LMFDB - Embedded newform 504.2.bm.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41266 + 0.0663565i) q^{2} +(1.99119 - 0.187478i) q^{4} +(1.02787 - 1.78033i) q^{5} +(-1.24680 + 2.33356i) q^{7} +(-2.80043 + 0.396971i) q^{8} +O(q^{10})$	\(q+(-1.41266 + 0.0663565i) q^{2} +(1.99119 - 0.187478i) q^{4} +(1.02787 - 1.78033i) q^{5} +(-1.24680 + 2.33356i) q^{7} +(-2.80043 + 0.396971i) q^{8} +(-1.33390 + 2.58320i) q^{10} +(-5.24912 + 3.03058i) q^{11} +1.77772i q^{13} +(1.60646 - 3.37924i) q^{14} +(3.92970 - 0.746610i) q^{16} +(-0.786233 + 0.453932i) q^{17} +(-3.37450 + 5.84481i) q^{19} +(1.71292 - 3.73769i) q^{20} +(7.21410 - 4.62948i) q^{22} +(0.351459 - 0.608746i) q^{23} +(0.386948 + 0.670213i) q^{25} +(-0.117963 - 2.51130i) q^{26} +(-2.04514 + 4.88031i) q^{28} +4.52576 q^{29} +(7.31501 - 4.22332i) q^{31} +(-5.50178 + 1.31546i) q^{32} +(1.08056 - 0.693421i) q^{34} +(2.87294 + 4.61833i) q^{35} +(-6.07548 - 3.50768i) q^{37} +(4.37917 - 8.48062i) q^{38} +(-2.17175 + 5.39373i) q^{40} +11.6289i q^{41} -4.69997 q^{43} +(-9.88385 + 7.01857i) q^{44} +(-0.456097 + 0.883270i) q^{46} +(-4.42306 + 7.66096i) q^{47} +(-3.89096 - 5.81897i) q^{49} +(-0.591097 - 0.921104i) q^{50} +(0.333282 + 3.53978i) q^{52} +(3.31595 + 5.74340i) q^{53} +12.4602i q^{55} +(2.56524 - 7.02990i) q^{56} +(-6.39334 + 0.300314i) q^{58} +(1.11754 - 0.645211i) q^{59} +(-7.95517 - 4.59292i) q^{61} +(-10.0533 + 6.45150i) q^{62} +(7.68483 - 2.22338i) q^{64} +(3.16492 + 1.82727i) q^{65} +(-0.562480 - 0.974244i) q^{67} +(-1.48044 + 1.05127i) q^{68} +(-4.36494 - 6.33347i) q^{70} +1.43897 q^{71} +(2.08692 + 3.61465i) q^{73} +(8.81532 + 4.55200i) q^{74} +(-5.62351 + 12.2708i) q^{76} +(-0.527404 - 16.0277i) q^{77} +(11.6339 + 6.71681i) q^{79} +(2.71003 - 7.76359i) q^{80} +(-0.771653 - 16.4276i) q^{82} -4.71682i q^{83} +1.86634i q^{85} +(6.63944 - 0.311874i) q^{86} +(13.4967 - 10.5707i) q^{88} +(4.08201 + 2.35675i) q^{89} +(-4.14840 - 2.21646i) q^{91} +(0.585697 - 1.27802i) q^{92} +(5.73991 - 11.1158i) q^{94} +(6.93713 + 12.0155i) q^{95} -12.2014 q^{97} +(5.88271 + 7.96201i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.41266	+	0.0663565i	−0.998899	+	0.0469212i
$2$	−1.41266	+	0.0663565i	−0.998899	+	0.0469212i
$3$		0			0
$3$		0			0
$4$	1.99119	−	0.187478i	0.995597	−	0.0937390i
$5$	1.02787	−	1.78033i	0.459679	−	0.796188i	−0.539264	−	0.842137i	$-0.681298\pi$
$5$	1.02787	−	1.78033i	0.459679	−	0.796188i	0.998944	+	0.0459483i	$0.0146310\pi$
$6$		0			0
$7$	−1.24680	+	2.33356i	−0.471248	+	0.882001i
$7$	−1.24680	+	2.33356i	−0.471248	+	0.882001i
$8$	−2.80043	+	0.396971i	−0.990102	+	0.140350i
$9$		0			0
$10$	−1.33390	+	2.58320i	−0.421815	+	0.816880i
$11$	−5.24912	+	3.03058i	−1.58267	+	0.913754i	−0.588201	+	0.808715i	$0.700164\pi$
$11$	−5.24912	+	3.03058i	−1.58267	+	0.913754i	−0.994468	+	0.105040i	$0.966503\pi$
$12$		0			0
$13$			1.77772i			0.493050i	0.969136	+	0.246525i	$0.0792887\pi$
$13$			1.77772i			0.493050i	−0.969136	+	0.246525i	$0.920711\pi$
$14$	1.60646	−	3.37924i	0.429344	−	0.903141i
$15$		0			0
$16$	3.92970	−	0.746610i	0.982426	−	0.186652i
$17$	−0.786233	+	0.453932i	−0.190690	+	0.110095i	−0.592305	−	0.805714i	$-0.701782\pi$
$17$	−0.786233	+	0.453932i	−0.190690	+	0.110095i	0.401616	+	0.915808i	$0.368449\pi$
$18$		0			0
$19$	−3.37450	+	5.84481i	−0.774164	+	1.34089i	0.161100	+	0.986938i	$0.448496\pi$
$19$	−3.37450	+	5.84481i	−0.774164	+	1.34089i	−0.935263	+	0.353953i	$0.884837\pi$
$20$	1.71292	−	3.73769i	0.383022	−	0.835772i
$21$		0			0
$22$	7.21410	−	4.62948i	1.53805	−	0.987009i
$23$	0.351459	−	0.608746i	0.0732843	−	0.126932i	−0.827055	−	0.562122i	$-0.809985\pi$
$23$	0.351459	−	0.608746i	0.0732843	−	0.126932i	0.900339	+	0.435189i	$0.143319\pi$
$24$		0			0
$25$	0.386948	+	0.670213i	0.0773896	+	0.134043i
$26$	−0.117963	−	2.51130i	−0.0231345	−	0.492506i
$27$		0			0
$28$	−2.04514	+	4.88031i	−0.386495	+	0.922292i
$29$	4.52576			0.840412			0.420206	−	0.907429i	$-0.361958\pi$
$29$	4.52576			0.840412			0.420206	+	0.907429i	$0.361958\pi$
$30$		0			0
$31$	7.31501	−	4.22332i	1.31381	−	0.758531i	0.331088	−	0.943600i	$-0.392584\pi$
$31$	7.31501	−	4.22332i	1.31381	−	0.758531i	0.982726	+	0.185069i	$0.0592508\pi$
$32$	−5.50178	+	1.31546i	−0.972586	+	0.232543i
$33$		0			0
$34$	1.08056	−	0.693421i	0.185314	−	0.118921i
$35$	2.87294	+	4.61833i	0.485616	+	0.780640i
$36$		0			0
$37$	−6.07548	−	3.50768i	−0.998803	−	0.576659i	−0.0909092	−	0.995859i	$-0.528977\pi$
$37$	−6.07548	−	3.50768i	−0.998803	−	0.576659i	−0.907894	+	0.419200i	$0.862311\pi$
$38$	4.37917	−	8.48062i	0.710395	−	1.37574i
$39$		0			0
$40$	−2.17175	+	5.39373i	−0.343384	+	0.852824i
$41$			11.6289i			1.81613i	0.418831	+	0.908064i	$0.362440\pi$
$41$			11.6289i			1.81613i	−0.418831	+	0.908064i	$0.637560\pi$
$42$		0			0
$43$	−4.69997			−0.716739			−0.358369	−	0.933580i	$-0.616667\pi$
$43$	−4.69997			−0.716739			−0.358369	+	0.933580i	$0.616667\pi$
$44$	−9.88385	+	7.01857i	−1.49005	+	1.05809i
$45$		0			0
$46$	−0.456097	+	0.883270i	−0.0672478	+	0.130231i
$47$	−4.42306	+	7.66096i	−0.645169	+	1.11747i	0.339093	+	0.940753i	$0.389880\pi$
$47$	−4.42306	+	7.66096i	−0.645169	+	1.11747i	−0.984262	+	0.176713i	$0.943453\pi$
$48$		0			0
$49$	−3.89096	−	5.81897i	−0.555851	−	0.831282i
$50$	−0.591097	−	0.921104i	−0.0835937	−	0.130264i
$51$		0			0
$52$	0.333282	+	3.53978i	0.0462179	+	0.490879i
$53$	3.31595	+	5.74340i	0.455481	+	0.788917i	0.998716	−	0.0506644i	$-0.0161339\pi$
$53$	3.31595	+	5.74340i	0.455481	+	0.788917i	−0.543235	+	0.839581i	$0.682801\pi$
$54$		0			0
$55$			12.4602i			1.68014i
$56$	2.56524	−	7.02990i	0.342794	−	0.939411i
$57$		0			0
$58$	−6.39334	+	0.300314i	−0.839487	+	0.0394331i
$59$	1.11754	−	0.645211i	0.145491	−	0.0839993i	−0.425487	−	0.904964i	$-0.639897\pi$
$59$	1.11754	−	0.645211i	0.145491	−	0.0839993i	0.570978	+	0.820965i	$0.306564\pi$
$60$		0			0
$61$	−7.95517	−	4.59292i	−1.01856	−	0.588063i	−0.104870	−	0.994486i	$-0.533443\pi$
$61$	−7.95517	−	4.59292i	−1.01856	−	0.588063i	−0.913685	+	0.406422i	$0.866776\pi$
$62$	−10.0533	+	6.45150i	−1.27678	+	0.819341i
$63$		0			0
$64$	7.68483	−	2.22338i	0.960604	−	0.277922i
$65$	3.16492	+	1.82727i	0.392560	+	0.226645i
$66$		0			0
$67$	−0.562480	−	0.974244i	−0.0687179	−	0.119023i	0.829619	−	0.558330i	$-0.188558\pi$
$67$	−0.562480	−	0.974244i	−0.0687179	−	0.119023i	−0.898337	+	0.439307i	$0.855224\pi$
$68$	−1.48044	+	1.05127i	−0.179530	+	0.127485i
$69$		0			0
$70$	−4.36494	−	6.33347i	−0.521710	−	0.756994i
$71$	1.43897			0.170774			0.0853869	−	0.996348i	$-0.472787\pi$
$71$	1.43897			0.170774			0.0853869	+	0.996348i	$0.472787\pi$
$72$		0			0
$73$	2.08692	+	3.61465i	0.244255	+	0.423063i	0.961922	−	0.273324i	$-0.0881231\pi$
$73$	2.08692	+	3.61465i	0.244255	+	0.423063i	−0.717667	+	0.696387i	$0.754790\pi$
$74$	8.81532	+	4.55200i	1.02476	+	0.529159i
$75$		0			0
$76$	−5.62351	+	12.2708i	−0.645061	+	1.40756i
$77$	−0.527404	−	16.0277i	−0.0601032	−	1.82652i
$78$		0			0
$79$	11.6339	+	6.71681i	1.30891	+	0.755701i	0.981915	−	0.189325i	$-0.0606299\pi$
$79$	11.6339	+	6.71681i	1.30891	+	0.755701i	0.326997	+	0.945025i	$0.393963\pi$
$80$	2.71003	−	7.76359i	0.302991	−	0.867996i
$81$		0			0
$82$	−0.771653	−	16.4276i	−0.0852148	−	1.81413i
$83$		−	4.71682i		−	0.517738i	−0.965912	−	0.258869i	$-0.916650\pi$
$83$		−	4.71682i		−	0.517738i	0.965912	−	0.258869i	$-0.0833499\pi$
$84$		0			0
$85$			1.86634i			0.202433i
