LMFDB - Embedded newform 684.2.bo.c.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(73,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("684.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bo (of order $9$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			253.2
Root			$-1.25236 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	684.253
Dual form			684.2.bo.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658711 + 3.73574i) q^{5} +(-0.0695116 + 0.120398i) q^{7} +(0.350493 + 0.607072i) q^{11} +(-1.47751 + 0.537771i) q^{13} +(-2.88131 + 2.41771i) q^{17} +(4.28653 - 0.790990i) q^{19} +(-1.02690 + 5.82385i) q^{23} +(-8.82337 + 3.21144i) q^{25} +(-5.28209 - 4.43220i) q^{29} +(1.43886 - 2.49217i) q^{31} +(-0.495562 - 0.180370i) q^{35} -6.33018 q^{37} +(4.40018 + 1.60154i) q^{41} +(0.935226 + 5.30393i) q^{43} +(1.42658 + 1.19704i) q^{47} +(3.49034 + 6.04544i) q^{49} +(-0.551093 + 3.12541i) q^{53} +(-2.03699 + 1.70923i) q^{55} +(-1.81608 + 1.52387i) q^{59} +(0.587398 - 3.33130i) q^{61} +(-2.98223 - 5.16537i) q^{65} +(7.61119 + 6.38655i) q^{67} +(-0.375070 - 2.12713i) q^{71} +(10.6967 + 3.89330i) q^{73} -0.0974533 q^{77} +(7.36033 + 2.67894i) q^{79} +(5.12849 - 8.88280i) q^{83} +(-10.9299 - 9.17125i) q^{85} +(12.2044 - 4.44204i) q^{89} +(0.0379580 - 0.215271i) q^{91} +(5.77852 + 15.4923i) q^{95} +(-0.581665 + 0.488075i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 3 q^{11} - 9 q^{13} + 3 q^{17} - 12 q^{19} + 12 q^{23} - 18 q^{25} - 27 q^{29} + 6 q^{31} - 33 q^{35} - 12 q^{37} - 3 q^{41} + 27 q^{43} + 15 q^{47} + 9 q^{49} + 21 q^{53} - 27 q^{55} + 48 q^{59}+ \cdots + 12 q^{97}+O(q^{100}) $ 12 * q + 3 * q^7 - 3 * q^11 - 9 * q^13 + 3 * q^17 - 12 * q^19 + 12 * q^23 - 18 * q^25 - 27 * q^29 + 6 * q^31 - 33 * q^35 - 12 * q^37 - 3 * q^41 + 27 * q^43 + 15 * q^47 + 9 * q^49 + 21 * q^53 - 27 * q^55 + 48 * q^59 - 6 * q^61 + 33 * q^65 + 24 * q^67 + 30 * q^73 - 24 * q^77 + 3 * q^79 - 3 * q^83 - 42 * q^85 + 18 * q^89 - 24 * q^91 - 9 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.658711	+	3.73574i	0.294585	+	1.67067i	0.668886	+	0.743365i	$0.266772\pi$
$5$	0.658711	+	3.73574i	0.294585	+	1.67067i	−0.374301	+	0.927307i	$0.622117\pi$
$6$		0			0
$7$	−0.0695116	+	0.120398i	−0.0262729	+	0.0455060i	−0.878863	−	0.477074i	$-0.841697\pi$
$7$	−0.0695116	+	0.120398i	−0.0262729	+	0.0455060i	0.852590	+	0.522580i	$0.175031\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.350493	+	0.607072i	0.105678	+	0.183039i	0.914015	−	0.405681i	$-0.132966\pi$
$11$	0.350493	+	0.607072i	0.105678	+	0.183039i	−0.808337	+	0.588720i	$0.799632\pi$
$12$		0			0
$13$	−1.47751	+	0.537771i	−0.409789	+	0.149151i	−0.538685	−	0.842507i	$-0.681079\pi$
$13$	−1.47751	+	0.537771i	−0.409789	+	0.149151i	0.128896	+	0.991658i	$0.458857\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.88131	+	2.41771i	−0.698820	+	0.586380i	−0.921438	−	0.388526i	$-0.872984\pi$
$17$	−2.88131	+	2.41771i	−0.698820	+	0.586380i	0.222617	+	0.974906i	$0.428540\pi$
$18$		0			0
$19$	4.28653	−	0.790990i	0.983397	−	0.181466i
$19$	4.28653	−	0.790990i	0.983397	−	0.181466i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.02690	+	5.82385i	−0.214124	+	1.21436i	0.668297	+	0.743895i	$0.267024\pi$
$23$	−1.02690	+	5.82385i	−0.214124	+	1.21436i	−0.882421	+	0.470461i	$0.844088\pi$
$24$		0			0
$25$	−8.82337	+	3.21144i	−1.76467	+	0.642289i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.28209	−	4.43220i	−0.980860	−	0.823039i	0.00335912	−	0.999994i	$-0.498931\pi$
$29$	−5.28209	−	4.43220i	−0.980860	−	0.823039i	−0.984219	+	0.176955i	$0.943375\pi$
$30$		0			0
$31$	1.43886	−	2.49217i	0.258426	−	0.447608i	−0.707394	−	0.706819i	$-0.750129\pi$
$31$	1.43886	−	2.49217i	0.258426	−	0.447608i	0.965821	+	0.259212i	$0.0834627\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.495562	−	0.180370i	−0.0837653	−	0.0304881i
$36$		0			0
$37$	−6.33018			−1.04067			−0.520337	−	0.853961i	$-0.674194\pi$
$37$	−6.33018			−1.04067			−0.520337	+	0.853961i	$0.674194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.40018	+	1.60154i	0.687193	+	0.250118i	0.661933	−	0.749563i	$-0.269736\pi$
$41$	4.40018	+	1.60154i	0.687193	+	0.250118i	0.0252602	+	0.999681i	$0.491959\pi$
$42$		0			0
$43$	0.935226	+	5.30393i	0.142621	+	0.808842i	0.969247	+	0.246091i	$0.0791461\pi$
$43$	0.935226	+	5.30393i	0.142621	+	0.808842i	−0.826626	+	0.562751i	$0.809743\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.42658	+	1.19704i	0.208088	+	0.174607i	0.740875	−	0.671643i	$-0.234411\pi$
$47$	1.42658	+	1.19704i	0.208088	+	0.174607i	−0.532787	+	0.846249i	$0.678855\pi$
$48$		0			0
$49$	3.49034	+	6.04544i	0.498619	+	0.863634i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.551093	+	3.12541i	−0.0756985	+	0.429307i	0.923280	+	0.384127i	$0.125497\pi$
$53$	−0.551093	+	3.12541i	−0.0756985	+	0.429307i	−0.998979	+	0.0451806i	$0.985614\pi$
$54$		0			0
$55$	−2.03699	+	1.70923i	−0.274667	+	0.230473i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.81608	+	1.52387i	−0.236433	+	0.198391i	−0.753304	−	0.657672i	$-0.771541\pi$
$59$	−1.81608	+	1.52387i	−0.236433	+	0.198391i	0.516871	+	0.856063i	$0.327097\pi$
$60$		0			0
$61$	0.587398	−	3.33130i	0.0752086	−	0.426529i	−0.923834	−	0.382792i	$-0.874963\pi$
$61$	0.587398	−	3.33130i	0.0752086	−	0.426529i	0.999043	−	0.0437370i	$-0.0139264\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.98223	−	5.16537i	−0.369900	−	0.640685i
$66$		0			0
$67$	7.61119	+	6.38655i	0.929855	+	0.780241i	0.975791	−	0.218704i	$-0.0701828\pi$
$67$	7.61119	+	6.38655i	0.929855	+	0.780241i	−0.0459367	+	0.998944i	$0.514627\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.375070	−	2.12713i	−0.0445127	−	0.252444i	0.954429	−	0.298438i	$-0.0964656\pi$
$71$	−0.375070	−	2.12713i	−0.0445127	−	0.252444i	−0.998942	+	0.0459940i	$0.985354\pi$
$72$		0			0
$73$	10.6967	+	3.89330i	1.25196	+	0.455676i	0.881063	−	0.472998i	$-0.156828\pi$
$73$	10.6967	+	3.89330i	1.25196	+	0.455676i	0.370896	+	0.928674i	$0.379051\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0974533			−0.0111058
$78$		0			0
$79$	7.36033	+	2.67894i	0.828102	+	0.301404i	0.721079	−	0.692852i	$-0.243646\pi$
