LMFDB - Embedded newform 738.2.v.b.659.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(137,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.v (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [168,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$21$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			659.13
Character	$\chi$	$=$	738.659
Dual form			738.2.v.b.383.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.897801 + 1.48120i) q^{3} +(0.866025 - 0.500000i) q^{4} +(3.25497 + 0.872167i) q^{5} +(1.25057 + 1.19836i) q^{6} +(-1.61407 - 2.10349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.38791 + 2.65965i) q^{9} +3.36980 q^{10} +(-1.11279 - 1.45021i) q^{11} +(1.51812 + 0.833856i) q^{12} +(0.894411 - 0.117751i) q^{13} +(-2.10349 - 1.61407i) q^{14} +(1.63046 + 5.60430i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.44629 - 2.67014i) q^{17} +(-0.652247 + 2.92824i) q^{18} +(1.57542 + 3.80341i) q^{19} +(3.25497 - 0.872167i) q^{20} +(1.66658 - 4.27928i) q^{21} +(-1.45021 - 1.11279i) q^{22} +(-0.394630 - 0.683520i) q^{23} +(1.68221 + 0.412525i) q^{24} +(5.50404 + 3.17776i) q^{25} +(0.833458 - 0.345230i) q^{26} +(-5.18553 + 0.332069i) q^{27} +(-2.44957 - 1.01465i) q^{28} +(-3.16401 + 2.42783i) q^{29} +(3.02541 + 4.99134i) q^{30} +(-8.28363 + 4.78256i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.14899 - 2.95026i) q^{33} +(5.53556 - 4.24758i) q^{34} +(-3.41915 - 8.25455i) q^{35} +(0.127862 + 2.99727i) q^{36} -6.35886 q^{37} +(2.50614 + 3.26606i) q^{38} +(0.977417 + 1.21908i) q^{39} +(2.91833 - 1.68490i) q^{40} +(-6.32106 - 1.02189i) q^{41} +(0.502237 - 4.56481i) q^{42} +(-1.08760 - 4.05897i) q^{43} +(-1.68881 - 0.699527i) q^{44} +(-6.83725 + 7.44659i) q^{45} +(-0.558092 - 0.558092i) q^{46} +(-1.50829 + 11.4566i) q^{47} +(1.73166 - 0.0369189i) q^{48} +(-0.00773902 + 0.0288824i) q^{49} +(6.13896 + 1.64493i) q^{50} +(9.74251 + 7.15099i) q^{51} +(0.715707 - 0.549181i) q^{52} +(5.50514 - 13.2906i) q^{53} +(-4.92289 + 1.66287i) q^{54} +(-2.35726 - 5.69094i) q^{55} +(-2.62871 - 0.346077i) q^{56} +(-4.21919 + 5.74823i) q^{57} +(-2.42783 + 3.16401i) q^{58} +(-5.12647 + 2.95977i) q^{59} +(4.21417 + 4.03823i) q^{60} +(0.698289 + 2.60605i) q^{61} +(-6.76356 + 6.76356i) q^{62} +(7.83472 - 1.37340i) q^{63} -1.00000i q^{64} +(3.01398 + 0.396798i) q^{65} +(0.346257 - 3.14712i) q^{66} +(1.97248 - 2.57059i) q^{67} +(4.24758 - 5.53556i) q^{68} +(0.658130 - 1.19819i) q^{69} +(-5.43908 - 7.08834i) q^{70} +(0.572841 + 0.237279i) q^{71} +(0.899257 + 2.86205i) q^{72} +(7.43536 - 7.43536i) q^{73} +(-6.14219 + 1.64579i) q^{74} +(0.234639 + 11.0056i) q^{75} +(3.26606 + 2.50614i) q^{76} +(-1.25440 + 4.68148i) q^{77} +(1.25963 + 0.924571i) q^{78} +(10.7226 - 8.22777i) q^{79} +(2.38281 - 2.38281i) q^{80} +(-5.14744 - 7.38268i) q^{81} +(-6.37016 + 0.648940i) q^{82} +(-8.58655 - 4.95745i) q^{83} +(-0.696335 - 4.53925i) q^{84} +(23.3113 - 3.06899i) q^{85} +(-2.10108 - 3.63918i) q^{86} +(-6.43674 - 2.50682i) q^{87} +(-1.81231 - 0.238596i) q^{88} +(-5.56027 - 2.30314i) q^{89} +(-4.67696 + 8.96246i) q^{90} +(-1.69133 - 1.69133i) q^{91} +(-0.683520 - 0.394630i) q^{92} +(-14.5210 - 7.97593i) q^{93} +(1.50829 + 11.4566i) q^{94} +(1.81075 + 13.7540i) q^{95} +(1.66310 - 0.483847i) q^{96} +(-0.890940 + 6.76736i) q^{97} +0.0299013i q^{98} +(5.40149 - 0.946862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{7} - 8 q^{9} + 16 q^{15} + 84 q^{16} + 12 q^{17} - 8 q^{21} + 4 q^{24} - 48 q^{25} - 8 q^{30} - 40 q^{33} + 48 q^{34} - 24 q^{35} - 8 q^{36} - 32 q^{42} - 12 q^{44} - 72 q^{45} + 12 q^{47}+ \cdots + 16 q^{99}+O(q^{100}) $ 168 * q + 12 * q^7 - 8 * q^9 + 16 * q^15 + 84 * q^16 + 12 * q^17 - 8 * q^21 + 4 * q^24 - 48 * q^25 - 8 * q^30 - 40 * q^33 + 48 * q^34 - 24 * q^35 - 8 * q^36 - 32 * q^42 - 12 * q^44 - 72 * q^45 + 12 * q^47 + 12 * q^48 + 12 * q^49 - 44 * q^51 - 20 * q^54 + 12 * q^56 - 64 * q^57 + 24 * q^58 + 108 * q^61 + 112 * q^63 - 84 * q^65 + 4 * q^66 + 48 * q^67 + 48 * q^69 + 12 * q^70 + 84 * q^75 - 12 * q^76 + 60 * q^79 - 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 40 * q^87 - 72 * q^89 - 96 * q^93 - 12 * q^94 - 72 * q^95 - 96 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.897801	+	1.48120i	0.518346	+	0.855171i
$3$	0.897801	+	1.48120i	0.518346	+	0.855171i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	3.25497	+	0.872167i	1.45567	+	0.390045i	0.897991	−	0.440013i	$-0.145026\pi$
$5$	3.25497	+	0.872167i	1.45567	+	0.390045i	0.557677	+	0.830058i	$0.311693\pi$
$6$	1.25057	+	1.19836i	0.510544	+	0.489229i
$7$	−1.61407	−	2.10349i	−0.610060	−	0.795046i	0.381545	−	0.924350i	$-0.375392\pi$
$7$	−1.61407	−	2.10349i	−0.610060	−	0.795046i	−0.991605	+	0.129304i	$0.958726\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.38791	+	2.65965i	−0.462635	+	0.886549i
$10$	3.36980			1.06562
$11$	−1.11279	−	1.45021i	−0.335518	−	0.437255i	0.594876	−	0.803818i	$-0.297201\pi$
$11$	−1.11279	−	1.45021i	−0.335518	−	0.437255i	−0.930393	+	0.366562i	$0.880535\pi$
$12$	1.51812	+	0.833856i	0.438243	+	0.240713i
$13$	0.894411	−	0.117751i	0.248065	−	0.0326584i	−0.00546825	−	0.999985i	$-0.501741\pi$
$13$	0.894411	−	0.117751i	0.248065	−	0.0326584i	0.253533	+	0.967327i	$0.418407\pi$
$14$	−2.10349	−	1.61407i	−0.562182	−	0.431378i
$15$	1.63046	+	5.60430i	0.420984	+	1.44702i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.44629	−	2.67014i	1.56346	−	0.647605i	0.577770	−	0.816199i	$-0.303923\pi$
$17$	6.44629	−	2.67014i	1.56346	−	0.647605i	0.985685	+	0.168595i	$0.0539229\pi$
$18$	−0.652247	+	2.92824i	−0.153736	+	0.690192i
$19$	1.57542	+	3.80341i	0.361427	+	0.872563i	0.995092	+	0.0989547i	$0.0315499\pi$
$19$	1.57542	+	3.80341i	0.361427	+	0.872563i	−0.633665	+	0.773608i	$0.718450\pi$
$20$	3.25497	−	0.872167i	0.727834	−	0.195023i
$21$	1.66658	−	4.27928i	0.363678	−	0.933815i
$22$	−1.45021	−	1.11279i	−0.309186	−	0.237247i
$23$	−0.394630	−	0.683520i	−0.0822861	−	0.142524i	0.821945	−	0.569566i	$-0.192889\pi$
$23$	−0.394630	−	0.683520i	−0.0822861	−	0.142524i	−0.904232	+	0.427042i	$0.859555\pi$
$24$	1.68221	+	0.412525i	0.343379	+	0.0842063i
$25$	5.50404	+	3.17776i	1.10081	+	0.635552i
$26$	0.833458	−	0.345230i	0.163455	−	0.0677051i
$27$	−5.18553	+	0.332069i	−0.997956	+	0.0639067i
$28$	−2.44957	−	1.01465i	−0.462925	−	0.191750i
$29$	−3.16401	+	2.42783i	−0.587541	+	0.450836i	−0.859259	−	0.511541i	$-0.829075\pi$
$29$	−3.16401	+	2.42783i	−0.587541	+	0.450836i	0.271718	+	0.962377i	$0.412408\pi$
$30$	3.02541	+	4.99134i	0.552361	+	0.911290i
$31$	−8.28363	+	4.78256i	−1.48778	+	0.858973i	−0.999903	−	0.0139373i	$-0.995563\pi$
$31$	−8.28363	+	4.78256i	−1.48778	+	0.858973i	−0.487881	+	0.872910i	$0.662230\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.14899	−	2.95026i	0.200014	−	0.513575i
$34$	5.53556	−	4.24758i	0.949340	−	0.728454i
$35$	−3.41915	−	8.25455i	−0.577941	−	1.39527i
$36$	0.127862	+	2.99727i	0.0213103	+	0.499546i
$37$	−6.35886			−1.04539			−0.522695	−	0.852520i	$-0.675073\pi$
$37$	−6.35886			−1.04539			−0.522695	+	0.852520i	$0.675073\pi$
$38$	2.50614	+	3.26606i	0.406549	+	0.529825i
$39$	0.977417	+	1.21908i	0.156512	+	0.195210i
$40$	2.91833	−	1.68490i	0.461428	−	0.266406i
$41$	−6.32106	−	1.02189i	−0.987183	−	0.159592i
$41$	−6.32106	−	1.02189i	−0.987183	−	0.159592i
$42$	0.502237	−	4.56481i	0.0774968	−	0.704365i
$43$	−1.08760	−	4.05897i	−0.165857	−	0.618988i	−0.997929	−	0.0643201i	$-0.979512\pi$
$43$	−1.08760	−	4.05897i	−0.165857	−	0.618988i	0.832072	−	0.554667i	$-0.187155\pi$
$44$	−1.68881	−	0.699527i	−0.254597	−	0.105458i
$45$	−6.83725	+	7.44659i	−1.01924	+	1.11007i
$46$	−0.558092	−	0.558092i	−0.0822861	−	0.0822861i
$47$	−1.50829	+	11.4566i	−0.220006	+	1.67111i	0.423670	+	0.905817i	$0.360742\pi$
$47$	−1.50829	+	11.4566i	−0.220006	+	1.67111i	−0.643677	+	0.765298i	$0.722592\pi$
$48$	1.73166	−	0.0369189i	0.249943	−	0.00532879i
$49$	−0.00773902	+	0.0288824i	−0.00110557	+	0.00412606i
$50$	6.13896	+	1.64493i	0.868181	+	0.232628i
$51$	9.74251	+	7.15099i	1.36422	+	1.00134i
$52$	0.715707	−	0.549181i	0.0992507	−	0.0761577i
$53$	5.50514	−	13.2906i	0.756189	−	1.82560i	0.235447	−	0.971887i	$-0.424345\pi$
$53$	5.50514	−	13.2906i	0.756189	−	1.82560i	0.520742	−	0.853714i	$-0.325655\pi$
$54$	−4.92289	+	1.66287i	−0.669921	+	0.226288i
$55$	−2.35726	−	5.69094i	−0.317853	−	0.767366i
$56$	−2.62871	−	0.346077i	−0.351277	−	0.0462464i
$57$	−4.21919	+	5.74823i	−0.558846	+	0.761371i
$58$	−2.42783	+	3.16401i	−0.318789	+	0.415454i
$59$	−5.12647	+	2.95977i	−0.667409	+	0.385329i	−0.795094	−	0.606486i	$-0.792579\pi$
$59$	−5.12647	+	2.95977i	−0.667409	+	0.385329i	0.127685	+	0.991815i	$0.459245\pi$
$60$	4.21417	+	4.03823i	0.544047	+	0.521333i
$61$	0.698289	+	2.60605i	0.0894067	+	0.333670i	0.996112	−	0.0880941i	$-0.0280776\pi$
$61$	0.698289	+	2.60605i	0.0894067	+	0.333670i	−0.906705	+	0.421764i	$0.861411\pi$
$62$	−6.76356	+	6.76356i	−0.858973	+	0.858973i
$63$	7.83472	−	1.37340i	0.987082	−	0.173032i
$64$		−	1.00000i		−	0.125000i
$65$	3.01398	+	0.396798i	0.373839	+	0.0492168i
$66$	0.346257	−	3.14712i	0.0426213	−	0.387383i
$67$	1.97248	−	2.57059i	0.240977	−	0.314048i	−0.657170	−	0.753742i	$-0.728247\pi$
$67$	1.97248	−	2.57059i	0.240977	−	0.314048i	0.898147	+	0.439695i	$0.144913\pi$
$68$	4.24758	−	5.53556i	0.515095	−	0.671285i
$69$	0.658130	−	1.19819i	0.0792295	−	0.144245i
$70$	−5.43908	−	7.08834i	−0.650094	−	0.847219i
