LMFDB - Embedded newform 1110.2.x.e.841.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (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:	$8.86339462436$
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} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 $ x^16 + 44x^14 + 724x^12 + 5750x^10 + 23344x^8 + 47024x^6 + 43297x^4 + 13976*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.8
Root			$-0.720074i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.e.751.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.04628 + 1.81222i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.04628 + 1.81222i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +5.41105 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.29896 + 2.48201i) q^{13} +2.09257i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.13772 - 1.81156i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.82628 - 2.20910i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.04628 + 1.81222i) q^{21} +(4.68611 + 2.70553i) q^{22} +7.06690i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -4.96402 q^{26} -1.00000 q^{27} +(-1.04628 + 1.81222i) q^{28} -1.37695i q^{29} +(-0.500000 - 0.866025i) q^{30} +4.90425i q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.70553 + 4.68611i) q^{33} +(-1.81156 - 3.13772i) q^{34} +(-1.81222 - 1.04628i) q^{35} -1.00000 q^{36} +(-4.57889 - 4.00422i) q^{37} +4.41821 q^{38} +(-4.29896 - 2.48201i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.54632 - 6.14241i) q^{41} +(-1.81222 + 1.04628i) q^{42} +4.69322i q^{43} +(2.70553 + 4.68611i) q^{44} -1.00000i q^{45} +(-3.53345 + 6.12012i) q^{46} +1.42519 q^{47} -1.00000 q^{48} +(1.31058 - 2.27000i) q^{49} +(0.866025 - 0.500000i) q^{50} -3.62313i q^{51} +(-4.29896 - 2.48201i) q^{52} +(-1.07681 + 1.86508i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-4.68611 + 2.70553i) q^{55} +(-1.81222 + 1.04628i) q^{56} +(3.82628 + 2.20910i) q^{57} +(0.688475 - 1.19247i) q^{58} +(12.3218 + 7.11401i) q^{59} -1.00000i q^{60} +(-2.87084 + 1.65748i) q^{61} +(-2.45212 + 4.24720i) q^{62} -2.09257 q^{63} -1.00000 q^{64} +(2.48201 - 4.29896i) q^{65} +5.41105i q^{66} +(-1.09149 - 1.89052i) q^{67} -3.62313i q^{68} +(-6.12012 + 3.53345i) q^{69} +(-1.04628 - 1.81222i) q^{70} +(7.21751 + 12.5011i) q^{71} +(-0.866025 - 0.500000i) q^{72} -13.3095 q^{73} +(-1.96332 - 5.75720i) q^{74} +1.00000 q^{75} +(3.82628 + 2.20910i) q^{76} +(5.66149 + 9.80599i) q^{77} +(-2.48201 - 4.29896i) q^{78} +(-0.685185 + 0.395592i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -7.09265i q^{82} +(7.95510 - 13.7786i) q^{83} -2.09257 q^{84} +3.62313 q^{85} +(-2.34661 + 4.06444i) q^{86} +(1.19247 - 0.688475i) q^{87} +5.41105i q^{88} +(-0.917239 - 0.529568i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-8.99587 - 5.19377i) q^{91} +(-6.12012 + 3.53345i) q^{92} +(-4.24720 + 2.45212i) q^{93} +(1.23425 + 0.712594i) q^{94} +(-2.20910 + 3.82628i) q^{95} +(-0.866025 - 0.500000i) q^{96} -9.37239i q^{97} +(2.27000 - 1.31058i) q^{98} +(-2.70553 + 4.68611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	1.04628	+	1.81222i	0.395458	+	0.684953i	0.993160	−	0.116766i	$-0.0372526\pi$
$7$	1.04628	+	1.81222i	0.395458	+	0.684953i	−0.597702	+	0.801719i	$0.703919\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	5.41105			1.63149			0.815747	−	0.578409i	$-0.196326\pi$
$11$	5.41105			1.63149			0.815747	+	0.578409i	$0.196326\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−4.29896	+	2.48201i	−1.19232	+	0.688385i	−0.958832	−	0.283975i	$-0.908347\pi$
$13$	−4.29896	+	2.48201i	−1.19232	+	0.688385i	−0.233486	+	0.972360i	$0.575013\pi$
$14$			2.09257i			0.559262i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.13772	−	1.81156i	−0.761009	−	0.439369i	0.0686487	−	0.997641i	$-0.478131\pi$
$17$	−3.13772	−	1.81156i	−0.761009	−	0.439369i	−0.829658	+	0.558272i	$0.811465\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	3.82628	−	2.20910i	0.877809	−	0.506803i	0.00787376	−	0.999969i	$-0.497494\pi$
$19$	3.82628	−	2.20910i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−1.04628	+	1.81222i	−0.228318	+	0.395458i
$22$	4.68611	+	2.70553i	0.999082	+	0.576820i
$23$			7.06690i			1.47355i	0.676137	+	0.736776i	$0.263653\pi$
$23$			7.06690i			1.47355i	−0.676137	+	0.736776i	$0.736347\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−4.96402			−0.973523
$27$	−1.00000			−0.192450
$28$	−1.04628	+	1.81222i	−0.197729	+	0.342477i
$29$		−	1.37695i		−	0.255693i	−0.991794	−	0.127847i	$-0.959193\pi$
$29$		−	1.37695i		−	0.255693i	0.991794	−	0.127847i	$-0.0408065\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			4.90425i			0.880829i	0.897794	+	0.440415i	$0.145169\pi$
$31$			4.90425i			0.880829i	−0.897794	+	0.440415i	$0.854831\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.70553	+	4.68611i	0.470972	+	0.815747i
$34$	−1.81156	−	3.13772i	−0.310681	−	0.538115i
$35$	−1.81222	−	1.04628i	−0.306320	−	0.176854i
$36$	−1.00000			−0.166667
$37$	−4.57889	−	4.00422i	−0.752765	−	0.658290i
$37$	−4.57889	−	4.00422i	−0.752765	−	0.658290i
$38$	4.41821			0.716728
$39$	−4.29896	−	2.48201i	−0.688385	−	0.397439i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−3.54632	−	6.14241i	−0.553843	−	0.959284i	−0.997993	−	0.0633311i	$-0.979828\pi$
$41$	−3.54632	−	6.14241i	−0.553843	−	0.959284i	0.444150	−	0.895952i	$-0.353506\pi$
$42$	−1.81222	+	1.04628i	−0.279631	+	0.161445i
$43$			4.69322i			0.715709i	0.933777	+	0.357854i	$0.116492\pi$
$43$			4.69322i			0.715709i	−0.933777	+	0.357854i	$0.883508\pi$
$44$	2.70553	+	4.68611i	0.407873	+	0.706458i
$45$		−	1.00000i		−	0.149071i
$46$	−3.53345	+	6.12012i	−0.520979	+	0.902362i
$47$	1.42519			0.207885			0.103942	−	0.994583i	$-0.466854\pi$
$47$	1.42519			0.207885			0.103942	+	0.994583i	$0.466854\pi$
$48$	−1.00000			−0.144338
$49$	1.31058	−	2.27000i	0.187226	−	0.324285i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	3.62313i		−	0.507340i
$52$	−4.29896	−	2.48201i	−0.596159	−	0.344193i
$53$	−1.07681	+	1.86508i	−0.147911	+	0.256189i	−0.930455	−	0.366406i	$-0.880588\pi$
$53$	−1.07681	+	1.86508i	−0.147911	+	0.256189i	0.782544	+	0.622595i	$0.213921\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−4.68611	+	2.70553i	−0.631875	+	0.364813i
$56$	−1.81222	+	1.04628i	−0.242167	+	0.139815i
$57$	3.82628	+	2.20910i	0.506803	+	0.292603i
$58$	0.688475	−	1.19247i	0.0904012	−	0.156580i
$59$	12.3218	+	7.11401i	1.60416	+	0.926165i	0.990642	+	0.136487i	$0.0435813\pi$
$59$	12.3218	+	7.11401i	1.60416	+	0.926165i	0.613522	+	0.789677i	$0.289752\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−2.87084	+	1.65748i	−0.367574	+	0.212219i	−0.672398	−	0.740190i	$-0.734736\pi$
$61$	−2.87084	+	1.65748i	−0.367574	+	0.212219i	0.304824	+	0.952409i	$0.401402\pi$
$62$	−2.45212	+	4.24720i	−0.311420	+	0.539396i
$63$	−2.09257			−0.263639
$64$	−1.00000			−0.125000
$65$	2.48201	−	4.29896i	0.307855	−	0.533221i
$66$			5.41105i			0.666055i
$67$	−1.09149	−	1.89052i	−0.133347	−	0.230963i	0.791618	−	0.611016i	$-0.209239\pi$
$67$	−1.09149	−	1.89052i	−0.133347	−	0.230963i	−0.924965	+	0.380053i	$0.875906\pi$
$68$		−	3.62313i		−	0.439369i
$69$	−6.12012	+	3.53345i	−0.736776	+	0.425378i
$70$	−1.04628	−	1.81222i	−0.125055	−	0.216601i
$71$	7.21751	+	12.5011i	0.856561	+	1.48361i	0.875190	+	0.483780i	$0.160737\pi$
$71$	7.21751	+	12.5011i	0.856561	+	1.48361i	−0.0186290	+	0.999826i	$0.505930\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	−13.3095			−1.55776			−0.778882	−	0.627170i	$-0.784213\pi$
$73$	−13.3095			−1.55776			−0.778882	+	0.627170i	$0.784213\pi$
$74$	−1.96332	−	5.75720i	−0.228232	−	0.669261i
$75$	1.00000			0.115470
$76$	3.82628	+	2.20910i	0.438905	+	0.253402i
$77$	5.66149	+	9.80599i	0.645187	+	1.11750i
$78$	−2.48201	−	4.29896i	−0.281032	−	0.486762i
$79$	−0.685185	+	0.395592i	−0.0770893	+	0.0445075i	−0.538049	−	0.842913i	$-0.680839\pi$
$79$	−0.685185	+	0.395592i	−0.0770893	+	0.0445075i	0.460960	+	0.887421i	$0.347505\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	7.09265i		−	0.783252i
$83$	7.95510	−	13.7786i	0.873185	−	1.51240i	0.0145023	−	0.999895i	$-0.495384\pi$
$83$	7.95510	−	13.7786i	0.873185	−	1.51240i	0.858683	−	0.512507i	$-0.171283\pi$
$84$	−2.09257			−0.228318
$85$	3.62313			0.392984
