LMFDB - Embedded newform 429.2.x.a.365.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(248,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 0]))

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

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

chi := DirichletCharacter("429.248");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.x (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			365.46
Character	$\chi$	$=$	429.365
Dual form			429.2.x.a.248.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.828482 - 2.54980i) q^{2} +(-0.629445 - 1.61363i) q^{3} +(-4.19709 - 3.04936i) q^{4} +(-2.56502 + 0.833425i) q^{5} +(-4.63592 + 0.268101i) q^{6} +(2.78275 - 3.83012i) q^{7} +(-6.91450 + 5.02368i) q^{8} +(-2.20760 + 2.03138i) q^{9} +O(q^{10})$	\(q+(0.828482 - 2.54980i) q^{2} +(-0.629445 - 1.61363i) q^{3} +(-4.19709 - 3.04936i) q^{4} +(-2.56502 + 0.833425i) q^{5} +(-4.63592 + 0.268101i) q^{6} +(2.78275 - 3.83012i) q^{7} +(-6.91450 + 5.02368i) q^{8} +(-2.20760 + 2.03138i) q^{9} +7.23077i q^{10} +(3.15751 - 1.01495i) q^{11} +(-2.27870 + 8.69195i) q^{12} +(0.951057 + 0.309017i) q^{13} +(-7.46061 - 10.2687i) q^{14} +(2.95938 + 3.61439i) q^{15} +(3.87457 + 11.9247i) q^{16} +(-0.622707 - 1.91649i) q^{17} +(3.35068 + 7.31190i) q^{18} +(1.49966 + 2.06411i) q^{19} +(13.3070 + 4.32371i) q^{20} +(-7.93199 - 2.07947i) q^{21} +(0.0280078 - 8.89190i) q^{22} -1.65219i q^{23} +(12.4587 + 7.99531i) q^{24} +(1.83963 - 1.33657i) q^{25} +(1.57587 - 2.16899i) q^{26} +(4.66746 + 2.28360i) q^{27} +(-23.3589 + 7.58976i) q^{28} +(-2.56908 - 1.86655i) q^{29} +(11.6678 - 4.55137i) q^{30} +(-0.419363 + 1.29067i) q^{31} +16.5221 q^{32} +(-3.62524 - 4.45619i) q^{33} -5.40259 q^{34} +(-3.94568 + 12.1435i) q^{35} +(15.4599 - 1.79413i) q^{36} +(-2.11663 - 1.53782i) q^{37} +(6.50551 - 2.11377i) q^{38} +(-0.0999994 - 1.72916i) q^{39} +(13.5490 - 18.6485i) q^{40} +(-8.73715 + 6.34791i) q^{41} +(-11.8737 + 18.5022i) q^{42} -8.47599i q^{43} +(-16.3473 - 5.36855i) q^{44} +(3.96952 - 7.05040i) q^{45} +(-4.21277 - 1.36881i) q^{46} +(-0.732957 - 1.00883i) q^{47} +(16.8032 - 13.7581i) q^{48} +(-4.76305 - 14.6592i) q^{49} +(-1.88389 - 5.79803i) q^{50} +(-2.70055 + 2.21115i) q^{51} +(-3.04936 - 4.19709i) q^{52} +(6.86533 + 2.23068i) q^{53} +(9.68963 - 10.0092i) q^{54} +(-7.25318 + 5.23492i) q^{55} +40.4630i q^{56} +(2.38675 - 3.71914i) q^{57} +(-6.88777 + 5.00426i) q^{58} +(3.97615 - 5.47270i) q^{59} +(-1.39917 - 24.1941i) q^{60} +(-0.891593 + 0.289696i) q^{61} +(2.94351 + 2.13859i) q^{62} +(1.63726 + 14.1082i) q^{63} +(5.93911 - 18.2787i) q^{64} -2.69702 q^{65} +(-14.3659 + 5.55177i) q^{66} +3.14422 q^{67} +(-3.23053 + 9.94255i) q^{68} +(-2.66603 + 1.03997i) q^{69} +(27.6948 + 20.1214i) q^{70} +(9.85531 - 3.20218i) q^{71} +(5.05941 - 25.1363i) q^{72} +(1.37666 - 1.89482i) q^{73} +(-5.67472 + 4.12293i) q^{74} +(-3.31468 - 2.12718i) q^{75} -13.2362i q^{76} +(4.89916 - 14.9180i) q^{77} +(-4.49187 - 1.17760i) q^{78} +(-11.1922 - 3.63657i) q^{79} +(-19.8767 - 27.3579i) q^{80} +(0.746968 - 8.96895i) q^{81} +(8.94737 + 27.5372i) q^{82} +(3.00150 + 9.23768i) q^{83} +(26.9502 + 32.9152i) q^{84} +(3.19451 + 4.39686i) q^{85} +(-21.6121 - 7.02220i) q^{86} +(-1.39482 + 5.32044i) q^{87} +(-16.7338 + 22.8802i) q^{88} -11.5947i q^{89} +(-14.6885 - 15.9626i) q^{90} +(3.83012 - 2.78275i) q^{91} +(-5.03814 + 6.93441i) q^{92} +(2.34662 - 0.135708i) q^{93} +(-3.17956 + 1.03310i) q^{94} +(-5.56694 - 4.04462i) q^{95} +(-10.3998 - 26.6605i) q^{96} +(-0.520822 + 1.60293i) q^{97} -41.3241 q^{98} +(-4.90875 + 8.65472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.828482	−	2.54980i	0.585825	−	1.80298i	−0.0101067	−	0.999949i	$-0.503217\pi$
$2$	0.828482	−	2.54980i	0.585825	−	1.80298i	0.595932	−	0.803035i	$-0.296783\pi$
$3$	−0.629445	−	1.61363i	−0.363411	−	0.931629i
$3$	−0.629445	−	1.61363i	−0.363411	−	0.931629i
$4$	−4.19709	−	3.04936i	−2.09854	−	1.52468i
$5$	−2.56502	+	0.833425i	−1.14711	+	0.372719i	−0.820054	−	0.572286i	$-0.806057\pi$
$5$	−2.56502	+	0.833425i	−1.14711	+	0.372719i	−0.327056	+	0.945005i	$0.606057\pi$
$6$	−4.63592	+	0.268101i	−1.89261	+	0.109452i
$7$	2.78275	−	3.83012i	1.05178	−	1.44765i	0.164525	−	0.986373i	$-0.447391\pi$
$7$	2.78275	−	3.83012i	1.05178	−	1.44765i	0.887256	−	0.461278i	$-0.152609\pi$
$8$	−6.91450	+	5.02368i	−2.44464	+	1.77614i
$9$	−2.20760	+	2.03138i	−0.735866	+	0.677128i
$10$			7.23077i			2.28657i
$11$	3.15751	−	1.01495i	0.952025	−	0.306020i
$11$	3.15751	−	1.01495i	0.952025	−	0.306020i
$12$	−2.27870	+	8.69195i	−0.657805	+	2.50915i
$13$	0.951057	+	0.309017i	0.263776	+	0.0857059i
$13$	0.951057	+	0.309017i	0.263776	+	0.0857059i
$14$	−7.46061	−	10.2687i	−1.99393	−	2.74441i
$15$	2.95938	+	3.61439i	0.764108	+	0.933232i
$16$	3.87457	+	11.9247i	0.968643	+	2.98118i
$17$	−0.622707	−	1.91649i	−0.151029	−	0.464818i	0.846708	−	0.532057i	$-0.178581\pi$
$17$	−0.622707	−	1.91649i	−0.151029	−	0.464818i	−0.997737	+	0.0672393i	$0.978581\pi$
$18$	3.35068	+	7.31190i	0.789762	+	1.72343i
$19$	1.49966	+	2.06411i	0.344046	+	0.473539i	0.945618	−	0.325280i	$-0.105459\pi$
$19$	1.49966	+	2.06411i	0.344046	+	0.473539i	−0.601572	+	0.798819i	$0.705459\pi$
$20$	13.3070	+	4.32371i	2.97554	+	0.966811i
$21$	−7.93199	−	2.07947i	−1.73090	−	0.453777i
$22$	0.0280078	−	8.89190i	0.00597128	−	1.89576i
$23$		−	1.65219i		−	0.344506i	−0.985053	−	0.172253i	$-0.944895\pi$
$23$		−	1.65219i		−	0.344506i	0.985053	−	0.172253i	$-0.0551047\pi$
$24$	12.4587	+	7.99531i	2.54311	+	1.63203i
$25$	1.83963	−	1.33657i	0.367926	−	0.267314i
$26$	1.57587	−	2.16899i	0.309053	−	0.425375i
$27$	4.66746	+	2.28360i	0.898253	+	0.439479i
$28$	−23.3589	+	7.58976i	−4.41441	+	1.43433i
$29$	−2.56908	−	1.86655i	−0.477067	−	0.346609i	0.323122	−	0.946357i	$-0.395268\pi$
$29$	−2.56908	−	1.86655i	−0.477067	−	0.346609i	−0.800189	+	0.599748i	$0.795268\pi$
$30$	11.6678	−	4.55137i	2.13024	−	0.830964i
$31$	−0.419363	+	1.29067i	−0.0753197	+	0.231810i	−0.981627	−	0.190808i	$-0.938889\pi$
$31$	−0.419363	+	1.29067i	−0.0753197	+	0.231810i	0.906308	+	0.422619i	$0.138889\pi$
$32$	16.5221			2.92072
$33$	−3.62524	−	4.45619i	−0.631073	−	0.775724i
$34$	−5.40259			−0.926536
$35$	−3.94568	+	12.1435i	−0.666941	+	2.05263i
$36$	15.4599	−	1.79413i	2.57665	−	0.299021i
$37$	−2.11663	−	1.53782i	−0.347971	−	0.252816i	0.400046	−	0.916495i	$-0.368994\pi$
$37$	−2.11663	−	1.53782i	−0.347971	−	0.252816i	−0.748017	+	0.663679i	$0.768994\pi$
$38$	6.50551	−	2.11377i	1.05533	−	0.342899i
$39$	−0.0999994	−	1.72916i	−0.0160127	−	0.276887i
$40$	13.5490	−	18.6485i	2.14228	−	2.94859i
$41$	−8.73715	+	6.34791i	−1.36451	+	0.991378i	−0.366371	+	0.930469i	$0.619400\pi$
$41$	−8.73715	+	6.34791i	−1.36451	+	0.991378i	−0.998143	+	0.0609087i	$0.980600\pi$
$42$	−11.8737	+	18.5022i	−1.83216	+	2.85495i
$43$		−	8.47599i		−	1.29258i	−0.763093	−	0.646288i	$-0.776320\pi$
$43$		−	8.47599i		−	1.29258i	0.763093	−	0.646288i	$-0.223680\pi$
$44$	−16.3473	−	5.36855i	−2.46445	−	0.809339i
$45$	3.96952	−	7.05040i	0.591741	−	1.05101i
$46$	−4.21277	−	1.36881i	−0.621140	−	0.201820i
$47$	−0.732957	−	1.00883i	−0.106913	−	0.147153i	0.752208	−	0.658926i	$-0.228989\pi$
$47$	−0.732957	−	1.00883i	−0.106913	−	0.147153i	−0.859121	+	0.511773i	$0.828989\pi$
$48$	16.8032	−	13.7581i	2.42534	−	1.98581i
$49$	−4.76305	−	14.6592i	−0.680435	−	2.09416i
$50$	−1.88389	−	5.79803i	−0.266423	−	0.819965i
$51$	−2.70055	+	2.21115i	−0.378153	+	0.309622i
$52$	−3.04936	−	4.19709i	−0.422870	−	0.582031i
$53$	6.86533	+	2.23068i	0.943025	+	0.306407i	0.739878	−	0.672741i	$-0.234883\pi$
$53$	6.86533	+	2.23068i	0.943025	+	0.306407i	0.203147	+	0.979148i	$0.434883\pi$
$54$	9.68963	−	10.0092i	1.31859	−	1.36208i
$55$	−7.25318	+	5.23492i	−0.978019	+	0.705876i
$56$			40.4630i			5.40710i
$57$	2.38675	−	3.71914i	0.316132	−	0.492612i
$58$	−6.88777	+	5.00426i	−0.904409	+	0.657092i
$59$	3.97615	−	5.47270i	0.517650	−	0.712484i	−0.467536	−	0.883974i	$-0.654858\pi$
$59$	3.97615	−	5.47270i	0.517650	−	0.712484i	0.985186	+	0.171490i	$0.0548581\pi$
$60$	−1.39917	−	24.1941i	−0.180633	−	3.12345i
$61$	−0.891593	+	0.289696i	−0.114157	+	0.0370918i	−0.365538	−	0.930796i	$-0.619115\pi$
$61$	−0.891593	+	0.289696i	−0.114157	+	0.0370918i	0.251382	+	0.967888i	$0.419115\pi$
$62$	2.94351	+	2.13859i	0.373826	+	0.271601i
$63$	1.63726	+	14.1082i	0.206276	+	1.77747i
$64$	5.93911	−	18.2787i	0.742389	−	2.28484i
$65$	−2.69702			−0.334524
$66$	−14.3659	+	5.55177i	−1.76832	+	0.683376i
$67$	3.14422			0.384127			0.192064	−	0.981382i	$-0.438482\pi$
$67$	3.14422			0.384127			0.192064	+	0.981382i	$0.438482\pi$
$68$	−3.23053	+	9.94255i	−0.391759	+	1.20571i
$69$	−2.66603	+	1.03997i	−0.320952	+	0.125197i
$70$	27.6948	+	20.1214i	3.31016	+	2.40497i
$71$	9.85531	−	3.20218i	1.16961	−	0.380029i	0.341113	−	0.940022i	$-0.389196\pi$
$71$	9.85531	−	3.20218i	1.16961	−	0.380029i	0.828497	+	0.559993i	$0.189196\pi$
$72$	5.05941	−	25.1363i	0.596258	−	2.96234i
$73$	1.37666	−	1.89482i	0.161126	−	0.221771i	−0.720819	−	0.693124i	$-0.756234\pi$
