LMFDB - Embedded newform 363.2.d.f.362.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(362,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("363.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.d (of order $2$, degree $1$, 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			362.3
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	363.362
Dual form			363.2.d.f.362.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17557 q^{2} +(-0.618034 - 1.61803i) q^{3} -0.618034 q^{4} -0.381966i q^{5} +(0.726543 + 1.90211i) q^{6} +3.07768i q^{7} +3.07768 q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q-1.17557 q^{2} +(-0.618034 - 1.61803i) q^{3} -0.618034 q^{4} -0.381966i q^{5} +(0.726543 + 1.90211i) q^{6} +3.07768i q^{7} +3.07768 q^{8} +(-2.23607 + 2.00000i) q^{9} +0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +0.726543i q^{13} -3.61803i q^{14} +(-0.618034 + 0.236068i) q^{15} -2.38197 q^{16} +4.25325 q^{17} +(2.62866 - 2.35114i) q^{18} +2.62866i q^{19} +0.236068i q^{20} +(4.97980 - 1.90211i) q^{21} -6.23607i q^{23} +(-1.90211 - 4.97980i) q^{24} +4.85410 q^{25} -0.854102i q^{26} +(4.61803 + 2.38197i) q^{27} -1.90211i q^{28} +2.35114 q^{29} +(0.726543 - 0.277515i) q^{30} +5.85410 q^{31} -3.35520 q^{32} -5.00000 q^{34} +1.17557 q^{35} +(1.38197 - 1.23607i) q^{36} +3.00000 q^{37} -3.09017i q^{38} +(1.17557 - 0.449028i) q^{39} -1.17557i q^{40} -0.726543 q^{41} +(-5.85410 + 2.23607i) q^{42} +6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +7.33094i q^{46} +8.32624i q^{47} +(1.47214 + 3.85410i) q^{48} -2.47214 q^{49} -5.70634 q^{50} +(-2.62866 - 6.88191i) q^{51} -0.449028i q^{52} -1.85410i q^{53} +(-5.42882 - 2.80017i) q^{54} +9.47214i q^{56} +(4.25325 - 1.62460i) q^{57} -2.76393 q^{58} -0.381966i q^{59} +(0.381966 - 0.145898i) q^{60} -2.62866i q^{61} -6.88191 q^{62} +(-6.15537 - 6.88191i) q^{63} +8.70820 q^{64} +0.277515 q^{65} +7.32624 q^{67} -2.62866 q^{68} +(-10.0902 + 3.85410i) q^{69} -1.38197 q^{70} +5.32624i q^{71} +(-6.88191 + 6.15537i) q^{72} +9.40456i q^{73} -3.52671 q^{74} +(-3.00000 - 7.85410i) q^{75} -1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +3.97574i q^{79} +0.909830i q^{80} +(1.00000 - 8.94427i) q^{81} +0.854102 q^{82} -6.32688 q^{83} +(-3.07768 + 1.17557i) q^{84} -1.62460i q^{85} -8.09017i q^{86} +(-1.45309 - 3.80423i) q^{87} +0.527864i q^{89} +(-0.898056 - 1.00406i) q^{90} -2.23607 q^{91} +3.85410i q^{92} +(-3.61803 - 9.47214i) q^{93} -9.78808i q^{94} +1.00406 q^{95} +(2.07363 + 5.42882i) q^{96} -4.38197 q^{97} +2.90617 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4	$ 8 q + 4 q^{3} + 4 q^{4} + 12 q^{12} + 4 q^{15} - 28 q^{16} + 12 q^{25} + 28 q^{27} + 20 q^{31} - 40 q^{34} + 20 q^{36} + 24 q^{37} - 20 q^{42} + 24 q^{45} - 24 q^{48} + 16 q^{49} - 40 q^{58} + 12 q^{60} + 16 q^{64} - 4 q^{67} - 36 q^{69} - 20 q^{70} - 24 q^{75} - 20 q^{78} + 8 q^{81} - 20 q^{82} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 + 12 * q^12 + 4 * q^15 - 28 * q^16 + 12 * q^25 + 28 * q^27 + 20 * q^31 - 40 * q^34 + 20 * q^36 + 24 * q^37 - 20 * q^42 + 24 * q^45 - 24 * q^48 + 16 * q^49 - 40 * q^58 + 12 * q^60 + 16 * q^64 - 4 * q^67 - 36 * q^69 - 20 * q^70 - 24 * q^75 - 20 * q^78 + 8 * q^81 - 20 * q^82 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.17557			−0.831254			−0.415627	−	0.909535i	$-0.636438\pi$
$2$	−1.17557			−0.831254			−0.415627	+	0.909535i	$0.636438\pi$
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$4$	−0.618034			−0.309017
$5$		−	0.381966i		−	0.170820i	−0.996346	−	0.0854102i	$-0.972780\pi$
$5$		−	0.381966i		−	0.170820i	0.996346	−	0.0854102i	$-0.0272201\pi$
$6$	0.726543	+	1.90211i	0.296610	+	0.776534i
$7$			3.07768i			1.16326i	0.813455	+	0.581628i	$0.197584\pi$
$7$			3.07768i			1.16326i	−0.813455	+	0.581628i	$0.802416\pi$
$8$	3.07768			1.08813
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$			0.449028i			0.141995i
$11$		0			0
$11$		0			0
$12$	0.381966	+	1.00000i	0.110264	+	0.288675i
$13$			0.726543i			0.201507i	0.994911	+	0.100753i	$0.0321253\pi$
$13$			0.726543i			0.201507i	−0.994911	+	0.100753i	$0.967875\pi$
$14$		−	3.61803i		−	0.966960i
$15$	−0.618034	+	0.236068i	−0.159576	+	0.0609525i
$16$	−2.38197			−0.595492
$17$	4.25325			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$17$	4.25325			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$18$	2.62866	−	2.35114i	0.619580	−	0.554169i
$19$			2.62866i			0.603055i	0.953457	+	0.301527i	$0.0974965\pi$
$19$			2.62866i			0.603055i	−0.953457	+	0.301527i	$0.902504\pi$
$20$			0.236068i			0.0527864i
$21$	4.97980	−	1.90211i	1.08668	−	0.415075i
$22$		0			0
$23$		−	6.23607i		−	1.30031i	−0.759802	−	0.650155i	$-0.774704\pi$
$23$		−	6.23607i		−	1.30031i	0.759802	−	0.650155i	$-0.225296\pi$
$24$	−1.90211	−	4.97980i	−0.388267	−	1.01650i
$25$	4.85410			0.970820
$26$		−	0.854102i		−	0.167503i
$27$	4.61803	+	2.38197i	0.888741	+	0.458410i
$28$		−	1.90211i		−	0.359466i
$29$	2.35114			0.436596			0.218298	−	0.975882i	$-0.429950\pi$
$29$	2.35114			0.436596			0.218298	+	0.975882i	$0.429950\pi$
$30$	0.726543	−	0.277515i	0.132648	−	0.0506670i
$31$	5.85410			1.05143			0.525714	−	0.850661i	$-0.323798\pi$
$31$	5.85410			1.05143			0.525714	+	0.850661i	$0.323798\pi$
$32$	−3.35520			−0.593121
$33$		0			0
$34$	−5.00000			−0.857493
$35$	1.17557			0.198708
$36$	1.38197	−	1.23607i	0.230328	−	0.206011i
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$		−	3.09017i		−	0.501292i
$39$	1.17557	−	0.449028i	0.188242	−	0.0719020i
$40$		−	1.17557i		−	0.185874i
$41$	−0.726543			−0.113467			−0.0567334	−	0.998389i	$-0.518069\pi$
$41$	−0.726543			−0.113467			−0.0567334	+	0.998389i	$0.518069\pi$
$42$	−5.85410	+	2.23607i	−0.903308	+	0.345033i
$43$			6.88191i			1.04948i	0.851262	+	0.524741i	$0.175838\pi$
$43$			6.88191i			1.04948i	−0.851262	+	0.524741i	$0.824162\pi$
$44$		0			0
$45$	0.763932	+	0.854102i	0.113880	+	0.127322i
$46$			7.33094i			1.08089i
$47$			8.32624i			1.21451i	0.794508	+	0.607253i	$0.207729\pi$
$47$			8.32624i			1.21451i	−0.794508	+	0.607253i	$0.792271\pi$
$48$	1.47214	+	3.85410i	0.212485	+	0.556292i
$49$	−2.47214			−0.353162
$50$	−5.70634			−0.806998
$51$	−2.62866	−	6.88191i	−0.368085	−	0.963660i
$52$		−	0.449028i		−	0.0622690i
$53$		−	1.85410i		−	0.254680i	−0.991859	−	0.127340i	$-0.959356\pi$
$53$		−	1.85410i		−	0.254680i	0.991859	−	0.127340i	$-0.0406440\pi$
$54$	−5.42882	−	2.80017i	−0.738769	−	0.381055i
$55$		0			0
$56$			9.47214i			1.26577i
$57$	4.25325	−	1.62460i	0.563357	−	0.215183i
$58$	−2.76393			−0.362922
$59$		−	0.381966i		−	0.0497277i	−0.999691	−	0.0248639i	$-0.992085\pi$
$59$		−	0.381966i		−	0.0497277i	0.999691	−	0.0248639i	$-0.00791523\pi$
$60$	0.381966	−	0.145898i	0.0493116	−	0.0188354i
$61$		−	2.62866i		−	0.336565i	−0.985739	−	0.168282i	$-0.946178\pi$
$61$		−	2.62866i		−	0.336565i	0.985739	−	0.168282i	$-0.0538221\pi$
$62$	−6.88191			−0.874003
$63$	−6.15537	−	6.88191i	−0.775503	−	0.867039i
$64$	8.70820			1.08853
$65$	0.277515			0.0344214
$66$		0			0
$67$	7.32624			0.895042			0.447521	−	0.894273i	$-0.352307\pi$
$67$	7.32624			0.895042			0.447521	+	0.894273i	$0.352307\pi$
$68$	−2.62866			−0.318771
$69$	−10.0902	+	3.85410i	−1.21471	+	0.463979i
$70$	−1.38197			−0.165177
$71$			5.32624i			0.632108i	0.948741	+	0.316054i	$0.102358\pi$
$71$			5.32624i			0.632108i	−0.948741	+	0.316054i	$0.897642\pi$
$72$	−6.88191	+	6.15537i	−0.811041	+	0.725417i
