LMFDB - Embedded newform 416.3.bb.c.191.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,3,Mod(159,416)] 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("416.159"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	416.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,-8,0,0,0,80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$11.3351789974$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.4
Character	$\chi$	$=$	416.191
Dual form			416.3.bb.c.159.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.45657 - 1.99565i) q^{3} +6.36955 q^{5} +(-5.32276 + 3.07310i) q^{7} +(3.46526 + 6.00201i) q^{9} +(-4.55705 - 2.63102i) q^{11} +(-0.635553 + 12.9845i) q^{13} +(-22.0168 - 12.7114i) q^{15} +(-16.0523 - 27.8035i) q^{17} +(-4.23804 + 2.44684i) q^{19} +24.5314 q^{21} +(8.99944 + 5.19583i) q^{23} +15.5712 q^{25} +8.25990i q^{27} +(-18.6765 + 32.3486i) q^{29} +39.4746i q^{31} +(10.5012 + 18.1886i) q^{33} +(-33.9036 + 19.5743i) q^{35} +(-16.8593 + 29.2011i) q^{37} +(28.1093 - 43.6134i) q^{39} +(-15.9547 + 27.6343i) q^{41} +(-7.50010 + 4.33019i) q^{43} +(22.0722 + 38.2301i) q^{45} -69.4026i q^{47} +(-5.61212 + 9.72047i) q^{49} +128.140i q^{51} -19.7488 q^{53} +(-29.0264 - 16.7584i) q^{55} +19.5321 q^{57} +(-80.1928 + 46.2993i) q^{59} +(29.2216 + 50.6133i) q^{61} +(-36.8896 - 21.2982i) q^{63} +(-4.04819 + 82.7052i) q^{65} +(113.408 + 65.4759i) q^{67} +(-20.7381 - 35.9195i) q^{69} +(-40.2747 + 23.2526i) q^{71} -28.9100 q^{73} +(-53.8229 - 31.0747i) q^{75} +32.3415 q^{77} -73.0898i q^{79} +(47.6713 - 82.5691i) q^{81} -6.44306i q^{83} +(-102.246 - 177.096i) q^{85} +(129.113 - 74.5436i) q^{87} +(-41.4095 + 71.7234i) q^{89} +(-36.5196 - 71.0663i) q^{91} +(78.7776 - 136.447i) q^{93} +(-26.9944 + 15.5852i) q^{95} +(28.4641 + 49.3012i) q^{97} -36.4687i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{5} + 80 q^{9} - 44 q^{13} + 16 q^{17} - 128 q^{21} + 272 q^{25} - 52 q^{29} - 72 q^{33} + 148 q^{37} + 72 q^{41} - 116 q^{45} + 328 q^{49} - 152 q^{53} - 224 q^{57} + 228 q^{61} - 352 q^{65}+ \cdots - 352 q^{97}+O(q^{100}) $ 32 * q - 8 * q^5 + 80 * q^9 - 44 * q^13 + 16 * q^17 - 128 * q^21 + 272 * q^25 - 52 * q^29 - 72 * q^33 + 148 * q^37 + 72 * q^41 - 116 * q^45 + 328 * q^49 - 152 * q^53 - 224 * q^57 + 228 * q^61 - 352 * q^65 + 200 * q^69 + 224 * q^73 + 832 * q^77 - 696 * q^81 - 84 * q^85 - 112 * q^89 + 152 * q^93 - 352 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.45657	−	1.99565i	−1.15219	−	0.665218i	−0.202771	−	0.979226i	$-0.564995\pi$
$3$	−3.45657	−	1.99565i	−1.15219	−	0.665218i	−0.949420	+	0.314009i	$0.898328\pi$
$4$		0			0
$5$	6.36955			1.27391			0.636955	−	0.770901i	$-0.280194\pi$
$5$	6.36955			1.27391			0.636955	+	0.770901i	$0.280194\pi$
$6$		0			0
$7$	−5.32276	+	3.07310i	−0.760395	+	0.439014i	−0.829438	−	0.558599i	$-0.811339\pi$
$7$	−5.32276	+	3.07310i	−0.760395	+	0.439014i	0.0690426	+	0.997614i	$0.478006\pi$
$8$		0			0
$9$	3.46526	+	6.00201i	0.385029	+	0.666890i
$10$		0			0
$11$	−4.55705	−	2.63102i	−0.414278	−	0.239183i	0.278348	−	0.960480i	$-0.410213\pi$
$11$	−4.55705	−	2.63102i	−0.414278	−	0.239183i	−0.692626	+	0.721297i	$0.743546\pi$
$12$		0			0
$13$	−0.635553	+	12.9845i	−0.0488887	+	0.998804i
$13$	−0.635553	+	12.9845i	−0.0488887	+	0.998804i
$14$		0			0
$15$	−22.0168	−	12.7114i	−1.46779	−	0.847428i
$16$		0			0
$17$	−16.0523	−	27.8035i	−0.944255	−	1.63550i	−0.757236	−	0.653142i	$-0.773451\pi$
$17$	−16.0523	−	27.8035i	−0.944255	−	1.63550i	−0.187019	−	0.982356i	$-0.559883\pi$
$18$		0			0
$19$	−4.23804	+	2.44684i	−0.223055	+	0.128781i	−0.607364	−	0.794424i	$-0.707773\pi$
$19$	−4.23804	+	2.44684i	−0.223055	+	0.128781i	0.384309	+	0.923204i	$0.374440\pi$
$20$		0			0
$21$	24.5314			1.16816
$22$		0			0
$23$	8.99944	+	5.19583i	0.391280	+	0.225906i	0.682715	−	0.730685i	$-0.260799\pi$
$23$	8.99944	+	5.19583i	0.391280	+	0.225906i	−0.291435	+	0.956591i	$0.594133\pi$
$24$		0			0
$25$	15.5712			0.622847
$26$		0			0
$27$			8.25990i			0.305922i
$28$		0			0
$29$	−18.6765	+	32.3486i	−0.644017	+	1.11547i	0.340511	+	0.940241i	$0.389400\pi$
$29$	−18.6765	+	32.3486i	−0.644017	+	1.11547i	−0.984528	+	0.175229i	$0.943933\pi$
$30$		0			0
$31$			39.4746i			1.27337i	0.771122	+	0.636687i	$0.219696\pi$
$31$			39.4746i			1.27337i	−0.771122	+	0.636687i	$0.780304\pi$
$32$		0			0
$33$	10.5012	+	18.1886i	0.318218	+	0.551170i
$34$		0			0
$35$	−33.9036	+	19.5743i	−0.968675	+	0.559265i
$36$		0			0
$37$	−16.8593	+	29.2011i	−0.455656	+	0.789219i	−0.998726	−	0.0504683i	$-0.983929\pi$
$37$	−16.8593	+	29.2011i	−0.455656	+	0.789219i	0.543070	+	0.839688i	$0.317262\pi$
$38$		0			0
$39$	28.1093	−	43.6134i	0.720751	−	1.11829i
$40$		0			0
$41$	−15.9547	+	27.6343i	−0.389139	+	0.674008i	−0.992334	−	0.123586i	$-0.960561\pi$
$41$	−15.9547	+	27.6343i	−0.389139	+	0.674008i	0.603195	+	0.797594i	$0.293894\pi$
$42$		0			0
$43$	−7.50010	+	4.33019i	−0.174421	+	0.100702i	−0.584669	−	0.811272i	$-0.698776\pi$
$43$	−7.50010	+	4.33019i	−0.174421	+	0.100702i	0.410248	+	0.911974i	$0.365442\pi$
$44$		0			0
$45$	22.0722	+	38.2301i	0.490493	+	0.849558i
$46$		0			0
$47$		−	69.4026i		−	1.47665i	−0.674445	−	0.738325i	$-0.735617\pi$
$47$		−	69.4026i		−	1.47665i	0.674445	−	0.738325i	$-0.264383\pi$
$48$		0			0
$49$	−5.61212	+	9.72047i	−0.114533	+	0.198377i
$50$		0			0
$51$			128.140i			2.51254i
$52$		0			0
$53$	−19.7488			−0.372619			−0.186310	−	0.982491i	$-0.559653\pi$
$53$	−19.7488			−0.372619			−0.186310	+	0.982491i	$0.559653\pi$
$54$		0			0
$55$	−29.0264	−	16.7584i	−0.527752	−	0.304698i
$56$		0			0
$57$	19.5321			0.342669
$58$		0			0
$59$	−80.1928	+	46.2993i	−1.35920	+	0.784734i	−0.989516	−	0.144423i	$-0.953867\pi$
$59$	−80.1928	+	46.2993i	−1.35920	+	0.784734i	−0.369684	+	0.929158i	$0.620534\pi$
$60$		0			0
$61$	29.2216	+	50.6133i	0.479043	+	0.829727i	0.999711	−	0.0240323i	$-0.00765044\pi$
$61$	29.2216	+	50.6133i	0.479043	+	0.829727i	−0.520668	+	0.853759i	$0.674317\pi$
$62$		0			0
$63$	−36.8896	−	21.2982i	−0.585549	−	0.338067i
$64$		0			0
$65$	−4.04819	+	82.7052i	−0.0622798	+	1.27239i
$66$		0			0
$67$	113.408	+	65.4759i	1.69265	+	0.977252i	0.952366	+	0.304957i	$0.0986422\pi$
$67$	113.408	+	65.4759i	1.69265	+	0.977252i	0.740284	+	0.672294i	$0.234691\pi$
$68$		0			0
$69$	−20.7381	−	35.9195i	−0.300553	−	0.520573i
$70$		0			0
$71$	−40.2747	+	23.2526i	−0.567250	+	0.327502i	−0.756050	−	0.654514i	$-0.772873\pi$
$71$	−40.2747	+	23.2526i	−0.567250	+	0.327502i	0.188800	+	0.982015i	$0.439540\pi$