$71$	0.572841	+	0.237279i	0.0679837	+	0.0281598i	0.416416	−	0.909174i	$-0.363286\pi$
$71$	0.572841	+	0.237279i	0.0679837	+	0.0281598i	−0.348432	+	0.937334i	$0.613286\pi$
$72$	0.899257	+	2.86205i	0.105978	+	0.337296i
$73$	7.43536	−	7.43536i	0.870243	−	0.870243i	−0.122256	−	0.992499i	$-0.539013\pi$
$73$	7.43536	−	7.43536i	0.870243	−	0.870243i	0.992499	+	0.122256i	$0.0390128\pi$
$74$	−6.14219	+	1.64579i	−0.714015	+	0.191320i
$75$	0.234639	+	11.0056i	0.0270938	+	1.27082i
$76$	3.26606	+	2.50614i	0.374643	+	0.287474i
$77$	−1.25440	+	4.68148i	−0.142952	+	0.533504i
$78$	1.25963	+	0.924571i	0.142626	+	0.104687i
$79$	10.7226	−	8.22777i	1.20639	−	0.925697i	0.207769	−	0.978178i	$-0.433380\pi$
$79$	10.7226	−	8.22777i	1.20639	−	0.925697i	0.998622	+	0.0524812i	$0.0167129\pi$
$80$	2.38281	−	2.38281i	0.266406	−	0.266406i
$81$	−5.14744	−	7.38268i	−0.571937	−	0.820297i
$82$	−6.37016	+	0.648940i	−0.703466	+	0.0716635i
$83$	−8.58655	−	4.95745i	−0.942497	−	0.544151i	−0.0517545	−	0.998660i	$-0.516481\pi$
$83$	−8.58655	−	4.95745i	−0.942497	−	0.544151i	−0.890742	+	0.454509i	$0.849815\pi$
$84$	−0.696335	−	4.53925i	−0.0759764	−	0.495273i
$85$	23.3113	−	3.06899i	2.52847	−	0.332879i
$86$	−2.10108	−	3.63918i	−0.226565	−	0.392422i
$87$	−6.43674	−	2.50682i	−0.690091	−	0.268759i
$88$	−1.81231	−	0.238596i	−0.193193	−	0.0254344i
$89$	−5.56027	−	2.30314i	−0.589387	−	0.244132i	0.0679997	−	0.997685i	$-0.478338\pi$
$89$	−5.56027	−	2.30314i	−0.589387	−	0.244132i	−0.657387	+	0.753553i	$0.728338\pi$
$90$	−4.67696	+	8.96246i	−0.492995	+	0.944727i
$91$	−1.69133	−	1.69133i	−0.177300	−	0.177300i
$92$	−0.683520	−	0.394630i	−0.0712619	−	0.0411431i
$93$	−14.5210	−	7.97593i	−1.50576	−	0.827065i
$94$	1.50829	+	11.4566i	0.155568	+	1.18166i
$95$	1.81075	+	13.7540i	0.185779	+	1.41113i
$96$	1.66310	−	0.483847i	0.169739	−	0.0493824i
$97$	−0.890940	+	6.76736i	−0.0904613	+	0.687122i	0.884785	+	0.466000i	$0.154305\pi$
$97$	−0.890940	+	6.76736i	−0.0904613	+	0.687122i	−0.975246	+	0.221122i	$0.929028\pi$
$98$			0.0299013i			0.00302049i
$99$	5.40149	−	0.946862i	0.542871	−	0.0951632i
$100$	6.35552			0.635552
$101$	−1.84025	+	13.9781i	−0.183112	+	1.39087i	0.615079	+	0.788466i	$0.289124\pi$
$101$	−1.84025	+	13.9781i	−0.183112	+	1.39087i	−0.798190	+	0.602405i	$0.794209\pi$
$102$	11.2614	+	4.38578i	1.11504	+	0.434257i
$103$	−1.05246	+	3.92783i	−0.103702	+	0.387020i	−0.998195	−	0.0600618i	$-0.980870\pi$
$103$	−1.05246	+	3.92783i	−0.103702	+	0.387020i	0.894493	+	0.447082i	$0.147537\pi$
$104$	0.549181	−	0.715707i	0.0538517	−	0.0701808i
$105$	9.15693	−	12.4754i	0.893624	−	1.21747i
$106$	1.87770	−	14.2625i	0.182378	−	1.38530i
$107$	−2.79045			−0.269763			−0.134881	−	0.990862i	$-0.543065\pi$
$107$	−2.79045			−0.269763			−0.134881	+	0.990862i	$0.543065\pi$
$108$	−4.32477	+	2.88035i	−0.416151	+	0.277161i
$109$	8.49392	−	3.51830i	0.813570	−	0.336992i	0.0631925	−	0.998001i	$-0.479872\pi$
$109$	8.49392	−	3.51830i	0.813570	−	0.336992i	0.750377	+	0.661010i	$0.229872\pi$
$110$	−3.74986	−	4.88692i	−0.357536	−	0.465949i
$111$	−5.70900	−	9.41875i	−0.541874	−	0.893988i
$112$	−2.62871	+	0.346077i	−0.248390	+	0.0327012i
$113$	0.711501	+	1.23236i	0.0669323	+	0.115930i	0.897550	−	0.440914i	$-0.145345\pi$
$113$	0.711501	+	1.23236i	0.0669323	+	0.115930i	−0.830617	+	0.556844i	$0.812012\pi$
$114$	−2.58768	+	6.64437i	−0.242358	+	0.622302i
$115$	−0.688367	−	2.56902i	−0.0641906	−	0.239563i
$116$	−1.52620	+	3.68456i	−0.141704	+	0.342103i
$117$	−0.928181	+	2.54224i	−0.0858103	+	0.235031i
$118$	−4.18574	+	4.18574i	−0.385329	+	0.385329i
$119$	−16.0214	−	9.24995i	−1.46868	−	0.847941i
$120$	5.11575	+	2.80992i	0.467002	+	0.256510i
$121$	1.98219	−	7.39763i	0.180199	−	0.672512i
$122$	1.34899	+	2.33652i	0.122132	+	0.211538i
$123$	−4.16143	−	10.2802i	−0.375224	−	0.926934i
$124$	−4.78256	+	8.28363i	−0.429486	+	0.743892i
$125$	3.22995	+	3.22995i	0.288895	+	0.288895i
$126$	7.21230	−	3.35438i	0.642523	−	0.298832i
$127$		−	12.5448i		−	1.11317i	−0.830789	−	0.556587i	$-0.812111\pi$
$127$		−	12.5448i		−	1.11317i	0.830789	−	0.556587i	$-0.187889\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	5.03570	−	5.25510i	0.443369	−	0.462686i
$130$	3.01398	−	0.396798i	0.264344	−	0.0348015i
$131$	−17.0020	−	4.55568i	−1.48548	−	0.398032i	−0.577269	−	0.816554i	$-0.695882\pi$
$131$	−17.0020	−	4.55568i	−1.48548	−	0.398032i	−0.908207	+	0.418522i	$0.862548\pi$
$132$	−0.480075	−	3.12950i	−0.0417851	−	0.272388i
$133$	5.45761	−	9.45286i	0.473235	−	0.819667i
$134$	1.23996	−	2.99352i	0.107116	−	0.258601i
$135$	−17.1684	−	3.44178i	−1.47762	−	0.296221i
$136$	2.67014	−	6.44629i	0.228963	−	0.552765i
$137$	1.49586	−	11.3622i	0.127800	−	0.970734i	−0.800613	−	0.599182i	$-0.795492\pi$
$137$	1.49586	−	11.3622i	0.127800	−	0.970734i	0.928412	−	0.371552i	$-0.121174\pi$
$138$	0.325590	−	1.32770i	0.0277160	−	0.113021i
$139$	4.96716	+	8.60337i	0.421309	+	0.729728i	0.996068	−	0.0885946i	$-0.0282376\pi$
$139$	4.96716	+	8.60337i	0.421309	+	0.729728i	−0.574759	+	0.818323i	$0.694904\pi$
$140$	−7.08834	−	5.43908i	−0.599074	−	0.459686i
$141$	−18.3236	+	8.05166i	−1.54313	+	0.678072i
$142$	0.614734	+	0.0809313i	0.0515874	+	0.00679161i
$143$	−1.16605	−	1.16605i	−0.0975103	−	0.0975103i
$144$	1.60937	+	2.53178i	0.134114	+	0.210982i
$145$	−12.4162	+	5.14297i	−1.03111	+	0.427100i
$146$	5.25759	−	9.10642i	0.435121	−	0.753652i
$147$	−0.0497287	+	0.0144676i	−0.00410156	+	0.00119327i
$148$	−5.50694	+	3.17943i	−0.452667	+	0.261348i
$149$	9.12384	+	7.00097i	0.747454	+	0.573542i	0.910712	−	0.413041i	$-0.135534\pi$
$149$	9.12384	+	7.00097i	0.747454	+	0.573542i	−0.163258	+	0.986583i	$0.552200\pi$
$150$	3.07510	+	10.5699i	0.251081	+	0.863025i
$151$	−4.40967	+	3.38366i	−0.358854	+	0.275358i	−0.772415	−	0.635118i	$-0.780951\pi$
$151$	−4.40967	+	3.38366i	−0.358854	+	0.275358i	0.413561	+	0.910476i	$0.364285\pi$
$152$	3.80341	+	1.57542i	0.308497	+	0.127784i
$153$	−1.84521	+	20.8508i	−0.149177	+	1.68568i
$154$			4.84663i			0.390552i
$155$	−31.1342	+	8.34238i	−2.50076	+	0.670076i
$156$	1.45601	+	0.567049i	0.116574	+	0.0454003i
$157$	1.36297	+	10.3528i	0.108777	+	0.826244i	0.955662	+	0.294467i	$0.0951421\pi$
$157$	1.36297	+	10.3528i	0.108777	+	0.826244i	−0.846885	+	0.531777i	$0.821525\pi$
$158$	8.22777	−	10.7226i	0.654566	−	0.853048i
$159$	24.6285	−	3.77809i	1.95317	−	0.299622i
$160$	1.68490	−	2.91833i	0.133203	−	0.230714i
$161$	−0.800820	+	1.93335i	−0.0631134	+	0.152369i
$162$	−6.88282	−	5.79886i	−0.540765	−	0.455602i
$163$		−	1.23582i		−	0.0967968i	−0.998828	−	0.0483984i	$-0.984588\pi$
$163$		−	1.23582i		−	0.0967968i	0.998828	−	0.0483984i	$-0.0154117\pi$
$164$	−5.98514	+	2.27555i	−0.467361	+	0.177690i
$165$	6.31306	−	8.60091i	0.491471	−	0.669580i
$166$	−9.57705	−	2.56616i	−0.743324	−	0.199173i
$167$	−2.27384	−	17.2716i	−0.175955	−	1.33651i	−0.820368	−	0.571836i	$-0.806232\pi$
$167$	−2.27384	−	17.2716i	−0.175955	−	1.33651i	0.644413	−	0.764678i	$-0.277102\pi$
$168$	−1.84745	−	4.20436i	−0.142534	−	0.324373i
$169$	−11.7709	+	3.15401i	−0.905456	+	0.242616i
$170$	21.7227	−	8.99783i	1.66605	−	0.690102i
$171$	−12.3023	−	1.08870i	−0.940778	−	0.0832552i
$172$	−2.97137	−	2.97137i	−0.226565	−	0.226565i
$173$	5.22647	+	19.5055i	0.397361	+	1.48297i	0.817721	+	0.575615i	$0.195237\pi$
$173$	5.22647	+	19.5055i	0.397361	+	1.48297i	−0.420360	+	0.907358i	$0.638096\pi$
$174$	−6.86623	−	0.755448i	−0.520528	−	0.0572704i
$175$	−2.19950	−	16.7068i	−0.166266	−	1.26292i
$176$	−1.81231	+	0.238596i	−0.136608	+	0.0179848i
$177$	−8.98655	−	4.93604i	−0.675471	−	0.371015i
$178$	−5.96690	−	0.785558i	−0.447238	−	0.0588800i
$179$	−3.10978	−	7.50768i	−0.232436	−	0.561151i	0.764027	−	0.645185i	$-0.223220\pi$
$179$	−3.10978	−	7.50768i	−0.232436	−	0.561151i	−0.996463	+	0.0840340i	$0.973220\pi$
$180$	−2.19794	+	9.86756i	−0.163825	+	0.735485i
$181$	3.58592	+	8.65717i	0.266539	+	0.643482i	0.999316	−	0.0369869i	$-0.0117760\pi$
$181$	3.58592	+	8.65717i	0.266539	+	0.643482i	−0.732777	+	0.680469i	$0.761776\pi$
$182$	−2.07145	−	1.19595i	−0.153546	−	0.0886498i
$183$	−3.23315	+	3.37402i	−0.239002	+	0.249415i
$184$	−0.762367	−	0.204276i	−0.0562025	−	0.0150594i
$185$	−20.6979	−	5.54599i	−1.52174	−	0.407749i
$186$	−16.0905	−	3.94585i	−1.17981	−	0.289324i
$187$	−11.0456	−	6.37719i	−0.807736	−	0.466347i
$188$	4.42208	+	10.6758i	0.322513	+	0.778615i
$189$	9.06830	+	10.3718i	0.659622	+	0.754434i
$190$	5.30886	+	12.8167i	0.385145	+	0.929823i
$191$	19.2360	+	2.53247i	1.39187	+	0.183243i	0.788900	−	0.614522i	$-0.210651\pi$
$191$	19.2360	+	2.53247i	1.39187	+	0.183243i	0.602968	+	0.797765i	$0.293984\pi$
$192$	1.48120	−	0.897801i	0.106896	−	0.0647932i
$193$	3.72052	−	0.489816i	0.267809	−	0.0352577i	0.00457415	−	0.999990i	$-0.498544\pi$
$193$	3.72052	−	0.489816i	0.267809	−	0.0352577i	0.263235	+	0.964732i	$0.415211\pi$
$194$	0.890940	+	6.76736i	0.0639658	+	0.485868i
$195$	2.11822	+	4.82056i	0.151689	+	0.345207i
$196$	0.00773902	+	0.0288824i	0.000552787	+	0.00206303i
$197$	15.1676	+	15.1676i	1.08065	+	1.08065i	0.996449	+	0.0841995i	$0.0268333\pi$
$197$	15.1676	+	15.1676i	1.08065	+	1.08065i	0.0841995	+	0.996449i	$0.473167\pi$
$198$	4.97238	−	2.31261i	0.353371	−	0.164350i
$199$	14.8839	−	6.16510i	1.05509	−	0.437032i	0.213384	−	0.976969i	$-0.431552\pi$
$199$	14.8839	−	6.16510i	1.05509	−	0.437032i	0.841706	+	0.539936i	$0.181552\pi$
$200$	6.13896	−	1.64493i	0.434090	−	0.116314i
$201$	5.57846	+	0.613763i	0.393474	+	0.0432915i
$202$	1.84025	+	13.9781i	0.129479	+	0.983494i
