LMFDB - Embedded newform 430.2.j.a.49.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.17
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.0417606 - 0.0241105i) q^{3} -1.00000 q^{4} +(-2.19004 + 0.451367i) q^{5} +(0.0241105 - 0.0417606i) q^{6} +(3.51224 - 2.02779i) q^{7} -1.00000i q^{8} +(-1.49884 - 2.59606i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.0417606 - 0.0241105i) q^{3} -1.00000 q^{4} +(-2.19004 + 0.451367i) q^{5} +(0.0241105 - 0.0417606i) q^{6} +(3.51224 - 2.02779i) q^{7} -1.00000i q^{8} +(-1.49884 - 2.59606i) q^{9} +(-0.451367 - 2.19004i) q^{10} +1.21075 q^{11} +(0.0417606 + 0.0241105i) q^{12} +(5.67052 - 3.27388i) q^{13} +(2.02779 + 3.51224i) q^{14} +(0.102340 + 0.0339535i) q^{15} +1.00000 q^{16} +(-0.427236 + 0.246665i) q^{17} +(2.59606 - 1.49884i) q^{18} +(-2.95660 + 5.12098i) q^{19} +(2.19004 - 0.451367i) q^{20} -0.195564 q^{21} +1.21075i q^{22} +(3.64025 + 2.10170i) q^{23} +(-0.0241105 + 0.0417606i) q^{24} +(4.59254 - 1.97702i) q^{25} +(3.27388 + 5.67052i) q^{26} +0.289214i q^{27} +(-3.51224 + 2.02779i) q^{28} +(1.43082 + 2.47825i) q^{29} +(-0.0339535 + 0.102340i) q^{30} +(4.02532 - 6.97207i) q^{31} +1.00000i q^{32} +(-0.0505617 - 0.0291918i) q^{33} +(-0.246665 - 0.427236i) q^{34} +(-6.77666 + 6.02625i) q^{35} +(1.49884 + 2.59606i) q^{36} +(-7.39356 - 4.26867i) q^{37} +(-5.12098 - 2.95660i) q^{38} -0.315739 q^{39} +(0.451367 + 2.19004i) q^{40} +8.65418 q^{41} -0.195564i q^{42} +(2.56640 - 6.03437i) q^{43} -1.21075 q^{44} +(4.45429 + 5.00895i) q^{45} +(-2.10170 + 3.64025i) q^{46} -3.61348i q^{47} +(-0.0417606 - 0.0241105i) q^{48} +(4.72388 - 8.18201i) q^{49} +(1.97702 + 4.59254i) q^{50} +0.0237888 q^{51} +(-5.67052 + 3.27388i) q^{52} +(-3.83572 - 2.21456i) q^{53} -0.289214 q^{54} +(-2.65159 + 0.546494i) q^{55} +(-2.02779 - 3.51224i) q^{56} +(0.246939 - 0.142570i) q^{57} +(-2.47825 + 1.43082i) q^{58} -15.0476 q^{59} +(-0.102340 - 0.0339535i) q^{60} +(-0.0822573 - 0.142474i) q^{61} +(6.97207 + 4.02532i) q^{62} +(-10.5286 - 6.07866i) q^{63} -1.00000 q^{64} +(-10.9409 + 9.72940i) q^{65} +(0.0291918 - 0.0505617i) q^{66} +(10.8917 + 6.28833i) q^{67} +(0.427236 - 0.246665i) q^{68} +(-0.101346 - 0.175537i) q^{69} +(-6.02625 - 6.77666i) q^{70} +(0.973463 + 1.68609i) q^{71} +(-2.59606 + 1.49884i) q^{72} +(-9.35998 + 5.40399i) q^{73} +(4.26867 - 7.39356i) q^{74} +(-0.239454 - 0.0281666i) q^{75} +(2.95660 - 5.12098i) q^{76} +(4.25245 - 2.45515i) q^{77} -0.315739i q^{78} +(0.639286 + 1.10728i) q^{79} +(-2.19004 + 0.451367i) q^{80} +(-4.48954 + 7.77611i) q^{81} +8.65418i q^{82} +(0.265472 + 0.153271i) q^{83} +0.195564 q^{84} +(0.824326 - 0.733045i) q^{85} +(6.03437 + 2.56640i) q^{86} -0.137991i q^{87} -1.21075i q^{88} +(2.37457 - 4.11288i) q^{89} +(-5.00895 + 4.45429i) q^{90} +(13.2775 - 22.9973i) q^{91} +(-3.64025 - 2.10170i) q^{92} +(-0.336200 + 0.194105i) q^{93} +3.61348 q^{94} +(4.16362 - 12.5497i) q^{95} +(0.0241105 - 0.0417606i) q^{96} +15.1388i q^{97} +(8.18201 + 4.72388i) q^{98} +(-1.81472 - 3.14319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.0417606	−	0.0241105i	−0.0241105	−	0.0139202i	0.487896	−	0.872902i	$-0.337764\pi$
$3$	−0.0417606	−	0.0241105i	−0.0241105	−	0.0139202i	−0.512007	+	0.858981i	$0.671098\pi$
$4$	−1.00000			−0.500000
$5$	−2.19004	+	0.451367i	−0.979415	+	0.201858i
$5$	−2.19004	+	0.451367i	−0.979415	+	0.201858i
$6$	0.0241105	−	0.0417606i	0.00984307	−	0.0170487i
$7$	3.51224	−	2.02779i	1.32750	−	0.766433i	0.342589	−	0.939485i	$-0.388696\pi$
$7$	3.51224	−	2.02779i	1.32750	−	0.766433i	0.984913	+	0.173052i	$0.0553628\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.49884	−	2.59606i	−0.499612	−	0.865354i
$10$	−0.451367	−	2.19004i	−0.142735	−	0.692551i
$11$	1.21075			0.365055			0.182528	−	0.983201i	$-0.441572\pi$
$11$	1.21075			0.365055			0.182528	+	0.983201i	$0.441572\pi$
$12$	0.0417606	+	0.0241105i	0.0120552	+	0.00696010i
$13$	5.67052	−	3.27388i	1.57272	−	0.908010i	0.576886	−	0.816825i	$-0.304268\pi$
$13$	5.67052	−	3.27388i	1.57272	−	0.908010i	0.995834	−	0.0911853i	$-0.0290656\pi$
$14$	2.02779	+	3.51224i	0.541950	+	0.938685i
$15$	0.102340	+	0.0339535i	0.0264241	+	0.00876677i
$16$	1.00000			0.250000
$17$	−0.427236	+	0.246665i	−0.103620	+	0.0598250i	−0.550914	−	0.834562i	$-0.685721\pi$
$17$	−0.427236	+	0.246665i	−0.103620	+	0.0598250i	0.447294	+	0.894387i	$0.352388\pi$
$18$	2.59606	−	1.49884i	0.611898	−	0.353279i
$19$	−2.95660	+	5.12098i	−0.678290	+	1.17483i	0.297205	+	0.954814i	$0.403945\pi$
$19$	−2.95660	+	5.12098i	−0.678290	+	1.17483i	−0.975495	+	0.220019i	$0.929388\pi$
$20$	2.19004	−	0.451367i	0.489707	−	0.100929i
$21$	−0.195564			−0.0426756
$22$			1.21075i			0.258133i
$23$	3.64025	+	2.10170i	0.759045	+	0.438235i	0.828953	−	0.559319i	$-0.188937\pi$
$23$	3.64025	+	2.10170i	0.759045	+	0.438235i	−0.0699077	+	0.997553i	$0.522270\pi$
$24$	−0.0241105	+	0.0417606i	−0.00492153	+	0.00852435i
$25$	4.59254	−	1.97702i	0.918507	−	0.395405i
$26$	3.27388	+	5.67052i	0.642060	+	1.11208i
$27$			0.289214i			0.0556592i
$28$	−3.51224	+	2.02779i	−0.663751	+	0.383217i
$29$	1.43082	+	2.47825i	0.265696	+	0.460199i	0.967746	−	0.251929i	$-0.0810650\pi$
$29$	1.43082	+	2.47825i	0.265696	+	0.460199i	−0.702050	+	0.712128i	$0.747732\pi$
$30$	−0.0339535	+	0.102340i	−0.00619904	+	0.0186846i
$31$	4.02532	−	6.97207i	0.722970	−	1.25222i	−0.236835	−	0.971550i	$-0.576110\pi$
$31$	4.02532	−	6.97207i	0.722970	−	1.25222i	0.959804	−	0.280670i	$-0.0905567\pi$
$32$			1.00000i			0.176777i
$33$	−0.0505617	−	0.0291918i	−0.00880166	−	0.00508164i
$34$	−0.246665	−	0.427236i	−0.0423026	−	0.0732703i
$35$	−6.77666	+	6.02625i	−1.14546	+	1.01862i
$36$	1.49884	+	2.59606i	0.249806	+	0.432677i
$37$	−7.39356	−	4.26867i	−1.21549	−	0.701765i	−0.251542	−	0.967846i	$-0.580938\pi$
$37$	−7.39356	−	4.26867i	−1.21549	−	0.701765i	−0.963951	+	0.266081i	$0.914271\pi$
$38$	−5.12098	−	2.95660i	−0.830732	−	0.479624i
$39$	−0.315739			−0.0505587
$40$	0.451367	+	2.19004i	0.0713674	+	0.346275i
$41$	8.65418			1.35156			0.675778	−	0.737106i	$-0.263808\pi$
$41$	8.65418			1.35156			0.675778	+	0.737106i	$0.263808\pi$
$42$		−	0.195564i		−	0.0301762i
$43$	2.56640	−	6.03437i	0.391372	−	0.920233i
$43$	2.56640	−	6.03437i	0.391372	−	0.920233i
$44$	−1.21075			−0.182528
$45$	4.45429	+	5.00895i	0.664006	+	0.746690i
$46$	−2.10170	+	3.64025i	−0.309879	+	0.536726i
$47$		−	3.61348i		−	0.527080i	−0.964649	−	0.263540i	$-0.915110\pi$
$47$		−	3.61348i		−	0.527080i	0.964649	−	0.263540i	$-0.0848900\pi$
$48$	−0.0417606	−	0.0241105i	−0.00602762	−	0.00348005i
$49$	4.72388	−	8.18201i	0.674840	−	1.16886i
$50$	1.97702	+	4.59254i	0.279593	+	0.649483i
$51$	0.0237888			0.00333110
$52$	−5.67052	+	3.27388i	−0.786360	+	0.454005i
$53$	−3.83572	−	2.21456i	−0.526877	−	0.304193i	0.212867	−	0.977081i	$-0.431720\pi$
$53$	−3.83572	−	2.21456i	−0.526877	−	0.304193i	−0.739744	+	0.672889i	$0.765053\pi$
$54$	−0.289214			−0.0393570
$55$	−2.65159	+	0.546494i	−0.357541	+	0.0736892i
$56$	−2.02779	−	3.51224i	−0.270975	−	0.469343i
$57$	0.246939	−	0.142570i	0.0327078	−	0.0188839i
$58$	−2.47825	+	1.43082i	−0.325410	+	0.187875i
$59$	−15.0476			−1.95903			−0.979515	−	0.201369i	$-0.935461\pi$
$59$	−15.0476			−1.95903			−0.979515	+	0.201369i	$0.935461\pi$
$60$	−0.102340	−	0.0339535i	−0.0132120	−	0.00438338i
$61$	−0.0822573	−	0.142474i	−0.0105320	−	0.0182419i	0.860711	−	0.509093i	$-0.170019\pi$
$61$	−0.0822573	−	0.142474i	−0.0105320	−	0.0182419i	−0.871243	+	0.490851i	$0.836686\pi$
$62$	6.97207	+	4.02532i	0.885453	+	0.511217i
$63$	−10.5286	−	6.07866i	−1.32647	−	0.765839i
$64$	−1.00000			−0.125000
$65$	−10.9409	+	9.72940i	−1.35706	+	1.20678i
$66$	0.0291918	−	0.0505617i	0.00359326	−	0.00622372i
$67$	10.8917	+	6.28833i	1.33063	+	0.768241i	0.985397	−	0.170275i	$-0.0544655\pi$
$67$	10.8917	+	6.28833i	1.33063	+	0.768241i	0.345236	+	0.938516i	$0.387799\pi$
$68$	0.427236	−	0.246665i	0.0518099	−	0.0299125i
$69$	−0.101346	−	0.175537i	−0.0122006	−	0.0211321i
$70$	−6.02625	−	6.77666i	−0.720275	−	0.809966i
$71$	0.973463	+	1.68609i	0.115529	+	0.200102i	0.917991	−	0.396601i	$-0.129810\pi$
$71$	0.973463	+	1.68609i	0.115529	+	0.200102i	−0.802462	+	0.596703i	$0.796477\pi$
$72$	−2.59606	+	1.49884i	−0.305949	+	0.176640i
$73$	−9.35998	+	5.40399i	−1.09550	+	0.632489i	−0.935036	−	0.354552i	$-0.884633\pi$
$73$	−9.35998	+	5.40399i	−1.09550	+	0.632489i	−0.160467	+	0.987041i	$0.551300\pi$
$74$	4.26867	−	7.39356i	0.496223	−	0.859483i
$75$	−0.239454	−	0.0281666i	−0.0276498	−	0.00325240i
$76$	2.95660	−	5.12098i	0.339145	−	0.587416i
$77$	4.25245	−	2.45515i	0.484612	−	0.279791i
$78$		−	0.315739i		−	0.0357504i
$79$	0.639286	+	1.10728i	0.0719253	+	0.124578i	0.899745	−	0.436416i	$-0.143752\pi$
