LMFDB - Embedded newform 935.2.u.e.86.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(86,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("935.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.u (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.2
Character	$\chi$	$=$	935.86
Dual form			935.2.u.e.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766629 + 2.35944i) q^{2} +(-0.0390857 + 0.0283975i) q^{3} +(-3.36120 - 2.44206i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0370378 - 0.113991i) q^{6} +(-0.163849 - 0.119043i) q^{7} +(4.32457 - 3.14198i) q^{8} +(-0.926330 + 2.85095i) q^{9} +O(q^{10})$	\(q+(-0.766629 + 2.35944i) q^{2} +(-0.0390857 + 0.0283975i) q^{3} +(-3.36120 - 2.44206i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0370378 - 0.113991i) q^{6} +(-0.163849 - 0.119043i) q^{7} +(4.32457 - 3.14198i) q^{8} +(-0.926330 + 2.85095i) q^{9} +2.48086 q^{10} +(3.31221 - 0.171089i) q^{11} +0.200723 q^{12} +(-0.838246 + 2.57986i) q^{13} +(0.406486 - 0.295329i) q^{14} +(0.0390857 + 0.0283975i) q^{15} +(1.53025 + 4.70962i) q^{16} +(-0.309017 - 0.951057i) q^{17} +(-6.01649 - 4.37124i) q^{18} +(-4.58014 + 3.32767i) q^{19} +(-1.28387 + 3.95133i) q^{20} +0.00978466 q^{21} +(-2.13556 + 7.94612i) q^{22} -5.26376 q^{23} +(-0.0798046 + 0.245613i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-5.44439 - 3.95558i) q^{26} +(-0.0895417 - 0.275581i) q^{27} +(0.260019 + 0.800256i) q^{28} +(-5.00313 - 3.63499i) q^{29} +(-0.0969663 + 0.0704502i) q^{30} +(0.545872 - 1.68002i) q^{31} -1.59428 q^{32} +(-0.124602 + 0.100745i) q^{33} +2.48086 q^{34} +(-0.0625846 + 0.192616i) q^{35} +(10.0758 - 7.32047i) q^{36} +(-2.13516 - 1.55128i) q^{37} +(-4.34016 - 13.3577i) q^{38} +(-0.0404979 - 0.124640i) q^{39} +(-4.32457 - 3.14198i) q^{40} +(5.35765 - 3.89256i) q^{41} +(-0.00750120 + 0.0230863i) q^{42} -0.651310 q^{43} +(-11.5508 - 7.51354i) q^{44} +2.99767 q^{45} +(4.03535 - 12.4195i) q^{46} +(-4.46871 + 3.24671i) q^{47} +(-0.193552 - 0.140624i) q^{48} +(-2.15044 - 6.61839i) q^{49} +(-0.766629 - 2.35944i) q^{50} +(0.0390857 + 0.0283975i) q^{51} +(9.11767 - 6.62438i) q^{52} +(-4.12038 + 12.6812i) q^{53} +0.718862 q^{54} +(-1.18624 - 3.09723i) q^{55} -1.08261 q^{56} +(0.0845209 - 0.260129i) q^{57} +(12.4121 - 9.01790i) q^{58} +(-7.53135 - 5.47185i) q^{59} +(-0.0620269 - 0.190899i) q^{60} +(-1.41658 - 4.35979i) q^{61} +(3.54543 + 2.57591i) q^{62} +(0.491164 - 0.356851i) q^{63} +(-1.83827 + 5.65762i) q^{64} +2.71262 q^{65} +(-0.142180 - 0.371224i) q^{66} -1.67769 q^{67} +(-1.28387 + 3.95133i) q^{68} +(0.205738 - 0.149477i) q^{69} +(-0.406486 - 0.295329i) q^{70} +(0.731579 + 2.25157i) q^{71} +(4.95165 + 15.2396i) q^{72} +(-10.9426 - 7.95027i) q^{73} +(5.29703 - 3.84852i) q^{74} +(0.0149294 - 0.0459480i) q^{75} +23.5211 q^{76} +(-0.563068 - 0.366263i) q^{77} +0.325127 q^{78} +(5.00553 - 15.4054i) q^{79} +(4.00624 - 2.91070i) q^{80} +(-7.26416 - 5.27772i) q^{81} +(5.07693 + 15.6252i) q^{82} +(1.91346 + 5.88903i) q^{83} +(-0.0328883 - 0.0238947i) q^{84} +(-0.809017 + 0.587785i) q^{85} +(0.499313 - 1.53673i) q^{86} +0.298775 q^{87} +(13.7863 - 11.1468i) q^{88} -14.1031 q^{89} +(-2.29810 + 7.07281i) q^{90} +(0.444459 - 0.322919i) q^{91} +(17.6926 + 12.8544i) q^{92} +(0.0263725 + 0.0811663i) q^{93} +(-4.23457 - 13.0327i) q^{94} +(4.58014 + 3.32767i) q^{95} +(0.0623137 - 0.0452736i) q^{96} +(-2.91793 + 8.98045i) q^{97} +17.2643 q^{98} +(-2.58043 + 9.60143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9}+O(q^{10}) $ 60 * q - q^2 + 10 * q^3 - 19 * q^4 + 15 * q^5 + 18 * q^6 + 14 * q^7 + 8 * q^8 - 9 * q^9	\( 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9} - 14 q^{10} + 15 q^{11} - 84 q^{12} + q^{13} - q^{14} - 10 q^{15} - 29 q^{16} + 15 q^{17} - 13 q^{18} - 8 q^{19} + 24 q^{20} + 28 q^{22} - 78 q^{23} + 15 q^{24} - 15 q^{25} + 20 q^{26} + 22 q^{27} - 47 q^{28} - 11 q^{29} + 12 q^{30} + 10 q^{32} - 12 q^{33} - 14 q^{34} + 11 q^{35} + 27 q^{36} + 26 q^{37} + 87 q^{38} - 14 q^{39} - 8 q^{40} - 14 q^{41} - 27 q^{42} + 28 q^{43} - 56 q^{45} + 39 q^{46} + 45 q^{47} + 16 q^{48} - 17 q^{49} - q^{50} - 10 q^{51} + 24 q^{52} + 65 q^{53} - 94 q^{54} + 5 q^{55} - 144 q^{56} + 32 q^{57} + 48 q^{58} + 29 q^{59} - 21 q^{60} - 70 q^{61} - 73 q^{62} + 12 q^{63} - 32 q^{64} - 6 q^{65} + 130 q^{66} - 124 q^{67} + 24 q^{68} + 17 q^{69} + q^{70} + 4 q^{71} - 154 q^{72} - 49 q^{73} + 60 q^{74} + 52 q^{76} - 37 q^{77} - 62 q^{78} - 28 q^{79} + 24 q^{80} - 9 q^{81} + 122 q^{82} - 48 q^{83} - 88 q^{84} - 15 q^{85} - 62 q^{86} - 14 q^{87} + 114 q^{88} - 116 q^{89} + 18 q^{90} + 21 q^{91} + 83 q^{92} + 101 q^{93} - 75 q^{94} + 8 q^{95} - 53 q^{96} + 36 q^{97} + 20 q^{98} - 85 q^{99}+O(q^{100}) \) 60 * q - q^2 + 10 * q^3 - 19 * q^4 + 15 * q^5 + 18 * q^6 + 14 * q^7 + 8 * q^8 - 9 * q^9 - 14 * q^10 + 15 * q^11 - 84 * q^12 + q^13 - q^14 - 10 * q^15 - 29 * q^16 + 15 * q^17 - 13 * q^18 - 8 * q^19 + 24 * q^20 + 28 * q^22 - 78 * q^23 + 15 * q^24 - 15 * q^25 + 20 * q^26 + 22 * q^27 - 47 * q^28 - 11 * q^29 + 12 * q^30 + 10 * q^32 - 12 * q^33 - 14 * q^34 + 11 * q^35 + 27 * q^36 + 26 * q^37 + 87 * q^38 - 14 * q^39 - 8 * q^40 - 14 * q^41 - 27 * q^42 + 28 * q^43 - 56 * q^45 + 39 * q^46 + 45 * q^47 + 16 * q^48 - 17 * q^49 - q^50 - 10 * q^51 + 24 * q^52 + 65 * q^53 - 94 * q^54 + 5 * q^55 - 144 * q^56 + 32 * q^57 + 48 * q^58 + 29 * q^59 - 21 * q^60 - 70 * q^61 - 73 * q^62 + 12 * q^63 - 32 * q^64 - 6 * q^65 + 130 * q^66 - 124 * q^67 + 24 * q^68 + 17 * q^69 + q^70 + 4 * q^71 - 154 * q^72 - 49 * q^73 + 60 * q^74 + 52 * q^76 - 37 * q^77 - 62 * q^78 - 28 * q^79 + 24 * q^80 - 9 * q^81 + 122 * q^82 - 48 * q^83 - 88 * q^84 - 15 * q^85 - 62 * q^86 - 14 * q^87 + 114 * q^88 - 116 * q^89 + 18 * q^90 + 21 * q^91 + 83 * q^92 + 101 * q^93 - 75 * q^94 + 8 * q^95 - 53 * q^96 + 36 * q^97 + 20 * q^98 - 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/935\mathbb{Z}\right)^\times$.

$n$	$496$	$562$	$596$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.766629	+	2.35944i	−0.542088	+	1.66838i	0.185726	+	0.982602i	$0.440536\pi$
$2$	−0.766629	+	2.35944i	−0.542088	+	1.66838i	−0.727814	+	0.685774i	$0.759464\pi$
$3$	−0.0390857	+	0.0283975i	−0.0225662	+	0.0163953i	−0.599011	−	0.800741i	$-0.704440\pi$
$3$	−0.0390857	+	0.0283975i	−0.0225662	+	0.0163953i	0.576445	+	0.817136i	$0.304440\pi$
$4$	−3.36120	−	2.44206i	−1.68060	−	1.22103i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.0370378	−	0.113991i	−0.0151206	−	0.0465365i
$7$	−0.163849	−	0.119043i	−0.0619290	−	0.0449940i	0.556390	−	0.830921i	$-0.312186\pi$
$7$	−0.163849	−	0.119043i	−0.0619290	−	0.0449940i	−0.618319	+	0.785927i	$0.712186\pi$
$8$	4.32457	−	3.14198i	1.52896	−	1.11086i
$9$	−0.926330	+	2.85095i	−0.308777	+	0.950317i
$10$	2.48086			0.784517
$11$	3.31221	−	0.171089i	0.998669	−	0.0515854i
$11$	3.31221	−	0.171089i	0.998669	−	0.0515854i
$12$	0.200723			0.0579438
$13$	−0.838246	+	2.57986i	−0.232488	+	0.715523i	0.764957	+	0.644081i	$0.222760\pi$
$13$	−0.838246	+	2.57986i	−0.232488	+	0.715523i	−0.997445	+	0.0714421i	$0.977240\pi$
$14$	0.406486	−	0.295329i	0.108638	−	0.0789301i
$15$	0.0390857	+	0.0283975i	0.0100919	+	0.00733219i
$16$	1.53025	+	4.70962i	0.382562	+	1.17740i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−6.01649	−	4.37124i	−1.41810	−	1.03031i
$19$	−4.58014	+	3.32767i	−1.05076	+	0.763419i	−0.972356	−	0.233503i	$-0.924981\pi$
$19$	−4.58014	+	3.32767i	−1.05076	+	0.763419i	−0.0784003	+	0.996922i	$0.524981\pi$
$20$	−1.28387	+	3.95133i	−0.287081	+	0.883545i
$21$	0.00978466			0.00213519
$22$	−2.13556	+	7.94612i	−0.455303	+	1.69412i
$23$	−5.26376			−1.09757			−0.548785	−	0.835964i	$-0.684909\pi$
$23$	−5.26376			−1.09757			−0.548785	+	0.835964i	$0.684909\pi$
$24$	−0.0798046	+	0.245613i	−0.0162900	+	0.0501356i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−5.44439	−	3.95558i	−1.06773	−	0.775754i
$27$	−0.0895417	−	0.275581i	−0.0172323	−	0.0530356i
$28$	0.260019	+	0.800256i	0.0491389	+	0.151234i
$29$	−5.00313	−	3.63499i	−0.929058	−	0.675000i	0.0167040	−	0.999860i	$-0.494683\pi$
$29$	−5.00313	−	3.63499i	−0.929058	−	0.675000i	−0.945762	+	0.324860i	$0.894683\pi$
$30$	−0.0969663	+	0.0704502i	−0.0177035	+	0.0128624i
$31$	0.545872	−	1.68002i	0.0980416	−	0.301741i	−0.889993	−	0.455975i	$-0.849291\pi$
$31$	0.545872	−	1.68002i	0.0980416	−	0.301741i	0.988034	+	0.154234i	$0.0492908\pi$
$32$	−1.59428			−0.281832
$33$	−0.124602	+	0.100745i	−0.0216904	+	0.0175375i
$34$	2.48086			0.425464
$35$	−0.0625846	+	0.192616i	−0.0105787	+	0.0325580i
$36$	10.0758	−	7.32047i	1.67929	−	1.22008i
$37$	−2.13516	−	1.55128i	−0.351018	−	0.255029i	0.398278	−	0.917265i	$-0.369608\pi$
$37$	−2.13516	−	1.55128i	−0.351018	−	0.255029i	−0.749296	+	0.662235i	$0.769608\pi$
$38$	−4.34016	−	13.3577i	−0.704068	−	2.16690i
$39$	−0.0404979	−	0.124640i	−0.00648485	−	0.0199583i
$40$	−4.32457	−	3.14198i	−0.683774	−	0.496791i
$41$	5.35765	−	3.89256i	0.836724	−	0.607916i	−0.0847295	−	0.996404i	$-0.527003\pi$
$41$	5.35765	−	3.89256i	0.836724	−	0.607916i	0.921454	+	0.388488i	$0.127003\pi$
$42$	−0.00750120	+	0.0230863i	−0.00115746	+	0.00356230i
$43$	−0.651310			−0.0993239			−0.0496619	−	0.998766i	$-0.515814\pi$
$43$	−0.651310			−0.0993239			−0.0496619	+	0.998766i	$0.515814\pi$
$44$	−11.5508	−	7.51354i	−1.74135	−	1.13271i
$45$	2.99767			0.446866
$46$	4.03535	−	12.4195i	0.594979	−	1.83116i
$47$	−4.46871	+	3.24671i	−0.651829	+	0.473581i	−0.863894	−	0.503674i	$-0.831981\pi$
$47$	−4.46871	+	3.24671i	−0.651829	+	0.473581i	0.212065	+	0.977256i	$0.431981\pi$