$203$	10.2138	+	2.73679i	0.716871	+	0.192085i
$204$	12.0128	+	1.32169i	0.841061	+	0.0925366i
$205$	−19.6836	−	8.83924i	−1.37476	−	0.617359i
$206$			4.06639i			0.283319i
$207$	2.36563	−	0.100916i	0.164423	−	0.00701417i
$208$	0.345230	−	0.833458i	0.0239374	−	0.0577899i
$209$	3.76264	−	6.51709i	0.260267	−	0.450796i
$210$	5.61604	−	14.4203i	0.387544	−	0.995094i
$211$	1.79291	−	2.33656i	0.123429	−	0.160856i	−0.727552	−	0.686053i	$-0.759342\pi$
$211$	1.79291	−	2.33656i	0.123429	−	0.160856i	0.850980	+	0.525197i	$0.176008\pi$
$212$	−1.87770	−	14.2625i	−0.128961	−	0.979556i
$213$	0.162841	+	1.06152i	0.0111577	+	0.0727342i
$214$	−2.69537	+	0.722222i	−0.184252	+	0.0493701i
$215$		−	14.1604i		−	0.965732i
$216$	−3.43192	+	3.90153i	−0.233512	+	0.265466i
$217$	23.4304	+	9.70520i	1.59056	+	0.658832i
$218$	7.29389	−	5.59680i	0.494005	−	0.379063i
$219$	17.6887	+	4.33778i	1.19529	+	0.293120i
$220$	−4.88692	−	3.74986i	−0.329476	−	0.252816i
$221$	5.45122	−	3.14727i	0.366689	−	0.211708i
$222$	−7.95222	−	7.62021i	−0.533718	−	0.511435i
$223$	6.86446	−	11.8896i	0.459679	−	0.796187i	−0.539265	−	0.842136i	$-0.681298\pi$
$223$	6.86446	−	11.8896i	0.459679	−	0.796187i	0.998944	+	0.0459494i	$0.0146313\pi$
$224$	−2.44957	+	1.01465i	−0.163669	+	0.0677938i
$225$	−16.0908	+	10.2284i	−1.07272	+	0.681892i
$226$	1.00621	+	1.00621i	0.0669323	+	0.0669323i
$227$	7.73416	+	1.01822i	0.513334	+	0.0675817i	0.382743	−	0.923855i	$-0.374979\pi$
$227$	7.73416	+	1.01822i	0.513334	+	0.0675817i	0.130591	+	0.991436i	$0.458313\pi$
$228$	−0.779816	+	7.08771i	−0.0516446	+	0.469395i
$229$	1.76168	+	1.35179i	0.116415	+	0.0893285i	0.665328	−	0.746551i	$-0.268292\pi$
$229$	1.76168	+	1.35179i	0.116415	+	0.0893285i	−0.548913	+	0.835879i	$0.684958\pi$
$230$	−1.32982	−	2.30332i	−0.0876860	−	0.151877i
$231$	−8.06041	+	2.34502i	−0.530336	+	0.154291i
$232$	−0.520557	+	3.95402i	−0.0341762	+	0.259594i
$233$	−1.84353	+	4.45067i	−0.120773	+	0.291573i	−0.972691	−	0.232102i	$-0.925440\pi$
$233$	−1.84353	+	4.45067i	−0.120773	+	0.291573i	0.851918	+	0.523675i	$0.175440\pi$
$234$	−0.238572	+	2.69585i	−0.0155960	+	0.176233i
$235$	−14.9015	+	35.9754i	−0.972066	+	2.34678i
$236$	−2.95977	+	5.12647i	−0.192664	+	0.333704i
$237$	21.8138	+	8.49547i	1.41696	+	0.551840i
$238$	−17.8695	−	4.78813i	−1.15831	−	0.310368i
$239$	−20.3632	+	2.68086i	−1.31718	+	0.173410i	−0.756158	−	0.654389i	$-0.772926\pi$
$239$	−20.3632	+	2.68086i	−1.31718	+	0.173410i	−0.561025	+	0.827799i	$0.689593\pi$
$240$	5.66870	+	1.39012i	0.365913	+	0.0897322i
$241$	2.80823	+	10.4805i	0.180894	+	0.675106i	0.995472	+	0.0950522i	$0.0303018\pi$
$241$	2.80823	+	10.4805i	0.180894	+	0.675106i	−0.814578	+	0.580054i	$0.803032\pi$
$242$		−	7.65859i		−	0.492313i
$243$	6.31384	−	14.2526i	0.405033	−	0.914302i
$244$	1.90776	+	1.90776i	0.122132	+	0.122132i
$245$	−0.0503806	+	0.0872618i	−0.00321870	+	0.00557495i
$246$	−6.68034	−	8.85285i	−0.425923	−	0.564437i
$247$	1.85693	+	3.21630i	0.118154	+	0.204649i
$248$	−2.47563	+	9.23919i	−0.157203	+	0.586689i
$249$	−0.366047	−	17.1692i	−0.0231973	−	1.08805i
$250$	3.95586	+	2.28392i	0.250191	+	0.144448i
$251$	−5.65353	+	5.65353i	−0.356848	+	0.356848i	−0.862650	−	0.505802i	$-0.831197\pi$
$251$	−5.65353	+	5.65353i	−0.356848	+	0.356848i	0.505802	+	0.862650i	$0.331197\pi$
$252$	6.09837	−	5.10676i	0.384161	−	0.321696i
$253$	−0.552109	+	1.33291i	−0.0347108	+	0.0837993i
$254$	−3.24684	−	12.1174i	−0.203725	−	0.760312i
$255$	25.4747	+	31.7734i	1.59529	+	1.98973i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.7438	+	3.12594i	−1.48110	+	0.194991i	−0.827336	−	0.561708i	$-0.810145\pi$
$257$	−23.7438	+	3.12594i	−1.48110	+	0.194991i	−0.653764	+	0.756698i	$0.726811\pi$
$258$	3.50399	−	6.37937i	0.218149	−	0.397162i
$259$	10.2636	+	13.3758i	0.637751	+	0.831134i
$260$	2.80858	−	1.16335i	0.174181	−	0.0721481i
$261$	−2.06582	−	11.7847i	−0.127871	−	0.729456i
$262$	−17.6018			−1.08744
$263$	−2.81930	+	21.4147i	−0.173846	+	1.32049i	0.652699	+	0.757618i	$0.273637\pi$
$263$	−2.81930	+	21.4147i	−0.173846	+	1.32049i	−0.826544	+	0.562872i	$0.809696\pi$
$264$	−1.27369	−	2.89861i	−0.0783902	−	0.178397i
$265$	29.5107	−	38.4591i	1.81283	−	2.36252i
$266$	2.82507	−	10.5433i	0.173216	−	0.646451i
$267$	−1.58061	−	10.3036i	−0.0967317	−	0.630572i
$268$	0.422926	−	3.21244i	0.0258343	−	0.196231i
$269$	−22.9668			−1.40031			−0.700156	−	0.713990i	$-0.746886\pi$
$269$	−22.9668			−1.40031			−0.700156	+	0.713990i	$0.746886\pi$
$270$	−17.4742	+	1.11900i	−1.06344	+	0.0681004i
$271$			12.8426i			0.780133i	0.920787	+	0.390067i	$0.127548\pi$
$271$			12.8426i			0.780133i	−0.920787	+	0.390067i	$0.872452\pi$
$272$	0.910736	−	6.91773i	0.0552215	−	0.419449i
$273$	0.986719	−	4.02367i	0.0597189	−	0.243524i
$274$	−1.49586	−	11.3622i	−0.0903680	−	0.686413i
$275$	−1.51640	−	11.5182i	−0.0914424	−	0.694574i
$276$	−0.0291386	−	1.36673i	−0.00175394	−	0.0822674i
$277$	15.2368	+	8.79696i	0.915490	+	0.528558i	0.882193	−	0.470887i	$-0.156066\pi$
$277$	15.2368	+	8.79696i	0.915490	+	0.528558i	0.0332963	+	0.999446i	$0.489399\pi$
$278$	7.02462	+	7.02462i	0.421309	+	0.421309i
$279$	−1.22301	−	28.6693i	−0.0732199	−	1.71638i
$280$	−8.25455	−	3.41915i	−0.493304	−	0.204333i
$281$	−11.2795	−	1.48497i	−0.672876	−	0.0885858i	−0.213657	−	0.976909i	$-0.568537\pi$
$281$	−11.2795	−	1.48497i	−0.672876	−	0.0885858i	−0.459219	+	0.888323i	$0.651871\pi$
$282$	−15.6153	+	12.5198i	−0.929880	+	0.745544i
$283$	6.57212	+	11.3832i	0.390672	+	0.676664i	0.992538	−	0.121933i	$-0.0389093\pi$
$283$	6.57212	+	11.3832i	0.390672	+	0.676664i	−0.601866	+	0.798597i	$0.705576\pi$
$284$	0.614734	−	0.0809313i	0.0364778	−	0.00480239i
$285$	−18.7468	+	15.0305i	−1.11046	+	0.890329i
$286$	−1.42812	−	0.824524i	−0.0844464	−	0.0487551i
$287$	8.05307	+	14.9457i	0.475358	+	0.882217i
$288$	2.20980	+	2.02898i	0.130214	+	0.119559i
$289$	22.4042	−	22.4042i	1.31790	−	1.31790i
$290$	−10.6621	+	8.18128i	−0.626097	+	0.480421i
$291$	−10.8237	+	4.75609i	−0.634497	+	0.278807i
$292$	2.72153	−	10.1569i	0.159266	−	0.594387i
$293$	−11.4766	−	8.80628i	−0.670468	−	0.514468i	0.216510	−	0.976280i	$-0.430533\pi$
$293$	−11.4766	−	8.80628i	−0.670468	−	0.514468i	−0.886978	+	0.461812i	$0.847199\pi$
$294$	−0.0442898	+	0.0268454i	−0.00258303	+	0.00156566i
$295$	−19.2679	+	5.16282i	−1.12182	+	0.300591i
$296$	−4.49639	+	4.49639i	−0.261348	+	0.261348i
$297$	6.25196	+	7.15060i	0.362776	+	0.414920i
$298$	10.6249	+	4.40099i	0.615486	+	0.254943i
$299$	−0.433447	−	0.564879i	−0.0250669	−	0.0326678i
$300$	5.70600	+	9.41380i	0.329436	+	0.543506i
$301$	−6.78257	+	8.83921i	−0.390941	+	0.509484i
$302$	−3.38366	+	4.40967i	−0.194708	+	0.253748i
$303$	−22.3565	+	9.82376i	−1.28435	+	0.564360i
$304$	4.08156	+	0.537348i	0.234094	+	0.0308190i
$305$			9.09164i			0.520586i
$306$	3.61424	+	20.6179i	0.206612	+	1.17865i
$307$	−11.2477	+	11.2477i	−0.641942	+	0.641942i	−0.951033	−	0.309091i	$-0.899975\pi$
$307$	−11.2477	+	11.2477i	−0.641942	+	0.641942i	0.309091	+	0.951033i	$0.399975\pi$
$308$	1.25440	+	4.68148i	0.0714760	+	0.266752i
$309$	−6.76280	+	1.96751i	−0.384722	+	0.111928i
$310$	−27.9141	+	16.1162i	−1.58542	+	0.915341i
$311$	12.1981	−	15.8969i	0.691691	−	0.901429i	−0.307045	−	0.951695i	$-0.599340\pi$
$311$	12.1981	−	15.8969i	0.691691	−	0.901429i	0.998736	+	0.0502662i	$0.0160070\pi$
$312$	1.55316	+	0.170884i	0.0879304	+	0.00967443i
$313$	16.0802	+	2.11700i	0.908909	+	0.119660i	0.570461	−	0.821325i	$-0.306765\pi$
$313$	16.0802	+	2.11700i	0.908909	+	0.119660i	0.338448	+	0.940985i	$0.390098\pi$
$314$	3.99603	+	9.64728i	0.225509	+	0.544427i
$315$	26.6996	+	2.36281i	1.50435	+	0.133130i
$316$	5.17219	−	12.4868i	0.290959	−	0.702436i
$317$	−12.1874	+	9.35175i	−0.684515	+	0.525246i	−0.891456	−	0.453107i	$-0.850316\pi$
$317$	−12.1874	+	9.35175i	−0.684515	+	0.525246i	0.206942	+	0.978353i	$0.433649\pi$
$318$	22.8115	−	10.0237i	1.27920	−	0.562100i
$319$	7.04173	+	1.88683i	0.394261	+	0.105642i
$320$	0.872167	−	3.25497i	0.0487556	−	0.181959i
$321$	−2.50527	−	4.13321i	−0.139831	−	0.230694i
$322$	−0.273145	+	2.07474i	−0.0152218	+	0.115621i
$323$	20.3113	+	20.3113i	1.13015	+	1.13015i
$324$	−8.14915	−	3.81987i	−0.452730	−	0.212215i
$325$	5.29706	+	2.19412i	0.293828	+	0.121708i
$326$	−0.319853	−	1.19371i	−0.0177150	−	0.0661134i
$327$	12.8372	+	9.42246i	0.709896	+	0.521063i
$328$	−5.19225	+	3.74708i	−0.286694	+	0.206898i
$329$	26.5333	−	15.3190i	1.46283	−	0.844565i
$330$	3.87187	−	9.94178i	0.213139	−	0.547277i
$331$	−15.0393	−	19.5996i	−0.826634	−	1.07729i	−0.995787	−	0.0917003i	$-0.970770\pi$
$331$	−15.0393	−	19.5996i	−0.826634	−	1.07729i	0.169153	−	0.985590i	$-0.445897\pi$
$332$	−9.91490			−0.544151
$333$	8.82550	−	16.9123i	0.483634	−	0.926790i
$334$	−6.66657	−	16.0945i	−0.364779	−	0.880653i
$335$	8.66237	−	6.64687i	0.473276	−	0.363157i
$336$	−2.87267	−	3.58294i	−0.156717	−	0.195465i
$337$	4.33399	−	16.1747i	0.236087	−	0.881090i	−0.741568	−	0.670877i	$-0.765918\pi$
$337$	4.33399	−	16.1747i	0.236087	−	0.881090i	0.977656	−	0.210213i	$-0.0674157\pi$
$338$	−10.5535	+	6.09308i	−0.574036	+	0.331420i
$339$	−1.18658	+	2.16028i	−0.0644461	+	0.117331i
$340$	18.6537	−	14.3135i	1.01164	−	0.776258i
$341$	16.1536	+	6.69106i	0.874769	+	0.362341i
$342$	−12.1649	+	2.13246i	−0.657800	+	0.115310i
$343$	−17.0737	+	7.07218i	−0.921896	+	0.381862i
$344$	−3.63918	−	2.10108i	−0.196211	−	0.113283i
$345$	3.18722	−	3.32608i	0.171594	−	0.179070i
$346$	10.0968	+	17.4881i	0.542806	+	0.940167i
