LMFDB - Embedded newform 384.4.j.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(97,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("384.97");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.j (of order $4$, 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:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	384.289
Dual form			384.4.j.b.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12132 - 2.12132i) q^{3} +(-0.644922 + 0.644922i) q^{5} -7.13926i q^{7} +9.00000i q^{9} +O(q^{10})$	\(q+(-2.12132 - 2.12132i) q^{3} +(-0.644922 + 0.644922i) q^{5} -7.13926i q^{7} +9.00000i q^{9} +(-25.4455 + 25.4455i) q^{11} +(14.6030 + 14.6030i) q^{13} +2.73617 q^{15} +71.4024 q^{17} +(43.6238 + 43.6238i) q^{19} +(-15.1447 + 15.1447i) q^{21} -211.845i q^{23} +124.168i q^{25} +(19.0919 - 19.0919i) q^{27} +(-5.84463 - 5.84463i) q^{29} -107.807 q^{31} +107.956 q^{33} +(4.60426 + 4.60426i) q^{35} +(184.865 - 184.865i) q^{37} -61.9551i q^{39} +360.146i q^{41} +(312.475 - 312.475i) q^{43} +(-5.80429 - 5.80429i) q^{45} +343.892 q^{47} +292.031 q^{49} +(-151.467 - 151.467i) q^{51} +(249.900 - 249.900i) q^{53} -32.8207i q^{55} -185.080i q^{57} +(152.755 - 152.755i) q^{59} +(525.985 + 525.985i) q^{61} +64.2534 q^{63} -18.8355 q^{65} +(35.3052 + 35.3052i) q^{67} +(-449.392 + 449.392i) q^{69} -784.715i q^{71} -800.215i q^{73} +(263.400 - 263.400i) q^{75} +(181.662 + 181.662i) q^{77} +548.062 q^{79} -81.0000 q^{81} +(-464.431 - 464.431i) q^{83} +(-46.0489 + 46.0489i) q^{85} +24.7967i q^{87} +302.977i q^{89} +(104.254 - 104.254i) q^{91} +(228.693 + 228.693i) q^{93} -56.2679 q^{95} +1567.24 q^{97} +(-229.009 - 229.009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 40 q^{11} + 120 q^{15} - 24 q^{19} - 400 q^{29} - 744 q^{31} + 456 q^{35} - 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} - 752 q^{53} + 1376 q^{59} + 912 q^{61} - 504 q^{63} + 976 q^{65} + 2256 q^{67} + 528 q^{69} - 1104 q^{75} - 1904 q^{77} + 5992 q^{79} - 1944 q^{81} - 2680 q^{83} + 240 q^{85} + 3496 q^{91} - 7728 q^{95} + 360 q^{99}+O(q^{100}) $ 24 * q + 40 * q^11 + 120 * q^15 - 24 * q^19 - 400 * q^29 - 744 * q^31 + 456 * q^35 - 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 - 752 * q^53 + 1376 * q^59 + 912 * q^61 - 504 * q^63 + 976 * q^65 + 2256 * q^67 + 528 * q^69 - 1104 * q^75 - 1904 * q^77 + 5992 * q^79 - 1944 * q^81 - 2680 * q^83 + 240 * q^85 + 3496 * q^91 - 7728 * q^95 + 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$		0			0
$5$	−0.644922	+	0.644922i	−0.0576835	+	0.0576835i	−0.735360	−	0.677677i	$-0.762987\pi$
$5$	−0.644922	+	0.644922i	−0.0576835	+	0.0576835i	0.677677	+	0.735360i	$0.262987\pi$
$6$		0			0
$7$		−	7.13926i		−	0.385484i	−0.981249	−	0.192742i	$-0.938262\pi$
$7$		−	7.13926i		−	0.385484i	0.981249	−	0.192742i	$-0.0617380\pi$
$8$		0			0
$9$			9.00000i			0.333333i
$10$		0			0
$11$	−25.4455	+	25.4455i	−0.697464	+	0.697464i	−0.963863	−	0.266399i	$-0.914166\pi$
$11$	−25.4455	+	25.4455i	−0.697464	+	0.697464i	0.266399	+	0.963863i	$0.414166\pi$
$12$		0			0
$13$	14.6030	+	14.6030i	0.311549	+	0.311549i	0.845509	−	0.533961i	$-0.179297\pi$
$13$	14.6030	+	14.6030i	0.311549	+	0.311549i	−0.533961	+	0.845509i	$0.679297\pi$
$14$		0			0
$15$	2.73617			0.0470984
$16$		0			0
$17$	71.4024			1.01868			0.509342	−	0.860564i	$-0.329889\pi$
$17$	71.4024			1.01868			0.509342	+	0.860564i	$0.329889\pi$
$18$		0			0
$19$	43.6238	+	43.6238i	0.526736	+	0.526736i	0.919598	−	0.392861i	$-0.128515\pi$
$19$	43.6238	+	43.6238i	0.526736	+	0.526736i	−0.392861	+	0.919598i	$0.628515\pi$
$20$		0			0
$21$	−15.1447	+	15.1447i	−0.157373	+	0.157373i
$22$		0			0
$23$		−	211.845i		−	1.92056i	−0.279045	−	0.960278i	$-0.590018\pi$
$23$		−	211.845i		−	1.92056i	0.279045	−	0.960278i	$-0.409982\pi$
$24$		0			0
$25$			124.168i			0.993345i
$26$		0			0
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$		0			0
$29$	−5.84463	−	5.84463i	−0.0374248	−	0.0374248i	0.688147	−	0.725572i	$-0.258425\pi$
$29$	−5.84463	−	5.84463i	−0.0374248	−	0.0374248i	−0.725572	+	0.688147i	$0.758425\pi$
$30$		0			0
$31$	−107.807			−0.624604			−0.312302	−	0.949983i	$-0.601100\pi$
$31$	−107.807			−0.624604			−0.312302	+	0.949983i	$0.601100\pi$
$32$		0			0
$33$	107.956			0.569477
$34$		0			0
$35$	4.60426	+	4.60426i	0.0222361	+	0.0222361i
$36$		0			0
$37$	184.865	−	184.865i	0.821395	−	0.821395i	−0.164913	−	0.986308i	$-0.552734\pi$
$37$	184.865	−	184.865i	0.821395	−	0.821395i	0.986308	+	0.164913i	$0.0527343\pi$
$38$		0			0
$39$		−	61.9551i		−	0.254379i
$40$		0			0
$41$			360.146i			1.37184i	0.727679	+	0.685918i	$0.240599\pi$
$41$			360.146i			1.37184i	−0.727679	+	0.685918i	$0.759401\pi$
$42$		0			0
$43$	312.475	−	312.475i	1.10818	−	1.10818i	0.114795	−	0.993389i	$-0.463379\pi$
$43$	312.475	−	312.475i	1.10818	−	1.10818i	0.993389	−	0.114795i	$-0.0366213\pi$
$44$		0			0
$45$	−5.80429	−	5.80429i	−0.0192278	−	0.0192278i
$46$		0			0
$47$	343.892			1.06727			0.533636	−	0.845715i	$-0.320825\pi$
$47$	343.892			1.06727			0.533636	+	0.845715i	$0.320825\pi$
$48$		0			0
$49$	292.031			0.851402
$50$		0			0
$51$	−151.467	−	151.467i	−0.415876	−	0.415876i
$52$		0			0
$53$	249.900	−	249.900i	0.647667	−	0.647667i	−0.304762	−	0.952429i	$-0.598577\pi$
$53$	249.900	−	249.900i	0.647667	−	0.647667i	0.952429	+	0.304762i	$0.0985768\pi$
$54$		0			0
$55$		−	32.8207i		−	0.0804644i
$56$		0			0
$57$		−	185.080i		−	0.430078i
$58$		0			0
$59$	152.755	−	152.755i	0.337067	−	0.337067i	−0.518195	−	0.855262i	$-0.673396\pi$
$59$	152.755	−	152.755i	0.337067	−	0.337067i	0.855262	+	0.518195i	$0.173396\pi$
$60$		0			0
$61$	525.985	+	525.985i	1.10402	+	1.10402i	0.993920	+	0.110104i	$0.0351183\pi$
$61$	525.985	+	525.985i	1.10402	+	1.10402i	0.110104	+	0.993920i	$0.464882\pi$
$62$		0			0
$63$	64.2534			0.128495
$64$		0			0
$65$	−18.8355			−0.0359425
$66$		0			0
$67$	35.3052	+	35.3052i	0.0643764	+	0.0643764i	0.738562	−	0.674186i	$-0.235505\pi$
$67$	35.3052	+	35.3052i	0.0643764	+	0.0643764i	−0.674186	+	0.738562i	$0.735505\pi$
$68$		0			0
$69$	−449.392	+	449.392i	−0.784064	+	0.784064i
$70$		0			0
$71$		−	784.715i		−	1.31167i	−0.754905	−	0.655834i	$-0.772317\pi$
$71$		−	784.715i		−	1.31167i	0.754905	−	0.655834i	$-0.227683\pi$
$72$		0			0
