LMFDB - Embedded newform 468.2.bp.d.251.7

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			251.7
Character	$\chi$	$=$	468.251
Dual form			468.2.bp.d.179.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00055 - 0.999454i) q^{2} +(0.00218229 + 2.00000i) q^{4} +3.86412 q^{5} +(-0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +O(q^{10})$	\(q+(-1.00055 - 0.999454i) q^{2} +(0.00218229 + 2.00000i) q^{4} +3.86412 q^{5} +(-0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +(-3.86622 - 3.86201i) q^{10} +(4.31382 + 2.49059i) q^{11} +(-3.19318 - 1.67439i) q^{13} +(-0.329088 + 1.23086i) q^{14} +(-3.99999 + 0.00872914i) q^{16} +(-2.93265 + 1.69317i) q^{17} +(3.89294 + 6.74276i) q^{19} +(0.00843260 + 7.72823i) q^{20} +(-1.82695 - 6.80341i) q^{22} +(3.15217 - 5.45971i) q^{23} +9.93140 q^{25} +(1.52144 + 4.86675i) q^{26} +(1.55945 - 0.902621i) q^{28} +(1.80867 + 1.04424i) q^{29} -4.02376 q^{31} +(4.01090 + 3.98907i) q^{32} +(4.62650 + 1.23696i) q^{34} +(-1.74063 - 3.01486i) q^{35} +(-3.49810 - 2.01963i) q^{37} +(2.84402 - 10.6373i) q^{38} +(7.71557 - 7.74087i) q^{40} +(2.26815 - 3.92854i) q^{41} +(-3.69023 + 2.13055i) q^{43} +(-4.97176 + 8.63307i) q^{44} +(-8.61062 + 2.31224i) q^{46} -9.87089i q^{47} +(3.09417 - 5.35926i) q^{49} +(-9.93681 - 9.92598i) q^{50} +(3.34182 - 6.39001i) q^{52} +5.39166i q^{53} +(16.6691 + 9.62392i) q^{55} +(-2.46243 - 0.655489i) q^{56} +(-0.765991 - 2.85249i) q^{58} +(8.43231 - 4.86840i) q^{59} +(1.64463 + 2.84858i) q^{61} +(4.02595 + 4.02156i) q^{62} +(-0.0261874 - 7.99996i) q^{64} +(-12.3388 - 6.47005i) q^{65} +(-1.48167 + 2.56634i) q^{67} +(-3.39273 - 5.86161i) q^{68} +(-1.27163 + 4.75618i) q^{70} +(-8.54844 + 4.93545i) q^{71} -2.37988i q^{73} +(1.48148 + 5.51693i) q^{74} +(-13.4770 + 7.80058i) q^{76} -4.48763i q^{77} -3.68370i q^{79} +(-15.4564 + 0.0337304i) q^{80} +(-6.19578 + 1.66378i) q^{82} +1.75782i q^{83} +(-11.3321 + 6.54260i) q^{85} +(5.82163 + 1.55650i) q^{86} +(13.6028 - 3.66874i) q^{88} +(0.982423 - 1.70161i) q^{89} +(0.132006 + 3.24563i) q^{91} +(10.9263 + 6.29242i) q^{92} +(-9.86550 + 9.87627i) q^{94} +(15.0428 + 26.0548i) q^{95} +(-7.46572 + 4.31034i) q^{97} +(-8.45220 + 2.26970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00055	−	0.999454i	−0.707492	−	0.706721i
$2$	−1.00055	−	0.999454i	−0.707492	−	0.706721i
$3$		0			0
$3$		0			0
$4$	0.00218229	+	2.00000i	0.00109114	+	0.999999i
$5$	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	$-0.221127\pi$
$7$	−0.450459	−	0.780219i	−0.170258	−	0.294895i	−0.938510	+	0.345252i	$0.887793\pi$
$8$	1.99672	−	2.00327i	0.705949	−	0.708263i
$9$		0			0
$10$	−3.86622	−	3.86201i	−1.22261	−	1.22127i
$11$	4.31382	+	2.49059i	1.30067	+	0.750940i	0.980518	−	0.196428i	$-0.0629340\pi$
$11$	4.31382	+	2.49059i	1.30067	+	0.750940i	0.320148	+	0.947368i	$0.396267\pi$
$12$		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
$16$	−3.99999	+	0.00872914i	−0.999998	+	0.00218228i
$17$	−2.93265	+	1.69317i	−0.711273	+	0.410654i	−0.811532	−	0.584308i	$-0.801366\pi$
$17$	−2.93265	+	1.69317i	−0.711273	+	0.410654i	0.100259	+	0.994961i	$0.468033\pi$
$18$		0			0
$19$	3.89294	+	6.74276i	0.893101	+	1.54690i	0.836138	+	0.548519i	$0.184808\pi$
$19$	3.89294	+	6.74276i	0.893101	+	1.54690i	0.0569627	+	0.998376i	$0.481858\pi$
$20$	0.00843260	+	7.72823i	0.00188559	+	1.72808i
$21$		0			0
$22$	−1.82695	−	6.80341i	−0.389507	−	1.45049i
$23$	3.15217	−	5.45971i	0.657272	−	1.13843i	−0.324047	−	0.946041i	$-0.605043\pi$
$23$	3.15217	−	5.45971i	0.657272	−	1.13843i	0.981319	−	0.192388i	$-0.0616232\pi$
$24$		0			0
$25$	9.93140			1.98628
$26$	1.52144	+	4.86675i	0.298380	+	0.954447i
$27$		0			0
$28$	1.55945	−	0.902621i	0.294709	−	0.170579i
$29$	1.80867	+	1.04424i	0.335862	+	0.193910i	0.658441	−	0.752633i	$-0.271216\pi$
$29$	1.80867	+	1.04424i	0.335862	+	0.193910i	−0.322579	+	0.946543i	$0.604550\pi$
$30$		0			0
$31$	−4.02376			−0.722688			−0.361344	−	0.932433i	$-0.617682\pi$
$31$	−4.02376			−0.722688			−0.361344	+	0.932433i	$0.617682\pi$
$32$	4.01090	+	3.98907i	0.709033	+	0.705175i
$33$		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	0.184093	−	0.982909i	$-0.441065\pi$
$37$	−3.49810	−	2.01963i	−0.575084	−	0.332025i	−0.759178	+	0.650884i	$0.774399\pi$
$38$	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	−0.632760	−	0.774348i	$-0.718078\pi$
$41$	2.26815	−	3.92854i	0.354225	−	0.613535i	0.986985	+	0.160812i	$0.0514114\pi$
$42$		0			0
$43$	−3.69023	+	2.13055i	−0.562754	+	0.324906i	−0.754250	−	0.656587i	$-0.771999\pi$
$43$	−3.69023	+	2.13055i	−0.562754	+	0.324906i	0.191496	+	0.981493i	$0.438666\pi$
$44$	−4.97176	+	8.63307i	−0.749520	+	1.30148i
$45$		0			0
$46$	−8.61062	+	2.31224i	−1.26957	+	0.340922i
$47$		−	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
$50$	−9.93681	−	9.92598i	−1.40528	−	1.40374i
$51$		0			0
$52$	3.34182	−	6.39001i	0.463427	−	0.886135i
$53$			5.39166i			0.740601i	0.928912	+	0.370300i	$0.120745\pi$
$53$			5.39166i			0.740601i	−0.928912	+	0.370300i	$0.879255\pi$
$54$		0			0
$55$	16.6691	+	9.62392i	2.24766	+	1.29769i
$56$	−2.46243	−	0.655489i	−0.329056	−	0.0875934i
$57$		0			0
$58$	−0.765991	−	2.85249i	−0.100580	−	0.374551i
$59$	8.43231	−	4.86840i	1.09779	−	0.633811i	0.162153	−	0.986766i	$-0.448156\pi$
$59$	8.43231	−	4.86840i	1.09779	−	0.633811i	0.935640	+	0.352954i	$0.114823\pi$
$60$		0			0
$61$	1.64463	+	2.84858i	0.210573	+	0.364723i	0.951894	−	0.306428i	$-0.0991338\pi$
$61$	1.64463	+	2.84858i	0.210573	+	0.364723i	−0.741321	+	0.671150i	$0.765800\pi$
$62$	4.02595	+	4.02156i	0.511296	+	0.510739i
$63$		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	$-0.891272\pi$
$67$	−1.48167	+	2.56634i	−0.181015	+	0.313528i	0.761211	+	0.648504i	$0.224605\pi$
$68$	−3.39273	−	5.86161i	−0.411429	−	0.710824i
$69$		0			0
$70$	−1.27163	+	4.75618i	−0.151989	+	0.568472i
$71$	−8.54844	+	4.93545i	−1.01451	+	0.585730i	−0.912510	−	0.409054i	$-0.865859\pi$
$71$	−8.54844	+	4.93545i	−1.01451	+	0.585730i	−0.102003	+	0.994784i	$0.532525\pi$
$72$		0			0
$73$		−	2.37988i		−	0.278544i	−0.990254	−	0.139272i	$-0.955524\pi$
$73$		−	2.37988i		−	0.278544i	0.990254	−	0.139272i	$-0.0444763\pi$
$74$	1.48148	+	5.51693i	0.172219	+	0.641330i
$75$		0			0
$76$	−13.4770	+	7.80058i	−1.54592	+	0.894788i
