LMFDB - Embedded newform 384.4.k.b.95.6

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			95.6
Character	$\chi$	$=$	384.95
Dual form			384.4.k.b.287.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.76578 - 3.58035i) q^{3} +(-4.71515 - 4.71515i) q^{5} +4.67595 q^{7} +(1.36225 + 26.9656i) q^{9} +(29.7408 - 29.7408i) q^{11} +(-36.9803 - 36.9803i) q^{13} +(0.874367 + 34.6381i) q^{15} -109.986i q^{17} +(-28.6283 + 28.6283i) q^{19} +(-17.6086 - 16.7415i) q^{21} +0.193203i q^{23} -80.5347i q^{25} +(91.4163 - 106.424i) q^{27} +(-162.554 + 162.554i) q^{29} +179.457i q^{31} +(-218.480 + 5.51507i) q^{33} +(-22.0478 - 22.0478i) q^{35} +(-194.940 + 194.940i) q^{37} +(6.85755 + 271.662i) q^{39} +49.2056 q^{41} +(336.318 + 336.318i) q^{43} +(120.724 - 133.570i) q^{45} -187.268 q^{47} -321.136 q^{49} +(-393.787 + 414.182i) q^{51} +(195.182 + 195.182i) q^{53} -280.465 q^{55} +(210.307 - 5.30877i) q^{57} +(-302.622 + 302.622i) q^{59} +(-501.230 - 501.230i) q^{61} +(6.36981 + 126.090i) q^{63} +348.736i q^{65} +(36.4798 - 36.4798i) q^{67} +(0.691733 - 0.727560i) q^{69} -637.743i q^{71} +90.3903i q^{73} +(-288.342 + 303.276i) q^{75} +(139.067 - 139.067i) q^{77} +1171.61i q^{79} +(-725.289 + 73.4678i) q^{81} +(-256.872 - 256.872i) q^{83} +(-518.599 + 518.599i) q^{85} +(1194.14 - 30.1437i) q^{87} -818.864 q^{89} +(-172.918 - 172.918i) q^{91} +(642.519 - 675.797i) q^{93} +269.973 q^{95} +667.747 q^{97} +(842.494 + 761.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

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

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
$3$	−3.76578	−	3.58035i	−0.724725	−	0.689038i
$3$	−3.76578	−	3.58035i	−0.724725	−	0.689038i
$4$		0			0
$5$	−4.71515	−	4.71515i	−0.421736	−	0.421736i	0.464065	−	0.885801i	$-0.346390\pi$
$5$	−4.71515	−	4.71515i	−0.421736	−	0.421736i	−0.885801	+	0.464065i	$0.846390\pi$
$6$		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	$-0.554444\pi$
$11$	29.7408	−	29.7408i	0.815200	−	0.815200i	0.985408	+	0.170208i	$0.0544440\pi$
$12$		0			0
$13$	−36.9803	−	36.9803i	−0.788961	−	0.788961i	0.192363	−	0.981324i	$-0.438385\pi$
$13$	−36.9803	−	36.9803i	−0.788961	−	0.788961i	−0.981324	+	0.192363i	$0.938385\pi$
$14$		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	−0.858495	−	0.512822i	$-0.828600\pi$
$19$	−28.6283	+	28.6283i	−0.345673	+	0.345673i	0.512822	+	0.858495i	$0.328600\pi$
$20$		0			0
$21$	−17.6086	−	16.7415i	−0.182977	−	0.173967i
$22$		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
$27$	91.4163	−	106.424i	0.651595	−	0.758567i
$28$		0			0
$29$	−162.554	+	162.554i	−1.04088	+	1.04088i	−0.0417521	+	0.999128i	$0.513294\pi$
$29$	−162.554	+	162.554i	−1.04088	+	1.04088i	−0.999128	+	0.0417521i	$0.986706\pi$
$30$		0			0
$31$			179.457i			1.03973i	0.854250	+	0.519863i	$0.174017\pi$
$31$			179.457i			1.03973i	−0.854250	+	0.519863i	$0.825983\pi$
$32$		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	−0.992045	−	0.125885i	$-0.959823\pi$
$37$	−194.940	+	194.940i	−0.866160	+	0.866160i	0.125885	+	0.992045i	$0.459823\pi$
$38$		0			0
$39$	6.85755	+	271.662i	0.0281561	+	1.11540i
$40$		0			0
$41$	49.2056			0.187430			0.0937149	−	0.995599i	$-0.470126\pi$
$41$	49.2056			0.187430			0.0937149	+	0.995599i	$0.470126\pi$
$42$		0			0
$43$	336.318	+	336.318i	1.19274	+	1.19274i	0.976294	+	0.216450i	$0.0694480\pi$
$43$	336.318	+	336.318i	1.19274	+	1.19274i	0.216450	+	0.976294i	$0.430552\pi$
$44$		0			0
$45$	120.724	−	133.570i	0.399921	−	0.442477i
$46$		0			0
$47$	−187.268			−0.581188			−0.290594	−	0.956846i	$-0.593853\pi$
$47$	−187.268			−0.581188			−0.290594	+	0.956846i	$0.593853\pi$
$48$		0			0
$49$	−321.136			−0.936255
$50$		0			0
$51$	−393.787	+	414.182i	−1.08120	+	1.13720i
$52$		0			0
$53$	195.182	+	195.182i	0.505855	+	0.505855i	0.913252	−	0.407396i	$-0.133563\pi$
$53$	195.182	+	195.182i	0.505855	+	0.505855i	−0.407396	+	0.913252i	$0.633563\pi$
$54$		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	$-0.906533\pi$