$73$		−	800.215i		−	1.28299i	−0.767128	−	0.641494i	$-0.778315\pi$
$73$		−	800.215i		−	1.28299i	0.767128	−	0.641494i	$-0.221685\pi$
$74$		0			0
$75$	263.400	−	263.400i	0.405531	−	0.405531i
$76$		0			0
$77$	181.662	+	181.662i	0.268861	+	0.268861i
$78$		0			0
$79$	548.062			0.780530			0.390265	−	0.920703i	$-0.372383\pi$
$79$	548.062			0.780530			0.390265	+	0.920703i	$0.372383\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	−464.431	−	464.431i	−0.614191	−	0.614191i	0.329844	−	0.944035i	$-0.393004\pi$
$83$	−464.431	−	464.431i	−0.614191	−	0.614191i	−0.944035	+	0.329844i	$0.893004\pi$
$84$		0			0
$85$	−46.0489	+	46.0489i	−0.0587613	+	0.0587613i
$86$		0			0
$87$			24.7967i			0.0305573i
$88$		0			0
$89$			302.977i			0.360849i	0.983589	+	0.180424i	$0.0577471\pi$
$89$			302.977i			0.360849i	−0.983589	+	0.180424i	$0.942253\pi$
$90$		0			0
$91$	104.254	−	104.254i	0.120097	−	0.120097i
$92$		0			0
$93$	228.693	+	228.693i	0.254994	+	0.254994i
$94$		0			0
$95$	−56.2679			−0.0607680
$96$		0			0
$97$	1567.24			1.64050			0.820252	−	0.572002i	$-0.193833\pi$
$97$	1567.24			1.64050			0.820252	+	0.572002i	$0.193833\pi$
$98$		0			0
$99$	−229.009	−	229.009i	−0.232488	−	0.232488i
$100$		0			0
$101$	−59.6129	+	59.6129i	−0.0587297	+	0.0587297i	−0.735862	−	0.677132i	$-0.763223\pi$
$101$	−59.6129	+	59.6129i	−0.0587297	+	0.0587297i	0.677132	+	0.735862i	$0.263223\pi$
$102$		0			0
$103$			1762.59i			1.68615i	0.537795	+	0.843076i	$0.319257\pi$
$103$			1762.59i			1.68615i	−0.537795	+	0.843076i	$0.680743\pi$
$104$		0			0
$105$		−	19.5342i		−	0.0181557i
$106$		0			0
$107$	−656.579	+	656.579i	−0.593214	+	0.593214i	−0.938498	−	0.345284i	$-0.887782\pi$
$107$	−656.579	+	656.579i	−0.593214	+	0.593214i	0.345284	+	0.938498i	$0.387782\pi$
$108$		0			0
$109$	327.776	+	327.776i	0.288030	+	0.288030i	0.836301	−	0.548271i	$-0.184714\pi$
$109$	327.776	+	327.776i	0.288030	+	0.288030i	−0.548271	+	0.836301i	$0.684714\pi$
$110$		0			0
$111$	−784.316			−0.670667
$112$		0			0
$113$	−1349.18			−1.12319			−0.561593	−	0.827414i	$-0.689811\pi$
$113$	−1349.18			−1.12319			−0.561593	+	0.827414i	$0.689811\pi$
$114$		0			0
$115$	136.624	+	136.624i	0.110784	+	0.110784i
$116$		0			0
$117$	−131.427	+	131.427i	−0.103850	+	0.103850i
$118$		0			0
$119$		−	509.761i		−	0.392686i
$120$		0			0
$121$			36.0534i			0.0270875i
$122$		0			0
$123$	763.984	−	763.984i	0.560050	−	0.560050i
$124$		0			0
$125$	−160.694	−	160.694i	−0.114983	−	0.114983i
$126$		0			0
$127$	52.2111			0.0364802			0.0182401	−	0.999834i	$-0.494194\pi$
$127$	52.2111			0.0364802			0.0182401	+	0.999834i	$0.494194\pi$
$128$		0			0
$129$	−1325.72			−0.904829
$130$		0			0
$131$	387.958	+	387.958i	0.258749	+	0.258749i	0.824545	−	0.565796i	$-0.191431\pi$
$131$	387.958	+	387.958i	0.258749	+	0.258749i	−0.565796	+	0.824545i	$0.691431\pi$
$132$		0			0
$133$	311.442	−	311.442i	0.203048	−	0.203048i
$134$		0			0
$135$			24.6255i			0.0156995i
$136$		0			0
$137$			795.048i			0.495807i	0.968785	+	0.247903i	$0.0797415\pi$
$137$			795.048i			0.495807i	−0.968785	+	0.247903i	$0.920258\pi$
$138$		0			0
$139$	−1708.70	+	1708.70i	−1.04266	+	1.04266i	−0.0436142	+	0.999048i	$0.513887\pi$
$139$	−1708.70	+	1708.70i	−1.04266	+	1.04266i	−0.999048	+	0.0436142i	$0.986113\pi$
$140$		0			0
$141$	−729.504	−	729.504i	−0.435712	−	0.435712i
$142$		0			0
$143$	−743.160			−0.434588
$144$		0			0
$145$	7.53865			0.00431759
$146$		0			0
$147$	−619.491	−	619.491i	−0.347583	−	0.347583i
$148$		0			0
$149$	69.6301	−	69.6301i	0.0382840	−	0.0382840i	−0.687706	−	0.725990i	$-0.741382\pi$
$149$	69.6301	−	69.6301i	0.0382840	−	0.0382840i	0.725990	+	0.687706i	$0.241382\pi$
$150$		0			0
$151$			1567.48i			0.844768i	0.906417	+	0.422384i	$0.138807\pi$
$151$			1567.48i			0.844768i	−0.906417	+	0.422384i	$0.861193\pi$
$152$		0			0
$153$			642.622i			0.339561i
$154$		0			0
$155$	69.5271	−	69.5271i	0.0360294	−	0.0360294i
$156$		0			0
$157$	−1738.35	−	1738.35i	−0.883667	−	0.883667i	0.110238	−	0.993905i	$-0.464839\pi$
$157$	−1738.35	−	1738.35i	−0.883667	−	0.883667i	−0.993905	+	0.110238i	$0.964839\pi$
$158$		0			0
$159$	−1060.23			−0.528818
$160$		0			0
$161$	−1512.42			−0.740344
$162$		0			0
$163$	2685.71	+	2685.71i	1.29056	+	1.29056i	0.934442	+	0.356116i	$0.115899\pi$
$163$	2685.71	+	2685.71i	1.29056	+	1.29056i	0.356116	+	0.934442i	$0.384101\pi$
$164$		0			0
$165$	−69.6232	+	69.6232i	−0.0328495	+	0.0328495i
$166$		0			0
$167$			27.5126i			0.0127484i	0.999980	+	0.00637422i	$0.00202899\pi$
$167$			27.5126i			0.0127484i	−0.999980	+	0.00637422i	$0.997971\pi$
$168$		0			0
$169$		−	1770.51i		−	0.805875i
$170$		0			0
$171$	−392.614	+	392.614i	−0.175579	+	0.175579i
$172$		0			0
$173$	−3044.87	−	3044.87i	−1.33813	−	1.33813i	−0.897867	−	0.440267i	$-0.854884\pi$
$173$	−3044.87	−	3044.87i	−1.33813	−	1.33813i	−0.440267	−	0.897867i	$-0.645116\pi$
$174$		0			0
$175$	886.469			0.382919
$176$		0			0
$177$	−648.083			−0.275214
$178$		0			0
$179$	365.808	+	365.808i	0.152747	+	0.152747i	0.779344	−	0.626597i	$-0.215553\pi$
$179$	365.808	+	365.808i	0.152747	+	0.152747i	−0.626597	+	0.779344i	$0.715553\pi$
$180$		0			0
$181$	1737.10	−	1737.10i	0.713359	−	0.713359i	−0.253877	−	0.967236i	$-0.581706\pi$
$181$	1737.10	−	1737.10i	0.713359	−	0.713359i	0.967236	+	0.253877i	$0.0817060\pi$
$182$		0			0
$183$		−	2231.56i		−	0.901432i
$184$		0			0
$185$			238.447i			0.0947620i
$186$		0			0
$187$	−1816.87	+	1816.87i	−0.710495	+	0.710495i
$188$		0			0
$189$	−136.302	−	136.302i	−0.0524577	−	0.0524577i
$190$		0			0
$191$	−1709.44			−0.647595			−0.323798	−	0.946126i	$-0.604960\pi$
$191$	−1709.44			−0.647595			−0.323798	+	0.946126i	$0.604960\pi$
$192$		0			0
$193$	2404.54			0.896800			0.448400	−	0.893833i	$-0.351994\pi$
$193$	2404.54			0.896800			0.448400	+	0.893833i	$0.351994\pi$
$194$		0			0
$195$	39.9562	+	39.9562i	0.0146735	+	0.0146735i
$196$		0			0
$197$	−2772.54	+	2772.54i	−1.00272	+	1.00272i	−0.00271983	+	0.999996i	$0.500866\pi$
$197$	−2772.54	+	2772.54i	−1.00272	+	1.00272i	−0.999996	+	0.00271983i	$0.999134\pi$
$198$		0			0
$199$			1506.90i			0.536790i	0.963309	+	0.268395i	$0.0864932\pi$
$199$			1506.90i			0.536790i	−0.963309	+	0.268395i	$0.913507\pi$
$200$		0			0
$201$		−	149.787i		−	0.0525631i
$202$		0			0
