LMFDB - Embedded newform 804.2.ba.b.41.1

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			41.1
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +O(q^{10})$	\(q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +(-1.16153 + 0.465006i) q^{11} +(-1.83241 - 1.92178i) q^{13} +(0.0769269 + 1.85784i) q^{15} +(-3.09077 + 1.06973i) q^{17} +(6.96190 + 0.664781i) q^{19} +(-1.63025 - 5.68258i) q^{21} +(-6.97890 + 0.332446i) q^{23} +(3.69165 + 1.08397i) q^{25} +(-4.42291 + 2.72724i) q^{27} +(-0.870238 + 0.502432i) q^{29} +(-4.01310 + 4.20882i) q^{31} +(1.83029 - 1.16024i) q^{33} +(3.66006 + 0.174350i) q^{35} +(-3.99087 + 6.91239i) q^{37} +(3.72976 + 2.69105i) q^{39} +(-3.54601 - 0.683437i) q^{41} +(1.94811 + 1.68805i) q^{43} +(-0.720320 - 3.13905i) q^{45} +(-5.36003 + 10.3970i) q^{47} +(-4.56579 + 0.879983i) q^{49} +(4.92350 - 2.80192i) q^{51} +(-4.61898 - 5.33059i) q^{53} +(0.316664 + 1.30531i) q^{55} +(-12.0653 + 1.07645i) q^{57} +(3.82125 + 13.0140i) q^{59} +(-3.61460 + 9.02884i) q^{61} +(4.57851 + 9.15891i) q^{63} +(-2.32208 + 1.65354i) q^{65} +(-7.45395 - 3.38209i) q^{67} +(11.7779 - 2.77987i) q^{69} +(10.5155 + 3.63946i) q^{71} +(-5.63753 - 2.25693i) q^{73} +(-6.62982 - 0.674690i) q^{75} +(-1.95681 - 3.79569i) q^{77} +(-9.16491 + 2.22338i) q^{79} +(6.66602 - 6.04683i) q^{81} +(8.90868 - 11.3283i) q^{83} +(0.664499 + 3.44775i) q^{85} +(1.32242 - 1.13157i) q^{87} +(-7.82886 + 12.1820i) q^{89} +(5.93517 - 6.84955i) q^{91} +(5.49823 - 8.43959i) q^{93} +(1.77006 - 7.29627i) q^{95} +(4.98536 + 2.87830i) q^{97} +(-2.74850 + 2.55620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

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
$3$	−1.70276	+	0.317213i	−0.983086	+	0.183143i
$3$	−1.70276	+	0.317213i	−0.983086	+	0.183143i
$4$		0			0
$5$	0.152781	−	1.06262i	0.0683259	−	0.475217i	−0.926716	−	0.375762i	$-0.877381\pi$
$5$	0.152781	−	1.06262i	0.0683259	−	0.475217i	0.995042	−	0.0994551i	$-0.0317100\pi$
$6$		0			0
$7$	0.324444	+	3.39773i	0.122628	+	1.28422i	0.822010	+	0.569472i	$0.192852\pi$
$7$	0.324444	+	3.39773i	0.122628	+	1.28422i	−0.699382	+	0.714748i	$0.746541\pi$
$8$		0			0
$9$	2.79875	−	1.08027i	0.932917	−	0.360091i
$10$		0			0
$11$	−1.16153	+	0.465006i	−0.350214	+	0.140204i	−0.540098	−	0.841602i	$-0.681613\pi$
$11$	−1.16153	+	0.465006i	−0.350214	+	0.140204i	0.189884	+	0.981806i	$0.439189\pi$
$12$		0			0
$13$	−1.83241	−	1.92178i	−0.508220	−	0.533006i	0.418770	−	0.908092i	$-0.362461\pi$
$13$	−1.83241	−	1.92178i	−0.508220	−	0.533006i	−0.926990	+	0.375087i	$0.877613\pi$
$14$		0			0
$15$	0.0769269	+	1.85784i	0.0198624	+	0.479693i
$16$		0			0
$17$	−3.09077	+	1.06973i	−0.749623	+	0.259447i	−0.675053	−	0.737769i	$-0.735879\pi$
$17$	−3.09077	+	1.06973i	−0.749623	+	0.259447i	−0.0745693	+	0.997216i	$0.523758\pi$
$18$		0			0
$19$	6.96190	+	0.664781i	1.59717	+	0.152511i	0.855336	−	0.518074i	$-0.173351\pi$
$19$	6.96190	+	0.664781i	1.59717	+	0.152511i	0.741833	+	0.670585i	$0.233957\pi$
$20$		0			0
$21$	−1.63025	−	5.68258i	−0.355750	−	1.24004i
$22$		0			0
$23$	−6.97890	+	0.332446i	−1.45520	+	0.0693197i	−0.760200	−	0.649689i	$-0.774899\pi$
$23$	−6.97890	+	0.332446i	−1.45520	+	0.0693197i	−0.695001	+	0.719009i	$0.744596\pi$
$24$		0			0
$25$	3.69165	+	1.08397i	0.738330	+	0.216793i
$26$		0			0
$27$	−4.42291	+	2.72724i	−0.851190	+	0.524858i
$28$		0			0
$29$	−0.870238	+	0.502432i	−0.161599	+	0.0932993i	−0.578619	−	0.815598i	$-0.696408\pi$
$29$	−0.870238	+	0.502432i	−0.161599	+	0.0932993i	0.417019	+	0.908898i	$0.363075\pi$
$30$		0			0
$31$	−4.01310	+	4.20882i	−0.720774	+	0.755926i	−0.977586	−	0.210536i	$-0.932479\pi$
$31$	−4.01310	+	4.20882i	−0.720774	+	0.755926i	0.256813	+	0.966461i	$0.417328\pi$
$32$		0			0
$33$	1.83029	−	1.16024i	0.318613	−	0.201972i
$34$		0			0
$35$	3.66006	+	0.174350i	0.618662	+	0.0294705i
$36$		0			0
$37$	−3.99087	+	6.91239i	−0.656095	+	1.13639i	0.325523	+	0.945534i	$0.394460\pi$
$37$	−3.99087	+	6.91239i	−0.656095	+	1.13639i	−0.981618	+	0.190856i	$0.938874\pi$
$38$		0			0
$39$	3.72976	+	2.69105i	0.597240	+	0.430914i
$40$		0			0
$41$	−3.54601	−	0.683437i	−0.553793	−	0.106735i	−0.0953258	−	0.995446i	$-0.530389\pi$
$41$	−3.54601	−	0.683437i	−0.553793	−	0.106735i	−0.458467	+	0.888711i	$0.651601\pi$
$42$		0			0
$43$	1.94811	+	1.68805i	0.297084	+	0.257424i	0.790629	−	0.612296i	$-0.209754\pi$
$43$	1.94811	+	1.68805i	0.297084	+	0.257424i	−0.493545	+	0.869720i	$0.664299\pi$
$44$		0			0
$45$	−0.720320	−	3.13905i	−0.107379	−	0.467942i
$46$		0			0
$47$	−5.36003	+	10.3970i	−0.781841	+	1.51656i	0.0728031	+	0.997346i	$0.476806\pi$
$47$	−5.36003	+	10.3970i	−0.781841	+	1.51656i	−0.854644	+	0.519214i	$0.826225\pi$
$48$		0			0
$49$	−4.56579	+	0.879983i	−0.652255	+	0.125712i
$50$		0			0
$51$	4.92350	−	2.80192i	0.689428	−	0.392347i
$52$		0			0
$53$	−4.61898	−	5.33059i	−0.634466	−	0.732213i	0.343920	−	0.938999i	$-0.388245\pi$
$53$	−4.61898	−	5.33059i	−0.634466	−	0.732213i	−0.978386	+	0.206786i	$0.933700\pi$
$54$		0			0
$55$	0.316664	+	1.30531i	0.0426989	+	0.176007i
$56$		0			0
$57$	−12.0653	+	1.07645i	−1.59809	+	0.142579i
$58$		0			0
$59$	3.82125	+	13.0140i	0.497484	+	1.69428i	0.699280	+	0.714848i	$0.253504\pi$
$59$	3.82125	+	13.0140i	0.497484	+	1.69428i	−0.201796	+	0.979428i	$0.564678\pi$
$60$		0			0
$61$	−3.61460	+	9.02884i	−0.462803	+	1.15603i	0.495075	+	0.868850i	$0.335140\pi$
$61$	−3.61460	+	9.02884i	−0.462803	+	1.15603i	−0.957878	+	0.287175i	$0.907284\pi$
$62$		0			0
$63$	4.57851	+	9.15891i	0.576838	+	1.15391i
$64$		0			0
$65$	−2.32208	+	1.65354i	−0.288018	+	0.205097i
$66$		0			0
$67$	−7.45395	−	3.38209i	−0.910646	−	0.413188i
$67$	−7.45395	−	3.38209i	−0.910646	−	0.413188i
$68$		0			0
$69$	11.7779	−	2.77987i	1.41789	−	0.334657i
$70$		0			0
$71$	10.5155	+	3.63946i	1.24796	+	0.431925i	0.869611	−	0.493737i	$-0.164369\pi$
$71$	10.5155	+	3.63946i	1.24796	+	0.431925i	0.378353	+	0.925661i	$0.376491\pi$
$72$		0			0
$73$	−5.63753	−	2.25693i	−0.659823	−	0.264153i	0.0174913	−	0.999847i	$-0.494432\pi$
$73$	−5.63753	−	2.25693i	−0.659823	−	0.264153i	−0.677314	+	0.735694i	$0.736856\pi$
$74$		0			0
$75$	−6.62982	−	0.674690i	−0.765546	−	0.0779065i
$76$		0			0
$77$	−1.95681	−	3.79569i	−0.223000	−	0.432559i
$78$		0			0
$79$	−9.16491	+	2.22338i	−1.03113	+	0.250150i	−0.715413	−	0.698702i	$-0.753761\pi$
$79$	−9.16491	+	2.22338i	−1.03113	+	0.250150i	−0.315720	+	0.948852i	$0.602246\pi$
$80$		0			0
$81$	6.66602	−	6.04683i	0.740669	−	0.671870i
$82$		0			0
$83$	8.90868	−	11.3283i	0.977855	−	1.24344i	0.00794744	−	0.999968i	$-0.497470\pi$
$83$	8.90868	−	11.3283i	0.977855	−	1.24344i	0.969907	−	0.243475i	$-0.0782874\pi$
$84$		0			0
$85$	0.664499	+	3.44775i	0.0720750	+	0.373961i
$86$		0			0
$87$	1.32242	−	1.13157i	0.141779	−	0.121317i
$88$		0			0
