LMFDB - Embedded newform 804.2.ba.b.353.6

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			353.6
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19819 - 1.25074i) q^{3} +(0.253886 + 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(-0.128702 + 2.99724i) q^{9} +O(q^{10})$	\(q+(-1.19819 - 1.25074i) q^{3} +(0.253886 + 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(-0.128702 + 2.99724i) q^{9} +(-2.31075 - 0.925084i) q^{11} +(2.62372 - 2.75167i) q^{13} +(1.90438 - 2.43332i) q^{15} +(-2.57618 - 0.891623i) q^{17} +(-8.04118 + 0.767839i) q^{19} +(2.29753 - 1.81553i) q^{21} +(-5.28862 - 0.251928i) q^{23} +(1.74381 - 0.512028i) q^{25} +(3.90298 - 3.43027i) q^{27} +(-3.12371 - 1.80347i) q^{29} +(-1.65164 - 1.73219i) q^{31} +(1.61167 + 3.99857i) q^{33} +(-3.01265 + 0.143510i) q^{35} +(-0.708877 - 1.22781i) q^{37} +(-6.58533 + 0.0154293i) q^{39} +(-8.80789 + 1.69758i) q^{41} +(-5.80208 + 5.02753i) q^{43} +(-5.32526 + 0.533693i) q^{45} +(4.31741 + 8.37461i) q^{47} +(4.06689 + 0.783828i) q^{49} +(1.97155 + 4.29046i) q^{51} +(0.681416 - 0.786397i) q^{53} +(1.04686 - 4.31523i) q^{55} +(10.5952 + 9.13741i) q^{57} +(-0.514512 + 1.75227i) q^{59} +(1.34703 + 3.36473i) q^{61} +(-5.02362 - 0.698277i) q^{63} +(5.52508 + 3.93439i) q^{65} +(-8.05494 - 1.45534i) q^{67} +(6.02165 + 6.91655i) q^{69} +(2.27699 - 0.788075i) q^{71} +(-10.7788 + 4.31518i) q^{73} +(-2.72982 - 1.56754i) q^{75} +(1.92825 - 3.74029i) q^{77} +(-7.15051 - 1.73470i) q^{79} +(-8.96687 - 0.771503i) q^{81} +(-7.76201 - 9.87019i) q^{83} +(0.920389 - 4.77543i) q^{85} +(1.48710 + 6.06784i) q^{87} +(6.70853 + 10.4387i) q^{89} +(4.20938 + 4.85788i) q^{91} +(-0.187548 + 4.14125i) q^{93} +(-3.39741 - 14.0043i) q^{95} +(-2.06706 + 1.19342i) q^{97} +(3.07010 - 6.80681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.19819	−	1.25074i	−0.691773	−	0.722115i
$3$	−1.19819	−	1.25074i	−0.691773	−	0.722115i
$4$		0			0
$5$	0.253886	+	1.76582i	0.113541	+	0.789698i	0.964427	+	0.264348i	$0.0851567\pi$
$5$	0.253886	+	1.76582i	0.113541	+	0.789698i	−0.850886	+	0.525350i	$0.823934\pi$
$6$		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
$9$	−0.128702	+	2.99724i	−0.0429008	+	0.999079i
$10$		0			0
$11$	−2.31075	−	0.925084i	−0.696717	−	0.278923i	−0.00385398	−	0.999993i	$-0.501227\pi$
$11$	−2.31075	−	0.925084i	−0.696717	−	0.278923i	−0.692863	+	0.721069i	$0.743651\pi$
$12$		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
$15$	1.90438	−	2.43332i	0.491708	−	0.628282i
$16$		0			0
$17$	−2.57618	−	0.891623i	−0.624814	−	0.216250i	−0.00372874	−	0.999993i	$-0.501187\pi$
$17$	−2.57618	−	0.891623i	−0.624814	−	0.216250i	−0.621086	+	0.783743i	$0.713308\pi$
$18$		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
$21$	2.29753	−	1.81553i	0.501363	−	0.396181i
$22$		0			0
$23$	−5.28862	−	0.251928i	−1.10275	−	0.0525306i	−0.511701	−	0.859163i	$-0.670985\pi$
$23$	−5.28862	−	0.251928i	−1.10275	−	0.0525306i	−0.591053	+	0.806633i	$0.701288\pi$
$24$		0			0
$25$	1.74381	−	0.512028i	0.348761	−	0.102406i
$26$		0			0
$27$	3.90298	−	3.43027i	0.751128	−	0.660157i
$28$		0			0
$29$	−3.12371	−	1.80347i	−0.580058	−	0.334896i	0.181099	−	0.983465i	$-0.442035\pi$
$29$	−3.12371	−	1.80347i	−0.580058	−	0.334896i	−0.761156	+	0.648569i	$0.775368\pi$
$30$		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
$33$	1.61167	+	3.99857i	0.280555	+	0.696062i
$34$		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
$39$	−6.58533	+	0.0154293i	−1.05450	+	0.00247066i
$40$		0			0
$41$	−8.80789	+	1.69758i	−1.37556	+	0.265118i	−0.822852	−	0.568256i	$-0.807618\pi$
$41$	−8.80789	+	1.69758i	−1.37556	+	0.265118i	−0.552710	+	0.833374i	$0.686406\pi$
$42$		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
$45$	−5.32526	+	0.533693i	−0.793842	+	0.0795583i
$46$		0			0
$47$	4.31741	+	8.37461i	0.629759	+	1.22156i	0.960615	+	0.277881i	$0.0896321\pi$
$47$	4.31741	+	8.37461i	0.629759	+	1.22156i	−0.330856	+	0.943681i	$0.607338\pi$
$48$		0			0
$49$	4.06689	+	0.783828i	0.580984	+	0.111975i
$50$		0			0
$51$	1.97155	+	4.29046i	0.276072	+	0.600784i
$52$		0			0
$53$	0.681416	−	0.786397i	0.0935998	−	0.108020i	−0.707017	−	0.707196i	$-0.749960\pi$
$53$	0.681416	−	0.786397i	0.0935998	−	0.108020i	0.800617	+	0.599176i	$0.204505\pi$
$54$		0			0
$55$	1.04686	−	4.31523i	0.141159	−	0.581866i
$56$		0			0
$57$	10.5952	+	9.13741i	1.40337	+	1.21028i
$58$		0			0
$59$	−0.514512	+	1.75227i	−0.0669838	+	0.228126i	−0.986181	−	0.165672i	$-0.947021\pi$
$59$	−0.514512	+	1.75227i	−0.0669838	+	0.228126i	0.919197	+	0.393798i	$0.128839\pi$
$60$		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
$63$	−5.02362	−	0.698277i	−0.632917	−	0.0879746i
$64$		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