$203$	−41.7263	+	41.7263i	−0.0144267	+	0.0144267i
$204$		0			0
$205$	−232.266	−	232.266i	−0.0791324	−	0.0791324i
$206$		0			0
$207$	1906.61			0.640185
$208$		0			0
$209$	−2220.06			−0.734760
$210$		0			0
$211$	1965.22	+	1965.22i	0.641190	+	0.641190i	0.950848	−	0.309658i	$-0.100215\pi$
$211$	1965.22	+	1965.22i	0.641190	+	0.641190i	−0.309658	+	0.950848i	$0.600215\pi$
$212$		0			0
$213$	−1664.63	+	1664.63i	−0.535487	+	0.535487i
$214$		0			0
$215$			403.043i			0.127848i
$216$		0			0
$217$			769.663i			0.240775i
$218$		0			0
$219$	−1697.51	+	1697.51i	−0.523778	+	0.523778i
$220$		0			0
$221$	1042.69	+	1042.69i	0.317370	+	0.317370i
$222$		0			0
$223$	85.7869			0.0257610			0.0128805	−	0.999917i	$-0.495900\pi$
$223$	85.7869			0.0257610			0.0128805	+	0.999917i	$0.495900\pi$
$224$		0			0
$225$	−1117.51			−0.331115
$226$		0			0
$227$	−2526.02	−	2526.02i	−0.738582	−	0.738582i	0.233722	−	0.972304i	$-0.424910\pi$
$227$	−2526.02	−	2526.02i	−0.738582	−	0.738582i	−0.972304	+	0.233722i	$0.924910\pi$
$228$		0			0
$229$	1116.65	−	1116.65i	0.322227	−	0.322227i	−0.527394	−	0.849621i	$-0.676831\pi$
$229$	1116.65	−	1116.65i	0.322227	−	0.322227i	0.849621	+	0.527394i	$0.176831\pi$
$230$		0			0
$231$		−	770.727i		−	0.219524i
$232$		0			0
$233$		−	5754.25i		−	1.61791i	−0.587869	−	0.808956i	$-0.700033\pi$
$233$		−	5754.25i		−	1.61791i	0.587869	−	0.808956i	$-0.299967\pi$
$234$		0			0
$235$	−221.783	+	221.783i	−0.0615640	+	0.0615640i
$236$		0			0
$237$	−1162.62	−	1162.62i	−0.318650	−	0.318650i
$238$		0			0
$239$	−641.784			−0.173697			−0.0868484	−	0.996222i	$-0.527680\pi$
$239$	−641.784			−0.173697			−0.0868484	+	0.996222i	$0.527680\pi$
$240$		0			0
$241$	−2887.45			−0.771771			−0.385885	−	0.922547i	$-0.626104\pi$
$241$	−2887.45			−0.771771			−0.385885	+	0.922547i	$0.626104\pi$
$242$		0			0
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−188.337	+	188.337i	−0.0491119	+	0.0491119i
$246$		0			0
$247$			1274.07i			0.328208i
$248$		0			0
$249$			1970.41i			0.501485i
$250$		0			0
$251$	2367.55	−	2367.55i	0.595372	−	0.595372i	−0.343706	−	0.939077i	$-0.611682\pi$
$251$	2367.55	−	2367.55i	0.595372	−	0.595372i	0.939077	+	0.343706i	$0.111682\pi$
$252$		0			0
$253$	5390.51	+	5390.51i	1.33952	+	1.33952i
$254$		0			0
$255$	195.369			0.0479784
$256$		0			0
$257$	5112.43			1.24087			0.620437	−	0.784256i	$-0.286955\pi$
$257$	5112.43			1.24087			0.620437	+	0.784256i	$0.286955\pi$
$258$		0			0
$259$	−1319.80	−	1319.80i	−0.316635	−	0.316635i
$260$		0			0
$261$	52.6017	−	52.6017i	0.0124749	−	0.0124749i
$262$		0			0
$263$			5496.36i			1.28867i	0.764744	+	0.644334i	$0.222866\pi$
$263$			5496.36i			1.28867i	−0.764744	+	0.644334i	$0.777134\pi$
$264$		0			0
$265$			322.331i			0.0747194i
$266$		0			0
$267$	642.712	−	642.712i	0.147316	−	0.147316i
$268$		0			0
$269$	2474.35	+	2474.35i	0.560831	+	0.560831i	0.929544	−	0.368712i	$-0.120201\pi$
$269$	2474.35	+	2474.35i	0.560831	+	0.560831i	−0.368712	+	0.929544i	$0.620201\pi$
$270$		0			0
$271$	−1718.58			−0.385226			−0.192613	−	0.981275i	$-0.561696\pi$
$271$	−1718.58			−0.385226			−0.192613	+	0.981275i	$0.561696\pi$
$272$		0			0
$273$	−442.314			−0.0980589
$274$		0			0
$275$	−3159.52	−	3159.52i	−0.692823	−	0.692823i
$276$		0			0
$277$	4722.69	−	4722.69i	1.02440	−	1.02440i	0.0247055	−	0.999695i	$-0.492135\pi$
$277$	4722.69	−	4722.69i	1.02440	−	1.02440i	0.999695	−	0.0247055i	$-0.00786482\pi$
$278$		0			0
$279$		−	970.264i		−	0.208201i
$280$		0			0
$281$			2543.21i			0.539911i	0.962873	+	0.269955i	$0.0870090\pi$
$281$			2543.21i			0.539911i	−0.962873	+	0.269955i	$0.912991\pi$
$282$		0			0
$283$	3206.82	−	3206.82i	0.673589	−	0.673589i	−0.284952	−	0.958542i	$-0.591978\pi$
$283$	3206.82	−	3206.82i	0.673589	−	0.673589i	0.958542	+	0.284952i	$0.0919778\pi$
$284$		0			0
$285$	119.362	+	119.362i	0.0248084	+	0.0248084i
$286$		0			0
$287$	2571.17			0.528821
$288$		0			0
$289$	185.302			0.0377167
$290$		0			0
$291$	−3324.61	−	3324.61i	−0.669733	−	0.669733i
$292$		0			0
$293$	−5911.40	+	5911.40i	−1.17866	+	1.17866i	−0.198575	+	0.980086i	$0.563631\pi$
$293$	−5911.40	+	5911.40i	−1.17866	+	1.17866i	−0.980086	+	0.198575i	$0.936369\pi$
$294$		0			0
$295$			197.030i			0.0388865i
$296$		0			0
$297$			971.605i			0.189826i
$298$		0			0
$299$	3093.57	−	3093.57i	0.598347	−	0.598347i
$300$		0			0
$301$	−2230.84	−	2230.84i	−0.427187	−	0.427187i
$302$		0			0
$303$	252.916			0.0479526
$304$		0			0
$305$	−678.438			−0.127368
$306$		0			0
$307$	−1162.25	−	1162.25i	−0.216068	−	0.216068i	0.590771	−	0.806839i	$-0.298824\pi$
$307$	−1162.25	−	1162.25i	−0.216068	−	0.216068i	−0.806839	+	0.590771i	$0.798824\pi$
$308$		0			0
$309$	3739.03	−	3739.03i	0.688368	−	0.688368i
$310$		0			0
$311$		−	2357.28i		−	0.429805i	−0.976636	−	0.214902i	$-0.931057\pi$
$311$		−	2357.28i		−	0.429805i	0.976636	−	0.214902i	$-0.0689433\pi$
$312$		0			0
$313$			3785.95i			0.683689i	0.939757	+	0.341844i	$0.111052\pi$
$313$			3785.95i			0.683689i	−0.939757	+	0.341844i	$0.888948\pi$
$314$		0			0
$315$	−41.4384	+	41.4384i	−0.00741203	+	0.00741203i
$316$		0			0
$317$	3135.51	+	3135.51i	0.555545	+	0.555545i	0.928036	−	0.372491i	$-0.121496\pi$
$317$	3135.51	+	3135.51i	0.555545	+	0.555545i	−0.372491	+	0.928036i	$0.621496\pi$
$318$		0			0
$319$	297.439			0.0522050
$320$		0			0
$321$	2785.63			0.484357
$322$		0			0
$323$	3114.85	+	3114.85i	0.536578	+	0.536578i
$324$		0			0
$325$	−1813.22	+	1813.22i	−0.309476	+	0.309476i
$326$		0			0
$327$		−	1390.64i		−	0.235176i
$328$		0			0
$329$		−	2455.13i		−	0.411416i
$330$		0			0
$331$	1734.12	−	1734.12i	0.287963	−	0.287963i	−0.548312	−	0.836274i	$-0.684729\pi$
$331$	1734.12	−	1734.12i	0.287963	−	0.287963i	0.836274	+	0.548312i	$0.184729\pi$
$332$		0			0
$333$	1663.79	+	1663.79i	0.273798	+	0.273798i
$334$		0			0
$335$	−45.5382			−0.00742691
$336$		0			0
$337$	5828.89			0.942196			0.471098	−	0.882081i	$-0.343858\pi$
$337$	5828.89			0.942196			0.471098	+	0.882081i	$0.343858\pi$
$338$		0			0
$339$	2862.04	+	2862.04i	0.458539	+	0.458539i
$340$		0			0
$341$	2743.21	−	2743.21i	0.435639	−	0.435639i
$342$		0			0
$343$		−	4533.65i		−	0.713686i
$344$		0			0
$345$		−	579.645i		−	0.0904551i
$346$		0			0
$347$	716.234	−	716.234i	0.110805	−	0.110805i	−0.649530	−	0.760336i	$-0.725034\pi$
