LMFDB - Embedded newform 529.2.c.b.170.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,2,Mod(118,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.118"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$529 = 23^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	529.c (of order $11$ , degree $10$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-7,4,-3,-3,-5,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			170.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	529.170
Dual form			529.2.c.b.501.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11435 + 0.620830i) q^{2} +(1.64589 + 1.89945i) q^{3} +(2.40255 - 1.54403i) q^{4} +(0.175969 + 1.22389i) q^{5} +(-4.65922 - 2.99430i) q^{6} +(-0.985691 + 2.15836i) q^{7} +(-1.23515 + 1.42544i) q^{8} +(-0.472039 + 3.28310i) q^{9} +(-1.13189 - 2.47850i) q^{10} +(1.83440 + 0.538629i) q^{11} +(6.88714 + 2.02225i) q^{12} +(0.0816181 + 0.178719i) q^{13} +(0.744123 - 5.17549i) q^{14} +(-2.03510 + 2.34863i) q^{15} +(-0.646201 + 1.41498i) q^{16} +(-1.31228 - 0.843349i) q^{17} +(-1.04019 - 7.23470i) q^{18} +(-6.71695 + 4.31672i) q^{19} +(2.31250 + 2.66877i) q^{20} +(-5.72204 + 1.68014i) q^{21} -4.21297 q^{22} -4.74046 q^{24} +(3.33052 - 0.977928i) q^{25} +(-0.283524 - 0.327204i) q^{26} +(-0.669961 + 0.430558i) q^{27} +(0.964395 + 6.70752i) q^{28} +(4.18718 + 2.69094i) q^{29} +(2.84482 - 6.22930i) q^{30} +(-1.16741 + 1.34726i) q^{31} +(1.02468 - 7.12680i) q^{32} +(1.99611 + 4.37088i) q^{33} +(3.29819 + 0.968437i) q^{34} +(-2.81506 - 0.826575i) q^{35} +(3.93510 + 8.61667i) q^{36} +(-0.552641 + 3.84370i) q^{37} +(11.5221 - 13.2972i) q^{38} +(-0.205134 + 0.449181i) q^{39} +(-1.96193 - 1.26086i) q^{40} +(-0.0606967 - 0.422155i) q^{41} +(11.0553 - 7.10483i) q^{42} +(-2.91621 - 3.36548i) q^{43} +(5.23891 - 1.53828i) q^{44} -4.10123 q^{45} -2.58842 q^{47} +(-3.75126 + 1.10147i) q^{48} +(0.897086 + 1.03529i) q^{49} +(-6.43476 + 4.13537i) q^{50} +(-0.557955 - 3.88066i) q^{51} +(0.472039 + 0.303361i) q^{52} +(4.07912 - 8.93203i) q^{53} +(1.14923 - 1.32628i) q^{54} +(-0.336426 + 2.33989i) q^{55} +(-1.85913 - 4.07093i) q^{56} +(-19.2548 - 5.65371i) q^{57} +(-10.5238 - 3.09007i) q^{58} +(-2.99884 - 6.56655i) q^{59} +(-1.26309 + 8.78498i) q^{60} +(-4.86539 + 5.61496i) q^{61} +(1.63189 - 3.57334i) q^{62} +(-6.62084 - 4.25495i) q^{63} +(1.81524 + 12.6253i) q^{64} +(-0.204370 + 0.131341i) q^{65} +(-6.93407 - 8.00234i) q^{66} +(-6.97216 + 2.04721i) q^{67} -4.45497 q^{68} +6.46519 q^{70} +(0.700702 - 0.205745i) q^{71} +(-4.09682 - 4.72798i) q^{72} +(-5.42132 + 3.48407i) q^{73} +(-1.21781 - 8.47004i) q^{74} +(7.33918 + 4.71660i) q^{75} +(-9.47270 + 20.7423i) q^{76} +(-2.97071 + 3.42838i) q^{77} +(0.154861 - 1.07708i) q^{78} +(-2.35876 - 5.16497i) q^{79} +(-1.84550 - 0.541887i) q^{80} +(7.62702 + 2.23949i) q^{81} +(0.390421 + 0.854902i) q^{82} +(1.83440 - 12.7585i) q^{83} +(-11.1533 + 12.8716i) q^{84} +(0.801248 - 1.75449i) q^{85} +(8.25528 + 5.30535i) q^{86} +(1.78031 + 12.3823i) q^{87} +(-3.03354 + 1.94954i) q^{88} +(9.10271 + 10.5051i) q^{89} +(8.67145 - 2.54617i) q^{90} -0.466190 q^{91} -4.48047 q^{93} +(5.47283 - 1.60697i) q^{94} +(-6.46519 - 7.46122i) q^{95} +(15.2235 - 9.78357i) q^{96} +(-0.615337 - 4.27976i) q^{97} +(-2.53950 - 1.63204i) q^{98} +(-2.63428 + 5.76827i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q - 7 q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 4 q^{8} + 9 q^{9} - 10 q^{10} - 4 q^{11} + 23 q^{12} + 8 q^{13} - 2 q^{14} - 10 q^{15} - 21 q^{16} + q^{17} + 8 q^{18} - 20 q^{19} + 24 q^{20}+ \cdots + 3 q^{99}+O(q^{100})$ 10 * q - 7 * q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 4 * q^8 + 9 * q^9 - 10 * q^10 - 4 * q^11 + 23 * q^12 + 8 * q^13 - 2 * q^14 - 10 * q^15 - 21 * q^16 + q^17 + 8 * q^18 - 20 * q^19 + 24 * q^20 - 2 * q^21 - 6 * q^22 - 38 * q^24 - 4 * q^25 + q^26 + 7 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 - q^31 - q^32 + 5 * q^33 + 18 * q^34 - 26 * q^35 + 5 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 32 * q^40 + 7 * q^41 + 30 * q^42 + 10 * q^44 - 6 * q^45 - 18 * q^47 - 4 * q^48 + 15 * q^49 - 39 * q^50 - 15 * q^51 - 9 * q^52 - 4 * q^53 - 28 * q^54 - q^55 - 13 * q^56 - 52 * q^57 - 23 * q^58 + q^59 - 8 * q^60 + 14 * q^61 + 15 * q^62 - 10 * q^63 + 2 * q^64 + 24 * q^65 - 42 * q^66 - 32 * q^67 - 30 * q^68 + 38 * q^70 + 19 * q^71 - 14 * q^72 + 19 * q^73 - 34 * q^74 + 16 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 + 40 * q^79 + 3 * q^80 + 33 * q^81 - 17 * q^82 - 4 * q^83 - 17 * q^84 + 3 * q^85 + 22 * q^86 - q^87 - 50 * q^88 + 14 * q^89 + 13 * q^90 - 4 * q^91 + 4 * q^93 + 17 * q^94 - 38 * q^95 + 37 * q^96 + 43 * q^97 - 5 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−2.11435	+	0.620830i	−1.49507	+	0.438993i	−0.924156	−	0.382014i	$-0.875231\pi$
$2$	−2.11435	+	0.620830i	−1.49507	+	0.438993i	−0.570917	+	0.821008i	$0.693412\pi$
$3$	1.64589	+	1.89945i	0.950253	+	1.09665i	0.995220	+	0.0976615i	$0.0311362\pi$
$3$	1.64589	+	1.89945i	0.950253	+	1.09665i	−0.0449671	+	0.998988i	$0.514318\pi$
$4$	2.40255	−	1.54403i	1.20128	−	0.772014i
$5$	0.175969	+	1.22389i	0.0786959	+	0.547342i	0.990584	+	0.136904i	$0.0437151\pi$
$5$	0.175969	+	1.22389i	0.0786959	+	0.547342i	−0.911888	+	0.410438i	$0.865376\pi$
$6$	−4.65922	−	2.99430i	−1.90212	−	1.22242i
$7$	−0.985691	+	2.15836i	−0.372556	+	0.815784i	0.626775	+	0.779201i	$0.284375\pi$
$7$	−0.985691	+	2.15836i	−0.372556	+	0.815784i	−0.999331	+	0.0365834i	$0.988353\pi$
$8$	−1.23515	+	1.42544i	−0.436691	+	0.503968i
$9$	−0.472039	+	3.28310i	−0.157346	+	1.09437i
$10$	−1.13189	−	2.47850i	−0.357935	−	0.783769i
$11$	1.83440	+	0.538629i	0.553093	+	0.162403i	0.546323	−	0.837574i	$-0.316027\pi$
$11$	1.83440	+	0.538629i	0.553093	+	0.162403i	0.00676945	+	0.999977i	$0.497845\pi$
$12$	6.88714	+	2.02225i	1.98815	+	0.583772i
$13$	0.0816181	+	0.178719i	0.0226368	+	0.0495677i	0.920613	−	0.390477i	$-0.127690\pi$
$13$	0.0816181	+	0.178719i	0.0226368	+	0.0495677i	−0.897976	+	0.440045i	$0.854963\pi$
$14$	0.744123	−	5.17549i	0.198875	−	1.38321i
$15$	−2.03510	+	2.34863i	−0.525461	+	0.606415i
$16$	−0.646201	+	1.41498i	−0.161550	+	0.353745i
$17$	−1.31228	−	0.843349i	−0.318274	−	0.204542i	0.371743	−	0.928336i	$-0.378760\pi$
$17$	−1.31228	−	0.843349i	−0.318274	−	0.204542i	−0.690016	+	0.723794i	$0.742397\pi$
$18$	−1.04019	−	7.23470i	−0.245176	−	1.70523i
$19$	−6.71695	+	4.31672i	−1.54097	+	0.990324i	−0.553446	+	0.832885i	$0.686687\pi$
$19$	−6.71695	+	4.31672i	−1.54097	+	0.990324i	−0.987529	+	0.157439i	$0.949676\pi$
$20$	2.31250	+	2.66877i	0.517091	+	0.596755i
$21$	−5.72204	+	1.68014i	−1.24865	+	0.366637i
$22$	−4.21297			−0.898208
$23$		0			0
$23$		0			0
$24$	−4.74046			−0.967643
$25$	3.33052	−	0.977928i	0.666103	−	0.195586i
$26$	−0.283524	−	0.327204i	−0.0556036	−	0.0641699i
$27$	−0.669961	+	0.430558i	−0.128934	+	0.0828609i
$28$	0.964395	+	6.70752i	0.182254	+	1.26760i
$29$	4.18718	+	2.69094i	0.777541	+	0.499695i	0.868217	−	0.496185i	$-0.165266\pi$
$29$	4.18718	+	2.69094i	0.777541	+	0.499695i	−0.0906760	+	0.995880i	$0.528903\pi$
$30$	2.84482	−	6.22930i	0.519392	−	1.13731i
$31$	−1.16741	+	1.34726i	−0.209672	+	0.241975i	−0.850839	−	0.525427i	$-0.823905\pi$
$31$	−1.16741	+	1.34726i	−0.209672	+	0.241975i	0.641166	+	0.767402i	$0.278451\pi$
$32$	1.02468	−	7.12680i	0.181139	−	1.25985i
$33$	1.99611	+	4.37088i	0.347479	+	0.760873i
$34$	3.29819	+	0.968437i	0.565635	+	0.166085i
$35$	−2.81506	−	0.826575i	−0.475831	−	0.139717i
$36$	3.93510	+	8.61667i	0.655850	+	1.43611i
$37$	−0.552641	+	3.84370i	−0.0908536	+	0.631900i	0.892615	+	0.450820i	$0.148868\pi$
$37$	−0.552641	+	3.84370i	−0.0908536	+	0.631900i	−0.983468	+	0.181080i	$0.942041\pi$
$38$	11.5221	−	13.2972i	1.86913	−	2.15709i
$39$	−0.205134	+	0.449181i	−0.0328477	+	0.0719265i
$40$	−1.96193	−	1.26086i	−0.310208	−	0.199359i
$41$	−0.0606967	−	0.422155i	−0.00947923	−	0.0659295i	0.984533	−	0.175201i	$-0.0560574\pi$
$41$	−0.0606967	−	0.422155i	−0.00947923	−	0.0659295i	−0.994012	+	0.109271i	$0.965148\pi$
$42$	11.0553	−	7.10483i	1.70588	−	1.09630i
$43$	−2.91621	−	3.36548i	−0.444717	−	0.513231i	0.488490	−	0.872569i	$-0.337548\pi$
$43$	−2.91621	−	3.36548i	−0.444717	−	0.513231i	−0.933207	+	0.359338i	$0.883002\pi$
$44$	5.23891	−	1.53828i	0.789795	−	0.231905i
$45$	−4.10123			−0.611375
$46$		0			0
$47$	−2.58842			−0.377559			−0.188780	−	0.982019i	$-0.560453\pi$
$47$	−2.58842			−0.377559			−0.188780	+	0.982019i	$0.560453\pi$
$48$	−3.75126	+	1.10147i	−0.541448	+	0.158984i
$49$	0.897086	+	1.03529i	0.128155	+	0.147899i
$50$	−6.43476	+	4.13537i	−0.910013	+	0.584830i
$51$	−0.557955	−	3.88066i	−0.0781293	−	0.543401i
$52$	0.472039	+	0.303361i	0.0654600	+	0.0420686i
$53$	4.07912	−	8.93203i	0.560311	−	1.22691i	−0.391487	−	0.920183i	$-0.628039\pi$
$53$	4.07912	−	8.93203i	0.560311	−	1.22691i	0.951798	−	0.306726i	$-0.0992334\pi$
$54$	1.14923	−	1.32628i	0.156391	−	0.180484i
