	−	1.80184i	−0.000371551	−	0.340515i
$29$	1.80867	−	1.04424i	0.335862	−	0.193910i	−0.322579	−	0.946543i	$-0.604550\pi$
$29$	1.80867	−	1.04424i	0.335862	−	0.193910i	0.658441	+	0.752633i	$0.271216\pi$
$30$		0			0
$31$	4.02376			0.722688			0.361344	−	0.932433i	$-0.382318\pi$
$31$	4.02376			0.722688			0.361344	+	0.932433i	$0.382318\pi$
$32$	1.44919	−	5.46808i	0.256183	−	0.966628i
$33$		0			0
$34$	−4.62650	−	1.23696i	−0.793438	−	0.212137i
$35$	1.74063	−	3.01486i	0.294220	−	0.509604i
$36$		0			0
$37$	−3.49810	+	2.01963i	−0.575084	+	0.332025i	−0.759178	−	0.650884i	$-0.774399\pi$
$37$	−3.49810	+	2.01963i	−0.575084	+	0.332025i	0.184093	+	0.982909i	$0.441065\pi$
$38$	−2.84402	+	10.6373i	−0.461362	+	1.72559i
$39$		0			0
$40$	7.71557	−	7.74087i	1.21994	−	1.22394i
$41$	2.26815	+	3.92854i	0.354225	+	0.613535i	0.986985	−	0.160812i	$-0.0514114\pi$
$41$	2.26815	+	3.92854i	0.354225	+	0.613535i	−0.632760	+	0.774348i	$0.718078\pi$
$42$		0			0
$43$	3.69023	+	2.13055i	0.562754	+	0.324906i	0.754250	−	0.656587i	$-0.228001\pi$
$43$	3.69023	+	2.13055i	0.562754	+	0.324906i	−0.191496	+	0.981493i	$0.561334\pi$
$44$	−4.97176	+	8.63307i	−0.749520	+	1.30148i
$45$		0			0
$46$	−6.30777	−	6.30089i	−0.930031	−	0.929016i
$47$		−	9.87089i		−	1.43982i	−0.694069	−	0.719909i	$-0.744184\pi$
$47$		−	9.87089i		−	1.43982i	0.694069	−	0.719909i	$-0.255816\pi$
$48$		0			0
$49$	3.09417	+	5.35926i	0.442025	+	0.765609i
$50$	13.5646	−	3.64254i	1.91832	−	0.515134i
$51$		0			0
$52$	−3.84971	+	6.09752i	−0.533858	+	0.845574i
$53$		−	5.39166i		−	0.740601i	−0.928912	−	0.370300i	$-0.879255\pi$
$53$		−	5.39166i		−	0.740601i	0.928912	−	0.370300i	$-0.120745\pi$
$54$		0			0
$55$	−16.6691	+	9.62392i	−2.24766	+	1.29769i
$56$	−0.663546	−	2.46027i	−0.0886701	−	0.328768i
$57$		0			0
$58$	2.08734	−	2.08961i	0.274081	−	0.274380i
$59$	−8.43231	−	4.86840i	−1.09779	−	0.633811i	−0.162153	−	0.986766i	$-0.551844\pi$
$59$	−8.43231	−	4.86840i	−1.09779	−	0.633811i	−0.935640	+	0.352954i	$0.885177\pi$
$60$		0			0
$61$	1.64463	−	2.84858i	0.210573	−	0.364723i	−0.741321	−	0.671150i	$-0.765800\pi$
$61$	1.64463	−	2.84858i	0.210573	−	0.364723i	0.951894	+	0.306428i	$0.0991338\pi$
$62$	5.49575	−	1.47580i	0.697961	−	0.187426i
$63$		0			0
$64$	−0.0261874	−	7.99996i	−0.00327342	−	0.999995i
$65$	−12.3388	+	6.47005i	−1.53044	+	0.802511i
$66$		0			0
$67$	1.48167	+	2.56634i	0.181015	+	0.313528i	0.942227	−	0.334976i	$-0.108728\pi$
$67$	1.48167	+	2.56634i	0.181015	+	0.313528i	−0.761211	+	0.648504i	$0.775395\pi$
$68$	−6.77267	+	0.00738995i	−0.821307	+	0.000896163i
$69$		0			0
$70$	1.27163	−	4.75618i	0.151989	−	0.568472i
$71$	8.54844	+	4.93545i	1.01451	+	0.585730i	0.912510	−	0.409054i	$-0.134141\pi$
$71$	8.54844	+	4.93545i	1.01451	+	0.585730i	0.102003	+	0.994784i	$0.467475\pi$
$72$		0			0
$73$			2.37988i			0.278544i	0.990254	+	0.139272i	$0.0444763\pi$
$73$			2.37988i			0.278544i	−0.990254	+	0.139272i	$0.955524\pi$
$74$	−4.03706	+	4.04146i	−0.469298	+	0.469811i
$75$		0			0
$76$	0.0169910	+	15.5717i	0.00194900	+	1.78620i
$77$			4.48763i			0.511413i
$78$		0			0
$79$		−	3.68370i		−	0.414448i	−0.978293	−	0.207224i	$-0.933557\pi$
$79$		−	3.68370i		−	0.414448i	0.978293	−	0.207224i	$-0.0664430\pi$
$80$	7.69900	−	13.4025i	0.860775	−	1.49845i
$81$		0			0
$82$	4.53876	+	4.53382i	0.501223	+	0.500676i
$83$			1.75782i			0.192946i	0.995336	+	0.0964728i	$0.0307561\pi$
$83$			1.75782i			0.192946i	−0.995336	+	0.0964728i	$0.969244\pi$
$84$		0			0
$85$	−11.3321	−	6.54260i	−1.22914	−	0.709645i
$86$	5.82163	+	1.55650i	0.627763	+	0.167841i
$87$		0			0
$88$	−3.62419	+	13.6148i	−0.386340	+	1.45134i
$89$	0.982423	+	1.70161i	0.104137	+	0.180370i	0.913385	−	0.407097i	$-0.133459\pi$
$89$	0.982423	+	1.70161i	0.104137	+	0.180370i	−0.809248	+	0.587466i	$0.800125\pi$
$90$		0			0
$91$	−0.132006	+	3.24563i	−0.0138379	+	0.340234i
$92$	−10.9263	−	6.29242i	−1.13915	−	0.656030i
$93$		0			0
$94$	−3.62035	−	13.4819i	−0.373411	−	1.39055i
$95$	−15.0428	+	26.0548i	−1.54335	+	2.67317i
$96$		0			0
$97$	−7.46572	−	4.31034i	−0.758029	−	0.437648i	0.0705585	−	0.997508i	$-0.477522\pi$
$97$	−7.46572	−	4.31034i	−0.758029	−	0.437648i	−0.828588	+	0.559859i	$0.810855\pi$
$98$	6.19172	+	6.18497i	0.625458	+	0.624776i
$99$		0			0
$100$	17.1908	−	9.95016i	1.71908	−	0.995016i
$101$	−3.42463	+	1.97721i	−0.340763	+	0.196740i	−0.660610	−	0.750730i	$-0.729702\pi$
$101$	−3.42463	+	1.97721i	−0.340763	+	0.196740i	0.319846	+	0.947469i	$0.396369\pi$
$102$		0			0
$103$			5.55288i			0.547141i	0.961852	+	0.273571i	$0.0882047\pi$
$103$			5.55288i			0.547141i	−0.961852	+	0.273571i	$0.911795\pi$
$104$	−3.02164	+	9.74011i	−0.296296	+	0.955096i
$105$		0			0
$106$	−1.97750	−	7.36406i	−0.192072	−	0.715261i
$107$	5.88542	+	10.1938i	0.568965	+	0.985476i	0.996669	+	0.0815568i	$0.0259892\pi$
$107$	5.88542	+	10.1938i	0.568965	+	0.985476i	−0.427704	+	0.903919i	$0.640677\pi$
$108$		0			0
$109$		−	0.508779i		−	0.0487321i	−0.999703	−	0.0243661i	$-0.992243\pi$
$109$		−	0.508779i		−	0.0487321i	0.999703	−	0.0243661i	$-0.00775673\pi$
$110$	−19.2373	+	19.2583i	−1.83421	+	1.83621i
$111$		0			0
$112$	−1.80864	−	3.11694i	−0.170901	−	0.294523i
$113$	−9.13432	−	5.27370i	−0.859285	−	0.496108i	0.00448796	−	0.999990i	$-0.498571\pi$
$113$	−9.13432	−	5.27370i	−0.859285	−	0.496108i	−0.863773	+	0.503882i	$0.831905\pi$
$114$		0			0
$115$	−12.1803	−	21.0970i	−1.13582	−	1.96730i
$116$	2.08453	−	3.61962i	0.193543	−	0.336074i
$117$		0			0
$118$	−13.3026	−	3.55666i	−1.22461	−	0.327417i
$119$	−2.64208	+	1.52541i	−0.242199	+	0.139834i
$120$		0			0
$121$	6.90604	−	11.9616i	0.627822	−	1.08742i
$122$	1.20150	−	4.49386i	0.108779	−	0.406855i
$123$		0			0
$124$	6.96496	−	4.03136i	0.625472	−	0.362027i
$125$	19.0555			1.70437
$126$		0			0
$127$	7.98858	−	4.61221i	0.708872	−	0.409267i	−0.101771	−	0.994808i	$-0.532451\pi$
$127$	7.98858	−	4.61221i	0.708872	−	0.409267i	0.810643	+	0.585541i	$0.199118\pi$
$128$	−2.96992	−	10.9169i	−0.262506	−	0.964930i
$129$		0			0
$130$	−14.4797	+	13.3625i	−1.26995	+	1.17197i
$131$	11.1725			0.976146			0.488073	−	0.872803i	$-0.337700\pi$
$131$	11.1725			0.976146			0.488073	+	0.872803i	$0.337700\pi$
$132$		0			0
$133$	3.50722	+	6.07468i	0.304114	+	0.526742i
$134$	2.96496	+	2.96173i	0.256134	+	0.255855i
$135$		0			0
$136$	−9.24757	+	2.49411i	−0.792973	+	0.213868i
$137$	−0.0460669	+	0.0797902i	−0.00393576	+	0.00681694i	−0.867987	−	0.496588i	$-0.834586\pi$
$137$	−0.0460669	+	0.0797902i	−0.00393576	+	0.00681694i	0.864051	+	0.503405i	$0.167919\pi$
$138$		0			0
$139$	2.97013	+	1.71481i	0.251923	+	0.145448i	0.620645	−	0.784092i	$-0.286871\pi$
$139$	2.97013	+	1.71481i	0.251923	+	0.145448i	−0.368721	+	0.929540i	$0.620204\pi$
$140$	−0.00759709	−	6.96251i	−0.000642072	−	0.588439i
$141$		0			0
$142$	13.4859	+	3.60564i	1.13171	+	0.302579i
$143$	9.60459	−	15.1759i	0.803176	−	1.26907i
$144$		0			0
$145$	6.98892	−	4.03506i	0.580398	−	0.335093i
