LMFDB - Embedded newform 117.2.bc.a.110.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(20,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.20"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			110.9
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.308060 - 1.14969i) q^{2} +(-0.781791 + 1.54558i) q^{3} +(0.505155 + 0.291651i) q^{4} +(-0.744040 + 2.77680i) q^{5} +(1.53610 + 1.37495i) q^{6} +(1.04357 + 1.04357i) q^{7} +(2.17420 - 2.17420i) q^{8} +(-1.77761 - 2.41663i) q^{9} +(2.96326 + 1.71084i) q^{10} +(-1.68335 - 0.451052i) q^{11} +(-0.845695 + 0.552745i) q^{12} +(1.90363 - 3.06206i) q^{13} +(1.52127 - 0.878303i) q^{14} +(-3.71006 - 3.32085i) q^{15} +(-1.24658 - 2.15913i) q^{16} +(-0.939625 - 1.62748i) q^{17} +(-3.32600 + 1.29924i) q^{18} +(4.34907 + 1.16533i) q^{19} +(-1.18571 + 1.18571i) q^{20} +(-2.42877 + 0.797061i) q^{21} +(-1.03714 + 1.79639i) q^{22} -5.65176 q^{23} +(1.66062 + 5.06015i) q^{24} +(-2.82688 - 1.63210i) q^{25} +(-2.93400 - 3.13189i) q^{26} +(5.12481 - 0.858121i) q^{27} +(0.222806 + 0.831522i) q^{28} +(5.80315 - 3.35045i) q^{29} +(-4.96088 + 3.24242i) q^{30} +(-2.52515 - 0.676611i) q^{31} +(3.07365 - 0.823583i) q^{32} +(2.01316 - 2.24911i) q^{33} +(-2.16056 + 0.578921i) q^{34} +(-3.67424 + 2.12132i) q^{35} +(-0.193152 - 1.73922i) q^{36} +(-11.1775 + 2.99499i) q^{37} +(2.67955 - 4.64111i) q^{38} +(3.24440 + 5.33609i) q^{39} +(4.41961 + 7.65499i) q^{40} +(-0.459167 - 0.459167i) q^{41} +(0.168172 + 3.03788i) q^{42} -2.05612i q^{43} +(-0.718802 - 0.718802i) q^{44} +(8.03311 - 3.13798i) q^{45} +(-1.74108 + 6.49779i) q^{46} +(0.619735 + 2.31288i) q^{47} +(4.31167 - 0.238686i) q^{48} -4.82193i q^{49} +(-2.74726 + 2.74726i) q^{50} +(3.24998 - 0.179913i) q^{51} +(1.85468 - 0.991618i) q^{52} -11.5633i q^{53} +(0.592168 - 6.15631i) q^{54} +(2.50496 - 4.33872i) q^{55} +4.53785 q^{56} +(-5.20117 + 5.81077i) q^{57} +(-2.06428 - 7.70398i) q^{58} +(3.35246 + 12.5115i) q^{59} +(-0.905629 - 2.75959i) q^{60} +10.4856 q^{61} +(-1.55579 + 2.69471i) q^{62} +(0.666869 - 4.37698i) q^{63} -8.77378i q^{64} +(7.08634 + 7.56428i) q^{65} +(-1.96562 - 3.00738i) q^{66} +(-2.56688 + 2.56688i) q^{67} -1.09617i q^{68} +(4.41849 - 8.73522i) q^{69} +(1.30699 + 4.87774i) q^{70} +(-2.99663 + 11.1836i) q^{71} +(-9.11910 - 1.38937i) q^{72} +(-8.97423 - 8.97423i) q^{73} +13.7733i q^{74} +(4.73256 - 3.09319i) q^{75} +(1.85709 + 1.85709i) q^{76} +(-1.28599 - 2.22739i) q^{77} +(7.13434 - 2.08624i) q^{78} +(-4.85927 + 8.41651i) q^{79} +(6.92298 - 1.85501i) q^{80} +(-2.68024 + 8.59164i) q^{81} +(-0.669352 + 0.386451i) q^{82} +(2.65776 - 0.712145i) q^{83} +(-1.45937 - 0.305713i) q^{84} +(5.21830 - 1.39824i) q^{85} +(-2.36391 - 0.633407i) q^{86} +(0.641522 + 11.5885i) q^{87} +(-4.64061 + 2.67926i) q^{88} +(1.57286 + 5.86998i) q^{89} +(-1.13304 - 10.2023i) q^{90} +(5.18203 - 1.20890i) q^{91} +(-2.85501 - 1.64834i) q^{92} +(3.01989 - 3.37384i) q^{93} +2.85002 q^{94} +(-6.47177 + 11.2094i) q^{95} +(-1.13004 + 5.39443i) q^{96} +(-3.70756 + 3.70756i) q^{97} +(-5.54374 - 1.48544i) q^{98} +(1.90230 + 4.86983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21}+ \cdots - 32 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.308060	−	1.14969i	0.217831	−	0.812956i	−0.767320	−	0.641265i	$-0.778410\pi$
$2$	0.308060	−	1.14969i	0.217831	−	0.812956i	0.985151	−	0.171692i	$-0.0549233\pi$
$3$	−0.781791	+	1.54558i	−0.451367	+	0.892338i
$3$	−0.781791	+	1.54558i	−0.451367	+	0.892338i
$4$	0.505155	+	0.291651i	0.252578	+	0.145826i
$5$	−0.744040	+	2.77680i	−0.332745	+	1.24182i	0.573548	+	0.819172i	$0.305567\pi$
$5$	−0.744040	+	2.77680i	−0.332745	+	1.24182i	−0.906293	+	0.422650i	$0.861100\pi$
$6$	1.53610	+	1.37495i	0.627110	+	0.561321i
$7$	1.04357	+	1.04357i	0.394432	+	0.394432i	0.876264	−	0.481832i	$-0.160028\pi$
$7$	1.04357	+	1.04357i	0.394432	+	0.394432i	−0.481832	+	0.876264i	$0.660028\pi$
$8$	2.17420	−	2.17420i	0.768695	−	0.768695i
$9$	−1.77761	−	2.41663i	−0.592535	−	0.805545i
$10$	2.96326	+	1.71084i	0.937065	+	0.541014i
$11$	−1.68335	−	0.451052i	−0.507549	−	0.135997i	−0.00404763	−	0.999992i	$-0.501288\pi$
$11$	−1.68335	−	0.451052i	−0.507549	−	0.135997i	−0.503501	+	0.863994i	$0.667955\pi$
$12$	−0.845695	+	0.552745i	−0.244131	+	0.159564i
$13$	1.90363	−	3.06206i	0.527971	−	0.849262i
$13$	1.90363	−	3.06206i	0.527971	−	0.849262i
$14$	1.52127	−	0.878303i	0.406575	−	0.234736i
$15$	−3.71006	−	3.32085i	−0.957935	−	0.857439i
$16$	−1.24658	−	2.15913i	−0.311644	−	0.539783i
$17$	−0.939625	−	1.62748i	−0.227893	−	0.394722i	0.729291	−	0.684204i	$-0.239850\pi$
$17$	−0.939625	−	1.62748i	−0.227893	−	0.394722i	−0.957183	+	0.289482i	$0.906517\pi$
$18$	−3.32600	+	1.29924i	−0.783945	+	0.306233i
$19$	4.34907	+	1.16533i	0.997745	+	0.267345i	0.720501	−	0.693454i	$-0.243912\pi$
$19$	4.34907	+	1.16533i	0.997745	+	0.267345i	0.277245	+	0.960799i	$0.410579\pi$
$20$	−1.18571	+	1.18571i	−0.265133	+	0.265133i
$21$	−2.42877	+	0.797061i	−0.530000	+	0.173933i
$22$	−1.03714	+	1.79639i	−0.221120	+	0.382991i
$23$	−5.65176			−1.17847			−0.589237	−	0.807961i	$-0.700571\pi$
$23$	−5.65176			−1.17847			−0.589237	+	0.807961i	$0.700571\pi$
$24$	1.66062	+	5.06015i	0.338972	+	1.03290i
$25$	−2.82688	−	1.63210i	−0.565376	−	0.326420i
$26$	−2.93400	−	3.13189i	−0.575405	−	0.614213i
$27$	5.12481	−	0.858121i	0.986269	−	0.165146i
$28$	0.222806	+	0.831522i	0.0421063	+	0.157143i
$29$	5.80315	−	3.35045i	1.07762	−	0.622162i	0.147364	−	0.989082i	$-0.452921\pi$
$29$	5.80315	−	3.35045i	1.07762	−	0.622162i	0.930253	+	0.366920i	$0.119588\pi$
$30$	−4.96088	+	3.24242i	−0.905728	+	0.591982i
$31$	−2.52515	−	0.676611i	−0.453530	−	0.121523i	0.0248208	−	0.999692i	$-0.492098\pi$
$31$	−2.52515	−	0.676611i	−0.453530	−	0.121523i	−0.478350	+	0.878169i	$0.658765\pi$
$32$	3.07365	−	0.823583i	0.543350	−	0.145590i
$33$	2.01316	−	2.24911i	0.350447	−	0.391521i
$34$	−2.16056	+	0.578921i	−0.370534	+	0.0992842i
$35$	−3.67424	+	2.12132i	−0.621059	+	0.358569i
$36$	−0.193152	−	1.73922i	−0.0321920	−	0.289869i
$37$	−11.1775	+	2.99499i	−1.83756	+	0.492374i	−0.998653	−	0.0518927i	$-0.983475\pi$
$37$	−11.1775	+	2.99499i	−1.83756	+	0.492374i	−0.838912	+	0.544267i	$0.816808\pi$
$38$	2.67955	−	4.64111i	0.434680	−	0.752888i
$39$	3.24440	+	5.33609i	0.519520	+	0.854458i
$40$	4.41961	+	7.65499i	0.698802	+	1.21036i
$41$	−0.459167	−	0.459167i	−0.0717098	−	0.0717098i	0.670342	−	0.742052i	$-0.266147\pi$
$41$	−0.459167	−	0.459167i	−0.0717098	−	0.0717098i	−0.742052	+	0.670342i	$0.766147\pi$
$42$	0.168172	+	3.03788i	0.0259495	+	0.468755i
$43$		−	2.05612i		−	0.313555i	−0.987634	−	0.156778i	$-0.949889\pi$
$43$		−	2.05612i		−	0.313555i	0.987634	−	0.156778i	$-0.0501106\pi$
$44$	−0.718802	−	0.718802i	−0.108364	−	0.108364i
$45$	8.03311	−	3.13798i	1.19751	−	0.467782i
$46$	−1.74108	+	6.49779i	−0.256708	+	0.958048i
$47$	0.619735	+	2.31288i	0.0903977	+	0.337369i	0.996282	−	0.0861575i	$-0.0274588\pi$
$47$	0.619735	+	2.31288i	0.0903977	+	0.337369i	−0.905884	+	0.423526i	$0.860792\pi$
$48$	4.31167	−	0.238686i	0.622335	−	0.0344514i
$49$		−	4.82193i		−	0.688847i
$50$	−2.74726	+	2.74726i	−0.388521	+	0.388521i
$51$	3.24998	−	0.179913i	0.455088	−	0.0251929i
$52$	1.85468	−	0.991618i	0.257198	−	0.137513i
$53$		−	11.5633i		−	1.58834i	−0.607698	−	0.794168i	$-0.707907\pi$
$53$		−	11.5633i		−	1.58834i	0.607698	−	0.794168i	$-0.292093\pi$
$54$	0.592168	−	6.15631i	0.0805839	−	0.837768i
$55$	2.50496	−	4.33872i	0.337769	−	0.585033i
$56$	4.53785			0.606395
$57$	−5.20117	+	5.81077i	−0.688912	+	0.769656i
$58$	−2.06428	−	7.70398i	−0.271053	−	1.01158i
$59$	3.35246	+	12.5115i	0.436453	+	1.62886i	0.737566	+	0.675275i	$0.235975\pi$
$59$	3.35246	+	12.5115i	0.436453	+	1.62886i	−0.301113	+	0.953589i	$0.597358\pi$
$60$	−0.905629	−	2.75959i	−0.116916	−	0.356261i
$61$	10.4856			1.34254			0.671269	−	0.741213i	$-0.265749\pi$
$61$	10.4856			1.34254			0.671269	+	0.741213i	$0.265749\pi$
$62$	−1.55579	+	2.69471i	−0.197586	+	0.342228i
$63$	0.666869	−	4.37698i	0.0840176	−	0.551447i
$64$		−	8.77378i		−	1.09672i
$65$	7.08634	+	7.56428i	0.878952	+	0.938234i
$66$	−1.96562	−	3.00738i	−0.241951	−	0.370183i
$67$	−2.56688	+	2.56688i	−0.313595	+	0.313595i	−0.846300	−	0.532706i	$-0.821175\pi$
$67$	−2.56688	+	2.56688i	−0.313595	+	0.313595i	0.532706	+	0.846300i	$0.321175\pi$
$68$		−	1.09617i		−	0.132930i
$69$	4.41849	−	8.73522i	0.531924	−	1.05160i
$70$	1.30699	+	4.87774i	0.156215	+	0.583001i
$71$	−2.99663	+	11.1836i	−0.355635	+	1.32725i	0.524049	+	0.851688i	$0.324421\pi$
$71$	−2.99663	+	11.1836i	−0.355635	+	1.32725i	−0.879684	+	0.475559i	$0.842246\pi$
$72$	−9.11910	−	1.38937i	−1.07470	−	0.163739i
$73$	−8.97423	−	8.97423i	−1.05035	−	1.05035i	−0.998663	−	0.0516906i	$-0.983539\pi$
$73$	−8.97423	−	8.97423i	−1.05035	−	1.05035i	−0.0516906	−	0.998663i	$-0.516461\pi$
$74$			13.7733i			1.60111i
$75$	4.73256	−	3.09319i	0.546469	−	0.357171i
$76$	1.85709	+	1.85709i	0.213022	+	0.213022i
$77$	−1.28599	−	2.22739i	−0.146552	−	0.253835i
$78$	7.13434	−	2.08624i	0.807805	−	0.236220i
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	−0.998497	+	0.0548048i	$0.982546\pi$
