LMFDB - Embedded newform 864.2.v.b.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33723 - 0.460244i) q^{2} +(1.57635 + 1.23090i) q^{4} +(-2.37116 + 0.982165i) q^{5} +(2.29537 - 2.29537i) q^{7} +(-1.54142 - 2.37150i) q^{8} +O(q^{10})$	\(q+(-1.33723 - 0.460244i) q^{2} +(1.57635 + 1.23090i) q^{4} +(-2.37116 + 0.982165i) q^{5} +(2.29537 - 2.29537i) q^{7} +(-1.54142 - 2.37150i) q^{8} +(3.62281 - 0.222067i) q^{10} +(0.00833427 + 0.0201207i) q^{11} +(-4.05547 - 1.67983i) q^{13} +(-4.12585 + 2.01300i) q^{14} +(0.969765 + 3.88066i) q^{16} +1.80284i q^{17} +(0.650151 + 0.269301i) q^{19} +(-4.94672 - 1.37042i) q^{20} +(-0.00188438 - 0.0307418i) q^{22} +(1.25771 + 1.25771i) q^{23} +(1.12220 - 1.12220i) q^{25} +(4.64996 + 4.11282i) q^{26} +(6.44367 - 0.792934i) q^{28} +(0.655744 - 1.58311i) q^{29} -1.65118 q^{31} +(0.489257 - 5.63566i) q^{32} +(0.829744 - 2.41080i) q^{34} +(-3.18824 + 7.69710i) q^{35} +(-11.0433 + 4.57430i) q^{37} +(-0.745455 - 0.659345i) q^{38} +(5.98416 + 4.10926i) q^{40} +(-3.27522 - 3.27522i) q^{41} +(-2.93287 - 7.08058i) q^{43} +(-0.0116289 + 0.0419760i) q^{44} +(-1.10299 - 2.26070i) q^{46} -9.31235i q^{47} -3.53740i q^{49} +(-2.01712 + 0.984150i) q^{50} +(-4.32514 - 7.63989i) q^{52} +(-5.35156 - 12.9198i) q^{53} +(-0.0395237 - 0.0395237i) q^{55} +(-8.98159 - 1.90533i) q^{56} +(-1.60549 + 1.81517i) q^{58} +(-8.36913 + 3.46661i) q^{59} +(-0.0511774 + 0.123553i) q^{61} +(2.20800 + 0.759946i) q^{62} +(-3.24802 + 7.31097i) q^{64} +11.2660 q^{65} +(-2.29687 + 5.54514i) q^{67} +(-2.21911 + 2.84190i) q^{68} +(7.80595 - 8.82540i) q^{70} +(-10.9401 + 10.9401i) q^{71} +(5.54998 + 5.54998i) q^{73} +(16.8727 - 1.03425i) q^{74} +(0.693383 + 1.22478i) q^{76} +(0.0653146 + 0.0270542i) q^{77} -1.71204i q^{79} +(-6.11092 - 8.24919i) q^{80} +(2.87231 + 5.88711i) q^{82} +(-8.31348 - 3.44356i) q^{83} +(-1.77068 - 4.27481i) q^{85} +(0.663121 + 10.8182i) q^{86} +(0.0348696 - 0.0507793i) q^{88} +(8.03010 - 8.03010i) q^{89} +(-13.1646 + 5.45296i) q^{91} +(0.434477 + 3.53072i) q^{92} +(-4.28595 + 12.4527i) q^{94} -1.80611 q^{95} -12.8284 q^{97} +(-1.62807 + 4.73031i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.33723	−	0.460244i	−0.945562	−	0.325442i
$2$	−1.33723	−	0.460244i	−0.945562	−	0.325442i
$3$		0			0
$3$		0			0
$4$	1.57635	+	1.23090i	0.788175	+	0.615451i
$5$	−2.37116	+	0.982165i	−1.06041	+	0.439238i	−0.843598	−	0.536975i	$-0.819567\pi$
$5$	−2.37116	+	0.982165i	−1.06041	+	0.439238i	−0.216815	+	0.976213i	$0.569567\pi$
$6$		0			0
$7$	2.29537	−	2.29537i	0.867566	−	0.867566i	−0.124636	−	0.992203i	$-0.539776\pi$
$7$	2.29537	−	2.29537i	0.867566	−	0.867566i	0.992203	+	0.124636i	$0.0397763\pi$
$8$	−1.54142	−	2.37150i	−0.544976	−	0.838452i
$9$		0			0
$10$	3.62281	−	0.222067i	1.14563	−	0.0702238i
$11$	0.00833427	+	0.0201207i	0.00251288	+	0.00606663i	0.925131	−	0.379648i	$-0.123955\pi$
$11$	0.00833427	+	0.0201207i	0.00251288	+	0.00606663i	−0.922618	+	0.385715i	$0.873955\pi$
$12$		0			0
$13$	−4.05547	−	1.67983i	−1.12479	−	0.465902i	−0.258781	−	0.965936i	$-0.583321\pi$
$13$	−4.05547	−	1.67983i	−1.12479	−	0.465902i	−0.866005	+	0.500035i	$0.833321\pi$
$14$	−4.12585	+	2.01300i	−1.10268	+	0.537996i
$15$		0			0
$16$	0.969765	+	3.88066i	0.242441	+	0.970166i
$17$			1.80284i			0.437252i	0.975809	+	0.218626i	$0.0701575\pi$
$17$			1.80284i			0.437252i	−0.975809	+	0.218626i	$0.929843\pi$
$18$		0			0
$19$	0.650151	+	0.269301i	0.149155	+	0.0617820i	0.456012	−	0.889974i	$-0.349277\pi$
$19$	0.650151	+	0.269301i	0.149155	+	0.0617820i	−0.306857	+	0.951756i	$0.599277\pi$
$20$	−4.94672	−	1.37042i	−1.10612	−	0.306436i
$21$		0			0
$22$	−0.00188438	−	0.0307418i	−0.000401750	−	0.00655417i
$23$	1.25771	+	1.25771i	0.262251	+	0.262251i	0.825968	−	0.563717i	$-0.190629\pi$
$23$	1.25771	+	1.25771i	0.262251	+	0.262251i	−0.563717	+	0.825968i	$0.690629\pi$
$24$		0			0
$25$	1.12220	−	1.12220i	0.224440	−	0.224440i
$26$	4.64996	+	4.11282i	0.911931	+	0.806591i
$27$		0			0
$28$	6.44367	−	0.792934i	1.21774	−	0.149850i
$29$	0.655744	−	1.58311i	0.121769	−	0.293976i	−0.851227	−	0.524797i	$-0.824141\pi$
$29$	0.655744	−	1.58311i	0.121769	−	0.293976i	0.972996	+	0.230821i	$0.0741413\pi$
$30$		0			0
$31$	−1.65118			−0.296561			−0.148280	−	0.988945i	$-0.547374\pi$
$31$	−1.65118			−0.296561			−0.148280	+	0.988945i	$0.547374\pi$
$32$	0.489257	−	5.63566i	0.0864892	−	0.996253i
$33$		0			0
$34$	0.829744	−	2.41080i	0.142300	−	0.413449i
$35$	−3.18824	+	7.69710i	−0.538911	+	1.30105i
$36$		0			0
$37$	−11.0433	+	4.57430i	−1.81551	+	0.752011i	−0.836577	+	0.547850i	$0.815446\pi$
$37$	−11.0433	+	4.57430i	−1.81551	+	0.752011i	−0.978937	+	0.204161i	$0.934554\pi$
$38$	−0.745455	−	0.659345i	−0.120929	−	0.106960i
$39$		0			0
$40$	5.98416	+	4.10926i	0.946179	+	0.649732i
$41$	−3.27522	−	3.27522i	−0.511503	−	0.511503i	0.403484	−	0.914987i	$-0.367799\pi$
$41$	−3.27522	−	3.27522i	−0.511503	−	0.511503i	−0.914987	+	0.403484i	$0.867799\pi$
$42$		0			0
$43$	−2.93287	−	7.08058i	−0.447259	−	1.07978i	−0.973345	−	0.229347i	$-0.926341\pi$
$43$	−2.93287	−	7.08058i	−0.447259	−	1.07978i	0.526086	−	0.850432i	$-0.323659\pi$
$44$	−0.0116289	+	0.0419760i	−0.00175312	+	0.00632812i
$45$		0			0
$46$	−1.10299	−	2.26070i	−0.162627	−	0.333322i
$47$		−	9.31235i		−	1.35835i	−0.733978	−	0.679173i	$-0.762339\pi$
$47$		−	9.31235i		−	1.35835i	0.733978	−	0.679173i	$-0.237661\pi$
$48$		0			0
$49$		−	3.53740i		−	0.505343i
$50$	−2.01712	+	0.984150i	−0.285264	+	0.139180i
$51$		0			0
$52$	−4.32514	−	7.63989i	−0.599789	−	1.05946i
$53$	−5.35156	−	12.9198i	−0.735094	−	1.77467i	−0.624815	−	0.780773i	$-0.714826\pi$
$53$	−5.35156	−	12.9198i	−0.735094	−	1.77467i	−0.110279	−	0.993901i	$-0.535174\pi$
$54$		0			0
$55$	−0.0395237	−	0.0395237i	−0.00532938	−	0.00532938i
$56$	−8.98159	−	1.90533i	−1.20022	−	0.254610i
$57$		0			0
$58$	−1.60549	+	1.81517i	−0.210812	+	0.238344i
$59$	−8.36913	+	3.46661i	−1.08957	+	0.451314i	−0.853856	−	0.520509i	$-0.825742\pi$
$59$	−8.36913	+	3.46661i	−1.08957	+	0.451314i	−0.235712	+	0.971823i	$0.575742\pi$
$60$		0			0
$61$	−0.0511774	+	0.123553i	−0.00655260	+	0.0158194i	−0.927122	−	0.374760i	$-0.877725\pi$
$61$	−0.0511774	+	0.123553i	−0.00655260	+	0.0158194i	0.920569	+	0.390579i	$0.127725\pi$
$62$	2.20800	+	0.759946i	0.280417	+	0.0965133i
$63$		0			0
$64$	−3.24802	+	7.31097i	−0.406003	+	0.913872i
$65$	11.2660			1.39738
$66$		0			0
$67$	−2.29687	+	5.54514i	−0.280608	+	0.677447i	−0.999850	−	0.0173122i	$-0.994489\pi$
$67$	−2.29687	+	5.54514i	−0.280608	+	0.677447i	0.719242	+	0.694759i	$0.244489\pi$
$68$	−2.21911	+	2.84190i	−0.269107	+	0.344631i
$69$		0			0
$70$	7.80595	−	8.82540i	0.932989	−	1.05484i
$71$	−10.9401	+	10.9401i	−1.29835	+	1.29835i	−0.368875	+	0.929479i	$0.620257\pi$
$71$	−10.9401	+	10.9401i	−1.29835	+	1.29835i	−0.929479	+	0.368875i	$0.879743\pi$
$72$		0			0
$73$	5.54998	+	5.54998i	0.649577	+	0.649577i	0.952891	−	0.303314i	$-0.0980931\pi$
$73$	5.54998	+	5.54998i	0.649577	+	0.649577i	−0.303314	+	0.952891i	$0.598093\pi$
$74$	16.8727	−	1.03425i	1.96142	−	0.120229i
$75$		0			0
$76$	0.693383	+	1.22478i	0.0795364	+	0.140492i
$77$	0.0653146	+	0.0270542i	0.00744329	+	0.00308311i
$78$		0			0
$79$		−	1.71204i		−	0.192620i	−0.995351	−	0.0963100i	$-0.969296\pi$
$79$		−	1.71204i		−	0.192620i	0.995351	−	0.0963100i	$-0.0307040\pi$
$80$	−6.11092	−	8.24919i	−0.683221	−	0.922288i
$81$		0			0
$82$	2.87231	+	5.88711i	0.317194	+	0.650123i
