LMFDB - Embedded newform 666.2.f.f.343.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(343,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.343"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			343.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	666.343
Dual form			666.2.f.f.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +4.00000 q^{10} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{20} +(1.00000 - 1.73205i) q^{22} +6.00000 q^{23} +(-5.50000 + 9.52628i) q^{25} +3.00000 q^{26} +(-1.50000 + 2.59808i) q^{28} +7.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(6.00000 - 10.3923i) q^{35} +(-5.00000 + 3.46410i) q^{37} +4.00000 q^{38} +(-2.00000 - 3.46410i) q^{40} +(3.00000 + 5.19615i) q^{41} +1.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{46} -10.0000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(5.50000 + 9.52628i) q^{50} +(1.50000 - 2.59808i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(4.00000 + 6.92820i) q^{55} +(1.50000 + 2.59808i) q^{56} +(5.00000 - 8.66025i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(3.50000 - 6.06218i) q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-4.50000 - 7.79423i) q^{67} -6.00000 q^{68} +(-6.00000 - 10.3923i) q^{70} +(-3.00000 - 5.19615i) q^{71} -11.0000 q^{73} +(0.500000 + 6.06218i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-4.50000 - 7.79423i) q^{79} -4.00000 q^{80} +6.00000 q^{82} +(5.00000 - 8.66025i) q^{83} +24.0000 q^{85} +(0.500000 - 0.866025i) q^{86} -2.00000 q^{88} +(-1.00000 + 1.73205i) q^{89} +(4.50000 - 7.79423i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-5.00000 + 8.66025i) q^{94} +(-8.00000 + 13.8564i) q^{95} -15.0000 q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 4 q^{5} - 3 q^{7} - 2 q^{8} + 8 q^{10} + 4 q^{11} + 3 q^{13} - 6 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 4 q^{20} + 2 q^{22} + 12 q^{23} - 11 q^{25} + 6 q^{26} - 3 q^{28} + 14 q^{31}+ \cdots + 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 4 * q^5 - 3 * q^7 - 2 * q^8 + 8 * q^10 + 4 * q^11 + 3 * q^13 - 6 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 4 * q^20 + 2 * q^22 + 12 * q^23 - 11 * q^25 + 6 * q^26 - 3 * q^28 + 14 * q^31 + q^32 - 6 * q^34 + 12 * q^35 - 10 * q^37 + 8 * q^38 - 4 * q^40 + 6 * q^41 + 2 * q^43 - 2 * q^44 + 6 * q^46 - 20 * q^47 - 2 * q^49 + 11 * q^50 + 3 * q^52 - 6 * q^53 + 8 * q^55 + 3 * q^56 + 10 * q^59 - 10 * q^61 + 7 * q^62 + 2 * q^64 - 12 * q^65 - 9 * q^67 - 12 * q^68 - 12 * q^70 - 6 * q^71 - 22 * q^73 + q^74 + 4 * q^76 - 6 * q^77 - 9 * q^79 - 8 * q^80 + 12 * q^82 + 10 * q^83 + 48 * q^85 + q^86 - 4 * q^88 - 2 * q^89 + 9 * q^91 - 6 * q^92 - 10 * q^94 - 16 * q^95 - 30 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	4.00000			1.26491
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	0.995535	−	0.0943882i	$-0.0300895\pi$
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	−0.579510	+	0.814965i	$0.696756\pi$
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	2.00000	−	3.46410i	0.447214	−	0.774597i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	3.00000			0.588348
$27$		0			0
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	7.00000			1.25724			0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000			1.25724			0.628619	+	0.777714i	$0.283621\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	6.00000	−	10.3923i	1.01419	−	1.75662i
$36$		0			0
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$37$	−5.00000	+	3.46410i	−0.821995	+	0.569495i
$38$	4.00000			0.648886
$39$		0			0
$40$	−2.00000	−	3.46410i	−0.316228	−	0.547723i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−10.0000			−1.45865			−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000			−1.45865			−0.729325	+	0.684167i	$0.760166\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	5.50000	+	9.52628i	0.777817	+	1.34722i
$51$		0			0
$52$	1.50000	−	2.59808i	0.208013	−	0.360288i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		0			0
$58$		0			0
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	3.50000	−	6.06218i	0.444500	−	0.769897i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	−0.998290	−	0.0584478i	$-0.981385\pi$
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	0.448528	−	0.893769i	$-0.351948\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$	−6.00000	−	10.3923i	−0.717137	−	1.24212i
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$		0			0
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	0.500000	+	6.06218i	0.0581238	+	0.704714i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−3.00000	−	5.19615i	−0.341882	−	0.592157i
$78$		0			0
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$	−4.00000			−0.447214
$81$		0			0
$82$	6.00000			0.662589
$83$	5.00000	−	8.66025i	0.548821	−	0.950586i	−0.449534	−	0.893263i	$-0.648410\pi$
$83$	5.00000	−	8.66025i	0.548821	−	0.950586i	0.998356	−	0.0573233i	$-0.0182566\pi$
$84$		0			0
$85$	24.0000			2.60317
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	−2.00000			−0.213201
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	4.50000	−	7.79423i	0.471728	−	0.817057i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$	−5.00000	+	8.66025i	−0.515711	+	0.893237i
$95$	−8.00000	+	13.8564i	−0.820783	+	1.42164i
$96$		0			0
$97$	−15.0000			−1.52302			−0.761510	−	0.648154i	$-0.775541\pi$
$97$	−15.0000			−1.52302			−0.761510	+	0.648154i	$0.775541\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$		0			0
$100$	11.0000			1.10000
