LMFDB - Embedded newform 666.2.f.h.433.1

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 = [4,-2,0,-2,2] 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$1.65831 - 2.87228i$ of defining polynomial
Character	$\chi$	$=$	666.433
Dual form			666.2.f.h.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.15831 + 2.00626i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.31662 q^{11} +(-1.00000 + 1.73205i) q^{13} +2.31662 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.65831 + 2.87228i) q^{17} +(-0.158312 + 0.274205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.15831 - 2.00626i) q^{22} +4.00000 q^{23} +(2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +(-1.15831 - 2.00626i) q^{28} +3.63325 q^{29} -2.31662 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.65831 - 2.87228i) q^{34} +(1.15831 + 2.00626i) q^{35} +(3.97494 + 4.60433i) q^{37} +0.316625 q^{38} +(0.500000 - 0.866025i) q^{40} +(2.34169 - 4.05592i) q^{41} +0.316625 q^{43} +(-1.15831 + 2.00626i) q^{44} +(-2.00000 - 3.46410i) q^{46} +4.31662 q^{47} +(0.816625 + 1.41444i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(2.31662 + 4.01251i) q^{53} +(1.15831 - 2.00626i) q^{55} +(-1.15831 + 2.00626i) q^{56} +(-1.81662 - 3.14649i) q^{58} +(-4.31662 - 7.47661i) q^{59} +(0.341688 - 0.591820i) q^{61} +(1.15831 + 2.00626i) q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(0.158312 - 0.274205i) q^{67} -3.31662 q^{68} +(1.15831 - 2.00626i) q^{70} +(0.158312 - 0.274205i) q^{71} +12.6332 q^{73} +(2.00000 - 5.74456i) q^{74} +(-0.158312 - 0.274205i) q^{76} +(-2.68338 + 4.64774i) q^{77} +(-3.47494 + 6.01877i) q^{79} -1.00000 q^{80} -4.68338 q^{82} +(-4.31662 - 7.47661i) q^{83} +3.31662 q^{85} +(-0.158312 - 0.274205i) q^{86} +2.31662 q^{88} +(1.34169 + 2.32387i) q^{89} +(-2.31662 - 4.01251i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-2.15831 - 3.73831i) q^{94} +(0.158312 + 0.274205i) q^{95} +13.6332 q^{97} +(0.816625 - 1.41444i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} + 4 q^{8} - 4 q^{10} - 4 q^{11} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{19} + 2 q^{20} + 2 q^{22} + 16 q^{23} + 8 q^{25} + 8 q^{26} + 2 q^{28} - 12 q^{29} + 4 q^{31}+ \cdots - 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 + 4 * q^8 - 4 * q^10 - 4 * q^11 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^19 + 2 * q^20 + 2 * q^22 + 16 * q^23 + 8 * q^25 + 8 * q^26 + 2 * q^28 - 12 * q^29 + 4 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 - 12 * q^38 + 2 * q^40 + 16 * q^41 - 12 * q^43 + 2 * q^44 - 8 * q^46 + 4 * q^47 - 10 * q^49 + 8 * q^50 - 4 * q^52 - 4 * q^53 - 2 * q^55 + 2 * q^56 + 6 * q^58 - 4 * q^59 + 8 * q^61 - 2 * q^62 + 4 * q^64 + 4 * q^65 - 6 * q^67 - 2 * q^70 - 6 * q^71 + 24 * q^73 + 8 * q^74 + 6 * q^76 - 24 * q^77 + 6 * q^79 - 4 * q^80 - 32 * q^82 - 4 * q^83 + 6 * q^86 - 4 * q^88 + 12 * q^89 + 4 * q^91 - 8 * q^92 - 2 * q^94 - 6 * q^95 + 28 * q^97 - 10 * q^98

Character values

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

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

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	−1.15831	+	2.00626i	−0.437801	+	0.758293i	−0.997520	−	0.0703892i	$-0.977576\pi$
$7$	−1.15831	+	2.00626i	−0.437801	+	0.758293i	0.559719	+	0.828683i	$0.310909\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	2.31662			0.698489			0.349244	−	0.937032i	$-0.386438\pi$
$11$	2.31662			0.698489			0.349244	+	0.937032i	$0.386438\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	2.31662			0.619144
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.65831	+	2.87228i	0.402200	+	0.696631i	0.993991	−	0.109461i	$-0.0349124\pi$
$17$	1.65831	+	2.87228i	0.402200	+	0.696631i	−0.591791	+	0.806091i	$0.701579\pi$
$18$		0			0
$19$	−0.158312	+	0.274205i	−0.0363194	+	0.0629070i	−0.883614	−	0.468217i	$-0.844897\pi$
$19$	−0.158312	+	0.274205i	−0.0363194	+	0.0629070i	0.847294	+	0.531124i	$0.178230\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−1.15831	−	2.00626i	−0.246953	−	0.427735i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.00000			0.392232
$27$		0			0
$28$	−1.15831	−	2.00626i	−0.218900	−	0.379147i
$29$	3.63325			0.674678			0.337339	−	0.941383i	$-0.390473\pi$
$29$	3.63325			0.674678			0.337339	+	0.941383i	$0.390473\pi$
$30$		0			0
$31$	−2.31662			−0.416078			−0.208039	−	0.978121i	$-0.566708\pi$
$31$	−2.31662			−0.416078			−0.208039	+	0.978121i	$0.566708\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.65831	−	2.87228i	0.284398	−	0.492592i
$35$	1.15831	+	2.00626i	0.195791	+	0.339119i
$36$		0			0
$37$	3.97494	+	4.60433i	0.653476	+	0.756948i
$37$	3.97494	+	4.60433i	0.653476	+	0.756948i
$38$	0.316625			0.0513633
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	2.34169	−	4.05592i	0.365710	−	0.633429i	−0.623180	−	0.782079i	$-0.714159\pi$
$41$	2.34169	−	4.05592i	0.365710	−	0.633429i	0.988890	+	0.148650i	$0.0474928\pi$
$42$		0			0
$43$	0.316625			0.0482848			0.0241424	−	0.999709i	$-0.492314\pi$
$43$	0.316625			0.0482848			0.0241424	+	0.999709i	$0.492314\pi$
$44$	−1.15831	+	2.00626i	−0.174622	+	0.302454i
$45$		0			0
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	4.31662			0.629644			0.314822	−	0.949151i	$-0.398055\pi$
$47$	4.31662			0.629644			0.314822	+	0.949151i	$0.398055\pi$
$48$		0			0
$49$	0.816625	+	1.41444i	0.116661	+	0.202062i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	2.31662	+	4.01251i	0.318213	+	0.551161i	0.980115	−	0.198429i	$-0.0635840\pi$
$53$	2.31662	+	4.01251i	0.318213	+	0.551161i	−0.661902	+	0.749590i	$0.730251\pi$
$54$		0			0
$55$	1.15831	−	2.00626i	0.156187	−	0.270523i
$56$	−1.15831	+	2.00626i	−0.154786	+	0.268097i
$57$		0			0
$58$	−1.81662	−	3.14649i	−0.238535	−	0.413154i
$59$	−4.31662	−	7.47661i	−0.561977	−	0.973372i	−0.997324	−	0.0731095i	$-0.976708\pi$
$59$	−4.31662	−	7.47661i	−0.561977	−	0.973372i	0.435347	−	0.900263i	$-0.356626\pi$
$60$		0			0
$61$	0.341688	−	0.591820i	0.0437486	−	0.0757748i	−0.843322	−	0.537409i	$-0.819403\pi$
$61$	0.341688	−	0.591820i	0.0437486	−	0.0757748i	0.887071	+	0.461634i	$0.152737\pi$
$62$	1.15831	+	2.00626i	0.147106	+	0.254795i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	0.158312	−	0.274205i	0.0193409	−	0.0334995i	−0.856193	−	0.516656i	$-0.827177\pi$
$67$	0.158312	−	0.274205i	0.0193409	−	0.0334995i	0.875534	+	0.483157i	$0.160510\pi$
$68$	−3.31662			−0.402200
$69$		0			0
$70$	1.15831	−	2.00626i	0.138445	−	0.239793i
$71$	0.158312	−	0.274205i	0.0187882	−	0.0325422i	−0.856478	−	0.516183i	$-0.827353\pi$
$71$	0.158312	−	0.274205i	0.0187882	−	0.0325422i	0.875267	+	0.483641i	$0.160686\pi$
$72$		0			0
$73$	12.6332			1.47861			0.739305	−	0.673371i	$-0.235154\pi$
$73$	12.6332			1.47861			0.739305	+	0.673371i	$0.235154\pi$
$74$	2.00000	−	5.74456i	0.232495	−	0.667792i
$75$		0			0
$76$	−0.158312	−	0.274205i	−0.0181597	−	0.0314535i
$77$	−2.68338	+	4.64774i	−0.305799	+	0.529659i
$78$		0			0