$79$	0.639286	+	1.10728i	0.0719253	+	0.124578i	−0.827820	+	0.560994i	$0.810419\pi$
$80$	−2.19004	+	0.451367i	−0.244854	+	0.0504644i
$81$	−4.48954	+	7.77611i	−0.498838	+	0.864012i
$82$			8.65418i			0.955694i
$83$	0.265472	+	0.153271i	0.0291394	+	0.0168236i	0.514499	−	0.857491i	$-0.327978\pi$
$83$	0.265472	+	0.153271i	0.0291394	+	0.0168236i	−0.485360	+	0.874315i	$0.661311\pi$
$84$	0.195564			0.0213378
$85$	0.824326	−	0.733045i	0.0894107	−	0.0795099i
$86$	6.03437	+	2.56640i	0.650703	+	0.276742i
$87$		−	0.137991i		−	0.0147942i
$88$		−	1.21075i		−	0.129067i
$89$	2.37457	−	4.11288i	0.251704	−	0.435964i	−0.712291	−	0.701884i	$-0.752342\pi$
$89$	2.37457	−	4.11288i	0.251704	−	0.435964i	0.963995	+	0.265920i	$0.0856758\pi$
$90$	−5.00895	+	4.45429i	−0.527990	+	0.469523i
$91$	13.2775	−	22.9973i	1.39186	−	2.41077i
$92$	−3.64025	−	2.10170i	−0.379523	−	0.219117i
$93$	−0.336200	+	0.194105i	−0.0348623	+	0.0201278i
$94$	3.61348			0.372702
$95$	4.16362	−	12.5497i	0.427179	−	1.28757i
$96$	0.0241105	−	0.0417606i	0.00246077	−	0.00426217i
$97$			15.1388i			1.53711i	0.639782	+	0.768556i	$0.279025\pi$
$97$			15.1388i			1.53711i	−0.639782	+	0.768556i	$0.720975\pi$
$98$	8.18201	+	4.72388i	0.826507	+	0.477184i
$99$	−1.81472	−	3.14319i	−0.182386	−	0.315902i
$100$	−4.59254	+	1.97702i	−0.459254	+	0.197702i
$101$	6.37904	+	11.0488i	0.634739	+	1.09940i	0.986570	+	0.163336i	$0.0522256\pi$
$101$	6.37904	+	11.0488i	0.634739	+	1.09940i	−0.351832	+	0.936063i	$0.614441\pi$
$102$			0.0237888i			0.00235545i
$103$	−0.402989	+	0.232666i	−0.0397077	+	0.0229253i	−0.519722	−	0.854335i	$-0.673965\pi$
$103$	−0.402989	+	0.232666i	−0.0397077	+	0.0229253i	0.480015	+	0.877260i	$0.340631\pi$
$104$	−3.27388	−	5.67052i	−0.321030	−	0.556040i
$105$	0.428293	−	0.0882713i	0.0417971	−	0.00861440i
$106$	2.21456	−	3.83572i	0.215097	−	0.372559i
$107$		−	9.61329i		−	0.929351i	−0.885481	−	0.464676i	$-0.846171\pi$
$107$		−	9.61329i		−	0.929351i	0.885481	−	0.464676i	$-0.153829\pi$
$108$		−	0.289214i		−	0.0278296i
$109$	−5.48415	+	9.49883i	−0.525286	+	0.909823i	0.474280	+	0.880374i	$0.342708\pi$
$109$	−5.48415	+	9.49883i	−0.525286	+	0.909823i	−0.999566	+	0.0294485i	$0.990625\pi$
$110$	−0.546494	−	2.65159i	−0.0521061	−	0.252819i
$111$	0.205840	+	0.356525i	0.0195374	+	0.0338398i
$112$	3.51224	−	2.02779i	0.331875	−	0.191608i
$113$		−	0.789393i		−	0.0742599i	−0.999310	−	0.0371299i	$-0.988178\pi$
$113$		−	0.789393i		−	0.0742599i	0.999310	−	0.0371299i	$-0.0118215\pi$
$114$	0.142570	+	0.246939i	0.0133529	+	0.0231279i
$115$	−8.92093	−	2.95971i	−0.831881	−	0.275995i
$116$	−1.43082	−	2.47825i	−0.132848	−	0.230099i
$117$	−16.9984	−	9.81402i	−1.57150	−	0.907306i
$118$		−	15.0476i		−	1.38524i
$119$	−1.00037	+	1.73269i	−0.0917037	+	0.158836i
$120$	0.0339535	−	0.102340i	0.00309952	−	0.00934232i
$121$	−9.53408			−0.866735
$122$	0.142474	−	0.0822573i	0.0128990	−	0.00744722i
$123$	−0.361404	−	0.208656i	−0.0325867	−	0.0188139i
$124$	−4.02532	+	6.97207i	−0.361485	+	0.626110i
$125$	−9.16546	+	6.40268i	−0.819784	+	0.572673i
$126$	6.07866	−	10.5286i	0.541530	−	0.937958i
$127$		−	4.35073i		−	0.386065i	−0.981192	−	0.193032i	$-0.938168\pi$
$127$		−	4.35073i		−	0.386065i	0.981192	−	0.193032i	$-0.0618322\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.252666	+	0.190122i	−0.0222460	+	0.0167393i
$130$	−9.72940	−	10.9409i	−0.853325	−	0.959584i
$131$	−10.0418			−0.877356			−0.438678	−	0.898644i	$-0.644553\pi$
$131$	−10.0418			−0.877356			−0.438678	+	0.898644i	$0.644553\pi$
$132$	0.0505617	+	0.0291918i	0.00440083	+	0.00254082i
$133$			23.9815i			2.07946i
$134$	−6.28833	+	10.8917i	−0.543229	+	0.940899i
$135$	−0.130542	−	0.633389i	−0.0112352	−	0.0545135i
$136$	0.246665	+	0.427236i	0.0211513	+	0.0366352i
$137$		−	4.44688i		−	0.379923i	−0.981792	−	0.189961i	$-0.939164\pi$
$137$		−	4.44688i		−	0.379923i	0.981792	−	0.189961i	$-0.0608363\pi$
$138$	0.175537	−	0.101346i	0.0149427	−	0.00862715i
$139$	3.49920	−	6.06079i	0.296798	−	0.514070i	−0.678603	−	0.734505i	$-0.737414\pi$
$139$	3.49920	−	6.06079i	0.296798	−	0.514070i	0.975402	+	0.220435i	$0.0707478\pi$
$140$	6.77666	−	6.02625i	0.572732	−	0.509311i
$141$	−0.0871227	+	0.150901i	−0.00733706	+	0.0127082i
$142$	−1.68609	+	0.973463i	−0.141493	+	0.0816912i
$143$	6.86559	−	3.96385i	0.574130	−	0.331474i
$144$	−1.49884	−	2.59606i	−0.124903	−	0.216339i
$145$	−4.25214	−	4.78163i	−0.353121	−	0.397093i
$146$	−5.40399	−	9.35998i	−0.447237	−	0.774638i
$147$	−0.394544	+	0.227790i	−0.0325415	+	0.0187878i
$148$	7.39356	+	4.26867i	0.607747	+	0.350883i
$149$	−7.09816	+	12.2944i	−0.581504	+	1.00719i	0.413798	+	0.910369i	$0.364202\pi$
$149$	−7.09816	+	12.2944i	−0.581504	+	1.00719i	−0.995301	+	0.0968249i	$0.969131\pi$
$150$	0.0281666	−	0.239454i	0.00229980	−	0.0195513i
$151$	4.04683			0.329326			0.164663	−	0.986350i	$-0.447346\pi$
$151$	4.04683			0.329326			0.164663	+	0.986350i	$0.447346\pi$
$152$	5.12098	+	2.95660i	0.415366	+	0.239812i
$153$	1.28071	+	0.739420i	0.103540	+	0.0597786i
$154$	2.45515	+	4.25245i	0.197842	+	0.342672i
$155$	−5.66865	+	17.0860i	−0.455317	+	1.37238i
$156$	0.315739			0.0252794
$157$	−6.75201	+	3.89828i	−0.538869	+	0.311116i	−0.744621	−	0.667488i	$-0.767370\pi$
$157$	−6.75201	+	3.89828i	−0.538869	+	0.311116i	0.205751	+	0.978604i	$0.434036\pi$
$158$	−1.10728	+	0.639286i	−0.0880901	+	0.0508589i
$159$	0.106788	+	0.184962i	0.00846885	+	0.0146685i
$160$	−0.451367	−	2.19004i	−0.0356837	−	0.173138i
$161$	17.0473			1.34351
$162$	−7.77611	−	4.48954i	−0.610949	−	0.352731i
$163$	8.85895	−	5.11472i	0.693887	−	0.400616i	−0.111180	−	0.993800i	$-0.535463\pi$
$163$	8.85895	−	5.11472i	0.693887	−	0.400616i	0.805066	+	0.593185i	$0.202130\pi$
$164$	−8.65418			−0.675778
$165$	0.123908	+	0.0411093i	0.00964625	+	0.00320035i
$166$	−0.153271	+	0.265472i	−0.0118961	+	0.0206046i
$167$	−12.4562	−	7.19156i	−0.963886	−	0.556500i	−0.0665191	−	0.997785i	$-0.521189\pi$
$167$	−12.4562	−	7.19156i	−0.963886	−	0.556500i	−0.897367	+	0.441285i	$0.854523\pi$
$168$			0.195564i			0.0150881i
$169$	14.9365	−	25.8709i	1.14896	−	1.99007i
$170$	0.733045	+	0.824326i	0.0562220	+	0.0632229i
$171$	17.7258			1.35553
$172$	−2.56640	+	6.03437i	−0.195686	+	0.460116i
$173$			23.7335i			1.80442i	0.431296	+	0.902210i	$0.358056\pi$
$173$			23.7335i			1.80442i	−0.431296	+	0.902210i	$0.641944\pi$
$174$	0.137991			0.0104610
$175$	12.1211	−	16.2565i	0.916268	−	1.22887i
$176$	1.21075			0.0912638
$177$	0.628397	+	0.362805i	0.0472332	+	0.0272701i
$178$	4.11288	+	2.37457i	0.308273	+	0.177982i
$179$	3.93437	+	6.81452i	0.294068	+	0.509341i	0.974768	−	0.223222i	$-0.0716573\pi$
$179$	3.93437	+	6.81452i	0.294068	+	0.509341i	−0.680699	+	0.732563i	$0.738324\pi$
$180$	−4.45429	−	5.00895i	−0.332003	−	0.373345i
$181$	12.2348	+	21.1913i	0.909406	+	1.57514i	0.814892	+	0.579613i	$0.196796\pi$
$181$	12.2348	+	21.1913i	0.909406	+	1.57514i	0.0945142	+	0.995524i	$0.469870\pi$
$182$	22.9973	+	13.2775i	1.70467	+	0.984193i
$183$			0.00793305i			0.000586428i
$184$	2.10170	−	3.64025i	0.154939	−	0.268363i
$185$	18.1189	+	6.01134i	1.33213	+	0.441963i
$186$	−0.194105	−	0.336200i	−0.0142325	−	0.0246514i
$187$	−0.517276	+	0.298650i	−0.0378270	+	0.0218394i
$188$			3.61348i			0.263540i
$189$	0.586466	+	1.01579i	0.0426591	+	0.0738877i
$190$	12.5497	+	4.16362i	0.910447	+	0.302061i
$191$	−8.98776	+	15.5673i	−0.650332	+	1.12641i	0.332711	+	0.943029i	$0.392037\pi$
$191$	−8.98776	+	15.5673i	−0.650332	+	1.12641i	−0.983042	+	0.183379i	$0.941297\pi$
$192$	0.0417606	+	0.0241105i	0.00301381	+	0.00174003i
$193$		−	2.67172i		−	0.192315i	−0.995366	−	0.0961574i	$-0.969345\pi$
$193$		−	2.67172i		−	0.192315i	0.995366	−	0.0961574i	$-0.0306552\pi$
$194$	−15.1388			−1.08690
$195$	0.691481	−	0.142514i	0.0495180	−	0.0102057i
$196$	−4.72388	+	8.18201i	−0.337420	+	0.584429i
$197$	14.2632	−	8.23486i	1.01621	−	0.586709i	0.103206	−	0.994660i	$-0.467090\pi$
$197$	14.2632	−	8.23486i	1.01621	−	0.586709i	0.913004	+	0.407951i	$0.133757\pi$
$198$	3.14319	−	1.81472i	0.223377	−	0.128966i
$199$	17.1893			1.21851			0.609257	−	0.792973i	$-0.291468\pi$
$199$	17.1893			1.21851			0.609257	+	0.792973i	$0.291468\pi$
$200$	−1.97702	−	4.59254i	−0.139797	−	0.324741i
$201$	−0.303229	−	0.525208i	−0.0213881	−	0.0370454i
$202$	−11.0488	+	6.37904i	−0.777393	+	0.448828i
$203$	10.0507	+	5.80279i	0.705423	+	0.407276i
$204$	−0.0237888			−0.00166555
$205$	−18.9530	+	3.90621i	−1.32373	+	0.272822i
$206$	−0.232666	−	0.402989i	−0.0162106	−	0.0280776i
$207$		−	12.6004i		−	0.875790i
$208$	5.67052	−	3.27388i	0.393180	−	0.227003i
$209$	−3.57971	+	6.20023i	−0.247613	+	0.428879i
$210$	0.0882713	+	0.428293i	0.00609130	+	0.0295550i
$211$	−13.4708			−0.927368			−0.463684	−	0.886001i	$-0.653473\pi$
