LMFDB - Embedded newform 287.2.h.a.78.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, 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:	$2.29170653801$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	287.78
Dual form			287.2.h.a.92.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.00000 q^{9} +O(q^{10})$	\(q-2.23607 q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.00000 q^{9} +(-1.11803 - 3.44095i) q^{11} +(1.38197 - 4.25325i) q^{12} +(-5.04508 + 3.66547i) q^{13} +(-0.690983 + 2.12663i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-1.88197 - 5.79210i) q^{17} +(-6.04508 - 4.39201i) q^{19} +(1.61803 + 1.17557i) q^{20} +(-1.80902 - 1.31433i) q^{21} +(0.118034 - 0.0857567i) q^{23} +(3.23607 + 2.35114i) q^{25} +2.23607 q^{27} +(-1.61803 + 1.17557i) q^{28} +(-1.19098 + 3.66547i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(2.50000 + 7.69421i) q^{33} +(0.809017 - 0.587785i) q^{35} +(-1.23607 + 3.80423i) q^{36} +(-0.781153 + 2.40414i) q^{37} +(11.2812 - 8.19624i) q^{39} +(-2.19098 + 6.01661i) q^{41} +(-3.04508 + 2.21238i) q^{43} +7.23607 q^{44} +(0.618034 - 1.90211i) q^{45} +(3.73607 - 2.71441i) q^{47} +(7.23607 + 5.25731i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.20820 + 12.9515i) q^{51} +(-3.85410 - 11.8617i) q^{52} +(-0.763932 + 2.35114i) q^{53} -3.61803 q^{55} +(13.5172 + 9.82084i) q^{57} +(-9.59017 + 6.96767i) q^{59} +(-3.61803 - 2.62866i) q^{60} +(-3.11803 - 2.26538i) q^{61} +(1.61803 + 1.17557i) q^{63} +(6.47214 - 4.70228i) q^{64} +(1.92705 + 5.93085i) q^{65} +(-2.47214 + 7.60845i) q^{67} +12.1803 q^{68} +(-0.263932 + 0.191758i) q^{69} +(-4.38197 - 13.4863i) q^{71} +13.3262 q^{73} +(-7.23607 - 5.25731i) q^{75} +(12.0902 - 8.78402i) q^{76} +(1.11803 - 3.44095i) q^{77} -1.76393 q^{79} +(-3.23607 + 2.35114i) q^{80} -11.0000 q^{81} +7.00000 q^{83} +(3.61803 - 2.62866i) q^{84} -6.09017 q^{85} +(2.66312 - 8.19624i) q^{87} +(-11.1631 - 8.11048i) q^{89} -6.23607 q^{91} +(0.0901699 + 0.277515i) q^{92} +(4.04508 + 12.4495i) q^{93} +(-6.04508 + 4.39201i) q^{95} +(-4.16312 + 12.8128i) q^{97} +(-2.23607 - 6.88191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - q^{5} + q^{7} + 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - q^5 + q^7 + 8 * q^9	$ 4 q + 2 q^{4} - q^{5} + q^{7} + 8 q^{9} + 10 q^{12} - 9 q^{13} - 5 q^{15} - 4 q^{16} - 12 q^{17} - 13 q^{19} + 2 q^{20} - 5 q^{21} - 4 q^{23} + 4 q^{25} - 2 q^{28} - 7 q^{29} - 5 q^{31} + 10 q^{33} + q^{35} + 4 q^{36} + 17 q^{37} + 25 q^{39} - 11 q^{41} - q^{43} + 20 q^{44} - 2 q^{45} + 6 q^{47} + 20 q^{48} - q^{49} - 10 q^{51} - 2 q^{52} - 12 q^{53} - 10 q^{55} + 25 q^{57} - 16 q^{59} - 10 q^{60} - 8 q^{61} + 2 q^{63} + 8 q^{64} + q^{65} + 8 q^{67} + 4 q^{68} - 10 q^{69} - 22 q^{71} + 22 q^{73} - 20 q^{75} + 26 q^{76} - 16 q^{79} - 4 q^{80} - 44 q^{81} + 28 q^{83} + 10 q^{84} - 2 q^{85} - 5 q^{87} - 29 q^{89} - 16 q^{91} - 22 q^{92} + 5 q^{93} - 13 q^{95} - q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - q^5 + q^7 + 8 * q^9 + 10 * q^12 - 9 * q^13 - 5 * q^15 - 4 * q^16 - 12 * q^17 - 13 * q^19 + 2 * q^20 - 5 * q^21 - 4 * q^23 + 4 * q^25 - 2 * q^28 - 7 * q^29 - 5 * q^31 + 10 * q^33 + q^35 + 4 * q^36 + 17 * q^37 + 25 * q^39 - 11 * q^41 - q^43 + 20 * q^44 - 2 * q^45 + 6 * q^47 + 20 * q^48 - q^49 - 10 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 + 25 * q^57 - 16 * q^59 - 10 * q^60 - 8 * q^61 + 2 * q^63 + 8 * q^64 + q^65 + 8 * q^67 + 4 * q^68 - 10 * q^69 - 22 * q^71 + 22 * q^73 - 20 * q^75 + 26 * q^76 - 16 * q^79 - 4 * q^80 - 44 * q^81 + 28 * q^83 + 10 * q^84 - 2 * q^85 - 5 * q^87 - 29 * q^89 - 16 * q^91 - 22 * q^92 + 5 * q^93 - 13 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$2$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$3$	−2.23607			−1.29099			−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607			−1.29099			−0.645497	+	0.763763i	$0.723350\pi$
$4$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	−0.857877	−	0.513855i	$-0.828217\pi$
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i	0.996074	+	0.0885298i	$0.0282169\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$		0			0
$9$	2.00000			0.666667
$10$		0			0
$11$	−1.11803	−	3.44095i	−0.337100	−	1.03749i	−0.965678	−	0.259741i	$-0.916363\pi$
$11$	−1.11803	−	3.44095i	−0.337100	−	1.03749i	0.628578	−	0.777746i	$-0.283637\pi$
$12$	1.38197	−	4.25325i	0.398939	−	1.22781i
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.404478	+	0.914548i	$0.632547\pi$
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.994777	+	0.102070i	$0.967453\pi$
$14$		0			0
$15$	−0.690983	+	2.12663i	−0.178411	+	0.549093i
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	−1.88197	−	5.79210i	−0.456444	−	1.40479i	−0.869432	−	0.494053i	$-0.835515\pi$
$17$	−1.88197	−	5.79210i	−0.456444	−	1.40479i	0.412988	−	0.910736i	$-0.364485\pi$
$18$		0			0
$19$	−6.04508	−	4.39201i	−1.38684	−	1.00760i	−0.996204	−	0.0870503i	$-0.972256\pi$
$19$	−6.04508	−	4.39201i	−1.38684	−	1.00760i	−0.390634	−	0.920546i	$-0.627744\pi$
$20$	1.61803	+	1.17557i	0.361803	+	0.262866i
$21$	−1.80902	−	1.31433i	−0.394760	−	0.286810i
$22$		0			0
$23$	0.118034	−	0.0857567i	0.0246118	−	0.0178815i	−0.575411	−	0.817864i	$-0.695158\pi$
$23$	0.118034	−	0.0857567i	0.0246118	−	0.0178815i	0.600023	+	0.799983i	$0.295158\pi$
$24$		0			0
$25$	3.23607	+	2.35114i	0.647214	+	0.470228i
$26$		0			0
$27$	2.23607			0.430331
$28$	−1.61803	+	1.17557i	−0.305780	+	0.222162i
$29$	−1.19098	+	3.66547i	−0.221160	+	0.680660i	0.777499	+	0.628885i	$0.216488\pi$
$29$	−1.19098	+	3.66547i	−0.221160	+	0.680660i	−0.998659	+	0.0517760i	$0.983512\pi$
$30$		0			0
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	−0.971482	−	0.237115i	$-0.923798\pi$
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	0.646573	−	0.762852i	$-0.276202\pi$
$32$		0			0
$33$	2.50000	+	7.69421i	0.435194	+	1.33939i
$34$		0			0
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−1.23607	+	3.80423i	−0.206011	+	0.634038i
$37$	−0.781153	+	2.40414i	−0.128421	+	0.395238i	−0.994509	−	0.104653i	$-0.966627\pi$
$37$	−0.781153	+	2.40414i	−0.128421	+	0.395238i	0.866088	+	0.499891i	$0.166627\pi$
$38$		0			0
$39$	11.2812	−	8.19624i	1.80643	−	1.31245i
$40$		0			0
$41$	−2.19098	+	6.01661i	−0.342174	+	0.939637i
$41$	−2.19098	+	6.01661i	−0.342174	+	0.939637i
$42$		0			0
$43$	−3.04508	+	2.21238i	−0.464371	+	0.337385i	−0.795244	−	0.606290i	$-0.792657\pi$
$43$	−3.04508	+	2.21238i	−0.464371	+	0.337385i	0.330872	+	0.943675i	$0.392657\pi$
$44$	7.23607			1.09088
$45$	0.618034	−	1.90211i	0.0921311	−	0.283550i
$46$		0			0
$47$	3.73607	−	2.71441i	0.544962	−	0.395938i	−0.280963	−	0.959719i	$-0.590654\pi$
$47$	3.73607	−	2.71441i	0.544962	−	0.395938i	0.825924	+	0.563781i	$0.190654\pi$
$48$	7.23607	+	5.25731i	1.04444	+	0.758827i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	4.20820	+	12.9515i	0.589266	+	1.81358i
$52$	−3.85410	−	11.8617i	−0.534468	−	1.64492i
$53$	−0.763932	+	2.35114i	−0.104934	+	0.322954i	−0.989715	−	0.143053i	$-0.954308\pi$
$53$	−0.763932	+	2.35114i	−0.104934	+	0.322954i	0.884781	+	0.466007i	$0.154308\pi$
$54$		0			0
$55$	−3.61803			−0.487856
$56$		0			0
$57$	13.5172	+	9.82084i	1.79040	+	1.30080i
$58$		0			0
$59$	−9.59017	+	6.96767i	−1.24853	+	0.907113i	−0.998136	−	0.0610301i	$-0.980561\pi$
$59$	−9.59017	+	6.96767i	−1.24853	+	0.907113i	−0.250398	+	0.968143i	$0.580561\pi$
$60$	−3.61803	−	2.62866i	−0.467086	−	0.339358i
$61$	−3.11803	−	2.26538i	−0.399223	−	0.290053i	0.370001	−	0.929031i	$-0.379357\pi$