$79$	−3.47494	+	6.01877i	−0.390961	+	0.677164i	−0.992577	−	0.121621i	$-0.961191\pi$
$79$	−3.47494	+	6.01877i	−0.390961	+	0.677164i	0.601616	+	0.798786i	$0.294524\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	−4.68338			−0.517192
$83$	−4.31662	−	7.47661i	−0.473811	−	0.820665i	0.525739	−	0.850646i	$-0.323789\pi$
$83$	−4.31662	−	7.47661i	−0.473811	−	0.820665i	−0.999550	+	0.0299808i	$0.990455\pi$
$84$		0			0
$85$	3.31662			0.359738
$86$	−0.158312	−	0.274205i	−0.0170713	−	0.0295683i
$87$		0			0
$88$	2.31662			0.246953
$89$	1.34169	+	2.32387i	0.142219	+	0.246330i	0.928332	−	0.371753i	$-0.121243\pi$
$89$	1.34169	+	2.32387i	0.142219	+	0.246330i	−0.786113	+	0.618083i	$0.787910\pi$
$90$		0			0
$91$	−2.31662	−	4.01251i	−0.242848	−	0.420626i
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$		0			0
$94$	−2.15831	−	3.73831i	−0.222613	−	0.385577i
$95$	0.158312	+	0.274205i	0.0162425	+	0.0281329i
$96$		0			0
$97$	13.6332			1.38425			0.692123	−	0.721779i	$-0.256675\pi$
$97$	13.6332			1.38425			0.692123	+	0.721779i	$0.256675\pi$
$98$	0.816625	−	1.41444i	0.0824916	−	0.142880i
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−8.26650			−0.822547			−0.411274	−	0.911512i	$-0.634916\pi$
$101$	−8.26650			−0.822547			−0.411274	+	0.911512i	$0.634916\pi$
$102$		0			0
$103$	−10.9499			−1.07892			−0.539462	−	0.842010i	$-0.681372\pi$
$103$	−10.9499			−1.07892			−0.539462	+	0.842010i	$0.681372\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	2.31662	−	4.01251i	0.225010	−	0.389730i
$107$	−7.79156	+	13.4954i	−0.753239	+	1.30465i	0.193006	+	0.981197i	$0.438176\pi$
$107$	−7.79156	+	13.4954i	−0.753239	+	1.30465i	−0.946245	+	0.323450i	$0.895157\pi$
$108$		0			0
$109$	−1.34169	−	2.32387i	−0.128510	−	0.222586i	0.794589	−	0.607147i	$-0.207686\pi$
$109$	−1.34169	−	2.32387i	−0.128510	−	0.222586i	−0.923100	+	0.384561i	$0.874353\pi$
$110$	−2.31662			−0.220882
$111$		0			0
$112$	2.31662			0.218900
$113$	−7.63325	−	13.2212i	−0.718076	−	1.24374i	−0.961761	−	0.273889i	$-0.911690\pi$
$113$	−7.63325	−	13.2212i	−0.718076	−	1.24374i	0.243686	−	0.969854i	$-0.421644\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−1.81662	+	3.14649i	−0.168669	+	0.292144i
$117$		0			0
$118$	−4.31662	+	7.47661i	−0.397378	+	0.688278i
$119$	−7.68338			−0.704334
$120$		0			0
$121$	−5.63325			−0.512114
$122$	−0.683375			−0.0618699
$123$		0			0
$124$	1.15831	−	2.00626i	0.104020	−	0.180167i
$125$	9.00000			0.804984
$126$		0			0
$127$	1.68338	+	2.91569i	0.149375	+	0.258726i	0.930997	−	0.365027i	$-0.118940\pi$
$127$	1.68338	+	2.91569i	0.149375	+	0.258726i	−0.781621	+	0.623753i	$0.785607\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−4.63325	−	8.02502i	−0.404809	−	0.701150i	0.589490	−	0.807775i	$-0.299329\pi$
$131$	−4.63325	−	8.02502i	−0.404809	−	0.701150i	−0.994299	+	0.106626i	$0.965995\pi$
$132$		0			0
$133$	−0.366750	−	0.635230i	−0.0318013	−	0.0550815i
$134$	−0.316625			−0.0273522
$135$		0			0
$136$	1.65831	+	2.87228i	0.142199	+	0.246296i
$137$	0.683375			0.0583847			0.0291923	−	0.999574i	$-0.490706\pi$
$137$	0.683375			0.0583847			0.0291923	+	0.999574i	$0.490706\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$	−2.31662			−0.195791
$141$		0			0
$142$	−0.316625			−0.0265706
$143$	−2.31662	+	4.01251i	−0.193726	+	0.335543i
$144$		0			0
$145$	1.81662	−	3.14649i	0.150862	−	0.261301i
$146$	−6.31662	−	10.9407i	−0.522768	−	0.905460i
$147$		0			0
$148$	−5.97494	+	1.14023i	−0.491137	+	0.0937264i
$149$	−19.6332			−1.60842			−0.804209	−	0.594346i	$-0.797411\pi$
$149$	−19.6332			−1.60842			−0.804209	+	0.594346i	$0.797411\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	−0.158312	+	0.274205i	−0.0128408	+	0.0222410i
$153$		0			0
$154$	5.36675			0.432465
$155$	−1.15831	+	2.00626i	−0.0930379	+	0.161146i
$156$		0			0
$157$	−1.34169	−	2.32387i	−0.107078	−	0.185465i	0.807507	−	0.589858i	$-0.200816\pi$
$157$	−1.34169	−	2.32387i	−0.107078	−	0.185465i	−0.914585	+	0.404393i	$0.867483\pi$
$158$	6.94987			0.552902
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−4.63325	+	8.02502i	−0.365151	+	0.632460i
$162$		0			0
$163$	−2.15831	−	3.73831i	−0.169052	−	0.292807i	0.769035	−	0.639207i	$-0.220737\pi$
$163$	−2.15831	−	3.73831i	−0.169052	−	0.292807i	−0.938087	+	0.346400i	$0.887404\pi$
$164$	2.34169	+	4.05592i	0.182855	+	0.316714i
$165$		0			0
$166$	−4.31662	+	7.47661i	−0.335035	+	0.580298i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−1.65831	−	2.87228i	−0.127187	−	0.220294i
$171$		0			0
$172$	−0.158312	+	0.274205i	−0.0120712	+	0.0209079i
$173$	−6.81662	−	11.8067i	−0.518258	−	0.897650i	−0.999775	−	0.0212129i	$-0.993247\pi$
$173$	−6.81662	−	11.8067i	−0.518258	−	0.897650i	0.481517	−	0.876437i	$-0.340086\pi$
$174$		0			0
$175$	−9.26650			−0.700481
$176$	−1.15831	−	2.00626i	−0.0873111	−	0.151227i
$177$		0			0
$178$	1.34169	−	2.32387i	0.100564	−	0.174182i
$179$	−0.633250			−0.0473313			−0.0236656	−	0.999720i	$-0.507534\pi$
$179$	−0.633250			−0.0473313			−0.0236656	+	0.999720i	$0.507534\pi$
$180$		0			0
$181$	−0.658312	+	1.14023i	−0.0489320	+	0.0847527i	−0.889454	−	0.457025i	$-0.848915\pi$
$181$	−0.658312	+	1.14023i	−0.0489320	+	0.0847527i	0.840522	+	0.541777i	$0.182248\pi$
$182$	−2.31662	+	4.01251i	−0.171720	+	0.297427i
$183$		0			0
$184$	4.00000			0.294884
$185$	5.97494	−	1.14023i	0.439286	−	0.0838314i
$186$		0			0
$187$	3.84169	+	6.65400i	0.280932	+	0.486589i
$188$	−2.15831	+	3.73831i	−0.157411	+	0.272644i
$189$		0			0
$190$	0.158312	−	0.274205i	0.0114852	−	0.0198929i
$191$	11.3668			0.822469			0.411235	−	0.911530i	$-0.365098\pi$
$191$	11.3668			0.822469			0.411235	+	0.911530i	$0.365098\pi$
$192$		0			0
$193$	1.00000			0.0719816			0.0359908	−	0.999352i	$-0.488541\pi$
$193$	1.00000			0.0719816			0.0359908	+	0.999352i	$0.488541\pi$
$194$	−6.81662	−	11.8067i	−0.489405	−	0.847675i
$195$		0			0
$196$	−1.63325			−0.116661
$197$	4.81662	+	8.34264i	0.343170	+	0.594388i	0.985020	−	0.172442i	$-0.0551659\pi$
$197$	4.81662	+	8.34264i	0.343170	+	0.594388i	−0.641849	+	0.766831i	$0.721833\pi$
$198$		0			0
$199$	−5.68338			−0.402884			−0.201442	−	0.979500i	$-0.564563\pi$
$199$	−5.68338			−0.402884			−0.201442	+	0.979500i	$0.564563\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	4.13325	+	7.15900i	0.290814	+	0.503705i
$203$	−4.20844	+	7.28923i	−0.295374	+	0.511604i
$204$		0			0
$205$	−2.34169	−	4.05592i	−0.163551	−	0.283278i
$206$	5.47494	+	9.48287i	0.381457	+	0.660703i
$207$		0			0
$208$	2.00000			0.138675
$209$	−0.366750	+	0.635230i	−0.0253687	+	0.0439398i
$210$		0			0
$211$	−16.9499			−1.16688			−0.583439	−	0.812157i	$-0.698293\pi$
$211$	−16.9499			−1.16688			−0.583439	+	0.812157i	$0.698293\pi$
$212$	−4.63325			−0.318213
$213$		0			0
$214$	15.5831			1.06524
$215$	0.158312	−	0.274205i	0.0107968	−	0.0187006i
$216$		0			0
$217$	2.68338	−	4.64774i	0.182159	−	0.315509i
$218$	−1.34169	+	2.32387i	−0.0908706	+	0.157392i
$219$		0			0
