LMFDB - Embedded newform 58.2.d.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(7,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	58.49
Dual form			58.2.d.a.45.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.900969 - 0.433884i) q^{2} +(0.500000 + 0.626980i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.92543 + 1.40881i) q^{5} +(0.722521 + 0.347948i) q^{6} +(-1.62349 - 2.03579i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.524459 - 2.29780i) q^{9} +(-2.02446 + 2.53859i) q^{10} +(1.20291 + 5.27028i) q^{11} +0.801938 q^{12} +(-0.425428 - 1.86392i) q^{13} +(-2.34601 - 1.12978i) q^{14} +(-2.34601 - 1.12978i) q^{15} +(-0.222521 - 0.974928i) q^{16} +2.85086 q^{17} +(-0.524459 - 2.29780i) q^{18} +(-3.20291 + 4.01632i) q^{19} +(-0.722521 + 3.16557i) q^{20} +(0.464656 - 2.03579i) q^{21} +(3.37047 + 4.22643i) q^{22} +(1.82640 + 0.879546i) q^{23} +(0.722521 - 0.347948i) q^{24} +(3.45593 - 4.33360i) q^{25} +(-1.19202 - 1.49475i) q^{26} +(3.87047 - 1.86392i) q^{27} -2.60388 q^{28} +(3.51357 - 4.08103i) q^{29} -2.60388 q^{30} +(-1.64795 + 0.793610i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-2.70291 + 3.38934i) q^{33} +(2.56853 - 1.23694i) q^{34} +(7.61745 + 3.66837i) q^{35} +(-1.46950 - 1.84270i) q^{36} +(1.50484 - 6.59315i) q^{37} +(-1.14310 + 5.00827i) q^{38} +(0.955927 - 1.19869i) q^{39} +(0.722521 + 3.16557i) q^{40} -9.78986 q^{41} +(-0.464656 - 2.03579i) q^{42} +(2.33728 + 1.12558i) q^{43} +(4.87047 + 2.34549i) q^{44} +(1.70291 + 7.46092i) q^{45} +2.02715 q^{46} +(0.500000 + 2.19064i) q^{47} +(0.500000 - 0.626980i) q^{48} +(0.0489173 - 0.214321i) q^{49} +(1.23341 - 5.40391i) q^{50} +(1.42543 + 1.78743i) q^{51} +(-1.72252 - 0.829522i) q^{52} +(-11.1773 + 5.38268i) q^{53} +(2.67845 - 3.35867i) q^{54} +(-10.9438 - 13.7231i) q^{55} +(-2.34601 + 1.12978i) q^{56} -4.11960 q^{57} +(1.39493 - 5.20136i) q^{58} -10.8509 q^{59} +(-2.34601 + 1.12978i) q^{60} +(5.56584 + 6.97935i) q^{61} +(-1.14042 + 1.43004i) q^{62} +(-5.52930 + 2.66277i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.87047 + 4.85342i) q^{65} +(-0.964656 + 4.22643i) q^{66} +(2.44773 - 10.7242i) q^{67} +(1.77748 - 2.22889i) q^{68} +(0.361740 + 1.58489i) q^{69} +8.45473 q^{70} +(1.40701 + 6.16451i) q^{71} +(-2.12349 - 1.02262i) q^{72} +(8.39977 + 4.04512i) q^{73} +(-1.50484 - 6.59315i) q^{74} +4.44504 q^{75} +(1.14310 + 5.00827i) q^{76} +(8.77628 - 11.0051i) q^{77} +(0.341166 - 1.49475i) q^{78} +(-1.69202 + 7.41323i) q^{79} +(2.02446 + 2.53859i) q^{80} +(-3.26659 - 1.57311i) q^{81} +(-8.82036 + 4.24766i) q^{82} +(4.76391 - 5.97375i) q^{83} +(-1.30194 - 1.63258i) q^{84} +(-8.33997 + 4.01632i) q^{85} +2.59419 q^{86} +(4.31551 + 0.162426i) q^{87} +5.40581 q^{88} +(7.30678 - 3.51876i) q^{89} +(4.77144 + 5.98319i) q^{90} +(-3.10388 + 3.89214i) q^{91} +(1.82640 - 0.879546i) q^{92} +(-1.32155 - 0.636426i) q^{93} +(1.40097 + 1.75676i) q^{94} +(3.71164 - 16.2617i) q^{95} +(0.178448 - 0.781831i) q^{96} +(1.41789 - 1.77798i) q^{97} +(-0.0489173 - 0.214321i) q^{98} +12.7409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} + q^{8} - 6 q^{9} - 3 q^{10} - 6 q^{11} - 4 q^{12} + 11 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - 10 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{20}+ \cdots + 48 q^{99}+O(q^{100}) $ 6 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 + q^8 - 6 * q^9 - 3 * q^10 - 6 * q^11 - 4 * q^12 + 11 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - 10 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^20 + 15 * q^21 + 6 * q^22 - 7 * q^23 + 4 * q^24 + 17 * q^25 + 3 * q^26 + 9 * q^27 + 2 * q^28 + 15 * q^29 + 2 * q^30 + 4 * q^31 + q^32 - 3 * q^33 + 10 * q^34 + 22 * q^35 + q^36 - 13 * q^37 - 15 * q^38 + 2 * q^39 + 4 * q^40 - 12 * q^41 - 15 * q^42 - 7 * q^43 + 15 * q^44 - 3 * q^45 + 3 * q^47 + 3 * q^48 - 18 * q^49 + 4 * q^50 - 5 * q^51 - 10 * q^52 - 22 * q^53 + 12 * q^54 - 24 * q^55 - 9 * q^56 + 18 * q^57 - 15 * q^58 - 38 * q^59 - 9 * q^60 + 31 * q^61 - 18 * q^62 - 2 * q^63 - q^64 + 9 * q^65 - 18 * q^66 + 11 * q^67 + 11 * q^68 - 28 * q^69 + 6 * q^70 + 23 * q^71 - 8 * q^72 + 5 * q^73 + 13 * q^74 + 26 * q^75 + 15 * q^76 + 12 * q^77 + 19 * q^78 + 3 * q^80 - 23 * q^81 - 16 * q^82 + 35 * q^83 + q^84 - 26 * q^85 + 42 * q^86 + 11 * q^87 + 6 * q^88 + 13 * q^89 + 10 * q^90 - q^91 - 7 * q^92 - 12 * q^93 + 4 * q^94 + 25 * q^95 - 3 * q^96 + 20 * q^97 + 18 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	0.500000	+	0.626980i	0.288675	+	0.361987i	0.904931	−	0.425559i	$-0.139923\pi$
$3$	0.500000	+	0.626980i	0.288675	+	0.361987i	−0.616255	+	0.787546i	$0.711351\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−2.92543	+	1.40881i	−1.30829	+	0.630040i	−0.952504	−	0.304527i	$-0.901502\pi$
$5$	−2.92543	+	1.40881i	−1.30829	+	0.630040i	−0.355787	+	0.934567i	$0.615787\pi$
$6$	0.722521	+	0.347948i	0.294968	+	0.142049i
$7$	−1.62349	−	2.03579i	−0.613621	−	0.769457i	0.373810	−	0.927505i	$-0.378051\pi$
$7$	−1.62349	−	2.03579i	−0.613621	−	0.769457i	−0.987431	+	0.158048i	$0.949480\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	0.524459	−	2.29780i	0.174820	−	0.765935i
$10$	−2.02446	+	2.53859i	−0.640190	+	0.802773i
$11$	1.20291	+	5.27028i	0.362690	+	1.58905i	0.746337	+	0.665569i	$0.231811\pi$
$11$	1.20291	+	5.27028i	0.362690	+	1.58905i	−0.383647	+	0.923480i	$0.625332\pi$
$12$	0.801938			0.231499
$13$	−0.425428	−	1.86392i	−0.117992	−	0.516958i	−0.999035	−	0.0439215i	$-0.986015\pi$
$13$	−0.425428	−	1.86392i	−0.117992	−	0.516958i	0.881043	−	0.473037i	$-0.156842\pi$
$14$	−2.34601	−	1.12978i	−0.626998	−	0.301946i
$15$	−2.34601	−	1.12978i	−0.605737	−	0.291708i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	2.85086			0.691434			0.345717	−	0.938339i	$-0.387636\pi$
$17$	2.85086			0.691434			0.345717	+	0.938339i	$0.387636\pi$
$18$	−0.524459	−	2.29780i	−0.123616	−	0.541597i
$19$	−3.20291	+	4.01632i	−0.734797	+	0.921407i	−0.999073	−	0.0430405i	$-0.986296\pi$
$19$	−3.20291	+	4.01632i	−0.734797	+	0.921407i	0.264276	+	0.964447i	$0.414867\pi$
$20$	−0.722521	+	3.16557i	−0.161561	+	0.707843i
$21$	0.464656	−	2.03579i	0.101396	−	0.444246i
$22$	3.37047	+	4.22643i	0.718586	+	0.901079i
$23$	1.82640	+	0.879546i	0.380830	+	0.183398i	0.614498	−	0.788918i	$-0.289359\pi$
$23$	1.82640	+	0.879546i	0.380830	+	0.183398i	−0.233668	+	0.972316i	$0.575073\pi$
$24$	0.722521	−	0.347948i	0.147484	−	0.0710245i
$25$	3.45593	−	4.33360i	0.691185	−	0.866719i
$26$	−1.19202	−	1.49475i	−0.233775	−	0.293144i
$27$	3.87047	−	1.86392i	0.744872	−	0.358712i
$28$	−2.60388			−0.492086
$29$	3.51357	−	4.08103i	0.652454	−	0.757828i
$29$	3.51357	−	4.08103i	0.652454	−	0.757828i
$30$	−2.60388			−0.475400
$31$	−1.64795	+	0.793610i	−0.295980	+	0.142537i	−0.575981	−	0.817463i	$-0.695380\pi$
$31$	−1.64795	+	0.793610i	−0.295980	+	0.142537i	0.280000	+	0.960000i	$0.409665\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−2.70291	+	3.38934i	−0.470516	+	0.590008i
$34$	2.56853	−	1.23694i	0.440500	−	0.212133i
$35$	7.61745	+	3.66837i	1.28758	+	0.620068i
$36$	−1.46950	−	1.84270i	−0.244917	−	0.307116i
$37$	1.50484	−	6.59315i	0.247395	−	1.08391i	−0.686716	−	0.726926i	$-0.740949\pi$
$37$	1.50484	−	6.59315i	0.247395	−	1.08391i	0.934111	−	0.356982i	$-0.116194\pi$
$38$	−1.14310	+	5.00827i	−0.185436	+	0.812448i
$39$	0.955927	−	1.19869i	0.153071	−	0.191945i
$40$	0.722521	+	3.16557i	0.114241	+	0.500521i
$41$	−9.78986			−1.52892			−0.764459	−	0.644672i	$-0.776994\pi$
$41$	−9.78986			−1.52892			−0.764459	+	0.644672i	$0.776994\pi$
$42$	−0.464656	−	2.03579i	−0.0716980	−	0.314129i
$43$	2.33728	+	1.12558i	0.356432	+	0.171649i	0.603527	−	0.797343i	$-0.293762\pi$
$43$	2.33728	+	1.12558i	0.356432	+	0.171649i	−0.247095	+	0.968991i	$0.579476\pi$
$44$	4.87047	+	2.34549i	0.734251	+	0.353597i
$45$	1.70291	+	7.46092i	0.253854	+	1.11221i
$46$	2.02715			0.298887
$47$	0.500000	+	2.19064i	0.0729325	+	0.319538i	0.998214	−	0.0597435i	$-0.0190283\pi$
$47$	0.500000	+	2.19064i	0.0729325	+	0.319538i	−0.925281	+	0.379282i	$0.876171\pi$
$48$	0.500000	−	0.626980i	0.0721688	−	0.0904968i
$49$	0.0489173	−	0.214321i	0.00698819	−	0.0306173i
$50$	1.23341	−	5.40391i	0.174430	−	0.764228i
$51$	1.42543	+	1.78743i	0.199600	+	0.250290i
$52$	−1.72252	−	0.829522i	−0.238871	−	0.115034i
$53$	−11.1773	+	5.38268i	−1.53531	+	0.739368i	−0.994789	−	0.101960i	$-0.967489\pi$
$53$	−11.1773	+	5.38268i	−1.53531	+	0.739368i	−0.540525	+	0.841328i	$0.681774\pi$
$54$	2.67845	−	3.35867i	0.364491	−	0.457057i
$55$	−10.9438	−	13.7231i	−1.47567	−	1.85043i
$56$	−2.34601	+	1.12978i	−0.313499	+	0.150973i
$57$	−4.11960			−0.545655
$58$	1.39493	−	5.20136i	0.183163	−	0.682972i
$59$	−10.8509			−1.41266			−0.706331	−	0.707882i	$-0.749651\pi$
$59$	−10.8509			−1.41266			−0.706331	+	0.707882i	$0.749651\pi$
$60$	−2.34601	+	1.12978i	−0.302869	+	0.145854i
$61$	5.56584	+	6.97935i	0.712633	+	0.893614i	0.997896	−	0.0648356i	$-0.0206523\pi$
$61$	5.56584	+	6.97935i	0.712633	+	0.893614i	−0.285263	+	0.958449i	$0.592081\pi$
$62$	−1.14042	+	1.43004i	−0.144833	+	0.181615i
$63$	−5.52930	+	2.66277i	−0.696627	+	0.335478i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	3.87047	+	4.85342i	0.480073	+	0.601992i
$66$	−0.964656	+	4.22643i	−0.118741	+	0.520238i
$67$	2.44773	−	10.7242i	0.299038	−	1.31017i	−0.572525	−	0.819887i	$-0.694036\pi$