$61$	−3.11803	−	2.26538i	−0.399223	−	0.290053i	−0.769225	+	0.638979i	$0.779357\pi$
$62$		0			0
$63$	1.61803	+	1.17557i	0.203853	+	0.148108i
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$	1.92705	+	5.93085i	0.239021	+	0.735632i
$66$		0			0
$67$	−2.47214	+	7.60845i	−0.302019	+	0.929520i	0.678753	+	0.734366i	$0.262521\pi$
$67$	−2.47214	+	7.60845i	−0.302019	+	0.929520i	−0.980773	+	0.195154i	$0.937479\pi$
$68$	12.1803			1.47708
$69$	−0.263932	+	0.191758i	−0.0317737	+	0.0230849i
$70$		0			0
$71$	−4.38197	−	13.4863i	−0.520044	−	1.60053i	−0.773913	−	0.633291i	$-0.781703\pi$
$71$	−4.38197	−	13.4863i	−0.520044	−	1.60053i	0.253870	−	0.967238i	$-0.418297\pi$
$72$		0			0
$73$	13.3262			1.55972			0.779859	−	0.625955i	$-0.215291\pi$
$73$	13.3262			1.55972			0.779859	+	0.625955i	$0.215291\pi$
$74$		0			0
$75$	−7.23607	−	5.25731i	−0.835549	−	0.607062i
$76$	12.0902	−	8.78402i	1.38684	−	1.00760i
$77$	1.11803	−	3.44095i	0.127412	−	0.392133i
$78$		0			0
$79$	−1.76393			−0.198458			−0.0992289	−	0.995065i	$-0.531638\pi$
$79$	−1.76393			−0.198458			−0.0992289	+	0.995065i	$0.531638\pi$
$80$	−3.23607	+	2.35114i	−0.361803	+	0.262866i
$81$	−11.0000			−1.22222
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$	3.61803	−	2.62866i	0.394760	−	0.286810i
$85$	−6.09017			−0.660572
$86$		0			0
$87$	2.66312	−	8.19624i	0.285516	−	0.878729i
$88$		0			0
$89$	−11.1631	−	8.11048i	−1.18329	−	0.859709i	−0.190749	−	0.981639i	$-0.561092\pi$
$89$	−11.1631	−	8.11048i	−1.18329	−	0.859709i	−0.992539	+	0.121930i	$0.961092\pi$
$90$		0			0
$91$	−6.23607			−0.653718
$92$	0.0901699	+	0.277515i	0.00940087	+	0.0289329i
$93$	4.04508	+	12.4495i	0.419456	+	1.29095i
$94$		0			0
$95$	−6.04508	+	4.39201i	−0.620213	+	0.450611i
$96$		0			0
$97$	−4.16312	+	12.8128i	−0.422701	+	1.30094i	0.482478	+	0.875908i	$0.339737\pi$
$97$	−4.16312	+	12.8128i	−0.422701	+	1.30094i	−0.905179	+	0.425031i	$0.860263\pi$
$98$		0			0
$99$	−2.23607	−	6.88191i	−0.224733	−	0.691658i
$100$	−6.47214	+	4.70228i	−0.647214	+	0.470228i
$101$	7.04508	+	5.11855i	0.701012	+	0.509315i	0.880262	−	0.474488i	$-0.157367\pi$
$101$	7.04508	+	5.11855i	0.701012	+	0.509315i	−0.179250	+	0.983804i	$0.557367\pi$
$102$		0			0
$103$	−10.2812	−	7.46969i	−1.01303	−	0.736011i	−0.0481892	−	0.998838i	$-0.515345\pi$
$103$	−10.2812	−	7.46969i	−1.01303	−	0.736011i	−0.964843	+	0.262827i	$0.915345\pi$
$104$		0			0
$105$	−1.80902	+	1.31433i	−0.176542	+	0.128265i
$106$		0			0
$107$	3.30902	+	2.40414i	0.319895	+	0.232417i	0.736131	−	0.676840i	$-0.236651\pi$
$107$	3.30902	+	2.40414i	0.319895	+	0.232417i	−0.416236	+	0.909257i	$0.636651\pi$
$108$	−1.38197	+	4.25325i	−0.132980	+	0.409270i
$109$	−3.85410			−0.369156			−0.184578	−	0.982818i	$-0.559092\pi$
$109$	−3.85410			−0.369156			−0.184578	+	0.982818i	$0.559092\pi$
$110$		0			0
$111$	1.74671	−	5.37582i	0.165790	−	0.510251i
$112$	−1.23607	−	3.80423i	−0.116797	−	0.359466i
$113$	6.38197	+	19.6417i	0.600365	+	1.84773i	0.525968	+	0.850504i	$0.323703\pi$
$113$	6.38197	+	19.6417i	0.600365	+	1.84773i	0.0743968	+	0.997229i	$0.476297\pi$
$114$		0			0
$115$	−0.0450850	−	0.138757i	−0.00420420	−	0.0129392i
$116$	−6.23607	−	4.53077i	−0.579004	−	0.420671i
$117$	−10.0902	+	7.33094i	−0.932837	+	0.677745i
$118$		0			0
$119$	1.88197	−	5.79210i	0.172520	−	0.530961i
$120$		0			0
$121$	−1.69098	+	1.22857i	−0.153726	+	0.111688i
$122$		0			0
$123$	4.89919	−	13.4535i	0.441745	−	1.21307i
$124$	11.7082			1.05143
$125$	7.28115	−	5.29007i	0.651246	−	0.473158i
$126$		0			0
$127$	3.21885	−	9.90659i	0.285626	−	0.879068i	−0.700584	−	0.713570i	$-0.747077\pi$
$127$	3.21885	−	9.90659i	0.285626	−	0.879068i	0.986210	−	0.165498i	$-0.0529230\pi$
$128$		0			0
$129$	6.80902	−	4.94704i	0.599501	−	0.435563i
$130$		0			0
$131$	3.52786	+	10.8576i	0.308231	+	0.948637i	0.978452	+	0.206475i	$0.0661994\pi$
$131$	3.52786	+	10.8576i	0.308231	+	0.948637i	−0.670221	+	0.742162i	$0.733801\pi$
$132$	−16.1803			−1.40832
$133$	−2.30902	−	7.10642i	−0.200217	−	0.616205i
$134$		0			0
$135$	0.690983	−	2.12663i	0.0594703	−	0.183031i
$136$		0			0
$137$	−1.70820			−0.145942			−0.0729709	−	0.997334i	$-0.523248\pi$
$137$	−1.70820			−0.145942			−0.0729709	+	0.997334i	$0.523248\pi$
$138$		0			0
$139$	−7.92705	−	5.75934i	−0.672364	−	0.488501i	0.198452	−	0.980111i	$-0.436409\pi$
$139$	−7.92705	−	5.75934i	−0.672364	−	0.488501i	−0.870816	+	0.491610i	$0.836409\pi$
$140$	0.618034	+	1.90211i	0.0522334	+	0.160758i
$141$	−8.35410	+	6.06961i	−0.703542	+	0.511153i
$142$		0			0
$143$	18.2533	+	13.2618i	1.52642	+	1.10901i
$144$	−6.47214	−	4.70228i	−0.539345	−	0.391857i
$145$	3.11803	+	2.26538i	0.258939	+	0.188130i
$146$		0			0
$147$	−0.690983	−	2.12663i	−0.0569913	−	0.175401i
$148$	−4.09017	−	2.97168i	−0.336210	−	0.244271i
$149$	−0.635255	+	1.95511i	−0.0520421	+	0.160169i	−0.973700	−	0.227835i	$-0.926835\pi$
$149$	−0.635255	+	1.95511i	−0.0520421	+	0.160169i	0.921658	+	0.388004i	$0.126835\pi$
$150$		0			0
$151$	−2.07295	+	1.50609i	−0.168694	+	0.122564i	−0.668929	−	0.743326i	$-0.733247\pi$
$151$	−2.07295	+	1.50609i	−0.168694	+	0.122564i	0.500235	+	0.865890i	$0.333247\pi$
$152$		0			0
$153$	−3.76393	−	11.5842i	−0.304296	−	0.936526i
$154$		0			0
$155$	−5.85410			−0.470213
$156$	8.61803	+	26.5236i	0.689995	+	2.12359i
$157$	−9.78115	−	7.10642i	−0.780621	−	0.567154i	0.124544	−	0.992214i	$-0.460253\pi$
$157$	−9.78115	−	7.10642i	−0.780621	−	0.567154i	−0.905165	+	0.425060i	$0.860253\pi$
$158$		0			0
$159$	1.70820	−	5.25731i	0.135469	−	0.416932i
$160$		0			0
$161$	0.145898			0.0114984
$162$		0			0
$163$	−11.0902			−0.868649			−0.434325	−	0.900756i	$-0.643013\pi$
$163$	−11.0902			−0.868649			−0.434325	+	0.900756i	$0.643013\pi$
$164$	−10.0902	−	7.88597i	−0.787910	−	0.615791i
$165$	8.09017			0.629819
$166$		0			0
$167$	16.9443			1.31119			0.655594	−	0.755114i	$-0.272418\pi$
$167$	16.9443			1.31119			0.655594	+	0.755114i	$0.272418\pi$
$168$		0			0
$169$	8.00000	−	24.6215i	0.615385	−	1.89396i
$170$		0			0
$171$	−12.0902	−	8.78402i	−0.924558	−	0.671731i
$172$	−2.32624	−	7.15942i	−0.177374	−	0.545901i
$173$	−11.1803			−0.850026			−0.425013	−	0.905187i	$-0.639730\pi$
$173$	−11.1803			−0.850026			−0.425013	+	0.905187i	$0.639730\pi$
$174$		0			0
$175$	1.23607	+	3.80423i	0.0934380	+	0.287572i
$176$	−4.47214	+	13.7638i	−0.337100	+	1.03749i
$177$	21.4443	−	15.5802i	1.61185	−	1.17108i
$178$		0			0
$179$	5.94427	−	18.2946i	0.444296	−	1.36740i	−0.438959	−	0.898507i	$-0.644652\pi$
$179$	5.94427	−	18.2946i	0.444296	−	1.36740i	0.883254	−	0.468894i	$-0.155348\pi$
$180$	3.23607	+	2.35114i	0.241202	+	0.175244i
$181$	0.663119	+	2.04087i	0.0492892	+	0.151697i	0.972672	−	0.232184i	$-0.0745873\pi$
$181$	0.663119	+	2.04087i	0.0492892	+	0.151697i	−0.923383	+	0.383881i	$0.874587\pi$
$182$		0			0
$183$	6.97214	+	5.06555i	0.515395	+	0.374456i
$184$		0			0
$185$	2.04508	+	1.48584i	0.150358	+	0.109241i
$186$		0			0
$187$	−17.8262	+	12.9515i	−1.30358	+	0.947109i
$188$	2.85410	+	8.78402i	0.208157	+	0.640641i
$189$	1.80902	+	1.31433i	0.131587	+	0.0956033i
$190$		0			0
$191$	−8.38197			−0.606498			−0.303249	−	0.952911i	$-0.598071\pi$
$191$	−8.38197			−0.606498			−0.303249	+	0.952911i	$0.598071\pi$
$192$	−14.4721	+	10.5146i	−1.04444	+	0.758827i
$193$	2.76393	−	8.50651i	0.198952	−	0.612312i	−0.800955	−	0.598724i	$-0.795675\pi$
$193$	2.76393	−	8.50651i	0.198952	−	0.612312i	0.999908	−	0.0135880i	$-0.00432532\pi$
$194$		0			0
$195$	−4.30902	−	13.2618i	−0.308575	−	0.949697i
$196$	−2.00000			−0.142857
$197$	−6.00000	−	18.4661i	−0.427482	−	1.31566i	−0.900597	−	0.434655i	$-0.856870\pi$
