LMFDB - Embedded newform 392.4.i.g.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,4,Mod(177,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("392.177");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	392.i (of order $3$, degree $2$, not 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:	$23.1287487223$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.4.i.g.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{3} +(1.00000 + 1.73205i) q^{5} +(5.50000 + 9.52628i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{3} +(1.00000 + 1.73205i) q^{5} +(5.50000 + 9.52628i) q^{9} +(22.0000 - 38.1051i) q^{11} +22.0000 q^{13} +8.00000 q^{15} +(-25.0000 + 43.3013i) q^{17} +(-22.0000 - 38.1051i) q^{19} +(28.0000 + 48.4974i) q^{23} +(60.5000 - 104.789i) q^{25} +152.000 q^{27} +198.000 q^{29} +(80.0000 - 138.564i) q^{31} +(-88.0000 - 152.420i) q^{33} +(81.0000 + 140.296i) q^{37} +(44.0000 - 76.2102i) q^{39} -198.000 q^{41} +52.0000 q^{43} +(-11.0000 + 19.0526i) q^{45} +(-264.000 - 457.261i) q^{47} +(100.000 + 173.205i) q^{51} +(121.000 - 209.578i) q^{53} +88.0000 q^{55} -176.000 q^{57} +(334.000 - 578.505i) q^{59} +(-275.000 - 476.314i) q^{61} +(22.0000 + 38.1051i) q^{65} +(-94.0000 + 162.813i) q^{67} +224.000 q^{69} +728.000 q^{71} +(-77.0000 + 133.368i) q^{73} +(-242.000 - 419.156i) q^{75} +(328.000 + 568.113i) q^{79} +(155.500 - 269.334i) q^{81} +236.000 q^{83} -100.000 q^{85} +(396.000 - 685.892i) q^{87} +(-357.000 - 618.342i) q^{89} +(-320.000 - 554.256i) q^{93} +(44.0000 - 76.2102i) q^{95} -478.000 q^{97} +484.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 2 q^{5} + 11 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 + 2 * q^5 + 11 * q^9	$ 2 q + 4 q^{3} + 2 q^{5} + 11 q^{9} + 44 q^{11} + 44 q^{13} + 16 q^{15} - 50 q^{17} - 44 q^{19} + 56 q^{23} + 121 q^{25} + 304 q^{27} + 396 q^{29} + 160 q^{31} - 176 q^{33} + 162 q^{37} + 88 q^{39} - 396 q^{41} + 104 q^{43} - 22 q^{45} - 528 q^{47} + 200 q^{51} + 242 q^{53} + 176 q^{55} - 352 q^{57} + 668 q^{59} - 550 q^{61} + 44 q^{65} - 188 q^{67} + 448 q^{69} + 1456 q^{71} - 154 q^{73} - 484 q^{75} + 656 q^{79} + 311 q^{81} + 472 q^{83} - 200 q^{85} + 792 q^{87} - 714 q^{89} - 640 q^{93} + 88 q^{95} - 956 q^{97} + 968 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 2 * q^5 + 11 * q^9 + 44 * q^11 + 44 * q^13 + 16 * q^15 - 50 * q^17 - 44 * q^19 + 56 * q^23 + 121 * q^25 + 304 * q^27 + 396 * q^29 + 160 * q^31 - 176 * q^33 + 162 * q^37 + 88 * q^39 - 396 * q^41 + 104 * q^43 - 22 * q^45 - 528 * q^47 + 200 * q^51 + 242 * q^53 + 176 * q^55 - 352 * q^57 + 668 * q^59 - 550 * q^61 + 44 * q^65 - 188 * q^67 + 448 * q^69 + 1456 * q^71 - 154 * q^73 - 484 * q^75 + 656 * q^79 + 311 * q^81 + 472 * q^83 - 200 * q^85 + 792 * q^87 - 714 * q^89 - 640 * q^93 + 88 * q^95 - 956 * q^97 + 968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.00000	−	3.46410i	0.384900	−	0.666667i	−0.606855	−	0.794812i	$-0.707569\pi$
$3$	2.00000	−	3.46410i	0.384900	−	0.666667i	0.991755	+	0.128146i	$0.0409025\pi$
$4$		0			0
$5$	1.00000	+	1.73205i	0.0894427	+	0.154919i	0.907276	−	0.420536i	$-0.138158\pi$
$5$	1.00000	+	1.73205i	0.0894427	+	0.154919i	−0.817833	+	0.575456i	$0.804825\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.50000	+	9.52628i	0.203704	+	0.352825i
$10$		0			0
$11$	22.0000	−	38.1051i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	22.0000	−	38.1051i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$	22.0000			0.469362			0.234681	−	0.972072i	$-0.424595\pi$
$13$	22.0000			0.469362			0.234681	+	0.972072i	$0.424595\pi$
$14$		0			0
$15$	8.00000			0.137706
$16$		0			0
$17$	−25.0000	+	43.3013i	−0.356670	+	0.617771i	−0.987402	−	0.158230i	$-0.949421\pi$
$17$	−25.0000	+	43.3013i	−0.356670	+	0.617771i	0.630732	+	0.776001i	$0.282755\pi$
$18$		0			0
$19$	−22.0000	−	38.1051i	−0.265639	−	0.460101i	0.702092	−	0.712087i	$-0.252250\pi$
$19$	−22.0000	−	38.1051i	−0.265639	−	0.460101i	−0.967731	+	0.251986i	$0.918916\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	28.0000	+	48.4974i	0.253844	+	0.439670i	0.964581	−	0.263788i	$-0.0849718\pi$
$23$	28.0000	+	48.4974i	0.253844	+	0.439670i	−0.710737	+	0.703458i	$0.751638\pi$
$24$		0			0
$25$	60.5000	−	104.789i	0.484000	−	0.838313i
$26$		0			0
$27$	152.000			1.08342
$28$		0			0
$29$	198.000			1.26785			0.633925	−	0.773394i	$-0.281443\pi$
$29$	198.000			1.26785			0.633925	+	0.773394i	$0.281443\pi$
$30$		0			0
$31$	80.0000	−	138.564i	0.463498	−	0.802801i	−0.535635	−	0.844450i	$-0.679928\pi$
$31$	80.0000	−	138.564i	0.463498	−	0.802801i	0.999132	+	0.0416484i	$0.0132609\pi$
$32$		0			0
$33$	−88.0000	−	152.420i	−0.464207	−	0.804030i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	0.987944	−	0.154812i	$-0.0494773\pi$
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	−0.628043	+	0.778178i	$0.716144\pi$
$38$		0			0
$39$	44.0000	−	76.2102i	0.180657	−	0.312908i
$40$		0			0
$41$	−198.000			−0.754205			−0.377102	−	0.926172i	$-0.623080\pi$
$41$	−198.000			−0.754205			−0.377102	+	0.926172i	$0.623080\pi$
$42$		0			0
$43$	52.0000			0.184417			0.0922084	−	0.995740i	$-0.470607\pi$
$43$	52.0000			0.184417			0.0922084	+	0.995740i	$0.470607\pi$
$44$		0			0
$45$	−11.0000	+	19.0526i	−0.0364396	+	0.0631153i
$46$		0			0
$47$	−264.000	−	457.261i	−0.819327	−	1.41912i	−0.906179	−	0.422894i	$-0.861014\pi$
$47$	−264.000	−	457.261i	−0.819327	−	1.41912i	0.0868522	−	0.996221i	$-0.472319\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	100.000	+	173.205i	0.274565	+	0.475560i
$52$		0			0
$53$	121.000	−	209.578i	0.313597	−	0.543166i	−0.665541	−	0.746361i	$-0.731799\pi$
$53$	121.000	−	209.578i	0.313597	−	0.543166i	0.979138	+	0.203195i	$0.0651327\pi$
$54$		0			0
$55$	88.0000			0.215744
$56$		0			0
$57$	−176.000			−0.408978
$58$		0			0
$59$	334.000	−	578.505i	0.737002	−	1.27652i	−0.216838	−	0.976208i	$-0.569574\pi$
$59$	334.000	−	578.505i	0.737002	−	1.27652i	0.953840	−	0.300317i	$-0.0970924\pi$
$60$		0			0
$61$	−275.000	−	476.314i	−0.577215	−	0.999766i	−0.995797	−	0.0915873i	$-0.970806\pi$
$61$	−275.000	−	476.314i	−0.577215	−	0.999766i	0.418582	−	0.908179i	$-0.362527\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	22.0000	+	38.1051i	0.0419810	+	0.0727132i
$66$		0			0
$67$	−94.0000	+	162.813i	−0.171402	+	0.296877i	−0.938910	−	0.344162i	$-0.888163\pi$
$67$	−94.0000	+	162.813i	−0.171402	+	0.296877i	0.767508	+	0.641039i	$0.221496\pi$
$68$		0			0
$69$	224.000			0.390818
$70$		0			0
$71$	728.000			1.21687			0.608435	−	0.793604i	$-0.291798\pi$
