LMFDB - Embedded newform 819.2.fy.a.50.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.6
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.663488 - 2.47617i) q^{2} +(-0.692898 - 1.58742i) q^{3} +(-3.95915 + 2.28582i) q^{4} +(-0.816615 - 3.04765i) q^{5} +(-3.47098 + 2.76896i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.66155 + 4.66155i) q^{8} +(-2.03979 + 2.19984i) q^{9} +O(q^{10})$	\(q+(-0.663488 - 2.47617i) q^{2} +(-0.692898 - 1.58742i) q^{3} +(-3.95915 + 2.28582i) q^{4} +(-0.816615 - 3.04765i) q^{5} +(-3.47098 + 2.76896i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.66155 + 4.66155i) q^{8} +(-2.03979 + 2.19984i) q^{9} +(-7.00468 + 4.04416i) q^{10} +(0.561751 - 0.150521i) q^{11} +(6.37183 + 4.70098i) q^{12} +(3.52364 + 0.764181i) q^{13} +(2.22007 + 1.28176i) q^{14} +(-4.27206 + 3.40802i) q^{15} +(3.87827 - 6.71736i) q^{16} +(-2.47344 + 4.28413i) q^{17} +(6.80054 + 3.59129i) q^{18} +(-6.25464 + 1.67592i) q^{19} +(10.1995 + 10.1995i) q^{20} +(1.61243 + 0.632521i) q^{21} +(-0.745430 - 1.29112i) q^{22} +6.69818 q^{23} +(4.16984 - 10.6298i) q^{24} +(-4.29119 + 2.47752i) q^{25} +(-0.445650 - 9.23215i) q^{26} +(4.90542 + 1.71373i) q^{27} +(1.18323 - 4.41586i) q^{28} +(-1.72023 - 0.993175i) q^{29} +(11.2733 + 8.31717i) q^{30} +(-6.40609 + 1.71651i) q^{31} +(-6.47093 - 1.73388i) q^{32} +(-0.628175 - 0.787438i) q^{33} +(12.2493 + 3.28219i) q^{34} +(2.73245 + 1.57758i) q^{35} +(3.04740 - 13.3720i) q^{36} +(-8.31622 - 2.22833i) q^{37} +(8.29975 + 14.3756i) q^{38} +(-1.22845 - 6.12298i) q^{39} +(10.4001 - 18.0135i) q^{40} +(-1.75242 + 1.75242i) q^{41} +(0.496404 - 4.41231i) q^{42} -1.53970i q^{43} +(-1.87999 + 1.87999i) q^{44} +(8.37005 + 4.42013i) q^{45} +(-4.44416 - 16.5858i) q^{46} +(-1.97692 + 7.37798i) q^{47} +(-13.3505 - 1.50199i) q^{48} -1.00000i q^{49} +(8.98190 + 8.98190i) q^{50} +(8.51454 + 0.957921i) q^{51} +(-15.6974 + 5.02888i) q^{52} -13.7627i q^{53} +(0.988799 - 13.2837i) q^{54} +(-0.917469 - 1.58910i) q^{55} -6.59242 q^{56} +(6.99421 + 8.76747i) q^{57} +(-1.31792 + 4.91854i) q^{58} +(-0.728588 + 2.71913i) q^{59} +(9.12362 - 23.2580i) q^{60} +3.69471 q^{61} +(8.50072 + 14.7237i) q^{62} +(-0.113172 - 2.99786i) q^{63} +1.66044i q^{64} +(-0.548502 - 11.3629i) q^{65} +(-1.53304 + 2.07792i) q^{66} +(-0.933331 - 0.933331i) q^{67} -22.6153i q^{68} +(-4.64115 - 10.6328i) q^{69} +(2.09341 - 7.81271i) q^{70} +(0.126849 + 0.473407i) q^{71} +(-19.7632 + 0.746080i) q^{72} +(-10.4071 + 10.4071i) q^{73} +22.0708i q^{74} +(6.90621 + 5.09523i) q^{75} +(20.9322 - 20.9322i) q^{76} +(-0.290784 + 0.503652i) q^{77} +(-14.3465 + 7.10437i) q^{78} +(4.07484 + 7.05783i) q^{79} +(-23.6392 - 6.33411i) q^{80} +(-0.678551 - 8.97438i) q^{81} +(5.50200 + 3.17658i) q^{82} +(-13.8670 - 3.71566i) q^{83} +(-7.82966 + 1.18147i) q^{84} +(15.0764 + 4.03970i) q^{85} +(-3.81257 + 1.02157i) q^{86} +(-0.384640 + 3.41889i) q^{87} +(3.32029 + 1.91697i) q^{88} +(-1.71262 + 6.39158i) q^{89} +(5.39157 - 23.6584i) q^{90} +(-3.03195 + 1.95123i) q^{91} +(-26.5191 + 15.3108i) q^{92} +(7.16357 + 8.97977i) q^{93} +19.5808 q^{94} +(10.2153 + 17.6934i) q^{95} +(1.73130 + 11.4735i) q^{96} +(11.6425 + 11.6425i) q^{97} +(-2.47617 + 0.663488i) q^{98} +(-0.814731 + 1.54279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.663488	−	2.47617i	−0.469157	−	1.75092i	−0.642728	−	0.766095i	$-0.722197\pi$
$2$	−0.663488	−	2.47617i	−0.469157	−	1.75092i	0.173571	−	0.984821i	$-0.444469\pi$
$3$	−0.692898	−	1.58742i	−0.400045	−	0.916496i
$3$	−0.692898	−	1.58742i	−0.400045	−	0.916496i
$4$	−3.95915	+	2.28582i	−1.97957	+	1.14291i
$5$	−0.816615	−	3.04765i	−0.365202	−	1.36295i	−0.867147	−	0.498052i	$-0.834049\pi$
$5$	−0.816615	−	3.04765i	−0.365202	−	1.36295i	0.501946	−	0.864899i	$-0.332618\pi$
$6$	−3.47098	+	2.76896i	−1.41702	+	1.13042i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	4.66155	+	4.66155i	1.64811	+	1.64811i
$9$	−2.03979	+	2.19984i	−0.679928	+	0.733278i
$10$	−7.00468	+	4.04416i	−2.21508	+	1.27887i
$11$	0.561751	−	0.150521i	0.169374	−	0.0453837i	−0.173135	−	0.984898i	$-0.555390\pi$
$11$	0.561751	−	0.150521i	0.169374	−	0.0453837i	0.342510	+	0.939514i	$0.388723\pi$
$12$	6.37183	+	4.70098i	1.83939	+	1.35706i
$13$	3.52364	+	0.764181i	0.977281	+	0.211946i
$13$	3.52364	+	0.764181i	0.977281	+	0.211946i
$14$	2.22007	+	1.28176i	0.593339	+	0.342565i
$15$	−4.27206	+	3.40802i	−1.10304	+	0.879947i
$16$	3.87827	−	6.71736i	0.969568	−	1.67934i
$17$	−2.47344	+	4.28413i	−0.599898	+	1.03905i	0.392938	+	0.919565i	$0.371459\pi$
$17$	−2.47344	+	4.28413i	−0.599898	+	1.03905i	−0.992836	+	0.119488i	$0.961875\pi$
$18$	6.80054	+	3.59129i	1.60290	+	0.846475i
$19$	−6.25464	+	1.67592i	−1.43491	+	0.384483i	−0.890749	−	0.454496i	$-0.849819\pi$
$19$	−6.25464	+	1.67592i	−1.43491	+	0.384483i	−0.544163	+	0.838980i	$0.683153\pi$
$20$	10.1995	+	10.1995i	2.28067	+	2.28067i
$21$	1.61243	+	0.632521i	0.351860	+	0.138027i
$22$	−0.745430	−	1.29112i	−0.158926	−	0.275268i
$23$	6.69818			1.39667			0.698333	−	0.715773i	$-0.253925\pi$
$23$	6.69818			1.39667			0.698333	+	0.715773i	$0.253925\pi$
$24$	4.16984	−	10.6298i	0.851166	−	2.16980i
$25$	−4.29119	+	2.47752i	−0.858237	+	0.495503i
$26$	−0.445650	−	9.23215i	−0.0873991	−	1.81057i
$27$	4.90542	+	1.71373i	0.944048	+	0.329807i
$28$	1.18323	−	4.41586i	0.223609	−	0.834518i
$29$	−1.72023	−	0.993175i	−0.319439	−	0.184428i	0.331704	−	0.943384i	$-0.392377\pi$
$29$	−1.72023	−	0.993175i	−0.319439	−	0.184428i	−0.651142	+	0.758956i	$0.725710\pi$
$30$	11.2733	+	8.31717i	2.05821	+	1.51850i
$31$	−6.40609	+	1.71651i	−1.15057	+	0.308294i	−0.783192	−	0.621779i	$-0.786410\pi$
$31$	−6.40609	+	1.71651i	−1.15057	+	0.308294i	−0.367375	+	0.930073i	$0.619743\pi$
$32$	−6.47093	−	1.73388i	−1.14391	−	0.306510i
$33$	−0.628175	−	0.787438i	−0.109351	−	0.137075i
$34$	12.2493	+	3.28219i	2.10074	+	0.562892i
$35$	2.73245	+	1.57758i	0.461868	+	0.266660i
$36$	3.04740	−	13.3720i	0.507899	−	2.22867i
$37$	−8.31622	−	2.22833i	−1.36718	−	0.366334i	−0.500731	−	0.865603i	$-0.666936\pi$
$37$	−8.31622	−	2.22833i	−1.36718	−	0.366334i	−0.866447	+	0.499268i	$0.833602\pi$
$38$	8.29975	+	14.3756i	1.34640	+	2.33203i
$39$	−1.22845	−	6.12298i	−0.196709	−	0.980462i
$40$	10.4001	−	18.0135i	1.64440	−	2.84818i
$41$	−1.75242	+	1.75242i	−0.273682	+	0.273682i	−0.830581	−	0.556899i	$-0.811991\pi$
$41$	−1.75242	+	1.75242i	−0.273682	+	0.273682i	0.556899	+	0.830581i	$0.311991\pi$
$42$	0.496404	−	4.41231i	0.0765967	−	0.680834i
$43$		−	1.53970i		−	0.234803i	−0.993085	−	0.117401i	$-0.962544\pi$
$43$		−	1.53970i		−	0.234803i	0.993085	−	0.117401i	$-0.0374564\pi$
$44$	−1.87999	+	1.87999i	−0.283420	+	0.283420i
$45$	8.37005	+	4.42013i	1.24773	+	0.658915i
$46$	−4.44416	−	16.5858i	−0.655255	−	2.44545i
$47$	−1.97692	+	7.37798i	−0.288364	+	1.07619i	0.657982	+	0.753034i	$0.271410\pi$
$47$	−1.97692	+	7.37798i	−0.288364	+	1.07619i	−0.946346	+	0.323155i	$0.895256\pi$
$48$	−13.3505	−	1.50199i	−1.92698	−	0.216793i
$49$		−	1.00000i		−	0.142857i
$50$	8.98190	+	8.98190i	1.27023	+	1.27023i
$51$	8.51454	+	0.957921i	1.19227	+	0.134136i
$52$	−15.6974	+	5.02888i	−2.17684	+	0.697381i
$53$		−	13.7627i		−	1.89045i	−0.326419	−	0.945225i	$-0.605842\pi$
$53$		−	13.7627i		−	1.89045i	0.326419	−	0.945225i	$-0.394158\pi$
$54$	0.988799	−	13.2837i	0.134558	−	1.80768i
$55$	−0.917469	−	1.58910i	−0.123712	−	0.214275i
$56$	−6.59242			−0.880950
$57$	6.99421	+	8.76747i	0.926406	+	1.16128i
$58$	−1.31792	+	4.91854i	−0.173051	+	0.645836i
$59$	−0.728588	+	2.71913i	−0.0948541	+	0.354000i	−0.996997	−	0.0774364i	$-0.975327\pi$
$59$	−0.728588	+	2.71913i	−0.0948541	+	0.354000i	0.902143	+	0.431437i	$0.141993\pi$
$60$	9.12362	−	23.2580i	1.17785	−	3.00259i
$61$	3.69471			0.473059			0.236530	−	0.971624i	$-0.423990\pi$
$61$	3.69471			0.473059			0.236530	+	0.971624i	$0.423990\pi$
$62$	8.50072	+	14.7237i	1.07959	+	1.86991i
$63$	−0.113172	−	2.99786i	−0.0142584	−	0.377695i
$64$			1.66044i			0.207555i
$65$	−0.548502	−	11.3629i	−0.0680334	−	1.40939i
$66$	−1.53304	+	2.07792i	−0.188704	+	0.255775i
$67$	−0.933331	−	0.933331i	−0.114025	−	0.114025i	0.647792	−	0.761817i	$-0.275692\pi$
$67$	−0.933331	−	0.933331i	−0.114025	−	0.114025i	−0.761817	+	0.647792i	$0.775692\pi$
$68$		−	22.6153i		−	2.74251i
$69$	−4.64115	−	10.6328i	−0.558729	−	1.28004i
$70$	2.09341	−	7.81271i	0.250210	−	0.933797i
$71$	0.126849	+	0.473407i	0.0150542	+	0.0561830i	0.973044	−	0.230618i	$-0.0740748\pi$
$71$	0.126849	+	0.473407i	0.0150542	+	0.0561830i	−0.957990	+	0.286801i	$0.907408\pi$
$72$	−19.7632	+	0.746080i	−2.32911	+	0.0879264i
$73$	−10.4071	+	10.4071i	−1.21806	+	1.21806i	−0.249747	+	0.968311i	$0.580348\pi$
$73$	−10.4071	+	10.4071i	−1.21806	+	1.21806i	−0.968311	+	0.249747i	$0.919652\pi$
$74$			22.0708i			2.56568i
$75$	6.90621	+	5.09523i	0.797460	+	0.588347i
$76$	20.9322	−	20.9322i	2.40108	−	2.40108i
$77$	−0.290784	+	0.503652i	−0.0331379	+	0.0573965i
$78$	−14.3465	+	7.10437i	−1.62442	+	0.804411i
$79$	4.07484	+	7.05783i	0.458455	+	0.794068i	0.998880	−	0.0473247i	$-0.0150696\pi$