$73$	1.37666	−	1.89482i	0.161126	−	0.221771i	0.881945	+	0.471352i	$0.156234\pi$
$74$	−5.67472	+	4.12293i	−0.659673	+	0.479280i
$75$	−3.31468	−	2.12718i	−0.382746	−	0.245626i
$76$		−	13.2362i		−	1.51830i
$77$	4.89916	−	14.9180i	0.558311	−	1.70007i
$78$	−4.49187	−	1.17760i	−0.508604	−	0.133337i
$79$	−11.1922	−	3.63657i	−1.25922	−	0.409147i	−0.398006	−	0.917383i	$-0.630298\pi$
$79$	−11.1922	−	3.63657i	−1.25922	−	0.409147i	−0.861218	+	0.508236i	$0.830298\pi$
$80$	−19.8767	−	27.3579i	−2.22228	−	3.05871i
$81$	0.746968	−	8.96895i	0.0829964	−	0.996550i
$82$	8.94737	+	27.5372i	0.988071	+	3.04097i
$83$	3.00150	+	9.23768i	0.329458	+	1.01397i	0.969388	+	0.245534i	$0.0789632\pi$
$83$	3.00150	+	9.23768i	0.329458	+	1.01397i	−0.639930	+	0.768433i	$0.721037\pi$
$84$	26.9502	+	32.9152i	2.94051	+	3.59134i
$85$	3.19451	+	4.39686i	0.346493	+	0.476907i
$86$	−21.6121	−	7.02220i	−2.33049	−	0.757224i
$87$	−1.39482	+	5.32044i	−0.149540	+	0.570411i
$88$	−16.7338	+	22.8802i	−1.78383	+	2.43904i
$89$		−	11.5947i		−	1.22903i	−0.788904	−	0.614516i	$-0.789351\pi$
$89$		−	11.5947i		−	1.22903i	0.788904	−	0.614516i	$-0.210649\pi$
$90$	−14.6885	−	15.9626i	−1.54830	−	1.68261i
$91$	3.83012	−	2.78275i	0.401506	−	0.291711i
$92$	−5.03814	+	6.93441i	−0.525262	+	0.722962i
$93$	2.34662	−	0.135708i	0.243333	−	0.0140722i
$94$	−3.17956	+	1.03310i	−0.327946	+	0.106556i
$95$	−5.56694	−	4.04462i	−0.571156	−	0.414969i
$96$	−10.3998	−	26.6605i	−1.06142	−	2.72103i
$97$	−0.520822	+	1.60293i	−0.0528815	+	0.162753i	−0.974009	−	0.226507i	$-0.927269\pi$
$97$	−0.520822	+	1.60293i	−0.0528815	+	0.162753i	0.921128	+	0.389260i	$0.127269\pi$
$98$	−41.3241			−4.17436
$99$	−4.90875	+	8.65472i	−0.493348	+	0.869832i
$100$	−11.7968			−1.17968
$101$	−2.89139	+	8.89880i	−0.287704	+	0.885463i	0.697870	+	0.716224i	$0.254131\pi$
$101$	−2.89139	+	8.89880i	−0.287704	+	0.885463i	−0.985575	+	0.169239i	$0.945869\pi$
$102$	3.40063	+	8.71777i	0.336713	+	0.863188i
$103$	0.708869	+	0.515024i	0.0698469	+	0.0507468i	0.622161	−	0.782889i	$-0.286255\pi$
$103$	0.708869	+	0.515024i	0.0698469	+	0.0507468i	−0.552314	+	0.833636i	$0.686255\pi$
$104$	−8.12848	+	2.64110i	−0.797063	+	0.258982i
$105$	22.0788	−	1.27684i	2.15467	−	0.124607i
$106$	11.3756	−	15.6572i	1.10490	−	1.52076i
$107$	8.83622	−	6.41989i	0.854230	−	0.620634i	−0.0720793	−	0.997399i	$-0.522963\pi$
$107$	8.83622	−	6.41989i	0.854230	−	0.620634i	0.926309	+	0.376765i	$0.122963\pi$
$108$	−12.6262	−	23.8172i	−1.21496	−	2.29181i
$109$			7.99407i			0.765693i	0.923812	+	0.382847i	$0.125056\pi$
$109$			7.99407i			0.765693i	−0.923812	+	0.382847i	$0.874944\pi$
$110$	7.33889	+	22.8312i	0.699736	+	2.17687i
$111$	−1.14917	+	4.38342i	−0.109074	+	0.416056i
$112$	56.4551	+	18.3434i	5.33450	+	1.73328i
$113$	8.92823	+	12.2887i	0.839898	+	1.15602i	0.985999	+	0.166750i	$0.0533274\pi$
$113$	8.92823	+	12.2887i	0.839898	+	1.15602i	−0.146102	+	0.989270i	$0.546673\pi$
$114$	−7.50570	−	9.16698i	−0.702974	−	0.858566i
$115$	1.37698	+	4.23791i	0.128404	+	0.395187i
$116$	5.09089	+	15.6681i	0.472677	+	1.45475i
$117$	−2.72728	+	1.24977i	−0.252137	+	0.115542i
$118$	−10.6601	−	14.6724i	−0.981345	−	1.35071i
$119$	−9.07325	−	2.94808i	−0.831743	−	0.270250i
$120$	−38.6201	−	10.1247i	−3.52552	−	0.924259i
$121$	8.93974	−	6.40945i	0.812704	−	0.582677i
$122$			2.51340i			0.227552i
$123$	15.7427	+	10.1029i	1.41948	+	0.910944i
$124$	5.69581	−	4.13825i	0.511499	−	0.371625i
$125$	4.32158	−	5.94815i	0.386534	−	0.532019i
$126$	37.3296	+	7.51368i	3.32558	+	0.669372i
$127$	−3.57402	+	1.16127i	−0.317143	+	0.103046i	−0.463263	−	0.886221i	$-0.653321\pi$
$127$	−3.57402	+	1.16127i	−0.317143	+	0.103046i	0.146120	+	0.989267i	$0.453321\pi$
$128$	−14.9534	−	10.8642i	−1.32170	−	0.960273i
$129$	−13.6771	+	5.33517i	−1.20420	+	0.469736i
$130$	−2.23443	+	6.87687i	−0.195973	+	0.603141i
$131$	5.35433			0.467810			0.233905	−	0.972259i	$-0.424850\pi$
$131$	5.35433			0.467810			0.233905	+	0.972259i	$0.424850\pi$
$132$	1.62689	+	29.7577i	0.141603	+	2.59007i
$133$	12.0790			1.04738
$134$	2.60493	−	8.01714i	0.225031	−	0.692575i
$135$	−13.8753	−	1.96749i	−1.19420	−	0.169335i
$136$	13.9336	+	10.1233i	1.19479	+	0.868067i
$137$	−5.04399	+	1.63889i	−0.430937	+	0.140020i	−0.516450	−	0.856317i	$-0.672747\pi$
$137$	−5.04399	+	1.63889i	−0.430937	+	0.140020i	0.0855135	+	0.996337i	$0.472747\pi$
$138$	0.442955	+	7.65945i	0.0377068	+	0.652015i
$139$	7.28089	−	10.0213i	0.617557	−	0.849995i	−0.379615	−	0.925145i	$-0.623944\pi$
$139$	7.28089	−	10.0213i	0.617557	−	0.849995i	0.997172	+	0.0751499i	$0.0239435\pi$
$140$	53.5904	−	38.9357i	4.52922	−	3.29067i
$141$	−1.16652	+	1.81772i	−0.0982385	+	0.153080i
$142$		−	27.7821i		−	2.33142i
$143$	3.31661	+	0.0104467i	0.277349	+	0.000873595i
$144$	−32.7771	−	18.4542i	−2.73143	−	1.53785i
$145$	8.14537	+	2.64659i	0.676436	+	0.219788i
$146$	−3.69087	−	5.08004i	−0.305458	−	0.420427i
$147$	−20.6564	+	16.9129i	−1.70371	+	1.39495i
$148$	4.19430	+	12.9087i	0.344769	+	1.06109i
$149$	−5.05975	−	15.5723i	−0.414511	−	1.27573i	−0.912688	−	0.408657i	$-0.865997\pi$
$149$	−5.05975	−	15.5723i	−0.414511	−	1.27573i	0.498177	−	0.867075i	$-0.334003\pi$
$150$	−8.17006	+	6.68945i	−0.667082	+	0.546191i
$151$	−12.5103	−	17.2190i	−1.01808	−	1.40126i	−0.913544	−	0.406741i	$-0.866665\pi$
$151$	−12.5103	−	17.2190i	−1.01808	−	1.40126i	−0.104533	−	0.994521i	$-0.533335\pi$
$152$	−20.7388	−	6.73845i	−1.68214	−	0.546561i
$153$	5.26782	+	2.96589i	0.425878	+	0.239778i
$154$	−33.9792	−	24.8512i	−2.73812	−	2.00257i
$155$		−	3.66009i		−	0.293985i
$156$	−4.85313	+	7.56238i	−0.388562	+	0.605475i
$157$	−3.17978	+	2.31025i	−0.253774	+	0.184378i	−0.707398	−	0.706816i	$-0.750131\pi$
$157$	−3.17978	+	2.31025i	−0.253774	+	0.184378i	0.453624	+	0.891193i	$0.350131\pi$
$158$	−18.5451	+	25.5251i	−1.47537	+	2.03067i
$159$	−0.721859	−	12.4822i	−0.0572472	−	0.989902i
$160$	−42.3795	+	13.7699i	−3.35039	+	1.08861i
$161$	−6.32811	−	4.59764i	−0.498725	−	0.362345i
$162$	−22.2502	−	9.33523i	−1.74814	−	0.733445i
$163$	6.24171	−	19.2100i	0.488889	−	1.50464i	−0.337380	−	0.941368i	$-0.609541\pi$
$163$	6.24171	−	19.2100i	0.488889	−	1.50464i	0.826269	−	0.563276i	$-0.190459\pi$
$164$	56.0277			4.37503
$165$	13.0127	+	8.40885i	1.01304	+	0.654628i
$166$	26.0410			2.02117
$167$	0.216874	−	0.667470i	0.0167822	−	0.0516504i	−0.942315	−	0.334728i	$-0.891355\pi$
$167$	0.216874	−	0.667470i	0.0167822	−	0.0516504i	0.959097	+	0.283078i	$0.0913555\pi$
$168$	65.2923	−	25.4693i	5.03741	−	1.96500i
$169$	0.809017	+	0.587785i	0.0622321	+	0.0452143i
$170$	13.8577	−	4.50265i	1.06284	−	0.345337i
$171$	−7.50364	−	1.51033i	−0.573818	−	0.115498i
$172$	−25.8464	+	35.5745i	−1.97077	+	2.71253i
$173$	18.6398	−	13.5426i	1.41715	−	1.02962i	0.424921	−	0.905230i	$-0.360302\pi$
$173$	18.6398	−	13.5426i	1.41715	−	1.02962i	0.992233	−	0.124393i	$-0.0396982\pi$
$174$	12.4105	+	7.96440i	0.940837	+	0.603780i
$175$		−	10.7654i		−	0.813785i
$176$	24.3370	+	33.7199i	1.83447	+	2.54173i
$177$	−11.3337	−	2.97126i	−0.851891	−	0.223334i
$178$	−29.5641	−	9.60597i	−2.21593	−	0.719998i
$179$	6.05148	+	8.32914i	0.452309	+	0.622549i	0.972892	−	0.231262i	$-0.0742853\pi$
$179$	6.05148	+	8.32914i	0.452309	+	0.622549i	−0.520583	+	0.853811i	$0.674285\pi$
$180$	−38.1596	+	17.4866i	−2.84425	+	1.30338i
$181$	6.43840	+	19.8153i	0.478562	+	1.47286i	0.841093	+	0.540891i	$0.181913\pi$
$181$	6.43840	+	19.8153i	0.478562	+	1.47286i	−0.362531	+	0.931972i	$0.618087\pi$
$182$	−3.92228	−	12.0715i	−0.290738	−	0.894801i
$183$	1.02867	+	1.25635i	0.0760415	+	0.0928722i
$184$	8.30010	+	11.4241i	0.611891	+	0.842196i
$185$	6.71084	+	2.18048i	0.493391	+	0.160312i
$186$	1.59810	−	6.09586i	0.117179	−	0.446970i
$187$	−3.91135	−	5.41933i	−0.286027	−	0.396301i
$188$			6.46919i			0.471814i
$189$	21.7348	−	11.5223i	1.58098	−	0.838122i
$190$	−14.9251	+	10.8437i	−1.08278	+	0.786685i
$191$	1.18004	−	1.62419i	0.0853848	−	0.117522i	−0.764188	−	0.644994i	$-0.776860\pi$
$191$	1.18004	−	1.62419i	0.0853848	−	0.117522i	0.849573	+	0.527472i	$0.176860\pi$
$192$	−33.2334	+	1.92193i	−2.39841	+	0.138703i
$193$	7.86391	−	2.55514i	0.566057	−	0.183923i	−0.0119879	−	0.999928i	$-0.503816\pi$
$193$	7.86391	−	2.55514i	0.566057	−	0.183923i	0.578045	+	0.816005i	$0.303816\pi$
$194$	3.65566	+	2.65599i	0.262461	+	0.190689i
$195$	1.69763	+	4.35199i	0.121570	+	0.311652i
$196$	−24.7101	+	76.0500i	−1.76501	+	5.43214i
$197$	1.99374			0.142048			0.0710239	−	0.997475i	$-0.477373\pi$
$197$	1.99374			0.142048			0.0710239	+	0.997475i	$0.477373\pi$
$198$	18.0010	+	19.6866i	1.27928	+	1.39907i
$199$	0.353143			0.0250337			0.0125168	−	0.999922i	$-0.496016\pi$
$199$	0.353143			0.0250337			0.0125168	+	0.999922i	$0.496016\pi$
$200$	−6.00563	+	18.4834i	−0.424662	+	1.30698i
$201$	−1.97911	−	5.07360i	−0.139596	−	0.357864i
$202$	20.2947	+	14.7450i	1.42793	+	1.03745i
$203$	−14.2982	+	4.64578i	−1.00354	+	0.326070i
$204$	18.0770	−	1.04542i	1.26565	−	0.0731937i
$205$	17.1204	−	23.5643i	1.19574	−	1.64580i
