LMFDB - Embedded newform 504.3.l.h.181.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] 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("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.9
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19641 - 1.60268i) q^{2} +(-1.13719 + 3.83494i) q^{4} -9.09019 q^{5} +(3.83254 - 5.85761i) q^{7} +(7.50675 - 2.76563i) q^{8} +(10.8756 + 14.5687i) q^{10} -14.8648i q^{11} +4.25079 q^{13} +(-13.9732 + 0.865781i) q^{14} +(-13.4136 - 8.72211i) q^{16} -4.31083i q^{17} -26.9453 q^{19} +(10.3373 - 34.8604i) q^{20} +(-23.8236 + 17.7845i) q^{22} -9.33910 q^{23} +57.6315 q^{25} +(-5.08570 - 6.81267i) q^{26} +(18.1053 + 21.3588i) q^{28} +34.2521i q^{29} +4.01283i q^{31} +(2.06943 + 31.9330i) q^{32} +(-6.90890 + 5.15754i) q^{34} +(-34.8385 + 53.2468i) q^{35} +64.5914i q^{37} +(32.2378 + 43.1849i) q^{38} +(-68.2378 + 25.1401i) q^{40} +36.7189i q^{41} -74.7186i q^{43} +(57.0058 + 16.9041i) q^{44} +(11.1734 + 14.9676i) q^{46} +52.5115i q^{47} +(-19.6233 - 44.8991i) q^{49} +(-68.9511 - 92.3650i) q^{50} +(-4.83395 + 16.3015i) q^{52} +19.3795i q^{53} +135.124i q^{55} +(12.5699 - 54.5710i) q^{56} +(54.8953 - 40.9797i) q^{58} -3.71348 q^{59} -79.8128 q^{61} +(6.43130 - 4.80100i) q^{62} +(48.7026 - 41.5217i) q^{64} -38.6404 q^{65} +66.3899i q^{67} +(16.5318 + 4.90223i) q^{68} +(127.019 - 7.87011i) q^{70} -0.994759 q^{71} -8.78191i q^{73} +(103.520 - 77.2781i) q^{74} +(30.6420 - 103.334i) q^{76} +(-87.0725 - 56.9701i) q^{77} -31.1944 q^{79} +(121.932 + 79.2856i) q^{80} +(58.8488 - 43.9310i) q^{82} +44.7600 q^{83} +39.1863i q^{85} +(-119.750 + 89.3943i) q^{86} +(-41.1106 - 111.587i) q^{88} +11.6296i q^{89} +(16.2913 - 24.8995i) q^{91} +(10.6203 - 35.8149i) q^{92} +(84.1594 - 62.8255i) q^{94} +244.938 q^{95} +91.4731i q^{97} +(-48.4814 + 85.1678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.19641	−	1.60268i	−0.598207	−	0.801342i
$2$	−1.19641	−	1.60268i	−0.598207	−	0.801342i
$3$		0			0
$3$		0			0
$4$	−1.13719	+	3.83494i	−0.284297	+	0.958736i
$5$	−9.09019			−1.81804			−0.909019	−	0.416756i	$-0.863167\pi$
$5$	−9.09019			−1.81804			−0.909019	+	0.416756i	$0.863167\pi$
$6$		0			0
$7$	3.83254	−	5.85761i	0.547506	−	0.836802i
$7$	3.83254	−	5.85761i	0.547506	−	0.836802i
$8$	7.50675	−	2.76563i	0.938344	−	0.345703i
$9$		0			0
$10$	10.8756	+	14.5687i	1.08756	+	1.45687i
$11$		−	14.8648i		−	1.35135i	−0.737200	−	0.675675i	$-0.763852\pi$
$11$		−	14.8648i		−	1.35135i	0.737200	−	0.675675i	$-0.236148\pi$
$12$		0			0
$13$	4.25079			0.326984			0.163492	−	0.986545i	$-0.447724\pi$
$13$	4.25079			0.326984			0.163492	+	0.986545i	$0.447724\pi$
$14$	−13.9732	+	0.865781i	−0.998086	+	0.0618415i
$15$		0			0
$16$	−13.4136	−	8.72211i	−0.838350	−	0.545132i
$17$		−	4.31083i		−	0.253578i	−0.991930	−	0.126789i	$-0.959533\pi$
$17$		−	4.31083i		−	0.253578i	0.991930	−	0.126789i	$-0.0404672\pi$
$18$		0			0
$19$	−26.9453			−1.41818			−0.709088	−	0.705120i	$-0.750893\pi$
$19$	−26.9453			−1.41818			−0.709088	+	0.705120i	$0.750893\pi$
$20$	10.3373	−	34.8604i	0.516863	−	1.74302i
$21$		0			0
$22$	−23.8236	+	17.7845i	−1.08289	+	0.808386i
$23$	−9.33910			−0.406048			−0.203024	−	0.979174i	$-0.565077\pi$
$23$	−9.33910			−0.406048			−0.203024	+	0.979174i	$0.565077\pi$
$24$		0			0
$25$	57.6315			2.30526
$26$	−5.08570	−	6.81267i	−0.195604	−	0.262026i
$27$		0			0
$28$	18.1053	+	21.3588i	0.646618	+	0.762814i
$29$			34.2521i			1.18111i	0.806999	+	0.590553i	$0.201090\pi$
$29$			34.2521i			1.18111i	−0.806999	+	0.590553i	$0.798910\pi$
$30$		0			0
$31$			4.01283i			0.129446i	0.997903	+	0.0647231i	$0.0206164\pi$
$31$			4.01283i			0.129446i	−0.997903	+	0.0647231i	$0.979384\pi$
$32$	2.06943	+	31.9330i	0.0646697	+	0.997907i
$33$		0			0
$34$	−6.90890	+	5.15754i	−0.203203	+	0.151692i
$35$	−34.8385	+	53.2468i	−0.995386	+	1.52134i
$36$		0			0
$37$			64.5914i			1.74571i	0.487976	+	0.872857i	$0.337735\pi$
$37$			64.5914i			1.74571i	−0.487976	+	0.872857i	$0.662265\pi$
$38$	32.2378	+	43.1849i	0.848363	+	1.13644i
$39$		0			0
$40$	−68.2378	+	25.1401i	−1.70594	+	0.628501i
$41$			36.7189i			0.895583i	0.894138	+	0.447792i	$0.147789\pi$
$41$			36.7189i			0.895583i	−0.894138	+	0.447792i	$0.852211\pi$
$42$		0			0
$43$		−	74.7186i		−	1.73764i	−0.495127	−	0.868821i	$-0.664878\pi$
$43$		−	74.7186i		−	1.73764i	0.495127	−	0.868821i	$-0.335122\pi$
$44$	57.0058	+	16.9041i	1.29559	+	0.384185i
$45$		0			0
$46$	11.1734	+	14.9676i	0.242900	+	0.325383i
$47$			52.5115i			1.11727i	0.829415	+	0.558633i	$0.188674\pi$
$47$			52.5115i			1.11727i	−0.829415	+	0.558633i	$0.811326\pi$
$48$		0			0
$49$	−19.6233	−	44.8991i	−0.400475	−	0.916308i
$50$	−68.9511	−	92.3650i	−1.37902	−	1.84730i
$51$		0			0
$52$	−4.83395	+	16.3015i	−0.0929605	+	0.313491i
$53$			19.3795i			0.365650i	0.983145	+	0.182825i	$0.0585242\pi$
$53$			19.3795i			0.365650i	−0.983145	+	0.182825i	$0.941476\pi$
$54$		0			0
$55$			135.124i			2.45680i
$56$	12.5699	−	54.5710i	0.224463	−	0.974483i
$57$		0			0
$58$	54.8953	−	40.9797i	0.946470	−	0.706546i
$59$	−3.71348			−0.0629404			−0.0314702	−	0.999505i	$-0.510019\pi$
$59$	−3.71348			−0.0629404			−0.0314702	+	0.999505i	$0.510019\pi$
$60$		0			0
$61$	−79.8128			−1.30841			−0.654203	−	0.756319i	$-0.726996\pi$
$61$	−79.8128			−1.30841			−0.654203	+	0.756319i	$0.726996\pi$
$62$	6.43130	−	4.80100i	0.103731	−	0.0774356i
$63$		0			0
$64$	48.7026	−	41.5217i	0.760978	−	0.648777i
$65$	−38.6404			−0.594468
$66$		0			0
$67$			66.3899i			0.990894i	0.868638	+	0.495447i	$0.164996\pi$
$67$			66.3899i			0.990894i	−0.868638	+	0.495447i	$0.835004\pi$
$68$	16.5318	+	4.90223i	0.243115	+	0.0720916i
$69$		0			0
$70$	127.019	−	7.87011i	1.81456	−	0.112430i
$71$	−0.994759			−0.0140107			−0.00700535	−	0.999975i	$-0.502230\pi$
$71$	−0.994759			−0.0140107			−0.00700535	+	0.999975i	$0.502230\pi$
$72$		0			0
$73$		−	8.78191i		−	0.120300i	−0.998189	−	0.0601501i	$-0.980842\pi$
$73$		−	8.78191i		−	0.120300i	0.998189	−	0.0601501i	$-0.0191579\pi$
$74$	103.520	−	77.2781i	1.39891	−	1.04430i
$75$		0			0
$76$	30.6420	−	103.334i	0.403184	−	1.35966i
$77$	−87.0725	−	56.9701i	−1.13081	−	0.739871i
$78$		0			0
$79$	−31.1944			−0.394866			−0.197433	−	0.980316i	$-0.563260\pi$
$79$	−31.1944			−0.394866			−0.197433	+	0.980316i	$0.563260\pi$
$80$	121.932	+	79.2856i	1.52415	+	0.991070i
$81$		0			0
$82$	58.8488	−	43.9310i	0.717668	−	0.535744i
$83$	44.7600			0.539277			0.269639	−	0.962962i	$-0.413096\pi$
$83$	44.7600			0.539277			0.269639	+	0.962962i	$0.413096\pi$
$84$		0			0
$85$			39.1863i			0.461015i
$86$	−119.750	+	89.3943i	−1.39244	+	1.03947i
