LMFDB - Embedded newform 471.2.q.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06747 - 0.509586i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.24385 + 1.17766i) q^{4} +(-0.929494 + 0.698469i) q^{5} +(1.47505 + 1.53569i) q^{6} +(-0.0122606 + 0.00643484i) q^{7} +(-0.851290 - 0.754178i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-2.06747 - 0.509586i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.24385 + 1.17766i) q^{4} +(-0.929494 + 0.698469i) q^{5} +(1.47505 + 1.53569i) q^{6} +(-0.0122606 + 0.00643484i) q^{7} +(-0.851290 - 0.754178i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.27763 - 0.970408i) q^{10} +(0.0361289 + 0.0376142i) q^{11} +(-1.26706 - 2.19461i) q^{12} +(2.59893 - 4.50148i) q^{13} +(0.0286275 - 0.00705603i) q^{14} +(1.15891 - 0.0935567i) q^{15} +(-1.50338 - 2.17802i) q^{16} +(-5.59347 + 4.20322i) q^{17} +(-0.425924 - 2.08631i) q^{18} +(0.358236 - 1.75476i) q^{19} +(-2.90820 + 0.472629i) q^{20} +(0.0138017 + 0.00111419i) q^{21} +(-0.0555278 - 0.0961769i) q^{22} +(-1.98020 - 2.86882i) q^{23} +(0.316420 + 1.09241i) q^{24} +(-1.01499 + 3.50414i) q^{25} +(-7.66710 + 7.98230i) q^{26} +(0.120537 - 0.992709i) q^{27} -0.0350889 q^{28} +(0.858933 - 7.07395i) q^{29} +(-2.44368 - 0.397137i) q^{30} +(4.20529 + 5.15054i) q^{31} +(2.80490 + 7.39591i) q^{32} +(-0.0104323 - 0.0511008i) q^{33} +(13.7062 - 5.83968i) q^{34} +(0.00690158 - 0.0145448i) q^{35} +(-0.102038 + 2.53206i) q^{36} +(-3.69819 - 2.77901i) q^{37} +(-1.63484 + 3.44536i) q^{38} +(-4.60248 + 2.41557i) q^{39} +(1.31804 + 0.106403i) q^{40} +(-5.89813 + 8.54492i) q^{41} +(-0.0279669 - 0.00933671i) q^{42} +(-10.5920 + 6.69795i) q^{43} +(0.0367709 + 0.126948i) q^{44} +(-1.02950 - 0.540323i) q^{45} +(2.63210 + 6.94028i) q^{46} +(-6.88960 - 2.93538i) q^{47} +(0.106564 + 2.64435i) q^{48} +(-3.97634 + 5.76073i) q^{49} +(3.88412 - 6.72749i) q^{50} +(6.97402 - 0.563001i) q^{51} +(11.1328 - 7.03996i) q^{52} +(-2.57240 + 0.858793i) q^{53} +(-0.755076 + 1.99097i) q^{54} +(-0.0598539 - 0.00972721i) q^{55} +(0.0152903 + 0.00376872i) q^{56} +(-1.24064 + 1.29164i) q^{57} +(-5.38061 + 14.1875i) q^{58} +(-0.00915945 + 0.00811457i) q^{59} +(2.71059 + 1.15487i) q^{60} +(-1.09452 + 5.36132i) q^{61} +(-6.06967 - 12.7916i) q^{62} +(-0.0110696 - 0.00831824i) q^{63} +(-1.39220 - 11.4658i) q^{64} +(0.728455 + 5.99937i) q^{65} +(-0.00447176 + 0.110965i) q^{66} +(3.43301 + 3.04138i) q^{67} +(-17.5009 + 2.84417i) q^{68} +(0.140362 + 3.48305i) q^{69} +(-0.0216806 + 0.0265539i) q^{70} +(3.27112 - 1.09206i) q^{71} +(0.316420 - 1.09241i) q^{72} +(-12.6395 - 7.99273i) q^{73} +(6.22976 + 7.63007i) q^{74} +(2.73070 - 2.41919i) q^{75} +(2.87034 - 3.51552i) q^{76} +(-0.000685001 - 0.000228687i) q^{77} +(10.7464 - 2.64876i) q^{78} +(-2.27074 + 0.559686i) q^{79} +(2.91867 + 0.974394i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(16.5486 - 14.6608i) q^{82} +(1.05454 + 1.29158i) q^{83} +(0.0296568 + 0.0187538i) q^{84} +(2.26328 - 7.81374i) q^{85} +(25.3118 - 8.45031i) q^{86} +(-4.50675 + 5.51976i) q^{87} +(-0.00238843 - 0.0592682i) q^{88} +(-3.02507 + 0.491622i) q^{89} +(1.85312 + 1.64172i) q^{90} +(-0.00289805 + 0.0719143i) q^{91} +(-1.06477 - 8.76920i) q^{92} +(-0.801479 - 6.60077i) q^{93} +(12.7482 + 9.57967i) q^{94} +(0.892666 + 1.88125i) q^{95} +(1.58219 - 7.75007i) q^{96} +(-13.7599 - 5.86254i) q^{97} +(11.1566 - 9.88385i) q^{98} +(-0.0184943 + 0.0487656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	−2.06747	−	0.509586i	−1.46192	−	0.360332i	−0.573442	−	0.819246i	$-0.694392\pi$
$2$	−2.06747	−	0.509586i	−1.46192	−	0.360332i	−0.888480	+	0.458914i	$0.848238\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	2.24385	+	1.17766i	1.12192	+	0.588831i
$5$	−0.929494	+	0.698469i	−0.415682	+	0.312365i	−0.787926	−	0.615770i	$-0.788845\pi$
$5$	−0.929494	+	0.698469i	−0.415682	+	0.312365i	0.372244	+	0.928135i	$0.378589\pi$
$6$	1.47505	+	1.53569i	0.602187	+	0.626943i
$7$	−0.0122606	+	0.00643484i	−0.00463406	+	0.00243214i	−0.467039	−	0.884237i	$-0.654679\pi$
$7$	−0.0122606	+	0.00643484i	−0.00463406	+	0.00243214i	0.462405	+	0.886669i	$0.346987\pi$
$8$	−0.851290	−	0.754178i	−0.300977	−	0.266642i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	2.27763	−	0.970408i	0.720250	−	0.306870i
$11$	0.0361289	+	0.0376142i	0.0108933	+	0.0113411i	0.726627	−	0.687032i	$-0.241087\pi$
$11$	0.0361289	+	0.0376142i	0.0108933	+	0.0113411i	−0.715734	+	0.698373i	$0.753907\pi$
$12$	−1.26706	−	2.19461i	−0.365768	−	0.633528i
$13$	2.59893	−	4.50148i	0.720813	−	1.24849i	−0.239861	−	0.970807i	$-0.577102\pi$
$13$	2.59893	−	4.50148i	0.720813	−	1.24849i	0.960674	−	0.277678i	$-0.0895649\pi$
$14$	0.0286275	−	0.00705603i	0.00765101	−	0.00188580i
$15$	1.15891	−	0.0935567i	0.299229	−	0.0241562i
$16$	−1.50338	−	2.17802i	−0.375845	−	0.544506i
$17$	−5.59347	+	4.20322i	−1.35662	+	1.01943i	−0.360375	+	0.932808i	$0.617351\pi$
$17$	−5.59347	+	4.20322i	−1.35662	+	1.01943i	−0.996241	+	0.0866231i	$0.972392\pi$
$18$	−0.425924	−	2.08631i	−0.100391	−	0.491749i
$19$	0.358236	−	1.75476i	0.0821850	−	0.402569i	−0.917800	−	0.397044i	$-0.870036\pi$
$19$	0.358236	−	1.75476i	0.0821850	−	0.402569i	0.999985	−	0.00552523i	$-0.00175875\pi$
$20$	−2.90820	+	0.472629i	−0.650294	+	0.105683i
$21$	0.0138017	+	0.00111419i	0.00301178	+	0.000243136i
$22$	−0.0555278	−	0.0961769i	−0.0118386	−	0.0205050i
$23$	−1.98020	−	2.86882i	−0.412901	−	0.598190i	0.560260	−	0.828317i	$-0.310701\pi$
$23$	−1.98020	−	2.86882i	−0.412901	−	0.598190i	−0.973161	+	0.230127i	$0.926086\pi$
$24$	0.316420	+	1.09241i	0.0645890	+	0.222987i
$25$	−1.01499	+	3.50414i	−0.202998	+	0.700829i
$26$	−7.66710	+	7.98230i	−1.50364	+	1.56546i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−0.0350889			−0.00663117
$29$	0.858933	−	7.07395i	0.159500	−	1.31360i	−0.664619	−	0.747183i	$-0.731406\pi$
$29$	0.858933	−	7.07395i	0.159500	−	1.31360i	0.824119	−	0.566417i	$-0.191671\pi$
$30$	−2.44368	−	0.397137i	−0.446153	−	0.0725070i
$31$	4.20529	+	5.15054i	0.755292	+	0.925065i	0.998997	−	0.0447846i	$-0.0142602\pi$
$31$	4.20529	+	5.15054i	0.755292	+	0.925065i	−0.243705	+	0.969850i	$0.578363\pi$
$32$	2.80490	+	7.39591i	0.495841	+	1.30742i
$33$	−0.0104323	−	0.0511008i	−0.00181603	−	0.00889550i
$34$	13.7062	−	5.83968i	2.35060	−	1.00150i
$35$	0.00690158	−	0.0145448i	0.00116658	−	0.00245852i
$36$	−0.102038	+	2.53206i	−0.0170064	+	0.422010i
$37$	−3.69819	−	2.77901i	−0.607979	−	0.456866i	0.251627	−	0.967824i	$-0.419034\pi$
$37$	−3.69819	−	2.77901i	−0.607979	−	0.456866i	−0.859606	+	0.510958i	$0.829291\pi$
$38$	−1.63484	+	3.44536i	−0.265206	+	0.558911i
$39$	−4.60248	+	2.41557i	−0.736986	+	0.386800i
$40$	1.31804	+	0.106403i	0.208400	+	0.0168238i
$41$	−5.89813	+	8.54492i	−0.921134	+	1.33449i	0.0211849	+	0.999776i	$0.493256\pi$
$41$	−5.89813	+	8.54492i	−0.921134	+	1.33449i	−0.942319	+	0.334717i	$0.891359\pi$
$42$	−0.0279669	−	0.00933671i	−0.00431538	−	0.00144069i
$43$	−10.5920	+	6.69795i	−1.61526	+	1.02143i	−0.650071	+	0.759873i	$0.725261\pi$
$43$	−10.5920	+	6.69795i	−1.61526	+	1.02143i	−0.965189	+	0.261555i	$0.915765\pi$
$44$	0.0367709	+	0.126948i	0.00554343	+	0.0191381i
$45$	−1.02950	−	0.540323i	−0.153469	−	0.0805466i
$46$	2.63210	+	6.94028i	0.388082	+	1.02329i
$47$	−6.88960	−	2.93538i	−1.00495	−	0.428170i	−0.174138	−	0.984721i	$-0.555714\pi$
$47$	−6.88960	−	2.93538i	−1.00495	−	0.428170i	−0.830813	+	0.556551i	$0.812124\pi$
$48$	0.106564	+	2.64435i	0.0153811	+	0.381679i
$49$	−3.97634	+	5.76073i	−0.568049	+	0.822961i
$50$	3.88412	−	6.72749i	0.549298	−	0.951411i
$51$	6.97402	−	0.563001i	0.976559	−	0.0788360i
$52$	11.1328	−	7.03996i	1.54384	−	0.976267i
$53$	−2.57240	+	0.858793i	−0.353346	+	0.117964i	−0.487800	−	0.872956i	$-0.662200\pi$
$53$	−2.57240	+	0.858793i	−0.353346	+	0.117964i	0.134453	+	0.990920i	$0.457072\pi$
$54$	−0.755076	+	1.99097i	−0.102753	+	0.270937i
$55$	−0.0598539	−	0.00972721i	−0.00807070	−	0.00131162i
$56$	0.0152903	+	0.00376872i	0.00204325	+	0.000503617i
$57$	−1.24064	+	1.29164i	−0.164326	+	0.171082i
$58$	−5.38061	+	14.1875i	−0.706508	+	1.86291i
$59$	−0.00915945	+	0.00811457i	−0.00119246	+	0.00105643i	−0.663719	−	0.747982i	$-0.731023\pi$
$59$	−0.00915945	+	0.00811457i	−0.00119246	+	0.00105643i	0.662526	+	0.749039i	$0.269484\pi$
$60$	2.71059	+	1.15487i	0.349935	+	0.149093i
$61$	−1.09452	+	5.36132i	−0.140139	+	0.686447i	0.847638	+	0.530575i	$0.178024\pi$
$61$	−1.09452	+	5.36132i	−0.140139	+	0.686447i	−0.987777	+	0.155872i	$0.950181\pi$
$62$	−6.06967	−	12.7916i	−0.770849	−	1.62453i
$63$	−0.0110696	−	0.00831824i	−0.00139463	−	0.00104800i
$64$	−1.39220	−	11.4658i	−0.174025	−	1.43322i
$65$	0.728455	+	5.99937i	0.0903538	+	0.744130i
$66$	−0.00447176	+	0.110965i	−0.000550435	+	0.0136589i
$67$	3.43301	+	3.04138i	0.419408	+	0.371563i	0.846271	−	0.532753i	$-0.178843\pi$
$67$	3.43301	+	3.04138i	0.419408	+	0.371563i	−0.426862	+	0.904317i	$0.640381\pi$
$68$	−17.5009	+	2.84417i	−2.12229	+	0.344906i
$69$	0.140362	+	3.48305i	0.0168976	+	0.419310i
$70$	−0.0216806	+	0.0265539i	−0.00259133	+	0.00317380i
$71$	3.27112	−	1.09206i	0.388210	−	0.129604i	−0.115862	−	0.993265i	$-0.536963\pi$
$71$	3.27112	−	1.09206i	0.388210	−	0.129604i	0.504072	+	0.863662i	$0.331835\pi$
$72$	0.316420	−	1.09241i	0.0372905	−	0.128742i
$73$	−12.6395	−	7.99273i	−1.47934	−	0.935478i	−0.998270	−	0.0587964i	$-0.981274\pi$
$73$	−12.6395	−	7.99273i	−1.47934	−	0.935478i	−0.481071	−	0.876682i	$-0.659752\pi$
$74$	6.22976	+	7.63007i	0.724195	+	0.886977i
$75$	2.73070	−	2.41919i	0.315314	−	0.279344i
$76$	2.87034	−	3.51552i	0.329250	−	0.403258i