$101$	16.0000			1.59206			0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000			1.59206			0.796030	+	0.605257i	$0.206930\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−1.50000	−	2.59808i	−0.147087	−	0.254762i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−8.50000	+	14.7224i	−0.814152	+	1.41015i	0.0957826	+	0.995402i	$0.469465\pi$
$109$	−8.50000	+	14.7224i	−0.814152	+	1.41015i	−0.909935	+	0.414751i	$0.863869\pi$
$110$	8.00000			0.762770
$111$		0			0
$112$	3.00000			0.283473
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	−0.909221	−	0.416314i	$-0.863322\pi$
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	0.815149	+	0.579252i	$0.196655\pi$
$114$		0			0
$115$	12.0000	+	20.7846i	1.11901	+	1.93817i
$116$		0			0
$117$		0			0
$118$	−5.00000	−	8.66025i	−0.460287	−	0.797241i
$119$	−18.0000			−1.65006
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−10.0000			−0.905357
$123$		0			0
$124$	−3.50000	−	6.06218i	−0.314309	−	0.544400i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	−0.986157	−	0.165812i	$-0.946976\pi$
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	0.636676	+	0.771132i	$0.280309\pi$
$132$		0			0
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	−9.00000			−0.777482
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	−12.0000			−1.01419
$141$		0			0
$142$	−6.00000			−0.503509
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$		0			0
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	5.50000	+	2.59808i	0.452097	+	0.213561i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	7.50000	+	12.9904i	0.610341	+	1.05714i	0.991183	+	0.132502i	$0.0423010\pi$
$151$	7.50000	+	12.9904i	0.610341	+	1.05714i	−0.380841	+	0.924640i	$0.624366\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$		0			0
$154$	−6.00000			−0.483494
$155$	14.0000	+	24.2487i	1.12451	+	1.94770i
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	−9.00000			−0.716002
$159$		0			0
$160$	−2.00000	+	3.46410i	−0.158114	+	0.273861i
$161$	−9.00000	−	15.5885i	−0.709299	−	1.22854i
$162$		0			0
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	−5.00000	−	8.66025i	−0.388075	−	0.672166i
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	0.902120	−	0.431486i	$-0.142010\pi$
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	−0.824737	+	0.565516i	$0.808677\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$	12.0000	−	20.7846i	0.920358	−	1.59411i
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$		0			0
$175$	33.0000			2.49457
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	−0.987184	−	0.159589i	$-0.948983\pi$
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	0.355383	−	0.934721i	$-0.384350\pi$
$182$	−4.50000	−	7.79423i	−0.333562	−	0.577747i
$183$		0			0
$184$	−6.00000			−0.442326
$185$	−22.0000	−	10.3923i	−1.61747	−	0.764057i
$186$		0			0
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$	5.00000	+	8.66025i	0.364662	+	0.631614i
$189$		0			0
$190$	8.00000	+	13.8564i	0.580381	+	1.00525i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	−7.50000	+	12.9904i	−0.538469	+	0.932655i
$195$		0			0
$196$	2.00000			0.142857
$197$	12.0000	−	20.7846i	0.854965	−	1.48084i	−0.0217133	−	0.999764i	$-0.506912\pi$
$197$	12.0000	−	20.7846i	0.854965	−	1.48084i	0.876678	−	0.481078i	$-0.159755\pi$
$198$		0			0
$199$	25.0000			1.77220			0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000			1.77220			0.886102	+	0.463491i	$0.153403\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$		0			0
$202$	8.00000	−	13.8564i	0.562878	−	0.974933i
$203$		0			0
$204$		0			0
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	−3.00000			−0.208013
$209$	4.00000	+	6.92820i	0.276686	+	0.479234i
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	6.00000			0.412082
$213$		0			0
$214$	4.00000			0.273434
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$		0			0
$217$	−10.5000	−	18.1865i	−0.712786	−	1.23458i
$218$	8.50000	+	14.7224i	0.575693	+	0.997129i
$219$		0			0
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	18.0000			1.21081
$222$		0			0
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$		0			0
$229$	−12.5000	−	21.6506i	−0.826023	−	1.43071i	−0.901135	−	0.433539i	$-0.857265\pi$
$229$	−12.5000	−	21.6506i	−0.826023	−	1.43071i	0.0751115	−	0.997175i	$-0.476069\pi$
$230$	24.0000			1.58251
$231$		0			0
$232$		0			0
$233$	2.00000			0.131024			0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000			0.131024			0.0655122	+	0.997852i	$0.479132\pi$
$234$		0			0
$235$	−20.0000	−	34.6410i	−1.30466	−	2.25973i
$236$	−10.0000			−0.650945
$237$		0			0
$238$	−9.00000	+	15.5885i	−0.583383	+	1.01045i
$239$	−11.0000	+	19.0526i	−0.711531	+	1.23241i	0.252752	+	0.967531i	$0.418664\pi$
$239$	−11.0000	+	19.0526i	−0.711531	+	1.23241i	−0.964282	+	0.264876i	$0.914669\pi$
$240$		0			0
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−5.00000	+	8.66025i	−0.320092	+	0.554416i
$245$	−8.00000			−0.511101
$246$		0			0
$247$	−6.00000	+	10.3923i	−0.381771	+	0.661247i
$248$	−7.00000			−0.444500
$249$		0			0
$250$	−12.0000	+	20.7846i	−0.758947	+	1.31453i
$251$	−4.00000			−0.252478			−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000			−0.252478			−0.126239	+	0.992000i	$0.540291\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	6.50000	+	11.2583i	0.407846	+	0.706410i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	−0.364992	−	0.931011i	$-0.618928\pi$
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	0.988775	−	0.149413i	$-0.0477384\pi$
$258$		0			0
$259$	16.5000	+	7.79423i	1.02526	+	0.484310i
$260$	12.0000			0.744208
$261$		0			0
