LMFDB - Embedded newform 126.2.m.a.41.7

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			41.7
Root			$-0.0967785 + 1.72934i$ of defining polynomial
Character	$\chi$	$=$	126.41
Dual form			126.2.m.a.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.0967785 - 1.72934i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.183299 - 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} +(-0.624224 + 2.57106i) q^{7} -1.00000i q^{8} +(-2.98127 - 0.334727i) q^{9} +O(q^{10})$	\(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} +(-0.624224 + 2.57106i) 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} +(0.744936 + 2.53871i) 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} +(4.38584 + 1.32832i) 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} +(4.46241 - 1.04256i) 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} +(-6.22069 - 3.20983i) 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} +(2.57106 + 0.624224i) 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} +(2.72158 - 7.45607i) 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} +(0.942545 + 0.228839i) 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} +(0.498700 + 1.69955i) 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} +(3.34328 - 3.13408i) 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.807211\pi$
$5$	0.183299	−	0.317483i	0.0819738	−	0.141983i	0.904098	+	0.427326i	$0.140544\pi$
$6$	−0.780860	−	1.54605i	−0.318785	−	0.631171i
$7$	−0.624224	+	2.57106i	−0.235935	+	0.971769i
$7$	−0.624224	+	2.57106i	−0.235935	+	0.971769i
$8$		−	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	−0.410044	−	0.912066i	$-0.634487\pi$
$11$	0.579764	−	0.334727i	0.174805	−	0.100924i	0.584850	+	0.811142i	$0.301153\pi$
$12$	−1.44927	−	0.948485i	−0.418367	−	0.273804i
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	0.615438	−	0.788185i	$-0.288979\pi$
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	−0.374870	+	0.927077i	$0.622313\pi$
$14$	0.744936	+	2.53871i	0.199092	+	0.678500i
$15$	−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	$-0.293168\pi$
$17$	4.98906			1.21003			0.605013	+	0.796216i	$0.293168\pi$
$18$	−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
$21$	4.38584	+	1.32832i	0.957068	+	0.289864i
$22$	0.334727	−	0.579764i	0.0713640	−	0.123606i
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.396223	−	0.918154i	$-0.629679\pi$
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.993256	+	0.115938i	$0.963012\pi$
$24$	−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	−0.345672	−	0.938355i	$-0.612349\pi$
$29$	1.58394	−	0.914490i	0.294131	−	0.169817i	0.639803	+	0.768539i	$0.279016\pi$
$30$	−0.633975	−	0.0354788i	−0.115747	−	0.00647751i
$31$	−5.47837	−	3.16294i	−0.983944	−	0.568081i	−0.0804857	−	0.996756i	$-0.525647\pi$
$31$	−5.47837	−	3.16294i	−0.983944	−	0.568081i	−0.903459	+	0.428675i	$0.858980\pi$
$32$	−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	$-0.723846\pi$
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	0.983909	+	0.178669i	$0.0571790\pi$
$42$	4.46241	−	1.04256i	0.688564	−	0.160870i
$43$	2.24922	+	3.89576i	0.343002	+	0.594098i	0.984989	−	0.172618i	$-0.0552228\pi$
$43$	2.24922	+	3.89576i	0.343002	+	0.594098i	−0.641986	+	0.766716i	$0.721889\pi$
$44$		−	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	−0.991658	−	0.128895i	$-0.958857\pi$
$47$	−4.16450	−	7.21313i	−0.607455	−	1.05214i	0.384203	−	0.923249i	$-0.374476\pi$
$48$	−1.54605	+	0.780860i	−0.223153	+	0.112707i
$49$	−6.22069	−	3.20983i	−0.888670	−	0.458548i
$50$	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
$56$	2.57106	+	0.624224i	0.343572	+	0.0834155i
$57$	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	0.428680	+	0.903456i	$0.358979\pi$
$59$	−4.36348	+	7.55776i	−0.568076	+	0.983937i	−0.996756	+	0.0804804i	$0.974355\pi$
$60$	−0.566778	+	0.286262i	−0.0731707	+	0.0369562i
$61$	4.29351	−	2.47886i	0.549727	−	0.317385i	−0.199285	−	0.979942i	$-0.563862\pi$
$61$	4.29351	−	2.47886i	0.549727	−	0.317385i	0.749012	+	0.662556i	$0.230529\pi$
$62$	−6.32588			−0.803387
$63$	2.72158	−	7.45607i	0.342887	−	0.939377i
$64$	−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	−0.313958	−	0.949437i	$-0.601655\pi$
$67$	5.44537	−	9.43166i	0.665258	−	1.15226i	0.979215	−	0.202823i	$-0.0650117\pi$
$68$	2.49453	−	4.32065i	0.302506	−	0.523956i
$69$	−7.29820	+	11.1515i	−0.878600	+	1.34248i
$70$	0.942545	+	0.228839i	0.112656	+	0.0273515i
$71$			5.49843i			0.652544i	0.945276	+	0.326272i	$0.105793\pi$
$71$			5.49843i			0.652544i	−0.945276	+	0.326272i	$0.894207\pi$
$72$	−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
$77$	0.498700	+	1.69955i	0.0568321	+	0.193682i
$78$	0.0969299	−	1.73205i	0.0109751	−	0.196116i
$79$	−4.17784	−	7.23623i	−0.470044	−	0.814140i	0.529370	−	0.848391i	$-0.322429\pi$
$79$	−4.17784	−	7.23623i	−0.470044	−	0.814140i	−0.999413	+	0.0342518i	$0.989095\pi$
$80$	−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	−0.776798	−	0.629750i	$-0.783158\pi$
$83$	−8.50712	−	14.7348i	−0.933778	−	1.61735i	−0.156980	−	0.987602i	$-0.550176\pi$