$77$		−	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	$-0.0664430\pi$
$80$	−15.4564	+	0.0337304i	−1.72808	+	0.00377117i
$81$		0			0
$82$	−6.19578	+	1.66378i	−0.684210	+	0.183734i
$83$			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
$88$	13.6028	−	3.66874i	1.45007	−	0.391089i
$89$	0.982423	−	1.70161i	0.104137	−	0.180370i	−0.809248	−	0.587466i	$-0.800125\pi$
$89$	0.982423	−	1.70161i	0.104137	−	0.180370i	0.913385	+	0.407097i	$0.133459\pi$
$90$		0			0
$91$	0.132006	+	3.24563i	0.0138379	+	0.340234i
$92$	10.9263	+	6.29242i	1.13915	+	0.656030i
$93$		0			0
$94$	−9.86550	+	9.87627i	−1.01755	+	1.01866i
$95$	15.0428	+	26.0548i	1.54335	+	2.67317i
$96$		0			0
$97$	−7.46572	+	4.31034i	−0.758029	+	0.437648i	−0.828588	−	0.559859i	$-0.810855\pi$
$97$	−7.46572	+	4.31034i	−0.758029	+	0.437648i	0.0705585	+	0.997508i	$0.477522\pi$
$98$	−8.45220	+	2.26970i	−0.853801	+	0.229275i
$99$		0			0
$100$	0.0216731	+	19.8628i	0.00216731	+	1.98628i
$101$	−3.42463	−	1.97721i	−0.340763	−	0.196740i	0.319846	−	0.947469i	$-0.396369\pi$
$101$	−3.42463	−	1.97721i	−0.340763	−	0.196740i	−0.660610	+	0.750730i	$0.729702\pi$
$102$		0			0
$103$			5.55288i			0.547141i	0.961852	+	0.273571i	$0.0882047\pi$
$103$			5.55288i			0.547141i	−0.961852	+	0.273571i	$0.911795\pi$
$104$	−9.73016	+	3.05350i	−0.954121	+	0.299421i
$105$		0			0
$106$	5.38871	−	5.39460i	0.523398	−	0.523970i
$107$	−5.88542	+	10.1938i	−0.568965	+	0.985476i	0.427704	+	0.903919i	$0.359323\pi$
$107$	−5.88542	+	10.1938i	−0.568965	+	0.985476i	−0.996669	+	0.0815568i	$0.974011\pi$
$108$		0			0
$109$			0.508779i			0.0487321i	0.999703	+	0.0243661i	$0.00775673\pi$
$109$			0.508779i			0.0487321i	−0.999703	+	0.0243661i	$0.992243\pi$
$110$	−7.05954	−	26.2892i	−0.673101	−	2.50657i
$111$		0			0
$112$	1.80864	+	3.11694i	0.170901	+	0.294523i
$113$	−9.13432	+	5.27370i	−0.859285	+	0.496108i	−0.863773	−	0.503882i	$-0.831905\pi$
$113$	−9.13432	+	5.27370i	−0.859285	+	0.496108i	0.00448796	+	0.999990i	$0.498571\pi$
$114$		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
$124$	−0.00878099	−	8.04751i	−0.000788556	−	0.722688i
$125$	19.0555			1.70437
$126$		0			0
$127$	−7.98858	−	4.61221i	−0.708872	−	0.409267i	0.101771	−	0.994808i	$-0.467549\pi$
$127$	−7.98858	−	4.61221i	−0.708872	−	0.409267i	−0.810643	+	0.585541i	$0.800882\pi$
$128$	−7.96939	+	8.03049i	−0.704401	+	0.709802i
$129$		0			0
$130$	5.87903	+	18.8057i	0.515625	+	1.64937i
$131$	−11.1725			−0.976146			−0.488073	−	0.872803i	$-0.662300\pi$
$131$	−11.1725			−0.976146			−0.488073	+	0.872803i	$0.662300\pi$
$132$		0			0
$133$	3.50722	−	6.07468i	0.304114	−	0.526742i
$134$	4.04742	−	1.08687i	0.349644	−	0.0938912i
$135$		0			0
$136$	−2.46382	+	9.25569i	−0.211271	+	0.793669i
$137$	−0.0460669	−	0.0797902i	−0.00393576	−	0.00681694i	0.864051	−	0.503405i	$-0.167919\pi$
$137$	−0.0460669	−	0.0797902i	−0.00393576	−	0.00681694i	−0.867987	+	0.496588i	$0.834586\pi$
$138$		0			0
$139$	−2.97013	+	1.71481i	−0.251923	+	0.145448i	−0.620645	−	0.784092i	$-0.713129\pi$
$139$	−2.97013	+	1.71481i	−0.251923	+	0.145448i	0.368721	+	0.929540i	$0.379796\pi$
$140$	6.02591	−	3.48783i	0.509282	−	0.294776i
$141$		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
$146$	−2.37858	+	2.38118i	−0.196853	+	0.197068i
$147$		0			0
$148$	4.03162	−	7.00061i	0.331397	−	0.575446i
$149$	−1.82501	−	3.16102i	−0.149511	−	0.258961i	0.781536	−	0.623860i	$-0.214437\pi$
$149$	−1.82501	−	3.16102i	−0.149511	−	0.258961i	−0.931047	+	0.364900i	$0.881103\pi$
$150$		0			0
$151$	−16.7634			−1.36419			−0.682093	−	0.731265i	$-0.738930\pi$
$151$	−16.7634			−1.36419			−0.682093	+	0.731265i	$0.738930\pi$
$152$	21.2807	+	5.66483i	1.72609	+	0.459478i
$153$		0			0
$154$	−4.48518	+	4.49008i	−0.361426	+	0.361821i
$155$	−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	$0.514474\pi$
$158$	−3.68169	+	3.68571i	−0.292899	+	0.293219i
$159$		0			0
$160$	15.4986	+	15.4142i	1.22527	+	1.21860i
$161$	−5.67969			−0.447623
$162$		0			0
$163$	−2.41126	−	4.17643i	−0.188865	−	0.327123i	0.756007	−	0.654563i	$-0.227147\pi$
$163$	−2.41126	−	4.17643i	−0.188865	−	0.327123i	−0.944872	+	0.327440i	$0.893814\pi$
$164$	7.86203	+	4.52771i	0.613921	+	0.353555i
$165$		0			0
$166$	1.75686	−	1.75878i	0.136359	−	0.136508i
$167$	−2.13657	−	1.23355i	−0.165333	−	0.0954549i	0.415050	−	0.909798i	$-0.363764\pi$
$167$	−2.13657	−	1.23355i	−0.165333	−	0.0954549i	−0.580383	+	0.814343i	$0.697097\pi$
$168$		0			0
$169$	7.39281	+	10.6933i	0.568678	+	0.822560i
$170$	17.8773	+	4.77976i	1.37113	+	0.366591i
$171$		0			0
$172$	−4.26916	−	7.37580i	−0.325520	−	0.562399i
$173$	15.3809	−	8.88015i	1.16939	−	0.675145i	0.215851	−	0.976426i	$-0.430748\pi$
$173$	15.3809	−	8.88015i	1.16939	−	0.675145i	0.953535	+	0.301281i	$0.0974142\pi$
$174$		0			0
$175$	−4.47369	−	7.74866i	−0.338179	−	0.585744i
$176$	−17.2770	−	9.92467i	−1.30230	−	0.748100i
$177$		0			0
$178$	−2.68364	+	0.720648i	−0.201147	+	0.0540149i
$179$	9.49178	−	16.4403i	0.709449	−	1.22880i	−0.255612	−	0.966779i	$-0.582277\pi$
$179$	9.49178	−	16.4403i	0.709449	−	1.22880i	0.965062	−	0.262023i	$-0.0843896\pi$
$180$		0			0
$181$	−22.8963			−1.70187			−0.850933	−	0.525275i	$-0.823963\pi$
$181$	−22.8963			−1.70187			−0.850933	+	0.525275i	$0.823963\pi$
$182$	3.11178	−	3.37933i	0.230660	−	0.250493i
$183$		0			0
$184$	−4.64328	−	17.2162i	−0.342307	−	1.26919i
$185$	−13.5171	−	7.80409i	−0.993795	−	0.573768i
$186$		0			0
$187$	−16.8679			−1.23350
$188$	19.7418	−	0.0215411i	1.43982	−	0.00157105i
$189$		0			0
$190$	10.9896	−	41.1036i	0.797272	−	2.98197i
$191$	−3.37946	−	5.85340i	−0.244529	−	0.423537i	0.717470	−	0.696589i	$-0.245300\pi$
$191$	−3.37946	−	5.85340i	−0.244529	−	0.423537i	−0.961999	+	0.273052i	$0.911967\pi$
$192$		0			0
$193$	−19.7363	−	11.3947i	−1.42065	−	0.820211i	−0.424293	−	0.905525i	$-0.639477\pi$
$193$	−19.7363	−	11.3947i	−1.42065	−	0.820211i	−0.996354	+	0.0853145i	$0.972810\pi$
$194$	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	0.0254792	+	0.999675i	$0.491889\pi$
$197$	−11.9725	+	20.7370i	−0.853005	+	1.47745i	−0.878484	+	0.477772i	$0.841444\pi$
$198$		0			0
$199$	−2.37752	+	1.37266i	−0.168538	+	0.0973053i	−0.581896	−	0.813263i	$-0.697689\pi$
$199$	−2.37752	+	1.37266i	−0.168538	+	0.0973053i	0.413358	+	0.910568i	$0.364356\pi$
$200$	19.8303	−	19.8953i	1.40221	−	1.40681i
$201$		0			0