$73$			9.40456i			1.10072i	0.834927	+	0.550360i	$0.185510\pi$
$73$			9.40456i			1.10072i	−0.834927	+	0.550360i	$0.814490\pi$
$74$	−3.52671			−0.409972
$75$	−3.00000	−	7.85410i	−0.346410	−	0.906914i
$76$		−	1.62460i		−	0.186354i
$77$		0			0
$78$	−1.38197	+	0.527864i	−0.156477	+	0.0597688i
$79$			3.97574i			0.447306i	0.974669	+	0.223653i	$0.0717982\pi$
$79$			3.97574i			0.447306i	−0.974669	+	0.223653i	$0.928202\pi$
$80$			0.909830i			0.101722i
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$	0.854102			0.0943198
$83$	−6.32688			−0.694465			−0.347233	−	0.937779i	$-0.612879\pi$
$83$	−6.32688			−0.694465			−0.347233	+	0.937779i	$0.612879\pi$
$84$	−3.07768	+	1.17557i	−0.335803	+	0.128265i
$85$		−	1.62460i		−	0.176212i
$86$		−	8.09017i		−	0.872385i
$87$	−1.45309	−	3.80423i	−0.155787	−	0.407856i
$88$		0			0
$89$			0.527864i			0.0559535i	0.999609	+	0.0279767i	$0.00890643\pi$
$89$			0.527864i			0.0559535i	−0.999609	+	0.0279767i	$0.991094\pi$
$90$	−0.898056	−	1.00406i	−0.0946634	−	0.105837i
$91$	−2.23607			−0.234404
$92$			3.85410i			0.401818i
$93$	−3.61803	−	9.47214i	−0.375173	−	0.982215i
$94$		−	9.78808i		−	1.00956i
$95$	1.00406			0.103014
$96$	2.07363	+	5.42882i	0.211639	+	0.554077i
$97$	−4.38197			−0.444921			−0.222461	−	0.974942i	$-0.571409\pi$
$97$	−4.38197			−0.444921			−0.222461	+	0.974942i	$0.571409\pi$
$98$	2.90617			0.293568
$99$		0			0
$100$	−3.00000			−0.300000
$101$	15.9434			1.58643			0.793216	−	0.608940i	$-0.208405\pi$
$101$	15.9434			1.58643			0.793216	+	0.608940i	$0.208405\pi$
$102$	3.09017	+	8.09017i	0.305972	+	0.801046i
$103$	−11.2361			−1.10712			−0.553561	−	0.832808i	$-0.686732\pi$
$103$	−11.2361			−1.10712			−0.553561	+	0.832808i	$0.686732\pi$
$104$			2.23607i			0.219265i
$105$	−0.726543	−	1.90211i	−0.0709033	−	0.185627i
$106$			2.17963i			0.211704i
$107$	−13.0373			−1.26036			−0.630181	−	0.776449i	$-0.717019\pi$
$107$	−13.0373			−1.26036			−0.630181	+	0.776449i	$0.717019\pi$
$108$	−2.85410	−	1.47214i	−0.274636	−	0.141656i
$109$		−	4.70228i		−	0.450397i	−0.974313	−	0.225198i	$-0.927697\pi$
$109$		−	4.70228i		−	0.450397i	0.974313	−	0.225198i	$-0.0723030\pi$
$110$		0			0
$111$	−1.85410	−	4.85410i	−0.175984	−	0.460731i
$112$		−	7.33094i		−	0.692708i
$113$			2.05573i			0.193387i	0.995314	+	0.0966933i	$0.0308266\pi$
$113$			2.05573i			0.193387i	−0.995314	+	0.0966933i	$0.969173\pi$
$114$	−5.00000	+	1.90983i	−0.468293	+	0.178872i
$115$	−2.38197			−0.222119
$116$	−1.45309			−0.134916
$117$	−1.45309	−	1.62460i	−0.134338	−	0.150194i
$118$			0.449028i			0.0413364i
$119$			13.0902i			1.19997i
$120$	−1.90211	+	0.726543i	−0.173638	+	0.0663240i
$121$		0			0
$122$			3.09017i			0.279771i
$123$	0.449028	+	1.17557i	0.0404875	+	0.105998i
$124$	−3.61803			−0.324909
$125$		−	3.76393i		−	0.336656i
$126$	7.23607	+	8.09017i	0.644640	+	0.720730i
$127$			12.8658i			1.14165i	0.821071	+	0.570826i	$0.193377\pi$
$127$			12.8658i			1.14165i	−0.821071	+	0.570826i	$0.806623\pi$
$128$	−3.52671			−0.311720
$129$	11.1352	−	4.25325i	0.980396	−	0.374478i
$130$	−0.326238			−0.0286130
$131$	10.4086			0.909405			0.454703	−	0.890643i	$-0.349746\pi$
$131$	10.4086			0.909405			0.454703	+	0.890643i	$0.349746\pi$
$132$		0			0
$133$	−8.09017			−0.701507
$134$	−8.61251			−0.744007
$135$	0.909830	−	1.76393i	0.0783057	−	0.151815i
$136$	13.0902			1.12247
$137$		−	4.70820i		−	0.402249i	−0.979566	−	0.201125i	$-0.935540\pi$
$137$		−	4.70820i		−	0.402249i	0.979566	−	0.201125i	$-0.0644596\pi$
$138$	11.8617	−	4.53077i	1.00974	−	0.385685i
$139$		−	14.2128i		−	1.20552i	−0.797923	−	0.602759i	$-0.794068\pi$
$139$		−	14.2128i		−	1.20552i	0.797923	−	0.602759i	$-0.205932\pi$
$140$	−0.726543			−0.0614041
$141$	13.4721	−	5.14590i	1.13456	−	0.433363i
$142$		−	6.26137i		−	0.525442i
$143$		0			0
$144$	5.32624	−	4.76393i	0.443853	−	0.396994i
$145$		−	0.898056i		−	0.0745795i
$146$		−	11.0557i		−	0.914979i
$147$	1.52786	+	4.00000i	0.126016	+	0.329914i
$148$	−1.85410			−0.152406
$149$	13.0373			1.06806			0.534028	−	0.845467i	$-0.320678\pi$
$149$	13.0373			1.06806			0.534028	+	0.845467i	$0.320678\pi$
$150$	3.52671	+	9.23305i	0.287955	+	0.753875i
$151$			5.60034i			0.455749i	0.973691	+	0.227875i	$0.0731776\pi$
$151$			5.60034i			0.455749i	−0.973691	+	0.227875i	$0.926822\pi$
$152$			8.09017i			0.656199i
$153$	−9.51057	+	8.50651i	−0.768884	+	0.687710i
$154$		0			0
$155$		−	2.23607i		−	0.179605i
$156$	−0.726543	+	0.277515i	−0.0581700	+	0.0222189i
$157$	9.70820			0.774799			0.387400	−	0.921912i	$-0.373373\pi$
$157$	9.70820			0.774799			0.387400	+	0.921912i	$0.373373\pi$
$158$		−	4.67376i		−	0.371825i
$159$	−3.00000	+	1.14590i	−0.237915	+	0.0908756i
$160$			1.28157i			0.101317i
$161$	19.1926			1.51259
$162$	−1.17557	+	10.5146i	−0.0923615	+	0.826107i
$163$	−14.6180			−1.14497			−0.572486	−	0.819914i	$-0.694021\pi$
$163$	−14.6180			−1.14497			−0.572486	+	0.819914i	$0.694021\pi$
$164$	0.449028			0.0350632
$165$		0			0
$166$	7.43769			0.577277
$167$	−21.0948			−1.63236			−0.816181	−	0.577797i	$-0.803913\pi$
$167$	−21.0948			−1.63236			−0.816181	+	0.577797i	$0.803913\pi$
$168$	15.3262	−	5.85410i	1.18244	−	0.451654i
$169$	12.4721			0.959395
$170$			1.90983i			0.146477i
$171$	−5.25731	−	5.87785i	−0.402037	−	0.449491i
$172$		−	4.25325i		−	0.324308i
$173$	23.1029			1.75648			0.878239	−	0.478221i	$-0.158718\pi$
$173$	23.1029			1.75648			0.878239	+	0.478221i	$0.158718\pi$
$174$	1.70820	+	4.47214i	0.129499	+	0.339032i
$175$			14.9394i			1.12931i
$176$		0			0
$177$	−0.618034	+	0.236068i	−0.0464543	+	0.0177440i
$178$		−	0.620541i		−	0.0465115i
$179$		−	13.9443i		−	1.04224i	−0.853482	−	0.521122i	$-0.825514\pi$
$179$		−	13.9443i		−	1.04224i	0.853482	−	0.521122i	$-0.174486\pi$
$180$	−0.472136	−	0.527864i	−0.0351909	−	0.0393447i
$181$	7.76393			0.577089			0.288544	−	0.957467i	$-0.406829\pi$
$181$	7.76393			0.577089			0.288544	+	0.957467i	$0.406829\pi$
$182$	2.62866			0.194849
$183$	−4.25325	+	1.62460i	−0.314410	+	0.120094i
$184$		−	19.1926i		−	1.41490i
$185$		−	1.14590i		−	0.0842481i
$186$	4.25325	+	11.1352i	0.311864	+	0.816470i
$187$		0			0
$188$		−	5.14590i		−	0.375303i
$189$	−7.33094	+	14.2128i	−0.533247	+	1.03383i
$190$	−1.18034			−0.0856309
$191$			24.2361i			1.75366i	0.480800	+	0.876830i	$0.340346\pi$
$191$			24.2361i			1.75366i	−0.480800	+	0.876830i	$0.659654\pi$
$192$	−5.38197	−	14.0902i	−0.388410	−	1.01687i
$193$			9.85359i			0.709277i	0.935003	+	0.354639i	$0.115396\pi$
$193$			9.85359i			0.709277i	−0.935003	+	0.354639i	$0.884604\pi$
$194$	5.15131			0.369843
$195$	−0.171513	−	0.449028i	−0.0122823	−	0.0321556i
$196$	1.52786			0.109133
$197$	−8.61251			−0.613616			−0.306808	−	0.951771i	$-0.599261\pi$
$197$	−8.61251			−0.613616			−0.306808	+	0.951771i	$0.599261\pi$
$198$		0			0
$199$	2.23607			0.158511			0.0792553	−	0.996854i	$-0.474746\pi$
$199$	2.23607			0.158511			0.0792553	+	0.996854i	$0.474746\pi$
$200$	14.9394			1.05637
$201$	−4.52786	−	11.8541i	−0.319371	−	0.836124i
$202$	−18.7426			−1.31873
$203$			7.23607i			0.507872i
$204$	1.62460	+	4.25325i	0.113745	+	0.297787i
$205$			0.277515i			0.0193825i
$206$	13.2088			0.920300
$207$	12.4721	+	13.9443i	0.866873	+	0.969194i
$208$		−	1.73060i		−	0.119995i
$209$		0			0
$210$	0.854102	+	2.23607i	0.0589386	+	0.154303i
$211$		−	19.4702i		−	1.34038i	−0.742189	−	0.670190i	$-0.766212\pi$
$211$		−	19.4702i		−	1.34038i	0.742189	−	0.670190i	$-0.233788\pi$
$212$			1.14590i			0.0787006i
