LMFDB - Embedded newform 126.2.m.a.83.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.m (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			83.6
Root			$0.0967785 + 1.72934i$ of defining polynomial
Character	$\chi$	$=$	126.83
Dual form			126.2.m.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.0967785 - 1.72934i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.183299 - 0.317483i) q^{5} +(0.780860 - 1.54605i) q^{6} +(2.53871 - 0.744936i) q^{7} +1.00000i q^{8} +(-2.98127 + 0.334727i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0967785 - 1.72934i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.183299 - 0.317483i) q^{5} +(0.780860 - 1.54605i) q^{6} +(2.53871 - 0.744936i) q^{7} +1.00000i q^{8} +(-2.98127 + 0.334727i) q^{9} -0.366598i q^{10} +(0.579764 + 0.334727i) q^{11} +(1.44927 - 0.948485i) q^{12} +(-0.867380 + 0.500782i) q^{13} +(2.57106 + 0.624224i) q^{14} +(-0.531299 + 0.347713i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.98906 q^{17} +(-2.74922 - 1.20075i) q^{18} +6.35722i q^{19} +(0.183299 - 0.317483i) q^{20} +(-1.53394 - 4.31822i) q^{21} +(0.334727 + 0.579764i) q^{22} +(-6.66371 + 3.84729i) q^{23} +(1.72934 - 0.0967785i) q^{24} +(2.43280 - 4.21374i) q^{25} -1.00156 q^{26} +(0.867380 + 5.12325i) q^{27} +(1.91449 + 1.82612i) q^{28} +(1.58394 + 0.914490i) q^{29} +(-0.633975 + 0.0354788i) q^{30} +(5.47837 - 3.16294i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.522749 - 1.03501i) q^{33} +(-4.32065 - 2.49453i) q^{34} +(-0.701849 - 0.669453i) q^{35} +(-1.78052 - 2.41449i) q^{36} -5.16789 q^{37} +(-3.17861 + 5.50552i) q^{38} +(0.949969 + 1.45154i) q^{39} +(0.317483 - 0.183299i) q^{40} +(-2.15928 - 3.73998i) q^{41} +(0.830676 - 4.50666i) q^{42} +(2.24922 - 3.89576i) q^{43} +0.669453i q^{44} +(0.652734 + 0.885148i) q^{45} -7.69459 q^{46} +(4.16450 - 7.21313i) q^{47} +(1.54605 + 0.780860i) q^{48} +(5.89014 - 3.78236i) q^{49} +(4.21374 - 2.43280i) q^{50} +(0.482834 + 8.62781i) q^{51} +(-0.867380 - 0.500782i) q^{52} +(-1.81045 + 4.87055i) q^{54} -0.245420i q^{55} +(0.744936 + 2.53871i) q^{56} +(10.9938 - 0.615242i) q^{57} +(0.914490 + 1.58394i) q^{58} +(4.36348 + 7.55776i) q^{59} +(-0.566778 - 0.286262i) q^{60} +(-4.29351 - 2.47886i) q^{61} +6.32588 q^{62} +(-7.31924 + 3.07063i) q^{63} -1.00000 q^{64} +(0.317980 + 0.183586i) q^{65} +(0.970217 - 0.634967i) q^{66} +(5.44537 + 9.43166i) q^{67} +(-2.49453 - 4.32065i) q^{68} +(7.29820 + 11.1515i) q^{69} +(-0.273092 - 0.930688i) q^{70} -5.49843i q^{71} +(-0.334727 - 2.98127i) q^{72} -4.07314i q^{73} +(-4.47552 - 2.58394i) q^{74} +(-7.52245 - 3.79936i) q^{75} +(-5.50552 + 3.17861i) q^{76} +(1.72120 + 0.417889i) q^{77} +(0.0969299 + 1.73205i) q^{78} +(-4.17784 + 7.23623i) q^{79} +0.366598 q^{80} +(8.77592 - 1.99582i) q^{81} -4.31856i q^{82} +(8.50712 - 14.7348i) q^{83} +(2.97272 - 3.48754i) q^{84} +(0.914490 + 1.58394i) q^{85} +(3.89576 - 2.24922i) q^{86} +(1.42818 - 2.82769i) q^{87} +(-0.334727 + 0.579764i) q^{88} +10.7113 q^{89} +(0.122710 + 1.09293i) q^{90} +(-1.82898 + 1.91749i) q^{91} +(-6.66371 - 3.84729i) q^{92} +(-6.00000 - 9.16789i) q^{93} +(7.21313 - 4.16450i) q^{94} +(2.01831 - 1.16527i) q^{95} +(0.948485 + 1.44927i) q^{96} +(-14.9093 - 8.60787i) q^{97} +(6.99219 - 0.330547i) q^{98} +(-1.84047 - 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.0967785	−	1.72934i	−0.0558751	−	0.998438i
$3$	−0.0967785	−	1.72934i	−0.0558751	−	0.998438i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.183299	−	0.317483i	−0.0819738	−	0.141983i	0.822124	−	0.569309i	$-0.192789\pi$
$5$	−0.183299	−	0.317483i	−0.0819738	−	0.141983i	−0.904098	+	0.427326i	$0.859456\pi$
$6$	0.780860	−	1.54605i	0.318785	−	0.631171i
$7$	2.53871	−	0.744936i	0.959544	−	0.281559i
$7$	2.53871	−	0.744936i	0.959544	−	0.281559i
$8$			1.00000i			0.353553i
$9$	−2.98127	+	0.334727i	−0.993756	+	0.111576i
$10$		−	0.366598i		−	0.115929i
$11$	0.579764	+	0.334727i	0.174805	+	0.100924i	0.584850	−	0.811142i	$-0.301153\pi$
$11$	0.579764	+	0.334727i	0.174805	+	0.100924i	−0.410044	+	0.912066i	$0.634487\pi$
$12$	1.44927	−	0.948485i	0.418367	−	0.273804i
$13$	−0.867380	+	0.500782i	−0.240568	+	0.138892i	−0.615438	−	0.788185i	$-0.711021\pi$
$13$	−0.867380	+	0.500782i	−0.240568	+	0.138892i	0.374870	+	0.927077i	$0.377687\pi$
$14$	2.57106	+	0.624224i	0.687144	+	0.166831i
$15$	−0.531299	+	0.347713i	−0.137181	+	0.0897791i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.98906			−1.21003			−0.605013	−	0.796216i	$-0.706832\pi$
$17$	−4.98906			−1.21003			−0.605013	+	0.796216i	$0.706832\pi$
$18$	−2.74922	−	1.20075i	−0.647997	−	0.283020i
$19$			6.35722i			1.45845i	0.684275	+	0.729224i	$0.260119\pi$
$19$			6.35722i			1.45845i	−0.684275	+	0.729224i	$0.739881\pi$
$20$	0.183299	−	0.317483i	0.0409869	−	0.0709914i
$21$	−1.53394	−	4.31822i	−0.334734	−	0.942313i
$22$	0.334727	+	0.579764i	0.0713640	+	0.123606i
$23$	−6.66371	+	3.84729i	−1.38948	+	0.802216i	−0.993256	−	0.115938i	$-0.963012\pi$
$23$	−6.66371	+	3.84729i	−1.38948	+	0.802216i	−0.396223	+	0.918154i	$0.629679\pi$
$24$	1.72934	−	0.0967785i	0.353001	−	0.0197548i
$25$	2.43280	−	4.21374i	0.486561	−	0.842748i
$26$	−1.00156			−0.196423
$27$	0.867380	+	5.12325i	0.166927	+	0.985969i
$28$	1.91449	+	1.82612i	0.361805	+	0.345105i
$29$	1.58394	+	0.914490i	0.294131	+	0.169817i	0.639803	−	0.768539i	$-0.279016\pi$
$29$	1.58394	+	0.914490i	0.294131	+	0.169817i	−0.345672	+	0.938355i	$0.612349\pi$
$30$	−0.633975	+	0.0354788i	−0.115747	+	0.00647751i
$31$	5.47837	−	3.16294i	0.983944	−	0.568081i	0.0804857	−	0.996756i	$-0.474353\pi$
$31$	5.47837	−	3.16294i	0.983944	−	0.568081i	0.903459	+	0.428675i	$0.141020\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.522749	−	1.03501i	0.0909990	−	0.180171i
$34$	−4.32065	−	2.49453i	−0.740986	−	0.427809i
$35$	−0.701849	−	0.669453i	−0.118634	−	0.113158i
$36$	−1.78052	−	2.41449i	−0.296753	−	0.402415i
$37$	−5.16789			−0.849595			−0.424798	−	0.905288i	$-0.639655\pi$
$37$	−5.16789			−0.849595			−0.424798	+	0.905288i	$0.639655\pi$
$38$	−3.17861	+	5.50552i	−0.515639	+	0.893113i
$39$	0.949969	+	1.45154i	0.152117	+	0.232432i
$40$	0.317483	−	0.183299i	0.0501985	−	0.0289821i
$41$	−2.15928	−	3.73998i	−0.337223	−	0.584087i	0.646686	−	0.762756i	$-0.276154\pi$
$41$	−2.15928	−	3.73998i	−0.337223	−	0.584087i	−0.983909	+	0.178669i	$0.942821\pi$
$42$	0.830676	−	4.50666i	0.128176	−	0.695393i
$43$	2.24922	−	3.89576i	0.343002	−	0.594098i	−0.641986	−	0.766716i	$-0.721889\pi$
$43$	2.24922	−	3.89576i	0.343002	−	0.594098i	0.984989	+	0.172618i	$0.0552228\pi$
$44$			0.669453i			0.100924i
$45$	0.652734	+	0.885148i	0.0973038	+	0.131950i
$46$	−7.69459			−1.13450
$47$	4.16450	−	7.21313i	0.607455	−	1.05214i	−0.384203	−	0.923249i	$-0.625524\pi$
$47$	4.16450	−	7.21313i	0.607455	−	1.05214i	0.991658	−	0.128895i	$-0.0411429\pi$
$48$	1.54605	+	0.780860i	0.223153	+	0.112707i
$49$	5.89014	−	3.78236i	0.841449	−	0.540337i
$50$	4.21374	−	2.43280i	0.595913	−	0.344050i
$51$	0.482834	+	8.62781i	0.0676102	+	1.20813i
$52$	−0.867380	−	0.500782i	−0.120284	−	0.0694460i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−1.81045	+	4.87055i	−0.246371	+	0.662798i
$55$		−	0.245420i		−	0.0330925i
$56$	0.744936	+	2.53871i	0.0995462	+	0.339250i
$57$	10.9938	−	0.615242i	1.45617	−	0.0814909i
$58$	0.914490	+	1.58394i	0.120078	+	0.207982i
$59$	4.36348	+	7.55776i	0.568076	+	0.983937i	0.996756	+	0.0804804i	$0.0256455\pi$
$59$	4.36348	+	7.55776i	0.568076	+	0.983937i	−0.428680	+	0.903456i	$0.641021\pi$
$60$	−0.566778	−	0.286262i	−0.0731707	−	0.0369562i
$61$	−4.29351	−	2.47886i	−0.549727	−	0.317385i	0.199285	−	0.979942i	$-0.436138\pi$
$61$	−4.29351	−	2.47886i	−0.549727	−	0.317385i	−0.749012	+	0.662556i	$0.769471\pi$
$62$	6.32588			0.803387
$63$	−7.31924	+	3.07063i	−0.922137	+	0.386863i
$64$	−1.00000			−0.125000
$65$	0.317980	+	0.183586i	0.0394406	+	0.0227710i
$66$	0.970217	−	0.634967i	0.119425	−	0.0781590i
$67$	5.44537	+	9.43166i	0.665258	+	1.15226i	0.979215	+	0.202823i	$0.0650117\pi$
$67$	5.44537	+	9.43166i	0.665258	+	1.15226i	−0.313958	+	0.949437i	$0.601655\pi$
$68$	−2.49453	−	4.32065i	−0.302506	−	0.523956i
$69$	7.29820	+	11.1515i	0.878600	+	1.34248i
$70$	−0.273092	−	0.930688i	−0.0326407	−	0.111238i
$71$		−	5.49843i		−	0.652544i	−0.945276	−	0.326272i	$-0.894207\pi$
$71$		−	5.49843i		−	0.652544i	0.945276	−	0.326272i	$-0.105793\pi$
$72$	−0.334727	−	2.98127i	−0.0394479	−	0.351346i
$73$		−	4.07314i		−	0.476725i	−0.971176	−	0.238363i	$-0.923389\pi$
$73$		−	4.07314i		−	0.476725i	0.971176	−	0.238363i	$-0.0766106\pi$
$74$	−4.47552	−	2.58394i	−0.520269	−	0.300377i
$75$	−7.52245	−	3.79936i	−0.868618	−	0.438712i
$76$	−5.50552	+	3.17861i	−0.631526	+	0.364612i
$77$	1.72120	+	0.417889i	0.196149	+	0.0476229i
$78$	0.0969299	+	1.73205i	0.0109751	+	0.196116i
$79$	−4.17784	+	7.23623i	−0.470044	+	0.814140i	−0.999413	−	0.0342518i	$-0.989095\pi$
$79$	−4.17784	+	7.23623i	−0.470044	+	0.814140i	0.529370	+	0.848391i	$0.322429\pi$
$80$	0.366598			0.0409869