$89$	−7.82886	+	12.1820i	−0.829858	+	1.29128i	0.124380	+	0.992235i	$0.460306\pi$
$89$	−7.82886	+	12.1820i	−0.829858	+	1.29128i	−0.954238	+	0.299050i	$0.903330\pi$
$90$		0			0
$91$	5.93517	−	6.84955i	0.622174	−	0.718028i
$92$		0			0
$93$	5.49823	−	8.43959i	0.570140	−	0.875145i
$94$		0			0
$95$	1.77006	−	7.29627i	0.181604	−	0.748582i
$96$		0			0
$97$	4.98536	+	2.87830i	0.506186	+	0.292247i	0.731265	−	0.682094i	$-0.238930\pi$
$97$	4.98536	+	2.87830i	0.506186	+	0.292247i	−0.225078	+	0.974341i	$0.572264\pi$
$98$		0			0
$99$	−2.74850	+	2.55620i	−0.276234	+	0.256908i
$100$		0			0
$101$	6.06907	−	8.52281i	0.603895	−	0.848052i	−0.393564	−	0.919297i	$-0.628758\pi$
$101$	6.06907	−	8.52281i	0.603895	−	0.848052i	0.997459	+	0.0712456i	$0.0226974\pi$
$102$		0			0
$103$	−9.39509	−	8.95820i	−0.925726	−	0.882678i	0.0676357	−	0.997710i	$-0.478454\pi$
$103$	−9.39509	−	8.95820i	−0.925726	−	0.882678i	−0.993362	+	0.115032i	$0.963303\pi$
$104$		0			0
$105$	−6.28749	+	0.864142i	−0.613596	+	0.0843316i
$106$		0			0
$107$	0.0851448	−	0.0122420i	0.00823125	−	0.00118348i	−0.138198	−	0.990405i	$-0.544131\pi$
$107$	0.0851448	−	0.0122420i	0.00823125	−	0.00118348i	0.146429	+	0.989221i	$0.453222\pi$
$108$		0			0
$109$	3.46042	−	11.7851i	0.331448	−	1.12881i	−0.610211	−	0.792239i	$-0.708915\pi$
$109$	3.46042	−	11.7851i	0.331448	−	1.12881i	0.941659	−	0.336569i	$-0.109267\pi$
$110$		0			0
$111$	4.60278	−	13.0361i	0.436876	−	1.23733i
$112$		0			0
$113$	−9.11844	+	7.17082i	−0.857790	+	0.674574i	−0.946928	−	0.321446i	$-0.895831\pi$
$113$	−9.11844	+	7.17082i	−0.857790	+	0.674574i	0.0891377	+	0.996019i	$0.471589\pi$
$114$		0			0
$115$	−0.712983	+	7.46669i	−0.0664860	+	0.696273i
$116$		0			0
$117$	−7.20451	−	3.39908i	−0.666057	−	0.314245i
$118$		0			0
$119$	−4.63742	−	10.1545i	−0.425112	−	0.930865i
$120$		0			0
$121$	−6.82816	+	6.51064i	−0.620742	+	0.591876i
$122$		0			0
$123$	6.25478	+	0.0388863i	0.563974	+	0.00350626i
$124$		0			0
$125$	3.94569	−	8.63986i	0.352913	−	0.772773i
$126$		0			0
$127$	9.48549	−	0.905754i	0.841701	−	0.0803727i	0.334707	−	0.942322i	$-0.391363\pi$
$127$	9.48549	−	0.905754i	0.841701	−	0.0803727i	0.506994	+	0.861950i	$0.330757\pi$
$128$		0			0
$129$	−3.85262	−	2.25636i	−0.339204	−	0.198662i
$130$		0			0
$131$	2.19930	+	3.42218i	0.192154	+	0.298997i	0.923940	−	0.382537i	$-0.124949\pi$
$131$	2.19930	+	3.42218i	0.192154	+	0.298997i	−0.731786	+	0.681534i	$0.761313\pi$
$132$		0			0
$133$			23.8703i			2.06982i
$134$		0			0
$135$	2.22228	+	5.11654i	0.191263	+	0.440362i
$136$		0			0
$137$	13.1710	−	8.46452i	1.12528	−	0.723173i	0.160709	−	0.987002i	$-0.448622\pi$
$137$	13.1710	−	8.46452i	1.12528	−	0.723173i	0.964569	+	0.263829i	$0.0849855\pi$
$138$		0			0
$139$	9.29511	+	1.33643i	0.788401	+	0.113355i	0.524742	−	0.851261i	$-0.324162\pi$
$139$	9.29511	+	1.33643i	0.788401	+	0.113355i	0.263658	+	0.964616i	$0.415071\pi$
$140$		0			0
$141$	5.82876	−	19.4038i	0.490870	−	1.63410i
$142$		0			0
$143$	3.02204	+	1.38012i	0.252715	+	0.115411i
$144$		0			0
$145$	0.400937	+	1.00149i	0.0332960	+	0.0831695i
$146$		0			0
$147$	7.49528	−	2.94672i	0.618200	−	0.243042i
$148$		0			0
$149$	13.8950	−	6.34561i	1.13832	−	0.519853i	0.245111	−	0.969495i	$-0.421176\pi$
$149$	13.8950	−	6.34561i	1.13832	−	0.519853i	0.893209	+	0.449642i	$0.148448\pi$
$150$		0			0
$151$	−0.869270	−	2.51159i	−0.0707402	−	0.204390i	0.904089	−	0.427345i	$-0.140551\pi$
$151$	−0.869270	−	2.51159i	−0.0707402	−	0.204390i	−0.974829	+	0.222955i	$0.928430\pi$
$152$		0			0
$153$	−7.49471	+	6.33278i	−0.605911	+	0.511975i
$154$		0			0
$155$	3.85924	+	4.90742i	0.309981	+	0.394173i
$156$		0			0
$157$	0.361765	+	7.59438i	0.0288720	+	0.606098i	0.966222	+	0.257710i	$0.0829678\pi$
$157$	0.361765	+	7.59438i	0.0288720	+	0.606098i	−0.937350	+	0.348388i	$0.886729\pi$
$158$		0			0
$159$	9.55593	+	7.61149i	0.757834	+	0.603630i
$160$		0			0
$161$	−3.39382	−	23.6045i	−0.267470	−	1.86030i
$162$		0			0
$163$	−3.22544	−	5.58663i	−0.252636	−	0.437579i	0.711615	−	0.702570i	$-0.247964\pi$
$163$	−3.22544	−	5.58663i	−0.252636	−	0.437579i	−0.964251	+	0.264991i	$0.914631\pi$
$164$		0			0
$165$	−0.953260	−	2.12217i	−0.0742112	−	0.165210i
$166$		0			0
$167$	9.05990	+	6.45152i	0.701076	+	0.499234i	0.874138	−	0.485677i	$-0.161427\pi$
$167$	9.05990	+	6.45152i	0.701076	+	0.499234i	−0.173062	+	0.984911i	$0.555366\pi$
$168$		0			0
$169$	0.283066	−	5.94229i	0.0217743	−	0.457099i
$170$		0			0
$171$	20.2028	−	5.66019i	1.54494	−	0.432845i
$172$		0			0
$173$	6.05483	+	1.46889i	0.460341	+	0.111677i	0.459221	−	0.888322i	$-0.348129\pi$
$173$	6.05483	+	1.46889i	0.460341	+	0.111677i	0.00111938	+	0.999999i	$0.499644\pi$
$174$		0			0
$175$	−2.48529	+	12.8949i	−0.187870	+	0.974763i
$176$		0			0
$177$	−10.6349	−	20.9475i	−0.799364	−	1.57451i
$178$		0			0
$179$	6.62139	+	4.25531i	0.494906	+	0.318057i	0.764176	−	0.645008i	$-0.223146\pi$
$179$	6.62139	+	4.25531i	0.494906	+	0.318057i	−0.269270	+	0.963065i	$0.586782\pi$
$180$		0			0
$181$	5.80714	+	2.99379i	0.431641	+	0.222526i	0.660334	−	0.750972i	$-0.270415\pi$
$181$	5.80714	+	2.99379i	0.431641	+	0.222526i	−0.228693	+	0.973499i	$0.573445\pi$
$182$		0			0
$183$	3.29072	−	16.5205i	0.243257	−	1.22123i
$184$		0			0
$185$	6.73550	+	5.29686i	0.495204	+	0.389433i
$186$		0			0
$187$	3.09259	−	2.67974i	0.226153	−	0.195962i
$188$		0			0
$189$	−10.7014	−	14.1430i	−0.778413	−	1.02875i
$190$		0			0
$191$	−13.6843	+	7.05474i	−0.990160	+	0.510463i	−0.875643	−	0.482958i	$-0.839562\pi$
$191$	−13.6843	+	7.05474i	−0.990160	+	0.510463i	−0.114517	+	0.993421i	$0.536532\pi$
$192$		0			0
$193$	10.8125	−	3.17484i	0.778301	−	0.228530i	0.131630	−	0.991299i	$-0.457979\pi$
$193$	10.8125	−	3.17484i	0.778301	−	0.228530i	0.646671	+	0.762769i	$0.276161\pi$
$194$		0			0
$195$	3.42940	−	3.55217i	0.245585	−	0.254376i
$196$		0			0
$197$	4.30693	−	12.4440i	0.306856	−	0.886602i	−0.681144	−	0.732149i	$-0.738517\pi$
$197$	4.30693	−	12.4440i	0.306856	−	0.886602i	0.988000	−	0.154453i	$-0.0493614\pi$
$198$		0			0
$199$	0.573623	+	0.805541i	0.0406631	+	0.0571033i	0.834407	−	0.551149i	$-0.185810\pi$
$199$	0.573623	+	0.805541i	0.0406631	+	0.0571033i	−0.793744	+	0.608252i	$0.791871\pi$
$200$		0			0
$201$	13.7651	+	3.39439i	0.970916	+	0.239422i
$202$		0			0
$203$	−1.98947	−	2.79382i	−0.139633	−	0.196088i
$204$		0			0
$205$	−1.26800	+	3.66364i	−0.0885607	+	0.255879i
$206$		0			0
$207$	−19.1731	+	8.46954i	−1.33262	+	0.588674i
$208$		0			0
$209$	−8.39556	+	2.46516i	−0.580733	+	0.170519i
$210$		0			0
$211$	−6.01206	+	3.09943i	−0.413888	+	0.213374i	−0.652578	−	0.757722i	$-0.726312\pi$
$211$	−6.01206	+	3.09943i	−0.413888	+	0.213374i	0.238690	+	0.971096i	$0.423282\pi$
$212$		0			0
$213$	−19.0599	−	2.86145i	−1.30596	−	0.196063i
$214$		0			0
$215$	2.09138	−	1.81219i	0.142631	−	0.123591i
$216$		0			0