$83$	−8.31348	−	3.44356i	−0.912523	−	0.377979i	−0.123501	−	0.992344i	$-0.539412\pi$
$83$	−8.31348	−	3.44356i	−0.912523	−	0.377979i	−0.789022	+	0.614365i	$0.789412\pi$
$84$		0			0
$85$	−1.77068	−	4.27481i	−0.192057	−	0.463668i
$86$	0.663121	+	10.8182i	0.0715062	+	1.16655i
$87$		0			0
$88$	0.0348696	−	0.0507793i	0.00371712	−	0.00541309i
$89$	8.03010	−	8.03010i	0.851189	−	0.851189i	−0.139090	−	0.990280i	$-0.544418\pi$
$89$	8.03010	−	8.03010i	0.851189	−	0.851189i	0.990280	+	0.139090i	$0.0444178\pi$
$90$		0			0
$91$	−13.1646	+	5.45296i	−1.38003	+	0.571626i
$92$	0.434477	+	3.53072i	0.0452973	+	0.368103i
$93$		0			0
$94$	−4.28595	+	12.4527i	−0.442062	+	1.28440i
$95$	−1.80611			−0.185303
$96$		0			0
$97$	−12.8284			−1.30252			−0.651261	−	0.758854i	$-0.725760\pi$
$97$	−12.8284			−1.30252			−0.651261	+	0.758854i	$0.725760\pi$
$98$	−1.62807	+	4.73031i	−0.164460	+	0.477833i
$99$		0			0
$100$	3.15030	−	0.387664i	0.315030	−	0.0387664i
$101$	8.56996	−	3.54980i	0.852743	−	0.353218i	0.0868780	−	0.996219i	$-0.472311\pi$
$101$	8.56996	−	3.54980i	0.852743	−	0.353218i	0.765865	+	0.643001i	$0.222311\pi$
$102$		0			0
$103$	5.27513	−	5.27513i	0.519774	−	0.519774i	−0.397729	−	0.917503i	$-0.630202\pi$
$103$	5.27513	−	5.27513i	0.519774	−	0.519774i	0.917503	+	0.397729i	$0.130202\pi$
$104$	2.26748	+	12.2069i	0.222345	+	1.19698i
$105$		0			0
$106$	1.20999	+	19.7398i	0.117524	+	1.91729i
$107$	−1.74387	−	4.21007i	−0.168586	−	0.407002i	0.816895	−	0.576786i	$-0.195693\pi$
$107$	−1.74387	−	4.21007i	−0.168586	−	0.407002i	−0.985481	+	0.169783i	$0.945693\pi$
$108$		0			0
$109$	−14.3642	−	5.94984i	−1.37584	−	0.569891i	−0.432473	−	0.901647i	$-0.642359\pi$
$109$	−14.3642	−	5.94984i	−1.37584	−	0.569891i	−0.943365	+	0.331756i	$0.892359\pi$
$110$	0.0346616	+	0.0710428i	0.00330486	+	0.00677366i
$111$		0			0
$112$	11.1335	+	6.68158i	1.05202	+	0.631350i
$113$			12.2588i			1.15322i	0.817021	+	0.576608i	$0.195624\pi$
$113$			12.2588i			1.15322i	−0.817021	+	0.576608i	$0.804376\pi$
$114$		0			0
$115$	−4.21752	−	1.74695i	−0.393285	−	0.162904i
$116$	2.98233	−	1.68838i	0.276903	−	0.156762i
$117$		0			0
$118$	12.7869	−	0.783798i	1.17713	−	0.0721545i
$119$	4.13817	+	4.13817i	0.379345	+	0.379345i
$120$		0			0
$121$	7.77784	−	7.77784i	0.707076	−	0.707076i
$122$	0.125300	−	0.141665i	0.0113442	−	0.0128257i
$123$		0			0
$124$	−2.60284	−	2.03244i	−0.233742	−	0.182519i
$125$	3.35210	−	8.09268i	0.299821	−	0.723832i
$126$		0			0
$127$	−17.5967			−1.56146			−0.780729	−	0.624870i	$-0.785152\pi$
$127$	−17.5967			−1.56146			−0.780729	+	0.624870i	$0.785152\pi$
$128$	7.70818	−	8.28155i	0.681313	−	0.731992i
$129$		0			0
$130$	−15.0652	−	5.18512i	−1.32131	−	0.454765i
$131$	−7.84827	+	18.9474i	−0.685707	+	1.65544i	0.0675499	+	0.997716i	$0.478482\pi$
$131$	−7.84827	+	18.9474i	−0.685707	+	1.65544i	−0.753257	+	0.657727i	$0.771518\pi$
$132$		0			0
$133$	2.11048	−	0.874189i	0.183002	−	0.0758018i
$134$	5.62356	−	6.35799i	0.485802	−	0.549247i
$135$		0			0
$136$	4.27543	−	2.77893i	0.366615	−	0.238292i
$137$	−2.91291	−	2.91291i	−0.248867	−	0.248867i	0.571639	−	0.820506i	$-0.306308\pi$
$137$	−2.91291	−	2.91291i	−0.248867	−	0.248867i	−0.820506	+	0.571639i	$0.806308\pi$
$138$		0			0
$139$	−0.374574	−	0.904302i	−0.0317710	−	0.0767019i	0.907198	−	0.420705i	$-0.138217\pi$
$139$	−0.374574	−	0.904302i	−0.0317710	−	0.0767019i	−0.938969	+	0.344003i	$0.888217\pi$
$140$	−14.5002	+	8.20892i	−1.22549	+	0.693780i
$141$		0			0
$142$	19.6646	−	9.59430i	1.65021	−	0.805136i
$143$		−	0.0955992i		−	0.00799441i
$144$		0			0
$145$			4.39784i			0.365221i
$146$	−4.86724	−	9.97593i	−0.402816	−	0.825614i
$147$		0			0
$148$	−23.0387	−	6.38256i	−1.89377	−	0.524643i
$149$	6.60678	+	15.9502i	0.541249	+	1.30669i	0.923842	+	0.382773i	$0.125031\pi$
$149$	6.60678	+	15.9502i	0.541249	+	1.30669i	−0.382594	+	0.923917i	$0.624969\pi$
$150$		0			0
$151$	−9.14148	−	9.14148i	−0.743923	−	0.743923i	0.229408	−	0.973330i	$-0.426321\pi$
$151$	−9.14148	−	9.14148i	−0.743923	−	0.743923i	−0.973330	+	0.229408i	$0.926321\pi$
$152$	−0.363510	−	1.95694i	−0.0294846	−	0.158729i
$153$		0			0
$154$	−0.0748889	−	0.0662382i	−0.00603472	−	0.00533763i
$155$	3.91521	−	1.62173i	0.314477	−	0.130261i
$156$		0			0
$157$	8.17583	−	19.7382i	0.652502	−	1.57528i	−0.156632	−	0.987657i	$-0.550064\pi$
$157$	8.17583	−	19.7382i	0.652502	−	1.57528i	0.809135	−	0.587623i	$-0.199936\pi$
$158$	−0.787958	+	2.28939i	−0.0626865	+	0.182134i
$159$		0			0
$160$	4.37504	+	13.8436i	0.345877	+	1.09443i
$161$	5.77382			0.455041
$162$		0			0
$163$	−5.62522	+	13.5805i	−0.440601	+	1.06371i	0.535137	+	0.844765i	$0.320260\pi$
$163$	−5.62522	+	13.5805i	−0.440601	+	1.06371i	−0.975738	+	0.218941i	$0.929740\pi$
$164$	−1.13142	−	9.19436i	−0.0883494	−	0.717959i
$165$		0			0
$166$	9.53213	+	8.43104i	0.739837	+	0.654376i
$167$	4.65503	−	4.65503i	0.360217	−	0.360217i	−0.503676	−	0.863893i	$-0.668019\pi$
$167$	4.65503	−	4.65503i	0.360217	−	0.360217i	0.863893	+	0.503676i	$0.168019\pi$
$168$		0			0
$169$	4.43264	+	4.43264i	0.340972	+	0.340972i
$170$	0.400351	+	6.53133i	0.0307055	+	0.500930i
$171$		0			0
$172$	4.09226	−	14.7716i	0.312032	−	1.12632i
$173$	5.44067	+	2.25360i	0.413647	+	0.171338i	0.579794	−	0.814763i	$-0.303133\pi$
$173$	5.44067	+	2.25360i	0.413647	+	0.171338i	−0.166148	+	0.986101i	$0.553133\pi$
$174$		0			0
$175$		−	5.15172i		−	0.389433i
$176$	−0.0699995	+	0.0518549i	−0.00527641	+	0.00390871i
$177$		0			0
$178$	−14.4339	+	7.04226i	−1.08186	+	0.527840i
$179$	20.2433	+	8.38506i	1.51306	+	0.626729i	0.976186	−	0.216935i	$-0.0696060\pi$
$179$	20.2433	+	8.38506i	1.51306	+	0.626729i	0.536872	+	0.843664i	$0.319606\pi$
$180$		0			0
$181$	2.50436	+	6.04607i	0.186148	+	0.449401i	0.989212	−	0.146492i	$-0.0467983\pi$
$181$	2.50436	+	6.04607i	0.186148	+	0.449401i	−0.803064	+	0.595893i	$0.796798\pi$
$182$	20.1138	−	1.23291i	1.49093	−	0.0913896i
$183$		0			0
$184$	1.04400	−	4.92134i	0.0769645	−	0.362806i
$185$	21.6928	−	21.6928i	1.59488	−	1.59488i
$186$		0			0
$187$	−0.0362744	+	0.0150253i	−0.00265264	+	0.00109876i
$188$	11.4626	−	14.6795i	0.835995	−	1.07062i
$189$		0			0
$190$	2.41518	+	0.831250i	0.175215	+	0.0603052i
$191$	−16.5358			−1.19649			−0.598244	−	0.801314i	$-0.704134\pi$
$191$	−16.5358			−1.19649			−0.598244	+	0.801314i	$0.704134\pi$
$192$		0			0
$193$	17.3317			1.24756			0.623780	−	0.781600i	$-0.285596\pi$
$193$	17.3317			1.24756			0.623780	+	0.781600i	$0.285596\pi$
$194$	17.1544	+	5.90417i	1.23162	+	0.423895i
$195$		0			0
$196$	4.35419	−	5.57619i	0.311014	−	0.398299i
$197$	16.3748	−	6.78268i	1.16666	−	0.483246i	0.286572	−	0.958059i	$-0.407484\pi$
$197$	16.3748	−	6.78268i	1.16666	−	0.483246i	0.880087	+	0.474813i	$0.157484\pi$
$198$		0			0
$199$	10.3808	−	10.3808i	0.735877	−	0.735877i	−0.235900	−	0.971777i	$-0.575804\pi$
$199$	10.3808	−	10.3808i	0.735877	−	0.735877i	0.971777	+	0.235900i	$0.0758038\pi$
$200$	−4.39108	−	0.931512i	−0.310497	−	0.0658678i
$201$		0			0
$202$	−13.0938	+	0.802607i	−0.921274	+	0.0564712i
$203$	−2.12864	−	5.13898i	−0.149401	−	0.360686i
$204$		0			0
$205$	10.9829	+	4.54925i	0.767076	+	0.317733i
$206$	−9.48190	+	4.62620i	−0.660635	+	0.322323i
$207$		0			0
$208$	2.58601	−	17.3670i	0.179307	−	1.20418i
$209$			0.0153259i			0.00106012i
$210$		0			0
$211$	17.7340	+	7.34566i	1.22086	+	0.505696i	0.897682	−	0.440643i	$-0.145250\pi$
$211$	17.7340	+	7.34566i	1.22086	+	0.505696i	0.323175	+	0.946339i	$0.395250\pi$
$212$	7.46708	−	26.9534i	0.512841	−	1.85117i