$84$	3.34328	−	3.13408i	0.364782	−	0.341957i
$85$	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	$-0.692166\pi$
$89$	−10.7113			−1.13540			−0.567699	+	0.823236i	$0.692166\pi$
$90$	−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	0.513937	−	0.857828i	$-0.328186\pi$
$97$	14.9093	−	8.60787i	1.51381	−	0.873997i	0.999869	−	0.0161687i	$-0.00514689\pi$
$98$	−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	0.930374	+	0.366613i	$0.119483\pi$
$101$	7.86586	+	13.6241i	0.782683	+	1.35565i	−0.147691	+	0.989034i	$0.547184\pi$
$102$	−3.89576	−	7.71332i	−0.385738	−	0.763732i
$103$	9.91124	+	5.72226i	0.976584	+	0.563831i	0.901237	−	0.433327i	$-0.142660\pi$
$103$	9.91124	+	5.72226i	0.976584	+	0.563831i	0.0753467	+	0.997157i	$0.475994\pi$
$104$	0.500782	−	0.867380i	0.0491057	−	0.0850537i
$105$	1.22564	−	1.14895i	0.119610	−	0.112126i
$106$		0			0
$107$			11.0618i			1.06938i	0.845048	+	0.534690i	$0.179572\pi$
$107$			11.0618i			1.06938i	−0.845048	+	0.534690i	$0.820428\pi$
$108$	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
$112$	2.53871	−	0.744936i	0.239886	−	0.0703898i
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	0.659773	−	0.751465i	$-0.270652\pi$
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	−0.320901	+	0.947113i	$0.603986\pi$
$114$	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
$119$	−3.11429	+	12.8272i	−0.285487	+	1.17586i
$120$	−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
$126$	−1.37108	−	7.81794i	−0.122145	−	0.696477i
$127$	−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	0.402923	+	0.915234i	$0.367994\pi$
$131$	−6.76607	+	11.7192i	−0.591154	+	1.02391i	−0.994077	+	0.108675i	$0.965339\pi$
$132$	−1.15772	−	0.0647887i	−0.100766	−	0.00563913i
$133$	−16.3448	−	3.96833i	−1.41727	−	0.344098i
$134$		−	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	−0.129145	−	0.991626i	$-0.541223\pi$
$137$	7.78428	−	4.49425i	0.665056	−	0.383970i	0.794201	+	0.607656i	$0.207890\pi$
$138$	−0.744670	+	13.3066i	−0.0633905	+	1.13273i
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	0.801014	−	0.598646i	$-0.204294\pi$
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	−0.117936	+	0.993021i	$0.537628\pi$
$140$	0.930688	−	0.273092i	0.0786575	−	0.0230805i
$141$	−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
$147$	−6.15294	+	10.4471i	−0.507486	+	0.861660i
$148$	−2.58394	+	4.47552i	−0.212399	+	0.367886i
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	0.396158	−	0.918182i	$-0.370343\pi$
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	−0.597090	+	0.802174i	$0.703676\pi$
$150$	4.61495	−	7.05156i	0.376809	−	0.575758i
$151$	8.27592	+	14.3343i	0.673484	+	1.16651i	0.976909	+	0.213654i	$0.0685365\pi$
$151$	8.27592	+	14.3343i	0.673484	+	1.16651i	−0.303425	+	0.952855i	$0.598130\pi$
$152$	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	$-0.369415\pi$
$157$	−2.45480	−	1.41728i	−0.195914	−	0.113111i	−0.594748	+	0.803912i	$0.702748\pi$
$158$	−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	−0.199874	−	0.979822i	$-0.564053\pi$
$167$	9.67422	−	16.7562i	0.748614	−	1.29664i	0.948487	−	0.316815i	$-0.102614\pi$
$168$	1.32832	−	4.38584i	0.102482	−	0.338375i
$169$	−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	$-0.107808\pi$
$173$	2.41827	+	4.18856i	0.183858	+	0.318451i	−0.759333	+	0.650702i	$0.774475\pi$
$174$	−2.65068	−	1.73476i	−0.200948	−	0.131512i
$175$	−12.3524	+	3.62456i	−0.933752	+	0.273991i
$176$	−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	$0.0436511\pi$
$179$			3.65796i			0.273409i	−0.990612	+	0.136704i	$0.956349\pi$
$180$	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	$-0.0675574\pi$
$182$	−0.625201	+	2.57508i	−0.0463430	+	0.190878i
$183$	−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
$189$	−12.6307	−	5.42814i	−0.918750	−	0.394839i
$190$	2.33055			0.169076
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.788996	−	0.614398i	$-0.210601\pi$
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.926583	−	0.376091i	$-0.122732\pi$
$192$	−0.0967785	+	1.72934i	−0.00698438	+	0.124805i
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	−0.627188	−	0.778868i	$-0.715794\pi$
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	0.988113	+	0.153727i	$0.0491276\pi$
$194$	8.60787	−	14.9093i	0.618009	−	1.07042i
$195$	−0.286710	−	0.567664i	−0.0205317	−	0.0406513i
$196$	−5.89014	+	3.78236i	−0.420724	+	0.270168i
$197$		−	18.8258i		−	1.34129i	−0.741780	−	0.670643i	$-0.766018\pi$
$197$		−	18.8258i		−	1.34129i	0.741780	−	0.670643i	$-0.233982\pi$
$198$	−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
$203$	1.36247	+	4.64326i	0.0956268	+	0.325893i
$204$	−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
$210$	0.486960	−	1.60784i	0.0336035	−	0.110951i
$211$	−0.828981	+	1.43584i	−0.0570694	+	0.0988471i	−0.893149	−	0.449762i	$-0.851509\pi$
$211$	−0.828981	+	1.43584i	−0.0570694	+	0.0988471i	0.836079	+	0.548609i	$0.184842\pi$
$212$		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	$-0.859897\pi$