$81$	8.77592	−	1.99582i	0.975102	−	0.221758i
$82$		−	4.31856i		−	0.476905i
$83$	8.50712	−	14.7348i	0.933778	−	1.61735i	0.156980	−	0.987602i	$-0.449824\pi$
$83$	8.50712	−	14.7348i	0.933778	−	1.61735i	0.776798	−	0.629750i	$-0.216842\pi$
$84$	2.97272	−	3.48754i	0.324350	−	0.380522i
$85$	0.914490	+	1.58394i	0.0991904	+	0.171803i
$86$	3.89576	−	2.24922i	0.420090	−	0.242539i
$87$	1.42818	−	2.82769i	0.153117	−	0.303160i
$88$	−0.334727	+	0.579764i	−0.0356820	+	0.0618030i
$89$	10.7113			1.13540			0.567699	−	0.823236i	$-0.307834\pi$
$89$	10.7113			1.13540			0.567699	+	0.823236i	$0.307834\pi$
$90$	0.122710	+	1.09293i	0.0129348	+	0.115205i
$91$	−1.82898	+	1.91749i	−0.191729	+	0.201007i
$92$	−6.66371	−	3.84729i	−0.694740	−	0.401108i
$93$	−6.00000	−	9.16789i	−0.622171	−	0.950666i
$94$	7.21313	−	4.16450i	0.743978	−	0.429536i
$95$	2.01831	−	1.16527i	0.207074	−	0.119555i
$96$	0.948485	+	1.44927i	0.0968044	+	0.147915i
$97$	−14.9093	−	8.60787i	−1.51381	−	0.873997i	−0.999869	−	0.0161687i	$-0.994853\pi$
$97$	−14.9093	−	8.60787i	−1.51381	−	0.873997i	−0.513937	−	0.857828i	$-0.671814\pi$
$98$	6.99219	−	0.330547i	0.706318	−	0.0333902i
$99$	−1.84047	−	0.803848i	−0.184974	−	0.0807897i
$100$	4.86561			0.486561
$101$	−7.86586	+	13.6241i	−0.782683	+	1.35565i	0.147691	+	0.989034i	$0.452816\pi$
$101$	−7.86586	+	13.6241i	−0.782683	+	1.35565i	−0.930374	+	0.366613i	$0.880517\pi$
$102$	−3.89576	+	7.71332i	−0.385738	+	0.763732i
$103$	−9.91124	+	5.72226i	−0.976584	+	0.563831i	−0.901237	−	0.433327i	$-0.857340\pi$
$103$	−9.91124	+	5.72226i	−0.976584	+	0.563831i	−0.0753467	+	0.997157i	$0.524006\pi$
$104$	−0.500782	−	0.867380i	−0.0491057	−	0.0850537i
$105$	−1.08979	+	1.27853i	−0.106353	+	0.124771i
$106$		0			0
$107$		−	11.0618i		−	1.06938i	−0.845048	−	0.534690i	$-0.820428\pi$
$107$		−	11.0618i		−	1.06938i	0.845048	−	0.534690i	$-0.179572\pi$
$108$	−4.00317	+	3.31280i	−0.385205	+	0.318774i
$109$	−10.5633			−1.01178			−0.505891	−	0.862597i	$-0.668836\pi$
$109$	−10.5633			−1.01178			−0.505891	+	0.862597i	$0.668836\pi$
$110$	0.122710	−	0.212540i	0.0117000	−	0.0202649i
$111$	0.500140	+	8.93706i	0.0474712	+	0.848268i
$112$	−0.624224	+	2.57106i	−0.0589836	+	0.242942i
$113$	3.60226	−	2.07976i	0.338872	−	0.195648i	−0.320901	−	0.947113i	$-0.603986\pi$
$113$	3.60226	−	2.07976i	0.338872	−	0.195648i	0.659773	+	0.751465i	$0.270652\pi$
$114$	9.82856	+	4.96410i	0.920529	+	0.464931i
$115$	2.44290	+	1.41041i	0.227802	+	0.131521i
$116$			1.82898i			0.169817i
$117$	2.41827	−	1.78330i	0.223569	−	0.164866i
$118$			8.72695i			0.803381i
$119$	−12.6658	+	3.71653i	−1.16107	+	0.340694i
$120$	−0.347713	−	0.531299i	−0.0317417	−	0.0485007i
$121$	−5.27592	−	9.13815i	−0.479629	−	0.830741i
$122$	−2.47886	−	4.29351i	−0.224425	−	0.388716i
$123$	−6.25875	+	4.09609i	−0.564332	+	0.369332i
$124$	5.47837	+	3.16294i	0.491972	+	0.284040i
$125$	−3.61671			−0.323489
$126$	−7.87396	−	1.00038i	−0.701468	−	0.0891207i
$127$	−1.66945			−0.148140			−0.0740700	−	0.997253i	$-0.523599\pi$
$127$	−1.66945			−0.148140			−0.0740700	+	0.997253i	$0.523599\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−6.95479	−	3.51265i	−0.612335	−	0.309271i
$130$	0.183586	+	0.317980i	0.0161015	+	0.0278887i
$131$	6.76607	+	11.7192i	0.591154	+	1.02391i	0.994077	+	0.108675i	$0.0346609\pi$
$131$	6.76607	+	11.7192i	0.591154	+	1.02391i	−0.402923	+	0.915234i	$0.632006\pi$
$132$	1.15772	−	0.0647887i	0.100766	−	0.00563913i
$133$	4.73572	+	16.1392i	0.410639	+	1.39944i
$134$			10.8907i			0.940817i
$135$	1.46755	−	1.21446i	0.126307	−	0.104525i
$136$		−	4.98906i		−	0.427809i
$137$	7.78428	+	4.49425i	0.665056	+	0.383970i	0.794201	−	0.607656i	$-0.207890\pi$
$137$	7.78428	+	4.49425i	0.665056	+	0.383970i	−0.129145	+	0.991626i	$0.541223\pi$
$138$	0.744670	+	13.3066i	0.0633905	+	1.13273i
$139$	−8.05336	+	4.64961i	−0.683077	+	0.394375i	−0.801014	−	0.598646i	$-0.795706\pi$
$139$	−8.05336	+	4.64961i	−0.683077	+	0.394375i	0.117936	+	0.993021i	$0.462372\pi$
$140$	0.228839	−	0.942545i	0.0193405	−	0.0796596i
$141$	−12.8770	−	6.50379i	−1.08444	−	0.547718i
$142$	2.74922	−	4.76178i	0.230709	−	0.399600i
$143$	−0.670501			−0.0560701
$144$	1.20075	−	2.74922i	0.100063	−	0.229101i
$145$		−	0.670501i		−	0.0556821i
$146$	2.03657	−	3.52744i	0.168548	−	0.291933i
$147$	−7.11104	−	9.82004i	−0.586509	−	0.809943i
$148$	−2.58394	−	4.47552i	−0.212399	−	0.367886i
$149$	−2.45268	+	1.41606i	−0.200931	+	0.116008i	−0.597090	−	0.802174i	$-0.703676\pi$
$149$	−2.45268	+	1.41606i	−0.200931	+	0.116008i	0.396158	+	0.918182i	$0.370343\pi$
$150$	−4.61495	−	7.05156i	−0.376809	−	0.575758i
$151$	8.27592	−	14.3343i	0.673484	−	1.16651i	−0.303425	−	0.952855i	$-0.598130\pi$
$151$	8.27592	−	14.3343i	0.673484	−	1.16651i	0.976909	−	0.213654i	$-0.0685365\pi$
$152$	−6.35722			−0.515639
$153$	14.8737	−	1.66997i	1.20247	−	0.135009i
$154$	1.28166	+	1.22250i	0.103279	+	0.0985122i
$155$	−2.00836	−	1.15953i	−0.161315	−	0.0931355i
$156$	−0.782082	+	1.54846i	−0.0626166	+	0.123976i
$157$	2.45480	−	1.41728i	0.195914	−	0.113111i	−0.398834	−	0.917023i	$-0.630585\pi$
$157$	2.45480	−	1.41728i	0.195914	−	0.113111i	0.594748	+	0.803912i	$0.297252\pi$
$158$	−7.23623	+	4.17784i	−0.575684	+	0.332371i
$159$		0			0
$160$	0.317483	+	0.183299i	0.0250993	+	0.0144911i
$161$	−14.0513	+	14.7312i	−1.10739	+	1.16098i
$162$	8.59808	+	2.65953i	0.675529	+	0.208952i
$163$	24.7281			1.93685			0.968426	−	0.249300i	$-0.0802005\pi$
$163$	24.7281			1.93685			0.968426	+	0.249300i	$0.0802005\pi$
$164$	2.15928	−	3.73998i	0.168611	−	0.292044i
$165$	−0.424416	+	0.0237514i	−0.0330408	+	0.00184904i
$166$	14.7348	−	8.50712i	1.14364	−	0.660281i
$167$	−9.67422	−	16.7562i	−0.748614	−	1.29664i	−0.948487	−	0.316815i	$-0.897386\pi$
$167$	−9.67422	−	16.7562i	−0.748614	−	1.29664i	0.199874	−	0.979822i	$-0.435947\pi$
$168$	4.31822	−	1.53394i	0.333158	−	0.118346i
$169$	−5.99843	+	10.3896i	−0.461418	+	0.799199i
$170$			1.82898i			0.140276i
$171$	−2.12793	−	18.9526i	−0.162727	−	1.44934i
$172$	4.49843			0.343002
$173$	−2.41827	+	4.18856i	−0.183858	+	0.318451i	−0.943191	−	0.332251i	$-0.892192\pi$
$173$	−2.41827	+	4.18856i	−0.183858	+	0.318451i	0.759333	+	0.650702i	$0.225525\pi$
$174$	2.65068	−	1.73476i	0.200948	−	0.131512i
$175$	3.03723	−	12.5098i	0.229593	−	0.945649i
$176$	−0.579764	+	0.334727i	−0.0437013	+	0.0252310i
$177$	12.6477	−	8.27738i	0.950658	−	0.622166i
$178$	9.27628	+	5.35566i	0.695286	+	0.401424i
$179$		−	3.65796i		−	0.273409i	−0.990612	−	0.136704i	$-0.956349\pi$
$179$		−	3.65796i		−	0.273409i	0.990612	−	0.136704i	$-0.0436511\pi$
$180$	−0.440193	+	1.00786i	−0.0328101	+	0.0751213i
$181$		−	5.66796i		−	0.421296i	−0.977562	−	0.210648i	$-0.932443\pi$
$181$		−	5.66796i		−	0.421296i	0.977562	−	0.210648i	$-0.0675574\pi$
$182$	−2.54269	+	0.746101i	−0.188476	+	0.0553047i
$183$	−3.87128	+	7.66485i	−0.286173	+	0.566602i
$184$	−3.84729	−	6.66371i	−0.283626	−	0.491255i
$185$	0.947269	+	1.64072i	0.0696446	+	0.120628i
$186$	−0.612209	−	10.9396i	−0.0448893	−	0.802132i
$187$	−2.89248	−	1.66997i	−0.211519	−	0.122120i
$188$	8.32901			0.607455
$189$	6.01852	+	12.3603i	0.437783	+	0.899081i
$190$	2.33055			0.169076
$191$	23.7098	+	13.6888i	1.71558	+	0.990490i	0.926583	+	0.376091i	$0.122732\pi$
$191$	23.7098	+	13.6888i	1.71558	+	0.990490i	0.788996	+	0.614398i	$0.210601\pi$
$192$	0.0967785	+	1.72934i	0.00698438	+	0.124805i
$193$	5.01413	+	8.68473i	0.360925	+	0.625141i	0.988113	−	0.153727i	$-0.0491276\pi$
$193$	5.01413	+	8.68473i	0.360925	+	0.625141i	−0.627188	+	0.778868i	$0.715794\pi$
$194$	−8.60787	−	14.9093i	−0.618009	−	1.07042i
$195$	0.286710	−	0.567664i	0.0205317	−	0.0406513i
$196$	6.22069	+	3.20983i	0.444335	+	0.229274i
$197$			18.8258i			1.34129i	0.741780	+	0.670643i	$0.233982\pi$
$197$			18.8258i			1.34129i	−0.741780	+	0.670643i	$0.766018\pi$
$198$	−1.19197	−	1.61639i	−0.0847098	−	0.114872i
$199$			5.36406i			0.380248i	0.981760	+	0.190124i	$0.0608890\pi$
$199$			5.36406i			0.380248i	−0.981760	+	0.190124i	$0.939111\pi$
$200$	4.21374	+	2.43280i	0.297956	+	0.172025i
$201$	15.7836	−	10.3297i	1.11329	−	0.728601i
$202$	−13.6241	+	7.86586i	−0.958587	+	0.553440i
$203$	4.70242	+	1.14169i	0.330045	+	0.0801312i
$204$	−7.23048	+	4.73205i	−0.506235	+	0.331310i
$205$	−0.791588	+	1.37107i	−0.0552869	+	0.0957597i
$206$	−11.4445			−0.797377
$207$	18.5785	−	13.7003i	1.29130	−	0.952239i
$208$		−	1.00156i		−	0.0694460i
$209$	−2.12793	+	3.68569i	−0.147192	+	0.254944i
$210$	−1.58305	+	0.562341i	−0.109241	+	0.0388052i
$211$	−0.828981	−	1.43584i	−0.0570694	−	0.0988471i	0.836079	−	0.548609i	$-0.184842\pi$
$211$	−0.828981	−	1.43584i	−0.0570694	−	0.0988471i	−0.893149	+	0.449762i	$0.851509\pi$
$212$		0			0
$213$	−9.50869	+	0.532130i	−0.651525	+	0.0364609i
$214$	5.53088	−	9.57976i	0.378083	−	0.654859i
$215$	−1.64912			−0.112469
$216$	−5.12325	+	0.867380i	−0.348593	+	0.0590178i
$217$	11.5518	−	12.1108i	0.784189	−	0.822137i
$218$	−9.14811	−	5.28166i	−0.619588	−	0.357719i
$219$	−7.04387	+	0.394192i	−0.475980	+	0.0266370i
$220$	0.212540	−	0.122710i	0.0143295	−	0.00827312i
