LMFDB - Embedded newform 392.4.i.g.177.1

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			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	392.177
Dual form			392.4.i.g.361.1

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.00000	+	3.46410i	0.384900	+	0.666667i	0.991755	−	0.128146i	$-0.0409025\pi$
$3$	2.00000	+	3.46410i	0.384900	+	0.666667i	−0.606855	+	0.794812i	$0.707569\pi$
$4$		0			0
$5$	1.00000	−	1.73205i	0.0894427	−	0.154919i	−0.817833	−	0.575456i	$-0.804825\pi$
$5$	1.00000	−	1.73205i	0.0894427	−	0.154919i	0.907276	+	0.420536i	$0.138158\pi$
$6$		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	0.992361	+	0.123371i	$0.0393705\pi$
$11$	22.0000	+	38.1051i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		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	0.630732	−	0.776001i	$-0.282755\pi$
$17$	−25.0000	−	43.3013i	−0.356670	−	0.617771i	−0.987402	+	0.158230i	$0.949421\pi$
$18$		0			0
$19$	−22.0000	+	38.1051i	−0.265639	+	0.460101i	−0.967731	−	0.251986i	$-0.918916\pi$
$19$	−22.0000	+	38.1051i	−0.265639	+	0.460101i	0.702092	+	0.712087i	$0.252250\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	28.0000	−	48.4974i	0.253844	−	0.439670i	−0.710737	−	0.703458i	$-0.751638\pi$
$23$	28.0000	−	48.4974i	0.253844	−	0.439670i	0.964581	+	0.263788i	$0.0849718\pi$
$24$		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	0.999132	−	0.0416484i	$-0.0132609\pi$
$31$	80.0000	+	138.564i	0.463498	+	0.802801i	−0.535635	+	0.844450i	$0.679928\pi$
$32$		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	−0.628043	−	0.778178i	$-0.716144\pi$
$37$	81.0000	−	140.296i	0.359900	−	0.623366i	0.987944	+	0.154812i	$0.0494773\pi$
$38$		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	0.0868522	+	0.996221i	$0.472319\pi$
$47$	−264.000	+	457.261i	−0.819327	+	1.41912i	−0.906179	+	0.422894i	$0.861014\pi$
$48$		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	0.979138	−	0.203195i	$-0.0651327\pi$
$53$	121.000	+	209.578i	0.313597	+	0.543166i	−0.665541	+	0.746361i	$0.731799\pi$
$54$		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	0.953840	+	0.300317i	$0.0970924\pi$
$59$	334.000	+	578.505i	0.737002	+	1.27652i	−0.216838	+	0.976208i	$0.569574\pi$
$60$		0			0
$61$	−275.000	+	476.314i	−0.577215	+	0.999766i	0.418582	+	0.908179i	$0.362527\pi$
$61$	−275.000	+	476.314i	−0.577215	+	0.999766i	−0.995797	+	0.0915873i	$0.970806\pi$
$62$		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	0.767508	−	0.641039i	$-0.221496\pi$
$67$	−94.0000	−	162.813i	−0.171402	−	0.296877i	−0.938910	+	0.344162i	$0.888163\pi$
$68$		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	0.797673	−	0.603090i	$-0.206064\pi$
$73$	−77.0000	−	133.368i	−0.123454	−	0.213829i	−0.921128	+	0.389261i	$0.872731\pi$
$74$		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	−0.532170	−	0.846638i	$-0.678623\pi$
$79$	328.000	−	568.113i	0.467125	−	0.809084i	0.999295	+	0.0375534i	$0.0119564\pi$
$80$		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	−0.996438	−	0.0843265i	$-0.973126\pi$
$89$	−357.000	+	618.342i	−0.425190	+	0.736451i	0.571248	+	0.820778i	$0.306459\pi$
$90$		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	−0.936796	−	0.349877i	$-0.886223\pi$
$101$	−783.000	−	1356.20i	−0.771400	−	1.33610i	0.165396	−	0.986227i	$-0.447110\pi$