$223$	−14.7546	+	8.51860i	−0.988044	+	0.570448i	−0.0833551	+	0.996520i	$0.526564\pi$
$224$	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	$-0.220911\pi$
$227$	−2.55512	−	4.42560i	−0.169589	−	0.293737i	−0.938276	+	0.345889i	$0.887577\pi$
$228$	6.02973	−	9.21332i	0.399329	−	0.610167i
$229$	13.2215	+	7.63345i	0.873703	+	0.504433i	0.868577	−	0.495554i	$-0.165035\pi$
$229$	13.2215	+	7.63345i	0.873703	+	0.504433i	0.00512595	+	0.999987i	$0.498368\pi$
$230$	−1.41041	+	2.44290i	−0.0929997	+	0.161080i
$231$	2.98737	−	0.697944i	0.196555	−	0.0459213i
$232$	−0.914490	−	1.58394i	−0.0600392	−	0.103991i
$233$			10.1930i			0.667767i	0.942614	+	0.333883i	$0.108359\pi$
$233$			10.1930i			0.667767i	−0.942614	+	0.333883i	$0.891641\pi$
$234$	−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
$238$	3.71653	+	12.6658i	0.240907	+	0.821002i
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.145108	−	0.989416i	$-0.546353\pi$
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.929413	+	0.369041i	$0.879686\pi$
$240$	−0.0354788	+	0.633975i	−0.00229015	+	0.0409229i
$241$	−17.9140	+	10.3426i	−1.15394	+	0.666227i	−0.949844	−	0.312724i	$-0.898759\pi$
$241$	−17.9140	+	10.3426i	−1.15394	+	0.666227i	−0.204095	+	0.978951i	$0.565425\pi$
$242$			10.5518i			0.678297i
$243$	4.30078	−	14.9834i	0.275895	−	0.961188i
$244$		−	4.95771i		−	0.317385i
$245$	−2.15931	+	1.38661i	−0.137954	+	0.0885869i
$246$	−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	$-0.481787\pi$
$251$	1.81200			0.114373			0.0571864	+	0.998364i	$0.481787\pi$
$252$	−5.09636	−	6.08499i	−0.321040	−	0.383319i
$253$	−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	$-0.897863\pi$
$257$	−3.22773	+	5.59059i	−0.201340	+	0.348731i	0.747620	+	0.664126i	$0.231196\pi$
$258$	4.26670	−	6.51943i	0.265633	−	0.405882i
$259$	3.22592	−	13.2869i	0.200449	−	0.825611i
$260$		−	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	−0.716672	−	0.697410i	$-0.754336\pi$
$263$	−7.63888	+	4.41031i	−0.471034	+	0.271951i	0.245639	+	0.969361i	$0.421002\pi$
$264$	−1.03501	+	0.522749i	−0.0637002	+	0.0321730i
$265$		0			0
$266$	−16.1392	+	4.73572i	−0.989557	+	0.290366i
$267$	−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	$-0.643212\pi$
$269$	−14.2653			−0.869773			−0.434886	+	0.900485i	$0.643212\pi$
$270$	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
$273$	3.13899	+	3.34851i	0.189980	+	0.202661i
$274$	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	0.846388	−	0.532567i	$-0.178773\pi$
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	−0.884411	+	0.466710i	$0.845439\pi$
$278$	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	−0.202795	−	0.979221i	$-0.565002\pi$
$281$	9.11639	−	5.26335i	0.543838	−	0.313985i	0.746633	+	0.665236i	$0.231669\pi$
$282$	−7.89994	+	12.0710i	−0.470434	+	0.718815i
$283$	17.2094	+	9.93588i	1.02300	+	0.590627i	0.914970	−	0.403522i	$-0.132214\pi$
$283$	17.2094	+	9.93588i	1.02300	+	0.590627i	0.108025	+	0.994148i	$0.465547\pi$
$284$	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	$-0.961471\pi$
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	0.600911	+	0.799316i	$0.294804\pi$
$294$	−0.105064	+	12.1239i	−0.00612748	+	0.707080i
$295$	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
$301$	−11.4202	+	3.35104i	−0.658252	+	0.193151i
$302$	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	$-0.00593845\pi$
$308$	1.72120	+	0.417889i	0.0980747	+	0.0238114i
$309$	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	$-0.917754\pi$
$311$	−4.62246	+	8.00634i	−0.262116	+	0.453998i	0.704688	+	0.709517i	$0.251087\pi$
$312$	−1.45154	−	0.949969i	−0.0821770	−	0.0537814i
$313$	5.33830	−	3.08207i	0.301739	−	0.174209i	−0.341485	−	0.939887i	$-0.610930\pi$
$313$	5.33830	−	3.08207i	0.301739	−	0.174209i	0.643224	+	0.765678i	$0.277597\pi$
$314$	−2.83456			−0.159963
$315$	−1.86831	−	2.23075i	−0.105268	−	0.125688i
$316$	−8.35568			−0.470044
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.909626	−	0.415428i	$-0.863632\pi$
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.0950420	+	0.995473i	$0.530299\pi$
$318$		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
$322$	4.80315	−	19.7832i	0.267669	−	1.10248i
$323$			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
$329$	21.1450	−	6.20457i	1.16576	−	0.342069i
$330$	−0.379431	+	0.191639i	−0.0208870	+	0.0105494i
$331$	−5.35568	−	9.27631i	−0.294375	−	0.509872i	0.680464	−	0.732781i	$-0.261778\pi$
$331$	−5.35568	−	9.27631i	−0.294375	−	0.509872i	−0.974839	+	0.222909i	$0.928445\pi$
$332$	−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
$336$	−1.04256	−	4.46241i	−0.0568762	−	0.243444i
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	−0.744664	−	0.667439i	$-0.767390\pi$
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	0.950351	+	0.311179i	$0.100724\pi$
$338$	−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	0.223873	−	0.974618i	$-0.428130\pi$
$347$	−9.46737	−	5.46599i	−0.508235	−	0.293430i	−0.732108	+	0.681189i	$0.761463\pi$
$348$	−3.16294	−	0.177006i	−0.169551	−	0.00948851i