$206$	1.90049	−	1.38079i	0.132414	−	0.0962042i
$207$	3.35624	+	3.64738i	0.233275	+	0.253510i
$208$			12.5384i			0.869380i
$209$	6.83017	+	4.99535i	0.472453	+	0.345536i
$210$	15.0362	−	57.3544i	1.03759	−	3.95783i
$211$	−12.5108	−	4.06499i	−0.861277	−	0.279846i	−0.155115	−	0.987896i	$-0.549575\pi$
$211$	−12.5108	−	4.06499i	−0.861277	−	0.279846i	−0.706162	+	0.708051i	$0.749575\pi$
$212$	−22.0122	−	30.2972i	−1.51181	−	2.08082i
$213$	−11.3705	−	13.8872i	−0.779095	−	0.951536i
$214$	−9.04882	−	27.8494i	−0.618564	−	1.90375i
$215$	7.06410	+	21.7411i	0.481768	+	1.48273i
$216$	−43.7452	+	7.65788i	−2.97648	+	0.521053i
$217$	3.77643	+	5.19781i	0.256361	+	0.352850i
$218$	20.3833	+	6.62294i	1.38053	+	0.448562i
$219$	−3.92406	−	1.02874i	−0.265164	−	0.0695159i
$220$	46.4054	+	0.146168i	3.12865	+	0.00985464i
$221$		−	2.01512i		−	0.135552i
$222$	10.2248	+	6.56174i	0.686244	+	0.440395i
$223$	−8.13660	+	5.91158i	−0.544867	+	0.395869i	−0.825889	−	0.563832i	$-0.809326\pi$
$223$	−8.13660	+	5.91158i	−0.544867	+	0.395869i	0.281022	+	0.959701i	$0.409326\pi$
$224$	45.9768	−	63.2817i	3.07196	−	4.22819i
$225$	−1.34608	+	6.68761i	−0.0897386	+	0.445840i
$226$	38.7306	−	12.5843i	2.57632	−	0.837097i
$227$	−7.03088	−	5.10823i	−0.466656	−	0.339045i	0.329481	−	0.944162i	$-0.393126\pi$
$227$	−7.03088	−	5.10823i	−0.466656	−	0.339045i	−0.796137	+	0.605117i	$0.793126\pi$
$228$	−21.3584	+	8.33150i	−1.41449	+	0.551767i
$229$	−3.07694	+	9.46984i	−0.203330	+	0.625785i	0.796448	+	0.604707i	$0.206710\pi$
$229$	−3.07694	+	9.46984i	−0.203330	+	0.625785i	−0.999778	+	0.0210779i	$0.993290\pi$
$230$	11.9466			0.787738
$231$	−27.1559	+	1.48465i	−1.78673	+	0.0976829i
$232$	27.1409			1.78189
$233$	−4.23102	+	13.0217i	−0.277184	+	0.853083i	0.711450	+	0.702737i	$0.248039\pi$
$233$	−4.23102	+	13.0217i	−0.277184	+	0.853083i	−0.988633	+	0.150346i	$0.951961\pi$
$234$	0.927179	+	7.98945i	0.0606116	+	0.522287i
$235$	2.72083	+	1.97680i	0.177487	+	0.128952i
$236$	−33.3765	+	10.8447i	−2.17262	+	0.705928i
$237$	1.17681	+	20.3491i	0.0764422	+	1.32182i
$238$	−15.0340	+	20.6926i	−0.974512	+	1.34130i
$239$	2.27647	−	1.65395i	0.147253	−	0.106985i	−0.511720	−	0.859152i	$-0.670991\pi$
$239$	2.27647	−	1.65395i	0.147253	−	0.106985i	0.658972	+	0.752167i	$0.270991\pi$
$240$	−31.6342	+	49.2939i	−2.04198	+	3.18191i
$241$			26.3546i			1.69765i	0.528675	+	0.848824i	$0.322689\pi$
$241$			26.3546i			1.69765i	−0.528675	+	0.848824i	$0.677311\pi$
$242$	−8.93643	−	28.1047i	−0.574455	−	1.80664i
$243$	−14.9427	+	4.44014i	−0.958577	+	0.284835i
$244$	4.62548	+	1.50291i	0.296116	+	0.0962139i
$245$	24.4346	+	33.6313i	1.56107	+	2.14863i
$246$	38.8029	−	31.7709i	2.47398	−	2.02564i
$247$	0.788419	+	2.42650i	0.0501659	+	0.154395i
$248$	−3.58420	−	11.0310i	−0.227597	−	0.700472i
$249$	13.0169	−	10.6579i	0.824913	−	0.675419i
$250$	−11.5863	−	15.9471i	−0.732780	−	1.00858i
$251$	16.1648	+	5.25226i	1.02031	+	0.331520i	0.770954	−	0.636891i	$-0.219780\pi$
$251$	16.1648	+	5.25226i	1.02031	+	0.331520i	0.249359	+	0.968411i	$0.419780\pi$
$252$	36.1493	−	64.2059i	2.27719	−	4.04459i
$253$	−1.67690	−	5.21682i	−0.105426	−	0.327979i
$254$			10.0751i			0.632171i
$255$	5.08413	−	7.92233i	0.318381	−	0.496116i
$256$	−8.99270	+	6.53358i	−0.562044	+	0.408349i
$257$	−11.2698	+	15.5116i	−0.702992	+	0.967586i	0.296927	+	0.954900i	$0.404038\pi$
$257$	−11.2698	+	15.5116i	−0.702992	+	0.967586i	−0.999920	+	0.0126857i	$0.995962\pi$
$258$	2.27242	+	39.2940i	0.141475	+	2.44634i
$259$	−11.7801	+	3.82758i	−0.731978	+	0.237834i
$260$	11.3196	+	8.22419i	0.702013	+	0.510042i
$261$	9.46318	−	1.09821i	0.585756	−	0.0679772i
$262$	4.43596	−	13.6525i	0.274055	−	0.843454i
$263$	−9.17853			−0.565972			−0.282986	−	0.959124i	$-0.591325\pi$
$263$	−9.17853			−0.565972			−0.282986	+	0.959124i	$0.591325\pi$
$264$	47.4532	+	12.6003i	2.92054	+	0.775496i
$265$	−19.4688			−1.19596
$266$	10.0072	−	30.7990i	0.613581	−	1.88841i
$267$	−18.7095	+	7.29821i	−1.14500	+	0.446643i
$268$	−13.1965	−	9.58785i	−0.806107	−	0.585671i
$269$	11.2413	−	3.65252i	0.685393	−	0.222698i	0.0544382	−	0.998517i	$-0.482663\pi$
$269$	11.2413	−	3.65252i	0.685393	−	0.222698i	0.630955	+	0.775819i	$0.282663\pi$
$270$	−16.5122	+	33.7493i	−1.00490	+	2.05392i
$271$	15.8932	−	21.8751i	0.965443	−	1.32882i	0.0211268	−	0.999777i	$-0.493275\pi$
$271$	15.8932	−	21.8751i	0.965443	−	1.32882i	0.944316	−	0.329041i	$-0.106725\pi$
$272$	20.4409	−	14.8512i	1.23941	−	0.900485i
$273$	−6.90118	−	4.42881i	−0.417678	−	0.268044i
$274$			14.2190i			0.858999i
$275$	4.45210	−	6.08738i	0.268472	−	0.367083i
$276$	14.3608	+	3.76486i	0.864418	+	0.226618i
$277$	27.6904	+	8.99716i	1.66375	+	0.540587i	0.981654	−	0.190671i	$-0.0610664\pi$
$277$	27.6904	+	8.99716i	1.66375	+	0.540587i	0.682101	+	0.731258i	$0.261066\pi$
$278$	−19.5202	−	26.8673i	−1.17075	−	1.61139i
$279$	−1.69605	−	3.70115i	−0.101540	−	0.221582i
$280$	−33.7229	−	103.788i	−2.01533	−	6.20254i
$281$	2.26750	+	6.97866i	0.135268	+	0.416312i	0.995632	−	0.0933689i	$-0.0297636\pi$
$281$	2.26750	+	6.97866i	0.135268	+	0.416312i	−0.860364	+	0.509681i	$0.829764\pi$
$282$	3.66840	+	4.48034i	0.218450	+	0.266801i
$283$	11.8845	+	16.3577i	0.706463	+	0.972362i	0.999866	+	0.0163737i	$0.00521214\pi$
$283$	11.8845	+	16.3577i	0.706463	+	0.972362i	−0.293403	+	0.955989i	$0.594788\pi$
$284$	−51.1282	−	16.6126i	−3.03390	−	0.985774i
$285$	−3.02243	+	11.5288i	−0.179033	+	0.682909i
$286$	2.77439	−	8.44805i	0.164053	−	0.499544i
$287$			51.1290i			3.01805i
$288$	−36.4741	+	33.5627i	−2.14926	+	1.97770i
$289$	10.4681	−	7.60552i	0.615771	−	0.447384i
$290$	13.4966	−	18.5765i	0.792547	−	1.09085i
$291$	2.91436	−	0.168541i	0.170843	−	0.00988003i
$292$	−11.5560	+	3.75476i	−0.676261	+	0.219731i
$293$	3.46625	+	2.51838i	0.202501	+	0.147125i	0.684414	−	0.729093i	$-0.260058\pi$
$293$	3.46625	+	2.51838i	0.202501	+	0.147125i	−0.481914	+	0.876219i	$0.660058\pi$
$294$	26.0113	+	66.6817i	1.51701	+	3.88896i
$295$	−5.63780	+	17.3514i	−0.328246	+	1.01024i
$296$	22.3609			1.29970
$297$	17.0553	+	2.47323i	0.989649	+	0.143511i
$298$	−43.8982			−2.54296
$299$	0.510556	−	1.57133i	0.0295262	−	0.0908724i
$300$	7.42543	+	19.0356i	0.428707	+	1.09902i
$301$	−32.4641	−	23.5866i	−1.87120	−	1.35951i
$302$	−54.2697	+	17.6333i	−3.12287	+	1.01468i
$303$	16.1793	−	0.935670i	0.929478	−	0.0537528i
$304$	−18.8033	+	25.8806i	−1.07844	+	1.48435i
$305$	2.04551	−	1.48615i	0.117126	−	0.0850967i
$306$	11.9267	−	10.9747i	0.681806	−	0.627383i
$307$			28.8866i			1.64865i	0.566120	+	0.824323i	$0.308444\pi$
$307$			28.8866i			1.64865i	−0.566120	+	0.824323i	$0.691556\pi$
$308$	−66.0526	+	47.6729i	−3.76370	+	2.71642i
$309$	0.384862	−	1.46803i	0.0218941	−	0.0835134i
$310$	−9.33250	−	3.03231i	−0.530051	−	0.172224i
$311$	−6.61481	−	9.10451i	−0.375092	−	0.516269i	0.579184	−	0.815197i	$-0.303371\pi$
$311$	−6.61481	−	9.10451i	−0.375092	−	0.516269i	−0.954276	+	0.298927i	$0.903371\pi$
$312$	9.37820	+	11.4539i	0.530936	+	0.648451i
$313$	7.17406	+	22.0795i	0.405502	+	1.24801i	0.920475	+	0.390800i	$0.127802\pi$
$313$	7.17406	+	22.0795i	0.405502	+	1.24801i	−0.514974	+	0.857206i	$0.672198\pi$
$314$	3.25628	+	10.0218i	0.183763	+	0.565564i
$315$	−15.9577	−	34.8232i	−0.899116	−	1.96207i
$316$	35.8855	+	49.3922i	2.01872	+	2.77853i
$317$	−27.5037	−	8.93649i	−1.54476	−	0.501924i	−0.592076	−	0.805882i	$-0.701692\pi$
$317$	−27.5037	−	8.93649i	−1.54476	−	0.501924i	−0.952685	+	0.303958i	$0.901692\pi$
$318$	−32.4252	−	8.50066i	−1.81831	−	0.476693i
$319$	−10.0064	−	3.28615i	−0.560249	−	0.183989i
$320$			51.8350i			2.89766i
$321$	−15.9212	−	10.2174i	−0.888637	−	0.570280i
$322$	−16.9658	+	12.3264i	−0.945468	+	0.686923i
$323$	3.02200	−	4.15943i	0.168149	−	0.231437i
$324$	−30.4847	+	35.3657i	−1.69359	+	1.96476i
$325$	2.16262	−	0.702677i	0.119960	−	0.0389775i
$326$	−43.8106	−	31.8303i	−2.42645	−	1.76292i
$327$	12.8995	−	5.03183i	0.713342	−	0.278261i
$328$	28.5232	−	87.7853i	1.57493	−	4.84713i
$329$	−5.90357			−0.325474
$330$	32.2217	−	26.2133i	1.77375	−	1.44299i
$331$	−24.1402			−1.32687			−0.663433	−	0.748235i	$-0.730901\pi$
$331$	−24.1402			−1.32687			−0.663433	+	0.748235i	$0.730901\pi$
$332$	15.5715	−	47.9240i	0.854594	−	2.63017i
$333$	7.79655	−	0.904794i	0.427248	−	0.0495824i
$334$	−1.52224	−	1.10597i	−0.0832933	−	0.0605162i
$335$	−8.06497	+	2.62047i	−0.440636	+	0.143171i
$336$	−5.93600	−	102.644i	−0.323836	−	5.59967i
$337$	3.43955	−	4.73413i	0.187364	−	0.257885i	−0.704993	−	0.709214i	$-0.749050\pi$
$337$	3.43955	−	4.73413i	0.187364	−	0.257885i	0.892357	+	0.451329i	$0.149050\pi$
$338$	2.16899	−	1.57587i	0.117978	−	0.0857158i
$339$	14.2095	−	22.1419i	0.771754	−	1.20258i
$340$		−	28.1952i		−	1.52910i
$341$	−0.0141770	+	4.50092i	−0.000767729	+	0.243739i
$342$	−10.0677	+	17.8815i	−0.544397	+	0.966923i
$343$	−37.8827	−	12.3088i	−2.04547	−	0.664614i
$344$	42.5806	+	58.6072i	2.29579	+	3.15989i
$345$	5.97168	−	4.88947i	0.321504	−	0.263240i
$346$	−19.0882	−	58.7475i	−1.02619	−	3.15829i