$221$	4.32741	−	2.49843i	0.291093	−	0.168063i
$222$	−4.03540	+	7.98979i	−0.270838	+	0.536240i
$223$	14.7546	+	8.51860i	0.988044	+	0.570448i	0.904689	−	0.426072i	$-0.140103\pi$
$223$	14.7546	+	8.51860i	0.988044	+	0.570448i	0.0833551	+	0.996520i	$0.473436\pi$
$224$	−1.82612	+	1.91449i	−0.122013	+	0.127917i
$225$	−5.84239	+	13.3766i	−0.389492	+	0.891774i
$226$	4.15953			0.276688
$227$	2.55512	−	4.42560i	0.169589	−	0.293737i	−0.768686	−	0.639626i	$-0.779089\pi$
$227$	2.55512	−	4.42560i	0.169589	−	0.293737i	0.938276	+	0.345889i	$0.112423\pi$
$228$	6.02973	+	9.21332i	0.399329	+	0.610167i
$229$	−13.2215	+	7.63345i	−0.873703	+	0.504433i	−0.868577	−	0.495554i	$-0.834965\pi$
$229$	−13.2215	+	7.63345i	−0.873703	+	0.504433i	−0.00512595	+	0.999987i	$0.501632\pi$
$230$	1.41041	+	2.44290i	0.0929997	+	0.161080i
$231$	0.556099	−	3.01700i	0.0365886	−	0.198504i
$232$	−0.914490	+	1.58394i	−0.0600392	+	0.103991i
$233$		−	10.1930i		−	0.667767i	−0.942614	−	0.333883i	$-0.891641\pi$
$233$		−	10.1930i		−	0.667767i	0.942614	−	0.333883i	$-0.108359\pi$
$234$	2.98593	−	0.335250i	0.195197	−	0.0219160i
$235$	−3.05340			−0.199182
$236$	−4.36348	+	7.55776i	−0.284038	+	0.491968i
$237$	12.9183	+	6.52461i	0.839131	+	0.423819i
$238$	−12.8272	−	3.11429i	−0.831462	−	0.201870i
$239$	−16.6117	+	9.59076i	−1.07452	+	0.620375i	−0.929413	−	0.369041i	$-0.879686\pi$
$239$	−16.6117	+	9.59076i	−1.07452	+	0.620375i	−0.145108	+	0.989416i	$0.546353\pi$
$240$	−0.0354788	−	0.633975i	−0.00229015	−	0.0409229i
$241$	17.9140	+	10.3426i	1.15394	+	0.666227i	0.949844	−	0.312724i	$-0.101241\pi$
$241$	17.9140	+	10.3426i	1.15394	+	0.666227i	0.204095	+	0.978951i	$0.434575\pi$
$242$		−	10.5518i		−	0.678297i
$243$	−4.30078	−	14.9834i	−0.275895	−	0.961188i
$244$		−	4.95771i		−	0.317385i
$245$	−2.28049	−	1.17672i	−0.145695	−	0.0751778i
$246$	−7.46828	+	0.417944i	−0.476160	+	0.0266471i
$247$	−3.18359	−	5.51413i	−0.202567	−	0.350856i
$248$	3.16294	+	5.47837i	0.200847	+	0.347877i
$249$	−26.3048	−	13.2857i	−1.66700	−	0.841950i
$250$	−3.13216	−	1.80836i	−0.198096	−	0.114370i
$251$	−1.81200			−0.114373			−0.0571864	−	0.998364i	$-0.518213\pi$
$251$	−1.81200			−0.114373			−0.0571864	+	0.998364i	$0.518213\pi$
$252$	−6.31886	−	4.80333i	−0.398051	−	0.302581i
$253$	−5.15117			−0.323851
$254$	−1.44579	−	0.834727i	−0.0907169	−	0.0523754i
$255$	2.65068	−	1.73476i	0.165992	−	0.108635i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.22773	+	5.59059i	0.201340	+	0.348731i	0.948960	−	0.315395i	$-0.102137\pi$
$257$	3.22773	+	5.59059i	0.201340	+	0.348731i	−0.747620	+	0.664126i	$0.768804\pi$
$258$	−4.26670	−	6.51943i	−0.265633	−	0.405882i
$259$	−13.1198	+	3.84974i	−0.815224	+	0.239211i
$260$			0.367172i			0.0227710i
$261$	−5.02826	−	2.19615i	−0.311242	−	0.135938i
$262$			13.5321i			0.836018i
$263$	−7.63888	−	4.41031i	−0.471034	−	0.271951i	0.245639	−	0.969361i	$-0.421002\pi$
$263$	−7.63888	−	4.41031i	−0.471034	−	0.271951i	−0.716672	+	0.697410i	$0.754336\pi$
$264$	1.03501	+	0.522749i	0.0637002	+	0.0321730i
$265$		0			0
$266$	−3.96833	+	16.3448i	−0.243314	+	1.00216i
$267$	−1.03663	−	18.5236i	−0.0634404	−	1.13362i
$268$	−5.44537	+	9.43166i	−0.332629	+	0.576130i
$269$	14.2653			0.869773			0.434886	−	0.900485i	$-0.356788\pi$
$269$	14.2653			0.869773			0.434886	+	0.900485i	$0.356788\pi$
$270$	1.87817	−	0.317980i	0.114302	−	0.0193516i
$271$		−	3.05281i		−	0.185445i	−0.995692	−	0.0927226i	$-0.970443\pi$
$271$		−	3.05281i		−	0.185445i	0.995692	−	0.0927226i	$-0.0295570\pi$
$272$	2.49453	−	4.32065i	0.151253	−	0.261978i
$273$	3.49300	+	2.97737i	0.211406	+	0.180198i
$274$	4.49425	+	7.78428i	0.271508	+	0.470265i
$275$	2.82090	−	1.62865i	0.170107	−	0.0982112i
$276$	−6.00839	+	11.8962i	−0.361663	+	0.716066i
$277$	−0.632828	+	1.09609i	−0.0380230	+	0.0658577i	−0.884411	−	0.466710i	$-0.845439\pi$
$277$	−0.632828	+	1.09609i	−0.0380230	+	0.0658577i	0.846388	+	0.532567i	$0.178773\pi$
$278$	−9.29922			−0.557730
$279$	−15.2738	+	11.2633i	−0.914417	+	0.674318i
$280$	0.669453	−	0.701849i	0.0400075	−	0.0419435i
$281$	9.11639	+	5.26335i	0.543838	+	0.313985i	0.746633	−	0.665236i	$-0.231669\pi$
$281$	9.11639	+	5.26335i	0.543838	+	0.313985i	−0.202795	+	0.979221i	$0.565002\pi$
$282$	−7.89994	−	12.0710i	−0.470434	−	0.718815i
$283$	−17.2094	+	9.93588i	−1.02300	+	0.590627i	−0.914970	−	0.403522i	$-0.867786\pi$
$283$	−17.2094	+	9.93588i	−1.02300	+	0.590627i	−0.108025	+	0.994148i	$0.534453\pi$
$284$	4.76178	−	2.74922i	0.282560	−	0.163136i
$285$	−2.21049	−	3.37759i	−0.130938	−	0.200071i
$286$	−0.580671	−	0.335250i	−0.0343358	−	0.0198238i
$287$	−8.26784	−	7.88623i	−0.488035	−	0.465509i
$288$	2.41449	−	1.78052i	0.142275	−	0.104918i
$289$	7.89074			0.464161
$290$	0.335250	−	0.580671i	0.0196866	−	0.0340982i
$291$	−13.4431	+	26.6163i	−0.788047	+	1.56028i
$292$	3.52744	−	2.03657i	0.206428	−	0.119181i
$293$	6.70606	+	11.6152i	0.391772	+	0.678569i	0.992683	−	0.120747i	$-0.0385289\pi$
$293$	6.70606	+	11.6152i	0.391772	+	0.678569i	−0.600911	+	0.799316i	$0.705196\pi$
$294$	−1.24832	−	12.0599i	−0.0728037	−	0.703349i
$295$	1.59964	−	2.77066i	0.0931348	−	0.161314i
$296$		−	5.16789i		−	0.300377i
$297$	−1.21201	+	3.26061i	−0.0703280	+	0.189200i
$298$	−2.83211			−0.164060
$299$	3.85331	−	6.67413i	0.222843	−	0.385975i
$300$	−0.470886	−	8.41431i	−0.0271866	−	0.485800i
$301$	2.80803	−	11.5657i	0.161852	−	0.666638i
$302$	14.3343	−	8.27592i	0.824847	−	0.476225i
$303$	24.3220	+	12.2843i	1.39726	+	0.705713i
$304$	−5.50552	−	3.17861i	−0.315763	−	0.182306i
$305$			1.81749i			0.104069i
$306$	13.7160	+	5.99063i	0.784092	+	0.342461i
$307$		−	0.653728i		−	0.0373102i	−0.999826	−	0.0186551i	$-0.994062\pi$
$307$		−	0.653728i		−	0.0373102i	0.999826	−	0.0186551i	$-0.00593845\pi$
$308$	0.498700	+	1.69955i	0.0284160	+	0.0968409i
$309$	10.8550	+	16.5862i	0.617517	+	0.943554i
$310$	−1.15953	−	2.00836i	−0.0658567	−	0.114067i
$311$	4.62246	+	8.00634i	0.262116	+	0.453998i	0.966804	−	0.255519i	$-0.0822464\pi$
$311$	4.62246	+	8.00634i	0.262116	+	0.453998i	−0.704688	+	0.709517i	$0.748913\pi$
$312$	−1.45154	+	0.949969i	−0.0821770	+	0.0537814i
$313$	−5.33830	−	3.08207i	−0.301739	−	0.174209i	0.341485	−	0.939887i	$-0.389070\pi$
$313$	−5.33830	−	3.08207i	−0.301739	−	0.174209i	−0.643224	+	0.765678i	$0.722403\pi$
$314$	2.83456			0.159963
$315$	2.31648	+	1.76089i	0.130519	+	0.0992150i
$316$	−8.35568			−0.470044
$317$	−17.8876	−	10.3274i	−1.00467	−	0.580045i	−0.0950420	−	0.995473i	$-0.530299\pi$
$317$	−17.8876	−	10.3274i	−1.00467	−	0.580045i	−0.909626	+	0.415428i	$0.863632\pi$
$318$		0			0
$319$	0.612209	+	1.06038i	0.0342771	+	0.0593697i
$320$	0.183299	+	0.317483i	0.0102467	+	0.0177479i
$321$	−19.1296	+	1.07054i	−1.06771	+	0.0597517i
$322$	−19.5344	+	5.73197i	−1.08861	+	0.319430i
$323$		−	31.7166i		−	1.76476i
$324$	6.11639	+	6.60226i	0.339799	+	0.366792i
$325$			4.87322i			0.270318i
$326$	21.4151	+	12.3640i	1.18608	+	0.684781i
$327$	1.02230	+	18.2676i	0.0565334	+	1.01020i
$328$	3.73998	−	2.15928i	0.206506	−	0.119226i
$329$	5.19917	−	21.4144i	0.286639	−	1.18061i
$330$	−0.379431	−	0.191639i	−0.0208870	−	0.0105494i
$331$	−5.35568	+	9.27631i	−0.294375	+	0.509872i	−0.974839	−	0.222909i	$-0.928445\pi$
$331$	−5.35568	+	9.27631i	−0.294375	+	0.509872i	0.680464	+	0.732781i	$0.261778\pi$
$332$	17.0142			0.933778
$333$	15.4069	−	1.72983i	0.844291	−	0.0947941i
$334$		−	19.3484i		−	1.05870i
$335$	1.99626	−	3.45763i	0.109067	−	0.188910i
$336$	4.50666	+	0.830676i	0.245858	+	0.0453171i
$337$	3.77592	+	6.54008i	0.205687	+	0.356261i	0.950351	−	0.311179i	$-0.100724\pi$
$337$	3.77592	+	6.54008i	0.205687	+	0.356261i	−0.744664	+	0.667439i	$0.767390\pi$
$338$	−10.3896	+	5.99843i	−0.565119	+	0.326272i
$339$	−3.94525	−	6.02827i	−0.214277	−	0.327411i
$340$	−0.914490	+	1.58394i	−0.0495952	+	0.0859014i
$341$	4.23488			0.229332
$342$	7.63345	−	17.4774i	0.412770	−	0.945069i
$343$	12.1358	−	13.9901i	0.655270	−	0.755394i
$344$	3.89576	+	2.24922i	0.210045	+	0.121270i
$345$	2.20267	−	4.36112i	0.118588	−	0.234795i
$346$	−4.18856	+	2.41827i	−0.225179	+	0.130007i
$347$	−9.46737	+	5.46599i	−0.508235	+	0.293430i	−0.732108	−	0.681189i	$-0.761463\pi$
$347$	−9.46737	+	5.46599i	−0.508235	+	0.293430i	0.223873	+	0.974618i	$0.428130\pi$
$348$	3.16294	−	0.177006i	0.169551	−	0.00948851i
$349$	1.02562	+	0.592145i	0.0549004	+	0.0316968i	0.527199	−	0.849742i	$-0.323242\pi$
$349$	1.02562	+	0.592145i	0.0549004	+	0.0316968i	−0.472299	+	0.881439i	$0.656576\pi$
$350$	8.88520	−	9.31516i	0.474934	−	0.497916i
$351$	−3.31798	−	4.00943i	−0.177101	−	0.214008i
$352$	−0.669453			−0.0356820
$353$	16.7912	−	29.0832i	0.893706	−	1.54794i	0.0583086	−	0.998299i	$-0.481429\pi$
$353$	16.7912	−	29.0832i	0.893706	−	1.54794i	0.835398	−	0.549646i	$-0.185237\pi$
$354$	15.0919	−	0.844581i	0.802126	−	0.0448890i
$355$	−1.74566	+	1.00786i	−0.0926501	+	0.0534915i
$356$	5.35566	+	9.27628i	0.283849	+	0.491642i
$357$	7.65294	+	21.5439i	0.405036	+	1.14022i
$358$	1.82898	−	3.16789i	0.0966646	−	0.167428i