$72$		0			0
$73$	−28.9100			−0.396027			−0.198014	−	0.980199i	$-0.563449\pi$
$73$	−28.9100			−0.396027			−0.198014	+	0.980199i	$0.563449\pi$
$74$		0			0
$75$	−53.8229	−	31.0747i	−0.717639	−	0.414329i
$76$		0			0
$77$	32.3415			0.420019
$78$		0			0
$79$		−	73.0898i		−	0.925187i	−0.886570	−	0.462594i	$-0.846919\pi$
$79$		−	73.0898i		−	0.925187i	0.886570	−	0.462594i	$-0.153081\pi$
$80$		0			0
$81$	47.6713	−	82.5691i	0.588534	−	1.01937i
$82$		0			0
$83$		−	6.44306i		−	0.0776272i	−0.999246	−	0.0388136i	$-0.987642\pi$
$83$		−	6.44306i		−	0.0776272i	0.999246	−	0.0388136i	$-0.0123579\pi$
$84$		0			0
$85$	−102.246	−	177.096i	−1.20290	−	2.08348i
$86$		0			0
$87$	129.113	−	74.5436i	1.48406	−	0.856823i
$88$		0			0
$89$	−41.4095	+	71.7234i	−0.465276	+	0.805881i	−0.999214	−	0.0396423i	$-0.987378\pi$
$89$	−41.4095	+	71.7234i	−0.465276	+	0.805881i	0.533938	+	0.845523i	$0.320711\pi$
$90$		0			0
$91$	−36.5196	−	71.0663i	−0.401315	−	0.780949i
$92$		0			0
$93$	78.7776	−	136.447i	0.847071	−	1.46717i
$94$		0			0
$95$	−26.9944	+	15.5852i	−0.284152	+	0.164055i
$96$		0			0
$97$	28.4641	+	49.3012i	0.293444	+	0.508260i	0.974622	−	0.223858i	$-0.0718652\pi$
$97$	28.4641	+	49.3012i	0.293444	+	0.508260i	−0.681178	+	0.732118i	$0.738532\pi$
$98$		0			0
$99$		−	36.4687i		−	0.368370i
$100$		0			0
$101$	81.7174	−	141.539i	0.809083	−	1.40137i	−0.104417	−	0.994534i	$-0.533298\pi$
$101$	81.7174	−	141.539i	0.809083	−	1.40137i	0.913500	−	0.406839i	$-0.133369\pi$
$102$		0			0
$103$		−	8.24875i		−	0.0800849i	−0.999198	−	0.0400425i	$-0.987251\pi$
$103$		−	8.24875i		−	0.0800849i	0.999198	−	0.0400425i	$-0.0127493\pi$
$104$		0			0
$105$	156.254			1.48813
$106$		0			0
$107$	−8.04003	−	4.64191i	−0.0751404	−	0.0433823i	0.461959	−	0.886901i	$-0.347147\pi$
$107$	−8.04003	−	4.64191i	−0.0751404	−	0.0433823i	−0.537099	+	0.843519i	$0.680480\pi$
$108$		0			0
$109$	−29.1142			−0.267103			−0.133551	−	0.991042i	$-0.542638\pi$
$109$	−29.1142			−0.267103			−0.133551	+	0.991042i	$0.542638\pi$
$110$		0			0
$111$	116.551	−	67.2905i	1.05001	−	0.606221i
$112$		0			0
$113$	−55.0757	−	95.3939i	−0.487395	−	0.844194i	0.512500	−	0.858687i	$-0.328720\pi$
$113$	−55.0757	−	95.3939i	−0.487395	−	0.844194i	−0.999895	+	0.0144939i	$0.995386\pi$
$114$		0			0
$115$	57.3224	+	33.0951i	0.498455	+	0.287783i
$116$		0			0
$117$	−80.1352	+	41.1800i	−0.684916	+	0.351965i
$118$		0			0
$119$	170.886	+	98.6609i	1.43601	+	0.829083i
$120$		0			0
$121$	−46.6555	−	80.8097i	−0.385583	−	0.667849i
$122$		0			0
$123$	110.297	−	63.6800i	0.896724	−	0.517724i
$124$		0			0
$125$	−60.0573			−0.480459
$126$		0			0
$127$	−217.522	−	125.586i	−1.71277	−	0.988869i	−0.930779	−	0.365582i	$-0.880870\pi$
$127$	−217.522	−	125.586i	−1.71277	−	0.988869i	−0.781993	−	0.623287i	$-0.785797\pi$
$128$		0			0
$129$	34.5662			0.267955
$130$		0			0
$131$		−	46.9658i		−	0.358518i	−0.983802	−	0.179259i	$-0.942630\pi$
$131$		−	46.9658i		−	0.358518i	0.983802	−	0.179259i	$-0.0573700\pi$
$132$		0			0
$133$	15.0387	−	26.0479i	0.113073	−	0.195849i
$134$		0			0
$135$			52.6119i			0.389718i
$136$		0			0
$137$	−123.862	−	214.535i	−0.904099	−	1.56595i	−0.822122	−	0.569312i	$-0.807210\pi$
$137$	−123.862	−	214.535i	−0.904099	−	1.56595i	−0.0819774	−	0.996634i	$-0.526124\pi$
$138$		0			0
$139$	48.7862	−	28.1667i	0.350980	−	0.202638i	−0.314137	−	0.949378i	$-0.601715\pi$
$139$	48.7862	−	28.1667i	0.350980	−	0.202638i	0.665117	+	0.746739i	$0.268382\pi$
$140$		0			0
$141$	−138.503	+	239.895i	−0.982294	+	1.70138i
$142$		0			0
$143$	37.0586	−	57.4987i	0.259151	−	0.402089i
$144$		0			0
$145$	−118.961	+	206.046i	−0.820420	+	1.42101i
$146$		0			0
$147$	38.7974	−	22.3997i	0.263928	−	0.152379i
$148$		0			0
$149$	22.6213	+	39.1812i	0.151821	+	0.262961i	0.931897	−	0.362724i	$-0.118153\pi$
$149$	22.6213	+	39.1812i	0.151821	+	0.262961i	−0.780076	+	0.625685i	$0.784820\pi$
$150$		0			0
$151$			213.294i			1.41254i	0.707943	+	0.706270i	$0.249624\pi$
$151$			213.294i			1.41254i	−0.707943	+	0.706270i	$0.750376\pi$
$152$		0			0
$153$	111.251	−	192.693i	0.727132	−	1.25943i
$154$		0			0
$155$			251.436i			1.62216i
$156$		0			0
$157$	117.158			0.746227			0.373114	−	0.927786i	$-0.378290\pi$
$157$	117.158			0.746227			0.373114	+	0.927786i	$0.378290\pi$
$158$		0			0
$159$	68.2632	+	39.4118i	0.429328	+	0.247873i
$160$		0			0
$161$	−63.8692			−0.396703
$162$		0			0
$163$	−45.2131	+	26.1038i	−0.277381	+	0.160146i	−0.632237	−	0.774775i	$-0.717863\pi$
$163$	−45.2131	+	26.1038i	−0.277381	+	0.160146i	0.354856	+	0.934921i	$0.384530\pi$
$164$		0			0
$165$	66.8879	+	115.853i	0.405381	+	0.702141i
$166$		0			0
$167$	109.301	+	63.1049i	0.654496	+	0.377874i	0.790177	−	0.612879i	$-0.209989\pi$
$167$	109.301	+	63.1049i	0.654496	+	0.377874i	−0.135680	+	0.990753i	$0.543322\pi$
$168$		0			0
$169$	−168.192	−	16.5046i	−0.995220	−	0.0976605i
$170$		0			0
$171$	−29.3719	−	16.9579i	−0.171765	−	0.0991687i
$172$		0			0
$173$	−22.3761	−	38.7565i	−0.129342	−	0.224026i	0.794080	−	0.607813i	$-0.207953\pi$
$173$	−22.3761	−	38.7565i	−0.129342	−	0.224026i	−0.923422	+	0.383787i	$0.874620\pi$
$174$		0			0
$175$	−82.8817	+	47.8518i	−0.473610	+	0.273439i
$176$		0			0
$177$	369.590			2.08808
$178$		0			0
$179$	252.618	+	145.849i	1.41128	+	0.814801i	0.995509	−	0.0946703i	$-0.0301797\pi$
$179$	252.618	+	145.849i	1.41128	+	0.814801i	0.415767	+	0.909471i	$0.363513\pi$
$180$		0			0
$181$	−236.676			−1.30760			−0.653802	−	0.756666i	$-0.726827\pi$
$181$	−236.676			−1.30760			−0.653802	+	0.756666i	$0.726827\pi$
$182$		0			0
$183$		−	233.265i		−	1.27467i
$184$		0			0
$185$	−107.386	+	185.998i	−0.580465	+	1.00539i
$186$		0			0
$187$			168.936i			0.903400i
$188$		0			0
$189$	−25.3835	−	43.9655i	−0.134304	−	0.232622i
$190$		0			0
$191$	313.094	−	180.765i	1.63923	−	0.946413i	0.658137	−	0.752898i	$-0.271345\pi$
$191$	313.094	−	180.765i	1.63923	−	0.946413i	0.981097	−	0.193515i	$-0.0619887\pi$
$192$		0			0
$193$	−93.6618	+	162.227i	−0.485294	+	0.840555i	−0.999857	−	0.0168980i	$-0.994621\pi$
$193$	−93.6618	+	162.227i	−0.485294	+	0.840555i	0.514563	+	0.857453i	$0.327954\pi$
$194$		0			0
$195$	179.044	−	277.798i	0.918173	−	1.42460i
$196$		0			0
$197$	83.5515	−	144.716i	0.424119	−	0.734597i	−0.572218	−	0.820101i	$-0.693917\pi$
$197$	83.5515	−	144.716i	0.424119	−	0.734597i	0.996338	+	0.0855049i	$0.0272503\pi$
$198$		0			0
$199$	−112.560	+	64.9863i	−0.565626	+	0.326564i	−0.755400	−	0.655263i	$-0.772558\pi$