$197$	−6.00000	−	18.4661i	−0.427482	−	1.31566i	0.473115	−	0.881001i	$-0.343130\pi$
$198$		0			0
$199$	−13.3713	+	9.71483i	−0.947868	+	0.688666i	−0.950302	−	0.311331i	$-0.899225\pi$
$199$	−13.3713	+	9.71483i	−0.947868	+	0.688666i	0.00243370	+	0.999997i	$0.499225\pi$
$200$		0			0
$201$	5.52786	−	17.0130i	0.389905	−	1.20001i
$202$		0			0
$203$	−3.11803	+	2.26538i	−0.218843	+	0.158999i
$204$	−27.2361			−1.90691
$205$	5.04508	+	3.94298i	0.352364	+	0.275390i
$206$		0			0
$207$	0.236068	−	0.171513i	0.0164079	−	0.0119210i
$208$	24.9443			1.72957
$209$	−8.35410	+	25.7113i	−0.577865	+	1.77849i
$210$		0			0
$211$	13.6631	−	9.92684i	0.940608	−	0.683392i	−0.00795902	−	0.999968i	$-0.502533\pi$
$211$	13.6631	−	9.92684i	0.940608	−	0.683392i	0.948567	+	0.316577i	$0.102533\pi$
$212$	−4.00000	−	2.90617i	−0.274721	−	0.199597i
$213$	9.79837	+	30.1563i	0.671374	+	2.06628i
$214$		0			0
$215$	1.16312	+	3.57971i	0.0793241	+	0.244134i
$216$		0			0
$217$	1.80902	−	5.56758i	0.122804	−	0.377952i
$218$		0			0
$219$	−29.7984			−2.01359
$220$	2.23607	−	6.88191i	0.150756	−	0.463978i
$221$	30.7254	+	22.3233i	2.06682	+	1.50163i
$222$		0			0
$223$	−21.0344	+	15.2824i	−1.40857	+	1.02339i	−0.415042	+	0.909802i	$0.636233\pi$
$223$	−21.0344	+	15.2824i	−1.40857	+	1.02339i	−0.993528	+	0.113584i	$0.963767\pi$
$224$		0			0
$225$	6.47214	+	4.70228i	0.431476	+	0.313485i
$226$		0			0
$227$	2.61803	+	1.90211i	0.173765	+	0.126248i	0.671268	−	0.741214i	$-0.265750\pi$
$227$	2.61803	+	1.90211i	0.173765	+	0.126248i	−0.497503	+	0.867462i	$0.665750\pi$
$228$	−27.0344	+	19.6417i	−1.79040	+	1.30080i
$229$	0.118034	+	0.363271i	0.00779991	+	0.0240056i	0.954881	−	0.296990i	$-0.0959827\pi$
$229$	0.118034	+	0.363271i	0.00779991	+	0.0240056i	−0.947081	+	0.320995i	$0.895983\pi$
$230$		0			0
$231$	−2.50000	+	7.69421i	−0.164488	+	0.506242i
$232$		0			0
$233$	8.89919	−	6.46564i	0.583005	−	0.423578i	−0.256801	−	0.966464i	$-0.582669\pi$
$233$	8.89919	−	6.46564i	0.583005	−	0.423578i	0.839806	+	0.542886i	$0.182669\pi$
$234$		0			0
$235$	−1.42705	−	4.39201i	−0.0930905	−	0.286503i
$236$	−7.32624	−	22.5478i	−0.476897	−	1.46774i
$237$	3.94427			0.256208
$238$		0			0
$239$	−2.19098	−	1.59184i	−0.141723	−	0.102968i	0.514665	−	0.857392i	$-0.327916\pi$
$239$	−2.19098	−	1.59184i	−0.141723	−	0.102968i	−0.656388	+	0.754424i	$0.727916\pi$
$240$	7.23607	−	5.25731i	0.467086	−	0.339358i
$241$	2.88197	−	8.86978i	0.185644	−	0.571353i	−0.814315	−	0.580423i	$-0.802887\pi$
$241$	2.88197	−	8.86978i	0.185644	−	0.571353i	0.999959	+	0.00907032i	$0.00288721\pi$
$242$		0			0
$243$	17.8885			1.14755
$244$	6.23607	−	4.53077i	0.399223	−	0.290053i
$245$	1.00000			0.0638877
$246$		0			0
$247$	46.5967			2.96488
$248$		0			0
$249$	−15.6525			−0.991935
$250$		0			0
$251$	3.71885	−	11.4454i	0.234732	−	0.722429i	−0.762425	−	0.647076i	$-0.775992\pi$
$251$	3.71885	−	11.4454i	0.234732	−	0.722429i	0.997157	−	0.0753532i	$-0.0240084\pi$
$252$	−3.23607	+	2.35114i	−0.203853	+	0.148108i
$253$	−0.427051	−	0.310271i	−0.0268485	−	0.0195066i
$254$		0			0
$255$	13.6180			0.852794
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−0.819660	−	2.52265i	−0.0511290	−	0.157359i	0.922232	−	0.386637i	$-0.126363\pi$
$257$	−0.819660	−	2.52265i	−0.0511290	−	0.157359i	−0.973361	+	0.229278i	$0.926363\pi$
$258$		0			0
$259$	−2.04508	+	1.48584i	−0.127075	+	0.0923257i
$260$	−12.4721			−0.773489
$261$	−2.38197	+	7.33094i	−0.147440	+	0.453774i
$262$		0			0
$263$	−1.06231	−	3.26944i	−0.0655046	−	0.201602i	0.912947	−	0.408078i	$-0.133801\pi$
$263$	−1.06231	−	3.26944i	−0.0655046	−	0.201602i	−0.978452	+	0.206475i	$0.933801\pi$
$264$		0			0
$265$	2.00000	+	1.45309i	0.122859	+	0.0892623i
$266$		0			0
$267$	24.9615	+	18.1356i	1.52762	+	1.10988i
$268$	−12.9443	−	9.40456i	−0.790697	−	0.574475i
$269$	23.2254	−	16.8743i	1.41608	−	1.02884i	0.423676	−	0.905814i	$-0.360740\pi$
$269$	23.2254	−	16.8743i	1.41608	−	1.02884i	0.992403	−	0.123028i	$-0.0392605\pi$
$270$		0			0
$271$	5.73607	+	4.16750i	0.348441	+	0.253157i	0.748215	−	0.663457i	$-0.230911\pi$
$271$	5.73607	+	4.16750i	0.348441	+	0.253157i	−0.399774	+	0.916614i	$0.630911\pi$
$272$	−7.52786	+	23.1684i	−0.456444	+	1.40479i
$273$	13.9443			0.843946
$274$		0			0
$275$	4.47214	−	13.7638i	0.269680	−	0.829990i
$276$	−0.201626	−	0.620541i	−0.0121365	−	0.0373522i
$277$	4.44427	+	13.6781i	0.267030	+	0.821835i	0.991219	+	0.132233i	$0.0422146\pi$
$277$	4.44427	+	13.6781i	0.267030	+	0.821835i	−0.724188	+	0.689602i	$0.757785\pi$
$278$		0			0
$279$	−3.61803	−	11.1352i	−0.216606	−	0.666645i
$280$		0			0
$281$	15.3992	−	11.1882i	0.918638	−	0.667430i	−0.0245463	−	0.999699i	$-0.507814\pi$
$281$	15.3992	−	11.1882i	0.918638	−	0.667430i	0.943185	+	0.332269i	$0.107814\pi$
$282$		0			0
$283$	−2.59017	+	7.97172i	−0.153970	+	0.473870i	−0.998055	−	0.0623390i	$-0.980144\pi$
$283$	−2.59017	+	7.97172i	−0.153970	+	0.473870i	0.844085	+	0.536209i	$0.180144\pi$
$284$	28.3607			1.68290
$285$	13.5172	−	9.82084i	0.800691	−	0.581736i
$286$		0			0
$287$	−5.30902	+	3.57971i	−0.313381	+	0.211304i
$288$		0			0
$289$	−16.2533	+	11.8087i	−0.956076	+	0.694630i
$290$		0			0
$291$	9.30902	−	28.6502i	0.545704	−	1.67950i
$292$	−8.23607	+	25.3480i	−0.481979	+	1.48338i
$293$	−10.8541	+	7.88597i	−0.634103	+	0.460703i	−0.857819	−	0.513951i	$-0.828181\pi$
$293$	−10.8541	+	7.88597i	−0.634103	+	0.460703i	0.223716	+	0.974654i	$0.428181\pi$
$294$		0			0
$295$	3.66312	+	11.2739i	0.213275	+	0.656393i
$296$		0			0
$297$	−2.50000	−	7.69421i	−0.145065	−	0.446463i
$298$		0			0
$299$	−0.281153	+	0.865300i	−0.0162595	+	0.0500416i
$300$	14.4721	−	10.5146i	0.835549	−	0.607062i
$301$	−3.76393			−0.216949
$302$		0			0
$303$	−15.7533	−	11.4454i	−0.905003	−	0.657523i
$304$	9.23607	+	28.4257i	0.529725	+	1.63033i
$305$	−3.11803	+	2.26538i	−0.178538	+	0.129716i
$306$		0			0
$307$	9.56231	+	6.94742i	0.545750	+	0.396510i	0.826216	−	0.563354i	$-0.190489\pi$
$307$	9.56231	+	6.94742i	0.545750	+	0.396510i	−0.280466	+	0.959864i	$0.590489\pi$
$308$	5.85410	+	4.25325i	0.333568	+	0.242352i
$309$	22.9894	+	16.7027i	1.30782	+	0.950186i
$310$		0			0
$311$	−0.937694	−	2.88593i	−0.0531718	−	0.163646i	0.920944	−	0.389694i	$-0.127419\pi$
$311$	−0.937694	−	2.88593i	−0.0531718	−	0.163646i	−0.974116	+	0.226048i	$0.927419\pi$
$312$		0			0
$313$	−3.65248	+	11.2412i	−0.206450	+	0.635388i	0.793201	+	0.608960i	$0.208413\pi$
$313$	−3.65248	+	11.2412i	−0.206450	+	0.635388i	−0.999651	+	0.0264277i	$0.991587\pi$
$314$		0			0
$315$	1.61803	−	1.17557i	0.0911659	−	0.0662359i
$316$	1.09017	−	3.35520i	0.0613269	−	0.188745i
$317$	−9.34346	−	28.7562i	−0.524781	−	1.61511i	−0.764749	−	0.644329i	$-0.777137\pi$
$317$	−9.34346	−	28.7562i	−0.524781	−	1.61511i	0.239968	−	0.970781i	$-0.422863\pi$
$318$		0			0
$319$	13.9443			0.780729
$320$	−2.47214	−	7.60845i	−0.138197	−	0.425325i
$321$	−7.39919	−	5.37582i	−0.412982	−	0.300049i
$322$		0			0
$323$	−14.0623	+	43.2793i	−0.782448	+	2.40813i
$324$	6.79837	−	20.9232i	0.377687	−	1.16240i
$325$	−24.9443			−1.38366
$326$		0			0
$327$	8.61803			0.476578
$328$		0			0
$329$	4.61803			0.254600
$330$		0			0
$331$	−9.00000			−0.494685			−0.247342	−	0.968928i	$-0.579557\pi$
$331$	−9.00000			−0.494685			−0.247342	+	0.968928i	$0.579557\pi$
$332$	−4.32624	+	13.3148i	−0.237433	+	0.730744i
$333$	−1.56231	+	4.80828i	−0.0856138	+	0.263492i
$334$		0			0
$335$	6.47214	+	4.70228i	0.353611	+	0.256913i
$336$	2.76393	+	8.50651i	0.150785	+	0.464068i
$337$	−7.76393			−0.422928			−0.211464	−	0.977386i	$-0.567823\pi$
$337$	−7.76393			−0.422928			−0.211464	+	0.977386i	$0.567823\pi$
$338$		0			0
