LMFDB - Embedded newform 384.4.k.b.287.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [384,4,Mod(95,384)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("384.95"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(384, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [44,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.17
Character	$\chi$	$=$	384.287
Dual form			384.4.k.b.95.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.58035 - 3.76578i) q^{3} +(4.71515 - 4.71515i) q^{5} +4.67595 q^{7} +(-1.36225 - 26.9656i) q^{9} +(-29.7408 - 29.7408i) q^{11} +(-36.9803 + 36.9803i) q^{13} +(-0.874367 - 34.6381i) q^{15} -109.986i q^{17} +(-28.6283 - 28.6283i) q^{19} +(16.7415 - 17.6086i) q^{21} +0.193203i q^{23} +80.5347i q^{25} +(-106.424 - 91.4163i) q^{27} +(162.554 + 162.554i) q^{29} -179.457i q^{31} +(-218.480 + 5.51507i) q^{33} +(22.0478 - 22.0478i) q^{35} +(-194.940 - 194.940i) q^{37} +(6.85755 + 271.662i) q^{39} -49.2056 q^{41} +(336.318 - 336.318i) q^{43} +(-133.570 - 120.724i) q^{45} +187.268 q^{47} -321.136 q^{49} +(-414.182 - 393.787i) q^{51} +(-195.182 + 195.182i) q^{53} -280.465 q^{55} +(-210.307 + 5.30877i) q^{57} +(302.622 + 302.622i) q^{59} +(-501.230 + 501.230i) q^{61} +(-6.36981 - 126.090i) q^{63} +348.736i q^{65} +(36.4798 + 36.4798i) q^{67} +(0.727560 + 0.691733i) q^{69} -637.743i q^{71} -90.3903i q^{73} +(303.276 + 288.342i) q^{75} +(-139.067 - 139.067i) q^{77} -1171.61i q^{79} +(-725.289 + 73.4678i) q^{81} +(256.872 - 256.872i) q^{83} +(-518.599 - 518.599i) q^{85} +(1194.14 - 30.1437i) q^{87} +818.864 q^{89} +(-172.918 + 172.918i) q^{91} +(-675.797 - 642.519i) q^{93} -269.973 q^{95} +667.747 q^{97} +(-761.465 + 842.494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Character values

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

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

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
$3$	3.58035	−	3.76578i	0.689038	−	0.724725i
$3$	3.58035	−	3.76578i	0.689038	−	0.724725i
$4$		0			0
$5$	4.71515	−	4.71515i	0.421736	−	0.421736i	−0.464065	−	0.885801i	$-0.653610\pi$
$5$	4.71515	−	4.71515i	0.421736	−	0.421736i	0.885801	+	0.464065i	$0.153610\pi$
$6$		0			0
$7$	4.67595			0.252477			0.126239	−	0.992000i	$-0.459709\pi$
$7$	4.67595			0.252477			0.126239	+	0.992000i	$0.459709\pi$
$8$		0			0
$9$	−1.36225	−	26.9656i	−0.0504537	−	0.998726i
$10$		0			0
$11$	−29.7408	−	29.7408i	−0.815200	−	0.815200i	0.170208	−	0.985408i	$-0.445556\pi$
$11$	−29.7408	−	29.7408i	−0.815200	−	0.815200i	−0.985408	+	0.170208i	$0.945556\pi$
$12$		0			0
$13$	−36.9803	+	36.9803i	−0.788961	+	0.788961i	−0.981324	−	0.192363i	$-0.938385\pi$
$13$	−36.9803	+	36.9803i	−0.788961	+	0.788961i	0.192363	+	0.981324i	$0.438385\pi$
$14$		0			0
$15$	−0.874367	−	34.6381i	−0.0150507	−	0.596235i
$16$		0			0
$17$		−	109.986i		−	1.56914i	−0.620037	−	0.784572i	$-0.712883\pi$
$17$		−	109.986i		−	1.56914i	0.620037	−	0.784572i	$-0.287117\pi$
$18$		0			0
$19$	−28.6283	−	28.6283i	−0.345673	−	0.345673i	0.512822	−	0.858495i	$-0.328600\pi$
$19$	−28.6283	−	28.6283i	−0.345673	−	0.345673i	−0.858495	+	0.512822i	$0.828600\pi$
$20$		0			0
$21$	16.7415	−	17.6086i	0.173967	−	0.182977i
$22$		0			0
$23$			0.193203i			0.00175155i	1.00000		0.000875773i	$0.000278767\pi$
$23$			0.193203i			0.00175155i	−1.00000		0.000875773i	$0.999721\pi$
$24$		0			0
$25$			80.5347i			0.644277i
$26$		0			0
$27$	−106.424	−	91.4163i	−0.758567	−	0.651595i
$28$		0			0
$29$	162.554	+	162.554i	1.04088	+	1.04088i	0.999128	+	0.0417521i	$0.0132940\pi$
$29$	162.554	+	162.554i	1.04088	+	1.04088i	0.0417521	+	0.999128i	$0.486706\pi$
$30$		0			0
$31$		−	179.457i		−	1.03973i	−0.854250	−	0.519863i	$-0.825983\pi$
$31$		−	179.457i		−	1.03973i	0.854250	−	0.519863i	$-0.174017\pi$
$32$		0			0
$33$	−218.480	+	5.51507i	−1.15250	+	0.0290925i
$34$		0			0
$35$	22.0478	−	22.0478i	0.106479	−	0.106479i
$36$		0			0
$37$	−194.940	−	194.940i	−0.866160	−	0.866160i	0.125885	−	0.992045i	$-0.459823\pi$
$37$	−194.940	−	194.940i	−0.866160	−	0.866160i	−0.992045	+	0.125885i	$0.959823\pi$
$38$		0			0
$39$	6.85755	+	271.662i	0.0281561	+	1.11540i
$40$		0			0
$41$	−49.2056			−0.187430			−0.0937149	−	0.995599i	$-0.529874\pi$
$41$	−49.2056			−0.187430			−0.0937149	+	0.995599i	$0.529874\pi$
$42$		0			0
$43$	336.318	−	336.318i	1.19274	−	1.19274i	0.216450	−	0.976294i	$-0.430552\pi$
$43$	336.318	−	336.318i	1.19274	−	1.19274i	0.976294	−	0.216450i	$-0.0694480\pi$
$44$		0			0
$45$	−133.570	−	120.724i	−0.442477	−	0.399921i
$46$		0			0
$47$	187.268			0.581188			0.290594	−	0.956846i	$-0.406147\pi$
$47$	187.268			0.581188			0.290594	+	0.956846i	$0.406147\pi$
$48$		0			0
$49$	−321.136			−0.936255
$50$		0			0
$51$	−414.182	−	393.787i	−1.13720	−	1.08120i
$52$		0			0
$53$	−195.182	+	195.182i	−0.505855	+	0.505855i	−0.913252	−	0.407396i	$-0.866437\pi$
$53$	−195.182	+	195.182i	−0.505855	+	0.505855i	0.407396	+	0.913252i	$0.366437\pi$
$54$		0			0
$55$	−280.465			−0.687598
$56$		0			0
$57$	−210.307	+	5.30877i	−0.488699	+	0.0123362i
$58$		0			0
$59$	302.622	+	302.622i	0.667763	+	0.667763i	0.957198	−	0.289435i	$-0.0934674\pi$
$59$	302.622	+	302.622i	0.667763	+	0.667763i	−0.289435	+	0.957198i	$0.593467\pi$
$60$		0			0
$61$	−501.230	+	501.230i	−1.05207	+	1.05207i	−0.0534972	+	0.998568i	$0.517037\pi$
$61$	−501.230	+	501.230i	−1.05207	+	1.05207i	−0.998568	+	0.0534972i	$0.982963\pi$
$62$		0			0
$63$	−6.36981	−	126.090i	−0.0127384	−	0.252156i
$64$		0			0
$65$			348.736i			0.665467i
$66$		0			0
$67$	36.4798	+	36.4798i	0.0665183	+	0.0665183i	0.739583	−	0.673065i	$-0.235023\pi$
$67$	36.4798	+	36.4798i	0.0665183	+	0.0665183i	−0.673065	+	0.739583i	$0.735023\pi$
$68$		0			0
$69$	0.727560	+	0.691733i	0.00126939	+	0.00120688i
$70$		0			0
$71$		−	637.743i		−	1.06600i	−0.846114	−	0.533001i	$-0.821064\pi$
$71$		−	637.743i		−	1.06600i	0.846114	−	0.533001i	$-0.178936\pi$
$72$		0			0
$73$		−	90.3903i		−	0.144923i	−0.997371	−	0.0724615i	$-0.976915\pi$
$73$		−	90.3903i		−	0.144923i	0.997371	−	0.0724615i	$-0.0230855\pi$
$74$		0			0
$75$	303.276	+	288.342i	0.466924	+	0.443932i
$76$		0			0
$77$	−139.067	−	139.067i	−0.205820	−	0.205820i
$78$		0			0
$79$		−	1171.61i		−	1.66856i	−0.551341	−	0.834280i	$-0.685884\pi$
$79$		−	1171.61i		−	1.66856i	0.551341	−	0.834280i	$-0.314116\pi$
$80$		0			0