$71$	728.000			1.21687			0.608435	+	0.793604i	$0.291798\pi$
$72$		0			0
$73$	−77.0000	+	133.368i	−0.123454	+	0.213829i	−0.921128	−	0.389261i	$-0.872731\pi$
$73$	−77.0000	+	133.368i	−0.123454	+	0.213829i	0.797673	+	0.603090i	$0.206064\pi$
$74$		0			0
$75$	−242.000	−	419.156i	−0.372583	−	0.645333i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	328.000	+	568.113i	0.467125	+	0.809084i	0.999295	−	0.0375534i	$-0.0119564\pi$
$79$	328.000	+	568.113i	0.467125	+	0.809084i	−0.532170	+	0.846638i	$0.678623\pi$
$80$		0			0
$81$	155.500	−	269.334i	0.213306	−	0.369457i
$82$		0			0
$83$	236.000			0.312101			0.156050	−	0.987749i	$-0.450124\pi$
$83$	236.000			0.312101			0.156050	+	0.987749i	$0.450124\pi$
$84$		0			0
$85$	−100.000			−0.127606
$86$		0			0
$87$	396.000	−	685.892i	0.487996	−	0.845234i
$88$		0			0
$89$	−357.000	−	618.342i	−0.425190	−	0.736451i	0.571248	−	0.820778i	$-0.306459\pi$
$89$	−357.000	−	618.342i	−0.425190	−	0.736451i	−0.996438	+	0.0843265i	$0.973126\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−320.000	−	554.256i	−0.356801	−	0.617997i
$94$		0			0
$95$	44.0000	−	76.2102i	0.0475190	−	0.0823053i
$96$		0			0
$97$	−478.000			−0.500346			−0.250173	−	0.968201i	$-0.580487\pi$
$97$	−478.000			−0.500346			−0.250173	+	0.968201i	$0.580487\pi$
$98$		0			0
$99$	484.000			0.491352
$100$		0			0
$101$	−783.000	+	1356.20i	−0.771400	+	1.33610i	0.165396	+	0.986227i	$0.447110\pi$
$101$	−783.000	+	1356.20i	−0.771400	+	1.33610i	−0.936796	+	0.349877i	$0.886223\pi$
$102$		0			0
$103$	484.000	+	838.313i	0.463009	+	0.801955i	0.999109	−	0.0421991i	$-0.0134364\pi$
$103$	484.000	+	838.313i	0.463009	+	0.801955i	−0.536100	+	0.844154i	$0.680103\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	390.000	+	675.500i	0.352362	+	0.610309i	0.986663	−	0.162778i	$-0.0520453\pi$
$107$	390.000	+	675.500i	0.352362	+	0.610309i	−0.634301	+	0.773086i	$0.718712\pi$
$108$		0			0
$109$	997.000	−	1726.85i	0.876103	−	1.51746i	0.0205209	−	0.999789i	$-0.493468\pi$
$109$	997.000	−	1726.85i	0.876103	−	1.51746i	0.855583	−	0.517666i	$-0.173199\pi$
$110$		0			0
$111$	648.000			0.554103
$112$		0			0
$113$	−942.000			−0.784212			−0.392106	−	0.919920i	$-0.628253\pi$
$113$	−942.000			−0.784212			−0.392106	+	0.919920i	$0.628253\pi$
$114$		0			0
$115$	−56.0000	+	96.9948i	−0.0454089	+	0.0786506i
$116$		0			0
$117$	121.000	+	209.578i	0.0956107	+	0.165603i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−302.500	−	523.945i	−0.227273	−	0.393648i
$122$		0			0
$123$	−396.000	+	685.892i	−0.290294	+	0.502803i
$124$		0			0
$125$	492.000			0.352047
$126$		0			0
$127$	1408.00			0.983778			0.491889	−	0.870658i	$-0.336307\pi$
$127$	1408.00			0.983778			0.491889	+	0.870658i	$0.336307\pi$
$128$		0			0
$129$	104.000	−	180.133i	0.0709821	−	0.122945i
$130$		0			0
$131$	1346.00	+	2331.34i	0.897714	+	1.55489i	0.830409	+	0.557154i	$0.188107\pi$
$131$	1346.00	+	2331.34i	0.897714	+	1.55489i	0.0673052	+	0.997732i	$0.478560\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	152.000	+	263.272i	0.0969043	+	0.167843i
$136$		0			0
$137$	−813.000	+	1408.16i	−0.507002	+	0.878153i	0.492965	+	0.870049i	$0.335913\pi$
$137$	−813.000	+	1408.16i	−0.507002	+	0.878153i	−0.999967	+	0.00810420i	$0.997420\pi$
$138$		0			0
$139$	−684.000			−0.417382			−0.208691	−	0.977982i	$-0.566920\pi$
$139$	−684.000			−0.417382			−0.208691	+	0.977982i	$0.566920\pi$
$140$		0			0
$141$	−2112.00			−1.26144
$142$		0			0
$143$	484.000	−	838.313i	0.283036	−	0.490232i
$144$		0			0
$145$	198.000	+	342.946i	0.113400	+	0.196415i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−151.000	−	261.540i	−0.0830228	−	0.143800i	0.821524	−	0.570174i	$-0.193124\pi$
$149$	−151.000	−	261.540i	−0.0830228	−	0.143800i	−0.904547	+	0.426374i	$0.859791\pi$
$150$		0			0
$151$	−676.000	+	1170.87i	−0.364319	+	0.631018i	−0.988667	−	0.150128i	$-0.952031\pi$
$151$	−676.000	+	1170.87i	−0.364319	+	0.631018i	0.624348	+	0.781146i	$0.285365\pi$
$152$		0			0
$153$	−550.000			−0.290620
$154$		0			0
$155$	320.000			0.165826
$156$		0			0
$157$	−1571.00	+	2721.05i	−0.798595	+	1.38321i	0.121936	+	0.992538i	$0.461090\pi$
$157$	−1571.00	+	2721.05i	−0.798595	+	1.38321i	−0.920531	+	0.390670i	$0.872244\pi$
$158$		0			0
$159$	−484.000	−	838.313i	−0.241407	−	0.418129i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1518.00	−	2629.25i	−0.729441	−	1.26343i	−0.957120	−	0.289693i	$-0.906447\pi$
$163$	−1518.00	−	2629.25i	−0.729441	−	1.26343i	0.227678	−	0.973736i	$-0.426887\pi$
$164$		0			0
$165$	176.000	−	304.841i	0.0830399	−	0.143829i
$166$		0			0
$167$	−264.000			−0.122329			−0.0611645	−	0.998128i	$-0.519481\pi$
$167$	−264.000			−0.122329			−0.0611645	+	0.998128i	$0.519481\pi$
$168$		0			0
$169$	−1713.00			−0.779700
$170$		0			0
$171$	242.000	−	419.156i	0.108223	−	0.187448i
$172$		0			0
$173$	1413.00	+	2447.39i	0.620973	+	1.07556i	0.989305	+	0.145863i	$0.0465959\pi$
$173$	1413.00	+	2447.39i	0.620973	+	1.07556i	−0.368331	+	0.929695i	$0.620071\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1336.00	−	2314.02i	−0.567344	−	0.982669i
$178$		0			0
$179$	−1542.00	+	2670.82i	−0.643880	+	1.11523i	0.340679	+	0.940180i	$0.389343\pi$
$179$	−1542.00	+	2670.82i	−0.643880	+	1.11523i	−0.984559	+	0.175053i	$0.943990\pi$
$180$		0			0
$181$	−2418.00			−0.992975			−0.496488	−	0.868044i	$-0.665377\pi$
$181$	−2418.00			−0.992975			−0.496488	+	0.868044i	$0.665377\pi$
$182$		0			0
$183$	−2200.00			−0.888681
$184$		0			0
$185$	−162.000	+	280.592i	−0.0643810	+	0.111511i
$186$		0			0
$187$	1100.00	+	1905.26i	0.430160	+	0.745059i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	480.000	+	831.384i	0.181841	+	0.314957i	0.942507	−	0.334185i	$-0.108461\pi$
$191$	480.000	+	831.384i	0.181841	+	0.314957i	−0.760667	+	0.649143i	$0.775128\pi$
$192$		0			0
$193$	−1441.00	+	2495.89i	−0.537438	+	0.930869i	0.461604	+	0.887086i	$0.347274\pi$
$193$	−1441.00	+	2495.89i	−0.537438	+	0.930869i	−0.999041	+	0.0437828i	$0.986059\pi$
$194$		0			0
$195$	176.000			0.0646340
$196$		0			0
$197$	1086.00			0.392763			0.196381	−	0.980528i	$-0.437081\pi$
$197$	1086.00			0.392763			0.196381	+	0.980528i	$0.437081\pi$
$198$		0			0
$199$	−44.0000	+	76.2102i	−0.0156738	+	0.0271477i	−0.873756	−	0.486365i	$-0.838323\pi$
$199$	−44.0000	+	76.2102i	−0.0156738	+	0.0271477i	0.858082	+	0.513512i	$0.171656\pi$
$200$		0			0
$201$	376.000	+	651.251i	0.131945	+	0.228536i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−198.000	−	342.946i	−0.0674581	−	0.116841i
$206$		0			0
$207$	−308.000	+	533.472i	−0.103418	+	0.179125i
$208$		0			0