$48$	−0.193552	−	0.140624i	−0.0279368	−	0.0202973i
$49$	−2.15044	−	6.61839i	−0.307206	−	0.945484i
$50$	−0.766629	−	2.35944i	−0.108418	−	0.333675i
$51$	0.0390857	+	0.0283975i	0.00547310	+	0.00397644i
$52$	9.11767	−	6.62438i	1.26439	−	0.918636i
$53$	−4.12038	+	12.6812i	−0.565977	+	1.74190i	0.0990527	+	0.995082i	$0.468419\pi$
$53$	−4.12038	+	12.6812i	−0.565977	+	1.74190i	−0.665030	+	0.746817i	$0.731581\pi$
$54$	0.718862			0.0978247
$55$	−1.18624	−	3.09723i	−0.159953	−	0.417630i
$56$	−1.08261			−0.144669
$57$	0.0845209	−	0.260129i	0.0111951	−	0.0344549i
$58$	12.4121	−	9.01790i	1.62979	−	1.18411i
$59$	−7.53135	−	5.47185i	−0.980499	−	0.712374i	−0.0226786	−	0.999743i	$-0.507219\pi$
$59$	−7.53135	−	5.47185i	−0.980499	−	0.712374i	−0.957820	+	0.287369i	$0.907219\pi$
$60$	−0.0620269	−	0.190899i	−0.00800764	−	0.0246450i
$61$	−1.41658	−	4.35979i	−0.181375	−	0.558214i	0.818493	−	0.574517i	$-0.194810\pi$
$61$	−1.41658	−	4.35979i	−0.181375	−	0.558214i	−0.999867	+	0.0163036i	$0.994810\pi$
$62$	3.54543	+	2.57591i	0.450270	+	0.327140i
$63$	0.491164	−	0.356851i	0.0618808	−	0.0449590i
$64$	−1.83827	+	5.65762i	−0.229784	+	0.707203i
$65$	2.71262			0.336459
$66$	−0.142180	−	0.371224i	−0.0175011	−	0.0456946i
$67$	−1.67769			−0.204962			−0.102481	−	0.994735i	$-0.532678\pi$
$67$	−1.67769			−0.204962			−0.102481	+	0.994735i	$0.532678\pi$
$68$	−1.28387	+	3.95133i	−0.155692	+	0.479169i
$69$	0.205738	−	0.149477i	0.0247679	−	0.0179950i
$70$	−0.406486	−	0.295329i	−0.0485844	−	0.0352986i
$71$	0.731579	+	2.25157i	0.0868225	+	0.267212i	0.985036	−	0.172347i	$-0.0551349\pi$
$71$	0.731579	+	2.25157i	0.0868225	+	0.267212i	−0.898214	+	0.439559i	$0.855135\pi$
$72$	4.95165	+	15.2396i	0.583558	+	1.79601i
$73$	−10.9426	−	7.95027i	−1.28073	−	0.930508i	−0.281160	−	0.959661i	$-0.590719\pi$
$73$	−10.9426	−	7.95027i	−1.28073	−	0.930508i	−0.999575	+	0.0291529i	$0.990719\pi$
$74$	5.29703	−	3.84852i	0.615768	−	0.447381i
$75$	0.0149294	−	0.0459480i	0.00172390	−	0.00530562i
$76$	23.5211			2.69806
$77$	−0.563068	−	0.366263i	−0.0641676	−	0.0417395i
$78$	0.325127			0.0368133
$79$	5.00553	−	15.4054i	0.563166	−	1.73325i	−0.110173	−	0.993912i	$-0.535141\pi$
$79$	5.00553	−	15.4054i	0.563166	−	1.73325i	0.673339	−	0.739334i	$-0.264859\pi$
$80$	4.00624	−	2.91070i	0.447911	−	0.325427i
$81$	−7.26416	−	5.27772i	−0.807129	−	0.586414i
$82$	5.07693	+	15.6252i	0.560654	+	1.72551i
$83$	1.91346	+	5.88903i	0.210030	+	0.646405i	0.999469	+	0.0325766i	$0.0103713\pi$
$83$	1.91346	+	5.88903i	0.210030	+	0.646405i	−0.789440	+	0.613828i	$0.789629\pi$
$84$	−0.0328883	−	0.0238947i	−0.00358840	−	0.00260713i
$85$	−0.809017	+	0.587785i	−0.0877502	+	0.0637543i
$86$	0.499313	−	1.53673i	0.0538423	−	0.165710i
$87$	0.298775			0.0320321
$88$	13.7863	−	11.1468i	1.46962	−	1.18825i
$89$	−14.1031			−1.49493			−0.747464	−	0.664302i	$-0.768729\pi$
$89$	−14.1031			−1.49493			−0.747464	+	0.664302i	$0.768729\pi$
$90$	−2.29810	+	7.07281i	−0.242241	+	0.745540i
$91$	0.444459	−	0.322919i	0.0465920	−	0.0338511i
$92$	17.6926	+	12.8544i	1.84458	+	1.34016i
$93$	0.0263725	+	0.0811663i	0.00273470	+	0.00841656i
$94$	−4.23457	−	13.0327i	−0.436763	−	1.34422i
$95$	4.58014	+	3.32767i	0.469913	+	0.341411i
$96$	0.0623137	−	0.0452736i	0.00635987	−	0.00462071i
$97$	−2.91793	+	8.98045i	−0.296271	+	0.911827i	0.686521	+	0.727110i	$0.259137\pi$
$97$	−2.91793	+	8.98045i	−0.296271	+	0.911827i	−0.982792	+	0.184717i	$0.940863\pi$
$98$	17.2643			1.74396
$99$	−2.58043	+	9.60143i	−0.259343	+	0.964980i
$100$	4.15468			0.415468
$101$	−1.48551	+	4.57192i	−0.147813	+	0.454923i	−0.997362	−	0.0725874i	$-0.976874\pi$
$101$	−1.48551	+	4.57192i	−0.147813	+	0.454923i	0.849549	+	0.527510i	$0.176874\pi$
$102$	−0.0969663	+	0.0704502i	−0.00960110	+	0.00697561i
$103$	11.3098	+	8.21706i	1.11439	+	0.809651i	0.983349	−	0.181726i	$-0.0581684\pi$
$103$	11.3098	+	8.21706i	1.11439	+	0.809651i	0.131040	+	0.991377i	$0.458168\pi$
$104$	4.48081	+	13.7905i	0.439379	+	1.35227i
$105$	−0.00302363	−	0.00930577i	−0.000295076	−	0.000908150i
$106$	−26.7618	−	19.4436i	−2.59933	−	1.88853i
$107$	−4.44727	+	3.23113i	−0.429934	+	0.312365i	−0.781622	−	0.623752i	$-0.785608\pi$
$107$	−4.44727	+	3.23113i	−0.429934	+	0.312365i	0.351689	+	0.936117i	$0.385608\pi$
$108$	−0.372017	+	1.14495i	−0.0357973	+	0.110173i
$109$	18.2737			1.75031			0.875153	−	0.483846i	$-0.160760\pi$
$109$	18.2737			1.75031			0.875153	+	0.483846i	$0.160760\pi$
$110$	8.21713	−	0.424449i	0.783473	−	0.0404697i
$111$	0.127507			0.0121024
$112$	0.309918	−	0.953830i	0.0292845	−	0.0901285i
$113$	−9.37444	+	6.81093i	−0.881873	+	0.640718i	−0.933746	−	0.357936i	$-0.883481\pi$
$113$	−9.37444	+	6.81093i	−0.881873	+	0.640718i	0.0518734	+	0.998654i	$0.483481\pi$
$114$	0.548962	+	0.398844i	0.0514150	+	0.0373552i
$115$	1.62659	+	5.00613i	0.151680	+	0.466824i
$116$	7.93969	+	24.4359i	0.737182	+	2.26881i
$117$	−6.57855	−	4.77959i	−0.608187	−	0.441874i
$118$	18.6842	−	13.5749i	1.72002	−	1.24967i
$119$	−0.0625846	+	0.192616i	−0.00573712	+	0.0176570i
$120$	0.258253			0.0235752
$121$	10.9415	−	1.13337i	0.994678	−	0.103033i
$122$	11.3726			1.02963
$123$	−0.0988689	+	0.304287i	−0.00891471	+	0.0274366i
$124$	−5.93750	+	4.31385i	−0.533203	+	0.387395i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	0.465429	+	1.43244i	0.0414637	+	0.127612i
$127$	1.19317	+	3.67221i	0.105877	+	0.325856i	0.989935	−	0.141521i	$-0.0451993\pi$
$127$	1.19317	+	3.67221i	0.105877	+	0.325856i	−0.884058	+	0.467376i	$0.845199\pi$
$128$	−14.5192	−	10.5488i	−1.28332	−	0.932389i
$129$	0.0254569	−	0.0184956i	0.00224136	−	0.00162844i
$130$	−2.07957	+	6.40027i	−0.182391	+	0.561341i
$131$	−9.90975			−0.865819			−0.432909	−	0.901437i	$-0.642513\pi$
$131$	−9.90975			−0.865819			−0.432909	+	0.901437i	$0.642513\pi$
$132$	0.664838	−	0.0343417i	0.0578667	−	0.00298906i
$133$	1.14659			0.0994216
$134$	1.28616	−	3.95840i	0.111108	−	0.341954i
$135$	−0.234423	+	0.170318i	−0.0201759	+	0.0146587i
$136$	−4.32457	−	3.14198i	−0.370828	−	0.269423i
$137$	−0.148291	−	0.456394i	−0.0126694	−	0.0389924i	0.944522	−	0.328448i	$-0.106526\pi$
$137$	−0.148291	−	0.456394i	−0.0126694	−	0.0389924i	−0.957191	+	0.289456i	$0.906526\pi$
$138$	0.194958	+	0.600020i	0.0165959	+	0.0510771i
$139$	−3.52903	−	2.56399i	−0.299328	−	0.217475i	0.427976	−	0.903790i	$-0.359227\pi$
$139$	−3.52903	−	2.56399i	−0.299328	−	0.217475i	−0.727304	+	0.686316i	$0.759227\pi$
$140$	0.680738	−	0.494585i	0.0575329	−	0.0418001i
$141$	0.0824646	−	0.253800i	0.00694477	−	0.0213738i
$142$	−5.87329			−0.492876
$143$	−2.33506	+	8.68844i	−0.195268	+	0.726564i
$144$	−14.8444			−1.23703
$145$	−1.91103	+	5.88153i	−0.158702	+	0.488435i
$146$	27.1471	−	19.7235i	2.24671	−	1.63233i
$147$	0.271997	+	0.197617i	0.0224339	+	0.0162992i
$148$	3.38838	+	10.4284i	0.278523	+	0.857206i
$149$	0.177326	+	0.545754i	0.0145271	+	0.0447099i	0.958057	−	0.286577i	$-0.0925173\pi$
$149$	0.177326	+	0.545754i	0.0145271	+	0.0447099i	−0.943530	+	0.331287i	$0.892517\pi$
$150$	0.0969663	+	0.0704502i	0.00791727	+	0.00575223i
$151$	−15.2389	+	11.0717i	−1.24013	+	0.901006i	−0.997607	−	0.0691403i	$-0.977974\pi$
$151$	−15.2389	+	11.0717i	−1.24013	+	0.901006i	−0.242521	+	0.970146i	$0.577974\pi$
$152$	−9.35165	+	28.7814i	−0.758519	+	2.33448i
$153$	2.99767			0.242347
$154$	1.29584	−	1.04774i	0.104422	−	0.0844291i
$155$	−1.76648			−0.141887
$156$	−0.168256	+	0.517837i	−0.0134712	+	0.0414602i
$157$	6.25207	−	4.54240i	0.498970	−	0.362523i	−0.309654	−	0.950849i	$-0.600213\pi$
$157$	6.25207	−	4.54240i	0.498970	−	0.362523i	0.808623	+	0.588327i	$0.200213\pi$
$158$	32.5108	+	23.6205i	2.58642	+	1.87914i
$159$	−0.199066	−	0.612663i	−0.0157870	−	0.0485873i
$160$	0.492660	+	1.51625i	0.0389482	+	0.119870i
$161$	0.862460	+	0.626614i	0.0679713	+	0.0493841i
$162$	18.0214	−	13.0933i	1.41589	−	1.02871i
$163$	3.69337	−	11.3670i	0.289287	−	0.890335i	−0.695793	−	0.718242i	$-0.744947\pi$
$163$	3.69337	−	11.3670i	0.289287	−	0.890335i	0.985081	−	0.172093i	$-0.0550529\pi$
$164$	−27.5140			−2.14848
$165$	0.134319	+	0.0873711i	0.0104567	+	0.00680183i
$166$	−15.3617			−1.19230
$167$	−2.93255	+	9.02547i	−0.226928	+	0.698412i	0.771162	+	0.636638i	$0.219676\pi$
$167$	−2.93255	+	9.02547i	−0.226928	+	0.698412i	−0.998090	+	0.0617734i	$0.980324\pi$
$168$	0.0423144	−	0.0307432i	0.00326463	−	0.00237189i
$169$	4.56422	+	3.31610i	0.351094	+	0.255085i
$170$	−0.766629	−	2.35944i	−0.0587977	−	0.180961i
$171$	−5.24429	−	16.1403i	−0.401041	−	1.23428i
$172$	2.18919	+	1.59054i	0.166924	+	0.121277i
$173$	14.4154	−	10.4734i	1.09598	−	0.796276i	0.115581	−	0.993298i	$-0.463127\pi$
$173$	14.4154	−	10.4734i	1.09598	−	0.796276i	0.980399	+	0.197022i	$0.0631269\pi$
$174$	−0.229050	+	0.704943i	−0.0173642	+	0.0534416i
$175$	0.202528			0.0153097
$176$	5.87427	+	15.3374i	0.442790	+	1.15610i
$177$	0.449755			0.0338057
$178$	10.8119	−	33.2755i	0.810383	−	2.49410i
$179$	−10.4021	+	7.55755i	−0.777488	+	0.564878i	−0.904224	−	0.427058i	$-0.859550\pi$
$179$	−10.4021	+	7.55755i	−0.777488	+	0.564878i	0.126736	+	0.991936i	$0.459550\pi$
$180$	−10.0758	−	7.32047i	−0.751003	−	0.545636i
$181$	3.90028	+	12.0038i	0.289906	+	0.892238i	0.984885	+	0.173208i	$0.0554134\pi$
$181$	3.90028	+	12.0038i	0.289906	+	0.892238i	−0.694980	+	0.719030i	$0.744587\pi$
$182$	0.421172	+	1.29623i	0.0312193	+	0.0960832i
$183$	0.179175	+	0.130178i	0.0132450	+	0.00962305i
$184$	−22.7635	+	16.5386i	−1.67814	+	1.21924i
$185$	−0.815558	+	2.51003i	−0.0599610	+	0.184541i
$186$	−0.211725			−0.0155244
$187$	−1.18624	−	3.09723i	−0.0867468	−	0.226492i
$188$	22.9489			1.67372
$189$	−0.0181347	+	0.0558129i	−0.00131911	+	0.00405979i
