LMFDB - Embedded newform 666.2.be.d.467.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			467.1
Root			$-0.912166 - 1.47240i$ of defining polynomial
Character	$\chi$	$=$	666.467
Dual form			666.2.be.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.43832 - 0.653347i) q^{5} +(0.762169 + 1.32012i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.43832 - 0.653347i) q^{5} +(0.762169 + 1.32012i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.52434 q^{10} -0.293751 q^{11} +(0.472172 - 1.76217i) q^{13} +(-1.07787 - 1.07787i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.0537601 - 0.200635i) q^{17} +(-0.213969 + 0.798543i) q^{19} +(-2.43832 + 0.653347i) q^{20} +(0.283741 - 0.0760282i) q^{22} +(5.10053 - 5.10053i) q^{23} +(1.18843 + 0.686141i) q^{25} +1.82433i q^{26} +(1.32012 + 0.762169i) q^{28} +(-4.72977 - 4.72977i) q^{29} +(4.39891 - 4.39891i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.103857 + 0.179885i) q^{34} +(-0.995921 - 3.71683i) q^{35} +(-1.03408 - 5.99422i) q^{37} -0.826712i q^{38} +(2.18614 - 1.26217i) q^{40} +(0.398951 + 0.691004i) q^{41} +(-5.60662 - 5.60662i) q^{43} +(-0.254395 + 0.146875i) q^{44} +(-3.60662 + 6.24685i) q^{46} -0.508791i q^{47} +(2.33820 - 4.04988i) q^{49} +(-1.32552 - 0.355173i) q^{50} +(-0.472172 - 1.76217i) q^{52} +(3.09167 + 1.78498i) q^{53} +(0.716259 + 0.191921i) q^{55} +(-1.47240 - 0.394528i) q^{56} +(5.79276 + 3.34445i) q^{58} +(-0.715281 - 2.66947i) q^{59} +(0.820115 + 0.219749i) q^{61} +(-3.11050 + 5.38754i) q^{62} -1.00000i q^{64} +(-2.30261 + 3.98825i) q^{65} +(-0.106871 + 0.0617022i) q^{67} +(-0.146875 - 0.146875i) q^{68} +(1.92397 + 3.33242i) q^{70} +(12.0471 - 6.95537i) q^{71} -2.83638i q^{73} +(2.55027 + 5.52233i) q^{74} +(0.213969 + 0.798543i) q^{76} +(-0.223888 - 0.387785i) q^{77} +(-0.472172 + 1.76217i) q^{79} +(-1.78498 + 1.78498i) q^{80} +(-0.564202 - 0.564202i) q^{82} +(-4.50265 - 2.59960i) q^{83} +0.524338i q^{85} +(6.86668 + 3.96448i) q^{86} +(0.207713 - 0.207713i) q^{88} +(10.2598 - 2.74910i) q^{89} +(2.68614 - 0.719749i) q^{91} +(1.86692 - 6.96746i) q^{92} +(0.131685 + 0.491454i) q^{94} +(1.04345 - 1.80731i) q^{95} +(-4.15831 - 4.15831i) q^{97} +(-1.21034 + 4.51705i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.43832	−	0.653347i	−1.09045	−	0.292186i	−0.331581	−	0.943427i	$-0.607582\pi$
$5$	−2.43832	−	0.653347i	−1.09045	−	0.292186i	−0.758871	+	0.651241i	$0.774249\pi$
$6$		0			0
$7$	0.762169	+	1.32012i	0.288073	+	0.498957i	0.973350	−	0.229326i	$-0.0736522\pi$
$7$	0.762169	+	1.32012i	0.288073	+	0.498957i	−0.685277	+	0.728283i	$0.740319\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	2.52434			0.798266
$11$	−0.293751			−0.0885691			−0.0442846	−	0.999019i	$-0.514101\pi$
$11$	−0.293751			−0.0885691			−0.0442846	+	0.999019i	$0.514101\pi$
$12$		0			0
$13$	0.472172	−	1.76217i	0.130957	−	0.488738i	−0.869025	−	0.494768i	$-0.835253\pi$
$13$	0.472172	−	1.76217i	0.130957	−	0.488738i	0.999982	+	0.00603057i	$0.00191960\pi$
$14$	−1.07787	−	1.07787i	−0.288073	−	0.288073i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.0537601	−	0.200635i	−0.0130387	−	0.0486612i	0.959100	−	0.283068i	$-0.0913521\pi$
$17$	−0.0537601	−	0.200635i	−0.0130387	−	0.0486612i	−0.972139	+	0.234406i	$0.924685\pi$
$18$		0			0
$19$	−0.213969	+	0.798543i	−0.0490878	+	0.183198i	−0.986117	−	0.166054i	$-0.946898\pi$
$19$	−0.213969	+	0.798543i	−0.0490878	+	0.183198i	0.937029	+	0.349252i	$0.113564\pi$
$20$	−2.43832	+	0.653347i	−0.545226	+	0.146093i
$21$		0			0
$22$	0.283741	−	0.0760282i	0.0604938	−	0.0162093i
$23$	5.10053	−	5.10053i	1.06353	−	1.06353i	0.0656950	−	0.997840i	$-0.479074\pi$
$23$	5.10053	−	5.10053i	1.06353	−	1.06353i	0.997840	−	0.0656950i	$-0.0209265\pi$
$24$		0			0
$25$	1.18843	+	0.686141i	0.237686	+	0.137228i
$26$			1.82433i			0.357781i
$27$		0			0
$28$	1.32012	+	0.762169i	0.249478	+	0.144036i
$29$	−4.72977	−	4.72977i	−0.878296	−	0.878296i	0.115062	−	0.993358i	$-0.463293\pi$
$29$	−4.72977	−	4.72977i	−0.878296	−	0.878296i	−0.993358	+	0.115062i	$0.963293\pi$
$30$		0			0
$31$	4.39891	−	4.39891i	0.790067	−	0.790067i	−0.191437	−	0.981505i	$-0.561315\pi$
$31$	4.39891	−	4.39891i	0.790067	−	0.790067i	0.981505	+	0.191437i	$0.0613149\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	0.103857	+	0.179885i	0.0178112	+	0.0308500i
$35$	−0.995921	−	3.71683i	−0.168341	−	0.628259i
$36$		0			0
$37$	−1.03408	−	5.99422i	−0.170002	−	0.985444i
$37$	−1.03408	−	5.99422i	−0.170002	−	0.985444i
$38$		−	0.826712i		−	0.134110i
$39$		0			0
$40$	2.18614	−	1.26217i	0.345659	−	0.199566i
$41$	0.398951	+	0.691004i	0.0623057	+	0.107917i	0.895496	−	0.445070i	$-0.146821\pi$
$41$	0.398951	+	0.691004i	0.0623057	+	0.107917i	−0.833190	+	0.552987i	$0.813488\pi$
$42$		0			0
$43$	−5.60662	−	5.60662i	−0.855002	−	0.855002i	0.135742	−	0.990744i	$-0.456658\pi$
$43$	−5.60662	−	5.60662i	−0.855002	−	0.855002i	−0.990744	+	0.135742i	$0.956658\pi$
$44$	−0.254395	+	0.146875i	−0.0383516	+	0.0221423i
$45$		0			0
$46$	−3.60662	+	6.24685i	−0.531767	+	0.921048i
$47$		−	0.508791i		−	0.0742148i	−0.999311	−	0.0371074i	$-0.988186\pi$
$47$		−	0.508791i		−	0.0742148i	0.999311	−	0.0371074i	$-0.0118144\pi$
$48$		0			0
$49$	2.33820	−	4.04988i	0.334028	−	0.578554i
$50$	−1.32552	−	0.355173i	−0.187457	−	0.0502290i
$51$		0			0
$52$	−0.472172	−	1.76217i	−0.0654784	−	0.244369i
$53$	3.09167	+	1.78498i	0.424674	+	0.245185i	0.697075	−	0.716998i	$-0.254485\pi$
$53$	3.09167	+	1.78498i	0.424674	+	0.245185i	−0.272401	+	0.962184i	$0.587818\pi$
$54$		0			0
$55$	0.716259	+	0.191921i	0.0965803	+	0.0258786i
$56$	−1.47240	−	0.394528i	−0.196757	−	0.0527210i
$57$		0			0
$58$	5.79276	+	3.34445i	0.760627	+	0.439148i
$59$	−0.715281	−	2.66947i	−0.0931217	−	0.347535i	0.903606	−	0.428364i	$-0.140910\pi$
$59$	−0.715281	−	2.66947i	−0.0931217	−	0.347535i	−0.996728	+	0.0808291i	$0.974243\pi$
$60$		0			0
$61$	0.820115	+	0.219749i	0.105005	+	0.0281360i	0.310939	−	0.950430i	$-0.399357\pi$
$61$	0.820115	+	0.219749i	0.105005	+	0.0281360i	−0.205934	+	0.978566i	$0.566023\pi$
$62$	−3.11050	+	5.38754i	−0.395034	+	0.684218i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.30261	+	3.98825i	−0.285604	+	0.494681i
$66$		0			0
$67$	−0.106871	+	0.0617022i	−0.0130564	+	0.00753812i	−0.506514	−	0.862232i	$-0.669066\pi$
$67$	−0.106871	+	0.0617022i	−0.0130564	+	0.00753812i	0.493458	+	0.869770i	$0.335733\pi$
$68$	−0.146875	−	0.146875i	−0.0178112	−	0.0178112i
$69$		0			0
$70$	1.92397	+	3.33242i	0.229959	+	0.398300i
$71$	12.0471	−	6.95537i	1.42972	−	0.825451i	0.432625	−	0.901574i	$-0.357588\pi$
$71$	12.0471	−	6.95537i	1.42972	−	0.825451i	0.997098	+	0.0761233i	$0.0242543\pi$
$72$		0			0
$73$		−	2.83638i		−	0.331974i	−0.986128	−	0.165987i	$-0.946919\pi$
$73$		−	2.83638i		−	0.331974i	0.986128	−	0.165987i	$-0.0530809\pi$
$74$	2.55027	+	5.52233i	0.296462	+	0.641958i
$75$		0			0
$76$	0.213969	+	0.798543i	0.0245439	+	0.0915992i
$77$	−0.223888	−	0.387785i	−0.0255144	−	0.0441922i
$78$		0			0
$79$	−0.472172	+	1.76217i	−0.0531235	+	0.198259i	−0.987387	−	0.158323i	$-0.949391\pi$
$79$	−0.472172	+	1.76217i	−0.0531235	+	0.198259i	0.934264	+	0.356582i	$0.116058\pi$
$80$	−1.78498	+	1.78498i	−0.199566	+	0.199566i
$81$		0			0
$82$	−0.564202	−	0.564202i	−0.0623057	−	0.0623057i
$83$	−4.50265	−	2.59960i	−0.494230	−	0.285344i	0.232098	−	0.972692i	$-0.425441\pi$
$83$	−4.50265	−	2.59960i	−0.494230	−	0.285344i	−0.726327	+	0.687349i	$0.758774\pi$