$69$	6.02165	+	6.91655i	0.724922	+	0.832655i
$70$		0			0
$71$	2.27699	−	0.788075i	0.270229	−	0.0935272i	−0.188593	−	0.982055i	$-0.560393\pi$
$71$	2.27699	−	0.788075i	0.270229	−	0.0935272i	0.458822	+	0.888528i	$0.348271\pi$
$72$		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
$75$	−2.72982	−	1.56754i	−0.315212	−	0.181005i
$76$		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
$81$	−8.96687	−	0.771503i	−0.996319	−	0.0857226i
$82$		0			0
$83$	−7.76201	−	9.87019i	−0.851991	−	1.08339i	−0.995595	−	0.0937592i	$-0.970112\pi$
$83$	−7.76201	−	9.87019i	−0.851991	−	1.08339i	0.143604	−	0.989635i	$-0.454131\pi$
$84$		0			0
$85$	0.920389	−	4.77543i	0.0998302	−	0.517968i
$86$		0			0
$87$	1.48710	+	6.06784i	0.159434	+	0.650541i
$88$		0			0
$89$	6.70853	+	10.4387i	0.711102	+	1.10650i	0.989289	+	0.145970i	$0.0466303\pi$
$89$	6.70853	+	10.4387i	0.711102	+	1.10650i	−0.278187	+	0.960527i	$0.589733\pi$
$90$		0			0
$91$	4.20938	+	4.85788i	0.441263	+	0.509245i
$92$		0			0
$93$	−0.187548	+	4.14125i	−0.0194479	+	0.429428i
$94$		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
$99$	3.07010	−	6.80681i	0.308556	−	0.684110i
$100$		0			0
$101$	−6.99812	−	9.82748i	−0.696339	−	0.977871i	−0.999688	−	0.0249915i	$-0.992044\pi$
$101$	−6.99812	−	9.82748i	−0.696339	−	0.977871i	0.303349	−	0.952880i	$-0.401895\pi$
$102$		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
$105$	3.78921	+	3.59609i	0.369789	+	0.350942i
$106$		0			0
$107$	14.0867	+	2.02537i	1.36182	+	0.195800i	0.784200	−	0.620508i	$-0.213074\pi$
$107$	14.0867	+	2.02537i	1.36182	+	0.195800i	0.577617	+	0.816308i	$0.303983\pi$
$108$		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
$111$	−0.686306	+	2.35777i	−0.0651413	+	0.223789i
$112$		0			0
$113$	5.92718	+	4.66119i	0.557582	+	0.438488i	0.856764	−	0.515708i	$-0.172471\pi$
$113$	5.92718	+	4.66119i	0.557582	+	0.438488i	−0.299182	+	0.954196i	$0.596714\pi$
$114$		0			0
$115$	−0.897850	−	9.40271i	−0.0837249	−	0.876807i
$116$		0			0
$117$	7.90974	+	8.21805i	0.731256	+	0.759759i
$118$		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
$123$	12.6767	+	8.98237i	1.14302	+	0.809913i
$124$		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
$129$	13.2401	+	1.23298i	1.16573	+	0.108558i
$130$		0			0
$131$	9.40847	−	14.6399i	0.822022	−	1.27909i	−0.135514	−	0.990775i	$-0.543269\pi$
$131$	9.40847	−	14.6399i	0.822022	−	1.27909i	0.957536	−	0.288315i	$-0.0930951\pi$
$132$		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	0.911412	−	0.411496i	$-0.134993\pi$
$137$	10.7182	+	6.88816i	0.915716	+	0.588495i	0.00430447	+	0.999991i	$0.498630\pi$
$138$		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
$141$	5.30140	−	15.4343i	0.446458	−	1.29980i
$142$		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
$147$	−3.89252	−	6.02579i	−0.321050	−	0.496999i
$148$		0			0
$149$	1.20508	+	0.550340i	0.0987237	+	0.0450856i	0.464165	−	0.885749i	$-0.346355\pi$
$149$	1.20508	+	0.550340i	0.0987237	+	0.0450856i	−0.365441	+	0.930834i	$0.619082\pi$
$150$		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
$153$	3.00397	−	7.60666i	0.242856	−	0.614962i
$154$		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
$159$	−1.80004	+	0.0899740i	−0.142753	+	0.00713540i
$160$		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
$165$	−6.65157	+	3.86109i	−0.517824	+	0.300586i
$166$		0			0
$167$	−17.5344	+	12.4862i	−1.35685	+	0.966208i	−0.357369	+	0.933963i	$0.616326\pi$
$167$	−17.5344	+	12.4862i	−1.35685	+	0.966208i	−0.999480	+	0.0322443i	$0.989735\pi$
$168$		0			0
$169$	−0.0692596	−	1.45394i	−0.00532766	−	0.111841i
$170$		0			0
$171$	−1.26648	−	24.2001i	−0.0968501	−	1.85063i
$172$		0			0
$173$	−3.43160	+	0.832498i	−0.260900	+	0.0632936i	−0.364075	−	0.931370i	$-0.618615\pi$
$173$	−3.43160	+	0.832498i	−0.260900	+	0.0632936i	0.103175	+	0.994663i	$0.467100\pi$
$174$		0			0
$175$	0.581496	+	3.01709i	0.0439570	+	0.228070i
$176$		0			0
$177$	2.80811	−	1.45602i	0.211071	−	0.109441i
$178$		0			0
$179$	15.1563	−	9.74037i	1.13284	−	0.728029i	0.166686	−	0.986010i	$-0.446693\pi$
$179$	15.1563	−	9.74037i	1.13284	−	0.728029i	0.966150	+	0.257981i	$0.0830571\pi$
$180$		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
$183$	2.59440	−	5.71636i	0.191784	−	0.422565i
$184$		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
$189$	5.14587	+	7.11991i	0.374307	+	0.517898i
$190$		0			0
$191$	21.1980	+	10.9284i	1.53384	+	0.790748i	0.998545	−	0.0539195i	$-0.0171714\pi$
$191$	21.1980	+	10.9284i	1.53384	+	0.790748i	0.535292	+	0.844667i	$0.320202\pi$
$192$		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
$195$	−1.69917	−	11.6246i	−0.121680	−	0.832453i
$196$		0			0
