LMFDB - Embedded newform 804.2.ba.b.353.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			353.20
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63546 + 0.570332i) q^{3} +(-0.253886 - 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(2.34944 + 1.86551i) q^{9} +O(q^{10})$	\(q+(1.63546 + 0.570332i) q^{3} +(-0.253886 - 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(2.34944 + 1.86551i) q^{9} +(2.31075 + 0.925084i) q^{11} +(2.62372 - 2.75167i) q^{13} +(0.591882 - 3.03272i) q^{15} +(2.57618 + 0.891623i) q^{17} +(-8.04118 + 0.767839i) q^{19} +(-1.22269 + 2.66080i) q^{21} +(5.28862 + 0.251928i) q^{23} +(1.74381 - 0.512028i) q^{25} +(2.77846 + 4.39092i) q^{27} +(3.12371 + 1.80347i) q^{29} +(-1.65164 - 1.73219i) q^{31} +(3.25153 + 2.83083i) q^{33} +(3.01265 - 0.143510i) q^{35} +(-0.708877 - 1.22781i) q^{37} +(5.86034 - 3.00386i) q^{39} +(8.80789 - 1.69758i) q^{41} +(-5.80208 + 5.02753i) q^{43} +(2.69766 - 4.62232i) q^{45} +(-4.31741 - 8.37461i) q^{47} +(4.06689 + 0.783828i) q^{49} +(3.70471 + 2.92749i) q^{51} +(-0.681416 + 0.786397i) q^{53} +(1.04686 - 4.31523i) q^{55} +(-13.5889 - 3.33037i) q^{57} +(0.514512 - 1.75227i) q^{59} +(1.34703 + 3.36473i) q^{61} +(-3.51719 + 3.65428i) q^{63} +(-5.52508 - 3.93439i) q^{65} +(-8.05494 - 1.45534i) q^{67} +(8.50564 + 3.42829i) q^{69} +(-2.27699 + 0.788075i) q^{71} +(-10.7788 + 4.31518i) q^{73} +(3.14395 + 0.157148i) q^{75} +(-1.92825 + 3.74029i) q^{77} +(-7.15051 - 1.73470i) q^{79} +(2.03977 + 8.76581i) q^{81} +(7.76201 + 9.87019i) q^{83} +(0.920389 - 4.77543i) q^{85} +(4.08011 + 4.73105i) q^{87} +(-6.70853 - 10.4387i) q^{89} +(4.20938 + 4.85788i) q^{91} +(-1.71326 - 3.77490i) q^{93} +(3.39741 + 14.0043i) q^{95} +(-2.06706 + 1.19342i) q^{97} +(3.70322 + 6.48415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{13}{66}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.63546	+	0.570332i	0.944232	+	0.329281i
$3$	1.63546	+	0.570332i	0.944232	+	0.329281i
$4$		0			0
$5$	−0.253886	−	1.76582i	−0.113541	−	0.789698i	−0.964427	−	0.264348i	$-0.914843\pi$
$5$	−0.253886	−	1.76582i	−0.113541	−	0.789698i	0.850886	−	0.525350i	$-0.176066\pi$
$6$		0			0
$7$	−0.160706	+	1.68299i	−0.0607410	+	0.636109i	0.912925	+	0.408128i	$0.133818\pi$
$7$	−0.160706	+	1.68299i	−0.0607410	+	0.636109i	−0.973666	+	0.227981i	$0.926788\pi$
$8$		0			0
$9$	2.34944	+	1.86551i	0.783148	+	0.621836i
$10$		0			0
$11$	2.31075	+	0.925084i	0.696717	+	0.278923i	0.692863	−	0.721069i	$-0.256349\pi$
$11$	2.31075	+	0.925084i	0.696717	+	0.278923i	0.00385398	+	0.999993i	$0.498773\pi$
$12$		0			0
$13$	2.62372	−	2.75167i	0.727688	−	0.763177i	−0.251121	−	0.967956i	$-0.580799\pi$
$13$	2.62372	−	2.75167i	0.727688	−	0.763177i	0.978808	+	0.204779i	$0.0656476\pi$
$14$		0			0
$15$	0.591882	−	3.03272i	0.152823	−	0.783045i
$16$		0			0
$17$	2.57618	+	0.891623i	0.624814	+	0.216250i	0.621086	−	0.783743i	$-0.286692\pi$
$17$	2.57618	+	0.891623i	0.624814	+	0.216250i	0.00372874	+	0.999993i	$0.498813\pi$
$18$		0			0
$19$	−8.04118	+	0.767839i	−1.84477	+	0.176154i	−0.958136	−	0.286313i	$-0.907570\pi$
$19$	−8.04118	+	0.767839i	−1.84477	+	0.176154i	−0.886636	+	0.462468i	$0.846964\pi$
$20$		0			0
$21$	−1.22269	+	2.66080i	−0.266812	+	0.580633i
$22$		0			0
$23$	5.28862	+	0.251928i	1.10275	+	0.0525306i	0.591053	−	0.806633i	$-0.298712\pi$
$23$	5.28862	+	0.251928i	1.10275	+	0.0525306i	0.511701	+	0.859163i	$0.329015\pi$
$24$		0			0
$25$	1.74381	−	0.512028i	0.348761	−	0.102406i
$26$		0			0
$27$	2.77846	+	4.39092i	0.534714	+	0.845033i
$28$		0			0
$29$	3.12371	+	1.80347i	0.580058	+	0.334896i	0.761156	−	0.648569i	$-0.224632\pi$
$29$	3.12371	+	1.80347i	0.580058	+	0.334896i	−0.181099	+	0.983465i	$0.557965\pi$
$30$		0			0
$31$	−1.65164	−	1.73219i	−0.296643	−	0.311110i	0.558498	−	0.829506i	$-0.311378\pi$
$31$	−1.65164	−	1.73219i	−0.296643	−	0.311110i	−0.855141	+	0.518396i	$0.826529\pi$
$32$		0			0
$33$	3.25153	+	2.83083i	0.566018	+	0.492784i
$34$		0			0
$35$	3.01265	−	0.143510i	0.509230	−	0.0242576i
$36$		0			0
$37$	−0.708877	−	1.22781i	−0.116539	−	0.201851i	0.801855	−	0.597519i	$-0.203847\pi$
$37$	−0.708877	−	1.22781i	−0.116539	−	0.201851i	−0.918394	+	0.395668i	$0.870513\pi$
$38$		0			0
$39$	5.86034	−	3.00386i	0.938406	−	0.481002i
$40$		0			0
$41$	8.80789	−	1.69758i	1.37556	−	0.265118i	0.552710	−	0.833374i	$-0.313594\pi$
$41$	8.80789	−	1.69758i	1.37556	−	0.265118i	0.822852	+	0.568256i	$0.192382\pi$
$42$		0			0
$43$	−5.80208	+	5.02753i	−0.884809	+	0.766691i	−0.973336	−	0.229382i	$-0.926329\pi$
$43$	−5.80208	+	5.02753i	−0.884809	+	0.766691i	0.0885273	+	0.996074i	$0.471784\pi$
$44$		0			0
$45$	2.69766	−	4.62232i	0.402143	−	0.689055i
$46$		0			0
$47$	−4.31741	−	8.37461i	−0.629759	−	1.22156i	−0.960615	−	0.277881i	$-0.910368\pi$
$47$	−4.31741	−	8.37461i	−0.629759	−	1.22156i	0.330856	−	0.943681i	$-0.392662\pi$
$48$		0			0
$49$	4.06689	+	0.783828i	0.580984	+	0.111975i
$50$		0			0
$51$	3.70471	+	2.92749i	0.518763	+	0.409930i
$52$		0			0
$53$	−0.681416	+	0.786397i	−0.0935998	+	0.108020i	−0.800617	−	0.599176i	$-0.795495\pi$
$53$	−0.681416	+	0.786397i	−0.0935998	+	0.108020i	0.707017	+	0.707196i	$0.250040\pi$
$54$		0			0
$55$	1.04686	−	4.31523i	0.141159	−	0.581866i
$56$		0			0
$57$	−13.5889	−	3.33037i	−1.79990	−	0.441118i
$58$		0			0
$59$	0.514512	−	1.75227i	0.0669838	−	0.228126i	−0.919197	−	0.393798i	$-0.871161\pi$
$59$	0.514512	−	1.75227i	0.0669838	−	0.228126i	0.986181	+	0.165672i	$0.0529792\pi$
$60$		0			0
$61$	1.34703	+	3.36473i	0.172470	+	0.430809i	0.989268	−	0.146115i	$-0.0466770\pi$
$61$	1.34703	+	3.36473i	0.172470	+	0.430809i	−0.816798	+	0.576924i	$0.804253\pi$
$62$		0			0
$63$	−3.51719	+	3.65428i	−0.443124	+	0.460396i
$64$		0			0
$65$	−5.52508	−	3.93439i	−0.685302	−	0.488001i
$66$		0			0
$67$	−8.05494	−	1.45534i	−0.984067	−	0.177798i
$67$	−8.05494	−	1.45534i	−0.984067	−	0.177798i
$68$		0			0
$69$	8.50564	+	3.42829i	1.02396	+	0.412717i
$70$		0			0
$71$	−2.27699	+	0.788075i	−0.270229	+	0.0935272i	−0.458822	−	0.888528i	$-0.651729\pi$
$71$	−2.27699	+	0.788075i	−0.270229	+	0.0935272i	0.188593	+	0.982055i	$0.439607\pi$
$72$		0			0
$73$	−10.7788	+	4.31518i	−1.26156	+	0.505054i	−0.903478	−	0.428635i	$-0.858995\pi$
$73$	−10.7788	+	4.31518i	−1.26156	+	0.505054i	−0.358085	+	0.933689i	$0.616570\pi$
$74$		0			0
$75$	3.14395	+	0.157148i	0.363032	+	0.0181459i
$76$		0			0
$77$	−1.92825	+	3.74029i	−0.219745	+	0.426246i
$78$		0			0
$79$	−7.15051	−	1.73470i	−0.804495	−	0.195168i	−0.187633	−	0.982239i	$-0.560081\pi$
$79$	−7.15051	−	1.73470i	−0.804495	−	0.195168i	−0.616863	+	0.787071i	$0.711597\pi$
$80$		0			0
$81$	2.03977	+	8.76581i	0.226641	+	0.973978i
$82$		0			0
$83$	7.76201	+	9.87019i	0.851991	+	1.08339i	0.995595	+	0.0937592i	$0.0298884\pi$
$83$	7.76201	+	9.87019i	0.851991	+	1.08339i	−0.143604	+	0.989635i	$0.545869\pi$