$79$	7.36033	+	2.67894i	0.828102	+	0.301404i	0.107022	+	0.994257i	$0.465868\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.12849	−	8.88280i	0.562925	−	0.975014i	−0.434315	−	0.900761i	$-0.643009\pi$
$83$	5.12849	−	8.88280i	0.562925	−	0.975014i	0.997239	−	0.0742528i	$-0.0236572\pi$
$84$		0			0
$85$	−10.9299	−	9.17125i	−1.18551	−	0.994761i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.2044	−	4.44204i	1.29366	−	0.470856i	0.398737	−	0.917066i	$-0.369449\pi$
$89$	12.2044	−	4.44204i	1.29366	−	0.470856i	0.894928	+	0.446210i	$0.147227\pi$
$90$		0			0
$91$	0.0379580	−	0.215271i	0.00397908	−	0.0225665i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.77852	+	15.4923i	0.592863	+	1.58948i
$96$		0			0
$97$	−0.581665	+	0.488075i	−0.0590591	+	0.0495565i	−0.671839	−	0.740697i	$-0.734496\pi$
$97$	−0.581665	+	0.488075i	−0.0590591	+	0.0495565i	0.612780	+	0.790253i	$0.290051\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.7847	+	4.28927i	−1.17262	+	0.426798i	−0.853589	−	0.520947i	$-0.825579\pi$
$101$	−11.7847	+	4.28927i	−1.17262	+	0.426798i	−0.319029	+	0.947745i	$0.603357\pi$
$102$		0			0
$103$	−4.32365	−	7.48879i	−0.426022	−	0.737892i	0.570493	−	0.821302i	$-0.306752\pi$
$103$	−4.32365	−	7.48879i	−0.426022	−	0.737892i	−0.996515	+	0.0834102i	$0.973419\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.492451	+	0.852950i	−0.0476070	+	0.0824578i	−0.888847	−	0.458204i	$-0.848493\pi$
$107$	−0.492451	+	0.852950i	−0.0476070	+	0.0824578i	0.841240	+	0.540662i	$0.181826\pi$
$108$		0			0
$109$	−2.47482	−	14.0354i	−0.237044	−	1.34435i	−0.838265	−	0.545263i	$-0.816430\pi$
$109$	−2.47482	−	14.0354i	−0.237044	−	1.34435i	0.601221	−	0.799083i	$-0.294681\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.86600			−0.269611			−0.134805	−	0.990872i	$-0.543041\pi$
$113$	−2.86600			−0.269611			−0.134805	+	0.990872i	$0.543041\pi$
$114$		0			0
$115$	−22.4328			−2.09187
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0908016	−	0.514962i	−0.00832377	−	0.0472065i
$120$		0			0
$121$	5.25431	−	9.10073i	0.477664	−	0.827339i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.32575	−	14.4206i	−0.744677	−	1.28982i
$126$		0			0
$127$	19.8223	−	7.21472i	1.75894	−	0.640203i	0.759002	−	0.651089i	$-0.225687\pi$
$127$	19.8223	−	7.21472i	1.75894	−	0.640203i	0.999941	+	0.0108860i	$0.00346520\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.87172	−	6.60516i	0.687756	−	0.577096i	−0.230505	−	0.973071i	$-0.574038\pi$
$131$	7.87172	−	6.60516i	0.687756	−	0.577096i	0.918261	+	0.395975i	$0.129593\pi$
$132$		0			0
$133$	−0.202730	+	0.571071i	−0.0175789	+	0.0495181i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.08375	−	11.8175i	0.178027	−	1.00964i	−0.756565	−	0.653919i	$-0.773124\pi$
$137$	2.08375	−	11.8175i	0.178027	−	1.00964i	0.934592	−	0.355722i	$-0.115765\pi$
$138$		0			0
$139$	−9.67258	+	3.52053i	−0.820417	+	0.298607i	−0.717920	−	0.696126i	$-0.754906\pi$
$139$	−9.67258	+	3.52053i	−0.820417	+	0.298607i	−0.102497	+	0.994733i	$0.532683\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.844324	−	0.708472i	−0.0706059	−	0.0592454i
$144$		0			0
$145$	13.0782	−	22.6520i	1.08608	−	1.88115i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.52238	−	1.28204i	−0.288565	−	0.105029i	0.193682	−	0.981064i	$-0.437957\pi$
$149$	−3.52238	−	1.28204i	−0.288565	−	0.105029i	−0.482247	+	0.876035i	$0.660179\pi$
$150$		0			0
$151$	−13.3866			−1.08939			−0.544693	−	0.838636i	$-0.683354\pi$
$151$	−13.3866			−1.08939			−0.544693	+	0.838636i	$0.683354\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.2579	+	3.73357i	0.823934	+	0.299888i
$156$		0			0
$157$	1.40711	+	7.98010i	0.112299	+	0.636881i	0.988052	+	0.154121i	$0.0492546\pi$
$157$	1.40711	+	7.98010i	0.112299	+	0.636881i	−0.875753	+	0.482760i	$0.839634\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.629796	−	0.528461i	−0.0496349	−	0.0416486i
$162$		0			0
$163$	4.12600	+	7.14644i	0.323173	+	0.559753i	0.981141	−	0.193294i	$-0.0619170\pi$
$163$	4.12600	+	7.14644i	0.323173	+	0.559753i	−0.657968	+	0.753046i	$0.728584\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.04523	−	11.5991i	0.158264	−	0.897562i	−0.797476	−	0.603351i	$-0.793832\pi$
$167$	2.04523	−	11.5991i	0.158264	−	0.897562i	0.955740	−	0.294211i	$-0.0950569\pi$
$168$		0			0
$169$	−8.06473	+	6.76711i	−0.620364	+	0.520547i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.17235	+	6.01832i	−0.545304	+	0.457564i	−0.873347	−	0.487098i	$-0.838055\pi$
$173$	−7.17235	+	6.01832i	−0.545304	+	0.457564i	0.328043	+	0.944663i	$0.393611\pi$
$174$		0			0
$175$	0.226676	−	1.28555i	0.0171351	−	0.0971781i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.64499	+	8.04536i	0.347183	+	0.601339i	0.985748	−	0.168229i	$-0.0538049\pi$
$179$	4.64499	+	8.04536i	0.347183	+	0.601339i	−0.638565	+	0.769568i	$0.720472\pi$
$180$		0			0
$181$	−2.07659	−	1.74246i	−0.154351	−	0.129516i	0.562342	−	0.826905i	$-0.309901\pi$
$181$	−2.07659	−	1.74246i	−0.154351	−	0.129516i	−0.716693	+	0.697389i	$0.754345\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.16976	−	23.6479i	−0.306567	−	1.73863i
$186$		0			0
$187$	−2.47760	−	0.901773i	−0.181180	−	0.0659441i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.8935			1.36709			0.683544	−	0.729910i	$-0.260438\pi$
$191$	18.8935			1.36709			0.683544	+	0.729910i	$0.260438\pi$
$192$		0			0
$193$	20.0362	+	7.29258i	1.44224	+	0.524931i	0.940412	−	0.340037i	$-0.110440\pi$
$193$	20.0362	+	7.29258i	1.44224	+	0.524931i	0.501825	+	0.864969i	$0.332662\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.29055	−	14.3597i	0.590677	−	1.02308i	−0.403464	−	0.914996i	$-0.632194\pi$
$197$	8.29055	−	14.3597i	0.590677	−	1.02308i	0.994141	−	0.108088i	$-0.0344727\pi$
$198$		0			0
$199$	12.3943	+	10.4001i	0.878610	+	0.737241i	0.965893	−	0.258943i	$-0.0833741\pi$
$199$	12.3943	+	10.4001i	0.878610	+	0.737241i	−0.0872832	+	0.996184i	$0.527819\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.900793	−	0.327862i	0.0632233	−	0.0230114i
$204$		0			0
$205$	−3.08447	+	17.4929i	−0.215428	+	1.22176i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.98259	+	2.32499i	0.137138	+	0.160823i