$217$	−15.6024	−	12.2699i	−1.05916	−	0.832934i
$218$		0			0
$219$	10.3153	+	2.05470i	0.697041	+	0.138844i
$220$		0			0
$221$	7.71935	+	3.97960i	0.519260	+	0.267697i
$222$		0			0
$223$	−3.72053	−	2.39104i	−0.249145	−	0.160116i	0.410108	−	0.912037i	$-0.365491\pi$
$223$	−3.72053	−	2.39104i	−0.249145	−	0.160116i	−0.659253	+	0.751921i	$0.729127\pi$
$224$		0			0
$225$	11.5030	−	0.954234i	0.766866	−	0.0636156i
$226$		0			0
$227$	−2.92214	+	15.1615i	−0.193949	+	1.00630i	0.746247	+	0.665669i	$0.231854\pi$
$227$	−2.92214	+	15.1615i	−0.193949	+	1.00630i	−0.940196	+	0.340634i	$0.889358\pi$
$228$		0			0
$229$	−1.16775	−	0.283294i	−0.0771672	−	0.0187206i	0.196989	−	0.980406i	$-0.436884\pi$
$229$	−1.16775	−	0.283294i	−0.0771672	−	0.0187206i	−0.274157	+	0.961685i	$0.588399\pi$
$230$		0			0
$231$	4.53601	+	5.84240i	0.298448	+	0.384402i
$232$		0			0
$233$	−0.0185739	+	0.389913i	−0.00121681	+	0.0255441i	−0.999394	−	0.0348060i	$-0.988919\pi$
$233$	−0.0185739	+	0.389913i	−0.00121681	+	0.0255441i	0.998177	+	0.0603501i	$0.0192217\pi$
$234$		0			0
$235$	10.2291	+	7.28414i	0.667276	+	0.475165i
$236$		0			0
$237$	14.9003	−	6.69311i	0.967879	−	0.434764i
$238$		0			0
$239$	−2.07881	−	3.60060i	−0.134467	−	0.232903i	0.790927	−	0.611911i	$-0.209599\pi$
$239$	−2.07881	−	3.60060i	−0.134467	−	0.232903i	−0.925394	+	0.379007i	$0.876266\pi$
$240$		0			0
$241$	1.04541	+	7.27101i	0.0673410	+	0.468367i	0.995390	+	0.0959090i	$0.0305758\pi$
$241$	1.04541	+	7.27101i	0.0673410	+	0.468367i	−0.928049	+	0.372458i	$0.878515\pi$
$242$		0			0
$243$	−9.43248	+	12.4108i	−0.605094	+	0.796154i
$244$		0			0
$245$	0.237519	+	4.98613i	0.0151745	+	0.318552i
$246$		0			0
$247$	−11.4795	−	14.5974i	−0.730423	−	0.928809i
$248$		0			0
$249$	−11.5758	+	22.1153i	−0.733588	+	1.40150i
$250$		0			0
$251$	−7.51263	−	21.7063i	−0.474193	−	1.37009i	−0.888049	−	0.459749i	$-0.847939\pi$
$251$	−7.51263	−	21.7063i	−0.474193	−	1.37009i	0.413856	−	0.910343i	$-0.364182\pi$
$252$		0			0
$253$	7.95159	−	3.63137i	0.499912	−	0.228302i
$254$		0			0
$255$	−2.22515	−	5.65988i	−0.139344	−	0.354436i
$256$		0			0
$257$	−0.867445	−	2.16677i	−0.0541098	−	0.135160i	0.898850	−	0.438256i	$-0.144404\pi$
$257$	−0.867445	−	2.16677i	−0.0541098	−	0.135160i	−0.952960	+	0.303097i	$0.901980\pi$
$258$		0			0
$259$	−24.7812	−	11.3172i	−1.53983	−	0.703218i
$260$		0			0
$261$	−1.89282	+	2.34628i	−0.117162	+	0.145231i
$262$		0			0
$263$	−15.9922	−	2.29933i	−0.986119	−	0.141783i	−0.369658	−	0.929168i	$-0.620525\pi$
$263$	−15.9922	−	2.29933i	−0.986119	−	0.141783i	−0.616461	+	0.787385i	$0.711434\pi$
$264$		0			0
$265$	−6.37008	+	4.09380i	−0.391311	+	0.251480i
$266$		0			0
$267$	9.46637	−	23.2263i	0.579332	−	1.42143i
$268$		0			0
$269$			22.0639i			1.34526i	0.739978	+	0.672631i	$0.234836\pi$
$269$			22.0639i			1.34526i	−0.739978	+	0.672631i	$0.765164\pi$
$270$		0			0
$271$	−10.4091	−	16.1968i	−0.632305	−	0.983886i	−0.998574	−	0.0533769i	$-0.983002\pi$
$271$	−10.4091	−	16.1968i	−0.632305	−	0.983886i	0.366269	−	0.930509i	$-0.380635\pi$
$272$		0			0
$273$	−7.93337	+	13.5458i	−0.480149	+	0.819830i
$274$		0			0
$275$	−4.79200	+	0.457581i	−0.288969	+	0.0275932i
$276$		0			0
$277$	−2.65963	+	5.82378i	−0.159802	+	0.349917i	−0.972549	−	0.232700i	$-0.925244\pi$
$277$	−2.65963	+	5.82378i	−0.159802	+	0.349917i	0.812747	+	0.582617i	$0.197971\pi$
$278$		0			0
$279$	−6.68500	+	16.1147i	−0.400220	+	0.964760i
$280$		0			0
$281$	12.9657	−	12.3628i	0.773468	−	0.737501i	−0.196560	−	0.980492i	$-0.562977\pi$
$281$	12.9657	−	12.3628i	0.773468	−	0.737501i	0.970028	+	0.242991i	$0.0781286\pi$
$282$		0			0
$283$	−5.54205	−	12.1354i	−0.329441	−	0.721375i	0.670345	−	0.742049i	$-0.266146\pi$
$283$	−5.54205	−	12.1354i	−0.329441	−	0.721375i	−0.999786	+	0.0206743i	$0.993419\pi$
$284$		0			0
$285$	−0.699501	+	12.9853i	−0.0414349	+	0.769180i
$286$		0			0
$287$	1.17165	−	12.2701i	0.0691605	−	0.724281i
$288$		0			0
$289$	−4.95434	+	3.89614i	−0.291432	+	0.229184i
$290$		0			0
$291$	−9.40188	−	3.31962i	−0.551148	−	0.194599i
$292$		0			0
$293$	−0.725462	+	2.47070i	−0.0423819	+	0.144340i	−0.977966	−	0.208765i	$-0.933056\pi$
$293$	−0.725462	+	2.47070i	−0.0423819	+	0.144340i	0.935584	+	0.353104i	$0.114874\pi$
$294$		0			0
$295$	14.4127	−	2.07223i	0.839140	−	0.120650i
$296$		0			0
$297$	3.86916	−	5.22444i	0.224511	−	0.303153i
$298$		0			0
$299$	13.4271	+	12.8027i	0.776509	+	0.740400i
$300$		0			0
$301$	−5.10347	+	7.16682i	−0.294159	+	0.413088i
$302$		0			0
$303$	−7.63059	+	16.4375i	−0.438366	+	0.944307i
$304$		0			0
$305$	9.04197	+	5.22038i	0.517742	+	0.298918i
$306$		0			0
$307$	−5.08377	+	20.9556i	−0.290146	+	1.19600i	0.620966	+	0.783838i	$0.286741\pi$
$307$	−5.08377	+	20.9556i	−0.290146	+	1.19600i	−0.911111	+	0.412160i	$0.864774\pi$
$308$		0			0
$309$	18.8392	+	12.2734i	1.07172	+	0.698208i
$310$		0			0
$311$	−7.70833	+	8.89589i	−0.437099	+	0.504440i	−0.930970	−	0.365096i	$-0.881036\pi$
$311$	−7.70833	+	8.89589i	−0.437099	+	0.504440i	0.493871	+	0.869535i	$0.335582\pi$
$312$		0			0
$313$	4.49750	−	6.99824i	0.254214	−	0.395564i	−0.690567	−	0.723269i	$-0.742639\pi$
$313$	4.49750	−	6.99824i	0.254214	−	0.395564i	0.944780	+	0.327705i	$0.106275\pi$
$314$		0			0
$315$	10.4319	−	3.46589i	0.587773	−	0.195281i
$316$		0			0
$317$	1.16133	+	6.02556i	0.0652268	+	0.338429i	0.999852	−	0.0172055i	$-0.00547695\pi$
$317$	1.16133	+	6.02556i	0.0652268	+	0.338429i	−0.934625	+	0.355634i	$0.884265\pi$
$318$		0			0
$319$	0.777172	−	0.988255i	0.0435133	−	0.0553316i
$320$		0			0
$321$	−0.141097	+	0.0478541i	−0.00787529	+	0.00267096i
$322$		0			0
$323$	−22.2288	+	5.39264i	−1.23684	+	0.300055i
$324$		0			0
$325$	−4.68148	−	9.08081i	−0.259682	−	0.503713i
$326$		0			0
$327$	−2.15386	+	21.1648i	−0.119109	+	1.17042i
$328$		0			0
$329$	−37.0652	−	14.8387i	−2.04347	−	0.818083i
$330$		0			0
$331$	4.35721	+	1.50804i	0.239494	+	0.0828896i	0.444178	−	0.895938i	$-0.353496\pi$
$331$	4.35721	+	1.50804i	0.239494	+	0.0828896i	−0.204685	+	0.978828i	$0.565617\pi$
$332$		0			0
$333$	−3.70219	+	23.6573i	−0.202879	+	1.29641i
$334$		0			0
$335$	−4.73270	+	7.40399i	−0.258575	+	0.404523i
$336$		0			0
$337$	26.3193	−	18.7419i	1.43370	−	1.02094i	0.441374	−	0.897323i	$-0.354491\pi$
$337$	26.3193	−	18.7419i	1.43370	−	1.02094i	0.992330	−	0.123613i	$-0.0394482\pi$
$338$		0			0
$339$	13.2518	−	15.1026i	0.719738	−	0.820263i
$340$		0			0
$341$	2.70420	−	6.75477i	0.146441	−	0.365791i
$342$		0			0
$343$	2.25995	+	7.69668i	0.122026	+	0.415581i
$344$		0			0
$345$	−1.15450	−	12.9401i	−0.0621560	−	0.696673i
$346$		0			0
$347$	1.90552	+	7.85464i	0.102293	+	0.421659i	0.999813	−	0.0193145i	$-0.00614837\pi$
$347$	1.90552	+	7.85464i	0.102293	+	0.421659i	−0.897520	+	0.440974i	$0.854633\pi$
$348$		0			0
$349$	−4.97083	−	5.73664i	−0.266082	−	0.307075i	0.606948	−	0.794742i	$-0.292394\pi$