$146$	0.872871	+	3.25050i	0.0722393	+	0.269014i
$147$		0			0
$148$	−4.03162	+	7.00061i	−0.331397	+	0.575446i
$149$	−1.82501	+	3.16102i	−0.149511	+	0.258961i	−0.931047	−	0.364900i	$-0.881103\pi$
$149$	−1.82501	+	3.16102i	−0.149511	+	0.258961i	0.781536	+	0.623860i	$0.214437\pi$
$150$		0			0
$151$	16.7634			1.36419			0.682093	−	0.731265i	$-0.261070\pi$
$151$	16.7634			1.36419			0.682093	+	0.731265i	$0.261070\pi$
$152$	5.73446	+	21.2620i	0.465126	+	1.72458i
$153$		0			0
$154$	1.64593	+	6.12932i	0.132633	+	0.493915i
$155$	15.5483			1.24887
$156$		0			0
$157$	−1.13909			−0.0909096			−0.0454548	−	0.998966i	$-0.514474\pi$
$157$	−1.13909			−0.0909096			−0.0454548	+	0.998966i	$0.514474\pi$
$158$	−1.35107	−	5.03129i	−0.107486	−	0.400268i
$159$		0			0
$160$	5.59984	−	21.1293i	0.442706	−	1.67042i
$161$	−5.67969			−0.447623
$162$		0			0
$163$	2.41126	−	4.17643i	0.188865	−	0.327123i	−0.756007	−	0.654563i	$-0.772853\pi$
$163$	2.41126	−	4.17643i	0.188865	−	0.327123i	0.944872	+	0.327440i	$0.106186\pi$
$164$	7.86203	+	4.52771i	0.613921	+	0.353555i
$165$		0			0
$166$	0.644716	+	2.40087i	0.0500397	+	0.186344i
$167$	2.13657	−	1.23355i	0.165333	−	0.0954549i	−0.415050	−	0.909798i	$-0.636236\pi$
$167$	2.13657	−	1.23355i	0.165333	−	0.0954549i	0.580383	+	0.814343i	$0.302903\pi$
$168$		0			0
$169$	7.39281	−	10.6933i	0.568678	−	0.822560i
$170$	−17.8773	−	4.77976i	−1.37113	−	0.366591i
$171$		0			0
$172$	8.52221	−	0.00929895i	0.649812	−	0.000709038i
$173$	15.3809	+	8.88015i	1.16939	+	0.675145i	0.953535	−	0.301281i	$-0.0974142\pi$
$173$	15.3809	+	8.88015i	1.16939	+	0.675145i	0.215851	+	0.976426i	$0.430748\pi$
$174$		0			0
$175$	4.47369	−	7.74866i	0.338179	−	0.585744i
$176$	0.0434813	+	19.9246i	0.00327753	+	1.50188i
$177$		0			0
$178$	1.96592	+	1.96377i	0.147352	+	0.147191i
$179$	−9.49178	−	16.4403i	−0.709449	−	1.22880i	−0.965062	−	0.262023i	$-0.915610\pi$
$179$	−9.49178	−	16.4403i	−0.709449	−	1.22880i	0.255612	−	0.966779i	$-0.417723\pi$
$180$		0			0
$181$	−22.8963			−1.70187			−0.850933	−	0.525275i	$-0.823963\pi$
$181$	−22.8963			−1.70187			−0.850933	+	0.525275i	$0.823963\pi$
$182$	1.01010	+	4.48137i	0.0748739	+	0.332182i
$183$		0			0
$184$	−17.2313	−	4.58690i	−1.27031	−	0.338151i
$185$	−13.5171	+	7.80409i	−0.993795	+	0.573768i
$186$		0			0
$187$	16.8679			1.23350
$188$	−9.88954	−	17.0861i	−0.721269	−	1.24613i
$189$		0			0
$190$	−10.9896	+	41.1036i	−0.797272	+	2.98197i
$191$	3.37946	−	5.85340i	0.244529	−	0.423537i	−0.717470	−	0.696589i	$-0.754700\pi$
$191$	3.37946	−	5.85340i	0.244529	−	0.423537i	0.961999	+	0.273052i	$0.0880333\pi$
$192$		0			0
$193$	−19.7363	+	11.3947i	−1.42065	+	0.820211i	−0.996354	−	0.0853145i	$-0.972810\pi$
$193$	−19.7363	+	11.3947i	−1.42065	+	0.820211i	−0.424293	+	0.905525i	$0.639477\pi$
$194$	−11.7778	−	3.14896i	−0.845595	−	0.226082i
$195$		0			0
$196$	10.7253	+	6.17665i	0.766091	+	0.441189i
$197$	−11.9725	−	20.7370i	−0.853005	−	1.47745i	−0.878484	−	0.477772i	$-0.841444\pi$
$197$	−11.9725	−	20.7370i	−0.853005	−	1.47745i	0.0254792	−	0.999675i	$-0.491889\pi$
$198$		0			0
$199$	2.37752	+	1.37266i	0.168538	+	0.0973053i	0.581896	−	0.813263i	$-0.302311\pi$
$199$	2.37752	+	1.37266i	0.168538	+	0.0973053i	−0.413358	+	0.910568i	$0.635644\pi$
$200$	19.8303	−	19.8953i	1.40221	−	1.40681i
$201$		0			0
$202$	−3.95226	+	3.95658i	−0.278080	+	0.278384i
$203$		−	1.88155i		−	0.132059i
$204$		0			0
$205$	8.76438	+	15.1803i	0.612131	+	1.06024i
$206$	2.03663	+	7.58426i	0.141899	+	0.528420i
$207$		0			0
$208$	−0.554644	+	14.4115i	−0.0384577	+	0.999260i
$209$		−	38.7828i		−	2.68266i
$210$		0			0
$211$	−11.3254	+	6.53874i	−0.779674	+	0.450145i	−0.836315	−	0.548249i	$-0.815294\pi$
$211$	−11.3254	+	6.53874i	−0.779674	+	0.450145i	0.0566404	+	0.998395i	$0.481961\pi$
$212$	−5.40184	−	9.33273i	−0.371000	−	0.640975i
$213$		0			0
$214$	11.7773	+	11.7644i	0.805076	+	0.804198i
$215$	14.2595	+	8.23271i	0.972488	+	0.561466i
$216$		0			0
$217$	1.81254	−	3.13941i	0.123043	−	0.213117i
$218$	−0.186605	−	0.694903i	−0.0126385	−	0.0470648i
$219$		0			0
$220$	−19.2114	+	33.3592i	−1.29524	+	2.24908i
$221$	12.1995	+	0.496177i	0.820629	+	0.0333765i
$222$		0			0
$223$	0.748761	+	1.29689i	0.0501408	+	0.0868464i	0.890006	−	0.455948i	$-0.150700\pi$
$223$	0.748761	+	1.29689i	0.0501408	+	0.0868464i	−0.839866	+	0.542794i	$0.817366\pi$
$224$	−3.61349	−	3.59383i	−0.241437	−	0.240123i
$225$		0			0
$226$	−14.4101	−	3.85276i	−0.958548	−	0.256282i
$227$	6.64444	+	3.83617i	0.441007	+	0.254615i	0.704025	−	0.710176i	$-0.251384\pi$
$227$	6.64444	+	3.83617i	0.441007	+	0.254615i	−0.263018	+	0.964791i	$0.584718\pi$
$228$		0			0
$229$			20.7703i			1.37254i	0.727348	+	0.686269i	$0.240753\pi$
$229$			20.7703i			1.37254i	−0.727348	+	0.686269i	$0.759247\pi$
$230$	−24.3740	−	24.3474i	−1.60717	−	1.60542i
$231$		0			0
$232$	1.51953	−	5.70832i	0.0997620	−	0.374769i
$233$			3.56192i			0.233349i	0.993170	+	0.116675i	$0.0372234\pi$
$233$			3.56192i			0.233349i	−0.993170	+	0.116675i	$0.962777\pi$
$234$		0			0
$235$		−	38.1423i		−	2.48813i
$236$	−19.4736	+	0.0212485i	−1.26762	+	0.00138316i
$237$		0			0
$238$	−3.04915	+	3.05248i	−0.197647	+	0.197863i
$239$			14.2446i			0.921407i	0.887554	+	0.460704i	$0.152403\pi$
$239$			14.2446i			0.921407i	−0.887554	+	0.460704i	$0.847597\pi$
$240$		0			0
$241$	0.863050	+	0.498282i	0.0555939	+	0.0320972i	0.527539	−	0.849531i	$-0.323115\pi$
$241$	0.863050	+	0.498282i	0.0555939	+	0.0320972i	−0.471945	+	0.881628i	$0.656448\pi$
$242$	5.04528	−	18.8704i	0.324323	−	1.21304i
$243$		0			0
$244$	−0.00717809	−	6.57850i	−0.000459530	−	0.421145i
$245$	11.9562	+	20.7088i	0.763856	+	1.32304i
$246$		0			0
$247$	1.14081	−	28.0492i	0.0725881	−	1.78473i
$248$	8.03433	−	8.06068i	0.510181	−	0.511853i
$249$		0			0
$250$	26.0265	−	6.98899i	1.64606	−	0.442023i
$251$	1.97988	−	3.42926i	0.124969	−	0.216453i	−0.796752	−	0.604307i	$-0.793450\pi$
$251$	1.97988	−	3.42926i	0.124969	−	0.216453i	0.921721	+	0.387854i	$0.126783\pi$
$252$		0			0
$253$	27.1958	+	15.7015i	1.70978	+	0.987144i
$254$	9.21938	−	9.22945i	0.578476	−	0.579107i
$255$		0			0
$256$	−8.06040	−	13.8214i	−0.503775	−	0.863835i
$257$	24.3137	−	14.0375i	1.51664	−	0.875635i	0.516836	−	0.856084i	$-0.327110\pi$
$257$	24.3137	−	14.0375i	1.51664	−	0.875635i	0.999809	−	0.0195508i	$-0.00622361\pi$
$258$		0			0
$259$			3.63905i			0.226119i
$260$	−14.8757	+	23.5615i	−0.922553	+	1.46122i
$261$		0			0
$262$	15.2597	−	4.09775i	0.942747	−	0.253160i
$263$	−10.8980	−	18.8758i	−0.671997	−	1.16393i	−0.977337	−	0.211690i	$-0.932103\pi$
$263$	−10.8980	−	18.8758i	−0.671997	−	1.16393i	0.305339	−	0.952244i	$-0.401230\pi$
$264$		0			0
$265$		−	20.8340i		−	1.27982i
$266$	7.01826	+	7.01061i	0.430317	+	0.429848i
$267$		0			0
$268$	5.13590	+	2.95775i	0.313725	+	0.180673i
$269$	8.35430	+	4.82336i	0.509371	+	0.294085i	0.732575	−	0.680686i	$-0.238318\pi$