$86$	−2.34661	+	4.06444i	−0.253041	+	0.438280i
$87$	1.19247	−	0.688475i	0.127847	−	0.0738123i
$88$			5.41105i			0.576820i
$89$	−0.917239	−	0.529568i	−0.0972271	−	0.0561341i	0.450598	−	0.892727i	$-0.351211\pi$
$89$	−0.917239	−	0.529568i	−0.0972271	−	0.0561341i	−0.547825	+	0.836593i	$0.684544\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−8.99587	−	5.19377i	−0.943023	−	0.544455i
$92$	−6.12012	+	3.53345i	−0.638066	+	0.368388i
$93$	−4.24720	+	2.45212i	−0.440415	+	0.254274i
$94$	1.23425	+	0.712594i	0.127303	+	0.0734984i
$95$	−2.20910	+	3.82628i	−0.226649	+	0.392568i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$		−	9.37239i		−	0.951622i	−0.879548	−	0.475811i	$-0.842155\pi$
$97$		−	9.37239i		−	0.951622i	0.879548	−	0.475811i	$-0.157845\pi$
$98$	2.27000	−	1.31058i	0.229304	−	0.132389i
$99$	−2.70553	+	4.68611i	−0.271916	+	0.470972i
$100$	1.00000			0.100000
$101$	14.9451			1.48710			0.743549	−	0.668682i	$-0.233141\pi$
$101$	14.9451			1.48710			0.743549	+	0.668682i	$0.233141\pi$
$102$	1.81156	−	3.13772i	0.179372	−	0.310681i
$103$		−	11.6299i		−	1.14593i	−0.819580	−	0.572965i	$-0.805793\pi$
$103$		−	11.6299i		−	1.14593i	0.819580	−	0.572965i	$-0.194207\pi$
$104$	−2.48201	−	4.29896i	−0.243381	−	0.421548i
$105$		−	2.09257i		−	0.204214i
$106$	−1.86508	+	1.07681i	−0.181153	+	0.104589i
$107$	−6.67277	−	11.5576i	−0.645081	−	1.11731i	−0.984283	−	0.176600i	$-0.943490\pi$
$107$	−6.67277	−	11.5576i	−0.645081	−	1.11731i	0.339202	−	0.940714i	$-0.389843\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.94813	+	5.74356i	0.952858	+	0.550133i	0.893968	−	0.448132i	$-0.147910\pi$
$109$	9.94813	+	5.74356i	0.952858	+	0.550133i	0.0588905	+	0.998264i	$0.481244\pi$
$110$	−5.41105			−0.515924
$111$	1.17831	−	5.96754i	0.111840	−	0.566414i
$112$	−2.09257			−0.197729
$113$	9.12279	+	5.26705i	0.858200	+	0.495482i	0.863409	−	0.504504i	$-0.168325\pi$
$113$	9.12279	+	5.26705i	0.858200	+	0.495482i	−0.00520889	+	0.999986i	$0.501658\pi$
$114$	2.20910	+	3.82628i	0.206902	+	0.358364i
$115$	−3.53345	−	6.12012i	−0.329496	−	0.570704i
$116$	1.19247	−	0.688475i	0.110718	−	0.0639233i
$117$		−	4.96402i		−	0.458923i
$118$	7.11401	+	12.3218i	0.654897	+	1.13432i
$119$		−	7.58164i		−	0.695008i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	18.2795			1.66177
$122$	−3.31496			−0.300123
$123$	3.54632	−	6.14241i	0.319761	−	0.553843i
$124$	−4.24720	+	2.45212i	−0.381410	+	0.220207i
$125$			1.00000i			0.0894427i
$126$	−1.81222	−	1.04628i	−0.161445	−	0.0932103i
$127$	4.41753	−	7.65139i	0.391993	−	0.678951i	−0.600720	−	0.799460i	$-0.705119\pi$
$127$	4.41753	−	7.65139i	0.391993	−	0.678951i	0.992712	+	0.120509i	$0.0384525\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.06444	+	2.34661i	−0.357854	+	0.206607i
$130$	4.29896	−	2.48201i	0.377044	−	0.217686i
$131$	−0.00468949	−	0.00270748i	−0.000409722	−	0.000236553i	0.499795	−	0.866144i	$-0.333409\pi$
$131$	−0.00468949	−	0.00270748i	−0.000409722	−	0.000236553i	−0.500205	+	0.865907i	$0.666742\pi$
$132$	−2.70553	+	4.68611i	−0.235486	+	0.407873i
$133$	8.00675	+	4.62270i	0.694273	+	0.400839i
$134$		−	2.18298i		−	0.188581i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	1.81156	−	3.13772i	0.155340	−	0.269057i
$137$	13.3214			1.13812			0.569061	−	0.822295i	$-0.307307\pi$
$137$	13.3214			1.13812			0.569061	+	0.822295i	$0.307307\pi$
$138$	−7.06690			−0.601575
$139$	5.26202	−	9.11408i	0.446319	−	0.773046i	−0.551824	−	0.833960i	$-0.686068\pi$
$139$	5.26202	−	9.11408i	0.446319	−	0.773046i	0.998143	+	0.0609139i	$0.0194015\pi$
$140$		−	2.09257i		−	0.176854i
$141$	0.712594	+	1.23425i	0.0600112	+	0.103942i
$142$			14.4350i			1.21136i
$143$	−23.2619	+	13.4303i	−1.94526	+	1.12310i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.688475	+	1.19247i	0.0571748	+	0.0990296i
$146$	−11.5264	−	6.65477i	−0.953932	−	0.550753i
$147$	2.62117			0.216190
$148$	1.17831	−	5.96754i	0.0968566	−	0.490529i
$149$	−0.469855			−0.0384921			−0.0192460	−	0.999815i	$-0.506127\pi$
$149$	−0.469855			−0.0384921			−0.0192460	+	0.999815i	$0.506127\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	−3.67900	−	6.37222i	−0.299393	−	0.518564i	0.676604	−	0.736347i	$-0.263451\pi$
$151$	−3.67900	−	6.37222i	−0.299393	−	0.518564i	−0.975997	+	0.217783i	$0.930117\pi$
$152$	2.20910	+	3.82628i	0.179182	+	0.310352i
$153$	3.13772	−	1.81156i	0.253670	−	0.146456i
$154$			11.3230i			0.912432i
$155$	−2.45212	−	4.24720i	−0.196959	−	0.341144i
$156$		−	4.96402i		−	0.397439i
$157$	−5.74720	+	9.95443i	−0.458676	+	0.794450i	−0.998891	−	0.0470766i	$-0.985010\pi$
$157$	−5.74720	+	9.95443i	−0.458676	+	0.794450i	0.540215	+	0.841527i	$0.318343\pi$
$158$	−0.791183			−0.0629431
$159$	−2.15361			−0.170793
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−12.8068	+	7.39398i	−1.00931	+	0.582727i
$162$		−	1.00000i		−	0.0785674i
$163$	4.95023	+	2.85802i	0.387732	+	0.223857i	0.681177	−	0.732119i	$-0.261468\pi$
$163$	4.95023	+	2.85802i	0.387732	+	0.223857i	−0.293445	+	0.955976i	$0.594802\pi$
$164$	3.54632	−	6.14241i	0.276921	−	0.479642i
$165$	−4.68611	−	2.70553i	−0.364813	−	0.210625i
$166$	13.7786	−	7.95510i	1.06943	−	0.617435i
$167$	15.7934	−	9.11832i	1.22213	−	0.705597i	0.256758	−	0.966476i	$-0.417346\pi$
$167$	15.7934	−	9.11832i	1.22213	−	0.705597i	0.965371	+	0.260879i	$0.0840124\pi$
$168$	−1.81222	−	1.04628i	−0.139815	−	0.0807225i
$169$	5.82072	−	10.0818i	0.447748	−	0.775522i
$170$	3.13772	+	1.81156i	0.240652	+	0.138941i
$171$			4.41821i			0.337869i
$172$	−4.06444	+	2.34661i	−0.309911	+	0.178927i
$173$	−5.26410	+	9.11769i	−0.400222	+	0.693205i	−0.993752	−	0.111607i	$-0.964400\pi$
$173$	−5.26410	+	9.11769i	−0.400222	+	0.693205i	0.593530	+	0.804812i	$0.297734\pi$
$174$	1.37695			0.104386
$175$	2.09257			0.158183
$176$	−2.70553	+	4.68611i	−0.203937	+	0.353229i
$177$			14.2280i			1.06944i
$178$	−0.529568	−	0.917239i	−0.0396928	−	0.0687500i
$179$			7.53789i			0.563408i	0.959501	+	0.281704i	$0.0908997\pi$
$179$			7.53789i			0.563408i	−0.959501	+	0.281704i	$0.909100\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−4.43672	−	7.68462i	−0.329778	−	0.571193i	0.652689	−	0.757626i	$-0.273641\pi$
$181$	−4.43672	−	7.68462i	−0.329778	−	0.571193i	−0.982468	+	0.186433i	$0.940307\pi$
$182$	−5.19377	−	8.99587i	−0.384987	−	0.666818i
$183$	−2.87084	−	1.65748i	−0.212219	−	0.122525i
$184$	−7.06690			−0.520979
$185$	5.96754	+	1.17831i	0.438743	+	0.0866312i
$186$	−4.90425			−0.359597
$187$	−16.9784	−	9.80247i	−1.24158	−	0.716828i
$188$	0.712594	+	1.23425i	0.0519712	+	0.0900168i
$189$	−1.04628	−	1.81222i	−0.0761059	−	0.131819i
$190$	−3.82628	+	2.20910i	−0.277588	+	0.160265i
$191$			10.9927i			0.795404i	0.917515	+	0.397702i	$0.130192\pi$
$191$			10.9927i			0.795404i	−0.917515	+	0.397702i	$0.869808\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$			8.29710i			0.597238i	0.954372	+	0.298619i	$0.0965260\pi$
$193$			8.29710i			0.597238i	−0.954372	+	0.298619i	$0.903474\pi$
$194$	4.68619	−	8.11672i	0.336449	−	0.582747i
$195$	4.96402			0.355481
$196$	2.62117			0.187226
$197$	7.57307	−	13.1169i	0.539559	−	0.934543i	−0.459369	−	0.888246i	$-0.651924\pi$
$197$	7.57307	−	13.1169i	0.539559	−	0.934543i	0.998928	−	0.0462977i	$-0.0147423\pi$
$198$	−4.68611	+	2.70553i	−0.333027	+	0.192273i
$199$		−	16.8242i		−	1.19264i	−0.802748	−	0.596319i	$-0.796630\pi$
$199$		−	16.8242i		−	1.19264i	0.802748	−	0.596319i	$-0.203370\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	1.09149	−	1.89052i	0.0769878	−	0.133347i
$202$	12.9429	+	7.47257i	0.910658	+	0.525768i
$203$	2.49533	−	1.44068i	0.175138	−	0.101116i
$204$	3.13772	−	1.81156i	0.219684	−	0.126835i
$205$	6.14241	+	3.54632i	0.429005	+	0.247686i
$206$	5.81496	−	10.0718i	0.405148	−	0.701736i
$207$	−6.12012	−	3.53345i	−0.425378	−	0.245592i
$208$		−	4.96402i		−	0.344193i
$209$	20.7042	−	11.9536i	1.43214	−	0.826847i
$210$	1.04628	−	1.81222i	0.0722004	−	0.125055i
$211$	−5.74948			−0.395810			−0.197905	−	0.980221i	$-0.563414\pi$
$211$	−5.74948			−0.395810			−0.197905	+	0.980221i	$0.563414\pi$
$212$	−2.15361			−0.147911
$213$	−7.21751	+	12.5011i	−0.494536	+	0.856561i
$214$		−	13.3455i		−	0.912282i
$215$	−2.34661	−	4.06444i	−0.160037	−	0.277193i
$216$		−	1.00000i		−	0.0680414i
$217$	−8.88756	+	5.13123i	−0.603327	+	0.348331i
$218$	5.74356	+	9.94813i	0.389003	+	0.673772i