$67$	2.44773	−	10.7242i	0.299038	−	1.31017i	0.871563	−	0.490283i	$-0.163107\pi$
$68$	1.77748	−	2.22889i	0.215551	−	0.270292i
$69$	0.361740	+	1.58489i	0.0435484	+	0.190798i
$70$	8.45473			1.01053
$71$	1.40701	+	6.16451i	0.166981	+	0.731593i	0.987193	+	0.159532i	$0.0509986\pi$
$71$	1.40701	+	6.16451i	0.166981	+	0.731593i	−0.820211	+	0.572061i	$0.806144\pi$
$72$	−2.12349	−	1.02262i	−0.250256	−	0.120517i
$73$	8.39977	+	4.04512i	0.983119	+	0.473445i	0.855177	−	0.518336i	$-0.173449\pi$
$73$	8.39977	+	4.04512i	0.983119	+	0.473445i	0.127942	+	0.991782i	$0.459163\pi$
$74$	−1.50484	−	6.59315i	−0.174935	−	0.766439i
$75$	4.44504			0.513269
$76$	1.14310	+	5.00827i	0.131123	+	0.574488i
$77$	8.77628	−	11.0051i	1.00015	−	1.25415i
$78$	0.341166	−	1.49475i	0.0386295	−	0.169247i
$79$	−1.69202	+	7.41323i	−0.190367	+	0.834054i	0.786050	+	0.618163i	$0.212123\pi$
$79$	−1.69202	+	7.41323i	−0.190367	+	0.834054i	−0.976417	+	0.215891i	$0.930734\pi$
$80$	2.02446	+	2.53859i	0.226341	+	0.283823i
$81$	−3.26659	−	1.57311i	−0.362955	−	0.174790i
$82$	−8.82036	+	4.24766i	−0.974045	+	0.469076i
$83$	4.76391	−	5.97375i	0.522907	−	0.655704i	−0.448317	−	0.893875i	$-0.647976\pi$
$83$	4.76391	−	5.97375i	0.522907	−	0.655704i	0.971223	+	0.238171i	$0.0765478\pi$
$84$	−1.30194	−	1.63258i	−0.142053	−	0.178129i
$85$	−8.33997	+	4.01632i	−0.904597	+	0.435631i
$86$	2.59419			0.279738
$87$	4.31551	+	0.162426i	0.462671	+	0.0174139i
$88$	5.40581			0.576262
$89$	7.30678	−	3.51876i	0.774517	−	0.372988i	−0.00450031	−	0.999990i	$-0.501432\pi$
$89$	7.30678	−	3.51876i	0.774517	−	0.372988i	0.779018	+	0.627002i	$0.215718\pi$
$90$	4.77144	+	5.98319i	0.502954	+	0.630684i
$91$	−3.10388	+	3.89214i	−0.325375	+	0.408007i
$92$	1.82640	−	0.879546i	0.190415	−	0.0916990i
$93$	−1.32155	−	0.636426i	−0.137039	−	0.0659943i
$94$	1.40097	+	1.75676i	0.144499	+	0.181196i
$95$	3.71164	−	16.2617i	0.380806	−	1.66842i
$96$	0.178448	−	0.781831i	0.0182128	−	0.0797953i
$97$	1.41789	−	1.77798i	0.143965	−	0.180527i	−0.704621	−	0.709584i	$-0.748883\pi$
$97$	1.41789	−	1.77798i	0.143965	−	0.180527i	0.848586	+	0.529057i	$0.177454\pi$
$98$	−0.0489173	−	0.214321i	−0.00494140	−	0.0216497i
$99$	12.7409			1.28051
$100$	−1.23341	−	5.40391i	−0.123341	−	0.540391i
$101$	−2.01573	−	0.970724i	−0.200573	−	0.0965907i	0.330901	−	0.943665i	$-0.392647\pi$
$101$	−2.01573	−	0.970724i	−0.200573	−	0.0965907i	−0.531474	+	0.847075i	$0.678362\pi$
$102$	2.05980	+	0.991949i	0.203951	+	0.0982175i
$103$	−0.338478	−	1.48297i	−0.0333512	−	0.146121i	0.955511	−	0.294956i	$-0.0953049\pi$
$103$	−0.338478	−	1.48297i	−0.0333512	−	0.146121i	−0.988862	+	0.148835i	$0.952448\pi$
$104$	−1.91185			−0.187473
$105$	1.50873	+	6.61017i	0.147237	+	0.645087i
$106$	−7.73490	+	9.69926i	−0.751280	+	0.942075i
$107$	−1.98158	+	8.68188i	−0.191567	+	0.839309i	0.784202	+	0.620505i	$0.213073\pi$
$107$	−1.98158	+	8.68188i	−0.191567	+	0.839309i	−0.975769	+	0.218803i	$0.929785\pi$
$108$	0.955927	−	4.18819i	0.0919841	−	0.403009i
$109$	6.41939	+	8.04966i	0.614866	+	0.771017i	0.987612	−	0.156916i	$-0.0501552\pi$
$109$	6.41939	+	8.04966i	0.614866	+	0.771017i	−0.372746	+	0.927933i	$0.621584\pi$
$110$	−15.8143	−	7.61577i	−1.50784	−	0.726135i
$111$	4.88620	−	2.35307i	0.463777	−	0.223343i
$112$	−1.62349	+	2.03579i	−0.153405	+	0.192364i
$113$	−2.26995	−	2.84642i	−0.213539	−	0.267769i	0.663513	−	0.748164i	$-0.269065\pi$
$113$	−2.26995	−	2.84642i	−0.213539	−	0.267769i	−0.877052	+	0.480395i	$0.840493\pi$
$114$	−3.71164	+	1.78743i	−0.347627	+	0.167408i
$115$	−6.58211			−0.613784
$116$	−1.00000	−	5.29150i	−0.0928477	−	0.491304i
$117$	−4.50604			−0.416584
$118$	−9.77628	+	4.70801i	−0.899980	+	0.433407i
$119$	−4.62833	−	5.80375i	−0.424279	−	0.532029i
$120$	−1.62349	+	2.03579i	−0.148204	+	0.185842i
$121$	−16.4182	+	7.90658i	−1.49256	+	0.718780i
$122$	8.04288	+	3.87325i	0.728168	+	0.350667i
$123$	−4.89493	−	6.13805i	−0.441361	−	0.553449i
$124$	−0.407010	+	1.78323i	−0.0365505	+	0.160138i
$125$	−0.392240	+	1.71851i	−0.0350830	+	0.153709i
$126$	−3.82640	+	4.79815i	−0.340882	+	0.427453i
$127$	−4.07553	−	17.8561i	−0.361645	−	1.58447i	−0.749020	−	0.662548i	$-0.769475\pi$
$127$	−4.07553	−	17.8561i	−0.361645	−	1.58447i	0.387375	−	0.921922i	$-0.373382\pi$
$128$	−1.00000			−0.0883883
$129$	0.462927	+	2.02822i	0.0407585	+	0.178575i
$130$	5.59299	+	2.69344i	0.490538	+	0.236231i
$131$	−6.06249	−	2.91954i	−0.529682	−	0.255082i	0.149874	−	0.988705i	$-0.452113\pi$
$131$	−6.06249	−	2.91954i	−0.529682	−	0.255082i	−0.679556	+	0.733624i	$0.737828\pi$
$132$	0.964656	+	4.22643i	0.0839625	+	0.367864i
$133$	13.3763			1.15987
$134$	−2.44773	−	10.7242i	−0.211452	−	0.926430i
$135$	−8.69687	+	10.9055i	−0.748507	+	0.938598i
$136$	0.634375	−	2.77938i	0.0543972	−	0.238330i
$137$	2.39008	−	10.4716i	0.204199	−	0.894653i	−0.764148	−	0.645042i	$-0.776840\pi$
$137$	2.39008	−	10.4716i	0.204199	−	0.894653i	0.968346	−	0.249611i	$-0.0803028\pi$
$138$	1.01357	+	1.27098i	0.0862811	+	0.108193i
$139$	15.6359	+	7.52984i	1.32622	+	0.638672i	0.956842	−	0.290608i	$-0.0938576\pi$
$139$	15.6359	+	7.52984i	1.32622	+	0.638672i	0.369375	+	0.929281i	$0.379572\pi$
$140$	7.61745	−	3.66837i	0.643792	−	0.310034i
$141$	−1.12349	+	1.40881i	−0.0946149	+	0.118643i
$142$	3.94235	+	4.94355i	0.330835	+	0.414854i
$143$	9.31163	−	4.48424i	0.778677	−	0.374991i
$144$	−2.35690			−0.196408
$145$	−4.52930	+	16.8887i	−0.376138	+	1.40253i
$146$	9.32304			0.771581
$147$	0.158834	−	0.0764902i	0.0131004	−	0.00630881i
$148$	−4.21648	−	5.28730i	−0.346593	−	0.434613i
$149$	−11.5809	+	14.5220i	−0.948745	+	1.18969i	0.0329939	+	0.999456i	$0.489496\pi$
$149$	−11.5809	+	14.5220i	−0.948745	+	1.18969i	−0.981739	+	0.190233i	$0.939076\pi$
$150$	4.00484	−	1.92863i	0.326994	−	0.157472i
$151$	5.50484	+	2.65099i	0.447978	+	0.215735i	0.644250	−	0.764815i	$-0.277169\pi$
$151$	5.50484	+	2.65099i	0.447978	+	0.215735i	−0.196273	+	0.980549i	$0.562884\pi$
$152$	3.20291	+	4.01632i	0.259790	+	0.325766i
$153$	1.49516	−	6.55070i	0.120876	−	0.529593i
$154$	3.13222	−	13.7231i	0.252401	−	1.10584i
$155$	3.70291	−	4.64330i	0.297425	−	0.372959i
$156$	−0.341166	−	1.49475i	−0.0273152	−	0.119676i
$157$	−6.52111			−0.520441			−0.260220	−	0.965549i	$-0.583795\pi$
$157$	−6.52111			−0.520441			−0.260220	+	0.965549i	$0.583795\pi$
$158$	1.69202	+	7.41323i	0.134610	+	0.589765i
$159$	−8.96346	−	4.31657i	−0.710849	−	0.342327i
$160$	2.92543	+	1.40881i	0.231275	+	0.111376i
$161$	−1.17456	−	5.14610i	−0.0925685	−	0.405569i
$162$	−3.62565			−0.284858
$163$	1.35743	+	5.94728i	0.106322	+	0.465827i	0.999858	+	0.0168361i	$0.00535934\pi$
$163$	1.35743	+	5.94728i	0.106322	+	0.465827i	−0.893536	+	0.448991i	$0.851784\pi$
$164$	−6.10388	+	7.65402i	−0.476633	+	0.597678i
$165$	3.13222	−	13.7231i	0.243843	−	1.06835i
$166$	1.70022	−	7.44914i	0.131963	−	0.578166i
$167$	−0.131023	−	0.164297i	−0.0101388	−	0.0127137i	0.776736	−	0.629826i	$-0.216874\pi$
$167$	−0.131023	−	0.164297i	−0.0101388	−	0.0127137i	−0.786875	+	0.617112i	$0.788302\pi$
$168$	−1.88135	−	0.906013i	−0.145150	−	0.0699004i
$169$	8.41939	−	4.05456i	0.647645	−	0.311889i
$170$	−5.77144	+	7.23715i	−0.442649	+	0.555064i
$171$	7.54892	+	9.46604i	0.577280	+	0.723886i
$172$	2.33728	−	1.12558i	0.178216	−	0.0858243i
$173$	17.8388			1.35626			0.678128	−	0.734943i	$-0.262791\pi$
$173$	17.8388			1.35626			0.678128	+	0.734943i	$0.262791\pi$
$174$	3.95862	−	1.72609i	0.300102	−	0.130854i
$175$	−14.4330			−1.09103
$176$	4.87047	−	2.34549i	0.367125	−	0.176798i
$177$	−5.42543	−	6.80327i	−0.407800	−	0.511365i
$178$	5.05645	−	6.34059i	0.378997	−	0.475247i
$179$	5.02446	−	2.41965i	0.375546	−	0.180853i	−0.236583	−	0.971611i	$-0.576028\pi$
$179$	5.02446	−	2.41965i	0.375546	−	0.180853i	0.612129	+	0.790758i	$0.290313\pi$
$180$	6.89493	+	3.32042i	0.513918	+	0.247490i
$181$	−8.63922	−	10.8332i	−0.642148	−	0.805228i	0.349122	−	0.937077i	$-0.386480\pi$
$181$	−8.63922	−	10.8332i	−0.642148	−	0.805228i	−0.991270	+	0.131849i	$0.957909\pi$
$182$	−1.10776	+	4.85342i	−0.0821127	+	0.359759i
$183$	−1.59299	+	6.97935i	−0.117757	+	0.515928i
$184$	1.26391	−	1.58489i	0.0931764	−	0.116839i
$185$	4.88620	+	21.4078i	0.359240	+	1.57394i
$186$	−1.46681			−0.107552
$187$	3.42931	+	15.0248i	0.250776	+	1.09872i
$188$	2.02446	+	0.974928i	0.147649	+	0.0711039i
$189$	−10.0782	−	4.85342i	−0.733083	−	0.353034i
$190$	−3.71164	−	16.2617i	−0.269270	−	1.17975i
$191$	6.24698			0.452016			0.226008	−	0.974125i	$-0.427433\pi$
$191$	6.24698			0.452016			0.226008	+	0.974125i	$0.427433\pi$
$192$	−0.178448	−	0.781831i	−0.0128784	−	0.0564238i
$193$	−1.15548	+	1.44893i	−0.0831734	+	0.104296i	−0.821677	−	0.569953i	$-0.806961\pi$
$193$	−1.15548	+	1.44893i	−0.0831734	+	0.104296i	0.738504	+	0.674249i	$0.235533\pi$
$194$	0.506041	−	2.21711i	0.0363316	−	0.159179i
$195$	−1.10776	+	4.85342i	−0.0793284	+	0.347560i
$196$	−0.137063	−	0.171872i	−0.00979024	−	0.0122766i
$197$	−6.43512	−	3.09899i	−0.458483	−	0.220794i	0.190363	−	0.981714i	$-0.439034\pi$
$197$	−6.43512	−	3.09899i	−0.458483	−	0.220794i	−0.648846	+	0.760920i	$0.724748\pi$
$198$	11.4792	−	5.52809i	0.815790	−	0.392864i
$199$	−6.47016	+	8.11333i	−0.458658	+	0.575139i	−0.956353	−	0.292213i	$-0.905608\pi$
$199$	−6.47016	+	8.11333i	−0.458658	+	0.575139i	0.497695	+	0.867352i	$0.334180\pi$