$79$	4.07484	+	7.05783i	0.458455	+	0.794068i	−0.540424	+	0.841393i	$0.681736\pi$
$80$	−23.6392	−	6.33411i	−2.64295	−	0.708175i
$81$	−0.678551	−	8.97438i	−0.0753946	−	0.997154i
$82$	5.50200	+	3.17658i	0.607594	+	0.350794i
$83$	−13.8670	−	3.71566i	−1.52210	−	0.407847i	−0.601670	−	0.798745i	$-0.705498\pi$
$83$	−13.8670	−	3.71566i	−1.52210	−	0.407847i	−0.920434	+	0.390898i	$0.872164\pi$
$84$	−7.82966	+	1.18147i	−0.854286	+	0.128908i
$85$	15.0764	+	4.03970i	1.63526	+	0.438167i
$86$	−3.81257	+	1.02157i	−0.411120	+	0.110159i
$87$	−0.384640	+	3.41889i	−0.0412377	+	0.366544i
$88$	3.32029	+	1.91697i	0.353944	+	0.204350i
$89$	−1.71262	+	6.39158i	−0.181537	+	0.677506i	0.813808	+	0.581134i	$0.197391\pi$
$89$	−1.71262	+	6.39158i	−0.181537	+	0.677506i	−0.995345	+	0.0963723i	$0.969276\pi$
$90$	5.39157	−	23.6584i	0.568322	−	2.49381i
$91$	−3.03195	+	1.95123i	−0.317834	+	0.204545i
$92$	−26.5191	+	15.3108i	−2.76480	+	1.59626i
$93$	7.16357	+	8.97977i	0.742828	+	0.931159i
$94$	19.5808			2.01960
$95$	10.2153	+	17.6934i	1.04806	+	1.81530i
$96$	1.73130	+	11.4735i	0.176700	+	1.17101i
$97$	11.6425	+	11.6425i	1.18212	+	1.18212i	0.979194	+	0.202925i	$0.0650448\pi$
$97$	11.6425	+	11.6425i	1.18212	+	1.18212i	0.202925	+	0.979194i	$0.434955\pi$
$98$	−2.47617	+	0.663488i	−0.250131	+	0.0670224i
$99$	−0.814731	+	1.54279i	−0.0818835	+	0.155056i
$100$	11.3263	−	19.6177i	1.13263	−	1.96177i
$101$	7.69689	−	13.3314i	0.765869	−	1.32652i	−0.173916	−	0.984760i	$-0.555642\pi$
$101$	7.69689	−	13.3314i	0.765869	−	1.32652i	0.939786	−	0.341764i	$-0.111024\pi$
$102$	−3.27731	−	21.7190i	−0.324502	−	2.15050i
$103$	3.65202	+	2.10849i	0.359844	+	0.207756i	0.669012	−	0.743251i	$-0.266717\pi$
$103$	3.65202	+	2.10849i	0.359844	+	0.207756i	−0.309168	+	0.951007i	$0.600051\pi$
$104$	12.8633	+	19.9879i	1.26135	+	1.95997i
$105$	0.610970	−	5.43064i	0.0596245	−	0.529976i
$106$	−34.0787	+	9.13137i	−3.31002	+	0.886917i
$107$	−7.58667	+	4.38017i	−0.733432	+	0.423447i	−0.819676	−	0.572827i	$-0.805847\pi$
$107$	−7.58667	+	4.38017i	−0.733432	+	0.423447i	0.0862447	+	0.996274i	$0.472513\pi$
$108$	−23.3385	+	4.42797i	−2.24575	+	0.426082i
$109$	−8.43495	−	8.43495i	−0.807922	−	0.807922i	0.176397	−	0.984319i	$-0.443556\pi$
$109$	−8.43495	−	8.43495i	−0.807922	−	0.807922i	−0.984319	+	0.176397i	$0.943556\pi$
$110$	−3.32616	+	3.32616i	−0.317137	+	0.317137i
$111$	2.22501	+	14.7453i	0.211189	+	1.39956i
$112$	2.00754	+	7.49225i	0.189695	+	0.707951i
$113$	3.20375	−	1.84968i	0.301383	−	0.174004i	−0.341681	−	0.939816i	$-0.610996\pi$
$113$	3.20375	−	1.84968i	0.301383	−	0.174004i	0.643064	+	0.765812i	$0.277663\pi$
$114$	17.0692	−	23.1360i	1.59867	−	2.16688i
$115$	−5.46984	−	20.4137i	−0.510065	−	1.90359i
$116$	9.08086			0.843137
$117$	−8.86854	+	6.19266i	−0.819897	+	0.572512i
$118$	7.21643			0.664326
$119$	−1.28035	−	4.77832i	−0.117369	−	0.438028i
$120$	−35.8011	−	4.02777i	−3.26817	−	0.367684i
$121$	−9.23337	+	5.33089i	−0.839397	+	0.484626i
$122$	−2.45140	−	9.14873i	−0.221939	−	0.828287i
$123$	3.99607	+	1.56757i	0.360313	+	0.141343i
$124$	21.4390	−	21.4390i	1.92528	−	1.92528i
$125$	−0.100320	−	0.100320i	−0.00897290	−	0.00897290i
$126$	−7.34813	+	2.26928i	−0.654624	+	0.202164i
$127$	1.85353	−	1.07013i	0.164474	−	0.0949590i	−0.415504	−	0.909591i	$-0.636395\pi$
$127$	1.85353	−	1.07013i	0.164474	−	0.0949590i	0.579978	+	0.814632i	$0.303061\pi$
$128$	−8.83032	+	2.36608i	−0.780498	+	0.209134i
$129$	−2.44415	+	1.06686i	−0.215196	+	0.0939316i
$130$	−27.7724	+	8.89730i	−2.43580	+	0.780345i
$131$	4.04928	+	2.33785i	0.353787	+	0.204259i	0.666352	−	0.745637i	$-0.267855\pi$
$131$	4.04928	+	2.33785i	0.353787	+	0.204259i	−0.312565	+	0.949896i	$0.601188\pi$
$132$	4.28698	+	1.68169i	0.373133	+	0.146372i
$133$	3.23764	−	5.60775i	0.280739	−	0.486254i
$134$	−1.69183	+	2.93034i	−0.146152	+	0.253143i
$135$	1.21701	−	16.3495i	0.104743	−	1.40714i
$136$	−31.5007	+	8.44059i	−2.70116	+	0.723775i
$137$	−2.87167	−	2.87167i	−0.245343	−	0.245343i	0.573713	−	0.819056i	$-0.305502\pi$
$137$	−2.87167	−	2.87167i	−0.245343	−	0.245343i	−0.819056	+	0.573713i	$0.805502\pi$
$138$	−23.2493	+	18.5470i	−1.97911	+	1.57883i
$139$	−7.34950	−	12.7297i	−0.623376	−	1.07972i	−0.988852	−	0.148898i	$-0.952427\pi$
$139$	−7.34950	−	12.7297i	−0.623376	−	1.07972i	0.365476	−	0.930821i	$-0.380906\pi$
$140$	−14.4242			−1.21907
$141$	13.0817	−	1.97398i	1.10168	−	0.166239i
$142$	1.08807	−	0.628199i	0.0913090	−	0.0527173i
$143$	2.09443	−	0.101101i	0.175145	−	0.00845453i
$144$	6.86625	+	22.2335i	0.572188	+	1.85280i
$145$	−1.62208	+	6.05370i	−0.134707	+	0.502732i
$146$	32.6747	+	18.8648i	2.70418	+	1.56126i
$147$	−1.58742	+	0.692898i	−0.130928	+	0.0571492i
$148$	38.0187	−	10.1871i	3.12512	−	0.837373i
$149$	9.00455	+	2.41276i	0.737681	+	0.197661i	0.608047	−	0.793901i	$-0.291953\pi$
$149$	9.00455	+	2.41276i	0.737681	+	0.197661i	0.129634	+	0.991562i	$0.458620\pi$
$150$	8.03448	−	20.4816i	0.656013	−	1.67231i
$151$	5.87788	+	1.57497i	0.478335	+	0.128170i	0.489927	−	0.871763i	$-0.337023\pi$
$151$	5.87788	+	1.57497i	0.478335	+	0.128170i	−0.0115922	+	0.999933i	$0.503690\pi$
$152$	−36.9687	−	21.3439i	−2.99856	−	1.73122i
$153$	−4.37908	−	14.1799i	−0.354028	−	1.14637i
$154$	1.44006	+	0.385863i	0.116043	+	0.0310937i
$155$	10.4626	+	18.1218i	0.840378	+	1.45558i
$156$	18.8596	+	21.4338i	1.50998	+	1.71608i
$157$	−5.89575	+	10.2117i	−0.470532	+	0.814986i	−0.999432	−	0.0336983i	$-0.989271\pi$
$157$	−5.89575	+	10.2117i	−0.470532	+	0.814986i	0.528900	+	0.848684i	$0.322605\pi$
$158$	14.7728	−	14.7728i	1.17526	−	1.17526i
$159$	−21.8471	+	9.53614i	−1.73259	+	0.756265i
$160$			21.1371i			1.67103i
$161$	−4.73633	+	4.73633i	−0.373275	+	0.373275i
$162$	−21.7719	+	7.63460i	−1.71056	+	0.599831i
$163$	6.22894	+	23.2467i	0.487888	+	1.82082i	0.566686	+	0.823934i	$0.308225\pi$
$163$	6.22894	+	23.2467i	0.487888	+	1.82082i	−0.0787977	+	0.996891i	$0.525108\pi$
$164$	2.93238	−	10.9438i	0.228980	−	0.854567i
$165$	−1.88686	+	2.55749i	−0.146892	+	0.199100i
$166$			36.8024i			2.85642i
$167$	9.84716	+	9.84716i	0.761996	+	0.761996i	0.976683	−	0.214687i	$-0.0688731\pi$
$167$	9.84716	+	9.84716i	0.761996	+	0.761996i	−0.214687	+	0.976683i	$0.568873\pi$
$168$	4.56788	+	10.4649i	0.352419	+	0.807387i
$169$	11.8321	+	5.38539i	0.910158	+	0.414261i
$170$		−	40.0119i		−	3.06877i
$171$	9.07136	−	17.1777i	0.693704	−	1.31361i
$172$	3.51948	+	6.09592i	0.268358	+	0.464809i
$173$	−5.83462			−0.443598			−0.221799	−	0.975092i	$-0.571193\pi$
$173$	−5.83462			−0.443598			−0.221799	+	0.975092i	$0.571193\pi$
$174$	8.72096	−	1.31596i	0.661134	−	0.0997625i
$175$	1.28246	−	4.78620i	0.0969447	−	0.361802i
$176$	1.16752	−	4.35725i	0.0880052	−	0.328440i
$177$	4.82123	−	0.727504i	0.362386	−	0.0546826i
$178$	16.9629			1.27143
$179$	3.74123	+	6.47999i	0.279632	+	0.484337i	0.971293	−	0.237885i	$-0.0764541\pi$
$179$	3.74123	+	6.47999i	0.279632	+	0.484337i	−0.691661	+	0.722222i	$0.743121\pi$
$180$	−43.2419	+	1.63242i	−3.22306	+	0.121674i
$181$			9.28576i			0.690205i	0.938565	+	0.345102i	$0.112156\pi$
$181$			9.28576i			0.690205i	−0.938565	+	0.345102i	$0.887844\pi$
$182$	6.84324	+	6.21299i	0.507255	+	0.460538i
$183$	−2.56006	−	5.86505i	−0.189245	−	0.433557i
$184$	31.2239	+	31.2239i	2.30185	+	2.30185i
$185$			27.1646i			1.99718i
$186$	17.4825	−	23.6962i	1.28188	−	1.73749i
$187$	−0.744608	+	2.77892i	−0.0544511	+	0.203214i
$188$	−9.03777	−	33.7294i	−0.659147	−	2.45997i
$189$	−4.68044	+	2.25687i	−0.340452	+	0.164163i
$190$	37.0340	−	37.0340i	2.68673	−	2.68673i
$191$			4.18824i			0.303050i	0.988453	+	0.151525i	$0.0484185\pi$
$191$			4.18824i			0.303050i	−0.988453	+	0.151525i	$0.951582\pi$
$192$	2.63582	−	1.15052i	0.190224	−	0.0830314i
$193$	4.80439	−	4.80439i	0.345827	−	0.345827i	−0.512725	−	0.858553i	$-0.671364\pi$
$193$	4.80439	−	4.80439i	0.345827	−	0.345827i	0.858553	+	0.512725i	$0.171364\pi$
$194$	21.1042	−	36.5535i	1.51519	−	2.62439i
$195$	−17.6575	+	8.74400i	−1.26448	+	0.626171i
$196$	2.28582	+	3.95915i	0.163273	+	0.282796i
$197$	−6.32730	−	1.69540i	−0.450802	−	0.120792i	0.0262728	−	0.999655i	$-0.491636\pi$
$197$	−6.32730	−	1.69540i	−0.450802	−	0.120792i	−0.477075	+	0.878863i	$0.658303\pi$
$198$	4.36077	+	0.993789i	0.309907	+	0.0706255i
$199$	3.51632	+	2.03015i	0.249265	+	0.143913i	0.619428	−	0.785054i	$-0.287365\pi$
$199$	3.51632	+	2.03015i	0.249265	+	0.143913i	−0.370163	+	0.928967i	$0.620698\pi$
$200$	−31.5526	−	8.45450i	−2.23111	−	0.597824i
$201$	−0.834882	+	2.12829i	−0.0588881	+	0.150118i
$202$	−38.1176	−	10.2136i	−2.68195	−	0.718625i
$203$	1.91867	−	0.514105i	0.134664	−	0.0360831i
$204$	−35.8999	+	15.6701i	−2.51350	+	1.09713i
$205$	6.77181	+	3.90971i	0.472964	+	0.273066i
$206$	2.79792	−	10.4420i	0.194940	−	0.727526i
$207$	−13.6628	+	14.7349i	−0.949633	+	1.02415i
$208$	18.7989	−	20.7059i	1.30347	−	1.43569i
$209$	−3.26129	+	1.88290i	−0.225588	+	0.130243i
$210$	−13.8525	+	2.09030i	−0.955917	+	0.144244i
$211$	5.76369			0.396789			0.198394	−	0.980122i	$-0.436427\pi$
$211$	5.76369			0.396789			0.198394	+	0.980122i	$0.436427\pi$