$84$		0			0
$85$			0.524338i			0.0568724i
$86$	6.86668	+	3.96448i	0.740453	+	0.427501i
$87$		0			0
$88$	0.207713	−	0.207713i	0.0221423	−	0.0221423i
$89$	10.2598	−	2.74910i	1.08753	−	0.291404i	0.329855	−	0.944032i	$-0.393000\pi$
$89$	10.2598	−	2.74910i	1.08753	−	0.291404i	0.757678	+	0.652628i	$0.226334\pi$
$90$		0			0
$91$	2.68614	−	0.719749i	0.281584	−	0.0754502i
$92$	1.86692	−	6.96746i	0.194640	−	0.726408i
$93$		0			0
$94$	0.131685	+	0.491454i	0.0135822	+	0.0506896i
$95$	1.04345	−	1.80731i	0.107056	−	0.185426i
$96$		0			0
$97$	−4.15831	−	4.15831i	−0.422213	−	0.422213i	0.463752	−	0.885965i	$-0.346503\pi$
$97$	−4.15831	−	4.15831i	−0.422213	−	0.422213i	−0.885965	+	0.463752i	$0.846503\pi$
$98$	−1.21034	+	4.51705i	−0.122263	+	0.456291i
$99$		0			0
$100$	1.37228			0.137228
$101$	−1.47059			−0.146329			−0.0731646	−	0.997320i	$-0.523310\pi$
$101$	−1.47059			−0.146329			−0.0731646	+	0.997320i	$0.523310\pi$
$102$		0			0
$103$	−9.09735	+	9.09735i	−0.896389	+	0.896389i	−0.995115	−	0.0987260i	$-0.968523\pi$
$103$	−9.09735	+	9.09735i	−0.896389	+	0.896389i	0.0987260	+	0.995115i	$0.468523\pi$
$104$	0.912166	+	1.57992i	0.0894452	+	0.154924i
$105$		0			0
$106$	−3.44831	−	0.923972i	−0.334929	−	0.0897441i
$107$	−0.455950	+	0.263243i	−0.0440783	+	0.0254486i	−0.521877	−	0.853021i	$-0.674768\pi$
$107$	−0.455950	+	0.263243i	−0.0440783	+	0.0254486i	0.477799	+	0.878469i	$0.341435\pi$
$108$		0			0
$109$	7.76264	−	2.07999i	0.743526	−	0.199227i	0.132882	−	0.991132i	$-0.457577\pi$
$109$	7.76264	−	2.07999i	0.743526	−	0.199227i	0.610645	+	0.791905i	$0.290910\pi$
$110$	−0.741526			−0.0707017
$111$		0			0
$112$	1.52434			0.144036
$113$	−3.37024	+	0.903052i	−0.317045	+	0.0849520i	−0.413832	−	0.910353i	$-0.635810\pi$
$113$	−3.37024	+	0.903052i	−0.317045	+	0.0849520i	0.0967872	+	0.995305i	$0.469143\pi$
$114$		0			0
$115$	−15.7692	+	9.10433i	−1.47048	+	0.848983i
$116$	−6.46099	−	1.73122i	−0.599888	−	0.160739i
$117$		0			0
$118$	1.38182	+	2.39338i	0.127207	+	0.220328i
$119$	0.223888	−	0.223888i	0.0205237	−	0.0205237i
$120$		0			0
$121$	−10.9137			−0.992156
$122$	−0.849046			−0.0768690
$123$		0			0
$124$	1.61011	−	6.00902i	0.144592	−	0.539626i
$125$	6.47539	+	6.47539i	0.579177	+	0.579177i
$126$		0			0
$127$	−4.01230	+	6.94951i	−0.356034	+	0.616669i	−0.987294	−	0.158902i	$-0.949205\pi$
$127$	−4.01230	+	6.94951i	−0.356034	+	0.616669i	0.631260	+	0.775571i	$0.282538\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	1.19192	−	4.44831i	0.104538	−	0.390143i
$131$	19.1702	−	5.13665i	1.67491	−	0.448791i	0.708483	−	0.705728i	$-0.249380\pi$
$131$	19.1702	−	5.13665i	1.67491	−	0.448791i	0.966428	+	0.256936i	$0.0827131\pi$
$132$		0			0
$133$	−1.21725	+	0.326161i	−0.105549	+	0.0282817i
$134$	0.0872601	−	0.0872601i	0.00753812	−	0.00753812i
$135$		0			0
$136$	0.179885	+	0.103857i	0.0154250	+	0.00890562i
$137$			5.01637i			0.428578i	0.976770	+	0.214289i	$0.0687434\pi$
$137$			5.01637i			0.428578i	−0.976770	+	0.214289i	$0.931257\pi$
$138$		0			0
$139$	−14.7067	−	8.49094i	−1.24741	−	0.720192i	−0.276817	−	0.960923i	$-0.589280\pi$
$139$	−14.7067	−	8.49094i	−1.24741	−	0.720192i	−0.970592	+	0.240730i	$0.922613\pi$
$140$	−2.72091	−	2.72091i	−0.229959	−	0.229959i
$141$		0			0
$142$	−9.83638	+	9.83638i	−0.825451	+	0.825451i
$143$	−0.138701	+	0.517638i	−0.0115987	+	0.0432871i
$144$		0			0
$145$	8.44253	+	14.6229i	0.701114	+	1.21436i
$146$	0.734110	+	2.73974i	0.0607554	+	0.226742i
$147$		0			0
$148$	−3.89265	−	4.67410i	−0.319974	−	0.384209i
$149$			18.2510i			1.49518i	0.664159	+	0.747592i	$0.268790\pi$
$149$			18.2510i			1.49518i	−0.664159	+	0.747592i	$0.731210\pi$
$150$		0			0
$151$	−3.12121	+	1.80203i	−0.254001	+	0.146647i	−0.621595	−	0.783339i	$-0.713515\pi$
$151$	−3.12121	+	1.80203i	−0.254001	+	0.146647i	0.367594	+	0.929986i	$0.380182\pi$
$152$	−0.413356	−	0.715954i	−0.0335276	−	0.0580715i
$153$		0			0
$154$	0.316625	+	0.316625i	0.0255144	+	0.0255144i
$155$	−13.6000	+	7.85195i	−1.09238	+	0.630684i
$156$		0			0
$157$	−7.50423	+	12.9977i	−0.598903	+	1.03733i	0.394080	+	0.919076i	$0.371063\pi$
$157$	−7.50423	+	12.9977i	−0.598903	+	1.03733i	−0.992983	+	0.118254i	$0.962270\pi$
$158$		−	1.82433i		−	0.145136i
$159$		0			0
$160$	1.26217	−	2.18614i	0.0997832	−	0.172830i
$161$	10.6208	+	2.84582i	0.837033	+	0.224282i
$162$		0			0
$163$	−1.13371	−	4.23106i	−0.0887990	−	0.331402i	0.907207	−	0.420683i	$-0.138210\pi$
$163$	−1.13371	−	4.23106i	−0.0887990	−	0.331402i	−0.996006	+	0.0892812i	$0.971543\pi$
$164$	0.691004	+	0.398951i	0.0539583	+	0.0311529i
$165$		0			0
$166$	5.02205	+	1.34565i	0.389787	+	0.104443i
$167$	−0.654266	−	0.175310i	−0.0506286	−	0.0135659i	0.233416	−	0.972377i	$-0.425010\pi$
$167$	−0.654266	−	0.175310i	−0.0506286	−	0.0135659i	−0.284044	+	0.958811i	$0.591676\pi$
$168$		0			0
$169$	8.37604	+	4.83591i	0.644311	+	0.371993i
$170$	−0.135709	−	0.506471i	−0.0104084	−	0.0388446i
$171$		0			0
$172$	−7.65879	−	2.05217i	−0.583977	−	0.156476i
$173$	−8.06143	+	13.9628i	−0.612899	+	1.06157i	0.377850	+	0.925867i	$0.376664\pi$
$173$	−8.06143	+	13.9628i	−0.612899	+	1.06157i	−0.990749	+	0.135706i	$0.956670\pi$
$174$		0			0
$175$			2.09182i			0.158127i
$176$	−0.146875	+	0.254395i	−0.0110711	+	0.0191758i
$177$		0			0
$178$	−9.19865	+	5.31084i	−0.689468	+	0.398065i
$179$	−13.0230	−	13.0230i	−0.973386	−	0.973386i	0.0262689	−	0.999655i	$-0.491637\pi$
$179$	−13.0230	−	13.0230i	−0.973386	−	0.973386i	−0.999655	+	0.0262689i	$0.991637\pi$
$180$		0			0
$181$	8.96540	+	15.5285i	0.666393	+	1.15423i	0.978906	+	0.204313i	$0.0654960\pi$
$181$	8.96540	+	15.5285i	0.666393	+	1.15423i	−0.312513	+	0.949914i	$0.601171\pi$
$182$	−2.40833	+	1.39045i	−0.178517	+	0.103067i
$183$		0			0
$184$			7.21324i			0.531767i
$185$	−1.39487	+	15.2915i	−0.102553	+	1.12425i
$186$		0			0
$187$	0.0157921	+	0.0589367i	0.00115483	+	0.00430988i
$188$	−0.254395	−	0.440626i	−0.0185537	−	0.0321359i
$189$		0			0
$190$	−0.540130	+	2.01579i	−0.0391851	+	0.146241i
$191$	−8.66401	+	8.66401i	−0.626906	+	0.626906i	−0.947288	−	0.320383i	$-0.896189\pi$
$191$	−8.66401	+	8.66401i	−0.626906	+	0.626906i	0.320383	+	0.947288i	$0.396189\pi$
$192$		0			0
$193$	−0.798543	−	0.798543i	−0.0574804	−	0.0574804i	0.677782	−	0.735263i	$-0.262941\pi$
$193$	−0.798543	−	0.798543i	−0.0574804	−	0.0574804i	−0.735263	+	0.677782i	$0.762941\pi$
$194$	5.09287	+	2.94037i	0.365647	+	0.211106i
$195$		0			0
$196$		−	4.67639i		−	0.334028i
$197$	0.621674	+	0.358924i	0.0442924	+	0.0255722i	0.521983	−	0.852956i	$-0.325193\pi$
$197$	0.621674	+	0.358924i	0.0442924	+	0.0255722i	−0.477690	+	0.878528i	$0.658526\pi$
$198$		0			0
$199$	8.78568	−	8.78568i	0.622801	−	0.622801i	−0.323446	−	0.946247i	$-0.604841\pi$
$199$	8.78568	−	8.78568i	0.622801	−	0.622801i	0.946247	+	0.323446i	$0.104841\pi$
$200$	−1.32552	+	0.355173i	−0.0937286	+	0.0251145i
$201$		0			0
$202$	1.42048	−	0.380617i	0.0999447	−	0.0267801i
$203$	2.63896	−	9.84873i	0.185219	−	0.691245i
$204$		0			0
$205$	−0.521307	−	1.94554i	−0.0364097	−	0.135883i
$206$	6.43280	−	11.1419i	0.448194	−	0.776295i
$207$		0			0
$208$	−1.29000	−	1.29000i	−0.0894452	−	0.0894452i
$209$	0.0628535	−	0.234572i	0.00434767	−	0.0162257i
$210$		0			0
$211$	−8.65930			−0.596131			−0.298065	−	0.954545i	$-0.596341\pi$
$211$	−8.65930			−0.596131			−0.298065	+	0.954545i	$0.596341\pi$
$212$	3.56995			0.245185
$213$		0			0
$214$	0.372281	−	0.372281i	0.0254486	−	0.0254486i