$55$	−0.336426	+	2.33989i	−0.0453637	+	0.315511i
$56$	−1.85913	−	4.07093i	−0.248437	−	0.544002i
$57$	−19.2548	−	5.65371i	−2.55035	−	0.748852i
$58$	−10.5238	−	3.09007i	−1.38184	−	0.405746i
$59$	−2.99884	−	6.56655i	−0.390416	−	0.854891i	−0.998153	−	0.0607530i	$-0.980650\pi$
$59$	−2.99884	−	6.56655i	−0.390416	−	0.854891i	0.607737	−	0.794138i	$-0.292077\pi$
$60$	−1.26309	+	8.78498i	−0.163064	+	1.13414i
$61$	−4.86539	+	5.61496i	−0.622950	+	0.718922i	−0.976264	−	0.216582i	$-0.930509\pi$
$61$	−4.86539	+	5.61496i	−0.622950	+	0.718922i	0.353315	+	0.935505i	$0.385055\pi$
$62$	1.63189	−	3.57334i	0.207250	−	0.453815i
$63$	−6.62084	−	4.25495i	−0.834147	−	0.536074i
$64$	1.81524	+	12.6253i	0.226905	+	1.57816i
$65$	−0.204370	+	0.131341i	−0.0253490	+	0.0162908i
$66$	−6.93407	−	8.00234i	−0.853525	−	0.985020i
$67$	−6.97216	+	2.04721i	−0.851784	+	0.250106i	−0.678350	−	0.734739i	$-0.737305\pi$
$67$	−6.97216	+	2.04721i	−0.851784	+	0.250106i	−0.173434	+	0.984845i	$0.555486\pi$
$68$	−4.45497			−0.540244
$69$		0			0
$70$	6.46519			0.772738
$71$	0.700702	−	0.205745i	0.0831580	−	0.0244174i	−0.239889	−	0.970800i	$-0.577111\pi$
$71$	0.700702	−	0.205745i	0.0831580	−	0.0244174i	0.323047	+	0.946383i	$0.395293\pi$
$72$	−4.09682	−	4.72798i	−0.482814	−	0.557198i
$73$	−5.42132	+	3.48407i	−0.634518	+	0.407780i	−0.817980	−	0.575247i	$-0.804906\pi$
$73$	−5.42132	+	3.48407i	−0.634518	+	0.407780i	0.183462	+	0.983027i	$0.441270\pi$
$74$	−1.21781	−	8.47004i	−0.141567	−	0.984622i
$75$	7.33918	+	4.71660i	0.847455	+	0.544626i
$76$	−9.47270	+	20.7423i	−1.08659	+	2.37931i
$77$	−2.97071	+	3.42838i	−0.338544	+	0.390700i
$78$	0.154861	−	1.07708i	0.0175345	−	0.121955i
$79$	−2.35876	−	5.16497i	−0.265381	−	0.581104i	0.729290	−	0.684205i	$-0.239851\pi$
$79$	−2.35876	−	5.16497i	−0.265381	−	0.581104i	−0.994671	+	0.103101i	$0.967123\pi$
$80$	−1.84550	−	0.541887i	−0.206333	−	0.0605848i
$81$	7.62702	+	2.23949i	0.847446	+	0.248833i
$82$	0.390421	+	0.854902i	0.0431148	+	0.0944081i
$83$	1.83440	−	12.7585i	0.201352	−	1.40043i	−0.598927	−	0.800804i	$-0.704406\pi$
$83$	1.83440	−	12.7585i	0.201352	−	1.40043i	0.800279	−	0.599628i	$-0.204685\pi$
$84$	−11.1533	+	12.8716i	−1.21693	+	1.40441i
$85$	0.801248	−	1.75449i	0.0869076	−	0.190301i
$86$	8.25528	+	5.30535i	0.890190	+	0.572090i
$87$	1.78031	+	12.3823i	0.190869	+	1.32753i
$88$	−3.03354	+	1.94954i	−0.323376	+	0.207821i
$89$	9.10271	+	10.5051i	0.964886	+	1.11354i	0.993487	+	0.113946i	$0.0363492\pi$
$89$	9.10271	+	10.5051i	0.964886	+	1.11354i	−0.0286012	+	0.999591i	$0.509105\pi$
$90$	8.67145	−	2.54617i	0.914052	−	0.268390i
$91$	−0.466190			−0.0488700
$92$		0			0
$93$	−4.48047			−0.464603
$94$	5.47283	−	1.60697i	0.564479	−	0.165746i
$95$	−6.46519	−	7.46122i	−0.663314	−	0.765505i
$96$	15.2235	−	9.78357i	1.55375	−	0.998532i
$97$	−0.615337	−	4.27976i	−0.0624780	−	0.434544i	−0.996920	−	0.0784280i	$-0.975010\pi$
$97$	−0.615337	−	4.27976i	−0.0624780	−	0.434544i	0.934442	−	0.356116i	$-0.115899\pi$
$98$	−2.53950	−	1.63204i	−0.256528	−	0.164861i
$99$	−2.63428	+	5.76827i	−0.264755	+	0.579733i
$100$	6.49180	−	7.49193i	0.649180	−	0.749193i
$101$	0.259052	−	1.80175i	0.0257767	−	0.179281i	−0.972866	−	0.231370i	$-0.925679\pi$
$101$	0.259052	−	1.80175i	0.0257767	−	0.179281i	0.998642	+	0.0520896i	$0.0165882\pi$
$102$	3.58895	+	7.85870i	0.355359	+	0.778127i
$103$	14.6929	+	4.31424i	1.44774	+	0.425094i	0.908793	−	0.417247i	$-0.137005\pi$
$103$	14.6929	+	4.31424i	1.44774	+	0.425094i	0.538945	+	0.842341i	$0.318823\pi$
$104$	−0.355563	−	0.104403i	−0.0348658	−	0.0102375i
$105$	−3.06322	−	6.70752i	−0.298940	−	0.654586i
$106$	−3.07943	+	21.4179i	−0.299101	+	2.08029i
$107$	−1.30208	+	1.50268i	−0.125877	+	0.145269i	−0.815189	−	0.579195i	$-0.803367\pi$
$107$	−1.30208	+	1.50268i	−0.125877	+	0.145269i	0.689313	+	0.724464i	$0.257913\pi$
$108$	−0.944825	+	2.06888i	−0.0909158	+	0.199078i
$109$	13.1192	+	8.43118i	1.25659	+	0.807560i	0.987813	−	0.155643i	$-0.0497449\pi$
$109$	13.1192	+	8.43118i	1.25659	+	0.807560i	0.268775	+	0.963203i	$0.413381\pi$
$110$	−0.741353	−	5.15623i	−0.0706853	−	0.491627i
$111$	−8.21051	+	5.27658i	−0.779307	+	0.500830i
$112$	−2.41709	−	2.78947i	−0.228393	−	0.263580i
$113$	1.42796	−	0.419287i	0.134331	−	0.0394432i	−0.213876	−	0.976861i	$-0.568609\pi$
$113$	1.42796	−	0.419287i	0.134331	−	0.0394432i	0.348207	+	0.937418i	$0.386791\pi$
$114$	44.2213			4.14171
$115$		0			0
$116$	14.2148			1.31981
$117$	−0.625279	+	0.183599i	−0.0578071	+	0.0169737i
$118$	10.4173	+	12.0222i	0.958992	+	1.10674i
$119$	3.11375	−	2.00109i	0.285437	−	0.183439i
$120$	−0.834176	−	5.80182i	−0.0761495	−	0.529631i
$121$	−6.17888	−	3.97093i	−0.561717	−	0.360993i
$122$	6.80122	−	14.8926i	0.615754	−	1.34831i
$123$	0.701963	−	0.810109i	0.0632939	−	0.0730451i
$124$	−0.724552	+	5.03937i	−0.0650667	+	0.452549i
$125$	4.35121	+	9.52781i	0.389184	+	0.852194i
$126$	16.6404	+	4.88606i	1.48244	+	0.435285i
$127$	−5.75155	−	1.68881i	−0.510368	−	0.149858i	0.0164020	−	0.999865i	$-0.494779\pi$
$127$	−5.75155	−	1.68881i	−0.510368	−	0.149858i	−0.526770	+	0.850008i	$0.676597\pi$
$128$	−5.69418	−	12.4685i	−0.503299	−	1.10207i
$129$	1.59283	−	11.0784i	0.140241	−	0.975398i
$130$	0.350571	−	0.404581i	0.0307471	−	0.0354841i
$131$	−5.30436	+	11.6149i	−0.463444	+	1.01480i	0.523245	+	0.852182i	$0.324721\pi$
$131$	−5.30436	+	11.6149i	−0.463444	+	1.01480i	−0.986689	+	0.162619i	$0.948006\pi$
$132$	11.5445	+	7.41922i	1.00482	+	0.645760i
$133$	−2.69621	−	18.7526i	−0.233791	−	1.62605i
$134$	13.4706	−	8.65705i	1.16369	−	0.747855i
$135$	−0.644850	−	0.744196i	−0.0554998	−	0.0640502i
$136$	2.82299	−	0.828906i	0.242070	−	0.0710781i
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$		0			0
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	−8.03958	+	2.36063i	−0.679468	+	0.199510i
$141$	−4.26024	−	4.91658i	−0.358777	−	0.414051i
$142$	−1.35380	+	0.870034i	−0.113608	+	0.0730116i
$143$	0.0534573	+	0.371804i	0.00447033	+	0.0310918i
$144$	−4.34050	−	2.78947i	−0.361708	−	0.232456i
$145$	−2.55661	+	5.59819i	−0.212315	+	0.464904i
$146$	9.29958	−	10.7323i	0.769638	−	0.888210i
$147$	−0.489989	+	3.40795i	−0.0404136	+	0.281083i
$148$	4.60703	+	10.0880i	0.378696	+	0.829228i
$149$	15.9650	+	4.68776i	1.30791	+	0.384036i	0.860114	−	0.510102i	$-0.170392\pi$
$149$	15.9650	+	4.68776i	1.30791	+	0.384036i	0.447792	+	0.894138i	$0.352210\pi$
$150$	−18.4458	−	5.41618i	−1.50610	−	0.442229i
$151$	5.47931	+	11.9980i	0.445900	+	0.976385i	0.990478	+	0.137674i	$0.0439627\pi$
$151$	5.47931	+	11.9980i	0.445900	+	0.976385i	−0.544578	+	0.838710i	$0.683310\pi$
$152$	2.14321	−	14.9064i	0.173838	−	1.20907i
$153$	3.38825	−	3.91024i	0.273923	−	0.316124i
$154$	4.15269	−	9.09311i	0.334633	−	0.732744i
$155$	−1.85433	−	1.19170i	−0.148943	−	0.0957200i
$156$	0.200702	+	1.39591i	0.0160690	+	0.111763i
$157$	3.47326	−	2.23213i	0.277197	−	0.178143i	−0.394655	−	0.918830i	$-0.629136\pi$
$157$	3.47326	−	2.23213i	0.277197	−	0.178143i	0.671851	+	0.740686i	$0.265499\pi$
$158$	8.19382	+	9.45617i	0.651865	+	0.752293i
$159$	23.6798	−	6.95300i	1.87793	−	0.551409i
$160$	8.90276			0.703825
$161$		0			0
$162$	−17.5166			−1.37623
$163$	14.1902	−	4.16663i	1.11147	−	0.326356i	0.326067	−	0.945347i	$-0.394276\pi$
$163$	14.1902	−	4.16663i	1.11147	−	0.326356i	0.785398	+	0.618991i	$0.212458\pi$
$164$	−0.797646	−	0.920532i	−0.0622857	−	0.0718815i
$165$	−4.99824	+	3.21217i	−0.389112	+	0.250067i
$166$	4.04231	+	28.1149i	0.313744	+	2.18214i
$167$	1.11865	+	0.718914i	0.0865639	+	0.0556312i	0.583207	−	0.812324i	$-0.301798\pi$
$167$	1.11865	+	0.718914i	0.0865639	+	0.0556312i	−0.496643	+	0.867955i	$0.665434\pi$
$168$	4.67263	−	10.2316i	0.360501	−	0.789388i
$169$	8.48791	−	9.79557i	0.652916	−	0.753505i
$170$	−0.604882	+	4.20705i	−0.0463924	+	0.322666i
$171$	−11.0016	−	24.0901i	−0.841312	−	1.84222i
$172$	−12.2027	−	3.58305i	−0.930450	−	0.273205i
$173$	16.2500	+	4.77144i	1.23547	+	0.362766i	0.833310	−	0.552806i	$-0.186443\pi$
$173$	16.2500	+	4.77144i	1.23547	+	0.362766i	0.402156	+	0.915571i	$0.368261\pi$
$174$	−11.4515	−	25.0754i	−0.868139	−	1.90096i
$175$	−1.17214	+	8.15239i	−0.0886052	+	0.616263i
$176$	−1.94754	+	2.24758i	−0.146801	+	0.169418i
$177$	7.53710	−	16.5039i	0.566523	−	1.24051i
$178$	−25.7682	−	16.5602i	−1.93141	−	1.24124i
$179$	0.203702	+	1.41678i	0.0152254	+	0.105895i	0.996017	−	0.0891635i	$-0.0284194\pi$
$179$	0.203702	+	1.41678i	0.0152254	+	0.105895i	−0.980792	+	0.195059i	$0.937510\pi$
$180$	−9.85343	+	6.33242i	−0.734431	+	0.471990i
$181$	10.5638	+	12.1913i	0.785201	+	0.906170i	0.997473	−	0.0710407i	$-0.0226320\pi$
$181$	10.5638	+	12.1913i	0.785201	+	0.906170i	−0.212273	+	0.977210i	$0.568087\pi$
$182$	0.985691	−	0.289425i	0.0730643	−	0.0214536i
$183$	−18.6732			−1.38037
$184$		0			0
$185$	−4.80153			−0.353015
$186$	9.47331	−	2.78161i	0.694617	−	0.203958i
$187$	−1.95299	−	2.25387i	−0.142817	−	0.164819i
$188$	−6.21881	+	3.99659i	−0.453554	+	0.291481i
