LMFDB - Embedded newform 363.2.e.b.202.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.b.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(0.500000 - 0.363271i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(0.500000 - 0.363271i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.61803 q^{10} -4.85410 q^{12} +(0.190983 + 0.138757i) q^{13} +(0.809017 - 2.48990i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-0.927051 + 0.673542i) q^{17} +(0.809017 + 2.48990i) q^{18} +(-1.80902 + 5.56758i) q^{19} +(2.42705 + 1.76336i) q^{20} -1.00000 q^{21} +0.236068 q^{23} +(6.04508 + 4.39201i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(-0.190983 - 0.587785i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(1.85410 + 5.70634i) q^{29} +(0.500000 - 1.53884i) q^{30} +(4.92705 + 3.57971i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(0.500000 + 0.363271i) q^{35} +(1.50000 - 4.61653i) q^{36} +(-1.92705 - 5.93085i) q^{37} +(12.3992 - 9.00854i) q^{38} +(-0.190983 + 0.138757i) q^{39} +(-1.42705 - 4.39201i) q^{40} +(-0.0729490 + 0.224514i) q^{41} +(2.11803 + 1.53884i) q^{42} +6.70820 q^{43} -0.618034 q^{45} +(-0.500000 - 0.363271i) q^{46} +(-3.11803 + 9.59632i) q^{47} +(-3.04508 - 9.37181i) q^{48} +(4.85410 - 3.52671i) q^{49} +(9.78115 - 7.10642i) q^{50} +(-0.354102 - 1.08981i) q^{51} +(-0.354102 + 1.08981i) q^{52} +(0.309017 + 0.224514i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(-4.73607 - 3.44095i) q^{57} +(4.85410 - 14.9394i) q^{58} +(2.28115 + 7.02067i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(-9.35410 + 6.79615i) q^{61} +(-4.92705 - 15.1639i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-7.04508 - 5.11855i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(-4.50000 - 3.26944i) q^{68} +(-0.0729490 + 0.224514i) q^{69} +(-0.500000 - 1.53884i) q^{70} +(-8.35410 + 6.06961i) q^{71} +(-6.04508 + 4.39201i) q^{72} +(1.76393 + 5.42882i) q^{73} +(-5.04508 + 15.5272i) q^{74} +(-3.73607 - 2.71441i) q^{75} -28.4164 q^{76} +0.618034 q^{78} +(8.89919 + 6.46564i) q^{79} +(-1.88197 + 5.79210i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.500000 - 0.363271i) q^{82} +(1.19098 - 0.865300i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(-0.218847 + 0.673542i) q^{85} +(-14.2082 - 10.3229i) q^{86} -6.00000 q^{87} -8.23607 q^{89} +(1.30902 + 0.951057i) q^{90} +(-0.0729490 + 0.224514i) q^{91} +(0.354102 + 1.08981i) q^{92} +(-4.92705 + 3.57971i) q^{93} +(21.3713 - 15.5272i) q^{94} +(1.11803 + 3.44095i) q^{95} +(-3.35410 + 10.3229i) q^{96} +(-6.35410 - 4.61653i) q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9	$ 4 q - 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9} - 2 q^{10} - 6 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 3 q^{20} - 4 q^{21} - 8 q^{23} + 13 q^{24} + q^{25} - 3 q^{26} + q^{27} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 13 q^{31} + 30 q^{32} + 12 q^{34} + 2 q^{35} + 6 q^{36} - q^{37} + 25 q^{38} - 3 q^{39} + q^{40} - 7 q^{41} + 4 q^{42} + 2 q^{45} - 2 q^{46} - 8 q^{47} - q^{48} + 6 q^{49} + 19 q^{50} + 12 q^{51} + 12 q^{52} - q^{53} - 6 q^{54} + 12 q^{56} - 10 q^{57} + 6 q^{58} - 11 q^{59} - 3 q^{60} - 24 q^{61} - 13 q^{62} - q^{63} - 17 q^{64} + 14 q^{65} - 6 q^{67} - 18 q^{68} - 7 q^{69} - 2 q^{70} - 20 q^{71} - 13 q^{72} + 16 q^{73} - 9 q^{74} - 6 q^{75} - 60 q^{76} - 2 q^{78} + 11 q^{79} - 12 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} - 6 q^{84} - 21 q^{85} - 30 q^{86} - 24 q^{87} - 24 q^{89} + 3 q^{90} - 7 q^{91} - 12 q^{92} - 13 q^{93} + 43 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9 - 2 * q^10 - 6 * q^12 + 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^23 + 13 * q^24 + q^25 - 3 * q^26 + q^27 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 13 * q^31 + 30 * q^32 + 12 * q^34 + 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 - 3 * q^39 + q^40 - 7 * q^41 + 4 * q^42 + 2 * q^45 - 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 + 19 * q^50 + 12 * q^51 + 12 * q^52 - q^53 - 6 * q^54 + 12 * q^56 - 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 - 24 * q^61 - 13 * q^62 - q^63 - 17 * q^64 + 14 * q^65 - 6 * q^67 - 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 - 13 * q^72 + 16 * q^73 - 9 * q^74 - 6 * q^75 - 60 * q^76 - 2 * q^78 + 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 + 7 * q^83 - 6 * q^84 - 21 * q^85 - 30 * q^86 - 24 * q^87 - 24 * q^89 + 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 + 43 * q^94 - 12 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.971295	−	0.237877i	$-0.923549\pi$
$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.526381	−	0.850249i	$-0.676451\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	1.50000	+	4.61653i	0.750000	+	2.30826i
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	−0.470342	−	0.882484i	$-0.655869\pi$
$5$	0.500000	−	0.363271i	0.223607	−	0.162460i	0.693949	+	0.720024i	$0.255869\pi$
$6$	2.11803	−	1.53884i	0.864684	−	0.628230i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	0.992318	−	0.123716i	$-0.0394811\pi$
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i	−0.875520	+	0.483181i	$0.839481\pi$
$8$	2.30902	−	7.10642i	0.816361	−	2.51250i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−1.61803			−0.511667
$11$		0			0
$11$		0			0
$12$	−4.85410			−1.40126
$13$	0.190983	+	0.138757i	0.0529692	+	0.0384843i	0.613955	−	0.789341i	$-0.289578\pi$
$13$	0.190983	+	0.138757i	0.0529692	+	0.0384843i	−0.560986	+	0.827826i	$0.689578\pi$
$14$	0.809017	−	2.48990i	0.216219	−	0.665453i
$15$	0.190983	+	0.587785i	0.0493116	+	0.151765i
$16$	−7.97214	+	5.79210i	−1.99303	+	1.44802i
$17$	−0.927051	+	0.673542i	−0.224843	+	0.163358i	−0.694504	−	0.719489i	$-0.744376\pi$
$17$	−0.927051	+	0.673542i	−0.224843	+	0.163358i	0.469661	+	0.882847i	$0.344376\pi$
$18$	0.809017	+	2.48990i	0.190687	+	0.586875i
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$	2.42705	+	1.76336i	0.542705	+	0.394298i
$21$	−1.00000			−0.218218
$22$		0			0
$23$	0.236068			0.0492236			0.0246118	−	0.999697i	$-0.492165\pi$
$23$	0.236068			0.0492236			0.0246118	+	0.999697i	$0.492165\pi$
$24$	6.04508	+	4.39201i	1.23395	+	0.896516i
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$	−0.190983	−	0.587785i	−0.0374548	−	0.115274i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−3.92705	+	2.85317i	−0.742143	+	0.539198i
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	0.961958	+	0.273196i	$0.0880806\pi$
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	−0.617660	+	0.786445i	$0.711919\pi$
$30$	0.500000	−	1.53884i	0.0912871	−	0.280953i
$31$	4.92705	+	3.57971i	0.884924	+	0.642935i	0.934550	−	0.355833i	$-0.115803\pi$
$31$	4.92705	+	3.57971i	0.884924	+	0.642935i	−0.0496252	+	0.998768i	$0.515803\pi$
$32$	10.8541			1.91875
$33$		0			0
$34$	3.00000			0.514496
$35$	0.500000	+	0.363271i	0.0845154	+	0.0614041i
$36$	1.50000	−	4.61653i	0.250000	−	0.769421i