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	−0.527199	−	0.849742i	$-0.676758\pi$
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	0.472299	+	0.881439i	$0.343424\pi$
$350$	−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	−0.835398	−	0.549646i	$-0.814763\pi$
$353$	−16.7912	−	29.0832i	−0.893706	−	1.54794i	−0.0583086	−	0.998299i	$-0.518571\pi$
$354$	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
$357$	21.8812	+	6.62708i	1.15808	+	0.350742i
$358$	1.82898	+	3.16789i	0.0966646	+	0.167428i
$359$		−	10.1281i		−	0.534542i	−0.963621	−	0.267271i	$-0.913878\pi$
$359$		−	10.1281i		−	0.534542i	0.963621	−	0.267271i	$-0.0861219\pi$
$360$	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
$364$	0.746101	+	2.54269i	0.0391063	+	0.133273i
$365$	−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	$-0.510975\pi$
$367$	15.5903	−	9.00104i	0.813805	−	0.469850i	0.848275	+	0.529555i	$0.177641\pi$
$368$			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	−0.996403	−	0.0847411i	$-0.972994\pi$
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	0.571589	+	0.820540i	$0.306327\pi$
$374$	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
$378$	−13.6526	+	1.61446i	−0.702214	+	0.0830387i
$379$	−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	$-0.763032\pi$
$383$	4.28721	−	7.42567i	0.219066	−	0.379434i	0.954523	+	0.298138i	$0.0963655\pi$
$384$	0.780860	+	1.54605i	0.0398481	+	0.0788963i
$385$	0.630990	+	0.153197i	0.0321582	+	0.00780766i
$386$		−	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	−0.564004	+	0.825772i	$0.690740\pi$
$389$	−30.7906	+	17.7770i	−1.56115	+	0.901328i	−0.997142	+	0.0755559i	$0.975927\pi$
$390$	−0.532130	−	0.348257i	−0.0269455	−	0.0176347i
$391$	−33.2456	−	19.1944i	−1.68130	−	0.970702i
$392$	−3.20983	+	6.22069i	−0.162121	+	0.314192i
$393$	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
$399$	−8.44444	+	27.8817i	−0.422751	+	1.39583i
$400$	2.43280	−	4.21374i	0.121640	−	0.210687i
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	0.504122	−	0.863633i	$-0.331816\pi$
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	−0.495867	+	0.868398i	$0.665150\pi$
$402$	−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	$-0.305963\pi$
$409$	3.00832	+	1.73685i	0.148752	+	0.0858819i	−0.423777	+	0.905767i	$0.639296\pi$
$410$	−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	$-0.844282\pi$
$419$	−0.703955	+	1.21929i	−0.0343905	+	0.0595660i	0.848318	+	0.529487i	$0.177616\pi$
$420$	−0.382200	−	1.63591i	−0.0186494	−	0.0798242i
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987268\pi$
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	−0.211822	+	0.977308i	$0.567940\pi$
$422$			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
$427$	3.69318	+	12.5862i	0.178725	+	0.609090i
$428$	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	$-0.771873\pi$
$431$		−	27.2747i		−	1.31378i	0.753988	−	0.656888i	$-0.228127\pi$
$432$	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	$-0.0627444\pi$
$434$	3.94876	−	16.2642i	0.189547	−	0.780707i
$435$	−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	$-0.761021\pi$
$439$	−10.6005	+	6.12020i	−0.505934	+	0.292101i	0.225226	+	0.974306i	$0.427688\pi$
$440$	−0.245420			−0.0117000
$441$	17.4711	+	11.6516i	0.831958	+	0.554838i
$442$	4.99687			0.237677
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	−0.326112	−	0.945331i	$-0.605739\pi$
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	0.655625	+	0.755087i	$0.272405\pi$
$444$	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
$448$	0.624224	−	2.57106i	0.0294918	−	0.121471i
$449$			14.5183i			0.685163i	0.939488	+	0.342581i	$0.111301\pi$
$449$			14.5183i			0.685163i	−0.939488	+	0.342581i	$0.888699\pi$
$450$	−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
$455$	0.273519	+	0.932144i	0.0128228	+	0.0436996i
$456$	0.615242	−	10.9938i	0.0288114	−	0.514833i
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	0.725804	−	0.687901i	$-0.241468\pi$
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	−0.958642	+	0.284614i	$0.908135\pi$
$458$	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	0.946456	+	0.322834i	$0.104636\pi$
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	−0.193645	+	0.981072i	$0.562031\pi$
$462$	2.23817	−	2.09812i	0.104129	−	0.0976135i
$463$	−4.72516	+	8.18421i	−0.219597	+	0.380353i	−0.954685	−	0.297619i	$-0.903807\pi$
$463$	−4.72516	+	8.18421i	−0.219597	+	0.380353i	0.735088	+	0.677972i	$0.237141\pi$
$464$	−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	$-0.658663\pi$
$467$	−20.6623			−0.956138			−0.478069	+	0.878322i	$0.658663\pi$
$468$	−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	$-0.0920970\pi$
$479$	5.08042	+	8.79955i	0.232131	+	0.402062i	−0.726304	+	0.687373i	$0.758764\pi$
$480$	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
$483$	−24.1155	−	25.7251i	−1.09729	−	1.17053i
$484$	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
$490$	−1.17672	+	2.28049i	−0.0531587	+	0.103022i