$219$	−6.65477	−	11.5264i	−0.449688	−	0.778882i
$220$	−4.68611	−	2.70553i	−0.315937	−	0.182407i
$221$	17.9853			1.20982
$222$	4.00422	−	4.57889i	0.268746	−	0.307315i
$223$	11.0812			0.742052			0.371026	−	0.928623i	$-0.379006\pi$
$223$	11.0812			0.742052			0.371026	+	0.928623i	$0.379006\pi$
$224$	−1.81222	−	1.04628i	−0.121084	−	0.0699077i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	5.26705	+	9.12279i	0.350359	+	0.606839i
$227$	19.0630	−	11.0060i	1.26526	−	0.730497i	0.291171	−	0.956671i	$-0.405955\pi$
$227$	19.0630	−	11.0060i	1.26526	−	0.730497i	0.974087	+	0.226174i	$0.0726219\pi$
$228$			4.41821i			0.292603i
$229$	−11.2114	−	19.4187i	−0.740871	−	1.28323i	−0.952099	−	0.305790i	$-0.901079\pi$
$229$	−11.2114	−	19.4187i	−0.740871	−	1.28323i	0.211228	−	0.977437i	$-0.432254\pi$
$230$		−	7.06690i		−	0.465978i
$231$	−5.66149	+	9.80599i	−0.372499	+	0.645187i
$232$	1.37695			0.0904012
$233$	16.1101			1.05541			0.527704	−	0.849428i	$-0.323053\pi$
$233$	16.1101			1.05541			0.527704	+	0.849428i	$0.323053\pi$
$234$	2.48201	−	4.29896i	0.162254	−	0.281032i
$235$	−1.23425	+	0.712594i	−0.0805135	+	0.0464845i
$236$			14.2280i			0.926165i
$237$	−0.685185	−	0.395592i	−0.0445075	−	0.0256964i
$238$	3.79082	−	6.56589i	0.245722	−	0.425603i
$239$	−15.3436	−	8.85862i	−0.992494	−	0.573017i	−0.0864753	−	0.996254i	$-0.527560\pi$
$239$	−15.3436	−	8.85862i	−0.992494	−	0.573017i	−0.906019	+	0.423237i	$0.860894\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	−7.55837	+	4.36383i	−0.486877	+	0.281099i	−0.723278	−	0.690557i	$-0.757366\pi$
$241$	−7.55837	+	4.36383i	−0.486877	+	0.281099i	0.236401	+	0.971656i	$0.424032\pi$
$242$	15.8305	+	9.13975i	1.01762	+	0.587525i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.87084	−	1.65748i	−0.183787	−	0.106109i
$245$			2.62117i			0.167460i
$246$	6.14241	−	3.54632i	0.391626	−	0.226105i
$247$	−10.9660	+	18.9937i	−0.697752	+	1.20854i
$248$	−4.90425			−0.311420
$249$	15.9102			1.00827
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$			28.4549i			1.79606i	0.439937	+	0.898029i	$0.355001\pi$
$251$			28.4549i			1.79606i	−0.439937	+	0.898029i	$0.644999\pi$
$252$	−1.04628	−	1.81222i	−0.0659096	−	0.114159i
$253$			38.2394i			2.40409i
$254$	7.65139	−	4.41753i	0.480091	−	0.277181i
$255$	1.81156	+	3.13772i	0.113445	+	0.196492i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.39967	+	1.38545i	0.149687	+	0.0864220i	0.572973	−	0.819574i	$-0.305790\pi$
$257$	2.39967	+	1.38545i	0.149687	+	0.0864220i	−0.423286	+	0.905996i	$0.639123\pi$
$258$	−4.69322			−0.292187
$259$	2.46569	−	12.4875i	0.153211	−	0.775934i
$260$	4.96402			0.307855
$261$	1.19247	+	0.688475i	0.0738123	+	0.0426155i
$262$	−0.00270748	−	0.00468949i	−0.000167268	−	0.000289717i
$263$	15.4986	+	26.8444i	0.955686	+	1.65530i	0.732791	+	0.680454i	$0.238217\pi$
$263$	15.4986	+	26.8444i	0.955686	+	1.65530i	0.222895	+	0.974843i	$0.428449\pi$
$264$	−4.68611	+	2.70553i	−0.288410	+	0.166514i
$265$		−	2.15361i		−	0.132295i
$266$	4.62270	+	8.00675i	0.283436	+	0.490925i
$267$		−	1.05914i		−	0.0648181i
$268$	1.09149	−	1.89052i	0.0666734	−	0.115482i
$269$	17.7605			1.08288			0.541439	−	0.840740i	$-0.317880\pi$
$269$	17.7605			1.08288			0.541439	+	0.840740i	$0.317880\pi$
$270$	1.00000			0.0608581
$271$	14.0101	−	24.2661i	0.851050	−	1.47406i	−0.0292112	−	0.999573i	$-0.509300\pi$
$271$	14.0101	−	24.2661i	0.851050	−	1.47406i	0.880261	−	0.474489i	$-0.157367\pi$
$272$	3.13772	−	1.81156i	0.190252	−	0.109842i
$273$		−	10.3875i		−	0.628682i
$274$	11.5367	+	6.66069i	0.696955	+	0.402387i
$275$	2.70553	−	4.68611i	0.163149	−	0.282583i
$276$	−6.12012	−	3.53345i	−0.368388	−	0.212689i
$277$	−9.50917	+	5.49012i	−0.571351	+	0.329869i	−0.757689	−	0.652616i	$-0.773671\pi$
$277$	−9.50917	+	5.49012i	−0.571351	+	0.329869i	0.186338	+	0.982486i	$0.440338\pi$
$278$	9.11408	−	5.26202i	0.546626	−	0.315595i
$279$	−4.24720	−	2.45212i	−0.254274	−	0.146805i
$280$	1.04628	−	1.81222i	0.0625274	−	0.108301i
$281$	−4.25746	−	2.45805i	−0.253979	−	0.146635i	0.367606	−	0.929982i	$-0.380178\pi$
$281$	−4.25746	−	2.45805i	−0.253979	−	0.146635i	−0.621585	+	0.783347i	$0.713511\pi$
$282$			1.42519i			0.0848687i
$283$	−22.2395	+	12.8400i	−1.32200	+	0.763257i	−0.984048	−	0.177905i	$-0.943068\pi$
$283$	−22.2395	+	12.8400i	−1.32200	+	0.763257i	−0.337953	+	0.941163i	$0.609735\pi$
$284$	−7.21751	+	12.5011i	−0.428280	+	0.741803i
$285$	−4.41821			−0.261712
$286$	−26.8605			−1.58830
$287$	7.42092	−	12.8534i	0.438043	−	0.758712i
$288$		−	1.00000i		−	0.0589256i
$289$	−1.93647	−	3.35406i	−0.113910	−	0.197298i
$290$			1.37695i			0.0808573i
$291$	8.11672	−	4.68619i	0.475811	−	0.274709i
$292$	−6.65477	−	11.5264i	−0.389441	−	0.674532i
$293$	−16.2196	−	28.0931i	−0.947557	−	1.64122i	−0.750548	−	0.660815i	$-0.770211\pi$
$293$	−16.2196	−	28.0931i	−0.947557	−	1.64122i	−0.197009	−	0.980402i	$-0.563123\pi$
$294$	2.27000	+	1.31058i	0.132389	+	0.0764348i
$295$	−14.2280			−0.828387
$296$	4.00422	−	4.57889i	0.232741	−	0.266143i
$297$	−5.41105			−0.313981
$298$	−0.406907	−	0.234928i	−0.0235715	−	0.0136090i
$299$	−17.5401	−	30.3804i	−1.01437	−	1.75694i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−8.50512	+	4.91043i	−0.490227	+	0.283033i
$302$		−	7.35800i		−	0.423406i
$303$	7.47257	+	12.9429i	0.429288	+	0.743549i
$304$			4.41821i			0.253402i
$305$	1.65748	−	2.87084i	0.0949072	−	0.164384i
$306$	3.62313			0.207121
$307$	−28.6918			−1.63753			−0.818765	−	0.574129i	$-0.805341\pi$
$307$	−28.6918			−1.63753			−0.818765	+	0.574129i	$0.805341\pi$
$308$	−5.66149	+	9.80599i	−0.322593	+	0.558748i
$309$	10.0718	−	5.81496i	0.572965	−	0.330802i
$310$		−	4.90425i		−	0.278543i
$311$	−12.6187	−	7.28540i	−0.715540	−	0.413117i	0.0975692	−	0.995229i	$-0.468893\pi$
$311$	−12.6187	−	7.28540i	−0.715540	−	0.413117i	−0.813109	+	0.582112i	$0.802227\pi$
$312$	2.48201	−	4.29896i	0.140516	−	0.243381i
$313$	0.735057	+	0.424385i	0.0415479	+	0.0239877i	0.520630	−	0.853782i	$-0.325697\pi$
$313$	0.735057	+	0.424385i	0.0415479	+	0.0239877i	−0.479082	+	0.877770i	$0.659030\pi$
$314$	−9.95443	+	5.74720i	−0.561761	+	0.324333i
$315$	1.81222	−	1.04628i	0.102107	−	0.0589514i
$316$	−0.685185	−	0.395592i	−0.0385446	−	0.0222538i
$317$	8.36127	−	14.4821i	0.469615	−	0.813398i	−0.529781	−	0.848134i	$-0.677726\pi$
$317$	8.36127	−	14.4821i	0.469615	−	0.813398i	0.999397	+	0.0347366i	$0.0110592\pi$
$318$	−1.86508	−	1.07681i	−0.104589	−	0.0603843i
$319$		−	7.45075i		−	0.417162i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	6.67277	−	11.5576i	0.372438	−	0.645081i
$322$	−14.7880			−0.824101
$323$	−16.0077			−0.890695
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			4.96402i			0.275354i
$326$	2.85802	+	4.95023i	0.158291	+	0.274168i
$327$			11.4871i			0.635239i
$328$	6.14241	−	3.54632i	0.339158	−	0.195813i
$329$	1.49115	+	2.58275i	0.0822097	+	0.142391i
$330$	−2.70553	−	4.68611i	−0.148934	−	0.257962i
$331$	25.0118	+	14.4406i	1.37477	+	0.793726i	0.991525	−	0.129919i	$-0.0414717\pi$
$331$	25.0118	+	14.4406i	1.37477	+	0.793726i	0.383249	+	0.923645i	$0.374805\pi$
$332$	15.9102			0.873185
$333$	5.75720	−	1.96332i	0.315493	−	0.107590i
$334$	18.2366			0.997864
$335$	1.89052	+	1.09149i	0.103290	+	0.0596345i
$336$	−1.04628	−	1.81222i	−0.0570794	−	0.0988645i
$337$	−12.2727	−	21.2570i	−0.668538	−	1.15794i	−0.978313	−	0.207132i	$-0.933587\pi$
$337$	−12.2727	−	21.2570i	−0.668538	−	1.15794i	0.309775	−	0.950810i	$-0.399746\pi$
$338$	10.0818	−	5.82072i	0.548377	−	0.316606i
$339$			10.5341i			0.572134i
$340$	1.81156	+	3.13772i	0.0982459	+	0.170167i
$341$			26.5372i			1.43707i
$342$	−2.20910	+	3.82628i	−0.119455	+	0.206902i
$343$	20.1329			1.08708
$344$	−4.69322			−0.253041
$345$	3.53345	−	6.12012i	0.190235	−	0.329496i
$346$	−9.11769	+	5.26410i	−0.490170	+	0.283000i
$347$		−	13.9012i		−	0.746257i	−0.927780	−	0.373129i	$-0.878285\pi$
$347$		−	13.9012i		−	0.746257i	0.927780	−	0.373129i	$-0.121715\pi$
$348$	1.19247	+	0.688475i	0.0639233	+	0.0369061i
$349$	−1.15032	+	1.99241i	−0.0615753	+	0.106652i	−0.895170	−	0.445725i	$-0.852946\pi$
$349$	−1.15032	+	1.99241i	−0.0615753	+	0.106652i	0.833594	+	0.552377i	$0.186279\pi$
$350$	1.81222	+	1.04628i	0.0968670	+	0.0559262i
$351$	4.29896	−	2.48201i	0.229462	−	0.132480i
$352$	−4.68611	+	2.70553i	−0.249770	+	0.144205i