$213$		0			0
$214$	0.394287	+	6.43242i	0.0269529	+	0.439711i
$215$	13.9086	+	13.9086i	0.948559	+	0.948559i
$216$		0			0
$217$	−3.79006	+	3.79006i	−0.257286	+	0.257286i
$218$	16.4698	+	14.5673i	1.11547	+	0.986622i
$219$		0			0
$220$	−0.0136535	−	0.110953i	−0.000920517	−	0.00748046i
$221$	3.02846	−	7.31135i	0.203716	−	0.491815i
$222$		0			0
$223$	19.4648			1.30346			0.651729	−	0.758452i	$-0.274044\pi$
$223$	19.4648			1.30346			0.651729	+	0.758452i	$0.274044\pi$
$224$	−11.8129	−	14.0589i	−0.789280	−	0.939351i
$225$		0			0
$226$	5.64206	−	16.3929i	0.375304	−	1.09044i
$227$	−0.180050	+	0.434679i	−0.0119503	+	0.0288507i	−0.929742	−	0.368211i	$-0.879970\pi$
$227$	−0.180050	+	0.434679i	−0.0119503	+	0.0288507i	0.917792	+	0.397062i	$0.129970\pi$
$228$		0			0
$229$	−11.2666	+	4.66678i	−0.744518	+	0.308389i	−0.722502	−	0.691368i	$-0.757008\pi$
$229$	−11.2666	+	4.66678i	−0.744518	+	0.308389i	−0.0220151	+	0.999758i	$0.507008\pi$
$230$	4.83575	+	4.27716i	0.318860	+	0.282027i
$231$		0			0
$232$	−4.76512	+	0.885141i	−0.312845	+	0.0581124i
$233$	−4.24009	−	4.24009i	−0.277778	−	0.277778i	0.554444	−	0.832221i	$-0.312931\pi$
$233$	−4.24009	−	4.24009i	−0.277778	−	0.277778i	−0.832221	+	0.554444i	$0.812931\pi$
$234$		0			0
$235$	9.14627	+	22.0810i	0.596637	+	1.44041i
$236$	−17.4597	−	4.83698i	−1.13653	−	0.314861i
$237$		0			0
$238$	−3.62910	−	7.43823i	−0.235240	−	0.482149i
$239$			24.9057i			1.61101i	0.592587	+	0.805507i	$0.298107\pi$
$239$			24.9057i			1.61101i	−0.592587	+	0.805507i	$0.701893\pi$
$240$		0			0
$241$			1.00972i			0.0650415i	0.999471	+	0.0325207i	$0.0103535\pi$
$241$			1.00972i			0.0650415i	−0.999471	+	0.0325207i	$0.989647\pi$
$242$	−13.9804	+	6.82103i	−0.898697	+	0.438473i
$243$		0			0
$244$	−0.232755	+	0.131769i	−0.0149006	+	0.00843564i
$245$	3.47431	+	8.38773i	0.221966	+	0.535873i
$246$		0			0
$247$	−2.18429	−	2.18429i	−0.138983	−	0.138983i
$248$	2.54517	+	3.91578i	0.161618	+	0.248652i
$249$		0			0
$250$	−8.20713	+	9.27897i	−0.519064	+	0.586854i
$251$	12.1217	−	5.02097i	0.765114	−	0.316921i	0.0342224	−	0.999414i	$-0.489105\pi$
$251$	12.1217	−	5.02097i	0.765114	−	0.316921i	0.730891	+	0.682494i	$0.239105\pi$
$252$		0			0
$253$	−0.0148240	+	0.0357882i	−0.000931975	+	0.00224999i
$254$	23.5308	+	8.09879i	1.47645	+	0.508163i
$255$		0			0
$256$	−14.1191	+	7.52666i	−0.882445	+	0.470417i
$257$	−19.3691			−1.20821			−0.604107	−	0.796903i	$-0.706470\pi$
$257$	−19.3691			−1.20821			−0.604107	+	0.796903i	$0.706470\pi$
$258$		0			0
$259$	−14.8488	+	35.8482i	−0.922660	+	2.22750i
$260$	17.7592	+	13.8674i	1.10138	+	0.860018i
$261$		0			0
$262$	19.2154	−	21.7249i	1.18713	−	1.34217i
$263$	0.669423	−	0.669423i	0.0412784	−	0.0412784i	−0.686166	−	0.727445i	$-0.740708\pi$
$263$	0.669423	−	0.669423i	0.0412784	−	0.0412784i	0.727445	+	0.686166i	$0.240708\pi$
$264$		0			0
$265$	25.3788	+	25.3788i	1.55901	+	1.55901i
$266$	−3.22453	+	0.197654i	−0.197709	+	0.0121189i
$267$		0			0
$268$	−10.4462	+	5.91387i	−0.638103	+	0.361247i
$269$	−23.1684	−	9.59667i	−1.41260	−	0.585120i	−0.459613	−	0.888119i	$-0.652012\pi$
$269$	−23.1684	−	9.59667i	−1.41260	−	0.585120i	−0.952991	+	0.303000i	$0.902012\pi$
$270$		0			0
$271$		−	30.0377i		−	1.82466i	−0.409455	−	0.912330i	$-0.634281\pi$
$271$		−	30.0377i		−	1.82466i	0.409455	−	0.912330i	$-0.365719\pi$
$272$	−6.99620	+	1.74833i	−0.424207	+	0.106008i
$273$		0			0
$274$	2.55457	+	5.23587i	0.154327	+	0.316311i
$275$	0.0319322	+	0.0132268i	0.00192558	+	0.000797603i
$276$		0			0
$277$	−2.22804	−	5.37897i	−0.133870	−	0.323191i	0.842702	−	0.538380i	$-0.180963\pi$
$277$	−2.22804	−	5.37897i	−0.133870	−	0.323191i	−0.976572	+	0.215189i	$0.930963\pi$
$278$	0.0846911	+	1.38165i	0.00507943	+	0.0828660i
$279$		0			0
$280$	23.1681	−	4.30357i	1.38456	−	0.257188i
$281$	−4.65189	+	4.65189i	−0.277508	+	0.277508i	−0.832114	−	0.554605i	$-0.812869\pi$
$281$	−4.65189	+	4.65189i	−0.277508	+	0.277508i	0.554605	+	0.832114i	$0.312869\pi$
$282$		0			0
$283$	8.25299	−	3.41850i	0.490589	−	0.203209i	−0.123654	−	0.992325i	$-0.539461\pi$
$283$	8.25299	−	3.41850i	0.490589	−	0.203209i	0.614243	+	0.789117i	$0.289461\pi$
$284$	−30.7117	+	3.77926i	−1.82240	+	0.224258i
$285$		0			0
$286$	−0.0439990	+	0.127838i	−0.00260171	+	0.00755921i
$287$	−15.0356			−0.887526
$288$		0			0
$289$	13.7498			0.808811
$290$	2.02408	−	5.88091i	0.118858	−	0.345339i
$291$		0			0
$292$	1.91724	+	15.5802i	0.112198	+	0.911763i
$293$	24.7969	−	10.2712i	1.44865	−	0.600050i	0.486771	−	0.873530i	$-0.338175\pi$
$293$	24.7969	−	10.2712i	1.44865	−	0.600050i	0.961878	+	0.273479i	$0.0881745\pi$
$294$		0			0
$295$	16.4397	−	16.4397i	0.957158	−	0.957158i
$296$	27.8704	+	19.1383i	1.61994	+	1.11239i
$297$		0			0
$298$	−1.49379	−	24.3697i	−0.0865330	−	1.41170i
$299$	−2.98788	−	7.21337i	−0.172793	−	0.417160i
$300$		0			0
$301$	−22.9845	−	9.52051i	−1.32481	−	0.548753i
$302$	8.01692	+	16.4315i	0.461322	+	0.945529i
$303$		0			0
$304$	−0.414575	+	2.78418i	−0.0237775	+	0.159683i
$305$		−	0.343229i		−	0.0196532i
$306$		0			0
$307$	5.48932	+	2.27375i	0.313292	+	0.129770i	0.533789	−	0.845618i	$-0.320768\pi$
$307$	5.48932	+	2.27375i	0.313292	+	0.129770i	−0.220497	+	0.975388i	$0.570768\pi$
$308$	0.0696577	+	0.123043i	0.00396912	+	0.00701101i
$309$		0			0
$310$	−5.98191	+	0.366673i	−0.339750	+	0.0208256i
$311$	1.40770	+	1.40770i	0.0798236	+	0.0798236i	0.745891	−	0.666068i	$-0.232024\pi$
$311$	1.40770	+	1.40770i	0.0798236	+	0.0798236i	−0.666068	+	0.745891i	$0.732024\pi$
$312$		0			0
$313$	11.2976	−	11.2976i	0.638580	−	0.638580i	−0.311625	−	0.950205i	$-0.600873\pi$
$313$	11.2976	−	11.2976i	0.638580	−	0.638580i	0.950205	+	0.311625i	$0.100873\pi$
$314$	−20.0173	+	22.6316i	−1.12964	+	1.27717i
$315$		0			0
$316$	2.10736	−	2.69878i	0.118548	−	0.151818i
$317$	−10.2347	+	24.7087i	−0.574836	+	1.38778i	0.322560	+	0.946549i	$0.395457\pi$
$317$	−10.2347	+	24.7087i	−0.574836	+	1.38778i	−0.897395	+	0.441227i	$0.854543\pi$
$318$		0			0
$319$	0.0373184			0.00208943
$320$	0.520990	−	20.5256i	0.0291242	−	1.14741i
$321$		0			0
$322$	−7.72091	−	2.65737i	−0.430269	−	0.148089i
$323$	−0.485506	+	1.17212i	−0.0270143	+	0.0652182i
$324$		0			0
$325$	−6.43616	+	2.66595i	−0.357014	+	0.147880i
$326$	13.7725	−	15.5712i	0.762790	−	0.862410i
$327$		0			0
$328$	−2.71868	+	12.8157i	−0.150114	+	0.707628i
$329$	−21.3752	−	21.3752i	−1.17846	−	1.17846i
$330$		0			0
$331$	7.23996	+	17.4788i	0.397944	+	0.960722i	0.988153	+	0.153471i	$0.0490453\pi$
$331$	7.23996	+	17.4788i	0.397944	+	0.960722i	−0.590209	+	0.807250i	$0.700955\pi$
$332$	−8.86628	−	15.6613i	−0.486600	−	0.859527i
$333$		0			0
$334$	−8.36728	+	4.08238i	−0.457837	+	0.223378i
$335$		−	15.4043i		−	0.841627i
$336$		0			0
$337$			16.3700i			0.891728i	0.895101	+	0.445864i	$0.147104\pi$
$337$			16.3700i			0.891728i	−0.895101	+	0.445864i	$0.852896\pi$
$338$	−3.88735	−	7.96754i	−0.211444	−	0.433377i
$339$		0			0
$340$	2.47065	−	8.91813i	0.133990	−	0.483653i
$341$	−0.0137614	−	0.0332230i	−0.000745221	−	0.00179912i
$342$		0			0
$343$	7.94793	+	7.94793i	0.429148	+	0.429148i
$344$	−12.2708	+	17.8695i	−0.661597	+	0.963458i
$345$		0			0
$346$	−6.23821	−	5.51761i	−0.335368	−	0.296629i
$347$	13.0473	−	5.40435i	0.700414	−	0.290121i	−0.00391756	−	0.999992i	$-0.501247\pi$
$347$	13.0473	−	5.40435i	0.700414	−	0.290121i	0.704331	+	0.709871i	$0.251247\pi$
$348$		0			0
$349$	−8.03613	+	19.4009i	−0.430164	+	1.03851i	0.549070	+	0.835776i	$0.314982\pi$