$262$	4.00000	+	6.92820i	0.247121	+	0.428026i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$		0			0
$268$	−4.50000	+	7.79423i	−0.274881	+	0.476108i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	−0.816864	−	0.576831i	$-0.804289\pi$
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	0.907982	+	0.419009i	$0.137622\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$		0			0
$275$	−11.0000	+	19.0526i	−0.663325	+	1.14891i
$276$		0			0
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	0.998861	+	0.0477206i	$0.0151957\pi$
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	−0.458103	+	0.888899i	$0.651471\pi$
$278$	2.50000	+	4.33013i	0.149940	+	0.259704i
$279$		0			0
$280$	−6.00000	+	10.3923i	−0.358569	+	0.621059i
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	−0.762561	−	0.646916i	$-0.776058\pi$
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	0.941526	+	0.336939i	$0.109392\pi$
$282$		0			0
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.124096	−	0.992270i	$-0.539603\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	6.00000			0.354787
$287$	9.00000	−	15.5885i	0.531253	−	0.920158i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	16.0000	+	27.7128i	0.934730	+	1.61900i	0.775115	+	0.631821i	$0.217692\pi$
$293$	16.0000	+	27.7128i	0.934730	+	1.61900i	0.159615	+	0.987179i	$0.448975\pi$
$294$		0			0
$295$	40.0000			2.32889
$296$	5.00000	−	3.46410i	0.290619	−	0.201347i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	9.00000	+	15.5885i	0.520483	+	0.901504i
$300$		0			0
$301$	−1.50000	−	2.59808i	−0.0864586	−	0.149751i
$302$	15.0000			0.863153
$303$		0			0
$304$	−4.00000			−0.229416
$305$	20.0000	−	34.6410i	1.14520	−	1.98354i
$306$		0			0
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$		0			0
$310$	28.0000			1.59029
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$		0			0
$316$	−4.50000	+	7.79423i	−0.253145	+	0.438460i
$317$	7.00000	−	12.1244i	0.393159	−	0.680972i	−0.599705	−	0.800221i	$-0.704715\pi$
$317$	7.00000	−	12.1244i	0.393159	−	0.680972i	0.992864	+	0.119249i	$0.0380488\pi$
$318$		0			0
$319$		0			0
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$		0			0
$322$	−18.0000			−1.00310
$323$	24.0000			1.33540
$324$		0			0
$325$	−33.0000			−1.83051
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	15.0000	+	25.9808i	0.826977	+	1.43237i
$330$		0			0
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	−0.674351	−	0.738411i	$-0.735576\pi$
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	0.976658	+	0.214799i	$0.0689098\pi$
$332$	−10.0000			−0.548821
$333$		0			0
$334$	2.00000			0.109435
$335$	18.0000	−	31.1769i	0.983445	−	1.70338i
$336$		0			0
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	0.954551	+	0.298047i	$0.0963352\pi$
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	−0.219159	+	0.975689i	$0.570331\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$		0			0
$340$	−12.0000	−	20.7846i	−0.650791	−	1.12720i
$341$	14.0000			0.758143
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−1.00000			−0.0539164
$345$		0			0
$346$	5.00000	+	8.66025i	0.268802	+	0.465578i
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$		0			0
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$	16.5000	−	28.5788i	0.881962	−	1.52760i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	12.0000	−	20.7846i	0.636894	−	1.10313i
$356$	2.00000			0.106000
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	4.00000			0.211112			0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000			0.211112			0.105556	+	0.994413i	$0.466338\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−17.0000			−0.893500
$363$		0			0
$364$	−9.00000			−0.471728
$365$	−22.0000	−	38.1051i	−1.15153	−	1.99451i
$366$		0			0
$367$	−14.5000	−	25.1147i	−0.756894	−	1.31098i	−0.944427	−	0.328720i	$-0.893383\pi$
$367$	−14.5000	−	25.1147i	−0.756894	−	1.31098i	0.187533	−	0.982258i	$-0.439951\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$	−20.0000	+	13.8564i	−1.03975	+	0.720360i
$371$	18.0000			0.934513
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$		0			0
$376$	10.0000			0.515711
$377$		0			0
$378$		0			0
$379$	−2.00000	+	3.46410i	−0.102733	+	0.177939i	−0.912810	−	0.408385i	$-0.866092\pi$
$379$	−2.00000	+	3.46410i	−0.102733	+	0.177939i	0.810077	+	0.586324i	$0.199425\pi$
$380$	16.0000			0.820783
$381$		0			0
$382$	−10.0000	+	17.3205i	−0.511645	+	0.886194i
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	0.839345	−	0.543599i	$-0.182939\pi$
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	−0.890443	+	0.455095i	$0.849605\pi$
$384$		0			0
$385$	12.0000	−	20.7846i	0.611577	−	1.05928i
$386$	5.50000	−	9.52628i	0.279943	−	0.484875i
$387$		0			0
$388$	7.50000	+	12.9904i	0.380755	+	0.659487i
$389$	11.0000	+	19.0526i	0.557722	+	0.966003i	0.997686	+	0.0679877i	$0.0216579\pi$
$389$	11.0000	+	19.0526i	0.557722	+	0.966003i	−0.439964	+	0.898015i	$0.645009\pi$
$390$		0			0
$391$	18.0000	−	31.1769i	0.910299	−	1.57668i
$392$	1.00000	−	1.73205i	0.0505076	−	0.0874818i
$393$		0			0
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$	18.0000	−	31.1769i	0.905678	−	1.56868i
$396$		0			0
$397$	−13.0000			−0.652451			−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000			−0.652451			−0.326226	+	0.945292i	$0.605777\pi$
$398$	12.5000	−	21.6506i	0.626568	−	1.08525i
$399$		0			0
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	−12.0000			−0.599251			−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000			−0.599251			−0.299626	+	0.954057i	$0.596862\pi$
$402$		0			0
$403$	10.5000	+	18.1865i	0.523042	+	0.905936i