$190$	−11.3627	+	8.25548i	−0.824337	+	0.598916i
$191$	−3.54224	−	2.57359i	−0.256308	−	0.186218i	0.452210	−	0.891911i	$-0.350636\pi$
$191$	−3.54224	−	2.57359i	−0.256308	−	0.186218i	−0.708518	+	0.705693i	$0.750636\pi$
$192$	−0.0888118	−	0.273335i	−0.00640944	−	0.0197262i
$193$	−3.86772	−	11.9036i	−0.278405	−	0.856841i	−0.988298	−	0.152533i	$-0.951257\pi$
$193$	−3.86772	−	11.9036i	−0.278405	−	0.856841i	0.709894	−	0.704309i	$-0.248743\pi$
$194$	−18.9519	−	13.7693i	−1.36067	−	0.988581i
$195$	−0.106025	+	0.0770315i	−0.00759259	+	0.00551634i
$196$	−8.93440	+	27.4973i	−0.638171	+	1.96409i
$197$	2.38963			0.170254			0.0851269	−	0.996370i	$-0.472870\pi$
$197$	2.38963			0.170254			0.0851269	+	0.996370i	$0.472870\pi$
$198$	−20.6758	−	13.4491i	−1.46936	−	0.955786i
$199$	8.67391			0.614877			0.307439	−	0.951568i	$-0.400528\pi$
$199$	8.67391			0.614877			0.307439	+	0.951568i	$0.400528\pi$
$200$	−1.65184	+	5.08383i	−0.116803	+	0.359481i
$201$	0.0655737	−	0.0476421i	0.00462521	−	0.00336041i
$202$	−9.64834	−	7.00993i	−0.678855	−	0.493217i
$203$	0.387036	+	1.19118i	0.0271646	+	0.0836041i
$204$	−0.0620269	−	0.190899i	−0.00434275	−	0.0133656i
$205$	−5.35765	−	3.89256i	−0.374194	−	0.271868i
$206$	−28.0581	+	20.3854i	−1.95490	+	1.42032i
$207$	4.87598	−	15.0067i	0.338904	−	1.04304i
$208$	−13.4329			−0.931402
$209$	−14.6011	+	11.8055i	−1.00998	+	0.816607i
$210$	0.0242744			0.00167509
$211$	3.90519	−	12.0189i	0.268844	−	0.827418i	−0.721939	−	0.691957i	$-0.756749\pi$
$211$	3.90519	−	12.0189i	0.268844	−	0.827418i	0.990783	−	0.135460i	$-0.0432513\pi$
$212$	44.8177	−	32.5620i	3.07809	−	2.23636i
$213$	−0.0925331	−	0.0672292i	−0.00634026	−	0.00460647i
$214$	−4.21426	−	12.9701i	−0.288081	−	0.886621i
$215$	0.201266	+	0.619433i	0.0137262	+	0.0422450i
$216$	−1.25310	−	0.910430i	−0.0852626	−	0.0619469i
$217$	−0.289435	+	0.210287i	−0.0196482	+	0.0142752i
$218$	−14.0092	+	43.1158i	−0.948821	+	2.92017i
$219$	0.653467			0.0441572
$220$	−3.57640	+	13.3073i	−0.241121	+	0.897178i
$221$	2.71262			0.182471
$222$	−0.0977503	+	0.300845i	−0.00656057	+	0.0201914i
$223$	−17.0799	+	12.4093i	−1.14375	+	0.830985i	−0.987638	−	0.156754i	$-0.949897\pi$
$223$	−17.0799	+	12.4093i	−1.14375	+	0.830985i	−0.156115	+	0.987739i	$0.549897\pi$
$224$	0.261221	+	0.189788i	0.0174536	+	0.0126808i
$225$	−0.926330	−	2.85095i	−0.0617553	−	0.190063i
$226$	−8.88326	−	27.3399i	−0.590906	−	1.81862i
$227$	−11.4528	−	8.32095i	−0.760150	−	0.552281i	0.138807	−	0.990320i	$-0.455673\pi$
$227$	−11.4528	−	8.32095i	−0.760150	−	0.552281i	−0.898956	+	0.438038i	$0.855673\pi$
$228$	−0.919341	+	0.667941i	−0.0608849	+	0.0442354i
$229$	2.20544	−	6.78764i	0.145740	−	0.448540i	−0.851366	−	0.524572i	$-0.824225\pi$
$229$	2.20544	−	6.78764i	0.145740	−	0.448540i	0.997105	+	0.0760323i	$0.0242252\pi$
$230$	−13.0587			−0.861062
$231$	0.0324089	−	0.00167405i	0.00213235	−	0.000110145i
$232$	−33.0574			−2.17033
$233$	−6.52667	+	20.0870i	−0.427576	+	1.31594i	0.472930	+	0.881100i	$0.343196\pi$
$233$	−6.52667	+	20.0870i	−0.427576	+	1.31594i	−0.900506	+	0.434844i	$0.856804\pi$
$234$	16.3205	−	11.8575i	1.06690	−	0.775150i
$235$	4.46871	+	3.24671i	0.291507	+	0.211792i
$236$	11.9518	+	36.7840i	0.777999	+	2.39443i
$237$	0.241830	+	0.744277i	0.0157086	+	0.0483460i
$238$	−0.406486	−	0.295329i	−0.0263486	−	0.0191434i
$239$	9.93969	−	7.22161i	0.642945	−	0.467127i	−0.217916	−	0.975968i	$-0.569926\pi$
$239$	9.93969	−	7.22161i	0.642945	−	0.467127i	0.860861	+	0.508841i	$0.169926\pi$
$240$	−0.0739303	+	0.227534i	−0.00477218	+	0.0146873i
$241$	−5.34748			−0.344461			−0.172231	−	0.985057i	$-0.555097\pi$
$241$	−5.34748			−0.344461			−0.172231	+	0.985057i	$0.555097\pi$
$242$	−5.71392	+	26.6846i	−0.367305	+	1.71535i
$243$	1.30309			0.0835931
$244$	−5.88544	+	18.1135i	−0.376776	+	1.15960i
$245$	−5.62994	+	4.09039i	−0.359683	+	0.261325i
$246$	−0.642152	−	0.466550i	−0.0409421	−	0.0297462i
$247$	−4.74562	−	14.6055i	−0.301956	−	0.929326i
$248$	−2.91794	−	8.98049i	−0.185289	−	0.570262i
$249$	−0.242022	−	0.175840i	−0.0153375	−	0.0111434i
$250$	−2.00706	+	1.45821i	−0.126938	+	0.0922256i
$251$	−9.22353	+	28.3871i	−0.582184	+	1.79178i	0.0281132	+	0.999605i	$0.491050\pi$
$251$	−9.22353	+	28.3871i	−0.582184	+	1.79178i	−0.610297	+	0.792173i	$0.708950\pi$
$252$	−2.52235			−0.158893
$253$	−17.4347	+	0.900573i	−1.09611	+	0.0566186i
$254$	−9.57907			−0.601044
$255$	0.0149294	−	0.0459480i	0.000934917	−	0.00287738i
$256$	26.3947	−	19.1769i	1.64967	−	1.19855i
$257$	14.7517	+	10.7178i	0.920188	+	0.668555i	0.943571	−	0.331171i	$-0.107444\pi$
$257$	14.7517	+	10.7178i	0.920188	+	0.668555i	−0.0233830	+	0.999727i	$0.507444\pi$
$258$	0.0241231	+	0.0742434i	0.00150184	+	0.00462219i
$259$	0.165173	+	0.508352i	0.0102634	+	0.0315874i
$260$	−9.11767	−	6.62438i	−0.565454	−	0.410826i
$261$	14.9977	−	10.8965i	0.928335	−	0.674475i
$262$	7.59710	−	23.3815i	0.469350	−	1.44451i
$263$	−15.2139			−0.938132			−0.469066	−	0.883163i	$-0.655409\pi$
$263$	−15.2139			−0.938132			−0.469066	+	0.883163i	$0.655409\pi$
$264$	−0.222308	+	0.827176i	−0.0136821	+	0.0509092i
$265$	13.3338			0.819090
$266$	−0.879005	+	2.70530i	−0.0538953	+	0.165873i
$267$	0.551231	−	0.400493i	0.0337348	−	0.0245098i
$268$	5.63905	+	4.09701i	0.344460	+	0.250265i
$269$	0.659514	+	2.02978i	0.0402113	+	0.123758i	0.969147	−	0.246483i	$-0.0792751\pi$
$269$	0.659514	+	2.02978i	0.0402113	+	0.123758i	−0.928936	+	0.370241i	$0.879275\pi$
$270$	−0.222141	−	0.683678i	−0.0135190	−	0.0416073i
$271$	3.37190	+	2.44983i	0.204828	+	0.148816i	0.685471	−	0.728100i	$-0.259597\pi$
$271$	3.37190	+	2.44983i	0.204828	+	0.148816i	−0.480642	+	0.876917i	$0.659597\pi$
$272$	4.00624	−	2.91070i	0.242914	−	0.176487i
$273$	−0.00820196	+	0.0252430i	−0.000496405	+	0.00152778i
$274$	1.19052			0.0719218
$275$	−2.57907	+	2.08528i	−0.155524	+	0.125747i
$276$	−1.05656			−0.0635974
$277$	−1.38022	+	4.24788i	−0.0829293	+	0.255230i	−0.983920	−	0.178607i	$-0.942841\pi$
$277$	−1.38022	+	4.24788i	−0.0829293	+	0.255230i	0.900991	+	0.433838i	$0.142841\pi$
$278$	8.75503	−	6.36090i	0.525092	−	0.381502i
$279$	4.28400	+	3.11251i	0.256477	+	0.186341i
$280$	0.334543	+	1.02962i	0.0199928	+	0.0615315i
$281$	6.59674	+	20.3027i	0.393528	+	1.21116i	0.930102	+	0.367302i	$0.119718\pi$
$281$	6.59674	+	20.3027i	0.393528	+	1.21116i	−0.536574	+	0.843854i	$0.680282\pi$
$282$	0.535606	+	0.389141i	0.0318949	+	0.0231730i
$283$	−4.52854	+	3.29018i	−0.269194	+	0.195581i	−0.714190	−	0.699952i	$-0.753205\pi$
$283$	−4.52854	+	3.29018i	−0.269194	+	0.195581i	0.444996	+	0.895532i	$0.353205\pi$
$284$	3.03947	−	9.35454i	0.180360	−	0.555090i
$285$	−0.273515			−0.0162017
$286$	−18.7097	−	12.1702i	−1.10633	−	0.719641i
$287$	−1.34123			−0.0791700
$288$	1.47683	−	4.54522i	0.0870231	−	0.267830i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−12.4121	−	9.01790i	−0.728862	−	0.529549i
$291$	−0.140973	−	0.433869i	−0.00826397	−	0.0254339i
$292$	17.3653	+	53.4449i	1.01623	+	3.12763i
$293$	9.93880	+	7.22096i	0.580631	+	0.421853i	0.838951	−	0.544206i	$-0.183169\pi$
$293$	9.93880	+	7.22096i	0.580631	+	0.421853i	−0.258321	+	0.966059i	$0.583169\pi$
$294$	−0.674787	+	0.490261i	−0.0393544	+	0.0285926i
$295$	−2.87672	+	8.85364i	−0.167489	+	0.515479i
$296$	−14.1077			−0.819995
$297$	−0.343730	−	0.897462i	−0.0199452	−	0.0520760i
$298$	−1.42362			−0.0824679
$299$	4.41232	−	13.5797i	0.255171	−	0.785337i
$300$	−0.162389	+	0.117982i	−0.00937551	+	0.00681171i
$301$	0.106716	+	0.0775339i	0.00615103	+	0.00446898i
$302$	−14.4405	−	44.4433i	−0.830958	−	2.55742i
$303$	−0.0717687	−	0.220881i	−0.00412301	−	0.0126893i
$304$	−22.6808	−	16.4786i	−1.30083	−	0.945110i
$305$	−3.70866	+	2.69450i	−0.212357	+	0.154286i
$306$	−2.29810	+	7.07281i	−0.131373	+	0.404326i
$307$	−22.8266			−1.30278			−0.651392	−	0.758742i	$-0.725815\pi$
$307$	−22.8266			−1.30278			−0.651392	+	0.758742i	$0.725815\pi$
$308$	0.998152	+	2.60613i	0.0568750	+	0.148498i
$309$	−0.675396			−0.0384219
$310$	1.35423	−	4.16790i	0.0769153	−	0.236721i
$311$	18.6977	−	13.5846i	1.06025	−	0.770315i	0.0861132	−	0.996285i	$-0.472555\pi$
$311$	18.6977	−	13.5846i	1.06025	−	0.770315i	0.974134	+	0.225971i	$0.0725553\pi$
$312$	−0.566751	−	0.411769i	−0.0320860	−	0.0233118i
$313$	2.33134	+	7.17513i	0.131775	+	0.405562i	0.995074	−	0.0991301i	$-0.0316060\pi$
$313$	2.33134	+	7.17513i	0.131775	+	0.405562i	−0.863299	+	0.504692i	$0.831606\pi$
$314$	5.92449	+	18.2337i	0.334339	+	1.02899i
$315$	−0.491164	−	0.356851i	−0.0276739	−	0.0201063i
$316$	−54.4455	+	39.5570i	−3.06280	+	2.22526i
$317$	5.06512	−	15.5888i	0.284486	−	0.875557i	−0.702067	−	0.712111i	$-0.747739\pi$
$317$	5.06512	−	15.5888i	0.284486	−	0.875557i	0.986552	−	0.163446i	$-0.0522608\pi$
$318$	1.59815			0.0896199
$319$	−17.1933	−	11.1839i	−0.962641	−	0.626176i
$320$	5.94878			0.332547
$321$	0.0820690	−	0.252582i	0.00458064	−	0.0140978i
$322$	−2.13964	+	1.55454i	−0.119238	+	0.0866312i
$323$	4.58014	+	3.32767i	0.254846	+	0.185156i
$324$	11.5278	+	35.4790i	0.640435	+	1.97106i
$325$	−0.838246	−	2.57986i	−0.0464975	−	0.143105i
$326$	23.9884	+	17.4286i	1.32859	+	0.965280i
$327$	−0.714242	+	0.518928i	−0.0394977	+	0.0286968i
$328$	10.9392	−	33.6673i	0.604014	−	1.85896i
$329$	1.11869			0.0616754
$330$	−0.309119	+	0.249936i	−0.0170165	+	0.0137585i
$331$	5.59288			0.307412			0.153706	−	0.988117i	$-0.450879\pi$
$331$	5.59288			0.307412			0.153706	+	0.988117i	$0.450879\pi$
$332$	7.94981	−	24.4670i	0.436303	−	1.34280i
$333$	6.40049	−	4.65023i	0.350745	−	0.254831i
$334$	−19.0469	−	13.8384i	−1.04220	−	0.757202i
$335$	0.518434	+	1.59558i	0.0283251	+	0.0871756i
