LMFDB - Embedded newform 336.2.w.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.1
Root			$1.10050 + 0.888196i$ of defining polynomial
Character	$\chi$	$=$	336.85
Dual form			336.2.w.a.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33348 + 0.470984i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.55635 - 1.25610i) q^{4} +(2.01011 + 2.01011i) q^{5} +(0.609878 - 1.27595i) q^{6} +1.00000i q^{7} +(-1.48376 + 2.40800i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.33348 + 0.470984i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.55635 - 1.25610i) q^{4} +(2.01011 + 2.01011i) q^{5} +(0.609878 - 1.27595i) q^{6} +1.00000i q^{7} +(-1.48376 + 2.40800i) q^{8} -1.00000i q^{9} +(-3.62718 - 1.73372i) q^{10} +(1.19999 + 1.19999i) q^{11} +(-0.212308 + 1.98870i) q^{12} +(1.92519 - 1.92519i) q^{13} +(-0.470984 - 1.33348i) q^{14} -2.84273 q^{15} +(0.844433 - 3.90985i) q^{16} +1.24973 q^{17} +(0.470984 + 1.33348i) q^{18} +(-0.720066 + 0.720066i) q^{19} +(5.65333 + 0.603534i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-2.16534 - 1.03499i) q^{22} +8.18862i q^{23} +(-0.653538 - 2.75189i) q^{24} +3.08110i q^{25} +(-1.66047 + 3.47394i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.25610 + 1.55635i) q^{28} +(-1.27746 + 1.27746i) q^{29} +(3.79073 - 1.33888i) q^{30} -10.8193 q^{31} +(0.715443 + 5.61143i) q^{32} -1.69704 q^{33} +(-1.66650 + 0.588605i) q^{34} +(-2.01011 + 2.01011i) q^{35} +(-1.25610 - 1.55635i) q^{36} +(5.38468 + 5.38468i) q^{37} +(0.621055 - 1.29934i) q^{38} +2.72263i q^{39} +(-7.82287 + 1.85783i) q^{40} +4.30290i q^{41} +(1.27595 + 0.609878i) q^{42} +(0.310922 + 0.310922i) q^{43} +(3.37490 + 0.360295i) q^{44} +(2.01011 - 2.01011i) q^{45} +(-3.85671 - 10.9194i) q^{46} +6.10797 q^{47} +(2.16758 + 3.36179i) q^{48} -1.00000 q^{49} +(-1.45115 - 4.10859i) q^{50} +(-0.883695 + 0.883695i) q^{51} +(0.578035 - 5.41448i) q^{52} +(-1.34951 - 1.34951i) q^{53} +(-1.27595 - 0.609878i) q^{54} +4.82422i q^{55} +(-2.40800 - 1.48376i) q^{56} -1.01833i q^{57} +(1.10180 - 2.30513i) q^{58} +(-10.2730 - 10.2730i) q^{59} +(-4.42427 + 3.57075i) q^{60} +(10.2386 - 10.2386i) q^{61} +(14.4273 - 5.09571i) q^{62} +1.00000 q^{63} +(-3.59693 - 7.14578i) q^{64} +7.73968 q^{65} +(2.26297 - 0.799279i) q^{66} +(1.99158 - 1.99158i) q^{67} +(1.94502 - 1.56979i) q^{68} +(-5.79023 - 5.79023i) q^{69} +(1.73372 - 3.62718i) q^{70} -4.97742i q^{71} +(2.40800 + 1.48376i) q^{72} +9.75342i q^{73} +(-9.71648 - 4.64427i) q^{74} +(-2.17867 - 2.17867i) q^{75} +(-0.216199 + 2.02515i) q^{76} +(-1.19999 + 1.19999i) q^{77} +(-1.28231 - 3.63057i) q^{78} +15.7018 q^{79} +(9.55664 - 6.16183i) q^{80} -1.00000 q^{81} +(-2.02660 - 5.73784i) q^{82} +(3.53556 - 3.53556i) q^{83} +(-1.98870 - 0.212308i) q^{84} +(2.51211 + 2.51211i) q^{85} +(-0.561049 - 0.268170i) q^{86} -1.80660i q^{87} +(-4.67006 + 1.10908i) q^{88} +2.86694i q^{89} +(-1.73372 + 3.62718i) q^{90} +(1.92519 + 1.92519i) q^{91} +(10.2857 + 12.7443i) q^{92} +(7.65037 - 7.65037i) q^{93} +(-8.14487 + 2.87676i) q^{94} -2.89483 q^{95} +(-4.47377 - 3.46199i) q^{96} -8.40145 q^{97} +(1.33348 - 0.470984i) q^{98} +(1.19999 - 1.19999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4}+O(q^{10}) $ 20 * q + 4 * q^4	$ 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.33348	+	0.470984i	−0.942914	+	0.333036i
$2$	−1.33348	+	0.470984i	−0.942914	+	0.333036i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.55635	−	1.25610i	0.778174	−	0.628049i
$5$	2.01011	+	2.01011i	0.898949	+	0.898949i	0.995343	−	0.0963939i	$-0.0307308\pi$
$5$	2.01011	+	2.01011i	0.898949	+	0.898949i	−0.0963939	+	0.995343i	$0.530731\pi$
$6$	0.609878	−	1.27595i	0.248982	−	0.520905i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.48376	+	2.40800i	−0.524588	+	0.851356i
$9$		−	1.00000i		−	0.333333i
$10$	−3.62718	−	1.73372i	−1.14701	−	0.548249i
$11$	1.19999	+	1.19999i	0.361810	+	0.361810i	0.864479	−	0.502669i	$-0.167649\pi$
$11$	1.19999	+	1.19999i	0.361810	+	0.361810i	−0.502669	+	0.864479i	$0.667649\pi$
$12$	−0.212308	+	1.98870i	−0.0612880	+	0.574088i
$13$	1.92519	−	1.92519i	0.533951	−	0.533951i	−0.387795	−	0.921746i	$-0.626763\pi$
$13$	1.92519	−	1.92519i	0.533951	−	0.533951i	0.921746	+	0.387795i	$0.126763\pi$
$14$	−0.470984	−	1.33348i	−0.125876	−	0.356388i
$15$	−2.84273			−0.733989
$16$	0.844433	−	3.90985i	0.211108	−	0.977463i
$17$	1.24973			0.303105			0.151553	−	0.988449i	$-0.451573\pi$
$17$	1.24973			0.303105			0.151553	+	0.988449i	$0.451573\pi$
$18$	0.470984	+	1.33348i	0.111012	+	0.314305i
$19$	−0.720066	+	0.720066i	−0.165195	+	0.165195i	−0.784863	−	0.619669i	$-0.787267\pi$
$19$	−0.720066	+	0.720066i	−0.165195	+	0.165195i	0.619669	+	0.784863i	$0.287267\pi$
$20$	5.65333	+	0.603534i	1.26412	+	0.134954i
$21$	−0.707107	−	0.707107i	−0.154303	−	0.154303i
$22$	−2.16534	−	1.03499i	−0.461651	−	0.220660i
$23$			8.18862i			1.70744i	0.520729	+	0.853722i	$0.325660\pi$
$23$			8.18862i			1.70744i	−0.520729	+	0.853722i	$0.674340\pi$
$24$	−0.653538	−	2.75189i	−0.133403	−	0.561727i
$25$			3.08110i			0.616220i
$26$	−1.66047	+	3.47394i	−0.325645	+	0.681295i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.25610	+	1.55635i	0.237380	+	0.294122i
$29$	−1.27746	+	1.27746i	−0.237218	+	0.237218i	−0.815697	−	0.578479i	$-0.803646\pi$
$29$	−1.27746	+	1.27746i	−0.237218	+	0.237218i	0.578479	+	0.815697i	$0.303646\pi$
$30$	3.79073	−	1.33888i	0.692089	−	0.244445i
$31$	−10.8193			−1.94320			−0.971599	−	0.236635i	$-0.923955\pi$
$31$	−10.8193			−1.94320			−0.971599	+	0.236635i	$0.923955\pi$
$32$	0.715443	+	5.61143i	0.126474	+	0.991970i
$33$	−1.69704			−0.295416
$34$	−1.66650	+	0.588605i	−0.285802	+	0.100945i
$35$	−2.01011	+	2.01011i	−0.339771	+	0.339771i
$36$	−1.25610	−	1.55635i	−0.209350	−	0.259391i
$37$	5.38468	+	5.38468i	0.885236	+	0.885236i	0.994061	−	0.108825i	$-0.0347087\pi$
$37$	5.38468	+	5.38468i	0.885236	+	0.885236i	−0.108825	+	0.994061i	$0.534709\pi$
$38$	0.621055	−	1.29934i	0.100748	−	0.210780i
$39$			2.72263i			0.435969i
$40$	−7.82287	+	1.85783i	−1.23690	+	0.293749i
$41$			4.30290i			0.672000i	0.941862	+	0.336000i	$0.109074\pi$
$41$			4.30290i			0.672000i	−0.941862	+	0.336000i	$0.890926\pi$
$42$	1.27595	+	0.609878i	0.196883	+	0.0941062i
$43$	0.310922	+	0.310922i	0.0474152	+	0.0474152i	0.730417	−	0.683002i	$-0.239326\pi$
$43$	0.310922	+	0.310922i	0.0474152	+	0.0474152i	−0.683002	+	0.730417i	$0.739326\pi$
$44$	3.37490	+	0.360295i	0.508785	+	0.0543165i
$45$	2.01011	−	2.01011i	0.299650	−	0.299650i
$46$	−3.85671	−	10.9194i	−0.568641	−	1.60997i
$47$	6.10797			0.890939			0.445470	−	0.895297i	$-0.353037\pi$
$47$	6.10797			0.890939			0.445470	+	0.895297i	$0.353037\pi$
$48$	2.16758	+	3.36179i	0.312863	+	0.485232i
$49$	−1.00000			−0.142857
$50$	−1.45115	−	4.10859i	−0.205224	−	0.581042i
$51$	−0.883695	+	0.883695i	−0.123742	+	0.123742i
$52$	0.578035	−	5.41448i	0.0801590	−	0.750854i
$53$	−1.34951	−	1.34951i	−0.185370	−	0.185370i	0.608321	−	0.793691i	$-0.291843\pi$
$53$	−1.34951	−	1.34951i	−0.185370	−	0.185370i	−0.793691	+	0.608321i	$0.791843\pi$
$54$	−1.27595	−	0.609878i	−0.173635	−	0.0829938i
$55$			4.82422i			0.650497i
$56$	−2.40800	−	1.48376i	−0.321783	−	0.198275i
$57$		−	1.01833i		−	0.134881i
$58$	1.10180	−	2.30513i	0.144674	−	0.302678i
$59$	−10.2730	−	10.2730i	−1.33743	−	1.33743i	−0.898545	−	0.438882i	$-0.855375\pi$
$59$	−10.2730	−	10.2730i	−1.33743	−	1.33743i	−0.438882	−	0.898545i	$-0.644625\pi$
$60$	−4.42427	+	3.57075i	−0.571171	+	0.460981i
$61$	10.2386	−	10.2386i	1.31092	−	1.31092i	0.390178	−	0.920740i	$-0.372414\pi$
$61$	10.2386	−	10.2386i	1.31092	−	1.31092i	0.920740	−	0.390178i	$-0.127586\pi$
$62$	14.4273	−	5.09571i	1.83227	−	0.647155i
$63$	1.00000			0.125988
$64$	−3.59693	−	7.14578i	−0.449616	−	0.893222i
$65$	7.73968			0.959990
$66$	2.26297	−	0.799279i	0.278552	−	0.0983844i
$67$	1.99158	−	1.99158i	0.243310	−	0.243310i	−0.574908	−	0.818218i	$-0.694962\pi$
$67$	1.99158	−	1.99158i	0.243310	−	0.243310i	0.818218	+	0.574908i	$0.194962\pi$
$68$	1.94502	−	1.56979i	0.235868	−	0.190365i
$69$	−5.79023	−	5.79023i	−0.697061	−	0.697061i
$70$	1.73372	−	3.62718i	0.207219	−	0.433531i
$71$		−	4.97742i		−	0.590711i	−0.955387	−	0.295356i	$-0.904562\pi$
$71$		−	4.97742i		−	0.590711i	0.955387	−	0.295356i	$-0.0954381\pi$
$72$	2.40800	+	1.48376i	0.283785	+	0.174863i
$73$			9.75342i			1.14155i	0.821106	+	0.570776i	$0.193357\pi$
$73$			9.75342i			1.14155i	−0.821106	+	0.570776i	$0.806643\pi$
$74$	−9.71648	−	4.64427i	−1.12952	−	0.539886i
$75$	−2.17867	−	2.17867i	−0.251571	−	0.251571i
$76$	−0.216199	+	2.02515i	−0.0247997	+	0.232300i
$77$	−1.19999	+	1.19999i	−0.136751	+	0.136751i