$202$	1.45037	+	5.40105i	0.102047	+	0.380016i
$203$		−	1.88155i		−	0.132059i
$204$		0			0
$205$	8.76438	−	15.1803i	0.612131	−	1.06024i
$206$	5.54984	−	5.55590i	0.386676	−	0.387098i
$207$		0			0
$208$	12.7873	+	6.66968i	0.886640	+	0.462459i
$209$			38.7828i			2.68266i
$210$		0			0
$211$	11.3254	+	6.53874i	0.779674	+	0.450145i	0.836315	−	0.548249i	$-0.184706\pi$
$211$	11.3254	+	6.53874i	0.779674	+	0.450145i	−0.0566404	+	0.998395i	$0.518039\pi$
$212$	−10.7833	+	0.0117661i	−0.740600	+	0.000808101i
$213$		0			0
$214$	16.0769	−	4.31719i	1.09899	−	0.295117i
$215$	−14.2595	+	8.23271i	−0.972488	+	0.561466i
$216$		0			0
$217$	1.81254	+	3.13941i	0.123043	+	0.213117i
$218$	0.508501	−	0.509056i	0.0344400	−	0.0344776i
$219$		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	$-0.849300\pi$
$223$	−0.748761	+	1.29689i	−0.0501408	+	0.0868464i	0.839866	+	0.542794i	$0.182634\pi$
$224$	1.30560	−	4.92629i	0.0872343	−	0.329152i
$225$		0			0
$226$	14.4101	+	3.85276i	0.958548	+	0.256282i
$227$	−6.64444	+	3.83617i	−0.441007	+	0.254615i	−0.704025	−	0.710176i	$-0.748616\pi$
$227$	−6.64444	+	3.83617i	−0.441007	+	0.254615i	0.263018	+	0.964791i	$0.415282\pi$
$228$		0			0
$229$		−	20.7703i		−	1.37254i	−0.727348	−	0.686269i	$-0.759247\pi$
$229$		−	20.7703i		−	1.37254i	0.727348	−	0.686269i	$-0.240753\pi$
$230$	−33.2724	+	8.93478i	−2.19392	+	0.589142i
$231$		0			0
$232$	5.70331	−	1.53821i	0.374441	−	0.100988i
$233$		−	3.56192i		−	0.233349i	−0.993170	−	0.116675i	$-0.962777\pi$
$233$		−	3.56192i		−	0.233349i	0.993170	−	0.116675i	$-0.0372234\pi$
$234$		0			0
$235$		−	38.1423i		−	2.48813i
$236$	9.75519	+	16.8540i	0.635009	+	1.09710i
$237$		0			0
$238$	−1.11895	−	4.16688i	−0.0725307	−	0.270099i
$239$			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	−0.471945	−	0.881628i	$-0.656448\pi$
$241$	0.863050	−	0.498282i	0.0555939	−	0.0320972i	0.527539	+	0.849531i	$0.323115\pi$
$242$	5.04528	−	18.8704i	0.324323	−	1.21304i
$243$		0			0
$244$	−5.69356	+	3.29547i	−0.364493	+	0.210971i
$245$	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
$250$	−19.0659	−	19.0451i	−1.20583	−	1.20452i
$251$	−1.97988	−	3.42926i	−0.124969	−	0.216453i	0.796752	−	0.604307i	$-0.206550\pi$
$251$	−1.97988	−	3.42926i	−0.124969	−	0.216453i	−0.921721	+	0.387854i	$0.873217\pi$
$252$		0			0
$253$	27.1958	−	15.7015i	1.70978	−	0.987144i
$254$	3.38324	+	12.5989i	0.212284	+	0.790528i
$255$		0			0
$256$	15.9998	−	0.0698329i	0.999990	−	0.00436456i
$257$	24.3137	+	14.0375i	1.51664	+	0.875635i	0.999809	+	0.0195508i	$0.00622361\pi$
$257$	24.3137	+	14.0375i	1.51664	+	0.875635i	0.516836	+	0.856084i	$0.327110\pi$
$258$		0			0
$259$			3.63905i			0.226119i
$260$	12.9132	−	24.6918i	0.800841	−	1.53132i
$261$		0			0
$262$	11.1786	+	11.1664i	0.690616	+	0.689863i
$263$	10.8980	−	18.8758i	0.671997	−	1.16393i	−0.305339	−	0.952244i	$-0.598770\pi$
$263$	10.8980	−	18.8758i	0.671997	−	1.16393i	0.977337	−	0.211690i	$-0.0678968\pi$
$264$		0			0
$265$			20.8340i			1.27982i
$266$	−9.58050	+	2.57269i	−0.587418	+	0.157742i
$267$		0			0
$268$	−5.13590	−	2.95775i	−0.313725	−	0.180673i
$269$	8.35430	−	4.82336i	0.509371	−	0.294085i	−0.223204	−	0.974772i	$-0.571652\pi$
$269$	8.35430	−	4.82336i	0.509371	−	0.294085i	0.732575	+	0.680686i	$0.238318\pi$
$270$		0			0
$271$	−5.52677	+	9.57264i	−0.335727	+	0.581497i	−0.983624	−	0.180231i	$-0.942315\pi$
$271$	−5.52677	+	9.57264i	−0.335727	+	0.581497i	0.647897	+	0.761728i	$0.275649\pi$
$272$	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	0.948335	−	0.317271i	$-0.102767\pi$
$277$	3.31872	+	5.74819i	0.199402	+	0.345375i	−0.748932	+	0.662646i	$0.769433\pi$
$278$	4.68562	+	1.25277i	0.281025	+	0.0751361i
$279$		0			0
$280$	−9.51513	−	2.53289i	−0.568637	−	0.151369i
$281$	−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	$-0.0475578\pi$
$283$	22.7842	+	13.1545i	1.35438	+	0.781951i	0.365520	+	0.930803i	$0.380891\pi$
$284$	−9.88954	−	17.0861i	−0.586836	−	1.01387i
$285$		0			0
$286$	−5.55782	+	24.7836i	−0.328641	+	1.46548i
$287$	−4.08683			−0.241238
$288$		0			0
$289$	−2.76636	+	4.79148i	−0.162727	+	0.281852i
$290$	−2.95988	−	11.0224i	−0.173810	−	0.647256i
$291$		0			0
$292$	4.75976	−	0.00519358i	0.278544	−	0.000303931i
$293$	−10.2477	−	17.7496i	−0.598678	−	1.03694i	−0.993017	−	0.117975i	$-0.962360\pi$
$293$	−10.2477	−	17.7496i	−0.598678	−	1.03694i	0.394339	−	0.918965i	$-0.370974\pi$
$294$		0			0
$295$	32.5834	−	18.8120i	1.89708	−	1.09528i
$296$	−11.0306	+	2.97500i	−0.641141	+	0.172918i
$297$		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
$302$	16.7725	+	16.7543i	0.965152	+	0.964099i
$303$		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	$-0.901202\pi$
$307$	−33.3684			−1.90443			−0.952217	+	0.305423i	$0.901202\pi$
$308$	8.97526	−	0.00979329i	0.511413	−	0.000558025i
$309$		0			0
$310$	15.5567	+	15.5398i	0.883564	+	0.882600i
$311$	10.5603			0.598819			0.299409	−	0.954125i	$-0.403210\pi$
$311$	10.5603			0.598819			0.299409	+	0.954125i	$0.403210\pi$
$312$		0			0
$313$	11.0233			0.623071			0.311536	−	0.950234i	$-0.399157\pi$
$313$	11.0233			0.623071			0.311536	+	0.950234i	$0.399157\pi$
$314$	1.13971	+	1.13847i	0.0643178	+	0.0642477i
$315$		0			0
$316$	7.36739	−	0.00803888i	0.414448	−	0.000452222i
$317$	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
$322$	5.68279	+	5.67660i	0.316690	+	0.316344i
$323$	−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
$328$	−3.34108	−	12.3879i	−0.184480	−	0.684009i
$329$	−7.70145	+	4.44644i	−0.424595	+	0.245140i
$330$		0			0
$331$	−4.06094	−	7.03376i	−0.223210	−	0.386610i	0.732571	−	0.680690i	$-0.238320\pi$
$331$	−4.06094	−	7.03376i	−0.223210	−	0.386610i	−0.955781	+	0.294080i	$0.904987\pi$
$332$	−3.51564	+	0.00383606i	−0.192946	+	0.000210531i
$333$		0			0
$334$	0.904859	+	3.36963i	0.0495117	+	0.184378i
$335$	−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	$0.569325\pi$
$338$	3.29060	−	18.0879i	0.178985	−	0.983852i
$339$		0			0
$340$	−13.1099	−	22.6499i	−0.710985	−	1.22837i
$341$	−17.3578	−	10.0215i	−0.939976	−	0.542696i
$342$		0			0
$343$	−11.8816			−0.641548
$344$	−3.10029	+	11.6467i	−0.167156	+	0.627945i
$345$		0			0
$346$	−24.2646	−	6.48748i	−1.30447	−	0.348769i
$347$	2.57523	+	4.46043i	0.138245	+	0.239448i	0.926833	−	0.375475i	$-0.122520\pi$