$336$	0.0149730	+	0.0460820i	0.000816842	+	0.00251398i
$337$	22.1512	+	16.0938i	1.20665	+	0.876685i	0.994923	−	0.100643i	$-0.0320900\pi$
$337$	22.1512	+	16.0938i	1.20665	+	0.876685i	0.211731	+	0.977328i	$0.432090\pi$
$338$	−11.3232	+	8.22679i	−0.615901	+	0.447478i
$339$	0.172994	−	0.532420i	0.00939574	−	0.0289171i
$340$	4.15468			0.225319
$341$	1.52061	−	5.65798i	0.0823456	−	0.306397i
$342$	42.1024			2.27664
$343$	−0.873618	+	2.68872i	−0.0471709	+	0.145177i
$344$	−2.81663	+	2.04640i	−0.151863	+	0.110335i
$345$	−0.205738	−	0.149477i	−0.0110766	−	0.00804759i
$346$	13.6601	+	42.0414i	0.734370	+	2.26016i
$347$	5.98761	+	18.4280i	0.321432	+	0.989266i	0.973026	+	0.230697i	$0.0741007\pi$
$347$	5.98761	+	18.4280i	0.321432	+	0.989266i	−0.651594	+	0.758568i	$0.725899\pi$
$348$	−1.00425	−	0.729627i	−0.0538332	−	0.0391121i
$349$	23.9692	−	17.4147i	1.28304	−	0.932186i	0.283404	−	0.959001i	$-0.408536\pi$
$349$	23.9692	−	17.4147i	1.28304	−	0.932186i	0.999640	+	0.0268145i	$0.00853636\pi$
$350$	−0.155264	+	0.477853i	−0.00829920	+	0.0255423i
$351$	0.786017			0.0419545
$352$	−5.28060	+	0.272765i	−0.281457	+	0.0145384i
$353$	17.1303			0.911756			0.455878	−	0.890042i	$-0.349325\pi$
$353$	17.1303			0.911756			0.455878	+	0.890042i	$0.349325\pi$
$354$	−0.344795	+	1.06117i	−0.0183257	+	0.0564006i
$355$	1.91530	−	1.39155i	0.101653	−	0.0738556i
$356$	47.4035	+	34.4407i	2.51238	+	1.82535i
$357$	−0.00302363	−	0.00930577i	−0.000160027	−	0.000492514i
$358$	−9.85706	−	30.3369i	−0.520962	−	1.60336i
$359$	−8.48246	−	6.16287i	−0.447687	−	0.325264i	0.340995	−	0.940065i	$-0.389236\pi$
$359$	−8.48246	−	6.16287i	−0.447687	−	0.325264i	−0.788682	+	0.614801i	$0.789236\pi$
$360$	12.9636	−	9.41861i	0.683242	−	0.496404i
$361$	4.03300	−	12.4123i	0.212263	−	0.653279i
$362$	−31.3124			−1.64574
$363$	−0.395470	+	0.355008i	−0.0207568	+	0.0186331i
$364$	−2.28250			−0.119636
$365$	−4.17970	+	12.8638i	−0.218776	+	0.673322i
$366$	−0.444508	+	0.322954i	−0.0232348	+	0.0168811i
$367$	−1.62800	−	1.18281i	−0.0849810	−	0.0617423i	0.544484	−	0.838772i	$-0.316726\pi$
$367$	−1.62800	−	1.18281i	−0.0849810	−	0.0617423i	−0.629464	+	0.777029i	$0.716726\pi$
$368$	−8.05485	−	24.7903i	−0.419888	−	1.29228i
$369$	6.13454	+	18.8802i	0.319352	+	0.982863i
$370$	−5.29703	−	3.84852i	−0.275380	−	0.200075i
$371$	2.18473	−	1.58730i	0.113425	−	0.0824084i
$372$	0.109569	−	0.337220i	0.00568091	−	0.0174840i
$373$	17.8871			0.926159			0.463079	−	0.886317i	$-0.346744\pi$
$373$	17.8871			0.926159			0.463079	+	0.886317i	$0.346744\pi$
$374$	8.21713	−	0.424449i	0.424898	−	0.0219478i
$375$	−0.0483126			−0.00249485
$376$	−9.12414	+	28.0812i	−0.470541	+	1.44818i
$377$	13.5716	−	9.86034i	0.698973	−	0.507833i
$378$	−0.117785	−	0.0855755i	−0.00605819	−	0.00440153i
$379$	11.4679	+	35.2946i	0.589067	+	1.81296i	0.582286	+	0.812984i	$0.302158\pi$
$379$	11.4679	+	35.2946i	0.589067	+	1.81296i	0.00678099	+	0.999977i	$0.497842\pi$
$380$	−7.26843	−	22.3699i	−0.372863	−	1.14755i
$381$	−0.150917	−	0.109648i	−0.00773173	−	0.00561743i
$382$	8.78781	−	6.38472i	0.449624	−	0.326671i
$383$	−4.32724	+	13.3179i	−0.221111	+	0.680511i	0.777552	+	0.628819i	$0.216461\pi$
$383$	−4.32724	+	13.3179i	−0.221111	+	0.680511i	−0.998663	+	0.0516920i	$0.983539\pi$
$384$	0.867050			0.0442465
$385$	−0.174339	+	0.648691i	−0.00888513	+	0.0330603i
$386$	31.0510			1.58045
$387$	0.603328	−	1.85685i	0.0306689	−	0.0943891i
$388$	31.7385	−	23.0594i	1.61128	−	1.17066i
$389$	28.1890	+	20.4805i	1.42924	+	1.03840i	0.990158	+	0.139957i	$0.0446964\pi$
$389$	28.1890	+	20.4805i	1.42924	+	1.03840i	0.439082	+	0.898447i	$0.355304\pi$
$390$	−0.100470	−	0.309214i	−0.00508748	−	0.0156576i
$391$	1.62659	+	5.00613i	0.0822602	+	0.253171i
$392$	−30.0946	−	21.8650i	−1.52001	−	1.10435i
$393$	0.387330	−	0.281412i	0.0195382	−	0.0141953i
$394$	−1.83196	+	5.63818i	−0.0922926	+	0.284048i
$395$	−16.1982			−0.815021
$396$	32.1206	−	25.9708i	1.61412	−	1.30508i
$397$	−17.6183			−0.884236			−0.442118	−	0.896957i	$-0.645773\pi$
$397$	−17.6183			−0.884236			−0.442118	+	0.896957i	$0.645773\pi$
$398$	−6.64967	+	20.4656i	−0.333318	+	1.02585i
$399$	−0.0448151	+	0.0325601i	−0.00224356	+	0.00163004i
$400$	−4.00624	−	2.91070i	−0.200312	−	0.145535i
$401$	−4.57616	−	14.0840i	−0.228522	−	0.703320i	−0.997915	−	0.0645433i	$-0.979441\pi$
$401$	−4.57616	−	14.0840i	−0.228522	−	0.703320i	0.769393	−	0.638776i	$-0.220559\pi$
$402$	0.0621380	+	0.191241i	0.00309916	+	0.00953823i
$403$	3.87664	+	2.81654i	0.193109	+	0.140302i
$404$	16.1580	−	11.7395i	0.803890	−	0.584060i
$405$	−2.77466	+	8.53953i	−0.137874	+	0.424333i
$406$	−3.10722			−0.154209
$407$	−7.33750	−	4.77287i	−0.363706	−	0.236583i
$408$	0.258253			0.0127854
$409$	7.01807	−	21.5994i	0.347021	−	1.06802i	−0.613472	−	0.789717i	$-0.710227\pi$
$409$	7.01807	−	21.5994i	0.347021	−	1.06802i	0.960493	−	0.278305i	$-0.0897725\pi$
$410$	13.2916	−	9.65690i	0.656425	−	0.476920i
$411$	0.0187565	+	0.0136274i	0.000925190	+	0.000672190i
$412$	−17.9481	−	55.2384i	−0.884237	−	2.72140i
$413$	0.582617	+	1.79311i	0.0286687	+	0.0882332i
$414$	31.6694	+	23.0091i	1.55646	+	1.13084i
$415$	5.00951	−	3.63962i	0.245907	−	0.178662i
$416$	1.33640	−	4.11302i	0.0655225	−	0.201657i
$417$	0.210745			0.0103202
$418$	−16.6609	−	43.5008i	−0.814911	−	2.12769i
$419$	−32.5160			−1.58851			−0.794256	−	0.607584i	$-0.792139\pi$
$419$	−32.5160			−1.58851			−0.794256	+	0.607584i	$0.792139\pi$
$420$	−0.0125622	+	0.0386625i	−0.000612972	+	0.00188654i
$421$	−6.49630	+	4.71984i	−0.316610	+	0.230031i	−0.734728	−	0.678362i	$-0.762690\pi$
$421$	−6.49630	+	4.71984i	−0.316610	+	0.230031i	0.418117	+	0.908393i	$0.362690\pi$
$422$	25.3641	+	18.4281i	1.23471	+	0.897067i
$423$	−5.11670	−	15.7476i	−0.248783	−	0.765674i
$424$	22.0253	+	67.7869i	1.06964	+	3.29202i
$425$	0.809017	+	0.587785i	0.0392431	+	0.0285118i
$426$	0.229562	−	0.166786i	0.0111223	−	0.00808083i
$427$	−0.286897	+	0.882979i	−0.0138839	+	0.0427304i
$428$	22.8388			1.10395
$429$	−0.155462	−	0.405904i	−0.00750577	−	0.0195972i
$430$	−1.61581			−0.0779213
$431$	3.52511	−	10.8492i	0.169799	−	0.522587i	−0.829559	−	0.558419i	$-0.811408\pi$
$431$	3.52511	−	10.8492i	0.169799	−	0.522587i	0.999358	+	0.0358323i	$0.0114082\pi$
$432$	1.16086	−	0.843415i	0.0558519	−	0.0405788i
$433$	30.2835	+	22.0022i	1.45533	+	1.05736i	0.984549	+	0.175110i	$0.0560279\pi$
$433$	30.2835	+	22.0022i	1.45533	+	1.05736i	0.470781	+	0.882250i	$0.343972\pi$
$434$	−0.274270	−	0.844118i	−0.0131654	−	0.0405189i
$435$	−0.0923267	−	0.284152i	−0.00442673	−	0.0136241i
$436$	−61.4218	−	44.6255i	−2.94157	−	2.13717i
$437$	24.1088	−	17.5160i	1.15328	−	0.837906i
$438$	−0.500966	+	1.54182i	−0.0239371	+	0.0736708i
$439$	−31.6803			−1.51202			−0.756010	−	0.654560i	$-0.772854\pi$
$439$	−31.6803			−1.51202			−0.756010	+	0.654560i	$0.772854\pi$
$440$	−14.8614	−	9.66701i	−0.708491	−	0.460857i
$441$	20.8607			0.993367
$442$	−2.07957	+	6.40027i	−0.0989152	+	0.304430i
$443$	−26.2655	+	19.0830i	−1.24791	+	0.906662i	−0.998099	−	0.0616319i	$-0.980370\pi$
$443$	−26.2655	+	19.0830i	−1.24791	+	0.906662i	−0.249814	+	0.968294i	$0.580370\pi$
$444$	−0.428576	−	0.311379i	−0.0203393	−	0.0147774i
$445$	4.35811	+	13.4129i	0.206594	+	0.635831i
$446$	−16.1850	−	49.8122i	−0.766381	−	2.35868i
$447$	−0.0224289	−	0.0162956i	−0.00106085	−	0.000770754i
$448$	0.974699	−	0.708160i	0.0460502	−	0.0334574i
$449$	−1.35654	+	4.17500i	−0.0640191	+	0.197030i	−0.977950	−	0.208839i	$-0.933031\pi$
$449$	−1.35654	+	4.17500i	−0.0640191	+	0.197030i	0.913931	+	0.405870i	$0.133031\pi$
$450$	7.43680			0.350574
$451$	17.0797	−	13.8096i	0.804251	−	0.650269i
$452$	48.1421			2.26441
$453$	0.281216	−	0.865495i	0.0132127	−	0.0406645i
$454$	28.4128	−	20.6431i	1.33348	−	0.968831i
$455$	−0.444459	−	0.322919i	−0.0208366	−	0.0151387i
$456$	−0.451803	−	1.39051i	−0.0211576	−	0.0651164i
$457$	−9.40088	−	28.9329i	−0.439755	−	1.35343i	−0.888135	−	0.459583i	$-0.847999\pi$
$457$	−9.40088	−	28.9329i	−0.439755	−	1.35343i	0.448380	−	0.893843i	$-0.352001\pi$
$458$	14.3243	+	10.4072i	0.669330	+	0.486297i
$459$	−0.234423	+	0.170318i	−0.0109419	+	0.00794978i
$460$	6.75796	−	20.7989i	0.315091	−	0.969752i
$461$	1.13602			0.0529099			0.0264549	−	0.999650i	$-0.491578\pi$
$461$	1.13602			0.0529099			0.0264549	+	0.999650i	$0.491578\pi$
$462$	−0.0208957	+	0.0777501i	−0.000972157	+	0.00361726i
$463$	20.3418			0.945365			0.472682	−	0.881233i	$-0.343286\pi$
$463$	20.3418			0.945365			0.472682	+	0.881233i	$0.343286\pi$
$464$	9.46337	−	29.1253i	0.439326	−	1.35211i
$465$	0.0690442	−	0.0501635i	0.00320185	−	0.00232628i
$466$	−42.3906	−	30.7986i	−1.96371	−	1.42672i
$467$	−7.66346	−	23.5857i	−0.354622	−	1.09142i	−0.956228	−	0.292622i	$-0.905472\pi$
$467$	−7.66346	−	23.5857i	−0.354622	−	1.09142i	0.601606	−	0.798793i	$-0.294528\pi$
$468$	10.4398	+	32.1304i	0.482580	+	1.48523i
$469$	0.274887	+	0.199717i	0.0126931	+	0.00922208i
$470$	−11.0863	+	8.05464i	−0.511371	+	0.371533i
$471$	−0.115374	+	0.355086i	−0.00531617	+	0.0163615i
$472$	−49.7623			−2.29049
$473$	−2.15728	+	0.111432i	−0.0991916	+	0.00512366i
$474$	−1.94147			−0.0891747
$475$	1.74946	−	5.38428i	0.0802706	−	0.247048i
$476$	0.680738	−	0.494585i	0.0312016	−	0.0226693i
$477$	−32.3367	−	23.4940i	−1.48059	−	1.07572i
$478$	9.41890	+	28.9884i	0.430811	+	1.32590i
$479$	7.81745	+	24.0596i	0.357189	+	1.09931i	0.954730	+	0.297475i	$0.0961445\pi$
$479$	7.81745	+	24.0596i	0.357189	+	1.09931i	−0.597541	+	0.801838i	$0.703856\pi$
$480$	−0.0623137	−	0.0452736i	−0.00284422	−	0.00206645i
$481$	5.79188	−	4.20805i	0.264087	−	0.191870i