$349$	−4.97083	−	5.73664i	−0.266082	−	0.307075i	−0.873030	+	0.487666i	$0.837848\pi$
$350$		0			0
$351$	13.3458	+	3.50243i	0.712344	+	0.186946i
$352$		0			0
$353$	6.62243	−	1.27637i	0.352476	−	0.0679343i	−0.00993986	−	0.999951i	$-0.503164\pi$
$353$	6.62243	−	1.27637i	0.352476	−	0.0679343i	0.362416	+	0.932016i	$0.381952\pi$
$354$		0			0
$355$	5.47394	−	10.6180i	0.290526	−	0.563543i
$356$		0			0
$357$	11.1175	+	15.8196i	0.588403	+	0.837264i
$358$		0			0
$359$	28.2755	+	24.5009i	1.49232	+	1.29311i	0.850141	+	0.526555i	$0.176517\pi$
$359$	28.2755	+	24.5009i	1.49232	+	1.29311i	0.642183	+	0.766551i	$0.278029\pi$
$360$		0			0
$361$	29.3694	+	5.66049i	1.54576	+	0.297921i
$362$		0			0
$363$	9.56142	−	13.2520i	0.501845	−	0.695550i
$364$		0			0
$365$	−3.25956	+	5.64573i	−0.170613	+	0.295511i
$366$		0			0
$367$	26.1307	+	1.24476i	1.36401	+	0.0649760i	0.716771	−	0.697308i	$-0.245619\pi$
$367$	26.1307	+	1.24476i	1.36401	+	0.0649760i	0.647242	+	0.762284i	$0.275922\pi$
$368$		0			0
$369$	−10.6627	+	1.91788i	−0.555078	+	0.0998410i
$370$		0			0
$371$	16.6133	−	17.4235i	0.862519	−	0.904584i
$372$		0			0
$373$	10.3411	−	5.97047i	0.535444	−	0.309139i	−0.207786	−	0.978174i	$-0.566626\pi$
$373$	10.3411	−	5.97047i	0.535444	−	0.309139i	0.743231	+	0.669035i	$0.233293\pi$
$374$		0			0
$375$	−3.97787	+	15.9632i	−0.205416	+	0.824336i
$376$		0			0
$377$	2.56020	+	0.751742i	0.131857	+	0.0387167i
$378$		0			0
$379$	−33.2501	+	1.58390i	−1.70794	+	0.0813592i	−0.878653	−	0.477462i	$-0.841557\pi$
$379$	−33.2501	+	1.58390i	−1.70794	+	0.0813592i	−0.829288	+	0.558821i	$0.811254\pi$
$380$		0			0
$381$	−15.8641	+	4.55120i	−0.812745	+	0.233165i
$382$		0			0
$383$	−18.4651	−	1.76320i	−0.943522	−	0.0900955i	−0.388057	−	0.921635i	$-0.626854\pi$
$383$	−18.4651	−	1.76320i	−0.943522	−	0.0900955i	−0.555465	+	0.831540i	$0.687460\pi$
$384$		0			0
$385$	−4.33233	+	1.49943i	−0.220796	+	0.0764183i
$386$		0			0
$387$	7.27582	+	2.61993i	0.369851	+	0.133179i
$388$		0			0
$389$	−12.6712	−	13.2892i	−0.642455	−	0.673787i	0.319314	−	0.947649i	$-0.396547\pi$
$389$	−12.6712	−	13.2892i	−0.642455	−	0.673787i	−0.961769	+	0.273862i	$0.911699\pi$
$390$		0			0
$391$	21.2146	−	8.49303i	1.07287	−	0.429511i
$392$		0			0
$393$	−4.83043	−	5.12949i	−0.243663	−	0.258749i
$394$		0			0
$395$	0.962379	+	10.0785i	0.0484226	+	0.507104i
$396$		0			0
$397$	−1.34766	+	9.37317i	−0.0676370	+	0.470426i	0.927650	+	0.373451i	$0.121826\pi$
$397$	−1.34766	+	9.37317i	−0.0676370	+	0.470426i	−0.995287	+	0.0969747i	$0.969083\pi$
$398$		0			0
$399$	−7.57197	−	40.6453i	−0.379073	−	2.03481i
$400$		0			0
$401$	28.6827			1.43235			0.716174	−	0.697922i	$-0.245892\pi$
$401$	28.6827			1.43235			0.716174	+	0.697922i	$0.245892\pi$
$402$		0			0
$403$	15.4421			0.769224
$404$		0			0
$405$	−5.40702	−	8.00728i	−0.268677	−	0.397885i
$406$		0			0
$407$	1.42121	−	9.88472i	0.0704467	−	0.489967i
$408$		0			0
$409$	1.22216	+	12.7991i	0.0604320	+	0.632872i	0.974055	+	0.226310i	$0.0726664\pi$
$409$	1.22216	+	12.7991i	0.0604320	+	0.632872i	−0.913623	+	0.406562i	$0.866728\pi$
$410$		0			0
$411$	−19.7420	+	18.5910i	−0.973802	+	0.917028i
$412$		0			0
$413$	−42.9782	+	17.2059i	−2.11482	+	0.846645i
$414$		0			0
$415$	−10.6766	−	11.1973i	−0.524093	−	0.549653i
$416$		0			0
$417$	−16.2512	+	0.672907i	−0.795826	+	0.0329524i
$418$		0			0
$419$	−1.30845	+	0.452859i	−0.0639220	+	0.0221236i	−0.358842	−	0.933398i	$-0.616828\pi$
$419$	−1.30845	+	0.452859i	−0.0639220	+	0.0221236i	0.294920	+	0.955522i	$0.404707\pi$
$420$		0			0
$421$	32.1300	+	3.06804i	1.56592	+	0.149527i	0.841663	−	0.540003i	$-0.181577\pi$
$421$	32.1300	+	3.06804i	1.56592	+	0.149527i	0.724257	+	0.689530i	$0.242183\pi$
$422$		0			0
$423$	−3.76980	+	34.8890i	−0.183294	+	1.69636i
$424$		0			0
$425$	−12.5696	+	0.598764i	−0.609715	+	0.0290443i
$426$		0			0
$427$	−31.8503	−	9.35209i	−1.54134	−	0.452579i
$428$		0			0
$429$	−5.58358	−	1.39137i	−0.269578	−	0.0671762i
$430$		0			0
$431$	−11.4511	+	6.61130i	−0.551580	+	0.318455i	−0.749759	−	0.661711i	$-0.769831\pi$
$431$	−11.4511	+	6.61130i	−0.551580	+	0.318455i	0.198179	+	0.980166i	$0.436497\pi$
$432$		0			0
$433$	−11.3091	+	11.8607i	−0.543482	+	0.569988i	−0.937000	−	0.349329i	$-0.886409\pi$
$433$	−11.3091	+	11.8607i	−0.543482	+	0.569988i	0.393518	+	0.919317i	$0.371258\pi$
$434$		0			0
$435$	−1.00038	−	1.57812i	−0.0479648	−	0.0756648i
$436$		0			0
$437$	−48.8074	−	2.32498i	−2.33477	−	0.111219i
$438$		0			0
$439$	−20.0048	+	34.6493i	−0.954777	+	1.65372i	−0.219899	+	0.975523i	$0.570573\pi$
$439$	−20.0048	+	34.6493i	−0.954777	+	1.65372i	−0.734878	+	0.678200i	$0.762760\pi$
$440$		0			0
$441$	−11.8279	+	7.39515i	−0.563233	+	0.352150i
$442$		0			0
$443$	13.9459	+	2.68786i	0.662591	+	0.127704i	0.509450	−	0.860500i	$-0.329849\pi$
$443$	13.9459	+	2.68786i	0.662591	+	0.127704i	0.153141	+	0.988204i	$0.451061\pi$
$444$		0			0
$445$	11.7487	+	10.1803i	0.556940	+	0.482591i
$446$		0			0
$447$	−21.6468	+	15.2127i	−1.02386	+	0.719536i
$448$		0			0
$449$	9.31873	−	18.0758i	0.439778	−	0.853051i	−0.559921	−	0.828546i	$-0.689169\pi$
$449$	9.31873	−	18.0758i	0.439778	−	0.853051i	0.999700	−	0.0245051i	$-0.00780099\pi$
$450$		0			0
$451$	4.43659	−	0.855082i	0.208911	−	0.0402643i
$452$		0			0
$453$	2.27686	+	4.00088i	0.106976	+	0.187978i
$454$		0			0
$455$	−6.37167	−	7.35330i	−0.298709	−	0.344728i
$456$		0			0
$457$	2.03728	+	8.39776i	0.0952997	+	0.392831i	0.999405	−	0.0344780i	$-0.0109769\pi$
$457$	2.03728	+	8.39776i	0.0952997	+	0.392831i	−0.904106	+	0.427309i	$0.859462\pi$
$458$		0			0
$459$	10.7528	−	13.1606i	0.501899	−	0.614284i
$460$		0			0
$461$	5.51343	+	18.7770i	0.256786	+	0.874533i	0.982457	+	0.186491i	$0.0597115\pi$
$461$	5.51343	+	18.7770i	0.256786	+	0.874533i	−0.725671	+	0.688042i	$0.758470\pi$
$462$		0			0
$463$	4.70448	−	11.7512i	0.218636	−	0.546125i	−0.777984	−	0.628284i	$-0.783757\pi$
$463$	4.70448	−	11.7512i	0.218636	−	0.546125i	0.996619	+	0.0821593i	$0.0261816\pi$
$464$		0			0
$465$	−8.12803	−	7.13193i	−0.376929	−	0.330736i
$466$		0			0
$467$	14.8938	−	10.6058i	0.689203	−	0.490779i	−0.180993	−	0.983484i	$-0.557931\pi$
$467$	14.8938	−	10.6058i	0.689203	−	0.490779i	0.870196	+	0.492705i	$0.163992\pi$
$468$		0			0
$469$	9.07304	−	26.4238i	0.418954	−	1.22014i
$470$		0			0
$471$	−3.02503	−	12.8166i	−0.139386	−	0.590559i
$472$		0			0
$473$	−3.04773	−	1.05483i	−0.140135	−	0.0485012i
$474$		0			0
$475$	24.9803	+	10.0006i	1.14617	+	0.458859i
$476$		0			0
$477$	−18.6859	−	9.92924i	−0.855567	−	0.454629i
$478$		0			0
$479$	−15.6875	−	30.4295i	−0.716780	−	1.39036i	−0.912243	−	0.409648i	$-0.865651\pi$
$479$	−15.6875	−	30.4295i	−0.716780	−	1.39036i	0.195463	−	0.980711i	$-0.437379\pi$
$480$		0			0
$481$	20.5970	−	4.99678i	0.939143	−	0.227834i