$84$		0			0
$85$	0.920389	−	4.77543i	0.0998302	−	0.517968i
$86$		0			0
$87$	4.08011	+	4.73105i	0.437434	+	0.507222i
$88$		0			0
$89$	−6.70853	−	10.4387i	−0.711102	−	1.10650i	−0.989289	−	0.145970i	$-0.953370\pi$
$89$	−6.70853	−	10.4387i	−0.711102	−	1.10650i	0.278187	−	0.960527i	$-0.410267\pi$
$90$		0			0
$91$	4.20938	+	4.85788i	0.441263	+	0.509245i
$92$		0			0
$93$	−1.71326	−	3.77490i	−0.177657	−	0.391439i
$94$		0			0
$95$	3.39741	+	14.0043i	0.348567	+	1.43681i
$96$		0			0
$97$	−2.06706	+	1.19342i	−0.209879	+	0.121173i	−0.601255	−	0.799057i	$-0.705332\pi$
$97$	−2.06706	+	1.19342i	−0.209879	+	0.121173i	0.391376	+	0.920231i	$0.371999\pi$
$98$		0			0
$99$	3.70322	+	6.48415i	0.372188	+	0.651682i
$100$		0			0
$101$	6.99812	+	9.82748i	0.696339	+	0.977871i	0.999688	+	0.0249915i	$0.00795588\pi$
$101$	6.99812	+	9.82748i	0.696339	+	0.977871i	−0.303349	+	0.952880i	$0.598105\pi$
$102$		0			0
$103$	6.27700	−	5.98510i	0.618491	−	0.589730i	−0.314665	−	0.949203i	$-0.601892\pi$
$103$	6.27700	−	5.98510i	0.618491	−	0.589730i	0.933155	+	0.359473i	$0.117044\pi$
$104$		0			0
$105$	5.00891	+	1.48350i	0.488819	+	0.144775i
$106$		0			0
$107$	−14.0867	−	2.02537i	−1.36182	−	0.195800i	−0.577617	−	0.816308i	$-0.696017\pi$
$107$	−14.0867	−	2.02537i	−1.36182	−	0.195800i	−0.784200	+	0.620508i	$0.786926\pi$
$108$		0			0
$109$	−3.38256	−	11.5200i	−0.323991	−	1.10341i	−0.947010	−	0.321205i	$-0.895912\pi$
$109$	−3.38256	−	11.5200i	−0.323991	−	1.10341i	0.623019	−	0.782207i	$-0.285906\pi$
$110$		0			0
$111$	−0.459079	−	2.41233i	−0.0435738	−	0.228968i
$112$		0			0
$113$	−5.92718	−	4.66119i	−0.557582	−	0.438488i	0.299182	−	0.954196i	$-0.403286\pi$
$113$	−5.92718	−	4.66119i	−0.557582	−	0.438488i	−0.856764	+	0.515708i	$0.827529\pi$
$114$		0			0
$115$	−0.897850	−	9.40271i	−0.0837249	−	0.876807i
$116$		0			0
$117$	11.2975	−	1.57034i	1.04446	−	0.145178i
$118$		0			0
$119$	−1.91459	+	4.19238i	−0.175511	+	0.384315i
$120$		0			0
$121$	−3.47729	−	3.31559i	−0.316118	−	0.301418i
$122$		0			0
$123$	15.3731	+	2.24710i	1.38615	+	0.202614i
$124$		0			0
$125$	−5.05233	−	11.0631i	−0.451894	−	0.989511i
$126$		0			0
$127$	−8.93571	−	0.853257i	−0.792916	−	0.0757143i	−0.309266	−	0.950976i	$-0.600083\pi$
$127$	−8.93571	−	0.853257i	−0.792916	−	0.0757143i	−0.483650	+	0.875261i	$0.660689\pi$
$128$		0			0
$129$	−12.3564	+	4.91320i	−1.08792	+	0.432584i
$130$		0			0
$131$	−9.40847	+	14.6399i	−0.822022	+	1.27909i	0.135514	+	0.990775i	$0.456731\pi$
$131$	−9.40847	+	14.6399i	−0.822022	+	1.27909i	−0.957536	+	0.288315i	$0.906905\pi$
$132$		0			0
$133$		−	13.6566i		−	1.18418i
$134$		0			0
$135$	7.04816	−	6.02105i	0.606609	−	0.518209i
$136$		0			0
$137$	−10.7182	−	6.88816i	−0.915716	−	0.588495i	−0.00430447	−	0.999991i	$-0.501370\pi$
$137$	−10.7182	−	6.88816i	−0.915716	−	0.588495i	−0.911412	+	0.411496i	$0.865007\pi$
$138$		0			0
$139$	7.19676	−	1.03474i	0.610421	−	0.0877653i	0.169830	−	0.985473i	$-0.445678\pi$
$139$	7.19676	−	1.03474i	0.610421	−	0.0877653i	0.440591	+	0.897708i	$0.354769\pi$
$140$		0			0
$141$	−2.28464	−	16.1587i	−0.192401	−	1.36081i
$142$		0			0
$143$	8.60828	−	3.93127i	0.719860	−	0.328749i
$144$		0			0
$145$	2.39154	−	5.97378i	0.198606	−	0.496095i
$146$		0			0
$147$	6.20418	+	3.60139i	0.511712	+	0.297038i
$148$		0			0
$149$	−1.20508	−	0.550340i	−0.0987237	−	0.0450856i	0.365441	−	0.930834i	$-0.380918\pi$
$149$	−1.20508	−	0.550340i	−0.0987237	−	0.0450856i	−0.464165	+	0.885749i	$0.653645\pi$
$150$		0			0
$151$	2.83488	−	8.19085i	0.230699	−	0.666562i	−0.768930	−	0.639333i	$-0.779211\pi$
$151$	2.83488	−	8.19085i	0.230699	−	0.666562i	0.999629	−	0.0272287i	$-0.00866824\pi$
$152$		0			0
$153$	4.38925	+	6.90069i	0.354850	+	0.557888i
$154$		0			0
$155$	−2.63940	+	3.35627i	−0.212002	+	0.269582i
$156$		0			0
$157$	−0.767166	+	16.1048i	−0.0612265	+	1.28530i	0.734066	+	0.679078i	$0.237620\pi$
$157$	−0.767166	+	16.1048i	−0.0612265	+	1.28530i	−0.795293	+	0.606225i	$0.792683\pi$
$158$		0			0
$159$	−1.56293	+	0.897485i	−0.123949	+	0.0711752i
$160$		0			0
$161$	−1.27390	+	8.86019i	−0.100398	+	0.698281i
$162$		0			0
$163$	−5.75503	+	9.96800i	−0.450769	+	0.780754i	−0.998434	−	0.0559432i	$-0.982183\pi$
$163$	−5.75503	+	9.96800i	−0.450769	+	0.780754i	0.547665	+	0.836698i	$0.315517\pi$
$164$		0			0
$165$	4.17321	−	6.46032i	0.324884	−	0.502935i
$166$		0			0
$167$	17.5344	−	12.4862i	1.35685	−	0.966208i	0.357369	−	0.933963i	$-0.383674\pi$
$167$	17.5344	−	12.4862i	1.35685	−	0.966208i	0.999480	−	0.0322443i	$-0.0102655\pi$
$168$		0			0
$169$	−0.0692596	−	1.45394i	−0.00532766	−	0.111841i
$170$		0			0
$171$	−20.3247	−	13.1969i	−1.55427	−	1.00919i
$172$		0			0
$173$	3.43160	−	0.832498i	0.260900	−	0.0632936i	−0.103175	−	0.994663i	$-0.532900\pi$
$173$	3.43160	−	0.832498i	0.260900	−	0.0632936i	0.364075	+	0.931370i	$0.381385\pi$
$174$		0			0
$175$	0.581496	+	3.01709i	0.0439570	+	0.228070i
$176$		0			0
$177$	1.84084	−	2.57232i	0.138366	−	0.193347i
$178$		0			0
$179$	−15.1563	+	9.74037i	−1.13284	+	0.728029i	−0.966150	−	0.257981i	$-0.916943\pi$
$179$	−15.1563	+	9.74037i	−1.13284	+	0.728029i	−0.166686	+	0.986010i	$0.553307\pi$
$180$		0			0
$181$	2.27315	−	1.17189i	0.168962	−	0.0871060i	−0.371671	−	0.928365i	$-0.621215\pi$
$181$	2.27315	−	1.17189i	0.168962	−	0.0871060i	0.540633	+	0.841258i	$0.318185\pi$
$182$		0			0
$183$	0.284006	+	6.27112i	0.0209943	+	0.463575i
$184$		0			0
$185$	−1.98812	+	1.56347i	−0.146169	+	0.114949i
$186$		0			0
$187$	5.12807	+	4.44350i	0.375002	+	0.324941i
$188$		0			0
$189$	−7.83637	+	3.97046i	−0.570012	+	0.288808i
$190$		0			0
$191$	−21.1980	−	10.9284i	−1.53384	−	0.790748i	−0.535292	−	0.844667i	$-0.679798\pi$
$191$	−21.1980	−	10.9284i	−1.53384	−	0.790748i	−0.998545	+	0.0539195i	$0.982829\pi$
$192$		0			0
$193$	−12.6834	−	3.72420i	−0.912975	−	0.268074i	−0.208682	−	0.977984i	$-0.566917\pi$
$193$	−12.6834	−	3.72420i	−0.912975	−	0.268074i	−0.704292	+	0.709910i	$0.748736\pi$
$194$		0			0
$195$	−6.79213	−	9.58566i	−0.486394	−	0.686444i
$196$		0			0
$197$	−0.686890	−	1.98464i	−0.0489389	−	0.141400i	0.917883	−	0.396851i	$-0.129897\pi$
$197$	−0.686890	−	1.98464i	−0.0489389	−	0.141400i	−0.966822	+	0.255452i	$0.917776\pi$
$198$		0			0
$199$	−10.0473	+	14.1094i	−0.712232	+	1.00019i	0.286876	+	0.957968i	$0.407383\pi$
$199$	−10.0473	+	14.1094i	−0.712232	+	1.00019i	−0.999108	+	0.0422228i	$0.986556\pi$
$200$		0			0
$201$	−12.3435	−	6.97413i	−0.870642	−	0.491917i
$202$		0			0
$203$	−3.53721	+	4.96732i	−0.248264	+	0.348638i
$204$		0			0
$205$	−5.23383	−	15.1222i	−0.365546	−	1.05618i
$206$		0			0
$207$	11.9553	+	10.4579i	0.830954	+	0.726871i
$208$		0			0
$209$	−19.2915	−	5.66448i	−1.33442	−	0.391820i
$210$		0			0
$211$	12.4013	+	6.39332i	0.853741	+	0.440134i	0.828793	−	0.559555i	$-0.189028\pi$
$211$	12.4013	+	6.39332i	0.853741	+	0.440134i	0.0249475	+	0.999689i	$0.492058\pi$