$211$	−13.4708			−0.927368			−0.463684	+	0.886001i	$0.653473\pi$
$212$	3.83572	+	2.21456i	0.263439	+	0.152096i
$213$		−	0.0938827i		−	0.00643274i
$214$	9.61329			0.657151
$215$	−2.89679	+	14.3739i	−0.197560	+	0.980291i
$216$	0.289214			0.0196785
$217$		−	32.6501i		−	2.21643i
$218$	−9.49883	−	5.48415i	−0.643342	−	0.371434i
$219$	0.521171			0.0352175
$220$	2.65159	−	0.546494i	0.178770	−	0.0368446i
$221$	−1.61510	+	2.79743i	−0.108643	+	0.188176i
$222$	−0.356525	+	0.205840i	−0.0239284	+	0.0138150i
$223$		−	0.772140i		−	0.0517063i	−0.999666	−	0.0258531i	$-0.991770\pi$
$223$		−	0.772140i		−	0.0517063i	0.999666	−	0.0258531i	$-0.00823023\pi$
$224$	2.02779	+	3.51224i	0.135488	+	0.234671i
$225$	−12.0159	−	8.95927i	−0.801063	−	0.597285i
$226$	0.789393			0.0525097
$227$	8.05329	+	4.64957i	0.534515	+	0.308603i	0.742853	−	0.669454i	$-0.233472\pi$
$227$	8.05329	+	4.64957i	0.534515	+	0.308603i	−0.208338	+	0.978057i	$0.566805\pi$
$228$	−0.246939	+	0.142570i	−0.0163539	+	0.00944194i
$229$	10.2542	+	17.7608i	0.677618	+	1.17367i	0.975696	+	0.219128i	$0.0703212\pi$
$229$	10.2542	+	17.7608i	0.677618	+	1.17367i	−0.298078	+	0.954542i	$0.596345\pi$
$230$	2.95971	−	8.92093i	0.195158	−	0.588229i
$231$	−0.236780			−0.0155790
$232$	2.47825	−	1.43082i	0.162705	−	0.0939377i
$233$	−1.83582	+	1.05991i	−0.120269	+	0.0694371i	−0.558927	−	0.829217i	$-0.688787\pi$
$233$	−1.83582	+	1.05991i	−0.120269	+	0.0694371i	0.438659	+	0.898654i	$0.355454\pi$
$234$	9.81402	−	16.9984i	0.641562	−	1.11122i
$235$	1.63100	+	7.91365i	0.106395	+	0.516230i
$236$	15.0476			0.979515
$237$		−	0.0616540i		−	0.00400486i
$238$	−1.73269	−	1.00037i	−0.112314	−	0.0648443i
$239$	0.385083	−	0.666984i	0.0249090	−	0.0431436i	−0.853302	−	0.521417i	$-0.825404\pi$
$239$	0.385083	−	0.666984i	0.0249090	−	0.0431436i	0.878211	+	0.478273i	$0.158737\pi$
$240$	0.102340	+	0.0339535i	0.00660602	+	0.00219169i
$241$	2.18888	+	3.79126i	0.140998	+	0.244216i	0.927873	−	0.372897i	$-0.121635\pi$
$241$	2.18888	+	3.79126i	0.140998	+	0.244216i	−0.786874	+	0.617113i	$0.788302\pi$
$242$		−	9.53408i		−	0.612874i
$243$	1.12637	−	0.650311i	0.0722567	−	0.0417175i
$244$	0.0822573	+	0.142474i	0.00526598	+	0.00912095i
$245$	−6.65240	+	20.0511i	−0.425006	+	1.28102i
$246$	0.208656	−	0.361404i	0.0133035	−	0.0230423i
$247$			38.7182i			2.46358i
$248$	−6.97207	−	4.02532i	−0.442727	−	0.255608i
$249$	−0.00739086	−	0.0128013i	−0.000468376	−	0.000811252i
$250$	−6.40268	−	9.16546i	−0.404941	−	0.579675i
$251$	4.13912	+	7.16916i	0.261259	+	0.452513i	0.966577	−	0.256378i	$-0.0825291\pi$
$251$	4.13912	+	7.16916i	0.261259	+	0.452513i	−0.705318	+	0.708891i	$0.749196\pi$
$252$	10.5286	+	6.07866i	0.663236	+	0.382920i
$253$	4.40744	+	2.54464i	0.277093	+	0.159980i
$254$	4.35073			0.272989
$255$	−0.0520985	+	0.0107375i	−0.00326253	+	0.000672408i
$256$	1.00000			0.0625000
$257$		−	10.8851i		−	0.678997i	−0.940607	−	0.339498i	$-0.889743\pi$
$257$		−	10.8851i		−	0.678997i	0.940607	−	0.339498i	$-0.110257\pi$
$258$	−0.190122	−	0.252666i	−0.0118365	−	0.0157303i
$259$	−34.6239			−2.15143
$260$	10.9409	−	9.72940i	0.678528	−	0.603392i
$261$	4.28912	−	7.42897i	0.265490	−	0.459842i
$262$		−	10.0418i		−	0.620385i
$263$	−3.86379	−	2.23076i	−0.238251	−	0.137555i	0.376121	−	0.926570i	$-0.377258\pi$
$263$	−3.86379	−	2.23076i	−0.238251	−	0.137555i	−0.614373	+	0.789016i	$0.710591\pi$
$264$	−0.0291918	+	0.0505617i	−0.00179663	+	0.00311186i
$265$	9.39996	+	3.11864i	0.577435	+	0.191577i
$266$	−23.9815			−1.47040
$267$	−0.198327	+	0.114504i	−0.0121374	+	0.00700754i
$268$	−10.8917	−	6.28833i	−0.665316	−	0.384121i
$269$	17.2374			1.05098			0.525491	−	0.850799i	$-0.323882\pi$
$269$	17.2374			1.05098			0.525491	+	0.850799i	$0.323882\pi$
$270$	0.633389	−	0.130542i	0.0385468	−	0.00794451i
$271$	−5.55959	−	9.62949i	−0.337721	−	0.584950i	0.646283	−	0.763098i	$-0.276323\pi$
$271$	−5.55959	−	9.62949i	−0.337721	−	0.584950i	−0.984004	+	0.178148i	$0.942989\pi$
$272$	−0.427236	+	0.246665i	−0.0259050	+	0.0149562i
$273$	−1.10895	+	0.640254i	−0.0671168	+	0.0387499i
$274$	4.44688			0.268646
$275$	5.56042	−	2.39368i	0.335306	−	0.144345i
$276$	0.101346	+	0.175537i	0.00610032	+	0.0105661i
$277$	−9.22273	−	5.32475i	−0.554140	−	0.319933i	0.196650	−	0.980474i	$-0.436994\pi$
$277$	−9.22273	−	5.32475i	−0.554140	−	0.319933i	−0.750790	+	0.660541i	$0.770327\pi$
$278$	6.06079	+	3.49920i	0.363502	+	0.209868i
$279$	−24.1332			−1.44482
$280$	6.02625	+	6.77666i	0.360137	+	0.404983i
$281$	7.86745	−	13.6268i	0.469333	−	0.812908i	−0.530052	−	0.847965i	$-0.677828\pi$
$281$	7.86745	−	13.6268i	0.469333	−	0.812908i	0.999385	+	0.0350565i	$0.0111611\pi$
$282$	−0.150901	−	0.0871227i	−0.00898602	−	0.00518808i
$283$	−15.3829	+	8.88133i	−0.914419	+	0.527940i	−0.881850	−	0.471529i	$-0.843702\pi$
$283$	−15.3829	+	8.88133i	−0.914419	+	0.527940i	−0.0325688	+	0.999469i	$0.510369\pi$
$284$	−0.973463	−	1.68609i	−0.0577644	−	0.100051i
$285$	−0.476454	+	0.423694i	−0.0282227	+	0.0250975i
$286$	3.96385	+	6.86559i	0.234387	+	0.405971i
$287$	30.3955	−	17.5489i	1.79419	−	1.03588i
$288$	2.59606	−	1.49884i	0.152974	−	0.0883198i
$289$	−8.37831	+	14.5117i	−0.492842	+	0.853627i
$290$	4.78163	−	4.25214i	0.280787	−	0.249694i
$291$	0.365004	−	0.632206i	0.0213969	−	0.0370605i
$292$	9.35998	−	5.40399i	0.547751	−	0.316244i
$293$			3.06126i			0.178840i	0.995994	+	0.0894202i	$0.0285014\pi$
$293$			3.06126i			0.178840i	−0.995994	+	0.0894202i	$0.971499\pi$
$294$	−0.227790	−	0.394544i	−0.0132850	−	0.0230103i
$295$	32.9548	−	6.79199i	1.91870	−	0.395445i
$296$	−4.26867	+	7.39356i	−0.248111	+	0.429742i
$297$			0.350166i			0.0203187i
$298$	−12.2944	−	7.09816i	−0.712193	−	0.411185i
$299$	27.5228			1.59169
$300$	0.239454	+	0.0281666i	0.0138249	+	0.00162620i
$301$	−3.22264	−	26.3983i	−0.185750	−	1.52157i
$302$			4.04683i			0.232869i
$303$		−	0.615208i		−	0.0353428i
$304$	−2.95660	+	5.12098i	−0.169573	+	0.293708i
$305$	0.244455	+	0.274895i	0.0139974	+	0.0157404i
$306$	−0.739420	+	1.28071i	−0.0422699	+	0.0732135i
$307$	−17.3305	−	10.0058i	−0.989103	−	0.571059i	−0.0840971	−	0.996458i	$-0.526801\pi$
$307$	−17.3305	−	10.0058i	−0.989103	−	0.571059i	−0.905006	+	0.425399i	$0.860134\pi$
$308$	−4.25245	+	2.45515i	−0.242306	+	0.139895i
$309$	0.0224388			0.00127650
$310$	−17.0860	−	5.66865i	−0.970419	−	0.321958i
$311$	−15.7288	+	27.2430i	−0.891896	+	1.54481i	−0.0542971	+	0.998525i	$0.517292\pi$
$311$	−15.7288	+	27.2430i	−0.891896	+	1.54481i	−0.837599	+	0.546285i	$0.816042\pi$
$312$			0.315739i			0.0178752i
$313$	−6.82928	−	3.94289i	−0.386014	−	0.222865i	0.294418	−	0.955677i	$-0.404874\pi$
$313$	−6.82928	−	3.94289i	−0.386014	−	0.222865i	−0.680432	+	0.732812i	$0.738208\pi$
$314$	−3.89828	−	6.75201i	−0.219992	−	0.381038i
$315$	25.8016	+	8.56026i	1.45376	+	0.482316i
$316$	−0.639286	−	1.10728i	−0.0359626	−	0.0622891i
$317$			15.3430i			0.861751i	0.902411	+	0.430876i	$0.141795\pi$
$317$			15.3430i			0.861751i	−0.902411	+	0.430876i	$0.858205\pi$
$318$	−0.184962	+	0.106788i	−0.0103722	+	0.00598838i
$319$	1.73236	+	3.00054i	0.0969937	+	0.167998i
$320$	2.19004	−	0.451367i	0.122427	−	0.0252322i
$321$	−0.231781	+	0.401457i	−0.0129368	+	0.0224071i
$322$			17.0473i			0.950006i
$323$		−	2.91715i		−	0.162315i
$324$	4.48954	−	7.77611i	0.249419	−	0.432006i
$325$	19.5695	−	26.2461i	1.08552	−	1.45587i
$326$	5.11472	+	8.85895i	0.283278	+	0.490652i
$327$	0.458043	−	0.264451i	0.0253298	−	0.0146242i
$328$		−	8.65418i		−	0.477847i
$329$	−7.32738	−	12.6914i	−0.403972	−	0.699699i
$330$	−0.0411093	+	0.123908i	−0.00226299	+	0.00682093i
$331$	−9.90401	−	17.1542i	−0.544374	−	0.942883i	−0.998646	−	0.0520199i	$-0.983434\pi$
$331$	−9.90401	−	17.1542i	−0.544374	−	0.942883i	0.454272	−	0.890863i	$-0.349899\pi$
$332$	−0.265472	−	0.153271i	−0.0145697	−	0.00841181i
$333$			25.5922i			1.40244i
$334$	7.19156	−	12.4562i	0.393505	−	0.681570i
$335$	−26.6916	−	8.85552i	−1.45832	−	0.483829i
$336$	−0.195564			−0.0106689
$337$	10.4455	−	6.03072i	0.569004	−	0.328514i	−0.187748	−	0.982217i	$-0.560119\pi$
$337$	10.4455	−	6.03072i	0.569004	−	0.328514i	0.756751	+	0.653703i	$0.226785\pi$
$338$	25.8709	+	14.9365i	1.40719	+	0.812441i
$339$	−0.0190327	+	0.0329655i	−0.00103371	+	0.00179044i
$340$	−0.824326	+	0.733045i	−0.0447054	+	0.0397550i
$341$	4.87367	−	8.44144i	0.263924	−	0.457130i
$342$			17.7258i			0.958504i
$343$		−	9.92712i		−	0.536014i
$344$	−6.03437	−	2.56640i	−0.325351	−	0.138371i
$345$	0.301183	+	0.338688i	0.0162152	+	0.0182343i
$346$	−23.7335			−1.27592
$347$	−9.49046	−	5.47932i	−0.509475	−	0.294145i	0.223143	−	0.974786i	$-0.428368\pi$
$347$	−9.49046	−	5.47932i	−0.509475	−	0.294145i	−0.732618	+	0.680640i	$0.761702\pi$
$348$			0.137991i			0.00739708i
$349$	−15.3720	+	26.6250i	−0.822842	+	1.42520i	0.0807146	+	0.996737i	$0.474280\pi$