$77$	−0.000685001	0	0.000228687i	−7.80632e−5	0	2.60613e-5i
$78$	10.7464	−	2.64876i	1.21679	−	0.299912i
$79$	−2.27074	+	0.559686i	−0.255478	+	0.0629696i	−0.364974	−	0.931018i	$-0.618922\pi$
$79$	−2.27074	+	0.559686i	−0.255478	+	0.0629696i	0.109497	+	0.993987i	$0.465076\pi$
$80$	2.91867	+	0.974394i	0.326317	+	0.108941i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	16.5486	−	14.6608i	1.82749	−	1.61901i
$83$	1.05454	+	1.29158i	0.115751	+	0.141769i	0.829230	−	0.558907i	$-0.188779\pi$
$83$	1.05454	+	1.29158i	0.115751	+	0.141769i	−0.713479	+	0.700676i	$0.752882\pi$
$84$	0.0296568	+	0.0187538i	0.00323582	+	0.00204621i
$85$	2.26328	−	7.81374i	0.245487	−	0.847519i
$86$	25.3118	−	8.45031i	2.72944	−	0.911220i
$87$	−4.50675	+	5.51976i	−0.483174	+	0.591781i
$88$	−0.00238843	−	0.0592682i	−0.000254607	−	0.00631801i
$89$	−3.02507	+	0.491622i	−0.320657	+	0.0521119i	−0.318610	−	0.947886i	$-0.603216\pi$
$89$	−3.02507	+	0.491622i	−0.320657	+	0.0521119i	−0.00204765	+	0.999998i	$0.500652\pi$
$90$	1.85312	+	1.64172i	0.195336	+	0.173053i
$91$	−0.00289805	+	0.0719143i	−0.000303798	+	0.00753867i
$92$	−1.06477	−	8.76920i	−0.111010	−	0.914252i
$93$	−0.801479	−	6.60077i	−0.0831095	−	0.684468i
$94$	12.7482	+	9.57967i	1.31488	+	0.988067i
$95$	0.892666	+	1.88125i	0.0915856	+	0.193013i
$96$	1.58219	−	7.75007i	0.161481	−	0.790989i
$97$	−13.7599	−	5.86254i	−1.39710	−	0.595251i	−0.443489	−	0.896280i	$-0.646260\pi$
$97$	−13.7599	−	5.86254i	−1.39710	−	0.595251i	−0.953615	+	0.301029i	$0.902670\pi$
$98$	11.1566	−	9.88385i	1.12698	−	0.998420i
$99$	−0.0184943	+	0.0487656i	−0.00185875	+	0.00490112i
$100$	−6.40417	+	6.66745i	−0.640417	+	0.666745i
$101$	−3.82135	−	0.941879i	−0.380239	−	0.0937205i	0.0445635	−	0.999007i	$-0.485810\pi$
$101$	−3.82135	−	0.941879i	−0.380239	−	0.0937205i	−0.424802	+	0.905286i	$0.639656\pi$
$102$	−14.7055	−	2.38987i	−1.45606	−	0.236633i
$103$	5.48175	−	14.4542i	0.540132	−	1.42421i	−0.335871	−	0.941908i	$-0.609031\pi$
$103$	5.48175	−	14.4542i	0.540132	−	1.42421i	0.876004	−	0.482304i	$-0.160200\pi$
$104$	−5.60736	+	1.87201i	−0.549847	+	0.183566i
$105$	−0.0136068	+	0.00860444i	−0.00132789	+	0.000839707i
$106$	5.75599	−	0.464672i	0.559071	−	0.0451329i
$107$	3.19185	−	5.52845i	0.308568	−	0.534455i	−0.669482	−	0.742829i	$-0.733484\pi$
$107$	3.19185	−	5.52845i	0.308568	−	0.534455i	0.978049	+	0.208374i	$0.0668170\pi$
$108$	1.43954	−	2.08553i	0.138520	−	0.200681i
$109$	−0.0222302	−	0.551637i	−0.00212927	−	0.0528372i	0.997775	−	0.0666705i	$-0.0212376\pi$
$109$	−0.0222302	−	0.551637i	−0.00212927	−	0.0528372i	−0.999904	+	0.0138333i	$0.995597\pi$
$110$	0.118789	+	0.0506114i	0.0113261	+	0.00482561i
$111$	1.64039	+	4.32535i	0.155699	+	0.410544i
$112$	0.0324475	+	0.0170298i	0.00306600	+	0.00160916i
$113$	1.24768	+	4.30748i	0.117371	+	0.405213i	0.997592	−	0.0693509i	$-0.0220928\pi$
$113$	1.24768	+	4.30748i	0.117371	+	0.405213i	−0.880221	+	0.474564i	$0.842606\pi$
$114$	3.22318	−	2.03821i	0.301878	−	0.190896i
$115$	3.84437	+	1.28344i	0.358489	+	0.119681i
$116$	10.2580	−	14.8613i	0.952435	−	1.37984i
$117$	5.18100	+	0.418254i	0.478984	+	0.0386676i
$118$	0.0230720	−	0.0121091i	0.00212395	−	0.00111473i
$119$	0.0415320	−	0.0875269i	0.00380724	−	0.00802358i
$120$	−1.05712	−	0.794378i	−0.0965019	−	0.0725164i
$121$	0.442816	−	10.9884i	0.0402560	−	0.998942i
$122$	4.99494	−	10.5266i	0.452221	−	0.953035i
$123$	9.55201	−	4.06973i	0.861276	−	0.366955i
$124$	3.37042	+	16.5094i	0.302673	+	1.48259i
$125$	−3.56557	−	9.40163i	−0.318914	−	0.840907i
$126$	0.0186472	+	0.0228386i	0.00166122	+	0.00203463i
$127$	−9.93618	−	1.61479i	−0.881694	−	0.143289i	−0.297324	−	0.954777i	$-0.596094\pi$
$127$	−9.93618	−	1.61479i	−0.881694	−	0.143289i	−0.584370	+	0.811487i	$0.698658\pi$
$128$	−1.05759	+	8.71008i	−0.0934791	+	0.769869i
$129$	12.5321			1.10339
$130$	1.55113	−	12.7747i	0.136043	−	1.12042i
$131$	1.09474	−	1.13974i	0.0956475	−	0.0995796i	−0.671658	−	0.740861i	$-0.734418\pi$
$131$	1.09474	−	1.13974i	0.0956475	−	0.0995796i	0.767305	+	0.641282i	$0.221597\pi$
$132$	0.0367709	−	0.126948i	0.00320050	−	0.0110494i
$133$	0.00689940	+	0.0238195i	0.000598254	+	0.00206541i
$134$	−5.54780	−	8.03737i	−0.479257	−	0.694323i
$135$	0.581339	+	1.00691i	0.0500337	+	0.0866608i
$136$	7.93164	+	0.640308i	0.680133	+	0.0549060i
$137$	4.56020	−	0.741105i	0.389604	−	0.0633169i	0.0375459	−	0.999295i	$-0.488046\pi$
$137$	4.56020	−	0.741105i	0.389604	−	0.0633169i	0.352058	+	0.935978i	$0.385482\pi$
$138$	1.48472	−	7.27263i	0.126388	−	0.619087i
$139$	3.99936	+	19.5902i	0.339221	+	1.66162i	0.688984	+	0.724777i	$0.258057\pi$
$139$	3.99936	+	19.5902i	0.339221	+	1.66162i	−0.349762	+	0.936838i	$0.613738\pi$
$140$	0.0326149	−	0.0245085i	0.00275646	−	0.00207135i
$141$	4.25416	+	6.16321i	0.358265	+	0.519036i
$142$	−7.31943	+	0.590886i	−0.614233	+	0.0495860i
$143$	0.263216	−	0.0648768i	0.0220112	−	0.00542527i
$144$	1.32325	−	2.29193i	0.110271	−	0.190994i
$145$	4.14257	+	7.17513i	0.344021	+	0.595863i
$146$	22.0588	+	22.9656i	1.82560	+	1.90065i
$147$	6.43968	−	2.74369i	0.531136	−	0.226296i
$148$	−5.02544	−	10.5909i	−0.413089	−	0.870566i
$149$	1.71718	+	1.52128i	0.140676	+	0.124628i	0.730527	−	0.682884i	$-0.239275\pi$
$149$	1.71718	+	1.52128i	0.140676	+	0.124628i	−0.589850	+	0.807513i	$0.700813\pi$
$150$	−6.87843	+	3.61008i	−0.561622	+	0.294762i
$151$	8.51096	+	8.86084i	0.692612	+	0.721085i	0.970919	−	0.239407i	$-0.0769530\pi$
$151$	8.51096	+	8.86084i	0.692612	+	0.721085i	−0.278308	+	0.960492i	$0.589773\pi$
$152$	−1.62836	+	1.22363i	−0.132078	+	0.0992499i
$153$	−6.19528	−	3.25153i	−0.500859	−	0.262871i
$154$	0.00129968		0.000821871i	0.000104732		6.62282e-5i
$155$	−7.50629	−	1.85013i	−0.602919	−	0.148606i
$156$	−13.1720			−1.05460
$157$	−8.78907	+	8.93041i	−0.701444	+	0.712725i
$157$	−8.78907	+	8.93041i	−0.701444	+	0.712725i
$158$	4.97989			0.396179
$159$	2.63316	+	0.649016i	0.208823	+	0.0514703i
$160$	−7.77296	−	4.91532i	−0.614506	−	0.388590i
$161$	0.0427388	+	0.0224310i	0.00336829	+	0.00176781i
$162$	1.70229	−	1.27919i	0.133745	−	0.100503i
$163$	0.0281678	+	0.0293258i	0.00220627	+	0.00229697i	0.722305	−	0.691575i	$-0.243083\pi$
$163$	0.0281678	+	0.0293258i	0.00220627	+	0.00229697i	−0.720098	+	0.693872i	$0.755903\pi$
$164$	−23.2975	+	12.2275i	−1.81923	+	0.954806i
$165$	0.0453891	+	0.0402112i	0.00353353	+	0.00313044i
$166$	−1.52206	−	3.20768i	−0.118135	−	0.248964i
$167$	16.7862	−	7.15193i	1.29895	−	0.553433i	0.371870	−	0.928285i	$-0.378717\pi$
$167$	16.7862	−	7.15193i	1.29895	−	0.553433i	0.927085	+	0.374852i	$0.122307\pi$
$168$	−0.0109090	−	0.0113574i	−0.000841645	−	0.000876245i
$169$	−7.00887	−	12.1397i	−0.539144	−	0.933824i
$170$	−8.66103	+	15.0013i	−0.664270	+	1.15055i
$171$	1.73891	−	0.428603i	0.132978	−	0.0327761i
$172$	−31.6547	+	2.55543i	−2.41365	+	0.194850i
$173$	0.177742	+	0.257503i	0.0135134	+	0.0195776i	0.829682	−	0.558236i	$-0.188522\pi$
$173$	0.177742	+	0.257503i	0.0135134	+	0.0195776i	−0.816169	+	0.577813i	$0.803906\pi$
$174$	12.1304	−	9.11538i	0.919600	−	0.691035i
$175$	−0.0101043	−	0.0494941i	−0.000763812	−	0.00374140i
$176$	0.0276090	−	0.135238i	0.00208111	−	0.0101939i
$177$	0.0120784	−	0.00196294i	0.000907871	−	0.000147543i
$178$	6.50478	+	0.525120i	0.487554	+	0.0393594i
$179$	−8.91867	−	15.4476i	−0.666613	−	1.15461i	−0.978845	−	0.204601i	$-0.934410\pi$
$179$	−8.91867	−	15.4476i	−0.666613	−	1.15461i	0.312233	−	0.950006i	$-0.398923\pi$
$180$	−1.67372	−	2.42480i	−0.124752	−	0.180734i
$181$	5.08021	+	17.5389i	0.377609	+	1.30366i	0.894293	+	0.447482i	$0.147679\pi$
$181$	5.08021	+	17.5389i	0.377609	+	1.30366i	−0.516684	+	0.856176i	$0.672834\pi$
$182$	0.0426382	−	0.147204i	0.00316055	−	0.0109115i
$183$	3.79052	−	3.94635i	0.280203	−	0.291723i
$184$	−0.477871	+	3.93562i	−0.0352291	+	0.290138i
$185$	5.37850			0.395435
$186$	−1.70663	+	14.0553i	−0.125136	+	1.03059i
$187$	−0.360186	−	0.0585360i	−0.0263394	−	0.00428058i
$188$	−12.0023	−	14.7002i	−0.875359	−	1.07212i
$189$	0.00491007	+	0.0129468i	0.000357155	+	0.000941741i
$190$	−0.886901	−	4.34433i	−0.0643425	−	0.315171i
$191$	−5.82454	+	2.48161i	−0.421449	+	0.179563i	−0.592270	−	0.805739i	$-0.701768\pi$
$191$	−5.82454	+	2.48161i	−0.421449	+	0.179563i	0.170821	+	0.985302i	$0.445358\pi$
$192$	−4.95139	+	10.4348i	−0.357336	+	0.753070i
$193$	−0.803108	+	19.9289i	−0.0578090	+	1.43451i	0.666740	+	0.745291i	$0.267689\pi$
$193$	−0.803108	+	19.9289i	−0.0578090	+	1.43451i	−0.724548	+	0.689224i	$0.757952\pi$
$194$	25.4607	+	19.1325i	1.82797	+	1.37363i
$195$	2.59077	−	5.45994i	0.185529	−	0.390995i
$196$	−15.7065	+	8.24340i	−1.12189	+	0.588814i
$197$	−26.3966	−	2.13096i	−1.88068	−	0.151824i	−0.913653	−	0.406495i	$-0.866751\pi$
$197$	−26.3966	−	2.13096i	−1.88068	−	0.151824i	−0.967028	+	0.254671i	$0.918033\pi$
$198$	0.0630867	−	0.0913969i	0.00448338	−	0.00649530i
$199$	−5.74022	−	1.91637i	−0.406913	−	0.135848i	0.105841	−	0.994383i	$-0.466247\pi$
$199$	−5.74022	−	1.91637i	−0.406913	−	0.135848i	−0.512754	+	0.858536i	$0.671375\pi$
$200$	3.50680	−	2.21756i	0.247968	−	0.156805i
$201$	−1.27603	−	4.40537i	−0.0900042	−	0.310731i
$202$	7.42057	+	3.89462i	0.522109	+	0.274024i
$203$	0.0349887	+	0.0922577i	0.00245573	+	0.00647522i
$204$	16.3117	+	6.94975i	1.14204	+	0.486580i
$205$	−0.486087	−	12.0621i	−0.0339498	−	0.842455i
$206$	−18.6990	+	27.0902i	−1.30282	+	1.88746i
$207$	1.74294	−	3.01886i	0.121143	−	0.209825i
$208$	−13.7115	+	1.10691i	−0.950722	+	0.0767502i
$209$	0.0789464	−	0.0499227i	0.00546084	−	0.00345322i
$210$	0.0325164	−	0.0108556i	0.00224385	−	0.000749106i
