LMFDB - Embedded newform 504.2.cj.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.2
Root			$-1.01214 + 0.987711i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01214 - 0.987711i) q^{2} +(0.0488544 + 1.99940i) q^{4} +(2.26303 - 1.30656i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.92538 - 2.07193i) q^{8} +O(q^{10})$	\(q+(-1.01214 - 0.987711i) q^{2} +(0.0488544 + 1.99940i) q^{4} +(2.26303 - 1.30656i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.92538 - 2.07193i) q^{8} +(-3.58101 - 0.912798i) q^{10} +(1.87476 + 1.08239i) q^{11} +6.50490i q^{13} +(-3.00745 - 2.22603i) q^{14} +(-3.99523 + 0.195359i) q^{16} +(0.797521 - 1.38135i) q^{17} +(-1.27620 + 0.736813i) q^{19} +(2.72291 + 4.46088i) q^{20} +(-0.828427 - 2.94725i) q^{22} +(-1.92538 - 3.33486i) q^{23} +(0.914214 - 1.58346i) q^{25} +(6.42496 - 6.58387i) q^{26} +(0.845288 + 5.22355i) q^{28} +7.39104i q^{29} +(1.79289 - 3.10538i) q^{31} +(4.23669 + 3.74840i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(5.46345 - 4.23671i) q^{35} +(6.69064 - 3.86285i) q^{37} +(2.01945 + 0.514756i) q^{38} +(1.65010 - 7.20448i) q^{40} +7.70154 q^{41} -2.69442i q^{43} +(-2.07255 + 3.80128i) q^{44} +(-1.34512 + 5.27707i) q^{46} +(-5.77615 - 10.0046i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.48932 + 0.699709i) q^{50} +(-13.0059 + 0.317793i) q^{52} +(-8.66386 - 5.00208i) q^{53} +5.65685 q^{55} +(4.30381 - 6.12186i) q^{56} +(7.30021 - 7.48076i) q^{58} +(-8.11475 - 4.68506i) q^{59} +(-3.60963 + 2.08402i) q^{61} +(-4.88188 + 1.37222i) q^{62} +(-0.585786 - 7.97852i) q^{64} +(8.49906 + 14.7208i) q^{65} +(9.99062 + 5.76809i) q^{67} +(2.80083 + 1.52708i) q^{68} +(-9.71442 - 1.10816i) q^{70} -14.7424 q^{71} +(1.50000 - 2.59808i) q^{73} +(-10.5872 - 2.69868i) q^{74} +(-1.53553 - 2.51564i) q^{76} +(5.30262 + 2.16478i) q^{77} +(-3.62132 - 6.27231i) q^{79} +(-8.78608 + 5.66212i) q^{80} +(-7.79504 - 7.60689i) q^{82} +7.20533i q^{83} -4.16804i q^{85} +(-2.66131 + 2.72713i) q^{86} +(5.85227 - 1.80035i) q^{88} +(3.85077 + 6.66973i) q^{89} +(2.33343 + 17.0514i) q^{91} +(6.57368 - 4.01254i) q^{92} +(-4.03537 + 15.8312i) q^{94} +(-1.92538 + 3.33486i) q^{95} +0.828427 q^{97} +(-8.68202 - 4.75631i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^4 + 8 * q^7	$ 16 q - 8 q^{4} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 32 q^{22} - 8 q^{25} - 16 q^{28} + 40 q^{31} - 80 q^{34} - 32 q^{40} - 8 q^{46} + 40 q^{49} + 8 q^{52} - 32 q^{64} - 16 q^{70} + 24 q^{73} + 32 q^{76} - 24 q^{79} - 16 q^{82} - 32 q^{88} - 24 q^{94} - 32 q^{97}+O(q^{100}) $ 16 * q - 8 * q^4 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 32 * q^22 - 8 * q^25 - 16 * q^28 + 40 * q^31 - 80 * q^34 - 32 * q^40 - 8 * q^46 + 40 * q^49 + 8 * q^52 - 32 * q^64 - 16 * q^70 + 24 * q^73 + 32 * q^76 - 24 * q^79 - 16 * q^82 - 32 * q^88 - 24 * q^94 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.01214	−	0.987711i	−0.715691	−	0.698417i
$2$	−1.01214	−	0.987711i	−0.715691	−	0.698417i
$3$		0			0
$3$		0			0
$4$	0.0488544	+	1.99940i	0.0244272	+	0.999702i
$5$	2.26303	−	1.30656i	1.01206	−	0.584313i	0.100265	−	0.994961i	$-0.468031\pi$
$5$	2.26303	−	1.30656i	1.01206	−	0.584313i	0.911794	+	0.410648i	$0.134697\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$	1.92538	−	2.07193i	0.680726	−	0.732538i
$9$		0			0
$10$	−3.58101	−	0.912798i	−1.13242	−	0.288652i
$11$	1.87476	+	1.08239i	0.565261	+	0.326354i	0.755254	−	0.655432i	$-0.227513\pi$
$11$	1.87476	+	1.08239i	0.565261	+	0.326354i	−0.189993	+	0.981785i	$0.560847\pi$
$12$		0			0
$13$			6.50490i			1.80413i	0.431596	+	0.902067i	$0.357951\pi$
$13$			6.50490i			1.80413i	−0.431596	+	0.902067i	$0.642049\pi$
$14$	−3.00745	−	2.22603i	−0.803776	−	0.594932i
$15$		0			0
$16$	−3.99523	+	0.195359i	−0.998807	+	0.0488398i
$17$	0.797521	−	1.38135i	0.193427	−	0.335026i	−0.752957	−	0.658070i	$-0.771373\pi$
$17$	0.797521	−	1.38135i	0.193427	−	0.335026i	0.946384	+	0.323045i	$0.104706\pi$
$18$		0			0
$19$	−1.27620	+	0.736813i	−0.292780	+	0.169036i	−0.639195	−	0.769045i	$-0.720732\pi$
$19$	−1.27620	+	0.736813i	−0.292780	+	0.169036i	0.346415	+	0.938081i	$0.387399\pi$
$20$	2.72291	+	4.46088i	0.608860	+	0.997484i
$21$		0			0
$22$	−0.828427	−	2.94725i	−0.176621	−	0.628356i
$23$	−1.92538	−	3.33486i	−0.401470	−	0.695367i	0.592433	−	0.805620i	$-0.298167\pi$
$23$	−1.92538	−	3.33486i	−0.401470	−	0.695367i	−0.993904	+	0.110252i	$0.964834\pi$
$24$		0			0
$25$	0.914214	−	1.58346i	0.182843	−	0.316693i
$26$	6.42496	−	6.58387i	1.26004	−	1.29120i
$27$		0			0
$28$	0.845288	+	5.22355i	0.159744	+	0.987158i
$29$			7.39104i			1.37248i	0.727375	+	0.686240i	$0.240740\pi$
$29$			7.39104i			1.37248i	−0.727375	+	0.686240i	$0.759260\pi$
$30$		0			0
$31$	1.79289	−	3.10538i	0.322013	−	0.557743i	−0.658890	−	0.752239i	$-0.728974\pi$
$31$	1.79289	−	3.10538i	0.322013	−	0.557743i	0.980903	+	0.194496i	$0.0623071\pi$
$32$	4.23669	+	3.74840i	0.748947	+	0.662629i
$33$		0			0
$34$	−2.17157	+	0.610396i	−0.372422	+	0.104682i
$35$	5.46345	−	4.23671i	0.923491	−	0.716135i
$36$		0			0
$37$	6.69064	−	3.86285i	1.09994	−	0.635048i	0.163731	−	0.986505i	$-0.447647\pi$
$37$	6.69064	−	3.86285i	1.09994	−	0.635048i	0.936204	+	0.351457i	$0.114314\pi$
$38$	2.01945	+	0.514756i	0.327598	+	0.0835045i
$39$		0			0
$40$	1.65010	−	7.20448i	0.260904	−	1.13913i
$41$	7.70154			1.20278			0.601389	−	0.798956i	$-0.294614\pi$
$41$	7.70154			1.20278			0.601389	+	0.798956i	$0.294614\pi$
$42$		0			0
$43$		−	2.69442i		−	0.410895i	−0.978668	−	0.205447i	$-0.934135\pi$
$43$		−	2.69442i		−	0.410895i	0.978668	−	0.205447i	$-0.0658649\pi$
$44$	−2.07255	+	3.80128i	−0.312448	+	0.573064i
$45$		0			0
$46$	−1.34512	+	5.27707i	−0.198328	+	0.778062i
$47$	−5.77615	−	10.0046i	−0.842539	−	1.45932i	−0.887742	−	0.460342i	$-0.847727\pi$
$47$	−5.77615	−	10.0046i	−0.842539	−	1.45932i	0.0452029	−	0.998978i	$-0.485607\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−2.48932	+	0.699709i	−0.352043	+	0.0989538i
$51$		0			0
$52$	−13.0059	+	0.317793i	−1.80360	+	0.0440700i
$53$	−8.66386	−	5.00208i	−1.19007	−	0.687089i	−0.231749	−	0.972776i	$-0.574445\pi$
$53$	−8.66386	−	5.00208i	−1.19007	−	0.687089i	−0.958323	+	0.285687i	$0.907778\pi$
$54$		0			0
$55$	5.65685			0.762770
$56$	4.30381	−	6.12186i	0.575121	−	0.818069i
$57$		0			0
$58$	7.30021	−	7.48076i	0.958564	−	0.982272i
$59$	−8.11475	−	4.68506i	−1.05645	−	0.609942i	−0.132003	−	0.991249i	$-0.542141\pi$
$59$	−8.11475	−	4.68506i	−1.05645	−	0.609942i	−0.924448	+	0.381307i	$0.875474\pi$
$60$		0			0
$61$	−3.60963	+	2.08402i	−0.462166	+	0.266832i	−0.712955	−	0.701210i	$-0.752643\pi$
$61$	−3.60963	+	2.08402i	−0.462166	+	0.266832i	0.250789	+	0.968042i	$0.419310\pi$
$62$	−4.88188	+	1.37222i	−0.619999	+	0.174272i
$63$		0			0
$64$	−0.585786	−	7.97852i	−0.0732233	−	0.997316i
$65$	8.49906	+	14.7208i	1.05418	+	1.82589i
$66$		0			0
$67$	9.99062	+	5.76809i	1.22055	+	0.704684i	0.965035	−	0.262122i	$-0.0844222\pi$
$67$	9.99062	+	5.76809i	1.22055	+	0.704684i	0.255513	+	0.966806i	$0.417756\pi$
$68$	2.80083	+	1.52708i	0.339651	+	0.185186i
$69$		0			0
$70$	−9.71442	−	1.10816i	−1.16110	−	0.132450i
$71$	−14.7424			−1.74960			−0.874800	−	0.484484i	$-0.839007\pi$
$71$	−14.7424			−1.74960			−0.874800	+	0.484484i	$0.839007\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	−10.5872	−	2.69868i	−1.23074	−	0.313715i
$75$		0			0
$76$	−1.53553	−	2.51564i	−0.176138	−	0.288563i
$77$	5.30262	+	2.16478i	0.604289	+	0.246700i
$78$		0			0
$79$	−3.62132	−	6.27231i	−0.407430	−	0.705690i	0.587171	−	0.809463i	$-0.300242\pi$