$86$	6.63944	−	0.311874i	0.715950	−	0.0336302i
$87$		0			0
$88$	13.4967	−	10.5707i	1.43876	−	1.12684i
$89$	4.08201	+	2.35675i	0.432692	+	0.249815i	0.700493	−	0.713660i	$-0.252964\pi$
$89$	4.08201	+	2.35675i	0.432692	+	0.249815i	−0.267801	+	0.963474i	$0.586297\pi$
$90$		0			0
$91$	−4.14840	−	2.21646i	−0.434870	−	0.232348i
$92$	0.585697	−	1.27802i	0.0610632	−	0.133243i
$93$		0			0
$94$	5.73991	−	11.1158i	0.592026	−	1.14651i
$95$	6.93713	+	12.0155i	0.711734	+	1.23276i
$96$		0			0
$97$	−12.2014			−1.23886			−0.619430	−	0.785052i	$-0.712636\pi$
$97$	−12.2014			−1.23886			−0.619430	+	0.785052i	$0.712636\pi$
$98$	5.88271	+	7.96201i	0.594244	+	0.804285i
$99$		0			0
$100$	0.896138	+	1.26198i	0.0896138	+	0.126198i
$101$	−5.20672	−	9.01831i	−0.518088	−	0.897355i	−0.999779	−	0.0210140i	$-0.993311\pi$
$101$	−5.20672	−	9.01831i	−0.518088	−	0.897355i	0.481691	−	0.876341i	$-0.340023\pi$
$102$		0			0
$103$	−5.65349	−	3.26404i	−0.557055	−	0.321616i	0.194908	−	0.980822i	$-0.437559\pi$
$103$	−5.65349	−	3.26404i	−0.557055	−	0.321616i	−0.751963	+	0.659206i	$0.770893\pi$
$104$	−0.705701	−	4.97837i	−0.0691996	−	0.488169i
$105$		0			0
$106$	−5.06541	−	7.89341i	−0.491996	−	0.766676i
$107$	−8.00556	−	4.62201i	−0.773926	−	0.446827i	0.0603472	−	0.998177i	$-0.480779\pi$
$107$	−8.00556	−	4.62201i	−0.773926	−	0.446827i	−0.834273	+	0.551351i	$0.814113\pi$
$108$		0			0
$109$	4.22453	−	2.43904i	0.404637	−	0.233617i	−0.283846	−	0.958870i	$-0.591610\pi$
$109$	4.22453	−	2.43904i	0.404637	−	0.233617i	0.688483	+	0.725253i	$0.258277\pi$
$110$	−0.826818	−	17.6020i	−0.0788340	−	1.67829i
$111$		0			0
$112$	−3.15732	+	10.1011i	−0.298338	+	0.954460i
$113$		−	2.39142i		−	0.224966i	−0.993654	−	0.112483i	$-0.964120\pi$
$113$		−	2.39142i		−	0.224966i	0.993654	−	0.112483i	$-0.0358803\pi$
$114$		0			0
$115$	−0.722512	−	1.25143i	−0.0673746	−	0.116696i
$116$	9.01166	−	0.848480i	0.836712	−	0.0787794i
$117$		0			0
$118$	−1.53588	+	0.985617i	−0.141389	+	0.0907334i
$119$	−0.0789966	−	2.40068i	−0.00724160	−	0.220070i
$120$		0			0
$121$	12.8688	−	22.2895i	1.16989	−	2.02632i
$122$	11.5427	+	5.96034i	1.04503	+	0.539624i
$123$		0			0
$124$	13.7738	−	9.78085i	1.23693	−	0.878346i
$125$	11.8697			1.06166
$126$		0			0
$127$			4.06366i			0.360591i	0.983612	+	0.180296i	$0.0577055\pi$
$127$			4.06366i			0.360591i	−0.983612	+	0.180296i	$0.942295\pi$
$128$	−10.7085	+	3.65081i	−0.946505	+	0.322689i
$129$		0			0
$130$	−4.59220	−	2.37129i	−0.402762	−	0.207976i
$131$	0.208033	+	0.120108i	0.0181760	+	0.0104939i	0.509060	−	0.860731i	$-0.329993\pi$
$131$	0.208033	+	0.120108i	0.0181760	+	0.0104939i	−0.490884	+	0.871225i	$0.663326\pi$
$132$		0			0
$133$	−9.43184	−	15.1619i	−0.817844	−	1.31470i
$134$	0.859239	+	1.33895i	0.0742269	+	0.115667i
$135$		0			0
$136$	2.02159	−	1.58332i	0.173350	−	0.135768i
$137$	13.2051	−	7.62397i	1.12819	−	0.651360i	0.184709	−	0.982793i	$-0.440866\pi$
$137$	13.2051	−	7.62397i	1.12819	−	0.651360i	0.943479	+	0.331434i	$0.107532\pi$
$138$		0			0
$139$	7.64300			0.648271			0.324135	−	0.946011i	$-0.394927\pi$
$139$	7.64300			0.648271			0.324135	+	0.946011i	$0.394927\pi$
$140$	6.58642	+	8.65737i	0.556654	+	0.731681i
$141$		0			0
$142$	−2.03276	+	0.0954848i	−0.170586	+	0.00801291i
$143$	−5.38751	−	9.33144i	−0.450526	−	0.780334i
$144$		0			0
$145$	4.65191	−	8.05735i	0.386320	−	0.669126i
$146$	−3.18795	−	4.96778i	−0.263837	−	0.411136i
$147$		0			0
$148$	−12.7551	−	5.84545i	−1.04846	−	0.480493i
$149$	−8.37831	+	14.5117i	−0.686378	+	1.18884i	0.286623	+	0.958043i	$0.407467\pi$
$149$	−8.37831	+	14.5117i	−0.686378	+	1.18884i	−0.973002	+	0.230798i	$0.925866\pi$
$150$		0			0
$151$	7.10302	−	4.10093i	0.578036	−	0.333729i	−0.182317	−	0.983240i	$-0.558360\pi$
$151$	7.10302	−	4.10093i	0.578036	−	0.333729i	0.760352	+	0.649511i	$0.225026\pi$
$152$	7.12984	−	17.7076i	0.578307	−	1.43627i
$153$		0			0
$154$	1.80858	+	22.6066i	0.145739	+	1.82169i
$155$		−	17.3642i		−	1.39472i
$156$		0			0
$157$	−1.87900	+	1.08484i	−0.149961	+	0.0865798i	−0.573103	−	0.819483i	$-0.694260\pi$
$157$	−1.87900	+	1.08484i	−0.149961	+	0.0865798i	0.423142	+	0.906063i	$0.360927\pi$
$158$	−16.8803	−	8.71656i	−1.34293	−	0.693453i
$159$		0			0
$160$	−3.31318	+	11.1471i	−0.261930	+	0.881257i
$161$	0.982340	+	1.57914i	0.0774193	+	0.124453i
$162$		0			0
$163$	−9.29429	+	16.0982i	−0.727985	+	1.26091i	0.229749	+	0.973250i	$0.426210\pi$
$163$	−9.29429	+	16.0982i	−0.727985	+	1.26091i	−0.957734	+	0.287657i	$0.907124\pi$
$164$	2.18016	+	23.1554i	0.170242	+	1.80813i
$165$		0			0
$166$	0.312992	+	6.66325i	0.0242929	+	0.517168i
$167$	−22.6164			−1.75011			−0.875056	−	0.484022i	$-0.839176\pi$
$167$	−22.6164			−1.75011			−0.875056	+	0.484022i	$0.839176\pi$
$168$		0			0
$169$	9.83973			0.756902
$170$	−0.123844	−	2.63650i	−0.00949839	−	0.202210i
$171$		0			0
$172$	−9.35855	+	0.881141i	−0.713583	+	0.0671864i
$173$	−0.544356	+	0.942851i	−0.0413866	+	0.0716837i	−0.885977	−	0.463730i	$-0.846511\pi$
$173$	−0.544356	+	0.942851i	−0.0413866	+	0.0716837i	0.844590	+	0.535413i	$0.179844\pi$
$174$		0			0
$175$	−2.04643	+	0.0673395i	−0.154695	+	0.00509039i
$176$	−18.3648	+	15.8283i	−1.38430	+	1.19311i
$177$		0			0
$178$	−5.92286	−	3.05841i	−0.443937	−	0.229237i
$179$	5.20593	−	3.00564i	0.389109	−	0.224652i	−0.292665	−	0.956215i	$-0.594542\pi$
$179$	5.20593	−	3.00564i	0.389109	−	0.224652i	0.681774	+	0.731563i	$0.261209\pi$
$180$		0			0
$181$			7.28891i			0.541780i	0.962610	+	0.270890i	$0.0873180\pi$
$181$			7.28891i			0.541780i	−0.962610	+	0.270890i	$0.912682\pi$
$182$	6.00733	+	2.85583i	0.445293	+	0.211688i
$183$		0			0
$184$	−0.742584	+	1.84427i	−0.0547440	+	0.135961i
$185$	−12.4897	+	7.21091i	−0.918259	+	0.530157i
$186$		0			0
$187$	2.75135	−	4.76549i	0.201199	−	0.348487i
$188$	−7.37091	+	16.0837i	−0.537579	+	1.17302i
$189$		0			0
$190$	−10.5971	−	16.5134i	−0.768793	−	1.19801i
$191$	2.21264	−	3.83240i	0.160101	−	0.277303i	−0.774804	−	0.632202i	$-0.782151\pi$
$191$	2.21264	−	3.83240i	0.160101	−	0.277303i	0.934905	+	0.354899i	$0.115485\pi$
$192$		0			0
$193$	1.26476	+	2.19063i	0.0910393	+	0.157685i	0.907949	−	0.419081i	$-0.137648\pi$
$193$	1.26476	+	2.19063i	0.0910393	+	0.157685i	−0.816909	+	0.576766i	$0.804314\pi$
$194$	17.2363	−	0.809640i	1.23750	−	0.0581288i
$195$		0			0
$196$	−8.83858	−	10.8572i	−0.631327	−	0.775516i
$197$	11.6259			0.828314			0.414157	−	0.910205i	$-0.364076\pi$
$197$	11.6259			0.828314			0.414157	+	0.910205i	$0.364076\pi$
$198$		0			0
$199$	16.8071	−	9.70356i	1.19142	−	0.687867i	0.232792	−	0.972527i	$-0.425214\pi$
$199$	16.8071	−	9.70356i	1.19142	−	0.687867i	0.958629	+	0.284659i	$0.0918805\pi$
$200$	−1.34968	−	1.72328i	−0.0954365	−	0.121854i
$201$		0			0
$202$	7.95373	+	12.3943i	0.559623	+	0.872058i
$203$	−5.64273	+	10.5611i	−0.396042	+	0.741244i
$204$		0			0
$205$	20.7033	+	11.9530i	1.44598	+	0.834837i
$206$	8.20303	+	4.23583i	0.571532	+	0.295124i
$207$		0			0
$208$	1.32726	+	6.98590i	0.0920289	+	0.484385i
$209$		−	40.9068i		−	2.82958i
$210$		0			0
$211$	5.73966			0.395135			0.197567	−	0.980289i	$-0.436696\pi$
$211$	5.73966			0.395135			0.197567	+	0.980289i	$0.436696\pi$
$212$	7.67947	+	10.8146i	0.527428	+	0.742746i
$213$		0			0
$214$	11.6158	+	5.99809i	0.794039	+	0.410021i
$215$	−4.83098	+	8.36750i	−0.329470	+	0.570659i
$216$		0			0
$217$	0.734973	+	22.3356i	0.0498932	+	1.51624i
$218$	−5.80597	+	3.72584i	−0.393230	+	0.252346i
$219$		0			0