$211$	3.93363	−	10.3721i	0.270802	−	0.714047i	−0.728769	−	0.684760i	$-0.759907\pi$
$211$	3.93363	−	10.3721i	0.270802	−	0.714047i	0.999571	−	0.0292868i	$-0.00932361\pi$
$212$	−6.78344	−	1.10242i	−0.465888	−	0.0757142i
$213$	−3.34838	−	0.825302i	−0.229427	−	0.0565488i
$214$	−9.41627	+	9.80338i	−0.643683	+	0.670145i
$215$	5.16685	−	13.6239i	0.352376	−	0.929140i
$216$	−0.851290	+	0.754178i	−0.0579230	+	0.0513153i
$217$	−0.0847021	−	0.0360882i	−0.00574995	−	0.00244983i
$218$	−0.235146	+	1.15182i	−0.0159261	+	0.0780111i
$219$	6.41093	+	13.5108i	0.433211	+	0.912972i
$220$	−0.122848	−	0.0923140i	−0.00828238	−	0.00622381i
$221$	4.38367	+	36.1028i	0.294877	+	2.42853i
$222$	−1.18732	−	9.77845i	−0.0796876	−	0.656287i
$223$	−0.480495	+	11.9234i	−0.0321763	+	0.798447i	0.899881	+	0.436136i	$0.143653\pi$
$223$	−0.480495	+	11.9234i	−0.0321763	+	0.798447i	−0.932057	+	0.362311i	$0.881988\pi$
$224$	−0.0819812	−	0.0726290i	−0.00547760	−	0.00485273i
$225$	−3.60094	+	0.585209i	−0.240063	+	0.0390140i
$226$	−0.384505	−	9.54138i	−0.0255769	−	0.634683i
$227$	1.84254	−	2.25670i	0.122294	−	0.149783i	−0.709829	−	0.704374i	$-0.751228\pi$
$227$	1.84254	−	2.25670i	0.122294	−	0.149783i	0.832123	+	0.554591i	$0.187125\pi$
$228$	−4.30491	+	1.43719i	−0.285099	+	0.0951802i
$229$	0.317579	−	1.09641i	0.0209862	−	0.0724528i	−0.949342	−	0.314246i	$-0.898248\pi$
$229$	0.317579	−	1.09641i	0.0209862	−	0.0724528i	0.970328	+	0.241793i	$0.0777355\pi$
$230$	−7.29410	−	4.61251i	−0.480959	−	0.304140i
$231$	0.000456731	0	0.000559394i	3.00507e−5	0	3.68054e-5i
$232$	−6.06622	+	5.37420i	−0.398267	+	0.352834i
$233$	3.79716	−	4.65068i	0.248760	−	0.304676i	−0.635097	−	0.772432i	$-0.719040\pi$
$233$	3.79716	−	4.65068i	0.248760	−	0.304676i	0.883858	+	0.467756i	$0.154937\pi$
$234$	−10.4984	−	3.50489i	−0.686304	−	0.229122i
$235$	8.45412	−	2.08375i	0.551486	−	0.135929i
$236$	−0.0301086	+	0.00742111i	−0.00195990	+	0.000483073i
$237$	2.21834	+	0.740589i	0.144096	+	0.0481065i
$238$	−0.130469	+	0.159795i	−0.00845703	+	0.0103580i
$239$	−9.67086	+	8.56764i	−0.625556	+	0.554194i	−0.915230	−	0.402931i	$-0.867991\pi$
$239$	−9.67086	+	8.56764i	−0.625556	+	0.554194i	0.289674	+	0.957125i	$0.406453\pi$
$240$	−1.94605	−	2.38348i	−0.125617	−	0.153853i
$241$	−19.7971	−	12.5189i	−1.27524	−	0.806413i	−0.286795	−	0.957992i	$-0.592590\pi$
$241$	−19.7971	−	12.5189i	−1.27524	−	0.806413i	−0.988445	+	0.151579i	$0.951564\pi$
$242$	−6.51502	+	22.4925i	−0.418801	+	1.44587i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−8.76975	+	10.7410i	−0.561426	+	0.687622i
$245$	−0.327705	−	8.13192i	−0.0209363	−	0.519529i
$246$	−21.8224	+	3.54648i	−1.39134	+	0.226116i
$247$	−6.96797	−	6.17308i	−0.443361	−	0.392784i
$248$	0.304502	−	7.55614i	0.0193359	−	0.479816i
$249$	−0.200983	−	1.65525i	−0.0127368	−	0.104897i
$250$	2.58077	+	21.2546i	0.163222	+	1.34426i
$251$	10.5094	+	7.89728i	0.663346	+	0.498472i	0.878274	−	0.478158i	$-0.158695\pi$
$251$	10.5094	+	7.89728i	0.663346	+	0.498472i	−0.214928	+	0.976630i	$0.568952\pi$
$252$	−0.0150423	−	0.0317011i	−0.000947578	−	0.00199698i
$253$	0.0363657	−	0.178131i	0.00228629	−	0.0111990i
$254$	19.7199	+	8.40186i	1.23734	+	0.527180i
$255$	−6.08907	+	5.39445i	−0.381313	+	0.337813i
$256$	−1.56628	+	4.12995i	−0.0978927	+	0.258122i
$257$	10.5840	−	11.0191i	0.660209	−	0.687351i	−0.303946	−	0.952689i	$-0.598304\pi$
$257$	10.5840	−	11.0191i	0.660209	−	0.687351i	0.964155	+	0.265339i	$0.0854837\pi$
$258$	−25.9097	−	6.38616i	−1.61306	−	0.397585i
$259$	0.0632244	+	0.0102750i	0.00392857	+	0.000638455i
$260$	−5.43068	+	14.3195i	−0.336797	+	0.888060i
$261$	6.75918	−	2.25655i	0.418383	−	0.139677i
$262$	−2.84413	+	1.79852i	−0.175711	+	0.111113i
$263$	19.3632	−	1.56316i	1.19399	−	0.0963886i	0.532556	−	0.846395i	$-0.321232\pi$
$263$	19.3632	−	1.56316i	1.19399	−	0.0963886i	0.661431	+	0.750006i	$0.269950\pi$
$264$	−0.0296581	+	0.0513694i	−0.00182533	+	0.00316157i
$265$	1.79119	−	2.59499i	0.110032	−	0.159409i
$266$	−0.00212623	−	0.0527620i	−0.000130368	−	0.00323504i
$267$	2.81952	+	1.20128i	0.172552	+	0.0735174i
$268$	4.12142	+	10.8673i	0.251756	+	0.663826i
$269$	6.92817	+	3.63618i	0.422418	+	0.221702i	0.662518	−	0.749046i	$-0.269488\pi$
$269$	6.92817	+	3.63618i	0.422418	+	0.221702i	−0.240100	+	0.970748i	$0.577180\pi$
$270$	−0.688795	−	2.37800i	−0.0419187	−	0.144720i
$271$	18.4185	−	11.6472i	1.11885	−	0.707516i	0.158788	−	0.987313i	$-0.449241\pi$
$271$	18.4185	−	11.6472i	1.11885	−	0.707516i	0.960059	+	0.279797i	$0.0902671\pi$
$272$	17.5638	+	5.86367i	1.06496	+	0.355537i
$273$	0.0408852	−	0.0592324i	0.00247448	−	0.00358491i
$274$	−9.80574	−	0.791601i	−0.592386	−	0.0478224i
$275$	−0.168476	+	0.0884229i	−0.0101595	+	0.00533210i
$276$	−3.78690	+	7.98072i	−0.227945	+	0.480383i
$277$	0.144957	+	0.108928i	0.00870963	+	0.00654486i	0.605088	−	0.796158i	$-0.293138\pi$
$277$	0.144957	+	0.108928i	0.00870963	+	0.00654486i	−0.596379	+	0.802703i	$0.703394\pi$
$278$	1.71431	−	42.5401i	0.102817	−	2.55139i
$279$	−2.85048	+	6.00727i	−0.170654	+	0.359646i
$280$	−0.0168446	+	0.00717681i	−0.00100666	+	0.000428896i
$281$	−4.67518	−	22.9006i	−0.278898	−	1.36613i	−0.841881	−	0.539664i	$-0.818551\pi$
$281$	−4.67518	−	22.9006i	−0.278898	−	1.36613i	0.562983	−	0.826469i	$-0.309654\pi$
$282$	−5.65467	−	14.9101i	−0.336730	−	0.887885i
$283$	16.1944	+	19.8345i	0.962655	+	1.17904i	0.983801	+	0.179262i	$0.0573709\pi$
$283$	16.1944	+	19.8345i	0.962655	+	1.17904i	−0.0211467	+	0.999776i	$0.506732\pi$
$284$	8.62595	+	1.40185i	0.511856	+	0.0831847i
$285$	0.250993	−	2.06712i	0.0148676	−	0.122445i
$286$	−0.577251			−0.0341336
$287$	0.0173292	−	0.142719i	0.00102291	−	0.00842444i
$288$	−5.47940	+	5.70466i	−0.322877	+	0.336150i
$289$	8.89015	−	30.6924i	0.522950	−	1.80543i
$290$	−4.90829	−	16.9454i	−0.288225	−	0.995067i
$291$	8.49639	+	12.3091i	0.498067	+	0.721575i
$292$	−18.9483	−	32.8195i	−1.10887	−	1.92062i
$293$	−18.2700	−	1.47491i	−1.06734	−	0.0861649i	−0.465710	−	0.884937i	$-0.654201\pi$
$293$	−18.2700	−	1.47491i	−1.06734	−	0.0861649i	−0.601633	+	0.798772i	$0.705483\pi$
$294$	−14.7120	+	2.39093i	−0.858021	+	0.139442i
$295$	0.00284588	−	0.0139400i	0.000165693	−	0.000811620i
$296$	1.05237	+	5.15484i	0.0611676	+	0.299619i
$297$	0.0416948	−	0.0313316i	0.00241938	−	0.00181804i
$298$	−2.77499	−	4.02026i	−0.160751	−	0.232887i
$299$	−18.0603	+	1.45798i	−1.04446	+	0.0843172i
$300$	8.97627	−	2.21245i	0.518245	−	0.127736i
$301$	0.0867632	−	0.150278i	0.00500095	−	0.00866190i
$302$	−13.0808	−	22.6566i	−0.752715	−	1.30374i
$303$	2.72637	+	2.83845i	0.156626	+	0.163065i
$304$	−4.36047	+	1.85782i	−0.250090	+	0.106553i
$305$	−2.72737	−	5.74780i	−0.156169	−	0.329118i
$306$	11.1516	+	9.87948i	0.637496	+	0.564772i
$307$	8.66162	−	4.54597i	0.494345	−	0.259452i	−0.199077	−	0.979984i	$-0.563794\pi$
$307$	8.66162	−	4.54597i	0.494345	−	0.259452i	0.693422	+	0.720532i	$0.256102\pi$
$308$	−0.00126772	−	0.00131984i	−7.22352e−5	−	7.52048e-5i
$309$	−12.3584	+	9.28672i	−0.703044	+	0.528303i
$310$	14.5762	+	7.65019i	0.827874	+	0.434502i
$311$	27.6710	+	17.4981i	1.56908	+	0.992225i	0.983351	+	0.181716i	$0.0581652\pi$
$311$	27.6710	+	17.4981i	1.56908	+	0.992225i	0.585727	+	0.810509i	$0.300809\pi$
$312$	5.73981	+	1.41474i	0.324953	+	0.0800936i
$313$	3.93241			0.222273			0.111136	−	0.993805i	$-0.464551\pi$
$313$	3.93241			0.222273			0.111136	+	0.993805i	$0.464551\pi$
$314$	22.7220	−	13.9846i	1.28227	−	0.789196i
$315$	0.0160991			0.000907084
$316$	−5.75430	−	1.41831i	−0.323705	−	0.0797861i
$317$	27.3628	+	17.3032i	1.53685	+	0.971844i	0.990985	+	0.133971i	$0.0427728\pi$
$317$	27.3628	+	17.3032i	1.53685	+	0.971844i	0.545864	+	0.837874i	$0.316202\pi$
$318$	−5.11326	−	2.68364i	−0.286737	−	0.150491i
$319$	0.297113	−	0.223266i	0.0166351	−	0.0125005i
$320$	9.30253	+	9.68496i	0.520027	+	0.541406i
$321$	−5.65248	+	2.96665i	−0.315491	+	0.165582i
$322$	−0.0769307	−	0.0681546i	−0.00428718	−	0.00379811i
$323$	5.37185	+	11.3209i	0.298898	+	0.629913i
$324$	−2.33133	+	0.993288i	−0.129518	+	0.0551827i
$325$	13.1359	+	13.6760i	0.728651	+	0.758606i
$326$	−0.0432921	−	0.0749840i	−0.00239773	−	0.00415298i
$327$	−0.276042	+	0.478119i	−0.0152652	+	0.0264400i
$328$	11.4654	−	2.82597i	0.633072	−	0.156038i
$329$	0.103359	−	0.00834401i	0.00569837	−	0.000460020i
$330$	−0.0733495	−	0.106265i	−0.00403776	−	0.00584970i
$331$	−7.95933	+	5.98105i	−0.437484	+	0.328748i	−0.796559	−	0.604561i	$-0.793349\pi$
$331$	−7.95933	+	5.98105i	−0.437484	+	0.328748i	0.359075	+	0.933309i	$0.383092\pi$
$332$	0.845186	+	4.14000i	0.0463856	+	0.227212i
$333$	0.925311	−	4.53247i	0.0507067	−	0.248378i
$334$	−38.3495	+	6.23240i	−2.09839	+	0.341022i
$335$	−5.31527	−	0.429093i	−0.290404	−	0.0234438i
$336$	−0.0183225	−	0.0317355i	−0.000999574	−	0.00173131i
$337$	−17.6304	−	25.5421i	−0.960390	−	1.39136i	−0.919886	−	0.392185i	$-0.871719\pi$
$337$	−17.6304	−	25.5421i	−0.960390	−	1.39136i	−0.0405031	−	0.999179i	$-0.512896\pi$
$338$	8.30441	+	28.6701i	0.451700	+	1.55945i
$339$	1.24768	−	4.30748i	0.0677645	−	0.233950i
$340$	14.2804	−	14.8674i	0.774462	−	0.806301i
$341$	−0.0418009	+	0.344262i	−0.00226365	+	0.0186428i
$342$	−3.81355			−0.206213
$343$	0.0233660	−	0.192436i	0.00126165	−	0.0103906i
$344$	14.0683	+	2.28632i	0.758511	+	0.123270i
$345$	−2.56327	−	3.13943i	−0.138002	−	0.169021i
$346$	−0.236256	−	0.622955i	−0.0127012	−	0.0334903i
$347$	0.0398745	+	0.195318i	0.00214057	+	0.0104852i	0.980847	−	0.194780i	$-0.0623994\pi$
$347$	0.0398745	+	0.195318i	0.00214057	+	0.0104852i	−0.978706	+	0.205265i	$0.934194\pi$
$348$	−16.6129	+	7.07808i	−0.890543	+	0.379425i