$79$	−3.62132	−	6.27231i	−0.407430	−	0.705690i	−0.994601	+	0.103773i	$0.966908\pi$
$80$	−8.78608	+	5.66212i	−0.982314	+	0.633044i
$81$		0			0
$82$	−7.79504	−	7.60689i	−0.860818	−	0.840041i
$83$			7.20533i			0.790887i	0.918490	+	0.395444i	$0.129409\pi$
$83$			7.20533i			0.790887i	−0.918490	+	0.395444i	$0.870591\pi$
$84$		0			0
$85$		−	4.16804i		−	0.452088i
$86$	−2.66131	+	2.72713i	−0.286976	+	0.294074i
$87$		0			0
$88$	5.85227	−	1.80035i	0.623854	−	0.191918i
$89$	3.85077	+	6.66973i	0.408181	+	0.706990i	0.994686	−	0.102956i	$-0.0328300\pi$
$89$	3.85077	+	6.66973i	0.408181	+	0.706990i	−0.586505	+	0.809945i	$0.699497\pi$
$90$		0			0
$91$	2.33343	+	17.0514i	0.244610	+	1.78747i
$92$	6.57368	−	4.01254i	0.685353	−	0.418337i
$93$		0			0
$94$	−4.03537	+	15.8312i	−0.416217	+	1.63287i
$95$	−1.92538	+	3.33486i	−0.197540	+	0.342150i
$96$		0			0
$97$	0.828427			0.0841140			0.0420570	−	0.999115i	$-0.486609\pi$
$97$	0.828427			0.0841140			0.0420570	+	0.999115i	$0.486609\pi$
$98$	−8.68202	−	4.75631i	−0.877017	−	0.480460i
$99$		0			0
$100$	3.21065	+	1.75052i	0.321065	+	0.175052i
$101$	−3.74952	−	2.16478i	−0.373091	−	0.215404i	0.301717	−	0.953398i	$-0.402440\pi$
$101$	−3.74952	−	2.16478i	−0.373091	−	0.215404i	−0.674808	+	0.737993i	$0.735774\pi$
$102$		0			0
$103$	5.20711	+	9.01897i	0.513071	+	0.888666i	0.999885	+	0.0151600i	$0.00482576\pi$
$103$	5.20711	+	9.01897i	0.513071	+	0.888666i	−0.486814	+	0.873506i	$0.661841\pi$
$104$	13.4777	+	12.5244i	1.32160	+	1.22812i
$105$		0			0
$106$	3.82843	+	13.6202i	0.371850	+	1.32291i
$107$	2.81214	−	1.62359i	0.271860	−	0.156958i	−0.357873	−	0.933770i	$-0.616498\pi$
$107$	2.81214	−	1.62359i	0.271860	−	0.156958i	0.629732	+	0.776812i	$0.283165\pi$
$108$		0			0
$109$	−9.24304	−	5.33647i	−0.885323	−	0.511141i	−0.0129129	−	0.999917i	$-0.504110\pi$
$109$	−9.24304	−	5.33647i	−0.885323	−	0.511141i	−0.872410	+	0.488775i	$0.837444\pi$
$110$	−5.72553	−	5.58734i	−0.545908	−	0.532732i
$111$		0			0
$112$	−10.4027	+	1.94526i	−0.982962	+	0.183810i
$113$	9.29658			0.874549			0.437274	−	0.899328i	$-0.355944\pi$
$113$	9.29658			0.874549			0.437274	+	0.899328i	$0.355944\pi$
$114$		0			0
$115$	−8.71442	−	5.03127i	−0.812624	−	0.469169i
$116$	−14.7777	+	0.361085i	−1.37207	+	0.0335259i
$117$		0			0
$118$	3.58579	+	12.7570i	0.330098	+	1.17437i
$119$	1.59504	−	3.90704i	0.146217	−	0.358157i
$120$		0			0
$121$	−3.15685	−	5.46783i	−0.286987	−	0.497076i
$122$	5.71186	+	1.45595i	0.517128	+	0.131816i
$123$		0			0
$124$	6.29650	+	3.43300i	0.565443	+	0.308293i
$125$			8.28772i			0.741276i
$126$		0			0
$127$	−10.0711			−0.893663			−0.446831	−	0.894618i	$-0.647448\pi$
$127$	−10.0711			−0.893663			−0.446831	+	0.894618i	$0.647448\pi$
$128$	−7.28758	+	8.65397i	−0.644137	+	0.764910i
$129$		0			0
$130$	5.93766	−	23.2941i	0.520767	−	2.04303i
$131$	4.52607	−	2.61313i	0.395444	−	0.228310i	−0.289072	−	0.957307i	$-0.593347\pi$
$131$	4.52607	−	2.61313i	0.395444	−	0.228310i	0.684516	+	0.728997i	$0.260013\pi$
$132$		0			0
$133$	−3.08101	+	2.38922i	−0.267158	+	0.207172i
$134$	−4.41470	−	15.7060i	−0.381372	−	1.35679i
$135$		0			0
$136$	−1.32652	−	4.31203i	−0.113748	−	0.369753i
$137$	−7.70154	+	13.3395i	−0.657987	+	1.13967i	0.323149	+	0.946348i	$0.395258\pi$
$137$	−7.70154	+	13.3395i	−0.657987	+	1.13967i	−0.981136	+	0.193319i	$0.938075\pi$
$138$		0			0
$139$		−	15.7042i		−	1.33201i	−0.745945	−	0.666007i	$-0.768002\pi$
$139$		−	15.7042i		−	1.33201i	0.745945	−	0.666007i	$-0.231998\pi$
$140$	8.73781	+	10.7166i	0.738480	+	0.905722i
$141$		0			0
$142$	14.9214	+	14.5612i	1.25217	+	1.22195i
$143$	−7.04085	+	12.1951i	−0.588786	+	1.01981i
$144$		0			0
$145$	9.65685	+	16.7262i	0.801958	+	1.38903i
$146$	−4.08436	+	1.14805i	−0.338024	+	0.0950133i
$147$		0			0
$148$	8.05025	+	13.1886i	0.661727	+	1.08409i
$149$	−9.05213	+	5.22625i	−0.741580	+	0.428151i	−0.822643	−	0.568558i	$-0.807502\pi$
$149$	−9.05213	+	5.22625i	−0.741580	+	0.428151i	0.0810637	+	0.996709i	$0.474168\pi$
$150$		0			0
$151$	−4.41421	+	7.64564i	−0.359224	+	0.622194i	−0.987831	−	0.155529i	$-0.950292\pi$
$151$	−4.41421	+	7.64564i	−0.359224	+	0.622194i	0.628608	+	0.777723i	$0.283625\pi$
$152$	−0.930546	+	4.06284i	−0.0754773	+	0.329540i
$153$		0			0
$154$	−3.22881	−	7.42852i	−0.260185	−	0.598607i
$155$		−	9.37011i		−	0.752625i
$156$		0			0
$157$	7.21926	+	4.16804i	0.576160	+	0.332646i	0.759606	−	0.650384i	$-0.225392\pi$
$157$	7.21926	+	4.16804i	0.576160	+	0.332646i	−0.183446	+	0.983030i	$0.558725\pi$
$158$	−2.52995	+	9.92527i	−0.201272	+	0.789612i
$159$		0			0
$160$	14.4853	+	2.94725i	1.14516	+	0.233001i
$161$	−6.24333	−	8.05107i	−0.492043	−	0.634514i
$162$		0			0
$163$	−8.71442	+	5.03127i	−0.682566	+	0.394080i	−0.800821	−	0.598904i	$-0.795603\pi$
$163$	−8.71442	+	5.03127i	−0.682566	+	0.394080i	0.118255	+	0.992983i	$0.462270\pi$
$164$	0.376254	+	15.3985i	0.0293805	+	1.20242i
$165$		0			0
$166$	7.11678	−	7.29280i	0.552369	−	0.566031i
$167$	14.7424			1.14080			0.570400	−	0.821367i	$-0.306788\pi$
$167$	14.7424			1.14080			0.570400	+	0.821367i	$0.306788\pi$
$168$		0			0
$169$	−29.3137			−2.25490
$170$	−4.11682	+	4.21864i	−0.315746	+	0.323555i
$171$		0			0
$172$	5.38723	−	0.131634i	0.410772	−	0.0100370i
$173$	−5.23600	+	3.02301i	−0.398086	+	0.229835i	−0.685658	−	0.727924i	$-0.740485\pi$
$173$	−5.23600	+	3.02301i	−0.398086	+	0.229835i	0.287572	+	0.957759i	$0.407152\pi$
$174$		0			0
$175$	1.82843	−	4.47871i	0.138216	−	0.338559i
$176$	−7.70154	−	3.95815i	−0.580525	−	0.298357i
$177$		0			0
$178$	2.69025	−	10.5541i	0.201642	−	0.791067i
$179$	−19.0416	−	10.9937i	−1.42324	−	0.821708i	−0.426665	−	0.904410i	$-0.640312\pi$
$179$	−19.0416	−	10.9937i	−1.42324	−	0.821708i	−0.996574	+	0.0827020i	$0.973645\pi$
$180$		0			0
$181$			4.77844i			0.355179i	0.984105	+	0.177589i	$0.0568299\pi$
$181$			4.77844i			0.355179i	−0.984105	+	0.177589i	$0.943170\pi$
$182$	14.4801	−	19.5632i	1.07334	−	1.45012i
$183$		0			0
$184$	−10.6167	−	2.43164i	−0.782674	−	0.179263i
$185$	10.0941	−	17.4835i	0.742133	−	1.28541i
$186$		0			0
$187$	2.99032	−	1.72646i	0.218674	−	0.126251i
$188$	19.7210	−	12.0376i	1.43830	−	0.877934i
$189$		0			0
$190$	5.24264	−	1.47363i	0.380341	−	0.106908i
$191$	−8.96624	−	15.5300i	−0.648774	−	1.12371i	−0.983416	−	0.181364i	$-0.941949\pi$
$191$	−8.96624	−	15.5300i	−0.648774	−	1.12371i	0.334642	−	0.942345i	$-0.391385\pi$
$192$		0			0
$193$	−5.15685	+	8.93193i	−0.371198	+	0.642935i	−0.989750	−	0.142809i	$-0.954386\pi$
$193$	−5.15685	+	8.93193i	−0.371198	+	0.642935i	0.618552	+	0.785744i	$0.287720\pi$
$194$	−0.838484	−	0.818246i	−0.0601997	−	0.0587467i
$195$		0			0
$196$	4.08956	+	13.3894i	0.292111	+	0.956384i
$197$		−	19.5600i		−	1.39359i	−0.717270	−	0.696796i	$-0.754608\pi$
$197$		−	19.5600i		−	1.39359i	0.717270	−	0.696796i	$-0.245392\pi$
$198$		0			0
$199$	0.414214	−	0.717439i	0.0293628	−	0.0508579i	−0.850971	−	0.525213i	$-0.823986\pi$
$199$	0.414214	−	0.717439i	0.0293628	−	0.0508579i	0.880333	+	0.474355i	$0.157319\pi$
$200$	−1.52061	−	4.94296i	−0.107524	−	0.349520i
$201$		0			0
$202$	1.65685	+	5.89450i	0.116576	+	0.414736i
$203$	2.65131	+	19.3743i	0.186085	+	1.35981i
$204$		0			0
$205$	17.4288	−	10.0625i	1.21728	−	0.702799i
$206$	3.63782	−	14.2716i	0.253459	−	0.994348i
$207$		0			0
$208$	−1.27079	−	25.9885i	−0.0881136	−	1.80198i
$209$	−3.19008			−0.220663
$210$		0			0
$211$		−	20.1251i		−	1.38547i	−0.721193	−	0.692734i	$-0.756406\pi$
$211$		−	20.1251i		−	1.38547i	0.721193	−	0.692734i	$-0.243594\pi$
$212$	9.57791	−	17.5669i	0.657814	−	1.20650i
$213$		0			0