$349$	−15.3720	+	26.6250i	−0.822842	+	1.42520i	−0.903557	+	0.428468i	$0.859054\pi$
$350$	16.2565	+	12.1211i	0.868946	+	0.647900i
$351$	0.946851	+	1.63999i	0.0505391	+	0.0875364i
$352$			1.21075i			0.0645333i
$353$	7.19391	−	4.15341i	0.382893	−	0.221063i	−0.296183	−	0.955131i	$-0.595714\pi$
$353$	7.19391	−	4.15341i	0.382893	−	0.221063i	0.679076	+	0.734068i	$0.262381\pi$
$354$	−0.362805	+	0.628397i	−0.0192829	+	0.0333989i
$355$	−2.89297	−	3.25321i	−0.153543	−	0.172662i
$356$	−2.37457	+	4.11288i	−0.125852	+	0.217982i
$357$	0.0835521	−	0.0482388i	0.00442204	−	0.00255307i
$358$	−6.81452	+	3.93437i	−0.360159	+	0.207938i
$359$	−11.6203	−	20.1270i	−0.613296	−	1.06226i	−0.990681	−	0.136204i	$-0.956510\pi$
$359$	−11.6203	−	20.1270i	−0.613296	−	1.06226i	0.377384	−	0.926057i	$-0.376824\pi$
$360$	5.00895	−	4.45429i	0.263995	−	0.234762i
$361$	−7.98295	−	13.8269i	−0.420155	−	0.727730i
$362$	−21.1913	+	12.2348i	−1.11379	+	0.643047i
$363$	0.398149	+	0.229871i	0.0208974	+	0.0120651i
$364$	−13.2775	+	22.9973i	−0.695929	+	1.20538i
$365$	18.0595	−	16.0597i	0.945279	−	0.840605i
$366$	−0.00793305			−0.000414667
$367$	−15.5413	−	8.97276i	−0.811248	−	0.468375i	0.0361408	−	0.999347i	$-0.488494\pi$
$367$	−15.5413	−	8.97276i	−0.811248	−	0.468375i	−0.847389	+	0.530972i	$0.821827\pi$
$368$	3.64025	+	2.10170i	0.189761	+	0.109559i
$369$	−12.9712	−	22.4668i	−0.675254	−	1.16957i
$370$	−6.01134	+	18.1189i	−0.312515	+	0.941957i
$371$	−17.9626			−0.932574
$372$	0.336200	−	0.194105i	0.0174312	−	0.0100639i
$373$	14.0303	−	8.10038i	0.726460	−	0.419422i	−0.0906657	−	0.995881i	$-0.528899\pi$
$373$	14.0303	−	8.10038i	0.726460	−	0.419422i	0.817126	+	0.576460i	$0.195566\pi$
$374$	−0.298650	−	0.517276i	−0.0154428	−	0.0267477i
$375$	0.537127	−	0.0463957i	0.0277371	−	0.00239586i
$376$	−3.61348			−0.186351
$377$	16.2269	+	9.36863i	0.835730	+	0.482509i
$378$	−1.01579	+	0.586466i	−0.0522465	+	0.0301645i
$379$	6.86184			0.352469			0.176235	−	0.984348i	$-0.443608\pi$
$379$	6.86184			0.352469			0.176235	+	0.984348i	$0.443608\pi$
$380$	−4.16362	+	12.5497i	−0.213589	+	0.643783i
$381$	−0.104898	+	0.181689i	−0.00537410	+	0.00930821i
$382$	−15.5673	−	8.98776i	−0.796491	−	0.459854i
$383$			11.1830i			0.571425i	0.958315	+	0.285713i	$0.0922303\pi$
$383$			11.1830i			0.571425i	−0.958315	+	0.285713i	$0.907770\pi$
$384$	−0.0241105	+	0.0417606i	−0.00123038	+	0.00213109i
$385$	−8.20485	+	7.29629i	−0.418158	+	0.371854i
$386$	2.67172			0.135987
$387$	−19.5122	+	2.38201i	−0.991861	+	0.121084i
$388$		−	15.1388i		−	0.768556i
$389$	−16.3355			−0.828244			−0.414122	−	0.910221i	$-0.635911\pi$
$389$	−16.3355			−0.828244			−0.414122	+	0.910221i	$0.635911\pi$
$390$	0.142514	+	0.691481i	0.00721649	+	0.0350145i
$391$	−2.07366			−0.104870
$392$	−8.18201	−	4.72388i	−0.413254	−	0.238592i
$393$	0.419352	+	0.242113i	0.0211535	+	0.0122130i
$394$	8.23486	+	14.2632i	0.414866	+	0.718569i
$395$	−1.89985	−	2.13642i	−0.0955918	−	0.107495i
$396$	1.81472	+	3.14319i	0.0911931	+	0.157951i
$397$	3.77245	+	2.17803i	0.189334	+	0.109312i	0.591671	−	0.806180i	$-0.298469\pi$
$397$	3.77245	+	2.17803i	0.189334	+	0.109312i	−0.402337	+	0.915492i	$0.631802\pi$
$398$			17.1893i			0.861620i
$399$	0.578205	−	1.00148i	0.0289465	−	0.0501367i
$400$	4.59254	−	1.97702i	0.229627	−	0.0988511i
$401$	−15.7137	−	27.2170i	−0.784706	−	1.35915i	−0.929175	−	0.369641i	$-0.879481\pi$
$401$	−15.7137	−	27.2170i	−0.784706	−	1.35915i	0.144469	−	0.989509i	$-0.453853\pi$
$402$	0.525208	−	0.303229i	0.0261950	−	0.0151237i
$403$		−	52.7137i		−	2.62585i
$404$	−6.37904	−	11.0488i	−0.317369	−	0.549700i
$405$	6.32238	−	19.0564i	0.314162	−	0.946921i
$406$	−5.80279	+	10.0507i	−0.287988	+	0.498810i
$407$	−8.95176	−	5.16830i	−0.443722	−	0.256183i
$408$		−	0.0237888i		−	0.00117772i
$409$	15.0079			0.742095			0.371047	−	0.928614i	$-0.378999\pi$
$409$	15.0079			0.742095			0.371047	+	0.928614i	$0.378999\pi$
$410$	−3.90621	−	18.9530i	−0.192914	−	0.936021i
$411$	−0.107217	+	0.185704i	−0.00528860	+	0.00916013i
$412$	0.402989	−	0.232666i	0.0198539	−	0.0114626i
$413$	−52.8508	+	30.5134i	−2.60062	+	1.50147i
$414$	12.6004			0.619277
$415$	−0.650576	−	0.215843i	−0.0319355	−	0.0105953i
$416$	3.27388	+	5.67052i	0.160515	+	0.278020i
$417$	−0.292257	+	0.168735i	−0.0143119	+	0.00826298i
$418$	−6.20023	−	3.57971i	−0.303263	−	0.175089i
$419$	33.5113			1.63713			0.818567	−	0.574411i	$-0.194769\pi$
$419$	33.5113			1.63713			0.818567	+	0.574411i	$0.194769\pi$
$420$	−0.428293	+	0.0882713i	−0.0208986	+	0.00430720i
$421$	−0.256913	−	0.444986i	−0.0125212	−	0.0216873i	0.859697	−	0.510804i	$-0.170652\pi$
$421$	−0.256913	−	0.444986i	−0.0125212	−	0.0216873i	−0.872218	+	0.489117i	$0.837319\pi$
$422$		−	13.4708i		−	0.655748i
$423$	−9.38081	+	5.41601i	−0.456111	+	0.263336i
$424$	−2.21456	+	3.83572i	−0.107548	+	0.186279i
$425$	−1.47443	+	1.97747i	−0.0715205	+	0.0959214i
$426$	0.0938827			0.00454863
$427$	−0.577814	−	0.333601i	−0.0279624	−	0.0161441i
$428$			9.61329i			0.464676i
$429$	−0.382282			−0.0184567
$430$	−14.3739	−	2.89679i	−0.693170	−	0.139696i
$431$	−12.1396			−0.584745			−0.292373	−	0.956304i	$-0.594445\pi$
$431$	−12.1396			−0.584745			−0.292373	+	0.956304i	$0.594445\pi$
$432$			0.289214i			0.0139148i
$433$	21.3158	+	12.3067i	1.02437	+	0.591422i	0.915368	−	0.402619i	$-0.131900\pi$
$433$	21.3158	+	12.3067i	1.02437	+	0.591422i	0.109006	+	0.994041i	$0.465233\pi$
$434$	32.6501			1.56725
$435$	0.0622845	+	0.302205i	0.00298631	+	0.0144896i
$436$	5.48415	−	9.49883i	0.262643	−	0.454911i
$437$	−21.5255	+	12.4278i	−1.02971	+	0.594501i
$438$			0.521171i			0.0249025i
$439$	5.58470	+	9.67298i	0.266543	+	0.461666i	0.967967	−	0.251078i	$-0.0807852\pi$
$439$	5.58470	+	9.67298i	0.266543	+	0.461666i	−0.701424	+	0.712745i	$0.747452\pi$
$440$	0.546494	+	2.65159i	0.0260531	+	0.126410i
$441$	−28.3213			−1.34863
$442$	−2.79743	−	1.61510i	−0.133060	−	0.0768225i
$443$	27.3686	−	15.8013i	1.30032	−	0.750742i	0.319864	−	0.947464i	$-0.396363\pi$
$443$	27.3686	−	15.8013i	1.30032	−	0.750742i	0.980459	+	0.196722i	$0.0630295\pi$
$444$	−0.205840	−	0.356525i	−0.00976871	−	0.0169199i
$445$	−3.34398	+	10.0792i	−0.158520	+	0.477798i
$446$	0.772140			0.0365619
$447$	0.592846	−	0.342280i	0.0280407	−	0.0161893i
$448$	−3.51224	+	2.02779i	−0.165938	+	0.0958042i
$449$	−2.87744	+	4.98388i	−0.135795	+	0.235204i	−0.925901	−	0.377767i	$-0.876692\pi$
$449$	−2.87744	+	4.98388i	−0.135795	+	0.235204i	0.790106	+	0.612970i	$0.210025\pi$
$450$	8.95927	−	12.0159i	0.422344	−	0.566437i
$451$	10.4781			0.493392
$452$			0.789393i			0.0371299i
$453$	−0.168998	−	0.0975710i	−0.00794022	−	0.00458429i
$454$	−4.64957	+	8.05329i	−0.218215	+	0.377960i
$455$	−18.6980	+	56.3579i	−0.876575	+	2.64210i
$456$	−0.142570	−	0.246939i	−0.00667646	−	0.0115640i
$457$			18.9183i			0.884960i	0.896778	+	0.442480i	$0.145901\pi$
$457$			18.9183i			0.884960i	−0.896778	+	0.442480i	$0.854099\pi$
$458$	−17.7608	+	10.2542i	−0.829910	+	0.479149i
$459$	−0.0713388	−	0.123562i	−0.00332981	−	0.00576740i
$460$	8.92093	+	2.95971i	0.415941	+	0.137997i
$461$	−9.19922	+	15.9335i	−0.428450	+	0.742098i	−0.996736	−	0.0807338i	$-0.974274\pi$
$461$	−9.19922	+	15.9335i	−0.428450	+	0.742098i	0.568285	+	0.822832i	$0.307607\pi$
$462$		−	0.236780i		−	0.0110160i
$463$	3.19944	+	1.84720i	0.148690	+	0.0858465i	0.572499	−	0.819905i	$-0.305974\pi$
$463$	3.19944	+	1.84720i	0.148690	+	0.0858465i	−0.423809	+	0.905752i	$0.639307\pi$
$464$	1.43082	+	2.47825i	0.0664240	+	0.115050i
$465$	0.648678	−	0.576847i	0.0300817	−	0.0267507i
$466$	−1.05991	−	1.83582i	−0.0490995	−	0.0850428i
$467$	27.5988	+	15.9342i	1.27712	+	0.737345i	0.976318	−	0.216342i	$-0.0694128\pi$
$467$	27.5988	+	15.9342i	1.27712	+	0.737345i	0.300801	+	0.953687i	$0.402746\pi$
$468$	16.9984	+	9.81402i	0.785750	+	0.453653i
$469$	51.0057			2.35522
$470$	−7.91365	+	1.63100i	−0.365030	+	0.0752326i
$471$	0.375957			0.0173232
$472$			15.0476i			0.692622i
$473$	3.10727	−	7.30612i	0.142872	−	0.335936i
$474$	0.0616540			0.00283186
$475$	−3.45399	+	29.3635i	−0.158480	+	1.34729i
$476$	1.00037	−	1.73269i	0.0458519	−	0.0794178i
$477$			13.2770i			0.607914i
$478$	0.666984	+	0.385083i	0.0305071	+	0.0176133i
$479$	17.8551	−	30.9260i	0.815823	−	1.41305i	−0.0929133	−	0.995674i	$-0.529618\pi$
$479$	17.8551	−	30.9260i	0.815823	−	1.41305i	0.908736	−	0.417372i	$-0.137049\pi$
$480$	−0.0339535	+	0.102340i	−0.00154976	+	0.00467116i
$481$	−55.9004			−2.54884
$482$	−3.79126	+	2.18888i	−0.172687	+	0.0997009i
$483$	−0.711903	−	0.411018i	−0.0323927	−	0.0187020i
$484$	9.53408			0.433367
$485$	−6.83316	−	33.1546i	−0.310278	−	1.50547i
$486$	0.650311	+	1.12637i	0.0294987	+	0.0510932i