$353$	−8.53811	−	4.92948i	−0.454438	−	0.262370i	0.255265	−	0.966871i	$-0.417837\pi$
$353$	−8.53811	−	4.92948i	−0.454438	−	0.262370i	−0.709703	+	0.704501i	$0.751171\pi$
$354$	−7.11401	+	12.3218i	−0.378105	+	0.654897i
$355$	−12.5011	−	7.21751i	−0.663489	−	0.383066i
$356$		−	1.05914i		−	0.0561341i
$357$	6.56589	−	3.79082i	0.347504	−	0.200631i
$358$	−3.76894	+	6.52800i	−0.199195	+	0.345016i
$359$	10.3058			0.543917			0.271959	−	0.962309i	$-0.412329\pi$
$359$	10.3058			0.543917			0.271959	+	0.962309i	$0.412329\pi$
$360$	1.00000			0.0527046
$361$	0.260287	−	0.450831i	0.0136993	−	0.0237279i
$362$		−	8.87343i		−	0.466377i
$363$	9.13975	+	15.8305i	0.479712	+	0.830886i
$364$		−	10.3875i		−	0.544455i
$365$	11.5264	−	6.65477i	0.603320	−	0.348327i
$366$	−1.65748	−	2.87084i	−0.0866380	−	0.150061i
$367$	13.5092	+	23.3986i	0.705174	+	1.22140i	0.966629	+	0.256181i	$0.0824643\pi$
$367$	13.5092	+	23.3986i	0.705174	+	1.22140i	−0.261455	+	0.965216i	$0.584202\pi$
$368$	−6.12012	−	3.53345i	−0.319033	−	0.184194i
$369$	7.09265			0.369228
$370$	4.57889	+	4.00422i	0.238045	+	0.208169i
$371$	−4.50658			−0.233970
$372$	−4.24720	−	2.45212i	−0.220207	−	0.127137i
$373$	8.86130	+	15.3482i	0.458821	+	0.794701i	0.998899	−	0.0469138i	$-0.0149386\pi$
$373$	8.86130	+	15.3482i	0.458821	+	0.794701i	−0.540078	+	0.841615i	$0.681605\pi$
$374$	−9.80247	−	16.9784i	−0.506874	−	0.877931i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$			1.42519i			0.0734984i
$377$	3.41760	+	5.91946i	0.176015	+	0.304868i
$378$		−	2.09257i		−	0.107630i
$379$	−1.27449	+	2.20749i	−0.0654663	+	0.113391i	−0.896901	−	0.442232i	$-0.854187\pi$
$379$	−1.27449	+	2.20749i	−0.0654663	+	0.113391i	0.831434	+	0.555623i	$0.187520\pi$
$380$	−4.41821			−0.226649
$381$	8.83506			0.452634
$382$	−5.49635	+	9.51996i	−0.281218	+	0.487084i
$383$	−10.9343	+	6.31291i	−0.558715	+	0.322574i	−0.752630	−	0.658444i	$-0.771215\pi$
$383$	−10.9343	+	6.31291i	−0.558715	+	0.322574i	0.193914	+	0.981018i	$0.437882\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−9.80599	−	5.66149i	−0.499760	−	0.288536i
$386$	−4.14855	+	7.18550i	−0.211156	+	0.365732i
$387$	−4.06444	−	2.34661i	−0.206607	−	0.119285i
$388$	8.11672	−	4.68619i	0.412064	−	0.237905i
$389$	6.66283	−	3.84679i	0.337819	−	0.195040i	−0.321488	−	0.946914i	$-0.604183\pi$
$389$	6.66283	−	3.84679i	0.337819	−	0.195040i	0.659307	+	0.751874i	$0.270850\pi$
$390$	4.29896	+	2.48201i	0.217686	+	0.125681i
$391$	12.8022	−	22.1740i	0.647433	−	1.12139i
$392$	2.27000	+	1.31058i	0.114652	+	0.0661945i
$393$		−	0.00541495i		−	0.000273148i
$394$	13.1169	−	7.57307i	0.660822	−	0.381526i
$395$	0.395592	−	0.685185i	0.0199044	−	0.0344754i
$396$	−5.41105			−0.271916
$397$	−12.4842			−0.626563			−0.313282	−	0.949660i	$-0.601428\pi$
$397$	−12.4842			−0.626563			−0.313282	+	0.949660i	$0.601428\pi$
$398$	8.41211	−	14.5702i	0.421661	−	0.730338i
$399$			9.24540i			0.462849i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	34.1762i		−	1.70668i	−0.521356	−	0.853339i	$-0.674574\pi$
$401$		−	34.1762i		−	1.70668i	0.521356	−	0.853339i	$-0.325426\pi$
$402$	1.89052	−	1.09149i	0.0942904	−	0.0544386i
$403$	−12.1724	−	21.0832i	−0.606350	−	1.05023i
$404$	7.47257	+	12.9429i	0.371774	+	0.643932i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	2.88136			0.142999
$407$	−24.7766	−	21.6670i	−1.22813	−	1.07400i
$408$	3.62313			0.179372
$409$	−12.0742	−	6.97104i	−0.597031	−	0.344696i	0.170842	−	0.985298i	$-0.445351\pi$
$409$	−12.0742	−	6.97104i	−0.597031	−	0.344696i	−0.767873	+	0.640603i	$0.778685\pi$
$410$	3.54632	+	6.14241i	0.175140	+	0.303352i
$411$	6.66069	+	11.5367i	0.328548	+	0.569061i
$412$	10.0718	−	5.81496i	0.496203	−	0.286483i
$413$			29.7731i			1.46504i
$414$	−3.53345	−	6.12012i	−0.173660	−	0.300787i
$415$			15.9102i			0.781001i
$416$	2.48201	−	4.29896i	0.121690	−	0.210774i
$417$	10.5240			0.515364
$418$	23.9072			1.16934
$419$	−16.2396	+	28.1278i	−0.793355	+	1.37413i	0.130523	+	0.991445i	$0.458334\pi$
$419$	−16.2396	+	28.1278i	−0.793355	+	1.37413i	−0.923878	+	0.382686i	$0.874999\pi$
$420$	1.81222	−	1.04628i	0.0884271	−	0.0510534i
$421$			30.8916i			1.50557i	0.658269	+	0.752783i	$0.271289\pi$
$421$			30.8916i			1.50557i	−0.658269	+	0.752783i	$0.728711\pi$
$422$	−4.97919	−	2.87474i	−0.242383	−	0.139940i
$423$	−0.712594	+	1.23425i	−0.0346475	+	0.0600112i
$424$	−1.86508	−	1.07681i	−0.0905765	−	0.0522943i
$425$	−3.13772	+	1.81156i	−0.152202	+	0.0878738i
$426$	−12.5011	+	7.21751i	−0.605680	+	0.349689i
$427$	−6.00743	−	3.46839i	−0.290720	−	0.167847i
$428$	6.67277	−	11.5576i	0.322541	−	0.558657i
$429$	−23.2619	−	13.4303i	−1.12310	−	0.648420i
$430$		−	4.69322i		−	0.226327i
$431$	−10.9435	+	6.31821i	−0.527128	+	0.304338i	−0.739846	−	0.672776i	$-0.765102\pi$
$431$	−10.9435	+	6.31821i	−0.527128	+	0.304338i	0.212718	+	0.977114i	$0.431768\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	6.06755			0.291588			0.145794	−	0.989315i	$-0.453426\pi$
$433$	6.06755			0.291588			0.145794	+	0.989315i	$0.453426\pi$
$434$	−10.2625			−0.492614
$435$	−0.688475	+	1.19247i	−0.0330099	+	0.0571748i
$436$			11.4871i			0.550133i
$437$	15.6115	+	27.0400i	0.746801	+	1.29350i
$438$		−	13.3095i		−	0.635955i
$439$	5.04570	−	2.91314i	0.240818	−	0.139036i	−0.374735	−	0.927132i	$-0.622266\pi$
$439$	5.04570	−	2.91314i	0.240818	−	0.139036i	0.615553	+	0.788096i	$0.288933\pi$
$440$	−2.70553	−	4.68611i	−0.128981	−	0.223401i
$441$	1.31058	+	2.27000i	0.0624087	+	0.108095i
$442$	15.5757	+	8.99263i	0.740861	+	0.427736i
$443$	−21.1567			−1.00518			−0.502592	−	0.864524i	$-0.667620\pi$
$443$	−21.1567			−1.00518			−0.502592	+	0.864524i	$0.667620\pi$
$444$	5.75720	−	1.96332i	0.273225	−	0.0931753i
$445$	1.05914			0.0502079
$446$	9.59660	+	5.54060i	0.454412	+	0.262355i
$447$	−0.234928	−	0.406907i	−0.0111117	−	0.0192460i
$448$	−1.04628	−	1.81222i	−0.0494322	−	0.0856191i
$449$	−10.7329	+	6.19665i	−0.506518	+	0.292438i	−0.731401	−	0.681948i	$-0.761133\pi$
$449$	−10.7329	+	6.19665i	−0.506518	+	0.292438i	0.224883	+	0.974386i	$0.427800\pi$
$450$			1.00000i			0.0471405i
$451$	−19.1893	−	33.2369i	−0.903591	−	1.56507i
$452$			10.5341i			0.495482i
$453$	3.67900	−	6.37222i	0.172855	−	0.299393i
$454$	22.0121			1.03308
$455$	10.3875			0.486975
$456$	−2.20910	+	3.82628i	−0.103451	+	0.179182i
$457$	−8.84100	+	5.10436i	−0.413565	+	0.238772i	−0.692320	−	0.721590i	$-0.743411\pi$
$457$	−8.84100	+	5.10436i	−0.413565	+	0.238772i	0.278755	+	0.960362i	$0.410078\pi$
$458$		−	22.4228i		−	1.04775i
$459$	3.13772	+	1.81156i	0.146456	+	0.0845566i
$460$	3.53345	−	6.12012i	0.164748	−	0.285352i
$461$	−12.6156	−	7.28362i	−0.587567	−	0.339232i	0.176568	−	0.984289i	$-0.443501\pi$
$461$	−12.6156	−	7.28362i	−0.587567	−	0.339232i	−0.764135	+	0.645056i	$0.776834\pi$
$462$	−9.80599	+	5.66149i	−0.456216	+	0.263396i
$463$	−0.123315	+	0.0711960i	−0.00573094	+	0.00330876i	−0.502863	−	0.864366i	$-0.667720\pi$
$463$	−0.123315	+	0.0711960i	−0.00573094	+	0.00330876i	0.497132	+	0.867675i	$0.334387\pi$
$464$	1.19247	+	0.688475i	0.0553592	+	0.0319617i
$465$	2.45212	−	4.24720i	0.113715	−	0.196959i
$466$	13.9518	+	8.05505i	0.646303	+	0.373143i
$467$			25.2649i			1.16912i	0.811350	+	0.584561i	$0.198733\pi$
$467$			25.2649i			1.16912i	−0.811350	+	0.584561i	$0.801267\pi$
$468$	4.29896	−	2.48201i	0.198720	−	0.114731i
$469$	2.28402	−	3.95603i	0.105466	−	0.182673i
$470$	−1.42519			−0.0657390
$471$	−11.4944			−0.529634
$472$	−7.11401	+	12.3218i	−0.327449	+	0.567158i
$473$			25.3952i			1.16767i
$474$	−0.395592	−	0.685185i	−0.0181701	−	0.0314716i
$475$		−	4.41821i		−	0.202721i
$476$	6.56589	−	3.79082i	0.300947	−	0.173752i
$477$	−1.07681	−	1.86508i	−0.0493036	−	0.0853963i
$478$	−8.85862	−	15.3436i	−0.405184	−	0.701799i
$479$	−9.77566	−	5.64398i	−0.446661	−	0.257880i	0.259758	−	0.965674i	$-0.416357\pi$
$479$	−9.77566	−	5.64398i	−0.446661	−	0.257880i	−0.706419	+	0.707794i	$0.749691\pi$
$480$	1.00000			0.0456435
$481$	29.6230	+	5.84915i	1.35069	+	0.266698i
$482$	−8.72766			−0.397534
$483$	−12.8068	−	7.39398i	−0.582727	−	0.336438i
$484$	9.13975	+	15.8305i	0.415443	+	0.719568i
$485$	4.68619	+	8.11672i	0.212789	+	0.368561i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	1.25338i		−	0.0567962i	−0.999597	−	0.0283981i	$-0.990959\pi$
$487$		−	1.25338i		−	0.0567962i	0.999597	−	0.0283981i	$-0.00904062\pi$