$87$		0			0
$88$	−41.1106	−	111.587i	−0.467166	−	1.26803i
$89$			11.6296i			0.130669i	0.997863	+	0.0653347i	$0.0208115\pi$
$89$			11.6296i			0.130669i	−0.997863	+	0.0653347i	$0.979188\pi$
$90$		0			0
$91$	16.2913	−	24.8995i	0.179025	−	0.273621i
$92$	10.6203	−	35.8149i	0.115438	−	0.389293i
$93$		0			0
$94$	84.1594	−	62.8255i	0.895312	−	0.668357i
$95$	244.938			2.57830
$96$		0			0
$97$			91.4731i			0.943021i	0.881860	+	0.471511i	$0.156291\pi$
$97$			91.4731i			0.943021i	−0.881860	+	0.471511i	$0.843709\pi$
$98$	−48.4814	+	85.1678i	−0.494709	+	0.869059i
$99$		0			0
$100$	−65.5379	+	221.013i	−0.655379	+	2.21013i
$101$	−35.1617			−0.348136			−0.174068	−	0.984734i	$-0.555691\pi$
$101$	−35.1617			−0.348136			−0.174068	+	0.984734i	$0.555691\pi$
$102$		0			0
$103$			45.5116i			0.441860i	0.975290	+	0.220930i	$0.0709093\pi$
$103$			45.5116i			0.441860i	−0.975290	+	0.220930i	$0.929091\pi$
$104$	31.9096	−	11.7561i	0.306823	−	0.113039i
$105$		0			0
$106$	31.0591	−	23.1858i	0.293011	−	0.218734i
$107$			64.2360i			0.600336i	0.953886	+	0.300168i	$0.0970428\pi$
$107$			64.2360i			0.600336i	−0.953886	+	0.300168i	$0.902957\pi$
$108$		0			0
$109$		−	39.3165i		−	0.360702i	−0.983602	−	0.180351i	$-0.942277\pi$
$109$		−	39.3165i		−	0.360702i	0.983602	−	0.180351i	$-0.0577234\pi$
$110$	216.561	−	161.664i	1.96874	−	1.46968i
$111$		0			0
$112$	−102.499	+	45.1439i	−0.915169	+	0.403070i
$113$	72.5108			0.641688			0.320844	−	0.947132i	$-0.396033\pi$
$113$	72.5108			0.641688			0.320844	+	0.947132i	$0.396033\pi$
$114$		0			0
$115$	84.8941			0.738210
$116$	−131.355	−	38.9511i	−1.13237	−	0.335785i
$117$		0			0
$118$	4.44286	+	5.95154i	0.0376514	+	0.0504368i
$119$	−25.2512	−	16.5214i	−0.212195	−	0.138836i
$120$		0			0
$121$	−99.9635			−0.826145
$122$	95.4892	+	127.915i	0.782698	+	1.04848i
$123$		0			0
$124$	−15.3890	−	4.56335i	−0.124105	−	0.0368012i
$125$	−296.626			−2.37301
$126$		0			0
$127$	−78.5274			−0.618326			−0.309163	−	0.951009i	$-0.600049\pi$
$127$	−78.5274			−0.618326			−0.309163	+	0.951009i	$0.600049\pi$
$128$	−124.815	−	28.3777i	−0.975115	−	0.221701i
$129$		0			0
$130$	46.2300	+	61.9284i	0.355615	+	0.476372i
$131$	−13.2698			−0.101296			−0.0506479	−	0.998717i	$-0.516129\pi$
$131$	−13.2698			−0.101296			−0.0506479	+	0.998717i	$0.516129\pi$
$132$		0			0
$133$	−103.269	+	157.835i	−0.776460	+	1.18673i
$134$	106.402	−	79.4298i	0.794045	−	0.592759i
$135$		0			0
$136$	−11.9222	−	32.3603i	−0.0876629	−	0.237944i
$137$	−101.465			−0.740623			−0.370311	−	0.928908i	$-0.620749\pi$
$137$	−101.465			−0.740623			−0.370311	+	0.928908i	$0.620749\pi$
$138$		0			0
$139$	163.338			1.17509			0.587546	−	0.809191i	$-0.300094\pi$
$139$	163.338			1.17509			0.587546	+	0.809191i	$0.300094\pi$
$140$	−164.581	−	194.155i	−1.17558	−	1.38682i
$141$		0			0
$142$	1.19014	+	1.59428i	0.00838129	+	0.0112274i
$143$		−	63.1873i		−	0.441869i
$144$		0			0
$145$		−	311.358i		−	2.14730i
$146$	−14.0746	+	10.5068i	−0.0964015	+	0.0719644i
$147$		0			0
$148$	−247.705	−	73.4526i	−1.67368	−	0.496302i
$149$			95.5068i			0.640985i	0.947251	+	0.320492i	$0.103848\pi$
$149$			95.5068i			0.640985i	−0.947251	+	0.320492i	$0.896152\pi$
$150$		0			0
$151$	194.643			1.28902			0.644512	−	0.764594i	$-0.277060\pi$
$151$	194.643			1.28902			0.644512	+	0.764594i	$0.277060\pi$
$152$	−202.272	+	74.5208i	−1.33074	+	0.490268i
$153$		0			0
$154$	12.8697	+	207.709i	0.0835694	+	1.34876i
$155$		−	36.4774i		−	0.235338i
$156$		0			0
$157$	−247.603			−1.57709			−0.788545	−	0.614977i	$-0.789165\pi$
$157$	−247.603			−1.57709			−0.788545	+	0.614977i	$0.789165\pi$
$158$	37.3214	+	49.9948i	0.236212	+	0.316423i
$159$		0			0
$160$	−18.8115	−	290.277i	−0.117572	−	1.81423i
$161$	−35.7925	+	54.7048i	−0.222313	+	0.339781i
$162$		0			0
$163$		−	42.2893i		−	0.259444i	−0.991550	−	0.129722i	$-0.958592\pi$
$163$		−	42.2893i		−	0.259444i	0.991550	−	0.129722i	$-0.0414085\pi$
$164$	−140.815	−	41.7563i	−0.858628	−	0.254612i
$165$		0			0
$166$	−53.5515	−	71.7361i	−0.322599	−	0.432145i
$167$		−	218.408i		−	1.30783i	−0.756568	−	0.653915i	$-0.773126\pi$
$167$		−	218.408i		−	1.30783i	0.756568	−	0.653915i	$-0.226874\pi$
$168$		0			0
$169$	−150.931			−0.893082
$170$	62.8032	−	46.8830i	0.369430	−	0.275782i
$171$		0			0
$172$	286.542	+	84.9691i	1.66594	+	0.494007i
$173$	270.029			1.56086			0.780431	−	0.625242i	$-0.215000\pi$
$173$	270.029			1.56086			0.780431	+	0.625242i	$0.215000\pi$
$174$		0			0
$175$	220.875	−	337.583i	1.26214	−	1.92905i
$176$	−129.653	+	199.391i	−0.736664	+	1.13290i
$177$		0			0
$178$	18.6385	−	13.9138i	0.104711	−	0.0781674i
$179$		−	150.910i		−	0.843071i	−0.906812	−	0.421535i	$-0.861491\pi$
$179$		−	150.910i		−	0.843071i	0.906812	−	0.421535i	$-0.138509\pi$
$180$		0			0
$181$	62.7742			0.346819			0.173409	−	0.984850i	$-0.444522\pi$
$181$	62.7742			0.346819			0.173409	+	0.984850i	$0.444522\pi$
$182$	−59.3971	+	3.68025i	−0.326358	+	0.0202212i
$183$		0			0
$184$	−70.1063	+	25.8285i	−0.381012	+	0.140372i
$185$		−	587.148i		−	3.17377i
$186$		0			0
$187$	−64.0798			−0.342673
$188$	−201.379	−	59.7155i	−1.07116	−	0.317636i
$189$		0			0
$190$	−293.047	−	392.558i	−1.54235	−	2.06610i
$191$	−152.844			−0.800231			−0.400115	−	0.916465i	$-0.631030\pi$
$191$	−152.844			−0.800231			−0.400115	+	0.916465i	$0.631030\pi$
$192$		0			0
$193$	−196.995			−1.02070			−0.510350	−	0.859967i	$-0.670484\pi$
$193$	−196.995			−1.02070			−0.510350	+	0.859967i	$0.670484\pi$
$194$	146.602	−	109.440i	0.755682	−	0.564122i
$195$		0			0
$196$	194.501	−	24.1955i	0.992351	−	0.123446i
$197$			58.4171i			0.296533i	0.988947	+	0.148267i	$0.0473694\pi$
$197$			58.4171i			0.296533i	−0.988947	+	0.148267i	$0.952631\pi$
$198$		0			0
$199$			31.9014i			0.160309i	0.996782	+	0.0801543i	$0.0255413\pi$
$199$			31.9014i			0.160309i	−0.996782	+	0.0801543i	$0.974459\pi$
$200$	432.625	−	159.387i	2.16313	−	0.796936i
$201$		0			0
$202$	42.0680	+	56.3531i	0.208257	+	0.278976i
$203$	200.636	+	131.273i	0.988352	+	0.646663i
$204$		0			0
$205$		−	333.782i		−	1.62820i
$206$	72.9407	−	54.4507i	0.354081	−	0.264324i
$207$		0			0
$208$	−57.0184	−	37.0758i	−0.274127	−	0.178249i
$209$			400.538i			1.91645i
$210$		0			0
$211$			77.3310i			0.366498i	0.983067	+	0.183249i	$0.0586614\pi$
$211$			77.3310i			0.366498i	−0.983067	+	0.183249i	$0.941339\pi$
$212$	−74.3191	−	22.0381i	−0.350562	−	0.103953i
$213$		0			0
$214$	102.950	−	76.8528i	0.481075	−	0.359125i
$215$			679.206i			3.15910i
$216$		0			0
$217$	23.5056	+	15.3793i	0.108321	+	0.0708725i
$218$	−63.0120	+	47.0388i	−0.289046	+	0.215775i
$219$		0			0