$482$	4.09953	−	12.6171i	0.186729	−	0.574691i
$483$	−0.0515041			−0.00234352
$484$	−39.5442	−	22.9102i	−1.79746	−	1.04137i
$485$	9.44261			0.428767
$486$	−0.998985	+	3.07456i	−0.0453149	+	0.139465i
$487$	−17.0727	+	12.4041i	−0.773639	+	0.562081i	−0.903063	−	0.429508i	$-0.858687\pi$
$487$	−17.0727	+	12.4041i	−0.773639	+	0.562081i	0.129424	+	0.991589i	$0.458687\pi$
$488$	−19.8245	−	14.4033i	−0.897411	−	0.652007i
$489$	0.178437	+	0.549171i	0.00806918	+	0.0248344i
$490$	−5.33495	−	16.4193i	−0.241009	−	0.741748i
$491$	−21.2271	−	15.4224i	−0.957966	−	0.696003i	−0.00528864	−	0.999986i	$-0.501683\pi$
$491$	−21.2271	−	15.4224i	−0.957966	−	0.696003i	−0.952677	+	0.303983i	$0.901683\pi$
$492$	1.07541	−	0.781328i	0.0484830	−	0.0352250i
$493$	−1.91103	+	5.88153i	−0.0860683	+	0.264891i
$494$	38.0990			1.71415
$495$	9.92890	−	0.512869i	0.446271	−	0.0230517i
$496$	8.74759			0.392778
$497$	0.148165	−	0.456006i	0.00664612	−	0.0204547i
$498$	0.600424	−	0.436234i	0.0269057	−	0.0195481i
$499$	26.5361	+	19.2796i	1.18792	+	0.863075i	0.993043	−	0.117752i	$-0.0375689\pi$
$499$	26.5361	+	19.2796i	1.18792	+	0.863075i	0.194878	+	0.980827i	$0.437569\pi$
$500$	−1.28387	−	3.95133i	−0.0574162	−	0.176709i
$501$	−0.141679	−	0.436044i	−0.00632977	−	0.0194810i
$502$	−59.9066	−	43.5247i	−2.67376	−	1.94260i
$503$	−5.98893	+	4.35121i	−0.267033	+	0.194011i	−0.713242	−	0.700918i	$-0.752774\pi$
$503$	−5.98893	+	4.35121i	−0.267033	+	0.194011i	0.446209	+	0.894929i	$0.352774\pi$
$504$	1.00285	−	3.08645i	0.0446705	−	0.137482i
$505$	4.80720			0.213918
$506$	11.2411	−	41.8265i	0.499726	−	1.85941i
$507$	−0.272565			−0.0121050
$508$	4.95724	−	15.2568i	0.219942	−	0.676912i
$509$	7.00238	−	5.08753i	0.310375	−	0.225501i	−0.421682	−	0.906744i	$-0.638560\pi$
$509$	7.00238	−	5.08753i	0.310375	−	0.225501i	0.732057	+	0.681243i	$0.238560\pi$
$510$	0.0969663	+	0.0704502i	0.00429374	+	0.00311959i
$511$	0.846507	+	2.60528i	0.0374473	+	0.115251i
$512$	13.9201	+	42.8417i	0.615187	+	1.89335i
$513$	1.32716	+	0.964235i	0.0585953	+	0.0425720i
$514$	−36.5970	+	26.5893i	−1.61422	+	1.17280i
$515$	4.31996	−	13.2955i	0.190360	−	0.585869i
$516$	−0.130733			−0.00575521
$517$	−14.2458	+	11.5183i	−0.626531	+	0.506575i
$518$	−1.32605			−0.0582634
$519$	−0.266018	+	0.818720i	−0.0116769	+	0.0359378i
$520$	11.7309	−	8.52300i	0.514434	−	0.373758i
$521$	0.000229779	0	0.000166944i	1.00668e−5	0	7.31395e-6i	0.587790	−	0.809013i	$-0.299998\pi$
$521$	0.000229779	0	0.000166944i	1.00668e−5	0	7.31395e-6i	−0.587780	+	0.809021i	$0.699998\pi$
$522$	14.2119	+	43.7398i	0.622038	+	1.91444i
$523$	4.96830	+	15.2909i	0.217249	+	0.668622i	0.998986	+	0.0450150i	$0.0143336\pi$
$523$	4.96830	+	15.2909i	0.217249	+	0.668622i	−0.781738	+	0.623607i	$0.785666\pi$
$524$	33.3087	+	24.2002i	1.45510	+	1.05719i
$525$	−0.00791596	+	0.00575128i	−0.000345481	+	0.000251007i
$526$	11.6634	−	35.8964i	0.508550	−	1.56516i
$527$	−1.76648			−0.0769491
$528$	−0.665144	−	0.432661i	−0.0289467	−	0.0188291i
$529$	4.70715			0.204658
$530$	−10.2221	+	31.4603i	−0.444019	+	1.36655i
$531$	22.5765	−	16.4028i	0.979736	−	0.711820i
$532$	−3.85391	−	2.80003i	−0.167088	−	0.121397i
$533$	5.55122	+	17.0849i	0.240450	+	0.740029i
$534$	0.522349	+	1.60763i	0.0226043	+	0.0695688i
$535$	4.44727	+	3.23113i	0.192272	+	0.139694i
$536$	−7.25527	+	5.27126i	−0.313380	+	0.227684i
$537$	0.191958	−	0.590785i	0.00828359	−	0.0254943i
$538$	−5.29474			−0.228272
$539$	−8.25506	−	21.5536i	−0.355570	−	0.928377i
$540$	1.20387			0.0518064
$541$	7.89414	−	24.2957i	0.339396	−	1.04455i	−0.625121	−	0.780528i	$-0.714950\pi$
$541$	7.89414	−	24.2957i	0.339396	−	1.04455i	0.964516	−	0.264024i	$-0.0850498\pi$
$542$	−8.36521	+	6.07768i	−0.359317	+	0.261059i
$543$	−0.493324	−	0.358421i	−0.0211705	−	0.0153813i
$544$	0.492660	+	1.51625i	0.0211226	+	0.0650088i
$545$	−5.64690	−	17.3794i	−0.241886	−	0.744450i
$546$	−0.0532716	−	0.0387041i	−0.00227981	−	0.00165638i
$547$	14.3968	−	10.4599i	0.615564	−	0.447234i	−0.235805	−	0.971800i	$-0.575773\pi$
$547$	14.3968	−	10.4599i	0.615564	−	0.447234i	0.851369	+	0.524567i	$0.175773\pi$
$548$	−0.616103	+	1.89617i	−0.0263186	+	0.0810003i
$549$	13.7418			0.586484
$550$	−2.94291	−	7.68380i	−0.125486	−	0.327638i
$551$	35.0111			1.49152
$552$	0.420072	−	1.29285i	0.0178795	−	0.0550273i
$553$	−2.65406	+	1.92829i	−0.112862	+	0.0819991i
$554$	−8.96450	−	6.51309i	−0.380865	−	0.276715i
$555$	−0.0394018	−	0.121266i	−0.00167251	−	0.00514746i
$556$	5.60037	+	17.2362i	0.237509	+	0.730977i
$557$	24.0104	+	17.4446i	1.01735	+	0.739151i	0.965739	−	0.259517i	$-0.0835632\pi$
$557$	24.0104	+	17.4446i	1.01735	+	0.739151i	0.0516148	+	0.998667i	$0.483563\pi$
$558$	−10.6280	+	7.72171i	−0.449920	+	0.326886i
$559$	0.545958	−	1.68029i	0.0230916	−	0.0710686i
$560$	−1.00292			−0.0423809
$561$	0.134319	+	0.0873711i	0.00567094	+	0.00368881i
$562$	−52.9602			−2.23399
$563$	8.39290	−	25.8307i	0.353719	−	1.08863i	−0.603030	−	0.797718i	$-0.706040\pi$
$563$	8.39290	−	25.8307i	0.353719	−	1.08863i	0.956749	−	0.290915i	$-0.0939598\pi$
$564$	−0.896975	+	0.651690i	−0.0377695	+	0.0274411i
$565$	9.37444	+	6.81093i	0.394386	+	0.286538i
$566$	−4.29127	−	13.2072i	−0.180375	−	0.555139i
$567$	0.561947	+	1.72950i	0.0235996	+	0.0726320i
$568$	10.2381	+	7.43845i	0.429583	+	0.312110i
$569$	−4.28303	+	3.11180i	−0.179554	+	0.130454i	−0.673932	−	0.738793i	$-0.735396\pi$
$569$	−4.28303	+	3.11180i	−0.179554	+	0.130454i	0.494378	+	0.869247i	$0.335396\pi$
$570$	0.209685	−	0.645343i	0.00878273	−	0.0270305i
$571$	17.4555			0.730491			0.365245	−	0.930911i	$-0.380985\pi$
$571$	17.4555			0.730491			0.365245	+	0.930911i	$0.380985\pi$
$572$	29.0663	−	23.5013i	1.21532	−	0.982637i
$573$	0.211534			0.00883698
$574$	1.02822	−	3.16454i	0.0429171	−	0.132085i
$575$	4.25847	−	3.09396i	0.177590	−	0.129027i
$576$	−14.4268	−	10.4816i	−0.601115	−	0.436735i
$577$	−9.29899	−	28.6194i	−0.387122	−	1.19144i	−0.934929	−	0.354835i	$-0.884537\pi$
$577$	−9.29899	−	28.6194i	−0.387122	−	1.19144i	0.547807	−	0.836605i	$-0.315463\pi$
$578$	−0.766629	−	2.35944i	−0.0318875	−	0.0981398i
$579$	0.489205	+	0.355428i	0.0203307	+	0.0147711i
$580$	20.7864	−	15.1022i	0.863108	−	0.627085i
$581$	0.387530	−	1.19269i	0.0160774	−	0.0494813i
$582$	1.13176			0.0469131
$583$	−11.4779	+	42.7078i	−0.475367	+	1.76878i
$584$	−72.3016			−2.99186
$585$	−2.51278	+	7.73355i	−0.103891	+	0.319743i
$586$	−24.6568	+	17.9142i	−1.01856	+	0.740029i
$587$	−18.9057	−	13.7358i	−0.780324	−	0.566938i	0.124752	−	0.992188i	$-0.460186\pi$
$587$	−18.9057	−	13.7358i	−0.780324	−	0.566938i	−0.905076	+	0.425250i	$0.860186\pi$
$588$	−0.431644	−	1.32846i	−0.0178007	−	0.0547850i
$589$	3.09038	+	9.51122i	0.127337	+	0.391903i
$590$	−18.6842	−	13.5749i	−0.769218	−	0.558870i
$591$	−0.0934003	+	0.0678593i	−0.00384198	+	0.00279136i
$592$	4.03863	−	12.4296i	0.165987	−	0.510855i
$593$	4.06553			0.166951			0.0834756	−	0.996510i	$-0.473398\pi$
$593$	4.06553			0.166951			0.0834756	+	0.996510i	$0.473398\pi$
$594$	2.38102	−	0.122990i	0.0976945	−	0.00504633i
$595$	0.202528			0.00830284
$596$	0.736733	−	2.26743i	0.0301778	−	0.0928776i
$597$	−0.339026	+	0.246317i	−0.0138754	+	0.0100811i
$598$	28.6580	+	20.8212i	1.17191	+	0.851443i
$599$	−10.0414	−	30.9042i	−0.410280	−	1.26271i	−0.916405	−	0.400253i	$-0.868922\pi$
$599$	−10.0414	−	30.9042i	−0.410280	−	1.26271i	0.506124	−	0.862460i	$-0.331078\pi$
$600$	−0.0798046	−	0.245613i	−0.00325801	−	0.0100271i
$601$	−18.9185	−	13.7451i	−0.771700	−	0.560673i	0.130776	−	0.991412i	$-0.458253\pi$
$601$	−18.9185	−	13.7451i	−0.771700	−	0.560673i	−0.902477	+	0.430739i	$0.858253\pi$
$602$	−0.264748	+	0.192351i	−0.0107903	+	0.00783964i
$603$	1.55409	−	4.78300i	0.0632875	−	0.194779i
$604$	78.2591			3.18432
$605$	−4.45899	−	10.0557i	−0.181284	−	0.408823i
$606$	0.576176			0.0234056
$607$	−8.81619	+	27.1335i	−0.357838	+	1.10131i	0.596507	+	0.802608i	$0.296555\pi$
$607$	−8.81619	+	27.1335i	−0.357838	+	1.10131i	−0.954345	+	0.298705i	$0.903445\pi$
$608$	7.30204	−	5.30524i	0.296137	−	0.215156i
$609$	−0.0489540	−	0.0355671i	−0.00198371	−	0.00144125i
$610$	−3.51434	−	10.8160i	−0.142292	−	0.437928i
$611$	−4.63016	−	14.2502i	−0.187316	−	0.576500i
$612$	−10.0758	−	7.32047i	−0.407289	−	0.295913i
$613$	12.7920	−	9.29396i	0.516666	−	0.375379i	−0.298681	−	0.954353i	$-0.596547\pi$
$613$	12.7920	−	9.29396i	0.516666	−	0.375379i	0.815346	+	0.578974i	$0.196547\pi$
$614$	17.4995	−	53.8580i	0.706224	−	2.17353i
$615$	0.319946			0.0129015
$616$	−3.58581	+	0.185222i	−0.144477	+	0.00746282i
$617$	−15.4491			−0.621959			−0.310979	−	0.950417i	$-0.600657\pi$
$617$	−15.4491			−0.621959			−0.310979	+	0.950417i	$0.600657\pi$
$618$	0.517778	−	1.59356i	0.0208281	−	0.0641022i
$619$	−32.8541	+	23.8699i	−1.32052	+	0.959411i	−0.320591	+	0.947218i	$0.603881\pi$
$619$	−32.8541	+	23.8699i	−1.32052	+	0.959411i	−0.999926	+	0.0121934i	$0.996119\pi$
$620$	5.93750	+	4.31385i	0.238456	+	0.173248i
$621$	0.471326	+	1.45059i	0.0189137	+	0.0582102i
$622$	17.7180	+	54.5304i	0.710427	+	2.18647i
$623$	2.31078	+	1.67888i	0.0925794	+	0.0672629i
$624$	0.525033	−	0.381459i	0.0210182	−	0.0152706i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−18.7166			−0.748064
$627$	0.235446	−	0.876061i	0.00940280	−	0.0349865i
$628$	−32.1073			−1.28122
$629$	−0.815558	+	2.51003i	−0.0325184	+	0.100081i
$630$	1.21851	−	0.885299i	0.0485466	−	0.0352711i
$631$	−1.50450	−	1.09308i	−0.0598931	−	0.0435149i	0.557436	−	0.830220i	$-0.311785\pi$
$631$	−1.50450	−	1.09308i	−0.0598931	−	0.0435149i	−0.617329	+	0.786705i	$0.711785\pi$
$632$	−26.7568	−	82.3490i	−1.06433	−	3.27567i