$347$	11.8465	+	9.09017i	0.635955	+	0.487986i	0.875703	−	0.482849i	$-0.160398\pi$
$347$	11.8465	+	9.09017i	0.635955	+	0.487986i	−0.239748	+	0.970835i	$0.577065\pi$
$348$	−6.82779	+	1.04740i	−0.366008	+	0.0561468i
$349$	−12.5695	+	3.36798i	−0.672828	+	0.180284i	−0.579029	−	0.815307i	$-0.696568\pi$
$349$	−12.5695	+	3.36798i	−0.672828	+	0.180284i	−0.0937998	+	0.995591i	$0.529901\pi$
$350$	−6.44860	−	15.5683i	−0.344692	−	0.832161i
$351$	−4.59889	+	0.907610i	−0.245471	+	0.0484446i
$352$	−1.68881	+	0.699527i	−0.0900138	+	0.0372849i
$353$	4.85845	−	8.41508i	0.258589	−	0.447890i	−0.707275	−	0.706938i	$-0.750076\pi$
$353$	4.85845	−	8.41508i	0.258589	−	0.447890i	0.965864	+	0.259049i	$0.0834091\pi$
$354$	−9.95788	−	2.44195i	−0.529256	−	0.129788i
$355$	1.65764	+	1.27195i	0.0879782	+	0.0675080i
$356$	−5.96690	+	0.785558i	−0.316245	+	0.0416345i
$357$	−0.682996	−	32.0355i	−0.0361480	−	1.69550i
$358$	−4.94695	−	6.44699i	−0.261455	−	0.340734i
$359$	−7.69659			−0.406210			−0.203105	−	0.979157i	$-0.565103\pi$
$359$	−7.69659			−0.406210			−0.203105	+	0.979157i	$0.565103\pi$
$360$	0.430868	+	10.1002i	0.0227087	+	0.532327i
$361$	1.45105	−	1.45105i	0.0763711	−	0.0763711i
$362$	5.70437	+	7.43408i	0.299815	+	0.390727i
$363$	12.7370	−	3.70558i	0.668518	−	0.194493i
$364$	−2.31040	−	0.619070i	−0.121098	−	0.0324481i
$365$	30.6868	−	17.7170i	1.60622	−	0.927351i
$366$	−2.24973	+	4.09585i	−0.117595	+	0.214094i
$367$	−13.3413	+	3.57478i	−0.696408	+	0.186602i	−0.589621	−	0.807680i	$-0.700723\pi$
$367$	−13.3413	+	3.57478i	−0.696408	+	0.186602i	−0.106787	+	0.994282i	$0.534056\pi$
$368$	−0.789261			−0.0411431
$369$	11.4909	−	15.3935i	0.598192	−	0.801353i
$370$	−21.4281			−1.11399
$371$	−36.8423	+	9.87187i	−1.91276	+	0.512522i
$372$	−16.5635	+	0.353134i	−0.858777	+	0.0183091i
$373$	8.02082	−	4.63082i	0.415302	−	0.239775i	−0.277763	−	0.960650i	$-0.589593\pi$
$373$	8.02082	−	4.63082i	0.415302	−	0.239775i	0.693065	+	0.720875i	$0.256260\pi$
$374$	−12.3198	−	3.30108i	−0.637041	−	0.170695i
$375$	−1.88435	+	7.68405i	−0.0973072	+	0.396803i
$376$	7.03451	+	9.16755i	0.362777	+	0.472780i
$377$	−2.54404	+	2.54404i	−0.131025	+	0.131025i
$378$	11.4437	+	7.67129i	0.588601	+	0.394569i
$379$	32.7079			1.68009			0.840046	−	0.542516i	$-0.182528\pi$
$379$	32.7079			1.68009			0.840046	+	0.542516i	$0.182528\pi$
$380$	8.44518	+	11.0060i	0.433228	+	0.564594i
$381$	18.5814	−	11.2628i	0.951954	−	0.577009i
$382$	19.2360	−	2.53247i	0.984199	−	0.129572i
$383$	7.55620	+	5.79807i	0.386104	+	0.296268i	0.783515	−	0.621373i	$-0.213425\pi$
$383$	7.55620	+	5.79807i	0.386104	+	0.296268i	−0.397411	+	0.917641i	$0.630091\pi$
$384$	1.19836	−	1.25057i	0.0611536	−	0.0638180i
$385$	−8.16607	+	14.1440i	−0.416181	+	0.720847i
$386$	3.46697	−	1.43607i	0.176464	−	0.0730939i
$387$	12.3049	+	2.74084i	0.625494	+	0.139325i
$388$	2.61211	+	6.30618i	0.132610	+	0.320148i
$389$	−19.8749	+	5.32547i	−1.00770	+	0.270012i	−0.724667	−	0.689099i	$-0.758007\pi$
$389$	−19.8749	+	5.32547i	−1.00770	+	0.270012i	−0.283031	+	0.959111i	$0.591340\pi$
$390$	3.29370	+	4.10806i	0.166783	+	0.208020i
$391$	−4.36900	−	3.35245i	−0.220950	−	0.169541i
$392$	0.0149506	+	0.0258953i	0.000755121	+	0.00130791i
$393$	−8.51658	−	29.2735i	−0.429605	−	1.47665i
$394$	18.5765	+	10.7251i	0.935869	+	0.540324i
$395$	42.0779	−	17.4292i	2.11717	−	0.876960i
$396$	4.20440	−	3.52075i	0.211279	−	0.176925i
$397$	19.3072	+	7.99731i	0.969002	+	0.401374i	0.810340	−	0.585959i	$-0.199282\pi$
$397$	19.3072	+	7.99731i	0.969002	+	0.401374i	0.158661	+	0.987333i	$0.449282\pi$
$398$	12.7811	−	9.80726i	0.640657	−	0.491593i
$399$	18.9014	−	0.402978i	0.946255	−	0.0201741i
$400$	5.50404	−	3.17776i	0.275202	−	0.158888i
$401$	1.20252	−	4.48786i	0.0600509	−	0.224113i	−0.929379	−	0.369128i	$-0.879656\pi$
$401$	1.20252	−	4.48786i	0.0600509	−	0.224113i	0.989429	+	0.145015i	$0.0463230\pi$
$402$	5.54723	−	0.850962i	0.276671	−	0.0424422i
$403$	−6.84582	+	5.25298i	−0.341015	+	0.261670i
$404$	5.39534	+	13.0255i	0.268428	+	0.648043i
$405$	−10.3158	−	28.5198i	−0.512598	−	1.41716i
$406$	10.5741			0.524786
$407$	7.07606	+	9.22170i	0.350747	+	0.457103i
$408$	11.9455	−	1.83248i	0.591391	−	0.0907211i
$409$	−29.4947	+	17.0288i	−1.45842	+	0.842018i	−0.998934	−	0.0461686i	$-0.985299\pi$
$409$	−29.4947	+	17.0288i	−1.45842	+	0.842018i	−0.459484	+	0.888186i	$0.651966\pi$
$410$	−21.3007	−	3.44356i	−1.05196	−	0.170065i
$411$	18.1726	−	7.98530i	0.896388	−	0.393886i
$412$	1.05246	+	3.92783i	0.0518509	+	0.193510i
$413$	14.5003	+	6.00623i	0.713514	+	0.295547i
$414$	2.25891	−	0.709748i	0.111019	−	0.0348822i
$415$	−23.6253	−	23.6253i	−1.15972	−	1.15972i
$416$	0.117751	−	0.894411i	0.00577324	−	0.0438521i
$417$	−8.28379	+	15.0815i	−0.405659	+	0.738543i
$418$	1.94769	−	7.26887i	0.0952645	−	0.355532i
$419$	28.9258	+	7.75064i	1.41312	+	0.378644i	0.883037	−	0.469304i	$-0.155495\pi$
$419$	28.9258	+	7.75064i	1.41312	+	0.378644i	0.530081	+	0.847947i	$0.322162\pi$
$420$	1.69244	−	15.3825i	0.0825824	−	0.750588i
$421$	11.0124	−	8.45011i	0.536711	−	0.411833i	−0.304522	−	0.952505i	$-0.598497\pi$
$421$	11.0124	−	8.45011i	0.536711	−	0.411833i	0.841233	+	0.540672i	$0.181830\pi$
$422$	1.12707	−	2.72098i	0.0548649	−	0.132455i
$423$	−28.3771	−	19.9122i	−1.37974	−	0.968162i
$424$	−5.50514	−	13.2906i	−0.267353	−	0.645448i
$425$	43.9658	+	5.78820i	2.13265	+	0.280769i
$426$	0.432034	+	0.983205i	0.0209321	+	0.0476364i
$427$	4.35472	−	5.67518i	0.210740	−	0.274641i
$428$	−2.41660	+	1.39523i	−0.116811	+	0.0674407i
$429$	0.680274	−	2.77404i	0.0328439	−	0.133932i
$430$	−3.66498	−	13.6779i	−0.176741	−	0.659607i
$431$	18.9281	−	18.9281i	0.911737	−	0.911737i	−0.0846723	−	0.996409i	$-0.526984\pi$
$431$	18.9281	−	18.9281i	0.911737	−	0.911737i	0.996409	+	0.0846723i	$0.0269843\pi$
$432$	−2.30519	+	4.65684i	−0.110908	+	0.224052i
$433$			5.13068i			0.246565i	0.992372	+	0.123282i	$0.0393421\pi$
$433$			5.13068i			0.246565i	−0.992372	+	0.123282i	$0.960658\pi$
$434$	25.1439	+	3.31026i	1.20695	+	0.158898i
$435$	−18.7651	−	13.7735i	−0.899716	−	0.660391i
$436$	5.59680	−	7.29389i	0.268038	−	0.349314i
$437$	1.97800	−	2.57778i	0.0946204	−	0.123312i
$438$	18.2087	−	0.388209i	0.870045	−	0.0185494i
$439$	23.1861	+	30.2167i	1.10661	+	1.44217i	0.884137	+	0.467228i	$0.154747\pi$
$439$	23.1861	+	30.2167i	1.10661	+	1.44217i	0.222476	+	0.974938i	$0.428586\pi$
$440$	−5.69094	−	2.35726i	−0.271305	−	0.112378i
$441$	−0.0660760	−	0.0606691i	−0.00314648	−	0.00288901i
$442$	4.45091	−	4.45091i	0.211708	−	0.211708i
$443$	−14.0534	+	3.76560i	−0.667698	+	0.178909i	−0.576718	−	0.816944i	$-0.695667\pi$
$443$	−14.0534	+	3.76560i	−0.667698	+	0.178909i	−0.0909804	+	0.995853i	$0.529000\pi$
$444$	−9.65351	−	5.30238i	−0.458135	−	0.251640i
$445$	−16.0898	−	12.3461i	−0.762730	−	0.585263i
$446$	3.55331	−	13.2611i	0.168254	−	0.627933i
$447$	−2.17844	+	19.7997i	−0.103037	+	0.936495i
$448$	−2.10349	+	1.61407i	−0.0993807	+	0.0762575i
$449$	−2.73035	+	2.73035i	−0.128853	+	0.128853i	−0.768592	−	0.639739i	$-0.779042\pi$
$449$	−2.73035	+	2.73035i	−0.128853	+	0.128853i	0.639739	+	0.768592i	$0.279042\pi$
$450$	−12.8952	+	14.0445i	−0.607887	+	0.662062i
$451$	5.55203	+	10.3040i	0.261435	+	0.485197i
$452$	1.23236	+	0.711501i	0.0579651	+	0.0334662i
$453$	−8.97088	−	3.49375i	−0.421489	−	0.164151i
$454$	7.73416	−	1.01822i	0.362982	−	0.0477875i
$455$	−4.03011	−	6.98035i	−0.188934	−	0.327244i
$456$	1.08119	+	7.04803i	0.0506313	+	0.330054i
$457$	21.5795	+	2.84099i	1.00945	+	0.132896i	0.617069	−	0.786909i	$-0.288320\pi$
$457$	21.5795	+	2.84099i	1.00945	+	0.132896i	0.392376	+	0.919805i	$0.371653\pi$
$458$	2.05152	+	0.849768i	0.0958613	+	0.0397071i
$459$	−32.5408	+	15.9867i	−1.51887	+	0.746196i
$460$	−1.88065	−	1.88065i	−0.0876860	−	0.0876860i
$461$	21.1162	+	12.1914i	0.983479	+	0.567812i	0.903319	−	0.428970i	$-0.141124\pi$
$461$	21.1162	+	12.1914i	0.983479	+	0.567812i	0.0801600	+	0.996782i	$0.474457\pi$
$462$	−7.17882	+	4.35131i	−0.333989	+	0.202441i
$463$	3.68867	+	28.0182i	0.171427	+	1.30212i	0.833434	+	0.552620i	$0.186372\pi$
$463$	3.68867	+	28.0182i	0.171427	+	1.30212i	−0.662006	+	0.749498i	$0.730295\pi$
$464$	0.520557	+	3.95402i	0.0241662	+	0.183561i
$465$	−40.3090	−	38.6261i	−1.86929	−	1.79124i
$466$	−0.628793	+	4.77616i	−0.0291283	+	0.221251i
$467$			14.2002i			0.657106i	0.944485	+	0.328553i	$0.106561\pi$
$467$			14.2002i			0.657106i	−0.944485	+	0.328553i	$0.893439\pi$
$468$	0.467294	+	2.66574i	0.0216007	+	0.123224i
$469$	−8.59095			−0.396693
$470$	−5.08262	+	38.6063i	−0.234444	+	1.78078i
$471$	−14.1109	+	11.3136i	−0.650195	+	0.521303i
$472$	−1.53209	+	5.71783i	−0.0705201	+	0.263184i
$473$	−4.67611	+	6.09402i	−0.215008	+	0.280203i
$474$	23.2693	+	2.56017i	1.06879	+	0.117593i
$475$	−3.41513	+	25.9405i	−0.156697	+	1.19023i
$476$	−18.4999			−0.847941
$477$	27.7076	+	33.0878i	1.26865	+	1.51499i
$478$	−18.9754	+	7.85988i	−0.867916	+	0.359503i
$479$	14.0904	+	18.3630i	0.643806	+	0.839025i	0.995267	−	0.0971779i	$-0.0309816\pi$
$479$	14.0904	+	18.3630i	0.643806	+	0.839025i	−0.351461	+	0.936203i	$0.614315\pi$
$480$	5.83533	−	0.124409i	0.266345	−	0.00567848i
$481$	−5.68744	+	0.748765i	−0.259325	+	0.0341408i
$482$	5.42509	+	9.39653i	0.247106	+	0.428000i
$483$	−3.58265	+	0.549590i	−0.163016	+	0.0250072i
$484$	−1.98219	−	7.39763i	−0.0900995	−	0.336256i
$485$	−8.80226	+	21.2505i	−0.399690	+	0.964937i
$486$	2.40987	−	15.4011i	0.109314	−	0.698606i