$212$		0			0
$213$	−4.17339	−	0.00977815i	−0.285956	−	0.000669988i
$214$		0			0
$215$	10.3508	+	8.96900i	0.705917	+	0.611681i
$216$		0			0
$217$	3.18067	−	2.50131i	0.215918	−	0.169800i
$218$		0			0
$219$	−20.0894	+	0.909803i	−1.35751	+	0.0614788i
$220$		0			0
$221$	9.21261	−	4.74943i	0.619707	−	0.319481i
$222$		0			0
$223$	23.0161	−	14.7915i	1.54127	−	0.990514i	0.553810	−	0.832643i	$-0.313173\pi$
$223$	23.0161	−	14.7915i	1.54127	−	0.990514i	0.987460	−	0.157871i	$-0.0504630\pi$
$224$		0			0
$225$	5.05217	+	2.05010i	0.336811	+	0.136674i
$226$		0			0
$227$	0.797905	+	4.13993i	0.0529588	+	0.274777i	0.998749	−	0.0500014i	$-0.0159226\pi$
$227$	0.797905	+	4.13993i	0.0529588	+	0.274777i	−0.945790	+	0.324778i	$0.894710\pi$
$228$		0			0
$229$	−17.7661	+	4.31001i	−1.17402	+	0.284814i	−0.774899	−	0.632086i	$-0.782199\pi$
$229$	−17.7661	+	4.31001i	−1.17402	+	0.284814i	−0.399119	+	0.916899i	$0.630684\pi$
$230$		0			0
$231$	−5.28678	+	5.01734i	−0.347845	+	0.330117i
$232$		0			0
$233$	−0.558031	−	11.7145i	−0.0365578	−	0.767443i	−0.940501	−	0.339791i	$-0.889644\pi$
$233$	−0.558031	−	11.7145i	−0.0365578	−	0.767443i	0.903943	−	0.427653i	$-0.140659\pi$
$234$		0			0
$235$	−13.6919	+	9.74997i	−0.893162	+	0.636018i
$236$		0			0
$237$	−10.7050	−	6.91518i	−0.695365	−	0.449189i
$238$		0			0
$239$	−4.72116	+	8.17729i	−0.305386	+	0.528945i	−0.977347	−	0.211642i	$-0.932119\pi$
$239$	−4.72116	+	8.17729i	−0.305386	+	0.528945i	0.671961	+	0.740587i	$0.265452\pi$
$240$		0			0
$241$	1.26707	−	8.81264i	0.0816189	−	0.567672i	−0.907443	−	0.420174i	$-0.861969\pi$
$241$	1.26707	−	8.81264i	0.0816189	−	0.567672i	0.989062	−	0.147498i	$-0.0471219\pi$
$242$		0			0
$243$	−1.66346	+	15.4994i	−0.106711	+	0.994290i
$244$		0			0
$245$	0.351571	−	7.38039i	0.0224611	−	0.471516i
$246$		0			0
$247$	−18.9849	+	24.1413i	−1.20798	+	1.53607i
$248$		0			0
$249$	7.06515	+	20.5692i	0.447735	+	1.30352i
$250$		0			0
$251$	0.167885	−	0.485072i	0.0105968	−	0.0306175i	−0.939578	−	0.342334i	$-0.888783\pi$
$251$	0.167885	−	0.485072i	0.0105968	−	0.0306175i	0.950175	+	0.311716i	$0.100904\pi$
$252$		0			0
$253$	11.9876	+	5.47457i	0.753656	+	0.344183i
$254$		0			0
$255$	4.22884	−	7.28509i	0.264820	−	0.456210i
$256$		0			0
$257$	1.25869	−	3.14406i	0.0785150	−	0.196121i	−0.883917	−	0.467644i	$-0.845103\pi$
$257$	1.25869	−	3.14406i	0.0785150	−	0.196121i	0.962432	+	0.271523i	$0.0875272\pi$
$258$		0			0
$259$	2.18031	−	0.995713i	0.135478	−	0.0618706i
$260$		0			0
$261$	3.97458	+	10.0644i	0.246020	+	0.622974i
$262$		0			0
$263$	16.9934	−	2.44328i	1.04786	−	0.150659i	0.403185	−	0.915119i	$-0.367903\pi$
$263$	16.9934	−	2.44328i	1.04786	−	0.150659i	0.644672	+	0.764459i	$0.276994\pi$
$264$		0			0
$265$	1.56164	+	1.00360i	0.0959306	+	0.0616508i
$266$		0			0
$267$	−5.01801	−	20.8981i	−0.307097	−	1.27894i
$268$		0			0
$269$		−	4.68589i		−	0.285704i	−0.989744	−	0.142852i	$-0.954373\pi$
$269$		−	4.68589i		−	0.285704i	0.989744	−	0.142852i	$-0.0456273\pi$
$270$		0			0
$271$	−4.90107	+	7.62621i	−0.297719	+	0.463259i	−0.957596	−	0.288114i	$-0.906972\pi$
$271$	−4.90107	+	7.62621i	−0.297719	+	0.463259i	0.659877	+	0.751373i	$0.270608\pi$
$272$		0			0
$273$	4.11366	+	10.3456i	0.248970	+	0.626144i
$274$		0			0
$275$	4.50317	+	0.430001i	0.271551	+	0.0259300i
$276$		0			0
$277$	−5.49945	−	12.0421i	−0.330430	−	0.723541i	0.669382	−	0.742918i	$-0.266559\pi$
$277$	−5.49945	−	12.0421i	−0.330430	−	0.723541i	−0.999812	+	0.0193774i	$0.993832\pi$
$278$		0			0
$279$	−0.649021	−	7.15082i	−0.0388559	−	0.428108i
$280$		0			0
$281$	−5.68312	−	5.41884i	−0.339026	−	0.323261i	0.501370	−	0.865233i	$-0.332829\pi$
$281$	−5.68312	−	5.41884i	−0.339026	−	0.323261i	−0.840397	+	0.541972i	$0.817678\pi$
$282$		0			0
$283$	−3.13847	+	6.87229i	−0.186563	+	0.408515i	−0.979684	−	0.200549i	$-0.935728\pi$
$283$	−3.13847	+	6.87229i	−0.186563	+	0.408515i	0.793121	+	0.609064i	$0.208455\pi$
$284$		0			0
$285$	−2.43079	+	24.8411i	−0.143987	+	1.47146i
$286$		0			0
$287$	1.44153	+	15.0964i	0.0850907	+	0.891110i
$288$		0			0
$289$	−7.52121	−	5.91475i	−0.442424	−	0.347926i
$290$		0			0
$291$	−4.06124	+	0.772876i	−0.238074	+	0.0453068i
$292$		0			0
$293$	−4.38699	−	14.9407i	−0.256291	−	0.872846i	−0.982640	−	0.185521i	$-0.940603\pi$
$293$	−4.38699	−	14.9407i	−0.256291	−	0.872846i	0.726350	−	0.687325i	$-0.241215\pi$
$294$		0			0
$295$	−3.22482	−	0.463659i	−0.187756	−	0.0269953i
$296$		0			0
$297$	2.35835	+	12.7166i	0.136845	+	0.737893i
$298$		0			0
$299$	14.5691	−	13.8916i	0.842551	−	0.803370i
$300$		0			0
$301$	−7.52883	−	10.5728i	−0.433955	−	0.609404i
$302$		0			0
$303$	5.84020	+	20.0637i	0.335511	+	1.15263i
$304$		0			0
$305$	5.59951	−	3.23288i	0.320627	−	0.185114i
$306$		0			0
$307$	−0.0892480	−	0.367885i	−0.00509365	−	0.0209963i	0.969208	−	0.246243i	$-0.0791962\pi$
$307$	−0.0892480	−	0.367885i	−0.00509365	−	0.0209963i	−0.974302	+	0.225247i	$0.927681\pi$
$308$		0			0
$309$	13.6793	−	6.20841i	0.778186	−	0.353184i
$310$		0			0
$311$	−9.37890	−	10.8238i	−0.531829	−	0.613763i	0.424724	−	0.905323i	$-0.360371\pi$
$311$	−9.37890	−	10.8238i	−0.531829	−	0.613763i	−0.956553	+	0.291560i	$0.905826\pi$
$312$		0			0
$313$	−13.1366	−	20.4409i	−0.742522	−	1.15539i	−0.982798	−	0.184682i	$-0.940874\pi$
$313$	−13.1366	−	20.4409i	−0.742522	−	1.15539i	0.240276	−	0.970704i	$-0.422762\pi$
$314$		0			0
$315$	7.34576	+	5.28295i	0.413887	+	0.297660i
$316$		0			0
$317$	−5.47509	+	28.4075i	−0.307512	+	1.59552i	0.418747	+	0.908103i	$0.362469\pi$
$317$	−5.47509	+	28.4075i	−0.307512	+	1.59552i	−0.726259	+	0.687421i	$0.758743\pi$
$318$		0			0
$319$	5.54974	+	7.05706i	0.310726	+	0.395120i
$320$		0			0
$321$	−21.8831	−	11.3465i	−1.22140	−	0.633301i
$322$		0			0
$323$	−21.4001	−	5.19161i	−1.19073	−	0.288869i
$324$		0			0
$325$	3.16632	−	6.14180i	0.175636	−	0.340686i
$326$		0			0
$327$	1.03816	−	20.7696i	0.0574101	−	1.14856i
$328$		0			0
$329$	14.7882	−	5.92029i	0.815298	−	0.326396i
$330$		0			0
$331$	28.7768	−	9.95974i	1.58171	−	0.547437i	0.611827	−	0.790991i	$-0.290435\pi$
$331$	28.7768	−	9.95974i	1.58171	−	0.547437i	0.969887	+	0.243555i	$0.0783135\pi$
$332$		0			0
$333$	0.625023	−	4.20709i	0.0342511	−	0.230547i
$334$		0			0
$335$	−0.524827	+	14.5930i	−0.0286744	+	0.797303i
$336$		0			0
$337$	20.5323	+	14.6210i	1.11846	+	0.796455i	0.980992	−	0.194051i	$-0.0621626\pi$
$337$	20.5323	+	14.6210i	1.11846	+	0.796455i	0.137473	+	0.990506i	$0.456102\pi$
$338$		0			0
$339$	−7.03523	−	11.0036i	−0.382101	−	0.597635i
$340$		0			0
$341$	−2.21410	−	5.53055i	−0.119900	−	0.299496i
$342$		0			0
$343$	−5.30690	+	18.0737i	−0.286546	+	0.975885i
$344$		0			0
$345$	3.89427	−	15.8898i	0.209660	−	0.855478i
$346$		0			0
$347$	0.356727	−	1.47045i	0.0191501	−	0.0789378i	−0.961435	−	0.275033i	$-0.911311\pi$
$347$	0.356727	−	1.47045i	0.0191501	−	0.0789378i	0.980585	+	0.196096i	$0.0628263\pi$