$347$	2.57523	+	4.46043i	0.138245	+	0.239448i	−0.788587	+	0.614923i	$0.789187\pi$
$348$		0			0
$349$	15.5889	+	9.00027i	0.834456	+	0.481774i	0.855376	−	0.518008i	$-0.173326\pi$
$349$	15.5889	+	9.00027i	0.834456	+	0.481774i	−0.0209196	+	0.999781i	$0.506659\pi$
$350$	−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	−0.998226	−	0.0595425i	$-0.981036\pi$
$353$	−8.40866	+	14.5642i	−0.447548	+	0.775175i	0.550678	+	0.834718i	$0.314369\pi$
$354$		0			0
$355$	−33.0322	+	19.0711i	−1.75317	+	1.01219i
$356$	3.40536	+	1.96113i	0.180484	+	0.103940i
$357$		0			0
$358$	−25.9282	+	6.96262i	−1.37035	+	0.367986i
$359$			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
$362$	22.9087	+	22.8838i	1.20406	+	1.20274i
$363$		0			0
$364$	−6.49096	+	0.271094i	−0.340219	+	0.0142092i
$365$		−	9.19614i		−	0.481348i
$366$		0			0
$367$	14.1130	+	8.14816i	0.736694	+	0.425330i	0.820866	−	0.571121i	$-0.193491\pi$
$367$	14.1130	+	8.14816i	0.736694	+	0.425330i	−0.0841721	+	0.996451i	$0.526825\pi$
$368$	−12.5610	+	21.8663i	−0.654786	+	1.13986i
$369$		0			0
$370$	5.72462	+	21.3180i	0.297609	+	1.10827i
$371$	4.20667	−	2.42872i	0.218399	−	0.126093i
$372$		0			0
$373$	1.46760	+	2.54195i	0.0759892	+	0.131617i	0.901516	−	0.432746i	$-0.142455\pi$
$373$	1.46760	+	2.54195i	0.0759892	+	0.131617i	−0.825527	+	0.564363i	$0.809122\pi$
$374$	16.8771	+	16.8587i	0.872695	+	0.871744i
$375$		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	0.325805	+	0.945437i	$0.394365\pi$
$379$	−12.7684	+	22.1156i	−0.655870	+	1.13600i	−0.981675	+	0.190563i	$0.938969\pi$
$380$	−52.0768	+	30.1424i	−2.67148	+	1.54627i
$381$		0			0
$382$	−2.46890	+	9.23421i	−0.126320	+	0.472463i
$383$	1.91909	−	1.10799i	0.0980607	−	0.0566154i	−0.450168	−	0.892944i	$-0.648636\pi$
$383$	1.91909	−	1.10799i	0.0980607	−	0.0566154i	0.548228	+	0.836329i	$0.315302\pi$
$384$		0			0
$385$		−	17.3407i		−	0.883766i
$386$	8.35850	+	31.1264i	0.425437	+	1.58429i
$387$		0			0
$388$	−8.63696	−	14.9220i	−0.438475	−	0.757551i
$389$		−	12.9878i		−	0.658505i	−0.944242	−	0.329253i	$-0.893203\pi$
$389$		−	12.9878i		−	0.658505i	0.944242	−	0.329253i	$-0.106797\pi$
$390$		0			0
$391$			21.3486i			1.07965i
$392$	−4.55785	−	16.8994i	−0.230206	−	0.853550i
$393$		0			0
$394$	32.7047	−	8.78232i	1.64764	−	0.442447i
$395$		−	14.2342i		−	0.716202i
$396$		0			0
$397$	17.1162	−	9.88206i	0.859039	−	0.495966i	−0.00465142	−	0.999989i	$-0.501481\pi$
$397$	17.1162	−	9.88206i	0.859039	−	0.495966i	0.863690	+	0.504023i	$0.168147\pi$
$398$	3.75073	+	1.00281i	0.188007	+	0.0502664i
$399$		0			0
$400$	−39.7255	+	0.0866925i	−1.98627	+	0.00433463i
$401$	−8.68520	+	15.0432i	−0.433718	+	0.751222i	−0.997190	−	0.0749133i	$-0.976132\pi$
$401$	−8.68520	+	15.0432i	−0.433718	+	0.751222i	0.563472	+	0.826135i	$0.309465\pi$
$402$		0			0
$403$	12.8486	+	6.73735i	0.640034	+	0.335612i
$404$	3.94695	−	6.85357i	0.196368	−	0.340978i
$405$		0			0
$406$	−1.88052	+	1.88257i	−0.0933287	+	0.0934305i
$407$	−10.0601	−	17.4247i	−0.498662	−	0.863708i
$408$		0			0
$409$	−21.8306	+	12.6039i	−1.07945	+	0.623223i	−0.930749	−	0.365659i	$-0.880844\pi$
$409$	−21.8306	+	12.6039i	−1.07945	+	0.623223i	−0.148705	+	0.988882i	$0.547510\pi$
$410$	−23.9412	+	6.42903i	−1.18237	+	0.317507i
$411$		0			0
$412$	−11.1057	+	0.0121180i	−0.547141	+	0.000597009i
$413$	−7.59683	−	4.38603i	−0.373815	−	0.215822i
$414$		0			0
$415$			6.79242i			0.333427i
$416$	−6.12824	−	19.4537i	−0.300462	−	0.953794i
$417$		0			0
$418$	38.7616	−	38.8039i	1.89589	−	1.89796i
$419$	18.3660	−	31.8108i	0.897237	−	1.55406i	0.0662264	−	0.997805i	$-0.478904\pi$
$419$	18.3660	−	31.8108i	0.897237	−	1.55406i	0.831011	−	0.556256i	$-0.187763\pi$
$420$		0			0
$421$		−	10.7389i		−	0.523384i	−0.965151	−	0.261692i	$-0.915720\pi$
$421$		−	10.7389i		−	0.523384i	0.965151	−	0.261692i	$-0.0842805\pi$
$422$	−4.79643	−	17.8615i	−0.233487	−	0.869487i
$423$		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	$-0.276713\pi$
$431$	6.36251	+	3.67340i	0.306471	+	0.176941i	−0.338875	+	0.940831i	$0.610046\pi$
$432$		0			0
$433$	10.3474	+	17.9222i	0.497265	+	0.861287i	0.999995	−	0.00315579i	$-0.00100452\pi$
$433$	10.3474	+	17.9222i	0.497265	+	0.861287i	−0.502731	+	0.864443i	$0.667671\pi$
$434$	1.32417	−	4.95267i	0.0635622	−	0.237736i
$435$		0			0
$436$	−1.01756	+	0.00111030i	−0.0487321	+	5.31737e-5i
$437$	49.0847			2.34804
$438$		0			0
$439$	−1.82985	−	1.05646i	−0.0873339	−	0.0504223i	0.455697	−	0.890135i	$-0.349390\pi$
$439$	−1.82985	−	1.05646i	−0.0873339	−	0.0504223i	−0.543031	+	0.839713i	$0.682723\pi$
$440$	52.5629	−	14.1764i	2.50584	−	0.675835i
$441$		0			0
$442$	−12.7021	−	11.6964i	−0.604177	−	0.556342i
$443$	27.2205			1.29329			0.646644	−	0.762792i	$-0.276172\pi$
$443$	27.2205			1.29329			0.646644	+	0.762792i	$0.276172\pi$
$444$		0			0
$445$	3.79620	−	6.57521i	0.179957	−	0.311695i
$446$	2.04535	−	0.549247i	0.0968504	−	0.0260076i
$447$		0			0
$448$	−6.22992	+	3.62409i	−0.294336	+	0.171222i
$449$	−13.9938	−	24.2381i	−0.660411	−	1.14386i	−0.980508	−	0.196480i	$-0.937049\pi$
$449$	−13.9938	−	24.2381i	−0.660411	−	1.14386i	0.320097	−	0.947385i	$-0.396284\pi$
$450$		0			0
$451$	19.5688	−	11.2980i	0.921456	−	0.532003i
$452$	−10.5673	−	18.2571i	−0.497046	−	0.858743i
$453$		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	0.944235	−	0.329272i	$-0.106803\pi$
$457$	24.1822	+	13.9616i	1.13120	+	0.653096i	0.186960	+	0.982368i	$0.440137\pi$
$458$	−20.7589	+	20.7816i	−0.970001	+	0.971060i
$459$		0			0
$460$	42.2205	+	24.3146i	1.96854	+	1.13368i
$461$	−15.7424	−	27.2667i	−0.733197	−	1.26994i	−0.955510	−	0.294960i	$-0.904694\pi$
$461$	−15.7424	−	27.2667i	−0.733197	−	1.26994i	0.222312	−	0.974975i	$-0.428640\pi$
$462$		0			0
$463$	35.7895			1.66328			0.831639	−	0.555316i	$-0.187403\pi$
$463$	35.7895			1.66328			0.831639	+	0.555316i	$0.187403\pi$
$464$	−7.24379	−	4.16115i	−0.336284	−	0.193177i
$465$		0			0
$466$	−3.55997	+	3.56386i	−0.164913	+	0.165093i
$467$	−7.80035			−0.360957			−0.180479	−	0.983579i	$-0.557765\pi$
$467$	−7.80035			−0.360957			−0.180479	+	0.983579i	$0.557765\pi$
$468$		0			0
$469$	2.66974			0.123277
$470$	−38.1215	+	38.1631i	−1.75841	+	1.76033i
$471$		0			0
$472$	7.08428	−	26.6130i	0.326080	−	1.22496i
$473$	−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
$478$	14.2368	−	14.2524i	0.651178	−	0.651889i