$199$	−112.560	+	64.9863i	−0.565626	+	0.326564i	0.189775	+	0.981828i	$0.439224\pi$
$200$		0			0
$201$	−261.334	−	452.644i	−1.30017	−	2.25196i
$202$		0			0
$203$		−	229.579i		−	1.13093i
$204$		0			0
$205$	−101.624	+	176.018i	−0.495728	+	0.858625i
$206$		0			0
$207$			72.0196i			0.347921i
$208$		0			0
$209$	25.7506			0.123209
$210$		0			0
$211$	−294.929	−	170.277i	−1.39777	−	0.807002i	−0.403610	−	0.914931i	$-0.632245\pi$
$211$	−294.929	−	170.277i	−1.39777	−	0.807002i	−0.994159	+	0.107930i	$0.965578\pi$
$212$		0			0
$213$	185.617			0.871440
$214$		0			0
$215$	−47.7723	+	27.5813i	−0.222197	+	0.128285i
$216$		0			0
$217$	−121.309	−	210.114i	−0.559030	−	0.968268i
$218$		0			0
$219$	99.9295	+	57.6943i	0.456299	+	0.263444i
$220$		0			0
$221$	371.215	−	190.760i	1.67971	−	0.863169i
$222$		0			0
$223$	−205.586	−	118.695i	−0.921912	−	0.532266i	−0.0376675	−	0.999290i	$-0.511993\pi$
$223$	−205.586	−	118.695i	−0.921912	−	0.532266i	−0.884245	+	0.467024i	$0.845326\pi$
$224$		0			0
$225$	53.9582	+	93.4584i	0.239814	+	0.415371i
$226$		0			0
$227$	−103.665	+	59.8513i	−0.456676	+	0.263662i	−0.710646	−	0.703550i	$-0.751597\pi$
$227$	−103.665	+	59.8513i	−0.456676	+	0.263662i	0.253970	+	0.967212i	$0.418264\pi$
$228$		0			0
$229$	192.387			0.840118			0.420059	−	0.907497i	$-0.362009\pi$
$229$	192.387			0.840118			0.420059	+	0.907497i	$0.362009\pi$
$230$		0			0
$231$	−111.791	−	64.5424i	−0.483943	−	0.279404i
$232$		0			0
$233$	299.621			1.28593			0.642963	−	0.765897i	$-0.277705\pi$
$233$	299.621			1.28593			0.642963	+	0.765897i	$0.277705\pi$
$234$		0			0
$235$		−	442.063i		−	1.88112i
$236$		0			0
$237$	−145.862	+	252.640i	−0.615451	+	1.06599i
$238$		0			0
$239$			318.987i			1.33468i	0.744755	+	0.667338i	$0.232566\pi$
$239$			318.987i			1.33468i	−0.744755	+	0.667338i	$0.767434\pi$
$240$		0			0
$241$	96.6529	+	167.408i	0.401049	+	0.694638i	0.993853	−	0.110709i	$-0.0353122\pi$
$241$	96.6529	+	167.408i	0.401049	+	0.694638i	−0.592803	+	0.805347i	$0.701979\pi$
$242$		0			0
$243$	−265.179	+	153.101i	−1.09127	+	0.630046i
$244$		0			0
$245$	−35.7467	+	61.9150i	−0.145905	+	0.252714i
$246$		0			0
$247$	−29.0773	−	56.5838i	−0.117722	−	0.229084i
$248$		0			0
$249$	−12.8581	+	22.2709i	−0.0516390	+	0.0894414i
$250$		0			0
$251$	−373.908	+	215.876i	−1.48967	+	0.860063i	−0.999930	−	0.0118049i	$-0.996242\pi$
$251$	−373.908	+	215.876i	−1.48967	+	0.860063i	−0.489742	+	0.871868i	$0.662909\pi$
$252$		0			0
$253$	−27.3406	−	47.3553i	−0.108066	−	0.187175i
$254$		0			0
$255$			816.192i			3.20075i
$256$		0			0
$257$	176.804	−	306.234i	0.687954	−	1.19157i	−0.284544	−	0.958663i	$-0.591842\pi$
$257$	176.804	−	306.234i	0.687954	−	1.19157i	0.972499	−	0.232909i	$-0.0748244\pi$
$258$		0			0
$259$		−	207.241i		−	0.800158i
$260$		0			0
$261$	−258.876			−0.991861
$262$		0			0
$263$	−83.9181	−	48.4501i	−0.319080	−	0.184221i	0.331902	−	0.943314i	$-0.392310\pi$
$263$	−83.9181	−	48.4501i	−0.319080	−	0.184221i	−0.650983	+	0.759093i	$0.725643\pi$
$264$		0			0
$265$	−125.791			−0.474683
$266$		0			0
$267$	286.270	−	165.278i	1.07217	−	0.619019i
$268$		0			0
$269$	190.353	+	329.702i	0.707633	+	1.22566i	0.965733	+	0.259539i	$0.0835705\pi$
$269$	190.353	+	329.702i	0.707633	+	1.22566i	−0.258099	+	0.966118i	$0.583096\pi$
$270$		0			0
$271$	−73.3675	−	42.3587i	−0.270729	−	0.156305i	0.358490	−	0.933534i	$-0.383292\pi$
$271$	−73.3675	−	42.3587i	−0.270729	−	0.156305i	−0.629219	+	0.777228i	$0.716625\pi$
$272$		0			0
$273$	−15.5910	+	318.526i	−0.0571098	+	1.16676i
$274$		0			0
$275$	−70.9587	−	40.9680i	−0.258032	−	0.148975i
$276$		0			0
$277$	101.853	+	176.415i	0.367702	+	0.636878i	0.989206	−	0.146533i	$-0.0468114\pi$
$277$	101.853	+	176.415i	0.367702	+	0.636878i	−0.621504	+	0.783411i	$0.713478\pi$
$278$		0			0
$279$	−236.927	+	136.790i	−0.849201	+	0.490286i
$280$		0			0
$281$	296.079			1.05366			0.526831	−	0.849970i	$-0.323380\pi$
$281$	296.079			1.05366			0.526831	+	0.849970i	$0.323380\pi$
$282$		0			0
$283$	−98.8953	−	57.0972i	−0.349453	−	0.201757i	0.314991	−	0.949095i	$-0.397998\pi$
$283$	−98.8953	−	57.0972i	−0.349453	−	0.201757i	−0.664445	+	0.747338i	$0.731332\pi$
$284$		0			0
$285$	124.411			0.436530
$286$		0			0
$287$		−	196.121i		−	0.683350i
$288$		0			0
$289$	−370.855	+	642.340i	−1.28324	+	2.22263i
$290$		0			0
$291$		−	227.218i		−	0.780817i
$292$		0			0
$293$	−245.335	−	424.933i	−0.837322	−	1.45028i	−0.892126	−	0.451787i	$-0.850787\pi$
$293$	−245.335	−	424.933i	−0.837322	−	1.45028i	0.0548042	−	0.998497i	$-0.482547\pi$
$294$		0			0
$295$	−510.792	+	294.906i	−1.73150	+	0.999681i
$296$		0			0
$297$	21.7319	−	37.6408i	0.0731715	−	0.126737i
$298$		0			0
$299$	−73.1846	+	113.551i	−0.244765	+	0.379768i
$300$		0			0
$301$	26.6142	−	46.0971i	0.0884192	−	0.153147i
$302$		0			0
$303$	−564.924	+	326.159i	−1.86444	+	1.07643i
$304$		0			0
$305$	186.129	+	322.384i	0.610258	+	1.05700i
$306$		0			0
$307$		−	369.169i		−	1.20251i	−0.799059	−	0.601253i	$-0.794669\pi$
$307$		−	369.169i		−	1.20251i	0.799059	−	0.601253i	$-0.205331\pi$
$308$		0			0
$309$	−16.4616	+	28.5124i	−0.0532739	+	0.0922731i
$310$		0			0
$311$		−	63.7658i		−	0.205035i	−0.994731	−	0.102517i	$-0.967310\pi$
$311$		−	63.7658i		−	0.205035i	0.994731	−	0.102517i	$-0.0326897\pi$
$312$		0			0
$313$	360.648			1.15223			0.576115	−	0.817368i	$-0.304568\pi$
$313$	360.648			1.15223			0.576115	+	0.817368i	$0.304568\pi$
$314$		0			0
$315$	−234.970	−	135.660i	−0.745936	−	0.430667i
$316$		0			0
$317$	−48.1951			−0.152035			−0.0760176	−	0.997106i	$-0.524221\pi$
$317$	−48.1951			−0.152035			−0.0760176	+	0.997106i	$0.524221\pi$
$318$		0			0
$319$	170.220	−	98.2763i	0.533603	−	0.308076i
$320$		0			0
$321$	18.5273	+	32.0902i	0.0577174	+	0.0999695i
$322$		0			0
$323$	136.061	+	78.5548i	0.421241	+	0.243204i
$324$		0			0
$325$	−9.89631	+	202.183i	−0.0304502	+	0.622103i
$326$		0			0
$327$	100.635	+	58.1019i	0.307754	+	0.177682i
$328$		0			0
$329$	213.281	+	369.413i	0.648270	+	1.12284i
$330$		0			0
$331$	506.834	−	292.621i	1.53122	−	0.884051i	0.531915	−	0.846798i	$-0.321472\pi$
$331$	506.834	−	292.621i	1.53122	−	0.884051i	0.999306	−	0.0372535i	$-0.0118609\pi$
$332$		0			0
$333$	−233.687			−0.701763
$334$		0			0
$335$	722.355	+	417.052i	2.15628	+	1.24493i
$336$		0			0
$337$	−42.7329			−0.126804			−0.0634019	−	0.997988i	$-0.520195\pi$
$337$	−42.7329			−0.126804			−0.0634019	+	0.997988i	$0.520195\pi$
$338$		0			0
$339$			439.648i			1.29690i
$340$		0			0
$341$	103.858	−	179.888i	0.304570	−	0.527530i
$342$		0			0