$210$		0			0
$211$	20.1088	−	16.8733i	1.38434	−	1.16160i	0.416772	−	0.909011i	$-0.363161\pi$
$211$	20.1088	−	16.8733i	1.38434	−	1.16160i	0.967573	−	0.252592i	$-0.0812831\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−19.1981	+	6.98752i	−1.30930	+	0.476545i
$216$		0			0
$217$	0.200035	+	0.346470i	0.0135792	+	0.0235199i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.95700	−	5.12168i	0.198910	−	0.344522i
$222$		0			0
$223$	0.397301	+	2.25321i	0.0266053	+	0.150886i	0.995216	−	0.0976949i	$-0.0311469\pi$
$223$	0.397301	+	2.25321i	0.0266053	+	0.150886i	−0.968611	+	0.248581i	$0.920036\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.4671			1.15934			0.579668	−	0.814853i	$-0.303182\pi$
$227$	17.4671			1.15934			0.579668	+	0.814853i	$0.303182\pi$
$228$		0			0
$229$	8.14952			0.538536			0.269268	−	0.963065i	$-0.413218\pi$
$229$	8.14952			0.538536			0.269268	+	0.963065i	$0.413218\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.69185	+	20.9375i	0.241861	+	1.37166i	0.827671	+	0.561214i	$0.189665\pi$
$233$	3.69185	+	20.9375i	0.241861	+	1.37166i	−0.585810	+	0.810449i	$0.699223\pi$
$234$		0			0
$235$	−3.53213	+	6.11783i	−0.230411	+	0.399083i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.3725	−	17.9657i	−0.670941	−	1.16210i	−0.977638	−	0.210296i	$-0.932557\pi$
$239$	−10.3725	−	17.9657i	−0.670941	−	1.16210i	0.306697	−	0.951807i	$-0.400776\pi$
$240$		0			0
$241$	−18.7960	+	6.84119i	−1.21076	+	0.440680i	−0.866966	−	0.498367i	$-0.833933\pi$
$241$	−18.7960	+	6.84119i	−1.21076	+	0.440680i	−0.343791	+	0.939046i	$0.611711\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−20.2851	+	17.0212i	−1.29596	+	1.08744i
$246$		0			0
$247$	−5.90804	+	3.47387i	−0.375919	+	0.221037i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.27528	−	7.23245i	0.0804948	−	0.456508i	−0.917743	−	0.397174i	$-0.869991\pi$
$251$	1.27528	−	7.23245i	0.0804948	−	0.456508i	0.998238	−	0.0593346i	$-0.0188979\pi$
$252$		0			0
$253$	−3.89541	+	1.41781i	−0.244903	+	0.0891372i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.7914	−	17.4460i	−1.29693	−	1.08825i	−0.990666	−	0.136308i	$-0.956476\pi$
$257$	−20.7914	−	17.4460i	−1.29693	−	1.08825i	−0.306265	−	0.951946i	$-0.599079\pi$
$258$		0			0
$259$	0.440021	−	0.762139i	0.0273416	−	0.0473570i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.3152	+	7.39413i	1.25269	+	0.455941i	0.881309	−	0.472540i	$-0.156663\pi$
$263$	20.3152	+	7.39413i	1.25269	+	0.455941i	0.371379	+	0.928481i	$0.378885\pi$
$264$		0			0
$265$	−12.0387			−0.739532
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.63396	+	2.05060i	0.343509	+	0.125027i	0.508013	−	0.861349i	$-0.330380\pi$
$269$	5.63396	+	2.05060i	0.343509	+	0.125027i	−0.164504	+	0.986376i	$0.552602\pi$
$270$		0			0
$271$	−4.11091	−	23.3141i	−0.249720	−	1.41623i	−0.809271	−	0.587436i	$-0.800137\pi$
$271$	−4.11091	−	23.3141i	−0.249720	−	1.41623i	0.559551	−	0.828796i	$-0.310974\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.04211	−	4.23083i	−0.304050	−	0.255129i
$276$		0			0
$277$	4.74294	+	8.21502i	0.284976	+	0.493593i	0.972603	−	0.232471i	$-0.0746811\pi$
$277$	4.74294	+	8.21502i	0.284976	+	0.493593i	−0.687628	+	0.726064i	$0.741348\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.22110	+	23.9391i	−0.251810	+	1.42808i	0.552321	+	0.833632i	$0.313742\pi$
$281$	−4.22110	+	23.9391i	−0.251810	+	1.42808i	−0.804131	+	0.594453i	$0.797369\pi$
$282$		0			0
$283$	−8.94917	+	7.50925i	−0.531973	+	0.446378i	−0.868782	−	0.495195i	$-0.835097\pi$
$283$	−8.94917	+	7.50925i	−0.531973	+	0.446378i	0.336809	+	0.941573i	$0.390652\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.498685	+	0.418446i	−0.0294364	+	0.0247001i
$288$		0			0
$289$	−0.495374	+	2.80941i	−0.0291397	+	0.165259i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.01571	+	12.1516i	0.409862	+	0.709902i	0.994874	−	0.101122i	$-0.0322434\pi$
$293$	7.01571	+	12.1516i	0.409862	+	0.709902i	−0.585012	+	0.811025i	$0.698910\pi$
$294$		0			0
$295$	−6.88905	−	5.78060i	−0.401096	−	0.336559i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.61464	−	9.15705i	−0.0933768	−	0.529566i
$300$		0			0
$301$	−0.703590	−	0.256086i	−0.0405543	−	0.0147605i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.8318			0.734746
$306$		0			0
$307$	0.522125	+	0.190038i	0.0297993	+	0.0108460i	0.356877	−	0.934151i	$-0.383842\pi$
$307$	0.522125	+	0.190038i	0.0297993	+	0.0108460i	−0.327078	+	0.944998i	$0.606064\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.89478	+	13.6742i	−0.447672	+	0.775390i	−0.998234	−	0.0594037i	$-0.981080\pi$
$311$	−7.89478	+	13.6742i	−0.447672	+	0.775390i	0.550562	+	0.834794i	$0.314413\pi$
$312$		0			0
$313$	−17.4399	−	14.6338i	−0.985763	−	0.827153i	−0.000814014	−	1.00000i	$-0.500259\pi$
$313$	−17.4399	−	14.6338i	−0.985763	−	0.827153i	−0.984949	+	0.172846i	$0.944704\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.8284	+	6.48900i	−1.00134	+	0.364458i	−0.790102	−	0.612976i	$-0.789972\pi$
$317$	−17.8284	+	6.48900i	−1.00134	+	0.364458i	−0.211240	+	0.977434i	$0.567750\pi$
$318$		0			0
$319$	0.839328	−	4.76006i	0.0469933	−	0.266512i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.4384	+	12.6427i	−0.580810	+	0.703456i
$324$		0			0
$325$	11.3096	−	9.48991i	0.627345	−	0.526405i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.243285	+	0.0885485i	−0.0134127	+	0.00488184i
$330$		0			0
$331$	7.38160	+	12.7853i	0.405729	+	0.702744i	0.994406	−	0.105625i	$-0.0336843\pi$
$331$	7.38160	+	12.7853i	0.405729	+	0.702744i	−0.588677	+	0.808368i	$0.700351\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−18.8449	+	32.6403i	−1.02961	+	1.78333i
$336$		0			0
$337$	−1.43116	−	8.11649i	−0.0779601	−	0.442134i	−0.998655	−	0.0518502i	$-0.983488\pi$
$337$	−1.43116	−	8.11649i	−0.0779601	−	0.442134i	0.920695	−	0.390283i	$-0.127623\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.01724			0.109240
$342$		0			0
$343$	−1.94364			−0.104947
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.39699	−	19.2653i	−0.182360	−	1.03421i	−0.929301	−	0.369324i	$-0.879589\pi$
$347$	−3.39699	−	19.2653i	−0.182360	−	1.03421i	0.746941	−	0.664891i	$-0.231522\pi$