$214$	−4.44991	−	1.13428i	−0.304190	−	0.0775378i
$215$	−3.52043	−	6.09756i	−0.240091	−	0.415850i
$216$		0			0
$217$	3.58579	−	8.78335i	0.243419	−	0.596252i
$218$	4.08436	+	14.5307i	0.276628	+	0.984144i
$219$		0			0
$220$	0.276362	+	11.3103i	0.0186323	+	0.762542i
$221$	8.98552	+	5.18779i	0.604431	+	0.348969i
$222$		0			0
$223$	−16.1421			−1.08096			−0.540479	−	0.841358i	$-0.681757\pi$
$223$	−16.1421			−1.08096			−0.540479	+	0.841358i	$0.681757\pi$
$224$	12.4503	+	8.30597i	0.831873	+	0.554966i
$225$		0			0
$226$	−9.40944	−	9.18233i	−0.625907	−	0.610800i
$227$	13.8999	+	8.02509i	0.922566	+	0.532644i	0.884453	−	0.466630i	$-0.154532\pi$
$227$	13.8999	+	8.02509i	0.922566	+	0.532644i	0.0381132	+	0.999273i	$0.487865\pi$
$228$		0			0
$229$	−13.9099	+	8.03089i	−0.919192	+	0.530696i	−0.883377	−	0.468662i	$-0.844736\pi$
$229$	−13.9099	+	8.03089i	−0.919192	+	0.530696i	−0.0358151	+	0.999358i	$0.511403\pi$
$230$	3.85077	+	13.6997i	0.253912	+	0.903330i
$231$		0			0
$232$	15.3137	+	14.2306i	1.00539	+	0.934284i
$233$	6.24333	+	10.8138i	0.409014	+	0.708433i	0.994780	−	0.102047i	$-0.0325393\pi$
$233$	6.24333	+	10.8138i	0.409014	+	0.708433i	−0.585765	+	0.810481i	$0.699206\pi$
$234$		0			0
$235$	−26.1433	−	15.0938i	−1.70540	−	0.984612i
$236$	8.97087	−	16.4536i	0.583954	−	1.07104i
$237$		0			0
$238$	−5.47343	+	2.37903i	−0.354790	+	0.154210i
$239$	−4.51146			−0.291822			−0.145911	−	0.989298i	$-0.546611\pi$
$239$	−4.51146			−0.291822			−0.145911	+	0.989298i	$0.546611\pi$
$240$		0			0
$241$	1.58579	−	2.74666i	0.102149	−	0.176928i	−0.810421	−	0.585849i	$-0.800761\pi$
$241$	1.58579	−	2.74666i	0.102149	−	0.176928i	0.912570	+	0.408920i	$0.134095\pi$
$242$	−2.20546	+	8.65227i	−0.141772	+	0.556189i
$243$		0			0
$244$	−4.34315	−	7.11529i	−0.278041	−	0.455510i
$245$	12.8017	−	13.0656i	0.817867	−	0.834732i
$246$		0			0
$247$	−4.79289	−	8.30153i	−0.304964	−	0.528214i
$248$	−2.98212	−	9.69380i	−0.189365	−	0.615557i
$249$		0			0
$250$	8.18587	−	8.38833i	0.517720	−	0.530525i
$251$			5.04054i			0.318156i	0.987266	+	0.159078i	$0.0508522\pi$
$251$			5.04054i			0.318156i	−0.987266	+	0.159078i	$0.949148\pi$
$252$		0			0
$253$		−	8.33609i		−	0.524085i
$254$	10.1933	+	9.94730i	0.639586	+	0.624149i
$255$		0			0
$256$	15.9237	−	1.56101i	0.995229	−	0.0975631i
$257$	−6.90402	−	11.9581i	−0.430661	−	0.745926i	0.566269	−	0.824220i	$-0.308386\pi$
$257$	−6.90402	−	11.9581i	−0.430661	−	0.745926i	−0.996930	+	0.0782937i	$0.975053\pi$
$258$		0			0
$259$	16.1526	−	12.5258i	1.00368	−	0.778317i
$260$	−29.0176	+	17.7122i	−1.79960	+	1.09847i
$261$		0			0
$262$	−7.16203	−	1.82560i	−0.442471	−	0.112786i
$263$	5.44581	−	9.43242i	0.335803	−	0.581628i	−0.647836	−	0.761780i	$-0.724326\pi$
$263$	5.44581	−	9.43242i	0.335803	−	0.581628i	0.983639	+	0.180152i	$0.0576590\pi$
$264$		0			0
$265$	−26.1421			−1.60590
$266$	5.47827	+	0.624926i	0.335895	+	0.0383167i
$267$		0			0
$268$	−11.0446	+	20.2571i	−0.674659	+	1.23740i
$269$	18.1043	+	10.4525i	1.10384	+	0.637300i	0.937226	−	0.348722i	$-0.113384\pi$
$269$	18.1043	+	10.4525i	1.10384	+	0.637300i	0.166611	+	0.986023i	$0.446718\pi$
$270$		0			0
$271$	12.0711	+	20.9077i	0.733265	+	1.27005i	0.955480	+	0.295055i	$0.0953379\pi$
$271$	12.0711	+	20.9077i	0.733265	+	1.27005i	−0.222215	+	0.974998i	$0.571329\pi$
$272$	−2.91642	+	5.67459i	−0.176834	+	0.344073i
$273$		0			0
$274$	20.9706	−	5.89450i	1.26688	−	0.356100i
$275$	3.42786	−	1.97908i	0.206708	−	0.119343i
$276$		0			0
$277$	−7.74788	−	4.47324i	−0.465525	−	0.268771i	0.248840	−	0.968545i	$-0.419951\pi$
$277$	−7.74788	−	4.47324i	−0.465525	−	0.268771i	−0.714365	+	0.699774i	$0.753284\pi$
$278$	−15.5112	+	15.8949i	−0.930301	+	0.953311i
$279$		0			0
$280$	1.74106	−	19.4772i	0.104048	−	1.16398i
$281$	4.78512			0.285457			0.142728	−	0.989762i	$-0.454413\pi$
$281$	4.78512			0.285457			0.142728	+	0.989762i	$0.454413\pi$
$282$		0			0
$283$	20.8195	+	12.0202i	1.23759	+	0.714524i	0.968601	−	0.248619i	$-0.0799768\pi$
$283$	20.8195	+	12.0202i	1.23759	+	0.714524i	0.268990	+	0.963143i	$0.413310\pi$
$284$	−0.720231	−	29.4760i	−0.0427378	−	1.74908i
$285$		0			0
$286$	19.1716	−	5.38883i	1.13364	−	0.318648i
$287$	20.1882	−	2.76269i	1.19167	−	0.163077i
$288$		0			0
$289$	7.22792	+	12.5191i	0.425172	+	0.736419i
$290$	6.74652	−	26.4674i	0.396170	−	1.55422i
$291$		0			0
$292$	5.26788	+	2.87218i	0.308280	+	0.168081i
$293$			10.8239i			0.632340i	0.948703	+	0.316170i	$0.102397\pi$
$293$			10.8239i			0.632340i	−0.948703	+	0.316170i	$0.897603\pi$
$294$		0			0
$295$	−24.4853			−1.42559
$296$	4.87852	−	21.3000i	0.283558	−	1.23804i
$297$		0			0
$298$	14.3241	+	3.65119i	0.829770	+	0.211508i
$299$	21.6930	−	12.5244i	1.25454	−	0.724307i
$300$		0			0
$301$	−0.966540	−	7.06293i	−0.0557104	−	0.407101i
$302$	12.0195	−	3.37849i	0.691644	−	0.194410i
$303$		0			0
$304$	4.95475	−	3.19305i	0.284175	−	0.183134i
$305$	−5.44581	+	9.43242i	−0.311826	+	0.540099i
$306$		0			0
$307$			10.3154i			0.588730i	0.955693	+	0.294365i	$0.0951081\pi$
$307$			10.3154i			0.588730i	−0.955693	+	0.294365i	$0.904892\pi$
$308$	−4.06922	+	10.7078i	−0.231865	+	0.610135i
$309$		0			0
$310$	−9.25496	+	9.48386i	−0.525646	+	0.538647i
$311$	−16.9981	+	29.4416i	−0.963875	+	1.66948i	−0.251267	+	0.967918i	$0.580847\pi$
$311$	−16.9981	+	29.4416i	−0.963875	+	1.66948i	−0.712608	+	0.701563i	$0.752486\pi$
$312$		0			0
$313$	−2.98528	−	5.17066i	−0.168738	−	0.292263i	0.769238	−	0.638962i	$-0.220636\pi$
$313$	−2.98528	−	5.17066i	−0.168738	−	0.292263i	−0.937976	+	0.346699i	$0.887303\pi$
$314$	−3.19008	−	11.3492i	−0.180027	−	0.640472i
$315$		0			0
$316$	12.3640	−	7.54691i	0.695527	−	0.424547i
$317$	−8.73048	+	5.04054i	−0.490352	+	0.283105i	−0.724721	−	0.689043i	$-0.758031\pi$
$317$	−8.73048	+	5.04054i	−0.490352	+	0.283105i	0.234368	+	0.972148i	$0.424698\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$	−11.7501	−	17.2903i	−0.656851	−	0.966557i
$321$		0			0
$322$	−1.63301	+	14.3154i	−0.0910041	+	0.797767i
$323$			2.35049i			0.130785i
$324$		0			0
$325$	10.3003	+	5.94687i	0.571356	+	0.329873i
$326$	13.7897	+	3.51498i	0.763738	+	0.194677i
$327$		0			0
$328$	14.8284	−	15.9570i	0.818763	−	0.881081i
$329$	−18.7300	−	24.1532i	−1.03262	−	1.33161i
$330$		0			0
$331$	4.88583	−	2.82083i	0.268549	−	0.155047i	−0.359679	−	0.933076i	$-0.617114\pi$
$331$	4.88583	−	2.82083i	0.268549	−	0.155047i	0.628228	+	0.778029i	$0.283780\pi$
$332$	−14.4064	+	0.352012i	−0.790651	+	0.0193192i
$333$		0			0
$334$	−14.9214	−	14.5612i	−0.816461	−	0.796755i
$335$	30.1455			1.64702
$336$		0			0
$337$	12.6569			0.689463			0.344731	−	0.938701i	$-0.387970\pi$
$337$	12.6569			0.689463			0.344731	+	0.938701i	$0.387970\pi$
$338$	29.6696	+	28.9535i	1.61381	+	1.57486i
$339$		0			0
$340$	8.33360	−	0.203627i	0.451953	−	0.0110432i
$341$	6.72248	−	3.88123i	0.364043	−	0.210180i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	−5.58264	−	5.18779i	−0.300996	−	0.279707i
$345$		0			0
$346$	8.28542	+	2.11195i	0.445427	+	0.113539i
$347$	11.5426	+	6.66413i	0.619640	+	0.357749i	0.776729	−	0.629835i	$-0.216878\pi$
$347$	11.5426	+	6.66413i	0.619640	+	0.357749i	−0.157089	+	0.987584i	$0.550211\pi$
$348$		0			0
$349$		−	24.2931i		−	1.30038i	−0.759771	−	0.650191i	$-0.774689\pi$
$349$		−	24.2931i		−	1.30038i	0.759771	−	0.650191i	$-0.225311\pi$
$350$	−6.27430	+	2.72713i	−0.335375	+	0.145771i
$351$		0			0
$352$	3.88553	+	11.6131i	0.207099	+	0.618980i
$353$	6.24333	−	10.8138i	0.332299	−	0.575559i	−0.650663	−	0.759366i	$-0.725509\pi$
$353$	6.24333	−	10.8138i	0.332299	−	0.575559i	0.982962	+	0.183808i	$0.0588424\pi$