$488$	−1.65748	−	2.87084i	−0.0750307	−	0.129957i
$489$			5.71603i			0.258488i
$490$	−1.31058	+	2.27000i	−0.0592061	+	0.102548i
$491$	−10.8592			−0.490068			−0.245034	−	0.969514i	$-0.578799\pi$
$491$	−10.8592			−0.490068			−0.245034	+	0.969514i	$0.578799\pi$
$492$	7.09265			0.319761
$493$	−2.49443	+	4.32049i	−0.112344	+	0.194585i
$494$	−18.9937	+	10.9660i	−0.854568	+	0.493385i
$495$		−	5.41105i		−	0.243209i
$496$	−4.24720	−	2.45212i	−0.190705	−	0.110104i
$497$	−15.1031	+	26.1594i	−0.677467	+	1.17341i
$498$	13.7786	+	7.95510i	0.617435	+	0.356476i
$499$	−26.6123	+	15.3646i	−1.19133	+	0.687815i	−0.958608	−	0.284728i	$-0.908097\pi$
$499$	−26.6123	+	15.3646i	−1.19133	+	0.687815i	−0.232722	+	0.972543i	$0.574763\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	15.7934	+	9.11832i	0.705597	+	0.407376i
$502$	−14.2274	+	24.6427i	−0.635002	+	1.09986i
$503$	−1.57866	−	0.911439i	−0.0703889	−	0.0406391i	0.464392	−	0.885630i	$-0.346273\pi$
$503$	−1.57866	−	0.911439i	−0.0703889	−	0.0406391i	−0.534781	+	0.844990i	$0.679606\pi$
$504$		−	2.09257i		−	0.0932103i
$505$	−12.9429	+	7.47257i	−0.575951	+	0.332525i
$506$	−19.1197	+	33.1163i	−0.849974	+	1.47220i
$507$	11.6414			0.517015
$508$	8.83506			0.391993
$509$	1.32942	−	2.30262i	0.0589254	−	0.102062i	−0.835058	−	0.550162i	$-0.814566\pi$
$509$	1.32942	−	2.30262i	0.0589254	−	0.102062i	0.893983	+	0.448100i	$0.147899\pi$
$510$			3.62313i			0.160435i
$511$	−13.9256	−	24.1198i	−0.616030	−	1.06700i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.82628	+	2.20910i	−0.168934	+	0.0975344i
$514$	1.38545	+	2.39967i	0.0611096	+	0.105845i
$515$	5.81496	+	10.0718i	0.256238	+	0.443817i
$516$	−4.06444	−	2.34661i	−0.178927	−	0.103304i
$517$	7.71176			0.339163
$518$	8.37909	−	9.58163i	0.368156	−	0.420993i
$519$	−10.5282			−0.462137
$520$	4.29896	+	2.48201i	0.188522	+	0.108843i
$521$	−17.4759	−	30.2691i	−0.765632	−	1.32611i	−0.939912	−	0.341418i	$-0.889093\pi$
$521$	−17.4759	−	30.2691i	−0.765632	−	1.32611i	0.174279	−	0.984696i	$-0.444240\pi$
$522$	0.688475	+	1.19247i	0.0301337	+	0.0521932i
$523$	−16.8022	+	9.70075i	−0.734708	+	0.424184i	−0.820142	−	0.572160i	$-0.806106\pi$
$523$	−16.8022	+	9.70075i	−0.734708	+	0.424184i	0.0854339	+	0.996344i	$0.472772\pi$
$524$		−	0.00541495i		−	0.000236553i
$525$	1.04628	+	1.81222i	0.0456635	+	0.0790916i
$526$			30.9972i			1.35154i
$527$	8.88437	−	15.3882i	0.387009	−	0.670319i
$528$	−5.41105			−0.235486
$529$	−26.9411			−1.17135
$530$	1.07681	−	1.86508i	0.0467735	−	0.0810140i
$531$	−12.3218	+	7.11401i	−0.534721	+	0.308722i
$532$			9.24540i			0.400839i
$533$	30.4910	+	17.6040i	1.32071	+	0.762514i
$534$	0.529568	−	0.917239i	0.0229167	−	0.0396928i
$535$	11.5576	+	6.67277i	0.499678	+	0.288489i
$536$	1.89052	−	1.09149i	0.0816579	−	0.0471452i
$537$	−6.52800	+	3.76894i	−0.281704	+	0.162642i
$538$	15.3811	+	8.88025i	0.663124	+	0.382855i
$539$	7.09164	−	12.2831i	0.305458	−	0.529069i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$		−	9.13669i		−	0.392817i	−0.980522	−	0.196409i	$-0.937072\pi$
$541$		−	9.13669i		−	0.392817i	0.980522	−	0.196409i	$-0.0629279\pi$
$542$	24.2661	−	14.0101i	1.04232	−	0.601783i
$543$	4.43672	−	7.68462i	0.190398	−	0.329778i
$544$	3.62313			0.155340
$545$	−11.4871			−0.492054
$546$	5.19377	−	8.99587i	0.222273	−	0.384987i
$547$			42.4052i			1.81312i	0.422081	+	0.906558i	$0.361300\pi$
$547$			42.4052i			1.81312i	−0.422081	+	0.906558i	$0.638700\pi$
$548$	6.66069	+	11.5367i	0.284531	+	0.492821i
$549$		−	3.31496i		−	0.141479i
$550$	4.68611	−	2.70553i	0.199816	−	0.115364i
$551$	−3.04183	−	5.26860i	−0.129586	−	0.224450i
$552$	−3.53345	−	6.12012i	−0.150394	−	0.260489i
$553$	−1.43379	−	0.827801i	−0.0609711	−	0.0352017i
$554$	−10.9802			−0.466506
$555$	1.96332	+	5.75720i	0.0833385	+	0.244380i
$556$	10.5240			0.446319
$557$	−22.9514	−	13.2510i	−0.972483	−	0.561463i	−0.0724905	−	0.997369i	$-0.523095\pi$
$557$	−22.9514	−	13.2510i	−0.972483	−	0.561463i	−0.899992	+	0.435906i	$0.856428\pi$
$558$	−2.45212	−	4.24720i	−0.103807	−	0.179799i
$559$	−11.6486	−	20.1760i	−0.492683	−	0.853352i
$560$	1.81222	−	1.04628i	0.0765801	−	0.0442135i
$561$		−	19.6049i		−	0.827721i
$562$	−2.45805	−	4.25746i	−0.103686	−	0.179590i
$563$			32.5079i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$563$			32.5079i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$564$	−0.712594	+	1.23425i	−0.0300056	+	0.0519712i
$565$	−10.5341			−0.443173
$566$	−25.6800			−1.07941
$567$	1.04628	−	1.81222i	0.0439398	−	0.0761059i
$568$	−12.5011	+	7.21751i	−0.524534	+	0.302840i
$569$		−	6.74560i		−	0.282790i	−0.989953	−	0.141395i	$-0.954841\pi$
$569$		−	6.74560i		−	0.282790i	0.989953	−	0.141395i	$-0.0451588\pi$
$570$	−3.82628	−	2.20910i	−0.160265	−	0.0925292i
$571$	−2.53825	+	4.39637i	−0.106222	+	0.183982i	−0.914237	−	0.405180i	$-0.867209\pi$
$571$	−2.53825	+	4.39637i	−0.106222	+	0.183982i	0.808015	+	0.589162i	$0.200542\pi$
$572$	−23.2619	−	13.4303i	−0.972630	−	0.561548i
$573$	−9.51996	+	5.49635i	−0.397702	+	0.229613i
$574$	12.8534	−	7.42092i	0.536491	−	0.309743i
$575$	6.12012	+	3.53345i	0.255227	+	0.147355i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	18.5127	+	10.6883i	0.770693	+	0.444960i	0.833122	−	0.553090i	$-0.186551\pi$
$577$	18.5127	+	10.6883i	0.770693	+	0.444960i	−0.0624290	+	0.998049i	$0.519885\pi$
$578$		−	3.87293i		−	0.161093i
$579$	−7.18550	+	4.14855i	−0.298619	+	0.172408i
$580$	−0.688475	+	1.19247i	−0.0285874	+	0.0495148i
$581$	33.2931			1.38123
$582$	9.37239			0.388498
$583$	−5.82666	+	10.0921i	−0.241315	+	0.417971i
$584$		−	13.3095i		−	0.550753i
$585$	2.48201	+	4.29896i	0.102618	+	0.177740i
$586$		−	32.4391i		−	1.34005i
$587$	31.5988	−	18.2436i	1.30422	−	0.752994i	0.323098	−	0.946366i	$-0.395276\pi$
$587$	31.5988	−	18.2436i	1.30422	−	0.752994i	0.981126	+	0.193372i	$0.0619423\pi$
$588$	1.31058	+	2.27000i	0.0540476	+	0.0936131i
$589$	10.8340	+	18.7650i	0.446407	+	0.773200i
$590$	−12.3218	−	7.11401i	−0.507281	−	0.292879i
$591$	15.1461			0.623029
$592$	5.75720	−	1.96332i	0.236619	−	0.0806921i
$593$	2.40920			0.0989340			0.0494670	−	0.998776i	$-0.484248\pi$
$593$	2.40920			0.0989340			0.0494670	+	0.998776i	$0.484248\pi$
$594$	−4.68611	−	2.70553i	−0.192273	−	0.111009i
$595$	3.79082	+	6.56589i	0.155408	+	0.269175i
$596$	−0.234928	−	0.406907i	−0.00962301	−	0.0166675i
$597$	14.5702	−	8.41211i	0.596319	−	0.344285i
$598$		−	35.0802i		−	1.43454i
$599$	−15.3048	−	26.5087i	−0.625338	−	1.08312i	−0.988475	−	0.151381i	$-0.951628\pi$
$599$	−15.3048	−	26.5087i	−0.625338	−	1.08312i	0.363138	−	0.931735i	$-0.381705\pi$
$600$			1.00000i			0.0408248i
$601$	4.73290	−	8.19762i	0.193059	−	0.334388i	−0.753204	−	0.657788i	$-0.771492\pi$
$601$	4.73290	−	8.19762i	0.193059	−	0.334388i	0.946262	+	0.323400i	$0.104826\pi$
$602$	−9.82087			−0.400269
$603$	2.18298			0.0888979
$604$	3.67900	−	6.37222i	0.149696	−	0.259282i
$605$	−15.8305	+	9.13975i	−0.643601	+	0.371583i
$606$			14.9451i			0.607105i
$607$	−5.46378	−	3.15451i	−0.221768	−	0.128038i	0.385001	−	0.922916i	$-0.374201\pi$
$607$	−5.46378	−	3.15451i	−0.221768	−	0.128038i	−0.606769	+	0.794879i	$0.707535\pi$
$608$	−2.20910	+	3.82628i	−0.0895910	+	0.155176i
$609$	2.49533	+	1.44068i	0.101116	+	0.0583793i
$610$	2.87084	−	1.65748i	0.116237	−	0.0671095i
$611$	−6.12683	+	3.53733i	−0.247865	+	0.143105i
$612$	3.13772	+	1.81156i	0.126835	+	0.0732282i
$613$	−6.91073	+	11.9697i	−0.279122	+	0.483453i	−0.971167	−	0.238401i	$-0.923377\pi$
$613$	−6.91073	+	11.9697i	−0.279122	+	0.483453i	0.692045	+	0.721854i	$0.256710\pi$
$614$	−24.8479	−	14.3459i	−1.00278	−	0.578954i
$615$			7.09265i			0.286003i
$616$	−9.80599	+	5.66149i	−0.395095	+	0.228108i
$617$	−12.5663	+	21.7655i	−0.505902	+	0.876248i	0.494075	+	0.869419i	$0.335507\pi$
$617$	−12.5663	+	21.7655i	−0.505902	+	0.876248i	−0.999977	+	0.00682855i	$0.997826\pi$
$618$	11.6299			0.467824
$619$	−3.76403			−0.151289			−0.0756446	−	0.997135i	$-0.524101\pi$
$619$	−3.76403			−0.151289			−0.0756446	+	0.997135i	$0.524101\pi$
$620$	2.45212	−	4.24720i	0.0984797	−	0.170572i
$621$		−	7.06690i		−	0.283585i
$622$	−7.28540	−	12.6187i	−0.292118	−	0.505963i
$623$		−	2.21631i		−	0.0887947i
$624$	4.29896	−	2.48201i	0.172096	−	0.0993598i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.424385	+	0.735057i	0.0169619	+	0.0293788i