$269$	8.35430	+	4.82336i	0.509371	+	0.294085i	−0.223204	+	0.974772i	$0.571652\pi$
$270$		0			0
$271$	5.52677	+	9.57264i	0.335727	+	0.581497i	0.983624	−	0.180231i	$-0.0576846\pi$
$271$	5.52677	+	9.57264i	0.335727	+	0.581497i	−0.647897	+	0.761728i	$0.724351\pi$
$272$	−11.7158	+	6.79826i	−0.710375	+	0.412205i
$273$		0			0
$274$	−0.0336547	+	0.125876i	−0.00203315	+	0.00760442i
$275$	−42.8423	+	24.7350i	−2.58349	+	1.49158i
$276$		0			0
$277$	3.31872	−	5.74819i	0.199402	−	0.345375i	−0.748932	−	0.662646i	$-0.769433\pi$
$277$	3.31872	−	5.74819i	0.199402	−	0.345375i	0.948335	+	0.317271i	$0.102767\pi$
$278$	4.68562	+	1.25277i	0.281025	+	0.0751361i
$279$		0			0
$280$	−2.56402	−	9.50678i	−0.153229	−	0.568139i
$281$	−15.1898			−0.906145			−0.453072	−	0.891474i	$-0.649672\pi$
$281$	−15.1898			−0.906145			−0.453072	+	0.891474i	$0.649672\pi$
$282$		0			0
$283$	−22.7842	+	13.1545i	−1.35438	+	0.781951i	−0.988859	−	0.148852i	$-0.952442\pi$
$283$	−22.7842	+	13.1545i	−1.35438	+	0.781951i	−0.365520	+	0.930803i	$0.619109\pi$
$284$	19.7418	−	0.0215411i	1.17146	−	0.00127823i
$285$		0			0
$286$	7.55211	−	24.2504i	0.446566	−	1.43395i
$287$	4.08683			0.241238
$288$		0			0
$289$	−2.76636	−	4.79148i	−0.162727	−	0.281852i
$290$	8.06571	−	8.07451i	0.473635	−	0.474152i
$291$		0			0
$292$	2.38438	+	4.11948i	0.139535	+	0.241074i
$293$	−10.2477	+	17.7496i	−0.598678	+	1.03694i	0.394339	+	0.918965i	$0.370974\pi$
$293$	−10.2477	+	17.7496i	−0.598678	+	1.03694i	−0.993017	+	0.117975i	$0.962360\pi$
$294$		0			0
$295$	−32.5834	−	18.8120i	−1.89708	−	1.09528i
$296$	−2.93888	+	11.0403i	−0.170819	+	0.641704i
$297$		0			0
$298$	−1.33328	+	4.98676i	−0.0772350	+	0.288875i
$299$	19.2072	+	12.1559i	1.11078	+	0.702993i
$300$		0			0
$301$	3.32460	−	1.91946i	0.191626	−	0.110636i
$302$	22.8959	−	6.14832i	1.31751	−	0.353796i
$303$		0			0
$304$	15.6306	+	26.9370i	0.896474	+	1.54494i
$305$	6.35502	−	11.0072i	0.363888	−	0.630272i
$306$		0			0
$307$	33.3684			1.90443			0.952217	−	0.305423i	$-0.0987978\pi$
$307$	33.3684			1.90443			0.952217	+	0.305423i	$0.0987978\pi$
$308$	4.49611	+	7.76791i	0.256190	+	0.442618i
$309$		0			0
$310$	21.2362	−	5.70265i	1.20614	−	0.323889i
$311$	−10.5603			−0.598819			−0.299409	−	0.954125i	$-0.596790\pi$
$311$	−10.5603			−0.598819			−0.299409	+	0.954125i	$0.596790\pi$
$312$		0			0
$313$	11.0233			0.623071			0.311536	−	0.950234i	$-0.399157\pi$
$313$	11.0233			0.623071			0.311536	+	0.950234i	$0.399157\pi$
$314$	−1.55580	+	0.417786i	−0.0877991	+	0.0235770i
$315$		0			0
$316$	−3.69066	−	6.37633i	−0.207616	−	0.358697i
$317$	29.0484			1.63152			0.815762	−	0.578388i	$-0.196318\pi$
$317$	29.0484			1.63152			0.815762	+	0.578388i	$0.196318\pi$
$318$		0			0
$319$	−5.20153	+	9.00931i	−0.291230	+	0.504425i
$320$	−0.101191	−	30.9128i	−0.00565675	−	1.72808i
$321$		0			0
$322$	−7.75747	+	2.08315i	−0.432307	+	0.116089i
$323$	22.8333	−	13.1828i	1.27048	−	0.733510i
$324$		0			0
$325$	−31.7127	+	16.6291i	−1.75911	+	0.922415i
$326$	1.76157	−	6.58865i	0.0975644	−	0.364912i
$327$		0			0
$328$	12.3988	+	3.30051i	0.684609	+	0.182240i
$329$	−7.70145	−	4.44644i	−0.424595	−	0.245140i
$330$		0			0
$331$	4.06094	−	7.03376i	0.223210	−	0.386610i	−0.732571	−	0.680690i	$-0.761680\pi$
$331$	4.06094	−	7.03376i	0.223210	−	0.386610i	0.955781	+	0.294080i	$0.0950133\pi$
$332$	1.76114	+	3.04271i	0.0966551	+	0.166990i
$333$		0			0
$334$	2.46575	−	2.46844i	0.134920	−	0.135067i
$335$	5.72536	+	9.91662i	0.312810	+	0.541803i
$336$		0			0
$337$	−7.93311			−0.432144			−0.216072	−	0.976377i	$-0.569325\pi$
$337$	−7.93311			−0.432144			−0.216072	+	0.976377i	$0.569325\pi$
$338$	6.17531	−	17.3166i	0.335893	−	0.941900i
$339$		0			0
$340$	−26.1704	+	0.0285556i	−1.41929	+	0.00154865i
$341$	−17.3578	+	10.0215i	−0.939976	+	0.542696i
$342$		0			0
$343$	11.8816			0.641548
$344$	11.6364	−	3.13840i	0.627395	−	0.169211i
$345$		0			0
$346$	24.2646	+	6.48748i	1.30447	+	0.348769i
$347$	−2.57523	+	4.46043i	−0.138245	+	0.239448i	−0.926833	−	0.375475i	$-0.877480\pi$
$347$	−2.57523	+	4.46043i	−0.138245	+	0.239448i	0.788587	+	0.614923i	$0.210813\pi$
$348$		0			0
$349$	15.5889	−	9.00027i	0.834456	−	0.481774i	−0.0209196	−	0.999781i	$-0.506659\pi$
$349$	15.5889	−	9.00027i	0.834456	−	0.481774i	0.855376	+	0.518008i	$0.173326\pi$
$350$	3.26830	−	12.2241i	0.174698	−	0.653408i
$351$		0			0
$352$	7.36716	+	27.1976i	0.392671	+	1.44964i
$353$	−8.40866	−	14.5642i	−0.447548	−	0.775175i	0.550678	−	0.834718i	$-0.314369\pi$
$353$	−8.40866	−	14.5642i	−0.447548	−	0.775175i	−0.998226	+	0.0595425i	$0.981036\pi$
$354$		0			0
$355$	33.0322	+	19.0711i	1.75317	+	1.01219i
$356$	3.40536	+	1.96113i	0.180484	+	0.103940i
$357$		0			0
$358$	−18.9939	−	18.9732i	−1.00386	−	1.00277i
$359$			3.83265i			0.202279i	0.994872	+	0.101140i	$0.0322489\pi$
$359$			3.83265i			0.202279i	−0.994872	+	0.101140i	$0.967751\pi$
$360$		0			0
$361$	−20.8099	−	36.0438i	−1.09526	−	1.89704i
$362$	−31.2723	+	8.39768i	−1.64364	+	0.441372i
$363$		0			0
$364$	3.02326	+	5.75030i	0.158462	+	0.301398i
$365$			9.19614i			0.481348i
$366$		0			0
$367$	−14.1130	+	8.14816i	−0.736694	+	0.425330i	−0.820866	−	0.571121i	$-0.806509\pi$
$367$	−14.1130	+	8.14816i	−0.736694	+	0.425330i	0.0841721	+	0.996451i	$0.473175\pi$
$368$	−25.2173	+	0.0550314i	−1.31454	+	0.00286871i
$369$		0			0
$370$	−15.5997	+	15.6167i	−0.810987	+	0.811873i
$371$	−4.20667	−	2.42872i	−0.218399	−	0.126093i
$372$		0			0
$373$	1.46760	−	2.54195i	0.0759892	−	0.131617i	−0.825527	−	0.564363i	$-0.809122\pi$
$373$	1.46760	−	2.54195i	0.0759892	−	0.131617i	0.901516	+	0.432746i	$0.142455\pi$
$374$	23.0386	−	6.18666i	1.19130	−	0.319905i
$375$		0			0
$376$	−19.7741	−	19.7094i	−1.01977	−	1.01644i
$377$	−4.02696	+	6.36287i	−0.207399	+	0.327705i
$378$		0			0
$379$	12.7684	+	22.1156i	0.655870	+	1.13600i	0.981675	+	0.190563i	$0.0610315\pi$
$379$	12.7684	+	22.1156i	0.655870	+	1.13600i	−0.325805	+	0.945437i	$0.605635\pi$
$380$	0.0656552	+	60.1710i	0.00336804	+	3.08671i
$381$		0			0
$382$	2.46890	−	9.23421i	0.126320	−	0.472463i
$383$	−1.91909	−	1.10799i	−0.0980607	−	0.0566154i	0.450168	−	0.892944i	$-0.351364\pi$
$383$	−1.91909	−	1.10799i	−0.0980607	−	0.0566154i	−0.548228	+	0.836329i	$0.684698\pi$
$384$		0			0
$385$			17.3407i			0.883766i
$386$	−22.7770	+	22.8019i	−1.15932	+	1.16059i
$387$		0			0
$388$	−17.2413	+	0.0188128i	−0.875296	+	0.000955074i
$389$			12.9878i			0.658505i	0.944242	+	0.329253i	$0.106797\pi$
$389$			12.9878i			0.658505i	−0.944242	+	0.329253i	$0.893203\pi$
$390$		0			0
$391$			21.3486i			1.07965i
$392$	16.9143	+	4.50251i	0.854299	+	0.227411i
$393$		0			0
$394$	−23.9580	−	23.9319i	−1.20699	−	1.20567i
$395$		−	14.2342i		−	0.716202i
$396$		0			0
$397$	17.1162	+	9.88206i	0.859039	+	0.495966i	0.863690	−	0.504023i	$-0.168147\pi$
$397$	17.1162	+	9.88206i	0.859039	+	0.495966i	−0.00465142	+	0.999989i	$0.501481\pi$
$398$	3.75073	+	1.00281i	0.188007	+	0.0502664i
$399$		0			0