$347$	−0.172266	−	0.530179i	−0.00924771	−	0.0284615i	0.946326	−	0.323213i	$-0.104763\pi$
$347$	−0.172266	−	0.530179i	−0.00924771	−	0.0284615i	−0.955574	+	0.294752i	$0.904763\pi$
$348$	22.0781	−	18.0770i	1.18351	−	0.969031i
$349$	2.65111	+	3.64894i	0.141911	+	0.195323i	0.874056	−	0.485825i	$-0.161481\pi$
$349$	2.65111	+	3.64894i	0.141911	+	0.195323i	−0.732145	+	0.681148i	$0.761481\pi$
$350$	−27.4496	−	8.91890i	−1.46724	−	0.476735i
$351$	3.73335	+	3.61415i	0.199271	+	0.192909i
$352$	52.1687	−	16.7691i	2.78060	−	0.893799i
$353$		−	19.1497i		−	1.01924i	−0.860400	−	0.509619i	$-0.829787\pi$
$353$		−	19.1497i		−	1.01924i	0.860400	−	0.509619i	$-0.170213\pi$
$354$	−16.9659	+	26.4370i	−0.901726	+	1.40511i
$355$	−22.6103	+	16.4273i	−1.20003	+	0.871871i
$356$	−35.3563	+	48.6638i	−1.87388	+	2.57918i
$357$	0.954012	+	16.4965i	0.0504917	+	0.873088i
$358$	26.2512	−	8.52954i	1.38742	−	0.450800i
$359$	−16.8579	−	12.2480i	−0.889725	−	0.646423i	0.0460813	−	0.998938i	$-0.485327\pi$
$359$	−16.8579	−	12.2480i	−0.889725	−	0.646423i	−0.935806	+	0.352515i	$0.885327\pi$
$360$	7.97169	+	68.6916i	0.420145	+	3.62036i
$361$	3.85977	−	11.8791i	0.203146	−	0.625218i
$362$	55.8593			2.93590
$363$	−15.9696	−	10.3910i	−0.838184	−	0.545387i
$364$	−24.5610			−1.28734
$365$	−1.95198	+	6.00758i	−0.102171	+	0.314451i
$366$	4.05569	−	1.58205i	0.211994	−	0.0826948i
$367$	−1.14880	−	0.834655i	−0.0599671	−	0.0435686i	0.557398	−	0.830245i	$-0.311800\pi$
$367$	−1.14880	−	0.834655i	−0.0599671	−	0.0435686i	−0.617365	+	0.786677i	$0.711800\pi$
$368$	19.7019	−	6.40155i	1.02703	−	0.333704i
$369$	6.39307	−	31.7621i	0.332810	−	1.65347i
$370$	11.1196	−	15.3048i	0.578081	−	0.795660i
$371$	27.6483	−	20.0876i	1.43543	−	1.04290i
$372$	−10.2628	−	6.58612i	−0.532101	−	0.341474i
$373$		−	29.6715i		−	1.53633i	−0.640251	−	0.768166i	$-0.721170\pi$
$373$		−	29.6715i		−	1.53633i	0.640251	−	0.768166i	$-0.278830\pi$
$374$	−17.0587	+	5.48337i	−0.882085	+	0.283538i
$375$	−12.3183	−	3.22940i	−0.636115	−	0.166765i
$376$	10.1361	+	3.29340i	0.522727	+	0.169844i
$377$	−1.86655	−	2.56908i	−0.0961322	−	0.132315i
$378$	−11.3726	−	64.9656i	−0.584946	−	3.34147i
$379$	5.93274	+	18.2591i	0.304744	+	0.937907i	0.979772	+	0.200115i	$0.0641315\pi$
$379$	5.93274	+	18.2591i	0.304744	+	0.937907i	−0.675028	+	0.737792i	$0.735869\pi$
$380$	11.0314	+	33.9512i	0.565900	+	1.74166i
$381$	4.12351	+	5.03619i	0.211254	+	0.258012i
$382$	−3.16372	−	4.35448i	−0.161870	−	0.222795i
$383$	0.0965525	+	0.0313718i	0.00493360	+	0.00160303i	0.311483	−	0.950252i	$-0.399174\pi$
$383$	0.0965525	+	0.0313718i	0.00493360	+	0.00160303i	−0.306549	+	0.951855i	$0.599174\pi$
$384$	−8.11854	+	30.9676i	−0.414298	+	1.58031i
$385$	−0.133388	+	42.3481i	−0.00679809	+	2.15826i
$386$		−	22.1683i		−	1.12834i
$387$	17.2180	+	18.7116i	0.875239	+	0.951163i
$388$	7.07384	−	5.13945i	0.359120	−	0.260916i
$389$	−2.86882	+	3.94859i	−0.145455	+	0.200202i	−0.875528	−	0.483168i	$-0.839486\pi$
$389$	−2.86882	+	3.94859i	−0.145455	+	0.200202i	0.730073	+	0.683369i	$0.239486\pi$
$390$	12.5032	−	0.723073i	0.633123	−	0.0366142i
$391$	−3.16642	+	1.02883i	−0.160133	+	0.0520303i
$392$	106.577	+	77.4327i	5.38295	+	3.91094i
$393$	−3.37026	−	8.63990i	−0.170007	−	0.435825i
$394$	1.65177	−	5.08364i	0.0832152	−	0.256110i
$395$	31.7391			1.59697
$396$	46.9938	−	21.3560i	2.36153	−	1.07318i
$397$	5.16938			0.259444			0.129722	−	0.991550i	$-0.458592\pi$
$397$	5.16938			0.259444			0.129722	+	0.991550i	$0.458592\pi$
$398$	0.292573	−	0.900447i	0.0146654	−	0.0451353i
$399$	−7.60305	−	19.4910i	−0.380629	−	0.975769i
$400$	23.0660	+	16.7584i	1.15330	+	0.837921i
$401$	−0.397172	+	0.129049i	−0.0198338	+	0.00644440i	−0.318917	−	0.947783i	$-0.603319\pi$
$401$	−0.397172	+	0.129049i	−0.0198338	+	0.00644440i	0.299083	+	0.954227i	$0.403319\pi$
$402$	−14.5763	+	0.842967i	−0.727002	+	0.0420434i
$403$	−0.797675	+	1.09791i	−0.0397350	+	0.0546906i
$404$	39.2711	−	28.5321i	1.95381	−	1.41953i
$405$	5.55896	+	23.6280i	0.276227	+	1.17409i
$406$			40.3066i			2.00038i
$407$	−8.24408	−	2.70740i	−0.408644	−	0.134201i
$408$	7.56487	−	28.8557i	0.374517	−	1.42857i
$409$	−1.40169	−	0.455435i	−0.0693089	−	0.0225198i	0.274157	−	0.961685i	$-0.411601\pi$
$409$	−1.40169	−	0.455435i	−0.0693089	−	0.0225198i	−0.343466	+	0.939165i	$0.611601\pi$
$410$	−45.9003	−	63.1763i	−2.26685	−	3.12006i
$411$	5.81948	+	7.10753i	0.287054	+	0.350589i
$412$	−1.40469	−	4.32320i	−0.0692042	−	0.212989i
$413$	−9.89649	−	30.4583i	−0.486975	−	1.49875i
$414$	12.0807	−	5.53597i	0.593734	−	0.272078i
$415$	−15.3978	−	21.1933i	−0.755849	−	1.04034i
$416$	15.7134	+	5.10561i	0.770415	+	0.250323i
$417$	−20.7536	−	5.44080i	−1.01631	−	0.266437i
$418$	18.3958	−	13.2770i	0.899770	−	0.649401i
$419$			21.5222i			1.05143i	0.850662	+	0.525713i	$0.176202\pi$
$419$			21.5222i			1.05143i	−0.850662	+	0.525713i	$0.823798\pi$
$420$	−96.5601	−	61.9671i	−4.71165	−	3.02369i
$421$	19.8298	−	14.4072i	0.966446	−	0.702164i	0.0118073	−	0.999930i	$-0.496242\pi$
$421$	19.8298	−	14.4072i	0.966446	−	0.702164i	0.954639	+	0.297766i	$0.0962415\pi$
$422$	−20.7299	+	28.5322i	−1.00911	+	1.38893i
$423$	3.66739	+	0.738170i	0.178315	+	0.0358911i
$424$	−58.6765	+	19.0652i	−2.84958	+	0.925886i
$425$	−3.70708	−	2.69335i	−0.179820	−	0.130647i
$426$	−44.8299	+	17.4873i	−2.17202	+	0.847262i
$427$	−1.37151	+	4.22106i	−0.0663719	+	0.204272i
$428$	−56.6630			−2.73891
$429$	−2.07077	−	5.35835i	−0.0999776	−	0.258704i
$430$	61.2879			2.95557
$431$	3.79465	−	11.6787i	0.182782	−	0.562544i	−0.817121	−	0.576466i	$-0.804431\pi$
$431$	3.79465	−	11.6787i	0.182782	−	0.562544i	0.999903	+	0.0139213i	$0.00443144\pi$
$432$	−9.14682	+	64.5060i	−0.440077	+	3.10355i
$433$	−6.26385	−	4.55096i	−0.301022	−	0.218705i	0.427013	−	0.904246i	$-0.359566\pi$
$433$	−6.26385	−	4.55096i	−0.301022	−	0.218705i	−0.728034	+	0.685541i	$0.759566\pi$
$434$	16.3821	−	5.32287i	0.786366	−	0.255506i
$435$	−0.856450	−	14.8095i	−0.0410637	−	0.710061i
$436$	24.3768	−	33.5518i	1.16744	−	1.60684i
$437$	3.41031	−	2.47773i	0.163137	−	0.118526i
$438$	−5.87411	+	9.15330i	−0.280676	+	0.437362i
$439$			38.8790i			1.85559i	0.373089	+	0.927796i	$0.378299\pi$
$439$			38.8790i			1.85559i	−0.373089	+	0.927796i	$0.621701\pi$
$440$	23.8536	−	72.6345i	1.13717	−	3.46271i
$441$	40.2932	+	22.6859i	1.91873	+	1.08028i
$442$	−5.13816	−	1.66949i	−0.244398	−	0.0794096i
$443$	5.29820	+	7.29235i	0.251725	+	0.346470i	0.916115	−	0.400917i	$-0.131308\pi$
$443$	5.29820	+	7.29235i	0.251725	+	0.346470i	−0.664389	+	0.747387i	$0.731308\pi$
$444$	18.1898	−	14.8934i	0.863249	−	0.706808i
$445$	9.66328	+	29.7405i	0.458083	+	1.40984i
$446$	8.33236	+	25.6444i	0.394549	+	1.21430i
$447$	−21.9431	+	17.9665i	−1.03787	+	0.849785i
$448$	−53.4826	−	73.6126i	−2.52682	−	3.47787i
$449$	−26.8900	−	8.73708i	−1.26902	−	0.412328i	−0.404317	−	0.914619i	$-0.632491\pi$
$449$	−26.8900	−	8.73708i	−1.26902	−	0.412328i	−0.864699	+	0.502291i	$0.832491\pi$
$450$	15.9369	+	8.97280i	0.751272	+	0.422982i
$451$	−21.1448	+	28.9114i	−0.995671	+	1.36138i
$452$		−	78.8020i		−	3.70653i
$453$	−19.9105	+	31.0255i	−0.935477	+	1.45770i
$454$	−18.8500	+	13.6953i	−0.884672	+	0.642752i
$455$	−7.50513	+	10.3299i	−0.351846	+	0.484274i
$456$	2.18060	+	37.7062i	0.102116	+	1.76576i
$457$	−8.11283	+	2.63602i	−0.379502	+	0.123308i	−0.492555	−	0.870281i	$-0.663937\pi$
$457$	−8.11283	+	2.63602i	−0.379502	+	0.123308i	0.113053	+	0.993589i	$0.463937\pi$
$458$	21.5971	+	15.6912i	1.00916	+	0.733201i
$459$	1.47004	−	10.3672i	0.0686157	−	0.483898i
$460$	7.14361	−	21.9858i	0.333073	−	1.02509i
$461$	−9.71386			−0.452419			−0.226210	−	0.974079i	$-0.572633\pi$
$461$	−9.71386			−0.452419			−0.226210	+	0.974079i	$0.572633\pi$
$462$	−18.7126	+	70.4722i	−0.870589	+	3.27867i
$463$	33.8515			1.57321			0.786607	−	0.617453i	$-0.211836\pi$
$463$	33.8515			1.57321			0.786607	+	0.617453i	$0.211836\pi$
$464$	12.3039	−	37.8676i	0.571196	−	1.75796i
$465$	−5.90602	+	2.30382i	−0.273885	+	0.106837i
$466$	29.6976	+	21.5766i	1.37571	+	0.999515i
$467$	23.0619	−	7.49326i	1.06718	−	0.346747i	0.277790	−	0.960642i	$-0.410398\pi$
$467$	23.0619	−	7.49326i	1.06718	−	0.346747i	0.789388	+	0.613895i	$0.210398\pi$
$468$	15.2577	+	3.07105i	0.705285	+	0.141960i
$469$	8.74956	−	12.0427i	0.404017	−	0.556082i
$470$	7.29460	−	5.29984i	0.336475	−	0.244463i
$471$	5.72938	+	3.67681i	0.263996	+	0.169419i
$472$			57.8158i			2.66119i
$473$	−8.60273	−	26.7630i	−0.395554	−	1.23057i
$474$	52.8612	+	13.8582i	2.42800	+	0.636530i
$475$	5.51765	+	1.79279i	0.253167	+	0.0822590i
$476$	29.0915	+	40.0409i	1.33340	+	1.83527i
$477$	−19.6872	+	9.02167i	−0.901417	+	0.413074i
$478$	−2.33124	−	7.17482i	−0.106629	−	0.328169i
$479$	4.29847	+	13.2293i	0.196402	+	0.604463i	0.999957	+	0.00923322i	$0.00293907\pi$
$479$	4.29847	+	13.2293i	0.196402	+	0.604463i	−0.803555	+	0.595230i	$0.797061\pi$
$480$	48.8951	+	59.7173i	2.23175	+	2.72571i
$481$	−1.53782	−	2.11663i	−0.0701185	−	0.0965098i
$482$	67.1991	+	21.8343i	3.06083	+	0.994525i
$483$	−3.43569	+	13.1052i	−0.156329	+	0.596307i