$102$		0			0
$103$	484.000	−	838.313i	0.463009	−	0.801955i	−0.536100	−	0.844154i	$-0.680103\pi$
$103$	484.000	−	838.313i	0.463009	−	0.801955i	0.999109	+	0.0421991i	$0.0134364\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	390.000	−	675.500i	0.352362	−	0.610309i	−0.634301	−	0.773086i	$-0.718712\pi$
$107$	390.000	−	675.500i	0.352362	−	0.610309i	0.986663	+	0.162778i	$0.0520453\pi$
$108$		0			0
$109$	997.000	+	1726.85i	0.876103	+	1.51746i	0.855583	+	0.517666i	$0.173199\pi$
$109$	997.000	+	1726.85i	0.876103	+	1.51746i	0.0205209	+	0.999789i	$0.493468\pi$
$110$		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	0.0673052	−	0.997732i	$-0.478560\pi$
$131$	1346.00	−	2331.34i	0.897714	−	1.55489i	0.830409	−	0.557154i	$-0.188107\pi$
$132$		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	−0.999967	−	0.00810420i	$-0.997420\pi$
$137$	−813.000	−	1408.16i	−0.507002	−	0.878153i	0.492965	−	0.870049i	$-0.335913\pi$
$138$		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	−0.904547	−	0.426374i	$-0.859791\pi$
$149$	−151.000	+	261.540i	−0.0830228	+	0.143800i	0.821524	+	0.570174i	$0.193124\pi$
$150$		0			0
$151$	−676.000	−	1170.87i	−0.364319	−	0.631018i	0.624348	−	0.781146i	$-0.285365\pi$
$151$	−676.000	−	1170.87i	−0.364319	−	0.631018i	−0.988667	+	0.150128i	$0.952031\pi$
$152$		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	−0.920531	−	0.390670i	$-0.872244\pi$
$157$	−1571.00	−	2721.05i	−0.798595	−	1.38321i	0.121936	−	0.992538i	$-0.461090\pi$
$158$		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	0.227678	+	0.973736i	$0.426887\pi$
$163$	−1518.00	+	2629.25i	−0.729441	+	1.26343i	−0.957120	+	0.289693i	$0.906447\pi$
$164$		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	−0.368331	−	0.929695i	$-0.620071\pi$
$173$	1413.00	−	2447.39i	0.620973	−	1.07556i	0.989305	−	0.145863i	$-0.0465959\pi$
$174$		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	−0.984559	−	0.175053i	$-0.943990\pi$
$179$	−1542.00	−	2670.82i	−0.643880	−	1.11523i	0.340679	−	0.940180i	$-0.389343\pi$
$180$		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	−0.760667	−	0.649143i	$-0.775128\pi$
$191$	480.000	−	831.384i	0.181841	−	0.314957i	0.942507	+	0.334185i	$0.108461\pi$
$192$		0			0
$193$	−1441.00	−	2495.89i	−0.537438	−	0.930869i	−0.999041	−	0.0437828i	$-0.986059\pi$
$193$	−1441.00	−	2495.89i	−0.537438	−	0.930869i	0.461604	−	0.887086i	$-0.347274\pi$
$194$		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	0.858082	−	0.513512i	$-0.171656\pi$
$199$	−44.0000	−	76.2102i	−0.0156738	−	0.0271477i	−0.873756	+	0.486365i	$0.838323\pi$
$200$		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	0.854397	−	0.519621i	$-0.173927\pi$
$227$	−78.0000	−	135.100i	−0.0228064	−	0.0395018i	−0.877203	+	0.480119i	$0.840593\pi$
$228$		0			0
$229$	817.000	−	1415.09i	0.235759	−	0.408347i	−0.723734	−	0.690079i	$-0.757576\pi$
$229$	817.000	−	1415.09i	0.235759	−	0.408347i	0.959493	+	0.281732i	$0.0909090\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	451.000	−	781.155i	0.126807	−	0.219636i	−0.795631	−	0.605782i	$-0.792860\pi$
$233$	451.000	−	781.155i	0.126807	−	0.219636i	0.922438	+	0.386146i	$0.126194\pi$
$234$		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	−0.984557	−	0.175065i	$-0.943986\pi$
$241$	−2409.00	−	4172.51i	−0.643889	−	1.11525i	0.340667	−	0.940184i	$-0.389347\pi$