$343$		−	370.150i		−	1.07915i
$344$		0			0
$345$	−132.093	−	228.791i	−0.382877	−	0.663163i
$346$		0			0
$347$	235.840	−	136.163i	0.679656	−	0.392399i	−0.120070	−	0.992765i	$-0.538312\pi$
$347$	235.840	−	136.163i	0.679656	−	0.392399i	0.799725	+	0.600366i	$0.204978\pi$
$348$		0			0
$349$	−85.4989	+	148.088i	−0.244983	+	0.424322i	−0.962127	−	0.272603i	$-0.912116\pi$
$349$	−85.4989	+	148.088i	−0.244983	+	0.424322i	0.717144	+	0.696925i	$0.245449\pi$
$350$		0			0
$351$	−107.250	−	5.24961i	−0.305557	−	0.0149561i
$352$		0			0
$353$	−108.204	+	187.414i	−0.306526	+	0.530919i	−0.977600	−	0.210472i	$-0.932500\pi$
$353$	−108.204	+	187.414i	−0.306526	+	0.530919i	0.671074	+	0.741391i	$0.265833\pi$
$354$		0			0
$355$	−256.532	+	148.109i	−0.722625	+	0.417208i
$356$		0			0
$357$	−393.786	−	682.057i	−1.10304	−	1.91052i
$358$		0			0
$359$			301.873i			0.840871i	0.907322	+	0.420435i	$0.138123\pi$
$359$			301.873i			0.840871i	−0.907322	+	0.420435i	$0.861877\pi$
$360$		0			0
$361$	−168.526	+	291.896i	−0.466831	+	0.808575i
$362$		0			0
$363$			372.433i			1.02599i
$364$		0			0
$365$	−184.144			−0.504503
$366$		0			0
$367$	201.170	+	116.146i	0.548148	+	0.316474i	0.748375	−	0.663276i	$-0.230834\pi$
$367$	201.170	+	116.146i	0.548148	+	0.316474i	−0.200226	+	0.979750i	$0.564168\pi$
$368$		0			0
$369$	−221.149			−0.599319
$370$		0			0
$371$	105.118	−	60.6901i	0.283338	−	0.163585i
$372$		0			0
$373$	135.082	+	233.969i	0.362150	+	0.627262i	0.988314	−	0.152429i	$-0.0487096\pi$
$373$	135.082	+	233.969i	0.362150	+	0.627262i	−0.626165	+	0.779691i	$0.715376\pi$
$374$		0			0
$375$	207.593	+	119.854i	0.553580	+	0.319610i
$376$		0			0
$377$	−408.159	−	263.063i	−1.08265	−	0.697781i
$378$		0			0
$379$	461.926	+	266.693i	1.21880	+	0.703675i	0.964662	−	0.263492i	$-0.0848742\pi$
$379$	461.926	+	266.693i	1.21880	+	0.703675i	0.254140	+	0.967167i	$0.418208\pi$
$380$		0			0
$381$	501.254	+	868.197i	1.31563	+	2.27873i
$382$		0			0
$383$	135.650	−	78.3177i	0.354178	−	0.204485i	−0.312346	−	0.949968i	$-0.601115\pi$
$383$	135.650	−	78.3177i	0.354178	−	0.204485i	0.666524	+	0.745484i	$0.267781\pi$
$384$		0			0
$385$	206.001			0.535067
$386$		0			0
$387$	−51.9797	−	30.0105i	−0.134314	−	0.0775464i
$388$		0			0
$389$	−143.862			−0.369826			−0.184913	−	0.982755i	$-0.559200\pi$
$389$	−143.862			−0.369826			−0.184913	+	0.982755i	$0.559200\pi$
$390$		0			0
$391$		−	333.621i		−	0.853250i
$392$		0			0
$393$	−93.7275	+	162.341i	−0.238492	+	0.413081i
$394$		0			0
$395$		−	465.549i		−	1.17861i
$396$		0			0
$397$	−189.348	−	327.961i	−0.476948	−	0.826098i	0.522703	−	0.852515i	$-0.324924\pi$
$397$	−189.348	−	327.961i	−0.476948	−	0.826098i	−0.999651	+	0.0264167i	$0.991590\pi$
$398$		0			0
$399$	−103.965	+	60.0242i	−0.260564	+	0.150437i
$400$		0			0
$401$	329.115	−	570.045i	0.820737	−	1.42156i	−0.0843975	−	0.996432i	$-0.526897\pi$
$401$	329.115	−	570.045i	0.820737	−	1.42156i	0.905134	−	0.425126i	$-0.139770\pi$
$402$		0			0
$403$	−512.556	−	25.0882i	−1.27185	−	0.0622536i
$404$		0			0
$405$	303.645	−	525.928i	0.749740	−	1.29859i
$406$		0			0
$407$	153.657	−	88.7140i	0.377536	−	0.217971i
$408$		0			0
$409$	−80.8009	−	139.951i	−0.197557	−	0.342179i	0.750179	−	0.661235i	$-0.229967\pi$
$409$	−80.8009	−	139.951i	−0.197557	−	0.342179i	−0.947736	+	0.319056i	$0.896634\pi$
$410$		0			0
$411$			988.739i			2.40569i
$412$		0			0
$413$	284.565	−	492.881i	0.689019	−	1.19342i
$414$		0			0
$415$		−	41.0394i		−	0.0988901i
$416$		0			0
$417$	−224.844			−0.539194
$418$		0			0
$419$	−688.383	−	397.438i	−1.64292	−	0.948540i	−0.979788	−	0.200037i	$-0.935894\pi$
$419$	−688.383	−	397.438i	−1.64292	−	0.948540i	−0.663131	−	0.748503i	$-0.730773\pi$
$420$		0			0
$421$	71.6524			0.170196			0.0850979	−	0.996373i	$-0.472880\pi$
$421$	71.6524			0.170196			0.0850979	+	0.996373i	$0.472880\pi$
$422$		0			0
$423$	416.555	−	240.498i	0.984764	−	0.568553i
$424$		0			0
$425$	−249.954	−	432.933i	−0.588127	−	1.01867i
$426$		0			0
$427$	−311.080	−	179.602i	−0.728524	−	0.420613i
$428$		0			0
$429$	−242.843	+	124.792i	−0.566068	+	0.290891i
$430$		0			0
$431$	−234.206	−	135.219i	−0.543402	−	0.313733i	0.203055	−	0.979167i	$-0.434913\pi$
$431$	−234.206	−	135.219i	−0.543402	−	0.313733i	−0.746457	+	0.665434i	$0.768246\pi$
$432$		0			0
$433$	150.640	+	260.917i	0.347899	+	0.602579i	0.985876	−	0.167476i	$-0.0535618\pi$
$433$	150.640	+	260.917i	0.347899	+	0.602579i	−0.637977	+	0.770056i	$0.720228\pi$
$434$		0			0
$435$	822.394	−	474.809i	1.89056	−	1.09152i
$436$		0			0
$437$	−50.8533			−0.116369
$438$		0			0
$439$	−100.433	−	57.9852i	−0.228777	−	0.132085i	0.381231	−	0.924480i	$-0.375500\pi$
$439$	−100.433	−	57.9852i	−0.228777	−	0.132085i	−0.610008	+	0.792395i	$0.708834\pi$
$440$		0			0
$441$	−77.7898			−0.176394
$442$		0			0
$443$			574.602i			1.29707i	0.761185	+	0.648535i	$0.224618\pi$
$443$			574.602i			1.29707i	−0.761185	+	0.648535i	$0.775382\pi$
$444$		0			0
$445$	−263.760	+	456.846i	−0.592720	+	1.02662i
$446$		0			0
$447$		−	180.577i		−	0.403975i
$448$		0			0
$449$	144.175	+	249.719i	0.321104	+	0.556168i	0.980716	−	0.195438i	$-0.0626129\pi$
$449$	144.175	+	249.719i	0.321104	+	0.556168i	−0.659612	+	0.751606i	$0.729280\pi$
$450$		0			0
$451$	145.413	−	83.9541i	0.322423	−	0.186151i
$452$		0			0
$453$	425.660	−	737.265i	0.939647	−	1.62752i
$454$		0			0
$455$	−232.614	−	452.661i	−0.511239	−	0.994858i
$456$		0			0
$457$	−89.6069	+	155.204i	−0.196076	+	0.339614i	−0.947253	−	0.320487i	$-0.896153\pi$
$457$	−89.6069	+	155.204i	−0.196076	+	0.339614i	0.751176	+	0.660101i	$0.229487\pi$
$458$		0			0
$459$	229.654	−	132.591i	0.500335	−	0.288869i
$460$		0			0
$461$	253.467	+	439.018i	0.549820	+	0.952316i	0.998286	+	0.0585166i	$0.0186370\pi$
$461$	253.467	+	439.018i	0.549820	+	0.952316i	−0.448466	+	0.893800i	$0.648030\pi$
$462$		0			0
$463$		−	464.130i		−	1.00244i	−0.865320	−	0.501220i	$-0.832885\pi$
$463$		−	464.130i		−	1.00244i	0.865320	−	0.501220i	$-0.167115\pi$
$464$		0			0
$465$	501.778	−	869.105i	1.07909	−	1.86904i
$466$		0			0
$467$			246.434i			0.527697i	0.964564	+	0.263848i	$0.0849918\pi$
$467$			246.434i			0.527697i	−0.964564	+	0.263848i	$0.915008\pi$
$468$		0			0
$469$	−804.856			−1.71611
$470$		0			0
$471$	−404.964	−	233.806i	−0.859796	−	0.496404i
$472$		0			0
$473$	45.5712			0.0963449
$474$		0			0
$475$	−65.9913	+	38.1001i	−0.138929	+	0.0802108i
$476$		0			0
$477$	−68.4348	−	118.533i	−0.143469	−	0.248496i
$478$		0			0