$404$	−8.00000	−	13.8564i	−0.398015	−	0.689382i
$405$		0			0
$406$		0			0
$407$	−10.0000	+	6.92820i	−0.495682	+	0.343418i
$408$		0			0
$409$	1.50000	−	2.59808i	0.0741702	−	0.128467i	−0.826555	−	0.562856i	$-0.809703\pi$
$409$	1.50000	−	2.59808i	0.0741702	−	0.128467i	0.900725	+	0.434389i	$0.143036\pi$
$410$	12.0000	+	20.7846i	0.592638	+	1.02648i
$411$		0			0
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$	−30.0000			−1.47620
$414$		0			0
$415$	40.0000			1.96352
$416$	−1.50000	+	2.59808i	−0.0735436	+	0.127381i
$417$		0			0
$418$	8.00000			0.391293
$419$	−10.0000	+	17.3205i	−0.488532	+	0.846162i	−0.999913	−	0.0131919i	$-0.995801\pi$
$419$	−10.0000	+	17.3205i	−0.488532	+	0.846162i	0.511381	+	0.859354i	$0.329134\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	−4.50000	+	7.79423i	−0.219057	+	0.379417i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	33.0000	+	57.1577i	1.60074	+	2.77255i
$426$		0			0
$427$	−15.0000	+	25.9808i	−0.725901	+	1.25730i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$		0			0
$430$	4.00000			0.192897
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$		0			0
$433$	6.00000			0.288342			0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000			0.288342			0.144171	+	0.989553i	$0.453949\pi$
$434$	−21.0000			−1.00803
$435$		0			0
$436$	17.0000			0.814152
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	5.50000	+	9.52628i	0.262501	+	0.454665i	0.966906	−	0.255134i	$-0.0821195\pi$
$439$	5.50000	+	9.52628i	0.262501	+	0.454665i	−0.704405	+	0.709798i	$0.748786\pi$
$440$	−4.00000	−	6.92820i	−0.190693	−	0.330289i
$441$		0			0
$442$	9.00000	−	15.5885i	0.428086	−	0.741467i
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$		0			0
$445$	−8.00000			−0.379236
$446$	−3.50000	+	6.06218i	−0.165730	+	0.287052i
$447$		0			0
$448$	−1.50000	−	2.59808i	−0.0708683	−	0.122748i
$449$	8.00000	+	13.8564i	0.377543	+	0.653924i	0.990704	−	0.136034i	$-0.0434356\pi$
$449$	8.00000	+	13.8564i	0.377543	+	0.653924i	−0.613161	+	0.789958i	$0.710102\pi$
$450$		0			0
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$	2.00000			0.0940721
$453$		0			0
$454$	−24.0000			−1.12638
$455$	36.0000			1.68771
$456$		0			0
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	0.575036	−	0.818128i	$-0.304988\pi$
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	−0.996038	+	0.0889312i	$0.971655\pi$
$458$	−25.0000			−1.16817
$459$		0			0
$460$	12.0000	−	20.7846i	0.559503	−	0.969087i
$461$	5.00000	−	8.66025i	0.232873	−	0.403348i	−0.725779	−	0.687928i	$-0.758521\pi$
$461$	5.00000	−	8.66025i	0.232873	−	0.403348i	0.958652	+	0.284579i	$0.0918539\pi$
$462$		0			0
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	0.965060	−	0.262029i	$-0.0843915\pi$
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	−0.709453	+	0.704752i	$0.751058\pi$
$464$		0			0
$465$		0			0
$466$	1.00000	−	1.73205i	0.0463241	−	0.0802357i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	−13.5000	+	23.3827i	−0.623372	+	1.07971i
$470$	−40.0000			−1.84506
$471$		0			0
$472$	−5.00000	+	8.66025i	−0.230144	+	0.398621i
$473$	2.00000			0.0919601
$474$		0			0
$475$	−44.0000			−2.01886
$476$	9.00000	+	15.5885i	0.412514	+	0.714496i
$477$		0			0
$478$	11.0000	+	19.0526i	0.503128	+	0.871444i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−16.5000	−	7.79423i	−0.752335	−	0.355386i
$482$	19.0000			0.865426
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−30.0000	−	51.9615i	−1.36223	−	2.35945i
$486$		0			0
$487$	28.0000			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$		0			0
$490$	−4.00000	+	6.92820i	−0.180702	+	0.312984i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$	6.00000	+	10.3923i	0.269953	+	0.467572i
$495$		0			0
$496$	−3.50000	+	6.06218i	−0.157155	+	0.272200i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$		0			0
$499$	12.0000	+	20.7846i	0.537194	+	0.930447i	0.999054	+	0.0434940i	$0.0138489\pi$
$499$	12.0000	+	20.7846i	0.537194	+	0.930447i	−0.461860	+	0.886953i	$0.652818\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$	−2.00000	+	3.46410i	−0.0892644	+	0.154610i
$503$	−16.0000	+	27.7128i	−0.713405	+	1.23565i	0.250167	+	0.968203i	$0.419515\pi$
$503$	−16.0000	+	27.7128i	−0.713405	+	1.23565i	−0.963572	+	0.267451i	$0.913819\pi$
$504$		0			0
$505$	32.0000	+	55.4256i	1.42398	+	2.46641i
$506$	6.00000	−	10.3923i	0.266733	−	0.461994i
$507$		0			0
$508$	13.0000			0.576782
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	16.5000	+	28.5788i	0.729917	+	1.26425i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.0000	−	17.3205i	−0.441081	−	0.763975i
$515$	−16.0000	−	27.7128i	−0.705044	−	1.22117i
$516$		0			0
$517$	−20.0000			−0.879599
$518$	15.0000	−	10.3923i	0.659062	−	0.456612i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	0.967002	−	0.254769i	$-0.0819994\pi$
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	−0.704137	+	0.710064i	$0.748666\pi$
$522$		0			0
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	0.539782	−	0.841805i	$-0.318507\pi$
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	−0.998915	+	0.0465630i	$0.985173\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$	−12.0000			−0.523225
$527$	21.0000	−	36.3731i	0.914774	−	1.58444i
$528$		0			0
$529$	13.0000			0.565217
$530$	−12.0000	+	20.7846i	−0.521247	+	0.902826i
$531$		0			0
$532$	−12.0000			−0.520266
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	−8.00000	+	13.8564i	−0.345870	+	0.599065i
$536$	4.50000	+	7.79423i	0.194370	+	0.336659i
$537$		0			0
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	−2.00000	+	3.46410i	−0.0861461	+	0.149209i