$209$	−1936.00			−0.640746
$210$		0			0
$211$	−3476.00			−1.13411			−0.567056	−	0.823679i	$-0.691918\pi$
$211$	−3476.00			−1.13411			−0.567056	+	0.823679i	$0.691918\pi$
$212$		0			0
$213$	1456.00	−	2521.87i	0.468373	−	0.811246i
$214$		0			0
$215$	52.0000	+	90.0666i	0.0164947	+	0.0285697i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	308.000	+	533.472i	0.0950352	+	0.164606i
$220$		0			0
$221$	−550.000	+	952.628i	−0.167407	+	0.289958i
$222$		0			0
$223$	928.000			0.278670			0.139335	−	0.990245i	$-0.455503\pi$
$223$	928.000			0.278670			0.139335	+	0.990245i	$0.455503\pi$
$224$		0			0
$225$	1331.00			0.394370
$226$		0			0
$227$	−78.0000	+	135.100i	−0.0228064	+	0.0395018i	−0.877203	−	0.480119i	$-0.840593\pi$
$227$	−78.0000	+	135.100i	−0.0228064	+	0.0395018i	0.854397	+	0.519621i	$0.173927\pi$
$228$		0			0
$229$	817.000	+	1415.09i	0.235759	+	0.408347i	0.959493	−	0.281732i	$-0.0909090\pi$
$229$	817.000	+	1415.09i	0.235759	+	0.408347i	−0.723734	+	0.690079i	$0.757576\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	451.000	+	781.155i	0.126807	+	0.219636i	0.922438	−	0.386146i	$-0.126194\pi$
$233$	451.000	+	781.155i	0.126807	+	0.219636i	−0.795631	+	0.605782i	$0.792860\pi$
$234$		0			0
$235$	528.000	−	914.523i	0.146566	−	0.253859i
$236$		0			0
$237$	2624.00			0.719186
$238$		0			0
$239$	1616.00			0.437365			0.218683	−	0.975796i	$-0.429824\pi$
$239$	1616.00			0.437365			0.218683	+	0.975796i	$0.429824\pi$
$240$		0			0
$241$	−2409.00	+	4172.51i	−0.643889	+	1.11525i	0.340667	+	0.940184i	$0.389347\pi$
$241$	−2409.00	+	4172.51i	−0.643889	+	1.11525i	−0.984557	+	0.175065i	$0.943986\pi$
$242$		0			0
$243$	1430.00	+	2476.83i	0.377508	+	0.653864i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−484.000	−	838.313i	−0.124681	−	0.215954i
$248$		0			0
$249$	472.000	−	817.528i	0.120128	−	0.208067i
$250$		0			0
$251$	−2140.00			−0.538150			−0.269075	−	0.963119i	$-0.586718\pi$
$251$	−2140.00			−0.538150			−0.269075	+	0.963119i	$0.586718\pi$
$252$		0			0
$253$	2464.00			0.612294
$254$		0			0
$255$	−200.000	+	346.410i	−0.0491156	+	0.0850708i
$256$		0			0
$257$	−385.000	−	666.840i	−0.0934461	−	0.161853i	0.815513	−	0.578739i	$-0.196455\pi$
$257$	−385.000	−	666.840i	−0.0934461	−	0.161853i	−0.908959	+	0.416886i	$0.863122\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1089.00	+	1886.20i	0.258266	+	0.447330i
$262$		0			0
$263$	3700.00	−	6408.59i	0.867497	−	1.50255i	0.00295121	−	0.999996i	$-0.499061\pi$
$263$	3700.00	−	6408.59i	0.867497	−	1.50255i	0.864546	−	0.502554i	$-0.167606\pi$
$264$		0			0
$265$	484.000			0.112196
$266$		0			0
$267$	−2856.00			−0.654623
$268$		0			0
$269$	1397.00	−	2419.67i	0.316642	−	0.548439i	−0.663143	−	0.748492i	$-0.730778\pi$
$269$	1397.00	−	2419.67i	0.316642	−	0.548439i	0.979785	+	0.200053i	$0.0641114\pi$
$270$		0			0
$271$	−4312.00	−	7468.60i	−0.966551	−	1.67412i	−0.705389	−	0.708821i	$-0.749228\pi$
$271$	−4312.00	−	7468.60i	−0.966551	−	1.67412i	−0.261162	−	0.965295i	$-0.584106\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2662.00	−	4610.72i	−0.583726	−	1.01104i
$276$		0			0
$277$	937.000	−	1622.93i	0.203245	−	0.352031i	−0.746327	−	0.665579i	$-0.768185\pi$
$277$	937.000	−	1622.93i	0.203245	−	0.352031i	0.949572	+	0.313549i	$0.101518\pi$
$278$		0			0
$279$	1760.00			0.377665
$280$		0			0
$281$	3338.00			0.708642			0.354321	−	0.935124i	$-0.384712\pi$
$281$	3338.00			0.708642			0.354321	+	0.935124i	$0.384712\pi$
$282$		0			0
$283$	−3586.00	+	6211.13i	−0.753235	+	1.30464i	0.193012	+	0.981196i	$0.438174\pi$
$283$	−3586.00	+	6211.13i	−0.753235	+	1.30464i	−0.946247	+	0.323445i	$0.895159\pi$
$284$		0			0
$285$	−176.000	−	304.841i	−0.0365801	−	0.0633587i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1206.50	+	2089.72i	0.245573	+	0.425345i
$290$		0			0
$291$	−956.000	+	1655.84i	−0.192583	+	0.333564i
$292$		0			0
$293$	5214.00			1.03961			0.519804	−	0.854286i	$-0.326005\pi$
$293$	5214.00			1.03961			0.519804	+	0.854286i	$0.326005\pi$
$294$		0			0
$295$	1336.00			0.263678
$296$		0			0
$297$	3344.00	−	5791.98i	0.653328	−	1.13160i
$298$		0			0
$299$	616.000	+	1066.94i	0.119144	+	0.206364i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3132.00	+	5424.78i	0.593824	+	1.02853i
$304$		0			0
$305$	550.000	−	952.628i	0.103255	−	0.178844i
$306$		0			0
$307$	396.000			0.0736186			0.0368093	−	0.999322i	$-0.488281\pi$
$307$	396.000			0.0736186			0.0368093	+	0.999322i	$0.488281\pi$
$308$		0			0
$309$	3872.00			0.712849
$310$		0			0
$311$	2028.00	−	3512.60i	0.369766	−	0.640454i	−0.619762	−	0.784789i	$-0.712771\pi$
$311$	2028.00	−	3512.60i	0.369766	−	0.640454i	0.989529	+	0.144335i	$0.0461044\pi$
$312$		0			0
$313$	−1077.00	−	1865.42i	−0.194491	−	0.336868i	0.752243	−	0.658886i	$-0.228972\pi$
$313$	−1077.00	−	1865.42i	−0.194491	−	0.336868i	−0.946733	+	0.322018i	$0.895639\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3693.00	+	6396.46i	0.654320	+	1.13332i	0.982064	+	0.188549i	$0.0603785\pi$
$317$	3693.00	+	6396.46i	0.654320	+	1.13332i	−0.327743	+	0.944767i	$0.606288\pi$
$318$		0			0
$319$	4356.00	−	7544.81i	0.764543	−	1.32423i
$320$		0			0
$321$	3120.00			0.542497
$322$		0			0
$323$	2200.00			0.378982
$324$		0			0
$325$	1331.00	−	2305.36i	0.227171	−	0.393472i
$326$		0			0
$327$	−3988.00	−	6907.42i	−0.674425	−	1.16814i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	566.000	+	980.341i	0.0939884	+	0.162793i	0.909186	−	0.416390i	$-0.136705\pi$
$331$	566.000	+	980.341i	0.0939884	+	0.162793i	−0.815198	+	0.579183i	$0.803372\pi$
$332$		0			0
$333$	−891.000	+	1543.26i	−0.146626	+	0.253964i
$334$		0			0
$335$	−376.000			−0.0613226
$336$		0			0
$337$	−3342.00			−0.540209			−0.270104	−	0.962831i	$-0.587058\pi$
$337$	−3342.00			−0.540209			−0.270104	+	0.962831i	$0.587058\pi$
$338$		0			0
$339$	−1884.00	+	3263.18i	−0.301843	+	0.522808i
$340$		0			0
$341$	−3520.00	−	6096.82i	−0.558999	−	0.968215i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	224.000	+	387.979i	0.0349558	+	0.0605452i
$346$		0			0
$347$	−1122.00	+	1943.36i	−0.173580	+	0.300649i	−0.939669	−	0.342086i	$-0.888867\pi$
$347$	−1122.00	+	1943.36i	−0.173580	+	0.300649i	0.766089	+	0.642734i	$0.222200\pi$
$348$		0			0
$349$	−6522.00			−1.00033			−0.500164	−	0.865931i	$-0.666727\pi$
$349$	−6522.00			−1.00033			−0.500164	+	0.865931i	$0.666727\pi$
$350$		0			0
$351$	3344.00			0.508517
$352$		0			0
$353$	5615.00	−	9725.47i	0.846618	−	1.46639i	−0.0375899	−	0.999293i	$-0.511968\pi$
$353$	5615.00	−	9725.47i	0.846618	−	1.46639i	0.884208	−	0.467093i	$-0.154699\pi$