$354$		0			0
$355$	−33.3625	+	19.2619i	−1.77070	+	1.02231i
$356$	−13.1474	+	8.02509i	−0.696808	+	0.425329i
$357$		0			0
$358$	8.41421	+	29.9348i	0.444705	+	1.58210i
$359$	−1.59504	−	2.76269i	−0.0841830	−	0.145809i	0.820860	−	0.571130i	$-0.193495\pi$
$359$	−1.59504	−	2.76269i	−0.0841830	−	0.145809i	−0.905043	+	0.425320i	$0.860161\pi$
$360$		0			0
$361$	−8.41421	+	14.5738i	−0.442853	+	0.767044i
$362$	4.71972	−	4.83645i	0.248063	−	0.254198i
$363$		0			0
$364$	−33.9787	+	5.49851i	−1.78097	+	0.288200i
$365$		−	7.83938i		−	0.410332i
$366$		0			0
$367$	15.6924	−	27.1800i	0.819136	−	1.41879i	−0.0871836	−	0.996192i	$-0.527787\pi$
$367$	15.6924	−	27.1800i	0.819136	−	1.41879i	0.906320	−	0.422593i	$-0.138880\pi$
$368$	8.34385	+	12.9474i	0.434953	+	0.674930i
$369$		0			0
$370$	−27.4853	+	7.72569i	−1.42889	+	0.401640i
$371$	−24.5051	−	10.0042i	−1.27224	−	0.519390i
$372$		0			0
$373$	−20.5099	+	11.8414i	−1.06196	+	0.613123i	−0.925974	−	0.377588i	$-0.876754\pi$
$373$	−20.5099	+	11.8414i	−1.06196	+	0.613123i	−0.135986	+	0.990711i	$0.543420\pi$
$374$	−4.73186	−	1.20615i	−0.244679	−	0.0623685i
$375$		0			0
$376$	−31.8501	−	7.29491i	−1.64255	−	0.376206i
$377$	−48.0779			−2.47614
$378$		0			0
$379$			16.2099i			0.832646i	0.909217	+	0.416323i	$0.136681\pi$
$379$			16.2099i			0.832646i	−0.909217	+	0.416323i	$0.863319\pi$
$380$	−6.76180	−	3.68670i	−0.346873	−	0.189124i
$381$		0			0
$382$	−6.26404	+	24.5746i	−0.320496	+	1.25734i
$383$	15.0727	+	26.1067i	0.770181	+	1.33399i	0.937464	+	0.348083i	$0.113167\pi$
$383$	15.0727	+	26.1067i	0.770181	+	1.33399i	−0.167283	+	0.985909i	$0.553499\pi$
$384$		0			0
$385$	14.8284	−	2.02922i	0.755727	−	0.103419i
$386$	14.0416	−	3.94689i	0.714700	−	0.200891i
$387$		0			0
$388$	0.0404723	+	1.65636i	0.00205467	+	0.0840889i
$389$	−7.88731	−	4.55374i	−0.399902	−	0.230884i	0.286539	−	0.958068i	$-0.407495\pi$
$389$	−7.88731	−	4.55374i	−0.399902	−	0.230884i	−0.686442	+	0.727185i	$0.740828\pi$
$390$		0			0
$391$	−6.14214			−0.310621
$392$	9.08563	−	17.5912i	0.458894	−	0.888491i
$393$		0			0
$394$	−19.3196	+	19.7974i	−0.973308	+	0.997381i
$395$	−16.3903	−	9.46297i	−0.824687	−	0.476133i
$396$		0			0
$397$	−15.4051	+	8.89412i	−0.773158	+	0.446383i	−0.834000	−	0.551764i	$-0.813955\pi$
$397$	−15.4051	+	8.89412i	−0.773158	+	0.446383i	0.0608420	+	0.998147i	$0.480621\pi$
$398$	−1.12786	+	0.317025i	−0.0565347	+	0.0158910i
$399$		0			0
$400$	−3.34315	+	6.50490i	−0.167157	+	0.325245i
$401$	−5.30898	−	9.19542i	−0.265118	−	0.459197i	0.702477	−	0.711707i	$-0.252077\pi$
$401$	−5.30898	−	9.19542i	−0.265118	−	0.459197i	−0.967594	+	0.252509i	$0.918744\pi$
$402$		0			0
$403$	20.2002	+	11.6626i	1.00624	+	0.580955i
$404$	4.14510	−	7.60255i	0.206226	−	0.378241i
$405$		0			0
$406$	16.4527	−	22.2282i	0.816533	−	1.10317i
$407$	16.7245			0.829000
$408$		0			0
$409$	14.4706	−	25.0637i	0.715523	−	1.23932i	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	14.4706	−	25.0637i	0.715523	−	1.23932i	0.962757	−	0.270367i	$-0.0871450\pi$
$410$	−27.5793	−	7.02995i	−1.36205	−	0.347185i
$411$		0			0
$412$	−17.7782	+	10.8517i	−0.875868	+	0.534626i
$413$	−22.9520	−	9.37011i	−1.12939	−	0.461073i
$414$		0			0
$415$	9.41421	+	16.3059i	0.462126	+	0.800425i
$416$	−24.3829	+	27.5592i	−1.19547	+	1.35120i
$417$		0			0
$418$	3.22881	+	3.15088i	0.157926	+	0.154115i
$419$			18.7402i			0.915520i	0.889076	+	0.457760i	$0.151348\pi$
$419$			18.7402i			0.915520i	−0.889076	+	0.457760i	$0.848652\pi$
$420$		0			0
$421$		−	0.610396i		−	0.0297489i	−0.999889	−	0.0148744i	$-0.995265\pi$
$421$		−	0.610396i		−	0.0297489i	0.999889	−	0.0148744i	$-0.00473485\pi$
$422$	−19.8778	+	20.3694i	−0.967635	+	0.991567i
$423$		0			0
$424$	−27.0452	+	8.31998i	−1.31343	+	0.404054i
$425$	−1.45821	−	2.52569i	−0.0707335	−	0.122514i
$426$		0			0
$427$	−8.71442	+	6.75773i	−0.421720	+	0.327030i
$428$	3.38359	+	5.54328i	0.163552	+	0.267944i
$429$		0			0
$430$	−2.45946	+	9.64874i	−0.118606	+	0.465304i
$431$	3.52043	−	6.09756i	0.169573	−	0.293709i	−0.768697	−	0.639613i	$-0.779094\pi$
$431$	3.52043	−	6.09756i	0.169573	−	0.293709i	0.938270	+	0.345904i	$0.112428\pi$
$432$		0			0
$433$	32.7990			1.57622			0.788109	−	0.615535i	$-0.211060\pi$
$433$	32.7990			1.57622			0.788109	+	0.615535i	$0.211060\pi$
$434$	−12.3047	+	5.34826i	−0.590646	+	0.256724i
$435$		0			0
$436$	10.2182	−	18.7413i	0.489363	−	0.897544i
$437$	4.91434	+	2.83730i	0.235085	+	0.135726i
$438$		0			0
$439$	−0.757359	−	1.31178i	−0.0361468	−	0.0626081i	0.847386	−	0.530977i	$-0.178175\pi$
$439$	−0.757359	−	1.31178i	−0.0361468	−	0.0626081i	−0.883533	+	0.468369i	$0.844842\pi$
$440$	10.8916	−	11.7206i	0.519238	−	0.558758i
$441$		0			0
$442$	−3.97056	−	14.1259i	−0.188860	−	0.671899i
$443$	−32.1650	+	18.5704i	−1.52820	+	0.882308i	−0.528766	+	0.848768i	$0.677345\pi$
$443$	−32.1650	+	18.5704i	−1.52820	+	0.882308i	−0.999437	+	0.0335407i	$0.989322\pi$
$444$		0			0
$445$	17.4288	+	10.0625i	0.826206	+	0.477010i
$446$	16.3381	+	15.9438i	0.773631	+	0.754959i
$447$		0			0
$448$	−4.39759	−	20.7041i	−0.207766	−	0.978178i
$449$	1.59504			0.0752746			0.0376373	−	0.999291i	$-0.488017\pi$
$449$	1.59504			0.0752746			0.0376373	+	0.999291i	$0.488017\pi$
$450$		0			0
$451$	14.4385	+	8.33609i	0.679884	+	0.392531i
$452$	0.454179	+	18.5876i	0.0213628	+	0.874288i
$453$		0			0
$454$	−6.14214	−	21.8516i	−0.288265	−	1.02554i
$455$	27.5594	+	35.5392i	1.29200	+	1.66610i
$456$		0			0
$457$	−21.2279	−	36.7678i	−0.993000	−	1.71993i	−0.598788	−	0.800908i	$-0.704351\pi$
$457$	−21.2279	−	36.7678i	−0.993000	−	1.71993i	−0.394212	−	0.919019i	$-0.628983\pi$
$458$	22.0110	+	5.61058i	1.02850	+	0.262165i
$459$		0			0
$460$	9.63381	−	17.6694i	0.449179	−	0.823842i
$461$		−	39.1200i		−	1.82200i	−0.412408	−	0.910999i	$-0.635312\pi$
$461$		−	39.1200i		−	1.82200i	0.412408	−	0.910999i	$-0.364688\pi$
$462$		0			0
$463$	18.2132			0.846439			0.423220	−	0.906027i	$-0.360900\pi$
$463$	18.2132			0.846439			0.423220	+	0.906027i	$0.360900\pi$
$464$	−1.44391	−	29.5289i	−0.0670317	−	1.37084i
$465$		0			0
$466$	4.36175	−	17.1117i	0.202054	−	0.792682i
$467$	−29.1920	+	16.8540i	−1.35084	+	0.779910i	−0.988368	−	0.152083i	$-0.951402\pi$
$467$	−29.1920	+	16.8540i	−1.35084	+	0.779910i	−0.362476	+	0.931993i	$0.618069\pi$
$468$		0			0
$469$	28.2577	+	11.5362i	1.30482	+	0.532691i
$470$	11.5523	+	41.0990i	0.532868	+	1.89576i
$471$		0			0
$472$	−25.3311	+	7.79267i	−1.16596	+	0.358687i
$473$	2.91642	−	5.05138i	0.134097	−	0.232263i
$474$		0			0
$475$			2.69442i			0.123628i
$476$	7.88967	+	2.99825i	0.361622	+	0.137425i
$477$		0			0
$478$	4.56623	+	4.45602i	0.208854	+	0.203813i
$479$	−14.4120	+	24.9624i	−0.658503	+	1.14056i	0.322500	+	0.946569i	$0.395477\pi$
$479$	−14.4120	+	24.9624i	−0.658503	+	1.14056i	−0.981003	+	0.193992i	$0.937857\pi$
$480$		0			0
$481$	25.1274	+	43.5220i	1.14571	+	1.98443i
$482$	−4.31795	+	1.21371i	−0.196677	+	0.0552829i
$483$		0			0
$484$	10.7782	−	6.57895i	0.489917	−	0.299043i
$485$	1.87476	−	1.08239i	0.0851284	−	0.0491489i
$486$		0			0
$487$	5.13604	−	8.89588i	0.232736	−	0.403111i	−0.725876	−	0.687825i	$-0.758565\pi$
$487$	5.13604	−	8.89588i	0.232736	−	0.403111i	0.958612	+	0.284715i	$0.0918988\pi$
$488$	−2.63198	+	11.4914i	−0.119144	+	0.520193i
$489$		0			0
$490$	−25.8621	+	0.579916i	−1.16833	+	0.0261979i
$491$		−	7.39104i		−	0.333553i	−0.985995	−	0.166776i	$-0.946664\pi$
$491$		−	7.39104i		−	0.333553i	0.985995	−	0.166776i	$-0.0533358\pi$
$492$		0			0
$493$	10.2096	+	5.89450i	0.459816	+	0.265475i
$494$	−3.34844	+	13.1363i	−0.150653	+	0.591030i