$78$	−1.28231	−	3.63057i	−0.145194	−	0.411081i
$79$	15.7018			1.76660			0.883298	−	0.468813i	$-0.155318\pi$
$79$	15.7018			1.76660			0.883298	+	0.468813i	$0.155318\pi$
$80$	9.55664	−	6.16183i	1.06847	−	0.688914i
$81$	−1.00000			−0.111111
$82$	−2.02660	−	5.73784i	−0.223800	−	0.633638i
$83$	3.53556	−	3.53556i	0.388078	−	0.388078i	−0.485923	−	0.874002i	$-0.661516\pi$
$83$	3.53556	−	3.53556i	0.388078	−	0.388078i	0.874002	+	0.485923i	$0.161516\pi$
$84$	−1.98870	−	0.212308i	−0.216985	−	0.0231647i
$85$	2.51211	+	2.51211i	0.272476	+	0.272476i
$86$	−0.561049	−	0.268170i	−0.0604994	−	0.0289175i
$87$		−	1.80660i		−	0.193687i
$88$	−4.67006	+	1.10908i	−0.497830	+	0.118228i
$89$			2.86694i			0.303895i	0.988389	+	0.151947i	$0.0485544\pi$
$89$			2.86694i			0.303895i	−0.988389	+	0.151947i	$0.951446\pi$
$90$	−1.73372	+	3.62718i	−0.182750	+	0.382338i
$91$	1.92519	+	1.92519i	0.201814	+	0.201814i
$92$	10.2857	+	12.7443i	1.07236	+	1.32869i
$93$	7.65037	−	7.65037i	0.793307	−	0.793307i
$94$	−8.14487	+	2.87676i	−0.840079	+	0.296715i
$95$	−2.89483			−0.297003
$96$	−4.47377	−	3.46199i	−0.456603	−	0.353337i
$97$	−8.40145			−0.853038			−0.426519	−	0.904478i	$-0.640260\pi$
$97$	−8.40145			−0.853038			−0.426519	+	0.904478i	$0.640260\pi$
$98$	1.33348	−	0.470984i	0.134702	−	0.0475766i
$99$	1.19999	−	1.19999i	0.120603	−	0.120603i
$100$	3.87017	+	4.79526i	0.387017	+	0.479526i
$101$	−7.84089	−	7.84089i	−0.780198	−	0.780198i	0.199666	−	0.979864i	$-0.436014\pi$
$101$	−7.84089	−	7.84089i	−0.780198	−	0.780198i	−0.979864	+	0.199666i	$0.936014\pi$
$102$	0.762185	−	1.59460i	0.0754676	−	0.157889i
$103$		−	4.47471i		−	0.440906i	−0.975398	−	0.220453i	$-0.929246\pi$
$103$		−	4.47471i		−	0.440906i	0.975398	−	0.220453i	$-0.0707536\pi$
$104$	1.77934	+	7.49236i	0.174479	+	0.734687i
$105$		−	2.84273i		−	0.277422i
$106$	2.43515	+	1.16395i	0.236523	+	0.113053i
$107$	−6.88767	−	6.88767i	−0.665856	−	0.665856i	0.290898	−	0.956754i	$-0.406046\pi$
$107$	−6.88767	−	6.88767i	−0.665856	−	0.665856i	−0.956754	+	0.290898i	$0.906046\pi$
$108$	1.98870	+	0.212308i	0.191363	+	0.0204293i
$109$	14.1226	−	14.1226i	1.35270	−	1.35270i	0.470062	−	0.882633i	$-0.344231\pi$
$109$	14.1226	−	14.1226i	1.35270	−	1.35270i	0.882633	−	0.470062i	$-0.155769\pi$
$110$	−2.27213	−	6.43301i	−0.216639	−	0.613363i
$111$	−7.61509			−0.722792
$112$	3.90985	+	0.844433i	0.369446	+	0.0797914i
$113$	−7.45355			−0.701171			−0.350585	−	0.936531i	$-0.614017\pi$
$113$	−7.45355			−0.701171			−0.350585	+	0.936531i	$0.614017\pi$
$114$	0.479616	+	1.35792i	0.0449202	+	0.127181i
$115$	−16.4600	+	16.4600i	−1.53491	+	1.53491i
$116$	−0.383555	+	3.59278i	−0.0356122	+	0.333581i
$117$	−1.92519	−	1.92519i	−0.177984	−	0.177984i
$118$	18.5372	+	8.86041i	1.70649	+	0.815667i
$119$			1.24973i			0.114563i
$120$	4.21792	−	6.84529i	0.385042	−	0.624886i
$121$		−	8.12006i		−	0.738187i
$122$	−8.83076	+	18.4752i	−0.799499	+	1.67267i
$123$	−3.04261	−	3.04261i	−0.274343	−	0.274343i
$124$	−16.8385	+	13.5901i	−1.51214	+	1.22042i
$125$	3.85720	−	3.85720i	0.344999	−	0.344999i
$126$	−1.33348	+	0.470984i	−0.118796	+	0.0419586i
$127$	14.8202			1.31508			0.657539	−	0.753421i	$-0.271598\pi$
$127$	14.8202			1.31508			0.657539	+	0.753421i	$0.271598\pi$
$128$	8.16199	+	7.83467i	0.721424	+	0.692493i
$129$	−0.439710			−0.0387144
$130$	−10.3207	+	3.64527i	−0.905188	+	0.319711i
$131$	−2.59589	+	2.59589i	−0.226804	+	0.226804i	−0.811356	−	0.584552i	$-0.801270\pi$
$131$	−2.59589	+	2.59589i	−0.226804	+	0.226804i	0.584552	+	0.811356i	$0.301270\pi$
$132$	−2.64118	+	2.13165i	−0.229885	+	0.185536i
$133$	−0.720066	−	0.720066i	−0.0624377	−	0.0624377i
$134$	−1.71773	+	3.59374i	−0.148389	+	0.310452i
$135$			2.84273i			0.244663i
$136$	−1.85430	+	3.00936i	−0.159005	+	0.258050i
$137$		−	4.13193i		−	0.353015i	−0.984299	−	0.176507i	$-0.943520\pi$
$137$		−	4.13193i		−	0.353015i	0.984299	−	0.176507i	$-0.0564799\pi$
$138$	10.4483	+	4.99405i	0.889416	+	0.425122i
$139$	5.21659	+	5.21659i	0.442465	+	0.442465i	0.892840	−	0.450374i	$-0.148709\pi$
$139$	5.21659	+	5.21659i	0.442465	+	0.442465i	−0.450374	+	0.892840i	$0.648709\pi$
$140$	−0.603534	+	5.65333i	−0.0510079	+	0.477794i
$141$	−4.31899	+	4.31899i	−0.363724	+	0.363724i
$142$	2.34429	+	6.63730i	0.196728	+	0.556990i
$143$	4.62040			0.386377
$144$	−3.90985	−	0.844433i	−0.325821	−	0.0703694i
$145$	−5.13566			−0.426493
$146$	−4.59371	−	13.0060i	−0.380178	−	1.07638i
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$	15.1441	+	1.61674i	1.24484	+	0.132896i
$149$	−0.139187	−	0.139187i	−0.0114027	−	0.0114027i	0.701382	−	0.712785i	$-0.252567\pi$
$149$	−0.139187	−	0.139187i	−0.0114027	−	0.0114027i	−0.712785	+	0.701382i	$0.752567\pi$
$150$	3.93133	+	1.87909i	0.320992	+	0.153427i
$151$			9.05020i			0.736495i	0.929728	+	0.368247i	$0.120042\pi$
$151$			9.05020i			0.736495i	−0.929728	+	0.368247i	$0.879958\pi$
$152$	−0.665515	−	2.80232i	−0.0539804	−	0.227298i
$153$		−	1.24973i		−	0.101035i
$154$	1.03499	−	2.16534i	0.0834015	−	0.174488i
$155$	−21.7479	−	21.7479i	−1.74684	−	1.74684i
$156$	3.41989	+	4.23735i	0.273810	+	0.339260i
$157$	9.76247	−	9.76247i	0.779130	−	0.779130i	−0.200553	−	0.979683i	$-0.564274\pi$
$157$	9.76247	−	9.76247i	0.779130	−	0.779130i	0.979683	+	0.200553i	$0.0642738\pi$
$158$	−20.9381	+	7.39532i	−1.66575	+	0.588340i
$159$	1.90850			0.151354
$160$	−9.84148	+	12.7177i	−0.778037	+	1.00542i
$161$	−8.18862			−0.645353
$162$	1.33348	−	0.470984i	0.104768	−	0.0370040i
$163$	−5.52971	+	5.52971i	−0.433121	+	0.433121i	−0.889689	−	0.456568i	$-0.849079\pi$
$163$	−5.52971	+	5.52971i	−0.433121	+	0.433121i	0.456568	+	0.889689i	$0.349079\pi$
$164$	5.40487	+	6.69681i	0.422049	+	0.522933i
$165$	−3.41124	−	3.41124i	−0.265564	−	0.265564i
$166$	−3.04941	+	6.37980i	−0.236680	+	0.495169i
$167$			3.97093i			0.307280i	0.988127	+	0.153640i	$0.0490996\pi$
$167$			3.97093i			0.307280i	−0.988127	+	0.153640i	$0.950900\pi$
$168$	2.75189	−	0.653538i	0.212313	−	0.0504215i
$169$			5.58731i			0.429793i
$170$	−4.53301	−	2.16668i	−0.347666	−	0.166177i
$171$	0.720066	+	0.720066i	0.0550648	+	0.0550648i
$172$	0.874452	+	0.0933540i	0.0666763	+	0.00711818i
$173$	−12.8323	+	12.8323i	−0.975619	+	0.975619i	−0.999710	−	0.0240906i	$-0.992331\pi$
$173$	−12.8323	+	12.8323i	−0.975619	+	0.975619i	0.0240906	+	0.999710i	$0.492331\pi$
$174$	0.850879	+	2.40906i	0.0645050	+	0.182631i
$175$	−3.08110			−0.232909
$176$	5.70508	−	3.67846i	0.430037	−	0.277275i
$177$	14.5282			1.09200
$178$	−1.35028	−	3.82301i	−0.101208	−	0.286547i
$179$	16.0865	−	16.0865i	1.20236	−	1.20236i	0.228917	−	0.973446i	$-0.426482\pi$
$179$	16.0865	−	16.0865i	1.20236	−	1.20236i	0.973446	−	0.228917i	$-0.0735183\pi$
$180$	0.603534	−	5.65333i	0.0449847	−	0.421374i
$181$	−5.13842	−	5.13842i	−0.381936	−	0.381936i	0.489863	−	0.871799i	$-0.337047\pi$
$181$	−5.13842	−	5.13842i	−0.381936	−	0.381936i	−0.871799	+	0.489863i	$0.837047\pi$
$182$	−3.47394	−	1.66047i	−0.257505	−	0.123082i
$183$			14.4796i			1.07036i
$184$	−19.7182	−	12.1499i	−1.45364	−	0.895704i
$185$			21.6476i			1.59157i
$186$	−6.59843	+	13.8048i	−0.483820	+	1.01222i
$187$	1.49967	+	1.49967i	0.109666	+	0.109666i
$188$	9.50612	−	7.67221i	0.693305	−	0.559554i
$189$	−0.707107	+	0.707107i	−0.0514344	+	0.0514344i
$190$	3.86020	−	1.36342i	0.280048	−	0.0989128i
$191$	21.8736			1.58272			0.791358	−	0.611354i	$-0.209375\pi$
$191$	21.8736			1.58272			0.791358	+	0.611354i	$0.209375\pi$
$192$	7.59624	+	2.50942i	0.548211	+	0.181102i
$193$	−4.53207			−0.326225			−0.163113	−	0.986607i	$-0.552153\pi$
$193$	−4.53207			−0.326225			−0.163113	+	0.986607i	$0.552153\pi$
$194$	11.2032	−	3.95695i	0.804342	−	0.284093i
$195$	−5.47278	+	5.47278i	−0.391914	+	0.391914i
$196$	−1.55635	+	1.25610i	−0.111168	+	0.0897213i
$197$	16.9905	+	16.9905i	1.21052	+	1.21052i	0.970855	+	0.239666i	$0.0770379\pi$
$197$	16.9905	+	16.9905i	1.21052	+	1.21052i	0.239666	+	0.970855i	$0.422962\pi$
$198$	−1.03499	+	2.16534i	−0.0735532	+	0.153884i
$199$		−	4.63377i		−	0.328479i	−0.986420	−	0.164240i	$-0.947483\pi$
$199$		−	4.63377i		−	0.328479i	0.986420	−	0.164240i	$-0.0525170\pi$
$200$	−7.41929	−	4.57161i	−0.524623	−	0.323261i
$201$			2.81652i			0.198662i
$202$	14.1486	+	6.76275i	0.995494	+	0.475825i
$203$	−1.27746	−	1.27746i	−0.0896599	−	0.0896599i
$204$	−0.265328	+	2.48535i	−0.0185767	+	0.174009i
$205$	−8.64931	+	8.64931i	−0.604094	+	0.604094i
$206$	2.10752	+	5.96694i	0.146838	+	0.415737i
$207$	8.18862			0.569148
$208$	−5.90150	−	9.15289i	−0.409196	−	0.634639i
$209$	−1.72814			−0.119538
$210$	1.33888	+	3.79073i	0.0923915	+	0.261585i
$211$	1.26697	−	1.26697i	0.0872219	−	0.0872219i	−0.662150	−	0.749372i	$-0.730356\pi$