$189$	−0.268925	−	1.87042i	−0.0195614	−	0.136053i
$190$	18.3018	+	11.7619i	1.32776	+	0.853297i
$191$	−8.61757	+	18.8699i	−0.623546	+	1.36537i	0.289366	+	0.957218i	$0.406555\pi$
$191$	−8.61757	+	18.8699i	−0.623546	+	1.36537i	−0.912912	+	0.408156i	$0.866172\pi$
$192$	−20.9935	+	24.2278i	−1.51507	+	1.74849i
$193$	−2.08523	+	14.5031i	−0.150098	+	1.04396i	0.765953	+	0.642896i	$0.222267\pi$
$193$	−2.08523	+	14.5031i	−0.150098	+	1.04396i	−0.916051	+	0.401061i	$0.868642\pi$
$194$	3.95804	+	8.66691i	0.284171	+	0.622248i
$195$	−0.585846	−	0.172020i	−0.0419533	−	0.0123186i
$196$	3.75382	+	1.10222i	0.268130	+	0.0787301i
$197$	4.85118	+	10.6226i	0.345632	+	0.756828i	1.00000		0.000651969i	$0.000207528\pi$
$197$	4.85118	+	10.6226i	0.345632	+	0.756828i	−0.654368	+	0.756176i	$0.727065\pi$
$198$	1.98869	−	13.8316i	0.141330	−	0.982970i
$199$	3.74804	−	4.32546i	0.265691	−	0.306624i	−0.607190	−	0.794557i	$-0.707703\pi$
$199$	3.74804	−	4.32546i	0.265691	−	0.306624i	0.872881	+	0.487933i	$0.162249\pi$
$200$	−2.71970	+	5.95532i	−0.192312	+	0.421105i
$201$	−15.3640	−	9.87381i	−1.08369	−	0.696445i
$202$	0.570852	+	3.97036i	0.0401650	+	0.279354i
$203$	−9.93529	+	6.38502i	−0.697321	+	0.448141i
$204$	−7.33237	−	8.46200i	−0.513368	−	0.592459i
$205$	0.505992	−	0.148573i	0.0353400	−	0.0103768i
$206$	−33.7445			−2.35109
$207$		0			0
$208$	−0.305626			−0.0211913
$209$	−14.6467	+	4.30066i	−1.01313	+	0.297483i
$210$	10.6410	+	12.2803i	0.734296	+	0.847423i
$211$	−11.8345	+	7.60559i	−0.814723	+	0.523591i	−0.880390	−	0.474251i	$-0.842719\pi$
$211$	−11.8345	+	7.60559i	−0.814723	+	0.523591i	0.0656667	+	0.997842i	$0.479083\pi$
$212$	−3.99099	−	27.7580i	−0.274103	−	1.90643i
$213$	1.54408	+	0.992319i	0.105798	+	0.0679926i
$214$	1.82014	−	3.98556i	0.124423	−	0.272447i
$215$	3.60583	−	4.16135i	0.245915	−	0.283801i
$216$	0.213768	−	1.48679i	0.0145451	−	0.101163i
$217$	−1.75717	−	3.84767i	−0.119285	−	0.261197i
$218$	−32.9729	−	9.68171i	−2.23321	−	0.655728i
$219$	−15.5407	−	4.56317i	−1.05014	−	0.308350i
$220$	2.80458	+	6.14117i	0.189085	+	0.414038i
$221$	0.0436167	−	0.303361i	0.00293398	−	0.0204063i
$222$	14.0841	−	16.2539i	0.945261	−	1.09089i
$223$	−1.74623	+	3.82372i	−0.116936	+	0.256055i	−0.959045	−	0.283252i	$-0.908587\pi$
$223$	−1.74623	+	3.82372i	−0.116936	+	0.256055i	0.842109	+	0.539307i	$0.181314\pi$
$224$	14.3722	+	9.23645i	0.960283	+	0.617136i
$225$	1.63850	+	11.3960i	0.109234	+	0.759736i
$226$	−2.75891	+	1.77304i	−0.183520	+	0.117941i
$227$	−12.0696	−	13.9290i	−0.801087	−	0.924503i	0.197354	−	0.980332i	$-0.436765\pi$
$227$	−12.0696	−	13.9290i	−0.801087	−	0.924503i	−0.998440	+	0.0558291i	$0.982220\pi$
$228$	−54.9901	+	16.1465i	−3.64181	+	1.06933i
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$		0			0
$231$	−11.4015			−0.750163
$232$	−9.00755	+	2.64486i	−0.591375	+	0.173643i
$233$	−2.72738	−	3.14757i	−0.178677	−	0.206204i	0.659345	−	0.751840i	$-0.270834\pi$
$233$	−2.72738	−	3.14757i	−0.178677	−	0.206204i	−0.838022	+	0.545636i	$0.816288\pi$
$234$	1.20808	−	0.776384i	0.0789745	−	0.0507538i
$235$	−0.455482	−	3.16795i	−0.0297124	−	0.206654i
$236$	−17.3438	−	11.1462i	−1.12899	−	0.725555i
$237$	5.92836	−	12.9813i	0.385088	−	0.843226i
$238$	−5.34123	+	6.16411i	−0.346221	+	0.399560i
$239$	3.20452	−	22.2880i	0.207283	−	1.44169i	−0.574687	−	0.818373i	$-0.694876\pi$
$239$	3.20452	−	22.2880i	0.207283	−	1.44169i	0.781971	−	0.623315i	$-0.214215\pi$
$240$	−2.00819	−	4.39732i	−0.129628	−	0.283846i
$241$	−5.68896	−	1.67043i	−0.366458	−	0.107602i	0.0933187	−	0.995636i	$-0.470252\pi$
$241$	−5.68896	−	1.67043i	−0.366458	−	0.107602i	−0.459777	+	0.888034i	$0.652071\pi$
$242$	15.5296	+	4.55991i	0.998281	+	0.293122i
$243$	9.29187	+	20.3464i	0.596074	+	1.30522i
$244$	−3.01971	+	21.0026i	−0.193317	+	1.34455i
$245$	−1.10923	+	1.28012i	−0.0708660	+	0.0817837i
$246$	−0.981259	+	2.14866i	−0.0625628	+	0.136993i
$247$	−1.31970	−	0.848123i	−0.0839708	−	0.0539648i
$248$	−0.478513	−	3.32813i	−0.0303856	−	0.211336i
$249$	27.2535	−	17.5147i	1.72712	−	1.10995i
$250$	−15.1151	−	17.4438i	−0.955966	−	1.10324i
$251$	1.48780	−	0.436858i	0.0939092	−	0.0275742i	−0.234440	−	0.972130i	$-0.575326\pi$
$251$	1.48780	−	0.436858i	0.0939092	−	0.0275742i	0.328350	+	0.944556i	$0.393508\pi$
$252$	−22.4767			−1.41590
$253$		0			0
$254$	13.2093			0.828824
$255$	4.65133	−	1.36575i	0.291278	−	0.0855269i
$256$	3.07468	+	3.54837i	0.192168	+	0.221773i
$257$	23.0990	−	14.8449i	1.44088	−	0.925997i	0.441289	−	0.897365i	$-0.354521\pi$
$257$	23.0990	−	14.8449i	1.44088	−	0.925997i	0.999590	−	0.0286314i	$-0.00911491\pi$
$258$	3.50999	+	24.4125i	0.218523	+	1.51986i
$259$	−7.75136	−	4.98150i	−0.481646	−	0.309535i
$260$	−0.288217	+	0.631107i	−0.0178745	+	0.0391396i
$261$	−10.8111	+	12.4767i	−0.669193	+	0.772290i
$262$	4.00440	−	27.8512i	0.247392	−	1.72065i
$263$	−5.37576	−	11.7713i	−0.331484	−	0.725848i	0.668355	−	0.743843i	$-0.266999\pi$
$263$	−5.37576	−	11.7713i	−0.331484	−	0.725848i	−0.999838	+	0.0179951i	$0.994272\pi$
$264$	−8.69591	−	2.55335i	−0.535196	−	0.157148i
$265$	11.6497	+	3.42065i	0.715633	+	0.210129i
$266$	17.3429	+	37.9757i	1.06336	+	2.32844i
$267$	−4.97191	+	34.5804i	−0.304276	+	2.11628i
$268$	−13.5900	+	15.6837i	−0.830144	+	0.958037i
$269$	−4.15318	+	9.09419i	−0.253224	+	0.554483i	−0.992965	−	0.118409i	$-0.962221\pi$
$269$	−4.15318	+	9.09419i	−0.253224	+	0.554483i	0.739741	+	0.672892i	$0.234948\pi$
$270$	1.82546	+	1.17315i	0.111094	+	0.0713957i
$271$	−0.627807	−	4.36649i	−0.0381365	−	0.265245i	0.961828	−	0.273654i	$-0.0882324\pi$
$271$	−0.627807	−	4.36649i	−0.0381365	−	0.265245i	−0.999965	+	0.00840891i	$0.997323\pi$
$272$	2.04132	−	1.31187i	0.123773	−	0.0795441i
$273$	−0.767296	−	0.885506i	−0.0464388	−	0.0535933i
$274$	−1.47489	+	0.433066i	−0.0891013	+	0.0261625i
$275$	6.63624			0.400180
$276$		0			0
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	−29.5077	+	8.66425i	−1.76976	+	0.519647i
$279$	−3.87213	−	4.46867i	−0.231818	−	0.267533i
$280$	4.65524	−	2.99174i	0.278204	−	0.178791i
$281$	0.509389	+	3.54288i	0.0303876	+	0.211350i	0.999358	−	0.0358263i	$-0.0114063\pi$
$281$	0.509389	+	3.54288i	0.0303876	+	0.211350i	−0.968970	+	0.247177i	$0.920497\pi$
$282$	12.0600	+	7.75050i	0.718163	+	0.461536i
$283$	6.14000	−	13.4447i	0.364985	−	0.799206i	−0.634666	−	0.772787i	$-0.718862\pi$
$283$	6.14000	−	13.4447i	0.364985	−	0.799206i	0.999651	−	0.0264195i	$-0.00841055\pi$
$284$	1.36580	−	1.57622i	0.0810453	−	0.0935312i
$285$	3.53129	−	24.5606i	0.209175	−	1.45485i
$286$	−0.343855	−	0.752937i	−0.0203326	−	0.0445221i
$287$	0.970991	+	0.285109i	0.0573158	+	0.0168294i
$288$	22.9143	+	6.72826i	1.35024	+	0.396466i
$289$	−6.05122	−	13.2503i	−0.355954	−	0.779431i
$290$	1.93005	−	13.4238i	0.113336	−	0.788271i
$291$	7.11643	−	8.21280i	0.417173	−	0.481443i
$292$	−7.64552	+	16.7413i	−0.447420	+	0.979713i
$293$	18.0983	+	11.6311i	1.05731	+	0.679493i	0.949209	−	0.314646i	$-0.101886\pi$
$293$	18.0983	+	11.6311i	1.05731	+	0.679493i	0.108103	+	0.994140i	$0.465522\pi$
$294$	−1.07975	−	7.50981i	−0.0629721	−	0.437981i
$295$	7.50905	−	4.82577i	0.437194	−	0.280967i
$296$	−4.79636	−	5.53529i	−0.278783	−	0.321732i
$297$	−1.46089	+	0.428955i	−0.0847693	+	0.0248905i
$298$	−36.6660			−2.12401
$299$		0			0
$300$	24.9153			1.43849
$301$	10.1384	−	2.97690i	0.584368	−	0.171586i
$302$	−19.0339	−	21.9663i	−1.09528	−	1.26402i
$303$	3.84871	−	2.47342i	0.221103	−	0.142094i
$304$	−1.76759	−	12.2938i	−0.101378	−	0.705100i
$305$	−7.72828	−	4.96666i	−0.442520	−	0.284390i
$306$	−4.73635	+	10.3712i	−0.270759	+	0.592880i
$307$	−9.26297	+	10.6900i	−0.528665	+	0.610112i	−0.955779	−	0.294086i	$-0.904985\pi$
$307$	−9.26297	+	10.6900i	−0.528665	+	0.610112i	0.427114	+	0.904198i	$0.359530\pi$
$308$	−1.84377	+	12.8237i	−0.105059	+	0.730699i
$309$	15.9882	+	35.0093i	0.909537	+	1.99161i
$310$	4.66055	+	1.36846i	0.264702	+	0.0777234i
$311$	−0.547045	−	0.160627i	−0.0310201	−	0.00910831i	0.266186	−	0.963922i	$-0.414237\pi$
$311$	−0.547045	−	0.160627i	−0.0310201	−	0.00910831i	−0.297206	+	0.954813i	$0.596055\pi$
$312$	−0.386908	−	0.847210i	−0.0219043	−	0.0479638i
$313$	3.00750	−	20.9176i	0.169994	−	1.18233i	−0.708897	−	0.705312i	$-0.750807\pi$
$313$	3.00750	−	20.9176i	0.169994	−	1.18233i	0.878891	−	0.477023i	$-0.158284\pi$
$314$	−5.95793	+	6.87582i	−0.336225	+	0.388025i
$315$	4.04255	−	8.85194i	0.227772	−	0.498750i
$316$	−13.6419	−	8.76712i	−0.767417	−	0.493189i
$317$	1.25410	+	8.72244i	0.0704371	+	0.489901i	0.994252	+	0.107062i	$0.0341444\pi$
$317$	1.25410	+	8.72244i	0.0704371	+	0.489901i	−0.923815	+	0.382839i	$0.874946\pi$
$318$	−45.7507	+	29.4022i	−2.56557	+	1.64879i
$319$	6.23156	+	7.19160i	0.348900	+	0.402652i
$320$	−15.1326	+	4.44333i	−0.845937	+	0.248390i
$321$	−4.99734			−0.278924
$322$		0			0
$323$	12.4550			0.693015
$324$	21.7822	−	6.39582i	1.21012	−	0.355323i
$325$	0.446605	+	0.515409i	0.0247732	+	0.0285898i
$326$	−27.4164	+	17.6195i	−1.51845	+	0.975852i