$495$		0			0
$496$	−6.55635	+	12.7570i	−0.294389	+	0.572805i
$497$	−38.6445	+	5.28838i	−1.73344	+	0.237216i
$498$		0			0
$499$	8.49546	−	4.90486i	0.380309	−	0.219572i	−0.297644	−	0.954677i	$-0.596201\pi$
$499$	8.49546	−	4.90486i	0.380309	−	0.219572i	0.677953	+	0.735106i	$0.262867\pi$
$500$	−16.5705	+	0.404892i	−0.741055	+	0.0181073i
$501$		0			0
$502$	4.97860	−	5.10173i	0.222206	−	0.227702i
$503$	24.9733			1.11351			0.556753	−	0.830678i	$-0.312047\pi$
$503$	24.9733			1.11351			0.556753	+	0.830678i	$0.312047\pi$
$504$		0			0
$505$	−11.3137			−0.503453
$506$	−8.23364	+	8.43729i	−0.366030	+	0.375083i
$507$		0			0
$508$	−0.492016	−	20.1361i	−0.0218297	−	0.893396i
$509$	14.2881	−	8.24926i	0.633310	−	0.365642i	−0.148723	−	0.988879i	$-0.547516\pi$
$509$	14.2881	−	8.24926i	0.633310	−	0.365642i	0.782033	+	0.623237i	$0.214183\pi$
$510$		0			0
$511$	3.00000	−	7.34847i	0.132712	−	0.325077i
$512$	−17.6588	−	14.1480i	−0.780416	−	0.625260i
$513$		0			0
$514$	−4.82332	+	18.9225i	−0.212748	+	0.834634i
$515$	23.5677	+	13.6068i	1.03852	+	0.599588i
$516$		0			0
$517$		−	25.0083i		−	1.09986i
$518$	−28.7206	−	3.27626i	−1.26191	−	0.143951i
$519$		0			0
$520$	46.8644	+	10.7338i	2.05514	+	0.470706i
$521$	14.7424	−	25.5346i	0.645876	−	1.11869i	−0.338223	−	0.941066i	$-0.609826\pi$
$521$	14.7424	−	25.5346i	0.645876	−	1.11869i	0.984098	−	0.177624i	$-0.0568410\pi$
$522$		0			0
$523$	19.7623	−	11.4098i	0.864144	−	0.498914i	−0.00125385	−	0.999999i	$-0.500399\pi$
$523$	19.7623	−	11.4098i	0.864144	−	0.498914i	0.865398	+	0.501085i	$0.167066\pi$
$524$	5.44581	+	8.92177i	0.237901	+	0.389749i
$525$		0			0
$526$	−14.8284	+	4.16804i	−0.646550	+	0.181735i
$527$	−2.85974	−	4.95321i	−0.124572	−	0.215765i
$528$		0			0
$529$	4.08579	−	7.07679i	0.177643	−	0.307687i
$530$	26.4595	+	25.8209i	1.14933	+	1.12159i
$531$		0			0
$532$	−4.92753	−	6.04346i	−0.213636	−	0.262017i
$533$			50.0977i			2.16997i
$534$		0			0
$535$	4.24264	−	7.34847i	0.183425	−	0.317702i
$536$	31.1869	−	9.59407i	1.34707	−	0.414401i
$537$		0			0
$538$	−8.00000	−	28.4612i	−0.344904	−	1.22705i
$539$	14.6764	+	3.77244i	0.632158	+	0.162491i
$540$		0			0
$541$	−36.8815	+	21.2935i	−1.58566	+	0.915480i	−0.591647	+	0.806197i	$0.701522\pi$
$541$	−36.8815	+	21.2935i	−1.58566	+	0.915480i	−0.994011	+	0.109283i	$0.965145\pi$
$542$	8.43316	−	33.0842i	0.362235	−	1.42109i
$543$		0			0
$544$	8.55668	−	2.86291i	0.366865	−	0.122746i
$545$	−27.8897			−1.19467
$546$		0			0
$547$		−	16.6722i		−	0.712851i	−0.934324	−	0.356425i	$-0.883995\pi$
$547$		−	16.6722i		−	0.712851i	0.934324	−	0.356425i	$-0.116005\pi$
$548$	−27.0472	−	14.7468i	−1.15540	−	0.629952i
$549$		0			0
$550$	−5.42423	−	1.38263i	−0.231290	−	0.0589556i
$551$	−5.44581	−	9.43242i	−0.231999	−	0.401835i
$552$		0			0
$553$	−11.7426	−	15.1427i	−0.499348	−	0.643933i
$554$	3.42367	+	12.1802i	0.145458	+	0.517488i
$555$		0			0
$556$	31.3991	−	0.767220i	1.33162	−	0.0325374i
$557$	−11.7034	−	6.75699i	−0.495891	−	0.286303i	0.231124	−	0.972924i	$-0.425760\pi$
$557$	−11.7034	−	6.75699i	−0.495891	−	0.286303i	−0.727015	+	0.686622i	$0.759093\pi$
$558$		0			0
$559$	17.5269			0.741309
$560$	−21.0000	+	17.9940i	−0.887413	+	0.760384i
$561$		0			0
$562$	−4.84321	−	4.72632i	−0.204299	−	0.199368i
$563$	−23.8894	−	13.7925i	−1.00682	−	0.581286i	−0.0965588	−	0.995327i	$-0.530784\pi$
$563$	−23.8894	−	13.7925i	−1.00682	−	0.581286i	−0.910258	+	0.414041i	$0.864117\pi$
$564$		0			0
$565$	21.0385	−	12.1466i	0.885095	−	0.511010i
$566$	−9.19982	−	32.7297i	−0.386697	−	1.37573i
$567$		0			0
$568$	−28.3848	+	30.5452i	−1.19100	+	1.28165i
$569$	14.7424	+	25.5346i	0.618033	+	1.07046i	0.989844	+	0.142156i	$0.0454036\pi$
$569$	14.7424	+	25.5346i	0.618033	+	1.07046i	−0.371811	+	0.928308i	$0.621263\pi$
$570$		0			0
$571$	−28.4767	−	16.4410i	−1.19171	−	0.688036i	−0.233018	−	0.972472i	$-0.574860\pi$
$571$	−28.4767	−	16.4410i	−1.19171	−	0.688036i	−0.958695	+	0.284437i	$0.908193\pi$
$572$	−24.7269	−	13.4817i	−1.03388	−	0.563699i
$573$		0			0
$574$	−23.1620	−	17.1439i	−0.966764	−	0.715572i
$575$	−7.04085			−0.293624
$576$		0			0
$577$	8.67157	−	15.0196i	0.361002	−	0.625274i	−0.627124	−	0.778920i	$-0.715768\pi$
$577$	8.67157	−	15.0196i	0.361002	−	0.625274i	0.988126	+	0.153645i	$0.0491013\pi$
$578$	5.04961	−	19.8102i	0.210036	−	0.823996i
$579$		0			0
$580$	−32.9706	+	20.1251i	−1.36903	+	0.835649i
$581$	2.58469	+	18.8875i	0.107231	+	0.783584i
$582$		0			0
$583$	−10.8284	−	18.7554i	−0.448468	−	0.776769i
$584$	−2.49495	−	8.11019i	−0.103242	−	0.335602i
$585$		0			0
$586$	10.6909	−	10.9553i	0.441637	−	0.452560i
$587$		−	20.5336i		−	0.847512i	−0.905776	−	0.423756i	$-0.860711\pi$
$587$		−	20.5336i		−	0.847512i	0.905776	−	0.423756i	$-0.139289\pi$
$588$		0			0
$589$			5.28411i			0.217728i
$590$	24.7825	+	24.1844i	1.02028	+	0.995655i
$591$		0			0
$592$	−25.9760	+	16.7400i	−1.06761	+	0.688011i
$593$	11.5523	+	20.0092i	0.474396	+	0.821679i	0.999570	−	0.0293163i	$-0.00933299\pi$
$593$	11.5523	+	20.0092i	0.474396	+	0.821679i	−0.525174	+	0.850995i	$0.676000\pi$
$594$		0			0
$595$	−1.49516	−	10.9258i	−0.0612955	−	0.447913i
$596$	−10.8916	−	17.8435i	−0.446138	−	0.730900i
$597$		0			0
$598$	−34.3268	−	8.74989i	−1.40373	−	0.357810i
$599$	−0.660688	+	1.14434i	−0.0269950	+	0.0467567i	−0.879207	−	0.476439i	$-0.841927\pi$
$599$	−0.660688	+	1.14434i	−0.0269950	+	0.0467567i	0.852212	+	0.523196i	$0.175260\pi$
$600$		0			0
$601$	−12.7990			−0.522082			−0.261041	−	0.965328i	$-0.584066\pi$
$601$	−12.7990			−0.522082			−0.261041	+	0.965328i	$0.584066\pi$
$602$	−5.99786	+	8.10334i	−0.244455	+	0.330267i
$603$		0			0
$604$	−15.5024	−	8.45227i	−0.630783	−	0.343918i
$605$	−14.2881	−	8.24926i	−0.580895	−	0.335380i
$606$		0			0
$607$	5.96447	+	10.3308i	0.242090	+	0.419313i	0.961309	−	0.275471i	$-0.0888337\pi$
$607$	5.96447	+	10.3308i	0.242090	+	0.419313i	−0.719219	+	0.694783i	$0.755500\pi$
$608$	−8.16872	−	1.66205i	−0.331285	−	0.0674050i
$609$		0			0
$610$	14.8284	−	4.16804i	0.600385	−	0.168759i
$611$	65.0789	−	37.5733i	2.63281	−	1.52005i
$612$		0			0
$613$	10.8289	+	6.25206i	0.437375	+	0.252519i	0.702483	−	0.711700i	$-0.252074\pi$
$613$	10.8289	+	6.25206i	0.437375	+	0.252519i	−0.265109	+	0.964219i	$0.585408\pi$
$614$	10.1886	−	10.4406i	0.411179	−	0.421349i
$615$		0			0
$616$	14.6949	−	6.81861i	0.592073	−	0.274730i
$617$	−3.19008			−0.128428			−0.0642139	−	0.997936i	$-0.520454\pi$
$617$	−3.19008			−0.128428			−0.0642139	+	0.997936i	$0.520454\pi$
$618$		0			0
$619$	5.32375	+	3.07367i	0.213980	+	0.123541i	0.603160	−	0.797621i	$-0.293908\pi$
$619$	5.32375	+	3.07367i	0.213980	+	0.123541i	−0.389180	+	0.921162i	$0.627242\pi$
$620$	18.7346	−	0.457771i	0.752401	−	0.0183845i
$621$		0			0
$622$	46.2843	−	13.0098i	1.85583	−	0.521645i
$623$	12.4867	+	16.1021i	0.500268	+	0.645119i
$624$		0			0
$625$	15.3995	+	26.6727i	0.615980	+	1.06691i
$626$	−2.08559	+	8.18203i	−0.0833571	+	0.327020i
$627$		0			0
$628$	−7.98091	+	14.6378i	−0.318473	+	0.584114i
$629$		−	12.3228i		−	0.491342i
$630$		0			0
$631$	−4.82843			−0.192217			−0.0961083	−	0.995371i	$-0.530640\pi$
$631$	−4.82843			−0.192217			−0.0961083	+	0.995371i	$0.530640\pi$
$632$	−19.9682	−	4.57349i	−0.794293	−	0.181924i
$633$		0			0
$634$	13.8151	+	3.52145i	0.548666	+	0.139855i
$635$	−22.7912	+	13.1585i	−0.904440	+	0.522179i
$636$		0			0
$637$	12.2334	+	43.8602i	0.484703	+	1.73780i
$638$	21.7832	−	6.12293i	0.862407	−	0.242409i
$639$		0			0
$640$	−5.18507	+	29.1059i	−0.204958	+	1.15051i
$641$	−0.797521	+	1.38135i	−0.0315002	+	0.0545599i	−0.881346	−	0.472472i	$-0.843362\pi$