$37$	−1.92705	−	5.93085i	−0.316805	−	0.975026i	−0.975005	−	0.222183i	$-0.928682\pi$
$37$	−1.92705	−	5.93085i	−0.316805	−	0.975026i	0.658200	−	0.752843i	$-0.271318\pi$
$38$	12.3992	−	9.00854i	2.01141	−	1.46138i
$39$	−0.190983	+	0.138757i	−0.0305818	+	0.0222189i
$40$	−1.42705	−	4.39201i	−0.225637	−	0.694438i
$41$	−0.0729490	+	0.224514i	−0.0113927	+	0.0350632i	−0.956591	−	0.291433i	$-0.905868\pi$
$41$	−0.0729490	+	0.224514i	−0.0113927	+	0.0350632i	0.945199	+	0.326496i	$0.105868\pi$
$42$	2.11803	+	1.53884i	0.326820	+	0.237448i
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$		0			0
$45$	−0.618034			−0.0921311
$46$	−0.500000	−	0.363271i	−0.0737210	−	0.0535614i
$47$	−3.11803	+	9.59632i	−0.454812	+	1.39977i	0.416544	+	0.909116i	$0.363241\pi$
$47$	−3.11803	+	9.59632i	−0.454812	+	1.39977i	−0.871356	+	0.490652i	$0.836759\pi$
$48$	−3.04508	−	9.37181i	−0.439520	−	1.35270i
$49$	4.85410	−	3.52671i	0.693443	−	0.503816i
$50$	9.78115	−	7.10642i	1.38326	−	1.00500i
$51$	−0.354102	−	1.08981i	−0.0495842	−	0.152604i
$52$	−0.354102	+	1.08981i	−0.0491051	+	0.151130i
$53$	0.309017	+	0.224514i	0.0424467	+	0.0308394i	0.608806	−	0.793319i	$-0.291649\pi$
$53$	0.309017	+	0.224514i	0.0424467	+	0.0308394i	−0.566360	+	0.824158i	$0.691649\pi$
$54$	−2.61803			−0.356269
$55$		0			0
$56$	7.47214			0.998506
$57$	−4.73607	−	3.44095i	−0.627308	−	0.455766i
$58$	4.85410	−	14.9394i	0.637375	−	1.96164i
$59$	2.28115	+	7.02067i	0.296981	+	0.914013i	0.982549	+	0.186004i	$0.0595539\pi$
$59$	2.28115	+	7.02067i	0.296981	+	0.914013i	−0.685568	+	0.728009i	$0.740446\pi$
$60$	−2.42705	+	1.76336i	−0.313331	+	0.227648i
$61$	−9.35410	+	6.79615i	−1.19767	+	0.870158i	−0.994054	−	0.108893i	$-0.965270\pi$
$61$	−9.35410	+	6.79615i	−1.19767	+	0.870158i	−0.203617	+	0.979051i	$0.565270\pi$
$62$	−4.92705	−	15.1639i	−0.625736	−	1.92582i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	0.145898			0.0180964
$66$		0			0
$67$	1.85410			0.226515			0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410			0.226515			0.113257	+	0.993566i	$0.463872\pi$
$68$	−4.50000	−	3.26944i	−0.545705	−	0.396478i
$69$	−0.0729490	+	0.224514i	−0.00878203	+	0.0270283i
$70$	−0.500000	−	1.53884i	−0.0597614	−	0.183927i
$71$	−8.35410	+	6.06961i	−0.991449	+	0.720330i	−0.960238	−	0.279183i	$-0.909937\pi$
$71$	−8.35410	+	6.06961i	−0.991449	+	0.720330i	−0.0312115	+	0.999513i	$0.509937\pi$
$72$	−6.04508	+	4.39201i	−0.712420	+	0.517603i
$73$	1.76393	+	5.42882i	0.206453	+	0.635396i	0.999651	+	0.0264320i	$0.00841455\pi$
$73$	1.76393	+	5.42882i	0.206453	+	0.635396i	−0.793198	+	0.608964i	$0.791585\pi$
$74$	−5.04508	+	15.5272i	−0.586479	+	1.80500i
$75$	−3.73607	−	2.71441i	−0.431404	−	0.313433i
$76$	−28.4164			−3.25959
$77$		0			0
$78$	0.618034			0.0699786
$79$	8.89919	+	6.46564i	1.00124	+	0.727441i	0.962353	−	0.271803i	$-0.0876198\pi$
$79$	8.89919	+	6.46564i	1.00124	+	0.727441i	0.0388837	+	0.999244i	$0.487620\pi$
$80$	−1.88197	+	5.79210i	−0.210410	+	0.647576i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.500000	−	0.363271i	0.0552158	−	0.0401166i
$83$	1.19098	−	0.865300i	0.130727	−	0.0949790i	−0.520500	−	0.853862i	$-0.674254\pi$
$83$	1.19098	−	0.865300i	0.130727	−	0.0949790i	0.651227	+	0.758883i	$0.274254\pi$
$84$	−1.50000	−	4.61653i	−0.163663	−	0.503704i
$85$	−0.218847	+	0.673542i	−0.0237373	+	0.0730559i
$86$	−14.2082	−	10.3229i	−1.53211	−	1.11314i
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−8.23607			−0.873021			−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607			−0.873021			−0.436511	+	0.899699i	$0.643786\pi$
$90$	1.30902	+	0.951057i	0.137983	+	0.100250i
$91$	−0.0729490	+	0.224514i	−0.00764713	+	0.0235355i
$92$	0.354102	+	1.08981i	0.0369177	+	0.113621i
$93$	−4.92705	+	3.57971i	−0.510911	+	0.371199i
$94$	21.3713	−	15.5272i	2.20428	−	1.60151i
$95$	1.11803	+	3.44095i	0.114708	+	0.353035i
$96$	−3.35410	+	10.3229i	−0.342327	+	1.05357i
$97$	−6.35410	−	4.61653i	−0.645161	−	0.468737i	0.216458	−	0.976292i	$-0.430549\pi$
$97$	−6.35410	−	4.61653i	−0.645161	−	0.468737i	−0.861620	+	0.507555i	$0.830549\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	−8.28115	−	6.01661i	−0.824006	−	0.598675i	0.0938515	−	0.995586i	$-0.470082\pi$
$101$	−8.28115	−	6.01661i	−0.824006	−	0.598675i	−0.917857	+	0.396911i	$0.870082\pi$
$102$	−0.927051	+	2.85317i	−0.0917917	+	0.282506i
$103$	−3.38197	−	10.4086i	−0.333235	−	1.02559i	−0.967585	−	0.252546i	$-0.918732\pi$
$103$	−3.38197	−	10.4086i	−0.333235	−	1.02559i	0.634350	−	0.773046i	$-0.281268\pi$
$104$	1.42705	−	1.03681i	0.139934	−	0.101668i
$105$	−0.500000	+	0.363271i	−0.0487950	+	0.0354516i
$106$	−0.309017	−	0.951057i	−0.0300144	−	0.0923748i
$107$	3.54508	−	10.9106i	0.342716	−	1.05477i	−0.620079	−	0.784540i	$-0.712899\pi$
$107$	3.54508	−	10.9106i	0.342716	−	1.05477i	0.962795	−	0.270233i	$-0.0871006\pi$
$108$	3.92705	+	2.85317i	0.377881	+	0.274546i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	6.23607			0.591901
$112$	−7.97214	−	5.79210i	−0.753296	−	0.547302i
$113$	4.16312	−	12.8128i	0.391633	−	1.20532i	−0.539919	−	0.841717i	$-0.681545\pi$
$113$	4.16312	−	12.8128i	0.391633	−	1.20532i	0.931553	−	0.363607i	$-0.118455\pi$
$114$	4.73607	+	14.5761i	0.443573	+	1.36518i
$115$	0.118034	−	0.0857567i	0.0110067	−	0.00799685i
$116$	−23.5623	+	17.1190i	−2.18771	+	1.58946i
$117$	−0.0729490	−	0.224514i	−0.00674414	−	0.0207563i
$118$	5.97214	−	18.3803i	0.549780	−	1.69205i
$119$	−0.927051	−	0.673542i	−0.0849826	−	0.0617435i
$120$	4.61803			0.421567
$121$		0			0
$122$	30.2705			2.74056
$123$	−0.190983	−	0.138757i	−0.0172204	−	0.0125113i
$124$	−9.13525	+	28.1154i	−0.820370	+	2.52484i
$125$	1.83688	+	5.65334i	0.164296	+	0.505650i
$126$	−2.11803	+	1.53884i	−0.188689	+	0.137091i
$127$	6.23607	−	4.53077i	0.553362	−	0.402041i	−0.275662	−	0.961255i	$-0.588897\pi$
$127$	6.23607	−	4.53077i	0.553362	−	0.402041i	0.829023	+	0.559214i	$0.188897\pi$
$128$	0.336881	+	1.03681i	0.0297764	+	0.0916422i
$129$	−2.07295	+	6.37988i	−0.182513	+	0.561717i
$130$	−0.309017	−	0.224514i	−0.0271026	−	0.0196912i
$131$	11.7984			1.03083			0.515414	−	0.856941i	$-0.327638\pi$
$131$	11.7984			1.03083			0.515414	+	0.856941i	$0.327638\pi$
$132$		0			0
$133$	−5.85410			−0.507615
$134$	−3.92705	−	2.85317i	−0.339246	−	0.246476i
$135$	0.190983	−	0.587785i	0.0164372	−	0.0505885i
$136$	2.64590	+	8.14324i	0.226884	+	0.698277i
$137$	−7.89919	+	5.73910i	−0.674873	+	0.490324i	−0.871653	−	0.490124i	$-0.836952\pi$
$137$	−7.89919	+	5.73910i	−0.674873	+	0.490324i	0.196780	+	0.980448i	$0.436952\pi$
$138$	0.500000	−	0.363271i	0.0425628	−	0.0309237i
$139$	−4.50000	−	13.8496i	−0.381685	−	1.17471i	−0.938857	−	0.344308i	$-0.888113\pi$
$139$	−4.50000	−	13.8496i	−0.381685	−	1.17471i	0.557172	−	0.830397i	$-0.311887\pi$
$140$	−0.927051	+	2.85317i	−0.0783501	+	0.241137i
$141$	−8.16312	−	5.93085i	−0.687459	−	0.499468i
$142$	27.0344			2.26868
$143$		0			0
$144$	9.85410			0.821175
$145$	3.00000	+	2.17963i	0.249136	+	0.181008i
$146$	4.61803	−	14.2128i	0.382191	−	1.17626i
$147$	1.85410	+	5.70634i	0.152924	+	0.470651i