$349$	−8.03613	+	19.4009i	−0.430164	+	1.03851i	−0.979234	+	0.202732i	$0.935018\pi$
$350$	−2.37105	+	6.88902i	−0.126738	+	0.368233i
$351$		0			0
$352$	0.117471	−	0.0371249i	0.00626123	−	0.00197876i
$353$	14.8115			0.788339			0.394170	−	0.919038i	$-0.371032\pi$
$353$	14.8115			0.788339			0.394170	+	0.919038i	$0.371032\pi$
$354$		0			0
$355$	15.1957	−	36.6858i	0.806506	−	1.94708i
$356$	22.5425	−	2.77400i	1.19475	−	0.147022i
$357$		0			0
$358$	−23.2108	−	20.5296i	−1.22673	−	1.08502i
$359$	−10.2009	+	10.2009i	−0.538385	+	0.538385i	−0.923055	−	0.384669i	$-0.874316\pi$
$359$	−10.2009	+	10.2009i	−0.538385	+	0.538385i	0.384669	+	0.923055i	$0.374316\pi$
$360$		0			0
$361$	−13.0849	−	13.0849i	−0.688677	−	0.688677i
$362$	−0.566236	−	9.23759i	−0.0297607	−	0.485517i
$363$		0			0
$364$	−27.4641	−	7.60856i	−1.43951	−	0.398797i
$365$	−18.6109	−	7.70888i	−0.974138	−	0.403501i
$366$		0			0
$367$			2.78290i			0.145266i	0.997359	+	0.0726331i	$0.0231402\pi$
$367$			2.78290i			0.145266i	−0.997359	+	0.0726331i	$0.976860\pi$
$368$	−3.66108	+	6.10045i	−0.190847	+	0.318008i
$369$		0			0
$370$	−38.9921	+	19.0242i	−2.02710	+	0.989020i
$371$	−41.9395	−	17.3719i	−2.17739	−	0.901905i
$372$		0			0
$373$	−9.13011	−	22.0420i	−0.472739	−	1.14129i	−0.962948	−	0.269688i	$-0.913079\pi$
$373$	−9.13011	−	22.0420i	−0.472739	−	1.14129i	0.490209	−	0.871605i	$-0.336921\pi$
$374$	0.0554224	−	0.00339722i	0.00286582	−	0.000175666i
$375$		0			0
$376$	−22.0842	+	14.3543i	−1.13891	+	0.740266i
$377$	−5.31871	+	5.31871i	−0.273927	+	0.273927i
$378$		0			0
$379$	−23.0464	+	9.54614i	−1.18382	+	0.490352i	−0.885736	−	0.464189i	$-0.846346\pi$
$379$	−23.0464	+	9.54614i	−1.18382	+	0.490352i	−0.298079	+	0.954541i	$0.596346\pi$
$380$	−2.84706	−	2.22314i	−0.146051	−	0.114045i
$381$		0			0
$382$	22.1121	+	7.61049i	1.13135	+	0.389387i
$383$	−24.7373			−1.26402			−0.632009	−	0.774961i	$-0.717770\pi$
$383$	−24.7373			−1.26402			−0.632009	+	0.774961i	$0.717770\pi$
$384$		0			0
$385$	−0.181443			−0.00924718
$386$	−23.1764	−	7.97679i	−1.17965	−	0.406008i
$387$		0			0
$388$	−20.2220	−	15.7904i	−1.02662	−	0.801638i
$389$	11.3906	−	4.71814i	0.577526	−	0.239219i	−0.0747478	−	0.997202i	$-0.523815\pi$
$389$	11.3906	−	4.71814i	0.577526	−	0.239219i	0.652274	+	0.757983i	$0.273815\pi$
$390$		0			0
$391$	−2.26745	+	2.26745i	−0.114670	+	0.114670i
$392$	−8.38895	+	5.45264i	−0.423706	+	0.275400i
$393$		0			0
$394$	−25.0186	+	1.53356i	−1.26042	+	0.0772597i
$395$	1.68151	+	4.05952i	0.0846059	+	0.204257i
$396$		0			0
$397$	−1.91024	−	0.791248i	−0.0958723	−	0.0397116i	0.334232	−	0.942491i	$-0.391523\pi$
$397$	−1.91024	−	0.791248i	−0.0958723	−	0.0397116i	−0.430104	+	0.902779i	$0.641523\pi$
$398$	−18.6592	+	9.10381i	−0.935303	+	0.456333i
$399$		0			0
$400$	5.44315	+	3.26661i	0.272158	+	0.163331i
$401$		−	3.78176i		−	0.188852i	−0.995532	−	0.0944261i	$-0.969898\pi$
$401$		−	3.78176i		−	0.188852i	0.995532	−	0.0944261i	$-0.0301016\pi$
$402$		0			0
$403$	6.69632	+	2.77371i	0.333568	+	0.138168i
$404$	17.8787	+	4.95305i	0.889499	+	0.246424i
$405$		0			0
$406$	0.481284	+	7.85168i	0.0238857	+	0.389672i
$407$	−0.184076	−	0.184076i	−0.00912433	−	0.00912433i
$408$		0			0
$409$	−2.70674	+	2.70674i	−0.133840	+	0.133840i	−0.770853	−	0.637013i	$-0.780170\pi$
$409$	−2.70674	+	2.70674i	−0.133840	+	0.133840i	0.637013	+	0.770853i	$0.280170\pi$
$410$	−12.5928	−	11.1382i	−0.621915	−	0.550075i
$411$		0			0
$412$	14.8086	−	1.82229i	0.729569	−	0.0897780i
$413$	−11.2531	+	27.1673i	−0.553728	+	1.33682i
$414$		0			0
$415$	23.0947			1.13367
$416$	−11.4511	+	22.0334i	−0.561438	+	1.08028i
$417$		0			0
$418$	0.00705367	−	0.0204943i	0.000345006	−	0.00100241i
$419$	−2.90452	+	7.01213i	−0.141895	+	0.342565i	−0.978811	−	0.204767i	$-0.934356\pi$
$419$	−2.90452	+	7.01213i	−0.141895	+	0.342565i	0.836916	+	0.547332i	$0.184356\pi$
$420$		0			0
$421$	3.14478	−	1.30261i	0.153267	−	0.0634854i	−0.304731	−	0.952438i	$-0.598567\pi$
$421$	3.14478	−	1.30261i	0.153267	−	0.0634854i	0.457998	+	0.888953i	$0.348567\pi$
$422$	−20.3336	−	17.9848i	−0.989822	−	0.875485i
$423$		0			0
$424$	−22.3903	+	32.6062i	−1.08737	+	1.58349i
$425$	2.02314	+	2.02314i	0.0981368	+	0.0981368i
$426$		0			0
$427$	0.166129	+	0.401070i	0.00803954	+	0.0194092i
$428$	2.43323	−	8.78307i	0.117615	−	0.424546i
$429$		0			0
$430$	−12.1976	−	25.0003i	−0.588221	−	1.20562i
$431$		−	10.0900i		−	0.486019i	−0.970024	−	0.243010i	$-0.921865\pi$
$431$		−	10.0900i		−	0.486019i	0.970024	−	0.243010i	$-0.0781347\pi$
$432$		0			0
$433$			6.33633i			0.304505i	0.988342	+	0.152252i	$0.0486526\pi$
$433$			6.33633i			0.304505i	−0.988342	+	0.152252i	$0.951347\pi$
$434$	6.81253	−	3.32382i	0.327012	−	0.159549i
$435$		0			0
$436$	−15.3193	−	27.0599i	−0.733662	−	1.29593i
$437$	0.479000	+	1.15641i	0.0229137	+	0.0553185i
$438$		0			0
$439$	−0.428160	−	0.428160i	−0.0204350	−	0.0204350i	0.696815	−	0.717250i	$-0.254600\pi$
$439$	−0.428160	−	0.428160i	−0.0204350	−	0.0204350i	−0.717250	+	0.696815i	$0.754600\pi$
$440$	−0.0328077	+	0.154653i	−0.00156405	+	0.00737281i
$441$		0			0
$442$	−7.41475	+	8.38311i	−0.352683	+	0.398744i
$443$	32.9600	−	13.6525i	1.56598	−	0.648649i	0.579862	−	0.814715i	$-0.303106\pi$
$443$	32.9600	−	13.6525i	1.56598	−	0.648649i	0.986115	+	0.166066i	$0.0531065\pi$
$444$		0			0
$445$	−11.1537	+	26.9275i	−0.528738	+	1.27649i
$446$	−26.0288	−	8.95855i	−1.23250	−	0.424200i
$447$		0			0
$448$	9.32595	+	24.2368i	0.440610	+	1.14508i
$449$	−29.2280			−1.37936			−0.689678	−	0.724116i	$-0.742248\pi$
$449$	−29.2280			−1.37936			−0.689678	+	0.724116i	$0.742248\pi$
$450$		0			0
$451$	0.0386032	−	0.0931963i	0.00181775	−	0.00438844i
$452$	−15.0894	+	19.3242i	−0.709747	+	0.908936i
$453$		0			0
$454$	0.440826	−	0.498398i	0.0206890	−	0.0233910i
$455$	25.8597	−	25.8597i	1.21232	−	1.21232i
$456$		0			0
$457$	8.48909	+	8.48909i	0.397103	+	0.397103i	0.877210	−	0.480107i	$-0.159402\pi$
$457$	8.48909	+	8.48909i	0.397103	+	0.397103i	−0.480107	+	0.877210i	$0.659402\pi$
$458$	17.2138	−	1.05516i	0.804350	−	0.0493042i
$459$		0			0
$460$	−4.49796	−	7.94516i	−0.209718	−	0.370445i
$461$	5.18907	+	2.14938i	0.241679	+	0.100107i	0.500235	−	0.865889i	$-0.333247\pi$
$461$	5.18907	+	2.14938i	0.241679	+	0.100107i	−0.258557	+	0.965996i	$0.583247\pi$
$462$		0			0
$463$		−	0.453268i		−	0.0210652i	−0.999945	−	0.0105326i	$-0.996647\pi$
$463$		−	0.453268i		−	0.0210652i	0.999945	−	0.0105326i	$-0.00335269\pi$
$464$	6.77943	+	1.00948i	0.314727	+	0.0468640i
$465$		0			0
$466$	3.71849	+	7.62145i	0.172256	+	0.353057i
$467$	−12.5351	−	5.19222i	−0.580056	−	0.240267i	0.0733099	−	0.997309i	$-0.476644\pi$
$467$	−12.5351	−	5.19222i	−0.580056	−	0.240267i	−0.653366	+	0.757042i	$0.726644\pi$
$468$		0			0
$469$	7.45597	+	18.0003i	0.344284	+	0.831176i
$470$	−2.06797	−	33.7369i	−0.0953882	−	1.55617i
$471$		0			0
$472$	21.1214	+	14.5039i	0.972192	+	0.667595i
$473$	0.118023	−	0.118023i	0.00542670	−	0.00542670i
$474$		0			0
$475$	1.03181	−	0.427390i	0.0473427	−	0.0196100i
$476$	1.42953	+	11.6169i	0.0655224	+	0.532459i
$477$		0			0
$478$	11.4627	−	33.3045i	0.524291	−	1.52331i
$479$	−21.2834			−0.972462			−0.486231	−	0.873830i	$-0.661629\pi$
$479$	−21.2834			−0.972462			−0.486231	+	0.873830i	$0.661629\pi$
$480$		0			0
$481$	52.4700			2.39243
$482$	0.464715	−	1.35022i	0.0211672	−	0.0615008i
$483$		0			0
$484$	21.8344	−	2.68685i	0.992471	−	0.122130i
$485$	30.4180	−	12.5996i	1.38121	−	0.572117i