$641$	−0.797521	+	1.38135i	−0.0315002	+	0.0545599i	0.849846	+	0.527032i	$0.176695\pi$
$642$		0			0
$643$			8.58892i			0.338714i	0.985555	+	0.169357i	$0.0541691\pi$
$643$			8.58892i			0.338714i	−0.985555	+	0.169357i	$0.945831\pi$
$644$	15.7923	−	12.8763i	0.622305	−	0.507396i
$645$		0			0
$646$	2.32161	−	2.37903i	0.0913424	−	0.0936016i
$647$	0.660688	−	1.14434i	0.0259743	−	0.0449888i	−0.852746	−	0.522326i	$-0.825065\pi$
$647$	0.660688	−	1.14434i	0.0259743	−	0.0449888i	0.878720	+	0.477337i	$0.158398\pi$
$648$		0			0
$649$	−10.1421	−	17.5667i	−0.398114	−	0.689553i
$650$	−4.55153	−	16.1928i	−0.178526	−	0.635132i
$651$		0			0
$652$	−10.4853	−	17.1778i	−0.410635	−	0.672736i
$653$	20.3007	−	11.7206i	0.794427	−	0.458663i	−0.0470917	−	0.998891i	$-0.514995\pi$
$653$	20.3007	−	11.7206i	0.794427	−	0.458663i	0.841519	+	0.540228i	$0.181662\pi$
$654$		0			0
$655$	6.82843	−	11.8272i	0.266809	−	0.462126i
$656$	−30.7694	+	1.50457i	−1.20134	+	0.0587435i
$657$		0			0
$658$	−4.89903	+	42.9463i	−0.190984	+	1.67422i
$659$			8.10201i			0.315610i	0.987470	+	0.157805i	$0.0504417\pi$
$659$			8.10201i			0.315610i	−0.987470	+	0.157805i	$0.949558\pi$
$660$		0			0
$661$	−9.68096	−	5.58931i	−0.376546	−	0.217399i	0.299769	−	0.954012i	$-0.403091\pi$
$661$	−9.68096	−	5.58931i	−0.376546	−	0.217399i	−0.676314	+	0.736613i	$0.736424\pi$
$662$	−7.73131	−	1.97071i	−0.300486	−	0.0765937i
$663$		0			0
$664$	14.9289	+	13.8730i	0.579355	+	0.538378i
$665$	−3.85077	+	9.43242i	−0.149326	+	0.365774i
$666$		0			0
$667$	24.6481	−	14.2306i	0.954378	−	0.551011i
$668$	0.720231	+	29.4760i	0.0278666	+	1.14046i
$669$		0			0
$670$	−30.5114	−	29.7750i	−1.17876	−	1.15031i
$671$	−9.02291			−0.348326
$672$		0			0
$673$	7.62742			0.294015			0.147008	−	0.989135i	$-0.453036\pi$
$673$	7.62742			0.294015			0.147008	+	0.989135i	$0.453036\pi$
$674$	−12.8105	−	12.5013i	−0.493442	−	0.481533i
$675$		0			0
$676$	−1.43210	−	58.6099i	−0.0550809	−	2.25423i
$677$	−0.776550	+	0.448342i	−0.0298453	+	0.0172312i	−0.514848	−	0.857281i	$-0.672152\pi$
$677$	−0.776550	+	0.448342i	−0.0298453	+	0.0172312i	0.485003	+	0.874512i	$0.338818\pi$
$678$		0			0
$679$	2.17157	−	0.297173i	0.0833373	−	0.0114045i
$680$	−8.63589	−	8.02509i	−0.331171	−	0.307748i
$681$		0			0
$682$	−10.6376	−	2.71152i	−0.407336	−	0.103830i
$683$	25.4425	+	14.6892i	0.973529	+	0.562067i	0.900310	−	0.435249i	$-0.143340\pi$
$683$	25.4425	+	14.6892i	0.973529	+	0.562067i	0.0732188	+	0.997316i	$0.476673\pi$
$684$		0			0
$685$			40.2502i			1.53788i
$686$	−24.4645	−	9.35341i	−0.934061	−	0.357115i
$687$		0			0
$688$	0.526379	+	10.7648i	0.0200680	+	0.410404i
$689$	32.5380	−	56.3575i	1.23960	−	2.14705i
$690$		0			0
$691$	−32.0863	+	18.5250i	−1.22062	+	0.704726i	−0.965050	−	0.262064i	$-0.915597\pi$
$691$	−32.0863	+	18.5250i	−1.22062	+	0.704726i	−0.255571	+	0.966790i	$0.582263\pi$
$692$	−6.30001	−	10.3212i	−0.239490	−	0.392353i
$693$		0			0
$694$	−5.10051	−	18.1458i	−0.193613	−	0.688805i
$695$	−20.5185	−	35.5392i	−0.778313	−	1.34808i
$696$		0			0
$697$	6.14214	−	10.6385i	0.232650	−	0.402962i
$698$	−23.9946	+	24.5881i	−0.908209	+	0.930671i
$699$		0			0
$700$	9.04408	+	3.43696i	0.341834	+	0.129905i
$701$			7.83938i			0.296089i	0.988981	+	0.148045i	$0.0472979\pi$
$701$			7.83938i			0.296089i	−0.988981	+	0.148045i	$0.952702\pi$
$702$		0			0
$703$	−5.69239	+	9.85951i	−0.214692	+	0.371858i
$704$	7.53768	−	15.5919i	0.284087	−	0.587640i
$705$		0			0
$706$	−17.0000	+	4.77844i	−0.639803	+	0.179839i
$707$	−10.6052	−	4.32957i	−0.398851	−	0.162830i
$708$		0			0
$709$	13.8192	−	7.97852i	0.518991	−	0.299640i	−0.217531	−	0.976054i	$-0.569800\pi$
$709$	13.8192	−	7.97852i	0.518991	−	0.299640i	0.736522	+	0.676414i	$0.236467\pi$
$710$	52.7927	+	13.4568i	1.98127	+	0.505026i
$711$		0			0
$712$	21.2334	+	4.86327i	0.795756	+	0.182259i
$713$	−13.8080			−0.517115
$714$		0			0
$715$			36.7973i			1.37614i
$716$	21.0506	−	38.6090i	0.786697	−	1.44289i
$717$		0			0
$718$	−1.11434	+	4.37167i	−0.0415867	+	0.163149i
$719$	−7.04085	−	12.1951i	−0.262579	−	0.454801i	0.704347	−	0.709856i	$-0.251240\pi$
$719$	−7.04085	−	12.1951i	−0.262579	−	0.454801i	−0.966927	+	0.255055i	$0.917907\pi$
$720$		0			0
$721$	16.8848	+	21.7737i	0.628822	+	0.810896i
$722$	22.9111	−	6.43996i	0.852663	−	0.239671i
$723$		0			0
$724$	−9.55403	+	0.233448i	−0.355073	+	0.00867602i
$725$	11.7034	+	6.75699i	0.434655	+	0.250948i
$726$		0			0
$727$	10.8995			0.404240			0.202120	−	0.979361i	$-0.435217\pi$
$727$	10.8995			0.404240			0.202120	+	0.979361i	$0.435217\pi$
$728$	39.8221	+	27.9958i	1.47591	+	1.03759i
$729$		0			0
$730$	−7.74304	+	7.93455i	−0.286583	+	0.293671i
$731$	−3.72192	−	2.14885i	−0.137660	−	0.0794782i
$732$		0			0
$733$	19.4526	−	11.2310i	0.718499	−	0.414825i	−0.0957011	−	0.995410i	$-0.530509\pi$
$733$	19.4526	−	11.2310i	0.718499	−	0.414825i	0.814200	+	0.580585i	$0.197176\pi$
$734$	−42.7289	+	12.0104i	−1.57715	+	0.443313i
$735$		0			0
$736$	4.34315	−	21.3459i	0.160090	−	0.786820i
$737$	12.4867	+	21.6275i	0.459952	+	0.796660i
$738$		0			0
$739$	−15.7147	−	9.07290i	−0.578075	−	0.333752i	0.182293	−	0.983244i	$-0.441648\pi$
$739$	−15.7147	−	9.07290i	−0.578075	−	0.333752i	−0.760368	+	0.649492i	$0.774981\pi$
$740$	35.4497	+	19.3280i	1.30316	+	0.710513i
$741$		0			0
$742$	14.9214	+	34.3296i	0.547780	+	1.26028i
$743$	−26.2947			−0.964659			−0.482329	−	0.875990i	$-0.660209\pi$
$743$	−26.2947			−0.964659			−0.482329	+	0.875990i	$0.660209\pi$
$744$		0			0
$745$	−13.6569	+	23.6544i	−0.500348	+	0.866629i
$746$	32.4547	+	8.27268i	1.18825	+	0.302884i
$747$		0			0
$748$	3.59798	+	5.89450i	0.131555	+	0.215524i
$749$	6.78910	−	5.26471i	0.248068	−	0.192368i
$750$		0			0
$751$	16.8640	+	29.2092i	0.615375	+	1.06586i	0.990319	+	0.138813i	$0.0443286\pi$
$751$	16.8640	+	29.2092i	0.615375	+	1.06586i	−0.374944	+	0.927047i	$0.622338\pi$
$752$	25.0315	+	38.8422i	0.912806	+	1.41643i
$753$		0			0
$754$	48.6616	+	47.4871i	1.77215	+	1.72938i
$755$			23.0698i			0.839596i
$756$		0			0
$757$		−	24.2931i		−	0.882949i	−0.897274	−	0.441475i	$-0.854456\pi$
$757$		−	24.2931i		−	0.882949i	0.897274	−	0.441475i	$-0.145544\pi$
$758$	16.0107	−	16.4067i	0.581534	−	0.595917i
$759$		0			0
$760$	3.20250	+	10.4102i	0.116167	+	0.377616i
$761$	−3.98760	−	6.90673i	−0.144550	−	0.250369i	0.784655	−	0.619933i	$-0.212840\pi$
$761$	−3.98760	−	6.90673i	−0.144550	−	0.250369i	−0.929205	+	0.369564i	$0.879507\pi$
$762$		0			0
$763$	−26.1433	−	10.6729i	−0.946450	−	0.386386i
$764$	30.6126	−	18.6858i	1.10753	−	0.676030i
$765$		0			0
$766$	10.5302	−	41.3112i	0.380471	−	1.49263i
$767$	30.4758	−	52.7857i	1.10042	−	1.90598i
$768$		0			0
$769$	16.1716			0.583162			0.291581	−	0.956546i	$-0.405819\pi$
$769$	16.1716			0.583162			0.291581	+	0.956546i	$0.405819\pi$
$770$	−17.0127	−	12.5923i	−0.613096	−	0.453796i
$771$		0			0
$772$	−18.1105	−	9.87427i	−0.651810	−	0.355383i
$773$	39.6364	+	22.8841i	1.42562	+	0.823083i	0.996771	−	0.0802922i	$-0.0255853\pi$
$773$	39.6364	+	22.8841i	1.42562	+	0.823083i	0.428851	+	0.903375i	$0.358919\pi$
$774$		0			0
$775$	−3.27817	−	5.67796i	−0.117756	−	0.203959i
$776$	1.59504	−	1.71644i	0.0572586	−	0.0616167i
$777$		0			0
$778$	3.48528	+	12.3994i	0.124953	+	0.444540i
$779$	−9.82868	+	5.67459i	−0.352149	+	0.203313i
$780$		0			0
$781$	−27.6384	−	15.9570i	−0.988980	−	0.570988i
$782$	6.21670	+	6.06665i	0.222309	+	0.216943i
$783$		0			0
$784$	−26.5710	+	8.83081i	−0.948963	+	0.315386i
$785$	21.7832			0.777477
$786$		0			0
$787$	8.71442	+	5.03127i	0.310636	+	0.179346i	0.647211	−	0.762311i	$-0.275935\pi$