$215$	10.0077	+	17.3338i	0.682519	+	1.18216i
$216$		0			0
$217$	9.15978	+	2.45436i	0.621806	+	0.166612i
$218$	−6.95980	+	4.01824i	−0.471377	+	0.272150i
$219$		0			0
$220$	0.716259	−	0.191921i	0.0482902	−	0.0129393i
$221$	−0.378937			−0.0254901
$222$		0			0
$223$	4.39273			0.294159			0.147079	−	0.989125i	$-0.453013\pi$
$223$	4.39273			0.294159			0.147079	+	0.989125i	$0.453013\pi$
$224$	−1.47240	+	0.394528i	−0.0983787	+	0.0263605i
$225$		0			0
$226$	3.02167	−	1.74456i	0.200999	−	0.116047i
$227$	−12.1730	−	3.26175i	−0.807951	−	0.216490i	−0.168879	−	0.985637i	$-0.554015\pi$
$227$	−12.1730	−	3.26175i	−0.807951	−	0.216490i	−0.639072	+	0.769147i	$0.720681\pi$
$228$		0			0
$229$	14.2912	+	24.7531i	0.944390	+	1.63573i	0.756968	+	0.653452i	$0.226680\pi$
$229$	14.2912	+	24.7531i	0.944390	+	1.63573i	0.187422	+	0.982279i	$0.439987\pi$
$230$	12.8755	−	12.8755i	0.848983	−	0.848983i
$231$		0			0
$232$	6.68891			0.439148
$233$	−10.4036			−0.681566			−0.340783	−	0.940142i	$-0.610692\pi$
$233$	−10.4036			−0.681566			−0.340783	+	0.940142i	$0.610692\pi$
$234$		0			0
$235$	−0.332417	+	1.24060i	−0.0216845	+	0.0809276i
$236$	−1.95418	−	1.95418i	−0.127207	−	0.127207i
$237$		0			0
$238$	−0.158312	+	0.274205i	−0.0102619	+	0.0177741i
$239$	−2.55377	−	9.53081i	−0.165190	−	0.616497i	−0.998016	−	0.0629619i	$-0.979945\pi$
$239$	−2.55377	−	9.53081i	−0.165190	−	0.616497i	0.832826	−	0.553535i	$-0.186721\pi$
$240$		0			0
$241$	4.68446	−	17.4827i	0.301753	−	1.12616i	−0.633952	−	0.773373i	$-0.718568\pi$
$241$	4.68446	−	17.4827i	0.301753	−	1.12616i	0.935705	−	0.352784i	$-0.114765\pi$
$242$	10.5418	−	2.82468i	0.677655	−	0.181577i
$243$		0			0
$244$	0.820115	−	0.219749i	0.0525025	−	0.0140680i
$245$	−8.34725	+	8.34725i	−0.533286	+	0.533286i
$246$		0			0
$247$	1.30614	+	0.754099i	0.0831075	+	0.0479822i
$248$			6.22100i			0.395034i
$249$		0			0
$250$	−7.93070	−	4.57879i	−0.501582	−	0.289588i
$251$	−3.15099	−	3.15099i	−0.198889	−	0.198889i	0.600635	−	0.799523i	$-0.294915\pi$
$251$	−3.15099	−	3.15099i	−0.198889	−	0.198889i	−0.799523	+	0.600635i	$0.794915\pi$
$252$		0			0
$253$	−1.49828	+	1.49828i	−0.0941963	+	0.0941963i
$254$	2.07692	−	7.75117i	0.130318	−	0.486352i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.73732	+	17.6799i	0.295506	+	1.10284i	0.940815	+	0.338922i	$0.110062\pi$
$257$	4.73732	+	17.6799i	0.295506	+	1.10284i	−0.645308	+	0.763922i	$0.723271\pi$
$258$		0			0
$259$	7.12491	−	5.93372i	0.442721	−	0.368703i
$260$			4.60523i			0.285604i
$261$		0			0
$262$	−17.1876	+	9.92325i	−1.06185	+	0.613060i
$263$	−11.0262	−	19.0980i	−0.679907	−	1.17763i	−0.975008	−	0.222168i	$-0.928687\pi$
$263$	−11.0262	−	19.0980i	−0.679907	−	1.17763i	0.295101	−	0.955466i	$-0.404647\pi$
$264$		0			0
$265$	−6.37228	−	6.37228i	−0.391446	−	0.391446i
$266$	1.09136	−	0.630095i	0.0669153	−	0.0386336i
$267$		0			0
$268$	−0.0617022	+	0.106871i	−0.00376906	+	0.00652821i
$269$		−	18.8850i		−	1.15144i	−0.817646	−	0.575721i	$-0.804722\pi$
$269$		−	18.8850i		−	1.15144i	0.817646	−	0.575721i	$-0.195278\pi$
$270$		0			0
$271$	12.1785	−	21.0939i	0.739794	−	1.28136i	−0.212794	−	0.977097i	$-0.568256\pi$
$271$	12.1785	−	21.0939i	0.739794	−	1.28136i	0.952588	−	0.304264i	$-0.0984104\pi$
$272$	−0.200635	−	0.0537601i	−0.0121653	−	0.00325968i
$273$		0			0
$274$	−1.29833	−	4.84544i	−0.0784351	−	0.292724i
$275$	−0.349102	−	0.201554i	−0.0210516	−	0.0121542i
$276$		0			0
$277$	−9.19793	−	2.46458i	−0.552650	−	0.148082i	−0.0283225	−	0.999599i	$-0.509017\pi$
$277$	−9.19793	−	2.46458i	−0.552650	−	0.148082i	−0.524327	+	0.851517i	$0.675683\pi$
$278$	16.4032	+	4.39523i	0.983801	+	0.263609i
$279$		0			0
$280$	3.33242	+	1.92397i	0.199150	+	0.114979i
$281$	−3.50203	−	13.0698i	−0.208914	−	0.779677i	−0.988221	−	0.153035i	$-0.951095\pi$
$281$	−3.50203	−	13.0698i	−0.208914	−	0.779677i	0.779307	−	0.626642i	$-0.215571\pi$
$282$		0			0
$283$	−9.24832	−	2.47808i	−0.549755	−	0.147307i	−0.0267598	−	0.999642i	$-0.508519\pi$
$283$	−9.24832	−	2.47808i	−0.549755	−	0.147307i	−0.522996	+	0.852335i	$0.675186\pi$
$284$	6.95537	−	12.0471i	0.412725	−	0.714861i
$285$		0			0
$286$		−	0.535898i		−	0.0316883i
$287$	−0.608136	+	1.05332i	−0.0358972	+	0.0621757i
$288$		0			0
$289$	14.6851	−	8.47843i	0.863827	−	0.498731i
$290$	−11.9395	−	11.9395i	−0.701114	−	0.701114i
$291$		0			0
$292$	−1.41819	−	2.45638i	−0.0829934	−	0.143749i
$293$	27.5304	−	15.8947i	1.60834	−	0.928576i	0.618599	−	0.785707i	$-0.287701\pi$
$293$	27.5304	−	15.8947i	1.60834	−	0.928576i	0.989742	−	0.142869i	$-0.0456328\pi$
$294$		0			0
$295$			6.97635i			0.406179i
$296$	4.96976	+	3.50735i	0.288862	+	0.203860i
$297$		0			0
$298$	−4.72372	−	17.6291i	−0.273637	−	1.02123i
$299$	−6.57967	−	11.3963i	−0.380512	−	0.659067i
$300$		0			0
$301$	3.12819	−	11.6746i	0.180306	−	0.672912i
$302$	2.54846	−	2.54846i	0.146647	−	0.146647i
$303$		0			0
$304$	0.584574	+	0.584574i	0.0335276	+	0.0335276i
$305$	−1.85613	−	1.07164i	−0.106282	−	0.0613619i
$306$		0			0
$307$		−	26.8349i		−	1.53155i	−0.643108	−	0.765775i	$-0.722355\pi$
$307$		−	26.8349i		−	1.53155i	0.643108	−	0.765775i	$-0.277645\pi$
$308$	−0.387785	−	0.223888i	−0.0220961	−	0.0127572i
$309$		0			0
$310$	11.1043	−	11.1043i	0.630684	−	0.630684i
$311$	19.8171	−	5.30997i	1.12372	−	0.301100i	0.351333	−	0.936250i	$-0.385728\pi$
$311$	19.8171	−	5.30997i	1.12372	−	0.301100i	0.772389	+	0.635150i	$0.219062\pi$
$312$		0			0
$313$	31.8946	−	8.54612i	1.80279	−	0.483055i	0.808379	−	0.588662i	$-0.200345\pi$
$313$	31.8946	−	8.54612i	1.80279	−	0.483055i	0.994408	+	0.105607i	$0.0336786\pi$
$314$	3.88448	−	14.4971i	0.219214	−	0.818117i
$315$		0			0
$316$	0.472172	+	1.76217i	0.0265617	+	0.0991297i
$317$	−16.7060	+	28.9357i	−0.938305	+	1.62519i	−0.169674	+	0.985500i	$0.554271\pi$
$317$	−16.7060	+	28.9357i	−0.938305	+	1.62519i	−0.768631	+	0.639692i	$0.779062\pi$
$318$		0			0
$319$	1.38937	+	1.38937i	0.0777899	+	0.0777899i
$320$	−0.653347	+	2.43832i	−0.0365232	+	0.136306i
$321$		0			0
$322$	−10.9954			−0.612751
$323$	0.171719			0.00955470
$324$		0			0
$325$	1.77024	−	1.77024i	0.0981952	−	0.0981952i
$326$	2.19016	+	3.79346i	0.121302	+	0.210101i
$327$		0			0
$328$	−0.770715	−	0.206512i	−0.0425556	−	0.0114027i
$329$	0.671663	−	0.387785i	0.0370300	−	0.0213793i
$330$		0			0
$331$	2.47087	−	0.662068i	0.135811	−	0.0363906i	−0.190273	−	0.981731i	$-0.560937\pi$
$331$	2.47087	−	0.662068i	0.135811	−	0.0363906i	0.326084	+	0.945341i	$0.394271\pi$
$332$	−5.19921			−0.285344
$333$		0			0
$334$	0.677346			0.0370627
$335$	0.300900	−	0.0806259i	0.0164399	−	0.00440506i
$336$		0			0
$337$	−20.9419	+	12.0908i	−1.14078	+	0.658629i	−0.946624	−	0.322341i	$-0.895530\pi$
$337$	−20.9419	+	12.0908i	−1.14078	+	0.658629i	−0.194156	+	0.980971i	$0.562197\pi$
$338$	−9.34226	−	2.50325i	−0.508152	−	0.136159i
$339$		0			0
$340$	0.262169	+	0.454090i	0.0142181	+	0.0246265i
$341$	−1.29218	+	1.29218i	−0.0699756	+	0.0699756i
$342$		0			0
$343$	17.7988			0.961043
$344$	7.92896			0.427501
$345$		0			0
$346$	4.17290	−	15.5735i	0.224337	−	0.837236i
$347$	−12.6017	−	12.6017i	−0.676494	−	0.676494i	0.282711	−	0.959205i	$-0.408766\pi$
$347$	−12.6017	−	12.6017i	−0.676494	−	0.676494i	−0.959205	+	0.282711i	$0.908766\pi$
$348$		0			0
$349$	−0.246377	+	0.426737i	−0.0131883	+	0.0228427i	−0.872544	−	0.488535i	$-0.837531\pi$
$349$	−0.246377	+	0.426737i	−0.0131883	+	0.0228427i	0.859356	+	0.511378i	$0.170865\pi$