$479$	−18.9832	−	10.9600i	−0.867366	−	0.500774i	−0.000893831	−	1.00000i	$-0.500285\pi$
$479$	−18.9832	−	10.9600i	−0.867366	−	0.500774i	−0.866472	+	0.499226i	$0.833618\pi$
$480$		0			0
$481$	7.78842	+	12.3062i	0.355121	+	0.561117i
$482$	−1.36153	−	0.364025i	−0.0620160	−	0.0165809i
$483$		0			0
$484$	−23.9081	+	13.8382i	−1.08673	+	0.629008i
$485$	−28.8484	+	16.6556i	−1.30994	+	0.756294i
$486$		0			0
$487$	−16.7338	−	28.9838i	−0.758280	−	1.31338i	−0.943727	−	0.330725i	$-0.892707\pi$
$487$	−16.7338	−	28.9838i	−0.758280	−	1.31338i	0.185447	−	0.982654i	$-0.440627\pi$
$488$	8.99033	+	2.39319i	0.406973	+	0.108335i
$489$		0			0
$490$	−32.6603	+	8.77040i	−1.47544	+	0.396206i
$491$	−9.97889	+	17.2839i	−0.450341	+	0.780014i	−0.998407	−	0.0564215i	$-0.982031\pi$
$491$	−9.97889	+	17.2839i	−0.450341	+	0.780014i	0.548066	+	0.836435i	$0.315364\pi$
$492$		0			0
$493$	−7.07228			−0.318520
$494$	−26.8924	+	29.2047i	−1.20995	+	1.31398i
$495$		0			0
$496$	16.0950	−	0.0351239i	0.722686	−	0.00157711i
$497$	7.70145	+	4.44644i	0.345457	+	0.199450i
$498$		0			0
$499$	17.3589			0.777092			0.388546	−	0.921429i	$-0.372978\pi$
$499$	17.3589			0.777092			0.388546	+	0.921429i	$0.372978\pi$
$500$	0.0415845	+	38.1109i	0.00185972	+	1.70437i
$501$		0			0
$502$	−1.44642	+	5.40993i	−0.0645571	+	0.241457i
$503$	7.31587	+	12.6715i	0.326198	+	0.564992i	0.981754	−	0.190155i	$-0.0608989\pi$
$503$	7.31587	+	12.6715i	0.326198	+	0.564992i	−0.655556	+	0.755147i	$0.727566\pi$
$504$		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	−0.333240	−	0.942842i	$-0.608142\pi$
$509$	14.6625	−	25.3962i	0.649905	−	1.12567i	0.983145	−	0.182826i	$-0.0585246\pi$
$510$		0			0
$511$	−1.85683	+	1.07204i	−0.0821413	+	0.0474243i
$512$	−16.0784	−	15.9212i	−0.710570	−	0.703626i
$513$		0			0
$514$	−10.2971	−	38.3456i	−0.454185	−	1.69135i
$515$			21.4570i			0.945506i
$516$		0			0
$517$	24.5843	−	42.5813i	1.08122	−	1.87272i
$518$	3.63706	−	3.64103i	0.159803	−	0.159978i
$519$		0			0
$520$	−37.5985	+	11.7991i	−1.64880	+	0.517425i
$521$		−	28.2001i		−	1.23547i	−0.786386	−	0.617735i	$-0.788051\pi$
$521$		−	28.2001i		−	1.23547i	0.786386	−	0.617735i	$-0.211949\pi$
$522$		0			0
$523$	27.7553	+	16.0245i	1.21365	+	0.700704i	0.963553	−	0.267516i	$-0.0862028\pi$
$523$	27.7553	+	16.0245i	1.21365	+	0.700704i	0.250101	+	0.968220i	$0.419536\pi$
$524$	−0.0243816	−	22.3450i	−0.00106511	−	0.976146i
$525$		0			0
$526$	−29.7694	+	7.99411i	−1.29801	+	0.348560i
$527$	11.8003	−	6.81290i	0.514029	−	0.296775i
$528$		0			0
$529$	−8.37232	−	14.5013i	−0.364014	−	0.630491i
$530$	20.8226	−	20.8453i	0.904477	−	0.905464i
$531$		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
$536$	2.18257	+	8.09246i	0.0942727	+	0.349541i
$537$		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	$0.286139\pi$
$541$			36.4085i			1.56532i	−0.622447	+	0.782662i	$0.713861\pi$
$542$	15.0972	−	4.05411i	0.648480	−	0.174139i
$543$		0			0
$544$	−18.5167	−	4.90745i	−0.793899	−	0.210405i
$545$			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	$-0.225253\pi$
$548$	0.159480	−	0.0923079i	0.00681264	−	0.00394320i
$549$		0			0
$550$	−18.1441	−	67.5674i	−0.773669	−	2.88108i
$551$			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
$556$	−3.43609	−	5.93652i	−0.145723	−	0.251765i
$557$	−4.57967	+	7.93223i	−0.194047	+	0.336099i	−0.946588	−	0.322447i	$-0.895495\pi$
$557$	−4.57967	+	7.93223i	−0.194047	+	0.336099i	0.752541	+	0.658546i	$0.228828\pi$
$558$		0			0
$559$	15.3509	−	0.624351i	0.649276	−	0.0264072i
$560$	6.98881	+	12.0442i	0.295331	+	0.508960i
$561$		0			0
$562$	15.1980	+	15.1815i	0.641091	+	0.640392i
$563$	14.1667	+	24.5374i	0.597053	+	1.03413i	0.993254	+	0.115962i	$0.0369952\pi$
$563$	14.1667	+	24.5374i	0.597053	+	1.03413i	−0.396200	+	0.918164i	$0.629671\pi$
$564$		0			0
$565$	−35.2961	+	20.3782i	−1.48492	+	0.857317i
$566$	−9.64934	−	35.9334i	−0.405592	−	1.51039i
$567$		0			0
$568$	−7.18185	+	26.9796i	−0.301344	+	1.13204i
$569$	−10.5468	−	6.08920i	−0.442145	−	0.255272i	0.262362	−	0.964969i	$-0.415499\pi$
$569$	−10.5468	−	6.08920i	−0.442145	−	0.255272i	−0.704507	+	0.709697i	$0.748832\pi$
$570$		0			0
$571$		−	42.7464i		−	1.78888i	−0.447185	−	0.894441i	$-0.647574\pi$
$571$		−	42.7464i		−	1.78888i	0.447185	−	0.894441i	$-0.352426\pi$
$572$	30.3309	−	19.2423i	1.26820	−	0.804561i
$573$		0			0
$574$	4.08906	+	4.08460i	0.170674	+	0.170488i
$575$	31.3054	−	54.2226i	1.30553	−	2.26124i
$576$		0			0
$577$		−	41.1803i		−	1.71436i	−0.515019	−	0.857179i	$-0.672215\pi$
$577$		−	41.1803i		−	1.71436i	0.515019	−	0.857179i	$-0.327785\pi$
$578$	7.55674	−	2.02924i	0.314319	−	0.0844053i
$579$		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	$-0.388248\pi$
$587$	−7.20380	−	4.15912i	−0.297333	−	0.171665i	−0.641244	+	0.767337i	$0.721581\pi$
$588$		0			0
$589$	−15.6642	−	27.1312i	−0.645433	−	1.11792i
$590$	−51.4030	−	13.7433i	−2.11623	−	0.565804i
$591$		0			0
$592$	14.0100	+	8.04797i	0.575808	+	0.330769i
$593$	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
$596$	6.31805	−	3.65692i	0.258797	−	0.149793i
$597$		0			0
$598$	31.3669	+	7.03415i	1.28269	+	0.287648i
$599$	27.0648			1.10584			0.552919	−	0.833235i	$-0.313514\pi$
$599$	27.0648			1.10584			0.552919	+	0.833235i	$0.313514\pi$
$600$		0			0
$601$	9.98919	−	17.3018i	0.407468	−	0.705755i	−0.587137	−	0.809487i	$-0.699745\pi$
$601$	9.98919	−	17.3018i	0.407468	−	0.705755i	0.994605	+	0.103732i	$0.0330785\pi$
$602$	−1.40800	−	5.24328i	−0.0573858	−	0.213700i
$603$		0			0
$604$	−0.0365825	−	33.5268i	−0.00148852	−	1.36419i
$605$	26.6857	+	46.2211i	1.08493	+	1.87915i
$606$		0			0
$607$	−5.41050	+	3.12375i	−0.219605	+	0.126789i	−0.605767	−	0.795642i	$-0.707134\pi$
$607$	−5.41050	+	3.12375i	−0.219605	+	0.126789i	0.386162	+	0.922431i	$0.373800\pi$
$608$	−11.2832	+	42.5737i	−0.457595	+	1.72659i
$609$		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	0.293247	−	0.956037i	$-0.405264\pi$
$613$	−9.60845	−	5.54744i	−0.388081	−	0.224059i	−0.681329	+	0.731978i	$0.738597\pi$
$614$	33.3866	+	33.3502i	1.34737	+	1.34590i
$615$		0			0
$616$	−8.98994	−	8.96056i	−0.362215	−	0.361031i
$617$	10.1490	+	17.5787i	0.408585	+	0.707691i	0.994731	−	0.102515i	$-0.0326889\pi$
$617$	10.1490	+	17.5787i	0.408585	+	0.707691i	−0.586146	+	0.810205i	$0.699356\pi$