$348$		0			0
$349$	15.4848	−	17.8705i	0.828885	−	0.956584i	−0.170702	−	0.985323i	$-0.554604\pi$
$349$	15.4848	−	17.8705i	0.828885	−	0.956584i	0.999587	+	0.0287388i	$0.00914910\pi$
$350$		0			0
$351$	19.3723	+	3.87511i	1.03401	+	0.206838i
$352$		0			0
$353$	26.7416	+	5.15403i	1.42331	+	0.274321i	0.842053	−	0.539395i	$-0.181347\pi$
$353$	26.7416	+	5.15403i	1.42331	+	0.274321i	0.581262	+	0.813717i	$0.302559\pi$
$354$		0			0
$355$	1.96969	+	3.82067i	0.104541	+	0.202780i
$356$		0			0
$357$	−5.52228	+	5.76450i	−0.292270	+	0.305090i
$358$		0			0
$359$	5.72078	−	4.95708i	0.301931	−	0.261625i	−0.490697	−	0.871330i	$-0.663258\pi$
$359$	5.72078	−	4.95708i	0.301931	−	0.261625i	0.792628	+	0.609705i	$0.208712\pi$
$360$		0			0
$361$	45.4143	−	8.75289i	2.39023	−	0.460678i
$362$		0			0
$363$	−3.79598	−	7.40572i	−0.199237	−	0.388700i
$364$		0			0
$365$	10.3564	+	17.9378i	0.542080	+	0.938909i
$366$		0			0
$367$	−5.69029	+	0.271062i	−0.297031	+	0.0141493i	−0.195568	−	0.980690i	$-0.562655\pi$
$367$	−5.69029	+	0.271062i	−0.297031	+	0.0141493i	−0.101462	+	0.994839i	$0.532352\pi$
$368$		0			0
$369$	23.8605	+	12.4428i	1.24213	+	0.647747i
$370$		0			0
$371$	−1.21399	−	1.27319i	−0.0630270	−	0.0661008i
$372$		0			0
$373$	9.97830	+	5.76097i	0.516657	+	0.298292i	0.735566	−	0.677453i	$-0.236916\pi$
$373$	9.97830	+	5.76097i	0.516657	+	0.298292i	−0.218909	+	0.975745i	$0.570250\pi$
$374$		0			0
$375$	−1.95326	−	20.9747i	−0.100866	−	1.08313i
$376$		0			0
$377$	13.1583	−	3.86362i	0.677686	−	0.198987i
$378$		0			0
$379$	−11.4588	−	0.545852i	−0.588601	−	0.0280385i	−0.248831	−	0.968547i	$-0.580046\pi$
$379$	−11.4588	−	0.545852i	−0.588601	−	0.0280385i	−0.339770	+	0.940508i	$0.610349\pi$
$380$		0			0
$381$	−14.1273	−	6.49179i	−0.723766	−	0.332584i
$382$		0			0
$383$	30.7291	−	2.93427i	1.57018	−	0.149934i	0.726648	−	0.687010i	$-0.241077\pi$
$383$	30.7291	−	2.93427i	1.57018	−	0.149934i	0.843534	+	0.537076i	$0.180471\pi$
$384$		0			0
$385$	7.09423	+	2.45534i	0.361556	+	0.125136i
$386$		0			0
$387$	−23.0106	+	0.988080i	−1.16969	+	0.0502269i
$388$		0			0
$389$	−4.77693	+	5.00990i	−0.242200	+	0.254012i	−0.833603	−	0.552364i	$-0.813726\pi$
$389$	−4.77693	+	5.00990i	−0.242200	+	0.254012i	0.591403	+	0.806376i	$0.298574\pi$
$390$		0			0
$391$	13.3998	+	5.36447i	0.677657	+	0.271293i
$392$		0			0
$393$	−23.7367	+	18.5769i	−1.19736	+	0.937082i
$394$		0			0
$395$	−1.24774	+	13.0669i	−0.0627806	+	0.657468i
$396$		0			0
$397$	2.02879	+	14.1105i	0.101822	+	0.708187i	0.975229	+	0.221197i	$0.0709963\pi$
$397$	2.02879	+	14.1105i	0.101822	+	0.708187i	−0.873407	+	0.486991i	$0.838095\pi$
$398$		0			0
$399$	7.78878	−	22.3348i	0.389927	−	1.11814i
$400$		0			0
$401$	12.9470			0.646540			0.323270	−	0.946307i	$-0.395218\pi$
$401$	12.9470			0.646540			0.323270	+	0.946307i	$0.395218\pi$
$402$		0			0
$403$	−9.09984			−0.453295
$404$		0			0
$405$	14.9610	−	5.82738i	0.743416	−	0.289565i
$406$		0			0
$407$	−0.502208	−	3.49293i	−0.0248935	−	0.173138i
$408$		0			0
$409$	−2.35057	+	24.6162i	−0.116228	+	1.21720i	0.729651	+	0.683820i	$0.239683\pi$
$409$	−2.35057	+	24.6162i	−0.116228	+	1.21720i	−0.845879	+	0.533375i	$0.820923\pi$
$410$		0			0
$411$	−13.6006	−	17.3782i	−0.670868	−	0.857204i
$412$		0			0
$413$	2.86636	+	1.14752i	0.141044	+	0.0564656i
$414$		0			0
$415$	15.4583	−	16.2122i	0.758818	−	0.795826i
$416$		0			0
$417$	12.3601	+	2.41227i	0.605279	+	0.118129i
$418$		0			0
$419$	−0.923996	−	0.319798i	−0.0451402	−	0.0156232i	0.304405	−	0.952543i	$-0.401543\pi$
$419$	−0.923996	−	0.319798i	−0.0451402	−	0.0156232i	−0.349545	+	0.936920i	$0.613664\pi$
$420$		0			0
$421$	7.90228	−	0.754577i	0.385134	−	0.0367758i	0.0993063	−	0.995057i	$-0.468338\pi$
$421$	7.90228	−	0.754577i	0.385134	−	0.0367758i	0.285827	+	0.958281i	$0.407732\pi$
$422$		0			0
$423$	5.47938	−	27.7298i	0.266416	−	1.34827i
$424$		0			0
$425$	4.94889	+	0.235745i	0.240056	+	0.0114353i
$426$		0			0
$427$	−5.87926	+	1.72631i	−0.284517	+	0.0835419i
$428$		0			0
$429$	16.3206	−	1.51985i	0.787966	−	0.0733790i
$430$		0			0
$431$	1.97236	+	1.13874i	0.0950054	+	0.0548514i	0.546750	−	0.837296i	$-0.315865\pi$
$431$	1.97236	+	1.13874i	0.0950054	+	0.0548514i	−0.451745	+	0.892147i	$0.649198\pi$
$432$		0			0
$433$	15.1719	+	15.9118i	0.729115	+	0.764673i	0.979057	−	0.203587i	$-0.0652601\pi$
$433$	15.1719	+	15.9118i	0.729115	+	0.764673i	−0.249942	+	0.968261i	$0.580412\pi$
$434$		0			0
$435$	7.31829	−	8.40589i	0.350885	−	0.403031i
$436$		0			0
$437$	−42.7202	+	2.03501i	−2.04358	+	0.0973479i
$438$		0			0
$439$	−3.27643	−	5.67495i	−0.156376	−	0.270850i	0.777183	−	0.629274i	$-0.216648\pi$
$439$	−3.27643	−	5.67495i	−0.156376	−	0.270850i	−0.933559	+	0.358424i	$0.883314\pi$
$440$		0			0
$441$	8.09269	+	9.42837i	0.385366	+	0.448970i
$442$		0			0
$443$	26.5066	−	5.10872i	1.25937	−	0.242723i	0.484467	−	0.874809i	$-0.339013\pi$
$443$	26.5066	−	5.10872i	1.25937	−	0.242723i	0.774898	+	0.632087i	$0.217801\pi$
$444$		0			0
$445$	−16.7296	+	14.4963i	−0.793059	+	0.687190i
$446$		0			0
$447$	−1.65697	−	1.58735i	−0.0783722	−	0.0750791i
$448$		0			0
$449$	10.4791	+	20.3265i	0.494537	+	0.959268i	0.995586	+	0.0938492i	$0.0299172\pi$
$449$	10.4791	+	20.3265i	0.494537	+	0.959268i	−0.501049	+	0.865419i	$0.667053\pi$
$450$		0			0
$451$	21.9232	+	4.22536i	1.03233	+	0.198964i
$452$		0			0
$453$	9.30783	−	11.7790i	0.437320	−	0.553424i
$454$		0			0
$455$	7.50944	−	8.66635i	0.352048	−	0.406285i
$456$		0			0
$457$	−7.84954	+	32.3562i	−0.367186	+	1.51356i	0.426080	+	0.904686i	$0.359894\pi$
$457$	−7.84954	+	32.3562i	−0.367186	+	1.51356i	−0.793266	+	0.608876i	$0.791621\pi$
$458$		0			0
$459$	3.24275	+	13.7891i	0.151359	+	0.643621i
$460$		0			0
$461$	−5.32358	+	18.1305i	−0.247944	+	0.844419i	0.737635	+	0.675200i	$0.235943\pi$
$461$	−5.32358	+	18.1305i	−0.247944	+	0.844419i	−0.985578	+	0.169219i	$0.945875\pi$
$462$		0			0
$463$	9.61241	+	24.0106i	0.446727	+	1.11587i	0.965371	+	0.260879i	$0.0840125\pi$
$463$	9.61241	+	24.0106i	0.446727	+	1.11587i	−0.518645	+	0.854990i	$0.673563\pi$
$464$		0			0
$465$	−6.23082	+	3.98370i	−0.288947	+	0.184740i
$466$		0			0
$467$	−2.18741	−	1.55764i	−0.101221	−	0.0720792i	0.528326	−	0.849042i	$-0.322820\pi$
$467$	−2.18741	−	1.55764i	−0.101221	−	0.0720792i	−0.629547	+	0.776963i	$0.716759\pi$
$468$		0			0
$469$	3.74379	−	13.3225i	0.172872	−	0.615174i
$470$		0			0
$471$	−10.4397	+	25.9012i	−0.481038	+	1.19346i
$472$		0			0
$473$	−18.0580	+	6.24995i	−0.830310	+	0.287373i
$474$		0			0
$475$	−13.6291	+	5.45627i	−0.625346	+	0.250351i
$476$		0			0
$477$	−3.06798	+	0.576407i	−0.140473	+	0.0263919i
$478$		0			0
$479$	14.2296	−	27.6015i	0.650166	−	1.26115i	−0.301340	−	0.953517i	$-0.597434\pi$
$479$	14.2296	−	27.6015i	0.650166	−	1.26115i	0.951506	−	0.307629i	$-0.0995356\pi$