$197$	0.686890	+	1.98464i	0.0489389	+	0.141400i	0.966822	−	0.255452i	$-0.0822241\pi$
$197$	0.686890	+	1.98464i	0.0489389	+	0.141400i	−0.917883	+	0.396851i	$0.870103\pi$
$198$		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
$201$	7.83106	+	11.8184i	0.552360	+	0.833606i
$202$		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
$207$	1.43575	−	15.8188i	0.0997913	−	1.09949i
$208$		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
$213$	−3.71394	−	1.90367i	−0.254475	−	0.130437i
$214$		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
$219$	18.3122	+	8.31109i	1.23742	+	0.561611i
$220$		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
$225$	1.31024	+	5.29250i	0.0873492	+	0.352834i
$226$		0			0
$227$	−0.797905	−	4.13993i	−0.0529588	−	0.274777i	0.945790	−	0.324778i	$-0.105290\pi$
$227$	−0.797905	−	4.13993i	−0.0529588	−	0.274777i	−0.998749	+	0.0500014i	$0.984077\pi$
$228$		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
$231$	−6.98854	+	2.06982i	−0.459812	+	0.136184i
$232$		0			0
$233$	0.558031	+	11.7145i	0.0365578	+	0.767443i	0.940501	+	0.339791i	$0.110356\pi$
$233$	0.558031	+	11.7145i	0.0365578	+	0.767443i	−0.903943	+	0.427653i	$0.859341\pi$
$234$		0			0
$235$	−13.6919	+	9.74997i	−0.893162	+	0.636018i
$236$		0			0
$237$	6.39799	+	11.0219i	0.415594	+	0.715951i
$238$		0			0
$239$	4.72116	−	8.17729i	0.305386	−	0.528945i	−0.671961	−	0.740587i	$-0.734548\pi$
$239$	4.72116	−	8.17729i	0.305386	−	0.528945i	0.977347	+	0.211642i	$0.0678810\pi$
$240$		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
$243$	9.77903	+	12.1396i	0.627325	+	0.778758i
$244$		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
$249$	−3.04472	+	21.5346i	−0.192952	+	1.36470i
$250$		0			0
$251$	−0.167885	+	0.485072i	−0.0105968	+	0.0306175i	−0.950175	−	0.311716i	$-0.899096\pi$
$251$	−0.167885	+	0.485072i	−0.0105968	+	0.0306175i	0.939578	+	0.342334i	$0.111217\pi$
$252$		0			0
$253$	11.9876	+	5.47457i	0.753656	+	0.344183i
$254$		0			0
$255$	−7.07562	+	4.57069i	−0.443093	+	0.286227i
$256$		0			0
$257$	−1.25869	+	3.14406i	−0.0785150	+	0.196121i	−0.962432	−	0.271523i	$-0.912473\pi$
$257$	−1.25869	+	3.14406i	−0.0785150	+	0.196121i	0.883917	+	0.467644i	$0.154897\pi$
$258$		0			0
$259$	2.18031	−	0.995713i	0.135478	−	0.0618706i
$260$		0			0
$261$	5.80746	−	9.13038i	0.359473	−	0.565156i
$262$		0			0
$263$	−16.9934	+	2.44328i	−1.04786	+	0.150659i	−0.644672	−	0.764459i	$-0.723006\pi$
$263$	−16.9934	+	2.44328i	−1.04786	+	0.150659i	−0.403185	+	0.915119i	$0.632097\pi$
$264$		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	$0.0456273\pi$
$269$			4.68589i			0.285704i	−0.989744	+	0.142852i	$0.954373\pi$
$270$		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
$273$	1.03233	−	11.0855i	0.0624795	−	0.670924i
$274$		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
$279$	5.40435	−	4.72741i	0.323550	−	0.283023i
$280$		0			0
$281$	5.68312	+	5.41884i	0.339026	+	0.323261i	0.840397	−	0.541972i	$-0.182322\pi$
$281$	5.68312	+	5.41884i	0.339026	+	0.323261i	−0.501370	+	0.865233i	$0.667171\pi$
$282$		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
$285$	−13.4450	+	21.0290i	−0.796415	+	1.24565i
$286$		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
$291$	3.96939	+	1.15542i	0.232689	+	0.0677320i
$292$		0			0
$293$	4.38699	+	14.9407i	0.256291	+	0.872846i	0.982640	+	0.185521i	$0.0593972\pi$
$293$	4.38699	+	14.9407i	0.256291	+	0.872846i	−0.726350	+	0.687325i	$0.758785\pi$
$294$		0			0
$295$	−3.22482	−	0.463659i	−0.187756	−	0.0269953i
$296$		0			0
$297$	−12.1921	+	4.31592i	−0.707457	+	0.250435i
$298$		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
$303$	−3.90658	+	20.5280i	−0.224427	+	1.17930i
$304$		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
$309$	−15.0068	−	0.679626i	−0.853708	−	0.0386626i
$310$		0			0
$311$	9.37890	+	10.8238i	0.531829	+	0.613763i	0.956553	−	0.291560i	$-0.0941742\pi$
$311$	9.37890	+	10.8238i	0.531829	+	0.613763i	−0.424724	+	0.905323i	$0.639629\pi$
$312$		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
$315$	−0.0423992	−	9.04809i	−0.00238892	−	0.509802i
$316$		0			0
$317$	5.47509	−	28.4075i	0.307512	−	1.59552i	−0.418747	−	0.908103i	$-0.637531\pi$
$317$	5.47509	−	28.4075i	0.307512	−	1.59552i	0.726259	−	0.687421i	$-0.241257\pi$
$318$		0			0
$319$	5.54974	+	7.05706i	0.310726	+	0.395120i
$320$		0			0
$321$	−14.3453	−	20.0456i	−0.800678	−	1.11884i
$322$		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
$327$	−10.3555	+	18.0338i	−0.572662	+	0.997269i
$328$		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
$333$	3.77128	−	1.96665i	0.206665	−	0.107772i
$334$		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
$339$	−1.27193	−	12.9983i	−0.0690817	−	0.705973i