$484$	−57.0656	−	0.359495i	−2.59389	−	0.0163407i
$485$		−	4.54560i		−	0.206405i
$486$	−1.05830	+	41.7796i	−0.0480055	+	1.89516i
$487$	0.556028	−	0.403978i	0.0251960	−	0.0183060i	−0.575116	−	0.818072i	$-0.695043\pi$
$487$	0.556028	−	0.403978i	0.0251960	−	0.0183060i	0.600312	+	0.799766i	$0.295043\pi$
$488$	4.70958	−	6.48218i	0.213193	−	0.293434i
$489$	−34.9267	+	2.01985i	−1.57944	+	0.0913407i
$490$	105.997	−	34.4405i	4.78845	−	1.55586i
$491$	33.4018	+	24.2678i	1.50740	+	1.09519i	0.967314	+	0.253580i	$0.0816082\pi$
$491$	33.4018	+	24.2678i	1.50740	+	1.09519i	0.540086	+	0.841610i	$0.318392\pi$
$492$	−35.2664	−	90.4079i	−1.58993	−	4.07590i
$493$	−1.97744	+	6.08595i	−0.0890596	+	0.274097i
$494$	6.84030			0.307760
$495$	5.37798	−	26.2906i	0.241722	−	1.18167i
$496$	−17.0157			−0.764025
$497$	15.1601	−	46.6579i	0.680023	−	2.09289i
$498$	−16.3914	−	42.0204i	−0.734515	−	1.88298i
$499$	12.5467	+	9.11569i	0.561666	+	0.408074i	0.832068	−	0.554673i	$-0.187157\pi$
$499$	12.5467	+	9.11569i	0.561666	+	0.408074i	−0.270402	+	0.962747i	$0.587157\pi$
$500$	−36.2761	+	11.7868i	−1.62232	+	0.527123i
$501$	−1.21356	+	0.0701815i	−0.0542178	+	0.00313548i
$502$	26.7845	−	36.8657i	1.19545	−	1.64540i
$503$	−19.6475	+	14.2748i	−0.876039	+	0.636480i	−0.932201	−	0.361942i	$-0.882114\pi$
$503$	−19.6475	+	14.2748i	−0.876039	+	0.636480i	0.0561613	+	0.998422i	$0.482114\pi$
$504$	−82.1959	−	89.3261i	−3.66130	−	3.97890i
$505$		−	25.2353i		−	1.12296i
$506$	−14.6912	−	0.0462743i	−0.653102	−	0.00205714i
$507$	0.439235	−	1.67543i	0.0195071	−	0.0744085i
$508$	18.5416	+	6.02454i	0.822651	+	0.267296i
$509$	5.88046	+	8.09375i	0.260647	+	0.358749i	0.919204	−	0.393781i	$-0.128833\pi$
$509$	5.88046	+	8.09375i	0.260647	+	0.358749i	−0.658558	+	0.752530i	$0.728833\pi$
$510$	−15.9883	−	19.5271i	−0.707973	−	0.864673i
$511$	−3.42647	−	10.5456i	−0.151578	−	0.466509i
$512$	−2.21428	−	6.81485i	−0.0978582	−	0.301177i
$513$	2.28602	+	13.0588i	0.100930	+	0.576558i
$514$	30.2147	+	41.5869i	1.33271	+	1.83432i
$515$	−2.24749	−	0.730255i	−0.0990364	−	0.0321789i
$516$	73.6729	+	19.3143i	3.24327	+	0.850263i
$517$	−3.33823	−	2.44147i	−0.146815	−	0.107376i
$518$			33.2080i			1.45907i
$519$	−33.5854	−	21.5533i	−1.47424	−	0.946086i
$520$	18.6485	−	13.5490i	0.817792	−	0.594161i
$521$	−11.7443	+	16.1647i	−0.514529	+	0.708188i	−0.984675	−	0.174400i	$-0.944201\pi$
$521$	−11.7443	+	16.1647i	−0.514529	+	0.708188i	0.470146	+	0.882589i	$0.344201\pi$
$522$	5.03986	−	25.0391i	0.220589	−	1.09593i
$523$	24.9773	−	8.11563i	1.09218	−	0.354872i	0.293093	−	0.956084i	$-0.405315\pi$
$523$	24.9773	−	8.11563i	1.09218	−	0.354872i	0.799090	+	0.601212i	$0.205315\pi$
$524$	−22.4726	−	16.3273i	−0.981719	−	0.713261i
$525$	−17.3713	+	6.77621i	−0.758146	+	0.295738i
$526$	−7.60424	+	23.4034i	−0.331561	+	1.02044i
$527$	2.73469			0.119125
$528$	39.0925	−	60.4957i	1.70128	−	2.63274i
$529$	20.2703			0.881315
$530$	−16.1295	+	49.6416i	−0.700622	+	2.15629i
$531$	2.33941	+	20.1586i	0.101522	+	0.874808i
$532$	−50.6965	−	36.8331i	−2.19797	−	1.59692i
$533$	−10.2711	+	3.33730i	−0.444892	+	0.144554i
$534$	3.10854	+	53.7520i	0.134520	+	2.32608i
$535$	−17.3146	+	23.8315i	−0.748574	+	1.03032i
$536$	−21.7407	+	15.7955i	−0.939054	+	0.682263i
$537$	9.63107	−	15.0076i	0.415611	−	0.647625i
$538$		−	31.6891i		−	1.36622i
$539$	−29.9177	−	41.4522i	−1.28865	−	1.78547i
$540$	52.2363	+	50.5686i	2.24789	+	2.17613i
$541$	−39.8069	−	12.9340i	−1.71143	−	0.556078i	−0.720861	−	0.693080i	$-0.756253\pi$
$541$	−39.8069	−	12.9340i	−1.71143	−	0.556078i	−0.990571	+	0.137002i	$0.956253\pi$
$542$	−42.6100	−	58.6476i	−1.83026	−	2.51913i
$543$	27.9220	−	22.8619i	1.19825	−	0.981096i
$544$	−10.2884	−	31.6645i	−0.441112	−	1.35760i
$545$	−6.66246	−	20.5049i	−0.285388	−	0.878335i
$546$	−17.0101	+	13.9275i	−0.727965	+	0.596041i
$547$	1.94968	+	2.68350i	0.0833623	+	0.114738i	0.848662	−	0.528936i	$-0.177409\pi$
$547$	1.94968	+	2.68350i	0.0833623	+	0.114738i	−0.765299	+	0.643675i	$0.777409\pi$
$548$	26.1676	+	8.50238i	1.11783	+	0.363204i
$549$	1.37979	−	2.45070i	0.0588882	−	0.104593i
$550$	−11.8331	−	16.3953i	−0.504567	−	0.699096i
$551$		−	8.10206i		−	0.345159i
$552$	13.2098	−	20.5841i	0.562247	−	0.876118i
$553$	−45.0737	+	32.7479i	−1.91673	+	1.39258i
$554$	45.8820	−	63.1511i	1.94934	−	2.68303i
$555$	−0.705615	−	12.2013i	−0.0299517	−	0.517916i
$556$	−61.1171	+	19.8581i	−2.59194	+	0.842173i
$557$	−6.63023	−	4.81714i	−0.280932	−	0.204109i	0.438392	−	0.898784i	$-0.355548\pi$
$557$	−6.63023	−	4.81714i	−0.280932	−	0.204109i	−0.719324	+	0.694675i	$0.755548\pi$
$558$	−10.8424	+	1.25826i	−0.458994	+	0.0532665i
$559$	2.61923	−	8.06115i	0.110781	−	0.340950i
$560$	−160.096			−6.76529
$561$	−6.28281	+	9.72265i	−0.265260	+	0.410490i
$562$	19.6728			0.829847
$563$	1.08862	−	3.35043i	0.0458799	−	0.141204i	−0.925492	−	0.378766i	$-0.876348\pi$
$563$	1.08862	−	3.35043i	0.0458799	−	0.141204i	0.971372	+	0.237562i	$0.0763484\pi$
$564$	10.4389	−	4.07200i	0.439556	−	0.171462i
$565$	−33.1427	−	24.0796i	−1.39433	−	1.01304i
$566$	51.5550	−	16.7512i	2.16702	−	0.704107i
$567$	−32.2736	−	27.8193i	−1.35536	−	1.16830i
$568$	−52.0578	+	71.6514i	−2.18430	+	3.00643i
$569$	−7.68520	+	5.58362i	−0.322180	+	0.234078i	−0.737105	−	0.675778i	$-0.763808\pi$
$569$	−7.68520	+	5.58362i	−0.322180	+	0.234078i	0.414925	+	0.909856i	$0.363808\pi$
$570$	26.8922	+	17.2580i	1.12639	+	0.722859i
$571$			4.76401i			0.199368i	0.995019	+	0.0996838i	$0.0317831\pi$
$571$			4.76401i			0.199368i	−0.995019	+	0.0996838i	$0.968217\pi$
$572$	−13.8882	−	10.1574i	−0.580696	−	0.424702i
$573$	−3.36361	−	0.881811i	−0.140517	−	0.0368382i
$574$	130.369	+	42.3595i	5.44150	+	1.76805i
$575$	−2.20828	−	3.03943i	−0.0920915	−	0.126753i
$576$	24.0199	+	52.4166i	1.00083	+	2.18403i
$577$	8.86569	+	27.2858i	0.369083	+	1.13592i	0.947384	+	0.320098i	$0.103716\pi$
$577$	8.86569	+	27.2858i	0.369083	+	1.13592i	−0.578301	+	0.815823i	$0.696284\pi$
$578$	−10.7200	−	32.9927i	−0.445892	−	1.37231i
$579$	−9.07295	−	11.0811i	−0.377059	−	0.460515i
$580$	−26.1164	−	35.9462i	−1.08443	−	1.49258i
$581$	43.7339	+	14.2100i	1.81439	+	0.589530i
$582$	1.98475	−	7.57068i	0.0822704	−	0.313815i
$583$	23.9414	+	0.0754107i	0.991551	+	0.00312319i
$584$			20.0176i			0.828335i
$585$	5.95393	−	5.47868i	0.246165	−	0.226515i
$586$	9.29310	−	6.75183i	0.383894	−	0.278916i
$587$	−13.1590	+	18.1118i	−0.543128	+	0.747552i	−0.989060	−	0.147515i	$-0.952872\pi$
$587$	−13.1590	+	18.1118i	−0.543128	+	0.747552i	0.445931	+	0.895067i	$0.352872\pi$
$588$	138.270	−	7.99633i	5.70217	−	0.329763i
$589$	−3.29297	+	1.06995i	−0.135685	+	0.0440866i
$590$	39.5718	+	28.7506i	1.62915	+	1.18364i
$591$	−1.25495	−	3.21715i	−0.0516217	−	0.132336i
$592$	10.1370	−	31.1985i	0.416629	−	1.28225i
$593$	−6.83961			−0.280869			−0.140435	−	0.990090i	$-0.544850\pi$
$593$	−6.83961			−0.280869			−0.140435	+	0.990090i	$0.544850\pi$
$594$	20.4363	−	41.4386i	0.838510	−	1.70025i
$595$	25.7300			1.05483
$596$	−26.2494	+	80.7873i	−1.07522	+	3.30918i
$597$	−0.222285	−	0.569842i	−0.00909750	−	0.0233221i
$598$	−3.58360	−	2.60364i	−0.146544	−	0.106471i
$599$	−11.7563	+	3.81985i	−0.480349	+	0.156075i	−0.539176	−	0.842193i	$-0.681264\pi$
$599$	−11.7563	+	3.81985i	−0.480349	+	0.156075i	0.0588266	+	0.998268i	$0.481264\pi$
$600$	33.6056	−	1.94345i	1.37194	−	0.0793411i
$601$	−3.04222	+	4.18726i	−0.124095	+	0.170802i	−0.866544	−	0.499100i	$-0.833664\pi$
$601$	−3.04222	+	4.18726i	−0.124095	+	0.170802i	0.742449	+	0.669902i	$0.233664\pi$
$602$	−87.0370	+	63.2361i	−3.54736	+	2.57731i
$603$	−6.94116	+	6.38711i	−0.282666	+	0.260103i
$604$			110.418i			4.49285i
$605$	−17.5888	+	23.8909i	−0.715086	+	0.971305i
$606$	11.0185	−	42.0293i	0.447596	−	1.70732i
$607$	−38.8772	−	12.6320i	−1.57798	−	0.512715i	−0.616441	−	0.787401i	$-0.711426\pi$
$607$	−38.8772	−	12.6320i	−1.57798	−	0.512715i	−0.961534	+	0.274686i	$0.911426\pi$
$608$	24.7775	+	34.1034i	1.00486	+	1.38307i
$609$	16.4965	+	20.1478i	0.668473	+	0.816429i
$610$	−2.09473	−	6.44690i	−0.0848129	−	0.261027i
$611$	−0.385338	−	1.18595i	−0.0155891	−	0.0479783i
$612$	−13.0654	−	28.5116i	−0.528138	−	1.15251i
$613$	−2.47720	−	3.40957i	−0.100053	−	0.137711i	0.756055	−	0.654508i	$-0.227124\pi$
$613$	−2.47720	−	3.40957i	−0.100053	−	0.137711i	−0.856108	+	0.516797i	$0.827124\pi$
$614$	73.6552	+	23.9320i	2.97248	+	0.965818i
$615$	−48.8004	−	12.7936i	−1.96782	−	0.515889i
$616$	41.0681	+	127.762i	1.65468	+	5.14770i
$617$			2.18020i			0.0877717i	0.999037	+	0.0438858i	$0.0139738\pi$
$617$			2.18020i			0.0877717i	−0.999037	+	0.0438858i	$0.986026\pi$
$618$	−3.42434	−	2.19756i	−0.137747	−	0.0883989i
$619$	13.6216	−	9.89670i	0.547500	−	0.397782i	−0.279363	−	0.960186i	$-0.590123\pi$
$619$	13.6216	−	9.89670i	0.547500	−	0.397782i	0.826863	+	0.562404i	$0.190123\pi$
$620$	−11.1609	+	15.3617i	−0.448234	+	0.616941i
$621$	3.77295	−	7.71155i	0.151403	−	0.309454i
$622$	−28.6950	+	9.32356i	−1.15056	+	0.373841i
$623$	−44.4090	−	32.2650i	−1.77921	−	1.29267i