$220$	1.15831	+	2.00626i	0.0780934	+	0.135262i
$221$	−6.63325			−0.446201
$222$		0			0
$223$	−0.633250			−0.0424055			−0.0212028	−	0.999775i	$-0.506750\pi$
$223$	−0.633250			−0.0424055			−0.0212028	+	0.999775i	$0.506750\pi$
$224$	−1.15831	−	2.00626i	−0.0773930	−	0.134049i
$225$		0			0
$226$	−7.63325	+	13.2212i	−0.507756	+	0.879460i
$227$	0.525063	−	0.909435i	0.0348496	−	0.0603614i	−0.848075	−	0.529877i	$-0.822238\pi$
$227$	0.525063	−	0.909435i	0.0348496	−	0.0603614i	0.882924	+	0.469516i	$0.155571\pi$
$228$		0			0
$229$	−1.02506	+	1.77546i	−0.0677381	+	0.117326i	−0.897905	−	0.440189i	$-0.854912\pi$
$229$	−1.02506	+	1.77546i	−0.0677381	+	0.117326i	0.830167	+	0.557514i	$0.188245\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	3.63325			0.238535
$233$	5.94987			0.389789			0.194895	−	0.980824i	$-0.437564\pi$
$233$	5.94987			0.389789			0.194895	+	0.980824i	$0.437564\pi$
$234$		0			0
$235$	2.15831	−	3.73831i	0.140793	−	0.243860i
$236$	8.63325			0.561977
$237$		0			0
$238$	3.84169	+	6.65400i	0.249020	+	0.431315i
$239$	−10.4749	−	18.1431i	−0.677567	−	1.17358i	−0.975711	−	0.219060i	$-0.929701\pi$
$239$	−10.4749	−	18.1431i	−0.677567	−	1.17358i	0.298144	−	0.954521i	$-0.403632\pi$
$240$		0			0
$241$	6.31662	−	10.9407i	0.406890	−	0.704753i	−0.587650	−	0.809115i	$-0.699947\pi$
$241$	6.31662	−	10.9407i	0.406890	−	0.704753i	0.994539	+	0.104362i	$0.0332800\pi$
$242$	2.81662	+	4.87854i	0.181059	+	0.313604i
$243$		0			0
$244$	0.341688	+	0.591820i	0.0218743	+	0.0378874i
$245$	1.63325			0.104344
$246$		0			0
$247$	−0.316625	−	0.548410i	−0.0201464	−	0.0348945i
$248$	−2.31662			−0.147106
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	18.3166			1.15614			0.578068	−	0.815989i	$-0.303807\pi$
$251$	18.3166			1.15614			0.578068	+	0.815989i	$0.303807\pi$
$252$		0			0
$253$	9.26650			0.582580
$254$	1.68338	−	2.91569i	0.105624	−	0.182947i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.34169	−	9.25207i	−0.333205	−	0.577129i	0.649933	−	0.759991i	$-0.274797\pi$
$257$	−5.34169	−	9.25207i	−0.333205	−	0.577129i	−0.983138	+	0.182863i	$0.941464\pi$
$258$		0			0
$259$	−13.8417	+	2.64149i	−0.860081	+	0.164134i
$260$	−2.00000			−0.124035
$261$		0			0
$262$	−4.63325	+	8.02502i	−0.286243	+	0.495788i
$263$	10.3166	−	17.8689i	0.636150	−	1.10184i	−0.350120	−	0.936705i	$-0.613859\pi$
$263$	10.3166	−	17.8689i	0.636150	−	1.10184i	0.986270	−	0.165140i	$-0.0528075\pi$
$264$		0			0
$265$	4.63325			0.284618
$266$	−0.366750	+	0.635230i	−0.0224869	+	0.0389485i
$267$		0			0
$268$	0.158312	+	0.274205i	0.00967047	+	0.0167497i
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$		0			0
$271$	−11.7916	−	20.4236i	−0.716286	−	1.24064i	−0.962461	−	0.271419i	$-0.912507\pi$
$271$	−11.7916	−	20.4236i	−0.716286	−	1.24064i	0.246175	−	0.969225i	$-0.420826\pi$
$272$	1.65831	−	2.87228i	0.100550	−	0.174158i
$273$		0			0
$274$	−0.341688	−	0.591820i	−0.0206421	−	0.0357532i
$275$	4.63325	+	8.02502i	0.279395	+	0.483927i
$276$		0			0
$277$	13.6583	−	23.6569i	0.820648	−	1.42140i	−0.0845516	−	0.996419i	$-0.526946\pi$
$277$	13.6583	−	23.6569i	0.820648	−	1.42140i	0.905200	−	0.424986i	$-0.139721\pi$
$278$		0			0
$279$		0			0
$280$	1.15831	+	2.00626i	0.0692224	+	0.119897i
$281$	−7.65831	−	13.2646i	−0.456857	−	0.791299i	0.541936	−	0.840420i	$-0.317691\pi$
$281$	−7.65831	−	13.2646i	−0.456857	−	0.791299i	−0.998793	+	0.0491207i	$0.984358\pi$
$282$		0			0
$283$	12.7916	−	22.1556i	0.760379	−	1.31702i	−0.182276	−	0.983247i	$-0.558346\pi$
$283$	12.7916	−	22.1556i	0.760379	−	1.31702i	0.942655	−	0.333768i	$-0.108320\pi$
$284$	0.158312	+	0.274205i	0.00939411	+	0.0162711i
$285$		0			0
$286$	4.63325			0.273970
$287$	5.42481	+	9.39605i	0.320217	+	0.554631i
$288$		0			0
$289$	3.00000	−	5.19615i	0.176471	−	0.305656i
$290$	−3.63325			−0.213352
$291$		0			0
$292$	−6.31662	+	10.9407i	−0.369653	+	0.640257i
$293$	10.8166	−	18.7349i	0.631914	−	1.09451i	−0.355246	−	0.934773i	$-0.615603\pi$
$293$	10.8166	−	18.7349i	0.631914	−	1.09451i	0.987160	−	0.159734i	$-0.0510637\pi$
$294$		0			0
$295$	−8.63325			−0.502647
$296$	3.97494	+	4.60433i	0.231039	+	0.267621i
$297$		0			0
$298$	9.81662	+	17.0029i	0.568662	+	0.984951i
$299$	−4.00000	+	6.92820i	−0.231326	+	0.400668i
$300$		0			0
$301$	−0.366750	+	0.635230i	−0.0211391	+	0.0366141i
$302$	20.0000			1.15087
$303$		0			0
$304$	0.316625			0.0181597
$305$	−0.341688	−	0.591820i	−0.0195650	−	0.0338875i
$306$		0			0
$307$	4.94987			0.282504			0.141252	−	0.989974i	$-0.454887\pi$
$307$	4.94987			0.282504			0.141252	+	0.989974i	$0.454887\pi$
$308$	−2.68338	−	4.64774i	−0.152899	−	0.264830i
$309$		0			0
$310$	2.31662			0.131575
$311$	4.15831	+	7.20241i	0.235796	+	0.408411i	0.959504	−	0.281696i	$-0.0908969\pi$
$311$	4.15831	+	7.20241i	0.235796	+	0.408411i	−0.723708	+	0.690107i	$0.757564\pi$
$312$		0			0
$313$	−3.13325	−	5.42695i	−0.177102	−	0.306749i	0.763785	−	0.645471i	$-0.223339\pi$
$313$	−3.13325	−	5.42695i	−0.177102	−	0.306749i	−0.940887	+	0.338722i	$0.890005\pi$
$314$	−1.34169	+	2.32387i	−0.0757158	+	0.131144i
$315$		0			0
$316$	−3.47494	−	6.01877i	−0.195480	−	0.338582i
$317$	14.1332	+	24.4795i	0.793802	+	1.37491i	0.923597	+	0.383365i	$0.125235\pi$
$317$	14.1332	+	24.4795i	0.793802	+	1.37491i	−0.129794	+	0.991541i	$0.541432\pi$
$318$		0			0
$319$	8.41688			0.471255
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	9.26650			0.516402
$323$	−1.05013			−0.0584306
$324$		0			0
$325$	−8.00000			−0.443760
$326$	−2.15831	+	3.73831i	−0.119538	+	0.207046i
$327$		0			0
$328$	2.34169	−	4.05592i	0.129298	−	0.223951i
$329$	−5.00000	+	8.66025i	−0.275659	+	0.477455i
$330$		0			0
$331$	−14.9499	−	25.8939i	−0.821719	−	1.42326i	−0.904401	−	0.426684i	$-0.859682\pi$
$331$	−14.9499	−	25.8939i	−0.821719	−	1.42326i	0.0826815	−	0.996576i	$-0.473652\pi$
$332$	8.63325			0.473811
$333$		0			0
$334$	12.0000			0.656611
$335$	−0.158312	−	0.274205i	−0.00864953	−	0.0149814i
$336$		0			0
$337$	10.7665	−	18.6481i	0.586489	−	1.01583i	−0.408199	−	0.912893i	$-0.633843\pi$
$337$	10.7665	−	18.6481i	0.586489	−	1.01583i	0.994688	−	0.102935i	$-0.0328235\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−1.65831	+	2.87228i	−0.0899346	+	0.155771i
$341$	−5.36675			−0.290626
$342$		0			0
$343$	−20.0000			−1.07990
$344$	0.316625			0.0170713
$345$		0			0
$346$	−6.81662	+	11.8067i	−0.366464	+	0.634734i
$347$	36.6332			1.96658			0.983288	−	0.182057i	$-0.0582756\pi$
$347$	36.6332			1.96658			0.983288	+	0.182057i	$0.0582756\pi$
$348$		0			0
$349$	9.60819	+	16.6419i	0.514314	+	0.890819i	0.999862	+	0.0166085i	$0.00528690\pi$
$349$	9.60819	+	16.6419i	0.514314	+	0.890819i	−0.485548	+	0.874210i	$0.661380\pi$
$350$	4.63325	+	8.02502i	0.247658	+	0.428956i
$351$		0			0
$352$	−1.15831	+	2.00626i	−0.0617383	+	0.106934i
$353$	12.9749	+	22.4733i	0.690586	+	1.19613i	0.971646	+	0.236440i	$0.0759807\pi$
$353$	12.9749	+	22.4733i	0.690586	+	1.19613i	−0.281060	+	0.959690i	$0.590686\pi$
$354$		0			0