$200$	−3.45593	−	4.33360i	−0.244371	−	0.306431i
$201$	7.94773	−	3.82743i	0.560590	−	0.269966i
$202$	−2.23729			−0.157415
$203$	−14.0124	−	0.527395i	−0.983476	−	0.0370158i
$204$	2.28621			0.160067
$205$	28.6395	−	13.7921i	2.00027	−	0.963279i
$206$	−0.948394	−	1.18925i	−0.0660778	−	0.0828589i
$207$	2.97889	−	3.73541i	0.207047	−	0.259629i
$208$	−1.72252	+	0.829522i	−0.119435	+	0.0575170i
$209$	−25.0199	−	12.0490i	−1.73066	−	0.833444i
$210$	4.22737	+	5.30095i	0.291716	+	0.365800i
$211$	−1.83848	+	8.05490i	−0.126566	+	0.554522i	0.871388	+	0.490594i	$0.163220\pi$
$211$	−1.83848	+	8.05490i	−0.126566	+	0.554522i	−0.997954	+	0.0639284i	$0.979637\pi$
$212$	−2.76055	+	12.0948i	−0.189596	+	0.830672i
$213$	−3.16152	+	3.96442i	−0.216624	+	0.271638i
$214$	1.98158	+	8.68188i	0.135458	+	0.593481i
$215$	−8.42327			−0.574462
$216$	−0.955927	−	4.18819i	−0.0650426	−	0.284970i
$217$	4.29105	+	2.06646i	0.291296	+	0.140281i
$218$	9.27628	+	4.46722i	0.628269	+	0.302558i
$219$	1.66368	+	7.28905i	0.112421	+	0.492548i
$220$	−17.5526			−1.18339
$221$	−1.21283	−	5.31377i	−0.0815839	−	0.357443i
$222$	3.38135	−	4.24008i	0.226942	−	0.284576i
$223$	−0.885239	+	3.87849i	−0.0592800	+	0.259723i	−0.995880	−	0.0906767i	$-0.971097\pi$
$223$	−0.885239	+	3.87849i	−0.0592800	+	0.259723i	0.936600	+	0.350399i	$0.113954\pi$
$224$	−0.579417	+	2.53859i	−0.0387139	+	0.169617i
$225$	−8.14526	−	10.2138i	−0.543017	−	0.680922i
$226$	−3.28017	−	1.57965i	−0.218193	−	0.105076i
$227$	−9.88889	+	4.76224i	−0.656349	+	0.316081i	−0.732251	−	0.681034i	$-0.761530\pi$
$227$	−9.88889	+	4.76224i	−0.656349	+	0.316081i	0.0759029	+	0.997115i	$0.475816\pi$
$228$	−2.56853	+	3.22084i	−0.170105	+	0.213305i
$229$	3.17510	+	3.98144i	0.209816	+	0.263101i	0.875593	−	0.483050i	$-0.160471\pi$
$229$	3.17510	+	3.98144i	0.209816	+	0.263101i	−0.665777	+	0.746151i	$0.731900\pi$
$230$	−5.93027	+	2.85587i	−0.391031	+	0.188310i
$231$	11.2881			0.742704
$232$	−3.19687	−	4.33360i	−0.209885	−	0.284514i
$233$	16.5526			1.08439			0.542197	−	0.840251i	$-0.317593\pi$
$233$	16.5526			1.08439			0.542197	+	0.840251i	$0.317593\pi$
$234$	−4.05980	+	1.95510i	−0.265398	+	0.127809i
$235$	−4.54892	−	5.70416i	−0.296739	−	0.372098i
$236$	−6.76540	+	8.48354i	−0.440390	+	0.552231i
$237$	−5.49396	+	2.64575i	−0.356871	+	0.171860i
$238$	−6.68814	−	3.22084i	−0.433528	−	0.208776i
$239$	3.64795	+	4.57438i	0.235966	+	0.295892i	0.885689	−	0.464279i	$-0.153686\pi$
$239$	3.64795	+	4.57438i	0.235966	+	0.295892i	−0.649723	+	0.760171i	$0.725115\pi$
$240$	−0.579417	+	2.53859i	−0.0374012	+	0.163865i
$241$	1.38620	−	6.07333i	0.0892929	−	0.391218i	−0.910456	−	0.413605i	$-0.864269\pi$
$241$	1.38620	−	6.07333i	0.0892929	−	0.391218i	0.999749	+	0.0223871i	$0.00712663\pi$
$242$	−11.3617	+	14.2472i	−0.730360	+	0.915843i
$243$	−3.51477	−	15.3992i	−0.225473	−	0.987860i
$244$	8.92692			0.571487
$245$	0.158834	+	0.695895i	0.0101475	+	0.0444591i
$246$	−7.07338	−	3.40636i	−0.450982	−	0.217181i
$247$	8.84870	+	4.26131i	0.563029	+	0.271141i
$248$	0.407010	+	1.78323i	0.0258451	+	0.113235i
$249$	6.12737			0.388307
$250$	0.392240	+	1.71851i	0.0248074	+	0.108688i
$251$	14.7669	−	18.5171i	0.932078	−	1.16879i	−0.0533297	−	0.998577i	$-0.516983\pi$
$251$	14.7669	−	18.5171i	0.932078	−	1.16879i	0.985408	−	0.170212i	$-0.0544451\pi$
$252$	−1.36563	+	5.98319i	−0.0860263	+	0.376906i
$253$	−2.43847	+	10.6836i	−0.153305	+	0.671674i
$254$	−11.4194	−	14.3195i	−0.716516	−	0.898483i
$255$	−6.68814	−	3.22084i	−0.418827	−	0.201697i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−5.83728	+	7.31972i	−0.364120	+	0.456592i	−0.929817	−	0.368021i	$-0.880035\pi$
$257$	−5.83728	+	7.31972i	−0.364120	+	0.456592i	0.565698	+	0.824613i	$0.308607\pi$
$258$	1.29709	+	1.62650i	0.0807535	+	0.101262i
$259$	−15.8654	+	7.64037i	−0.985827	+	0.474749i
$260$	6.20775			0.384988
$261$	−7.53468	−	10.2138i	−0.466385	−	0.632220i
$262$	−6.72886			−0.415710
$263$	−18.4535	+	8.88675i	−1.13789	+	0.547981i	−0.905376	−	0.424611i	$-0.860411\pi$
$263$	−18.4535	+	8.88675i	−1.13789	+	0.547981i	−0.232518	+	0.972592i	$0.574696\pi$
$264$	2.70291	+	3.38934i	0.166352	+	0.208599i
$265$	25.1151	−	31.4933i	1.54281	−	1.93462i
$266$	12.0516	−	5.80375i	0.738931	−	0.355851i
$267$	5.85958	+	2.82183i	0.358601	+	0.172693i
$268$	−6.85839	−	8.60015i	−0.418943	−	0.525338i
$269$	−1.50634	+	6.59969i	−0.0918429	+	0.402390i	−0.999863	−	0.0165359i	$-0.994736\pi$
$269$	−1.50634	+	6.59969i	−0.0918429	+	0.402390i	0.908020	+	0.418926i	$0.137593\pi$
$270$	−3.10388	+	13.5990i	−0.188896	+	0.827607i
$271$	8.49210	−	10.6488i	0.515858	−	0.646866i	−0.453866	−	0.891070i	$-0.649955\pi$
$271$	8.49210	−	10.6488i	0.515858	−	0.646866i	0.969724	+	0.244204i	$0.0785268\pi$
$272$	−0.634375	−	2.77938i	−0.0384646	−	0.168525i
$273$	−3.99223			−0.241621
$274$	−2.39008	−	10.4716i	−0.144390	−	0.632615i
$275$	26.9964	+	13.0008i	1.62794	+	0.783977i
$276$	1.46466	+	0.705341i	0.0881619	+	0.0424566i
$277$	2.27091	+	9.94949i	0.136446	+	0.597807i	0.996200	+	0.0870987i	$0.0277596\pi$
$277$	2.27091	+	9.94949i	0.136446	+	0.597807i	−0.859754	+	0.510708i	$0.829383\pi$
$278$	17.3545			1.04085
$279$	0.959279	+	4.20288i	0.0574306	+	0.251620i
$280$	5.27144	−	6.61017i	0.315029	−	0.395033i
$281$	−1.60441	+	7.02937i	−0.0957110	+	0.419337i	−0.999971	−	0.00764556i	$-0.997566\pi$
$281$	−1.60441	+	7.02937i	−0.0957110	+	0.419337i	0.904260	+	0.426983i	$0.140423\pi$
$282$	−0.400969	+	1.75676i	−0.0238773	+	0.104613i
$283$	−17.5737	−	22.0367i	−1.04465	−	1.30995i	−0.949256	−	0.314505i	$-0.898161\pi$
$283$	−17.5737	−	22.0367i	−1.04465	−	1.30995i	−0.0953906	−	0.995440i	$-0.530410\pi$
$284$	5.69687	+	2.74347i	0.338047	+	0.162795i
$285$	12.0516	−	5.80375i	0.713876	−	0.343784i
$286$	6.44385	−	8.08033i	0.381033	−	0.477800i
$287$	15.8937	+	19.9301i	0.938177	+	1.17644i
$288$	−2.12349	+	1.02262i	−0.125128	+	0.0602584i
$289$	−8.87263			−0.521919
$290$	3.24698	+	17.1814i	0.190669	+	1.00893i
$291$	1.82371			0.106908
$292$	8.39977	−	4.04512i	0.491559	−	0.236723i
$293$	7.75332	+	9.72235i	0.452954	+	0.567986i	0.954906	−	0.296910i	$-0.0959560\pi$
$293$	7.75332	+	9.72235i	0.452954	+	0.567986i	−0.501952	+	0.864895i	$0.667385\pi$
$294$	0.109916	−	0.137831i	0.00641045	−	0.00803845i
$295$	31.7434	−	15.2868i	1.84817	−	0.890033i
$296$	−6.09299	−	2.93423i	−0.354148	−	0.170549i
$297$	14.4792	+	18.1563i	0.840168	+	1.05354i
$298$	−4.13318	+	18.1086i	−0.239429	+	1.04901i
$299$	0.862404	−	3.77844i	0.0498741	−	0.218513i
$300$	2.77144	−	3.47527i	0.160009	−	0.200645i
$301$	−1.50312	−	6.58558i	−0.0866381	−	0.379586i
$302$	6.10992			0.351586
$303$	−0.399240	−	1.74918i	−0.0229357	−	0.100488i
$304$	4.62833	+	2.22889i	0.265453	+	0.127836i
$305$	−26.1151	−	12.5763i	−1.49534	−	0.720120i
$306$	−1.49516	−	6.55070i	−0.0854724	−	0.374479i
$307$	−33.3139			−1.90133			−0.950664	−	0.310223i	$-0.899596\pi$
$307$	−33.3139			−1.90133			−0.950664	+	0.310223i	$0.899596\pi$
$308$	−3.13222	−	13.7231i	−0.178475	−	0.781949i
$309$	0.760553	−	0.953703i	0.0432664	−	0.0542543i
$310$	1.32155	−	5.79010i	0.0750591	−	0.328855i
$311$	−1.78956	+	7.84058i	−0.101477	+	0.444598i	0.898507	+	0.438958i	$0.144652\pi$
$311$	−1.78956	+	7.84058i	−0.101477	+	0.444598i	−0.999984	+	0.00564003i	$0.998205\pi$
$312$	−0.955927	−	1.19869i	−0.0541187	−	0.0678627i
$313$	8.43243	+	4.06084i	0.476629	+	0.229532i	0.656745	−	0.754113i	$-0.271933\pi$
$313$	8.43243	+	4.06084i	0.476629	+	0.229532i	−0.180116	+	0.983645i	$0.557647\pi$
$314$	−5.87531	+	2.82940i	−0.331563	+	0.159672i
$315$	12.4242	−	15.5795i	0.700026	−	0.877805i
$316$	4.74094	+	5.94495i	0.266699	+	0.334430i
$317$	−3.24309	+	1.56179i	−0.182150	+	0.0877190i	−0.522736	−	0.852494i	$-0.675089\pi$
$317$	−3.24309	+	1.56179i	−0.182150	+	0.0877190i	0.340586	+	0.940213i	$0.389375\pi$
$318$	−9.94869			−0.557895
$319$	25.7347	+	13.6084i	1.44086	+	0.761925i
$320$	3.24698			0.181512
$321$	−6.43416	+	3.09853i	−0.359120	+	0.172943i
$322$	−3.29105	−	4.12685i	−0.183403	−	0.229980i
$323$	−9.13102	+	11.4499i	−0.508064	+	0.637092i
$324$	−3.26659	+	1.57311i	−0.181477	+	0.0873949i
$325$	−9.54772	−	4.59794i	−0.529612	−	0.255048i
$326$	3.80343	+	4.76935i	0.210652	+	0.264150i
$327$	−1.83728	+	8.04966i	−0.101602	+	0.445147i
$328$	−2.17845	+	9.54440i	−0.120285	+	0.527002i
$329$	3.64795	−	4.57438i	0.201118	−	0.252194i
$330$	−3.13222	−	13.7231i	−0.172423	−	0.755434i
$331$	−7.46681			−0.410413			−0.205207	−	0.978719i	$-0.565787\pi$
$331$	−7.46681			−0.410413			−0.205207	+	0.978719i	$0.565787\pi$
$332$	−1.70022	−	7.44914i	−0.0933116	−	0.408825i
$333$	−14.3605	−	6.91567i	−0.786953	−	0.378977i
$334$	−0.189333	−	0.0911780i	−0.0103598	−	0.00498904i
$335$	7.94773	+	34.8213i	0.434231	+	1.90249i
$336$	−2.08815			−0.113918
$337$	0.261513	+	1.14576i	0.0142455	+	0.0624136i	0.981551	−	0.191200i	$-0.0612379\pi$
$337$	0.261513	+	1.14576i	0.0142455	+	0.0624136i	−0.967306	+	0.253614i	$0.918381\pi$
$338$	5.82640	−	7.30607i	0.316914	−	0.397398i
$339$	0.649677	−	2.84642i	0.0352856	−	0.154596i
$340$	−2.05980	+	9.02458i	−0.111708	+	0.489427i
$341$	−6.16487	−	7.73051i	−0.333847	−	0.418630i
$342$	10.9085	+	5.25326i	0.589864	+	0.284064i
$343$	−16.9378	+	8.15682i	−0.914555	+	0.440427i
$344$	1.61745	−	2.02822i	0.0872070	−	0.109354i
$345$	−3.29105	−	4.12685i	−0.177184	−	0.222182i
$346$	16.0722	−	7.73995i	0.864046	−	0.416102i