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	0.845119	−	0.534578i	$-0.179529\pi$
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	−0.0403987	+	0.999184i	$0.512863\pi$
$492$	−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
$497$	−14.1368	−	3.43226i	−0.634122	−	0.153958i
$498$	−16.1378	+	24.6582i	−0.723150	+	1.10496i
$499$	12.5766	−	21.7834i	0.563007	−	0.975157i	−0.434225	−	0.900805i	$-0.642978\pi$
$499$	12.5766	−	21.7834i	0.563007	−	0.975157i	0.997232	−	0.0743527i	$-0.0236891\pi$
$500$	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	$-0.255593\pi$
$503$	31.1553			1.38915			0.694574	+	0.719421i	$0.255593\pi$
$504$	−7.45607	−	2.72158i	−0.332120	−	0.121229i
$505$	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	$-0.799170\pi$
$509$	2.41674	−	4.18591i	0.107120	−	0.185537i	0.914602	+	0.404354i	$0.132504\pi$
$510$	−3.16294	−	0.177006i	−0.140057	−	0.00783796i
$511$	10.4723	+	2.54255i	0.463267	+	0.112476i
$512$			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
$518$	−3.84974	−	13.1198i	−0.169148	−	0.576451i
$519$	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	$-0.625471\pi$
$521$	−17.5322			−0.768101			−0.384050	+	0.923312i	$0.625471\pi$
$522$	−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
$525$	5.07267	+	21.7123i	0.221390	+	0.947603i
$526$	−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
$546$	4.39270	+	1.33040i	0.187990	+	0.0569359i
$547$	4.94380	+	8.56292i	0.211382	+	0.366124i	0.952147	−	0.305640i	$-0.0988703\pi$
$547$	4.94380	+	8.56292i	0.211382	+	0.366124i	−0.740765	+	0.671764i	$0.765537\pi$
$548$		−	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
$553$	21.2127	−	6.22444i	0.902055	−	0.264690i
$554$	−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	$-0.914127\pi$
$557$		−	12.5800i		−	0.533034i	0.963830	−	0.266517i	$-0.0858728\pi$
$558$	18.8591	+	2.11744i	0.798371	+	0.0896384i
$559$			4.50547i			0.190561i
$560$	0.228839	−	0.942545i	0.00967023	−	0.0398298i
$561$	−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	0.487127	+	0.873331i	$0.338045\pi$
$563$	−12.1666	+	21.0732i	−0.512763	+	0.888132i	−0.999890	+	0.0148007i	$0.995289\pi$
$564$	−0.806068	+	14.4037i	−0.0339416	+	0.606506i
$565$	1.32058	−	0.762437i	0.0555572	−	0.0320760i
$566$	19.8718			0.835272
$567$	−10.6095	+	21.3176i	−0.445557	+	0.895253i
$568$	5.49843			0.230709
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	−0.661702	−	0.749767i	$-0.730166\pi$
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	0.318466	+	0.947934i	$0.396832\pi$
$570$	0.225547	−	4.03032i	0.00944711	−	0.168811i
$571$	15.7843	−	27.3392i	0.660551	−	1.14411i	−0.319920	−	0.947445i	$-0.603656\pi$
$571$	15.7843	−	27.3392i	0.660551	−	1.14411i	0.980471	−	0.196664i	$-0.0630108\pi$
$572$	0.335250	−	0.580671i	0.0140175	−	0.0242791i
$573$	−21.3781	−	42.3272i	−0.893084	−	1.76824i
$574$	11.1033	+	2.69575i	0.463442	+	0.112518i
$575$		−	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
$581$	43.1943	−	12.6745i	1.79200	−	0.525828i
$582$	−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	$-0.0361452\pi$
$587$	9.65855	+	16.7291i	0.398651	+	0.690484i	−0.594909	+	0.803793i	$0.702812\pi$
$588$	5.97096	+	10.5521i	0.246238	+	0.435163i
$589$	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	$-0.504792\pi$
$593$	−0.733196			−0.0301088			−0.0150544	+	0.999887i	$0.504792\pi$
$594$	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	0.933333	−	0.359011i	$-0.116886\pi$
$599$	26.6548	+	15.3892i	1.08909	+	0.628785i	0.155754	+	0.987796i	$0.450219\pi$
$600$	−3.79936	−	7.52245i	−0.155108	−	0.307103i
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	−0.483864	−	0.875143i	$-0.660767\pi$
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	0.515964	+	0.856610i	$0.327434\pi$
$602$	−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	−0.995676	−	0.0928949i	$-0.970388\pi$
$607$	−38.7783	−	22.3887i	−1.57396	−	0.908728i	−0.578287	−	0.815833i	$-0.696279\pi$
$608$	3.17861	−	5.50552i	0.128910	−	0.223278i
$609$	8.16166	−	1.90682i	0.330727	−	0.0772682i
$610$	−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
$616$	1.69955	−	0.498700i	0.0684769	−	0.0200932i
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	0.0469315	−	0.998898i	$-0.485056\pi$
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	−0.841605	+	0.540093i	$0.818389\pi$
$618$	1.10758	−	19.7915i	0.0445535	−	0.796132i
$619$	38.4228	−	22.1834i	1.54434	−	0.891626i	0.545785	−	0.837925i	$-0.316232\pi$
$619$	38.4228	−	22.1834i	1.54434	−	0.891626i	0.998557	−	0.0537011i	$-0.0171018\pi$
$620$			2.31905i			0.0931355i
$621$	25.4906	−	30.8027i	1.02290	−	1.23607i
$622$			9.24493i			0.370688i
$623$	6.68626	−	27.5394i	0.267880	−	1.10334i
$624$	−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
$630$	−2.73338	−	0.997727i	−0.108901	−	0.0397504i
$631$	−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
$637$	−3.78828	−	5.89936i	−0.150097	−	0.233741i
$638$		−	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	−0.688184	−	0.725537i	$-0.741592\pi$