$400$	19.7877	−	34.4466i	0.989383	−	1.72233i
$401$	−8.68520	−	15.0432i	−0.433718	−	0.751222i	0.563472	−	0.826135i	$-0.309465\pi$
$401$	−8.68520	−	15.0432i	−0.433718	−	0.751222i	−0.997190	+	0.0749133i	$0.976132\pi$
$402$		0			0
$403$	−12.8486	+	6.73735i	−0.640034	+	0.335612i
$404$	−3.94695	+	6.85357i	−0.196368	+	0.340978i
$405$		0			0
$406$	−0.690096	−	2.56986i	−0.0342489	−	0.127540i
$407$	10.0601	−	17.4247i	0.498662	−	0.863708i
$408$		0			0
$409$	−21.8306	−	12.6039i	−1.07945	−	0.623223i	−0.148705	−	0.988882i	$-0.547510\pi$
$409$	−21.8306	−	12.6039i	−1.07945	−	0.623223i	−0.930749	+	0.365659i	$0.880844\pi$
$410$	17.5383	+	17.5192i	0.866156	+	0.865211i
$411$		0			0
$412$	5.56337	+	9.61180i	0.274087	+	0.473539i
$413$	−7.59683	+	4.38603i	−0.373815	+	0.215822i
$414$		0			0
$415$			6.79242i			0.333427i
$416$	4.52818	+	19.8871i	0.222012	+	0.975044i
$417$		0			0
$418$	−14.2244	−	52.9705i	−0.695737	−	2.59087i
$419$	−18.3660	−	31.8108i	−0.897237	−	1.55406i	−0.831011	−	0.556256i	$-0.812237\pi$
$419$	−18.3660	−	31.8108i	−0.897237	−	1.55406i	−0.0662264	−	0.997805i	$-0.521096\pi$
$420$		0			0
$421$			10.7389i			0.523384i	0.965151	+	0.261692i	$0.0842805\pi$
$421$			10.7389i			0.523384i	−0.965151	+	0.261692i	$0.915720\pi$
$422$	−13.0703	+	13.0846i	−0.636254	+	0.636949i
$423$		0			0
$424$	−10.8009	−	10.7656i	−0.524540	−	0.522826i
$425$	−29.1253	−	16.8155i	−1.41279	−	0.815673i
$426$		0			0
$427$	−1.48167	−	2.56634i	−0.0717032	−	0.124194i
$428$	20.4005	+	11.7486i	0.986096	+	0.567889i
$429$		0			0
$430$	22.4955	+	6.01449i	1.08483	+	0.290044i
$431$	−6.36251	+	3.67340i	−0.306471	+	0.176941i	−0.645346	−	0.763890i	$-0.723287\pi$
$431$	−6.36251	+	3.67340i	−0.306471	+	0.176941i	0.338875	+	0.940831i	$0.389954\pi$
$432$		0			0
$433$	10.3474	−	17.9222i	0.497265	−	0.861287i	−0.502731	−	0.864443i	$-0.667671\pi$
$433$	10.3474	−	17.9222i	0.497265	−	0.861287i	0.999995	+	0.00315579i	$0.00100452\pi$
$434$	1.32417	−	4.95267i	0.0635622	−	0.237736i
$435$		0			0
$436$	−0.509740	−	0.880675i	−0.0244121	−	0.0421767i
$437$	49.0847			2.34804
$438$		0			0
$439$	1.82985	−	1.05646i	0.0873339	−	0.0504223i	−0.455697	−	0.890135i	$-0.650610\pi$
$439$	1.82985	−	1.05646i	0.0873339	−	0.0504223i	0.543031	+	0.839713i	$0.317277\pi$
$440$	−14.0043	+	52.6090i	−0.667629	+	2.50804i
$441$		0			0
$442$	16.8444	−	3.79674i	0.801207	−	0.180592i
$443$	−27.2205			−1.29329			−0.646644	−	0.762792i	$-0.723828\pi$
$443$	−27.2205			−1.29329			−0.646644	+	0.762792i	$0.723828\pi$
$444$		0			0
$445$	3.79620	+	6.57521i	0.179957	+	0.311695i
$446$	1.49834	+	1.49671i	0.0709484	+	0.0708711i
$447$		0			0
$448$	−6.25351	−	3.58322i	−0.295451	−	0.169291i
$449$	−13.9938	+	24.2381i	−0.660411	+	1.14386i	0.320097	+	0.947385i	$0.396284\pi$
$449$	−13.9938	+	24.2381i	−0.660411	+	1.14386i	−0.980508	+	0.196480i	$0.937049\pi$
$450$		0			0
$451$	−19.5688	−	11.2980i	−0.921456	−	0.532003i
$452$	−21.0948	+	0.0230175i	−0.992216	+	0.00108265i
$453$		0			0
$454$	10.4821	+	2.80255i	0.491951	+	0.131530i
$455$	−0.510085	+	12.5415i	−0.0239131	+	0.587953i
$456$		0			0
$457$	24.1822	−	13.9616i	1.13120	−	0.653096i	0.186960	−	0.982368i	$-0.440137\pi$
$457$	24.1822	−	13.9616i	1.13120	−	0.653096i	0.944235	+	0.329272i	$0.106803\pi$
$458$	7.61792	+	28.3685i	0.355962	+	1.32558i
$459$		0			0
$460$	−42.2205	−	24.3146i	−1.96854	−	1.13368i
$461$	−15.7424	+	27.2667i	−0.733197	+	1.26994i	0.222312	+	0.974975i	$0.428640\pi$
$461$	−15.7424	+	27.2667i	−0.733197	+	1.26994i	−0.955510	+	0.294960i	$0.904694\pi$
$462$		0			0
$463$	−35.7895			−1.66328			−0.831639	−	0.555316i	$-0.812597\pi$
$463$	−35.7895			−1.66328			−0.831639	+	0.555316i	$0.812597\pi$
$464$	−0.0182306	−	8.35388i	−0.000846334	−	0.387819i
$465$		0			0
$466$	1.30641	+	4.86496i	0.0605181	+	0.225365i
$467$	7.80035			0.360957			0.180479	−	0.983579i	$-0.442235\pi$
$467$	7.80035			0.360957			0.180479	+	0.983579i	$0.442235\pi$
$468$		0			0
$469$	2.66974			0.123277
$470$	−13.9895	−	52.0957i	−0.645286	−	2.40299i
$471$		0			0
$472$	−26.5897	+	7.17136i	−1.22389	+	0.330088i
$473$	−21.2253			−0.975941
$474$		0			0
$475$	−38.6623	+	66.9650i	−1.77395	+	3.07257i
$476$	−3.04505	+	5.28749i	−0.139569	+	0.242352i
$477$		0			0
$478$	5.22450	+	19.4556i	0.238963	+	0.889881i
$479$	18.9832	−	10.9600i	0.867366	−	0.500774i	0.000893831	−	1.00000i	$-0.499715\pi$
$479$	18.9832	−	10.9600i	0.867366	−	0.500774i	0.866472	+	0.499226i	$0.166382\pi$
$480$		0			0
$481$	7.78842	−	12.3062i	0.355121	−	0.561117i
$482$	1.36153	+	0.364025i	0.0620160	+	0.0165809i
$483$		0			0
$484$	−0.0301419	−	27.6241i	−0.00137009	−	1.25564i
$485$	−28.8484	−	16.6556i	−1.30994	−	0.756294i
$486$		0			0
$487$	16.7338	−	28.9838i	0.758280	−	1.31338i	−0.185447	−	0.982654i	$-0.559373\pi$
$487$	16.7338	−	28.9838i	0.758280	−	1.31338i	0.943727	−	0.330725i	$-0.107293\pi$
$488$	−2.42260	−	8.98245i	−0.109666	−	0.406616i
$489$		0			0
$490$	23.9255	+	23.8994i	1.08085	+	1.07967i
$491$	9.97889	+	17.2839i	0.450341	+	0.780014i	0.998407	−	0.0564215i	$-0.0179691\pi$
$491$	9.97889	+	17.2839i	0.450341	+	0.780014i	−0.548066	+	0.836435i	$0.684636\pi$
$492$		0			0
$493$	−7.07228			−0.318520
$494$	−8.72946	−	38.7287i	−0.392757	−	1.74249i
$495$		0			0
$496$	8.01708	−	13.9562i	0.359977	−	0.626653i
$497$	7.70145	−	4.44644i	0.345457	−	0.199450i
$498$		0			0
$499$	−17.3589			−0.777092			−0.388546	−	0.921429i	$-0.627022\pi$
$499$	−17.3589			−0.777092			−0.388546	+	0.921429i	$0.627022\pi$
$500$	32.9843	−	19.0915i	1.47510	−	0.853797i
$501$		0			0
$502$	1.44642	−	5.40993i	0.0645571	−	0.241457i
$503$	−7.31587	+	12.6715i	−0.326198	+	0.564992i	−0.981754	−	0.190155i	$-0.939101\pi$
$503$	−7.31587	+	12.6715i	−0.326198	+	0.564992i	0.655556	+	0.755147i	$0.272434\pi$
$504$		0			0
$505$	−13.2332	+	7.64017i	−0.588868	+	0.339983i
$506$	42.9035	+	11.4709i	1.90729	+	0.509943i
$507$		0			0
$508$	9.20698	−	15.9872i	0.408494	−	0.709318i
$509$	14.6625	+	25.3962i	0.649905	+	1.12567i	0.983145	+	0.182826i	$0.0585246\pi$
$509$	14.6625	+	25.3962i	0.649905	+	1.12567i	−0.333240	+	0.942842i	$0.608142\pi$
$510$		0			0
$511$	1.85683	+	1.07204i	0.0821413	+	0.0474243i
$512$	−16.0784	−	15.9212i	−0.710570	−	0.703626i
$513$		0			0
$514$	28.0597	−	28.0903i	1.23766	−	1.23901i
$515$			21.4570i			0.945506i
$516$		0			0
$517$	24.5843	+	42.5813i	1.08122	+	1.87272i
$518$	1.33470	+	4.97030i	0.0586431	+	0.218383i
$519$		0			0
$520$	−11.6760	+	37.6369i	−0.512025	+	1.65049i
$521$			28.2001i			1.23547i	0.786386	+	0.617735i	$0.211949\pi$
$521$			28.2001i			1.23547i	−0.786386	+	0.617735i	$0.788051\pi$
$522$		0			0
$523$	−27.7553	+	16.0245i	−1.21365	+	0.700704i	−0.963553	−	0.267516i	$-0.913797\pi$
$523$	−27.7553	+	16.0245i	−1.21365	+	0.700704i	−0.250101	+	0.968220i	$0.580464\pi$
$524$	19.3391	−	11.1936i	0.844834	−	0.488995i
$525$		0			0
$526$	−21.8078	−	21.7840i	−0.950866	−	0.949829i
$527$	−11.8003	−	6.81290i	−0.514029	−	0.296775i
$528$		0			0