$350$	−0.541403	−	2.02054i	−0.0289392	−	0.108003i
$351$		0			0
$352$	0.0760282	−	0.283741i	0.00405232	−	0.0151235i
$353$	−4.76187	+	1.27594i	−0.253449	+	0.0679114i	−0.383306	−	0.923621i	$-0.625215\pi$
$353$	−4.76187	+	1.27594i	−0.253449	+	0.0679114i	0.129858	+	0.991533i	$0.458548\pi$
$354$		0			0
$355$	−33.9189	+	9.08854i	−1.80023	+	0.482370i
$356$	7.51067	−	7.51067i	0.398065	−	0.398065i
$357$		0			0
$358$	15.9499	+	9.20866i	0.842977	+	0.486693i
$359$			6.79501i			0.358627i	0.983792	+	0.179313i	$0.0573876\pi$
$359$			6.79501i			0.358627i	−0.983792	+	0.179313i	$0.942612\pi$
$360$		0			0
$361$	15.8626	+	9.15827i	0.834873	+	0.482014i
$362$	−12.6790	−	12.6790i	−0.666393	−	0.666393i
$363$		0			0
$364$	1.96639	−	1.96639i	0.103067	−	0.103067i
$365$	−1.85314	+	6.91602i	−0.0969979	+	0.362001i
$366$		0			0
$367$	7.39614	+	12.8105i	0.386076	+	0.668702i	0.991918	−	0.126882i	$-0.0404971\pi$
$367$	7.39614	+	12.8105i	0.386076	+	0.668702i	−0.605842	+	0.795585i	$0.707164\pi$
$368$	−1.86692	−	6.96746i	−0.0973202	−	0.363204i
$369$		0			0
$370$	−2.61038	−	15.1314i	−0.135707	−	0.786646i
$371$			5.44181i			0.282525i
$372$		0			0
$373$	29.4642	−	17.0112i	1.52560	−	0.880805i	0.526060	−	0.850447i	$-0.323669\pi$
$373$	29.4642	−	17.0112i	1.52560	−	0.880805i	0.999539	−	0.0303578i	$-0.00966468\pi$
$374$	−0.0305079	−	0.0528412i	−0.00157753	−	0.00273236i
$375$		0			0
$376$	0.359769	+	0.359769i	0.0185537	+	0.0185537i
$377$	−10.5679	+	6.10139i	−0.544276	+	0.314238i
$378$		0			0
$379$	−6.19287	+	10.7264i	−0.318106	+	0.550977i	−0.980093	−	0.198539i	$-0.936380\pi$
$379$	−6.19287	+	10.7264i	−0.318106	+	0.550977i	0.661986	+	0.749516i	$0.269714\pi$
$380$		−	2.08690i		−	0.107056i
$381$		0			0
$382$	6.12638	−	10.6112i	0.313453	−	0.542916i
$383$	24.2072	+	6.48631i	1.23693	+	0.331435i	0.817275	−	0.576248i	$-0.195484\pi$
$383$	24.2072	+	6.48631i	1.23693	+	0.331435i	0.419657	+	0.907683i	$0.362150\pi$
$384$		0			0
$385$	0.292552	+	1.09182i	0.0149098	+	0.0556443i
$386$	0.978011	+	0.564655i	0.0497795	+	0.0287402i
$387$		0			0
$388$	−5.68036	−	1.52205i	−0.288377	−	0.0772703i
$389$	−20.4360	−	5.47581i	−1.03615	−	0.277634i	−0.299630	−	0.954055i	$-0.596863\pi$
$389$	−20.4360	−	5.47581i	−1.03615	−	0.277634i	−0.736515	+	0.676421i	$0.763530\pi$
$390$		0			0
$391$	−1.29755	−	0.749142i	−0.0656201	−	0.0378858i
$392$	1.21034	+	4.51705i	0.0611314	+	0.228145i
$393$		0			0
$394$	−0.693387	−	0.185792i	−0.0349323	−	0.00936009i
$395$	2.30261	−	3.98825i	0.115857	−	0.200670i
$396$		0			0
$397$			4.90600i			0.246225i	0.992393	+	0.123113i	$0.0392876\pi$
$397$			4.90600i			0.246225i	−0.992393	+	0.123113i	$0.960712\pi$
$398$	−6.21242	+	10.7602i	−0.311400	+	0.539361i
$399$		0			0
$400$	1.18843	−	0.686141i	0.0594215	−	0.0343070i
$401$	10.9589	+	10.9589i	0.547263	+	0.547263i	0.925648	−	0.378385i	$-0.123520\pi$
$401$	10.9589	+	10.9589i	0.547263	+	0.547263i	−0.378385	+	0.925648i	$0.623520\pi$
$402$		0			0
$403$	−5.67458	−	9.82866i	−0.282671	−	0.489600i
$404$	−1.27357	+	0.735295i	−0.0633624	+	0.0365823i
$405$		0			0
$406$			10.1962i			0.506027i
$407$	0.303763	+	1.76081i	0.0150570	+	0.0872799i
$408$		0			0
$409$	8.04108	+	30.0097i	0.397606	+	1.48389i	0.817296	+	0.576218i	$0.195472\pi$
$409$	8.04108	+	30.0097i	0.397606	+	1.48389i	−0.419690	+	0.907667i	$0.637861\pi$
$410$	1.00709	+	1.74433i	0.0497365	+	0.0861462i
$411$		0			0
$412$	−3.32986	+	12.4272i	−0.164051	+	0.612245i
$413$	2.97884	−	2.97884i	0.146579	−	0.146579i
$414$		0			0
$415$	9.28046	+	9.28046i	0.455560	+	0.455560i
$416$	1.57992	+	0.912166i	0.0774618	+	0.0447226i
$417$		0			0
$418$			0.242847i			0.0118780i
$419$	−8.00956	−	4.62432i	−0.391293	−	0.225913i	0.291427	−	0.956593i	$-0.405870\pi$
$419$	−8.00956	−	4.62432i	−0.391293	−	0.225913i	−0.682720	+	0.730680i	$0.739203\pi$
$420$		0			0
$421$	22.5565	−	22.5565i	1.09934	−	1.09934i	0.104850	−	0.994488i	$-0.466564\pi$
$421$	22.5565	−	22.5565i	1.09934	−	1.09934i	0.994488	−	0.104850i	$-0.0334361\pi$
$422$	8.36424	−	2.24119i	0.407165	−	0.109100i
$423$		0			0
$424$	−3.44831	+	0.923972i	−0.167465	+	0.0448720i
$425$	0.0737740	−	0.275328i	0.00357856	−	0.0133554i
$426$		0			0
$427$	0.334972	+	1.25013i	0.0162104	+	0.0604982i
$428$	−0.263243	+	0.455950i	−0.0127243	+	0.0220392i
$429$		0			0
$430$	−14.1530	−	14.1530i	−0.682519	−	0.682519i
$431$	−7.01773	+	26.1905i	−0.338032	+	1.26155i	0.562512	+	0.826789i	$0.309835\pi$
$431$	−7.01773	+	26.1905i	−0.338032	+	1.26155i	−0.900544	+	0.434765i	$0.856832\pi$
$432$		0			0
$433$	−15.2439			−0.732574			−0.366287	−	0.930502i	$-0.619371\pi$
$433$	−15.2439			−0.732574			−0.366287	+	0.930502i	$0.619371\pi$
$434$	−9.48290			−0.455194
$435$		0			0
$436$	5.68265	−	5.68265i	0.272150	−	0.272150i
$437$	2.98164	+	5.16435i	0.142631	+	0.247044i
$438$		0			0
$439$	24.9751	+	6.69205i	1.19199	+	0.319394i	0.799674	−	0.600434i	$-0.205006\pi$
$439$	24.9751	+	6.69205i	1.19199	+	0.319394i	0.392321	+	0.919828i	$0.371672\pi$
$440$	−0.642180	+	0.370763i	−0.0306147	+	0.0176754i
$441$		0			0
$442$	0.366025	−	0.0980762i	0.0174101	−	0.00466501i
$443$	−12.3490			−0.586718			−0.293359	−	0.956002i	$-0.594773\pi$
$443$	−12.3490			−0.586718			−0.293359	+	0.956002i	$0.594773\pi$
$444$		0			0
$445$	−26.8127			−1.27105
$446$	−4.24305	+	1.13692i	−0.200914	+	0.0538348i
$447$		0			0
$448$	1.32012	−	0.762169i	0.0623696	−	0.0360091i
$449$	−26.3577	−	7.06252i	−1.24390	−	0.333301i	−0.423920	−	0.905700i	$-0.639346\pi$
$449$	−26.3577	−	7.06252i	−1.24390	−	0.333301i	−0.819975	+	0.572399i	$0.806013\pi$
$450$		0			0
$451$	−0.117192	−	0.202983i	−0.00551836	−	0.00955808i
$452$	−2.46718	+	2.46718i	−0.116047	+	0.116047i
$453$		0			0
$454$	12.6024			0.591461
$455$	−7.01992			−0.329099
$456$		0			0
$457$	−3.26110	+	12.1706i	−0.152548	+	0.569315i	0.846755	+	0.531983i	$0.178553\pi$
$457$	−3.26110	+	12.1706i	−0.152548	+	0.569315i	−0.999303	+	0.0373328i	$0.988114\pi$
$458$	−20.2108	−	20.2108i	−0.944390	−	0.944390i
$459$		0			0
$460$	−9.10433	+	15.7692i	−0.424492	+	0.735241i
$461$	−7.73576	−	28.8703i	−0.360290	−	1.34462i	−0.873695	−	0.486475i	$-0.838283\pi$
$461$	−7.73576	−	28.8703i	−0.360290	−	1.34462i	0.513404	−	0.858147i	$-0.328384\pi$
$462$		0			0
$463$	4.94528	−	18.4560i	0.229827	−	0.857725i	−0.750586	−	0.660772i	$-0.770229\pi$
$463$	4.94528	−	18.4560i	0.229827	−	0.857725i	0.980413	−	0.196952i	$-0.0631044\pi$
$464$	−6.46099	+	1.73122i	−0.299944	+	0.0803697i
$465$		0			0
$466$	10.0492	−	2.69266i	0.465518	−	0.124735i
$467$	7.82381	−	7.82381i	0.362043	−	0.362043i	−0.502522	−	0.864565i	$-0.667594\pi$
$467$	7.82381	−	7.82381i	0.362043	−	0.362043i	0.864565	+	0.502522i	$0.167594\pi$
$468$		0			0
$469$	−0.162908	−	0.0940550i	−0.00752239	−	0.00434306i
$470$		−	1.28436i		−	0.0592431i
$471$		0			0
$472$	2.39338	+	1.38182i	0.110164	+	0.0636033i
$473$	1.64695	+	1.64695i	0.0757268	+	0.0757268i
$474$		0			0
$475$	−0.802200	+	0.802200i	−0.0368075	+	0.0368075i
$476$	0.0819485	−	0.305836i	0.00375610	−	0.0140180i
$477$		0			0
$478$	4.93351	+	8.54509i	0.225653	+	0.390843i
$479$	−0.672493	−	2.50978i	−0.0307270	−	0.114675i	0.948859	−	0.315700i	$-0.102239\pi$
$479$	−0.672493	−	2.50978i	−0.0307270	−	0.114675i	−0.979586	+	0.201025i	$0.935573\pi$
$480$		0			0
$481$	−11.0511	−	1.00807i	−0.503886	−	0.0459640i
$482$			18.0994i			0.824404i
$483$		0			0
$484$	−9.45155	+	5.45686i	−0.429616	+	0.248039i
$485$	7.42249	+	12.8561i	0.337038	+	0.583767i
$486$		0			0
