LMFDB - Embedded newform 529.2.c.i.334.1

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 = [10,4,4,8,8,-5,-5] 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			334.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	529.334
Dual form			529.2.c.i.255.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85380 - 1.19136i) q^{2} +(0.357685 - 2.48775i) q^{3} +(1.18639 - 2.59784i) q^{4} +(1.18639 - 0.348356i) q^{5} +(-2.30075 - 5.03793i) q^{6} +(1.55384 + 1.79323i) q^{7} +(-0.268423 - 1.86692i) q^{8} +(-3.18251 - 0.934468i) q^{9} +(1.78431 - 2.05921i) q^{10} +(-1.60835 - 1.03362i) q^{11} +(-6.03843 - 3.88066i) q^{12} +(-0.128663 + 0.148485i) q^{13} +(5.01691 + 1.47310i) q^{14} +(-0.442270 - 3.07606i) q^{15} +(1.01867 + 1.17561i) q^{16} +(-0.648008 - 1.41894i) q^{17} +(-7.01302 + 2.05921i) q^{18} +(-3.31686 + 7.26292i) q^{19} +(0.502555 - 3.49534i) q^{20} +(5.01691 - 3.22417i) q^{21} -4.21297 q^{22} -4.74046 q^{24} +(-2.92009 + 1.87663i) q^{25} +(-0.0616156 + 0.428546i) q^{26} +(-0.330830 + 0.724417i) q^{27} +(6.50199 - 1.90916i) q^{28} +(2.06765 + 4.52753i) q^{29} +(-4.48458 - 5.17549i) q^{30} +(-0.253702 - 1.76453i) q^{31} +(6.90843 + 2.02850i) q^{32} +(-3.14668 + 3.63146i) q^{33} +(-2.89175 - 1.85842i) q^{34} +(2.46815 + 1.58619i) q^{35} +(-6.20330 + 7.15899i) q^{36} +(-3.72593 - 1.09403i) q^{37} +(2.50398 + 17.4156i) q^{38} +(0.323373 + 0.373193i) q^{39} +(-0.968810 - 2.12140i) q^{40} +(-0.409220 + 0.120158i) q^{41} +(5.45918 - 11.9539i) q^{42} +(-0.633752 + 4.40784i) q^{43} +(-4.59331 + 2.95194i) q^{44} -4.10123 q^{45} -2.58842 q^{47} +(3.28899 - 2.11371i) q^{48} +(0.194955 - 1.35595i) q^{49} +(-3.17752 + 6.95779i) q^{50} +(-3.76176 + 1.10455i) q^{51} +(0.233095 + 0.510407i) q^{52} +(-6.43033 - 7.42100i) q^{53} +(0.249752 + 1.73706i) q^{54} +(-2.26820 - 0.666003i) q^{55} +(2.93074 - 3.38226i) q^{56} +(16.8820 + 10.8494i) q^{57} +(9.22694 + 5.92980i) q^{58} +(4.72738 - 5.45568i) q^{59} +(-8.51580 - 2.50047i) q^{60} +(-1.05735 - 7.35404i) q^{61} +(-2.57252 - 2.96884i) q^{62} +(-3.26940 - 7.15899i) q^{63} +(12.2384 - 3.59353i) q^{64} +(-0.100919 + 0.220982i) q^{65} +(-1.50692 + 10.4808i) q^{66} +(6.11297 - 3.92857i) q^{67} -4.45497 q^{68} +6.46519 q^{70} +(-0.614354 + 0.394821i) q^{71} +(-0.890323 + 6.19233i) q^{72} +(-2.67708 + 5.86198i) q^{73} +(-8.21051 + 2.41082i) q^{74} +(3.62412 + 7.93572i) q^{75} +(14.9328 + 17.2333i) q^{76} +(-0.645596 - 4.49022i) q^{77} +(1.04408 + 0.306569i) q^{78} +(3.71835 - 4.29121i) q^{79} +(1.61808 + 1.03987i) q^{80} +(-6.68713 - 4.29756i) q^{81} +(-0.615460 + 0.710278i) q^{82} +(12.3676 + 3.63146i) q^{83} +(-2.42385 - 16.8582i) q^{84} +(-1.26309 - 1.45768i) q^{85} +(4.07650 + 8.92629i) q^{86} +(12.0029 - 3.52438i) q^{87} +(-1.49798 + 3.28011i) q^{88} +(1.97821 - 13.7587i) q^{89} +(-7.60286 + 4.88606i) q^{90} -0.466190 q^{91} -4.48047 q^{93} +(-4.79841 + 3.08375i) q^{94} +(-1.40502 + 9.77212i) q^{95} +(7.51745 - 16.4609i) q^{96} +(-4.14863 + 1.21815i) q^{97} +(-1.25402 - 2.74591i) q^{98} +(4.15269 + 4.79245i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 4 q^{2} + 4 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} - 5 q^{7} - 7 q^{8} - 13 q^{9} - 10 q^{10} + 7 q^{11} - 21 q^{12} - 3 q^{13} + 9 q^{14} - 10 q^{15} - 10 q^{16} + 12 q^{17} - 14 q^{18} + 2 q^{19}+ \cdots + 14 q^{99}+O(q^{100})$ 10 * q + 4 * q^2 + 4 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 - 5 * q^7 - 7 * q^8 - 13 * q^9 - 10 * q^10 + 7 * q^11 - 21 * q^12 - 3 * q^13 + 9 * q^14 - 10 * q^15 - 10 * q^16 + 12 * q^17 - 14 * q^18 + 2 * q^19 + 2 * q^20 + 9 * q^21 - 6 * q^22 - 38 * q^24 - 15 * q^25 - 10 * q^26 + 7 * q^27 + 18 * q^28 + 3 * q^29 - 26 * q^30 + 10 * q^31 + 10 * q^32 + 5 * q^33 - 26 * q^34 - 4 * q^35 - 17 * q^36 + 3 * q^37 + 14 * q^38 - 10 * q^39 + q^40 - 4 * q^41 + 19 * q^42 + 21 * q^44 - 6 * q^45 - 18 * q^47 - 4 * q^48 + 4 * q^49 + 5 * q^50 - 15 * q^51 + 2 * q^52 + 18 * q^53 + 27 * q^54 - 12 * q^55 + 31 * q^56 + 36 * q^57 + 43 * q^58 + q^59 - 41 * q^60 - 30 * q^61 + 15 * q^62 + q^63 + 13 * q^64 - 42 * q^65 + 24 * q^66 + q^67 - 30 * q^68 + 38 * q^70 + 8 * q^71 - 14 * q^72 - 25 * q^73 - 23 * q^74 + 5 * q^75 + 50 * q^76 - 31 * q^77 + 7 * q^78 + 18 * q^79 - 8 * q^80 - 11 * q^81 + 5 * q^82 + 29 * q^83 + 16 * q^84 - 8 * q^85 - 11 * q^86 + 54 * q^87 + 5 * q^88 - 63 * q^89 - 42 * q^90 - 4 * q^91 + 4 * q^93 + 17 * q^94 + 28 * q^95 - 7 * q^96 - 12 * q^97 - 27 * q^98 + 14 * q^99

Character values

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

$n$	$5$
$\chi(n)$	$e\left(\frac{10}{11}\right)$

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

)

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

$2$	1.85380	−	1.19136i	1.31083	−	0.842422i	0.316487	−	0.948597i	$-0.397497\pi$
$2$	1.85380	−	1.19136i	1.31083	−	0.842422i	0.994347	+	0.106175i	$0.0338604\pi$
$3$	0.357685	−	2.48775i	0.206510	−	1.43631i	−0.577923	−	0.816092i	$-0.696136\pi$
$3$	0.357685	−	2.48775i	0.206510	−	1.43631i	0.784432	−	0.620214i	$-0.212954\pi$
$4$	1.18639	−	2.59784i	0.593196	−	1.29892i
$5$	1.18639	−	0.348356i	0.530571	−	0.155790i	−0.00546462	−	0.999985i	$-0.501739\pi$
$5$	1.18639	−	0.348356i	0.530571	−	0.155790i	0.536036	+	0.844195i	$0.319921\pi$
$6$	−2.30075	−	5.03793i	−0.939276	−	2.05673i
$7$	1.55384	+	1.79323i	0.587298	+	0.677778i	0.969157	−	0.246442i	$-0.0792616\pi$
$7$	1.55384	+	1.79323i	0.587298	+	0.677778i	−0.381860	+	0.924220i	$0.624716\pi$
$8$	−0.268423	−	1.86692i	−0.0949019	−	0.660058i
$9$	−3.18251	−	0.934468i	−1.06084	−	0.311489i
$10$	1.78431	−	2.05921i	0.564250	−	0.651179i
$11$	−1.60835	−	1.03362i	−0.484934	−	0.311648i	0.275231	−	0.961378i	$-0.411246\pi$
$11$	−1.60835	−	1.03362i	−0.484934	−	0.311648i	−0.760165	+	0.649730i	$0.774882\pi$
$12$	−6.03843	−	3.88066i	−1.74314	−	1.12025i
$13$	−0.128663	+	0.148485i	−0.0356847	+	0.0411823i	−0.773311	−	0.634026i	$-0.781401\pi$
$13$	−0.128663	+	0.148485i	−0.0356847	+	0.0411823i	0.737627	+	0.675209i	$0.235946\pi$
$14$	5.01691	+	1.47310i	1.34083	+	0.393702i
$15$	−0.442270	−	3.07606i	−0.114194	−	0.794234i
$16$	1.01867	+	1.17561i	0.254668	+	0.293902i
$17$	−0.648008	−	1.41894i	−0.157165	−	0.344143i	0.814626	−	0.579986i	$-0.196942\pi$
$17$	−0.648008	−	1.41894i	−0.157165	−	0.344143i	−0.971791	+	0.235843i	$0.924215\pi$
$18$	−7.01302	+	2.05921i	−1.65299	+	0.485360i
$19$	−3.31686	+	7.26292i	−0.760941	+	1.66623i	−0.0152967	+	0.999883i	$0.504869\pi$
$19$	−3.31686	+	7.26292i	−0.760941	+	1.66623i	−0.745644	+	0.666345i	$0.767858\pi$
$20$	0.502555	−	3.49534i	0.112375	−	0.781583i
$21$	5.01691	−	3.22417i	1.09478	−	0.703572i
$22$	−4.21297			−0.898208
$23$		0			0
$23$		0			0
$24$	−4.74046			−0.967643
$25$	−2.92009	+	1.87663i	−0.584018	+	0.375326i
$26$	−0.0616156	+	0.428546i	−0.0120838	+	0.0840447i
$27$	−0.330830	+	0.724417i	−0.0636683	+	0.139414i
$28$	6.50199	−	1.90916i	1.22876	−	0.360797i
$29$	2.06765	+	4.52753i	0.383953	+	0.840740i	0.998648	+	0.0519755i	$0.0165518\pi$
$29$	2.06765	+	4.52753i	0.383953	+	0.840740i	−0.614695	+	0.788765i	$0.710721\pi$
$30$	−4.48458	−	5.17549i	−0.818769	−	0.944910i
$31$	−0.253702	−	1.76453i	−0.0455662	−	0.316920i	−0.999838	−	0.0179805i	$-0.994276\pi$
$31$	−0.253702	−	1.76453i	−0.0455662	−	0.316920i	0.954272	−	0.298939i	$-0.0966328\pi$
$32$	6.90843	+	2.02850i	1.22125	+	0.358591i
$33$	−3.14668	+	3.63146i	−0.547766	+	0.632156i
$34$	−2.89175	−	1.85842i	−0.495931	−	0.318716i
$35$	2.46815	+	1.58619i	0.417194	+	0.268114i
$36$	−6.20330	+	7.15899i	−1.03388	+	1.19317i
$37$	−3.72593	−	1.09403i	−0.612539	−	0.179858i	−0.0392749	−	0.999228i	$-0.512505\pi$
$37$	−3.72593	−	1.09403i	−0.612539	−	0.179858i	−0.573264	+	0.819371i	$0.694323\pi$
$38$	2.50398	+	17.4156i	0.406200	+	2.82518i
$39$	0.323373	+	0.373193i	0.0517812	+	0.0597587i
$40$	−0.968810	−	2.12140i	−0.153182	−	0.335423i
$41$	−0.409220	+	0.120158i	−0.0639094	+	0.0187655i	−0.313531	−	0.949578i	$-0.601512\pi$
$41$	−0.409220	+	0.120158i	−0.0639094	+	0.0187655i	0.249622	+	0.968343i	$0.419694\pi$
$42$	5.45918	−	11.9539i	0.842369	−	1.84453i
$43$	−0.633752	+	4.40784i	−0.0966463	+	0.672190i	0.882691	+	0.469954i	$0.155730\pi$
$43$	−0.633752	+	4.40784i	−0.0966463	+	0.672190i	−0.979337	+	0.202235i	$0.935179\pi$
$44$	−4.59331	+	2.95194i	−0.692467	+	0.445022i
$45$	−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	$0.560453\pi$
$48$	3.28899	−	2.11371i	0.474725	−	0.305087i
$49$	0.194955	−	1.35595i	0.0278508	−	0.193706i
$50$	−3.17752	+	6.95779i	−0.449369	+	0.983980i
$51$	−3.76176	+	1.10455i	−0.526751	+	0.154668i
$52$	0.233095	+	0.510407i	0.0323245	+	0.0707807i
$53$	−6.43033	−	7.42100i	−0.883274	−	1.01935i	−0.999658	−	0.0261486i	$-0.991676\pi$
$53$	−6.43033	−	7.42100i	−0.883274	−	1.01935i	0.116384	−	0.993204i	$-0.462870\pi$
$54$	0.249752	+	1.73706i	0.0339869	+	0.236384i
$55$	−2.26820	−	0.666003i	−0.305844	−	0.0898038i
$56$	2.93074	−	3.38226i	0.391637	−	0.451973i