$339$	−14.2705	−	43.9201i	−0.775068	−	2.38541i
$340$	3.76393	−	11.5842i	0.204128	−	0.628241i
$341$	−17.1353	+	12.4495i	−0.927926	+	0.674178i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$		0			0
$345$	0.100813	+	0.310271i	0.00542759	+	0.0167044i
$346$		0			0
$347$	−12.9271	−	9.39205i	−0.693960	−	0.504192i	0.183999	−	0.982926i	$-0.441096\pi$
$347$	−12.9271	−	9.39205i	−0.693960	−	0.504192i	−0.877960	+	0.478735i	$0.841096\pi$
$348$	13.9443	+	10.1311i	0.747491	+	0.543084i
$349$	−14.6631	−	10.6534i	−0.784899	−	0.570262i	0.121546	−	0.992586i	$-0.461215\pi$
$349$	−14.6631	−	10.6534i	−0.784899	−	0.570262i	−0.906445	+	0.422323i	$0.861215\pi$
$350$		0			0
$351$	−11.2812	+	8.19624i	−0.602143	+	0.437483i
$352$		0			0
$353$	−9.06231	−	6.58415i	−0.482338	−	0.350439i	0.319892	−	0.947454i	$-0.396353\pi$
$353$	−9.06231	−	6.58415i	−0.482338	−	0.350439i	−0.802230	+	0.597015i	$0.796353\pi$
$354$		0			0
$355$	−14.1803			−0.752614
$356$	22.3262	−	16.2210i	1.18329	−	0.859709i
$357$	−4.20820	+	12.9515i	−0.222722	+	0.685467i
$358$		0			0
$359$	−3.23607	−	9.95959i	−0.170793	−	0.525647i	0.828623	−	0.559807i	$-0.189125\pi$
$359$	−3.23607	−	9.95959i	−0.170793	−	0.525647i	−0.999416	+	0.0341594i	$0.989125\pi$
$360$		0			0
$361$	11.3820	+	35.0301i	0.599051	+	1.84369i
$362$		0			0
$363$	3.78115	−	2.74717i	0.198459	−	0.144189i
$364$	3.85410	−	11.8617i	0.202010	−	0.621722i
$365$	4.11803	−	12.6740i	0.215548	−	0.663388i
$366$		0			0
$367$	14.4443	−	10.4944i	0.753985	−	0.547802i	−0.143075	−	0.989712i	$-0.545699\pi$
$367$	14.4443	−	10.4944i	0.753985	−	0.547802i	0.897059	+	0.441910i	$0.145699\pi$
$368$	−0.583592			−0.0304218
$369$	−4.38197	+	12.0332i	−0.228116	+	0.626424i
$370$		0			0
$371$	−2.00000	+	1.45309i	−0.103835	+	0.0754404i
$372$	−26.1803			−1.35739
$373$	1.06231	−	3.26944i	0.0550041	−	0.169285i	−0.919780	−	0.392433i	$-0.871633\pi$
$373$	1.06231	−	3.26944i	0.0550041	−	0.169285i	0.974785	+	0.223148i	$0.0716334\pi$
$374$		0			0
$375$	−16.2812	+	11.8290i	−0.840755	+	0.610844i
$376$		0			0
$377$	−7.42705	−	22.8581i	−0.382513	−	1.17725i
$378$		0			0
$379$	3.78115	+	11.6372i	0.194225	+	0.597762i	0.999985	+	0.00552019i	$0.00175714\pi$
$379$	3.78115	+	11.6372i	0.194225	+	0.597762i	−0.805760	+	0.592242i	$0.798243\pi$
$380$	−4.61803	−	14.2128i	−0.236900	−	0.729104i
$381$	−7.19756	+	22.1518i	−0.368742	+	1.13487i
$382$		0			0
$383$	3.41641			0.174570			0.0872851	−	0.996183i	$-0.472181\pi$
$383$	3.41641			0.174570			0.0872851	+	0.996183i	$0.472181\pi$
$384$		0			0
$385$	−2.92705	−	2.12663i	−0.149176	−	0.108383i
$386$		0			0
$387$	−6.09017	+	4.42477i	−0.309581	+	0.224924i
$388$	−21.7984	−	15.8374i	−1.10664	−	0.804024i
$389$	−2.11803	−	1.53884i	−0.107389	−	0.0780224i	0.532795	−	0.846244i	$-0.321142\pi$
$389$	−2.11803	−	1.53884i	−0.107389	−	0.0780224i	−0.640184	+	0.768222i	$0.721142\pi$
$390$		0			0
$391$	−0.718847	−	0.522273i	−0.0363537	−	0.0264125i
$392$		0			0
$393$	−7.88854	−	24.2784i	−0.397924	−	1.22469i
$394$		0			0
$395$	−0.545085	+	1.67760i	−0.0274262	+	0.0844092i
$396$	14.4721			0.727252
$397$	−9.69098	+	7.04091i	−0.486376	+	0.353373i	−0.803789	−	0.594914i	$-0.797186\pi$
$397$	−9.69098	+	7.04091i	−0.486376	+	0.353373i	0.317413	+	0.948288i	$0.397186\pi$
$398$		0			0
$399$	5.16312	+	15.8904i	0.258479	+	0.795517i
$400$	−4.94427	−	15.2169i	−0.247214	−	0.760845i
$401$	−21.3262			−1.06498			−0.532491	−	0.846436i	$-0.678744\pi$
$401$	−21.3262			−1.06498			−0.532491	+	0.846436i	$0.678744\pi$
$402$		0			0
$403$	29.5344	+	21.4580i	1.47122	+	1.06890i
$404$	−14.0902	+	10.2371i	−0.701012	+	0.509315i
$405$	−3.39919	+	10.4616i	−0.168907	+	0.519842i
$406$		0			0
$407$	9.14590			0.453345
$408$		0			0
$409$	9.79837			0.484498			0.242249	−	0.970214i	$-0.422115\pi$
$409$	9.79837			0.484498			0.242249	+	0.970214i	$0.422115\pi$
$410$		0			0
$411$	3.81966			0.188410
$412$	20.5623	−	14.9394i	1.01303	−	0.736011i
$413$	−11.8541			−0.583302
$414$		0			0
$415$	2.16312	−	6.65740i	0.106183	−	0.326799i
$416$		0			0
$417$	17.7254	+	12.8783i	0.868018	+	0.630652i
$418$		0			0
$419$	−21.1246			−1.03200			−0.516002	−	0.856587i	$-0.672580\pi$
$419$	−21.1246			−1.03200			−0.516002	+	0.856587i	$0.672580\pi$
$420$	−1.38197	−	4.25325i	−0.0674330	−	0.207538i
$421$	−9.94427	−	30.6053i	−0.484654	−	1.49161i	−0.832481	−	0.554053i	$-0.813080\pi$
$421$	−9.94427	−	30.6053i	−0.484654	−	1.49161i	0.347827	−	0.937559i	$-0.386920\pi$
$422$		0			0
$423$	7.47214	−	5.42882i	0.363308	−	0.263958i
$424$		0			0
$425$	7.52786	−	23.1684i	0.365155	−	1.12383i
$426$		0			0
$427$	−1.19098	−	3.66547i	−0.0576357	−	0.177384i
$428$	−6.61803	+	4.80828i	−0.319895	+	0.232417i
$429$	−40.8156	−	29.6543i	−1.97060	−	1.43172i
$430$		0			0
$431$	−20.5623	−	14.9394i	−0.990451	−	0.719605i	−0.0304315	−	0.999537i	$-0.509688\pi$
$431$	−20.5623	−	14.9394i	−0.990451	−	0.719605i	−0.960020	+	0.279932i	$0.909688\pi$
$432$	−7.23607	−	5.25731i	−0.348145	−	0.252942i
$433$	3.89919	−	2.83293i	0.187383	−	0.136142i	−0.490139	−	0.871644i	$-0.663054\pi$
$433$	3.89919	−	2.83293i	0.187383	−	0.136142i	0.677522	+	0.735503i	$0.263054\pi$
$434$		0			0
$435$	−6.97214	−	5.06555i	−0.334288	−	0.242875i
$436$	2.38197	−	7.33094i	0.114075	−	0.351088i
$437$	−1.09017			−0.0521499
$438$		0			0
$439$	3.72542	−	11.4657i	0.177805	−	0.547227i	−0.821946	−	0.569566i	$-0.807111\pi$
$439$	3.72542	−	11.4657i	0.177805	−	0.547227i	0.999750	+	0.0223390i	$0.00711131\pi$
$440$		0			0
$441$	0.618034	+	1.90211i	0.0294302	+	0.0905768i
$442$		0			0
$443$	−6.54508	−	20.1437i	−0.310966	−	0.957056i	−0.977383	−	0.211477i	$-0.932173\pi$
$443$	−6.54508	−	20.1437i	−0.310966	−	0.957056i	0.666417	−	0.745580i	$-0.267827\pi$
$444$	9.14590	+	6.64488i	0.434045	+	0.315352i
$445$	−11.1631	+	8.11048i	−0.529183	+	0.384474i
$446$		0			0
$447$	1.42047	−	4.37177i	0.0671861	−	0.206777i
$448$	8.00000			0.377964
$449$	0.645898	−	0.469272i	0.0304818	−	0.0221463i	−0.572440	−	0.819947i	$-0.694003\pi$
$449$	0.645898	−	0.469272i	0.0304818	−	0.0221463i	0.602922	+	0.797800i	$0.294003\pi$
$450$		0			0
$451$	23.1525	+	0.812299i	1.09021	+	0.0382497i
$452$	−41.3050			−1.94282
$453$	4.63525	−	3.36771i	0.217783	−	0.158229i
$454$		0			0
$455$	−1.92705	+	5.93085i	−0.0903415	+	0.278043i
$456$		0			0
$457$	−4.78115	+	3.47371i	−0.223653	+	0.162493i	−0.693969	−	0.720004i	$-0.744140\pi$
$457$	−4.78115	+	3.47371i	−0.223653	+	0.162493i	0.470317	+	0.882498i	$0.344140\pi$
$458$		0			0
$459$	−4.20820	−	12.9515i	−0.196422	−	0.604525i
$460$	0.291796			0.0136051
$461$	11.2361	+	34.5811i	0.523316	+	1.61060i	0.767622	+	0.640903i	$0.221440\pi$
$461$	11.2361	+	34.5811i	0.523316	+	1.61060i	−0.244306	+	0.969698i	$0.578560\pi$
$462$		0			0
$463$	−0.437694	+	1.34708i	−0.0203414	+	0.0626043i	−0.960712	−	0.277547i	$-0.910478\pi$
$463$	−0.437694	+	1.34708i	−0.0203414	+	0.0626043i	0.940371	+	0.340152i	$0.110478\pi$
$464$	12.4721	−	9.06154i	0.579004	−	0.420671i
$465$	13.0902			0.607042
$466$		0			0
$467$	24.2533	+	17.6210i	1.12231	+	0.815405i	0.984557	−	0.175062i	$-0.0560126\pi$
$467$	24.2533	+	17.6210i	1.12231	+	0.815405i	0.137751	+	0.990467i	$0.456013\pi$
$468$	−7.70820	−	23.7234i	−0.356312	−	1.09662i
$469$	−6.47214	+	4.70228i	−0.298855	+	0.217131i
$470$		0			0
$471$	21.8713	+	15.8904i	1.00778	+	0.732193i
$472$		0			0
$473$	11.0172	+	8.00448i	0.506572	+	0.368046i
$474$		0			0
$475$	−9.23607	−	28.4257i	−0.423780	−	1.30426i
$476$	9.85410	+	7.15942i	0.451662	+	0.328152i
$477$	−1.52786	+	4.70228i	−0.0699561	+	0.215303i
$478$		0			0
$479$	−6.70820	+	4.87380i	−0.306506	+	0.222689i	−0.730396	−	0.683024i	$-0.760664\pi$