$479$	−112.600	−	65.0096i	−0.235073	−	0.135719i	0.377837	−	0.925872i	$-0.376668\pi$
$479$	−112.600	−	65.0096i	−0.235073	−	0.135719i	−0.612910	+	0.790153i	$0.710001\pi$
$480$		0			0
$481$	−368.446	−	237.467i	−0.765999	−	0.493695i
$482$		0			0
$483$	220.768	+	127.461i	0.457078	+	0.263894i
$484$		0			0
$485$	181.303	+	314.027i	0.373822	+	0.647478i
$486$		0			0
$487$	362.273	−	209.158i	0.743887	−	0.429483i	−0.0795939	−	0.996827i	$-0.525362\pi$
$487$	362.273	−	209.158i	0.743887	−	0.429483i	0.823481	+	0.567344i	$0.192029\pi$
$488$		0			0
$489$	208.376			0.426128
$490$		0			0
$491$	64.3021	+	37.1249i	0.130962	+	0.0756107i	0.564049	−	0.825741i	$-0.309243\pi$
$491$	64.3021	+	37.1249i	0.130962	+	0.0756107i	−0.433088	+	0.901352i	$0.642576\pi$
$492$		0			0
$493$	1199.21			2.43246
$494$		0			0
$495$		−	232.289i		−	0.469271i
$496$		0			0
$497$	142.915	−	247.537i	0.287556	−	0.498061i
$498$		0			0
$499$			520.278i			1.04264i	0.853361	+	0.521320i	$0.174560\pi$
$499$			520.278i			1.04264i	−0.853361	+	0.521320i	$0.825440\pi$
$500$		0			0
$501$	−251.871	−	436.253i	−0.502737	−	0.870765i
$502$		0			0
$503$	−152.046	+	87.7838i	−0.302278	+	0.174521i	−0.643466	−	0.765475i	$-0.722504\pi$
$503$	−152.046	+	87.7838i	−0.302278	+	0.174521i	0.341188	+	0.939995i	$0.389171\pi$
$504$		0			0
$505$	520.503	−	901.538i	1.03070	−	1.78522i
$506$		0			0
$507$	548.431	+	392.703i	1.08172	+	0.774561i
$508$		0			0
$509$	−117.308	+	203.183i	−0.230467	+	0.399180i	−0.957946	−	0.286950i	$-0.907359\pi$
$509$	−117.308	+	203.183i	−0.230467	+	0.399180i	0.727479	+	0.686130i	$0.240692\pi$
$510$		0			0
$511$	153.881	−	88.8433i	0.301137	−	0.173862i
$512$		0			0
$513$	−20.2106	−	35.0058i	−0.0393969	−	0.0682375i
$514$		0			0
$515$		−	52.5408i		−	0.102021i
$516$		0			0
$517$	−182.599	+	316.271i	−0.353190	+	0.611743i
$518$		0			0
$519$			178.620i			0.344161i
$520$		0			0
$521$	−319.194			−0.612656			−0.306328	−	0.951926i	$-0.599100\pi$
$521$	−319.194			−0.612656			−0.306328	+	0.951926i	$0.599100\pi$
$522$		0			0
$523$	−774.518	−	447.168i	−1.48091	−	0.855006i	−0.481147	−	0.876640i	$-0.659780\pi$
$523$	−774.518	−	447.168i	−1.48091	−	0.855006i	−0.999766	+	0.0216341i	$0.993113\pi$
$524$		0			0
$525$	381.982			0.727585
$526$		0			0
$527$	1097.53	−	633.660i	2.08260	−	1.20239i
$528$		0			0
$529$	−210.507	−	364.608i	−0.397933	−	0.689241i
$530$		0			0
$531$	−555.778	−	320.879i	−1.04666	−	0.604291i
$532$		0			0
$533$	−348.677	−	224.726i	−0.654177	−	0.421625i
$534$		0			0
$535$	−51.2114	−	29.5669i	−0.0957222	−	0.0552652i
$536$		0			0
$537$	−582.129	−	1008.28i	−1.08404	−	1.87761i
$538$		0			0
$539$	51.1494	−	29.5311i	0.0948969	−	0.0547887i
$540$		0			0
$541$	663.170			1.22582			0.612911	−	0.790152i	$-0.289998\pi$
$541$	663.170			1.22582			0.612911	+	0.790152i	$0.289998\pi$
$542$		0			0
$543$	818.089	+	472.324i	1.50661	+	0.869841i
$544$		0			0
$545$	−185.445			−0.340265
$546$		0			0
$547$			279.261i			0.510531i	0.966871	+	0.255266i	$0.0821629\pi$
$547$			279.261i			0.510531i	−0.966871	+	0.255266i	$0.917837\pi$
$548$		0			0
$549$	−202.521	+	350.777i	−0.368891	+	0.638938i
$550$		0			0
$551$		−	182.793i		−	0.331748i
$552$		0			0
$553$	224.612	+	389.040i	0.406170	+	0.703508i
$554$		0			0
$555$	742.375	−	428.610i	1.33761	−	0.772271i
$556$		0			0
$557$	−360.197	+	623.880i	−0.646674	+	1.12007i	0.337238	+	0.941419i	$0.390507\pi$
$557$	−360.197	+	623.880i	−0.646674	+	1.12007i	−0.983912	+	0.178653i	$0.942826\pi$
$558$		0			0
$559$	−51.4584	−	100.137i	−0.0920544	−	0.179136i
$560$		0			0
$561$	337.137	−	583.939i	0.600958	−	1.04089i
$562$		0			0
$563$	−335.019	+	193.423i	−0.595060	+	0.343558i	−0.767096	−	0.641533i	$-0.778299\pi$
$563$	−335.019	+	193.423i	−0.595060	+	0.343558i	0.172036	+	0.985091i	$0.444966\pi$
$564$		0			0
$565$	−350.807	−	607.616i	−0.620898	−	1.07543i
$566$		0			0
$567$			585.994i			1.03350i
$568$		0			0
$569$	−319.829	+	553.961i	−0.562090	+	0.973569i	0.435224	+	0.900322i	$0.356669\pi$
$569$	−319.829	+	553.961i	−0.562090	+	0.973569i	−0.997314	+	0.0732464i	$0.976664\pi$
$570$		0			0
$571$		−	70.3895i		−	0.123274i	−0.998099	−	0.0616370i	$-0.980368\pi$
$571$		−	70.3895i		−	0.123274i	0.998099	−	0.0616370i	$-0.0196321\pi$
$572$		0			0
$573$	−1442.98			−2.51828
$574$		0			0
$575$	140.132	+	80.9052i	0.243708	+	0.140705i
$576$		0			0
$577$	−99.4850			−0.172418			−0.0862089	−	0.996277i	$-0.527475\pi$
$577$	−99.4850			−0.172418			−0.0862089	+	0.996277i	$0.527475\pi$
$578$		0			0
$579$	647.498	−	373.833i	1.11830	−	0.645653i
$580$		0			0
$581$	19.8002	+	34.2949i	0.0340795	+	0.0590274i
$582$		0			0
$583$	89.9964	+	51.9594i	0.154368	+	0.0891243i
$584$		0			0
$585$	−510.425	+	262.298i	−0.872522	+	0.448372i
$586$		0			0
$587$	−130.564	−	75.3811i	−0.222426	−	0.128418i	0.384647	−	0.923064i	$-0.374323\pi$
$587$	−130.564	−	75.3811i	−0.222426	−	0.128418i	−0.607073	+	0.794646i	$0.707656\pi$
$588$		0			0
$589$	−96.5879	−	167.295i	−0.163986	−	0.284032i
$590$		0			0
$591$	−577.604	+	333.480i	−0.977333	+	0.564264i
$592$		0			0
$593$	14.1594			0.0238775			0.0119388	−	0.999929i	$-0.496200\pi$
$593$	14.1594			0.0238775			0.0119388	+	0.999929i	$0.496200\pi$
$594$		0			0
$595$	1088.46	+	628.425i	1.82935	+	1.05618i
$596$		0			0
$597$	518.760			0.868945
$598$		0			0
$599$			49.5504i			0.0827219i	0.999144	+	0.0413610i	$0.0131694\pi$
$599$			49.5504i			0.0827219i	−0.999144	+	0.0413610i	$0.986831\pi$
$600$		0			0
$601$	71.9058	−	124.545i	0.119644	−	0.207229i	−0.799983	−	0.600023i	$-0.795158\pi$
$601$	71.9058	−	124.545i	0.119644	−	0.207229i	0.919626	+	0.392794i	$0.128491\pi$
$602$		0			0
$603$			907.564i			1.50508i
$604$		0			0
$605$	−297.175	−	514.722i	−0.491198	−	0.850780i
$606$		0			0
$607$	−493.343	+	284.832i	−0.812756	+	0.469245i	−0.847912	−	0.530137i	$-0.822141\pi$
$607$	−493.343	+	284.832i	−0.812756	+	0.469245i	0.0351558	+	0.999382i	$0.488807\pi$
$608$		0			0
$609$	−458.160	+	793.556i	−0.752315	+	1.30305i
$610$		0			0
$611$	901.154	+	44.1090i	1.47488	+	0.0721915i
$612$		0			0
$613$	−15.0863	+	26.1302i	−0.0246106	+	0.0426267i	−0.878068	−	0.478535i	$-0.841168\pi$
$613$	−15.0863	+	26.1302i	−0.0246106	+	0.0426267i	0.853458	+	0.521162i	$0.174501\pi$
$614$		0			0
$615$	702.543	−	405.613i	1.14235	−	0.659534i
$616$		0			0
$617$	155.101	+	268.644i	0.251380	+	0.435403i	0.963906	−	0.266243i	$-0.0857823\pi$
$617$	155.101	+	268.644i	0.251380	+	0.435403i	−0.712526	+	0.701646i	$0.752449\pi$
$618$		0			0
$619$			514.549i			0.831259i	0.909534	+	0.415629i	$0.136439\pi$