$348$		0			0
$349$	−12.8829	+	22.3139i	−0.689607	+	1.19443i	0.282358	+	0.959309i	$0.408884\pi$
$349$	−12.8829	+	22.3139i	−0.689607	+	1.19443i	−0.971965	+	0.235126i	$0.924450\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.712979	−	1.23492i	−0.0379480	−	0.0657279i	0.846428	−	0.532504i	$-0.178749\pi$
$353$	−0.712979	−	1.23492i	−0.0379480	−	0.0657279i	−0.884376	+	0.466776i	$0.845415\pi$
$354$		0			0
$355$	7.69934	−	2.80233i	0.408638	−	0.148732i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.55106	+	6.33609i	−0.398530	+	0.334406i	−0.819925	−	0.572471i	$-0.805985\pi$
$359$	−7.55106	+	6.33609i	−0.398530	+	0.334406i	0.421395	+	0.906877i	$0.361540\pi$
$360$		0			0
$361$	17.7487	−	6.78120i	0.934141	−	0.356905i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.49827	+	42.5248i	−0.392477	+	2.22585i
$366$		0			0
$367$	−10.7351	+	3.90726i	−0.560368	+	0.203957i	−0.606647	−	0.794971i	$-0.707486\pi$
$367$	−10.7351	+	3.90726i	−0.560368	+	0.203957i	0.0462791	+	0.998929i	$0.485264\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.337984	−	0.283602i	−0.0175473	−	0.0147239i
$372$		0			0
$373$	−13.3194	+	23.0699i	−0.689653	+	1.19451i	0.282297	+	0.959327i	$0.408903\pi$
$373$	−13.3194	+	23.0699i	−0.689653	+	1.19451i	−0.971950	+	0.235187i	$0.924430\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.1879	+	3.70808i	0.524702	+	0.190976i
$378$		0			0
$379$	19.8016			1.01714			0.508569	−	0.861021i	$-0.330174\pi$
$379$	19.8016			1.01714			0.508569	+	0.861021i	$0.330174\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.8435	+	6.13052i	0.860661	+	0.313255i	0.734379	−	0.678739i	$-0.237473\pi$
$383$	16.8435	+	6.13052i	0.860661	+	0.313255i	0.126282	+	0.991994i	$0.459696\pi$
$384$		0			0
$385$	−0.0641936	−	0.364060i	−0.00327161	−	0.0185542i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.4626	+	13.8137i	0.834685	+	0.700384i	0.956362	−	0.292186i	$-0.0943826\pi$
$389$	16.4626	+	13.8137i	0.834685	+	0.700384i	−0.121676	+	0.992570i	$0.538827\pi$
$390$		0			0
$391$	−11.1215	−	19.2631i	−0.562440	−	0.974175i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.15949	+	29.2609i	−0.259602	+	1.47228i
$396$		0			0
$397$	4.26129	−	3.57565i	0.213868	−	0.179457i	−0.529560	−	0.848272i	$-0.677643\pi$
$397$	4.26129	−	3.57565i	0.213868	−	0.179457i	0.743428	+	0.668816i	$0.233199\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	27.9884	−	23.4850i	1.39767	−	1.17279i	0.435550	−	0.900164i	$-0.356554\pi$
$401$	27.9884	−	23.4850i	1.39767	−	1.17279i	0.962121	−	0.272621i	$-0.0878906\pi$
$402$		0			0
$403$	−0.785713	+	4.45600i	−0.0391391	+	0.221969i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.21868	−	3.84287i	−0.109976	−	0.190484i
$408$		0			0
$409$	−0.581665	−	0.488075i	−0.0287615	−	0.0241338i	0.628294	−	0.777976i	$-0.283754\pi$
$409$	−0.581665	−	0.488075i	−0.0287615	−	0.0241338i	−0.657055	+	0.753843i	$0.728198\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.0572319	−	0.324578i	−0.00281620	−	0.0159714i
$414$		0			0
$415$	36.5620	+	13.3075i	1.79476	+	0.653238i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.2619			−0.794446			−0.397223	−	0.917722i	$-0.630026\pi$
$419$	−16.2619			−0.794446			−0.397223	+	0.917722i	$0.630026\pi$
$420$		0			0
$421$	−14.1059	−	5.13414i	−0.687481	−	0.250223i	−0.0254245	−	0.999677i	$-0.508094\pi$
$421$	−14.1059	−	5.13414i	−0.687481	−	0.250223i	−0.662056	+	0.749454i	$0.730316\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	17.6585	−	30.5855i	0.856565	−	1.48361i
$426$		0			0
$427$	0.360250	+	0.302285i	0.0174337	+	0.0146286i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.41358	−	3.42626i	0.453436	−	0.165037i	−0.105198	−	0.994451i	$-0.533548\pi$
$431$	9.41358	−	3.42626i	0.453436	−	0.165037i	0.558634	+	0.829414i	$0.311326\pi$
$432$		0			0
$433$	0.711701	−	4.03626i	0.0342022	−	0.193970i	−0.962919	−	0.269789i	$-0.913046\pi$
$433$	0.711701	−	4.03626i	0.0342022	−	0.193970i	0.997122	+	0.0758190i	$0.0241571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.204761	+	25.7764i	0.00979506	+	1.23305i
$438$		0			0
$439$	−4.00981	+	3.36463i	−0.191378	+	0.160585i	−0.733442	−	0.679752i	$-0.762087\pi$
$439$	−4.00981	+	3.36463i	−0.191378	+	0.160585i	0.542064	+	0.840337i	$0.317643\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−31.8347	+	11.5869i	−1.51251	+	0.550509i	−0.959265	−	0.282508i	$-0.908834\pi$
$443$	−31.8347	+	11.5869i	−1.51251	+	0.550509i	−0.553247	+	0.833017i	$0.686611\pi$
$444$		0			0
$445$	24.6335	+	42.6664i	1.16774	+	2.02258i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.545695	+	0.945172i	−0.0257530	+	0.0446054i	−0.878615	−	0.477531i	$-0.841532\pi$
$449$	−0.545695	+	0.945172i	−0.0257530	+	0.0446054i	0.852862	+	0.522137i	$0.174865\pi$
$450$		0			0
$451$	0.569986	+	3.23255i	0.0268396	+	0.152215i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.829198			0.0388734
$456$		0			0
$457$	16.9280			0.791858			0.395929	−	0.918281i	$-0.370423\pi$
$457$	16.9280			0.791858			0.395929	+	0.918281i	$0.370423\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.62318	−	9.20551i	−0.0755991	−	0.428744i	−0.998992	−	0.0448876i	$-0.985707\pi$
$461$	−1.62318	−	9.20551i	−0.0755991	−	0.428744i	0.923393	−	0.383856i	$-0.125404\pi$
$462$		0			0
$463$	−3.80227	+	6.58572i	−0.176706	+	0.306064i	−0.940750	−	0.339100i	$-0.889878\pi$
$463$	−3.80227	+	6.58572i	−0.176706	+	0.306064i	0.764044	+	0.645164i	$0.223211\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.7403	−	30.7272i	−0.820925	−	1.42188i	−0.904994	−	0.425424i	$-0.860125\pi$
$467$	−17.7403	−	30.7272i	−0.820925	−	1.42188i	0.0840686	−	0.996460i	$-0.473208\pi$
$468$		0			0
$469$	−1.29799	+	0.472430i	−0.0599357	+	0.0218148i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.89208	+	2.42674i	−0.132978	+	0.111582i
$474$		0			0
$475$	−35.2814	+	20.7451i	−1.61882	+	0.951853i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.87224	−	27.6318i	0.222618	−	1.26253i	−0.644568	−	0.764547i	$-0.722963\pi$
$479$	4.87224	−	27.6318i	0.222618	−	1.26253i	0.867186	−	0.497984i	$-0.165926\pi$
$480$		0			0
$481$	9.35293	−	3.40419i	0.426457	−	0.155218i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.20647	−	1.85145i	−0.100191	−	0.0840699i