$480$		0			0
$481$	−5.23843	−	1.27083i	−0.238852	−	0.0579448i
$482$		0			0
$483$	−7.13666	+	13.7639i	−0.324729	+	0.626280i
$484$		0			0
$485$	2.63216	+	3.34707i	0.119520	+	0.151983i
$486$		0			0
$487$	3.92931	−	20.3872i	0.178054	−	0.923832i	−0.777470	−	0.628920i	$-0.783497\pi$
$487$	3.92931	−	20.3872i	0.178054	−	0.923832i	0.955524	−	0.294912i	$-0.0952905\pi$
$488$		0			0
$489$	−15.0972	+	13.0200i	−0.682718	+	0.588784i
$490$		0			0
$491$	17.7200	+	27.5728i	0.799691	+	1.24434i	0.966070	+	0.258282i	$0.0831564\pi$
$491$	17.7200	+	27.5728i	0.799691	+	1.24434i	−0.166378	+	0.986062i	$0.553207\pi$
$492$		0			0
$493$	6.43920	+	7.43123i	0.290007	+	0.334686i
$494$		0			0
$495$	10.5096	−	8.18546i	0.472373	−	0.367909i
$496$		0			0
$497$	−0.960392	−	3.95879i	−0.0430795	−	0.177576i
$498$		0			0
$499$	−12.7635	+	7.36899i	−0.571371	+	0.329881i	−0.757697	−	0.652607i	$-0.773675\pi$
$499$	−12.7635	+	7.36899i	−0.571371	+	0.329881i	0.186326	+	0.982488i	$0.440342\pi$
$500$		0			0
$501$	35.7979	−	10.4202i	1.59933	−	0.465539i
$502$		0			0
$503$	4.61392	+	6.47934i	0.205724	+	0.288899i	0.904528	−	0.426414i	$-0.140223\pi$
$503$	4.61392	+	6.47934i	0.205724	+	0.288899i	−0.698804	+	0.715313i	$0.746284\pi$
$504$		0			0
$505$	15.5768	−	14.8525i	0.693160	−	0.660926i
$506$		0			0
$507$	0.715956	−	2.41736i	0.0317967	−	0.107359i
$508$		0			0
$509$	33.2815	+	4.78515i	1.47517	+	0.212098i	0.832493	−	0.554035i	$-0.186913\pi$
$509$	33.2815	+	4.78515i	1.47517	+	0.212098i	0.642682	+	0.766133i	$0.277822\pi$
$510$		0			0
$511$	−5.53017	−	18.8340i	−0.244640	−	0.833168i
$512$		0			0
$513$	−25.7136	−	33.1747i	−1.13528	−	1.46470i
$514$		0			0
$515$	−12.1623	−	9.56450i	−0.535933	−	0.421462i
$516$		0			0
$517$	−2.22923	−	23.3456i	−0.0980416	−	1.02674i
$518$		0			0
$519$	6.08704	+	0.595637i	0.267191	+	0.0261456i
$520$		0			0
$521$	4.05822	−	8.88626i	0.177794	−	0.389314i	−0.799663	−	0.600449i	$-0.794989\pi$
$521$	4.05822	−	8.88626i	0.177794	−	0.389314i	0.977457	+	0.211135i	$0.0677159\pi$
$522$		0			0
$523$	14.7738	+	14.0868i	0.646013	+	0.615972i	0.940545	−	0.339670i	$-0.110315\pi$
$523$	14.7738	+	14.0868i	0.646013	+	0.615972i	−0.294532	+	0.955642i	$0.595164\pi$
$524$		0			0
$525$	−0.769729	+	5.26596i	−0.0335937	+	0.229825i
$526$		0			0
$527$	−2.71045	−	5.93506i	−0.118069	−	0.258535i
$528$		0			0
$529$	5.01020	+	0.478416i	0.217835	+	0.0208007i
$530$		0			0
$531$	4.47769	−	3.15703i	0.194315	−	0.137003i
$532$		0			0
$533$	18.4382	−	28.6904i	0.798648	−	1.24272i
$534$		0			0
$535$			25.3889i			1.09766i
$536$		0			0
$537$	−30.3427	+	7.28584i	−1.30939	+	0.314407i
$538$		0			0
$539$	8.67245	+	5.57345i	0.373549	+	0.240065i
$540$		0			0
$541$	−45.6957	+	6.57004i	−1.96461	+	0.282468i	−0.964800	+	0.262985i	$0.915293\pi$
$541$	−45.6957	+	6.57004i	−1.96461	+	0.282468i	−0.999810	+	0.0194832i	$0.993798\pi$
$542$		0			0
$543$	4.38601	−	0.620128i	0.188222	−	0.0266123i
$544$		0			0
$545$	−19.4834	+	8.89775i	−0.834576	+	0.381138i
$546$		0			0
$547$	−6.21299	+	15.5193i	−0.265648	+	0.663557i	−0.999882	−	0.0153392i	$-0.995117\pi$
$547$	−6.21299	+	15.5193i	−0.265648	+	0.663557i	0.734234	+	0.678896i	$0.237541\pi$
$548$		0			0
$549$	−3.11214	+	10.4181i	−0.132823	+	0.444635i
$550$		0			0
$551$	−26.5030	−	12.1035i	−1.12907	−	0.515628i
$552$		0			0
$553$	4.06859	−	11.7554i	0.173014	−	0.499892i
$554$		0			0
$555$	−4.14318	+	1.42311i	−0.175868	+	0.0604075i
$556$		0			0
$557$	−13.3933	+	17.0309i	−0.567491	+	0.721624i	−0.982097	−	0.188378i	$-0.939677\pi$
$557$	−13.3933	+	17.0309i	−0.567491	+	0.721624i	0.414606	+	0.910001i	$0.363920\pi$
$558$		0			0
$559$	−1.38888	+	29.1562i	−0.0587435	+	1.23318i
$560$		0			0
$561$	5.85247	+	10.1919i	0.247092	+	0.430300i
$562$		0			0
$563$	5.77668	−	40.1777i	0.243458	−	1.69329i	−0.391048	−	0.920370i	$-0.627887\pi$
$563$	5.77668	−	40.1777i	0.243458	−	1.69329i	0.634506	−	0.772918i	$-0.281204\pi$
$564$		0			0
$565$	−6.72598	+	11.6497i	−0.282964	+	0.490108i
$566$		0			0
$567$	−15.0805	+	2.02419i	−0.633322	+	0.0850079i
$568$		0			0
$569$	−33.4521	+	23.8211i	−1.40238	+	0.998633i	−0.405982	+	0.913881i	$0.633070\pi$
$569$	−33.4521	+	23.8211i	−1.40238	+	0.998633i	−0.996402	+	0.0847518i	$0.972990\pi$
$570$		0			0
$571$	−0.821796	−	17.2516i	−0.0343911	−	0.721958i	−0.948555	−	0.316613i	$-0.897454\pi$
$571$	−0.821796	−	17.2516i	−0.0343911	−	0.721958i	0.914164	−	0.405345i	$-0.132849\pi$
$572$		0			0
$573$	−28.4357	−	29.9628i	−1.18792	−	1.25171i
$574$		0			0
$575$	9.35133	−	2.26861i	0.389977	−	0.0946075i
$576$		0			0
$577$	−3.67128	−	19.0484i	−0.152837	−	0.792996i	−0.974736	−	0.223362i	$-0.928297\pi$
$577$	−3.67128	−	19.0484i	−0.152837	−	0.792996i	0.821898	−	0.569634i	$-0.192915\pi$
$578$		0			0
$579$	−18.6192	−	13.3245i	−0.773788	−	0.553749i
$580$		0			0
$581$	−17.8588	+	11.4771i	−0.740907	+	0.476152i
$582$		0			0
$583$	−2.30207	+	1.18680i	−0.0953418	+	0.0491521i
$584$		0			0
$585$	−5.64123	−	19.5507i	−0.233236	−	0.808323i
$586$		0			0
$587$	−16.9004	+	13.2906i	−0.697554	+	0.548563i	−0.902754	−	0.430157i	$-0.858458\pi$
$587$	−16.9004	+	13.2906i	−0.697554	+	0.548563i	0.205200	+	0.978720i	$0.434216\pi$
$588$		0			0
$589$	14.6111	+	12.6606i	0.602042	+	0.521672i
$590$		0			0
$591$	0.00852269	−	3.63755i	0.000350577	−	0.149629i
$592$		0			0
$593$	38.4008	+	19.7970i	1.57693	+	0.812965i	0.999993	−	0.00382154i	$-0.00121644\pi$
$593$	38.4008	+	19.7970i	1.57693	+	0.812965i	0.576940	+	0.816787i	$0.304247\pi$
$594$		0			0
$595$	7.88907	+	2.31644i	0.323420	+	0.0949648i
$596$		0			0
$597$	−24.4789	+	17.3451i	−1.00186	+	0.709887i
$598$		0			0
$599$	−15.0809	−	43.5734i	−0.616189	−	1.78036i	−0.625277	−	0.780403i	$-0.715014\pi$
$599$	−15.0809	−	43.5734i	−0.616189	−	1.78036i	0.00908805	−	0.999959i	$-0.497107\pi$
$600$		0			0
$601$	10.4442	−	14.6668i	0.426026	−	0.598270i	−0.544650	−	0.838664i	$-0.683337\pi$
$601$	10.4442	−	14.6668i	0.426026	−	0.598270i	0.970675	+	0.240394i	$0.0772767\pi$
$602$		0			0
$603$	−16.2097	−	18.4458i	−0.660109	−	0.751170i
$604$		0			0
$605$	−4.97190	+	6.98205i	−0.202136	+	0.283861i
$606$		0			0
$607$	8.85669	+	25.5897i	0.359482	+	1.03865i	0.969251	+	0.246075i	$0.0791411\pi$
$607$	8.85669	+	25.5897i	0.359482	+	1.03865i	−0.609769	+	0.792579i	$0.708738\pi$
$608$		0			0
$609$	−8.61798	+	6.10646i	−0.349218	+	0.247446i
$610$		0			0
$611$	−34.3718	−	10.0925i	−1.39054	−	0.408298i
$612$		0			0
$613$	29.5624	+	15.2405i	1.19401	+	0.615557i	0.936483	−	0.350714i	$-0.114061\pi$
$613$	29.5624	+	15.2405i	1.19401	+	0.615557i	0.257530	+	0.966270i	$0.417091\pi$
$614$		0			0
$615$	0.0649395	−	27.7167i	0.00261861	−	1.11764i
$616$		0			0
$617$	−3.97513	−	3.44447i	−0.160033	−	0.138669i	0.571164	−	0.820836i	$-0.306492\pi$
$617$	−3.97513	−	3.44447i	−0.160033	−	0.138669i	−0.731196	+	0.682167i	$0.761038\pi$
$618$		0			0
$619$	25.0888	−	19.7300i	1.00840	−	0.793018i	0.0299642	−	0.999551i	$-0.490461\pi$