$347$	−30.4698			−1.63570			−0.817852	−	0.575428i	$-0.804835\pi$
$347$	−30.4698			−1.63570			−0.817852	+	0.575428i	$0.804835\pi$
$348$	2.81767	−	3.27273i	0.151043	−	0.175437i
$349$	5.31037			0.284258			0.142129	−	0.989848i	$-0.454605\pi$
$349$	5.31037			0.284258			0.142129	+	0.989848i	$0.454605\pi$
$350$	−13.0036	+	6.26223i	−0.695074	+	0.334730i
$351$	−5.12080	−	6.42128i	−0.273328	−	0.342743i
$352$	3.37047	−	4.22643i	0.179647	−	0.225270i
$353$	9.48403	−	4.56727i	0.504784	−	0.243091i	−0.164119	−	0.986440i	$-0.552478\pi$
$353$	9.48403	−	4.56727i	0.504784	−	0.243091i	0.668904	+	0.743349i	$0.266764\pi$
$354$	−7.83997	−	3.77553i	−0.416690	−	0.200667i
$355$	−12.8007	−	16.0516i	−0.679393	−	0.851932i
$356$	1.80463	−	7.90658i	0.0956450	−	0.419048i
$357$	1.32467	−	5.80375i	0.0701088	−	0.307167i
$358$	3.47703	−	4.36006i	0.183767	−	0.230436i
$359$	−5.25236	−	23.0121i	−0.277209	−	1.21453i	−0.901306	−	0.433184i	$-0.857390\pi$
$359$	−5.25236	−	23.0121i	−0.277209	−	1.21453i	0.624097	−	0.781347i	$-0.285467\pi$
$360$	7.65279			0.403338
$361$	−1.64430	−	7.20415i	−0.0865421	−	0.379166i
$362$	−12.4840	−	6.01199i	−0.656146	−	0.315983i
$363$	−13.1664	−	6.34059i	−0.691055	−	0.332795i
$364$	1.10776	+	4.85342i	0.0580624	+	0.254388i
$365$	−30.2717			−1.58449
$366$	1.59299	+	6.97935i	0.0832669	+	0.364816i
$367$	−6.10388	+	7.65402i	−0.318620	+	0.399536i	−0.915189	−	0.403025i	$-0.867959\pi$
$367$	−6.10388	+	7.65402i	−0.318620	+	0.399536i	0.596569	+	0.802562i	$0.296530\pi$
$368$	0.451083	−	1.97632i	0.0235143	−	0.103023i
$369$	−5.13437	+	22.4952i	−0.267285	+	1.17105i
$370$	13.6908	+	17.1678i	0.711752	+	0.892509i
$371$	29.1042	+	14.0158i	1.51101	+	0.727666i
$372$	−1.32155	+	0.636426i	−0.0685193	+	0.0329971i
$373$	−17.2627	+	21.6468i	−0.893829	+	1.12083i	0.0982437	+	0.995162i	$0.468678\pi$
$373$	−17.2627	+	21.6468i	−0.893829	+	1.12083i	−0.992073	+	0.125664i	$0.959894\pi$
$374$	9.60872	+	12.0490i	0.496855	+	0.623037i
$375$	−1.27359	+	0.613331i	−0.0657681	+	0.0316723i
$376$	2.24698			0.115879
$377$	−9.10148	−	4.81284i	−0.468750	−	0.247874i
$378$	−11.1860			−0.575345
$379$	−6.27359	+	3.02120i	−0.322253	+	0.155189i	−0.588015	−	0.808850i	$-0.700091\pi$
$379$	−6.27359	+	3.02120i	−0.322253	+	0.155189i	0.265763	+	0.964039i	$0.414376\pi$
$380$	−10.3998	−	13.0409i	−0.533497	−	0.668984i
$381$	9.15764	−	11.4833i	0.469160	−	0.588308i
$382$	5.62833	−	2.71046i	0.287971	−	0.138679i
$383$	−6.05161	−	2.91430i	−0.309223	−	0.148914i	0.272836	−	0.962061i	$-0.412038\pi$
$383$	−6.05161	−	2.91430i	−0.309223	−	0.148914i	−0.582059	+	0.813147i	$0.697753\pi$
$384$	−0.500000	−	0.626980i	−0.0255155	−	0.0319954i
$385$	−10.1703	+	44.5588i	−0.518324	+	2.27093i
$386$	−0.412386	+	1.80678i	−0.0209899	+	0.0919628i
$387$	3.81216	−	4.78030i	0.193783	−	0.242996i
$388$	−0.506041	−	2.21711i	−0.0256903	−	0.112557i
$389$	12.7560			0.646755			0.323378	−	0.946270i	$-0.395182\pi$
$389$	12.7560			0.646755			0.323378	+	0.946270i	$0.395182\pi$
$390$	1.10776	+	4.85342i	0.0560936	+	0.245762i
$391$	5.20679	+	2.50746i	0.263319	+	0.126808i
$392$	−0.198062	−	0.0953818i	−0.0100037	−	0.00481751i
$393$	−1.20075	−	5.26083i	−0.0605699	−	0.265374i
$394$	−7.14244			−0.359831
$395$	−5.49396	−	24.0706i	−0.276431	−	1.21112i
$396$	7.94385	−	9.96127i	0.399193	−	0.500573i
$397$	4.64646	−	20.3575i	0.233199	−	1.02171i	−0.713768	−	0.700382i	$-0.753013\pi$
$397$	4.64646	−	20.3575i	0.233199	−	1.02171i	0.946967	−	0.321330i	$-0.104130\pi$
$398$	−2.30917	+	10.1172i	−0.115748	+	0.507127i
$399$	6.68814	+	8.38666i	0.334826	+	0.419858i
$400$	−4.99396	−	2.40496i	−0.249698	−	0.120248i
$401$	27.0846	−	13.0432i	1.35254	−	0.651348i	0.389578	−	0.920993i	$-0.372621\pi$
$401$	27.0846	−	13.0432i	1.35254	−	0.651348i	0.962960	+	0.269645i	$0.0869064\pi$
$402$	5.50000	−	6.89678i	0.274315	−	0.343980i
$403$	2.18031	+	2.73402i	0.108609	+	0.136191i
$404$	−2.01573	+	0.970724i	−0.100286	+	0.0482953i
$405$	11.7724			0.584975
$406$	−12.8535	+	5.60458i	−0.637911	+	0.278150i
$407$	36.5579			1.81211
$408$	2.05980	−	0.991949i	0.101975	−	0.0491088i
$409$	16.5740	+	20.7832i	0.819534	+	1.02766i	0.999036	+	0.0439050i	$0.0139799\pi$
$409$	16.5740	+	20.7832i	0.819534	+	1.02766i	−0.179502	+	0.983758i	$0.557449\pi$
$410$	19.8192	−	24.8524i	0.978799	−	1.22737i
$411$	7.76055	−	3.73729i	0.382800	−	0.184347i
$412$	−1.37047	−	0.659983i	−0.0675182	−	0.0325150i
$413$	17.6163	+	22.0901i	0.866839	+	1.08698i
$414$	1.06315	−	4.65799i	0.0522512	−	0.228928i
$415$	−5.52057	+	24.1872i	−0.270994	+	1.18730i
$416$	−1.19202	+	1.49475i	−0.0584437	+	0.0732860i
$417$	3.09688	+	13.5683i	0.151655	+	0.664442i
$418$	−27.7700			−1.35828
$419$	−8.45808	−	37.0573i	−0.413204	−	1.81037i	−0.568718	−	0.822533i	$-0.692560\pi$
$419$	−8.45808	−	37.0573i	−0.413204	−	1.81037i	0.155513	−	0.987834i	$-0.450297\pi$
$420$	6.10872	+	2.94180i	0.298075	+	0.143545i
$421$	13.0151	+	6.26773i	0.634315	+	0.305470i	0.723270	−	0.690565i	$-0.242638\pi$
$421$	13.0151	+	6.26773i	0.634315	+	0.305470i	−0.0889544	+	0.996036i	$0.528353\pi$
$422$	1.83848	+	8.05490i	0.0894957	+	0.392106i
$423$	5.29590			0.257495
$424$	2.76055	+	12.0948i	0.134064	+	0.587374i
$425$	9.85235	−	12.3545i	0.477909	−	0.599279i
$426$	−1.12833	+	4.94355i	−0.0546680	+	0.239516i
$427$	5.17241	−	22.6618i	0.250310	−	1.09668i
$428$	5.55227	+	6.96233i	0.268379	+	0.336537i
$429$	7.46734	+	3.59608i	0.360527	+	0.173621i
$430$	−7.58911	+	3.65472i	−0.365979	+	0.176246i
$431$	−1.75720	+	2.20346i	−0.0846414	+	0.106137i	−0.822349	−	0.568983i	$-0.807337\pi$
$431$	−1.75720	+	2.20346i	−0.0846414	+	0.106137i	0.737708	+	0.675120i	$0.235908\pi$
$432$	−2.67845	−	3.35867i	−0.128867	−	0.161594i
$433$	14.7772	−	7.11634i	0.710149	−	0.341990i	−0.0436935	−	0.999045i	$-0.513912\pi$
$433$	14.7772	−	7.11634i	0.710149	−	0.341990i	0.753842	+	0.657055i	$0.228198\pi$
$434$	4.76271			0.228617
$435$	−12.8535	+	5.60458i	−0.616280	+	0.268719i
$436$	10.2959			0.493084
$437$	−9.38231	+	4.51828i	−0.448817	+	0.216139i
$438$	4.66152	+	5.84536i	0.222736	+	0.279302i
$439$	12.6935	−	15.9172i	0.605828	−	0.759685i	−0.380445	−	0.924803i	$-0.624229\pi$
$439$	12.6935	−	15.9172i	0.605828	−	0.759685i	0.986274	+	0.165119i	$0.0528007\pi$
$440$	−15.8143	+	7.61577i	−0.753918	+	0.363068i
$441$	−0.466812	−	0.224805i	−0.0222291	−	0.0107050i
$442$	−3.39828	−	4.26131i	−0.161640	−	0.202690i
$443$	4.21672	−	18.4746i	0.200342	−	0.877757i	−0.770386	−	0.637577i	$-0.779937\pi$
$443$	4.21672	−	18.4746i	0.200342	−	0.877757i	0.970729	−	0.240179i	$-0.0772063\pi$
$444$	1.20679	−	5.28730i	0.0572718	−	0.250924i
$445$	−16.4182	+	20.5878i	−0.778297	+	0.975953i
$446$	0.885239	+	3.87849i	0.0419173	+	0.183652i
$447$	−14.8955			−0.704531
$448$	0.579417	+	2.53859i	0.0273749	+	0.119937i
$449$	−19.5407	−	9.41032i	−0.922184	−	0.444100i	−0.0883334	−	0.996091i	$-0.528154\pi$
$449$	−19.5407	−	9.41032i	−0.922184	−	0.444100i	−0.833850	+	0.551991i	$0.813868\pi$
$450$	−11.7702	−	5.66825i	−0.554855	−	0.267204i
$451$	−11.7763	−	51.5953i	−0.554523	−	2.42953i
$452$	−3.64071			−0.171245
$453$	1.09030	+	4.77692i	0.0512269	+	0.224440i
$454$	−6.84332	+	8.58125i	−0.321173	+	0.402738i
$455$	3.59688	−	15.7589i	0.168624	−	0.738790i
$456$	−0.916698	+	4.01632i	−0.0429283	+	0.188081i
$457$	−7.70775	−	9.66521i	−0.360553	−	0.452120i	0.568160	−	0.822918i	$-0.307655\pi$
$457$	−7.70775	−	9.66521i	−0.360553	−	0.452120i	−0.928713	+	0.370798i	$0.879084\pi$
$458$	4.58815	+	2.20953i	0.214390	+	0.103245i
$459$	11.0341	−	5.31377i	0.515030	−	0.248025i
$460$	−4.10388	+	5.14610i	−0.191344	+	0.239938i
$461$	−1.73945	−	2.18120i	−0.0810141	−	0.101588i	0.739673	−	0.672967i	$-0.234980\pi$
$461$	−1.73945	−	2.18120i	−0.0810141	−	0.101588i	−0.820687	+	0.571378i	$0.806409\pi$
$462$	10.1703	−	4.89773i	0.473163	−	0.227863i
$463$	39.2911			1.82601			0.913006	−	0.407945i	$-0.133755\pi$
$463$	39.2911			1.82601			0.913006	+	0.407945i	$0.133755\pi$
$464$	−4.76055	−	2.51737i	−0.221003	−	0.116866i
$465$	4.76271			0.220865
$466$	14.9133	−	7.18189i	0.690847	−	0.332695i
$467$	9.14005	+	11.4613i	0.422951	+	0.530364i	0.946961	−	0.321348i	$-0.104136\pi$
$467$	9.14005	+	11.4613i	0.422951	+	0.530364i	−0.524010	+	0.851712i	$0.675565\pi$
$468$	−2.80947	+	3.52296i	−0.129868	+	0.162849i
$469$	−25.8061	+	12.4276i	−1.19162	+	0.573852i
$470$	−6.57338	−	3.16557i	−0.303207	−	0.146017i
$471$	−3.26055	−	4.08860i	−0.150238	−	0.188393i
$472$	−2.41454	+	10.5788i	−0.111138	+	0.486929i
$473$	−3.12056	+	13.6721i	−0.143484	+	0.628643i
$474$	−3.80194	+	4.76748i	−0.174629	+	0.218978i
$475$	6.33609	+	27.7602i	0.290720	+	1.27373i
$476$	−7.42327			−0.340245
$477$	6.50634	+	28.5061i	0.297905	+	1.30521i
$478$	5.27144	+	2.53859i	0.241110	+	0.116112i
$479$	−15.5025	−	7.46559i	−0.708325	−	0.341111i	0.0447934	−	0.998996i	$-0.485737\pi$
$479$	−15.5025	−	7.46559i	−0.708325	−	0.341111i	−0.753118	+	0.657885i	$0.771451\pi$
$480$	0.579417	+	2.53859i	0.0264466	+	0.115870i
$481$	−12.9293			−0.589526
$482$	−1.38620	−	6.07333i	−0.0631396	−	0.276633i
$483$	2.63922	−	3.30948i	0.120089	−	0.150586i
$484$	−4.05496	+	17.7659i	−0.184316	+	0.807542i
$485$	−1.64310	+	7.19891i	−0.0746095	+	0.326886i
$486$	−9.84817	−	12.3492i	−0.446722	−	0.560172i
$487$	11.9596	+	5.75943i	0.541940	+	0.260985i	0.684766	−	0.728763i	$-0.259905\pi$
$487$	11.9596	+	5.75943i	0.541940	+	0.260985i	−0.142826	+	0.989748i	$0.545619\pi$