$349$	4.80384	−	10.1239i	0.257144	−	0.541919i	−0.733289	−	0.679917i	$-0.762016\pi$
$349$	4.80384	−	10.1239i	0.257144	−	0.541919i	0.990432	+	0.137998i	$0.0440669\pi$
$350$	−0.00433116	+	0.107477i	−0.000231510	+	0.00574486i
$351$	−4.15539	−	3.12257i	−0.221798	−	0.166671i
$352$	−0.176853	+	0.372710i	−0.00942630	+	0.0198655i
$353$	3.13520	−	1.64548i	0.166870	−	0.0875802i	−0.379220	−	0.925306i	$-0.623808\pi$
$353$	3.13520	−	1.64548i	0.166870	−	0.0875802i	0.546090	+	0.837726i	$0.316115\pi$
$354$	−0.0259721	−	0.00209668i	−0.00138040	−	0.000111438i
$355$	−2.27771	+	3.29984i	−0.120888	+	0.175137i
$356$	−7.36677	−	2.45939i	−0.390438	−	0.130347i
$357$	−0.0818826	+	0.0517794i	−0.00433369	+	0.00274046i
$358$	10.5672	+	36.4823i	0.558495	+	1.92815i
$359$	−28.2117	−	14.8067i	−1.48896	−	0.781466i	−0.492893	−	0.870090i	$-0.664061\pi$
$359$	−28.2117	−	14.8067i	−1.48896	−	0.781466i	−0.996065	+	0.0886242i	$0.971753\pi$
$360$	0.468904	+	1.23640i	0.0247134	+	0.0651639i
$361$	14.5288	+	6.19013i	0.764672	+	0.325796i
$362$	−1.56560	−	38.8500i	−0.0822862	−	2.04191i
$363$	−6.24717	+	9.05058i	−0.327891	+	0.475032i
$364$	−0.0911935	+	0.157952i	−0.00477984	+	0.00827892i
$365$	17.3310	−	1.39910i	0.907146	−	0.0732324i
$366$	−9.84779	+	6.22737i	−0.514752	+	0.325510i
$367$	10.0255	−	3.34700i	0.523326	−	0.174712i	−0.0427176	−	0.999087i	$-0.513602\pi$
$367$	10.0255	−	3.34700i	0.523326	−	0.174712i	0.566044	+	0.824375i	$0.308473\pi$
$368$	−3.27136	+	8.62586i	−0.170531	+	0.449654i
$369$	−10.2484	−	1.66553i	−0.533510	−	0.0867039i
$370$	−11.1199	−	2.74081i	−0.578096	−	0.142488i
$371$	0.0260129	−	0.0270823i	0.00135052	−	0.00140604i
$372$	5.97508	−	15.7550i	0.309793	−	0.816858i
$373$	−13.6584	+	12.1003i	−0.707207	+	0.626531i	−0.938066	−	0.346456i	$-0.887385\pi$
$373$	−13.6584	+	12.1003i	−0.707207	+	0.626531i	0.230859	+	0.972987i	$0.425846\pi$
$374$	0.714846	+	0.304567i	0.0369638	+	0.0157488i
$375$	−2.01127	+	9.85184i	−0.103861	+	0.508747i
$376$	3.65125	+	7.69485i	0.188299	+	0.396831i
$377$	−29.6109	−	22.2512i	−1.52504	−	1.14599i
$378$	−0.00355393	−	0.0292692i	−0.000182794	−	0.00150545i
$379$	−0.298137	−	2.45538i	−0.0153143	−	0.126124i	0.983047	−	0.183355i	$-0.0586959\pi$
$379$	−0.298137	−	2.45538i	−0.0153143	−	0.126124i	−0.998361	+	0.0572310i	$0.981773\pi$
$380$	−0.212475	+	5.27250i	−0.0108997	+	0.270474i
$381$	7.53492	+	6.67535i	0.386025	+	0.341989i
$382$	13.3067	−	2.16254i	0.680828	−	0.110645i
$383$	1.13309	+	28.1172i	0.0578979	+	1.43672i	0.723453	+	0.690374i	$0.242554\pi$
$383$	1.13309	+	28.1172i	0.0578979	+	1.43672i	−0.665555	+	0.746349i	$0.731805\pi$
$384$	5.54911	−	6.79642i	0.283177	−	0.346828i
$385$	0.000796436	0	0.000265889i	4.05901e−5	0	1.35510e-5i
$386$	11.8159	−	40.7932i	0.601413	−	2.07632i
$387$	−10.5920	−	6.69795i	−0.538420	−	0.340476i
$388$	−23.9710	−	29.3591i	−1.21694	−	1.49048i
$389$	15.7852	−	13.9845i	0.800343	−	0.709042i	−0.160227	−	0.987080i	$-0.551223\pi$
$389$	15.7852	−	13.9845i	0.800343	−	0.709042i	0.960570	+	0.278038i	$0.0896842\pi$
$390$	−8.13866	+	9.96805i	−0.412117	+	0.504752i
$391$	23.1345	+	7.72343i	1.16996	+	0.390590i
$392$	7.72964	−	1.90518i	0.390406	−	0.0962263i
$393$	−1.53441	+	0.378199i	−0.0774008	+	0.0190776i
$394$	53.4883	+	17.8570i	2.69470	+	0.899624i
$395$	1.71971	−	2.10626i	0.0865281	−	0.105978i
$396$	−0.0989278	+	0.0876423i	−0.00497131	+	0.00440419i
$397$	−5.54476	−	6.79110i	−0.278284	−	0.340836i	0.616484	−	0.787367i	$-0.288556\pi$
$397$	−5.54476	−	6.79110i	−0.278284	−	0.340836i	−0.894768	+	0.446532i	$0.852659\pi$
$398$	10.8912	+	6.88716i	0.545925	+	0.345222i
$399$	0.00689940	−	0.0238195i	0.000345402	−	0.00119247i
$400$	9.15802	−	3.05740i	0.457901	−	0.152870i
$401$	−9.41041	+	11.5257i	−0.469933	+	0.575564i	−0.954129	−	0.299396i	$-0.903215\pi$
$401$	−9.41041	+	11.5257i	−0.469933	+	0.575564i	0.484196	+	0.874960i	$0.339112\pi$
$402$	0.393242	+	9.75821i	0.0196132	+	0.486695i
$403$	34.1143	−	5.54411i	1.69935	−	0.276172i
$404$	−7.46531	−	6.61369i	−0.371413	−	0.329043i
$405$	0.0468163	−	1.16173i	0.00232632	−	0.0577270i
$406$	−0.0253250	−	0.208570i	−0.00125686	−	0.0103512i
$407$	−0.0290814	−	0.239507i	−0.00144151	−	0.0118719i
$408$	−6.36152	−	4.78037i	−0.314942	−	0.236664i
$409$	2.93744	+	6.19052i	0.145247	+	0.306102i	0.963016	−	0.269446i	$-0.0868404\pi$
$409$	2.93744	+	6.19052i	0.145247	+	0.306102i	−0.817769	+	0.575547i	$0.804789\pi$
$410$	−5.14171	+	25.1858i	−0.253931	+	1.24384i
$411$	−4.25033	−	1.81090i	−0.209653	−	0.0893250i
$412$	29.3223	−	25.9773i	1.44461	−	1.27981i
$413$	6.00841e−5	0	0.000158429i	2.95655e−6	0	7.79577e-6i
$414$	−5.14184	+	5.35322i	−0.252708	+	0.263096i
$415$	−1.88232	−	0.463950i	−0.0923994	−	0.0227744i
$416$	40.5823	+	6.59526i	1.98971	+	0.323359i
$417$	7.09005	−	18.6949i	0.347201	−	0.915494i
$418$	−0.188659	+	0.0629837i	−0.00922763	+	0.00308063i
$419$	14.8322	−	9.37929i	0.724598	−	0.458208i	−0.120573	−	0.992705i	$-0.538473\pi$
$419$	14.8322	−	9.37929i	0.724598	−	0.458208i	0.845171	+	0.534496i	$0.179499\pi$
$420$	−0.0406647	+	0.00328280i	−0.00198424	+	0.000160184i
$421$	6.82535	−	11.8218i	0.332647	−	0.576162i	−0.650383	−	0.759606i	$-0.725392\pi$
$421$	6.82535	−	11.8218i	0.332647	−	0.576162i	0.983030	+	0.183445i	$0.0587249\pi$
$422$	−13.4181	+	19.4395i	−0.653185	+	0.946302i
$423$	−0.301546	−	7.48279i	−0.0146617	−	0.363826i
$424$	2.83754	+	1.20896i	0.137803	+	0.0587125i
$425$	−9.05139	−	23.8665i	−0.439057	−	1.15770i
$426$	6.50212	+	3.41258i	0.315029	+	0.165340i
$427$	−0.0210798	−	0.0727759i	−0.00102012	−	0.00352187i
$428$	13.6727	−	8.64606i	0.660893	−	0.417923i
$429$	−0.257142	−	0.0858465i	−0.0124149	−	0.00414471i
$430$	−17.6249	+	25.5340i	−0.849946	+	1.23136i
$431$	17.9104	+	1.44588i	0.862713	+	0.0696454i	0.503898	−	0.863763i	$-0.331899\pi$
$431$	17.9104	+	1.44588i	0.862713	+	0.0696454i	0.358815	+	0.933409i	$0.383181\pi$
$432$	−2.34336	+	1.22989i	−0.112745	+	0.0591730i
$433$	−4.42683	+	9.32935i	−0.212740	+	0.448340i	−0.981567	−	0.191116i	$-0.938789\pi$
$433$	−4.42683	+	9.32935i	−0.212740	+	0.448340i	0.768827	+	0.639456i	$0.220841\pi$
$434$	0.156729	+	0.117774i	0.00752324	+	0.00565335i
$435$	0.333609	−	8.27841i	0.0159953	−	0.396920i
$436$	0.599760	−	1.26397i	0.0287233	−	0.0605330i
$437$	−5.74346	+	2.44706i	−0.274747	+	0.117059i
$438$	−6.36953	−	31.2000i	−0.304348	−	1.49079i
$439$	3.23556	+	8.53147i	0.154425	+	0.407185i	0.989794	−	0.142504i	$-0.0455154\pi$
$439$	3.23556	+	8.53147i	0.154425	+	0.407185i	−0.835369	+	0.549689i	$0.814746\pi$
$440$	0.0436170	+	0.0534212i	0.00207936	+	0.00254675i
$441$	−6.90916	−	1.12285i	−0.329008	−	0.0534690i
$442$	9.33435	−	76.8753i	0.443990	−	3.65658i
$443$	−2.23183			−0.106037			−0.0530187	−	0.998594i	$-0.516884\pi$
$443$	−2.23183			−0.106037			−0.0530187	+	0.998594i	$0.516884\pi$
$444$	−1.41302	+	11.6372i	−0.0670588	+	0.552279i
$445$	2.46841	−	2.56988i	0.117014	−	0.121824i
$446$	7.06938	−	24.4063i	0.334745	−	1.15567i
$447$	−0.638265	−	2.20355i	−0.0301889	−	0.104224i
$448$	0.0908495	+	0.131618i	0.00429224	+	0.00621838i
$449$	−17.9375	−	31.0686i	−0.846523	−	1.46622i	−0.884292	−	0.466934i	$-0.845359\pi$
$449$	−17.9375	−	31.0686i	−0.846523	−	1.46622i	0.0377697	−	0.999286i	$-0.487975\pi$
$450$	7.74305	+	0.625084i	0.365011	+	0.0294667i
$451$	−0.534503	+	0.0868652i	−0.0251688	+	0.00409032i
$452$	−2.27316	+	11.1347i	−0.106920	+	0.523730i
$453$	−2.45756	−	12.0379i	−0.115466	−	0.565590i
$454$	−4.95939	+	3.72674i	−0.232756	+	0.174904i
$455$	−0.0475363	−	0.0688682i	−0.00222853	−	0.00322859i
$456$	2.03027	−	0.163900i	0.0950759	−	0.00767532i
$457$	2.68356	−	0.661439i	0.125532	−	0.0309408i	−0.176049	−	0.984381i	$-0.556332\pi$
$457$	2.68356	−	0.661439i	0.125532	−	0.0309408i	0.301581	+	0.953441i	$0.402486\pi$
$458$	−1.21530	+	2.10496i	−0.0567872	+	0.0983584i
$459$	3.49836	+	6.05933i	0.163289	+	0.282825i
$460$	7.11471	+	7.40720i	0.331725	+	0.345363i
$461$	−26.9209	+	11.4699i	−1.25383	+	0.534207i	−0.913784	−	0.406201i	$-0.866853\pi$
$461$	−26.9209	+	11.4699i	−1.25383	+	0.534207i	−0.340047	+	0.940408i	$0.610443\pi$
$462$	−0.000659219	−	0.00138927i	−3.06696e−5	−	6.46349e-5i
$463$	−15.6835	−	13.8944i	−0.728874	−	0.645726i	0.214779	−	0.976663i	$-0.431097\pi$
$463$	−15.6835	−	13.8944i	−0.728874	−	0.645726i	−0.943653	+	0.330937i	$0.892635\pi$
$464$	−16.6985	+	8.76407i	−0.775210	+	0.406862i
$465$	5.35541	+	5.57557i	0.248351	+	0.258561i
$466$	−10.2204	+	7.68016i	−0.473453	+	0.355777i
$467$	3.89285	+	2.04312i	0.180139	+	0.0945445i	0.552382	−	0.833591i	$-0.313719\pi$
$467$	3.89285	+	2.04312i	0.180139	+	0.0945445i	−0.372243	+	0.928135i	$0.621411\pi$
$468$	11.1328	+	7.03996i	0.514615	+	0.325422i
$469$	−0.0616613	−	0.0151982i	−0.00284726	−	0.000701786i
$470$	−18.5405			−0.855209
$471$	12.2014	−	2.85044i	0.562212	−	0.131341i
$472$	0.0139172			0.000640590
$473$	−0.634614	−	0.156418i	−0.0291796	−	0.00719212i
$474$	−4.20895	−	2.66158i	−0.193324	−	0.122250i
$475$	5.78532	+	3.03637i	0.265449	+	0.139318i
$476$	0.196269	−	0.147486i	0.00899596	−	0.00676002i
$477$	−1.87865	−	1.95588i	−0.0860173	−	0.0895535i
$478$	24.3602	−	12.7852i	1.11421	−	0.584782i
$479$	−23.7432	−	21.0347i	−1.08486	−	0.961098i	−0.0854768	−	0.996340i	$-0.527241\pi$
$479$	−23.7432	−	21.0347i	−1.08486	−	0.961098i	−0.999379	+	0.0352420i	$0.988780\pi$
$480$	3.94255	+	8.30876i	0.179952	+	0.379241i
$481$	−22.1210	+	9.42487i	−1.00863	+	0.429737i
$482$	34.5504	+	35.9708i	1.57373	+	1.63842i
$483$	−0.0241338	−	0.0418009i	−0.00109812	−	0.00190201i
$484$	13.9342	−	24.1347i	0.633372	−	1.09703i
$485$	16.8845	−	4.16166i	0.766687	−	0.188971i