$487$	−26.7694	+	26.7694i	−1.21304	+	1.21304i	−0.243014	+	0.970023i	$0.578136\pi$
$487$	−26.7694	+	26.7694i	−1.21304	+	1.21304i	−0.970023	+	0.243014i	$0.921864\pi$
$488$	2.33652	+	1.34899i	0.105769	+	0.0610659i
$489$	1.83049	−	1.10952i	0.0827778	−	0.0501742i
$490$	−0.0260789	+	0.0973278i	−0.00117813	+	0.00439682i
$491$	−11.8270	−	20.4849i	−0.533744	−	0.924471i	−0.999223	−	0.0394126i	$-0.987451\pi$
$491$	−11.8270	−	20.4849i	−0.533744	−	0.924471i	0.465479	−	0.885059i	$-0.345882\pi$
$492$	−8.74400	−	6.82220i	−0.394210	−	0.307568i
$493$	−13.9135	+	24.0988i	−0.626631	+	1.08536i
$494$	2.62610	+	2.62610i	0.118154	+	0.118154i
$495$	18.4075	+	1.62900i	0.827357	+	0.0732179i
$496$			9.56511i			0.429486i
$497$	−0.425490	−	1.58795i	−0.0190859	−	0.0712294i
$498$	−4.79729	−	16.4894i	−0.214972	−	0.738909i
$499$	22.1548	−	2.91674i	0.991787	−	0.130571i	0.382867	−	0.923803i	$-0.374937\pi$
$499$	22.1548	−	2.91674i	0.991787	−	0.130571i	0.608919	+	0.793232i	$0.291603\pi$
$500$	4.41219	+	1.18224i	0.197319	+	0.0528715i
$501$	23.5412	−	18.8744i	1.05174	−	0.843248i
$502$	−3.99765	+	6.92414i	−0.178424	+	0.309039i
$503$	16.9072	−	40.8175i	0.753853	−	1.81996i	0.217278	−	0.976110i	$-0.430282\pi$
$503$	16.9072	−	40.8175i	0.753853	−	1.81996i	0.536575	−	0.843853i	$-0.319718\pi$
$504$	4.56885	−	6.51113i	0.203513	−	0.290029i
$505$	−18.1812	+	43.8933i	−0.809052	+	1.95322i
$506$	−0.188314	+	1.43039i	−0.00837159	+	0.0635885i
$507$	−15.2397	−	14.6034i	−0.676818	−	0.648561i
$508$	−6.27242	−	10.8641i	−0.278293	−	0.482018i
$509$	26.8881	+	20.6320i	1.19179	+	0.914496i	0.997786	−	0.0665042i	$-0.0211846\pi$
$509$	26.8881	+	20.6320i	1.19179	+	0.914496i	0.194008	+	0.981000i	$0.437851\pi$
$510$	32.8303	+	24.0974i	1.45375	+	1.06705i
$511$	−27.6414	−	3.63906i	−1.22278	−	0.160983i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−9.43241	−	19.1996i	−0.416451	−	0.847681i
$514$	−22.1257	+	9.16478i	−0.975925	+	0.404241i
$515$	−6.85145	+	11.8671i	−0.301911	+	0.522925i
$516$	1.73349	−	7.06890i	0.0763129	−	0.311191i
$517$	18.2929	−	10.5614i	0.804520	−	0.464490i
$518$	13.3758	+	10.2636i	0.587700	+	0.450958i
$519$	−24.1991	+	25.2535i	−1.06222	+	1.10850i
$520$	2.41179	−	1.85063i	0.105764	−	0.0811554i
$521$	−7.16805	−	2.96910i	−0.314038	−	0.130079i	0.220097	−	0.975478i	$-0.429363\pi$
$521$	−7.16805	−	2.96910i	−0.314038	−	0.130079i	−0.534135	+	0.845399i	$0.679363\pi$
$522$	−5.04554	−	10.8485i	−0.220837	−	0.474826i
$523$		−	13.8896i		−	0.607350i	−0.952776	−	0.303675i	$-0.901786\pi$
$523$		−	13.8896i		−	0.607350i	0.952776	−	0.303675i	$-0.0982138\pi$
$524$	−17.0020	+	4.55568i	−0.742738	+	0.199016i
$525$	22.7715	−	18.2573i	0.993828	−	0.796815i
$526$	2.81930	+	21.4147i	0.122928	+	0.933727i
$527$	−40.6286	+	52.9482i	−1.76981	+	2.30646i
$528$	−1.98051	−	2.47019i	−0.0861905	−	0.107501i
$529$	11.1885	−	19.3791i	0.486458	−	0.842570i
$530$	18.5512	−	44.7865i	0.805812	−	1.94540i
$531$	−0.756882	−	17.7425i	−0.0328459	−	0.769957i
$532$		−	10.9152i		−	0.473235i
$533$	−5.77395	−	0.169676i	−0.250098	−	0.00734947i
$534$	−4.19353	−	9.54345i	−0.181472	−	0.412985i
$535$	−9.08284	−	2.43374i	−0.392685	−	0.105220i
$536$	−0.422926	−	3.21244i	−0.0182676	−	0.138756i
$537$	8.32841	−	11.3466i	0.359397	−	0.489643i
$538$	−22.1842	+	5.94425i	−0.956431	+	0.256275i
$539$	0.0504975	−	0.0209168i	0.00217508	−	0.000900948i
$540$	−16.5891	+	5.60353i	−0.713883	+	0.241137i
$541$	12.6663	+	12.6663i	0.544566	+	0.544566i	0.924864	−	0.380298i	$-0.124179\pi$
$541$	12.6663	+	12.6663i	0.544566	+	0.544566i	−0.380298	+	0.924864i	$0.624179\pi$
$542$	3.32391	+	12.4050i	0.142774	+	0.532841i
$543$	−9.60356	+	13.0839i	−0.412128	+	0.561483i
$544$	−0.910736	−	6.91773i	−0.0390475	−	0.296595i
$545$	30.7160	−	4.04384i	1.31573	−	0.173219i
$546$	−0.0883064	−	4.14195i	−0.00377916	−	0.177259i
$547$	11.5461	+	1.52008i	0.493677	+	0.0649937i	0.373254	−	0.927729i	$-0.378242\pi$
$547$	11.5461	+	1.52008i	0.493677	+	0.0649937i	0.120422	+	0.992723i	$0.461575\pi$
$548$	−4.38563	−	10.5878i	−0.187345	−	0.452290i
$549$	−7.90033	−	1.75975i	−0.337178	−	0.0751042i
$550$	−4.44586	−	10.7333i	−0.189572	−	0.457668i
$551$	−14.2187	−	8.20916i	−0.605736	−	0.349722i
$552$	−0.381881	−	1.31262i	−0.0162539	−	0.0558687i
$553$	−34.6141	−	9.27483i	−1.47194	−	0.394406i
$554$	16.9944	+	4.55364i	0.722024	+	0.193466i
$555$	−10.3679	−	35.6370i	−0.440093	−	1.51270i
$556$	8.60337	+	4.96716i	0.364864	+	0.210654i
$557$	12.9176	+	31.1859i	0.547338	+	1.32139i	0.919452	+	0.393203i	$0.128633\pi$
$557$	12.9176	+	31.1859i	0.547338	+	1.32139i	−0.372114	+	0.928187i	$0.621367\pi$
$558$	−8.60149	−	27.3758i	−0.364130	−	1.15891i
$559$	−1.45071	−	3.50232i	−0.0613585	−	0.148133i
$560$	−8.85823	−	1.16621i	−0.374328	−	0.0492813i
$561$	−0.470878	−	22.0862i	−0.0198805	−	0.932481i
$562$	−11.2795	+	1.48497i	−0.475795	+	0.0626397i
$563$	−1.72171	−	13.0777i	−0.0725615	−	0.551159i	−0.988656	−	0.150197i	$-0.952009\pi$
$563$	−1.72171	−	13.0777i	−0.0725615	−	0.551159i	0.916095	−	0.400962i	$-0.131324\pi$
$564$	−11.8429	+	16.1348i	−0.498676	+	0.679396i
$565$	1.24110	+	4.63183i	0.0522133	+	0.194863i
$566$	9.29438	+	9.29438i	0.390672	+	0.390672i
$567$	−7.22110	+	22.7437i	−0.303258	+	0.955147i
$568$	0.572841	−	0.237279i	0.0240359	−	0.00995599i
$569$	22.3672	−	5.99327i	0.937681	−	0.251251i	0.242554	−	0.970138i	$-0.422015\pi$
$569$	22.3672	−	5.99327i	0.937681	−	0.251251i	0.695127	+	0.718887i	$0.255348\pi$
$570$	−14.2178	+	19.3704i	−0.595519	+	0.811335i
$571$	−0.632629	−	4.80529i	−0.0264747	−	0.201095i	0.973096	−	0.230401i	$-0.0740037\pi$
$571$	−0.632629	−	4.80529i	−0.0264747	−	0.201095i	−0.999570	+	0.0293056i	$0.990670\pi$
$572$	−1.59286	−	0.426805i	−0.0666008	−	0.0178456i
$573$	13.5190	+	30.7660i	0.564765	+	1.28527i
$574$	11.6469	+	12.3521i	0.486132	+	0.515569i
$575$		−	5.01617i		−	0.209189i
$576$	2.65965	+	1.38791i	0.110819	+	0.0578294i
$577$	−9.09835	+	21.9654i	−0.378769	+	0.914430i	0.613428	+	0.789751i	$0.289790\pi$
$577$	−9.09835	+	21.9654i	−0.378769	+	0.914430i	−0.992197	+	0.124679i	$0.960210\pi$
$578$	15.8422	−	27.4395i	0.658948	−	1.14133i
$579$	4.06580	+	5.07107i	0.168969	+	0.210747i
$580$	−8.18128	+	10.6621i	−0.339709	+	0.442718i
$581$	3.43131	+	26.0634i	0.142355	+	1.08129i
$582$	−9.22393	+	7.39541i	−0.382344	+	0.306550i
$583$	−25.4002	+	6.80596i	−1.05197	+	0.281874i
$584$		−	10.5152i		−	0.435121i
$585$	−5.23847	+	7.46541i	−0.216584	+	0.308657i
$586$	−13.3647	−	5.53586i	−0.552092	−	0.228684i
$587$	27.8610	−	21.3785i	1.14995	−	0.882384i	0.155520	−	0.987833i	$-0.450295\pi$
$587$	27.8610	−	21.3785i	1.14995	−	0.882384i	0.994425	+	0.105449i	$0.0336279\pi$
$588$	−0.0358325	+	0.0373937i	−0.00147771	+	0.00154209i
$589$	−31.2403	−	23.9715i	−1.28723	−	0.987729i
$590$	−17.2751	+	9.97381i	−0.711206	+	0.410615i
$591$	−8.84877	+	36.0838i	−0.363990	+	1.48429i
$592$	−3.17943	+	5.50694i	−0.130674	+	0.226334i
$593$	−1.74742	+	0.723805i	−0.0717580	+	0.0297231i	−0.418274	−	0.908321i	$-0.637365\pi$
$593$	−1.74742	+	0.723805i	−0.0717580	+	0.0297231i	0.346516	+	0.938044i	$0.387365\pi$
$594$	7.88964	+	5.28882i	0.323716	+	0.217003i
$595$	−44.0817	−	44.0817i	−1.80717	−	1.80717i
$596$	11.4020	+	1.50110i	0.467043	+	0.0614873i
$597$	22.4945	+	16.5109i	0.920639	+	0.675748i
$598$	−0.564879	−	0.433447i	−0.0230996	−	0.0177250i
$599$	−16.9266	−	29.3177i	−0.691600	−	1.19789i	−0.971313	−	0.237803i	$-0.923573\pi$
$599$	−16.9266	−	29.3177i	−0.691600	−	1.19789i	0.279713	−	0.960084i	$-0.409761\pi$
$600$	7.94804	+	7.61621i	0.324477	+	0.310931i
$601$	3.18051	−	24.1584i	0.129736	−	0.985441i	−0.795475	−	0.605987i	$-0.792778\pi$
$601$	3.18051	−	24.1584i	0.129736	−	0.985441i	0.925210	−	0.379454i	$-0.123888\pi$
$602$	−4.26370	+	10.2935i	−0.173775	+	0.419531i
$603$	4.09924	+	8.81385i	0.166934	+	0.358928i
$604$	−2.12706	+	5.13517i	−0.0865487	+	0.208947i
$605$	12.9039	−	22.3503i	0.524620	−	0.908668i
$606$	−19.0522	+	15.2753i	−0.773941	+	0.620517i
$607$	8.24802	+	2.21005i	0.334777	+	0.0897032i	0.422292	−	0.906460i	$-0.361226\pi$
$607$	8.24802	+	2.21005i	0.334777	+	0.0897032i	−0.0875148	+	0.996163i	$0.527893\pi$
$608$	4.08156	−	0.537348i	0.165529	−	0.0217923i
$609$	5.11627	+	17.5858i	0.207322	+	0.712614i
$610$	2.35309	+	8.78185i	0.0952738	+	0.355567i
$611$			10.4245i			0.421730i
$612$	8.82738	+	18.9799i	0.356826	+	0.767217i
$613$	−20.5922	−	20.5922i	−0.831709	−	0.831709i	0.156041	−	0.987751i	$-0.450127\pi$
$613$	−20.5922	−	20.5922i	−0.831709	−	0.831709i	−0.987751	+	0.156041i	$0.950127\pi$
$614$	−7.95334	+	13.7756i	−0.320971	+	0.555938i
$615$	−4.57929	−	37.0912i	−0.184655	−	1.49566i
$616$	2.42331	+	4.19730i	0.0976381	+	0.169114i
$617$	−2.90118	+	10.8273i	−0.116797	+	0.435892i	−0.999415	−	0.0341985i	$-0.989112\pi$
$617$	−2.90118	+	10.8273i	−0.116797	+	0.435892i	0.882618	+	0.470091i	$0.155779\pi$
$618$	−6.02313	+	3.65081i	−0.242286	+	0.146857i
$619$	−20.0163	−	11.5564i	−0.804522	−	0.464491i	0.0405279	−	0.999178i	$-0.487096\pi$
$619$	−20.0163	−	11.5564i	−0.804522	−	0.464491i	−0.845050	+	0.534687i	$0.820429\pi$
$620$	−22.7918	+	22.7918i	−0.915341	+	0.915341i
$621$	2.27334	+	3.41337i	0.0912262	+	0.136974i
$622$	7.66804	−	18.5123i	0.307461	−	0.742275i
$623$	4.13001	+	15.4134i	0.165465	+	0.617525i
$624$	1.54447	−	0.236926i	0.0618281	−	0.00948462i
$625$	−8.19247	−	14.1898i	−0.327699	−	0.567591i
$626$	16.0802	−	2.11700i	0.642696	−	0.0846125i
$627$	13.0312	−	0.277825i	0.520416	−	0.0110953i
$628$	6.35677	+	8.28430i	0.253663	+	0.330580i
$629$	−40.9911	+	16.9791i	−1.63442	+	0.677000i