$540$		0			0
$541$	33.0000			1.41878			0.709390	−	0.704816i	$-0.248970\pi$
$541$	33.0000			1.41878			0.709390	+	0.704816i	$0.248970\pi$
$542$	−1.50000	−	2.59808i	−0.0644305	−	0.111597i
$543$		0			0
$544$	6.00000			0.257248
$545$	−68.0000			−2.91280
$546$		0			0
$547$	−9.00000			−0.384812			−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000			−0.384812			−0.192406	+	0.981315i	$0.561629\pi$
$548$		0			0
$549$		0			0
$550$	11.0000	+	19.0526i	0.469042	+	0.812404i
$551$		0			0
$552$		0			0
$553$	−13.5000	+	23.3827i	−0.574078	+	0.994333i
$554$	18.0000			0.764747
$555$		0			0
$556$	5.00000			0.212047
$557$	11.0000	−	19.0526i	0.466085	−	0.807283i	−0.533165	−	0.846011i	$-0.678997\pi$
$557$	11.0000	−	19.0526i	0.466085	−	0.807283i	0.999250	+	0.0387286i	$0.0123308\pi$
$558$		0			0
$559$	1.50000	+	2.59808i	0.0634432	+	0.109887i
$560$	6.00000	+	10.3923i	0.253546	+	0.439155i
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	34.0000			1.43293			0.716465	−	0.697623i	$-0.245759\pi$
$563$	34.0000			1.43293			0.716465	+	0.697623i	$0.245759\pi$
$564$		0			0
$565$	−8.00000			−0.336563
$566$	−31.0000			−1.30303
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−16.0000			−0.670755			−0.335377	−	0.942084i	$-0.608864\pi$
$569$	−16.0000			−0.670755			−0.335377	+	0.942084i	$0.608864\pi$
$570$		0			0
$571$	−4.50000	+	7.79423i	−0.188319	+	0.326178i	−0.944690	−	0.327965i	$-0.893637\pi$
$571$	−4.50000	+	7.79423i	−0.188319	+	0.326178i	0.756371	+	0.654143i	$0.226971\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$	−9.00000	−	15.5885i	−0.375653	−	0.650650i
$575$	−33.0000	+	57.1577i	−1.37620	+	2.38364i
$576$		0			0
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−19.0000			−0.790296
$579$		0			0
$580$		0			0
$581$	−30.0000			−1.24461
$582$		0			0
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	11.0000			0.455183
$585$		0			0
$586$	32.0000			1.32191
$587$	−15.0000	−	25.9808i	−0.619116	−	1.07234i	−0.989647	−	0.143521i	$-0.954158\pi$
$587$	−15.0000	−	25.9808i	−0.619116	−	1.07234i	0.370531	−	0.928820i	$-0.379176\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$	20.0000	−	34.6410i	0.823387	−	1.42615i
$591$		0			0
$592$	−0.500000	−	6.06218i	−0.0205499	−	0.249154i
$593$	−8.00000			−0.328521			−0.164260	−	0.986417i	$-0.552524\pi$
$593$	−8.00000			−0.328521			−0.164260	+	0.986417i	$0.552524\pi$
$594$		0			0
$595$	−36.0000	−	62.3538i	−1.47586	−	2.55626i
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	18.0000			0.736075
$599$	−23.0000	−	39.8372i	−0.939755	−	1.62770i	−0.765928	−	0.642926i	$-0.777720\pi$
$599$	−23.0000	−	39.8372i	−0.939755	−	1.62770i	−0.173826	−	0.984776i	$-0.555613\pi$
$600$		0			0
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$	−3.00000			−0.122271
$603$		0			0
$604$	7.50000	−	12.9904i	0.305171	−	0.528571i
$605$	−14.0000	−	24.2487i	−0.569181	−	0.985850i
$606$		0			0
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$		0			0
$610$	−20.0000	−	34.6410i	−0.809776	−	1.40257i
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	−6.50000	+	11.2583i	−0.262319	+	0.454349i
$615$		0			0
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	−0.994037	−	0.109043i	$-0.965221\pi$
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	0.591452	+	0.806340i	$0.298555\pi$
$618$		0			0
$619$	19.0000			0.763674			0.381837	−	0.924230i	$-0.375291\pi$
$619$	19.0000			0.763674			0.381837	+	0.924230i	$0.375291\pi$
$620$	14.0000	−	24.2487i	0.562254	−	0.973852i
$621$		0			0
$622$	12.0000	+	20.7846i	0.481156	+	0.833387i
$623$	6.00000			0.240385
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$		0			0
$628$	7.00000			0.279330
$629$	3.00000	+	36.3731i	0.119618	+	1.45029i
$630$		0			0
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	−0.645748	−	0.763550i	$-0.723455\pi$
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	0.984128	+	0.177459i	$0.0567879\pi$
$632$	4.50000	+	7.79423i	0.179000	+	0.310038i
$633$		0			0
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$	−52.0000			−2.06356
$636$		0			0
$637$	−6.00000			−0.237729
$638$		0			0
$639$		0			0
$640$	4.00000			0.158114
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$		0			0
$643$	−31.0000			−1.22252			−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000			−1.22252			−0.611260	+	0.791430i	$0.709337\pi$
$644$	−9.00000	+	15.5885i	−0.354650	+	0.614271i
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	4.00000	+	6.92820i	0.157256	+	0.272376i	0.933878	−	0.357591i	$-0.116402\pi$
$647$	4.00000	+	6.92820i	0.157256	+	0.272376i	−0.776622	+	0.629967i	$0.783068\pi$
$648$		0			0
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$	−16.5000	+	28.5788i	−0.647183	+	1.12095i
$651$		0			0
$652$	−20.0000			−0.783260
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	0.999396	−	0.0347583i	$-0.0110661\pi$
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	−0.529799	+	0.848123i	$0.677733\pi$
$654$		0			0
$655$	−32.0000			−1.25034
$656$	−6.00000			−0.234261
$657$		0			0
$658$	30.0000			1.16952
$659$	7.00000	+	12.1244i	0.272681	+	0.472298i	0.969548	−	0.244903i	$-0.0787562\pi$
$659$	7.00000	+	12.1244i	0.272681	+	0.472298i	−0.696866	+	0.717201i	$0.745423\pi$
$660$		0			0
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	0.835379	−	0.549675i	$-0.185248\pi$
$661$	−1.50000	−	2.59808i	−0.0583432	−	0.101053i	−0.893722	+	0.448622i	$0.851915\pi$
$662$	−5.50000	−	9.52628i	−0.213764	−	0.370249i
$663$		0			0
$664$	−5.00000	+	8.66025i	−0.194038	+	0.336083i
$665$	48.0000			1.86136
$666$		0			0
$667$		0			0