$57$	16.8820	+	10.8494i	2.23607	+	1.43704i
$58$	9.22694	+	5.92980i	1.21156	+	0.778620i
$59$	4.72738	−	5.45568i	0.615452	−	0.710269i	−0.359385	−	0.933189i	$-0.617013\pi$
$59$	4.72738	−	5.45568i	0.615452	−	0.710269i	0.974837	+	0.222920i	$0.0715589\pi$
$60$	−8.51580	−	2.50047i	−1.09939	−	0.322809i
$61$	−1.05735	−	7.35404i	−0.135380	−	0.941588i	−0.938379	−	0.345608i	$-0.887673\pi$
$61$	−1.05735	−	7.35404i	−0.135380	−	0.941588i	0.802999	−	0.595980i	$-0.203236\pi$
$62$	−2.57252	−	2.96884i	−0.326710	−	0.377043i
$63$	−3.26940	−	7.15899i	−0.411906	−	0.901948i
$64$	12.2384	−	3.59353i	1.52981	−	0.449192i
$65$	−0.100919	+	0.220982i	−0.0125175	+	0.0274094i
$66$	−1.50692	+	10.4808i	−0.185489	+	1.29010i
$67$	6.11297	−	3.92857i	0.746818	−	0.479951i	−0.111054	−	0.993814i	$-0.535423\pi$
$67$	6.11297	−	3.92857i	0.746818	−	0.479951i	0.857872	+	0.513864i	$0.171786\pi$
$68$	−4.45497			−0.540244
$69$		0			0
$70$	6.46519			0.772738
$71$	−0.614354	+	0.394821i	−0.0729104	+	0.0468567i	−0.576588	−	0.817035i	$-0.695616\pi$
$71$	−0.614354	+	0.394821i	−0.0729104	+	0.0468567i	0.503678	+	0.863892i	$0.331980\pi$
$72$	−0.890323	+	6.19233i	−0.104926	+	0.729774i
$73$	−2.67708	+	5.86198i	−0.313328	+	0.686093i	−0.999130	−	0.0416952i	$-0.986724\pi$
$73$	−2.67708	+	5.86198i	−0.313328	+	0.686093i	0.685802	+	0.727788i	$0.259451\pi$
$74$	−8.21051	+	2.41082i	−0.954453	+	0.280253i
$75$	3.62412	+	7.93572i	0.418477	+	0.916338i
$76$	14.9328	+	17.2333i	1.71291	+	1.97680i
$77$	−0.645596	−	4.49022i	−0.0735725	−	0.511708i
$78$	1.04408	+	0.306569i	0.118219	+	0.0347121i
$79$	3.71835	−	4.29121i	0.418347	−	0.482799i	−0.506985	−	0.861955i	$-0.669240\pi$
$79$	3.71835	−	4.29121i	0.418347	−	0.482799i	0.925333	+	0.379156i	$0.123786\pi$
$80$	1.61808	+	1.03987i	0.180906	+	0.116261i
$81$	−6.68713	−	4.29756i	−0.743015	−	0.477506i
$82$	−0.615460	+	0.710278i	−0.0679662	+	0.0784371i
$83$	12.3676	+	3.63146i	1.35752	+	0.398604i	0.877889	−	0.478865i	$-0.158952\pi$
$83$	12.3676	+	3.63146i	1.35752	+	0.398604i	0.479633	+	0.877469i	$0.340770\pi$
$84$	−2.42385	−	16.8582i	−0.264464	−	1.83939i
$85$	−1.26309	−	1.45768i	−0.137001	−	0.158108i
$86$	4.07650	+	8.92629i	0.439580	+	0.962546i
$87$	12.0029	−	3.52438i	1.28685	−	0.377853i
$88$	−1.49798	+	3.28011i	−0.159685	+	0.349661i
$89$	1.97821	−	13.7587i	0.209690	−	1.45842i	−0.564481	−	0.825446i	$-0.690923\pi$
$89$	1.97821	−	13.7587i	0.209690	−	1.45842i	0.774170	−	0.632977i	$-0.218167\pi$
$90$	−7.60286	+	4.88606i	−0.801412	+	0.515036i
$91$	−0.466190			−0.0488700
$92$		0			0
$93$	−4.48047			−0.464603
$94$	−4.79841	+	3.08375i	−0.494918	+	0.318064i
$95$	−1.40502	+	9.77212i	−0.144152	+	1.00260i
$96$	7.51745	−	16.4609i	0.767247	−	1.68004i
$97$	−4.14863	+	1.21815i	−0.421229	+	0.123684i	−0.485476	−	0.874250i	$-0.661354\pi$
$97$	−4.14863	+	1.21815i	−0.421229	+	0.123684i	0.0642468	+	0.997934i	$0.479536\pi$
$98$	−1.25402	−	2.74591i	−0.126675	−	0.277379i
$99$	4.15269	+	4.79245i	0.417361	+	0.481660i
$100$	1.41080	+	9.81234i	0.141080	+	0.981234i
$101$	1.74654	+	0.512831i	0.173788	+	0.0510286i	0.367469	−	0.930036i	$-0.380225\pi$
$101$	1.74654	+	0.512831i	0.173788	+	0.0510286i	−0.193681	+	0.981065i	$0.562043\pi$
$102$	−5.65762	+	6.52924i	−0.560188	+	0.646491i
$103$	−12.8823	−	8.27896i	−1.26933	−	0.815750i	−0.279799	−	0.960059i	$-0.590268\pi$
$103$	−12.8823	−	8.27896i	−1.26933	−	0.815750i	−0.989533	+	0.144309i	$0.953904\pi$
$104$	0.311746	+	0.200347i	0.0305692	+	0.0196457i
$105$	4.82886	−	5.57281i	0.471249	−	0.543850i
$106$	−20.7617	−	6.09618i	−2.01655	−	0.592113i
$107$	−0.282969	−	1.96809i	−0.0273556	−	0.190262i	0.971562	−	0.236787i	$-0.0760944\pi$
$107$	−0.282969	−	1.96809i	−0.0273556	−	0.190262i	−0.998917	+	0.0465248i	$0.985185\pi$
$108$	1.48942	+	1.71889i	0.143320	+	0.165400i
$109$	6.47831	+	14.1855i	0.620509	+	1.35873i	0.915148	+	0.403117i	$0.132073\pi$
$109$	6.47831	+	14.1855i	0.620509	+	1.35873i	−0.294639	+	0.955609i	$0.595199\pi$
$110$	−4.99824	+	1.46761i	−0.476563	+	0.139932i
$111$	−4.05439	+	8.87788i	−0.384826	+	0.842651i
$112$	−0.525284	+	3.65343i	−0.0496346	+	0.345216i
$113$	−1.25199	+	0.804606i	−0.117777	+	0.0756910i	−0.598203	−	0.801344i	$-0.704118\pi$
$113$	−1.25199	+	0.804606i	−0.117777	+	0.0756910i	0.480426	+	0.877035i	$0.340482\pi$
$114$	44.2213			4.14171
$115$		0			0
$116$	14.2148			1.31981
$117$	0.548225	−	0.352323i	0.0506834	−	0.0325723i
$118$	2.26390	−	15.7458i	0.208409	−	1.44952i
$119$	1.53758	−	3.36684i	0.140950	−	0.308638i
$120$	−5.62405	+	1.65137i	−0.513403	+	0.150749i
$121$	−3.05116	−	6.68111i	−0.277378	−	0.607374i
$122$	−10.7215	−	12.3732i	−0.970675	−	1.12022i
$123$	0.152551	+	1.06102i	0.0137551	+	0.0956687i
$124$	−4.88496	−	1.43435i	−0.438683	−	0.128809i
$125$	−6.85925	+	7.91599i	−0.613510	+	0.708028i
$126$	−14.5898	−	9.37628i	−1.29976	−	0.835306i
$127$	5.04278	+	3.24080i	0.447475	+	0.287574i	0.744907	−	0.667168i	$-0.232494\pi$
$127$	5.04278	+	3.24080i	0.447475	+	0.287574i	−0.297432	+	0.954743i	$0.596130\pi$
$128$	8.97631	−	10.3592i	0.793401	−	0.915634i
$129$	10.7389	+	3.15324i	0.945512	+	0.277627i
$130$	0.0761864	+	0.529888i	0.00668199	+	0.0464742i
$131$	8.36180	+	9.65003i	0.730574	+	0.843127i	0.992536	−	0.121951i	$-0.0389150\pi$
$131$	8.36180	+	9.65003i	0.730574	+	0.843127i	−0.261962	+	0.965078i	$0.584370\pi$
$132$	5.70075	+	12.4829i	0.496186	+	1.08650i
$133$	−18.1780	+	5.33754i	−1.57623	+	0.462823i
$134$	6.65186	−	14.5655i	0.574634	−	1.25827i
$135$	−0.140139	+	0.974690i	−0.0120613	+	0.0838879i
$136$	−2.47511	+	1.59066i	−0.212239	+	0.136398i
$137$	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	$0.298393\pi$
$140$	7.04885	−	4.53002i	0.595737	−	0.382857i
$141$	−0.925839	+	6.43935i	−0.0779697	+	0.542291i
$142$	−0.668513	+	1.46384i	−0.0561003	+	0.122843i
$143$	0.360412	−	0.105826i	0.0301391	−	0.00884965i
$144$	−2.14336	−	4.69330i	−0.178613	−	0.391108i
$145$	4.03024	+	4.65114i	0.334693	+	0.386256i
$146$	2.02099	+	14.0563i	0.167258	+	1.16331i
$147$	−3.30353	−	0.970003i	−0.272470	−	0.0800045i
$148$	−7.26253	+	8.38141i	−0.596976	+	0.688947i
$149$	−13.9976	−	8.99574i	−1.14673	−	0.736960i	−0.177746	−	0.984076i	$-0.556881\pi$
$149$	−13.9976	−	8.99574i	−1.14673	−	0.736960i	−0.968986	+	0.247117i	$0.920517\pi$
$150$	16.1727	+	10.3936i	1.32050	+	0.848632i
$151$	−8.63759	+	9.96831i	−0.702917	+	0.811210i	−0.989144	−	0.146952i	$-0.953054\pi$
$151$	−8.63759	+	9.96831i	−0.702917	+	0.811210i	0.286226	+	0.958162i	$0.407599\pi$
$152$	14.4496	+	4.24280i	1.17202	+	0.344136i
$153$	0.736336	+	5.12133i	0.0595292	+	0.414035i
$154$	−6.54630	−	7.55483i	−0.527516	−	0.608786i
$155$	−0.915677	−	2.00505i	−0.0735489	−	0.161050i
$156$	1.35314	−	0.397318i	0.108338	−	0.0318109i
$157$	1.71511	−	3.75557i	0.136881	−	0.299727i	−0.828761	−	0.559602i	$-0.810954\pi$
$157$	1.71511	−	3.75557i	0.136881	−	0.299727i	0.965642	+	0.259875i	$0.0836812\pi$
$158$	1.78069	−	12.3850i	0.141664	−	0.985294i
$159$	−20.7617	+	13.3427i	−1.64651	+	1.05815i
$160$	8.90276			0.703825
$161$		0			0
$162$	−17.5166			−1.37623
$163$	−12.4416	+	7.99570i	−0.974498	+	0.626272i	−0.927974	−	0.372645i	$-0.878451\pi$
$163$	−12.4416	+	7.99570i	−0.974498	+	0.626272i	−0.0465243	+	0.998917i	$0.514814\pi$
$164$	−0.173345	+	1.20564i	−0.0135360	+	0.0941447i
$165$	−2.46815	+	5.40450i	−0.192145	+	0.420740i
$166$	27.2535	−	8.00234i	2.11528	−	0.621102i
$167$	0.552396	+	1.20958i	0.0427457	+	0.0935999i	0.929800	−	0.368065i	$-0.119980\pi$
$167$	0.552396	+	1.20958i	0.0427457	+	0.0935999i	−0.887054	+	0.461665i	$0.847252\pi$
$168$	−7.36594	−	8.50075i	−0.568295	−	0.655847i
$169$	1.84460	+	12.8295i	0.141892	+	0.986882i
$170$	−4.07814	−	1.19745i	−0.312779	−	0.0918403i
$171$	17.3429	−	20.0148i	1.32625	−	1.53057i
$172$	10.6990	+	6.87582i	0.815790	+	0.524276i
$173$	−14.2475	−	9.15632i	−1.08322	−	0.696142i	−0.127920	−	0.991785i	$-0.540830\pi$
$173$	−14.2475	−	9.15632i	−1.08322	−	0.696142i	−0.955299	+	0.295642i	$0.904466\pi$
$174$	18.0522	−	20.8334i	1.36854	−	1.57937i
$175$	−7.90260	−	2.32041i	−0.597380	−	0.175407i
$176$	−0.423241	−	2.94371i	−0.0319030	−	0.221890i
$177$	−11.8815	−	13.7120i	−0.893067	−	1.03065i
$178$	−12.7245	−	27.8627i	−0.953740	−	2.08840i
$179$	1.37337	−	0.403258i	0.102650	−	0.0301409i	−0.230004	−	0.973190i	$-0.573874\pi$
$179$	1.37337	−	0.403258i	0.102650	−	0.0301409i	0.332654	+	0.943049i	$0.392056\pi$
$180$	−4.86567	+	10.6543i	−0.362666	+	0.794127i
$181$	2.29573	−	15.9672i	0.170640	−	1.18683i	−0.706895	−	0.707318i	$-0.749905\pi$
$181$	2.29573	−	15.9672i	0.170640	−	1.18683i	0.877536	−	0.479512i	$-0.159186\pi$
$182$	−0.864223	+	0.555402i	−0.0640605	+	0.0411692i
$183$	−18.6732			−1.38037
$184$		0			0
$185$	−4.80153			−0.353015
$186$	−8.30590	+	5.33788i	−0.609018	+	0.391392i
$187$	−0.424425	+	2.95194i	−0.0310370	+	0.215867i
$188$	−3.07088	+	6.72429i	−0.223967	+	0.490419i
$189$	−1.81311	+	0.532376i	−0.131884	+	0.0387246i