$347$	716.234	−	716.234i	0.110805	−	0.110805i	0.760336	+	0.649530i	$0.225034\pi$
$348$		0			0
$349$	4388.39	+	4388.39i	0.673081	+	0.673081i	0.958425	−	0.285344i	$-0.0921080\pi$
$349$	4388.39	+	4388.39i	0.673081	+	0.673081i	−0.285344	+	0.958425i	$0.592108\pi$
$350$		0			0
$351$	557.596			0.0847928
$352$		0			0
$353$	9348.76			1.40959			0.704794	−	0.709412i	$-0.251040\pi$
$353$	9348.76			1.40959			0.704794	+	0.709412i	$0.251040\pi$
$354$		0			0
$355$	506.079	+	506.079i	0.0756617	+	0.0756617i
$356$		0			0
$357$	−1081.37	+	1081.37i	−0.160314	+	0.160314i
$358$		0			0
$359$		−	12531.1i		−	1.84224i	−0.389275	−	0.921122i	$-0.627274\pi$
$359$		−	12531.1i		−	1.84224i	0.389275	−	0.921122i	$-0.372726\pi$
$360$		0			0
$361$		−	3052.92i		−	0.445097i
$362$		0			0
$363$	76.4808	−	76.4808i	0.0110584	−	0.0110584i
$364$		0			0
$365$	516.076	+	516.076i	0.0740073	+	0.0740073i
$366$		0			0
$367$	9276.83			1.31947			0.659736	−	0.751497i	$-0.270668\pi$
$367$	9276.83			1.31947			0.659736	+	0.751497i	$0.270668\pi$
$368$		0			0
$369$	−3241.31			−0.457279
$370$		0			0
$371$	−1784.10	−	1784.10i	−0.249665	−	0.249665i
$372$		0			0
$373$	−1765.32	+	1765.32i	−0.245053	+	0.245053i	−0.818937	−	0.573884i	$-0.805436\pi$
$373$	−1765.32	+	1765.32i	−0.245053	+	0.245053i	0.573884	+	0.818937i	$0.305436\pi$
$374$		0			0
$375$			681.766i			0.0938834i
$376$		0			0
$377$		−	170.698i		−	0.0233193i
$378$		0			0
$379$	−2909.05	+	2909.05i	−0.394269	+	0.394269i	−0.876206	−	0.481937i	$-0.839933\pi$
$379$	−2909.05	+	2909.05i	−0.394269	+	0.394269i	0.481937	+	0.876206i	$0.339933\pi$
$380$		0			0
$381$	−110.757	−	110.757i	−0.0148930	−	0.0148930i
$382$		0			0
$383$	1520.26			0.202824			0.101412	−	0.994845i	$-0.467664\pi$
$383$	1520.26			0.202824			0.101412	+	0.994845i	$0.467664\pi$
$384$		0			0
$385$	−234.316			−0.0310177
$386$		0			0
$387$	2812.27	+	2812.27i	0.369395	+	0.369395i
$388$		0			0
$389$	8093.35	−	8093.35i	1.05488	−	1.05488i	0.0564785	−	0.998404i	$-0.482013\pi$
$389$	8093.35	−	8093.35i	1.05488	−	1.05488i	0.998404	−	0.0564785i	$-0.0179872\pi$
$390$		0			0
$391$		−	15126.3i		−	1.95644i
$392$		0			0
$393$		−	1645.97i		−	0.211267i
$394$		0			0
$395$	−353.457	+	353.457i	−0.0450237	+	0.0450237i
$396$		0			0
$397$	−8897.26	−	8897.26i	−1.12479	−	1.12479i	−0.991012	−	0.133776i	$-0.957290\pi$
$397$	−8897.26	−	8897.26i	−1.12479	−	1.12479i	−0.133776	−	0.991012i	$-0.542710\pi$
$398$		0			0
$399$	−1321.34			−0.165788
$400$		0			0
$401$	−4199.74			−0.523004			−0.261502	−	0.965203i	$-0.584218\pi$
$401$	−4199.74			−0.523004			−0.261502	+	0.965203i	$0.584218\pi$
$402$		0			0
$403$	−1574.30	−	1574.30i	−0.194595	−	0.194595i
$404$		0			0
$405$	52.2386	−	52.2386i	0.00640928	−	0.00640928i
$406$		0			0
$407$			9407.97i			1.14579i
$408$		0			0
$409$			7881.87i			0.952894i	0.879203	+	0.476447i	$0.158076\pi$
$409$			7881.87i			0.952894i	−0.879203	+	0.476447i	$0.841924\pi$
$410$		0			0
$411$	1686.55	−	1686.55i	0.202412	−	0.202412i
$412$		0			0
$413$	−1090.56	−	1090.56i	−0.129934	−	0.129934i
$414$		0			0
$415$	599.043			0.0708575
$416$		0			0
$417$	7249.40			0.851331
$418$		0			0
$419$	5502.69	+	5502.69i	0.641585	+	0.641585i	0.950945	−	0.309360i	$-0.100115\pi$
$419$	5502.69	+	5502.69i	0.641585	+	0.641585i	−0.309360	+	0.950945i	$0.600115\pi$
$420$		0			0
$421$	−11302.2	+	11302.2i	−1.30840	+	1.30840i	−0.385823	+	0.922573i	$0.626082\pi$
$421$	−11302.2	+	11302.2i	−1.30840	+	1.30840i	−0.922573	+	0.385823i	$0.873918\pi$
$422$		0			0
$423$			3095.02i			0.355757i
$424$		0			0
$425$			8865.90i			1.01190i
$426$		0			0
$427$	3755.14	−	3755.14i	0.425584	−	0.425584i
$428$		0			0
$429$	1576.48	+	1576.48i	0.177420	+	0.177420i
$430$		0			0
$431$	−5428.20			−0.606652			−0.303326	−	0.952887i	$-0.598097\pi$
$431$	−5428.20			−0.606652			−0.303326	+	0.952887i	$0.598097\pi$
$432$		0			0
$433$	−5143.78			−0.570888			−0.285444	−	0.958395i	$-0.592141\pi$
$433$	−5143.78			−0.570888			−0.285444	+	0.958395i	$0.592141\pi$
$434$		0			0
$435$	−15.9919	−	15.9919i	−0.00176265	−	0.00176265i
$436$		0			0
$437$	9241.50	−	9241.50i	1.01163	−	1.01163i
$438$		0			0
$439$		−	2183.50i		−	0.237386i	−0.992931	−	0.118693i	$-0.962130\pi$
$439$		−	2183.50i		−	0.237386i	0.992931	−	0.118693i	$-0.0378705\pi$
$440$		0			0
$441$			2628.28i			0.283801i
$442$		0			0
$443$	−561.821	+	561.821i	−0.0602549	+	0.0602549i	−0.736592	−	0.676337i	$-0.763566\pi$
$443$	−561.821	+	561.821i	−0.0602549	+	0.0602549i	0.676337	+	0.736592i	$0.263566\pi$
$444$		0			0
$445$	−195.397	−	195.397i	−0.0208150	−	0.0208150i
$446$		0			0
$447$	−295.415			−0.0312588
$448$		0			0
$449$	−2639.02			−0.277378			−0.138689	−	0.990336i	$-0.544289\pi$
$449$	−2639.02			−0.277378			−0.138689	+	0.990336i	$0.544289\pi$
$450$		0			0
$451$	−9164.08	−	9164.08i	−0.956807	−	0.956807i
$452$		0			0
$453$	3325.13	−	3325.13i	0.344875	−	0.344875i
$454$		0			0
$455$			134.472i			0.0138552i
$456$		0			0
$457$		−	5546.69i		−	0.567753i	−0.958861	−	0.283876i	$-0.908379\pi$
$457$		−	5546.69i		−	0.567753i	0.958861	−	0.283876i	$-0.0916205\pi$
$458$		0			0
$459$	1363.21	−	1363.21i	0.138625	−	0.138625i
$460$		0			0
$461$	−8475.23	−	8475.23i	−0.856249	−	0.856249i	0.134645	−	0.990894i	$-0.457011\pi$
$461$	−8475.23	−	8475.23i	−0.856249	−	0.856249i	−0.990894	+	0.134645i	$0.957011\pi$
$462$		0			0
$463$	−16410.6			−1.64722			−0.823612	−	0.567154i	$-0.808044\pi$
$463$	−16410.6			−1.64722			−0.823612	+	0.567154i	$0.808044\pi$
$464$		0			0
$465$	−294.979			−0.0294179
$466$		0			0
$467$	6689.53	+	6689.53i	0.662858	+	0.662858i	0.956053	−	0.293195i	$-0.0947185\pi$
$467$	6689.53	+	6689.53i	0.662858	+	0.662858i	−0.293195	+	0.956053i	$0.594719\pi$
$468$		0			0
$469$	252.053	−	252.053i	0.0248161	−	0.0248161i
$470$		0			0
$471$			7375.21i			0.721511i
$472$		0			0
$473$			15902.1i			1.54584i
$474$		0			0
$475$	−5416.69	+	5416.69i	−0.523231	+	0.523231i
$476$		0			0
$477$	2249.10	+	2249.10i	0.215889	+	0.215889i
$478$		0			0
$479$	7188.55			0.685707			0.342853	−	0.939389i	$-0.388607\pi$
$479$	7188.55			0.685707			0.342853	+	0.939389i	$0.388607\pi$
$480$		0			0
$481$	5399.16			0.511810
$482$		0			0
$483$	3208.33	+	3208.33i	0.302244	+	0.302244i
$484$		0			0
$485$	−1010.75	+	1010.75i	−0.0946301	+	0.0946301i
$486$		0			0