$327$	5.57802	+	38.7960i	0.308465	+	2.14542i
$328$	0.676724	+	0.434904i	0.0373658	+	0.0240136i
$329$	2.55138	−	5.58674i	0.140662	−	0.308007i
$330$	8.57383	−	9.89472i	0.471974	−	0.544687i
$331$	−4.29613	+	29.8802i	−0.236137	+	1.64237i	0.434566	+	0.900640i	$0.356902\pi$
$331$	−4.29613	+	29.8802i	−0.236137	+	1.64237i	−0.670703	+	0.741726i	$0.734007\pi$
$332$	−15.2923	−	33.4854i	−0.839274	−	1.83775i
$333$	−12.3584	−	3.62875i	−0.677236	−	0.198854i
$334$	−2.81155	−	0.825545i	−0.153841	−	0.0451718i
$335$	−3.73245	−	8.17293i	−0.203926	−	0.446535i
$336$	1.32021	−	9.18230i	0.0720236	−	0.500935i
$337$	3.24534	−	3.74532i	0.176785	−	0.204020i	−0.660441	−	0.750878i	$-0.729631\pi$
$337$	3.24534	−	3.74532i	0.176785	−	0.204020i	0.837226	+	0.546858i	$0.184176\pi$
$338$	−11.8651	+	25.9809i	−0.645374	+	1.41317i
$339$	3.14668	+	2.02225i	0.170904	+	0.109833i
$340$	−0.783938	−	5.45241i	−0.0425150	−	0.295698i
$341$	−2.86716	+	1.84261i	−0.155266	+	0.0997832i
$342$	38.2171	+	44.1049i	2.06654	+	2.38492i
$343$	−19.0555	+	5.59519i	−1.02890	+	0.302112i
$344$	8.39923			0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	6.49285	−	1.90647i	0.348554	−	0.102345i	−0.102769	−	0.994705i	$-0.532770\pi$
$347$	6.49285	−	1.90647i	0.348554	−	0.102345i	0.451323	+	0.892360i	$0.350952\pi$
$348$	23.3960	+	27.0004i	1.25416	+	1.44737i
$349$	8.48980	−	5.45606i	0.454449	−	0.292056i	−0.293322	−	0.956014i	$-0.594761\pi$
$349$	8.48980	−	5.45606i	0.454449	−	0.292056i	0.747770	+	0.663957i	$0.231124\pi$
$350$	−2.58294	−	17.9647i	−0.138064	−	0.960255i
$351$	−0.131630	−	0.0845933i	−0.00702588	−	0.00451526i
$352$	5.71837	−	12.5215i	0.304790	−	0.667398i
$353$	−16.0240	+	18.4926i	−0.852869	+	0.984264i	−0.999988	−	0.00485521i	$-0.998455\pi$
$353$	−16.0240	+	18.4926i	−0.852869	+	0.984264i	0.147119	+	0.989119i	$0.453000\pi$
$354$	−5.68994	+	39.5744i	−0.302417	+	2.10336i
$355$	0.375112	+	0.821380i	0.0199089	+	0.0435943i
$356$	38.0899	+	11.1842i	2.01876	+	0.592762i
$357$	8.92584	+	2.62086i	0.472406	+	0.138711i
$358$	−1.31028	−	2.86911i	−0.0692504	−	0.151637i
$359$	−0.0596033	+	0.414550i	−0.00314574	+	0.0218791i	−0.991334	−	0.131367i	$-0.958064\pi$
$359$	−0.0596033	+	0.414550i	−0.00314574	+	0.0218791i	0.988188	+	0.153246i	$0.0489726\pi$
$360$	5.06563	−	5.84604i	0.266982	−	0.308114i
$361$	18.5905	−	40.7074i	0.978446	−	2.14250i
$362$	−29.9043	−	19.2183i	−1.57174	−	1.01009i
$363$	−2.62714	−	18.2722i	−0.137889	−	0.959041i
$364$	−1.12005	+	0.719811i	−0.0587064	+	0.0377283i
$365$	−5.21812	−	6.02203i	−0.273129	−	0.315208i
$366$	39.4818	−	11.5929i	2.06375	−	0.605971i
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$		0			0
$369$	1.41463			0.0736426
$370$	10.1521	−	2.98093i	0.527784	−	0.154971i
$371$	15.2578	+	17.6084i	0.792146	+	0.914185i
$372$	−10.7646	+	6.91798i	−0.558118	+	0.358680i
$373$	−2.05044	−	14.2611i	−0.106168	−	0.738413i	−0.971470	−	0.237162i	$-0.923783\pi$
$373$	−2.05044	−	14.2611i	−0.106168	−	0.738413i	0.865302	−	0.501250i	$-0.167126\pi$
$374$	5.52858	+	3.55300i	0.285876	+	0.183721i
$375$	−10.9360	+	23.9466i	−0.564735	+	1.23660i
$376$	3.19708	−	3.68962i	0.164877	−	0.190278i
$377$	−0.139171	+	0.967958i	−0.00716769	+	0.0498524i
$378$	1.72981	+	3.78776i	0.0889720	+	0.194822i
$379$	5.39919	+	1.58534i	0.277338	+	0.0814336i	0.417444	−	0.908703i	$-0.362926\pi$
$379$	5.39919	+	1.58534i	0.277338	+	0.0814336i	−0.140106	+	0.990137i	$0.544744\pi$
$380$	−27.0533	−	7.94356i	−1.38780	−	0.407496i
$381$	−6.25859	−	13.7044i	−0.320637	−	0.702097i
$382$	6.50562	−	45.2476i	0.332857	−	2.31507i
$383$	−0.151705	+	0.175077i	−0.00775177	+	0.00894601i	−0.759612	−	0.650376i	$-0.774611\pi$
$383$	−0.151705	+	0.175077i	−0.00775177	+	0.00894601i	0.751860	+	0.659322i	$0.229157\pi$
$384$	14.3114	−	31.3376i	0.730325	−	1.59919i
$385$	−4.71872	−	3.03254i	−0.240488	−	0.154553i
$386$	−4.59505	−	31.9593i	−0.233882	−	1.62669i
$387$	12.4258	−	7.98557i	0.631638	−	0.405929i
$388$	−8.08645	−	9.33226i	−0.410527	−	0.473774i
$389$	28.9477	−	8.49982i	1.46771	−	0.430958i	0.552355	−	0.833609i	$-0.313729\pi$
$389$	28.9477	−	8.49982i	1.46771	−	0.430958i	0.915353	+	0.402651i	$0.131911\pi$
$390$	1.34548			0.0681311
$391$		0			0
$392$	−2.58378			−0.130500
$393$	−30.7924	+	9.04146i	−1.55327	+	0.456081i
$394$	−16.8519	−	19.4482i	−0.848988	−	0.979784i
$395$	5.90630	−	3.79575i	0.297178	−	0.190985i
$396$	2.57737	+	17.9260i	0.129518	+	0.900815i
$397$	−10.9744	−	7.05281i	−0.550788	−	0.353970i	0.235457	−	0.971885i	$-0.424341\pi$
$397$	−10.9744	−	7.05281i	−0.550788	−	0.353970i	−0.786245	+	0.617915i	$0.787978\pi$
$398$	−5.23929	+	11.4725i	−0.262622	+	0.575062i
$399$	31.1820	−	35.9859i	1.56105	−	1.80155i
$400$	−0.768431	+	5.34456i	−0.0384216	+	0.267228i
$401$	−8.85904	−	19.3986i	−0.442399	−	0.968719i	−0.991152	−	0.132734i	$-0.957624\pi$
$401$	−8.85904	−	19.3986i	−0.442399	−	0.968719i	0.548753	−	0.835985i	$-0.315103\pi$
$402$	38.6148	+	11.3383i	1.92593	+	0.565504i
$403$	−0.336062	−	0.0986767i	−0.0167404	−	0.00491544i
$404$	−2.15956	−	4.72879i	−0.107442	−	0.235266i
$405$	−1.39878	+	9.72874i	−0.0695060	+	0.483425i
$406$	17.0427	−	19.6683i	0.845815	−	0.976123i
$407$	−3.08409	+	6.75322i	−0.152873	+	0.334745i
$408$	6.22079	+	3.99786i	0.307975	+	0.197924i
$409$	1.30204	+	9.05590i	0.0643818	+	0.447785i	0.996358	+	0.0852664i	$0.0271741\pi$
$409$	1.30204	+	9.05590i	0.0643818	+	0.447785i	−0.931976	+	0.362519i	$0.881917\pi$
$410$	−0.977607	+	0.628270i	−0.0482806	+	0.0310280i
$411$	1.14810	+	1.32498i	0.0566318	+	0.0653566i
$412$	41.9619	−	12.3211i	2.06731	−	0.607018i
$413$	17.1289			0.842859
$414$		0			0
$415$	15.9379			0.782360
$416$	1.35733	−	0.398547i	0.0665484	−	0.0195404i
$417$	22.9698	+	26.5086i	1.12484	+	1.29813i
$418$	28.2983	−	18.1862i	1.38412	−	0.889517i
$419$	1.27716	+	8.88285i	0.0623934	+	0.433956i	0.996944	+	0.0781244i	$0.0248931\pi$
$419$	1.27716	+	8.88285i	0.0623934	+	0.433956i	−0.934550	+	0.355831i	$0.884198\pi$
$420$	−17.7161	−	11.3855i	−0.864459	−	0.555554i
$421$	13.0741	−	28.6282i	0.637191	−	1.39525i	−0.265141	−	0.964210i	$-0.585418\pi$
$421$	13.0741	−	28.6282i	0.637191	−	1.39525i	0.902331	−	0.431043i	$-0.141854\pi$
$422$	20.3006	−	23.4282i	0.988218	−	1.14046i
$423$	1.22183	−	8.49804i	0.0594076	−	0.413189i
$424$	7.69373	+	16.8469i	0.373640	+	0.818158i
$425$	−5.19529	−	1.52547i	−0.252009	−	0.0739964i
$426$	−3.88079	−	1.13950i	−0.188025	−	0.0552091i
$427$	−7.32335	−	16.0359i	−0.354402	−	0.776031i
$428$	−0.808136	+	5.62071i	−0.0390627	+	0.271687i
$429$	−0.618239	+	0.713486i	−0.0298489	+	0.0344474i
$430$	−5.04050	+	11.0372i	−0.243075	+	0.532259i
$431$	−18.5937	−	11.9495i	−0.895628	−	0.575585i	0.00986260	−	0.999951i	$-0.496861\pi$
$431$	−18.5937	−	11.9495i	−0.895628	−	0.575585i	−0.905491	+	0.424366i	$0.860497\pi$
$432$	−0.176302	−	1.22621i	−0.00848235	−	0.0589960i
$433$	10.6799	−	6.86357i	0.513244	−	0.329842i	−0.258250	−	0.966078i	$-0.583146\pi$
$433$	10.6799	−	6.86357i	0.513244	−	0.329842i	0.771495	+	0.636236i	$0.219510\pi$
$434$	6.10403	+	7.04442i	0.293003	+	0.338143i
$435$	−14.8414	+	4.35782i	−0.711590	+	0.208942i
$436$	44.5375			2.13296
$437$		0			0
$438$	35.6915			1.70541
$439$	−17.6748	+	5.18980i	−0.843573	+	0.247695i	−0.674838	−	0.737966i	$-0.735787\pi$
$439$	−17.6748	+	5.18980i	−0.843573	+	0.247695i	−0.168735	+	0.985661i	$0.553968\pi$
$440$	−2.91983	−	3.36967i	−0.139198	−	0.160643i
$441$	−3.82243	+	2.45653i	−0.182021	+	0.116978i
$442$	0.0961145	+	0.668491i	0.00457170	+	0.0317969i
$443$	−11.7042	−	7.52182i	−0.556082	−	0.357372i	0.232217	−	0.972664i	$-0.425402\pi$
$443$	−11.7042	−	7.52182i	−0.556082	−	0.357372i	−0.788300	+	0.615292i	$0.789038\pi$
$444$	−11.5790	+	25.3545i	−0.549516	+	1.20327i
$445$	−11.2553	+	12.9893i	−0.533553	+	0.615753i
$446$	1.31827	−	9.16880i	0.0624221	−	0.434155i
$447$	17.3724	+	38.0403i	0.821688	+	1.79925i
$448$	−29.0392	−	8.52668i	−1.37197	−	0.402848i
$449$	−28.8735	−	8.47803i	−1.36263	−	0.400103i	−0.482938	−	0.875655i	$-0.660430\pi$
$449$	−28.8735	−	8.47803i	−1.36263	−	0.400103i	−0.879688	+	0.475552i	$0.842248\pi$
$450$	−10.5394	−	23.0780i	−0.496831	−	1.08791i
$451$	0.116043	−	0.807094i	0.00546423	−	0.0380046i
$452$	2.78336	−	3.21217i	0.130918	−	0.151088i
$453$	−13.7714	+	30.1551i	−0.647035	+	1.41681i
$454$	34.1669	+	21.9578i	1.60353	+	1.03053i
$455$	−0.0820351	−	0.570567i	−0.00384587	−	0.0267486i
$456$	31.8415	−	20.4633i	1.49111	−	0.958280i
$457$	−24.9158	−	28.7544i	−1.16551	−	1.34507i	−0.927505	−	0.373812i	$-0.878051\pi$
$457$	−24.9158	−	28.7544i	−1.16551	−	1.34507i	−0.238009	−	0.971263i	$-0.576495\pi$
$458$	−23.0986	+	6.78237i	−1.07933	+	0.316919i
$459$	1.24228			0.0579849
$460$		0			0
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$	24.1068	−	7.07839i	1.12155	−	0.329317i
$463$	18.2292	+	21.0376i	0.847181	+	0.977699i	0.999944	−	0.0105636i	$-0.00336255\pi$
$463$	18.2292	+	21.0376i	0.847181	+	0.977699i	−0.152763	+	0.988263i	$0.548817\pi$
$464$	−6.51339	+	4.18590i	−0.302377	+	0.194326i