$787$	8.71442	+	5.03127i	0.310636	+	0.179346i	−0.336575	+	0.941657i	$0.609269\pi$
$788$	39.1083	−	0.955591i	1.39318	−	0.0340415i
$789$		0			0
$790$	7.24264	+	25.7668i	0.257682	+	0.916740i
$791$	24.3693	−	3.33486i	0.866473	−	0.118574i
$792$		0			0
$793$	−13.5563	−	23.4803i	−0.481400	−	0.833809i
$794$	24.3769	+	6.21366i	0.865104	+	0.220514i
$795$		0			0
$796$	1.45469	+	0.793130i	0.0515600	+	0.0281117i
$797$		−	41.3617i		−	1.46511i	−0.680710	−	0.732553i	$-0.738329\pi$
$797$		−	41.3617i		−	1.46511i	0.680710	−	0.732553i	$-0.261671\pi$
$798$		0			0
$799$	−18.4264			−0.651879
$800$	9.80869	−	3.28181i	0.346790	−	0.116029i
$801$		0			0
$802$	−3.70899	+	14.5508i	−0.130969	+	0.513806i
$803$	5.62427	−	3.24718i	0.198476	−	0.114590i
$804$		0			0
$805$	−24.6481	−	10.0625i	−0.868731	−	0.354658i
$806$	−8.92616	−	31.7561i	−0.314411	−	1.11856i
$807$		0			0
$808$	−11.7045	+	3.60069i	−0.411764	+	0.126672i
$809$	9.43341	−	16.3392i	0.331661	−	0.574454i	−0.651177	−	0.758926i	$-0.725724\pi$
$809$	9.43341	−	16.3392i	0.331661	−	0.574454i	0.982838	+	0.184472i	$0.0590576\pi$
$810$		0			0
$811$			16.6722i			0.585439i	0.956198	+	0.292720i	$0.0945602\pi$
$811$			16.6722i			0.585439i	−0.956198	+	0.292720i	$0.905440\pi$
$812$	−38.6075	+	6.24755i	−1.35486	+	0.219246i
$813$		0			0
$814$	−16.9275	−	16.5189i	−0.593308	−	0.578988i
$815$	−13.1474	+	22.7719i	−0.460532	+	0.797664i
$816$		0			0
$817$	1.98528	+	3.43861i	0.0694562	+	0.120302i
$818$	−39.4020	+	11.0753i	−1.37766	+	0.387238i
$819$		0			0
$820$	20.9706	+	34.3557i	0.732324	+	1.19975i
$821$	−0.709933	+	0.409880i	−0.0247768	+	0.0143049i	−0.512337	−	0.858784i	$-0.671220\pi$
$821$	−0.709933	+	0.409880i	−0.0247768	+	0.0143049i	0.487560	+	0.873089i	$0.337887\pi$
$822$		0			0
$823$	6.89949	−	11.9503i	0.240501	−	0.416560i	−0.720356	−	0.693605i	$-0.756022\pi$
$823$	6.89949	−	11.9503i	0.240501	−	0.416560i	0.960857	+	0.277044i	$0.0893548\pi$
$824$	28.7124	+	6.57623i	1.00024	+	0.229094i
$825$		0			0
$826$	13.9757	+	32.1538i	0.486276	+	1.11877i
$827$			16.2359i			0.564577i	0.959330	+	0.282288i	$0.0910935\pi$
$827$			16.2359i			0.564577i	−0.959330	+	0.282288i	$0.908906\pi$
$828$		0			0
$829$	−47.7104	−	27.5456i	−1.65705	−	0.956698i	−0.974066	−	0.226263i	$-0.927349\pi$
$829$	−47.7104	−	27.5456i	−1.65705	−	0.956698i	−0.682983	−	0.730434i	$-0.739318\pi$
$830$	6.57701	−	25.8024i	0.228291	−	0.895613i
$831$		0			0
$832$	51.8995	−	3.81048i	1.79929	−	0.132105i
$833$	2.77958	−	10.8138i	0.0963069	−	0.374675i
$834$		0			0
$835$	33.3625	−	19.2619i	1.15456	−	0.666584i
$836$	−0.155850	−	6.37826i	−0.00539017	−	0.220597i
$837$		0			0
$838$	18.5099	−	18.9677i	0.639415	−	0.655229i
$839$	−23.1046			−0.797660			−0.398830	−	0.917025i	$-0.630584\pi$
$839$	−23.1046			−0.797660			−0.398830	+	0.917025i	$0.630584\pi$
$840$		0			0
$841$	−25.6274			−0.883704
$842$	−0.602895	+	0.617806i	−0.0207771	+	0.0212910i
$843$		0			0
$844$	40.2382	−	0.983199i	1.38506	−	0.0338431i
$845$	−66.3379	+	38.3002i	−2.28209	+	1.31757i
$846$		0			0
$847$	−10.2365	−	13.2005i	−0.351732	−	0.453575i
$848$	35.5913	+	18.2919i	1.22221	+	0.628146i
$849$		0			0
$850$	−1.01874	+	3.99664i	−0.0349425	+	0.137084i
$851$	−25.7641	−	14.8749i	−0.883183	−	0.509906i
$852$		0			0
$853$		−	7.01057i		−	0.240037i	−0.992772	−	0.120019i	$-0.961705\pi$
$853$		−	7.01057i		−	0.240037i	0.992772	−	0.120019i	$-0.0382954\pi$
$854$	15.4949	+	1.76756i	0.530225	+	0.0604845i
$855$		0			0
$856$	2.05049	−	8.95258i	0.0700842	−	0.305993i
$857$	−2.91642	+	5.05138i	−0.0996229	+	0.172552i	−0.911529	−	0.411237i	$-0.865097\pi$
$857$	−2.91642	+	5.05138i	−0.0996229	+	0.172552i	0.811906	+	0.583789i	$0.198430\pi$
$858$		0			0
$859$	7.21926	−	4.16804i	0.246318	−	0.142212i	−0.371759	−	0.928329i	$-0.621245\pi$
$859$	7.21926	−	4.16804i	0.246318	−	0.142212i	0.618077	+	0.786117i	$0.287912\pi$
$860$	12.0195	−	7.33664i	0.409861	−	0.250177i
$861$		0			0
$862$	−9.58579	+	2.69442i	−0.326493	+	0.0917722i
$863$	−17.6588	−	30.5860i	−0.601113	−	1.04116i	−0.992653	−	0.120997i	$-0.961391\pi$
$863$	−17.6588	−	30.5860i	−0.601113	−	1.04116i	0.391540	−	0.920161i	$-0.371942\pi$
$864$		0			0
$865$	−7.89949	+	13.6823i	−0.268591	+	0.465213i
$866$	−33.1972	−	32.3959i	−1.12809	−	1.10086i
$867$		0			0
$868$	17.7366	+	6.74033i	0.602021	+	0.228782i
$869$		−	15.6788i		−	0.531865i
$870$		0			0
$871$	−37.5208	+	64.9880i	−1.27134	+	2.20203i
$872$	−28.8532	+	8.87617i	−0.977093	+	0.300585i
$873$		0			0
$874$	−2.17157	−	7.72569i	−0.0734545	−	0.261325i
$875$	2.97297	+	21.7248i	0.100505	+	0.734431i
$876$		0			0
$877$	24.0288	−	13.8730i	0.811395	−	0.468459i	−0.0360454	−	0.999350i	$-0.511476\pi$
$877$	24.0288	−	13.8730i	0.811395	−	0.468459i	0.847440	+	0.530891i	$0.178143\pi$
$878$	−0.529111	+	2.07576i	−0.0178566	+	0.0700536i
$879$		0			0
$880$	−22.6004	+	1.10512i	−0.761860	+	0.0372536i
$881$	−23.3783			−0.787634			−0.393817	−	0.919189i	$-0.628846\pi$
$881$	−23.3783			−0.787634			−0.393817	+	0.919189i	$0.628846\pi$
$882$		0			0
$883$		−	12.0418i		−	0.405240i	−0.979257	−	0.202620i	$-0.935054\pi$
$883$		−	12.0418i		−	0.405240i	0.979257	−	0.202620i	$-0.0649457\pi$
$884$	−9.93350	+	18.2191i	−0.334100	+	0.612775i
$885$		0			0
$886$	50.8977	+	12.9738i	1.70994	+	0.435863i
$887$	9.29658	+	16.1021i	0.312149	+	0.540657i	0.978827	−	0.204688i	$-0.0656180\pi$
$887$	9.29658	+	16.1021i	0.312149	+	0.540657i	−0.666679	+	0.745345i	$0.732285\pi$
$888$		0			0
$889$	−26.3995	+	3.61269i	−0.885411	+	0.121166i
$890$	−7.70154	−	27.3994i	−0.258156	−	0.918429i
$891$		0			0
$892$	−0.788614	−	32.2746i	−0.0264048	−	1.08063i
$893$	14.7430	+	8.51189i	0.493357	+	0.284840i
$894$		0			0
$895$	−57.4558			−1.92054
$896$	−15.9987	+	25.2990i	−0.534480	+	0.845181i
$897$		0			0
$898$	−1.61440	−	1.57544i	−0.0538734	−	0.0525731i
$899$	22.9520	+	13.2513i	0.765492	+	0.441957i
$900$		0			0
$901$	−13.8192	+	7.97852i	−0.460385	+	0.265803i
$902$	−6.38016	−	22.6984i	−0.212436	−	0.755773i
$903$		0			0
$904$	17.8995	−	19.2619i	0.595328	−	0.640640i
$905$	6.24333	+	10.8138i	0.207535	+	0.359462i
$906$		0			0
$907$	36.7532	+	21.2195i	1.22037	+	0.704581i	0.964997	−	0.262262i	$-0.0844684\pi$
$907$	36.7532	+	21.2195i	1.22037	+	0.704581i	0.255373	+	0.966843i	$0.417802\pi$
$908$	−15.3663	+	28.1835i	−0.509949	+	0.935302i
$909$		0			0
$910$	7.20845	−	63.1913i	0.238958	−	2.09477i
$911$	−28.8241			−0.954985			−0.477492	−	0.878636i	$-0.658454\pi$
$911$	−28.8241			−0.954985			−0.477492	+	0.878636i	$0.658454\pi$
$912$		0			0
$913$	−7.79899	+	13.5082i	−0.258109	+	0.447058i
$914$	−14.8304	+	58.1812i	−0.490545	+	1.92446i
$915$		0			0
$916$	−16.7365	−	27.4192i	−0.552991	−	0.905955i
$917$	10.9269	−	8.47343i	0.360838	−	0.279817i
$918$		0			0
$919$	−10.6213	−	18.3967i	−0.350365	−	0.606850i	0.635948	−	0.771732i	$-0.280609\pi$
$919$	−10.6213	−	18.3967i	−0.350365	−	0.606850i	−0.986313	+	0.164882i	$0.947276\pi$
$920$	−27.2031	+	8.36853i	−0.896858	+	0.275902i
$921$		0			0
$922$	−38.6392	+	39.5949i	−1.27251	+	1.30399i
$923$		−	95.8978i		−	3.15651i
$924$		0			0
$925$		−	14.1259i		−	0.464455i
$926$	−18.4343	−	17.9894i	−0.605789	−	0.591168i
$927$		0			0
$928$	−27.7045	+	31.3135i	−0.909446	+	1.02792i
$929$	21.6464	+	37.4927i	0.710196	+	1.23009i	0.964783	+	0.263045i	$0.0847269\pi$
$929$	21.6464	+	37.4927i	0.710196	+	1.23009i	−0.254588	+	0.967050i	$0.581940\pi$
$930$		0			0
$931$	−7.21926	+	7.36813i	−0.236602	+	0.241481i
$932$	−21.3161	+	13.0112i	−0.698231	+	0.426197i
$933$		0			0
$934$	46.1933	+	11.7746i	1.51149	+	0.385278i