$487$			11181.6i			1.04042i	0.854038	+	0.520210i	$0.174146\pi$
$487$			11181.6i			1.04042i	−0.854038	+	0.520210i	$0.825854\pi$
$488$		0			0
$489$		−	11394.5i		−	1.05374i
$490$		0			0
$491$	−11679.8	+	11679.8i	−1.07353	+	1.07353i	−0.0764529	+	0.997073i	$0.524359\pi$
$491$	−11679.8	+	11679.8i	−1.07353	+	1.07353i	−0.997073	+	0.0764529i	$0.975641\pi$
$492$		0			0
$493$	−417.321	−	417.321i	−0.0381241	−	0.0381241i
$494$		0			0
$495$	295.386			0.0268215
$496$		0			0
$497$	−5602.28			−0.505627
$498$		0			0
$499$	2094.26	+	2094.26i	0.187880	+	0.187880i	0.794779	−	0.606899i	$-0.207587\pi$
$499$	2094.26	+	2094.26i	0.187880	+	0.187880i	−0.606899	+	0.794779i	$0.707587\pi$
$500$		0			0
$501$	58.3631	−	58.3631i	0.00520453	−	0.00520453i
$502$		0			0
$503$			4293.63i			0.380604i	0.981726	+	0.190302i	$0.0609466\pi$
$503$			4293.63i			0.380604i	−0.981726	+	0.190302i	$0.939053\pi$
$504$		0			0
$505$		−	76.8912i		−	0.00677548i
$506$		0			0
$507$	−3755.81	+	3755.81i	−0.328997	+	0.328997i
$508$		0			0
$509$	9115.13	+	9115.13i	0.793755	+	0.793755i	0.982102	−	0.188348i	$-0.0603132\pi$
$509$	9115.13	+	9115.13i	0.793755	+	0.793755i	−0.188348	+	0.982102i	$0.560313\pi$
$510$		0			0
$511$	−5712.95			−0.494571
$512$		0			0
$513$	1665.72			0.143359
$514$		0			0
$515$	−1136.73	−	1136.73i	−0.0972631	−	0.0972631i
$516$		0			0
$517$	−8750.49	+	8750.49i	−0.744383	+	0.744383i
$518$		0			0
$519$			12918.3i			1.09258i
$520$		0			0
$521$		−	23150.3i		−	1.94671i	−0.229309	−	0.973354i	$-0.573647\pi$
$521$		−	23150.3i		−	1.94671i	0.229309	−	0.973354i	$-0.426353\pi$
$522$		0			0
$523$	8510.52	−	8510.52i	0.711547	−	0.711547i	−0.255312	−	0.966859i	$-0.582178\pi$
$523$	8510.52	−	8510.52i	0.711547	−	0.711547i	0.966859	+	0.255312i	$0.0821781\pi$
$524$		0			0
$525$	−1880.49	−	1880.49i	−0.156326	−	0.156326i
$526$		0			0
$527$	−7697.69			−0.636274
$528$		0			0
$529$	−32711.4			−2.68854
$530$		0			0
$531$	1374.79	+	1374.79i	0.112356	+	0.112356i
$532$		0			0
$533$	−5259.19	+	5259.19i	−0.427394	+	0.427394i
$534$		0			0
$535$		−	846.884i		−	0.0684373i
$536$		0			0
$537$		−	1551.99i		−	0.124718i
$538$		0			0
$539$	−7430.87	+	7430.87i	−0.593822	+	0.593822i
$540$		0			0
$541$	−3403.84	−	3403.84i	−0.270504	−	0.270504i	0.558799	−	0.829303i	$-0.311262\pi$
$541$	−3403.84	−	3403.84i	−0.270504	−	0.270504i	−0.829303	+	0.558799i	$0.811262\pi$
$542$		0			0
$543$	−7369.91			−0.582455
$544$		0			0
$545$	−422.780			−0.0332292
$546$		0			0
$547$	−15672.4	−	15672.4i	−1.22505	−	1.22505i	−0.965814	−	0.259237i	$-0.916529\pi$
$547$	−15672.4	−	15672.4i	−1.22505	−	1.22505i	−0.259237	−	0.965814i	$-0.583471\pi$
$548$		0			0
$549$	−4733.86	+	4733.86i	−0.368008	+	0.368008i
$550$		0			0
$551$		−	509.930i		−	0.0394261i
$552$		0			0
$553$		−	3912.76i		−	0.300882i
$554$		0			0
$555$	505.822	−	505.822i	0.0386864	−	0.0386864i
$556$		0			0
$557$	−6285.58	−	6285.58i	−0.478149	−	0.478149i	0.426391	−	0.904539i	$-0.359785\pi$
$557$	−6285.58	−	6285.58i	−0.478149	−	0.478149i	−0.904539	+	0.426391i	$0.859785\pi$
$558$		0			0
$559$	9126.11			0.690507
$560$		0			0
$561$	7708.32			0.580117
$562$		0			0
$563$	1763.14	+	1763.14i	0.131985	+	0.131985i	0.770013	−	0.638028i	$-0.220250\pi$
$563$	1763.14	+	1763.14i	0.131985	+	0.131985i	−0.638028	+	0.770013i	$0.720250\pi$
$564$		0			0
$565$	870.114	−	870.114i	0.0647894	−	0.0647894i
$566$		0			0
$567$			578.280i			0.0428316i
$568$		0			0
$569$			1150.05i			0.0847323i	0.999102	+	0.0423662i	$0.0134896\pi$
$569$			1150.05i			0.0847323i	−0.999102	+	0.0423662i	$0.986510\pi$
$570$		0			0
$571$	4853.30	−	4853.30i	0.355699	−	0.355699i	−0.506526	−	0.862225i	$-0.669070\pi$
$571$	4853.30	−	4853.30i	0.355699	−	0.355699i	0.862225	+	0.506526i	$0.169070\pi$
$572$		0			0
$573$	3626.27	+	3626.27i	0.264380	+	0.264380i
$574$		0			0
$575$	26304.4			1.90778
$576$		0			0
$577$	−5152.84			−0.371777			−0.185889	−	0.982571i	$-0.559516\pi$
$577$	−5152.84			−0.371777			−0.185889	+	0.982571i	$0.559516\pi$
$578$		0			0
$579$	−5100.80	−	5100.80i	−0.366117	−	0.366117i
$580$		0			0
$581$	−3315.69	+	3315.69i	−0.236761	+	0.236761i
$582$		0			0
$583$			12717.6i			0.903449i
$584$		0			0
$585$		−	169.520i		−	0.0119808i
$586$		0			0
$587$	−12549.2	+	12549.2i	−0.882387	+	0.882387i	−0.993777	−	0.111390i	$-0.964470\pi$
$587$	−12549.2	+	12549.2i	−0.882387	+	0.882387i	0.111390	+	0.993777i	$0.464470\pi$
$588$		0			0
$589$	−4702.96	−	4702.96i	−0.329002	−	0.329002i
$590$		0			0
$591$	11762.9			0.818714
$592$		0			0
$593$	−1116.75			−0.0773347			−0.0386674	−	0.999252i	$-0.512311\pi$
$593$	−1116.75			−0.0773347			−0.0386674	+	0.999252i	$0.512311\pi$
$594$		0			0
$595$	328.756	+	328.756i	0.0226515	+	0.0226515i
$596$		0			0
$597$	3196.61	−	3196.61i	0.219143	−	0.219143i
$598$		0			0
$599$			15827.4i			1.07962i	0.841788	+	0.539808i	$0.181503\pi$
$599$			15827.4i			1.07962i	−0.841788	+	0.539808i	$0.818497\pi$
$600$		0			0
$601$		−	12216.9i		−	0.829180i	−0.910008	−	0.414590i	$-0.863925\pi$
$601$		−	12216.9i		−	0.829180i	0.910008	−	0.414590i	$-0.136075\pi$
$602$		0			0
$603$	−317.747	+	317.747i	−0.0214588	+	0.0214588i
$604$		0			0
$605$	−23.2516	−	23.2516i	−0.00156250	−	0.00156250i
$606$		0			0
$607$	−24175.5			−1.61656			−0.808282	−	0.588795i	$-0.799602\pi$
$607$	−24175.5			−1.61656			−0.808282	+	0.588795i	$0.799602\pi$
$608$		0			0
$609$	177.030			0.0117793
$610$		0			0
$611$	5021.84	+	5021.84i	0.332507	+	0.332507i
$612$		0			0
$613$	−12893.7	+	12893.7i	−0.849544	+	0.849544i	−0.990076	−	0.140532i	$-0.955119\pi$
$613$	−12893.7	+	12893.7i	−0.849544	+	0.849544i	0.140532	+	0.990076i	$0.455119\pi$
$614$		0			0
$615$			985.420i			0.0646113i
$616$		0			0
$617$		−	13762.7i		−	0.897998i	−0.893532	−	0.448999i	$-0.851781\pi$
$617$		−	13762.7i		−	0.897998i	0.893532	−	0.448999i	$-0.148219\pi$
$618$		0			0
$619$	326.797	−	326.797i	0.0212199	−	0.0212199i	−0.696417	−	0.717637i	$-0.745224\pi$
$619$	326.797	−	326.797i	0.0212199	−	0.0212199i	0.717637	+	0.696417i	$0.245224\pi$
$620$		0			0
$621$	−4044.52	−	4044.52i	−0.261355	−	0.261355i
$622$		0			0
$623$	2163.04			0.139101
$624$		0			0
$625$	−15313.7			−0.980080
$626$		0			0
$627$	4709.46	+	4709.46i	0.299964	+	0.299964i
$628$		0			0
$629$	13199.8	−	13199.8i	0.836742	−	0.836742i
$630$		0			0