$488$	8.04288	−	3.87325i	0.364084	−	0.175334i
$489$	−3.05011	+	3.82472i	−0.137931	+	0.172960i
$490$	0.445042	+	0.558065i	0.0201049	+	0.0252108i
$491$	−2.61865	+	1.26107i	−0.118178	+	0.0569114i	−0.492039	−	0.870573i	$-0.663748\pi$
$491$	−2.61865	+	1.26107i	−0.118178	+	0.0569114i	0.373861	+	0.927485i	$0.378034\pi$
$492$	−7.85086			−0.353944
$493$	10.0167	−	11.6344i	0.451129	−	0.523988i
$494$	9.82132			0.441882
$495$	−37.2727	+	17.9496i	−1.67528	+	0.806774i
$496$	1.14042	+	1.43004i	0.0512062	+	0.0642105i
$497$	10.2654	−	12.8724i	0.460466	−	0.577406i
$498$	5.52057	−	2.65857i	0.247383	−	0.119133i
$499$	−2.25571	−	1.08629i	−0.100979	−	0.0486291i	0.382712	−	0.923868i	$-0.374990\pi$
$499$	−2.25571	−	1.08629i	−0.100979	−	0.0486291i	−0.483692	+	0.875238i	$0.660704\pi$
$500$	1.09903	+	1.37814i	0.0491502	+	0.0616324i
$501$	0.0374997	−	0.164297i	0.00167536	−	0.00734025i
$502$	5.27024	−	23.0904i	0.235222	−	1.03058i
$503$	4.00418	−	5.02108i	0.178538	−	0.223879i	−0.684508	−	0.729006i	$-0.739983\pi$
$503$	4.00418	−	5.02108i	0.178538	−	0.223879i	0.863045	+	0.505127i	$0.168554\pi$
$504$	1.36563	+	5.98319i	0.0608298	+	0.266513i
$505$	7.26444			0.323263
$506$	2.43847	+	10.6836i	0.108403	+	0.474945i
$507$	6.75182	+	3.25151i	0.299859	+	0.144404i
$508$	−16.5015	−	7.94670i	−0.732135	−	0.352578i
$509$	−7.15117	−	31.3313i	−0.316970	−	1.38874i	−0.842837	−	0.538169i	$-0.819116\pi$
$509$	−7.15117	−	31.3313i	−0.316970	−	1.38874i	0.525867	−	0.850567i	$-0.323741\pi$
$510$	−7.42327			−0.328708
$511$	−5.40193	−	23.6674i	−0.238967	−	1.04698i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−4.91066	+	21.5150i	−0.216811	+	0.949910i
$514$	−2.08330	+	9.12754i	−0.0918905	+	0.402599i
$515$	3.07942	+	3.86147i	0.135695	+	0.170157i
$516$	1.87435	+	0.902641i	0.0825138	+	0.0397366i
$517$	−10.9438	+	5.27028i	−0.481310	+	0.231787i
$518$	−10.9792	+	13.7675i	−0.482398	+	0.604908i
$519$	8.91939	+	11.1846i	0.391518	+	0.490948i
$520$	5.59299	−	2.69344i	0.245269	−	0.118115i
$521$	−2.51334			−0.110111			−0.0550556	−	0.998483i	$-0.517534\pi$
$521$	−2.51334			−0.110111			−0.0550556	+	0.998483i	$0.517534\pi$
$522$	−11.2201	−	5.93317i	−0.491092	−	0.259688i
$523$	−3.65040			−0.159621			−0.0798104	−	0.996810i	$-0.525431\pi$
$523$	−3.65040			−0.159621			−0.0798104	+	0.996810i	$0.525431\pi$
$524$	−6.06249	+	2.91954i	−0.264841	+	0.127541i
$525$	−7.21648	−	9.04918i	−0.314953	−	0.394939i
$526$	−12.7702	+	16.0134i	−0.556809	+	0.698216i
$527$	−4.69806	+	2.26247i	−0.204651	+	0.0985546i
$528$	3.90581	+	1.88094i	0.169979	+	0.0818574i
$529$	−11.7781	−	14.7693i	−0.512093	−	0.642145i
$530$	8.96346	−	39.2715i	0.389348	−	1.70584i
$531$	−5.69083	+	24.9331i	−0.246961	+	1.08201i
$532$	8.33997	−	10.4580i	0.361584	−	0.453411i
$533$	4.16487	+	18.2475i	0.180401	+	0.790387i
$534$	6.50365			0.281440
$535$	−6.43416	−	28.1899i	−0.278173	−	1.21875i
$536$	−9.91066	−	4.77272i	−0.428075	−	0.206150i
$537$	4.02930	+	1.94041i	0.173877	+	0.0837349i
$538$	1.50634	+	6.59969i	0.0649428	+	0.284533i
$539$	1.18837			0.0511869
$540$	3.10388	+	13.5990i	0.133570	+	0.585206i
$541$	5.12080	−	6.42128i	0.220160	−	0.276072i	−0.659469	−	0.751731i	$-0.729219\pi$
$541$	5.12080	−	6.42128i	0.220160	−	0.276072i	0.879630	+	0.475659i	$0.157790\pi$
$542$	3.03079	−	13.2788i	0.130184	−	0.570372i
$543$	2.47262	−	10.8332i	0.106110	−	0.464899i
$544$	−1.77748	−	2.22889i	−0.0762088	−	0.0955628i
$545$	−30.1199	−	14.5050i	−1.29019	−	0.621325i
$546$	−3.59688	+	1.73216i	−0.153932	+	0.0741298i
$547$	−23.6177	+	29.6157i	−1.00982	+	1.26628i	−0.0462210	+	0.998931i	$0.514718\pi$
$547$	−23.6177	+	29.6157i	−1.00982	+	1.26628i	−0.963601	+	0.267345i	$0.913854\pi$
$548$	−6.69687	−	8.39760i	−0.286076	−	0.358728i
$549$	18.9562	−	9.12884i	0.809032	−	0.389609i
$550$	29.9638			1.27766
$551$	5.13706	+	27.1828i	0.218846	+	1.15803i
$552$	1.62565			0.0691921
$553$	17.8388	−	8.59070i	0.758582	−	0.365314i
$554$	6.36294	+	7.97887i	0.270335	+	0.338990i
$555$	−10.9792	+	13.7675i	−0.466041	+	0.584396i
$556$	15.6359	−	7.52984i	0.663108	−	0.319336i
$557$	14.7446	+	7.10062i	0.624748	+	0.300863i	0.719345	−	0.694653i	$-0.244442\pi$
$557$	14.7446	+	7.10062i	0.624748	+	0.300863i	−0.0945970	+	0.995516i	$0.530156\pi$
$558$	2.68784	+	3.37045i	0.113785	+	0.142682i
$559$	1.10364	−	4.83536i	0.0466789	−	0.204514i
$560$	1.88135	−	8.24275i	0.0795017	−	0.348320i
$561$	−7.70560	+	9.66251i	−0.325330	+	0.407952i
$562$	1.60441	+	7.02937i	0.0676779	+	0.296516i
$563$	4.41657			0.186136			0.0930680	−	0.995660i	$-0.470333\pi$
$563$	4.41657			0.186136			0.0930680	+	0.995660i	$0.470333\pi$
$564$	0.400969	+	1.75676i	0.0168838	+	0.0739729i
$565$	10.6506	+	5.12908i	0.448076	+	0.215782i
$566$	−25.3947	−	12.2294i	−1.06742	−	0.514042i
$567$	2.10076	+	9.20403i	0.0882236	+	0.386533i
$568$	6.32304			0.265309
$569$	5.80098	+	25.4157i	0.243190	+	1.06548i	0.938094	+	0.346381i	$0.112590\pi$
$569$	5.80098	+	25.4157i	0.243190	+	1.06548i	−0.694904	+	0.719102i	$0.744553\pi$
$570$	8.33997	−	10.4580i	0.349323	−	0.438037i
$571$	−10.1681	+	44.5493i	−0.425522	+	1.86433i	0.0728111	+	0.997346i	$0.476803\pi$
$571$	−10.1681	+	44.5493i	−0.425522	+	1.86433i	−0.498333	+	0.866986i	$0.666054\pi$
$572$	2.29978	−	10.0760i	0.0961587	−	0.421299i
$573$	3.12349	+	3.91673i	0.130486	+	0.163624i
$574$	22.9671	+	11.0604i	0.958629	+	0.461651i
$575$	10.1235	−	4.87522i	0.422179	−	0.203311i
$576$	−1.46950	+	1.84270i	−0.0612292	+	0.0767790i
$577$	−19.0628	−	23.9040i	−0.793594	−	0.995136i	−0.999862	−	0.0166400i	$-0.994703\pi$
$577$	−19.0628	−	23.9040i	−0.793594	−	0.995136i	0.206267	−	0.978496i	$-0.433868\pi$
$578$	−7.99396	+	3.84969i	−0.332505	+	0.160126i
$579$	−1.48619			−0.0617639
$580$	10.3802	+	14.0711i	0.431013	+	0.584270i
$581$	−19.8955			−0.825403
$582$	1.64310	−	0.791277i	0.0681089	−	0.0327995i
$583$	−41.8134	−	52.4324i	−1.73173	−	2.17153i
$584$	5.81282	−	7.28905i	0.240536	−	0.301623i
$585$	13.1821	−	6.34816i	0.545013	−	0.262464i
$586$	11.2039	+	5.39550i	0.462827	+	0.222886i
$587$	−2.96615	−	3.71943i	−0.122426	−	0.153517i	0.716841	−	0.697236i	$-0.245587\pi$
$587$	−2.96615	−	3.71943i	−0.122426	−	0.153517i	−0.839267	+	0.543719i	$0.817016\pi$
$588$	0.0392287	−	0.171872i	0.00161776	−	0.00708788i
$589$	2.09083	−	9.16054i	0.0861513	−	0.377454i
$590$	21.9671	−	27.5459i	0.904372	−	1.13405i
$591$	−1.27455	−	5.58418i	−0.0524281	−	0.229703i
$592$	−6.76271			−0.277946
$593$	0.295601	+	1.29511i	0.0121389	+	0.0531840i	0.980635	−	0.195846i	$-0.0627453\pi$
$593$	0.295601	+	1.29511i	0.0121389	+	0.0531840i	−0.968496	+	0.249030i	$0.919888\pi$
$594$	20.9230	+	10.0760i	0.858483	+	0.413423i
$595$	21.7162	+	10.4580i	0.890279	+	0.428736i
$596$	4.13318	+	18.1086i	0.169302	+	0.741759i
$597$	−8.32198			−0.340596
$598$	−0.862404	−	3.77844i	−0.0352663	−	0.154512i
$599$	−19.4242	+	24.3572i	−0.793653	+	0.995209i	0.206208	+	0.978508i	$0.433888\pi$
$599$	−19.4242	+	24.3572i	−0.793653	+	0.995209i	−0.999861	+	0.0167007i	$0.994684\pi$
$600$	0.989115	−	4.33360i	0.0403804	−	0.176918i
$601$	−0.752783	+	3.29816i	−0.0307067	+	0.134535i	−0.987958	−	0.154723i	$-0.950551\pi$
$601$	−0.752783	+	3.29816i	−0.0307067	+	0.134535i	0.957251	+	0.289258i	$0.0934085\pi$
$602$	−4.21164	−	5.28122i	−0.171653	−	0.215247i
$603$	−23.3584	−	11.2488i	−0.951227	−	0.458087i
$604$	5.50484	−	2.65099i	0.223989	−	0.107867i
$605$	36.8913	−	46.2603i	1.49985	−	1.88075i
$606$	−1.11865	−	1.40274i	−0.0454419	−	0.0569823i
$607$	25.3811	−	12.2229i	1.03019	−	0.496112i	0.159112	−	0.987261i	$-0.449137\pi$
$607$	25.3811	−	12.2229i	1.03019	−	0.496112i	0.871076	+	0.491148i	$0.163423\pi$
$608$	5.13706			0.208335
$609$	−6.67552	−	9.04918i	−0.270506	−	0.366691i
$610$	−28.9855			−1.17359
$611$	3.87047	−	1.86392i	0.156582	−	0.0754061i
$612$	−4.18933	−	5.25326i	−0.169344	−	0.212350i
$613$	8.69232	−	10.8998i	0.351079	−	0.440240i	−0.574665	−	0.818388i	$-0.694868\pi$
$613$	8.69232	−	10.8998i	0.351079	−	0.440240i	0.925745	+	0.378149i	$0.123439\pi$
$614$	−30.0148	+	14.4544i	−1.21130	+	0.583331i
$615$	22.9671	+	11.0604i	0.926123	+	0.445997i
$616$	−8.77628	−	11.0051i	−0.353607	−	0.443409i
$617$	−5.33244	+	23.3629i	−0.214676	+	0.940556i	0.746666	+	0.665199i	$0.231653\pi$
$617$	−5.33244	+	23.3629i	−0.214676	+	0.940556i	−0.961342	+	0.275357i	$0.911204\pi$
$618$	0.271438	−	1.18925i	0.0109188	−	0.0478386i
$619$	−15.6618	+	19.6393i	−0.629502	+	0.789370i	−0.989646	−	0.143526i	$-0.954156\pi$
$619$	−15.6618	+	19.6393i	−0.629502	+	0.789370i	0.360145	+	0.932896i	$0.382727\pi$
$620$	−1.32155	−	5.79010i	−0.0530748	−	0.232536i
$621$	8.70841			0.349457
$622$	1.78956	+	7.84058i	0.0717548	+	0.314379i
$623$	−19.0260	−	9.16241i	−0.762259	−	0.367084i
$624$	−1.38135	−	0.665225i	−0.0552984	−	0.0266303i
$625$	4.89344	+	21.4395i	0.195737	+	0.857582i
$626$	9.35929			0.374072
$627$	−4.95550	−	21.7115i	−0.197904	−	0.867072i
$628$	−4.06584	+	5.09841i	−0.162245	+	0.203449i
$629$	4.29009	−	18.7961i	0.171057	−	0.749451i
$630$	4.43416	−	19.4273i	0.176661	−	0.774003i
$631$	28.8857	+	36.2215i	1.14992	+	1.44195i	0.877371	+	0.479812i	$0.159295\pi$
$631$	28.8857	+	36.2215i	1.14992	+	1.44195i	0.272549	+	0.962142i	$0.412133\pi$
$632$	6.85086	+	3.29920i	0.272512	+	0.131235i
$633$	−5.96950	+	2.87476i	−0.237266	+	0.114261i
$634$	−2.24429	+	2.81425i	−0.0891322	+	0.111768i