$148$	24.4894	−	17.7926i	2.01301	−	1.46254i
$149$	−3.42705	+	2.48990i	−0.280755	+	0.203980i	−0.719247	−	0.694755i	$-0.755513\pi$
$149$	−3.42705	+	2.48990i	−0.280755	+	0.203980i	0.438492	+	0.898735i	$0.355513\pi$
$150$	3.73607	+	11.4984i	0.305049	+	0.938843i
$151$	−0.326238	+	1.00406i	−0.0265489	+	0.0817090i	−0.963453	−	0.267877i	$-0.913678\pi$
$151$	−0.326238	+	1.00406i	−0.0265489	+	0.0817090i	0.936904	+	0.349586i	$0.113678\pi$
$152$	35.3885	+	25.7113i	2.87039	+	2.08546i
$153$	1.14590			0.0926404
$154$		0			0
$155$	3.76393			0.302326
$156$	−0.927051	−	0.673542i	−0.0742235	−	0.0539265i
$157$	4.85410	−	14.9394i	0.387400	−	1.19229i	−0.547325	−	0.836920i	$-0.684354\pi$
$157$	4.85410	−	14.9394i	0.387400	−	1.19229i	0.934725	−	0.355373i	$-0.115646\pi$
$158$	−8.89919	−	27.3889i	−0.707981	−	2.17894i
$159$	−0.309017	+	0.224514i	−0.0245066	+	0.0178051i
$160$	5.42705	−	3.94298i	0.429046	−	0.311720i
$161$	0.0729490	+	0.224514i	0.00574919	+	0.0176942i
$162$	0.809017	−	2.48990i	0.0635624	−	0.195625i
$163$	4.16312	+	3.02468i	0.326081	+	0.236911i	0.738766	−	0.673962i	$-0.235409\pi$
$163$	4.16312	+	3.02468i	0.326081	+	0.236911i	−0.412685	+	0.910874i	$0.635409\pi$
$164$	−1.14590			−0.0894796
$165$		0			0
$166$	−3.85410			−0.299136
$167$	9.73607	+	7.07367i	0.753400	+	0.547377i	0.896879	−	0.442277i	$-0.145829\pi$
$167$	9.73607	+	7.07367i	0.753400	+	0.547377i	−0.143479	+	0.989653i	$0.545829\pi$
$168$	−2.30902	+	7.10642i	−0.178145	+	0.548272i
$169$	−4.00000	−	12.3107i	−0.307692	−	0.946980i
$170$	1.50000	−	1.08981i	0.115045	−	0.0835849i
$171$	4.73607	−	3.44095i	0.362176	−	0.263136i
$172$	10.0623	+	30.9686i	0.767244	+	2.36133i
$173$	5.57295	−	17.1518i	0.423703	−	1.30403i	−0.480527	−	0.876980i	$-0.659555\pi$
$173$	5.57295	−	17.1518i	0.423703	−	1.30403i	0.904230	−	0.427045i	$-0.140445\pi$
$174$	12.7082	+	9.23305i	0.963406	+	0.699956i
$175$	−4.61803			−0.349091
$176$		0			0
$177$	−7.38197			−0.554863
$178$	17.4443	+	12.6740i	1.30750	+	0.949957i
$179$	−2.63525	+	8.11048i	−0.196968	+	0.606206i	0.802980	+	0.596006i	$0.203247\pi$
$179$	−2.63525	+	8.11048i	−0.196968	+	0.606206i	−0.999948	+	0.0101995i	$0.996753\pi$
$180$	−0.927051	−	2.85317i	−0.0690983	−	0.212663i
$181$	−2.04508	+	1.48584i	−0.152010	+	0.110442i	−0.661191	−	0.750218i	$-0.729949\pi$
$181$	−2.04508	+	1.48584i	−0.152010	+	0.110442i	0.509181	+	0.860660i	$0.329949\pi$
$182$	0.500000	−	0.363271i	0.0370625	−	0.0269275i
$183$	−3.57295	−	10.9964i	−0.264120	−	0.812878i
$184$	0.545085	−	1.67760i	0.0401842	−	0.123674i
$185$	−3.11803	−	2.26538i	−0.229242	−	0.166554i
$186$	15.9443			1.16909
$187$		0			0
$188$	−48.9787			−3.57214
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	2.92705	−	9.00854i	0.212351	−	0.653548i
$191$	−0.253289	−	0.779543i	−0.0183273	−	0.0564058i	0.941475	−	0.337084i	$-0.109441\pi$
$191$	−0.253289	−	0.779543i	−0.0183273	−	0.0564058i	−0.959802	+	0.280678i	$0.909441\pi$
$192$	7.04508	−	5.11855i	0.508435	−	0.369400i
$193$	−2.54508	+	1.84911i	−0.183199	+	0.133102i	−0.675605	−	0.737264i	$-0.736118\pi$
$193$	−2.54508	+	1.84911i	−0.183199	+	0.133102i	0.492406	+	0.870366i	$0.336118\pi$
$194$	6.35410	+	19.5559i	0.456198	+	1.40403i
$195$	−0.0450850	+	0.138757i	−0.00322860	+	0.00993661i
$196$	23.5623	+	17.1190i	1.68302	+	1.22279i
$197$	−13.0344			−0.928666			−0.464333	−	0.885661i	$-0.653706\pi$
$197$	−13.0344			−0.928666			−0.464333	+	0.885661i	$0.653706\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	27.9164	+	20.2825i	1.97399	+	1.43419i
$201$	−0.572949	+	1.76336i	−0.0404127	+	0.124378i
$202$	8.28115	+	25.4868i	0.582660	+	1.79324i
$203$	−4.85410	+	3.52671i	−0.340691	+	0.247527i
$204$	4.50000	−	3.26944i	0.315063	−	0.228907i
$205$	0.0450850	+	0.138757i	0.00314887	+	0.00969123i
$206$	−8.85410	+	27.2501i	−0.616895	+	1.89861i
$207$	−0.190983	−	0.138757i	−0.0132742	−	0.00964430i
$208$	−2.32624			−0.161296
$209$		0			0
$210$	1.61803			0.111655
$211$	2.92705	+	2.12663i	0.201506	+	0.146403i	0.683963	−	0.729517i	$-0.260255\pi$
$211$	2.92705	+	2.12663i	0.201506	+	0.146403i	−0.482456	+	0.875920i	$0.660255\pi$
$212$	−0.572949	+	1.76336i	−0.0393503	+	0.121108i
$213$	−3.19098	−	9.82084i	−0.218643	−	0.672913i
$214$	−24.2984	+	17.6538i	−1.66100	+	1.20679i
$215$	3.35410	−	2.43690i	0.228748	−	0.166195i
$216$	−2.30902	−	7.10642i	−0.157109	−	0.483531i
$217$	−1.88197	+	5.79210i	−0.127756	+	0.393193i
$218$	−25.4164	−	18.4661i	−1.72142	−	1.25068i
$219$	−5.70820			−0.385725
$220$		0			0
$221$	−0.270510			−0.0181965
$222$	−13.2082	−	9.59632i	−0.886477	−	0.644063i
$223$	2.21885	−	6.82891i	0.148585	−	0.457298i	−0.848870	−	0.528602i	$-0.822716\pi$
$223$	2.21885	−	6.82891i	0.148585	−	0.457298i	0.997455	+	0.0713048i	$0.0227163\pi$
$224$	3.35410	+	10.3229i	0.224105	+	0.689725i
$225$	3.73607	−	2.71441i	0.249071	−	0.180961i
$226$	−28.5344	+	20.7315i	−1.89808	+	1.37904i
$227$	−4.07295	−	12.5352i	−0.270331	−	0.831994i	−0.990417	−	0.138109i	$-0.955898\pi$
$227$	−4.07295	−	12.5352i	−0.270331	−	0.831994i	0.720086	−	0.693885i	$-0.244102\pi$
$228$	8.78115	−	27.0256i	0.581546	−	1.78981i
$229$	−0.381966	−	0.277515i	−0.0252410	−	0.0183387i	0.575093	−	0.818088i	$-0.304966\pi$
$229$	−0.381966	−	0.277515i	−0.0252410	−	0.0183387i	−0.600334	+	0.799749i	$0.704966\pi$
$230$	−0.381966			−0.0251861
$231$		0			0
$232$	44.8328			2.94342
$233$	−3.35410	−	2.43690i	−0.219735	−	0.159646i	0.472473	−	0.881345i	$-0.343362\pi$
$233$	−3.35410	−	2.43690i	−0.219735	−	0.159646i	−0.692207	+	0.721699i	$0.743362\pi$
$234$	−0.190983	+	0.587785i	−0.0124849	+	0.0384247i
$235$	1.92705	+	5.93085i	0.125707	+	0.386886i
$236$	−28.9894	+	21.0620i	−1.88705	+	1.37102i
$237$	−8.89919	+	6.46564i	−0.578064	+	0.419988i
$238$	0.927051	+	2.85317i	0.0600918	+	0.184944i
$239$	−0.118034	+	0.363271i	−0.00763498	+	0.0234981i	−0.954801	−	0.297244i	$-0.903932\pi$
$239$	−0.118034	+	0.363271i	−0.00763498	+	0.0234981i	0.947166	+	0.320742i	$0.103932\pi$
$240$	−4.92705	−	3.57971i	−0.318040	−	0.231069i
$241$	−8.29180			−0.534122			−0.267061	−	0.963680i	$-0.586052\pi$
$241$	−8.29180			−0.534122			−0.267061	+	0.963680i	$0.586052\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	−45.4058	−	32.9892i	−2.90681	−	2.11192i
$245$	1.14590	−	3.52671i	0.0732087	−	0.225313i
$246$	0.190983	+	0.587785i	0.0121766	+	0.0374758i
$247$	−1.11803	+	0.812299i	−0.0711388	+	0.0516854i
$248$	36.8156	−	26.7481i	2.33779	−	1.69851i
$249$	0.454915	+	1.40008i	0.0288291	+	0.0887267i
$250$	4.80902	−	14.8006i	0.304149	−	0.936074i
$251$	17.7812	+	12.9188i	1.12234	+	0.815425i	0.984562	−	0.175038i	$-0.0560050\pi$
$251$	17.7812	+	12.9188i	1.12234	+	0.815425i	0.137775	+	0.990464i	$0.456005\pi$
$252$	4.85410			0.305780
$253$		0			0
$254$	−20.1803			−1.26623
$255$	−0.572949	−	0.416272i	−0.0358795	−	0.0260680i
$256$	−4.50000	+	13.8496i	−0.281250	+	0.865598i
$257$	9.19098	+	28.2869i	0.573318	+	1.76449i	0.641837	+	0.766841i	$0.278172\pi$
$257$	9.19098	+	28.2869i	0.573318	+	1.76449i	−0.0685195	+	0.997650i	$0.521828\pi$