$190$	9.03754	+	19.7894i	0.655652	+	1.43568i
$191$	13.5848	+	15.6776i	0.982958	+	1.13439i	0.990924	+	0.134426i	$0.0429190\pi$
$191$	13.5848	+	15.6776i	0.982958	+	1.13439i	−0.00796543	+	0.999968i	$0.502536\pi$
$192$	−4.56232	−	31.7316i	−0.329257	−	2.29003i
$193$	−14.0587	−	4.12802i	−1.01197	−	0.297141i	−0.266611	−	0.963804i	$-0.585904\pi$
$193$	−14.0587	−	4.12802i	−1.01197	−	0.297141i	−0.745359	+	0.666663i	$0.767722\pi$
$194$	−6.23947	+	7.20073i	−0.447968	+	0.516982i
$195$	0.513652	+	0.330104i	0.0367834	+	0.0236392i
$196$	−3.29123	−	2.11515i	−0.235088	−	0.151082i
$197$	−7.64740	+	8.82557i	−0.544855	+	0.628796i	−0.959676	−	0.281107i	$-0.909298\pi$
$197$	−7.64740	+	8.82557i	−0.544855	+	0.628796i	0.414822	+	0.909903i	$0.363844\pi$
$198$	13.4078	+	3.93689i	0.952851	+	0.279782i
$199$	0.814526	+	5.66515i	0.0577402	+	0.401592i	0.998111	+	0.0614403i	$0.0195694\pi$
$199$	0.814526	+	5.66515i	0.0577402	+	0.401592i	−0.940371	+	0.340152i	$0.889522\pi$
$200$	4.28735	+	4.94786i	0.303161	+	0.349867i
$201$	−7.58679	−	16.6128i	−0.535131	−	1.17177i
$202$	3.84871	−	1.13008i	0.270794	−	0.0795124i
$203$	−4.90609	+	10.7428i	−0.344340	+	0.754000i
$204$	−1.59348	+	11.0829i	−0.111566	+	0.775956i
$205$	−0.443638	+	0.285109i	−0.0309850	+	0.0199129i
$206$	−33.7445			−2.35109
$207$		0			0
$208$	−0.305626			−0.0211913
$209$	12.8418	−	8.25290i	0.888284	−	0.570865i
$210$	2.31250	−	16.0838i	0.159578	−	1.10989i
$211$	−5.84395	+	12.7965i	−0.402314	+	0.880945i	0.594716	+	0.803936i	$0.297264\pi$
$211$	−5.84395	+	12.7965i	−0.402314	+	0.880945i	−0.997030	+	0.0770093i	$0.975463\pi$
$212$	−26.9075	+	7.90074i	−1.84801	+	0.542625i
$213$	0.762473	+	1.66958i	0.0522438	+	0.114398i
$214$	−2.86928	−	3.31132i	−0.196140	−	0.226357i
$215$	0.783621	+	5.45021i	0.0534425	+	0.371701i
$216$	1.44123	+	0.423184i	0.0980635	+	0.0287941i
$217$	2.77001	−	3.19676i	0.188040	−	0.217010i
$218$	28.9096	+	18.5791i	1.95800	+	1.25833i
$219$	13.6256	+	8.75665i	0.920734	+	0.591720i
$220$	−4.42114	+	5.10227i	−0.298073	+	0.343995i
$221$	0.294066	+	0.0863455i	0.0197810	+	0.00580823i
$222$	3.06076	+	21.2881i	0.205425	+	1.42876i
$223$	2.75276	+	3.17686i	0.184339	+	0.212738i	0.840396	−	0.541973i	$-0.182322\pi$
$223$	2.75276	+	3.17686i	0.184339	+	0.212738i	−0.656057	+	0.754711i	$0.727777\pi$
$224$	7.09706	+	15.5404i	0.474192	+	1.03834i
$225$	11.0469	−	3.24365i	0.736458	−	0.216243i
$226$	−1.36236	+	2.98316i	−0.0906230	+	0.198437i
$227$	−2.62297	+	18.2432i	−0.174093	+	1.21084i	0.696032	+	0.718011i	$0.254947\pi$
$227$	−2.62297	+	18.2432i	−0.174093	+	1.21084i	−0.870125	+	0.492831i	$0.835962\pi$
$228$	48.2136	−	30.9850i	3.19302	−	2.05203i
$229$	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
$232$	7.89754	−	5.07544i	0.518499	−	0.333219i
$233$	−0.592717	+	4.12244i	−0.0388302	+	0.270070i	−0.999982	−	0.00594940i	$-0.998106\pi$
$233$	−0.592717	+	4.12244i	−0.0388302	+	0.270070i	0.961152	+	0.276019i	$0.0890153\pi$
$234$	0.596555	−	1.30627i	0.0389980	−	0.0853937i
$235$	−3.07088	+	0.901692i	−0.200322	+	0.0588199i
$236$	−8.56445	−	18.7535i	−0.557499	−	1.22075i
$237$	−9.34548	−	10.7853i	−0.607054	−	0.700578i
$238$	−1.16076	−	8.07327i	−0.0752410	−	0.523312i
$239$	21.6050	+	6.34381i	1.39751	+	0.410347i	0.891830	−	0.452371i	$-0.149422\pi$
$239$	21.6050	+	6.34381i	1.39751	+	0.410347i	0.505684	+	0.862719i	$0.331240\pi$
$240$	3.16571	−	3.65343i	0.204346	−	0.235828i
$241$	4.98790	+	3.20553i	0.321299	+	0.206486i	0.691341	−	0.722529i	$-0.257020\pi$
$241$	4.98790	+	3.20553i	0.321299	+	0.206486i	−0.370042	+	0.929015i	$0.620657\pi$
$242$	−13.6159	−	8.75040i	−0.875262	−	0.562497i
$243$	−14.6477	+	16.9044i	−0.939652	+	1.08442i
$244$	−20.3590	−	5.97795i	−1.30335	−	0.382699i
$245$	−0.241058	−	1.67660i	−0.0154007	−	0.107114i
$246$	1.54686	+	1.78517i	0.0986240	+	0.113818i
$247$	−0.651677	−	1.42697i	−0.0414652	−	0.0907961i
$248$	−3.22615	+	0.947284i	−0.204861	+	0.0601526i
$249$	13.4579	−	29.4687i	0.852859	−	1.86750i
$250$	−3.28484	+	22.8465i	−0.207751	+	1.44494i
$251$	−1.30446	+	0.838324i	−0.0823366	+	0.0529146i	−0.581161	−	0.813788i	$-0.697401\pi$
$251$	−1.30446	+	0.838324i	−0.0823366	+	0.0529146i	0.498825	+	0.866703i	$0.333765\pi$
$252$	−22.4767			−1.41590
$253$		0			0
$254$	13.2093			0.828824
$255$	−4.07814	+	2.62086i	−0.255383	+	0.164125i
$256$	0.668192	−	4.64738i	0.0417620	−	0.290461i
$257$	11.4064	−	24.9766i	0.711513	−	1.55800i	−0.113917	−	0.993490i	$-0.536340\pi$
$257$	11.4064	−	24.9766i	0.711513	−	1.55800i	0.825429	−	0.564505i	$-0.190933\pi$
$258$	23.6645	−	6.94853i	1.47329	−	0.432597i
$259$	−3.82766	−	8.38141i	−0.237839	−	0.520795i
$260$	0.454346	+	0.524343i	0.0281773	+	0.0325184i
$261$	−2.34949	−	16.3410i	−0.145430	−	1.01148i
$262$	26.9978	+	7.92727i	1.66793	+	0.489749i
$263$	8.47435	−	9.77993i	0.522551	−	0.603056i	−0.431717	−	0.902009i	$-0.642092\pi$
$263$	8.47435	−	9.77993i	0.522551	−	0.603056i	0.954268	+	0.298953i	$0.0966374\pi$
$264$	7.62430	+	4.89984i	0.469243	+	0.301564i
$265$	−10.2141	−	6.56417i	−0.627444	−	0.403234i
$266$	−27.3394	+	31.5513i	−1.67629	+	1.93454i
$267$	−33.5208	−	9.84260i	−2.05144	−	0.602357i
$268$	−2.95340	−	20.5413i	−0.180407	−	1.25476i
$269$	6.54708	+	7.55573i	0.399182	+	0.460681i	0.919383	−	0.393363i	$-0.128688\pi$
$269$	6.54708	+	7.55573i	0.399182	+	0.460681i	−0.520201	+	0.854044i	$0.674143\pi$
$270$	0.901421	+	1.97384i	0.0548587	+	0.120124i
$271$	−4.23270	+	1.24283i	−0.257118	+	0.0754967i	−0.407751	−	0.913093i	$-0.633687\pi$
$271$	−4.23270	+	1.24283i	−0.257118	+	0.0754967i	0.150633	+	0.988590i	$0.451869\pi$
$272$	1.00801	−	2.20724i	0.0611197	−	0.133833i
$273$	−0.166749	+	1.15977i	−0.0100921	+	0.0701923i
$274$	1.29314	−	0.831048i	0.0781212	−	0.0502055i
$275$	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	$0.876290\pi$
$278$	25.8715	−	16.6266i	1.55167	−	0.997196i
$279$	−0.841494	+	5.85272i	−0.0503789	+	0.350393i
$280$	2.29878	−	5.03363i	0.137378	−	0.300817i
$281$	3.43432	−	1.00841i	0.204874	−	0.0601565i	−0.177685	−	0.984087i	$-0.556861\pi$
$281$	3.43432	−	1.00841i	0.204874	−	0.0601565i	0.382560	+	0.923931i	$0.375043\pi$
$282$	5.95529	+	13.0403i	0.354633	+	0.776537i
$283$	−9.67911	−	11.1703i	−0.575363	−	0.664005i	0.391238	−	0.920290i	$-0.372047\pi$
$283$	−9.67911	−	11.1703i	−0.575363	−	0.664005i	−0.966601	+	0.256285i	$0.917501\pi$
$284$	0.296817	+	2.06440i	0.0176128	+	0.122500i
$285$	23.8081	+	6.99069i	1.41027	+	0.414093i
$286$	0.542053	−	0.625563i	0.0320523	−	0.0369903i
$287$	−0.851334	−	0.547119i	−0.0502527	−	0.0322954i
$288$	−20.0906	−	12.9114i	−1.18385	−	0.760813i
$289$	9.53916	−	11.0088i	0.561127	−	0.647575i
$290$	13.0125	+	3.82080i	0.764118	+	0.224365i
$291$	1.54655	+	10.7565i	0.0906603	+	0.630556i
$292$	12.0524	+	13.9092i	0.705314	+	0.813975i
$293$	8.93701	+	19.5693i	0.522106	+	1.14325i	0.968636	+	0.248484i	$0.0799323\pi$
$293$	8.93701	+	19.5693i	0.522106	+	1.14325i	−0.446530	+	0.894769i	$0.647340\pi$
$294$	−7.27970	+	2.13751i	−0.424561	+	0.124662i
$295$	3.70800	−	8.11939i	0.215888	−	0.472729i
$296$	−1.04235	+	7.24969i	−0.0605852	+	0.421380i
$297$	1.28086	−	0.823160i	0.0743231	−	0.0477646i
$298$	−36.6660			−2.12401
$299$		0			0
$300$	24.9153			1.43849
$301$	−8.88904	+	5.71264i	−0.512356	+	0.329271i
$302$	−4.13647	+	28.7698i	−0.238027	+	1.65551i
$303$	1.90051	−	4.16154i	0.109182	−	0.239074i
$304$	−11.9171	+	3.49919i	−0.683495	+	0.200692i
$305$	−3.81626	−	8.35644i	−0.218518	−	0.478488i
$306$	7.46639	+	8.61667i	0.426825	+	0.492582i
$307$	−2.01303	−	14.0010i	−0.114890	−	0.799077i	−0.963047	−	0.269333i	$-0.913197\pi$
$307$	−2.01303	−	14.0010i	−0.114890	−	0.799077i	0.848157	−	0.529745i	$-0.177712\pi$
$308$	−12.4308	−	3.65001i	−0.708311	−	0.207979i
$309$	−25.2038	+	29.0868i	−1.43380	+	1.65469i
$310$	−4.08623	−	2.62606i	−0.232082	−	0.149150i
$311$	0.479632	+	0.308241i	0.0271974	+	0.0174787i	0.554169	−	0.832404i	$-0.313036\pi$
$311$	0.479632	+	0.308241i	0.0271974	+	0.0174787i	−0.526971	+	0.849883i	$0.676673\pi$
$312$	0.609922	−	0.703887i	0.0345300	−	0.0398498i
$313$	20.2767	+	5.95378i	1.14611	+	0.336528i	0.799020	−	0.601305i	$-0.205352\pi$
$313$	20.2767	+	5.95378i	1.14611	+	0.336528i	0.347088	+	0.937833i	$0.387170\pi$
$314$	−1.29478	−	9.00541i	−0.0730688	−	0.508205i
$315$	−6.37267	−	7.35446i	−0.359060	−	0.414377i
$316$	−6.73644	−	14.7507i	−0.378954	−	0.829794i
$317$	8.45518	−	2.48267i	0.474890	−	0.139440i	−0.0355243	−	0.999369i	$-0.511310\pi$
$317$	8.45518	−	2.48267i	0.474890	−	0.139440i	0.510415	+	0.859928i	$0.329492\pi$
$318$	−22.5919	+	49.4694i	−1.26689	+	2.77411i
$319$	1.35425	−	9.41899i	0.0758233	−	0.527362i
$320$	13.2678	−	8.52668i	0.741691	−	0.476656i
$321$	−4.99734			−0.278924
$322$		0			0
$323$	12.4550			0.693015
$324$	−19.0979	+	12.2735i	−1.06100	+	0.681861i
$325$	0.0970564	−	0.675042i	0.00538372	−	0.0374446i
$326$	−13.5384	+	29.6449i	−0.749820	+	1.64188i