$211$	1.26697	−	1.26697i	0.0872219	−	0.0872219i	0.749372	+	0.662150i	$0.230356\pi$
$212$	−3.79543	−	0.405189i	−0.260671	−	0.0278285i
$213$	3.51957	+	3.51957i	0.241157	+	0.241157i
$214$	12.4286	+	5.94060i	0.849599	+	0.406091i
$215$			1.24998i			0.0852477i
$216$	−2.75189	+	0.653538i	−0.187242	+	0.0444676i
$217$		−	10.8193i		−	0.734459i
$218$	−12.1807	+	25.4837i	−0.824979	+	1.72597i
$219$	−6.89671	−	6.89671i	−0.466036	−	0.466036i
$220$	6.05969	+	7.50816i	0.408544	+	0.506200i
$221$	2.40597	−	2.40597i	0.161843	−	0.161843i
$222$	10.1546	−	3.58659i	0.681531	−	0.240716i
$223$	−6.29832			−0.421767			−0.210884	−	0.977511i	$-0.567634\pi$
$223$	−6.29832			−0.421767			−0.210884	+	0.977511i	$0.567634\pi$
$224$	−5.61143	+	0.715443i	−0.374929	+	0.0478025i
$225$	3.08110			0.205407
$226$	9.93917	−	3.51051i	0.661144	−	0.233515i
$227$	17.8116	−	17.8116i	1.18220	−	1.18220i	0.203025	−	0.979173i	$-0.434923\pi$
$227$	17.8116	−	17.8116i	1.18220	−	1.18220i	0.979173	−	0.203025i	$-0.0650774\pi$
$228$	−1.27912	−	1.58487i	−0.0847117	−	0.104961i
$229$	1.15235	+	1.15235i	0.0761496	+	0.0761496i	0.744156	−	0.668006i	$-0.232852\pi$
$229$	1.15235	+	1.15235i	0.0761496	+	0.0761496i	−0.668006	+	0.744156i	$0.732852\pi$
$230$	14.1967	−	29.7016i	0.936105	−	1.95846i
$231$		−	1.69704i		−	0.111657i
$232$	−1.18068	−	4.97155i	−0.0775154	−	0.326398i
$233$		−	11.7361i		−	0.768857i	−0.923155	−	0.384429i	$-0.874398\pi$
$233$		−	11.7361i		−	0.768857i	0.923155	−	0.384429i	$-0.125602\pi$
$234$	3.47394	+	1.66047i	0.227098	+	0.108548i
$235$	12.2777	+	12.2777i	0.800909	+	0.800909i
$236$	−28.8922	−	3.08445i	−1.88072	−	0.200780i
$237$	−11.1029	+	11.1029i	−0.721209	+	0.721209i
$238$	−0.588605	−	1.66650i	−0.0381536	−	0.108023i
$239$	−15.4758			−1.00105			−0.500524	−	0.865723i	$-0.666859\pi$
$239$	−15.4758			−1.00105			−0.500524	+	0.865723i	$0.666859\pi$
$240$	−2.40049	+	11.1146i	−0.154951	+	0.717447i
$241$	−17.3101			−1.11504			−0.557522	−	0.830162i	$-0.688248\pi$
$241$	−17.3101			−1.11504			−0.557522	+	0.830162i	$0.688248\pi$
$242$	3.82442	+	10.8280i	0.245843	+	0.696047i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	3.07412	−	28.7955i	0.196801	−	1.84344i
$245$	−2.01011	−	2.01011i	−0.128421	−	0.128421i
$246$	5.49029	+	2.62424i	0.350048	+	0.167316i
$247$			2.77252i			0.176412i
$248$	16.0532	−	26.0528i	1.01938	−	1.65435i
$249$			5.00004i			0.316865i
$250$	−3.32683	+	6.96019i	−0.210407	+	0.440201i
$251$	−4.97541	−	4.97541i	−0.314045	−	0.314045i	0.532429	−	0.846475i	$-0.321279\pi$
$251$	−4.97541	−	4.97541i	−0.314045	−	0.314045i	−0.846475	+	0.532429i	$0.821279\pi$
$252$	1.55635	−	1.25610i	0.0980407	−	0.0791268i
$253$	−9.82624	+	9.82624i	−0.617770	+	0.617770i
$254$	−19.7624	+	6.98007i	−1.24000	+	0.437969i
$255$	−3.55265			−0.222476
$256$	−14.5739	−	6.60322i	−0.910867	−	0.412701i
$257$	−17.6065			−1.09827			−0.549133	−	0.835735i	$-0.685042\pi$
$257$	−17.6065			−1.09827			−0.549133	+	0.835735i	$0.685042\pi$
$258$	0.586346	−	0.207097i	0.0365043	−	0.0128933i
$259$	−5.38468	+	5.38468i	−0.334588	+	0.334588i
$260$	12.0456	−	9.72181i	0.747039	−	0.602921i
$261$	1.27746	+	1.27746i	0.0790726	+	0.0790726i
$262$	2.23895	−	4.68419i	0.138323	−	0.289391i
$263$		−	31.6849i		−	1.95377i	−0.213759	−	0.976886i	$-0.568571\pi$
$263$		−	31.6849i		−	1.95377i	0.213759	−	0.976886i	$-0.431429\pi$
$264$	2.51799	−	4.08647i	0.154972	−	0.251505i
$265$		−	5.42534i		−	0.333276i
$266$	1.29934	+	0.621055i	0.0796673	+	0.0380793i
$267$	−2.02723	−	2.02723i	−0.124064	−	0.124064i
$268$	0.597969	−	5.60121i	0.0365268	−	0.342148i
$269$	5.40521	−	5.40521i	0.329561	−	0.329561i	−0.522858	−	0.852420i	$-0.675134\pi$
$269$	5.40521	−	5.40521i	0.329561	−	0.329561i	0.852420	+	0.522858i	$0.175134\pi$
$270$	−1.33888	−	3.79073i	−0.0814817	−	0.230696i
$271$	11.1293			0.676057			0.338028	−	0.941136i	$-0.390240\pi$
$271$	11.1293			0.676057			0.338028	+	0.941136i	$0.390240\pi$
$272$	1.05532	−	4.88627i	0.0639880	−	0.296274i
$273$	−2.72263			−0.164781
$274$	1.94607	+	5.50985i	0.117567	+	0.332862i
$275$	−3.69728	+	3.69728i	−0.222954	+	0.222954i
$276$	−16.2847	−	1.73851i	−0.980223	−	0.104646i
$277$	16.4865	+	16.4865i	0.990580	+	0.990580i	0.999956	−	0.00937626i	$-0.00298460\pi$
$277$	16.4865	+	16.4865i	0.990580	+	0.990580i	−0.00937626	+	0.999956i	$0.502985\pi$
$278$	−9.41316	−	4.49929i	−0.564564	−	0.269850i
$279$			10.8193i			0.647732i
$280$	−1.85783	−	7.82287i	−0.111027	−	0.467506i
$281$			16.9337i			1.01018i	0.863067	+	0.505089i	$0.168540\pi$
$281$			16.9337i			1.01018i	−0.863067	+	0.505089i	$0.831460\pi$
$282$	3.72512	−	7.79347i	0.221827	−	0.464094i
$283$	−4.26162	−	4.26162i	−0.253327	−	0.253327i	0.569006	−	0.822333i	$-0.307328\pi$
$283$	−4.26162	−	4.26162i	−0.253327	−	0.253327i	−0.822333	+	0.569006i	$0.807328\pi$
$284$	−6.25213	−	7.74659i	−0.370996	−	0.459676i
$285$	2.04695	−	2.04695i	0.121251	−	0.121251i
$286$	−6.16122	+	2.17614i	−0.364321	+	0.128678i
$287$	−4.30290			−0.253992
$288$	5.61143	−	0.715443i	0.330657	−	0.0421579i
$289$	−15.4382			−0.908127
$290$	6.84831	−	2.41882i	0.402147	−	0.142038i
$291$	5.94073	−	5.94073i	0.348252	−	0.348252i
$292$	12.2513	+	15.1797i	0.716950	+	0.888325i
$293$	−10.5179	−	10.5179i	−0.614464	−	0.614464i	0.329642	−	0.944106i	$-0.393072\pi$
$293$	−10.5179	−	10.5179i	−0.614464	−	0.614464i	−0.944106	+	0.329642i	$0.893072\pi$
$294$	−0.609878	+	1.27595i	−0.0355688	+	0.0744149i
$295$		−	41.2996i		−	2.40456i
$296$	−20.9559	+	4.97675i	−1.21804	+	0.289268i
$297$			1.69704i			0.0984722i
$298$	0.251159	+	0.120049i	0.0145492	+	0.00695423i
$299$	15.7646	+	15.7646i	0.911691	+	0.911691i
$300$	−6.12738	−	0.654142i	−0.353765	−	0.0377669i
$301$	−0.310922	+	0.310922i	−0.0179213	+	0.0179213i
$302$	−4.26250	−	12.0683i	−0.245279	−	0.694451i
$303$	11.0887			0.637029
$304$	2.20730	+	3.42340i	0.126598	+	0.196345i
$305$	41.1614			2.35690
$306$	0.588605	+	1.66650i	0.0336483	+	0.0952673i
$307$	12.5856	−	12.5856i	0.718300	−	0.718300i	−0.249957	−	0.968257i	$-0.580416\pi$
$307$	12.5856	−	12.5856i	0.718300	−	0.718300i	0.968257	+	0.249957i	$0.0804164\pi$
$308$	−0.360295	+	3.37490i	−0.0205297	+	0.192303i
$309$	3.16410	+	3.16410i	0.179999	+	0.179999i
$310$	39.2434	+	18.7575i	2.22888	+	1.06536i
$311$		−	7.29408i		−	0.413609i	−0.978382	−	0.206805i	$-0.933694\pi$
$311$		−	7.29408i		−	0.413609i	0.978382	−	0.206805i	$-0.0663064\pi$
$312$	−6.55608	−	4.03972i	−0.371165	−	0.228704i
$313$		−	17.6793i		−	0.999293i	−0.866229	−	0.499646i	$-0.833463\pi$
$313$		−	17.6793i		−	0.999293i	0.866229	−	0.499646i	$-0.166537\pi$
$314$	−8.42010	+	17.6160i	−0.475174	+	0.994131i
$315$	2.01011	+	2.01011i	0.113257	+	0.113257i
$316$	24.4375	−	19.7231i	1.37472	−	1.10951i
$317$	−17.1763	+	17.1763i	−0.964714	+	0.964714i	−0.999398	−	0.0346839i	$-0.988958\pi$
$317$	−17.1763	+	17.1763i	−0.964714	+	0.964714i	0.0346839	+	0.999398i	$0.488958\pi$
$318$	−2.54495	+	0.898874i	−0.142714	+	0.0504063i
$319$	−3.06586			−0.171655
$320$	7.13359	−	21.5940i	0.398780	−	1.20714i
$321$	9.74064			0.543669
$322$	10.9194	−	3.85671i	0.608513	−	0.214926i
$323$	−0.899891	+	0.899891i	−0.0500713	+	0.0500713i
$324$	−1.55635	+	1.25610i	−0.0864637	+	0.0697832i
$325$	5.93170	+	5.93170i	0.329031	+	0.329031i
$326$	4.76936	−	9.97818i	0.264151	−	0.552640i
$327$			19.9723i			1.10447i
$328$	−10.3614	−	6.38446i	−0.572112	−	0.352523i
$329$			6.10797i			0.336743i
$330$	6.15546	+	2.94218i	0.338847	+	0.161962i
$331$	−1.24559	−	1.24559i	−0.0684641	−	0.0684641i	0.672046	−	0.740510i	$-0.265416\pi$
$331$	−1.24559	−	1.24559i	−0.0684641	−	0.0684641i	−0.740510	+	0.672046i	$0.765416\pi$
$332$	1.06155	−	9.94358i	0.0582600	−	0.545725i
$333$	5.38468	−	5.38468i	0.295079	−	0.295079i
$334$	−1.87025	−	5.29516i	−0.102335	−	0.289738i
$335$	8.00659			0.437447
$336$	−3.36179	+	2.16758i	−0.183400	+	0.118251i
$337$	21.7737			1.18609			0.593045	−	0.805169i	$-0.297925\pi$
$337$	21.7737			1.18609			0.593045	+	0.805169i	$0.297925\pi$
$338$	−2.63154	−	7.45057i	−0.143137	−	0.405258i
$339$	5.27046	−	5.27046i	0.286252	−	0.286252i
$340$	7.06516	+	0.754256i	0.383162	+	0.0409053i
$341$	−12.9830	−	12.9830i	−0.703068	−	0.703068i
$342$	−1.29934	−	0.621055i	−0.0702600	−	0.0335828i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.21003	+	0.287367i	−0.0652407	+	0.0154938i
$345$		−	23.2780i		−	1.25325i
$346$	11.0678	−	23.1554i	0.595008	−	1.24484i
$347$	20.7830	+	20.7830i	1.11569	+	1.11569i	0.992367	+	0.123321i	$0.0393546\pi$
$347$	20.7830	+	20.7830i	1.11569	+	1.11569i	0.123321	+	0.992367i	$0.460645\pi$
$348$	−2.26926	−	2.81169i	−0.121645	−	0.150722i
$349$	−9.63121	+	9.63121i	−0.515547	+	0.515547i	−0.916221	−	0.400674i	$-0.868776\pi$