$220$	2.33602	+	24.8107i	0.157494	+	1.67274i
$221$	−0.806962	−	1.39770i	−0.0542821	−	0.0940194i
$222$		0			0
$223$			5.21414i			0.349164i	0.984643	+	0.174582i	$0.0558575\pi$
$223$			5.21414i			0.349164i	−0.984643	+	0.174582i	$0.944143\pi$
$224$	3.78993	−	14.4788i	0.253225	−	0.967407i
$225$		0			0
$226$	0.158686	+	3.37825i	0.0105557	+	0.224718i
$227$	6.08667	−	3.51414i	0.403986	−	0.233242i	−0.284216	−	0.958760i	$-0.591733\pi$
$227$	6.08667	−	3.51414i	0.403986	−	0.233242i	0.688203	+	0.725519i	$0.258400\pi$
$228$		0			0
$229$	−22.0239	−	12.7155i	−1.45538	−	0.840264i	−0.456601	−	0.889672i	$-0.650933\pi$
$229$	−22.0239	−	12.7155i	−1.45538	−	0.840264i	−0.998779	+	0.0494076i	$0.984267\pi$
$230$	1.10370	+	1.71989i	0.0727759	+	0.113406i
$231$		0			0
$232$	−12.6741	+	1.79659i	−0.832094	+	0.117952i
$233$	−10.0196	−	5.78482i	−0.656406	−	0.378976i	0.134500	−	0.990914i	$-0.457057\pi$
$233$	−10.0196	−	5.78482i	−0.656406	−	0.378976i	−0.790906	+	0.611937i	$0.790390\pi$
$234$		0			0
$235$	9.09270	+	15.7490i	0.593142	+	1.02735i
$236$	2.10427	−	1.49425i	0.136976	−	0.0972676i
$237$		0			0
$238$	0.270896	+	3.38610i	0.0175596	+	0.219488i
$239$	17.2023			1.11272			0.556362	−	0.830940i	$-0.312197\pi$
$239$	17.2023			1.11272			0.556362	+	0.830940i	$0.312197\pi$
$240$		0			0
$241$	6.84594	+	11.8575i	0.440986	+	0.763810i	0.997763	−	0.0668522i	$-0.0212956\pi$
$241$	6.84594	+	11.8575i	0.440986	+	0.763810i	−0.556777	+	0.830662i	$0.687962\pi$
$242$	−16.7002	+	32.3413i	−1.07353	+	2.07898i
$243$		0			0
$244$	−16.7014	−	7.65398i	−1.06920	−	0.489996i
$245$	−14.3591	+	0.946023i	−0.917370	+	0.0604392i
$246$		0			0
$247$	−10.3904	−	5.99890i	−0.661126	−	0.381701i
$248$	−18.8086	+	14.7310i	−1.19435	+	0.935417i
$249$		0			0
$250$	−16.7678	+	0.787631i	−1.06049	+	0.0498142i
$251$			9.77570i			0.617037i	0.951218	+	0.308518i	$0.0998332\pi$
$251$			9.77570i			0.617037i	−0.951218	+	0.308518i	$0.900167\pi$
$252$		0			0
$253$			4.26050i			0.267856i
$254$	−0.269650	−	5.74055i	−0.0169194	−	0.360194i
$255$		0			0
$256$	14.8851	−	5.86791i	0.930322	−	0.366744i
$257$	17.9664	+	10.3729i	1.12071	+	0.647043i	0.941582	−	0.336783i	$-0.109339\pi$
$257$	17.9664	+	10.3729i	1.12071	+	0.647043i	0.179129	+	0.983826i	$0.442672\pi$
$258$		0			0
$259$	15.7603	−	9.80408i	0.979298	−	0.609196i
$260$	6.64454	+	3.04509i	0.412077	+	0.188849i
$261$		0			0
$262$	−0.301850	−	0.155867i	−0.0186483	−	0.00962950i
$263$	6.61692	+	11.4608i	0.408016	+	0.706705i	0.994667	−	0.103135i	$-0.0328873\pi$
$263$	6.61692	+	11.4608i	0.408016	+	0.706705i	−0.586651	+	0.809840i	$0.699554\pi$
$264$		0			0
$265$	13.6335			0.837501
$266$	14.3300	+	20.7927i	0.878631	+	1.27488i
$267$		0			0
$268$	−1.30266	−	1.83446i	−0.0795724	−	0.112057i
$269$	−6.00719	−	10.4048i	−0.366265	−	0.634390i	0.622713	−	0.782450i	$-0.286030\pi$
$269$	−6.00719	−	10.4048i	−0.366265	−	0.634390i	−0.988978	+	0.148060i	$0.952697\pi$
$270$		0			0
$271$	−25.7592	−	14.8721i	−1.56476	−	0.903414i	−0.996764	−	0.0803814i	$-0.974386\pi$
$271$	−25.7592	−	14.8721i	−1.56476	−	0.903414i	−0.567994	−	0.823032i	$-0.692280\pi$
$272$	−2.75075	+	2.37083i	−0.166789	+	0.143753i
$273$		0			0
$274$	−18.1484	+	11.6463i	−1.09638	+	0.703578i
$275$	−4.06227	−	2.34535i	−0.244964	−	0.141430i
$276$		0			0
$277$	7.23966	−	4.17982i	0.434989	−	0.251141i	−0.266481	−	0.963840i	$-0.585861\pi$
$277$	7.23966	−	4.17982i	0.434989	−	0.251141i	0.701470	+	0.712699i	$0.252528\pi$
$278$	−10.7969	+	0.507163i	−0.647557	+	0.0304176i
$279$		0			0
$280$	−9.87882	−	11.7928i	−0.590372	−	0.704756i
$281$			3.58062i			0.213602i	0.994280	+	0.106801i	$0.0340608\pi$
$281$			3.58062i			0.213602i	−0.994280	+	0.106801i	$0.965939\pi$
$282$		0			0
$283$	−10.8564	−	18.8038i	−0.645346	−	1.11777i	−0.984222	−	0.176940i	$-0.943380\pi$
$283$	−10.8564	−	18.8038i	−0.645346	−	1.11777i	0.338876	−	0.940831i	$-0.389953\pi$
$284$	2.86526	−	0.269774i	0.170022	−	0.0160082i
$285$		0			0
$286$	8.22990	+	12.8246i	0.486644	+	0.758336i
$287$	−27.1367	−	14.4990i	−1.60183	−	0.855846i
$288$		0			0
$289$	−8.08789	+	14.0086i	−0.475758	+	0.824038i
$290$	−6.03689	+	11.6909i	−0.354499	+	0.686516i
$291$		0			0
$292$	4.83313	+	6.80622i	0.282837	+	0.398304i
$293$	−14.2584			−0.832986			−0.416493	−	0.909139i	$-0.636741\pi$
$293$	−14.2584			−0.832986			−0.416493	+	0.909139i	$0.636741\pi$
$294$		0			0
$295$		−	2.65278i		−	0.154451i
$296$	18.4064	+	7.41123i	1.06985	+	0.430769i
$297$		0			0
$298$	10.8727	−	21.0559i	0.629840	−	1.21974i
$299$	1.08218	+	0.624795i	0.0625839	+	0.0361328i
$300$		0			0
$301$	5.85994	−	10.9676i	0.337762	−	0.632164i
$302$	−9.76200	+	6.26454i	−0.561740	+	0.360484i
$303$		0			0
$304$	−8.89700	+	25.4878i	−0.510278	+	1.46183i
$305$	−16.3538	+	9.44190i	−0.936418	+	0.540641i
$306$		0			0
$307$	12.0680			0.688757			0.344378	−	0.938831i	$-0.388090\pi$
$307$	12.0680			0.688757			0.344378	+	0.938831i	$0.388090\pi$
$308$	−4.05499	−	31.8153i	−0.231055	−	1.81284i
$309$		0			0
$310$	1.15223	+	24.5296i	0.0654421	+	1.39319i
$311$	4.88095	+	8.45405i	0.276773	+	0.479385i	0.970581	−	0.240775i	$-0.0774016\pi$
$311$	4.88095	+	8.45405i	0.276773	+	0.479385i	−0.693808	+	0.720160i	$0.744068\pi$
$312$		0			0
$313$	−14.1208	+	24.4580i	−0.798155	+	1.38245i	0.122661	+	0.992449i	$0.460857\pi$
$313$	−14.1208	+	24.4580i	−0.798155	+	1.38245i	−0.920816	+	0.389997i	$0.872476\pi$
$314$	2.58240	−	1.65719i	0.145733	−	0.0935208i
$315$		0			0
$316$	24.4245	+	11.1934i	1.37399	+	0.629677i
$317$	12.7790	−	22.1338i	0.717738	−	1.24316i	−0.244157	−	0.969736i	$-0.578511\pi$
$317$	12.7790	−	22.1338i	0.717738	−	1.24316i	0.961894	−	0.273422i	$-0.0881556\pi$
$318$		0			0
$319$	−23.7563	+	13.7157i	−1.33009	+	0.767931i
$320$	3.94069	−	15.9669i	0.220291	−	0.892576i
$321$		0			0
$322$	−1.49249	−	2.16559i	−0.0831735	−	0.120684i
$323$		−	6.12718i		−	0.340925i
$324$		0			0
$325$	−1.19145	+	0.687883i	−0.0660897	+	0.0381569i
$326$	12.0614	−	23.3579i	0.668020	−	1.29368i
$327$		0			0
$328$	−4.61633	−	32.5659i	−0.254894	−	1.79815i
$329$	−12.3626	−	19.8732i	−0.681572	−	1.09564i
$330$		0			0
$331$	−5.83423	+	10.1052i	−0.320678	+	0.555431i	−0.980628	−	0.195879i	$-0.937244\pi$
$331$	−5.83423	+	10.1052i	−0.320678	+	0.555431i	0.659950	+	0.751310i	$0.270577\pi$
$332$	−0.884300	−	9.39211i	−0.0485323	−	0.515459i
$333$		0			0
$334$	31.9492	−	1.50075i	1.74818	−	0.0821173i
$335$	−2.31264			−0.126353
$336$		0			0
$337$	22.5456			1.22814			0.614068	−	0.789253i	$-0.289532\pi$
$337$	22.5456			1.22814			0.614068	+	0.789253i	$0.289532\pi$
$338$	−13.9002	+	0.652930i	−0.756069	+	0.0355147i
$339$		0			0
$340$	0.349898	+	3.71625i	0.0189759	+	0.201542i
$341$	−25.5982	+	44.3374i	−1.38622	+	2.40101i
$342$		0			0
$343$	18.4302	−	1.82465i	0.995135	−	0.0985219i
$344$	13.1619	−	1.86575i	0.709645	−	0.100595i
$345$		0			0
$346$	0.706423	−	1.36805i	0.0379775	−	0.0735466i
$347$	6.94457	−	4.00945i	0.372804	−	0.215238i	−0.301879	−	0.953346i	$-0.597614\pi$
$347$	6.94457	−	4.00945i	0.372804	−	0.215238i	0.674683	+	0.738108i	$0.264280\pi$
$348$		0			0
$349$			18.5648i			0.993750i	0.867822	+	0.496875i	$0.165519\pi$
$349$			18.5648i			0.993750i	−0.867822	+	0.496875i	$0.834481\pi$
$350$	2.88643	−	0.230921i	0.154286	−	0.0123433i
$351$		0			0
$352$	24.8929	−	23.5786i	1.32679	−	1.25674i
$353$	−16.1137	+	9.30324i	−0.857645	+	0.495161i	−0.863223	−	0.504823i	$-0.831558\pi$
$353$	−16.1137	+	9.30324i	−0.857645	+	0.495161i	0.00557823	+	0.999984i	$0.498224\pi$