$59$	−302.622	+	302.622i	−0.667763	+	0.667763i	0.289435	+	0.957198i	$0.406533\pi$
$60$		0			0
$61$	−501.230	−	501.230i	−1.05207	−	1.05207i	−0.998568	−	0.0534972i	$-0.982963\pi$
$61$	−501.230	−	501.230i	−1.05207	−	1.05207i	−0.0534972	−	0.998568i	$-0.517037\pi$
$62$		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	−0.673065	−	0.739583i	$-0.735023\pi$
$67$	36.4798	−	36.4798i	0.0665183	−	0.0665183i	0.739583	+	0.673065i	$0.235023\pi$
$68$		0			0
$69$	0.691733	−	0.727560i	0.00120688	−	0.00126939i
$70$		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	$0.0230855\pi$
$73$			90.3903i			0.144923i	−0.997371	+	0.0724615i	$0.976915\pi$
$74$		0			0
$75$	−288.342	+	303.276i	−0.443932	+	0.466924i
$76$		0			0
$77$	139.067	−	139.067i	0.205820	−	0.205820i
$78$		0			0
$79$			1171.61i			1.66856i	0.551341	+	0.834280i	$0.314116\pi$
$79$			1171.61i			1.66856i	−0.551341	+	0.834280i	$0.685884\pi$
$80$		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	$-0.327215\pi$
$83$	−256.872	−	256.872i	−0.339703	−	0.339703i	−0.856256	+	0.516553i	$0.827215\pi$
$84$		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	$-0.662141\pi$
$89$	−818.864			−0.975274			−0.487637	+	0.873047i	$0.662141\pi$
$90$		0			0
$91$	−172.918	−	172.918i	−0.199195	−	0.199195i
$92$		0			0
$93$	642.519	−	675.797i	0.716410	−	0.753515i
$94$		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
$99$	842.494	+	761.465i	0.855292	+	0.773032i
$100$		0			0
$101$	−794.088	−	794.088i	−0.782324	−	0.782324i	0.197899	−	0.980222i	$-0.436588\pi$
$101$	−794.088	−	794.088i	−0.782324	−	0.782324i	−0.980222	+	0.197899i	$0.936588\pi$
$102$		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	$-0.649054\pi$
$107$	488.119	−	488.119i	0.441011	−	0.441011i	0.892352	+	0.451341i	$0.149054\pi$
$108$		0			0
$109$	131.638	+	131.638i	0.115675	+	0.115675i	0.762575	−	0.646900i	$-0.223935\pi$
$109$	131.638	+	131.638i	0.115675	+	0.115675i	−0.646900	+	0.762575i	$0.723935\pi$
$110$		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
$117$	946.821	−	1047.57i	0.748151	−	0.827763i
$118$		0			0
$119$		−	514.288i		−	0.396174i
$120$		0			0
$121$		−	438.035i		−	0.329102i
$122$		0			0
$123$	−185.298	−	176.173i	−0.135835	−	0.129146i
$124$		0			0
$125$	−969.127	+	969.127i	−0.693451	+	0.693451i
$126$		0			0
$127$		−	2564.42i		−	1.79178i	−0.444281	−	0.895888i	$-0.646541\pi$
$127$		−	2564.42i		−	1.79178i	0.444281	−	0.895888i	$-0.353459\pi$
$128$		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	$-0.449181\pi$
$131$	−1241.94	−	1241.94i	−0.828309	−	0.828309i	−0.987283	+	0.158974i	$0.949181\pi$
$132$		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	$-0.641810\pi$
$137$	−1381.99			−0.861835			−0.430917	+	0.902391i	$0.641810\pi$
$138$		0			0
$139$	643.732	+	643.732i	0.392810	+	0.392810i	0.875688	−	0.482877i	$-0.160408\pi$
$139$	643.732	+	643.732i	0.392810	+	0.392810i	−0.482877	+	0.875688i	$0.660408\pi$
$140$		0			0
$141$	705.210	+	670.484i	0.421201	+	0.400460i
$142$		0			0
$143$	−2199.65			−1.28632
$144$		0			0
$145$	1532.93			0.877953
$146$		0			0
$147$	1209.33	+	1149.78i	0.678528	+	0.645115i
$148$		0			0
$149$	604.581	+	604.581i	0.332411	+	0.332411i	0.853501	−	0.521091i	$-0.174475\pi$
$149$	604.581	+	604.581i	0.332411	+	0.332411i	−0.521091	+	0.853501i	$0.674475\pi$
$150$		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	0.982064	−	0.188548i	$-0.0603780\pi$
$157$	1561.01	+	1561.01i	0.793516	+	0.793516i	−0.188548	+	0.982064i	$0.560378\pi$
$158$		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	−0.0221997	−	0.999754i	$-0.507067\pi$
$163$	2034.33	−	2034.33i	0.977554	−	0.977554i	0.999754	+	0.0221997i	$0.00706698\pi$
$164$		0			0
$165$	1056.17	+	1004.16i	0.498320	+	0.473781i
$166$		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
$171$	−810.978	−	732.980i	−0.362673	−	0.327792i
$172$		0			0
$173$	−867.517	+	867.517i	−0.381249	+	0.381249i	−0.871552	−	0.490303i	$-0.836886\pi$
$173$	−867.517	+	867.517i	−0.381249	+	0.381249i	0.490303	+	0.871552i	$0.336886\pi$