$349$	−9.63121	+	9.63121i	−0.515547	+	0.515547i	0.400674	+	0.916221i	$0.368776\pi$
$350$	4.10859	−	1.45115i	0.219613	−	0.0775673i
$351$	2.72263			0.145323
$352$	−5.87512	+	7.59217i	−0.313145	+	0.404664i
$353$	−35.5556			−1.89243			−0.946217	−	0.323531i	$-0.895130\pi$
$353$	−35.5556			−1.89243			−0.946217	+	0.323531i	$0.895130\pi$
$354$	−19.3730	+	6.84254i	−1.02967	+	0.363677i
$355$	10.0052	−	10.0052i	0.531019	−	0.531019i
$356$	3.60115	+	4.46195i	0.190861	+	0.236483i
$357$	−0.883695	−	0.883695i	−0.0467701	−	0.0467701i
$358$	−13.8746	+	29.0276i	−0.733294	+	1.53415i
$359$			14.5283i			0.766776i	0.923587	+	0.383388i	$0.125243\pi$
$359$			14.5283i			0.766776i	−0.923587	+	0.383388i	$0.874757\pi$
$360$	1.85783	+	7.82287i	0.0979162	+	0.412301i
$361$			17.9630i			0.945422i
$362$	9.27211	+	4.43188i	0.487331	+	0.232934i
$363$	5.74175	+	5.74175i	0.301364	+	0.301364i
$364$	5.41448	+	0.578035i	0.283796	+	0.0302973i
$365$	−19.6055	+	19.6055i	−1.02620	+	1.02620i
$366$	−6.81965	−	19.3082i	−0.356469	−	1.00926i
$367$	−19.1601			−1.00015			−0.500075	−	0.865982i	$-0.666694\pi$
$367$	−19.1601			−1.00015			−0.500075	+	0.865982i	$0.666694\pi$
$368$	32.0163	+	6.91474i	1.66896	+	0.360456i
$369$	4.30290			0.224000
$370$	−10.1957	−	28.8667i	−0.530049	−	1.50071i
$371$	1.34951	−	1.34951i	0.0700632	−	0.0700632i
$372$	2.29702	−	21.5163i	0.119095	−	1.11557i
$373$	−23.3748	−	23.3748i	−1.21030	−	1.21030i	−0.970927	−	0.239374i	$-0.923058\pi$
$373$	−23.3748	−	23.3748i	−1.21030	−	1.21030i	−0.239374	−	0.970927i	$-0.576942\pi$
$374$	−2.70610	−	1.29346i	−0.139929	−	0.0668831i
$375$			5.45491i			0.281690i
$376$	−9.06275	+	14.7080i	−0.467376	+	0.758507i
$377$			4.91869i			0.253325i
$378$	0.609878	−	1.27595i	0.0313687	−	0.0656278i
$379$	−5.03700	−	5.03700i	−0.258734	−	0.258734i	0.565805	−	0.824539i	$-0.308565\pi$
$379$	−5.03700	−	5.03700i	−0.258734	−	0.258734i	−0.824539	+	0.565805i	$0.808565\pi$
$380$	−4.50536	+	3.63619i	−0.231120	+	0.186533i
$381$	−10.4794	+	10.4794i	−0.536878	+	0.536878i
$382$	−29.1680	+	10.3021i	−1.49236	+	0.527102i
$383$	−4.80910			−0.245734			−0.122867	−	0.992423i	$-0.539209\pi$
$383$	−4.80910			−0.245734			−0.122867	+	0.992423i	$0.539209\pi$
$384$	−11.3113	+	0.231450i	−0.577229	+	0.0118111i
$385$	−4.82422			−0.245865
$386$	6.04343	−	2.13453i	0.307602	−	0.108645i
$387$	0.310922	−	0.310922i	0.0158051	−	0.0158051i
$388$	−13.0756	+	10.5531i	−0.663812	+	0.535750i
$389$	18.7727	+	18.7727i	0.951813	+	0.951813i	0.998891	−	0.0470783i	$-0.0149910\pi$
$389$	18.7727	+	18.7727i	0.951813	+	0.951813i	−0.0470783	+	0.998891i	$0.514991\pi$
$390$	4.72026	−	9.87545i	0.239020	−	0.500063i
$391$			10.2336i			0.517535i
$392$	1.48376	−	2.40800i	0.0749411	−	0.121622i
$393$		−	3.67114i		−	0.185185i
$394$	−30.6587	−	14.6542i	−1.54457	−	0.738270i
$395$	31.5625	+	31.5625i	1.58808	+	1.58808i
$396$	0.360295	−	3.37490i	0.0181055	−	0.169595i
$397$	24.8947	−	24.8947i	1.24943	−	1.24943i	0.293455	−	0.955973i	$-0.405195\pi$
$397$	24.8947	−	24.8947i	1.24943	−	1.24943i	0.955973	−	0.293455i	$-0.0948051\pi$
$398$	2.18243	+	6.17905i	0.109396	+	0.309728i
$399$	1.01833			0.0509801
$400$	12.0466	+	2.60178i	0.602332	+	0.130089i
$401$	−2.62482			−0.131077			−0.0655386	−	0.997850i	$-0.520877\pi$
$401$	−2.62482			−0.131077			−0.0655386	+	0.997850i	$0.520877\pi$
$402$	−1.32654	−	3.75578i	−0.0661616	−	0.187321i
$403$	−20.8291	+	20.8291i	−1.03757	+	1.03757i
$404$	−22.0521	−	2.35422i	−1.09713	−	0.117127i
$405$	−2.01011	−	2.01011i	−0.0998833	−	0.0998833i
$406$	2.30513	+	1.10180i	0.114402	+	0.0546816i
$407$			12.9231i			0.640574i
$408$	−0.816749	−	3.43913i	−0.0404351	−	0.170262i
$409$			16.5394i			0.817822i	0.912574	+	0.408911i	$0.134091\pi$
$409$			16.5394i			0.817822i	−0.912574	+	0.408911i	$0.865909\pi$
$410$	7.46001	−	15.6074i	0.368423	−	0.770794i
$411$	2.92172	+	2.92172i	0.144118	+	0.144118i
$412$	−5.62068	−	6.96420i	−0.276911	−	0.343102i
$413$	10.2730	−	10.2730i	0.505500	−	0.505500i
$414$	−10.9194	+	3.85671i	−0.536658	+	0.189547i
$415$	14.2138			0.697726
$416$	12.1804	+	9.42569i	0.597194	+	0.462133i
$417$	−7.37737			−0.361271
$418$	2.30444	−	0.813927i	0.112714	−	0.0398105i
$419$	−4.06764	+	4.06764i	−0.198717	+	0.198717i	−0.799450	−	0.600733i	$-0.794876\pi$
$419$	−4.06764	+	4.06764i	−0.198717	+	0.198717i	0.600733	+	0.799450i	$0.294876\pi$
$420$	−3.57075	−	4.42427i	−0.174235	−	0.215882i
$421$	13.2281	+	13.2281i	0.644699	+	0.644699i	0.951707	−	0.307008i	$-0.0993279\pi$
$421$	13.2281	+	13.2281i	0.644699	+	0.644699i	−0.307008	+	0.951707i	$0.599328\pi$
$422$	−1.09276	+	2.28621i	−0.0531947	+	0.111291i
$423$		−	6.10797i		−	0.296980i
$424$	5.25198	−	1.24728i	0.255059	−	0.0605731i
$425$			3.85056i			0.186779i
$426$	−6.35094	−	3.03562i	−0.307704	−	0.147076i
$427$	10.2386	+	10.2386i	0.495480	+	0.495480i
$428$	−19.3712	−	2.06801i	−0.936342	−	0.0999612i
$429$	−3.26712	+	3.26712i	−0.157738	+	0.157738i
$430$	−0.588720	−	1.66682i	−0.0283906	−	0.0803813i
$431$	−25.5013			−1.22836			−0.614178	−	0.789167i	$-0.710512\pi$
$431$	−25.5013			−1.22836			−0.614178	+	0.789167i	$0.710512\pi$
$432$	3.36179	−	2.16758i	0.161744	−	0.104288i
$433$	−38.3125			−1.84118			−0.920592	−	0.390526i	$-0.872293\pi$
$433$	−38.3125			−1.84118			−0.920592	+	0.390526i	$0.872293\pi$
$434$	5.09571	+	14.4273i	0.244602	+	0.692532i
$435$	3.63146	−	3.63146i	0.174115	−	0.174115i
$436$	4.24028	−	39.7189i	0.203073	−	1.90219i
$437$	−5.89635	−	5.89635i	−0.282060	−	0.282060i
$438$	12.4449	+	5.94839i	0.594639	+	0.284225i
$439$		−	15.1503i		−	0.723082i	−0.932356	−	0.361541i	$-0.882251\pi$
$439$		−	15.1503i		−	0.723082i	0.932356	−	0.361541i	$-0.117749\pi$
$440$	−11.6167	−	7.15797i	−0.553805	−	0.341243i
$441$			1.00000i			0.0476190i
$442$	−2.07514	+	4.34150i	−0.0987046	+	0.206504i
$443$	−2.78395	−	2.78395i	−0.132270	−	0.132270i	0.637872	−	0.770142i	$-0.279815\pi$
$443$	−2.78395	−	2.78395i	−0.132270	−	0.132270i	−0.770142	+	0.637872i	$0.779815\pi$
$444$	−11.8517	+	9.56530i	−0.562458	+	0.453949i
$445$	−5.76286	+	5.76286i	−0.273186	+	0.273186i
$446$	8.39870	−	2.96641i	0.397690	−	0.140464i
$447$	0.196840			0.00931023
$448$	7.14578	−	3.59693i	0.337606	−	0.169939i
$449$	17.0189			0.803172			0.401586	−	0.915821i	$-0.368459\pi$
$449$	17.0189			0.803172			0.401586	+	0.915821i	$0.368459\pi$
$450$	−4.10859	+	1.45115i	−0.193681	+	0.0684079i
$451$	−5.16343	+	5.16343i	−0.243136	+	0.243136i
$452$	−11.6003	+	9.36239i	−0.545633	+	0.440370i
$453$	−6.39946	−	6.39946i	−0.300673	−	0.300673i
$454$	−15.3625	+	32.1405i	−0.720997	+	1.50843i
$455$			7.73968i			0.362842i
$456$	2.45213	+	1.51095i	0.114832	+	0.0707568i
$457$			12.0596i			0.564123i	0.959396	+	0.282061i	$0.0910182\pi$
$457$			12.0596i			0.564123i	−0.959396	+	0.282061i	$0.908982\pi$
$458$	−2.07938	−	0.993901i	−0.0971631	−	0.0464419i
$459$	0.883695	+	0.883695i	0.0412474	+	0.0412474i
$460$	−4.94210	+	46.2930i	−0.230427	+	2.15842i
$461$	5.72644	−	5.72644i	0.266707	−	0.266707i	−0.561065	−	0.827772i	$-0.689608\pi$
$461$	5.72644	−	5.72644i	0.266707	−	0.266707i	0.827772	+	0.561065i	$0.189608\pi$
$462$	0.799279	+	2.26297i	0.0371858	+	0.105283i
$463$	−35.9237			−1.66952			−0.834758	−	0.550618i	$-0.814392\pi$
$463$	−35.9237			−1.66952			−0.834758	+	0.550618i	$0.814392\pi$
$464$	3.91594	+	6.07339i	0.181793	+	0.281950i
$465$	30.7562			1.42629
$466$	5.52752	+	15.6499i	0.256057	+	0.724966i
$467$	0.383033	−	0.383033i	0.0177247	−	0.0177247i	−0.698189	−	0.715914i	$-0.746010\pi$
$467$	0.383033	−	0.383033i	0.0177247	−	0.0177247i	0.715914	+	0.698189i	$0.246010\pi$
$468$	−5.41448	−	0.578035i	−0.250285	−	0.0267197i
$469$	1.99158	+	1.99158i	0.0919626	+	0.0919626i
$470$	−22.1547	−	10.5895i	−1.02192	−	0.488457i
$471$			13.8062i			0.636157i
$472$	39.9799	−	9.49471i	1.84022	−	0.437029i
$473$			0.746206i			0.0343106i
$474$	9.57620	−	20.0348i	0.439850	−	0.920227i
$475$	−2.21860	−	2.21860i	−0.101796	−	0.101796i
$476$	1.56979	+	1.94502i	0.0719512	+	0.0891499i
$477$	−1.34951	+	1.34951i	−0.0617899	+	0.0617899i
$478$	20.6367	−	7.28888i	0.943903	−	0.333385i
$479$	40.7375			1.86135			0.930673	−	0.365853i	$-0.119223\pi$
$479$	40.7375			1.86135			0.930673	+	0.365853i	$0.119223\pi$
$480$	−2.03381	−	15.9518i	−0.0928302	−	0.728095i
$481$	20.7330			0.945345
$482$	23.0828	−	8.15281i	1.05139	−	0.371350i
$483$	5.79023	−	5.79023i	0.263464	−	0.263464i
$484$	−10.1996	−	12.6376i	−0.463618	−	0.574438i
$485$	−16.8879	−	16.8879i	−0.766838	−	0.766838i
$486$	−0.609878	+	1.27595i	−0.0276646	+	0.0578783i
$487$		−	17.2478i		−	0.781573i	−0.920481	−	0.390786i	$-0.872203\pi$
$487$		−	17.2478i		−	0.781573i	0.920481	−	0.390786i	$-0.127797\pi$