$465$	−0.788426	−	5.48362i	−0.0365624	−	0.254297i
$466$	7.72076	+	4.96183i	0.357657	+	0.229852i
$467$	−7.21424	+	15.7970i	−0.333835	+	0.730997i	−0.999889	−	0.0149067i	$-0.995255\pi$
$467$	−7.21424	+	15.7970i	−0.333835	+	0.730997i	0.666054	+	0.745904i	$0.267982\pi$
$468$	−1.21879	+	1.40655i	−0.0563384	+	0.0650180i
$469$	2.45377	−	17.0664i	0.113305	−	0.788051i
$470$	2.92981	+	6.41538i	0.135142	+	0.295920i
$471$	9.95642	+	2.92347i	0.458768	+	0.134706i
$472$	13.0642	+	3.83600i	0.601329	+	0.176566i
$473$	−3.53675	−	7.74439i	−0.162620	−	0.356088i
$474$	−4.47547	+	31.1276i	−0.205565	+	1.42974i
$475$	−18.1495	+	20.9456i	−0.832755	+	0.961050i
$476$	4.39122	−	9.61543i	0.201271	−	0.440723i
$477$	27.3993	+	17.6084i	1.25453	+	0.806235i
$478$	7.06154	+	49.1141i	0.322987	+	2.24643i
$479$	−21.4333	+	13.7743i	−0.979311	+	0.629365i	−0.929277	−	0.369382i	$-0.879569\pi$
$479$	−21.4333	+	13.7743i	−0.979311	+	0.629365i	−0.0500338	+	0.998748i	$0.515933\pi$
$480$	14.6529	+	16.9104i	0.668811	+	0.771849i
$481$	−0.732047	+	0.214948i	−0.0333785	+	0.00980080i
$482$	13.0655			0.595119
$483$		0			0
$484$	−20.9763			−0.953469
$485$	5.12969	−	1.50621i	0.232927	−	0.0683936i
$486$	−32.2779	−	37.2507i	−1.46416	−	1.68973i
$487$	−5.18302	+	3.33093i	−0.234865	+	0.150939i	−0.652780	−	0.757547i	$-0.726397\pi$
$487$	−5.18302	+	3.33093i	−0.234865	+	0.150939i	0.417915	+	0.908486i	$0.362761\pi$
$488$	−1.99429	−	13.8706i	−0.0902774	−	0.627893i
$489$	31.2698	+	20.0959i	1.41407	+	0.908768i
$490$	1.55056	−	3.39526i	0.0700474	−	0.153382i
$491$	21.3796	−	24.6734i	0.964850	−	1.11350i	−0.0286418	−	0.999590i	$-0.509118\pi$
$491$	21.3796	−	24.6734i	0.964850	−	1.11350i	0.993492	−	0.113906i	$-0.0363363\pi$
$492$	0.435674	−	3.03018i	0.0196417	−	0.136611i
$493$	−3.22534	−	7.06251i	−0.145262	−	0.318080i
$494$	3.31686	+	0.973919i	0.149233	+	0.0438187i
$495$	−7.52330	−	2.20904i	−0.338147	−	0.0992890i
$496$	−1.15197	−	2.52246i	−0.0517249	−	0.113262i
$497$	−0.246604	+	1.71517i	−0.0110617	+	0.0769358i
$498$	−46.7498	+	53.9521i	−2.09491	+	2.41765i
$499$	−3.56164	+	7.79890i	−0.159441	+	0.349127i	−0.972445	−	0.233130i	$-0.925103\pi$
$499$	−3.56164	+	7.79890i	−0.159441	+	0.349127i	0.813005	+	0.582257i	$0.197830\pi$
$500$	25.1652	+	16.1727i	1.12542	+	0.723265i
$501$	0.475630	+	3.30808i	0.0212496	+	0.147794i
$502$	−2.87452	+	1.84734i	−0.128296	+	0.0824510i
$503$	−4.42394	−	5.10549i	−0.197254	−	0.227643i	0.648502	−	0.761213i	$-0.275396\pi$
$503$	−4.42394	−	5.10549i	−0.197254	−	0.227643i	−0.845756	+	0.533570i	$0.820850\pi$
$504$	14.2429	−	4.18209i	0.634428	−	0.186285i
$505$	2.25073			0.100156
$506$		0			0
$507$	32.5764			1.44677
$508$	−16.4260	+	4.82311i	−0.728785	+	0.213991i
$509$	−26.8313	−	30.9650i	−1.18928	−	1.37250i	−0.911213	−	0.411937i	$-0.864853\pi$
$509$	−26.8313	−	30.9650i	−1.18928	−	1.37250i	−0.278065	−	0.960562i	$-0.589693\pi$
$510$	−8.98666	+	5.77538i	−0.397936	+	0.255738i
$511$	−2.17614	−	15.1354i	−0.0962668	−	0.669550i
$512$	14.3586	+	9.22769i	0.634565	+	0.407810i
$513$	2.64150	−	5.78407i	0.116625	−	0.255373i
$514$	−39.6234	+	45.7279i	−1.74771	+	2.01697i
$515$	−2.69466	+	18.7418i	−0.118741	+	0.825861i
$516$	−13.2785	−	29.0758i	−0.584553	−	1.27999i
$517$	−4.74820	−	1.39420i	−0.208825	−	0.0613167i
$518$	19.4818	+	5.72037i	0.855981	+	0.251339i
$519$	17.6826	+	38.7194i	0.776178	+	1.69959i
$520$	0.0652096	−	0.453543i	0.00285963	−	0.0198892i
$521$	12.2635	−	14.1528i	0.537273	−	0.620046i	−0.420598	−	0.907247i	$-0.638180\pi$
$521$	12.2635	−	14.1528i	0.537273	−	0.620046i	0.957870	+	0.287202i	$0.0927250\pi$
$522$	15.1127	−	33.0921i	0.661463	−	1.44840i
$523$	19.8233	+	12.7397i	0.866813	+	0.557067i	0.896776	−	0.442484i	$-0.145903\pi$
$523$	19.8233	+	12.7397i	0.866813	+	0.557067i	−0.0299636	+	0.999551i	$0.509539\pi$
$524$	5.18976	+	36.0956i	0.226716	+	1.57684i
$525$	−17.4143	+	11.1915i	−0.760022	+	0.488436i
$526$	18.6742	+	21.5512i	0.814235	+	0.939677i
$527$	2.66817	−	0.783445i	0.116227	−	0.0341274i
$528$	−7.47461			−0.325291
$529$		0			0
$530$	−26.7551			−1.16217
$531$	22.9742	−	6.74584i	0.996996	−	0.292744i
$532$	−35.4323	−	40.8910i	−1.53618	−	1.77285i
$533$	0.0704930	−	0.0453031i	0.00305339	−	0.00196230i
$534$	−10.9562	−	76.2018i	−0.474120	−	3.29758i
$535$	−2.06824	−	1.32918i	−0.0894179	−	0.0574654i
$536$	5.69348	−	12.4670i	0.245921	−	0.538491i
$537$	−2.35584	+	2.71878i	−0.101662	+	0.117324i
$538$	3.13534	−	21.8068i	0.135174	−	0.940156i
$539$	1.08798	+	2.38234i	0.0468625	+	0.102615i
$540$	−2.69835	−	0.792306i	−0.116118	−	0.0340954i
$541$	−0.914673	−	0.268572i	−0.0393249	−	0.0115468i	0.262011	−	0.965065i	$-0.415614\pi$
$541$	−0.914673	−	0.268572i	−0.0393249	−	0.0115468i	−0.301336	+	0.953518i	$0.597433\pi$
$542$	4.03825	+	8.84254i	0.173458	+	0.379820i
$543$	−5.76995	+	40.1309i	−0.247612	+	1.72218i
$544$	−7.35504	+	8.48817i	−0.315345	+	0.363927i
$545$	−8.01029	+	17.5401i	−0.343123	+	0.751335i
$546$	2.17208	+	1.39591i	0.0929566	+	0.0597396i
$547$	−4.23899	−	29.4828i	−0.181246	−	1.26059i	−0.853821	−	0.520566i	$-0.825721\pi$
$547$	−4.23899	−	29.4828i	−0.181246	−	1.26059i	0.672575	−	0.740029i	$-0.265188\pi$
$548$	1.67593	−	1.07705i	0.0715920	−	0.0460094i
$549$	−16.1378	−	18.6241i	−0.688746	−	0.794856i
$550$	−14.0314	+	4.11998i	−0.598299	+	0.175676i
$551$	−39.7412			−1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$	65.1310	−	19.1242i	2.76715	−	0.812509i
$555$	−7.90276	−	9.12028i	−0.335454	−	0.387134i
$556$	33.5298	−	21.5483i	1.42198	−	0.913852i
$557$	0.855129	+	5.94755i	0.0362330	+	0.252006i	0.999885	−	0.0151540i	$-0.00482386\pi$
$557$	0.855129	+	5.94755i	0.0362330	+	0.252006i	−0.963652	+	0.267160i	$0.913915\pi$
$558$	10.9613	+	7.04442i	0.464030	+	0.298214i
$559$	0.363459	−	0.795865i	0.0153727	−	0.0336615i
$560$	2.98868	−	3.44912i	0.126295	−	0.145752i
$561$	1.06672	−	7.41922i	0.0450371	−	0.313240i
$562$	−3.27655	−	7.17465i	−0.138213	−	0.302644i
$563$	−0.0855772	−	0.0251277i	−0.00360665	−	0.00105901i	0.279929	−	0.960021i	$-0.409689\pi$
$563$	−0.0855772	−	0.0251277i	−0.00360665	−	0.00105901i	−0.283535	+	0.958962i	$0.591507\pi$
$564$	−17.8268	−	5.23442i	−0.750643	−	0.220409i
$565$	0.764440	+	1.67389i	0.0321602	+	0.0704211i
$566$	−4.63524	+	32.2388i	−0.194834	+	1.35510i
$567$	−12.3515	+	14.2544i	−0.518715	+	0.598629i
$568$	−0.572195	+	1.25293i	−0.0240087	+	0.0525718i
$569$	−34.7939	−	22.3607i	−1.45864	−	0.937408i	−0.998778	−	0.0494153i	$-0.984264\pi$
$569$	−34.7939	−	22.3607i	−1.45864	−	0.937408i	−0.459857	−	0.887993i	$-0.652099\pi$
$570$	7.78160	+	54.1222i	0.325935	+	2.26693i
$571$	21.6963	−	13.9434i	0.907963	−	0.583513i	−0.00117841	−	0.999999i	$-0.500375\pi$
$571$	21.6963	−	13.9434i	0.907963	−	0.583513i	0.909142	+	0.416487i	$0.136739\pi$
$572$	0.702510	+	0.810739i	0.0293734	+	0.0338987i
$573$	−50.0259	+	14.6889i	−2.08986	+	0.613639i
$574$	−2.23002			−0.0930793
$575$		0			0
$576$	−42.3070			−1.76279
$577$	−26.0447	+	7.64741i	−1.08425	+	0.318366i	−0.774579	−	0.632477i	$-0.782038\pi$
$577$	−26.0447	+	7.64741i	−1.08425	+	0.318366i	−0.309675	+	0.950842i	$0.600220\pi$
$578$	21.0206	+	24.2591i	0.874343	+	1.00905i
$579$	−30.9801	+	19.9097i	−1.28749	+	0.827418i
$580$	2.50137	+	17.3974i	0.103864	+	0.722389i
$581$	25.7294	+	16.5353i	1.06743	+	0.685999i
$582$	−9.94790	+	21.7829i	−0.412354	+	0.902929i
$583$	12.2938	−	14.1878i	0.509157	−	0.587599i
$584$	1.72981	−	12.0311i	0.0715801	−	0.497850i
$585$	−0.334735	−	0.732967i	−0.0138396	−	0.0303045i
$586$	−45.4871	−	13.3562i	−1.87905	−	0.551740i
$587$	−30.3534	−	8.91255i	−1.25282	−	0.367860i	−0.413001	−	0.910731i	$-0.635519\pi$
$587$	−30.3534	−	8.91255i	−1.25282	−	0.367860i	−0.839816	+	0.542870i	$0.817337\pi$
$588$	4.08474	+	8.94433i	0.168452	+	0.368858i
$589$	2.02567	−	14.0888i	0.0834663	−	0.580521i
$590$	−12.8808	+	14.8652i	−0.530294	+	0.611992i
$591$	−12.1926	+	26.6982i	−0.501538	+	1.09822i
$592$	−5.08165	−	3.26578i	−0.208854	−	0.134223i
$593$	3.66403	+	25.4839i	0.150464	+	1.04650i	0.915444	+	0.402445i	$0.131840\pi$
$593$	3.66403	+	25.4839i	0.150464	+	1.04650i	−0.764980	+	0.644054i	$0.777251\pi$
$594$	2.82253	−	1.81393i	0.115810	−	0.0744263i
$595$	2.99704	+	3.45877i	0.122867	+	0.141796i
$596$	45.5949	−	13.3879i	1.86764	−	0.548388i
$597$	14.3849			0.588733
$598$		0			0
$599$	16.9434			0.692289			0.346144	−	0.938181i	$-0.387491\pi$
$599$	16.9434			0.692289			0.346144	+	0.938181i	$0.387491\pi$
$600$	−15.7882	+	4.63583i	−0.644550	+	0.189257i
$601$	6.32265	+	7.29673i	0.257906	+	0.297640i	0.869905	−	0.493219i	$-0.164180\pi$
$601$	6.32265	+	7.29673i	0.257906	+	0.297640i	−0.611999	+	0.790859i	$0.709634\pi$
$602$	−19.5880	+	12.5885i	−0.798348	+	0.513067i
$603$	−3.43007	−	23.8567i	−0.139683	−	0.971519i
$604$	31.6896	+	20.3657i	1.28943	+	0.828668i
$605$	3.77270	−	8.26105i	0.153382	−	0.335860i
$606$	−6.60196	+	7.61907i	−0.268186	+	0.309504i
$607$	−0.461850	+	3.21224i	−0.0187459	+	0.130381i	−0.997045	−	0.0768155i	$-0.975525\pi$