$633$	0.188670	+	0.580666i	0.00749896	+	0.0230794i
$634$	32.8979	+	23.9017i	1.30654	+	0.949258i
$635$	3.12376	−	2.26955i	0.123963	−	0.0900643i
$636$	−0.827056	+	2.54542i	−0.0327949	+	0.100932i
$637$	18.8771			0.747937
$638$	39.5685	−	31.9927i	1.56653	−	1.26661i
$639$	−7.09679			−0.280745
$640$	−5.54582	+	17.0683i	−0.219218	+	0.674683i
$641$	−36.9061	+	26.8139i	−1.45770	+	1.05908i	−0.473750	+	0.880659i	$0.657100\pi$
$641$	−36.9061	+	26.8139i	−1.45770	+	1.05908i	−0.983954	+	0.178424i	$0.942900\pi$
$642$	0.533036	+	0.387274i	0.0210373	+	0.0152845i
$643$	2.20897	+	6.79850i	0.0871131	+	0.268106i	0.985118	−	0.171879i	$-0.0549837\pi$
$643$	2.20897	+	6.79850i	0.0871131	+	0.268106i	−0.898005	+	0.439985i	$0.854984\pi$
$644$	−1.36868	−	4.21235i	−0.0539334	−	0.165990i
$645$	−0.0254569	−	0.0184956i	−0.00100237	−	0.000728262i
$646$	−11.3627	+	8.25548i	−0.447059	+	0.324808i
$647$	−6.30039	+	19.3906i	−0.247694	+	0.762324i	0.747488	+	0.664276i	$0.231260\pi$
$647$	−6.30039	+	19.3906i	−0.247694	+	0.762324i	−0.995182	+	0.0980482i	$0.968740\pi$
$648$	−47.9968			−1.88549
$649$	−25.8816	−	16.8354i	−1.01594	−	0.660846i
$650$	6.72964			0.263958
$651$	0.00534118	−	0.0164385i	0.000209337	−	0.000644274i
$652$	−40.1731	+	29.1875i	−1.57330	+	1.14307i
$653$	4.75778	+	3.45673i	0.186186	+	0.135272i	0.676974	−	0.736007i	$-0.263291\pi$
$653$	4.75778	+	3.45673i	0.186186	+	0.135272i	−0.490788	+	0.871279i	$0.663291\pi$
$654$	−0.676820	−	2.08304i	−0.0264657	−	0.0814532i
$655$	3.06228	+	9.42473i	0.119653	+	0.368255i
$656$	26.5310	+	19.2759i	1.03586	+	0.752598i
$657$	32.8023	−	23.8322i	1.27974	−	0.929784i
$658$	−0.857620	+	2.63948i	−0.0334335	+	0.102898i
$659$	29.9479			1.16660			0.583302	−	0.812255i	$-0.301760\pi$
$659$	29.9479			1.16660			0.583302	+	0.812255i	$0.301760\pi$
$660$	−0.238107	−	0.621686i	−0.00926830	−	0.0241991i
$661$	27.7229			1.07830			0.539148	−	0.842211i	$-0.318746\pi$
$661$	27.7229			1.07830			0.539148	+	0.842211i	$0.318746\pi$
$662$	−4.28766	+	13.1961i	−0.166645	+	0.512879i
$663$	−0.106025	+	0.0770315i	−0.00411766	+	0.00299166i
$664$	26.7781	+	19.4554i	1.03919	+	0.755017i
$665$	−0.354314	−	1.09047i	−0.0137397	−	0.0422865i
$666$	6.06514	+	18.6666i	0.235019	+	0.723315i
$667$	26.3353	+	19.1337i	1.01971	+	0.740859i
$668$	31.8976	−	23.1750i	1.23416	−	0.896667i
$669$	0.315188	−	0.970050i	0.0121859	−	0.0375043i
$670$	−4.16211			−0.160796
$671$	−5.43793	−	14.1982i	−0.209929	−	0.548114i
$672$	−0.0155995			−0.000601765
$673$	−10.4201	+	32.0698i	−0.401666	+	1.23620i	0.521981	+	0.852957i	$0.325193\pi$
$673$	−10.4201	+	32.0698i	−0.401666	+	1.23620i	−0.923647	+	0.383244i	$0.874807\pi$
$674$	−54.9541	+	39.9265i	−2.11675	+	1.53791i
$675$	0.234423	+	0.170318i	0.00902295	+	0.00655556i
$676$	−7.24317	−	22.2922i	−0.278583	−	0.857391i
$677$	3.61407	+	11.1230i	0.138900	+	0.427491i	0.996176	−	0.0873663i	$-0.0278451\pi$
$677$	3.61407	+	11.1230i	0.138900	+	0.427491i	−0.857276	+	0.514857i	$0.827845\pi$
$678$	1.12359	+	0.816337i	0.0431513	+	0.0313512i
$679$	1.54716	−	1.12408i	0.0593745	−	0.0431381i
$680$	−1.65184	+	5.08383i	−0.0633451	+	0.194956i
$681$	0.683935			0.0262085
$682$	12.1839	+	7.92536i	0.466546	+	0.303478i
$683$	−2.93692			−0.112378			−0.0561891	−	0.998420i	$-0.517895\pi$
$683$	−2.93692			−0.112378			−0.0561891	+	0.998420i	$0.517895\pi$
$684$	−21.7883	+	67.0576i	−0.833098	+	2.56401i
$685$	−0.388232	+	0.282067i	−0.0148336	+	0.0107772i
$686$	−5.67413	−	4.12250i	−0.216639	−	0.157398i
$687$	0.106551	+	0.327929i	0.00406516	+	0.0125113i
$688$	−0.996666	−	3.06742i	−0.0379975	−	0.116944i
$689$	−29.2618	−	21.2600i	−1.11479	−	0.809940i
$690$	0.510407	−	0.370833i	0.0194309	−	0.0141174i
$691$	−1.82056	+	5.60311i	−0.0692574	+	0.213152i	−0.979695	−	0.200494i	$-0.935745\pi$
$691$	−1.82056	+	5.60311i	−0.0692574	+	0.213152i	0.910437	+	0.413647i	$0.135745\pi$
$692$	−74.0296			−2.81418
$693$	1.56578	−	1.26600i	0.0594792	−	0.0480913i
$694$	−48.0700			−1.82471
$695$	−1.34797	+	4.14862i	−0.0511314	+	0.157366i
$696$	1.29207	−	0.938746i	0.0489759	−	0.0355831i
$697$	−5.35765	−	3.89256i	−0.202935	−	0.147441i
$698$	22.7134	+	69.9046i	0.859714	+	2.64593i
$699$	−0.315320	−	0.970456i	−0.0119265	−	0.0367060i
$700$	−0.680738	−	0.494585i	−0.0257295	−	0.0186936i
$701$	13.8176	−	10.0391i	0.521884	−	0.379171i	−0.295429	−	0.955365i	$-0.595463\pi$
$701$	13.8176	−	10.0391i	0.521884	−	0.379171i	0.817313	+	0.576194i	$0.195463\pi$
$702$	−0.602583	+	1.85456i	−0.0227430	+	0.0699959i
$703$	14.9415			0.563529
$704$	−5.12079	+	19.0537i	−0.192997	+	0.718115i
$705$	−0.266861			−0.0100506
$706$	−13.1326	+	40.4180i	−0.494252	+	1.52115i
$707$	0.787653	−	0.572264i	0.0296228	−	0.0215222i
$708$	−1.51172	−	1.09833i	−0.0568139	−	0.0412777i
$709$	4.58625	+	14.1150i	0.172240	+	0.530101i	0.999497	−	0.0317237i	$-0.0100997\pi$
$709$	4.58625	+	14.1150i	0.172240	+	0.530101i	−0.827257	+	0.561824i	$0.810100\pi$
$710$	1.81495	+	5.58583i	0.0681137	+	0.209633i
$711$	39.2833	+	28.5410i	1.47324	+	1.07037i
$712$	−60.9899	+	44.3118i	−2.28569	+	1.66065i
$713$	−2.87334	+	8.84323i	−0.107607	+	0.331182i
$714$	0.0242744			0.000908447
$715$	8.98477	−	0.464101i	0.336011	−	0.0173564i
$716$	53.4195			1.99638
$717$	−0.183425	+	0.564524i	−0.00685013	+	0.0210825i
$718$	21.0438	−	15.2892i	0.785348	−	0.570589i
$719$	19.4349	+	14.1203i	0.724798	+	0.526597i	0.887914	−	0.460010i	$-0.152154\pi$
$719$	19.4349	+	14.1203i	0.724798	+	0.526597i	−0.163115	+	0.986607i	$0.552154\pi$
$720$	4.58717	+	14.1179i	0.170954	+	0.526142i
$721$	−0.874914	−	2.69271i	−0.0325835	−	0.100282i
$722$	26.1943	+	19.0312i	0.974849	+	0.708270i
$723$	0.209010	−	0.151855i	0.00777317	−	0.00564754i
$724$	16.2044	−	49.8720i	0.602232	−	1.85348i
$725$	6.18421			0.229676
$726$	−0.534441	−	1.20525i	−0.0198350	−	0.0447309i
$727$	−21.9522			−0.814163			−0.407082	−	0.913392i	$-0.633454\pi$
$727$	−21.9522			−0.814163			−0.407082	+	0.913392i	$0.633454\pi$
$728$	0.907489	−	2.79297i	0.0336338	−	0.103514i
$729$	21.7416	−	15.7962i	0.805243	−	0.585043i
$730$	−27.1471	−	19.7235i	−1.00476	−	0.730000i
$731$	0.201266	+	0.619433i	0.00744409	+	0.0229106i
$732$	−0.284341	−	0.875111i	−0.0105095	−	0.0323450i
$733$	−23.8958	−	17.3613i	−0.882611	−	0.641255i	0.0513298	−	0.998682i	$-0.483654\pi$
$733$	−23.8958	−	17.3613i	−0.882611	−	0.641255i	−0.933941	+	0.357427i	$0.883654\pi$
$734$	4.03885	−	2.93439i	0.149077	−	0.108310i
$735$	0.103894	−	0.319752i	0.00383217	−	0.0117942i
$736$	8.39192			0.309330
$737$	−5.55685	+	0.287035i	−0.204689	+	0.0105731i
$738$	−49.2496			−1.81290
$739$	−8.41270	+	25.8916i	−0.309466	+	0.952438i	0.668507	+	0.743706i	$0.266934\pi$
$739$	−8.41270	+	25.8916i	−0.309466	+	0.952438i	−0.977973	+	0.208732i	$0.933066\pi$
$740$	8.87089	−	6.44508i	0.326101	−	0.236926i
$741$	0.600245	+	0.436104i	0.0220506	+	0.0160207i
$742$	2.07026	+	6.37160i	0.0760016	+	0.233909i
$743$	−5.98419	−	18.4174i	−0.219538	−	0.675670i	−0.998800	−	0.0489713i	$-0.984406\pi$
$743$	−5.98419	−	18.4174i	−0.219538	−	0.675670i	0.779262	−	0.626699i	$-0.215594\pi$
$744$	0.369073	+	0.268147i	0.0135309	+	0.00983075i
$745$	0.464246	−	0.337294i	0.0170087	−	0.0123575i
$746$	−13.7128	+	42.2035i	−0.502060	+	1.54518i
$747$	−18.5618			−0.679141
$748$	−3.57640	+	13.3073i	−0.130766	+	0.486563i
$749$	1.11332			0.0406799
$750$	0.0370378	−	0.113991i	0.00135243	−	0.00416235i
$751$	−32.0405	+	23.2788i	−1.16917	+	0.849455i	−0.990910	−	0.134528i	$-0.957048\pi$
$751$	−32.0405	+	23.2788i	−1.16917	+	0.849455i	−0.178264	+	0.983983i	$0.557048\pi$
$752$	−22.1290	−	16.0777i	−0.806962	−	0.586292i
$753$	−0.445613	−	1.37146i	−0.0162390	−	0.0499786i
$754$	12.8605	+	39.5806i	0.468352	+	1.44144i
$755$	15.2389	+	11.0717i	0.554602	+	0.402942i
$756$	0.197253	−	0.143313i	0.00717401	−	0.00521223i
$757$	6.58843	−	20.2771i	0.239460	−	0.736983i	−0.757038	−	0.653371i	$-0.773354\pi$
$757$	6.58843	−	20.2771i	0.239460	−	0.736983i	0.996498	−	0.0836124i	$-0.0266458\pi$
$758$	−92.0671			−3.34403
$759$	0.655873	−	0.530300i	0.0238067	−	0.0192487i
$760$	30.2626			1.09774
$761$	−4.11813	+	12.6743i	−0.149282	+	0.459443i	−0.997537	−	0.0701455i	$-0.977654\pi$
$761$	−4.11813	+	12.6743i	−0.149282	+	0.459443i	0.848255	+	0.529588i	$0.177654\pi$
$762$	0.374405	−	0.272021i	0.0135633	−	0.00985429i
$763$	−2.99413	−	2.17536i	−0.108395	−	0.0787533i
$764$	5.62134	+	17.3007i	0.203373	+	0.625918i
$765$	−0.926330	−	2.85095i	−0.0334915	−	0.103076i
$766$	−28.1053	−	20.4197i	−1.01549	−	0.737794i
$767$	20.4297	−	14.8431i	0.737674	−	0.535952i
$768$	−0.487082	+	1.49908i	−0.0175761	+	0.0540935i
$769$	−46.3110			−1.67002			−0.835009	−	0.550236i	$-0.814538\pi$
$769$	−46.3110			−1.67002			−0.835009	+	0.550236i	$0.814538\pi$
$770$	−1.39689	−	0.908647i	−0.0503406	−	0.0327454i
$771$	−0.880939			−0.0317263
$772$	−16.0691	+	49.4557i	−0.578341	+	1.77995i
$773$	−34.3785	+	24.9774i	−1.23651	+	0.898375i	−0.997361	−	0.0726083i	$-0.976868\pi$
$773$	−34.3785	+	24.9774i	−1.23651	+	0.898375i	−0.239147	+	0.970983i	$0.576868\pi$
$774$	3.91860	+	2.84703i	0.140851	+	0.102334i
$775$	0.545872	+	1.68002i	0.0196083	+	0.0603482i
$776$	15.5976	+	48.0046i	0.559923	+	1.72327i
$777$	−0.0208918	−	0.0151788i	−0.000749490	−	0.000544536i
$778$	−69.9331	+	50.8093i	−2.50722	+	1.82160i
$779$	−11.5856	+	35.6569i	−0.415099	+	1.27754i
$780$	0.544486			0.0194957
$781$	2.80836	+	7.33250i	0.100491	+	0.262377i
$782$	−13.0587			−0.466977
$783$	−0.553745	+	1.70425i	−0.0197892	+	0.0609049i
$784$	27.8794	−	20.2555i	0.995691	−	0.723412i
$785$	−6.25207	−	4.54240i	−0.223146	−	0.162125i
$786$	0.367036	+	1.12962i	0.0130917	+	0.0402922i