$213$	8.61803	−	3.29180i	0.590498	−	0.225550i
$214$	15.3262			1.04768
$215$	2.62866			0.179273
$216$	14.2128	+	7.33094i	0.967062	+	0.498807i
$217$			18.0171i			1.22308i
$218$			5.52786i			0.374394i
$219$	15.2169	−	5.81234i	1.02826	−	0.392762i
$220$		0			0
$221$			3.09017i			0.207867i
$222$	2.17963	+	5.70634i	0.146287	+	0.382984i
$223$	1.76393			0.118122			0.0590608	−	0.998254i	$-0.481189\pi$
$223$	1.76393			0.118122			0.0590608	+	0.998254i	$0.481189\pi$
$224$		−	10.3262i		−	0.689951i
$225$	−10.8541	+	9.70820i	−0.723607	+	0.647214i
$226$		−	2.41665i		−	0.160753i
$227$	−14.4904			−0.961759			−0.480880	−	0.876787i	$-0.659683\pi$
$227$	−14.4904			−0.961759			−0.480880	+	0.876787i	$0.659683\pi$
$228$	−2.62866	+	1.00406i	−0.174087	+	0.0664953i
$229$	−15.1246			−0.999462			−0.499731	−	0.866181i	$-0.666568\pi$
$229$	−15.1246			−0.999462			−0.499731	+	0.866181i	$0.666568\pi$
$230$	2.80017			0.184638
$231$		0			0
$232$	7.23607			0.475071
$233$	−9.68208			−0.634294			−0.317147	−	0.948376i	$-0.602725\pi$
$233$	−9.68208			−0.634294			−0.317147	+	0.948376i	$0.602725\pi$
$234$	1.70820	+	1.90983i	0.111669	+	0.124849i
$235$	3.18034			0.207462
$236$			0.236068i			0.0153667i
$237$	6.43288	−	2.45714i	0.417861	−	0.159609i
$238$		−	15.3884i		−	0.997483i
$239$	−7.71445			−0.499006			−0.249503	−	0.968374i	$-0.580267\pi$
$239$	−7.71445			−0.499006			−0.249503	+	0.968374i	$0.580267\pi$
$240$	1.47214	−	0.562306i	0.0950260	−	0.0362967i
$241$		−	27.8707i		−	1.79531i	−0.440702	−	0.897654i	$-0.645270\pi$
$241$		−	27.8707i		−	1.79531i	0.440702	−	0.897654i	$-0.354730\pi$
$242$		0			0
$243$	−15.0902	+	3.90983i	−0.968035	+	0.250816i
$244$			1.62460i			0.104004i
$245$			0.944272i			0.0603273i
$246$	−0.527864	−	1.38197i	−0.0336554	−	0.0881109i
$247$	−1.90983			−0.121520
$248$	18.0171			1.14409
$249$	3.91023	+	10.2371i	0.247801	+	0.648750i
$250$			4.42477i			0.279847i
$251$		−	20.3262i		−	1.28298i	−0.767131	−	0.641490i	$-0.778316\pi$
$251$		−	20.3262i		−	1.28298i	0.767131	−	0.641490i	$-0.221684\pi$
$252$	3.80423	+	4.25325i	0.239644	+	0.267930i
$253$		0			0
$254$		−	15.1246i		−	0.949003i
$255$	−2.62866	+	1.00406i	−0.164613	+	0.0628765i
$256$	−13.2705			−0.829407
$257$		−	22.2705i		−	1.38920i	−0.719398	−	0.694598i	$-0.755582\pi$
$257$		−	22.2705i		−	1.38920i	0.719398	−	0.694598i	$-0.244418\pi$
$258$	−13.0902	+	5.00000i	−0.814958	+	0.311286i
$259$			9.23305i			0.573714i
$260$	−0.171513			−0.0106368
$261$	−5.25731	+	4.70228i	−0.325419	+	0.291064i
$262$	−12.2361			−0.755947
$263$	−9.12705			−0.562798			−0.281399	−	0.959591i	$-0.590798\pi$
$263$	−9.12705			−0.562798			−0.281399	+	0.959591i	$0.590798\pi$
$264$		0			0
$265$	−0.708204			−0.0435046
$266$	9.51057			0.583130
$267$	0.854102	−	0.326238i	0.0522702	−	0.0199654i
$268$	−4.52786			−0.276583
$269$		−	18.7639i		−	1.14406i	−0.820234	−	0.572029i	$-0.806157\pi$
$269$		−	18.7639i		−	1.14406i	0.820234	−	0.572029i	$-0.193843\pi$
$270$	−1.06957	+	2.07363i	−0.0650919	+	0.126197i
$271$			16.9475i			1.02949i	0.857344	+	0.514744i	$0.172113\pi$
$271$			16.9475i			1.02949i	−0.857344	+	0.514744i	$0.827887\pi$
$272$	−10.1311			−0.614289
$273$	1.38197	+	3.61803i	0.0836404	+	0.218973i
$274$			5.53483i			0.334371i
$275$		0			0
$276$	6.23607	−	2.38197i	0.375367	−	0.143378i
$277$		−	16.2210i		−	0.974623i	−0.873228	−	0.487312i	$-0.837978\pi$
$277$		−	16.2210i		−	0.974623i	0.873228	−	0.487312i	$-0.162022\pi$
$278$			16.7082i			1.00209i
$279$	−13.0902	+	11.7082i	−0.783688	+	0.700952i
$280$	3.61803			0.216219
$281$	−26.6296			−1.58859			−0.794294	−	0.607534i	$-0.792159\pi$
$281$	−26.6296			−1.58859			−0.794294	+	0.607534i	$0.792159\pi$
$282$	−15.8374	+	6.04937i	−0.943106	+	0.360234i
$283$		−	21.3723i		−	1.27045i	−0.772327	−	0.635225i	$-0.780907\pi$
$283$		−	21.3723i		−	1.27045i	0.772327	−	0.635225i	$-0.219093\pi$
$284$		−	3.29180i		−	0.195332i
$285$	−0.620541	−	1.62460i	−0.0367577	−	0.0962329i
$286$		0			0
$287$		−	2.23607i		−	0.131991i
$288$	7.50245	−	6.71040i	0.442086	−	0.395414i
$289$	1.09017			0.0641276
$290$			1.05573i			0.0619945i
$291$	2.70820	+	7.09017i	0.158758	+	0.415633i
$292$		−	5.81234i		−	0.340141i
$293$	−13.9353			−0.814111			−0.407055	−	0.913403i	$-0.633444\pi$
$293$	−13.9353			−0.814111			−0.407055	+	0.913403i	$0.633444\pi$
$294$	−1.79611	−	4.70228i	−0.104751	−	0.274243i
$295$	−0.145898			−0.00849451
$296$	9.23305			0.536660
$297$		0			0
$298$	−15.3262			−0.887825
$299$	4.53077			0.262021
$300$	1.85410	+	4.85410i	0.107047	+	0.280252i
$301$	−21.1803			−1.22081
$302$		−	6.58359i		−	0.378843i
$303$	−9.85359	−	25.7970i	−0.566074	−	1.48200i
$304$		−	6.26137i		−	0.359114i
$305$	−1.00406			−0.0574921
$306$	11.1803	−	10.0000i	0.639137	−	0.571662i
$307$		−	9.51057i		−	0.542797i	−0.962467	−	0.271398i	$-0.912514\pi$
$307$		−	9.51057i		−	0.542797i	0.962467	−	0.271398i	$-0.0874861\pi$
$308$		0			0
$309$	6.94427	+	18.1803i	0.395046	+	1.03424i
$310$			2.62866i			0.149298i
$311$			5.00000i			0.283524i	0.989901	+	0.141762i	$0.0452768\pi$
$311$			5.00000i			0.283524i	−0.989901	+	0.141762i	$0.954723\pi$
$312$	3.61803	−	1.38197i	0.204831	−	0.0782384i
$313$	11.0000			0.621757			0.310878	−	0.950450i	$-0.399377\pi$
$313$	11.0000			0.621757			0.310878	+	0.950450i	$0.399377\pi$
$314$	−11.4127			−0.644055
$315$	−2.62866	+	2.35114i	−0.148108	+	0.132472i
$316$		−	2.45714i		−	0.138225i
$317$			4.23607i			0.237921i	0.992899	+	0.118961i	$0.0379562\pi$
$317$			4.23607i			0.237921i	−0.992899	+	0.118961i	$0.962044\pi$
$318$	3.52671	−	1.34708i	0.197768	−	0.0755407i
$319$		0			0
$320$		−	3.32624i		−	0.185942i
$321$	8.05748	+	21.0948i	0.449725	+	1.17739i
$322$	−22.5623			−1.25735
$323$			11.1803i			0.622091i
$324$	−0.618034	+	5.52786i	−0.0343352	+	0.307104i
$325$			3.52671i			0.195627i
$326$	17.1845			0.951763
$327$	−7.60845	+	2.90617i	−0.420748	+	0.160712i
$328$	−2.23607			−0.123466
$329$	−25.6255			−1.41278
$330$		0			0
$331$	12.8885			0.708418			0.354209	−	0.935166i	$-0.384750\pi$
$331$	12.8885			0.708418			0.354209	+	0.935166i	$0.384750\pi$
$332$	3.91023			0.214602
$333$	−6.70820	+	6.00000i	−0.367607	+	0.328798i
$334$	24.7984			1.35691
$335$		−	2.79837i		−	0.152891i
$336$	−11.8617	+	4.53077i	−0.647109	+	0.247174i
$337$		−	25.1765i		−	1.37145i	−0.727860	−	0.685726i	$-0.759485\pi$
$337$		−	25.1765i		−	1.37145i	0.727860	−	0.685726i	$-0.240515\pi$
$338$	−14.6619			−0.797501
$339$	3.32624	−	1.27051i	0.180656	−	0.0690046i
$340$			1.00406i			0.0544526i
$341$		0			0
$342$	6.18034	+	6.90983i	0.334195	+	0.373641i
$343$			13.9353i			0.752437i
$344$			21.1803i			1.14197i
$345$	1.47214	+	3.85410i	0.0792571	+	0.207498i
$346$	−27.1591			−1.46008
$347$	−7.26543			−0.390028			−0.195014	−	0.980800i	$-0.562475\pi$
$347$	−7.26543			−0.390028			−0.195014	+	0.980800i	$0.562475\pi$
$348$	0.898056	+	2.35114i	0.0481409	+	0.126034i
$349$			13.5923i			0.727579i	0.931481	+	0.363790i	$0.118517\pi$
$349$			13.5923i			0.727579i	−0.931481	+	0.363790i	$0.881483\pi$
$350$		−	17.5623i		−	0.938745i
$351$	−1.73060	+	3.35520i	−0.0923726	+	0.179087i
$352$		0			0
$353$			33.5967i			1.78817i	0.447893	+	0.894087i	$0.352175\pi$
$353$			33.5967i			1.78817i	−0.447893	+	0.894087i	$0.647825\pi$
$354$	0.726543	−	0.277515i	0.0386153	−	0.0147497i
$355$	2.03444			0.107977
$356$		−	0.326238i		−	0.0172906i
$357$	21.1803	−	8.09017i	1.12098	−	0.428177i
$358$			16.3925i			0.866369i
$359$	−31.8869			−1.68293			−0.841463	−	0.540315i	$-0.818305\pi$