$354$		0			0
$355$	728.000	+	1260.93i	0.108840	+	0.188517i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−924.000	−	1600.41i	−0.135841	−	0.235283i	0.790078	−	0.613007i	$-0.210040\pi$
$359$	−924.000	−	1600.41i	−0.135841	−	0.235283i	−0.925918	+	0.377724i	$0.876707\pi$
$360$		0			0
$361$	2461.50	−	4263.44i	0.358872	−	0.621584i
$362$		0			0
$363$	−2420.00			−0.349909
$364$		0			0
$365$	−308.000			−0.0441684
$366$		0			0
$367$	−3560.00	+	6166.10i	−0.506350	+	0.877024i	0.493623	+	0.869676i	$0.335672\pi$
$367$	−3560.00	+	6166.10i	−0.506350	+	0.877024i	−0.999973	+	0.00734805i	$0.997661\pi$
$368$		0			0
$369$	−1089.00	−	1886.20i	−0.153634	−	0.266103i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−3175.00	−	5499.26i	−0.440738	−	0.763381i	0.557006	−	0.830508i	$-0.311950\pi$
$373$	−3175.00	−	5499.26i	−0.440738	−	0.763381i	−0.997744	+	0.0671276i	$0.978617\pi$
$374$		0			0
$375$	984.000	−	1704.34i	0.135503	−	0.234698i
$376$		0			0
$377$	4356.00			0.595081
$378$		0			0
$379$	−7900.00			−1.07070			−0.535351	−	0.844630i	$-0.679821\pi$
$379$	−7900.00			−1.07070			−0.535351	+	0.844630i	$0.679821\pi$
$380$		0			0
$381$	2816.00	−	4877.46i	0.378656	−	0.655852i
$382$		0			0
$383$	−5184.00	−	8978.95i	−0.691619	−	1.19792i	−0.971307	−	0.237828i	$-0.923564\pi$
$383$	−5184.00	−	8978.95i	−0.691619	−	1.19792i	0.279688	−	0.960091i	$-0.409769\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	286.000	+	495.367i	0.0375664	+	0.0650669i
$388$		0			0
$389$	−4415.00	+	7647.00i	−0.575448	+	0.996706i	0.420544	+	0.907272i	$0.361839\pi$
$389$	−4415.00	+	7647.00i	−0.575448	+	0.996706i	−0.995993	+	0.0894338i	$0.971494\pi$
$390$		0			0
$391$	−2800.00			−0.362154
$392$		0			0
$393$	10768.0			1.38212
$394$		0			0
$395$	−656.000	+	1136.23i	−0.0835619	+	0.144733i
$396$		0			0
$397$	−4939.00	−	8554.60i	−0.624386	−	1.08147i	−0.988659	−	0.150176i	$-0.952016\pi$
$397$	−4939.00	−	8554.60i	−0.624386	−	1.08147i	0.364273	−	0.931292i	$-0.381317\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6567.00	+	11374.4i	0.817806	+	1.41648i	0.907295	+	0.420494i	$0.138143\pi$
$401$	6567.00	+	11374.4i	0.817806	+	1.41648i	−0.0894889	+	0.995988i	$0.528523\pi$
$402$		0			0
$403$	1760.00	−	3048.41i	0.217548	−	0.376804i
$404$		0			0
$405$	622.000			0.0763146
$406$		0			0
$407$	7128.00			0.868113
$408$		0			0
$409$	−453.000	+	784.619i	−0.0547663	+	0.0948580i	−0.892109	−	0.451821i	$-0.850775\pi$
$409$	−453.000	+	784.619i	−0.0547663	+	0.0948580i	0.837343	+	0.546679i	$0.184108\pi$
$410$		0			0
$411$	3252.00	+	5632.63i	0.390290	+	0.676003i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	236.000	+	408.764i	0.0279151	+	0.0483504i
$416$		0			0
$417$	−1368.00	+	2369.45i	−0.160650	+	0.278255i
$418$		0			0
$419$	−5412.00			−0.631011			−0.315505	−	0.948924i	$-0.602174\pi$
$419$	−5412.00			−0.631011			−0.315505	+	0.948924i	$0.602174\pi$
$420$		0			0
$421$	−4642.00			−0.537381			−0.268690	−	0.963227i	$-0.586591\pi$
$421$	−4642.00			−0.537381			−0.268690	+	0.963227i	$0.586591\pi$
$422$		0			0
$423$	2904.00	−	5029.88i	0.333800	−	0.578158i
$424$		0			0
$425$	3025.00	+	5239.45i	0.345257	+	0.598002i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1936.00	−	3353.25i	−0.217881	−	0.377381i
$430$		0			0
$431$	−328.000	+	568.113i	−0.0366571	+	0.0634919i	−0.883772	−	0.467918i	$-0.845004\pi$
$431$	−328.000	+	568.113i	−0.0366571	+	0.0634919i	0.847115	+	0.531410i	$0.178338\pi$
$432$		0			0
$433$	9490.00			1.05326			0.526629	−	0.850096i	$-0.323456\pi$
$433$	9490.00			1.05326			0.526629	+	0.850096i	$0.323456\pi$
$434$		0			0
$435$	1584.00			0.174591
$436$		0			0
$437$	1232.00	−	2133.89i	0.134862	−	0.233587i
$438$		0			0
$439$	−2772.00	−	4801.24i	−0.301368	−	0.521984i	0.675078	−	0.737746i	$-0.264110\pi$
$439$	−2772.00	−	4801.24i	−0.301368	−	0.521984i	−0.976446	+	0.215762i	$0.930776\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3826.00	−	6626.83i	−0.410336	−	0.710722i	0.584591	−	0.811328i	$-0.301255\pi$
$443$	−3826.00	−	6626.83i	−0.410336	−	0.710722i	−0.994926	+	0.100606i	$0.967922\pi$
$444$		0			0
$445$	714.000	−	1236.68i	0.0760603	−	0.131740i
$446$		0			0
$447$	−1208.00			−0.127822
$448$		0			0
$449$	−446.000			−0.0468776			−0.0234388	−	0.999725i	$-0.507461\pi$
$449$	−446.000			−0.0468776			−0.0234388	+	0.999725i	$0.507461\pi$
$450$		0			0
$451$	−4356.00	+	7544.81i	−0.454803	+	0.787741i
$452$		0			0
$453$	2704.00	+	4683.47i	0.280453	+	0.485758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−781.000	−	1352.73i	−0.0799423	−	0.138464i	0.823283	−	0.567632i	$-0.192140\pi$
$457$	−781.000	−	1352.73i	−0.0799423	−	0.138464i	−0.903225	+	0.429168i	$0.858807\pi$
$458$		0			0
$459$	−3800.00	+	6581.79i	−0.386424	+	0.669307i
$460$		0			0
$461$	10582.0			1.06910			0.534548	−	0.845138i	$-0.320482\pi$
$461$	10582.0			1.06910			0.534548	+	0.845138i	$0.320482\pi$
$462$		0			0
$463$	−10768.0			−1.08085			−0.540423	−	0.841394i	$-0.681736\pi$
$463$	−10768.0			−1.08085			−0.540423	+	0.841394i	$0.681736\pi$
$464$		0			0
$465$	640.000	−	1108.51i	0.0638264	−	0.110551i
$466$		0			0
$467$	4938.00	+	8552.87i	0.489301	+	0.847494i	0.999924	−	0.0123108i	$-0.00391876\pi$
$467$	4938.00	+	8552.87i	0.489301	+	0.847494i	−0.510624	+	0.859804i	$0.670585\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6284.00	+	10884.2i	0.614759	+	1.06479i
$472$		0			0
$473$	1144.00	−	1981.47i	0.111208	−	0.192617i
$474$		0			0
$475$	−5324.00			−0.514278
$476$		0			0
$477$	2662.00			0.255523
$478$		0			0
$479$	176.000	−	304.841i	0.0167884	−	0.0290784i	−0.857509	−	0.514469i	$-0.827989\pi$
$479$	176.000	−	304.841i	0.0167884	−	0.0290784i	0.874298	+	0.485390i	$0.161323\pi$
$480$		0			0
$481$	1782.00	+	3086.51i	0.168924	+	0.292584i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−478.000	−	827.920i	−0.0447523	−	0.0775132i
$486$		0			0
$487$	7588.00	−	13142.8i	0.706047	−	1.22291i	−0.260265	−	0.965537i	$-0.583810\pi$
$487$	7588.00	−	13142.8i	0.706047	−	1.22291i	0.966312	−	0.257373i	$-0.0828568\pi$
$488$		0			0
$489$	−12144.0			−1.12305
$490$		0			0
$491$	−8844.00			−0.812880			−0.406440	−	0.913677i	$-0.633230\pi$
$491$	−8844.00			−0.812880			−0.406440	+	0.913677i	$0.633230\pi$
$492$		0			0
$493$	−4950.00	+	8573.65i	−0.452204	+	0.783241i
$494$		0			0
$495$	484.000	+	838.313i	0.0439478	+	0.0761199i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−9702.00	−	16804.4i	−0.870383	−	1.50755i	−0.861601	−	0.507586i	$-0.830538\pi$
$499$	−9702.00	−	16804.4i	−0.870383	−	1.50755i	−0.00878220	−	0.999961i	$-0.502795\pi$
$500$		0			0