$354$		0			0
$355$	1.47908	−	2.56184i	0.0785012	−	0.135968i
$356$	8.56990	+	3.92746i	0.454204	+	0.208155i
$357$		0			0
$358$	−7.15474	+	4.59139i	−0.378140	+	0.242662i
$359$	16.9950	−	29.4361i	0.896959	−	1.55358i	0.0655985	−	0.997846i	$-0.479104\pi$
$359$	16.9950	−	29.4361i	0.896959	−	1.55358i	0.831361	−	0.555733i	$-0.187562\pi$
$360$		0			0
$361$	−13.2745	−	22.9921i	−0.698659	−	1.21011i
$362$	−0.483667	−	10.2967i	−0.0254210	−	0.541184i
$363$		0			0
$364$	−8.67580	−	3.63567i	−0.454735	−	0.190561i
$365$	8.58037			0.449117
$366$		0			0
$367$	4.41003	−	2.54613i	0.230202	−	0.132907i	−0.380463	−	0.924796i	$-0.624235\pi$
$367$	4.41003	−	2.54613i	0.230202	−	0.132907i	0.610665	+	0.791889i	$0.290902\pi$
$368$	0.926636	−	2.65459i	0.0483042	−	0.138380i
$369$		0			0
$370$	17.1651	−	11.0153i	0.892372	−	0.572659i
$371$	−17.5369	+	0.577066i	−0.910470	+	0.0299598i
$372$		0			0
$373$	14.7870	+	8.53728i	0.765642	+	0.442044i	0.831318	−	0.555797i	$-0.187587\pi$
$373$	14.7870	+	8.53728i	0.765642	+	0.442044i	−0.0656756	+	0.997841i	$0.520920\pi$
$374$	−3.57050	+	6.91456i	−0.184626	+	0.357544i
$375$		0			0
$376$	9.34530	−	23.2098i	0.481947	−	1.19696i
$377$			8.04551i			0.414365i
$378$		0			0
$379$	11.2872			0.579783			0.289892	−	0.957059i	$-0.406381\pi$
$379$	11.2872			0.579783			0.289892	+	0.957059i	$0.406381\pi$
$380$	16.0658	+	22.6245i	0.824158	+	1.16061i
$381$		0			0
$382$	−2.87139	+	5.56069i	−0.146913	+	0.284510i
$383$	10.2813	−	17.8078i	0.525352	−	0.909936i	−0.474212	−	0.880410i	$-0.657267\pi$
$383$	10.2813	−	17.8078i	0.525352	−	0.909936i	0.999564	−	0.0295252i	$-0.00939952\pi$
$384$		0			0
$385$	−29.0766	−	15.5355i	−1.48188	−	0.791760i
$386$	−1.93203	−	3.01068i	−0.0983378	−	0.153239i
$387$		0			0
$388$	−24.2953	+	2.28749i	−1.23341	+	0.116130i
$389$	6.92881	+	12.0011i	0.351305	+	0.608478i	0.986478	−	0.163892i	$-0.0524048\pi$
$389$	6.92881	+	12.0011i	0.351305	+	0.608478i	−0.635174	+	0.772369i	$0.719071\pi$
$390$		0			0
$391$			0.638155i			0.0322729i
$392$	13.2063	+	14.7510i	0.667020	+	0.745040i
$393$		0			0
$394$	−16.4235	+	0.771457i	−0.827402	+	0.0388655i
$395$	23.9163	−	13.8081i	1.20336	−	0.694760i
$396$		0			0
$397$	29.9634	+	17.2993i	1.50382	+	0.868229i	0.999990	+	0.00442498i	$0.00140852\pi$
$397$	29.9634	+	17.2993i	1.50382	+	0.868229i	0.503827	+	0.863804i	$0.331925\pi$
$398$	−23.0987	+	14.8231i	−1.15783	+	0.743012i
$399$		0			0
$400$	2.02098	+	2.34484i	0.101049	+	0.117242i
$401$	12.1249	+	7.00029i	0.605486	+	0.349578i	0.771197	−	0.636597i	$-0.219658\pi$
$401$	12.1249	+	7.00029i	0.605486	+	0.349578i	−0.165711	+	0.986174i	$0.552992\pi$
$402$		0			0
$403$	7.50786	+	13.0040i	0.373993	+	0.647775i
$404$	−12.0583	−	16.9811i	−0.599924	−	0.844839i
$405$		0			0
$406$	7.27044	−	15.2936i	0.360826	−	0.759011i
$407$	42.5212			2.10770
$408$		0			0
$409$	−2.76388	−	4.78718i	−0.136665	−	0.236711i	0.789567	−	0.613664i	$-0.210305\pi$
$409$	−2.76388	−	4.78718i	−0.136665	−	0.236711i	−0.926232	+	0.376953i	$0.876972\pi$
$410$	−30.0398	−	15.5117i	−1.48356	−	0.766070i
$411$		0			0
$412$	−11.8691	−	5.43944i	−0.584750	−	0.267982i
$413$	0.112284	+	3.41229i	0.00552515	+	0.167908i
$414$		0			0
$415$	−8.39750	−	4.84830i	−0.412217	−	0.237994i
$416$	−2.33852	−	9.78059i	−0.114655	−	0.479533i
$417$		0			0
$418$	2.71443	+	57.7872i	0.132767	+	2.82647i
$419$			13.1122i			0.640574i	0.947320	+	0.320287i	$0.103779\pi$
$419$			13.1122i			0.640574i	−0.947320	+	0.320287i	$0.896221\pi$
$420$		0			0
$421$			22.0752i			1.07588i	0.842983	+	0.537941i	$0.180798\pi$
$421$			22.0752i			1.07588i	−0.842983	+	0.537941i	$0.819202\pi$
$422$	−8.10817	+	0.380864i	−0.394699	+	0.0185402i
$423$		0			0
$424$	−11.5661	−	14.7677i	−0.561697	−	0.717181i
$425$	−0.608462	−	0.351296i	−0.0295148	−	0.0170404i
$426$		0			0
$427$	20.6364	−	12.8374i	0.998664	−	0.621244i
$428$	−16.8071	−	7.70245i	−0.812404	−	0.372312i
$429$		0			0
$430$	6.26928	−	12.1410i	0.302331	−	0.585490i
$431$	−12.9464	−	22.4237i	−0.623604	−	1.08011i	−0.988809	−	0.149187i	$-0.952334\pi$
$431$	−12.9464	−	22.4237i	−0.623604	−	1.08011i	0.365205	−	0.930927i	$-0.380999\pi$
$432$		0			0
$433$	−32.4535			−1.55961			−0.779807	−	0.626020i	$-0.784683\pi$
$433$	−32.4535			−1.55961			−0.779807	+	0.626020i	$0.784683\pi$
$434$	−2.52038	−	31.5038i	−0.120982	−	1.51223i
$435$		0			0
$436$	7.95460	−	5.64860i	0.380956	−	0.270519i
$437$	2.37200	+	4.10843i	0.113468	+	0.196533i
$438$		0			0
$439$	−11.7422	−	6.77937i	−0.560425	−	0.323561i	0.192891	−	0.981220i	$-0.438214\pi$
$439$	−11.7422	−	6.77937i	−0.560425	−	0.323561i	−0.753316	+	0.657659i	$0.771547\pi$
$440$	−4.94634	−	34.8940i	−0.235808	−	1.66351i
$441$		0			0
$442$	1.23271	+	1.92092i	0.0586338	+	0.0913689i
$443$	3.78628	+	2.18601i	0.179892	+	0.103860i	0.587242	−	0.809412i	$-0.300214\pi$
$443$	3.78628	+	2.18601i	0.179892	+	0.103860i	−0.407350	+	0.913272i	$0.633547\pi$
$444$		0			0
$445$	8.39158	−	4.84488i	0.397799	−	0.229669i
$446$	−0.345992	−	7.36578i	−0.0163832	−	0.348780i
$447$		0			0
$448$	−4.39310	+	20.7051i	−0.207555	+	0.978223i
$449$			13.7570i			0.649235i	0.945845	+	0.324618i	$0.105236\pi$
$449$			13.7570i			0.649235i	−0.945845	+	0.324618i	$0.894764\pi$
$450$		0			0
$451$	−35.2423	−	61.0415i	−1.65950	−	2.87433i
$452$	−0.448338	−	4.76178i	−0.0210880	−	0.223975i
$453$		0			0
$454$	−8.36518	+	5.36816i	−0.392598	+	0.251940i
$455$	−8.21007	+	5.10727i	−0.384894	+	0.239433i
$456$		0			0
$457$	5.88182	−	10.1876i	0.275140	−	0.476557i	−0.695030	−	0.718980i	$-0.744609\pi$
$457$	5.88182	−	10.1876i	0.275140	−	0.476557i	0.970170	+	0.242424i	$0.0779424\pi$
$458$	31.9559	+	16.5012i	1.49320	+	0.771050i
$459$		0			0
$460$	−1.67328	−	2.35638i	−0.0780169	−	0.109867i
$461$	11.1624			0.519887			0.259943	−	0.965624i	$-0.416296\pi$
$461$	11.1624			0.519887			0.259943	+	0.965624i	$0.416296\pi$
$462$		0			0
$463$		−	16.0864i		−	0.747599i	−0.927510	−	0.373799i	$-0.878055\pi$
$463$		−	16.0864i		−	0.747599i	0.927510	−	0.373799i	$-0.121945\pi$
$464$	17.7849	−	3.37898i	0.825643	−	0.156865i
$465$		0			0
$466$	14.5381	+	7.50709i	0.673465	+	0.347759i
$467$	18.8715	+	10.8955i	0.873268	+	0.504181i	0.868433	−	0.495807i	$-0.165128\pi$
$467$	18.8715	+	10.8955i	0.873268	+	0.504181i	0.00483503	+	0.999988i	$0.498461\pi$
$468$		0			0
$469$	2.97476	−	0.0978869i	0.137361	−	0.00452000i
$470$	−13.8899	−	21.6446i	−0.640694	−	0.998390i
$471$		0			0
$472$	−2.87346	+	2.25050i	−0.132262	+	0.103588i
$473$	24.6707	−	14.2436i	1.13436	−	0.654923i
$474$		0			0
$475$	−5.22302			−0.239649
$476$	−0.607372	−	4.76541i	−0.0278389	−	0.218422i
$477$		0			0
$478$	−24.3009	+	1.14149i	−1.11150	+	0.0522103i
$479$	10.9014	+	18.8818i	0.498099	+	0.862734i	0.999998	−	0.00219321i	$-0.000698121\pi$
$479$	10.9014	+	18.8818i	0.498099	+	0.862734i	−0.501898	+	0.864927i	$0.667365\pi$
$480$		0			0
$481$	6.23566	−	10.8005i	0.284322	−	0.492459i
$482$	−10.4578	−	16.2963i	−0.476339	−	0.742277i
$483$		0			0
$484$	21.4456	−	46.7953i	0.974798	−	2.12706i
$485$	−12.5415	+	21.7225i	−0.569479	+	0.986366i
$486$		0			0
$487$	−5.03965	+	2.90964i	−0.228368	+	0.131849i	−0.609819	−	0.792541i	$-0.708758\pi$
$487$	−5.03965	+	2.90964i	−0.228368	+	0.131849i	0.381451	+	0.924389i	$0.375425\pi$
$488$	24.1012	+	9.70419i	1.09101	+	0.439288i
$489$		0			0
$490$	20.2217	−	2.28923i	0.913524	−	0.103417i
$491$			17.6807i			0.797919i	0.916969	+	0.398959i	$0.130629\pi$
$491$			17.6807i			0.797919i	−0.916969	+	0.398959i	$0.869371\pi$