$212$	31.4590	+	54.4885i	2.16061	+	3.74229i
$213$	0.663600	−	0.529384i	0.0454691	−	0.0362728i
$214$	15.8797	+	15.8797i	1.08551	+	1.08551i
$215$	−4.69248	+	1.25735i	−0.320024	+	0.0857503i
$216$	14.8782	+	30.8555i	1.01233	+	2.09945i
$217$	3.31604	−	5.74354i	0.225107	−	0.389897i
$218$	−15.2899	+	26.4829i	−1.03556	+	1.79365i
$219$	23.7315	+	9.30935i	1.60362	+	0.629067i
$220$	7.26479	+	4.19433i	0.489792	+	0.282782i
$221$	−11.9894	+	13.2056i	−0.806491	+	0.888302i
$222$	35.0356	−	15.2928i	2.35144	−	1.02639i
$223$	−24.7505	+	6.63188i	−1.65742	+	0.444104i	−0.961676	−	0.274189i	$-0.911591\pi$
$223$	−24.7505	+	6.63188i	−1.65742	+	0.444104i	−0.695741	+	0.718292i	$0.744924\pi$
$224$	5.80168	−	3.34960i	0.387641	−	0.223805i
$225$	3.30297	−	14.4935i	0.220198	−	0.966234i
$226$	−6.70578	−	6.70578i	−0.446062	−	0.446062i
$227$	4.22979	−	4.22979i	0.280741	−	0.280741i	−0.552664	−	0.833404i	$-0.686389\pi$
$227$	4.22979	−	4.22979i	0.280741	−	0.280741i	0.833404	+	0.552664i	$0.186389\pi$
$228$	−47.7319	−	18.7242i	−3.16113	−	1.24004i
$229$	−0.677413	−	2.52814i	−0.0447647	−	0.167064i	0.939925	−	0.341381i	$-0.110895\pi$
$229$	−0.677413	−	2.52814i	−0.0447647	−	0.167064i	−0.984690	+	0.174317i	$0.944228\pi$
$230$	−46.9186	+	27.0885i	−3.09372	+	1.78616i
$231$	1.00099	+	0.112616i	0.0658603	+	0.00740956i
$232$	−3.38920	−	12.6487i	−0.222512	−	0.830426i
$233$	5.04648			0.330606			0.165303	−	0.986243i	$-0.447140\pi$
$233$	5.04648			0.330606			0.165303	+	0.986243i	$0.447140\pi$
$234$	21.2182	+	17.8512i	1.38708	+	1.16697i
$235$	24.0999			1.57210
$236$	−3.33084	−	12.4308i	−0.216819	−	0.809179i
$237$	8.38027	−	11.3588i	0.544357	−	0.737835i
$238$	−10.9824	+	6.34071i	−0.711886	+	0.411007i
$239$	−3.10979	−	11.6059i	−0.201155	−	0.750722i	−0.990587	−	0.136884i	$-0.956291\pi$
$239$	−3.10979	−	11.6059i	−0.201155	−	0.750722i	0.789432	−	0.613839i	$-0.210375\pi$
$240$	6.32469	+	41.9142i	0.408257	+	2.70555i
$241$	−11.5688	+	11.5688i	−0.745214	+	0.745214i	−0.973576	−	0.228362i	$-0.926663\pi$
$241$	−11.5688	+	11.5688i	−0.745214	+	0.745214i	0.228362	+	0.973576i	$0.426663\pi$
$242$	19.3264	+	19.3264i	1.24235	+	1.24235i
$243$	−13.7759	+	7.29547i	−0.883726	+	0.468005i
$244$	−14.6279	+	8.44543i	−0.936456	+	0.540663i
$245$	−3.04765	+	0.816615i	−0.194707	+	0.0521716i
$246$	1.23023	−	10.9350i	0.0784369	−	0.697190i
$247$	−23.3198	+	1.12568i	−1.48380	+	0.0716254i
$248$	−37.8639	−	21.8607i	−2.40436	−	1.38816i
$249$	3.71013	+	24.5873i	0.235120	+	1.55816i
$250$	−0.181848	+	0.314971i	−0.0115011	+	0.0199205i
$251$	−5.51066	+	9.54475i	−0.347830	+	0.602459i	−0.985864	−	0.167549i	$-0.946415\pi$
$251$	−5.51066	+	9.54475i	−0.347830	+	0.602459i	0.638034	+	0.770008i	$0.279748\pi$
$252$	7.30063	+	11.6103i	0.459897	+	0.731380i
$253$	3.76271	−	1.00821i	0.236559	−	0.0633859i
$254$	−3.87962	−	3.87962i	−0.243429	−	0.243429i
$255$	−4.03369	−	26.7316i	−0.252600	−	1.67400i
$256$	13.3781	+	23.1715i	0.836129	+	1.44822i
$257$	−9.84904			−0.614366			−0.307183	−	0.951650i	$-0.599386\pi$
$257$	−9.84904			−0.614366			−0.307183	+	0.951650i	$0.599386\pi$
$258$	4.26338	+	5.34429i	0.265427	+	0.332721i
$259$	7.45612	−	4.30479i	0.463301	−	0.267487i
$260$	28.1450	+	43.7335i	1.74548	+	2.71223i
$261$	5.69372	−	1.75836i	0.352432	−	0.108840i
$262$	3.10227	−	11.5778i	0.191659	−	0.715281i
$263$	10.4496	+	6.03306i	0.644348	+	0.372015i	0.786288	−	0.617861i	$-0.212000\pi$
$263$	10.4496	+	6.03306i	0.644348	+	0.372015i	−0.141939	+	0.989875i	$0.545334\pi$
$264$	0.742409	−	6.59895i	0.0456921	−	0.406137i
$265$	−41.9439	+	11.2388i	−2.57659	+	0.690395i
$266$	−16.0339	−	4.29626i	−0.983100	−	0.263421i
$267$	11.3328	−	1.71007i	0.693554	−	0.104655i
$268$	5.82862	+	1.56177i	0.356039	+	0.0954005i
$269$	−3.48831	−	2.01397i	−0.212686	−	0.122794i	0.389873	−	0.920869i	$-0.372519\pi$
$269$	−3.48831	−	2.01397i	−0.212686	−	0.122794i	−0.602559	+	0.798074i	$0.705852\pi$
$270$	−41.2915	+	7.83415i	−2.51292	+	0.476771i
$271$	−23.2195	−	6.22164i	−1.41048	−	0.377938i	−0.528385	−	0.849005i	$-0.677202\pi$
$271$	−23.2195	−	6.22164i	−1.41048	−	0.377938i	−0.882097	+	0.471067i	$0.843869\pi$
$272$	19.1854	+	33.2300i	1.16328	+	2.01487i
$273$	5.19825	+	3.46096i	0.314612	+	0.209467i
$274$	−5.20542	+	9.01606i	−0.314471	+	0.544680i
$275$	−2.03766	+	2.03766i	−0.122876	+	0.122876i
$276$	42.6796	+	31.4880i	2.56901	+	1.89536i
$277$		−	24.3826i		−	1.46501i	−0.680764	−	0.732503i	$-0.738352\pi$
$277$		−	24.3826i		−	1.46501i	0.680764	−	0.732503i	$-0.261648\pi$
$278$	−26.6446	+	26.6446i	−1.59804	+	1.59804i
$279$	9.29101	−	17.5936i	0.556238	−	1.05330i
$280$	5.38348	+	20.0914i	0.321724	+	1.20069i
$281$	2.59978	−	9.70250i	0.155090	−	0.578803i	−0.844008	−	0.536331i	$-0.819810\pi$
$281$	2.59978	−	9.70250i	0.155090	−	0.578803i	0.999098	−	0.0424720i	$-0.0135233\pi$
$282$	−13.5675	−	31.0829i	−0.807932	−	1.85096i
$283$		−	5.14094i		−	0.305597i	−0.988257	−	0.152799i	$-0.951171\pi$
$283$		−	5.14094i		−	0.305597i	0.988257	−	0.152799i	$-0.0488286\pi$
$284$	−1.58433	−	1.58433i	−0.0940129	−	0.0940129i
$285$	21.0086	−	28.4756i	1.24444	−	1.68675i
$286$	−1.63997	−	5.11909i	−0.0969737	−	0.302698i
$287$		−	2.47830i		−	0.146289i
$288$	17.0136	−	10.6982i	1.00253	−	0.630400i
$289$	−3.73582	−	6.47063i	−0.219754	−	0.380625i
$290$	16.0662			0.943441
$291$	10.4145	−	26.5486i	0.610507	−	1.55631i
$292$	17.4145	−	64.9919i	1.01911	−	3.80337i
$293$	7.40343	−	27.6300i	0.432513	−	1.61416i	−0.314436	−	0.949279i	$-0.601815\pi$
$293$	7.40343	−	27.6300i	0.432513	−	1.61416i	0.746949	−	0.664881i	$-0.231518\pi$
$294$	2.76896	+	3.47098i	0.161489	+	0.202432i
$295$	8.88193			0.517126
$296$	−28.3790	−	49.1539i	−1.64950	−	2.85701i
$297$	3.01358	+	0.224322i	0.174865	+	0.0130165i
$298$		−	23.8976i		−	1.38435i
$299$	23.6020	+	5.11862i	1.36494	+	0.296017i
$300$	−38.9895	−	4.38648i	−2.25106	−	0.253253i
$301$	1.08874	+	1.08874i	0.0627537	+	0.0627537i
$302$		−	15.5996i		−	0.897656i
$303$	−26.4957	−	2.98087i	−1.52214	−	0.171247i
$304$	−12.9994	+	48.5144i	−0.745566	+	2.78249i
$305$	−3.01716	−	11.2602i	−0.172762	−	0.644757i
$306$	−32.2063	+	20.2515i	−1.84111	+	1.15770i
$307$	−16.6477	+	16.6477i	−0.950135	+	0.950135i	−0.998814	−	0.0486798i	$-0.984499\pi$
$307$	−16.6477	+	16.6477i	−0.950135	+	0.950135i	0.0486798	+	0.998814i	$0.484499\pi$
$308$		−	2.65871i		−	0.151494i
$309$	0.816583	−	7.25824i	0.0464538	−	0.412907i
$310$	37.9308	−	37.9308i	2.15433	−	2.15433i
$311$	9.13366	−	15.8200i	0.517922	−	0.897068i	−0.481861	−	0.876248i	$-0.660039\pi$
$311$	9.13366	−	15.8200i	0.517922	−	0.897068i	0.999783	−	0.0208201i	$-0.00662772\pi$
$312$	22.8161	−	34.2690i	1.29171	−	1.94010i
$313$	−5.88760	−	10.1976i	−0.332787	−	0.576403i	0.650271	−	0.759703i	$-0.274656\pi$
$313$	−5.88760	−	10.1976i	−0.332787	−	0.576403i	−0.983057	+	0.183299i	$0.941322\pi$
$314$	29.1978	+	7.82352i	1.64773	+	0.441507i
$315$	−9.04403	+	2.79301i	−0.509573	+	0.157368i
$316$	−32.2658	−	18.6287i	−1.81509	−	1.04794i
$317$	−25.8520	−	6.92701i	−1.45199	−	0.389060i	−0.555275	−	0.831667i	$-0.687387\pi$
$317$	−25.8520	−	6.92701i	−1.45199	−	0.389060i	−0.896716	+	0.442607i	$0.854054\pi$
$318$	38.1084	+	47.7701i	2.13701	+	2.67881i
$319$	−1.11583	−	0.298987i	−0.0624747	−	0.0167400i
$320$	5.06045	−	1.35594i	0.282888	−	0.0757996i
$321$	12.2099	+	9.00821i	0.681493	+	0.502789i
$322$	14.8704	+	8.58545i	0.828697	+	0.478449i
$323$	8.29060	−	30.9409i	0.461301	−	1.72160i
$324$	23.2003	+	33.9799i	1.28890	+	1.88777i
$325$	−17.0139	+	5.45063i	−0.943759	+	0.302347i
$326$	53.4300	−	30.8478i	2.95921	−	1.70850i
$327$	−7.54523	+	19.2343i	−0.417252	+	1.06366i
$328$	−16.3380			−0.902114
$329$	−3.81912	−	6.61492i	−0.210555	−	0.364692i
$330$	7.58469	+	2.97531i	0.417523	+	0.163786i
$331$	−1.91630	−	1.91630i	−0.105329	−	0.105329i	0.652478	−	0.757808i	$-0.273729\pi$
$331$	−1.91630	−	1.91630i	−0.105329	−	0.105329i	−0.757808	+	0.652478i	$0.773729\pi$
$332$	63.3949	−	16.9866i	3.47925	−	0.932262i
$333$	21.8653	−	13.7490i	1.19821	−	0.753442i
$334$	17.8498	−	30.9167i	0.976696	−	1.69169i
$335$	−2.08229	+	3.60664i	−0.113768	+	0.197052i
$336$	10.5023	−	8.37817i	0.572947	−	0.457066i
$337$	−12.0716	−	6.96956i	−0.657583	−	0.379656i	0.133772	−	0.991012i	$-0.457291\pi$
$337$	−12.0716	−	6.96956i	−0.657583	−	0.379656i	−0.791356	+	0.611356i	$0.790624\pi$
$338$	5.48472	−	32.8713i	0.298329	−	1.78796i
$339$	−5.15609	−	3.80404i	−0.280040	−	0.206607i
$340$	−68.9236	+	18.4680i	−3.73791	+	1.00157i
$341$	−3.34026	+	1.92850i	−0.180885	+	0.104434i
$342$	−48.5536	−	11.0650i	−2.62548	−	0.598328i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	7.17740	−	7.17740i	0.386980	−	0.386980i
$345$	−28.6150	+	22.8275i	−1.54058	+	1.22899i
$346$	3.87120	+	14.4475i	0.208117	+	0.776703i
$347$	−21.1623	+	12.2180i	−1.13605	+	0.655899i	−0.945450	−	0.325769i	$-0.894377\pi$
$347$	−21.1623	+	12.2180i	−1.13605	+	0.655899i	−0.190601	+	0.981668i	$0.561044\pi$
$348$	−6.29211	−	14.4151i	−0.337292	−	0.772731i
$349$	7.35327	+	27.4428i	0.393611	+	1.46898i	0.824132	+	0.566397i	$0.191663\pi$