$486$	−2.12244	+	0.171341i	−0.0962759	+	0.00777219i
$487$	−5.78707	−	8.38401i	−0.262237	−	0.379916i	0.669643	−	0.742683i	$-0.266447\pi$
$487$	−5.78707	−	8.38401i	−0.262237	−	0.379916i	−0.931880	+	0.362768i	$0.881832\pi$
$488$	4.97514	−	3.73858i	0.225214	−	0.169237i
$489$	−0.00813351	−	0.0398405i	−0.000367810	−	0.00180165i
$490$	−3.46639	+	16.9795i	−0.156595	+	0.767055i
$491$	−6.54878	+	1.06428i	−0.295542	+	0.0480303i	−0.306375	−	0.951911i	$-0.599116\pi$
$491$	−6.54878	+	1.06428i	−0.295542	+	0.0480303i	0.0108323	+	0.999941i	$0.496552\pi$
$492$	26.2260	+	2.11718i	1.18236	+	0.0954500i
$493$	24.9290	+	43.1782i	1.12274	+	1.94465i
$494$	11.2604	+	16.3134i	0.506628	+	0.733977i
$495$	−0.0168709	−	0.0582450i	−0.000758290	−	0.00261792i
$496$	4.89585	−	16.9024i	0.219830	−	0.758942i
$497$	−0.0330785	+	0.0344384i	−0.00148377	+	0.00154477i
$498$	−0.427963	+	3.52459i	−0.0191775	+	0.157941i
$499$	35.2458			1.57782			0.788910	−	0.614508i	$-0.210646\pi$
$499$	35.2458			1.57782			0.788910	+	0.614508i	$0.210646\pi$
$500$	3.07135	−	25.2948i	0.137355	−	1.13122i
$501$	−18.0100	−	2.92691i	−0.804627	−	0.130765i
$502$	−17.7035	−	21.6828i	−0.790145	−	0.967752i
$503$	−1.84906	−	4.87558i	−0.0824457	−	0.217391i	0.887454	−	0.460896i	$-0.152472\pi$
$503$	−1.84906	−	4.87558i	−0.0824457	−	0.217391i	−0.969900	+	0.243505i	$0.921703\pi$
$504$	0.00314999	+	0.0154297i	0.000140312	+	0.000687292i
$505$	4.20980	−	1.79363i	0.187334	−	0.0798154i
$506$	−0.165958	+	0.349749i	−0.00737773	+	0.0155482i
$507$	−0.564437	+	14.0064i	−0.0250675	+	0.622045i
$508$	−20.3936	−	15.3248i	−0.904820	−	0.679928i
$509$	−5.16899	+	10.8934i	−0.229111	+	0.482842i	−0.985152	−	0.171682i	$-0.945080\pi$
$509$	−5.16899	+	10.8934i	−0.229111	+	0.482842i	0.756041	+	0.654524i	$0.227131\pi$
$510$	15.3379	−	8.04996i	0.679174	−	0.356458i
$511$	0.206399	+	0.0166623i	0.00913056	+	0.000737095i
$512$	15.3113	−	22.1822i	0.676669	−	0.980324i
$513$	−1.69878	−	0.567137i	−0.0750031	−	0.0250397i
$514$	−27.4972	+	17.3882i	−1.21285	+	0.766959i
$515$	5.00055	+	17.2639i	0.220351	+	0.760738i
$516$	28.1200	+	14.7585i	1.23791	+	0.649707i
$517$	−0.138502	−	0.365199i	−0.00609129	−	0.0160614i
$518$	−0.125479	−	0.0534614i	−0.00551321	−	0.00234896i
$519$	−0.0125988	−	0.312636i	−0.000553026	−	0.0137232i
$520$	3.90446	−	5.65659i	0.171222	−	0.248058i
$521$	−20.1596	+	34.9174i	−0.883206	+	1.52976i	−0.0354502	+	0.999371i	$0.511287\pi$
$521$	−20.1596	+	34.9174i	−0.883206	+	1.52976i	−0.847756	+	0.530387i	$0.822047\pi$
$522$	−15.1243	+	1.22096i	−0.661974	+	0.0534400i
$523$	8.65876	−	5.47547i	0.378621	−	0.239425i	−0.331576	−	0.943429i	$-0.607580\pi$
$523$	8.65876	−	5.47547i	0.378621	−	0.239425i	0.710197	+	0.704003i	$0.248606\pi$
$524$	3.79865	−	1.26817i	0.165945	−	0.0554005i
$525$	−0.0179128	+	0.0472323i	−0.000781781	+	0.00206139i
$526$	−40.8294	−	6.63543i	−1.78025	−	0.289318i
$527$	−45.1710	−	11.1337i	−1.96768	−	0.484990i
$528$	−0.0956149	+	0.0995457i	−0.00416111	+	0.00433217i
$529$	3.84699	−	10.1437i	0.167261	−	0.441030i
$530$	−5.02560	+	4.45229i	−0.218298	+	0.193395i
$531$	−0.0112577	−	0.00479646i	−0.000488542	−	0.000208148i
$532$	−0.0125701	+	0.0615725i	−0.000544983	+	0.00266950i
$533$	23.1359	+	48.7580i	1.00213	+	2.11194i
$534$	−5.21711	−	3.92041i	−0.225767	−	0.169653i
$535$	0.894645	+	7.36807i	0.0386789	+	0.318549i
$536$	−0.628746	−	5.17819i	−0.0271577	−	0.223664i
$537$	−0.718237	+	17.8229i	−0.0309942	+	0.769114i
$538$	−12.4708	−	11.0482i	−0.537656	−	0.476322i
$539$	−0.360346	+	0.0585619i	−0.0155212	+	0.00252244i
$540$	0.118638	+	2.94397i	0.00510536	+	0.126688i
$541$	−9.06392	+	11.1013i	−0.389688	+	0.477282i	−0.931773	−	0.363042i	$-0.881738\pi$
$541$	−9.06392	+	11.1013i	−0.389688	+	0.477282i	0.542084	+	0.840324i	$0.317635\pi$
$542$	−44.0150	+	14.6944i	−1.89061	+	0.631178i
$543$	5.08021	−	17.5389i	0.218013	−	0.752667i
$544$	−46.7758	−	29.5792i	−2.00549	−	1.26820i
$545$	0.405964	+	0.497216i	0.0173896	+	0.0212984i
$546$	−0.114713	+	0.101627i	−0.00490926	+	0.00434922i
$547$	14.6886	−	17.9902i	0.628038	−	0.769207i	−0.358360	−	0.933584i	$-0.616664\pi$
$547$	14.6886	−	17.9902i	0.628038	−	0.769207i	0.986398	+	0.164377i	$0.0525613\pi$
$548$	11.1052	+	3.70745i	0.474389	+	0.158374i
$549$	−5.31290	+	1.30951i	−0.226749	+	0.0558886i
$550$	0.393378	−	0.0969589i	0.0167737	−	0.00413434i
$551$	−12.1054	−	4.04137i	−0.515706	−	0.172168i
$552$	2.50735	−	3.07094i	0.106720	−	0.130708i
$553$	0.0242390	−	0.0214739i	0.00103075	−	0.000913162i
$554$	−0.244186	−	0.299074i	−0.0103745	−	0.0127064i
$555$	−4.54585	−	2.87462i	−0.192961	−	0.122021i
$556$	−14.0966	+	48.6672i	−0.597830	+	2.06395i
$557$	−25.6764	+	8.57203i	−1.08794	+	0.363209i	−0.803391	−	0.595452i	$-0.796973\pi$
$557$	−25.6764	+	8.57203i	−1.08794	+	0.363209i	−0.284552	+	0.958661i	$0.591845\pi$
$558$	8.95451	−	10.9673i	0.379075	−	0.464282i
$559$	2.62292	+	65.0870i	0.110938	+	2.75289i
$560$	−0.0420546	+	0.00683453i	−0.00177713	+	0.000288812i
$561$	0.273141	+	0.241981i	0.0115320	+	0.0102165i
$562$	−2.00400	+	49.7286i	−0.0845335	+	2.09768i
$563$	−0.000783851	−	0.00645560i	−3.30354e−5	−	0.000272071i	0.992692	−	0.120673i	$-0.0385052\pi$
$563$	−0.000783851	−	0.00645560i	−3.30354e−5	−	0.000272071i	−0.992725	+	0.120401i	$0.961582\pi$
$564$	2.28750	+	18.8393i	0.0963212	+	0.793276i
$565$	−4.16835	−	3.13231i	−0.175364	−	0.131777i
$566$	−23.3740	−	49.2596i	−0.982482	−	2.07054i
$567$	0.00276968	−	0.0135668i	0.000116316	−	0.000569751i
$568$	−3.60828	−	1.53734i	−0.151400	−	0.0645055i
$569$	15.3224	−	13.5744i	0.642347	−	0.569069i	−0.277802	−	0.960638i	$-0.589606\pi$
$569$	15.3224	−	13.5744i	0.642347	−	0.569069i	0.920149	+	0.391569i	$0.128068\pi$
$570$	−1.57229	+	4.14580i	−0.0658562	+	0.173648i
$571$	19.4030	−	20.2007i	0.811992	−	0.845373i	−0.178357	−	0.983966i	$-0.557078\pi$
$571$	19.4030	−	20.2007i	0.811992	−	0.845373i	0.990350	+	0.138592i	$0.0442578\pi$
$572$	0.667018	+	0.164405i	0.0278894	+	0.00687413i
$573$	6.24918	+	1.01559i	0.261063	+	0.0424269i
$574$	−0.108555	+	0.286237i	−0.00453101	+	0.0119473i
$575$	12.0626	−	4.02710i	0.503047	−	0.167942i
$576$	9.76193	−	6.17307i	0.406747	−	0.257211i
$577$	17.7846	−	1.43572i	0.740381	−	0.0597698i	0.295479	−	0.955349i	$-0.404521\pi$
$577$	17.7846	−	1.43572i	0.740381	−	0.0597698i	0.444902	+	0.895579i	$0.353239\pi$
$578$	−34.0205	+	58.9253i	−1.41507	+	2.45097i
$579$	11.3301	−	16.4145i	0.470863	−	0.682163i
$580$	0.845402	+	20.9784i	0.0351034	+	0.871082i
$581$	−0.0212404	−	0.00904968i	−0.000881199	−	0.000375444i
$582$	−11.2935	−	29.7784i	−0.468129	−	1.23436i
$583$	−0.125241	−	0.0657314i	−0.00518694	−	0.00272232i
$584$	4.73194	+	16.3366i	0.195809	+	0.676011i
$585$	−5.10785	+	3.23001i	−0.211184	+	0.133544i
$586$	37.0211	+	12.3594i	1.52933	+	0.510564i
$587$	−13.9445	+	20.2022i	−0.575553	+	0.833832i	−0.997342	−	0.0728615i	$-0.976787\pi$
$587$	−13.9445	+	20.2022i	−0.575553	+	0.833832i	0.421789	+	0.906694i	$0.361402\pi$
$588$	17.6808	+	1.42734i	0.729143	+	0.0588625i
$589$	10.5444	−	5.53415i	0.434476	−	0.228031i
$590$	−0.0129874	+	0.0273704i	−0.000534683	+	0.00112682i
$591$	21.1712	+	15.9092i	0.870868	+	0.654415i
$592$	−0.492959	+	12.2327i	−0.0202605	+	0.502759i
$593$	2.14463	−	4.51972i	0.0880695	−	0.185603i	−0.854637	−	0.519226i	$-0.826220\pi$
$593$	2.14463	−	4.51972i	0.0880695	−	0.185603i	0.942706	+	0.333624i	$0.108271\pi$
$594$	−0.102169	+	0.0435301i	−0.00419204	+	0.00178606i
$595$	0.0225311	+	0.110365i	0.000923685	+	0.00452451i
$596$	2.06152	+	5.43578i	0.0844431	+	0.222658i
$597$	3.82734	+	4.68764i	0.156643	+	0.191852i
$598$	38.0822	+	6.18896i	1.55730	+	0.253085i
$599$	3.00271	−	24.7295i	0.122687	−	1.01042i	−0.793193	−	0.608970i	$-0.791583\pi$
$599$	3.00271	−	24.7295i	0.122687	−	1.01042i	0.915881	−	0.401451i	$-0.131494\pi$
$600$	−4.14912			−0.169387
$601$	−3.78750	+	31.1928i	−0.154495	+	1.27238i	0.684810	+	0.728722i	$0.259885\pi$
$601$	−3.78750	+	31.1928i	−0.154495	+	1.27238i	−0.839305	+	0.543661i	$0.817038\pi$
$602$	−0.255960	+	0.266483i	−0.0104322	+	0.0108610i
$603$	−1.27603	+	4.40537i	−0.0519639	+	0.179400i
$604$	8.66220	+	29.9054i	0.352460	+	1.21683i
$605$	7.26344	+	10.5229i	0.295301	+	0.427817i
$606$	−4.19025	−	7.25773i	−0.170217	−	0.294825i
$607$	−26.3466	−	2.12692i	−1.06937	−	0.0863289i	−0.466778	−	0.884375i	$-0.654585\pi$
$607$	−26.3466	−	2.12692i	−1.06937	−	0.0863289i	−0.602597	+	0.798046i	$0.705867\pi$
$608$	13.9828	−	2.27243i	0.567079	−	0.0921594i
$609$	0.0197365	−	0.0966756i	0.000799762	−	0.00391749i
$610$	2.70975	+	13.2732i	0.109715	+	0.537418i
$611$	−31.1192	+	23.3845i	−1.25895	+	0.946037i
$612$	−10.0721	−	14.5919i	−0.407138	−	0.589842i
$613$	−36.4239	+	2.94044i	−1.47115	+	0.118763i	−0.789876	−	0.613267i	$-0.789855\pi$
$613$	−36.4239	+	2.94044i	−1.47115	+	0.118763i	−0.681272	+	0.732030i	$0.738573\pi$
$614$	−20.2242	+	4.98482i	−0.816183	+	0.201171i
$615$	−6.03595	+	10.4546i	−0.243393	+	0.421569i
$616$	0.000410665	0	0.000711292i	1.65461e−5	0	2.86588e-5i
$617$	8.07094	+	8.40274i	0.324924	+	0.338282i	0.863550	−	0.504263i	$-0.168236\pi$
$617$	8.07094	+	8.40274i	0.324924	+	0.338282i	−0.538626	+	0.842545i	$0.681056\pi$
$618$	30.2830	−	12.9024i	1.21816	−	0.519009i
$619$	6.97226	+	14.6937i	0.280239	+	0.590591i	0.993948	−	0.109851i	$-0.0350375\pi$
$619$	6.97226	+	14.6937i	0.280239	+	0.590591i	−0.713709	+	0.700442i	$0.752986\pi$
$620$	−14.6641	−	12.9913i	−0.588925	−	0.521742i
$621$	−3.08659	+	1.61997i	−0.123861	+	0.0650070i
$622$	−48.2922	−	50.2775i	−1.93634	−	2.01594i
$623$	0.0339256	−	0.0254934i	0.00135920	−	0.00102137i
$624$	12.1804	+	6.39278i	0.487608	+	0.255916i