$174$		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	$-0.409670\pi$
$179$	−1628.54	−	1628.54i	−0.680017	−	0.680017i	−0.960004	+	0.279987i	$0.909670\pi$
$180$		0			0
$181$	2209.08	−	2209.08i	0.907181	−	0.907181i	−0.0888632	−	0.996044i	$-0.528323\pi$
$181$	2209.08	−	2209.08i	0.907181	−	0.907181i	0.996044	+	0.0888632i	$0.0283234\pi$
$182$		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
$189$	427.458	−	497.633i	0.164513	−	0.191521i
$190$		0			0
$191$	−1746.47			−0.661623			−0.330812	−	0.943697i	$-0.607322\pi$
$191$	−1746.47			−0.661623			−0.330812	+	0.943697i	$0.607322\pi$
$192$		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
$195$	1248.59	−	1313.26i	0.458532	−	0.482281i
$196$		0			0
$197$	31.6458	+	31.6458i	0.0114450	+	0.0114450i	0.712806	−	0.701361i	$-0.247424\pi$
$197$	31.6458	+	31.6458i	0.0114450	+	0.0114450i	−0.701361	+	0.712806i	$0.747424\pi$
$198$		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	−0.840703	−	0.541496i	$-0.817858\pi$
$211$	−917.057	+	917.057i	−0.299208	+	0.299208i	0.541496	+	0.840703i	$0.317858\pi$
$212$		0			0
$213$	−2283.34	+	2401.60i	−0.734516	+	0.772559i
$214$		0			0
$215$		−	3171.58i		−	1.00605i
$216$		0			0
$217$			839.133i			0.262507i
$218$		0			0
$219$	323.628	−	340.390i	0.0998575	−	0.105029i
$220$		0			0
$221$	−4067.31	+	4067.31i	−1.23799	+	1.23799i
$222$		0			0
$223$		−	332.177i		−	0.0997499i	−0.998755	−	0.0498749i	$-0.984118\pi$
$223$		−	332.177i		−	0.0997499i	0.998755	−	0.0498749i	$-0.0158823\pi$
$224$		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	$-0.170125\pi$
$227$	1201.02	+	1201.02i	0.351164	+	0.351164i	−0.509378	+	0.860543i	$0.670125\pi$
$228$		0			0
$229$	2969.95	−	2969.95i	0.857031	−	0.857031i	−0.133957	−	0.990987i	$-0.542768\pi$
$229$	2969.95	−	2969.95i	0.857031	−	0.857031i	0.990987	+	0.133957i	$0.0427683\pi$
$230$		0			0
$231$	−1021.60	+	25.7882i	−0.290980	+	0.00734519i
$232$		0			0
$233$	−4481.22			−1.25998			−0.629988	−	0.776605i	$-0.716940\pi$
$233$	−4481.22			−1.25998			−0.629988	+	0.776605i	$0.716940\pi$
$234$		0			0
$235$	882.996	+	882.996i	0.245108	+	0.245108i
$236$		0			0
$237$	4194.76	−	4412.02i	1.14970	−	1.20925i
$238$		0			0
$239$	2196.96			0.594602			0.297301	−	0.954784i	$-0.403914\pi$
$239$	2196.96			0.594602			0.297301	+	0.954784i	$0.403914\pi$
$240$		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
$243$	2994.32	+	2320.12i	0.790476	+	0.612493i
$244$		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	$-0.814684\pi$
$251$	−1134.95	+	1134.95i	−0.285409	+	0.285409i	0.549853	+	0.835262i	$0.314684\pi$
$252$		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
$261$	−4604.81	−	4161.93i	−1.09207	−	0.987038i
$262$		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
$267$	3083.66	+	2931.82i	0.706806	+	0.672001i
$268$		0			0
$269$	3967.07	−	3967.07i	0.899169	−	0.899169i	−0.0961936	−	0.995363i	$-0.530667\pi$
$269$	3967.07	−	3967.07i	0.899169	−	0.899169i	0.995363	+	0.0961936i	$0.0306668\pi$
$270$		0			0
$271$		−	2659.35i		−	0.596103i	−0.954550	−	0.298051i	$-0.903663\pi$
$271$		−	2659.35i		−	0.596103i	0.954550	−	0.298051i	$-0.0963367\pi$
$272$		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	−0.975321	−	0.220791i	$-0.929136\pi$
$277$	−3478.53	+	3478.53i	−0.754530	+	0.754530i	0.220791	+	0.975321i	$0.429136\pi$
$278$		0			0
$279$	−4839.18	+	244.466i	−1.03840	+	0.0524580i
$280$		0			0
$281$	−555.076			−0.117840			−0.0589200	−	0.998263i	$-0.518766\pi$
$281$	−555.076			−0.117840			−0.0589200	+	0.998263i	$0.518766\pi$
$282$		0			0
$283$	2673.37	+	2673.37i	0.561538	+	0.561538i	0.929744	−	0.368206i	$-0.120028\pi$
$283$	2673.37	+	2673.37i	0.561538	+	0.561538i	−0.368206	+	0.929744i	$0.620028\pi$
$284$		0			0
$285$	−1016.66	−	966.598i	−0.211305	−	0.200899i
$286$		0			0
$287$	230.083			0.0473218
$288$		0			0
$289$	−7183.86			−1.46221
$290$		0			0
$291$	−2514.59	−	2390.77i	−0.506557	−	0.481612i
$292$		0			0
$293$	−5234.64	−	5234.64i	−1.04372	−	1.04372i	−0.998999	−	0.0447231i	$-0.985759\pi$