$242$		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	−0.908959	−	0.416886i	$-0.863122\pi$
$257$	−385.000	+	666.840i	−0.0934461	+	0.161853i	0.815513	+	0.578739i	$0.196455\pi$
$258$		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	0.864546	+	0.502554i	$0.167606\pi$
$263$	3700.00	+	6408.59i	0.867497	+	1.50255i	0.00295121	+	0.999996i	$0.499061\pi$
$264$		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	0.979785	−	0.200053i	$-0.0641114\pi$
$269$	1397.00	+	2419.67i	0.316642	+	0.548439i	−0.663143	+	0.748492i	$0.730778\pi$
$270$		0			0
$271$	−4312.00	+	7468.60i	−0.966551	+	1.67412i	−0.261162	+	0.965295i	$0.584106\pi$
$271$	−4312.00	+	7468.60i	−0.966551	+	1.67412i	−0.705389	+	0.708821i	$0.749228\pi$
$272$		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	0.949572	−	0.313549i	$-0.101518\pi$
$277$	937.000	+	1622.93i	0.203245	+	0.352031i	−0.746327	+	0.665579i	$0.768185\pi$
$278$		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	−0.946247	−	0.323445i	$-0.895159\pi$
$283$	−3586.00	−	6211.13i	−0.753235	−	1.30464i	0.193012	−	0.981196i	$-0.438174\pi$
$284$		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	0.989529	−	0.144335i	$-0.0461044\pi$
$311$	2028.00	+	3512.60i	0.369766	+	0.640454i	−0.619762	+	0.784789i	$0.712771\pi$
$312$		0			0
$313$	−1077.00	+	1865.42i	−0.194491	+	0.336868i	−0.946733	−	0.322018i	$-0.895639\pi$
$313$	−1077.00	+	1865.42i	−0.194491	+	0.336868i	0.752243	+	0.658886i	$0.228972\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3693.00	−	6396.46i	0.654320	−	1.13332i	−0.327743	−	0.944767i	$-0.606288\pi$
$317$	3693.00	−	6396.46i	0.654320	−	1.13332i	0.982064	−	0.188549i	$-0.0603785\pi$
$318$		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	−0.815198	−	0.579183i	$-0.803372\pi$
$331$	566.000	−	980.341i	0.0939884	−	0.162793i	0.909186	+	0.416390i	$0.136705\pi$
$332$		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	0.766089	−	0.642734i	$-0.222200\pi$
$347$	−1122.00	−	1943.36i	−0.173580	−	0.300649i	−0.939669	+	0.342086i	$0.888867\pi$
$348$		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	0.884208	+	0.467093i	$0.154699\pi$
$353$	5615.00	+	9725.47i	0.846618	+	1.46639i	−0.0375899	+	0.999293i	$0.511968\pi$
$354$		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	−0.925918	−	0.377724i	$-0.876707\pi$
$359$	−924.000	+	1600.41i	−0.135841	+	0.235283i	0.790078	+	0.613007i	$0.210040\pi$
$360$		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	−0.999973	−	0.00734805i	$-0.997661\pi$
$367$	−3560.00	−	6166.10i	−0.506350	−	0.877024i	0.493623	−	0.869676i	$-0.335672\pi$
$368$		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	−0.997744	−	0.0671276i	$-0.978617\pi$
$373$	−3175.00	+	5499.26i	−0.440738	+	0.763381i	0.557006	+	0.830508i	$0.311950\pi$
$374$		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	0.279688	+	0.960091i	$0.409769\pi$
$383$	−5184.00	+	8978.95i	−0.691619	+	1.19792i	−0.971307	+	0.237828i	$0.923564\pi$
$384$		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	−0.995993	−	0.0894338i	$-0.971494\pi$
$389$	−4415.00	−	7647.00i	−0.575448	−	0.996706i	0.420544	−	0.907272i	$-0.361839\pi$
$390$		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	0.364273	+	0.931292i	$0.381317\pi$