$501$	−528.000	+	914.523i	−0.0470844	+	0.0815526i
$502$		0			0
$503$	16488.0			1.46156			0.730779	−	0.682614i	$-0.239157\pi$
$503$	16488.0			1.46156			0.730779	+	0.682614i	$0.239157\pi$
$504$		0			0
$505$	−3132.00			−0.275984
$506$		0			0
$507$	−3426.00	+	5934.01i	−0.300107	+	0.519800i
$508$		0			0
$509$	6477.00	+	11218.5i	0.564024	+	0.976917i	0.997140	+	0.0755793i	$0.0240806\pi$
$509$	6477.00	+	11218.5i	0.564024	+	0.976917i	−0.433116	+	0.901338i	$0.642586\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3344.00	−	5791.98i	−0.287800	−	0.498484i
$514$		0			0
$515$	−968.000	+	1676.63i	−0.0828256	+	0.143458i
$516$		0			0
$517$	−23232.0			−1.97629
$518$		0			0
$519$	11304.0			0.956051
$520$		0			0
$521$	−5485.00	+	9500.30i	−0.461233	+	0.798878i	−0.999023	−	0.0442004i	$-0.985926\pi$
$521$	−5485.00	+	9500.30i	−0.461233	+	0.798878i	0.537790	+	0.843079i	$0.319259\pi$
$522$		0			0
$523$	8470.00	+	14670.5i	0.708159	+	1.22657i	0.965539	+	0.260257i	$0.0838074\pi$
$523$	8470.00	+	14670.5i	0.708159	+	1.22657i	−0.257380	+	0.966310i	$0.582859\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4000.00	+	6928.20i	0.330631	+	0.572670i
$528$		0			0
$529$	4515.50	−	7821.08i	0.371127	−	0.642811i
$530$		0			0
$531$	7348.00			0.600520
$532$		0			0
$533$	−4356.00			−0.353995
$534$		0			0
$535$	−780.000	+	1351.00i	−0.0630324	+	0.109175i
$536$		0			0
$537$	6168.00	+	10683.3i	0.495659	+	0.858506i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−99.0000	−	171.473i	−0.00786755	−	0.0136270i	0.862065	−	0.506798i	$-0.169171\pi$
$541$	−99.0000	−	171.473i	−0.00786755	−	0.0136270i	−0.869932	+	0.493171i	$0.835838\pi$
$542$		0			0
$543$	−4836.00	+	8376.20i	−0.382196	+	0.661984i
$544$		0			0
$545$	3988.00			0.313444
$546$		0			0
$547$	−15268.0			−1.19344			−0.596721	−	0.802449i	$-0.703530\pi$
$547$	−15268.0			−1.19344			−0.596721	+	0.802449i	$0.703530\pi$
$548$		0			0
$549$	3025.00	−	5239.45i	0.235162	−	0.407312i
$550$		0			0
$551$	−4356.00	−	7544.81i	−0.336791	−	0.583339i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	648.000	+	1122.37i	0.0495605	+	0.0858413i
$556$		0			0
$557$	−10427.0	+	18060.1i	−0.793189	+	1.37384i	0.130794	+	0.991410i	$0.458247\pi$
$557$	−10427.0	+	18060.1i	−0.793189	+	1.37384i	−0.923983	+	0.382434i	$0.875086\pi$
$558$		0			0
$559$	1144.00			0.0865582
$560$		0			0
$561$	8800.00			0.662275
$562$		0			0
$563$	9658.00	−	16728.1i	0.722977	−	1.25223i	−0.236824	−	0.971553i	$-0.576106\pi$
$563$	9658.00	−	16728.1i	0.722977	−	1.25223i	0.959801	−	0.280681i	$-0.0905602\pi$
$564$		0			0
$565$	−942.000	−	1631.59i	−0.0701420	−	0.121490i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3509.00	−	6077.77i	−0.258532	−	0.447791i	0.707317	−	0.706897i	$-0.249906\pi$
$569$	−3509.00	−	6077.77i	−0.258532	−	0.447791i	−0.965849	+	0.259106i	$0.916572\pi$
$570$		0			0
$571$	−12210.0	+	21148.3i	−0.894873	+	1.54997i	−0.0609117	+	0.998143i	$0.519401\pi$
$571$	−12210.0	+	21148.3i	−0.894873	+	1.54997i	−0.833961	+	0.551823i	$0.813933\pi$
$572$		0			0
$573$	3840.00			0.279962
$574$		0			0
$575$	6776.00			0.491441
$576$		0			0
$577$	−11617.0	+	20121.2i	−0.838166	+	1.45175i	0.0532596	+	0.998581i	$0.483039\pi$
$577$	−11617.0	+	20121.2i	−0.838166	+	1.45175i	−0.891426	+	0.453166i	$0.850294\pi$
$578$		0			0
$579$	5764.00	+	9983.54i	0.413720	+	0.716583i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−5324.00	−	9221.44i	−0.378212	−	0.655082i
$584$		0			0
$585$	−242.000	+	419.156i	−0.0171034	+	0.0296239i
$586$		0			0
$587$	−10604.0			−0.745611			−0.372806	−	0.927909i	$-0.621604\pi$
$587$	−10604.0			−0.745611			−0.372806	+	0.927909i	$0.621604\pi$
$588$		0			0
$589$	−7040.00			−0.492493
$590$		0			0
$591$	2172.00	−	3762.01i	0.151175	−	0.261842i
$592$		0			0
$593$	6919.00	+	11984.1i	0.479139	+	0.829893i	0.999714	−	0.0239233i	$-0.00761574\pi$
$593$	6919.00	+	11984.1i	0.479139	+	0.829893i	−0.520575	+	0.853816i	$0.674282\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	176.000	+	304.841i	0.0120657	+	0.0208983i
$598$		0			0
$599$	1980.00	−	3429.46i	0.135059	−	0.233930i	−0.790561	−	0.612384i	$-0.790211\pi$
$599$	1980.00	−	3429.46i	0.135059	−	0.233930i	0.925620	+	0.378454i	$0.123544\pi$
$600$		0			0
$601$	−5942.00			−0.403293			−0.201647	−	0.979458i	$-0.564629\pi$
$601$	−5942.00			−0.403293			−0.201647	+	0.979458i	$0.564629\pi$
$602$		0			0
$603$	−2068.00			−0.139661
$604$		0			0
$605$	605.000	−	1047.89i	0.0406558	−	0.0704179i
$606$		0			0
$607$	1520.00	+	2632.72i	0.101639	+	0.176044i	0.912360	−	0.409389i	$-0.134258\pi$
$607$	1520.00	+	2632.72i	0.101639	+	0.176044i	−0.810721	+	0.585433i	$0.800925\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5808.00	−	10059.8i	−0.384561	−	0.666079i
$612$		0			0
$613$	1265.00	−	2191.04i	0.0833489	−	0.144365i	−0.821338	−	0.570442i	$-0.806772\pi$
$613$	1265.00	−	2191.04i	0.0833489	−	0.144365i	0.904686	+	0.426078i	$0.140105\pi$
$614$		0			0
$615$	−1584.00			−0.103859
$616$		0			0
$617$	−19206.0			−1.25317			−0.626584	−	0.779354i	$-0.715547\pi$
$617$	−19206.0			−1.25317			−0.626584	+	0.779354i	$0.715547\pi$
$618$		0			0
$619$	−5498.00	+	9522.82i	−0.357000	+	0.618343i	−0.987458	−	0.157881i	$-0.949534\pi$
$619$	−5498.00	+	9522.82i	−0.357000	+	0.618343i	0.630458	+	0.776224i	$0.282867\pi$
$620$		0			0
$621$	4256.00	+	7371.61i	0.275020	+	0.476349i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7070.50	−	12246.5i	−0.452512	−	0.783774i
$626$		0			0
$627$	−3872.00	+	6706.50i	−0.246623	+	0.427164i
$628$		0			0
$629$	−8100.00			−0.513463
$630$		0			0
$631$	−6680.00			−0.421437			−0.210718	−	0.977547i	$-0.567580\pi$
$631$	−6680.00			−0.421437			−0.210718	+	0.977547i	$0.567580\pi$
$632$		0			0
$633$	−6952.00	+	12041.2i	−0.436520	+	0.756075i
$634$		0			0
$635$	1408.00	+	2438.73i	0.0879918	+	0.152406i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4004.00	+	6935.13i	0.247881	+	0.429342i
$640$		0			0
$641$	−3137.00	+	5433.44i	−0.193298	+	0.334802i	−0.946341	−	0.323169i	$-0.895252\pi$
$641$	−3137.00	+	5433.44i	−0.193298	+	0.334802i	0.753043	+	0.657971i	$0.228585\pi$
$642$		0			0
$643$	9084.00			0.557135			0.278568	−	0.960417i	$-0.410140\pi$
$643$	9084.00			0.557135			0.278568	+	0.960417i	$0.410140\pi$
$644$		0			0
$645$	416.000			0.0253953
$646$		0			0
$647$	11828.0	−	20486.7i	0.718712	−	1.24485i	−0.242798	−	0.970077i	$-0.578065\pi$
$647$	11828.0	−	20486.7i	0.718712	−	1.24485i	0.961510	−	0.274769i	$-0.0886013\pi$
$648$		0			0
$649$	−14696.0	−	25454.2i	−0.888857	−	1.53955i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3381.00	+	5856.06i	0.202617	+	0.350943i	0.949371	−	0.314158i	$-0.101722\pi$