$487$	21.4302	−	12.3727i	0.971094	−	0.560661i	0.0715242	−	0.997439i	$-0.477214\pi$
$487$	21.4302	−	12.3727i	0.971094	−	0.560661i	0.899569	+	0.436778i	$0.143880\pi$
$488$	−0.142474	+	0.0822573i	−0.00644948	+	0.00372361i
$489$	−0.493274			−0.0223066
$490$	−20.0511	−	6.65240i	−0.905817	−	0.300525i
$491$	−4.84781	−	8.39665i	−0.218779	−	0.378936i	0.735656	−	0.677355i	$-0.236874\pi$
$491$	−4.84781	−	8.39665i	−0.218779	−	0.378936i	−0.954435	+	0.298419i	$0.903541\pi$
$492$	0.361404	+	0.208656i	0.0162933	+	0.00940696i
$493$	−1.22259	−	0.705863i	−0.0550627	−	0.0317905i
$494$	−38.7182			−1.74201
$495$	5.39304	+	6.06459i	0.242399	+	0.272583i
$496$	4.02532	−	6.97207i	0.180742	−	0.313055i
$497$	6.83807	+	3.94796i	0.306729	+	0.177090i
$498$	0.0128013	−	0.00739086i	0.000573642	−	0.000331192i
$499$	−5.51631	−	9.55453i	−0.246944	−	0.427720i	0.715732	−	0.698375i	$-0.246093\pi$
$499$	−5.51631	−	9.55453i	−0.246944	−	0.427720i	−0.962676	+	0.270655i	$0.912760\pi$
$500$	9.16546	−	6.40268i	0.409892	−	0.286336i
$501$	0.346784	+	0.600648i	0.0154932	+	0.0268350i
$502$	−7.16916	+	4.13912i	−0.319975	+	0.184738i
$503$	4.16656	−	2.40556i	0.185778	−	0.107259i	−0.404227	−	0.914659i	$-0.632459\pi$
$503$	4.16656	−	2.40556i	0.185778	−	0.107259i	0.590004	+	0.807400i	$0.299126\pi$
$504$	−6.07866	+	10.5286i	−0.270765	+	0.468979i
$505$	−18.9574	−	21.3181i	−0.843595	−	0.948641i
$506$	−2.54464	+	4.40744i	−0.113123	+	0.195935i
$507$	−1.24752	+	0.720255i	−0.0554042	+	0.0319876i
$508$			4.35073i			0.193032i
$509$	−21.8678	−	37.8761i	−0.969272	−	1.67883i	−0.697671	−	0.716418i	$-0.745780\pi$
$509$	−21.8678	−	37.8761i	−0.969272	−	1.67883i	−0.271601	−	0.962410i	$-0.587553\pi$
$510$	−0.0107375	−	0.0520985i	−0.000475464	−	0.00230696i
$511$	−21.9163	+	37.9602i	−0.969521	+	1.67926i
$512$			1.00000i			0.0441942i
$513$	−1.48106	−	0.855089i	−0.0653903	−	0.0377531i
$514$	10.8851			0.480123
$515$	0.777544	−	0.691444i	0.0342627	−	0.0304687i
$516$	0.252666	−	0.190122i	0.0111230	−	0.00836964i
$517$		−	4.37502i		−	0.192413i
$518$		−	34.6239i		−	1.52129i
$519$	0.572225	−	0.991123i	0.0251179	−	0.0435055i
$520$	9.72940	+	10.9409i	0.426663	+	0.479792i
$521$	−7.03978	+	12.1933i	−0.308418	+	0.534196i	−0.978017	−	0.208527i	$-0.933133\pi$
$521$	−7.03978	+	12.1933i	−0.308418	+	0.534196i	0.669598	+	0.742723i	$0.266466\pi$
$522$	7.42897	+	4.28912i	0.325157	+	0.187730i
$523$	−30.2896	+	17.4877i	−1.32447	+	0.764684i	−0.984438	−	0.175730i	$-0.943771\pi$
$523$	−30.2896	+	17.4877i	−1.32447	+	0.764684i	−0.340033	+	0.940414i	$0.610438\pi$
$524$	10.0418			0.438678
$525$	−0.898136	+	0.386635i	−0.0391979	+	0.0168741i
$526$	2.23076	−	3.86379i	0.0972657	−	0.168469i
$527$			3.97162i			0.173007i
$528$	−0.0505617	−	0.0291918i	−0.00220042	−	0.00127041i
$529$	−2.66571	−	4.61714i	−0.115900	−	0.200745i
$530$	−3.11864	+	9.39996i	−0.135465	+	0.408308i
$531$	22.5539	+	39.0645i	0.978756	+	1.69526i
$532$		−	23.9815i		−	1.03973i
$533$	49.0737	−	28.3327i	2.12562	−	1.22723i
$534$	−0.114504	−	0.198327i	−0.00495508	−	0.00858244i
$535$	4.33912	+	21.0535i	0.187597	+	0.910221i
$536$	6.28833	−	10.8917i	0.271614	−	0.470450i
$537$		−	0.379438i		−	0.0163740i
$538$			17.2374i			0.743157i
$539$	5.71945	−	9.90638i	0.246354	−	0.426698i
$540$	0.130542	+	0.633389i	0.00561762	+	0.0272567i
$541$	13.9143	+	24.1003i	0.598224	+	1.03615i	0.993083	+	0.117413i	$0.0374601\pi$
$541$	13.9143	+	24.1003i	0.598224	+	1.03615i	−0.394859	+	0.918742i	$0.629207\pi$
$542$	9.62949	−	5.55959i	0.413622	−	0.238805i
$543$		−	1.17995i		−	0.0506364i
$544$	−0.246665	−	0.427236i	−0.0105757	−	0.0183176i
$545$	7.72304	−	23.2782i	0.330819	−	0.997127i
$546$	−0.640254	−	1.10895i	−0.0274003	−	0.0474587i
$547$	−8.80742	−	5.08497i	−0.376578	−	0.217417i	0.299750	−	0.954018i	$-0.403097\pi$
$547$	−8.80742	−	5.08497i	−0.376578	−	0.217417i	−0.676328	+	0.736600i	$0.736430\pi$
$548$			4.44688i			0.189961i
$549$	−0.246580	+	0.427090i	−0.0105238	+	0.0182278i
$550$	2.39368	+	5.56042i	0.102067	+	0.237097i
$551$	−16.9214			−0.720875
$552$	−0.175537	+	0.101346i	−0.00747133	+	0.00431358i
$553$	4.49065	+	2.59268i	0.190962	+	0.110252i
$554$	5.32475	−	9.22273i	0.226227	−	0.391836i
$555$	−0.611720	−	0.687893i	−0.0259661	−	0.0291994i
$556$	−3.49920	+	6.06079i	−0.148399	+	0.257035i
$557$		−	38.3850i		−	1.62642i	−0.581967	−	0.813212i	$-0.697717\pi$
$557$		−	38.3850i		−	1.62642i	0.581967	−	0.813212i	$-0.302283\pi$
$558$		−	24.1332i		−	1.02164i
$559$	−5.20297	−	42.6201i	−0.220062	−	1.80264i
$560$	−6.77666	+	6.02625i	−0.286366	+	0.254656i
$561$	0.0288024			0.00121604
$562$	13.6268	+	7.86745i	0.574813	+	0.331868i
$563$		−	33.2895i		−	1.40299i	−0.712676	−	0.701494i	$-0.752517\pi$
$563$		−	33.2895i		−	1.40299i	0.712676	−	0.701494i	$-0.247483\pi$
$564$	0.0871227	−	0.150901i	0.00366853	−	0.00635408i
$565$	0.356306	+	1.72880i	0.0149899	+	0.0727312i
$566$	−8.88133	−	15.3829i	−0.373310	−	0.646592i
$567$			36.4154i			1.52930i
$568$	1.68609	−	0.973463i	0.0707467	−	0.0408456i
$569$	−11.1034	+	19.2317i	−0.465480	+	0.806234i	−0.999223	−	0.0394120i	$-0.987452\pi$
$569$	−11.1034	+	19.2317i	−0.465480	+	0.806234i	0.533743	+	0.845647i	$0.320785\pi$
$570$	−0.423694	−	0.476454i	−0.0177466	−	0.0199564i
$571$	19.5228	−	33.8144i	0.817002	−	1.41509i	−0.0908792	−	0.995862i	$-0.528968\pi$
$571$	19.5228	−	33.8144i	0.817002	−	1.41509i	0.907881	−	0.419227i	$-0.137699\pi$
$572$	−6.86559	+	3.96385i	−0.287065	+	0.165737i
$573$	0.750669	−	0.433399i	0.0313596	−	0.0181055i
$574$	17.5489	+	30.3955i	0.732476	+	1.26869i
$575$	20.8731	+	2.45527i	0.870468	+	0.102392i
$576$	1.49884	+	2.59606i	0.0624516	+	0.108169i
$577$	17.2326	−	9.94923i	0.717402	−	0.414192i	−0.0963939	−	0.995343i	$-0.530731\pi$
$577$	17.2326	−	9.94923i	0.717402	−	0.414192i	0.813796	+	0.581151i	$0.197398\pi$
$578$	−14.5117	−	8.37831i	−0.603606	−	0.348492i
$579$	−0.0644165	+	0.111573i	−0.00267706	+	0.00463680i
$580$	4.25214	+	4.78163i	0.176561	+	0.198546i
$581$	1.24320			0.0515768
$582$	0.632206	+	0.365004i	0.0262058	+	0.0151299i
$583$	−4.64411	−	2.68128i	−0.192339	−	0.111047i
$584$	5.40399	+	9.35998i	0.223619	+	0.387319i
$585$	41.6568	+	13.8206i	1.72230	+	0.571410i
$586$	−3.06126			−0.126459
$587$	−31.0210	+	17.9100i	−1.28037	+	0.739224i	−0.976917	−	0.213621i	$-0.931474\pi$
$587$	−31.0210	+	17.9100i	−1.28037	+	0.739224i	−0.303457	+	0.952845i	$0.598141\pi$
$588$	0.394544	−	0.227790i	0.0162707	−	0.00939391i
$589$	23.8025	+	41.2272i	0.980766	+	1.69874i
$590$	6.79199	+	32.9548i	0.279622	+	1.35673i
$591$	−0.794186			−0.0326684
$592$	−7.39356	−	4.26867i	−0.303873	−	0.175441i
$593$	−2.49336	+	1.43954i	−0.102390	+	0.0591149i	−0.550321	−	0.834953i	$-0.685494\pi$
$593$	−2.49336	+	1.43954i	−0.102390	+	0.0591149i	0.447931	+	0.894068i	$0.352161\pi$
$594$	−0.350166			−0.0143675
$595$	1.40877	−	4.24619i	0.0577538	−	0.174077i
$596$	7.09816	−	12.2944i	0.290752	−	0.503597i
$597$	−0.717834	−	0.414442i	−0.0293790	−	0.0169620i
$598$			27.5228i			1.12549i
$599$	−6.97965	+	12.0891i	−0.285181	+	0.493948i	−0.972653	−	0.232263i	$-0.925387\pi$
$599$	−6.97965	+	12.0891i	−0.285181	+	0.493948i	0.687472	+	0.726211i	$0.258720\pi$
$600$	−0.0281666	+	0.239454i	−0.00114990	+	0.00977567i
$601$	−29.8205			−1.21640			−0.608202	−	0.793782i	$-0.708109\pi$
$601$	−29.8205			−1.21640			−0.608202	+	0.793782i	$0.708109\pi$
$602$	26.3983	−	3.22264i	1.07591	−	0.131345i
$603$		−	37.7007i		−	1.53529i
$604$	−4.04683			−0.164663
$605$	20.8800	−	4.30337i	0.848893	−	0.174957i
$606$	0.615208			0.0249911
$607$	20.7228	+	11.9643i	0.841111	+	0.485615i	0.857642	−	0.514248i	$-0.171929\pi$
$607$	20.7228	+	11.9643i	0.841111	+	0.485615i	−0.0165310	+	0.999863i	$0.505262\pi$
$608$	−5.12098	−	2.95660i	−0.207683	−	0.119906i
$609$	−0.279817	−	0.484656i	−0.0113387	−	0.0196393i
$610$	−0.274895	+	0.244455i	−0.0111302	+	0.00989767i
$611$	−11.8301	−	20.4903i	−0.478594	−	0.828949i
$612$	−1.28071	−	0.739420i	−0.0517698	−	0.0298893i
$613$			12.8718i			0.519887i	0.965624	+	0.259944i	$0.0837040\pi$
$613$			12.8718i			0.519887i	−0.965624	+	0.259944i	$0.916296\pi$
$614$	10.0058	−	17.3305i	0.403800	−	0.699402i
$615$	0.885668	+	0.293840i	0.0357136	+	0.0118488i
$616$	−2.45515	−	4.25245i	−0.0989209	−	0.171336i
$617$	−8.90746	+	5.14272i	−0.358601	+	0.207038i	−0.668467	−	0.743742i	$-0.733049\pi$
$617$	−8.90746	+	5.14272i	−0.358601	+	0.207038i	0.309866	+	0.950780i	$0.399716\pi$
$618$			0.0224388i			0.000902620i
$619$	13.1239	+	22.7312i	0.527493	+	0.913645i	0.999486	+	0.0320429i	$0.0102013\pi$
$619$	13.1239	+	22.7312i	0.527493	+	0.913645i	−0.471993	+	0.881602i	$0.656465\pi$
$620$	5.66865	−	17.0860i	0.227659	−	0.686190i
$621$	−0.607841	+	1.05281i	−0.0243918	+	0.0422479i
$622$	−27.2430	−	15.7288i	−1.09235	−	0.630666i
$623$		−	19.2605i		−	0.771657i