$359$			10.1281i			0.534542i	0.963621	+	0.267271i	$0.0861219\pi$
$359$			10.1281i			0.534542i	−0.963621	+	0.267271i	$0.913878\pi$
$360$	−0.885148	+	0.652734i	−0.0466514	+	0.0344021i
$361$	−21.4143			−1.12707
$362$	2.83398	−	4.90860i	0.148951	−	0.257990i
$363$	−15.2924	+	10.0083i	−0.802644	+	0.525297i
$364$	−2.57508	−	0.625201i	−0.134971	−	0.0327694i
$365$	−1.29315	+	0.746603i	−0.0676868	+	0.0390790i
$366$	−7.18505	+	4.70232i	−0.375569	+	0.245794i
$367$	−15.5903	−	9.00104i	−0.813805	−	0.469850i	0.0344706	−	0.999406i	$-0.489025\pi$
$367$	−15.5903	−	9.00104i	−0.813805	−	0.469850i	−0.848275	+	0.529555i	$0.822359\pi$
$368$		−	7.69459i		−	0.401108i
$369$	7.68927	+	10.4271i	0.400287	+	0.542814i
$370$			1.89454i			0.0984923i
$371$		0			0
$372$	4.93962	−	9.78010i	0.256108	−	0.507074i
$373$	−8.20451	−	14.2106i	−0.424814	−	0.735799i	0.571589	−	0.820540i	$-0.306327\pi$
$373$	−8.20451	−	14.2106i	−0.424814	−	0.735799i	−0.996403	+	0.0847411i	$0.972994\pi$
$374$	−1.66997	−	2.89248i	−0.0863522	−	0.149566i
$375$	0.350020	+	6.25454i	0.0180749	+	0.322983i
$376$	7.21313	+	4.16450i	0.371989	+	0.214768i
$377$	−1.83184			−0.0943447
$378$	−0.967967	+	13.7136i	−0.0497869	+	0.705352i
$379$	−2.91372			−0.149668			−0.0748339	−	0.997196i	$-0.523843\pi$
$379$	−2.91372			−0.149668			−0.0748339	+	0.997196i	$0.523843\pi$
$380$	2.01831	+	1.16527i	0.103537	+	0.0597773i
$381$	0.161567	+	2.88706i	0.00827734	+	0.147909i
$382$	13.6888	+	23.7098i	0.700382	+	1.21310i
$383$	−4.28721	−	7.42567i	−0.219066	−	0.379434i	0.735456	−	0.677572i	$-0.236968\pi$
$383$	−4.28721	−	7.42567i	−0.219066	−	0.379434i	−0.954523	+	0.298138i	$0.903634\pi$
$384$	−0.780860	+	1.54605i	−0.0398481	+	0.0788963i
$385$	−0.182822	−	0.623052i	−0.00931749	−	0.0317537i
$386$			10.0283i			0.510425i
$387$	−5.40150	+	12.3672i	−0.274574	+	0.628659i
$388$		−	17.2157i		−	0.873997i
$389$	−30.7906	−	17.7770i	−1.56115	−	0.901328i	−0.997142	−	0.0755559i	$-0.975927\pi$
$389$	−30.7906	−	17.7770i	−1.56115	−	0.901328i	−0.564004	−	0.825772i	$-0.690740\pi$
$390$	0.532130	−	0.348257i	0.0269455	−	0.0176347i
$391$	33.2456	−	19.1944i	1.68130	−	0.970702i
$392$	3.78236	+	5.89014i	0.191038	+	0.297497i
$393$	19.6117	−	12.8350i	0.989279	−	0.647442i
$394$	−9.41292	+	16.3037i	−0.474216	+	0.821367i
$395$	3.06318			0.154125
$396$	−0.224084	−	1.99582i	−0.0112606	−	0.100294i
$397$			3.58034i			0.179692i	0.995956	+	0.0898460i	$0.0286375\pi$
$397$			3.58034i			0.179692i	−0.995956	+	0.0898460i	$0.971363\pi$
$398$	−2.68203	+	4.64541i	−0.134438	+	0.232853i
$399$	27.4519	−	9.75162i	1.37431	−	0.488192i
$400$	2.43280	+	4.21374i	0.121640	+	0.210687i
$401$	0.165300	−	0.0954357i	0.00825467	−	0.00476583i	−0.495867	−	0.868398i	$-0.665150\pi$
$401$	0.165300	−	0.0954357i	0.00825467	−	0.00476583i	0.504122	+	0.863633i	$0.331816\pi$
$402$	18.8338	−	1.05399i	0.939347	−	0.0525682i
$403$	−3.16789	+	5.48694i	−0.157804	+	0.273324i
$404$	−15.7317			−0.782683
$405$	−2.24226	−	2.42037i	−0.111419	−	0.120269i
$406$	3.50157	+	3.33994i	0.173780	+	0.165759i
$407$	−2.99615	−	1.72983i	−0.148514	−	0.0857445i
$408$	−8.62781	+	0.482834i	−0.427140	+	0.0239038i
$409$	−3.00832	+	1.73685i	−0.148752	+	0.0858819i	−0.572529	−	0.819885i	$-0.694037\pi$
$409$	−3.00832	+	1.73685i	−0.148752	+	0.0858819i	0.423777	+	0.905767i	$0.360704\pi$
$410$	−1.37107	+	0.791588i	−0.0677124	+	0.0390938i
$411$	7.01877	−	13.8966i	0.346210	−	0.685471i
$412$	−9.91124	−	5.72226i	−0.488292	−	0.281915i
$413$	16.7077	+	15.9365i	0.822130	+	0.784183i
$414$	22.9396	−	2.57558i	1.12742	−	0.126583i
$415$	−6.23739			−0.306182
$416$	0.500782	−	0.867380i	0.0245529	−	0.0425268i
$417$	8.82017	+	13.4771i	0.431926	+	0.659975i
$418$	−3.68569	+	2.12793i	−0.180273	+	0.104081i
$419$	0.703955	+	1.21929i	0.0343905	+	0.0595660i	0.882708	−	0.469921i	$-0.155718\pi$
$419$	0.703955	+	1.21929i	0.0343905	+	0.0595660i	−0.848318	+	0.529487i	$0.822384\pi$
$420$	−1.65213	−	0.304524i	−0.0806158	−	0.0148593i
$421$	15.1930	−	26.3151i	0.740463	−	1.28252i	−0.211822	−	0.977308i	$-0.567940\pi$
$421$	15.1930	−	26.3151i	0.740463	−	1.28252i	0.952285	−	0.305211i	$-0.0987268\pi$
$422$		−	1.65796i		−	0.0807083i
$423$	−10.0011	+	22.8982i	−0.486269	+	1.11335i
$424$		0			0
$425$	−12.1374	+	21.0226i	−0.588751	+	1.01975i
$426$	−8.50083	−	4.29351i	−0.411867	−	0.208021i
$427$	−12.7466	−	3.09472i	−0.616850	−	0.149764i
$428$	9.57976	−	5.53088i	0.463055	−	0.267345i
$429$	0.0648900	+	1.15953i	0.00313292	+	0.0559825i
$430$	−1.42818	−	0.824559i	−0.0688728	−	0.0397638i
$431$			27.2747i			1.31378i	0.753988	+	0.656888i	$0.228127\pi$
$431$			27.2747i			1.31378i	−0.753988	+	0.656888i	$0.771873\pi$
$432$	−4.87055	−	1.81045i	−0.234335	−	0.0871053i
$433$		−	8.15047i		−	0.391686i	−0.980635	−	0.195843i	$-0.937256\pi$
$433$		−	8.15047i		−	0.391686i	0.980635	−	0.195843i	$-0.0627444\pi$
$434$	16.0596	−	4.71237i	0.770885	−	0.226201i
$435$	−1.15953	+	0.0648900i	−0.0555951	+	0.00311124i
$436$	−5.28166	−	9.14811i	−0.252946	−	0.438115i
$437$	−24.4581	−	42.3627i	−1.16999	−	2.02648i
$438$	−6.29726	−	3.18055i	−0.300895	−	0.151973i
$439$	10.6005	+	6.12020i	0.505934	+	0.292101i	0.731161	−	0.682205i	$-0.238979\pi$
$439$	10.6005	+	6.12020i	0.505934	+	0.292101i	−0.225226	+	0.974306i	$0.572312\pi$
$440$	0.245420			0.0117000
$441$	−16.2940	+	13.2478i	−0.775906	+	0.630848i
$442$	4.99687			0.237677
$443$	6.93544	+	4.00418i	0.329513	+	0.190244i	0.655625	−	0.755087i	$-0.272405\pi$
$443$	6.93544	+	4.00418i	0.329513	+	0.190244i	−0.326112	+	0.945331i	$0.605739\pi$
$444$	−7.48965	+	4.90166i	−0.355443	+	0.232623i
$445$	−1.96337	−	3.40067i	−0.0930729	−	0.161207i
$446$	8.51860	+	14.7546i	0.403367	+	0.698653i
$447$	2.68622	+	4.10449i	0.127054	+	0.194136i
$448$	−2.53871	+	0.744936i	−0.119943	+	0.0351949i
$449$		−	14.5183i		−	0.685163i	−0.939488	−	0.342581i	$-0.888699\pi$
$449$		−	14.5183i		−	0.685163i	0.939488	−	0.342581i	$-0.111301\pi$
$450$	−11.7480	+	8.66329i	−0.553804	+	0.408391i
$451$		−	2.89108i		−	0.136135i
$452$	3.60226	+	2.07976i	0.169436	+	0.0978239i
$453$	−25.5899	−	12.9247i	−1.20232	−	0.607254i
$454$	4.42560	−	2.55512i	0.207704	−	0.119918i
$455$	0.944020	+	0.229197i	0.0442563	+	0.0107449i
$456$	0.615242	+	10.9938i	0.0288114	+	0.514833i
$457$	−4.97751	+	8.62130i	−0.232838	+	0.403287i	−0.958642	−	0.284614i	$-0.908135\pi$
$457$	−4.97751	+	8.62130i	−0.232838	+	0.403287i	0.725804	+	0.687901i	$0.241468\pi$
$458$	−15.2669			−0.713375
$459$	−4.32741	−	25.5602i	−0.201986	−	1.19305i
$460$			2.82082i			0.131521i
$461$	−16.1635	+	27.9960i	−0.752810	+	1.30391i	0.193645	+	0.981072i	$0.437969\pi$
$461$	−16.1635	+	27.9960i	−0.752810	+	1.30391i	−0.946456	+	0.322834i	$0.895364\pi$
$462$	1.99009	−	2.33475i	0.0925876	−	0.108622i
$463$	−4.72516	−	8.18421i	−0.219597	−	0.380353i	0.735088	−	0.677972i	$-0.237141\pi$
$463$	−4.72516	−	8.18421i	−0.219597	−	0.380353i	−0.954685	+	0.297619i	$0.903807\pi$
$464$	−1.58394	+	0.914490i	−0.0735327	+	0.0424541i
$465$	−1.81086	+	3.58536i	−0.0839765	+	0.166267i
$466$	5.09651	−	8.82741i	0.236091	−	0.408922i
$467$	20.6623			0.956138			0.478069	−	0.878322i	$-0.341337\pi$
$467$	20.6623			0.956138			0.478069	+	0.878322i	$0.341337\pi$
$468$	2.75352	+	1.20263i	0.127281	+	0.0555916i
$469$	20.8502	+	19.8878i	0.962773	+	0.918335i
$470$	−2.64432	−	1.52670i	−0.121973	−	0.0704214i
$471$	−2.68853	−	4.10803i	−0.123881	−	0.189288i
$472$	−7.55776	+	4.36348i	−0.347874	+	0.200845i
$473$	2.60803	−	1.50575i	0.119917	−	0.0692343i
$474$	7.92524	+	12.1096i	0.364018	+	0.556213i
$475$	26.7877	+	15.4659i	1.22910	+	0.709623i
$476$	−9.55151	−	9.11064i	−0.437793	−	0.417586i
$477$		0			0
$478$	−19.1815			−0.877343
$479$	−5.08042	+	8.79955i	−0.232131	+	0.402062i	−0.958435	−	0.285311i	$-0.907903\pi$
$479$	−5.08042	+	8.79955i	−0.232131	+	0.402062i	0.726304	+	0.687373i	$0.241236\pi$
$480$	0.286262	−	0.566778i	0.0130660	−	0.0258697i
$481$	4.48252	−	2.58799i	0.204386	−	0.118002i
$482$	10.3426	+	17.9140i	0.471094	+	0.815958i
$483$	26.8352	+	22.8738i	1.22104	+	1.04079i
$484$	5.27592	−	9.13815i	0.239814	−	0.415371i
$485$			6.31126i			0.286579i
$486$	3.76713	−	15.1264i	0.170881	−	0.686149i
$487$	−31.2296			−1.41515			−0.707575	−	0.706638i	$-0.750211\pi$
$487$	−31.2296			−1.41515			−0.707575	+	0.706638i	$0.750211\pi$
$488$	2.47886	−	4.29351i	0.112213	−	0.194358i
$489$	−2.39315	−	42.7634i	−0.108222	−	1.93383i
$490$	−1.38661	−	2.15931i	−0.0626404	−	0.0975479i
$491$	17.8314	−	10.2950i	0.804720	−	0.464605i	−0.0403987	−	0.999184i	$-0.512863\pi$
$491$	17.8314	−	10.2950i	0.804720	−	0.464605i	0.845119	+	0.534578i	$0.179529\pi$
$492$	−6.67669	−	3.37219i	−0.301009	−	0.152030i
$493$	−7.90239	−	4.56245i	−0.355906	−	0.205482i
$494$		−	6.36717i		−	0.286473i
$495$	0.0821487	+	0.731664i	0.00369231	+	0.0328858i
$496$			6.32588i			0.284040i
$497$	−4.09598	−	13.9590i	−0.183730	−	0.626145i
$498$	−16.1378	−	24.6582i	−0.723150	−	1.10496i
$499$	12.5766	+	21.7834i	0.563007	+	0.975157i	0.997232	+	0.0743527i	$0.0236891\pi$
$499$	12.5766	+	21.7834i	0.563007	+	0.975157i	−0.434225	+	0.900805i	$0.642978\pi$