$653$	3381.00	+	5856.06i	0.202617	+	0.350943i	−0.746754	+	0.665100i	$0.768389\pi$
$654$		0			0
$655$	−2692.00	+	4662.68i	−0.160588	+	0.278147i
$656$		0			0
$657$	−1694.00			−0.100592
$658$		0			0
$659$	15276.0			0.902987			0.451494	−	0.892274i	$-0.350891\pi$
$659$	15276.0			0.902987			0.451494	+	0.892274i	$0.350891\pi$
$660$		0			0
$661$	−5527.00	+	9573.04i	−0.325228	+	0.563311i	−0.981558	−	0.191163i	$-0.938774\pi$
$661$	−5527.00	+	9573.04i	−0.325228	+	0.563311i	0.656331	+	0.754473i	$0.272108\pi$
$662$		0			0
$663$	2200.00	+	3810.51i	0.128870	+	0.223210i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5544.00	+	9602.49i	0.321836	+	0.557436i
$668$		0			0
$669$	1856.00	−	3214.69i	0.107260	−	0.185780i
$670$		0			0
$671$	−24200.0			−1.39230
$672$		0			0
$673$	−21278.0			−1.21873			−0.609366	−	0.792889i	$-0.708576\pi$
$673$	−21278.0			−1.21873			−0.609366	+	0.792889i	$0.708576\pi$
$674$		0			0
$675$	9196.00	−	15927.9i	0.524377	−	0.908247i
$676$		0			0
$677$	−4463.00	−	7730.14i	−0.253363	−	0.438838i	0.711086	−	0.703105i	$-0.248204\pi$
$677$	−4463.00	−	7730.14i	−0.253363	−	0.438838i	−0.964450	+	0.264266i	$0.914870\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	312.000	+	540.400i	0.0175563	+	0.0304085i
$682$		0			0
$683$	−4058.00	+	7028.66i	−0.227343	+	0.393769i	−0.957020	−	0.290023i	$-0.906337\pi$
$683$	−4058.00	+	7028.66i	−0.227343	+	0.393769i	0.729677	+	0.683792i	$0.239670\pi$
$684$		0			0
$685$	−3252.00			−0.181391
$686$		0			0
$687$	6536.00			0.362975
$688$		0			0
$689$	2662.00	−	4610.72i	0.147190	−	0.254941i
$690$		0			0
$691$	5882.00	+	10187.9i	0.323823	+	0.560878i	0.981273	−	0.192620i	$-0.0616984\pi$
$691$	5882.00	+	10187.9i	0.323823	+	0.560878i	−0.657450	+	0.753498i	$0.728365\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−684.000	−	1184.72i	−0.0373318	−	0.0646606i
$696$		0			0
$697$	4950.00	−	8573.65i	0.269002	−	0.465926i
$698$		0			0
$699$	3608.00			0.195232
$700$		0			0
$701$	−4698.00			−0.253126			−0.126563	−	0.991959i	$-0.540395\pi$
$701$	−4698.00			−0.253126			−0.126563	+	0.991959i	$0.540395\pi$
$702$		0			0
$703$	3564.00	−	6173.03i	0.191207	−	0.331181i
$704$		0			0
$705$	−2112.00	−	3658.09i	−0.112826	−	0.195421i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−12319.0	−	21337.1i	−0.652538	−	1.13023i	−0.982505	−	0.186237i	$-0.940371\pi$
$709$	−12319.0	−	21337.1i	−0.652538	−	1.13023i	0.329966	−	0.943993i	$-0.392963\pi$
$710$		0			0
$711$	−3608.00	+	6249.24i	−0.190310	+	0.329627i
$712$		0			0
$713$	8960.00			0.470624
$714$		0			0
$715$	1936.00			0.101262
$716$		0			0
$717$	3232.00	−	5597.99i	0.168342	−	0.291577i
$718$		0			0
$719$	−8312.00	−	14396.8i	−0.431134	−	0.746746i	0.565837	−	0.824517i	$-0.308553\pi$
$719$	−8312.00	−	14396.8i	−0.431134	−	0.746746i	−0.996971	+	0.0777710i	$0.975220\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9636.00	+	16690.0i	0.495666	+	0.858519i
$724$		0			0
$725$	11979.0	−	20748.2i	0.613640	−	1.06286i
$726$		0			0
$727$	30216.0			1.54147			0.770735	−	0.637155i	$-0.219889\pi$
$727$	30216.0			1.54147			0.770735	+	0.637155i	$0.219889\pi$
$728$		0			0
$729$	19837.0			1.00782
$730$		0			0
$731$	−1300.00	+	2251.67i	−0.0657760	+	0.113927i
$732$		0			0
$733$	1661.00	+	2876.94i	0.0836977	+	0.144969i	0.904836	−	0.425761i	$-0.139994\pi$
$733$	1661.00	+	2876.94i	0.0836977	+	0.144969i	−0.821138	+	0.570730i	$0.806660\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4136.00	+	7163.76i	0.206718	+	0.358047i
$738$		0			0
$739$	7346.00	−	12723.6i	0.365666	−	0.633352i	−0.623217	−	0.782049i	$-0.714175\pi$
$739$	7346.00	−	12723.6i	0.365666	−	0.633352i	0.988883	+	0.148697i	$0.0475080\pi$
$740$		0			0
$741$	−3872.00			−0.191959
$742$		0			0
$743$	28600.0			1.41216			0.706078	−	0.708134i	$-0.250463\pi$
$743$	28600.0			1.41216			0.706078	+	0.708134i	$0.250463\pi$
$744$		0			0
$745$	302.000	−	523.079i	0.0148516	−	0.0257237i
$746$		0			0
$747$	1298.00	+	2248.20i	0.0635761	+	0.110117i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	14808.0	+	25648.2i	0.719509	+	1.24623i	0.961194	+	0.275872i	$0.0889666\pi$
$751$	14808.0	+	25648.2i	0.719509	+	1.24623i	−0.241685	+	0.970355i	$0.577700\pi$
$752$		0			0
$753$	−4280.00	+	7413.18i	−0.207134	+	0.358767i
$754$		0			0
$755$	−2704.00			−0.130343
$756$		0			0
$757$	2894.00			0.138949			0.0694744	−	0.997584i	$-0.477868\pi$
$757$	2894.00			0.138949			0.0694744	+	0.997584i	$0.477868\pi$
$758$		0			0
$759$	4928.00	−	8535.55i	0.235672	−	0.408196i
$760$		0			0
$761$	−7381.00	−	12784.3i	−0.351591	−	0.608974i	0.634937	−	0.772564i	$-0.281026\pi$
$761$	−7381.00	−	12784.3i	−0.351591	−	0.608974i	−0.986528	+	0.163590i	$0.947693\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−550.000	−	952.628i	−0.0259938	−	0.0450227i
$766$		0			0
$767$	7348.00	−	12727.1i	0.345920	−	0.599152i
$768$		0			0
$769$	−7678.00			−0.360047			−0.180023	−	0.983662i	$-0.557617\pi$
$769$	−7678.00			−0.360047			−0.180023	+	0.983662i	$0.557617\pi$
$770$		0			0
$771$	−3080.00			−0.143870
$772$		0			0
$773$	−13695.0	+	23720.4i	−0.637225	+	1.10371i	0.348814	+	0.937192i	$0.386584\pi$
$773$	−13695.0	+	23720.4i	−0.637225	+	1.10371i	−0.986039	+	0.166514i	$0.946749\pi$
$774$		0			0
$775$	−9680.00	−	16766.3i	−0.448666	−	0.777112i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4356.00	+	7544.81i	0.200346	+	0.347010i
$780$		0			0
$781$	16016.0	−	27740.5i	0.733800	−	1.27098i
$782$		0			0
$783$	30096.0			1.37362
$784$		0			0
$785$	−6284.00			−0.285714
$786$		0			0
$787$	−9878.00	+	17109.2i	−0.447411	+	0.774939i	−0.998217	−	0.0596946i	$-0.980987\pi$
$787$	−9878.00	+	17109.2i	−0.447411	+	0.774939i	0.550805	+	0.834634i	$0.314321\pi$
$788$		0			0
$789$	−14800.0	−	25634.4i	−0.667800	−	1.15666i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6050.00	−	10478.9i	−0.270923	−	0.469252i
$794$		0			0
$795$	968.000	−	1676.63i	0.0431842	−	0.0747972i
$796$		0			0
$797$	38854.0			1.72682			0.863412	−	0.504499i	$-0.168323\pi$
$797$	38854.0			1.72682			0.863412	+	0.504499i	$0.168323\pi$
$798$		0			0
$799$	26400.0			1.16892
$800$		0			0
$801$	3927.00	−	6801.76i	0.173226	−	0.300036i
$802$		0			0
$803$	3388.00	+	5868.19i	0.148892	+	0.257888i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5588.00	−	9678.70i	−0.243751	−	0.422189i
$808$		0			0
$809$	7139.00	−	12365.1i	0.310252	−	0.537372i	−0.668165	−	0.744013i	$-0.732920\pi$
$809$	7139.00	−	12365.1i	0.310252	−	0.537372i	0.978417	+	0.206641i	$0.0662532\pi$
$810$		0			0