$220$	−518.194	−	153.662i	−2.35543	−	0.698462i
$221$		−	18.3244i		−	0.0829160i
$222$		0			0
$223$			145.310i			0.651614i	0.945436	+	0.325807i	$0.105636\pi$
$223$			145.310i			0.651614i	−0.945436	+	0.325807i	$0.894364\pi$
$224$	194.982	+	110.263i	0.870457	+	0.492244i
$225$		0			0
$226$	−86.7529	−	116.212i	−0.383862	−	0.514212i
$227$	−357.567			−1.57519			−0.787593	−	0.616196i	$-0.788673\pi$
$227$	−357.567			−1.57519			−0.787593	+	0.616196i	$0.788673\pi$
$228$		0			0
$229$	127.298			0.555886			0.277943	−	0.960598i	$-0.410347\pi$
$229$	127.298			0.555886			0.277943	+	0.960598i	$0.410347\pi$
$230$	−101.568	−	136.058i	−0.441602	−	0.591558i
$231$		0			0
$232$	94.7285	+	257.122i	0.408312	+	1.10828i
$233$	−80.4881			−0.345442			−0.172721	−	0.984971i	$-0.555256\pi$
$233$	−80.4881			−0.345442			−0.172721	+	0.984971i	$0.555256\pi$
$234$		0			0
$235$		−	477.340i		−	2.03123i
$236$	4.22293	−	14.2410i	0.0178938	−	0.0603432i
$237$		0			0
$238$	3.73224	+	60.2361i	0.0156817	+	0.253093i
$239$	−343.515			−1.43730			−0.718650	−	0.695372i	$-0.755240\pi$
$239$	−343.515			−1.43730			−0.718650	+	0.695372i	$0.755240\pi$
$240$		0			0
$241$			201.772i			0.837229i	0.908164	+	0.418614i	$0.137484\pi$
$241$			201.772i			0.837229i	−0.908164	+	0.418614i	$0.862516\pi$
$242$	119.598	+	160.210i	0.494205	+	0.662024i
$243$		0			0
$244$	90.7623	−	306.078i	0.371976	−	1.25442i
$245$	178.379	+	408.141i	0.728079	+	1.66588i
$246$		0			0
$247$	−114.539			−0.463720
$248$	11.0980	+	30.1233i	0.0447500	+	0.121465i
$249$		0			0
$250$	354.888	+	475.398i	1.41955	+	1.90159i
$251$	388.278			1.54692			0.773461	−	0.633844i	$-0.218524\pi$
$251$	388.278			1.54692			0.773461	+	0.633844i	$0.218524\pi$
$252$		0			0
$253$			138.824i			0.548712i
$254$	93.9513	+	125.855i	0.369887	+	0.495490i
$255$		0			0
$256$	103.849	+	233.990i	0.405662	+	0.914023i
$257$		−	290.061i		−	1.12864i	−0.825555	−	0.564322i	$-0.809138\pi$
$257$		−	290.061i		−	1.12864i	0.825555	−	0.564322i	$-0.190862\pi$
$258$		0			0
$259$	378.352	+	247.549i	1.46082	+	0.955788i
$260$	43.9415	−	148.184i	0.169006	−	0.569938i
$261$		0			0
$262$	15.8761	+	21.2672i	0.0605958	+	0.0811726i
$263$	−289.474			−1.10066			−0.550331	−	0.834947i	$-0.685498\pi$
$263$	−289.474			−1.10066			−0.550331	+	0.834947i	$0.685498\pi$
$264$		0			0
$265$		−	176.163i		−	0.664765i
$266$	376.513	−	23.3288i	1.41546	−	0.0877021i
$267$		0			0
$268$	−254.602	−	75.4978i	−0.950006	−	0.281708i
$269$	130.290			0.484348			0.242174	−	0.970233i	$-0.422139\pi$
$269$	130.290			0.484348			0.242174	+	0.970233i	$0.422139\pi$
$270$		0			0
$271$			317.150i			1.17030i	0.810927	+	0.585148i	$0.198964\pi$
$271$			317.150i			1.17030i	−0.810927	+	0.585148i	$0.801036\pi$
$272$	−37.5996	+	57.8238i	−0.138234	+	0.212587i
$273$		0			0
$274$	121.394	+	162.617i	0.443046	+	0.593492i
$275$		−	856.683i		−	3.11521i
$276$		0			0
$277$			526.555i			1.90092i	0.310843	+	0.950461i	$0.399389\pi$
$277$			526.555i			1.90092i	−0.310843	+	0.950461i	$0.600611\pi$
$278$	−195.420	−	261.779i	−0.702948	−	0.941651i
$279$		0			0
$280$	−114.263	+	496.061i	−0.408083	+	1.77165i
$281$	−165.241			−0.588046			−0.294023	−	0.955798i	$-0.594994\pi$
$281$	−165.241			−0.588046			−0.294023	+	0.955798i	$0.594994\pi$
$282$		0			0
$283$	170.636			0.602953			0.301477	−	0.953474i	$-0.402520\pi$
$283$	170.636			0.602953			0.301477	+	0.953474i	$0.402520\pi$
$284$	1.13123	−	3.81485i	0.00398320	−	0.0134326i
$285$		0			0
$286$	−101.269	+	75.5981i	−0.354088	+	0.264329i
$287$	215.085	+	140.727i	0.749426	+	0.490337i
$288$		0			0
$289$	270.417			0.935698
$290$	−499.008	+	372.513i	−1.72072	+	1.28453i
$291$		0			0
$292$	33.6781	+	9.98669i	0.115336	+	0.0342010i
$293$	−16.1118			−0.0549892			−0.0274946	−	0.999622i	$-0.508753\pi$
$293$	−16.1118			−0.0549892			−0.0274946	+	0.999622i	$0.508753\pi$
$294$		0			0
$295$	33.7562			0.114428
$296$	178.636	+	484.872i	0.603499	+	1.63808i
$297$		0			0
$298$	153.067	−	114.266i	0.513648	−	0.383442i
$299$	−39.6985			−0.132771
$300$		0			0
$301$	−437.673	−	286.362i	−1.45406	−	0.951369i
$302$	−232.873	−	311.951i	−0.771103	−	1.03295i
$303$		0			0
$304$	361.434	+	235.020i	1.18893	+	0.773093i
$305$	725.513			2.37873
$306$		0			0
$307$	−5.96095			−0.0194168			−0.00970839	−	0.999953i	$-0.503090\pi$
$307$	−5.96095			−0.0194168			−0.00970839	+	0.999953i	$0.503090\pi$
$308$	317.495	−	269.132i	1.03083	−	0.873807i
$309$		0			0
$310$	−58.4617	+	43.6420i	−0.188586	+	0.140781i
$311$			261.056i			0.839408i	0.907661	+	0.419704i	$0.137866\pi$
$311$			261.056i			0.839408i	−0.907661	+	0.419704i	$0.862134\pi$
$312$		0			0
$313$		−	285.715i		−	0.912826i	−0.889768	−	0.456413i	$-0.849134\pi$
$313$		−	285.715i		−	0.912826i	0.889768	−	0.456413i	$-0.150866\pi$
$314$	296.236	+	396.830i	0.943426	+	1.26379i
$315$		0			0
$316$	35.4739	−	119.629i	0.112259	−	0.378572i
$317$		−	593.885i		−	1.87345i	−0.350060	−	0.936727i	$-0.613839\pi$
$317$		−	593.885i		−	1.87345i	0.350060	−	0.936727i	$-0.386161\pi$
$318$		0			0
$319$	509.152			1.59609
$320$	−442.716	+	377.440i	−1.38349	+	1.17950i
$321$		0			0
$322$	130.497	−	8.08561i	0.405270	−	0.0251106i
$323$			116.157i			0.359619i
$324$		0			0
$325$	244.979			0.753782
$326$	−67.7764	+	50.5956i	−0.207903	+	0.155201i
$327$		0			0
$328$	101.551	+	275.640i	0.309606	+	0.840365i
$329$	307.592	+	201.253i	0.934931	+	0.611710i
$330$		0			0
$331$			25.5772i			0.0772725i	0.999253	+	0.0386362i	$0.0123014\pi$
$331$			25.5772i			0.0772725i	−0.999253	+	0.0386362i	$0.987699\pi$
$332$	−50.9006	+	171.652i	−0.153315	+	0.517024i
$333$		0			0
$334$	−350.038	+	261.306i	−1.04802	+	0.782352i
$335$		−	603.496i		−	1.80148i
$336$		0			0
$337$	−565.903			−1.67924			−0.839619	−	0.543176i	$-0.817222\pi$
$337$	−565.903			−1.67924			−0.839619	+	0.543176i	$0.817222\pi$
$338$	180.576	+	241.894i	0.534248	+	0.715664i
$339$		0			0
$340$	−150.277	−	44.5622i	−0.441992	−	0.131065i
$341$	59.6501			0.174927
$342$		0			0
$343$	−338.208	−	57.1319i	−0.986030	−	0.166565i
$344$	−206.644	−	560.894i	−0.600708	−	1.63051i
$345$		0			0
$346$	−323.066	−	432.771i	−0.933718	−	1.25078i
$347$			85.1612i			0.245421i	0.992442	+	0.122711i	$0.0391587\pi$
$347$			85.1612i			0.245421i	−0.992442	+	0.122711i	$0.960841\pi$
$348$		0			0
$349$	−275.035			−0.788066			−0.394033	−	0.919096i	$-0.628920\pi$
$349$	−275.035			−0.788066			−0.394033	+	0.919096i	$0.628920\pi$
$350$	−805.296	+	49.8962i	−2.30085	+	0.142561i
$351$		0			0
$352$	474.679	−	30.7618i	1.34852	−	0.0873914i
$353$		−	145.204i		−	0.411342i	−0.978621	−	0.205671i	$-0.934062\pi$