$359$	−31.8869			−1.68293			−0.841463	+	0.540315i	$0.818305\pi$
$360$	2.35114	+	2.62866i	0.123916	+	0.138542i
$361$	12.0902			0.636325
$362$	−9.12705			−0.479707
$363$		0			0
$364$	1.38197			0.0724347
$365$	3.59222			0.188026
$366$	5.00000	−	1.90983i	0.261354	−	0.0998284i
$367$	23.9787			1.25168			0.625839	−	0.779952i	$-0.284757\pi$
$367$	23.9787			1.25168			0.625839	+	0.779952i	$0.284757\pi$
$368$			14.8541i			0.774324i
$369$	1.62460	−	1.45309i	0.0845732	−	0.0756446i
$370$			1.34708i			0.0700316i
$371$	5.70634			0.296258
$372$	2.23607	+	5.85410i	0.115935	+	0.303521i
$373$			27.3561i			1.41645i	0.705989	+	0.708223i	$0.250503\pi$
$373$			27.3561i			1.41645i	−0.705989	+	0.708223i	$0.749497\pi$
$374$		0			0
$375$	−6.09017	+	2.32624i	−0.314495	+	0.120126i
$376$			25.6255i			1.32154i
$377$			1.70820i			0.0879770i
$378$	8.61803	−	16.7082i	0.443264	−	0.859377i
$379$	2.88854			0.148375			0.0741873	−	0.997244i	$-0.476364\pi$
$379$	2.88854			0.148375			0.0741873	+	0.997244i	$0.476364\pi$
$380$	−0.620541			−0.0318331
$381$	20.8172	−	7.95148i	1.06650	−	0.407367i
$382$		−	28.4912i		−	1.45774i
$383$		−	12.4164i		−	0.634449i	−0.948351	−	0.317224i	$-0.897249\pi$
$383$		−	12.4164i		−	0.634449i	0.948351	−	0.317224i	$-0.102751\pi$
$384$	2.17963	+	5.70634i	0.111229	+	0.291200i
$385$		0			0
$386$		−	11.5836i		−	0.589589i
$387$	−13.7638	−	15.3884i	−0.699654	−	0.782237i
$388$	2.70820			0.137488
$389$		−	7.38197i		−	0.374281i	−0.982333	−	0.187140i	$-0.940078\pi$
$389$		−	7.38197i		−	0.374281i	0.982333	−	0.187140i	$-0.0599219\pi$
$390$	0.201626	+	0.527864i	0.0102097	+	0.0267294i
$391$		−	26.5236i		−	1.34136i
$392$	−7.60845			−0.384285
$393$	−6.43288	−	16.8415i	−0.324496	−	0.849541i
$394$	10.1246			0.510071
$395$	1.51860			0.0764089
$396$		0			0
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	−2.62866			−0.131763
$399$	5.00000	+	13.0902i	0.250313	+	0.655328i
$400$	−11.5623			−0.578115
$401$			27.8541i			1.39097i	0.718542	+	0.695484i	$0.244810\pi$
$401$			27.8541i			1.39097i	−0.718542	+	0.695484i	$0.755190\pi$
$402$	5.32282	+	13.9353i	0.265478	+	0.695031i
$403$			4.25325i			0.211870i
$404$	−9.85359			−0.490235
$405$	−3.41641	−	0.381966i	−0.169763	−	0.0189800i
$406$		−	8.50651i		−	0.422171i
$407$		0			0
$408$	−8.09017	−	21.1803i	−0.400523	−	1.04858i
$409$		−	21.1603i		−	1.04631i	−0.852238	−	0.523154i	$-0.824755\pi$
$409$		−	21.1603i		−	1.04631i	0.852238	−	0.523154i	$-0.175245\pi$
$410$		−	0.326238i		−	0.0161117i
$411$	−7.61803	+	2.90983i	−0.375770	+	0.143531i
$412$	6.94427			0.342120
$413$	1.17557			0.0578460
$414$	−14.6619	−	16.3925i	−0.720592	−	0.805646i
$415$			2.41665i			0.118629i
$416$		−	2.43769i		−	0.119518i
$417$	−22.9969	+	8.78402i	−1.12616	+	0.430155i
$418$		0			0
$419$		−	0.854102i		−	0.0417256i	−0.999782	−	0.0208628i	$-0.993359\pi$
$419$		−	0.854102i		−	0.0417256i	0.999782	−	0.0208628i	$-0.00664132\pi$
$420$	0.449028	+	1.17557i	0.0219103	+	0.0573620i
$421$	19.1459			0.933114			0.466557	−	0.884491i	$-0.345494\pi$
$421$	19.1459			0.933114			0.466557	+	0.884491i	$0.345494\pi$
$422$			22.8885i			1.11420i
$423$	−16.6525	−	18.6180i	−0.809671	−	0.905240i
$424$		−	5.70634i		−	0.277124i
$425$	20.6457			1.00146
$426$	−10.1311	+	3.86974i	−0.490854	+	0.187489i
$427$	8.09017			0.391511
$428$	8.05748			0.389473
$429$		0			0
$430$	−3.09017			−0.149021
$431$	6.04937			0.291388			0.145694	−	0.989330i	$-0.453459\pi$
$431$	6.04937			0.291388			0.145694	+	0.989330i	$0.453459\pi$
$432$	−11.0000	−	5.67376i	−0.529238	−	0.272979i
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$		−	21.1803i		−	1.01669i
$435$	−1.45309	+	0.555029i	−0.0696701	+	0.0266116i
$436$			2.90617i			0.139180i
$437$	16.3925			0.784158
$438$	−17.8885	+	6.83282i	−0.854748	+	0.326485i
$439$		−	2.73466i		−	0.130518i	−0.997868	−	0.0652590i	$-0.979213\pi$
$439$		−	2.73466i		−	0.130518i	0.997868	−	0.0652590i	$-0.0207874\pi$
$440$		0			0
$441$	5.52786	−	4.94427i	0.263232	−	0.235442i
$442$		−	3.63271i		−	0.172791i
$443$		−	1.52786i		−	0.0725910i	−0.999341	−	0.0362955i	$-0.988444\pi$
$443$		−	1.52786i		−	0.0725910i	0.999341	−	0.0362955i	$-0.0115558\pi$
$444$	1.14590	+	3.00000i	0.0543819	+	0.142374i
$445$	0.201626			0.00955799
$446$	−2.07363			−0.0981891
$447$	−8.05748	−	21.0948i	−0.381106	−	0.997748i
$448$			26.8011i			1.26623i
$449$			27.8885i			1.31614i	0.752956	+	0.658071i	$0.228627\pi$
$449$			27.8885i			1.31614i	−0.752956	+	0.658071i	$0.771373\pi$
$450$	12.7598	−	11.4127i	0.601501	−	0.537999i
$451$		0			0
$452$		−	1.27051i		−	0.0597598i
$453$	9.06154	−	3.46120i	0.425748	−	0.162621i
$454$	17.0344			0.799466
$455$			0.854102i			0.0400409i
$456$	13.0902	−	5.00000i	0.613003	−	0.234146i
$457$		−	25.0705i		−	1.17275i	−0.810040	−	0.586374i	$-0.800555\pi$
$457$		−	25.0705i		−	1.17275i	0.810040	−	0.586374i	$-0.199445\pi$
$458$	17.7800			0.830807
$459$	19.6417	+	10.1311i	0.916795	+	0.472880i
$460$	1.47214			0.0686387
$461$	30.7113			1.43037			0.715184	−	0.698936i	$-0.246343\pi$
$461$	30.7113			1.43037			0.715184	+	0.698936i	$0.246343\pi$
$462$		0			0
$463$	33.2705			1.54621			0.773106	−	0.634277i	$-0.218702\pi$
$463$	33.2705			1.54621			0.773106	+	0.634277i	$0.218702\pi$
$464$	−5.60034			−0.259989
$465$	−3.61803	+	1.38197i	−0.167782	+	0.0640871i
$466$	11.3820			0.527259
$467$		−	7.65248i		−	0.354114i	−0.984201	−	0.177057i	$-0.943342\pi$
$467$		−	7.65248i		−	0.354114i	0.984201	−	0.177057i	$-0.0566578\pi$
$468$	0.898056	+	1.00406i	0.0415127	+	0.0464126i
$469$			22.5478i			1.04116i
$470$	−3.73871			−0.172454
$471$	−6.00000	−	15.7082i	−0.276465	−	0.723796i
$472$		−	1.17557i		−	0.0541100i
$473$		0			0
$474$	−7.56231	+	2.88854i	−0.347348	+	0.132675i
$475$			12.7598i			0.585458i
$476$		−	8.09017i		−	0.370812i
$477$	3.70820	+	4.14590i	0.169787	+	0.189828i
$478$	9.06888			0.414801
$479$	20.0252			0.914974			0.457487	−	0.889216i	$-0.348750\pi$
$479$	20.0252			0.914974			0.457487	+	0.889216i	$0.348750\pi$
$480$	2.07363	−	0.792055i	0.0946477	−	0.0361522i
$481$			2.17963i			0.0993825i
$482$			32.7639i			1.49236i
$483$	−11.8617	−	31.0543i	−0.539726	−	1.41302i
$484$		0			0
$485$			1.67376i			0.0760016i
$486$	17.7396	−	4.59628i	0.804683	−	0.208492i
$487$	1.47214			0.0667088			0.0333544	−	0.999444i	$-0.489381\pi$
$487$	1.47214			0.0667088			0.0333544	+	0.999444i	$0.489381\pi$
$488$		−	8.09017i		−	0.366225i
$489$	9.03444	+	23.6525i	0.408552	+	1.06960i
$490$		−	1.11006i		−	0.0501473i
$491$	17.6740			0.797619			0.398809	−	0.917034i	$-0.369424\pi$
$491$	17.6740			0.797619			0.398809	+	0.917034i	$0.369424\pi$
$492$	−0.277515	−	0.726543i	−0.0125113	−	0.0327551i
$493$	10.0000			0.450377
$494$	2.24514			0.101014
$495$		0			0
$496$	−13.9443			−0.626116
$497$	−16.3925			−0.735303
$498$	−4.59675	−	12.0344i	−0.205985	−	0.539276i
$499$	−35.9787			−1.61063			−0.805314	−	0.592848i	$-0.798003\pi$
$499$	−35.9787			−1.61063			−0.805314	+	0.592848i	$0.798003\pi$
$500$			2.32624i			0.104033i
$501$	13.0373	+	34.1320i	0.582463	+	1.52491i
$502$			23.8949i			1.06648i
$503$	−8.50651			−0.379286			−0.189643	−	0.981853i	$-0.560733\pi$
$503$	−8.50651			−0.379286			−0.189643	+	0.981853i	$0.560733\pi$
$504$	−18.9443	−	21.1803i	−0.843845	−	0.943447i
$505$		−	6.08985i		−	0.270995i
$506$		0			0
$507$	−7.70820	−	20.1803i	−0.342333	−	0.896240i
$508$		−	7.95148i		−	0.352790i
$509$		−	33.2705i		−	1.47469i	−0.675517	−	0.737345i	$-0.736079\pi$