$607$	−0.461850	+	3.21224i	−0.0187459	+	0.130381i	0.978299	+	0.207196i	$0.0664338\pi$
$608$	23.8817	+	52.2937i	0.968531	+	2.12079i
$609$	−28.4804	−	8.36260i	−1.15408	−	0.338870i
$610$	19.4238	+	5.70333i	0.786445	+	0.230921i
$611$	−0.211262	−	0.462599i	−0.00854674	−	0.0187147i
$612$	2.10292	−	14.6261i	0.0850054	−	0.591226i
$613$	21.5543	−	24.8750i	0.870569	−	1.00469i	−0.129345	−	0.991600i	$-0.541287\pi$
$613$	21.5543	−	24.8750i	0.870569	−	1.00469i	0.999914	−	0.0130910i	$-0.00416711\pi$
$614$	12.9485	−	28.3532i	0.522559	−	1.14424i
$615$	1.11501	+	0.716574i	0.0449616	+	0.0288951i
$616$	−1.21767	−	8.46911i	−0.0490615	−	0.341230i
$617$	2.54431	−	1.63513i	0.102430	−	0.0658278i	−0.488423	−	0.872607i	$-0.662428\pi$
$617$	2.54431	−	1.63513i	0.102430	−	0.0658278i	0.590853	+	0.806779i	$0.298791\pi$
$618$	−55.5395	−	64.0961i	−2.23413	−	2.57832i
$619$	−10.0002	+	2.93632i	−0.401942	+	0.118021i	−0.476454	−	0.879199i	$-0.658078\pi$
$619$	−10.0002	+	2.93632i	−0.401942	+	0.118021i	0.0745122	+	0.997220i	$0.476260\pi$
$620$	−6.29515			−0.252819
$621$		0			0
$622$	1.25637			0.0503758
$623$	−31.6462	+	9.29218i	−1.26788	+	0.372283i
$624$	−0.503025	−	0.580522i	−0.0201371	−	0.0232395i
$625$	3.70511	−	2.38113i	0.148204	−	0.0952452i
$626$	6.62738	+	46.0944i	0.264883	+	1.84230i
$627$	−32.2757	−	20.7423i	−1.28897	−	0.828369i
$628$	4.89823	−	10.7256i	0.195461	−	0.427999i
$629$	3.96680	−	4.57793i	0.158167	−	0.182534i
$630$	−3.05182	+	21.2259i	−0.121587	+	0.845659i
$631$	14.1662	+	31.0196i	0.563947	+	1.23487i	0.949958	+	0.312378i	$0.101126\pi$
$631$	14.1662	+	31.0196i	0.563947	+	1.23487i	−0.386011	+	0.922494i	$0.626147\pi$
$632$	10.2757	+	3.01723i	0.408747	+	0.120019i
$633$	−33.9248	−	9.96121i	−1.34839	−	0.395923i
$634$	−8.06676	−	17.6637i	−0.320372	−	0.701517i
$635$	1.05482	−	7.33647i	0.0418594	−	0.291139i
$636$	46.1563	−	53.2672i	1.83021	−	2.11218i
$637$	−0.111808	+	0.244825i	−0.00442998	+	0.00970031i
$638$	−17.6405	−	11.3368i	−0.698393	−	0.448830i
$639$	0.344722	+	2.39760i	0.0136370	+	0.0948474i
$640$	14.2581	−	9.16314i	0.563602	−	0.362205i
$641$	5.89746	+	6.80603i	0.232936	+	0.268822i	0.860169	−	0.510010i	$-0.170358\pi$
$641$	5.89746	+	6.80603i	0.232936	+	0.268822i	−0.627233	+	0.778832i	$0.715813\pi$
$642$	10.5661	−	3.10250i	0.417012	−	0.122446i
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$		0			0
$645$	13.8391			0.544913
$646$	−26.3343	+	7.73244i	−1.03611	+	0.304229i
$647$	29.4388	+	33.9742i	1.15736	+	1.33566i	0.932456	+	0.361283i	$0.117661\pi$
$647$	29.4388	+	33.9742i	1.15736	+	1.33566i	0.224903	+	0.974381i	$0.427793\pi$
$648$	−12.6127	+	8.10572i	−0.495476	+	0.318423i
$649$	−1.96415	−	13.6609i	−0.0770995	−	0.536239i
$650$	−1.26426	−	0.812492i	−0.0495884	−	0.0318685i
$651$	4.41636	−	9.67048i	0.173091	−	0.379016i
$652$	27.6594	−	31.9207i	1.08323	−	1.25011i
$653$	4.17884	−	29.0645i	0.163531	−	1.13738i	−0.728381	−	0.685172i	$-0.759727\pi$
$653$	4.17884	−	29.0645i	0.163531	−	1.13738i	0.891912	−	0.452209i	$-0.149364\pi$
$654$	−35.8796	−	78.5654i	−1.40300	−	3.07215i
$655$	−15.1488	−	4.44810i	−0.591914	−	0.173802i
$656$	0.636564	+	0.186912i	0.0248536	+	0.00729768i
$657$	−8.87949	−	19.4434i	−0.346422	−	0.758558i
$658$	−1.92610	+	13.3963i	−0.0750872	+	0.522243i
$659$	26.2951	−	30.3461i	1.02431	−	1.18212i	0.0411919	−	0.999151i	$-0.486884\pi$
$659$	26.2951	−	30.3461i	1.02431	−	1.18212i	0.983119	−	0.182967i	$-0.0585701\pi$
$660$	−7.04885	+	15.4348i	−0.274376	+	0.600800i
$661$	8.38444	+	5.38835i	0.326117	+	0.209583i	0.693446	−	0.720508i	$-0.256091\pi$
$661$	8.38444	+	5.38835i	0.326117	+	0.209583i	−0.367329	+	0.930091i	$0.619728\pi$
$662$	−9.46702	−	65.8445i	−0.367946	−	2.55912i
$663$	0.648008	−	0.416450i	0.0251666	−	0.0161736i
$664$	15.9207	+	18.3735i	0.617844	+	0.713030i
$665$	22.4767	−	6.59975i	0.871609	−	0.255927i
$666$	28.3829			1.09981
$667$		0			0
$668$	3.79764			0.146935
$669$	−10.1371	+	2.97651i	−0.391922	+	0.115079i
$670$	12.9657	+	14.9632i	0.500910	+	0.578081i
$671$	−11.9495	+	7.67945i	−0.461304	+	0.296462i
$672$	6.11079	+	42.5015i	0.235729	+	1.63953i
$673$	−28.6504	−	18.4125i	−1.10439	−	0.709748i	−0.144326	−	0.989530i	$-0.546101\pi$
$673$	−28.6504	−	18.4125i	−1.10439	−	0.709748i	−0.960064	+	0.279782i	$0.909738\pi$
$674$	−4.53658	+	9.93373i	−0.174743	+	0.382633i
$675$	−1.81026	+	2.08915i	−0.0696770	+	0.0804115i
$676$	5.26803	−	36.6400i	0.202617	−	1.40923i
$677$	−10.3817	−	22.7327i	−0.399000	−	0.873689i	−0.997371	−	0.0724692i	$-0.976912\pi$
$677$	−10.3817	−	22.7327i	−0.399000	−	0.873689i	0.598370	−	0.801220i	$-0.295815\pi$
$678$	−7.90866	−	2.32219i	−0.303730	−	0.0891832i
$679$	9.84380	+	2.89040i	0.377771	+	0.110923i
$680$	1.51125	+	3.30918i	0.0579539	+	0.126901i
$681$	6.59241	−	45.8512i	0.252622	−	1.75702i
$682$	4.91825	−	5.67596i	0.188329	−	0.217344i
$683$	14.3219	−	31.3606i	0.548013	−	1.19998i	−0.409691	−	0.912225i	$-0.634363\pi$
$683$	14.3219	−	31.3606i	0.548013	−	1.19998i	0.957704	−	0.287756i	$-0.0929094\pi$
$684$	−63.6277	−	40.8910i	−2.43287	−	1.56351i
$685$	0.122749	+	0.853739i	0.00469000	+	0.0326197i
$686$	36.8164	−	23.6604i	1.40566	−	0.903360i
$687$	17.9808	+	20.7509i	0.686009	+	0.791697i
$688$	6.64655	−	1.95160i	0.253397	−	0.0744042i
$689$	1.92925			0.0734987
$690$		0			0
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	46.4088	−	13.6269i	1.76420	−	0.518015i
$693$	−9.85343	−	11.3715i	−0.374301	−	0.431966i
$694$	−12.5446	+	8.06191i	−0.476186	+	0.306026i
$695$	2.45581	+	17.0805i	0.0931543	+	0.647902i
$696$	−19.8492	−	12.7563i	−0.752381	−	0.483526i
$697$	−0.276373	+	0.605172i	−0.0104684	+	0.0229225i
$698$	−14.5632	+	16.8068i	−0.551224	+	0.636146i
$699$	1.48970	−	10.3611i	0.0563455	−	0.391892i
$700$	9.77140	+	21.3964i	0.369324	+	0.808707i
$701$	23.1489	+	6.79712i	0.874320	+	0.256724i	0.687952	−	0.725756i	$-0.258510\pi$
$701$	23.1489	+	6.79712i	0.874320	+	0.256724i	0.186369	+	0.982480i	$0.440328\pi$
$702$	0.330830	+	0.0971405i	0.0124864	+	0.00366633i
$703$	−12.8801	−	28.2035i	−0.485783	−	1.06372i
$704$	−3.47046	+	24.1376i	−0.130798	+	0.909720i
$705$	5.26770	−	6.07925i	0.198393	−	0.228958i
$706$	22.3995	−	49.0481i	0.843017	−	1.84595i
$707$	3.63348	+	2.33510i	0.136651	+	0.0878204i
$708$	−7.37426	−	51.2891i	−0.277142	−	1.92756i
$709$	5.91984	−	3.80445i	0.222324	−	0.142879i	−0.424738	−	0.905316i	$-0.639634\pi$
$709$	5.91984	−	3.80445i	0.222324	−	0.142879i	0.647062	+	0.762437i	$0.275997\pi$
$710$	−1.30306	−	1.50381i	−0.0489028	−	0.0564369i
$711$	18.0705	−	5.30599i	0.677698	−	0.198990i
$712$	−26.2175			−0.982544
$713$		0			0
$714$	−20.4995			−0.767175
$715$	−0.445641	+	0.130852i	−0.0166660	+	0.00489359i
$716$	2.67695	+	3.08937i	0.100042	+	0.115455i
$717$	47.6092	−	30.5966i	1.77800	−	1.14265i
$718$	−0.131343	−	0.913509i	−0.00490167	−	0.0340918i
$719$	22.3506	+	14.3639i	0.833538	+	0.535682i	0.886400	−	0.462919i	$-0.153198\pi$
$719$	22.3506	+	14.3639i	0.833538	+	0.535682i	−0.0528623	+	0.998602i	$0.516834\pi$
$720$	2.65022	−	5.80317i	0.0987678	−	0.216271i
$721$	−23.7944	+	27.4602i	−0.886149	+	1.02267i
$722$	−14.0344	+	97.6115i	−0.522307	+	3.63272i
$723$	−6.19048	−	13.5553i	−0.230226	−	0.504125i
$724$	44.2037	+	12.9794i	1.64282	+	0.482375i
$725$	16.5770	+	4.86745i	0.615655	+	0.180773i
$726$	16.8986	+	37.0029i	0.627167	+	1.37331i
$727$	0.743959	−	5.17435i	0.0275919	−	0.191906i	−0.971364	−	0.237598i	$-0.923640\pi$
$727$	0.743959	−	5.17435i	0.0275919	−	0.191906i	0.998956	+	0.0456916i	$0.0145492\pi$
$728$	0.575814	−	0.664524i	0.0213411	−	0.0246289i
$729$	−13.4472	+	29.4453i	−0.498044	+	1.09057i
$730$	14.7716	+	9.49314i	0.546722	+	0.351357i
$731$	0.988594	+	6.87582i	0.0365645	+	0.254311i
$732$	−44.8635	+	28.8320i	−1.65820	+	1.06566i
$733$	17.4775	+	20.1701i	0.645546	+	0.745000i	0.980345	−	0.197289i	$-0.0632139\pi$
$733$	17.4775	+	20.1701i	0.645546	+	0.745000i	−0.334799	+	0.942290i	$0.608668\pi$
$734$	−60.4033	+	17.7360i	−2.22953	+	0.654648i
$735$	−4.25719			−0.157029
$736$		0			0
$737$	−13.8924			−0.511734
$738$	−2.99103	+	0.878244i	−0.110101	+	0.0323286i
$739$	1.46659	+	1.69254i	0.0539495	+	0.0622610i	0.782083	−	0.623174i	$-0.214157\pi$
$739$	1.46659	+	1.69254i	0.0539495	+	0.0622610i	−0.728133	+	0.685435i	$0.759612\pi$
$740$	−11.5359	+	7.41369i	−0.424069	+	0.272533i
$741$	−0.561114	−	3.90263i	−0.0206130	−	0.143367i
$742$	−43.1923	−	27.7580i	−1.58564	−	1.01903i
$743$	7.53568	−	16.5008i	0.276457	−	0.605357i	−0.719568	−	0.694421i	$-0.755660\pi$
$743$	7.53568	−	16.5008i	0.276457	−	0.605357i	0.996026	+	0.0890642i	$0.0283876\pi$
$744$	5.53405	−	6.38663i	0.202888	−	0.234145i
$745$	−2.92796	+	20.3644i	−0.107272	+	0.746094i
$746$	13.1891	+	28.8801i	0.482887	+	1.05737i
$747$	41.0217	+	12.0451i	1.50090	+	0.440705i
$748$	−8.17220	−	2.39957i	−0.298805	−	0.0877371i
$749$	−1.95988	−	4.29153i	−0.0716123	−	0.156809i
$750$	8.25590	−	57.4210i	0.301463	−	2.09672i
$751$	−18.4846	+	21.3323i	−0.674511	+	0.778427i	−0.985075	−	0.172125i	$-0.944937\pi$