$327$	37.6073	−	11.0425i	2.07969	−	0.610651i
$328$	0.334170	+	0.731729i	0.0184514	+	0.0404030i
$329$	−4.02200	−	4.64163i	−0.221740	−	0.255901i
$330$	1.86327	+	12.9593i	0.102570	+	0.713388i
$331$	−28.9647	−	8.50480i	−1.59204	−	0.467466i	−0.638726	−	0.769435i	$-0.720538\pi$
$331$	−28.9647	−	8.50480i	−1.59204	−	0.467466i	−0.953318	+	0.301968i	$0.902356\pi$
$332$	24.1068	−	27.8207i	1.32303	−	1.52686i
$333$	10.8355	+	6.96352i	0.593779	+	0.381599i
$334$	2.46508	+	1.58421i	0.134883	+	0.0866841i
$335$	5.88384	−	6.79032i	0.321469	−	0.370995i
$336$	8.90095	+	2.61355i	0.485586	+	0.142581i
$337$	0.705279	+	4.90532i	0.0384190	+	0.267210i	0.999973	−	0.00740745i	$-0.00235788\pi$
$337$	0.705279	+	4.90532i	0.0384190	+	0.267210i	−0.961554	+	0.274617i	$0.911449\pi$
$338$	18.7041	+	21.5857i	1.01737	+	1.17411i
$339$	1.55384	+	3.40244i	0.0843932	+	0.184795i
$340$	−5.28534	+	1.55192i	−0.286638	+	0.0841645i
$341$	−1.41582	+	3.10021i	−0.0766709	+	0.167886i
$342$	8.30537	−	57.7651i	0.449103	−	3.12358i
$343$	16.7073	−	10.7371i	0.902107	−	0.579749i
$344$	8.39923			0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	−5.69273	+	3.65849i	−0.305602	+	0.196398i	−0.684449	−	0.729061i	$-0.739957\pi$
$347$	−5.69273	+	3.65849i	−0.305602	+	0.196398i	0.378847	+	0.925459i	$0.376321\pi$
$348$	5.08443	−	35.3630i	0.272554	−	1.89566i
$349$	4.19230	−	9.17987i	0.224409	−	0.491387i	−0.763618	−	0.645668i	$-0.776579\pi$
$349$	4.19230	−	9.17987i	0.224409	−	0.491387i	0.988027	+	0.154281i	$0.0493062\pi$
$350$	−17.4143	+	5.11330i	−0.930833	+	0.273317i
$351$	−0.0649994	−	0.142329i	−0.00346941	−	0.00759695i
$352$	−9.01445	−	10.4032i	−0.480472	−	0.554494i
$353$	−3.48234	−	24.2202i	−0.185346	−	1.28911i	−0.843869	−	0.536550i	$-0.819727\pi$
$353$	−3.48234	−	24.2202i	−0.185346	−	1.28911i	0.658522	−	0.752561i	$-0.271182\pi$
$354$	−38.3619	−	11.2641i	−2.03891	−	0.598678i
$355$	−0.591326	+	0.682427i	−0.0313843	+	0.0362195i
$356$	−33.3961	−	21.4623i	−1.76999	−	1.13750i
$357$	−7.82590	−	5.02940i	−0.414191	−	0.266184i
$358$	2.06553	−	2.38374i	0.109166	−	0.125985i
$359$	−0.401848	−	0.117993i	−0.0212087	−	0.00622744i	0.271111	−	0.962548i	$-0.412609\pi$
$359$	−0.401848	−	0.117993i	−0.0212087	−	0.00622744i	−0.292320	+	0.956321i	$0.594427\pi$
$360$	1.10087	+	7.65669i	0.0580207	+	0.403543i
$361$	−29.3060	−	33.8210i	−1.54242	−	1.78005i
$362$	−14.7669	−	32.3350i	−0.776130	−	1.69949i
$363$	−17.7123	+	5.20081i	−0.929656	+	0.272972i
$364$	−0.553085	+	1.21109i	−0.0289895	+	0.0634782i
$365$	−1.13401	+	7.88718i	−0.0593566	+	0.412834i
$366$	−34.6164	+	22.2466i	−1.80943	+	1.16285i
$367$	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
$370$	−8.90107	+	5.72037i	−0.462744	+	0.297388i
$371$	3.31584	−	23.0622i	0.172150	−	1.19733i
$372$	−5.31560	+	11.6395i	−0.275601	+	0.603482i
$373$	−13.8242	+	4.05914i	−0.715787	+	0.210174i	−0.619294	−	0.785159i	$-0.712581\pi$
$373$	−13.8242	+	4.05914i	−0.715787	+	0.210174i	−0.0964938	+	0.995334i	$0.530763\pi$
$374$	2.73004	+	5.97795i	0.141167	+	0.309112i
$375$	17.2396	+	19.8956i	0.890249	+	1.02740i
$376$	0.694791	+	4.83238i	0.0358311	+	0.249211i
$377$	−0.938300	−	0.275510i	−0.0483249	−	0.0141895i
$378$	−2.72688	+	3.14699i	−0.140256	+	0.161864i
$379$	−4.73384	−	3.04225i	−0.243161	−	0.156270i	0.413384	−	0.910557i	$-0.364347\pi$
$379$	−4.73384	−	3.04225i	−0.243161	−	0.156270i	−0.656545	+	0.754287i	$0.727983\pi$
$380$	23.7195	+	15.2436i	1.21678	+	0.781980i
$381$	9.86604	−	11.3860i	0.505453	−	0.583324i
$382$	43.8612	+	12.8788i	2.24413	+	0.658937i
$383$	−0.0329687	−	0.229302i	−0.00168462	−	0.0117168i	0.988962	−	0.148171i	$-0.0473385\pi$
$383$	−0.0329687	−	0.229302i	−0.00168462	−	0.0117168i	−0.990646	+	0.136454i	$0.956429\pi$
$384$	−22.5605	−	26.0362i	−1.15129	−	1.32865i
$385$	−2.33013	−	5.10227i	−0.118754	−	0.260036i
$386$	−30.9801	+	9.09656i	−1.57684	+	0.463003i
$387$	6.13591	−	13.4358i	0.311906	−	0.682979i
$388$	−1.75735	+	12.2227i	−0.0892161	+	0.620512i
$389$	−25.3805	+	16.3110i	−1.28684	+	0.827002i	−0.991715	−	0.128456i	$-0.958998\pi$
$389$	−25.3805	+	16.3110i	−1.28684	+	0.827002i	−0.295125	+	0.955459i	$0.595361\pi$
$390$	1.34548			0.0681311
$391$		0			0
$392$	−2.58378			−0.130500
$393$	26.9978	−	17.3504i	1.36186	−	0.875214i
$394$	−3.66227	+	25.4717i	−0.184503	+	1.28324i
$395$	2.91656	−	6.38637i	0.146748	−	0.321333i
$396$	17.3767	−	5.10227i	0.873214	−	0.256399i
$397$	−5.41920	−	11.8664i	−0.271982	−	0.595557i	0.723520	−	0.690304i	$-0.242523\pi$
$397$	−5.41920	−	11.8664i	−0.271982	−	0.595557i	−0.995501	+	0.0947466i	$0.969796\pi$
$398$	8.25923	+	9.53166i	0.413998	+	0.477779i
$399$	6.77649	+	47.1315i	0.339249	+	2.35953i
$400$	−5.18080	−	1.52122i	−0.259040	−	0.0760610i
$401$	13.9654	−	16.1169i	0.697399	−	0.804841i	−0.291000	−	0.956723i	$-0.593988\pi$
$401$	13.9654	−	16.1169i	0.697399	−	0.804841i	0.988399	+	0.151882i	$0.0485334\pi$
$402$	−33.8562	−	21.7581i	−1.68860	−	1.08519i
$403$	0.294649	+	0.189359i	0.0146775	+	0.00943266i
$404$	3.40434	−	3.92882i	0.169372	−	0.195466i
$405$	−9.43065	−	2.76909i	−0.468613	−	0.137597i
$406$	3.70373	+	25.7600i	0.183813	+	1.27845i
$407$	4.86177	+	5.61078i	0.240989	+	0.278116i
$408$	3.07186	+	6.72643i	0.152080	+	0.333008i
$409$	8.77842	−	2.57758i	0.434065	−	0.127453i	−0.0573981	−	0.998351i	$-0.518280\pi$
$409$	8.77842	−	2.57758i	0.434065	−	0.127453i	0.491463	+	0.870898i	$0.336462\pi$
$410$	−0.482747	+	1.05707i	−0.0238412	+	0.0522049i
$411$	0.249507	−	1.73536i	0.0123073	−	0.0855989i
$412$	−36.7909	+	23.6441i	−1.81256	+	1.16486i
$413$	17.1289			0.842859
$414$		0			0
$415$	15.9379			0.782360
$416$	−1.19006	+	0.764806i	−0.0583476	+	0.0374977i
$417$	4.99182	−	34.7189i	0.244451	−	1.70019i
$418$	13.9738	−	30.5985i	0.683483	−	1.49662i
$419$	8.61068	−	2.52832i	0.420659	−	0.123517i	−0.0645506	−	0.997914i	$-0.520561\pi$
$419$	8.61068	−	2.52832i	0.420659	−	0.123517i	0.485210	+	0.874398i	$0.338743\pi$
$420$	−8.74832	−	19.1561i	−0.426874	−	0.934724i
$421$	−20.6100	−	23.7852i	−1.00447	−	1.15922i	−0.987219	−	0.159367i	$-0.949055\pi$
$421$	−20.6100	−	23.7852i	−1.00447	−	1.15922i	−0.0172487	−	0.999851i	$-0.505491\pi$
$422$	4.41174	+	30.6844i	0.214760	+	1.49369i
$423$	8.23766	+	2.41879i	0.400529	+	0.117606i
$424$	−12.1284	+	13.9969i	−0.589007	+	0.679751i
$425$	4.55507	+	2.92736i	0.220953	+	0.141998i
$426$	3.40255	+	2.18669i	0.164854	+	0.105945i
$427$	11.5445	−	13.3231i	0.558679	−	0.644750i
$428$	−5.44849	−	1.59982i	−0.263363	−	0.0773303i
$429$	−0.134356	−	0.934468i	−0.00648678	−	0.0451166i
$430$	7.94586	+	9.17001i	0.383183	+	0.442217i
$431$	−9.18167	−	20.1051i	−0.442265	−	0.968426i	−0.991177	−	0.132546i	$-0.957685\pi$
$431$	−9.18167	−	20.1051i	−0.442265	−	0.968426i	0.548911	−	0.835880i	$-0.315042\pi$
$432$	−1.18864	+	0.349016i	−0.0571884	+	0.0167920i
$433$	5.27380	−	11.5480i	0.253442	−	0.554962i	−0.739555	−	0.673096i	$-0.764964\pi$
$433$	5.27380	−	11.5480i	0.253442	−	0.554962i	0.992998	+	0.118134i	$0.0376913\pi$
$434$	1.32653	−	9.22623i	0.0636756	−	0.442873i
$435$	13.0125	−	8.36260i	0.623900	−	0.400956i
$436$	44.5375			2.13296
$437$		0			0
$438$	35.6915			1.70541
$439$	15.4967	−	9.95915i	0.739619	−	0.475324i	−0.115793	−	0.993273i	$-0.536941\pi$
$439$	15.4967	−	9.95915i	0.739619	−	0.475324i	0.855411	+	0.517949i	$0.173304\pi$
$440$	−0.634540	+	4.41333i	−0.0302505	+	0.210397i
$441$	−1.88753	+	4.13312i	−0.0898826	+	0.196815i
$442$	0.648008	−	0.190272i	0.0308226	−	0.00905033i
$443$	−5.77958	−	12.6555i	−0.274596	−	0.601281i	0.721216	−	0.692711i	$-0.243584\pi$
$443$	−5.77958	−	12.6555i	−0.274596	−	0.601281i	−0.995812	+	0.0914293i	$0.970856\pi$
$444$	18.2532	+	21.0653i	0.866258	+	0.999715i
$445$	−2.44601	−	17.0124i	−0.115952	−	0.806465i
$446$	8.88787	+	2.60971i	0.420853	+	0.123573i
$447$	−27.3859	+	31.6051i	−1.29531	+	1.49487i
$448$	25.4607	+	16.3626i	1.20290	+	0.773059i
$449$	25.3154	+	16.2692i	1.19471	+	0.767792i	0.978033	−	0.208452i	$-0.0668425\pi$
$449$	25.3154	+	16.2692i	1.19471	+	0.767792i	0.216675	+	0.976244i	$0.430479\pi$
$450$	16.6143	−	19.1739i	0.783206	−	0.903867i
$451$	0.782364	+	0.229723i	0.0368401	+	0.0108172i
$452$	0.604882	+	4.20705i	0.0284513	+	0.197883i
$453$	21.7092	+	25.0537i	1.01999	+	1.17713i
$454$	16.8718	+	36.9441i	0.791833	+	1.73387i
$455$	−0.553085	+	0.162400i	−0.0259290	+	0.00761344i
$456$	15.7235	−	34.4296i	0.736319	−	1.61231i
$457$	−5.41473	+	37.6603i	−0.253290	+	1.76167i	0.324878	+	0.945756i	$0.394677\pi$
$457$	−5.41473	+	37.6603i	−0.253290	+	1.76167i	−0.578168	+	0.815917i	$0.696232\pi$
$458$	20.2522	−	13.0153i	0.946321	−	0.608164i
$459$	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	$0.434606\pi$
$462$	−21.1361	+	13.5833i	−0.983339	+	0.631954i
$463$	3.96158	−	27.5534i	0.184110	−	1.28051i	−0.662808	−	0.748790i	$-0.730635\pi$
$463$	3.96158	−	27.5534i	0.184110	−	1.28051i	0.846918	−	0.531724i	$-0.178456\pi$
$464$	−3.21634	+	7.04281i	−0.149315	+	0.326954i