$353$		−	145.204i		−	0.411342i	0.978621	−	0.205671i	$-0.0659376\pi$
$354$		0			0
$355$	9.04255			0.0254720
$356$	−44.5988	−	13.2250i	−0.125278	−	0.0371490i
$357$		0			0
$358$	−241.860	+	180.550i	−0.675588	+	0.504331i
$359$	40.1294			0.111781			0.0558906	−	0.998437i	$-0.482200\pi$
$359$	40.1294			0.111781			0.0558906	+	0.998437i	$0.482200\pi$
$360$		0			0
$361$	365.052			1.01122
$362$	−75.1039	−	100.607i	−0.207469	−	0.277920i
$363$		0			0
$364$	76.9618	+	90.7917i	0.211434	+	0.249428i
$365$			79.8292i			0.218710i
$366$		0			0
$367$			373.965i			1.01898i	0.860477	+	0.509489i	$0.170166\pi$
$367$			373.965i			1.01898i	−0.860477	+	0.509489i	$0.829834\pi$
$368$	125.271	+	81.4566i	0.340410	+	0.221350i
$369$		0			0
$370$	−941.012	+	702.472i	−2.54328	+	1.89857i
$371$	113.517	+	74.2725i	0.305977	+	0.200195i
$372$		0			0
$373$		−	222.942i		−	0.597699i	−0.954300	−	0.298849i	$-0.903397\pi$
$373$		−	222.942i		−	0.597699i	0.954300	−	0.298849i	$-0.0966028\pi$
$374$	76.6660	+	102.700i	0.204989	+	0.274598i
$375$		0			0
$376$	145.227	+	394.191i	0.386243	+	1.04838i
$377$			145.598i			0.386203i
$378$		0			0
$379$		−	445.711i		−	1.17602i	−0.808854	−	0.588010i	$-0.799912\pi$
$379$		−	445.711i		−	1.17602i	0.808854	−	0.588010i	$-0.200088\pi$
$380$	−278.541	+	939.325i	−0.733003	+	2.47191i
$381$		0			0
$382$	182.865	+	244.961i	0.478704	+	0.641258i
$383$		−	463.682i		−	1.21066i	−0.795975	−	0.605329i	$-0.793042\pi$
$383$		−	463.682i		−	1.21066i	0.795975	−	0.605329i	$-0.206958\pi$
$384$		0			0
$385$	791.505	+	517.869i	2.05586	+	1.34511i
$386$	235.687	+	315.721i	0.610589	+	0.817929i
$387$		0			0
$388$	−350.794	−	104.022i	−0.904109	−	0.268098i
$389$		−	170.836i		−	0.439167i	−0.975594	−	0.219584i	$-0.929530\pi$
$389$		−	170.836i		−	0.439167i	0.975594	−	0.219584i	$-0.0704699\pi$
$390$		0			0
$391$			40.2593i			0.102965i
$392$	−271.481	−	282.776i	−0.692554	−	0.721366i
$393$		0			0
$394$	93.6240	−	69.8910i	0.237624	−	0.177388i
$395$	283.563			0.717881
$396$		0			0
$397$	537.521			1.35396			0.676979	−	0.736003i	$-0.263289\pi$
$397$	537.521			1.35396			0.676979	+	0.736003i	$0.263289\pi$
$398$	51.1278	−	38.1673i	0.128462	−	0.0958977i
$399$		0			0
$400$	−773.046	−	502.668i	−1.93261	−	1.25667i
$401$	−490.979			−1.22439			−0.612193	−	0.790709i	$-0.709712\pi$
$401$	−490.979			−1.22439			−0.612193	+	0.790709i	$0.709712\pi$
$402$		0			0
$403$			17.0577i			0.0423268i
$404$	39.9855	−	134.843i	0.0989740	−	0.333770i
$405$		0			0
$406$	−29.6548	−	478.611i	−0.0730414	−	1.17885i
$407$	960.141			2.35907
$408$		0			0
$409$			426.048i			1.04168i	0.853654	+	0.520841i	$0.174382\pi$
$409$			426.048i			1.04168i	−0.853654	+	0.520841i	$0.825618\pi$
$410$	−534.946	+	399.341i	−1.30475	+	0.974002i
$411$		0			0
$412$	−174.535	−	51.7553i	−0.423628	−	0.125620i
$413$	−14.2321	+	21.7521i	−0.0344602	+	0.0526686i
$414$		0			0
$415$	−406.877			−0.980426
$416$	8.79671	+	135.740i	0.0211459	+	0.326299i
$417$		0			0
$418$	641.936	−	479.210i	1.53573	−	1.14643i
$419$	725.389			1.73124			0.865619	−	0.500704i	$-0.166925\pi$
$419$	725.389			1.73124			0.865619	+	0.500704i	$0.166925\pi$
$420$		0			0
$421$			30.0999i			0.0714963i	0.999361	+	0.0357481i	$0.0113814\pi$
$421$			30.0999i			0.0714963i	−0.999361	+	0.0357481i	$0.988619\pi$
$422$	123.937	−	92.5199i	0.293690	−	0.219241i
$423$		0			0
$424$	53.5963	+	145.477i	0.126406	+	0.343105i
$425$		−	248.440i		−	0.584564i
$426$		0			0
$427$	−305.886	+	467.513i	−0.716360	+	1.09488i
$428$	−246.341	−	73.0484i	−0.575564	−	0.170674i
$429$		0			0
$430$	1088.55	−	812.611i	2.53152	−	1.88979i
$431$	265.508			0.616027			0.308013	−	0.951382i	$-0.400336\pi$
$431$	265.508			0.616027			0.308013	+	0.951382i	$0.400336\pi$
$432$		0			0
$433$		−	716.150i		−	1.65393i	−0.562256	−	0.826963i	$-0.690067\pi$
$433$		−	716.150i		−	1.65393i	0.562256	−	0.826963i	$-0.309933\pi$
$434$	−3.47423	−	56.0721i	−0.00800514	−	0.129198i
$435$		0			0
$436$	150.777	+	44.7103i	0.345818	+	0.102547i
$437$	251.645			0.575847
$438$		0			0
$439$		−	294.401i		−	0.670617i	−0.942108	−	0.335308i	$-0.891160\pi$
$439$		−	294.401i		−	0.670617i	0.942108	−	0.335308i	$-0.108840\pi$
$440$	373.703	+	1014.34i	0.849325	+	2.30533i
$441$		0			0
$442$	−29.3683	+	21.9236i	−0.0664440	+	0.0496009i
$443$			488.734i			1.10324i	0.834096	+	0.551619i	$0.185990\pi$
$443$			488.734i			1.10324i	−0.834096	+	0.551619i	$0.814010\pi$
$444$		0			0
$445$		−	105.715i		−	0.237562i
$446$	232.886	−	173.851i	0.522165	−	0.389800i
$447$		0			0
$448$	−56.5636	−	444.415i	−0.126258	−	0.991997i
$449$	−430.945			−0.959788			−0.479894	−	0.877326i	$-0.659325\pi$
$449$	−430.945			−0.959788			−0.479894	+	0.877326i	$0.659325\pi$
$450$		0			0
$451$	545.821			1.21025
$452$	−82.4584	+	278.075i	−0.182430	+	0.615210i
$453$		0			0
$454$	427.798	+	573.067i	0.942287	+	1.26226i
$455$	−148.091	+	226.341i	−0.325475	+	0.497452i
$456$		0			0
$457$	−699.398			−1.53041			−0.765206	−	0.643785i	$-0.777363\pi$
$457$	−699.398			−1.53041			−0.765206	+	0.643785i	$0.777363\pi$
$458$	−152.301	−	204.018i	−0.332535	−	0.445454i
$459$		0			0
$460$	−96.5406	+	325.564i	−0.209871	+	0.707748i
$461$	−387.880			−0.841389			−0.420695	−	0.907202i	$-0.638214\pi$
$461$	−387.880			−0.841389			−0.420695	+	0.907202i	$0.638214\pi$
$462$		0			0
$463$	−293.086			−0.633015			−0.316508	−	0.948590i	$-0.602510\pi$
$463$	−293.086			−0.633015			−0.316508	+	0.948590i	$0.602510\pi$
$464$	298.751	−	459.444i	0.643859	−	0.990181i
$465$		0			0
$466$	96.2970	+	128.997i	0.206646	+	0.276817i
$467$	−588.136			−1.25939			−0.629696	−	0.776842i	$-0.716820\pi$
$467$	−588.136			−1.25939			−0.629696	+	0.776842i	$0.716820\pi$
$468$		0			0
$469$	388.886	+	254.442i	0.829182	+	0.542520i
$470$	−765.024	+	571.096i	−1.62771	+	1.21510i
$471$		0			0
$472$	−27.8762	+	10.2701i	−0.0590597	+	0.0217587i
$473$	−1110.68			−2.34816
$474$		0			0
$475$	−1552.90			−3.26926
$476$	92.0742	−	78.0489i	0.193433	−	0.163968i
$477$		0			0
$478$	410.986	+	550.546i	0.859803	+	1.15177i
$479$			389.912i			0.814012i	0.913425	+	0.407006i	$0.133427\pi$
$479$			389.912i			0.814012i	−0.913425	+	0.407006i	$0.866573\pi$
$480$		0			0
$481$			274.564i			0.570820i
$482$	323.377	−	241.403i	0.670906	−	0.500836i
$483$		0			0
$484$	113.677	−	383.355i	0.234871	−	0.792055i
$485$		−	831.507i		−	1.71445i
$486$		0			0
$487$	−307.232			−0.630867			−0.315433	−	0.948948i	$-0.602150\pi$
$487$	−307.232			−0.630867			−0.315433	+	0.948948i	$0.602150\pi$
$488$	−599.135	+	220.732i	−1.22774	+	0.452321i
$489$		0			0
$490$	440.705	−	774.191i	0.899399	−	1.57998i
$491$			751.084i			1.52970i	0.644207	+	0.764851i	$0.277188\pi$