$488$	9.46294	+	39.8461i	0.428367	+	1.80375i
$489$		−	7.82020i		−	0.353641i
$490$	3.62718	+	1.73372i	0.163859	+	0.0783213i
$491$	−12.5443	−	12.5443i	−0.566118	−	0.566118i	0.364921	−	0.931039i	$-0.381096\pi$
$491$	−12.5443	−	12.5443i	−0.566118	−	0.566118i	−0.931039	+	0.364921i	$0.881096\pi$
$492$	−8.55717	−	0.913540i	−0.385787	−	0.0411855i
$493$	−1.59648	+	1.59648i	−0.0719019	+	0.0719019i
$494$	−1.30582	−	3.69711i	−0.0587514	−	0.166341i
$495$	4.82422			0.216832
$496$	−9.13615	+	42.3017i	−0.410225	+	1.89940i
$497$	4.97742			0.223268
$498$	−2.35494	−	6.66746i	−0.105527	−	0.298776i
$499$	−8.56236	+	8.56236i	−0.383304	+	0.383304i	−0.872291	−	0.488987i	$-0.837366\pi$
$499$	−8.56236	+	8.56236i	−0.383304	+	0.383304i	0.488987	+	0.872291i	$0.337366\pi$
$500$	1.15812	−	10.8482i	0.0517927	−	0.485145i
$501$	−2.80787	−	2.80787i	−0.125446	−	0.125446i
$502$	8.97796	+	4.29128i	0.400706	+	0.191529i
$503$			21.5863i			0.962488i	0.876587	+	0.481244i	$0.159815\pi$
$503$			21.5863i			0.962488i	−0.876587	+	0.481244i	$0.840185\pi$
$504$	−1.48376	+	2.40800i	−0.0660918	+	0.107261i
$505$		−	31.5221i		−	1.40272i
$506$	8.47510	−	17.7311i	0.376764	−	0.788244i
$507$	−3.95082	−	3.95082i	−0.175462	−	0.175462i
$508$	23.0653	−	18.6156i	1.02336	−	0.825933i
$509$	13.1322	−	13.1322i	0.582074	−	0.582074i	−0.353398	−	0.935473i	$-0.614974\pi$
$509$	13.1322	−	13.1322i	0.582074	−	0.582074i	0.935473	+	0.353398i	$0.114974\pi$
$510$	4.73740	−	1.67324i	0.209776	−	0.0740925i
$511$	−9.75342			−0.431466
$512$	22.5440	+	1.94120i	0.996313	+	0.0857899i
$513$	−1.01833			−0.0449602
$514$	23.4780	−	8.29241i	1.03557	−	0.365762i
$515$	8.99467	−	8.99467i	0.396352	−	0.396352i
$516$	−0.684342	+	0.552320i	−0.0301265	+	0.0243145i
$517$	7.32949	+	7.32949i	0.322351	+	0.322351i
$518$	4.64427	−	9.71648i	0.204058	−	0.426917i
$519$		−	18.1476i		−	0.796590i
$520$	−11.4838	+	18.6372i	−0.503599	+	0.817293i
$521$			11.9641i			0.524155i	0.965047	+	0.262077i	$0.0844076\pi$
$521$			11.9641i			0.524155i	−0.965047	+	0.262077i	$0.915592\pi$
$522$	−2.30513	−	1.10180i	−0.100893	−	0.0482246i
$523$	28.2756	+	28.2756i	1.23640	+	1.23640i	0.961461	+	0.274943i	$0.0886590\pi$
$523$	28.2756	+	28.2756i	1.23640	+	1.23640i	0.274943	+	0.961461i	$0.411341\pi$
$524$	−0.779413	+	7.30080i	−0.0340488	+	0.318937i
$525$	2.17867	−	2.17867i	0.0950848	−	0.0950848i
$526$	14.9231	+	42.2512i	0.650677	+	1.84224i
$527$	−13.5212			−0.588993
$528$	−1.43304	+	6.63517i	−0.0623649	+	0.288759i
$529$	−44.0534			−1.91537
$530$	2.55525	+	7.23460i	0.110993	+	0.314251i
$531$	−10.2730	+	10.2730i	−0.445809	+	0.445809i
$532$	−2.02515	−	0.216199i	−0.0878013	−	0.00937341i
$533$	8.28389	+	8.28389i	0.358815	+	0.358815i
$534$	3.65807	+	1.74848i	0.158300	+	0.0756642i
$535$		−	27.6900i		−	1.19714i
$536$	1.84070	+	7.75074i	0.0795062	+	0.334781i
$537$			22.7498i			0.981725i
$538$	−4.66198	+	9.75352i	−0.200992	+	0.420504i
$539$	−1.19999	−	1.19999i	−0.0516871	−	0.0516871i
$540$	3.57075	+	4.42427i	0.153660	+	0.190390i
$541$	−25.0102	+	25.0102i	−1.07527	+	1.07527i	−0.0783484	+	0.996926i	$0.524965\pi$
$541$	−25.0102	+	25.0102i	−1.07527	+	1.07527i	−0.996926	+	0.0783484i	$0.975035\pi$
$542$	−14.8407	+	5.24173i	−0.637463	+	0.225151i
$543$	7.26683			0.311849
$544$	0.894113	+	7.01279i	0.0383348	+	0.300671i
$545$	56.7758			2.43201
$546$	3.63057	−	1.28231i	0.155374	−	0.0548780i
$547$	8.31314	−	8.31314i	0.355444	−	0.355444i	−0.506686	−	0.862130i	$-0.669130\pi$
$547$	8.31314	−	8.31314i	0.355444	−	0.355444i	0.862130	+	0.506686i	$0.169130\pi$
$548$	−5.19011	−	6.43072i	−0.221711	−	0.274707i
$549$	−10.2386	−	10.2386i	−0.436972	−	0.436972i
$550$	3.18890	−	6.67162i	0.135975	−	0.284479i
$551$		−	1.83971i		−	0.0783741i
$552$	22.5342	−	5.35157i	0.959117	−	0.227778i
$553$			15.7018i			0.667710i
$554$	−29.7494	−	14.2196i	−1.26393	−	0.604132i
$555$	−15.3072	−	15.3072i	−0.649754	−	0.649754i
$556$	14.6714	+	1.56627i	0.622205	+	0.0664248i
$557$	−16.8478	+	16.8478i	−0.713866	+	0.713866i	−0.967342	−	0.253476i	$-0.918426\pi$
$557$	−16.8478	+	16.8478i	−0.713866	+	0.713866i	0.253476	+	0.967342i	$0.418426\pi$
$558$	−5.09571	−	14.4273i	−0.215718	−	0.610756i
$559$	1.19717			0.0506348
$560$	6.16183	+	9.55664i	0.260385	+	0.403842i
$561$	−2.12085			−0.0895422
$562$	−7.97550	−	22.5807i	−0.336426	−	0.952511i
$563$	−14.8909	+	14.8909i	−0.627577	+	0.627577i	−0.947458	−	0.319881i	$-0.896357\pi$
$563$	−14.8909	+	14.8909i	−0.627577	+	0.627577i	0.319881	+	0.947458i	$0.396357\pi$
$564$	−1.29677	+	12.1469i	−0.0546039	+	0.511478i
$565$	−14.9825	−	14.9825i	−0.630317	−	0.630317i
$566$	7.68994	+	3.67563i	0.323232	+	0.154498i
$567$		−	1.00000i		−	0.0419961i
$568$	11.9856	+	7.38528i	0.502906	+	0.309880i
$569$		−	37.7158i		−	1.58113i	−0.612380	−	0.790564i	$-0.709788\pi$
$569$		−	37.7158i		−	1.58113i	0.612380	−	0.790564i	$-0.290212\pi$
$570$	−1.76549	+	3.69366i	−0.0739483	+	0.154710i
$571$	−21.6472	−	21.6472i	−0.905906	−	0.905906i	0.0900329	−	0.995939i	$-0.471303\pi$
$571$	−21.6472	−	21.6472i	−0.905906	−	0.905906i	−0.995939	+	0.0900329i	$0.971303\pi$
$572$	7.19095	−	5.80368i	0.300669	−	0.242664i
$573$	−15.4669	+	15.4669i	−0.646141	+	0.646141i
$574$	5.73784	−	2.02660i	0.239493	−	0.0845886i
$575$	−25.2299			−1.05216
$576$	−7.14578	+	3.59693i	−0.297741	+	0.149872i
$577$	22.0735			0.918934			0.459467	−	0.888195i	$-0.348041\pi$
$577$	22.0735			0.918934			0.459467	+	0.888195i	$0.348041\pi$
$578$	20.5865	−	7.27114i	0.856286	−	0.302439i
$579$	3.20466	−	3.20466i	0.133181	−	0.133181i
$580$	−7.99287	+	6.45090i	−0.331886	+	0.267859i
$581$	3.53556	+	3.53556i	0.146680	+	0.146680i
$582$	−5.12386	+	10.7198i	−0.212391	+	0.444352i
$583$		−	3.23880i		−	0.134137i
$584$	−23.4862	−	14.4717i	−0.971867	−	0.598843i
$585$		−	7.73968i		−	0.319997i
$586$	18.9792	+	9.07169i	0.784026	+	0.374748i
$587$	−15.9766	−	15.9766i	−0.659426	−	0.659426i	0.295818	−	0.955244i	$-0.404408\pi$
$587$	−15.9766	−	15.9766i	−0.659426	−	0.659426i	−0.955244	+	0.295818i	$0.904408\pi$
$588$	0.212308	−	1.98870i	0.00875543	−	0.0820126i
$589$	7.79059	−	7.79059i	0.321005	−	0.321005i
$590$	19.4515	+	55.0723i	0.800805	+	2.26729i
$591$	−24.0282			−0.988387
$592$	25.6003	−	16.5063i	1.05217	−	0.678405i
$593$	−2.13357			−0.0876150			−0.0438075	−	0.999040i	$-0.513949\pi$
$593$	−2.13357			−0.0876150			−0.0438075	+	0.999040i	$0.513949\pi$
$594$	−0.799279	−	2.26297i	−0.0327948	−	0.0928508i
$595$	−2.51211	+	2.51211i	−0.102986	+	0.102986i
$596$	−0.391457	−	0.0417908i	−0.0160347	−	0.00171182i
$597$	3.27657	+	3.27657i	0.134101	+	0.134101i
$598$	−28.4467	−	13.5969i	−1.16327	−	0.556020i
$599$		−	16.0735i		−	0.656743i	−0.944549	−	0.328372i	$-0.893500\pi$
$599$		−	16.0735i		−	0.656743i	0.944549	−	0.328372i	$-0.106500\pi$
$600$	8.47884	−	2.01362i	0.346147	−	0.0822055i
$601$		−	38.7107i		−	1.57904i	−0.613722	−	0.789522i	$-0.710328\pi$
$601$		−	38.7107i		−	1.57904i	0.613722	−	0.789522i	$-0.289672\pi$
$602$	0.268170	−	0.561049i	0.0109298	−	0.0228666i
$603$	−1.99158	−	1.99158i	−0.0811034	−	0.0811034i
$604$	11.3679	+	14.0852i	0.462555	+	0.573121i
$605$	16.3222	−	16.3222i	0.663593	−	0.663593i
$606$	−14.7866	+	5.22260i	−0.600663	+	0.212154i
$607$	−0.471089			−0.0191209			−0.00956045	−	0.999954i	$-0.503043\pi$
$607$	−0.471089			−0.0191209			−0.00956045	+	0.999954i	$0.503043\pi$
$608$	−4.55577	−	3.52543i	−0.184761	−	0.142975i
$609$	1.80660			0.0732070
$610$	−54.8880	+	19.3864i	−2.22235	+	0.784932i
$611$	11.7590	−	11.7590i	0.475718	−	0.475718i
$612$	−1.56979	−	1.94502i	−0.0634550	−	0.0786228i
$613$	−12.2091	−	12.2091i	−0.493120	−	0.493120i	0.416168	−	0.909288i	$-0.363373\pi$
$613$	−12.2091	−	12.2091i	−0.493120	−	0.493120i	−0.909288	+	0.416168i	$0.863373\pi$
$614$	−10.8551	+	22.7104i	−0.438075	+	0.916516i
$615$		−	12.2320i		−	0.493241i
$616$	−1.10908	−	4.67006i	−0.0446861	−	0.188162i
$617$			15.2964i			0.615808i	0.951417	+	0.307904i	$0.0996275\pi$
$617$			15.2964i			0.615808i	−0.951417	+	0.307904i	$0.900372\pi$
$618$	−5.70951	−	2.72903i	−0.229670	−	0.109777i
$619$	1.21290	+	1.21290i	0.0487507	+	0.0487507i	0.731062	−	0.682311i	$-0.239025\pi$
$619$	1.21290	+	1.21290i	0.0487507	+	0.0487507i	−0.682311	+	0.731062i	$0.739025\pi$
$620$	−61.1649	−	6.52979i	−2.45644	−	0.262243i
$621$	−5.79023	+	5.79023i	−0.232354	+	0.232354i
$622$	3.43540	+	9.72652i	0.137747	+	0.389998i
$623$	−2.86694			−0.114861
$624$	10.6451	+	2.29908i	0.426144	+	0.0920367i
$625$	30.9123			1.23649
$626$	8.32667	+	23.5750i	0.332801	+	0.942247i
$627$	1.22198	−	1.22198i	0.0488012	−	0.0488012i
$628$	2.93117	−	27.4564i	0.116966	−	1.09563i
$629$	6.72942	+	6.72942i	0.268320	+	0.268320i
$630$	−3.62718	−	1.73372i	−0.144510	−	0.0690729i