$465$	−5.31560	+	1.56080i	−0.246505	+	0.0723804i
$466$	3.81255	+	8.34831i	0.176613	+	0.386728i
$467$	11.3725	+	13.1246i	0.526258	+	0.607334i	0.955187	−	0.296004i	$-0.0956542\pi$
$467$	11.3725	+	13.1246i	0.526258	+	0.607334i	−0.428928	+	0.903338i	$0.641109\pi$
$468$	−0.264867	−	1.84219i	−0.0122435	−	0.0851554i
$469$	16.5434	+	4.85759i	0.763905	+	0.224303i
$470$	−4.61855	+	5.33009i	−0.213038	+	0.245859i
$471$	−8.72948	−	5.61010i	−0.402233	−	0.258500i
$472$	−11.4543	−	7.36122i	−0.527226	−	0.338828i
$473$	5.57533	−	6.43428i	0.256354	−	0.295848i
$474$	−30.1738	−	8.85983i	−1.38593	−	0.406945i
$475$	−3.94426	−	27.4329i	−0.180975	−	1.25871i
$476$	−6.92233	−	7.98879i	−0.317284	−	0.366166i
$477$	13.5299	+	29.6263i	0.619491	+	1.35650i
$478$	47.6092	−	13.9793i	2.17759	−	0.639400i
$479$	−10.5839	+	23.1754i	−0.483589	+	1.05891i	0.497873	+	0.867250i	$0.334115\pi$
$479$	−10.5839	+	23.1754i	−0.483589	+	1.05891i	−0.981461	+	0.191661i	$0.938613\pi$
$480$	3.18438	−	22.1479i	0.145347	−	1.01091i
$481$	0.641836	−	0.412483i	0.0292652	−	0.0188076i
$482$	13.0655			0.595119
$483$		0			0
$484$	−20.9763			−0.953469
$485$	−4.49755	+	2.89040i	−0.204223	+	0.131246i
$486$	−7.01467	+	48.7881i	−0.318192	+	2.21307i
$487$	−2.55940	+	5.60431i	−0.115978	+	0.253955i	−0.958715	−	0.284370i	$-0.908216\pi$
$487$	−2.55940	+	5.60431i	−0.115978	+	0.253955i	0.842737	+	0.538325i	$0.180943\pi$
$488$	−13.4456	+	3.94799i	−0.608654	+	0.178717i
$489$	15.4412	+	33.8115i	0.698275	+	1.52901i
$490$	−2.44431	−	2.82089i	−0.110423	−	0.127435i
$491$	4.64624	+	32.3153i	0.209682	+	1.45837i	0.774196	+	0.632946i	$0.218155\pi$
$491$	4.64624	+	32.3153i	0.209682	+	1.45837i	−0.564514	+	0.825423i	$0.690936\pi$
$492$	2.93734	+	0.862480i	0.132425	+	0.0388836i
$493$	5.08443	−	5.86775i	0.228991	−	0.264270i
$494$	−2.90812	−	1.86894i	−0.130843	−	0.0840874i
$495$	6.59620	+	4.23912i	0.296477	+	0.190534i
$496$	1.81596	−	2.09573i	0.0815392	−	0.0941013i
$497$	−1.66262	−	0.488188i	−0.0745785	−	0.0218982i
$498$	−10.1597	−	70.6623i	−0.455267	−	3.16645i
$499$	5.61457	+	6.47956i	0.251343	+	0.290065i	0.867374	−	0.497657i	$-0.165806\pi$
$499$	5.61457	+	6.47956i	0.251343	+	0.290065i	−0.616031	+	0.787722i	$0.711261\pi$
$500$	12.4267	+	27.2107i	0.555739	+	1.21690i
$501$	3.20672	−	0.941577i	0.143266	−	0.0420666i
$502$	−1.41945	+	3.10817i	−0.0633533	+	0.138724i
$503$	−0.961413	+	6.68678i	−0.0428673	+	0.298149i	0.957098	+	0.289766i	$0.0935774\pi$
$503$	−0.961413	+	6.68678i	−0.0428673	+	0.298149i	−0.999965	+	0.00838273i	$0.997332\pi$
$504$	−12.4877	+	8.02537i	−0.556247	+	0.357478i
$505$	2.25073			0.100156
$506$		0			0
$507$	32.5764			1.44677
$508$	14.4018	−	9.25547i	0.638976	−	0.410645i
$509$	−5.83100	+	40.5555i	−0.258455	+	1.79759i	0.285396	+	0.958410i	$0.407875\pi$
$509$	−5.83100	+	40.5555i	−0.258455	+	1.79759i	−0.543851	+	0.839182i	$0.683034\pi$
$510$	−4.43766	+	9.71711i	−0.196503	+	0.430281i
$511$	−14.6716	+	4.30798i	−0.649035	+	0.190574i
$512$	7.09033	+	15.5257i	0.313351	+	0.686143i
$513$	−4.16406	−	4.80558i	−0.183848	−	0.212172i
$514$	−8.61099	−	59.8908i	−0.379815	−	2.64167i
$515$	−18.1675	−	5.33446i	−0.800556	−	0.235064i
$516$	20.9322	−	24.1571i	0.921490	−	1.06346i
$517$	4.16307	+	2.67544i	0.183092	+	0.117666i
$518$	−17.0810	−	10.9773i	−0.750497	−	0.482315i
$519$	−27.8748	+	32.1692i	−1.22357	+	1.41207i
$520$	0.439646	+	0.129092i	0.0192797	+	0.00566104i
$521$	2.66511	+	18.5362i	0.116760	+	0.812087i	0.961085	+	0.276254i	$0.0890932\pi$
$521$	2.66511	+	18.5362i	0.116760	+	0.812087i	−0.844324	+	0.535833i	$0.819998\pi$
$522$	−23.8236	−	27.4939i	−1.04273	−	1.20338i
$523$	9.78884	+	21.4346i	0.428036	+	0.937269i	0.993641	+	0.112592i	$0.0359154\pi$
$523$	9.78884	+	21.4346i	0.428036	+	0.937269i	−0.565605	+	0.824676i	$0.691357\pi$
$524$	34.9896	−	10.2739i	1.52853	−	0.448816i
$525$	−8.59926	+	18.8298i	−0.375302	+	0.821798i
$526$	4.05830	−	28.2261i	0.176950	−	1.23072i
$527$	−2.33937	+	1.50342i	−0.101904	+	0.0654900i
$528$	−7.47461			−0.325291
$529$		0			0
$530$	−26.7551			−1.16217
$531$	−20.1431	+	12.9452i	−0.874135	+	0.561772i
$532$	−7.70017	+	53.5559i	−0.333845	+	2.32194i
$533$	0.0348098	−	0.0762228i	0.00150778	−	0.00330158i
$534$	−73.8670	+	21.6893i	−3.19654	+	0.938588i
$535$	−1.02131	−	2.23635i	−0.0441550	−	0.0966860i
$536$	−8.97520	−	10.3579i	−0.387670	−	0.447395i
$537$	−0.511972	−	3.56085i	−0.0220932	−	0.153662i
$538$	21.1386	+	6.20685i	0.911349	+	0.267596i
$539$	−1.71509	+	1.97932i	−0.0738741	+	0.0852553i
$540$	2.36583	+	1.52042i	0.101809	+	0.0654286i
$541$	0.801957	+	0.515386i	0.0344788	+	0.0221582i	0.557767	−	0.829998i	$-0.311658\pi$
$541$	0.801957	+	0.515386i	0.0344788	+	0.0221582i	−0.523288	+	0.852156i	$0.675295\pi$
$542$	−6.36591	+	7.34665i	−0.273439	+	0.315566i
$543$	−38.9012	−	11.4224i	−1.66941	−	0.490184i
$544$	−1.59840	−	11.1171i	−0.0685310	−	0.476643i
$545$	12.6274	+	14.5728i	0.540900	+	0.624231i
$546$	1.07259	+	2.34863i	0.0459024	+	0.100512i
$547$	−28.5795	+	8.39169i	−1.22197	+	0.358803i	−0.828214	−	0.560412i	$-0.810643\pi$
$547$	−28.5795	+	8.39169i	−1.22197	+	0.358803i	−0.393756	+	0.919215i	$0.628824\pi$
$548$	0.827580	−	1.81215i	0.0353525	−	0.0774111i
$549$	−3.50709	+	24.3923i	−0.149679	+	1.04104i
$550$	12.3023	−	7.90618i	0.524570	−	0.337121i
$551$	−39.7412			−1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$	−57.1049	+	36.6991i	−2.42615	+	1.55919i
$555$	−1.71743	+	11.9450i	−0.0729010	+	0.507038i
$556$	16.5572	−	36.2552i	0.702181	−	1.53756i
$557$	5.76532	−	1.69285i	0.244284	−	0.0717284i	−0.157298	−	0.987551i	$-0.550278\pi$
$557$	5.76532	−	1.69285i	0.244284	−	0.0717284i	0.401583	+	0.915823i	$0.368460\pi$
$558$	5.41276	+	11.8523i	0.229140	+	0.501748i
$559$	−0.572958	−	0.661229i	−0.0242335	−	0.0279670i
$560$	0.649502	+	4.51739i	0.0274465	+	0.190894i
$561$	7.19189	+	2.11173i	0.303642	+	0.0891573i
$562$	5.16516	−	5.96091i	0.217879	−	0.251446i
$563$	0.0750314	+	0.0482198i	0.00316220	+	0.00203222i	0.542221	−	0.840236i	$-0.317584\pi$
$563$	0.0750314	+	0.0482198i	0.00316220	+	0.00203222i	−0.539059	+	0.842268i	$0.681220\pi$
$564$	15.6300	+	10.0448i	0.658141	+	0.422961i
$565$	−1.20506	+	1.39072i	−0.0506974	+	0.0585080i
$566$	−31.2510	−	9.17612i	−1.31358	−	0.385701i
$567$	−2.68424	−	18.6693i	−0.112728	−	0.784037i
$568$	0.902008	+	1.04097i	0.0378474	+	0.0436783i
$569$	−17.1814	−	37.6220i	−0.720281	−	1.57720i	−0.813510	−	0.581551i	$-0.802446\pi$
$569$	−17.1814	−	37.6220i	−0.720281	−	1.57720i	0.0932287	−	0.995645i	$-0.470281\pi$
$570$	52.4639	−	15.4048i	2.19747	−	0.645236i
$571$	10.7138	−	23.4599i	0.448357	−	0.981764i	−0.541632	−	0.840616i	$-0.682193\pi$
$571$	10.7138	−	23.4599i	0.448357	−	0.981764i	0.989988	−	0.141148i	$-0.0450794\pi$
$572$	0.152670	−	1.06184i	0.00638345	−	0.0443979i
$573$	43.8612	−	28.1879i	1.83233	−	1.17757i
$574$	−2.23002			−0.0930793
$575$		0			0
$576$	−42.3070			−1.76279
$577$	22.8352	−	14.6753i	0.950640	−	0.610939i	0.0292476	−	0.999572i	$-0.490689\pi$
$577$	22.8352	−	14.6753i	0.950640	−	0.610939i	0.921393	+	0.388633i	$0.127053\pi$
$578$	4.56822	−	31.7727i	0.190013	−	1.32157i
$579$	−15.2981	+	33.4982i	−0.635767	+	1.39214i
$580$	16.8644	−	4.95182i	0.700255	−	0.205613i
$581$	12.7053	+	27.8207i	0.527104	+	1.15420i
$582$	15.6819	+	18.0979i	0.650035	+	0.750180i
$583$	2.67170	+	18.5821i	0.110650	+	0.769590i
$584$	11.6625	+	3.42441i	0.482596	+	0.141703i
$585$	0.527677	−	0.608971i	0.0218167	−	0.0251779i
$586$	39.8816	+	25.6304i	1.64750	+	1.05878i
$587$	26.6129	+	17.1031i	1.09843	+	0.705919i	0.958742	−	0.284277i	$-0.0917534\pi$
$587$	26.6129	+	17.1031i	1.09843	+	0.705919i	0.139689	+	0.990195i	$0.455390\pi$
$588$	−6.43919	+	7.43122i	−0.265548	+	0.306458i
$589$	13.6572	+	4.01010i	0.562733	+	0.165233i
$590$	−2.79926	−	19.4693i	−0.115244	−	0.801539i
$591$	19.2205	+	22.1816i	0.790625	+	0.912430i
$592$	−2.50934	−	5.49469i	−0.103133	−	0.225831i
$593$	24.7031	−	7.25348i	1.01443	−	0.297865i	0.268068	−	0.963400i	$-0.413615\pi$
$593$	24.7031	−	7.25348i	1.01443	−	0.297865i	0.746366	+	0.665535i	$0.231797\pi$
$594$	1.39378	−	3.05195i	0.0571874	−	0.125223i
$595$	0.651319	−	4.53002i	0.0267015	−	0.185713i
$596$	−39.9762	+	25.6911i	−1.63749	+	1.05235i
$597$	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	$0.387491\pi$
$600$	13.8426	−	8.89609i	0.565121	−	0.363181i
$601$	1.37404	−	9.55668i	0.0560484	−	0.389825i	−0.942417	−	0.334441i	$-0.891453\pi$
$601$	1.37404	−	9.55668i	0.0560484	−	0.389825i	0.998465	−	0.0553843i	$-0.0176384\pi$
$602$	−9.67266	+	21.1802i	−0.394228	+	0.863239i
$603$	−23.1257	+	6.79032i	−0.941751	+	0.276523i
$604$	15.6485	+	34.2654i	0.636728	+	1.39424i
$605$	−5.94728	−	6.86353i	−0.241791	−	0.279042i
$606$	−1.43474	−	9.97886i	−0.0582825	−	0.405364i
$607$	−3.11381	−	0.914298i	−0.126386	−	0.0371102i	0.217928	−	0.975965i	$-0.430070\pi$
$607$	−3.11381	−	0.914298i	−0.126386	−	0.0371102i	−0.344314	+	0.938855i	$0.611888\pi$