$293$	−5234.64	−	5234.64i	−1.04372	−	1.04372i	−0.0447231	−	0.998999i	$-0.514241\pi$
$294$		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	−0.182502	+	0.983205i	$0.558420\pi$
$307$	−6270.43	+	6270.43i	−1.16571	+	1.16571i	−0.983205	+	0.182502i	$0.941580\pi$
$308$		0			0
$309$	4090.88	+	3889.43i	0.753145	+	0.716058i
$310$		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	$0.0214068\pi$
$313$			744.254i			0.134402i	−0.997739	+	0.0672008i	$0.978593\pi$
$314$		0			0
$315$	564.498	−	624.567i	0.100971	−	0.111715i
$316$		0			0
$317$	−105.984	+	105.984i	−0.0187782	+	0.0187782i	−0.716434	−	0.697655i	$-0.754227\pi$
$317$	−105.984	+	105.984i	−0.0187782	+	0.0187782i	0.697655	+	0.716434i	$0.254227\pi$
$318$		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	0.466157	−	0.884702i	$-0.345638\pi$
$331$	−2520.49	−	2520.49i	−0.418545	−	0.418545i	−0.884702	+	0.466157i	$0.845638\pi$
$332$		0			0
$333$	−5522.23	−	4991.12i	−0.908758	−	0.821356i
$334$		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
$339$	4305.90	−	4528.92i	0.689866	−	0.725596i
$340$		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	$-0.864078\pi$
$347$	−3206.45	+	3206.45i	−0.496056	+	0.496056i	0.414152	+	0.910208i	$0.364078\pi$
$348$		0			0
$349$	−2228.50	−	2228.50i	−0.341802	−	0.341802i	0.515242	−	0.857045i	$-0.327702\pi$
$349$	−2228.50	−	2228.50i	−0.341802	−	0.341802i	−0.857045	+	0.515242i	$0.827702\pi$
$350$		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
$357$	−1841.33	+	1936.70i	−0.272979	+	0.287117i
$358$		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
$363$	−1568.32	+	1649.54i	−0.226764	+	0.238509i
$364$		0			0
$365$	426.204	−	426.204i	0.0611193	−	0.0611193i
$366$		0			0
$367$			2019.62i			0.287257i	0.989632	+	0.143628i	$0.0458770\pi$
$367$			2019.62i			0.287257i	−0.989632	+	0.143628i	$0.954123\pi$
$368$		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	−0.715368	−	0.698748i	$-0.753741\pi$
$373$	−119.726	+	119.726i	−0.0166197	+	0.0166197i	0.698748	+	0.715368i	$0.253741\pi$
$374$		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	0.942642	−	0.333804i	$-0.108332\pi$
$379$	4492.22	+	4492.22i	0.608838	+	0.608838i	−0.333804	+	0.942642i	$0.608332\pi$
$380$		0			0
$381$	−9181.51	+	9657.05i	−1.23460	+	1.29854i
$382$		0			0
$383$	1574.45			0.210054			0.105027	−	0.994469i	$-0.466507\pi$
$383$	1574.45			0.210054			0.105027	+	0.994469i	$0.466507\pi$
$384$		0			0
$385$	−1311.44			−0.173603
$386$		0			0
$387$	−8610.87	+	9527.17i	−1.13105	+	1.25140i
$388$		0			0
$389$	−619.930	−	619.930i	−0.0808013	−	0.0808013i	0.665551	−	0.746352i	$-0.268197\pi$
$389$	−619.930	−	619.930i	−0.0808013	−	0.0808013i	−0.746352	+	0.665551i	$0.768197\pi$
$390$		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	−0.920607	−	0.390491i	$-0.872305\pi$
$397$	−10371.0	−	10371.0i	−1.31110	−	1.31110i	−0.390491	−	0.920607i	$-0.627695\pi$
$398$		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
$405$	3766.26	+	3073.43i	0.462091	+	0.377087i
$406$		0			0
$407$			11595.4i			1.41219i
$408$		0			0
$409$		−	1734.25i		−	0.209665i	−0.994490	−	0.104833i	$-0.966569\pi$
$409$		−	1734.25i		−	0.209665i	0.994490	−	0.104833i	$-0.0334307\pi$
$410$		0			0
$411$	5204.27	+	4948.00i	0.624594	+	0.593837i
$412$		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	$-0.369169\pi$
$419$	−4435.64	−	4435.64i	−0.517172	−	0.517172i	−0.916715	+	0.399543i	$0.869169\pi$
$420$		0			0
$421$	1602.03	−	1602.03i	0.185459	−	0.185459i	−0.608271	−	0.793730i	$-0.708137\pi$
$421$	1602.03	−	1602.03i	0.185459	−	0.185459i	0.793730	+	0.608271i	$0.208137\pi$
$422$		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
$429$	8283.41	+	7875.51i	0.932231	+	0.886325i
$430$		0			0
$431$	−11106.8			−1.24129			−0.620645	−	0.784092i	$-0.713129\pi$
$431$	−11106.8			−1.24129			−0.620645	+	0.784092i	$0.713129\pi$
$432$		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
$435$	−5772.70	−	5488.43i	−0.636275	−	0.604943i
$436$		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	$-0.559122\pi$