$751$	−18.4846	+	21.3323i	−0.674511	+	0.778427i	0.310564	+	0.950552i	$0.399482\pi$
$752$	1.67264	−	3.66256i	0.0609948	−	0.133560i
$753$	3.27854	+	2.10699i	0.119477	+	0.0767830i
$754$	−0.306680	−	2.13301i	−0.0111686	−	0.0776796i
$755$	−13.7201	+	8.81737i	−0.499326	+	0.320897i
$756$	−3.53408	−	4.07855i	−0.128533	−	0.148335i
$757$	−0.117071	+	0.0343752i	−0.00425502	+	0.00124939i	−0.283859	−	0.958866i	$-0.591615\pi$
$757$	−0.117071	+	0.0343752i	−0.00425502	+	0.00124939i	0.279604	+	0.960115i	$0.409797\pi$
$758$	−12.4000			−0.450389
$759$		0			0
$760$	18.6210			0.675453
$761$	25.6236	−	7.52378i	0.928856	−	0.272737i	0.217898	−	0.975971i	$-0.430080\pi$
$761$	25.6236	−	7.52378i	0.928856	−	0.272737i	0.710958	+	0.703235i	$0.248262\pi$
$762$	21.7410	+	25.0904i	0.787592	+	0.908930i
$763$	−31.1290	+	20.0054i	−1.12694	+	0.724243i
$764$	8.43139	+	58.6416i	0.305037	+	2.12158i
$765$	5.38195	+	3.45877i	0.194585	+	0.125052i
$766$	0.212065	−	0.464358i	0.00766222	−	0.0167779i
$767$	0.928805	−	1.07190i	0.0335372	−	0.0387040i
$768$	−1.67939	+	11.6804i	−0.0605998	+	0.421481i
$769$	−3.26144	−	7.14156i	−0.117611	−	0.257531i	0.841667	−	0.539997i	$-0.181575\pi$
$769$	−3.26144	−	7.14156i	−0.117611	−	0.257531i	−0.959277	+	0.282466i	$0.908847\pi$
$770$	11.8597	+	3.48234i	0.427396	+	0.125495i
$771$	66.2155	+	19.4426i	2.38469	+	0.700209i
$772$	17.3833	+	38.0642i	0.625640	+	1.36996i
$773$	4.87879	−	33.9327i	0.175478	−	1.22048i	−0.691592	−	0.722289i	$-0.743090\pi$
$773$	4.87879	−	33.9327i	0.175478	−	1.22048i	0.867070	−	0.498187i	$-0.166001\pi$
$774$	−21.3148	+	24.5986i	−0.766145	+	0.884179i
$775$	−2.57054	+	5.62871i	−0.0923367	+	0.202189i
$776$	6.86056	+	4.40901i	0.246280	+	0.158274i
$777$	−3.29573	−	22.9223i	−0.118234	−	0.822334i
$778$	−55.9288	+	35.9432i	−2.00514	+	1.28863i
$779$	2.23002	+	2.57358i	0.0798988	+	0.0922082i
$780$	−1.67313	+	0.491276i	−0.0599077	+	0.0175905i
$781$	1.39619			0.0499596
$782$		0			0
$783$	−3.96386			−0.141657
$784$	−2.04462	+	0.600354i	−0.0730221	+	0.0214412i
$785$	3.34308	+	3.85812i	0.119320	+	0.137702i
$786$	59.4928	−	38.2337i	2.12204	−	1.36375i
$787$	−2.27882	−	15.8495i	−0.0812312	−	0.564975i	−0.989271	−	0.146091i	$-0.953331\pi$
$787$	−2.27882	−	15.8495i	−0.0812312	−	0.564975i	0.908040	−	0.418884i	$-0.137578\pi$
$788$	28.0568	+	18.0310i	0.999482	+	0.642328i
$789$	13.5111	−	29.5852i	0.481008	−	1.05326i
$790$	−10.1315	+	11.6924i	−0.360462	+	0.415996i
$791$	−0.502555	+	3.49534i	−0.0178688	+	0.124280i
$792$	−4.96858	−	10.8797i	−0.176551	−	0.386592i
$793$	−1.40060	−	0.411254i	−0.0497369	−	0.0146041i
$794$	27.5823	+	8.09890i	0.978860	+	0.287419i
$795$	12.6766	+	27.7580i	0.449594	+	0.984474i
$796$	2.32622	−	16.1792i	0.0824508	−	0.573458i
$797$	−14.0950	+	16.2665i	−0.499272	+	0.576190i	−0.948319	−	0.317317i	$-0.897218\pi$
$797$	−14.0950	+	16.2665i	−0.499272	+	0.576190i	0.449047	+	0.893508i	$0.351763\pi$
$798$	−43.5886	+	95.4457i	−1.54302	+	3.37874i
$799$	3.39672	+	2.18294i	0.120167	+	0.0772268i
$800$	−3.55679	−	24.7380i	−0.125751	−	0.874620i
$801$	−38.7861	+	24.9263i	−1.37044	+	0.880729i
$802$	30.7744	+	35.5155i	1.08668	+	1.25410i
$803$	−11.8215	+	3.47111i	−0.417172	+	0.122493i
$804$	−52.1582			−1.83948
$805$		0			0
$806$	0.771816			0.0271860
$807$	−24.1097	+	7.07923i	−0.848700	+	0.249201i
$808$	2.24831	+	2.59469i	0.0790953	+	0.0912809i
$809$	20.2953	−	13.0430i	0.713546	−	0.458568i	−0.132840	−	0.991137i	$-0.542410\pi$
$809$	20.2953	−	13.0430i	0.713546	−	0.458568i	0.846386	+	0.532569i	$0.178773\pi$
$810$	−3.08238	−	21.4384i	−0.108304	−	0.753269i
$811$	12.0621	+	7.75187i	0.423559	+	0.272205i	0.735009	−	0.678058i	$-0.237178\pi$
$811$	12.0621	+	7.75187i	0.423559	+	0.272205i	−0.311450	+	0.950263i	$0.600814\pi$
$812$	−14.0114	+	30.6807i	−0.491704	+	1.07668i
$813$	7.26065	−	8.37923i	0.254642	−	0.293873i
$814$	2.32826	−	16.1934i	0.0816054	−	0.567578i
$815$	7.59656	+	16.6341i	0.266096	+	0.582669i
$816$	5.85162	+	1.71819i	0.204848	+	0.0601487i
$817$	34.1159	+	10.0173i	1.19356	+	0.350462i
$818$	−8.37515	−	18.3390i	−0.292830	−	0.641209i
$819$	0.220060	−	1.53055i	0.00768951	−	0.0534817i
$820$	0.986272	−	1.13822i	0.0344421	−	0.0397483i
$821$	5.90241	−	12.9245i	0.205995	−	0.451067i	−0.778232	−	0.627977i	$-0.783883\pi$
$821$	5.90241	−	12.9245i	0.205995	−	0.451067i	0.984227	+	0.176910i	$0.0566103\pi$
$822$	−3.25009	−	2.08870i	−0.113360	−	0.0728519i
$823$	−2.28033	−	15.8600i	−0.0794871	−	0.552845i	−0.990184	−	0.139770i	$-0.955364\pi$
$823$	−2.28033	−	15.8600i	−0.0794871	−	0.552845i	0.910697	−	0.413075i	$-0.135545\pi$
$824$	−24.2976	+	15.6151i	−0.846448	+	0.543979i
$825$	10.9225	+	12.6052i	0.380272	+	0.438858i
$826$	−36.2166	+	10.6341i	−1.26014	+	0.370009i
$827$	35.1240			1.22138			0.610690	−	0.791870i	$-0.290892\pi$
$827$	35.1240			1.22138			0.610690	+	0.791870i	$0.290892\pi$
$828$		0			0
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	−33.6983	+	9.89472i	−1.16969	+	0.343451i
$831$	−50.7002	−	58.5112i	−1.75877	−	2.02973i
$832$	−2.10822	+	1.35487i	−0.0730894	+	0.0469717i
$833$	−0.304112	−	2.11515i	−0.0105369	−	0.0732855i
$834$	−65.0237	−	41.7882i	−2.25159	−	1.44701i
$835$	−0.683025	+	1.49562i	−0.0236371	+	0.0517580i
$836$	−28.5491	+	32.9475i	−0.987393	+	1.13951i
$837$	0.202044	−	1.40525i	0.00698366	−	0.0485725i
$838$	−8.21511	−	17.9886i	−0.283786	−	0.621406i
$839$	−37.0476	−	10.8782i	−1.27903	−	0.375556i	−0.429483	−	0.903075i	$-0.641304\pi$
$839$	−37.0476	−	10.8782i	−1.27903	−	0.375556i	−0.849543	+	0.527519i	$0.823122\pi$
$840$	13.3447	+	3.91835i	0.460435	+	0.135196i
$841$	−1.75568	−	3.84441i	−0.0605408	−	0.132566i
$842$	−9.86994	+	68.6469i	−0.340140	+	2.36573i
$843$	−5.89113	+	6.79873i	−0.202901	+	0.234161i
$844$	−16.6899	+	36.5457i	−0.574489	+	1.25796i
$845$	13.4823	+	8.66458i	0.463807	+	0.298071i
$846$	2.69245	+	18.7264i	0.0925684	+	0.643827i
$847$	14.6612	−	9.42216i	0.503764	−	0.323749i
$848$	10.0027	+	11.5438i	0.343495	+	0.396415i
$849$	35.6434	−	10.4658i	1.22328	−	0.359187i
$850$	11.9317			0.409255
$851$		0			0
$852$	5.24190			0.179584
$853$	36.8727	−	10.8268i	1.26250	−	0.370703i	0.419074	−	0.907952i	$-0.362355\pi$
$853$	36.8727	−	10.8268i	1.26250	−	0.370703i	0.843424	+	0.537249i	$0.180537\pi$
$854$	25.4397	+	29.3590i	0.870529	+	1.00464i
$855$	27.5478	−	17.7039i	0.942114	−	0.605460i
$856$	−0.533713	−	3.71206i	−0.0182419	−	0.126876i
$857$	−42.8109	−	27.5129i	−1.46239	−	0.939824i	−0.998546	−	0.0539088i	$-0.982832\pi$
$857$	−42.8109	−	27.5129i	−1.46239	−	0.939824i	−0.463848	−	0.885915i	$-0.653532\pi$
$858$	0.864223	−	1.89238i	0.0295041	−	0.0646049i
$859$	−5.99008	+	6.91292i	−0.204379	+	0.235866i	−0.848681	−	0.528905i	$-0.822603\pi$
$859$	−5.99008	+	6.91292i	−0.204379	+	0.235866i	0.644302	+	0.764771i	$0.277148\pi$
$860$	2.23796	−	15.5654i	0.0763138	−	0.530774i
$861$	1.05659	+	2.31361i	0.0360085	+	0.0788476i
$862$	46.7323	+	13.7218i	1.59171	+	0.467368i
$863$	−11.8390	−	3.47626i	−0.403006	−	0.118333i	0.0739469	−	0.997262i	$-0.476440\pi$
$863$	−11.8390	−	3.47626i	−0.403006	−	0.118333i	−0.476953	+	0.878929i	$0.658259\pi$
$864$	2.38201	+	5.21586i	0.0810375	+	0.177447i
$865$	−2.98022	+	20.7279i	−0.101331	+	0.704770i
$866$	−18.3200	+	21.1424i	−0.622540	+	0.718449i
$867$	15.2088	−	33.3026i	0.516517	−	1.13101i
$868$	−10.1626	−	6.53111i	−0.344941	−	0.221680i
$869$	−1.54491	−	10.7451i	−0.0524076	−	0.364503i
$870$	28.6745	−	18.4280i	0.972155	−	0.624766i
$871$	−0.934929	−	1.07897i	−0.0316789	−	0.0365594i
$872$	−28.2222	+	8.28679i	−0.955725	+	0.280626i
$873$	14.3414			0.485381
$874$		0			0
$875$	−24.8534			−0.840199
$876$	−44.3831	+	13.0320i	−1.49956	+	0.440312i
$877$	−1.51089	−	1.74366i	−0.0510193	−	0.0588794i	0.729666	−	0.683803i	$-0.239675\pi$
$877$	−1.51089	−	1.74366i	−0.0510193	−	0.0588794i	−0.780686	+	0.624924i	$0.785130\pi$
$878$	34.1488	−	21.9461i	1.15247	−	0.740646i
$879$	7.69504	+	53.5202i	0.259547	+	1.80519i
$880$	−3.09351	−	1.98808i	−0.104282	−	0.0670181i
$881$	−14.7889	+	32.3832i	−0.498252	+	1.09102i	0.478782	+	0.877934i	$0.341078\pi$
$881$	−14.7889	+	32.3832i	−0.498252	+	1.09102i	−0.977034	+	0.213085i	$0.931649\pi$
$882$	6.55689	−	7.56705i	0.220782	−	0.254796i
$883$	−4.33698	+	30.1643i	−0.145951	+	1.01511i	0.776809	+	0.629736i	$0.216837\pi$
$883$	−4.33698	+	30.1643i	−0.145951	+	1.01511i	−0.922760	+	0.385375i	$0.874072\pi$
$884$	−0.363606	−	0.796187i	−0.0122294	−	0.0267787i
$885$	21.5254	+	6.32042i	0.723567	+	0.212458i
$886$	29.4165	+	8.63748i	0.988268	+	0.290182i
$887$	8.63696	+	18.9123i	0.290001	+	0.635013i	0.997420	−	0.0717808i	$-0.0228682\pi$
$887$	8.63696	+	18.9123i	0.290001	+	0.635013i	−0.707420	+	0.706794i	$0.750141\pi$
$888$	2.61977	−	18.2209i	0.0879138	−	0.611454i
$889$	9.31431	−	10.7493i	0.312392	−	0.360520i
$890$	15.7335	−	34.4517i	0.527390	−	1.15482i
$891$	12.7848	+	8.21626i	0.428305	+	0.275255i
$892$	1.70851	+	11.8829i	0.0572050	+	0.397869i
$893$	17.3863	−	11.1735i	0.581810	−	0.373906i
$894$	−60.3481	−	69.6454i	−2.01834	−	2.32929i