$349$	7.35327	+	27.4428i	0.393611	+	1.46898i	−0.430521	+	0.902581i	$0.641670\pi$
$350$	−12.7023			−0.678968
$351$	15.9753	+	9.78719i	0.852700	+	0.522401i
$352$	−3.89604			−0.207659
$353$	−7.19266	−	26.8434i	−0.382827	−	1.42873i	−0.841564	−	0.540157i	$-0.818365\pi$
$353$	−7.19266	−	26.8434i	−0.382827	−	1.42873i	0.458737	−	0.888572i	$-0.348302\pi$
$354$	−5.00025	−	11.4555i	−0.265760	−	0.608852i
$355$	1.33919	−	0.773182i	0.0710769	−	0.0410363i
$356$	−7.82946	−	29.2199i	−0.414960	−	1.54865i
$357$	−6.69804	+	5.34333i	−0.354498	+	0.282799i
$358$	13.5633	−	13.5633i	0.716843	−	0.716843i
$359$	4.48701	+	4.48701i	0.236815	+	0.236815i	0.815530	−	0.578715i	$-0.196445\pi$
$359$	4.48701	+	4.48701i	0.236815	+	0.236815i	−0.578715	+	0.815530i	$0.696445\pi$
$360$	18.4127	+	59.6220i	0.970436	+	3.14236i
$361$	19.8573	−	11.4646i	1.04512	−	0.603400i
$362$	22.9931	−	6.16098i	1.20849	−	0.323814i
$363$	14.8601	+	10.9634i	0.779954	+	0.575432i
$364$	7.54377	−	14.6557i	0.395401	−	0.768166i
$365$	40.2158	+	23.2186i	2.10499	+	1.21532i
$366$	−12.8243	+	10.2305i	−0.670336	+	0.534758i
$367$	−14.6249	+	25.3311i	−0.763415	+	1.32227i	0.177665	+	0.984091i	$0.443146\pi$
$367$	−14.6249	+	25.3311i	−0.763415	+	1.32227i	−0.941080	+	0.338183i	$0.890188\pi$
$368$	25.9774	−	44.9941i	1.35416	−	2.34548i
$369$	−0.280475	−	7.42959i	−0.0146009	−	0.386769i
$370$	67.2642	−	18.0234i	3.49690	−	0.936992i
$371$	9.73169	+	9.73169i	0.505244	+	0.505244i
$372$	−48.8877	−	19.1776i	−2.53471	−	0.994314i
$373$	−10.1585	−	17.5950i	−0.525985	−	0.911033i	−0.999542	−	0.0302694i	$-0.990363\pi$
$373$	−10.1585	−	17.5950i	−0.525985	−	0.911033i	0.473557	−	0.880763i	$-0.342970\pi$
$374$	7.37510			0.381358
$375$	−0.0897382	+	0.228761i	−0.00463406	+	0.0118132i
$376$	−43.6083	+	25.1773i	−2.24893	+	1.29842i
$377$	−5.30250	−	4.81416i	−0.273093	−	0.247942i
$378$	8.69380	+	10.0922i	0.447161	+	0.519085i
$379$	−3.94229	+	14.7128i	−0.202502	+	0.755748i	0.787694	+	0.616066i	$0.211275\pi$
$379$	−3.94229	+	14.7128i	−0.202502	+	0.755748i	−0.990196	+	0.139682i	$0.955392\pi$
$380$	−80.8875	−	46.7004i	−4.14944	−	2.39568i
$381$	−2.98305	−	2.20083i	−0.152826	−	0.112752i
$382$	10.3708	−	2.77885i	0.530616	−	0.142178i
$383$	10.1934	+	2.73133i	0.520861	+	0.139564i	0.509665	−	0.860373i	$-0.329769\pi$
$383$	10.1934	+	2.73133i	0.520861	+	0.139564i	0.0111960	+	0.999937i	$0.496436\pi$
$384$	9.87447	+	12.3780i	0.503904	+	0.631660i
$385$	1.77241	+	0.474917i	0.0903306	+	0.0242040i
$386$	−15.0841	−	8.70882i	−0.767762	−	0.443267i
$387$	3.38710	+	3.14067i	0.172176	+	0.159649i
$388$	−72.7071	−	19.4818i	−3.69115	−	0.989040i
$389$	−4.94787	−	8.56996i	−0.250867	−	0.434514i	0.712898	−	0.701268i	$-0.247382\pi$
$389$	−4.94787	−	8.56996i	−0.250867	−	0.434514i	−0.963765	+	0.266754i	$0.914049\pi$
$390$	33.3672	+	37.9215i	1.68961	+	1.92023i
$391$	−16.5675	+	28.6958i	−0.837857	+	1.45121i
$392$	4.66155	−	4.66155i	0.235444	−	0.235444i
$393$	0.905409	−	8.04778i	0.0456719	−	0.405957i
$394$			16.7923i			0.845986i
$395$	18.1822	−	18.1822i	0.914847	−	0.914847i
$396$	−0.300893	−	7.97046i	−0.0151204	−	0.400531i
$397$	−8.57668	−	32.0086i	−0.430451	−	1.60647i	−0.751723	−	0.659479i	$-0.770777\pi$
$397$	−8.57668	−	32.0086i	−0.430451	−	1.60647i	0.321271	−	0.946987i	$-0.395890\pi$
$398$	2.69395	−	10.0540i	0.135036	−	0.503960i
$399$	−11.1452	−	1.25388i	−0.557958	−	0.0627726i
$400$			38.4339i			1.92170i
$401$	−14.8359	−	14.8359i	−0.740870	−	0.740870i	0.231875	−	0.972746i	$-0.425514\pi$
$401$	−14.8359	−	14.8359i	−0.740870	−	0.740870i	−0.972746	+	0.231875i	$0.925514\pi$
$402$	5.82394	+	0.655218i	0.290472	+	0.0326793i
$403$	−23.8845	+	1.15294i	−1.18977	+	0.0574320i
$404$			70.3747i			3.50127i
$405$	−26.7967	+	9.39661i	−1.33154	+	0.466921i
$406$	−2.54602	−	4.40984i	−0.126357	−	0.218857i
$407$	−5.00706			−0.248191
$408$	35.2255	+	44.1563i	1.74392	+	2.18606i
$409$	8.21192	−	30.6473i	0.406053	−	1.51541i	−0.396051	−	0.918229i	$-0.629620\pi$
$409$	8.21192	−	30.6473i	0.406053	−	1.51541i	0.802104	−	0.597184i	$-0.203714\pi$
$410$	5.18809	−	19.3622i	0.256221	−	0.956231i
$411$	−2.56876	+	6.54831i	−0.126708	+	0.323004i
$412$	−19.2785			−0.949783
$413$	−1.40752	−	2.43790i	−0.0692597	−	0.119961i
$414$	45.5512	+	24.0551i	2.23872	+	1.18224i
$415$			45.2961i			2.22350i
$416$	−21.4762	−	11.0545i	−1.05296	−	0.541993i
$417$	−15.1149	+	20.4871i	−0.740179	+	1.00326i
$418$	6.82621	+	6.82621i	0.333881	+	0.333881i
$419$			18.3766i			0.897756i	0.893593	+	0.448878i	$0.148176\pi$
$419$			18.3766i			0.897756i	−0.893593	+	0.448878i	$0.851824\pi$
$420$	9.99451	+	22.8973i	0.487682	+	1.11727i
$421$	−0.0726400	+	0.271096i	−0.00354026	+	0.0132124i	−0.967673	−	0.252207i	$-0.918844\pi$
$421$	−0.0726400	+	0.271096i	−0.00354026	+	0.0132124i	0.964133	+	0.265419i	$0.0855104\pi$
$422$	−3.82413	−	14.2719i	−0.186156	−	0.694744i
$423$	−12.1978	−	19.3984i	−0.593079	−	0.943183i
$424$	64.1554	−	64.1554i	3.11566	−	3.11566i
$425$		−	24.5120i		−	1.18901i
$426$	−1.75114	−	1.29195i	−0.0848428	−	0.0625950i
$427$	−2.61256	+	2.61256i	−0.126430	+	0.126430i
$428$	20.0245	−	34.6835i	0.967921	−	1.67649i
$429$	−1.61172	−	3.25468i	−0.0778145	−	0.157138i
$430$	6.22680	+	10.7851i	0.300283	+	0.520106i
$431$	−7.74972	−	2.07653i	−0.373291	−	0.100023i	0.0672957	−	0.997733i	$-0.478563\pi$
$431$	−7.74972	−	2.07653i	−0.373291	−	0.100023i	−0.440587	+	0.897710i	$0.645230\pi$
$432$	30.5363	−	26.3052i	1.46918	−	1.26561i
$433$	−19.1562	−	11.0598i	−0.920586	−	0.531501i	−0.0367643	−	0.999324i	$-0.511705\pi$
$433$	−19.1562	−	11.0598i	−0.920586	−	0.531501i	−0.883822	+	0.467823i	$0.845038\pi$
$434$	−16.4221	−	4.40030i	−0.788287	−	0.211221i
$435$	10.7337	−	1.61967i	0.514641	−	0.0776573i
$436$	52.6760	+	14.1145i	2.52272	+	0.675961i
$437$	−41.8947	+	11.2256i	−2.00409	+	0.536995i
$438$	7.30600	−	64.9397i	0.349094	−	3.10294i
$439$	−22.4824	−	12.9802i	−1.07303	−	0.619513i	−0.144021	−	0.989575i	$-0.546003\pi$
$439$	−22.4824	−	12.9802i	−1.07303	−	0.619513i	−0.929007	+	0.370062i	$0.879337\pi$
$440$	3.13085	−	11.6845i	0.149258	−	0.557037i
$441$	2.19984	+	2.03979i	0.104754	+	0.0971326i
$442$	40.6540	+	20.9260i	1.93371	+	0.995346i
$443$	−8.91991	+	5.14991i	−0.423798	+	0.244680i	−0.696701	−	0.717362i	$-0.745350\pi$
$443$	−8.91991	+	5.14991i	−0.423798	+	0.244680i	0.272903	+	0.962042i	$0.412016\pi$
$444$	−42.5142	−	53.2929i	−2.01764	−	2.52917i
$445$	20.8778			0.989705
$446$	32.8433	+	56.8863i	1.55518	+	2.69364i
$447$	−2.40917	−	15.9658i	−0.113950	−	0.755155i
$448$	−1.17411	−	1.17411i	−0.0554715	−	0.0554715i
$449$	−27.0696	+	7.25329i	−1.27750	+	0.342304i	−0.832898	−	0.553426i	$-0.813320\pi$
$449$	−27.0696	+	7.25329i	−1.27750	+	0.342304i	−0.444598	+	0.895730i	$0.646653\pi$
$450$	−38.0799	+	1.43755i	−1.79510	+	0.0677669i
$451$	−0.720648	+	1.24820i	−0.0339340	+	0.0587754i
$452$	−8.45607	+	14.6463i	−0.397740	+	0.688906i
$453$	−1.57263	−	10.4219i	−0.0738886	−	0.489666i
$454$	−13.2801	−	7.66726i	−0.623265	−	0.359842i
$455$	8.42261	+	7.64691i	0.394858	+	0.358492i
$456$	−8.26612	+	73.4738i	−0.387096	+	3.44073i
$457$	6.44588	−	1.72717i	0.301526	−	0.0807935i	−0.104884	−	0.994484i	$-0.533447\pi$
$457$	6.44588	−	1.72717i	0.301526	−	0.0807935i	0.406410	+	0.913691i	$0.366781\pi$
$458$	−5.81065	+	3.35478i	−0.271514	+	0.156758i
$459$	−19.4751	+	16.7766i	−0.909020	+	0.783066i
$460$	68.3178	+	68.3178i	3.18534	+	3.18534i
$461$	11.9578	−	11.9578i	0.556931	−	0.556931i	−0.371502	−	0.928432i	$-0.621157\pi$
$461$	11.9578	−	11.9578i	0.556931	−	0.556931i	0.928432	+	0.371502i	$0.121157\pi$
$462$	−0.385289	−	2.55334i	−0.0179253	−	0.118792i
$463$	8.87365	+	33.1169i	0.412394	+	1.53907i	0.789999	+	0.613108i	$0.210081\pi$
$463$	8.87365	+	33.1169i	0.412394	+	1.53907i	−0.377606	+	0.925966i	$0.623253\pi$
$464$	−13.3430	+	7.70361i	−0.619435	+	0.357631i
$465$	21.5173	−	29.1651i	0.997842	−	1.35250i
$466$	−3.34828	−	12.4959i	−0.155106	−	0.578863i
$467$	−29.0738			−1.34538			−0.672688	−	0.739927i	$-0.734860\pi$
$467$	−29.0738			−1.34538			−0.672688	+	0.739927i	$0.734860\pi$
$468$	20.9566	−	44.7895i	0.968718	−	2.07040i
$469$	1.31993			0.0609487
$470$	−15.9900	−	59.6754i	−0.737563	−	2.75262i
$471$	20.2955	+	2.28332i	0.935165	+	0.105210i
$472$	−16.0717	+	9.27900i	−0.739760	+	0.427100i
$473$	−0.231757	−	0.864930i	−0.0106562	−	0.0397695i
$474$	−33.6866	−	13.2145i	−1.54728	−	0.606964i
$475$	22.6877	−	22.6877i	1.04098	−	1.04098i
$476$	15.9914	+	15.9914i	0.732967	+	0.732967i
$477$	30.2756	+	28.0729i	1.38623	+	1.28537i
$478$	−26.6748	+	15.4007i	−1.22008	+	0.704413i
$479$	41.0413	−	10.9970i	1.87523	−	0.502465i	0.875408	−	0.483386i	$-0.160593\pi$
$479$	41.0413	−	10.9970i	1.87523	−	0.502465i	0.999818	−	0.0190795i	$-0.00607356\pi$
$480$	33.5533	−	14.6458i	1.53149	−	0.668487i
$481$	−27.6005	−	14.2069i	−1.25848	−	0.647779i
$482$	36.3222	+	20.9706i	1.65443	+	0.955186i
$483$	10.8003	+	4.23674i	0.491431	+	0.192778i
$484$	24.3709	−	42.2116i	1.10777	−	1.91871i
$485$	25.9749	−	44.9898i	1.17946	−	2.04288i
$486$	27.2050	+	29.2711i	1.23404	+	1.32776i
$487$	−4.56264	+	1.22256i	−0.206753	+	0.0553993i	−0.360709	−	0.932678i	$-0.617465\pi$