$624$	−0.315739			−0.0126397
$625$	17.1828	−	18.1591i	0.687310	−	0.726364i
$626$	3.94289	−	6.82928i	0.157590	−	0.272953i
$627$	0.298981	−	0.172617i	0.0119402	−	0.00689366i
$628$	6.75201	−	3.89828i	0.269435	−	0.155558i
$629$	4.21172			0.167932
$630$	−8.56026	+	25.8016i	−0.341049	+	1.02796i
$631$	4.44896	+	7.70583i	0.177110	+	0.306764i	0.940890	−	0.338713i	$-0.109992\pi$
$631$	4.44896	+	7.70583i	0.177110	+	0.306764i	−0.763779	+	0.645478i	$0.776658\pi$
$632$	1.10728	−	0.639286i	0.0440451	−	0.0254294i
$633$	0.562549	+	0.324788i	0.0223593	+	0.0129091i
$634$	−15.3430			−0.609350
$635$	1.96378	+	9.52826i	0.0779301	+	0.378118i
$636$	−0.106788	−	0.184962i	−0.00423442	−	0.00733424i
$637$		−	61.8617i		−	2.45105i
$638$	−3.00054	+	1.73236i	−0.118793	+	0.0685849i
$639$	2.91813	−	5.05434i	0.115439	−	0.199947i
$640$	0.451367	+	2.19004i	0.0178419	+	0.0865689i
$641$	32.5954			1.28744			0.643720	−	0.765261i	$-0.277390\pi$
$641$	32.5954			1.28744			0.643720	+	0.765261i	$0.277390\pi$
$642$	−0.401457	−	0.231781i	−0.0158442	−	0.00914767i
$643$			34.0896i			1.34436i	0.740386	+	0.672182i	$0.234643\pi$
$643$			34.0896i			1.34436i	−0.740386	+	0.672182i	$0.765357\pi$
$644$	−17.0473			−0.671756
$645$	0.467533	−	0.530419i	0.0184091	−	0.0208852i
$646$	2.91715			0.114774
$647$		−	17.3941i		−	0.683832i	−0.939731	−	0.341916i	$-0.888924\pi$
$647$		−	17.3941i		−	0.683832i	0.939731	−	0.341916i	$-0.111076\pi$
$648$	7.77611	+	4.48954i	0.305474	+	0.176366i
$649$	−18.2189			−0.715155
$650$	26.2461	+	19.5695i	1.02946	+	0.767581i
$651$	−0.787210	+	1.36349i	−0.0308532	+	0.0534393i
$652$	−8.85895	+	5.11472i	−0.346943	+	0.200308i
$653$		−	28.5268i		−	1.11634i	−0.829726	−	0.558171i	$-0.811503\pi$
$653$		−	28.5268i		−	1.11634i	0.829726	−	0.558171i	$-0.188497\pi$
$654$	0.264451	+	0.458043i	0.0103409	+	0.0179109i
$655$	21.9919	−	4.53254i	0.859296	−	0.177101i
$656$	8.65418			0.337889
$657$	28.0582	+	16.1994i	1.09465	+	0.631999i
$658$	12.6914	−	7.32738i	0.494762	−	0.285651i
$659$	8.15199	+	14.1197i	0.317556	+	0.550024i	0.979978	−	0.199108i	$-0.0638044\pi$
$659$	8.15199	+	14.1197i	0.317556	+	0.550024i	−0.662421	+	0.749132i	$0.730471\pi$
$660$	−0.123908	−	0.0411093i	−0.00482312	−	0.00160018i
$661$	12.5760			0.489150			0.244575	−	0.969630i	$-0.421352\pi$
$661$	12.5760			0.489150			0.244575	+	0.969630i	$0.421352\pi$
$662$	17.1542	−	9.90401i	0.666719	−	0.384930i
$663$	0.134895	−	0.0778817i	0.00523889	−	0.00302467i
$664$	0.153271	−	0.265472i	0.00594805	−	0.0103023i
$665$	−10.8244	−	52.5203i	−0.419754	−	2.03665i
$666$	−25.5922			−0.991677
$667$			12.0286i			0.465749i
$668$	12.4562	+	7.19156i	0.481943	+	0.278250i
$669$	−0.0186167	+	0.0322450i	−0.000719762	+	0.00124666i
$670$	8.85552	−	26.6916i	0.342118	−	1.03119i
$671$	−0.0995931	−	0.172500i	−0.00384475	−	0.00665930i
$672$		−	0.195564i		−	0.00754406i
$673$	−25.1492	+	14.5199i	−0.969429	+	0.559700i	−0.899062	−	0.437821i	$-0.855750\pi$
$673$	−25.1492	+	14.5199i	−0.969429	+	0.559700i	−0.0703671	+	0.997521i	$0.522417\pi$
$674$	6.03072	+	10.4455i	0.232295	+	0.402346i
$675$	0.571782	+	1.32822i	0.0220079	+	0.0511234i
$676$	−14.9365	+	25.8709i	−0.574482	+	0.995033i
$677$		−	1.09298i		−	0.0420067i	−0.999779	−	0.0210033i	$-0.993314\pi$
$677$		−	1.09298i		−	0.0420067i	0.999779	−	0.0210033i	$-0.00668606\pi$
$678$	−0.0329655	−	0.0190327i	−0.00126603	−	0.000730945i
$679$	30.6983	+	53.1711i	1.17809	+	2.04052i
$680$	−0.733045	−	0.824326i	−0.0281110	−	0.0316115i
$681$	−0.224207	−	0.388338i	−0.00859162	−	0.0148811i
$682$	8.44144	+	4.87367i	0.323239	+	0.186622i
$683$	−35.6656	−	20.5916i	−1.36471	−	0.787914i	−0.374461	−	0.927242i	$-0.622172\pi$
$683$	−35.6656	−	20.5916i	−1.36471	−	0.787914i	−0.990246	+	0.139328i	$0.955506\pi$
$684$	−17.7258			−0.677764
$685$	2.00718	+	9.73884i	0.0766903	+	0.372102i
$686$	9.92712			0.379019
$687$		−	0.988938i		−	0.0377303i
$688$	2.56640	−	6.03437i	0.0978430	−	0.230058i
$689$	−29.0007			−1.10484
$690$	−0.338688	+	0.301183i	−0.0128936	+	0.0114659i
$691$	5.77430	−	10.0014i	0.219665	−	0.380470i	−0.735041	−	0.678023i	$-0.762837\pi$
$691$	5.77430	−	10.0014i	0.219665	−	0.380470i	0.954705	+	0.297553i	$0.0961704\pi$
$692$		−	23.7335i		−	0.902210i
$693$	−12.7475	−	7.35975i	−0.484236	−	0.279574i
$694$	5.47932	−	9.49046i	0.207992	−	0.360253i
$695$	−4.92774	+	14.8528i	−0.186920	+	0.563398i
$696$	−0.137991			−0.00523052
$697$	−3.69737	+	2.13468i	−0.140048	+	0.0808568i
$698$	−26.6250	−	15.3720i	−1.00777	−	0.581837i
$699$	0.102220			0.00386631
$700$	−12.1211	+	16.2565i	−0.458134	+	0.614437i
$701$	0.895381	+	1.55084i	0.0338181	+	0.0585746i	0.882439	−	0.470427i	$-0.155900\pi$
$701$	0.895381	+	1.55084i	0.0338181	+	0.0585746i	−0.848621	+	0.529001i	$0.822567\pi$
$702$	−1.63999	+	0.946851i	−0.0618976	+	0.0357366i
$703$	43.7195	−	25.2415i	1.64891	−	0.952001i
$704$	−1.21075			−0.0456319
$705$	0.122690	−	0.369803i	0.00462078	−	0.0139276i
$706$	4.15341	+	7.19391i	0.156315	+	0.270746i
$707$	44.8095	+	25.8708i	1.68523	+	0.972970i
$708$	−0.628397	−	0.362805i	−0.0236166	−	0.0136351i
$709$	−17.5539			−0.659252			−0.329626	−	0.944112i	$-0.606923\pi$
$709$	−17.5539			−0.659252			−0.329626	+	0.944112i	$0.606923\pi$
$710$	3.25321	−	2.89297i	0.122091	−	0.108571i
$711$	1.91637	−	3.31925i	0.0718695	−	0.124482i
$712$	−4.11288	−	2.37457i	−0.154137	−	0.0889908i
$713$	29.3064	−	16.9201i	1.09753	−	0.633661i
$714$	0.0482388	+	0.0835521i	0.00180529	+	0.00312686i
$715$	−13.2468	+	11.7799i	−0.495401	+	0.440543i
$716$	−3.93437	−	6.81452i	−0.147034	−	0.254671i
$717$	−0.0321626	+	0.0185691i	−0.00120114	+	0.000693476i
$718$	20.1270	−	11.6203i	0.751132	−	0.433666i
$719$	0.902336	−	1.56289i	0.0336515	−	0.0582860i	−0.848709	−	0.528860i	$-0.822620\pi$
$719$	0.902336	−	1.56289i	0.0336515	−	0.0582860i	0.882361	+	0.470574i	$0.155953\pi$
$720$	4.45429	+	5.00895i	0.166002	+	0.186673i
$721$	−0.943597	+	1.63436i	−0.0351414	+	0.0608667i
$722$	13.8269	−	7.98295i	0.514583	−	0.297094i
$723$		−	0.211100i		−	0.00785091i
$724$	−12.2348	−	21.1913i	−0.454703	−	0.787568i
$725$	11.4706	+	8.55268i	0.426008	+	0.317638i
$726$	−0.229871	+	0.398149i	−0.00853133	+	0.0147767i
$727$			7.42381i			0.275334i	0.990479	+	0.137667i	$0.0439603\pi$
$727$			7.42381i			0.275334i	−0.990479	+	0.137667i	$0.956040\pi$
$728$	−22.9973	−	13.2775i	−0.852336	−	0.492096i
$729$	26.8745			0.995352
$730$	16.0597	+	18.0595i	0.594397	+	0.668413i
$731$	0.392009	+	3.21114i	0.0144990	+	0.118768i
$732$		−	0.00793305i		−	0.000293214i
$733$			23.8888i			0.882352i	0.897421	+	0.441176i	$0.145439\pi$
$733$			23.8888i			0.882352i	−0.897421	+	0.441176i	$0.854561\pi$
$734$	8.97276	−	15.5413i	0.331191	−	0.573639i
$735$	0.761250	−	0.676954i	0.0280791	−	0.0249698i
$736$	−2.10170	+	3.64025i	−0.0774697	+	0.134181i
$737$	13.1871	+	7.61360i	0.485755	+	0.280451i
$738$	22.4668	−	12.9712i	0.827014	−	0.477477i
$739$	42.8600			1.57663			0.788314	−	0.615273i	$-0.210954\pi$
$739$	42.8600			1.57663			0.788314	+	0.615273i	$0.210954\pi$
$740$	−18.1189	−	6.01134i	−0.666064	−	0.220981i
$741$	0.933514	−	1.61689i	0.0342935	−	0.0593981i
$742$		−	17.9626i		−	0.659429i
$743$	−28.9362	−	16.7063i	−1.06157	−	0.612896i	−0.135701	−	0.990750i	$-0.543329\pi$
$743$	−28.9362	−	16.7063i	−1.06157	−	0.612896i	−0.925865	+	0.377854i	$0.876662\pi$
$744$	0.194105	+	0.336200i	0.00711624	+	0.0123257i
$745$	9.99596	−	30.1290i	0.366224	−	1.10384i
$746$	8.10038	+	14.0303i	0.296576	+	0.513685i
$747$		−	0.918910i		−	0.0336212i
$748$	0.517276	−	0.298650i	0.0189135	−	0.0109197i
$749$	−19.4937	−	33.7642i	−0.712286	−	1.23372i
$750$	0.0463957	+	0.537127i	0.00169413	+	0.0196131i
$751$	−7.01641	+	12.1528i	−0.256032	+	0.443461i	−0.965175	−	0.261603i	$-0.915749\pi$
$751$	−7.01641	+	12.1528i	−0.256032	+	0.443461i	0.709143	+	0.705065i	$0.249082\pi$
$752$		−	3.61348i		−	0.131770i
$753$		−	0.399185i		−	0.0145471i
$754$	−9.36863	+	16.2269i	−0.341185	+	0.590950i
$755$	−8.86271	+	1.82661i	−0.322547	+	0.0664770i
$756$	−0.586466	−	1.01579i	−0.0213295	−	0.0369439i
$757$	−11.3518	+	6.55397i	−0.412589	+	0.238208i	−0.691901	−	0.721992i	$-0.743227\pi$
$757$	−11.3518	+	6.55397i	−0.412589	+	0.238208i	0.279313	+	0.960200i	$0.409893\pi$
$758$			6.86184i			0.249233i
$759$	−0.122705	−	0.212531i	−0.00445391	−	0.00771439i
$760$	−12.5497	−	4.16362i	−0.455224	−	0.151030i
$761$	25.8549	+	44.7820i	0.937239	+	1.62335i	0.770592	+	0.637329i	$0.219961\pi$
$761$	25.8549	+	44.7820i	0.937239	+	1.62335i	0.166647	+	0.986017i	$0.446706\pi$
$762$	−0.181689	−	0.104898i	−0.00658190	−	0.00380006i
$763$			44.4829i			1.61039i
$764$	8.98776	−	15.5673i	0.325166	−	0.563204i
$765$	−3.13856	−	1.04129i	−0.113475	−	0.0376478i
$766$	−11.1830			−0.404059
$767$	−85.3277	+	49.2640i	−3.08101	+	1.77882i