$81$	−725.289	+	73.4678i	−0.994909	+	0.100779i
$82$		0			0
$83$	256.872	−	256.872i	0.339703	−	0.339703i	−0.516553	−	0.856256i	$-0.672785\pi$
$83$	256.872	−	256.872i	0.339703	−	0.339703i	0.856256	+	0.516553i	$0.172785\pi$
$84$		0			0
$85$	−518.599	−	518.599i	−0.661765	−	0.661765i
$86$		0			0
$87$	1194.14	−	30.1437i	1.47156	−	0.0371464i
$88$		0			0
$89$	818.864			0.975274			0.487637	−	0.873047i	$-0.337859\pi$
$89$	818.864			0.975274			0.487637	+	0.873047i	$0.337859\pi$
$90$		0			0
$91$	−172.918	+	172.918i	−0.199195	+	0.199195i
$92$		0			0
$93$	−675.797	−	642.519i	−0.753515	−	0.716410i
$94$		0			0
$95$	−269.973			−0.291565
$96$		0			0
$97$	667.747			0.698964			0.349482	−	0.936943i	$-0.386358\pi$
$97$	667.747			0.698964			0.349482	+	0.936943i	$0.386358\pi$
$98$		0			0
$99$	−761.465	+	842.494i	−0.773032	+	0.855292i
$100$		0			0
$101$	794.088	−	794.088i	0.782324	−	0.782324i	−0.197899	−	0.980222i	$-0.563412\pi$
$101$	794.088	−	794.088i	0.782324	−	0.782324i	0.980222	+	0.197899i	$0.0634118\pi$
$102$		0			0
$103$	−1086.33			−1.03921			−0.519607	−	0.854405i	$-0.673922\pi$
$103$	−1086.33			−1.03921			−0.519607	+	0.854405i	$0.673922\pi$
$104$		0			0
$105$	−4.08850	−	161.966i	−0.00379997	−	0.150536i
$106$		0			0
$107$	−488.119	−	488.119i	−0.441011	−	0.441011i	0.451341	−	0.892352i	$-0.350946\pi$
$107$	−488.119	−	488.119i	−0.441011	−	0.441011i	−0.892352	+	0.451341i	$0.850946\pi$
$108$		0			0
$109$	131.638	−	131.638i	0.115675	−	0.115675i	−0.646900	−	0.762575i	$-0.723935\pi$
$109$	131.638	−	131.638i	0.115675	−	0.115675i	0.762575	+	0.646900i	$0.223935\pi$
$110$		0			0
$111$	−1432.05	+	36.1492i	−1.22455	+	0.0309111i
$112$		0			0
$113$			1202.65i			1.00120i	0.865678	+	0.500601i	$0.166887\pi$
$113$			1202.65i			1.00120i	−0.865678	+	0.500601i	$0.833113\pi$
$114$		0			0
$115$	0.910981	+	0.910981i	0.000738690	+	0.000738690i
$116$		0			0
$117$	1047.57	+	946.821i	0.827763	+	0.748151i
$118$		0			0
$119$		−	514.288i		−	0.396174i
$120$		0			0
$121$			438.035i			0.329102i
$122$		0			0
$123$	−176.173	+	185.298i	−0.129146	+	0.135835i
$124$		0			0
$125$	969.127	+	969.127i	0.693451	+	0.693451i
$126$		0			0
$127$			2564.42i			1.79178i	0.444281	+	0.895888i	$0.353459\pi$
$127$			2564.42i			1.79178i	−0.444281	+	0.895888i	$0.646541\pi$
$128$		0			0
$129$	−62.3660	−	2470.63i	−0.0425661	−	1.68626i
$130$		0			0
$131$	1241.94	−	1241.94i	0.828309	−	0.828309i	−0.158974	−	0.987283i	$-0.550819\pi$
$131$	1241.94	−	1241.94i	0.828309	−	0.828309i	0.987283	+	0.158974i	$0.0508186\pi$
$132$		0			0
$133$	−133.864	−	133.864i	−0.0872746	−	0.0872746i
$134$		0			0
$135$	−932.847	+	70.7636i	−0.594716	+	0.0451138i
$136$		0			0
$137$	1381.99			0.861835			0.430917	−	0.902391i	$-0.358190\pi$
$137$	1381.99			0.861835			0.430917	+	0.902391i	$0.358190\pi$
$138$		0			0
$139$	643.732	−	643.732i	0.392810	−	0.392810i	−0.482877	−	0.875688i	$-0.660408\pi$
$139$	643.732	−	643.732i	0.392810	−	0.392810i	0.875688	+	0.482877i	$0.160408\pi$
$140$		0			0
$141$	670.484	−	705.210i	0.400460	−	0.421201i
$142$		0			0
$143$	2199.65			1.28632
$144$		0			0
$145$	1532.93			0.877953
$146$		0			0
$147$	−1149.78	+	1209.33i	−0.645115	+	0.678528i
$148$		0			0
$149$	−604.581	+	604.581i	−0.332411	+	0.332411i	−0.853501	−	0.521091i	$-0.825525\pi$
$149$	−604.581	+	604.581i	−0.332411	+	0.332411i	0.521091	+	0.853501i	$0.325525\pi$
$150$		0			0
$151$	1368.69			0.737631			0.368815	−	0.929503i	$-0.379763\pi$
$151$	1368.69			0.737631			0.368815	+	0.929503i	$0.379763\pi$
$152$		0			0
$153$	−2965.83	+	149.828i	−1.56715	+	0.0791691i
$154$		0			0
$155$	−846.168	−	846.168i	−0.438490	−	0.438490i
$156$		0			0
$157$	1561.01	−	1561.01i	0.793516	−	0.793516i	−0.188548	−	0.982064i	$-0.560378\pi$
$157$	1561.01	−	1561.01i	0.793516	−	0.793516i	0.982064	+	0.188548i	$0.0603780\pi$
$158$		0			0
$159$	36.1941	+	1433.83i	0.0180527	+	0.715160i
$160$		0			0
$161$			0.903406i			0.000442226i
$162$		0			0
$163$	2034.33	+	2034.33i	0.977554	+	0.977554i	0.999754	−	0.0221997i	$-0.00706698\pi$
$163$	2034.33	+	2034.33i	0.977554	+	0.977554i	−0.0221997	+	0.999754i	$0.507067\pi$
$164$		0			0
$165$	−1004.16	+	1056.17i	−0.473781	+	0.498320i
$166$		0			0
$167$			1459.42i			0.676249i	0.941101	+	0.338125i	$0.109793\pi$
$167$			1459.42i			0.676249i	−0.941101	+	0.338125i	$0.890207\pi$
$168$		0			0
$169$		−	538.090i		−	0.244920i
$170$		0			0
$171$	−732.980	+	810.978i	−0.327792	+	0.362673i
$172$		0			0
$173$	867.517	+	867.517i	0.381249	+	0.381249i	0.871552	−	0.490303i	$-0.163114\pi$
$173$	867.517	+	867.517i	0.381249	+	0.381249i	−0.490303	+	0.871552i	$0.663114\pi$
$174$		0			0
$175$			376.576i			0.162666i
$176$		0			0
$177$	2223.10	−	56.1175i	0.944058	−	0.0238308i
$178$		0			0
$179$	1628.54	−	1628.54i	0.680017	−	0.680017i	−0.279987	−	0.960004i	$-0.590330\pi$
$179$	1628.54	−	1628.54i	0.680017	−	0.680017i	0.960004	+	0.279987i	$0.0903300\pi$
$180$		0			0
$181$	2209.08	+	2209.08i	0.907181	+	0.907181i	0.996044	−	0.0888632i	$-0.0283234\pi$
$181$	2209.08	+	2209.08i	0.907181	+	0.907181i	−0.0888632	+	0.996044i	$0.528323\pi$
$182$		0			0
$183$	92.9470	+	3682.10i	0.0375456	+	1.48737i
$184$		0			0
$185$	−1838.34			−0.730582
$186$		0			0
$187$	−3271.07	+	3271.07i	−1.27917	+	1.27917i
$188$		0			0
$189$	−497.633	−	427.458i	−0.191521	−	0.164513i
$190$		0			0
$191$	1746.47			0.661623			0.330812	−	0.943697i	$-0.392678\pi$
$191$	1746.47			0.661623			0.330812	+	0.943697i	$0.392678\pi$
$192$		0			0
$193$	1250.64			0.466441			0.233220	−	0.972424i	$-0.425074\pi$
$193$	1250.64			0.466441			0.233220	+	0.972424i	$0.425074\pi$
$194$		0			0
$195$	1313.26	+	1248.59i	0.482281	+	0.458532i
$196$		0			0
$197$	−31.6458	+	31.6458i	−0.0114450	+	0.0114450i	−0.712806	−	0.701361i	$-0.752576\pi$
$197$	−31.6458	+	31.6458i	−0.0114450	+	0.0114450i	0.701361	+	0.712806i	$0.252576\pi$
$198$		0			0
$199$	268.802			0.0957530			0.0478765	−	0.998853i	$-0.484755\pi$
$199$	268.802			0.0957530			0.0478765	+	0.998853i	$0.484755\pi$
$200$		0			0
$201$	267.986	−	6.76474i	0.0940411	−	0.00237387i
$202$		0			0
$203$	760.094	+	760.094i	0.262799	+	0.262799i
$204$		0			0
$205$	−232.012	+	232.012i	−0.0790459	+	0.0790459i
$206$		0			0
$207$	5.20983	−	0.263190i	0.00174932	−	8.83720e-5i
$208$		0			0
$209$			1702.86i			0.563585i
$210$		0			0
$211$	−917.057	−	917.057i	−0.299208	−	0.299208i	0.541496	−	0.840703i	$-0.317858\pi$