$355$	−0.158312	−	0.274205i	−0.00840235	−	0.0145533i
$356$	−2.68338			−0.142219
$357$		0			0
$358$	0.316625	+	0.548410i	0.0167341	+	0.0289844i
$359$	24.6332			1.30009			0.650047	−	0.759894i	$-0.274749\pi$
$359$	24.6332			1.30009			0.650047	+	0.759894i	$0.274749\pi$
$360$		0			0
$361$	9.44987	+	16.3677i	0.497362	+	0.861456i
$362$	1.31662			0.0692003
$363$		0			0
$364$	4.63325			0.242848
$365$	6.31662	−	10.9407i	0.330627	−	0.572663i
$366$		0			0
$367$	−4.94987	+	8.57343i	−0.258381	+	0.447530i	−0.965808	−	0.259257i	$-0.916522\pi$
$367$	−4.94987	+	8.57343i	−0.258381	+	0.447530i	0.707427	+	0.706786i	$0.249856\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	−3.97494	−	4.60433i	−0.206647	−	0.239368i
$371$	−10.7335			−0.557256
$372$		0			0
$373$	−4.02506	+	6.97161i	−0.208410	+	0.360976i	−0.951214	−	0.308533i	$-0.900162\pi$
$373$	−4.02506	+	6.97161i	−0.208410	+	0.360976i	0.742804	+	0.669509i	$0.233495\pi$
$374$	3.84169	−	6.65400i	0.198649	−	0.344070i
$375$		0			0
$376$	4.31662			0.222613
$377$	−3.63325	+	6.29297i	−0.187122	+	0.324105i
$378$		0			0
$379$	−12.7916	−	22.1556i	−0.657058	−	1.13806i	−0.981374	−	0.192109i	$-0.938467\pi$
$379$	−12.7916	−	22.1556i	−0.657058	−	1.13806i	0.324315	−	0.945949i	$-0.394866\pi$
$380$	−0.316625			−0.0162425
$381$		0			0
$382$	−5.68338	−	9.84389i	−0.290787	−	0.503657i
$383$	6.79156	−	11.7633i	0.347033	−	0.601078i	−0.638688	−	0.769466i	$-0.720523\pi$
$383$	6.79156	−	11.7633i	0.347033	−	0.601078i	0.985721	+	0.168387i	$0.0538560\pi$
$384$		0			0
$385$	2.68338	+	4.64774i	0.136757	+	0.236871i
$386$	−0.500000	−	0.866025i	−0.0254493	−	0.0440795i
$387$		0			0
$388$	−6.81662	+	11.8067i	−0.346062	+	0.599396i
$389$	−3.50000	+	6.06218i	−0.177457	+	0.307365i	−0.941009	−	0.338382i	$-0.890120\pi$
$389$	−3.50000	+	6.06218i	−0.177457	+	0.307365i	0.763552	+	0.645747i	$0.223454\pi$
$390$		0			0
$391$	6.63325	+	11.4891i	0.335458	+	0.581030i
$392$	0.816625	+	1.41444i	0.0412458	+	0.0714398i
$393$		0			0
$394$	4.81662	−	8.34264i	0.242658	−	0.420296i
$395$	3.47494	+	6.01877i	0.174843	+	0.302837i
$396$		0			0
$397$	18.5831			0.932660			0.466330	−	0.884611i	$-0.345576\pi$
$397$	18.5831			0.932660			0.466330	+	0.884611i	$0.345576\pi$
$398$	2.84169	+	4.92195i	0.142441	+	0.246715i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	16.5330			0.825619			0.412809	−	0.910817i	$-0.364548\pi$
$401$	16.5330			0.825619			0.412809	+	0.910817i	$0.364548\pi$
$402$		0			0
$403$	2.31662	−	4.01251i	0.115399	−	0.199877i
$404$	4.13325	−	7.15900i	0.205637	−	0.356173i
$405$		0			0
$406$	8.41688			0.417723
$407$	9.20844	+	10.6665i	0.456445	+	0.528719i
$408$		0			0
$409$	5.13325	+	8.89105i	0.253823	+	0.439634i	0.964575	−	0.263808i	$-0.0849786\pi$
$409$	5.13325	+	8.89105i	0.253823	+	0.439634i	−0.710752	+	0.703442i	$0.751645\pi$
$410$	−2.34169	+	4.05592i	−0.115648	+	0.200308i
$411$		0			0
$412$	5.47494	−	9.48287i	0.269731	−	0.467187i
$413$	20.0000			0.984136
$414$		0			0
$415$	−8.63325			−0.423790
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	0.733501			0.0358767
$419$	−11.4749	−	19.8752i	−0.560587	−	0.970966i	−0.997445	−	0.0714353i	$-0.977242\pi$
$419$	−11.4749	−	19.8752i	−0.560587	−	0.970966i	0.436858	−	0.899531i	$-0.356091\pi$
$420$		0			0
$421$	−11.2164			−0.546653			−0.273326	−	0.961921i	$-0.588124\pi$
$421$	−11.2164			−0.546653			−0.273326	+	0.961921i	$0.588124\pi$
$422$	8.47494	+	14.6790i	0.412553	+	0.714564i
$423$		0			0
$424$	2.31662	+	4.01251i	0.112505	+	0.194865i
$425$	−6.63325	+	11.4891i	−0.321760	+	0.557304i
$426$		0			0
$427$	0.791562	+	1.37103i	0.0383064	+	0.0663486i
$428$	−7.79156	−	13.4954i	−0.376619	−	0.652324i
$429$		0			0
$430$	−0.316625			−0.0152690
$431$	−16.7916	+	29.0838i	−0.808821	+	1.40092i	0.104860	+	0.994487i	$0.466561\pi$
$431$	−16.7916	+	29.0838i	−0.808821	+	1.40092i	−0.913681	+	0.406432i	$0.866773\pi$
$432$		0			0
$433$	−1.73350			−0.0833067			−0.0416534	−	0.999132i	$-0.513263\pi$
$433$	−1.73350			−0.0833067			−0.0416534	+	0.999132i	$0.513263\pi$
$434$	−5.36675			−0.257612
$435$		0			0
$436$	2.68338			0.128510
$437$	−0.633250	+	1.09682i	−0.0302924	+	0.0524680i
$438$		0			0
$439$	−19.2665	+	33.3706i	−0.919540	+	1.59269i	−0.119425	+	0.992843i	$0.538105\pi$
$439$	−19.2665	+	33.3706i	−0.919540	+	1.59269i	−0.800115	+	0.599846i	$0.795228\pi$
$440$	1.15831	−	2.00626i	0.0552204	−	0.0956445i
$441$		0			0
$442$	3.31662	+	5.74456i	0.157756	+	0.273241i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	2.68338			0.127204
$446$	0.316625	+	0.548410i	0.0149926	+	0.0259680i
$447$		0			0
$448$	−1.15831	+	2.00626i	−0.0547251	+	0.0947867i
$449$	15.6332	−	27.0776i	0.737779	−	1.27787i	−0.215715	−	0.976456i	$-0.569208\pi$
$449$	15.6332	−	27.0776i	0.737779	−	1.27787i	0.953493	−	0.301414i	$-0.0974585\pi$
$450$		0			0
$451$	5.42481	−	9.39605i	0.255444	−	0.442443i
$452$	15.2665			0.718076
$453$		0			0
$454$	−1.05013			−0.0492848
$455$	−4.63325			−0.217210
$456$		0			0
$457$	−10.8166	+	18.7349i	−0.505980	+	0.876384i	0.493996	+	0.869464i	$0.335536\pi$
$457$	−10.8166	+	18.7349i	−0.505980	+	0.876384i	−0.999976	+	0.00691935i	$0.997797\pi$
$458$	2.05013			0.0957961
$459$		0			0
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	−5.68338	−	9.84389i	−0.264701	−	0.458476i	0.702784	−	0.711403i	$-0.251940\pi$
$461$	−5.68338	−	9.84389i	−0.264701	−	0.458476i	−0.967485	+	0.252927i	$0.918607\pi$
$462$		0			0
$463$	6.52506	−	11.3017i	0.303245	−	0.525236i	−0.673624	−	0.739074i	$-0.735263\pi$
$463$	6.52506	−	11.3017i	0.303245	−	0.525236i	0.976869	+	0.213838i	$0.0685965\pi$
$464$	−1.81662	−	3.14649i	−0.0843347	−	0.146072i
$465$		0			0
$466$	−2.97494	−	5.15274i	−0.137811	−	0.238696i
$467$	3.36675			0.155795			0.0778973	−	0.996961i	$-0.475179\pi$
$467$	3.36675			0.155795			0.0778973	+	0.996961i	$0.475179\pi$
$468$		0			0
$469$	0.366750	+	0.635230i	0.0169350	+	0.0293322i
$470$	−4.31662			−0.199111
$471$		0			0
$472$	−4.31662	−	7.47661i	−0.198689	−	0.344139i
$473$	0.733501			0.0337264
$474$		0			0
$475$	−1.26650			−0.0581110
$476$	3.84169	−	6.65400i	0.176083	−	0.304986i
$477$		0			0
$478$	−10.4749	+	18.1431i	−0.479112	+	0.829847i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	−11.9499	+	2.28046i	−0.544867	+	0.103980i
$482$	−12.6332			−0.575429
$483$		0			0
$484$	2.81662	−	4.87854i	0.128028	−	0.221752i
$485$	6.81662	−	11.8067i	0.309527	−	0.536116i
$486$		0			0
$487$	−0.633250			−0.0286953			−0.0143476	−	0.999897i	$-0.504567\pi$
$487$	−0.633250			−0.0286953			−0.0143476	+	0.999897i	$0.504567\pi$
$488$	0.341688	−	0.591820i	0.0154675	−	0.0267904i
$489$		0			0
$490$	−0.816625	−	1.41444i	−0.0368913	−	0.0638977i
$491$	−14.3166			−0.646100			−0.323050	−	0.946382i	$-0.604708\pi$
$491$	−14.3166			−0.646100			−0.323050	+	0.946382i	$0.604708\pi$
$492$		0			0
$493$	6.02506	+	10.4357i	0.271355	+	0.470001i
$494$	−0.316625	+	0.548410i	−0.0142456	+	0.0246741i
$495$		0			0
$496$	1.15831	+	2.00626i	0.0520098	+	0.0900836i