$509$		−	33.2705i		−	1.47469i	0.675517	−	0.737345i	$-0.263921\pi$
$510$	3.09017	−	1.18034i	0.136835	−	0.0522663i
$511$	−28.9443			−1.28042
$512$	22.6538			1.00117
$513$	−6.26137	+	12.1392i	−0.276446	+	0.535960i
$514$			26.1806i			1.15477i
$515$			4.29180i			0.189119i
$516$	−6.88191	+	2.62866i	−0.302959	+	0.115720i
$517$		0			0
$518$		−	10.8541i		−	0.476902i
$519$	−14.2784	−	37.3812i	−0.626750	−	1.64085i
$520$	0.854102			0.0374548
$521$		−	33.7082i		−	1.47678i	−0.674372	−	0.738392i	$-0.735586\pi$
$521$		−	33.7082i		−	1.47678i	0.674372	−	0.738392i	$-0.264414\pi$
$522$	6.18034	−	5.52786i	0.270506	−	0.241948i
$523$			20.3682i			0.890640i	0.895372	+	0.445320i	$0.146910\pi$
$523$			20.3682i			0.890640i	−0.895372	+	0.445320i	$0.853090\pi$
$524$	−6.43288			−0.281022
$525$	24.1724	−	9.23305i	1.05497	−	0.402963i
$526$	10.7295			0.467828
$527$	24.8990			1.08462
$528$		0			0
$529$	−15.8885			−0.690806
$530$	0.832544			0.0361634
$531$	0.763932	+	0.854102i	0.0331518	+	0.0370649i
$532$	5.00000			0.216777
$533$		−	0.527864i		−	0.0228643i
$534$	−1.00406	+	0.383516i	−0.0434498	+	0.0165963i
$535$			4.97980i			0.215295i
$536$	22.5478			0.973918
$537$	−22.5623	+	8.61803i	−0.973635	+	0.371896i
$538$			22.0583i			0.951002i
$539$		0			0
$540$	−0.562306	+	1.09017i	−0.0241978	+	0.0469134i
$541$			15.2824i			0.657042i	0.944497	+	0.328521i	$0.106550\pi$
$541$			15.2824i			0.657042i	−0.944497	+	0.328521i	$0.893450\pi$
$542$		−	19.9230i		−	0.855766i
$543$	−4.79837	−	12.5623i	−0.205918	−	0.539100i
$544$	−14.2705			−0.611843
$545$	−1.79611			−0.0769370
$546$	−1.62460	−	4.25325i	−0.0695264	−	0.182022i
$547$		−	26.8666i		−	1.14873i	−0.818598	−	0.574367i	$-0.805248\pi$
$547$		−	26.8666i		−	1.14873i	0.818598	−	0.574367i	$-0.194752\pi$
$548$			2.90983i			0.124302i
$549$	5.25731	+	5.87785i	0.224377	+	0.250861i
$550$		0			0
$551$			6.18034i			0.263291i
$552$	−31.0543	+	11.8617i	−1.32176	+	0.504868i
$553$	−12.2361			−0.520331
$554$			19.0689i			0.810159i
$555$	−1.85410	+	0.708204i	−0.0787022	+	0.0300616i
$556$			8.78402i			0.372526i
$557$	−0.277515			−0.0117587			−0.00587933	−	0.999983i	$-0.501871\pi$
$557$	−0.277515			−0.0117587			−0.00587933	+	0.999983i	$0.501871\pi$
$558$	15.3884	−	13.7638i	0.651444	−	0.582669i
$559$	−5.00000			−0.211477
$560$	−2.80017			−0.118329
$561$		0			0
$562$	31.3050			1.32052
$563$	−1.06957			−0.0450770			−0.0225385	−	0.999746i	$-0.507175\pi$
$563$	−1.06957			−0.0450770			−0.0225385	+	0.999746i	$0.507175\pi$
$564$	−8.32624	+	3.18034i	−0.350598	+	0.133916i
$565$	0.785218			0.0330344
$566$			25.1246i			1.05607i
$567$	27.5276	+	3.07768i	1.15605	+	0.129251i
$568$			16.3925i			0.687813i
$569$	−20.8172			−0.872704			−0.436352	−	0.899776i	$-0.643730\pi$
$569$	−20.8172			−0.872704			−0.436352	+	0.899776i	$0.643730\pi$
$570$	0.729490	+	1.90983i	0.0305550	+	0.0799940i
$571$			22.5478i			0.943598i	0.881706	+	0.471799i	$0.156395\pi$
$571$			22.5478i			0.943598i	−0.881706	+	0.471799i	$0.843605\pi$
$572$		0			0
$573$	39.2148	−	14.9787i	1.63822	−	0.625745i
$574$			2.62866i			0.109718i
$575$		−	30.2705i		−	1.26237i
$576$	−19.4721	+	17.4164i	−0.811339	+	0.725684i
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	−1.28157			−0.0533064
$579$	15.9434	−	6.08985i	0.662587	−	0.253086i
$580$			0.555029i			0.0230463i
$581$		−	19.4721i		−	0.807840i
$582$	−3.18368	−	8.33499i	−0.131968	−	0.345497i
$583$		0			0
$584$			28.9443i			1.19772i
$585$	−0.620541	+	0.555029i	−0.0256562	+	0.0229476i
$586$	16.3820			0.676733
$587$			11.9443i			0.492993i	0.969144	+	0.246496i	$0.0792794\pi$
$587$			11.9443i			0.492993i	−0.969144	+	0.246496i	$0.920721\pi$
$588$	−0.944272	−	2.47214i	−0.0389411	−	0.101949i
$589$			15.3884i			0.634069i
$590$	0.171513			0.00706110
$591$	5.32282	+	13.9353i	0.218952	+	0.573223i
$592$	−7.14590			−0.293695
$593$	−7.33094			−0.301046			−0.150523	−	0.988607i	$-0.548096\pi$
$593$	−7.33094			−0.301046			−0.150523	+	0.988607i	$0.548096\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$	−8.05748			−0.330047
$597$	−1.38197	−	3.61803i	−0.0565601	−	0.148076i
$598$	−5.32624			−0.217806
$599$		−	21.7082i		−	0.886973i	−0.896281	−	0.443487i	$-0.853741\pi$
$599$		−	21.7082i		−	0.886973i	0.896281	−	0.443487i	$-0.146259\pi$
$600$	−9.23305	−	24.1724i	−0.376938	−	0.986836i
$601$			18.6376i			0.760244i	0.924936	+	0.380122i	$0.124118\pi$
$601$			18.6376i			0.760244i	−0.924936	+	0.380122i	$0.875882\pi$
$602$	24.8990			1.01481
$603$	−16.3820	+	14.6525i	−0.667125	+	0.596695i
$604$		−	3.46120i		−	0.140834i
$605$		0			0
$606$	11.5836	+	30.3262i	0.470551	+	1.23192i
$607$			37.0382i			1.50333i	0.659543	+	0.751667i	$0.270750\pi$
$607$			37.0382i			1.50333i	−0.659543	+	0.751667i	$0.729250\pi$
$608$		−	8.81966i		−	0.357684i
$609$	11.7082	−	4.47214i	0.474440	−	0.181220i
$610$	1.18034			0.0477906
$611$	−6.04937			−0.244731
$612$	5.87785	−	5.25731i	0.237598	−	0.212514i
$613$			38.0423i			1.53651i	0.640142	+	0.768256i	$0.278875\pi$
$613$			38.0423i			1.53651i	−0.640142	+	0.768256i	$0.721125\pi$
$614$			11.1803i			0.451202i
$615$	0.449028	−	0.171513i	0.0181066	−	0.00691609i
$616$		0			0
$617$		−	15.7639i		−	0.634632i	−0.948320	−	0.317316i	$-0.897218\pi$
$617$		−	15.7639i		−	0.634632i	0.948320	−	0.317316i	$-0.102782\pi$
$618$	−8.16348	−	21.3723i	−0.328383	−	0.859719i
$619$	−14.4164			−0.579444			−0.289722	−	0.957111i	$-0.593563\pi$
$619$	−14.4164			−0.579444			−0.289722	+	0.957111i	$0.593563\pi$
$620$			1.38197i			0.0555011i
$621$	14.8541	−	28.7984i	0.596075	−	1.15564i
$622$		−	5.87785i		−	0.235680i
$623$	−1.62460			−0.0650882
$624$	−2.80017	+	1.06957i	−0.112096	+	0.0428170i
$625$	22.8328			0.913313
$626$	−12.9313			−0.516838
$627$		0			0
$628$	−6.00000			−0.239426
$629$	12.7598			0.508765
$630$	3.09017	−	2.76393i	0.123115	−	0.110118i
$631$	43.4508			1.72975			0.864876	−	0.501986i	$-0.167397\pi$
$631$	43.4508			1.72975			0.864876	+	0.501986i	$0.167397\pi$
$632$			12.2361i			0.486725i
$633$	−31.5034	+	12.0332i	−1.25215	+	0.478278i
$634$		−	4.97980i		−	0.197773i
$635$	4.91428			0.195017
$636$	1.85410	−	0.708204i	0.0735199	−	0.0280821i
$637$		−	1.79611i		−	0.0711645i
$638$		0			0
$639$	−10.6525	−	11.9098i	−0.421405	−	0.471146i
$640$			1.34708i			0.0532482i
$641$			11.1459i			0.440237i	0.975473	+	0.220118i	$0.0706443\pi$
$641$			11.1459i			0.440237i	−0.975473	+	0.220118i	$0.929356\pi$
$642$	−9.47214	−	24.7984i	−0.373835	−	0.978714i
$643$	19.0902			0.752843			0.376421	−	0.926449i	$-0.377154\pi$
$643$	19.0902			0.752843			0.376421	+	0.926449i	$0.377154\pi$
$644$	−11.8617			−0.467417
$645$	−1.62460	−	4.25325i	−0.0639685	−	0.167472i
$646$		−	13.1433i		−	0.517115i
$647$			25.1591i			0.989104i	0.869148	+	0.494552i	$0.164668\pi$
$647$			25.1591i			0.989104i	−0.869148	+	0.494552i	$0.835332\pi$
$648$	3.07768	−	27.5276i	0.120903	−	1.08139i
$649$		0			0
$650$		−	4.14590i		−	0.162615i
$651$	29.1522	−	11.1352i	1.14257	−	0.436421i
$652$	9.03444			0.353816
$653$			41.8541i			1.63788i	0.573881	+	0.818939i	$0.305437\pi$
$653$			41.8541i			1.63788i	−0.573881	+	0.818939i	$0.694563\pi$
$654$	8.94427	−	3.41641i	0.349749	−	0.133592i
$655$		−	3.97574i		−	0.155345i
$656$	1.73060			0.0675686
$657$	−18.8091	−	21.0292i	−0.733814	−	0.820429i
$658$	30.1246			1.17438
$659$	3.59222			0.139933			0.0699666	−	0.997549i	$-0.477711\pi$
$659$	3.59222			0.139933			0.0699666	+	0.997549i	$0.477711\pi$
$660$		0			0
$661$	−23.4508			−0.912132			−0.456066	−	0.889946i	$-0.650742\pi$