$631$		−	27.4265i		−	1.09183i	−0.837841	−	0.545915i	$-0.816182\pi$
$631$		−	27.4265i		−	1.09183i	0.837841	−	0.545915i	$-0.183818\pi$
$632$	−23.2977	+	37.8100i	−0.926734	+	1.50400i
$633$			1.79177i			0.0712164i
$634$	14.8145	−	30.9940i	0.588358	−	1.23093i
$635$	29.7902	+	29.7902i	1.18219	+	1.18219i
$636$	2.97029	−	2.39726i	0.117780	−	0.0950577i
$637$	−1.92519	+	1.92519i	−0.0762787	+	0.0762787i
$638$	4.08827	−	1.44397i	0.161856	−	0.0571675i
$639$	−4.97742			−0.196904
$640$	0.657948	+	32.1551i	0.0260077	+	1.27104i
$641$	43.1622			1.70480			0.852401	−	0.522888i	$-0.175145\pi$
$641$	43.1622			1.70480			0.852401	+	0.522888i	$0.175145\pi$
$642$	−12.9890	+	4.58769i	−0.512633	+	0.181062i
$643$	−11.6984	+	11.6984i	−0.461342	+	0.461342i	−0.899095	−	0.437753i	$-0.855774\pi$
$643$	−11.6984	+	11.6984i	−0.461342	+	0.461342i	0.437753	+	0.899095i	$0.355774\pi$
$644$	−12.7443	+	10.2857i	−0.502197	+	0.405314i
$645$	−0.883867	−	0.883867i	−0.0348022	−	0.0348022i
$646$	0.776154	−	1.62382i	0.0305374	−	0.0638885i
$647$		−	9.25148i		−	0.363713i	−0.983325	−	0.181857i	$-0.941789\pi$
$647$		−	9.25148i		−	0.363713i	0.983325	−	0.181857i	$-0.0582107\pi$
$648$	1.48376	−	2.40800i	0.0582875	−	0.0945952i
$649$		−	24.6549i		−	0.967788i
$650$	−10.7035	−	5.11607i	−0.419828	−	0.200669i
$651$	7.65037	+	7.65037i	0.299842	+	0.299842i
$652$	−1.66029	+	15.5520i	−0.0650219	+	0.609064i
$653$	−18.0872	+	18.0872i	−0.707808	+	0.707808i	−0.966074	−	0.258266i	$-0.916849\pi$
$653$	−18.0872	+	18.0872i	−0.707808	+	0.707808i	0.258266	+	0.966074i	$0.416849\pi$
$654$	−9.40665	−	26.6327i	−0.367829	−	1.04142i
$655$	−10.4361			−0.407770
$656$	16.8237	+	3.63351i	0.656855	+	0.141865i
$657$	9.75342			0.380517
$658$	−2.87676	−	8.14487i	−0.112148	−	0.317520i
$659$	−14.5814	+	14.5814i	−0.568011	+	0.568011i	−0.931571	−	0.363560i	$-0.881561\pi$
$659$	−14.5814	+	14.5814i	−0.568011	+	0.568011i	0.363560	+	0.931571i	$0.381561\pi$
$660$	−9.59392	−	1.02422i	−0.373443	−	0.0398677i
$661$	20.4492	+	20.4492i	0.795382	+	0.795382i	0.982363	−	0.186982i	$-0.0598705\pi$
$661$	20.4492	+	20.4492i	0.795382	+	0.795382i	−0.186982	+	0.982363i	$0.559871\pi$
$662$	2.24763	+	1.07432i	0.0873568	+	0.0417547i
$663$			3.40256i			0.132144i
$664$	3.26772	+	13.7596i	0.126812	+	0.533974i
$665$		−	2.89483i		−	0.112257i
$666$	−4.64427	+	9.71648i	−0.179962	+	0.376506i
$667$	−10.4606	−	10.4606i	−0.405036	−	0.405036i
$668$	4.98788	+	6.18015i	0.192987	+	0.239117i
$669$	4.45359	−	4.45359i	0.172186	−	0.172186i
$670$	−10.6766	+	3.77098i	−0.412475	+	0.145686i
$671$	24.5724			0.948606
$672$	3.46199	−	4.47377i	0.133549	−	0.172580i
$673$	−19.3984			−0.747755			−0.373878	−	0.927478i	$-0.621972\pi$
$673$	−19.3984			−0.747755			−0.373878	+	0.927478i	$0.621972\pi$
$674$	−29.0349	+	10.2551i	−1.11838	+	0.395011i
$675$	−2.17867	+	2.17867i	−0.0838569	+	0.0838569i
$676$	7.01821	+	8.69579i	0.269931	+	0.334453i
$677$	−0.258487	−	0.258487i	−0.00993446	−	0.00993446i	0.702122	−	0.712057i	$-0.252236\pi$
$677$	−0.258487	−	0.258487i	−0.00993446	−	0.00993446i	−0.712057	+	0.702122i	$0.752236\pi$
$678$	−4.54575	+	9.51036i	−0.174579	+	0.365243i
$679$		−	8.40145i		−	0.322418i
$680$	−9.77651	+	2.32179i	−0.374912	+	0.0890367i
$681$			25.1894i			0.965261i
$682$	23.4274	+	11.1978i	0.897080	+	0.428785i
$683$	−1.04397	−	1.04397i	−0.0399462	−	0.0399462i	0.686852	−	0.726798i	$-0.258992\pi$
$683$	−1.04397	−	1.04397i	−0.0399462	−	0.0399462i	−0.726798	+	0.686852i	$0.758992\pi$
$684$	2.02515	+	0.216199i	0.0774334	+	0.00826657i
$685$	8.30564	−	8.30564i	0.317342	−	0.317342i
$686$	0.470984	+	1.33348i	0.0179823	+	0.0509126i
$687$	−1.62967			−0.0621759
$688$	1.47821	−	0.953107i	0.0563563	−	0.0363368i
$689$	−5.19613			−0.197957
$690$	10.9636	+	31.0408i	0.417376	+	1.18170i
$691$	−18.2172	+	18.2172i	−0.693013	+	0.693013i	−0.962894	−	0.269880i	$-0.913016\pi$
$691$	−18.2172	+	18.2172i	−0.693013	+	0.693013i	0.269880	+	0.962894i	$0.413016\pi$
$692$	−3.85287	+	36.0901i	−0.146464	+	1.37194i
$693$	1.19999	+	1.19999i	0.0455838	+	0.0455838i
$694$	−37.5022	−	17.9253i	−1.42356	−	0.680433i
$695$			20.9719i			0.795508i
$696$	4.35028	+	2.68055i	0.164897	+	0.101606i
$697$			5.37748i			0.203687i
$698$	8.30689	−	17.3792i	0.314420	−	0.657812i
$699$	8.29867	+	8.29867i	0.313885	+	0.313885i
$700$	−4.79526	+	3.87017i	−0.181244	+	0.146278i
$701$	21.2401	−	21.2401i	0.802226	−	0.802226i	−0.181217	−	0.983443i	$-0.558004\pi$
$701$	21.2401	−	21.2401i	0.802226	−	0.802226i	0.983443	+	0.181217i	$0.0580037\pi$
$702$	−3.63057	+	1.28231i	−0.137027	+	0.0483978i
$703$	−7.75465			−0.292472
$704$	4.25858	−	12.8911i	0.160501	−	0.485852i
$705$	−17.3633			−0.653940
$706$	47.4128	−	16.7461i	1.78440	−	0.630250i
$707$	7.84089	−	7.84089i	0.294887	−	0.294887i
$708$	22.6109	−	18.2488i	0.849769	−	0.685832i
$709$	23.9787	+	23.9787i	0.900539	+	0.900539i	0.995483	−	0.0949439i	$-0.0302672\pi$
$709$	23.9787	+	23.9787i	0.900539	+	0.900539i	−0.0949439	+	0.995483i	$0.530267\pi$
$710$	−8.62943	+	18.0540i	−0.323857	+	0.677554i
$711$		−	15.7018i		−	0.588865i
$712$	−6.90358	−	4.25384i	−0.258723	−	0.159419i
$713$		−	88.5948i		−	3.31790i
$714$	1.59460	+	0.762185i	0.0596764	+	0.0285241i
$715$	9.28752	+	9.28752i	0.347334	+	0.347334i
$716$	4.82996	−	45.2425i	0.180504	−	1.69079i
$717$	10.9431	−	10.9431i	0.408676	−	0.408676i
$718$	−6.84262	−	19.3733i	−0.255364	−	0.723004i
$719$	−45.9476			−1.71356			−0.856779	−	0.515684i	$-0.827538\pi$
$719$	−45.9476			−1.71356			−0.856779	+	0.515684i	$0.827538\pi$
$720$	−6.16183	−	9.55664i	−0.229638	−	0.356155i
$721$	4.47471			0.166647
$722$	−8.46030	−	23.9533i	−0.314860	−	0.891451i
$723$	12.2401	−	12.2401i	0.455215	−	0.455215i
$724$	−14.4515	−	1.54281i	−0.537087	−	0.0573379i
$725$	−3.93597	−	3.93597i	−0.146178	−	0.146178i
$726$	−10.3608	−	4.95224i	−0.384525	−	0.183795i
$727$			14.9397i			0.554082i	0.960858	+	0.277041i	$0.0893538\pi$
$727$			14.9397i			0.554082i	−0.960858	+	0.277041i	$0.910646\pi$
$728$	−7.49236	+	1.77934i	−0.277685	+	0.0659467i
$729$			1.00000i			0.0370370i
$730$	16.9097	−	35.3774i	0.625854	−	1.30938i
$731$	0.388570	+	0.388570i	0.0143718	+	0.0143718i
$732$	18.1877	+	22.5352i	0.672238	+	0.832925i
$733$	25.5679	−	25.5679i	0.944371	−	0.944371i	−0.0541608	−	0.998532i	$-0.517248\pi$
$733$	25.5679	−	25.5679i	0.944371	−	0.944371i	0.998532	+	0.0541608i	$0.0172483\pi$
$734$	25.5496	−	9.02411i	0.943055	−	0.333086i
$735$	2.84273			0.104856
$736$	−45.9498	+	5.85849i	−1.69373	+	0.215947i
$737$	4.77974			0.176064
$738$	−5.73784	+	2.02660i	−0.211213	+	0.0746001i
$739$	19.6495	−	19.6495i	0.722819	−	0.722819i	−0.246360	−	0.969178i	$-0.579234\pi$
$739$	19.6495	−	19.6495i	0.722819	−	0.722819i	0.969178	+	0.246360i	$0.0792344\pi$
$740$	27.1916	+	33.6912i	0.999581	+	1.23851i
$741$	−1.96047	−	1.96047i	−0.0720197	−	0.0720197i
$742$	−1.16395	+	2.43515i	−0.0427300	+	0.0893972i
$743$			26.0555i			0.955885i	0.878391	+	0.477942i	$0.158617\pi$
$743$			26.0555i			0.955885i	−0.878391	+	0.477942i	$0.841383\pi$
$744$	7.07080	+	29.7734i	0.259228	+	1.09155i
$745$		−	0.559564i		−	0.0205008i
$746$	42.1791	+	20.1607i	1.54428	+	0.738136i
$747$	−3.53556	−	3.53556i	−0.129359	−	0.129359i
$748$	4.21773	+	0.450273i	0.154215	+	0.0164636i
$749$	6.88767	−	6.88767i	0.251670	−	0.251670i
$750$	−2.56918	−	7.27402i	−0.0938131	−	0.265610i
$751$	−34.2020			−1.24805			−0.624024	−	0.781405i	$-0.714503\pi$
$751$	−34.2020			−1.24805			−0.624024	+	0.781405i	$0.714503\pi$
$752$	5.15777	−	23.8813i	0.188085	−	0.870860i
$753$	7.03630			0.256417
$754$	−2.31663	−	6.55898i	−0.0843665	−	0.238864i
$755$	−18.1919	+	18.1919i	−0.662071	+	0.662071i
$756$	−0.212308	+	1.98870i	−0.00772156	+	0.0723283i
$757$	−23.5059	−	23.5059i	−0.854337	−	0.854337i	0.136327	−	0.990664i	$-0.456470\pi$
$757$	−23.5059	−	23.5059i	−0.854337	−	0.854337i	−0.990664	+	0.136327i	$0.956470\pi$
$758$	9.08910	+	4.34440i	0.330131	+	0.157796i
$759$		−	13.8964i		−	0.504407i
$760$	4.29522	−	6.97074i	0.155804	−	0.252855i
$761$		−	19.1706i		−	0.694932i	−0.937692	−	0.347466i	$-0.887042\pi$
$761$		−	19.1706i		−	0.694932i	0.937692	−	0.347466i	$-0.112958\pi$
$762$	9.03849	−	18.9098i	0.327430	−	0.685030i
$763$	14.1226	+	14.1226i	0.511271	+	0.511271i
$764$	34.0429	−	27.4753i	1.23163	−	0.994023i
$765$	2.51211	−	2.51211i	0.0908254	−	0.0908254i
$766$	6.41285	−	2.26501i	0.231706	−	0.0818383i
$767$	−39.5548			−1.42824
$768$	14.9745	−	5.63610i	0.540344	−	0.203375i
$769$	10.8534			0.391385			0.195692	−	0.980665i	$-0.437305\pi$
$769$	10.8534			0.391385			0.195692	+	0.980665i	$0.437305\pi$
$770$	6.43301	−	2.27213i	0.231829	−	0.0818820i
$771$	12.4497	−	12.4497i	0.448365	−	0.448365i
$772$	−7.05347	+	5.69272i	−0.253860	+	0.204886i