$397$	−4939.00	+	8554.60i	−0.624386	+	1.08147i	−0.988659	+	0.150176i	$0.952016\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6567.00	−	11374.4i	0.817806	−	1.41648i	−0.0894889	−	0.995988i	$-0.528523\pi$
$401$	6567.00	−	11374.4i	0.817806	−	1.41648i	0.907295	−	0.420494i	$-0.138143\pi$
$402$		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	0.837343	−	0.546679i	$-0.184108\pi$
$409$	−453.000	−	784.619i	−0.0547663	−	0.0948580i	−0.892109	+	0.451821i	$0.850775\pi$
$410$		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	0.847115	−	0.531410i	$-0.178338\pi$
$431$	−328.000	−	568.113i	−0.0366571	−	0.0634919i	−0.883772	+	0.467918i	$0.845004\pi$
$432$		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	−0.976446	−	0.215762i	$-0.930776\pi$
$439$	−2772.00	+	4801.24i	−0.301368	+	0.521984i	0.675078	+	0.737746i	$0.264110\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3826.00	+	6626.83i	−0.410336	+	0.710722i	−0.994926	−	0.100606i	$-0.967922\pi$
$443$	−3826.00	+	6626.83i	−0.410336	+	0.710722i	0.584591	+	0.811328i	$0.301255\pi$
$444$		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	−0.903225	−	0.429168i	$-0.858807\pi$
$457$	−781.000	+	1352.73i	−0.0799423	+	0.138464i	0.823283	+	0.567632i	$0.192140\pi$
$458$		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	−0.510624	−	0.859804i	$-0.670585\pi$
$467$	4938.00	−	8552.87i	0.489301	−	0.847494i	0.999924	+	0.0123108i	$0.00391876\pi$
$468$		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	0.874298	−	0.485390i	$-0.161323\pi$
$479$	176.000	+	304.841i	0.0167884	+	0.0290784i	−0.857509	+	0.514469i	$0.827989\pi$
$480$		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	0.966312	+	0.257373i	$0.0828568\pi$
$487$	7588.00	+	13142.8i	0.706047	+	1.22291i	−0.260265	+	0.965537i	$0.583810\pi$
$488$		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	−0.00878220	+	0.999961i	$0.502795\pi$
$499$	−9702.00	+	16804.4i	−0.870383	+	1.50755i	−0.861601	+	0.507586i	$0.830538\pi$
$500$		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	−0.433116	−	0.901338i	$-0.642586\pi$
$509$	6477.00	−	11218.5i	0.564024	−	0.976917i	0.997140	−	0.0755793i	$-0.0240806\pi$
$510$		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	0.537790	−	0.843079i	$-0.319259\pi$
$521$	−5485.00	−	9500.30i	−0.461233	−	0.798878i	−0.999023	+	0.0442004i	$0.985926\pi$
$522$		0			0
$523$	8470.00	−	14670.5i	0.708159	−	1.22657i	−0.257380	−	0.966310i	$-0.582859\pi$
$523$	8470.00	−	14670.5i	0.708159	−	1.22657i	0.965539	−	0.260257i	$-0.0838074\pi$
$524$		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	−0.869932	−	0.493171i	$-0.835838\pi$
$541$	−99.0000	+	171.473i	−0.00786755	+	0.0136270i	0.862065	+	0.506798i	$0.169171\pi$
$542$		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	−0.923983	−	0.382434i	$-0.875086\pi$
$557$	−10427.0	−	18060.1i	−0.793189	−	1.37384i	0.130794	−	0.991410i	$-0.458247\pi$
$558$		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	0.959801	+	0.280681i	$0.0905602\pi$
$563$	9658.00	+	16728.1i	0.722977	+	1.25223i	−0.236824	+	0.971553i	$0.576106\pi$
$564$		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	−0.965849	−	0.259106i	$-0.916572\pi$
$569$	−3509.00	+	6077.77i	−0.258532	+	0.447791i	0.707317	+	0.706897i	$0.249906\pi$
$570$		0			0
$571$	−12210.0	−	21148.3i	−0.894873	−	1.54997i	−0.833961	−	0.551823i	$-0.813933\pi$