$768$	−0.0417606	−	0.0241105i	−0.00150691	−	0.000870013i
$769$	−13.1751	+	22.8200i	−0.475107	+	0.822909i	−0.999594	−	0.0285095i	$-0.990924\pi$
$769$	−13.1751	+	22.8200i	−0.475107	+	0.822909i	0.524487	+	0.851419i	$0.324257\pi$
$770$	−7.29629	−	8.20485i	−0.262940	−	0.295682i
$771$	−0.262446	+	0.454570i	−0.00945177	+	0.0163709i
$772$			2.67172i			0.0961574i
$773$			47.8910i			1.72252i	0.508166	+	0.861259i	$0.330324\pi$
$773$			47.8910i			1.72252i	−0.508166	+	0.861259i	$0.669676\pi$
$774$	−2.38201	−	19.5122i	−0.0856196	−	0.701352i
$775$	4.70251	−	39.9776i	0.168919	−	1.43604i
$776$	15.1388			0.543451
$777$	1.44592	+	0.834800i	0.0518719	+	0.0299483i
$778$		−	16.3355i		−	0.585657i
$779$	−25.5869	+	44.3178i	−0.916747	+	1.58785i
$780$	−0.691481	+	0.142514i	−0.0247590	+	0.00510283i
$781$	1.17862	+	2.04143i	0.0421744	+	0.0730482i
$782$		−	2.07366i		−	0.0741540i
$783$	−0.716743	+	0.413812i	−0.0256143	+	0.0147884i
$784$	4.72388	−	8.18201i	0.168710	−	0.292214i
$785$	13.0276	−	11.5850i	0.464975	−	0.413487i
$786$	−0.242113	+	0.419352i	−0.00863588	+	0.0149578i
$787$	13.7430	−	7.93452i	0.489885	−	0.282835i	−0.234642	−	0.972082i	$-0.575392\pi$
$787$	13.7430	−	7.93452i	0.489885	−	0.282835i	0.724527	+	0.689247i	$0.242058\pi$
$788$	−14.2632	+	8.23486i	−0.508105	+	0.293355i
$789$	0.107569	+	0.186316i	0.00382957	+	0.00663302i
$790$	2.13642	−	1.89985i	0.0760105	−	0.0675936i
$791$	−1.60073	−	2.77254i	−0.0569153	−	0.0985801i
$792$	−3.14319	+	1.81472i	−0.111688	+	0.0644832i
$793$	−0.932883	−	0.538600i	−0.0331276	−	0.0191263i
$794$	−2.17803	+	3.77245i	−0.0772952	+	0.133879i
$795$	−0.317356	−	0.356874i	−0.0112555	−	0.0126570i
$796$	−17.1893			−0.609257
$797$	3.86855	+	2.23351i	0.137031	+	0.0791149i	0.566948	−	0.823753i	$-0.308124\pi$
$797$	3.86855	+	2.23351i	0.137031	+	0.0791149i	−0.429917	+	0.902868i	$0.641457\pi$
$798$	1.00148	+	0.578205i	0.0354520	+	0.0204682i
$799$	0.891317	+	1.54381i	0.0315325	+	0.0546159i
$800$	1.97702	+	4.59254i	0.0698983	+	0.162371i
$801$	−14.2364			−0.503018
$802$	27.2170	−	15.7137i	0.961064	−	0.554871i
$803$	−11.3326	+	6.54289i	−0.399919	+	0.230893i
$804$	0.303229	+	0.525208i	0.0106941	+	0.0185227i
$805$	−37.3341	+	7.69457i	−1.31586	+	0.271198i
$806$	52.7137			1.85676
$807$	−0.719844	−	0.415602i	−0.0253397	−	0.0146299i
$808$	11.0488	−	6.37904i	0.388696	−	0.224414i
$809$	5.40141			0.189903			0.0949516	−	0.995482i	$-0.469730\pi$
$809$	5.40141			0.189903			0.0949516	+	0.995482i	$0.469730\pi$
$810$	19.0564	+	6.32238i	0.669574	+	0.222146i
$811$	15.6118	−	27.0404i	0.548205	−	0.949518i	−0.450193	−	0.892931i	$-0.648645\pi$
$811$	15.6118	−	27.0404i	0.548205	−	0.949518i	0.998398	−	0.0565869i	$-0.0180218\pi$
$812$	−10.0507	−	5.80279i	−0.352712	−	0.203638i
$813$			0.536178i			0.0188046i
$814$	5.16830	−	8.95176i	0.181149	−	0.313759i
$815$	−17.0928	+	15.2001i	−0.598736	+	0.532435i
$816$	0.0237888			0.000832776
$817$	23.3141	+	30.9837i	0.815656	+	1.08398i
$818$			15.0079i			0.524740i
$819$	−79.6032			−2.78156
$820$	18.9530	−	3.90621i	0.661867	−	0.136411i
$821$	−35.3968			−1.23536			−0.617679	−	0.786430i	$-0.711927\pi$
$821$	−35.3968			−1.23536			−0.617679	+	0.786430i	$0.711927\pi$
$822$	−0.185704	−	0.107217i	−0.00647719	−	0.00373961i
$823$	12.7180	+	7.34274i	0.443321	+	0.255952i	0.705005	−	0.709202i	$-0.250945\pi$
$823$	12.7180	+	7.34274i	0.443321	+	0.255952i	−0.261684	+	0.965154i	$0.584278\pi$
$824$	0.232666	+	0.402989i	0.00810531	+	0.0140388i
$825$	−0.289919	−	0.0341028i	−0.0100937	−	0.00118731i
$826$	−30.5134	−	52.8508i	−1.06170	−	1.83891i
$827$	−6.90064	−	3.98408i	−0.239959	−	0.138540i	0.375199	−	0.926944i	$-0.377574\pi$
$827$	−6.90064	−	3.98408i	−0.239959	−	0.138540i	−0.615158	+	0.788404i	$0.710908\pi$
$828$			12.6004i			0.437895i
$829$	13.6198	−	23.5902i	0.473035	−	0.819321i	−0.526488	−	0.850182i	$-0.676492\pi$
$829$	13.6198	−	23.5902i	0.473035	−	0.819321i	0.999524	+	0.0308613i	$0.00982501\pi$
$830$	0.215843	−	0.650576i	0.00749201	−	0.0225818i
$831$	0.256765	+	0.444729i	0.00890706	+	0.0154275i
$832$	−5.67052	+	3.27388i	−0.196590	+	0.113501i
$833$			4.66086i			0.161489i
$834$	−0.168735	−	0.292257i	−0.00584281	−	0.0101200i
$835$	30.5255	+	10.1275i	1.05638	+	0.350477i
$836$	3.57971	−	6.20023i	0.123807	−	0.214440i
$837$	2.01642	+	1.16418i	0.0696976	+	0.0402399i
$838$			33.5113i			1.15763i
$839$	9.83244			0.339453			0.169727	−	0.985491i	$-0.445712\pi$
$839$	9.83244			0.339453			0.169727	+	0.985491i	$0.445712\pi$
$840$	−0.0882713	−	0.428293i	−0.00304565	−	0.0147775i
$841$	10.4055	−	18.0229i	0.358811	−	0.621480i
$842$	0.444986	−	0.256913i	0.0153352	−	0.00885380i
$843$	−0.657099	+	0.379376i	−0.0226317	+	0.0130664i
$844$	13.4708			0.463684
$845$	−21.0343	+	63.4000i	−0.723604	+	2.18103i
$846$	−5.41601	−	9.38081i	−0.186206	−	0.322519i
$847$	−33.4860	+	19.3331i	−1.15059	+	0.664294i
$848$	−3.83572	−	2.21456i	−0.131719	−	0.0760482i
$849$	0.856533			0.0293961
$850$	−1.97747	−	1.47443i	−0.0678267	−	0.0505727i
$851$	−17.9429	−	31.0781i	−0.615076	−	1.06534i
$852$			0.0938827i			0.00321637i
$853$	−22.0168	+	12.7114i	−0.753842	+	0.435231i	−0.827080	−	0.562084i	$-0.810000\pi$
$853$	−22.0168	+	12.7114i	−0.753842	+	0.435231i	0.0732385	+	0.997314i	$0.476667\pi$
$854$	0.333601	−	0.577814i	0.0114156	−	0.0197724i
$855$	−38.8203	+	8.00086i	−1.32763	+	0.273624i
$856$	−9.61329			−0.328575
$857$	5.48079	+	3.16433i	0.187220	+	0.108092i	0.590681	−	0.806906i	$-0.298859\pi$
$857$	5.48079	+	3.16433i	0.187220	+	0.108092i	−0.403460	+	0.914997i	$0.632193\pi$
$858$		−	0.382282i		−	0.0130509i
$859$	−12.1759			−0.415435			−0.207717	−	0.978189i	$-0.566603\pi$
$859$	−12.1759			−0.415435			−0.207717	+	0.978189i	$0.566603\pi$
$860$	2.89679	−	14.3739i	0.0987798	−	0.490145i
$861$	−1.69245			−0.0576785
$862$		−	12.1396i		−	0.413477i
$863$	−43.7819	−	25.2775i	−1.49035	−	0.860455i	−0.490412	−	0.871490i	$-0.663154\pi$
$863$	−43.7819	−	25.2775i	−1.49035	−	0.860455i	−0.999939	+	0.0110356i	$0.996487\pi$
$864$	−0.289214			−0.00983925
$865$	−10.7125	−	51.9772i	−0.364236	−	1.76728i
$866$	−12.3067	+	21.3158i	−0.418199	+	0.724342i
$867$	0.699767	−	0.404011i	0.0237653	−	0.0137209i
$868$			32.6501i			1.10822i
$869$	0.774016	+	1.34064i	0.0262567	+	0.0454779i
$870$	−0.302205	+	0.0622845i	−0.0102457	+	0.00211164i
$871$	82.3488			2.79028
$872$	9.49883	+	5.48415i	0.321671	+	0.185717i
$873$	39.3013	−	22.6906i	1.33015	−	0.767961i
$874$	−12.4278	−	21.5255i	−0.420376	−	0.728112i
$875$	−19.2080	+	41.0734i	−0.649349	+	1.38853i
$876$	−0.521171			−0.0176087
$877$	2.94396	−	1.69970i	0.0994105	−	0.0573947i	−0.449471	−	0.893295i	$-0.648387\pi$
$877$	2.94396	−	1.69970i	0.0994105	−	0.0573947i	0.548881	+	0.835900i	$0.315054\pi$
$878$	−9.67298	+	5.58470i	−0.326447	+	0.188474i
$879$	0.0738084	−	0.127840i	0.00248950	−	0.00431193i
$880$	−2.65159	+	0.546494i	−0.0893851	+	0.0184223i
$881$	48.7148			1.64124			0.820622	−	0.571471i	$-0.193627\pi$
$881$	48.7148			1.64124			0.820622	+	0.571471i	$0.193627\pi$
$882$		−	28.3213i		−	0.953629i
$883$	3.10907	+	1.79502i	0.104628	+	0.0604072i	0.551401	−	0.834240i	$-0.314093\pi$
$883$	3.10907	+	1.79502i	0.104628	+	0.0604072i	−0.446773	+	0.894648i	$0.647427\pi$
$884$	1.61510	−	2.79743i	0.0543217	−	0.0940879i
$885$	−1.53997	−	0.510919i	−0.0517656	−	0.0171744i
$886$	15.8013	+	27.3686i	0.530855	+	0.919467i
$887$			28.0343i			0.941301i	0.882320	+	0.470651i	$0.155981\pi$
$887$			28.0343i			0.941301i	−0.882320	+	0.470651i	$0.844019\pi$
$888$	0.356525	−	0.205840i	0.0119642	−	0.00690752i
$889$	−8.82237	−	15.2808i	−0.295893	−	0.512502i
$890$	−10.0792	−	3.34398i	−0.337854	−	0.112091i
$891$	−5.43572	+	9.41494i	−0.182103	+	0.315412i
$892$			0.772140i			0.0258531i
$893$	18.5045	+	10.6836i	0.619231	+	0.357513i
$894$	0.342280	+	0.592846i	0.0114476	+	0.0198278i
$895$	−11.6923	−	13.1482i	−0.390829	−	0.439496i
$896$	−2.02779	−	3.51224i	−0.0677438	−	0.117336i
$897$	−1.14937	−	0.663589i	−0.0383764	−	0.0221566i
$898$	−4.98388	−	2.87744i	−0.166314	−	0.0960215i
$899$	23.0380			0.768360
$900$	12.0159	+	8.95927i	0.400531	+	0.298642i
$901$	2.18501			0.0727933
$902$			10.4781i			0.348881i
$903$	−0.501896	+	1.18011i	−0.0167020	+	0.0392715i
$904$	−0.789393			−0.0262548
$905$	−36.3597	−	40.8874i	−1.20864	−	1.35914i
$906$	0.0975710	−	0.168998i	0.00324158	−	0.00561458i
$907$			46.8204i			1.55465i	0.629101	+	0.777323i	$0.283423\pi$
$907$			46.8204i			1.55465i	−0.629101	+	0.777323i	$0.716577\pi$
$908$	−8.05329	−	4.64957i	−0.267258	−	0.154301i
$909$	19.1223	−	33.1208i	0.634247	−	1.09855i
$910$	−56.3579	−	18.6980i	−1.86825	−	0.619832i
$911$	20.0109			0.662992			0.331496	−	0.943457i	$-0.392447\pi$
$911$	20.0109			0.662992			0.331496	+	0.943457i	$0.392447\pi$
$912$	0.246939	−	0.142570i	0.00817696	−	0.00472097i