$486$		0			0
$487$	−21.5368	+	37.3029i	−0.975926	+	1.69035i	−0.299082	+	0.954228i	$0.596680\pi$
$487$	−21.5368	+	37.3029i	−0.975926	+	1.69035i	−0.676844	+	0.736126i	$0.736653\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.4166	−	6.33912i	−0.786000	−	0.286080i	−0.0823275	−	0.996605i	$-0.526235\pi$
$491$	−17.4166	−	6.33912i	−0.786000	−	0.286080i	−0.703672	+	0.710525i	$0.748458\pi$
$492$		0			0
$493$	25.9351			1.16806
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.282173	+	0.102703i	0.0126572	+	0.00460684i
$498$		0			0
$499$	−7.54046	−	42.7641i	−0.337557	−	1.91438i	−0.400361	−	0.916358i	$-0.631115\pi$
$499$	−7.54046	−	42.7641i	−0.337557	−	1.91438i	0.0628031	−	0.998026i	$-0.479996\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.819590	+	0.687718i	0.0365437	+	0.0306638i	0.660877	−	0.750495i	$-0.270185\pi$
$503$	0.819590	+	0.687718i	0.0365437	+	0.0306638i	−0.624333	+	0.781158i	$0.714629\pi$
$504$		0			0
$505$	−23.7863	−	41.1990i	−1.05847	−	1.83333i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.01402	+	5.75077i	−0.0449455	+	0.254899i	−0.998999	−	0.0447386i	$-0.985755\pi$
$509$	−1.01402	+	5.75077i	−0.0449455	+	0.254899i	0.954053	+	0.299637i	$0.0968656\pi$
$510$		0			0
$511$	−1.21229	+	1.01723i	−0.0536286	+	0.0449998i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	25.1281	−	21.0850i	1.10728	−	0.929116i
$516$		0			0
$517$	−0.226684	+	1.28559i	−0.00996957	+	0.0565402i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.78321	−	10.0168i	−0.253367	−	0.438844i	0.711084	−	0.703107i	$-0.248205\pi$
$521$	−5.78321	−	10.0168i	−0.253367	−	0.438844i	−0.964451	+	0.264263i	$0.914871\pi$
$522$		0			0
$523$	2.87535	+	2.41270i	0.125730	+	0.105500i	0.703485	−	0.710710i	$-0.251626\pi$
$523$	2.87535	+	2.41270i	0.125730	+	0.105500i	−0.577754	+	0.816211i	$0.696071\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.87955	+	10.6595i	0.0818745	+	0.464333i
$528$		0			0
$529$	−11.2497	−	4.09457i	−0.489119	−	0.178025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.36259			−0.318909
$534$		0			0
$535$	−3.51078	−	1.27782i	−0.151784	−	0.0552450i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.44668	+	4.23777i	−0.105386	+	0.182534i
$540$		0			0
$541$	−11.2927	−	9.47568i	−0.485510	−	0.407391i	0.366904	−	0.930259i	$-0.380418\pi$
$541$	−11.2927	−	9.47568i	−0.485510	−	0.407391i	−0.852414	+	0.522867i	$0.824862\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	50.8023	−	18.4905i	2.17613	−	0.792047i
$546$		0			0
$547$	−1.35734	+	7.69785i	−0.0580356	+	0.329136i	−0.999978	−	0.00663836i	$-0.997887\pi$
$547$	−1.35734	+	7.69785i	−0.0580356	+	0.329136i	0.941942	+	0.335775i	$0.108998\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−26.1477	−	14.8207i	−1.11393	−	0.631382i
$552$		0			0
$553$	−0.834166	+	0.699949i	−0.0354724	+	0.0297648i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.775402	−	0.282223i	0.0328549	−	0.0119582i	−0.325540	−	0.945528i	$-0.605546\pi$
$557$	0.775402	−	0.282223i	0.0328549	−	0.0119582i	0.358395	+	0.933570i	$0.383324\pi$
$558$		0			0
$559$	−4.23411	−	7.33370i	−0.179084	−	0.310182i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.41715	+	4.18662i	−0.101871	+	0.176445i	−0.912455	−	0.409176i	$-0.865816\pi$
$563$	−2.41715	+	4.18662i	−0.101871	+	0.176445i	0.810585	+	0.585621i	$0.199149\pi$
$564$		0			0
$565$	−1.88787	−	10.7066i	−0.0794232	−	0.450431i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.7045			0.867977			0.433989	−	0.900918i	$-0.357106\pi$
$569$	20.7045			0.867977			0.433989	+	0.900918i	$0.357106\pi$
$570$		0			0
$571$	−8.15233			−0.341164			−0.170582	−	0.985343i	$-0.554565\pi$
$571$	−8.15233			−0.341164			−0.170582	+	0.985343i	$0.554565\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.64223	−	54.6838i	−0.402109	−	2.28047i
$576$		0			0
$577$	2.61121	−	4.52275i	0.108706	−	0.188285i	−0.806540	−	0.591179i	$-0.798663\pi$
$577$	2.61121	−	4.52275i	0.108706	−	0.188285i	0.915246	+	0.402895i	$0.131996\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.712979	+	1.23492i	0.0295793	+	0.0512329i
$582$		0			0
$583$	−2.09050	+	0.760879i	−0.0865796	+	0.0315124i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.74153	+	3.97861i	−0.195704	+	0.164215i	−0.735374	−	0.677662i	$-0.762993\pi$
$587$	−4.74153	+	3.97861i	−0.195704	+	0.164215i	0.539670	+	0.841877i	$0.318549\pi$
$588$		0			0
$589$	4.19642	−	11.8209i	0.172910	−	0.487072i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.92199	+	16.5715i	−0.119992	+	0.680508i	0.864165	+	0.503209i	$0.167847\pi$
$593$	−2.92199	+	16.5715i	−0.119992	+	0.680508i	−0.984157	+	0.177300i	$0.943264\pi$
$594$		0			0
$595$	1.86395	−	0.678422i	0.0764145	−	0.0278126i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.5345	−	22.2651i	−1.08417	−	0.909726i	−0.0879086	−	0.996129i	$-0.528018\pi$
$599$	−26.5345	−	22.2651i	−1.08417	−	0.909726i	−0.996260	+	0.0864028i	$0.972463\pi$
$600$		0			0
$601$	10.0714	−	17.4442i	0.410822	−	0.711564i	−0.584158	−	0.811640i	$-0.698575\pi$
$601$	10.0714	−	17.4442i	0.410822	−	0.711564i	0.994980	+	0.100076i	$0.0319085\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	37.4590	+	13.6340i	1.52293	+	0.554300i
$606$		0			0
$607$	30.9282			1.25534			0.627668	−	0.778481i	$-0.284010\pi$
$607$	30.9282			1.25534			0.627668	+	0.778481i	$0.284010\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.75153	−	1.00147i	−0.111315	−	0.0405153i
$612$		0			0
$613$	1.55289	+	8.80687i	0.0627206	+	0.355706i	0.999975	+	0.00706025i	$0.00224737\pi$
$613$	1.55289	+	8.80687i	0.0627206	+	0.355706i	−0.937254	+	0.348646i	$0.886642\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.4246	−	13.7819i	−0.661230	−	0.554838i	0.249225	−	0.968446i	$-0.419824\pi$
$617$	−16.4246	−	13.7819i	−0.661230	−	0.554838i	−0.910455	+	0.413607i	$0.864269\pi$
$618$		0			0
$619$	−12.7984	−	22.1675i	−0.514413	−	0.890989i	−0.999860	−	0.0167229i	$-0.994677\pi$
$619$	−12.7984	−	22.1675i	−0.514413	−	0.890989i	0.485448	−	0.874266i	$-0.338657\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.313537	+	1.77816i	−0.0125616	+	0.0712403i
$624$		0			0