$627$	20.7042	+	11.9536i	0.826847	+	0.477380i
$628$	−11.4944			−0.458676
$629$	7.11338	+	20.8591i	0.283629	+	0.831706i
$630$	2.09257			0.0833698
$631$	−34.1150	−	19.6963i	−1.35810	−	0.784097i	−0.368728	−	0.929537i	$-0.620207\pi$
$631$	−34.1150	−	19.6963i	−1.35810	−	0.784097i	−0.989367	+	0.145440i	$0.953540\pi$
$632$	−0.395592	−	0.685185i	−0.0157358	−	0.0272552i
$633$	−2.87474	−	4.97919i	−0.114261	−	0.197905i
$634$	14.4821	−	8.36127i	0.575159	−	0.332068i
$635$			8.83506i			0.350609i
$636$	−1.07681	−	1.86508i	−0.0426982	−	0.0739554i
$637$			13.0115i			0.515535i
$638$	3.72538	−	6.45254i	0.147489	−	0.255459i
$639$	−14.4350			−0.571040
$640$	1.00000			0.0395285
$641$	−12.9263	+	22.3890i	−0.510559	+	0.884314i	0.489366	+	0.872078i	$0.337228\pi$
$641$	−12.9263	+	22.3890i	−0.510559	+	0.884314i	−0.999925	+	0.0122354i	$0.996105\pi$
$642$	11.5576	−	6.67277i	0.456141	−	0.263353i
$643$		−	50.1531i		−	1.97785i	−0.148428	−	0.988923i	$-0.547421\pi$
$643$		−	50.1531i		−	1.97785i	0.148428	−	0.988923i	$-0.452579\pi$
$644$	−12.8068	−	7.39398i	−0.504657	−	0.291364i
$645$	2.34661	−	4.06444i	0.0923976	−	0.160037i
$646$	−13.8631	−	8.00387i	−0.545437	−	0.314908i
$647$	33.5403	−	19.3645i	1.31860	−	0.761296i	0.335100	−	0.942183i	$-0.391230\pi$
$647$	33.5403	−	19.3645i	1.31860	−	0.761296i	0.983504	+	0.180886i	$0.0578967\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	66.6740	+	38.4943i	2.61718	+	1.51103i
$650$	−2.48201	+	4.29896i	−0.0973523	+	0.168619i
$651$	−8.88756	−	5.13123i	−0.348331	−	0.201109i
$652$			5.71603i			0.223857i
$653$	−4.82012	+	2.78290i	−0.188626	+	0.108903i	−0.591339	−	0.806423i	$-0.701401\pi$
$653$	−4.82012	+	2.78290i	−0.188626	+	0.108903i	0.402713	+	0.915326i	$0.368067\pi$
$654$	−5.74356	+	9.94813i	−0.224591	+	0.389003i
$655$	0.00541495			0.000211580
$656$	7.09265			0.276921
$657$	6.65477	−	11.5264i	0.259627	−	0.449688i
$658$			2.98230i			0.116262i
$659$	6.95647	+	12.0490i	0.270986	+	0.469361i	0.969114	−	0.246611i	$-0.0793171\pi$
$659$	6.95647	+	12.0490i	0.270986	+	0.469361i	−0.698129	+	0.715972i	$0.745984\pi$
$660$		−	5.41105i		−	0.210625i
$661$	6.24556	−	3.60588i	0.242924	−	0.140252i	−0.373596	−	0.927592i	$-0.621875\pi$
$661$	6.24556	−	3.60588i	0.242924	−	0.140252i	0.616520	+	0.787339i	$0.288542\pi$
$662$	14.4406	+	25.0118i	0.561249	+	0.972112i
$663$	8.99263	+	15.5757i	0.349245	+	0.604910i
$664$	13.7786	+	7.95510i	0.534715	+	0.308718i
$665$	−9.24540			−0.358521
$666$	5.96754	+	1.17831i	0.231238	+	0.0456586i
$667$	9.73078			0.376777
$668$	15.7934	+	9.11832i	0.611065	+	0.352798i
$669$	5.54060	+	9.59660i	0.214212	+	0.371026i
$670$	1.09149	+	1.89052i	0.0421680	+	0.0730370i
$671$	−15.5343	+	8.96872i	−0.599694	+	0.346234i
$672$		−	2.09257i		−	0.0807225i
$673$	−12.8878	−	22.3224i	−0.496789	−	0.860464i	0.503204	−	0.864168i	$-0.332154\pi$
$673$	−12.8878	−	22.3224i	−0.496789	−	0.860464i	−0.999993	+	0.00370382i	$0.998821\pi$
$674$		−	24.5455i		−	0.945456i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	11.6414			0.447748
$677$	−17.4978			−0.672496			−0.336248	−	0.941774i	$-0.609158\pi$
$677$	−17.4978			−0.672496			−0.336248	+	0.941774i	$0.609158\pi$
$678$	−5.26705	+	9.12279i	−0.202280	+	0.350359i
$679$	16.9848	−	9.80617i	0.651816	−	0.376326i
$680$			3.62313i			0.138941i
$681$	19.0630	+	11.0060i	0.730497	+	0.421753i
$682$	−13.2686	+	22.9818i	−0.508080	+	0.880021i
$683$	−26.1499	−	15.0977i	−1.00060	−	0.577697i	−0.0921742	−	0.995743i	$-0.529382\pi$
$683$	−26.1499	−	15.0977i	−1.00060	−	0.577697i	−0.908426	+	0.418046i	$0.862715\pi$
$684$	−3.82628	+	2.20910i	−0.146302	+	0.0844672i
$685$	−11.5367	+	6.66069i	−0.440793	+	0.254492i
$686$	17.4356	+	10.0665i	0.665695	+	0.384339i
$687$	11.2114	−	19.4187i	0.427742	−	0.740871i
$688$	−4.06444	−	2.34661i	−0.154955	−	0.0894636i
$689$		−	10.6906i		−	0.407278i
$690$	6.12012	−	3.53345i	0.232989	−	0.134516i
$691$	1.71675	−	2.97350i	0.0653084	−	0.113117i	−0.831522	−	0.555491i	$-0.812530\pi$
$691$	1.71675	−	2.97350i	0.0653084	−	0.113117i	0.896831	+	0.442374i	$0.145864\pi$
$692$	−10.5282			−0.400222
$693$	−11.3230			−0.430125
$694$	6.95062	−	12.0388i	0.263842	−	0.456987i
$695$			10.5240i			0.399199i
$696$	0.688475	+	1.19247i	0.0260966	+	0.0452006i
$697$			25.6976i			0.973365i
$698$	−1.99241	+	1.15032i	−0.0754140	+	0.0435403i
$699$	8.05505	+	13.9518i	0.304670	+	0.527704i
$700$	1.04628	+	1.81222i	0.0395458	+	0.0684953i
$701$	−36.7040	−	21.1911i	−1.38629	−	0.800375i	−0.393395	−	0.919369i	$-0.628700\pi$
$701$	−36.7040	−	21.1911i	−1.38629	−	0.800375i	−0.992895	+	0.118994i	$0.962033\pi$
$702$	4.96402			0.187355
$703$	−26.3659	−	5.20603i	−0.994407	−	0.196349i
$704$	−5.41105			−0.203937
$705$	−1.23425	−	0.712594i	−0.0464845	−	0.0268378i
$706$	−4.92948	−	8.53811i	−0.185523	−	0.321336i
$707$	15.6369	+	27.0838i	0.588084	+	1.01859i
$708$	−12.3218	+	7.11401i	−0.463082	+	0.267361i
$709$			13.5081i			0.507308i	0.967295	+	0.253654i	$0.0816325\pi$
$709$			13.5081i			0.507308i	−0.967295	+	0.253654i	$0.918367\pi$
$710$	−7.21751	−	12.5011i	−0.270868	−	0.469158i
$711$		−	0.791183i		−	0.0296717i
$712$	0.529568	−	0.917239i	0.0198464	−	0.0343750i
$713$	−34.6579			−1.29795
$714$	7.58164			0.283736
$715$	13.4303	−	23.2619i	0.502264	−	0.869946i
$716$	−6.52800	+	3.76894i	−0.243963	+	0.140852i
$717$		−	17.7172i		−	0.661663i
$718$	8.92505	+	5.15288i	0.333080	+	0.192304i
$719$	−14.8863	+	25.7839i	−0.555167	+	0.961578i	0.442723	+	0.896658i	$0.354012\pi$
$719$	−14.8863	+	25.7839i	−0.555167	+	0.961578i	−0.997891	+	0.0649193i	$0.979321\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	21.0759	−	12.1682i	0.784909	−	0.453167i
$722$	0.450831	−	0.260287i	0.0167782	−	0.00968689i
$723$	−7.55837	−	4.36383i	−0.281099	−	0.162292i
$724$	4.43672	−	7.68462i	0.164889	−	0.285597i
$725$	−1.19247	−	0.688475i	−0.0442874	−	0.0255693i
$726$			18.2795i			0.678416i
$727$	−24.1236	+	13.9277i	−0.894694	+	0.516552i	−0.875475	−	0.483264i	$-0.839451\pi$
$727$	−24.1236	+	13.9277i	−0.894694	+	0.516552i	−0.0192187	+	0.999815i	$0.506118\pi$
$728$	5.19377	−	8.99587i	0.192494	−	0.333409i
$729$	1.00000			0.0370370
$730$	13.3095			0.492608
$731$	8.50206	−	14.7260i	0.314460	−	0.544661i
$732$		−	3.31496i		−	0.122525i
$733$	25.0936	+	43.4634i	0.926853	+	1.60536i	0.788554	+	0.614965i	$0.210830\pi$
$733$	25.0936	+	43.4634i	0.926853	+	1.60536i	0.138298	+	0.990391i	$0.455837\pi$
$734$			27.0184i			0.997266i
$735$	−2.27000	+	1.31058i	−0.0837301	+	0.0483416i
$736$	−3.53345	−	6.12012i	−0.130245	−	0.225591i
$737$	−5.90611	−	10.2297i	−0.217554	−	0.376815i
$738$	6.14241	+	3.54632i	0.226105	+	0.130542i
$739$	−5.34756			−0.196713			−0.0983566	−	0.995151i	$-0.531359\pi$
$739$	−5.34756			−0.196713			−0.0983566	+	0.995151i	$0.531359\pi$
$740$	1.96332	+	5.75720i	0.0721732	+	0.211639i
$741$	−21.9321			−0.805694
$742$	−3.90281	−	2.25329i	−0.143277	−	0.0827208i
$743$	21.1205	+	36.5817i	0.774835	+	1.34205i	0.934887	+	0.354945i	$0.115500\pi$
$743$	21.1205	+	36.5817i	0.774835	+	1.34205i	−0.160052	+	0.987109i	$0.551166\pi$
$744$	−2.45212	−	4.24720i	−0.0898993	−	0.155710i
$745$	0.406907	−	0.234928i	0.0149079	−	0.00860708i
$746$			17.7226i			0.648871i
$747$	7.95510	+	13.7786i	0.291062	+	0.504134i
$748$		−	19.6049i		−	0.716828i
$749$	13.9632	−	24.1850i	0.510205	−	0.883701i
$750$	−1.00000			−0.0365148
$751$	−18.0497			−0.658643			−0.329321	−	0.944218i	$-0.606820\pi$
$751$	−18.0497			−0.658643			−0.329321	+	0.944218i	$0.606820\pi$
$752$	−0.712594	+	1.23425i	−0.0259856	+	0.0450084i
$753$	−24.6427	+	14.2274i	−0.898029	+	0.518477i
$754$			6.83520i			0.248923i
$755$	6.37222	+	3.67900i	0.231909	+	0.133893i
$756$	1.04628	−	1.81222i	0.0380529	−	0.0659096i
$757$	−17.8525	−	10.3072i	−0.648862	−	0.374621i	0.139158	−	0.990270i	$-0.455560\pi$
$757$	−17.8525	−	10.3072i	−0.648862	−	0.374621i	−0.788020	+	0.615650i	$0.788894\pi$
$758$	−2.20749	+	1.27449i	−0.0801795	+	0.0462917i
$759$	−33.1163	+	19.1197i	−1.20204	+	0.694001i
$760$	−3.82628	−	2.20910i	−0.138794	−	0.0801327i
$761$	−18.6379	+	32.2819i	−0.675625	+	1.17022i	0.300661	+	0.953731i	$0.402793\pi$
$761$	−18.6379	+	32.2819i	−0.675625	+	1.17022i	−0.976286	+	0.216485i	$0.930541\pi$
$762$	7.65139	+	4.41753i	0.277181	+	0.160030i
$763$			24.0375i			0.870217i
$764$	−9.51996	+	5.49635i	−0.344420	+	0.198851i