$773$	−3.57093	−	3.57093i	−0.128437	−	0.128437i	0.639966	−	0.768403i	$-0.278948\pi$
$773$	−3.57093	−	3.57093i	−0.128437	−	0.128437i	−0.768403	+	0.639966i	$0.778948\pi$
$774$	−0.268170	+	0.561049i	−0.00963916	+	0.0201665i
$775$		−	33.3352i		−	1.19744i
$776$	12.4657	−	20.2307i	0.447493	−	0.726240i
$777$		−	7.61509i		−	0.273190i
$778$	−33.8747	−	16.1914i	−1.21447	−	0.580489i
$779$	−3.09837	−	3.09837i	−0.111011	−	0.111011i
$780$	−1.64320	+	15.3919i	−0.0588359	+	0.551119i
$781$	5.97284	−	5.97284i	0.213725	−	0.213725i
$782$	−4.81986	−	13.6463i	−0.172358	−	0.487991i
$783$	−1.80660			−0.0645625
$784$	−0.844433	+	3.90985i	−0.0301583	+	0.139638i
$785$	39.2473			1.40080
$786$	1.72905	+	4.89540i	0.0616732	+	0.174613i
$787$	21.8242	−	21.8242i	0.777950	−	0.777950i	−0.201532	−	0.979482i	$-0.564592\pi$
$787$	21.8242	−	21.8242i	0.777950	−	0.777950i	0.979482	+	0.201532i	$0.0645919\pi$
$788$	47.7848	+	5.10137i	1.70226	+	0.181729i
$789$	22.4046	+	22.4046i	0.797624	+	0.797624i
$790$	−56.9534	−	27.2225i	−2.02631	−	0.968534i
$791$		−	7.45355i		−	0.265018i
$792$	1.10908	+	4.67006i	0.0394094	+	0.165943i
$793$		−	39.4224i		−	1.39993i
$794$	−21.4716	+	44.9216i	−0.761998	+	1.59421i
$795$	3.83630	+	3.83630i	0.136059	+	0.136059i
$796$	−5.82047	−	7.21175i	−0.206301	−	0.255614i
$797$	−25.5382	+	25.5382i	−0.904610	+	0.904610i	−0.995831	−	0.0912205i	$-0.970923\pi$
$797$	−25.5382	+	25.5382i	−0.904610	+	0.904610i	0.0912205	+	0.995831i	$0.470923\pi$
$798$	−1.35792	+	0.479616i	−0.0480699	+	0.0169782i
$799$	7.63334			0.270048
$800$	−17.2894	+	2.20435i	−0.611272	+	0.0779356i
$801$	2.86694			0.101298
$802$	3.50015	−	1.23625i	0.123595	−	0.0436535i
$803$	−11.7040	+	11.7040i	−0.413024	+	0.413024i
$804$	3.53782	+	4.38348i	0.124769	+	0.154593i
$805$	−16.4600	−	16.4600i	−0.580140	−	0.580140i
$806$	17.9651	−	37.5854i	0.632792	−	1.32389i
$807$			7.64412i			0.269086i
$808$	30.5148	−	7.24688i	1.07351	−	0.254944i
$809$		−	32.2906i		−	1.13528i	−0.823278	−	0.567638i	$-0.807857\pi$
$809$		−	32.2906i		−	1.13528i	0.823278	−	0.567638i	$-0.192143\pi$
$810$	3.62718	+	1.73372i	0.127446	+	0.0609166i
$811$	−5.25871	−	5.25871i	−0.184658	−	0.184658i	0.608724	−	0.793382i	$-0.291682\pi$
$811$	−5.25871	−	5.25871i	−0.184658	−	0.184658i	−0.793382	+	0.608724i	$0.791682\pi$
$812$	−3.59278	−	0.383555i	−0.126082	−	0.0134601i
$813$	−7.86960	+	7.86960i	−0.275999	+	0.275999i
$814$	−6.08658	−	17.2327i	−0.213335	−	0.604007i
$815$	−22.2307			−0.778707
$816$	2.70890	+	4.20134i	0.0948303	+	0.147076i
$817$	−0.447769			−0.0156655
$818$	−7.78981	−	22.0550i	−0.272364	−	0.771136i
$819$	1.92519	−	1.92519i	0.0672715	−	0.0672715i
$820$	−2.59694	+	24.3257i	−0.0906892	+	0.849491i
$821$	−6.11075	−	6.11075i	−0.213267	−	0.213267i	0.592387	−	0.805654i	$-0.298186\pi$
$821$	−6.11075	−	6.11075i	−0.213267	−	0.213267i	−0.805654	+	0.592387i	$0.798186\pi$
$822$	−5.27214	−	2.51997i	−0.183887	−	0.0878941i
$823$			37.3133i			1.30066i	0.759652	+	0.650330i	$0.225369\pi$
$823$			37.3133i			1.30066i	−0.759652	+	0.650330i	$0.774631\pi$
$824$	10.7751	+	6.63938i	0.375368	+	0.231294i
$825$		−	5.22875i		−	0.182042i
$826$	−8.86041	+	18.5372i	−0.308293	+	0.644992i
$827$	−21.0461	−	21.0461i	−0.731846	−	0.731846i	0.239139	−	0.970985i	$-0.423135\pi$
$827$	−21.0461	−	21.0461i	−0.731846	−	0.731846i	−0.970985	+	0.239139i	$0.923135\pi$
$828$	12.7443	−	10.2857i	0.442896	−	0.357453i
$829$	11.5168	−	11.5168i	0.399995	−	0.399995i	−0.478236	−	0.878231i	$-0.658724\pi$
$829$	11.5168	−	11.5168i	0.399995	−	0.399995i	0.878231	+	0.478236i	$0.158724\pi$
$830$	−18.9538	+	6.69446i	−0.657895	+	0.232368i
$831$	−23.3155			−0.808805
$832$	−20.6817	−	6.83220i	−0.717009	−	0.236864i
$833$	−1.24973			−0.0433007
$834$	9.83759	−	3.47463i	0.340648	−	0.120317i
$835$	−7.98202	+	7.98202i	−0.276229	+	0.276229i
$836$	−2.68959	+	2.17071i	−0.0930213	+	0.0750757i
$837$	−7.65037	−	7.65037i	−0.264436	−	0.264436i
$838$	3.50832	−	7.33991i	0.121193	−	0.253553i
$839$		−	18.3880i		−	0.634824i	−0.948288	−	0.317412i	$-0.897186\pi$
$839$		−	18.3880i		−	0.634824i	0.948288	−	0.317412i	$-0.102814\pi$
$840$	6.84529	+	4.21792i	0.236185	+	0.145532i
$841$			25.7362i			0.887455i
$842$	−23.8697	−	11.4092i	−0.822604	−	0.393187i
$843$	−11.9739	−	11.9739i	−0.412403	−	0.412403i
$844$	0.380406	−	3.56329i	0.0130941	−	0.122653i
$845$	−11.2311	+	11.2311i	−0.386362	+	0.386362i
$846$	2.87676	+	8.14487i	0.0989050	+	0.280026i
$847$	8.12006			0.279009
$848$	−6.41597	+	4.13682i	−0.220325	+	0.142059i
$849$	6.02684			0.206841
$850$	−1.81355	−	5.13465i	−0.0622043	−	0.176117i
$851$	−44.0931	+	44.0931i	−1.51149	+	1.51149i
$852$	9.89859	+	1.05675i	0.339120	+	0.0362035i
$853$	25.9771	+	25.9771i	0.889439	+	0.889439i	0.994469	−	0.105030i	$-0.0334938\pi$
$853$	25.9771	+	25.9771i	0.889439	+	0.889439i	−0.105030	+	0.994469i	$0.533494\pi$
$854$	−18.4752	−	8.83076i	−0.632208	−	0.302182i
$855$			2.89483i			0.0990010i
$856$	26.8051	−	6.36587i	0.916181	−	0.217581i
$857$		−	26.4386i		−	0.903126i	−0.892239	−	0.451563i	$-0.850867\pi$
$857$		−	26.4386i		−	0.903126i	0.892239	−	0.451563i	$-0.149133\pi$
$858$	2.81788	−	5.89540i	0.0962008	−	0.201266i
$859$	16.9656	+	16.9656i	0.578860	+	0.578860i	0.934589	−	0.355729i	$-0.115768\pi$
$859$	16.9656	+	16.9656i	0.578860	+	0.578860i	−0.355729	+	0.934589i	$0.615768\pi$
$860$	1.57009	+	1.94540i	0.0535398	+	0.0663375i
$861$	3.04261	−	3.04261i	0.103692	−	0.103692i
$862$	34.0056	−	12.0107i	1.15823	−	0.409087i
$863$	35.3210			1.20234			0.601171	−	0.799121i	$-0.294701\pi$
$863$	35.3210			1.20234			0.601171	+	0.799121i	$0.294701\pi$
$864$	−3.46199	+	4.47377i	−0.117779	+	0.152201i
$865$	−51.5886			−1.75406
$866$	51.0891	−	18.0446i	1.73608	−	0.613181i
$867$	10.9164	−	10.9164i	0.370741	−	0.370741i
$868$	−13.5901	−	16.8385i	−0.461277	−	0.571537i
$869$	18.8420	+	18.8420i	0.639171	+	0.639171i
$870$	−3.13213	+	6.55285i	−0.106189	+	0.222162i
$871$		−	7.66833i		−	0.259831i
$872$	13.0527	+	54.9616i	0.442019	+	1.86123i
$873$			8.40145i			0.284346i
$874$	10.6398	+	5.08558i	0.359895	+	0.172022i
$875$	3.85720	+	3.85720i	0.130397	+	0.130397i
$876$	−19.3966	−	2.07073i	−0.655351	−	0.0699634i
$877$	−18.3579	+	18.3579i	−0.619902	+	0.619902i	−0.945506	−	0.325604i	$-0.894432\pi$
$877$	−18.3579	+	18.3579i	−0.619902	+	0.619902i	0.325604	+	0.945506i	$0.394432\pi$
$878$	7.13554	+	20.2026i	0.240813	+	0.681804i
$879$	14.8746			0.501708
$880$	18.8620	+	4.07373i	0.635837	+	0.137325i
$881$	−26.3703			−0.888438			−0.444219	−	0.895918i	$-0.646519\pi$
$881$	−26.3703			−0.888438			−0.444219	+	0.895918i	$0.646519\pi$
$882$	−0.470984	−	1.33348i	−0.0158589	−	0.0449007i
$883$	−1.91831	+	1.91831i	−0.0645564	+	0.0645564i	−0.738648	−	0.674091i	$-0.764535\pi$
$883$	−1.91831	+	1.91831i	−0.0645564	+	0.0645564i	0.674091	+	0.738648i	$0.264535\pi$
$884$	0.722390	−	6.76667i	0.0242966	−	0.227588i
$885$	29.2032	+	29.2032i	0.981656	+	0.981656i
$886$	5.02355	+	2.40115i	0.168769	+	0.0806683i
$887$			44.2379i			1.48536i	0.669644	+	0.742682i	$0.266447\pi$
$887$			44.2379i			1.48536i	−0.669644	+	0.742682i	$0.733553\pi$
$888$	11.2989	−	18.3371i	0.379168	−	0.615354i
$889$			14.8202i			0.497053i
$890$	4.97045	−	10.3989i	0.166610	−	0.348572i
$891$	−1.19999	−	1.19999i	−0.0402011	−	0.0402011i
$892$	−9.80238	+	7.91132i	−0.328208	+	0.264890i
$893$	−4.39814	+	4.39814i	−0.147178	+	0.147178i
$894$	−0.262483	+	0.0927088i	−0.00877875	+	0.00310065i
$895$	64.6714			2.16173
$896$	−7.83467	+	8.16199i	−0.261738	+	0.272673i
$897$	−22.2945			−0.744393
$898$	−22.6944	+	8.01564i	−0.757322	+	0.267486i
$899$	13.8211	−	13.8211i	0.460961	−	0.460961i
$900$	4.79526	−	3.87017i	0.159842	−	0.129006i
$901$	−1.68653	−	1.68653i	−0.0561865	−	0.0561865i
$902$	4.45344	−	9.31723i	0.148283	−	0.310230i
$903$		−	0.439710i		−	0.0146326i
$904$	11.0593	−	17.9481i	0.367826	−	0.596946i
$905$		−	20.6576i		−	0.686682i
$906$	11.5476	+	5.51951i	0.383643	+	0.183374i
$907$	5.39604	+	5.39604i	0.179173	+	0.179173i	0.790995	−	0.611822i	$-0.209563\pi$
$907$	5.39604	+	5.39604i	0.179173	+	0.179173i	−0.611822	+	0.790995i	$0.709563\pi$
$908$	5.34792	−	50.0942i	0.177477	−	1.66244i
$909$	−7.84089	+	7.84089i	−0.260066	+	0.260066i
$910$	−3.64527	−	10.3207i	−0.120840	−	0.342129i
$911$	26.8905			0.890924			0.445462	−	0.895301i	$-0.353040\pi$
$911$	26.8905			0.890924			0.445462	+	0.895301i	$0.353040\pi$
$912$	−3.98151	−	0.859909i	−0.131841	−	0.0284744i
$913$	8.48526			0.280821
$914$	−5.67987	−	16.0812i	−0.187873	−	0.531919i
$915$	−29.1055	+	29.1055i	−0.962199	+	0.962199i
$916$	3.24093	+	0.345992i	0.107083	+	0.0114319i
$917$	−2.59589	−	2.59589i	−0.0857238	−	0.0857238i