$211$	−917.057	−	917.057i	−0.299208	−	0.299208i	−0.840703	+	0.541496i	$0.817858\pi$
$212$		0			0
$213$	−2401.60	−	2283.34i	−0.772559	−	0.734516i
$214$		0			0
$215$		−	3171.58i		−	1.00605i
$216$		0			0
$217$		−	839.133i		−	0.262507i
$218$		0			0
$219$	−340.390	−	323.628i	−0.105029	−	0.0998575i
$220$		0			0
$221$	4067.31	+	4067.31i	1.23799	+	1.23799i
$222$		0			0
$223$			332.177i			0.0997499i	0.998755	+	0.0498749i	$0.0158823\pi$
$223$			332.177i			0.0997499i	−0.998755	+	0.0498749i	$0.984118\pi$
$224$		0			0
$225$	2171.67	−	109.708i	0.643457	−	0.0325062i
$226$		0			0
$227$	−1201.02	+	1201.02i	−0.351164	+	0.351164i	−0.860543	−	0.509378i	$-0.829875\pi$
$227$	−1201.02	+	1201.02i	−0.351164	+	0.351164i	0.509378	+	0.860543i	$0.329875\pi$
$228$		0			0
$229$	2969.95	+	2969.95i	0.857031	+	0.857031i	0.990987	−	0.133957i	$-0.0427683\pi$
$229$	2969.95	+	2969.95i	0.857031	+	0.857031i	−0.133957	+	0.990987i	$0.542768\pi$
$230$		0			0
$231$	−1021.60	+	25.7882i	−0.290980	+	0.00734519i
$232$		0			0
$233$	4481.22			1.25998			0.629988	−	0.776605i	$-0.283060\pi$
$233$	4481.22			1.25998			0.629988	+	0.776605i	$0.283060\pi$
$234$		0			0
$235$	882.996	−	882.996i	0.245108	−	0.245108i
$236$		0			0
$237$	−4412.02	−	4194.76i	−1.20925	−	1.14970i
$238$		0			0
$239$	−2196.96			−0.594602			−0.297301	−	0.954784i	$-0.596086\pi$
$239$	−2196.96			−0.594602			−0.297301	+	0.954784i	$0.596086\pi$
$240$		0			0
$241$	−2608.91			−0.697322			−0.348661	−	0.937249i	$-0.613363\pi$
$241$	−2608.91			−0.697322			−0.348661	+	0.937249i	$0.613363\pi$
$242$		0			0
$243$	−2320.12	+	2994.32i	−0.612493	+	0.790476i
$244$		0			0
$245$	−1514.20	+	1514.20i	−0.394852	+	0.394852i
$246$		0			0
$247$	2117.37			0.545445
$248$		0			0
$249$	−47.6337	−	1887.01i	−0.0121232	−	0.480260i
$250$		0			0
$251$	1134.95	+	1134.95i	0.285409	+	0.285409i	0.835262	−	0.549853i	$-0.185316\pi$
$251$	1134.95	+	1134.95i	0.285409	+	0.285409i	−0.549853	+	0.835262i	$0.685316\pi$
$252$		0			0
$253$	5.74601	−	5.74601i	0.00142786	−	0.00142786i
$254$		0			0
$255$	−3809.70	+	96.1679i	−0.935579	+	0.0236167i
$256$		0			0
$257$		−	1979.45i		−	0.480446i	−0.970718	−	0.240223i	$-0.922779\pi$
$257$		−	1979.45i		−	0.480446i	0.970718	−	0.240223i	$-0.0772206\pi$
$258$		0			0
$259$	−911.529	−	911.529i	−0.218686	−	0.218686i
$260$		0			0
$261$	4161.93	−	4604.81i	0.987038	−	1.09207i
$262$		0			0
$263$		−	5494.40i		−	1.28821i	−0.764937	−	0.644105i	$-0.777230\pi$
$263$		−	5494.40i		−	1.28821i	0.764937	−	0.644105i	$-0.222770\pi$
$264$		0			0
$265$			1840.63i			0.426675i
$266$		0			0
$267$	2931.82	−	3083.66i	0.672001	−	0.706806i
$268$		0			0
$269$	−3967.07	−	3967.07i	−0.899169	−	0.899169i	0.0961936	−	0.995363i	$-0.469333\pi$
$269$	−3967.07	−	3967.07i	−0.899169	−	0.899169i	−0.995363	+	0.0961936i	$0.969333\pi$
$270$		0			0
$271$			2659.35i			0.596103i	0.954550	+	0.298051i	$0.0963367\pi$
$271$			2659.35i			0.596103i	−0.954550	+	0.298051i	$0.903663\pi$
$272$		0			0
$273$	32.0656	+	1270.28i	0.00710877	+	0.281615i
$274$		0			0
$275$	2395.17	−	2395.17i	0.525215	−	0.525215i
$276$		0			0
$277$	−3478.53	−	3478.53i	−0.754530	−	0.754530i	0.220791	−	0.975321i	$-0.429136\pi$
$277$	−3478.53	−	3478.53i	−0.754530	−	0.754530i	−0.975321	+	0.220791i	$0.929136\pi$
$278$		0			0
$279$	−4839.18	+	244.466i	−1.03840	+	0.0524580i
$280$		0			0
$281$	555.076			0.117840			0.0589200	−	0.998263i	$-0.481234\pi$
$281$	555.076			0.117840			0.0589200	+	0.998263i	$0.481234\pi$
$282$		0			0
$283$	2673.37	−	2673.37i	0.561538	−	0.561538i	−0.368206	−	0.929744i	$-0.620028\pi$
$283$	2673.37	−	2673.37i	0.561538	−	0.561538i	0.929744	+	0.368206i	$0.120028\pi$
$284$		0			0
$285$	−966.598	+	1016.66i	−0.200899	+	0.211305i
$286$		0			0
$287$	−230.083			−0.0473218
$288$		0			0
$289$	−7183.86			−1.46221
$290$		0			0
$291$	2390.77	−	2514.59i	0.481612	−	0.506557i
$292$		0			0
$293$	5234.64	−	5234.64i	1.04372	−	1.04372i	0.0447231	−	0.998999i	$-0.485759\pi$
$293$	5234.64	−	5234.64i	1.04372	−	1.04372i	0.998999	−	0.0447231i	$-0.0142406\pi$
$294$		0			0
$295$	2853.82			0.563239
$296$		0			0
$297$	446.342	+	5883.93i	0.0872033	+	1.14956i
$298$		0			0
$299$	−7.14470	−	7.14470i	−0.00138190	−	0.00138190i
$300$		0			0
$301$	1572.61	−	1572.61i	0.301141	−	0.301141i
$302$		0			0
$303$	−147.254	−	5833.47i	−0.0279192	−	1.10602i
$304$		0			0
$305$			4726.75i			0.887388i
$306$		0			0
$307$	−6270.43	−	6270.43i	−1.16571	−	1.16571i	−0.983205	−	0.182502i	$-0.941580\pi$
$307$	−6270.43	−	6270.43i	−1.16571	−	1.16571i	−0.182502	−	0.983205i	$-0.558420\pi$
$308$		0			0
$309$	−3889.43	+	4090.88i	−0.716058	+	0.753145i
$310$		0			0
$311$		−	2819.71i		−	0.514119i	−0.966396	−	0.257059i	$-0.917246\pi$
$311$		−	2819.71i		−	0.514119i	0.966396	−	0.257059i	$-0.0827536\pi$
$312$		0			0
$313$		−	744.254i		−	0.134402i	−0.997739	−	0.0672008i	$-0.978593\pi$
$313$		−	744.254i		−	0.134402i	0.997739	−	0.0672008i	$-0.0214068\pi$
$314$		0			0
$315$	−624.567	−	564.498i	−0.111715	−	0.100971i
$316$		0			0
$317$	105.984	+	105.984i	0.0187782	+	0.0187782i	0.716434	−	0.697655i	$-0.245773\pi$
$317$	105.984	+	105.984i	0.0187782	+	0.0187782i	−0.697655	+	0.716434i	$0.745773\pi$
$318$		0			0
$319$		−	9668.99i		−	1.69705i
$320$		0			0
$321$	−3585.78	+	90.5156i	−0.623486	+	0.0157386i
$322$		0			0
$323$	−3148.70	+	3148.70i	−0.542410	+	0.542410i
$324$		0			0
$325$	−2978.20	−	2978.20i	−0.508310	−	0.508310i
$326$		0			0
$327$	−24.4106	−	967.027i	−0.00412816	−	0.163537i
$328$		0			0
$329$	875.655			0.146737
$330$		0			0
$331$	−2520.49	+	2520.49i	−0.418545	+	0.418545i	−0.884702	−	0.466157i	$-0.845638\pi$
$331$	−2520.49	+	2520.49i	−0.418545	+	0.418545i	0.466157	+	0.884702i	$0.345638\pi$
$332$		0			0
$333$	−4991.12	+	5522.23i	−0.821356	+	0.908758i
$334$		0			0
$335$	344.016			0.0561063
$336$		0			0
$337$	−1969.50			−0.318355			−0.159178	−	0.987250i	$-0.550884\pi$
$337$	−1969.50			−0.318355			−0.159178	+	0.987250i	$0.550884\pi$
$338$		0			0
$339$	4528.92	+	4305.90i	0.725596	+	0.689866i
$340$		0			0
$341$	−5337.21	+	5337.21i	−0.847584	+	0.847584i
$342$		0			0
$343$	−3105.46			−0.488861
$344$		0			0
$345$	6.69218	−	0.168930i	0.00104433	−	2.63620e-5i
$346$		0			0
$347$	3206.45	+	3206.45i	0.496056	+	0.496056i	0.910208	−	0.414152i	$-0.135922\pi$
$347$	3206.45	+	3206.45i	0.496056	+	0.496056i	−0.414152	+	0.910208i	$0.635922\pi$
$348$		0			0