$482$		0			0
$483$	13.2665	+	39.1162i	0.603647	+	1.77985i
$484$		0			0
$485$	3.82020	−	4.85778i	0.173466	−	0.220580i
$486$		0			0
$487$	−3.77448	−	19.5839i	−0.171038	−	0.887430i	−0.961476	−	0.274888i	$-0.911359\pi$
$487$	−3.77448	−	19.5839i	−0.171038	−	0.887430i	0.790438	−	0.612542i	$-0.209853\pi$
$488$		0			0
$489$	7.26429	+	8.48951i	0.328503	+	0.383909i
$490$		0			0
$491$	15.4080	−	23.9753i	0.695352	−	1.08199i	−0.296554	−	0.955016i	$-0.595838\pi$
$491$	15.4080	−	23.9753i	0.695352	−	1.08199i	0.991906	−	0.126973i	$-0.0405260\pi$
$492$		0			0
$493$	2.15224	−	2.48382i	0.0969321	−	0.111866i
$494$		0			0
$495$	2.29635	+	3.31114i	0.103213	+	0.148825i
$496$		0			0
$497$	−8.95420	+	36.9097i	−0.401651	+	1.65563i
$498$		0			0
$499$	−29.8604	−	17.2399i	−1.33674	−	0.771765i	−0.350414	−	0.936595i	$-0.613959\pi$
$499$	−29.8604	−	17.2399i	−1.33674	−	0.771765i	−0.986322	+	0.164830i	$0.947292\pi$
$500$		0			0
$501$	−17.4733	−	8.11145i	−0.780649	−	0.362393i
$502$		0			0
$503$	−24.5267	+	34.4430i	−1.09359	+	1.53574i	−0.274929	+	0.961464i	$0.588654\pi$
$503$	−24.5267	+	34.4430i	−1.09359	+	1.53574i	−0.818664	+	0.574272i	$0.805285\pi$
$504$		0			0
$505$	−8.12926	−	7.75123i	−0.361747	−	0.344925i
$506$		0			0
$507$	1.40298	+	10.2081i	0.0623085	+	0.453356i
$508$		0			0
$509$	25.5162	−	3.66868i	1.13099	−	0.162611i	0.448690	−	0.893687i	$-0.351891\pi$
$509$	25.5162	−	3.66868i	1.13099	−	0.162611i	0.682296	+	0.731076i	$0.260982\pi$
$510$		0			0
$511$	5.83936	−	19.8870i	0.258318	−	0.879751i
$512$		0			0
$513$	−32.6049	+	16.0465i	−1.43954	+	0.708470i
$514$		0			0
$515$	−10.9545	+	8.61475i	−0.482715	+	0.379611i
$516$		0			0
$517$	1.39116	−	14.5689i	0.0611831	−	0.640738i
$518$		0			0
$519$	−10.7759	−	0.580483i	−0.473007	−	0.0254804i
$520$		0			0
$521$	5.35842	+	11.7333i	0.234756	+	0.514045i	0.989943	−	0.141465i	$-0.0451811\pi$
$521$	5.35842	+	11.7333i	0.234756	+	0.514045i	−0.755187	+	0.655510i	$0.772454\pi$
$522$		0			0
$523$	8.37239	−	7.98306i	0.366099	−	0.349075i	−0.484592	−	0.874740i	$-0.661032\pi$
$523$	8.37239	−	7.98306i	0.366099	−	0.349075i	0.850691	+	0.525665i	$0.176184\pi$
$524$		0			0
$525$	0.141408	−	22.7452i	0.00617157	−	0.992683i
$526$		0			0
$527$	7.90129	−	17.3014i	0.344186	−	0.753661i
$528$		0			0
$529$	25.6986	−	2.45392i	1.11733	−	0.106692i
$530$		0			0
$531$	24.7534	+	32.2949i	1.07420	+	1.40148i
$532$		0			0
$533$	5.18433	+	8.06698i	0.224558	+	0.349420i
$534$		0			0
$535$		−	0.0923467i		−	0.00399250i
$536$		0			0
$537$	−12.6245	−	5.14536i	−0.544785	−	0.222039i
$538$		0			0
$539$	4.89409	−	3.14524i	0.210803	−	0.135475i
$540$		0			0
$541$	18.6189	+	2.67700i	0.800490	+	0.115093i	0.530406	−	0.847744i	$-0.322039\pi$
$541$	18.6189	+	2.67700i	0.800490	+	0.115093i	0.270084	+	0.962837i	$0.412949\pi$
$542$		0			0
$543$	−10.8378	−	3.25559i	−0.465095	−	0.139711i
$544$		0			0
$545$	−11.9944	−	5.47765i	−0.513783	−	0.234637i
$546$		0			0
$547$	11.5509	+	28.8527i	0.493879	+	1.23365i	0.940765	+	0.339059i	$0.110109\pi$
$547$	11.5509	+	28.8527i	0.493879	+	1.23365i	−0.446886	+	0.894591i	$0.647467\pi$
$548$		0			0
$549$	−0.362770	+	29.1743i	−0.0154826	+	1.24513i
$550$		0			0
$551$	−6.39251	+	2.91936i	−0.272330	+	0.124369i
$552$		0			0
$553$	−10.5279	−	30.4185i	−0.447694	−	1.29353i
$554$		0			0
$555$	−13.1491	−	6.88267i	−0.558150	−	0.292153i
$556$		0			0
$557$	21.7296	+	27.6314i	0.920712	+	1.17078i	0.984949	+	0.172846i	$0.0552962\pi$
$557$	21.7296	+	27.6314i	0.920712	+	1.17078i	−0.0642371	+	0.997935i	$0.520461\pi$
$558$		0			0
$559$	−0.325688	−	6.83703i	−0.0137751	−	0.289175i
$560$		0			0
$561$	−4.41588	+	5.54396i	−0.186438	+	0.234066i
$562$		0			0
$563$	5.63565	+	39.1968i	0.237515	+	1.65195i	0.664204	+	0.747552i	$0.268771\pi$
$563$	5.63565	+	39.1968i	0.237515	+	1.65195i	−0.426689	+	0.904398i	$0.640320\pi$
$564$		0			0
$565$	6.22671	+	10.7850i	0.261960	+	0.453728i
$566$		0			0
$567$	22.7082	+	20.6875i	0.953656	+	0.868792i
$568$		0			0
$569$	−1.61100	−	1.14719i	−0.0675368	−	0.0480927i	0.545790	−	0.837922i	$-0.316230\pi$
$569$	−1.61100	−	1.14719i	−0.0675368	−	0.0480927i	−0.613327	+	0.789829i	$0.710169\pi$
$570$		0			0
$571$	2.04251	−	42.8776i	0.0854765	−	1.79437i	−0.396344	−	0.918102i	$-0.629721\pi$
$571$	2.04251	−	42.8776i	0.0854765	−	1.79437i	0.481821	−	0.876270i	$-0.339976\pi$
$572$		0			0
$573$	21.0631	−	16.3533i	0.879925	−	0.683170i
$574$		0			0
$575$	−26.1240	−	6.33761i	−1.08945	−	0.264297i
$576$		0			0
$577$	−1.44529	+	7.49887i	−0.0601682	+	0.312182i	−0.999527	−	0.0307538i	$-0.990209\pi$
$577$	−1.44529	+	7.49887i	−0.0601682	+	0.312182i	0.939359	+	0.342936i	$0.111421\pi$
$578$		0			0
$579$	−17.4039	+	8.83583i	−0.723283	+	0.367205i
$580$		0			0
$581$	41.3809	+	26.5939i	1.71677	+	1.10330i
$582$		0			0
$583$	7.84383	+	4.04378i	0.324858	+	0.167476i
$584$		0			0
$585$	−4.71264	+	7.13633i	−0.194844	+	0.295051i
$586$		0			0
$587$	26.2994	+	20.6821i	1.08549	+	0.853641i	0.989898	−	0.141779i	$-0.0452824\pi$
$587$	26.2994	+	20.6821i	1.08549	+	0.853641i	0.0955945	+	0.995420i	$0.469525\pi$
$588$		0			0
$589$	−30.7367	+	26.6335i	−1.26648	+	1.09741i
$590$		0			0
$591$	−3.38623	+	22.5554i	−0.139291	+	0.927805i
$592$		0			0
$593$	−32.6745	+	16.8449i	−1.34178	+	0.691736i	−0.971468	−	0.237172i	$-0.923780\pi$
$593$	−32.6745	+	16.8449i	−1.34178	+	0.691736i	−0.370312	+	0.928907i	$0.620749\pi$
$594$		0			0
$595$	−11.4989	+	3.37638i	−0.471409	+	0.138418i
$596$		0			0
$597$	−1.23227	−	1.18968i	−0.0504334	−	0.0486903i
$598$		0			0
$599$	3.14596	−	9.08965i	0.128540	−	0.371393i	−0.862306	−	0.506388i	$-0.830981\pi$
$599$	3.14596	−	9.08965i	0.128540	−	0.371393i	0.990846	+	0.134995i	$0.0431017\pi$
$600$		0			0
$601$	−4.55869	−	6.40178i	−0.185953	−	0.261134i	0.711067	−	0.703124i	$-0.248212\pi$
$601$	−4.55869	−	6.40178i	−0.185953	−	0.261134i	−0.897020	+	0.441990i	$0.854273\pi$
$602$		0			0
$603$	−24.5154	−	1.41334i	−0.998342	−	0.0575556i
$604$		0			0
$605$	5.87510	+	8.25043i	0.238857	+	0.335428i
$606$		0			0
$607$	2.62671	−	7.58939i	0.106615	−	0.308044i	−0.879057	−	0.476716i	$-0.841827\pi$
$607$	2.62671	−	7.58939i	0.106615	−	0.308044i	0.985672	+	0.168673i	$0.0539481\pi$
$608$		0			0
$609$	4.27382	+	4.12611i	0.173184	+	0.167198i
$610$		0			0
$611$	29.8026	−	8.75082i	1.20568	−	0.354020i
$612$		0			0
$613$	−15.3235	+	7.89982i	−0.618911	+	0.319071i	−0.739013	−	0.673691i	$-0.764708\pi$
$613$	−15.3235	+	7.89982i	−0.618911	+	0.319071i	0.120102	+	0.992762i	$0.461678\pi$
$614$		0			0
$615$	0.996935	−	6.64050i	0.0402003	−	0.267771i
$616$		0			0
$617$	7.70303	−	6.67472i	0.310112	−	0.268714i	−0.485873	−	0.874029i	$-0.661498\pi$
$617$	7.70303	−	6.67472i	0.310112	−	0.268714i	0.795986	+	0.605315i	$0.206953\pi$
$618$		0			0
$619$	29.4092	+	23.1276i	1.18205	+	0.929578i	0.998571	−	0.0534445i	$-0.0170200\pi$