$668$	1.00000	−	1.73205i	0.0386912	−	0.0670151i
$669$		0			0
$670$	−18.0000	−	31.1769i	−0.695401	−	1.20447i
$671$	−10.0000	−	17.3205i	−0.386046	−	0.668651i
$672$		0			0
$673$	−17.0000	−	29.4449i	−0.655302	−	1.13502i	−0.981818	−	0.189824i	$-0.939208\pi$
$673$	−17.0000	−	29.4449i	−0.655302	−	1.13502i	0.326516	−	0.945192i	$-0.394125\pi$
$674$	27.0000			1.04000
$675$		0			0
$676$	−4.00000			−0.153846
$677$	50.0000			1.92166			0.960828	−	0.277145i	$-0.0893883\pi$
$677$	50.0000			1.92166			0.960828	+	0.277145i	$0.0893883\pi$
$678$		0			0
$679$	22.5000	+	38.9711i	0.863471	+	1.49558i
$680$	−24.0000			−0.920358
$681$		0			0
$682$	7.00000	−	12.1244i	0.268044	−	0.464266i
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	−0.917697	−	0.397282i	$-0.869953\pi$
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	0.802905	+	0.596107i	$0.203287\pi$
$684$		0			0
$685$		0			0
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	−18.0000			−0.685745
$690$		0			0
$691$	18.5000	−	32.0429i	0.703773	−	1.21897i	−0.263359	−	0.964698i	$-0.584830\pi$
$691$	18.5000	−	32.0429i	0.703773	−	1.21897i	0.967132	−	0.254273i	$-0.0818362\pi$
$692$	10.0000			0.380143
$693$		0			0
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$	−20.0000			−0.758643
$696$		0			0
$697$	36.0000			1.36360
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$	−16.5000	−	28.5788i	−0.623641	−	1.08018i
$701$	−14.0000	+	24.2487i	−0.528773	+	0.915861i	0.470664	+	0.882312i	$0.344014\pi$
$701$	−14.0000	+	24.2487i	−0.528773	+	0.915861i	−0.999437	+	0.0335489i	$0.989319\pi$
$702$		0			0
$703$	−22.0000	−	10.3923i	−0.829746	−	0.391953i
$704$	2.00000			0.0753778
$705$		0			0
$706$	−6.00000	−	10.3923i	−0.225813	−	0.391120i
$707$	−24.0000	−	41.5692i	−0.902613	−	1.56337i
$708$		0			0
$709$	−3.00000			−0.112667			−0.0563337	−	0.998412i	$-0.517941\pi$
$709$	−3.00000			−0.112667			−0.0563337	+	0.998412i	$0.517941\pi$
$710$	−12.0000	−	20.7846i	−0.450352	−	0.780033i
$711$		0			0
$712$	1.00000	−	1.73205i	0.0374766	−	0.0649113i
$713$	42.0000			1.57291
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.448775	+	0.777300i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$		0			0
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	12.0000	+	20.7846i	0.446903	+	0.774059i
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	−8.50000	+	14.7224i	−0.315900	+	0.547155i
$725$		0			0
$726$		0			0
$727$	21.5000	+	37.2391i	0.797391	+	1.38112i	0.921310	+	0.388829i	$0.127120\pi$
$727$	21.5000	+	37.2391i	0.797391	+	1.38112i	−0.123919	+	0.992292i	$0.539546\pi$
$728$	−4.50000	+	7.79423i	−0.166781	+	0.288873i
$729$		0			0
$730$	−44.0000			−1.62851
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	0.986406	−	0.164328i	$-0.0525456\pi$
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	−0.635515	+	0.772088i	$0.719212\pi$
$734$	−29.0000			−1.07041
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−9.00000	−	15.5885i	−0.331519	−	0.574208i
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	2.00000	+	24.2487i	0.0735215	+	0.891400i
$741$		0			0
$742$	9.00000	−	15.5885i	0.330400	−	0.572270i
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$	12.0000	+	20.7846i	0.439646	+	0.761489i
$746$	−11.0000			−0.402739
$747$		0			0
$748$	−12.0000			−0.438763
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$	5.00000	−	8.66025i	0.182331	−	0.315807i
$753$		0			0
$754$		0			0
$755$	−30.0000	+	51.9615i	−1.09181	+	1.89107i
$756$		0			0
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	−0.577761	−	0.816206i	$-0.696073\pi$
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	0.995736	+	0.0922527i	$0.0294068\pi$
$758$	2.00000	+	3.46410i	0.0726433	+	0.125822i
$759$		0			0
$760$	8.00000	−	13.8564i	0.290191	−	0.502625i
$761$	2.00000	−	3.46410i	0.0724999	−	0.125574i	−0.827496	−	0.561471i	$-0.810236\pi$
$761$	2.00000	−	3.46410i	0.0724999	−	0.125574i	0.899996	+	0.435897i	$0.143569\pi$
$762$		0			0
$763$	51.0000			1.84632
$764$	10.0000	+	17.3205i	0.361787	+	0.626634i
$765$		0			0
$766$	−2.00000			−0.0722629
$767$	30.0000			1.08324
$768$		0			0
$769$	−1.00000			−0.0360609			−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000			−0.0360609			−0.0180305	+	0.999837i	$0.505740\pi$
$770$	−12.0000	−	20.7846i	−0.432450	−	0.749025i
$771$		0			0
$772$	−5.50000	−	9.52628i	−0.197949	−	0.342858i
$773$	2.00000	+	3.46410i	0.0719350	+	0.124595i	0.899749	−	0.436407i	$-0.143749\pi$
$773$	2.00000	+	3.46410i	0.0719350	+	0.124595i	−0.827814	+	0.561002i	$0.810416\pi$
$774$		0			0
$775$	−38.5000	+	66.6840i	−1.38296	+	2.39536i
$776$	15.0000			0.538469
$777$		0			0
$778$	22.0000			0.788738
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$		0			0
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−28.0000			−0.999363
$786$		0			0
$787$	−23.0000			−0.819861			−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000			−0.819861			−0.409931	+	0.912117i	$0.634447\pi$
$788$	−24.0000			−0.854965
$789$		0			0
$790$	−18.0000	−	31.1769i	−0.640411	−	1.10922i
$791$	6.00000			0.213335
$792$		0			0
$793$	15.0000	−	25.9808i	0.532666	−	0.922604i
$794$	−6.50000	+	11.2583i	−0.230676	+	0.399543i
$795$		0			0
$796$	−12.5000	−	21.6506i	−0.443051	−	0.767386i
$797$	5.00000	−	8.66025i	0.177109	−	0.306762i	−0.763780	−	0.645477i	$-0.776659\pi$
$797$	5.00000	−	8.66025i	0.177109	−	0.306762i	0.940889	+	0.338715i	$0.109992\pi$
$798$		0			0
$799$	−30.0000	+	51.9615i	−1.06132	+	1.83827i
$800$	−11.0000			−0.388909
$801$		0			0
$802$	−6.00000	+	10.3923i	−0.211867	+	0.366965i
$803$	−22.0000			−0.776363
$804$		0			0