$349$	−2228.50	+	2228.50i	−0.341802	+	0.341802i	−0.857045	−	0.515242i	$-0.827702\pi$
$349$	−2228.50	+	2228.50i	−0.341802	+	0.341802i	0.515242	+	0.857045i	$0.327702\pi$
$350$		0			0
$351$	7316.20	−	554.990i	1.11256	−	0.0843965i
$352$		0			0
$353$		−	8425.61i		−	1.27040i	−0.772349	−	0.635198i	$-0.780918\pi$
$353$		−	8425.61i		−	1.27040i	0.772349	−	0.635198i	$-0.219082\pi$
$354$		0			0
$355$	−3007.06	−	3007.06i	−0.449572	−	0.449572i
$356$		0			0
$357$	−1936.70	−	1841.33i	−0.287117	−	0.272979i
$358$		0			0
$359$			12048.7i			1.77133i	0.464325	+	0.885665i	$0.346297\pi$
$359$			12048.7i			1.77133i	−0.464325	+	0.885665i	$0.653703\pi$
$360$		0			0
$361$		−	5219.84i		−	0.761021i
$362$		0			0
$363$	1649.54	+	1568.32i	0.238509	+	0.226764i
$364$		0			0
$365$	−426.204	−	426.204i	−0.0611193	−	0.0611193i
$366$		0			0
$367$		−	2019.62i		−	0.287257i	−0.989632	−	0.143628i	$-0.954123\pi$
$367$		−	2019.62i		−	0.287257i	0.989632	−	0.143628i	$-0.0458770\pi$
$368$		0			0
$369$	67.0303	+	1326.86i	0.00945652	+	0.187191i
$370$		0			0
$371$	−912.662	+	912.662i	−0.127717	+	0.127717i
$372$		0			0
$373$	−119.726	−	119.726i	−0.0166197	−	0.0166197i	0.698748	−	0.715368i	$-0.253741\pi$
$373$	−119.726	−	119.726i	−0.0166197	−	0.0166197i	−0.715368	+	0.698748i	$0.753741\pi$
$374$		0			0
$375$	7119.33	−	179.713i	0.980376	−	0.0247475i
$376$		0			0
$377$	−12022.6			−1.64243
$378$		0			0
$379$	4492.22	−	4492.22i	0.608838	−	0.608838i	−0.333804	−	0.942642i	$-0.608332\pi$
$379$	4492.22	−	4492.22i	0.608838	−	0.608838i	0.942642	+	0.333804i	$0.108332\pi$
$380$		0			0
$381$	9657.05	+	9181.51i	1.29854	+	1.23460i
$382$		0			0
$383$	−1574.45			−0.210054			−0.105027	−	0.994469i	$-0.533493\pi$
$383$	−1574.45			−0.210054			−0.105027	+	0.994469i	$0.533493\pi$
$384$		0			0
$385$	−1311.44			−0.173603
$386$		0			0
$387$	−9527.17	−	8610.87i	−1.25140	−	1.13105i
$388$		0			0
$389$	619.930	−	619.930i	0.0808013	−	0.0808013i	−0.665551	−	0.746352i	$-0.731803\pi$
$389$	619.930	−	619.930i	0.0808013	−	0.0808013i	0.746352	+	0.665551i	$0.231803\pi$
$390$		0			0
$391$	21.2496			0.00274843
$392$		0			0
$393$	−230.302	−	9123.42i	−0.0295603	−	1.17103i
$394$		0			0
$395$	−5524.31	−	5524.31i	−0.703692	−	0.703692i
$396$		0			0
$397$	−10371.0	+	10371.0i	−1.31110	+	1.31110i	−0.390491	+	0.920607i	$0.627695\pi$
$397$	−10371.0	+	10371.0i	−1.31110	+	1.31110i	−0.920607	+	0.390491i	$0.872305\pi$
$398$		0			0
$399$	−983.385	+	24.8235i	−0.123386	+	0.00311461i
$400$		0			0
$401$			10287.3i			1.28110i	0.767915	+	0.640552i	$0.221294\pi$
$401$			10287.3i			1.28110i	−0.767915	+	0.640552i	$0.778706\pi$
$402$		0			0
$403$	6636.39	+	6636.39i	0.820303	+	0.820303i
$404$		0			0
$405$	−3073.43	+	3766.26i	−0.377087	+	0.462091i
$406$		0			0
$407$			11595.4i			1.41219i
$408$		0			0
$409$			1734.25i			0.209665i	0.994490	+	0.104833i	$0.0334307\pi$
$409$			1734.25i			0.209665i	−0.994490	+	0.104833i	$0.966569\pi$
$410$		0			0
$411$	4948.00	−	5204.27i	0.593837	−	0.624594i
$412$		0			0
$413$	1415.04	+	1415.04i	0.168595	+	0.168595i
$414$		0			0
$415$		−	2422.38i		−	0.286530i
$416$		0			0
$417$	−119.372	−	4728.94i	−0.0140184	−	0.555341i
$418$		0			0
$419$	4435.64	−	4435.64i	0.517172	−	0.517172i	−0.399543	−	0.916715i	$-0.630831\pi$
$419$	4435.64	−	4435.64i	0.517172	−	0.517172i	0.916715	+	0.399543i	$0.130831\pi$
$420$		0			0
$421$	1602.03	+	1602.03i	0.185459	+	0.185459i	0.793730	−	0.608271i	$-0.208137\pi$
$421$	1602.03	+	1602.03i	0.185459	+	0.185459i	−0.608271	+	0.793730i	$0.708137\pi$
$422$		0			0
$423$	−255.106	−	5049.79i	−0.0293231	−	0.580447i
$424$		0			0
$425$	8857.67			1.01096
$426$		0			0
$427$	−2343.73	+	2343.73i	−0.265623	+	0.265623i
$428$		0			0
$429$	7875.51	−	8283.41i	0.886325	−	0.932231i
$430$		0			0
$431$	11106.8			1.24129			0.620645	−	0.784092i	$-0.286871\pi$
$431$	11106.8			1.24129			0.620645	+	0.784092i	$0.286871\pi$
$432$		0			0
$433$	400.999			0.0445053			0.0222527	−	0.999752i	$-0.492916\pi$
$433$	400.999			0.0445053			0.0222527	+	0.999752i	$0.492916\pi$
$434$		0			0
$435$	5488.43	−	5772.70i	0.604943	−	0.636275i
$436$		0			0
$437$	5.53107	−	5.53107i	0.000605462	−	0.000605462i
$438$		0			0
$439$	−9964.43			−1.08332			−0.541658	−	0.840599i	$-0.682203\pi$
$439$	−9964.43			−1.08332			−0.541658	+	0.840599i	$0.682203\pi$
$440$		0			0
$441$	437.467	+	8659.62i	0.0472375	+	0.935063i
$442$		0			0
$443$	−7441.81	−	7441.81i	−0.798129	−	0.798129i	0.184671	−	0.982800i	$-0.440878\pi$
$443$	−7441.81	−	7441.81i	−0.798129	−	0.798129i	−0.982800	+	0.184671i	$0.940878\pi$
$444$		0			0
$445$	3861.07	−	3861.07i	0.411308	−	0.411308i
$446$		0			0
$447$	112.112	+	4441.33i	0.0118629	+	0.469950i
$448$		0			0
$449$		−	15032.1i		−	1.57997i	−0.613124	−	0.789987i	$-0.710087\pi$
$449$		−	15032.1i		−	1.57997i	0.613124	−	0.789987i	$-0.289913\pi$
$450$		0			0
$451$	1463.41	+	1463.41i	0.152793	+	0.152793i
$452$		0			0
$453$	4900.38	−	5154.18i	0.508256	−	0.534580i
$454$		0			0
$455$			1630.67i			0.168015i
$456$		0			0
$457$			12925.5i			1.32304i	0.749927	+	0.661521i	$0.230089\pi$
$457$			12925.5i			1.32304i	−0.749927	+	0.661521i	$0.769911\pi$
$458$		0			0
$459$	−10054.5	+	11705.1i	−1.02245	+	1.19030i
$460$		0			0
$461$	−9557.64	−	9557.64i	−0.965604	−	0.965604i	0.0338235	−	0.999428i	$-0.489232\pi$
$461$	−9557.64	−	9557.64i	−0.965604	−	0.965604i	−0.999428	+	0.0338235i	$0.989232\pi$
$462$		0			0
$463$			7779.26i			0.780849i	0.920635	+	0.390424i	$0.127672\pi$
$463$			7779.26i			0.780849i	−0.920635	+	0.390424i	$0.872328\pi$
$464$		0			0
$465$	−6216.06	+	156.912i	−0.619920	+	0.0156486i
$466$		0			0
$467$	−8196.34	+	8196.34i	−0.812166	+	0.812166i	−0.984958	−	0.172792i	$-0.944721\pi$
$467$	−8196.34	+	8196.34i	−0.812166	+	0.812166i	0.172792	+	0.984958i	$0.444721\pi$
$468$		0			0
$469$	170.578	+	170.578i	0.0167944	+	0.0167944i
$470$		0			0
$471$	−289.470	−	11467.4i	−0.0283186	−	1.12184i
$472$		0			0
$473$	−20004.7			−1.94465
$474$		0			0
$475$	2305.57	−	2305.57i	0.222709	−	0.222709i
$476$		0			0
$477$	5529.09	+	4997.32i	0.530733	+	0.479689i
$478$		0			0
$479$	−15149.0			−1.44504			−0.722522	−	0.691348i	$-0.757017\pi$
$479$	−15149.0			−1.44504			−0.722522	+	0.691348i	$0.757017\pi$
$480$		0			0
$481$	14417.9			1.36673
$482$		0			0
$483$	3.40203	+	3.23451i	0.000320492	+	0.000304711i
$484$		0			0
$485$	3148.53	−	3148.53i	0.294778	−	0.294778i