$491$			751.084i			1.52970i	−0.644207	+	0.764851i	$0.722812\pi$
$492$		0			0
$493$	147.655			0.299503
$494$	137.036	+	183.570i	0.277401	+	0.371599i
$495$		0			0
$496$	35.0004	−	53.8265i	0.0705652	−	0.108521i
$497$	−3.81246	+	5.82692i	−0.00767094	+	0.0117242i
$498$		0			0
$499$		−	252.238i		−	0.505487i	−0.967533	−	0.252744i	$-0.918667\pi$
$499$		−	252.238i		−	0.505487i	0.967533	−	0.252744i	$-0.0813329\pi$
$500$	337.320	−	1137.54i	0.674640	−	2.27509i
$501$		0			0
$502$	−464.541	−	622.286i	−0.925380	−	1.23961i
$503$		−	840.895i		−	1.67176i	−0.548912	−	0.835880i	$-0.684958\pi$
$503$		−	840.895i		−	1.67176i	0.548912	−	0.835880i	$-0.315042\pi$
$504$		0			0
$505$	319.626			0.632924
$506$	222.491	−	166.091i	0.439706	−	0.328243i
$507$		0			0
$508$	89.3005	−	301.148i	0.175788	−	0.592812i
$509$	−532.050			−1.04528			−0.522642	−	0.852552i	$-0.675054\pi$
$509$	−532.050			−1.04528			−0.522642	+	0.852552i	$0.675054\pi$
$510$		0			0
$511$	−51.4410	−	33.6570i	−0.100667	−	0.0658650i
$512$	250.765	−	446.387i	0.489775	−	0.871849i
$513$		0			0
$514$	−464.877	+	347.033i	−0.904429	+	0.675162i
$515$		−	413.709i		−	0.803318i
$516$		0			0
$517$	780.576			1.50982
$518$	−55.9220	−	902.549i	−0.107958	−	1.74237i
$519$		0			0
$520$	−290.064	+	106.865i	−0.557816	+	0.205510i
$521$			673.016i			1.29178i	0.763432	+	0.645889i	$0.223513\pi$
$521$			673.016i			1.29178i	−0.763432	+	0.645889i	$0.776487\pi$
$522$		0			0
$523$	131.940			0.252276			0.126138	−	0.992013i	$-0.459742\pi$
$523$	131.940			0.252276			0.126138	+	0.992013i	$0.459742\pi$
$524$	15.0902	−	50.8888i	0.0287981	−	0.0971160i
$525$		0			0
$526$	346.331	+	463.935i	0.658424	+	0.882006i
$527$	17.2986			0.0328247
$528$		0			0
$529$	−441.781			−0.835125
$530$	−282.333	+	210.764i	−0.532704	+	0.397667i
$531$		0			0
$532$	−487.854	−	575.520i	−0.917018	−	1.08180i
$533$			156.084i			0.292841i
$534$		0			0
$535$		−	583.917i		−	1.09143i
$536$	183.610	+	498.372i	0.342555	+	0.929799i
$537$		0			0
$538$	−155.880	−	208.813i	−0.289740	−	0.388129i
$539$	−667.418	+	291.697i	−1.23825	+	0.541182i
$540$		0			0
$541$		−	413.321i		−	0.763995i	−0.924163	−	0.381997i	$-0.875236\pi$
$541$		−	413.321i		−	0.763995i	0.924163	−	0.381997i	$-0.124764\pi$
$542$	508.291	−	379.443i	0.937807	−	0.700079i
$543$		0			0
$544$	137.658	−	8.92097i	0.253048	−	0.0163988i
$545$			357.395i			0.655770i
$546$		0			0
$547$			869.058i			1.58877i	0.607414	+	0.794385i	$0.292207\pi$
$547$			869.058i			1.58877i	−0.607414	+	0.794385i	$0.707793\pi$
$548$	115.385	−	389.114i	0.210557	−	0.710062i
$549$		0			0
$550$	−1372.99	+	1024.95i	−2.49635	+	1.86354i
$551$		−	922.935i		−	1.67502i
$552$		0			0
$553$	−119.554	+	182.725i	−0.216191	+	0.330425i
$554$	843.902	−	629.978i	1.52329	−	1.13714i
$555$		0			0
$556$	−185.746	+	626.392i	−0.334075	+	1.12660i
$557$			238.943i			0.428982i	0.976726	+	0.214491i	$0.0688092\pi$
$557$			238.943i			0.428982i	−0.976726	+	0.214491i	$0.931191\pi$
$558$		0			0
$559$		−	317.613i		−	0.568180i
$560$	931.734	−	410.366i	1.66381	−	0.732797i
$561$		0			0
$562$	197.697	+	264.829i	0.351773	+	0.471226i
$563$	−349.331			−0.620481			−0.310240	−	0.950658i	$-0.600410\pi$
$563$	−349.331			−0.620481			−0.310240	+	0.950658i	$0.600410\pi$
$564$		0			0
$565$	−659.136			−1.16661
$566$	−204.151	−	273.475i	−0.360691	−	0.483172i
$567$		0			0
$568$	−7.46741	+	2.75113i	−0.0131469	+	0.00484354i
$569$	905.015			1.59054			0.795268	−	0.606258i	$-0.207330\pi$
$569$	905.015			1.59054			0.795268	+	0.606258i	$0.207330\pi$
$570$		0			0
$571$		−	469.382i		−	0.822035i	−0.911627	−	0.411017i	$-0.865174\pi$
$571$		−	469.382i		−	0.822035i	0.911627	−	0.411017i	$-0.134826\pi$
$572$	242.320	+	71.8559i	0.423636	+	0.125622i
$573$		0			0
$574$	−31.7905	−	513.081i	−0.0553842	−	0.893869i
$575$	−538.226			−0.936045
$576$		0			0
$577$			607.599i			1.05303i	0.850165	+	0.526516i	$0.176502\pi$
$577$			607.599i			1.05303i	−0.850165	+	0.526516i	$0.823498\pi$
$578$	−323.530	−	433.392i	−0.559741	−	0.749814i
$579$		0			0
$580$	1194.04	+	354.073i	2.05869	+	0.610470i
$581$	171.544	−	262.187i	0.295257	−	0.451268i
$582$		0			0
$583$	288.073			0.494121
$584$	−24.2875	−	65.9236i	−0.0415882	−	0.112883i
$585$		0			0
$586$	19.2764	+	25.8222i	0.0328949	+	0.0440651i
$587$	−374.034			−0.637196			−0.318598	−	0.947890i	$-0.603212\pi$
$587$	−374.034			−0.637196			−0.318598	+	0.947890i	$0.603212\pi$
$588$		0			0
$589$		−	108.127i		−	0.183577i
$590$	−40.3864	−	54.1006i	−0.0684516	−	0.0916959i
$591$		0			0
$592$	563.374	−	866.404i	0.951645	−	1.46352i
$593$			1159.14i			1.95471i	0.211614	+	0.977353i	$0.432128\pi$
$593$			1159.14i			1.95471i	−0.211614	+	0.977353i	$0.567872\pi$
$594$		0			0
$595$	229.538	+	150.183i	0.385778	+	0.252408i
$596$	−366.263	−	108.609i	−0.614536	−	0.182230i
$597$		0			0
$598$	47.4958	+	63.6242i	0.0794245	+	0.106395i
$599$	−154.662			−0.258200			−0.129100	−	0.991632i	$-0.541209\pi$
$599$	−154.662			−0.258200			−0.129100	+	0.991632i	$0.541209\pi$
$600$		0			0
$601$		−	924.074i		−	1.53756i	−0.639513	−	0.768780i	$-0.720864\pi$
$601$		−	924.074i		−	1.53756i	0.639513	−	0.768780i	$-0.279136\pi$
$602$	64.6899	+	1044.06i	0.107458	+	1.73432i
$603$		0			0
$604$	−221.346	+	746.444i	−0.366466	+	1.23583i
$605$	908.687			1.50196
$606$		0			0
$607$		−	61.7356i		−	0.101706i	−0.998706	−	0.0508531i	$-0.983806\pi$
$607$		−	61.7356i		−	0.101706i	0.998706	−	0.0508531i	$-0.0161940\pi$
$608$	−55.7616	−	860.446i	−0.0917131	−	1.41521i
$609$		0			0
$610$	−868.014	−	1162.77i	−1.42297	−	1.90618i
$611$			223.215i			0.365328i
$612$		0			0
$613$			661.600i			1.07928i	0.841895	+	0.539641i	$0.181440\pi$
$613$			661.600i			1.07928i	−0.841895	+	0.539641i	$0.818560\pi$
$614$	7.13176	+	9.55352i	0.0116153	+	0.0155595i
$615$		0			0
$616$	−811.190	−	186.850i	−1.31687	−	0.303328i
$617$	−354.372			−0.574347			−0.287174	−	0.957879i	$-0.592716\pi$
$617$	−354.372			−0.574347			−0.287174	+	0.957879i	$0.592716\pi$
$618$		0			0
$619$	−636.341			−1.02801			−0.514007	−	0.857786i	$-0.671839\pi$
$619$	−636.341			−1.02801			−0.514007	+	0.857786i	$0.671839\pi$
$620$	139.889	+	41.4817i	0.225627	+	0.0669059i
$621$		0			0
$622$	418.390	−	312.331i	0.672653	−	0.502140i
$623$	68.1216	+	44.5708i	0.109344	+	0.0715423i
$624$		0			0
$625$	1255.60			2.00896
$626$	−457.910	+	341.833i	−0.731486	+	0.546059i
$627$		0			0
$628$	281.572	−	949.545i	0.448362	−	1.51201i
$629$	278.443			0.442675
$630$		0			0
$631$	−199.202			−0.315693			−0.157847	−	0.987464i	$-0.550455\pi$
$631$	−199.202			−0.315693			−0.157847	+	0.987464i	$0.550455\pi$
$632$	−234.169	+	86.2721i	−0.370520	+	0.136506i