$487$	−16.5058	−	16.5058i	−0.747949	−	0.747949i	0.226145	−	0.974094i	$-0.427388\pi$
$487$	−16.5058	−	16.5058i	−0.747949	−	0.747949i	−0.974094	+	0.226145i	$0.927388\pi$
$488$	−0.735295	+	0.424523i	−0.0332853	+	0.0192172i
$489$		0			0
$490$	5.90240	−	10.2233i	0.266643	−	0.461840i
$491$		−	15.7257i		−	0.709693i	−0.934925	−	0.354846i	$-0.884533\pi$
$491$		−	15.7257i		−	0.709693i	0.934925	−	0.354846i	$-0.115467\pi$
$492$		0			0
$493$	−0.694686	+	1.20323i	−0.0312871	+	0.0541909i
$494$	−1.45681	−	0.390350i	−0.0655448	−	0.0175627i
$495$		0			0
$496$	−1.61011	−	6.00902i	−0.0722962	−	0.269813i
$497$	18.3638	+	10.6023i	0.823728	+	0.475580i
$498$		0			0
$499$	28.6335	+	7.67232i	1.28181	+	0.343460i	0.834544	−	0.550941i	$-0.185731\pi$
$499$	28.6335	+	7.67232i	1.28181	+	0.343460i	0.447266	+	0.894401i	$0.352398\pi$
$500$	8.84555	+	2.37016i	0.395585	+	0.105997i
$501$		0			0
$502$	3.85916	+	2.22808i	0.172243	+	0.0994443i
$503$	2.43638	+	9.09269i	0.108633	+	0.405423i	0.998732	−	0.0503439i	$-0.0160317\pi$
$503$	2.43638	+	9.09269i	0.108633	+	0.405423i	−0.890099	+	0.455767i	$0.849365\pi$
$504$		0			0
$505$	3.58577	+	0.960805i	0.159565	+	0.0427553i
$506$	1.05945	−	1.83502i	0.0470982	−	0.0815764i
$507$		0			0
$508$			8.02460i			0.356034i
$509$	−2.56030	+	4.43457i	−0.113483	+	0.196559i	−0.917172	−	0.398491i	$-0.869534\pi$
$509$	−2.56030	+	4.43457i	−0.113483	+	0.196559i	0.803689	+	0.595049i	$0.202868\pi$
$510$		0			0
$511$	3.74435	−	2.16180i	0.165640	−	0.0956325i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−9.15181	−	15.8514i	−0.403669	−	0.699175i
$515$	28.1260	−	16.2386i	1.23938	−	0.715556i
$516$		0			0
$517$			0.149458i			0.00657314i
$518$	−5.34638	+	7.57560i	−0.234906	+	0.332853i
$519$		0			0
$520$	−1.19192	−	4.44831i	−0.0522692	−	0.195071i
$521$	0.531797	+	0.921099i	0.0232984	+	0.0403541i	0.877440	−	0.479687i	$-0.159250\pi$
$521$	0.531797	+	0.921099i	0.0232984	+	0.0403541i	−0.854141	+	0.520041i	$0.825917\pi$
$522$		0			0
$523$	−6.27785	+	23.4293i	−0.274511	+	1.02449i	0.681657	+	0.731672i	$0.261260\pi$
$523$	−6.27785	+	23.4293i	−0.274511	+	1.02449i	−0.956168	+	0.292818i	$0.905407\pi$
$524$	14.0336	−	14.0336i	0.613060	−	0.613060i
$525$		0			0
$526$	15.5935	+	15.5935i	0.679907	+	0.679907i
$527$	−1.11906	−	0.646091i	−0.0487471	−	0.0281442i
$528$		0			0
$529$		−	29.0309i		−	1.26221i
$530$	7.80442	+	4.50588i	0.339002	+	0.195723i
$531$		0			0
$532$	−0.891088	+	0.891088i	−0.0386336	+	0.0386336i
$533$	1.40604	−	0.376747i	0.0609023	−	0.0163187i
$534$		0			0
$535$	1.28374	−	0.343977i	0.0555010	−	0.0148714i
$536$	0.0319394	−	0.119199i	0.00137957	−	0.00514863i
$537$		0			0
$538$	4.88781	+	18.2415i	0.210728	+	0.786449i
$539$	−0.686847	+	1.18965i	−0.0295846	+	0.0512420i
$540$		0			0
$541$	−29.7879	−	29.7879i	−1.28068	−	1.28068i	−0.940279	−	0.340404i	$-0.889436\pi$
$541$	−29.7879	−	29.7879i	−1.28068	−	1.28068i	−0.340404	−	0.940279i	$-0.610564\pi$
$542$	−6.30408	+	23.5271i	−0.270783	+	1.01058i
$543$		0			0
$544$	0.207713			0.00890562
$545$	−20.2868			−0.868991
$546$		0			0
$547$	−30.2623	+	30.2623i	−1.29392	+	1.29392i	−0.361582	+	0.932340i	$0.617763\pi$
$547$	−30.2623	+	30.2623i	−1.29392	+	1.29392i	−0.932340	+	0.361582i	$0.882237\pi$
$548$	2.50819	+	4.34431i	0.107144	+	0.185580i
$549$		0			0
$550$	0.389373	+	0.104332i	0.0166029	+	0.00444874i
$551$	4.78895	−	2.76490i	0.204016	−	0.117789i
$552$		0			0
$553$	−2.68614	+	0.719749i	−0.114226	+	0.0306069i
$554$	9.52240			0.404568
$555$		0			0
$556$	−16.9819			−0.720192
$557$	4.61499	−	1.23658i	0.195544	−	0.0523958i	−0.159718	−	0.987163i	$-0.551058\pi$
$557$	4.61499	−	1.23658i	0.195544	−	0.0523958i	0.355262	+	0.934767i	$0.384392\pi$
$558$		0			0
$559$	−12.5271	+	7.23253i	−0.529840	+	0.305903i
$560$	−3.71683	−	0.995921i	−0.157065	−	0.0420853i
$561$		0			0
$562$	6.76541	+	11.7180i	0.285382	+	0.494295i
$563$	20.0154	−	20.0154i	0.843548	−	0.843548i	−0.145771	−	0.989318i	$-0.546566\pi$
$563$	20.0154	−	20.0154i	0.843548	−	0.843548i	0.989318	+	0.145771i	$0.0465662\pi$
$564$		0			0
$565$	8.80773			0.370544
$566$	9.57456			0.402449
$567$		0			0
$568$	−3.60037	+	13.4367i	−0.151068	+	0.563793i
$569$	−17.3227	−	17.3227i	−0.726206	−	0.726206i	0.243656	−	0.969862i	$-0.421653\pi$
$569$	−17.3227	−	17.3227i	−0.726206	−	0.726206i	−0.969862	+	0.243656i	$0.921653\pi$
$570$		0			0
$571$	−3.28265	+	5.68572i	−0.137375	+	0.237940i	−0.926502	−	0.376290i	$-0.877200\pi$
$571$	−3.28265	+	5.68572i	−0.137375	+	0.237940i	0.789127	+	0.614230i	$0.210533\pi$
$572$	0.138701	+	0.517638i	0.00579937	+	0.0216435i
$573$		0			0
$574$	0.314795	−	1.17483i	0.0131393	−	0.0490364i
$575$	9.56131	−	2.56195i	0.398734	−	0.106841i
$576$		0			0
$577$	−32.2224	+	8.63397i	−1.34144	+	0.359437i	−0.856967	−	0.515371i	$-0.827654\pi$
$577$	−32.2224	+	8.63397i	−1.34144	+	0.359437i	−0.484470	+	0.874808i	$0.660988\pi$
$578$	−11.9903	+	11.9903i	−0.498731	+	0.498731i
$579$		0			0
$580$	14.6229	+	8.44253i	0.607182	+	0.350557i
$581$		−	7.92535i		−	0.328799i
$582$		0			0
$583$	−0.908180	−	0.524338i	−0.0376130	−	0.0217159i
$584$	2.00563	+	2.00563i	0.0829934	+	0.0829934i
$585$		0			0
$586$	−22.4784	+	22.4784i	−0.928576	+	0.928576i
$587$	−2.59467	+	9.68343i	−0.107093	+	0.399678i	−0.998574	−	0.0533804i	$-0.983000\pi$
$587$	−2.59467	+	9.68343i	−0.107093	+	0.399678i	0.891481	+	0.453058i	$0.149667\pi$
$588$		0			0
$589$	2.57149	+	4.45395i	0.105956	+	0.183522i
$590$	−1.80561	−	6.73863i	−0.0743359	−	0.277425i
$591$		0			0
$592$	−5.70819	−	2.10157i	−0.234605	−	0.0863739i
$593$			11.4901i			0.471840i	0.971772	+	0.235920i	$0.0758104\pi$
$593$			11.4901i			0.471840i	−0.971772	+	0.235920i	$0.924190\pi$
$594$		0			0
$595$	−0.692186	+	0.399634i	−0.0283769	+	0.0163834i
$596$	9.12552	+	15.8059i	0.373796	+	0.647433i
$597$		0			0
$598$	9.30506	+	9.30506i	0.380512	+	0.380512i
$599$	−20.2142	+	11.6707i	−0.825931	+	0.476851i	−0.852457	−	0.522797i	$-0.824889\pi$
$599$	−20.2142	+	11.6707i	−0.825931	+	0.476851i	0.0265266	+	0.999648i	$0.491555\pi$
$600$		0			0
$601$	−10.8100	+	18.7235i	−0.440950	+	0.763748i	−0.997760	−	0.0668920i	$-0.978692\pi$
$601$	−10.8100	+	18.7235i	−0.440950	+	0.763748i	0.556810	+	0.830640i	$0.312025\pi$
$602$			12.0864i			0.492605i
$603$		0			0
$604$	−1.80203	+	3.12121i	−0.0733237	+	0.127000i
$605$	26.6112	+	7.13044i	1.08190	+	0.289893i
$606$		0			0
$607$	10.0032	+	37.3323i	0.406016	+	1.51527i	0.802175	+	0.597089i	$0.203676\pi$
$607$	10.0032	+	37.3323i	0.406016	+	1.51527i	−0.396159	+	0.918182i	$0.629657\pi$
$608$	−0.715954	−	0.413356i	−0.0290358	−	0.0167638i
$609$		0			0
$610$	2.07025	+	0.554721i	0.0838219	+	0.0224600i
$611$	−0.896575	−	0.240237i	−0.0362716	−	0.00971894i
$612$		0			0
$613$	2.81721	+	1.62652i	0.113786	+	0.0656944i	0.555813	−	0.831307i	$-0.312407\pi$
$613$	2.81721	+	1.62652i	0.113786	+	0.0656944i	−0.442027	+	0.897002i	$0.645740\pi$
$614$	6.94539	+	25.9206i	0.280293	+	1.04607i
$615$		0			0
$616$	0.432518	+	0.115893i	0.0174266	+	0.00466945i
$617$	3.67631	−	6.36755i	0.148003	−	0.256348i	−0.782487	−	0.622667i	$-0.786049\pi$
$617$	3.67631	−	6.36755i	0.148003	−	0.256348i	0.930489	+	0.366319i	$0.119382\pi$
$618$		0			0
$619$			1.36167i			0.0547302i	0.999626	+	0.0273651i	$0.00871167\pi$
$619$			1.36167i			0.0547302i	−0.999626	+	0.0273651i	$0.991288\pi$
$620$	−7.85195	+	13.6000i	−0.315342	+	0.546188i
$621$		0			0
$622$	−17.7675	+	10.2581i	−0.712411	+	0.411311i
$623$	11.4488	+	11.4488i	0.458686	+	0.458686i
$624$		0			0