$608$	−37.6472	+	43.4471i	−1.52679	+	1.76201i
$609$	24.9707	+	16.0477i	1.01187	+	0.650286i
$610$	−17.0301	−	10.9446i	−0.689531	−	0.443134i
$611$	0.333033	−	0.384341i	0.0134731	−	0.0155488i
$612$	14.1780	+	4.16303i	0.573110	+	0.168280i
$613$	4.68419	+	32.5793i	0.189193	+	1.31586i	0.834104	+	0.551607i	$0.185985\pi$
$613$	4.68419	+	32.5793i	0.189193	+	1.31586i	−0.644911	+	0.764258i	$0.723106\pi$
$614$	−20.4120	−	23.5567i	−0.823762	−	0.950672i
$615$	0.550598	+	1.20564i	0.0222022	+	0.0486161i
$616$	−8.20961	+	2.41056i	−0.330775	+	0.0971242i
$617$	1.25639	−	2.75111i	0.0505804	−	0.110756i	−0.882655	−	0.470022i	$-0.844246\pi$
$617$	1.25639	−	2.75111i	0.0505804	−	0.110756i	0.933235	+	0.359267i	$0.116973\pi$
$618$	−12.0699	+	83.9480i	−0.485522	+	3.37688i
$619$	8.76787	−	5.63477i	0.352410	−	0.226480i	−0.352443	−	0.935833i	$-0.614649\pi$
$619$	8.76787	−	5.63477i	0.352410	−	0.226480i	0.704854	+	0.709353i	$0.251013\pi$
$620$	−6.29515			−0.252819
$621$		0			0
$622$	1.25637			0.0503758
$623$	27.7464	−	17.8316i	1.11164	−	0.714406i
$624$	−0.109318	+	0.760322i	−0.00437621	+	0.0304372i
$625$	1.82960	−	4.00627i	0.0731841	−	0.160251i
$626$	44.6821	−	13.1198i	1.78586	−	0.524374i
$627$	−15.9379	−	34.8991i	−0.636498	−	1.39374i
$628$	−7.72158	−	8.91117i	−0.308124	−	0.355595i
$629$	0.862067	+	5.99581i	0.0343729	+	0.239069i
$630$	−20.5755	−	6.04151i	−0.819748	−	0.240700i
$631$	−22.3316	+	25.7720i	−0.889007	+	1.02597i	0.110478	+	0.993879i	$0.464762\pi$
$631$	−22.3316	+	25.7720i	−0.889007	+	1.02597i	−0.999485	+	0.0320904i	$0.989784\pi$
$632$	−9.00946	−	5.79003i	−0.358377	−	0.230315i
$633$	29.7442	+	19.1154i	1.18222	+	0.759770i
$634$	12.7165	−	14.6756i	0.505035	−	0.582841i
$635$	7.11167	+	2.08818i	0.282218	+	0.0828667i
$636$	10.0307	+	69.7651i	0.397744	+	2.76637i
$637$	0.176254	+	0.203408i	0.00698343	+	0.00805931i
$638$	−8.71095	−	19.0743i	−0.344870	−	0.755160i
$639$	2.32413	−	0.682427i	0.0919413	−	0.0269964i
$640$	7.04073	−	15.4171i	0.278309	−	0.609412i
$641$	1.28164	−	8.91400i	0.0506217	−	0.352082i	−0.948730	−	0.316087i	$-0.897631\pi$
$641$	1.28164	−	8.91400i	0.0506217	−	0.352082i	0.999352	−	0.0359950i	$-0.0114600\pi$
$642$	−9.26406	+	5.95365i	−0.365623	+	0.234972i
$643$	−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
$646$	23.0891	−	14.8384i	0.908427	−	0.583811i
$647$	6.39767	−	44.4968i	0.251518	−	1.74935i	−0.337589	−	0.941293i	$-0.609612\pi$
$647$	6.39767	−	44.4968i	0.251518	−	1.74935i	0.589108	−	0.808055i	$-0.299479\pi$
$648$	−6.22824	+	13.6379i	−0.244668	+	0.535749i
$649$	−13.2424	+	3.88831i	−0.519808	+	0.152629i
$650$	−0.624298	−	1.36702i	−0.0244870	−	0.0536190i
$651$	−6.96196	−	8.03453i	−0.272861	−	0.314898i
$652$	6.01097	+	41.8072i	0.235408	+	1.63730i
$653$	28.1739	+	8.27262i	1.10253	+	0.323733i	0.781858	−	0.623457i	$-0.214272\pi$
$653$	28.1739	+	8.27262i	1.10253	+	0.323733i	0.320674	+	0.947190i	$0.396091\pi$
$654$	56.5607	−	65.2745i	2.21170	−	2.55244i
$655$	13.2820	+	8.53584i	0.518972	+	0.333523i
$656$	−0.558119	−	0.358681i	−0.0217909	−	0.0140042i
$657$	13.9976	−	16.1541i	0.546100	−	0.630233i
$658$	−12.9859	−	3.81299i	−0.506241	−	0.148646i
$659$	5.71447	+	39.7450i	0.222604	+	1.54825i	0.728133	+	0.685436i	$0.240388\pi$
$659$	5.71447	+	39.7450i	0.222604	+	1.54825i	−0.505529	+	0.862810i	$0.668703\pi$
$660$	11.1118	+	12.8237i	0.432527	+	0.499163i
$661$	4.14027	+	9.06594i	0.161038	+	0.352624i	0.972900	−	0.231225i	$-0.0742733\pi$
$661$	4.14027	+	9.06594i	0.161038	+	0.352624i	−0.811862	+	0.583849i	$0.801546\pi$
$662$	−63.8270	+	18.7413i	−2.48071	+	0.728402i
$663$	0.319990	−	0.700679i	0.0124274	−	0.0272121i
$664$	3.45991	−	24.0642i	0.134270	−	0.933871i
$665$	−19.7069	+	12.6648i	−0.764199	+	0.491121i
$666$	28.3829			1.09981
$667$		0			0
$668$	3.79764			0.146935
$669$	8.88787	−	5.71188i	0.343625	−	0.220834i
$670$	2.81772	−	19.5977i	0.108858	−	0.757125i
$671$	−5.90070	+	12.9207i	−0.227794	+	0.498799i
$672$	41.1992	−	12.0972i	1.58929	−	0.466659i
$673$	−14.1477	−	30.9791i	−0.545353	−	1.19416i	−0.958918	−	0.283682i	$-0.908444\pi$
$673$	−14.1477	−	30.9791i	−0.545353	−	1.19416i	0.413565	−	0.910474i	$-0.364283\pi$
$674$	7.15147	+	8.25324i	0.275464	+	0.317903i
$675$	−0.393407	−	2.73621i	−0.0151423	−	0.105317i
$676$	35.5173	+	10.4288i	1.36605	+	0.401108i
$677$	16.3657	−	18.8870i	0.628985	−	0.725887i	−0.348402	−	0.937345i	$-0.613276\pi$
$677$	16.3657	−	18.8870i	0.628985	−	0.725887i	0.977387	+	0.211458i	$0.0678212\pi$
$678$	6.93407	+	4.45625i	0.266301	+	0.171141i
$679$	−8.63074	−	5.54664i	−0.331217	−	0.212860i
$680$	−2.38234	+	2.74937i	−0.0913586	+	0.105433i
$681$	44.4463	+	13.0506i	1.70319	+	0.500101i
$682$	1.06884	+	7.43393i	0.0409279	+	0.284660i
$683$	−22.5771	−	26.0553i	−0.863888	−	0.996980i	−0.999980	−	0.00628404i	$-0.998000\pi$
$683$	−22.5771	−	26.0553i	−0.863888	−	0.996980i	0.136092	−	0.990696i	$-0.456546\pi$
$684$	−31.4197	−	68.7995i	−1.20136	−	2.63061i
$685$	0.827580	−	0.242999i	0.0316202	−	0.00928453i
$686$	18.1801	−	39.8089i	0.694119	−	1.51991i
$687$	3.90759	−	27.1779i	0.149084	−	1.03690i
$688$	−5.82749	+	3.74510i	−0.222171	+	0.142781i
$689$	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	$0.632288\pi$
$692$	−40.6898	+	26.1497i	−1.54679	+	0.994064i
$693$	−2.14136	+	14.8935i	−0.0813434	+	0.565756i
$694$	−6.19457	+	13.5642i	−0.235143	+	0.514891i
$695$	16.5572	−	4.86163i	0.628050	−	0.184412i
$696$	−9.80162	−	21.4626i	−0.371530	−	0.813536i
$697$	0.435674	+	0.502795i	0.0165023	+	0.0190447i
$698$	−3.16488	−	22.0122i	−0.119792	−	0.833174i
$699$	10.0436	+	2.94907i	0.379884	+	0.111544i
$700$	−15.4036	+	17.7767i	−0.582203	+	0.671898i
$701$	−20.2962	−	13.0436i	−0.766577	−	0.492649i	0.0979773	−	0.995189i	$-0.468763\pi$
$701$	−20.2962	−	13.0436i	−0.766577	−	0.492649i	−0.864554	+	0.502540i	$0.832399\pi$
$702$	−0.290061	−	0.186411i	−0.0109477	−	0.00703564i
$703$	20.3043	−	23.4324i	0.765789	−	0.883768i
$704$	−23.3980	−	6.87027i	−0.881845	−	0.258933i
$705$	1.14478	+	7.96212i	0.0431149	+	0.299871i
$706$	−35.3106	−	40.7507i	−1.32893	−	1.53367i
$707$	1.79423	+	3.92882i	0.0674790	+	0.147758i
$708$	−49.7176	+	14.5984i	−1.86850	+	0.548642i
$709$	2.92325	−	6.40102i	0.109785	−	0.240395i	−0.846763	−	0.531970i	$-0.821452\pi$
$709$	2.92325	−	6.40102i	0.109785	−	0.240395i	0.956548	+	0.291575i	$0.0941792\pi$
$710$	−0.283181	+	1.96957i	−0.0106276	+	0.0739166i
$711$	−15.8437	+	10.1821i	−0.594185	+	0.381859i
$712$	−26.2175			−0.982544
$713$		0			0
$714$	−20.4995			−0.767175
$715$	0.390724	−	0.251103i	0.0146123	−	0.00939073i
$716$	0.581758	−	4.04621i	0.0217413	−	0.151214i
$717$	23.5097	−	51.4790i	0.877984	−	1.92252i
$718$	−0.885519	+	0.260012i	−0.0330473	+	0.00970355i
$719$	11.0368	+	24.1673i	0.411605	+	0.901289i	0.995961	+	0.0897916i	$0.0286201\pi$
$719$	11.0368	+	24.1673i	0.411605	+	0.901289i	−0.584356	+	0.811498i	$0.698653\pi$
$720$	−4.17781	−	4.82145i	−0.155698	−	0.179685i
$721$	−5.17101	−	35.9652i	−0.192579	−	1.33941i
$722$	−94.6206	−	27.7831i	−3.52141	−	1.03398i
$723$	9.75868	−	11.2621i	0.362929	−	0.418843i
$724$	−38.7565	−	24.9073i	−1.44037	−	0.925671i
$725$	−14.5342	−	9.34057i	−0.539787	−	0.346900i
$726$	−26.6390	+	30.7431i	−0.988668	+	1.14098i
$727$	5.01580	+	1.47277i	0.186026	+	0.0546221i	0.373419	−	0.927663i	$-0.378186\pi$
$727$	5.01580	+	1.47277i	0.186026	+	0.0546221i	−0.187393	+	0.982285i	$0.560004\pi$
$728$	0.125136	+	0.870342i	0.00463786	+	0.0322570i
$729$	21.1982	+	24.4640i	0.785118	+	0.906074i
$730$	7.29429	+	15.9723i	0.269974	+	0.591160i
$731$	6.66514	−	1.95706i	0.246519	−	0.0723846i
$732$	−22.1538	+	48.5101i	−0.818828	+	1.79298i
$733$	3.79822	−	26.4172i	0.140291	−	0.975743i	−0.791091	−	0.611698i	$-0.790487\pi$
$733$	3.79822	−	26.4172i	0.140291	−	0.975743i	0.931382	−	0.364044i	$-0.118604\pi$
$734$	52.9597	−	34.0351i	1.95478	−	1.25626i
$735$	−4.25719			−0.157029
$736$		0			0
$737$	−13.8924			−0.511734
$738$	2.62244	−	1.68534i	0.0965333	−	0.0620382i
$739$	0.318721	−	2.21675i	0.0117243	−	0.0815446i	−0.983119	−	0.182966i	$-0.941430\pi$
$739$	0.318721	−	2.21675i	0.0117243	−	0.0815446i	0.994844	+	0.101422i	$0.0323392\pi$
$740$	−5.69650	+	12.4736i	−0.209407	+	0.458538i
$741$	−3.78305	+	1.11080i	−0.138974	+	0.0408064i
$742$	−21.3285	−	46.7030i	−0.782995	−	1.71452i
$743$	−11.8793	−	13.7094i	−0.435808	−	0.502949i	0.494780	−	0.869018i	$-0.335249\pi$
$743$	−11.8793	−	13.7094i	−0.435808	−	0.502949i	−0.930588	+	0.366069i	$0.880703\pi$
$744$	1.20266	+	8.36471i	0.0440918	+	0.306665i
$745$	−19.7404	−	5.79631i	−0.723233	−	0.212360i
$746$	−20.7913	+	23.9944i	−0.761223	+	0.878499i
$747$	−35.9665	−	23.1143i	−1.31595	−	0.845708i
$748$	7.16513	+	4.60475i	0.261983	+	0.168366i
$749$	3.08955	−	3.56553i	0.112890	−	0.130282i
$750$	55.6616	+	16.3437i	2.03248	+	0.596789i
$751$	−4.01708	−	27.9394i	−0.146585	−	1.01952i	−0.921756	−	0.387771i	$-0.873245\pi$