$624$	20.2323	−	7.89222i	0.809940	−	0.315942i
$625$	−9.64099	+	29.6719i	−0.385639	+	1.18688i
$626$	62.2419			2.48769
$627$	3.76143	−	14.1657i	0.150217	−	0.565722i
$628$	20.3906			0.813673
$629$	−1.62918	+	5.01411i	−0.0649598	+	0.199926i
$630$	−102.013	+	11.8387i	−4.06430	+	0.471664i
$631$	−31.2997	−	22.7405i	−1.24602	−	0.905286i	−0.248036	−	0.968751i	$-0.579785\pi$
$631$	−31.2997	−	22.7405i	−1.24602	−	0.905286i	−0.997984	+	0.0634645i	$0.979785\pi$
$632$	95.6576	−	31.0810i	3.80506	−	1.23634i
$633$	1.31545	+	22.7464i	0.0522845	+	0.904089i
$634$	−45.5726	+	62.7253i	−1.80992	+	2.49114i
$635$	8.19960	−	5.95736i	0.325391	−	0.236411i
$636$	−35.0330	+	54.5900i	−1.38915	+	2.16463i
$637$		−	15.4135i		−	0.610707i
$638$	−16.6691	+	22.7918i	−0.659937	+	0.902335i
$639$	−15.2517	+	27.0890i	−0.603347	+	1.07163i
$640$	47.4101	+	15.4045i	1.87405	+	0.608916i
$641$	23.1549	+	31.8700i	0.914564	+	1.25879i	0.965584	+	0.260091i	$0.0837527\pi$
$641$	23.1549	+	31.8700i	0.914564	+	1.25879i	−0.0510203	+	0.998698i	$0.516247\pi$
$642$	−39.2429	+	32.1311i	−1.54879	+	1.26811i
$643$	2.50399	+	7.70649i	0.0987477	+	0.303914i	0.988212	−	0.153090i	$-0.0489224\pi$
$643$	2.50399	+	7.70649i	0.0987477	+	0.303914i	−0.889465	+	0.457004i	$0.848922\pi$
$644$	12.5398	+	38.5934i	0.494136	+	1.52079i
$645$	30.6355	−	25.0836i	1.20627	−	0.987668i
$646$	−8.10205	−	11.1515i	−0.318771	−	0.438750i
$647$	10.7460	+	3.49158i	0.422468	+	0.137268i	0.512533	−	0.858668i	$-0.328707\pi$
$647$	10.7460	+	3.49158i	0.422468	+	0.137268i	−0.0900645	+	0.995936i	$0.528707\pi$
$648$	39.8922	+	65.7683i	1.56711	+	2.58362i
$649$	7.00019	−	21.3157i	0.274782	−	0.836714i
$650$		−	6.09641i		−	0.239121i
$651$	6.01028	−	9.36549i	0.235561	−	0.367063i
$652$	−84.7753	+	61.5929i	−3.32006	+	2.41216i
$653$	23.3707	−	32.1670i	0.914567	−	1.25879i	−0.0510155	−	0.998698i	$-0.516246\pi$
$653$	23.3707	−	32.1670i	0.914567	−	1.25879i	0.965583	−	0.260096i	$-0.0837542\pi$
$654$	−2.14322	−	37.0599i	−0.0838064	−	1.44916i
$655$	−13.7339	+	4.46243i	−0.536630	+	0.174362i
$656$	−109.550	−	79.5925i	−4.27720	−	3.10757i
$657$	0.809976	+	6.97952i	0.0316002	+	0.272297i
$658$	−4.89100	+	15.0530i	−0.190671	+	0.586825i
$659$	35.4799			1.38210			0.691050	−	0.722807i	$-0.257148\pi$
$659$	35.4799			1.38210			0.691050	+	0.722807i	$0.257148\pi$
$660$	−28.9738	−	74.9731i	−1.12780	−	2.91832i
$661$	14.3024			0.556299			0.278149	−	0.960538i	$-0.410279\pi$
$661$	14.3024			0.556299			0.278149	+	0.960538i	$0.410279\pi$
$662$	−19.9997	+	61.5528i	−0.777312	+	2.39232i
$663$	−3.25166	+	1.26841i	−0.126284	+	0.0492609i
$664$	−67.1610	−	48.7953i	−2.60635	−	1.89363i
$665$	−30.9828	+	10.0669i	−1.20146	+	0.390378i
$666$	4.15226	−	20.6293i	0.160897	−	0.799369i
$667$	−3.08390	+	4.24463i	−0.119409	+	0.164353i
$668$	−2.94560	+	2.14010i	−0.113969	+	0.0828030i
$669$	14.6606	+	9.40843i	0.566813	+	0.363751i
$670$			22.7351i			0.878334i
$671$	−2.52119	+	1.81964i	−0.0973293	+	0.0702465i
$672$	−131.053	−	34.3572i	−5.05548	−	1.32536i
$673$	16.1796	+	5.25707i	0.623678	+	0.202645i	0.603773	−	0.797157i	$-0.293664\pi$
$673$	16.1796	+	5.25707i	0.623678	+	0.202645i	0.0199053	+	0.999802i	$0.493664\pi$
$674$	−9.22151	−	12.6923i	−0.355199	−	0.488890i
$675$	11.6386	−	2.03741i	0.447970	−	0.0784200i
$676$	−1.60314	−	4.93397i	−0.0616594	−	0.189768i
$677$	−13.7183	−	42.2206i	−0.527237	−	1.62267i	−0.759849	−	0.650100i	$-0.774727\pi$
$677$	−13.7183	−	42.2206i	−0.527237	−	1.62267i	0.232611	−	0.972570i	$-0.425273\pi$
$678$	−44.6852	−	54.5756i	−1.71612	−	2.09596i
$679$	4.69009	+	6.45536i	0.179989	+	0.247734i
$680$	−44.1768	−	14.3539i	−1.69410	−	0.550448i
$681$	−3.81724	+	14.5606i	−0.146277	+	0.557963i
$682$	11.4647	+	3.76508i	0.439007	+	0.144172i
$683$		−	7.37477i		−	0.282188i	−0.989996	−	0.141094i	$-0.954938\pi$
$683$		−	7.37477i		−	0.282188i	0.989996	−	0.141094i	$-0.0450620\pi$
$684$	26.8879	+	29.2203i	1.02808	+	1.11727i
$685$	11.5720	−	8.40757i	0.442144	−	0.321237i
$686$	−62.7702	+	86.3958i	−2.39658	+	3.29861i
$687$	17.2176	−	0.995713i	0.656892	−	0.0379888i
$688$	101.074	−	32.8408i	3.85340	−	1.25204i
$689$	5.84000	+	4.24301i	0.222486	+	0.161646i
$690$	−7.51976	−	19.2774i	−0.286272	−	0.733880i
$691$	1.81891	−	5.59802i	0.0691944	−	0.212959i	−0.910480	−	0.413553i	$-0.864287\pi$
$691$	1.81891	−	5.59802i	0.0691944	−	0.212959i	0.979674	+	0.200595i	$0.0642875\pi$
$692$	−119.529			−4.54381
$693$	19.4888	+	42.8850i	0.740320	+	1.62907i
$694$	−1.49457			−0.0567332
$695$	−10.3236	+	31.7729i	−0.391597	+	1.20521i
$696$	−17.0837	−	43.7953i	−0.647556	−	1.66006i
$697$	17.6064	+	12.7918i	0.666891	+	0.484525i
$698$	11.5005	−	3.73673i	0.435299	−	0.141437i
$699$	23.6755	−	1.36918i	0.895489	−	0.0517871i
$700$	−32.8275	+	45.1832i	−1.24076	+	1.70776i
$701$	15.3653	−	11.1635i	0.580339	−	0.421641i	−0.258508	−	0.966009i	$-0.583231\pi$
$701$	15.3653	−	11.1635i	0.580339	−	0.421641i	0.838846	+	0.544369i	$0.183231\pi$
$702$	12.3084	−	6.52505i	0.464551	−	0.246272i
$703$		−	6.67515i		−	0.251758i
$704$	0.200778	−	63.7431i	0.00756712	−	2.40241i
$705$	1.47720	−	5.63469i	0.0556347	−	0.212215i
$706$	−48.8281	−	15.8652i	−1.83767	−	0.597095i
$707$	26.0375	+	35.8375i	0.979240	+	1.34781i
$708$	38.5079	+	47.0311i	1.44722	+	1.76754i
$709$	5.64860	+	17.3846i	0.212137	+	0.652892i	0.999344	+	0.0362031i	$0.0115263\pi$
$709$	5.64860	+	17.3846i	0.212137	+	0.652892i	−0.787207	+	0.616689i	$0.788474\pi$
$710$	23.1542	+	71.2615i	0.868963	+	2.67439i
$711$	32.0952	−	14.7076i	1.20366	−	0.551578i
$712$	58.2479	+	80.1713i	2.18293	+	3.00455i
$713$	2.13243	+	0.692869i	0.0798602	+	0.0259481i
$714$	42.8532	+	11.2345i	1.60374	+	0.420441i
$715$	−8.51586	+	2.73735i	−0.318475	+	0.102371i
$716$		−	53.4113i		−	1.99607i
$717$	−4.10178	−	2.63231i	−0.153184	−	0.0983053i
$718$	−45.1964	+	32.8371i	−1.68671	+	1.22547i
$719$	0.890195	−	1.22525i	0.0331987	−	0.0456941i	−0.792095	−	0.610398i	$-0.791010\pi$
$719$	0.890195	−	1.22525i	0.0331987	−	0.0456941i	0.825294	+	0.564704i	$0.191010\pi$
$720$	99.4541	+	20.0181i	3.70644	+	0.746030i
$721$	3.94521	−	1.28188i	0.146927	−	0.0477396i
$722$	−27.0918	−	19.6833i	−1.00825	−	0.732537i
$723$	42.5265	−	16.5888i	1.58158	−	0.616943i
$724$	33.4017	−	102.800i	1.24136	−	3.82052i
$725$	−7.22094			−0.268179
$726$	−39.7256	+	32.1105i	−1.47435	+	1.19173i
$727$	23.1638			0.859098			0.429549	−	0.903043i	$-0.358672\pi$
$727$	23.1638			0.859098			0.429549	+	0.903043i	$0.358672\pi$
$728$	−12.5038	+	38.4826i	−0.463420	+	1.42626i
$729$	16.5704	+	21.3172i	0.613717	+	0.789526i
$730$	13.7010	+	9.95434i	0.507096	+	0.368427i
$731$	−16.2442	+	5.27806i	−0.600813	+	0.195216i
$732$	−0.486349	−	8.40981i	−0.0179760	−	0.310835i
$733$	15.8488	−	21.8140i	0.585388	−	0.805717i	−0.408885	−	0.912586i	$-0.634082\pi$
$733$	15.8488	−	21.8140i	0.585388	−	0.805717i	0.994273	+	0.106868i	$0.0340823\pi$
$734$	−3.07997	+	2.23773i	−0.113684	+	0.0825961i
$735$	38.8883	−	60.5975i	1.43442	−	2.23517i
$736$		−	27.2977i		−	1.00621i
$737$	9.92789	−	3.19123i	0.365699	−	0.117551i
$738$	−75.6907	−	42.6154i	−2.78621	−	1.56870i
$739$	−4.50351	−	1.46328i	−0.165664	−	0.0538275i	0.225011	−	0.974356i	$-0.427758\pi$
$739$	−4.50351	−	1.46328i	−0.165664	−	0.0538275i	−0.390675	+	0.920529i	$0.627758\pi$
$740$	−21.5169	−	29.6154i	−0.790976	−	1.08869i
$741$	3.41921	−	2.79957i	0.125608	−	0.102845i
$742$	−28.3135	−	87.1399i	−1.03942	−	3.19901i
$743$	0.208530	+	0.641789i	0.00765022	+	0.0235450i	0.954809	−	0.297221i	$-0.0960598\pi$
$743$	0.208530	+	0.641789i	0.00765022	+	0.0235450i	−0.947159	+	0.320766i	$0.896060\pi$
$744$	−15.5440	+	12.7270i	−0.569869	+	0.466595i
$745$	25.9567	+	35.7263i	0.950979	+	1.30891i
$746$	−75.6565	−	24.5823i	−2.76998	−	0.900021i
$747$	−25.3914	−	14.2959i	−0.929022	−	0.523058i
$748$	−0.109212	+	34.6725i	−0.00399318	+	1.26775i
$749$		−	51.7088i		−	1.88940i
$750$	−18.4398	+	28.7338i	−0.673327	+	1.04921i
$751$	31.9826	−	23.2367i	1.16706	−	0.847921i	0.176409	−	0.984317i	$-0.443552\pi$
$751$	31.9826	−	23.2367i	1.16706	−	0.847921i	0.990654	+	0.136396i	$0.0435520\pi$
$752$	9.19009	−	12.6491i	0.335128	−	0.461264i
$753$	−1.69966	−	29.3900i	−0.0619390	−	1.07103i
$754$	−8.09706	+	2.63090i	−0.294878	+	0.0958116i
$755$	46.4400	+	33.7406i	1.69012	+	1.22795i
$756$	−126.359	−	17.9174i	−4.59562	−	0.651649i
$757$	−11.1578	+	34.3403i	−0.405538	+	1.24812i	0.514907	+	0.857246i	$0.327826\pi$
$757$	−11.1578	+	34.3403i	−0.405538	+	1.24812i	−0.920445	+	0.390872i	$0.872174\pi$
$758$	51.4723			1.86956
$759$	−7.36250	+	5.98960i	−0.267242	+	0.217409i
$760$	58.8114			2.13331
$761$	−11.7560	+	36.1814i	−0.426156	+	1.31157i	0.475726	+	0.879593i	$0.342185\pi$
$761$	−11.7560	+	36.1814i	−0.426156	+	1.31157i	−0.901883	+	0.431981i	$0.857815\pi$
$762$	16.2576	−	6.34176i	0.588949	−	0.229738i
$763$	30.6183	+	22.2455i	1.10846	+	0.805341i
$764$	−9.90547	+	3.21848i	−0.358367	+	0.116441i
$765$	−15.9839	−	3.21723i	−0.577899	−	0.116319i
$766$	0.159984	−	0.220199i	0.00578046	−	0.00795612i
$767$	5.47270	−	3.97615i	0.197608	−	0.143570i