$619$	29.4092	+	23.1276i	1.18205	+	0.929578i	0.183484	+	0.983023i	$0.441262\pi$
$620$		0			0
$621$	29.9604	−	20.5035i	1.20227	−	0.822777i
$622$		0			0
$623$	−43.9310	−	22.6480i	−1.76006	−	0.907373i
$624$		0			0
$625$	7.60557	+	4.88780i	0.304223	+	0.195512i
$626$		0			0
$627$	13.5136	−	6.86075i	0.539682	−	0.273992i
$628$		0			0
$629$	4.94051	−	25.6338i	0.196991	−	1.02209i
$630$		0			0
$631$	−36.1058	−	8.75918i	−1.43735	−	0.348698i	−0.559978	−	0.828507i	$-0.689190\pi$
$631$	−36.1058	−	8.75918i	−1.43735	−	0.348698i	−0.877373	+	0.479810i	$0.840706\pi$
$632$		0			0
$633$	9.25389	−	7.18468i	0.367809	−	0.285566i
$634$		0			0
$635$	0.486735	−	10.2178i	0.0193155	−	0.405482i
$636$		0			0
$637$	10.0575	+	7.16194i	0.398494	+	0.283766i
$638$		0			0
$639$	33.3620	−	1.17369i	1.31978	−	0.0464304i
$640$		0			0
$641$	−4.70490	−	8.14913i	−0.185833	−	0.321871i	0.758024	−	0.652226i	$-0.226165\pi$
$641$	−4.70490	−	8.14913i	−0.185833	−	0.321871i	−0.943857	+	0.330355i	$0.892832\pi$
$642$		0			0
$643$	−4.78557	−	33.2844i	−0.188724	−	1.31261i	−0.835316	−	0.549771i	$-0.814715\pi$
$643$	−4.78557	−	33.2844i	−0.188724	−	1.31261i	0.646591	−	0.762837i	$-0.276194\pi$
$644$		0			0
$645$	−2.98626	+	3.74913i	−0.117584	+	0.147622i
$646$		0			0
$647$	−0.466056	−	9.78372i	−0.0183226	−	0.384638i	−0.989340	−	0.145627i	$-0.953480\pi$
$647$	−0.466056	−	9.78372i	−0.0183226	−	0.384638i	0.971017	−	0.239011i	$-0.0768230\pi$
$648$		0			0
$649$	−10.4901	−	13.3392i	−0.411771	−	0.523609i
$650$		0			0
$651$	30.4593	+	15.9433i	1.19379	+	0.624868i
$652$		0			0
$653$	−7.31137	−	21.1248i	−0.286116	−	0.826678i	−0.992868	−	0.119217i	$-0.961962\pi$
$653$	−7.31137	−	21.1248i	−0.286116	−	0.826678i	0.706752	−	0.707461i	$-0.250159\pi$
$654$		0			0
$655$	3.97248	−	1.81417i	0.155218	−	0.0708856i
$656$		0			0
$657$	−18.2161	−	0.226510i	−0.710679	−	0.00883701i
$658$		0			0
$659$	−16.3965	−	40.9565i	−0.638718	−	1.59544i	−0.794238	−	0.607607i	$-0.792130\pi$
$659$	−16.3965	−	40.9565i	−0.638718	−	1.59544i	0.155520	−	0.987833i	$-0.450295\pi$
$660$		0			0
$661$	−43.2103	−	19.7335i	−1.68069	−	0.767544i	−0.999368	−	0.0355573i	$-0.988679\pi$
$661$	−43.2103	−	19.7335i	−1.68069	−	0.767544i	−0.681319	−	0.731987i	$-0.738593\pi$
$662$		0			0
$663$	−14.4065	−	4.32761i	−0.559504	−	0.168070i
$664$		0			0
$665$	25.3650	+	3.64694i	0.983614	+	0.141422i
$666$		0			0
$667$	5.90627	−	3.79573i	0.228692	−	0.146971i
$668$		0			0
$669$	7.09363	+	2.89116i	0.274255	+	0.111779i
$670$		0			0
$671$		−	12.1681i		−	0.469743i
$672$		0			0
$673$	23.9329	+	37.2404i	0.922547	+	1.43551i	0.900061	+	0.435763i	$0.143522\pi$
$673$	23.9329	+	37.2404i	0.922547	+	1.43551i	0.0224854	+	0.999747i	$0.492842\pi$
$674$		0			0
$675$	−19.2841	+	5.27373i	−0.742245	+	0.202986i
$676$		0			0
$677$	−19.4425	+	1.85653i	−0.747236	+	0.0713524i	−0.461725	−	0.887023i	$-0.652769\pi$
$677$	−19.4425	+	1.85653i	−0.747236	+	0.0713524i	−0.285511	+	0.958375i	$0.592163\pi$
$678$		0			0
$679$	−8.16220	+	17.8727i	−0.313237	+	0.685892i
$680$		0			0
$681$	0.166264	−	26.7432i	0.00637126	−	1.02480i
$682$		0			0
$683$	26.8772	−	25.6273i	1.02843	−	0.980603i	0.0286069	−	0.999591i	$-0.490893\pi$
$683$	26.8772	−	25.6273i	1.02843	−	0.980603i	0.999820	+	0.0189880i	$0.00604442\pi$
$684$		0			0
$685$	−6.98226	−	15.2890i	−0.266778	−	0.584163i
$686$		0			0
$687$	2.07826	+	0.111954i	0.0792906	+	0.00427130i
$688$		0			0
$689$	−1.78033	+	18.6445i	−0.0678253	+	0.710299i
$690$		0			0
$691$	8.55640	−	6.72883i	0.325501	−	0.255977i	−0.442014	−	0.897008i	$-0.645736\pi$
$691$	8.55640	−	6.72883i	0.325501	−	0.255977i	0.767514	+	0.641032i	$0.221493\pi$
$692$		0			0
$693$	−9.57701	−	8.50930i	−0.363800	−	0.323241i
$694$		0			0
$695$	2.84024	−	9.67297i	0.107736	−	0.366917i
$696$		0			0
$697$	11.6910	−	1.68091i	0.442828	−	0.0636690i
$698$		0			0
$699$	−0.0920588	−	0.669819i	−0.00348198	−	0.0253349i
$700$		0			0
$701$	16.5837	+	15.8125i	0.626358	+	0.597231i	0.935303	−	0.353849i	$-0.115127\pi$
$701$	16.5837	+	15.8125i	0.626358	+	0.597231i	−0.308945	+	0.951080i	$0.599976\pi$
$702$		0			0
$703$	−32.3793	+	45.4703i	−1.22121	+	1.71495i
$704$		0			0
$705$	−19.7284	−	9.15829i	−0.743013	−	0.344921i
$706$		0			0
$707$	30.9273	+	17.8559i	1.16314	+	0.671539i
$708$		0			0
$709$	5.35357	−	22.0677i	0.201058	−	0.828771i	−0.778506	−	0.627637i	$-0.784022\pi$
$709$	5.35357	−	22.0677i	0.201058	−	0.828771i	0.979564	−	0.201134i	$-0.0644626\pi$
$710$		0			0
$711$	−23.2485	+	16.1233i	−0.871885	+	0.604671i
$712$		0			0
$713$	26.6078	−	30.7070i	0.996470	−	1.14999i
$714$		0			0
$715$	1.92825	−	3.00041i	0.0721124	−	0.112209i
$716$		0			0
$717$	4.68186	+	5.47152i	0.174847	+	0.204338i
$718$		0			0
$719$	−2.01198	−	10.4392i	−0.0750343	−	0.389315i	−0.999958	−	0.00916223i	$-0.997084\pi$
$719$	−2.01198	−	10.4392i	−0.0750343	−	0.389315i	0.924924	−	0.380153i	$-0.124129\pi$
$720$		0			0
$721$	27.3894	−	34.8284i	1.02003	−	1.29708i
$722$		0			0
$723$	−4.08654	−	12.0491i	−0.151980	−	0.448112i
$724$		0			0
$725$	−3.75723	+	0.911495i	−0.139540	+	0.0338521i
$726$		0			0
$727$	−5.86785	−	11.3820i	−0.217627	−	0.422137i	0.754598	−	0.656188i	$-0.227832\pi$
$727$	−5.86785	−	11.3820i	−0.217627	−	0.422137i	−0.972224	+	0.234051i	$0.924802\pi$
$728$		0			0
$729$	12.1243	−	24.1247i	0.449049	−	0.893507i
$730$		0			0
$731$	−7.82691	−	3.13342i	−0.289489	−	0.115894i
$732$		0			0
$733$	−16.0598	−	5.55836i	−0.593183	−	0.205303i	0.0139503	−	0.999903i	$-0.495559\pi$
$733$	−16.0598	−	5.55836i	−0.593183	−	0.205303i	−0.607133	+	0.794600i	$0.707681\pi$
$734$		0			0
$735$	−1.98610	−	8.41482i	−0.0732585	−	0.310385i
$736$		0			0
$737$	10.2307	+	0.462265i	0.376852	+	0.0170277i
$738$		0			0
$739$	−36.7435	+	26.1649i	−1.35163	+	0.962491i	−0.351981	+	0.936007i	$0.614492\pi$
$739$	−36.7435	+	26.1649i	−1.35163	+	0.962491i	−0.999649	+	0.0264840i	$0.991569\pi$
$740$		0			0
$741$	24.1773	+	21.2143i	0.888174	+	0.779327i
$742$		0			0
$743$	−12.6837	+	31.6823i	−0.465319	+	1.16231i	0.491305	+	0.870987i	$0.336520\pi$
$743$	−12.6837	+	31.6823i	−0.465319	+	1.16231i	−0.956625	+	0.291324i	$0.905904\pi$
$744$		0			0
$745$	−4.62007	−	15.7345i	−0.169266	−	0.576469i
$746$		0			0
$747$	12.6955	−	41.3289i	0.464505	−	1.51215i
$748$		0			0
$749$	0.0692195	+	0.285327i	0.00252923	+	0.0104256i
$750$		0			0
$751$	−12.4611	−	14.3809i	−0.454713	−	0.524767i	0.481383	−	0.876510i	$-0.340135\pi$
$751$	−12.4611	−	14.3809i	−0.454713	−	0.524767i	−0.936097	+	0.351743i	$0.885589\pi$
$752$		0			0
$753$	19.6777	+	34.5775i	0.717096	+	1.26007i
$754$		0			0
$755$	−2.80167	+	0.539977i	−0.101963	+	0.0196518i
$756$		0			0
$757$	9.08557	−	17.6236i	0.330221	−	0.640539i	−0.664019	−	0.747716i	$-0.731151\pi$
$757$	9.08557	−	17.6236i	0.330221	−	0.640539i	0.994240	+	0.107177i	$0.0341810\pi$
$758$		0			0