$479$	−6.70820	+	4.87380i	−0.306506	+	0.222689i	0.423890	+	0.905714i	$0.360664\pi$
$480$		0			0
$481$	−4.87132	−	14.9924i	−0.222113	−	0.683594i
$482$		0			0
$483$	−0.326238			−0.0148443
$484$	−1.29180	−	3.97574i	−0.0587180	−	0.180715i
$485$	10.8992	+	7.91872i	0.494907	+	0.359571i
$486$		0			0
$487$	−10.4894	+	32.2829i	−0.475318	+	1.46288i	0.370210	+	0.928948i	$0.379286\pi$
$487$	−10.4894	+	32.2829i	−0.475318	+	1.46288i	−0.845528	+	0.533931i	$0.820714\pi$
$488$		0			0
$489$	24.7984			1.12142
$490$		0			0
$491$	37.3607			1.68606			0.843032	−	0.537864i	$-0.180768\pi$
$491$	37.3607			1.68606			0.843032	+	0.537864i	$0.180768\pi$
$492$	22.5623	+	17.6336i	1.01719	+	0.794982i
$493$	23.4721			1.05713
$494$		0			0
$495$	−7.23607			−0.325237
$496$	−7.23607	+	22.2703i	−0.324909	+	0.999967i
$497$	4.38197	−	13.4863i	0.196558	−	0.604943i
$498$		0			0
$499$	−5.23607	−	3.80423i	−0.234399	−	0.170301i	0.464386	−	0.885633i	$-0.346275\pi$
$499$	−5.23607	−	3.80423i	−0.234399	−	0.170301i	−0.698784	+	0.715333i	$0.746275\pi$
$500$	5.56231	+	17.1190i	0.248754	+	0.765586i
$501$	−37.8885			−1.69274
$502$		0			0
$503$	−6.97214	−	21.4580i	−0.310872	−	0.956766i	−0.977420	−	0.211304i	$-0.932229\pi$
$503$	−6.97214	−	21.4580i	−0.310872	−	0.956766i	0.666548	−	0.745462i	$-0.267771\pi$
$504$		0			0
$505$	7.04508	−	5.11855i	0.313502	−	0.227773i
$506$		0			0
$507$	−17.8885	+	55.0553i	−0.794458	+	2.44509i
$508$	16.8541	+	12.2452i	0.747780	+	0.543294i
$509$	−0.590170	−	1.81636i	−0.0261588	−	0.0805086i	0.937125	−	0.348994i	$-0.113477\pi$
$509$	−0.590170	−	1.81636i	−0.0261588	−	0.0805086i	−0.963284	+	0.268486i	$0.913477\pi$
$510$		0			0
$511$	10.7812	+	7.83297i	0.476930	+	0.346510i
$512$		0			0
$513$	−13.5172	−	9.82084i	−0.596800	−	0.433600i
$514$		0			0
$515$	−10.2812	+	7.46969i	−0.453042	+	0.329154i
$516$	5.20163	+	16.0090i	0.228989	+	0.704755i
$517$	−13.5172	−	9.82084i	−0.594487	−	0.431920i
$518$		0			0
$519$	25.0000			1.09738
$520$		0			0
$521$	−5.89261	+	18.1356i	−0.258160	+	0.794534i	0.735031	+	0.678034i	$0.237168\pi$
$521$	−5.89261	+	18.1356i	−0.258160	+	0.794534i	−0.993191	+	0.116501i	$0.962832\pi$
$522$		0			0
$523$	5.19756	+	15.9964i	0.227273	+	0.699476i	0.998053	+	0.0623737i	$0.0198671\pi$
$523$	5.19756	+	15.9964i	0.227273	+	0.699476i	−0.770779	+	0.637102i	$0.780133\pi$
$524$	−22.8328			−0.997456
$525$	−2.76393	−	8.50651i	−0.120628	−	0.371254i
$526$		0			0
$527$	−28.8435	+	20.9560i	−1.25644	+	0.912858i
$528$	10.0000	−	30.7768i	0.435194	−	1.33939i
$529$	−7.10081	+	21.8541i	−0.308731	+	0.950176i
$530$		0			0
$531$	−19.1803	+	13.9353i	−0.832356	+	0.604742i
$532$	14.9443			0.647916
$533$	−11.0000	−	38.3853i	−0.476463	−	1.66265i
$534$		0			0
$535$	3.30902	−	2.40414i	0.143061	−	0.103940i
$536$		0			0
$537$	−13.2918	+	40.9079i	−0.573583	+	1.76531i
$538$		0			0
$539$	2.92705	−	2.12663i	0.126077	−	0.0916003i
$540$	3.61803	+	2.62866i	0.155695	+	0.113119i
$541$	−5.47214	−	16.8415i	−0.235266	−	0.724073i	−0.997086	−	0.0762847i	$-0.975694\pi$
$541$	−5.47214	−	16.8415i	−0.235266	−	0.724073i	0.761821	−	0.647788i	$-0.224306\pi$
$542$		0			0
$543$	−1.48278	−	4.56352i	−0.0636321	−	0.195840i
$544$		0			0
$545$	−1.19098	+	3.66547i	−0.0510161	+	0.157011i
$546$		0			0
$547$	−17.7639			−0.759531			−0.379765	−	0.925083i	$-0.623995\pi$
$547$	−17.7639			−0.759531			−0.379765	+	0.925083i	$0.623995\pi$
$548$	1.05573	−	3.24920i	0.0450985	−	0.138799i
$549$	−6.23607	−	4.53077i	−0.266149	−	0.193368i
$550$		0			0
$551$	23.2984	−	16.9273i	0.992544	−	0.721125i
$552$		0			0
$553$	−1.42705	−	1.03681i	−0.0606844	−	0.0440898i
$554$		0			0
$555$	−4.57295	−	3.32244i	−0.194111	−	0.141030i
$556$	15.8541	−	11.5187i	0.672364	−	0.488501i
$557$	−13.6074	−	41.8792i	−0.576564	−	1.77448i	−0.630792	−	0.775952i	$-0.717270\pi$
$557$	−13.6074	−	41.8792i	−0.576564	−	1.77448i	0.0542284	−	0.998529i	$-0.482730\pi$
$558$		0			0
$559$	7.25329	−	22.3233i	0.306781	−	0.944176i
$560$	−4.00000			−0.169031
$561$	39.8607	−	28.9605i	1.68292	−	1.22271i
$562$		0			0
$563$	−0.253289	−	0.779543i	−0.0106749	−	0.0328538i	0.945577	−	0.325398i	$-0.105498\pi$
$563$	−0.253289	−	0.779543i	−0.0106749	−	0.0328538i	−0.956252	+	0.292544i	$0.905498\pi$
$564$	−6.38197	−	19.6417i	−0.268729	−	0.827064i
$565$	20.6525			0.868856
$566$		0			0
$567$	−8.89919	−	6.46564i	−0.373731	−	0.271531i
$568$		0			0
$569$	−0.274575	+	0.845055i	−0.0115108	+	0.0354266i	−0.956647	−	0.291250i	$-0.905929\pi$
$569$	−0.274575	+	0.845055i	−0.0115108	+	0.0354266i	0.945136	+	0.326677i	$0.105929\pi$
$570$		0			0
$571$	−6.58359			−0.275515			−0.137757	−	0.990466i	$-0.543989\pi$
$571$	−6.58359			−0.275515			−0.137757	+	0.990466i	$0.543989\pi$
$572$	−36.5066	+	26.5236i	−1.52642	+	1.10901i
$573$	18.7426			0.782985
$574$		0			0
$575$	0.583592			0.0243375
$576$	12.9443	−	9.40456i	0.539345	−	0.391857i
$577$	−13.9656			−0.581394			−0.290697	−	0.956815i	$-0.593887\pi$
$577$	−13.9656			−0.581394			−0.290697	+	0.956815i	$0.593887\pi$
$578$		0			0
$579$	−6.18034	+	19.0211i	−0.256846	+	0.790491i
$580$	−6.23607	+	4.53077i	−0.258939	+	0.188130i
$581$	5.66312	+	4.11450i	0.234946	+	0.170698i
$582$		0			0
$583$	8.94427			0.370434
$584$		0			0
$585$	3.85410	+	11.8617i	0.159348	+	0.490421i
$586$		0			0
$587$	−15.8262	+	11.4984i	−0.653219	+	0.474591i	−0.864366	−	0.502863i	$-0.832280\pi$
$587$	−15.8262	+	11.4984i	−0.653219	+	0.474591i	0.211147	+	0.977454i	$0.432280\pi$
$588$	4.47214			0.184428
$589$	−13.5172	+	41.6017i	−0.556967	+	1.71417i
$590$		0			0
$591$	13.4164	+	41.2915i	0.551877	+	1.69850i
$592$	8.18034	−	5.94336i	0.336210	−	0.244271i
$593$	−8.23607	−	5.98385i	−0.338215	−	0.245727i	0.405693	−	0.914009i	$-0.367030\pi$
$593$	−8.23607	−	5.98385i	−0.338215	−	0.245727i	−0.743908	+	0.668282i	$0.767030\pi$
$594$		0			0
$595$	−4.92705	−	3.57971i	−0.201989	−	0.146754i
$596$	−3.32624	−	2.41665i	−0.136248	−	0.0989900i
$597$	29.8992	−	21.7230i	1.22369	−	0.889064i
$598$		0			0
$599$	12.0623	+	8.76378i	0.492852	+	0.358078i	0.806280	−	0.591534i	$-0.201477\pi$
$599$	12.0623	+	8.76378i	0.492852	+	0.358078i	−0.313428	+	0.949612i	$0.601477\pi$
$600$		0			0
$601$	26.3607			1.07527			0.537637	−	0.843176i	$-0.319317\pi$
$601$	26.3607			1.07527			0.537637	+	0.843176i	$0.319317\pi$
$602$		0			0
$603$	−4.94427	+	15.2169i	−0.201346	+	0.619680i
$604$	−1.58359	−	4.87380i	−0.0644355	−	0.198312i
$605$	0.645898	+	1.98787i	0.0262595	+	0.0808184i
$606$		0			0
$607$	8.57953	+	26.4051i	0.348232	+	1.07175i	0.959831	+	0.280580i	$0.0905269\pi$
$607$	8.57953	+	26.4051i	0.348232	+	1.07175i	−0.611598	+	0.791168i	$0.709473\pi$
$608$		0			0
$609$	6.97214	−	5.06555i	0.282525	−	0.205267i
$610$		0			0
$611$	−8.89919	+	27.3889i	−0.360023	+	1.10804i
$612$	24.3607			0.984722
$613$	21.9615	−	15.9560i	0.887016	−	0.644455i	−0.0480820	−	0.998843i	$-0.515311\pi$
$613$	21.9615	−	15.9560i	0.887016	−	0.644455i	0.935098	+	0.354388i	$0.115311\pi$
$614$		0			0
$615$	−11.2812	−	8.81678i	−0.454900	−	0.355527i
$616$		0			0
$617$	0.399187	−	0.290026i	0.0160707	−	0.0116760i	−0.579721	−	0.814815i	$-0.696838\pi$
$617$	0.399187	−	0.290026i	0.0160707	−	0.0116760i	0.595792	+	0.803139i	$0.296838\pi$
$618$		0			0
$619$	1.46149	−	4.49801i	0.0587424	−	0.180790i	−0.917380	−	0.398013i	$-0.869700\pi$
$619$	1.46149	−	4.49801i	0.0587424	−	0.180790i	0.976122	+	0.217223i	$0.0696998\pi$
$620$	3.61803	−	11.1352i	0.145304	−	0.447199i
$621$	0.263932	−	0.191758i	0.0105912	−	0.00769498i
$622$		0			0
$623$	−4.26393	−	13.1230i	−0.170831	−	0.525763i
$624$	−55.7771			−2.23287
$625$	3.39919	+	10.4616i	0.135967	+	0.418465i
$626$		0			0