$340$		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
$345$	−10.6846	+	12.3892i	−0.575237	+	0.667010i
$346$		0			0
$347$	−0.356727	+	1.47045i	−0.0191501	+	0.0789378i	−0.980585	−	0.196096i	$-0.937174\pi$
$347$	−0.356727	+	1.47045i	−0.0191501	+	0.0789378i	0.961435	+	0.275033i	$0.0886889\pi$
$348$		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
$351$	0.801302	−	19.7398i	0.0427703	−	1.05363i
$352$		0			0
$353$	−26.7416	−	5.15403i	−1.42331	−	0.274321i	−0.581262	−	0.813717i	$-0.697441\pi$
$353$	−26.7416	−	5.15403i	−1.42331	−	0.274321i	−0.842053	+	0.539395i	$0.818653\pi$
$354$		0			0
$355$	1.96969	+	3.82067i	0.104541	+	0.202780i
$356$		0			0
$357$	−7.53761	+	2.62859i	−0.398933	+	0.139119i
$358$		0			0
$359$	−5.72078	+	4.95708i	−0.301931	+	0.261625i	−0.792628	−	0.609705i	$-0.791288\pi$
$359$	−5.72078	+	4.95708i	−0.301931	+	0.261625i	0.490697	+	0.871330i	$0.336742\pi$
$360$		0			0
$361$	45.4143	−	8.75289i	2.39023	−	0.460678i
$362$		0			0
$363$	0.0194980	+	8.32189i	0.00102338	+	0.436786i
$364$		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
$369$	−3.95446	−	26.6178i	−0.205861	−	1.38567i
$370$		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
$375$	7.78339	−	19.5748i	0.401932	−	1.01084i
$376$		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
$381$	9.63944	+	12.1986i	0.493843	+	0.624954i
$382$		0			0
$383$	−30.7291	+	2.93427i	−1.57018	+	0.149934i	−0.843534	−	0.537076i	$-0.819529\pi$
$383$	−30.7291	+	2.93427i	−1.57018	+	0.149934i	−0.726648	+	0.687010i	$0.758923\pi$
$384$		0			0
$385$	7.09423	+	2.45534i	0.361556	+	0.125136i
$386$		0			0
$387$	−14.3220	−	18.0373i	−0.728027	−	0.916886i
$388$		0			0
$389$	4.77693	−	5.00990i	0.242200	−	0.254012i	−0.591403	−	0.806376i	$-0.701426\pi$
$389$	4.77693	−	5.00990i	0.242200	−	0.254012i	0.833603	+	0.552364i	$0.186274\pi$
$390$		0			0
$391$	13.3998	+	5.36447i	0.677657	+	0.271293i
$392$		0			0
$393$	−29.5838	+	5.77372i	−1.49230	+	0.291246i
$394$		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
$399$	−17.0808	+	16.3631i	−0.855111	+	0.819180i
$400$		0			0
$401$	−12.9470			−0.646540			−0.323270	−	0.946307i	$-0.604782\pi$
$401$	−12.9470			−0.646540			−0.323270	+	0.946307i	$0.604782\pi$
$402$		0			0
$403$	−9.09984			−0.453295
$404$		0			0
$405$	−0.914232	−	16.0297i	−0.0454286	−	0.796524i
$406$		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
$411$	−4.22708	−	21.6590i	−0.208506	−	1.06836i
$412$		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
$417$	−9.91725	−	7.76147i	−0.485650	−	0.380081i
$418$		0			0
$419$	0.923996	+	0.319798i	0.0451402	+	0.0156232i	0.349545	−	0.936920i	$-0.386336\pi$
$419$	0.923996	+	0.319798i	0.0451402	+	0.0156232i	−0.304405	+	0.952543i	$0.598457\pi$
$420$		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
$423$	−25.6564	+	11.8625i	−1.24745	+	0.576773i
$424$		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
$429$	15.2313	+	6.05633i	0.735375	+	0.292402i
$430$		0			0
$431$	−1.97236	−	1.13874i	−0.0950054	−	0.0548514i	0.451745	−	0.892147i	$-0.350802\pi$
$431$	−1.97236	−	1.13874i	−0.0950054	−	0.0548514i	−0.546750	+	0.837296i	$0.684135\pi$
$432$		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
$435$	−10.3371	+	4.16650i	−0.495628	+	0.199768i
$436$		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
$441$	−2.87274	+	12.0886i	−0.136797	+	0.575645i
$442$		0			0
$443$	−26.5066	+	5.10872i	−1.25937	+	0.242723i	−0.774898	−	0.632087i	$-0.782199\pi$
$443$	−26.5066	+	5.10872i	−1.25937	+	0.242723i	−0.484467	+	0.874809i	$0.660987\pi$
$444$		0			0
$445$	−16.7296	+	14.4963i	−0.793059	+	0.687190i
$446$		0			0
$447$	−0.755573	−	2.16665i	−0.0357374	−	0.102479i
$448$		0			0
$449$	−10.4791	−	20.3265i	−0.494537	−	0.959268i	−0.995586	−	0.0938492i	$-0.970083\pi$
$449$	−10.4791	−	20.3265i	−0.494537	−	0.959268i	0.501049	−	0.865419i	$-0.332947\pi$
$450$		0			0
$451$	21.9232	+	4.22536i	1.03233	+	0.198964i
$452$		0			0
$453$	−13.6413	+	6.26846i	−0.640926	+	0.294518i
$454$		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
$459$	−13.1133	+	5.35701i	−0.612075	+	0.250044i
$460$		0			0
$461$	5.32358	−	18.1305i	0.247944	−	0.844419i	−0.737635	−	0.675200i	$-0.764057\pi$
$461$	5.32358	−	18.1305i	0.247944	−	0.844419i	0.985578	−	0.169219i	$-0.0541246\pi$
$462$		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
$465$	−7.36031	+	0.720231i	−0.341326	+	0.0333999i
$466$		0			0
$467$	2.18741	+	1.55764i	0.101221	+	0.0720792i	0.629547	−	0.776963i	$-0.283241\pi$
$467$	2.18741	+	1.55764i	0.101221	+	0.0720792i	−0.528326	+	0.849042i	$0.677180\pi$
$468$		0			0
$469$	3.74379	−	13.3225i	0.172872	−	0.615174i
$470$		0			0
$471$	21.0621	−	18.3370i	0.970492	−	0.844925i