$631$		−	12260.2i		−	0.773487i	−0.922187	−	0.386744i	$-0.873600\pi$
$631$		−	12260.2i		−	0.773487i	0.922187	−	0.386744i	$-0.126400\pi$
$632$		0			0
$633$		−	8337.71i		−	0.523529i
$634$		0			0
$635$	−33.6721	+	33.6721i	−0.00210431	+	0.00210431i
$636$		0			0
$637$	4264.52	+	4264.52i	0.265253	+	0.265253i
$638$		0			0
$639$	7062.43			0.437223
$640$		0			0
$641$	10329.4			0.636485			0.318242	−	0.948009i	$-0.396907\pi$
$641$	10329.4			0.636485			0.318242	+	0.948009i	$0.396907\pi$
$642$		0			0
$643$	19299.9	+	19299.9i	1.18369	+	1.18369i	0.978781	+	0.204911i	$0.0656905\pi$
$643$	19299.9	+	19299.9i	1.18369	+	1.18369i	0.204911	+	0.978781i	$0.434309\pi$
$644$		0			0
$645$	854.984	−	854.984i	0.0521937	−	0.0521937i
$646$		0			0
$647$		−	8657.07i		−	0.526035i	−0.964791	−	0.263017i	$-0.915282\pi$
$647$		−	8657.07i		−	0.526035i	0.964791	−	0.263017i	$-0.0847177\pi$
$648$		0			0
$649$			7773.84i			0.470185i
$650$		0			0
$651$	1632.70	−	1632.70i	0.0982960	−	0.0982960i
$652$		0			0
$653$	−5966.31	−	5966.31i	−0.357549	−	0.357549i	0.505360	−	0.862909i	$-0.331360\pi$
$653$	−5966.31	−	5966.31i	−0.357549	−	0.357549i	−0.862909	+	0.505360i	$0.831360\pi$
$654$		0			0
$655$	−500.405			−0.0298511
$656$		0			0
$657$	7201.94			0.427663
$658$		0			0
$659$	−7127.52	−	7127.52i	−0.421318	−	0.421318i	0.464339	−	0.885657i	$-0.346292\pi$
$659$	−7127.52	−	7127.52i	−0.421318	−	0.421318i	−0.885657	+	0.464339i	$0.846292\pi$
$660$		0			0
$661$	−2386.19	+	2386.19i	−0.140412	+	0.140412i	−0.773819	−	0.633407i	$-0.781656\pi$
$661$	−2386.19	+	2386.19i	−0.140412	+	0.140412i	0.633407	+	0.773819i	$0.281656\pi$
$662$		0			0
$663$		−	4423.75i		−	0.259131i
$664$		0			0
$665$			401.711i			0.0234251i
$666$		0			0
$667$	−1238.16	+	1238.16i	−0.0718765	+	0.0718765i
$668$		0			0
$669$	−181.981	−	181.981i	−0.0105169	−	0.0105169i
$670$		0			0
$671$	−26767.9			−1.54003
$672$		0			0
$673$	−3709.39			−0.212461			−0.106231	−	0.994342i	$-0.533878\pi$
$673$	−3709.39			−0.212461			−0.106231	+	0.994342i	$0.533878\pi$
$674$		0			0
$675$	2370.60	+	2370.60i	0.135177	+	0.135177i
$676$		0			0
$677$	1602.20	−	1602.20i	0.0909564	−	0.0909564i	−0.660165	−	0.751121i	$-0.729513\pi$
$677$	1602.20	−	1602.20i	0.0909564	−	0.0909564i	0.751121	+	0.660165i	$0.229513\pi$
$678$		0			0
$679$		−	11188.9i		−	0.632388i
$680$		0			0
$681$			10717.0i			0.603050i
$682$		0			0
$683$	15495.9	−	15495.9i	0.868130	−	0.868130i	−0.124135	−	0.992265i	$-0.539616\pi$
$683$	15495.9	−	15495.9i	0.868130	−	0.868130i	0.992265	+	0.124135i	$0.0396157\pi$
$684$		0			0
$685$	−512.743	−	512.743i	−0.0285999	−	0.0285999i
$686$		0			0
$687$	−4737.52			−0.263097
$688$		0			0
$689$	7298.55			0.403560
$690$		0			0
$691$	−6337.43	−	6337.43i	−0.348896	−	0.348896i	0.510802	−	0.859698i	$-0.329348\pi$
$691$	−6337.43	−	6337.43i	−0.348896	−	0.348896i	−0.859698	+	0.510802i	$0.829348\pi$
$692$		0			0
$693$	−1634.96	+	1634.96i	−0.0896204	+	0.0896204i
$694$		0			0
$695$		−	2203.96i		−	0.120289i
$696$		0			0
$697$			25715.3i			1.39747i
$698$		0			0
$699$	−12206.6	+	12206.6i	−0.660510	+	0.660510i
$700$		0			0
$701$	952.656	+	952.656i	0.0513285	+	0.0513285i	0.732305	−	0.680977i	$-0.238444\pi$
$701$	952.656	+	952.656i	0.0513285	+	0.0513285i	−0.680977	+	0.732305i	$0.738444\pi$
$702$		0			0
$703$	16129.0			0.865318
$704$		0			0
$705$	940.946			0.0502668
$706$		0			0
$707$	425.592	+	425.592i	0.0226394	+	0.0226394i
$708$		0			0
$709$	20781.1	−	20781.1i	1.10078	−	1.10078i	0.106461	−	0.994317i	$-0.466048\pi$
$709$	20781.1	−	20781.1i	1.10078	−	1.10078i	0.994317	−	0.106461i	$-0.0339519\pi$
$710$		0			0
$711$			4932.56i			0.260177i
$712$		0			0
$713$			22838.4i			1.19959i
$714$		0			0
$715$	479.280	−	479.280i	0.0250686	−	0.0250686i
$716$		0			0
$717$	1361.43	+	1361.43i	0.0709114	+	0.0709114i
$718$		0			0
$719$	−1927.96			−0.100001			−0.0500006	−	0.998749i	$-0.515922\pi$
$719$	−1927.96			−0.100001			−0.0500006	+	0.998749i	$0.515922\pi$
$720$		0			0
$721$	12583.6			0.649984
$722$		0			0
$723$	6125.20	+	6125.20i	0.315074	+	0.315074i
$724$		0			0
$725$	725.717	−	725.717i	0.0371758	−	0.0371758i
$726$		0			0
$727$		−	5482.27i		−	0.279678i	−0.990174	−	0.139839i	$-0.955341\pi$
$727$		−	5482.27i		−	0.279678i	0.990174	−	0.139839i	$-0.0446585\pi$
$728$		0			0
$729$		−	729.000i		−	0.0370370i
$730$		0			0
$731$	22311.4	−	22311.4i	1.12889	−	1.12889i
$732$		0			0
$733$	−15048.8	−	15048.8i	−0.758311	−	0.758311i	0.217704	−	0.976015i	$-0.430143\pi$
$733$	−15048.8	−	15048.8i	−0.758311	−	0.758311i	−0.976015	+	0.217704i	$0.930143\pi$
$734$		0			0
$735$	799.046			0.0400997
$736$		0			0
$737$	−1796.72			−0.0898004
$738$		0			0
$739$	−12622.3	−	12622.3i	−0.628306	−	0.628306i	0.319335	−	0.947642i	$-0.396540\pi$
$739$	−12622.3	−	12622.3i	−0.628306	−	0.628306i	−0.947642	+	0.319335i	$0.896540\pi$
$740$		0			0
$741$	2702.72	−	2702.72i	0.133990	−	0.133990i
$742$		0			0
$743$			2335.45i			0.115315i	0.998336	+	0.0576576i	$0.0183632\pi$
$743$			2335.45i			0.115315i	−0.998336	+	0.0576576i	$0.981637\pi$
$744$		0			0
$745$			89.8119i			0.00441672i
$746$		0			0
$747$	4179.88	−	4179.88i	0.204730	−	0.204730i
$748$		0			0
$749$	4687.49	+	4687.49i	0.228674	+	0.228674i
$750$		0			0
$751$	−3513.73			−0.170729			−0.0853647	−	0.996350i	$-0.527206\pi$
$751$	−3513.73			−0.170729			−0.0853647	+	0.996350i	$0.527206\pi$
$752$		0			0
$753$	−10044.7			−0.486119
$754$		0			0
$755$	−1010.90	−	1010.90i	−0.0487292	−	0.0487292i
$756$		0			0
$757$	10416.0	−	10416.0i	0.500102	−	0.500102i	−0.411368	−	0.911470i	$-0.634949\pi$
$757$	10416.0	−	10416.0i	0.500102	−	0.500102i	0.911470	+	0.411368i	$0.134949\pi$
$758$		0			0
$759$		−	22870.0i		−	1.09371i
$760$		0			0
$761$			17937.9i			0.854464i	0.904142	+	0.427232i	$0.140511\pi$
$761$			17937.9i			0.854464i	−0.904142	+	0.427232i	$0.859489\pi$
$762$		0			0
$763$	2340.08	−	2340.08i	0.111031	−	0.111031i
$764$		0			0
$765$	−414.440	−	414.440i	−0.0195871	−	0.0195871i
$766$		0			0
$767$	4461.34			0.210026
$768$		0			0
$769$	32224.0			1.51109			0.755544	−	0.655097i	$-0.227372\pi$
$769$	32224.0			1.51109			0.755544	+	0.655097i	$0.227372\pi$
$770$		0			0
$771$	−10845.1	−	10845.1i	−0.506585	−	0.506585i
$772$		0			0
$773$	−13719.5	+	13719.5i	−0.638365	+	0.638365i	−0.950152	−	0.311787i	$-0.899072\pi$