$633$		0			0
$634$	−951.810	+	710.532i	−1.50128	+	1.12071i
$635$	713.829			1.12414
$636$		0			0
$637$	−83.4144	−	190.856i	−0.130949	−	0.299618i
$638$	−609.156	−	816.009i	−0.954790	−	1.27901i
$639$		0			0
$640$	1134.59	+	257.959i	1.77279	+	0.403060i
$641$	−19.2310			−0.0300016			−0.0150008	−	0.999887i	$-0.504775\pi$
$641$	−19.2310			−0.0300016			−0.0150008	+	0.999887i	$0.504775\pi$
$642$		0			0
$643$	783.597			1.21866			0.609329	−	0.792918i	$-0.291439\pi$
$643$	783.597			1.21866			0.609329	+	0.792918i	$0.291439\pi$
$644$	−169.087	−	199.472i	−0.262558	−	0.309739i
$645$		0			0
$646$	186.163	−	138.972i	0.288178	−	0.215126i
$647$			321.191i			0.496431i	0.968705	+	0.248216i	$0.0798442\pi$
$647$			321.191i			0.496431i	−0.968705	+	0.248216i	$0.920156\pi$
$648$		0			0
$649$			55.2003i			0.0850544i
$650$	−293.096	−	392.624i	−0.450917	−	0.604037i
$651$		0			0
$652$	162.177	+	48.0910i	0.248738	+	0.0737592i
$653$		−	567.084i		−	0.868428i	−0.900810	−	0.434214i	$-0.857026\pi$
$653$		−	567.084i		−	0.868428i	0.900810	−	0.434214i	$-0.142974\pi$
$654$		0			0
$655$	120.625			0.184160
$656$	320.266	−	492.533i	0.488211	−	0.750812i
$657$		0			0
$658$	−45.4635	−	733.754i	−0.0690934	−	1.11513i
$659$		−	76.3245i		−	0.115819i	−0.998322	−	0.0579094i	$-0.981557\pi$
$659$		−	76.3245i		−	0.115819i	0.998322	−	0.0579094i	$-0.0184434\pi$
$660$		0			0
$661$	−422.507			−0.639193			−0.319597	−	0.947554i	$-0.603547\pi$
$661$	−422.507			−0.639193			−0.319597	+	0.947554i	$0.603547\pi$
$662$	40.9921	−	30.6009i	0.0619216	−	0.0462249i
$663$		0			0
$664$	336.002	−	123.789i	0.506027	−	0.186430i
$665$	938.735	−	1434.75i	1.41163	−	2.15752i
$666$		0			0
$667$		−	319.884i		−	0.479586i
$668$	837.581	+	248.371i	1.25386	+	0.371812i
$669$		0			0
$670$	−967.214	+	722.031i	−1.44360	+	1.07766i
$671$			1186.41i			1.76811i
$672$		0			0
$673$	523.984			0.778579			0.389289	−	0.921115i	$-0.372721\pi$
$673$	523.984			0.778579			0.389289	+	0.921115i	$0.372721\pi$
$674$	677.054	+	906.964i	1.00453	+	1.34564i
$675$		0			0
$676$	171.637	−	578.811i	0.253901	−	0.856230i
$677$	−523.084			−0.772650			−0.386325	−	0.922363i	$-0.626256\pi$
$677$	−523.084			−0.772650			−0.386325	+	0.922363i	$0.626256\pi$
$678$		0			0
$679$	535.814	+	350.574i	0.789122	+	0.516310i
$680$	108.375	+	294.161i	0.159374	+	0.432590i
$681$		0			0
$682$	−71.3662	−	95.6002i	−0.104642	−	0.140176i
$683$		−	243.110i		−	0.355945i	−0.984036	−	0.177972i	$-0.943046\pi$
$683$		−	243.110i		−	0.355945i	0.984036	−	0.177972i	$-0.0569537\pi$
$684$		0			0
$685$	922.339			1.34648
$686$	313.073	+	610.394i	0.456374	+	0.889788i
$687$		0			0
$688$	−651.704	+	1002.25i	−0.947244	+	1.45675i
$689$			82.3779i			0.119562i
$690$		0			0
$691$	−1129.66			−1.63482			−0.817409	−	0.576057i	$-0.804590\pi$
$691$	−1129.66			−1.63482			−0.817409	+	0.576057i	$0.804590\pi$
$692$	−307.074	+	1035.55i	−0.443749	+	1.49645i
$693$		0			0
$694$	136.486	−	101.888i	0.196666	−	0.146813i
$695$	−1484.77			−2.13636
$696$		0			0
$697$	158.289			0.227100
$698$	329.056	+	440.794i	0.471426	+	0.631510i
$699$		0			0
$700$	1043.44	+	1230.94i	1.49062	+	1.75848i
$701$			1291.80i			1.84280i	0.388616	+	0.921400i	$0.372953\pi$
$701$			1291.80i			1.84280i	−0.388616	+	0.921400i	$0.627047\pi$
$702$		0			0
$703$		−	1740.44i		−	2.47573i
$704$	−617.214	−	723.957i	−0.876725	−	1.02835i
$705$		0			0
$706$	−232.715	+	173.724i	−0.329625	+	0.246067i
$707$	−134.759	+	205.964i	−0.190606	+	0.291321i
$708$		0			0
$709$		−	748.254i		−	1.05537i	−0.849442	−	0.527683i	$-0.823061\pi$
$709$		−	748.254i		−	1.05537i	0.849442	−	0.527683i	$-0.176939\pi$
$710$	−10.8186	−	14.4923i	−0.0152375	−	0.0204117i
$711$		0			0
$712$	32.1631	+	87.3004i	0.0451729	+	0.122613i
$713$		−	37.4762i		−	0.0525613i
$714$		0			0
$715$			574.384i			0.803334i
$716$	578.730	+	171.613i	0.808282	+	0.239683i
$717$		0			0
$718$	−48.0114	−	64.3148i	−0.0668682	−	0.0895749i
$719$			612.811i			0.852310i	0.904650	+	0.426155i	$0.140132\pi$
$719$			612.811i			0.852310i	−0.904650	+	0.426155i	$0.859868\pi$
$720$		0			0
$721$	266.589	+	174.425i	0.369750	+	0.241921i
$722$	−436.753	−	585.063i	−0.604921	−	0.810336i
$723$		0			0
$724$	−71.3861	+	240.736i	−0.0985996	+	0.332508i
$725$			1974.00i			2.72276i
$726$		0			0
$727$			138.017i			0.189845i	0.995485	+	0.0949223i	$0.0302603\pi$
$727$			138.017i			0.189845i	−0.995485	+	0.0949223i	$0.969740\pi$
$728$	53.4322	−	231.970i	0.0733959	−	0.318640i
$729$		0			0
$730$	127.941	−	95.5087i	0.175262	−	0.130834i
$731$	−322.099			−0.440628
$732$		0			0
$733$	644.555			0.879338			0.439669	−	0.898160i	$-0.355096\pi$
$733$	644.555			0.879338			0.439669	+	0.898160i	$0.355096\pi$
$734$	599.347	−	447.417i	0.816550	−	0.609560i
$735$		0			0
$736$	−19.3266	−	298.225i	−0.0262590	−	0.405198i
$737$	986.875			1.33904
$738$		0			0
$739$			712.278i			0.963841i	0.876215	+	0.481920i	$0.160061\pi$
$739$			712.278i			0.963841i	−0.876215	+	0.481920i	$0.839939\pi$
$740$	2251.68	+	667.698i	3.04281	+	0.902295i
$741$		0			0
$742$	−16.7784	−	270.793i	−0.0226123	−	0.364950i
$743$	−10.1719			−0.0136903			−0.00684515	−	0.999977i	$-0.502179\pi$
$743$	−10.1719			−0.0136903			−0.00684515	+	0.999977i	$0.502179\pi$
$744$		0			0
$745$		−	868.174i		−	1.16533i
$746$	−357.305	+	266.730i	−0.478961	+	0.357547i
$747$		0			0
$748$	72.8709	−	245.743i	0.0974209	−	0.328533i
$749$	376.270	+	246.187i	0.502363	+	0.328688i
$750$		0			0
$751$	−1079.30			−1.43715			−0.718573	−	0.695451i	$-0.755204\pi$
$751$	−1079.30			−1.43715			−0.718573	+	0.695451i	$0.755204\pi$
$752$	458.012	−	704.369i	0.609058	−	0.936661i
$753$		0			0
$754$	233.348	−	174.196i	0.309480	−	0.231029i
$755$	−1769.34			−2.34349
$756$		0			0
$757$		−	1200.34i		−	1.58566i	−0.609445	−	0.792828i	$-0.708608\pi$
$757$		−	1200.34i		−	1.58566i	0.609445	−	0.792828i	$-0.291392\pi$
$758$	−714.334	+	533.255i	−0.942394	+	0.703503i
$759$		0			0
$760$	1838.69	−	677.408i	2.41933	−	0.891326i
$761$		−	965.128i		−	1.26824i	−0.773236	−	0.634118i	$-0.781363\pi$
$761$		−	965.128i		−	1.26824i	0.773236	−	0.634118i	$-0.218637\pi$
$762$		0			0
$763$	−230.301	−	150.682i	−0.301836	−	0.197486i
$764$	173.813	−	586.149i	0.227503	−	0.767210i
$765$		0			0
$766$	−743.135	+	554.755i	−0.970151	+	0.724224i
$767$	−15.7852			−0.0205805
$768$		0			0
$769$			999.555i			1.29981i	0.760015	+	0.649906i	$0.225192\pi$
$769$			999.555i			1.29981i	−0.760015	+	0.649906i	$0.774808\pi$
$770$	−116.988	−	1888.12i	−0.151932	−	2.45210i
$771$		0			0
$772$	224.020	−	755.465i	0.290182	−	0.978581i
$773$	−1048.92			−1.35694			−0.678471	−	0.734628i	$-0.737357\pi$