$80$	6.92298	−	1.85501i	0.774012	−	0.207396i
$81$	−2.68024	+	8.59164i	−0.297804	+	0.954627i
$82$	−0.669352	+	0.386451i	−0.0739176	+	0.0426763i
$83$	2.65776	−	0.712145i	0.291727	−	0.0781681i	−0.109987	−	0.993933i	$-0.535081\pi$
$83$	2.65776	−	0.712145i	0.291727	−	0.0781681i	0.401715	+	0.915765i	$0.368414\pi$
$84$	−1.45937	−	0.305713i	−0.159230	−	0.0333561i
$85$	5.21830	−	1.39824i	0.566004	−	0.151660i
$86$	−2.36391	−	0.633407i	−0.254907	−	0.0683020i
$87$	0.641522	+	11.5885i	0.0687784	+	1.24242i
$88$	−4.64061	+	2.67926i	−0.494690	+	0.285610i
$89$	1.57286	+	5.86998i	0.166722	+	0.622217i	0.997814	+	0.0660814i	$0.0210497\pi$
$89$	1.57286	+	5.86998i	0.166722	+	0.622217i	−0.831092	+	0.556135i	$0.812284\pi$
$90$	−1.13304	−	10.2023i	−0.119433	−	1.07542i
$91$	5.18203	−	1.20890i	0.543225	−	0.126727i
$92$	−2.85501	−	1.64834i	−0.297656	−	0.171852i
$93$	3.01989	−	3.37384i	0.313148	−	0.349850i
$94$	2.85002			0.293957
$95$	−6.47177	+	11.2094i	−0.663990	+	1.15006i
$96$	−1.13004	+	5.39443i	−0.115335	+	0.550567i
$97$	−3.70756	+	3.70756i	−0.376446	+	0.376446i	−0.869818	−	0.493372i	$-0.835764\pi$
$97$	−3.70756	+	3.70756i	−0.376446	+	0.376446i	0.493372	+	0.869818i	$0.335764\pi$
$98$	−5.54374	−	1.48544i	−0.560003	−	0.150052i
$99$	1.90230	+	4.86983i	0.191189	+	0.489436i
$100$	−0.952008	−	1.64893i	−0.0952008	−	0.164893i
$101$	−1.51426	−	2.62277i	−0.150674	−	0.260975i	0.780801	−	0.624779i	$-0.214811\pi$
$101$	−1.51426	−	2.62277i	−0.150674	−	0.260975i	−0.931475	+	0.363804i	$0.881478\pi$
$102$	0.794343	−	3.79191i	0.0786516	−	0.375455i
$103$	−15.9431	+	9.20475i	−1.57092	+	0.906971i	−0.574864	+	0.818249i	$0.694945\pi$
$103$	−15.9431	+	9.20475i	−1.57092	+	0.906971i	−0.996056	+	0.0887220i	$0.971722\pi$
$104$	−2.51865	−	10.7964i	−0.246974	−	1.05867i
$105$	−0.406177	−	7.33724i	−0.0396388	−	0.716041i
$106$	−13.2942	−	3.56217i	−1.29125	−	0.345989i
$107$	−3.97340	−	2.29404i	−0.384123	−	0.221774i	0.295487	−	0.955347i	$-0.404518\pi$
$107$	−3.97340	−	2.29404i	−0.384123	−	0.221774i	−0.679611	+	0.733573i	$0.737851\pi$
$108$	2.83909	+	1.06117i	0.273192	+	0.102111i
$109$	0.138592	−	0.138592i	0.0132747	−	0.0132747i	−0.700438	−	0.713713i	$-0.747012\pi$
$109$	0.138592	−	0.138592i	0.0132747	−	0.0132747i	0.713713	+	0.700438i	$0.247012\pi$
$110$	−4.21652	−	4.21652i	−0.402030	−	0.402030i
$111$	4.10946	−	19.6171i	0.390052	−	1.86197i
$112$	0.952316	−	3.55409i	0.0899854	−	0.335830i
$113$	6.46742	+	3.73397i	0.608404	+	0.351262i	0.772341	−	0.635209i	$-0.219086\pi$
$113$	6.46742	+	3.73397i	0.608404	+	0.351262i	−0.163937	+	0.986471i	$0.552419\pi$
$114$	5.07834	+	7.76982i	0.475630	+	0.727710i
$115$	4.20514	−	15.6938i	0.392131	−	1.46345i
$116$	3.90865			0.362909
$117$	−10.7838	+	0.842761i	−0.996960	+	0.0779133i
$118$	15.4172			1.41927
$119$	0.717822	−	2.67895i	0.0658027	−	0.245579i
$120$	−15.2866	+	0.846239i	−1.39547	+	0.0772507i
$121$	−6.89606	−	3.98144i	−0.626915	−	0.361949i
$122$	3.23018	−	12.0552i	0.292447	−	1.09143i
$123$	1.06865	−	0.350704i	0.0963569	−	0.0316220i
$124$	−1.07826	−	1.07826i	−0.0968302	−	0.0968302i
$125$	−3.52846	+	3.52846i	−0.315595	+	0.315595i
$126$	−4.82675	−	2.11507i	−0.430001	−	0.188425i
$127$	−9.37062	−	5.41013i	−0.831508	−	0.480071i	0.0228608	−	0.999739i	$-0.492723\pi$
$127$	−9.37062	−	5.41013i	−0.831508	−	0.480071i	−0.854369	+	0.519667i	$0.826056\pi$
$128$	−3.93985	−	1.05568i	−0.348237	−	0.0933099i
$129$	3.17789	+	1.60745i	0.279797	+	0.141528i
$130$	10.8796	−	5.81687i	0.954206	−	0.510173i
$131$	6.84566	−	3.95234i	0.598108	−	0.345318i	−0.170189	−	0.985411i	$-0.554438\pi$
$131$	6.84566	−	3.95234i	0.598108	−	0.345318i	0.768297	+	0.640094i	$0.221104\pi$
$132$	1.67292	−	0.549010i	0.145609	−	0.0477852i
$133$	3.32245	+	5.75466i	0.288093	+	0.498992i
$134$	2.16038	+	3.74188i	0.186628	+	0.323249i
$135$	−1.43023	+	14.8690i	−0.123095	+	1.27972i
$136$	−5.58139	−	1.49553i	−0.478600	−	0.128241i
$137$	5.98485	−	5.98485i	0.511320	−	0.511320i	−0.403611	−	0.914931i	$-0.632245\pi$
$137$	5.98485	−	5.98485i	0.511320	−	0.511320i	0.914931	+	0.403611i	$0.132245\pi$
$138$	−8.68167	−	7.77089i	−0.739033	−	0.661502i
$139$	−0.234959	+	0.406962i	−0.0199290	+	0.0345180i	−0.875818	−	0.482642i	$-0.839677\pi$
$139$	−0.234959	+	0.406962i	−0.0199290	+	0.0345180i	0.855889	+	0.517160i	$0.173011\pi$
$140$	−2.47474			−0.209154
$141$	−4.05924	−	0.850344i	−0.341849	−	0.0716119i
$142$	11.9346	+	6.89042i	1.00153	+	0.578231i
$143$	−4.58562	+	4.29588i	−0.383469	+	0.359239i
$144$	−3.00191	+	6.85061i	−0.250159	+	0.570884i
$145$	4.98574	+	18.6070i	0.414043	+	1.54523i
$146$	−13.0822	+	7.55302i	−1.08269	+	0.625092i
$147$	7.45266	+	3.76974i	0.614685	+	0.310923i
$148$	−6.51985	−	1.74699i	−0.535928	−	0.143602i
$149$	−5.24080	+	1.40427i	−0.429343	+	0.115042i	−0.467018	−	0.884248i	$-0.654672\pi$
$149$	−5.24080	+	1.40427i	−0.429343	+	0.115042i	0.0376745	+	0.999290i	$0.488005\pi$
$150$	−2.09831	−	6.39388i	−0.171327	−	0.522058i
$151$	19.1087	−	5.12016i	1.55504	−	0.416673i	0.623953	−	0.781462i	$-0.285525\pi$
$151$	19.1087	−	5.12016i	1.55504	−	0.416673i	0.931090	+	0.364789i	$0.118859\pi$
$152$	11.9894	−	6.92208i	0.972468	−	0.561455i
$153$	−2.26274	+	5.16375i	−0.182931	+	0.417464i
$154$	−2.95698	+	0.792321i	−0.238280	+	0.0638470i
$155$	3.75762	−	6.50839i	0.301819	−	0.522767i
$156$	0.0826480	+	3.64179i	0.00661714	+	0.291576i
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.798796	+	0.601602i	$0.205471\pi$
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.121605	+	0.992579i	$0.461196\pi$
$158$	8.17946	+	8.17946i	0.650723	+	0.650723i
$159$	17.8719	+	9.04005i	1.41733	+	0.716923i
$160$			9.14769i			0.723188i
$161$	−5.89800	−	5.89800i	−0.464827	−	0.464827i
$162$	9.05209	+	5.72819i	0.711199	+	0.450049i
$163$	1.15428	−	4.30782i	0.0904100	−	0.337415i	−0.905874	−	0.423548i	$-0.860784\pi$
$163$	1.15428	−	4.30782i	0.0904100	−	0.337415i	0.996284	+	0.0861334i	$0.0274511\pi$
$164$	−0.0980338	−	0.365867i	−0.00765515	−	0.0285694i
$165$	4.74746	+	7.26357i	0.369589	+	0.565469i
$166$		−	3.27500i		−	0.254189i
$167$	0.251999	−	0.251999i	0.0195002	−	0.0195002i	−0.697289	−	0.716790i	$-0.745611\pi$
$167$	0.251999	−	0.251999i	0.0195002	−	0.0195002i	0.716790	+	0.697289i	$0.245611\pi$
$168$	−3.54765	+	7.01358i	−0.273707	+	0.541110i
$169$	−5.75240	−	11.6580i	−0.442492	−	0.896772i
$170$		−	6.43019i		−	0.493173i
$171$	−4.91476	−	12.5816i	−0.375841	−	0.962140i
$172$	0.599670	−	1.03866i	0.0457244	−	0.0791970i
$173$	−11.8976			−0.904559			−0.452280	−	0.891876i	$-0.649389\pi$
$173$	−11.8976			−0.904559			−0.452280	+	0.891876i	$0.649389\pi$
$174$	13.5209	+	2.83241i	1.02502	+	0.214724i
$175$	−1.24683	−	4.65325i	−0.0942518	−	0.351752i
$176$	1.12454	+	4.19685i	0.0847655	+	0.316349i
$177$	−21.9585	−	4.59993i	−1.65050	−	0.345752i
$178$	7.23322			0.542152
$179$	2.92970	−	5.07439i	0.218976	−	0.379278i	−0.735519	−	0.677504i	$-0.763062\pi$
$179$	2.92970	−	5.07439i	0.218976	−	0.379278i	0.954495	+	0.298226i	$0.0963950\pi$
$180$	4.97316	+	0.757703i	0.370678	+	0.0564759i
$181$			8.29778i			0.616769i	0.951262	+	0.308384i	$0.0997883\pi$
$181$			8.29778i			0.616769i	−0.951262	+	0.308384i	$0.900212\pi$
$182$	0.206509	−	6.33017i	0.0153075	−	0.469223i
$183$	−8.19752	+	16.2062i	−0.605978	+	1.19800i
$184$	−12.2880	+	12.2880i	−0.905886	+	0.905886i
$185$		−	33.2660i		−	2.44576i
$186$	−2.94857	−	4.51129i	−0.216200	−	0.330784i
$187$	0.847640	+	3.16344i	0.0619856	+	0.231333i
$188$	−0.361493	+	1.34911i	−0.0263646	+	0.0983940i
$189$	6.24359	+	4.45258i	0.454155	+	0.323877i
$190$	10.8937	+	10.8937i	0.790314	+	0.790314i
$191$		−	7.16012i		−	0.518088i	−0.965865	−	0.259044i	$-0.916592\pi$
$191$		−	7.16012i		−	0.518088i	0.965865	−	0.259044i	$-0.0834075\pi$
$192$	13.5605	+	6.85926i	0.978647	+	0.495024i
$193$	−1.93708	−	1.93708i	−0.139434	−	0.139434i	0.633945	−	0.773378i	$-0.281435\pi$
$193$	−1.93708	−	1.93708i	−0.139434	−	0.139434i	−0.773378	+	0.633945i	$0.781435\pi$
$194$	3.12041	+	5.40471i	0.224033	+	0.388036i
$195$	−17.2312	+	5.03878i	−1.23395	+	0.360834i
$196$	1.40632	−	2.43582i	0.100452	−	0.173987i
$197$	23.1428	−	6.20110i	1.64886	−	0.441810i	0.689564	−	0.724224i	$-0.257802\pi$
$197$	23.1428	−	6.20110i	1.64886	−	0.441810i	0.959292	+	0.282414i	$0.0911353\pi$
$198$	6.18484	−	0.686869i	0.439537	−	0.0488137i
$199$	8.08608	−	4.66850i	0.573207	−	0.330941i	−0.185222	−	0.982697i	$-0.559300\pi$
$199$	8.08608	−	4.66850i	0.573207	−	0.330941i	0.758429	+	0.651755i	$0.225967\pi$
$200$	−9.69469	+	2.59768i	−0.685518	+	0.183684i
$201$	−1.96054	−	5.97407i	−0.138286	−	0.421379i
$202$	−3.48186	+	0.932962i	−0.244983	+	0.0656429i
$203$	9.55240	+	2.55956i	0.670447	+	0.179646i
$204$	1.69422	+	0.856978i	0.118619	+	0.0600004i
$205$	1.61665	−	0.933374i	0.112912	−	0.0651897i
$206$	5.67122	+	21.1653i	0.395133	+	1.47466i
$207$	10.0466	+	13.6582i	0.698287	+	0.949313i
$208$	−8.98441	−	0.293098i	−0.622957	−	0.0203227i
$209$	−6.79538	−	3.92332i	−0.470046	−	0.271381i
$210$	−8.56070	−	1.79333i	−0.590745	−	0.123751i
$211$	5.21114			0.358750			0.179375	−	0.983781i	$-0.442592\pi$
$211$	5.21114			0.358750			0.179375	+	0.983781i	$0.442592\pi$