$768$	16.2032	+	10.3984i	0.584682	+	0.375218i
$769$		−	38.0757i		−	1.37305i	−0.727108	−	0.686523i	$-0.759136\pi$
$769$		−	38.0757i		−	1.37305i	0.727108	−	0.686523i	$-0.240864\pi$
$770$	107.869	+	35.4247i	3.88732	+	1.27662i
$771$	32.1237	+	8.42162i	1.15691	+	0.303297i
$772$	−40.7971	−	13.2558i	−1.46832	−	0.477086i
$773$	−18.5016	−	25.4653i	−0.665457	−	0.915923i	0.334189	−	0.942506i	$-0.391538\pi$
$773$	−18.5016	−	25.4653i	−0.665457	−	0.915923i	−0.999647	+	0.0265826i	$0.991538\pi$
$774$	61.9756	−	28.4003i	2.22767	−	1.02083i
$775$	0.953593	+	2.93486i	0.0342541	+	0.105423i
$776$	−4.45136	−	13.6999i	−0.159795	−	0.491797i
$777$	13.5912	+	16.5994i	0.487582	+	0.595501i
$778$	7.69138	+	10.5863i	0.275749	+	0.379536i
$779$	−26.2055	−	8.51470i	−0.938911	−	0.305071i
$780$	6.14570	−	23.4423i	0.220051	−	0.839371i
$781$	27.8682	−	20.1136i	0.997201	−	0.719721i
$782$			8.92612i			0.319198i
$783$	−7.72865	−	14.5788i	−0.276199	−	0.521004i
$784$	156.351	−	113.596i	5.58398	−	4.05700i
$785$	6.23078	−	8.57593i	0.222386	−	0.306088i
$786$	−24.8222	+	1.43550i	−0.885380	+	0.0512026i
$787$	−26.3853	+	8.57311i	−0.940535	+	0.305598i	−0.738864	−	0.673855i	$-0.764637\pi$
$787$	−26.3853	+	8.57311i	−0.940535	+	0.305598i	−0.201672	+	0.979453i	$0.564637\pi$
$788$	−8.36789	−	6.07962i	−0.298094	−	0.216578i
$789$	5.77738	+	14.8107i	0.205680	+	0.527276i
$790$	26.2952	−	80.9284i	0.935542	−	2.87930i
$791$	71.9121			2.55690
$792$	−9.53696	−	84.5030i	−0.338881	−	3.00268i
$793$	−0.937476			−0.0332908
$794$	4.28274	−	13.1809i	0.151989	−	0.467773i
$795$	12.2545	+	31.4154i	0.434624	+	1.11419i
$796$	−1.48217	−	1.07686i	−0.0525342	−	0.0381684i
$797$	11.5559	−	3.75472i	0.409329	−	0.132999i	−0.0971123	−	0.995273i	$-0.530961\pi$
$797$	11.5559	−	3.75472i	0.409329	−	0.132999i	0.506442	+	0.862274i	$0.330961\pi$
$798$	−55.9972	+	3.23838i	−1.98228	+	0.114637i
$799$	−1.47700	+	2.03291i	−0.0522524	+	0.0719192i
$800$	30.3946	−	22.0829i	1.07461	−	0.780750i
$801$	23.5532	+	25.5963i	0.832212	+	0.904402i
$802$			1.11963i			0.0395354i
$803$	2.42368	−	7.38015i	0.0855299	−	0.260440i
$804$	−7.16473	+	27.3294i	−0.252681	+	0.963832i
$805$	20.0635	+	6.51903i	0.707146	+	0.229766i
$806$	2.13859	+	2.94351i	0.0753285	+	0.103681i
$807$	−12.9696	−	15.8402i	−0.456551	−	0.557602i
$808$	−24.7121	−	76.0562i	−0.869370	−	2.67565i
$809$	1.11555	+	3.43329i	0.0392205	+	0.120708i	0.968750	−	0.248040i	$-0.0797865\pi$
$809$	1.11555	+	3.43329i	0.0392205	+	0.120708i	−0.929529	+	0.368748i	$0.879786\pi$
$810$	64.8524	+	5.40115i	2.27868	+	0.189777i
$811$	12.1925	+	16.7816i	0.428137	+	0.589281i	0.967524	−	0.252777i	$-0.0813440\pi$
$811$	12.1925	+	16.7816i	0.428137	+	0.589281i	−0.539387	+	0.842058i	$0.681344\pi$
$812$	74.1776	+	24.1018i	2.60312	+	0.845806i
$813$	−45.3022	−	11.8765i	−1.58882	−	0.416528i
$814$	−13.7334	+	18.7778i	−0.481356	+	0.658160i
$815$			54.4760i			1.90821i
$816$	−36.8307	−	23.6360i	−1.28933	−	0.827426i
$817$	17.4954	−	12.7111i	0.612085	−	0.444706i
$818$	−2.32254	+	3.19670i	−0.0812058	+	0.111770i
$819$	−2.80254	+	13.9236i	−0.0979288	+	0.486531i
$820$	−143.712	+	46.6949i	−5.01864	+	1.63065i
$821$	18.1406	+	13.1799i	0.633110	+	0.459981i	0.857476	−	0.514524i	$-0.172031\pi$
$821$	18.1406	+	13.1799i	0.633110	+	0.459981i	−0.224366	+	0.974505i	$0.572031\pi$
$822$	22.9441	−	8.95007i	0.800269	−	0.312169i
$823$	−4.84051	+	14.8975i	−0.168729	+	0.519296i	−0.999292	−	0.0376299i	$-0.988019\pi$
$823$	−4.84051	+	14.8975i	−0.168729	+	0.519296i	0.830562	+	0.556926i	$0.188019\pi$
$824$	−7.48879			−0.260884
$825$	−12.6251	−	3.35237i	−0.439550	−	0.116714i
$826$	−85.8617			−2.98751
$827$	−11.8109	+	36.3503i	−0.410706	+	1.26402i	0.505329	+	0.862927i	$0.331371\pi$
$827$	−11.8109	+	36.3503i	−0.410706	+	1.26402i	−0.916036	+	0.401097i	$0.868629\pi$
$828$	−2.96425	−	25.5428i	−0.103015	−	0.887672i
$829$	−30.9134	−	22.4599i	−1.07367	−	0.780064i	−0.0970988	−	0.995275i	$-0.530956\pi$
$829$	−30.9134	−	22.4599i	−1.07367	−	0.780064i	−0.976568	+	0.215210i	$0.930956\pi$
$830$	−66.7955	+	21.7032i	−2.31851	+	0.753328i
$831$	−2.91152	−	50.3453i	−0.101000	−	1.74646i
$832$	11.2969	−	15.5488i	0.391648	−	0.539057i
$833$	−25.1282	+	18.2567i	−0.870640	+	0.632557i
$834$	−31.0669	+	48.4099i	−1.07576	+	1.67630i
$835$			1.89282i			0.0655037i
$836$	−13.4342	−	41.7936i	−0.464630	−	1.44546i
$837$	−4.90472	+	5.06647i	−0.169532	+	0.175123i
$838$	54.8773	+	17.8307i	1.89571	+	0.615952i
$839$	16.0184	+	22.0474i	0.553015	+	0.761160i	0.990417	−	0.138106i	$-0.0441014\pi$
$839$	16.0184	+	22.0474i	0.553015	+	0.761160i	−0.437402	+	0.899266i	$0.644101\pi$
$840$	−146.249	+	119.745i	−5.04608	+	4.13161i
$841$	−5.84530	−	17.9900i	−0.201562	−	0.620345i
$842$	−20.3069	−	62.4983i	−0.699823	−	2.15383i
$843$	9.83369	−	8.05159i	0.338690	−	0.277312i
$844$	40.1131	+	55.2110i	1.38075	+	1.90044i
$845$	−2.56502	−	0.833425i	−0.0882393	−	0.0286707i
$846$	4.92055	−	8.73956i	0.169172	−	0.300472i
$847$	0.328063	−	52.0762i	0.0112724	−	1.78936i
$848$			90.5099i			3.10812i
$849$	18.9145	−	29.4735i	0.649145	−	1.01153i
$850$	−9.93877	+	7.22094i	−0.340897	+	0.247676i
$851$	−2.54078	+	3.49708i	−0.0870967	+	0.119878i
$852$	5.37591	+	92.9586i	0.184176	+	3.18471i
$853$	40.3971	−	13.1258i	1.38317	−	0.449419i	0.479460	−	0.877564i	$-0.340833\pi$
$853$	40.3971	−	13.1258i	1.38317	−	0.449419i	0.903710	+	0.428145i	$0.140833\pi$
$854$	9.62662	+	6.99415i	0.329416	+	0.239335i
$855$	20.5057	−	2.37970i	0.701281	−	0.0813839i
$856$	−28.8466	+	88.7807i	−0.985956	+	3.03446i
$857$	−31.4917			−1.07573			−0.537867	−	0.843029i	$-0.680770\pi$
$857$	−31.4917			−1.07573			−0.537867	+	0.843029i	$0.680770\pi$
$858$	−15.3783	+	0.840755i	−0.525008	+	0.0287029i
$859$	6.53487			0.222967			0.111484	−	0.993766i	$-0.464440\pi$
$859$	6.53487			0.222967			0.111484	+	0.993766i	$0.464440\pi$
$860$	36.6477	−	112.790i	1.24968	−	3.84611i
$861$	82.5033	−	32.1829i	2.81170	−	1.09679i
$862$	−26.6347	−	19.3512i	−0.907180	−	0.659105i
$863$	13.2144	−	4.29362i	0.449824	−	0.146157i	−0.0753398	−	0.997158i	$-0.524004\pi$
$863$	13.2144	−	4.29362i	0.449824	−	0.146157i	0.525164	+	0.851001i	$0.324004\pi$
$864$	77.1162	+	37.7298i	2.62355	+	1.28359i
$865$	−36.5246	+	50.2718i	−1.24187	+	1.70929i
$866$	−16.7935	+	12.2012i	−0.570668	+	0.414614i
$867$	−18.8616	−	12.1044i	−0.640573	−	0.411086i
$868$		−	33.3314i		−	1.13134i
$869$	−39.0305	−	0.122939i	−1.32402	−	0.00417040i
$870$	−38.4709	−	10.0856i	−1.30428	−	0.341934i
$871$	2.99033	+	0.971616i	0.101323	+	0.0329220i
$872$	−40.1596	−	55.2750i	−1.35998	−	1.87185i
$873$	−2.10639	−	4.59661i	−0.0712906	−	0.155572i
$874$	−3.49236	−	10.7484i	−0.118131	−	0.363569i
$875$	−10.7563	−	33.1044i	−0.363628	−	1.11913i
$876$	13.3326	+	16.2836i	0.450468	+	0.550172i
$877$	6.64790	+	9.15005i	0.224484	+	0.308975i	0.906372	−	0.422481i	$-0.138841\pi$
$877$	6.64790	+	9.15005i	0.224484	+	0.308975i	−0.681888	+	0.731457i	$0.738841\pi$
$878$	99.1337	+	32.2105i	3.34560	+	1.08705i
$879$	1.88191	−	7.17843i	0.0634754	−	0.242122i
$880$	−90.5278	−	66.2090i	−3.05169	−	2.23190i
$881$		−	23.9859i		−	0.808105i	−0.914736	−	0.404052i	$-0.867601\pi$
$881$		−	23.9859i		−	0.808105i	0.914736	−	0.404052i	$-0.132399\pi$
$882$	91.2269	−	83.9450i	3.07177	−	2.82658i
$883$	−6.44103	+	4.67968i	−0.216758	+	0.157484i	−0.690866	−	0.722983i	$-0.742771\pi$
$883$	−6.44103	+	4.67968i	−0.216758	+	0.157484i	0.474108	+	0.880467i	$0.342771\pi$
$884$	−6.14483	+	8.45764i	−0.206673	+	0.284461i
$885$	31.5474	−	1.82442i	1.06045	−	0.0613273i
$886$	22.9835	−	7.46780i	0.772147	−	0.250886i
$887$	−13.9297	−	10.1205i	−0.467715	−	0.339815i	0.328835	−	0.944387i	$-0.393344\pi$
$887$	−13.9297	−	10.1205i	−0.467715	−	0.339815i	−0.796550	+	0.604573i	$0.793344\pi$
$888$	−14.0750	−	36.0822i	−0.472325	−	1.21084i
$889$	−5.49780	+	16.9205i	−0.184390	+	0.567495i
$890$	83.8383			2.81027
$891$	−6.74450	−	29.0777i	−0.225949	−	0.974139i
$892$	52.1766			1.74700
$893$	0.983143	−	3.02580i	0.0328996	−	0.101255i
$894$	27.6315	+	70.8355i	0.924137	+	2.36909i
$895$	−22.4639	−	16.3209i	−0.750884	−	0.545549i
$896$	−83.2228	+	27.0407i	−2.78028	+	0.903368i
$897$	−2.85691	+	0.165219i	−0.0953895	+	0.00551649i
$898$	−44.5557	+	61.3256i	−1.48684	+	2.04646i
$899$	3.48647	−	2.53307i	0.116280	−	0.0844825i
$900$	26.0425	−	23.9638i	0.868085	−	0.798793i
$901$		−	14.5464i		−	0.484611i
$902$	56.2003	+	77.8677i	1.87127	+	2.59271i
$903$	−17.6256	+	67.2315i	−0.586542	+	2.23732i
$904$	−123.469	−	40.1174i	−4.10650	−	1.33428i
$905$	−33.0292	−	45.4608i	−1.09793	−	1.51117i
$906$	62.6134	+	76.4719i	2.08019	+	2.54061i
$907$	9.80606	+	30.1799i	0.325605	+	1.00211i	0.971167	+	0.238401i	$0.0766232\pi$
$907$	9.80606	+	30.1799i	0.325605	+	1.00211i	−0.645562	+	0.763708i	$0.723377\pi$
$908$	13.9324	+	42.8794i	0.462362	+	1.42300i
$909$	−11.6938	−	25.5185i	−0.387860	−	0.846395i
$910$	20.1214	+	27.6948i	0.667018	+	0.918072i
$911$	5.61768	+	1.82530i	0.186122	+	0.0604747i	0.400595	−	0.916255i	$-0.368803\pi$
$911$	5.61768	+	1.82530i	0.186122	+	0.0604747i	−0.214473	+	0.976730i	$0.568803\pi$