$619$			514.549i			0.831259i	−0.909534	+	0.415629i	$0.863561\pi$
$620$		0			0
$621$	−42.9170	+	74.3345i	−0.0691096	+	0.119701i
$622$		0			0
$623$		−	509.023i		−	0.817051i
$624$		0			0
$625$	−771.818			−1.23491
$626$		0			0
$627$	−89.0090	−	51.3894i	−0.141960	−	0.0819607i
$628$		0			0
$629$	1082.52			1.72102
$630$		0			0
$631$	366.774	−	211.757i	0.581259	−	0.335590i	−0.180375	−	0.983598i	$-0.557731\pi$
$631$	366.774	−	211.757i	0.581259	−	0.335590i	0.761633	+	0.648008i	$0.224398\pi$
$632$		0			0
$633$	679.629	+	1177.15i	1.07366	+	1.85964i
$634$		0			0
$635$	−1385.52	−	799.929i	−2.18192	−	1.25973i
$636$		0			0
$637$	−122.648	−	79.0481i	−0.192540	−	0.124094i
$638$		0			0
$639$	−279.125	−	161.153i	−0.436815	−	0.252196i
$640$		0			0
$641$	593.215	+	1027.48i	0.925453	+	1.60293i	0.790832	+	0.612034i	$0.209648\pi$
$641$	593.215	+	1027.48i	0.925453	+	1.60293i	0.134621	+	0.990897i	$0.457018\pi$
$642$		0			0
$643$	−96.1108	+	55.4896i	−0.149472	+	0.0862980i	−0.572871	−	0.819646i	$-0.694170\pi$
$643$	−96.1108	+	55.4896i	−0.149472	+	0.0862980i	0.423398	+	0.905944i	$0.360837\pi$
$644$		0			0
$645$	220.171			0.341351
$646$		0			0
$647$	659.017	+	380.484i	1.01857	+	0.588074i	0.913690	−	0.406411i	$-0.133220\pi$
$647$	659.017	+	380.484i	1.01857	+	0.588074i	0.104883	+	0.994485i	$0.466553\pi$
$648$		0			0
$649$	487.257			0.750781
$650$		0			0
$651$			968.366i			1.48751i
$652$		0			0
$653$	165.207	−	286.147i	0.252997	−	0.438203i	−0.711353	−	0.702835i	$-0.751917\pi$
$653$	165.207	−	286.147i	0.252997	−	0.438203i	0.964349	+	0.264632i	$0.0852505\pi$
$654$		0			0
$655$		−	299.151i		−	0.456719i
$656$		0			0
$657$	−100.181	−	173.518i	−0.152482	−	0.264107i
$658$		0			0
$659$	−1022.23	+	590.184i	−1.55118	+	0.895575i	−0.553135	+	0.833092i	$0.686569\pi$
$659$	−1022.23	+	590.184i	−1.55118	+	0.895575i	−0.998046	+	0.0624831i	$0.980098\pi$
$660$		0			0
$661$	−430.720	+	746.029i	−0.651619	+	1.12864i	0.331111	+	0.943592i	$0.392577\pi$
$661$	−430.720	+	746.029i	−0.651619	+	1.12864i	−0.982730	+	0.185046i	$0.940757\pi$
$662$		0			0
$663$	−1663.82	−	81.4395i	−2.50954	−	0.122835i
$664$		0			0
$665$	95.7900	−	165.913i	0.144045	−	0.249493i
$666$		0			0
$667$	−336.156	+	194.080i	−0.503982	+	0.290974i
$668$		0			0
$669$	473.749	+	820.558i	0.708146	+	1.22654i
$670$		0			0
$671$		−	307.530i		−	0.458316i
$672$		0			0
$673$	−340.739	+	590.176i	−0.506298	+	0.876934i	0.493675	+	0.869646i	$0.335653\pi$
$673$	−340.739	+	590.176i	−0.506298	+	0.876934i	−0.999973	+	0.00728760i	$0.997680\pi$
$674$		0			0
$675$			128.616i			0.190543i
$676$		0			0
$677$	308.569			0.455789			0.227894	−	0.973686i	$-0.426816\pi$
$677$	308.569			0.455789			0.227894	+	0.973686i	$0.426816\pi$
$678$		0			0
$679$	−303.015	−	174.946i	−0.446267	−	0.257652i
$680$		0			0
$681$	477.769			0.701570
$682$		0			0
$683$	−172.109	+	99.3669i	−0.251989	+	0.145486i	−0.620675	−	0.784068i	$-0.713141\pi$
$683$	−172.109	+	99.3669i	−0.251989	+	0.145486i	0.368686	+	0.929554i	$0.379808\pi$
$684$		0			0
$685$	−788.943	−	1366.49i	−1.15174	−	1.99487i
$686$		0			0
$687$	−664.999	−	383.938i	−0.967976	−	0.558861i
$688$		0			0
$689$	12.5514	−	256.428i	0.0182169	−	0.372174i
$690$		0			0
$691$	86.2576	+	49.8009i	0.124830	+	0.0720707i	0.561115	−	0.827738i	$-0.310373\pi$
$691$	86.2576	+	49.8009i	0.124830	+	0.0720707i	−0.436285	+	0.899809i	$0.643706\pi$
$692$		0			0
$693$	112.072	+	194.114i	0.161720	+	0.280107i
$694$		0			0
$695$	310.746	−	179.409i	0.447117	−	0.258143i
$696$		0			0
$697$	1024.44			1.46978
$698$		0			0
$699$	−1035.66	−	597.939i	−1.48163	−	0.855421i
$700$		0			0
$701$	−90.4437			−0.129021			−0.0645105	−	0.997917i	$-0.520549\pi$
$701$	−90.4437			−0.129021			−0.0645105	+	0.997917i	$0.520549\pi$
$702$		0			0
$703$		−	165.007i		−	0.234719i
$704$		0			0
$705$	−882.205	+	1528.02i	−1.25135	+	2.16741i
$706$		0			0
$707$			1004.50i			1.42080i
$708$		0			0
$709$	680.857	+	1179.28i	0.960306	+	1.66330i	0.721729	+	0.692175i	$0.243348\pi$
$709$	680.857	+	1179.28i	0.960306	+	1.66330i	0.238577	+	0.971124i	$0.423319\pi$
$710$		0			0
$711$	438.686	−	253.275i	0.616998	−	0.356224i
$712$		0			0
$713$	−205.103	+	355.249i	−0.287662	+	0.498246i
$714$		0			0
$715$	236.046	−	366.241i	0.330135	−	0.512225i
$716$		0			0
$717$	636.588	−	1102.60i	0.887850	−	1.53780i
$718$		0			0
$719$	−41.7335	+	24.0949i	−0.0580438	+	0.0335116i	−0.528741	−	0.848783i	$-0.677336\pi$
$719$	−41.7335	+	24.0949i	−0.0580438	+	0.0335116i	0.470697	+	0.882295i	$0.344002\pi$
$720$		0			0
$721$	25.3492	+	43.9062i	0.0351584	+	0.0608962i
$722$		0			0
$723$		−	771.543i		−	1.06714i
$724$		0			0
$725$	−290.815	+	503.706i	−0.401124	+	0.694767i
$726$		0			0
$727$			1279.06i			1.75937i	0.475554	+	0.879687i	$0.342248\pi$
$727$			1279.06i			1.75937i	−0.475554	+	0.879687i	$0.657752\pi$
$728$		0			0
$729$	364.064			0.499402
$730$		0			0
$731$	240.788	+	139.019i	0.329396	+	0.190177i
$732$		0			0
$733$	−1170.50			−1.59687			−0.798434	−	0.602082i	$-0.794338\pi$
$733$	−1170.50			−1.59687			−0.798434	+	0.602082i	$0.794338\pi$
$734$		0			0
$735$	247.122	−	142.676i	0.336220	−	0.194117i
$736$		0			0
$737$	−344.536	−	596.754i	−0.467485	−	0.809707i
$738$		0			0
$739$	−1136.93	−	656.406i	−1.53847	−	0.888236i	−0.998929	−	0.0462762i	$-0.985265\pi$
$739$	−1136.93	−	656.406i	−1.53847	−	0.888236i	−0.539541	−	0.841959i	$-0.681402\pi$
$740$		0			0
$741$	−12.4137	+	253.614i	−0.0167526	+	0.342259i
$742$		0			0
$743$	292.325	+	168.774i	0.393439	+	0.227152i	0.683649	−	0.729811i	$-0.260392\pi$
$743$	292.325	+	168.774i	0.393439	+	0.227152i	−0.290210	+	0.956963i	$0.593725\pi$
$744$		0			0
$745$	144.087	+	249.567i	0.193406	+	0.334989i
$746$		0			0
$747$	38.6713	−	22.3269i	0.0517688	−	0.0298888i
$748$		0			0
$749$	57.0602			0.0761819
$750$		0			0
$751$	−986.025	−	569.282i	−1.31295	−	0.758032i	−0.330366	−	0.943853i	$-0.607172\pi$
$751$	−986.025	−	569.282i	−1.31295	−	0.758032i	−0.982584	+	0.185821i	$0.940505\pi$
$752$		0			0
$753$	1723.25			2.28852
$754$		0			0
$755$			1358.58i			1.79945i
$756$		0			0
$757$	272.960	−	472.781i	0.360581	−	0.624545i	−0.627475	−	0.778636i	$-0.715912\pi$
$757$	272.960	−	472.781i	0.360581	−	0.624545i	0.988057	+	0.154091i	$0.0492450\pi$
$758$		0			0
$759$			218.249i			0.287549i
$760$		0			0
$761$	−580.449	−	1005.37i	−0.762745	−	1.32111i	−0.941431	−	0.337207i	$-0.890518\pi$
$761$	−580.449	−	1005.37i	−0.762745	−	1.32111i	0.178686	−	0.983906i	$-0.442816\pi$
$762$		0			0
$763$	154.968	−	89.4709i	0.203104	−	0.117262i