$212$	3.37244	−	5.84124i	0.231620	−	0.401178i
$213$	−14.9423	−	13.3747i	−1.02383	−	0.916422i
$214$	−3.86149	+	3.86149i	−0.263966	+	0.263966i
$215$	5.70942	+	1.52984i	0.389379	+	0.104334i
$216$	9.27661	−	13.0081i	0.631193	−	0.885086i
$217$	−1.92907	−	3.34125i	−0.130954	−	0.226819i
$218$	−0.116643	−	0.202032i	−0.00790009	−	0.0136834i
$219$	20.8863	−	6.85437i	1.41137	−	0.463176i
$220$	2.53079	−	1.46115i	0.170626	−	0.0985107i
$221$	−6.77213	−	0.220927i	−0.455543	−	0.0148612i
$222$	−21.2877	−	10.7678i	−1.42874	−	0.722691i
$223$	−6.61056	−	1.77129i	−0.442676	−	0.118615i	0.0305945	−	0.999532i	$-0.490260\pi$
$223$	−6.61056	−	1.77129i	−0.442676	−	0.118615i	−0.473270	+	0.880917i	$0.656927\pi$
$224$	4.06703	+	2.34810i	0.271740	+	0.156889i
$225$	1.08089	+	9.73276i	0.0720593	+	0.648850i
$226$	6.28527	−	6.28527i	0.418090	−	0.418090i
$227$	−9.03058	−	9.03058i	−0.599381	−	0.599381i	0.340767	−	0.940148i	$-0.389313\pi$
$227$	−9.03058	−	9.03058i	−0.599381	−	0.599381i	−0.940148	+	0.340767i	$0.889313\pi$
$228$	−4.32212	+	1.41841i	−0.286239	+	0.0939367i
$229$	−4.71861	+	17.6101i	−0.311815	+	1.16371i	0.615104	+	0.788446i	$0.289114\pi$
$229$	−4.71861	+	17.6101i	−0.311815	+	1.16371i	−0.926919	+	0.375263i	$0.877553\pi$
$230$	−16.7476	−	9.66924i	−1.10431	−	0.637571i
$231$	4.44798	−	0.246232i	0.292655	−	0.0162009i
$232$	5.33265	−	19.9017i	0.350105	−	1.30661i
$233$	−4.27048			−0.279769			−0.139884	−	0.990168i	$-0.544673\pi$
$233$	−4.27048			−0.279769			−0.139884	+	0.990168i	$0.544673\pi$
$234$	−2.35313	+	12.6577i	−0.153829	+	0.827457i
$235$	−6.88351			−0.449031
$236$	−1.95550	+	7.29802i	−0.127292	+	0.475060i
$237$	−9.20941	−	14.0903i	−0.598216	−	0.915265i
$238$	−2.85884	−	1.65055i	−0.185311	−	0.106989i
$239$	−0.291572	+	1.08816i	−0.0188603	+	0.0703874i	−0.974715	−	0.223453i	$-0.928267\pi$
$239$	−0.291572	+	1.08816i	−0.0188603	+	0.0703874i	0.955854	+	0.293841i	$0.0949336\pi$
$240$	−2.54527	+	12.1502i	−0.164296	+	0.784293i
$241$	−6.24227	−	6.24227i	−0.402100	−	0.402100i	0.476872	−	0.878972i	$-0.341770\pi$
$241$	−6.24227	−	6.24227i	−0.402100	−	0.402100i	−0.878972	+	0.476872i	$0.841770\pi$
$242$	−6.70184	+	6.70184i	−0.430811	+	0.430811i
$243$	−11.1836	−	10.8594i	−0.717431	−	0.696629i
$244$	5.29684	+	3.05813i	0.339095	+	0.195777i
$245$	13.3895	+	3.58771i	0.855425	+	0.229210i
$246$	−0.0739951	−	1.33666i	−0.00471776	−	0.0852222i
$247$	11.8473	−	11.0988i	0.753827	−	0.706197i
$248$	−6.96125	+	4.01908i	−0.442040	+	0.255212i
$249$	−0.977140	+	4.66452i	−0.0619237	+	0.295602i
$250$	2.96968	+	5.14363i	0.187819	+	0.325312i
$251$	−8.72352	−	15.1096i	−0.550624	−	0.953708i	−0.998230	−	0.0594773i	$-0.981057\pi$
$251$	−8.72352	−	15.1096i	−0.550624	−	0.953708i	0.447606	−	0.894231i	$-0.352277\pi$
$252$	1.61342	−	2.01656i	0.101636	−	0.127031i
$253$	9.51388	+	2.54924i	0.598133	+	0.160269i
$254$	−9.10670	+	9.10670i	−0.571405	+	0.571405i
$255$	−1.91853	+	9.15840i	−0.120143	+	0.573521i
$256$	6.34636	−	10.9922i	0.396647	−	0.687013i
$257$	3.25035			0.202751			0.101376	−	0.994848i	$-0.467676\pi$
$257$	3.25035			0.202751			0.101376	+	0.994848i	$0.467676\pi$
$258$	2.82706	−	3.15840i	0.176005	−	0.196634i
$259$	−14.7899	−	8.53897i	−0.919002	−	0.530586i
$260$	1.37356	+	5.88788i	0.0851849	+	0.365151i
$261$	−18.4125	−	8.06830i	−1.13971	−	0.499415i
$262$	−2.43511	−	9.08797i	−0.150442	−	0.561457i
$263$	−15.6551	+	9.03849i	−0.965337	+	0.557337i	−0.897811	−	0.440380i	$-0.854844\pi$
$263$	−15.6551	+	9.03849i	−0.965337	+	0.557337i	−0.0675253	+	0.997718i	$0.521510\pi$
$264$	−0.513007	−	9.26703i	−0.0315734	−	0.570346i
$265$	32.1088	+	8.60353i	1.97243	+	0.528511i
$266$	7.63961	−	2.04703i	0.468414	−	0.125511i
$267$	−10.3021	−	2.15813i	−0.630481	−	0.132075i
$268$	−2.04531	+	0.548039i	−0.124937	+	0.0334768i
$269$	0.992035	−	0.572752i	0.0604854	−	0.0349213i	−0.469452	−	0.882958i	$-0.655549\pi$
$269$	0.992035	−	0.572752i	0.0604854	−	0.0349213i	0.529938	+	0.848037i	$0.322215\pi$
$270$	16.6542	+	6.22488i	1.01354	+	0.378834i
$271$	−8.64641	+	2.31680i	−0.525232	+	0.140736i	−0.511686	−	0.859173i	$-0.670979\pi$
$271$	−8.64641	+	2.31680i	−0.525232	+	0.140736i	−0.0135464	+	0.999908i	$0.504312\pi$
$272$	−2.34263	+	4.05755i	−0.142043	+	0.246025i
$273$	−2.18282	+	8.95433i	−0.132110	+	0.541941i
$274$	−5.03705	−	8.72443i	−0.304299	−	0.527062i
$275$	4.02246	+	4.02246i	0.242564	+	0.242564i
$276$	4.77966	−	3.12398i	0.287702	−	0.188041i
$277$			25.7028i			1.54433i	0.635422	+	0.772165i	$0.280826\pi$
$277$			25.7028i			1.54433i	−0.635422	+	0.772165i	$0.719174\pi$
$278$	0.395500	+	0.395500i	0.0237205	+	0.0237205i
$279$	2.85359	+	7.30510i	0.170840	+	0.437345i
$280$	−3.37634	+	12.6007i	−0.201775	+	0.753035i
$281$	0.232804	+	0.868838i	0.0138879	+	0.0518305i	0.972522	−	0.232811i	$-0.0747922\pi$
$281$	0.232804	+	0.868838i	0.0138879	+	0.0518305i	−0.958634	+	0.284641i	$0.908126\pi$
$282$	−2.22812	+	4.40493i	−0.132683	+	0.262309i
$283$		−	18.1950i		−	1.08158i	−0.841157	−	0.540791i	$-0.818125\pi$
$283$		−	18.1950i		−	1.08158i	0.841157	−	0.540791i	$-0.181875\pi$
$284$	−4.77547	+	4.77547i	−0.283372	+	0.283372i
$285$	−12.2655	−	18.7660i	−0.726543	−	1.11160i
$286$	3.52630	+	6.59544i	0.208515	+	0.389997i
$287$		−	0.958344i		−	0.0565693i
$288$	−7.45404	−	5.96389i	−0.439234	−	0.351425i
$289$	6.73421	−	11.6640i	0.396130	−	0.686117i
$290$	22.9283			1.34640
$291$	−2.83178	−	8.62886i	−0.166002	−	0.505833i
$292$	−1.91603	−	7.15072i	−0.112127	−	0.418464i
$293$	1.18857	+	4.43581i	0.0694371	+	0.259143i	0.991914	−	0.126908i	$-0.0405054\pi$
$293$	1.18857	+	4.43581i	0.0694371	+	0.259143i	−0.922477	+	0.386051i	$0.873839\pi$
$294$	6.62991	−	7.40697i	0.386664	−	0.431983i
$295$	−37.2364			−2.16799
$296$	−17.7903	+	30.8137i	−1.03404	+	1.79101i
$297$	−9.01389	−	0.867036i	−0.523039	−	0.0503105i
$298$			6.45792i			0.374097i
$299$	−10.7588	+	17.3060i	−0.622200	+	1.00083i
$300$	3.29281	−	0.182284i	0.190110	−	0.0105242i
$301$	2.14570	−	2.14570i	0.123676	−	0.123676i
$302$		−	23.5465i		−	1.35495i
$303$	5.23751	−	0.289940i	0.300887	−	0.0166566i
$304$	−2.90535	−	10.8429i	−0.166633	−	0.621883i
$305$	−7.80168	+	29.1163i	−0.446723	+	1.66719i
$306$	5.23967	+	4.19220i	0.299532	+	0.239652i
$307$	3.93098	+	3.93098i	0.224353	+	0.224353i	0.810329	−	0.585976i	$-0.199289\pi$
$307$	3.93098	+	3.93098i	0.224353	+	0.224353i	−0.585976	+	0.810329i	$0.699289\pi$
$308$		−	1.50024i		−	0.0854840i
$309$	−1.76247	−	31.8375i	−0.100263	−	1.81117i
$310$	−6.32509	−	6.32509i	−0.359241	−	0.359241i
$311$	10.9466	+	18.9600i	0.620724	+	1.07513i	0.989351	+	0.145548i	$0.0464945\pi$
$311$	10.9466	+	18.9600i	0.620724	+	1.07513i	−0.368627	+	0.929577i	$0.620172\pi$
$312$	18.6557	+	4.54774i	1.05617	+	0.257465i
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	−0.952935	−	0.303176i	$-0.901953\pi$
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	0.739025	+	0.673678i	$0.235286\pi$
$314$	26.5179	−	7.10545i	1.49649	−	0.400984i
$315$	11.6578	+	5.10841i	0.656842	+	0.287826i
$316$	−4.90937	+	2.83443i	−0.276174	+	0.159449i
$317$	28.5136	−	7.64018i	1.60148	−	0.429116i	0.655992	−	0.754768i	$-0.272251\pi$
$317$	28.5136	−	7.64018i	1.60148	−	0.429116i	0.945489	+	0.325653i	$0.105584\pi$
$318$	15.8989	−	17.7623i	0.891566	−	0.996062i
$319$	−11.2799	+	3.02245i	−0.631556	+	0.169225i
$320$	24.3630	+	6.52805i	1.36193	+	0.364929i
$321$	6.65199	−	4.34773i	0.371278	−	0.242667i
$322$	−8.59783	+	4.96396i	−0.479138	+	0.276631i
$323$	−2.18995	−	8.17300i	−0.121852	−	0.454758i
$324$	−3.85970	+	3.55842i	−0.214428	+	0.197690i
$325$	−10.3789	+	5.54916i	−0.575718	+	0.307812i
$326$	−4.59709	−	2.65413i	−0.254609	−	0.146999i
$327$	0.105854	+	0.322553i	0.00585374	+	0.0178372i
$328$	−1.99664			−0.110246
$329$	−1.76692	+	3.06039i	−0.0974132	+	0.168725i
$330$	9.81339	−	3.22051i	0.540209	−	0.177283i
$331$	13.6196	−	13.6196i	0.748603	−	0.748603i	−0.225614	−	0.974217i	$-0.572439\pi$
$331$	13.6196	−	13.6196i	0.748603	−	0.748603i	0.974217	+	0.225614i	$0.0724387\pi$
$332$	1.55028	+	0.415396i	0.0850827	+	0.0227978i
$333$	27.1069	+	21.6879i	1.48545	+	1.18849i
$334$	−0.212091	−	0.367352i	−0.0116051	−	0.0201006i
$335$	−5.21785	−	9.03757i	−0.285081	−	0.493775i
$336$	4.74860	+	4.25043i	0.259058	+	0.231880i
$337$	15.6291	−	9.02348i	0.851373	−	0.491541i	−0.00974077	−	0.999953i	$-0.503101\pi$
$337$	15.6291	−	9.02348i	0.851373	−	0.491541i	0.861114	+	0.508412i	$0.169767\pi$
$338$	−15.1753	+	3.02213i	−0.825425	+	0.164382i
$339$	−10.8273	+	7.07671i	−0.588058	+	0.384354i
$340$	3.04385	+	0.815596i	0.165076	+	0.0442319i
$341$	3.94552	+	2.27794i	0.213662	+	0.123358i
$342$	−15.9790	+	1.77458i	−0.864048	+	0.0959585i
$343$	12.3370	−	12.3370i	0.666135	−	0.666135i
$344$	−4.47041	−	4.47041i	−0.241028	−	0.241028i
$345$	20.9684	+	18.7686i	1.12890	+	1.01047i
$346$	−3.66518	+	13.6786i	−0.197041	+	0.735367i
$347$	−21.7625	−	12.5646i	−1.16827	−	0.674503i	−0.215000	−	0.976614i	$-0.568975\pi$
$347$	−21.7625	−	12.5646i	−1.16827	−	0.674503i	−0.953273	+	0.302111i	$0.902309\pi$
$348$	−3.05575	+	6.04111i	−0.163805	+	0.323838i
$349$	−6.03993	+	22.5413i	−0.323310	+	1.20661i	0.592689	+	0.805431i	$0.298066\pi$