$472$		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
$477$	2.26932	+	2.14358i	0.103905	+	0.0981477i
$478$		0			0
$479$	−14.2296	+	27.6015i	−0.650166	+	1.26115i	0.301340	+	0.953517i	$0.402566\pi$
$479$	−14.2296	+	27.6015i	−0.650166	+	1.26115i	−0.951506	+	0.307629i	$0.900464\pi$
$480$		0			0
$481$	−5.23843	−	1.27083i	−0.238852	−	0.0579448i
$482$		0			0
$483$	−12.6082	+	9.02283i	−0.573691	+	0.410553i
$484$		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
$489$	19.3630	−	4.74547i	0.875624	−	0.214598i
$490$		0			0
$491$	−17.7200	−	27.5728i	−0.799691	−	1.24434i	−0.966070	−	0.258282i	$-0.916844\pi$
$491$	−17.7200	−	27.5728i	−0.799691	−	1.24434i	0.166378	−	0.986062i	$-0.446793\pi$
$492$		0			0
$493$	6.43920	+	7.43123i	0.290007	+	0.334686i
$494$		0			0
$495$	12.7990	+	3.69308i	0.575274	+	0.165992i
$496$		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
$501$	36.6263	+	6.97019i	1.63634	+	0.311405i
$502$		0			0
$503$	−4.61392	−	6.47934i	−0.205724	−	0.288899i	0.698804	−	0.715313i	$-0.253716\pi$
$503$	−4.61392	−	6.47934i	−0.205724	−	0.288899i	−0.904528	+	0.426414i	$0.859777\pi$
$504$		0			0
$505$	15.5768	−	14.8525i	0.693160	−	0.660926i
$506$		0			0
$507$	−1.73551	+	1.82871i	−0.0770769	+	0.0812161i
$508$		0			0
$509$	−33.2815	−	4.78515i	−1.47517	−	0.212098i	−0.642682	−	0.766133i	$-0.722178\pi$
$509$	−33.2815	−	4.78515i	−1.47517	−	0.212098i	−0.832493	+	0.554035i	$0.813087\pi$
$510$		0			0
$511$	−5.53017	−	18.8340i	−0.244640	−	0.833168i
$512$		0			0
$513$	−28.7506	+	30.5803i	−1.26937	+	1.35015i
$514$		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
$519$	5.15293	+	3.29456i	0.226189	+	0.144615i
$520$		0			0
$521$	−4.05822	+	8.88626i	−0.177794	+	0.389314i	−0.977457	−	0.211135i	$-0.932284\pi$
$521$	−4.05822	+	8.88626i	−0.177794	+	0.389314i	0.799663	+	0.600449i	$0.205011\pi$
$522$		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
$525$	3.07685	−	4.34233i	0.134285	−	0.189515i
$526$		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
$531$	−5.18575	−	1.76764i	−0.225042	−	0.0767089i
$532$		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
$543$	−4.18939	−	1.43898i	−0.179784	−	0.0617526i
$544$		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
$549$	−10.2583	+	3.60433i	−0.437812	+	0.153829i
$550$		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
$555$	−4.33763	−	0.613288i	−0.184122	−	0.0260326i
$556$		0			0
$557$	13.3933	−	17.0309i	0.567491	−	0.721624i	−0.414606	−	0.910001i	$-0.636080\pi$
$557$	13.3933	−	17.0309i	0.567491	−	0.721624i	0.982097	+	0.188378i	$0.0603229\pi$
$558$		0			0
$559$	−1.38888	+	29.1562i	−0.0587435	+	1.23318i
$560$		0			0
$561$	−0.586718	−	11.7380i	−0.0247713	−	0.495580i
$562$		0			0
$563$	−5.77668	+	40.1777i	−0.243458	+	1.69329i	0.391048	+	0.920370i	$0.372113\pi$
$563$	−5.77668	+	40.1777i	−0.243458	+	1.69329i	−0.634506	+	0.772918i	$0.718796\pi$
$564$		0			0
$565$	−6.72598	+	11.6497i	−0.282964	+	0.490108i
$566$		0			0
$567$	2.73945	−	14.9671i	0.115046	−	0.628560i
$568$		0			0
$569$	33.4521	−	23.8211i	1.40238	−	0.998633i	0.405982	−	0.913881i	$-0.366930\pi$
$569$	33.4521	−	23.8211i	1.40238	−	0.998633i	0.996402	−	0.0847518i	$-0.0270097\pi$
$570$		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
$573$	−11.7307	−	39.6074i	−0.490056	−	1.65462i
$574$		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
$579$	10.5391	+	20.3260i	0.437991	+	0.844719i
$580$		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
$585$	−12.5034	+	16.0536i	−0.516952	+	0.663736i
$586$		0			0
$587$	16.9004	−	13.2906i	0.697554	−	0.548563i	−0.205200	−	0.978720i	$-0.565784\pi$
$587$	16.9004	−	13.2906i	0.697554	−	0.548563i	0.902754	+	0.430157i	$0.141542\pi$
$588$		0			0
$589$	14.6111	+	12.6606i	0.602042	+	0.521672i
$590$		0			0
$591$	1.65925	−	3.23709i	0.0682523	−	0.133156i
$592$		0			0
$593$	−38.4008	−	19.7970i	−1.57693	−	0.812965i	−0.576940	−	0.816787i	$-0.695753\pi$
$593$	−38.4008	−	19.7970i	−1.57693	−	0.812965i	−0.999993	+	0.00382154i	$0.998784\pi$
$594$		0			0
$595$	7.88907	+	2.31644i	0.323420	+	0.0949648i
$596$		0			0
$597$	29.6857	−	4.33918i	1.21496	−	0.177591i
$598$		0			0
$599$	15.0809	+	43.5734i	0.616189	+	1.78036i	0.625277	+	0.780403i	$0.284986\pi$
$599$	15.0809	+	43.5734i	0.616189	+	1.78036i	−0.00908805	+	0.999959i	$0.502893\pi$
$600$		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
$603$	5.39869	−	23.9553i	0.219852	−	0.975533i
$604$		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
$609$	−10.4511	+	1.52764i	−0.423499	+	0.0619030i
$610$		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
$615$	−12.6428	+	24.6653i	−0.509806	+	0.994601i
$616$		0			0
$617$	3.97513	+	3.44447i	0.160033	+	0.138669i	0.731196	−	0.682167i	$-0.238962\pi$