$258$	14.2082	−	10.3229i	0.884564	−	0.642673i
$259$	5.04508	−	3.66547i	0.313486	−	0.227761i
$260$	0.218847	+	0.673542i	0.0135723	+	0.0417713i
$261$	1.85410	−	5.70634i	0.114766	−	0.353214i
$262$	−24.9894	−	18.1558i	−1.54385	−	1.12167i
$263$	15.2705			0.941620			0.470810	−	0.882235i	$-0.343962\pi$
$263$	15.2705			0.941620			0.470810	+	0.882235i	$0.343962\pi$
$264$		0			0
$265$	0.236068			0.0145015
$266$	12.3992	+	9.00854i	0.760243	+	0.552349i
$267$	2.54508	−	7.83297i	0.155757	−	0.479370i
$268$	2.78115	+	8.55951i	0.169886	+	0.522855i
$269$	20.5623	−	14.9394i	1.25371	−	0.910871i	0.255275	−	0.966868i	$-0.417834\pi$
$269$	20.5623	−	14.9394i	1.25371	−	0.910871i	0.998431	+	0.0559978i	$0.0178340\pi$
$270$	−1.30902	+	0.951057i	−0.0796642	+	0.0578795i
$271$	−5.75329	−	17.7068i	−0.349487	−	1.07561i	−0.959137	−	0.282941i	$-0.908690\pi$
$271$	−5.75329	−	17.7068i	−0.349487	−	1.07561i	0.609650	−	0.792671i	$-0.291310\pi$
$272$	3.48936	−	10.7391i	0.211573	−	0.651156i
$273$	−0.190983	−	0.138757i	−0.0115588	−	0.00839797i
$274$	25.5623			1.54428
$275$		0			0
$276$	−1.14590			−0.0689750
$277$	−23.6353	−	17.1720i	−1.42010	−	1.03177i	−0.991754	−	0.128154i	$-0.959095\pi$
$277$	−23.6353	−	17.1720i	−1.42010	−	1.03177i	−0.428351	−	0.903613i	$-0.640905\pi$
$278$	−11.7812	+	36.2587i	−0.706587	+	2.17465i
$279$	−1.88197	−	5.79210i	−0.112670	−	0.346764i
$280$	3.73607	−	2.71441i	0.223273	−	0.162217i
$281$	20.0344	−	14.5559i	1.19515	−	0.868331i	0.201355	−	0.979518i	$-0.435465\pi$
$281$	20.0344	−	14.5559i	1.19515	−	0.868331i	0.993799	+	0.111188i	$0.0354655\pi$
$282$	8.16312	+	25.1235i	0.486107	+	1.49608i
$283$	1.76393	−	5.42882i	0.104855	−	0.322710i	−0.884841	−	0.465892i	$-0.845733\pi$
$283$	1.76393	−	5.42882i	0.104855	−	0.322710i	0.989696	+	0.143182i	$0.0457335\pi$
$284$	−40.5517	−	29.4625i	−2.40630	−	1.74828i
$285$	−3.61803			−0.214314
$286$		0			0
$287$	−0.236068			−0.0139347
$288$	−8.78115	−	6.37988i	−0.517434	−	0.375938i
$289$	−4.84752	+	14.9191i	−0.285148	+	0.877597i
$290$	−3.00000	−	9.23305i	−0.176166	−	0.542183i
$291$	6.35410	−	4.61653i	0.372484	−	0.270626i
$292$	−22.4164	+	16.2865i	−1.31182	+	0.953094i
$293$	6.69098	+	20.5927i	0.390891	+	1.20304i	0.932115	+	0.362162i	$0.117961\pi$
$293$	6.69098	+	20.5927i	0.390891	+	1.20304i	−0.541224	+	0.840878i	$0.682039\pi$
$294$	4.85410	−	14.9394i	0.283097	−	0.871283i
$295$	3.69098	+	2.68166i	0.214897	+	0.156132i
$296$	−46.5967			−2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	0.0450850	+	0.0327561i	0.00260733	+	0.00189434i
$300$	6.92705	−	21.3193i	0.399933	−	1.23087i
$301$	2.07295	+	6.37988i	0.119483	+	0.367730i
$302$	2.23607	−	1.62460i	0.128671	−	0.0934851i
$303$	8.28115	−	6.01661i	0.475740	−	0.345645i
$304$	−17.8262	−	54.8635i	−1.02240	−	3.14664i
$305$	−2.20820	+	6.79615i	−0.126441	+	0.389147i
$306$	−2.42705	−	1.76336i	−0.138745	−	0.100804i
$307$	−27.9787			−1.59683			−0.798415	−	0.602108i	$-0.794328\pi$
$307$	−27.9787			−1.59683			−0.798415	+	0.602108i	$0.794328\pi$
$308$		0			0
$309$	10.9443			0.622598
$310$	−7.97214	−	5.79210i	−0.452787	−	0.328969i
$311$	3.60081	−	11.0822i	0.204183	−	0.628412i	−0.795563	−	0.605871i	$-0.792825\pi$
$311$	3.60081	−	11.0822i	0.204183	−	0.628412i	0.999746	−	0.0225404i	$-0.00717543\pi$
$312$	0.545085	+	1.67760i	0.0308594	+	0.0949753i
$313$	2.04508	−	1.48584i	0.115595	−	0.0839847i	−0.528486	−	0.848942i	$-0.677240\pi$
$313$	2.04508	−	1.48584i	0.115595	−	0.0839847i	0.644081	+	0.764957i	$0.277240\pi$
$314$	−33.2705	+	24.1724i	−1.87756	+	1.36413i
$315$	−0.190983	−	0.587785i	−0.0107607	−	0.0331179i
$316$	−16.5000	+	50.7818i	−0.928198	+	2.85670i
$317$	5.51722	+	4.00850i	0.309878	+	0.225140i	0.731844	−	0.681472i	$-0.238660\pi$
$317$	5.51722	+	4.00850i	0.309878	+	0.225140i	−0.421966	+	0.906612i	$0.638660\pi$
$318$	1.00000			0.0560772
$319$		0			0
$320$	−5.38197			−0.300861
$321$	9.28115	+	6.74315i	0.518023	+	0.376366i
$322$	0.190983	−	0.587785i	0.0106431	−	0.0327560i
$323$	−2.07295	−	6.37988i	−0.115342	−	0.354986i
$324$	−3.92705	+	2.85317i	−0.218169	+	0.158509i
$325$	−0.881966	+	0.640786i	−0.0489227	+	0.0355444i
$326$	−4.16312	−	12.8128i	−0.230574	−	0.709633i
$327$	−3.70820	+	11.4127i	−0.205064	+	0.631123i
$328$	1.42705	+	1.03681i	0.0787957	+	0.0572484i
$329$	−10.0902			−0.556289
$330$		0			0
$331$	16.7082			0.918366			0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082			0.918366			0.459183	+	0.888342i	$0.348142\pi$
$332$	5.78115	+	4.20025i	0.317282	+	0.230519i
$333$	−1.92705	+	5.93085i	−0.105602	+	0.325009i
$334$	−9.73607	−	29.9645i	−0.532734	−	1.63959i
$335$	0.927051	−	0.673542i	0.0506502	−	0.0367995i
$336$	7.97214	−	5.79210i	0.434916	−	0.315985i
$337$	5.61803	+	17.2905i	0.306034	+	0.941875i	0.979289	+	0.202465i	$0.0648954\pi$
$337$	5.61803	+	17.2905i	0.306034	+	0.941875i	−0.673256	+	0.739410i	$0.735105\pi$
$338$	−10.4721	+	32.2299i	−0.569609	+	1.75308i
$339$	10.8992	+	7.91872i	0.591963	+	0.430086i
$340$	−3.43769			−0.186435
$341$		0			0
$342$	−15.3262			−0.828748
$343$	10.5172	+	7.64121i	0.567877	+	0.412586i
$344$	15.4894	−	47.6713i	0.835130	−	2.57027i
$345$	0.0450850	+	0.138757i	0.00242729	+	0.00747044i
$346$	−38.1976	+	27.7522i	−2.05351	+	1.49196i
$347$	−1.23607	+	0.898056i	−0.0663556	+	0.0482102i	−0.620469	−	0.784231i	$-0.713058\pi$
$347$	−1.23607	+	0.898056i	−0.0663556	+	0.0482102i	0.554113	+	0.832441i	$0.313058\pi$
$348$	−9.00000	−	27.6992i	−0.482451	−	1.48483i
$349$	−3.92705	+	12.0862i	−0.210210	+	0.646961i	0.789249	+	0.614073i	$0.210470\pi$
$349$	−3.92705	+	12.0862i	−0.210210	+	0.646961i	−0.999459	+	0.0328870i	$0.989530\pi$
$350$	9.78115	+	7.10642i	0.522825	+	0.379854i
$351$	0.236068			0.0126004
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	15.6353	+	11.3597i	0.831004	+	0.603760i
$355$	−1.97214	+	6.06961i	−0.104670	+	0.322141i
$356$	−12.3541	−	38.0220i	−0.654766	−	2.01516i
$357$	0.927051	−	0.673542i	0.0490647	−	0.0356476i
$358$	18.0623	−	13.1230i	0.954623	−	0.693574i
$359$	3.00000	+	9.23305i	0.158334	+	0.487302i	0.998483	−	0.0550531i	$-0.0175328\pi$
$359$	3.00000	+	9.23305i	0.158334	+	0.487302i	−0.840149	+	0.542355i	$0.817533\pi$
$360$	−1.42705	+	4.39201i	−0.0752122	+	0.231479i
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	6.61803			0.347836
$363$		0			0
$364$	−1.14590			−0.0600614
$365$	2.85410	+	2.07363i	0.149391	+	0.108539i
$366$	−9.35410	+	28.7890i	−0.488947	+	1.50482i
$367$	6.84346	+	21.0620i	0.357226	+	1.09943i	0.954708	+	0.297545i	$0.0961679\pi$
$367$	6.84346	+	21.0620i	0.357226	+	1.09943i	−0.597482	+	0.801882i	$0.703832\pi$
$368$	−1.88197	+	1.36733i	−0.0981043	+	0.0712769i
$369$	0.190983	−	0.138757i	0.00994218	−	0.00722342i
$370$	3.11803	+	9.59632i	0.162099	+	0.498889i
$371$	−0.118034	+	0.363271i	−0.00612802	+	0.0188601i
$372$	−23.9164	−	17.3763i	−1.24001	−	0.900919i
$373$	−0.888544			−0.0460071			−0.0230035	−	0.999735i	$-0.507323\pi$
$373$	−0.888544			−0.0460071			−0.0230035	+	0.999735i	$0.507323\pi$
$374$		0			0
$375$	−5.94427			−0.306961
$376$	60.9959	+	44.3161i	3.14563	+	2.28543i