$913$	0.321421	+	0.185573i	0.0106375	+	0.00614155i
$914$	−18.9183			−0.625761
$915$	−0.00358072	−	0.0173737i	−0.000118375	−	0.000574356i
$916$	−10.2542	−	17.7608i	−0.338809	−	0.586835i
$917$	−35.2692	+	20.3627i	−1.16469	+	0.672435i
$918$	0.123562	−	0.0713388i	0.00407817	−	0.00235453i
$919$	−7.47561			−0.246598			−0.123299	−	0.992370i	$-0.539347\pi$
$919$	−7.47561			−0.246598			−0.123299	+	0.992370i	$0.539347\pi$
$920$	−2.95971	+	8.92093i	−0.0975789	+	0.294114i
$921$	0.482488	+	0.835693i	0.0158985	+	0.0275370i
$922$	−15.9335	−	9.19922i	−0.524742	−	0.302960i
$923$	11.0401	+	6.37400i	0.363389	+	0.209803i
$924$	0.236780			0.00778948
$925$	−42.3944	−	4.98679i	−1.39392	−	0.163965i
$926$	−1.84720	+	3.19944i	−0.0607026	+	0.105140i
$927$	1.20803	+	0.697457i	0.0396769	+	0.0229075i
$928$	−2.47825	+	1.43082i	−0.0813524	+	0.0469688i
$929$	−0.886490	−	1.53545i	−0.0290848	−	0.0503763i	0.851117	−	0.524977i	$-0.175926\pi$
$929$	−0.886490	−	1.53545i	−0.0290848	−	0.0503763i	−0.880201	+	0.474600i	$0.842593\pi$
$930$	0.576847	+	0.648678i	0.0189156	+	0.0212710i
$931$	27.9332	+	48.3818i	0.915475	+	1.58565i
$932$	1.83582	−	1.05991i	0.0601343	−	0.0347186i
$933$	1.31369	−	0.758457i	0.0430081	−	0.0248308i
$934$	−15.9342	+	27.5988i	−0.521381	+	0.903059i
$935$	0.998054	−	0.887536i	0.0326399	−	0.0290255i
$936$	−9.81402	+	16.9984i	−0.320781	+	0.555609i
$937$	−19.8476	+	11.4590i	−0.648392	+	0.374350i	−0.787840	−	0.615880i	$-0.788801\pi$
$937$	−19.8476	+	11.4590i	−0.648392	+	0.374350i	0.139448	+	0.990229i	$0.455467\pi$
$938$			51.0057i			1.66539i
$939$	0.190130	+	0.329315i	0.00620466	+	0.0107468i
$940$	−1.63100	−	7.91365i	−0.0531975	−	0.258115i
$941$	14.0422	−	24.3217i	0.457761	−	0.792866i	−0.541081	−	0.840970i	$-0.681985\pi$
$941$	14.0422	−	24.3217i	0.457761	−	0.792866i	0.998842	+	0.0481046i	$0.0153181\pi$
$942$			0.375957i			0.0122494i
$943$	31.5034	+	18.1885i	1.02589	+	0.592299i
$944$	−15.0476			−0.489758
$945$	−1.74288	−	1.95990i	−0.0566957	−	0.0637557i
$946$	7.30612	+	3.10727i	0.237542	+	0.101026i
$947$		−	42.6476i		−	1.38586i	−0.721005	−	0.692930i	$-0.756319\pi$
$947$		−	42.6476i		−	1.38586i	0.721005	−	0.692930i	$-0.243681\pi$
$948$			0.0616540i			0.00200243i
$949$	−35.3840	+	61.2869i	−1.14861	+	1.98946i
$950$	−29.3635	−	3.45399i	−0.952679	−	0.112062i
$951$	0.369928	−	0.640735i	0.0119957	−	0.0207772i
$952$	1.73269	+	1.00037i	0.0561568	+	0.0324222i
$953$	−1.90536	+	1.10006i	−0.0617205	+	0.0356344i	−0.530543	−	0.847658i	$-0.678012\pi$
$953$	−1.90536	+	1.10006i	−0.0617205	+	0.0356344i	0.468822	+	0.883293i	$0.344679\pi$
$954$	−13.2770			−0.429860
$955$	12.6570	−	38.1497i	0.409571	−	1.23449i
$956$	−0.385083	+	0.666984i	−0.0124545	+	0.0215718i
$957$		−	0.167072i		−	0.00540069i
$958$	30.9260	+	17.8551i	0.999174	+	0.576874i
$959$	−9.01735	−	15.6185i	−0.291186	−	0.504348i
$960$	−0.102340	−	0.0339535i	−0.00330301	−	0.00109585i
$961$	−16.9065	−	29.2829i	−0.545370	−	0.944609i
$962$		−	55.9004i		−	1.80230i
$963$	−24.9567	+	14.4088i	−0.804218	+	0.464316i
$964$	−2.18888	−	3.79126i	−0.0704992	−	0.122108i
$965$	1.20593	+	5.85117i	0.0388202	+	0.188356i
$966$	0.411018	−	0.711903i	0.0132243	−	0.0229051i
$967$		−	23.5356i		−	0.756855i	−0.925631	−	0.378428i	$-0.876465\pi$
$967$		−	23.5356i		−	0.756855i	0.925631	−	0.378428i	$-0.123535\pi$
$968$			9.53408i			0.306437i
$969$	−0.0703340	+	0.121822i	−0.00225945	+	0.00391349i
$970$	33.1546	−	6.83316i	1.06453	−	0.219400i
$971$	3.94946	+	6.84066i	0.126744	+	0.219527i	0.922413	−	0.386204i	$-0.126214\pi$
$971$	3.94946	+	6.84066i	0.126744	+	0.219527i	−0.795669	+	0.605731i	$0.792881\pi$
$972$	−1.12637	+	0.650311i	−0.0361284	+	0.0208587i
$973$		−	28.3826i		−	0.909904i
$974$	12.3727	+	21.4302i	0.396447	+	0.686667i
$975$	−1.45004	+	0.624224i	−0.0464386	+	0.0199912i
$976$	−0.0822573	−	0.142474i	−0.00263299	−	0.00456047i
$977$	−44.5642	−	25.7292i	−1.42574	−	0.823149i	−0.428955	−	0.903326i	$-0.641118\pi$
$977$	−44.5642	−	25.7292i	−1.42574	−	0.823149i	−0.996781	+	0.0801770i	$0.974451\pi$
$978$		−	0.493274i		−	0.0157731i
$979$	2.87501	−	4.97967i	0.0918858	−	0.159151i
$980$	6.65240	−	20.0511i	0.212503	−	0.640509i
$981$	32.8794			1.04976
$982$	8.39665	−	4.84781i	0.267948	−	0.154700i
$983$	−32.4652	−	18.7438i	−1.03548	−	0.597834i	−0.116929	−	0.993140i	$-0.537305\pi$
$983$	−32.4652	−	18.7438i	−1.03548	−	0.597834i	−0.918549	+	0.395306i	$0.870638\pi$
$984$	−0.208656	+	0.361404i	−0.00665173	+	0.0115211i
$985$	−27.5200	+	24.4726i	−0.876860	+	0.779761i
$986$	0.705863	−	1.22259i	0.0224793	−	0.0389352i
$987$			0.706667i			0.0224935i
$988$		−	38.7182i		−	1.23179i
$989$	22.0248	−	16.5728i	0.700347	−	0.526985i
$990$	−6.06459	+	5.39304i	−0.192745	+	0.171402i
$991$	−25.3855			−0.806396			−0.403198	−	0.915113i	$-0.632101\pi$
$991$	−25.3855			−0.806396			−0.403198	+	0.915113i	$0.632101\pi$
$992$	6.97207	+	4.02532i	0.221363	+	0.127804i
$993$			0.955162i			0.0303112i
$994$	−3.94796	+	6.83807i	−0.125222	+	0.216890i
$995$	−37.6451	+	7.75867i	−1.19343	+	0.245966i
$996$	0.00739086	+	0.0128013i	0.000234188	+	0.000405626i
$997$		−	26.0720i		−	0.825708i	−0.910797	−	0.412854i	$-0.864532\pi$
$997$		−	26.0720i		−	0.825708i	0.910797	−	0.412854i	$-0.135468\pi$
$998$	9.55453	−	5.51631i	0.302443	−	0.174616i
$999$	1.23456	−	2.13832i	0.0390597	−	0.0676534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.17	yes	44
5.4	even	2	inner	430.2.j.a.49.6	✓	44
43.36	even	3	inner	430.2.j.a.79.17	yes	44
215.79	even	6	inner	430.2.j.a.79.6	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.6	✓	44	5.4	even	2	inner
430.2.j.a.49.17	yes	44	1.1	even	1	trivial
430.2.j.a.79.6	yes	44	215.79	even	6	inner
430.2.j.a.79.17	yes	44	43.36	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.0417606 - 0.0241105i) q^{3} -1.00000 q^{4} +(-2.19004 + 0.451367i) q^{5} +(0.0241105 - 0.0417606i) q^{6} +(3.51224 - 2.02779i) q^{7} -1.00000i q^{8} +(-1.49884 - 2.59606i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.0417606 - 0.0241105i) q^{3} -1.00000 q^{4} +(-2.19004 + 0.451367i) q^{5} +(0.0241105 - 0.0417606i) q^{6} +(3.51224 - 2.02779i) q^{7} -1.00000i q^{8} +(-1.49884 - 2.59606i) q^{9} +(-0.451367 - 2.19004i) q^{10} +1.21075 q^{11} +(0.0417606 + 0.0241105i) q^{12} +(5.67052 - 3.27388i) q^{13} +(2.02779 + 3.51224i) q^{14} +(0.102340 + 0.0339535i) q^{15} +1.00000 q^{16} +(-0.427236 + 0.246665i) q^{17} +(2.59606 - 1.49884i) q^{18} +(-2.95660 + 5.12098i) q^{19} +(2.19004 - 0.451367i) q^{20} -0.195564 q^{21} +1.21075i q^{22} +(3.64025 + 2.10170i) q^{23} +(-0.0241105 + 0.0417606i) q^{24} +(4.59254 - 1.97702i) q^{25} +(3.27388 + 5.67052i) q^{26} +0.289214i q^{27} +(-3.51224 + 2.02779i) q^{28} +(1.43082 + 2.47825i) q^{29} +(-0.0339535 + 0.102340i) q^{30} +(4.02532 - 6.97207i) q^{31} +1.00000i q^{32} +(-0.0505617 - 0.0291918i) q^{33} +(-0.246665 - 0.427236i) q^{34} +(-6.77666 + 6.02625i) q^{35} +(1.49884 + 2.59606i) q^{36} +(-7.39356 - 4.26867i) q^{37} +(-5.12098 - 2.95660i) q^{38} -0.315739 q^{39} +(0.451367 + 2.19004i) q^{40} +8.65418 q^{41} -0.195564i q^{42} +(2.56640 - 6.03437i) q^{43} -1.21075 q^{44} +(4.45429 + 5.00895i) q^{45} +(-2.10170 + 3.64025i) q^{46} -3.61348i q^{47} +(-0.0417606 - 0.0241105i) q^{48} +(4.72388 - 8.18201i) q^{49} +(1.97702 + 4.59254i) q^{50} +0.0237888 q^{51} +(-5.67052 + 3.27388i) q^{52} +(-3.83572 - 2.21456i) q^{53} -0.289214 q^{54} +(-2.65159 + 0.546494i) q^{55} +(-2.02779 - 3.51224i) q^{56} +(0.246939 - 0.142570i) q^{57} +(-2.47825 + 1.43082i) q^{58} -15.0476 q^{59} +(-0.102340 - 0.0339535i) q^{60} +(-0.0822573 - 0.142474i) q^{61} +(6.97207 + 4.02532i) q^{62} +(-10.5286 - 6.07866i) q^{63} -1.00000 q^{64} +(-10.9409 + 9.72940i) q^{65} +(0.0291918 - 0.0505617i) q^{66} +(10.8917 + 6.28833i) q^{67} +(0.427236 - 0.246665i) q^{68} +(-0.101346 - 0.175537i) q^{69} +(-6.02625 - 6.77666i) q^{70} +(0.973463 + 1.68609i) q^{71} +(-2.59606 + 1.49884i) q^{72} +(-9.35998 + 5.40399i) q^{73} +(4.26867 - 7.39356i) q^{74} +(-0.239454 - 0.0281666i) q^{75} +(2.95660 - 5.12098i) q^{76} +(4.25245 - 2.45515i) q^{77} -0.315739i q^{78} +(0.639286 + 1.10728i) q^{79} +(-2.19004 + 0.451367i) q^{80} +(-4.48954 + 7.77611i) q^{81} +8.65418i q^{82} +(0.265472 + 0.153271i) q^{83} +0.195564 q^{84} +(0.824326 - 0.733045i) q^{85} +(6.03437 + 2.56640i) q^{86} -0.137991i q^{87} -1.21075i q^{88} +(2.37457 - 4.11288i) q^{89} +(-5.00895 + 4.45429i) q^{90} +(13.2775 - 22.9973i) q^{91} +(-3.64025 - 2.10170i) q^{92} +(-0.336200 + 0.194105i) q^{93} +3.61348 q^{94} +(4.16362 - 12.5497i) q^{95} +(0.0241105 - 0.0417606i) q^{96} +15.1388i q^{97} +(8.18201 + 4.72388i) q^{98} +(-1.81472 - 3.14319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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