$635$	37.0785	+	46.4950i	1.47142	+	1.84510i
$636$	−8.96346	+	4.31657i	−0.355424	+	0.171163i
$637$	−0.420288			−0.0166524
$638$	29.0906	+	1.09491i	1.15171	+	0.0433477i
$639$	14.9028			0.589544
$640$	2.92543	−	1.40881i	0.115638	−	0.0556882i
$641$	13.4194	+	16.8274i	0.530034	+	0.664641i	0.972706	−	0.232042i	$-0.0745407\pi$
$641$	13.4194	+	16.8274i	0.530034	+	0.664641i	−0.442672	+	0.896684i	$0.645969\pi$
$642$	−4.45257	+	5.58335i	−0.175729	+	0.220357i
$643$	28.3218	−	13.6391i	1.11690	−	0.537873i	0.217970	−	0.975955i	$-0.430057\pi$
$643$	28.3218	−	13.6391i	1.11690	−	0.537873i	0.898935	+	0.438083i	$0.144342\pi$
$644$	−4.75571	−	2.29023i	−0.187401	−	0.0902477i
$645$	−4.21164	−	5.28122i	−0.165833	−	0.207948i
$646$	−3.25882	+	14.2778i	−0.128217	+	0.561754i
$647$	0.641908	−	2.81238i	0.0252360	−	0.110566i	−0.960741	−	0.277446i	$-0.910512\pi$
$647$	0.641908	−	2.81238i	0.0252360	−	0.110566i	0.985977	+	0.166880i	$0.0533692\pi$
$648$	−2.26055	+	2.83464i	−0.0888029	+	0.111355i
$649$	−13.0526	−	57.1870i	−0.512358	−	2.24479i
$650$	−10.5972			−0.415655
$651$	0.849896	+	3.72364i	0.0333100	+	0.145941i
$652$	5.49612	+	2.64679i	0.215244	+	0.103656i
$653$	39.6405	+	19.0898i	1.55125	+	0.747043i	0.996390	−	0.0848989i	$-0.0270567\pi$
$653$	39.6405	+	19.0898i	1.55125	+	0.747043i	0.554862	+	0.831942i	$0.312771\pi$
$654$	1.83728	+	8.04966i	0.0718434	+	0.314766i
$655$	21.8485			0.853690
$656$	2.17845	+	9.54440i	0.0850541	+	0.372646i
$657$	13.7002	−	17.1795i	0.534496	−	0.670237i
$658$	1.30194	−	5.70416i	0.0507548	−	0.222371i
$659$	8.70184	−	38.1253i	0.338976	−	1.48515i	−0.462230	−	0.886760i	$-0.652951\pi$
$659$	8.70184	−	38.1253i	0.338976	−	1.48515i	0.801206	−	0.598389i	$-0.204192\pi$
$660$	−8.77628	−	11.0051i	−0.341616	−	0.428373i
$661$	−22.5758	−	10.8719i	−0.878098	−	0.422870i	−0.0601685	−	0.998188i	$-0.519164\pi$
$661$	−22.5758	−	10.8719i	−0.878098	−	0.422870i	−0.817929	+	0.575319i	$0.804878\pi$
$662$	−6.72737	+	3.23973i	−0.261466	+	0.125916i
$663$	2.72521	−	3.41730i	0.105838	−	0.132717i
$664$	−4.76391	−	5.97375i	−0.184875	−	0.231826i
$665$	−39.1313	+	18.8446i	−1.51745	+	0.730764i
$666$	−15.9390			−0.617624
$667$	10.0066	−	4.36323i	0.387458	−	0.168945i
$668$	−0.210144			−0.00813071
$669$	−2.87435	+	1.38422i	−0.111129	+	0.0535169i
$670$	22.2690	+	27.9245i	0.860328	+	1.07882i
$671$	−30.0879	+	37.7290i	−1.16153	+	1.45651i
$672$	−1.88135	+	0.906013i	−0.0725748	+	0.0349502i
$673$	−30.5937	−	14.7332i	−1.17930	−	0.567921i	−0.261593	−	0.965178i	$-0.584248\pi$
$673$	−30.5937	−	14.7332i	−1.17930	−	0.567921i	−0.917708	+	0.397257i	$0.869962\pi$
$674$	0.732742	+	0.918830i	0.0282242	+	0.0353920i
$675$	5.29859	−	23.2146i	0.203943	−	0.893531i
$676$	2.07942	−	9.11052i	0.0799776	−	0.350405i
$677$	−9.80612	+	12.2965i	−0.376880	+	0.472592i	−0.933708	−	0.358035i	$-0.883447\pi$
$677$	−9.80612	+	12.2965i	−0.376880	+	0.472592i	0.556828	+	0.830628i	$0.312018\pi$
$678$	−0.649677	−	2.84642i	−0.0249507	−	0.109316i
$679$	−5.92154			−0.227248
$680$	2.05980	+	9.02458i	0.0789898	+	0.346077i
$681$	−7.93027	−	3.81902i	−0.303889	−	0.146345i
$682$	−8.90850	−	4.29011i	−0.341124	−	0.164277i
$683$	−2.46748	−	10.8107i	−0.0944153	−	0.413661i	0.905528	−	0.424286i	$-0.139475\pi$
$683$	−2.46748	−	10.8107i	−0.0944153	−	0.413661i	−0.999944	+	0.0106254i	$0.996618\pi$
$684$	12.1075			0.462943
$685$	7.76055	+	34.0012i	0.296515	+	1.29912i
$686$	−11.7213	+	14.6981i	−0.447522	+	0.561175i
$687$	−0.908739	+	3.98144i	−0.0346705	+	0.151902i
$688$	0.577261	−	2.52915i	0.0220079	−	0.0964228i
$689$	14.7880	+	18.5436i	0.563378	+	0.706453i
$690$	−4.75571	−	2.29023i	−0.181047	−	0.0871875i
$691$	−30.3768	+	14.6287i	−1.15559	+	0.556502i	−0.910708	−	0.413051i	$-0.864463\pi$
$691$	−30.3768	+	14.6287i	−1.15559	+	0.556502i	−0.244880	+	0.969553i	$0.578749\pi$
$692$	11.1223	−	13.9469i	0.422806	−	0.530182i
$693$	−20.6848	−	25.9379i	−0.785750	−	0.985299i
$694$	−27.4523	+	13.2203i	−1.04208	+	0.501838i
$695$	−56.3497			−2.13747
$696$	1.11865	−	4.17117i	0.0424021	−	0.158108i
$697$	−27.9095			−1.05715
$698$	4.78448	−	2.30408i	0.181095	−	0.0872109i
$699$	8.27628	+	10.3781i	0.313038	+	0.392537i
$700$	−8.99880	+	11.2841i	−0.340123	+	0.426501i
$701$	−4.66368	+	2.24591i	−0.176145	+	0.0848268i	−0.519878	−	0.854240i	$-0.674023\pi$
$701$	−4.66368	+	2.24591i	−0.176145	+	0.0848268i	0.343733	+	0.939067i	$0.388308\pi$
$702$	−7.39977	−	3.56354i	−0.279286	−	0.134497i
$703$	21.6603	+	27.1612i	0.816935	+	1.02440i
$704$	1.20291	−	5.27028i	0.0453362	−	0.198631i
$705$	1.30194	−	5.70416i	0.0490338	−	0.214831i
$706$	6.56315	−	8.22994i	0.247008	−	0.309738i
$707$	1.29632	+	5.67957i	0.0487533	+	0.213602i
$708$	−8.70171			−0.327030
$709$	−8.30074	−	36.3679i	−0.311741	−	1.36583i	−0.851654	−	0.524105i	$-0.824400\pi$
$709$	−8.30074	−	36.3679i	−0.311741	−	1.36583i	0.539913	−	0.841721i	$-0.318457\pi$
$710$	−18.4976	−	8.90798i	−0.694203	−	0.334310i
$711$	16.1468	+	7.77587i	0.605551	+	0.291618i
$712$	−1.80463	−	7.90658i	−0.0676312	−	0.296312i
$713$	−3.70782			−0.138859
$714$	−1.32467	−	5.80375i	−0.0495744	−	0.217200i
$715$	−20.9230	+	26.2367i	−0.782477	+	0.981195i
$716$	1.24094	−	5.43691i	0.0463761	−	0.203187i
$717$	−1.04407	+	4.57438i	−0.0389916	+	0.170833i
$718$	−14.7168	−	18.4543i	−0.549225	−	0.688707i
$719$	−36.9698	−	17.8037i	−1.37874	−	0.663967i	−0.410010	−	0.912081i	$-0.634475\pi$
$719$	−36.9698	−	17.8037i	−1.37874	−	0.663967i	−0.968731	+	0.248114i	$0.920189\pi$
$720$	6.89493	−	3.32042i	0.256959	−	0.123745i
$721$	−2.46950	+	3.09666i	−0.0919690	+	0.115325i
$722$	−4.60723	−	5.77728i	−0.171463	−	0.215008i
$723$	4.50096	−	2.16755i	0.167392	−	0.0806120i
$724$	−13.8562			−0.514963
$725$	−5.54288	−	29.3301i	−0.205857	−	1.08929i
$726$	−14.6136			−0.542360
$727$	38.1051	−	18.3505i	1.41324	−	0.680581i	0.437441	−	0.899247i	$-0.355885\pi$
$727$	38.1051	−	18.3505i	1.41324	−	0.680581i	0.975800	+	0.218666i	$0.0701705\pi$
$728$	3.10388	+	3.89214i	0.115037	+	0.144252i
$729$	1.11596	−	1.39937i	0.0413317	−	0.0518284i
$730$	−27.2739	+	13.1344i	−1.00945	+	0.486126i
$731$	6.66325	+	3.20885i	0.246449	+	0.118684i
$732$	4.46346	+	5.59700i	0.164974	+	0.206871i
$733$	−3.38082	+	14.8123i	−0.124874	+	0.547107i	0.873327	+	0.487135i	$0.161958\pi$
$733$	−3.38082	+	14.8123i	−0.124874	+	0.547107i	−0.998200	+	0.0599714i	$0.980899\pi$
$734$	−2.17845	+	9.54440i	−0.0804080	+	0.352290i
$735$	−0.356896	+	0.447533i	−0.0131643	+	0.0165075i
$736$	−0.451083	−	1.97632i	−0.0166271	−	0.0728482i
$737$	59.4639			2.19038
$738$	5.13437	+	22.4952i	0.188999	+	0.828059i
$739$	30.3523	+	14.6169i	1.11653	+	0.537692i	0.898818	−	0.438321i	$-0.144427\pi$
$739$	30.3523	+	14.6169i	1.11653	+	0.537692i	0.217711	+	0.976013i	$0.430141\pi$
$740$	19.7838	+	9.52738i	0.727268	+	0.350234i
$741$	1.75259	+	7.67861i	0.0643831	+	0.282081i
$742$	32.3032			1.18589
$743$	−0.975114	−	4.27225i	−0.0357735	−	0.156734i	0.953886	−	0.300168i	$-0.0970427\pi$
$743$	−0.975114	−	4.27225i	−0.0357735	−	0.156734i	−0.989660	+	0.143434i	$0.954186\pi$
$744$	−0.914542	+	1.14680i	−0.0335288	+	0.0420437i
$745$	13.4203	−	58.7984i	0.491683	−	2.15421i
$746$	−6.16099	+	26.9931i	−0.225570	+	0.988286i
$747$	−11.2280	−	14.0795i	−0.410812	−	0.515142i
$748$	13.8850	+	6.68666i	0.507686	+	0.244489i
$749$	20.8916	−	10.0609i	0.763362	−	0.367616i
$750$	−0.881355	+	1.10518i	−0.0321825	+	0.0403556i
$751$	−25.6911	−	32.2156i	−0.937482	−	1.17557i	−0.984272	−	0.176661i	$-0.943470\pi$
$751$	−25.6911	−	32.2156i	−0.937482	−	1.17557i	0.0467895	−	0.998905i	$-0.485101\pi$
$752$	2.02446	−	0.974928i	0.0738244	−	0.0355520i
$753$	18.9933			0.692154
$754$	−10.2884	−	0.387231i	−0.374680	−	0.0141021i
$755$	−19.8388			−0.722007
$756$	−10.0782	+	4.85342i	−0.366541	+	0.176517i
$757$	11.2899	+	14.1570i	0.410337	+	0.514546i	0.943458	−	0.331493i	$-0.107552\pi$
$757$	11.2899	+	14.1570i	0.410337	+	0.514546i	−0.533121	+	0.846039i	$0.678981\pi$
$758$	−4.34146	+	5.44402i	−0.157689	+	0.197736i
$759$	−7.91766	+	3.81294i	−0.287393	+	0.138401i
$760$	−15.0281	−	7.23715i	−0.545127	−	0.262519i
$761$	18.9696	+	23.7872i	0.687649	+	0.862284i	0.996034	−	0.0889775i	$-0.0283599\pi$
$761$	18.9696	+	23.7872i	0.687649	+	0.862284i	−0.308385	+	0.951262i	$0.599789\pi$
$762$	3.26832	−	14.3195i	0.118399	−	0.518739i
$763$	5.96562	−	26.1371i	0.215970	−	0.946225i
$764$	3.89493	−	4.88409i	0.140914	−	0.176700i
$765$	4.85474	+	21.2700i	0.175523	+	0.769019i
$766$	−6.71678			−0.242687
$767$	4.61625	+	20.2251i	0.166683	+	0.730287i
$768$	−0.722521	−	0.347948i	−0.0260717	−	0.0125555i
$769$	32.8630	+	15.8260i	1.18507	+	0.570700i	0.919384	−	0.393360i	$-0.128687\pi$
$769$	32.8630	+	15.8260i	1.18507	+	0.570700i	0.265685	+	0.964060i	$0.414402\pi$
$770$	10.1703	+	44.5588i	0.366510	+	1.60579i
$771$	−7.50796			−0.270393
$772$	0.412386	+	1.80678i	0.0148421	+	0.0650275i
$773$	−2.84899	+	3.57253i	−0.102471	+	0.128495i	−0.830423	−	0.557134i	$-0.811901\pi$
$773$	−2.84899	+	3.57253i	−0.102471	+	0.128495i	0.727952	+	0.685628i	$0.240473\pi$
$774$	1.36054	−	5.96093i	0.0489037	−	0.214261i
$775$	−2.25600	+	9.88420i	−0.0810381	+	0.355051i
$776$	−1.41789	−	1.77798i	−0.0508995	−	0.0638259i
$777$	−12.7231	−	6.12710i	−0.456437	−	0.219808i
$778$	11.4928	−	5.53462i	0.412036	−	0.198426i
$779$	31.3560	−	39.3192i	1.12345	−	1.40876i
$780$	3.10388	+	3.89214i	0.111137	+	0.139361i