$625$	−5.53611	−	3.50082i	−0.221444	−	0.140033i
$626$	−8.13014	−	2.00390i	−0.324946	−	0.0800919i
$627$	−0.0934067			−0.00373030
$628$	−30.2383	+	9.68793i	−1.20664	+	0.386590i
$629$	32.3665			1.29054
$630$	−0.0332845	−	0.00820389i	−0.00132609	−	0.000326851i
$631$	−4.79425	−	3.03170i	−0.190856	−	0.120690i	0.435620	−	0.900131i	$-0.356529\pi$
$631$	−4.79425	−	3.03170i	−0.190856	−	0.120690i	−0.626476	+	0.779441i	$0.715503\pi$
$632$	2.35516	+	1.23608i	0.0936832	+	0.0491687i
$633$	−8.86821	+	6.66403i	−0.352480	+	0.264871i
$634$	−47.7544	−	49.7176i	−1.89657	−	1.97454i
$635$	10.3635	−	5.43919i	0.411263	−	0.215848i
$636$	5.14409	+	4.55727i	0.203976	+	0.180707i
$637$	15.5976	+	32.8712i	0.617998	+	1.30240i
$638$	−0.728046	+	0.310191i	−0.0288236	+	0.0122806i
$639$	2.38892	+	2.48713i	0.0945044	+	0.0983895i
$640$	−5.10069	−	8.83466i	−0.201623	−	0.349221i
$641$	17.4127	−	30.1596i	0.687759	−	1.19123i	−0.284802	−	0.958586i	$-0.591928\pi$
$641$	17.4127	−	30.1596i	0.687759	−	1.19123i	0.972561	−	0.232648i	$-0.0747389\pi$
$642$	13.1981	−	3.25304i	0.520888	−	0.128387i
$643$	−17.1986	+	1.38842i	−0.678248	+	0.0547538i	−0.414790	−	0.909917i	$-0.636145\pi$
$643$	−17.1986	+	1.38842i	−0.678248	+	0.0547538i	−0.263458	+	0.964671i	$0.584863\pi$
$644$	0.0694831	+	0.100664i	0.00273802	+	0.00396670i
$645$	−11.6485	+	8.75326i	−0.458658	+	0.344659i
$646$	−5.33715	−	26.1431i	−0.209988	−	1.02859i
$647$	−7.62503	+	37.3499i	−0.299771	+	1.46838i	0.498927	+	0.866644i	$0.333727\pi$
$647$	−7.62503	+	37.3499i	−0.299771	+	1.46838i	−0.798698	+	0.601732i	$0.794478\pi$
$648$	1.12258	−	0.182438i	0.0440993	−	0.00716683i
$649$	−0.000636143	0	5.13548e-5i	−2.49708e−5	0	2.01585e-6i
$650$	−20.1891	−	34.9686i	−0.791882	−	1.37158i
$651$	0.0523015	+	0.0757718i	0.00204986	+	0.00296973i
$652$	0.0286683	+	0.0989746i	0.00112274	+	0.00387614i
$653$	−4.20697	+	14.5242i	−0.164632	+	0.568374i	0.835199	+	0.549948i	$0.185353\pi$
$653$	−4.20697	+	14.5242i	−0.164632	+	0.568374i	−0.999830	+	0.0184258i	$0.994135\pi$
$654$	0.814352	−	0.847830i	0.0318437	−	0.0331528i
$655$	−0.221476	+	1.82402i	−0.00865379	+	0.0712704i
$656$	27.4782			1.07284
$657$	1.80258	−	14.8456i	0.0703253	−	0.579181i
$658$	−0.217944	−	0.0354193i	−0.00849634	−	0.00138079i
$659$	−26.7834	−	32.8037i	−1.04333	−	1.27785i	−0.959602	−	0.281362i	$-0.909214\pi$
$659$	−26.7834	−	32.8037i	−1.04333	−	1.27785i	−0.0837309	−	0.996488i	$-0.526684\pi$
$660$	0.0544909	+	0.143681i	0.00212106	+	0.00559276i
$661$	−8.01360	−	39.2532i	−0.311693	−	1.52677i	−0.770038	−	0.637998i	$-0.779763\pi$
$661$	−8.01360	−	39.2532i	−0.311693	−	1.52677i	0.458345	−	0.888774i	$-0.348442\pi$
$662$	19.5035	−	8.30968i	0.758026	−	0.322965i
$663$	15.5907	−	32.8566i	0.605491	−	1.27605i
$664$	0.0763586	−	1.89482i	0.00296329	−	0.0735333i
$665$	−0.0230502	−	0.0173211i	−0.000893847	−	0.000671682i
$666$	−4.22274	+	8.89923i	−0.163628	+	0.344838i
$667$	−21.9947	+	11.5437i	−0.851640	+	0.446975i
$668$	46.0882	+	3.72062i	1.78320	+	0.143955i
$669$	6.77874	−	9.82069i	0.262081	−	0.379690i
$670$	10.7705	+	3.59572i	0.416101	+	0.138915i
$671$	−0.241205	+	0.152529i	−0.00931163	+	0.00588832i
$672$	0.0304720	+	0.105201i	0.00117548	+	0.00405823i
$673$	12.2851	+	6.44770i	0.473555	+	0.248541i	0.684577	−	0.728941i	$-0.259987\pi$
$673$	12.2851	+	6.44770i	0.473555	+	0.248541i	−0.211022	+	0.977481i	$0.567679\pi$
$674$	23.4345	+	61.7917i	0.902663	+	2.38013i
$675$	3.35625	+	1.42997i	0.129182	+	0.0550394i
$676$	−1.43035	−	35.4937i	−0.0550134	−	1.36514i
$677$	9.35588	−	13.5543i	0.359576	−	0.520935i	−0.600891	−	0.799331i	$-0.705187\pi$
$677$	9.35588	−	13.5543i	0.359576	−	0.520935i	0.960466	+	0.278396i	$0.0898028\pi$
$678$	−4.77456	+	8.26979i	−0.183366	+	0.317599i
$679$	0.206428	−	0.0166646i	0.00792199	−	0.000639529i
$680$	−7.81965	+	4.94485i	−0.299870	+	0.189626i
$681$	−2.76343	+	0.922568i	−0.105895	+	0.0353529i
$682$	0.261853	−	0.690450i	0.0100269	−	0.0264387i
$683$	−31.4211	−	5.10642i	−1.20229	−	0.195392i	−0.473918	−	0.880569i	$-0.657161\pi$
$683$	−31.4211	−	5.10642i	−1.20229	−	0.195392i	−0.728377	+	0.685177i	$0.759725\pi$
$684$	4.40659	+	1.08613i	0.168490	+	0.0415291i
$685$	−3.72104	+	3.87401i	−0.142174	+	0.148018i
$686$	−0.146371	+	0.385950i	−0.00558849	+	0.0147356i
$687$	−0.854408	+	0.756939i	−0.0325977	+	0.0288790i
$688$	30.5121	+	13.0000i	1.16326	+	0.495619i
$689$	−2.81965	+	13.8115i	−0.107420	+	0.526178i
$690$	3.69967	+	7.79689i	0.140844	+	0.296823i
$691$	−16.5359	−	12.4260i	−0.629057	−	0.472706i	0.237766	−	0.971323i	$-0.423585\pi$
$691$	−16.5359	−	12.4260i	−0.629057	−	0.472706i	−0.866822	+	0.498617i	$0.833841\pi$
$692$	0.0955733	+	0.787117i	0.00363315	+	0.0299217i
$693$	−8.70476e−5	0	0.000716901i	−3.30666e−6	0	2.72328e-5i
$694$	0.0170920	−	0.424134i	0.000648804	−	0.0160999i
$695$	−17.4005	−	15.4155i	−0.660039	−	0.584743i
$696$	7.99943	−	1.30003i	0.303218	−	0.0492777i
$697$	−2.92515	−	72.5869i	−0.110798	−	2.74943i
$698$	−15.0908	+	18.4829i	−0.571195	+	0.699587i
$699$	−5.69495	+	1.90125i	−0.215403	+	0.0719120i
$700$	0.0356148	−	0.122956i	0.00134611	−	0.00464732i
$701$	−8.23108	−	5.20502i	−0.310883	−	0.196591i	0.369907	−	0.929069i	$-0.379389\pi$
$701$	−8.23108	−	5.20502i	−0.310883	−	0.196591i	−0.680791	+	0.732478i	$0.738364\pi$
$702$	6.99993	+	8.57336i	0.264195	+	0.323581i
$703$	−6.20132	+	5.49389i	−0.233887	+	0.207206i
$704$	0.380977	−	0.466612i	0.0143586	−	0.0175861i
$705$	−8.25903	−	2.75727i	−0.311053	−	0.103845i
$706$	−7.32046	+	1.80433i	−0.275509	+	0.0679069i
$707$	0.0529128	−	0.0130418i	0.00198999	−	0.000490489i
$708$	0.0294138	+	0.00981978i	0.00110544	+	0.000369050i
$709$	−0.0611058	+	0.0748411i	−0.00229488	+	0.00281072i	−0.775751	−	0.631039i	$-0.782629\pi$
$709$	−0.0611058	+	0.0748411i	−0.00229488	+	0.00281072i	0.773456	+	0.633850i	$0.218526\pi$
$710$	6.39065	−	5.66162i	0.239837	−	0.212477i
$711$	−1.47910	−	1.81156i	−0.0554704	−	0.0679390i
$712$	2.94599	+	1.86293i	0.110406	+	0.0698162i
$713$	6.44865	−	22.2633i	0.241504	−	0.833768i
$714$	0.195676	−	0.0653263i	0.00732299	−	0.00244477i
$715$	−0.199343	+	0.244151i	−0.00745500	+	0.00913072i
$716$	−1.82009	−	45.1652i	−0.0680201	−	1.68790i
$717$	12.7528	−	2.07254i	0.476263	−	0.0774003i
$718$	50.7817	+	44.9886i	1.89516	+	1.67896i
$719$	1.78364	−	44.2607i	0.0665187	−	1.65065i	−0.529965	−	0.848020i	$-0.677795\pi$
$719$	1.78364	−	44.2607i	0.0665187	−	1.65065i	0.596483	−	0.802625i	$-0.296564\pi$
$720$	0.370894	+	3.05459i	0.0138224	+	0.113838i
$721$	0.0258010	+	0.212490i	0.000960880	+	0.00791356i
$722$	−26.8834	−	20.2016i	−1.00050	−	0.751825i
$723$	10.0414	+	21.1617i	0.373442	+	0.787012i
$724$	−9.25570	+	45.3374i	−0.343985	+	1.68495i
$725$	23.9163	+	10.1898i	0.888231	+	0.378440i
$726$	17.5279	−	15.5284i	0.650521	−	0.576311i
$727$	−6.77808	+	17.8723i	−0.251385	+	0.662848i	−1.00000		0.000157298i	$-0.999950\pi$
$727$	−6.77808	+	17.8723i	−0.251385	+	0.662848i	0.748615	+	0.663005i	$0.230719\pi$
$728$	0.0567033	−	0.0590344i	0.00210156	−	0.00218796i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−36.5443	−	5.93903i	−1.35257	−	0.219813i
$731$	31.0929	−	81.9852i	1.15001	−	3.03233i
$732$	13.1528	−	4.39105i	0.486142	−	0.162298i
$733$	1.70734	−	1.07965i	0.0630619	−	0.0398779i	−0.502563	−	0.864541i	$-0.667609\pi$
$733$	1.70734	−	1.07965i	0.0630619	−	0.0398779i	0.565625	+	0.824663i	$0.308635\pi$
$734$	−22.4330	+	1.81098i	−0.828016	+	0.0668444i
$735$	−4.06926	+	7.04816i	−0.150097	+	0.259975i
$736$	15.6633	−	22.6922i	0.577356	−	0.836444i
$737$	0.00963182	+	0.239011i	0.000354793	+	0.00880409i
$738$	20.3395	+	8.66587i	0.748709	+	0.318995i
$739$	−4.82880	−	12.7325i	−0.177630	−	0.468373i	0.816399	−	0.577489i	$-0.195967\pi$
$739$	−4.82880	−	12.7325i	−0.177630	−	0.468373i	−0.994029	+	0.109116i	$0.965198\pi$
$740$	12.0685	+	6.33405i	0.443648	+	0.232844i
$741$	2.58996	+	8.94157i	0.0951445	+	0.328477i
$742$	−0.0675816	+	0.0427360i	−0.00248100	+	0.00156889i
$743$	29.0385	+	9.69449i	1.06532	+	0.355656i	0.794683	−	0.607025i	$-0.207637\pi$
$743$	29.0385	+	9.69449i	1.06532	+	0.355656i	0.270638	+	0.962681i	$0.412765\pi$
$744$	−4.29586	+	6.22363i	−0.157494	+	0.228169i
$745$	−2.65867	−	0.214630i	−0.0974063	−	0.00786345i
$746$	34.4046	−	18.0569i	1.25964	−	0.661111i
$747$	−0.714803	+	1.50642i	−0.0261533	+	0.0551169i
$748$	−0.739267	−	0.555523i	−0.0270303	−	0.0203119i
$749$	−0.00355921	+	0.0883209i	−0.000130051	+	0.00322717i
$750$	9.17859	−	19.3435i	0.335155	−	0.706324i
$751$	−30.0265	+	12.7931i	−1.09568	+	0.466827i	−0.862732	−	0.505662i	$-0.831248\pi$
$751$	−30.0265	+	12.7931i	−1.09568	+	0.466827i	−0.232951	+	0.972488i	$0.574838\pi$
$752$	3.96436	+	19.4187i	0.144565	+	0.708128i
$753$	−4.66159	−	12.2916i	−0.169878	−	0.447931i
$754$	49.8809	+	61.0930i	1.81655	+	2.22487i
$755$	−14.0999	−	2.29146i	−0.513148	−	0.0833947i
$756$	−0.00422950	+	0.0348330i	−0.000153825	+	0.00126687i
$757$	50.7416			1.84423			0.922117	−	0.386911i	$-0.126458\pi$
$757$	50.7416			1.84423			0.922117	+	0.386911i	$0.126458\pi$
$758$	−0.634837	+	5.22835i	−0.0230583	+	0.189902i
$759$	−0.125941	+	0.131118i	−0.00457136	+	0.00475929i
$760$	0.658881	−	2.27472i	0.0239001	−	0.0825128i
$761$	8.24991	+	28.4820i	0.299059	+	1.03247i	0.959527	+	0.281617i	$0.0908708\pi$
$761$	8.24991	+	28.4820i	0.299059	+	1.03247i	−0.660468	+	0.750854i	$0.729642\pi$
$762$	−12.1766	−	17.6408i	−0.441110	−	0.639058i
$763$	0.00382225	+	0.00662033i	0.000138375	+	0.000239672i
$764$	−15.9919	−	1.29100i	−0.578566	−	0.0467066i
$765$	8.02957	−	1.30493i	0.290310	−	0.0471799i
$766$	11.9855	−	58.7089i	0.433054	−	2.12124i
$767$	0.0127228	+	0.0623202i	0.000459393	+	0.00225025i