$661$	−23.4508			−0.912132			−0.456066	+	0.889946i	$0.650742\pi$
$662$	−15.1514			−0.588876
$663$	5.00000	−	1.90983i	0.194184	−	0.0741717i
$664$	−19.4721			−0.755665
$665$			3.09017i			0.119832i
$666$	7.88597	−	7.05342i	0.305575	−	0.273315i
$667$		−	14.6619i		−	0.567710i
$668$	13.0373			0.504427
$669$	−1.09017	−	2.85410i	−0.0421484	−	0.110346i
$670$			3.28969i			0.127092i
$671$		0			0
$672$	−16.7082	+	6.38197i	−0.644533	+	0.246190i
$673$			10.3431i			0.398698i	0.979929	+	0.199349i	$0.0638827\pi$
$673$			10.3431i			0.398698i	−0.979929	+	0.199349i	$0.936117\pi$
$674$			29.5967i			1.14002i
$675$	22.4164	+	11.5623i	0.862808	+	0.445033i
$676$	−7.70820			−0.296469
$677$	29.6668			1.14019			0.570093	−	0.821580i	$-0.306907\pi$
$677$	29.6668			1.14019			0.570093	+	0.821580i	$0.306907\pi$
$678$	−3.91023	+	1.49357i	−0.150171	+	0.0573604i
$679$		−	13.4863i		−	0.517557i
$680$		−	5.00000i		−	0.191741i
$681$	8.95554	+	23.4459i	0.343177	+	0.898449i
$682$		0			0
$683$		−	9.00000i		−	0.344375i	−0.985064	−	0.172188i	$-0.944916\pi$
$683$		−	9.00000i		−	0.344375i	0.985064	−	0.172188i	$-0.0550836\pi$
$684$	3.24920	+	3.63271i	0.124236	+	0.138900i
$685$	−1.79837			−0.0687123
$686$		−	16.3820i		−	0.625466i
$687$	9.34752	+	24.4721i	0.356630	+	0.933670i
$688$		−	16.3925i		−	0.624957i
$689$	1.34708			0.0513198
$690$	−1.73060	−	4.53077i	−0.0658828	−	0.172483i
$691$	−10.3607			−0.394139			−0.197069	−	0.980390i	$-0.563142\pi$
$691$	−10.3607			−0.394139			−0.197069	+	0.980390i	$0.563142\pi$
$692$	−14.2784			−0.542782
$693$		0			0
$694$	8.54102			0.324213
$695$	−5.42882			−0.205927
$696$	−4.47214	−	11.7082i	−0.169516	−	0.443798i
$697$	−3.09017			−0.117049
$698$		−	15.9787i		−	0.604803i
$699$	5.98385	+	15.6659i	0.226330	+	0.592540i
$700$		−	9.23305i		−	0.348977i
$701$	−15.4944			−0.585216			−0.292608	−	0.956232i	$-0.594523\pi$
$701$	−15.4944			−0.585216			−0.292608	+	0.956232i	$0.594523\pi$
$702$	2.03444	−	3.94427i	0.0767851	−	0.148867i
$703$			7.88597i			0.297425i
$704$		0			0
$705$	−1.96556	−	5.14590i	−0.0740272	−	0.193806i
$706$		−	39.4953i		−	1.48643i
$707$			49.0689i			1.84543i
$708$	0.381966	−	0.145898i	0.0143552	−	0.00548318i
$709$	−20.5066			−0.770141			−0.385070	−	0.922887i	$-0.625823\pi$
$709$	−20.5066			−0.770141			−0.385070	+	0.922887i	$0.625823\pi$
$710$	−2.39163			−0.0897563
$711$	−7.95148	−	8.89002i	−0.298204	−	0.333402i
$712$			1.62460i			0.0608844i
$713$		−	36.5066i		−	1.36718i
$714$	−24.8990	+	9.51057i	−0.931821	+	0.355924i
$715$		0			0
$716$			8.61803i			0.322071i
$717$	4.76779	+	12.4822i	0.178057	+	0.466158i
$718$	37.4853			1.39894
$719$		−	30.1246i		−	1.12346i	−0.827321	−	0.561729i	$-0.810136\pi$
$719$		−	30.1246i		−	1.12346i	0.827321	−	0.561729i	$-0.189864\pi$
$720$	−1.81966	−	2.03444i	−0.0678147	−	0.0758192i
$721$		−	34.5811i		−	1.28787i
$722$	−14.2128			−0.528947
$723$	−45.0957	+	17.2250i	−1.67713	+	0.640605i
$724$	−4.79837			−0.178330
$725$	11.4127			0.423856
$726$		0			0
$727$	−27.8541			−1.03305			−0.516526	−	0.856272i	$-0.672775\pi$
$727$	−27.8541			−1.03305			−0.516526	+	0.856272i	$0.672775\pi$
$728$	−6.88191			−0.255061
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$	−4.22291			−0.156297
$731$			29.2705i			1.08261i
$732$	2.62866	−	1.00406i	0.0971579	−	0.0371110i
$733$		−	47.1038i		−	1.73982i	−0.493212	−	0.869909i	$-0.664177\pi$
$733$		−	47.1038i		−	1.73982i	0.493212	−	0.869909i	$-0.335823\pi$
$734$	−28.1887			−1.04046
$735$	1.52786	−	0.583592i	0.0563561	−	0.0215261i
$736$			20.9232i			0.771241i
$737$		0			0
$738$	−1.90983	+	1.70820i	−0.0703018	+	0.0628799i
$739$			13.5923i			0.500001i	0.968246	+	0.250001i	$0.0804308\pi$
$739$			13.5923i			0.500001i	−0.968246	+	0.250001i	$0.919569\pi$
$740$			0.708204i			0.0260341i
$741$	1.18034	+	3.09017i	0.0433609	+	0.113520i
$742$	−6.70820			−0.246266
$743$	−29.3642			−1.07727			−0.538635	−	0.842539i	$-0.681060\pi$
$743$	−29.3642			−1.07727			−0.538635	+	0.842539i	$0.681060\pi$
$744$	−11.1352	−	29.1522i	−0.408235	−	1.06877i
$745$		−	4.97980i		−	0.182446i
$746$		−	32.1591i		−	1.17743i
$747$	14.1473	−	12.6538i	0.517624	−	0.462977i
$748$		0			0
$749$		−	40.1246i		−	1.46612i
$750$	7.15942	−	2.73466i	0.261425	−	0.0998555i
$751$	−14.5623			−0.531386			−0.265693	−	0.964058i	$-0.585601\pi$
$751$	−14.5623			−0.531386			−0.265693	+	0.964058i	$0.585601\pi$
$752$		−	19.8328i		−	0.723228i
$753$	−32.8885	+	12.5623i	−1.19853	+	0.457796i
$754$		−	2.00811i		−	0.0731312i
$755$	2.13914			0.0778512
$756$	4.53077	−	8.78402i	0.164782	−	0.319472i
$757$	10.8885			0.395751			0.197875	−	0.980227i	$-0.436596\pi$
$757$	10.8885			0.395751			0.197875	+	0.980227i	$0.436596\pi$
$758$	−3.39569			−0.123337
$759$		0			0
$760$	3.09017			0.112092
$761$	33.1685			1.20236			0.601178	−	0.799115i	$-0.294698\pi$
$761$	33.1685			1.20236			0.601178	+	0.799115i	$0.294698\pi$
$762$	−24.4721	+	9.34752i	−0.886532	+	0.338625i
$763$	14.4721			0.523926
$764$		−	14.9787i		−	0.541911i
$765$	3.24920	+	3.63271i	0.117475	+	0.131341i
$766$			14.5964i			0.527388i
$767$	0.277515			0.0100205
$768$	8.20163	+	21.4721i	0.295951	+	0.774809i
$769$		−	30.7113i		−	1.10748i	−0.832690	−	0.553739i	$-0.813200\pi$
$769$		−	30.7113i		−	1.10748i	0.832690	−	0.553739i	$-0.186800\pi$
$770$		0			0
$771$	−36.0344	+	13.7639i	−1.29775	+	0.495696i
$772$		−	6.08985i		−	0.219179i
$773$			45.8328i			1.64849i	0.566232	+	0.824246i	$0.308401\pi$
$773$			45.8328i			1.64849i	−0.566232	+	0.824246i	$0.691599\pi$
$774$	16.1803	+	18.0902i	0.581590	+	0.650238i
$775$	28.4164			1.02075
$776$	−13.4863			−0.484130
$777$	14.9394	−	5.70634i	0.535948	−	0.204714i
$778$			8.67802i			0.311122i
$779$		−	1.90983i		−	0.0684268i
$780$	0.106001	+	0.277515i	0.00379545	+	0.00993661i
$781$		0			0
$782$			31.1803i			1.11501i
$783$	10.8576	+	5.60034i	0.388021	+	0.200140i
$784$	5.88854			0.210305
$785$		−	3.70820i		−	0.132351i
$786$	7.56231	+	19.7984i	0.269739	+	0.706185i
$787$		−	3.11817i		−	0.111151i	−0.998454	−	0.0555754i	$-0.982301\pi$
$787$		−	3.11817i		−	0.111151i	0.998454	−	0.0555754i	$-0.0176993\pi$
$788$	5.32282			0.189618
$789$	5.64083	+	14.7679i	0.200819	+	0.525750i
$790$	−1.78522			−0.0635152
$791$	−6.32688			−0.224958
$792$		0			0
$793$	1.90983			0.0678201
$794$	27.0381			0.959547
$795$	0.437694	+	1.14590i	0.0155234	+	0.0406408i
$796$	−1.38197			−0.0489825
$797$		−	36.0689i		−	1.27763i	−0.769362	−	0.638813i	$-0.779426\pi$
$797$		−	36.0689i		−	1.27763i	0.769362	−	0.638813i	$-0.220574\pi$
$798$	−5.87785	−	15.3884i	−0.208074	−	0.544744i
$799$			35.4136i			1.25284i
$800$	−16.2865			−0.575814
$801$	−1.05573	−	1.18034i	−0.0373023	−	0.0417053i
$802$		−	32.7445i		−	1.15625i
$803$		0			0
$804$	2.79837	+	7.32624i	0.0986910	+	0.258376i
$805$		−	7.33094i		−	0.258382i
$806$		−	5.00000i		−	0.176117i
$807$	−30.3607	+	11.5967i	−1.06875	+	0.408225i
$808$	49.0689			1.72624
$809$	−21.4378			−0.753712			−0.376856	−	0.926272i	$-0.622995\pi$
$809$	−21.4378			−0.753712			−0.376856	+	0.926272i	$0.622995\pi$
$810$	4.01623	+	0.449028i	0.141116	+	0.0157772i
$811$		−	20.9232i		−	0.734714i	−0.930080	−	0.367357i	$-0.880263\pi$
$811$		−	20.9232i		−	0.734714i	0.930080	−	0.367357i	$-0.119737\pi$
$812$		−	4.47214i		−	0.156941i
$813$	27.4216	−	10.4741i	0.961719	−	0.367344i
$814$		0			0
$815$			5.58359i			0.195585i
$816$	6.26137	+	16.3925i	0.219192	+	0.573851i
$817$	−18.0902			−0.632895
$818$			24.8754i			0.869748i