$349$	−6.03993	+	22.5413i	−0.323310	+	1.20661i	−0.916000	+	0.401179i	$0.868601\pi$
$350$	−5.73391			−0.306490
$351$	7.12811	−	17.3260i	0.380470	−	0.924793i
$352$	−5.54551			−0.295577
$353$	−5.17925	+	19.3292i	−0.275663	+	1.02879i	0.679732	+	0.733461i	$0.262096\pi$
$353$	−5.17925	+	19.3292i	−0.275663	+	1.02879i	−0.955395	+	0.295329i	$0.904571\pi$
$354$	−12.0530	+	23.8284i	−0.640611	+	1.26647i
$355$	−28.8249	−	16.6421i	−1.52987	−	0.883269i
$356$	−0.917452	+	3.42398i	−0.0486248	+	0.181470i
$357$	3.57933	+	3.20383i	0.189438	+	0.169564i
$358$	−4.93147	−	4.93147i	−0.260636	−	0.260636i
$359$	1.97346	−	1.97346i	0.104155	−	0.104155i	−0.653109	−	0.757264i	$-0.726536\pi$
$359$	1.97346	−	1.97346i	0.104155	−	0.104155i	0.757264	+	0.653109i	$0.226536\pi$
$360$	10.6430	−	24.2881i	0.560935	−	1.28010i
$361$	1.10195	+	0.636209i	0.0579972	+	0.0334847i
$362$	9.53991	+	2.55621i	0.501406	+	0.134351i
$363$	11.5449	−	7.54573i	0.605950	−	0.396048i
$364$	2.97031	+	0.900665i	0.155686	+	0.0472077i
$365$	31.5968	−	18.2424i	1.65385	−	0.954852i
$366$	16.1069	+	14.4171i	0.841920	+	0.753595i
$367$	16.4946	+	28.5695i	0.861011	+	1.49131i	0.870954	+	0.491364i	$0.163502\pi$
$367$	16.4946	+	28.5695i	0.861011	+	1.49131i	−0.00994343	+	0.999951i	$0.503165\pi$
$368$	7.04535	+	12.2029i	0.367264	+	0.636120i
$369$	−0.293420	+	1.92586i	−0.0152749	+	0.100256i
$370$	−38.2457	−	10.2479i	−1.98830	−	0.532763i
$371$	12.0671	−	12.0671i	0.626490	−	0.626490i
$372$	2.50950	−	0.823555i	0.130111	−	0.0426993i
$373$	2.35231	−	4.07432i	0.121798	−	0.210960i	−0.798679	−	0.601758i	$-0.794467\pi$
$373$	2.35231	−	4.07432i	0.121798	−	0.210960i	0.920477	+	0.390797i	$0.127801\pi$
$374$	3.89811			0.201566
$375$	−2.69499	−	8.21203i	−0.139168	−	0.424067i
$376$	6.37609	+	3.68124i	0.328822	+	0.189845i
$377$	0.787765	−	24.1476i	0.0405720	−	1.24366i
$378$	7.04250	−	5.80656i	0.362227	−	0.298657i
$379$	5.09903	+	19.0299i	0.261920	+	0.977498i	0.964109	+	0.265507i	$0.0855394\pi$
$379$	5.09903	+	19.0299i	0.261920	+	0.977498i	−0.702189	+	0.711991i	$0.747794\pi$
$380$	−6.53849	+	3.77500i	−0.335418	+	0.193653i
$381$	15.6876	−	10.2534i	0.803701	−	0.525298i
$382$	−8.23195	−	2.20574i	−0.421183	−	0.112856i
$383$	5.52669	−	1.48087i	0.282401	−	0.0756690i	−0.114838	−	0.993384i	$-0.536635\pi$
$383$	5.52669	−	1.48087i	0.282401	−	0.0756690i	0.397239	+	0.917715i	$0.369968\pi$
$384$	4.71178	−	5.26402i	0.240447	−	0.268628i
$385$	7.14185	−	1.91365i	0.363982	−	0.0975287i
$386$	−2.82378	+	1.63031i	−0.143727	+	0.0829806i
$387$	−4.96888	+	3.65497i	−0.252583	+	0.185792i
$388$	−2.95421	+	0.791578i	−0.149977	+	0.0401863i
$389$	−8.59884	+	14.8936i	−0.435978	+	0.755137i	−0.997375	−	0.0724102i	$-0.976931\pi$
$389$	−8.59884	+	14.8936i	−0.435978	+	0.755137i	0.561397	+	0.827547i	$0.310264\pi$
$390$	0.484816	+	21.3629i	0.0245496	+	1.08175i
$391$	5.31054	+	9.19812i	0.268565	+	0.465169i
$392$	−10.4838	−	10.4838i	−0.529513	−	0.529513i
$393$	0.756770	+	13.6704i	0.0381740	+	0.689580i
$394$		−	28.5175i		−	1.43669i
$395$	−19.7554	−	19.7554i	−0.994004	−	0.994004i
$396$	−0.459335	+	3.01483i	−0.0230824	+	0.151501i
$397$	−0.701121	+	2.61662i	−0.0351882	+	0.131324i	−0.981286	−	0.192558i	$-0.938322\pi$
$397$	−0.701121	+	2.61662i	−0.0351882	+	0.131324i	0.946097	+	0.323882i	$0.104988\pi$
$398$	−2.87635	−	10.7347i	−0.144179	−	0.538082i
$399$	−11.4917	+	0.636162i	−0.575305	+	0.0318479i
$400$			8.13814i			0.406907i
$401$	5.47997	−	5.47997i	0.273657	−	0.273657i	−0.556914	−	0.830570i	$-0.688015\pi$
$401$	5.47997	−	5.47997i	0.273657	−	0.273657i	0.830570	+	0.556914i	$0.188015\pi$
$402$	−7.47232	+	0.413655i	−0.372686	+	0.0206312i
$403$	−6.87876	+	6.44413i	−0.342655	+	0.321005i
$404$		−	1.76654i		−	0.0878886i
$405$	−21.8630	−	13.8350i	−1.08638	−	0.687467i
$406$	5.88542	−	10.1938i	0.292088	−	0.505912i
$407$	20.1665			0.999616
$408$	6.67493	−	7.45727i	0.330458	−	0.369190i
$409$	−2.05083	−	7.65382i	−0.101407	−	0.378457i	0.896506	−	0.443032i	$-0.146097\pi$
$409$	−2.05083	−	7.65382i	−0.101407	−	0.378457i	−0.997913	+	0.0645754i	$0.979431\pi$
$410$	−0.575070	−	2.14619i	−0.0284007	−	0.105993i
$411$	4.57113	+	13.9289i	0.225477	+	0.687063i
$412$	−10.7383			−0.529039
$413$	−9.55813	+	16.5552i	−0.470325	+	0.814627i
$414$	18.7977	−	7.34297i	0.923858	−	0.360887i
$415$			7.90993i			0.388283i
$416$	3.32923	−	10.9795i	0.163229	−	0.538314i
$417$	−0.445301	−	0.681306i	−0.0218065	−	0.0333637i
$418$	−6.60400	+	6.60400i	−0.323012	+	0.323012i
$419$			30.4873i			1.48940i	0.667399	+	0.744700i	$0.267408\pi$
$419$			30.4873i			1.48940i	−0.667399	+	0.744700i	$0.732592\pi$
$420$	1.93473	−	3.82490i	0.0944053	−	0.186636i
$421$	2.02029	+	7.53981i	0.0984628	+	0.367468i	0.997522	−	0.0703596i	$-0.0224147\pi$
$421$	2.02029	+	7.53981i	0.0984628	+	0.367468i	−0.899059	+	0.437828i	$0.855748\pi$
$422$	1.60534	−	5.99122i	0.0781469	−	0.291648i
$423$	4.48775	−	5.60907i	0.218202	−	0.272722i
$424$	−25.1408	−	25.1408i	−1.22095	−	1.22095i
$425$			6.13425i			0.297555i
$426$	−19.9800	+	13.0589i	−0.968034	+	0.632705i
$427$	10.9424	+	10.9424i	0.529540	+	0.529540i
$428$	−1.33812	−	2.31770i	−0.0646806	−	0.112030i
$429$	−3.05461	−	10.4459i	−0.147478	−	0.504333i
$430$	3.51769	−	6.09281i	0.169638	−	0.293821i
$431$	−30.9395	+	8.29022i	−1.49030	+	0.399326i	−0.909840	−	0.414960i	$-0.863796\pi$
$431$	−30.9395	+	8.29022i	−1.49030	+	0.399326i	−0.580465	+	0.814285i	$0.697129\pi$
$432$	−8.24126	−	9.99542i	−0.396508	−	0.480905i
$433$	19.6303	−	11.3335i	0.943371	−	0.544655i	0.0523555	−	0.998629i	$-0.483327\pi$
$433$	19.6303	−	11.3335i	0.943371	−	0.544655i	0.891015	+	0.453973i	$0.149994\pi$
$434$	−4.43569	+	1.18854i	−0.212920	+	0.0570517i
$435$	−32.6564	−	6.84097i	−1.56575	−	0.327999i
$436$	0.110431	−	0.0295898i	0.00528867	−	0.00141709i
$437$	−24.5799	−	6.58617i	−1.17582	−	0.315059i
$438$	−1.44620	−	26.1244i	−0.0691023	−	1.24827i
$439$	28.0428	−	16.1905i	1.33841	−	0.772730i	0.351836	−	0.936062i	$-0.385557\pi$
$439$	28.0428	−	16.1905i	1.33841	−	0.772730i	0.986571	+	0.163332i	$0.0522241\pi$
$440$	−3.98695	−	14.8795i	−0.190070	−	0.709352i
$441$	−11.6528	+	8.57149i	−0.554897	+	0.408166i
$442$	−2.34022	+	7.71782i	−0.111313	+	0.367099i
$443$	21.0067	+	12.1282i	0.998059	+	0.576230i	0.907673	−	0.419677i	$-0.137857\pi$
$443$	21.0067	+	12.1282i	0.998059	+	0.576230i	0.0903854	+	0.995907i	$0.471190\pi$
$444$	7.79726	−	8.71114i	0.370042	−	0.413412i
$445$	−17.4700			−0.828158
$446$	−4.07289	+	7.05446i	−0.192857	+	0.334038i
$447$	1.92681	−	9.19790i	0.0911350	−	0.435046i
$448$	9.15604	−	9.15604i	0.432582	−	0.432582i
$449$	10.4048	+	2.78796i	0.491032	+	0.131572i	0.495835	−	0.868417i	$-0.334862\pi$
$449$	10.4048	+	2.78796i	0.491032	+	0.131572i	−0.00480262	+	0.999988i	$0.501529\pi$
$450$	11.5227	+	1.75558i	0.543184	+	0.0827586i
$451$	0.565830	+	0.980046i	0.0266439	+	0.0461486i
$452$	2.17803	+	3.77247i	0.102446	+	0.177442i
$453$	−7.02541	+	33.5368i	−0.330083	+	1.57570i
$454$	−13.1644	+	7.60045i	−0.617834	+	0.356707i
$455$	−0.498770	+	15.2889i	−0.0233827	+	0.716756i
$456$	1.32540	+	23.9421i	0.0620673	+	1.12119i
$457$	23.2711	+	6.23548i	1.08858	+	0.291684i	0.758106	−	0.652132i	$-0.226125\pi$
$457$	23.2711	+	6.23548i	1.08858	+	0.291684i	0.330473	+	0.943816i	$0.392792\pi$
$458$	18.7926	+	10.8499i	0.878122	+	0.506984i
$459$	−6.21197	−	7.53420i	−0.289950	−	0.351666i
$460$	6.70136	−	6.70136i	0.312453	−	0.312453i
$461$	2.08882	+	2.08882i	0.0972863	+	0.0972863i	0.754075	−	0.656789i	$-0.228086\pi$
$461$	2.08882	+	2.08882i	0.0972863	+	0.0972863i	−0.656789	+	0.754075i	$0.728086\pi$
$462$	1.08715	−	5.18967i	0.0505788	−	0.241445i
$463$	−0.480789	+	1.79433i	−0.0223442	+	0.0833896i	−0.976198	−	0.216883i	$-0.930411\pi$
$463$	−0.480789	+	1.79433i	−0.0223442	+	0.0833896i	0.953853	+	0.300273i	$0.0970776\pi$
$464$	−14.4681	−	8.35318i	−0.671666	−	0.387786i
$465$	7.12154	+	10.8959i	0.330253	+	0.505285i
$466$	−1.31556	+	4.90975i	−0.0609423	+	0.227440i
$467$	16.0374			0.742122			0.371061	−	0.928608i	$-0.378994\pi$
$467$	16.0374			0.742122			0.371061	+	0.928608i	$0.378994\pi$
$468$	−5.69327	−	2.71938i	−0.263171	−	0.125703i
$469$	−5.35743			−0.247383
$470$	−2.12053	+	7.91394i	−0.0978129	+	0.365043i
$471$	−39.8890	+	2.20819i	−1.83799	+	0.101748i
$472$	34.4915	+	19.9137i	1.58760	+	0.916600i
$473$	−0.927416	+	3.46117i	−0.0426427	+	0.159145i
$474$	−19.0366	+	6.24735i	−0.874380	+	0.286950i
$475$	−10.3924	−	10.3924i	−0.476834	−	0.476834i
$476$	1.14393	−	1.14393i	0.0524320	−	0.0524320i
$477$	−27.9442	+	20.5549i	−1.27948	+	0.941145i
$478$	1.16123	+	0.670438i	0.0531136	+	0.0306651i
$479$	−35.7803	−	9.58729i	−1.63484	−	0.438055i	−0.679528	−	0.733649i	$-0.737816\pi$
$479$	−35.7803	−	9.58729i	−1.63484	−	0.438055i	−0.955313	+	0.295595i	$0.904482\pi$
$480$	−14.1384	−	7.15158i	−0.645329	−	0.326424i
$481$	−12.1069	+	39.9274i	−0.552027	+	1.82053i
$482$	−9.09969	+	5.25371i	−0.414480	+	0.239300i
$483$	13.7268	−	4.50480i	0.624591	−	0.204975i
$484$	−2.32239	−	4.02249i	−0.105563	−	0.182841i
$485$	−7.53657	−	13.0537i	−0.342218	−	0.592739i
$486$	−15.9302	+	9.51244i	−0.722608	+	0.431493i
$487$	19.5635	+	5.24201i	0.886505	+	0.237538i	0.673212	−	0.739450i	$-0.264914\pi$