$811$	−716.000			−0.0310014			−0.0155007	−	0.999880i	$-0.504934\pi$
$811$	−716.000			−0.0310014			−0.0155007	+	0.999880i	$0.504934\pi$
$812$		0			0
$813$	−34496.0			−1.48810
$814$		0			0
$815$	3036.00	−	5258.51i	0.130486	−	0.226009i
$816$		0			0
$817$	−1144.00	−	1981.47i	−0.0489884	−	0.0848503i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11769.0	+	20384.5i	0.500293	+	0.866534i	1.00000		0.000338894i	$0.000107873\pi$
$821$	11769.0	+	20384.5i	0.500293	+	0.866534i	−0.499706	+	0.866195i	$0.666559\pi$
$822$		0			0
$823$	3308.00	−	5729.62i	0.140109	−	0.242676i	−0.787429	−	0.616406i	$-0.788588\pi$
$823$	3308.00	−	5729.62i	0.140109	−	0.242676i	0.927537	+	0.373730i	$0.121921\pi$
$824$		0			0
$825$	−21296.0			−0.898705
$826$		0			0
$827$	27236.0			1.14521			0.572605	−	0.819831i	$-0.305933\pi$
$827$	27236.0			1.14521			0.572605	+	0.819831i	$0.305933\pi$
$828$		0			0
$829$	−6035.00	+	10452.9i	−0.252840	+	0.437931i	−0.964307	−	0.264788i	$-0.914698\pi$
$829$	−6035.00	+	10452.9i	−0.252840	+	0.437931i	0.711467	+	0.702720i	$0.248031\pi$
$830$		0			0
$831$	−3748.00	−	6491.73i	−0.156458	−	0.270993i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−264.000	−	457.261i	−0.0109414	−	0.0189511i
$836$		0			0
$837$	12160.0	−	21061.7i	0.502164	−	0.869773i
$838$		0			0
$839$	−42024.0			−1.72924			−0.864618	−	0.502429i	$-0.832440\pi$
$839$	−42024.0			−1.72924			−0.864618	+	0.502429i	$0.832440\pi$
$840$		0			0
$841$	14815.0			0.607446
$842$		0			0
$843$	6676.00	−	11563.2i	0.272756	−	0.472428i
$844$		0			0
$845$	−1713.00	−	2967.00i	−0.0697385	−	0.120791i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	14344.0	+	24844.5i	0.579841	+	1.00431i
$850$		0			0
$851$	−4536.00	+	7856.58i	−0.182717	+	0.316475i
$852$		0			0
$853$	2414.00			0.0968978			0.0484489	−	0.998826i	$-0.484572\pi$
$853$	2414.00			0.0968978			0.0484489	+	0.998826i	$0.484572\pi$
$854$		0			0
$855$	968.000			0.0387192
$856$		0			0
$857$	18843.0	−	32637.0i	0.751067	−	1.30089i	−0.196239	−	0.980556i	$-0.562873\pi$
$857$	18843.0	−	32637.0i	0.751067	−	1.30089i	0.947306	−	0.320330i	$-0.103794\pi$
$858$		0			0
$859$	−20322.0	−	35198.7i	−0.807192	−	1.39810i	−0.914801	−	0.403904i	$-0.867653\pi$
$859$	−20322.0	−	35198.7i	−0.807192	−	1.39810i	0.107610	−	0.994193i	$-0.465680\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9328.00	+	16156.6i	0.367936	+	0.637284i	0.989243	−	0.146284i	$-0.0467312\pi$
$863$	9328.00	+	16156.6i	0.367936	+	0.637284i	−0.621307	+	0.783568i	$0.713398\pi$
$864$		0			0
$865$	−2826.00	+	4894.78i	−0.111083	+	0.192402i
$866$		0			0
$867$	9652.00			0.378084
$868$		0			0
$869$	28864.0			1.12675
$870$		0			0
$871$	−2068.00	+	3581.88i	−0.0804495	+	0.139343i
$872$		0			0
$873$	−2629.00	−	4553.56i	−0.101922	−	0.176535i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6501.00	+	11260.1i	0.250311	+	0.433552i	0.963612	−	0.267307i	$-0.0861336\pi$
$877$	6501.00	+	11260.1i	0.250311	+	0.433552i	−0.713300	+	0.700859i	$0.752800\pi$
$878$		0			0
$879$	10428.0	−	18061.8i	0.400145	−	0.693072i
$880$		0			0
$881$	49490.0			1.89258			0.946289	−	0.323323i	$-0.104800\pi$
$881$	49490.0			1.89258			0.946289	+	0.323323i	$0.104800\pi$
$882$		0			0
$883$	1100.00			0.0419229			0.0209615	−	0.999780i	$-0.493327\pi$
$883$	1100.00			0.0419229			0.0209615	+	0.999780i	$0.493327\pi$
$884$		0			0
$885$	2672.00	−	4628.04i	0.101490	−	0.175785i
$886$		0			0
$887$	7052.00	+	12214.4i	0.266948	+	0.462368i	0.968072	−	0.250672i	$-0.0806514\pi$
$887$	7052.00	+	12214.4i	0.266948	+	0.462368i	−0.701124	+	0.713039i	$0.747318\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6842.00	−	11850.7i	−0.257257	−	0.445581i
$892$		0			0
$893$	−11616.0	+	20119.5i	−0.435291	+	0.753946i
$894$		0			0
$895$	−6168.00			−0.230361
$896$		0			0
$897$	4928.00			0.183435
$898$		0			0
$899$	15840.0	−	27435.7i	0.587646	−	1.01783i
$900$		0			0
$901$	6050.00	+	10478.9i	0.223701	+	0.387462i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2418.00	−	4188.10i	−0.0888144	−	0.153831i
$906$		0			0
$907$	6358.00	−	11012.4i	0.232761	−	0.403153i	−0.725859	−	0.687844i	$-0.758557\pi$
$907$	6358.00	−	11012.4i	0.232761	−	0.403153i	0.958620	+	0.284690i	$0.0918908\pi$
$908$		0			0
$909$	−17226.0			−0.628548
$910$		0			0
$911$	−39632.0			−1.44135			−0.720673	−	0.693275i	$-0.756167\pi$
$911$	−39632.0			−1.44135			−0.720673	+	0.693275i	$0.756167\pi$
$912$		0			0
$913$	5192.00	−	8992.81i	0.188204	−	0.325979i
$914$		0			0
$915$	−2200.00	−	3810.51i	−0.0794861	−	0.137674i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−2852.00	−	4939.81i	−0.102371	−	0.177311i	0.810290	−	0.586029i	$-0.199310\pi$
$919$	−2852.00	−	4939.81i	−0.102371	−	0.177311i	−0.912661	+	0.408717i	$0.865976\pi$
$920$		0			0
$921$	792.000	−	1371.78i	0.0283358	−	0.0490791i
$922$		0			0
$923$	16016.0			0.571152
$924$		0			0
$925$	19602.0			0.696767
$926$		0			0
$927$	−5324.00	+	9221.44i	−0.188633	+	0.326723i
$928$		0			0
$929$	−4081.00	−	7068.50i	−0.144126	−	0.249634i	0.784920	−	0.619597i	$-0.212704\pi$
$929$	−4081.00	−	7068.50i	−0.144126	−	0.249634i	−0.929047	+	0.369963i	$0.879370\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−8112.00	−	14050.4i	−0.284646	−	0.493022i
$934$		0			0
$935$	−2200.00	+	3810.51i	−0.0769494	+	0.133280i
$936$		0			0
$937$	−55110.0			−1.92141			−0.960707	−	0.277564i	$-0.910473\pi$
$937$	−55110.0			−1.92141			−0.960707	+	0.277564i	$0.910473\pi$
$938$		0			0
$939$	−8616.00			−0.299438
$940$		0			0
$941$	−8187.00	+	14180.3i	−0.283622	+	0.491248i	−0.972274	−	0.233844i	$-0.924870\pi$
$941$	−8187.00	+	14180.3i	−0.283622	+	0.491248i	0.688652	+	0.725092i	$0.258203\pi$
$942$		0			0
$943$	−5544.00	−	9602.49i	−0.191450	−	0.331601i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4230.00	−	7326.57i	−0.145149	−	0.251406i	0.784279	−	0.620408i	$-0.213033\pi$
$947$	−4230.00	−	7326.57i	−0.145149	−	0.251406i	−0.929429	+	0.369002i	$0.879700\pi$
$948$		0			0
$949$	−1694.00	+	2934.09i	−0.0579447	+	0.100363i
$950$		0			0
$951$	29544.0			1.00739
$952$		0			0
$953$	−20502.0			−0.696878			−0.348439	−	0.937331i	$-0.613288\pi$
$953$	−20502.0			−0.696878			−0.348439	+	0.937331i	$0.613288\pi$
$954$		0			0
$955$	−960.000	+	1662.77i	−0.0325287	+	0.0563413i
$956$		0			0
$957$	−17424.0	−	30179.3i	−0.588545	−	1.01939i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2095.50	+	3629.51i	0.0703400	+	0.121833i
$962$		0			0
$963$	−4290.00	+	7430.50i	−0.143555	+	0.248644i
$964$		0			0
$965$	−5764.00			−0.192280
$966$		0			0
$967$	−36520.0			−1.21448			−0.607241	−	0.794518i	$-0.707724\pi$