$529$	−8.37232	+	14.5013i	−0.364014	+	0.630491i
$530$	−7.64129	−	28.4556i	−0.331917	−	1.23603i
$531$		0			0
$532$	12.1570	+	7.00118i	0.527073	+	0.303540i
$533$	−13.8205	−	8.74678i	−0.598633	−	0.378865i
$534$		0			0
$535$	22.7419	+	39.3902i	0.983219	+	1.70299i
$536$	8.09956	+	2.15607i	0.349848	+	0.0931280i
$537$		0			0
$538$	13.1796	+	3.52375i	0.568212	+	0.151920i
$539$	−26.6954	−	15.4126i	−1.14985	−	0.663868i
$540$		0			0
$541$		−	36.4085i		−	1.56532i	−0.622447	−	0.782662i	$-0.713861\pi$
$541$		−	36.4085i		−	1.56532i	0.622447	−	0.782662i	$-0.286139\pi$
$542$	11.0596	+	11.0475i	0.475049	+	0.474531i
$543$		0			0
$544$	−13.5083	+	13.5822i	−0.579166	+	0.582334i
$545$		−	1.96598i		−	0.0842133i
$546$		0			0
$547$		−	30.4069i		−	1.30011i	−0.759889	−	0.650053i	$-0.774747\pi$
$547$		−	30.4069i		−	1.30011i	0.759889	−	0.650053i	$-0.225253\pi$
$548$	0.000201062		0.184268i	8.58896e−6		0.00787152i
$549$		0			0
$550$	−49.4430	+	49.4970i	−2.10826	+	2.11056i
$551$			16.2606i			0.692725i
$552$		0			0
$553$	−2.87409	−	1.65936i	−0.122219	−	0.0705630i
$554$	2.42452	−	9.06823i	0.103008	−	0.385272i
$555$		0			0
$556$	6.85922	−	0.00748440i	0.290896	−	0.000317409i
$557$	−4.57967	−	7.93223i	−0.194047	−	0.336099i	0.752541	−	0.658546i	$-0.228828\pi$
$557$	−4.57967	−	7.93223i	−0.194047	−	0.336099i	−0.946588	+	0.322447i	$0.895495\pi$
$558$		0			0
$559$	−15.3509	−	0.624351i	−0.649276	−	0.0264072i
$560$	−6.98881	−	12.0442i	−0.295331	−	0.508960i
$561$		0			0
$562$	−20.7466	+	5.57116i	−0.875141	+	0.235005i
$563$	−14.1667	+	24.5374i	−0.597053	+	1.03413i	0.396200	+	0.918164i	$0.370329\pi$
$563$	−14.1667	+	24.5374i	−0.597053	+	1.03413i	−0.993254	+	0.115962i	$0.963005\pi$
$564$		0			0
$565$	−35.2961	−	20.3782i	−1.48492	−	0.857317i
$566$	−26.2946	+	26.3233i	−1.10524	+	1.10645i
$567$		0			0
$568$	26.9559	−	7.27012i	1.13104	−	0.305048i
$569$	−10.5468	+	6.08920i	−0.442145	+	0.255272i	−0.704507	−	0.709697i	$-0.748832\pi$
$569$	−10.5468	+	6.08920i	−0.442145	+	0.255272i	0.262362	+	0.964969i	$0.415499\pi$
$570$		0			0
$571$		−	42.7464i		−	1.78888i	−0.447185	−	0.894441i	$-0.647574\pi$
$571$		−	42.7464i		−	1.78888i	0.447185	−	0.894441i	$-0.352426\pi$
$572$	1.42055	−	35.8916i	0.0593963	−	1.50071i
$573$		0			0
$574$	5.58190	−	1.49893i	0.232984	−	0.0625641i
$575$	−31.3054	−	54.2226i	−1.30553	−	2.26124i
$576$		0			0
$577$			41.1803i			1.71436i	0.515019	+	0.857179i	$0.327785\pi$
$577$			41.1803i			1.71436i	−0.515019	+	0.857179i	$0.672215\pi$
$578$	−5.53574	−	5.52971i	−0.230257	−	0.230005i
$579$		0			0
$580$	8.05486	−	13.9866i	0.334460	−	0.580764i
$581$	1.37148	+	0.791826i	0.0568987	+	0.0328505i
$582$		0			0
$583$	13.4284	+	23.2586i	0.556147	+	0.963275i
$584$	4.76755	+	4.75197i	0.197283	+	0.196638i
$585$		0			0
$586$	−7.48657	+	28.0013i	−0.309267	+	1.15673i
$587$	7.20380	−	4.15912i	0.297333	−	0.171665i	−0.343911	−	0.939002i	$-0.611752\pi$
$587$	7.20380	−	4.15912i	0.297333	−	0.171665i	0.641244	+	0.767337i	$0.278419\pi$
$588$		0			0
$589$	−15.6642	+	27.1312i	−0.645433	+	1.11792i
$590$	−51.4030	−	13.7433i	−2.11623	−	0.565804i
$591$		0			0
$592$	0.0352593	+	16.1570i	0.00144915	+	0.664049i
$593$	23.0225			0.945420			0.472710	−	0.881218i	$-0.343276\pi$
$593$	23.0225			0.945420			0.472710	+	0.881218i	$0.343276\pi$
$594$		0			0
$595$	−10.2093	+	5.89435i	−0.418541	+	0.241645i
$596$	0.00796540	+	7.30005i	0.000326276	+	0.299022i
$597$		0			0
$598$	30.6920	+	9.55820i	1.25509	+	0.390864i
$599$	−27.0648			−1.10584			−0.552919	−	0.833235i	$-0.686486\pi$
$599$	−27.0648			−1.10584			−0.552919	+	0.833235i	$0.686486\pi$
$600$		0			0
$601$	9.98919	+	17.3018i	0.407468	+	0.705755i	0.994605	−	0.103732i	$-0.0330785\pi$
$601$	9.98919	+	17.3018i	0.407468	+	0.705755i	−0.587137	+	0.809487i	$0.699745\pi$
$602$	3.83682	−	3.84101i	0.156377	−	0.156548i
$603$		0			0
$604$	29.0168	−	16.7951i	1.18068	−	0.683382i
$605$	26.6857	−	46.2211i	1.08493	−	1.87915i
$606$		0			0
$607$	5.41050	+	3.12375i	0.219605	+	0.126789i	0.605767	−	0.795642i	$-0.292866\pi$
$607$	5.41050	+	3.12375i	0.219605	+	0.126789i	−0.386162	+	0.922431i	$0.626200\pi$
$608$	31.2283	+	31.0584i	1.26648	+	1.25958i
$609$		0			0
$610$	4.64273	−	17.3648i	0.187979	−	0.703080i
$611$	16.5278	+	31.5195i	0.668641	+	1.27514i
$612$		0			0
$613$	−9.60845	+	5.54744i	−0.388081	+	0.224059i	−0.681329	−	0.731978i	$-0.738597\pi$
$613$	−9.60845	+	5.54744i	−0.388081	+	0.224059i	0.293247	+	0.956037i	$0.405264\pi$
$614$	45.5754	−	12.2385i	1.83927	−	0.493907i
$615$		0			0
$616$	8.98994	+	8.96056i	0.362215	+	0.361031i
$617$	10.1490	−	17.5787i	0.408585	−	0.707691i	−0.586146	−	0.810205i	$-0.699356\pi$
$617$	10.1490	−	17.5787i	0.408585	−	0.707691i	0.994731	+	0.102515i	$0.0326889\pi$
$618$		0			0
$619$	15.4853			0.622407			0.311203	−	0.950343i	$-0.399268\pi$
$619$	15.4853			0.622407			0.311203	+	0.950343i	$0.399268\pi$
$620$	26.9134	−	15.5776i	1.08087	−	0.625613i
$621$		0			0
$622$	−14.4235	+	3.87320i	−0.578330	+	0.155301i
$623$	1.77017			0.0709203
$624$		0			0
$625$	23.9756			0.959025
$626$	15.0558	−	4.04301i	0.601752	−	0.161591i
$627$		0			0
$628$	−1.97172	+	1.14125i	−0.0786804	+	0.0455407i
$629$	13.6783			0.545389
$630$		0			0
$631$	−19.7995	+	34.2937i	−0.788206	+	1.36521i	0.138859	+	0.990312i	$0.455656\pi$
$631$	−19.7995	+	34.2937i	−0.788206	+	1.36521i	−0.927065	+	0.374900i	$0.877677\pi$
$632$	−7.37944	−	7.35533i	−0.293539	−	0.292579i
$633$		0			0
$634$	39.6751	−	10.6541i	1.57570	−	0.423129i
$635$	30.8688	−	17.8221i	1.22499	−	0.707249i
$636$		0			0
$637$	−18.8538	−	11.9322i	−0.747014	−	0.472773i
$638$	−3.80003	+	14.2129i	−0.150445	+	0.562695i
$639$		0			0
$640$	−11.4761	−	42.1843i	−0.453633	−	1.66748i
$641$	15.2012	+	8.77639i	0.600410	+	0.346647i	0.769203	−	0.639005i	$-0.220654\pi$
$641$	15.2012	+	8.77639i	0.600410	+	0.346647i	−0.168793	+	0.985652i	$0.553987\pi$
$642$		0			0
$643$	9.25566	−	16.0313i	0.365008	−	0.632212i	−0.623770	−	0.781608i	$-0.714400\pi$
$643$	9.25566	−	16.0313i	0.365008	−	0.632212i	0.988777	+	0.149396i	$0.0477330\pi$
$644$	−9.83132	+	5.69043i	−0.387408	+	0.224234i
$645$		0			0
$646$	26.3512	−	26.3800i	1.03677	−	1.03791i
$647$	−6.06305	−	10.5015i	−0.238363	−	0.412857i	0.721882	−	0.692016i	$-0.243277\pi$
$647$	−6.06305	−	10.5015i	−0.238363	−	0.412857i	−0.960245	+	0.279160i	$0.909944\pi$
$648$		0			0
$649$	48.5006			1.90382
$650$	−37.2150	+	34.3437i	−1.45969	+	1.34707i
$651$		0			0
$652$	−0.0105241	−	9.64504i	−0.000412156	−	0.377729i
$653$	5.26965	−	3.04243i	0.206217	−	0.119060i	−0.393335	−	0.919395i	$-0.628679\pi$
$653$	5.26965	−	3.04243i	0.206217	−	0.119060i	0.599552	+	0.800336i	$0.295345\pi$
$654$		0			0
$655$	43.1719			1.68686
$656$	18.1451	−	0.0395979i	0.708448	−	0.00154604i
$657$		0			0
$658$	−12.1497	−	3.24839i	−0.473643	−	0.126635i
$659$	12.5803	−	21.7898i	0.490060	−	0.848809i	−0.509874	−	0.860249i	$-0.670308\pi$
$659$	12.5803	−	21.7898i	0.490060	−	0.848809i	0.999935	+	0.0114396i	$0.00364141\pi$