$443$	7441.81	−	7441.81i	0.798129	−	0.798129i	0.982800	+	0.184671i	$0.0591221\pi$
$444$		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
$453$	−5154.18	−	4900.38i	−0.534580	−	0.508256i
$454$		0			0
$455$			1630.67i			0.168015i
$456$		0			0
$457$		−	12925.5i		−	1.32304i	−0.749927	−	0.661521i	$-0.769911\pi$
$457$		−	12925.5i		−	1.32304i	0.749927	−	0.661521i	$-0.230089\pi$
$458$		0			0
$459$	−11705.1	−	10054.5i	−1.19030	−	1.02245i
$460$		0			0
$461$	9557.64	−	9557.64i	0.965604	−	0.965604i	−0.0338235	−	0.999428i	$-0.510768\pi$
$461$	9557.64	−	9557.64i	0.965604	−	0.965604i	0.999428	+	0.0338235i	$0.0107684\pi$
$462$		0			0
$463$		−	7779.26i		−	0.780849i	−0.920635	−	0.390424i	$-0.872328\pi$
$463$		−	7779.26i		−	0.780849i	0.920635	−	0.390424i	$-0.127672\pi$
$464$		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	$-0.0552789\pi$
$467$	8196.34	+	8196.34i	0.812166	+	0.812166i	−0.172792	+	0.984958i	$0.555279\pi$
$468$		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
$477$	−4997.32	+	5529.09i	−0.479689	+	0.530733i
$478$		0			0
$479$	15149.0			1.44504			0.722522	−	0.691348i	$-0.242983\pi$
$479$	15149.0			1.44504			0.722522	+	0.691348i	$0.242983\pi$
$480$		0			0
$481$	14417.9			1.36673
$482$		0			0
$483$	3.23451	−	3.40203i	0.000304711	−	0.000320492i
$484$		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	$-0.789736\pi$
$491$	−1915.75	+	1915.75i	−0.176083	+	0.176083i	0.613563	+	0.789646i	$0.289736\pi$
$492$		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	−0.221437	−	0.975175i	$-0.571075\pi$
$499$	8401.78	−	8401.78i	0.753738	−	0.753738i	0.975175	+	0.221437i	$0.0710746\pi$
$500$		0			0
$501$	5225.24	−	5495.88i	0.465961	−	0.490095i
$502$		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
$507$	1926.55	−	2026.33i	0.168759	−	0.177500i
$508$		0			0
$509$	1636.10	−	1636.10i	0.142473	−	0.142473i	−0.632273	−	0.774746i	$-0.717878\pi$
$509$	1636.10	−	1636.10i	0.142473	−	0.142473i	0.774746	+	0.632273i	$0.217878\pi$
$510$		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	$-0.714297\pi$
$521$	−14829.8			−1.24703			−0.623517	+	0.781810i	$0.714297\pi$
$522$		0			0
$523$	7012.23	+	7012.23i	0.586278	+	0.586278i	0.936621	−	0.350343i	$-0.113935\pi$
$523$	7012.23	+	7012.23i	0.586278	+	0.586278i	−0.350343	+	0.936621i	$0.613935\pi$
$524$		0			0
$525$	−1348.27	+	1418.10i	−0.112083	+	0.117888i
$526$		0			0
$527$	19737.7			1.63148
$528$		0			0
$529$	12167.0			0.999997
$530$		0			0
$531$	−8572.63	−	7748.14i	−0.700603	−	0.633221i
$532$		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	−0.999812	−	0.0193853i	$-0.993829\pi$
$541$	−12824.9	−	12824.9i	−1.01920	−	1.01920i	−0.0193853	−	0.999812i	$-0.506171\pi$
$542$		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	−0.336853	−	0.941557i	$-0.609362\pi$
$547$	7736.14	−	7736.14i	0.604705	−	0.604705i	0.941557	+	0.336853i	$0.109362\pi$
$548$		0			0
$549$	12833.2	−	14198.8i	0.997645	−	1.10381i
$550$		0			0
$551$		−	9307.29i		−	0.719608i
$552$		0			0
$553$			5478.38i			0.421274i
$554$		0			0
$555$	−6922.80	−	6581.90i	−0.529471	−	0.503399i
$556$		0			0
$557$	11943.2	−	11943.2i	0.908528	−	0.908528i	−0.0876259	−	0.996153i	$-0.527928\pi$
$557$	11943.2	−	11943.2i	0.908528	−	0.908528i	0.996153	+	0.0876259i	$0.0279280\pi$
$558$		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	$-0.103196\pi$
$563$	8407.34	+	8407.34i	0.629355	+	0.629355i	−0.318550	+	0.947906i	$0.603196\pi$
$564$		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	$-0.499548\pi$
$569$	38.5252			0.00283842			0.00141921	+	0.999999i	$0.499548\pi$
$570$		0			0
$571$	−17899.6	−	17899.6i	−1.31186	−	1.31186i	−0.920041	−	0.391822i	$-0.871845\pi$
$571$	−17899.6	−	17899.6i	−1.31186	−	1.31186i	−0.391822	−	0.920041i	$-0.628155\pi$
$572$		0			0
$573$	6576.82	+	6252.96i	0.479495	+	0.455883i
$574$		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
$579$	−4709.64	−	4477.72i	−0.338041	−	0.321395i
$580$		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	$-0.845571\pi$