$641$	−10.2270	+	5.90456i	−0.403942	+	0.233216i	0.284241	+	0.958753i	$0.408258\pi$
$642$	17.1020	−	8.63768i	0.674962	−	0.340902i
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.0921392	−	0.995746i	$-0.529370\pi$
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.908411	+	0.418078i	$0.862704\pi$
$644$	−5.73197	−	19.5344i	−0.225871	−	0.769762i
$645$	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	$-0.313214\pi$
$647$	28.1683			1.10741			0.553705	+	0.832713i	$0.313214\pi$
$648$	1.99582	−	8.77592i	0.0784032	−	0.344751i
$649$			5.84229i			0.229330i
$650$	2.43661	+	4.22033i	0.0955717	+	0.165535i
$651$	−19.8258	−	21.1492i	−0.777036	−	0.828901i
$652$	12.3640	−	21.4151i	0.484213	−	0.838682i
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.999431	+	0.0337326i	$0.0107394\pi$
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.528929	+	0.848666i	$0.322594\pi$
$654$	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	0.143958	−	0.989584i	$-0.454017\pi$
$659$	27.5435	−	15.9022i	1.07294	−	0.619463i	0.928984	+	0.370121i	$0.120684\pi$
$660$	−0.232778	+	0.355680i	−0.00906085	+	0.0138448i
$661$	−17.1234	−	9.88619i	−0.666022	−	0.384528i	0.128546	−	0.991704i	$-0.458969\pi$
$661$	−17.1234	−	9.88619i	−0.666022	−	0.384528i	−0.794568	+	0.607175i	$0.792302\pi$
$662$	−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
$672$	−3.13408	−	3.34328i	−0.120900	−	0.128970i
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	0.847230	−	0.531227i	$-0.178269\pi$
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	−0.883671	+	0.468109i	$0.844936\pi$
$674$		−	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	$-0.299774\pi$
$677$	−10.5661	−	18.3010i	−0.406088	−	0.703364i	−0.994447	+	0.105235i	$0.966441\pi$
$678$	0.402553	−	7.19326i	0.0154599	−	0.276255i
$679$	12.8246	+	43.7058i	0.492164	+	1.67728i
$680$	−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	$-0.946648\pi$
$683$		−	8.71972i		−	0.333651i	0.985986	−	0.166825i	$-0.0533516\pi$
$684$	−15.3495	−	11.3191i	−0.586901	−	0.432798i
$685$		−	3.29517i		−	0.125902i
$686$	3.51484	−	18.1837i	0.134197	−	0.694256i
$687$	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	$-0.554552\pi$
$691$	15.7071	−	9.06850i	0.597526	−	0.344982i	0.768068	+	0.640369i	$0.221218\pi$
$692$	4.83654			0.183858
$693$	−0.917872	−	5.23374i	−0.0348671	−	0.198814i
$694$	−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
$700$	−3.03723	+	12.5098i	−0.114796	+	0.472824i
$701$			35.6167i			1.34523i	0.739995	+	0.672613i	$0.234828\pi$
$701$			35.6167i			1.34523i	−0.739995	+	0.672613i	$0.765172\pi$
$702$	−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
$707$	−39.9384	+	11.7191i	−1.50204	+	0.440743i
$708$	13.4923	−	6.81453i	0.507071	−	0.256106i
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$	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
$714$	22.2632	−	5.20138i	0.833180	−	0.194657i
$715$	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	$-0.340357\pi$
$719$	25.7829			0.961540			0.480770	+	0.876847i	$0.340357\pi$
$720$	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	$-0.675694\pi$
$727$	−1.32423	+	0.764544i	−0.0491129	+	0.0283554i	0.475242	+	0.879855i	$0.342360\pi$
$728$	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	$-0.208000\pi$
$733$	17.9908	+	10.3870i	0.664504	+	0.383651i	−0.129487	+	0.991581i	$0.541333\pi$
$734$	9.00104	−	15.5903i	0.332234	−	0.575447i
$735$	2.18894	+	3.86839i	0.0807404	+	0.142688i
$736$	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	−0.387019	−	0.922072i	$-0.626495\pi$
$743$	−37.5906	−	21.7029i	−1.37907	−	0.796204i	−0.992047	+	0.125868i	$0.959828\pi$
$744$	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
$749$	−28.4404	−	6.90502i	−1.03919	−	0.252304i
$750$	−2.82415	−	5.59160i	−0.103123	−	0.204176i
$751$	−1.15691	+	2.00383i	−0.0422164	+	0.0731209i	−0.886362	−	0.462994i	$-0.846775\pi$
$751$	−1.15691	+	2.00383i	−0.0422164	+	0.0731209i	0.844145	+	0.536115i	$0.180109\pi$
$752$	−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
$756$	−11.0163	+	8.22446i	−0.400658	+	0.299121i
$757$	−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	$-0.972356\pi$
$761$	−11.6690	+	20.2112i	−0.422999	+	0.732656i	0.573232	+	0.819393i	$0.305689\pi$
$762$	1.30361	+	2.58105i	0.0472248	+	0.0935016i
$763$	6.59388	−	27.1589i	0.238715	−	0.983219i
$764$		−	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	$-0.226451\pi$
$769$	15.8266	+	9.13748i	0.570721	+	0.329506i	−0.186716	+	0.982414i	$0.559784\pi$
$770$	0.623052	−	0.182822i	0.0224532	−	0.00658846i
$771$	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	$-0.497490\pi$
$773$	0.438507			0.0157720			0.00788600	+	0.999969i	$0.497490\pi$
$774$	−10.8614	−	8.00953i	−0.390406	−	0.287897i
$775$		−	30.7792i		−	1.10562i
$776$	−8.60787	−	14.9093i	−0.309004	−	0.535211i
$777$	−22.6655	−	6.86462i	−0.813121	−	0.246267i
$778$	−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	$-0.0945040\pi$
$787$	33.1317	+	19.1286i	1.18102	+	0.681861i	0.224769	+	0.974412i	$0.427837\pi$
$788$	−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	0.362832	+	0.931855i	$0.381810\pi$