$660$		0			0
$661$	39.1674	−	22.6133i	1.52344	−	0.879556i	0.523821	−	0.851829i	$-0.324506\pi$
$661$	39.1674	−	22.6133i	1.52344	−	0.879556i	0.999616	−	0.0277278i	$-0.00882715\pi$
$662$	2.96676	−	11.0963i	0.115306	−	0.431271i
$663$		0			0
$664$	3.52139	+	3.50988i	0.136656	+	0.136210i
$665$	13.5523	+	23.4733i	0.525536	+	0.910255i
$666$		0			0
$667$	−11.4025	−	6.58323i	−0.441506	−	0.254903i
$668$	2.46243	−	4.27583i	0.0952745	−	0.165437i
$669$		0			0
$670$	11.4570	+	11.4445i	0.442621	+	0.442139i
$671$			16.3843i			0.632510i
$672$		0			0
$673$	−6.02206	−	10.4305i	−0.232133	−	0.402067i	0.726302	−	0.687375i	$-0.241237\pi$
$673$	−6.02206	−	10.4305i	−0.232133	−	0.402067i	−0.958436	+	0.285309i	$0.907904\pi$
$674$	−10.8352	+	2.90963i	−0.417358	+	0.112075i
$675$		0			0
$676$	2.08317	−	25.9164i	0.0801217	−	0.996785i
$677$			1.50657i			0.0579022i	0.999581	+	0.0289511i	$0.00921671\pi$
$677$			1.50657i			0.0579022i	−0.999581	+	0.0289511i	$0.990783\pi$
$678$		0			0
$679$	−6.72601	+	3.88326i	−0.258121	+	0.149026i
$680$	−35.7337	+	9.63753i	−1.37032	+	0.369582i
$681$		0			0
$682$	−20.0321	+	20.0540i	−0.767069	+	0.767906i
$683$	−13.3271	−	7.69440i	−0.509947	−	0.294418i	0.222865	−	0.974849i	$-0.428459\pi$
$683$	−13.3271	−	7.69440i	−0.509947	−	0.294418i	−0.732812	+	0.680431i	$0.761792\pi$
$684$		0			0
$685$	−0.178008	+	0.308319i	−0.00680133	+	0.0117803i
$686$	16.2282	−	4.35783i	0.619597	−	0.166383i
$687$		0			0
$688$	14.7423	−	8.55441i	0.562044	−	0.326134i
$689$	9.02775	+	17.2165i	0.343930	+	0.655898i
$690$		0			0
$691$	14.3101	+	24.7858i	0.544382	+	0.942898i	0.998646	+	0.0520302i	$0.0165692\pi$
$691$	14.3101	+	24.7858i	0.544382	+	0.942898i	−0.454263	+	0.890867i	$0.650097\pi$
$692$	35.5206	−	0.0387580i	1.35029	−	0.00147336i
$693$		0			0
$694$	−1.88136	+	7.03668i	−0.0714154	+	0.267109i
$695$	11.4769	+	6.62621i	0.435345	+	0.251347i
$696$		0			0
$697$		−	15.3614i		−	0.581855i
$698$	17.9907	−	18.0104i	0.680959	−	0.681702i
$699$		0			0
$700$	−0.0195257	−	17.8948i	−0.000738004	−	0.676358i
$701$		−	41.2699i		−	1.55874i	−0.626563	−	0.779371i	$-0.715539\pi$
$701$		−	41.2699i		−	1.55874i	0.626563	−	0.779371i	$-0.284461\pi$
$702$		0			0
$703$		−	31.4492i		−	1.18613i
$704$	20.0376	+	34.4452i	0.755194	+	1.29820i
$705$		0			0
$706$	−16.8265	−	16.8081i	−0.633273	−	0.632582i
$707$			3.56261i			0.133986i
$708$		0			0
$709$	−14.6578	−	8.46268i	−0.550485	−	0.317823i	0.198832	−	0.980033i	$-0.436285\pi$
$709$	−14.6578	−	8.46268i	−0.550485	−	0.317823i	−0.749318	+	0.662211i	$0.769618\pi$
$710$	52.1109	+	13.9326i	1.95569	+	0.522882i
$711$		0			0
$712$	5.37041	+	1.42958i	0.201265	+	0.0535758i
$713$	−12.6836	−	21.9686i	−0.475003	−	0.822729i
$714$		0			0
$715$	37.1133	−	58.6416i	1.38796	−	2.19307i
$716$	−32.9012	−	18.9477i	−1.22958	−	0.708108i
$717$		0			0
$718$	1.40570	+	5.23472i	0.0524603	+	0.195358i
$719$	1.35328	−	2.34395i	0.0504689	−	0.0874147i	−0.839687	−	0.543070i	$-0.817262\pi$
$719$	1.35328	−	2.34395i	0.0504689	−	0.0874147i	0.890156	+	0.455655i	$0.150595\pi$
$720$		0			0
$721$	4.33246	+	2.50135i	0.161349	+	0.0931550i
$722$	−41.6425	−	41.5971i	−1.54977	−	1.54808i
$723$		0			0
$724$	−39.6325	+	22.9395i	−1.47293	+	0.852540i
$725$	17.9626	−	10.3707i	0.667116	−	0.385160i
$726$		0			0
$727$		−	47.7125i		−	1.76956i	−0.466010	−	0.884779i	$-0.654309\pi$
$727$		−	47.7125i		−	1.76956i	0.466010	−	0.884779i	$-0.345691\pi$
$728$	6.23829	+	6.74506i	0.231206	+	0.249989i
$729$		0			0
$730$	3.37287	+	12.5603i	0.124836	+	0.464879i
$731$	−7.21477	−	12.4964i	−0.266848	−	0.462194i
$732$		0			0
$733$			12.8449i			0.474436i	0.971456	+	0.237218i	$0.0762356\pi$
$733$			12.8449i			0.474436i	−0.971456	+	0.237218i	$0.923764\pi$
$734$	−16.2874	+	16.3052i	−0.601180	+	0.601836i
$735$		0			0
$736$	−34.4222	+	9.32412i	−1.26882	+	0.343692i
$737$	−12.7834	−	7.38048i	−0.470881	−	0.271863i
$738$		0			0
$739$	18.9646	+	32.8477i	0.697625	+	1.20832i	0.969288	+	0.245929i	$0.0790932\pi$
$739$	18.9646	+	32.8477i	0.697625	+	1.20832i	−0.271663	+	0.962393i	$0.587574\pi$
$740$	−15.5787	+	27.0512i	−0.572683	+	0.994421i
$741$		0			0
$742$	−6.63636	−	1.77433i	−0.243628	−	0.0651376i
$743$	2.15190	−	1.24240i	0.0789455	−	0.0455792i	−0.460008	−	0.887915i	$-0.652153\pi$
$743$	2.15190	−	1.24240i	0.0789455	−	0.0455792i	0.538953	+	0.842336i	$0.318820\pi$
$744$		0			0
$745$	−7.05207	+	12.2145i	−0.258368	+	0.447506i
$746$	1.07217	−	4.01013i	0.0392548	−	0.146821i
$747$		0			0
$748$	29.1977	−	16.8998i	1.06757	−	0.617918i
$749$	10.6046			0.387482
$750$		0			0
$751$	7.71464	−	4.45405i	0.281511	−	0.162531i	−0.352596	−	0.935776i	$-0.614701\pi$
$751$	7.71464	−	4.45405i	0.281511	−	0.162531i	0.634107	+	0.773245i	$0.281368\pi$
$752$	−34.2368	−	19.6671i	−1.24849	−	0.717186i
$753$		0			0
$754$	−3.16640	+	10.1675i	−0.115314	+	0.370280i
$755$	64.7758			2.35743
$756$		0			0
$757$	−20.0254	−	34.6850i	−0.727835	−	1.26065i	−0.957796	−	0.287447i	$-0.907193\pi$
$757$	−20.0254	−	34.6850i	−0.727835	−	1.26065i	0.229962	−	0.973200i	$-0.426140\pi$
$758$	25.5508	+	25.5229i	0.928046	+	0.927034i
$759$		0			0
$760$	22.1586	+	82.1590i	0.803778	+	2.98022i
$761$	−17.8174	+	30.8606i	−0.645879	+	1.11869i	0.338219	+	0.941067i	$0.390176\pi$
$761$	−17.8174	+	30.8606i	−0.645879	+	1.11869i	−0.984098	+	0.177627i	$0.943158\pi$
$762$		0			0
$763$	−0.396959	−	0.229184i	−0.0143709	−	0.00829702i
$764$	−0.0147499	−	13.5178i	−0.000533632	−	0.489058i
$765$		0			0
$766$	−3.02751	−	0.809450i	−0.109389	−	0.0292466i
$767$	35.0775	+	1.42667i	1.26658	+	0.0515139i
$768$		0			0
$769$	47.1682	−	27.2326i	1.70093	−	0.982032i	0.756107	−	0.654448i	$-0.227099\pi$
$769$	47.1682	−	27.2326i	1.70093	−	0.982032i	0.944822	−	0.327584i	$-0.106235\pi$
$770$	6.36007	+	23.6844i	0.229201	+	0.853527i
$771$		0			0
$772$	−22.7464	+	39.4973i	−0.818660	+	1.42154i
$773$	−6.47414	+	11.2135i	−0.232859	+	0.403323i	−0.958648	−	0.284594i	$-0.908141\pi$
$773$	−6.47414	+	11.2135i	−0.232859	+	0.403323i	0.725789	+	0.687917i	$0.241475\pi$
$774$		0			0
$775$	39.9615			1.43546
$776$	−23.5418	+	6.34931i	−0.845100	+	0.227927i
$777$		0			0
$778$	4.76353	+	17.7390i	0.170781	+	0.635974i
$779$	−35.3190			−1.26543
$780$		0			0
$781$	−49.1686			−1.75939
$782$	7.83004	+	29.1585i	0.280002	+	1.04270i
$783$		0			0
$784$	24.7533	−	0.0540189i	0.884047	−	0.00192925i
$785$	−4.40159			−0.157099
$786$		0			0
$787$	20.9524	−	36.2906i	0.746872	−	1.29362i	−0.202443	−	0.979294i	$-0.564888\pi$
$787$	20.9524	−	36.2906i	0.746872	−	1.29362i	0.949315	−	0.314326i	$-0.101779\pi$
$788$	−41.5000	−	23.8997i	−1.47838	−	0.851392i
$789$		0			0
$790$	−5.22070	−	19.4415i	−0.185744	−	0.691697i
$791$	−8.22928	+	4.75118i	−0.292600	+	0.168932i
$792$		0			0
$793$	−0.481952	+	11.8498i	−0.0171146	+	0.420798i
$794$	27.0022	+	7.21944i	0.958273	+	0.256208i
$795$		0			0
$796$	5.49064	−	0.00599107i	0.194611	−	0.000212348i
$797$	−30.5379	−	17.6311i	−1.08171	−	0.624524i	−0.150351	−	0.988633i	$-0.548040\pi$