$764$		0			0
$765$	708.620	−	1227.37i	0.926300	−	1.60440i
$766$		0			0
$767$	−550.205	−	1070.69i	−0.717346	−	1.39594i
$768$		0			0
$769$	332.076	−	575.173i	0.431828	−	0.747949i	−0.565202	−	0.824952i	$-0.691202\pi$
$769$	332.076	−	575.173i	0.431828	−	0.747949i	0.997031	+	0.0770035i	$0.0245353\pi$
$770$		0			0
$771$	−1222.27	+	705.680i	−1.58531	+	0.915279i
$772$		0			0
$773$	−115.578	−	200.187i	−0.149519	−	0.258974i	0.781531	−	0.623866i	$-0.214439\pi$
$773$	−115.578	−	200.187i	−0.149519	−	0.258974i	−0.931050	+	0.364893i	$0.881106\pi$
$774$		0			0
$775$			614.666i			0.793118i
$776$		0			0
$777$	−413.581	+	716.343i	−0.532279	+	0.921935i
$778$		0			0
$779$		−	156.154i		−	0.200454i
$780$		0			0
$781$	244.712			0.313332
$782$		0			0
$783$	−267.197	−	154.266i	−0.341247	−	0.197019i
$784$		0			0
$785$	746.242			0.950627
$786$		0			0
$787$	684.091	−	394.960i	0.869238	−	0.501855i	0.00214338	−	0.999998i	$-0.499318\pi$
$787$	684.091	−	394.960i	0.869238	−	0.501855i	0.867095	+	0.498143i	$0.165984\pi$
$788$		0			0
$789$	193.379	+	334.943i	0.245094	+	0.424516i
$790$		0			0
$791$	586.310	+	338.506i	0.741226	+	0.427947i
$792$		0			0
$793$	−675.759	+	347.259i	−0.852155	+	0.437906i
$794$		0			0
$795$	434.806	+	251.035i	0.546926	+	0.315768i
$796$		0			0
$797$	−28.8314	−	49.9374i	−0.0361749	−	0.0626568i	0.847371	−	0.531001i	$-0.178184\pi$
$797$	−28.8314	−	49.9374i	−0.0361749	−	0.0626568i	−0.883546	+	0.468344i	$0.844851\pi$
$798$		0			0
$799$	−1929.63	+	1114.07i	−2.41506	+	1.39433i
$800$		0			0
$801$	−573.980			−0.716579
$802$		0			0
$803$	131.744	+	76.0626i	0.164065	+	0.0947231i
$804$		0			0
$805$	−406.818			−0.505364
$806$		0			0
$807$		−	1519.52i		−	1.88292i
$808$		0			0
$809$	389.647	−	674.888i	0.481640	−	0.834225i	−0.518138	−	0.855297i	$-0.673375\pi$
$809$	389.647	−	674.888i	0.481640	−	0.834225i	0.999778	+	0.0210719i	$0.00670790\pi$
$810$		0			0
$811$		−	1205.71i		−	1.48669i	−0.668906	−	0.743347i	$-0.733237\pi$
$811$		−	1205.71i		−	1.48669i	0.668906	−	0.743347i	$-0.266763\pi$
$812$		0			0
$813$	169.067	+	292.832i	0.207954	+	0.360187i
$814$		0			0
$815$	−287.987	+	166.269i	−0.353358	+	0.204011i
$816$		0			0
$817$	21.1905	−	36.7030i	0.0259370	−	0.0449241i
$818$		0			0
$819$	299.991	−	465.455i	0.366289	−	0.568321i
$820$		0			0
$821$	−462.021	+	800.244i	−0.562754	+	0.974718i	0.434501	+	0.900671i	$0.356925\pi$
$821$	−462.021	+	800.244i	−0.562754	+	0.974718i	−0.997255	+	0.0740468i	$0.976409\pi$
$822$		0			0
$823$	928.989	−	536.352i	1.12878	−	0.651703i	0.185155	−	0.982709i	$-0.440721\pi$
$823$	928.989	−	536.352i	1.12878	−	0.651703i	0.943629	+	0.331006i	$0.107388\pi$
$824$		0			0
$825$	163.516	+	283.218i	0.198201	+	0.343295i
$826$		0			0
$827$			193.910i			0.234474i	0.993104	+	0.117237i	$0.0374037\pi$
$827$			193.910i			0.234474i	−0.993104	+	0.117237i	$0.962596\pi$
$828$		0			0
$829$	221.962	−	384.449i	0.267746	−	0.463750i	−0.700533	−	0.713620i	$-0.747055\pi$
$829$	221.962	−	384.449i	0.267746	−	0.463750i	0.968279	+	0.249870i	$0.0803878\pi$
$830$		0			0
$831$		−	813.056i		−	0.978407i
$832$		0			0
$833$	360.350			0.432593
$834$		0			0
$835$	696.198	+	401.950i	0.833770	+	0.481377i
$836$		0			0
$837$	−326.056			−0.389554
$838$		0			0
$839$	−220.248	+	127.160i	−0.262513	+	0.151562i	−0.625480	−	0.780240i	$-0.715097\pi$
$839$	−220.248	+	127.160i	−0.262513	+	0.151562i	0.362967	+	0.931802i	$0.381764\pi$
$840$		0			0
$841$	−277.122	−	479.990i	−0.329515	−	0.570737i
$842$		0			0
$843$	−1023.42	−	590.871i	−1.21402	−	0.700915i
$844$		0			0
$845$	−1071.31	−	105.127i	−1.26782	−	0.124411i
$846$		0			0
$847$	496.673	+	286.754i	0.586390	+	0.338553i
$848$		0			0
$849$	227.893	+	394.722i	0.268425	+	0.464925i
$850$		0			0
$851$	−303.448	+	175.196i	−0.356578	+	0.205870i
$852$		0			0
$853$	−684.756			−0.802762			−0.401381	−	0.915911i	$-0.631470\pi$
$853$	−684.756			−0.802762			−0.401381	+	0.915911i	$0.631470\pi$
$854$		0			0
$855$	−187.086	−	108.014i	−0.218814	−	0.126332i
$856$		0			0
$857$	−807.484			−0.942221			−0.471111	−	0.882074i	$-0.656147\pi$
$857$	−807.484			−0.942221			−0.471111	+	0.882074i	$0.656147\pi$
$858$		0			0
$859$		−	691.998i		−	0.805586i	−0.915291	−	0.402793i	$-0.868039\pi$
$859$		−	691.998i		−	0.805586i	0.915291	−	0.402793i	$-0.131961\pi$
$860$		0			0
$861$	−391.390	+	677.908i	−0.454576	+	0.787349i
$862$		0			0
$863$			488.730i			0.566315i	0.959073	+	0.283158i	$0.0913820\pi$
$863$			488.730i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$864$		0			0
$865$	−142.526	−	246.862i	−0.164770	−	0.285389i
$866$		0			0
$867$	2563.78	−	1480.20i	2.95706	−	1.70726i
$868$		0			0
$869$	−192.300	+	333.074i	−0.221289	+	0.383284i
$870$		0			0
$871$	−922.245	+	1430.92i	−1.05883	+	1.64285i
$872$		0			0
$873$	−197.271	+	341.684i	−0.225969	+	0.391390i
$874$		0			0
$875$	319.671	−	184.562i	0.365338	−	0.210928i
$876$		0			0
$877$	521.429	+	903.142i	0.594560	+	1.02981i	0.993609	+	0.112878i	$0.0360070\pi$
$877$	521.429	+	903.142i	0.594560	+	1.02981i	−0.399049	+	0.916930i	$0.630660\pi$
$878$		0			0
$879$			1958.42i			2.22801i
$880$		0			0
$881$	516.530	−	894.656i	0.586299	−	1.01550i	−0.408413	−	0.912797i	$-0.633918\pi$
$881$	516.530	−	894.656i	0.586299	−	1.01550i	0.994712	−	0.102703i	$-0.0327491\pi$
$882$		0			0
$883$			1565.94i			1.77343i	0.462316	+	0.886715i	$0.347019\pi$
$883$			1565.94i			1.77343i	−0.462316	+	0.886715i	$0.652981\pi$
$884$		0			0
$885$	2354.12			2.66002
$886$		0			0
$887$	886.201	+	511.648i	0.999099	+	0.576830i	0.907981	−	0.419010i	$-0.137623\pi$
$887$	886.201	+	511.648i	0.999099	+	0.576830i	0.0911172	+	0.995840i	$0.470956\pi$
$888$		0			0
$889$	1543.76			1.73651
$890$		0			0
$891$	−434.481	+	250.848i	−0.487633	+	0.281535i
$892$		0			0
$893$	169.817	+	294.131i	0.190164	+	0.329374i
$894$		0			0
$895$	1609.07	+	928.995i	1.79784	+	1.03798i
$896$		0			0
$897$	479.575	−	246.445i	0.534644	−	0.274743i
$898$		0			0
$899$	−1276.95	−	737.247i	−1.42041	−	0.820075i
$900$		0			0
$901$	317.015	+	549.085i	0.351848	+	0.609418i
$902$		0			0
$903$	−183.988	+	106.225i	−0.203752	+	0.117636i
$904$		0			0
$905$	−1507.52			−1.66577
$906$		0			0
$907$	−300.595	−	173.549i	−0.331417	−	0.191344i	0.325053	−	0.945696i	$-0.394618\pi$
$907$	−300.595	−	173.549i	−0.331417	−	0.191344i	−0.656470	+	0.754352i	$0.727951\pi$
$908$		0			0
$909$	1132.69			1.24608
$910$		0			0
$911$			280.057i			0.307417i	0.988116	+	0.153708i	$0.0491216\pi$
$911$			280.057i			0.307417i	−0.988116	+	0.153708i	$0.950878\pi$