$497$	0.366750	+	0.635230i	0.0164510	+	0.0284940i
$498$		0			0
$499$	8.47494	−	14.6790i	0.379390	−	0.657123i	−0.611583	−	0.791180i	$-0.709467\pi$
$499$	8.47494	−	14.6790i	0.379390	−	0.657123i	0.990974	+	0.134057i	$0.0428004\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$		0			0
$502$	−9.15831	−	15.8627i	−0.408755	−	0.707985i
$503$	−11.8417	−	20.5104i	−0.527995	−	0.914514i	−0.999467	−	0.0326331i	$-0.989611\pi$
$503$	−11.8417	−	20.5104i	−0.527995	−	0.914514i	0.471473	−	0.881881i	$-0.343723\pi$
$504$		0			0
$505$	−4.13325	+	7.15900i	−0.183927	+	0.318571i
$506$	−4.63325	−	8.02502i	−0.205973	−	0.356756i
$507$		0			0
$508$	−3.36675			−0.149375
$509$	−20.3997	−	35.3334i	−0.904203	−	1.56613i	−0.821984	−	0.569511i	$-0.807133\pi$
$509$	−20.3997	−	35.3334i	−0.904203	−	1.56613i	−0.0822194	−	0.996614i	$-0.526201\pi$
$510$		0			0
$511$	−14.6332	+	25.3455i	−0.647337	+	1.12122i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−5.34169	+	9.25207i	−0.235612	+	0.408092i
$515$	−5.47494	+	9.48287i	−0.241255	+	0.417865i
$516$		0			0
$517$	10.0000			0.439799
$518$	9.20844	+	10.6665i	0.404596	+	0.468660i
$519$		0			0
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.120656	+	0.992694i	$0.538500\pi$
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.799370	+	0.600839i	$0.794833\pi$
$522$		0			0
$523$	7.68338	−	13.3080i	0.335971	−	0.581918i	−0.647700	−	0.761895i	$-0.724269\pi$
$523$	7.68338	−	13.3080i	0.335971	−	0.581918i	0.983671	+	0.179977i	$0.0576024\pi$
$524$	9.26650			0.404809
$525$		0			0
$526$	−20.6332			−0.899652
$527$	−3.84169	−	6.65400i	−0.167347	−	0.289853i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−2.31662	−	4.01251i	−0.100628	−	0.174292i
$531$		0			0
$532$	0.733501			0.0318013
$533$	4.68338	+	8.11184i	0.202859	+	0.351363i
$534$		0			0
$535$	7.79156	+	13.4954i	0.336859	+	0.583456i
$536$	0.158312	−	0.274205i	0.00683805	−	0.0118439i
$537$		0			0
$538$	−5.00000	−	8.66025i	−0.215565	−	0.373370i
$539$	1.89181	+	3.27672i	0.0814862	+	0.141138i
$540$		0			0
$541$	28.6834			1.23319			0.616597	−	0.787279i	$-0.288511\pi$
$541$	28.6834			1.23319			0.616597	+	0.787279i	$0.288511\pi$
$542$	−11.7916	+	20.4236i	−0.506491	+	0.877268i
$543$		0			0
$544$	−3.31662			−0.142199
$545$	−2.68338			−0.114943
$546$		0			0
$547$	−19.6834			−0.841600			−0.420800	−	0.907153i	$-0.638251\pi$
$547$	−19.6834			−0.841600			−0.420800	+	0.907153i	$0.638251\pi$
$548$	−0.341688	+	0.591820i	−0.0145962	+	0.0252813i
$549$		0			0
$550$	4.63325	−	8.02502i	0.197562	−	0.342188i
$551$	−0.575188	+	0.996256i	−0.0245039	+	0.0424419i
$552$		0			0
$553$	−8.05013	−	13.9432i	−0.342326	−	0.592926i
$554$	−27.3166			−1.16057
$555$		0			0
$556$		0			0
$557$	4.44987	+	7.70741i	0.188547	+	0.326573i	0.944766	−	0.327745i	$-0.106289\pi$
$557$	4.44987	+	7.70741i	0.188547	+	0.326573i	−0.756219	+	0.654319i	$0.772955\pi$
$558$		0			0
$559$	−0.316625	+	0.548410i	−0.0133918	+	0.0231953i
$560$	1.15831	−	2.00626i	0.0489476	−	0.0847798i
$561$		0			0
$562$	−7.65831	+	13.2646i	−0.323046	+	0.559533i
$563$	−18.5330			−0.781073			−0.390536	−	0.920587i	$-0.627710\pi$
$563$	−18.5330			−0.781073			−0.390536	+	0.920587i	$0.627710\pi$
$564$		0			0
$565$	−15.2665			−0.642266
$566$	−25.5831			−1.07534
$567$		0			0
$568$	0.158312	−	0.274205i	0.00664264	−	0.0115054i
$569$	9.41688			0.394776			0.197388	−	0.980325i	$-0.436754\pi$
$569$	9.41688			0.394776			0.197388	+	0.980325i	$0.436754\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	−2.31662	−	4.01251i	−0.0968629	−	0.167772i
$573$		0			0
$574$	5.42481	−	9.39605i	0.226427	−	0.392184i
$575$	8.00000	+	13.8564i	0.333623	+	0.577852i
$576$		0			0
$577$	−8.31662	−	14.4048i	−0.346226	−	0.599680i	0.639350	−	0.768916i	$-0.279204\pi$
$577$	−8.31662	−	14.4048i	−0.346226	−	0.599680i	−0.985576	+	0.169235i	$0.945870\pi$
$578$	−6.00000			−0.249567
$579$		0			0
$580$	1.81662	+	3.14649i	0.0754312	+	0.130651i
$581$	20.0000			0.829740
$582$		0			0
$583$	5.36675	+	9.29548i	0.222268	+	0.384980i
$584$	12.6332			0.522768
$585$		0			0
$586$	−21.6332			−0.893661
$587$	8.63325	−	14.9532i	0.356332	−	0.617186i	−0.631013	−	0.775773i	$-0.717360\pi$
$587$	8.63325	−	14.9532i	0.356332	−	0.617186i	0.987345	+	0.158587i	$0.0506938\pi$
$588$		0			0
$589$	0.366750	−	0.635230i	0.0151117	−	0.0261742i
$590$	4.31662	+	7.47661i	0.177713	+	0.307807i
$591$		0			0
$592$	2.00000	−	5.74456i	0.0821995	−	0.236100i
$593$	−39.9499			−1.64054			−0.820272	−	0.571973i	$-0.806178\pi$
$593$	−39.9499			−1.64054			−0.820272	+	0.571973i	$0.806178\pi$
$594$		0			0
$595$	−3.84169	+	6.65400i	−0.157494	+	0.272787i
$596$	9.81662	−	17.0029i	0.402105	−	0.696466i
$597$		0			0
$598$	8.00000			0.327144
$599$	−1.20844	+	2.09308i	−0.0493754	+	0.0855208i	−0.889657	−	0.456630i	$-0.849056\pi$
$599$	−1.20844	+	2.09308i	−0.0493754	+	0.0855208i	0.840281	+	0.542151i	$0.182390\pi$
$600$		0			0
$601$	0.449874	+	0.779205i	0.0183508	+	0.0317844i	0.875055	−	0.484024i	$-0.160825\pi$
$601$	0.449874	+	0.779205i	0.0183508	+	0.0317844i	−0.856704	+	0.515808i	$0.827492\pi$
$602$	0.733501			0.0298953
$603$		0			0
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	−2.81662	+	4.87854i	−0.114512	+	0.198341i
$606$		0			0
$607$	19.7916	+	34.2800i	0.803315	+	1.39138i	0.917423	+	0.397914i	$0.130266\pi$
$607$	19.7916	+	34.2800i	0.803315	+	1.39138i	−0.114108	+	0.993468i	$0.536401\pi$
$608$	−0.158312	−	0.274205i	−0.00642042	−	0.0111205i
$609$		0			0
$610$	−0.341688	+	0.591820i	−0.0138345	+	0.0239621i
$611$	−4.31662	+	7.47661i	−0.174632	+	0.302471i
$612$		0			0
$613$	10.2916	+	17.8255i	0.415672	+	0.719965i	0.995499	−	0.0947745i	$-0.0302130\pi$
$613$	10.2916	+	17.8255i	0.415672	+	0.719965i	−0.579826	+	0.814740i	$0.696880\pi$
$614$	−2.47494	−	4.28672i	−0.0998803	−	0.172998i
$615$		0			0
$616$	−2.68338	+	4.64774i	−0.108116	+	0.187263i
$617$	8.63325	+	14.9532i	0.347562	+	0.601994i	0.985816	−	0.167831i	$-0.0536764\pi$
$617$	8.63325	+	14.9532i	0.347562	+	0.601994i	−0.638254	+	0.769826i	$0.720343\pi$
$618$		0			0
$619$	36.9499			1.48514			0.742570	−	0.669768i	$-0.233606\pi$
$619$	36.9499			1.48514			0.742570	+	0.669768i	$0.233606\pi$
$620$	−1.15831	−	2.00626i	−0.0465189	−	0.0805732i
$621$		0			0
$622$	4.15831	−	7.20241i	0.166733	−	0.288790i
$623$	−6.21637			−0.249054
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−3.13325	+	5.42695i	−0.125230	+	0.216904i
$627$		0			0
$628$	2.68338			0.107078
$629$	−6.63325	+	19.0526i	−0.264485	+	0.759675i
$630$		0			0
$631$	6.00000	+	10.3923i	0.238856	+	0.413711i	0.960386	−	0.278672i	$-0.0898942\pi$
$631$	6.00000	+	10.3923i	0.238856	+	0.413711i	−0.721530	+	0.692383i	$0.756561\pi$
$632$	−3.47494	+	6.01877i	−0.138226	+	0.239414i
$633$		0			0
$634$	14.1332	−	24.4795i	0.561303	−	0.972205i
$635$	3.36675			0.133605
$636$		0			0
$637$	−3.26650			−0.129423
$638$	−4.20844	−	7.28923i	−0.166614	−	0.288583i
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−6.34169	−	10.9841i	−0.250482	−	0.433847i	0.713177	−	0.700984i	$-0.247256\pi$