$377$	−0.437694	+	1.34708i	−0.0225424	+	0.0693784i
$378$	−0.809017	−	2.48990i	−0.0416113	−	0.128067i
$379$	20.1353	−	14.6291i	1.03428	−	0.751447i	0.0651180	−	0.997878i	$-0.479258\pi$
$379$	20.1353	−	14.6291i	1.03428	−	0.751447i	0.969161	+	0.246430i	$0.0792576\pi$
$380$	−14.2082	+	10.3229i	−0.728865	+	0.529552i
$381$	2.38197	+	7.33094i	0.122032	+	0.375575i
$382$	−0.663119	+	2.04087i	−0.0339281	+	0.104420i
$383$	10.2812	+	7.46969i	0.525342	+	0.381684i	0.818613	−	0.574346i	$-0.194744\pi$
$383$	10.2812	+	7.46969i	0.525342	+	0.381684i	−0.293270	+	0.956030i	$0.594744\pi$
$384$	−1.09017			−0.0556325
$385$		0			0
$386$	8.23607			0.419205
$387$	−5.42705	−	3.94298i	−0.275873	−	0.200433i
$388$	11.7812	−	36.2587i	0.598097	−	1.84075i
$389$	−11.3541	−	34.9443i	−0.575676	−	1.77175i	−0.633866	−	0.773443i	$-0.718533\pi$
$389$	−11.3541	−	34.9443i	−0.575676	−	1.77175i	0.0581906	−	0.998305i	$-0.481467\pi$
$390$	0.309017	−	0.224514i	0.0156477	−	0.0113687i
$391$	−0.218847	+	0.159002i	−0.0110676	+	0.00804106i
$392$	−13.8541	−	42.6385i	−0.699738	−	2.15357i
$393$	−3.64590	+	11.2209i	−0.183911	+	0.566021i
$394$	27.6074	+	20.0579i	1.39084	+	1.01050i
$395$	6.79837			0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$	−14.2082	−	10.3229i	−0.712193	−	0.517438i
$399$	1.80902	−	5.56758i	0.0905641	−	0.278728i
$400$	−14.0623	−	43.2793i	−0.703115	−	2.16397i
$401$	25.6353	−	18.6251i	1.28016	−	0.930093i	0.280606	−	0.959823i	$-0.409465\pi$
$401$	25.6353	−	18.6251i	1.28016	−	0.930093i	0.999558	+	0.0297299i	$0.00946472\pi$
$402$	3.92705	−	2.85317i	0.195864	−	0.142303i
$403$	0.444272	+	1.36733i	0.0221308	+	0.0681115i
$404$	15.3541	−	47.2551i	0.763895	−	2.35103i
$405$	0.500000	+	0.363271i	0.0248452	+	0.0180511i
$406$	15.7082			0.779585
$407$		0			0
$408$	−8.56231			−0.423897
$409$	−5.23607	−	3.80423i	−0.258907	−	0.188107i	0.450758	−	0.892646i	$-0.351154\pi$
$409$	−5.23607	−	3.80423i	−0.258907	−	0.188107i	−0.709665	+	0.704539i	$0.751154\pi$
$410$	0.118034	−	0.363271i	0.00582928	−	0.0179407i
$411$	−3.01722	−	9.28605i	−0.148829	−	0.458047i
$412$	42.9787	−	31.2259i	2.11741	−	1.53839i
$413$	−5.97214	+	4.33901i	−0.293870	+	0.213509i
$414$	0.190983	+	0.587785i	0.00938630	+	0.0288881i
$415$	0.281153	−	0.865300i	0.0138013	−	0.0424759i
$416$	2.07295	+	1.50609i	0.101635	+	0.0738419i
$417$	14.5623			0.713119
$418$		0			0
$419$	31.4508			1.53647			0.768237	−	0.640165i	$-0.221134\pi$
$419$	31.4508			1.53647			0.768237	+	0.640165i	$0.221134\pi$
$420$	−2.42705	−	1.76336i	−0.118428	−	0.0860430i
$421$	3.24671	−	9.99235i	0.158235	−	0.486997i	−0.840239	−	0.542216i	$-0.817586\pi$
$421$	3.24671	−	9.99235i	0.158235	−	0.486997i	0.998474	+	0.0552185i	$0.0175855\pi$
$422$	−2.92705	−	9.00854i	−0.142487	−	0.438529i
$423$	8.16312	−	5.93085i	0.396904	−	0.288368i
$424$	2.30902	−	1.67760i	0.112136	−	0.0814714i
$425$	−1.63525	−	5.03280i	−0.0793215	−	0.244127i
$426$	−8.35410	+	25.7113i	−0.404758	+	1.24572i
$427$	−9.35410	−	6.79615i	−0.452677	−	0.328889i
$428$	55.6869			2.69173
$429$		0			0
$430$	−10.8541			−0.523431
$431$	−4.78115	−	3.47371i	−0.230300	−	0.167323i	0.466651	−	0.884442i	$-0.345460\pi$
$431$	−4.78115	−	3.47371i	−0.230300	−	0.167323i	−0.696951	+	0.717119i	$0.745460\pi$
$432$	−3.04508	+	9.37181i	−0.146507	+	0.450901i
$433$	10.9098	+	33.5770i	0.524293	+	1.61361i	0.765710	+	0.643186i	$0.222388\pi$
$433$	10.9098	+	33.5770i	0.524293	+	1.61361i	−0.241417	+	0.970422i	$0.577612\pi$
$434$	12.8992	−	9.37181i	0.619181	−	0.449861i
$435$	−3.00000	+	2.17963i	−0.143839	+	0.104505i
$436$	18.0000	+	55.3983i	0.862044	+	2.65310i
$437$	−0.427051	+	1.31433i	−0.0204286	+	0.0628728i
$438$	12.0902	+	8.78402i	0.577691	+	0.419717i
$439$	−23.2918			−1.11166			−0.555828	−	0.831297i	$-0.687599\pi$
$439$	−23.2918			−1.11166			−0.555828	+	0.831297i	$0.687599\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	0.572949	+	0.416272i	0.0272524	+	0.0198000i
$443$	−9.76393	+	30.0503i	−0.463898	+	1.42773i	0.396464	+	0.918050i	$0.370237\pi$
$443$	−9.76393	+	30.0503i	−0.463898	+	1.42773i	−0.860363	+	0.509682i	$0.829763\pi$
$444$	9.35410	+	28.7890i	0.443926	+	1.36626i
$445$	−4.11803	+	2.99193i	−0.195214	+	0.141831i
$446$	−15.2082	+	11.0494i	−0.720129	+	0.523205i
$447$	−1.30902	−	4.02874i	−0.0619144	−	0.190553i
$448$	2.69098	−	8.28199i	0.127137	−	0.391287i
$449$	7.32624	+	5.32282i	0.345747	+	0.251200i	0.747082	−	0.664731i	$-0.231454\pi$
$449$	7.32624	+	5.32282i	0.345747	+	0.251200i	−0.401336	+	0.915931i	$0.631454\pi$
$450$	−12.0902			−0.569936
$451$		0			0
$452$	65.3951			3.07593
$453$	−0.854102	−	0.620541i	−0.0401292	−	0.0291556i
$454$	−10.6631	+	32.8177i	−0.500445	+	1.54021i
$455$	0.0450850	+	0.138757i	0.00211362	+	0.00650504i
$456$	−35.3885	+	25.7113i	−1.65722	+	1.20404i
$457$	19.3992	−	14.0943i	0.907456	−	0.659305i	−0.0329144	−	0.999458i	$-0.510479\pi$
$457$	19.3992	−	14.0943i	0.907456	−	0.659305i	0.940370	+	0.340153i	$0.110479\pi$
$458$	0.381966	+	1.17557i	0.0178481	+	0.0549308i
$459$	−0.354102	+	1.08981i	−0.0165281	+	0.0508682i
$460$	0.572949	+	0.416272i	0.0267139	+	0.0194088i
$461$	−9.27051			−0.431771			−0.215885	−	0.976419i	$-0.569264\pi$
$461$	−9.27051			−0.431771			−0.215885	+	0.976419i	$0.569264\pi$
$462$		0			0
$463$	1.72949			0.0803762			0.0401881	−	0.999192i	$-0.487204\pi$
$463$	1.72949			0.0803762			0.0401881	+	0.999192i	$0.487204\pi$
$464$	−47.8328	−	34.7526i	−2.22058	−	1.61335i
$465$	−1.16312	+	3.57971i	−0.0539384	+	0.166005i
$466$	3.35410	+	10.3229i	0.155376	+	0.478197i
$467$	−16.8992	+	12.2780i	−0.782001	+	0.568157i	−0.905579	−	0.424178i	$-0.860563\pi$
$467$	−16.8992	+	12.2780i	−0.782001	+	0.568157i	0.123578	+	0.992335i	$0.460563\pi$
$468$	0.927051	−	0.673542i	0.0428529	−	0.0311345i
$469$	0.572949	+	1.76336i	0.0264563	+	0.0814242i
$470$	5.04508	−	15.5272i	0.232712	−	0.716215i
$471$	12.7082	+	9.23305i	0.585563	+	0.425437i
$472$	55.1591			2.53890
$473$		0			0
$474$	28.7984			1.32275
$475$	−21.8713	−	15.8904i	−1.00353	−	0.729104i
$476$	1.71885	−	5.29007i	0.0787832	−	0.242470i
$477$	−0.118034	−	0.363271i	−0.00540441	−	0.0166330i
$478$	0.809017	−	0.587785i	0.0370036	−	0.0268847i
$479$	−22.9615	+	16.6825i	−1.04914	+	0.762243i	−0.972048	−	0.234781i	$-0.924563\pi$
$479$	−22.9615	+	16.6825i	−1.04914	+	0.762243i	−0.0770892	+	0.997024i	$0.524563\pi$
$480$	2.07295	+	6.37988i	0.0946167	+	0.291200i
$481$	0.454915	−	1.40008i	0.0207423	−	0.0638384i
$482$	17.5623	+	12.7598i	0.799941	+	0.581191i
$483$	−0.236068			−0.0107415
$484$		0			0
$485$	−4.85410			−0.220413
$486$	2.11803	+	1.53884i	0.0960760	+	0.0698033i
$487$	−3.92705	+	12.0862i	−0.177952	+	0.547679i	−0.999756	−	0.0220909i	$-0.992968\pi$
$487$	−3.92705	+	12.0862i	−0.177952	+	0.547679i	0.821804	+	0.569770i	$0.192968\pi$
$488$	26.6976	+	82.1666i	1.20854	+	3.71951i
$489$	−4.16312	+	3.02468i	−0.188263	+	0.136781i
$490$	−7.85410	+	5.70634i	−0.354812	+	0.257786i
$491$	5.53444	+	17.0333i	0.249766	+	0.768700i	0.994816	+	0.101692i	$0.0324255\pi$