$797$	−30.5379	−	17.6311i	−1.08171	−	0.624524i	−0.931356	+	0.364109i	$0.881374\pi$
$798$		0			0
$799$	−16.7131	+	28.9479i	−0.591266	+	1.02410i
$800$	14.3925	−	54.3056i	0.508851	−	1.91999i
$801$		0			0
$802$	−17.3799	−	17.3609i	−0.613705	−	0.613035i
$803$	−5.92730	−	10.2664i	−0.209170	−	0.362293i
$804$		0			0
$805$	−21.9470			−0.773530
$806$	−15.0779	+	13.9145i	−0.531095	+	0.490119i
$807$		0			0
$808$	−2.87715	+	10.8084i	−0.101218	+	0.380238i
$809$	17.9997	−	10.3922i	0.632837	−	0.365369i	−0.149013	−	0.988835i	$-0.547610\pi$
$809$	17.9997	−	10.3922i	0.632837	−	0.365369i	0.781850	+	0.623466i	$0.214276\pi$
$810$		0			0
$811$	−30.1143			−1.05746			−0.528728	−	0.848792i	$-0.677331\pi$
$811$	−30.1143			−1.05746			−0.528728	+	0.848792i	$0.677331\pi$
$812$	−1.88510	−	3.25688i	−0.0661541	−	0.114294i
$813$		0			0
$814$	7.34953	−	27.4888i	0.257601	−	0.963482i
$815$	9.31739	−	16.1382i	0.326374	−	0.565296i
$816$		0			0
$817$	−28.7316	+	16.5882i	−1.00519	+	0.580348i
$818$	−34.4395	−	9.20791i	−1.20415	−	0.321947i
$819$		0			0
$820$	30.3798	+	17.4956i	1.06091	+	0.610973i
$821$	8.14237	+	14.1030i	0.284171	+	0.492198i	0.972408	−	0.233288i	$-0.0749485\pi$
$821$	8.14237	+	14.1030i	0.284171	+	0.492198i	−0.688237	+	0.725486i	$0.741615\pi$
$822$		0			0
$823$	18.6155	+	10.7477i	0.648895	+	0.374640i	0.788033	−	0.615633i	$-0.211100\pi$
$823$	18.6155	+	10.7477i	0.648895	+	0.374640i	−0.139138	+	0.990273i	$0.544433\pi$
$824$	11.1239	+	11.0876i	0.387520	+	0.386253i
$825$		0			0
$826$	−8.76727	+	8.77684i	−0.305052	+	0.305385i
$827$			8.19871i			0.285097i	0.989788	+	0.142548i	$0.0455297\pi$
$827$			8.19871i			0.285097i	−0.989788	+	0.142548i	$0.954470\pi$
$828$		0			0
$829$	18.1725	+	31.4757i	0.631156	+	1.09320i	0.987316	+	0.158770i	$0.0507528\pi$
$829$	18.1725	+	31.4757i	0.631156	+	1.09320i	−0.356159	+	0.934425i	$0.615914\pi$
$830$	2.49126	+	9.27725i	0.0864728	+	0.322018i
$831$		0			0
$832$	13.4787	+	25.5015i	0.467290	+	0.884104i
$833$		−	20.9558i		−	0.726076i
$834$		0			0
$835$	8.25596	−	4.76658i	0.285709	−	0.164954i
$836$	−38.8560	−	67.1314i	−1.34386	−	2.32179i
$837$		0			0
$838$	−36.7520	−	36.7119i	−1.26958	−	1.26819i
$839$	−19.2667	−	11.1237i	−0.665162	−	0.384031i	0.129079	−	0.991634i	$-0.458798\pi$
$839$	−19.2667	−	11.1237i	−0.665162	−	0.384031i	−0.794241	+	0.607603i	$0.792131\pi$
$840$		0			0
$841$	−12.3191	+	21.3374i	−0.424798	+	0.735771i
$842$	3.93873	+	14.6675i	0.135738	+	0.505476i
$843$		0			0
$844$	−13.0528	+	22.6651i	−0.449294	+	0.780165i
$845$	28.5667	−	41.3201i	0.982724	−	1.42145i
$846$		0			0
$847$	−6.22178	−	10.7764i	−0.213783	−	0.370283i
$848$	−18.7007	−	10.7425i	−0.642186	−	0.368900i
$849$		0			0
$850$	−45.9476	−	12.2848i	−1.57599	−	0.421363i
$851$	22.0532	+	12.7324i	0.755974	+	0.436462i
$852$		0			0
$853$		−	29.6161i		−	1.01404i	−0.861935	−	0.507018i	$-0.830748\pi$
$853$		−	29.6161i		−	1.01404i	0.861935	−	0.507018i	$-0.169252\pi$
$854$	−2.96496	−	2.96173i	−0.101459	−	0.101348i
$855$		0			0
$856$	32.1726	+	8.56420i	1.09964	+	0.292718i
$857$			14.0190i			0.478879i	0.970911	+	0.239439i	$0.0769636\pi$
$857$			14.0190i			0.478879i	−0.970911	+	0.239439i	$0.923036\pi$
$858$		0			0
$859$			28.1857i			0.961683i	0.876808	+	0.480841i	$0.159669\pi$
$859$			28.1857i			0.961683i	−0.876808	+	0.480841i	$0.840331\pi$
$860$	32.9308	−	0.0359322i	1.12293	−	0.00122528i
$861$		0			0
$862$	−7.34278	+	7.35080i	−0.250096	+	0.250369i
$863$			36.8439i			1.25418i	0.778946	+	0.627091i	$0.215755\pi$
$863$			36.8439i			1.25418i	−0.778946	+	0.627091i	$0.784245\pi$
$864$		0			0
$865$	59.4335	+	34.3139i	2.02080	+	1.16671i
$866$	7.55940	−	28.2738i	0.256879	−	0.960782i
$867$		0			0
$868$	−0.00791096	−	7.25015i	−0.000268515	−	0.246086i
$869$	9.17457	+	15.8908i	0.311226	+	0.539059i
$870$		0			0
$871$	−9.02831	−	5.71387i	−0.305913	−	0.193607i
$872$	−1.01922	−	1.01589i	−0.0345152	−	0.0344024i
$873$		0			0
$874$	67.0412	−	18.0028i	2.26770	−	0.608955i
$875$	8.58372	−	14.8674i	0.290183	−	0.502611i
$876$		0			0
$877$	9.44822	+	5.45493i	0.319044	+	0.184200i	0.650966	−	0.759107i	$-0.274364\pi$
$877$	9.44822	+	5.45493i	0.319044	+	0.184200i	−0.331922	+	0.943307i	$0.607697\pi$
$878$	2.11177	−	2.11408i	0.0712689	−	0.0713467i
$879$		0			0
$880$	0.168017	+	76.9911i	0.00566385	+	2.59537i
$881$	−10.4498	+	6.03317i	−0.352061	+	0.203263i	−0.665593	−	0.746315i	$-0.731821\pi$
$881$	−10.4498	+	6.03317i	−0.352061	+	0.203263i	0.313532	+	0.949578i	$0.398488\pi$
$882$		0			0
$883$			2.66359i			0.0896371i	0.998995	+	0.0448185i	$0.0142710\pi$
$883$			2.66359i			0.0896371i	−0.998995	+	0.0448185i	$0.985729\pi$
$884$	21.6140	−	11.3637i	0.726957	−	0.382203i
$885$		0			0
$886$	−37.1785	+	9.98370i	−1.24904	+	0.335409i
$887$	27.5037	+	47.6378i	0.923485	+	1.59952i	0.793981	+	0.607943i	$0.208005\pi$
$887$	27.5037	+	47.6378i	0.923485	+	1.59952i	0.129504	+	0.991579i	$0.458661\pi$
$888$		0			0
$889$		−	8.31045i		−	0.278724i
$890$	7.59654	+	7.58825i	0.254636	+	0.254359i
$891$		0			0
$892$	2.59542	+	1.49469i	0.0869010	+	0.0500460i
$893$	66.5571	+	38.4267i	2.22725	+	1.28590i
$894$		0			0
$895$	−36.6774	−	63.5270i	−1.22599	−	2.12348i
$896$	−9.85543	−	2.60045i	−0.329247	−	0.0868751i
$897$		0			0
$898$	−10.2233	+	38.2375i	−0.341158	+	1.27600i
$899$	7.27766	−	4.20176i	0.242724	−	0.140137i
$900$		0			0
$901$	−9.12898	+	15.8119i	−0.304130	+	0.526769i
$902$	−30.8713	−	8.25389i	−1.02790	−	0.274824i
$903$		0			0
$904$	−28.8034	+	7.76839i	−0.957986	+	0.258373i
$905$	−88.4738			−2.94097
$906$		0			0
$907$	36.6320	−	21.1495i	1.21635	−	0.702258i	0.252212	−	0.967672i	$-0.418842\pi$
$907$	36.6320	−	21.1495i	1.21635	−	0.702258i	0.964134	+	0.265414i	$0.0855088\pi$
$908$	15.3447	−	0.0167432i	0.509231	−	0.000555643i
$909$		0			0
$910$	3.90316	+	17.3166i	0.129388	+	0.574038i
$911$	−10.7252			−0.355341			−0.177670	−	0.984090i	$-0.556856\pi$
$911$	−10.7252			−0.355341			−0.177670	+	0.984090i	$0.556856\pi$
$912$		0			0
$913$	−4.37800	−	7.58292i	−0.144891	−	0.250958i
$914$	27.9079	−	27.9384i	0.923113	−	0.924121i
$915$		0			0
$916$	20.8095	+	35.9525i	0.687565	+	1.18790i
$917$	5.03276	−	8.71700i	0.166196	−	0.287861i
$918$		0			0
$919$	−49.1677	−	28.3870i	−1.62189	−	0.936400i	−0.986413	−	0.164282i	$-0.947469\pi$
$919$	−49.1677	−	28.3870i	−1.62189	−	0.936400i	−0.635479	−	0.772118i	$-0.719197\pi$
$920$	−66.5837	−	17.7243i	−2.19520	−	0.584353i
$921$		0			0
$922$	−11.5008	+	43.0154i	−0.378758	+	1.41664i
$923$	−35.5606	−	1.44631i	−1.17049	−	0.0476060i
$924$		0			0
$925$	−34.7410	+	20.0577i	−1.14228	+	0.659495i
$926$	−48.8822	+	13.1265i	−1.60637	+	0.431365i
$927$		0			0
$928$	−3.08886	−	11.4033i	−0.101397	−	0.374330i
$929$	21.7847	−	37.7322i	0.714732	−	1.23795i	−0.248330	−	0.968675i	$-0.579882\pi$
$929$	21.7847	−	37.7322i	0.714732	−	1.23795i	0.963063	−	0.269277i	$-0.0867849\pi$
$930$		0			0
$931$	−48.1817			−1.57909