$587$	−5948.44	+	5948.44i	−0.418259	+	0.418259i	0.466344	+	0.884603i	$0.345571\pi$
$588$		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
$597$	−1012.25	−	962.403i	−0.0693946	−	0.0659774i
$598$		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	$-0.818953\pi$
$601$		−	15871.2i		−	1.07720i	0.842561	−	0.538601i	$-0.181047\pi$
$602$		0			0
$603$	1033.40	+	934.007i	0.0697896	+	0.0630774i
$604$		0			0
$605$	−2065.40	+	2065.40i	−0.138794	+	0.138794i
$606$		0			0
$607$			7884.67i			0.527231i	0.964628	+	0.263615i	$0.0849149\pi$
$607$			7884.67i			0.527231i	−0.964628	+	0.263615i	$0.915085\pi$
$608$		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	−0.495637	−	0.868530i	$-0.665066\pi$
$613$	5659.45	−	5659.45i	0.372892	−	0.372892i	0.868530	+	0.495637i	$0.165066\pi$
$614$		0			0
$615$	43.0237	+	1704.39i	0.00282095	+	0.111752i
$616$		0			0
$617$	20422.8			1.33257			0.666283	−	0.745699i	$-0.267884\pi$
$617$	20422.8			1.33257			0.666283	+	0.745699i	$0.267884\pi$
$618$		0			0
$619$	−1382.80	−	1382.80i	−0.0897888	−	0.0897888i	0.660786	−	0.750575i	$-0.270223\pi$
$619$	−1382.80	−	1382.80i	−0.0897888	−	0.0897888i	−0.750575	+	0.660786i	$0.770223\pi$
$620$		0			0
$621$	20.5614	+	17.6619i	0.00132867	+	0.00114130i
$622$		0			0
$623$	−3828.96			−0.246235
$624$		0			0
$625$	−927.672			−0.0593710
$626$		0			0
$627$	6096.82	−	6412.60i	0.388331	−	0.408444i
$628$		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	−0.534300	−	0.845295i	$-0.679425\pi$
$643$	5070.72	−	5070.72i	0.310995	−	0.310995i	0.845295	+	0.534300i	$0.179425\pi$
$644$		0			0
$645$	−11355.4	+	11943.5i	−0.693204	+	0.729107i
$646$		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
$651$	3004.39	−	3159.99i	0.180877	−	0.190246i
$652$		0			0
$653$	2132.91	−	2132.91i	0.127821	−	0.127821i	−0.640302	−	0.768123i	$-0.721191\pi$
$653$	2132.91	−	2132.91i	0.127821	−	0.127821i	0.768123	+	0.640302i	$0.221191\pi$
$654$		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	$-0.323837\pi$
$659$	−5500.01	−	5500.01i	−0.325114	−	0.325114i	−0.850725	+	0.525611i	$0.823837\pi$
$660$		0			0
$661$	−4321.74	+	4321.74i	−0.254306	+	0.254306i	−0.822733	−	0.568428i	$-0.807552\pi$
$661$	−4321.74	+	4321.74i	−0.254306	+	0.254306i	0.568428	+	0.822733i	$0.307552\pi$
$662$		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
$669$	−1189.31	+	1250.91i	−0.0687314	+	0.0722912i
$670$		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
$675$	−8570.82	−	7362.18i	−0.488728	−	0.419808i
$676$		0			0
$677$	−14002.2	−	14002.2i	−0.794904	−	0.794904i	0.187383	−	0.982287i	$-0.440000\pi$
$677$	−14002.2	−	14002.2i	−0.794904	−	0.794904i	−0.982287	+	0.187383i	$0.940000\pi$
$678$		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	$-0.728058\pi$
$683$	1738.73	−	1738.73i	0.0974093	−	0.0974093i	0.754132	+	0.656723i	$0.228058\pi$
$684$		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	−0.941019	−	0.338355i	$-0.890130\pi$
$691$	−10946.9	+	10946.9i	−0.602664	+	0.602664i	0.338355	+	0.941019i	$0.390130\pi$
$692$		0			0
$693$	3939.46	+	3560.57i	0.215942	+	0.195173i
$694$		0			0
$695$		−	6070.59i		−	0.331325i
$696$		0			0
$697$		−	5411.91i		−	0.294104i
$698$		0			0
$699$	16875.3	+	16044.3i	0.913137	+	0.868171i
$700$		0			0
$701$	−18915.0	+	18915.0i	−1.01913	+	1.01913i	−0.0193143	+	0.999813i	$0.506148\pi$
$701$	−18915.0	+	18915.0i	−1.01913	+	1.01913i	−0.999813	+	0.0193143i	$0.993852\pi$
$702$		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	−0.910920	−	0.412582i	$-0.864627\pi$
$709$	−9407.92	+	9407.92i	−0.498338	+	0.498338i	0.412582	+	0.910920i	$0.364627\pi$
$710$		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
$717$	−8273.29	−	7865.89i	−0.430923	−	0.409703i
$718$		0			0
$719$	20278.9			1.05184			0.525921	−	0.850533i	$-0.323721\pi$
$719$	20278.9			1.05184			0.525921	+	0.850533i	$0.323721\pi$
$720$		0			0
$721$	−5079.61			−0.262378
$722$		0			0
$723$	9824.58	+	9340.79i	0.505367	+	0.480481i
$724$		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	0.714183	−	0.699959i	$-0.246798\pi$