$618$		0			0
$619$	−15.4853			−0.622407			−0.311203	−	0.950343i	$-0.600732\pi$
$619$	−15.4853			−0.622407			−0.311203	+	0.950343i	$0.600732\pi$
$620$	−0.0339308	−	31.0965i	−0.00136269	−	1.24887i
$621$		0			0
$622$	−10.5660	−	10.5545i	−0.423660	−	0.423198i
$623$	−1.77017			−0.0709203
$624$		0			0
$625$	23.9756			0.959025
$626$	−11.0293	−	11.0172i	−0.440818	−	0.440337i
$627$		0			0
$628$	−0.00248583	−	2.27819i	−9.91953e−5	−	0.0909095i
$629$	13.6783			0.545389
$630$		0			0
$631$	19.7995	+	34.2937i	0.788206	+	1.36521i	0.927065	+	0.374900i	$0.122323\pi$
$631$	19.7995	+	34.2937i	0.788206	+	1.36521i	−0.138859	+	0.990312i	$0.544344\pi$
$632$	−7.37944	−	7.35533i	−0.293539	−	0.292579i
$633$		0			0
$634$	−29.0643	−	29.0326i	−1.15429	−	1.15303i
$635$	−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
$640$	−30.7946	+	31.0308i	−1.21727	+	1.22660i
$641$	15.2012	−	8.77639i	0.600410	−	0.346647i	−0.168793	−	0.985652i	$-0.553987\pi$
$641$	15.2012	−	8.77639i	0.600410	−	0.346647i	0.769203	+	0.639005i	$0.220654\pi$
$642$		0			0
$643$	−9.25566	−	16.0313i	−0.365008	−	0.632212i	0.623770	−	0.781608i	$-0.285600\pi$
$643$	−9.25566	−	16.0313i	−0.365008	−	0.632212i	−0.988777	+	0.149396i	$0.952267\pi$
$644$	−0.0123947	−	11.3594i	−0.000488420	−	0.447622i
$645$		0			0
$646$	9.67012	+	36.0108i	0.380466	+	1.41683i
$647$	6.06305	−	10.5015i	0.238363	−	0.412857i	−0.721882	−	0.692016i	$-0.756723\pi$
$647$	6.06305	−	10.5015i	0.238363	−	0.412857i	0.960245	+	0.279160i	$0.0900559\pi$
$648$		0			0
$649$	48.5006			1.90382
$650$	15.1101	+	48.3336i	0.592665	+	1.89580i
$651$		0			0
$652$	8.34759	−	4.83163i	0.326917	−	0.189221i
$653$	5.26965	+	3.04243i	0.206217	+	0.119060i	0.599552	−	0.800336i	$-0.295345\pi$
$653$	5.26965	+	3.04243i	0.206217	+	0.119060i	−0.393335	+	0.919395i	$0.628679\pi$
$654$		0			0
$655$	−43.1719			−1.68686
$656$	−9.03827	+	15.7339i	−0.352885	+	0.614307i
$657$		0			0
$658$	12.1497	+	3.24839i	0.473643	+	0.126635i
$659$	−12.5803	−	21.7898i	−0.490060	−	0.848809i	0.509874	−	0.860249i	$-0.329692\pi$
$659$	−12.5803	−	21.7898i	−0.490060	−	0.848809i	−0.999935	+	0.0114396i	$0.996359\pi$
$660$		0			0
$661$	39.1674	+	22.6133i	1.52344	+	0.879556i	0.999616	+	0.0277278i	$0.00882715\pi$
$661$	39.1674	+	22.6133i	1.52344	+	0.879556i	0.523821	+	0.851829i	$0.324506\pi$
$662$	−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
$670$	15.6397	−	4.19979i	0.604214	−	0.162252i
$671$			16.3843i			0.632510i
$672$		0			0
$673$	−6.02206	+	10.4305i	−0.232133	+	0.402067i	−0.958436	−	0.285309i	$-0.907904\pi$
$673$	−6.02206	+	10.4305i	−0.232133	+	0.402067i	0.726302	+	0.687375i	$0.241237\pi$
$674$	7.93744	+	7.92878i	0.305739	+	0.305405i
$675$		0			0
$676$	−21.3704	+	14.8090i	−0.821939	+	0.569575i
$677$		−	1.50657i		−	0.0579022i	−0.999581	−	0.0289511i	$-0.990783\pi$
$677$		−	1.50657i		−	0.0579022i	0.999581	−	0.0289511i	$-0.00921671\pi$
$678$		0			0
$679$	6.72601	+	3.88326i	0.258121	+	0.149026i
$680$	−9.52051	+	35.7651i	−0.365095	+	1.37153i
$681$		0			0
$682$	7.35119	+	27.3753i	0.281492	+	1.04825i
$683$	13.3271	−	7.69440i	0.509947	−	0.294418i	−0.222865	−	0.974849i	$-0.571541\pi$
$683$	13.3271	−	7.69440i	0.509947	−	0.294418i	0.732812	+	0.680431i	$0.238208\pi$
$684$		0			0
$685$	−0.178008	−	0.308319i	−0.00680133	−	0.0117803i
$686$	11.8881	+	11.8751i	0.453890	+	0.453395i
$687$		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	0.454263	+	0.890867i	$0.349903\pi$
$691$	−14.3101	+	24.7858i	−0.544382	+	0.942898i	−0.998646	+	0.0520302i	$0.983431\pi$
$692$	17.7939	+	30.7423i	0.676421	+	1.16865i
$693$		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
$698$	−6.60207	−	24.5856i	−0.249892	−	0.930579i
$699$		0			0
$700$	15.4875	−	8.96429i	0.585374	−	0.338818i
$701$			41.2699i			1.55874i	0.626563	+	0.779371i	$0.284461\pi$
$701$			41.2699i			1.55874i	−0.626563	+	0.779371i	$0.715539\pi$
$702$		0			0
$703$		−	31.4492i		−	1.18613i
$704$	19.8116	−	34.5756i	0.746678	−	1.30312i
$705$		0			0
$706$	22.9695	−	6.16810i	0.864469	−	0.232139i
$707$			3.56261i			0.133986i
$708$		0			0
$709$	−14.6578	+	8.46268i	−0.550485	+	0.317823i	−0.749318	−	0.662211i	$-0.769618\pi$
$709$	−14.6578	+	8.46268i	−0.550485	+	0.317823i	0.198832	+	0.980033i	$0.436285\pi$
$710$	52.1109	+	13.9326i	1.95569	+	0.522882i
$711$		0			0
$712$	−1.44715	−	5.36570i	−0.0542343	−	0.201088i
$713$	−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
$718$	3.83055	−	3.83474i	0.142955	−	0.143111i
$719$	−1.35328	−	2.34395i	−0.0504689	−	0.0874147i	0.839687	−	0.543070i	$-0.182738\pi$
$719$	−1.35328	−	2.34395i	−0.0504689	−	0.0874147i	−0.890156	+	0.455655i	$0.849405\pi$
$720$		0			0
$721$	4.33246	−	2.50135i	0.161349	−	0.0931550i
$722$	56.8454	−	15.2649i	2.11557	−	0.568101i
$723$		0			0
$724$	−0.0499662	−	45.7925i	−0.00185698	−	1.70186i
$725$	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	$-0.345691\pi$
$728$	6.76545	+	6.21618i	0.250744	+	0.230387i
$729$		0			0
$730$	−9.19112	+	9.20116i	−0.340179	+	0.340550i
$731$	7.21477	−	12.4964i	0.266848	−	0.462194i
$732$		0			0
$733$		−	12.8449i		−	0.474436i	−0.971456	−	0.237218i	$-0.923764\pi$
$733$		−	12.8449i		−	0.474436i	0.971456	−	0.237218i	$-0.0762356\pi$
$734$	−5.97701	−	22.2579i	−0.220615	−	0.821555i
$735$		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	0.271663	+	0.962393i	$0.412426\pi$
$739$	−18.9646	+	32.8477i	−0.697625	+	1.20832i	−0.969288	+	0.245929i	$0.920907\pi$
$740$	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	$-0.347847\pi$
$743$	−2.15190	−	1.24240i	−0.0789455	−	0.0455792i	−0.538953	+	0.842336i	$0.681180\pi$
$744$		0			0
$745$	−7.05207	−	12.2145i	−0.258368	−	0.447506i
$746$	1.07217	−	4.01013i	0.0392548	−	0.146821i
$747$		0			0
$748$	−0.0368106	−	33.7358i	−0.00134593	−	1.23350i
$749$	10.6046			0.387482
$750$		0			0
$751$	−7.71464	−	4.45405i	−0.281511	−	0.162531i	0.352596	−	0.935776i	$-0.385299\pi$
$751$	−7.71464	−	4.45405i	−0.281511	−	0.162531i	−0.634107	+	0.773245i	$0.718632\pi$
$752$	0.0861643	+	39.4835i	0.00314209	+	1.43981i
$753$		0			0
$754$	−2.33025	+	10.3911i	−0.0848626	+	0.378421i
$755$	−64.7758			−2.35743
$756$		0			0
$757$	−20.0254	+	34.6850i	−0.727835	+	1.26065i	0.229962	+	0.973200i	$0.426140\pi$
$757$	−20.0254	+	34.6850i	−0.727835	+	1.26065i	−0.957796	+	0.287447i	$0.907193\pi$