$486$		0			0
$487$	5601.13			0.521173			0.260587	−	0.965450i	$-0.416084\pi$
$487$	5601.13			0.521173			0.260587	+	0.965450i	$0.416084\pi$
$488$		0			0
$489$	14944.5	−	377.242i	1.38203	−	0.0348865i
$490$		0			0
$491$	1915.75	+	1915.75i	0.176083	+	0.176083i	0.789646	−	0.613563i	$-0.210264\pi$
$491$	1915.75	+	1915.75i	0.176083	+	0.176083i	−0.613563	+	0.789646i	$0.710264\pi$
$492$		0			0
$493$	17878.6	−	17878.6i	1.63329	−	1.63329i
$494$		0			0
$495$	382.064	+	7562.91i	0.0346919	+	0.686723i
$496$		0			0
$497$		−	2982.06i		−	0.269142i
$498$		0			0
$499$	8401.78	+	8401.78i	0.753738	+	0.753738i	0.975175	−	0.221437i	$-0.0710746\pi$
$499$	8401.78	+	8401.78i	0.753738	+	0.753738i	−0.221437	+	0.975175i	$0.571075\pi$
$500$		0			0
$501$	5495.88	+	5225.24i	0.490095	+	0.465961i
$502$		0			0
$503$		−	7484.92i		−	0.663491i	−0.943369	−	0.331746i	$-0.892362\pi$
$503$		−	7484.92i		−	0.663491i	0.943369	−	0.331746i	$-0.107638\pi$
$504$		0			0
$505$		−	7488.49i		−	0.659868i
$506$		0			0
$507$	−2026.33	−	1926.55i	−0.177500	−	0.168759i
$508$		0			0
$509$	−1636.10	−	1636.10i	−0.142473	−	0.142473i	0.632273	−	0.774746i	$-0.282122\pi$
$509$	−1636.10	−	1636.10i	−0.142473	−	0.142473i	−0.774746	+	0.632273i	$0.782122\pi$
$510$		0			0
$511$		−	422.660i		−	0.0365898i
$512$		0			0
$513$	429.645	+	5663.83i	0.0369772	+	0.487454i
$514$		0			0
$515$	−5122.20	+	5122.20i	−0.438274	+	0.438274i
$516$		0			0
$517$	−5569.50	−	5569.50i	−0.473784	−	0.473784i
$518$		0			0
$519$	6372.89	−	160.870i	0.538996	−	0.0136058i
$520$		0			0
$521$	14829.8			1.24703			0.623517	−	0.781810i	$-0.285703\pi$
$521$	14829.8			1.24703			0.623517	+	0.781810i	$0.285703\pi$
$522$		0			0
$523$	7012.23	−	7012.23i	0.586278	−	0.586278i	−0.350343	−	0.936621i	$-0.613935\pi$
$523$	7012.23	−	7012.23i	0.586278	−	0.586278i	0.936621	+	0.350343i	$0.113935\pi$
$524$		0			0
$525$	1418.10	+	1348.27i	0.117888	+	0.112083i
$526$		0			0
$527$	−19737.7			−1.63148
$528$		0			0
$529$	12167.0			0.999997
$530$		0			0
$531$	7748.14	−	8572.63i	0.633221	−	0.700603i
$532$		0			0
$533$	1819.64	−	1819.64i	0.147875	−	0.147875i
$534$		0			0
$535$	−4603.11			−0.371981
$536$		0			0
$537$	−301.994	−	11963.5i	−0.0242681	−	0.961384i
$538$		0			0
$539$	9550.84	+	9550.84i	0.763235	+	0.763235i
$540$		0			0
$541$	−12824.9	+	12824.9i	−1.01920	+	1.01920i	−0.0193853	+	0.999812i	$0.506171\pi$
$541$	−12824.9	+	12824.9i	−1.01920	+	1.01920i	−0.999812	+	0.0193853i	$0.993829\pi$
$542$		0			0
$543$	16228.2	−	409.647i	1.28254	−	0.0323750i
$544$		0			0
$545$		−	1241.38i		−	0.0975688i
$546$		0			0
$547$	7736.14	+	7736.14i	0.604705	+	0.604705i	0.941557	−	0.336853i	$-0.109362\pi$
$547$	7736.14	+	7736.14i	0.604705	+	0.604705i	−0.336853	+	0.941557i	$0.609362\pi$
$548$		0			0
$549$	14198.8	+	12833.2i	1.10381	+	0.997645i
$550$		0			0
$551$		−	9307.29i		−	0.719608i
$552$		0			0
$553$		−	5478.38i		−	0.421274i
$554$		0			0
$555$	−6581.90	+	6922.80i	−0.503399	+	0.529471i
$556$		0			0
$557$	−11943.2	−	11943.2i	−0.908528	−	0.908528i	0.0876259	−	0.996153i	$-0.472072\pi$
$557$	−11943.2	−	11943.2i	−0.908528	−	0.908528i	−0.996153	+	0.0876259i	$0.972072\pi$
$558$		0			0
$559$			24874.3i			1.88206i
$560$		0			0
$561$	606.579	+	24029.7i	0.0456503	+	1.80844i
$562$		0			0
$563$	−8407.34	+	8407.34i	−0.629355	+	0.629355i	−0.947906	−	0.318550i	$-0.896804\pi$
$563$	−8407.34	+	8407.34i	−0.629355	+	0.629355i	0.318550	+	0.947906i	$0.396804\pi$
$564$		0			0
$565$	5670.67	+	5670.67i	0.422243	+	0.422243i
$566$		0			0
$567$	−3391.41	+	343.532i	−0.251192	+	0.0254444i
$568$		0			0
$569$	−38.5252			−0.00283842			−0.00141921	−	0.999999i	$-0.500452\pi$
$569$	−38.5252			−0.00283842			−0.00141921	+	0.999999i	$0.500452\pi$
$570$		0			0
$571$	−17899.6	+	17899.6i	−1.31186	+	1.31186i	−0.391822	+	0.920041i	$0.628155\pi$
$571$	−17899.6	+	17899.6i	−1.31186	+	1.31186i	−0.920041	+	0.391822i	$0.871845\pi$
$572$		0			0
$573$	6252.96	−	6576.82i	0.455883	−	0.479495i
$574$		0			0
$575$	−15.5595			−0.00112848
$576$		0			0
$577$	19242.4			1.38834			0.694171	−	0.719810i	$-0.255771\pi$
$577$	19242.4			1.38834			0.694171	+	0.719810i	$0.255771\pi$
$578$		0			0
$579$	4477.72	−	4709.64i	0.321395	−	0.338041i
$580$		0			0
$581$	1201.12	−	1201.12i	0.0857674	−	0.0857674i
$582$		0			0
$583$	11609.8			0.824746
$584$		0			0
$585$	9403.87	−	475.065i	0.664619	−	0.0335753i
$586$		0			0
$587$	5948.44	+	5948.44i	0.418259	+	0.418259i	0.884603	−	0.466344i	$-0.154429\pi$
$587$	5948.44	+	5948.44i	0.418259	+	0.418259i	−0.466344	+	0.884603i	$0.654429\pi$
$588$		0			0
$589$	−5137.56	+	5137.56i	−0.359405	+	0.359405i
$590$		0			0
$591$	5.86833	+	232.474i	0.000408445	+	0.0161806i
$592$		0			0
$593$			13100.7i			0.907222i	0.891200	+	0.453611i	$0.149864\pi$
$593$			13100.7i			0.907222i	−0.891200	+	0.453611i	$0.850136\pi$
$594$		0			0
$595$	−2424.94	−	2424.94i	−0.167081	−	0.167081i
$596$		0			0
$597$	962.403	−	1012.25i	0.0659774	−	0.0693946i
$598$		0			0
$599$			16819.3i			1.14728i	0.819109	+	0.573638i	$0.194468\pi$
$599$			16819.3i			1.14728i	−0.819109	+	0.573638i	$0.805532\pi$
$600$		0			0
$601$			15871.2i			1.07720i	0.842561	+	0.538601i	$0.181047\pi$
$601$			15871.2i			1.07720i	−0.842561	+	0.538601i	$0.818953\pi$
$602$		0			0
$603$	934.007	−	1033.40i	0.0630774	−	0.0697896i
$604$		0			0
$605$	2065.40	+	2065.40i	0.138794	+	0.138794i
$606$		0			0
$607$		−	7884.67i		−	0.527231i	−0.964628	−	0.263615i	$-0.915085\pi$
$607$		−	7884.67i		−	0.527231i	0.964628	−	0.263615i	$-0.0849149\pi$
$608$		0			0
$609$	5583.75	−	140.950i	0.371535	−	0.00937864i
$610$		0			0
$611$	−6925.23	+	6925.23i	−0.458535	+	0.458535i
$612$		0			0
$613$	5659.45	+	5659.45i	0.372892	+	0.372892i	0.868530	−	0.495637i	$-0.165066\pi$
$613$	5659.45	+	5659.45i	0.372892	+	0.372892i	−0.495637	+	0.868530i	$0.665066\pi$
$614$		0			0
$615$	43.0237	+	1704.39i	0.00282095	+	0.111752i
$616$		0			0
$617$	−20422.8			−1.33257			−0.666283	−	0.745699i	$-0.732116\pi$
$617$	−20422.8			−1.33257			−0.666283	+	0.745699i	$0.732116\pi$
$618$		0			0
$619$	−1382.80	+	1382.80i	−0.0897888	+	0.0897888i	−0.750575	−	0.660786i	$-0.770223\pi$
$619$	−1382.80	+	1382.80i	−0.0897888	+	0.0897888i	0.660786	+	0.750575i	$0.270223\pi$
$620$		0			0
$621$	17.6619	−	20.5614i	0.00114130	−	0.00132867i
$622$		0			0
$623$	3828.96			0.246235
$624$		0			0
$625$	−927.672			−0.0593710
$626$		0			0