$751$	−4.01708	−	27.9394i	−0.146585	−	1.01952i	0.775171	−	0.631752i	$-0.217664\pi$
$752$	−2.63675	−	3.04297i	−0.0961523	−	0.110966i
$753$	1.61896	+	3.54503i	0.0589982	+	0.129188i
$754$	−2.06765	+	0.607117i	−0.0752994	+	0.0221099i
$755$	−6.77505	+	14.8353i	−0.246569	+	0.539912i
$756$	−0.768029	+	5.34176i	−0.0279330	+	0.194278i
$757$	0.102644	−	0.0659655i	0.00373067	−	0.00239756i	−0.538774	−	0.842450i	$-0.681112\pi$
$757$	0.102644	−	0.0659655i	0.00373067	−	0.00239756i	0.542505	+	0.840053i	$0.317476\pi$
$758$	−12.4000			−0.450389
$759$		0			0
$760$	18.6210			0.675453
$761$	−22.4660	+	14.4380i	−0.814392	+	0.523378i	−0.880283	−	0.474449i	$-0.842647\pi$
$761$	−22.4660	+	14.4380i	−0.814392	+	0.523378i	0.0658911	+	0.997827i	$0.479011\pi$
$762$	4.72476	−	32.8615i	0.171160	−	1.19045i
$763$	−15.3716	+	33.6592i	−0.556490	+	1.21854i
$764$	56.8448	−	16.6911i	2.05657	−	0.603864i
$765$	2.65763	+	5.81940i	0.0960869	+	0.210401i
$766$	−0.334300	−	0.385802i	−0.0120787	−	0.0139396i
$767$	0.201849	+	1.40389i	0.00728833	+	0.0506915i
$768$	−11.3225	−	3.32460i	−0.408567	−	0.119966i
$769$	5.14134	−	5.93342i	0.185401	−	0.213965i	−0.655438	−	0.755249i	$-0.727516\pi$
$769$	5.14134	−	5.93342i	0.185401	−	0.213965i	0.840840	+	0.541284i	$0.182062\pi$
$770$	−10.3983	−	6.68255i	−0.374727	−	0.240822i
$771$	−58.0557	−	37.3101i	−2.09082	−	1.34369i
$772$	−27.4031	+	31.6249i	−0.986259	+	1.13820i
$773$	32.8930	+	9.65826i	1.18308	+	0.347384i	0.813361	−	0.581760i	$-0.197636\pi$
$773$	32.8930	+	9.65826i	1.18308	+	0.347384i	0.369719	+	0.929143i	$0.379454\pi$
$774$	−4.63215	−	32.2173i	−0.166499	−	1.15803i
$775$	4.05221	+	4.67650i	0.145560	+	0.167985i
$776$	3.38778	+	7.41820i	0.121614	+	0.266298i
$777$	−22.2200	+	6.52437i	−0.797137	+	0.234061i
$778$	−27.6179	+	60.4748i	−0.990150	+	2.16813i
$779$	0.484630	−	3.37068i	0.0173637	−	0.120767i
$780$	1.46695	−	0.942751i	0.0525252	−	0.0337559i
$781$	1.39619			0.0499596
$782$		0			0
$783$	−3.96386			−0.141657
$784$	1.79266	−	1.15207i	0.0640235	−	0.0411454i
$785$	0.726520	−	5.05306i	0.0259306	−	0.180351i
$786$	29.3778	−	64.3285i	1.04787	−	2.29452i
$787$	−15.3639	+	4.51125i	−0.547664	+	0.160809i	−0.543848	−	0.839184i	$-0.683033\pi$
$787$	−15.3639	+	4.51125i	−0.547664	+	0.160809i	−0.00381653	+	0.999993i	$0.501215\pi$
$788$	13.8546	+	30.3373i	0.493549	+	1.08072i
$789$	−21.2989	−	24.5803i	−0.758261	−	0.875080i
$790$	−2.20178	−	15.3137i	−0.0783359	−	0.544838i
$791$	−3.38825	−	0.994879i	−0.120472	−	0.0353738i
$792$	7.83247	−	9.03916i	0.278315	−	0.321192i
$793$	1.22801	+	0.789191i	0.0436078	+	0.0280250i
$794$	−24.1833	−	15.5417i	−0.858234	−	0.551553i
$795$	−19.9835	+	23.0622i	−0.708741	+	0.817931i
$796$	15.6835	+	4.60509i	0.555887	+	0.163223i
$797$	−3.06314	−	21.3046i	−0.108502	−	0.754649i	−0.969332	−	0.245756i	$-0.920964\pi$
$797$	−3.06314	−	21.3046i	−0.108502	−	0.754649i	0.860830	−	0.508893i	$-0.169945\pi$
$798$	68.7131	+	79.2991i	2.43242	+	2.80716i
$799$	1.67732	+	3.67281i	0.0593392	+	0.129935i
$800$	−23.9800	+	7.04117i	−0.847821	+	0.248943i
$801$	−19.1528	+	41.9387i	−0.676730	+	1.48183i
$802$	6.68791	−	46.5154i	0.236158	−	1.64252i
$803$	10.3647	−	6.66100i	0.365763	−	0.235062i
$804$	−52.1582			−1.83948
$805$		0			0
$806$	0.771816			0.0271860
$807$	21.1386	−	13.5849i	0.744114	−	0.478213i
$808$	0.488605	−	3.39832i	0.0171891	−	0.119553i
$809$	10.0219	−	21.9450i	0.352353	−	0.771544i	−0.647602	−	0.761979i	$-0.724228\pi$
$809$	10.0219	−	21.9450i	0.352353	−	0.771544i	0.999954	−	0.00956540i	$-0.00304481\pi$
$810$	−20.7815	+	6.10200i	−0.730188	+	0.214403i
$811$	5.95634	+	13.0426i	0.209155	+	0.457987i	0.984914	−	0.173043i	$-0.0553600\pi$
$811$	5.95634	+	13.0426i	0.209155	+	0.457987i	−0.775759	+	0.631029i	$0.782633\pi$
$812$	22.0876	+	25.4905i	0.775123	+	0.894540i
$813$	1.57789	+	10.9745i	0.0553390	+	0.384891i
$814$	15.6972	+	4.60912i	0.550187	+	0.161550i
$815$	−11.9752	+	13.8201i	−0.419474	+	0.484098i
$816$	−5.13052	−	3.29718i	−0.179604	−	0.115424i
$817$	−29.9117	−	19.2231i	−1.04648	−	0.672531i
$818$	13.2026	−	15.2366i	0.461618	−	0.532736i
$819$	1.48365	+	0.435640i	0.0518430	+	0.0152225i
$820$	0.214337	+	1.49075i	0.00748499	+	0.0520592i
$821$	−9.30456	−	10.7380i	−0.324732	−	0.374760i	0.569786	−	0.821793i	$-0.307026\pi$
$821$	−9.30456	−	10.7380i	−0.324732	−	0.374760i	−0.894517	+	0.447033i	$0.852481\pi$
$822$	−1.60491	−	3.51426i	−0.0559776	−	0.122574i
$823$	−15.3741	+	4.51423i	−0.535906	+	0.157356i	−0.538476	−	0.842641i	$-0.681000\pi$
$823$	−15.3741	+	4.51423i	−0.535906	+	0.157356i	0.00257065	+	0.999997i	$0.499182\pi$
$824$	−11.9983	+	26.2726i	−0.417980	+	0.915248i
$825$	2.37368	−	16.5093i	0.0826411	−	0.574781i
$826$	31.7536	−	20.4068i	1.10485	−	0.710043i
$827$	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	$0.512695\pi$
$830$	29.5456	−	18.9878i	1.02554	−	0.659077i
$831$	−11.0182	+	76.6334i	−0.382218	+	2.65838i
$832$	−1.04105	+	2.27958i	−0.0360919	+	0.0790302i
$833$	−2.05034	+	0.602033i	−0.0710400	+	0.0208592i
$834$	−32.1090	−	70.3089i	−1.11184	−	2.43460i
$835$	1.07672	+	1.24260i	0.0372615	+	0.0430021i
$836$	−6.20432	−	43.1520i	−0.214581	−	1.49244i
$837$	1.36219	+	0.399975i	0.0470842	+	0.0138252i
$838$	12.9503	−	14.9455i	0.447361	−	0.516282i
$839$	32.4822	+	20.8750i	1.12141	+	0.720687i	0.963750	−	0.266807i	$-0.0859686\pi$
$839$	32.4822	+	20.8750i	1.12141	+	0.720687i	0.157660	+	0.987493i	$0.449605\pi$
$840$	−11.7002	−	7.51925i	−0.403695	−	0.259439i
$841$	2.76766	−	3.19405i	0.0954365	−	0.110140i
$842$	−66.5435	−	19.5389i	−2.29324	−	0.673357i
$843$	−1.28027	−	8.90444i	−0.0440947	−	0.306685i
$844$	26.3099	+	30.3633i	0.905625	+	1.04515i
$845$	6.65765	+	14.5782i	0.229030	+	0.501506i
$846$	18.1526	−	5.33009i	0.624100	−	0.183252i
$847$	7.23975	−	15.8528i	0.248761	−	0.544710i
$848$	2.17380	−	15.1191i	0.0746487	−	0.519193i
$849$	−31.2510	+	20.0838i	−1.07253	+	0.689274i
$850$	11.9317			0.409255
$851$		0			0
$852$	5.24190			0.179584
$853$	−32.3289	+	20.7765i	−1.10692	+	0.711374i	−0.960620	−	0.277867i	$-0.910373\pi$
$853$	−32.3289	+	20.7765i	−1.10692	+	0.711374i	−0.146299	+	0.989240i	$0.546736\pi$
$854$	5.52858	−	38.4521i	0.189184	−	1.31580i
$855$	13.6032	−	29.7869i	0.465220	−	1.01869i
$856$	−3.59832	+	1.05656i	−0.122988	+	0.0361125i
$857$	−21.1402	−	46.2907i	−0.722137	−	1.58126i	−0.810885	−	0.585206i	$-0.801014\pi$
$857$	−21.1402	−	46.2907i	−0.722137	−	1.58126i	0.0887478	−	0.996054i	$-0.471713\pi$
$858$	−1.36236	−	1.57225i	−0.0465103	−	0.0536757i
$859$	−1.30177	−	9.05400i	−0.0444158	−	0.308919i	−0.999904	−	0.0138879i	$-0.995579\pi$
$859$	−1.30177	−	9.05400i	−0.0444158	−	0.308919i	0.955488	−	0.295031i	$-0.0953299\pi$
$860$	15.0884	+	4.43036i	0.514511	+	0.151074i
$861$	−1.66561	+	1.92222i	−0.0567638	+	0.0655089i
$862$	−40.9734	−	26.3320i	−1.39556	−	0.896872i
$863$	10.3801	+	6.67089i	0.353343	+	0.227080i	0.705256	−	0.708953i	$-0.250832\pi$
$863$	10.3801	+	6.67089i	0.353343	+	0.227080i	−0.351913	+	0.936033i	$0.614469\pi$
$864$	−3.75500	+	4.33350i	−0.127748	+	0.147429i
$865$	−20.0928	−	5.89978i	−0.683176	−	0.200599i
$866$	−3.98132	−	27.6907i	−0.135291	−	0.940968i
$867$	−23.9751	−	27.6688i	−0.814238	−	0.939680i
$868$	−5.01834	−	10.9886i	−0.170334	−	0.372979i
$869$	−10.4159	+	3.05838i	−0.353335	+	0.103748i
$870$	14.1596	−	31.0052i	0.480055	−	1.05117i
$871$	−0.203180	+	1.41314i	−0.00688448	+	0.0478826i
$872$	24.7444	−	15.9022i	0.837950	−	0.538517i
$873$	14.3414			0.485381
$874$		0			0
$875$	−24.8534			−0.840199
$876$	38.9137	−	25.0083i	1.31477	−	0.844952i
$877$	−0.328349	+	2.28371i	−0.0110875	+	0.0771156i	−0.994614	−	0.103649i	$-0.966948\pi$
$877$	−0.328349	+	2.28371i	−0.0110875	+	0.0771156i	0.983526	+	0.180765i	$0.0578572\pi$
$878$	16.8629	−	36.9245i	0.569094	−	1.24614i
$879$	51.8803	−	15.2334i	1.74988	−	0.513811i
$880$	−1.52759	−	3.34495i	−0.0514950	−	0.112758i
$881$	23.3133	+	26.9050i	0.785444	+	0.906451i	0.997490	−	0.0708087i	$-0.0225580\pi$
$881$	23.3133	+	26.9050i	0.785444	+	0.906451i	−0.212046	+	0.977260i	$0.568013\pi$
$882$	1.42495	+	9.91073i	0.0479805	+	0.333712i
$883$	−29.2401	−	8.58567i	−0.984008	−	0.288931i	−0.250130	−	0.968212i	$-0.580473\pi$
$883$	−29.2401	−	8.58567i	−0.984008	−	0.288931i	−0.733878	+	0.679282i	$0.762292\pi$
$884$	0.573189	−	0.661496i	0.0192784	−	0.0222485i
$885$	−18.8728	−	12.1288i	−0.634401	−	0.407705i
$886$	−25.7915	−	16.5752i	−0.866483	−	0.556855i
$887$	−13.6153	+	15.7129i	−0.457157	+	0.527588i	−0.936795	−	0.349879i	$-0.886223\pi$
$887$	−13.6153	+	15.7129i	−0.457157	+	0.527588i	0.479638	+	0.877467i	$0.340768\pi$
$888$	17.6626	+	5.18621i	0.592719	+	0.174038i
$889$	2.02419	+	14.0786i	0.0678893	+	0.472180i
$890$	−24.8024	−	28.6235i	−0.831378	−	0.959461i
$891$	6.31317	+	13.8239i	0.211499	+	0.463119i
$892$	11.5188	−	3.38223i	0.385679	−	0.113245i
$893$	8.58543	−	18.7995i	0.287300	−	0.629100i
$894$	−13.1149	+	91.2161i	−0.438628	+	3.05072i
$895$	1.48888	−	0.956844i	0.0497677	−	0.0319838i