$486$		0			0
$487$	−10.3460	+	10.3460i	−0.468823	+	0.468823i	−0.901533	−	0.432710i	$-0.857557\pi$
$487$	−10.3460	+	10.3460i	−0.468823	+	0.468823i	0.432710	+	0.901533i	$0.357557\pi$
$488$	0.371892	−	0.0690806i	0.0168348	−	0.00312713i
$489$		0			0
$490$	−0.785541	−	12.8153i	−0.0354871	−	0.578938i
$491$	2.47658	+	5.97900i	0.111767	+	0.269828i	0.969859	−	0.243667i	$-0.0783504\pi$
$491$	2.47658	+	5.97900i	0.111767	+	0.269828i	−0.858092	+	0.513495i	$0.828350\pi$
$492$		0			0
$493$	2.85408	+	1.18220i	0.128541	+	0.0532436i
$494$	1.91558	+	3.92619i	0.0861862	+	0.176648i
$495$		0			0
$496$	−1.60126	−	6.40768i	−0.0718986	−	0.287713i
$497$			50.2232i			2.25282i
$498$		0			0
$499$	−25.7814	−	10.6790i	−1.15413	−	0.478058i	−0.278216	−	0.960519i	$-0.589743\pi$
$499$	−25.7814	−	10.6790i	−1.15413	−	0.478058i	−0.875918	+	0.482461i	$0.839743\pi$
$500$	15.2454	−	8.63081i	0.681794	−	0.385981i
$501$		0			0
$502$	−18.5203	+	1.13524i	−0.826602	+	0.0506682i
$503$	24.9477	+	24.9477i	1.11237	+	1.11237i	0.992830	+	0.119535i	$0.0381404\pi$
$503$	24.9477	+	24.9477i	1.11237	+	1.11237i	0.119535	+	0.992830i	$0.461860\pi$
$504$		0			0
$505$	−16.8342	+	16.8342i	−0.749114	+	0.749114i
$506$	0.0362943	−	0.0410343i	0.00161348	−	0.00182420i
$507$		0			0
$508$	−27.7386	−	21.6598i	−1.23070	−	0.961000i
$509$	3.65347	−	8.82027i	0.161937	−	0.390952i	−0.821995	−	0.569495i	$-0.807139\pi$
$509$	3.65347	−	8.82027i	0.161937	−	0.390952i	0.983932	+	0.178544i	$0.0571386\pi$
$510$		0			0
$511$	25.4785			1.12710
$512$	22.3446	−	3.56662i	0.987499	−	0.157624i
$513$		0			0
$514$	25.9009	+	8.91453i	1.14244	+	0.393203i
$515$	−7.32711	+	17.6892i	−0.322871	+	0.779480i
$516$		0			0
$517$	0.187371	−	0.0776117i	0.00824058	−	0.00341336i
$518$	36.3551	−	41.1031i	1.59735	−	1.80597i
$519$		0			0
$520$	−17.3657	−	26.7174i	−0.761538	−	1.17164i
$521$	4.37482	+	4.37482i	0.191664	+	0.191664i	0.796415	−	0.604751i	$-0.206727\pi$
$521$	4.37482	+	4.37482i	0.191664	+	0.191664i	−0.604751	+	0.796415i	$0.706727\pi$
$522$		0			0
$523$	0.160814	+	0.388239i	0.00703191	+	0.0169765i	0.927356	−	0.374179i	$-0.122075\pi$
$523$	0.160814	+	0.388239i	0.00703191	+	0.0169765i	−0.920325	+	0.391156i	$0.872075\pi$
$524$	−35.6940	+	20.2073i	−1.55930	+	0.882761i
$525$		0			0
$526$	−1.20327	+	0.587072i	−0.0524650	+	0.0255976i
$527$		−	2.97681i		−	0.129672i
$528$		0			0
$529$		−	19.8363i		−	0.862448i
$530$	−22.2568	−	45.6176i	−0.966772	−	1.98150i
$531$		0			0
$532$	4.40289	+	1.21976i	0.190890	+	0.0528834i
$533$	7.78074	+	18.7844i	0.337021	+	0.813642i
$534$		0			0
$535$	8.26996	+	8.26996i	0.357542	+	0.357542i
$536$	16.6908	−	3.10038i	0.720931	−	0.133916i
$537$		0			0
$538$	26.5646	+	23.4961i	1.14528	+	1.01299i
$539$	0.0711751	−	0.0294817i	0.00306573	−	0.00126987i
$540$		0			0
$541$	3.14750	−	7.59873i	0.135321	−	0.326695i	−0.841664	−	0.540002i	$-0.818423\pi$
$541$	3.14750	−	7.59873i	0.135321	−	0.326695i	0.976985	+	0.213307i	$0.0684235\pi$
$542$	−13.8247	+	40.1672i	−0.593820	+	1.72533i
$543$		0			0
$544$	10.1602	+	0.882050i	0.435613	+	0.0378176i
$545$	39.9034			1.70927
$546$		0			0
$547$	−9.55144	+	23.0592i	−0.408390	+	0.985941i	0.577171	+	0.816623i	$0.304156\pi$
$547$	−9.55144	+	23.0592i	−0.408390	+	0.985941i	−0.985562	+	0.169318i	$0.945844\pi$
$548$	−1.00627	−	8.17728i	−0.0429855	−	0.349316i
$549$		0			0
$550$	−0.0366131	−	0.0323838i	−0.00156119	−	0.00138085i
$551$	0.852666	−	0.852666i	0.0363248	−	0.0363248i
$552$		0			0
$553$	−3.92976	−	3.92976i	−0.167111	−	0.167111i
$554$	0.503759	+	8.21834i	0.0214027	+	0.349164i
$555$		0			0
$556$	0.522646	−	1.88656i	0.0221651	−	0.0800080i
$557$	−42.6425	−	17.6631i	−1.80682	−	0.748409i	−0.983520	−	0.180801i	$-0.942131\pi$
$557$	−42.6425	−	17.6631i	−1.80682	−	0.748409i	−0.823299	−	0.567608i	$-0.807869\pi$
$558$		0			0
$559$			33.6418i			1.42290i
$560$	−32.9617	−	4.90812i	−1.39289	−	0.207406i
$561$		0			0
$562$	8.36163	−	4.07962i	0.352714	−	0.172089i
$563$	−18.3038	−	7.58169i	−0.771414	−	0.319530i	−0.0379689	−	0.999279i	$-0.512089\pi$
$563$	−18.3038	−	7.58169i	−0.771414	−	0.319530i	−0.733445	+	0.679749i	$0.762089\pi$
$564$		0			0
$565$	−12.0402	−	29.0676i	−0.506535	−	1.22288i
$566$	−12.6095	+	0.772921i	−0.530015	+	0.0324883i
$567$		0			0
$568$	42.8079	+	9.08113i	1.79618	+	0.381036i
$569$	−4.50857	+	4.50857i	−0.189009	+	0.189009i	−0.795268	−	0.606258i	$-0.792670\pi$
$569$	−4.50857	+	4.50857i	−0.189009	+	0.189009i	0.606258	+	0.795268i	$0.292670\pi$
$570$		0			0
$571$	27.3177	−	11.3154i	1.14321	−	0.473533i	0.270959	−	0.962591i	$-0.412659\pi$
$571$	27.3177	−	11.3154i	1.14321	−	0.473533i	0.872251	+	0.489058i	$0.162659\pi$
$572$	0.117673	−	0.150698i	0.00492016	−	0.00630100i
$573$		0			0
$574$	20.1061	+	6.92007i	0.839211	+	0.288838i
$575$	2.82281			0.117719
$576$		0			0
$577$	21.6260			0.900302			0.450151	−	0.892953i	$-0.351370\pi$
$577$	21.6260			0.900302			0.450151	+	0.892953i	$0.351370\pi$
$578$	−18.3866	−	6.32825i	−0.764781	−	0.263221i
$579$		0			0
$580$	−5.41331	+	6.93255i	−0.224776	+	0.287858i
$581$	−26.9867	+	11.1782i	−1.11960	+	0.463752i
$582$		0			0
$583$	0.215355	−	0.215355i	0.00891908	−	0.00891908i
$584$	4.60691	−	21.7167i	0.190635	−	0.898642i
$585$		0			0
$586$	−37.8863	+	2.32231i	−1.56507	+	0.0959339i
$587$	−8.34082	−	20.1365i	−0.344262	−	0.831123i	−0.997275	−	0.0737756i	$-0.976495\pi$
$587$	−8.34082	−	20.1365i	−0.344262	−	0.831123i	0.653013	−	0.757347i	$-0.273505\pi$
$588$		0			0
$589$	−1.07352	−	0.444665i	−0.0442335	−	0.0183221i
$590$	−29.5499	+	14.4174i	−1.21655	+	0.593553i
$591$		0			0
$592$	−28.4608	−	38.4195i	−1.16973	−	1.57903i
$593$		−	36.8773i		−	1.51437i	−0.653202	−	0.757184i	$-0.726575\pi$
$593$		−	36.8773i		−	1.51437i	0.653202	−	0.757184i	$-0.273425\pi$
$594$		0			0
$595$	−13.8766	−	5.74788i	−0.568885	−	0.235640i
$596$	−9.21849	+	33.2754i	−0.377604	+	1.36301i
$597$		0			0
$598$	0.675557	+	11.0211i	0.0276256	+	0.450685i
$599$	10.2572	+	10.2572i	0.419097	+	0.419097i	0.884892	−	0.465796i	$-0.154232\pi$
$599$	10.2572	+	10.2572i	0.419097	+	0.419097i	−0.465796	+	0.884892i	$0.654232\pi$
$600$		0			0
$601$	24.5884	−	24.5884i	1.00298	−	1.00298i	0.00298783	−	0.999996i	$-0.499049\pi$
$601$	24.5884	−	24.5884i	1.00298	−	1.00298i	0.999996	−	0.00298783i	$-0.000951058\pi$
$602$	26.3538	+	23.3096i	1.07410	+	0.950027i
$603$		0			0
$604$	−3.15792	−	25.6624i	−0.128494	−	1.04419i
$605$	−10.8034	+	26.0816i	−0.439219	+	1.06037i
$606$		0			0
$607$	−3.85036			−0.156281			−0.0781407	−	0.996942i	$-0.524898\pi$
$607$	−3.85036			−0.156281			−0.0781407	+	0.996942i	$0.524898\pi$
$608$	1.83578	−	3.53227i	0.0744507	−	0.143252i
$609$		0			0
$610$	−0.157969	+	0.458974i	−0.00639597	+	0.0185833i
$611$	−15.6432	+	37.7660i	−0.632856	+	1.52785i
$612$		0			0
$613$	9.96357	−	4.12705i	0.402425	−	0.166690i	−0.172285	−	0.985047i	$-0.555115\pi$
$613$	9.96357	−	4.12705i	0.402425	−	0.166690i	0.574710	+	0.818357i	$0.305115\pi$
$614$	−6.29398	−	5.56695i	−0.254005	−	0.224664i
$615$		0			0
$616$	−0.0365185	−	0.196596i	−0.00147137	−	0.00792106i
$617$	−7.03734	−	7.03734i	−0.283313	−	0.283313i	0.551116	−	0.834429i	$-0.314202\pi$
$617$	−7.03734	−	7.03734i	−0.283313	−	0.283313i	−0.834429	+	0.551116i	$0.814202\pi$
$618$		0			0
$619$	5.66666	+	13.6805i	0.227762	+	0.549867i	0.995904	−	0.0904125i	$-0.0288186\pi$
$619$	5.66666	+	13.6805i	0.227762	+	0.549867i	−0.768142	+	0.640279i	$0.778819\pi$
$620$	8.16794	+	2.26282i	0.328032	+	0.0908768i
$621$		0			0