$487$	19.5635	+	5.24201i	0.886505	+	0.237538i	0.213293	+	0.976988i	$0.431581\pi$
$488$	22.7977	−	22.7977i	1.03200	−	1.03200i
$489$	5.75566	+	5.15184i	0.260280	+	0.232974i
$490$	8.24954	−	14.2886i	0.372676	−	0.645494i
$491$	11.3387			0.511707			0.255854	−	0.966716i	$-0.417644\pi$
$491$	11.3387			0.511707			0.255854	+	0.966716i	$0.417644\pi$
$492$	0.642117	+	0.134513i	0.0289489	+	0.00606431i
$493$	−10.9056	−	6.29633i	−0.491162	−	0.283572i
$494$	−9.11049	−	17.0399i	−0.409900	−	0.766660i
$495$	−14.9379	+	1.65896i	−0.671410	+	0.0745647i
$496$	1.68689	+	6.29557i	0.0757438	+	0.282680i
$497$	−14.7980	+	8.54364i	−0.663782	+	0.383235i
$498$	5.06175	+	2.56036i	0.226823	+	0.114733i
$499$	4.93618	+	1.32264i	0.220974	+	0.0592097i	0.367607	−	0.929981i	$-0.380177\pi$
$499$	4.93618	+	1.32264i	0.220974	+	0.0592097i	−0.146634	+	0.989191i	$0.546844\pi$
$500$	−2.81150	+	0.753340i	−0.125734	+	0.0336904i
$501$	0.192473	+	0.586493i	0.00859905	+	0.0262026i
$502$	−20.0588	+	5.37473i	−0.895266	+	0.239886i
$503$	16.1644	−	9.33251i	0.720734	−	0.416116i	−0.0942889	−	0.995545i	$-0.530058\pi$
$503$	16.1644	−	9.33251i	0.720734	−	0.416116i	0.815023	+	0.579429i	$0.196724\pi$
$504$	−8.06650	−	10.9663i	−0.359311	−	0.488478i
$505$	8.40956	−	2.25333i	0.374220	−	0.100272i
$506$	5.86169	−	10.1527i	0.260584	−	0.451344i
$507$	22.5156	+	0.223383i	0.999951	+	0.00992078i
$508$	−3.15574	−	5.46591i	−0.140013	−	0.242510i
$509$	−2.28498	−	2.28498i	−0.101280	−	0.101280i	0.654651	−	0.755931i	$-0.272815\pi$
$509$	−2.28498	−	2.28498i	−0.101280	−	0.101280i	−0.755931	+	0.654651i	$0.772815\pi$
$510$	9.93834	+	5.02706i	0.440077	+	0.222602i
$511$		−	18.7304i		−	0.828586i
$512$	−16.4510	−	16.4510i	−0.727037	−	0.727037i
$513$	23.2881	+	2.24006i	1.02820	+	0.0989010i
$514$	1.00130	−	3.73691i	0.0441655	−	0.164828i
$515$	−13.6974	−	51.1195i	−0.603580	−	2.25259i
$516$	1.13651	+	1.73885i	0.0500320	+	0.0765485i
$517$		−	4.17292i		−	0.183525i
$518$	−14.3734	+	14.3734i	−0.631531	+	0.631531i
$519$	9.30145	−	18.3887i	0.408288	−	0.807173i
$520$	31.8533	+	1.03915i	1.39686	+	0.0455698i
$521$		−	21.9128i		−	0.960018i	−0.877263	−	0.480009i	$-0.840633\pi$
$521$		−	21.9128i		−	0.960018i	0.877263	−	0.480009i	$-0.159367\pi$
$522$	−14.9482	+	18.6832i	−0.654266	+	0.817743i
$523$	9.66002	−	16.7316i	0.422403	−	0.731624i	−0.573771	−	0.819016i	$-0.694520\pi$
$523$	9.66002	−	16.7316i	0.422403	−	0.731624i	0.996174	+	0.0873922i	$0.0278533\pi$
$524$	4.61083			0.201425
$525$	8.16671	+	1.71079i	0.356424	+	0.0746650i
$526$	5.56879	+	20.7830i	0.242811	+	0.906182i
$527$	1.27152	+	4.74538i	0.0553883	+	0.206712i
$528$	−7.36570	−	1.54299i	−0.320551	−	0.0671501i
$529$	8.94238			0.388799
$530$	19.7829	−	34.2649i	0.859313	−	1.48837i
$531$	24.2765	−	30.3423i	1.05351	−	1.31674i
$532$			3.87599i			0.168046i
$533$	−2.28008	+	0.531913i	−0.0987612	+	0.0230397i
$534$	−5.65486	+	11.1795i	−0.244710	+	0.483783i
$535$	9.32647	−	9.32647i	0.403218	−	0.403218i
$536$			11.1618i			0.482117i
$537$	5.55244	+	8.49518i	0.239605	+	0.366594i
$538$	−0.352883	−	1.31698i	−0.0152139	−	0.0567790i
$539$	−2.17494	+	8.11699i	−0.0936814	+	0.349624i
$540$	−5.05906	+	7.09403i	−0.217707	+	0.305278i
$541$	−1.88126	−	1.88126i	−0.0808815	−	0.0808815i	0.665509	−	0.746390i	$-0.268215\pi$
$541$	−1.88126	−	1.88126i	−0.0808815	−	0.0808815i	−0.746390	+	0.665509i	$0.768215\pi$
$542$			10.6544i			0.457647i
$543$	−12.8248	−	6.48713i	−0.550367	−	0.278389i
$544$	−4.22845	−	4.22845i	−0.181293	−	0.181293i
$545$	0.281723	+	0.487958i	0.0120677	+	0.0209018i
$546$	9.62230	+	5.26804i	0.411797	+	0.225451i
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	−0.392281	−	0.919846i	$-0.628314\pi$
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	0.992750	−	0.120198i	$-0.0383529\pi$
$548$	4.76876	−	1.27779i	0.203711	−	0.0545843i
$549$	−18.6392	−	25.3398i	−0.795502	−	1.08147i
$550$	5.86376	−	3.38544i	0.250031	−	0.144356i
$551$	29.1427	−	7.80876i	1.24152	−	0.332664i
$552$	−9.38541	−	28.5988i	−0.399470	−	1.21724i
$553$	−13.8542	+	3.71222i	−0.589140	+	0.157860i
$554$	29.5503	+	7.91798i	1.25547	+	0.336403i
$555$	51.4151	+	26.0070i	2.18245	+	1.10394i
$556$	−0.237382	+	0.137052i	−0.0100672	+	0.00581232i
$557$	3.91190	+	14.5994i	0.165753	+	0.618597i	0.997943	+	0.0641073i	$0.0204200\pi$
$557$	3.91190	+	14.5994i	0.165753	+	0.618597i	−0.832190	+	0.554490i	$0.812913\pi$
$558$	9.27771	−	1.03035i	0.392757	−	0.0436184i
$559$	−6.29595	−	3.91408i	−0.266290	−	0.165548i
$560$	9.16043	+	5.28878i	0.387099	+	0.223492i
$561$	−5.55200	−	1.16305i	−0.234406	−	0.0491042i
$562$	1.07062			0.0451612
$563$	−12.7053	+	22.0062i	−0.535463	+	0.927450i	0.463677	+	0.886004i	$0.346530\pi$
$563$	−12.7053	+	22.0062i	−0.535463	+	0.927450i	−0.999141	+	0.0414457i	$0.986804\pi$
$564$	−1.80254	−	1.61344i	−0.0759006	−	0.0679380i
$565$	−15.1805	+	15.1805i	−0.638648	+	0.638648i
$566$	−20.9187	−	5.60516i	−0.879280	−	0.235602i
$567$	−11.7630	+	6.16896i	−0.493999	+	0.259072i
$568$	17.8000	+	30.8306i	0.746873	+	1.29362i
$569$	12.5182	+	21.6821i	0.524789	+	0.908962i	0.999583	+	0.0288649i	$0.00918926\pi$
$569$	12.5182	+	21.6821i	0.524789	+	0.908962i	−0.474794	+	0.880097i	$0.657477\pi$
$570$	−25.3537	+	8.32046i	−1.06195	+	0.348506i
$571$	23.2909	−	13.4470i	0.974693	−	0.562739i	0.0740294	−	0.997256i	$-0.476414\pi$
$571$	23.2909	−	13.4470i	0.974693	−	0.562739i	0.900664	+	0.434517i	$0.143081\pi$
$572$	−3.56935	+	0.832682i	−0.149242	+	0.0348162i
$573$	11.0665	+	5.59772i	0.462310	+	0.233848i
$574$	−1.10180	−	0.295227i	−0.0459884	−	0.0123225i
$575$	15.9768	+	9.22423i	0.666280	+	0.384677i
$576$	−21.2030	+	15.5963i	−0.883459	+	0.649847i
$577$	−12.8490	+	12.8490i	−0.534912	+	0.534912i	−0.922030	−	0.387118i	$-0.873470\pi$
$577$	−12.8490	+	12.8490i	−0.534912	+	0.534912i	0.387118	+	0.922030i	$0.373470\pi$
$578$	−11.3355	−	11.3355i	−0.471494	−	0.471494i
$579$	4.50828	−	1.47951i	0.187358	−	0.0614862i
$580$	−2.90819	+	10.8535i	−0.120756	+	0.450668i
$581$	3.51673	+	2.03038i	0.145899	+	0.0842345i
$582$	−10.7929	+	0.597477i	−0.447380	+	0.0247662i
$583$	−5.21563	+	19.4650i	−0.216009	+	0.806158i
$584$	−39.0235			−1.61480
$585$	5.68339	−	30.5714i	0.234979	−	1.26397i
$586$	5.46598			0.225797
$587$	3.68465	−	13.7513i	0.152082	−	0.567576i	−0.847256	−	0.531185i	$-0.821747\pi$
$587$	3.68465	−	13.7513i	0.152082	−	0.567576i	0.999338	−	0.0363915i	$-0.0115863\pi$
$588$	2.66530	+	4.07788i	0.109915	+	0.168169i
$589$	−10.1936	−	5.88526i	−0.420019	−	0.242498i
$590$	−11.4710	+	42.8104i	−0.472255	+	1.76248i
$591$	−8.50858	+	40.6169i	−0.349996	+	1.67076i
$592$	20.4002	+	20.4002i	0.838441	+	0.838441i
$593$	14.8629	−	14.8629i	0.610345	−	0.610345i	−0.332691	−	0.943036i	$-0.607957\pi$
$593$	14.8629	−	14.8629i	0.610345	−	0.610345i	0.943036	+	0.332691i	$0.107957\pi$
$594$	−3.77364	+	10.0961i	−0.154834	+	0.414249i
$595$	6.90481	+	3.98649i	0.283070	+	0.163430i
$596$	−3.05698	−	0.819114i	−0.125219	−	0.0335522i
$597$	0.893895	+	16.1474i	0.0365847	+	0.660871i
$598$	16.5823	+	17.7007i	0.678099	+	0.723834i
$599$	−29.6012	+	17.0903i	−1.20947	+	0.698289i	−0.962644	−	0.270770i	$-0.912722\pi$
$599$	−29.6012	+	17.0903i	−1.20947	+	0.698289i	−0.246828	+	0.969059i	$0.579388\pi$
$600$	3.56430	−	17.0147i	0.145512	−	0.694623i
$601$	−4.47135	−	7.74461i	−0.182390	−	0.315909i	0.760304	−	0.649568i	$-0.225050\pi$
$601$	−4.47135	−	7.74461i	−0.182390	−	0.315909i	−0.942694	+	0.333659i	$0.891717\pi$
$602$	−1.80590	−	3.12790i	−0.0736028	−	0.127484i
$603$	10.7661	+	1.64031i	0.438430	+	0.0667985i
$604$	11.1462	+	2.98660i	0.453531	+	0.121523i
$605$	16.1866	−	16.1866i	0.658079	−	0.658079i
$606$	1.28012	−	6.11086i	0.0520015	−	0.248237i
$607$	−4.58314	+	7.93823i	−0.186024	+	0.322203i	−0.943921	−	0.330171i	$-0.892894\pi$
$607$	−4.58314	+	7.93823i	−0.186024	+	0.322203i	0.757897	+	0.652374i	$0.226227\pi$
$608$	14.3273			0.581048
$609$	−11.4240	+	12.7629i	−0.462923	+	0.517179i
$610$	31.0714	+	17.9391i	1.25805	+	0.726333i
$611$	8.26193	+	2.50520i	0.334242	+	0.101350i
$612$	−2.64905	+	1.94856i	−0.107081	+	0.0787660i
$613$	−0.197913	−	0.738622i	−0.00799364	−	0.0298327i	0.961814	−	0.273705i	$-0.0882490\pi$
$613$	−0.197913	−	0.738622i	−0.00799364	−	0.0298327i	−0.969807	+	0.243872i	$0.921582\pi$
$614$	5.73041	−	3.30845i	0.231260	−	0.133518i
$615$	0.178717	+	3.22836i	0.00720655	+	0.130180i
$616$	−7.63878	−	2.04680i	−0.307775	−	0.0824681i
$617$	16.1154	−	4.31810i	0.648780	−	0.173840i	0.0806029	−	0.996746i	$-0.474315\pi$
$617$	16.1154	−	4.31810i	0.648780	−	0.173840i	0.568177	+	0.822906i	$0.307649\pi$
$618$	−37.1463	−	7.78153i	−1.49424	−	0.313019i
$619$	3.71367	−	0.995076i	0.149265	−	0.0399955i	−0.183413	−	0.983036i	$-0.558714\pi$
$619$	3.71367	−	0.995076i	0.149265	−	0.0399955i	0.332678	+	0.943041i	$0.392048\pi$
$620$	3.79636	−	2.19183i	0.152466	−	0.0880261i
$621$	−28.9642	+	4.84990i	−1.16229	+	0.194620i
$622$	25.1704	−	6.74440i	1.00924	−	0.270426i
$623$	−4.48434	+	7.76711i	−0.179661	+	0.311183i
$624$	7.47693	−	13.6569i	0.299317	−	0.546715i
$625$	−15.3330	−	26.5575i	−0.613320	−	1.06230i
$626$	6.37023	+	6.37023i	0.254606	+	0.254606i