$492$		0			0
$493$	−3.55830	+	2.05439i	−0.160258	+	0.0925249i
$494$	15.0761	+	7.78491i	0.678307	+	0.350260i
$495$		0			0
$496$	25.5926	−	22.0579i	1.14914	−	0.990427i
$497$	−1.79411	+	3.35791i	−0.0804768	+	0.150623i
$498$		0			0
$499$	4.79931	−	8.31264i	0.214846	−	0.372125i	−0.738379	−	0.674386i	$-0.764408\pi$
$499$	4.79931	−	8.31264i	0.214846	−	0.372125i	0.953225	+	0.302261i	$0.0977416\pi$
$500$	23.6348	−	2.22530i	1.05698	−	0.0995186i
$501$		0			0
$502$	−0.648682	−	13.8097i	−0.0289521	−	0.616357i
$503$	21.6062			0.963375			0.481687	−	0.876343i	$-0.340024\pi$
$503$	21.6062			0.963375			0.481687	+	0.876343i	$0.340024\pi$
$504$		0			0
$505$	−21.4074			−0.952618
$506$	−0.282712	−	6.01863i	−0.0125681	−	0.267561i
$507$		0			0
$508$	0.761846	+	8.09153i	0.0338015	+	0.359004i
$509$	8.22302	−	14.2427i	0.364479	−	0.631296i	−0.624213	−	0.781254i	$-0.714580\pi$
$509$	8.22302	−	14.2427i	0.364479	−	0.631296i	0.988692	+	0.149958i	$0.0479138\pi$
$510$		0			0
$511$	−11.0370	+	0.363181i	−0.488247	+	0.0160662i
$512$	−20.6382	+	9.27706i	−0.912089	+	0.409992i
$513$		0			0
$514$	−26.0686	−	13.4611i	−1.14984	−	0.593745i
$515$	−11.6222	+	6.71006i	−0.512133	+	0.295680i
$516$		0			0
$517$		−	53.6178i		−	2.35811i
$518$	−21.6133	+	14.8956i	−0.949635	+	0.654475i
$519$		0			0
$520$	−9.58852	−	3.86076i	−0.420484	−	0.169305i
$521$	−22.2819	+	12.8645i	−0.976189	+	0.563603i	−0.901117	−	0.433575i	$-0.857252\pi$
$521$	−22.2819	+	12.8645i	−0.976189	+	0.563603i	−0.0750717	+	0.997178i	$0.523919\pi$
$522$		0			0
$523$	−19.2515	+	33.3445i	−0.841808	+	1.45805i	0.0465564	+	0.998916i	$0.485175\pi$
$523$	−19.2515	+	33.3445i	−0.841808	+	1.45805i	−0.888365	+	0.459139i	$0.848158\pi$
$524$	0.436752	+	0.200157i	0.0190796	+	0.00874389i
$525$		0			0
$526$	−10.1079	−	15.7511i	−0.440727	−	0.686782i
$527$	−3.83420	+	6.64103i	−0.167020	+	0.289288i
$528$		0			0
$529$	11.2530	+	19.4907i	0.489259	+	0.847421i
$530$	−19.2595	+	0.904674i	−0.836579	+	0.0392965i
$531$		0			0
$532$	−21.6231	−	28.4220i	−0.937482	−	1.23225i
$533$	−20.6729			−0.895441
$534$		0			0
$535$	−16.4574	+	9.50169i	−0.711516	+	0.410794i
$536$	1.96193	+	2.50502i	0.0847426	+	0.108200i
$537$		0			0
$538$	9.17652	+	14.2997i	0.395628	+	0.616505i
$539$	38.0590	+	18.7526i	1.63932	+	0.807732i
$540$		0			0
$541$	32.4037	+	18.7083i	1.39314	+	0.804331i	0.993662	−	0.112410i	$-0.0358570\pi$
$541$	32.4037	+	18.7083i	1.39314	+	0.804331i	0.399481	+	0.916741i	$0.369190\pi$
$542$	37.3757	+	19.2998i	1.60542	+	0.828998i
$543$		0			0
$544$	3.72855	−	3.53169i	0.159860	−	0.151420i
$545$		−	10.0281i		−	0.429556i
$546$		0			0
$547$	−31.1153			−1.33039			−0.665197	−	0.746668i	$-0.731652\pi$
$547$	−31.1153			−1.33039			−0.665197	+	0.746668i	$0.731652\pi$
$548$	24.8646	−	17.6565i	1.06216	−	0.754247i
$549$		0			0
$550$	5.89422	+	3.04362i	0.251330	+	0.129780i
$551$	−15.2722	+	26.4522i	−0.650617	+	1.12690i
$552$		0			0
$553$	−30.1792	+	18.7737i	−1.28335	+	0.798339i
$554$	−9.94978	+	6.38504i	−0.422726	+	0.271274i
$555$		0			0
$556$	15.2187	−	1.43289i	0.645417	−	0.0607682i
$557$	15.0725	+	26.1063i	0.638641	+	1.10616i	0.985731	+	0.168327i	$0.0538364\pi$
$557$	15.0725	+	26.1063i	0.638641	+	1.10616i	−0.347090	+	0.937832i	$0.612830\pi$
$558$		0			0
$559$		−	8.35521i		−	0.353388i
$560$	14.7379	+	16.0037i	0.622790	+	0.676279i
$561$		0			0
$562$	−0.237598	−	5.05819i	−0.0100225	−	0.213367i
$563$	−26.6333	+	15.3767i	−1.12246	+	0.648051i	−0.942027	−	0.335536i	$-0.891082\pi$
$563$	−26.6333	+	15.3767i	−1.12246	+	0.648051i	−0.180431	+	0.983588i	$0.557749\pi$
$564$		0			0
$565$	−4.25752	−	2.45808i	−0.179115	−	0.103412i
$566$	16.5841	+	25.8429i	0.697082	+	1.08626i
$567$		0			0
$568$	−4.02973	+	0.571227i	−0.169084	+	0.0239682i
$569$	38.4227	+	22.1833i	1.61076	+	0.929974i	0.989194	+	0.146613i	$0.0468372\pi$
$569$	38.4227	+	22.1833i	1.61076	+	0.929974i	0.621568	+	0.783361i	$0.286496\pi$
$570$		0			0
$571$	−16.2431	−	28.1338i	−0.679751	−	1.17736i	−0.975056	−	0.221961i	$-0.928754\pi$
$571$	−16.2431	−	28.1338i	−0.679751	−	1.17736i	0.295304	−	0.955403i	$-0.404579\pi$
$572$	−12.4770	−	17.5707i	−0.521690	−	0.734666i
$573$		0			0
$574$	39.2969	+	18.6813i	1.64022	+	0.779744i
$575$	0.543986			0.0226858
$576$		0			0
$577$	19.6946	+	34.1120i	0.819896	+	1.42010i	0.905758	+	0.423795i	$0.139302\pi$
$577$	19.6946	+	34.1120i	0.819896	+	1.42010i	−0.0858615	+	0.996307i	$0.527364\pi$
$578$	10.4958	−	20.3261i	0.436570	−	0.845453i
$579$		0			0
$580$	7.75228	−	16.9159i	0.321896	−	0.702393i
$581$	11.0070	+	5.88095i	0.456646	+	0.243983i
$582$		0			0
$583$	−34.8117	−	20.0985i	−1.44175	−	0.832396i
$584$	−7.27918	−	9.29413i	−0.301215	−	0.384594i
$585$		0			0
$586$	20.1422	−	0.946139i	0.832068	−	0.0390846i
$587$			24.9178i			1.02847i	0.857650	+	0.514233i	$0.171923\pi$
$587$			24.9178i			1.02847i	−0.857650	+	0.514233i	$0.828077\pi$
$588$		0			0
$589$			57.0064i			2.34891i
$590$	0.176030	+	3.74747i	0.00724702	+	0.154281i
$591$		0			0
$592$	−26.4937	−	9.24814i	−1.08889	−	0.380096i
$593$	−12.1405	−	7.00931i	−0.498550	−	0.287838i	0.229565	−	0.973293i	$-0.426270\pi$
$593$	−12.1405	−	7.00931i	−0.498550	−	0.287838i	−0.728114	+	0.685456i	$0.759603\pi$
$594$		0			0
$595$	−4.35521	−	2.32696i	−0.178546	−	0.0953961i
$596$	−13.9622	+	30.4663i	−0.571915	+	1.24795i
$597$		0			0
$598$	−1.57020	−	0.810811i	−0.0642103	−	0.0331565i
$599$	−12.2437	−	21.2067i	−0.500264	−	0.866483i	−1.00000		0.000304857i	$-0.999903\pi$
$599$	−12.2437	−	21.2067i	−0.500264	−	0.866483i	0.499736	−	0.866178i	$-0.333430\pi$
$600$		0			0
$601$	−17.0204			−0.694275			−0.347138	−	0.937814i	$-0.612846\pi$
$601$	−17.0204			−0.694275			−0.347138	+	0.937814i	$0.612846\pi$
$602$	−7.55031	+	15.8824i	−0.307728	+	0.647316i
$603$		0			0
$604$	13.3747	−	9.49741i	0.544207	−	0.386444i
$605$	−26.4551	−	45.8216i	−1.07555	−	1.86291i
$606$		0			0
$607$	21.1481	+	12.2099i	0.858375	+	0.495583i	0.863468	−	0.504404i	$-0.168288\pi$
$607$	21.1481	+	12.2099i	0.858375	+	0.495583i	−0.00509301	+	0.999987i	$0.501621\pi$
$608$	10.8771	−	36.5959i	0.441125	−	1.48416i
$609$		0			0
$610$	22.4758	−	14.4233i	0.910019	−	0.583984i
$611$	−13.6190	−	7.86294i	−0.550966	−	0.318101i
$612$		0			0
$613$	−34.0566	+	19.6626i	−1.37553	+	0.794164i	−0.991618	−	0.129205i	$-0.958758\pi$
$613$	−34.0566	+	19.6626i	−1.37553	+	0.794164i	−0.383915	+	0.923369i	$0.625424\pi$
$614$	−17.0479	+	0.800790i	−0.687998	+	0.0323173i
$615$		0			0
$616$	7.83946	+	44.6750i	0.315861	+	1.80001i
$617$		−	14.5542i		−	0.585932i	−0.956123	−	0.292966i	$-0.905358\pi$
$617$		−	14.5542i		−	0.585932i	0.956123	−	0.292966i	$-0.0946422\pi$
$618$		0			0
$619$	8.16451	+	14.1413i	0.328159	+	0.568389i	0.982147	−	0.188117i	$-0.0602383\pi$
$619$	8.16451	+	14.1413i	0.328159	+	0.568389i	−0.653987	+	0.756506i	$0.726905\pi$
$620$	−3.25540	−	34.5754i	−0.130740	−	1.38858i
$621$		0			0
$622$	−7.45608	−	11.6188i	−0.298962	−	0.465871i
$623$	−10.5891	+	6.58719i	−0.424242	+	0.263910i
$624$		0			0
$625$	10.2658	−	17.7809i	0.410632	−	0.711236i
$626$	18.3249	−	35.4877i	0.732410	−	1.41837i
$627$		0			0
$628$	−3.53807	+	2.51240i	−0.141184	+	0.100256i
$629$	6.36899			0.253948
$630$		0			0
$631$			32.9828i			1.31302i	0.754315	+	0.656512i	$0.227969\pi$
$631$			32.9828i			1.31302i	−0.754315	+	0.656512i	$0.772031\pi$
$632$	−35.2462	−	14.1917i	−1.40202	−	0.564514i
$633$		0			0
$634$	−16.5835	+	32.1154i	−0.658617	+	1.27547i