$805$	36.0000	−	62.3538i	1.26883	−	2.19768i
$806$	21.0000			0.739693
$807$		0			0
$808$	−16.0000			−0.562878
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$		0			0
$811$	6.00000	+	10.3923i	0.210688	+	0.364923i	0.951930	−	0.306315i	$-0.0990961\pi$
$811$	6.00000	+	10.3923i	0.210688	+	0.364923i	−0.741242	+	0.671238i	$0.765763\pi$
$812$		0			0
$813$		0			0
$814$	1.00000	+	12.1244i	0.0350500	+	0.424958i
$815$	80.0000			2.80228
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	−1.50000	−	2.59808i	−0.0524463	−	0.0908396i
$819$		0			0
$820$	24.0000			0.838116
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.817654	+	0.575710i	$0.195274\pi$
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.0897520	+	0.995964i	$0.471393\pi$
$822$		0			0
$823$	−4.50000	+	7.79423i	−0.156860	+	0.271690i	−0.933735	−	0.357966i	$-0.883471\pi$
$823$	−4.50000	+	7.79423i	−0.156860	+	0.271690i	0.776875	+	0.629655i	$0.216804\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	−15.0000	+	25.9808i	−0.521917	+	0.903986i
$827$	−19.0000	−	32.9090i	−0.660695	−	1.14436i	−0.980433	−	0.196851i	$-0.936928\pi$
$827$	−19.0000	−	32.9090i	−0.660695	−	1.14436i	0.319739	−	0.947506i	$-0.396405\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	20.0000	−	34.6410i	0.694210	−	1.20241i
$831$		0			0
$832$	1.50000	+	2.59808i	0.0520031	+	0.0900721i
$833$	6.00000	+	10.3923i	0.207888	+	0.360072i
$834$		0			0
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$		0			0
$838$	10.0000	+	17.3205i	0.345444	+	0.598327i
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	−0.970435	−	0.241363i	$-0.922405\pi$
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	0.694244	+	0.719740i	$0.255739\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$		0			0
$844$	4.50000	+	7.79423i	0.154896	+	0.268288i
$845$	16.0000			0.550417
$846$		0			0
$847$	10.5000	+	18.1865i	0.360784	+	0.624897i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	66.0000			2.26378
$851$	−30.0000	+	20.7846i	−1.02839	+	0.712487i
$852$		0			0
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$	15.0000	+	25.9808i	0.513289	+	0.889043i
$855$		0			0
$856$	−2.00000	−	3.46410i	−0.0683586	−	0.118401i
$857$	−32.0000			−1.09310			−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000			−1.09310			−0.546550	+	0.837427i	$0.684059\pi$
$858$		0			0
$859$	−35.0000			−1.19418			−0.597092	−	0.802173i	$-0.703677\pi$
$859$	−35.0000			−1.19418			−0.597092	+	0.802173i	$0.703677\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$		0			0
$862$	2.00000			0.0681203
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	−0.671200	−	0.741276i	$-0.734221\pi$
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	0.977564	+	0.210639i	$0.0675543\pi$
$864$		0			0
$865$	−40.0000			−1.36004
$866$	3.00000	−	5.19615i	0.101944	−	0.176572i
$867$		0			0
$868$	−10.5000	+	18.1865i	−0.356393	+	0.617291i
$869$	−9.00000	−	15.5885i	−0.305304	−	0.528802i
$870$		0			0
$871$	13.5000	−	23.3827i	0.457430	−	0.792292i
$872$	8.50000	−	14.7224i	0.287846	−	0.498564i
$873$		0			0
$874$	24.0000			0.811812
$875$	36.0000	+	62.3538i	1.21702	+	2.10794i
$876$		0			0
$877$	−5.00000			−0.168838			−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000			−0.168838			−0.0844190	+	0.996430i	$0.526903\pi$
$878$	11.0000			0.371232
$879$		0			0
$880$	−8.00000			−0.269680
$881$	−9.00000	−	15.5885i	−0.303218	−	0.525188i	0.673645	−	0.739055i	$-0.264728\pi$
$881$	−9.00000	−	15.5885i	−0.303218	−	0.525188i	−0.976863	+	0.213866i	$0.931394\pi$
$882$		0			0
$883$	−14.0000	−	24.2487i	−0.471138	−	0.816034i	0.528317	−	0.849047i	$-0.322823\pi$
$883$	−14.0000	−	24.2487i	−0.471138	−	0.816034i	−0.999455	+	0.0330128i	$0.989490\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	28.0000			0.940148			0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000			0.940148			0.470074	+	0.882627i	$0.344227\pi$
$888$		0			0
$889$	39.0000			1.30802
$890$	−4.00000	+	6.92820i	−0.134080	+	0.232234i
$891$		0			0
$892$	3.50000	+	6.06218i	0.117189	+	0.202977i
$893$	−20.0000	−	34.6410i	−0.669274	−	1.15922i
$894$		0			0
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	16.0000			0.533927
$899$		0			0
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	12.0000			0.399556
$903$		0			0
$904$	1.00000	−	1.73205i	0.0332595	−	0.0576072i
$905$	34.0000	−	58.8897i	1.13020	−	1.95756i
$906$		0			0
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	0.874207	−	0.485553i	$-0.161382\pi$
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	−0.857605	+	0.514309i	$0.828048\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$		0			0
$910$	18.0000	−	31.1769i	0.596694	−	1.03350i
$911$	38.0000			1.25900			0.629498	−	0.777002i	$-0.283261\pi$
$911$	38.0000			1.25900			0.629498	+	0.777002i	$0.283261\pi$
$912$		0			0
$913$	10.0000	−	17.3205i	0.330952	−	0.573225i
$914$	−18.0000			−0.595387
$915$		0			0
$916$	−12.5000	+	21.6506i	−0.413012	+	0.715357i
$917$	24.0000			0.792550
$918$		0			0
$919$	31.0000			1.02260			0.511298	−	0.859404i	$-0.329165\pi$
$919$	31.0000			1.02260			0.511298	+	0.859404i	$0.329165\pi$
$920$	−12.0000	−	20.7846i	−0.395628	−	0.685248i
$921$		0			0
$922$	−5.00000	−	8.66025i	−0.164666	−	0.285210i
$923$	9.00000	−	15.5885i	0.296239	−	0.513100i
$924$		0			0
$925$	−5.50000	−	66.6840i	−0.180839	−	2.19255i
$926$	11.0000			0.361482
$927$		0			0
$928$		0			0
$929$	−16.0000	−	27.7128i	−0.524943	−	0.909228i	−0.999578	−	0.0290452i	$-0.990753\pi$
$929$	−16.0000	−	27.7128i	−0.524943	−	0.909228i	0.474635	−	0.880183i	$-0.342580\pi$
$930$		0			0
$931$	−8.00000			−0.262189