$625$	−14.9891	−	25.9619i	−0.599565	−	1.03848i
$626$	−28.5959	+	16.5098i	−1.14292	+	0.659866i
$627$		0			0
$628$			15.0085i			0.598903i
$629$	−1.14706	+	0.529724i	−0.0457363	+	0.0211215i
$630$		0			0
$631$	−4.59997	−	17.1673i	−0.183122	−	0.683421i	−0.995025	−	0.0996280i	$-0.968235\pi$
$631$	−4.59997	−	17.1673i	−0.183122	−	0.683421i	0.811903	−	0.583793i	$-0.198432\pi$
$632$	−0.912166	−	1.57992i	−0.0362840	−	0.0628457i
$633$		0			0
$634$	8.64769	−	32.2736i	0.343444	−	1.28175i
$635$	14.3237	−	14.3237i	0.568420	−	0.568420i
$636$		0			0
$637$	−6.03254	−	6.03254i	−0.239018	−	0.239018i
$638$	−1.70163	−	0.982435i	−0.0673681	−	0.0388950i
$639$		0			0
$640$		−	2.52434i		−	0.0997832i
$641$	29.4108	+	16.9803i	1.16166	+	0.670683i	0.951700	−	0.307028i	$-0.0993346\pi$
$641$	29.4108	+	16.9803i	1.16166	+	0.670683i	0.209956	+	0.977711i	$0.432668\pi$
$642$		0			0
$643$	9.17799	−	9.17799i	0.361945	−	0.361945i	−0.502584	−	0.864528i	$-0.667617\pi$
$643$	9.17799	−	9.17799i	0.361945	−	0.361945i	0.864528	+	0.502584i	$0.167617\pi$
$644$	10.6208	−	2.84582i	0.418517	−	0.112141i
$645$		0			0
$646$	−0.165868	+	0.0444441i	−0.00652598	+	0.00174863i
$647$	−8.62703	+	32.1965i	−0.339163	+	1.26577i	0.560121	+	0.828411i	$0.310755\pi$
$647$	−8.62703	+	32.1965i	−0.339163	+	1.26577i	−0.899284	+	0.437364i	$0.855912\pi$
$648$		0			0
$649$	0.210114	+	0.784157i	0.00824771	+	0.0307809i
$650$	−1.25175	+	2.16809i	−0.0490976	+	0.0850395i
$651$		0			0
$652$	−3.09735	−	3.09735i	−0.121302	−	0.121302i
$653$	−8.11599	+	30.2893i	−0.317603	+	1.18531i	0.603938	+	0.797031i	$0.293597\pi$
$653$	−8.11599	+	30.2893i	−0.317603	+	1.18531i	−0.921541	+	0.388280i	$0.873069\pi$
$654$		0			0
$655$	−50.0993			−1.95754
$656$	0.797903			0.0311529
$657$		0			0
$658$	−0.548410	+	0.548410i	−0.0213793	+	0.0213793i
$659$	1.46411	+	2.53592i	0.0570338	+	0.0987854i	0.893133	−	0.449793i	$-0.148502\pi$
$659$	1.46411	+	2.53592i	0.0570338	+	0.0987854i	−0.836099	+	0.548579i	$0.815169\pi$
$660$		0			0
$661$	13.4584	+	3.60616i	0.523470	+	0.140263i	0.510871	−	0.859657i	$-0.329323\pi$
$661$	13.4584	+	3.60616i	0.523470	+	0.140263i	0.0125990	+	0.999921i	$0.495990\pi$
$662$	−2.21532	+	1.27902i	−0.0861010	+	0.0497104i
$663$		0			0
$664$	5.02205	−	1.34565i	0.194893	−	0.0522215i
$665$	3.18114			0.123359
$666$		0			0
$667$	−48.2487			−1.86820
$668$	−0.654266	+	0.175310i	−0.0253143	+	0.00678294i
$669$		0			0
$670$	−0.269779	+	0.155757i	−0.0104225	+	0.00601743i
$671$	−0.240909	−	0.0645515i	−0.00930020	−	0.00249198i
$672$		0			0
$673$	10.0952	+	17.4854i	0.389140	+	0.674011i	0.992334	−	0.123584i	$-0.0394388\pi$
$673$	10.0952	+	17.4854i	0.389140	+	0.674011i	−0.603194	+	0.797595i	$0.706105\pi$
$674$	17.0990	−	17.0990i	0.658629	−	0.658629i
$675$		0			0
$676$	9.67181			0.371993
$677$	−4.96831			−0.190948			−0.0954738	−	0.995432i	$-0.530437\pi$
$677$	−4.96831			−0.190948			−0.0954738	+	0.995432i	$0.530437\pi$
$678$		0			0
$679$	2.32012	−	8.65879i	0.0890379	−	0.332294i
$680$	−0.370763	−	0.370763i	−0.0142181	−	0.0142181i
$681$		0			0
$682$	0.913711	−	1.58259i	0.0349878	−	0.0606006i
$683$	−12.3107	−	45.9441i	−0.471055	−	1.75800i	−0.635991	−	0.771697i	$-0.719408\pi$
$683$	−12.3107	−	45.9441i	−0.471055	−	1.75800i	0.164936	−	0.986304i	$-0.447258\pi$
$684$		0			0
$685$	3.27743	−	12.2315i	0.125224	−	0.467343i
$686$	−17.1923	+	4.60666i	−0.656405	+	0.175883i
$687$		0			0
$688$	−7.65879	+	2.05217i	−0.291989	+	0.0782381i
$689$	4.60523	−	4.60523i	0.175445	−	0.175445i
$690$		0			0
$691$	21.2329	+	12.2588i	0.807737	+	0.466347i	0.846169	−	0.532914i	$-0.178903\pi$
$691$	21.2329	+	12.2588i	0.807737	+	0.466347i	−0.0384326	+	0.999261i	$0.512237\pi$
$692$			16.1229i			0.612899i
$693$		0			0
$694$	15.4338	+	8.91073i	0.585861	+	0.338247i
$695$	30.3123	+	30.3123i	1.14981	+	1.14981i
$696$		0			0
$697$	0.117192	−	0.117192i	0.00443897	−	0.00443897i
$698$	0.127534	−	0.475964i	0.00482723	−	0.0180155i
$699$		0			0
$700$	1.04591	+	1.81157i	0.0395317	+	0.0684709i
$701$	−1.70435	−	6.36072i	−0.0643724	−	0.240241i	0.926242	−	0.376931i	$-0.123020\pi$
$701$	−1.70435	−	6.36072i	−0.0643724	−	0.240241i	−0.990614	+	0.136689i	$0.956354\pi$
$702$		0			0
$703$	5.00790	+	0.456816i	0.188877	+	0.0172291i
$704$			0.293751i			0.0110711i
$705$		0			0
$706$	4.26938	−	2.46493i	0.160680	−	0.0927687i
$707$	−1.12084	−	1.94135i	−0.0421535	−	0.0730119i
$708$		0			0
$709$	10.5921	+	10.5921i	0.397796	+	0.397796i	0.877455	−	0.479659i	$-0.159240\pi$
$709$	10.5921	+	10.5921i	0.397796	+	0.397796i	−0.479659	+	0.877455i	$0.659240\pi$
$710$	30.4108	−	17.5577i	1.14130	−	0.658929i
$711$		0			0
$712$	−5.31084	+	9.19865i	−0.199032	+	0.344734i
$713$		−	44.8736i		−	1.68053i
$714$		0			0
$715$	0.676394	−	1.17155i	0.0252957	−	0.0438135i
$716$	−17.7898	−	4.76676i	−0.664835	−	0.178142i
$717$		0			0
$718$	−1.75868	−	6.56348i	−0.0656333	−	0.244947i
$719$	27.7757	+	16.0363i	1.03586	+	0.598054i	0.918658	−	0.395054i	$-0.129274\pi$
$719$	27.7757	+	16.0363i	1.03586	+	0.598054i	0.117202	+	0.993108i	$0.462607\pi$
$720$		0			0
$721$	−18.9433	−	5.07583i	−0.705484	−	0.189034i
$722$	−17.6924	−	4.74067i	−0.658444	−	0.176430i
$723$		0			0
$724$	15.5285	+	8.96540i	0.577113	+	0.333197i
$725$	−2.37572	−	8.86629i	−0.0882319	−	0.329286i
$726$		0			0
$727$	−7.24206	−	1.94050i	−0.268593	−	0.0719693i	0.122009	−	0.992529i	$-0.461066\pi$
$727$	−7.24206	−	1.94050i	−0.268593	−	0.0719693i	−0.390602	+	0.920560i	$0.627733\pi$
$728$	−1.39045	+	2.40833i	−0.0515335	+	0.0892586i
$729$		0			0
$730$		−	7.15999i		−	0.265003i
$731$	−0.823474	+	1.42630i	−0.0304573	+	0.0527536i
$732$		0			0
$733$	−34.6612	+	20.0116i	−1.28024	+	0.739147i	−0.976892	−	0.213733i	$-0.931438\pi$
$733$	−34.6612	+	20.0116i	−1.28024	+	0.739147i	−0.303348	+	0.952880i	$0.598105\pi$
$734$	−10.4597	−	10.4597i	−0.386076	−	0.386076i
$735$		0			0
$736$	3.60662	+	6.24685i	0.132942	+	0.230262i
$737$	0.0313935	−	0.0181251i	0.00115640	−	0.000667645i
$738$		0			0
$739$		−	2.76959i		−	0.101881i	−0.998702	−	0.0509404i	$-0.983778\pi$
$739$		−	2.76959i		−	0.101881i	0.998702	−	0.0509404i	$-0.0162219\pi$
$740$	6.43773	+	13.9402i	0.236656	+	0.512453i
$741$		0			0
$742$	−1.40845	−	5.25639i	−0.0517056	−	0.192968i
$743$	16.7349	+	28.9857i	0.613944	+	1.06338i	0.990569	+	0.137017i	$0.0437514\pi$
$743$	16.7349	+	28.9857i	0.613944	+	1.06338i	−0.376624	+	0.926366i	$0.622915\pi$
$744$		0			0
$745$	11.9243	−	44.5019i	0.436871	−	1.63042i
$746$	−24.0574	+	24.0574i	−0.880805	+	0.880805i
$747$		0			0
$748$	0.0431447	+	0.0431447i	0.00157753	+	0.00157753i
$749$	−0.695021	−	0.401271i	−0.0253955	−	0.0146621i
$750$		0			0
$751$		−	50.0879i		−	1.82773i	−0.406014	−	0.913867i	$-0.633081\pi$
$751$		−	50.0879i		−	1.82773i	0.406014	−	0.913867i	$-0.366919\pi$
$752$	−0.440626	−	0.254395i	−0.0160680	−	0.00927685i
$753$		0			0
$754$	8.62867	−	8.62867i	0.314238	−	0.314238i
$755$	8.78788	−	2.35471i	0.319824	−	0.0856965i
$756$		0			0
$757$	−7.51674	+	2.01411i	−0.273201	+	0.0732039i	−0.392818	−	0.919616i	$-0.628500\pi$
$757$	−7.51674	+	2.01411i	−0.273201	+	0.0732039i	0.119618	+	0.992820i	$0.461833\pi$
$758$	3.20567	−	11.9637i	0.116435	−	0.434542i
$759$		0			0
$760$	0.540130	+	2.01579i	0.0195926	+	0.0731205i
$761$	2.73324	−	4.73411i	0.0990798	−	0.171611i	−0.812224	−	0.583345i	$-0.801743\pi$
$761$	2.73324	−	4.73411i	0.0990798	−	0.171611i	0.911304	+	0.411734i	$0.135077\pi$
$762$		0			0
$763$	8.66228	+	8.66228i	0.313596	+	0.313596i