$627$	18.6803	−	57.4922i	0.746021	−	2.29602i
$628$	19.5623	−	14.2128i	0.780621	−	0.567154i
$629$	15.3951			0.613844
$630$		0			0
$631$	−27.0623	−	19.6619i	−1.07733	−	0.782729i	−0.100117	−	0.994976i	$-0.531922\pi$
$631$	−27.0623	−	19.6619i	−1.07733	−	0.782729i	−0.977216	+	0.212247i	$0.931922\pi$
$632$		0			0
$633$	−30.5517	+	22.1971i	−1.21432	+	0.882255i
$634$		0			0
$635$	−8.42705	−	6.12261i	−0.334417	−	0.242968i
$636$	8.94427	+	6.49839i	0.354663	+	0.257678i
$637$	−5.04508	−	3.66547i	−0.199894	−	0.145231i
$638$		0			0
$639$	−8.76393	−	26.9726i	−0.346696	−	1.06702i
$640$		0			0
$641$	−13.8885	+	42.7445i	−0.548564	+	1.68831i	0.163796	+	0.986494i	$0.447626\pi$
$641$	−13.8885	+	42.7445i	−0.548564	+	1.68831i	−0.712361	+	0.701814i	$0.752374\pi$
$642$		0			0
$643$	22.9443	−	16.6700i	0.904834	−	0.657400i	−0.0348692	−	0.999392i	$-0.511101\pi$
$643$	22.9443	−	16.6700i	0.904834	−	0.657400i	0.939703	+	0.341992i	$0.111101\pi$
$644$	−0.0901699	+	0.277515i	−0.00355319	+	0.0109356i
$645$	−2.60081	−	8.00448i	−0.102407	−	0.315176i
$646$		0			0
$647$	33.4721			1.31593			0.657963	−	0.753050i	$-0.271418\pi$
$647$	33.4721			1.31593			0.657963	+	0.753050i	$0.271418\pi$
$648$		0			0
$649$	34.6976	+	25.2093i	1.36200	+	0.989550i
$650$		0			0
$651$	−4.04508	+	12.4495i	−0.158539	+	0.487934i
$652$	6.85410	−	21.0948i	0.268427	−	0.826134i
$653$	8.50658			0.332888			0.166444	−	0.986051i	$-0.446771\pi$
$653$	8.50658			0.332888			0.166444	+	0.986051i	$0.446771\pi$
$654$		0			0
$655$	11.4164			0.446076
$656$	21.2361	−	14.3188i	0.829129	−	0.559057i
$657$	26.6525			1.03981
$658$		0			0
$659$	12.1246			0.472308			0.236154	−	0.971716i	$-0.424113\pi$
$659$	12.1246			0.472308			0.236154	+	0.971716i	$0.424113\pi$
$660$	−5.00000	+	15.3884i	−0.194625	+	0.598993i
$661$	−13.4721	+	41.4630i	−0.524005	+	1.61272i	0.242269	+	0.970209i	$0.422108\pi$
$661$	−13.4721	+	41.4630i	−0.524005	+	1.61272i	−0.766274	+	0.642514i	$0.777892\pi$
$662$		0			0
$663$	−68.7041	−	49.9165i	−2.66825	−	1.93860i
$664$		0			0
$665$	−7.47214			−0.289757
$666$		0			0
$667$	0.173762	+	0.534785i	0.00672809	+	0.0207069i
$668$	−10.4721	+	32.2299i	−0.405179	+	1.24701i
$669$	47.0344	−	34.1725i	1.81846	−	1.32119i
$670$		0			0
$671$	−4.30902	+	13.2618i	−0.166348	+	0.511966i
$672$		0			0
$673$	8.36475	+	25.7440i	0.322437	+	0.992360i	0.972584	+	0.232551i	$0.0747073\pi$
$673$	8.36475	+	25.7440i	0.322437	+	0.992360i	−0.650147	+	0.759809i	$0.725293\pi$
$674$		0			0
$675$	7.23607	+	5.25731i	0.278516	+	0.202354i
$676$	41.8885	+	30.4338i	1.61110	+	1.17053i
$677$	−2.66312	−	1.93487i	−0.102352	−	0.0743631i	0.535432	−	0.844578i	$-0.320149\pi$
$677$	−2.66312	−	1.93487i	−0.102352	−	0.0743631i	−0.637784	+	0.770215i	$0.720149\pi$
$678$		0			0
$679$	−10.8992	+	7.91872i	−0.418272	+	0.303893i
$680$		0			0
$681$	−5.85410	−	4.25325i	−0.224330	−	0.162985i
$682$		0			0
$683$	−17.8328			−0.682354			−0.341177	−	0.939999i	$-0.610826\pi$
$683$	−17.8328			−0.682354			−0.341177	+	0.939999i	$0.610826\pi$
$684$	24.1803	−	17.5680i	0.924558	−	0.671731i
$685$	−0.527864	+	1.62460i	−0.0201686	+	0.0620727i
$686$		0			0
$687$	−0.263932	−	0.812299i	−0.0100696	−	0.0309911i
$688$	15.0557			0.573994
$689$	−4.76393	−	14.6619i	−0.181491	−	0.558573i
$690$		0			0
$691$	−4.57295	+	3.32244i	−0.173963	+	0.126392i	−0.671360	−	0.741132i	$-0.734289\pi$
$691$	−4.57295	+	3.32244i	−0.173963	+	0.126392i	0.497397	+	0.867523i	$0.334289\pi$
$692$	6.90983	−	21.2663i	0.262672	−	0.808422i
$693$	2.23607	−	6.88191i	0.0849412	−	0.261422i
$694$		0			0
$695$	−7.92705	+	5.75934i	−0.300690	+	0.218464i
$696$		0			0
$697$	38.9721	+	1.36733i	1.47617	+	0.0517913i
$698$		0			0
$699$	−19.8992	+	14.4576i	−0.752656	+	0.546837i
$700$	−8.00000			−0.302372
$701$	8.69098	−	26.7481i	0.328254	−	1.01026i	−0.641696	−	0.766959i	$-0.721769\pi$
$701$	8.69098	−	26.7481i	0.328254	−	1.01026i	0.969950	−	0.243303i	$-0.0782309\pi$
$702$		0			0
$703$	15.2812	−	11.1024i	0.576340	−	0.418735i
$704$	−23.4164	−	17.0130i	−0.882539	−	0.641202i
$705$	3.19098	+	9.82084i	0.120179	+	0.369874i
$706$		0			0
$707$	2.69098	+	8.28199i	0.101205	+	0.311476i
$708$	16.3820	+	50.4185i	0.615672	+	1.89484i
$709$	−8.24265	+	25.3683i	−0.309559	+	0.952725i	0.668377	+	0.743822i	$0.266989\pi$
$709$	−8.24265	+	25.3683i	−0.309559	+	0.952725i	−0.977936	+	0.208903i	$0.933011\pi$
$710$		0			0
$711$	−3.52786			−0.132305
$712$		0			0
$713$	−0.690983	−	0.502029i	−0.0258775	−	0.0188011i
$714$		0			0
$715$	18.2533	−	13.2618i	0.682634	−	0.495963i
$716$	31.1246	+	22.6134i	1.16318	+	0.845101i
$717$	4.89919	+	3.55947i	0.182963	+	0.132931i
$718$		0			0
$719$	37.2254	+	27.0459i	1.38827	+	1.00864i	0.996052	+	0.0887695i	$0.0282935\pi$
$719$	37.2254	+	27.0459i	1.38827	+	1.00864i	0.392222	+	0.919871i	$0.371707\pi$
$720$	−6.47214	+	4.70228i	−0.241202	+	0.175244i
$721$	−3.92705	−	12.0862i	−0.146251	−	0.450114i
$722$		0			0
$723$	−6.44427	+	19.8334i	−0.239665	+	0.737613i
$724$	−4.29180			−0.159503
$725$	−12.4721	+	9.06154i	−0.463204	+	0.336537i
$726$		0			0
$727$	8.98278	+	27.6462i	0.333153	+	1.02534i	0.967625	+	0.252393i	$0.0812176\pi$
$727$	8.98278	+	27.6462i	0.333153	+	1.02534i	−0.634472	+	0.772946i	$0.718782\pi$
$728$		0			0
$729$	−7.00000			−0.259259
$730$		0			0
$731$	18.5451	+	13.4738i	0.685915	+	0.498346i
$732$	−13.9443	+	10.1311i	−0.515395	+	0.374456i
$733$	−11.4549	+	35.2546i	−0.423097	+	1.30216i	0.481708	+	0.876332i	$0.340017\pi$
$733$	−11.4549	+	35.2546i	−0.423097	+	1.30216i	−0.904805	+	0.425827i	$0.859983\pi$
$734$		0			0
$735$	−2.23607			−0.0824786
$736$		0			0
$737$	28.9443			1.06618
$738$		0			0
$739$	−51.3050			−1.88728			−0.943642	−	0.330969i	$-0.892624\pi$
$739$	−51.3050			−1.88728			−0.943642	+	0.330969i	$0.892624\pi$
$740$	−4.09017	+	2.97168i	−0.150358	+	0.109241i
$741$	−104.193			−3.82764
$742$		0			0
$743$	−7.88854	+	24.2784i	−0.289403	+	0.890690i	0.695642	+	0.718389i	$0.255120\pi$
$743$	−7.88854	+	24.2784i	−0.289403	+	0.890690i	−0.985044	+	0.172301i	$0.944880\pi$
$744$		0			0
$745$	1.66312	+	1.20833i	0.0609320	+	0.0442697i
$746$		0			0
$747$	14.0000			0.512233
$748$	−13.6180	−	41.9120i	−0.497925	−	1.53245i
$749$	1.26393	+	3.88998i	0.0461831	+	0.142137i
$750$		0			0
$751$	−0.118034	+	0.0857567i	−0.00430712	+	0.00312931i	−0.589937	−	0.807449i	$-0.700847\pi$
$751$	−0.118034	+	0.0857567i	−0.00430712	+	0.00312931i	0.585630	+	0.810579i	$0.300847\pi$
$752$	−18.4721			−0.673609
$753$	−8.31559	+	25.5928i	−0.303037	+	0.932652i
$754$		0			0
$755$	0.791796	+	2.43690i	0.0288164	+	0.0886878i
$756$	−3.61803	+	2.62866i	−0.131587	+	0.0956033i
$757$	−7.73607	−	5.62058i	−0.281172	−	0.204284i	0.438256	−	0.898850i	$-0.355596\pi$
$757$	−7.73607	−	5.62058i	−0.281172	−	0.204284i	−0.719429	+	0.694566i	$0.755596\pi$
$758$		0			0
$759$	0.954915	+	0.693786i	0.0346612	+	0.0251829i
$760$		0			0
$761$	31.1803	−	22.6538i	1.13029	−	0.821201i	0.144550	−	0.989497i	$-0.453827\pi$
$761$	31.1803	−	22.6538i	1.13029	−	0.821201i	0.985736	+	0.168296i	$0.0538266\pi$
$762$		0			0
$763$	−3.11803	−	2.26538i	−0.112880	−	0.0820124i
$764$	5.18034	−	15.9434i	0.187418	−	0.576814i
$765$	−12.1803			−0.440381
$766$		0			0
$767$	22.8435	−	70.3049i	0.824829	−	2.53856i
$768$	−11.0557	−	34.0260i	−0.398939	−	1.22781i
$769$	0.128677	+	0.396027i	0.00464022	+	0.0142811i	0.953350	−	0.301868i	$-0.0976101\pi$
$769$	0.128677	+	0.396027i	0.00464022	+	0.0142811i	−0.948710	+	0.316149i	$0.897610\pi$
$770$		0			0
$771$	1.83282	+	5.64083i	0.0660072	+	0.203149i
$772$	14.4721	+	10.5146i	0.520864	+	0.378430i
$773$	−21.7705	+	15.8172i	−0.783031	+	0.568905i	−0.905887	−	0.423519i	$-0.860795\pi$