$819$	5.00000	−	4.47214i	0.174714	−	0.156269i
$820$		−	0.171513i		−	0.00598951i
$821$	−46.5083			−1.62315			−0.811575	−	0.584248i	$-0.801389\pi$
$821$	−46.5083			−1.62315			−0.811575	+	0.584248i	$0.801389\pi$
$822$	8.95554	−	3.42071i	0.312360	−	0.119311i
$823$	26.1246			0.910647			0.455323	−	0.890326i	$-0.349524\pi$
$823$	26.1246			0.910647			0.455323	+	0.890326i	$0.349524\pi$
$824$	−34.5811			−1.20469
$825$		0			0
$826$	−1.38197			−0.0480847
$827$	26.0746			0.906701			0.453351	−	0.891332i	$-0.350229\pi$
$827$	26.0746			0.906701			0.453351	+	0.891332i	$0.350229\pi$
$828$	−7.70820	−	8.61803i	−0.267879	−	0.299497i
$829$	−5.27051			−0.183052			−0.0915262	−	0.995803i	$-0.529175\pi$
$829$	−5.27051			−0.183052			−0.0915262	+	0.995803i	$0.529175\pi$
$830$		−	2.84095i		−	0.0986107i
$831$	−26.2461	+	10.0251i	−0.910466	+	0.347767i
$832$			6.32688i			0.219345i
$833$	−10.5146			−0.364310
$834$	27.0344	−	10.3262i	0.936126	−	0.357568i
$835$			8.05748i			0.278841i
$836$		0			0
$837$	27.0344	+	13.9443i	0.934447	+	0.481985i
$838$			1.00406i			0.0346846i
$839$		−	1.65248i		−	0.0570498i	−0.999593	−	0.0285249i	$-0.990919\pi$
$839$		−	1.65248i		−	0.0570498i	0.999593	−	0.0285249i	$-0.00908099\pi$
$840$	−2.23607	−	5.85410i	−0.0771517	−	0.201986i
$841$	−23.4721			−0.809384
$842$	−22.5074			−0.775655
$843$	16.4580	+	43.0876i	0.566843	+	1.48401i
$844$			12.0332i			0.414201i
$845$		−	4.76393i		−	0.163884i
$846$	19.5762	+	21.8868i	0.673042	+	0.752484i
$847$		0			0
$848$			4.41641i			0.151660i
$849$	−34.5811	+	13.2088i	−1.18682	+	0.453325i
$850$	−24.2705			−0.832472
$851$		−	18.7082i		−	0.641309i
$852$	−5.32624	+	2.03444i	−0.182474	+	0.0696988i
$853$			0.938545i			0.0321352i	0.999871	+	0.0160676i	$0.00511469\pi$
$853$			0.938545i			0.0321352i	−0.999871	+	0.0160676i	$0.994885\pi$
$854$	−9.51057			−0.325445
$855$	−2.24514	+	2.00811i	−0.0767822	+	0.0686761i
$856$	−40.1246			−1.37143
$857$	−34.9646			−1.19437			−0.597184	−	0.802105i	$-0.703714\pi$
$857$	−34.9646			−1.19437			−0.597184	+	0.802105i	$0.703714\pi$
$858$		0			0
$859$	43.4721			1.48325			0.741625	−	0.670815i	$-0.234055\pi$
$859$	43.4721			1.48325			0.741625	+	0.670815i	$0.234055\pi$
$860$	−1.62460			−0.0553983
$861$	−3.61803	+	1.38197i	−0.123302	+	0.0470973i
$862$	−7.11146			−0.242217
$863$			1.12461i			0.0382822i	0.999817	+	0.0191411i	$0.00609318\pi$
$863$			1.12461i			0.0382822i	−0.999817	+	0.0191411i	$0.993907\pi$
$864$	−15.4944	−	7.99197i	−0.527131	−	0.271892i
$865$		−	8.82451i		−	0.300042i
$866$	7.05342			0.239685
$867$	−0.673762	−	1.76393i	−0.0228822	−	0.0599063i
$868$		−	11.1352i		−	0.377952i
$869$		0			0
$870$	1.70820	−	0.652476i	0.0579135	−	0.0221210i
$871$			5.32282i			0.180357i
$872$		−	14.4721i		−	0.490088i
$873$	9.79837	−	8.76393i	0.331625	−	0.296614i
$874$	−19.2705			−0.651835
$875$	11.5842			0.391617
$876$	−9.40456	+	3.59222i	−0.317751	+	0.121370i
$877$		−	34.4095i		−	1.16193i	−0.813929	−	0.580964i	$-0.802676\pi$
$877$		−	34.4095i		−	1.16193i	0.813929	−	0.580964i	$-0.197324\pi$
$878$			3.21478i			0.108494i
$879$	8.61251	+	22.5478i	0.290493	+	0.760520i
$880$		0			0
$881$		−	29.9230i		−	1.00813i	−0.863665	−	0.504066i	$-0.831837\pi$
$881$		−	29.9230i		−	1.00813i	0.863665	−	0.504066i	$-0.168163\pi$
$882$	−6.49839	+	5.81234i	−0.218812	+	0.195712i
$883$	−40.1803			−1.35218			−0.676088	−	0.736821i	$-0.736326\pi$
$883$	−40.1803			−1.35218			−0.676088	+	0.736821i	$0.736326\pi$
$884$		−	1.90983i		−	0.0642345i
$885$	0.0901699	+	0.236068i	0.00303103	+	0.00793534i
$886$			1.79611i			0.0603416i
$887$	13.9353			0.467903			0.233951	−	0.972248i	$-0.424834\pi$
$887$	13.9353			0.467903			0.233951	+	0.972248i	$0.424834\pi$
$888$	−5.70634	−	14.9394i	−0.191492	−	0.501333i
$889$	−39.5967			−1.32803
$890$	−0.237026			−0.00794512
$891$		0			0
$892$	−1.09017			−0.0365016
$893$	−21.8868			−0.732414
$894$	9.47214	+	24.7984i	0.316796	+	0.829382i
$895$	−5.32624			−0.178036
$896$		−	10.8541i		−	0.362610i
$897$	−2.80017	−	7.33094i	−0.0934949	−	0.244773i
$898$		−	32.7849i		−	1.09405i
$899$	13.7638			0.459049
$900$	6.70820	−	6.00000i	0.223607	−	0.200000i
$901$		−	7.88597i		−	0.262720i
$902$		0			0
$903$	13.0902	+	34.2705i	0.435614	+	1.14045i
$904$			6.32688i			0.210429i
$905$		−	2.96556i		−	0.0985785i
$906$	−10.6525	+	4.06888i	−0.353905	+	0.135180i
$907$	−31.3951			−1.04246			−0.521229	−	0.853417i	$-0.674526\pi$
$907$	−31.3951			−1.04246			−0.521229	+	0.853417i	$0.674526\pi$
$908$	8.95554			0.297200
$909$	−35.6506	+	31.8869i	−1.18246	+	1.05762i
$910$		−	1.00406i		−	0.0332842i
$911$		−	31.7214i		−	1.05098i	−0.850801	−	0.525488i	$-0.823883\pi$
$911$		−	31.7214i		−	1.05098i	0.850801	−	0.525488i	$-0.176117\pi$
$912$	−10.1311	+	3.86974i	−0.335474	+	0.128140i
$913$		0			0
$914$			29.4721i			0.974852i
$915$	0.620541	+	1.62460i	0.0205145	+	0.0537076i
$916$	9.34752			0.308851
$917$			32.0344i			1.05787i
$918$	−23.0902	−	11.9098i	−0.762089	−	0.393083i
$919$			46.3773i			1.52984i	0.644123	+	0.764922i	$0.277223\pi$
$919$			46.3773i			1.52984i	−0.644123	+	0.764922i	$0.722777\pi$
$920$	−7.33094			−0.241694
$921$	−15.3884	+	5.87785i	−0.507066	+	0.193682i
$922$	−36.1033			−1.18900
$923$	−3.86974			−0.127374
$924$		0			0
$925$	14.5623			0.478806
$926$	−39.1118			−1.28529
$927$	25.1246	−	22.4721i	0.825201	−	0.738082i
$928$	−7.88854			−0.258954
$929$			32.3050i			1.05989i	0.848032	+	0.529946i	$0.177788\pi$
$929$			32.3050i			1.05989i	−0.848032	+	0.529946i	$0.822212\pi$
$930$	4.25325	−	1.62460i	0.139470	−	0.0532727i
$931$		−	6.49839i		−	0.212976i
$932$	5.98385			0.196008
$933$	8.09017	−	3.09017i	0.264860	−	0.101168i
$934$			8.99602i			0.294359i
$935$		0			0
$936$	−4.47214	−	5.00000i	−0.146176	−	0.163430i
$937$		−	36.5487i		−	1.19399i	−0.802244	−	0.596997i	$-0.796361\pi$
$937$		−	36.5487i		−	1.19399i	0.802244	−	0.596997i	$-0.203639\pi$
$938$		−	26.5066i		−	0.865470i
$939$	−6.79837	−	17.7984i	−0.221857	−	0.580828i
$940$	−1.96556			−0.0641094
$941$	35.7971			1.16695			0.583476	−	0.812130i	$-0.301692\pi$
$941$	35.7971			1.16695			0.583476	+	0.812130i	$0.301692\pi$
$942$	7.05342	+	18.4661i	0.229813	+	0.601658i
$943$			4.53077i			0.147542i
$944$			0.909830i			0.0296124i
$945$	5.42882	+	2.80017i	0.176600	+	0.0910895i
$946$		0			0
$947$		−	17.1459i		−	0.557167i	−0.960412	−	0.278583i	$-0.910135\pi$
$947$		−	17.1459i		−	0.557167i	0.960412	−	0.278583i	$-0.0898649\pi$
$948$	−3.97574	+	1.51860i	−0.129126	+	0.0493217i
$949$	−6.83282			−0.221803
$950$		−	15.0000i		−	0.486664i
$951$	6.85410	−	2.61803i	0.222259	−	0.0848956i
$952$			40.2874i			1.30572i
$953$	−4.01623			−0.130098			−0.0650492	−	0.997882i	$-0.520720\pi$
$953$	−4.01623			−0.130098			−0.0650492	+	0.997882i	$0.520720\pi$
$954$	−4.35926	−	4.87380i	−0.141136	−	0.157795i
$955$	9.25735			0.299561
$956$	4.76779			0.154201
$957$		0			0
$958$	−23.5410			−0.760576
$959$	14.4904			0.467918
$960$	−5.38197	+	2.05573i	−0.173702	+	0.0663483i
$961$	3.27051			0.105500
$962$		−	2.56231i		−	0.0826121i
$963$	29.1522	−	26.0746i	0.939418	−	0.840241i
$964$			17.2250i			0.554780i
$965$	3.76374			0.121159
$966$	13.9443	+	36.5066i	0.448650	+	1.17458i
$967$			12.9313i			0.415842i	0.978146	+	0.207921i	$0.0666697\pi$
$967$			12.9313i			0.415842i	−0.978146	+	0.207921i	$0.933330\pi$
$968$		0			0
$969$	18.0902	−	6.90983i	0.581140	−	0.221976i
$970$		−	1.96763i		−	0.0631766i
$971$		−	8.18034i		−	0.262520i	−0.991348	−	0.131260i	$-0.958098\pi$