$487$	−4.56264	+	1.22256i	−0.206753	+	0.0553993i	0.153956	+	0.988078i	$0.450799\pi$
$488$	17.2231	+	17.2231i	0.779652	+	0.779652i
$489$	32.5862	−	25.9955i	1.47360	−	1.17556i
$490$	4.04416	+	7.00468i	0.182696	+	0.316439i
$491$	6.31163			0.284840			0.142420	−	0.989806i	$-0.454512\pi$
$491$	6.31163			0.284840			0.142420	+	0.989806i	$0.454512\pi$
$492$	−19.4042	+	2.92802i	−0.874809	+	0.132005i
$493$	8.50977	−	4.91312i	0.383261	−	0.221276i
$494$	18.2598	+	56.9969i	0.821546	+	2.56441i
$495$	5.36721	+	1.22315i	0.241238	+	0.0549764i
$496$	−13.3142	+	49.6891i	−0.597823	+	2.23111i
$497$	−0.424445	−	0.245053i	−0.0190389	−	0.0109921i
$498$	58.4208	−	25.5003i	2.61790	−	1.14270i
$499$	22.3236	−	5.98159i	0.999341	−	0.267773i	0.278172	−	0.960531i	$-0.410272\pi$
$499$	22.3236	−	5.98159i	0.999341	−	0.267773i	0.721169	+	0.692759i	$0.243605\pi$
$500$	0.626495	+	0.167869i	0.0280177	+	0.00750732i
$501$	8.80848	−	22.4546i	0.393534	−	1.00320i
$502$	27.2907	+	7.31251i	1.21804	+	0.326373i
$503$	22.0338	+	12.7212i	0.982438	+	0.567211i	0.903005	−	0.429629i	$-0.141356\pi$
$503$	22.0338	+	12.7212i	0.982438	+	0.567211i	0.0794327	+	0.996840i	$0.474689\pi$
$504$	13.4471	−	14.5022i	0.598983	−	0.645981i
$505$	−46.9149	−	12.5708i	−2.08768	−	0.559393i
$506$	−4.99302	−	8.64816i	−0.221967	−	0.384458i
$507$	0.350458	−	22.5139i	0.0155644	−	0.999879i
$508$	−4.89226	+	8.47364i	−0.217059	+	0.375957i
$509$	2.19648	−	2.19648i	0.0973574	−	0.0973574i	−0.656750	−	0.754108i	$-0.728070\pi$
$509$	2.19648	−	2.19648i	0.0973574	−	0.0973574i	0.754108	+	0.656750i	$0.228070\pi$
$510$	−63.5156	+	27.7242i	−2.81252	+	1.22765i
$511$		−	14.7179i		−	0.651080i
$512$	35.5719	−	35.5719i	1.57207	−	1.57207i
$513$	−33.5537	−	2.49764i	−1.48143	−	0.110273i
$514$	6.53471	+	24.3879i	0.288234	+	1.07570i
$515$	3.44365	−	12.8519i	0.151746	−	0.566322i
$516$	7.23812	−	9.81073i	0.318641	−	0.431893i
$517$			4.44216i			0.195366i
$518$	−15.6064	−	15.6064i	−0.685708	−	0.685708i
$519$	4.04280	+	9.26198i	0.177459	+	0.406556i
$520$	50.4116	−	55.5254i	2.21070	−	2.43495i
$521$			0.403015i			0.0176564i	0.999961	+	0.00882821i	$0.00281014\pi$
$521$			0.403015i			0.0176564i	−0.999961	+	0.00882821i	$0.997190\pi$
$522$	−8.13171	−	12.9320i	−0.355915	−	0.566017i
$523$	8.22407	+	14.2445i	0.359613	+	0.622869i	0.987896	−	0.155116i	$-0.0495753\pi$
$523$	8.22407	+	14.2445i	0.359613	+	0.622869i	−0.628283	+	0.777985i	$0.716242\pi$
$524$	−21.3756			−0.933796
$525$	−8.48630	+	1.28055i	−0.370372	+	0.0558878i
$526$	8.00572	−	29.8778i	0.349066	−	1.30273i
$527$	8.49135	−	31.6902i	0.369889	−	1.38045i
$528$	−7.72574	+	1.16578i	−0.336220	+	0.0507342i
$529$	21.8656			0.950677
$530$	55.6585	+	96.4033i	2.41765	+	4.18749i
$531$	−4.49547	−	7.14921i	−0.195087	−	0.310249i
$532$			29.6026i			1.28343i
$533$	−7.51406	+	4.83573i	−0.325470	+	0.209459i
$534$	−11.7536	−	26.9272i	−0.508627	−	1.16526i
$535$	19.5446	+	19.5446i	0.844988	+	0.844988i
$536$		−	8.70153i		−	0.375849i
$537$	7.69416	−	10.4289i	0.332028	−	0.450038i
$538$	−2.67249	+	9.97388i	−0.115219	+	0.430005i
$539$	−0.150521	−	0.561751i	−0.00648339	−	0.0241963i
$540$	32.5535	+	67.5118i	1.40088	+	2.90524i
$541$	−24.6486	+	24.6486i	−1.05972	+	1.05972i	−0.0616253	+	0.998099i	$0.519628\pi$
$541$	−24.6486	+	24.6486i	−1.05972	+	1.05972i	−0.998099	+	0.0616253i	$0.980372\pi$
$542$			61.6233i			2.64695i
$543$	14.7404	−	6.43408i	0.632570	−	0.276113i
$544$	23.4336	−	23.4336i	1.00471	−	1.00471i
$545$	−18.8187	+	32.5949i	−0.806103	+	1.39621i
$546$	5.12095	−	15.1680i	0.219156	−	0.649132i
$547$	−6.95077	−	12.0391i	−0.297193	−	0.514754i	0.678299	−	0.734786i	$-0.262717\pi$
$547$	−6.95077	−	12.0391i	−0.297193	−	0.514754i	−0.975493	+	0.220032i	$0.929384\pi$
$548$	17.9335	+	4.80526i	0.766080	+	0.205271i
$549$	−7.53642	+	8.12776i	−0.321647	+	0.346884i
$550$	6.39755	+	3.69363i	0.272793	+	0.157497i
$551$	12.4239	+	3.32897i	0.529276	+	0.141819i
$552$	27.9304	−	71.2003i	1.18879	−	3.03048i
$553$	−7.87199	−	2.10929i	−0.334751	−	0.0896962i
$554$	−60.3754	+	16.1775i	−2.56510	+	0.687317i
$555$	43.1216	−	18.8223i	1.83041	−	0.798963i
$556$	58.1955	+	33.5992i	2.46804	+	1.42492i
$557$	−4.74951	+	17.7254i	−0.201243	+	0.751050i	0.789319	+	0.613984i	$0.210434\pi$
$557$	−4.74951	+	17.7254i	−0.201243	+	0.751050i	−0.990562	+	0.137066i	$0.956233\pi$
$558$	−49.7293	−	11.3330i	−2.10521	−	0.479762i
$559$	1.17661	−	5.42536i	0.0497654	−	0.229468i
$560$	21.1944	−	12.2366i	0.895625	−	0.517089i
$561$	4.92724	−	0.743501i	0.208028	−	0.0313906i
$562$	−25.7500			−1.08620
$563$	8.41024	+	14.5670i	0.354449	+	0.613924i	0.987024	−	0.160575i	$-0.0513350\pi$
$563$	8.41024	+	14.5670i	0.354449	+	0.613924i	−0.632574	+	0.774500i	$0.718002\pi$
$564$	−47.2804	+	37.7177i	−1.99086	+	1.58820i
$565$	−8.25342	−	8.25342i	−0.347224	−	0.347224i
$566$	−12.7298	+	3.41095i	−0.535075	+	0.143373i
$567$	6.82566	+	5.86604i	0.286651	+	0.246351i
$568$	−1.61550	+	2.79812i	−0.0677847	+	0.117406i
$569$	1.23938	−	2.14667i	0.0519575	−	0.0899931i	−0.838877	−	0.544321i	$-0.816787\pi$
$569$	1.23938	−	2.14667i	0.0519575	−	0.0899931i	0.890834	+	0.454328i	$0.150121\pi$
$570$	−84.4493	−	33.1277i	−3.53719	−	1.38757i
$571$	−14.6454	−	8.45552i	−0.612890	−	0.353852i	0.161206	−	0.986921i	$-0.448462\pi$
$571$	−14.6454	−	8.45552i	−0.612890	−	0.353852i	−0.774096	+	0.633069i	$0.781795\pi$
$572$	−8.06107	+	5.18776i	−0.337050	+	0.216911i
$573$	6.64849	−	2.90202i	0.277744	−	0.121234i
$574$	−6.13668	+	1.64432i	−0.256140	+	0.0686325i
$575$	−28.7431	+	16.5948i	−1.19867	+	0.692053i
$576$	−3.65270	−	3.38695i	−0.152196	−	0.141123i
$577$	24.6642	+	24.6642i	1.02678	+	1.02678i	0.999631	+	0.0271507i	$0.00864339\pi$
$577$	24.6642	+	24.6642i	1.02678	+	1.02678i	0.0271507	+	0.999631i	$0.491357\pi$
$578$	−13.5437	+	13.5437i	−0.563344	+	0.563344i
$579$	−10.9555	−	4.29762i	−0.455296	−	0.178603i
$580$	−7.41557	−	27.6753i	−0.307915	−	1.14915i
$581$	12.4328	−	7.17810i	0.515801	−	0.297798i
$582$	−72.6487	−	8.17329i	−3.01139	−	0.338794i
$583$	−2.07157	−	7.73120i	−0.0857957	−	0.320194i
$584$	−97.0263			−4.01498
$585$	26.1152	+	21.9712i	1.07973	+	0.908397i
$586$	−73.3286			−3.02918
$587$	0.675221	+	2.51996i	0.0278694	+	0.104010i	0.978460	−	0.206439i	$-0.0661874\pi$
$587$	0.675221	+	2.51996i	0.0278694	+	0.104010i	−0.950590	+	0.310449i	$0.899521\pi$
$588$	4.70098	−	6.37183i	0.193865	−	0.262770i
$589$	37.1910	−	21.4722i	1.53243	−	0.884748i
$590$	−5.89305	−	21.9932i	−0.242613	−	0.905444i
$591$	1.69287	+	11.2188i	0.0696355	+	0.461480i
$592$	−47.2211	+	47.2211i	−1.94077	+	1.94077i
$593$	−14.9377	−	14.9377i	−0.613419	−	0.613419i	0.330416	−	0.943835i	$-0.392811\pi$
$593$	−14.9377	−	14.9377i	−0.613419	−	0.613419i	−0.943835	+	0.330416i	$0.892811\pi$
$594$	−1.44401	−	7.61096i	−0.0592485	−	0.312281i
$595$	−13.5171	+	7.80410i	−0.554147	+	0.319937i
$596$	−41.1655	+	11.0303i	−1.68620	+	0.451817i
$597$	0.786241	−	6.98854i	0.0321787	−	0.286022i
$598$	−2.98504	−	61.8386i	−0.122067	−	2.52877i
$599$	−27.2486	−	15.7320i	−1.11335	−	0.642791i	−0.173652	−	0.984807i	$-0.555557\pi$
$599$	−27.2486	−	15.7320i	−1.11335	−	0.642791i	−0.939694	+	0.342016i	$0.888890\pi$
$600$	8.44193	+	55.9453i	0.344640	+	2.28396i
$601$	11.5096	−	19.9352i	0.469486	−	0.813174i	−0.529905	−	0.848057i	$-0.677772\pi$
$601$	11.5096	−	19.9352i	0.469486	−	0.813174i	0.999391	+	0.0348828i	$0.0111058\pi$
$602$	1.97353	−	3.41825i	0.0804351	−	0.139318i
$603$	3.95697	−	0.149380i	0.161140	−	0.00608321i
$604$	−26.8715	+	7.20020i	−1.09339	+	0.292972i
$605$	23.7868	+	23.7868i	0.967071	+	0.967071i
$606$	10.1984	+	67.5855i	0.414281	+	2.74547i
$607$	4.67657	+	8.10005i	0.189816	+	0.328771i	0.945189	−	0.326524i	$-0.105878\pi$
$607$	4.67657	+	8.10005i	0.189816	+	0.328771i	−0.755373	+	0.655295i	$0.772544\pi$
$608$	43.3792			1.75926
$609$	−2.14554	−	2.68950i	−0.0869416	−	0.108984i
$610$	−25.8803	+	14.9420i	−1.04786	+	0.604984i
$611$	−12.6041	+	24.4866i	−0.509906	+	0.990622i
$612$	49.7500	+	46.1304i	2.01102	+	1.86471i
$613$	−0.721317	+	2.69199i	−0.0291337	+	0.108729i	−0.978962	−	0.204045i	$-0.934591\pi$
$613$	−0.721317	+	2.69199i	−0.0291337	+	0.108729i	0.949828	+	0.312773i	$0.101258\pi$
$614$	52.2681	+	30.1770i	2.10937	+	1.21784i
$615$	1.51416	−	13.4587i	0.0610570	−	0.542708i
$616$	−3.70330	+	0.992296i	−0.149210	+	0.0399808i
$617$	5.52730	+	1.48103i	0.222521	+	0.0596242i	0.368357	−	0.929685i	$-0.379921\pi$
$617$	5.52730	+	1.48103i	0.222521	+	0.0596242i	−0.145836	+	0.989309i	$0.546587\pi$
$618$	−18.5144	+	2.79376i	−0.744760	+	0.112381i
$619$	−34.2266	−	9.17098i	−1.37568	−	0.368613i	−0.506131	−	0.862456i	$-0.668925\pi$
$619$	−34.2266	−	9.17098i	−1.37568	−	0.368613i	−0.869551	+	0.493843i	$0.835592\pi$
$620$	−82.8461	−	47.8312i	−3.32718	−	1.92095i
$621$	32.8574	+	11.4789i	1.31852	+	0.460631i
$622$	−45.2330	−	12.1201i	−1.81368	−	0.485973i
$623$	−3.30852	−	5.73053i	−0.132553	−	0.229589i
$624$	−45.8946	−	15.4947i	−1.83725	−	0.620283i
$625$	−12.6114	+	21.8436i	−0.504456	+	0.873744i
$626$	−21.3447	+	21.3447i	−0.853105	+	0.853105i