$627$	11.3763	−	7.43556i	0.454328	−	0.296948i
$628$			13.4540i			0.536872i
$629$	15.3769	+	15.3769i	0.613118	+	0.613118i
$630$	9.46440	−	11.8292i	0.377071	−	0.471287i
$631$	3.46710	−	12.9394i	0.138023	−	0.515110i	−0.861944	−	0.507004i	$-0.830753\pi$
$631$	3.46710	−	12.9394i	0.138023	−	0.515110i	0.999967	−	0.00810607i	$-0.00258027\pi$
$632$	7.73413	+	28.8642i	0.307647	+	1.14815i
$633$	−4.07403	+	8.05422i	−0.161928	+	0.320126i
$634$		−	35.1355i		−	1.39541i
$635$	21.9949	−	21.9949i	0.872843	−	0.872843i
$636$	6.39153	+	9.77899i	0.253441	+	0.387762i
$637$	−14.7650	−	9.17916i	−0.585012	−	0.363692i
$638$			13.8996i			0.550290i
$639$	32.3534	−	12.6382i	1.27988	−	0.499961i
$640$	5.86282	−	10.1547i	0.231748	−	0.401400i
$641$	−25.4888			−1.00675			−0.503375	−	0.864068i	$-0.667908\pi$
$641$	−25.4888			−1.00675			−0.503375	+	0.864068i	$0.667908\pi$
$642$	−2.94935	−	8.98711i	−0.116402	−	0.354693i
$643$	−1.44538	−	5.39422i	−0.0570001	−	0.212727i	0.931552	−	0.363609i	$-0.118455\pi$
$643$	−1.44538	−	5.39422i	−0.0570001	−	0.212727i	−0.988552	+	0.150881i	$0.951789\pi$
$644$	−1.25924	−	4.69956i	−0.0496212	−	0.185189i
$645$	−6.82805	+	7.62833i	−0.268854	+	0.300365i
$646$	−10.0711			−0.396241
$647$	−1.23117	+	2.13245i	−0.0484024	+	0.0838354i	−0.889212	−	0.457496i	$-0.848746\pi$
$647$	−1.23117	+	2.13245i	−0.0484024	+	0.0838354i	0.840809	+	0.541332i	$0.182080\pi$
$648$	12.8526	+	24.5073i	0.504896	+	0.962737i
$649$		−	22.5734i		−	0.886085i
$650$	3.18251	+	13.6420i	0.124828	+	0.535085i
$651$	6.67229	−	0.369367i	0.261508	−	0.0144766i
$652$	1.83947	−	1.83947i	0.0720393	−	0.0720393i
$653$		−	32.0947i		−	1.25596i	−0.778229	−	0.627981i	$-0.783882\pi$
$653$		−	32.0947i		−	1.25596i	0.778229	−	0.627981i	$-0.216118\pi$
$654$	0.403447	−	0.0223341i	0.0157760	−	0.000873334i
$655$	5.88141	+	21.9497i	0.229806	+	0.857646i
$656$	−0.419016	+	1.56379i	−0.0163598	+	0.0610557i
$657$	−5.73478	+	37.6401i	−0.223735	+	1.46848i
$658$	2.97419	+	2.97419i	0.115946	+	0.115946i
$659$			5.31859i			0.207183i	0.994620	+	0.103591i	$0.0330335\pi$
$659$			5.31859i			0.207183i	−0.994620	+	0.103591i	$0.966967\pi$
$660$	0.279772	+	5.05383i	0.0108901	+	0.196720i
$661$	−16.1836	−	16.1836i	−0.629470	−	0.629470i	0.318464	−	0.947935i	$-0.396833\pi$
$661$	−16.1836	−	16.1836i	−0.629470	−	0.629470i	−0.947935	+	0.318464i	$0.896833\pi$
$662$	−11.4628	−	19.8541i	−0.445513	−	0.771651i
$663$	5.63585	−	10.2941i	0.218878	−	0.399791i
$664$	4.23015	−	7.32684i	0.164162	−	0.284337i
$665$	−18.4516	+	4.94408i	−0.715520	+	0.191723i
$666$	33.2850	−	24.4835i	1.28977	−	0.948717i
$667$	−32.7980	+	18.9359i	−1.26994	+	0.733202i
$668$	0.200794	−	0.0538026i	0.00776896	−	0.00208169i
$669$	7.90574	−	8.83233i	0.305654	−	0.341478i
$670$	−11.9979	+	3.21481i	−0.463517	+	0.124199i
$671$	−17.6509	−	4.72954i	−0.681404	−	0.182582i
$672$	−6.80874	+	4.45018i	−0.262653	+	0.171669i
$673$	−24.6097	+	14.2084i	−0.948633	+	0.547693i	−0.892656	−	0.450739i	$-0.851161\pi$
$673$	−24.6097	+	14.2084i	−0.948633	+	0.547693i	−0.0559769	+	0.998432i	$0.517827\pi$
$674$	−5.55954	−	20.7485i	−0.214146	−	0.799202i
$675$	−15.8877	−	5.93838i	−0.611519	−	0.228568i
$676$	0.494230	−	7.56681i	0.0190088	−	0.291031i
$677$	19.5004	+	11.2586i	0.749461	+	0.432701i	0.825499	−	0.564404i	$-0.190894\pi$
$677$	19.5004	+	11.2586i	0.749461	+	0.432701i	−0.0760383	+	0.997105i	$0.524227\pi$
$678$	4.80059	+	14.6281i	0.184366	+	0.561790i
$679$	−7.73819			−0.296965
$680$	8.30556	−	14.3857i	0.318504	−	0.551665i
$681$	21.0175	−	6.89741i	0.805391	−	0.264309i
$682$	3.83439	−	3.83439i	0.146827	−	0.146827i
$683$	−38.9958	−	10.4489i	−1.49213	−	0.399816i	−0.581677	−	0.813420i	$-0.697603\pi$
$683$	−38.9958	−	10.4489i	−1.49213	−	0.399816i	−0.910457	+	0.413604i	$0.864270\pi$
$684$	1.18673	−	7.78906i	0.0453757	−	0.297822i
$685$	12.1657	+	21.0717i	0.464829	+	0.805107i
$686$	−10.3832	−	17.9843i	−0.396434	−	0.686644i
$687$	−23.5288	−	21.0604i	−0.897679	−	0.803504i
$688$	−4.43943	+	2.56311i	−0.169252	+	0.0977176i
$689$	−35.4074	−	22.0121i	−1.34891	−	0.838596i
$690$	28.0377	−	18.3254i	1.06738	−	0.697635i
$691$	−32.4618	−	8.69813i	−1.23491	−	0.330892i	−0.418419	−	0.908254i	$-0.637415\pi$
$691$	−32.4618	−	8.69813i	−1.23491	−	0.330892i	−0.816488	+	0.577362i	$0.804082\pi$
$692$	−6.01014	−	3.46996i	−0.228471	−	0.131908i
$693$	−3.09682	+	7.06719i	−0.117638	+	0.268460i
$694$	−21.1496	+	21.1496i	−0.802828	+	0.802828i
$695$	−0.955230	−	0.955230i	−0.0362339	−	0.0362339i
$696$	26.5906	+	23.8010i	1.00791	+	0.902174i
$697$	−0.315840	+	1.17873i	−0.0119633	+	0.0446476i
$698$	24.0550	+	13.8882i	0.910495	+	0.525674i
$699$	3.33862	−	6.60035i	0.126278	−	0.249648i
$700$	0.727282	−	2.71425i	0.0274887	−	0.102589i
$701$	34.8493			1.31624			0.658120	−	0.752913i	$-0.271352\pi$
$701$	34.8493			1.31624			0.658120	+	0.752913i	$0.271352\pi$
$702$	−17.7237	−	13.5326i	−0.668938	−	0.510754i
$703$	−52.1018			−1.96506
$704$	−3.95743	+	14.7693i	−0.149151	+	0.556640i
$705$	5.38147	−	10.6390i	0.202678	−	0.400687i
$706$	20.6272	+	11.9091i	0.776313	+	0.448205i
$707$	1.15681	−	4.31727i	0.0435062	−	0.162367i
$708$	−9.75084	−	8.72789i	−0.366459	−	0.328014i
$709$	−6.24720	−	6.24720i	−0.234619	−	0.234619i	0.579999	−	0.814617i	$-0.303053\pi$
$709$	−6.24720	−	6.24720i	−0.234619	−	0.234619i	−0.814617	+	0.579999i	$0.803053\pi$
$710$	−28.0131	+	28.0131i	−1.05131	+	1.05131i
$711$	28.9775	−	3.21815i	1.08674	−	0.120690i
$712$	16.1822	+	9.34279i	0.606453	+	0.350136i
$713$	14.2715	+	3.82404i	0.534473	+	0.143211i
$714$	4.78607	−	3.12817i	0.179114	−	0.117069i
$715$	−8.51689	−	15.9296i	−0.318514	−	0.595735i
$716$	2.95991	−	1.70890i	0.110617	−	0.0638647i
$717$	−1.45389	−	1.30136i	−0.0542965	−	0.0486003i
$718$	−1.66094	−	2.87683i	−0.0619856	−	0.107362i
$719$	−12.4677	−	21.5947i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$719$	−12.4677	−	21.5947i	−0.464966	−	0.805345i	−0.999200	+	0.0399915i	$0.987267\pi$
$720$	−16.7892	−	13.4328i	−0.625696	−	0.500612i
$721$	−26.2435	−	7.03193i	−0.977359	−	0.261883i
$722$	1.07091	−	1.07091i	0.0398552	−	0.0398552i
$723$	14.5281	−	4.76775i	0.540304	−	0.177314i
$724$	−2.42006	+	4.19166i	−0.0899408	+	0.155782i
$725$	−21.8730			−0.812344
$726$	−5.11876	−	15.5976i	−0.189975	−	0.578883i
$727$	−15.7972	−	9.12055i	−0.585888	−	0.338262i	0.177582	−	0.984106i	$-0.443172\pi$
$727$	−15.7972	−	9.12055i	−0.585888	−	0.338262i	−0.763470	+	0.645844i	$0.776506\pi$
$728$	8.63837	−	13.8951i	0.320159	−	0.514989i
$729$	25.5273	−	8.79541i	0.945454	−	0.325756i
$730$	−11.2395	−	41.9464i	−0.415993	−	1.55251i
$731$	−3.34629	+	1.93198i	−0.123767	+	0.0714569i
$732$	−8.86759	+	5.79584i	−0.327755	+	0.214220i
$733$	−22.3310	−	5.98357i	−0.824814	−	0.221008i	−0.178364	−	0.983965i	$-0.557081\pi$
$733$	−22.3310	−	5.98357i	−0.824814	−	0.221008i	−0.646450	+	0.762956i	$0.723747\pi$
$734$	37.9275	−	10.1626i	1.39993	−	0.375110i
$735$	−16.0129	+	17.8897i	−0.590644	+	0.659870i
$736$	−17.3715	+	4.65469i	−0.640324	+	0.171574i
$737$	5.47876	−	3.16316i	0.201813	−	0.116517i
$738$	2.12375	+	0.930622i	0.0781765	+	0.0342567i
$739$	11.4323	−	3.06326i	0.420542	−	0.112684i	−0.0423409	−	0.999103i	$-0.513482\pi$
$739$	11.4323	−	3.06326i	0.420542	−	0.112684i	0.462883	+	0.886419i	$0.346815\pi$
$740$	9.70206	−	16.8045i	0.356655	−	0.617745i
$741$	7.89183	+	26.9878i	0.289914	+	0.991423i
$742$	−10.1560	−	17.5908i	−0.372840	−	0.645778i
$743$	−31.1023	−	31.1023i	−1.14103	−	1.14103i	−0.988262	−	0.152771i	$-0.951180\pi$
$743$	−31.1023	−	31.1023i	−1.14103	−	1.14103i	−0.152771	−	0.988262i	$-0.548820\pi$
$744$	−0.769548	−	13.9012i	−0.0282130	−	0.509643i
$745$		−	15.5975i		−	0.571448i
$746$	−3.95957	−	3.95957i	−0.144970	−	0.144970i
$747$	−6.44545	−	5.15692i	−0.235827	−	0.188682i
$748$	−0.494431	+	1.84524i	−0.0180782	+	0.0674687i
$749$	−1.75252	−	6.54051i	−0.0640358	−	0.238985i
$750$	−10.2715	+	0.568615i	−0.375063	+	0.0207629i
$751$			37.0028i			1.35025i	0.737702	+	0.675126i	$0.235911\pi$
$751$			37.0028i			1.35025i	−0.737702	+	0.675126i	$0.764089\pi$
$752$	4.22128	−	4.22128i	0.153934	−	0.153934i
$753$	30.1730	−	1.67032i	1.09956	−	0.0608700i
$754$	−27.5196	−	8.34458i	−1.00221	−	0.303892i
$755$			56.8706i			2.06973i
$756$	1.85538	+	4.07019i	0.0674796	+	0.148032i
$757$	−23.2842	+	40.3294i	−0.846278	+	1.46580i	0.0382287	+	0.999269i	$0.487828\pi$
$757$	−23.2842	+	40.3294i	−0.846278	+	1.46580i	−0.884507	+	0.466527i	$0.845505\pi$
$758$	23.4493			0.851717
$759$	−11.3779	+	12.7115i	−0.412992	+	0.461397i
$760$	10.3006	+	38.4424i	0.373643	+	1.39445i
$761$	7.83690	+	29.2477i	0.284088	+	1.06023i	0.949504	+	0.313756i	$0.101588\pi$
$761$	7.83690	+	29.2477i	0.284088	+	1.06023i	−0.665416	+	0.746473i	$0.731746\pi$
$762$	−6.95556	−	21.1946i	−0.251973	−	0.767800i
$763$	0.289259			0.0104719
$764$	2.08826	−	3.61697i	0.0755506	−	0.130857i
$765$	−12.6551	−	10.1252i	−0.457546	−	0.366077i
$766$		−	6.81020i		−	0.246062i
$767$	44.6929	+	13.5519i	1.61377	+	0.489331i
$768$	12.0278	+	18.4024i	0.434015	+	0.664039i
$769$	37.1880	−	37.1880i	1.34103	−	1.34103i	0.445999	−	0.895033i	$-0.352848\pi$
$769$	37.1880	−	37.1880i	1.34103	−	1.34103i	0.895033	−	0.445999i	$-0.147152\pi$