$635$	7.23466	+	4.17693i	0.287099	+	0.165756i
$636$		0			0
$637$	10.3445	−	6.91702i	0.409863	−	0.274062i
$638$	32.6493	−	20.9519i	1.29260	−	0.829494i
$639$		0			0
$640$	−4.50734	+	22.8172i	−0.178168	+	0.901930i
$641$	−11.8256	+	6.82749i	−0.467081	+	0.269669i	−0.715017	−	0.699107i	$-0.753581\pi$
$641$	−11.8256	+	6.82749i	−0.467081	+	0.269669i	0.247936	+	0.968776i	$0.420248\pi$
$642$		0			0
$643$	46.5621			1.83623			0.918115	−	0.396315i	$-0.129711\pi$
$643$	46.5621			1.83623			0.918115	+	0.396315i	$0.129711\pi$
$644$	2.25208	+	2.96020i	0.0887445	+	0.116648i
$645$		0			0
$646$	0.406578	+	8.65559i	0.0159966	+	0.340550i
$647$	−17.7299	−	30.7090i	−0.697033	−	1.20730i	−0.969491	−	0.245128i	$-0.921170\pi$
$647$	−17.7299	−	30.7090i	−0.697033	−	1.20730i	0.272458	−	0.962168i	$-0.412163\pi$
$648$		0			0
$649$	−3.91073	+	6.77358i	−0.153509	+	0.265886i
$650$	1.63746	−	1.05080i	0.0642265	−	0.0412159i
$651$		0			0
$652$	−15.4887	+	33.7971i	−0.606583	+	1.32360i
$653$	10.6086	−	18.3747i	0.415148	−	0.719057i	−0.580296	−	0.814405i	$-0.697063\pi$
$653$	10.6086	−	18.3747i	0.415148	−	0.719057i	0.995444	+	0.0953486i	$0.0303966\pi$
$654$		0			0
$655$	0.427664	−	0.246912i	0.0167102	−	0.00964766i
$656$	8.68224	+	45.6981i	0.338985	+	1.78421i
$657$		0			0
$658$	18.7828	+	27.2536i	0.732230	+	1.06246i
$659$			7.62196i			0.296909i	0.988919	+	0.148455i	$0.0474299\pi$
$659$			7.62196i			0.296909i	−0.988919	+	0.148455i	$0.952570\pi$
$660$		0			0
$661$	−35.1044	+	20.2675i	−1.36540	+	0.788315i	−0.990337	−	0.138683i	$-0.955713\pi$
$661$	−35.1044	+	20.2675i	−1.36540	+	0.788315i	−0.375065	+	0.926998i	$0.622380\pi$
$662$	7.57121	−	14.6623i	0.294264	−	0.569866i
$663$		0			0
$664$	1.87244	+	13.2091i	0.0726647	+	0.512614i
$665$	−36.6880	+	1.20725i	−1.42270	+	0.0468151i
$666$		0			0
$667$	1.59062	−	2.75504i	0.0615891	−	0.106675i
$668$	−45.0337	+	4.24008i	−1.74241	+	0.164054i
$669$		0			0
$670$	3.26696	−	0.153459i	0.126214	−	0.00592862i
$671$	55.6769			2.14938
$672$		0			0
$673$	25.1754			0.970440			0.485220	−	0.874392i	$-0.338739\pi$
$673$	25.1754			0.970440			0.485220	+	0.874392i	$0.338739\pi$
$674$	−31.8491	+	1.49605i	−1.22678	+	0.0576255i
$675$		0			0
$676$	19.5928	−	1.84473i	0.753569	−	0.0709512i
$677$	−18.0389	+	31.2442i	−0.693290	+	1.20081i	0.277464	+	0.960736i	$0.410506\pi$
$677$	−18.0389	+	31.2442i	−0.693290	+	1.20081i	−0.970754	+	0.240077i	$0.922827\pi$
$678$		0			0
$679$	15.2127	−	28.4726i	0.583810	−	1.09268i
$680$	−0.740882	−	5.22656i	−0.0284115	−	0.200429i
$681$		0			0
$682$	33.2194	−	64.3321i	1.27204	−	2.46341i
$683$	−2.69000	+	1.55307i	−0.102930	+	0.0594268i	−0.550581	−	0.834781i	$-0.685594\pi$
$683$	−2.69000	+	1.55307i	−0.102930	+	0.0594268i	0.447651	+	0.894208i	$0.352261\pi$
$684$		0			0
$685$		−	31.3459i		−	1.19767i
$686$	−25.9144	+	3.80057i	−0.989416	+	0.145106i
$687$		0			0
$688$	−18.4695	+	3.50904i	−0.704143	+	0.133781i
$689$	−10.2101	+	5.89482i	−0.388975	+	0.224575i
$690$		0			0
$691$	3.31148	−	5.73566i	0.125975	−	0.218195i	−0.796139	−	0.605114i	$-0.793128\pi$
$691$	3.31148	−	5.73566i	0.125975	−	0.218195i	0.922114	+	0.386919i	$0.126461\pi$
$692$	−0.907153	+	1.97945i	−0.0344848	+	0.0752476i
$693$		0			0
$694$	−9.54423	+	6.12479i	−0.362294	+	0.232494i
$695$	7.85605	−	13.6071i	0.297997	−	0.516146i
$696$		0			0
$697$	−5.27873	−	9.14302i	−0.199946	−	0.346317i
$698$	−1.23189	−	26.2256i	−0.0466279	−	0.992655i
$699$		0			0
$700$	−4.06221	+	0.517746i	−0.153537	+	0.0195690i
$701$	30.4248			1.14913			0.574565	−	0.818459i	$-0.305171\pi$
$701$	30.4248			1.14913			0.574565	+	0.818459i	$0.305171\pi$
$702$		0			0
$703$	41.0034	−	23.6734i	1.54647	−	0.892857i
$704$	−33.6005	+	34.9603i	−1.26637	+	1.31761i
$705$		0			0
$706$	22.1458	−	14.2115i	0.833466	−	0.534858i
$707$	27.5365	−	0.906112i	1.03562	−	0.0340778i
$708$		0			0
$709$	4.73691	+	2.73486i	0.177899	+	0.102710i	0.586305	−	0.810090i	$-0.300582\pi$
$709$	4.73691	+	2.73486i	0.177899	+	0.102710i	−0.408406	+	0.912800i	$0.633915\pi$
$710$	−1.91943	+	3.71714i	−0.0720350	+	0.139502i
$711$		0			0
$712$	−12.3669	−	4.97947i	−0.463471	−	0.186614i
$713$		−	5.93730i		−	0.222354i
$714$		0			0
$715$	−22.1507			−0.828391
$716$	9.80251	−	6.96081i	0.366337	−	0.260138i
$717$		0			0
$718$	−22.0547	+	42.7108i	−0.823076	+	1.59395i
$719$	−4.25219	+	7.36501i	−0.158580	+	0.274669i	−0.934357	−	0.356339i	$-0.884025\pi$
$719$	−4.25219	+	7.36501i	−0.158580	+	0.274669i	0.775777	+	0.631007i	$0.217358\pi$
$720$		0			0
$721$	14.6656	−	9.12311i	0.546176	−	0.339762i
$722$	20.2780	+	31.5991i	0.754669	+	1.17600i
$723$		0			0
$724$	1.36651	+	14.5136i	0.0507859	+	0.539395i
$725$	1.75123	+	3.03322i	0.0650391	+	0.112651i
$726$		0			0
$727$			31.9931i			1.18656i	0.804997	+	0.593280i	$0.202167\pi$
$727$			31.9931i			1.18656i	−0.804997	+	0.593280i	$0.797833\pi$
$728$	12.4972	+	4.56026i	0.463176	+	0.169014i
$729$		0			0
$730$	−12.1211	+	0.569363i	−0.448622	+	0.0210731i
$731$	3.69527	−	2.13347i	0.136675	−	0.0789091i
$732$		0			0
$733$	12.6276	+	7.29054i	0.466411	+	0.269282i	0.714736	−	0.699394i	$-0.246547\pi$
$733$	12.6276	+	7.29054i	0.466411	+	0.269282i	−0.248325	+	0.968677i	$0.579880\pi$
$734$	−6.06091	+	3.88945i	−0.223712	+	0.143562i
$735$		0			0
$736$	−1.13287	+	3.81151i	−0.0417581	+	0.140494i
$737$	5.90505	+	3.40928i	0.217515	+	0.125583i
$738$		0			0
$739$	12.3199	+	21.3387i	0.453194	+	0.784955i	0.998582	−	0.0532282i	$-0.0169511\pi$
$739$	12.3199	+	21.3387i	0.453194	+	0.784955i	−0.545388	+	0.838184i	$0.683618\pi$
$740$	−23.5175	+	16.6999i	−0.864519	+	0.613899i
$741$		0			0
$742$	24.7353	−	1.97888i	0.908061	−	0.0726471i
$743$	−44.0203			−1.61495			−0.807474	−	0.589903i	$-0.799166\pi$
$743$	−44.0203			−1.61495			−0.807474	+	0.589903i	$0.799166\pi$
$744$		0			0
$745$	17.2237	+	29.8323i	0.631028	+	1.09297i
$746$	−21.4555	−	11.0790i	−0.785540	−	0.405632i
$747$		0			0
$748$	4.58506	−	10.0048i	0.167646	−	0.365813i
$749$	20.7671	−	12.9187i	0.758812	−	0.472038i
$750$		0			0
$751$	−7.28019	−	4.20322i	−0.265658	−	0.153378i	0.361255	−	0.932467i	$-0.382348\pi$
$751$	−7.28019	−	4.20322i	−0.265658	−	0.153378i	−0.626913	+	0.779089i	$0.715682\pi$
$752$	−11.6616	+	33.4076i	−0.425253	+	1.21825i
$753$		0			0
$754$	−0.533872	−	11.3655i	−0.0194425	−	0.413909i
$755$		−	16.8610i		−	0.613634i
$756$		0			0
$757$		−	44.5161i		−	1.61797i	−0.587831	−	0.808983i	$-0.700018\pi$
$757$		−	44.5161i		−	1.61797i	0.587831	−	0.808983i	$-0.299982\pi$
$758$	−15.9449	+	0.748978i	−0.579145	+	0.0272041i
$759$		0			0
$760$	−24.1967	−	30.8946i	−0.877708	−	1.12067i
$761$	−21.8857	−	12.6357i	−0.793357	−	0.458045i	0.0477862	−	0.998858i	$-0.484783\pi$
$761$	−21.8857	−	12.6357i	−0.793357	−	0.458045i	−0.841143	+	0.540813i	$0.818117\pi$
$762$		0			0
$763$	0.424459	+	12.8992i	0.0153664	+	0.466982i
$764$	3.68730	−	8.04588i	0.133402	−	0.291090i
$765$		0			0
$766$	−13.3423	+	25.8385i	−0.482078	+	0.933584i
$767$	1.14700	+	1.98666i	0.0414158	+	0.0717343i
$768$		0			0
$769$	−12.1185			−0.437005			−0.218502	−	0.975836i	$-0.570117\pi$
$769$	−12.1185			−0.437005			−0.218502	+	0.975836i	$0.570117\pi$
$770$	42.1062	+	20.0168i	1.51740	+	0.721357i
$771$		0			0
$772$	2.92907	+	4.12485i	0.105420	+	0.148457i
$773$	9.15261	+	15.8528i	0.329196	+	0.570185i	0.982353	−	0.187038i	$-0.0598888\pi$
$773$	9.15261	+	15.8528i	0.329196	+	0.570185i	−0.653156	+	0.757223i	$0.726555\pi$
$774$		0			0
$775$	5.66105	+	3.26841i	0.203351	+	0.117405i