$773$	−21.7705	+	15.8172i	−0.783031	+	0.568905i	0.122856	+	0.992424i	$0.460795\pi$
$774$		0			0
$775$	7.23607	−	22.2703i	0.259927	−	0.799974i
$776$		0			0
$777$	4.57295	−	3.32244i	0.164054	−	0.119192i
$778$		0			0
$779$	39.6697	−	26.7481i	1.42131	−	0.958350i
$780$	27.8885			0.998570
$781$	−41.5066	+	30.1563i	−1.48522	+	1.07908i
$782$		0			0
$783$	−2.66312	+	8.19624i	−0.0951721	+	0.292910i
$784$	1.23607	−	3.80423i	0.0441453	−	0.135865i
$785$	−9.78115	+	7.10642i	−0.349104	+	0.253639i
$786$		0			0
$787$	−14.0729	−	43.3121i	−0.501646	−	1.54391i	−0.806336	−	0.591457i	$-0.798553\pi$
$787$	−14.0729	−	43.3121i	−0.501646	−	1.54391i	0.304690	−	0.952452i	$-0.401447\pi$
$788$	38.8328			1.38336
$789$	2.37539	+	7.31069i	0.0845661	+	0.260268i
$790$		0			0
$791$	−6.38197	+	19.6417i	−0.226917	+	0.698377i
$792$		0			0
$793$	24.0344			0.853488
$794$		0			0
$795$	−4.47214	−	3.24920i	−0.158610	−	0.115237i
$796$	−10.2148	−	31.4379i	−0.362053	−	1.11429i
$797$	6.89919	−	5.01255i	0.244382	−	0.177554i	−0.458851	−	0.888513i	$-0.651739\pi$
$797$	6.89919	−	5.01255i	0.244382	−	0.177554i	0.703233	+	0.710959i	$0.251739\pi$
$798$		0			0
$799$	−22.7533	−	16.5312i	−0.804953	−	0.584833i
$800$		0			0
$801$	−22.3262	−	16.2210i	−0.788859	−	0.573139i
$802$		0			0
$803$	−14.8992	−	45.8550i	−0.525781	−	1.61819i
$804$	28.9443	+	21.0292i	1.02079	+	0.741644i
$805$	0.0450850	−	0.138757i	0.00158904	−	0.00489055i
$806$		0			0
$807$	−51.9336	+	37.7320i	−1.82815	+	1.32823i
$808$		0			0
$809$	−6.12461	−	18.8496i	−0.215330	−	0.662717i	−0.999130	−	0.0417041i	$-0.986721\pi$
$809$	−6.12461	−	18.8496i	−0.215330	−	0.662717i	0.783800	−	0.621013i	$-0.213279\pi$
$810$		0			0
$811$	−8.45085			−0.296749			−0.148375	−	0.988931i	$-0.547404\pi$
$811$	−8.45085			−0.296749			−0.148375	+	0.988931i	$0.547404\pi$
$812$	−2.38197	−	7.33094i	−0.0835906	−	0.257265i
$813$	−12.8262	−	9.31881i	−0.449836	−	0.326825i
$814$		0			0
$815$	−3.42705	+	10.5474i	−0.120044	+	0.369459i
$816$	16.8328	−	51.8061i	0.589266	−	1.81358i
$817$	28.1246			0.983956
$818$		0			0
$819$	−12.4721			−0.435812
$820$	−10.6180	+	7.15942i	−0.370798	+	0.250018i
$821$	−31.4508			−1.09764			−0.548821	−	0.835940i	$-0.684923\pi$
$821$	−31.4508			−1.09764			−0.548821	+	0.835940i	$0.684923\pi$
$822$		0			0
$823$	14.2016			0.495038			0.247519	−	0.968883i	$-0.420385\pi$
$823$	14.2016			0.495038			0.247519	+	0.968883i	$0.420385\pi$
$824$		0			0
$825$	−10.0000	+	30.7768i	−0.348155	+	1.07151i
$826$		0			0
$827$	17.4164	+	12.6538i	0.605628	+	0.440014i	0.847872	−	0.530201i	$-0.177884\pi$
$827$	17.4164	+	12.6538i	0.605628	+	0.440014i	−0.242244	+	0.970215i	$0.577884\pi$
$828$	0.180340	+	0.555029i	0.00626724	+	0.0192886i
$829$	7.94427			0.275916			0.137958	−	0.990438i	$-0.455946\pi$
$829$	7.94427			0.275916			0.137958	+	0.990438i	$0.455946\pi$
$830$		0			0
$831$	−9.93769	−	30.5851i	−0.344735	−	1.06098i
$832$	−15.4164	+	47.4468i	−0.534468	+	1.64492i
$833$	4.92705	−	3.57971i	0.170712	−	0.124030i
$834$		0			0
$835$	5.23607	−	16.1150i	0.181202	−	0.557681i
$836$	−43.7426	−	31.7809i	−1.51287	−	1.09917i
$837$	−4.04508	−	12.4495i	−0.139819	−	0.430317i
$838$		0			0
$839$	−3.82624	−	2.77992i	−0.132096	−	0.0959737i	0.519775	−	0.854303i	$-0.326016\pi$
$839$	−3.82624	−	2.77992i	−0.132096	−	0.0959737i	−0.651871	+	0.758330i	$0.726016\pi$
$840$		0			0
$841$	11.4443	+	8.31475i	0.394630	+	0.286716i
$842$		0			0
$843$	−34.4336	+	25.0175i	−1.18596	+	0.861648i
$844$	10.4377	+	32.1239i	0.359280	+	1.10575i
$845$	−20.9443	−	15.2169i	−0.720505	−	0.523477i
$846$		0			0
$847$	−2.09017			−0.0718191
$848$	8.00000	−	5.81234i	0.274721	−	0.199597i
$849$	5.79180	−	17.8253i	0.198774	−	0.611763i
$850$		0			0
$851$	0.113969	+	0.350760i	0.00390680	+	0.0120239i
$852$	−63.4164			−2.17261
$853$	−13.9656	−	42.9816i	−0.478172	−	1.47166i	−0.841632	−	0.540051i	$-0.818405\pi$
$853$	−13.9656	−	42.9816i	−0.478172	−	1.47166i	0.363461	−	0.931610i	$-0.381595\pi$
$854$		0			0
$855$	−12.0902	+	8.78402i	−0.413475	+	0.300407i
$856$		0			0
$857$	4.70163	−	14.4701i	0.160604	−	0.494290i	−0.838081	−	0.545546i	$-0.816322\pi$
$857$	4.70163	−	14.4701i	0.160604	−	0.494290i	0.998686	+	0.0512559i	$0.0163224\pi$
$858$		0			0
$859$	−12.8090	+	9.30630i	−0.437038	+	0.317527i	−0.784457	−	0.620183i	$-0.787058\pi$
$859$	−12.8090	+	9.30630i	−0.437038	+	0.317527i	0.347419	+	0.937710i	$0.387058\pi$
$860$	−7.52786			−0.256698
$861$	11.8713	−	8.00448i	0.404574	−	0.272792i
$862$		0			0
$863$	−17.8713	+	12.9843i	−0.608347	+	0.441990i	−0.848832	−	0.528663i	$-0.822694\pi$
$863$	−17.8713	+	12.9843i	−0.608347	+	0.441990i	0.240485	+	0.970653i	$0.422694\pi$
$864$		0			0
$865$	−3.45492	+	10.6331i	−0.117471	+	0.361537i
$866$		0			0
$867$	36.3435	−	26.4051i	1.23429	−	0.896763i
$868$	9.47214	+	6.88191i	0.321505	+	0.233587i
$869$	1.97214	+	6.06961i	0.0669001	+	0.205897i
$870$		0			0
$871$	−15.4164	−	47.4468i	−0.522365	−	1.60767i
$872$		0			0
$873$	−8.32624	+	25.6255i	−0.281800	+	0.867293i
$874$		0			0
$875$	9.00000			0.304256
$876$	18.4164	−	56.6799i	0.622233	−	1.91504i
$877$	3.02786	+	2.19987i	0.102244	+	0.0742844i	0.637732	−	0.770258i	$-0.279873\pi$
$877$	3.02786	+	2.19987i	0.102244	+	0.0742844i	−0.535489	+	0.844542i	$0.679873\pi$
$878$		0			0
$879$	24.2705	−	17.6336i	0.818624	−	0.594765i
$880$	11.7082	+	8.50651i	0.394683	+	0.286754i
$881$	−2.09017	−	1.51860i	−0.0704196	−	0.0511628i	0.552019	−	0.833832i	$-0.313858\pi$
$881$	−2.09017	−	1.51860i	−0.0704196	−	0.0511628i	−0.622438	+	0.782669i	$0.713858\pi$
$882$		0			0
$883$	27.7426	+	20.1562i	0.933614	+	0.678311i	0.946875	−	0.321602i	$-0.104221\pi$
$883$	27.7426	+	20.1562i	0.933614	+	0.678311i	−0.0132607	+	0.999912i	$0.504221\pi$
$884$	−61.4508	+	44.6467i	−2.06682	+	1.50163i
$885$	−8.19098	−	25.2093i	−0.275337	−	0.847400i
$886$		0			0
$887$	−2.27458	+	7.00042i	−0.0763728	+	0.235051i	−0.981953	−	0.189123i	$-0.939436\pi$
$887$	−2.27458	+	7.00042i	−0.0763728	+	0.235051i	0.905581	+	0.424174i	$0.139436\pi$
$888$		0			0
$889$	8.42705	−	6.12261i	0.282634	−	0.205346i
$890$		0			0
$891$	12.2984	+	37.8505i	0.412011	+	1.26804i
$892$	−16.0689	−	49.4549i	−0.538026	−	1.65587i
$893$	−34.5066			−1.15472
$894$		0			0
$895$	−15.5623	−	11.3067i	−0.520191	−	0.377941i
$896$		0			0
$897$	0.628677	−	1.93487i	0.0209909	−	0.0646034i
$898$		0			0
$899$	22.5623			0.752495
$900$	−12.9443	+	9.40456i	−0.431476	+	0.313485i
$901$	15.0557			0.501579
$902$		0			0
$903$	8.41641			0.280081
$904$		0			0
$905$	2.14590			0.0713321
$906$		0			0
$907$	7.90983	−	24.3440i	0.262642	−	0.808328i	−0.729586	−	0.683889i	$-0.760287\pi$
$907$	7.90983	−	24.3440i	0.262642	−	0.808328i	0.992227	−	0.124438i	$-0.0397129\pi$
$908$	−5.23607	+	3.80423i	−0.173765	+	0.126248i
$909$	14.0902	+	10.2371i	0.467341	+	0.339543i
$910$		0			0
$911$	−56.4296			−1.86959			−0.934797	−	0.355181i	$-0.884419\pi$
$911$	−56.4296			−1.86959			−0.934797	+	0.355181i	$0.884419\pi$
$912$	−20.6525	−	63.5618i	−0.683872	−	2.10474i
$913$	−7.82624	−	24.0867i	−0.259011	−	0.797153i
$914$		0			0
$915$	6.97214	−	5.06555i	0.230492	−	0.167462i
$916$	−0.763932			−0.0252410
$917$	−3.52786	+	10.8576i	−0.116500	+	0.358551i
$918$		0			0
$919$	7.92705	+	24.3970i	0.261489	+	0.804781i	0.992481	+	0.122395i	$0.0390576\pi$
$919$	7.92705	+	24.3970i	0.261489	+	0.804781i	−0.730992	+	0.682386i	$0.760942\pi$
$920$		0			0
$921$	−21.3820	−	15.5349i	−0.704560	−	0.511893i
$922$		0			0
$923$	71.5410	+	51.9776i	2.35480	+	1.71086i
$924$	−13.0902	−	9.51057i	−0.430635	−	0.312875i
$925$	−8.18034	+	5.94336i	−0.268968	+	0.195417i