$491$	5.53444	+	17.0333i	0.249766	+	0.768700i	−0.745050	+	0.667009i	$0.767574\pi$
$492$	0.354102	−	1.08981i	0.0159641	−	0.0491326i
$493$	−5.56231	−	4.04125i	−0.250514	−	0.182009i
$494$	3.61803			0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	−8.35410	−	6.06961i	−0.374733	−	0.272259i
$498$	1.19098	−	3.66547i	0.0533692	−	0.164254i
$499$	−5.60739	−	17.2578i	−0.251021	−	0.772564i	−0.994588	−	0.103902i	$-0.966867\pi$
$499$	−5.60739	−	17.2578i	−0.251021	−	0.772564i	0.743566	−	0.668662i	$-0.233133\pi$
$500$	−23.3435	+	16.9600i	−1.04395	+	0.758475i
$501$	−9.73607	+	7.07367i	−0.434975	+	0.316028i
$502$	−17.7812	−	54.7248i	−0.793612	−	2.44249i
$503$	−2.67376	+	8.22899i	−0.119217	+	0.366913i	−0.992803	−	0.119757i	$-0.961788\pi$
$503$	−2.67376	+	8.22899i	−0.119217	+	0.366913i	0.873586	+	0.486670i	$0.161788\pi$
$504$	−6.04508	−	4.39201i	−0.269269	−	0.195636i
$505$	−6.32624			−0.281514
$506$		0			0
$507$	12.9443			0.574875
$508$	30.2705	+	21.9928i	1.34304	+	0.975773i
$509$	11.9721	−	36.8464i	0.530656	−	1.63319i	−0.222198	−	0.975002i	$-0.571323\pi$
$509$	11.9721	−	36.8464i	0.530656	−	1.63319i	0.752853	−	0.658188i	$-0.228677\pi$
$510$	0.572949	+	1.76336i	0.0253706	+	0.0780827i
$511$	−4.61803	+	3.35520i	−0.204290	+	0.148425i
$512$	32.6074	−	23.6907i	1.44106	−	1.04699i
$513$	1.80902	+	5.56758i	0.0798701	+	0.245815i
$514$	24.0623	−	74.0562i	1.06134	−	3.26648i
$515$	−5.47214	−	3.97574i	−0.241131	−	0.175192i
$516$	−32.5623			−1.43348
$517$		0			0
$518$	−16.3262			−0.717334
$519$	14.5902	+	10.6004i	0.640437	+	0.465305i
$520$	0.336881	−	1.03681i	0.0147732	−	0.0454673i
$521$	2.76393	+	8.50651i	0.121090	+	0.372677i	0.993168	−	0.116689i	$-0.0372282\pi$
$521$	2.76393	+	8.50651i	0.121090	+	0.372677i	−0.872078	+	0.489366i	$0.837228\pi$
$522$	−12.7082	+	9.23305i	−0.556223	+	0.404120i
$523$	14.7812	−	10.7391i	0.646335	−	0.469590i	−0.215686	−	0.976463i	$-0.569199\pi$
$523$	14.7812	−	10.7391i	0.646335	−	0.469590i	0.862021	+	0.506873i	$0.169199\pi$
$524$	17.6976	+	54.4675i	0.773122	+	2.37942i
$525$	1.42705	−	4.39201i	0.0622816	−	0.191683i
$526$	−32.3435	−	23.4989i	−1.41024	−	1.02460i
$527$	−6.97871			−0.303998
$528$		0			0
$529$	−22.9443			−0.997577
$530$	−0.500000	−	0.363271i	−0.0217186	−	0.0157795i
$531$	2.28115	−	7.02067i	0.0989936	−	0.304671i
$532$	−8.78115	−	27.0256i	−0.380711	−	1.17171i
$533$	−0.0450850	+	0.0327561i	−0.00195285	+	0.00141883i
$534$	−17.4443	+	12.6740i	−0.754887	+	0.548458i
$535$	−2.19098	−	6.74315i	−0.0947245	−	0.291532i
$536$	4.28115	−	13.1760i	0.184918	−	0.569118i
$537$	−6.89919	−	5.01255i	−0.297722	−	0.216308i
$538$	−66.5410			−2.86879
$539$		0			0
$540$	3.00000			0.129099
$541$	−6.06231	−	4.40452i	−0.260639	−	0.189365i	0.449790	−	0.893134i	$-0.351499\pi$
$541$	−6.06231	−	4.40452i	−0.260639	−	0.189365i	−0.710429	+	0.703769i	$0.751499\pi$
$542$	−15.0623	+	46.3570i	−0.646981	+	1.99120i
$543$	−0.781153	−	2.40414i	−0.0335225	−	0.103172i
$544$	−10.0623	+	7.31069i	−0.431418	+	0.313443i
$545$	6.00000	−	4.35926i	0.257012	−	0.186730i
$546$	0.190983	+	0.587785i	0.00817332	+	0.0251549i
$547$	9.50000	−	29.2380i	0.406191	−	1.25013i	−0.513706	−	0.857966i	$-0.671728\pi$
$547$	9.50000	−	29.2380i	0.406191	−	1.25013i	0.919897	−	0.392160i	$-0.128272\pi$
$548$	−38.3435	−	27.8582i	−1.63795	−	1.19004i
$549$	11.5623			0.493467
$550$		0			0
$551$	−35.1246			−1.49636
$552$	1.42705	+	1.03681i	0.0607393	+	0.0441297i
$553$	−3.39919	+	10.4616i	−0.144548	+	0.444873i
$554$	23.6353	+	72.7418i	1.00417	+	3.09050i
$555$	3.11803	−	2.26538i	0.132353	−	0.0961602i
$556$	57.1869	−	41.5487i	2.42527	−	1.76206i
$557$	−11.6287	−	35.7894i	−0.492723	−	1.51645i	−0.820476	−	0.571682i	$-0.806291\pi$
$557$	−11.6287	−	35.7894i	−0.492723	−	1.51645i	0.327753	−	0.944764i	$-0.393709\pi$
$558$	−4.92705	+	15.1639i	−0.208579	+	0.641939i
$559$	1.28115	+	0.930812i	0.0541870	+	0.0393692i
$560$	−6.09017			−0.257357
$561$		0			0
$562$	−64.8328			−2.73481
$563$	32.8435	+	23.8622i	1.38419	+	1.00567i	0.996475	+	0.0838899i	$0.0267344\pi$
$563$	32.8435	+	23.8622i	1.38419	+	1.00567i	0.387712	+	0.921781i	$0.373266\pi$
$564$	15.1353	−	46.5815i	0.637309	−	1.96144i
$565$	−2.57295	−	7.91872i	−0.108245	−	0.333143i
$566$	−12.0902	+	8.78402i	−0.508188	+	0.369220i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	23.8435	+	73.3826i	1.00045	+	3.07907i
$569$	−10.5623	+	32.5074i	−0.442795	+	1.36278i	0.442089	+	0.896971i	$0.354237\pi$
$569$	−10.5623	+	32.5074i	−0.442795	+	1.36278i	−0.884884	+	0.465811i	$0.845763\pi$
$570$	7.66312	+	5.56758i	0.320973	+	0.233200i
$571$	9.09017			0.380412			0.190206	−	0.981744i	$-0.439084\pi$
$571$	9.09017			0.380412			0.190206	+	0.981744i	$0.439084\pi$
$572$		0			0
$573$	0.819660			0.0342418
$574$	0.500000	+	0.363271i	0.0208696	+	0.0151626i
$575$	−0.336881	+	1.03681i	−0.0140489	+	0.0432381i
$576$	2.69098	+	8.28199i	0.112124	+	0.345083i
$577$	−25.6525	+	18.6376i	−1.06793	+	0.775894i	−0.975538	−	0.219829i	$-0.929450\pi$
$577$	−25.6525	+	18.6376i	−1.06793	+	0.775894i	−0.0923881	+	0.995723i	$0.529450\pi$
$578$	33.2254	−	24.1397i	1.38200	−	1.00408i
$579$	−0.972136	−	2.99193i	−0.0404006	−	0.124340i
$580$	−5.56231	+	17.1190i	−0.230962	+	0.710829i
$581$	1.19098	+	0.865300i	0.0494103	+	0.0358987i
$582$	−20.5623			−0.852335
$583$		0			0
$584$	42.6525			1.76497
$585$	−0.118034	−	0.0857567i	−0.00488010	−	0.00354560i
$586$	17.5172	−	53.9125i	0.723630	−	2.22710i
$587$	−0.656541	−	2.02063i	−0.0270984	−	0.0834002i	0.936593	−	0.350420i	$-0.113961\pi$
$587$	−0.656541	−	2.02063i	−0.0270984	−	0.0834002i	−0.963691	+	0.267020i	$0.913961\pi$
$588$	−23.5623	+	17.1190i	−0.971693	+	0.705976i
$589$	−28.8435	+	20.9560i	−1.18847	+	0.863477i
$590$	−3.69098	−	11.3597i	−0.151955	−	0.467671i
$591$	4.02786	−	12.3965i	0.165684	−	0.509923i
$592$	49.7148	+	36.1199i	2.04326	+	1.48452i
$593$	14.0344			0.576325			0.288163	−	0.957581i	$-0.406956\pi$
$593$	14.0344			0.576325			0.288163	+	0.957581i	$0.406956\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	−16.6353	−	12.0862i	−0.681407	−	0.495071i
$597$	−2.07295	+	6.37988i	−0.0848402	+	0.261111i
$598$	−0.0450850	−	0.138757i	−0.00184366	−	0.00567421i
$599$	−10.2361	+	7.43694i	−0.418234	+	0.303865i	−0.776927	−	0.629591i	$-0.783223\pi$
$599$	−10.2361	+	7.43694i	−0.418234	+	0.303865i	0.358693	+	0.933456i	$0.383223\pi$
$600$	−27.9164	+	20.2825i	−1.13968	+	0.828028i
$601$	2.12868	+	6.55139i	0.0868306	+	0.267237i	0.985039	−	0.172334i	$-0.0551307\pi$
$601$	2.12868	+	6.55139i	0.0868306	+	0.267237i	−0.898208	+	0.439570i	$0.855131\pi$
$602$	5.42705	−	16.7027i	0.221190	−	0.680753i
$603$	−1.50000	−	1.08981i	−0.0610847	−	0.0443806i
$604$	−5.12461			−0.208517
$605$		0			0
$606$	−26.7984			−1.08861
$607$	−13.3992	−	9.73508i	−0.543856	−	0.395135i	0.281659	−	0.959515i	$-0.409115\pi$
$607$	−13.3992	−	9.73508i	−0.543856	−	0.395135i	−0.825515	+	0.564380i	$0.809115\pi$
$608$	−19.6353	+	60.4311i	−0.796315	+	2.45080i
$609$	−1.85410	−	5.70634i	−0.0751320	−	0.231233i
$610$	15.1353	−	10.9964i	0.612809	−	0.445231i
$611$	−1.92705	+	1.40008i	−0.0779601	+	0.0566414i