$765$	−1.81156	+	3.13772i	−0.0654973	+	0.113445i
$766$	−12.6258			−0.456189
$767$	−70.6281			−2.55023
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	41.7173i		−	1.50437i	−0.658955	−	0.752183i	$-0.729001\pi$
$769$		−	41.7173i		−	1.50437i	0.658955	−	0.752183i	$-0.270999\pi$
$770$	−5.66149	−	9.80599i	−0.204026	−	0.353383i
$771$			2.77090i			0.0997915i
$772$	−7.18550	+	4.14855i	−0.258612	+	0.149310i
$773$	−13.0027	−	22.5213i	−0.467674	−	0.810035i	0.531644	−	0.846968i	$-0.321574\pi$
$773$	−13.0027	−	22.5213i	−0.467674	−	0.810035i	−0.999318	+	0.0369333i	$0.988241\pi$
$774$	−2.34661	−	4.06444i	−0.0843471	−	0.146093i
$775$	4.24720	+	2.45212i	0.152564	+	0.0880829i
$776$	9.37239			0.336449
$777$	12.0473	−	4.10839i	0.432195	−	0.147388i
$778$	7.69358			0.275828
$779$	−27.1385	−	15.6684i	−0.972336	−	0.561379i
$780$	2.48201	+	4.29896i	0.0888701	+	0.153928i
$781$	39.0543	+	67.6441i	1.39747	+	2.42049i
$782$	22.1740	−	12.8022i	0.792940	−	0.457804i
$783$			1.37695i			0.0492082i
$784$	1.31058	+	2.27000i	0.0468066	+	0.0810713i
$785$		−	11.4944i		−	0.410252i
$786$	0.00270748	−	0.00468949i	9.65725e−5	−	0.000167268i
$787$	31.5096			1.12320			0.561598	−	0.827410i	$-0.310187\pi$
$787$	31.5096			1.12320			0.561598	+	0.827410i	$0.310187\pi$
$788$	15.1461			0.539559
$789$	−15.4986	+	26.8444i	−0.551765	+	0.955686i
$790$	0.685185	−	0.395592i	0.0243778	−	0.0140745i
$791$			22.0433i			0.783769i
$792$	−4.68611	−	2.70553i	−0.166514	−	0.0961367i
$793$	8.22777	−	14.2509i	0.292177	−	0.506065i
$794$	−10.8116	−	6.24209i	−0.383690	−	0.221524i
$795$	1.86508	−	1.07681i	0.0661477	−	0.0381904i
$796$	14.5702	−	8.41211i	0.516427	−	0.298159i
$797$	14.9898	+	8.65439i	0.530968	+	0.306554i	0.741410	−	0.671052i	$-0.234157\pi$
$797$	14.9898	+	8.65439i	0.530968	+	0.306554i	−0.210443	+	0.977606i	$0.567491\pi$
$798$	−4.62270	+	8.00675i	−0.163642	+	0.283436i
$799$	−4.47184	−	2.58182i	−0.158202	−	0.0913382i
$800$			1.00000i			0.0353553i
$801$	0.917239	−	0.529568i	0.0324090	−	0.0187114i
$802$	17.0881	−	29.5975i	0.603402	−	1.04512i
$803$	−72.0187			−2.54148
$804$	2.18298			0.0769878
$805$	7.39398	−	12.8068i	0.260604	−	0.451379i
$806$		−	24.3448i		−	0.857508i
$807$	8.88025	+	15.3811i	0.312600	+	0.541439i
$808$			14.9451i			0.525768i
$809$	33.1143	−	19.1185i	1.16424	−	0.672172i	0.211920	−	0.977287i	$-0.432028\pi$
$809$	33.1143	−	19.1185i	1.16424	−	0.672172i	0.952316	+	0.305115i	$0.0986949\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	1.04886	+	1.81667i	0.0368304	+	0.0637921i	0.883853	−	0.467765i	$-0.154941\pi$
$811$	1.04886	+	1.81667i	0.0368304	+	0.0637921i	−0.847023	+	0.531557i	$0.821607\pi$
$812$	2.49533	+	1.44068i	0.0875689	+	0.0505580i
$813$	28.0201			0.982708
$814$	−10.6237	−	31.1525i	−0.372359	−	1.09190i
$815$	−5.71603			−0.200224
$816$	3.13772	+	1.81156i	0.109842	+	0.0634174i
$817$	10.3678	+	17.9576i	0.362724	+	0.628256i
$818$	−6.97104	−	12.0742i	−0.243737	−	0.422164i
$819$	8.99587	−	5.19377i	0.314341	−	0.181485i
$820$			7.09265i			0.247686i
$821$	−10.0829	−	17.4641i	−0.351896	−	0.609502i	0.634686	−	0.772770i	$-0.281130\pi$
$821$	−10.0829	−	17.4641i	−0.351896	−	0.609502i	−0.986582	+	0.163269i	$0.947796\pi$
$822$			13.3214i			0.464636i
$823$	19.6384	−	34.0146i	0.684550	−	1.18568i	−0.289028	−	0.957321i	$-0.593332\pi$
$823$	19.6384	−	34.0146i	0.684550	−	1.18568i	0.973578	−	0.228355i	$-0.0733346\pi$
$824$	11.6299			0.405148
$825$	5.41105			0.188389
$826$	−14.8865	+	25.7842i	−0.517969	+	0.897148i
$827$	−10.2489	+	5.91721i	−0.356390	+	0.205762i	−0.667496	−	0.744613i	$-0.732634\pi$
$827$	−10.2489	+	5.91721i	−0.356390	+	0.205762i	0.311106	+	0.950375i	$0.399300\pi$
$828$		−	7.06690i		−	0.245592i
$829$	−5.13044	−	2.96206i	−0.178188	−	0.102877i	0.408253	−	0.912869i	$-0.366138\pi$
$829$	−5.13044	−	2.96206i	−0.178188	−	0.102877i	−0.586441	+	0.809992i	$0.699471\pi$
$830$	−7.95510	+	13.7786i	−0.276125	+	0.478263i
$831$	−9.50917	−	5.49012i	−0.329869	−	0.190450i
$832$	4.29896	−	2.48201i	0.149040	−	0.0860481i
$833$	−8.22449	+	4.74841i	−0.284962	+	0.164523i
$834$	9.11408	+	5.26202i	0.315595	+	0.182209i
$835$	−9.11832	+	15.7934i	−0.315552	+	0.546553i
$836$	20.7042	+	11.9536i	0.716070	+	0.413423i
$837$		−	4.90425i		−	0.169516i
$838$	−28.1278	+	16.2396i	−0.971658	+	0.560987i
$839$	−13.6379	+	23.6215i	−0.470832	+	0.815506i	−0.999443	−	0.0333584i	$-0.989380\pi$
$839$	−13.6379	+	23.6215i	−0.470832	+	0.815506i	0.528611	+	0.848864i	$0.322713\pi$
$840$	2.09257			0.0722004
$841$	27.1040			0.934621
$842$	−15.4458	+	26.7529i	−0.532298	+	0.921967i
$843$		−	4.91609i		−	0.169319i
$844$	−2.87474	−	4.97919i	−0.0989526	−	0.171391i
$845$			11.6414i			0.400478i
$846$	−1.23425	+	0.712594i	−0.0424343	+	0.0244995i
$847$	19.1255	+	33.1264i	0.657161	+	1.13824i
$848$	−1.07681	−	1.86508i	−0.0369777	−	0.0640472i
$849$	−22.2395	−	12.8400i	−0.763257	−	0.440667i
$850$	−3.62313			−0.124272
$851$	28.2974	−	32.3586i	0.970023	−	1.10924i
$852$	−14.4350			−0.494536
$853$	28.9444	+	16.7111i	0.991038	+	0.572176i	0.905584	−	0.424166i	$-0.139433\pi$
$853$	28.9444	+	16.7111i	0.991038	+	0.572176i	0.0854536	+	0.996342i	$0.472766\pi$
$854$	−3.46839	−	6.00743i	−0.118686	−	0.205570i
$855$	−2.20910	−	3.82628i	−0.0755498	−	0.130856i
$856$	11.5576	−	6.67277i	0.395030	−	0.228071i
$857$		−	3.11052i		−	0.106253i	−0.998588	−	0.0531267i	$-0.983081\pi$
$857$		−	3.11052i		−	0.106253i	0.998588	−	0.0531267i	$-0.0169187\pi$
$858$	−13.4303	−	23.2619i	−0.458502	−	0.794149i
$859$			35.9055i			1.22508i	0.790440	+	0.612540i	$0.209852\pi$
$859$			35.9055i			1.22508i	−0.790440	+	0.612540i	$0.790148\pi$
$860$	2.34661	−	4.06444i	0.0800187	−	0.138596i
$861$	14.8418			0.505808
$862$	−12.6364			−0.430398
$863$	1.64827	−	2.85488i	0.0561076	−	0.0971813i	−0.836607	−	0.547803i	$-0.815464\pi$
$863$	1.64827	−	2.85488i	0.0561076	−	0.0971813i	0.892715	+	0.450622i	$0.148798\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		−	10.5282i		−	0.357970i
$866$	5.25465	+	3.03377i	0.178560	+	0.103092i
$867$	1.93647	−	3.35406i	0.0657659	−	0.113910i
$868$	−8.88756	−	5.13123i	−0.301663	−	0.174165i
$869$	−3.70757	+	2.14057i	−0.125771	+	0.0726137i
$870$	−1.19247	+	0.688475i	−0.0404287	+	0.0233415i
$871$	9.38456	+	5.41818i	0.317984	+	0.183588i
$872$	−5.74356	+	9.94813i	−0.194501	+	0.336886i
$873$	8.11672	+	4.68619i	0.274709	+	0.158604i
$874$			31.2231i			1.05614i
$875$	−1.81222	+	1.04628i	−0.0612641	+	0.0353708i
$876$	6.65477	−	11.5264i	0.224844	−	0.389441i
$877$	−6.01214			−0.203016			−0.101508	−	0.994835i	$-0.532367\pi$
$877$	−6.01214			−0.203016			−0.101508	+	0.994835i	$0.532367\pi$
$878$	5.82627			0.196627
$879$	16.2196	−	28.0931i	0.547072	−	0.947557i
$880$		−	5.41105i		−	0.182407i
$881$	−8.21596	−	14.2305i	−0.276803	−	0.479436i	0.693786	−	0.720182i	$-0.255941\pi$
$881$	−8.21596	−	14.2305i	−0.276803	−	0.479436i	−0.970588	+	0.240745i	$0.922608\pi$
$882$			2.62117i			0.0882593i
$883$	41.8608	−	24.1684i	1.40873	−	0.813330i	0.413464	−	0.910521i	$-0.364319\pi$
$883$	41.8608	−	24.1684i	1.40873	−	0.813330i	0.995266	+	0.0971901i	$0.0309855\pi$
$884$	8.99263	+	15.5757i	0.302455	+	0.523867i
$885$	−7.11401	−	12.3218i	−0.239135	−	0.414193i
$886$	−18.3222	−	10.5783i	−0.615547	−	0.355386i
$887$	20.1938			0.678041			0.339020	−	0.940779i	$-0.389904\pi$
$887$	20.1938			0.678041			0.339020	+	0.940779i	$0.389904\pi$
$888$	5.96754	+	1.17831i	0.200258	+	0.0395415i
$889$	18.4880			0.620066
$890$	0.917239	+	0.529568i	0.0307459	+	0.0177512i
$891$	−2.70553	−	4.68611i	−0.0906385	−	0.156991i
$892$	5.54060	+	9.59660i	0.185513	+	0.321318i
$893$	5.45317	−	3.14839i	0.182483	−	0.105357i
$894$		−	0.469855i		−	0.0157143i
$895$	−3.76894	−	6.52800i	−0.125982	−	0.218207i
$896$		−	2.09257i		−	0.0699077i
$897$	17.5401	−	30.3804i	0.585647	−	1.01437i
$898$	−12.3933			−0.413570
$899$	6.75291			0.225222
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	6.75744	−	3.90141i	0.225123	−	0.129975i
$902$		−	38.3787i		−	1.27787i
$903$	−8.50512	−	4.91043i	−0.283033	−	0.163409i
$904$	−5.26705	+	9.12279i	−0.175179	+	0.303420i
$905$	7.68462	+	4.43672i	0.255445	+	0.147481i
$906$	6.37222	−	3.67900i	0.211703	−	0.122227i
$907$	18.2056	−	10.5110i	0.604508	−	0.349013i	−0.166305	−	0.986074i	$-0.553184\pi$
$907$	18.2056	−	10.5110i	0.604508	−	0.349013i	0.770813	+	0.637062i	$0.219850\pi$