$627$	6412.60	+	6096.82i	0.408444	+	0.388331i
$628$		0			0
$629$	−21440.6	+	21440.6i	−1.35913	+	1.35913i
$630$		0			0
$631$	−21039.0			−1.32734			−0.663669	−	0.748026i	$-0.731002\pi$
$631$	−21039.0			−1.32734			−0.663669	+	0.748026i	$0.731002\pi$
$632$		0			0
$633$	−6736.82	+	170.057i	−0.423009	+	0.0106780i
$634$		0			0
$635$	12091.6	+	12091.6i	0.755656	+	0.755656i
$636$		0			0
$637$	11875.7	−	11875.7i	0.738669	−	0.738669i
$638$		0			0
$639$	−17197.1	+	868.766i	−1.06465	+	0.0537838i
$640$		0			0
$641$		−	13567.3i		−	0.835997i	−0.908448	−	0.417999i	$-0.862732\pi$
$641$		−	13567.3i		−	0.835997i	0.908448	−	0.417999i	$-0.137268\pi$
$642$		0			0
$643$	5070.72	+	5070.72i	0.310995	+	0.310995i	0.845295	−	0.534300i	$-0.179425\pi$
$643$	5070.72	+	5070.72i	0.310995	+	0.310995i	−0.534300	+	0.845295i	$0.679425\pi$
$644$		0			0
$645$	−11943.5	−	11355.4i	−0.729107	−	0.693204i
$646$		0			0
$647$		−	4134.58i		−	0.251232i	−0.992079	−	0.125616i	$-0.959909\pi$
$647$		−	4134.58i		−	0.251232i	0.992079	−	0.125616i	$-0.0400907\pi$
$648$		0			0
$649$		−	18000.5i		−	1.08872i
$650$		0			0
$651$	−3159.99	−	3004.39i	−0.190246	−	0.180877i
$652$		0			0
$653$	−2132.91	−	2132.91i	−0.127821	−	0.127821i	0.640302	−	0.768123i	$-0.278809\pi$
$653$	−2132.91	−	2132.91i	−0.127821	−	0.127821i	−0.768123	+	0.640302i	$0.778809\pi$
$654$		0			0
$655$		−	11711.8i		−	0.698655i
$656$		0			0
$657$	−2437.43	+	123.134i	−0.144738	+	0.00731190i
$658$		0			0
$659$	5500.01	−	5500.01i	0.325114	−	0.325114i	−0.525611	−	0.850725i	$-0.676163\pi$
$659$	5500.01	−	5500.01i	0.325114	−	0.325114i	0.850725	+	0.525611i	$0.176163\pi$
$660$		0			0
$661$	−4321.74	−	4321.74i	−0.254306	−	0.254306i	0.568428	−	0.822733i	$-0.307552\pi$
$661$	−4321.74	−	4321.74i	−0.254306	−	0.254306i	−0.822733	+	0.568428i	$0.807552\pi$
$662$		0			0
$663$	29879.0	−	754.233i	1.75023	−	0.0441809i
$664$		0			0
$665$	−1262.38			−0.0736136
$666$		0			0
$667$	−31.4059	+	31.4059i	−0.00182315	+	0.00182315i
$668$		0			0
$669$	1250.91	+	1189.31i	0.0722912	+	0.0687314i
$670$		0			0
$671$	29814.0			1.71529
$672$		0			0
$673$	−24564.4			−1.40696			−0.703482	−	0.710713i	$-0.748372\pi$
$673$	−24564.4			−1.40696			−0.703482	+	0.710713i	$0.748372\pi$
$674$		0			0
$675$	7362.18	−	8570.82i	0.419808	−	0.488728i
$676$		0			0
$677$	14002.2	−	14002.2i	0.794904	−	0.794904i	−0.187383	−	0.982287i	$-0.560000\pi$
$677$	14002.2	−	14002.2i	0.794904	−	0.794904i	0.982287	+	0.187383i	$0.0600005\pi$
$678$		0			0
$679$	3122.35			0.176473
$680$		0			0
$681$	222.714	+	8822.83i	0.0125322	+	0.496463i
$682$		0			0
$683$	−1738.73	−	1738.73i	−0.0974093	−	0.0974093i	0.656723	−	0.754132i	$-0.271942\pi$
$683$	−1738.73	−	1738.73i	−0.0974093	−	0.0974093i	−0.754132	+	0.656723i	$0.771942\pi$
$684$		0			0
$685$	6516.29	−	6516.29i	0.363467	−	0.363467i
$686$		0			0
$687$	21817.7	−	550.741i	1.21164	−	0.0305853i
$688$		0			0
$689$		−	14435.8i		−	0.798201i
$690$		0			0
$691$	−10946.9	−	10946.9i	−0.602664	−	0.602664i	0.338355	−	0.941019i	$-0.390130\pi$
$691$	−10946.9	−	10946.9i	−0.602664	−	0.602664i	−0.941019	+	0.338355i	$0.890130\pi$
$692$		0			0
$693$	−3560.57	+	3939.46i	−0.195173	+	0.215942i
$694$		0			0
$695$		−	6070.59i		−	0.331325i
$696$		0			0
$697$			5411.91i			0.294104i
$698$		0			0
$699$	16044.3	−	16875.3i	0.868171	−	0.913137i
$700$		0			0
$701$	18915.0	+	18915.0i	1.01913	+	1.01913i	0.999813	+	0.0193143i	$0.00614832\pi$
$701$	18915.0	+	18915.0i	1.01913	+	1.01913i	0.0193143	+	0.999813i	$0.493852\pi$
$702$		0			0
$703$			11161.6i			0.598816i
$704$		0			0
$705$	−163.741	−	6486.60i	−0.00874729	−	0.346524i
$706$		0			0
$707$	3713.11	−	3713.11i	0.197519	−	0.197519i
$708$		0			0
$709$	−9407.92	−	9407.92i	−0.498338	−	0.498338i	0.412582	−	0.910920i	$-0.364627\pi$
$709$	−9407.92	−	9407.92i	−0.498338	−	0.498338i	−0.910920	+	0.412582i	$0.864627\pi$
$710$		0			0
$711$	−31593.1	+	1596.02i	−1.66644	+	0.0841850i
$712$		0			0
$713$	34.6717			0.00182113
$714$		0			0
$715$	10371.7	−	10371.7i	0.542489	−	0.542489i
$716$		0			0
$717$	−7865.89	+	8273.29i	−0.409703	+	0.430923i
$718$		0			0
$719$	−20278.9			−1.05184			−0.525921	−	0.850533i	$-0.676279\pi$
$719$	−20278.9			−1.05184			−0.525921	+	0.850533i	$0.676279\pi$
$720$		0			0
$721$	−5079.61			−0.262378
$722$		0			0
$723$	−9340.79	+	9824.58i	−0.480481	+	0.505367i
$724$		0			0
$725$	−13091.2	+	13091.2i	−0.670616	+	0.670616i
$726$		0			0
$727$	−5358.43			−0.273361			−0.136680	−	0.990615i	$-0.543643\pi$
$727$	−5358.43			−0.273361			−0.136680	+	0.990615i	$0.543643\pi$
$728$		0			0
$729$	2969.13	+	19457.8i	0.150847	+	0.988557i
$730$		0			0
$731$	−36990.2	−	36990.2i	−1.87159	−	1.87159i
$732$		0			0
$733$	282.297	−	282.297i	0.0142250	−	0.0142250i	−0.699959	−	0.714183i	$-0.746798\pi$
$733$	282.297	−	282.297i	0.0142250	−	0.0142250i	0.714183	+	0.699959i	$0.246798\pi$
$734$		0			0
$735$	280.790	+	11123.5i	0.0140913	+	0.558228i
$736$		0			0
$737$		−	2169.88i		−	0.108451i
$738$		0			0
$739$	−9969.28	−	9969.28i	−0.496246	−	0.496246i	0.414021	−	0.910267i	$-0.364124\pi$
$739$	−9969.28	−	9969.28i	−0.496246	−	0.496246i	−0.910267	+	0.414021i	$0.864124\pi$
$740$		0			0
$741$	7580.91	−	7973.55i	0.375832	−	0.395298i
$742$		0			0
$743$			29235.1i			1.44351i	0.692147	+	0.721757i	$0.256665\pi$
$743$			29235.1i			1.44351i	−0.692147	+	0.721757i	$0.743335\pi$
$744$		0			0
$745$			5701.39i			0.280379i
$746$		0			0
$747$	−7276.63	−	6576.78i	−0.356410	−	0.322131i
$748$		0			0
$749$	−2282.42	−	2282.42i	−0.111345	−	0.111345i
$750$		0			0
$751$		−	16830.9i		−	0.817802i	−0.912579	−	0.408901i	$-0.865912\pi$
$751$		−	16830.9i		−	0.817802i	0.912579	−	0.408901i	$-0.134088\pi$
$752$		0			0
$753$	8337.51	−	210.463i	0.403500	−	0.0101855i
$754$		0			0
$755$	6453.57	−	6453.57i	0.311086	−	0.311086i
$756$		0			0
$757$	15563.2	+	15563.2i	0.747231	+	0.747231i	0.973958	−	0.226728i	$-0.0728027\pi$
$757$	15563.2	+	15563.2i	0.747231	+	0.747231i	−0.226728	+	0.973958i	$0.572803\pi$
$758$		0			0
$759$	−1.06553	−	42.2110i	−5.09568e−5	−	0.00201866i
$760$		0			0
$761$	4967.50			0.236625			0.118313	−	0.992976i	$-0.462251\pi$
$761$	4967.50			0.236625			0.118313	+	0.992976i	$0.462251\pi$
$762$		0			0
$763$	615.531	−	615.531i	0.0292054	−	0.0292054i
$764$		0			0
$765$	−13277.9	+	14690.8i	−0.627533	+	0.694310i
$766$		0			0
$767$	−22382.1			−1.05368
$768$		0			0