$500$	−1.80836	−	3.13216i	−0.0808722	−	0.140075i
$501$	−28.0411	+	18.3517i	−1.25278	+	0.819894i
$502$	−1.56924	−	0.906002i	−0.0700387	−	0.0404369i
$503$	−31.1553			−1.38915			−0.694574	−	0.719421i	$-0.744407\pi$
$503$	−31.1553			−1.38915			−0.694574	+	0.719421i	$0.744407\pi$
$504$	−3.07063	−	7.31924i	−0.136777	−	0.326025i
$505$	5.76722			0.256638
$506$	−4.46104	−	2.57558i	−0.198317	−	0.114499i
$507$	18.5477	+	9.36787i	0.823733	+	0.416042i
$508$	−0.834727	−	1.44579i	−0.0370350	−	0.0641465i
$509$	−2.41674	−	4.18591i	−0.107120	−	0.185537i	0.807482	−	0.589892i	$-0.200830\pi$
$509$	−2.41674	−	4.18591i	−0.107120	−	0.185537i	−0.914602	+	0.404354i	$0.867496\pi$
$510$	3.16294	−	0.177006i	0.140057	−	0.00783796i
$511$	−3.03423	−	10.3405i	−0.134226	−	0.457439i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.5696	+	5.51413i	−1.43798	+	0.243455i
$514$			6.45545i			0.284738i
$515$	3.63344	+	2.09777i	0.160109	+	0.0924387i
$516$	−0.435352	−	7.77934i	−0.0191653	−	0.342467i
$517$	4.82886	−	2.78794i	0.212373	−	0.122613i
$518$	−13.2869	−	3.22592i	−0.583795	−	0.141739i
$519$	7.47751	+	3.77666i	0.328226	+	0.165777i
$520$	−0.183586	+	0.317980i	−0.00805077	+	0.0139443i
$521$	17.5322			0.768101			0.384050	−	0.923312i	$-0.374529\pi$
$521$	17.5322			0.768101			0.384050	+	0.923312i	$0.374529\pi$
$522$	−3.25653	−	4.41606i	−0.142534	−	0.193286i
$523$			19.1019i			0.835267i	0.908616	+	0.417633i	$0.137140\pi$
$523$			19.1019i			0.835267i	−0.908616	+	0.417633i	$0.862860\pi$
$524$	−6.76607	+	11.7192i	−0.295577	+	0.511955i
$525$	−21.9276	−	4.04174i	−0.957000	−	0.176396i
$526$	−4.41031	−	7.63888i	−0.192299	−	0.333071i
$527$	−27.3319	+	15.7801i	−1.19060	+	0.687392i
$528$	0.634967	+	0.970217i	0.0276334	+	0.0422233i
$529$	18.1033	−	31.3559i	0.787101	−	1.36330i
$530$		0			0
$531$	−15.5385	−	21.0711i	−0.674312	−	0.914410i
$532$	−11.6091	+	12.1708i	−0.503317	+	0.527673i
$533$	3.74584	+	2.16266i	0.162250	+	0.0936752i
$534$	8.36404	−	16.5602i	0.361947	−	0.716630i
$535$	−3.51192	+	2.02761i	−0.151834	+	0.0876612i
$536$	−9.43166	+	5.44537i	−0.407386	+	0.235204i
$537$	−6.32588	+	0.354012i	−0.272982	+	0.0152767i
$538$	12.3541	+	7.13267i	0.532625	+	0.307511i
$539$	4.68095	−	0.221286i	0.201623	−	0.00953144i
$540$	1.78554	+	0.663707i	0.0768372	+	0.0285614i
$541$	13.6642			0.587471			0.293735	−	0.955887i	$-0.405102\pi$
$541$	13.6642			0.587471			0.293735	+	0.955887i	$0.405102\pi$
$542$	1.52641	−	2.64381i	0.0655648	−	0.113562i
$543$	−9.80186	+	0.548537i	−0.420638	+	0.0235400i
$544$	4.32065	−	2.49453i	0.185247	−	0.106952i
$545$	1.93625	+	3.35368i	0.0829397	+	0.143656i
$546$	1.53634	+	4.32498i	0.0657494	+	0.185092i
$547$	4.94380	−	8.56292i	0.211382	−	0.366124i	−0.740765	−	0.671764i	$-0.765537\pi$
$547$	4.94380	−	8.56292i	0.211382	−	0.366124i	0.952147	+	0.305640i	$0.0988703\pi$
$548$			8.98851i			0.383970i
$549$	13.6298	+	5.95299i	0.581707	+	0.254067i
$550$	3.25730			0.138892
$551$	−5.81362	+	10.0695i	−0.247669	+	0.428975i
$552$	−11.1515	+	7.29820i	−0.474640	+	0.310632i
$553$	−5.21582	+	21.4829i	−0.221799	+	0.913548i
$554$	−1.09609	+	0.632828i	−0.0465684	+	0.0268863i
$555$	2.74569	−	1.79694i	0.116548	−	0.0762759i
$556$	−8.05336	−	4.64961i	−0.341539	−	0.197187i
$557$			12.5800i			0.533034i	0.963830	+	0.266517i	$0.0858728\pi$
$557$			12.5800i			0.533034i	−0.963830	+	0.266517i	$0.914127\pi$
$558$	−18.8591	+	2.11744i	−0.798371	+	0.0896384i
$559$			4.50547i			0.190561i
$560$	0.930688	−	0.273092i	0.0393287	−	0.0115402i
$561$	−2.60803	+	5.16371i	−0.110111	+	0.218012i
$562$	5.26335	+	9.11639i	0.222021	+	0.384552i
$563$	12.1666	+	21.0732i	0.512763	+	0.888132i	0.999890	+	0.0148007i	$0.00471137\pi$
$563$	12.1666	+	21.0732i	0.512763	+	0.888132i	−0.487127	+	0.873331i	$0.661955\pi$
$564$	−0.806068	−	14.4037i	−0.0339416	−	0.606506i
$565$	−1.32058	−	0.762437i	−0.0555572	−	0.0320760i
$566$	−19.8718			−0.835272
$567$	20.7928	−	11.6043i	0.873215	−	0.487335i
$568$	5.49843			0.230709
$569$	−8.18746	−	4.72703i	−0.343236	−	0.198167i	0.318466	−	0.947934i	$-0.396832\pi$
$569$	−8.18746	−	4.72703i	−0.343236	−	0.198167i	−0.661702	+	0.749767i	$0.730166\pi$
$570$	−0.225547	−	4.03032i	−0.00944711	−	0.168811i
$571$	15.7843	+	27.3392i	0.660551	+	1.14411i	0.980471	+	0.196664i	$0.0630108\pi$
$571$	15.7843	+	27.3392i	0.660551	+	1.14411i	−0.319920	+	0.947445i	$0.603656\pi$
$572$	−0.335250	−	0.580671i	−0.0140175	−	0.0242791i
$573$	21.3781	−	42.3272i	0.893084	−	1.76824i
$574$	−3.21705	−	10.9636i	−0.134277	−	0.457612i
$575$			37.4388i			1.56131i
$576$	2.98127	−	0.334727i	0.124219	−	0.0139469i
$577$			33.5794i			1.39793i	0.715157	+	0.698964i	$0.246355\pi$
$577$			33.5794i			1.39793i	−0.715157	+	0.698964i	$0.753645\pi$
$578$	6.83358	+	3.94537i	0.284239	+	0.164106i
$579$	14.5336	−	9.51166i	0.603997	−	0.395291i
$580$	0.580671	−	0.335250i	0.0241110	−	0.0139205i
$581$	10.6207	−	43.7446i	0.440621	−	1.81483i
$582$	−24.9502	+	16.3289i	−1.03422	+	0.676853i
$583$		0			0
$584$	4.07314			0.168548
$585$	−1.00943	−	0.440882i	−0.0417350	−	0.0182282i
$586$			13.4121i			0.554049i
$587$	−9.65855	+	16.7291i	−0.398651	+	0.690484i	−0.993560	−	0.113310i	$-0.963855\pi$
$587$	−9.65855	+	16.7291i	−0.398651	+	0.690484i	0.594909	+	0.803793i	$0.297188\pi$
$588$	4.94888	−	11.0684i	0.204088	−	0.456451i
$589$	20.1075	+	34.8272i	0.828516	+	1.43503i
$590$	2.77066	−	1.59964i	0.114066	−	0.0658562i
$591$	32.5564	−	1.82194i	1.33919	−	0.0749445i
$592$	2.58394	−	4.47552i	0.106199	−	0.183943i
$593$	0.733196			0.0301088			0.0150544	−	0.999887i	$-0.495208\pi$
$593$	0.733196			0.0301088			0.0150544	+	0.999887i	$0.495208\pi$
$594$	−2.67994	+	2.21776i	−0.109959	+	0.0909959i
$595$	3.50157	+	3.33994i	0.143550	+	0.136924i
$596$	−2.45268	−	1.41606i	−0.100466	−	0.0580039i
$597$	9.27631	−	0.519125i	0.379654	−	0.0212464i
$598$	6.67413	−	3.85331i	0.272926	−	0.157574i
$599$	26.6548	−	15.3892i	1.08909	−	0.628785i	0.155754	−	0.987796i	$-0.450219\pi$
$599$	26.6548	−	15.3892i	1.08909	−	0.628785i	0.933333	+	0.359011i	$0.116886\pi$
$600$	3.79936	−	7.52245i	0.155108	−	0.307103i
$601$	−0.786931	−	0.454335i	−0.0320996	−	0.0185327i	0.483864	−	0.875143i	$-0.339233\pi$
$601$	−0.786931	−	0.454335i	−0.0320996	−	0.0185327i	−0.515964	+	0.856610i	$0.672566\pi$
$602$	8.21470	−	8.61221i	0.334806	−	0.351007i
$603$	−19.3911	−	26.2956i	−0.789668	−	1.07084i
$604$	16.5518			0.673484
$605$	−1.93414	+	3.35003i	−0.0786340	+	0.136198i
$606$	14.9213	+	22.7995i	0.606137	+	0.926166i
$607$	38.7783	−	22.3887i	1.57396	−	0.908728i	0.578287	−	0.815833i	$-0.303721\pi$
$607$	38.7783	−	22.3887i	1.57396	−	0.908728i	0.995676	−	0.0928949i	$-0.0296121\pi$
$608$	−3.17861	−	5.50552i	−0.128910	−	0.223278i
$609$	1.51929	−	8.24259i	0.0615647	−	0.334007i
$610$	−0.908744	+	1.57399i	−0.0367940	+	0.0637290i
$611$			8.34204i			0.337483i
$612$	8.88310	+	12.0460i	0.359078	+	0.486932i
$613$	18.1480			0.732992			0.366496	−	0.930420i	$-0.380557\pi$
$613$	18.1480			0.732992			0.366496	+	0.930420i	$0.380557\pi$
$614$	0.326864	−	0.566145i	0.0131912	−	0.0228478i
$615$	2.44766	+	1.23624i	0.0986993	+	0.0498500i
$616$	−0.417889	+	1.72120i	−0.0168372	+	0.0693493i
$617$	−19.7393	+	11.3965i	−0.794674	+	0.458805i	−0.841605	−	0.540093i	$-0.818389\pi$
$617$	−19.7393	+	11.3965i	−0.794674	+	0.458805i	0.0469315	+	0.998898i	$0.485056\pi$
$618$	1.10758	+	19.7915i	0.0445535	+	0.796132i
$619$	−38.4228	−	22.1834i	−1.54434	−	0.891626i	−0.998557	−	0.0537011i	$-0.982898\pi$
$619$	−38.4228	−	22.1834i	−1.54434	−	0.891626i	−0.545785	−	0.837925i	$-0.683768\pi$
$620$		−	2.31905i		−	0.0931355i
$621$	−25.4906	−	30.8027i	−1.02290	−	1.23607i
$622$			9.24493i			0.370688i
$623$	27.1930	−	7.97924i	1.08946	−	0.319682i
$624$	−1.73205	+	0.0969299i	−0.0693375	+	0.00388030i
$625$	−11.5011	−	19.9204i	−0.460043	−	0.796818i
$626$	−3.08207	−	5.33830i	−0.123184	−	0.213361i
$627$	6.57976	+	3.32323i	0.262770	+	0.132717i
$628$	2.45480	+	1.41728i	0.0979571	+	0.0565555i
$629$	25.7829			1.02803
$630$	1.12569	+	2.68322i	0.0448484	+	0.106902i
$631$	−32.5707			−1.29662			−0.648310	−	0.761377i	$-0.724524\pi$
$631$	−32.5707			−1.29662			−0.648310	+	0.761377i	$0.724524\pi$
$632$	−7.23623	−	4.17784i	−0.287842	−	0.166186i
$633$	−2.40283	+	1.57255i	−0.0955039	+	0.0625033i
$634$	−10.3274	−	17.8876i	−0.410154	−	0.710408i
$635$	0.306009	+	0.530024i	0.0121436	+	0.0210333i
$636$		0			0
$637$	−3.21486	+	6.23042i	−0.127377	+	0.246858i
$638$			1.22442i			0.0484751i
$639$	1.84047	+	16.3923i	0.0728080	+	0.648470i
$640$			0.366598i			0.0144911i
$641$	−10.2270	−	5.90456i	−0.403942	−	0.233216i	0.284241	−	0.958753i	$-0.408258\pi$
$641$	−10.2270	−	5.90456i	−0.403942	−	0.233216i	−0.688184	+	0.725537i	$0.741592\pi$
$642$	−17.1020	−	8.63768i	−0.674962	−	0.340902i
$643$	25.3714	−	14.6482i	1.00055	−	0.577668i	0.0921392	−	0.995746i	$-0.470630\pi$
$643$	25.3714	−	14.6482i	1.00055	−	0.577668i	0.908411	+	0.418078i	$0.137296\pi$
$644$	−19.7832	−	4.80315i	−0.779569	−	0.189270i
$645$	0.159599	+	2.85189i	0.00628421	+	0.112293i
$646$	15.8583	−	27.4674i	0.623936	−	1.08069i