$619$	25.0888	−	19.7300i	1.00840	−	0.793018i	0.978440	+	0.206533i	$0.0662182\pi$
$620$		0			0
$621$	13.5880	+	23.9219i	0.545268	+	0.959952i
$622$		0			0
$623$	18.6462	−	9.61280i	0.747045	−	0.385129i
$624$		0			0
$625$	−10.6081	+	6.81739i	−0.424323	+	0.272696i
$626$		0			0
$627$	−28.3197	−	20.2666i	−1.13098	−	0.809368i
$628$		0			0
$629$	−0.731447	−	3.79511i	−0.0291647	−	0.151321i
$630$		0			0
$631$	−21.3715	+	5.18467i	−0.850786	+	0.206398i	−0.637365	−	0.770562i	$-0.719976\pi$
$631$	−21.3715	+	5.18467i	−0.850786	+	0.206398i	−0.213421	+	0.976960i	$0.568461\pi$
$632$		0			0
$633$	16.6355	+	17.5289i	0.661202	+	0.696709i
$634$		0			0
$635$	0.761959	+	15.9955i	0.0302374	+	0.634761i
$636$		0			0
$637$	12.8272	−	9.13421i	0.508232	−	0.361910i
$638$		0			0
$639$	−6.81982	−	2.39621i	−0.269788	−	0.0947925i
$640$		0			0
$641$	−6.01612	+	10.4202i	−0.237623	+	0.411574i	−0.960032	−	0.279892i	$-0.909701\pi$
$641$	−6.01612	+	10.4202i	−0.237623	+	0.411574i	0.722409	+	0.691466i	$0.243035\pi$
$642$		0			0
$643$	4.91187	−	34.1628i	0.193705	−	1.34725i	−0.628389	−	0.777899i	$-0.716285\pi$
$643$	4.91187	−	34.1628i	0.193705	−	1.34725i	0.822094	−	0.569351i	$-0.192806\pi$
$644$		0			0
$645$	11.8130	+	20.5718i	0.465135	+	0.810014i
$646$		0			0
$647$	1.70736	−	35.8419i	0.0671232	−	1.40909i	−0.674501	−	0.738274i	$-0.735641\pi$
$647$	1.70736	−	35.8419i	0.0671232	−	1.40909i	0.741624	−	0.670816i	$-0.234056\pi$
$648$		0			0
$649$	2.80991	−	3.57309i	0.110298	−	0.140256i
$650$		0			0
$651$	6.62843	−	2.27675i	0.259789	−	0.0892327i
$652$		0			0
$653$	5.84298	−	16.8822i	0.228653	−	0.660650i	−0.771061	−	0.636761i	$-0.780274\pi$
$653$	5.84298	−	16.8822i	0.228653	−	0.660650i	0.999715	−	0.0238894i	$-0.00760496\pi$
$654$		0			0
$655$	28.2400	+	12.8968i	1.10343	+	0.503919i
$656$		0			0
$657$	−33.3742	−	9.96965i	−1.30205	−	0.388953i
$658$		0			0
$659$	−3.78120	+	9.44497i	−0.147295	+	0.367924i	−0.983606	−	0.180331i	$-0.942283\pi$
$659$	−3.78120	+	9.44497i	−0.147295	+	0.367924i	0.836312	+	0.548255i	$0.184707\pi$
$660$		0			0
$661$	−16.7896	+	7.66757i	−0.653041	+	0.298234i	−0.714249	−	0.699891i	$-0.753232\pi$
$661$	−16.7896	+	7.66757i	−0.653041	+	0.298234i	0.0612086	+	0.998125i	$0.480505\pi$
$662$		0			0
$663$	17.7756	−	2.51325i	0.690346	−	0.0976065i
$664$		0			0
$665$	−24.1150	+	3.46722i	−0.935141	+	0.134453i
$666$		0			0
$667$	16.0658	+	10.3248i	0.622068	+	0.399779i
$668$		0			0
$669$	46.0779	−	11.0641i	1.78147	−	0.427764i
$670$		0			0
$671$			9.02116i			0.348258i
$672$		0			0
$673$	−4.46752	+	6.95160i	−0.172210	+	0.267965i	−0.916621	−	0.399758i	$-0.869094\pi$
$673$	−4.46752	+	6.95160i	−0.172210	+	0.267965i	0.744410	+	0.667722i	$0.232731\pi$
$674$		0			0
$675$	7.09337	+	6.23427i	0.273024	+	0.239957i
$676$		0			0
$677$	22.7437	+	2.17176i	0.874113	+	0.0834677i	0.522461	−	0.852663i	$-0.325014\pi$
$677$	22.7437	+	2.17176i	0.874113	+	0.0834677i	0.351652	+	0.936131i	$0.385620\pi$
$678$		0			0
$679$	−1.67632	−	3.67063i	−0.0643312	−	0.140866i
$680$		0			0
$681$	−1.05619	+	7.22574i	−0.0404733	+	0.276891i
$682$		0			0
$683$	13.0913	+	12.4826i	0.500926	+	0.477632i	0.897901	−	0.440197i	$-0.145091\pi$
$683$	13.0913	+	12.4826i	0.500926	+	0.477632i	−0.396975	+	0.917830i	$0.629940\pi$
$684$		0			0
$685$	−9.44204	+	20.6752i	−0.360762	+	0.789958i
$686$		0			0
$687$	−31.5139	−	3.08373i	−1.20233	−	0.117652i
$688$		0			0
$689$	0.376064	+	3.93832i	0.0143269	+	0.150038i
$690$		0			0
$691$	−40.6166	−	31.9412i	−1.54513	−	1.21510i	−0.886594	−	0.462549i	$-0.846935\pi$
$691$	−40.6166	−	31.9412i	−1.54513	−	1.21510i	−0.658533	−	0.752552i	$-0.728823\pi$
$692$		0			0
$693$	−11.5079	+	5.19043i	−0.437147	+	0.197168i
$694$		0			0
$695$	−3.65432	−	12.4455i	−0.138616	−	0.472084i
$696$		0			0
$697$	24.2043	+	3.48005i	0.916803	+	0.131816i
$698$		0			0
$699$	5.76852	−	19.4769i	0.218186	−	0.736682i
$700$		0			0
$701$	11.3286	−	10.8018i	0.427876	−	0.407979i	−0.445302	−	0.895381i	$-0.646904\pi$
$701$	11.3286	−	10.8018i	0.427876	−	0.407979i	0.873178	+	0.487401i	$0.162055\pi$
$702$		0			0
$703$	6.64297	+	9.32874i	0.250544	+	0.351840i
$704$		0			0
$705$	−27.9533	+	8.13672i	−1.05278	+	0.306447i
$706$		0			0
$707$	−17.6641	+	10.1984i	−0.664329	+	0.383550i
$708$		0			0
$709$	−8.94123	−	36.8563i	−0.335795	−	1.38417i	−0.850128	−	0.526576i	$-0.823476\pi$
$709$	−8.94123	−	36.8563i	−0.335795	−	1.38417i	0.514333	−	0.857590i	$-0.328040\pi$
$710$		0			0
$711$	−13.5636	−	17.4149i	−0.508676	−	0.653110i
$712$		0			0
$713$	−8.29850	−	9.57698i	−0.310781	−	0.358661i
$714$		0			0
$715$	−9.12743	−	14.2026i	−0.341347	−	0.531146i
$716$		0			0
$717$	−12.3850	+	10.6810i	−0.462527	+	0.398889i
$718$		0			0
$719$	−8.19919	+	42.5414i	−0.305778	+	1.58653i	0.425830	+	0.904803i	$0.359982\pi$
$719$	−8.19919	+	42.5414i	−0.305778	+	1.58653i	−0.731608	+	0.681725i	$0.761230\pi$
$720$		0			0
$721$	9.06409	+	11.5259i	0.337564	+	0.429248i
$722$		0			0
$723$	7.09836	−	13.6901i	0.263991	−	0.509138i
$724$		0			0
$725$	6.37057	+	1.54548i	0.236597	+	0.0573978i
$726$		0			0
$727$	−9.17982	+	17.8064i	−0.340461	+	0.660402i	−0.995455	−	0.0952320i	$-0.969641\pi$
$727$	−9.17982	+	17.8064i	−0.340461	+	0.660402i	0.654994	+	0.755634i	$0.272671\pi$
$728$		0			0
$729$	−11.5603	+	24.4000i	−0.428161	+	0.903702i
$730$		0			0
$731$	−19.4298	+	7.77854i	−0.718639	+	0.287700i
$732$		0			0
$733$	−4.55566	+	1.57673i	−0.168267	+	0.0582378i	−0.409903	−	0.912129i	$-0.634437\pi$
$733$	−4.55566	+	1.57673i	−0.168267	+	0.0582378i	0.241636	+	0.970367i	$0.422316\pi$
$734$		0			0
$735$	4.78425	−	11.8698i	0.176470	−	0.437824i
$736$		0			0
$737$	−17.2666	−	10.8144i	−0.636024	−	0.398354i
$738$		0			0
$739$	7.51972	+	5.35477i	0.276617	+	0.196978i	0.709943	−	0.704259i	$-0.248721\pi$
$739$	7.51972	+	5.35477i	0.276617	+	0.196978i	−0.433326	+	0.901237i	$0.642660\pi$
$740$		0			0
$741$	−44.8176	+	28.6543i	−1.64641	+	1.05264i
$742$		0			0
$743$	−17.9176	−	44.7560i	−0.657333	−	1.64194i	−0.762115	−	0.647442i	$-0.775839\pi$
$743$	−17.9176	−	44.7560i	−0.657333	−	1.64194i	0.104782	−	0.994495i	$-0.466586\pi$
$744$		0			0
$745$	−0.665848	+	2.26767i	−0.0243948	+	0.0830810i
$746$		0			0
$747$	−0.176519	+	37.6695i	−0.00645848	+	1.37826i
$748$		0			0
$749$	5.67248	−	23.3823i	0.207268	−	0.854371i
$750$		0			0
$751$	20.1566	−	23.2620i	0.735526	−	0.848842i	−0.257556	−	0.966263i	$-0.582917\pi$
$751$	20.1566	−	23.2620i	0.735526	−	0.848842i	0.993082	+	0.117421i	$0.0374627\pi$
$752$		0			0
$753$	0.551221	−	0.697565i	0.0200876	−	0.0254207i
$754$		0			0
$755$	−15.1833	−	2.92634i	−0.552577	−	0.106500i
$756$		0			0
$757$	−3.34716	−	6.49259i	−0.121655	−	0.235977i	0.820142	−	0.572160i	$-0.193894\pi$
$757$	−3.34716	−	6.49259i	−0.121655	−	0.235977i	−0.941797	+	0.336183i	$0.890864\pi$
$758$		0			0
$759$	16.4829	+	15.7903i	0.598293	+	0.573153i