$630$	26.4014	−	4.62807i	1.05186	−	0.184387i
$631$	27.5775			1.09784			0.548921	−	0.835874i	$-0.315039\pi$
$631$	27.5775			1.09784			0.548921	+	0.835874i	$0.315039\pi$
$632$	1.76414	−	13.4000i	0.0701737	−	0.533022i
$633$	5.07059	+	0.557885i	0.201538	+	0.0221739i
$634$	−9.35175	+	12.1874i	−0.371405	+	0.484025i
$635$	10.9412	−	40.8331i	0.434188	−	1.62041i
$636$	19.4399	−	15.5862i	0.770841	−	0.618032i
$637$	−0.00352092	+	0.0267440i	−0.000139504	+	0.00105964i
$638$	7.29013			0.288619
$639$	−1.42613	+	1.19423i	−0.0564167	+	0.0472432i
$640$		−	3.36980i		−	0.133203i
$641$	6.21721	−	47.2244i	0.245565	−	1.86525i	−0.213630	−	0.976915i	$-0.568529\pi$
$641$	6.21721	−	47.2244i	0.245565	−	1.86525i	0.459195	−	0.888336i	$-0.348138\pi$
$642$	−3.48966	−	3.34397i	−0.137726	−	0.131976i
$643$	−0.282530	−	2.14603i	−0.0111419	−	0.0846310i	0.984970	−	0.172723i	$-0.0552565\pi$
$643$	−0.282530	−	2.14603i	−0.0111419	−	0.0846310i	−0.996112	+	0.0880918i	$0.971923\pi$
$644$	0.273145	+	2.07474i	0.0107634	+	0.0817562i
$645$	20.9744	−	12.7132i	0.825866	−	0.500583i
$646$	24.8762	+	14.3623i	0.978740	+	0.565076i
$647$	−6.90273	−	6.90273i	−0.271374	−	0.271374i	0.558279	−	0.829653i	$-0.311462\pi$
$647$	−6.90273	−	6.90273i	−0.271374	−	0.271374i	−0.829653	+	0.558279i	$0.811462\pi$
$648$	−8.86013	−	1.58055i	−0.348059	−	0.0620899i
$649$	9.99695	+	4.14087i	0.392415	+	0.162543i
$650$	5.68445	+	0.748372i	0.222962	+	0.0293536i
$651$	6.66053	+	43.4185i	0.261047	+	1.70170i
$652$	−0.617909	−	1.07025i	−0.0241992	−	0.0419142i
$653$	−35.7246	+	4.70323i	−1.39801	+	0.184051i	−0.791570	−	0.611078i	$-0.790736\pi$
$653$	−35.7246	+	4.70323i	−1.39801	+	0.184051i	−0.606440	+	0.795130i	$0.707403\pi$
$654$	14.8384	+	5.77890i	0.580229	+	0.225973i
$655$	−51.3679	−	29.6573i	−2.00711	−	1.15880i
$656$	−4.04551	+	4.96325i	−0.157951	+	0.193782i
$657$	9.45585	+	30.0950i	0.368908	+	1.17412i
$658$	21.6644	−	21.6644i	0.844565	−	0.844565i
$659$	26.8612	−	20.6113i	1.04636	−	0.802902i	0.0655489	−	0.997849i	$-0.479120\pi$
$659$	26.8612	−	20.6113i	1.04636	−	0.802902i	0.980814	+	0.194947i	$0.0624535\pi$
$660$	1.16682	−	10.6051i	0.0454183	−	0.412804i
$661$	4.65674	−	17.3792i	0.181126	−	0.675972i	−0.814300	−	0.580444i	$-0.802879\pi$
$661$	4.65674	−	17.3792i	0.181126	−	0.675972i	0.995427	−	0.0955288i	$-0.0304542\pi$
$662$	−19.5996	−	15.0393i	−0.761759	−	0.584518i
$663$	9.55584	+	5.24873i	0.371118	+	0.203844i
$664$	−9.57705	+	2.56616i	−0.371662	+	0.0995865i
$665$	26.0089	−	26.0089i	1.00858	−	1.00858i
$666$	4.14755	−	18.6203i	0.160714	−	0.721520i
$667$	2.90808	+	1.20457i	0.112601	+	0.0466410i
$668$	−10.6050	−	13.8207i	−0.410319	−	0.534738i
$669$	23.7738	−	0.506857i	0.919148	−	0.0195962i
$670$	6.64687	−	8.66237i	0.256791	−	0.334657i
$671$	3.00228	−	3.91264i	0.115902	−	0.151046i
$672$	−3.70212	−	2.71735i	−0.142812	−	0.104824i
$673$	2.36125	+	0.310864i	0.0910195	+	0.0119829i	0.175898	−	0.984408i	$-0.443717\pi$
$673$	2.36125	+	0.310864i	0.0910195	+	0.0119829i	−0.0848789	+	0.996391i	$0.527050\pi$
$674$		−	16.7452i		−	0.645003i
$675$	−29.5966	−	14.6507i	−1.13917	−	0.563904i
$676$	−8.61692	+	8.61692i	−0.331420	+	0.331420i
$677$	−6.12645	−	22.8642i	−0.235459	−	0.878743i	−0.977942	−	0.208878i	$-0.933019\pi$
$677$	−6.12645	−	22.8642i	−0.235459	−	0.878743i	0.742483	−	0.669865i	$-0.233648\pi$
$678$	−0.587024	+	2.39378i	−0.0225445	+	0.0919327i
$679$	15.6731	−	9.04890i	0.601480	−	0.347265i
$680$	14.3135	−	18.6537i	0.548897	−	0.715337i
$681$	5.43555	+	12.3700i	0.208291	+	0.474019i
$682$	17.3350	+	2.28219i	0.663791	+	0.0873898i
$683$	6.87187	+	16.5901i	0.262945	+	0.634804i	0.999118	−	0.0419884i	$-0.0133693\pi$
$683$	6.87187	+	16.5901i	0.262945	+	0.634804i	−0.736173	+	0.676793i	$0.763369\pi$
$684$	−11.1984	+	5.20829i	−0.428183	+	0.199144i
$685$	14.7787	−	35.6789i	0.564664	−	1.36322i
$686$	−14.6616	+	11.2502i	−0.559781	+	0.429535i
$687$	−0.420625	+	3.82304i	−0.0160478	+	0.145858i
$688$	−4.05897	−	1.08760i	−0.154747	−	0.0414643i
$689$	3.35887	−	12.5355i	0.127963	−	0.477564i
$690$	2.21776	−	4.03766i	0.0844288	−	0.153711i
$691$	−4.51572	+	34.3003i	−0.171786	+	1.30485i	0.660637	+	0.750706i	$0.270286\pi$
$691$	−4.51572	+	34.3003i	−0.171786	+	1.30485i	−0.832423	+	0.554140i	$0.813047\pi$
$692$	14.2790	+	14.2790i	0.542806	+	0.542806i
$693$	−10.7101	−	9.83371i	−0.406843	−	0.373552i
$694$	13.7956	+	5.71432i	0.523673	+	0.216913i
$695$	8.66438	+	32.3359i	0.328659	+	1.22657i
$696$	−6.32405	+	2.77888i	−0.239713	+	0.105333i
$697$	−43.4760	+	10.2907i	−1.64677	+	0.389789i
$698$	−11.2695	+	6.50644i	−0.426556	+	0.246272i
$699$	−8.24745	+	1.26518i	−0.311947	+	0.0478537i
$700$	−10.2582	−	13.3688i	−0.387725	−	0.505293i
$701$	−30.0325			−1.13431			−0.567156	−	0.823611i	$-0.691956\pi$
$701$	−30.0325			−1.13431			−0.567156	+	0.823611i	$0.691956\pi$
$702$	−4.20728	+	2.06697i	−0.158794	+	0.0780126i
$703$	−10.0179	−	24.1854i	−0.377833	−	0.912169i
$704$	−1.45021	+	1.11279i	−0.0546569	+	0.0419397i
$705$	−66.6653	+	10.2267i	−2.51076	+	0.385158i
$706$	2.51492	−	9.38580i	0.0946502	−	0.353239i
$707$	32.3731	−	18.6906i	1.21752	−	0.702933i
$708$	−10.2506	+	0.218543i	−0.385241	+	0.00821334i
$709$	24.4232	−	18.7406i	0.917234	−	0.703819i	−0.0381226	−	0.999273i	$-0.512138\pi$
$709$	24.4232	−	18.7406i	0.917234	−	0.703819i	0.955357	+	0.295454i	$0.0954711\pi$
$710$	1.93036	+	0.799580i	0.0724450	+	0.0300077i
$711$	7.00095	+	39.9378i	0.262556	+	1.49778i
$712$	−5.56027	+	2.30314i	−0.208380	+	0.0863138i
$713$	6.53795	+	3.77469i	0.244848	+	0.141363i
$714$	−8.95112	−	30.7671i	−0.334987	−	1.15143i
$715$	−2.77848	−	4.81247i	−0.103909	−	0.179976i
$716$	−6.44699	−	4.94695i	−0.240935	−	0.184876i
$717$	−22.2530	−	27.7550i	−0.831052	−	1.03653i
$718$	−7.43433	+	1.99202i	−0.277447	+	0.0743417i
$719$	14.9167	+	36.0121i	0.556299	+	1.34303i	0.912676	+	0.408683i	$0.134012\pi$
$719$	14.9167	+	36.0121i	0.556299	+	1.34303i	−0.356377	+	0.934342i	$0.615988\pi$
$720$	3.03031	+	9.64453i	0.112933	+	0.359430i
$721$	9.96090	−	4.12594i	0.370963	−	0.153658i
$722$	1.02605	−	1.77717i	0.0381856	−	0.0661393i
$723$	−13.0024	+	13.5689i	−0.483565	+	0.504634i
$724$	7.43408	+	5.70437i	0.276285	+	0.212001i
$725$	−25.1299	+	3.30841i	−0.933300	+	0.122871i
$726$	11.3439	−	6.87589i	0.421012	−	0.255188i
$727$	4.02694	+	5.24801i	0.149351	+	0.194638i	0.862037	−	0.506845i	$-0.169188\pi$
$727$	4.02694	+	5.24801i	0.149351	+	0.194638i	−0.712686	+	0.701483i	$0.752522\pi$
$728$	−2.39190			−0.0886498
$729$	26.7795	−	3.44391i	0.991832	−	0.127552i
$730$	25.0556	−	25.0556i	0.927351	−	0.927351i
$731$	−17.8490	−	23.2613i	−0.660170	−	0.860350i
$732$	−1.11298	+	4.53856i	−0.0411371	+	0.167750i
$733$	14.5700	+	3.90401i	0.538154	+	0.144198i	0.517651	−	0.855592i	$-0.326807\pi$
$733$	14.5700	+	3.90401i	0.538154	+	0.144198i	0.0205029	+	0.999790i	$0.493473\pi$
$734$	−11.9614	+	6.90594i	−0.441505	+	0.254903i
$735$	−0.174484	+	0.00371999i	−0.00643593	+	0.000137214i
$736$	−0.762367	+	0.204276i	−0.0281012	+	0.00752970i
$737$	−5.92286			−0.218171
$738$	7.11522	−	17.8430i	0.261915	−	0.656811i
$739$	3.29887			0.121351			0.0606755	−	0.998158i	$-0.480675\pi$
$739$	3.29887			0.121351			0.0606755	+	0.998158i	$0.480675\pi$
$740$	−20.6979	+	5.54599i	−0.760871	+	0.203875i
$741$	−3.09683	+	5.63809i	−0.113765	+	0.207121i
$742$	−33.0319	+	19.0710i	−1.21264	+	0.700118i
$743$	21.6025	+	5.78836i	0.792517	+	0.212354i	0.632296	−	0.774727i	$-0.282113\pi$
$743$	21.6025	+	5.78836i	0.792517	+	0.212354i	0.160221	+	0.987081i	$0.448779\pi$
$744$	−15.9077	+	4.62805i	−0.583205	+	0.169673i
$745$	23.5918	+	30.7455i	0.864338	+	1.12643i
$746$	6.54897	−	6.54897i	0.239775	−	0.239775i
$747$	25.1024	−	15.9567i	0.918448	−	0.583826i
$748$	−12.7544			−0.466347
$749$	4.50398	+	5.86969i	0.164572	+	0.214474i
$750$	0.168639	+	7.90992i	0.00615784	+	0.288830i
$751$	−16.1858	+	2.13089i	−0.590627	+	0.0777575i	−0.419915	−	0.907564i	$-0.637940\pi$
$751$	−16.1858	+	2.13089i	−0.590627	+	0.0777575i	−0.170712	+	0.985321i	$0.554607\pi$
$752$	9.16755	+	7.03451i	0.334306	+	0.256522i
$753$	−13.4498	−	3.29826i	−0.490137	−	0.120195i
$754$	−1.79891	+	3.11580i	−0.0655124	+	0.113471i
$755$	−17.3045	+	7.16774i	−0.629774	+	0.260861i
$756$	13.0393	+	4.44805i	0.474233	+	0.161774i
$757$	−15.2727	−	36.8716i	−0.555096	−	1.34012i	−0.913608	−	0.406596i	$-0.866716\pi$
$757$	−15.2727	−	36.8716i	−0.555096	−	1.34012i	0.358512	−	0.933525i	$-0.383284\pi$
$758$	31.5934	−	8.46542i	1.14752	−	0.307478i
$759$	−2.46999	+	0.378904i	−0.0896550	+	0.0137533i
$760$	11.0060	+	8.44518i	0.399228	+	0.306339i
$761$	−18.2613	−	31.6295i	−0.661971	−	1.14657i	−0.980097	−	0.198519i	$-0.936387\pi$
$761$	−18.2613	−	31.6295i	−0.661971	−	1.14657i	0.318126	−	0.948048i	$-0.396946\pi$
$762$	15.0332	−	15.6882i	0.544597	−	0.568324i
$763$	−21.1105	−	12.1881i	−0.764251	−	0.441240i
$764$	17.9251	−	7.42482i	0.648507	−	0.268621i
$765$	−24.1915	+	66.2593i	−0.874645	+	2.39561i
$766$	8.79938	+	3.64482i	0.317934	+	0.131693i
$767$	−4.23665	+	3.25090i	−0.152977	+	0.117383i
$768$	0.833856	−	1.51812i	0.0300892	−	0.0547804i
$769$	−16.5985	+	9.58317i	−0.598559	+	0.345578i	−0.768474	−	0.639881i	$-0.778984\pi$
$769$	−16.5985	+	9.58317i	−0.598559	+	0.345578i	0.169916	+	0.985459i	$0.445650\pi$
$770$	−4.22707	+	15.7756i	−0.152333	+	0.568514i
$771$	−25.9474	−	32.3629i	−0.934473	−	1.16552i
$772$	2.97716	−	2.28445i	0.107150	−	0.0822192i
$773$	−14.5486	−	35.1233i	−0.523275	−	1.26330i	−0.935858	−	0.352378i	$-0.885373\pi$