$769$	−31721.3			−1.48752			−0.743758	−	0.668449i	$-0.766959\pi$
$769$	−31721.3			−1.48752			−0.743758	+	0.668449i	$0.766959\pi$
$770$		0			0
$771$	−7454.18	−	7087.11i	−0.348191	−	0.331046i
$772$		0			0
$773$	21018.6	−	21018.6i	0.977989	−	0.977989i	−0.0217738	−	0.999763i	$-0.506931\pi$
$773$	21018.6	−	21018.6i	0.977989	−	0.977989i	0.999763	+	0.0217738i	$0.00693135\pi$
$774$		0			0
$775$	14452.5			0.669872
$776$		0			0
$777$	−6696.21	+	169.032i	−0.309170	+	0.00780436i
$778$		0			0
$779$	1408.67	+	1408.67i	0.0647893	+	0.0647893i
$780$		0			0
$781$	−18967.0	+	18967.0i	−0.869006	+	0.869006i
$782$		0			0
$783$	−2439.56	−	32159.7i	−0.111345	−	1.46781i
$784$		0			0
$785$		−	14720.8i		−	0.669309i
$786$		0			0
$787$	−15691.0	−	15691.0i	−0.710703	−	0.710703i	0.255979	−	0.966682i	$-0.417602\pi$
$787$	−15691.0	−	15691.0i	−0.710703	−	0.710703i	−0.966682	+	0.255979i	$0.917602\pi$
$788$		0			0
$789$	−20690.7	−	19671.9i	−0.933598	−	0.887625i
$790$		0			0
$791$			5623.53i			0.252781i
$792$		0			0
$793$		−	37071.3i		−	1.66008i
$794$		0			0
$795$	6931.40	+	6590.08i	0.309222	+	0.293995i
$796$		0			0
$797$	392.159	+	392.159i	0.0174291	+	0.0174291i	0.715768	−	0.698339i	$-0.246077\pi$
$797$	392.159	+	392.159i	0.0174291	+	0.0174291i	−0.698339	+	0.715768i	$0.746077\pi$
$798$		0			0
$799$		−	20596.8i		−	0.911967i
$800$		0			0
$801$	−1115.50	−	22081.2i	−0.0492062	−	0.974032i
$802$		0			0
$803$	−2688.28	+	2688.28i	−0.118141	+	0.118141i
$804$		0			0
$805$	4.25970	+	4.25970i	0.000186503	+	0.000186503i
$806$		0			0
$807$	−29142.6	+	735.644i	−1.27121	+	0.0320891i
$808$		0			0
$809$	1365.11			0.0593259			0.0296629	−	0.999560i	$-0.490557\pi$
$809$	1365.11			0.0593259			0.0296629	+	0.999560i	$0.490557\pi$
$810$		0			0
$811$	19620.1	−	19620.1i	0.849512	−	0.849512i	−0.140560	−	0.990072i	$-0.544890\pi$
$811$	19620.1	−	19620.1i	0.849512	−	0.849512i	0.990072	+	0.140560i	$0.0448903\pi$
$812$		0			0
$813$	10014.5	+	9521.38i	0.432011	+	0.410737i
$814$		0			0
$815$	19184.4			0.824539
$816$		0			0
$817$	−19256.4			−0.824598
$818$		0			0
$819$	4898.40	+	4427.29i	0.208991	+	0.188891i
$820$		0			0
$821$	21308.6	−	21308.6i	0.905818	−	0.905818i	−0.0901139	−	0.995931i	$-0.528723\pi$
$821$	21308.6	−	21308.6i	0.905818	−	0.905818i	0.995931	+	0.0901139i	$0.0287231\pi$
$822$		0			0
$823$	42077.4			1.78217			0.891086	−	0.453835i	$-0.149944\pi$
$823$	42077.4			1.78217			0.891086	+	0.453835i	$0.149944\pi$
$824$		0			0
$825$	−444.155	−	17595.2i	−0.0187436	−	0.742530i
$826$		0			0
$827$	−3135.69	−	3135.69i	−0.131848	−	0.131848i	0.638103	−	0.769951i	$-0.279719\pi$
$827$	−3135.69	−	3135.69i	−0.131848	−	0.131848i	−0.769951	+	0.638103i	$0.779719\pi$
$828$		0			0
$829$	−12487.8	+	12487.8i	−0.523184	+	0.523184i	−0.918532	−	0.395348i	$-0.870624\pi$
$829$	−12487.8	+	12487.8i	−0.523184	+	0.523184i	0.395348	+	0.918532i	$0.370624\pi$
$830$		0			0
$831$	−25553.8	+	645.051i	−1.06673	+	0.0269273i
$832$		0			0
$833$			35320.3i			1.46912i
$834$		0			0
$835$	6881.41	+	6881.41i	0.285199	+	0.285199i
$836$		0			0
$837$	−16405.3	+	19098.6i	−0.677480	+	0.788701i
$838$		0			0
$839$		−	39451.5i		−	1.62338i	−0.584087	−	0.811691i	$-0.698547\pi$
$839$		−	39451.5i		−	1.62338i	0.584087	−	0.811691i	$-0.301453\pi$
$840$		0			0
$841$			28458.6i			1.16686i
$842$		0			0
$843$	1987.36	−	2090.30i	0.0811963	−	0.0854017i
$844$		0			0
$845$	−2537.18	−	2537.18i	−0.103292	−	0.103292i
$846$		0			0
$847$			2048.23i			0.0830908i
$848$		0			0
$849$	−495.743	−	19638.9i	−0.0200399	−	0.793882i
$850$		0			0
$851$	37.6629	−	37.6629i	0.00151712	−	0.00151712i
$852$		0			0
$853$	−28218.6	−	28218.6i	−1.13269	−	1.13269i	−0.989728	−	0.142966i	$-0.954336\pi$
$853$	−28218.6	−	28218.6i	−1.13269	−	1.13269i	−0.142966	−	0.989728i	$-0.545664\pi$
$854$		0			0
$855$	367.771	+	7280.00i	0.0147105	+	0.291194i
$856$		0			0
$857$	27268.2			1.08689			0.543444	−	0.839446i	$-0.317120\pi$
$857$	27268.2			1.08689			0.543444	+	0.839446i	$0.317120\pi$
$858$		0			0
$859$	−20537.8	+	20537.8i	−0.815764	+	0.815764i	−0.985491	−	0.169727i	$-0.945711\pi$
$859$	−20537.8	+	20537.8i	−0.815764	+	0.815764i	0.169727	+	0.985491i	$0.445711\pi$
$860$		0			0
$861$	−823.776	+	866.442i	−0.0326065	+	0.0342953i
$862$		0			0
$863$	27756.3			1.09483			0.547414	−	0.836862i	$-0.315612\pi$
$863$	27756.3			1.09483			0.547414	+	0.836862i	$0.315612\pi$
$864$		0			0
$865$	8180.95			0.321573
$866$		0			0
$867$	−25720.7	+	27052.9i	−1.00752	+	1.05970i
$868$		0			0
$869$	−34844.6	+	34844.6i	−1.36021	+	1.36021i
$870$		0			0
$871$	−2698.07			−0.104961
$872$		0			0
$873$	−909.639	−	18006.2i	−0.0352653	−	0.698074i
$874$		0			0
$875$	4531.59	+	4531.59i	0.175081	+	0.175081i
$876$		0			0
$877$	−1240.18	+	1240.18i	−0.0477512	+	0.0477512i	−0.730579	−	0.682828i	$-0.760750\pi$
$877$	−1240.18	+	1240.18i	−0.0477512	+	0.0477512i	0.682828	+	0.730579i	$0.260750\pi$
$878$		0			0
$879$	−970.699	−	38454.3i	−0.0372479	−	1.47558i
$880$		0			0
$881$			31267.9i			1.19574i	0.801595	+	0.597868i	$0.203985\pi$
$881$			31267.9i			1.19574i	−0.801595	+	0.597868i	$0.796015\pi$
$882$		0			0
$883$	−26119.6	−	26119.6i	−0.995464	−	0.995464i	0.00452604	−	0.999990i	$-0.498559\pi$
$883$	−26119.6	−	26119.6i	−0.995464	−	0.995464i	−0.999990	+	0.00452604i	$0.998559\pi$
$884$		0			0
$885$	10217.6	−	10746.9i	0.388093	−	0.408194i
$886$		0			0
$887$		−	13730.5i		−	0.519758i	−0.965641	−	0.259879i	$-0.916317\pi$
$887$		−	13730.5i		−	0.519758i	0.965641	−	0.259879i	$-0.0836827\pi$
$888$		0			0
$889$			11991.1i			0.452383i
$890$		0			0
$891$	23755.7	+	19385.7i	0.893205	+	0.728895i
$892$		0			0
$893$	−5361.16	−	5361.16i	−0.200901	−	0.200901i
$894$		0			0
$895$		−	15357.7i		−	0.573576i
$896$		0			0
$897$	−52.4859	+	1.32490i	−0.00195368	+	4.93167e-5i
$898$		0			0
$899$	29171.5	−	29171.5i	1.08223	−	1.08223i
$900$		0			0
$901$	21467.3	+	21467.3i	0.793760	+	0.793760i
$902$		0			0
$903$	−291.620	−	11552.6i	−0.0107470	−	0.425742i
$904$		0			0
$905$	20832.3			0.765181
$906$		0			0
$907$	−9646.24	+	9646.24i	−0.353140	+	0.353140i	−0.861277	−	0.508136i	$-0.830335\pi$
$907$	−9646.24	+	9646.24i	−0.353140	+	0.353140i	0.508136	+	0.861277i	$0.330335\pi$
$908$		0			0
$909$	−22494.8	−	20331.3i	−0.820798	−	0.741856i
$910$		0			0
$911$	−3435.47			−0.124942			−0.0624710	−	0.998047i	$-0.519898\pi$
$911$	−3435.47			−0.124942			−0.0624710	+	0.998047i	$0.519898\pi$