$759$	−12.3877	+	8.70569i	−0.449645	+	0.315996i
$760$		0			0
$761$	11.7391	+	10.1720i	0.425542	+	0.368734i	0.841143	−	0.540813i	$-0.181883\pi$
$761$	11.7391	+	10.1720i	0.425542	+	0.368734i	−0.415601	+	0.909547i	$0.636429\pi$
$762$		0			0
$763$	41.1653	+	7.93396i	1.49028	+	0.287228i
$764$		0			0
$765$	5.58427	+	8.93155i	0.201900	+	0.322921i
$766$		0			0
$767$	18.0079	−	31.1906i	0.650227	−	1.12623i
$768$		0			0
$769$	33.5752	+	1.59938i	1.21075	+	0.0576752i	0.643223	−	0.765679i	$-0.277597\pi$
$769$	33.5752	+	1.59938i	1.21075	+	0.0576752i	0.567528	+	0.823354i	$0.307900\pi$
$770$		0			0
$771$	2.16438	+	3.41432i	0.0779481	+	0.122964i
$772$		0			0
$773$	6.40397	−	6.71629i	0.230335	−	0.241568i	−0.598417	−	0.801185i	$-0.704203\pi$
$773$	6.40397	−	6.71629i	0.230335	−	0.241568i	0.828751	+	0.559617i	$0.189052\pi$
$774$		0			0
$775$	−19.3772	+	11.1874i	−0.696048	+	0.401864i
$776$		0			0
$777$	45.7864	+	11.4095i	1.64258	+	0.409314i
$778$		0			0
$779$	−24.2326	−	7.11533i	−0.868223	−	0.254933i
$780$		0			0
$781$	−13.9065	+	0.662446i	−0.497612	+	0.0237042i
$782$		0			0
$783$	2.47873	−	4.59556i	0.0885827	−	0.164232i
$784$		0			0
$785$	8.12520	+	0.775863i	0.290001	+	0.0276917i
$786$		0			0
$787$	24.0043	−	8.30797i	0.855661	−	0.296147i	0.136201	−	0.990681i	$-0.456511\pi$
$787$	24.0043	−	8.30797i	0.855661	−	0.296147i	0.719460	+	0.694534i	$0.244389\pi$
$788$		0			0
$789$	27.9601	−	1.15773i	0.995407	−	0.0412164i
$790$		0			0
$791$	−27.3229	−	28.6554i	−0.971491	−	1.01887i
$792$		0			0
$793$	23.9749	−	9.59810i	0.851373	−	0.340838i
$794$		0			0
$795$	9.54807	−	8.99141i	0.338635	−	0.318892i
$796$		0			0
$797$	−2.83359	−	29.6747i	−0.100371	−	1.05113i	−0.895611	−	0.444838i	$-0.853261\pi$
$797$	−2.83359	−	29.6747i	−0.100371	−	1.05113i	0.795240	−	0.606295i	$-0.207345\pi$
$798$		0			0
$799$	5.44468	−	37.8686i	0.192619	−	1.33969i
$800$		0			0
$801$	−8.75123	+	42.5516i	−0.309209	+	1.50349i
$802$		0			0
$803$	7.59763			0.268115
$804$		0			0
$805$	−25.6011			−0.902321
$806$		0			0
$807$	−6.99896	−	37.5695i	−0.246375	−	1.32251i
$808$		0			0
$809$	1.33584	−	9.29101i	0.0469658	−	0.326654i	−0.952771	−	0.303691i	$-0.901781\pi$
$809$	1.33584	−	9.29101i	0.0469658	−	0.326654i	0.999736	−	0.0229631i	$-0.00731003\pi$
$810$		0			0
$811$	−4.16515	−	43.6194i	−0.146258	−	1.53169i	−0.709092	−	0.705116i	$-0.750895\pi$
$811$	−4.16515	−	43.6194i	−0.146258	−	1.53169i	0.562834	−	0.826570i	$-0.309711\pi$
$812$		0			0
$813$	22.8619	+	24.2773i	0.801802	+	0.851442i
$814$		0			0
$815$	−6.42924	+	2.57388i	−0.225207	+	0.0901591i
$816$		0			0
$817$	12.4403	+	13.0471i	0.435233	+	0.456459i
$818$		0			0
$819$	9.21168	−	25.5818i	0.321882	−	0.893900i
$820$		0			0
$821$	12.8999	−	4.46471i	0.450211	−	0.155819i	−0.0925478	−	0.995708i	$-0.529501\pi$
$821$	12.8999	−	4.46471i	0.450211	−	0.155819i	0.542759	+	0.839889i	$0.317380\pi$
$822$		0			0
$823$	17.7364	+	1.69362i	0.618253	+	0.0590360i	0.399483	−	0.916740i	$-0.369190\pi$
$823$	17.7364	+	1.69362i	0.618253	+	0.0590360i	0.218770	+	0.975776i	$0.429796\pi$
$824$		0			0
$825$	8.01446	−	2.29923i	0.279028	−	0.0800491i
$826$		0			0
$827$	−13.0139	+	0.619930i	−0.452539	+	0.0215571i	−0.272614	−	0.962123i	$-0.587888\pi$
$827$	−13.0139	+	0.619930i	−0.452539	+	0.0215571i	−0.179924	+	0.983680i	$0.557585\pi$
$828$		0			0
$829$	−15.6247	−	4.58782i	−0.542667	−	0.159341i	−0.00110076	−	0.999999i	$-0.500350\pi$
$829$	−15.6247	−	4.58782i	−0.542667	−	0.159341i	−0.541567	+	0.840658i	$0.682169\pi$
$830$		0			0
$831$	2.68132	−	10.7601i	0.0930140	−	0.373265i
$832$		0			0
$833$	13.1705	−	7.60398i	0.456330	−	0.263462i
$834$		0			0
$835$	8.23969	−	8.64154i	0.285146	−	0.299053i
$836$		0			0
$837$	6.27113	−	29.5599i	0.216762	−	1.02174i
$838$		0			0
$839$	46.6955	+	2.22438i	1.61211	+	0.0767941i	0.834155	−	0.551530i	$-0.185956\pi$
$839$	46.6955	+	2.22438i	1.61211	+	0.0767941i	0.777952	+	0.628324i	$0.216259\pi$
$840$		0			0
$841$	−13.9951	+	24.2403i	−0.482590	+	0.835871i
$842$		0			0
$843$	−18.1558	+	25.1636i	−0.625318	+	0.866682i
$844$		0			0
$845$	−6.27114	−	1.20866i	−0.215734	−	0.0415793i
$846$		0			0
$847$	−24.3367	−	21.0879i	−0.836219	−	0.724588i
$848$		0			0
$849$	13.2863	+	18.9056i	0.455984	+	0.648839i
$850$		0			0
$851$	25.5539	−	49.5676i	0.875976	−	1.69916i
$852$		0			0
$853$	24.4914	−	4.72034i	0.838571	−	0.161621i	0.248155	−	0.968720i	$-0.420176\pi$
$853$	24.4914	−	4.72034i	0.838571	−	0.161621i	0.590416	+	0.807099i	$0.298964\pi$
$854$		0			0
$855$	−2.92801	−	22.3326i	−0.100136	−	0.763759i
$856$		0			0
$857$	1.11046	+	1.28154i	0.0379326	+	0.0437766i	0.774399	−	0.632698i	$-0.218052\pi$
$857$	1.11046	+	1.28154i	0.0379326	+	0.0437766i	−0.736466	+	0.676474i	$0.763507\pi$
$858$		0			0
$859$	−8.29405	−	34.1885i	−0.282989	−	1.16650i	−0.918822	−	0.394671i	$-0.870858\pi$
$859$	−8.29405	−	34.1885i	−0.282989	−	1.16650i	0.635833	−	0.771827i	$-0.280657\pi$
$860$		0			0
$861$	1.89720	+	21.2646i	0.0646563	+	0.724697i
$862$		0			0
$863$	11.5478	+	39.3283i	0.393093	+	1.33875i	0.883979	+	0.467527i	$0.154855\pi$
$863$	11.5478	+	39.3283i	0.393093	+	1.33875i	−0.490886	+	0.871224i	$0.663327\pi$
$864$		0			0
$865$	2.48593	−	6.20956i	0.0845242	−	0.211131i
$866$		0			0
$867$	7.20012	−	8.20575i	0.244529	−	0.278682i
$868$		0			0
$869$	9.61141	−	6.84426i	0.326045	−	0.232176i
$870$		0			0
$871$	7.15908	+	20.5222i	0.242576	+	0.695370i
$872$		0			0
$873$	17.0621	+	2.67010i	0.577465	+	0.0903691i
$874$		0			0
$875$	30.6360	+	10.6032i	1.03569	+	0.358455i
$876$		0			0
$877$	−25.6951	−	10.2868i	−0.867662	−	0.347359i	−0.105245	−	0.994446i	$-0.533563\pi$
$877$	−25.6951	−	10.2868i	−0.867662	−	0.347359i	−0.762416	+	0.647087i	$0.775987\pi$
$878$		0			0
$879$	0.451547	−	4.43712i	0.0152303	−	0.149660i
$880$		0			0
$881$	−8.04165	−	15.5986i	−0.270930	−	0.525531i	0.713642	−	0.700510i	$-0.247044\pi$
$881$	−8.04165	−	15.5986i	−0.270930	−	0.525531i	−0.984572	+	0.174980i	$0.944014\pi$
$882$		0			0
$883$	−15.7707	+	3.82592i	−0.530725	+	0.128753i	−0.492162	−	0.870504i	$-0.663793\pi$
$883$	−15.7707	+	3.82592i	−0.530725	+	0.128753i	−0.0385631	+	0.999256i	$0.512278\pi$
$884$		0			0
$885$	−23.8840	+	8.10040i	−0.802851	+	0.272292i
$886$		0			0
$887$	−28.9700	+	36.8384i	−0.972717	+	1.23691i	−0.00118616	+	0.999999i	$0.500378\pi$
$887$	−28.9700	+	36.8384i	−0.972717	+	1.23691i	−0.971531	+	0.236911i	$0.923865\pi$
$888$		0			0
$889$	6.15501	+	31.9352i	0.206432	+	1.07107i
$890$		0			0
$891$	−4.93096	+	10.1233i	−0.165194	+	0.339143i
$892$		0			0
$893$	−44.2277	+	68.8197i	−1.48002	+	2.30296i
$894$		0			0
$895$	5.53340	−	6.38588i	0.184961	−	0.213457i
$896$		0			0
$897$	−26.9243	−	17.5406i	−0.898975	−	0.585665i
$898$		0			0
$899$	1.37771	−	5.67898i	0.0459491	−	0.189405i
$900$		0			0
$901$	19.9785	+	11.5346i	0.665580	+	0.384273i
$902$		0			0