$617$	3.97513	+	3.44447i	0.160033	+	0.138669i	−0.571164	+	0.820836i	$0.693508\pi$
$618$		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
$621$	−21.5055	+	17.1582i	−0.862988	+	0.688533i
$622$		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
$627$	−16.0300	−	30.9157i	−0.640175	−	1.23465i
$628$		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
$633$	−6.86269	−	23.1712i	−0.272767	−	0.920972i
$634$		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
$639$	2.06899	+	6.92611i	0.0818481	+	0.273993i
$640$		0			0
$641$	6.01612	−	10.4202i	0.237623	−	0.411574i	−0.722409	−	0.691466i	$-0.756965\pi$
$641$	6.01612	−	10.4202i	0.237623	−	0.411574i	0.960032	+	0.279892i	$0.0902985\pi$
$642$		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
$645$	1.18426	+	23.6927i	0.0466304	+	0.932898i
$646$		0			0
$647$	−1.70736	+	35.8419i	−0.0671232	+	1.40909i	0.674501	+	0.738274i	$0.264359\pi$
$647$	−1.70736	+	35.8419i	−0.0671232	+	1.40909i	−0.741624	+	0.670816i	$0.765944\pi$
$648$		0			0
$649$	2.80991	−	3.57309i	0.110298	−	0.140256i
$650$		0			0
$651$	−6.93952	−	0.981163i	−0.271981	−	0.0384548i
$652$		0			0
$653$	−5.84298	+	16.8822i	−0.228653	+	0.660650i	0.771061	+	0.636761i	$0.219726\pi$
$653$	−5.84298	+	16.8822i	−0.228653	+	0.660650i	−0.999715	+	0.0238894i	$0.992395\pi$
$654$		0			0
$655$	28.2400	+	12.8968i	1.10343	+	0.503919i
$656$		0			0
$657$	−11.5464	−	32.8620i	−0.450467	−	1.28207i
$658$		0			0
$659$	3.78120	−	9.44497i	0.147295	−	0.367924i	−0.836312	−	0.548255i	$-0.815293\pi$
$659$	3.78120	−	9.44497i	0.147295	−	0.367924i	0.983606	+	0.180331i	$0.0577167\pi$
$660$		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
$663$	16.9787	+	5.83188i	0.659399	+	0.226491i
$664$		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
$675$	5.04964	−	7.98017i	0.194361	−	0.307157i
$676$		0			0
$677$	−22.7437	−	2.17176i	−0.874113	−	0.0834677i	−0.351652	−	0.936131i	$-0.614380\pi$
$677$	−22.7437	−	2.17176i	−0.874113	−	0.0834677i	−0.522461	+	0.852663i	$0.674986\pi$
$678$		0			0
$679$	−1.67632	−	3.67063i	−0.0643312	−	0.140866i
$680$		0			0
$681$	−4.22193	+	5.95837i	−0.161785	+	0.228325i
$682$		0			0
$683$	−13.0913	−	12.4826i	−0.500926	−	0.477632i	0.396975	−	0.917830i	$-0.370060\pi$
$683$	−13.0913	−	12.4826i	−0.500926	−	0.477632i	−0.897901	+	0.440197i	$0.854909\pi$
$684$		0			0
$685$	−9.44204	+	20.6752i	−0.360762	+	0.789958i
$686$		0			0
$687$	26.6778	+	17.0566i	1.01782	+	0.650750i
$688$		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
$693$	10.9624	+	6.26082i	0.416426	+	0.237829i
$694$		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
$699$	13.9832	−	14.7341i	0.528893	−	0.557295i
$700$		0			0
$701$	−11.3286	+	10.8018i	−0.427876	+	0.407979i	−0.873178	−	0.487401i	$-0.837945\pi$
$701$	−11.3286	+	10.8018i	−0.427876	+	0.407979i	0.445302	+	0.895381i	$0.353096\pi$
$702$		0			0
$703$	6.64297	+	9.32874i	0.250544	+	0.351840i
$704$		0			0
$705$	28.6001	+	5.44275i	1.07714	+	0.204986i
$706$		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
$711$	6.11958	−	21.2085i	0.229502	−	0.795382i
$712$		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
$717$	−15.8845	+	3.89296i	−0.593217	+	0.145385i
$718$		0			0
$719$	8.19919	−	42.5414i	0.305778	−	1.58653i	−0.425830	−	0.904803i	$-0.640018\pi$
$719$	8.19919	−	42.5414i	0.305778	−	1.58653i	0.731608	−	0.681725i	$-0.238770\pi$
$720$		0			0
$721$	9.06409	+	11.5259i	0.337564	+	0.429248i
$722$		0			0
$723$	−12.5405	+	8.97441i	−0.466386	+	0.333762i
$724$		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
$729$	3.46644	−	26.7766i	0.128386	−	0.991724i
$730$		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
$735$	9.65220	−	8.40335i	0.356027	−	0.309962i
$736$		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
$741$	52.9419	−	5.18054i	1.94487	−	0.190312i
$742$		0			0
$743$	17.9176	+	44.7560i	0.657333	+	1.64194i	0.762115	+	0.647442i	$0.224161\pi$
$743$	17.9176	+	44.7560i	0.657333	+	1.64194i	−0.104782	+	0.994495i	$0.533414\pi$
$744$		0			0
$745$	−0.665848	+	2.26767i	−0.0243948	+	0.0830810i
$746$		0			0
$747$	30.5823	−	21.9943i	1.11895	−	0.804728i
$748$		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
$753$	0.807857	−	0.371226i	0.0294399	−	0.0135282i
$754$		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
$759$	−7.51614	−	21.5530i	−0.272819	−	0.782323i
$760$		0			0
$761$	32.6450	−	28.2870i	1.18338	−	1.02540i	0.184284	−	0.982873i	$-0.441003\pi$
$761$	32.6450	−	28.2870i	1.18338	−	1.02540i	0.999095	−	0.0425313i	$-0.0135422\pi$
$762$		0			0
$763$	19.9315	−	3.84148i	0.721569	−	0.139071i
$764$		0			0
$765$	14.1946	+	3.37323i	0.513209	+	0.121960i
$766$		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