$641$	−6.34169	−	10.9841i	−0.250482	−	0.433847i	−0.963658	+	0.267137i	$0.913922\pi$
$642$		0			0
$643$	45.5831			1.79762			0.898811	−	0.438335i	$-0.144432\pi$
$643$	45.5831			1.79762			0.898811	+	0.438335i	$0.144432\pi$
$644$	−4.63325	−	8.02502i	−0.182576	−	0.316230i
$645$		0			0
$646$	0.525063	+	0.909435i	0.0206583	+	0.0357813i
$647$	−17.7414	+	30.7291i	−0.697488	+	1.20808i	0.271847	+	0.962340i	$0.412366\pi$
$647$	−17.7414	+	30.7291i	−0.697488	+	1.20808i	−0.969335	+	0.245744i	$0.920968\pi$
$648$		0			0
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$	4.00000	+	6.92820i	0.156893	+	0.271746i
$651$		0			0
$652$	4.31662			0.169052
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	−0.989837	−	0.142207i	$-0.954580\pi$
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	0.618073	+	0.786121i	$0.287914\pi$
$654$		0			0
$655$	−9.26650			−0.362072
$656$	−4.68338			−0.182855
$657$		0			0
$658$	10.0000			0.389841
$659$	15.2665	−	26.4424i	0.594698	−	1.03005i	−0.398891	−	0.916998i	$-0.630605\pi$
$659$	15.2665	−	26.4424i	0.594698	−	1.03005i	0.993589	−	0.113049i	$-0.0360618\pi$
$660$		0			0
$661$	17.2414	−	29.8630i	0.670614	−	1.16154i	−0.307116	−	0.951672i	$-0.599364\pi$
$661$	17.2414	−	29.8630i	0.670614	−	1.16154i	0.977730	−	0.209866i	$-0.0673027\pi$
$662$	−14.9499	+	25.8939i	−0.581043	+	1.00640i
$663$		0			0
$664$	−4.31662	−	7.47661i	−0.167518	−	0.290149i
$665$	−0.733501			−0.0284439
$666$		0			0
$667$	14.5330			0.562720
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$	−0.158312	+	0.274205i	−0.00611614	+	0.0105935i
$671$	0.791562	−	1.37103i	0.0305579	−	0.0529279i
$672$		0			0
$673$	−14.9499	+	25.8939i	−0.576275	+	0.998138i	0.419626	+	0.907697i	$0.362161\pi$
$673$	−14.9499	+	25.8939i	−0.576275	+	0.998138i	−0.995902	+	0.0904412i	$0.971172\pi$
$674$	−21.5330			−0.829420
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−38.1662			−1.46685			−0.733424	−	0.679771i	$-0.762079\pi$
$677$	−38.1662			−1.46685			−0.733424	+	0.679771i	$0.762079\pi$
$678$		0			0
$679$	−15.7916	+	27.3518i	−0.606025	+	1.04967i
$680$	3.31662			0.127187
$681$		0			0
$682$	2.68338	+	4.64774i	0.102752	+	0.177971i
$683$	−13.4749	−	23.3393i	−0.515604	−	0.893053i	−0.999836	−	0.0181128i	$-0.994234\pi$
$683$	−13.4749	−	23.3393i	−0.515604	−	0.893053i	0.484232	−	0.874940i	$-0.339099\pi$
$684$		0			0
$685$	0.341688	−	0.591820i	0.0130552	−	0.0226123i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$		0			0
$688$	−0.158312	−	0.274205i	−0.00603560	−	0.0104540i
$689$	−9.26650			−0.353026
$690$		0			0
$691$	1.10819	+	1.91944i	0.0421574	+	0.0730188i	0.886334	−	0.463046i	$-0.153244\pi$
$691$	1.10819	+	1.91944i	0.0421574	+	0.0730188i	−0.844177	+	0.536065i	$0.819910\pi$
$692$	13.6332			0.518258
$693$		0			0
$694$	−18.3166	−	31.7253i	−0.695290	−	1.20428i
$695$		0			0
$696$		0			0
$697$	15.5330			0.588354
$698$	9.60819	−	16.6419i	0.363675	−	0.629904i
$699$		0			0
$700$	4.63325	−	8.02502i	0.175120	−	0.303317i
$701$	−18.9499	−	32.8221i	−0.715727	−	1.23968i	−0.962679	−	0.270648i	$-0.912762\pi$
$701$	−18.9499	−	32.8221i	−0.715727	−	1.23968i	0.246952	−	0.969028i	$-0.420571\pi$
$702$		0			0
$703$	−1.89181	+	0.361025i	−0.0713511	+	0.0136163i
$704$	2.31662			0.0873111
$705$		0			0
$706$	12.9749	−	22.4733i	0.488318	−	0.845792i
$707$	9.57519	−	16.5847i	0.360112	−	0.623732i
$708$		0			0
$709$	−22.5330			−0.846245			−0.423122	−	0.906073i	$-0.639066\pi$
$709$	−22.5330			−0.846245			−0.423122	+	0.906073i	$0.639066\pi$
$710$	−0.158312	+	0.274205i	−0.00594136	+	0.0102907i
$711$		0			0
$712$	1.34169	+	2.32387i	0.0502819	+	0.0870908i
$713$	−9.26650			−0.347033
$714$		0			0
$715$	2.31662	+	4.01251i	0.0866369	+	0.150059i
$716$	0.316625	−	0.548410i	0.0118328	−	0.0204951i
$717$		0			0
$718$	−12.3166	−	21.3330i	−0.459652	−	0.796141i
$719$	−17.8997	−	31.0033i	−0.667548	−	1.15623i	−0.978588	−	0.205830i	$-0.934011\pi$
$719$	−17.8997	−	31.0033i	−0.667548	−	1.15623i	0.311040	−	0.950397i	$-0.399323\pi$
$720$		0			0
$721$	12.6834	−	21.9683i	0.472354	−	0.818140i
$722$	9.44987	−	16.3677i	0.351688	−	0.609141i
$723$		0			0
$724$	−0.658312	−	1.14023i	−0.0244660	−	0.0423763i
$725$	7.26650	+	12.5859i	0.269871	+	0.467430i
$726$		0			0
$727$	1.05013	−	1.81887i	0.0389470	−	0.0674582i	−0.845895	−	0.533350i	$-0.820933\pi$
$727$	1.05013	−	1.81887i	0.0389470	−	0.0674582i	0.884842	+	0.465892i	$0.154266\pi$
$728$	−2.31662	−	4.01251i	−0.0858598	−	0.148714i
$729$		0			0
$730$	−12.6332			−0.467578
$731$	0.525063	+	0.909435i	0.0194201	+	0.0336367i
$732$		0			0
$733$	5.63325	−	9.75707i	0.208069	−	0.360386i	−0.743037	−	0.669250i	$-0.766616\pi$
$733$	5.63325	−	9.75707i	0.208069	−	0.360386i	0.951106	+	0.308864i	$0.0999489\pi$
$734$	9.89975			0.365406
$735$		0			0
$736$	−2.00000	+	3.46410i	−0.0737210	+	0.127688i
$737$	0.366750	−	0.635230i	0.0135094	−	0.0233990i
$738$		0			0
$739$	14.5330			0.534605			0.267302	−	0.963613i	$-0.413868\pi$
$739$	14.5330			0.534605			0.267302	+	0.963613i	$0.413868\pi$
$740$	−2.00000	+	5.74456i	−0.0735215	+	0.211174i
$741$		0			0
$742$	5.36675	+	9.29548i	0.197020	+	0.341248i
$743$	−23.1082	+	40.0246i	−0.847757	+	1.46836i	0.0354480	+	0.999372i	$0.488714\pi$
$743$	−23.1082	+	40.0246i	−0.847757	+	1.46836i	−0.883205	+	0.468987i	$0.844619\pi$
$744$		0			0
$745$	−9.81662	+	17.0029i	−0.359653	+	0.622938i
$746$	8.05013			0.294736
$747$		0			0
$748$	−7.68338			−0.280932
$749$	−18.0501	−	31.2637i	−0.659537	−	1.14235i
$750$		0			0
$751$	−10.3166			−0.376459			−0.188229	−	0.982125i	$-0.560275\pi$
$751$	−10.3166			−0.376459			−0.188229	+	0.982125i	$0.560275\pi$
$752$	−2.15831	−	3.73831i	−0.0787056	−	0.136322i
$753$		0			0
$754$	7.26650			0.264630
$755$	10.0000	+	17.3205i	0.363937	+	0.630358i
$756$		0			0
$757$	−4.97494	−	8.61684i	−0.180817	−	0.313185i	0.761342	−	0.648351i	$-0.224541\pi$
$757$	−4.97494	−	8.61684i	−0.180817	−	0.313185i	−0.942159	+	0.335166i	$0.891208\pi$
$758$	−12.7916	+	22.1556i	−0.464610	+	0.804729i
$759$		0			0
$760$	0.158312	+	0.274205i	0.00574259	+	0.00994646i
$761$	−8.92481	−	15.4582i	−0.323524	−	0.560360i	0.657688	−	0.753290i	$-0.271534\pi$
$761$	−8.92481	−	15.4582i	−0.323524	−	0.560360i	−0.981213	+	0.192930i	$0.938201\pi$
$762$		0			0
$763$	6.21637			0.225048
$764$	−5.68338	+	9.84389i	−0.205617	+	0.356140i
$765$		0			0
$766$	−13.5831			−0.490778
$767$	17.2665			0.623457
$768$		0			0
$769$	−24.6332			−0.888298			−0.444149	−	0.895953i	$-0.646494\pi$
$769$	−24.6332			−0.888298			−0.444149	+	0.895953i	$0.646494\pi$
$770$	2.68338	−	4.64774i	0.0967021	−	0.167493i
$771$		0			0
$772$	−0.500000	+	0.866025i	−0.0179954	+	0.0311689i
$773$	−6.55013	+	11.3452i	−0.235592	+	0.408057i	−0.959444	−	0.281898i	$-0.909036\pi$
$773$	−6.55013	+	11.3452i	−0.235592	+	0.408057i	0.723853	+	0.689954i	$0.242369\pi$
$774$		0			0
$775$	−4.63325	−	8.02502i	−0.166431	−	0.288267i
$776$	13.6332			0.489405
$777$		0			0
$778$	7.00000			0.250962