$932$	3.56865	+	6.16553i	0.116895	+	0.201959i
$933$		0			0
$934$	10.6539	−	2.86094i	0.348607	−	0.0936128i
$935$	65.1796			2.13160
$936$		0			0
$937$	−7.56787			−0.247232			−0.123616	−	0.992330i	$-0.539449\pi$
$937$	−7.56787			−0.247232			−0.123616	+	0.992330i	$0.539449\pi$
$938$	3.64639	−	0.979181i	0.119059	−	0.0319714i
$939$		0			0
$940$	−38.2143	−	66.0227i	−1.24641	−	2.15342i
$941$	−28.6444			−0.933782			−0.466891	−	0.884315i	$-0.654626\pi$
$941$	−28.6444			−0.933782			−0.466891	+	0.884315i	$0.654626\pi$
$942$		0			0
$943$	14.2991	−	24.7669i	0.465644	−	0.806520i
$944$	−33.6867	+	19.5471i	−1.09641	+	0.636205i
$945$		0			0
$946$	−28.9901	+	7.78482i	−0.942548	+	0.253106i
$947$	−39.5732	+	22.8476i	−1.28596	+	0.742447i	−0.977930	−	0.208931i	$-0.933002\pi$
$947$	−39.5732	+	22.8476i	−1.28596	+	0.742447i	−0.308026	+	0.951378i	$0.599668\pi$
$948$		0			0
$949$	−3.98486	−	7.59940i	−0.129354	−	0.246687i
$950$	−28.2451	+	105.643i	−0.916393	+	3.42750i
$951$		0			0
$952$	−2.21971	+	8.33862i	−0.0719411	+	0.270256i
$953$	31.9834	+	18.4656i	1.03604	+	0.598161i	0.918710	−	0.394932i	$-0.129232\pi$
$953$	31.9834	+	18.4656i	1.03604	+	0.598161i	0.117334	+	0.993092i	$0.462565\pi$
$954$		0			0
$955$	13.0586	−	22.6182i	0.422567	−	0.731908i
$956$	14.2715	+	24.6568i	0.461574	+	0.797459i
$957$		0			0
$958$	21.9080	−	21.9319i	0.707815	−	0.708587i
$959$	0.0415026	+	0.0718845i	0.00134019	+	0.00232127i
$960$		0			0
$961$	−14.8094			−0.477722
$962$	6.12405	−	19.6647i	0.197447	−	0.634017i
$963$		0			0
$964$	1.99313	−	0.00217479i	0.0641943	−	7.00452e-5i
$965$	−76.2632	+	44.0306i	−2.45500	+	1.41739i
$966$		0			0
$967$	−4.36992			−0.140527			−0.0702636	−	0.997528i	$-0.522384\pi$
$967$	−4.36992			−0.140527			−0.0702636	+	0.997528i	$0.522384\pi$
$968$	−10.1729	−	37.7187i	−0.326969	−	1.21233i
$969$		0			0
$970$	−45.5107	−	12.1679i	−1.46126	−	0.390689i
$971$	9.26820	−	16.0530i	0.297431	−	0.515165i	−0.678117	−	0.734954i	$-0.737204\pi$
$971$	9.26820	−	16.0530i	0.297431	−	0.515165i	0.975547	+	0.219789i	$0.0705370\pi$
$972$		0			0
$973$	2.67585	−	1.54490i	0.0857838	−	0.0495273i
$974$	12.2250	−	45.7242i	0.391715	−	1.46510i
$975$		0			0
$976$	−6.60335	−	11.3799i	−0.211368	−	0.364262i
$977$	6.60452	+	11.4394i	0.211297	+	0.365978i	0.952121	−	0.305722i	$-0.0988978\pi$
$977$	6.60452	+	11.4394i	0.211297	+	0.365978i	−0.740823	+	0.671700i	$0.765564\pi$
$978$		0			0
$979$	−8.47600	−	4.89362i	−0.270894	−	0.156401i
$980$	41.4437	+	23.8673i	1.32387	+	0.762412i
$981$		0			0
$982$	19.9687	+	19.9469i	0.637226	+	0.636531i
$983$			27.1608i			0.866294i	0.901323	+	0.433147i	$0.142597\pi$
$983$			27.1608i			0.866294i	−0.901323	+	0.433147i	$0.857403\pi$
$984$		0			0
$985$	−46.2631	−	80.1300i	−1.47406	−	2.55316i
$986$	−9.65950	+	2.59390i	−0.307621	+	0.0826068i
$987$		0			0
$988$	−26.1275	−	49.6949i	−0.831225	−	1.58101i
$989$		−	26.8634i		−	0.854208i
$990$		0			0
$991$	−20.6051	+	11.8964i	−0.654544	+	0.377901i	−0.790195	−	0.612856i	$-0.790021\pi$
$991$	−20.6051	+	11.8964i	−0.654544	+	0.377901i	0.135651	+	0.990757i	$0.456687\pi$
$992$	5.83119	−	22.0022i	0.185141	−	0.698571i
$993$		0			0
$994$	8.88802	−	8.89772i	0.281911	−	0.282219i
$995$	9.18701	+	5.30412i	0.291248	+	0.168152i
$996$		0			0
$997$	1.44752	−	2.50718i	0.0458435	−	0.0794032i	−0.842193	−	0.539176i	$-0.818736\pi$
$997$	1.44752	−	2.50718i	0.0458435	−	0.0794032i	0.888037	+	0.459773i	$0.152069\pi$
$998$	−23.7092	+	6.36674i	−0.750503	+	0.201536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.bp.d.179.18	yes	40
3.2	odd	2	inner	468.2.bp.d.179.3	✓	40
4.3	odd	2	inner	468.2.bp.d.179.7	yes	40
12.11	even	2	inner	468.2.bp.d.179.14	yes	40
13.4	even	6	inner	468.2.bp.d.251.14	yes	40
39.17	odd	6	inner	468.2.bp.d.251.7	yes	40
52.43	odd	6	inner	468.2.bp.d.251.3	yes	40
156.95	even	6	inner	468.2.bp.d.251.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bp.d.179.3	✓	40	3.2	odd	2	inner
468.2.bp.d.179.7	yes	40	4.3	odd	2	inner
468.2.bp.d.179.14	yes	40	12.11	even	2	inner
468.2.bp.d.179.18	yes	40	1.1	even	1	trivial
468.2.bp.d.251.3	yes	40	52.43	odd	6	inner
468.2.bp.d.251.7	yes	40	39.17	odd	6	inner
468.2.bp.d.251.14	yes	40	13.4	even	6	inner
468.2.bp.d.251.18	yes	40	156.95	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.bp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36583 - 0.366771i) q^{2} +(1.73096 - 1.00189i) q^{4} +3.86412 q^{5} +(0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +O(q^{10})\)	\(q+(1.36583 - 0.366771i) q^{2} +(1.73096 - 1.00189i) q^{4} +3.86412 q^{5} +(0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +(5.27771 - 1.41724i) q^{10} +(-4.31382 + 2.49059i) q^{11} +(-3.19318 + 1.67439i) q^{13} +(0.329088 - 1.23086i) q^{14} +(1.99244 - 3.46846i) q^{16} +(-2.93265 - 1.69317i) q^{17} +(-3.89294 + 6.74276i) q^{19} +(6.68863 - 3.87142i) q^{20} +(-4.97845 + 4.98389i) q^{22} +(-3.15217 - 5.45971i) q^{23} +9.93140 q^{25} +(-3.74721 + 3.45809i) q^{26} +(-0.00196606 - 1.80184i) q^{28} +(1.80867 - 1.04424i) q^{29} +4.02376 q^{31} +(1.44919 - 5.46808i) q^{32} +(-4.62650 - 1.23696i) q^{34} +(1.74063 - 3.01486i) q^{35} +(-3.49810 + 2.01963i) q^{37} +(-2.84402 + 10.6373i) q^{38} +(7.71557 - 7.74087i) q^{40} +(2.26815 + 3.92854i) q^{41} +(3.69023 + 2.13055i) q^{43} +(-4.97176 + 8.63307i) q^{44} +(-6.30777 - 6.30089i) q^{46} -9.87089i q^{47} +(3.09417 + 5.35926i) q^{49} +(13.5646 - 3.64254i) q^{50} +(-3.84971 + 6.09752i) q^{52} -5.39166i q^{53} +(-16.6691 + 9.62392i) q^{55} +(-0.663546 - 2.46027i) q^{56} +(2.08734 - 2.08961i) q^{58} +(-8.43231 - 4.86840i) q^{59} +(1.64463 - 2.84858i) q^{61} +(5.49575 - 1.47580i) q^{62} +(-0.0261874 - 7.99996i) q^{64} +(-12.3388 + 6.47005i) q^{65} +(1.48167 + 2.56634i) q^{67} +(-6.77267 + 0.00738995i) q^{68} +(1.27163 - 4.75618i) q^{70} +(8.54844 + 4.93545i) q^{71} +2.37988i q^{73} +(-4.03706 + 4.04146i) q^{74} +(0.0169910 + 15.5717i) q^{76} +4.48763i q^{77} -3.68370i q^{79} +(7.69900 - 13.4025i) q^{80} +(4.53876 + 4.53382i) q^{82} +1.75782i q^{83} +(-11.3321 - 6.54260i) q^{85} +(5.82163 + 1.55650i) q^{86} +(-3.62419 + 13.6148i) q^{88} +(0.982423 + 1.70161i) q^{89} +(-0.132006 + 3.24563i) q^{91} +(-10.9263 - 6.29242i) q^{92} +(-3.62035 - 13.4819i) q^{94} +(-15.0428 + 26.0548i) q^{95} +(-7.46572 - 4.31034i) q^{97} +(6.19172 + 6.18497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4}+O(q^{10}) \) 40 * q + 12 * q^4	\( 40 q + 12 q^{4} + 16 q^{10} - 44 q^{13} - 24 q^{25} - 48 q^{37} + 40 q^{40} - 48 q^{46} - 24 q^{49} + 28 q^{52} - 72 q^{58} - 4 q^{61} + 60 q^{76} - 64 q^{82} - 24 q^{85} - 4 q^{88} - 24 q^{94} + 84 q^{97}+O(q^{100}) \) 40 * q + 12 * q^4 + 16 * q^10 - 44 * q^13 - 24 * q^25 - 48 * q^37 + 40 * q^40 - 48 * q^46 - 24 * q^49 + 28 * q^52 - 72 * q^58 - 4 * q^61 + 60 * q^76 - 64 * q^82 - 24 * q^85 - 4 * q^88 - 24 * q^94 + 84 * q^97

Introduction

L-functions

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