$771$	5.44055	−	2.19287i	0.195937	−	0.0789743i
$772$		0			0
$773$	−25.9204	−	27.1845i	−0.932291	−	0.977759i	0.0675095	−	0.997719i	$-0.478495\pi$
$773$	−25.9204	−	27.1845i	−0.932291	−	0.977759i	−0.999801	+	0.0199597i	$0.993646\pi$
$774$		0			0
$775$	−3.76706	−	2.17492i	−0.135317	−	0.0781253i
$776$		0			0
$777$	−3.85779	−	1.53395i	−0.138398	−	0.0550301i
$778$		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
$783$	−18.3782	+	3.67626i	−0.656782	+	0.131379i
$784$		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
$789$	23.4171	+	18.3268i	0.833672	+	0.652451i
$790$		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
$795$	−0.615884	−	3.15570i	−0.0218432	−	0.111921i
$796$		0			0
$797$	0.514775	−	5.39097i	0.0182343	−	0.190958i	−0.981765	−	0.190097i	$-0.939120\pi$
$797$	0.514775	−	5.39097i	0.0182343	−	0.190958i	1.00000		0.000861116i	$-0.000274102\pi$
$798$		0			0
$799$	−3.65541	−	25.4240i	−0.129319	−	0.899435i
$800$		0			0
$801$	−32.1506	+	18.7636i	−1.13599	+	0.662978i
$802$		0			0
$803$	28.8990			1.01982
$804$		0			0
$805$	15.9689			0.562830
$806$		0			0
$807$	5.86083	−	5.61457i	0.206311	−	0.197642i
$808$		0			0
$809$	−2.09565	−	14.5756i	−0.0736793	−	0.512451i	−0.992923	−	0.118761i	$-0.962108\pi$
$809$	−2.09565	−	14.5756i	−0.0736793	−	0.512451i	0.919244	−	0.393689i	$-0.128801\pi$
$810$		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
$813$	15.4108	−	3.00765i	0.540480	−	0.105483i
$814$		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
$819$	−15.1020	+	11.9913i	−0.527706	+	0.419010i
$820$		0			0
$821$	17.4854	+	6.05177i	0.610246	+	0.211208i	0.614673	−	0.788782i	$-0.289288\pi$
$821$	17.4854	+	6.05177i	0.610246	+	0.211208i	−0.00442701	+	0.999990i	$0.501409\pi$
$822$		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
$825$	4.85781	+	6.14752i	0.169127	+	0.214029i
$826$		0			0
$827$	−5.88925	−	0.280540i	−0.204789	−	0.00975532i	−0.0550634	−	0.998483i	$-0.517536\pi$
$827$	−5.88925	−	0.280540i	−0.204789	−	0.00975532i	−0.149726	+	0.988728i	$0.547839\pi$
$828$		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
$831$	−8.47220	+	21.3071i	−0.293897	+	0.739134i
$832$		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
$837$	−12.3882	−	1.09512i	−0.428198	−	0.0378527i
$838$		0			0
$839$	0.453948	−	0.0216242i	0.0156720	−	0.000746550i	−0.0397444	−	0.999210i	$-0.512654\pi$
$839$	0.453948	−	0.0216242i	0.0156720	−	0.000746550i	0.0554165	+	0.998463i	$0.482351\pi$
$840$		0			0
$841$	−7.99498	−	13.8477i	−0.275689	−	0.477507i
$842$		0			0
$843$	−0.0318665	−	13.6009i	−0.00109754	−	0.468439i
$844$		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
$849$	12.3559	−	4.30887i	0.424054	−	0.147880i
$850$		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
$855$	42.4115	−	8.38046i	1.45044	−	0.286606i
$856$		0			0
$857$	−20.1855	+	23.2953i	−0.689523	+	0.795752i	−0.987297	−	0.158885i	$-0.949210\pi$
$857$	−20.1855	+	23.2953i	−0.689523	+	0.795752i	0.297774	+	0.954636i	$0.403756\pi$
$858$		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
$861$	−17.1544	+	19.8912i	−0.584621	+	0.677891i
$862$		0			0
$863$	−5.63172	+	19.1799i	−0.191706	+	0.652891i	0.806400	+	0.591371i	$0.201413\pi$
$863$	−5.63172	+	19.1799i	−0.191706	+	0.652891i	−0.998106	+	0.0615200i	$0.980405\pi$
$864$		0			0
$865$	−2.34128	−	5.84823i	−0.0796058	−	0.198846i
$866$		0			0
$867$	1.61400	+	16.4940i	0.0548142	+	0.560167i
$868$		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
$873$	−3.31093	−	6.34908i	−0.112058	−	0.214884i
$874$		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
$879$	13.4305	−	23.3887i	0.453001	−	0.788883i
$880$		0			0
$881$	−16.7445	+	32.4797i	−0.564135	+	1.09427i	0.418413	+	0.908257i	$0.362587\pi$
$881$	−16.7445	+	32.4797i	−0.564135	+	1.09427i	−0.982547	+	0.186012i	$0.940444\pi$
$882$		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
$885$	3.28401	+	4.58896i	0.110391	+	0.154256i
$886$		0			0
$887$	−32.4462	−	41.2587i	−1.08944	−	1.38533i	−0.916327	−	0.400430i	$-0.868861\pi$
$887$	−32.4462	−	41.2587i	−1.08944	−	1.38533i	−0.173110	−	0.984902i	$-0.555382\pi$
$888$		0			0
$889$	2.87204	−	14.9015i	0.0963251	−	0.499782i
$890$		0			0
$891$	20.0065	+	10.0779i	0.670243	+	0.337621i
$892$		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
$897$	34.8312	+	1.57743i	1.16298	+	0.0526688i
$898$		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
$903$	−4.20285	+	22.0848i	−0.139862	+	0.734935i
$904$		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
$909$	30.3560	−	19.7102i	1.00684	−	0.653746i
$910$		0			0
$911$	21.9892	+	3.16157i	0.728536	+	0.104748i	0.496595	−	0.867982i	$-0.334583\pi$
$911$	21.9892	+	3.16157i	0.728536	+	0.104748i	0.231941	+	0.972730i	$0.425493\pi$