$622$	−1.23453	−	2.53031i	−0.0495003	−	0.101456i
$623$		−	36.8640i		−	1.47693i
$624$		0			0
$625$			30.4165i			1.21666i
$626$	−20.3072	+	9.90783i	−0.811637	+	0.395996i
$627$		0			0
$628$	37.1838	−	21.0507i	1.48379	−	0.840014i
$629$	−8.24671	−	19.9093i	−0.328818	−	0.793837i
$630$		0			0
$631$	−2.08745	−	2.08745i	−0.0830999	−	0.0830999i	0.664335	−	0.747435i	$-0.268715\pi$
$631$	−2.08745	−	2.08745i	−0.0830999	−	0.0830999i	−0.747435	+	0.664335i	$0.768715\pi$
$632$	−4.06011	+	2.63898i	−0.161503	+	0.104973i
$633$		0			0
$634$	25.0581	−	28.3306i	0.995183	−	1.12515i
$635$	41.7246	−	17.2829i	1.65579	−	0.685851i
$636$		0			0
$637$	−5.94224	+	14.3458i	−0.235440	+	0.568403i
$638$	−0.0499032	−	0.0171756i	−0.00197569	−	0.000679987i
$639$		0			0
$640$	−10.1434	+	27.2075i	−0.400955	+	1.07547i
$641$	−15.4167			−0.608923			−0.304461	−	0.952525i	$-0.598476\pi$
$641$	−15.4167			−0.608923			−0.304461	+	0.952525i	$0.598476\pi$
$642$		0			0
$643$	0.00709645	−	0.0171323i	0.000279857	−	0.000675633i	−0.923740	−	0.383021i	$-0.874884\pi$
$643$	0.00709645	−	0.0171323i	0.000279857	−	0.000675633i	0.924019	+	0.382346i	$0.124884\pi$
$644$	9.10157	+	7.10700i	0.358652	+	0.280055i
$645$		0			0
$646$	1.18869	−	1.34393i	0.0467684	−	0.0528763i
$647$	9.06988	−	9.06988i	0.356574	−	0.356574i	−0.505975	−	0.862548i	$-0.668867\pi$
$647$	9.06988	−	9.06988i	0.356574	−	0.356574i	0.862548	+	0.505975i	$0.168867\pi$
$648$		0			0
$649$	−0.139501	−	0.139501i	−0.00547590	−	0.00547590i
$650$	9.83359	−	0.602769i	0.385705	−	0.0236426i
$651$		0			0
$652$	−25.5836	+	14.4835i	−1.00193	+	0.567219i
$653$	−18.1374	−	7.51276i	−0.709772	−	0.293997i	−0.00156147	−	0.999999i	$-0.500497\pi$
$653$	−18.1374	−	7.51276i	−0.709772	−	0.293997i	−0.708210	+	0.706002i	$0.750497\pi$
$654$		0			0
$655$		−	52.6356i		−	2.05664i
$656$	9.53383	−	15.8862i	0.372234	−	0.620253i
$657$		0			0
$658$	18.7457	+	38.4214i	0.730784	+	1.49782i
$659$	23.8149	+	9.86444i	0.927695	+	0.384264i	0.794804	−	0.606867i	$-0.207574\pi$
$659$	23.8149	+	9.86444i	0.927695	+	0.384264i	0.132892	+	0.991131i	$0.457574\pi$
$660$		0			0
$661$	−2.61299	−	6.30831i	−0.101633	−	0.245365i	0.864881	−	0.501977i	$-0.167394\pi$
$661$	−2.61299	−	6.30831i	−0.101633	−	0.245365i	−0.966514	+	0.256612i	$0.917394\pi$
$662$	−1.63695	−	26.7053i	−0.0636219	−	1.03793i
$663$		0			0
$664$	4.64820	+	25.0234i	0.180385	+	0.971096i
$665$	−4.14568	+	4.14568i	−0.160762	+	0.160762i
$666$		0			0
$667$	2.81583	−	1.16636i	0.109029	−	0.0451615i
$668$	13.0678	−	1.60808i	0.505610	−	0.0622185i
$669$		0			0
$670$	−7.08974	+	20.5991i	−0.273901	+	0.795811i
$671$	−0.00291251			−0.000112436
$672$		0			0
$673$	0.864773			0.0333345			0.0166673	−	0.999861i	$-0.494694\pi$
$673$	0.864773			0.0333345			0.0166673	+	0.999861i	$0.494694\pi$
$674$	7.53417	−	21.8903i	0.290206	−	0.843185i
$675$		0			0
$676$	1.53126	+	12.4435i	0.0588944	+	0.478598i
$677$	−5.26132	+	2.17931i	−0.202209	+	0.0837577i	−0.481490	−	0.876452i	$-0.659904\pi$
$677$	−5.26132	+	2.17931i	−0.202209	+	0.0837577i	0.279281	+	0.960210i	$0.409904\pi$
$678$		0			0
$679$	−29.4458	+	29.4458i	−1.13002	+	1.13002i
$680$	−7.40833	+	10.7885i	−0.284096	+	0.413719i
$681$		0			0
$682$	0.00311145	+	0.0507602i	0.000119143	+	0.00194371i
$683$	0.341011	+	0.823273i	0.0130484	+	0.0315017i	0.930269	−	0.366877i	$-0.119573\pi$
$683$	0.341011	+	0.823273i	0.0130484	+	0.0315017i	−0.917221	+	0.398379i	$0.869573\pi$
$684$		0			0
$685$	9.76793	+	4.04601i	0.373213	+	0.154590i
$686$	−6.97019	−	14.2862i	−0.266123	−	0.545448i
$687$		0			0
$688$	24.6332	−	18.2480i	0.939131	−	0.695698i
$689$			61.3857i			2.33861i
$690$		0			0
$691$	−29.9466	−	12.4043i	−1.13922	−	0.471881i	−0.268315	−	0.963331i	$-0.586467\pi$
$691$	−29.9466	−	12.4043i	−1.13922	−	0.471881i	−0.870906	+	0.491450i	$0.836467\pi$
$692$	5.80245	+	10.2494i	0.220576	+	0.389624i
$693$		0			0
$694$	−19.9345	+	1.22192i	−0.756702	+	0.0463835i
$695$	1.77635	+	1.77635i	0.0673807	+	0.0673807i
$696$		0			0
$697$	5.90468	−	5.90468i	0.223656	−	0.223656i
$698$	19.6753	−	22.2449i	0.744720	−	0.841980i
$699$		0			0
$700$	6.34126	−	8.12092i	0.239677	−	0.306942i
$701$	−12.3191	+	29.7410i	−0.465287	+	1.12330i	0.500910	+	0.865499i	$0.332999\pi$
$701$	−12.3191	+	29.7410i	−0.465287	+	1.12330i	−0.966197	+	0.257804i	$0.917001\pi$
$702$		0			0
$703$	−8.41170			−0.317253
$704$	−0.174172	−	0.00442092i	−0.00656435	−	0.000166620i
$705$		0			0
$706$	−19.8064	−	6.81692i	−0.745424	−	0.256558i
$707$	11.5231	−	27.8193i	0.433372	−	1.04625i
$708$		0			0
$709$	4.59063	−	1.90150i	0.172405	−	0.0714123i	−0.294812	−	0.955555i	$-0.595257\pi$
$709$	4.59063	−	1.90150i	0.172405	−	0.0714123i	0.467216	+	0.884143i	$0.345257\pi$
$710$	−37.2045	+	42.0634i	−1.39626	+	1.57861i
$711$		0			0
$712$	−31.4212	−	6.66560i	−1.17756	−	0.249804i
$713$	−2.07671	−	2.07671i	−0.0777735	−	0.0777735i
$714$		0			0
$715$	0.0938942	+	0.226681i	0.00351145	+	0.00847738i
$716$	21.5894	+	38.1353i	0.806834	+	1.42518i
$717$		0			0
$718$	18.3359	−	8.94606i	0.684290	−	0.333864i
$719$		−	44.5016i		−	1.65963i	−0.558038	−	0.829815i	$-0.688446\pi$
$719$		−	44.5016i		−	1.65963i	0.558038	−	0.829815i	$-0.311554\pi$
$720$		0			0
$721$		−	24.2167i		−	0.901877i
$722$	11.4752	+	23.5196i	0.427062	+	0.875311i
$723$		0			0
$724$	−3.49436	+	12.6134i	−0.129867	+	0.468772i
$725$	−1.04069	−	2.51244i	−0.0386501	−	0.0933097i
$726$		0			0
$727$	−31.9535	−	31.9535i	−1.18509	−	1.18509i	−0.978408	−	0.206681i	$-0.933734\pi$
$727$	−31.9535	−	31.9535i	−1.18509	−	1.18509i	−0.206681	−	0.978408i	$-0.566266\pi$
$728$	33.2240	+	22.8146i	1.23136	+	0.845564i
$729$		0			0
$730$	21.3390	+	18.8741i	0.789792	+	0.698561i
$731$	12.7651	−	5.28749i	0.472135	−	0.195565i
$732$		0			0
$733$	7.44452	−	17.9727i	0.274970	−	0.663835i	−0.724712	−	0.689052i	$-0.758027\pi$
$733$	7.44452	−	17.9727i	0.274970	−	0.663835i	0.999682	+	0.0252160i	$0.00802737\pi$
$734$	1.28081	−	3.72137i	0.0472757	−	0.137358i
$735$		0			0
$736$	7.70338	−	6.47270i	0.283951	−	0.238587i
$737$	−0.130715			−0.00481495
$738$		0			0
$739$	16.3990	−	39.5907i	0.603247	−	1.45637i	−0.266974	−	0.963704i	$-0.586024\pi$
$739$	16.3990	−	39.5907i	0.603247	−	1.45637i	0.870221	−	0.492662i	$-0.163976\pi$
$740$	60.8971	−	7.49376i	2.23862	−	0.275476i
$741$		0			0
$742$	48.0873	+	42.5326i	1.76534	+	1.56142i
$743$	19.2131	−	19.2131i	0.704860	−	0.704860i	−0.260590	−	0.965450i	$-0.583917\pi$
$743$	19.2131	−	19.2131i	0.704860	−	0.704860i	0.965450	+	0.260590i	$0.0839169\pi$
$744$		0			0
$745$	−31.3314	−	31.3314i	−1.14789	−	1.14789i
$746$	2.06431	+	33.6773i	0.0755799	+	1.23301i
$747$		0			0
$748$	−0.0756758	−	0.0209649i	−0.00276698	−	0.000766554i
$749$	−13.6664	−	5.66083i	−0.499361	−	0.206842i
$750$		0			0
$751$			10.1963i			0.372069i	0.982543	+	0.186034i	$0.0595636\pi$
$751$			10.1963i			0.372069i	−0.982543	+	0.186034i	$0.940436\pi$
$752$	36.1381	−	9.03079i	1.31782	−	0.329319i
$753$		0			0
$754$	9.56022	−	4.66442i	0.348163	−	0.169868i
$755$	30.6543	+	12.6974i	1.11562	+	0.462107i
$756$		0			0
$757$	−7.98935	−	19.2880i	−0.290378	−	0.701034i	0.709616	−	0.704589i	$-0.248868\pi$
$757$	−7.98935	−	19.2880i	−0.290378	−	0.701034i	−0.999994	+	0.00355482i	$0.998868\pi$
$758$	35.2119	−	2.15838i	1.27895	−	0.0783958i
$759$		0			0
$760$	2.78398	+	4.28318i	0.100985	+	0.155367i
$761$	−10.3837	+	10.3837i	−0.376409	+	0.376409i	−0.869805	−	0.493396i	$-0.835755\pi$
$761$	−10.3837	+	10.3837i	−0.376409	+	0.376409i	0.493396	+	0.869805i	$0.335755\pi$