$776$	34.1691	−	4.84358i	1.22660	−	0.173874i
$777$		0			0
$778$	−10.5844	−	16.4936i	−0.379468	−	0.591324i
$779$	−67.9687	−	39.2417i	−2.43523	−	1.40598i
$780$		0			0
$781$	−7.55330	+	4.36090i	−0.270278	+	0.156045i
$782$	−0.0423457	−	0.901493i	−0.00151428	−	0.0322373i
$783$		0			0
$784$	−19.6348	−	19.9618i	−0.701244	−	0.712922i
$785$			4.46033i			0.159196i
$786$		0			0
$787$	11.0540	+	19.1461i	0.394033	+	0.682485i	0.992977	−	0.118306i	$-0.0377462\pi$
$787$	11.0540	+	19.1461i	0.394033	+	0.682485i	−0.598944	+	0.800791i	$0.704413\pi$
$788$	23.1495	−	2.17961i	0.824667	−	0.0776453i
$789$		0			0
$790$	−32.8692	+	21.0931i	−1.16944	+	0.750458i
$791$	5.58051	+	2.98163i	0.198420	+	0.106015i
$792$		0			0
$793$	8.16491	−	14.1420i	0.289944	−	0.502198i
$794$	−43.4758	−	22.4498i	−1.54290	−	0.796712i
$795$		0			0
$796$	31.6469	−	22.4726i	1.12169	−	0.796521i
$797$	11.9294			0.422563			0.211281	−	0.977425i	$-0.432236\pi$
$797$	11.9294			0.422563			0.211281	+	0.977425i	$0.432236\pi$
$798$		0			0
$799$		−	8.03107i		−	0.284119i
$800$	−3.01054	−	3.17835i	−0.106439	−	0.112372i
$801$		0			0
$802$	−17.5928	−	9.08443i	−0.621222	−	0.320783i
$803$	−21.9090	−	12.6492i	−0.773151	−	0.446379i
$804$		0			0
$805$	3.82111	−	0.125737i	0.134676	−	0.00443164i
$806$	−11.4689	−	17.8720i	−0.403976	−	0.629514i
$807$		0			0
$808$	18.1611	+	23.1882i	0.638904	+	0.815759i
$809$	13.1494	−	7.59184i	0.462310	−	0.266915i	−0.250705	−	0.968064i	$-0.580662\pi$
$809$	13.1494	−	7.59184i	0.462310	−	0.266915i	0.713015	+	0.701149i	$0.247329\pi$
$810$		0			0
$811$	31.1176			1.09269			0.546344	−	0.837561i	$-0.316019\pi$
$811$	31.1176			1.09269			0.546344	+	0.837561i	$0.316019\pi$
$812$	−9.25580	+	22.0871i	−0.324815	+	0.775105i
$813$		0			0
$814$	−60.0679	+	2.82156i	−2.10538	+	0.0988957i
$815$	19.1067	+	33.0938i	0.669279	+	1.15923i
$816$		0			0
$817$	15.8601	−	27.4704i	0.554873	−	0.961069i
$818$	4.22207	+	6.57923i	0.147621	+	0.230037i
$819$		0			0
$820$	43.4652	+	19.9194i	1.51787	+	0.695616i
$821$	−2.78548	+	4.82459i	−0.0972139	+	0.168379i	−0.910530	−	0.413442i	$-0.864326\pi$
$821$	−2.78548	+	4.82459i	−0.0972139	+	0.168379i	0.813317	+	0.581821i	$0.197660\pi$
$822$		0			0
$823$	−8.34067	+	4.81549i	−0.290737	+	0.167857i	−0.638274	−	0.769809i	$-0.720351\pi$
$823$	−8.34067	+	4.81549i	−0.290737	+	0.167857i	0.347537	+	0.937666i	$0.387018\pi$
$824$	17.1279	+	6.89646i	0.596680	+	0.240250i
$825$		0			0
$826$	−0.385047	−	4.81294i	−0.0133975	−	0.167464i
$827$		−	52.4810i		−	1.82494i	−0.409139	−	0.912472i	$-0.634171\pi$
$827$		−	52.4810i		−	1.82494i	0.409139	−	0.912472i	$-0.365829\pi$
$828$		0			0
$829$	24.0623	−	13.8924i	0.835717	−	0.482501i	−0.0200891	−	0.999798i	$-0.506395\pi$
$829$	24.0623	−	13.8924i	0.835717	−	0.482501i	0.855806	+	0.517297i	$0.173062\pi$
$830$	12.1845	+	6.29175i	0.422930	+	0.218390i
$831$		0			0
$832$	3.95253	+	13.6614i	0.137029	+	0.473625i
$833$	5.70062	+	2.80884i	0.197515	+	0.0973205i
$834$		0			0
$835$	−23.2469	+	40.2647i	−0.804491	+	1.39342i
$836$	−7.66912	−	81.4533i	−0.265242	−	2.81712i
$837$		0			0
$838$	−0.870082	−	18.5231i	−0.0300565	−	0.639869i
$839$	−22.6418			−0.781681			−0.390841	−	0.920458i	$-0.627816\pi$
$839$	−22.6418			−0.781681			−0.390841	+	0.920458i	$0.627816\pi$
$840$		0			0
$841$	−8.51751			−0.293707
$842$	−1.46484	−	31.1847i	−0.0504816	−	1.07470i
$843$		0			0
$844$	11.4288	−	1.07606i	0.393395	−	0.0370395i
$845$	10.1140	−	17.5180i	0.347932	−	0.602637i
$846$		0			0
$847$	35.9688	+	57.8208i	1.23590	+	1.98674i
$848$	17.3188	+	20.0941i	0.594730	+	0.690035i
$849$		0			0
$850$	0.882859	+	0.455885i	0.0302818	+	0.0156367i
$851$	−4.27057	+	2.46562i	−0.146393	+	0.0845202i
$852$		0			0
$853$		−	26.2579i		−	0.899053i	−0.893267	−	0.449526i	$-0.851593\pi$
$853$		−	26.2579i		−	0.899053i	0.893267	−	0.449526i	$-0.148407\pi$
$854$	−28.3003	+	19.5041i	−0.968415	+	0.667418i
$855$		0			0
$856$	24.2538	+	9.76565i	0.828978	+	0.333783i
$857$	23.8430	−	13.7658i	0.814461	−	0.470229i	−0.0340416	−	0.999420i	$-0.510838\pi$
$857$	23.8430	−	13.7658i	0.814461	−	0.470229i	0.848503	+	0.529191i	$0.177505\pi$
$858$		0			0
$859$	4.71373	−	8.16443i	0.160831	−	0.278567i	−0.774336	−	0.632774i	$-0.781916\pi$
$859$	4.71373	−	8.16443i	0.160831	−	0.278567i	0.935167	+	0.354208i	$0.115249\pi$
$860$	−8.05070	+	17.5670i	−0.274526	+	0.599031i
$861$		0			0
$862$	19.7767	+	30.8180i	0.673597	+	1.04966i
$863$	−2.57590	+	4.46158i	−0.0876846	+	0.151874i	−0.906532	−	0.422137i	$-0.861280\pi$
$863$	−2.57590	+	4.46158i	−0.0876846	+	0.151874i	0.818847	+	0.574011i	$0.194613\pi$
$864$		0			0
$865$	1.11906	+	1.93827i	0.0380491	+	0.0659030i
$866$	45.8456	−	2.15350i	1.55790	−	0.0731789i
$867$		0			0
$868$	5.65091	+	44.3368i	0.191804	+	1.50489i
$869$	−81.4234			−2.76210
$870$		0			0
$871$	1.73193	−	0.999930i	0.0586842	−	0.0338813i
$872$	−10.8623	+	8.50737i	−0.367844	+	0.288096i
$873$		0			0
$874$	−3.62344	−	5.64639i	−0.122565	−	0.190992i
$875$	−14.7992	+	27.6986i	−0.500303	+	0.936382i
$876$		0			0
$877$	−33.4832	−	19.3315i	−1.13065	−	0.652779i	−0.186550	−	0.982446i	$-0.559730\pi$
$877$	−33.4832	−	19.3315i	−1.13065	−	0.652779i	−0.944098	+	0.329666i	$0.893064\pi$
$878$	17.0376	+	8.79774i	0.574990	+	0.296909i
$879$		0			0
$880$	9.30293	+	48.9650i	0.313602	+	1.65061i
$881$			19.8610i			0.669134i	0.942372	+	0.334567i	$0.108590\pi$
$881$			19.8610i			0.669134i	−0.942372	+	0.334567i	$0.891410\pi$
$882$		0			0
$883$	−16.9587			−0.570707			−0.285353	−	0.958422i	$-0.592111\pi$
$883$	−16.9587			−0.570707			−0.285353	+	0.958422i	$0.592111\pi$
$884$	−1.86885	−	2.63180i	−0.0628564	−	0.0885171i
$885$		0			0
$886$	−5.49377	−	2.83683i	−0.184567	−	0.0953053i
$887$	1.65637	−	2.86892i	0.0556154	−	0.0963287i	−0.836877	−	0.547391i	$-0.815621\pi$
$887$	1.65637	−	2.86892i	0.0556154	−	0.0963287i	0.892493	+	0.451062i	$0.148955\pi$
$888$		0			0
$889$	−9.48277	−	5.06659i	−0.318042	−	0.169928i
$890$	−11.5329	+	7.40099i	−0.386585	+	0.248082i
$891$		0			0
$892$	0.977536	+	10.3824i	0.0327303	+	0.347627i
$893$	−29.8512	−	51.7039i	−0.998934	−	1.73020i
$894$		0			0
$895$		−	12.3577i		−	0.413072i
$896$	4.83202	−	29.5407i	0.161427	−	0.986885i
$897$		0			0
$898$	−0.912870	−	19.4340i	−0.0304629	−	0.648520i
$899$	33.1060	−	19.1137i	1.10415	−	0.637479i
$900$		0			0
$901$	−5.21422	−	3.01043i	−0.173711	−	0.100292i
$902$	53.8357	+	83.8920i	1.79253	+	2.79330i
$903$		0			0
$904$	0.949322	+	6.69700i	0.0315740	+	0.222739i
$905$	12.9767	+	7.49208i	0.431359	+	0.249045i
$906$		0			0
$907$	8.58088	+	14.8625i	0.284923	+	0.493502i	0.972591	−	0.232524i	$-0.0746985\pi$
$907$	8.58088	+	14.8625i	0.284923	+	0.493502i	−0.687667	+	0.726026i	$0.741365\pi$
$908$	11.4609	−	8.13845i	0.380344	−	0.270084i
$909$		0			0
$910$	11.2591	−	7.75961i	0.373236	−	0.257229i
$911$	−12.8972			−0.427303			−0.213652	−	0.976910i	$-0.568536\pi$
$911$	−12.8972			−0.427303			−0.213652	+	0.976910i	$0.568536\pi$
$912$		0			0
$913$	14.2947	+	24.7592i	0.473086	+	0.819409i
$914$	−7.63298	+	14.7819i	−0.252476	+	0.488942i
$915$		0			0
$916$	−46.2377	−	21.1900i	−1.52774	−	0.700138i
$917$	−0.539656	+	0.335706i	−0.0178210	+	0.0110860i
$918$		0			0
$919$	−31.2492	−	18.0418i	−1.03082	−	0.595142i	−0.113598	−	0.993527i	$-0.536238\pi$
$919$	−31.2492	−	18.0418i	−1.03082	−	0.595142i	−0.917219	+	0.398384i	$0.869571\pi$
$920$	2.52013	+	3.21772i	0.0830861	+	0.106085i
$921$		0			0
$922$	−15.7687	+	0.740701i	−0.519314	+	0.0243937i