$773$	−13719.5	+	13719.5i	−0.638365	+	0.638365i	0.311787	+	0.950152i	$0.399072\pi$
$774$		0			0
$775$		−	13386.2i		−	0.620448i
$776$		0			0
$777$			5599.44i			0.258531i
$778$		0			0
$779$	−15710.9	+	15710.9i	−0.722596	+	0.722596i
$780$		0			0
$781$	19967.5	+	19967.5i	0.914842	+	0.914842i
$782$		0			0
$783$	−223.170			−0.0101858
$784$		0			0
$785$	2242.20			0.101946
$786$		0			0
$787$	9919.72	+	9919.72i	0.449301	+	0.449301i	0.895122	−	0.445821i	$-0.147088\pi$
$787$	9919.72	+	9919.72i	0.449301	+	0.449301i	−0.445821	+	0.895122i	$0.647088\pi$
$788$		0			0
$789$	11659.5	−	11659.5i	0.526097	−	0.526097i
$790$		0			0
$791$			9632.14i			0.432970i
$792$		0			0
$793$			15361.9i			0.687915i
$794$		0			0
$795$	683.768	−	683.768i	0.0305041	−	0.0305041i
$796$		0			0
$797$	20018.0	+	20018.0i	0.889679	+	0.889679i	0.994492	−	0.104813i	$-0.0334243\pi$
$797$	20018.0	+	20018.0i	0.889679	+	0.889679i	−0.104813	+	0.994492i	$0.533424\pi$
$798$		0			0
$799$	24554.7			1.08721
$800$		0			0
$801$	−2726.80			−0.120283
$802$		0			0
$803$	20361.9	+	20361.9i	0.894838	+	0.894838i
$804$		0			0
$805$	975.392	−	975.392i	0.0427056	−	0.0427056i
$806$		0			0
$807$		−	10497.8i		−	0.457917i
$808$		0			0
$809$		−	9967.99i		−	0.433196i	−0.976261	−	0.216598i	$-0.930504\pi$
$809$		−	9967.99i		−	0.433196i	0.976261	−	0.216598i	$-0.0694961\pi$
$810$		0			0
$811$	−16080.2	+	16080.2i	−0.696243	+	0.696243i	−0.963598	−	0.267355i	$-0.913850\pi$
$811$	−16080.2	+	16080.2i	−0.696243	+	0.696243i	0.267355	+	0.963598i	$0.413850\pi$
$812$		0			0
$813$	3645.66	+	3645.66i	0.157268	+	0.157268i
$814$		0			0
$815$	−3464.14			−0.148888
$816$		0			0
$817$	27262.7			1.16744
$818$		0			0
$819$	938.290	+	938.290i	0.0400324	+	0.0400324i
$820$		0			0
$821$	−8235.64	+	8235.64i	−0.350092	+	0.350092i	−0.860144	−	0.510051i	$-0.829626\pi$
$821$	−8235.64	+	8235.64i	−0.350092	+	0.350092i	0.510051	+	0.860144i	$0.329626\pi$
$822$		0			0
$823$		−	21762.8i		−	0.921752i	−0.887464	−	0.460876i	$-0.847535\pi$
$823$		−	21762.8i		−	0.921752i	0.887464	−	0.460876i	$-0.152465\pi$
$824$		0			0
$825$			13404.7i			0.565687i
$826$		0			0
$827$	30211.4	−	30211.4i	1.27032	−	1.27032i	0.324396	−	0.945921i	$-0.394839\pi$
$827$	30211.4	−	30211.4i	1.27032	−	1.27032i	0.945921	−	0.324396i	$-0.105161\pi$
$828$		0			0
$829$	16821.1	+	16821.1i	0.704729	+	0.704729i	0.965422	−	0.260692i	$-0.0839509\pi$
$829$	16821.1	+	16821.1i	0.704729	+	0.704729i	−0.260692	+	0.965422i	$0.583951\pi$
$830$		0			0
$831$	−20036.7			−0.836419
$832$		0			0
$833$	20851.7			0.867310
$834$		0			0
$835$	−17.7435	−	17.7435i	−0.000735375	−	0.000735375i
$836$		0			0
$837$	−2058.24	+	2058.24i	−0.0849979	+	0.0849979i
$838$		0			0
$839$		−	21686.9i		−	0.892389i	−0.894936	−	0.446194i	$-0.852779\pi$
$839$		−	21686.9i		−	0.892389i	0.894936	−	0.446194i	$-0.147221\pi$
$840$		0			0
$841$		−	24320.7i		−	0.997199i
$842$		0			0
$843$	5394.95	−	5394.95i	0.220418	−	0.220418i
$844$		0			0
$845$	1141.84	+	1141.84i	0.0464857	+	0.0464857i
$846$		0			0
$847$	257.395			0.0104418
$848$		0			0
$849$	−13605.4			−0.549983
$850$		0			0
$851$	−39162.8	−	39162.8i	−1.57754	−	1.57754i
$852$		0			0
$853$	−12612.5	+	12612.5i	−0.506266	+	0.506266i	−0.913378	−	0.407112i	$-0.866536\pi$
$853$	−12612.5	+	12612.5i	−0.506266	+	0.506266i	0.407112	+	0.913378i	$0.366536\pi$
$854$		0			0
$855$		−	506.411i		−	0.0202560i
$856$		0			0
$857$		−	46080.3i		−	1.83672i	−0.395741	−	0.918362i	$-0.629512\pi$
$857$		−	46080.3i		−	1.83672i	0.395741	−	0.918362i	$-0.370488\pi$
$858$		0			0
$859$	−8935.85	+	8935.85i	−0.354933	+	0.354933i	−0.861941	−	0.507008i	$-0.830751\pi$
$859$	−8935.85	+	8935.85i	−0.354933	+	0.354933i	0.507008	+	0.861941i	$0.330751\pi$
$860$		0			0
$861$	−5454.28	−	5454.28i	−0.215890	−	0.215890i
$862$		0			0
$863$	19360.8			0.763674			0.381837	−	0.924230i	$-0.375292\pi$
$863$	19360.8			0.763674			0.381837	+	0.924230i	$0.375292\pi$
$864$		0			0
$865$	3927.40			0.154377
$866$		0			0
$867$	−393.086	−	393.086i	−0.0153978	−	0.0153978i
$868$		0			0
$869$	−13945.7	+	13945.7i	−0.544391	+	0.544391i
$870$		0			0
$871$			1031.12i			0.0401128i
$872$		0			0
$873$			14105.1i			0.546835i
$874$		0			0
$875$	−1147.24	+	1147.24i	−0.0443242	+	0.0443242i
$876$		0			0
$877$	−19139.4	−	19139.4i	−0.736933	−	0.736933i	0.235050	−	0.971983i	$-0.424475\pi$
$877$	−19139.4	−	19139.4i	−0.736933	−	0.736933i	−0.971983	+	0.235050i	$0.924475\pi$
$878$		0			0
$879$	25079.9			0.962372
$880$		0			0
$881$	4836.79			0.184967			0.0924833	−	0.995714i	$-0.470520\pi$
$881$	4836.79			0.184967			0.0924833	+	0.995714i	$0.470520\pi$
$882$		0			0
$883$	7730.89	+	7730.89i	0.294638	+	0.294638i	0.838909	−	0.544271i	$-0.183194\pi$
$883$	7730.89	+	7730.89i	0.294638	+	0.294638i	−0.544271	+	0.838909i	$0.683194\pi$
$884$		0			0
$885$	417.963	−	417.963i	0.0158753	−	0.0158753i
$886$		0			0
$887$		−	12163.5i		−	0.460442i	−0.973138	−	0.230221i	$-0.926055\pi$
$887$		−	12163.5i		−	0.460442i	0.973138	−	0.230221i	$-0.0739448\pi$
$888$		0			0
$889$		−	372.749i		−	0.0140625i
$890$		0			0
$891$	2061.09	−	2061.09i	0.0774960	−	0.0774960i
$892$		0			0
$893$	15001.9	+	15001.9i	0.562171	+	0.562171i
$894$		0			0
$895$	−471.835			−0.0176220
$896$		0			0
$897$	−13124.9			−0.488548
$898$		0			0
$899$	630.093	+	630.093i	0.0233757	+	0.0233757i
$900$		0			0
$901$	17843.4	−	17843.4i	0.659768	−	0.659768i
$902$		0			0
$903$			9464.65i			0.348797i
$904$		0			0
$905$			2240.59i			0.0822981i
$906$		0			0
$907$	8264.83	−	8264.83i	0.302568	−	0.302568i	−0.539450	−	0.842018i	$-0.681368\pi$
$907$	8264.83	−	8264.83i	0.302568	−	0.302568i	0.842018	+	0.539450i	$0.181368\pi$
$908$		0			0
$909$	−536.516	−	536.516i	−0.0195766	−	0.0195766i
$910$		0			0
$911$	−41364.8			−1.50437			−0.752183	−	0.658955i	$-0.770999\pi$
$911$	−41364.8			−1.50437			−0.752183	+	0.658955i	$0.770999\pi$
$912$		0			0
$913$	23635.3			0.856753
$914$		0			0
$915$	1439.18	+	1439.18i	0.0519978	+	0.0519978i
$916$		0			0
$917$	2769.74	−	2769.74i	0.0997434	−	0.0997434i
$918$		0			0
$919$			36966.7i			1.32690i	0.748221	+	0.663449i	$0.230908\pi$
$919$			36966.7i			1.32690i	−0.748221	+	0.663449i	$0.769092\pi$
$920$		0			0
$921$			4930.99i			0.176419i
$922$		0			0
$923$	11459.2	−	11459.2i	0.408649	−	0.408649i