$733$	282.297	+	282.297i	0.0142250	+	0.0142250i	−0.699959	+	0.714183i	$0.746798\pi$
$734$		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	−0.910267	−	0.414021i	$-0.864124\pi$
$739$	−9969.28	+	9969.28i	−0.496246	+	0.496246i	0.414021	+	0.910267i	$0.364124\pi$
$740$		0			0
$741$	−7973.55	−	7580.91i	−0.395298	−	0.375832i
$742$		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
$747$	6576.78	−	7276.63i	0.322131	−	0.356410i
$748$		0			0
$749$	2282.42	−	2282.42i	0.111345	−	0.111345i
$750$		0			0
$751$			16830.9i			0.817802i	0.912579	+	0.408901i	$0.134088\pi$
$751$			16830.9i			0.817802i	−0.912579	+	0.408901i	$0.865912\pi$
$752$		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	−0.226728	−	0.973958i	$-0.572803\pi$
$757$	15563.2	−	15563.2i	0.747231	−	0.747231i	0.973958	+	0.226728i	$0.0728027\pi$
$758$		0			0
$759$	−1.06553	−	42.2110i	−5.09568e−5	−	0.00201866i
$760$		0			0
$761$	−4967.50			−0.236625			−0.118313	−	0.992976i	$-0.537749\pi$
$761$	−4967.50			−0.236625			−0.118313	+	0.992976i	$0.537749\pi$
$762$		0			0
$763$	615.531	+	615.531i	0.0292054	+	0.0292054i
$764$		0			0
$765$	−14690.8	−	13277.9i	−0.694310	−	0.627533i
$766$		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
$771$	−7087.11	+	7454.18i	−0.331046	+	0.348191i
$772$		0			0
$773$	−21018.6	−	21018.6i	−0.977989	−	0.977989i	0.0217738	−	0.999763i	$-0.493069\pi$
$773$	−21018.6	−	21018.6i	−0.977989	−	0.977989i	−0.999763	+	0.0217738i	$0.993069\pi$
$774$		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	−0.966682	−	0.255979i	$-0.917602\pi$
$787$	−15691.0	+	15691.0i	−0.710703	+	0.710703i	0.255979	+	0.966682i	$0.417602\pi$
$788$		0			0
$789$	−19671.9	+	20690.7i	−0.887625	+	0.933598i
$790$		0			0
$791$			5623.53i			0.252781i
$792$		0			0
$793$			37071.3i			1.66008i
$794$		0			0
$795$	−6590.08	+	6931.40i	−0.293995	+	0.309222i
$796$		0			0
$797$	−392.159	+	392.159i	−0.0174291	+	0.0174291i	−0.715768	−	0.698339i	$-0.753923\pi$
$797$	−392.159	+	392.159i	−0.0174291	+	0.0174291i	0.698339	+	0.715768i	$0.253923\pi$
$798$		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	$-0.509443\pi$
$809$	−1365.11			−0.0593259			−0.0296629	+	0.999560i	$0.509443\pi$
$810$		0			0
$811$	19620.1	+	19620.1i	0.849512	+	0.849512i	0.990072	−	0.140560i	$-0.0448903\pi$
$811$	19620.1	+	19620.1i	0.849512	+	0.849512i	−0.140560	+	0.990072i	$0.544890\pi$
$812$		0			0
$813$	−9521.38	+	10014.5i	−0.410737	+	0.432011i
$814$		0			0
$815$	−19184.4			−0.824539
$816$		0			0
$817$	−19256.4			−0.824598
$818$		0			0
$819$	4427.29	−	4898.40i	0.188891	−	0.208991i
$820$		0			0
$821$	−21308.6	−	21308.6i	−0.905818	−	0.905818i	0.0901139	−	0.995931i	$-0.471277\pi$
$821$	−21308.6	−	21308.6i	−0.905818	−	0.905818i	−0.995931	+	0.0901139i	$0.971277\pi$
$822$		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	$-0.720281\pi$
$827$	3135.69	−	3135.69i	0.131848	−	0.131848i	0.769951	+	0.638103i	$0.220281\pi$
$828$		0			0
$829$	−12487.8	−	12487.8i	−0.523184	−	0.523184i	0.395348	−	0.918532i	$-0.370624\pi$
$829$	−12487.8	−	12487.8i	−0.523184	−	0.523184i	−0.918532	+	0.395348i	$0.870624\pi$
$830$		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
$837$	19098.6	+	16405.3i	0.788701	+	0.677480i
$838$		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
$843$	2090.30	+	1987.36i	0.0854017	+	0.0811963i
$844$		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	−0.142966	+	0.989728i	$0.545664\pi$
$853$	−28218.6	+	28218.6i	−1.13269	+	1.13269i	−0.989728	+	0.142966i	$0.954336\pi$
$854$		0			0
$855$	367.771	+	7280.00i	0.0147105	+	0.291194i
$856$		0			0
$857$	−27268.2			−1.08689			−0.543444	−	0.839446i	$-0.682880\pi$
$857$	−27268.2			−1.08689			−0.543444	+	0.839446i	$0.682880\pi$
$858$		0			0
$859$	−20537.8	−	20537.8i	−0.815764	−	0.815764i	0.169727	−	0.985491i	$-0.445711\pi$
$859$	−20537.8	−	20537.8i	−0.815764	−	0.815764i	−0.985491	+	0.169727i	$0.945711\pi$
$860$		0			0
$861$	−866.442	−	823.776i	−0.0342953	−	0.0326065i
$862$		0			0