$787$	−4.45158	−	13.7005i	−0.158682	−	0.488372i	0.839834	−	0.542844i	$-0.182652\pi$
$787$	−4.45158	−	13.7005i	−0.158682	−	0.488372i	−0.998515	+	0.0544720i	$0.982652\pi$
$788$	−8.03202	−	5.83561i	−0.286129	−	0.207885i
$789$	0.594648	−	0.432037i	0.0211700	−	0.0153809i
$790$	12.4180	−	38.2187i	0.441813	−	1.35976i
$791$	2.34678			0.0834420
$792$	19.0083	+	49.6297i	0.675429	+	1.76351i
$793$	12.4351			0.441582
$794$	13.5067	−	41.5693i	0.479334	−	1.47524i
$795$	−0.521162	+	0.378646i	−0.0184837	+	0.0134292i
$796$	−29.1548	−	21.1822i	−1.03336	−	0.750783i
$797$	−14.8525	−	45.7113i	−0.526103	−	1.61918i	−0.762124	−	0.647431i	$-0.775843\pi$
$797$	−14.8525	−	45.7113i	−0.526103	−	1.61918i	0.236021	−	0.971748i	$-0.424157\pi$
$798$	−0.0424671	−	0.130700i	−0.00150332	−	0.00462674i
$799$	4.46871	+	3.24671i	0.158092	+	0.114860i
$800$	1.28980	−	0.937096i	0.0456014	−	0.0331313i
$801$	13.0641	−	40.2073i	0.461599	−	1.42066i
$802$	36.7385			1.29728
$803$	−37.6044	−	24.4608i	−1.32703	−	0.863202i
$804$	−0.336751			−0.0118763
$805$	0.329430	−	1.01388i	0.0116109	−	0.0357346i
$806$	−9.61741	+	6.98746i	−0.338759	+	0.246123i
$807$	−0.0834181	−	0.0606068i	−0.00293646	−	0.00213346i
$808$	7.94071	+	24.4390i	0.279353	+	0.859761i
$809$	−10.9248	−	33.6232i	−0.384097	−	1.18213i	−0.937133	−	0.348972i	$-0.886531\pi$
$809$	−10.9248	−	33.6232i	−0.384097	−	1.18213i	0.553036	−	0.833157i	$-0.313469\pi$
$810$	−18.0214	−	13.0933i	−0.633207	−	0.460052i
$811$	20.9170	−	15.1971i	0.734494	−	0.533641i	−0.156488	−	0.987680i	$-0.550017\pi$
$811$	20.9170	−	15.1971i	0.734494	−	0.533641i	0.890982	+	0.454039i	$0.150017\pi$
$812$	1.60801	−	4.94895i	0.0564301	−	0.173674i
$813$	−0.201362			−0.00706207
$814$	16.8864	−	13.6534i	0.591870	−	0.478550i
$815$	−11.9520			−0.418660
$816$	−0.0739303	+	0.227534i	−0.00258808	+	0.00796529i
$817$	2.98309	−	2.16734i	0.104365	−	0.0758258i
$818$	45.5822	+	33.1174i	1.59375	+	1.15792i
$819$	0.508909	+	1.56626i	0.0177827	+	0.0547296i
$820$	8.50230	+	26.1674i	0.296913	+	0.913804i
$821$	28.8496	+	20.9604i	1.00686	+	0.731524i	0.963547	−	0.267537i	$-0.0862099\pi$
$821$	28.8496	+	20.9604i	1.00686	+	0.731524i	0.0433093	+	0.999062i	$0.486210\pi$
$822$	−0.0465323	+	0.0338077i	−0.00162300	+	0.00117918i
$823$	14.2888	−	43.9763i	0.498075	−	1.53292i	−0.314034	−	0.949412i	$-0.601681\pi$
$823$	14.2888	−	43.9763i	0.498075	−	1.53292i	0.812109	−	0.583506i	$-0.198319\pi$
$824$	74.7279			2.60327
$825$	0.0415881	−	0.154744i	0.00144791	−	0.00538749i
$826$	−4.67739			−0.162747
$827$	−8.01325	+	24.6622i	−0.278648	+	0.857590i	0.709583	+	0.704622i	$0.248883\pi$
$827$	−8.01325	+	24.6622i	−0.278648	+	0.857590i	−0.988231	+	0.152968i	$0.951117\pi$
$828$	−53.0364	+	38.5332i	−1.84314	+	1.33912i
$829$	−3.34906	−	2.43323i	−0.116317	−	0.0845096i	0.528106	−	0.849179i	$-0.322902\pi$
$829$	−3.34906	−	2.43323i	−0.116317	−	0.0845096i	−0.644423	+	0.764669i	$0.722902\pi$
$830$	4.74703	+	14.6099i	0.164772	+	0.507116i
$831$	−0.0666820	−	0.205226i	−0.00231317	−	0.00711922i
$832$	−13.0549	−	9.48496i	−0.452598	−	0.328832i
$833$	−5.62994	+	4.09039i	−0.195066	+	0.141724i
$834$	−0.161563	+	0.497241i	−0.00559448	+	0.0172181i
$835$	9.48994			0.328413
$836$	77.9069	−	4.02422i	2.69447	−	0.139181i
$837$	−0.511861			−0.0176925
$838$	24.9277	−	76.7196i	0.861113	−	2.65023i
$839$	13.8611	−	10.0707i	0.478538	−	0.347678i	−0.322222	−	0.946664i	$-0.604430\pi$
$839$	13.8611	−	10.0707i	0.478538	−	0.347678i	0.800759	+	0.598986i	$0.204430\pi$
$840$	−0.0423144	−	0.0307432i	−0.00145999	−	0.00106074i
$841$	2.85669	+	8.79199i	0.0985065	+	0.303172i
$842$	−6.15593	−	18.9460i	−0.212147	−	0.652922i
$843$	−0.834382	−	0.606214i	−0.0287376	−	0.0208791i
$844$	−42.4771	+	30.8614i	−1.46212	+	1.06229i
$845$	1.74338	−	5.36556i	0.0599740	−	0.184581i
$846$	41.0781			1.41229
$847$	−1.92766	−	1.11680i	−0.0662353	−	0.0383738i
$848$	−66.0289			−2.26744
$849$	0.0835687	−	0.257198i	0.00286807	−	0.00882702i
$850$	−2.00706	+	1.45821i	−0.0688416	+	0.0500163i
$851$	11.2390	+	8.16558i	0.385267	+	0.279913i
$852$	0.146845	+	0.451942i	0.00503083	+	0.0154833i
$853$	−10.5816	−	32.5670i	−0.362309	−	1.11507i	−0.951649	−	0.307187i	$-0.900612\pi$
$853$	−10.5816	−	32.5670i	−0.362309	−	1.11507i	0.589341	−	0.807885i	$-0.299388\pi$
$854$	−1.86339	−	1.35383i	−0.0637640	−	0.0463273i
$855$	−13.7297	+	9.97523i	−0.469547	+	0.341146i
$856$	−9.08036	+	27.9465i	−0.310360	+	0.955191i
$857$	−56.5769			−1.93263			−0.966315	−	0.257361i	$-0.917147\pi$
$857$	−56.5769			−1.93263			−0.966315	+	0.257361i	$0.917147\pi$
$858$	1.07689	−	0.0556257i	0.0367643	−	0.00189903i
$859$	27.7226			0.945881			0.472941	−	0.881094i	$-0.343192\pi$
$859$	27.7226			0.945881			0.472941	+	0.881094i	$0.343192\pi$
$860$	0.836195	−	2.57354i	0.0285140	−	0.0877571i
$861$	0.0524228	−	0.0380874i	0.00178656	−	0.00129801i
$862$	22.8955	+	16.6346i	0.779825	+	0.566576i
$863$	−11.7602	−	36.1941i	−0.400321	−	1.23206i	−0.924740	−	0.380600i	$-0.875717\pi$
$863$	−11.7602	−	36.1941i	−0.400321	−	1.23206i	0.524419	−	0.851461i	$-0.324283\pi$
$864$	0.142755	+	0.439354i	0.00485662	+	0.0149471i
$865$	−14.4154	−	10.4734i	−0.490137	−	0.356106i
$866$	−75.1291	+	54.5845i	−2.55299	+	1.85486i
$867$	0.0149294	−	0.0459480i	0.000507030	−	0.00156048i
$868$	1.48639			0.0504512
$869$	13.9436	−	51.8824i	0.473006	−	1.75999i
$870$	0.741221			0.0251297
$871$	1.40632	−	4.32819i	0.0476512	−	0.146655i
$872$	79.0260	−	57.4157i	2.67616	−	1.94434i
$873$	−22.8999	−	16.6377i	−0.775043	−	0.563102i
$874$	22.8456	+	70.3115i	0.772763	+	2.37832i
$875$	−0.0625846	−	0.192616i	−0.00211575	−	0.00651160i
$876$	−2.19644	−	1.59580i	−0.0742107	−	0.0539172i
$877$	13.7114	−	9.96191i	0.463001	−	0.336390i	−0.331706	−	0.943383i	$-0.607624\pi$
$877$	13.7114	−	9.96191i	0.463001	−	0.336390i	0.794707	+	0.606993i	$0.207624\pi$
$878$	24.2870	−	74.7478i	0.819648	−	2.52262i
$879$	−0.593522			−0.0200190
$880$	12.7715	−	10.3263i	0.430528	−	0.348099i
$881$	20.2221			0.681301			0.340651	−	0.940190i	$-0.389353\pi$
$881$	20.2221			0.681301			0.340651	+	0.940190i	$0.389353\pi$
$882$	−15.9924	+	49.2196i	−0.538493	+	1.65731i
$883$	30.4170	−	22.0993i	1.02362	−	0.743700i	0.0565943	−	0.998397i	$-0.481976\pi$
$883$	30.4170	−	22.0993i	1.02362	−	0.743700i	0.967021	+	0.254697i	$0.0819759\pi$
$884$	−9.11767	−	6.62438i	−0.306661	−	0.222802i
$885$	−0.138982	−	0.427742i	−0.00467183	−	0.0143784i
$886$	−24.8893	−	76.6015i	−0.836174	−	2.57348i
$887$	−18.9747	−	13.7859i	−0.637109	−	0.462887i	0.221747	−	0.975104i	$-0.428824\pi$
$887$	−18.9747	−	13.7859i	−0.637109	−	0.462887i	−0.858856	+	0.512217i	$0.828824\pi$
$888$	0.551411	−	0.400624i	0.0185042	−	0.0134441i
$889$	0.241651	−	0.743725i	0.00810471	−	0.0249437i
$890$	−34.9879			−1.17280
$891$	−24.9634	−	16.2381i	−0.836305	−	0.543997i
$892$	87.7130			2.93685
$893$	9.66336	−	29.7408i	0.323372	−	0.995237i
$894$	0.0556431	−	0.0404271i	0.00186098	−	0.00135208i
$895$	10.4021	+	7.55755i	0.347703	+	0.252621i
$896$	1.12318	+	3.45681i	0.0375230	+	0.115484i
$897$	0.213171	+	0.656073i	0.00711757	+	0.0219056i
$898$	−8.81070	−	6.40135i	−0.294017	−	0.213616i
$899$	−8.83793	+	6.42113i	−0.294762	+	0.214157i
$900$	−3.84860	+	11.8448i	−0.128287	+	0.394826i
$901$	13.3338			0.444214
$902$	19.4892	+	50.8853i	0.648919	+	1.69430i
$903$	−0.00637285			−0.000212075
$904$	−19.1406	+	58.9086i	−0.636606	+	1.95927i
$905$	10.2111	−	7.41878i	0.339427	−	0.246608i
$906$	1.82649	+	1.32703i	0.0606812	+	0.0440875i
$907$	−12.1346	−	37.3466i	−0.402924	−	1.24007i	−0.922616	−	0.385719i	$-0.873954\pi$
$907$	−12.1346	−	37.3466i	−0.402924	−	1.24007i	0.519693	−	0.854353i	$-0.326046\pi$
$908$	18.1750	+	55.9369i	0.603158	+	1.85633i
$909$	−11.6582	−	8.47021i	−0.386679	−	0.280939i
$910$	1.10264	−	0.801117i	0.0365522	−	0.0265568i
$911$	−2.44182	+	7.51516i	−0.0809012	+	0.248988i	−0.983324	−	0.181864i	$-0.941787\pi$
$911$	−2.44182	+	7.51516i	−0.0809012	+	0.248988i	0.902423	+	0.430852i	$0.141787\pi$
$912$	1.35444			0.0448502
$913$	7.34533	+	19.1783i	0.243095	+	0.634710i
$914$	75.4725			2.49641
$915$	0.0684387	−	0.210633i	0.00226252	−	0.00696331i
$916$	−23.9888	+	17.4288i	−0.792611	+	0.575865i
$917$	1.62370	+	1.17969i	0.0536193	+	0.0389567i
$918$	−0.222141	−	0.683678i	−0.00733173	−	0.0225648i
$919$	−1.53088	−	4.71156i	−0.0504990	−	0.155420i	0.922627	−	0.385694i	$-0.126038\pi$
$919$	−1.53088	−	4.71156i	−0.0504990	−	0.155420i	−0.973126	+	0.230274i	$0.926038\pi$
$920$	22.7635	+	16.5386i	0.750489	+	0.545262i
$921$	0.892195	−	0.648218i	0.0293988	−	0.0213595i
$922$	−0.870908	+	2.68038i	−0.0286818	+	0.0882735i
$923$	−6.42197			−0.211382
$924$	−0.113021	−	0.0735175i	−0.00371811	−	0.00241855i
$925$	2.63920			0.0867764
$926$	−15.5946	+	47.9953i	−0.512471	+	1.57722i
$927$	−33.9030	+	24.6320i	−1.11352	+	0.809021i
$928$	7.97640	+	5.79520i	0.261838	+	0.190237i
$929$	−4.82493	−	14.8496i	−0.158301	−	0.487200i	0.840179	−	0.542308i	$-0.182450\pi$
$929$	−4.82493	−	14.8496i	−0.158301	−	0.487200i	−0.998480	+	0.0551083i	$0.982450\pi$
$930$	0.0654266	+	0.201362i	0.00214542	+	0.00660293i
$931$	31.8731	+	23.1572i	1.04460	+	0.758946i
$932$	70.9911	−	51.5781i	2.32539	−	1.68950i
$933$	−0.345043	+	1.06193i	−0.0112962	+	0.0347661i
$934$	61.5241			2.01313
$935$	−2.57907	+	2.08528i	−0.0843446	+	0.0681960i
$936$	−43.4668			−1.42076
$937$	2.88002	−	8.86378i	0.0940860	−	0.289567i	−0.892928	−	0.450199i	$-0.851353\pi$
$937$	2.88002	−	8.86378i	0.0940860	−	0.289567i	0.987014	+	0.160632i	$0.0513531\pi$
$938$	−0.681957	+	0.495471i	−0.0222667	+	0.0161777i
$939$	−0.294877	−	0.214241i	−0.00962296	−	0.00699149i
$940$	−7.09160	−	21.8257i	−0.231303	−	0.711876i