$924$		0			0
$925$	22954.4	+	22954.4i	0.815929	+	0.815929i
$926$		0			0
$927$	−15863.3			−0.562050
$928$		0			0
$929$	−18882.5			−0.666862			−0.333431	−	0.942774i	$-0.608206\pi$
$929$	−18882.5			−0.666862			−0.333431	+	0.942774i	$0.608206\pi$
$930$		0			0
$931$	12739.5	+	12739.5i	0.448464	+	0.448464i
$932$		0			0
$933$	−5000.55	+	5000.55i	−0.175467	+	0.175467i
$934$		0			0
$935$		−	2343.48i		−	0.0819678i
$936$		0			0
$937$		−	8581.23i		−	0.299185i	−0.988748	−	0.149593i	$-0.952204\pi$
$937$		−	8581.23i		−	0.299185i	0.988748	−	0.149593i	$-0.0477962\pi$
$938$		0			0
$939$	8031.21	−	8031.21i	0.279115	−	0.279115i
$940$		0			0
$941$	5618.83	+	5618.83i	0.194653	+	0.194653i	0.797703	−	0.603050i	$-0.206048\pi$
$941$	5618.83	+	5618.83i	0.194653	+	0.194653i	−0.603050	+	0.797703i	$0.706048\pi$
$942$		0			0
$943$	76295.1			2.63469
$944$		0			0
$945$	175.808			0.00605189
$946$		0			0
$947$	−18722.7	−	18722.7i	−0.642456	−	0.642456i	0.308702	−	0.951159i	$-0.400105\pi$
$947$	−18722.7	−	18722.7i	−0.642456	−	0.642456i	−0.951159	+	0.308702i	$0.900105\pi$
$948$		0			0
$949$	11685.5	−	11685.5i	0.399713	−	0.399713i
$950$		0			0
$951$		−	13302.8i		−	0.453600i
$952$		0			0
$953$		−	17197.8i		−	0.584565i	−0.956332	−	0.292282i	$-0.905585\pi$
$953$		−	17197.8i		−	0.584565i	0.956332	−	0.292282i	$-0.0944147\pi$
$954$		0			0
$955$	1102.45	−	1102.45i	0.0373556	−	0.0373556i
$956$		0			0
$957$	−630.963	−	630.963i	−0.0213126	−	0.0213126i
$958$		0			0
$959$	5676.06			0.191126
$960$		0			0
$961$	−18168.6			−0.609870
$962$		0			0
$963$	−5909.21	−	5909.21i	−0.197738	−	0.197738i
$964$		0			0
$965$	−1550.74	+	1550.74i	−0.0517306	+	0.0517306i
$966$		0			0
$967$			58259.3i			1.93743i	0.248182	+	0.968713i	$0.420167\pi$
$967$			58259.3i			1.93743i	−0.248182	+	0.968713i	$0.579833\pi$
$968$		0			0
$969$		−	13215.2i		−	0.438114i
$970$		0			0
$971$	19203.8	−	19203.8i	0.634685	−	0.634685i	−0.314555	−	0.949239i	$-0.601855\pi$
$971$	19203.8	−	19203.8i	0.634685	−	0.634685i	0.949239	+	0.314555i	$0.101855\pi$
$972$		0			0
$973$	12198.9	+	12198.9i	0.401930	+	0.401930i
$974$		0			0
$975$	7692.86			0.252686
$976$		0			0
$977$	−16691.4			−0.546578			−0.273289	−	0.961932i	$-0.588112\pi$
$977$	−16691.4			−0.546578			−0.273289	+	0.961932i	$0.588112\pi$
$978$		0			0
$979$	−7709.41	−	7709.41i	−0.251679	−	0.251679i
$980$		0			0
$981$	−2949.99	+	2949.99i	−0.0960101	+	0.0960101i
$982$		0			0
$983$			36043.6i			1.16949i	0.811216	+	0.584747i	$0.198806\pi$
$983$			36043.6i			1.16949i	−0.811216	+	0.584747i	$0.801194\pi$
$984$		0			0
$985$		−	3576.14i		−	0.115680i
$986$		0			0
$987$	−5208.12	+	5208.12i	−0.167960	+	0.167960i
$988$		0			0
$989$	−66196.3	−	66196.3i	−2.12833	−	2.12833i
$990$		0			0
$991$	−48948.9			−1.56904			−0.784518	−	0.620107i	$-0.787089\pi$
$991$	−48948.9			−1.56904			−0.784518	+	0.620107i	$0.787089\pi$
$992$		0			0
$993$	−7357.23			−0.235120
$994$		0			0
$995$	−971.831	−	971.831i	−0.0309639	−	0.0309639i
$996$		0			0
$997$	22542.1	−	22542.1i	0.716062	−	0.716062i	−0.251734	−	0.967796i	$-0.581001\pi$
$997$	22542.1	−	22542.1i	0.716062	−	0.716062i	0.967796	+	0.251734i	$0.0810008\pi$
$998$		0			0
$999$		−	7058.84i		−	0.223556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.j.b.289.4		24
4.3	odd	2		384.4.j.a.289.9		24
8.3	odd	2		192.4.j.a.145.3		24
8.5	even	2		48.4.j.a.13.10	✓	24
16.3	odd	4		192.4.j.a.49.3		24
16.5	even	4	inner	384.4.j.b.97.4		24
16.11	odd	4		384.4.j.a.97.9		24
16.13	even	4		48.4.j.a.37.10	yes	24
24.5	odd	2		144.4.k.b.109.3		24
24.11	even	2		576.4.k.b.145.7		24
48.29	odd	4		144.4.k.b.37.3		24
48.35	even	4		576.4.k.b.433.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.10	✓	24	8.5	even	2
48.4.j.a.37.10	yes	24	16.13	even	4
144.4.k.b.37.3		24	48.29	odd	4
144.4.k.b.109.3		24	24.5	odd	2
192.4.j.a.49.3		24	16.3	odd	4
192.4.j.a.145.3		24	8.3	odd	2
384.4.j.a.97.9		24	16.11	odd	4
384.4.j.a.289.9		24	4.3	odd	2
384.4.j.b.97.4		24	16.5	even	4	inner
384.4.j.b.289.4		24	1.1	even	1	trivial
576.4.k.b.145.7		24	24.11	even	2
576.4.k.b.433.7		24	48.35	even	4

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-0.644922 + 0.644922i) q^{5} -7.13926i q^{7} +9.00000i q^{9} +O(q^{10})\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-0.644922 + 0.644922i) q^{5} -7.13926i q^{7} +9.00000i q^{9} +(-25.4455 + 25.4455i) q^{11} +(14.6030 + 14.6030i) q^{13} +2.73617 q^{15} +71.4024 q^{17} +(43.6238 + 43.6238i) q^{19} +(-15.1447 + 15.1447i) q^{21} -211.845i q^{23} +124.168i q^{25} +(19.0919 - 19.0919i) q^{27} +(-5.84463 - 5.84463i) q^{29} -107.807 q^{31} +107.956 q^{33} +(4.60426 + 4.60426i) q^{35} +(184.865 - 184.865i) q^{37} -61.9551i q^{39} +360.146i q^{41} +(312.475 - 312.475i) q^{43} +(-5.80429 - 5.80429i) q^{45} +343.892 q^{47} +292.031 q^{49} +(-151.467 - 151.467i) q^{51} +(249.900 - 249.900i) q^{53} -32.8207i q^{55} -185.080i q^{57} +(152.755 - 152.755i) q^{59} +(525.985 + 525.985i) q^{61} +64.2534 q^{63} -18.8355 q^{65} +(35.3052 + 35.3052i) q^{67} +(-449.392 + 449.392i) q^{69} -784.715i q^{71} -800.215i q^{73} +(263.400 - 263.400i) q^{75} +(181.662 + 181.662i) q^{77} +548.062 q^{79} -81.0000 q^{81} +(-464.431 - 464.431i) q^{83} +(-46.0489 + 46.0489i) q^{85} +24.7967i q^{87} +302.977i q^{89} +(104.254 - 104.254i) q^{91} +(228.693 + 228.693i) q^{93} -56.2679 q^{95} +1567.24 q^{97} +(-229.009 - 229.009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 40 q^{11} + 120 q^{15} - 24 q^{19} - 400 q^{29} - 744 q^{31} + 456 q^{35} - 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} - 752 q^{53} + 1376 q^{59} + 912 q^{61} - 504 q^{63} + 976 q^{65} + 2256 q^{67} + 528 q^{69} - 1104 q^{75} - 1904 q^{77} + 5992 q^{79} - 1944 q^{81} - 2680 q^{83} + 240 q^{85} + 3496 q^{91} - 7728 q^{95} + 360 q^{99}+O(q^{100}) \) 24 * q + 40 * q^11 + 120 * q^15 - 24 * q^19 - 400 * q^29 - 744 * q^31 + 456 * q^35 - 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 - 752 * q^53 + 1376 * q^59 + 912 * q^61 - 504 * q^63 + 976 * q^65 + 2256 * q^67 + 528 * q^69 - 1104 * q^75 - 1904 * q^77 + 5992 * q^79 - 1944 * q^81 - 2680 * q^83 + 240 * q^85 + 3496 * q^91 - 7728 * q^95 + 360 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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