$912$		0			0
$913$	8.80529	+	29.9881i	0.291412	+	0.992460i
$914$		0			0
$915$	10.7527	+	3.12994i	0.355474	+	0.103473i
$916$		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
$921$	−0.353193	+	0.552421i	−0.0116381	+	0.0182029i
$922$		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
$927$	17.1309	+	19.5839i	0.562653	+	0.643221i
$928$		0			0
$929$	−0.284591	−	0.623168i	−0.00933714	−	0.0204455i	0.904906	−	0.425612i	$-0.139941\pi$
$929$	−0.284591	−	0.623168i	−0.00933714	−	0.0204455i	−0.914243	+	0.405166i	$0.867214\pi$
$930$		0			0
$931$	−33.3044	−	3.18019i	−1.09151	−	0.104226i
$932$		0			0
$933$	2.30013	−	24.6995i	0.0753030	−	0.808626i
$934$		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	0.855638	−	0.517574i	$-0.173165\pi$
$941$	22.7087	+	14.5940i	0.740281	+	0.475750i	−0.115357	+	0.993324i	$0.536801\pi$
$942$		0			0
$943$	47.0093	−	6.75892i	1.53083	−	0.220101i
$944$		0			0
$945$	−11.2660	+	10.8943i	−0.366483	+	0.354392i
$946$		0			0
$947$	30.9226	−	14.1219i	1.00485	−	0.458900i	0.156127	−	0.987737i	$-0.450099\pi$
$947$	30.9226	−	14.1219i	1.00485	−	0.458900i	0.848723	+	0.528837i	$0.177372\pi$
$948$		0			0
$949$	−16.4065	+	40.9815i	−0.532579	+	1.33032i
$950$		0			0
$951$	−42.0906	+	27.1895i	−1.36488	+	0.881681i
$952$		0			0
$953$	21.3229	+	9.73785i	0.690717	+	0.315440i	0.729668	−	0.683801i	$-0.239674\pi$
$953$	21.3229	+	9.73785i	0.690717	+	0.315440i	−0.0389514	+	0.999241i	$0.512402\pi$
$954$		0			0
$955$	−13.9156	+	40.2065i	−0.450298	+	1.30105i
$956$		0			0
$957$	2.17694	−	15.3970i	0.0703705	−	0.497713i
$958$		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
$963$	−7.88351	+	41.9607i	−0.254043	+	1.35216i
$964$		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
$969$	−19.1479	−	32.9865i	−0.615121	−	1.05968i
$970$		0			0
$971$	1.75017	−	1.24629i	0.0561657	−	0.0399954i	−0.551629	−	0.834089i	$-0.685994\pi$
$971$	1.75017	−	1.24629i	0.0561657	−	0.0399954i	0.607795	+	0.794094i	$0.292054\pi$
$972$		0			0
$973$	0.584889	+	12.2783i	0.0187507	+	0.393625i
$974$		0			0
$975$	−11.4756	+	3.39878i	−0.367515	+	0.108848i
$976$		0			0
$977$	−30.0280	+	7.28471i	−0.960680	+	0.233058i	−0.685287	−	0.728273i	$-0.740323\pi$
$977$	−30.0280	+	7.28471i	−0.960680	+	0.233058i	−0.275393	+	0.961332i	$0.588808\pi$
$978$		0			0
$979$	−5.84507	−	30.3271i	−0.186809	−	0.969259i
$980$		0			0
$981$	34.9634	−	8.65570i	1.11630	−	0.276355i
$982$		0			0
$983$	−16.3758	+	10.5241i	−0.522307	+	0.335666i	−0.775084	−	0.631858i	$-0.782293\pi$
$983$	−16.3758	+	10.5241i	−0.522307	+	0.335666i	0.252777	+	0.967525i	$0.418656\pi$
$984$		0			0
$985$	−3.33012	+	1.71680i	−0.106106	+	0.0547017i
$986$		0			0
$987$	25.1237	+	11.4026i	0.799697	+	0.362947i
$988$		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
$993$	−46.9370	−	24.0587i	−1.48950	−	0.763478i
$994$		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
$999$	−6.97846	−	2.36047i	−0.220789	−	0.0746821i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.19819 - 1.25074i) q^{3} +(0.253886 + 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(-0.128702 + 2.99724i) q^{9} +O(q^{10})\)	\(q+(-1.19819 - 1.25074i) q^{3} +(0.253886 + 1.76582i) q^{5} +(-0.160706 + 1.68299i) q^{7} +(-0.128702 + 2.99724i) q^{9} +(-2.31075 - 0.925084i) q^{11} +(2.62372 - 2.75167i) q^{13} +(1.90438 - 2.43332i) q^{15} +(-2.57618 - 0.891623i) q^{17} +(-8.04118 + 0.767839i) q^{19} +(2.29753 - 1.81553i) q^{21} +(-5.28862 - 0.251928i) q^{23} +(1.74381 - 0.512028i) q^{25} +(3.90298 - 3.43027i) q^{27} +(-3.12371 - 1.80347i) q^{29} +(-1.65164 - 1.73219i) q^{31} +(1.61167 + 3.99857i) q^{33} +(-3.01265 + 0.143510i) q^{35} +(-0.708877 - 1.22781i) q^{37} +(-6.58533 + 0.0154293i) q^{39} +(-8.80789 + 1.69758i) q^{41} +(-5.80208 + 5.02753i) q^{43} +(-5.32526 + 0.533693i) q^{45} +(4.31741 + 8.37461i) q^{47} +(4.06689 + 0.783828i) q^{49} +(1.97155 + 4.29046i) q^{51} +(0.681416 - 0.786397i) q^{53} +(1.04686 - 4.31523i) q^{55} +(10.5952 + 9.13741i) q^{57} +(-0.514512 + 1.75227i) q^{59} +(1.34703 + 3.36473i) q^{61} +(-5.02362 - 0.698277i) q^{63} +(5.52508 + 3.93439i) q^{65} +(-8.05494 - 1.45534i) q^{67} +(6.02165 + 6.91655i) q^{69} +(2.27699 - 0.788075i) q^{71} +(-10.7788 + 4.31518i) q^{73} +(-2.72982 - 1.56754i) q^{75} +(1.92825 - 3.74029i) q^{77} +(-7.15051 - 1.73470i) q^{79} +(-8.96687 - 0.771503i) q^{81} +(-7.76201 - 9.87019i) q^{83} +(0.920389 - 4.77543i) q^{85} +(1.48710 + 6.06784i) q^{87} +(6.70853 + 10.4387i) q^{89} +(4.20938 + 4.85788i) q^{91} +(-0.187548 + 4.14125i) q^{93} +(-3.39741 - 14.0043i) q^{95} +(-2.06706 + 1.19342i) q^{97} +(3.07010 - 6.80681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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