$941$	−11.9246	−	36.7000i	−0.388729	−	1.19639i	−0.933738	−	0.357956i	$-0.883474\pi$
$941$	−11.9246	−	36.7000i	−0.388729	−	1.19639i	0.545009	−	0.838430i	$-0.316526\pi$
$942$	−0.749354	−	0.544438i	−0.0244153	−	0.0177387i
$943$	−28.2014	+	20.4895i	−0.918363	+	0.667230i
$944$	14.2455	−	43.8431i	0.463651	−	1.42697i
$945$	0.0586851			0.00190903
$946$	1.39091	−	5.17539i	0.0452224	−	0.168266i
$947$	−17.6813			−0.574565			−0.287283	−	0.957846i	$-0.592752\pi$
$947$	−17.6813			−0.574565			−0.287283	+	0.957846i	$0.592752\pi$
$948$	1.00473	−	3.09223i	0.0326320	−	0.100431i
$949$	29.6831	−	21.5661i	0.963555	−	0.700064i
$950$	11.3627	+	8.25548i	0.368655	+	0.267843i
$951$	0.244709	+	0.753138i	0.00793525	+	0.0244222i
$952$	0.334543	+	1.02962i	0.0108426	+	0.0333701i
$953$	48.3573	+	35.1336i	1.56645	+	1.13809i	0.930463	+	0.366385i	$0.119405\pi$
$953$	48.3573	+	35.1336i	1.56645	+	1.13809i	0.635982	+	0.771704i	$0.280595\pi$
$954$	80.2228	−	58.2853i	2.59731	−	1.88706i
$955$	−1.35302	+	4.16415i	−0.0437826	+	0.134749i
$956$	−51.0449			−1.65091
$957$	0.989607	−	0.0511173i	0.0319894	−	0.00165239i
$958$	−62.7604			−2.02770
$959$	−0.0300332	+	0.0924326i	−0.000969821	+	0.00298480i
$960$	−0.232512	+	0.168930i	−0.00750430	+	0.00545220i
$961$	22.5550	+	16.3872i	0.727582	+	0.528619i
$962$	5.48841	+	16.8916i	0.176953	+	0.544607i
$963$	−5.09215	−	15.6720i	−0.164092	−	0.505024i
$964$	17.9740	+	13.0589i	0.578903	+	0.420597i
$965$	−10.1258	+	7.35684i	−0.325962	+	0.236825i
$966$	0.0394845	−	0.121521i	0.00127039	−	0.00390987i
$967$	52.6880			1.69433			0.847166	−	0.531329i	$-0.178307\pi$
$967$	52.6880			1.69433			0.847166	+	0.531329i	$0.178307\pi$
$968$	43.7560	−	39.2792i	1.40637	−	1.26248i
$969$	−0.273515			−0.00878658
$970$	−7.23897	+	22.2793i	−0.232429	+	0.715344i
$971$	−33.3658	+	24.2417i	−1.07076	+	0.777953i	−0.976049	−	0.217552i	$-0.930193\pi$
$971$	−33.3658	+	24.2417i	−1.07076	+	0.777953i	−0.0947114	+	0.995505i	$0.530193\pi$
$972$	−4.37995	−	3.18222i	−0.140487	−	0.102070i
$973$	0.273001	+	0.840212i	0.00875203	+	0.0269360i
$974$	−16.1782	−	49.7914i	−0.518383	−	1.59542i
$975$	0.106025	+	0.0770315i	0.00339551	+	0.00246698i
$976$	18.3652	−	13.3431i	0.587856	−	0.427103i
$977$	−15.6516	+	48.1706i	−0.500738	+	1.54111i	0.307081	+	0.951684i	$0.400648\pi$
$977$	−15.6516	+	48.1706i	−0.500738	+	1.54111i	−0.807819	+	0.589431i	$0.799352\pi$
$978$	−1.43253			−0.0458073
$979$	−46.7125	+	2.41290i	−1.49294	+	0.0771165i
$980$	28.9123			0.923570
$981$	−16.9275	+	52.0975i	−0.540454	+	1.66335i
$982$	52.6615	−	38.2608i	1.68050	−	1.22095i
$983$	4.30769	+	3.12972i	0.137394	+	0.0998226i	0.654359	−	0.756184i	$-0.272938\pi$
$983$	4.30769	+	3.12972i	0.137394	+	0.0998226i	−0.516965	+	0.856006i	$0.672938\pi$
$984$	0.528499	+	1.62655i	0.0168479	+	0.0518526i
$985$	−0.738435	−	2.27267i	−0.0235285	−	0.0724133i
$986$	−12.4121	−	9.01790i	−0.395281	−	0.287188i
$987$	−0.0437248	+	0.0317680i	−0.00139178	+	0.00101119i
$988$	−19.7165	+	60.6812i	−0.627266	+	1.93053i
$989$	3.42834			0.109015
$990$	−6.40169	+	23.8198i	−0.203459	+	0.757043i
$991$	−48.6006			−1.54385			−0.771925	−	0.635714i	$-0.780706\pi$
$991$	−48.6006			−1.54385			−0.771925	+	0.635714i	$0.780706\pi$
$992$	−0.870275	+	2.67843i	−0.0276313	+	0.0850403i
$993$	−0.218602	+	0.158823i	−0.00693712	+	0.00504011i
$994$	0.962331	+	0.699174i	0.0305233	+	0.0221765i
$995$	−2.68039	−	8.24938i	−0.0849740	−	0.261523i
$996$	0.384076	+	1.18207i	0.0121699	+	0.0374552i
$997$	31.4157	+	22.8248i	0.994945	+	0.722870i	0.960998	−	0.276554i	$-0.0891924\pi$
$997$	31.4157	+	22.8248i	0.994945	+	0.722870i	0.0339465	+	0.999424i	$0.489192\pi$
$998$	−65.8325	+	47.8301i	−2.08389	+	1.51404i
$999$	−0.236319	+	0.727314i	−0.00747679	+	0.0230112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.u.e.86.2	✓	60
11.5	even	5	inner	935.2.u.e.511.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.u.e.86.2	✓	60	1.1	even	1	trivial
935.2.u.e.511.2	yes	60	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766629 + 2.35944i) q^{2} +(-0.0390857 + 0.0283975i) q^{3} +(-3.36120 - 2.44206i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0370378 - 0.113991i) q^{6} +(-0.163849 - 0.119043i) q^{7} +(4.32457 - 3.14198i) q^{8} +(-0.926330 + 2.85095i) q^{9} +O(q^{10})\)	\(q+(-0.766629 + 2.35944i) q^{2} +(-0.0390857 + 0.0283975i) q^{3} +(-3.36120 - 2.44206i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0370378 - 0.113991i) q^{6} +(-0.163849 - 0.119043i) q^{7} +(4.32457 - 3.14198i) q^{8} +(-0.926330 + 2.85095i) q^{9} +2.48086 q^{10} +(3.31221 - 0.171089i) q^{11} +0.200723 q^{12} +(-0.838246 + 2.57986i) q^{13} +(0.406486 - 0.295329i) q^{14} +(0.0390857 + 0.0283975i) q^{15} +(1.53025 + 4.70962i) q^{16} +(-0.309017 - 0.951057i) q^{17} +(-6.01649 - 4.37124i) q^{18} +(-4.58014 + 3.32767i) q^{19} +(-1.28387 + 3.95133i) q^{20} +0.00978466 q^{21} +(-2.13556 + 7.94612i) q^{22} -5.26376 q^{23} +(-0.0798046 + 0.245613i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-5.44439 - 3.95558i) q^{26} +(-0.0895417 - 0.275581i) q^{27} +(0.260019 + 0.800256i) q^{28} +(-5.00313 - 3.63499i) q^{29} +(-0.0969663 + 0.0704502i) q^{30} +(0.545872 - 1.68002i) q^{31} -1.59428 q^{32} +(-0.124602 + 0.100745i) q^{33} +2.48086 q^{34} +(-0.0625846 + 0.192616i) q^{35} +(10.0758 - 7.32047i) q^{36} +(-2.13516 - 1.55128i) q^{37} +(-4.34016 - 13.3577i) q^{38} +(-0.0404979 - 0.124640i) q^{39} +(-4.32457 - 3.14198i) q^{40} +(5.35765 - 3.89256i) q^{41} +(-0.00750120 + 0.0230863i) q^{42} -0.651310 q^{43} +(-11.5508 - 7.51354i) q^{44} +2.99767 q^{45} +(4.03535 - 12.4195i) q^{46} +(-4.46871 + 3.24671i) q^{47} +(-0.193552 - 0.140624i) q^{48} +(-2.15044 - 6.61839i) q^{49} +(-0.766629 - 2.35944i) q^{50} +(0.0390857 + 0.0283975i) q^{51} +(9.11767 - 6.62438i) q^{52} +(-4.12038 + 12.6812i) q^{53} +0.718862 q^{54} +(-1.18624 - 3.09723i) q^{55} -1.08261 q^{56} +(0.0845209 - 0.260129i) q^{57} +(12.4121 - 9.01790i) q^{58} +(-7.53135 - 5.47185i) q^{59} +(-0.0620269 - 0.190899i) q^{60} +(-1.41658 - 4.35979i) q^{61} +(3.54543 + 2.57591i) q^{62} +(0.491164 - 0.356851i) q^{63} +(-1.83827 + 5.65762i) q^{64} +2.71262 q^{65} +(-0.142180 - 0.371224i) q^{66} -1.67769 q^{67} +(-1.28387 + 3.95133i) q^{68} +(0.205738 - 0.149477i) q^{69} +(-0.406486 - 0.295329i) q^{70} +(0.731579 + 2.25157i) q^{71} +(4.95165 + 15.2396i) q^{72} +(-10.9426 - 7.95027i) q^{73} +(5.29703 - 3.84852i) q^{74} +(0.0149294 - 0.0459480i) q^{75} +23.5211 q^{76} +(-0.563068 - 0.366263i) q^{77} +0.325127 q^{78} +(5.00553 - 15.4054i) q^{79} +(4.00624 - 2.91070i) q^{80} +(-7.26416 - 5.27772i) q^{81} +(5.07693 + 15.6252i) q^{82} +(1.91346 + 5.88903i) q^{83} +(-0.0328883 - 0.0238947i) q^{84} +(-0.809017 + 0.587785i) q^{85} +(0.499313 - 1.53673i) q^{86} +0.298775 q^{87} +(13.7863 - 11.1468i) q^{88} -14.1031 q^{89} +(-2.29810 + 7.07281i) q^{90} +(0.444459 - 0.322919i) q^{91} +(17.6926 + 12.8544i) q^{92} +(0.0263725 + 0.0811663i) q^{93} +(-4.23457 - 13.0327i) q^{94} +(4.58014 + 3.32767i) q^{95} +(0.0623137 - 0.0452736i) q^{96} +(-2.91793 + 8.98045i) q^{97} +17.2643 q^{98} +(-2.58043 + 9.60143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9}+O(q^{10}) \) 60 * q - q^2 + 10 * q^3 - 19 * q^4 + 15 * q^5 + 18 * q^6 + 14 * q^7 + 8 * q^8 - 9 * q^9	\( 60 q - q^{2} + 10 q^{3} - 19 q^{4} + 15 q^{5} + 18 q^{6} + 14 q^{7} + 8 q^{8} - 9 q^{9} - 14 q^{10} + 15 q^{11} - 84 q^{12} + q^{13} - q^{14} - 10 q^{15} - 29 q^{16} + 15 q^{17} - 13 q^{18} - 8 q^{19} + 24 q^{20} + 28 q^{22} - 78 q^{23} + 15 q^{24} - 15 q^{25} + 20 q^{26} + 22 q^{27} - 47 q^{28} - 11 q^{29} + 12 q^{30} + 10 q^{32} - 12 q^{33} - 14 q^{34} + 11 q^{35} + 27 q^{36} + 26 q^{37} + 87 q^{38} - 14 q^{39} - 8 q^{40} - 14 q^{41} - 27 q^{42} + 28 q^{43} - 56 q^{45} + 39 q^{46} + 45 q^{47} + 16 q^{48} - 17 q^{49} - q^{50} - 10 q^{51} + 24 q^{52} + 65 q^{53} - 94 q^{54} + 5 q^{55} - 144 q^{56} + 32 q^{57} + 48 q^{58} + 29 q^{59} - 21 q^{60} - 70 q^{61} - 73 q^{62} + 12 q^{63} - 32 q^{64} - 6 q^{65} + 130 q^{66} - 124 q^{67} + 24 q^{68} + 17 q^{69} + q^{70} + 4 q^{71} - 154 q^{72} - 49 q^{73} + 60 q^{74} + 52 q^{76} - 37 q^{77} - 62 q^{78} - 28 q^{79} + 24 q^{80} - 9 q^{81} + 122 q^{82} - 48 q^{83} - 88 q^{84} - 15 q^{85} - 62 q^{86} - 14 q^{87} + 114 q^{88} - 116 q^{89} + 18 q^{90} + 21 q^{91} + 83 q^{92} + 101 q^{93} - 75 q^{94} + 8 q^{95} - 53 q^{96} + 36 q^{97} + 20 q^{98} - 85 q^{99}+O(q^{100}) \) 60 * q - q^2 + 10 * q^3 - 19 * q^4 + 15 * q^5 + 18 * q^6 + 14 * q^7 + 8 * q^8 - 9 * q^9 - 14 * q^10 + 15 * q^11 - 84 * q^12 + q^13 - q^14 - 10 * q^15 - 29 * q^16 + 15 * q^17 - 13 * q^18 - 8 * q^19 + 24 * q^20 + 28 * q^22 - 78 * q^23 + 15 * q^24 - 15 * q^25 + 20 * q^26 + 22 * q^27 - 47 * q^28 - 11 * q^29 + 12 * q^30 + 10 * q^32 - 12 * q^33 - 14 * q^34 + 11 * q^35 + 27 * q^36 + 26 * q^37 + 87 * q^38 - 14 * q^39 - 8 * q^40 - 14 * q^41 - 27 * q^42 + 28 * q^43 - 56 * q^45 + 39 * q^46 + 45 * q^47 + 16 * q^48 - 17 * q^49 - q^50 - 10 * q^51 + 24 * q^52 + 65 * q^53 - 94 * q^54 + 5 * q^55 - 144 * q^56 + 32 * q^57 + 48 * q^58 + 29 * q^59 - 21 * q^60 - 70 * q^61 - 73 * q^62 + 12 * q^63 - 32 * q^64 - 6 * q^65 + 130 * q^66 - 124 * q^67 + 24 * q^68 + 17 * q^69 + q^70 + 4 * q^71 - 154 * q^72 - 49 * q^73 + 60 * q^74 + 52 * q^76 - 37 * q^77 - 62 * q^78 - 28 * q^79 + 24 * q^80 - 9 * q^81 + 122 * q^82 - 48 * q^83 - 88 * q^84 - 15 * q^85 - 62 * q^86 - 14 * q^87 + 114 * q^88 - 116 * q^89 + 18 * q^90 + 21 * q^91 + 83 * q^92 + 101 * q^93 - 75 * q^94 + 8 * q^95 - 53 * q^96 + 36 * q^97 + 20 * q^98 - 85 * q^99

Introduction

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