$647$	−28.1683			−1.10741			−0.553705	−	0.832713i	$-0.686786\pi$
$647$	−28.1683			−1.10741			−0.553705	+	0.832713i	$0.686786\pi$
$648$	1.99582	+	8.77592i	0.0784032	+	0.344751i
$649$			5.84229i			0.229330i
$650$	−2.43661	+	4.22033i	−0.0955717	+	0.165535i
$651$	−22.0618	−	18.8050i	−0.864669	−	0.737027i
$652$	12.3640	+	21.4151i	0.484213	+	0.838682i
$653$	39.0555	−	22.5487i	1.52836	−	0.882399i	0.528929	−	0.848666i	$-0.322594\pi$
$653$	39.0555	−	22.5487i	1.52836	−	0.882399i	0.999431	−	0.0337326i	$-0.0107394\pi$
$654$	−8.24848	+	16.3314i	−0.322541	+	0.638608i
$655$	2.48043	−	4.29623i	0.0969184	−	0.167868i
$656$	4.31856			0.168611
$657$	1.36339	+	12.1431i	0.0531909	+	0.473748i
$658$	15.2098	−	15.9458i	0.592939	−	0.621632i
$659$	27.5435	+	15.9022i	1.07294	+	0.619463i	0.928984	−	0.370121i	$-0.120684\pi$
$659$	27.5435	+	15.9022i	1.07294	+	0.619463i	0.143958	+	0.989584i	$0.454017\pi$
$660$	−0.232778	−	0.355680i	−0.00906085	−	0.0138448i
$661$	17.1234	−	9.88619i	0.666022	−	0.384528i	−0.128546	−	0.991704i	$-0.541031\pi$
$661$	17.1234	−	9.88619i	0.666022	−	0.384528i	0.794568	+	0.607175i	$0.207698\pi$
$662$	−9.27631	+	5.35568i	−0.360534	+	0.208154i
$663$	−4.73945	−	7.24180i	−0.184065	−	0.281248i
$664$	14.7348	+	8.50712i	0.571820	+	0.330140i
$665$	4.25587	−	4.46181i	0.165035	−	0.173022i
$666$	14.2076	+	6.20535i	0.550535	+	0.240452i
$667$	−14.0733			−0.544918
$668$	9.67422	−	16.7562i	0.374307	−	0.648318i
$669$	13.3037	−	26.3403i	0.514349	−	1.01837i
$670$	3.45763	−	1.99626i	0.133580	−	0.0771223i
$671$	−1.65948	−	2.87430i	−0.0640635	−	0.110961i
$672$	3.48754	+	2.97272i	0.134535	+	0.114675i
$673$	−0.945369	+	1.63743i	−0.0364413	+	0.0631182i	−0.883671	−	0.468109i	$-0.844936\pi$
$673$	−0.945369	+	1.63743i	−0.0364413	+	0.0631182i	0.847230	+	0.531227i	$0.178269\pi$
$674$			7.55183i			0.290886i
$675$	23.6982	+	8.80893i	0.912144	+	0.339056i
$676$	−11.9969			−0.461418
$677$	10.5661	−	18.3010i	0.406088	−	0.703364i	−0.588360	−	0.808599i	$-0.700226\pi$
$677$	10.5661	−	18.3010i	0.406088	−	0.703364i	0.994447	+	0.105235i	$0.0335595\pi$
$678$	−0.402553	−	7.19326i	−0.0154599	−	0.276255i
$679$	−44.2627	−	10.7465i	−1.69865	−	0.412412i
$680$	−1.58394	+	0.914490i	−0.0607415	+	0.0350691i
$681$	−7.90067	−	3.99038i	−0.302754	−	0.152912i
$682$	3.66751	+	2.11744i	0.140436	+	0.0810810i
$683$			8.71972i			0.333651i	0.985986	+	0.166825i	$0.0533516\pi$
$683$			8.71972i			0.333651i	−0.985986	+	0.166825i	$0.946648\pi$
$684$	15.3495	−	11.3191i	0.586901	−	0.432798i
$685$		−	3.29517i		−	0.125902i
$686$	17.5049	−	6.04790i	0.668342	−	0.230910i
$687$	14.4804	+	22.1258i	0.552463	+	0.844153i
$688$	2.24922	+	3.89576i	0.0857506	+	0.148524i
$689$		0			0
$690$	4.08812	−	2.67551i	0.155632	−	0.101855i
$691$	−15.7071	−	9.06850i	−0.597526	−	0.344982i	0.170542	−	0.985350i	$-0.445448\pi$
$691$	−15.7071	−	9.06850i	−0.597526	−	0.344982i	−0.768068	+	0.640369i	$0.778782\pi$
$692$	−4.83654			−0.183858
$693$	−5.27125	−	0.669706i	−0.200238	−	0.0254400i
$694$	−10.9320			−0.414972
$695$	2.95235	+	1.70454i	0.111989	+	0.0646568i
$696$	2.82769	+	1.42818i	0.107183	+	0.0541349i
$697$	10.7728	+	18.6590i	0.408048	+	0.706760i
$698$	0.592145	+	1.02562i	0.0224130	+	0.0388205i
$699$	−17.6272	+	0.986465i	−0.666724	+	0.0373115i
$700$	12.3524	−	3.62456i	0.466876	−	0.136996i
$701$		−	35.6167i		−	1.34523i	−0.739995	−	0.672613i	$-0.765172\pi$
$701$		−	35.6167i		−	1.34523i	0.739995	−	0.672613i	$-0.234828\pi$
$702$	−0.868738	−	5.13126i	−0.0327884	−	0.193667i
$703$		−	32.8534i		−	1.23909i
$704$	−0.579764	−	0.334727i	−0.0218507	−	0.0126155i
$705$	0.295503	+	5.28038i	0.0111293	+	0.198871i
$706$	29.0832	−	16.7912i	1.09456	−	0.631946i
$707$	−9.82012	+	40.4472i	−0.369324	+	1.52117i
$708$	13.4923	+	6.81453i	0.507071	+	0.256106i
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$	−2.01572			−0.0756485
$711$	10.0331	−	22.9716i	0.376271	−	0.861501i
$712$			10.7113i			0.401424i
$713$	−24.3375	+	42.1538i	−0.911447	+	1.57867i
$714$	−4.14429	+	22.4840i	−0.155096	+	0.841443i
$715$	0.122902	+	0.212873i	0.00459628	+	0.00796099i
$716$	3.16789	−	1.82898i	0.118390	−	0.0683522i
$717$	18.1934	+	27.7992i	0.679445	+	1.03818i
$718$	−5.06407	+	8.77122i	−0.188989	+	0.327339i
$719$	−25.7829			−0.961540			−0.480770	−	0.876847i	$-0.659643\pi$
$719$	−25.7829			−0.961540			−0.480770	+	0.876847i	$0.659643\pi$
$720$	−1.09293	+	0.122710i	−0.0407310	+	0.00457314i
$721$	−20.8991	+	21.9104i	−0.778323	+	0.815987i
$722$	−18.5453	−	10.7072i	−0.690186	−	0.398479i
$723$	16.1523	−	31.9804i	0.600710	−	1.18936i
$724$	4.90860	−	2.83398i	0.182427	−	0.105324i
$725$	7.70685	−	4.44955i	0.286225	−	0.165252i
$726$	−18.2478	+	1.02119i	−0.677238	+	0.0378999i
$727$	1.32423	+	0.764544i	0.0491129	+	0.0283554i	0.524355	−	0.851499i	$-0.324306\pi$
$727$	1.32423	+	0.764544i	0.0491129	+	0.0283554i	−0.475242	+	0.879855i	$0.657640\pi$
$728$	−1.91749	−	1.82898i	−0.0710668	−	0.0677865i
$729$	−25.4953	+	8.88761i	−0.944270	+	0.329171i
$730$	−1.49321			−0.0552660
$731$	−11.2215	+	19.4362i	−0.415042	+	0.718873i
$732$	−8.57360	+	0.479800i	−0.316889	+	0.0177339i
$733$	−17.9908	+	10.3870i	−0.664504	+	0.383651i	−0.793991	−	0.607930i	$-0.792000\pi$
$733$	−17.9908	+	10.3870i	−0.664504	+	0.383651i	0.129487	+	0.991581i	$0.458667\pi$
$734$	−9.00104	−	15.5903i	−0.332234	−	0.575447i
$735$	−1.81425	+	4.05764i	−0.0669196	+	0.149668i
$736$	3.84729	−	6.66371i	0.141813	−	0.245628i
$737$			7.29084i			0.268562i
$738$	1.44554	+	12.8748i	0.0532110	+	0.473927i
$739$	−11.8709			−0.436678			−0.218339	−	0.975873i	$-0.570064\pi$
$739$	−11.8709			−0.436678			−0.218339	+	0.975873i	$0.570064\pi$
$740$	−0.947269	+	1.64072i	−0.0348223	+	0.0603140i
$741$	−9.22773	+	6.03917i	−0.338989	+	0.221854i
$742$		0			0
$743$	−37.5906	+	21.7029i	−1.37907	+	0.796204i	−0.992047	−	0.125868i	$-0.959828\pi$
$743$	−37.5906	+	21.7029i	−1.37907	+	0.796204i	−0.387019	+	0.922072i	$0.626495\pi$
$744$	9.16789	−	6.00000i	0.336111	−	0.219971i
$745$	0.899148	+	0.519124i	0.0329422	+	0.0190192i
$746$		−	16.4090i		−	0.600777i
$747$	−20.4299	+	46.7759i	−0.747491	+	1.71144i
$748$		−	3.33994i		−	0.122120i
$749$	−8.24030	−	28.0826i	−0.301094	−	1.02612i
$750$	−2.82415	+	5.59160i	−0.103123	+	0.204176i
$751$	−1.15691	−	2.00383i	−0.0422164	−	0.0731209i	0.844145	−	0.536115i	$-0.180109\pi$
$751$	−1.15691	−	2.00383i	−0.0422164	−	0.0731209i	−0.886362	+	0.462994i	$0.846775\pi$
$752$	4.16450	+	7.21313i	0.151864	+	0.263036i
$753$	0.175363	+	3.13358i	0.00639058	+	0.114194i
$754$	−1.58642	−	0.915921i	−0.0577741	−	0.0333559i
$755$	−6.06787			−0.220832
$756$	−7.69509	+	11.3923i	−0.279868	+	0.414336i
$757$	−15.0946			−0.548624			−0.274312	−	0.961641i	$-0.588450\pi$
$757$	−15.0946			−0.548624			−0.274312	+	0.961641i	$0.588450\pi$
$758$	−2.52336	−	1.45686i	−0.0916525	−	0.0529156i
$759$	0.498522	+	8.90814i	0.0180952	+	0.323345i
$760$	1.16527	+	2.01831i	0.0422689	+	0.0732119i
$761$	11.6690	+	20.2112i	0.422999	+	0.732656i	0.996231	−	0.0867370i	$-0.0276440\pi$
$761$	11.6690	+	20.2112i	0.422999	+	0.732656i	−0.573232	+	0.819393i	$0.694311\pi$
$762$	−1.30361	+	2.58105i	−0.0472248	+	0.0935016i
$763$	−26.8173	+	7.86900i	−0.970850	+	0.284877i
$764$			27.3777i			0.990490i
$765$	−3.25653	−	4.41606i	−0.117740	−	0.159663i
$766$		−	8.57443i		−	0.309807i
$767$	−7.56959	−	4.37030i	−0.273322	−	0.157803i
$768$	−1.44927	+	0.948485i	−0.0522959	+	0.0342255i
$769$	−15.8266	+	9.13748i	−0.570721	+	0.329506i	−0.757437	−	0.652908i	$-0.773549\pi$
$769$	−15.8266	+	9.13748i	−0.570721	+	0.329506i	0.186716	+	0.982414i	$0.440216\pi$
$770$	0.153197	−	0.630990i	0.00552085	−	0.0227393i
$771$	9.35568	−	6.12290i	0.336937	−	0.220511i
$772$	−5.01413	+	8.68473i	−0.180463	+	0.312570i
$773$	−0.438507			−0.0157720			−0.00788600	−	0.999969i	$-0.502510\pi$
$773$	−0.438507			−0.0157720			−0.00788600	+	0.999969i	$0.502510\pi$
$774$	−10.8614	+	8.00953i	−0.390406	+	0.287897i
$775$		−	30.7792i		−	1.10562i
$776$	8.60787	−	14.9093i	0.309004	−	0.535211i
$777$	7.92725	+	22.3161i	0.284388	+	0.800585i
$778$	−17.7770	−	30.7906i	−0.637335	−	1.10390i
$779$	23.7759	−	13.7270i	0.851861	−	0.491822i
$780$	0.634967	−	0.0355343i	0.0227354	−	0.00127233i
$781$	1.84047	−	3.18779i	0.0658573	−	0.114068i
$782$	38.3888			1.37278
$783$	−3.31128	+	8.90814i	−0.118335	+	0.318351i
$784$	0.330547	+	6.99219i	0.0118052	+	0.249721i
$785$	−0.899924	−	0.519571i	−0.0321197	−	0.0185443i
$786$	23.4017	−	1.30962i	0.834712	−	0.0467126i
$787$	−33.1317	+	19.1286i	−1.18102	+	0.681861i	−0.956250	−	0.292551i	$-0.905496\pi$
$787$	−33.1317	+	19.1286i	−1.18102	+	0.681861i	−0.224769	+	0.974412i	$0.572163\pi$
$788$	−16.3037	+	9.41292i	−0.580794	+	0.335322i
$789$	−6.88767	+	13.6371i	−0.245207	+	0.485493i
$790$	2.65279	+	1.53159i	0.0943820	+	0.0544915i
$791$	7.59581	−	7.96337i	0.270076	−	0.283145i
$792$	0.803848	−	1.84047i	0.0285635	−	0.0653983i
$793$	4.96547			0.176329
$794$	−1.79017	+	3.10066i	−0.0635307	+	0.110038i
$795$		0			0
$796$	−4.64541	+	2.68203i	−0.164652	+	0.0950620i