$918$	−1.59460	−	0.762185i	−0.0526296	−	0.0251559i
$919$			33.9472i			1.11981i	0.828555	+	0.559907i	$0.189163\pi$
$919$			33.9472i			1.11981i	−0.828555	+	0.559907i	$0.810837\pi$
$920$	−15.2131	−	64.0585i	−0.501560	−	2.11195i
$921$			17.7988i			0.586490i
$922$	−4.93904	+	10.3332i	−0.162659	+	0.340305i
$923$	−9.58246	−	9.58246i	−0.315411	−	0.315411i
$924$	−2.13165	−	2.64118i	−0.0701261	−	0.0868885i
$925$	−16.5907	+	16.5907i	−0.545500	+	0.545500i
$926$	47.9036	−	16.9195i	1.57421	−	0.556009i
$927$	−4.47471			−0.146969
$928$	−8.08231	−	6.25441i	−0.265315	−	0.205311i
$929$	−19.8940			−0.652700			−0.326350	−	0.945249i	$-0.605819\pi$
$929$	−19.8940			−0.652700			−0.326350	+	0.945249i	$0.605819\pi$
$930$	−41.0129	+	14.4857i	−1.34486	+	0.475005i
$931$	0.720066	−	0.720066i	0.0235992	−	0.0235992i
$932$	−14.7417	−	18.2654i	−0.482880	−	0.598304i
$933$	5.15769	+	5.15769i	0.168855	+	0.168855i
$934$	−0.330365	+	0.691171i	−0.0108099	+	0.0226158i
$935$			6.02899i			0.197169i
$936$	7.49236	−	1.77934i	0.244896	−	0.0581595i
$937$		−	7.81612i		−	0.255341i	−0.991817	−	0.127671i	$-0.959250\pi$
$937$		−	7.81612i		−	0.255341i	0.991817	−	0.127671i	$-0.0407501\pi$
$938$	−3.59374	−	1.71773i	−0.117340	−	0.0560859i
$939$	12.5011	+	12.5011i	0.407960	+	0.407960i
$940$	34.5304	+	3.68637i	1.12626	+	0.120236i
$941$	−9.80534	+	9.80534i	−0.319645	+	0.319645i	−0.848631	−	0.528986i	$-0.822573\pi$
$941$	−9.80534	+	9.80534i	−0.319645	+	0.319645i	0.528986	+	0.848631i	$0.322573\pi$
$942$	−6.50251	−	18.4103i	−0.211863	−	0.599841i
$943$	−35.2348			−1.14740
$944$	−48.8406	+	31.4909i	−1.58963	+	1.02494i
$945$	−2.84273			−0.0924739
$946$	−0.351451	−	0.995052i	−0.0114267	−	0.0323519i
$947$	4.80786	−	4.80786i	0.156235	−	0.156235i	−0.624661	−	0.780896i	$-0.714763\pi$
$947$	4.80786	−	4.80786i	0.156235	−	0.156235i	0.780896	+	0.624661i	$0.214763\pi$
$948$	−3.33363	+	31.2262i	−0.108271	+	1.01418i
$949$	18.7772	+	18.7772i	0.609532	+	0.609532i
$950$	4.00338	+	1.91353i	0.129887	+	0.0620832i
$951$		−	24.2909i		−	0.787686i
$952$	−3.00936	−	1.85430i	−0.0975339	−	0.0600983i
$953$			23.2445i			0.752963i	0.926424	+	0.376482i	$0.122866\pi$
$953$			23.2445i			0.752963i	−0.926424	+	0.376482i	$0.877134\pi$
$954$	1.16395	−	2.43515i	0.0376843	−	0.0788409i
$955$	43.9683	+	43.9683i	1.42278	+	1.42278i
$956$	−24.0858	+	19.4392i	−0.778989	+	0.628708i
$957$	2.16789	−	2.16789i	0.0700780	−	0.0700780i
$958$	−54.3228	+	19.1867i	−1.75509	+	0.619896i
$959$	4.13193			0.133427
$960$	10.2251	+	20.3135i	0.330013	+	0.655615i
$961$	86.0565			2.77602
$962$	−27.6471	+	9.76494i	−0.891379	+	0.314834i
$963$	−6.88767	+	6.88767i	−0.221952	+	0.221952i
$964$	−26.9406	+	21.7432i	−0.867698	+	0.700303i
$965$	−9.10996	−	9.10996i	−0.293260	−	0.293260i
$966$	−4.99405	+	10.4483i	−0.160681	+	0.336167i
$967$			26.3657i			0.847865i	0.905694	+	0.423932i	$0.139351\pi$
$967$			26.3657i			0.847865i	−0.905694	+	0.423932i	$0.860649\pi$
$968$	19.5531	+	12.0482i	0.628461	+	0.387244i
$969$		−	1.27264i		−	0.0408830i
$970$	30.4736	+	14.5657i	0.978448	+	0.467678i
$971$	6.90103	+	6.90103i	0.221464	+	0.221464i	0.809115	−	0.587650i	$-0.199947\pi$
$971$	6.90103	+	6.90103i	0.221464	+	0.221464i	−0.587650	+	0.809115i	$0.699947\pi$
$972$	0.212308	−	1.98870i	0.00680978	−	0.0637876i
$973$	−5.21659	+	5.21659i	−0.167236	+	0.167236i
$974$	8.12345	+	22.9996i	0.260292	+	0.736956i
$975$	−8.38868			−0.268653
$976$	−31.3856	−	48.6772i	−1.00463	−	1.55812i
$977$	−51.4493			−1.64601			−0.823004	−	0.568035i	$-0.807704\pi$
$977$	−51.4493			−1.64601			−0.823004	+	0.568035i	$0.807704\pi$
$978$	3.68319	+	10.4281i	0.117775	+	0.333453i
$979$	−3.44029	+	3.44029i	−0.109952	+	0.109952i
$980$	−5.65333	−	0.603534i	−0.180589	−	0.0192792i
$981$	−14.1226	−	14.1226i	−0.450898	−	0.450898i
$982$	22.6358	+	10.8194i	0.722338	+	0.345262i
$983$			15.4509i			0.492807i	0.969167	+	0.246403i	$0.0792488\pi$
$983$			15.4509i			0.492807i	−0.969167	+	0.246403i	$0.920751\pi$
$984$	11.8411	−	2.81211i	0.377480	−	0.0896467i
$985$			68.3055i			2.17639i
$986$	1.37696	−	2.88080i	0.0438514	−	0.0917432i
$987$	−4.31899	−	4.31899i	−0.137475	−	0.137475i
$988$	3.48256	+	4.31501i	0.110795	+	0.137279i
$989$	−2.54602	+	2.54602i	−0.0809588	+	0.0809588i
$990$	−6.43301	+	2.27213i	−0.204454	+	0.0722131i
$991$	19.5894			0.622279			0.311140	−	0.950364i	$-0.399289\pi$
$991$	19.5894			0.622279			0.311140	+	0.950364i	$0.399289\pi$
$992$	−7.74056	−	60.7115i	−0.245763	−	1.92759i
$993$	1.76154			0.0559007
$994$	−6.63730	+	2.34429i	−0.210522	+	0.0743563i
$995$	9.31440	−	9.31440i	0.295286	−	0.295286i
$996$	6.28054	+	7.78180i	0.199007	+	0.246576i
$997$	30.4417	+	30.4417i	0.964097	+	0.964097i	0.999377	−	0.0352807i	$-0.0112325\pi$
$997$	30.4417	+	30.4417i	0.964097	+	0.964097i	−0.0352807	+	0.999377i	$0.511233\pi$
$998$	7.38501	−	15.4505i	0.233768	−	0.489077i
$999$			7.61509i			0.240931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.a.85.1	✓	20
4.3	odd	2		1344.2.w.a.1009.10		20
8.3	odd	2		2688.2.w.b.2017.1		20
8.5	even	2		2688.2.w.a.2017.6		20
16.3	odd	4		1344.2.w.a.337.10		20
16.5	even	4		2688.2.w.a.673.6		20
16.11	odd	4		2688.2.w.b.673.1		20
16.13	even	4	inner	336.2.w.a.253.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.1	✓	20	1.1	even	1	trivial
336.2.w.a.253.1	yes	20	16.13	even	4	inner
1344.2.w.a.337.10		20	16.3	odd	4
1344.2.w.a.1009.10		20	4.3	odd	2
2688.2.w.a.673.6		20	16.5	even	4
2688.2.w.a.2017.6		20	8.5	even	2
2688.2.w.b.673.1		20	16.11	odd	4
2688.2.w.b.2017.1		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33348 + 0.470984i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.55635 - 1.25610i) q^{4} +(2.01011 + 2.01011i) q^{5} +(0.609878 - 1.27595i) q^{6} +1.00000i q^{7} +(-1.48376 + 2.40800i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.33348 + 0.470984i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.55635 - 1.25610i) q^{4} +(2.01011 + 2.01011i) q^{5} +(0.609878 - 1.27595i) q^{6} +1.00000i q^{7} +(-1.48376 + 2.40800i) q^{8} -1.00000i q^{9} +(-3.62718 - 1.73372i) q^{10} +(1.19999 + 1.19999i) q^{11} +(-0.212308 + 1.98870i) q^{12} +(1.92519 - 1.92519i) q^{13} +(-0.470984 - 1.33348i) q^{14} -2.84273 q^{15} +(0.844433 - 3.90985i) q^{16} +1.24973 q^{17} +(0.470984 + 1.33348i) q^{18} +(-0.720066 + 0.720066i) q^{19} +(5.65333 + 0.603534i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-2.16534 - 1.03499i) q^{22} +8.18862i q^{23} +(-0.653538 - 2.75189i) q^{24} +3.08110i q^{25} +(-1.66047 + 3.47394i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.25610 + 1.55635i) q^{28} +(-1.27746 + 1.27746i) q^{29} +(3.79073 - 1.33888i) q^{30} -10.8193 q^{31} +(0.715443 + 5.61143i) q^{32} -1.69704 q^{33} +(-1.66650 + 0.588605i) q^{34} +(-2.01011 + 2.01011i) q^{35} +(-1.25610 - 1.55635i) q^{36} +(5.38468 + 5.38468i) q^{37} +(0.621055 - 1.29934i) q^{38} +2.72263i q^{39} +(-7.82287 + 1.85783i) q^{40} +4.30290i q^{41} +(1.27595 + 0.609878i) q^{42} +(0.310922 + 0.310922i) q^{43} +(3.37490 + 0.360295i) q^{44} +(2.01011 - 2.01011i) q^{45} +(-3.85671 - 10.9194i) q^{46} +6.10797 q^{47} +(2.16758 + 3.36179i) q^{48} -1.00000 q^{49} +(-1.45115 - 4.10859i) q^{50} +(-0.883695 + 0.883695i) q^{51} +(0.578035 - 5.41448i) q^{52} +(-1.34951 - 1.34951i) q^{53} +(-1.27595 - 0.609878i) q^{54} +4.82422i q^{55} +(-2.40800 - 1.48376i) q^{56} -1.01833i q^{57} +(1.10180 - 2.30513i) q^{58} +(-10.2730 - 10.2730i) q^{59} +(-4.42427 + 3.57075i) q^{60} +(10.2386 - 10.2386i) q^{61} +(14.4273 - 5.09571i) q^{62} +1.00000 q^{63} +(-3.59693 - 7.14578i) q^{64} +7.73968 q^{65} +(2.26297 - 0.799279i) q^{66} +(1.99158 - 1.99158i) q^{67} +(1.94502 - 1.56979i) q^{68} +(-5.79023 - 5.79023i) q^{69} +(1.73372 - 3.62718i) q^{70} -4.97742i q^{71} +(2.40800 + 1.48376i) q^{72} +9.75342i q^{73} +(-9.71648 - 4.64427i) q^{74} +(-2.17867 - 2.17867i) q^{75} +(-0.216199 + 2.02515i) q^{76} +(-1.19999 + 1.19999i) q^{77} +(-1.28231 - 3.63057i) q^{78} +15.7018 q^{79} +(9.55664 - 6.16183i) q^{80} -1.00000 q^{81} +(-2.02660 - 5.73784i) q^{82} +(3.53556 - 3.53556i) q^{83} +(-1.98870 - 0.212308i) q^{84} +(2.51211 + 2.51211i) q^{85} +(-0.561049 - 0.268170i) q^{86} -1.80660i q^{87} +(-4.67006 + 1.10908i) q^{88} +2.86694i q^{89} +(-1.73372 + 3.62718i) q^{90} +(1.92519 + 1.92519i) q^{91} +(10.2857 + 12.7443i) q^{92} +(7.65037 - 7.65037i) q^{93} +(-8.14487 + 2.87676i) q^{94} -2.89483 q^{95} +(-4.47377 - 3.46199i) q^{96} -8.40145 q^{97} +(1.33348 - 0.470984i) q^{98} +(1.19999 - 1.19999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4}+O(q^{10}) \) 20 * q + 4 * q^4	\( 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

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