$627$	5.24869	+	3.87236i	0.209613	+	0.154647i
$628$		−	53.9064i		−	2.15110i
$629$	30.1161	−	30.1161i	1.20081	−	1.20081i
$630$	12.9166	+	20.5414i	0.514608	+	0.818389i
$631$	10.8947	+	40.6595i	0.433710	+	1.61863i	0.744135	+	0.668030i	$0.232862\pi$
$631$	10.8947	+	40.6595i	0.433710	+	1.61863i	−0.310425	+	0.950598i	$0.600471\pi$
$632$	−13.9054	+	51.8955i	−0.553125	+	2.06429i
$633$	−3.99365	−	9.14937i	−0.158733	−	0.363655i
$634$			68.6098i			2.72484i
$635$	−4.77501	−	4.77501i	−0.189491	−	0.189491i
$636$	64.6982	−	87.6935i	2.56545	−	3.47727i
$637$	0.764181	−	3.52364i	0.0302779	−	0.139612i
$638$			2.96137i			0.117242i
$639$	−1.30016	−	0.686601i	−0.0514336	−	0.0271615i
$640$	14.4220	+	24.9796i	0.570078	+	0.987404i
$641$	−17.6032			−0.695286			−0.347643	−	0.937627i	$-0.613018\pi$
$641$	−17.6032			−0.695286			−0.347643	+	0.937627i	$0.613018\pi$
$642$	14.2047	−	36.2107i	0.560615	−	1.42912i
$643$	3.84780	−	14.3602i	0.151742	−	0.566311i	−0.847620	−	0.530604i	$-0.821965\pi$
$643$	3.84780	−	14.3602i	0.151742	−	0.566311i	0.999362	−	0.0357066i	$-0.0113682\pi$
$644$	7.92545	−	29.5782i	0.312307	−	1.16554i
$645$	5.24734	+	6.57771i	0.206614	+	0.258997i
$646$	−82.1157			−3.23080
$647$	15.5851	+	26.9942i	0.612714	+	1.06125i	0.990781	+	0.135473i	$0.0432554\pi$
$647$	15.5851	+	26.9942i	0.612714	+	1.06125i	−0.378067	+	0.925778i	$0.623411\pi$
$648$	38.6714	−	44.9976i	1.51916	−	1.76767i
$649$			1.63714i			0.0642634i
$650$	24.7852	+	38.5128i	0.972155	+	1.51059i
$651$	−11.4151	−	1.28424i	−0.447392	−	0.0503335i
$652$	−77.7990	−	77.7990i	−3.04685	−	3.04685i
$653$			21.7116i			0.849642i	0.905277	+	0.424821i	$0.139663\pi$
$653$			21.7116i			0.849642i	−0.905277	+	0.424821i	$0.860337\pi$
$654$	52.6337	+	5.92151i	2.05814	+	0.231549i
$655$	3.81825	−	14.2499i	0.149191	−	0.556790i
$656$	4.97528	+	18.5680i	0.194252	+	0.724959i
$657$	−1.66566	−	44.1221i	−0.0649834	−	1.72137i
$658$	−13.8457	+	13.8457i	−0.539762	+	0.539762i
$659$		−	0.137034i		−	0.00533810i	−0.999996	−	0.00266905i	$-0.999150\pi$
$659$		−	0.137034i		−	0.00533810i	0.999996	−	0.00266905i	$-0.000849587\pi$
$660$	1.62439	−	14.4385i	0.0632294	−	0.562018i
$661$	−11.9150	+	11.9150i	−0.463439	+	0.463439i	−0.899781	−	0.436342i	$-0.856274\pi$
$661$	−11.9150	+	11.9150i	−0.463439	+	0.463439i	0.436342	+	0.899781i	$0.356274\pi$
$662$	−3.47365	+	6.01653i	−0.135007	+	0.233839i
$663$	29.2701	+	9.88201i	1.13676	+	0.383785i
$664$	−47.3211	−	81.9625i	−1.83641	−	3.18076i
$665$	−19.7344	−	5.28781i	−0.765266	−	0.205052i
$666$	−48.5522	−	45.0198i	−1.88136	−	1.74448i
$667$	−11.5224	−	6.65246i	−0.446149	−	0.257584i
$668$	−61.4952	−	16.4776i	−2.37932	−	0.637537i
$669$	27.6771	+	34.6942i	1.07006	+	1.34135i
$670$	10.3122	+	2.76315i	0.398396	+	0.106750i
$671$	2.07551	−	0.556131i	0.0801241	−	0.0214692i
$672$	−9.33718	−	6.88875i	−0.360190	−	0.265739i
$673$	35.8568	+	20.7019i	1.38218	+	0.798001i	0.992417	−	0.122915i	$-0.0392241\pi$
$673$	35.8568	+	20.7019i	1.38218	+	0.798001i	0.389762	+	0.920916i	$0.372557\pi$
$674$	−9.24843	+	34.5156i	−0.356236	+	1.32949i
$675$	−25.2959	+	4.79933i	−0.973638	+	0.184726i
$676$	−59.1549	+	5.72433i	−2.27519	+	0.220167i
$677$	−16.6401	+	9.60716i	−0.639530	+	0.369233i	−0.784434	−	0.620213i	$-0.787046\pi$
$677$	−16.6401	+	9.60716i	−0.639530	+	0.369233i	0.144903	+	0.989446i	$0.453713\pi$
$678$	−5.99845	+	15.2913i	−0.230369	+	0.587258i
$679$	−16.4650			−0.631869
$680$	51.4479	+	89.1105i	1.97294	+	3.41723i
$681$	−9.64525	−	3.78363i	−0.369607	−	0.144989i
$682$	6.99151	+	6.99151i	0.267719	+	0.267719i
$683$	40.6094	−	10.8813i	1.55388	−	0.416360i	0.623158	−	0.782096i	$-0.285850\pi$
$683$	40.6094	−	10.8813i	1.55388	−	0.416360i	0.930718	+	0.365736i	$0.119183\pi$
$684$	3.35019	+	88.7445i	0.128098	+	3.39323i
$685$	−6.40680	+	11.0969i	−0.244791	+	0.423991i
$686$	1.28176	−	2.22007i	0.0489378	−	0.0847628i
$687$	−3.54383	+	2.82708i	−0.135206	+	0.107860i
$688$	−10.3428	−	5.97139i	−0.394314	−	0.227657i
$689$	10.5172	−	48.4947i	0.400673	−	1.84750i
$690$	75.5105	+	55.7099i	2.87464	+	2.12084i
$691$	33.2013	−	8.89625i	1.26304	−	0.338429i	0.435677	−	0.900103i	$-0.356509\pi$
$691$	33.2013	−	8.89625i	1.26304	−	0.338429i	0.827359	+	0.561674i	$0.189842\pi$
$692$	23.1001	−	13.3369i	0.878135	−	0.506992i
$693$	−0.514815	−	1.66702i	−0.0195562	−	0.0633248i
$694$	44.2949	+	44.2949i	1.68141	+	1.68141i
$695$	−32.7940	+	32.7940i	−1.24395	+	1.24395i
$696$	−17.7303	+	14.1443i	−0.672067	+	0.536138i
$697$	−3.17308	−	11.8421i	−0.120189	−	0.448551i
$698$	63.0742	−	36.4159i	2.38739	−	1.37836i
$699$	−3.49670	−	8.01087i	−0.132257	−	0.302999i
$700$	5.86292	+	21.8807i	0.221598	+	0.827013i
$701$	0.518691			0.0195907			0.00979534	−	0.999952i	$-0.496882\pi$
$701$	0.518691			0.0195907			0.00979534	+	0.999952i	$0.496882\pi$
$702$	13.6353	−	46.0513i	0.514631	−	1.73809i
$703$	55.7495			2.10263
$704$	0.249931	+	0.932756i	0.00941963	+	0.0351546i
$705$	−16.6988	−	38.2566i	−0.628912	−	1.44083i
$706$	−61.6965	+	35.6205i	−2.32198	+	1.34060i
$707$	3.98420	+	14.8693i	0.149841	+	0.559216i
$708$	−17.4250	+	13.9007i	−0.654872	+	0.522421i
$709$	−0.124715	+	0.124715i	−0.00468378	+	0.00468378i	−0.709445	−	0.704761i	$-0.751054\pi$
$709$	−0.124715	+	0.124715i	−0.00468378	+	0.00468378i	0.704761	+	0.709445i	$0.251054\pi$
$710$	−2.80307	−	2.80307i	−0.105197	−	0.105197i
$711$	−23.8379	−	5.43248i	−0.893990	−	0.203734i
$712$	−37.7781	+	21.8112i	−1.41579	+	0.817409i
$713$	−42.9091	+	11.4975i	−1.60696	+	0.430583i
$714$	17.6751	+	13.0402i	0.661473	+	0.488019i
$715$	−2.01847	−	6.30054i	−0.0754864	−	0.235627i
$716$	−29.6241	−	17.1035i	−1.10711	−	0.639188i
$717$	−16.2686	+	12.9782i	−0.607563	+	0.484681i
$718$	8.13353	−	14.0877i	0.303540	−	0.525748i
$719$	−9.40670	+	16.2929i	−0.350811	+	0.607622i	−0.986392	−	0.164412i	$-0.947427\pi$
$719$	−9.40670	+	16.2929i	−0.350811	+	0.607622i	0.635581	+	0.772034i	$0.280761\pi$
$720$	62.1530	−	39.0822i	2.31630	−	1.45651i
$721$	−4.07329	+	1.09144i	−0.151697	+	0.0406472i
$722$	−41.5633	−	41.5633i	−1.54683	−	1.54683i
$723$	26.3806	+	10.3485i	0.981105	+	0.384867i
$724$	−21.2255	−	36.7637i	−0.788840	−	1.36631i
$725$	9.84243			0.365539
$726$	17.2878	−	44.0703i	0.641612	−	1.63560i
$727$	−20.3528	+	11.7507i	−0.754843	+	0.435809i	−0.827441	−	0.561552i	$-0.810204\pi$
$727$	−20.3528	+	11.7507i	−0.754843	+	0.435809i	0.0725979	+	0.997361i	$0.476871\pi$
$728$	−23.2293	−	5.03780i	−0.860936	−	0.186713i
$729$	21.1263	+	16.8131i	0.782454	+	0.622708i
$730$	30.8105	−	114.986i	1.14035	−	4.25584i
$731$	6.59629	+	3.80837i	0.243972	+	0.140858i
$732$	23.5421	+	17.3688i	0.870140	+	0.641968i
$733$	18.2968	−	4.90262i	0.675808	−	0.181082i	0.0954385	−	0.995435i	$-0.469575\pi$
$733$	18.2968	−	4.90262i	0.675808	−	0.181082i	0.580370	+	0.814353i	$0.302908\pi$
$734$	72.4276	+	19.4069i	2.67335	+	0.716323i
$735$	3.40802	+	4.27206i	0.125707	+	0.157577i
$736$	−43.3434	−	11.6138i	−1.59766	−	0.428092i
$737$	−0.664785	−	0.383814i	−0.0244877	−	0.0141380i
$738$	−18.2108	+	5.62395i	−0.670350	+	0.207020i
$739$	42.5064	+	11.3896i	1.56362	+	0.418972i	0.933809	−	0.357773i	$-0.116464\pi$
$739$	42.5064	+	11.3896i	1.56362	+	0.418972i	0.629816	+	0.776744i	$0.283130\pi$
$740$	−62.0933	−	107.549i	−2.28260	−	3.95357i
$741$	17.9452	+	36.2382i	0.659232	+	1.33124i
$742$	17.6405	−	30.5542i	0.647602	−	1.12168i
$743$	−13.2793	+	13.2793i	−0.487171	+	0.487171i	−0.907412	−	0.420241i	$-0.861945\pi$
$743$	−13.2793	+	13.2793i	−0.487171	+	0.487171i	0.420241	+	0.907412i	$0.361945\pi$
$744$	−8.46628	+	75.2530i	−0.310389	+	2.75891i
$745$		−	29.4130i		−	1.07761i
$746$	−36.8281	+	36.8281i	−1.34837	+	1.34837i
$747$	36.4596	−	22.9260i	1.33399	−	0.838820i
$748$	−3.40407	−	12.7042i	−0.124465	−	0.464511i
$749$	2.26734	−	8.46184i	0.0828469	−	0.309189i
$750$	0.625992	+	0.0704267i	0.0228580	+	0.00257162i
$751$		−	38.2653i		−	1.39632i	−0.715941	−	0.698161i	$-0.754002\pi$
$751$		−	38.2653i		−	1.39632i	0.715941	−	0.698161i	$-0.245998\pi$
$752$	41.8935	+	41.8935i	1.52770	+	1.52770i
$753$	18.9698	+	2.13419i	0.691299	+	0.0777740i
$754$	−8.40252	+	16.3240i	−0.306002	+	0.594486i
$755$		−	19.1999i		−	0.698755i
$756$	13.3718	−	19.6339i	0.486327	−	0.714078i
$757$	−7.71838	−	13.3686i	−0.280529	−	0.485891i	0.690986	−	0.722868i	$-0.257177\pi$
$757$	−7.71838	−	13.3686i	−0.280529	−	0.485891i	−0.971515	+	0.236977i	$0.923843\pi$
$758$	39.0471			1.41826
$759$	−4.20763	−	5.27440i	−0.152727	−	0.191448i
$760$	−34.8595	+	130.097i	−1.26449	+	4.71913i
$761$	8.93299	−	33.3384i	0.323821	−	1.20851i	−0.591672	−	0.806179i	$-0.701532\pi$
$761$	8.93299	−	33.3384i	0.323821	−	1.20851i	0.915492	−	0.402336i	$-0.131801\pi$
$762$	−3.47040	+	8.84676i	−0.125719	+	0.320484i
$763$	11.9288			0.431852
$764$	−9.57355	−	16.5819i	−0.346359	−	0.599911i
$765$	−39.6392	+	24.9254i	−1.43316	+	0.901180i
$766$		−	27.0529i		−	0.977461i
$767$	−4.64519	+	9.02445i	−0.167728	+	0.325854i
$768$	27.5132	−	37.2920i	0.992796	−	1.34566i
$769$	8.22657	+	8.22657i	0.296658	+	0.296658i	0.839703	−	0.543046i	$-0.182729\pi$