$773$	−1048.92			−1.35694			−0.678471	+	0.734628i	$0.737357\pi$
$774$		0			0
$775$			231.265i			0.298407i
$776$	252.980	+	686.666i	0.326006	+	0.884878i
$777$		0			0
$778$	−273.796	+	204.391i	−0.351923	+	0.262713i
$779$		−	989.404i		−	1.27009i
$780$		0			0
$781$			14.7869i			0.0189333i
$782$	64.5229	−	48.1667i	0.0825101	−	0.0615943i
$783$		0			0
$784$	−128.396	+	773.415i	−0.163770	+	0.986498i
$785$	2250.76			2.86721
$786$		0			0
$787$	−1269.73			−1.61338			−0.806690	−	0.590975i	$-0.798743\pi$
$787$	−1269.73			−1.61338			−0.806690	+	0.590975i	$0.798743\pi$
$788$	−224.026	−	66.4312i	−0.284297	−	0.0843036i
$789$		0			0
$790$	−339.259	−	454.462i	−0.429441	−	0.575268i
$791$	277.900	−	424.740i	0.351328	−	0.536966i
$792$		0			0
$793$	−339.267			−0.427828
$794$	−643.098	−	861.476i	−0.809947	−	1.08498i
$795$		0			0
$796$	−122.340	−	36.2779i	−0.153694	−	0.0455753i
$797$	−792.144			−0.993908			−0.496954	−	0.867777i	$-0.665548\pi$
$797$	−792.144			−0.993908			−0.496954	+	0.867777i	$0.665548\pi$
$798$		0			0
$799$	226.368			0.283315
$800$	119.264	+	1840.35i	0.149080	+	2.30043i
$801$		0			0
$802$	587.413	+	786.883i	0.732436	+	0.981151i
$803$	−130.542			−0.162568
$804$		0			0
$805$	325.360	−	497.277i	0.404174	−	0.617735i
$806$	27.3381	−	20.4080i	0.0339182	−	0.0253202i
$807$		0			0
$808$	−263.950	+	97.2442i	−0.326671	+	0.120352i
$809$	−1282.81			−1.58568			−0.792838	−	0.609433i	$-0.791397\pi$
$809$	−1282.81			−1.58568			−0.792838	+	0.609433i	$0.791397\pi$
$810$		0			0
$811$	−272.683			−0.336231			−0.168115	−	0.985767i	$-0.553768\pi$
$811$	−272.683			−0.336231			−0.168115	+	0.985767i	$0.553768\pi$
$812$	−731.583	+	620.145i	−0.900965	+	0.763725i
$813$		0			0
$814$	−1148.73	−	1538.80i	−1.41121	−	1.89042i
$815$			384.418i			0.471679i
$816$		0			0
$817$			2013.32i			2.46428i
$818$	682.820	−	509.729i	0.834743	−	0.623141i
$819$		0			0
$820$	1280.03	+	379.573i	1.56102	+	0.462894i
$821$		−	1350.30i		−	1.64470i	−0.568985	−	0.822348i	$-0.692664\pi$
$821$		−	1350.30i		−	1.64470i	0.568985	−	0.822348i	$-0.307336\pi$
$822$		0			0
$823$	126.866			0.154150			0.0770752	−	0.997025i	$-0.475442\pi$
$823$	126.866			0.154150			0.0770752	+	0.997025i	$0.475442\pi$
$824$	125.868	+	341.644i	0.152753	+	0.414617i
$825$		0			0
$826$	51.8893	−	3.21506i	0.0628199	−	0.00389233i
$827$			138.892i			0.167946i	0.996468	+	0.0839731i	$0.0267610\pi$
$827$			138.892i			0.167946i	−0.996468	+	0.0839731i	$0.973239\pi$
$828$		0			0
$829$	−951.755			−1.14808			−0.574038	−	0.818829i	$-0.694624\pi$
$829$	−951.755			−1.14808			−0.574038	+	0.818829i	$0.694624\pi$
$830$	486.793	+	652.095i	0.586497	+	0.785656i
$831$		0			0
$832$	207.024	−	176.500i	0.248828	−	0.212140i
$833$	−193.552	+	84.5926i	−0.232356	+	0.101552i
$834$		0			0
$835$			1985.36i			2.37768i
$836$	−1536.04	−	455.488i	−1.83737	−	0.544842i
$837$		0			0
$838$	−867.865	−	1162.57i	−1.03564	−	1.38731i
$839$			724.563i			0.863603i	0.901969	+	0.431802i	$0.142122\pi$
$839$			724.563i			0.863603i	−0.901969	+	0.431802i	$0.857878\pi$
$840$		0			0
$841$	−332.206			−0.395013
$842$	48.2407	−	36.0120i	0.0572930	−	0.0427696i
$843$		0			0
$844$	−296.560	−	87.9400i	−0.351375	−	0.104194i
$845$	1371.99			1.62366
$846$		0			0
$847$	−383.114	+	585.548i	−0.452319	+	0.691320i
$848$	169.030	−	259.948i	0.199328	−	0.306543i
$849$		0			0
$850$	−398.170	+	297.236i	−0.468435	+	0.349690i
$851$		−	603.225i		−	0.708843i
$852$		0			0
$853$	−1219.96			−1.43020			−0.715100	−	0.699022i	$-0.753619\pi$
$853$	−1219.96			−1.43020			−0.715100	+	0.699022i	$0.753619\pi$
$854$	1115.24	−	69.1004i	1.30590	−	0.0809138i
$855$		0			0
$856$	177.653	+	482.204i	0.207538	+	0.563322i
$857$		−	169.761i		−	0.198088i	−0.995083	−	0.0990440i	$-0.968422\pi$
$857$		−	169.761i		−	0.198088i	0.995083	−	0.0990440i	$-0.0315785\pi$
$858$		0			0
$859$	687.207			0.800009			0.400004	−	0.916513i	$-0.369009\pi$
$859$	687.207			0.800009			0.400004	+	0.916513i	$0.369009\pi$
$860$	−2604.72	−	772.385i	−3.02874	−	0.898122i
$861$		0			0
$862$	−317.657	−	425.525i	−0.368511	−	0.493648i
$863$	246.094			0.285161			0.142581	−	0.989783i	$-0.454460\pi$
$863$	246.094			0.285161			0.142581	+	0.989783i	$0.454460\pi$
$864$		0			0
$865$	−2454.61			−2.83770
$866$	−1147.76	+	856.812i	−1.32536	+	0.989390i
$867$		0			0
$868$	−85.7092	+	72.6535i	−0.0987433	+	0.0837022i
$869$			463.700i			0.533602i
$870$		0			0
$871$			282.209i			0.324006i
$872$	−108.735	−	295.139i	−0.124696	−	0.338463i
$873$		0			0
$874$	−301.072	−	403.308i	−0.344476	−	0.461450i
$875$	−1136.83	+	1737.52i	−1.29924	+	1.98574i
$876$		0			0
$877$			487.171i			0.555497i	0.960654	+	0.277749i	$0.0895882\pi$
$877$			487.171i			0.555497i	−0.960654	+	0.277749i	$0.910412\pi$
$878$	−471.831	+	352.225i	−0.537393	+	0.401167i
$879$		0			0
$880$	1178.57	−	1812.50i	1.33928	−	2.05966i
$881$		−	343.877i		−	0.390325i	−0.980771	−	0.195163i	$-0.937477\pi$
$881$		−	343.877i		−	0.390325i	0.980771	−	0.195163i	$-0.0625235\pi$
$882$		0			0
$883$		−	755.288i		−	0.855366i	−0.903929	−	0.427683i	$-0.859330\pi$
$883$		−	755.288i		−	0.855366i	0.903929	−	0.427683i	$-0.140670\pi$
$884$	70.2732	+	20.8383i	0.0794945	+	0.0235728i
$885$		0			0
$886$	783.287	−	584.729i	0.884071	−	0.659965i
$887$		−	1633.02i		−	1.84106i	−0.390668	−	0.920532i	$-0.627756\pi$
$887$		−	1633.02i		−	1.84106i	0.390668	−	0.920532i	$-0.372244\pi$
$888$		0			0
$889$	−300.959	+	459.983i	−0.338537	+	0.517416i
$890$	−169.428	+	126.479i	−0.190368	+	0.142111i
$891$		0			0
$892$	−557.255	−	165.245i	−0.624726	−	0.185252i
$893$		−	1414.94i		−	1.58448i
$894$		0			0
$895$			1371.80i			1.53273i
$896$	−644.583	+	622.358i	−0.719401	+	0.694595i
$897$		0			0
$898$	515.588	+	690.668i	0.574152	+	0.769119i
$899$	−137.448			−0.152890
$900$		0			0
$901$	83.5416			0.0927209
$902$	−653.027	−	874.778i	−0.723977	−	0.969820i
$903$		0			0
$904$	544.320	−	200.538i	0.602124	−	0.221834i
$905$	−570.629			−0.630530
$906$		0			0
$907$		−	579.901i		−	0.639361i	−0.947525	−	0.319681i	$-0.896424\pi$
$907$		−	579.901i		−	0.639361i	0.947525	−	0.319681i	$-0.103576\pi$
$908$	406.621	−	1371.25i	0.447821	−	1.51019i
$909$		0			0
$910$	539.931	−	33.4542i	0.593331	−	0.0367628i
$911$	−169.237			−0.185770			−0.0928852	−	0.995677i	$-0.529609\pi$
$911$	−169.237			−0.185770			−0.0928852	+	0.995677i	$0.529609\pi$
$912$		0			0
$913$		−	665.350i		−	0.728752i
$914$	836.770	+	1120.91i	0.915503	+	1.22638i
$915$		0			0
$916$	−144.762	+	488.180i	−0.158037	+	0.532948i
$917$	−50.8569	+	77.7291i	−0.0554600	+	0.0847645i
$918$		0			0
$919$	910.454			0.990701			0.495351	−	0.868693i	$-0.335040\pi$