$612$	1.71885	+	5.29007i	0.0694803	+	0.213838i
$613$	4.41641	−	13.5923i	0.178377	−	0.548988i	−0.821395	−	0.570360i	$-0.806804\pi$
$613$	4.41641	−	13.5923i	0.178377	−	0.548988i	0.999772	+	0.0213723i	$0.00680355\pi$
$614$	59.2599	+	43.0548i	2.39153	+	1.73755i
$615$	−0.145898			−0.00588318
$616$		0			0
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$	−23.1803	−	16.8415i	−0.932450	−	0.677465i
$619$	7.45492	−	22.9439i	0.299638	−	0.922192i	−0.681985	−	0.731366i	$-0.738883\pi$
$619$	7.45492	−	22.9439i	0.299638	−	0.922192i	0.981624	−	0.190826i	$-0.0611167\pi$
$620$	5.64590	+	17.3763i	0.226745	+	0.697848i
$621$	0.190983	−	0.138757i	0.00766388	−	0.00556814i
$622$	−24.6803	+	17.9313i	−0.989591	+	0.718980i
$623$	−2.54508	−	7.83297i	−0.101967	−	0.313821i
$624$	0.718847	−	2.21238i	0.0287769	−	0.0885662i
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$	−6.61803			−0.264510
$627$		0			0
$628$	76.2492			3.04268
$629$	5.78115	+	4.20025i	0.230510	+	0.167475i
$630$	−0.500000	+	1.53884i	−0.0199205	+	0.0613089i
$631$	5.93769	+	18.2743i	0.236376	+	0.727490i	0.996936	+	0.0782225i	$0.0249245\pi$
$631$	5.93769	+	18.2743i	0.236376	+	0.727490i	−0.760560	+	0.649268i	$0.775076\pi$
$632$	66.4959	−	48.3121i	2.64507	−	1.92175i
$633$	−2.92705	+	2.12663i	−0.116340	+	0.0845258i
$634$	−5.51722	−	16.9803i	−0.219117	−	0.674372i
$635$	1.47214	−	4.53077i	0.0584199	−	0.179798i
$636$	−1.50000	−	1.08981i	−0.0594789	−	0.0432139i
$637$	1.41641			0.0561201
$638$		0			0
$639$	10.3262			0.408500
$640$	0.545085	+	0.396027i	0.0215464	+	0.0156544i
$641$	−7.75329	+	23.8622i	−0.306236	+	0.942499i	0.672976	+	0.739664i	$0.265016\pi$
$641$	−7.75329	+	23.8622i	−0.306236	+	0.942499i	−0.979213	+	0.202835i	$0.934984\pi$
$642$	−9.28115	−	28.5645i	−0.366298	−	1.12735i
$643$	−16.8713	+	12.2577i	−0.665340	+	0.483398i	−0.868462	−	0.495756i	$-0.834891\pi$
$643$	−16.8713	+	12.2577i	−0.665340	+	0.483398i	0.203122	+	0.979153i	$0.434891\pi$
$644$	−0.927051	+	0.673542i	−0.0365309	+	0.0265413i
$645$	1.28115	+	3.94298i	0.0504453	+	0.155255i
$646$	−5.42705	+	16.7027i	−0.213524	+	0.657161i
$647$	−36.4336	−	26.4706i	−1.43235	−	1.04067i	−0.989572	−	0.144036i	$-0.953992\pi$
$647$	−36.4336	−	26.4706i	−1.43235	−	1.04067i	−0.442781	−	0.896630i	$-0.646008\pi$
$648$	7.47214			0.293533
$649$		0			0
$650$	2.85410			0.111947
$651$	−4.92705	−	3.57971i	−0.193106	−	0.140300i
$652$	−7.71885	+	23.7562i	−0.302293	+	0.930363i
$653$	−1.73607	−	5.34307i	−0.0679376	−	0.209090i	0.911324	−	0.411690i	$-0.135061\pi$
$653$	−1.73607	−	5.34307i	−0.0679376	−	0.209090i	−0.979262	+	0.202599i	$0.935061\pi$
$654$	25.4164	−	18.4661i	0.993860	−	0.722082i
$655$	5.89919	−	4.28601i	0.230500	−	0.167468i
$656$	−0.718847	−	2.21238i	−0.0280663	−	0.0863791i
$657$	1.76393	−	5.42882i	0.0688175	−	0.211799i
$658$	21.3713	+	15.5272i	0.833141	+	0.605312i
$659$	41.1246			1.60199			0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246			1.60199			0.800994	+	0.598673i	$0.204305\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$	−35.3885	−	25.7113i	−1.37541	−	0.999297i
$663$	0.0835921	−	0.257270i	0.00324645	−	0.00999154i
$664$	−3.39919	−	10.4616i	−0.131914	−	0.405990i
$665$	−2.92705	+	2.12663i	−0.113506	+	0.0824671i
$666$	13.2082	−	9.59632i	0.511808	−	0.371850i
$667$	0.437694	+	1.34708i	0.0169476	+	0.0521593i
$668$	−18.0517	+	55.5573i	−0.698440	+	2.14958i
$669$	5.80902	+	4.22050i	0.224590	+	0.163174i
$670$	−3.00000			−0.115900
$671$		0			0
$672$	−10.8541			−0.418706
$673$	28.9894	+	21.0620i	1.11746	+	0.811880i	0.983822	−	0.179150i	$-0.0573348\pi$
$673$	28.9894	+	21.0620i	1.11746	+	0.811880i	0.133636	+	0.991031i	$0.457335\pi$
$674$	14.7082	−	45.2672i	0.566539	−	1.74363i
$675$	1.42705	+	4.39201i	0.0549272	+	0.169049i
$676$	50.8328	−	36.9322i	1.95511	−	1.42047i
$677$	10.9443	−	7.95148i	0.420623	−	0.305600i	−0.357266	−	0.934003i	$-0.616291\pi$
$677$	10.9443	−	7.95148i	0.420623	−	0.305600i	0.777888	+	0.628403i	$0.216291\pi$
$678$	−10.8992	−	33.5442i	−0.418581	−	1.28826i
$679$	2.42705	−	7.46969i	0.0931417	−	0.286661i
$680$	4.28115	+	3.11044i	0.164175	+	0.119280i
$681$	13.1803			0.505072
$682$		0			0
$683$	9.06888			0.347011			0.173506	−	0.984833i	$-0.444491\pi$
$683$	9.06888			0.347011			0.173506	+	0.984833i	$0.444491\pi$
$684$	22.9894	+	16.7027i	0.879020	+	0.638645i
$685$	−1.86475	+	5.73910i	−0.0712482	+	0.219280i
$686$	−10.5172	−	32.3687i	−0.401549	−	1.23584i
$687$	0.381966	−	0.277515i	0.0145729	−	0.0105878i
$688$	−53.4787	+	38.8546i	−2.03886	+	1.48132i
$689$	0.0278640	+	0.0857567i	0.00106154	+	0.00326707i
$690$	0.118034	−	0.363271i	0.00449348	−	0.0138295i
$691$	−1.09017	−	0.792055i	−0.0414720	−	0.0301312i	0.566856	−	0.823817i	$-0.308160\pi$
$691$	−1.09017	−	0.792055i	−0.0414720	−	0.0301312i	−0.608328	+	0.793686i	$0.708160\pi$
$692$	87.5410			3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	−7.28115	−	5.29007i	−0.276190	−	0.200664i
$696$	−13.8541	+	42.6385i	−0.525138	+	1.61621i
$697$	−0.0835921	−	0.257270i	−0.00316628	−	0.00974480i
$698$	26.9164	−	19.5559i	1.01880	−	0.740202i
$699$	3.35410	−	2.43690i	0.126864	−	0.0921719i
$700$	−6.92705	−	21.3193i	−0.261818	−	0.805793i
$701$	10.7533	−	33.0952i	0.406146	−	1.24999i	−0.513788	−	0.857917i	$-0.671758\pi$
$701$	10.7533	−	33.0952i	0.406146	−	1.24999i	0.919934	−	0.392072i	$-0.128242\pi$
$702$	−0.500000	−	0.363271i	−0.0188713	−	0.0137108i
$703$	36.5066			1.37687
$704$		0			0
$705$	−6.23607			−0.234864
$706$	25.4164	+	18.4661i	0.956559	+	0.694981i
$707$	3.16312	−	9.73508i	0.118961	−	0.366125i
$708$	−11.0729	−	34.0790i	−0.416147	−	1.28077i
$709$	−9.07295	+	6.59188i	−0.340742	+	0.247563i	−0.744975	−	0.667093i	$-0.767538\pi$
$709$	−9.07295	+	6.59188i	−0.340742	+	0.247563i	0.404233	+	0.914656i	$0.367538\pi$
$710$	13.5172	−	9.82084i	0.507292	−	0.368569i
$711$	−3.39919	−	10.4616i	−0.127479	−	0.392341i
$712$	−19.0172	+	58.5290i	−0.712700	+	2.19347i
$713$	1.16312	+	0.845055i	0.0435591	+	0.0316476i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	−41.3951			−1.54701
$717$	−0.309017	−	0.224514i	−0.0115405	−	0.00838463i
$718$	7.85410	−	24.1724i	0.293112	−	0.902107i
$719$	−11.8926	−	36.6017i	−0.443519	−	1.36501i	−0.884099	−	0.467299i	$-0.845227\pi$
$719$	−11.8926	−	36.6017i	−0.443519	−	1.36501i	0.440580	−	0.897713i	$-0.354773\pi$
$720$	4.92705	−	3.57971i	0.183620	−	0.133408i
$721$	8.85410	−	6.43288i	0.329744	−	0.239573i
$722$	12.3541	+	38.0220i	0.459772	+	1.41503i
$723$	2.56231	−	7.88597i	0.0952932	−	0.293282i
$724$	−9.92705	−	7.21242i	−0.368936	−	0.268048i
$725$	−27.7082			−1.02906
$726$		0			0
$727$	−9.14590			−0.339203			−0.169601	−	0.985513i	$-0.554248\pi$
$727$	−9.14590			−0.339203			−0.169601	+	0.985513i	$0.554248\pi$
$728$	1.42705	+	1.03681i	0.0528900	+	0.0384269i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−2.85410	−	8.78402i	−0.105635	−	0.325111i
$731$	−6.21885	+	4.51826i	−0.230012	+	0.167114i
$732$	45.4058	−	32.9892i	1.67825	−	1.21932i