$769$	8.22657	+	8.22657i	0.296658	+	0.296658i	−0.543046	+	0.839703i	$0.682729\pi$
$770$		−	4.70390i		−	0.169517i
$771$	6.82438	+	15.6345i	0.245774	+	0.563064i
$772$	−8.03934	+	30.0032i	−0.289342	+	1.07984i
$773$	12.2125	+	45.5776i	0.439252	+	1.63931i	0.730680	+	0.682720i	$0.239203\pi$
$773$	12.2125	+	45.5776i	0.439252	+	1.63931i	−0.291428	+	0.956593i	$0.594130\pi$
$774$	5.52952	−	10.4708i	0.198755	−	0.376366i
$775$	23.2370	−	23.2370i	0.834699	−	0.834699i
$776$			108.544i			3.89652i
$777$	−11.9998	−	8.85319i	−0.430492	−	0.317607i
$778$	−17.9378	+	17.9378i	−0.643102	+	0.643102i
$779$	8.02382	−	13.8977i	0.287483	−	0.497936i
$780$	49.9216	−	74.9807i	1.78748	−	2.68474i
$781$	0.142515	+	0.246843i	0.00509959	+	0.00883274i
$782$	82.0481	+	21.9847i	2.93403	+	0.786172i
$783$	−6.73641	−	7.81995i	−0.240740	−	0.279462i
$784$	−6.71736	−	3.87827i	−0.239906	−	0.138510i
$785$	35.9364	+	9.62913i	1.28263	+	0.343678i
$786$	−20.5284	+	3.09766i	−0.732224	+	0.110490i
$787$	−22.0900	−	5.91899i	−0.787422	−	0.210989i	−0.157368	−	0.987540i	$-0.550301\pi$
$787$	−22.0900	−	5.91899i	−0.787422	−	0.210989i	−0.630054	+	0.776551i	$0.716967\pi$
$788$	28.9261	−	7.75072i	1.03045	−	0.276108i
$789$	2.33650	−	20.7681i	0.0831817	−	0.739365i
$790$	−57.0859	−	32.9586i	−2.03103	−	1.17261i
$791$	−0.957467	+	3.57331i	−0.0340436	+	0.127052i
$792$	−10.9897	+	3.39388i	−0.390502	+	0.120596i
$793$	13.0188	+	2.82343i	0.462312	+	0.100263i
$794$	−73.5682	+	42.4746i	−2.61084	+	1.50737i
$795$	46.9035	+	58.7950i	1.66350	+	2.08525i
$796$	−18.5622			−0.657918
$797$	−7.17533	−	12.4280i	−0.254163	−	0.440223i	0.710505	−	0.703692i	$-0.248467\pi$
$797$	−7.17533	−	12.4280i	−0.254163	−	0.440223i	−0.964668	+	0.263469i	$0.915133\pi$
$798$	4.28987	+	28.4293i	0.151860	+	1.00639i
$799$	−26.7184	−	26.7184i	−0.945229	−	0.945229i
$800$	32.0637	−	8.59144i	1.13362	−	0.303753i
$801$	−10.5670	−	16.8049i	−0.373368	−	0.593773i
$802$	−26.8928	+	46.5797i	−0.949618	+	1.64479i
$803$	−4.27971	+	7.41268i	−0.151028	+	0.261588i
$804$	−1.55945	−	10.3346i	−0.0549976	−	0.364473i
$805$	18.3024	+	10.5669i	0.645076	+	0.372435i
$806$	18.7019	+	58.3770i	0.658747	+	2.05624i
$807$	−0.779978	+	6.93287i	−0.0274565	+	0.244049i
$808$	98.0244	−	26.2656i	3.44849	−	0.924019i
$809$	−30.0319	+	17.3389i	−1.05587	+	0.609605i	−0.924286	−	0.381701i	$-0.875339\pi$
$809$	−30.0319	+	17.3389i	−1.05587	+	0.609605i	−0.131581	+	0.991305i	$0.542005\pi$
$810$	41.0468	+	60.1186i	1.44224	+	2.11235i
$811$	1.42519	+	1.42519i	0.0500454	+	0.0500454i	0.731687	−	0.681641i	$-0.238733\pi$
$811$	1.42519	+	1.42519i	0.0500454	+	0.0500454i	−0.681641	+	0.731687i	$0.738733\pi$
$812$	−6.42114	+	6.42114i	−0.225338	+	0.225338i
$813$	6.21239	+	41.1699i	0.217878	+	1.44389i
$814$	3.32212	+	12.3983i	0.116440	+	0.434561i
$815$	65.7613	−	37.9673i	2.30352	−	1.32994i
$816$	39.4564	−	53.4802i	1.38125	−	1.87218i
$817$	2.58043	+	9.63029i	0.0902777	+	0.336921i
$818$	−81.3365			−2.84386
$819$	1.89213	−	10.6499i	0.0661164	−	0.372137i
$820$	−35.7475			−1.24836
$821$	8.95869	+	33.4343i	0.312660	+	1.16686i	0.926148	+	0.377160i	$0.123099\pi$
$821$	8.95869	+	33.4343i	0.312660	+	1.16686i	−0.613488	+	0.789704i	$0.710234\pi$
$822$	17.9191	+	2.01597i	0.624999	+	0.0703151i
$823$	−27.8047	+	16.0530i	−0.969209	+	0.559573i	−0.898995	−	0.437959i	$-0.855702\pi$
$823$	−27.8047	+	16.0530i	−0.969209	+	0.559573i	−0.0702141	+	0.997532i	$0.522368\pi$
$824$	7.19521	+	26.8529i	0.250657	+	0.935465i
$825$	4.64651	+	1.82273i	0.161771	+	0.0634592i
$826$	−5.10279	+	5.10279i	−0.177549	+	0.177549i
$827$	−12.4366	−	12.4366i	−0.432462	−	0.432462i	0.457003	−	0.889465i	$-0.348923\pi$
$827$	−12.4366	−	12.4366i	−0.432462	−	0.432462i	−0.889465	+	0.457003i	$0.848923\pi$
$828$	20.4120	−	89.5683i	0.709366	−	3.11272i
$829$	−18.0440	+	10.4177i	−0.626694	+	0.361822i	−0.779471	−	0.626439i	$-0.784512\pi$
$829$	−18.0440	+	10.4177i	−0.626694	+	0.361822i	0.152777	+	0.988261i	$0.451178\pi$
$830$	112.161	−	30.0534i	3.89316	−	1.04317i
$831$	−38.7053	+	16.8946i	−1.34267	+	0.586068i
$832$	−1.26888	+	5.85080i	−0.0439904	+	0.202840i
$833$	4.28413	+	2.47344i	0.148436	+	0.0856996i
$834$	60.7581	+	23.8341i	2.10388	+	0.825307i
$835$	21.9694	−	38.0520i	0.760281	−	1.31685i
$836$	8.60794	−	14.9094i	0.297712	−	0.515652i
$837$	−34.3662	−	2.55812i	−1.18787	−	0.0884215i
$838$	45.5036	−	12.1926i	1.57189	−	0.421188i
$839$	−18.3381	−	18.3381i	−0.633101	−	0.633101i	0.315743	−	0.948845i	$-0.397746\pi$
$839$	−18.3381	−	18.3381i	−0.633101	−	0.633101i	−0.948845	+	0.315743i	$0.897746\pi$
$840$	28.1632	−	22.4671i	0.971724	−	0.775189i
$841$	−12.5272	−	21.6978i	−0.431973	−	0.748199i
$842$	0.719476			0.0247948
$843$	−17.2033	+	2.59591i	−0.592513	+	0.0894079i
$844$	−22.8193	+	13.1747i	−0.785472	+	0.453493i
$845$	6.75055	−	40.4578i	0.232226	−	1.39179i
$846$	−39.9406	+	43.0745i	−1.37319	+	1.48093i
$847$	2.75947	−	10.2985i	0.0948166	−	0.353860i
$848$	−92.4490	−	53.3754i	−3.17471	−	1.83292i
$849$	−8.16082	+	3.56215i	−0.280078	+	0.122253i
$850$	−60.6958	+	16.2634i	−2.08185	+	0.557830i
$851$	−55.7035	−	14.9257i	−1.90949	−	0.511647i
$852$	−1.41722	+	3.61278i	−0.0485530	+	0.123772i
$853$	48.6244	+	13.0289i	1.66487	+	0.446100i	0.963720	−	0.266915i	$-0.0860041\pi$
$853$	48.6244	+	13.0289i	1.66487	+	0.446100i	0.701149	+	0.713015i	$0.252671\pi$
$854$	8.20253	+	4.73573i	0.280685	+	0.162053i
$855$	−59.7594	−	13.6188i	−2.04373	−	0.465751i
$856$	−55.7840	−	14.9473i	−1.90666	−	0.510888i
$857$	24.7907	+	42.9387i	0.846834	+	1.46676i	0.884019	+	0.467451i	$0.154828\pi$
$857$	24.7907	+	42.9387i	0.846834	+	1.46676i	−0.0371852	+	0.999308i	$0.511839\pi$
$858$	−6.98980	+	6.15033i	−0.238628	+	0.209969i
$859$	2.49414	−	4.31998i	0.0850990	−	0.147396i	−0.820334	−	0.571884i	$-0.806213\pi$
$859$	2.49414	−	4.31998i	0.0850990	−	0.147396i	0.905433	+	0.424488i	$0.139546\pi$
$860$	15.7042	−	15.7042i	0.535507	−	0.535507i
$861$	−3.93409	+	1.71721i	−0.134073	+	0.0585222i
$862$			20.5674i			0.700528i
$863$	8.08826	−	8.08826i	0.275328	−	0.275328i	−0.555913	−	0.831241i	$-0.687631\pi$
$863$	8.08826	−	8.08826i	0.275328	−	0.275328i	0.831241	+	0.555913i	$0.187631\pi$
$864$	−28.7712	−	19.5948i	−0.978817	−	0.666630i
$865$	4.76464	+	17.7819i	0.162003	+	0.604602i
$866$	−14.6761	+	54.7719i	−0.498714	+	1.86123i
$867$	−7.68305	+	10.4138i	−0.260930	+	0.353671i
$868$			30.3194i			1.02911i
$869$	3.35140	+	3.35140i	0.113688	+	0.113688i
$870$	−11.1322	−	25.5038i	−0.377419	−	0.864660i
$871$	−2.57549	−	4.00195i	−0.0872671	−	0.135601i
$872$		−	78.6399i		−	2.66308i
$873$	−49.3599	+	1.86339i	−1.67058	+	0.0630660i
$874$	55.5932	+	96.2902i	1.88047	+	3.25706i
$875$	0.141874			0.00479622
$876$	−115.236	+	17.3886i	−3.89346	+	0.587508i
$877$	−10.2342	+	38.1945i	−0.345584	+	1.28974i	0.546345	+	0.837560i	$0.316019\pi$
$877$	−10.2342	+	38.1945i	−0.345584	+	1.28974i	−0.891929	+	0.452175i	$0.850648\pi$
$878$	−17.2245	+	64.2825i	−0.581297	+	2.16943i
$879$	−48.9901	+	7.39242i	−1.65240	+	0.249340i
$880$	−14.2328			−0.479787
$881$	−22.7301	−	39.3698i	−0.765798	−	1.32640i	−0.939824	−	0.341660i	$-0.889011\pi$
$881$	−22.7301	−	39.3698i	−0.765798	−	1.32640i	0.174025	−	0.984741i	$-0.444323\pi$
$882$	3.59129	−	6.80054i	0.120925	−	0.228986i
$883$			16.8337i			0.566499i	0.959046	+	0.283249i	$0.0914124\pi$
$883$			16.8337i			0.566499i	−0.959046	+	0.283249i	$0.908588\pi$
$884$	17.2822	−	79.6882i	0.581263	−	2.68020i
$885$	−6.15427	−	14.0993i	−0.206873	−	0.473944i
$886$	18.6703	+	18.6703i	0.627241	+	0.627241i
$887$		−	41.1481i		−	1.38162i	−0.723037	−	0.690809i	$-0.757255\pi$
$887$		−	41.1481i		−	1.38162i	0.723037	−	0.690809i	$-0.242745\pi$
$888$	−58.3640	+	79.1080i	−1.95857	+	2.65469i
$889$	−0.553942	+	2.06734i	−0.0185786	+	0.0693363i
$890$	−13.8522	−	51.6971i	−0.464326	−	1.73289i
$891$	−1.73201	−	4.93923i	−0.0580244	−	0.165471i
$892$	82.8317	−	82.8317i	2.77341	−	2.77341i
$893$		−	49.4598i		−	1.65511i
$894$	−37.9355	+	16.5586i	−1.26875	+	0.553803i
$895$	16.6936	−	16.6936i	0.558006	−	0.558006i
$896$	4.57091	−	7.91705i	0.152703	−	0.264490i
$897$	−8.22836	−	41.0128i	−0.274737	−	1.36938i
$898$	35.9207	+	62.2166i	1.19869	+	2.07619i
$899$	12.7247	+	3.40958i	0.424394	+	0.113716i
$900$	20.0525	+	64.9319i	0.668418	+	2.16440i
$901$	58.9611	+	34.0412i	1.96428	+	1.13408i
$902$	3.56889	+	0.956282i	0.118831	+	0.0318407i
$903$	0.973895	−	2.48266i	0.0324092	−	0.0826177i
$904$	23.5568	+	6.31203i	0.783488	+	0.209935i
$905$	28.2997	−	7.58289i	0.940715	−	0.252064i
$906$	−24.7631	+	10.8089i	−0.822698	+	0.359103i
$907$	31.4003	+	18.1290i	1.04263	+	0.601962i	0.920577	−	0.390561i	$-0.127719\pi$
$907$	31.4003	+	18.1290i	1.04263	+	0.601962i	0.122052	+	0.992524i	$0.461052\pi$
$908$	−7.07785	+	26.4149i	−0.234887	+	0.876609i
$909$	13.6269	+	44.1251i	0.451976	+	1.46354i
$910$	13.3467	−	25.9294i	0.442440	−	0.859552i
$911$	47.5755	−	27.4677i	1.57625	−	0.910046i	0.580870	−	0.813996i	$-0.302712\pi$
$911$	47.5755	−	27.4677i	1.57625	−	0.910046i	0.995377	−	0.0960500i	$-0.0306209\pi$
$912$	86.0198	−	12.9800i	2.84840	−	0.429812i
$913$	−8.34910			−0.276315