$903$	6.41655	−	13.8222i	0.213529	−	0.459975i
$904$		0			0
$905$	4.06848	−	5.71338i	0.135241	−	0.189919i
$906$		0			0
$907$	7.50255	+	7.15367i	0.249118	+	0.237534i	0.804341	−	0.594168i	$-0.202519\pi$
$907$	7.50255	+	7.15367i	0.249118	+	0.237534i	−0.555223	+	0.831702i	$0.687367\pi$
$908$		0			0
$909$	7.77886	−	30.4095i	0.258008	−	1.00862i
$910$		0			0
$911$	28.5137	−	4.09965i	0.944700	−	0.135827i	0.347285	−	0.937760i	$-0.387104\pi$
$911$	28.5137	−	4.09965i	0.944700	−	0.135827i	0.597415	+	0.801932i	$0.296194\pi$
$912$		0			0
$913$	−5.07995	+	17.3007i	−0.168122	+	0.572571i
$914$		0			0
$915$	−17.0522	−	6.02081i	−0.563730	−	0.199042i
$916$		0			0
$917$	−10.9141	+	8.58293i	−0.360415	+	0.283433i
$918$		0			0
$919$	−1.50413	+	15.7520i	−0.0496167	+	0.519610i	0.936163	+	0.351567i	$0.114351\pi$
$919$	−1.50413	+	15.7520i	−0.0496167	+	0.519610i	−0.985780	+	0.168043i	$0.946255\pi$
$920$		0			0
$921$	2.00903	−	37.2949i	0.0661999	−	1.22891i
$922$		0			0
$923$	−12.2746	−	26.8775i	−0.404022	−	0.884685i
$924$		0			0
$925$	−22.2257	+	21.1922i	−0.730777	+	0.696794i
$926$		0			0
$927$	−35.9718	−	14.9225i	−1.18147	−	0.490120i
$928$		0			0
$929$	−16.9192	+	37.0480i	−0.555102	+	1.21550i	0.399256	+	0.916840i	$0.369269\pi$
$929$	−16.9192	+	37.0480i	−0.555102	+	1.21550i	−0.954358	+	0.298665i	$0.903459\pi$
$930$		0			0
$931$	−32.3715	+	3.09111i	−1.06093	+	0.101307i
$932$		0			0
$933$	10.3035	−	17.5927i	0.337322	−	0.575959i
$934$		0			0
$935$	−2.37506	−	3.69566i	−0.0776726	−	0.120861i
$936$		0			0
$937$			41.4600i			1.35444i	0.735781	+	0.677220i	$0.236815\pi$
$937$			41.4600i			1.35444i	−0.735781	+	0.677220i	$0.763185\pi$
$938$		0			0
$939$	−5.43820	+	13.3430i	−0.177469	+	0.435431i
$940$		0			0
$941$	−23.7722	+	15.2775i	−0.774952	+	0.498032i	−0.867355	−	0.497690i	$-0.834182\pi$
$941$	−23.7722	+	15.2775i	−0.774952	+	0.498032i	0.0924026	+	0.995722i	$0.470545\pi$
$942$		0			0
$943$	24.9744	+	3.59078i	0.813279	+	0.116932i
$944$		0			0
$945$	−16.6636	+	9.21072i	−0.542067	+	0.299625i
$946$		0			0
$947$	1.15515	+	0.527538i	0.0375372	+	0.0171427i	0.434095	−	0.900867i	$-0.357068\pi$
$947$	1.15515	+	0.527538i	0.0375372	+	0.0171427i	−0.396558	+	0.918010i	$0.629795\pi$
$948$		0			0
$949$	5.99297	+	14.9697i	0.194540	+	0.485937i
$950$		0			0
$951$	−3.88885	−	9.89166i	−0.126104	−	0.320759i
$952$		0			0
$953$	−19.3910	+	8.85559i	−0.628137	+	0.286861i	−0.703937	−	0.710262i	$-0.748576\pi$
$953$	−19.3910	+	8.85559i	−0.628137	+	0.286861i	0.0757999	+	0.997123i	$0.475849\pi$
$954$		0			0
$955$	5.40579	+	15.6190i	0.174927	+	0.505419i
$956$		0			0
$957$	−1.00985	+	1.92928i	−0.0326437	+	0.0623649i
$958$		0			0
$959$	33.0334	+	42.0054i	1.06670	+	1.35642i
$960$		0			0
$961$	−0.134137	−	2.81589i	−0.00432701	−	0.0908351i
$962$		0			0
$963$	0.225074	−	0.126242i	0.00725292	−	0.00406808i
$964$		0			0
$965$	−1.72169	−	11.9746i	−0.0554231	−	0.385476i
$966$		0			0
$967$	21.4066	+	37.0773i	0.688390	+	1.19233i	0.972359	+	0.233493i	$0.0750155\pi$
$967$	21.4066	+	37.0773i	0.688390	+	1.19233i	−0.283969	+	0.958834i	$0.591651\pi$
$968$		0			0
$969$	36.1396	−	16.2336i	1.16097	−	0.521499i
$970$		0			0
$971$	2.70122	+	1.92353i	0.0866862	+	0.0617290i	0.622578	−	0.782558i	$-0.286085\pi$
$971$	2.70122	+	1.92353i	0.0866862	+	0.0617290i	−0.535892	+	0.844286i	$0.680025\pi$
$972$		0			0
$973$	−1.52510	+	32.0158i	−0.0488925	+	1.02638i
$974$		0			0
$975$	10.8520	+	13.9774i	0.347541	+	0.447634i
$976$		0			0
$977$	45.5433	+	11.0487i	1.45706	+	0.353479i	0.884560	−	0.466427i	$-0.154459\pi$
$977$	45.5433	+	11.0487i	1.45706	+	0.353479i	0.572499	+	0.819905i	$0.305974\pi$
$978$		0			0
$979$	3.42877	−	17.7901i	0.109584	−	0.568575i
$980$		0			0
$981$	−3.04627	−	36.7218i	−0.0972598	−	1.17244i
$982$		0			0
$983$	−18.0559	−	11.6038i	−0.575894	−	0.370105i	0.220037	−	0.975492i	$-0.429382\pi$
$983$	−18.0559	−	11.6038i	−0.575894	−	0.370105i	−0.795932	+	0.605387i	$0.793019\pi$
$984$		0			0
$985$	−12.5653	−	6.47784i	−0.400362	−	0.206401i
$986$		0			0
$987$	67.8201	+	13.5091i	2.15874	+	0.429999i
$988$		0			0
$989$	−14.1568	−	11.1331i	−0.450161	−	0.354010i
$990$		0			0
$991$	−25.7176	+	22.2844i	−0.816945	+	0.707887i	−0.959441	−	0.281908i	$-0.909033\pi$
$991$	−25.7176	+	22.2844i	−0.816945	+	0.707887i	0.142496	+	0.989795i	$0.454487\pi$
$992$		0			0
$993$	−7.89763	−	1.18567i	−0.250624	−	0.0376260i
$994$		0			0
$995$	0.943621	−	0.486471i	0.0299148	−	0.0154222i
$996$		0			0
$997$	−35.8027	+	10.5126i	−1.13388	+	0.332938i	−0.794232	−	0.607614i	$-0.792127\pi$
$997$	−35.8027	+	10.5126i	−1.13388	+	0.332938i	−0.339650	+	0.940552i	$0.610308\pi$
$998$		0			0
$999$	−1.20047	−	41.4570i	−0.0379813	−	1.31164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.1	✓	440
3.2	odd	2	inner	804.2.ba.b.41.16	yes	440
67.18	odd	66	inner	804.2.ba.b.353.16	yes	440
201.152	even	66	inner	804.2.ba.b.353.1	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.1	✓	440	1.1	even	1	trivial
804.2.ba.b.41.16	yes	440	3.2	odd	2	inner
804.2.ba.b.353.1	yes	440	201.152	even	66	inner
804.2.ba.b.353.16	yes	440	67.18	odd	66	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)

\(f(q)\)	\(=\)	\(q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +O(q^{10})\)	\(q+(-1.70276 + 0.317213i) q^{3} +(0.152781 - 1.06262i) q^{5} +(0.324444 + 3.39773i) q^{7} +(2.79875 - 1.08027i) q^{9} +(-1.16153 + 0.465006i) q^{11} +(-1.83241 - 1.92178i) q^{13} +(0.0769269 + 1.85784i) q^{15} +(-3.09077 + 1.06973i) q^{17} +(6.96190 + 0.664781i) q^{19} +(-1.63025 - 5.68258i) q^{21} +(-6.97890 + 0.332446i) q^{23} +(3.69165 + 1.08397i) q^{25} +(-4.42291 + 2.72724i) q^{27} +(-0.870238 + 0.502432i) q^{29} +(-4.01310 + 4.20882i) q^{31} +(1.83029 - 1.16024i) q^{33} +(3.66006 + 0.174350i) q^{35} +(-3.99087 + 6.91239i) q^{37} +(3.72976 + 2.69105i) q^{39} +(-3.54601 - 0.683437i) q^{41} +(1.94811 + 1.68805i) q^{43} +(-0.720320 - 3.13905i) q^{45} +(-5.36003 + 10.3970i) q^{47} +(-4.56579 + 0.879983i) q^{49} +(4.92350 - 2.80192i) q^{51} +(-4.61898 - 5.33059i) q^{53} +(0.316664 + 1.30531i) q^{55} +(-12.0653 + 1.07645i) q^{57} +(3.82125 + 13.0140i) q^{59} +(-3.61460 + 9.02884i) q^{61} +(4.57851 + 9.15891i) q^{63} +(-2.32208 + 1.65354i) q^{65} +(-7.45395 - 3.38209i) q^{67} +(11.7779 - 2.77987i) q^{69} +(10.5155 + 3.63946i) q^{71} +(-5.63753 - 2.25693i) q^{73} +(-6.62982 - 0.674690i) q^{75} +(-1.95681 - 3.79569i) q^{77} +(-9.16491 + 2.22338i) q^{79} +(6.66602 - 6.04683i) q^{81} +(8.90868 - 11.3283i) q^{83} +(0.664499 + 3.44775i) q^{85} +(1.32242 - 1.13157i) q^{87} +(-7.82886 + 12.1820i) q^{89} +(5.93517 - 6.84955i) q^{91} +(5.49823 - 8.43959i) q^{93} +(1.77006 - 7.29627i) q^{95} +(4.98536 + 2.87830i) q^{97} +(-2.74850 + 2.55620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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