$758$	34.8789	−	9.36617i	1.26686	−	0.340195i
$759$		0			0
$760$	82.2311	+	21.8896i	2.98283	+	0.794018i
$761$	−17.8174	−	30.8606i	−0.645879	−	1.11869i	−0.984098	−	0.177627i	$-0.943158\pi$
$761$	−17.8174	−	30.8606i	−0.645879	−	1.11869i	0.338219	−	0.941067i	$-0.390176\pi$
$762$		0			0
$763$	0.396959	−	0.229184i	0.0143709	−	0.00829702i
$764$	11.6994	−	6.77169i	0.423270	−	0.244991i
$765$		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	0.944822	+	0.327584i	$0.106235\pi$
$769$	47.1682	+	27.2326i	1.70093	+	0.982032i	0.756107	+	0.654448i	$0.227099\pi$
$770$	−17.3313	+	17.3502i	−0.624576	+	0.625258i
$771$		0			0
$772$	22.7464	−	39.4973i	0.818660	−	1.42154i
$773$	−6.47414	−	11.2135i	−0.232859	−	0.403323i	0.725789	−	0.687917i	$-0.241475\pi$
$773$	−6.47414	−	11.2135i	−0.232859	−	0.403323i	−0.958648	+	0.284594i	$0.908141\pi$
$774$		0			0
$775$	−39.9615			−1.43546
$776$	−6.27221	+	23.5624i	−0.225159	+	0.845841i
$777$		0			0
$778$	−12.9807	+	12.9948i	−0.465379	+	0.465887i
$779$	35.3190			1.26543
$780$		0			0
$781$	−49.1686			−1.75939
$782$	21.3370	−	21.3602i	0.763008	−	0.763841i
$783$		0			0
$784$	−12.3299	+	21.4640i	−0.440353	+	0.766572i
$785$	−4.40159			−0.157099
$786$		0			0
$787$	−20.9524	−	36.2906i	−0.746872	−	1.29362i	−0.949315	−	0.314326i	$-0.898221\pi$
$787$	−20.9524	−	36.2906i	−0.746872	−	1.29362i	0.202443	−	0.979294i	$-0.435112\pi$
$788$	−41.5000	−	23.8997i	−1.47838	−	0.851392i
$789$		0			0
$790$	−14.2265	+	14.2420i	−0.506155	+	0.506708i
$791$	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
$796$	−2.75051	−	4.75204i	−0.0974892	−	0.168432i
$797$	−30.5379	+	17.6311i	−1.08171	+	0.624524i	−0.931356	−	0.364109i	$-0.881374\pi$
$797$	−30.5379	+	17.6311i	−1.08171	+	0.624524i	−0.150351	+	0.988633i	$0.548040\pi$
$798$		0			0
$799$	16.7131	+	28.9479i	0.591266	+	1.02410i
$800$	39.8338	+	39.6171i	1.40834	+	1.40067i
$801$		0			0
$802$	23.7249	−	6.37095i	0.837757	−	0.224966i
$803$	5.92730	−	10.2664i	0.209170	−	0.362293i
$804$		0			0
$805$	−21.9470			−0.773530
$806$	−6.12192	−	19.5826i	−0.215635	−	0.689768i
$807$		0			0
$808$	−10.7989	+	2.91252i	−0.379905	+	0.102462i
$809$	17.9997	+	10.3922i	0.632837	+	0.365369i	0.781850	−	0.623466i	$-0.214276\pi$
$809$	17.9997	+	10.3922i	0.632837	+	0.365369i	−0.149013	+	0.988835i	$0.547610\pi$
$810$		0			0
$811$	30.1143			1.05746			0.528728	−	0.848792i	$-0.322669\pi$
$811$	30.1143			1.05746			0.528728	+	0.848792i	$0.322669\pi$
$812$	3.76309	−	0.00410607i	0.132059	−	0.000144095i
$813$		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	−0.688237	−	0.725486i	$-0.741615\pi$
$821$	8.14237	−	14.1030i	0.284171	−	0.492198i	0.972408	+	0.233288i	$0.0749485\pi$
$822$		0			0
$823$	−18.6155	+	10.7477i	−0.648895	+	0.374640i	−0.788033	−	0.615633i	$-0.788900\pi$
$823$	−18.6155	+	10.7477i	−0.648895	+	0.374640i	0.139138	+	0.990273i	$0.455567\pi$
$824$	11.1239	+	11.0876i	0.387520	+	0.386253i
$825$		0			0
$826$	3.21733	+	11.9811i	0.111945	+	0.416876i
$827$			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	−0.356159	−	0.934425i	$-0.615914\pi$
$829$	18.1725	−	31.4757i	0.631156	−	1.09320i	0.987316	−	0.158770i	$-0.0507528\pi$
$830$	6.78871	−	6.79612i	0.235640	−	0.235897i
$831$		0			0
$832$	−13.3115	+	25.5892i	−0.461492	+	0.887145i
$833$			20.9558i			0.726076i
$834$		0			0
$835$	−8.25596	−	4.76658i	−0.285709	−	0.164954i
$836$	−77.5655	+	0.0846351i	−2.68266	+	0.00292716i
$837$		0			0
$838$	−50.1695	+	13.4722i	−1.73308	+	0.465390i
$839$	19.2667	−	11.1237i	0.665162	−	0.384031i	−0.129079	−	0.991634i	$-0.541202\pi$
$839$	19.2667	−	11.1237i	0.665162	−	0.384031i	0.794241	+	0.607603i	$0.207869\pi$
$840$		0			0
$841$	−12.3191	−	21.3374i	−0.424798	−	0.735771i
$842$	−10.7331	+	10.7448i	−0.369886	+	0.370290i
$843$		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
$848$	−0.0470645	−	21.5666i	−0.00161620	−	0.740599i
$849$		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	$0.169252\pi$
$853$			29.6161i			1.01404i	−0.861935	+	0.507018i	$0.830748\pi$
$854$	−4.04742	+	1.08687i	−0.138500	+	0.0371919i
$855$		0			0
$856$	8.66947	+	32.1444i	0.296316	+	1.09867i
$857$		−	14.0190i		−	0.478879i	−0.970911	−	0.239439i	$-0.923036\pi$
$857$		−	14.0190i		−	0.478879i	0.970911	−	0.239439i	$-0.0769636\pi$
$858$		0			0
$859$			28.1857i			0.961683i	0.876808	+	0.480841i	$0.159669\pi$
$859$			28.1857i			0.961683i	−0.876808	+	0.480841i	$0.840331\pi$
$860$	−16.4965	−	28.5009i	−0.562527	−	0.971874i
$861$		0			0
$862$	−2.69459	−	10.0344i	−0.0917780	−	0.341774i
$863$			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
$868$	−6.27486	+	3.63193i	−0.212983	+	0.123276i
$869$	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
$874$	−49.1115	−	49.0580i	−1.66122	−	1.65941i
$875$	−8.58372	−	14.8674i	−0.290183	−	0.502611i
$876$		0			0
$877$	9.44822	−	5.45493i	0.319044	−	0.184200i	−0.331922	−	0.943307i	$-0.607697\pi$
$877$	9.44822	−	5.45493i	0.319044	−	0.184200i	0.650966	+	0.759107i	$0.274364\pi$
$878$	0.774960	+	2.88589i	0.0261536	+	0.0973941i
$879$		0			0
$880$	−66.7603	−	38.3501i	−2.25049	−	1.29278i
$881$	−10.4498	−	6.03317i	−0.352061	−	0.203263i	0.313532	−	0.949578i	$-0.398488\pi$
$881$	−10.4498	−	6.03317i	−0.352061	−	0.203263i	−0.665593	+	0.746315i	$0.731821\pi$
$882$		0			0
$883$			2.66359i			0.0896371i	0.998995	+	0.0448185i	$0.0142710\pi$
$883$			2.66359i			0.0896371i	−0.998995	+	0.0448185i	$0.985729\pi$
$884$	1.01898	+	24.3980i	0.0342719	+	0.820592i
$885$		0			0
$886$	−27.2354	−	27.2057i	−0.914991	−	0.913993i
$887$	−27.5037	+	47.6378i	−0.923485	+	1.59952i	−0.129504	+	0.991579i	$0.541339\pi$
$887$	−27.5037	+	47.6378i	−0.923485	+	1.59952i	−0.793981	+	0.607943i	$0.791995\pi$
$888$		0			0
$889$			8.31045i			0.278724i
$890$	−10.3699	+	2.78467i	−0.347599	+	0.0933423i
$891$		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
$904$	−7.67406	+	28.8286i	−0.255236	+	0.958827i
$905$	−88.4738			−2.94097
$906$		0			0
$907$	−36.6320	−	21.1495i	−1.21635	−	0.702258i	−0.252212	−	0.967672i	$-0.581158\pi$
$907$	−36.6320	−	21.1495i	−1.21635	−	0.702258i	−0.964134	+	0.265414i	$0.914491\pi$
$908$	−7.68683	−	13.2805i	−0.255096	−	0.440729i
$909$		0			0
$910$	12.0243	−	13.0581i	0.398601	−	0.432873i
$911$	10.7252			0.355341			0.177670	−	0.984090i	$-0.443144\pi$
$911$	10.7252			0.355341			0.177670	+	0.984090i	$0.443144\pi$