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	−0.988426	+	0.151706i	$0.951523\pi$
$798$	6.62777	+	28.3685i	0.234621	+	1.00423i
$799$	−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
$805$	−2.10133	−	7.16126i	−0.0740621	−	0.252401i
$806$	−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	$0.124985\pi$
$809$			21.7669i			0.765282i	−0.923897	+	0.382641i	$0.875015\pi$
$810$	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	$0.903414\pi$
$812$	4.70242	+	1.14169i	0.165022	+	0.0400656i
$813$	−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
$819$	6.09452	−	5.10433i	0.212960	−	0.178360i
$820$	−1.58318			−0.0552869
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	−0.825552	−	0.564326i	$-0.809136\pi$
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	0.0759445	+	0.997112i	$0.475803\pi$
$822$	−13.0268	−	8.52547i	−0.454360	−	0.297360i
$823$	−10.6572	+	18.4588i	−0.371486	+	0.643433i	−0.989794	−	0.142503i	$-0.954485\pi$
$823$	−10.6572	+	18.4588i	−0.371486	+	0.643433i	0.618308	+	0.785936i	$0.287818\pi$
$824$	5.72226	−	9.91124i	0.199344	−	0.345274i
$825$	3.08950	−	4.72069i	0.107562	−	0.164353i
$826$	−22.4375	−	5.44757i	−0.780701	−	0.189545i
$827$			49.7585i			1.73027i	0.501537	+	0.865136i	$0.332768\pi$
$827$			49.7585i			1.73027i	−0.501537	+	0.865136i	$0.667232\pi$
$828$	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
$833$	−31.0354	−	16.0141i	−1.07531	−	0.554854i
$834$	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	−0.999786	−	0.0206851i	$-0.993415\pi$
$839$	−14.9985	−	25.9782i	−0.517807	−	0.896868i	0.481979	−	0.876183i	$-0.339918\pi$
$840$	−1.14895	−	1.22564i	−0.0396425	−	0.0422886i
$841$	−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	$-0.496530\pi$
$853$	25.7693	−	14.8779i	0.882325	−	0.509411i	0.871424	+	0.490530i	$0.163197\pi$
$854$	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	−0.930033	−	0.367476i	$-0.880222\pi$
$857$	−22.9296	−	39.7152i	−0.783260	−	1.35665i	0.146773	−	0.989170i	$-0.453111\pi$
$858$	−0.523567	−	1.03663i	−0.0178743	−	0.0353898i
$859$	3.24073	+	1.87104i	0.110572	+	0.0638390i	0.554266	−	0.832339i	$-0.312999\pi$
$859$	3.24073	+	1.87104i	0.110572	+	0.0638390i	−0.443694	+	0.896178i	$0.646332\pi$
$860$	0.824559	−	1.42818i	0.0281172	−	0.0487005i
$861$	14.4382	−	13.5347i	0.492051	−	0.461263i
$862$	−13.6373	−	23.6206i	−0.464490	−	0.804520i
$863$			31.3944i			1.06868i	0.845270	+	0.534339i	$0.179439\pi$
$863$			31.3944i			1.06868i	−0.845270	+	0.534339i	$0.820561\pi$
$864$	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
$868$	−4.71237	−	16.0596i	−0.159948	−	0.545098i
$869$	−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
$875$	−2.25764	+	9.29878i	−0.0763221	+	0.314356i
$876$	−3.86331	+	5.90307i	−0.130529	+	0.199446i
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$	−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	$-0.616248\pi$
$881$	−21.2010			−0.714280			−0.357140	+	0.934051i	$0.616248\pi$
$882$	20.9562	+	1.35503i	0.705633	+	0.0456261i
$883$	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	$-0.800183\pi$
$887$	3.09606	−	5.36253i	0.103955	−	0.180056i	0.913311	+	0.407263i	$0.133517\pi$
$888$	8.93706	+	0.500140i	0.299908	+	0.0167836i
$889$	1.04211	−	4.29226i	0.0349513	−	0.143958i
$890$			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
$896$	−0.744936	−	2.53871i	−0.0248866	−	0.0848125i
$897$	−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
$903$	4.68988	+	20.0738i	0.156069	+	0.668016i
$904$	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	0.867095	−	0.498142i	$-0.165984\pi$
$907$	0.0645566	+	0.111815i	0.00214357	+	0.00371277i	−0.864952	+	0.501855i	$0.832651\pi$
$908$	−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	0.0797919	−	0.996812i	$-0.474574\pi$
$911$	29.6682	−	17.1290i	0.982952	−	0.567508i	0.903160	+	0.429304i	$0.141241\pi$
$912$	−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
$924$	0.889250	−	2.93611i	0.0292542	−	0.0965910i
$925$	−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	$-0.228394\pi$
$929$	−5.87364	−	10.1734i	−0.192708	−	0.333780i	−0.946147	+	0.323738i	$0.895060\pi$
$930$	3.36093	+	2.19959i	0.110209	+	0.0721274i
$931$	20.4056	−	39.5463i	0.668768	−	1.29608i
$932$	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	$-0.0137103\pi$
$938$	28.0007	+	6.79826i	0.914256	+	0.221971i
$939$	−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	$-0.771034\pi$
$941$	5.96557	−	10.3327i	0.194472	−	0.336836i	0.946727	+	0.322036i	$0.104367\pi$
$942$	−0.274324	+	4.90192i	−0.00893796	+	0.159713i
$943$	−28.7776	+	16.6148i	−0.937128	+	0.541051i
$944$	8.72695			0.284038
$945$	−4.03854	+	3.01507i	−0.131374	+	0.0980803i
$946$	3.01149			0.0979121
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	−0.387127	−	0.922026i	$-0.626533\pi$
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	0.604935	+	0.796275i	$0.293199\pi$
$948$	−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
$952$	12.8272	+	3.11429i	0.415731	+	0.100935i