$912$		0			0
$913$	−15279.2			−0.553852
$914$		0			0
$915$	17799.9	+	16923.4i	0.643112	+	0.611444i
$916$		0			0
$917$	5807.23	−	5807.23i	0.209129	−	0.209129i
$918$		0			0
$919$	−4868.66			−0.174758			−0.0873788	−	0.996175i	$-0.527849\pi$
$919$	−4868.66			−0.174758			−0.0873788	+	0.996175i	$0.527849\pi$
$920$		0			0
$921$	−46063.4	+	1162.77i	−1.64803	+	0.0416012i
$922$		0			0
$923$	23584.0	+	23584.0i	0.841035	+	0.841035i
$924$		0			0
$925$	15699.4	−	15699.4i	0.558047	−	0.558047i
$926$		0			0
$927$	1479.85	+	29293.5i	0.0524322	+	1.03789i
$928$		0			0
$929$			17567.8i			0.620431i	0.950666	+	0.310216i	$0.100401\pi$
$929$			17567.8i			0.620431i	−0.950666	+	0.310216i	$0.899599\pi$
$930$		0			0
$931$	9193.56	+	9193.56i	0.323638	+	0.323638i
$932$		0			0
$933$	−10618.4	−	10095.5i	−0.372595	−	0.354247i
$934$		0			0
$935$			30847.2i			1.07894i
$936$		0			0
$937$			13154.3i			0.458625i	0.973353	+	0.229312i	$0.0736477\pi$
$937$			13154.3i			0.458625i	−0.973353	+	0.229312i	$0.926352\pi$
$938$		0			0
$939$	−2802.70	−	2664.69i	−0.0974043	−	0.0926078i
$940$		0			0
$941$	385.039	+	385.039i	0.0133389	+	0.0133389i	0.713745	−	0.700406i	$-0.246998\pi$
$941$	385.039	+	385.039i	0.0133389	+	0.0133389i	−0.700406	+	0.713745i	$0.746998\pi$
$942$		0			0
$943$		−	9.50666i		−	0.000328292i
$944$		0			0
$945$	−4361.94	+	330.887i	−0.150152	+	0.0113902i
$946$		0			0
$947$	8878.86	−	8878.86i	0.304672	−	0.304672i	−0.538167	−	0.842838i	$-0.680883\pi$
$947$	8878.86	−	8878.86i	0.304672	−	0.304672i	0.842838	+	0.538167i	$0.180883\pi$
$948$		0			0
$949$	3342.66	+	3342.66i	0.114339	+	0.114339i
$950$		0			0
$951$	778.575	−	19.6535i	0.0265479	−	0.000670146i
$952$		0			0
$953$	−28727.2			−0.976457			−0.488229	−	0.872716i	$-0.662357\pi$
$953$	−28727.2			−0.976457			−0.488229	+	0.872716i	$0.662357\pi$
$954$		0			0
$955$	8234.87	−	8234.87i	0.279030	−	0.279030i
$956$		0			0
$957$	−36411.3	−	34618.3i	−1.22990	−	1.16933i
$958$		0			0
$959$	6462.11			0.217594
$960$		0			0
$961$	−2413.93			−0.0810288
$962$		0			0
$963$	−12497.5	+	13827.4i	−0.418199	+	0.462700i
$964$		0			0
$965$	5896.96	−	5896.96i	0.196715	−	0.196715i
$966$		0			0
$967$	−24789.2			−0.824373			−0.412186	−	0.911100i	$-0.635235\pi$
$967$	−24789.2			−0.824373			−0.412186	+	0.911100i	$0.635235\pi$
$968$		0			0
$969$	583.888	+	23130.8i	0.0193573	+	0.766840i
$970$		0			0
$971$	23458.4	+	23458.4i	0.775299	+	0.775299i	0.979028	−	0.203728i	$-0.0653058\pi$
$971$	23458.4	+	23458.4i	0.775299	+	0.775299i	−0.203728	+	0.979028i	$0.565306\pi$
$972$		0			0
$973$	3010.06	−	3010.06i	0.0991758	−	0.0991758i
$974$		0			0
$975$	−21878.2	+	552.271i	−0.718630	+	0.0181403i
$976$		0			0
$977$			28932.0i			0.947407i	0.880684	+	0.473704i	$0.157083\pi$
$977$			28932.0i			0.947407i	−0.880684	+	0.473704i	$0.842917\pi$
$978$		0			0
$979$	−24353.7	−	24353.7i	−0.795043	−	0.795043i
$980$		0			0
$981$	−3729.01	−	3370.37i	−0.121364	−	0.109692i
$982$		0			0
$983$		−	28504.9i		−	0.924889i	−0.886648	−	0.462445i	$-0.846972\pi$
$983$		−	28504.9i		−	0.924889i	0.886648	−	0.462445i	$-0.153028\pi$
$984$		0			0
$985$			298.430i			0.00965357i
$986$		0			0
$987$	3135.15	−	3297.53i	0.101107	−	0.106344i
$988$		0			0
$989$	64.9776	+	64.9776i	0.00208915	+	0.00208915i
$990$		0			0
$991$			32691.4i			1.04791i	0.851747	+	0.523953i	$0.175543\pi$
$991$			32691.4i			1.04791i	−0.851747	+	0.523953i	$0.824457\pi$
$992$		0			0
$993$	467.393	+	18515.8i	0.0149368	+	0.591724i
$994$		0			0
$995$	1267.44	−	1267.44i	0.0403825	−	0.0403825i
$996$		0			0
$997$	14405.9	+	14405.9i	0.457613	+	0.457613i	0.897871	−	0.440258i	$-0.145113\pi$
$997$	14405.9	+	14405.9i	0.457613	+	0.457613i	−0.440258	+	0.897871i	$0.645113\pi$
$998$		0			0
$999$	2925.60	+	38567.0i	0.0926546	+	1.22143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.k.b.287.17		44
3.2	odd	2	inner	384.4.k.b.287.6		44
4.3	odd	2		384.4.k.a.287.6		44
8.3	odd	2		192.4.k.a.143.17		44
8.5	even	2		48.4.k.a.11.19	yes	44
12.11	even	2		384.4.k.a.287.17		44
16.3	odd	4	inner	384.4.k.b.95.6		44
16.5	even	4		192.4.k.a.47.6		44
16.11	odd	4		48.4.k.a.35.4	yes	44
16.13	even	4		384.4.k.a.95.17		44
24.5	odd	2		48.4.k.a.11.4	✓	44
24.11	even	2		192.4.k.a.143.6		44
48.5	odd	4		192.4.k.a.47.17		44
48.11	even	4		48.4.k.a.35.19	yes	44
48.29	odd	4		384.4.k.a.95.6		44
48.35	even	4	inner	384.4.k.b.95.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.4	✓	44	24.5	odd	2
48.4.k.a.11.19	yes	44	8.5	even	2
48.4.k.a.35.4	yes	44	16.11	odd	4
48.4.k.a.35.19	yes	44	48.11	even	4
192.4.k.a.47.6		44	16.5	even	4
192.4.k.a.47.17		44	48.5	odd	4
192.4.k.a.143.6		44	24.11	even	2
192.4.k.a.143.17		44	8.3	odd	2
384.4.k.a.95.6		44	48.29	odd	4
384.4.k.a.95.17		44	16.13	even	4
384.4.k.a.287.6		44	4.3	odd	2
384.4.k.a.287.17		44	12.11	even	2
384.4.k.b.95.6		44	16.3	odd	4	inner
384.4.k.b.95.17		44	48.35	even	4	inner
384.4.k.b.287.6		44	3.2	odd	2	inner
384.4.k.b.287.17		44	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(3.58035 - 3.76578i) q^{3} +(4.71515 - 4.71515i) q^{5} +4.67595 q^{7} +(-1.36225 - 26.9656i) q^{9} +(-29.7408 - 29.7408i) q^{11} +(-36.9803 + 36.9803i) q^{13} +(-0.874367 - 34.6381i) q^{15} -109.986i q^{17} +(-28.6283 - 28.6283i) q^{19} +(16.7415 - 17.6086i) q^{21} +0.193203i q^{23} +80.5347i q^{25} +(-106.424 - 91.4163i) q^{27} +(162.554 + 162.554i) q^{29} -179.457i q^{31} +(-218.480 + 5.51507i) q^{33} +(22.0478 - 22.0478i) q^{35} +(-194.940 - 194.940i) q^{37} +(6.85755 + 271.662i) q^{39} -49.2056 q^{41} +(336.318 - 336.318i) q^{43} +(-133.570 - 120.724i) q^{45} +187.268 q^{47} -321.136 q^{49} +(-414.182 - 393.787i) q^{51} +(-195.182 + 195.182i) q^{53} -280.465 q^{55} +(-210.307 + 5.30877i) q^{57} +(302.622 + 302.622i) q^{59} +(-501.230 + 501.230i) q^{61} +(-6.36981 - 126.090i) q^{63} +348.736i q^{65} +(36.4798 + 36.4798i) q^{67} +(0.727560 + 0.691733i) q^{69} -637.743i q^{71} -90.3903i q^{73} +(303.276 + 288.342i) q^{75} +(-139.067 - 139.067i) q^{77} -1171.61i q^{79} +(-725.289 + 73.4678i) q^{81} +(256.872 - 256.872i) q^{83} +(-518.599 - 518.599i) q^{85} +(1194.14 - 30.1437i) q^{87} +818.864 q^{89} +(-172.918 + 172.918i) q^{91} +(-675.797 - 642.519i) q^{93} -269.973 q^{95} +667.747 q^{97} +(-761.465 + 842.494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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