$773$	−14.5486	−	35.1233i	−0.523275	−	1.26330i	0.412582	−	0.910920i	$-0.364627\pi$
$774$	12.5950	−	0.537295i	0.452719	−	0.0193127i
$775$	−60.7913			−2.18369
$776$	4.15526	+	5.41524i	0.149165	+	0.194396i
$777$	−10.5976	+	27.2113i	−0.380186	+	0.976201i
$778$	−17.8194	+	10.2880i	−0.638855	+	0.368843i
$779$	−6.07168	−	25.6515i	−0.217541	−	0.919060i
$780$	4.24471	+	3.11561i	0.151985	+	0.111557i
$781$	−0.293346	−	1.09478i	−0.0104967	−	0.0391744i
$782$	−5.08781	−	2.10744i	−0.181940	−	0.0753619i
$783$	15.6008	−	13.6402i	0.557529	−	0.487462i
$784$	0.0211434	+	0.0211434i	0.000755121	+	0.000755121i
$785$	−4.59294	+	34.8868i	−0.163929	+	1.24516i
$786$	−15.8029	−	26.0718i	−0.563672	−	0.929950i
$787$	−9.39146	+	35.0494i	−0.334769	+	1.24938i	0.569350	+	0.822095i	$0.307195\pi$
$787$	−9.39146	+	35.0494i	−0.334769	+	1.24938i	−0.904119	+	0.427281i	$0.859472\pi$
$788$	20.7194	+	5.55174i	0.738097	+	0.197772i
$789$	−34.2507	+	15.0502i	−1.21936	+	0.535802i
$790$	36.1331	−	27.7259i	1.28556	−	0.986444i
$791$	1.44384	−	3.48574i	0.0513371	−	0.123939i
$792$	3.14990	−	4.48897i	0.111927	−	0.159508i
$793$	0.931423	+	2.24865i	0.0330758	+	0.0798520i
$794$	20.7192	+	2.72773i	0.735297	+	0.0968037i
$795$	83.4603	+	9.18261i	2.96003	+	0.325674i
$796$	9.80726	−	12.7811i	0.347609	−	0.453013i
$797$	−43.0610	+	24.8613i	−1.52530	+	0.880631i	−0.525747	+	0.850641i	$0.676214\pi$
$797$	−43.0610	+	24.8613i	−1.52530	+	0.880631i	−0.999550	+	0.0299902i	$0.990452\pi$
$798$	18.1531	−	5.28130i	0.642612	−	0.186956i
$799$	20.8678	+	77.8798i	0.738251	+	2.75519i
$800$	4.49403	−	4.49403i	0.158888	−	0.158888i
$801$	13.8427	−	11.5918i	0.489106	−	0.409576i
$802$		−	4.64618i		−	0.164062i
$803$	−19.0568	−	2.50888i	−0.672500	−	0.0885364i
$804$	5.13797	−	2.25770i	0.181202	−	0.0796228i
$805$	−4.29285	+	5.59455i	−0.151303	+	0.197182i
$806$	−5.25298	+	6.84582i	−0.185028	+	0.241134i
$807$	−20.6196	−	34.0185i	−0.725846	−	1.19751i
$808$	8.58274	+	11.1852i	0.301940	+	0.393496i
$809$	−21.6266	−	8.95802i	−0.760350	−	0.314947i	−0.0313933	−	0.999507i	$-0.509994\pi$
$809$	−21.6266	−	8.95802i	−0.760350	−	0.314947i	−0.728957	+	0.684560i	$0.759994\pi$
$810$	−17.3458	−	24.8781i	−0.609470	−	0.874128i
$811$	−10.0815	+	10.0815i	−0.354010	+	0.354010i	−0.861599	−	0.507589i	$-0.830537\pi$
$811$	−10.0815	+	10.0815i	−0.354010	+	0.354010i	0.507589	+	0.861599i	$0.330537\pi$
$812$	10.2138	−	2.73679i	0.358435	−	0.0960425i
$813$	−19.0225	+	11.5301i	−0.667147	+	0.404379i
$814$	9.22170	+	7.07606i	0.323220	+	0.248016i
$815$	1.07784	−	4.02255i	0.0377551	−	0.140904i
$816$	11.0642	−	4.86176i	0.387324	−	0.170196i
$817$	13.7245	−	10.5312i	0.480160	−	0.368440i
$818$	−24.0823	+	24.0823i	−0.842018	+	0.842018i
$819$	6.84574	−	2.15093i	0.239210	−	0.0751597i
$820$	−21.4661	+	2.18680i	−0.749629	+	0.0763662i
$821$	33.2792	+	19.2137i	1.16145	+	0.670564i	0.951651	−	0.307180i	$-0.0993853\pi$
$821$	33.2792	+	19.2137i	1.16145	+	0.670564i	0.209800	+	0.977744i	$0.432719\pi$
$822$	15.4866	−	12.4166i	0.540159	−	0.433079i
$823$	−12.6487	+	1.66523i	−0.440905	+	0.0580462i	−0.347711	−	0.937602i	$-0.613041\pi$
$823$	−12.6487	+	1.66523i	−0.440905	+	0.0580462i	−0.0931937	+	0.995648i	$0.529708\pi$
$824$	2.03319	+	3.52160i	0.0708297	+	0.122681i
$825$	15.6993	−	12.5871i	0.546581	−	0.438228i
$826$	15.5608	+	2.04861i	0.541428	+	0.0712803i
$827$	4.00343	+	1.65828i	0.139213	+	0.0576639i	0.451202	−	0.892422i	$-0.350995\pi$
$827$	4.00343	+	1.65828i	0.139213	+	0.0576639i	−0.311989	+	0.950086i	$0.600995\pi$
$828$	1.99824	−	1.27021i	0.0694436	−	0.0441429i
$829$	15.4015	+	15.4015i	0.534915	+	0.534915i	0.922031	−	0.387116i	$-0.126529\pi$
$829$	15.4015	+	15.4015i	0.534915	+	0.534915i	−0.387116	+	0.922031i	$0.626529\pi$
$830$	−28.9349	−	16.7056i	−1.00435	−	0.579859i
$831$	0.649549	+	30.4666i	0.0225326	+	1.05688i
$832$	−0.117751	−	0.894411i	−0.00408230	−	0.0310081i
$833$	0.0272322	+	0.206849i	0.000943539	+	0.00716689i
$834$	−4.09815	+	16.7116i	−0.141907	+	0.578675i
$835$	7.66239	−	58.2016i	0.265168	−	2.01415i
$836$		−	7.52528i		−	0.260267i
$837$	41.3669	−	27.5508i	1.42985	−	0.952296i
$838$	29.9462			1.03447
$839$	2.75305	−	20.9115i	0.0950459	−	0.721945i	−0.875874	−	0.482540i	$-0.839714\pi$
$839$	2.75305	−	20.9115i	0.0950459	−	0.721945i	0.970920	−	0.239405i	$-0.0769524\pi$
$840$	−2.34651	−	15.2964i	−0.0809622	−	0.527774i
$841$	−3.38916	+	12.6485i	−0.116868	+	0.436156i
$842$	8.45011	−	11.0124i	0.291210	−	0.379512i
$843$	−7.92718	−	18.0403i	−0.273027	−	0.621342i
$844$	0.384422	−	2.91998i	0.0132324	−	0.100510i
$845$	−41.0649			−1.41267
$846$	−32.5638	−	11.8891i	−1.11957	−	0.408757i
$847$	−18.7603	+	7.77075i	−0.644610	+	0.267006i
$848$	−8.75741	−	11.4129i	−0.300731	−	0.391920i
$849$	−10.9604	+	19.9545i	−0.376160	+	0.684837i
$850$	43.9658	−	5.78820i	1.50801	−	0.198534i
$851$	2.50940	+	4.34641i	0.0860211	+	0.148993i
$852$	0.671785	+	0.837884i	0.0230150	+	0.0287054i
$853$	−4.17148	−	15.5682i	−0.142829	−	0.533044i	−0.999842	−	0.0177503i	$-0.994350\pi$
$853$	−4.17148	−	15.5682i	−0.142829	−	0.533044i	0.857014	−	0.515293i	$-0.172317\pi$
$854$	2.73749	−	6.60889i	0.0936751	−	0.226152i
$855$	−39.0940	−	14.2733i	−1.33699	−	0.488138i
$856$	−1.97315	+	1.97315i	−0.0674407	+	0.0674407i
$857$	−30.4354	−	17.5719i	−1.03965	−	0.600245i	−0.119919	−	0.992784i	$-0.538264\pi$
$857$	−30.4354	−	17.5719i	−1.03965	−	0.600245i	−0.919736	+	0.392539i	$0.871597\pi$
$858$	−0.0608811	−	2.85559i	−0.00207845	−	0.0974881i
$859$	11.2766	−	42.0847i	0.384751	−	1.43591i	−0.453807	−	0.891100i	$-0.649934\pi$
$859$	11.2766	−	42.0847i	0.384751	−	1.43591i	0.838558	−	0.544812i	$-0.183399\pi$
$860$	−7.08021	−	12.2633i	−0.241433	−	0.418174i
$861$	−14.9075	+	25.3465i	−0.508046	+	0.863806i
$862$	13.3842	−	23.1821i	0.455868	−	0.789587i
$863$	−0.834058	−	0.834058i	−0.0283917	−	0.0283917i	0.692768	−	0.721160i	$-0.256391\pi$
$863$	−0.834058	−	0.834058i	−0.0283917	−	0.0283917i	−0.721160	+	0.692768i	$0.756391\pi$
$864$	−1.02136	+	5.09478i	−0.0347474	+	0.173328i
$865$			68.0481i			2.31370i
$866$	1.32792	+	4.95586i	0.0451245	+	0.168407i
$867$	53.2997	+	13.0706i	1.81015	+	0.443901i
$868$	25.1439	−	3.31026i	0.853441	−	0.112358i
$869$	−23.8640	−	6.39435i	−0.809532	−	0.216913i
$870$	−21.6905	−	8.44746i	−0.735377	−	0.286396i
$871$	1.46152	−	2.53143i	0.0495218	−	0.0857742i
$872$	3.51830	−	8.49392i	0.119145	−	0.287640i
$873$	−16.7623	−	11.7620i	−0.567316	−	0.398085i
$874$	1.24342	−	3.00188i	0.0420593	−	0.101540i
$875$	1.58082	−	12.0075i	0.0534415	−	0.405929i
$876$	17.4878	−	5.08774i	0.590857	−	0.171899i
$877$	−5.17655	−	8.96605i	−0.174800	−	0.302762i	0.765292	−	0.643683i	$-0.222594\pi$
$877$	−5.17655	−	8.96605i	−0.174800	−	0.302762i	−0.940092	+	0.340921i	$0.889261\pi$
$878$	30.2167	+	23.1861i	1.01977	+	0.782494i
$879$	2.74018	−	24.9054i	0.0924240	−	0.840037i
$880$	−6.10713	−	0.804019i	−0.205871	−	0.0271035i
$881$	33.3264	+	33.3264i	1.12280	+	1.12280i	0.991319	+	0.131476i	$0.0419717\pi$
$881$	33.3264	+	33.3264i	1.12280	+	1.12280i	0.131476	+	0.991319i	$0.458028\pi$
$882$	−0.0795268	−	0.0415001i	−0.00267781	−	0.00139738i
$883$	6.26658	−	2.59570i	0.210887	−	0.0873524i	−0.274739	−	0.961519i	$-0.588592\pi$
$883$	6.26658	−	2.59570i	0.210887	−	0.0873524i	0.485626	+	0.874166i	$0.338592\pi$
$884$	3.14727	−	5.45122i	0.105854	−	0.183344i
$885$	−24.9459	−	23.9044i	−0.838548	−	0.803539i
$886$	−12.6000	+	7.27459i	−0.423304	+	0.244394i
$887$	−22.9295	−	17.5945i	−0.769899	−	0.590764i	0.147347	−	0.989085i	$-0.452926\pi$
$887$	−22.9295	−	17.5945i	−0.769899	−	0.590764i	−0.917246	+	0.398321i	$0.869593\pi$
$888$	−10.6969	−	2.62319i	−0.358965	−	0.0880285i
$889$	−26.3880	+	20.2482i	−0.885024	+	0.679103i
$890$	−18.7370	−	7.76111i	−0.628065	−	0.260153i
$891$	−4.97844	+	15.6802i	−0.166784	+	0.525307i
$892$		−	13.7289i		−	0.459679i
$893$	−45.9503	+	12.3123i	−1.53767	+	0.412017i
$894$	3.02033	+	19.6889i	0.101015	+	0.658495i
$895$	−3.57431	−	27.1496i	−0.119476	−	0.907510i
$896$	−1.61407	+	2.10349i	−0.0539222	+	0.0702728i
$897$	0.447550	−	1.14917i	0.0149433	−	0.0383697i
$898$	−1.93065	+	3.34398i	−0.0644265	+	0.111590i
$899$	14.5982	−	35.2433i	0.486878	−	1.17543i
$900$	−8.82086	+	16.9034i	−0.294029	+	0.563448i
$901$		−	100.374i		−	3.34396i
$902$	8.02973	+	8.51594i	0.267361	+	0.283550i
$903$	−19.1820	−	2.11048i	−0.638338	−	0.0702323i
$904$	1.37451	+	0.368300i	0.0457156	+	0.0122495i
$905$	4.12156	+	31.3064i	0.137005	+	1.04066i
$906$	−9.56945	−	1.05287i	−0.317924	−	0.0349791i
$907$	10.6825	−	2.86236i	0.354705	−	0.0950430i	−0.0770663	−	0.997026i	$-0.524555\pi$
$907$	10.6825	−	2.86236i	0.354705	−	0.0950430i	0.431772	+	0.901983i	$0.357889\pi$
$908$	7.20709	−	2.98527i	0.239176	−	0.0990698i
$909$	−34.6227	−	24.2947i	−1.14836	−	0.805803i
$910$	−5.69943	−	5.69943i	−0.188934	−	0.188934i
$911$	−6.85729	−	25.5918i	−0.227192	−	0.847893i	−0.981514	−	0.191389i	$-0.938701\pi$
$911$	−6.85729	−	25.5918i	−0.227192	−	0.847893i	0.754322	−	0.656505i	$-0.227966\pi$
$912$	2.86851	+	6.52804i	0.0949860	+	0.216165i
$913$	2.36565	+	17.9689i	0.0782916	+	0.594684i
$914$	21.5795	−	2.84099i	0.713786	−	0.0939717i
$915$	−13.4665	+	8.16249i	−0.445190	+	0.269844i
$916$	2.20155	+	0.289840i	0.0727414	+	0.00957659i
$917$	17.8596	+	43.1169i	0.589776	+	1.42384i
$918$	−27.2943	+	23.8642i	−0.900847	+	0.787635i
$919$	−0.193684	−	0.467594i	−0.00638905	−	0.0154245i	0.920653	−	0.390382i	$-0.127657\pi$
$919$	−0.193684	−	0.467594i	−0.00638905	−	0.0154245i	−0.927042	+	0.374958i	$0.877657\pi$