$908$	19.0630	+	11.0060i	0.632629	+	0.365248i
$909$	−7.47257	+	12.9429i	−0.247850	+	0.429288i
$910$	8.99587	+	5.19377i	0.298210	+	0.172172i
$911$		−	30.4267i		−	1.00808i	−0.863680	−	0.504041i	$-0.831846\pi$
$911$		−	30.4267i		−	1.00808i	0.863680	−	0.504041i	$-0.168154\pi$
$912$	−3.82628	+	2.20910i	−0.126701	+	0.0731508i
$913$	43.0455	−	74.5569i	1.42460	−	2.46747i
$914$	−10.2087			−0.337674
$915$	3.31496			0.109589
$916$	11.2114	−	19.4187i	0.370436	−	0.641613i
$917$		−	0.0113311i		−	0.000374187i
$918$	1.81156	+	3.13772i	0.0597905	+	0.103560i
$919$			3.14496i			0.103743i	0.998654	+	0.0518713i	$0.0165186\pi$
$919$			3.14496i			0.103743i	−0.998654	+	0.0518713i	$0.983481\pi$
$920$	6.12012	−	3.53345i	0.201774	−	0.116494i
$921$	−14.3459	−	24.8479i	−0.472714	−	0.818765i
$922$	−7.28362	−	12.6156i	−0.239873	−	0.415473i
$923$	−62.0556	−	35.8278i	−2.04259	−	1.17929i
$924$	−11.3230			−0.372499
$925$	−5.75720	+	1.96332i	−0.189296	+	0.0645537i
$926$	−0.142392			−0.00467929
$927$	10.0718	+	5.81496i	0.330802	+	0.190988i
$928$	0.688475	+	1.19247i	0.0226003	+	0.0391449i
$929$	14.3792	+	24.9055i	0.471766	+	0.817122i	0.999478	−	0.0323010i	$-0.0102835\pi$
$929$	14.3792	+	24.9055i	0.471766	+	0.817122i	−0.527713	+	0.849423i	$0.676950\pi$
$930$	4.24720	−	2.45212i	0.139271	−	0.0804083i
$931$		−	11.5809i		−	0.379548i
$932$	8.05505	+	13.9518i	0.263852	+	0.457005i
$933$		−	14.5708i		−	0.477026i
$934$	−12.6325	+	21.8801i	−0.413347	+	0.715938i
$935$	19.6049			0.641150
$936$	4.96402			0.162254
$937$	−28.5706	+	49.4858i	−0.933362	+	1.61663i	−0.155832	+	0.987784i	$0.549806\pi$
$937$	−28.5706	+	49.4858i	−0.933362	+	1.61663i	−0.777529	+	0.628847i	$0.783527\pi$
$938$	3.95603	−	2.28402i	0.129169	−	0.0745758i
$939$			0.848771i			0.0276986i
$940$	−1.23425	−	0.712594i	−0.0402567	−	0.0232422i
$941$	−20.3755	+	35.2913i	−0.664221	+	1.15047i	0.315274	+	0.949001i	$0.397903\pi$
$941$	−20.3755	+	35.2913i	−0.664221	+	1.15047i	−0.979496	+	0.201465i	$0.935430\pi$
$942$	−9.95443	−	5.74720i	−0.324333	−	0.187254i
$943$	43.4078	−	25.0615i	1.41355	−	0.816115i
$944$	−12.3218	+	7.11401i	−0.401041	+	0.231541i
$945$	1.81222	+	1.04628i	0.0589514	+	0.0340356i
$946$	−12.6976	+	21.9929i	−0.412835	+	0.715052i
$947$	23.3276	+	13.4682i	0.758046	+	0.437658i	0.828594	−	0.559850i	$-0.189141\pi$
$947$	23.3276	+	13.4682i	0.758046	+	0.437658i	−0.0705479	+	0.997508i	$0.522475\pi$
$948$		−	0.791183i		−	0.0256964i
$949$	57.2173	−	33.0344i	1.85735	−	1.07234i
$950$	2.20910	−	3.82628i	0.0716728	−	0.124141i
$951$	16.7225			0.542265
$952$	7.58164			0.245722
$953$	15.1718	−	26.2783i	0.491462	−	0.851237i	−0.508490	−	0.861068i	$-0.669796\pi$
$953$	15.1718	−	26.2783i	0.491462	−	0.851237i	0.999952	+	0.00983074i	$0.00312927\pi$
$954$		−	2.15361i		−	0.0697258i
$955$	−5.49635	−	9.51996i	−0.177858	−	0.308059i
$956$		−	17.7172i		−	0.573017i
$957$	6.45254	−	3.72538i	0.208581	−	0.120424i
$958$	−5.64398	−	9.77566i	−0.182349	−	0.315837i
$959$	13.9379	+	24.1412i	0.450079	+	0.779560i
$960$	0.866025	+	0.500000i	0.0279508	+	0.0161374i
$961$	6.94833			0.224140
$962$	22.7297	+	19.8770i	0.732834	+	0.640860i
$963$	13.3455			0.430054
$964$	−7.55837	−	4.36383i	−0.243439	−	0.140549i
$965$	−4.14855	−	7.18550i	−0.133547	−	0.231309i
$966$	−7.39398	−	12.8068i	−0.237897	−	0.412050i
$967$	50.2231	−	28.9963i	1.61506	−	0.932458i	0.626893	−	0.779105i	$-0.284326\pi$
$967$	50.2231	−	28.9963i	1.61506	−	0.932458i	0.988171	−	0.153353i	$-0.0490072\pi$
$968$			18.2795i			0.587525i
$969$	−8.00387	−	13.8631i	−0.257121	−	0.445347i
$970$			9.37239i			0.300929i
$971$	−30.2927	+	52.4684i	−0.972138	+	1.68379i	−0.283063	+	0.959101i	$0.591350\pi$
$971$	−30.2927	+	52.4684i	−0.972138	+	1.68379i	−0.689075	+	0.724690i	$0.741983\pi$
$972$	1.00000			0.0320750
$973$	22.0222			0.706001
$974$	0.626692	−	1.08546i	0.0200805	−	0.0347804i
$975$	−4.29896	+	2.48201i	−0.137677	+	0.0794879i
$976$		−	3.31496i		−	0.106109i
$977$	−15.2738	−	8.81834i	−0.488652	−	0.282124i	0.235363	−	0.971908i	$-0.424372\pi$
$977$	−15.2738	−	8.81834i	−0.488652	−	0.282124i	−0.724015	+	0.689784i	$0.757706\pi$
$978$	−2.85802	+	4.95023i	−0.0913893	+	0.158291i
$979$	−4.96323	−	2.86552i	−0.158625	−	0.0915824i
$980$	−2.27000	+	1.31058i	−0.0725124	+	0.0418651i
$981$	−9.94813	+	5.74356i	−0.317619	+	0.183378i
$982$	−9.40433	−	5.42959i	−0.300104	−	0.173265i
$983$	26.2965	−	45.5469i	0.838728	−	1.45272i	−0.0522299	−	0.998635i	$-0.516633\pi$
$983$	26.2965	−	45.5469i	0.838728	−	1.45272i	0.890958	−	0.454085i	$-0.150034\pi$
$984$	6.14241	+	3.54632i	0.195813	+	0.113053i
$985$			15.1461i			0.482596i
$986$	−4.32049	+	2.49443i	−0.137592	+	0.0794390i
$987$	−1.49115	+	2.58275i	−0.0474638	+	0.0822097i
$988$	−21.9321			−0.697752
$989$	−33.1665			−1.05463
$990$	2.70553	−	4.68611i	0.0859873	−	0.148934i
$991$		−	23.1257i		−	0.734611i	−0.930100	−	0.367305i	$-0.880280\pi$
$991$		−	23.1257i		−	0.734611i	0.930100	−	0.367305i	$-0.119720\pi$
$992$	−2.45212	−	4.24720i	−0.0778550	−	0.134849i
$993$			28.8812i			0.916516i
$994$	−26.1594	+	15.1031i	−0.829724	+	0.479042i
$995$	8.41211	+	14.5702i	0.266682	+	0.461906i
$996$	7.95510	+	13.7786i	0.252067	+	0.436593i
$997$	−47.0590	−	27.1695i	−1.49037	−	0.860467i	−0.490434	−	0.871478i	$-0.663162\pi$
$997$	−47.0590	−	27.1695i	−1.49037	−	0.860467i	−0.999939	+	0.0110110i	$0.996495\pi$
$998$	−30.7292			−0.972717
$999$	4.57889	+	4.00422i	0.144870	+	0.126688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.841.8	yes	16
37.11	even	6	inner	1110.2.x.e.751.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.8	✓	16	37.11	even	6	inner
1110.2.x.e.841.8	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.04628 + 1.81222i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.04628 + 1.81222i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +5.41105 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.29896 + 2.48201i) q^{13} +2.09257i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.13772 - 1.81156i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.82628 - 2.20910i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.04628 + 1.81222i) q^{21} +(4.68611 + 2.70553i) q^{22} +7.06690i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -4.96402 q^{26} -1.00000 q^{27} +(-1.04628 + 1.81222i) q^{28} -1.37695i q^{29} +(-0.500000 - 0.866025i) q^{30} +4.90425i q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.70553 + 4.68611i) q^{33} +(-1.81156 - 3.13772i) q^{34} +(-1.81222 - 1.04628i) q^{35} -1.00000 q^{36} +(-4.57889 - 4.00422i) q^{37} +4.41821 q^{38} +(-4.29896 - 2.48201i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.54632 - 6.14241i) q^{41} +(-1.81222 + 1.04628i) q^{42} +4.69322i q^{43} +(2.70553 + 4.68611i) q^{44} -1.00000i q^{45} +(-3.53345 + 6.12012i) q^{46} +1.42519 q^{47} -1.00000 q^{48} +(1.31058 - 2.27000i) q^{49} +(0.866025 - 0.500000i) q^{50} -3.62313i q^{51} +(-4.29896 - 2.48201i) q^{52} +(-1.07681 + 1.86508i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-4.68611 + 2.70553i) q^{55} +(-1.81222 + 1.04628i) q^{56} +(3.82628 + 2.20910i) q^{57} +(0.688475 - 1.19247i) q^{58} +(12.3218 + 7.11401i) q^{59} -1.00000i q^{60} +(-2.87084 + 1.65748i) q^{61} +(-2.45212 + 4.24720i) q^{62} -2.09257 q^{63} -1.00000 q^{64} +(2.48201 - 4.29896i) q^{65} +5.41105i q^{66} +(-1.09149 - 1.89052i) q^{67} -3.62313i q^{68} +(-6.12012 + 3.53345i) q^{69} +(-1.04628 - 1.81222i) q^{70} +(7.21751 + 12.5011i) q^{71} +(-0.866025 - 0.500000i) q^{72} -13.3095 q^{73} +(-1.96332 - 5.75720i) q^{74} +1.00000 q^{75} +(3.82628 + 2.20910i) q^{76} +(5.66149 + 9.80599i) q^{77} +(-2.48201 - 4.29896i) q^{78} +(-0.685185 + 0.395592i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -7.09265i q^{82} +(7.95510 - 13.7786i) q^{83} -2.09257 q^{84} +3.62313 q^{85} +(-2.34661 + 4.06444i) q^{86} +(1.19247 - 0.688475i) q^{87} +5.41105i q^{88} +(-0.917239 - 0.529568i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-8.99587 - 5.19377i) q^{91} +(-6.12012 + 3.53345i) q^{92} +(-4.24720 + 2.45212i) q^{93} +(1.23425 + 0.712594i) q^{94} +(-2.20910 + 3.82628i) q^{95} +(-0.866025 - 0.500000i) q^{96} -9.37239i q^{97} +(2.27000 - 1.31058i) q^{98} +(-2.70553 + 4.68611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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