$953$			3.76685i			0.122020i	0.998137	+	0.0610102i	$0.0194322\pi$
$953$			3.76685i			0.122020i	−0.998137	+	0.0610102i	$0.980568\pi$
$954$		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
$959$	6.69586	+	22.8193i	0.216221	+	0.736872i
$960$	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
$966$	−33.7472	−	10.2209i	−1.08580	−	0.328852i
$967$	−2.28741	+	3.96191i	−0.0735581	+	0.127406i	−0.900458	−	0.434942i	$-0.856769\pi$
$967$	−2.28741	+	3.96191i	−0.0735581	+	0.127406i	0.826900	+	0.562349i	$0.190102\pi$
$968$	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	$-0.363889\pi$
$971$	25.8445			0.829388			0.414694	+	0.909961i	$0.363889\pi$
$972$	−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	0.0206590	−	0.999787i	$-0.493424\pi$
$977$	−26.0950	−	15.0659i	−0.834852	−	0.482002i	−0.855511	+	0.517785i	$0.826757\pi$
$978$	−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	$-0.102237\pi$
$983$	6.30293	+	10.9170i	0.201032	+	0.348198i	−0.747829	+	0.663891i	$0.768904\pi$
$984$	−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
$987$	−8.68347	−	37.1674i	−0.276398	−	1.18305i
$988$	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
$994$	−13.9590	+	4.09598i	−0.442751	+	0.129917i
$995$	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	$-0.888834\pi$
$997$	−35.1469	+	20.2921i	−1.11311	+	0.642656i	−0.173479	+	0.984837i	$0.555501\pi$
$998$		−	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.41.7	yes	16
3.2	odd	2		378.2.m.a.125.2		16
4.3	odd	2		1008.2.cc.b.545.4		16
7.2	even	3		882.2.t.b.815.4		16
7.3	odd	6		882.2.l.a.509.8		16
7.4	even	3		882.2.l.a.509.5		16
7.5	odd	6		882.2.t.b.815.1		16
7.6	odd	2	inner	126.2.m.a.41.6	✓	16
9.2	odd	6	inner	126.2.m.a.83.6	yes	16
9.4	even	3		1134.2.d.a.1133.12		16
9.5	odd	6		1134.2.d.a.1133.5		16
9.7	even	3		378.2.m.a.251.3		16
12.11	even	2		3024.2.cc.b.881.4		16
21.2	odd	6		2646.2.t.a.2285.7		16
21.5	even	6		2646.2.t.a.2285.6		16
21.11	odd	6		2646.2.l.b.1097.2		16
21.17	even	6		2646.2.l.b.1097.3		16
21.20	even	2		378.2.m.a.125.3		16
28.27	even	2		1008.2.cc.b.545.5		16
36.7	odd	6		3024.2.cc.b.2897.5		16
36.11	even	6		1008.2.cc.b.209.5		16
63.2	odd	6		882.2.l.a.227.4		16
63.11	odd	6		882.2.t.b.803.1		16
63.13	odd	6		1134.2.d.a.1133.13		16
63.16	even	3		2646.2.l.b.521.7		16
63.20	even	6	inner	126.2.m.a.83.7	yes	16
63.25	even	3		2646.2.t.a.1979.6		16
63.34	odd	6		378.2.m.a.251.2		16
63.38	even	6		882.2.t.b.803.4		16
63.41	even	6		1134.2.d.a.1133.4		16
63.47	even	6		882.2.l.a.227.1		16
63.52	odd	6		2646.2.t.a.1979.7		16
63.61	odd	6		2646.2.l.b.521.6		16
84.83	odd	2		3024.2.cc.b.881.5		16
252.83	odd	6		1008.2.cc.b.209.4		16
252.223	even	6		3024.2.cc.b.2897.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	7.6	odd	2	inner
126.2.m.a.41.7	yes	16	1.1	even	1	trivial
126.2.m.a.83.6	yes	16	9.2	odd	6	inner
126.2.m.a.83.7	yes	16	63.20	even	6	inner
378.2.m.a.125.2		16	3.2	odd	2
378.2.m.a.125.3		16	21.20	even	2
378.2.m.a.251.2		16	63.34	odd	6
378.2.m.a.251.3		16	9.7	even	3
882.2.l.a.227.1		16	63.47	even	6
882.2.l.a.227.4		16	63.2	odd	6
882.2.l.a.509.5		16	7.4	even	3
882.2.l.a.509.8		16	7.3	odd	6
882.2.t.b.803.1		16	63.11	odd	6
882.2.t.b.803.4		16	63.38	even	6
882.2.t.b.815.1		16	7.5	odd	6
882.2.t.b.815.4		16	7.2	even	3
1008.2.cc.b.209.4		16	252.83	odd	6
1008.2.cc.b.209.5		16	36.11	even	6
1008.2.cc.b.545.4		16	4.3	odd	2
1008.2.cc.b.545.5		16	28.27	even	2
1134.2.d.a.1133.4		16	63.41	even	6
1134.2.d.a.1133.5		16	9.5	odd	6
1134.2.d.a.1133.12		16	9.4	even	3
1134.2.d.a.1133.13		16	63.13	odd	6
2646.2.l.b.521.6		16	63.61	odd	6
2646.2.l.b.521.7		16	63.16	even	3
2646.2.l.b.1097.2		16	21.11	odd	6
2646.2.l.b.1097.3		16	21.17	even	6
2646.2.t.a.1979.6		16	63.25	even	3
2646.2.t.a.1979.7		16	63.52	odd	6
2646.2.t.a.2285.6		16	21.5	even	6
2646.2.t.a.2285.7		16	21.2	odd	6
3024.2.cc.b.881.4		16	12.11	even	2
3024.2.cc.b.881.5		16	84.83	odd	2
3024.2.cc.b.2897.4		16	252.223	even	6
3024.2.cc.b.2897.5		16	36.7	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.0967785 - 1.72934i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.183299 - 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} +(-0.624224 + 2.57106i) q^{7} -1.00000i q^{8} +(-2.98127 - 0.334727i) q^{9} +O(q^{10})\)	\(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} +(-0.624224 + 2.57106i) 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} +(0.744936 + 2.53871i) 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} +(4.38584 + 1.32832i) 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} +(4.46241 - 1.04256i) 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} +(-6.22069 - 3.20983i) 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} +(2.57106 + 0.624224i) 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} +(2.72158 - 7.45607i) 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} +(0.942545 + 0.228839i) 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} +(0.498700 + 1.69955i) 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} +(3.34328 - 3.13408i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more