$762$		0			0
$763$	−46.6281	+	19.3140i	−1.68805	+	0.699213i
$764$	−26.0662	−	20.3539i	−0.943042	−	0.736379i
$765$		0			0
$766$	33.0794	+	11.3852i	1.19521	+	0.411364i
$767$	39.7641			1.43580
$768$		0			0
$769$	−30.4099			−1.09661			−0.548305	−	0.836278i	$-0.684727\pi$
$769$	−30.4099			−1.09661			−0.548305	+	0.836278i	$0.684727\pi$
$770$	0.242630	+	0.0835080i	0.00874379	+	0.00300942i
$771$		0			0
$772$	27.3208	+	21.3336i	0.983296	+	0.767812i
$773$	22.7017	−	9.40336i	0.816524	−	0.338215i	0.0649702	−	0.997887i	$-0.479305\pi$
$773$	22.7017	−	9.40336i	0.816524	−	0.338215i	0.751554	+	0.659672i	$0.229305\pi$
$774$		0			0
$775$	−1.85296	+	1.85296i	−0.0665601	+	0.0665601i
$776$	19.7739	+	30.4224i	0.709843	+	1.09210i
$777$		0			0
$778$	−17.4033	+	1.06677i	−0.623939	+	0.0382455i
$779$	−1.24737	−	3.01141i	−0.0446915	−	0.107895i
$780$		0			0
$781$	−0.311301	−	0.128945i	−0.0111392	−	0.00461402i
$782$	4.07568	−	1.98851i	0.145746	−	0.0711091i
$783$		0			0
$784$	13.7275	−	3.43045i	0.490267	−	0.122516i
$785$			54.8324i			1.95705i
$786$		0			0
$787$	28.9404	+	11.9875i	1.03161	+	0.427309i	0.833295	−	0.552829i	$-0.186452\pi$
$787$	28.9404	+	11.9875i	1.03161	+	0.427309i	0.198319	+	0.980137i	$0.436452\pi$
$788$	34.1613	+	9.46392i	1.21695	+	0.337138i
$789$		0			0
$790$	−0.380189	−	6.20241i	−0.0135265	−	0.220672i
$791$	28.1385	+	28.1385i	1.00049	+	1.00049i
$792$		0			0
$793$	0.415097	−	0.415097i	0.0147405	−	0.0147405i
$794$	2.19026	+	1.93726i	0.0777294	+	0.0687506i
$795$		0			0
$796$	29.1416	−	3.58606i	1.03290	−	0.127104i
$797$	−0.480051	+	1.15895i	−0.0170043	+	0.0410519i	−0.932154	−	0.362063i	$-0.882073\pi$
$797$	−0.480051	+	1.15895i	−0.0170043	+	0.0410519i	0.915149	+	0.403115i	$0.132073\pi$
$798$		0			0
$799$	16.7886			0.593939
$800$	−5.77529	−	6.87338i	−0.204187	−	0.243011i
$801$		0			0
$802$	−1.74053	+	5.05708i	−0.0614604	+	0.178572i
$803$	−0.0654146	+	0.157925i	−0.00230843	+	0.00557304i
$804$		0			0
$805$	−13.6906	+	5.67085i	−0.482531	+	0.199871i
$806$	−7.67792	−	6.79102i	−0.270443	−	0.239203i
$807$		0			0
$808$	−21.6283	−	14.8519i	−0.760880	−	0.522489i
$809$	−14.8375	−	14.8375i	−0.521659	−	0.521659i	0.396413	−	0.918072i	$-0.370255\pi$
$809$	−14.8375	−	14.8375i	−0.521659	−	0.521659i	−0.918072	+	0.396413i	$0.870255\pi$
$810$		0			0
$811$	2.94797	+	7.11704i	0.103517	+	0.249913i	0.967149	−	0.254211i	$-0.0818156\pi$
$811$	2.94797	+	7.11704i	0.103517	+	0.249913i	−0.863632	+	0.504124i	$0.831816\pi$
$812$	2.97010	−	10.7210i	0.104230	−	0.376233i
$813$		0			0
$814$	0.161432	+	0.330872i	0.00565819	+	0.0115971i
$815$		−	37.7264i		−	1.32150i
$816$		0			0
$817$		−	5.39327i		−	0.188687i
$818$	4.86529	−	2.37377i	0.170111	−	0.0829968i
$819$		0			0
$820$	11.7132	+	20.6900i	0.409042	+	0.722527i
$821$	−7.95342	−	19.2013i	−0.277576	−	0.670128i	0.722191	−	0.691693i	$-0.243135\pi$
$821$	−7.95342	−	19.2013i	−0.277576	−	0.670128i	−0.999767	+	0.0215651i	$0.993135\pi$
$822$		0			0
$823$	−9.98675	−	9.98675i	−0.348116	−	0.348116i	0.511291	−	0.859407i	$-0.329167\pi$
$823$	−9.98675	−	9.98675i	−0.348116	−	0.348116i	−0.859407	+	0.511291i	$0.829167\pi$
$824$	−20.6412	−	4.37876i	−0.719070	−	0.152541i
$825$		0			0
$826$	27.5515	−	31.1497i	0.958640	−	1.08384i
$827$	−27.3084	+	11.3115i	−0.949607	+	0.393340i	−0.803083	−	0.595867i	$-0.796808\pi$
$827$	−27.3084	+	11.3115i	−0.949607	+	0.393340i	−0.146524	+	0.989207i	$0.546808\pi$
$828$		0			0
$829$	−0.846683	+	2.04407i	−0.0294065	+	0.0709936i	−0.937901	−	0.346904i	$-0.887233\pi$
$829$	−0.846683	+	2.04407i	−0.0294065	+	0.0709936i	0.908494	+	0.417898i	$0.137233\pi$
$830$	−30.8828	−	10.6292i	−1.07196	−	0.368945i
$831$		0			0
$832$	25.4535	−	24.1933i	0.882441	−	0.838753i
$833$	6.37736			0.220962
$834$		0			0
$835$	−6.46580	+	15.6098i	−0.223758	+	0.540200i
$836$	−0.0188647	+	0.0241591i	−0.000652450	+	0.000835558i
$837$		0			0
$838$	7.11130	−	8.04003i	0.245656	−	0.277738i
$839$	18.3481	−	18.3481i	0.633446	−	0.633446i	−0.315484	−	0.948931i	$-0.602167\pi$
$839$	18.3481	−	18.3481i	0.633446	−	0.633446i	0.948931	+	0.315484i	$0.102167\pi$
$840$		0			0
$841$	18.4299	+	18.4299i	0.635513	+	0.635513i
$842$	−4.80480	+	0.294520i	−0.165584	+	0.0101498i
$843$		0			0
$844$	18.9132	+	33.4081i	0.651019	+	1.14995i
$845$	−14.8641	−	6.15690i	−0.511340	−	0.211804i
$846$		0			0
$847$		−	35.7060i		−	1.22687i
$848$	44.9477	−	33.2968i	1.54351	−	1.14342i
$849$		0			0
$850$	−1.77426	−	3.63654i	−0.0608567	−	0.124732i
$851$	−19.6425	−	8.13620i	−0.673337	−	0.278905i
$852$		0			0
$853$	16.4689	+	39.7595i	0.563885	+	1.36134i	0.906636	+	0.421913i	$0.138641\pi$
$853$	16.4689	+	39.7595i	0.563885	+	1.36134i	−0.342751	+	0.939426i	$0.611359\pi$
$854$	−0.0375617	−	0.612782i	−0.00128533	−	0.0209690i
$855$		0			0
$856$	−7.29613	+	10.6251i	−0.249377	+	0.363158i
$857$	19.1990	−	19.1990i	0.655827	−	0.655827i	−0.298563	−	0.954390i	$-0.596507\pi$
$857$	19.1990	−	19.1990i	0.655827	−	0.655827i	0.954390	+	0.298563i	$0.0965074\pi$
$858$		0			0
$859$	−20.9206	+	8.66558i	−0.713800	+	0.295666i	−0.709876	−	0.704327i	$-0.751249\pi$
$859$	−20.9206	+	8.66558i	−0.713800	+	0.295666i	−0.00392405	+	0.999992i	$0.501249\pi$
$860$	4.80472	+	39.0450i	0.163840	+	1.33142i
$861$		0			0
$862$	−4.64387	+	13.4926i	−0.158171	+	0.459561i
$863$	35.6482			1.21348			0.606740	−	0.794901i	$-0.292477\pi$
$863$	35.6482			1.21348			0.606740	+	0.794901i	$0.292477\pi$
$864$		0			0
$865$	−15.1141			−0.513895
$866$	2.91626	−	8.47311i	0.0990985	−	0.287928i
$867$		0			0
$868$	−10.6397	+	1.30928i	−0.361134	+	0.0444398i
$869$	0.0344475	−	0.0142686i	0.00116855	−	0.000484030i
$870$		0			0
$871$	18.6298	−	18.6298i	0.631247	−	0.631247i
$872$	8.03125	+	43.2359i	0.271972	+	1.46415i
$873$		0			0
$874$	−0.108302	−	1.76684i	−0.00366336	−	0.0597641i
$875$	−10.8814	−	26.2700i	−0.367858	−	0.888087i
$876$		0			0
$877$	−39.7520	−	16.4658i	−1.34233	−	0.556011i	−0.408183	−	0.912900i	$-0.633838\pi$
$877$	−39.7520	−	16.4658i	−1.34233	−	0.556011i	−0.934147	+	0.356889i	$0.883838\pi$
$878$	0.375489	+	0.769606i	0.0126721	+	0.0259729i
$879$		0			0
$880$	0.115050	−	0.191707i	0.00387832	−	0.00646244i
$881$		−	2.87702i		−	0.0969292i	−0.998825	−	0.0484646i	$-0.984567\pi$
$881$		−	2.87702i		−	0.0969292i	0.998825	−	0.0484646i	$-0.0154328\pi$
$882$		0			0
$883$	−14.6026	−	6.04860i	−0.491417	−	0.203552i	0.123193	−	0.992383i	$-0.460687\pi$
$883$	−14.6026	−	6.04860i	−0.491417	−	0.203552i	−0.614610	+	0.788831i	$0.710687\pi$
$884$	13.7735	−	7.79752i	0.463252	−	0.262259i
$885$		0			0
$886$	−50.3585	+	3.08682i	−1.69183	+	0.103704i
$887$	2.13617	+	2.13617i	0.0717256	+	0.0717256i	0.742060	−	0.670334i	$-0.233849\pi$
$887$	2.13617	+	2.13617i	0.0717256	+	0.0717256i	−0.670334	+	0.742060i	$0.733849\pi$
$888$		0			0
$889$	−40.3909	+	40.3909i	−1.35467	+	1.35467i
$890$	27.3083	−	30.8748i	0.915377	−	1.03492i
$891$		0			0
$892$	30.6833	+	23.9592i	1.02735	+	0.802214i
$893$	2.50783	−	6.05443i	0.0839213	−	0.202604i
$894$		0			0
$895$	−56.2356			−1.87975
$896$	−1.31609	−	36.7023i	−0.0439676	−	1.22614i
$897$		0			0
$898$	39.0845	+	13.4520i	1.30427	+	0.448900i
$899$	−1.08275	+	2.61400i	−0.0361118	+	0.0871817i
$900$		0			0
$901$	23.2923	−	9.64799i	0.775979	−	0.321421i
$902$	−0.0945143	+	0.106858i	−0.00314698	+	0.00355797i
$903$		0			0
$904$	29.0719	−	18.8961i	0.966915	−	0.628474i
$905$	−11.8765	−	11.8765i	−0.394788	−	0.394788i
$906$		0			0
$907$	9.74667	+	23.5305i	0.323633	+	0.781319i	0.999037	+	0.0438711i	$0.0139691\pi$