$781$	−30.7962	+	14.8307i	−1.10197	+	0.530683i
$782$	5.77910			0.206660
$783$	5.99247	−	22.3445i	0.214153	−	0.798528i
$784$	−0.219833			−0.00785116
$785$	19.0770	−	9.18701i	0.680888	−	0.327898i
$786$	−3.36443	−	4.21886i	−0.120005	−	0.150482i
$787$	−18.6523	+	23.3892i	−0.664881	+	0.833735i	−0.993865	−	0.110601i	$-0.964722\pi$
$787$	−18.6523	+	23.3892i	−0.664881	+	0.833735i	0.328984	+	0.944336i	$0.393294\pi$
$788$	−6.43512	+	3.09899i	−0.229242	+	0.110397i
$789$	−14.7986	−	7.12662i	−0.526844	−	0.253715i
$790$	−15.3937	−	19.3031i	−0.547684	−	0.686775i
$791$	−2.10949	+	9.24228i	−0.0750048	+	0.328618i
$792$	2.83513	−	12.4215i	0.100742	−	0.441379i
$793$	10.6411	−	13.3435i	0.377876	−	0.473841i
$794$	−4.64646	−	20.3575i	−0.164897	−	0.722459i
$795$	32.3032			1.14568
$796$	2.30917	+	10.1172i	0.0818465	+	0.358593i
$797$	−25.8436	−	12.4456i	−0.915428	−	0.440847i	−0.0839913	−	0.996466i	$-0.526767\pi$
$797$	−25.8436	−	12.4456i	−0.915428	−	0.440847i	−0.831437	+	0.555620i	$0.812481\pi$
$798$	9.66464	+	4.65424i	0.342124	+	0.164758i
$799$	1.42543	+	6.24521i	0.0504280	+	0.220940i
$800$	−5.54288			−0.195970
$801$	−4.25332	−	18.6350i	−0.150284	−	0.658435i
$802$	18.7431	−	23.5031i	0.661842	−	0.829923i
$803$	−11.2148	+	49.1350i	−0.395760	+	1.73394i
$804$	1.96293	−	8.60015i	0.0692271	−	0.303304i
$805$	10.6860	+	13.3998i	0.376631	+	0.472281i
$806$	3.15064	+	1.51727i	0.110976	+	0.0534434i
$807$	−4.89104	+	2.35540i	−0.172173	+	0.0829141i
$808$	−1.39493	+	1.74918i	−0.0490734	+	0.0615361i
$809$	19.6035	+	24.5820i	0.689223	+	0.864258i	0.996167	−	0.0874696i	$-0.0278781\pi$
$809$	19.6035	+	24.5820i	0.689223	+	0.864258i	−0.306945	+	0.951727i	$0.599307\pi$
$810$	10.6066	−	5.10785i	0.372677	−	0.179472i
$811$	2.63235			0.0924343			0.0462172	−	0.998931i	$-0.485283\pi$
$811$	2.63235			0.0924343			0.0462172	+	0.998931i	$0.485283\pi$
$812$	−9.14891	+	10.6265i	−0.321064	+	0.372917i
$813$	10.9226			0.383073
$814$	32.9376	−	15.8619i	1.15446	−	0.555959i
$815$	−12.3497	−	15.4860i	−0.432590	−	0.542450i
$816$	1.42543	−	1.78743i	0.0498999	−	0.0625726i
$817$	−12.0068	+	5.78215i	−0.420063	+	0.202292i
$818$	23.9502	+	11.5338i	0.837398	+	0.403270i
$819$	7.31551	+	9.17336i	0.255625	+	0.320543i
$820$	7.07338	−	30.9905i	0.247013	−	1.08223i
$821$	5.44816	−	23.8699i	0.190142	−	0.833067i	−0.786396	−	0.617722i	$-0.788056\pi$
$821$	5.44816	−	23.8699i	0.190142	−	0.833067i	0.976538	−	0.215344i	$-0.0690873\pi$
$822$	5.37047	−	6.73436i	0.187317	−	0.234888i
$823$	5.16099	+	22.6118i	0.179901	+	0.788197i	0.981674	+	0.190568i	$0.0610331\pi$
$823$	5.16099	+	22.6118i	0.179901	+	0.788197i	−0.801773	+	0.597629i	$0.796110\pi$
$824$	−1.52111			−0.0529902
$825$	5.34697	+	23.4266i	0.186158	+	0.815610i
$826$	25.4562	+	12.2591i	0.885735	+	0.426548i
$827$	−6.16637	−	2.96957i	−0.214426	−	0.103262i	0.323588	−	0.946198i	$-0.395111\pi$
$827$	−6.16637	−	2.96957i	−0.214426	−	0.103262i	−0.538014	+	0.842936i	$0.680825\pi$
$828$	−1.06315	−	4.65799i	−0.0369472	−	0.161876i
$829$	53.3139			1.85167			0.925835	−	0.377928i	$-0.123363\pi$
$829$	53.3139			1.85167			0.925835	+	0.377928i	$0.123363\pi$
$830$	5.52057	+	24.1872i	0.191622	+	0.839550i
$831$	−5.10268	+	6.39856i	−0.177010	+	0.221963i
$832$	−0.425428	+	1.86392i	−0.0147490	+	0.0646198i
$833$	0.139456	−	0.610998i	0.00483187	−	0.0211698i
$834$	8.67725	+	10.8809i	0.300469	+	0.376776i
$835$	0.614761	+	0.296053i	0.0212747	+	0.0102453i
$836$	−25.0199	+	12.0490i	−0.865332	+	0.416722i
$837$	−4.89911	+	6.14329i	−0.169338	+	0.212343i
$838$	−23.6990	−	29.7176i	−0.818669	−	1.02658i
$839$	−22.0318	+	10.6099i	−0.760621	+	0.366296i	−0.773645	−	0.633620i	$-0.781568\pi$
$839$	−22.0318	+	10.6099i	−0.760621	+	0.366296i	0.0130241	+	0.999915i	$0.495854\pi$
$840$	6.78017			0.233938
$841$	−4.30960	−	28.6780i	−0.148607	−	0.988896i
$842$	14.4456			0.497829
$843$	−5.20948	+	2.50875i	−0.179424	+	0.0864061i
$844$	5.15130	+	6.45953i	0.177315	+	0.222346i
$845$	−18.9182	+	23.7227i	−0.650806	+	0.816084i
$846$	4.77144	−	2.29780i	0.164045	−	0.0790001i
$847$	42.7509	+	20.5878i	1.46894	+	0.707404i
$848$	7.73490	+	9.69926i	0.265617	+	0.333074i
$849$	5.02973	−	22.0367i	0.172620	−	0.756297i
$850$	3.51626	−	15.4058i	0.120607	−	0.528413i
$851$	8.54743	−	10.7181i	0.293002	−	0.367413i
$852$	1.12833	+	4.94355i	0.0386561	+	0.169363i
$853$	−16.3394			−0.559452			−0.279726	−	0.960080i	$-0.590244\pi$
$853$	−16.3394			−0.559452			−0.279726	+	0.960080i	$0.590244\pi$
$854$	−5.17241	−	22.6618i	−0.176996	−	0.775471i
$855$	−35.4197	−	17.0572i	−1.21133	−	0.583345i
$856$	8.02326	+	3.86380i	0.274229	+	0.132062i
$857$	−9.82908	−	43.0640i	−0.335755	−	1.47104i	−0.807796	−	0.589463i	$-0.799340\pi$
$857$	−9.82908	−	43.0640i	−0.335755	−	1.47104i	0.472041	−	0.881577i	$-0.343518\pi$
$858$	8.28813			0.282952
$859$	−3.60633	−	15.8004i	−0.123046	−	0.539101i	−0.998447	−	0.0557037i	$-0.982260\pi$
$859$	−3.60633	−	15.8004i	−0.123046	−	0.539101i	0.875401	−	0.483397i	$-0.160597\pi$
$860$	−5.25182	+	6.58558i	−0.179086	+	0.224566i
$861$	−4.54892	+	19.9301i	−0.155027	+	0.679216i
$862$	−0.627138	+	2.74767i	−0.0213604	+	0.0935860i
$863$	−4.06734	−	5.10028i	−0.138454	−	0.173615i	0.707771	−	0.706442i	$-0.249701\pi$
$863$	−4.06734	−	5.10028i	−0.138454	−	0.173615i	−0.846224	+	0.532827i	$0.821130\pi$
$864$	−3.87047	−	1.86392i	−0.131676	−	0.0634118i
$865$	−52.1860	+	25.1315i	−1.77438	+	0.854496i
$866$	10.2262	−	12.8232i	0.347499	−	0.435750i
$867$	−4.43631	−	5.56296i	−0.150665	−	0.188928i
$868$	4.29105	−	2.06646i	0.145648	−	0.0701403i
$869$	−41.1051			−1.39440
$870$	−9.14891	+	10.6265i	−0.310177	+	0.360272i
$871$	−21.0304			−0.712588
$872$	9.27628	−	4.46722i	0.314135	−	0.151279i
$873$	−3.34183	−	4.19052i	−0.113104	−	0.141828i
$874$	−6.49276	+	8.14167i	−0.219621	+	0.275396i
$875$	4.13533	−	1.99147i	0.139800	−	0.0673240i
$876$	6.73609	+	3.24393i	0.227592	+	0.109602i
$877$	−29.9061	−	37.5011i	−1.00986	−	1.26632i	−0.963588	−	0.267392i	$-0.913838\pi$
$877$	−29.9061	−	37.5011i	−1.00986	−	1.26632i	−0.0462698	−	0.998929i	$-0.514733\pi$
$878$	4.53026	−	19.8484i	0.152889	−	0.669850i
$879$	−2.21906	+	9.72235i	−0.0748471	+	0.327927i
$880$	−10.9438	+	13.7231i	−0.368917	+	0.462607i
$881$	1.15979	+	5.08139i	0.0390744	+	0.171196i	0.990700	−	0.136063i	$-0.0434451\pi$
$881$	1.15979	+	5.08139i	0.0390744	+	0.171196i	−0.951626	+	0.307260i	$0.900588\pi$
$882$	−0.518122			−0.0174461
$883$	6.46575	+	28.3283i	0.217590	+	0.953323i	0.959253	+	0.282550i	$0.0911803\pi$
$883$	6.46575	+	28.3283i	0.217590	+	0.953323i	−0.741663	+	0.670773i	$0.765963\pi$
$884$	−4.91066	−	2.36485i	−0.165163	−	0.0795384i
$885$	25.4562	+	12.2591i	0.855702	+	0.412084i
$886$	−4.21672	−	18.4746i	−0.141663	−	0.620668i
$887$	27.1400			0.911274			0.455637	−	0.890166i	$-0.349412\pi$
$887$	27.1400			0.911274			0.455637	+	0.890166i	$0.349412\pi$
$888$	−1.20679	−	5.28730i	−0.0404973	−	0.177430i
$889$	−29.7347	+	37.2861i	−0.997269	+	1.25054i
$890$	−5.85958	+	25.6725i	−0.196414	+	0.860545i
$891$	4.36131	−	19.1082i	0.146109	−	0.640148i
$892$	2.48039	+	3.11031i	0.0830495	+	0.104141i
$893$	−10.3998	−	5.00827i	−0.348015	−	0.167595i
$894$	−13.4203	+	6.46290i	−0.448844	+	0.216152i
$895$	−11.2899	+	14.1570i	−0.377378	+	0.473217i
$896$	1.62349	+	2.03579i	0.0542370	+	0.0680110i
$897$	2.80021	−	1.34851i	0.0934963	−	0.0450254i
$898$	−21.6886			−0.723757
$899$	−2.55144	+	9.51373i	−0.0850953	+	0.317301i
$900$	−13.0640			−0.435466
$901$	−31.8647	+	15.3452i	−1.06157	+	0.511224i
$902$	−32.9964	−	41.3762i	−1.09866	−	1.37768i
$903$	3.37747	−	4.23521i	0.112395	−	0.140939i
$904$	−3.28017	+	1.57965i	−0.109097	+	0.0525382i
$905$	40.5354	+	19.5208i	1.34744	+	0.648894i
$906$	3.05496	+	3.83080i	0.101494	+	0.127270i
$907$	3.18532	−	13.9558i	0.105767	−	0.463394i	−0.894112	−	0.447843i	$-0.852192\pi$
$907$	3.18532	−	13.9558i	0.105767	−	0.463394i	0.999879	−	0.0155515i	$-0.00495040\pi$
$908$	−2.44235	+	10.7006i	−0.0810523	+	0.355114i
$909$	−3.28770	+	4.12265i	−0.109046	+	0.136740i
$910$	−3.59688	−	15.7589i	−0.119235	−	0.522404i
$911$	−1.53079			−0.0507175			−0.0253587	−	0.999678i	$-0.508073\pi$
$911$	−1.53079			−0.0507175			−0.0253587	+	0.999678i	$0.508073\pi$
$912$	0.916698	+	4.01632i	0.0303549	+	0.132994i
$913$	37.2139	+	17.9212i	1.23160	+	0.593107i
$914$	−11.1380	−	5.36379i	−0.368413	−	0.177418i
$915$	−5.17241	−	22.6618i	−0.170995	−	0.749176i
$916$	5.09246			0.168260
$917$	3.89881	+	17.0818i	0.128750	+	0.564091i
$918$	7.63587	−	9.57507i	0.252021	−	0.316025i
$919$	4.57529	−	20.0457i	0.150925	−	0.661246i	−0.841692	−	0.539958i	$-0.818440\pi$
$919$	4.57529	−	20.0457i	0.150925	−	0.661246i	0.992617	−	0.121288i	$-0.0387026\pi$
$920$	−1.46466	+	6.41708i	−0.0482883	+	0.211565i
$921$	−16.6570	−	20.8872i	−0.548866	−	0.688256i
$922$	−2.51357	−	1.21047i	−0.0827801	−	0.0398648i
$923$	10.8916	−	5.24511i	0.358501	−	0.172645i
$924$	7.03803	−	8.82541i	0.231534	−	0.290335i
$925$	−23.3714	−	29.3068i	−0.768448	−	0.963603i
$926$	35.4001	−	17.0478i	1.16332	−	0.560225i
$927$	−3.58509			−0.117750
$928$	−5.38135	−	0.202542i	−0.176652	−	0.00664877i
$929$	22.1903			0.728040			0.364020	−	0.931391i	$-0.381404\pi$
$929$	22.1903			0.728040			0.364020	+	0.931391i	$0.381404\pi$
$930$	4.29105	−	2.06646i	0.140709	−	0.0677620i
$931$	0.704103	+	0.882917i	0.0230760	+	0.0289364i
$932$	10.3204	−	12.9413i	0.338054	−	0.423907i