$895$	−1.69814	+	0.498620i	−0.0567627	+	0.0166670i
$896$	32.5243			1.08656
$897$		0			0
$898$	66.3122			2.21287
$899$	−8.51354	+	2.49980i	−0.283942	+	0.0833730i
$900$	21.5324	+	24.8497i	0.717747	+	0.828324i
$901$	−12.8858	+	8.28117i	−0.429287	+	0.275886i
$902$	0.255713	+	1.77853i	0.00851432	+	0.0592184i
$903$	22.3411	+	14.3578i	0.743467	+	0.477797i
$904$	−1.16608	+	2.55335i	−0.0387831	+	0.0849231i
$905$	−13.0619	+	15.0742i	−0.434192	+	0.501085i
$906$	10.3963	−	72.3081i	0.345395	−	2.40228i
$907$	−9.43483	−	20.6594i	−0.313278	−	0.685984i	0.685849	−	0.727744i	$-0.259431\pi$
$907$	−9.43483	−	20.6594i	−0.313278	−	0.685984i	−0.999128	+	0.0417596i	$0.986704\pi$
$908$	−50.5047	−	14.8295i	−1.67606	−	0.492135i
$909$	5.79305	+	1.70099i	0.192143	+	0.0564183i
$910$	0.527677	+	1.15545i	0.0174923	+	0.0383028i
$911$	−0.118697	+	0.825554i	−0.00393260	+	0.0273518i	−0.991693	−	0.128625i	$-0.958944\pi$
$911$	−0.118697	+	0.825554i	−0.00393260	+	0.0273518i	0.987761	+	0.155977i	$0.0498526\pi$
$912$	20.4423	−	23.5917i	0.676913	−	0.781199i
$913$	10.2371	−	22.4162i	0.338800	−	0.741868i
$914$	70.5325	+	45.3285i	2.33301	+	1.49933i
$915$	−3.28592	−	22.8541i	−0.108629	−	0.755532i
$916$	26.2471	−	16.8680i	0.867229	−	0.557334i
$917$	−19.8408	−	22.8975i	−0.655200	−	0.756141i
$918$	−2.62663	+	0.771248i	−0.0866917	+	0.0254550i
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$		0			0
$921$	−35.5510			−1.17145
$922$	−18.5221	+	5.43857i	−0.609992	+	0.179110i
$923$	0.0939604	+	0.108436i	0.00309275	+	0.00356922i
$924$	−27.3927	+	17.6042i	−0.901154	+	0.579136i
$925$	1.91828	+	13.3419i	0.0630727	+	0.438680i
$926$	−51.6037	−	33.1637i	−1.69580	−	1.08983i
$927$	−21.0997	+	46.2019i	−0.693006	+	1.51747i
$928$	23.4683	−	27.0839i	0.770385	−	0.889072i
$929$	2.52000	−	17.5270i	0.0826785	−	0.575042i	−0.905803	−	0.423699i	$-0.860731\pi$
$929$	2.52000	−	17.5270i	0.0826785	−	0.575042i	0.988481	−	0.151342i	$-0.0483596\pi$
$930$	5.07141	+	11.1048i	0.166298	+	0.364142i
$931$	−10.4948	−	3.08154i	−0.343952	−	0.100993i
$932$	−11.4126	−	3.35105i	−0.373833	−	0.109767i
$933$	−0.595270	−	1.30346i	−0.0194883	−	0.0426734i
$934$	5.44621	−	37.8792i	0.178205	−	1.23945i
$935$	2.41483	−	2.78686i	0.0789734	−	0.0911401i
$936$	0.510604	−	1.11807i	0.0166896	−	0.0365452i
$937$	−19.6231	−	12.6110i	−0.641059	−	0.411983i	0.179330	−	0.983789i	$-0.442607\pi$
$937$	−19.6231	−	12.6110i	−0.641059	−	0.411983i	−0.820389	+	0.571805i	$0.806243\pi$
$938$	5.40717	+	37.6077i	0.176550	+	1.22793i
$939$	44.6821	−	28.7154i	1.45814	−	0.937093i
$940$	−5.98572	−	6.90789i	−0.195233	−	0.225310i
$941$	−11.1443	+	3.27226i	−0.363293	+	0.106673i	−0.458284	−	0.888806i	$-0.651536\pi$
$941$	−11.1443	+	3.27226i	−0.363293	+	0.106673i	0.0949912	+	0.995478i	$0.469718\pi$
$942$	−22.8664			−0.745027
$943$		0			0
$944$	11.2294			0.365486
$945$	2.24187	−	0.658271i	0.0729279	−	0.0214136i
$946$	12.2859	+	14.1787i	0.399449	+	0.460988i
$947$	5.04579	−	3.24273i	0.163966	−	0.105375i	−0.456084	−	0.889937i	$-0.650748\pi$
$947$	5.04579	−	3.24273i	0.163966	−	0.105375i	0.620050	+	0.784562i	$0.287112\pi$
$948$	−5.80028	−	40.3418i	−0.188384	−	1.31024i
$949$	−1.06515	−	0.684529i	−0.0345762	−	0.0222207i
$950$	25.3707	−	55.5542i	0.823135	−	1.80241i
$951$	−14.5038	+	16.7382i	−0.470317	+	0.542775i
$952$	−0.993521	+	6.91009i	−0.0322002	+	0.223957i
$953$	−7.43870	−	16.2885i	−0.240963	−	0.527636i	0.750053	−	0.661378i	$-0.230028\pi$
$953$	−7.43870	−	16.2885i	−0.240963	−	0.527636i	−0.991016	+	0.133742i	$0.957301\pi$
$954$	−68.8636	−	20.2202i	−2.22954	−	0.654653i
$955$	−24.6111	−	7.22648i	−0.796397	−	0.233843i
$956$	−26.7142	−	58.4959i	−0.863998	−	1.89189i
$957$	−3.40368	+	23.6731i	−0.110025	+	0.765243i
$958$	36.7660	−	42.4302i	1.18786	−	1.37086i
$959$	−0.687578	+	1.50559i	−0.0222031	+	0.0486179i
$960$	−33.3464	−	21.4304i	−1.07625	−	0.691664i
$961$	3.95949	+	27.5389i	0.127726	+	0.888351i
$962$	1.41436	−	0.908954i	0.0456008	−	0.0293058i
$963$	−4.31881	−	4.98418i	−0.139172	−	0.160613i
$964$	−16.2472	+	4.77062i	−0.523288	+	0.153651i
$965$	−18.1172			−0.583213
$966$		0			0
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	13.2921	−	3.90292i	0.427225	−	0.125445i
$969$	20.4995	+	23.6577i	0.658539	+	0.759994i
$970$	−9.91088	+	6.36933i	−0.318219	+	0.204507i
$971$	−8.43728	−	58.6825i	−0.270765	−	1.88321i	−0.440545	−	0.897731i	$-0.645215\pi$
$971$	−8.43728	−	58.6825i	−0.270765	−	1.88321i	0.169780	−	0.985482i	$-0.445694\pi$
$972$	53.7396	+	34.5363i	1.72370	+	1.10775i
$973$	−13.7562	+	30.1219i	−0.441004	+	0.965664i
$974$	8.89081	−	10.2605i	0.284880	−	0.328769i
$975$	−0.243936	+	1.69661i	−0.00781219	+	0.0543350i
$976$	−4.80105	−	10.5128i	−0.153678	−	0.336508i
$977$	12.1299	+	3.56165i	0.388069	+	0.113947i	0.469946	−	0.882695i	$-0.344273\pi$
$977$	12.1299	+	3.56165i	0.388069	+	0.113947i	−0.0818770	+	0.996642i	$0.526091\pi$
$978$	−78.5916	−	23.0766i	−2.51308	−	0.737908i
$979$	11.0397	+	24.1735i	0.352830	+	0.772589i
$980$	−0.688444	+	4.78823i	−0.0219915	+	0.152954i
$981$	−33.8732	+	39.0917i	−1.08149	+	1.24810i
$982$	−29.8861	+	65.4415i	−0.953704	+	2.08832i
$983$	−49.0998	−	31.5545i	−1.56604	−	1.00643i	−0.980671	−	0.195666i	$-0.937313\pi$
$983$	−49.0998	−	31.5545i	−1.56604	−	1.00643i	−0.585369	−	0.810767i	$-0.699050\pi$
$984$	0.287730	+	2.00121i	0.00917251	+	0.0637962i
$985$	−12.1473	+	7.80657i	−0.387044	+	0.248738i
$986$	11.2041	+	12.9303i	0.356812	+	0.411783i
$987$	14.8110	−	4.34891i	0.471440	−	0.138427i
$988$	−4.48019			−0.142534
$989$		0			0
$990$	17.2784			0.549142
$991$	43.9362	−	12.9008i	1.39568	−	0.409809i	0.504481	−	0.863423i	$-0.331684\pi$
$991$	43.9362	−	12.9008i	1.39568	−	0.409809i	0.891198	+	0.453614i	$0.149866\pi$
$992$	8.40543	+	9.70039i	0.266873	+	0.307988i
$993$	−63.8270	+	41.0192i	−2.02549	+	1.30170i
$994$	−0.543421	−	3.77957i	−0.0172363	−	0.119881i
$995$	5.95345	+	3.82605i	0.188737	+	0.121294i
$996$	38.4347	−	84.1602i	1.21785	−	2.66672i
$997$	25.7701	−	29.7403i	0.816149	−	0.941886i	−0.183001	−	0.983113i	$-0.558581\pi$
$997$	25.7701	−	29.7403i	0.816149	−	0.941886i	0.999150	+	0.0412270i	$0.0131267\pi$
$998$	2.68877	−	18.7008i	0.0851116	−	0.591964i
$999$	−1.28469	−	2.81307i	−0.0406457	−	0.0890017i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.b.170.1		10
23.2	even	11		529.2.c.d.266.1		10
23.3	even	11		529.2.c.i.334.1		10
23.4	even	11		529.2.c.g.466.1		10
23.5	odd	22		529.2.c.c.501.1		10
23.6	even	11		529.2.c.i.255.1		10
23.7	odd	22		529.2.c.f.487.1		10
23.8	even	11		529.2.a.i.1.5		5
23.9	even	11		529.2.c.d.177.1		10
23.10	odd	22		529.2.c.a.118.1		10
23.11	odd	22		529.2.c.a.399.1		10
23.12	even	11		23.2.c.a.8.1	yes	10
23.13	even	11		23.2.c.a.3.1	✓	10
23.14	odd	22		529.2.c.e.177.1		10
23.15	odd	22		529.2.a.j.1.5		5
23.16	even	11		529.2.c.g.487.1		10
23.17	odd	22		529.2.c.h.255.1		10
23.18	even	11	inner	529.2.c.b.501.1		10
23.19	odd	22		529.2.c.f.466.1		10
23.20	odd	22		529.2.c.h.334.1		10
23.21	odd	22		529.2.c.e.266.1		10
23.22	odd	2		529.2.c.c.170.1		10
69.8	odd	22		4761.2.a.bo.1.1		5
69.35	odd	22		207.2.i.c.100.1		10
69.38	even	22		4761.2.a.bn.1.1		5
69.59	odd	22		207.2.i.c.118.1		10
92.15	even	22		8464.2.a.bt.1.5		5
92.31	odd	22		8464.2.a.bs.1.5		5
92.35	odd	22		368.2.m.c.353.1		10
92.59	odd	22		368.2.m.c.49.1		10
115.12	odd	44		575.2.p.b.399.1		20
115.13	odd	44		575.2.p.b.49.1		20
115.58	odd	44		575.2.p.b.399.2		20
115.59	even	22		575.2.k.b.26.1		10
115.82	odd	44		575.2.p.b.49.2		20
115.104	even	22		575.2.k.b.376.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.13	even	11
23.2.c.a.8.1	yes	10	23.12	even	11
207.2.i.c.100.1		10	69.35	odd	22
207.2.i.c.118.1		10	69.59	odd	22
368.2.m.c.49.1		10	92.59	odd	22
368.2.m.c.353.1		10	92.35	odd	22
529.2.a.i.1.5		5	23.8	even	11
529.2.a.j.1.5		5	23.15	odd	22
529.2.c.a.118.1		10	23.10	odd	22
529.2.c.a.399.1		10	23.11	odd	22
529.2.c.b.170.1		10	1.1	even	1	trivial
529.2.c.b.501.1		10	23.18	even	11	inner
529.2.c.c.170.1		10	23.22	odd	2
529.2.c.c.501.1		10	23.5	odd	22
529.2.c.d.177.1		10	23.9	even	11
529.2.c.d.266.1		10	23.2	even	11
529.2.c.e.177.1		10	23.14	odd	22
529.2.c.e.266.1		10	23.21	odd	22
529.2.c.f.466.1		10	23.19	odd	22
529.2.c.f.487.1		10	23.7	odd	22
529.2.c.g.466.1		10	23.4	even	11
529.2.c.g.487.1		10	23.16	even	11
529.2.c.h.255.1		10	23.17	odd	22
529.2.c.h.334.1		10	23.20	odd	22
529.2.c.i.255.1		10	23.6	even	11
529.2.c.i.334.1		10	23.3	even	11
575.2.k.b.26.1		10	115.59	even	22
575.2.k.b.376.1		10	115.104	even	22
575.2.p.b.49.1		20	115.13	odd	44
575.2.p.b.49.2		20	115.82	odd	44
575.2.p.b.399.1		20	115.12	odd	44
575.2.p.b.399.2		20	115.58	odd	44
4761.2.a.bn.1.1		5	69.38	even	22
4761.2.a.bo.1.1		5	69.8	odd	22
8464.2.a.bs.1.5		5	92.31	odd	22
8464.2.a.bt.1.5		5	92.15	even	22

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	529.2.c.b.170.1

Level	$529$
Weight	$2$
Character	529.170
Analytic conductor	$4.224$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$