$768$	3.53112	−	2.65347i	0.127418	−	0.0957488i
$769$	−25.2721	−	36.6129i	−0.911334	−	1.32029i	−0.947101	−	0.320935i	$-0.896003\pi$
$769$	−25.2721	−	36.6129i	−0.911334	−	1.32029i	0.0357675	−	0.999360i	$-0.488612\pi$
$770$	−0.00178210		0.000143866i	−6.42225e−5		5.18457e-6i
$771$	−14.8348	+	3.65644i	−0.534261	+	0.131684i
$772$	−25.2716	+	43.7716i	−0.909543	+	1.57538i
$773$	0.875636	+	1.51665i	0.0314944	+	0.0545500i	0.881343	−	0.472477i	$-0.156640\pi$
$773$	0.875636	+	1.51665i	0.0314944	+	0.0545500i	−0.849849	+	0.527027i	$0.823307\pi$
$774$	18.4854	+	19.2453i	0.664444	+	0.691760i
$775$	−22.3166	+	9.50820i	−0.801635	+	0.341545i
$776$	7.29226	+	15.3681i	0.261777	+	0.551683i
$777$	−0.0479450	−	0.0424756i	−0.00172002	−	0.00152380i
$778$	−39.7618	+	20.8686i	−1.42553	+	0.748176i
$779$	12.8813	+	13.4109i	0.461522	+	0.480495i
$780$	12.2433	−	9.20021i	0.438379	−	0.329421i
$781$	0.159259	+	0.0835854i	0.00569872	+	0.00299092i
$782$	−43.8941	−	27.7570i	−1.56965	−	0.992587i
$783$	−6.91884	−	1.70534i	−0.247259	−	0.0609439i
$784$	18.5250			0.661606
$785$	1.93176	−	14.4397i	0.0689476	−	0.515374i
$786$	3.36508			0.120028
$787$	35.2954	+	8.69954i	1.25815	+	0.310105i	0.811366	−	0.584539i	$-0.198724\pi$
$787$	35.2954	+	8.69954i	1.25815	+	0.310105i	0.446780	+	0.894644i	$0.352571\pi$
$788$	−56.7204	−	35.8678i	−2.02058	−	1.27774i
$789$	−17.2010	−	9.02781i	−0.612374	−	0.321398i
$790$	−4.62878	+	3.47830i	−0.164684	+	0.123752i
$791$	−0.0430151	−	0.0447835i	−0.00152944	−	0.00159232i
$792$	0.0525219	−	0.0275656i	0.00186629	−	0.000979502i
$793$	21.2893	+	18.8607i	0.756004	+	0.669761i
$794$	8.00299	+	16.8659i	0.284015	+	0.598550i
$795$	−2.90083	+	1.23593i	−0.102882	+	0.0438338i
$796$	−10.6233	−	11.0601i	−0.376534	−	0.392013i
$797$	15.5074	+	26.8596i	0.549301	+	0.951417i	0.998323	+	0.0578961i	$0.0184392\pi$
$797$	15.5074	+	26.8596i	0.549301	+	0.951417i	−0.449022	+	0.893521i	$0.648227\pi$
$798$	−0.0264024	+	0.0457303i	−0.000934635	+	0.00161883i
$799$	50.8749	−	12.5395i	1.79982	−	0.443617i
$800$	−28.7633	+	2.32201i	−1.01694	+	0.0820955i
$801$	−1.74098	−	2.52225i	−0.0615146	−	0.0891193i
$802$	25.3291	−	19.0335i	0.894400	−	0.672098i
$803$	−0.156011	−	0.764192i	−0.00550551	−	0.0269678i
$804$	2.32481	−	11.3877i	0.0819899	−	0.401613i
$805$	−0.0553928	+	0.00900221i	−0.00195234	+	0.000317286i
$806$	−73.3555	−	5.92187i	−2.58384	−	0.208589i
$807$	−3.91220	−	6.77614i	−0.137716	−	0.238531i
$808$	2.54274	+	3.68379i	0.0894532	+	0.129595i
$809$	15.0237	+	51.8677i	0.528204	+	1.82357i	0.566163	+	0.824293i	$0.308427\pi$
$809$	15.0237	+	51.8677i	0.528204	+	1.82357i	−0.0379588	+	0.999279i	$0.512086\pi$
$810$	−0.688795	+	2.37800i	−0.0242018	+	0.0835542i
$811$	−31.6650	+	32.9668i	−1.11191	+	1.15762i	−0.125708	+	0.992067i	$0.540120\pi$
$811$	−31.6650	+	32.9668i	−1.11191	+	1.15762i	−0.986201	+	0.165552i	$0.947059\pi$
$812$	−0.0301390	+	0.248217i	−0.00105767	+	0.00871071i
$813$	−21.7922			−0.764286
$814$	−0.0619244	+	0.509993i	−0.00217045	+	0.0178752i
$815$	−0.0466649	−	0.00758379i	−0.00163460	−	0.000265648i
$816$	−11.7108	−	14.3432i	−0.409962	−	0.502112i
$817$	7.95886	+	20.9858i	0.278445	+	0.734200i
$818$	−2.91847	−	14.2956i	−0.102042	−	0.499834i
$819$	−0.0662134	+	0.0282109i	−0.00231368	+	0.000985769i
$820$	13.1144	−	27.6380i	0.457974	−	0.965160i
$821$	−0.361956	+	8.98186i	−0.0126324	+	0.313469i	0.980503	+	0.196502i	$0.0629582\pi$
$821$	−0.361956	+	8.98186i	−0.0126324	+	0.313469i	−0.993136	+	0.116967i	$0.962683\pi$
$822$	7.86463	+	5.90989i	0.274310	+	0.206131i
$823$	−12.0813	+	25.4607i	−0.421126	+	0.887505i	0.576397	+	0.817170i	$0.304458\pi$
$823$	−12.0813	+	25.4607i	−0.421126	+	0.887505i	−0.997523	+	0.0703352i	$0.977593\pi$
$824$	−15.5676	+	8.17049i	−0.542322	+	0.284633i
$825$	0.189653	+	0.0153104i	0.00660287	+	0.000533039i
$826$	−0.000204955	0	0.000296929i	−7.13130e−6	0	1.03315e-5i
$827$	−0.0447183	−	0.0149292i	−0.00155501	−	0.000519138i	0.315890	−	0.948796i	$-0.397697\pi$
$827$	−0.0447183	−	0.0149292i	−0.00155501	−	0.000519138i	−0.317445	+	0.948277i	$0.602825\pi$
$828$	7.46607	−	4.72126i	0.259464	−	0.164075i
$829$	−11.8409	−	40.8796i	−0.411252	−	1.41981i	−0.852644	−	0.522492i	$-0.825002\pi$
$829$	−11.8409	−	40.8796i	−0.411252	−	1.41981i	0.441392	−	0.897314i	$-0.354485\pi$
$830$	3.65522	+	1.91841i	0.126874	+	0.0665888i
$831$	−0.0642979	−	0.169540i	−0.00223047	−	0.00588127i
$832$	−55.2311	−	23.5318i	−1.91480	−	0.815818i
$833$	−1.97205	−	48.9359i	−0.0683275	−	1.69553i
$834$	−24.1851	+	35.0382i	−0.837463	+	1.21327i
$835$	−10.6073	+	18.3723i	−0.367079	+	0.635800i
$836$	0.235936	−	0.0190467i	0.00816000	−	0.000658743i
$837$	5.61988	−	3.55380i	0.194252	−	0.122837i
$838$	−35.4446	+	11.8331i	−1.22441	+	0.408769i
$839$	−1.79190	+	4.72485i	−0.0618632	+	0.163120i	−0.962384	−	0.271693i	$-0.912416\pi$
$839$	−1.79190	+	4.72485i	−0.0618632	+	0.163120i	0.900521	+	0.434813i	$0.143186\pi$
$840$	0.0180726	+	0.00293709i	0.000623565	+	0.000101339i
$841$	−21.1457	−	5.21195i	−0.729163	−	0.179723i
$842$	−20.1354	+	20.9632i	−0.693913	+	0.722440i
$843$	−8.28815	+	21.8540i	−0.285459	+	0.752693i
$844$	21.0413	−	18.6410i	0.724272	−	0.641649i
$845$	14.9939	+	6.38831i	0.515807	+	0.219765i
$846$	−3.18969	+	15.6241i	−0.109664	+	0.537168i
$847$	0.0652792	+	0.137573i	0.00224302	+	0.00472706i
$848$	5.73777	+	4.31165i	0.197036	+	0.148063i
$849$	−3.08646	−	25.4192i	−0.105927	−	0.872386i
$850$	6.55143	+	53.9558i	0.224712	+	1.85067i
$851$	−0.649309	+	16.1124i	−0.0222580	+	0.552327i
$852$	−6.54133	−	5.79511i	−0.224102	−	0.198537i
$853$	−16.0296	+	2.60506i	−0.548842	+	0.0891955i	−0.428508	−	0.903538i	$-0.640961\pi$
$853$	−16.0296	+	2.60506i	−0.548842	+	0.0891955i	−0.120334	+	0.992733i	$0.538396\pi$
$854$	0.00649630	+	0.161204i	0.000222299	+	0.00551628i
$855$	−1.31694	+	1.61296i	−0.0450384	+	0.0551620i
$856$	−6.88662	+	2.29909i	−0.235380	+	0.0785813i
$857$	−6.77285	+	23.3826i	−0.231356	+	0.798734i	0.757878	+	0.652396i	$0.226236\pi$
$857$	−6.77285	+	23.3826i	−0.231356	+	0.798734i	−0.989235	+	0.146338i	$0.953251\pi$
$858$	0.487887	+	0.308521i	0.0166562	+	0.0105327i
$859$	13.3484	+	16.3488i	0.455442	+	0.557815i	0.950371	−	0.311118i	$-0.100703\pi$
$859$	13.3484	+	16.3488i	0.455442	+	0.557815i	−0.494929	+	0.868933i	$0.664806\pi$
$860$	27.6379	−	24.4851i	0.942446	−	0.834934i
$861$	−0.0909250	+	0.111363i	−0.00309872	+	0.00379524i
$862$	−36.2924	−	12.1162i	−1.23612	−	0.412679i
$863$	28.1238	−	6.93190i	0.957346	−	0.235965i	0.270461	−	0.962731i	$-0.412824\pi$
$863$	28.1238	−	6.93190i	0.957346	−	0.235965i	0.686885	+	0.726766i	$0.258978\pi$
$864$	7.68008	−	1.89297i	0.261282	−	0.0644001i
$865$	−0.345068	−	0.115201i	−0.0117327	−	0.00391694i
$866$	13.9065	−	17.0323i	0.472561	−	0.578782i
$867$	−23.9179	+	21.1894i	−0.812294	+	0.719630i
$868$	−0.147559	−	0.180727i	−0.00500847	−	0.00613427i
$869$	−0.103091	−	0.0651910i	−0.00349713	−	0.00221145i
$870$	−4.90829	+	16.9454i	−0.166407	+	0.574502i
$871$	22.6128	−	7.54927i	0.766207	−	0.255797i
$872$	−0.397108	+	0.486368i	−0.0134478	+	0.0164705i
$873$	−0.602247	−	14.9446i	−0.0203830	−	0.505798i
$874$	13.1214	−	2.13244i	0.443839	−	0.0721308i
$875$	0.104214	+	0.0923254i	0.00352307	+	0.00312117i
$876$	−1.52595	+	37.8660i	−0.0515569	+	1.27937i
$877$	−4.46949	−	36.8096i	−0.150924	−	1.24297i	−0.849559	−	0.527493i	$-0.823132\pi$
$877$	−4.46949	−	36.8096i	−0.150924	−	1.24297i	0.698635	−	0.715478i	$-0.253791\pi$
$878$	−2.34191	−	19.2874i	−0.0790356	−	0.650917i
$879$	14.6533	+	11.0113i	0.494244	+	0.371401i
$880$	0.0687971	+	0.144987i	0.00231915	+	0.00488751i
$881$	−9.12849	+	44.7143i	−0.307547	+	1.50646i	0.472830	+	0.881154i	$0.343232\pi$
$881$	−9.12849	+	44.7143i	−0.307547	+	1.50646i	−0.780377	+	0.625310i	$0.784973\pi$
$882$	13.7123	+	5.84227i	0.461717	+	0.196719i
$883$	10.1657	−	9.00605i	0.342104	−	0.303078i	−0.474523	−	0.880243i	$-0.657380\pi$
$883$	10.1657	−	9.00605i	0.342104	−	0.303078i	0.816627	+	0.577165i	$0.195841\pi$
$884$	−32.6805	+	86.1715i	−1.09917	+	2.89826i
$885$	−0.00985578	+	0.0102610i	−0.000331298	+	0.000344918i
$886$	4.61424	+	1.13731i	0.155019	+	0.0382086i
$887$	−56.8838	−	9.24452i	−1.90997	−	0.310401i	−0.914432	−	0.404739i	$-0.867362\pi$
$887$	−56.8838	−	9.24452i	−1.90997	−	0.310401i	−0.995540	+	0.0943380i	$0.969927\pi$
$888$	1.86563	−	4.91927i	0.0626066	−	0.165080i
$889$	0.132214	−	0.0441396i	0.00443432	−	0.00148039i
$890$	−6.41293	+	4.05529i	−0.214962	+	0.135934i
$891$	−0.0519857	+	0.00419672i	−0.00174158	+	0.000140595i
$892$	−15.1198	+	26.1883i	−0.506249	+	0.876850i
$893$	−7.61899	+	11.0380i	−0.254960	+	0.369373i
$894$	0.196698	+	4.88102i	0.00657858	+	0.163246i
$895$	19.0795	+	8.12902i	0.637758	+	0.271723i
$896$	−0.0430812	−	0.113596i	−0.00143924	−	0.00379497i
$897$	16.0437	+	8.42036i	0.535682	+	0.281148i
$898$	21.2531	+	73.3742i	0.709225	+	2.44853i
$899$	40.0468	−	25.3240i	1.33563	−	0.844604i
$900$	−8.76913	−	2.92757i	−0.292304	−	0.0975855i
$901$	10.7789	−	15.6160i	0.359099	−	0.520244i
$902$	1.14933	+	0.0927839i	0.0382687	+	0.00308937i
$903$	−0.153650	+	0.0806418i	−0.00511315	+	0.00268359i
$904$	2.18647	−	4.60788i	0.0727208	−	0.153256i
$905$	−16.9724	−	12.7540i	−0.564183	−	0.423956i
$906$	−1.05342	+	26.1404i	−0.0349976	+	0.868456i
$907$	5.28426	−	11.1363i	0.175461	−	0.369776i	−0.796599	−	0.604508i	$-0.793370\pi$
$907$	5.28426	−	11.1363i	0.175461	−	0.369776i	0.972060	+	0.234732i	$0.0754212\pi$
$908$	6.79201	−	2.89381i	0.225401	−	0.0960343i
$909$	−0.787245	−	3.85618i	−0.0261113	−	0.127901i
$910$	0.0631856	+	0.166607i	0.00209458	+	0.00552296i