$923$			2.55807i			0.0842000i
$924$		0			0
$925$		−	5.42916i		−	0.178510i
$926$	1.06744	+	22.7246i	0.0350782	+	0.746775i
$927$		0			0
$928$	−24.8997	+	5.95347i	−0.817373	+	0.195432i
$929$	32.7215	+	18.8918i	1.07356	+	0.619818i	0.929151	−	0.369700i	$-0.120540\pi$
$929$	32.7215	+	18.8918i	1.07356	+	0.619818i	0.144406	+	0.989519i	$0.453873\pi$
$930$		0			0
$931$	47.1408	−	3.10578i	1.54498	−	0.101788i
$932$	−21.0355	−	9.64024i	−0.689040	−	0.315777i
$933$		0			0
$934$	−27.3819	−	14.1393i	−0.895963	−	0.462651i
$935$	−5.65610	−	9.79664i	−0.184974	−	0.320385i
$936$		0			0
$937$	26.6280			0.869899			0.434949	−	0.900455i	$-0.356766\pi$
$937$	26.6280			0.869899			0.434949	+	0.900455i	$0.356766\pi$
$938$	−4.19581	+	0.335675i	−0.136998	+	0.0109602i
$939$		0			0
$940$	21.0579	+	29.6547i	0.686834	+	0.967229i
$941$	−5.35475	−	9.27469i	−0.174560	−	0.302346i	0.765449	−	0.643496i	$-0.222517\pi$
$941$	−5.35475	−	9.27469i	−0.174560	−	0.302346i	−0.940009	+	0.341150i	$0.889184\pi$
$942$		0			0
$943$	7.07904	+	4.08708i	0.230525	+	0.133094i
$944$	3.90987	−	3.36985i	0.127256	−	0.109679i
$945$		0			0
$946$	−33.9061	+	21.7584i	−1.10238	+	0.707428i
$947$	24.4571	+	14.1203i	0.794749	+	0.458849i	0.841632	−	0.540052i	$-0.181595\pi$
$947$	24.4571	+	14.1203i	0.794749	+	0.458849i	−0.0468825	+	0.998900i	$0.514929\pi$
$948$		0			0
$949$	−6.42582	+	3.70995i	−0.208591	+	0.120430i
$950$	7.37833	−	0.346582i	0.239385	−	0.0112446i
$951$		0			0
$952$	1.17422	+	6.69159i	0.0380568	+	0.216876i
$953$		−	21.4320i		−	0.694250i	−0.937819	−	0.347125i	$-0.887158\pi$
$953$		−	21.4320i		−	0.694250i	0.937819	−	0.347125i	$-0.112842\pi$
$954$		0			0
$955$	−4.54863	−	7.87846i	−0.147190	−	0.254941i
$956$	34.2531	−	3.22505i	1.10782	−	0.104306i
$957$		0			0
$958$	−16.6529	−	25.9502i	−0.538031	−	0.838412i
$959$	1.32678	+	40.3204i	0.0428439	+	1.30201i
$960$		0			0
$961$	20.1729	−	34.9405i	0.650738	−	1.12711i
$962$	−8.09216	+	15.6711i	−0.260902	+	0.505258i
$963$		0			0
$964$	15.8546	+	22.3271i	0.510643	+	0.719109i
$965$	5.20005			0.167396
$966$		0			0
$967$		−	16.5003i		−	0.530613i	−0.964164	−	0.265307i	$-0.914527\pi$
$967$		−	16.5003i		−	0.530613i	0.964164	−	0.265307i	$-0.0854732\pi$
$968$	−27.1900	+	67.5287i	−0.873921	+	2.17045i
$969$		0			0
$970$	16.2754	−	31.5186i	0.522570	−	1.01200i
$971$	−20.4371	−	11.7994i	−0.655858	−	0.378660i	0.134839	−	0.990868i	$-0.456948\pi$
$971$	−20.4371	−	11.7994i	−0.655858	−	0.378660i	−0.790697	+	0.612208i	$0.790282\pi$
$972$		0			0
$973$	−9.52933	+	17.8354i	−0.305496	+	0.571776i
$974$	6.92622	−	4.44474i	0.221930	−	0.142419i
$975$		0			0
$976$	−34.6906	−	12.1094i	−1.11042	−	0.387613i
$977$	26.7355	−	15.4358i	0.855346	−	0.493834i	−0.00710519	−	0.999975i	$-0.502262\pi$
$977$	26.7355	−	15.4358i	0.855346	−	0.493834i	0.862451	+	0.506141i	$0.168928\pi$
$978$		0			0
$979$	−28.5693			−0.913077
$980$	−28.4144	+	4.57573i	−0.907665	+	0.146166i
$981$		0			0
$982$	−1.17323	−	24.9767i	−0.0374393	−	0.797040i
$983$	9.83164	+	17.0289i	0.313581	+	0.543138i	0.979135	−	0.203212i	$-0.0651381\pi$
$983$	9.83164	+	17.0289i	0.313581	+	0.543138i	−0.665554	+	0.746350i	$0.731805\pi$
$984$		0			0
$985$	11.9500	−	20.6980i	0.380759	−	0.659494i
$986$	4.89033	−	3.13826i	0.155740	−	0.0999425i
$987$		0			0
$988$	−21.8140	−	9.99701i	−0.693995	−	0.318047i
$989$	−1.65185	+	2.86109i	−0.0525257	+	0.0909773i
$990$		0			0
$991$	−28.9635	+	16.7221i	−0.920057	+	0.531195i	−0.883653	−	0.468142i	$-0.844924\pi$
$991$	−28.9635	+	16.7221i	−0.920057	+	0.531195i	−0.0364036	+	0.999337i	$0.511590\pi$
$992$	−34.6899	+	32.8584i	−1.10141	+	1.04326i
$993$		0			0
$994$	2.31164	−	4.86262i	0.0733207	−	0.154233i
$995$		−	39.8962i		−	1.26479i
$996$		0			0
$997$	−7.84528	+	4.52948i	−0.248463	+	0.143450i	−0.619060	−	0.785344i	$-0.712486\pi$
$997$	−7.84528	+	4.52948i	−0.248463	+	0.143450i	0.370597	+	0.928794i	$0.379153\pi$
$998$	−6.22817	+	12.0614i	−0.197149	+	0.381796i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.1	✓	48
3.2	odd	2	inner	504.2.bm.c.107.24	yes	48
4.3	odd	2		2016.2.bu.c.1871.20		48
7.4	even	3	inner	504.2.bm.c.179.16	yes	48
8.3	odd	2	inner	504.2.bm.c.107.9	yes	48
8.5	even	2		2016.2.bu.c.1871.6		48
12.11	even	2		2016.2.bu.c.1871.5		48
21.11	odd	6	inner	504.2.bm.c.179.9	yes	48
24.5	odd	2		2016.2.bu.c.1871.19		48
24.11	even	2	inner	504.2.bm.c.107.16	yes	48
28.11	odd	6		2016.2.bu.c.431.19		48
56.11	odd	6	inner	504.2.bm.c.179.24	yes	48
56.53	even	6		2016.2.bu.c.431.5		48
84.11	even	6		2016.2.bu.c.431.6		48
168.11	even	6	inner	504.2.bm.c.179.1	yes	48
168.53	odd	6		2016.2.bu.c.431.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.1	✓	48	1.1	even	1	trivial
504.2.bm.c.107.9	yes	48	8.3	odd	2	inner
504.2.bm.c.107.16	yes	48	24.11	even	2	inner
504.2.bm.c.107.24	yes	48	3.2	odd	2	inner
504.2.bm.c.179.1	yes	48	168.11	even	6	inner
504.2.bm.c.179.9	yes	48	21.11	odd	6	inner
504.2.bm.c.179.16	yes	48	7.4	even	3	inner
504.2.bm.c.179.24	yes	48	56.11	odd	6	inner
2016.2.bu.c.431.5		48	56.53	even	6
2016.2.bu.c.431.6		48	84.11	even	6
2016.2.bu.c.431.19		48	28.11	odd	6
2016.2.bu.c.431.20		48	168.53	odd	6
2016.2.bu.c.1871.5		48	12.11	even	2
2016.2.bu.c.1871.6		48	8.5	even	2
2016.2.bu.c.1871.19		48	24.5	odd	2
2016.2.bu.c.1871.20		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41266 + 0.0663565i) q^{2} +(1.99119 - 0.187478i) q^{4} +(1.02787 - 1.78033i) q^{5} +(-1.24680 + 2.33356i) q^{7} +(-2.80043 + 0.396971i) q^{8} +O(q^{10})\)	\(q+(-1.41266 + 0.0663565i) q^{2} +(1.99119 - 0.187478i) q^{4} +(1.02787 - 1.78033i) q^{5} +(-1.24680 + 2.33356i) q^{7} +(-2.80043 + 0.396971i) q^{8} +(-1.33390 + 2.58320i) q^{10} +(-5.24912 + 3.03058i) q^{11} +1.77772i q^{13} +(1.60646 - 3.37924i) q^{14} +(3.92970 - 0.746610i) q^{16} +(-0.786233 + 0.453932i) q^{17} +(-3.37450 + 5.84481i) q^{19} +(1.71292 - 3.73769i) q^{20} +(7.21410 - 4.62948i) q^{22} +(0.351459 - 0.608746i) q^{23} +(0.386948 + 0.670213i) q^{25} +(-0.117963 - 2.51130i) q^{26} +(-2.04514 + 4.88031i) q^{28} +4.52576 q^{29} +(7.31501 - 4.22332i) q^{31} +(-5.50178 + 1.31546i) q^{32} +(1.08056 - 0.693421i) q^{34} +(2.87294 + 4.61833i) q^{35} +(-6.07548 - 3.50768i) q^{37} +(4.37917 - 8.48062i) q^{38} +(-2.17175 + 5.39373i) q^{40} +11.6289i q^{41} -4.69997 q^{43} +(-9.88385 + 7.01857i) q^{44} +(-0.456097 + 0.883270i) q^{46} +(-4.42306 + 7.66096i) q^{47} +(-3.89096 - 5.81897i) q^{49} +(-0.591097 - 0.921104i) q^{50} +(0.333282 + 3.53978i) q^{52} +(3.31595 + 5.74340i) q^{53} +12.4602i q^{55} +(2.56524 - 7.02990i) q^{56} +(-6.39334 + 0.300314i) q^{58} +(1.11754 - 0.645211i) q^{59} +(-7.95517 - 4.59292i) q^{61} +(-10.0533 + 6.45150i) q^{62} +(7.68483 - 2.22338i) q^{64} +(3.16492 + 1.82727i) q^{65} +(-0.562480 - 0.974244i) q^{67} +(-1.48044 + 1.05127i) q^{68} +(-4.36494 - 6.33347i) q^{70} +1.43897 q^{71} +(2.08692 + 3.61465i) q^{73} +(8.81532 + 4.55200i) q^{74} +(-5.62351 + 12.2708i) q^{76} +(-0.527404 - 16.0277i) q^{77} +(11.6339 + 6.71681i) q^{79} +(2.71003 - 7.76359i) q^{80} +(-0.771653 - 16.4276i) q^{82} -4.71682i q^{83} +1.86634i q^{85} +(6.63944 - 0.311874i) q^{86} +(13.4967 - 10.5707i) q^{88} +(4.08201 + 2.35675i) q^{89} +(-4.14840 - 2.21646i) q^{91} +(0.585697 - 1.27802i) q^{92} +(5.73991 - 11.1158i) q^{94} +(6.93713 + 12.0155i) q^{95} -12.2014 q^{97} +(5.88271 + 7.96201i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

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