$797$	17.6613	+	30.5902i	0.625594	+	1.08356i	0.988426	+	0.151706i	$0.0484767\pi$
$797$	17.6613	+	30.5902i	0.625594	+	1.08356i	−0.362832	+	0.931855i	$0.618190\pi$
$798$	28.6498	+	5.28079i	1.01419	+	0.186938i
$799$	−20.7770	+	35.9868i	−0.735036	+	1.27312i
$800$			4.86561i			0.172025i
$801$	−31.9333	+	3.58536i	−1.12831	+	0.126683i
$802$	0.190871			0.00673991
$803$	1.36339	−	2.36146i	0.0481130	−	0.0833341i
$804$	16.8376	+	8.50414i	0.593816	+	0.299918i
$805$	7.25250	+	1.76082i	0.255617	+	0.0620609i
$806$	−5.48694	+	3.16789i	−0.193269	+	0.111584i
$807$	−1.38058	−	24.6697i	−0.0485986	−	0.868414i
$808$	−13.6241	−	7.86586i	−0.479293	−	0.276720i
$809$		−	21.7669i		−	0.765282i	−0.923897	−	0.382641i	$-0.875015\pi$
$809$		−	21.7669i		−	0.765282i	0.923897	−	0.382641i	$-0.124985\pi$
$810$	−0.731664	−	3.21723i	−0.0257080	−	0.113042i
$811$			17.0184i			0.597598i	0.954316	+	0.298799i	$0.0965860\pi$
$811$			17.0184i			0.597598i	−0.954316	+	0.298799i	$0.903414\pi$
$812$	1.36247	+	4.64326i	0.0478134	+	0.162946i
$813$	−5.27937	+	0.295447i	−0.185156	+	0.0103618i
$814$	−1.72983	−	2.99615i	−0.0606305	−	0.105015i
$815$	−4.53263	−	7.85075i	−0.158771	−	0.275000i
$816$	−7.71332	−	3.89576i	−0.270020	−	0.136379i
$817$	24.7662	+	14.2988i	0.866460	+	0.500251i
$818$	−3.47371			−0.121455
$819$	4.81085	−	6.32875i	0.168105	−	0.221144i
$820$	−1.58318			−0.0552869
$821$	−21.4786	−	12.4007i	−0.749608	−	0.432786i	0.0759445	−	0.997112i	$-0.475803\pi$
$821$	−21.4786	−	12.4007i	−0.749608	−	0.432786i	−0.825552	+	0.564326i	$0.809136\pi$
$822$	13.0268	−	8.52547i	0.454360	−	0.297360i
$823$	−10.6572	−	18.4588i	−0.371486	−	0.643433i	0.618308	−	0.785936i	$-0.287818\pi$
$823$	−10.6572	−	18.4588i	−0.371486	−	0.643433i	−0.989794	+	0.142503i	$0.954485\pi$
$824$	−5.72226	−	9.91124i	−0.199344	−	0.345274i
$825$	−3.08950	−	4.72069i	−0.107562	−	0.164353i
$826$	6.50102	+	22.1552i	0.226199	+	0.770879i
$827$		−	49.7585i		−	1.73027i	−0.501537	−	0.865136i	$-0.667232\pi$
$827$		−	49.7585i		−	1.73027i	0.501537	−	0.865136i	$-0.332768\pi$
$828$	21.1541	+	9.23929i	0.735155	+	0.321088i
$829$		−	43.1190i		−	1.49759i	−0.662804	−	0.748793i	$-0.730634\pi$
$829$		−	43.1190i		−	1.49759i	0.662804	−	0.748793i	$-0.269366\pi$
$830$	−5.40174	−	3.11870i	−0.187497	−	0.108252i
$831$	1.95676	+	0.988300i	0.0678794	+	0.0342838i
$832$	0.867380	−	0.500782i	0.0300710	−	0.0173615i
$833$	−29.3863	+	18.8704i	−1.01817	+	0.653821i
$834$	0.899965	+	16.0816i	0.0311632	+	0.556859i
$835$	−3.54655	+	6.14281i	−0.122733	+	0.212581i
$836$	−4.25587			−0.147192
$837$	20.9563	+	25.3236i	0.724357	+	0.875311i
$838$			1.40791i			0.0486354i
$839$	14.9985	−	25.9782i	0.517807	−	0.896868i	−0.481979	−	0.876183i	$-0.660082\pi$
$839$	14.9985	−	25.9782i	0.517807	−	0.896868i	0.999786	−	0.0206851i	$-0.00658476\pi$
$840$	−1.27853	−	1.08979i	−0.0441134	−	0.0376014i
$841$	−12.8274	−	22.2177i	−0.442325	−	0.766129i
$842$	26.3151	−	15.1930i	0.906878	−	0.523586i
$843$	8.21988	−	16.2748i	0.283108	−	0.560532i
$844$	0.828981	−	1.43584i	0.0285347	−	0.0494235i
$845$	4.39803			0.151297
$846$	−20.1103	+	14.8299i	−0.691407	+	0.509863i
$847$	−20.2014	−	19.2689i	−0.694128	−	0.662089i
$848$		0			0
$849$	18.8481	+	28.7995i	0.646864	+	0.988396i
$850$	−21.0226	+	12.1374i	−0.721069	+	0.416310i
$851$	34.4373	−	19.8824i	1.18050	−	0.681559i
$852$	−5.21518	−	7.96870i	−0.178669	−	0.273003i
$853$	−25.7693	−	14.8779i	−0.882325	−	0.509411i	−0.0109007	−	0.999941i	$-0.503470\pi$
$853$	−25.7693	−	14.8779i	−0.882325	−	0.509411i	−0.871424	+	0.490530i	$0.836803\pi$
$854$	−9.49150	−	9.05340i	−0.324792	−	0.309801i
$855$	−5.62708	+	4.14957i	−0.192442	+	0.141912i
$856$	11.0618			0.378083
$857$	22.9296	−	39.7152i	0.783260	−	1.35665i	−0.146773	−	0.989170i	$-0.546889\pi$
$857$	22.9296	−	39.7152i	0.783260	−	1.35665i	0.930033	−	0.367476i	$-0.119778\pi$
$858$	−0.523567	+	1.03663i	−0.0178743	+	0.0353898i
$859$	−3.24073	+	1.87104i	−0.110572	+	0.0638390i	−0.554266	−	0.832339i	$-0.687001\pi$
$859$	−3.24073	+	1.87104i	−0.110572	+	0.0638390i	0.443694	+	0.896178i	$0.353668\pi$
$860$	−0.824559	−	1.42818i	−0.0281172	−	0.0487005i
$861$	−12.8379	+	15.0612i	−0.437513	+	0.513283i
$862$	−13.6373	+	23.6206i	−0.464490	+	0.804520i
$863$		−	31.3944i		−	1.06868i	−0.845270	−	0.534339i	$-0.820561\pi$
$863$		−	31.3944i		−	1.06868i	0.845270	−	0.534339i	$-0.179439\pi$
$864$	−3.31280	−	4.00317i	−0.112704	−	0.136191i
$865$	1.77307			0.0602860
$866$	4.07523	−	7.05851i	0.138482	−	0.239858i
$867$	−0.763654	−	13.6458i	−0.0259350	−	0.463436i
$868$	16.2642	+	3.94876i	0.552043	+	0.134030i
$869$	−4.84432	+	2.79687i	−0.164332	+	0.0948773i
$870$	−1.03663	−	0.523567i	−0.0351449	−	0.0177506i
$871$	−9.44641	−	5.45389i	−0.320080	−	0.184798i
$872$		−	10.5633i		−	0.357719i
$873$	47.3298	+	20.6718i	1.60187	+	0.699635i
$874$		−	48.9162i		−	1.65462i
$875$	−9.18180	+	2.69422i	−0.310402	+	0.0910812i
$876$	−3.86331	−	5.90307i	−0.130529	−	0.199446i
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	6.12020	+	10.6005i	0.206547	+	0.357750i
$879$	19.4377	−	12.7212i	0.655619	−	0.429075i
$880$	0.212540	+	0.122710i	0.00716473	+	0.00413656i
$881$	21.2010			0.714280			0.357140	−	0.934051i	$-0.383752\pi$
$881$	21.2010			0.714280			0.357140	+	0.934051i	$0.383752\pi$
$882$	−20.7350	+	3.32592i	−0.698182	+	0.111990i
$883$	38.6157			1.29952			0.649761	−	0.760139i	$-0.274869\pi$
$883$	38.6157			1.29952			0.649761	+	0.760139i	$0.274869\pi$
$884$	4.32741	+	2.49843i	0.145547	+	0.0840314i
$885$	−4.94624	−	2.49819i	−0.166266	−	0.0839758i
$886$	4.00418	+	6.93544i	0.134523	+	0.233001i
$887$	−3.09606	−	5.36253i	−0.103955	−	0.180056i	0.809356	−	0.587319i	$-0.199817\pi$
$887$	−3.09606	−	5.36253i	−0.103955	−	0.180056i	−0.913311	+	0.407263i	$0.866483\pi$
$888$	−8.93706	+	0.500140i	−0.299908	+	0.0167836i
$889$	−4.23827	+	1.24364i	−0.142147	+	0.0417102i
$890$		−	3.92675i		−	0.131625i
$891$	5.75601	+	1.78043i	0.192834	+	0.0596466i
$892$			17.0372i			0.570448i
$893$	45.8555	+	26.4747i	1.53450	+	0.885941i
$894$	0.274088	+	4.89770i	0.00916686	+	0.163804i
$895$	−1.16134	+	0.670501i	−0.0388194	+	0.0224124i
$896$	−2.57106	−	0.624224i	−0.0858931	−	0.0208539i
$897$	−11.9148	−	6.01779i	−0.397824	−	0.200928i
$898$	7.25917	−	12.5733i	0.242242	−	0.419575i
$899$	11.5699			0.385878
$900$	−14.5057	+	1.62865i	−0.483522	+	0.0542883i
$901$		0			0
$902$	1.44554	−	2.50374i	0.0481311	−	0.0833656i
$903$	−20.2729	−	3.73674i	−0.674640	−	0.124351i
$904$	2.07976	+	3.60226i	0.0691719	+	0.119809i
$905$	−1.79948	+	1.03893i	−0.0598168	+	0.0345353i
$906$	−15.6992	−	23.9880i	−0.521570	−	0.796949i
$907$	0.0645566	−	0.111815i	0.00214357	−	0.00371277i	−0.864952	−	0.501855i	$-0.832651\pi$
$907$	0.0645566	−	0.111815i	0.00214357	−	0.00371277i	0.867095	+	0.498142i	$0.165984\pi$
$908$	5.11024			0.169589
$909$	18.8899	−	43.2499i	0.626539	−	1.43451i
$910$	0.702947	+	0.670501i	0.0233025	+	0.0222269i
$911$	29.6682	+	17.1290i	0.982952	+	0.567508i	0.903160	−	0.429304i	$-0.141241\pi$
$911$	29.6682	+	17.1290i	0.982952	+	0.567508i	0.0797919	+	0.996812i	$0.474574\pi$
$912$	−4.96410	+	9.82856i	−0.164378	+	0.325456i
$913$	9.86424	−	5.69512i	0.326459	−	0.188481i
$914$	−8.62130	+	4.97751i	−0.285167	+	0.164641i
$915$	3.14306	−	0.175894i	0.103907	−	0.00581487i
$916$	−13.2215	−	7.63345i	−0.436851	−	0.252216i
$917$	25.9072	+	24.7114i	0.855530	+	0.816041i
$918$	9.03245	−	24.2995i	0.298115	−	0.802002i
$919$	14.3054			0.471892			0.235946	−	0.971766i	$-0.424181\pi$
$919$	14.3054			0.471892			0.235946	+	0.971766i	$0.424181\pi$
$920$	−1.41041	+	2.44290i	−0.0464999	+	0.0805401i
$921$	−1.13052	+	0.0632668i	−0.0372519	+	0.00208471i
$922$	−27.9960	+	16.1635i	−0.922001	+	0.532317i
$923$	2.75352	+	4.76923i	0.0906332	+	0.156981i
$924$	2.89085	−	1.02690i	0.0951019	−	0.0337827i
$925$	−12.5725	+	21.7761i	−0.413380	+	0.715995i
$926$		−	9.45032i		−	0.310557i
$927$	27.6327	−	20.3771i	0.907576	−	0.669273i
$928$	−1.82898			−0.0600392
$929$	5.87364	−	10.1734i	0.192708	−	0.333780i	−0.753439	−	0.657518i	$-0.771606\pi$
$929$	5.87364	−	10.1734i	0.192708	−	0.333780i	0.946147	+	0.323738i	$0.104940\pi$
$930$	−3.36093	+	2.19959i	−0.110209	+	0.0721274i
$931$	24.0453	+	37.4450i	0.788053	+	1.22721i
$932$	8.82741	−	5.09651i	0.289152	−	0.166942i
$933$	13.3984	−	8.76868i	0.438643	−	0.287074i
$934$	17.8941	+	10.3312i	0.585512	+	0.338046i
$935$			1.22442i			0.0400427i
$936$	1.78330	+	2.41827i	0.0582890	+	0.0790436i
$937$		−	2.63611i		−	0.0861179i	−0.999073	−	0.0430589i	$-0.986290\pi$
$937$		−	2.63611i		−	0.0861179i	0.999073	−	0.0430589i	$-0.0137103\pi$
$938$	8.11290	+	27.6485i	0.264896	+	0.902755i
$939$	−4.81333	+	9.53004i	−0.157077	+	0.311001i
$940$	−1.52670	−	2.64432i	−0.0497954	−	0.0862482i
$941$	−5.96557	−	10.3327i	−0.194472	−	0.336836i	0.752255	−	0.658872i	$-0.228966\pi$
$941$	−5.96557	−	10.3327i	−0.194472	−	0.336836i	−0.946727	+	0.322036i	$0.895633\pi$
$942$	−0.274324	−	4.90192i	−0.00893796	−	0.159713i
$943$	28.7776	+	16.6148i	0.937128	+	0.541051i
$944$	−8.72695			−0.284038
$945$	2.82100	−	4.17641i	0.0917673	−	0.135859i