$919$	910.454			0.990701			0.495351	+	0.868693i	$0.335040\pi$
$920$	637.279	−	234.785i	0.692695	−	0.255202i
$921$		0			0
$922$	464.065	+	621.650i	0.503325	+	0.674240i
$923$	−4.22851			−0.00458127
$924$		0			0
$925$			3722.50i			4.02432i
$926$	350.652	+	469.724i	0.378674	+	0.507261i
$927$		0			0
$928$	−1093.77	+	70.8824i	−1.17863	+	0.0763819i
$929$			1560.39i			1.67965i	0.542859	+	0.839824i	$0.317342\pi$
$929$			1560.39i			1.67965i	−0.542859	+	0.839824i	$0.682658\pi$
$930$		0			0
$931$	528.756	+	1209.82i	0.567944	+	1.29949i
$932$	91.5301	−	308.667i	0.0982083	−	0.331188i
$933$		0			0
$934$	703.654	+	942.596i	0.753377	+	1.00920i
$935$	582.498			0.622992
$936$		0			0
$937$			1529.70i			1.63255i	0.577664	+	0.816275i	$0.303964\pi$
$937$			1529.70i			1.63255i	−0.577664	+	0.816275i	$0.696036\pi$
$938$	−57.4791	−	927.679i	−0.0612783	−	0.988997i
$939$		0			0
$940$	1830.57	+	542.825i	1.94742	+	0.577474i
$941$	−509.889			−0.541859			−0.270929	−	0.962599i	$-0.587331\pi$
$941$	−509.889			−0.541859			−0.270929	+	0.962599i	$0.587331\pi$
$942$		0			0
$943$		−	342.921i		−	0.363649i
$944$	49.8112	+	32.3894i	0.0527661	+	0.0343108i
$945$		0			0
$946$	1328.83	+	1780.07i	1.40469	+	1.88168i
$947$		−	227.835i		−	0.240586i	−0.992738	−	0.120293i	$-0.961617\pi$
$947$		−	227.835i		−	0.240586i	0.992738	−	0.120293i	$-0.0383833\pi$
$948$		0			0
$949$		−	37.3300i		−	0.0393362i
$950$	1857.91	+	2488.81i	1.95570	+	2.61980i
$951$		0			0
$952$	−235.246	−	54.1869i	−0.247108	−	0.0569191i
$953$	−488.011			−0.512079			−0.256040	−	0.966666i	$-0.582418\pi$
$953$	−488.011			−0.512079			−0.256040	+	0.966666i	$0.582418\pi$
$954$		0			0
$955$	1389.38			1.45485
$956$	390.641	−	1317.36i	0.408621	−	1.37799i
$957$		0			0
$958$	624.905	−	466.496i	0.652302	−	0.486948i
$959$	−388.870	+	594.345i	−0.405495	+	0.619755i
$960$		0			0
$961$	944.897			0.983244
$962$	440.040	−	328.493i	0.457422	−	0.341468i
$963$		0			0
$964$	−773.785	−	229.453i	−0.802682	−	0.238022i
$965$	1790.72			1.85567
$966$		0			0
$967$	976.631			1.00996			0.504980	−	0.863131i	$-0.331500\pi$
$967$	976.631			1.00996			0.504980	+	0.863131i	$0.331500\pi$
$968$	−750.401	+	276.462i	−0.775208	+	0.285601i
$969$		0			0
$970$	−1332.64	+	994.827i	−1.37386	+	1.02559i
$971$	1709.72			1.76078			0.880390	−	0.474250i	$-0.157281\pi$
$971$	1709.72			1.76078			0.880390	+	0.474250i	$0.157281\pi$
$972$		0			0
$973$	625.999	−	956.770i	0.643370	−	0.983320i
$974$	367.577	+	492.396i	0.377389	+	0.505540i
$975$		0			0
$976$	1070.58	+	696.136i	1.09690	+	0.713255i
$977$	1387.42			1.42009			0.710043	−	0.704158i	$-0.248675\pi$
$977$	1387.42			1.42009			0.710043	+	0.704158i	$0.248675\pi$
$978$		0			0
$979$	172.872			0.176580
$980$	−1768.05	+	219.941i	−1.80413	+	0.224430i
$981$		0			0
$982$	1203.75	−	898.607i	1.22581	−	0.915079i
$983$		−	910.425i		−	0.926170i	−0.886314	−	0.463085i	$-0.846742\pi$
$983$		−	910.425i		−	0.926170i	0.886314	−	0.463085i	$-0.153258\pi$
$984$		0			0
$985$		−	531.022i		−	0.539108i
$986$	−176.656	−	236.644i	−0.179165	−	0.240004i
$987$		0			0
$988$	130.252	−	439.251i	0.131834	−	0.444586i
$989$			697.804i			0.705565i
$990$		0			0
$991$	474.575			0.478885			0.239443	−	0.970910i	$-0.423035\pi$
$991$	474.575			0.478885			0.239443	+	0.970910i	$0.423035\pi$
$992$	−128.142	+	8.30428i	−0.129175	+	0.00837125i
$993$		0			0
$994$	13.9000	−	0.861244i	0.0139839	−	0.000866442i
$995$		−	289.990i		−	0.291447i
$996$		0			0
$997$	545.379			0.547020			0.273510	−	0.961869i	$-0.411815\pi$
$997$	545.379			0.547020			0.273510	+	0.961869i	$0.411815\pi$
$998$	−404.258	+	301.781i	−0.405068	+	0.302386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.9		32
3.2	odd	2		168.3.l.a.13.23	yes	32
4.3	odd	2		2016.3.l.h.433.1		32
7.6	odd	2	inner	504.3.l.h.181.10		32
8.3	odd	2		2016.3.l.h.433.32		32
8.5	even	2	inner	504.3.l.h.181.12		32
12.11	even	2		672.3.l.a.433.18		32
21.20	even	2		168.3.l.a.13.24	yes	32
24.5	odd	2		168.3.l.a.13.22	yes	32
24.11	even	2		672.3.l.a.433.15		32
28.27	even	2		2016.3.l.h.433.31		32
56.13	odd	2	inner	504.3.l.h.181.11		32
56.27	even	2		2016.3.l.h.433.2		32
84.83	odd	2		672.3.l.a.433.2		32
168.83	odd	2		672.3.l.a.433.31		32
168.125	even	2		168.3.l.a.13.21	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.21	✓	32	168.125	even	2
168.3.l.a.13.22	yes	32	24.5	odd	2
168.3.l.a.13.23	yes	32	3.2	odd	2
168.3.l.a.13.24	yes	32	21.20	even	2
504.3.l.h.181.9		32	1.1	even	1	trivial
504.3.l.h.181.10		32	7.6	odd	2	inner
504.3.l.h.181.11		32	56.13	odd	2	inner
504.3.l.h.181.12		32	8.5	even	2	inner
672.3.l.a.433.2		32	84.83	odd	2
672.3.l.a.433.15		32	24.11	even	2
672.3.l.a.433.18		32	12.11	even	2
672.3.l.a.433.31		32	168.83	odd	2
2016.3.l.h.433.1		32	4.3	odd	2
2016.3.l.h.433.2		32	56.27	even	2
2016.3.l.h.433.31		32	28.27	even	2
2016.3.l.h.433.32		32	8.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19641 - 1.60268i) q^{2} +(-1.13719 + 3.83494i) q^{4} -9.09019 q^{5} +(3.83254 - 5.85761i) q^{7} +(7.50675 - 2.76563i) q^{8} +(10.8756 + 14.5687i) q^{10} -14.8648i q^{11} +4.25079 q^{13} +(-13.9732 + 0.865781i) q^{14} +(-13.4136 - 8.72211i) q^{16} -4.31083i q^{17} -26.9453 q^{19} +(10.3373 - 34.8604i) q^{20} +(-23.8236 + 17.7845i) q^{22} -9.33910 q^{23} +57.6315 q^{25} +(-5.08570 - 6.81267i) q^{26} +(18.1053 + 21.3588i) q^{28} +34.2521i q^{29} +4.01283i q^{31} +(2.06943 + 31.9330i) q^{32} +(-6.90890 + 5.15754i) q^{34} +(-34.8385 + 53.2468i) q^{35} +64.5914i q^{37} +(32.2378 + 43.1849i) q^{38} +(-68.2378 + 25.1401i) q^{40} +36.7189i q^{41} -74.7186i q^{43} +(57.0058 + 16.9041i) q^{44} +(11.1734 + 14.9676i) q^{46} +52.5115i q^{47} +(-19.6233 - 44.8991i) q^{49} +(-68.9511 - 92.3650i) q^{50} +(-4.83395 + 16.3015i) q^{52} +19.3795i q^{53} +135.124i q^{55} +(12.5699 - 54.5710i) q^{56} +(54.8953 - 40.9797i) q^{58} -3.71348 q^{59} -79.8128 q^{61} +(6.43130 - 4.80100i) q^{62} +(48.7026 - 41.5217i) q^{64} -38.6404 q^{65} +66.3899i q^{67} +(16.5318 + 4.90223i) q^{68} +(127.019 - 7.87011i) q^{70} -0.994759 q^{71} -8.78191i q^{73} +(103.520 - 77.2781i) q^{74} +(30.6420 - 103.334i) q^{76} +(-87.0725 - 56.9701i) q^{77} -31.1944 q^{79} +(121.932 + 79.2856i) q^{80} +(58.8488 - 43.9310i) q^{82} +44.7600 q^{83} +39.1863i q^{85} +(-119.750 + 89.3943i) q^{86} +(-41.1106 - 111.587i) q^{88} +11.6296i q^{89} +(16.2913 - 24.8995i) q^{91} +(10.6203 - 35.8149i) q^{92} +(84.1594 - 62.8255i) q^{94} +244.938 q^{95} +91.4731i q^{97} +(-48.4814 + 85.1678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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