$733$	0.124612	+	0.383516i	0.00460264	+	0.0141655i	0.953331	−	0.301926i	$-0.0976295\pi$
$733$	0.124612	+	0.383516i	0.00460264	+	0.0141655i	−0.948729	+	0.316091i	$0.897629\pi$
$734$	17.9164	−	55.1410i	0.661307	−	2.03529i
$735$	3.00000	+	2.17963i	0.110657	+	0.0803968i
$736$	2.56231			0.0944478
$737$		0			0
$738$	−0.618034			−0.0227501
$739$	2.42705	+	1.76336i	0.0892805	+	0.0648661i	0.631530	−	0.775351i	$-0.282427\pi$
$739$	2.42705	+	1.76336i	0.0892805	+	0.0648661i	−0.542250	+	0.840218i	$0.682427\pi$
$740$	5.78115	−	17.7926i	0.212519	−	0.654067i
$741$	−0.427051	−	1.31433i	−0.0156881	−	0.0482830i
$742$	0.809017	−	0.587785i	0.0296999	−	0.0215783i
$743$	−34.6976	+	25.2093i	−1.27293	+	0.924838i	−0.999315	−	0.0370015i	$-0.988219\pi$
$743$	−34.6976	+	25.2093i	−1.27293	+	0.924838i	−0.273615	+	0.961839i	$0.588219\pi$
$744$	14.0623	+	43.2793i	0.515549	+	1.58670i
$745$	−0.809017	+	2.48990i	−0.0296401	+	0.0912228i
$746$	1.88197	+	1.36733i	0.0689037	+	0.0500614i
$747$	−1.47214			−0.0538626
$748$		0			0
$749$	11.4721			0.419183
$750$	12.5902	+	9.14729i	0.459728	+	0.334012i
$751$	4.98936	−	15.3557i	0.182064	−	0.560336i	−0.817821	−	0.575472i	$-0.804818\pi$
$751$	4.98936	−	15.3557i	0.182064	−	0.560336i	0.999885	+	0.0151363i	$0.00481823\pi$
$752$	−30.7254	−	94.5631i	−1.12044	−	3.44836i
$753$	−17.7812	+	12.9188i	−0.647981	+	0.470786i
$754$	3.00000	−	2.17963i	0.109254	−	0.0793774i
$755$	0.201626	+	0.620541i	0.00733793	+	0.0225838i
$756$	−1.50000	+	4.61653i	−0.0545545	+	0.167901i
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	0.511843	−	0.859079i	$-0.328963\pi$
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	−0.658864	+	0.752262i	$0.728963\pi$
$758$	−65.1591			−2.36668
$759$		0			0
$760$	27.0344			0.980642
$761$	23.6976	+	17.2173i	0.859036	+	0.624126i	0.927623	−	0.373519i	$-0.121849\pi$
$761$	23.6976	+	17.2173i	0.859036	+	0.624126i	−0.0685866	+	0.997645i	$0.521849\pi$
$762$	6.23607	−	19.1926i	0.225909	−	0.695276i
$763$	3.70820	+	11.4127i	0.134246	+	0.413167i
$764$	3.21885	−	2.33863i	0.116454	−	0.0846086i
$765$	0.572949	−	0.416272i	0.0207150	−	0.0150503i
$766$	−10.2812	−	31.6421i	−0.371473	−	1.14328i
$767$	−0.538507	+	1.65735i	−0.0194444	+	0.0598436i
$768$	−11.7812	−	8.55951i	−0.425116	−	0.308865i
$769$	34.5066			1.24434			0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066			1.24434			0.622170	+	0.782883i	$0.286251\pi$
$770$		0

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.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(0.500000 - 0.363271i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 + 4.61653i) q^{4} +(0.500000 - 0.363271i) q^{5} +(2.11803 - 1.53884i) q^{6} +(0.309017 + 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.61803 q^{10} -4.85410 q^{12} +(0.190983 + 0.138757i) q^{13} +(0.809017 - 2.48990i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-0.927051 + 0.673542i) q^{17} +(0.809017 + 2.48990i) q^{18} +(-1.80902 + 5.56758i) q^{19} +(2.42705 + 1.76336i) q^{20} -1.00000 q^{21} +0.236068 q^{23} +(6.04508 + 4.39201i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(-0.190983 - 0.587785i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(1.85410 + 5.70634i) q^{29} +(0.500000 - 1.53884i) q^{30} +(4.92705 + 3.57971i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(0.500000 + 0.363271i) q^{35} +(1.50000 - 4.61653i) q^{36} +(-1.92705 - 5.93085i) q^{37} +(12.3992 - 9.00854i) q^{38} +(-0.190983 + 0.138757i) q^{39} +(-1.42705 - 4.39201i) q^{40} +(-0.0729490 + 0.224514i) q^{41} +(2.11803 + 1.53884i) q^{42} +6.70820 q^{43} -0.618034 q^{45} +(-0.500000 - 0.363271i) q^{46} +(-3.11803 + 9.59632i) q^{47} +(-3.04508 - 9.37181i) q^{48} +(4.85410 - 3.52671i) q^{49} +(9.78115 - 7.10642i) q^{50} +(-0.354102 - 1.08981i) q^{51} +(-0.354102 + 1.08981i) q^{52} +(0.309017 + 0.224514i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(-4.73607 - 3.44095i) q^{57} +(4.85410 - 14.9394i) q^{58} +(2.28115 + 7.02067i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(-9.35410 + 6.79615i) q^{61} +(-4.92705 - 15.1639i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-7.04508 - 5.11855i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(-4.50000 - 3.26944i) q^{68} +(-0.0729490 + 0.224514i) q^{69} +(-0.500000 - 1.53884i) q^{70} +(-8.35410 + 6.06961i) q^{71} +(-6.04508 + 4.39201i) q^{72} +(1.76393 + 5.42882i) q^{73} +(-5.04508 + 15.5272i) q^{74} +(-3.73607 - 2.71441i) q^{75} -28.4164 q^{76} +0.618034 q^{78} +(8.89919 + 6.46564i) q^{79} +(-1.88197 + 5.79210i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.500000 - 0.363271i) q^{82} +(1.19098 - 0.865300i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(-0.218847 + 0.673542i) q^{85} +(-14.2082 - 10.3229i) q^{86} -6.00000 q^{87} -8.23607 q^{89} +(1.30902 + 0.951057i) q^{90} +(-0.0729490 + 0.224514i) q^{91} +(0.354102 + 1.08981i) q^{92} +(-4.92705 + 3.57971i) q^{93} +(21.3713 - 15.5272i) q^{94} +(1.11803 + 3.44095i) q^{95} +(-3.35410 + 10.3229i) q^{96} +(-6.35410 - 4.61653i) q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9	\( 4 q - 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9} - 2 q^{10} - 6 q^{12} + 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 3 q^{20} - 4 q^{21} - 8 q^{23} + 13 q^{24} + q^{25} - 3 q^{26} + q^{27} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 13 q^{31} + 30 q^{32} + 12 q^{34} + 2 q^{35} + 6 q^{36} - q^{37} + 25 q^{38} - 3 q^{39} + q^{40} - 7 q^{41} + 4 q^{42} + 2 q^{45} - 2 q^{46} - 8 q^{47} - q^{48} + 6 q^{49} + 19 q^{50} + 12 q^{51} + 12 q^{52} - q^{53} - 6 q^{54} + 12 q^{56} - 10 q^{57} + 6 q^{58} - 11 q^{59} - 3 q^{60} - 24 q^{61} - 13 q^{62} - q^{63} - 17 q^{64} + 14 q^{65} - 6 q^{67} - 18 q^{68} - 7 q^{69} - 2 q^{70} - 20 q^{71} - 13 q^{72} + 16 q^{73} - 9 q^{74} - 6 q^{75} - 60 q^{76} - 2 q^{78} + 11 q^{79} - 12 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} - 6 q^{84} - 21 q^{85} - 30 q^{86} - 24 q^{87} - 24 q^{89} + 3 q^{90} - 7 q^{91} - 12 q^{92} - 13 q^{93} + 43 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9 - 2 * q^10 - 6 * q^12 + 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^23 + 13 * q^24 + q^25 - 3 * q^26 + q^27 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 13 * q^31 + 30 * q^32 + 12 * q^34 + 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 - 3 * q^39 + q^40 - 7 * q^41 + 4 * q^42 + 2 * q^45 - 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 + 19 * q^50 + 12 * q^51 + 12 * q^52 - q^53 - 6 * q^54 + 12 * q^56 - 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 - 24 * q^61 - 13 * q^62 - q^63 - 17 * q^64 + 14 * q^65 - 6 * q^67 - 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 - 13 * q^72 + 16 * q^73 - 9 * q^74 - 6 * q^75 - 60 * q^76 - 2 * q^78 + 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 + 7 * q^83 - 6 * q^84 - 21 * q^85 - 30 * q^86 - 24 * q^87 - 24 * q^89 + 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 + 43 * q^94 - 12 * q^97 - 36 * q^98

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