$571$	−12210.0	−	21148.3i	−0.894873	−	1.54997i	−0.0609117	−	0.998143i	$-0.519401\pi$
$572$		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	−0.891426	−	0.453166i	$-0.850294\pi$
$577$	−11617.0	−	20121.2i	−0.838166	−	1.45175i	0.0532596	−	0.998581i	$-0.483039\pi$
$578$		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	−0.520575	−	0.853816i	$-0.674282\pi$
$593$	6919.00	−	11984.1i	0.479139	−	0.829893i	0.999714	+	0.0239233i	$0.00761574\pi$
$594$		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	0.925620	−	0.378454i	$-0.123544\pi$
$599$	1980.00	+	3429.46i	0.135059	+	0.233930i	−0.790561	+	0.612384i	$0.790211\pi$
$600$		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	−0.810721	−	0.585433i	$-0.800925\pi$
$607$	1520.00	−	2632.72i	0.101639	−	0.176044i	0.912360	+	0.409389i	$0.134258\pi$
$608$		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	0.904686	−	0.426078i	$-0.140105\pi$
$613$	1265.00	+	2191.04i	0.0833489	+	0.144365i	−0.821338	+	0.570442i	$0.806772\pi$
$614$		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	0.630458	−	0.776224i	$-0.282867\pi$
$619$	−5498.00	−	9522.82i	−0.357000	−	0.618343i	−0.987458	+	0.157881i	$0.949534\pi$
$620$		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	0.753043	−	0.657971i	$-0.228585\pi$
$641$	−3137.00	−	5433.44i	−0.193298	−	0.334802i	−0.946341	+	0.323169i	$0.895252\pi$
$642$		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	0.961510	+	0.274769i	$0.0886013\pi$
$647$	11828.0	+	20486.7i	0.718712	+	1.24485i	−0.242798	+	0.970077i	$0.578065\pi$
$648$		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	−0.746754	−	0.665100i	$-0.768389\pi$
$653$	3381.00	−	5856.06i	0.202617	−	0.350943i	0.949371	+	0.314158i	$0.101722\pi$
$654$		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	0.656331	−	0.754473i	$-0.272108\pi$
$661$	−5527.00	−	9573.04i	−0.325228	−	0.563311i	−0.981558	+	0.191163i	$0.938774\pi$
$662$		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	−0.964450	−	0.264266i	$-0.914870\pi$
$677$	−4463.00	+	7730.14i	−0.253363	+	0.438838i	0.711086	+	0.703105i	$0.248204\pi$
$678$		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	0.729677	−	0.683792i	$-0.239670\pi$
$683$	−4058.00	−	7028.66i	−0.227343	−	0.393769i	−0.957020	+	0.290023i	$0.906337\pi$
$684$		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	−0.657450	−	0.753498i	$-0.728365\pi$
$691$	5882.00	−	10187.9i	0.323823	−	0.560878i	0.981273	+	0.192620i	$0.0616984\pi$
$692$		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	0.329966	+	0.943993i	$0.392963\pi$
$709$	−12319.0	+	21337.1i	−0.652538	+	1.13023i	−0.982505	+	0.186237i	$0.940371\pi$
$710$		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	−0.996971	−	0.0777710i	$-0.975220\pi$
$719$	−8312.00	+	14396.8i	−0.431134	+	0.746746i	0.565837	+	0.824517i	$0.308553\pi$
$720$		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	−0.821138	−	0.570730i	$-0.806660\pi$
$733$	1661.00	−	2876.94i	0.0836977	−	0.144969i	0.904836	+	0.425761i	$0.139994\pi$
$734$		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	0.988883	−	0.148697i	$-0.0475080\pi$
$739$	7346.00	+	12723.6i	0.365666	+	0.633352i	−0.623217	+	0.782049i	$0.714175\pi$
$740$		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	−0.241685	−	0.970355i	$-0.577700\pi$