$770$		−	8.80046i		−	0.317146i
$771$	−2.54109	+	5.02366i	−0.0915152	+	0.180923i
$772$	−0.413573	−	1.54347i	−0.0148848	−	0.0555508i
$773$	−5.09988	+	19.0330i	−0.183430	+	0.684570i	0.811531	+	0.584309i	$0.198634\pi$
$773$	−5.09988	+	19.0330i	−0.183430	+	0.684570i	−0.994961	+	0.100261i	$0.968032\pi$
$774$	2.67138	+	6.83865i	0.0960209	+	0.245810i
$775$	6.03398	+	6.03398i	0.216747	+	0.216747i
$776$			16.1219i			0.578744i
$777$	24.7603	−	16.1833i	0.888270	−	0.580572i
$778$	14.4742	+	14.4742i	0.518924	+	0.518924i
$779$	−1.46187	−	2.53203i	−0.0523769	−	0.0907194i
$780$	−10.1740	−	2.48014i	−0.364287	−	0.0888033i
$781$	10.0888	−	17.4742i	0.361004	−	0.625277i
$782$	12.2110	−	3.27192i	0.436664	−	0.117004i
$783$	26.8649	−	22.1502i	0.960073	−	0.791583i
$784$	−10.4112	+	6.01090i	−0.371828	+	0.214675i
$785$	−64.0473	+	17.1614i	−2.28595	+	0.612517i
$786$	15.9499	+	3.34124i	0.568914	+	0.119178i
$787$	9.80128	−	2.62624i	0.349378	−	0.0936155i	−0.0798623	−	0.996806i	$-0.525448\pi$
$787$	9.80128	−	2.62624i	0.349378	−	0.0936155i	0.429240	+	0.903190i	$0.358781\pi$
$788$	13.4993	+	3.61712i	0.480891	+	0.128854i
$789$	−1.73063	−	31.2624i	−0.0616122	−	1.11297i
$790$	−28.7986	+	16.6269i	−1.02461	+	0.591557i
$791$	2.85255	+	10.6459i	0.101425	+	0.378523i
$792$	14.7240	+	6.45199i	0.523193	+	0.229261i
$793$	19.9606	−	32.1074i	0.708822	−	1.14017i
$794$	2.79232	+	1.61215i	0.0990958	+	0.0572130i
$795$	−38.3998	+	42.9004i	−1.36190	+	1.52152i
$796$	5.44630			0.193039
$797$	−20.6189	+	35.7129i	−0.730358	+	1.26502i	0.226373	+	0.974041i	$0.427313\pi$
$797$	−20.6189	+	35.7129i	−0.730358	+	1.26502i	−0.956730	+	0.290976i	$0.906020\pi$
$798$	−2.80874	+	13.4079i	−0.0994284	+	0.474636i
$799$	3.18185	−	3.18185i	0.112566	−	0.112566i
$800$	−10.0330	−	2.68834i	−0.354720	−	0.0950471i
$801$	11.3897	−	14.2355i	0.402434	−	0.502988i
$802$	−4.61213	−	7.98844i	−0.162860	−	0.282082i
$803$	11.0589	+	19.1546i	0.390261	+	0.675951i
$804$	0.751968	−	3.58963i	0.0265199	−	0.126596i
$805$	20.7659	−	11.9892i	0.731902	−	0.422564i
$806$	5.28971	+	9.89365i	0.186322	+	0.348489i
$807$	0.109667	+	1.98104i	0.00386045	+	0.0697358i
$808$	−8.99470	−	2.41012i	−0.316432	−	0.0847878i
$809$	22.9401	+	13.2445i	0.806532	+	0.465651i	0.845750	−	0.533579i	$-0.179153\pi$
$809$	22.9401	+	13.2445i	0.806532	+	0.465651i	−0.0392184	+	0.999231i	$0.512487\pi$
$810$	−22.6411	+	20.8738i	−0.795529	+	0.733431i
$811$	−27.7759	+	27.7759i	−0.975343	+	0.975343i	−0.999703	−	0.0243602i	$-0.992245\pi$
$811$	−27.7759	+	27.7759i	−0.975343	+	0.975343i	0.0243602	+	0.999703i	$0.492245\pi$
$812$	4.07894	+	4.07894i	0.143143	+	0.143143i
$813$	3.17890	−	15.1749i	0.111489	−	0.532208i
$814$	6.21248	−	23.1853i	0.217747	−	0.812644i
$815$	11.1031	+	6.41039i	0.388925	+	0.224546i
$816$	−4.43981	−	6.79287i	−0.155424	−	0.237798i
$817$	2.39606	−	8.94221i	0.0838274	−	0.312848i
$818$	−9.43133			−0.329759
$819$	−12.1331	−	10.3741i	−0.423964	−	0.362501i
$820$	1.08888			0.0380253
$821$	7.32634	−	27.3423i	0.255691	−	0.954251i	−0.712014	−	0.702165i	$-0.752217\pi$
$821$	7.32634	−	27.3423i	0.255691	−	0.954251i	0.967705	−	0.252086i	$-0.0811166\pi$
$822$	17.4222	−	0.964463i	0.607669	−	0.0336395i
$823$	2.76090	+	1.59401i	0.0962390	+	0.0555636i	0.547347	−	0.836906i	$-0.315638\pi$
$823$	2.76090	+	1.59401i	0.0962390	+	0.0555636i	−0.451108	+	0.892469i	$0.648971\pi$
$824$	−14.6505	+	54.6764i	−0.510374	+	1.90474i
$825$	−9.36174	+	3.07229i	−0.325934	+	0.106963i
$826$	16.0889	+	16.0889i	0.559805	+	0.559805i
$827$	−40.4226	+	40.4226i	−1.40563	+	1.40563i	−0.625027	+	0.780603i	$0.714912\pi$
$827$	−40.4226	+	40.4226i	−1.40563	+	1.40563i	−0.780603	+	0.625027i	$0.785088\pi$
$828$	1.09165	+	9.82963i	0.0379374	+	0.341603i
$829$	0.372721	+	0.215190i	0.0129451	+	0.00747387i	0.506459	−	0.862264i	$-0.330954\pi$
$829$	0.372721	+	0.215190i	0.0129451	+	0.00747387i	−0.493513	+	0.869738i	$0.664288\pi$
$830$	9.09400	+	2.43673i	0.315657	+	0.0845801i
$831$	−39.7256	−	20.0942i	−1.37806	−	0.697060i
$832$	−26.8658	−	16.7020i	−0.931405	−	0.579038i
$833$	−7.84759	+	4.53081i	−0.271903	+	0.156983i
$834$	−0.920473	+	0.302077i	−0.0318734	+	0.0104601i
$835$	0.512252	+	0.887247i	0.0177272	+	0.0307044i
$836$	−2.28848	−	3.96376i	−0.0791488	−	0.137090i
$837$	−13.5215	−	1.30062i	−0.467371	−	0.0449559i
$838$	35.0510	+	9.39190i	1.21082	+	0.324438i
$839$	−3.41628	+	3.41628i	−0.117943	+	0.117943i	−0.763615	−	0.645672i	$-0.776577\pi$
$839$	−3.41628	+	3.41628i	−0.117943	+	0.117943i	0.645672	+	0.763615i	$0.276577\pi$
$840$	−16.8357	−	15.0695i	−0.580887	−	0.519947i
$841$	7.95100	−	13.7715i	0.274172	−	0.474880i
$842$	9.29085			0.320184
$843$	−1.52486	−	0.319433i	−0.0525189	−	0.0110019i
$844$	2.63244	+	1.51984i	0.0906122	+	0.0523150i
$845$	36.6520	−	7.29919i	1.26087	−	0.251100i
$846$	−5.06622	−	6.88746i	−0.174180	−	0.236796i
$847$	−3.04160	−	11.3514i	−0.104511	−	0.390040i
$848$	−24.9666	+	14.4145i	−0.857357	+	0.494995i
$849$	28.1218	+	14.2247i	0.965138	+	0.488191i
$850$	7.05251	+	1.88971i	0.241899	+	0.0648166i
$851$	63.1724	−	16.9270i	2.16552	−	0.580250i
$852$	−3.64743	−	11.1143i	−0.124959	−	0.380769i
$853$	43.1437	−	11.5603i	1.47721	−	0.395818i	0.571815	−	0.820383i	$-0.306240\pi$
$853$	43.1437	−	11.5603i	1.47721	−	0.395818i	0.905397	+	0.424565i	$0.139573\pi$
$854$	15.9513	−	9.20951i	0.545843	−	0.315143i
$855$	38.5934	−	4.28606i	1.31986	−	0.146580i
$856$	−13.6267	+	3.65125i	−0.465750	+	0.124797i
$857$	−25.1388	+	43.5417i	−0.858725	+	1.48736i	0.0144207	+	0.999896i	$0.495410\pi$
$857$	−25.1388	+	43.5417i	−0.858725	+	1.48736i	−0.873146	+	0.487459i	$0.837924\pi$
$858$	−12.9506	+	0.293905i	−0.442126	+	0.0100338i
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	0.873153	+	0.487445i	$0.162071\pi$
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	−0.0144366	+	0.999896i	$0.504595\pi$
$860$	2.43796	+	2.43796i	0.0831339	+	0.0831339i
$861$	1.48119	+	0.749225i	0.0504789	+	0.0255335i
$862$			38.1249i			1.29854i
$863$	29.3689	+	29.3689i	0.999728	+	0.999728i	1.00000		0.000272025i	$-8.65883e-5\pi$
$863$	29.3689	+	29.3689i	0.999728	+	0.999728i	−0.000272025		1.00000i	$0.500087\pi$
$864$	15.0451	−	6.85827i	0.511846	−	0.233323i
$865$	8.85231	−	33.0373i	0.300988	−	1.12330i
$866$	−6.98281	−	26.0602i	−0.237286	−	0.885562i
$867$	12.7628	+	19.5270i	0.433449	+	0.663173i
$868$		−	2.25047i		−	0.0763858i
$869$	11.9761	−	11.9761i	0.406263	−	0.406263i
$870$	−17.9251	+	35.4374i	−0.607719	+	1.20144i
$871$	2.97355	+	12.7463i	0.100755	+	0.431893i
$872$		−	0.602650i		−	0.0204083i
$873$	15.5504	+	2.36924i	0.526302	+	0.0801865i
$874$	−15.1442	+	26.2304i	−0.512259	+	0.887258i
$875$	−7.36439			−0.248962
$876$	12.5499	+	2.62900i	0.424022	+	0.0888257i
$877$	−4.54744	−	16.9713i	−0.153556	−	0.573080i	−0.999225	−	0.0393710i	$-0.987465\pi$
$877$	−4.54744	−	16.9713i	−0.153556	−	0.573080i	0.845668	−	0.533709i	$-0.179202\pi$
$878$	−9.97527	−	37.2282i	−0.336649	−	1.25639i
$879$	−7.78510	−	1.63085i	−0.262585	−	0.0550072i
$880$	−12.4905			−0.421054
$881$	11.7668	−	20.3807i	0.396434	−	0.686644i	−0.596849	−	0.802354i	$-0.703581\pi$
$881$	11.7668	−	20.3807i	0.396434	−	0.686644i	0.993283	+	0.115710i	$0.0369142\pi$
$882$	6.26482	+	16.0377i	0.210948	+	0.540018i
$883$		−	5.09275i		−	0.171385i	−0.996322	−	0.0856923i	$-0.972690\pi$
$883$		−	5.09275i		−	0.171385i	0.996322	−	0.0856923i	$-0.0273102\pi$
$884$	−3.35654	−	2.08670i	−0.112893	−	0.0701835i
$885$	29.1111	−	57.5516i	0.978558	−	1.93458i
$886$	20.4151	−	20.4151i	0.685858	−	0.685858i
$887$		−	13.2225i		−	0.443969i	−0.975050	−	0.221985i	$-0.928747\pi$
$887$		−	13.2225i		−	0.443969i	0.975050	−	0.221985i	$-0.0712535\pi$
$888$	−33.7166	−	51.5862i	−1.13146	−	1.73112i
$889$	−4.13304	−	15.4247i	−0.138618	−	0.517329i
$890$	−5.38181	+	20.0852i	−0.180399	+	0.673256i
$891$	8.38705	−	13.2538i	0.280977	−	0.444019i
$892$	−2.82276	−	2.82276i	−0.0945129	−	0.0945129i
$893$			10.7811i			0.360775i
$894$	−9.98120	−	5.04874i	−0.333821	−	0.168855i
$895$	11.9107	+	11.9107i	0.398132	+	0.398132i
$896$	−3.00983	−	5.21318i	−0.100551	−	0.174160i
$897$	−18.3366	−	30.1583i	−0.612241	−	1.00696i
$898$	6.41059	−	11.1035i	0.213924	−	0.370528i
$899$	−16.9207	+	4.53390i	−0.564338	+	0.151214i
$900$	−2.29255	+	5.23179i	−0.0764185	+	0.174393i
$901$	−18.8190	+	10.8651i	−0.626951	+	0.361970i
$902$	1.30106	−	0.348619i	0.0433207	−	0.0116077i
$903$	1.63885	+	4.99383i	0.0545376	+	0.166184i
$904$	22.1798	−	5.94307i	0.737690	−	0.197664i
$905$	−23.0412	−	6.17388i	−0.765917	−	0.205227i
$906$	36.3928	+	18.4084i	1.20907	+	0.611579i
$907$	8.56612	−	4.94565i	0.284433	−	0.164218i	−0.350995	−	0.936377i	$-0.614157\pi$
$907$	8.56612	−	4.94565i	0.284433	−	0.164218i	0.635429	+	0.772160i	$0.280823\pi$
$908$	−1.92806	−	7.19562i	−0.0639850	−	0.238795i
$909$	−3.64652	+	8.32164i	−0.120947	+	0.276012i
$910$	17.4239	+	5.28333i	0.577598	+	0.175141i
$911$	−10.2559	−	5.92123i	−0.339792	−	0.196179i	0.320388	−	0.947286i	$-0.396187\pi$
$911$	−10.2559	−	5.92123i	−0.339792	−	0.196179i	−0.660180	+	0.751107i	$0.729520\pi$
$912$	19.0299	+	3.98645i	0.630143	+	0.132005i
$913$	−4.79516			−0.158697