$932$	−1.00000	−	1.73205i	−0.0327561	−	0.0567352i
$933$		0			0
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$	48.0000			1.56977
$936$		0			0
$937$	6.50000	−	11.2583i	0.212346	−	0.367794i	−0.740102	−	0.672494i	$-0.765223\pi$
$937$	6.50000	−	11.2583i	0.212346	−	0.367794i	0.952448	+	0.304700i	$0.0985564\pi$
$938$	13.5000	+	23.3827i	0.440791	+	0.763472i
$939$		0			0
$940$	−20.0000	+	34.6410i	−0.652328	+	1.12987i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$	5.00000	+	8.66025i	0.162736	+	0.281867i
$945$		0			0
$946$	1.00000	−	1.73205i	0.0325128	−	0.0563138i
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	−0.602494	−	0.798123i	$-0.705826\pi$
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	0.992442	+	0.122714i	$0.0391598\pi$
$948$		0			0
$949$	−16.5000	−	28.5788i	−0.535613	−	0.927708i
$950$	−22.0000	+	38.1051i	−0.713774	+	1.23629i
$951$		0			0
$952$	18.0000			0.583383
$953$	4.00000	−	6.92820i	0.129573	−	0.224427i	−0.793938	−	0.607998i	$-0.791973\pi$
$953$	4.00000	−	6.92820i	0.129573	−	0.224427i	0.923511	+	0.383572i	$0.125306\pi$
$954$		0			0
$955$	−40.0000	−	69.2820i	−1.29437	−	2.24191i
$956$	22.0000			0.711531
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$		0			0
$960$		0			0
$961$	18.0000			0.580645
$962$	−15.0000	+	10.3923i	−0.483619	+	0.335061i
$963$		0			0
$964$	9.50000	−	16.4545i	0.305974	−	0.529963i
$965$	22.0000	+	38.1051i	0.708205	+	1.22665i
$966$		0			0
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	0.993964	−	0.109707i	$-0.0349913\pi$
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	−0.591991	+	0.805945i	$0.701658\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	−60.0000			−1.92648
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$		0			0
$973$	15.0000			0.480878
$974$	14.0000	−	24.2487i	0.448589	−	0.776979i
$975$		0			0
$976$	10.0000			0.320092
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.236768	−	0.971566i	$-0.423912\pi$
$977$	30.0000	−	51.9615i	0.959785	−	1.66240i	0.723017	−	0.690830i	$-0.242755\pi$
$978$		0			0
$979$	−2.00000	+	3.46410i	−0.0639203	+	0.110713i
$980$	4.00000	+	6.92820i	0.127775	+	0.221313i
$981$		0			0
$982$		0			0
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$		0			0
$985$	96.0000			3.05881
$986$		0			0
$987$		0			0
$988$	12.0000			0.381771
$989$	6.00000			0.190789
$990$		0			0
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	3.50000	+	6.06218i	0.111125	+	0.192474i
$993$		0			0
$994$	9.00000	+	15.5885i	0.285463	+	0.494436i
$995$	50.0000	+	86.6025i	1.58511	+	2.74549i
$996$		0			0
$997$	27.0000	−	46.7654i	0.855099	−	1.48107i	−0.0214550	−	0.999770i	$-0.506830\pi$
$997$	27.0000	−	46.7654i	0.855099	−	1.48107i	0.876554	−	0.481304i	$-0.159837\pi$
$998$	24.0000			0.759707
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.f.343.1	yes	2
3.2	odd	2		666.2.f.a.343.1	✓	2
37.26	even	3	inner	666.2.f.f.433.1	yes	2
111.26	odd	6		666.2.f.a.433.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.f.a.343.1	✓	2	3.2	odd	2
666.2.f.a.433.1	yes	2	111.26	odd	6
666.2.f.f.343.1	yes	2	1.1	even	1	trivial
666.2.f.f.433.1	yes	2	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +4.00000 q^{10} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{20} +(1.00000 - 1.73205i) q^{22} +6.00000 q^{23} +(-5.50000 + 9.52628i) q^{25} +3.00000 q^{26} +(-1.50000 + 2.59808i) q^{28} +7.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(6.00000 - 10.3923i) q^{35} +(-5.00000 + 3.46410i) q^{37} +4.00000 q^{38} +(-2.00000 - 3.46410i) q^{40} +(3.00000 + 5.19615i) q^{41} +1.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{46} -10.0000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(5.50000 + 9.52628i) q^{50} +(1.50000 - 2.59808i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(4.00000 + 6.92820i) q^{55} +(1.50000 + 2.59808i) q^{56} +(5.00000 - 8.66025i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(3.50000 - 6.06218i) q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-4.50000 - 7.79423i) q^{67} -6.00000 q^{68} +(-6.00000 - 10.3923i) q^{70} +(-3.00000 - 5.19615i) q^{71} -11.0000 q^{73} +(0.500000 + 6.06218i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-4.50000 - 7.79423i) q^{79} -4.00000 q^{80} +6.00000 q^{82} +(5.00000 - 8.66025i) q^{83} +24.0000 q^{85} +(0.500000 - 0.866025i) q^{86} -2.00000 q^{88} +(-1.00000 + 1.73205i) q^{89} +(4.50000 - 7.79423i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-5.00000 + 8.66025i) q^{94} +(-8.00000 + 13.8564i) q^{95} -15.0000 q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 4 q^{5} - 3 q^{7} - 2 q^{8} + 8 q^{10} + 4 q^{11} + 3 q^{13} - 6 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 4 q^{20} + 2 q^{22} + 12 q^{23} - 11 q^{25} + 6 q^{26} - 3 q^{28} + 14 q^{31}+ \cdots + 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 4 * q^5 - 3 * q^7 - 2 * q^8 + 8 * q^10 + 4 * q^11 + 3 * q^13 - 6 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 4 * q^20 + 2 * q^22 + 12 * q^23 - 11 * q^25 + 6 * q^26 - 3 * q^28 + 14 * q^31 + q^32 - 6 * q^34 + 12 * q^35 - 10 * q^37 + 8 * q^38 - 4 * q^40 + 6 * q^41 + 2 * q^43 - 2 * q^44 + 6 * q^46 - 20 * q^47 - 2 * q^49 + 11 * q^50 + 3 * q^52 - 6 * q^53 + 8 * q^55 + 3 * q^56 + 10 * q^59 - 10 * q^61 + 7 * q^62 + 2 * q^64 - 12 * q^65 - 9 * q^67 - 12 * q^68 - 12 * q^70 - 6 * q^71 - 22 * q^73 + q^74 + 4 * q^76 - 6 * q^77 - 9 * q^79 - 8 * q^80 + 12 * q^82 + 10 * q^83 + 48 * q^85 + q^86 - 4 * q^88 - 2 * q^89 + 9 * q^91 - 6 * q^92 - 10 * q^94 - 16 * q^95 - 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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