$912$		0			0
$913$	−4.37800	+	7.58292i	−0.144891	+	0.250958i
$914$	−10.2414	−	38.1382i	−0.338756	−	1.26150i
$915$		0			0
$916$	41.5405	−	0.0453266i	1.37254	−	0.00149763i
$917$	5.03276	+	8.71700i	0.166196	+	0.287861i
$918$		0			0
$919$	49.1677	−	28.3870i	1.62189	−	0.936400i	0.635479	−	0.772118i	$-0.280803\pi$
$919$	49.1677	−	28.3870i	1.62189	−	0.936400i	0.986413	−	0.164282i	$-0.0525307\pi$
$920$	−17.9422	−	66.5254i	−0.591536	−	2.19328i
$921$		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
$926$	−35.8090	−	35.7700i	−1.17676	−	1.17547i
$927$		0			0
$928$	3.08886	+	11.4033i	0.101397	+	0.374330i
$929$	21.7847	+	37.7322i	0.714732	+	1.23795i	0.963063	+	0.269277i	$0.0867849\pi$
$929$	21.7847	+	37.7322i	0.714732	+	1.23795i	−0.248330	+	0.968675i	$0.579882\pi$
$930$		0			0
$931$	48.1817			1.57909
$932$	7.12383	−	0.00777312i	0.233349	−	0.000254617i
$933$		0			0
$934$	7.80460	+	7.79609i	0.255374	+	0.255096i
$935$	−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	$0.539449\pi$
$938$	−2.67119	−	2.66828i	−0.0872175	−	0.0871224i
$939$		0			0
$940$	76.2845	−	0.0832373i	2.48813	−	0.00271490i
$941$	−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
$946$	21.2369	+	21.2137i	0.690471	+	0.689718i
$947$	39.5732	+	22.8476i	1.28596	+	0.742447i	0.977930	−	0.208931i	$-0.0669983\pi$
$947$	39.5732	+	22.8476i	1.28596	+	0.742447i	0.308026	+	0.951378i	$0.400332\pi$
$948$		0			0
$949$	−3.98486	+	7.59940i	−0.129354	+	0.246687i
$950$	28.2451	−	105.643i	0.916393	−	3.42750i
$951$		0			0
$952$	8.33131	−	2.24699i	0.270019	−	0.0728254i
$953$	31.9834	−	18.4656i	1.03604	−	0.598161i	0.117334	−	0.993092i	$-0.462565\pi$
$953$	31.9834	−	18.4656i	1.03604	−	0.598161i	0.918710	+	0.394932i	$0.129232\pi$
$954$		0			0
$955$	−13.0586	−	22.6182i	−0.422567	−	0.731908i
$956$	−28.4892	+	0.0310858i	−0.921407	+	0.00100539i
$957$		0			0
$958$	8.03959	+	29.9388i	0.259747	+	0.967279i
$959$	−0.0415026	+	0.0718845i	−0.00134019	+	0.00232127i
$960$		0			0
$961$	−14.8094			−0.477722
$962$	4.50686	−	20.0971i	0.145307	−	0.647957i
$963$		0			0
$964$	0.998447	+	1.72501i	0.0321578	+	0.0555589i
$965$	−76.2632	−	44.0306i	−2.45500	−	1.41739i
$966$		0			0
$967$	4.36992			0.140527			0.0702636	−	0.997528i	$-0.477616\pi$
$967$	4.36992			0.140527			0.0702636	+	0.997528i	$0.477616\pi$
$968$	37.7518	+	10.0494i	1.21339	+	0.322999i
$969$		0			0
$970$	45.5107	+	12.1679i	1.46126	+	0.390689i
$971$	−9.26820	−	16.0530i	−0.297431	−	0.515165i	0.678117	−	0.734954i	$-0.262796\pi$
$971$	−9.26820	−	16.0530i	−0.297431	−	0.515165i	−0.975547	+	0.219789i	$0.929463\pi$
$972$		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	−0.740823	−	0.671700i	$-0.765564\pi$
$977$	6.60452	−	11.4394i	0.211297	−	0.365978i	0.952121	+	0.305722i	$0.0988978\pi$
$978$		0			0
$979$	8.47600	−	4.89362i	0.270894	−	0.156401i
$980$	41.4437	+	23.8673i	1.32387	+	0.762412i
$981$		0			0
$982$	27.2588	−	7.31993i	0.869865	−	0.233588i
$983$			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
$986$	7.07614	+	7.06842i	0.225350	+	0.225104i
$987$		0			0
$988$	56.0958	−	2.34283i	1.78465	−	0.0745354i
$989$			26.8634i			0.854208i
$990$		0			0
$991$	20.6051	+	11.8964i	0.654544	+	0.377901i	0.790195	−	0.612856i	$-0.209979\pi$
$991$	20.6051	+	11.8964i	0.654544	+	0.377901i	−0.135651	+	0.990757i	$0.543313\pi$
$992$	−16.1389	−	16.0511i	−0.512410	−	0.509622i
$993$		0			0
$994$	−3.26164	−	12.1461i	−0.103453	−	0.385251i
$995$	−9.18701	+	5.30412i	−0.291248	+	0.168152i
$996$		0			0
$997$	1.44752	+	2.50718i	0.0458435	+	0.0794032i	0.888037	−	0.459773i	$-0.152069\pi$
$997$	1.44752	+	2.50718i	0.0458435	+	0.0794032i	−0.842193	+	0.539176i	$0.818736\pi$
$998$	−17.3684	−	17.3494i	−0.549787	−	0.549187i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bp.d.179.3	✓	40	13.10	even	6	inner
468.2.bp.d.179.7	yes	40	156.23	even	6	inner
468.2.bp.d.179.14	yes	40	52.23	odd	6	inner
468.2.bp.d.179.18	yes	40	39.23	odd	6	inner
468.2.bp.d.251.3	yes	40	12.11	even	2	inner
468.2.bp.d.251.7	yes	40	1.1	even	1	trivial
468.2.bp.d.251.14	yes	40	3.2	odd	2	inner
468.2.bp.d.251.18	yes	40	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.00055 - 0.999454i) q^{2} +(0.00218229 + 2.00000i) q^{4} +3.86412 q^{5} +(-0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +O(q^{10})\)	\(q+(-1.00055 - 0.999454i) q^{2} +(0.00218229 + 2.00000i) q^{4} +3.86412 q^{5} +(-0.450459 - 0.780219i) q^{7} +(1.99672 - 2.00327i) q^{8} +(-3.86622 - 3.86201i) q^{10} +(4.31382 + 2.49059i) q^{11} +(-3.19318 - 1.67439i) q^{13} +(-0.329088 + 1.23086i) q^{14} +(-3.99999 + 0.00872914i) q^{16} +(-2.93265 + 1.69317i) q^{17} +(3.89294 + 6.74276i) q^{19} +(0.00843260 + 7.72823i) q^{20} +(-1.82695 - 6.80341i) q^{22} +(3.15217 - 5.45971i) q^{23} +9.93140 q^{25} +(1.52144 + 4.86675i) q^{26} +(1.55945 - 0.902621i) q^{28} +(1.80867 + 1.04424i) q^{29} -4.02376 q^{31} +(4.01090 + 3.98907i) q^{32} +(4.62650 + 1.23696i) q^{34} +(-1.74063 - 3.01486i) q^{35} +(-3.49810 - 2.01963i) q^{37} +(2.84402 - 10.6373i) q^{38} +(7.71557 - 7.74087i) q^{40} +(2.26815 - 3.92854i) q^{41} +(-3.69023 + 2.13055i) q^{43} +(-4.97176 + 8.63307i) q^{44} +(-8.61062 + 2.31224i) q^{46} -9.87089i q^{47} +(3.09417 - 5.35926i) q^{49} +(-9.93681 - 9.92598i) q^{50} +(3.34182 - 6.39001i) q^{52} +5.39166i q^{53} +(16.6691 + 9.62392i) q^{55} +(-2.46243 - 0.655489i) q^{56} +(-0.765991 - 2.85249i) q^{58} +(8.43231 - 4.86840i) q^{59} +(1.64463 + 2.84858i) q^{61} +(4.02595 + 4.02156i) q^{62} +(-0.0261874 - 7.99996i) q^{64} +(-12.3388 - 6.47005i) q^{65} +(-1.48167 + 2.56634i) q^{67} +(-3.39273 - 5.86161i) q^{68} +(-1.27163 + 4.75618i) q^{70} +(-8.54844 + 4.93545i) q^{71} -2.37988i q^{73} +(1.48148 + 5.51693i) q^{74} +(-13.4770 + 7.80058i) q^{76} -4.48763i q^{77} -3.68370i q^{79} +(-15.4564 + 0.0337304i) q^{80} +(-6.19578 + 1.66378i) q^{82} +1.75782i q^{83} +(-11.3321 + 6.54260i) q^{85} +(5.82163 + 1.55650i) q^{86} +(13.6028 - 3.66874i) q^{88} +(0.982423 - 1.70161i) q^{89} +(0.132006 + 3.24563i) q^{91} +(10.9263 + 6.29242i) q^{92} +(-9.86550 + 9.87627i) q^{94} +(15.0428 + 26.0548i) q^{95} +(-7.46572 + 4.31034i) q^{97} +(-8.45220 + 2.26970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4}+O(q^{10}) \) 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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