$625$	12.4230	−	10.4241i	0.496919	−	0.416965i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.2392	−	15.3045i	0.727245	−	0.610231i
$630$		0			0
$631$	−0.493858	+	2.80081i	−0.0196602	+	0.111498i	−0.993059	−	0.117621i	$-0.962473\pi$
$631$	−0.493858	+	2.80081i	−0.0196602	+	0.111498i	0.973398	+	0.229119i	$0.0735845\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	40.0094	+	69.2984i	1.58773	+	2.75002i
$636$		0			0
$637$	−8.40808	−	7.05522i	−0.333140	−	0.279538i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.07050	−	45.7701i	−0.318765	−	1.80781i	−0.550283	−	0.834978i	$-0.685480\pi$
$641$	−8.07050	−	45.7701i	−0.318765	−	1.80781i	0.231518	−	0.972831i	$-0.425631\pi$
$642$		0			0
$643$	−8.80807	−	3.20587i	−0.347356	−	0.126427i	0.162450	−	0.986717i	$-0.448061\pi$
$643$	−8.80807	−	3.20587i	−0.347356	−	0.126427i	−0.509806	+	0.860290i	$0.670283\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.27319			0.207311			0.103655	−	0.994613i	$-0.466946\pi$
$647$	5.27319			0.207311			0.103655	+	0.994613i	$0.466946\pi$
$648$		0			0
$649$	−1.56162	−	0.568383i	−0.0612990	−	0.0223110i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0269	+	36.4197i	−0.822848	+	1.42521i	0.0807056	+	0.996738i	$0.474283\pi$
$653$	−21.0269	+	36.4197i	−0.822848	+	1.42521i	−0.903553	+	0.428476i	$0.859051\pi$
$654$		0			0
$655$	29.8603	+	25.0558i	1.16674	+	0.979011i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−31.5671	+	11.4895i	−1.22968	+	0.447567i	−0.873488	−	0.486846i	$-0.838147\pi$
$659$	−31.5671	+	11.4895i	−1.22968	+	0.447567i	−0.356192	+	0.934413i	$0.615925\pi$
$660$		0			0
$661$	−3.70331	+	21.0025i	−0.144042	+	0.816903i	0.824089	+	0.566460i	$0.191687\pi$
$661$	−3.70331	+	21.0025i	−0.144042	+	0.816903i	−0.968131	+	0.250443i	$0.919424\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.26691	−	0.381176i	−0.0879071	−	0.0147814i
$666$		0			0
$667$	31.2366	−	26.2107i	1.20949	−	1.01488i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.22822	−	0.811004i	0.0860193	−	0.0313085i
$672$		0			0
$673$	16.8335	+	29.1564i	0.648882	+	1.12390i	0.983390	+	0.181504i	$0.0580964\pi$
$673$	16.8335	+	29.1564i	0.648882	+	1.12390i	−0.334508	+	0.942393i	$0.608570\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.2965	−	28.2264i	0.626327	−	1.08483i	−0.361956	−	0.932195i	$-0.617891\pi$
$677$	16.2965	−	28.2264i	0.626327	−	1.08483i	0.988283	−	0.152635i	$-0.0487758\pi$
$678$		0			0
$679$	−0.0183306	−	0.103958i	−0.000703464	−	0.00398954i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.1071			1.11375			0.556875	−	0.830596i	$-0.312000\pi$
$683$	29.1071			1.11375			0.556875	+	0.830596i	$0.312000\pi$
$684$		0			0
$685$	45.5198			1.73922
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.866505	−	4.91419i	−0.0330112	−	0.187216i
$690$		0			0
$691$	17.4572	−	30.2367i	0.664102	−	1.15026i	−0.315425	−	0.948950i	$-0.602147\pi$
$691$	17.4572	−	30.2367i	0.664102	−	1.15026i	0.979528	−	0.201309i	$-0.0645195\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.5232	−	33.8152i	−0.740558	−	1.28268i
$696$		0			0
$697$	−16.5503	+	6.02383i	−0.626889	+	0.228169i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.84929	+	1.55174i	−0.0698467	+	0.0586084i	−0.677043	−	0.735944i	$-0.736739\pi$
$701$	−1.84929	+	1.55174i	−0.0698467	+	0.0586084i	0.607196	+	0.794552i	$0.292294\pi$
$702$		0			0
$703$	−27.1345	+	5.00711i	−1.02340	+	0.188847i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.302753	−	1.71700i	0.0113862	−	0.0645744i
$708$		0			0
$709$	−4.00623	+	1.45815i	−0.150457	+	0.0547619i	−0.416151	−	0.909296i	$-0.636621\pi$
$709$	−4.00623	+	1.45815i	−0.150457	+	0.0547619i	0.265694	+	0.964057i	$0.414399\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.0365	+	10.9389i	0.488220	+	0.409665i
$714$		0			0
$715$	2.09050	−	3.62085i	0.0781802	−	0.135412i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	27.5194	+	10.0162i	1.02630	+	0.373543i	0.799671	−	0.600438i	$-0.205007\pi$
$719$	27.5194	+	10.0162i	1.02630	+	0.373543i	0.226630	+	0.973981i	$0.427229\pi$
$720$		0			0
$721$	1.20218			0.0447714
$722$		0			0
$723$		0			0
$724$		0			0
$725$	60.8396	+	22.1438i	2.25953	+	0.822400i
$726$		0			0
$727$	−7.25564	−	41.1488i	−0.269097	−	1.52612i	−0.757110	−	0.653287i	$-0.773389\pi$
$727$	−7.25564	−	41.1488i	−0.269097	−	1.52612i	0.488013	−	0.872836i	$-0.337722\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.5180	−	13.0212i	−0.573955	−	0.481605i
$732$		0			0
$733$	−1.63173	−	2.82624i	−0.0602693	−	0.104390i	0.834316	−	0.551286i	$-0.185863\pi$
$733$	−1.63173	−	2.82624i	−0.0602693	−	0.104390i	−0.894586	+	0.446896i	$0.852529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.20942	+	6.85898i	−0.0445496	+	0.252654i
$738$		0			0
$739$	3.24786	−	2.72528i	0.119474	−	0.100251i	−0.581093	−	0.813837i	$-0.697375\pi$
$739$	3.24786	−	2.72528i	0.119474	−	0.100251i	0.700567	+	0.713586i	$0.252930\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.3449	−	10.3586i	0.452889	−	0.380019i	−0.387618	−	0.921820i	$-0.626702\pi$
$743$	12.3449	−	10.3586i	0.452889	−	0.380019i	0.840507	+	0.541801i	$0.182258\pi$
$744$		0			0
$745$	2.46914	−	14.0032i	0.0904623	−	0.513037i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.0684621	−	0.118580i	−0.00250155	−	0.00433281i
$750$		0			0
$751$	−26.4072	−	22.1583i	−0.963614	−	0.808568i	0.0179232	−	0.999839i	$-0.494295\pi$
$751$	−26.4072	−	22.1583i	−0.963614	−	0.808568i	−0.981537	+	0.191271i	$0.938739\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.81790	−	50.0088i	−0.320916	−	1.82001i
$756$		0			0
$757$	−23.7846	−	8.65689i	−0.864466	−	0.314640i	−0.128542	−	0.991704i	$-0.541030\pi$
$757$	−23.7846	−	8.65689i	−0.864466	−	0.314640i	−0.735924	+	0.677064i	$0.763252\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.6889			0.496223			0.248111	−	0.968731i	$-0.420190\pi$
$761$	13.6889			0.496223			0.248111	+	0.968731i	$0.420190\pi$
$762$		0			0
$763$	1.86186	+	0.677660i	0.0674037	+	0.0245329i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.86379	−	3.22817i	0.0672974	−	0.116563i
$768$		0			0
$769$	26.4169	+	22.1664i	0.952616	+	0.799340i	0.979736	−	0.200292i	$-0.0641891\pi$