$863$	−27756.3			−1.09483			−0.547414	−	0.836862i	$-0.684388\pi$
$863$	−27756.3			−1.09483			−0.547414	+	0.836862i	$0.684388\pi$
$864$		0			0
$865$	8180.95			0.321573
$866$		0			0
$867$	27052.9	+	25720.7i	1.05970	+	1.00752i
$868$		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	0.682828	−	0.730579i	$-0.260750\pi$
$877$	−1240.18	−	1240.18i	−0.0477512	−	0.0477512i	−0.730579	+	0.682828i	$0.760750\pi$
$878$		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	−0.999990	−	0.00452604i	$-0.998559\pi$
$883$	−26119.6	+	26119.6i	−0.995464	+	0.995464i	0.00452604	+	0.999990i	$0.498559\pi$
$884$		0			0
$885$	−10746.9	−	10217.6i	−0.408194	−	0.388093i
$886$		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
$891$	−19385.7	+	23755.7i	−0.728895	+	0.893205i
$892$		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	0.508136	−	0.861277i	$-0.330335\pi$
$907$	−9646.24	−	9646.24i	−0.353140	−	0.353140i	−0.861277	+	0.508136i	$0.830335\pi$
$908$		0			0
$909$	20331.3	−	22494.8i	0.741856	−	0.820798i
$910$		0			0
$911$	3435.47			0.124942			0.0624710	−	0.998047i	$-0.480102\pi$
$911$	3435.47			0.124942			0.0624710	+	0.998047i	$0.480102\pi$
$912$		0			0
$913$	−15279.2			−0.553852
$914$		0			0
$915$	16923.4	−	17799.9i	0.611444	−	0.643112i
$916$		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
$933$	−10095.5	+	10618.4i	−0.354247	+	0.372595i
$934$		0			0
$935$			30847.2i			1.07894i
$936$		0			0
$937$		−	13154.3i		−	0.458625i	−0.973353	−	0.229312i	$-0.926352\pi$
$937$		−	13154.3i		−	0.458625i	0.973353	−	0.229312i	$-0.0736477\pi$
$938$		0			0
$939$	2664.69	−	2802.70i	0.0926078	−	0.0974043i
$940$		0			0
$941$	−385.039	+	385.039i	−0.0133389	+	0.0133389i	−0.713745	−	0.700406i	$-0.753002\pi$
$941$	−385.039	+	385.039i	−0.0133389	+	0.0133389i	0.700406	+	0.713745i	$0.253002\pi$
$942$		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	$-0.319117\pi$
$947$	−8878.86	−	8878.86i	−0.304672	−	0.304672i	−0.842838	+	0.538167i	$0.819117\pi$
$948$		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	$-0.337643\pi$
$953$	28727.2			0.976457			0.488229	+	0.872716i	$0.337643\pi$
$954$		0			0
$955$	8234.87	+	8234.87i	0.279030	+	0.279030i
$956$		0			0
$957$	34618.3	−	36411.3i	1.16933	−	1.22990i
$958$		0			0
$959$	−6462.11			−0.217594
$960$		0			0
$961$	−2413.93			−0.0810288
$962$		0			0
$963$	13827.4	+	12497.5i	0.462700	+	0.418199i
$964$		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	$-0.934694\pi$
$971$	−23458.4	+	23458.4i	−0.775299	+	0.775299i	0.203728	+	0.979028i	$0.434694\pi$
$972$		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
$981$	−3370.37	+	3729.01i	−0.109692	+	0.121364i
$982$		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
$987$	3297.53	+	3135.15i	0.106344	+	0.101107i
$988$		0			0
$989$	−64.9776	+	64.9776i	−0.00208915	+	0.00208915i
$990$		0			0
$991$		−	32691.4i		−	1.04791i	−0.851747	−	0.523953i	$-0.824457\pi$
$991$		−	32691.4i		−	1.04791i	0.851747	−	0.523953i	$-0.175543\pi$
$992$		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	−0.440258	−	0.897871i	$-0.645113\pi$
$997$	14405.9	−	14405.9i	0.457613	−	0.457613i	0.897871	+	0.440258i	$0.145113\pi$
$998$		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.95.6		44
3.2	odd	2	inner	384.4.k.b.95.17		44
4.3	odd	2		384.4.k.a.95.17		44
8.3	odd	2		192.4.k.a.47.6		44
8.5	even	2		48.4.k.a.35.4	yes	44
12.11	even	2		384.4.k.a.95.6		44
16.3	odd	4		48.4.k.a.11.19	yes	44
16.5	even	4		384.4.k.a.287.6		44
16.11	odd	4	inner	384.4.k.b.287.17		44
16.13	even	4		192.4.k.a.143.17		44
24.5	odd	2		48.4.k.a.35.19	yes	44
24.11	even	2		192.4.k.a.47.17		44
48.5	odd	4		384.4.k.a.287.17		44
48.11	even	4	inner	384.4.k.b.287.6		44
48.29	odd	4		192.4.k.a.143.6		44
48.35	even	4		48.4.k.a.11.4	✓	44

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

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)

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

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Database

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