$764$	−3.17125	+	11.8353i	−0.114732	+	0.428185i
$765$		0			0
$766$	−25.0612			−0.905498
$767$	−5.04179			−0.182048
$768$		0			0
$769$	−6.48375	+	6.48375i	−0.233810	+	0.233810i	−0.814281	−	0.580471i	$-0.802868\pi$
$769$	−6.48375	+	6.48375i	−0.233810	+	0.233810i	0.580471	+	0.814281i	$0.302868\pi$
$770$	−0.565168	−	0.978899i	−0.0203672	−	0.0352771i
$771$		0			0
$772$	−1.09083	−	0.292287i	−0.0392598	−	0.0105196i
$773$	39.7347	−	22.9408i	1.42916	−	0.825124i	0.432103	−	0.901824i	$-0.357772\pi$
$773$	39.7347	−	22.9408i	1.42916	−	0.825124i	0.997054	+	0.0767000i	$0.0244384\pi$
$774$		0			0
$775$	8.24607	−	2.20953i	0.296207	−	0.0793686i
$776$	5.88074			0.211106
$777$		0			0
$778$	21.1569			0.758511
$779$	−0.637159	+	0.170726i	−0.0228286	+	0.00611691i
$780$		0			0
$781$	−3.53883	+	2.04314i	−0.126629	+	0.0731095i
$782$	1.44723	+	0.387785i	0.0517529	+	0.0138671i
$783$		0			0
$784$	−2.33820	−	4.04988i	−0.0835070	−	0.144638i
$785$	26.7898	−	26.7898i	0.956167	−	0.956167i
$786$		0			0
$787$	−32.7660			−1.16798			−0.583990	−	0.811761i	$-0.698509\pi$
$787$	−32.7660			−1.16798			−0.583990	+	0.811761i	$0.698509\pi$
$788$	0.717847			0.0255722
$789$		0			0
$790$	−1.19192	+	4.44831i	−0.0424066	+	0.158264i
$791$	−3.76082	−	3.76082i	−0.133719	−	0.133719i
$792$		0			0
$793$	0.774470	−	1.34142i	0.0275023	−	0.0476353i
$794$	−1.26977	−	4.73883i	−0.0450623	−	0.168175i
$795$		0			0
$796$	3.21578	−	12.0015i	0.113980	−	0.425381i
$797$	17.7625	−	4.75945i	0.629180	−	0.168588i	0.0698825	−	0.997555i	$-0.477738\pi$
$797$	17.7625	−	4.75945i	0.629180	−	0.168588i	0.559298	+	0.828967i	$0.311071\pi$
$798$		0			0
$799$	−0.102081	+	0.0273526i	−0.00361138	+	0.000967667i
$800$	−0.970349	+	0.970349i	−0.0343070	+	0.0343070i
$801$		0			0
$802$	−13.4219	−	7.74914i	−0.473944	−	0.273632i
$803$			0.833189i			0.0294026i
$804$		0			0
$805$	−24.0375	−	13.8781i	−0.847212	−	0.489138i
$806$	8.02507	+	8.02507i	0.282671	+	0.282671i
$807$		0			0
$808$	1.03986	−	1.03986i	0.0365823	−	0.0365823i
$809$	0.166680	−	0.622060i	0.00586017	−	0.0218705i	−0.962934	−	0.269738i	$-0.913063\pi$
$809$	0.166680	−	0.622060i	0.00586017	−	0.0218705i	0.968794	+	0.247867i	$0.0797297\pi$
$810$		0			0
$811$	22.1780	+	38.4135i	0.778776	+	1.34888i	0.932648	+	0.360789i	$0.117492\pi$
$811$	22.1780	+	38.4135i	0.778776	+	1.34888i	−0.153872	+	0.988091i	$0.549174\pi$
$812$	−2.63896	−	9.84873i	−0.0926093	−	0.345623i
$813$		0			0
$814$	−0.749142	−	1.62219i	−0.0262574	−	0.0568577i
$815$			11.0574i			0.387324i
$816$		0			0
$817$	5.67677	−	3.27749i	0.198605	−	0.114665i
$818$	−15.5342	−	26.9060i	−0.543140	−	0.940746i
$819$		0			0
$820$	−1.42424	−	1.42424i	−0.0497365	−	0.0497365i
$821$	37.9523	−	21.9118i	1.32455	−	0.764726i	0.340095	−	0.940391i	$-0.389541\pi$
$821$	37.9523	−	21.9118i	1.32455	−	0.764726i	0.984450	+	0.175665i	$0.0562074\pi$
$822$		0			0
$823$	18.1624	−	31.4582i	0.633101	−	1.09656i	−0.353813	−	0.935316i	$-0.615115\pi$
$823$	18.1624	−	31.4582i	0.633101	−	1.09656i	0.986914	−	0.161247i	$-0.0515514\pi$
$824$		−	12.8656i		−	0.448194i
$825$		0			0
$826$	−2.10636	+	3.64832i	−0.0732895	+	0.126941i
$827$	23.0386	+	6.17317i	0.801130	+	0.214662i	0.636080	−	0.771623i	$-0.280555\pi$
$827$	23.0386	+	6.17317i	0.801130	+	0.214662i	0.165050	+	0.986285i	$0.447221\pi$
$828$		0			0
$829$	10.9231	+	40.7656i	0.379375	+	1.41585i	0.846846	+	0.531839i	$0.178499\pi$
$829$	10.9231	+	40.7656i	0.379375	+	1.41585i	−0.467470	+	0.884009i	$0.654835\pi$
$830$	−11.3662	−	6.56228i	−0.394526	−	0.227780i
$831$		0			0
$832$	−1.76217	−	0.472172i	−0.0610922	−	0.0163696i
$833$	−0.938250	−	0.251403i	−0.0325084	−	0.00871061i
$834$		0			0
$835$	1.48077	+	0.854924i	0.0512442	+	0.0295859i
$836$	−0.0628535	−	0.234572i	−0.00217383	−	0.00811286i
$837$		0			0
$838$	8.93351	+	2.39373i	0.308603	+	0.0826899i
$839$	14.9148	−	25.8333i	0.514918	−	0.891863i	−0.484933	−	0.874552i	$-0.661156\pi$
$839$	14.9148	−	25.8333i	0.514918	−	0.891863i	0.999850	−	0.0173118i	$-0.00551079\pi$
$840$		0			0
$841$			15.7415i			0.542809i
$842$	−15.9499	+	27.6260i	−0.549669	+	0.952054i
$843$		0			0
$844$	−7.49918	+	4.32965i	−0.258132	+	0.149033i
$845$	−17.2640	−	17.2640i	−0.593898	−	0.593898i
$846$		0			0
$847$	−8.31809	−	14.4074i	−0.285813	−	0.495043i
$848$	3.09167	−	1.78498i	0.106168	−	0.0612963i
$849$		0			0
$850$			0.285041i			0.00977681i
$851$	−35.8481	−	25.2993i	−1.22886	−	0.867250i
$852$		0			0
$853$	−4.23131	−	15.7915i	−0.144877	−	0.540689i	−0.999761	−	0.0218695i	$-0.993038\pi$
$853$	−4.23131	−	15.7915i	−0.144877	−	0.540689i	0.854884	−	0.518820i	$-0.173628\pi$
$854$	−0.647116	−	1.12084i	−0.0221439	−	0.0383543i
$855$		0			0
$856$	0.136264	−	0.508546i	0.00465742	−	0.0173817i
$857$	−27.6848	+	27.6848i	−0.945695	+	0.945695i	−0.998600	−	0.0529045i	$-0.983152\pi$
$857$	−27.6848	+	27.6848i	−0.945695	+	0.945695i	0.0529045	+	0.998600i	$0.483152\pi$
$858$		0			0
$859$	33.2037	+	33.2037i	1.13290	+	1.13290i	0.989693	+	0.143202i	$0.0457400\pi$
$859$	33.2037	+	33.2037i	1.13290	+	1.13290i	0.143202	+	0.989693i	$0.454260\pi$
$860$	17.3338	+	10.0077i	0.591078	+	0.341259i
$861$		0			0
$862$		−	27.1144i		−	0.923522i
$863$	−40.9185	−	23.6243i	−1.39288	−	0.804182i	−0.399250	−	0.916842i	$-0.630729\pi$
$863$	−40.9185	−	23.6243i	−1.39288	−	0.804182i	−0.993634	+	0.112661i	$0.964063\pi$
$864$		0			0
$865$	28.7789	−	28.7789i	0.978513	−	0.978513i
$866$	14.7245	−	3.94541i	0.500357	−	0.134070i
$867$		0			0
$868$	9.15978	−	2.45436i	0.310903	−	0.0833062i
$869$	0.138701	−	0.517638i	0.00470510	−	0.0175597i
$870$		0			0
$871$	0.0582681	+	0.217459i	0.00197434	+	0.00736833i
$872$	−4.01824	+	6.95980i	−0.136075	+	0.235688i
$873$		0			0
$874$	−4.21667	−	4.21667i	−0.142631	−	0.142631i
$875$	−3.61292	+	13.4836i	−0.122139	+	0.455829i
$876$		0			0
$877$	−24.9993			−0.844167			−0.422083	−	0.906557i	$-0.638701\pi$
$877$	−24.9993			−0.844167			−0.422083	+	0.906557i	$0.638701\pi$
$878$	−25.8561			−0.872601
$879$		0			0
$880$	0.524338	−	0.524338i	0.0176754	−	0.0176754i
$881$	10.8865	+	18.8559i	0.366774	+	0.635272i	0.989059	−	0.147519i	$-0.0471288\pi$
$881$	10.8865	+	18.8559i	0.366774	+	0.635272i	−0.622285	+	0.782791i	$0.713795\pi$
$882$		0			0
$883$	2.49969	+	0.669790i	0.0841213	+	0.0225402i	0.300634	−	0.953740i	$-0.402802\pi$
$883$	2.49969	+	0.669790i	0.0841213	+	0.0225402i	−0.216513	+	0.976280i	$0.569468\pi$
$884$	−0.328169	+	0.189469i	−0.0110375	+	0.00637252i
$885$		0			0
$886$	11.9282	−	3.19615i	0.400736	−	0.107377i
$887$	−1.60876			−0.0540168			−0.0270084	−	0.999635i	$-0.508598\pi$
$887$	−1.60876			−0.0540168			−0.0270084	+	0.999635i	$0.508598\pi$
$888$		0			0
$889$	−12.2322			−0.410255
$890$	25.8991	−	6.93965i	0.868140	−	0.232617i
$891$		0			0
$892$	3.80421	−	2.19636i	0.127374	−	0.0735397i
$893$	0.406291	+	0.108865i	0.0135960	+	0.00364304i
$894$		0			0
$895$	23.2458	+	40.2629i	0.777021	+	1.34584i
$896$	−1.07787	+	1.07787i	−0.0360091	+	0.0360091i
$897$		0			0
$898$	27.2875			0.910595
$899$	−41.6117			−1.38783
$900$		0			0
$901$	0.191921	−	0.716259i	0.00639381	−	0.0238620i
$902$	0.165735	+	0.165735i	0.00551836	+	0.00551836i
$903$		0			0
$904$	1.74456	−	3.02167i	0.0580233	−	0.100499i
$905$	−11.7150	−	43.7211i	−0.389421	−	1.45334i
$906$		0			0
$907$	7.43979	−	27.7657i	0.247034	−	0.921944i	−0.725316	−	0.688416i	$-0.758306\pi$
$907$	7.43979	−	27.7657i	0.247034	−	0.921944i	0.972350	−	0.233528i	$-0.0750270\pi$
$908$	−12.1730	+	3.26175i	−0.403975	+	0.108245i