$946$	3.01149			0.0979121
$947$	6.70267	+	3.86979i	0.217807	+	0.125751i	0.604935	−	0.796275i	$-0.293199\pi$
$947$	6.70267	+	3.86979i	0.217807	+	0.125751i	−0.387127	+	0.922026i	$0.626533\pi$
$948$	0.808650	+	14.4499i	0.0262637	+	0.469309i
$949$	2.03976	+	3.53296i	0.0662133	+	0.114685i
$950$	15.4659	+	26.7877i	0.501779	+	0.869107i
$951$	−16.1285	+	31.9333i	−0.523003	+	1.03551i
$952$	−3.71653	−	12.6658i	−0.120453	−	0.410501i
$953$		−	3.76685i		−	0.122020i	−0.998137	−	0.0610102i	$-0.980568\pi$
$953$		−	3.76685i		−	0.122020i	0.998137	−	0.0610102i	$-0.0194322\pi$
$954$		0			0
$955$		−	10.0366i		−	0.324777i
$956$	−16.6117	−	9.59076i	−0.537260	−	0.310187i
$957$	1.77451	−	1.16134i	0.0573617	−	0.0375408i
$958$	−8.79955	+	5.08042i	−0.284301	+	0.164141i
$959$	23.1100	+	5.61084i	0.746260	+	0.181184i
$960$	0.531299	−	0.347713i	0.0171476	−	0.0112224i
$961$	4.50836	−	7.80871i	0.145431	−	0.251894i
$962$	5.17597			0.166880
$963$	3.70267	+	32.9781i	0.119317	+	1.06270i
$964$			20.6853i			0.666227i
$965$	1.83817	−	3.18381i	0.0591728	−	0.102490i
$966$	11.8031	+	33.2269i	0.379757	+	1.06906i
$967$	−2.28741	−	3.96191i	−0.0735581	−	0.127406i	0.826900	−	0.562349i	$-0.190102\pi$
$967$	−2.28741	−	3.96191i	−0.0735581	−	0.127406i	−0.900458	+	0.434942i	$0.856769\pi$
$968$	9.13815	−	5.27592i	0.293711	−	0.169574i
$969$	−54.8489	+	3.06948i	−1.76200	+	0.0986060i
$970$	−3.15563	+	5.46571i	−0.101321	+	0.175493i
$971$	−25.8445			−0.829388			−0.414694	−	0.909961i	$-0.636111\pi$
$971$	−25.8445			−0.829388			−0.414694	+	0.909961i	$0.636111\pi$
$972$	10.8256	−	11.2163i	0.347233	−	0.359763i
$973$	−16.9815	+	17.8033i	−0.544403	+	0.570747i
$974$	−27.0457	−	15.6148i	−0.866599	−	0.500331i
$975$	8.42748	−	0.471623i	0.269895	−	0.0151040i
$976$	4.29351	−	2.47886i	0.137432	−	0.0793463i
$977$	−26.0950	+	15.0659i	−0.834852	+	0.482002i	−0.855511	−	0.517785i	$-0.826757\pi$
$977$	−26.0950	+	15.0659i	−0.834852	+	0.482002i	0.0206590	+	0.999787i	$0.493424\pi$
$978$	19.3092	−	38.2307i	0.617439	−	1.22248i
$979$	6.21003	+	3.58536i	0.198474	+	0.114589i
$980$	−0.121178	−	2.56332i	−0.00387088	−	0.0818824i
$981$	31.4921	−	3.53583i	1.00547	−	0.112890i
$982$	20.5899			0.657051
$983$	−6.30293	+	10.9170i	−0.201032	+	0.348198i	−0.948861	−	0.315693i	$-0.897763\pi$
$983$	−6.30293	+	10.9170i	−0.201032	+	0.348198i	0.747829	+	0.663891i	$0.231096\pi$
$984$	−4.09609	−	6.25875i	−0.130579	−	0.199522i
$985$	5.97689	−	3.45076i	0.190440	−	0.109950i
$986$	−4.56245	−	7.90239i	−0.145298	−	0.251663i
$987$	−37.5360	−	6.91870i	−1.19478	−	0.220225i
$988$	3.18359	−	5.51413i	0.101283	−	0.175428i
$989$			34.6136i			1.10065i
$990$	−0.294689	+	0.674714i	−0.00936583	+	0.0214438i
$991$	51.6852			1.64184			0.820918	−	0.571046i	$-0.193462\pi$
$991$	51.6852			1.64184			0.820918	+	0.571046i	$0.193462\pi$
$992$	−3.16294	+	5.47837i	−0.100423	+	0.173938i
$993$	16.5603	+	8.36407i	0.525524	+	0.265426i
$994$	3.43226	−	14.1368i	0.108865	−	0.448392i
$995$	1.70300	−	0.983227i	0.0539887	−	0.0311704i
$996$	−1.64661	−	29.4235i	−0.0521749	−	0.932319i
$997$	35.1469	+	20.2921i	1.11311	+	0.642656i	0.939634	−	0.342181i	$-0.111166\pi$
$997$	35.1469	+	20.2921i	1.11311	+	0.642656i	0.173479	+	0.984837i	$0.444499\pi$
$998$			25.1533i			0.796213i
$999$	−4.48252	−	26.4764i	−0.141821	−	0.837675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.m.a.83.6	yes	16
3.2	odd	2		378.2.m.a.251.3		16
4.3	odd	2		1008.2.cc.b.209.5		16
7.2	even	3		882.2.l.a.227.4		16
7.3	odd	6		882.2.t.b.803.4		16
7.4	even	3		882.2.t.b.803.1		16
7.5	odd	6		882.2.l.a.227.1		16
7.6	odd	2	inner	126.2.m.a.83.7	yes	16
9.2	odd	6		1134.2.d.a.1133.12		16
9.4	even	3		378.2.m.a.125.2		16
9.5	odd	6	inner	126.2.m.a.41.7	yes	16
9.7	even	3		1134.2.d.a.1133.5		16
12.11	even	2		3024.2.cc.b.2897.5		16
21.2	odd	6		2646.2.l.b.521.7		16
21.5	even	6		2646.2.l.b.521.6		16
21.11	odd	6		2646.2.t.a.1979.6		16
21.17	even	6		2646.2.t.a.1979.7		16
21.20	even	2		378.2.m.a.251.2		16
28.27	even	2		1008.2.cc.b.209.4		16
36.23	even	6		1008.2.cc.b.545.4		16
36.31	odd	6		3024.2.cc.b.881.4		16
63.4	even	3		2646.2.l.b.1097.2		16
63.5	even	6		882.2.t.b.815.1		16
63.13	odd	6		378.2.m.a.125.3		16
63.20	even	6		1134.2.d.a.1133.13		16
63.23	odd	6		882.2.t.b.815.4		16
63.31	odd	6		2646.2.l.b.1097.3		16
63.32	odd	6		882.2.l.a.509.5		16
63.34	odd	6		1134.2.d.a.1133.4		16
63.40	odd	6		2646.2.t.a.2285.6		16
63.41	even	6	inner	126.2.m.a.41.6	✓	16
63.58	even	3		2646.2.t.a.2285.7		16
63.59	even	6		882.2.l.a.509.8		16
84.83	odd	2		3024.2.cc.b.2897.4		16
252.139	even	6		3024.2.cc.b.881.5		16
252.167	odd	6		1008.2.cc.b.545.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	63.41	even	6	inner
126.2.m.a.41.7	yes	16	9.5	odd	6	inner
126.2.m.a.83.6	yes	16	1.1	even	1	trivial
126.2.m.a.83.7	yes	16	7.6	odd	2	inner
378.2.m.a.125.2		16	9.4	even	3
378.2.m.a.125.3		16	63.13	odd	6
378.2.m.a.251.2		16	21.20	even	2
378.2.m.a.251.3		16	3.2	odd	2
882.2.l.a.227.1		16	7.5	odd	6
882.2.l.a.227.4		16	7.2	even	3
882.2.l.a.509.5		16	63.32	odd	6
882.2.l.a.509.8		16	63.59	even	6
882.2.t.b.803.1		16	7.4	even	3
882.2.t.b.803.4		16	7.3	odd	6
882.2.t.b.815.1		16	63.5	even	6
882.2.t.b.815.4		16	63.23	odd	6
1008.2.cc.b.209.4		16	28.27	even	2
1008.2.cc.b.209.5		16	4.3	odd	2
1008.2.cc.b.545.4		16	36.23	even	6
1008.2.cc.b.545.5		16	252.167	odd	6
1134.2.d.a.1133.4		16	63.34	odd	6
1134.2.d.a.1133.5		16	9.7	even	3
1134.2.d.a.1133.12		16	9.2	odd	6
1134.2.d.a.1133.13		16	63.20	even	6
2646.2.l.b.521.6		16	21.5	even	6
2646.2.l.b.521.7		16	21.2	odd	6
2646.2.l.b.1097.2		16	63.4	even	3
2646.2.l.b.1097.3		16	63.31	odd	6
2646.2.t.a.1979.6		16	21.11	odd	6
2646.2.t.a.1979.7		16	21.17	even	6
2646.2.t.a.2285.6		16	63.40	odd	6
2646.2.t.a.2285.7		16	63.58	even	3
3024.2.cc.b.881.4		16	36.31	odd	6
3024.2.cc.b.881.5		16	252.139	even	6
3024.2.cc.b.2897.4		16	84.83	odd	2
3024.2.cc.b.2897.5		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0967785 - 1.72934i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.183299 - 0.317483i) q^{5} +(0.780860 - 1.54605i) q^{6} +(2.53871 - 0.744936i) q^{7} +1.00000i q^{8} +(-2.98127 + 0.334727i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.0967785 - 1.72934i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.183299 - 0.317483i) q^{5} +(0.780860 - 1.54605i) q^{6} +(2.53871 - 0.744936i) q^{7} +1.00000i q^{8} +(-2.98127 + 0.334727i) q^{9} -0.366598i q^{10} +(0.579764 + 0.334727i) q^{11} +(1.44927 - 0.948485i) q^{12} +(-0.867380 + 0.500782i) q^{13} +(2.57106 + 0.624224i) q^{14} +(-0.531299 + 0.347713i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.98906 q^{17} +(-2.74922 - 1.20075i) q^{18} +6.35722i q^{19} +(0.183299 - 0.317483i) q^{20} +(-1.53394 - 4.31822i) q^{21} +(0.334727 + 0.579764i) q^{22} +(-6.66371 + 3.84729i) q^{23} +(1.72934 - 0.0967785i) q^{24} +(2.43280 - 4.21374i) q^{25} -1.00156 q^{26} +(0.867380 + 5.12325i) q^{27} +(1.91449 + 1.82612i) q^{28} +(1.58394 + 0.914490i) q^{29} +(-0.633975 + 0.0354788i) q^{30} +(5.47837 - 3.16294i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.522749 - 1.03501i) q^{33} +(-4.32065 - 2.49453i) q^{34} +(-0.701849 - 0.669453i) q^{35} +(-1.78052 - 2.41449i) q^{36} -5.16789 q^{37} +(-3.17861 + 5.50552i) q^{38} +(0.949969 + 1.45154i) q^{39} +(0.317483 - 0.183299i) q^{40} +(-2.15928 - 3.73998i) q^{41} +(0.830676 - 4.50666i) q^{42} +(2.24922 - 3.89576i) q^{43} +0.669453i q^{44} +(0.652734 + 0.885148i) q^{45} -7.69459 q^{46} +(4.16450 - 7.21313i) q^{47} +(1.54605 + 0.780860i) q^{48} +(5.89014 - 3.78236i) q^{49} +(4.21374 - 2.43280i) q^{50} +(0.482834 + 8.62781i) q^{51} +(-0.867380 - 0.500782i) q^{52} +(-1.81045 + 4.87055i) q^{54} -0.245420i q^{55} +(0.744936 + 2.53871i) q^{56} +(10.9938 - 0.615242i) q^{57} +(0.914490 + 1.58394i) q^{58} +(4.36348 + 7.55776i) q^{59} +(-0.566778 - 0.286262i) q^{60} +(-4.29351 - 2.47886i) q^{61} +6.32588 q^{62} +(-7.31924 + 3.07063i) q^{63} -1.00000 q^{64} +(0.317980 + 0.183586i) q^{65} +(0.970217 - 0.634967i) q^{66} +(5.44537 + 9.43166i) q^{67} +(-2.49453 - 4.32065i) q^{68} +(7.29820 + 11.1515i) q^{69} +(-0.273092 - 0.930688i) q^{70} -5.49843i q^{71} +(-0.334727 - 2.98127i) q^{72} -4.07314i q^{73} +(-4.47552 - 2.58394i) q^{74} +(-7.52245 - 3.79936i) q^{75} +(-5.50552 + 3.17861i) q^{76} +(1.72120 + 0.417889i) q^{77} +(0.0969299 + 1.73205i) q^{78} +(-4.17784 + 7.23623i) q^{79} +0.366598 q^{80} +(8.77592 - 1.99582i) q^{81} -4.31856i q^{82} +(8.50712 - 14.7348i) q^{83} +(2.97272 - 3.48754i) q^{84} +(0.914490 + 1.58394i) q^{85} +(3.89576 - 2.24922i) q^{86} +(1.42818 - 2.82769i) q^{87} +(-0.334727 + 0.579764i) q^{88} +10.7113 q^{89} +(0.122710 + 1.09293i) q^{90} +(-1.82898 + 1.91749i) q^{91} +(-6.66371 - 3.84729i) q^{92} +(-6.00000 - 9.16789i) q^{93} +(7.21313 - 4.16450i) q^{94} +(2.01831 - 1.16527i) q^{95} +(0.948485 + 1.44927i) q^{96} +(-14.9093 - 8.60787i) q^{97} +(6.99219 - 0.330547i) q^{98} +(-1.84047 - 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

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