$769$	26.4169	+	22.1664i	0.952616	+	0.799340i	−0.0271198	+	0.999632i	$0.508634\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−45.5996	+	16.5969i	−1.64010	+	0.596948i	−0.987057	−	0.160371i	$-0.948731\pi$
$773$	−45.5996	+	16.5969i	−1.64010	+	0.596948i	−0.653045	+	0.757319i	$0.726509\pi$
$774$		0			0
$775$	−4.69209	+	26.6102i	−0.168545	+	0.955866i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20.1283	+	3.38453i	0.721172	+	0.121263i
$780$		0			0
$781$	1.15986	−	0.973239i	0.0415031	−	0.0348252i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−28.8847	+	10.5132i	−1.03094	+	0.375231i
$786$		0			0
$787$	−23.4705	−	40.6521i	−0.836633	−	1.44909i	−0.892694	−	0.450663i	$-0.851188\pi$
$787$	−23.4705	−	40.6521i	−0.836633	−	1.44909i	0.0560615	−	0.998427i	$-0.482146\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.199220	−	0.345060i	0.00708346	−	0.0122689i
$792$		0			0
$793$	0.923588	+	5.23793i	0.0327976	+	0.186004i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−45.6388			−1.61661			−0.808305	−	0.588764i	$-0.799615\pi$
$797$	−45.6388			−1.61661			−0.808305	+	0.588764i	$0.799615\pi$
$798$		0			0
$799$	−7.00452			−0.247802
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.38562	+	7.85826i	0.0488976	+	0.277312i
$804$		0			0
$805$	1.55934	−	2.70086i	0.0549595	−	0.0951926i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	15.7365	+	27.2565i	0.553267	+	0.958286i	0.998036	+	0.0626411i	$0.0199524\pi$
$809$	15.7365	+	27.2565i	0.553267	+	0.958286i	−0.444769	+	0.895645i	$0.646714\pi$
$810$		0			0
$811$	−39.7312	+	14.4610i	−1.39515	+	0.507793i	−0.926735	−	0.375716i	$-0.877397\pi$
$811$	−39.7312	+	14.4610i	−1.39515	+	0.507793i	−0.468415	+	0.883509i	$0.655175\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−23.9794	+	20.1211i	−0.839962	+	0.704811i
$816$		0			0
$817$	8.20423	+	21.9957i	0.287030	+	0.769532i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.33917	−	18.9374i	0.116538	−	0.660919i	−0.869440	−	0.494039i	$-0.835520\pi$
$821$	3.33917	−	18.9374i	0.116538	−	0.660919i	0.985977	−	0.166879i	$-0.0533690\pi$
$822$		0			0
$823$	24.9230	−	9.07122i	0.868760	−	0.316203i	0.131095	−	0.991370i	$-0.458151\pi$
$823$	24.9230	−	9.07122i	0.868760	−	0.316203i	0.737665	+	0.675167i	$0.235928\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.3929	+	11.2380i	0.465718	+	0.390784i	0.845230	−	0.534403i	$-0.179464\pi$
$827$	13.3929	+	11.2380i	0.465718	+	0.390784i	−0.379512	+	0.925187i	$0.623908\pi$
$828$		0			0
$829$	−12.9372	+	22.4079i	−0.449328	+	0.778259i	−0.998342	−	0.0575537i	$-0.981670\pi$
$829$	−12.9372	+	22.4079i	−0.449328	+	0.778259i	0.549014	+	0.835813i	$0.315003\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−24.6728	−	8.98018i	−0.854863	−	0.311145i
$834$		0			0
$835$	44.6782			1.54615
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−37.2066	−	13.5421i	−1.28451	−	0.467524i	−0.392591	−	0.919713i	$-0.628421\pi$
$839$	−37.2066	−	13.5421i	−1.28451	−	0.467524i	−0.891922	+	0.452189i	$0.850643\pi$
$840$		0			0
$841$	3.22029	+	18.2632i	0.111044	+	0.629764i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−30.5925	−	25.6701i	−1.05241	−	0.883079i
$846$		0			0
$847$	0.730471	+	1.26521i	0.0250993	+	0.0434732i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.50047	−	36.8660i	0.222833	−	1.26375i
$852$		0			0
$853$	−23.9929	+	20.1325i	−0.821502	+	0.689322i	−0.953323	−	0.301951i	$-0.902362\pi$
$853$	−23.9929	+	20.1325i	−0.821502	+	0.689322i	0.131821	+	0.991274i	$0.457918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.5482	−	10.5292i	0.428637	−	0.359669i	−0.402800	−	0.915288i	$-0.631963\pi$
$857$	12.5482	−	10.5292i	0.428637	−	0.359669i	0.831437	+	0.555619i	$0.187519\pi$
$858$		0			0
$859$	−6.23449	+	35.3576i	−0.212718	+	1.20638i	0.672105	+	0.740456i	$0.265391\pi$
$859$	−6.23449	+	35.3576i	−0.212718	+	1.20638i	−0.884823	+	0.465928i	$0.845721\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.3886	+	33.5820i	0.659995	+	1.14314i	0.980616	+	0.195938i	$0.0627750\pi$
$863$	19.3886	+	33.5820i	0.659995	+	1.14314i	−0.320621	+	0.947207i	$0.603892\pi$
$864$		0			0
$865$	−27.2074	−	22.8297i	−0.925078	−	0.776233i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.953434	+	5.40720i	0.0323430	+	0.183427i
$870$		0			0
$871$	−14.6801	−	5.34313i	−0.497418	−	0.181045i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.31494			0.0782594
$876$		0			0
$877$	−12.6819	−	4.61584i	−0.428238	−	0.155866i	0.118904	−	0.992906i	$-0.462062\pi$
$877$	−12.6819	−	4.61584i	−0.428238	−	0.155866i	−0.547142	+	0.837040i	$0.684284\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.03251	+	5.25246i	−0.102168	+	0.176960i	−0.912578	−	0.408904i	$-0.865911\pi$
$881$	−3.03251	+	5.25246i	−0.102168	+	0.176960i	0.810410	+	0.585864i	$0.199245\pi$
$882$		0			0
$883$	−5.42261	−	4.55011i	−0.182485	−	0.153123i	0.546969	−	0.837153i	$-0.315782\pi$
$883$	−5.42261	−	4.55011i	−0.182485	−	0.153123i	−0.729454	+	0.684029i	$0.760226\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	42.7141	−	15.5466i	1.43420	−	0.522005i	0.496066	−	0.868285i	$-0.334777\pi$
$887$	42.7141	−	15.5466i	1.43420	−	0.522005i	0.938132	+	0.346279i	$0.112555\pi$
$888$		0			0
$889$	−0.509243	+	2.88806i	−0.0170795	+	0.0968625i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.06192	+	4.00275i	0.236318	+	0.133947i
$894$		0			0
$895$	−26.9957	+	22.6520i	−0.902365	+	0.757174i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.6460	+	6.78659i	−0.621879	+	0.226345i
$900$		0			0
$901$	−5.96844	−	10.3376i	−0.198838	−	0.344397i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.14151	−	8.90536i	0.170910	−	0.296024i
$906$		0			0
$907$	−6.82814	−	38.7243i	−0.226725	−	1.28582i	−0.859360	−	0.511370i	$-0.829138\pi$
$907$	−6.82814	−	38.7243i	−0.226725	−	1.28582i	0.632636	−	0.774450i	$-0.281973\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.52856			0.315695			0.157848	−	0.987463i	$-0.449545\pi$
$911$	9.52856			0.315695			0.157848	+	0.987463i	$0.449545\pi$
$912$		0			0
$913$	7.18999			0.237954
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.248070	+	1.40687i	0.00819198	+	0.0464590i
$918$		0			0
$919$	8.36681	−	14.4917i	0.275996	−	0.478039i	−0.694390	−	0.719599i	$-0.744326\pi$