$914$	−8.55352	−	14.8151i	−0.282925	−	0.490041i
$915$	−15.7840	+	12.5917i	−0.521804	+	0.416267i
$916$	8.46084	+	8.46084i	0.279554	+	0.279554i
$917$	−4.51638	+	1.21016i	−0.149144	+	0.0399630i
$918$	54.4632	+	37.0926i	1.79755	+	1.22424i
$919$	14.8178	−	25.6652i	0.488794	−	0.846615i	−0.511123	−	0.859507i	$-0.670770\pi$
$919$	14.8178	−	25.6652i	0.488794	−	0.846615i	0.999917	+	0.0128920i	$0.00410377\pi$
$920$	69.6616	−	120.657i	2.29667	−	3.97796i
$921$	37.9620	+	14.8917i	1.25089	+	0.490698i
$922$	−37.5434	−	21.6757i	−1.23643	−	0.713851i
$923$	0.0852016	+	1.76505i	0.00280444	+	0.0580973i
$924$	−4.22048	+	1.84222i	−0.138844	+	0.0606044i
$925$	41.2072	−	11.0414i	1.35488	−	0.363040i
$926$	76.1156	−	43.9453i	2.50131	−	1.44413i
$927$	−12.0877	+	3.73296i	−0.397011	+	0.122607i
$928$	9.40944	+	9.40944i	0.308880	+	0.308880i
$929$	−13.5013	+	13.5013i	−0.442963	+	0.442963i	−0.893007	−	0.450043i	$-0.851409\pi$
$929$	−13.5013	+	13.5013i	−0.442963	+	0.442963i	0.450043	+	0.893007i	$0.351409\pi$
$930$	−86.4942	−	33.9298i	−2.83626	−	1.11260i
$931$	1.67592	+	6.25464i	0.0549262	+	0.204987i
$932$	−19.9798	+	11.5353i	−0.654459	+	0.377852i
$933$	−31.4416	−	3.53731i	−1.02935	−	0.115806i
$934$	19.2901	+	71.9917i	0.631192	+	2.35564i
$935$	9.07722			0.296857
$936$	−70.2085	−	12.4737i	−2.29484	−	0.407717i
$937$	−15.2534			−0.498307			−0.249153	−	0.968464i	$-0.580152\pi$
$937$	−15.2534			−0.498307			−0.249153	+	0.968464i	$0.580152\pi$
$938$	−0.875757	−	3.26837i	−0.0285945	−	0.106716i
$939$	−12.1084	+	16.4120i	−0.395142	+	0.535585i
$940$	−95.4150	+	55.0879i	−3.11210	+	1.79677i
$941$	−7.68792	−	28.6917i	−0.250619	−	0.935323i	−0.970475	−	0.241200i	$-0.922459\pi$
$941$	−7.68792	−	28.6917i	−0.250619	−	0.935323i	0.719856	−	0.694123i	$-0.244208\pi$
$942$	−7.81188	−	51.7699i	−0.254525	−	1.68676i
$943$	−11.7380	+	11.7380i	−0.382242	+	0.382242i
$944$	15.4397	+	15.4397i	0.502520	+	0.502520i
$945$	10.7003	+	12.4214i	0.348079	+	0.404067i
$946$	−1.98795	+	1.14774i	−0.0646337	+	0.0373163i
$947$	−48.3591	+	12.9578i	−1.57146	+	0.421071i	−0.936269	−	0.351284i	$-0.885745\pi$
$947$	−48.3591	+	12.9578i	−1.57146	+	0.421071i	−0.635190	+	0.772356i	$0.719078\pi$
$948$	−7.21456	+	64.1270i	−0.234318	+	2.08275i
$949$	−44.6237	+	28.7179i	−1.44855	+	0.932224i
$950$	−71.2315	−	41.1255i	−2.31105	−	1.33429i
$951$	6.91671	+	45.8376i	0.224290	+	1.48638i
$952$	16.3060	−	28.2428i	0.528480	−	0.915353i
$953$	12.0625	−	20.8929i	0.390743	−	0.676787i	−0.601805	−	0.798643i	$-0.705551\pi$
$953$	12.0625	−	20.8929i	0.390743	−	0.676787i	0.992548	+	0.121856i	$0.0388847\pi$
$954$	49.4258	−	93.5937i	1.60022	−	3.03021i
$955$	12.7643	−	3.42018i	0.413043	−	0.110675i
$956$	38.8410	+	38.8410i	1.25621	+	1.25621i
$957$	0.298542	+	1.97846i	0.00965050	+	0.0639546i
$958$	−54.4608	−	94.3289i	−1.75955	−	3.04763i
$959$	4.06116			0.131142
$960$	−5.65882	−	7.09352i	−0.182638	−	0.228942i
$961$	11.2448	−	6.49218i	0.362735	−	0.209425i
$962$	−16.8661	+	77.7697i	−0.543785	+	2.50740i
$963$	5.83954	−	25.6240i	0.188177	−	0.825723i
$964$	19.3585	−	72.2470i	0.623496	−	2.32692i
$965$	−18.5654	−	10.7188i	−0.597642	−	0.345049i
$966$	3.32500	−	29.5544i	0.106980	−	0.950898i
$967$	12.3369	−	3.30566i	0.396727	−	0.106303i	−0.0549389	−	0.998490i	$-0.517496\pi$
$967$	12.3369	−	3.30566i	0.396727	−	0.106303i	0.451666	+	0.892187i	$0.350830\pi$
$968$	−67.8920	−	18.1916i	−2.18213	−	0.584700i
$969$	−54.8607	+	8.27827i	−1.76238	+	0.265936i
$970$	−128.636	−	34.4680i	−4.13027	−	1.10670i
$971$	1.67606	+	0.967671i	0.0537872	+	0.0310541i	0.526652	−	0.850081i	$-0.323447\pi$
$971$	1.67606	+	0.967671i	0.0537872	+	0.0310541i	−0.472865	+	0.881135i	$0.656780\pi$
$972$	37.8648	−	60.3731i	1.21451	−	1.93647i
$973$	14.1981	+	3.80438i	0.455171	+	0.121963i
$974$	6.05451	+	10.4867i	0.193999	+	0.336016i
$975$	20.4413	+	23.2314i	0.654645	+	0.743999i
$976$	14.3291	−	24.8187i	0.458663	−	0.794428i
$977$	9.40591	−	9.40591i	0.300922	−	0.300922i	−0.540453	−	0.841374i	$-0.681747\pi$
$977$	9.40591	−	9.40591i	0.300922	−	0.300922i	0.841374	+	0.540453i	$0.181747\pi$
$978$	−85.9899	−	63.4413i	−2.74965	−	2.02863i
$979$			3.84826i			0.122991i
$980$	10.1995	−	10.1995i	0.325810	−	0.325810i
$981$	35.7610	−	1.35001i	1.14176	−	0.0431026i
$982$	−4.18769	−	15.6287i	−0.133634	−	0.498730i
$983$	−1.84851	+	6.89875i	−0.0589585	+	0.220036i	−0.989119	−	0.147117i	$-0.953001\pi$
$983$	−1.84851	+	6.89875i	−0.0589585	+	0.220036i	0.930161	+	0.367153i	$0.119667\pi$
$984$	11.3205	+	25.9352i	0.360886	+	0.826783i
$985$			20.6679i			0.658534i
$986$	−17.8118	−	17.8118i	−0.567245	−	0.567245i
$987$	−7.85437	+	10.6460i	−0.250007	+	0.338866i
$988$	89.7534	−	57.7615i	2.85544	−	1.83764i
$989$		−	10.3132i		−	0.327941i
$990$	−0.532352	−	14.1017i	−0.0169192	−	0.448180i
$991$	−5.02163	−	8.69772i	−0.159517	−	0.276292i	0.775177	−	0.631744i	$-0.217660\pi$
$991$	−5.02163	−	8.69772i	−0.159517	−	0.276292i	−0.934695	+	0.355451i	$0.884327\pi$
$992$	44.4296			1.41064
$993$	−1.71417	+	4.36977i	−0.0543975	+	0.138671i
$994$	−0.325180	+	1.21359i	−0.0103141	+	0.0384926i
$995$	3.31570	−	12.3744i	0.105115	−	0.392293i
$996$	−70.8911	−	88.8642i	−2.24627	−	2.81577i
$997$	7.02370			0.222443			0.111221	−	0.993796i	$-0.464524\pi$
$997$	7.02370			0.222443			0.111221	+	0.993796i	$0.464524\pi$
$998$	−29.6228	−	51.3083i	−0.937695	−	1.62413i
$999$	−36.9758	−	25.1826i	−1.16986	−	0.796743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.6	yes	336
9.2	odd	6		819.2.ew.a.596.79	✓	336
13.6	odd	12		819.2.ew.a.617.79	yes	336
117.110	even	12	inner	819.2.fy.a.344.6	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.79	✓	336	9.2	odd	6
819.2.ew.a.617.79	yes	336	13.6	odd	12
819.2.fy.a.50.6	yes	336	1.1	even	1	trivial
819.2.fy.a.344.6	yes	336	117.110	even	12	inner

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.663488 - 2.47617i) q^{2} +(-0.692898 - 1.58742i) q^{3} +(-3.95915 + 2.28582i) q^{4} +(-0.816615 - 3.04765i) q^{5} +(-3.47098 + 2.76896i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.66155 + 4.66155i) q^{8} +(-2.03979 + 2.19984i) q^{9} +O(q^{10})\)	\(q+(-0.663488 - 2.47617i) q^{2} +(-0.692898 - 1.58742i) q^{3} +(-3.95915 + 2.28582i) q^{4} +(-0.816615 - 3.04765i) q^{5} +(-3.47098 + 2.76896i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.66155 + 4.66155i) q^{8} +(-2.03979 + 2.19984i) q^{9} +(-7.00468 + 4.04416i) q^{10} +(0.561751 - 0.150521i) q^{11} +(6.37183 + 4.70098i) q^{12} +(3.52364 + 0.764181i) q^{13} +(2.22007 + 1.28176i) q^{14} +(-4.27206 + 3.40802i) q^{15} +(3.87827 - 6.71736i) q^{16} +(-2.47344 + 4.28413i) q^{17} +(6.80054 + 3.59129i) q^{18} +(-6.25464 + 1.67592i) q^{19} +(10.1995 + 10.1995i) q^{20} +(1.61243 + 0.632521i) q^{21} +(-0.745430 - 1.29112i) q^{22} +6.69818 q^{23} +(4.16984 - 10.6298i) q^{24} +(-4.29119 + 2.47752i) q^{25} +(-0.445650 - 9.23215i) q^{26} +(4.90542 + 1.71373i) q^{27} +(1.18323 - 4.41586i) q^{28} +(-1.72023 - 0.993175i) q^{29} +(11.2733 + 8.31717i) q^{30} +(-6.40609 + 1.71651i) q^{31} +(-6.47093 - 1.73388i) q^{32} +(-0.628175 - 0.787438i) q^{33} +(12.2493 + 3.28219i) q^{34} +(2.73245 + 1.57758i) q^{35} +(3.04740 - 13.3720i) q^{36} +(-8.31622 - 2.22833i) q^{37} +(8.29975 + 14.3756i) q^{38} +(-1.22845 - 6.12298i) q^{39} +(10.4001 - 18.0135i) q^{40} +(-1.75242 + 1.75242i) q^{41} +(0.496404 - 4.41231i) q^{42} -1.53970i q^{43} +(-1.87999 + 1.87999i) q^{44} +(8.37005 + 4.42013i) q^{45} +(-4.44416 - 16.5858i) q^{46} +(-1.97692 + 7.37798i) q^{47} +(-13.3505 - 1.50199i) q^{48} -1.00000i q^{49} +(8.98190 + 8.98190i) q^{50} +(8.51454 + 0.957921i) q^{51} +(-15.6974 + 5.02888i) q^{52} -13.7627i q^{53} +(0.988799 - 13.2837i) q^{54} +(-0.917469 - 1.58910i) q^{55} -6.59242 q^{56} +(6.99421 + 8.76747i) q^{57} +(-1.31792 + 4.91854i) q^{58} +(-0.728588 + 2.71913i) q^{59} +(9.12362 - 23.2580i) q^{60} +3.69471 q^{61} +(8.50072 + 14.7237i) q^{62} +(-0.113172 - 2.99786i) q^{63} +1.66044i q^{64} +(-0.548502 - 11.3629i) q^{65} +(-1.53304 + 2.07792i) q^{66} +(-0.933331 - 0.933331i) q^{67} -22.6153i q^{68} +(-4.64115 - 10.6328i) q^{69} +(2.09341 - 7.81271i) q^{70} +(0.126849 + 0.473407i) q^{71} +(-19.7632 + 0.746080i) q^{72} +(-10.4071 + 10.4071i) q^{73} +22.0708i q^{74} +(6.90621 + 5.09523i) q^{75} +(20.9322 - 20.9322i) q^{76} +(-0.290784 + 0.503652i) q^{77} +(-14.3465 + 7.10437i) q^{78} +(4.07484 + 7.05783i) q^{79} +(-23.6392 - 6.33411i) q^{80} +(-0.678551 - 8.97438i) q^{81} +(5.50200 + 3.17658i) q^{82} +(-13.8670 - 3.71566i) q^{83} +(-7.82966 + 1.18147i) q^{84} +(15.0764 + 4.03970i) q^{85} +(-3.81257 + 1.02157i) q^{86} +(-0.384640 + 3.41889i) q^{87} +(3.32029 + 1.91697i) q^{88} +(-1.71262 + 6.39158i) q^{89} +(5.39157 - 23.6584i) q^{90} +(-3.03195 + 1.95123i) q^{91} +(-26.5191 + 15.3108i) q^{92} +(7.16357 + 8.97977i) q^{93} +19.5808 q^{94} +(10.2153 + 17.6934i) q^{95} +(1.73130 + 11.4735i) q^{96} +(11.6425 + 11.6425i) q^{97} +(-2.47617 + 0.663488i) q^{98} +(-0.814731 + 1.54279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

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