$760$		0			0
$761$	−32.6450	+	28.2870i	−1.18338	+	1.02540i	−0.184284	+	0.982873i	$0.558997\pi$
$761$	−32.6450	+	28.2870i	−1.18338	+	1.02540i	−0.999095	+	0.0425313i	$0.986458\pi$
$762$		0			0
$763$	19.9315	−	3.84148i	0.721569	−	0.139071i
$764$		0			0
$765$	11.0710	−	9.50261i	0.400273	−	0.343568i
$766$		0			0
$767$	−3.47174	−	6.01322i	−0.125357	−	0.217125i
$768$		0			0
$769$	18.0875	−	0.861614i	0.652252	−	0.0310706i	0.281152	−	0.959663i	$-0.409284\pi$
$769$	18.0875	−	0.861614i	0.652252	−	0.0310706i	0.371100	+	0.928593i	$0.378981\pi$
$770$		0			0
$771$	3.85169	−	4.42411i	0.138715	−	0.159330i
$772$		0			0
$773$	25.9204	+	27.1845i	0.932291	+	0.977759i	0.999801	−	0.0199597i	$-0.00635379\pi$
$773$	25.9204	+	27.1845i	0.932291	+	0.977759i	−0.0675095	+	0.997719i	$0.521505\pi$
$774$		0			0
$775$	−3.76706	−	2.17492i	−0.135317	−	0.0781253i
$776$		0			0
$777$	4.13369	−	0.384948i	0.148295	−	0.0138099i
$778$		0			0
$779$	−69.5223	+	20.4136i	−2.49090	+	0.731393i
$780$		0			0
$781$	−5.99059	−	0.285367i	−0.214360	−	0.0102112i
$782$		0			0
$783$	0.760182	+	18.7268i	0.0271667	+	0.669242i
$784$		0			0
$785$	28.6329	−	2.73411i	1.02195	−	0.0975847i
$786$		0			0
$787$	−6.35181	−	2.19838i	−0.226417	−	0.0783638i	0.211504	−	0.977377i	$-0.432164\pi$
$787$	−6.35181	−	2.19838i	−0.226417	−	0.0783638i	−0.437921	+	0.899013i	$0.644285\pi$
$788$		0			0
$789$	29.1854	+	5.69598i	1.03903	+	0.202782i
$790$		0			0
$791$	8.79724	−	9.22628i	0.312794	−	0.328049i
$792$		0			0
$793$	12.7929	+	5.12149i	0.454288	+	0.181869i
$794$		0			0
$795$	1.98160	+	2.53200i	0.0702802	+	0.0898008i
$796$		0			0
$797$	−0.514775	+	5.39097i	−0.0182343	+	0.190958i	0.981765	+	0.190097i	$0.0608802\pi$
$797$	−0.514775	+	5.39097i	−0.0182343	+	0.190958i	−1.00000		0.000861116i	$0.999726\pi$
$798$		0			0
$799$	−3.65541	−	25.4240i	−0.129319	−	0.899435i
$800$		0			0
$801$	3.71211	−	37.0399i	0.131161	−	1.30874i
$802$		0			0
$803$	−28.8990			−1.01982
$804$		0			0
$805$	15.9689			0.562830
$806$		0			0
$807$	2.67251	−	7.66358i	0.0940769	−	0.269771i
$808$		0			0
$809$	2.09565	+	14.5756i	0.0736793	+	0.512451i	0.992923	+	0.118761i	$0.0378923\pi$
$809$	2.09565	+	14.5756i	0.0736793	+	0.512451i	−0.919244	+	0.393689i	$0.871199\pi$
$810$		0			0
$811$	−3.88114	+	40.6452i	−0.136285	+	1.42724i	0.625909	+	0.779896i	$0.284728\pi$
$811$	−3.88114	+	40.6452i	−0.136285	+	1.42724i	−0.762194	+	0.647348i	$0.775878\pi$
$812$		0			0
$813$	−12.3650	+	9.67711i	−0.433658	+	0.339391i
$814$		0			0
$815$	19.0628	+	7.63160i	0.667741	+	0.267323i
$816$		0			0
$817$	42.7952	−	44.8823i	1.49722	−	1.57023i
$818$		0			0
$819$	0.827286	+	19.2659i	0.0289077	+	0.673207i
$820$		0			0
$821$	−17.4854	−	6.05177i	−0.610246	−	0.211208i	0.00442701	−	0.999990i	$-0.498591\pi$
$821$	−17.4854	−	6.05177i	−0.610246	−	0.211208i	−0.614673	+	0.788782i	$0.710712\pi$
$822$		0			0
$823$	17.1109	−	1.63389i	0.596448	−	0.0569538i	0.207534	−	0.978228i	$-0.433456\pi$
$823$	17.1109	−	1.63389i	0.596448	−	0.0569538i	0.388914	+	0.921274i	$0.372850\pi$
$824$		0			0
$825$	7.11950	+	3.27155i	0.247869	+	0.113901i
$826$		0			0
$827$	5.88925	+	0.280540i	0.204789	+	0.00975532i	0.149726	−	0.988728i	$-0.452161\pi$
$827$	5.88925	+	0.280540i	0.204789	+	0.00975532i	0.0550634	+	0.998483i	$0.482464\pi$
$828$		0			0
$829$	−37.2121	+	10.9265i	−1.29243	+	0.379492i	−0.854470	−	0.519502i	$-0.826118\pi$
$829$	−37.2121	+	10.9265i	−1.29243	+	0.379492i	−0.437962	+	0.898994i	$0.644299\pi$
$830$		0			0
$831$	−2.12612	−	22.8309i	−0.0737542	−	0.791995i
$832$		0			0
$833$	9.77814	+	5.64541i	0.338792	+	0.195602i
$834$		0			0
$835$	−26.5000	−	27.7924i	−0.917071	−	0.961796i
$836$		0			0
$837$	3.01689	−	12.0650i	0.104279	−	0.417028i
$838$		0			0
$839$	−0.453948	+	0.0216242i	−0.0156720	+	0.000746550i	−0.0554165	−	0.998463i	$-0.517649\pi$
$839$	−0.453948	+	0.0216242i	−0.0156720	+	0.000746550i	0.0397444	+	0.999210i	$0.487346\pi$
$840$		0			0
$841$	−7.99498	−	13.8477i	−0.275689	−	0.477507i
$842$		0			0
$843$	−6.20396	−	12.1035i	−0.213676	−	0.416868i
$844$		0			0
$845$	−2.54981	+	0.491435i	−0.0877161	+	0.0169059i
$846$		0			0
$847$	6.13891	−	5.31940i	0.210936	−	0.182777i
$848$		0			0
$849$	−9.05232	+	9.44938i	−0.310675	+	0.324302i
$850$		0			0
$851$	−3.43966	−	6.67202i	−0.117910	−	0.228714i
$852$		0			0
$853$	−31.8174	−	6.13231i	−1.08941	−	0.209966i	−0.387241	−	0.921979i	$-0.626572\pi$
$853$	−31.8174	−	6.13231i	−1.08941	−	0.209966i	−0.702167	+	0.712012i	$0.747784\pi$
$854$		0			0
$855$	−18.1431	+	39.2402i	−0.620482	+	1.34199i
$856$		0			0
$857$	20.1855	−	23.2953i	0.689523	−	0.795752i	−0.297774	−	0.954636i	$-0.596244\pi$
$857$	20.1855	−	23.2953i	0.689523	−	0.795752i	0.987297	+	0.158885i	$0.0507898\pi$
$858$		0			0
$859$	−4.79753	+	19.7757i	−0.163690	+	0.674737i	0.829528	+	0.558465i	$0.188610\pi$
$859$	−4.79753	+	19.7757i	−0.163690	+	0.674737i	−0.993217	+	0.116272i	$0.962906\pi$
$860$		0			0
$861$	−6.25238	+	25.5116i	−0.213080	+	0.869433i
$862$		0			0
$863$	5.63172	−	19.1799i	0.191706	−	0.652891i	−0.806400	−	0.591371i	$-0.798587\pi$
$863$	5.63172	−	19.1799i	0.191706	−	0.652891i	0.998106	−	0.0615200i	$-0.0195948\pi$
$864$		0			0
$865$	−2.34128	−	5.84823i	−0.0796058	−	0.198846i
$866$		0			0
$867$	−8.92726	−	13.9629i	−0.303186	−	0.474205i
$868$		0			0
$869$	−14.9183	−	10.6233i	−0.506069	−	0.360370i
$870$		0			0
$871$	−25.1385	+	18.3462i	−0.851785	+	0.621636i
$872$		0			0
$873$	−7.08278	−	1.05225i	−0.239716	−	0.0356132i
$874$		0			0
$875$	19.4309	−	6.72510i	0.656885	−	0.227350i
$876$		0			0
$877$	2.43256	−	0.973849i	0.0821416	−	0.0328845i	−0.330228	−	0.943901i	$-0.607126\pi$
$877$	2.43256	−	0.973849i	0.0821416	−	0.0328845i	0.412369	+	0.911017i	$0.364701\pi$
$878$		0			0
$879$	1.34643	−	26.9370i	0.0454139	−	0.908561i
$880$		0			0
$881$	16.7445	−	32.4797i	0.564135	−	1.09427i	−0.418413	−	0.908257i	$-0.637413\pi$
$881$	16.7445	−	32.4797i	0.564135	−	1.09427i	0.982547	−	0.186012i	$-0.0595563\pi$
$882$		0			0
$883$	15.6112	+	3.78723i	0.525357	+	0.127450i	0.489662	−	0.871912i	$-0.337120\pi$
$883$	15.6112	+	3.78723i	0.525357	+	0.127450i	0.0356955	+	0.999363i	$0.488635\pi$
$884$		0			0
$885$	−5.00961	−	2.59751i	−0.168396	−	0.0873143i
$886$		0			0
$887$	32.4462	+	41.2587i	1.08944	+	1.38533i	0.916327	+	0.400430i	$0.131139\pi$
$887$	32.4462	+	41.2587i	1.08944	+	1.38533i	0.173110	+	0.984902i	$0.444618\pi$
$888$		0			0
$889$	2.87204	−	14.9015i	0.0963251	−	0.499782i
$890$		0			0
$891$	−3.39572	+	22.1425i	−0.113761	+	0.741803i
$892$		0			0
$893$	41.1474	+	64.0266i	1.37695	+	2.14257i
$894$		0			0
$895$	21.0477	+	24.2903i	0.703547	+	0.811937i
$896$		0			0
$897$	31.7499	−	14.4099i	1.06010	−	0.481132i
$898$		0			0
$899$	−2.03528	−	8.38952i	−0.0678803	−	0.279806i
$900$		0			0
$901$	−2.45662	+	1.41833i	−0.0818418	+	0.0472514i
$902$		0			0