$896$	32.5243			1.08656
$897$		0			0
$898$	66.3122			2.21287
$899$	7.46441	−	4.79708i	0.248952	−	0.159992i
$900$	4.67944	−	32.5462i	0.155981	−	1.08487i
$901$	−6.36305	+	13.9331i	−0.211984	+	0.464180i
$902$	1.72403	−	0.506221i	0.0574039	−	0.0168553i
$903$	11.0322	+	24.1571i	0.367127	+	0.803897i
$904$	1.83820	+	2.12140i	0.0611377	+	0.0705567i
$905$	−2.83862	−	19.7431i	−0.0943590	−	0.656282i
$906$	70.0926	+	20.5810i	2.32867	+	0.683759i
$907$	14.8731	−	17.1644i	0.493852	−	0.569936i	−0.453039	−	0.891491i	$-0.649660\pi$
$907$	14.8731	−	17.1644i	0.493852	−	0.569936i	0.946891	+	0.321555i	$0.104205\pi$
$908$	44.2809	+	28.4576i	1.46951	+	0.944399i
$909$	−5.07916	−	3.26418i	−0.168465	−	0.108266i
$910$	−0.831830	+	0.959983i	−0.0275749	+	0.0318231i
$911$	−0.800259	−	0.234977i	−0.0265138	−	0.00778514i	0.268449	−	0.963294i	$-0.413489\pi$
$911$	−0.800259	−	0.234977i	−0.0265138	−	0.00778514i	−0.294963	+	0.955509i	$0.595307\pi$
$912$	4.44254	+	30.8986i	0.147107	+	1.02315i
$913$	−16.1378	−	18.6241i	−0.534085	−	0.616367i
$914$	34.8293	+	76.2655i	1.15205	+	2.52264i
$915$	−22.1538	+	6.50494i	−0.732382	+	0.215047i
$916$	12.9610	−	28.3805i	0.428242	−	0.937719i
$917$	−4.31181	+	29.9893i	−0.142389	+	0.990334i
$918$	2.30295	−	1.48001i	0.0760085	−	0.0488477i
$919$	−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
$922$	16.2396	−	10.4365i	0.534822	−	0.343709i
$923$	0.0204196	−	0.142021i	0.000672118	−	0.00467468i
$924$	−13.5266	+	29.6192i	−0.444994	+	0.974401i
$925$	12.9331	−	3.79751i	0.425239	−	0.124861i
$926$	−25.4821	−	55.7981i	−0.837395	−	1.83364i
$927$	33.2616	+	38.3860i	1.09245	+	1.26076i
$928$	5.10015	+	35.4723i	0.167421	+	1.16444i
$929$	16.9899	+	4.98870i	0.557422	+	0.163674i	0.548296	−	0.836284i	$-0.315277\pi$
$929$	16.9899	+	4.98870i	0.557422	+	0.163674i	0.00912630	+	0.999958i	$0.497095\pi$
$930$	−7.99458	+	9.22623i	−0.262152	+	0.302540i
$931$	9.20148	+	5.91343i	0.301566	+	0.193805i
$932$	10.0062	+	6.43061i	0.327765	+	0.210642i
$933$	0.938384	−	1.08295i	0.0307213	−	0.0354543i
$934$	36.7186	+	10.7816i	1.20147	+	0.352783i
$935$	0.524793	+	3.65001i	0.0171626	+	0.119368i
$936$	−0.804917	−	0.928924i	−0.0263095	−	0.0303628i
$937$	−9.68998	−	21.2181i	−0.316558	−	0.693165i	0.682739	−	0.730663i	$-0.260789\pi$
$937$	−9.68998	−	21.2181i	−0.316558	−	0.693165i	−0.999297	+	0.0374974i	$0.988061\pi$
$938$	36.4554	−	10.7043i	1.19031	−	0.349507i
$939$	22.0642	−	48.3139i	0.720039	−	1.57667i
$940$	−1.30082	+	9.04741i	−0.0424281	+	0.295094i
$941$	9.77096	−	6.27941i	0.318524	−	0.204703i	−0.371602	−	0.928392i	$-0.621191\pi$
$941$	9.77096	−	6.27941i	0.318524	−	0.204703i	0.690126	+	0.723689i	$0.257555\pi$
$942$	−22.8664			−0.745027
$943$		0			0
$944$	11.2294			0.365486
$945$	−1.96560	+	1.26321i	−0.0639409	+	0.0410923i
$946$	2.66998	−	18.5701i	0.0868085	−	0.603766i
$947$	2.49163	−	5.45592i	0.0809672	−	0.177293i	−0.864819	−	0.502084i	$-0.832567\pi$
$947$	2.49163	−	5.45592i	0.0809672	−	0.177293i	0.945786	+	0.324791i	$0.105294\pi$
$948$	−39.1057	+	11.4825i	−1.27010	+	0.372934i
$949$	−0.525975	−	1.15172i	−0.0170739	−	0.0373866i
$950$	−39.9945	−	46.1561i	−1.29759	−	1.49750i
$951$	−3.15197	−	21.9224i	−0.102210	−	0.710884i
$952$	−6.69836	−	1.96682i	−0.217095	−	0.0637449i
$953$	11.7264	−	13.5330i	0.379854	−	0.438375i	−0.533339	−	0.845902i	$-0.679063\pi$
$953$	11.7264	−	13.5330i	0.379854	−	0.438375i	0.913194	+	0.407526i	$0.133608\pi$
$954$	60.3775	+	38.8022i	1.95479	+	1.25627i
$955$	21.5783	+	13.8675i	0.698256	+	0.448742i
$956$	42.1123	−	48.6001i	1.36201	−	1.57184i
$957$	−22.9478	−	6.73807i	−0.741795	−	0.217811i
$958$	7.99002	+	55.5718i	0.258146	+	1.79544i
$959$	1.08390	+	1.25089i	0.0350009	+	0.0403932i
$960$	−16.4666	−	36.0568i	−0.531458	−	1.16373i
$961$	26.6951	−	7.83838i	0.861131	−	0.252851i
$962$	0.698418	−	1.52932i	0.0225179	−	0.0493073i
$963$	−0.938568	+	6.52788i	−0.0302449	+	0.210358i
$964$	14.2451	−	9.15475i	0.458803	−	0.294855i
$965$	−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	$0.318896\pi$
$968$	−11.6541	+	7.48966i	−0.374578	+	0.240727i
$969$	4.45497	−	30.9850i	0.143114	−	0.995381i
$970$	−4.89404	+	10.7164i	−0.157138	+	0.344084i
$971$	−56.8845	+	16.7028i	−1.82551	+	0.536018i	−0.999613	−	0.0278029i	$-0.991149\pi$
$971$	−56.8845	+	16.7028i	−1.82551	+	0.536018i	−0.825897	+	0.563821i	$0.809331\pi$
$972$	26.5369	+	58.1076i	0.851170	+	1.86380i
$973$	21.6853	+	25.0262i	0.695199	+	0.802303i
$974$	1.93216	+	13.4384i	0.0619103	+	0.430596i
$975$	−1.64462	−	0.482905i	−0.0526701	−	0.0154653i
$976$	7.56838	−	8.73438i	0.242258	−	0.279581i
$977$	−10.6351	−	6.83476i	−0.340247	−	0.218663i	0.359347	−	0.933204i	$-0.382999\pi$
$977$	−10.6351	−	6.83476i	−0.340247	−	0.218663i	−0.699594	+	0.714541i	$0.746636\pi$
$978$	68.9067	+	44.2836i	2.20339	+	1.41603i
$979$	−17.4030	+	20.0841i	−0.556201	+	0.641890i
$980$	−4.64152	−	1.36287i	−0.148268	−	0.0435354i
$981$	−7.36134	−	51.1993i	−0.235030	−	1.63467i
$982$	47.1125	+	54.3707i	1.50342	+	1.73504i
$983$	−24.2457	−	53.0907i	−0.773318	−	1.69333i	−0.719208	−	0.694795i	$-0.755495\pi$
$983$	−24.2457	−	53.0907i	−0.773318	−	1.69333i	−0.0541102	−	0.998535i	$-0.517232\pi$
$984$	1.93989	−	0.569603i	0.0618415	−	0.0181583i
$985$	−5.99838	+	13.1346i	−0.191124	+	0.418503i
$986$	2.43489	−	16.9350i	0.0775427	−	0.539321i
$987$	−12.9859	+	8.34550i	−0.413344	+	0.265640i
$988$	−4.48019			−0.142534
$989$		0			0
$990$	17.2784			0.549142
$991$	−38.5219	+	24.7565i	−1.22369	+	0.786417i	−0.982896	−	0.184160i	$-0.941044\pi$
$991$	−38.5219	+	24.7565i	−1.22369	+	0.786417i	−0.240792	+	0.970577i	$0.577407\pi$
$992$	1.82667	−	12.7048i	0.0579970	−	0.403378i
$993$	−31.5181	+	69.0150i	−1.00020	+	2.19013i
$994$	−3.66377	+	1.07578i	−0.116208	+	0.0341216i
$995$	2.93984	+	6.43735i	0.0931992	+	0.204078i
$996$	−60.5885	−	69.9228i	−1.91982	−	2.21559i
$997$	5.60039	+	38.9515i	0.177366	+	1.23361i	0.862827	+	0.505499i	$0.168691\pi$
$997$	5.60039	+	38.9515i	0.177366	+	1.23361i	−0.685461	+	0.728109i	$0.740399\pi$
$998$	18.1278	+	5.32281i	0.573826	+	0.168490i
$999$	2.02518	−	2.33719i	0.0640740	−	0.0739453i

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.i.334.1		10
23.2	even	11	inner	529.2.c.i.255.1		10
23.3	even	11		529.2.c.d.177.1		10
23.4	even	11		23.2.c.a.8.1	yes	10
23.5	odd	22		529.2.a.j.1.5		5
23.6	even	11		529.2.c.b.501.1		10
23.7	odd	22		529.2.c.e.266.1		10
23.8	even	11		529.2.c.b.170.1		10
23.9	even	11		529.2.c.g.466.1		10
23.10	odd	22		529.2.c.f.487.1		10
23.11	odd	22		529.2.c.a.118.1		10
23.12	even	11		23.2.c.a.3.1	✓	10
23.13	even	11		529.2.c.g.487.1		10
23.14	odd	22		529.2.c.f.466.1		10
23.15	odd	22		529.2.c.c.170.1		10
23.16	even	11		529.2.c.d.266.1		10
23.17	odd	22		529.2.c.c.501.1		10
23.18	even	11		529.2.a.i.1.5		5
23.19	odd	22		529.2.c.a.399.1		10
23.20	odd	22		529.2.c.e.177.1		10
23.21	odd	22		529.2.c.h.255.1		10
23.22	odd	2		529.2.c.h.334.1		10
69.5	even	22		4761.2.a.bn.1.1		5
69.35	odd	22		207.2.i.c.118.1		10
69.41	odd	22		4761.2.a.bo.1.1		5
69.50	odd	22		207.2.i.c.100.1		10
92.27	odd	22		368.2.m.c.353.1		10
92.35	odd	22		368.2.m.c.49.1		10
92.51	even	22		8464.2.a.bt.1.5		5
92.87	odd	22		8464.2.a.bs.1.5		5
115.4	even	22		575.2.k.b.376.1		10
115.12	odd	44		575.2.p.b.49.2		20
115.27	odd	44		575.2.p.b.399.1		20
115.58	odd	44		575.2.p.b.49.1		20
115.73	odd	44		575.2.p.b.399.2		20
115.104	even	22		575.2.k.b.26.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	23.12	even	11
23.2.c.a.8.1	yes	10	23.4	even	11
207.2.i.c.100.1		10	69.50	odd	22
207.2.i.c.118.1		10	69.35	odd	22
368.2.m.c.49.1		10	92.35	odd	22
368.2.m.c.353.1		10	92.27	odd	22
529.2.a.i.1.5		5	23.18	even	11
529.2.a.j.1.5		5	23.5	odd	22
529.2.c.a.118.1		10	23.11	odd	22
529.2.c.a.399.1		10	23.19	odd	22
529.2.c.b.170.1		10	23.8	even	11
529.2.c.b.501.1		10	23.6	even	11
529.2.c.c.170.1		10	23.15	odd	22
529.2.c.c.501.1		10	23.17	odd	22
529.2.c.d.177.1		10	23.3	even	11
529.2.c.d.266.1		10	23.16	even	11
529.2.c.e.177.1		10	23.20	odd	22
529.2.c.e.266.1		10	23.7	odd	22
529.2.c.f.466.1		10	23.14	odd	22
529.2.c.f.487.1		10	23.10	odd	22
529.2.c.g.466.1		10	23.9	even	11
529.2.c.g.487.1		10	23.13	even	11
529.2.c.h.255.1		10	23.21	odd	22
529.2.c.h.334.1		10	23.22	odd	2
529.2.c.i.255.1		10	23.2	even	11	inner
529.2.c.i.334.1		10	1.1	even	1	trivial
575.2.k.b.26.1		10	115.104	even	22
575.2.k.b.376.1		10	115.4	even	22
575.2.p.b.49.1		20	115.58	odd	44
575.2.p.b.49.2		20	115.12	odd	44
575.2.p.b.399.1		20	115.27	odd	44
575.2.p.b.399.2		20	115.73	odd	44
4761.2.a.bn.1.1		5	69.5	even	22
4761.2.a.bo.1.1		5	69.41	odd	22
8464.2.a.bs.1.5		5	92.87	odd	22
8464.2.a.bt.1.5		5	92.51	even	22

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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.i.334.1

Level	$529$
Weight	$2$
Character	529.334
Analytic conductor	$4.224$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$