$935$	4.51146	−	7.81407i	0.147540	−	0.255548i
$936$		0			0
$937$	−28.1716			−0.920325			−0.460163	−	0.887835i	$-0.652209\pi$
$937$	−28.1716			−0.920325			−0.460163	+	0.887835i	$0.652209\pi$
$938$	−17.2064	−	39.5867i	−0.561808	−	1.29255i
$939$		0			0
$940$	28.9014	−	53.0083i	0.942660	−	1.72894i
$941$	−8.66386	−	5.00208i	−0.282434	−	0.163063i	0.352091	−	0.935966i	$-0.385471\pi$
$941$	−8.66386	−	5.00208i	−0.282434	−	0.163063i	−0.634525	+	0.772903i	$0.718804\pi$
$942$		0			0
$943$	−14.8284	−	25.6836i	−0.482880	−	0.836373i
$944$	33.3356	+	17.1326i	1.08498	+	0.557618i
$945$		0			0
$946$	−7.94113	+	2.23213i	−0.258188	+	0.0725728i
$947$	41.0563	−	23.7038i	1.33415	−	0.770271i	0.348216	−	0.937414i	$-0.386787\pi$
$947$	41.0563	−	23.7038i	1.33415	−	0.770271i	0.985933	+	0.167143i	$0.0534541\pi$
$948$		0			0
$949$	16.9002	+	9.75735i	0.548604	+	0.316737i
$950$	2.66131	−	2.72713i	0.0863441	−	0.0884797i
$951$		0			0
$952$	−5.02404	−	10.8274i	−0.162830	−	0.350917i
$953$	49.6730			1.60907			0.804533	−	0.593908i	$-0.202416\pi$
$953$	49.6730			1.60907			0.804533	+	0.593908i	$0.202416\pi$
$954$		0			0
$955$	−40.5818	−	23.4299i	−1.31320	−	0.758174i
$956$	−0.220405	−	9.02022i	−0.00712839	−	0.291735i
$957$		0			0
$958$	39.2426	−	11.0305i	1.26787	−	0.356379i
$959$	−15.4031	+	37.7297i	−0.497391	+	1.21836i
$960$		0			0
$961$	9.07107	+	15.7116i	0.292615	+	0.506824i
$962$	17.5547	−	68.8689i	0.565985	−	2.22042i
$963$		0			0
$964$	5.56916	+	3.03644i	0.179371	+	0.0977971i
$965$			26.9510i			0.867584i
$966$		0			0
$967$	−7.58579			−0.243942			−0.121971	−	0.992534i	$-0.538922\pi$
$967$	−7.58579			−0.243942			−0.121971	+	0.992534i	$0.538922\pi$
$968$	−17.4071	−	3.98690i	−0.559486	−	0.128144i
$969$		0			0
$970$	−2.96661	−	0.756187i	−0.0952521	−	0.0242797i
$971$	7.65986	−	4.42242i	0.245817	−	0.141922i	−0.372031	−	0.928220i	$-0.621338\pi$
$971$	7.65986	−	4.42242i	0.245817	−	0.141922i	0.617847	+	0.786298i	$0.288005\pi$
$972$		0			0
$973$	−5.63341	−	41.1658i	−0.180599	−	1.31971i
$974$	−13.9849	+	3.93095i	−0.448107	+	0.125956i
$975$		0			0
$976$	14.0142	−	9.03131i	0.448582	−	0.289085i
$977$	−10.8916	+	18.8648i	−0.348454	+	0.603540i	−0.985975	−	0.166893i	$-0.946627\pi$
$977$	−10.8916	+	18.8648i	−0.348454	+	0.603540i	0.637521	+	0.770433i	$0.279960\pi$
$978$		0			0
$979$			16.6722i			0.532845i
$980$	26.7489	+	24.9573i	0.854462	+	0.797233i
$981$		0			0
$982$	−7.30021	+	7.48076i	−0.232959	+	0.238721i
$983$	−6.71051	+	11.6229i	−0.214032	+	0.370714i	−0.952973	−	0.303056i	$-0.901993\pi$
$983$	−6.71051	+	11.6229i	−0.214032	+	0.370714i	0.738941	+	0.673770i	$0.235326\pi$
$984$		0			0
$985$	−25.5563	−	44.2649i	−0.814293	−	1.41040i
$986$	−4.51146	−	16.0502i	−0.143674	−	0.511142i
$987$		0			0
$988$	16.3640	−	9.98849i	0.520607	−	0.317776i
$989$	−8.98552	+	5.18779i	−0.285723	+	0.164962i
$990$		0			0
$991$	−25.7635	+	44.6236i	−0.818403	+	1.41752i	0.0884551	+	0.996080i	$0.471807\pi$
$991$	−25.7635	+	44.6236i	−0.818403	+	1.41752i	−0.906858	+	0.421436i	$0.861526\pi$
$992$	19.2361	−	6.43605i	0.610748	−	0.204345i
$993$		0			0
$994$	44.3371	+	32.8170i	1.40629	+	1.04089i
$995$		−	2.16478i		−	0.0686283i
$996$		0			0
$997$	−7.30996	−	4.22041i	−0.231509	−	0.133662i	0.379759	−	0.925085i	$-0.376007\pi$
$997$	−7.30996	−	4.22041i	−0.231509	−	0.133662i	−0.611268	+	0.791424i	$0.709340\pi$
$998$	−13.4432	−	3.42666i	−0.425536	−	0.108469i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.d.109.2	yes	16
3.2	odd	2	inner	504.2.cj.d.109.7	yes	16
4.3	odd	2		2016.2.cr.d.1873.8		16
7.2	even	3	inner	504.2.cj.d.37.3	yes	16
8.3	odd	2		2016.2.cr.d.1873.1		16
8.5	even	2	inner	504.2.cj.d.109.3	yes	16
12.11	even	2		2016.2.cr.d.1873.2		16
21.2	odd	6	inner	504.2.cj.d.37.6	yes	16
24.5	odd	2	inner	504.2.cj.d.109.6	yes	16
24.11	even	2		2016.2.cr.d.1873.7		16
28.23	odd	6		2016.2.cr.d.1297.2		16
56.37	even	6	inner	504.2.cj.d.37.2	✓	16
56.51	odd	6		2016.2.cr.d.1297.7		16
84.23	even	6		2016.2.cr.d.1297.8		16
168.107	even	6		2016.2.cr.d.1297.1		16
168.149	odd	6	inner	504.2.cj.d.37.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cj.d.37.2	✓	16	56.37	even	6	inner
504.2.cj.d.37.3	yes	16	7.2	even	3	inner
504.2.cj.d.37.6	yes	16	21.2	odd	6	inner
504.2.cj.d.37.7	yes	16	168.149	odd	6	inner
504.2.cj.d.109.2	yes	16	1.1	even	1	trivial
504.2.cj.d.109.3	yes	16	8.5	even	2	inner
504.2.cj.d.109.6	yes	16	24.5	odd	2	inner
504.2.cj.d.109.7	yes	16	3.2	odd	2	inner
2016.2.cr.d.1297.1		16	168.107	even	6
2016.2.cr.d.1297.2		16	28.23	odd	6
2016.2.cr.d.1297.7		16	56.51	odd	6
2016.2.cr.d.1297.8		16	84.23	even	6
2016.2.cr.d.1873.1		16	8.3	odd	2
2016.2.cr.d.1873.2		16	12.11	even	2
2016.2.cr.d.1873.7		16	24.11	even	2
2016.2.cr.d.1873.8		16	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.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01214 - 0.987711i) q^{2} +(0.0488544 + 1.99940i) q^{4} +(2.26303 - 1.30656i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.92538 - 2.07193i) q^{8} +O(q^{10})\)	\(q+(-1.01214 - 0.987711i) q^{2} +(0.0488544 + 1.99940i) q^{4} +(2.26303 - 1.30656i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.92538 - 2.07193i) q^{8} +(-3.58101 - 0.912798i) q^{10} +(1.87476 + 1.08239i) q^{11} +6.50490i q^{13} +(-3.00745 - 2.22603i) q^{14} +(-3.99523 + 0.195359i) q^{16} +(0.797521 - 1.38135i) q^{17} +(-1.27620 + 0.736813i) q^{19} +(2.72291 + 4.46088i) q^{20} +(-0.828427 - 2.94725i) q^{22} +(-1.92538 - 3.33486i) q^{23} +(0.914214 - 1.58346i) q^{25} +(6.42496 - 6.58387i) q^{26} +(0.845288 + 5.22355i) q^{28} +7.39104i q^{29} +(1.79289 - 3.10538i) q^{31} +(4.23669 + 3.74840i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(5.46345 - 4.23671i) q^{35} +(6.69064 - 3.86285i) q^{37} +(2.01945 + 0.514756i) q^{38} +(1.65010 - 7.20448i) q^{40} +7.70154 q^{41} -2.69442i q^{43} +(-2.07255 + 3.80128i) q^{44} +(-1.34512 + 5.27707i) q^{46} +(-5.77615 - 10.0046i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-2.48932 + 0.699709i) q^{50} +(-13.0059 + 0.317793i) q^{52} +(-8.66386 - 5.00208i) q^{53} +5.65685 q^{55} +(4.30381 - 6.12186i) q^{56} +(7.30021 - 7.48076i) q^{58} +(-8.11475 - 4.68506i) q^{59} +(-3.60963 + 2.08402i) q^{61} +(-4.88188 + 1.37222i) q^{62} +(-0.585786 - 7.97852i) q^{64} +(8.49906 + 14.7208i) q^{65} +(9.99062 + 5.76809i) q^{67} +(2.80083 + 1.52708i) q^{68} +(-9.71442 - 1.10816i) q^{70} -14.7424 q^{71} +(1.50000 - 2.59808i) q^{73} +(-10.5872 - 2.69868i) q^{74} +(-1.53553 - 2.51564i) q^{76} +(5.30262 + 2.16478i) q^{77} +(-3.62132 - 6.27231i) q^{79} +(-8.78608 + 5.66212i) q^{80} +(-7.79504 - 7.60689i) q^{82} +7.20533i q^{83} -4.16804i q^{85} +(-2.66131 + 2.72713i) q^{86} +(5.85227 - 1.80035i) q^{88} +(3.85077 + 6.66973i) q^{89} +(2.33343 + 17.0514i) q^{91} +(6.57368 - 4.01254i) q^{92} +(-4.03537 + 15.8312i) q^{94} +(-1.92538 + 3.33486i) q^{95} +0.828427 q^{97} +(-8.68202 - 4.75631i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^4 + 8 * q^7	\( 16 q - 8 q^{4} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 32 q^{22} - 8 q^{25} - 16 q^{28} + 40 q^{31} - 80 q^{34} - 32 q^{40} - 8 q^{46} + 40 q^{49} + 8 q^{52} - 32 q^{64} - 16 q^{70} + 24 q^{73} + 32 q^{76} - 24 q^{79} - 16 q^{82} - 32 q^{88} - 24 q^{94} - 32 q^{97}+O(q^{100}) \) 16 * q - 8 * q^4 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 32 * q^22 - 8 * q^25 - 16 * q^28 + 40 * q^31 - 80 * q^34 - 32 * q^40 - 8 * q^46 + 40 * q^49 + 8 * q^52 - 32 * q^64 - 16 * q^70 + 24 * q^73 + 32 * q^76 - 24 * q^79 - 16 * q^82 - 32 * q^88 - 24 * q^94 - 32 * q^97

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