$933$	−5.81067	+	2.79827i	−0.190233	+	0.0916112i
$934$	13.2078	+	6.36052i	0.432171	+	0.208122i
$935$	−31.1993	−	39.1227i	−1.02033	−	1.27945i
$936$	−1.00269	+	4.39306i	−0.0327739	+	0.143592i
$937$	−9.22223	+	40.4052i	−0.301277	+	1.31998i	0.566925	+	0.823769i	$0.308133\pi$
$937$	−9.22223	+	40.4052i	−0.301277	+	1.31998i	−0.868202	+	0.496211i	$0.834724\pi$
$938$	−17.8584	+	22.3937i	−0.583097	+	0.731181i
$939$	1.67015	+	7.31739i	0.0545031	+	0.238794i
$940$	−7.29590			−0.237966
$941$	7.32736	+	32.1032i	0.238865	+	1.04654i	0.942035	+	0.335514i	$0.108910\pi$
$941$	7.32736	+	32.1032i	0.238865	+	1.04654i	−0.703170	+	0.711022i	$0.748233\pi$
$942$	−4.71164	−	2.26900i	−0.153513	−	0.0739282i
$943$	−17.8802	−	8.61063i	−0.582258	−	0.280401i
$944$	2.41454	+	10.5788i	0.0785867	+	0.344311i
$945$	36.3207			1.18151
$946$	3.12056	+	13.6721i	0.101458	+	0.444518i
$947$	−5.71164	+	7.16216i	−0.185603	+	0.232739i	−0.865924	−	0.500175i	$-0.833269\pi$
$947$	−5.71164	+	7.16216i	−0.185603	+	0.232739i	0.680321	+	0.732914i	$0.261840\pi$
$948$	−1.35690	+	5.94495i	−0.0440699	+	0.193083i
$949$	3.96628	−	17.3774i	0.128751	−	0.564094i
$950$	17.7533	+	22.2620i	0.575994	+	0.722273i
$951$	−2.60076	−	1.25246i	−0.0843354	−	0.0406138i
$952$	−6.68814	+	3.22084i	−0.216764	+	0.104388i
$953$	−20.6546	+	25.9000i	−0.669067	+	0.838984i	−0.994296	−	0.106651i	$-0.965987\pi$
$953$	−20.6546	+	25.9000i	−0.669067	+	0.838984i	0.325229	+	0.945635i	$0.394559\pi$
$954$	18.2303	+	22.8601i	0.590229	+	0.740124i
$955$	−18.2751	+	8.80082i	−0.591368	+	0.284788i
$956$	5.85086			0.189230
$957$	4.33513	+	22.9393i	0.140135	+	0.741523i
$958$	−17.2064			−0.555914
$959$	−25.1984	+	12.1349i	−0.813697	+	0.391856i
$960$	1.62349	+	2.03579i	0.0523979	+	0.0657049i
$961$	−17.2423	+	21.6211i	−0.556202	+	0.697455i
$962$	−11.6489	+	5.60982i	−0.375576	+	0.180868i
$963$	18.9100	+	9.10657i	0.609366	+	0.293455i
$964$	−3.88404	−	4.87044i	−0.125097	−	0.156866i
$965$	1.33901	−	5.86659i	0.0431043	−	0.188852i
$966$	0.941926	−	4.12685i	0.0303060	−	0.132779i
$967$	15.3919	−	19.3008i	0.494969	−	0.620672i	−0.470117	−	0.882604i	$-0.655788\pi$
$967$	15.3919	−	19.3008i	0.494969	−	0.620672i	0.965086	+	0.261932i	$0.0843597\pi$
$968$	4.05496	+	17.7659i	0.130331	+	0.571019i
$969$	−11.7444			−0.377284
$970$	1.64310	+	7.19891i	0.0527569	+	0.231143i
$971$	31.2211	+	15.0353i	1.00193	+	0.482505i	0.861594	−	0.507598i	$-0.169467\pi$
$971$	31.2211	+	15.0353i	1.00193	+	0.482505i	0.140339	+	0.990104i	$0.455181\pi$
$972$	−14.2310	−	6.85329i	−0.456460	−	0.219820i
$973$	−10.0555	−	44.0560i	−0.322364	−	1.41237i
$974$	13.2741			0.425330
$975$	−1.89104	−	8.28520i	−0.0605619	−	0.265339i
$976$	5.56584	−	6.97935i	0.178158	−	0.223403i
$977$	6.44557	−	28.2399i	0.206212	−	0.903475i	−0.760849	−	0.648929i	$-0.775217\pi$
$977$	6.44557	−	28.2399i	0.206212	−	0.903475i	0.967061	−	0.254545i	$-0.0819258\pi$
$978$	−1.08857	+	4.76935i	−0.0348087	+	0.152507i
$979$	27.3342	+	34.2760i	0.873606	+	1.09547i
$980$	0.643104	+	0.309703i	0.0205432	+	0.00989309i
$981$	21.8632	−	10.5288i	0.698039	−	0.336158i
$982$	−1.81216	+	2.27238i	−0.0578283	+	0.0725144i
$983$	−29.4435	−	36.9210i	−0.939101	−	1.17760i	−0.983922	−	0.178600i	$-0.942843\pi$
$983$	−29.4435	−	36.9210i	−0.939101	−	1.17760i	0.0448206	−	0.998995i	$-0.485728\pi$
$984$	−7.07338	+	3.40636i	−0.225491	+	0.108591i
$985$	23.1914			0.738938
$986$	3.97674	−	14.8283i	0.126645	−	0.472230i
$987$	4.69202			0.149349
$988$	8.84870	−	4.26131i	0.281515	−	0.135570i
$989$	3.27881	+	4.11149i	0.104260	+	0.130738i
$990$	−25.7935	+	32.3440i	−0.819771	+	1.02796i
$991$	53.2948	−	25.6654i	1.69296	−	0.815288i	0.697884	−	0.716211i	$-0.254125\pi$
$991$	53.2948	−	25.6654i	1.69296	−	0.815288i	0.995080	−	0.0990777i	$-0.0315892\pi$
$992$	1.64795	+	0.793610i	0.0523224	+	0.0251971i
$993$	−3.73341	−	4.68154i	−0.118476	−	0.148564i
$994$	3.66368	−	16.0516i	0.116205	−	0.509127i
$995$	7.49784	−	32.8502i	0.237698	−	1.04142i
$996$	3.82036	−	4.79057i	0.121053	−	0.151795i
$997$	10.7236	+	46.9831i	0.339619	+	1.48797i	0.799866	+	0.600179i	$0.204904\pi$
$997$	10.7236	+	46.9831i	0.339619	+	1.48797i	−0.460247	+	0.887791i	$0.652239\pi$
$998$	−2.50365			−0.0792516
$999$	−6.46466	−	28.3235i	−0.204533	−	0.896116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.d.a.49.1	yes	6
3.2	odd	2		522.2.k.c.397.1		6
4.3	odd	2		464.2.u.b.49.1		6
29.4	even	14		1682.2.a.n.1.1		3
29.10	odd	28		1682.2.b.g.1681.3		6
29.16	even	7	inner	58.2.d.a.45.1	✓	6
29.19	odd	28		1682.2.b.g.1681.4		6
29.25	even	7		1682.2.a.m.1.3		3
87.74	odd	14		522.2.k.c.451.1		6
116.103	odd	14		464.2.u.b.161.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.a.45.1	✓	6	29.16	even	7	inner
58.2.d.a.49.1	yes	6	1.1	even	1	trivial
464.2.u.b.49.1		6	4.3	odd	2
464.2.u.b.161.1		6	116.103	odd	14
522.2.k.c.397.1		6	3.2	odd	2
522.2.k.c.451.1		6	87.74	odd	14
1682.2.a.m.1.3		3	29.25	even	7
1682.2.a.n.1.1		3	29.4	even	14
1682.2.b.g.1681.3		6	29.10	odd	28
1682.2.b.g.1681.4		6	29.19	odd	28

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

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(0.500000 + 0.626980i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.92543 + 1.40881i) q^{5} +(0.722521 + 0.347948i) q^{6} +(-1.62349 - 2.03579i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.524459 - 2.29780i) q^{9} +(-2.02446 + 2.53859i) q^{10} +(1.20291 + 5.27028i) q^{11} +0.801938 q^{12} +(-0.425428 - 1.86392i) q^{13} +(-2.34601 - 1.12978i) q^{14} +(-2.34601 - 1.12978i) q^{15} +(-0.222521 - 0.974928i) q^{16} +2.85086 q^{17} +(-0.524459 - 2.29780i) q^{18} +(-3.20291 + 4.01632i) q^{19} +(-0.722521 + 3.16557i) q^{20} +(0.464656 - 2.03579i) q^{21} +(3.37047 + 4.22643i) q^{22} +(1.82640 + 0.879546i) q^{23} +(0.722521 - 0.347948i) q^{24} +(3.45593 - 4.33360i) q^{25} +(-1.19202 - 1.49475i) q^{26} +(3.87047 - 1.86392i) q^{27} -2.60388 q^{28} +(3.51357 - 4.08103i) q^{29} -2.60388 q^{30} +(-1.64795 + 0.793610i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-2.70291 + 3.38934i) q^{33} +(2.56853 - 1.23694i) q^{34} +(7.61745 + 3.66837i) q^{35} +(-1.46950 - 1.84270i) q^{36} +(1.50484 - 6.59315i) q^{37} +(-1.14310 + 5.00827i) q^{38} +(0.955927 - 1.19869i) q^{39} +(0.722521 + 3.16557i) q^{40} -9.78986 q^{41} +(-0.464656 - 2.03579i) q^{42} +(2.33728 + 1.12558i) q^{43} +(4.87047 + 2.34549i) q^{44} +(1.70291 + 7.46092i) q^{45} +2.02715 q^{46} +(0.500000 + 2.19064i) q^{47} +(0.500000 - 0.626980i) q^{48} +(0.0489173 - 0.214321i) q^{49} +(1.23341 - 5.40391i) q^{50} +(1.42543 + 1.78743i) q^{51} +(-1.72252 - 0.829522i) q^{52} +(-11.1773 + 5.38268i) q^{53} +(2.67845 - 3.35867i) q^{54} +(-10.9438 - 13.7231i) q^{55} +(-2.34601 + 1.12978i) q^{56} -4.11960 q^{57} +(1.39493 - 5.20136i) q^{58} -10.8509 q^{59} +(-2.34601 + 1.12978i) q^{60} +(5.56584 + 6.97935i) q^{61} +(-1.14042 + 1.43004i) q^{62} +(-5.52930 + 2.66277i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.87047 + 4.85342i) q^{65} +(-0.964656 + 4.22643i) q^{66} +(2.44773 - 10.7242i) q^{67} +(1.77748 - 2.22889i) q^{68} +(0.361740 + 1.58489i) q^{69} +8.45473 q^{70} +(1.40701 + 6.16451i) q^{71} +(-2.12349 - 1.02262i) q^{72} +(8.39977 + 4.04512i) q^{73} +(-1.50484 - 6.59315i) q^{74} +4.44504 q^{75} +(1.14310 + 5.00827i) q^{76} +(8.77628 - 11.0051i) q^{77} +(0.341166 - 1.49475i) q^{78} +(-1.69202 + 7.41323i) q^{79} +(2.02446 + 2.53859i) q^{80} +(-3.26659 - 1.57311i) q^{81} +(-8.82036 + 4.24766i) q^{82} +(4.76391 - 5.97375i) q^{83} +(-1.30194 - 1.63258i) q^{84} +(-8.33997 + 4.01632i) q^{85} +2.59419 q^{86} +(4.31551 + 0.162426i) q^{87} +5.40581 q^{88} +(7.30678 - 3.51876i) q^{89} +(4.77144 + 5.98319i) q^{90} +(-3.10388 + 3.89214i) q^{91} +(1.82640 - 0.879546i) q^{92} +(-1.32155 - 0.636426i) q^{93} +(1.40097 + 1.75676i) q^{94} +(3.71164 - 16.2617i) q^{95} +(0.178448 - 0.781831i) q^{96} +(1.41789 - 1.77798i) q^{97} +(-0.0489173 - 0.214321i) q^{98} +12.7409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} + q^{8} - 6 q^{9} - 3 q^{10} - 6 q^{11} - 4 q^{12} + 11 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - 10 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{20}+ \cdots + 48 q^{99}+O(q^{100}) \) 6 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 + q^8 - 6 * q^9 - 3 * q^10 - 6 * q^11 - 4 * q^12 + 11 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - 10 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^20 + 15 * q^21 + 6 * q^22 - 7 * q^23 + 4 * q^24 + 17 * q^25 + 3 * q^26 + 9 * q^27 + 2 * q^28 + 15 * q^29 + 2 * q^30 + 4 * q^31 + q^32 - 3 * q^33 + 10 * q^34 + 22 * q^35 + q^36 - 13 * q^37 - 15 * q^38 + 2 * q^39 + 4 * q^40 - 12 * q^41 - 15 * q^42 - 7 * q^43 + 15 * q^44 - 3 * q^45 + 3 * q^47 + 3 * q^48 - 18 * q^49 + 4 * q^50 - 5 * q^51 - 10 * q^52 - 22 * q^53 + 12 * q^54 - 24 * q^55 - 9 * q^56 + 18 * q^57 - 15 * q^58 - 38 * q^59 - 9 * q^60 + 31 * q^61 - 18 * q^62 - 2 * q^63 - q^64 + 9 * q^65 - 18 * q^66 + 11 * q^67 + 11 * q^68 - 28 * q^69 + 6 * q^70 + 23 * q^71 - 8 * q^72 + 5 * q^73 + 13 * q^74 + 26 * q^75 + 15 * q^76 + 12 * q^77 + 19 * q^78 + 3 * q^80 - 23 * q^81 - 16 * q^82 + 35 * q^83 + q^84 - 26 * q^85 + 42 * q^86 + 11 * q^87 + 6 * q^88 + 13 * q^89 + 10 * q^90 - q^91 - 7 * q^92 - 12 * q^93 + 4 * q^94 + 25 * q^95 - 3 * q^96 + 20 * q^97 + 18 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more