$907$	9.74667	+	23.5305i	0.323633	+	0.781319i	−0.675404	+	0.737448i	$0.736031\pi$
$908$	−0.818869	+	0.463583i	−0.0271751	+	0.0153845i
$909$		0			0
$910$	−46.4820	+	22.6785i	−1.54086	+	0.751784i
$911$			26.3712i			0.873717i	0.899530	+	0.436859i	$0.143909\pi$
$911$			26.3712i			0.873717i	−0.899530	+	0.436859i	$0.856091\pi$
$912$		0			0
$913$		−	0.195973i		−	0.00648575i
$914$	−7.44478	−	15.2589i	−0.246252	−	0.504719i
$915$		0			0
$916$	−23.5044	−	6.51159i	−0.776609	−	0.215149i
$917$	25.4766	+	61.5059i	0.841310	+	2.03110i
$918$		0			0
$919$	12.7406	+	12.7406i	0.420274	+	0.420274i	0.885298	−	0.465024i	$-0.153954\pi$
$919$	12.7406	+	12.7406i	0.420274	+	0.420274i	−0.465024	+	0.885298i	$0.653954\pi$
$920$	2.35808	+	12.6946i	0.0777437	+	0.418530i
$921$		0			0
$922$	−5.94972	−	5.26245i	−0.195943	−	0.173309i
$923$	62.7450	−	25.9898i	2.06528	−	0.855465i
$924$		0			0
$925$	−7.25956	+	17.5261i	−0.238693	+	0.576255i
$926$	−0.208614	+	0.606122i	−0.00685548	+	0.0199184i
$927$		0			0
$928$	−8.60102	−	4.47010i	−0.282342	−	0.146738i
$929$	3.69455			0.121214			0.0606071	−	0.998162i	$-0.480696\pi$
$929$	3.69455			0.121214			0.0606071	+	0.998162i	$0.480696\pi$
$930$		0			0
$931$	0.952627	−	2.29985i	0.0312211	−	0.0753744i
$932$	−1.46474	−	11.9030i	−0.0479792	−	0.389896i
$933$		0			0
$934$	14.3726	+	12.7124i	0.470286	+	0.415962i
$935$	0.0712548	−	0.0712548i	0.00233028	−	0.00233028i
$936$		0			0
$937$	−10.9918	−	10.9918i	−0.359086	−	0.359086i	0.504390	−	0.863476i	$-0.331717\pi$
$937$	−10.9918	−	10.9918i	−0.359086	−	0.359086i	−0.863476	+	0.504390i	$0.831717\pi$
$938$	−1.68579	−	27.5020i	−0.0550430	−	0.897973i
$939$		0			0
$940$	−12.7619	+	46.0656i	−0.416246	+	1.50250i
$941$	25.8484	+	10.7067i	0.842632	+	0.349030i	0.761891	−	0.647705i	$-0.224271\pi$
$941$	25.8484	+	10.7067i	0.842632	+	0.349030i	0.0807415	+	0.996735i	$0.474271\pi$
$942$		0			0
$943$		−	8.23857i		−	0.268285i
$944$	−21.5688	−	29.1160i	−0.702005	−	0.947644i
$945$		0			0
$946$	−0.212143	+	0.103504i	−0.00689736	+	0.00336521i
$947$	14.6973	+	6.08784i	0.477599	+	0.197828i	0.608479	−	0.793570i	$-0.291780\pi$
$947$	14.6973	+	6.08784i	0.477599	+	0.197828i	−0.130879	+	0.991398i	$0.541780\pi$
$948$		0			0
$949$	−13.1848	−	31.8309i	−0.427996	−	1.03327i
$950$	−1.57647	+	0.0966326i	−0.0511473	+	0.00313518i
$951$		0			0
$952$	3.43499	−	16.1923i	0.111329	−	0.524796i
$953$	15.7973	−	15.7973i	0.511725	−	0.511725i	−0.403329	−	0.915055i	$-0.632147\pi$
$953$	15.7973	−	15.7973i	0.511725	−	0.511725i	0.915055	+	0.403329i	$0.132147\pi$
$954$		0			0
$955$	39.2089	−	16.2409i	1.26877	−	0.525542i
$956$	−30.6564	+	39.2601i	−0.991499	+	1.26976i
$957$		0			0
$958$	28.4607	+	9.79554i	0.919523	+	0.316480i
$959$	−13.3724			−0.431817
$960$		0			0
$961$	−28.2736			−0.912052
$962$	−70.1643	−	24.1490i	−2.26219	−	0.778596i
$963$		0			0
$964$	−1.24286	+	1.59167i	−0.0400298	+	0.0512641i
$965$	−41.0961	+	17.0226i	−1.32293	+	0.547975i
$966$		0			0
$967$	−21.8340	+	21.8340i	−0.702133	+	0.702133i	−0.964868	−	0.262735i	$-0.915376\pi$
$967$	−21.8340	+	21.8340i	−0.702133	+	0.702133i	0.262735	+	0.964868i	$0.415376\pi$
$968$	−30.4341	−	6.45620i	−0.978189	−	0.207510i
$969$		0			0
$970$	−46.4747	+	2.84876i	−1.49221	+	0.0914680i
$971$	−9.34114	−	22.5515i	−0.299771	−	0.723712i	−0.999952	−	0.00974679i	$-0.996897\pi$
$971$	−9.34114	−	22.5515i	−0.299771	−	0.723712i	0.700181	−	0.713965i	$-0.253103\pi$
$972$		0			0
$973$	−2.93549	−	1.21592i	−0.0941075	−	0.0389806i
$974$	18.5967	−	9.07329i	0.595876	−	0.290727i
$975$		0			0
$976$	−0.529098	−	0.0787848i	−0.0169360	−	0.00252184i
$977$			56.1827i			1.79744i	0.438518	+	0.898722i	$0.355503\pi$
$977$			56.1827i			1.79744i	−0.438518	+	0.898722i	$0.644497\pi$
$978$		0			0
$979$	0.228497	+	0.0946464i	0.00730278	+	0.00302491i
$980$	−4.84773	+	17.4985i	−0.154855	+	0.558971i
$981$		0			0
$982$	−0.559954	−	9.13511i	−0.0178689	−	0.291513i
$983$	−19.2076	−	19.2076i	−0.612629	−	0.612629i	0.331002	−	0.943630i	$-0.392613\pi$
$983$	−19.2076	−	19.2076i	−0.612629	−	0.612629i	−0.943630	+	0.331002i	$0.892613\pi$
$984$		0			0
$985$	−32.1656	+	32.1656i	−1.02488	+	1.02488i
$986$	−3.27246	−	2.89444i	−0.104216	−	0.0921778i
$987$		0			0
$988$	−0.754562	−	6.13185i	−0.0240058	−	0.195080i
$989$	5.21663	−	12.5941i	0.165879	−	0.400468i
$990$		0			0
$991$	0.759661			0.0241314			0.0120657	−	0.999927i	$-0.496159\pi$
$991$	0.759661			0.0241314			0.0120657	+	0.999927i	$0.496159\pi$
$992$	−0.807852	+	9.30549i	−0.0256493	+	0.295450i
$993$		0			0
$994$	23.1149	−	67.1598i	0.733160	−	2.13018i
$995$	−14.4189	+	34.8103i	−0.457109	+	1.10356i
$996$		0			0
$997$	−5.82662	+	2.41346i	−0.184531	+	0.0764352i	−0.473036	−	0.881043i	$-0.656842\pi$
$997$	−5.82662	+	2.41346i	−0.184531	+	0.0764352i	0.288505	+	0.957478i	$0.406842\pi$
$998$	29.5606	+	26.1460i	0.935725	+	0.827636i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.3	✓	128
3.2	odd	2	inner	864.2.v.b.109.30	yes	128
32.5	even	8	inner	864.2.v.b.325.3	yes	128
96.5	odd	8	inner	864.2.v.b.325.30	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.3	✓	128	1.1	even	1	trivial
864.2.v.b.109.30	yes	128	3.2	odd	2	inner
864.2.v.b.325.3	yes	128	32.5	even	8	inner
864.2.v.b.325.30	yes	128	96.5	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33723 - 0.460244i) q^{2} +(1.57635 + 1.23090i) q^{4} +(-2.37116 + 0.982165i) q^{5} +(2.29537 - 2.29537i) q^{7} +(-1.54142 - 2.37150i) q^{8} +O(q^{10})\)	\(q+(-1.33723 - 0.460244i) q^{2} +(1.57635 + 1.23090i) q^{4} +(-2.37116 + 0.982165i) q^{5} +(2.29537 - 2.29537i) q^{7} +(-1.54142 - 2.37150i) q^{8} +(3.62281 - 0.222067i) q^{10} +(0.00833427 + 0.0201207i) q^{11} +(-4.05547 - 1.67983i) q^{13} +(-4.12585 + 2.01300i) q^{14} +(0.969765 + 3.88066i) q^{16} +1.80284i q^{17} +(0.650151 + 0.269301i) q^{19} +(-4.94672 - 1.37042i) q^{20} +(-0.00188438 - 0.0307418i) q^{22} +(1.25771 + 1.25771i) q^{23} +(1.12220 - 1.12220i) q^{25} +(4.64996 + 4.11282i) q^{26} +(6.44367 - 0.792934i) q^{28} +(0.655744 - 1.58311i) q^{29} -1.65118 q^{31} +(0.489257 - 5.63566i) q^{32} +(0.829744 - 2.41080i) q^{34} +(-3.18824 + 7.69710i) q^{35} +(-11.0433 + 4.57430i) q^{37} +(-0.745455 - 0.659345i) q^{38} +(5.98416 + 4.10926i) q^{40} +(-3.27522 - 3.27522i) q^{41} +(-2.93287 - 7.08058i) q^{43} +(-0.0116289 + 0.0419760i) q^{44} +(-1.10299 - 2.26070i) q^{46} -9.31235i q^{47} -3.53740i q^{49} +(-2.01712 + 0.984150i) q^{50} +(-4.32514 - 7.63989i) q^{52} +(-5.35156 - 12.9198i) q^{53} +(-0.0395237 - 0.0395237i) q^{55} +(-8.98159 - 1.90533i) q^{56} +(-1.60549 + 1.81517i) q^{58} +(-8.36913 + 3.46661i) q^{59} +(-0.0511774 + 0.123553i) q^{61} +(2.20800 + 0.759946i) q^{62} +(-3.24802 + 7.31097i) q^{64} +11.2660 q^{65} +(-2.29687 + 5.54514i) q^{67} +(-2.21911 + 2.84190i) q^{68} +(7.80595 - 8.82540i) q^{70} +(-10.9401 + 10.9401i) q^{71} +(5.54998 + 5.54998i) q^{73} +(16.8727 - 1.03425i) q^{74} +(0.693383 + 1.22478i) q^{76} +(0.0653146 + 0.0270542i) q^{77} -1.71204i q^{79} +(-6.11092 - 8.24919i) q^{80} +(2.87231 + 5.88711i) q^{82} +(-8.31348 - 3.44356i) q^{83} +(-1.77068 - 4.27481i) q^{85} +(0.663121 + 10.8182i) q^{86} +(0.0348696 - 0.0507793i) q^{88} +(8.03010 - 8.03010i) q^{89} +(-13.1646 + 5.45296i) q^{91} +(0.434477 + 3.53072i) q^{92} +(-4.28595 + 12.4527i) q^{94} -1.80611 q^{95} -12.8284 q^{97} +(-1.62807 + 4.73031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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