$919$	8.36681	−	14.4917i	0.275996	−	0.478039i	0.970386	+	0.241560i	$0.0776591\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.69808	+	2.94116i	0.0558930	+	0.0968096i
$924$		0			0
$925$	55.8535	−	20.3290i	1.83645	−	0.668414i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.66832	+	4.75629i	−0.185972	+	0.156049i	−0.731020	−	0.682356i	$-0.760956\pi$
$929$	−5.66832	+	4.75629i	−0.185972	+	0.156049i	0.545049	+	0.838404i	$0.316511\pi$
$930$		0			0
$931$	19.7433	+	23.1531i	0.647061	+	0.758813i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.73676	−	9.84967i	0.0567982	−	0.322119i
$936$		0			0
$937$	−26.4994	+	9.64498i	−0.865697	+	0.315088i	−0.736423	−	0.676521i	$-0.763487\pi$
$937$	−26.4994	+	9.64498i	−0.865697	+	0.315088i	−0.129273	+	0.991609i	$0.541265\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.9787	−	33.5461i	−1.30327	−	1.09357i	−0.989570	−	0.144050i	$-0.953988\pi$
$941$	−39.9787	−	33.5461i	−1.30327	−	1.09357i	−0.313698	−	0.949523i	$-0.601568\pi$
$942$		0			0
$943$	−13.8457	+	23.9814i	−0.450877	+	0.780941i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.1023	+	8.04458i	0.718228	+	0.261414i	0.675174	−	0.737659i	$-0.264069\pi$
$947$	22.1023	+	8.04458i	0.718228	+	0.261414i	0.0430549	+	0.999073i	$0.486291\pi$
$948$		0			0
$949$	−17.8983			−0.581003
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.1886	+	12.8076i	1.13987	+	0.414879i	0.841867	−	0.539686i	$-0.181457\pi$
$953$	35.1886	+	12.8076i	1.13987	+	0.414879i	0.298004	+	0.954565i	$0.403679\pi$
$954$		0			0
$955$	12.4454	+	70.5812i	0.402723	+	2.28395i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.27796	+	1.07234i	0.0412675	+	0.0346275i
$960$		0			0
$961$	11.3594	+	19.6750i	0.366432	+	0.634678i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.0451	+	79.6537i	−0.452128	+	2.56414i
$966$		0			0
$967$	−25.3924	+	21.3068i	−0.816565	+	0.685179i	−0.952165	−	0.305585i	$-0.901148\pi$
$967$	−25.3924	+	21.3068i	−0.816565	+	0.685179i	0.135600	+	0.990764i	$0.456704\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.1983	−	10.2356i	0.391462	−	0.328476i	−0.425720	−	0.904855i	$-0.639979\pi$
$971$	12.1983	−	10.2356i	0.391462	−	0.328476i	0.817182	+	0.576379i	$0.195535\pi$
$972$		0			0
$973$	0.248493	−	1.40927i	0.00796632	−	0.0451792i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.950197	+	1.64579i	0.0303995	+	0.0526535i	0.880825	−	0.473442i	$-0.156989\pi$
$977$	0.950197	+	1.64579i	0.0303995	+	0.0526535i	−0.850425	+	0.526096i	$0.823655\pi$
$978$		0			0
$979$	6.97420	+	5.85205i	0.222896	+	0.187032i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.74254	+	15.5537i	0.0874733	+	0.496086i	0.996795	+	0.0799929i	$0.0254898\pi$
$983$	2.74254	+	15.5537i	0.0874733	+	0.496086i	−0.909322	+	0.416093i	$0.863399\pi$
$984$		0			0
$985$	59.1050	+	21.5125i	1.88324	+	0.685444i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−31.8497			−1.01276
$990$		0			0
$991$	36.1131	+	13.1441i	1.14717	+	0.417536i	0.844498	−	0.535559i	$-0.179899\pi$
$991$	36.1131	+	13.1441i	1.14717	+	0.417536i	0.302672	+	0.953095i	$0.402121\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−30.6876	+	53.1525i	−0.972863	+	1.68505i
$996$		0			0
$997$	6.30982	+	5.29457i	0.199834	+	0.167681i	0.737213	−	0.675660i	$-0.236141\pi$
$997$	6.30982	+	5.29457i	0.199834	+	0.167681i	−0.537379	+	0.843341i	$0.680586\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bo.c.253.2		12
3.2	odd	2		76.2.i.a.25.1	✓	12
12.11	even	2		304.2.u.e.177.2		12
19.16	even	9	inner	684.2.bo.c.73.2		12
57.23	odd	18		1444.2.a.h.1.6		6
57.29	even	18		1444.2.e.h.429.6		12
57.32	even	18		1444.2.e.h.653.6		12
57.35	odd	18		76.2.i.a.73.1	yes	12
57.44	odd	18		1444.2.e.g.653.1		12
57.47	odd	18		1444.2.e.g.429.1		12
57.53	even	18		1444.2.a.g.1.1		6
228.23	even	18		5776.2.a.bw.1.1		6
228.35	even	18		304.2.u.e.225.2		12
228.167	odd	18		5776.2.a.by.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.25.1	✓	12	3.2	odd	2
76.2.i.a.73.1	yes	12	57.35	odd	18
304.2.u.e.177.2		12	12.11	even	2
304.2.u.e.225.2		12	228.35	even	18
684.2.bo.c.73.2		12	19.16	even	9	inner
684.2.bo.c.253.2		12	1.1	even	1	trivial
1444.2.a.g.1.1		6	57.53	even	18
1444.2.a.h.1.6		6	57.23	odd	18
1444.2.e.g.429.1		12	57.47	odd	18
1444.2.e.g.653.1		12	57.44	odd	18
1444.2.e.h.429.6		12	57.29	even	18
1444.2.e.h.653.6		12	57.32	even	18
5776.2.a.bw.1.1		6	228.23	even	18
5776.2.a.by.1.6		6	228.167	odd	18

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658711 + 3.73574i) q^{5} +(-0.0695116 + 0.120398i) q^{7} +(0.350493 + 0.607072i) q^{11} +(-1.47751 + 0.537771i) q^{13} +(-2.88131 + 2.41771i) q^{17} +(4.28653 - 0.790990i) q^{19} +(-1.02690 + 5.82385i) q^{23} +(-8.82337 + 3.21144i) q^{25} +(-5.28209 - 4.43220i) q^{29} +(1.43886 - 2.49217i) q^{31} +(-0.495562 - 0.180370i) q^{35} -6.33018 q^{37} +(4.40018 + 1.60154i) q^{41} +(0.935226 + 5.30393i) q^{43} +(1.42658 + 1.19704i) q^{47} +(3.49034 + 6.04544i) q^{49} +(-0.551093 + 3.12541i) q^{53} +(-2.03699 + 1.70923i) q^{55} +(-1.81608 + 1.52387i) q^{59} +(0.587398 - 3.33130i) q^{61} +(-2.98223 - 5.16537i) q^{65} +(7.61119 + 6.38655i) q^{67} +(-0.375070 - 2.12713i) q^{71} +(10.6967 + 3.89330i) q^{73} -0.0974533 q^{77} +(7.36033 + 2.67894i) q^{79} +(5.12849 - 8.88280i) q^{83} +(-10.9299 - 9.17125i) q^{85} +(12.2044 - 4.44204i) q^{89} +(0.0379580 - 0.215271i) q^{91} +(5.77852 + 15.4923i) q^{95} +(-0.581665 + 0.488075i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 3 q^{11} - 9 q^{13} + 3 q^{17} - 12 q^{19} + 12 q^{23} - 18 q^{25} - 27 q^{29} + 6 q^{31} - 33 q^{35} - 12 q^{37} - 3 q^{41} + 27 q^{43} + 15 q^{47} + 9 q^{49} + 21 q^{53} - 27 q^{55} + 48 q^{59}+ \cdots + 12 q^{97}+O(q^{100}) \) 12 * q + 3 * q^7 - 3 * q^11 - 9 * q^13 + 3 * q^17 - 12 * q^19 + 12 * q^23 - 18 * q^25 - 27 * q^29 + 6 * q^31 - 33 * q^35 - 12 * q^37 - 3 * q^41 + 27 * q^43 + 15 * q^47 + 9 * q^49 + 21 * q^53 - 27 * q^55 + 48 * q^59 - 6 * q^61 + 33 * q^65 + 24 * q^67 + 30 * q^73 - 24 * q^77 + 3 * q^79 - 3 * q^83 - 42 * q^85 + 18 * q^89 - 24 * q^91 - 9 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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