$779$	0.741436	+	1.28421i	0.0265647	+	0.0460114i
$780$		0			0
$781$	0.366750	−	0.635230i	0.0131234	−	0.0227303i
$782$	6.63325	−	11.4891i	0.237205	−	0.410850i
$783$		0			0
$784$	0.816625	−	1.41444i	0.0291652	−	0.0505156i
$785$	−2.68338			−0.0957738
$786$		0			0
$787$	15.1662			0.540618			0.270309	−	0.962774i	$-0.412874\pi$
$787$	15.1662			0.540618			0.270309	+	0.962774i	$0.412874\pi$
$788$	−9.63325			−0.343170
$789$		0			0
$790$	3.47494	−	6.01877i	0.123633	−	0.214138i
$791$	35.3668			1.25750
$792$		0			0
$793$	0.683375	+	1.18364i	0.0242674	+	0.0420323i
$794$	−9.29156	−	16.0935i	−0.329745	−	0.571135i
$795$		0			0
$796$	2.84169	−	4.92195i	0.100721	−	0.174454i
$797$	22.9499	+	39.7503i	0.812926	+	1.40803i	0.910807	+	0.412831i	$0.135460\pi$
$797$	22.9499	+	39.7503i	0.812926	+	1.40803i	−0.0978812	+	0.995198i	$0.531207\pi$
$798$		0			0
$799$	7.15831	+	12.3986i	0.253243	+	0.438630i
$800$	−4.00000			−0.141421
$801$		0			0
$802$	−8.26650	−	14.3180i	−0.291900	−	0.505586i
$803$	29.2665			1.03279
$804$		0			0
$805$	4.63325	+	8.02502i	0.163301	+	0.282845i
$806$	−4.63325			−0.163199
$807$		0			0
$808$	−8.26650			−0.290814
$809$	1.00000	−	1.73205i	0.0351581	−	0.0608957i	−0.847911	−	0.530139i	$-0.822140\pi$
$809$	1.00000	−	1.73205i	0.0351581	−	0.0608957i	0.883069	+	0.469243i	$0.155473\pi$
$810$		0			0
$811$	8.94987	−	15.5016i	0.314273	−	0.544336i	−0.665010	−	0.746834i	$-0.731573\pi$
$811$	8.94987	−	15.5016i	0.314273	−	0.544336i	0.979283	+	0.202498i	$0.0649061\pi$
$812$	−4.20844	−	7.28923i	−0.147687	−	0.255802i
$813$		0			0
$814$	4.63325	−	13.3080i	0.162395	−	0.466445i
$815$	−4.31662			−0.151205
$816$		0			0
$817$	−0.0501256	+	0.0868201i	−0.00175367	+	0.00303745i
$818$	5.13325	−	8.89105i	0.179480	−	0.310868i
$819$		0			0
$820$	4.68338			0.163551
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	−0.882948	−	0.469471i	$-0.844445\pi$
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	0.848048	+	0.529920i	$0.177778\pi$
$822$		0			0
$823$	2.31662	+	4.01251i	0.0807525	+	0.139867i	0.903573	−	0.428433i	$-0.140934\pi$
$823$	2.31662	+	4.01251i	0.0807525	+	0.139867i	−0.822821	+	0.568301i	$0.807601\pi$
$824$	−10.9499			−0.381457
$825$		0			0
$826$	−10.0000	−	17.3205i	−0.347945	−	0.602658i
$827$	1.26650	−	2.19364i	0.0440405	−	0.0762804i	−0.843165	−	0.537655i	$-0.819310\pi$
$827$	1.26650	−	2.19364i	0.0440405	−	0.0762804i	0.887205	+	0.461375i	$0.152644\pi$
$828$		0			0
$829$	15.6332	+	27.0776i	0.542965	+	0.940443i	0.998732	+	0.0503441i	$0.0160318\pi$
$829$	15.6332	+	27.0776i	0.542965	+	0.940443i	−0.455767	+	0.890099i	$0.650635\pi$
$830$	4.31662	+	7.47661i	0.149832	+	0.259517i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−2.70844	+	4.69115i	−0.0938418	+	0.162539i
$834$		0			0
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	−0.366750	−	0.635230i	−0.0126843	−	0.0219699i
$837$		0			0
$838$	−11.4749	+	19.8752i	−0.396395	+	0.686577i
$839$	−13.5831	−	23.5267i	−0.468942	−	0.812231i	0.530428	−	0.847730i	$-0.322031\pi$
$839$	−13.5831	−	23.5267i	−0.468942	−	0.812231i	−0.999370	+	0.0354993i	$0.988698\pi$
$840$		0			0
$841$	−15.7995			−0.544810
$842$	5.60819	+	9.71366i	0.193271	+	0.334755i
$843$		0			0
$844$	8.47494	−	14.6790i	0.291719	−	0.505273i
$845$	9.00000			0.309609
$846$		0			0
$847$	6.52506	−	11.3017i	0.224204	−	0.388332i
$848$	2.31662	−	4.01251i	0.0795532	−	0.137790i
$849$		0			0
$850$	13.2665			0.455037
$851$	15.8997	+	18.4173i	0.545036	+	0.631338i
$852$		0			0
$853$	−10.6082	−	18.3739i	−0.363217	−	0.629111i	0.625271	−	0.780408i	$-0.284988\pi$
$853$	−10.6082	−	18.3739i	−0.363217	−	0.629111i	−0.988488	+	0.151297i	$0.951655\pi$
$854$	0.791562	−	1.37103i	0.0270867	−	0.0469155i
$855$		0			0
$856$	−7.79156	+	13.4954i	−0.266310	+	0.461263i
$857$	54.4829			1.86110			0.930550	−	0.366166i	$-0.119330\pi$
$857$	54.4829			1.86110			0.930550	+	0.366166i	$0.119330\pi$
$858$		0			0
$859$	52.9499			1.80663			0.903313	−	0.428982i	$-0.141128\pi$
$859$	52.9499			1.80663			0.903313	+	0.428982i	$0.141128\pi$
$860$	0.158312	+	0.274205i	0.00539841	+	0.00935032i
$861$		0			0
$862$	33.5831			1.14385
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	0.949891	−	0.312581i	$-0.101194\pi$
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	−0.745649	+	0.666339i	$0.767860\pi$
$864$		0			0
$865$	−13.6332			−0.463544
$866$	0.866750	+	1.50126i	0.0294534	+	0.0510147i
$867$		0			0
$868$	2.68338	+	4.64774i	0.0910797	+	0.157755i
$869$	−8.05013	+	13.9432i	−0.273082	+	0.472992i
$870$		0			0
$871$	0.316625	+	0.548410i	0.0107284	+	0.0185822i
$872$	−1.34169	−	2.32387i	−0.0454353	−	0.0786962i
$873$		0			0
$874$	1.26650			0.0428400
$875$	−10.4248	+	18.0563i	−0.352423	+	0.610414i
$876$		0			0
$877$	−17.9499			−0.606124			−0.303062	−	0.952971i	$-0.598009\pi$
$877$	−17.9499			−0.606124			−0.303062	+	0.952971i	$0.598009\pi$
$878$	38.5330			1.30043
$879$		0			0
$880$	−2.31662			−0.0780934
$881$	19.3417	−	33.5008i	0.651638	−	1.12867i	−0.331087	−	0.943600i	$-0.607415\pi$
$881$	19.3417	−	33.5008i	0.651638	−	1.12867i	0.982725	−	0.185070i	$-0.0592512\pi$
$882$		0			0
$883$	4.63325	−	8.02502i	0.155921	−	0.270064i	−0.777473	−	0.628917i	$-0.783499\pi$
$883$	4.63325	−	8.02502i	0.155921	−	0.270064i	0.933394	+	0.358853i	$0.116832\pi$
$884$	3.31662	−	5.74456i	0.111550	−	0.193211i
$885$		0			0
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	−30.7335			−1.03193			−0.515965	−	0.856610i	$-0.672567\pi$
$887$	−30.7335			−1.03193			−0.515965	+	0.856610i	$0.672567\pi$
$888$		0			0
$889$	−7.79950			−0.261587
$890$	−1.34169	−	2.32387i	−0.0449735	−	0.0778963i
$891$		0			0
$892$	0.316625	−	0.548410i	0.0106014	−	0.0183621i
$893$	−0.683375	+	1.18364i	−0.0228683	+	0.0396090i
$894$		0			0
$895$	−0.316625	+	0.548410i	−0.0105836	+	0.0183313i
$896$	2.31662			0.0773930
$897$		0			0
$898$	−31.2665			−1.04338
$899$	−8.41688			−0.280719
$900$		0			0
$901$	−7.68338	+	13.3080i	−0.255970	+	0.443354i
$902$	−10.8496			−0.361253
$903$		0			0
$904$	−7.63325	−	13.2212i	−0.253878	−	0.439730i
$905$	0.658312	+	1.14023i	0.0218830	+	0.0379025i
$906$		0			0
$907$	10.1583	−	17.5947i	0.337301	−	0.584223i	−0.646623	−	0.762810i	$-0.723819\pi$
$907$	10.1583	−	17.5947i	0.337301	−	0.584223i	0.983924	+	0.178587i	$0.0571526\pi$
$908$	0.525063	+	0.909435i	0.0174248	+	0.0301807i
$909$		0			0
$910$	2.31662	+	4.01251i	0.0767954	+	0.133013i
$911$	9.26650			0.307013			0.153506	−	0.988148i	$-0.450943\pi$
$911$	9.26650			0.307013			0.153506	+	0.988148i	$0.450943\pi$
$912$		0			0
$913$	−10.0000	−	17.3205i	−0.330952	−	0.573225i
$914$	21.6332			0.715564
$915$		0			0
$916$	−1.02506	−	1.77546i	−0.0338690	−	0.0586629i
$917$	21.4670			0.708903
$918$		0			0
$919$	−27.1662			−0.896132			−0.448066	−	0.894001i	$-0.647887\pi$
$919$	−27.1662			−0.896132			−0.448066	+	0.894001i	$0.647887\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$		0			0
$922$	−5.68338	+	9.84389i	−0.187172	+	0.324191i