$751$	14808.0	−	25648.2i	0.719509	−	1.24623i	0.961194	−	0.275872i	$-0.0889666\pi$
$752$		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	−0.986528	−	0.163590i	$-0.947693\pi$
$761$	−7381.00	+	12784.3i	−0.351591	+	0.608974i	0.634937	+	0.772564i	$0.281026\pi$
$762$		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	−0.986039	−	0.166514i	$-0.946749\pi$
$773$	−13695.0	−	23720.4i	−0.637225	−	1.10371i	0.348814	−	0.937192i	$-0.386584\pi$
$774$		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	0.550805	−	0.834634i	$-0.314321\pi$
$787$	−9878.00	−	17109.2i	−0.447411	−	0.774939i	−0.998217	+	0.0596946i	$0.980987\pi$
$788$		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	0.978417	−	0.206641i	$-0.0662532\pi$
$809$	7139.00	+	12365.1i	0.310252	+	0.537372i	−0.668165	+	0.744013i	$0.732920\pi$
$810$		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	−0.499706	−	0.866195i	$-0.666559\pi$
$821$	11769.0	−	20384.5i	0.500293	−	0.866534i	1.00000		0.000338894i	$-0.000107873\pi$
$822$		0			0
$823$	3308.00	+	5729.62i	0.140109	+	0.242676i	0.927537	−	0.373730i	$-0.121921\pi$
$823$	3308.00	+	5729.62i	0.140109	+	0.242676i	−0.787429	+	0.616406i	$0.788588\pi$
$824$		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	0.711467	−	0.702720i	$-0.248031\pi$
$829$	−6035.00	−	10452.9i	−0.252840	−	0.437931i	−0.964307	+	0.264788i	$0.914698\pi$
$830$		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	0.947306	+	0.320330i	$0.103794\pi$
$857$	18843.0	+	32637.0i	0.751067	+	1.30089i	−0.196239	+	0.980556i	$0.562873\pi$
$858$		0			0
$859$	−20322.0	+	35198.7i	−0.807192	+	1.39810i	0.107610	+	0.994193i	$0.465680\pi$
$859$	−20322.0	+	35198.7i	−0.807192	+	1.39810i	−0.914801	+	0.403904i	$0.867653\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9328.00	−	16156.6i	0.367936	−	0.637284i	−0.621307	−	0.783568i	$-0.713398\pi$
$863$	9328.00	−	16156.6i	0.367936	−	0.637284i	0.989243	+	0.146284i	$0.0467312\pi$
$864$		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	−0.713300	−	0.700859i	$-0.752800\pi$
$877$	6501.00	−	11260.1i	0.250311	−	0.433552i	0.963612	+	0.267307i	$0.0861336\pi$
$878$		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	−0.701124	−	0.713039i	$-0.747318\pi$
$887$	7052.00	−	12214.4i	0.266948	−	0.462368i	0.968072	+	0.250672i	$0.0806514\pi$
$888$		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	0.958620	−	0.284690i	$-0.0918908\pi$
$907$	6358.00	+	11012.4i	0.232761	+	0.403153i	−0.725859	+	0.687844i	$0.758557\pi$
$908$		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	−0.912661	−	0.408717i	$-0.865976\pi$
$919$	−2852.00	+	4939.81i	−0.102371	+	0.177311i	0.810290	+	0.586029i	$0.199310\pi$
$920$		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	−0.929047	−	0.369963i	$-0.879370\pi$
$929$	−4081.00	+	7068.50i	−0.144126	+	0.249634i	0.784920	+	0.619597i	$0.212704\pi$
$930$		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	0.688652	−	0.725092i	$-0.258203\pi$
$941$	−8187.00	−	14180.3i	−0.283622	−	0.491248i	−0.972274	+	0.233844i	$0.924870\pi$
$942$		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	−0.929429	−	0.369002i	$-0.879700\pi$
$947$	−4230.00	+	7326.57i	−0.145149	+	0.251406i	0.784279	+	0.620408i	$0.213033\pi$
$948$		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	−0.983395	−	0.181479i	$-0.941912\pi$