$903$	−6.28310	−	21.5852i	−0.209089	−	0.718312i
$904$		0			0
$905$	−2.64647	−	3.71645i	−0.0879717	−	0.123539i
$906$		0			0
$907$	1.05114	−	1.00226i	0.0349026	−	0.0332795i	−0.672427	−	0.740163i	$-0.734748\pi$
$907$	1.05114	−	1.00226i	0.0349026	−	0.0332795i	0.707330	+	0.706884i	$0.249900\pi$
$908$		0			0
$909$	−1.89155	+	36.1442i	−0.0627388	+	1.19883i
$910$		0			0
$911$	−21.9892	−	3.16157i	−0.728536	−	0.104748i	−0.231941	−	0.972730i	$-0.574507\pi$
$911$	−21.9892	−	3.16157i	−0.728536	−	0.104748i	−0.496595	+	0.867982i	$0.665417\pi$
$912$		0			0
$913$	8.80529	+	29.9881i	0.291412	+	0.992460i
$914$		0			0
$915$	11.0016	−	2.09366i	0.363701	−	0.0692141i
$916$		0			0
$917$	−23.1267	−	18.1870i	−0.763710	−	0.600588i
$918$		0			0
$919$	−4.44697	−	46.5707i	−0.146692	−	1.53623i	−0.706565	−	0.707648i	$-0.749756\pi$
$919$	−4.44697	−	46.5707i	−0.146692	−	1.53623i	0.559873	−	0.828578i	$-0.310850\pi$
$920$		0			0
$921$	0.0638553	−	0.652562i	0.00210410	−	0.0215026i
$922$		0			0
$923$	−3.80565	+	8.33322i	−0.125265	+	0.274291i
$924$		0			0
$925$	−1.86482	−	1.77810i	−0.0613148	−	0.0584636i
$926$		0			0
$927$	25.9127	−	2.35188i	0.851085	−	0.0772460i
$928$		0			0
$929$	0.284591	+	0.623168i	0.00933714	+	0.0204455i	0.914243	−	0.405166i	$-0.132786\pi$
$929$	0.284591	+	0.623168i	0.00933714	+	0.0204455i	−0.904906	+	0.425612i	$0.860059\pi$
$930$		0			0
$931$	−33.3044	−	3.18019i	−1.09151	−	0.104226i
$932$		0			0
$933$	−9.16563	−	23.0510i	−0.300069	−	0.754656i
$934$		0			0
$935$	6.54446	−	10.1834i	0.214027	−	0.333032i
$936$		0			0
$937$		−	41.0330i		−	1.34049i	−0.742140	−	0.670245i	$-0.766189\pi$
$937$		−	41.0330i		−	1.34049i	0.742140	−	0.670245i	$-0.233811\pi$
$938$		0			0
$939$	−9.82620	−	40.9224i	−0.320666	−	1.33545i
$940$		0			0
$941$	−22.7087	−	14.5940i	−0.740281	−	0.475750i	0.115357	−	0.993324i	$-0.463199\pi$
$941$	−22.7087	−	14.5940i	−0.740281	−	0.475750i	−0.855638	+	0.517574i	$0.826835\pi$
$942$		0			0
$943$	47.0093	−	6.75892i	1.53083	−	0.220101i
$944$		0			0
$945$	9.00066	+	12.8296i	0.292791	+	0.417346i
$946$		0			0
$947$	−30.9226	+	14.1219i	−1.00485	+	0.458900i	−0.848723	−	0.528837i	$-0.822628\pi$
$947$	−30.9226	+	14.1219i	−1.00485	+	0.458900i	−0.156127	+	0.987737i	$0.549901\pi$
$948$		0			0
$949$	−16.4065	+	40.9815i	−0.532579	+	1.33032i
$950$		0			0
$951$	−25.1560	+	43.3366i	−0.815738	+	1.40529i
$952$		0			0
$953$	−21.3229	−	9.73785i	−0.690717	−	0.315440i	0.0389514	−	0.999241i	$-0.487598\pi$
$953$	−21.3229	−	9.73785i	−0.690717	−	0.315440i	−0.729668	+	0.683801i	$0.760326\pi$
$954$		0			0
$955$	−13.9156	+	40.2065i	−0.450298	+	1.30105i
$956$		0			0
$957$	5.05149	+	14.7067i	0.163292	+	0.475401i
$958$		0			0
$959$	13.3151	−	16.9316i	0.429968	−	0.546749i
$960$		0			0
$961$	1.20247	−	25.2430i	0.0387894	−	0.814290i
$962$		0			0
$963$	−29.3177	−	31.0374i	−0.944749	−	1.00017i
$964$		0			0
$965$	−3.35610	+	23.3422i	−0.108037	+	0.751412i
$966$		0			0
$967$	3.81216	−	6.60285i	0.122591	−	0.212333i	−0.798198	−	0.602395i	$-0.794213\pi$
$967$	3.81216	−	6.60285i	0.122591	−	0.212333i	0.920789	+	0.390062i	$0.127546\pi$
$968$		0			0
$969$	−32.0380	−	20.6958i	−1.02921	−	0.664845i
$970$		0			0
$971$	−1.75017	+	1.24629i	−0.0561657	+	0.0399954i	−0.607795	−	0.794094i	$-0.707946\pi$
$971$	−1.75017	+	1.24629i	−0.0561657	+	0.0399954i	0.551629	+	0.834089i	$0.314006\pi$
$972$		0			0
$973$	0.584889	+	12.2783i	0.0187507	+	0.393625i
$974$		0			0
$975$	8.68125	−	8.23881i	0.278022	−	0.263853i
$976$		0			0
$977$	30.0280	−	7.28471i	0.960680	−	0.233058i	0.275393	−	0.961332i	$-0.411192\pi$
$977$	30.0280	−	7.28471i	0.960680	−	0.233058i	0.685287	+	0.728273i	$0.259677\pi$
$978$		0			0
$979$	−5.84507	−	30.3271i	−0.186809	−	0.969259i
$980$		0			0
$981$	13.5434	−	33.3757i	0.432408	−	1.06560i
$982$		0			0
$983$	16.3758	−	10.5241i	0.522307	−	0.335666i	−0.252777	−	0.967525i	$-0.581344\pi$
$983$	16.3758	−	10.5241i	0.522307	−	0.335666i	0.775084	+	0.631858i	$0.217707\pi$
$984$		0			0
$985$	−3.33012	+	1.71680i	−0.106106	+	0.0547017i
$986$		0			0
$987$	27.5620	−	1.24822i	0.877307	−	0.0397313i
$988$		0			0
$989$	−31.9516	+	25.1270i	−1.01600	+	0.798992i
$990$		0			0
$991$	11.3596	+	9.84316i	0.360850	+	0.312678i	0.816350	−	0.577557i	$-0.195994\pi$
$991$	11.3596	+	9.84316i	0.360850	+	0.312678i	−0.455500	+	0.890236i	$0.650540\pi$
$992$		0			0
$993$	52.7435	+	0.123577i	1.67377	+	0.00392159i
$994$		0			0
$995$	27.4656	+	14.1595i	0.870717	+	0.448886i
$996$		0			0
$997$	−39.4985	−	11.5978i	−1.25093	−	0.367306i	−0.411819	−	0.911266i	$-0.635106\pi$
$997$	−39.4985	−	11.5978i	−1.25093	−	0.367306i	−0.839112	+	0.543959i	$0.816925\pi$
$998$		0			0
$999$	3.42163	−	6.52404i	0.108256	−	0.206412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.353.20	yes	440
3.2	odd	2	inner	804.2.ba.b.353.6	yes	440
67.41	odd	66	inner	804.2.ba.b.41.6	✓	440
201.41	even	66	inner	804.2.ba.b.41.20	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.6	✓	440	67.41	odd	66	inner
804.2.ba.b.41.20	yes	440	201.41	even	66	inner
804.2.ba.b.353.6	yes	440	3.2	odd	2	inner
804.2.ba.b.353.20	yes	440	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63546 + 0.570332i) q^{3} +(-0.253886 - 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(2.34944 + 1.86551i) q^{9} +O(q^{10})\)	\(q+(1.63546 + 0.570332i) q^{3} +(-0.253886 - 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(2.34944 + 1.86551i) q^{9} +(2.31075 + 0.925084i) q^{11} +(2.62372 - 2.75167i) q^{13} +(0.591882 - 3.03272i) q^{15} +(2.57618 + 0.891623i) q^{17} +(-8.04118 + 0.767839i) q^{19} +(-1.22269 + 2.66080i) q^{21} +(5.28862 + 0.251928i) q^{23} +(1.74381 - 0.512028i) q^{25} +(2.77846 + 4.39092i) q^{27} +(3.12371 + 1.80347i) q^{29} +(-1.65164 - 1.73219i) q^{31} +(3.25153 + 2.83083i) q^{33} +(3.01265 - 0.143510i) q^{35} +(-0.708877 - 1.22781i) q^{37} +(5.86034 - 3.00386i) q^{39} +(8.80789 - 1.69758i) q^{41} +(-5.80208 + 5.02753i) q^{43} +(2.69766 - 4.62232i) q^{45} +(-4.31741 - 8.37461i) q^{47} +(4.06689 + 0.783828i) q^{49} +(3.70471 + 2.92749i) q^{51} +(-0.681416 + 0.786397i) q^{53} +(1.04686 - 4.31523i) q^{55} +(-13.5889 - 3.33037i) q^{57} +(0.514512 - 1.75227i) q^{59} +(1.34703 + 3.36473i) q^{61} +(-3.51719 + 3.65428i) q^{63} +(-5.52508 - 3.93439i) q^{65} +(-8.05494 - 1.45534i) q^{67} +(8.50564 + 3.42829i) q^{69} +(-2.27699 + 0.788075i) q^{71} +(-10.7788 + 4.31518i) q^{73} +(3.14395 + 0.157148i) q^{75} +(-1.92825 + 3.74029i) q^{77} +(-7.15051 - 1.73470i) q^{79} +(2.03977 + 8.76581i) q^{81} +(7.76201 + 9.87019i) q^{83} +(0.920389 - 4.77543i) q^{85} +(4.08011 + 4.73105i) q^{87} +(-6.70853 - 10.4387i) q^{89} +(4.20938 + 4.85788i) q^{91} +(-1.71326 - 3.77490i) q^{93} +(3.39741 + 14.0043i) q^{95} +(-2.06706 + 1.19342i) q^{97} +(3.70322 + 6.48415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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