$967$	−36520.0			−1.21448			−0.607241	+	0.794518i	$0.707724\pi$
$968$		0			0
$969$	4400.00	−	7621.02i	0.145870	−	0.252655i
$970$		0			0
$971$	−10122.0	−	17531.8i	−0.334532	−	0.579426i	0.648863	−	0.760905i	$-0.275245\pi$
$971$	−10122.0	−	17531.8i	−0.334532	−	0.579426i	−0.983395	+	0.181479i	$0.941912\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5324.00	−	9221.44i	−0.174876	−	0.302895i
$976$		0			0
$977$	−25017.0	+	43330.7i	−0.819206	+	1.41891i	0.0870612	+	0.996203i	$0.472252\pi$
$977$	−25017.0	+	43330.7i	−0.819206	+	1.41891i	−0.906268	+	0.422704i	$0.861081\pi$
$978$		0			0
$979$	−31416.0			−1.02560
$980$		0			0
$981$	21934.0			0.713862
$982$		0			0
$983$	−18564.0	+	32153.8i	−0.602339	+	1.04328i	0.390126	+	0.920761i	$0.372431\pi$
$983$	−18564.0	+	32153.8i	−0.602339	+	1.04328i	−0.992466	+	0.122521i	$0.960902\pi$
$984$		0			0
$985$	1086.00	+	1881.01i	0.0351298	+	0.0608466i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1456.00	+	2521.87i	0.0468131	+	0.0810826i
$990$		0			0
$991$	−13904.0	+	24082.4i	−0.445686	+	0.771951i	−0.998100	−	0.0616190i	$-0.980374\pi$
$991$	−13904.0	+	24082.4i	−0.445686	+	0.771951i	0.552413	+	0.833570i	$0.313707\pi$
$992$		0			0
$993$	4528.00			0.144705
$994$		0			0
$995$	−176.000			−0.00560761
$996$		0			0
$997$	14257.0	−	24693.8i	0.452882	−	0.784415i	−0.545681	−	0.837993i	$-0.683729\pi$
$997$	14257.0	−	24693.8i	0.452882	−	0.784415i	0.998564	+	0.0535775i	$0.0170624\pi$
$998$		0			0
$999$	12312.0	+	21325.0i	0.389924	+	0.675369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.4.i.g.361.1		2
7.2	even	3	inner	392.4.i.g.177.1		2
7.3	odd	6		392.4.a.e.1.1		1
7.4	even	3		8.4.a.a.1.1	✓	1
7.5	odd	6		392.4.i.b.177.1		2
7.6	odd	2		392.4.i.b.361.1		2
21.11	odd	6		72.4.a.c.1.1		1
28.3	even	6		784.4.a.e.1.1		1
28.11	odd	6		16.4.a.a.1.1		1
35.4	even	6		200.4.a.g.1.1		1
35.18	odd	12		200.4.c.e.49.1		2
35.32	odd	12		200.4.c.e.49.2		2
56.11	odd	6		64.4.a.b.1.1		1
56.53	even	6		64.4.a.d.1.1		1
63.4	even	3		648.4.i.h.217.1		2
63.11	odd	6		648.4.i.e.433.1		2
63.25	even	3		648.4.i.h.433.1		2
63.32	odd	6		648.4.i.e.217.1		2
77.32	odd	6		968.4.a.a.1.1		1
84.11	even	6		144.4.a.e.1.1		1
91.25	even	6		1352.4.a.a.1.1		1
105.32	even	12		1800.4.f.u.649.2		2
105.53	even	12		1800.4.f.u.649.1		2
105.74	odd	6		1800.4.a.d.1.1		1
112.11	odd	12		256.4.b.g.129.1		2
112.53	even	12		256.4.b.a.129.2		2
112.67	odd	12		256.4.b.g.129.2		2
112.109	even	12		256.4.b.a.129.1		2
119.67	even	6		2312.4.a.a.1.1		1
140.39	odd	6		400.4.a.g.1.1		1
140.67	even	12		400.4.c.i.49.1		2
140.123	even	12		400.4.c.i.49.2		2
168.11	even	6		576.4.a.j.1.1		1
168.53	odd	6		576.4.a.k.1.1		1
280.109	even	6		1600.4.a.o.1.1		1
280.179	odd	6		1600.4.a.bm.1.1		1
308.263	even	6		1936.4.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.4.a.a.1.1	✓	1	7.4	even	3
16.4.a.a.1.1		1	28.11	odd	6
64.4.a.b.1.1		1	56.11	odd	6
64.4.a.d.1.1		1	56.53	even	6
72.4.a.c.1.1		1	21.11	odd	6
144.4.a.e.1.1		1	84.11	even	6
200.4.a.g.1.1		1	35.4	even	6
200.4.c.e.49.1		2	35.18	odd	12
200.4.c.e.49.2		2	35.32	odd	12
256.4.b.a.129.1		2	112.109	even	12
256.4.b.a.129.2		2	112.53	even	12
256.4.b.g.129.1		2	112.11	odd	12
256.4.b.g.129.2		2	112.67	odd	12
392.4.a.e.1.1		1	7.3	odd	6
392.4.i.b.177.1		2	7.5	odd	6
392.4.i.b.361.1		2	7.6	odd	2
392.4.i.g.177.1		2	7.2	even	3	inner
392.4.i.g.361.1		2	1.1	even	1	trivial
400.4.a.g.1.1		1	140.39	odd	6
400.4.c.i.49.1		2	140.67	even	12
400.4.c.i.49.2		2	140.123	even	12
576.4.a.j.1.1		1	168.11	even	6
576.4.a.k.1.1		1	168.53	odd	6
648.4.i.e.217.1		2	63.32	odd	6
648.4.i.e.433.1		2	63.11	odd	6
648.4.i.h.217.1		2	63.4	even	3
648.4.i.h.433.1		2	63.25	even	3
784.4.a.e.1.1		1	28.3	even	6
968.4.a.a.1.1		1	77.32	odd	6
1352.4.a.a.1.1		1	91.25	even	6
1600.4.a.o.1.1		1	280.109	even	6
1600.4.a.bm.1.1		1	280.179	odd	6
1800.4.a.d.1.1		1	105.74	odd	6
1800.4.f.u.649.1		2	105.53	even	12
1800.4.f.u.649.2		2	105.32	even	12
1936.4.a.l.1.1		1	308.263	even	6
2312.4.a.a.1.1		1	119.67	even	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	392.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{3} +(1.00000 + 1.73205i) q^{5} +(5.50000 + 9.52628i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{3} +(1.00000 + 1.73205i) q^{5} +(5.50000 + 9.52628i) q^{9} +(22.0000 - 38.1051i) q^{11} +22.0000 q^{13} +8.00000 q^{15} +(-25.0000 + 43.3013i) q^{17} +(-22.0000 - 38.1051i) q^{19} +(28.0000 + 48.4974i) q^{23} +(60.5000 - 104.789i) q^{25} +152.000 q^{27} +198.000 q^{29} +(80.0000 - 138.564i) q^{31} +(-88.0000 - 152.420i) q^{33} +(81.0000 + 140.296i) q^{37} +(44.0000 - 76.2102i) q^{39} -198.000 q^{41} +52.0000 q^{43} +(-11.0000 + 19.0526i) q^{45} +(-264.000 - 457.261i) q^{47} +(100.000 + 173.205i) q^{51} +(121.000 - 209.578i) q^{53} +88.0000 q^{55} -176.000 q^{57} +(334.000 - 578.505i) q^{59} +(-275.000 - 476.314i) q^{61} +(22.0000 + 38.1051i) q^{65} +(-94.0000 + 162.813i) q^{67} +224.000 q^{69} +728.000 q^{71} +(-77.0000 + 133.368i) q^{73} +(-242.000 - 419.156i) q^{75} +(328.000 + 568.113i) q^{79} +(155.500 - 269.334i) q^{81} +236.000 q^{83} -100.000 q^{85} +(396.000 - 685.892i) q^{87} +(-357.000 - 618.342i) q^{89} +(-320.000 - 554.256i) q^{93} +(44.0000 - 76.2102i) q^{95} -478.000 q^{97} +484.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 2 q^{5} + 11 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 + 2 * q^5 + 11 * q^9	\( 2 q + 4 q^{3} + 2 q^{5} + 11 q^{9} + 44 q^{11} + 44 q^{13} + 16 q^{15} - 50 q^{17} - 44 q^{19} + 56 q^{23} + 121 q^{25} + 304 q^{27} + 396 q^{29} + 160 q^{31} - 176 q^{33} + 162 q^{37} + 88 q^{39} - 396 q^{41} + 104 q^{43} - 22 q^{45} - 528 q^{47} + 200 q^{51} + 242 q^{53} + 176 q^{55} - 352 q^{57} + 668 q^{59} - 550 q^{61} + 44 q^{65} - 188 q^{67} + 448 q^{69} + 1456 q^{71} - 154 q^{73} - 484 q^{75} + 656 q^{79} + 311 q^{81} + 472 q^{83} - 200 q^{85} + 792 q^{87} - 714 q^{89} - 640 q^{93} + 88 q^{95} - 956 q^{97} + 968 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 2 * q^5 + 11 * q^9 + 44 * q^11 + 44 * q^13 + 16 * q^15 - 50 * q^17 - 44 * q^19 + 56 * q^23 + 121 * q^25 + 304 * q^27 + 396 * q^29 + 160 * q^31 - 176 * q^33 + 162 * q^37 + 88 * q^39 - 396 * q^41 + 104 * q^43 - 22 * q^45 - 528 * q^47 + 200 * q^51 + 242 * q^53 + 176 * q^55 - 352 * q^57 + 668 * q^59 - 550 * q^61 + 44 * q^65 - 188 * q^67 + 448 * q^69 + 1456 * q^71 - 154 * q^73 - 484 * q^75 + 656 * q^79 + 311 * q^81 + 472 * q^83 - 200 * q^85 + 792 * q^87 - 714 * q^89 - 640 * q^93 + 88 * q^95 - 956 * q^97 + 968 * q^99

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