$911$	14.1850	+	17.3734i	0.469969	+	0.575608i	0.954138	−	0.299367i	$-0.0967754\pi$
$911$	14.1850	+	17.3734i	0.469969	+	0.575608i	−0.484169	+	0.874975i	$0.660878\pi$
$912$	4.67837	+	0.760309i	0.154916	+	0.0251763i
$913$	−0.0104822	+	0.0863290i	−0.000346911	+	0.00285707i
$914$	−5.88525			−0.194667
$915$	−0.766861	+	6.31567i	−0.0253516	+	0.208790i
$916$	2.00380	−	2.08617i	0.0662073	−	0.0689291i
$917$	−0.00608803	+	0.0210183i	−0.000201044	+	0.000694086i
$918$	−4.14500	−	14.3102i	−0.136805	−	0.472307i
$919$	−5.49375	−	7.95907i	−0.181222	−	0.262545i	0.721836	−	0.692064i	$-0.243299\pi$
$919$	−5.49375	−	7.95907i	−0.181222	−	0.262545i	−0.903058	+	0.429519i	$0.858683\pi$
$920$	−2.30473	−	3.99192i	−0.0759848	−	0.131610i
$921$	−9.75038	−	0.787132i	−0.321286	−	0.0259369i
$922$	61.5031	−	9.99522i	2.02550	−	0.329175i
$923$	3.58552	−	17.5630i	0.118019	−	0.578094i
$924$	0.000366058		0.00179307i	1.20424e−5		5.89876e-5i
$925$	13.4917	−	10.1383i	0.443603	−	0.333346i
$926$	25.3448	+	36.7183i	0.832882	+	1.20664i
$927$	15.4086	−	1.24391i	0.506085	−	0.0408554i
$928$	54.7276	−	13.4891i	1.79652	−	0.442802i
$929$	−19.1679	+	33.1998i	−0.628880	+	1.08925i	0.358897	+	0.933377i	$0.383153\pi$
$929$	−19.1679	+	33.1998i	−0.628880	+	1.08925i	−0.987777	+	0.155874i	$0.950180\pi$
$930$	−8.23092	−	14.2564i	−0.269902	−	0.467485i
$931$	8.68421	+	9.04122i	0.284614	+	0.296314i
$932$	13.9972	−	5.96363i	0.458492	−	0.195345i
$933$	−14.0351	−	29.5784i	−0.459489	−	0.968353i
$934$	−7.00720	−	6.20784i	−0.229283	−	0.203127i
$935$	0.375677	−	0.197170i	0.0122859	−	0.00644816i
$936$	−4.09510	−	4.26345i	−0.133853	−	0.139355i
$937$	10.7098	−	8.04793i	0.349875	−	0.262914i	−0.411245	−	0.911525i	$-0.634906\pi$
$937$	10.7098	−	8.04793i	0.349875	−	0.262914i	0.761121	+	0.648610i	$0.224650\pi$
$938$	0.119738	+	0.0628435i	0.00390959	+	0.00205191i
$939$	−3.32363	−	2.10174i	−0.108463	−	0.0685876i
$940$	21.4237	+	5.28047i	0.698764	+	0.172230i
$941$	−36.7868			−1.19922			−0.599608	−	0.800294i	$-0.704677\pi$
$941$	−36.7868			−1.19922			−0.599608	+	0.800294i	$0.704677\pi$
$942$	−26.6787	−	0.324474i	−0.869237	−	0.0105719i
$943$	36.1933			1.17862
$944$	0.0314439	+	0.00775021i	0.00102341	+	0.000252248i
$945$	−0.0136068	−	0.00860444i	−0.000442630	−	0.000279902i
$946$	1.23234	+	0.646780i	0.0400667	+	0.0210286i
$947$	23.6360	−	17.7613i	0.768068	−	0.577166i	−0.142854	−	0.989744i	$-0.545628\pi$
$947$	23.6360	−	17.7613i	0.768068	−	0.577166i	0.910922	+	0.412578i	$0.135372\pi$
$948$	4.10544	+	4.27422i	0.133339	+	0.138820i
$949$	−68.8282	+	36.1238i	−2.23426	+	1.17263i
$950$	−10.4137	−	9.22572i	−0.337865	−	0.299322i
$951$	−13.8788	−	29.2490i	−0.450051	−	0.948463i
$952$	−0.101367	+	0.0431883i	−0.00328531	+	0.00139974i
$953$	5.64145	+	5.87337i	0.182745	+	0.190257i	0.806273	−	0.591543i	$-0.201481\pi$
$953$	5.64145	+	5.87337i	0.182745	+	0.190257i	−0.623529	+	0.781800i	$0.714302\pi$
$954$	2.88736	+	5.00105i	0.0934817	+	0.161915i
$955$	3.68055	−	6.37490i	0.119100	−	0.206287i
$956$	−31.7897	+	7.83546i	−1.02815	+	0.253417i
$957$	−0.370445	+	0.0299054i	−0.0119748	+	0.000966705i
$958$	38.3695	+	55.5878i	1.23966	+	1.79596i
$959$	−0.0511417	+	0.0384305i	−0.00165145	+	0.00124099i
$960$	−2.68613	−	13.1575i	−0.0866943	−	0.424657i
$961$	−2.64285	+	12.9455i	−0.0852532	+	0.417598i
$962$	50.5373	−	8.21311i	1.62939	−	0.264801i
$963$	6.36300	+	0.513674i	0.205045	+	0.0165529i
$964$	−29.6785	−	51.4047i	−0.955881	−	1.65563i
$965$	−13.1733	−	19.0848i	−0.424062	−	0.614360i
$966$	0.0285947	+	0.0987204i	0.000920020	+	0.00317628i
$967$	15.5041	−	53.5263i	0.498578	−	1.72129i	−0.177190	−	0.984177i	$-0.556701\pi$
$967$	15.5041	−	53.5263i	0.498578	−	1.72129i	0.675768	−	0.737114i	$-0.263812\pi$
$968$	−8.66414	+	9.02033i	−0.278476	+	0.289924i
$969$	1.51042	−	12.4394i	0.0485216	−	0.399611i
$970$	−37.0290			−1.18893
$971$	−2.87246	+	23.6568i	−0.0921816	+	0.759184i	0.871177	+	0.490968i	$0.163357\pi$
$971$	−2.87246	+	23.6568i	−0.0921816	+	0.759184i	−0.963359	+	0.268215i	$0.913566\pi$
$972$	2.50130	+	0.406500i	0.0802292	+	0.0130385i
$973$	−0.175094	−	0.214451i	−0.00561325	−	0.00687499i
$974$	7.69222	+	20.2827i	0.246475	+	0.649900i
$975$	−3.79303	−	18.5795i	−0.121474	−	0.595020i
$976$	13.3226	−	5.67621i	0.426445	−	0.181691i
$977$	−13.8199	+	29.1247i	−0.442137	+	0.931783i	0.552991	+	0.833187i	$0.313486\pi$
$977$	−13.8199	+	29.1247i	−0.442137	+	0.931783i	−0.995128	+	0.0985959i	$0.968565\pi$
$978$	−0.00348639	+	0.0865139i	−0.000111482	+	0.00276641i
$979$	−0.127785	−	0.0960238i	−0.00408401	−	0.00306894i
$980$	8.84132	−	18.6327i	0.282426	−	0.595200i
$981$	0.488846	−	0.256566i	0.0156077	−	0.00819153i
$982$	14.0818	+	1.13680i	0.449367	+	0.0362766i
$983$	−11.7460	+	17.0170i	−0.374638	+	0.542757i	−0.964272	−	0.264914i	$-0.914657\pi$
$983$	−11.7460	+	17.0170i	−0.374638	+	0.542757i	0.589634	+	0.807670i	$0.299272\pi$
$984$	−11.2008	−	3.73939i	−0.357070	−	0.119207i
$985$	26.0239	−	16.4565i	0.829190	−	0.524348i
$986$	−29.5369	−	101.973i	−0.940646	−	3.24749i
$987$	−0.0918177	−	0.0481896i	−0.00292259	−	0.00153389i
$988$	−8.36525	−	22.0574i	−0.266134	−	0.701738i
$989$	40.1895	+	17.1231i	1.27795	+	0.544484i
$990$	0.00519921	+	0.129017i	0.000165242	+	0.00410043i
$991$	−33.3825	+	48.3630i	−1.06043	+	1.53630i	−0.234838	+	0.972034i	$0.575456\pi$
$991$	−33.3825	+	48.3630i	−1.06043	+	1.53630i	−0.825593	+	0.564266i	$0.809159\pi$
$992$	−26.2976	+	45.5487i	−0.834948	+	1.44617i
$993$	9.92381	−	0.801133i	0.314923	−	0.0254232i
$994$	0.0859381	−	0.0543440i	0.00272579	−	0.00172369i
$995$	6.67402	−	2.22811i	0.211581	−	0.0706360i
$996$	1.49834	−	3.95081i	0.0474768	−	0.125186i
$997$	10.4231	+	1.69392i	0.330103	+	0.0536470i	0.323204	−	0.946329i	$-0.395240\pi$
$997$	10.4231	+	1.69392i	0.330103	+	0.0536470i	0.00689890	+	0.999976i	$0.497804\pi$
$998$	−72.8697	−	17.9608i	−2.30665	−	0.568539i
$999$	−3.20452	+	3.33625i	−0.101386	+	0.105554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.3	✓	336
157.124	even	39	inner	471.2.q.b.124.3	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.3	✓	336	1.1	even	1	trivial
471.2.q.b.124.3	yes	336	157.124	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06747 - 0.509586i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.24385 + 1.17766i) q^{4} +(-0.929494 + 0.698469i) q^{5} +(1.47505 + 1.53569i) q^{6} +(-0.0122606 + 0.00643484i) q^{7} +(-0.851290 - 0.754178i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-2.06747 - 0.509586i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.24385 + 1.17766i) q^{4} +(-0.929494 + 0.698469i) q^{5} +(1.47505 + 1.53569i) q^{6} +(-0.0122606 + 0.00643484i) q^{7} +(-0.851290 - 0.754178i) q^{8} +(0.428693 + 0.903450i) q^{9} +(2.27763 - 0.970408i) q^{10} +(0.0361289 + 0.0376142i) q^{11} +(-1.26706 - 2.19461i) q^{12} +(2.59893 - 4.50148i) q^{13} +(0.0286275 - 0.00705603i) q^{14} +(1.15891 - 0.0935567i) q^{15} +(-1.50338 - 2.17802i) q^{16} +(-5.59347 + 4.20322i) q^{17} +(-0.425924 - 2.08631i) q^{18} +(0.358236 - 1.75476i) q^{19} +(-2.90820 + 0.472629i) q^{20} +(0.0138017 + 0.00111419i) q^{21} +(-0.0555278 - 0.0961769i) q^{22} +(-1.98020 - 2.86882i) q^{23} +(0.316420 + 1.09241i) q^{24} +(-1.01499 + 3.50414i) q^{25} +(-7.66710 + 7.98230i) q^{26} +(0.120537 - 0.992709i) q^{27} -0.0350889 q^{28} +(0.858933 - 7.07395i) q^{29} +(-2.44368 - 0.397137i) q^{30} +(4.20529 + 5.15054i) q^{31} +(2.80490 + 7.39591i) q^{32} +(-0.0104323 - 0.0511008i) q^{33} +(13.7062 - 5.83968i) q^{34} +(0.00690158 - 0.0145448i) q^{35} +(-0.102038 + 2.53206i) q^{36} +(-3.69819 - 2.77901i) q^{37} +(-1.63484 + 3.44536i) q^{38} +(-4.60248 + 2.41557i) q^{39} +(1.31804 + 0.106403i) q^{40} +(-5.89813 + 8.54492i) q^{41} +(-0.0279669 - 0.00933671i) q^{42} +(-10.5920 + 6.69795i) q^{43} +(0.0367709 + 0.126948i) q^{44} +(-1.02950 - 0.540323i) q^{45} +(2.63210 + 6.94028i) q^{46} +(-6.88960 - 2.93538i) q^{47} +(0.106564 + 2.64435i) q^{48} +(-3.97634 + 5.76073i) q^{49} +(3.88412 - 6.72749i) q^{50} +(6.97402 - 0.563001i) q^{51} +(11.1328 - 7.03996i) q^{52} +(-2.57240 + 0.858793i) q^{53} +(-0.755076 + 1.99097i) q^{54} +(-0.0598539 - 0.00972721i) q^{55} +(0.0152903 + 0.00376872i) q^{56} +(-1.24064 + 1.29164i) q^{57} +(-5.38061 + 14.1875i) q^{58} +(-0.00915945 + 0.00811457i) q^{59} +(2.71059 + 1.15487i) q^{60} +(-1.09452 + 5.36132i) q^{61} +(-6.06967 - 12.7916i) q^{62} +(-0.0110696 - 0.00831824i) q^{63} +(-1.39220 - 11.4658i) q^{64} +(0.728455 + 5.99937i) q^{65} +(-0.00447176 + 0.110965i) q^{66} +(3.43301 + 3.04138i) q^{67} +(-17.5009 + 2.84417i) q^{68} +(0.140362 + 3.48305i) q^{69} +(-0.0216806 + 0.0265539i) q^{70} +(3.27112 - 1.09206i) q^{71} +(0.316420 - 1.09241i) q^{72} +(-12.6395 - 7.99273i) q^{73} +(6.22976 + 7.63007i) q^{74} +(2.73070 - 2.41919i) q^{75} +(2.87034 - 3.51552i) q^{76} +(-0.000685001 - 0.000228687i) q^{77} +(10.7464 - 2.64876i) q^{78} +(-2.27074 + 0.559686i) q^{79} +(2.91867 + 0.974394i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(16.5486 - 14.6608i) q^{82} +(1.05454 + 1.29158i) q^{83} +(0.0296568 + 0.0187538i) q^{84} +(2.26328 - 7.81374i) q^{85} +(25.3118 - 8.45031i) q^{86} +(-4.50675 + 5.51976i) q^{87} +(-0.00238843 - 0.0592682i) q^{88} +(-3.02507 + 0.491622i) q^{89} +(1.85312 + 1.64172i) q^{90} +(-0.00289805 + 0.0719143i) q^{91} +(-1.06477 - 8.76920i) q^{92} +(-0.801479 - 6.60077i) q^{93} +(12.7482 + 9.57967i) q^{94} +(0.892666 + 1.88125i) q^{95} +(1.58219 - 7.75007i) q^{96} +(-13.7599 - 5.86254i) q^{97} +(11.1566 - 9.88385i) q^{98} +(-0.0184943 + 0.0487656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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