$971$	−10122.0	+	17531.8i	−0.334532	+	0.579426i	0.648863	+	0.760905i	$0.275245\pi$
$972$		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	−0.906268	−	0.422704i	$-0.861081\pi$
$977$	−25017.0	−	43330.7i	−0.819206	−	1.41891i	0.0870612	−	0.996203i	$-0.472252\pi$
$978$		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	−0.992466	−	0.122521i	$-0.960902\pi$
$983$	−18564.0	−	32153.8i	−0.602339	−	1.04328i	0.390126	−	0.920761i	$-0.372431\pi$
$984$		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	0.552413	−	0.833570i	$-0.313707\pi$
$991$	−13904.0	−	24082.4i	−0.445686	−	0.771951i	−0.998100	+	0.0616190i	$0.980374\pi$
$992$		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	0.998564	−	0.0535775i	$-0.0170624\pi$
$997$	14257.0	+	24693.8i	0.452882	+	0.784415i	−0.545681	+	0.837993i	$0.683729\pi$
$998$		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.177.1		2
7.2	even	3		8.4.a.a.1.1	✓	1
7.3	odd	6		392.4.i.b.361.1		2
7.4	even	3	inner	392.4.i.g.361.1		2
7.5	odd	6		392.4.a.e.1.1		1
7.6	odd	2		392.4.i.b.177.1		2
21.2	odd	6		72.4.a.c.1.1		1
28.19	even	6		784.4.a.e.1.1		1
28.23	odd	6		16.4.a.a.1.1		1
35.2	odd	12		200.4.c.e.49.2		2
35.9	even	6		200.4.a.g.1.1		1
35.23	odd	12		200.4.c.e.49.1		2
56.37	even	6		64.4.a.d.1.1		1
56.51	odd	6		64.4.a.b.1.1		1
63.2	odd	6		648.4.i.e.433.1		2
63.16	even	3		648.4.i.h.433.1		2
63.23	odd	6		648.4.i.e.217.1		2
63.58	even	3		648.4.i.h.217.1		2
77.65	odd	6		968.4.a.a.1.1		1
84.23	even	6		144.4.a.e.1.1		1
91.51	even	6		1352.4.a.a.1.1		1
105.2	even	12		1800.4.f.u.649.2		2
105.23	even	12		1800.4.f.u.649.1		2
105.44	odd	6		1800.4.a.d.1.1		1
112.37	even	12		256.4.b.a.129.2		2
112.51	odd	12		256.4.b.g.129.2		2
112.93	even	12		256.4.b.a.129.1		2
112.107	odd	12		256.4.b.g.129.1		2
119.16	even	6		2312.4.a.a.1.1		1
140.23	even	12		400.4.c.i.49.2		2
140.79	odd	6		400.4.a.g.1.1		1
140.107	even	12		400.4.c.i.49.1		2
168.107	even	6		576.4.a.j.1.1		1
168.149	odd	6		576.4.a.k.1.1		1
280.149	even	6		1600.4.a.o.1.1		1
280.219	odd	6		1600.4.a.bm.1.1		1
308.219	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	7.2	even	3
16.4.a.a.1.1		1	28.23	odd	6
64.4.a.b.1.1		1	56.51	odd	6
64.4.a.d.1.1		1	56.37	even	6
72.4.a.c.1.1		1	21.2	odd	6
144.4.a.e.1.1		1	84.23	even	6
200.4.a.g.1.1		1	35.9	even	6
200.4.c.e.49.1		2	35.23	odd	12
200.4.c.e.49.2		2	35.2	odd	12
256.4.b.a.129.1		2	112.93	even	12
256.4.b.a.129.2		2	112.37	even	12
256.4.b.g.129.1		2	112.107	odd	12
256.4.b.g.129.2		2	112.51	odd	12
392.4.a.e.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	7.3	odd	6
392.4.i.g.177.1		2	1.1	even	1	trivial
392.4.i.g.361.1		2	7.4	even	3	inner
400.4.a.g.1.1		1	140.79	odd	6
400.4.c.i.49.1		2	140.107	even	12
400.4.c.i.49.2		2	140.23	even	12
576.4.a.j.1.1		1	168.107	even	6
576.4.a.k.1.1		1	168.149	odd	6
648.4.i.e.217.1		2	63.23	odd	6
648.4.i.e.433.1		2	63.2	odd	6
648.4.i.h.217.1		2	63.58	even	3
648.4.i.h.433.1		2	63.16	even	3
784.4.a.e.1.1		1	28.19	even	6
968.4.a.a.1.1		1	77.65	odd	6
1352.4.a.a.1.1		1	91.51	even	6
1600.4.a.o.1.1		1	280.149	even	6
1600.4.a.bm.1.1		1	280.219	odd	6
1800.4.a.d.1.1		1	105.44	odd	6
1800.4.f.u.649.1		2	105.23	even	12
1800.4.f.u.649.2		2	105.2	even	12
1936.4.a.l.1.1		1	308.219	even	6
2312.4.a.a.1.1		1	119.16	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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