$912$		0			0
$913$	−16.9518	+	29.3614i	−0.0185671	+	0.0321592i
$914$		0			0
$915$		−	1485.79i		−	1.62382i
$916$		0			0
$917$	144.331	+	249.988i	0.157394	+	0.272615i
$918$		0			0
$919$	−966.759	+	558.159i	−1.05197	+	0.607354i	−0.923200	−	0.384320i	$-0.874436\pi$
$919$	−966.759	+	558.159i	−1.05197	+	0.607354i	−0.128769	+	0.991675i	$0.541103\pi$
$920$		0			0
$921$	−736.733	+	1276.06i	−0.799928	+	1.38552i
$922$		0			0
$923$	−276.326	−	537.724i	−0.299378	−	0.582583i
$924$		0			0
$925$	−262.519	+	454.696i	−0.283804	+	0.491563i
$926$		0			0
$927$	49.5091	−	28.5841i	0.0534079	−	0.0308350i
$928$		0			0
$929$	−461.597	−	799.509i	−0.496875	−	0.860612i	0.503119	−	0.864217i	$-0.332186\pi$
$929$	−461.597	−	799.509i	−0.496875	−	0.860612i	−0.999994	+	0.00360505i	$0.998852\pi$
$930$		0			0
$931$		−	54.9277i		−	0.0589986i
$932$		0			0
$933$	−127.254	+	220.411i	−0.136393	+	0.236239i
$934$		0			0
$935$			1076.05i			1.15085i
$936$		0			0
$937$	−1107.45			−1.18191			−0.590955	−	0.806705i	$-0.701249\pi$
$937$	−1107.45			−1.18191			−0.590955	+	0.806705i	$0.701249\pi$
$938$		0			0
$939$	−1246.61	−	719.729i	−1.32759	−	0.766484i
$940$		0			0
$941$	227.712			0.241989			0.120994	−	0.992653i	$-0.461392\pi$
$941$	227.712			0.241989			0.120994	+	0.992653i	$0.461392\pi$
$942$		0			0
$943$	−287.166	+	165.796i	−0.304524	+	0.175817i
$944$		0			0
$945$	−161.682	−	280.041i	−0.171092	−	0.296339i
$946$		0			0
$947$	889.479	+	513.541i	0.939260	+	0.542282i	0.889728	−	0.456490i	$-0.150894\pi$
$947$	889.479	+	513.541i	0.939260	+	0.542282i	0.0495318	+	0.998773i	$0.484227\pi$
$948$		0			0
$949$	18.3738	−	375.380i	0.0193612	−	0.395554i
$950$		0			0
$951$	166.590	+	96.1808i	0.175173	+	0.101136i
$952$		0			0
$953$	342.572	+	593.352i	0.359467	+	0.622615i	0.987872	−	0.155271i	$-0.0496252\pi$
$953$	342.572	+	593.352i	0.359467	+	0.622615i	−0.628405	+	0.777887i	$0.716292\pi$
$954$		0			0
$955$	1994.27	−	1151.39i	2.08824	−	1.20564i
$956$		0			0
$957$	−784.501			−0.819751
$958$		0			0
$959$	1318.57	+	761.278i	1.37495	+	0.793825i
$960$		0			0
$961$	−597.245			−0.621482
$962$		0			0
$963$		−	64.3418i		−	0.0668139i
$964$		0			0
$965$	−596.584	+	1033.31i	−0.618222	+	1.07079i
$966$		0			0
$967$			237.349i			0.245449i	0.992441	+	0.122724i	$0.0391631\pi$
$967$			237.349i			0.245449i	−0.992441	+	0.122724i	$0.960837\pi$
$968$		0			0
$969$	−313.536	−	543.061i	−0.323567	−	0.560435i
$970$		0			0
$971$	−850.603	+	491.096i	−0.876007	+	0.505763i	−0.869340	−	0.494215i	$-0.835456\pi$
$971$	−850.603	+	491.096i	−0.876007	+	0.505763i	−0.00666729	+	0.999978i	$0.502122\pi$
$972$		0			0
$973$	−173.118	+	299.850i	−0.177922	+	0.308170i
$974$		0			0
$975$	437.695	−	679.112i	0.448918	−	0.696525i
$976$		0			0
$977$	605.979	−	1049.59i	0.620245	−	1.07430i	−0.369195	−	0.929352i	$-0.620366\pi$
$977$	605.979	−	1049.59i	0.620245	−	1.07430i	0.989440	−	0.144944i	$-0.0463002\pi$
$978$		0			0
$979$	377.411	−	217.898i	0.385507	−	0.222572i
$980$		0			0
$981$	−100.888	−	174.744i	−0.102842	−	0.178128i
$982$		0			0
$983$		−	106.912i		−	0.108760i	−0.998520	−	0.0543802i	$-0.982682\pi$
$983$		−	106.912i		−	0.108760i	0.998520	−	0.0543802i	$-0.0173183\pi$
$984$		0			0
$985$	532.186	−	921.773i	0.540290	−	0.935810i
$986$		0			0
$987$		−	1702.54i		−	1.72496i
$988$		0			0
$989$	−89.9956			−0.0909966
$990$		0			0
$991$	752.804	+	434.632i	0.759641	+	0.438579i	0.829167	−	0.559001i	$-0.188815\pi$
$991$	752.804	+	434.632i	0.759641	+	0.438579i	−0.0695258	+	0.997580i	$0.522149\pi$
$992$		0			0
$993$	−2335.88			−2.35235
$994$		0			0
$995$	−716.954	+	413.933i	−0.720556	+	0.416013i
$996$		0			0
$997$	−228.875	−	396.423i	−0.229564	−	0.397616i	0.728115	−	0.685455i	$-0.240397\pi$
$997$	−228.875	−	396.423i	−0.229564	−	0.397616i	−0.957679	+	0.287839i	$0.907063\pi$
$998$		0			0
$999$	−241.198	−	139.256i	−0.241440	−	0.139395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.3.bb.c.191.4	yes	32
4.3	odd	2	inner	416.3.bb.c.191.13	yes	32
13.3	even	3	inner	416.3.bb.c.159.13	yes	32
52.3	odd	6	inner	416.3.bb.c.159.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.3.bb.c.159.4	✓	32	52.3	odd	6	inner
416.3.bb.c.159.13	yes	32	13.3	even	3	inner
416.3.bb.c.191.4	yes	32	1.1	even	1	trivial
416.3.bb.c.191.13	yes	32	4.3	odd	2	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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	416.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.45657 - 1.99565i) q^{3} +6.36955 q^{5} +(-5.32276 + 3.07310i) q^{7} +(3.46526 + 6.00201i) q^{9} +(-4.55705 - 2.63102i) q^{11} +(-0.635553 + 12.9845i) q^{13} +(-22.0168 - 12.7114i) q^{15} +(-16.0523 - 27.8035i) q^{17} +(-4.23804 + 2.44684i) q^{19} +24.5314 q^{21} +(8.99944 + 5.19583i) q^{23} +15.5712 q^{25} +8.25990i q^{27} +(-18.6765 + 32.3486i) q^{29} +39.4746i q^{31} +(10.5012 + 18.1886i) q^{33} +(-33.9036 + 19.5743i) q^{35} +(-16.8593 + 29.2011i) q^{37} +(28.1093 - 43.6134i) q^{39} +(-15.9547 + 27.6343i) q^{41} +(-7.50010 + 4.33019i) q^{43} +(22.0722 + 38.2301i) q^{45} -69.4026i q^{47} +(-5.61212 + 9.72047i) q^{49} +128.140i q^{51} -19.7488 q^{53} +(-29.0264 - 16.7584i) q^{55} +19.5321 q^{57} +(-80.1928 + 46.2993i) q^{59} +(29.2216 + 50.6133i) q^{61} +(-36.8896 - 21.2982i) q^{63} +(-4.04819 + 82.7052i) q^{65} +(113.408 + 65.4759i) q^{67} +(-20.7381 - 35.9195i) q^{69} +(-40.2747 + 23.2526i) q^{71} -28.9100 q^{73} +(-53.8229 - 31.0747i) q^{75} +32.3415 q^{77} -73.0898i q^{79} +(47.6713 - 82.5691i) q^{81} -6.44306i q^{83} +(-102.246 - 177.096i) q^{85} +(129.113 - 74.5436i) q^{87} +(-41.4095 + 71.7234i) q^{89} +(-36.5196 - 71.0663i) q^{91} +(78.7776 - 136.447i) q^{93} +(-26.9944 + 15.5852i) q^{95} +(28.4641 + 49.3012i) q^{97} -36.4687i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{5} + 80 q^{9} - 44 q^{13} + 16 q^{17} - 128 q^{21} + 272 q^{25} - 52 q^{29} - 72 q^{33} + 148 q^{37} + 72 q^{41} - 116 q^{45} + 328 q^{49} - 152 q^{53} - 224 q^{57} + 228 q^{61} - 352 q^{65}+ \cdots - 352 q^{97}+O(q^{100}) \) 32 * q - 8 * q^5 + 80 * q^9 - 44 * q^13 + 16 * q^17 - 128 * q^21 + 272 * q^25 - 52 * q^29 - 72 * q^33 + 148 * q^37 + 72 * q^41 - 116 * q^45 + 328 * q^49 - 152 * q^53 - 224 * q^57 + 228 * q^61 - 352 * q^65 + 200 * q^69 + 224 * q^73 + 832 * q^77 - 696 * q^81 - 84 * q^85 - 112 * q^89 + 152 * q^93 - 352 * q^97

Introduction

L-functions

Modular forms

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Database

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