$912$	53.5973	+	14.0512i	1.77478	+	0.465281i
$913$	18.8531	+	26.1217i	0.623946	+	0.864501i
$914$			22.8700i			0.756473i
$915$	−3.68563	−	2.36524i	−0.121843	−	0.0781926i
$916$	41.7912	−	30.3631i	1.38082	−	1.00322i
$917$	14.8997	−	20.5077i	0.492033	−	0.677225i
$918$	−25.2164	−	12.3373i	−0.832264	−	0.407193i
$919$	−27.9470	+	9.08052i	−0.921886	+	0.299539i	−0.731240	−	0.682120i	$-0.761058\pi$
$919$	−27.9470	+	9.08052i	−0.921886	+	0.299539i	−0.190645	+	0.981659i	$0.561058\pi$
$920$	−30.8110	−	22.3855i	−1.01581	−	0.738029i
$921$	46.6123	−	18.1825i	1.53593	−	0.599135i
$922$	−8.04775	+	24.7684i	−0.265039	+	0.815705i
$923$	10.3625			0.341085
$924$	118.503	+	76.5770i	3.89846	+	2.51920i
$925$	−5.94921			−0.195609
$926$	28.0454	−	86.3148i	0.921629	−	2.83648i
$927$	−2.61111	+	0.303020i	−0.0857600	+	0.00995249i
$928$	−42.4466	−	30.8393i	−1.39338	−	1.01235i
$929$	39.4439	−	12.8161i	1.29411	−	0.420482i	0.420582	−	0.907254i	$-0.361826\pi$
$929$	39.4439	−	12.8161i	1.29411	−	0.420482i	0.873529	+	0.486772i	$0.161826\pi$
$930$	0.981272	+	16.9679i	0.0321772	+	0.556399i
$931$	23.1151	−	31.8152i	0.757567	−	1.04270i
$932$	57.4660	−	41.7515i	1.88236	−	1.36762i
$933$	−10.5276	+	16.4046i	−0.344659	+	0.537064i
$934$		−	65.0114i		−	2.12724i
$935$	14.5493	+	10.6409i	0.475813	+	0.347993i
$936$	12.5793	−	22.3426i	0.411168	−	0.730289i
$937$	19.5508	+	6.35244i	0.638697	+	0.207525i	0.610424	−	0.792075i	$-0.290999\pi$
$937$	19.5508	+	6.35244i	0.638697	+	0.207525i	0.0282734	+	0.999600i	$0.490999\pi$
$938$	−23.4578	−	32.2869i	−0.765924	−	1.05420i
$939$	31.1124	−	25.4741i	1.01532	−	0.831316i
$940$	−5.39158	−	16.5936i	−0.175854	−	0.541223i
$941$	7.14449	+	21.9885i	0.232904	+	0.716804i	0.997393	+	0.0721670i	$0.0229915\pi$
$941$	7.14449	+	21.9885i	0.232904	+	0.716804i	−0.764489	+	0.644637i	$0.777009\pi$
$942$	14.1218	−	11.5626i	0.460114	−	0.376731i
$943$	10.4880	+	14.4355i	0.341536	+	0.470084i
$944$	80.6662	+	26.2100i	2.62546	+	0.853064i
$945$	−46.1473	+	47.6692i	−1.50117	+	1.55068i
$946$	−75.3677	−	0.237394i	−2.45041	−	0.00771833i
$947$		−	13.7576i		−	0.447061i	−0.974697	−	0.223531i	$-0.928242\pi$
$947$		−	13.7576i		−	0.447061i	0.974697	−	0.223531i	$-0.0717583\pi$
$948$	57.1126	−	88.9956i	1.85493	−	2.89044i
$949$	1.89482	−	1.37666i	0.0615083	−	0.0446884i
$950$	9.14254	−	12.5836i	0.296623	−	0.408267i
$951$	2.89189	+	50.0058i	0.0937761	+	1.62155i
$952$	77.5472	−	25.1966i	2.51332	−	0.816626i
$953$	15.6735	+	11.3875i	0.507715	+	0.368877i	0.811956	−	0.583718i	$-0.198403\pi$
$953$	15.6735	+	11.3875i	0.507715	+	0.368877i	−0.304241	+	0.952595i	$0.598403\pi$
$954$	6.69297	+	57.6729i	0.216693	+	1.86723i
$955$	−1.67319	+	5.14954i	−0.0541431	+	0.166635i
$956$	−14.5980			−0.472135
$957$	0.995840	+	18.2150i	0.0321910	+	0.588808i
$958$	37.2934			1.20489
$959$	−7.75899	+	23.8797i	−0.250551	+	0.771116i
$960$	83.6424	−	32.6273i	2.69955	−	1.05304i
$961$	23.5896	+	17.1388i	0.760954	+	0.552865i
$962$	−6.67104	+	2.16755i	−0.215083	+	0.0698846i
$963$	−6.46556	+	32.1223i	−0.208350	+	1.03513i
$964$	80.3647	−	110.613i	2.58837	−	3.56259i
$965$	−18.0416	+	13.1080i	−0.580778	+	0.421960i
$966$	30.5693	+	19.6177i	0.983550	+	0.631191i
$967$		−	20.4595i		−	0.657933i	−0.944342	−	0.328967i	$-0.893300\pi$
$967$		−	20.4595i		−	0.657933i	0.944342	−	0.328967i	$-0.106700\pi$
$968$	−29.6148	+	89.2285i	−0.951857	+	2.86791i
$969$	−8.61395	−	2.25825i	−0.276720	−	0.0725456i
$970$	−11.5904	−	3.76595i	−0.372145	−	0.120917i
$971$	3.54995	+	4.88609i	0.113923	+	0.156802i	0.862171	−	0.506618i	$-0.169104\pi$
$971$	3.54995	+	4.88609i	0.113923	+	0.156802i	−0.748247	+	0.663420i	$0.769104\pi$
$972$	76.2555	+	26.9302i	2.44590	+	0.863785i
$973$	−18.1219	−	55.7735i	−0.580961	−	1.78801i
$974$	−0.569406	−	1.75245i	−0.0182449	−	0.0561522i
$975$	−2.49511	−	3.04736i	−0.0799074	−	0.0975938i
$976$	−6.90908	−	9.50953i	−0.221154	−	0.304393i
$977$	3.26120	+	1.05963i	0.104335	+	0.0339005i	0.360719	−	0.932674i	$-0.382531\pi$
$977$	3.26120	+	1.05963i	0.104335	+	0.0339005i	−0.256384	+	0.966575i	$0.582531\pi$
$978$	−23.7859	+	90.7295i	−0.760588	+	2.90121i
$979$	−11.7680	−	36.6103i	−0.376108	−	1.17007i
$980$		−	215.664i		−	6.88912i
$981$	−16.2390	−	17.6477i	−0.518472	−	0.563447i
$982$	89.5509	−	65.0625i	2.85768	−	2.07623i
$983$	−9.36146	+	12.8849i	−0.298584	+	0.410966i	−0.931779	−	0.363027i	$-0.881743\pi$
$983$	−9.36146	+	12.8849i	−0.298584	+	0.410966i	0.633195	+	0.773993i	$0.281743\pi$
$984$	−159.607	+	9.23024i	−5.08808	+	0.294249i
$985$	−5.11397	+	1.66163i	−0.162945	+	0.0529439i
$986$	13.8797	+	10.0842i	0.442020	+	0.321146i
$987$	3.71598	+	9.52617i	0.118281	+	0.303221i
$988$	4.09023	−	12.5884i	0.130127	−	0.400491i
$989$	−14.0040			−0.445301
$990$	−62.5803	−	35.4940i	−1.98893	−	1.12807i
$991$	−1.15562			−0.0367096			−0.0183548	−	0.999832i	$-0.505843\pi$
$991$	−1.15562			−0.0367096			−0.0183548	+	0.999832i	$0.505843\pi$
$992$	−6.92875	+	21.3245i	−0.219988	+	0.677053i
$993$	15.1950	+	38.9534i	0.482197	+	1.23615i
$994$	−106.409	−	77.3105i	−3.37508	−	2.45214i
$995$	−0.905819	+	0.294318i	−0.0287164	+	0.00933052i
$996$	−87.1329	+	5.03900i	−2.76091	+	0.159667i
$997$	−26.7467	+	36.8137i	−0.847077	+	1.16590i	0.137422	+	0.990513i	$0.456118\pi$
$997$	−26.7467	+	36.8137i	−0.847077	+	1.16590i	−0.984499	+	0.175389i	$0.943882\pi$
$998$	33.6379	−	24.4394i	1.06479	−	0.773615i
$999$	−6.36751	−	12.0112i	−0.201459	−	0.380018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.x.a.365.46	yes	192
3.2	odd	2	inner	429.2.x.a.365.3	yes	192
11.6	odd	10	inner	429.2.x.a.248.3	✓	192
33.17	even	10	inner	429.2.x.a.248.46	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.x.a.248.3	✓	192	11.6	odd	10	inner
429.2.x.a.248.46	yes	192	33.17	even	10	inner
429.2.x.a.365.3	yes	192	3.2	odd	2	inner
429.2.x.a.365.46	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.828482 - 2.54980i) q^{2} +(-0.629445 - 1.61363i) q^{3} +(-4.19709 - 3.04936i) q^{4} +(-2.56502 + 0.833425i) q^{5} +(-4.63592 + 0.268101i) q^{6} +(2.78275 - 3.83012i) q^{7} +(-6.91450 + 5.02368i) q^{8} +(-2.20760 + 2.03138i) q^{9} +O(q^{10})\)	\(q+(0.828482 - 2.54980i) q^{2} +(-0.629445 - 1.61363i) q^{3} +(-4.19709 - 3.04936i) q^{4} +(-2.56502 + 0.833425i) q^{5} +(-4.63592 + 0.268101i) q^{6} +(2.78275 - 3.83012i) q^{7} +(-6.91450 + 5.02368i) q^{8} +(-2.20760 + 2.03138i) q^{9} +7.23077i q^{10} +(3.15751 - 1.01495i) q^{11} +(-2.27870 + 8.69195i) q^{12} +(0.951057 + 0.309017i) q^{13} +(-7.46061 - 10.2687i) q^{14} +(2.95938 + 3.61439i) q^{15} +(3.87457 + 11.9247i) q^{16} +(-0.622707 - 1.91649i) q^{17} +(3.35068 + 7.31190i) q^{18} +(1.49966 + 2.06411i) q^{19} +(13.3070 + 4.32371i) q^{20} +(-7.93199 - 2.07947i) q^{21} +(0.0280078 - 8.89190i) q^{22} -1.65219i q^{23} +(12.4587 + 7.99531i) q^{24} +(1.83963 - 1.33657i) q^{25} +(1.57587 - 2.16899i) q^{26} +(4.66746 + 2.28360i) q^{27} +(-23.3589 + 7.58976i) q^{28} +(-2.56908 - 1.86655i) q^{29} +(11.6678 - 4.55137i) q^{30} +(-0.419363 + 1.29067i) q^{31} +16.5221 q^{32} +(-3.62524 - 4.45619i) q^{33} -5.40259 q^{34} +(-3.94568 + 12.1435i) q^{35} +(15.4599 - 1.79413i) q^{36} +(-2.11663 - 1.53782i) q^{37} +(6.50551 - 2.11377i) q^{38} +(-0.0999994 - 1.72916i) q^{39} +(13.5490 - 18.6485i) q^{40} +(-8.73715 + 6.34791i) q^{41} +(-11.8737 + 18.5022i) q^{42} -8.47599i q^{43} +(-16.3473 - 5.36855i) q^{44} +(3.96952 - 7.05040i) q^{45} +(-4.21277 - 1.36881i) q^{46} +(-0.732957 - 1.00883i) q^{47} +(16.8032 - 13.7581i) q^{48} +(-4.76305 - 14.6592i) q^{49} +(-1.88389 - 5.79803i) q^{50} +(-2.70055 + 2.21115i) q^{51} +(-3.04936 - 4.19709i) q^{52} +(6.86533 + 2.23068i) q^{53} +(9.68963 - 10.0092i) q^{54} +(-7.25318 + 5.23492i) q^{55} +40.4630i q^{56} +(2.38675 - 3.71914i) q^{57} +(-6.88777 + 5.00426i) q^{58} +(3.97615 - 5.47270i) q^{59} +(-1.39917 - 24.1941i) q^{60} +(-0.891593 + 0.289696i) q^{61} +(2.94351 + 2.13859i) q^{62} +(1.63726 + 14.1082i) q^{63} +(5.93911 - 18.2787i) q^{64} -2.69702 q^{65} +(-14.3659 + 5.55177i) q^{66} +3.14422 q^{67} +(-3.23053 + 9.94255i) q^{68} +(-2.66603 + 1.03997i) q^{69} +(27.6948 + 20.1214i) q^{70} +(9.85531 - 3.20218i) q^{71} +(5.05941 - 25.1363i) q^{72} +(1.37666 - 1.89482i) q^{73} +(-5.67472 + 4.12293i) q^{74} +(-3.31468 - 2.12718i) q^{75} -13.2362i q^{76} +(4.89916 - 14.9180i) q^{77} +(-4.49187 - 1.17760i) q^{78} +(-11.1922 - 3.63657i) q^{79} +(-19.8767 - 27.3579i) q^{80} +(0.746968 - 8.96895i) q^{81} +(8.94737 + 27.5372i) q^{82} +(3.00150 + 9.23768i) q^{83} +(26.9502 + 32.9152i) q^{84} +(3.19451 + 4.39686i) q^{85} +(-21.6121 - 7.02220i) q^{86} +(-1.39482 + 5.32044i) q^{87} +(-16.7338 + 22.8802i) q^{88} -11.5947i q^{89} +(-14.6885 - 15.9626i) q^{90} +(3.83012 - 2.78275i) q^{91} +(-5.03814 + 6.93441i) q^{92} +(2.34662 - 0.135708i) q^{93} +(-3.17956 + 1.03310i) q^{94} +(-5.56694 - 4.04462i) q^{95} +(-10.3998 - 26.6605i) q^{96} +(-0.520822 + 1.60293i) q^{97} -41.3241 q^{98} +(-4.90875 + 8.65472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more