$920$	−2.30332	−	1.32982i	−0.0759383	−	0.0438430i
$921$	−26.7584	−	6.56191i	−0.881718	−	0.216222i
$922$	23.5520	+	6.31075i	0.775645	+	0.207833i
$923$	0.540295	+	0.144772i	0.0177840	+	0.00476522i
$924$	−5.80801	+	6.06106i	−0.191069	+	0.199394i
$925$	−34.9995	−	20.2069i	−1.15078	−	0.664400i
$926$	10.8146	+	26.1088i	0.355391	+	0.857990i
$927$	−8.98592	−	8.25062i	−0.295136	−	0.270986i
$928$	1.52620	+	3.68456i	0.0500998	+	0.120952i
$929$	−40.2692	−	5.30154i	−1.32119	−	0.173938i	−0.563263	−	0.826278i	$-0.690454\pi$
$929$	−40.2692	−	5.30154i	−1.32119	−	0.173938i	−0.757926	+	0.652340i	$0.773787\pi$
$930$	−48.9327	−	26.8772i	−1.60457	−	0.881340i
$931$	−0.122044	+	0.0160674i	−0.00399983	+	0.000526588i
$932$	0.628793	+	4.77616i	0.0205968	+	0.156448i
$933$	34.4979	+	3.79559i	1.12941	+	0.124262i
$934$	3.67528	+	13.7163i	0.120259	+	0.448812i
$935$	−30.3912	−	30.3912i	−0.993899	−	0.993899i
$936$	1.14132	+	2.45396i	0.0373051	+	0.0802102i
$937$	45.4140	−	18.8111i	1.48361	−	0.614532i	0.513695	−	0.857973i	$-0.328276\pi$
$937$	45.4140	−	18.8111i	1.48361	−	0.614532i	0.969916	+	0.243441i	$0.0782762\pi$
$938$	−8.29822	+	2.22350i	−0.270947	+	0.0725999i
$939$	11.3012	+	25.7187i	0.368799	+	0.839298i
$940$	5.08262	+	38.6063i	0.165777	+	1.25920i
$941$	−7.23152	−	1.93768i	−0.235741	−	0.0631665i	0.139014	−	0.990290i	$-0.455607\pi$
$941$	−7.23152	−	1.93768i	−0.235741	−	0.0631665i	−0.374755	+	0.927124i	$0.622273\pi$
$942$	−10.7019	+	14.5803i	−0.348687	+	0.475051i
$943$	1.79600	+	4.72384i	0.0584858	+	0.153829i
$944$			5.91953i			0.192664i
$945$	20.4712	+	41.6688i	0.665927	+	1.35549i
$946$	−2.93952	+	7.09664i	−0.0955721	+	0.230732i
$947$	5.34388	−	9.25588i	0.173653	−	0.300776i	−0.766041	−	0.642791i	$-0.777776\pi$
$947$	5.34388	−	9.25588i	0.173653	−	0.300776i	0.939694	+	0.342016i	$0.111110\pi$
$948$	23.1390	−	3.54960i	0.751520	−	0.115286i
$949$	5.77474	−	7.52579i	0.187456	−	0.244298i
$950$	3.41513	+	25.9405i	0.110801	+	0.841620i
$951$	−24.7937	−	9.65601i	−0.803991	−	0.313118i
$952$	−17.8695	+	4.78813i	−0.579155	+	0.155184i
$953$			31.1380i			1.00866i	0.863511	+	0.504329i	$0.168260\pi$
$953$			31.1380i			1.00866i	−0.863511	+	0.504329i	$0.831740\pi$
$954$	35.3273	+	24.7891i	1.14376	+	0.802576i
$955$	60.4039	+	25.0201i	1.95462	+	0.809632i
$956$	−16.2946	+	12.5033i	−0.527004	+	0.404385i
$957$	3.52731	+	12.1242i	0.114022	+	0.391920i
$958$	18.3630	+	14.0904i	0.593280	+	0.455240i
$959$	−26.3146	+	15.1928i	−0.849744	+	0.490600i
$960$	5.60430	−	1.63046i	0.180878	−	0.0526230i
$961$	30.2457	−	52.3871i	0.975668	−	1.68991i
$962$	−5.29985	+	2.19527i	−0.170874	+	0.0707783i
$963$	3.87288	−	7.42161i	0.124802	−	0.239158i
$964$	7.67223	+	7.67223i	0.247106	+	0.247106i
$965$	12.5374	+	1.65058i	0.403593	+	0.0531340i
$966$	−3.31833	+	1.45812i	−0.106766	+	0.0469143i
$967$	21.3531	+	16.3848i	0.686670	+	0.526901i	0.892138	−	0.451763i	$-0.149205\pi$
$967$	21.3531	+	16.3848i	0.686670	+	0.526901i	−0.205467	+	0.978664i	$0.565871\pi$
$968$	−3.82930	−	6.63253i	−0.123078	−	0.213178i
$969$	−11.8496	+	48.3206i	−0.380663	+	1.55228i
$970$	−3.00229	+	22.8046i	−0.0963976	+	0.732213i
$971$	12.9457	−	31.2537i	0.415448	−	1.00298i	−0.568202	−	0.822889i	$-0.692361\pi$
$971$	12.9457	−	31.2537i	0.415448	−	1.00298i	0.983650	−	0.180091i	$-0.0576391\pi$
$972$	−1.65833	−	15.5000i	−0.0531910	−	0.497163i
$973$	10.0798	−	24.3348i	0.323144	−	0.780138i
$974$	−18.9288	+	32.7857i	−0.606518	+	1.05052i
$975$	1.50579	+	9.81589i	0.0482238	+	0.314360i
$976$	2.60605	+	0.698289i	0.0834176	+	0.0223517i
$977$	−9.02093	+	1.18763i	−0.288605	+	0.0379956i	−0.273439	−	0.961889i	$-0.588161\pi$
$977$	−9.02093	+	1.18763i	−0.288605	+	0.0379956i	−0.0151663	+	0.999885i	$0.504828\pi$
$978$	1.48096	−	1.54548i	0.0473558	−	0.0494190i
$979$	2.84735	+	10.6265i	0.0910018	+	0.339623i
$980$			0.100761i			0.00321870i
$981$	−2.43133	+	27.4739i	−0.0776265	+	0.877174i
$982$	−16.7259	−	16.7259i	−0.533744	−	0.533744i
$983$	4.20694	−	7.28664i	0.134181	−	0.232408i	−0.791104	−	0.611682i	$-0.790493\pi$
$983$	4.20694	−	7.28664i	0.134181	−	0.232408i	0.925284	+	0.379275i	$0.123826\pi$
$984$	−10.2118	−	4.32662i	−0.325539	−	0.137928i
$985$	36.1415	+	62.5989i	1.15156	+	1.99457i
$986$	−7.20214	+	26.8788i	−0.229363	+	0.855994i
$987$	46.5122	+	25.5477i	1.48050	+	0.813193i
$988$	3.21630	+	1.85693i	0.102324	+	0.0590770i
$989$	−2.34519	+	2.34519i	−0.0745727	+	0.0745727i
$990$	18.2019	−	3.19073i	0.578495	−	0.101408i
$991$	−21.2211	+	51.2322i	−0.674110	+	1.62745i	0.100448	+	0.994942i	$0.467972\pi$
$991$	−21.2211	+	51.2322i	−0.674110	+	1.62745i	−0.774558	+	0.632503i	$0.782028\pi$
$992$	2.47563	+	9.23919i	0.0786015	+	0.293345i
$993$	15.5286	−	39.8727i	0.492785	−	1.26532i
$994$	−0.821984	−	1.42372i	−0.0260718	−	0.0451576i
$995$	53.8236	−	7.08601i	1.70632	−	0.224642i
$996$	−8.90161	−	14.6859i	−0.282058	−	0.465342i
$997$	22.5296	+	29.3612i	0.713520	+	0.929878i	0.999599	−	0.0283283i	$-0.00901838\pi$
$997$	22.5296	+	29.3612i	0.713520	+	0.929878i	−0.286078	+	0.958206i	$0.592352\pi$
$998$	20.6450	−	8.55145i	0.653507	−	0.270691i
$999$	32.9741	−	2.11158i	1.04325	−	0.0668074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.v.b.659.13	yes	168
9.5	odd	6		738.2.v.a.167.3	yes	168
41.14	odd	8		738.2.v.a.137.3	✓	168
369.14	even	24	inner	738.2.v.b.383.13	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.v.a.137.3	✓	168	41.14	odd	8
738.2.v.a.167.3	yes	168	9.5	odd	6
738.2.v.b.383.13	yes	168	369.14	even	24	inner
738.2.v.b.659.13	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.v (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.897801 + 1.48120i) q^{3} +(0.866025 - 0.500000i) q^{4} +(3.25497 + 0.872167i) q^{5} +(1.25057 + 1.19836i) q^{6} +(-1.61407 - 2.10349i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.38791 + 2.65965i) q^{9} +3.36980 q^{10} +(-1.11279 - 1.45021i) q^{11} +(1.51812 + 0.833856i) q^{12} +(0.894411 - 0.117751i) q^{13} +(-2.10349 - 1.61407i) q^{14} +(1.63046 + 5.60430i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.44629 - 2.67014i) q^{17} +(-0.652247 + 2.92824i) q^{18} +(1.57542 + 3.80341i) q^{19} +(3.25497 - 0.872167i) q^{20} +(1.66658 - 4.27928i) q^{21} +(-1.45021 - 1.11279i) q^{22} +(-0.394630 - 0.683520i) q^{23} +(1.68221 + 0.412525i) q^{24} +(5.50404 + 3.17776i) q^{25} +(0.833458 - 0.345230i) q^{26} +(-5.18553 + 0.332069i) q^{27} +(-2.44957 - 1.01465i) q^{28} +(-3.16401 + 2.42783i) q^{29} +(3.02541 + 4.99134i) q^{30} +(-8.28363 + 4.78256i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.14899 - 2.95026i) q^{33} +(5.53556 - 4.24758i) q^{34} +(-3.41915 - 8.25455i) q^{35} +(0.127862 + 2.99727i) q^{36} -6.35886 q^{37} +(2.50614 + 3.26606i) q^{38} +(0.977417 + 1.21908i) q^{39} +(2.91833 - 1.68490i) q^{40} +(-6.32106 - 1.02189i) q^{41} +(0.502237 - 4.56481i) q^{42} +(-1.08760 - 4.05897i) q^{43} +(-1.68881 - 0.699527i) q^{44} +(-6.83725 + 7.44659i) q^{45} +(-0.558092 - 0.558092i) q^{46} +(-1.50829 + 11.4566i) q^{47} +(1.73166 - 0.0369189i) q^{48} +(-0.00773902 + 0.0288824i) q^{49} +(6.13896 + 1.64493i) q^{50} +(9.74251 + 7.15099i) q^{51} +(0.715707 - 0.549181i) q^{52} +(5.50514 - 13.2906i) q^{53} +(-4.92289 + 1.66287i) q^{54} +(-2.35726 - 5.69094i) q^{55} +(-2.62871 - 0.346077i) q^{56} +(-4.21919 + 5.74823i) q^{57} +(-2.42783 + 3.16401i) q^{58} +(-5.12647 + 2.95977i) q^{59} +(4.21417 + 4.03823i) q^{60} +(0.698289 + 2.60605i) q^{61} +(-6.76356 + 6.76356i) q^{62} +(7.83472 - 1.37340i) q^{63} -1.00000i q^{64} +(3.01398 + 0.396798i) q^{65} +(0.346257 - 3.14712i) q^{66} +(1.97248 - 2.57059i) q^{67} +(4.24758 - 5.53556i) q^{68} +(0.658130 - 1.19819i) q^{69} +(-5.43908 - 7.08834i) q^{70} +(0.572841 + 0.237279i) q^{71} +(0.899257 + 2.86205i) q^{72} +(7.43536 - 7.43536i) q^{73} +(-6.14219 + 1.64579i) q^{74} +(0.234639 + 11.0056i) q^{75} +(3.26606 + 2.50614i) q^{76} +(-1.25440 + 4.68148i) q^{77} +(1.25963 + 0.924571i) q^{78} +(10.7226 - 8.22777i) q^{79} +(2.38281 - 2.38281i) q^{80} +(-5.14744 - 7.38268i) q^{81} +(-6.37016 + 0.648940i) q^{82} +(-8.58655 - 4.95745i) q^{83} +(-0.696335 - 4.53925i) q^{84} +(23.3113 - 3.06899i) q^{85} +(-2.10108 - 3.63918i) q^{86} +(-6.43674 - 2.50682i) q^{87} +(-1.81231 - 0.238596i) q^{88} +(-5.56027 - 2.30314i) q^{89} +(-4.67696 + 8.96246i) q^{90} +(-1.69133 - 1.69133i) q^{91} +(-0.683520 - 0.394630i) q^{92} +(-14.5210 - 7.97593i) q^{93} +(1.50829 + 11.4566i) q^{94} +(1.81075 + 13.7540i) q^{95} +(1.66310 - 0.483847i) q^{96} +(-0.890940 + 6.76736i) q^{97} +0.0299013i q^{98} +(5.40149 - 0.946862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{7} - 8 q^{9} + 16 q^{15} + 84 q^{16} + 12 q^{17} - 8 q^{21} + 4 q^{24} - 48 q^{25} - 8 q^{30} - 40 q^{33} + 48 q^{34} - 24 q^{35} - 8 q^{36} - 32 q^{42} - 12 q^{44} - 72 q^{45} + 12 q^{47}+ \cdots + 16 q^{99}+O(q^{100}) \) 168 * q + 12 * q^7 - 8 * q^9 + 16 * q^15 + 84 * q^16 + 12 * q^17 - 8 * q^21 + 4 * q^24 - 48 * q^25 - 8 * q^30 - 40 * q^33 + 48 * q^34 - 24 * q^35 - 8 * q^36 - 32 * q^42 - 12 * q^44 - 72 * q^45 + 12 * q^47 + 12 * q^48 + 12 * q^49 - 44 * q^51 - 20 * q^54 + 12 * q^56 - 64 * q^57 + 24 * q^58 + 108 * q^61 + 112 * q^63 - 84 * q^65 + 4 * q^66 + 48 * q^67 + 48 * q^69 + 12 * q^70 + 84 * q^75 - 12 * q^76 + 60 * q^79 - 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 40 * q^87 - 72 * q^89 - 96 * q^93 - 12 * q^94 - 72 * q^95 - 96 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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