$909$		0			0
$910$	6.78073	−	1.81689i	0.224779	−	0.0602293i
$911$	−37.4862	+	37.4862i	−1.24197	+	1.24197i	−0.282792	+	0.959181i	$0.591261\pi$
$911$	−37.4862	+	37.4862i	−1.24197	+	1.24197i	−0.959181	+	0.282792i	$0.908739\pi$
$912$		0			0
$913$	1.32265	+	0.763635i	0.0437735	+	0.0252726i
$914$		−	12.5999i		−	0.416768i
$915$		0			0
$916$	24.7531	+	14.2912i	0.817866	+	0.472195i
$917$	21.3919	+	21.3919i	0.706424	+	0.706424i
$918$		0			0
$919$	34.9478	−	34.9478i	1.15282	−	1.15282i	0.166839	−	0.985984i	$-0.446644\pi$
$919$	34.9478	−	34.9478i	1.15282	−	1.15282i	0.985984	−	0.166839i	$-0.0533560\pi$
$920$	4.71275	−	17.5882i	0.155375	−	0.579866i
$921$		0			0
$922$	14.9443	+	25.8844i	0.492166	+	0.852456i
$923$	−6.56826	−	24.5131i	−0.216197	−	0.806858i
$924$		0			0
$925$	2.88394	−	7.83324i	0.0948234	−	0.257555i
$926$			19.1071i			0.627898i
$927$		0			0
$928$	5.79276	−	3.34445i	0.190157	−	0.109787i
$929$	0.851663	+	1.47512i	0.0279421	+	0.0483972i	0.879658	−	0.475606i	$-0.157771\pi$
$929$	0.851663	+	1.47512i	0.0279421	+	0.0483972i	−0.851716	+	0.524003i	$0.824438\pi$
$930$		0			0
$931$	2.73370	+	2.73370i	0.0895933	+	0.0895933i
$932$	−9.00982	+	5.20182i	−0.295127	+	0.170391i
$933$		0			0
$934$	−5.53227	+	9.58217i	−0.181021	+	0.313538i
$935$		−	0.154025i		−	0.00503714i
$936$		0			0
$937$	−23.4657	+	40.6437i	−0.766590	+	1.32777i	0.172812	+	0.984955i	$0.444715\pi$
$937$	−23.4657	+	40.6437i	−0.766590	+	1.32777i	−0.939402	+	0.342818i	$0.888619\pi$
$938$	0.181700	+	0.0486864i	0.00593273	+	0.00158967i
$939$		0			0
$940$	0.332417	+	1.24060i	0.0108422	+	0.0404638i
$941$	−22.4359	−	12.9534i	−0.731391	−	0.422269i	0.0875398	−	0.996161i	$-0.472099\pi$
$941$	−22.4359	−	12.9534i	−0.731391	−	0.422269i	−0.818931	+	0.573892i	$0.805433\pi$
$942$		0			0
$943$	5.55935	+	1.48962i	0.181037	+	0.0485088i
$944$	−2.66947	−	0.715281i	−0.0868837	−	0.0232804i
$945$		0			0
$946$	−2.01709	−	1.16457i	−0.0655813	−	0.0378634i
$947$	−0.308026	−	1.14957i	−0.0100095	−	0.0373560i	0.960740	−	0.277449i	$-0.0894888\pi$
$947$	−0.308026	−	1.14957i	−0.0100095	−	0.0373560i	−0.970750	+	0.240093i	$0.922822\pi$
$948$		0			0
$949$	−4.99819	−	1.33926i	−0.162248	−	0.0434742i
$950$	0.567241	−	0.982490i	0.0184037	−	0.0318762i
$951$		0			0
$952$			0.316625i			0.0102619i
$953$	24.9714	−	43.2517i	0.808903	−	1.40106i	−0.104721	−	0.994502i	$-0.533395\pi$
$953$	24.9714	−	43.2517i	0.808903	−	1.40106i	0.913624	−	0.406560i	$-0.133272\pi$
$954$		0			0
$955$	26.7863	−	15.4651i	0.866783	−	0.500437i
$956$	−6.97703	−	6.97703i	−0.225653	−	0.225653i
$957$		0			0
$958$	1.29916	+	2.25021i	0.0419738	+	0.0727008i
$959$	−6.62219	+	3.82332i	−0.213842	+	0.123462i
$960$		0			0
$961$		−	7.70080i		−	0.248413i
$962$	10.9354	−	1.88651i	0.352573	−	0.0608236i
$963$		0			0
$964$	−4.68446	−	17.4827i	−0.150876	−	0.563079i
$965$	1.42538	+	2.46883i	0.0458846	+	0.0794745i
$966$		0			0
$967$	8.35018	−	31.1633i	0.268524	−	1.00214i	−0.691535	−	0.722343i	$-0.743065\pi$
$967$	8.35018	−	31.1633i	0.268524	−	1.00214i	0.960058	−	0.279800i	$-0.0902683\pi$
$968$	7.71716	−	7.71716i	0.248039	−	0.248039i
$969$		0			0
$970$	−10.4970	−	10.4970i	−0.337038	−	0.337038i
$971$	2.02484	+	1.16904i	0.0649801	+	0.0375163i	0.532138	−	0.846658i	$-0.321389\pi$
$971$	2.02484	+	1.16904i	0.0649801	+	0.0375163i	−0.467158	+	0.884174i	$0.654722\pi$
$972$		0			0
$973$		−	25.8861i		−	0.829871i
$974$	20.2154	+	11.6714i	0.647743	+	0.373975i
$975$		0			0
$976$	0.600366	−	0.600366i	0.0192172	−	0.0192172i
$977$	−39.6993	+	10.6374i	−1.27009	+	0.340321i	−0.830067	−	0.557664i	$-0.811698\pi$
$977$	−39.6993	+	10.6374i	−1.27009	+	0.340321i	−0.440027	+	0.897984i	$0.645031\pi$
$978$		0			0
$979$	−3.01381	+	0.807548i	−0.0963218	+	0.0258094i
$980$	−3.05531	+	11.4026i	−0.0975982	+	0.364241i
$981$		0			0
$982$	4.07012	+	15.1899i	0.129883	+	0.484729i
$983$	−7.82705	+	13.5568i	−0.249644	+	0.432396i	−0.963427	−	0.267971i	$-0.913647\pi$
$983$	−7.82705	+	13.5568i	−0.249644	+	0.432396i	0.713783	+	0.700367i	$0.246980\pi$
$984$		0			0
$985$	−1.28134	−	1.28134i	−0.0408269	−	0.0408269i
$986$	0.359596	−	1.34203i	0.0114519	−	0.0427390i
$987$		0			0
$988$	1.50820			0.0479822
$989$	−57.1935			−1.81865
$990$		0			0
$991$	18.4593	−	18.4593i	0.586379	−	0.586379i	−0.350270	−	0.936649i	$-0.613910\pi$
$991$	18.4593	−	18.4593i	0.586379	−	0.586379i	0.936649	+	0.350270i	$0.113910\pi$
$992$	3.11050	+	5.38754i	0.0987584	+	0.171055i
$993$		0			0
$994$	−20.4821	−	5.48817i	−0.649654	−	0.174074i
$995$	−27.1624	+	15.6822i	−0.861107	+	0.497160i
$996$		0			0
$997$	56.6218	−	15.1718i	1.79323	−	0.480495i	0.800343	−	0.599542i	$-0.204651\pi$
$997$	56.6218	−	15.1718i	1.79323	−	0.480495i	0.992889	+	0.119047i	$0.0379841\pi$
$998$	−29.6436			−0.938350
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.d.467.1	yes	16
3.2	odd	2	inner	666.2.be.d.467.4	yes	16
37.29	odd	12	inner	666.2.be.d.251.4	yes	16
111.29	even	12	inner	666.2.be.d.251.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.d.251.1	✓	16	111.29	even	12	inner
666.2.be.d.251.4	yes	16	37.29	odd	12	inner
666.2.be.d.467.1	yes	16	1.1	even	1	trivial
666.2.be.d.467.4	yes	16	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.43832 - 0.653347i) q^{5} +(0.762169 + 1.32012i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.43832 - 0.653347i) q^{5} +(0.762169 + 1.32012i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.52434 q^{10} -0.293751 q^{11} +(0.472172 - 1.76217i) q^{13} +(-1.07787 - 1.07787i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.0537601 - 0.200635i) q^{17} +(-0.213969 + 0.798543i) q^{19} +(-2.43832 + 0.653347i) q^{20} +(0.283741 - 0.0760282i) q^{22} +(5.10053 - 5.10053i) q^{23} +(1.18843 + 0.686141i) q^{25} +1.82433i q^{26} +(1.32012 + 0.762169i) q^{28} +(-4.72977 - 4.72977i) q^{29} +(4.39891 - 4.39891i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.103857 + 0.179885i) q^{34} +(-0.995921 - 3.71683i) q^{35} +(-1.03408 - 5.99422i) q^{37} -0.826712i q^{38} +(2.18614 - 1.26217i) q^{40} +(0.398951 + 0.691004i) q^{41} +(-5.60662 - 5.60662i) q^{43} +(-0.254395 + 0.146875i) q^{44} +(-3.60662 + 6.24685i) q^{46} -0.508791i q^{47} +(2.33820 - 4.04988i) q^{49} +(-1.32552 - 0.355173i) q^{50} +(-0.472172 - 1.76217i) q^{52} +(3.09167 + 1.78498i) q^{53} +(0.716259 + 0.191921i) q^{55} +(-1.47240 - 0.394528i) q^{56} +(5.79276 + 3.34445i) q^{58} +(-0.715281 - 2.66947i) q^{59} +(0.820115 + 0.219749i) q^{61} +(-3.11050 + 5.38754i) q^{62} -1.00000i q^{64} +(-2.30261 + 3.98825i) q^{65} +(-0.106871 + 0.0617022i) q^{67} +(-0.146875 - 0.146875i) q^{68} +(1.92397 + 3.33242i) q^{70} +(12.0471 - 6.95537i) q^{71} -2.83638i q^{73} +(2.55027 + 5.52233i) q^{74} +(0.213969 + 0.798543i) q^{76} +(-0.223888 - 0.387785i) q^{77} +(-0.472172 + 1.76217i) q^{79} +(-1.78498 + 1.78498i) q^{80} +(-0.564202 - 0.564202i) q^{82} +(-4.50265 - 2.59960i) q^{83} +0.524338i q^{85} +(6.86668 + 3.96448i) q^{86} +(0.207713 - 0.207713i) q^{88} +(10.2598 - 2.74910i) q^{89} +(2.68614 - 0.719749i) q^{91} +(1.86692 - 6.96746i) q^{92} +(0.131685 + 0.491454i) q^{94} +(1.04345 - 1.80731i) q^{95} +(-4.15831 - 4.15831i) q^{97} +(-1.21034 + 4.51705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67} + 28 q^{70} - 16 q^{76} - 4 q^{79} + 12 q^{82} + 16 q^{88} + 20 q^{91} + 12 q^{94} - 40 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Introduction

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