$971$		−	8.18034i		−	0.262520i	0.991348	−	0.131260i	$-0.0419022\pi$
$972$	9.32624	−	2.41641i	0.299139	−	0.0775063i
$973$	43.7426			1.40232
$974$	−1.73060			−0.0554520
$975$	5.70634	−	2.17963i	0.182749	−	0.0698039i
$976$			6.26137i			0.200422i
$977$			34.0557i			1.08954i	0.838586	+	0.544770i	$0.183383\pi$
$977$			34.0557i			1.08954i	−0.838586	+	0.544770i	$0.816617\pi$
$978$	−10.6206	−	27.8052i	−0.339610	−	0.889111i
$979$		0			0
$980$		−	0.583592i		−	0.0186422i
$981$	9.40456	+	10.5146i	0.300265	+	0.335706i
$982$	−20.7771			−0.663024
$983$		−	57.3050i		−	1.82774i	−0.406002	−	0.913872i	$-0.633078\pi$
$983$		−	57.3050i		−	1.82774i	0.406002	−	0.913872i	$-0.366922\pi$
$984$	1.38197	+	3.61803i	0.0440555	+	0.115339i
$985$			3.28969i			0.104818i
$986$	−11.7557			−0.374378
$987$	15.8374	+	41.4630i	0.504111	+	1.31978i
$988$	1.18034			0.0375516
$989$	42.9161			1.36465
$990$		0			0
$991$	−12.5623			−0.399055			−0.199527	−	0.979892i	$-0.563941\pi$
$991$	−12.5623			−0.399055			−0.199527	+	0.979892i	$0.563941\pi$
$992$	−19.6417			−0.623624
$993$	−7.96556	−	20.8541i	−0.252779	−	0.661785i
$994$	19.2705			0.611223
$995$		−	0.854102i		−	0.0270769i
$996$	−2.41665	−	6.32688i	−0.0765746	−	0.200475i
$997$		−	14.7274i		−	0.466421i	−0.972426	−	0.233211i	$-0.925077\pi$
$997$		−	14.7274i		−	0.466421i	0.972426	−	0.233211i	$-0.0749231\pi$
$998$	42.2955			1.33884
$999$	13.8541	+	7.14590i	0.438324	+	0.226086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.d.f.362.3		8
3.2	odd	2	inner	363.2.d.f.362.6		8
11.2	odd	10		363.2.f.b.161.1		8
11.3	even	5		363.2.f.d.233.1		8
11.4	even	5		363.2.f.e.215.1		8
11.5	even	5		363.2.f.b.239.2		8
11.6	odd	10		33.2.f.a.8.1	✓	8
11.7	odd	10		363.2.f.d.215.2		8
11.8	odd	10		363.2.f.e.233.2		8
11.9	even	5		33.2.f.a.29.2	yes	8
11.10	odd	2	inner	363.2.d.f.362.5		8
33.2	even	10		363.2.f.b.161.2		8
33.5	odd	10		363.2.f.b.239.1		8
33.8	even	10		363.2.f.e.233.1		8
33.14	odd	10		363.2.f.d.233.2		8
33.17	even	10		33.2.f.a.8.2	yes	8
33.20	odd	10		33.2.f.a.29.1	yes	8
33.26	odd	10		363.2.f.e.215.2		8
33.29	even	10		363.2.f.d.215.1		8
33.32	even	2	inner	363.2.d.f.362.4		8
44.31	odd	10		528.2.bn.c.161.2		8
44.39	even	10		528.2.bn.c.305.1		8
55.9	even	10		825.2.bi.b.326.1		8
55.17	even	20		825.2.bs.a.74.1		8
55.28	even	20		825.2.bs.d.74.2		8
55.39	odd	10		825.2.bi.b.701.2		8
55.42	odd	20		825.2.bs.a.524.2		8
55.53	odd	20		825.2.bs.d.524.1		8
99.20	odd	30		891.2.u.a.458.1		16
99.31	even	15		891.2.u.a.755.1		16
99.50	even	30		891.2.u.a.107.2		16
99.61	odd	30		891.2.u.a.701.2		16
99.83	even	30		891.2.u.a.701.1		16
99.86	odd	30		891.2.u.a.755.2		16
99.94	odd	30		891.2.u.a.107.1		16
99.97	even	15		891.2.u.a.458.2		16
132.83	odd	10		528.2.bn.c.305.2		8
132.119	even	10		528.2.bn.c.161.1		8
165.17	odd	20		825.2.bs.d.74.1		8
165.53	even	20		825.2.bs.a.524.1		8
165.83	odd	20		825.2.bs.a.74.2		8
165.119	odd	10		825.2.bi.b.326.2		8
165.149	even	10		825.2.bi.b.701.1		8
165.152	even	20		825.2.bs.d.524.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.8.1	✓	8	11.6	odd	10
33.2.f.a.8.2	yes	8	33.17	even	10
33.2.f.a.29.1	yes	8	33.20	odd	10
33.2.f.a.29.2	yes	8	11.9	even	5
363.2.d.f.362.3		8	1.1	even	1	trivial
363.2.d.f.362.4		8	33.32	even	2	inner
363.2.d.f.362.5		8	11.10	odd	2	inner
363.2.d.f.362.6		8	3.2	odd	2	inner
363.2.f.b.161.1		8	11.2	odd	10
363.2.f.b.161.2		8	33.2	even	10
363.2.f.b.239.1		8	33.5	odd	10
363.2.f.b.239.2		8	11.5	even	5
363.2.f.d.215.1		8	33.29	even	10
363.2.f.d.215.2		8	11.7	odd	10
363.2.f.d.233.1		8	11.3	even	5
363.2.f.d.233.2		8	33.14	odd	10
363.2.f.e.215.1		8	11.4	even	5
363.2.f.e.215.2		8	33.26	odd	10
363.2.f.e.233.1		8	33.8	even	10
363.2.f.e.233.2		8	11.8	odd	10
528.2.bn.c.161.1		8	132.119	even	10
528.2.bn.c.161.2		8	44.31	odd	10
528.2.bn.c.305.1		8	44.39	even	10
528.2.bn.c.305.2		8	132.83	odd	10
825.2.bi.b.326.1		8	55.9	even	10
825.2.bi.b.326.2		8	165.119	odd	10
825.2.bi.b.701.1		8	165.149	even	10
825.2.bi.b.701.2		8	55.39	odd	10
825.2.bs.a.74.1		8	55.17	even	20
825.2.bs.a.74.2		8	165.83	odd	20
825.2.bs.a.524.1		8	165.53	even	20
825.2.bs.a.524.2		8	55.42	odd	20
825.2.bs.d.74.1		8	165.17	odd	20
825.2.bs.d.74.2		8	55.28	even	20
825.2.bs.d.524.1		8	55.53	odd	20
825.2.bs.d.524.2		8	165.152	even	20
891.2.u.a.107.1		16	99.94	odd	30
891.2.u.a.107.2		16	99.50	even	30
891.2.u.a.458.1		16	99.20	odd	30
891.2.u.a.458.2		16	99.97	even	15
891.2.u.a.701.1		16	99.83	even	30
891.2.u.a.701.2		16	99.61	odd	30
891.2.u.a.755.1		16	99.31	even	15
891.2.u.a.755.2		16	99.86	odd	30

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.17557 q^{2} +(-0.618034 - 1.61803i) q^{3} -0.618034 q^{4} -0.381966i q^{5} +(0.726543 + 1.90211i) q^{6} +3.07768i q^{7} +3.07768 q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q-1.17557 q^{2} +(-0.618034 - 1.61803i) q^{3} -0.618034 q^{4} -0.381966i q^{5} +(0.726543 + 1.90211i) q^{6} +3.07768i q^{7} +3.07768 q^{8} +(-2.23607 + 2.00000i) q^{9} +0.449028i q^{10} +(0.381966 + 1.00000i) q^{12} +0.726543i q^{13} -3.61803i q^{14} +(-0.618034 + 0.236068i) q^{15} -2.38197 q^{16} +4.25325 q^{17} +(2.62866 - 2.35114i) q^{18} +2.62866i q^{19} +0.236068i q^{20} +(4.97980 - 1.90211i) q^{21} -6.23607i q^{23} +(-1.90211 - 4.97980i) q^{24} +4.85410 q^{25} -0.854102i q^{26} +(4.61803 + 2.38197i) q^{27} -1.90211i q^{28} +2.35114 q^{29} +(0.726543 - 0.277515i) q^{30} +5.85410 q^{31} -3.35520 q^{32} -5.00000 q^{34} +1.17557 q^{35} +(1.38197 - 1.23607i) q^{36} +3.00000 q^{37} -3.09017i q^{38} +(1.17557 - 0.449028i) q^{39} -1.17557i q^{40} -0.726543 q^{41} +(-5.85410 + 2.23607i) q^{42} +6.88191i q^{43} +(0.763932 + 0.854102i) q^{45} +7.33094i q^{46} +8.32624i q^{47} +(1.47214 + 3.85410i) q^{48} -2.47214 q^{49} -5.70634 q^{50} +(-2.62866 - 6.88191i) q^{51} -0.449028i q^{52} -1.85410i q^{53} +(-5.42882 - 2.80017i) q^{54} +9.47214i q^{56} +(4.25325 - 1.62460i) q^{57} -2.76393 q^{58} -0.381966i q^{59} +(0.381966 - 0.145898i) q^{60} -2.62866i q^{61} -6.88191 q^{62} +(-6.15537 - 6.88191i) q^{63} +8.70820 q^{64} +0.277515 q^{65} +7.32624 q^{67} -2.62866 q^{68} +(-10.0902 + 3.85410i) q^{69} -1.38197 q^{70} +5.32624i q^{71} +(-6.88191 + 6.15537i) q^{72} +9.40456i q^{73} -3.52671 q^{74} +(-3.00000 - 7.85410i) q^{75} -1.62460i q^{76} +(-1.38197 + 0.527864i) q^{78} +3.97574i q^{79} +0.909830i q^{80} +(1.00000 - 8.94427i) q^{81} +0.854102 q^{82} -6.32688 q^{83} +(-3.07768 + 1.17557i) q^{84} -1.62460i q^{85} -8.09017i q^{86} +(-1.45309 - 3.80423i) q^{87} +0.527864i q^{89} +(-0.898056 - 1.00406i) q^{90} -2.23607 q^{91} +3.85410i q^{92} +(-3.61803 - 9.47214i) q^{93} -9.78808i q^{94} +1.00406 q^{95} +(2.07363 + 5.42882i) q^{96} -4.38197 q^{97} +2.90617 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4	\( 8 q + 4 q^{3} + 4 q^{4} + 12 q^{12} + 4 q^{15} - 28 q^{16} + 12 q^{25} + 28 q^{27} + 20 q^{31} - 40 q^{34} + 20 q^{36} + 24 q^{37} - 20 q^{42} + 24 q^{45} - 24 q^{48} + 16 q^{49} - 40 q^{58} + 12 q^{60} + 16 q^{64} - 4 q^{67} - 36 q^{69} - 20 q^{70} - 24 q^{75} - 20 q^{78} + 8 q^{81} - 20 q^{82} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 + 12 * q^12 + 4 * q^15 - 28 * q^16 + 12 * q^25 + 28 * q^27 + 20 * q^31 - 40 * q^34 + 20 * q^36 + 24 * q^37 - 20 * q^42 + 24 * q^45 - 24 * q^48 + 16 * q^49 - 40 * q^58 + 12 * q^60 + 16 * q^64 - 4 * q^67 - 36 * q^69 - 20 * q^70 - 24 * q^75 - 20 * q^78 + 8 * q^81 - 20 * q^82 - 20 * q^93 - 44 * q^97

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