$923$	0.316625	+	0.548410i	0.0104218	+	0.0180511i
$924$		0			0
$925$	−8.00000	+	22.9783i	−0.263038	+	0.755520i
$926$	−13.0501			−0.428854
$927$		0			0
$928$	−1.81662	+	3.14649i	−0.0596336	+	0.103288i
$929$	28.6082	−	49.5508i	0.938604	−	1.62571i	0.170527	−	0.985353i	$-0.445453\pi$
$929$	28.6082	−	49.5508i	0.938604	−	1.62571i	0.768077	−	0.640357i	$-0.221214\pi$
$930$		0			0
$931$	−0.517127			−0.0169482
$932$	−2.97494	+	5.15274i	−0.0974473	+	0.168784i
$933$		0			0
$934$	−1.68338	−	2.91569i	−0.0550817	−	0.0954043i
$935$	7.68338			0.251273
$936$		0			0
$937$	23.7665	+	41.1648i	0.776418	+	1.34479i	0.933994	+	0.357288i	$0.116299\pi$
$937$	23.7665	+	41.1648i	0.776418	+	1.34479i	−0.157577	+	0.987507i	$0.550368\pi$
$938$	0.366750	−	0.635230i	0.0119748	−	0.0207410i
$939$		0			0
$940$	2.15831	+	3.73831i	0.0703964	+	0.121930i
$941$	11.1332	+	19.2834i	0.362934	+	0.628619i	0.988442	−	0.151598i	$-0.0484419\pi$
$941$	11.1332	+	19.2834i	0.362934	+	0.628619i	−0.625509	+	0.780217i	$0.715109\pi$
$942$		0			0
$943$	9.36675	−	16.2237i	0.305023	−	0.528316i
$944$	−4.31662	+	7.47661i	−0.140494	+	0.243343i
$945$		0			0
$946$	−0.366750	−	0.635230i	−0.0119241	−	0.0206531i
$947$	23.8997	+	41.3956i	0.776637	+	1.34518i	0.933870	+	0.357614i	$0.116410\pi$
$947$	23.8997	+	41.3956i	0.776637	+	1.34518i	−0.157232	+	0.987562i	$0.550257\pi$
$948$		0			0
$949$	−12.6332	+	21.8814i	−0.410093	+	0.710301i
$950$	0.633250	+	1.09682i	0.0205453	+	0.0355856i
$951$		0			0
$952$	−7.68338			−0.249020
$953$	−27.6332	−	47.8622i	−0.895129	−	1.55041i	−0.833645	−	0.552300i	$-0.813750\pi$
$953$	−27.6332	−	47.8622i	−0.895129	−	1.55041i	−0.0614836	−	0.998108i	$-0.519583\pi$
$954$		0			0
$955$	5.68338	−	9.84389i	0.183910	−	0.318541i
$956$	20.9499			0.677567
$957$		0			0
$958$	−14.0000	+	24.2487i	−0.452319	+	0.783440i
$959$	−0.791562	+	1.37103i	−0.0255609	+	0.0442727i
$960$		0			0
$961$	−25.6332			−0.826879
$962$	7.94987	+	9.20866i	0.256314	+	0.296899i
$963$		0			0
$964$	6.31662	+	10.9407i	0.203445	+	0.352377i
$965$	0.500000	−	0.866025i	0.0160956	−	0.0278783i
$966$		0			0
$967$	−25.8997	+	44.8597i	−0.832880	+	1.44259i	0.0628653	+	0.998022i	$0.479976\pi$
$967$	−25.8997	+	44.8597i	−0.832880	+	1.44259i	−0.895745	+	0.444568i	$0.853357\pi$
$968$	−5.63325			−0.181059
$969$		0			0
$970$	−13.6332			−0.437737
$971$	−30.6332	−	53.0583i	−0.983068	−	1.70272i	−0.650226	−	0.759740i	$-0.725326\pi$
$971$	−30.6332	−	53.0583i	−0.983068	−	1.70272i	−0.332841	−	0.942983i	$-0.608007\pi$
$972$		0			0
$973$		0			0
$974$	0.316625	+	0.548410i	0.0101453	+	0.0175722i
$975$		0			0
$976$	−0.683375			−0.0218743
$977$	29.5330	+	51.1527i	0.944844	+	1.63652i	0.756063	+	0.654499i	$0.227121\pi$
$977$	29.5330	+	51.1527i	0.944844	+	1.63652i	0.188782	+	0.982019i	$0.439546\pi$
$978$		0			0
$979$	3.10819	+	5.38354i	0.0993381	+	0.172059i
$980$	−0.816625	+	1.41444i	−0.0260861	+	0.0451825i
$981$		0			0
$982$	7.15831	+	12.3986i	0.228431	+	0.395654i
$983$	11.7414	+	20.3368i	0.374494	+	0.648642i	0.990251	−	0.139294i	$-0.0444832\pi$
$983$	11.7414	+	20.3368i	0.374494	+	0.648642i	−0.615757	+	0.787936i	$0.711150\pi$
$984$		0			0
$985$	9.63325			0.306941
$986$	6.02506	−	10.4357i	0.191877	−	0.332341i
$987$		0			0
$988$	0.633250			0.0201464
$989$	1.26650			0.0402723
$990$		0			0
$991$	−6.94987			−0.220770			−0.110385	−	0.993889i	$-0.535208\pi$
$991$	−6.94987			−0.220770			−0.110385	+	0.993889i	$0.535208\pi$
$992$	1.15831	−	2.00626i	0.0367765	−	0.0636987i
$993$		0			0
$994$	0.366750	−	0.635230i	0.0116326	−	0.0201483i
$995$	−2.84169	+	4.92195i	−0.0900876	+	0.156036i
$996$		0			0
$997$	−21.6332	−	37.4699i	−0.685132	−	1.18668i	−0.973395	−	0.229132i	$-0.926411\pi$
$997$	−21.6332	−	37.4699i	−0.685132	−	1.18668i	0.288263	−	0.957551i	$-0.406922\pi$
$998$	−16.9499			−0.536539
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.h.433.1	yes	4
3.2	odd	2		666.2.f.i.433.1	yes	4
37.10	even	3	inner	666.2.f.h.343.1	✓	4
111.47	odd	6		666.2.f.i.343.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.f.h.343.1	✓	4	37.10	even	3	inner
666.2.f.h.433.1	yes	4	1.1	even	1	trivial
666.2.f.i.343.1	yes	4	111.47	odd	6
666.2.f.i.433.1	yes	4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.15831 + 2.00626i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +2.31662 q^{11} +(-1.00000 + 1.73205i) q^{13} +2.31662 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.65831 + 2.87228i) q^{17} +(-0.158312 + 0.274205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.15831 - 2.00626i) q^{22} +4.00000 q^{23} +(2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +(-1.15831 - 2.00626i) q^{28} +3.63325 q^{29} -2.31662 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.65831 - 2.87228i) q^{34} +(1.15831 + 2.00626i) q^{35} +(3.97494 + 4.60433i) q^{37} +0.316625 q^{38} +(0.500000 - 0.866025i) q^{40} +(2.34169 - 4.05592i) q^{41} +0.316625 q^{43} +(-1.15831 + 2.00626i) q^{44} +(-2.00000 - 3.46410i) q^{46} +4.31662 q^{47} +(0.816625 + 1.41444i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(2.31662 + 4.01251i) q^{53} +(1.15831 - 2.00626i) q^{55} +(-1.15831 + 2.00626i) q^{56} +(-1.81662 - 3.14649i) q^{58} +(-4.31662 - 7.47661i) q^{59} +(0.341688 - 0.591820i) q^{61} +(1.15831 + 2.00626i) q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(0.158312 - 0.274205i) q^{67} -3.31662 q^{68} +(1.15831 - 2.00626i) q^{70} +(0.158312 - 0.274205i) q^{71} +12.6332 q^{73} +(2.00000 - 5.74456i) q^{74} +(-0.158312 - 0.274205i) q^{76} +(-2.68338 + 4.64774i) q^{77} +(-3.47494 + 6.01877i) q^{79} -1.00000 q^{80} -4.68338 q^{82} +(-4.31662 - 7.47661i) q^{83} +3.31662 q^{85} +(-0.158312 - 0.274205i) q^{86} +2.31662 q^{88} +(1.34169 + 2.32387i) q^{89} +(-2.31662 - 4.01251i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-2.15831 - 3.73831i) q^{94} +(0.158312 + 0.274205i) q^{95} +13.6332 q^{97} +(0.816625 - 1.41444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} + 4 q^{8} - 4 q^{10} - 4 q^{11} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{19} + 2 q^{20} + 2 q^{22} + 16 q^{23} + 8 q^{25} + 8 q^{26} + 2 q^{28} - 12 q^{29} + 4 q^{31}+ \cdots - 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 + 4 * q^8 - 4 * q^10 - 4 * q^11 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^19 + 2 * q^20 + 2 * q^22 + 16 * q^23 + 8 * q^25 + 8 * q^26 + 2 * q^28 - 12 * q^29 + 4 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 - 12 * q^38 + 2 * q^40 + 16 * q^41 - 12 * q^43 + 2 * q^44 - 8 * q^46 + 4 * q^47 - 10 * q^49 + 8 * q^50 - 4 * q^52 - 4 * q^53 - 2 * q^55 + 2 * q^56 + 6 * q^58 - 4 * q^59 + 8 * q^61 - 2 * q^62 + 4 * q^64 + 4 * q^65 - 6 * q^67 - 2 * q^70 - 6 * q^71 + 24 * q^73 + 8 * q^74 + 6 * q^76 - 24 * q^77 + 6 * q^79 - 4 * q^80 - 32 * q^82 - 4 * q^83 + 6 * q^86 - 4 * q^88 + 12 * q^89 + 4 * q^91 - 8 * q^92 - 2 * q^94 - 6 * q^95 + 28 * q^97 - 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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