$914$	14.3378	−	24.8338i	0.474252	−	0.821429i
$915$	−38.9021	−	34.8209i	−1.28606	−	1.15114i
$916$	−7.51964	+	7.51964i	−0.248456	+	0.248456i
$917$	11.2685	+	3.01937i	0.372117	+	0.0997085i
$918$	−10.5757	+	4.82088i	−0.349050	+	0.159113i
$919$	−1.00599	−	1.74243i	−0.0331846	−	0.0574775i	0.848956	−	0.528463i	$-0.177232\pi$
$919$	−1.00599	−	1.74243i	−0.0331846	−	0.0574775i	−0.882141	+	0.470986i	$0.843898\pi$
$920$	−24.9786	−	43.2642i	−0.823520	−	1.42638i
$921$	−9.14884	+	3.00242i	−0.301465	+	0.0989333i
$922$	3.04499	−	1.75803i	0.100281	−	0.0578975i
$923$	28.5403	+	30.4652i	0.939415	+	1.00278i
$924$	2.31873	+	1.17287i	0.0762807	+	0.0385847i
$925$	36.4855	+	9.77625i	1.19963	+	0.321441i
$926$	1.91482	+	1.10552i	0.0629248	+	0.0363297i
$927$	50.5851	+	22.1662i	1.66143	+	0.728034i
$928$	15.0775	−	15.0775i	0.494943	−	0.494943i
$929$	−29.4569	−	29.4569i	−0.966450	−	0.966450i	0.0330054	−	0.999455i	$-0.489492\pi$
$929$	−29.4569	−	29.4569i	−0.966450	−	0.966450i	−0.999455	+	0.0330054i	$0.989492\pi$
$930$	14.7208	−	4.83100i	0.482714	−	0.158415i
$931$	5.61914	−	20.9709i	0.184160	−	0.687294i
$932$	−2.15726	−	1.24549i	−0.0706633	−	0.0407974i
$933$	−37.8621	+	2.09598i	−1.23955	+	0.0686194i
$934$	4.94048	−	18.4381i	0.161657	−	0.603313i
$935$	−9.41490			−0.307900
$936$	−21.6137	+	25.2784i	−0.706466	+	0.826249i
$937$	47.9819			1.56750			0.783750	−	0.621077i	$-0.213304\pi$
$937$	47.9819			1.56750			0.783750	+	0.621077i	$0.213304\pi$
$938$	−1.65041	+	6.15941i	−0.0538878	+	0.201112i
$939$	−7.17236	−	10.9737i	−0.234061	−	0.358112i
$940$	−3.47724	−	2.00759i	−0.113415	−	0.0654802i
$941$	6.36477	−	23.7536i	0.207485	−	0.774346i	−0.781192	−	0.624291i	$-0.785388\pi$
$941$	6.36477	−	23.7536i	0.207485	−	0.774346i	0.988678	−	0.150056i	$-0.0479453\pi$
$942$	−9.74945	+	46.5404i	−0.317654	+	1.51637i
$943$	2.59510	+	2.59510i	0.0845081	+	0.0845081i
$944$	22.8350	−	22.8350i	0.743216	−	0.743216i
$945$	−17.0094	+	14.0243i	−0.553315	+	0.456210i
$946$	3.69358	+	2.13249i	0.120089	+	0.0693332i
$947$	−40.3879	−	10.8219i	−1.31243	−	0.351665i	−0.466294	−	0.884630i	$-0.654411\pi$
$947$	−40.3879	−	10.8219i	−1.31243	−	0.351665i	−0.846138	+	0.532965i	$0.821078\pi$
$948$	−0.542718	−	9.80373i	−0.0176267	−	0.318410i
$949$	−44.5632	+	10.3960i	−1.44658	+	0.337469i
$950$	−15.1495	+	8.74657i	−0.491515	+	0.283776i
$951$	−10.4832	+	50.0429i	−0.339940	+	1.62275i
$952$	−4.26388	−	7.38525i	−0.138193	−	0.239357i
$953$	3.67150	+	6.35923i	0.118932	+	0.205996i	0.919345	−	0.393453i	$-0.128720\pi$
$953$	3.67150	+	6.35923i	0.118932	+	0.205996i	−0.800413	+	0.599449i	$0.795386\pi$
$954$	15.0234	+	38.4594i	0.486401	+	1.24517i
$955$	19.8822	+	5.32742i	0.643373	+	0.172391i
$956$	−0.464654	+	0.464654i	−0.0150280	+	0.0150280i
$957$	4.14713	−	19.7969i	0.134058	−	0.639944i
$958$	−22.0449	+	38.1829i	−0.712239	+	1.23363i
$959$	12.4912			0.403362
$960$	−29.1364	+	32.5513i	−0.940372	+	1.05059i
$961$	−20.9282	−	12.0829i	−0.675104	−	0.389772i
$962$	42.1747	+	26.2193i	1.35977	+	0.845343i
$963$	1.51928	+	13.6802i	0.0489580	+	0.440837i
$964$	−1.33275	−	4.97388i	−0.0429249	−	0.160198i
$965$	6.82013	−	3.93760i	0.219548	−	0.126756i
$966$	−0.950467	−	17.1694i	−0.0305808	−	0.552415i
$967$	−25.3368	−	6.78898i	−0.814778	−	0.218319i	−0.172716	−	0.984972i	$-0.555254\pi$
$967$	−25.3368	−	6.78898i	−0.814778	−	0.218319i	−0.642062	+	0.766653i	$0.721921\pi$
$968$	−23.6498	+	6.33696i	−0.760135	+	0.203677i
$969$	14.3441	+	3.00485i	0.460798	+	0.0965295i
$970$	−17.3295	+	4.64343i	−0.556417	+	0.149091i
$971$	11.1860	−	6.45823i	0.358975	−	0.207255i	−0.309656	−	0.950849i	$-0.600214\pi$
$971$	11.1860	−	6.45823i	0.358975	−	0.207255i	0.668631	+	0.743594i	$0.266880\pi$
$972$	−2.48232	−	8.74739i	−0.0796206	−	0.280573i
$973$	−0.669888	+	0.179496i	−0.0214756	+	0.00575438i
$974$	12.0534	−	20.8771i	0.386217	−	0.668947i
$975$	−0.462503	−	20.3797i	−0.0148120	−	0.652671i
$976$	−13.0711	−	22.6397i	−0.418394	−	0.724680i
$977$	−24.5234	−	24.5234i	−0.784573	−	0.784573i	0.196026	−	0.980599i	$-0.437196\pi$
$977$	−24.5234	−	24.5234i	−0.784573	−	0.784573i	−0.980599	+	0.196026i	$0.937196\pi$
$978$	7.69613	−	5.03018i	0.246095	−	0.160847i
$979$		−	10.5907i		−	0.338479i
$980$	5.71742	+	5.71742i	0.182636	+	0.182636i
$981$	−0.581286	−	0.0885638i	−0.0185590	−	0.00282763i
$982$	3.49299	−	13.0360i	0.111466	−	0.415996i
$983$	7.33678	+	27.3813i	0.234007	+	0.873326i	0.978594	+	0.205801i	$0.0659799\pi$
$983$	7.33678	+	27.3813i	0.234007	+	0.873326i	−0.744587	+	0.667526i	$0.767353\pi$
$984$	1.56095	−	3.08595i	0.0497614	−	0.0983766i
$985$			68.8768i			2.19460i
$986$	−10.5984	+	10.5984i	−0.337522	+	0.337522i
$987$	−3.34870	−	5.12348i	−0.106590	−	0.163082i
$988$	9.22170	−	2.15130i	0.293381	−	0.0684421i
$989$			11.6207i			0.369516i
$990$	−2.69447	+	17.6851i	−0.0856360	+	0.562069i
$991$	0.249119	−	0.431486i	0.00791352	−	0.0137066i	−0.862042	−	0.506838i	$-0.830814\pi$
$991$	0.249119	−	0.431486i	0.00791352	−	0.0137066i	0.869955	+	0.493131i	$0.164148\pi$
$992$	−8.31867			−0.264118
$993$	10.4025	+	31.6979i	0.330112	+	1.00590i
$994$	5.26390	+	19.6451i	0.166961	+	0.623106i
$995$	6.94711	+	25.9270i	0.220238	+	0.821940i
$996$	−1.85402	+	2.07132i	−0.0587469	+	0.0656323i
$997$	39.9905			1.26651			0.633255	−	0.773943i	$-0.281718\pi$
$997$	39.9905			1.26651			0.633255	+	0.773943i	$0.281718\pi$
$998$	3.04127	−	5.26764i	0.0962698	−	0.166744i
$999$	−54.7123	+	24.9404i	−1.73102	+	0.789079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.110.9	yes	48
3.2	odd	2		351.2.bf.a.305.4		48
9.4	even	3		351.2.ba.a.71.9		48
9.5	odd	6		117.2.x.a.32.4	yes	48
13.11	odd	12		117.2.x.a.11.4	✓	48
39.11	even	12		351.2.ba.a.89.9		48
117.50	even	12	inner	117.2.bc.a.50.9	yes	48
117.76	odd	12		351.2.bf.a.206.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.4	✓	48	13.11	odd	12
117.2.x.a.32.4	yes	48	9.5	odd	6
117.2.bc.a.50.9	yes	48	117.50	even	12	inner
117.2.bc.a.110.9	yes	48	1.1	even	1	trivial
351.2.ba.a.71.9		48	9.4	even	3
351.2.ba.a.89.9		48	39.11	even	12
351.2.bf.a.206.4		48	117.76	odd	12
351.2.bf.a.305.4		48	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.308060 - 1.14969i) q^{2} +(-0.781791 + 1.54558i) q^{3} +(0.505155 + 0.291651i) q^{4} +(-0.744040 + 2.77680i) q^{5} +(1.53610 + 1.37495i) q^{6} +(1.04357 + 1.04357i) q^{7} +(2.17420 - 2.17420i) q^{8} +(-1.77761 - 2.41663i) q^{9} +(2.96326 + 1.71084i) q^{10} +(-1.68335 - 0.451052i) q^{11} +(-0.845695 + 0.552745i) q^{12} +(1.90363 - 3.06206i) q^{13} +(1.52127 - 0.878303i) q^{14} +(-3.71006 - 3.32085i) q^{15} +(-1.24658 - 2.15913i) q^{16} +(-0.939625 - 1.62748i) q^{17} +(-3.32600 + 1.29924i) q^{18} +(4.34907 + 1.16533i) q^{19} +(-1.18571 + 1.18571i) q^{20} +(-2.42877 + 0.797061i) q^{21} +(-1.03714 + 1.79639i) q^{22} -5.65176 q^{23} +(1.66062 + 5.06015i) q^{24} +(-2.82688 - 1.63210i) q^{25} +(-2.93400 - 3.13189i) q^{26} +(5.12481 - 0.858121i) q^{27} +(0.222806 + 0.831522i) q^{28} +(5.80315 - 3.35045i) q^{29} +(-4.96088 + 3.24242i) q^{30} +(-2.52515 - 0.676611i) q^{31} +(3.07365 - 0.823583i) q^{32} +(2.01316 - 2.24911i) q^{33} +(-2.16056 + 0.578921i) q^{34} +(-3.67424 + 2.12132i) q^{35} +(-0.193152 - 1.73922i) q^{36} +(-11.1775 + 2.99499i) q^{37} +(2.67955 - 4.64111i) q^{38} +(3.24440 + 5.33609i) q^{39} +(4.41961 + 7.65499i) q^{40} +(-0.459167 - 0.459167i) q^{41} +(0.168172 + 3.03788i) q^{42} -2.05612i q^{43} +(-0.718802 - 0.718802i) q^{44} +(8.03311 - 3.13798i) q^{45} +(-1.74108 + 6.49779i) q^{46} +(0.619735 + 2.31288i) q^{47} +(4.31167 - 0.238686i) q^{48} -4.82193i q^{49} +(-2.74726 + 2.74726i) q^{50} +(3.24998 - 0.179913i) q^{51} +(1.85468 - 0.991618i) q^{52} -11.5633i q^{53} +(0.592168 - 6.15631i) q^{54} +(2.50496 - 4.33872i) q^{55} +4.53785 q^{56} +(-5.20117 + 5.81077i) q^{57} +(-2.06428 - 7.70398i) q^{58} +(3.35246 + 12.5115i) q^{59} +(-0.905629 - 2.75959i) q^{60} +10.4856 q^{61} +(-1.55579 + 2.69471i) q^{62} +(0.666869 - 4.37698i) q^{63} -8.77378i q^{64} +(7.08634 + 7.56428i) q^{65} +(-1.96562 - 3.00738i) q^{66} +(-2.56688 + 2.56688i) q^{67} -1.09617i q^{68} +(4.41849 - 8.73522i) q^{69} +(1.30699 + 4.87774i) q^{70} +(-2.99663 + 11.1836i) q^{71} +(-9.11910 - 1.38937i) q^{72} +(-8.97423 - 8.97423i) q^{73} +13.7733i q^{74} +(4.73256 - 3.09319i) q^{75} +(1.85709 + 1.85709i) q^{76} +(-1.28599 - 2.22739i) q^{77} +(7.13434 - 2.08624i) q^{78} +(-4.85927 + 8.41651i) q^{79} +(6.92298 - 1.85501i) q^{80} +(-2.68024 + 8.59164i) q^{81} +(-0.669352 + 0.386451i) q^{82} +(2.65776 - 0.712145i) q^{83} +(-1.45937 - 0.305713i) q^{84} +(5.21830 - 1.39824i) q^{85} +(-2.36391 - 0.633407i) q^{86} +(0.641522 + 11.5885i) q^{87} +(-4.64061 + 2.67926i) q^{88} +(1.57286 + 5.86998i) q^{89} +(-1.13304 - 10.2023i) q^{90} +(5.18203 - 1.20890i) q^{91} +(-2.85501 - 1.64834i) q^{92} +(3.01989 - 3.37384i) q^{93} +2.85002 q^{94} +(-6.47177 + 11.2094i) q^{95} +(-1.13004 + 5.39443i) q^{96} +(-3.70756 + 3.70756i) q^{97} +(-5.54374 - 1.48544i) q^{98} +(1.90230 + 4.86983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21}+ \cdots - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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