$926$		0			0
$927$	−20.5623	−	14.9394i	−0.675355	−	0.490674i
$928$		0			0
$929$	−18.0344			−0.591691			−0.295845	−	0.955236i	$-0.595601\pi$
$929$	−18.0344			−0.591691			−0.295845	+	0.955236i	$0.595601\pi$
$930$		0			0
$931$	2.30902	−	7.10642i	0.0756750	−	0.232904i
$932$	6.79837	+	20.9232i	0.222688	+	0.685364i
$933$	2.09675	+	6.45313i	0.0686444	+	0.211266i
$934$		0			0
$935$	6.80902	+	20.9560i	0.222679	+	0.685334i
$936$		0			0
$937$	26.1353	−	18.9884i	0.853802	−	0.620323i	−0.0723900	−	0.997376i	$-0.523063\pi$
$937$	26.1353	−	18.9884i	0.853802	−	0.620323i	0.926192	+	0.377053i	$0.123063\pi$
$938$		0			0
$939$	8.16718	−	25.1360i	0.266526	−	0.820283i
$940$	9.23607			0.301247
$941$	2.75329	−	2.00038i	0.0897547	−	0.0652106i	−0.542003	−	0.840377i	$-0.682334\pi$
$941$	2.75329	−	2.00038i	0.0897547	−	0.0652106i	0.631758	+	0.775166i	$0.282334\pi$
$942$		0			0
$943$	0.257354	+	0.898056i	0.00838061	+	0.0292447i
$944$	47.4164			1.54327
$945$	1.80902	−	1.31433i	0.0588473	−	0.0427551i
$946$		0			0
$947$	8.91641	−	27.4419i	0.289744	−	0.891741i	−0.695192	−	0.718824i	$-0.744681\pi$
$947$	8.91641	−	27.4419i	0.289744	−	0.891741i	0.984936	−	0.172917i	$-0.0553193\pi$
$948$	−2.43769	+	7.50245i	−0.0791726	+	0.243668i
$949$	−67.2320	+	48.8469i	−2.18244	+	1.58564i
$950$		0			0
$951$	20.8926	+	64.3008i	0.677489	+	2.08510i
$952$		0			0
$953$	−11.8541	−	36.4832i	−0.383992	−	1.18181i	−0.937209	−	0.348769i	$-0.886600\pi$
$953$	−11.8541	−	36.4832i	−0.383992	−	1.18181i	0.553217	−	0.833037i	$-0.313400\pi$
$954$		0			0
$955$	−2.59017	+	7.97172i	−0.0838159	+	0.257959i
$956$	4.38197	−	3.18368i	0.141723	−	0.102968i
$957$	−31.1803			−1.00792
$958$		0			0
$959$	−1.38197	−	1.00406i	−0.0446260	−	0.0324227i
$960$	5.52786	+	17.0130i	0.178411	+	0.549093i
$961$	−2.64590	+	1.92236i	−0.0853515	+	0.0620115i
$962$		0			0
$963$	6.61803	+	4.80828i	0.213263	+	0.154945i
$964$	15.0902	+	10.9637i	0.486022	+	0.353115i
$965$	−7.23607	−	5.25731i	−0.232937	−	0.169239i
$966$		0			0
$967$	13.4443	+	41.3772i	0.432339	+	1.33060i	0.895789	+	0.444479i	$0.146611\pi$
$967$	13.4443	+	41.3772i	0.432339	+	1.33060i	−0.463451	+	0.886123i	$0.653389\pi$
$968$		0			0
$969$	31.4443	−	96.7755i	1.01014	−	3.10888i
$970$		0			0
$971$	−29.1976	+	21.2133i	−0.936994	+	0.680766i	−0.947695	−	0.319177i	$-0.896594\pi$
$971$	−29.1976	+	21.2133i	−0.936994	+	0.680766i	0.0107010	+	0.999943i	$0.496594\pi$
$972$	−11.0557	+	34.0260i	−0.354613	+	1.09139i
$973$	−3.02786	−	9.31881i	−0.0970689	−	0.298747i
$974$		0			0
$975$	55.7771			1.78630
$976$	4.76393	+	14.6619i	0.152490	+	0.469315i
$977$	22.0795	+	16.0417i	0.706387	+	0.513220i	0.882006	−	0.471238i	$-0.156193\pi$
$977$	22.0795	+	16.0417i	0.706387	+	0.513220i	−0.175619	+	0.984458i	$0.556193\pi$
$978$		0			0
$979$	−15.4271	+	47.4796i	−0.493051	+	1.51745i
$980$	−0.618034	+	1.90211i	−0.0197424	+	0.0607608i
$981$	−7.70820			−0.246104
$982$		0			0
$983$	−6.21478			−0.198221			−0.0991104	−	0.995076i	$-0.531600\pi$
$983$	−6.21478			−0.198221			−0.0991104	+	0.995076i	$0.531600\pi$
$984$		0			0
$985$	−19.4164			−0.618658
$986$		0			0
$987$	−10.3262			−0.328688
$988$	−28.7984	+	88.6323i	−0.916198	+	2.81977i
$989$	−0.169697	+	0.522273i	−0.00539604	+	0.0166073i
$990$		0			0
$991$	−6.39919	−	4.64928i	−0.203277	−	0.147689i	0.481490	−	0.876452i	$-0.340096\pi$
$991$	−6.39919	−	4.64928i	−0.203277	−	0.147689i	−0.684767	+	0.728762i	$0.740096\pi$
$992$		0			0
$993$	20.1246			0.638635
$994$		0			0
$995$	5.10739	+	15.7189i	0.161915	+	0.498324i
$996$	9.67376	−	29.7728i	0.306525	−	0.943387i
$997$	6.20820	−	4.51052i	0.196616	−	0.142850i	−0.485122	−	0.874447i	$-0.661225\pi$
$997$	6.20820	−	4.51052i	0.196616	−	0.142850i	0.681737	+	0.731597i	$0.261225\pi$
$998$		0			0
$999$	−1.74671	+	5.37582i	−0.0552635	+	0.170084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.a.78.1	✓	4
41.10	even	5	inner	287.2.h.a.92.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.a.78.1	✓	4	1.1	even	1	trivial
287.2.h.a.92.1	yes	4	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.23607 q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.00000 q^{9} +O(q^{10})\)	\(q-2.23607 q^{3} +(-0.618034 + 1.90211i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.00000 q^{9} +(-1.11803 - 3.44095i) q^{11} +(1.38197 - 4.25325i) q^{12} +(-5.04508 + 3.66547i) q^{13} +(-0.690983 + 2.12663i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-1.88197 - 5.79210i) q^{17} +(-6.04508 - 4.39201i) q^{19} +(1.61803 + 1.17557i) q^{20} +(-1.80902 - 1.31433i) q^{21} +(0.118034 - 0.0857567i) q^{23} +(3.23607 + 2.35114i) q^{25} +2.23607 q^{27} +(-1.61803 + 1.17557i) q^{28} +(-1.19098 + 3.66547i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(2.50000 + 7.69421i) q^{33} +(0.809017 - 0.587785i) q^{35} +(-1.23607 + 3.80423i) q^{36} +(-0.781153 + 2.40414i) q^{37} +(11.2812 - 8.19624i) q^{39} +(-2.19098 + 6.01661i) q^{41} +(-3.04508 + 2.21238i) q^{43} +7.23607 q^{44} +(0.618034 - 1.90211i) q^{45} +(3.73607 - 2.71441i) q^{47} +(7.23607 + 5.25731i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.20820 + 12.9515i) q^{51} +(-3.85410 - 11.8617i) q^{52} +(-0.763932 + 2.35114i) q^{53} -3.61803 q^{55} +(13.5172 + 9.82084i) q^{57} +(-9.59017 + 6.96767i) q^{59} +(-3.61803 - 2.62866i) q^{60} +(-3.11803 - 2.26538i) q^{61} +(1.61803 + 1.17557i) q^{63} +(6.47214 - 4.70228i) q^{64} +(1.92705 + 5.93085i) q^{65} +(-2.47214 + 7.60845i) q^{67} +12.1803 q^{68} +(-0.263932 + 0.191758i) q^{69} +(-4.38197 - 13.4863i) q^{71} +13.3262 q^{73} +(-7.23607 - 5.25731i) q^{75} +(12.0902 - 8.78402i) q^{76} +(1.11803 - 3.44095i) q^{77} -1.76393 q^{79} +(-3.23607 + 2.35114i) q^{80} -11.0000 q^{81} +7.00000 q^{83} +(3.61803 - 2.62866i) q^{84} -6.09017 q^{85} +(2.66312 - 8.19624i) q^{87} +(-11.1631 - 8.11048i) q^{89} -6.23607 q^{91} +(0.0901699 + 0.277515i) q^{92} +(4.04508 + 12.4495i) q^{93} +(-6.04508 + 4.39201i) q^{95} +(-4.16312 + 12.8128i) q^{97} +(-2.23607 - 6.88191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - q^{5} + q^{7} + 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - q^5 + q^7 + 8 * q^9	\( 4 q + 2 q^{4} - q^{5} + q^{7} + 8 q^{9} + 10 q^{12} - 9 q^{13} - 5 q^{15} - 4 q^{16} - 12 q^{17} - 13 q^{19} + 2 q^{20} - 5 q^{21} - 4 q^{23} + 4 q^{25} - 2 q^{28} - 7 q^{29} - 5 q^{31} + 10 q^{33} + q^{35} + 4 q^{36} + 17 q^{37} + 25 q^{39} - 11 q^{41} - q^{43} + 20 q^{44} - 2 q^{45} + 6 q^{47} + 20 q^{48} - q^{49} - 10 q^{51} - 2 q^{52} - 12 q^{53} - 10 q^{55} + 25 q^{57} - 16 q^{59} - 10 q^{60} - 8 q^{61} + 2 q^{63} + 8 q^{64} + q^{65} + 8 q^{67} + 4 q^{68} - 10 q^{69} - 22 q^{71} + 22 q^{73} - 20 q^{75} + 26 q^{76} - 16 q^{79} - 4 q^{80} - 44 q^{81} + 28 q^{83} + 10 q^{84} - 2 q^{85} - 5 q^{87} - 29 q^{89} - 16 q^{91} - 22 q^{92} + 5 q^{93} - 13 q^{95} - q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - q^5 + q^7 + 8 * q^9 + 10 * q^12 - 9 * q^13 - 5 * q^15 - 4 * q^16 - 12 * q^17 - 13 * q^19 + 2 * q^20 - 5 * q^21 - 4 * q^23 + 4 * q^25 - 2 * q^28 - 7 * q^29 - 5 * q^31 + 10 * q^33 + q^35 + 4 * q^36 + 17 * q^37 + 25 * q^39 - 11 * q^41 - q^43 + 20 * q^44 - 2 * q^45 + 6 * q^47 + 20 * q^48 - q^49 - 10 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 + 25 * q^57 - 16 * q^59 - 10 * q^60 - 8 * q^61 + 2 * q^63 + 8 * q^64 + q^65 + 8 * q^67 + 4 * q^68 - 10 * q^69 - 22 * q^71 + 22 * q^73 - 20 * q^75 + 26 * q^76 - 16 * q^79 - 4 * q^80 - 44 * q^81 + 28 * q^83 + 10 * q^84 - 2 * q^85 - 5 * q^87 - 29 * q^89 - 16 * q^91 - 22 * q^92 + 5 * q^93 - 13 * q^95 - q^97

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