LMFDB - Embedded newform 168.4.u.a.17.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(17,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.17"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	168.17
Dual form			168.4.u.a.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35065 - 5.01754i) q^{3} +(2.40532 + 4.16613i) q^{5} +(-3.40309 + 18.2049i) q^{7} +(-23.3515 + 13.5539i) q^{9} +(29.6911 + 17.1421i) q^{11} +17.1571i q^{13} +(17.6550 - 17.6958i) q^{15} +(-50.4770 + 87.4288i) q^{17} +(119.893 - 69.2205i) q^{19} +(95.9403 - 7.51333i) q^{21} +(0.541507 - 0.312639i) q^{23} +(50.9289 - 88.2114i) q^{25} +(99.5470 + 98.8605i) q^{27} +222.968i q^{29} +(247.848 + 143.095i) q^{31} +(45.9092 - 172.129i) q^{33} +(-84.0296 + 29.6109i) q^{35} +(9.19197 + 15.9210i) q^{37} +(86.0864 - 23.1732i) q^{39} -219.751 q^{41} -370.491 q^{43} +(-112.635 - 64.6839i) q^{45} +(143.066 + 247.797i) q^{47} +(-319.838 - 123.906i) q^{49} +(506.855 + 135.185i) q^{51} +(29.3942 + 16.9708i) q^{53} +164.929i q^{55} +(-509.251 - 508.078i) q^{57} +(-127.350 + 220.577i) q^{59} +(-29.2617 + 16.8943i) q^{61} +(-167.280 - 471.237i) q^{63} +(-71.4787 + 41.2683i) q^{65} +(87.9473 - 152.329i) q^{67} +(-2.30007 - 2.29477i) q^{69} -626.114i q^{71} +(189.125 + 109.191i) q^{73} +(-511.392 - 136.395i) q^{75} +(-413.113 + 482.187i) q^{77} +(-263.456 - 456.319i) q^{79} +(361.583 - 633.008i) q^{81} +370.957 q^{83} -485.653 q^{85} +(1118.75 - 301.152i) q^{87} +(-412.449 - 714.383i) q^{89} +(-312.343 - 58.3872i) q^{91} +(383.230 - 1436.86i) q^{93} +(576.764 + 332.995i) q^{95} +1309.69i q^{97} +(-925.674 + 2.13549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 14 q^{9} - 88 q^{15} - 270 q^{19} + 50 q^{21} - 438 q^{25} + 216 q^{31} - 372 q^{33} + 66 q^{37} + 242 q^{39} + 900 q^{43} - 294 q^{45} + 60 q^{49} - 138 q^{51} + 1384 q^{57} + 108 q^{61}+ \cdots + 1988 q^{99}+O(q^{100}) $ 48 * q + 12 * q^7 + 14 * q^9 - 88 * q^15 - 270 * q^19 + 50 * q^21 - 438 * q^25 + 216 * q^31 - 372 * q^33 + 66 * q^37 + 242 * q^39 + 900 * q^43 - 294 * q^45 + 60 * q^49 - 138 * q^51 + 1384 * q^57 + 108 * q^61 + 1096 * q^63 + 6 * q^67 - 1206 * q^73 - 594 * q^75 - 588 * q^79 - 54 * q^81 - 240 * q^85 - 3522 * q^87 + 234 * q^91 - 608 * q^93 + 1988 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.35065	−	5.01754i	−0.259933	−	0.965627i
$3$	−1.35065	−	5.01754i	−0.259933	−	0.965627i
$4$		0			0
$5$	2.40532	+	4.16613i	0.215138	+	0.372630i	0.953315	−	0.301977i	$-0.0976465\pi$
$5$	2.40532	+	4.16613i	0.215138	+	0.372630i	−0.738177	+	0.674607i	$0.764313\pi$
$6$		0			0
$7$	−3.40309	+	18.2049i	−0.183750	+	0.982973i
$7$	−3.40309	+	18.2049i	−0.183750	+	0.982973i
$8$		0			0
$9$	−23.3515	+	13.5539i	−0.864870	+	0.501997i
$10$		0			0
$11$	29.6911	+	17.1421i	0.813836	+	0.469868i	0.848286	−	0.529538i	$-0.177635\pi$
$11$	29.6911	+	17.1421i	0.813836	+	0.469868i	−0.0344503	+	0.999406i	$0.510968\pi$
$12$		0			0
$13$			17.1571i			0.366040i	0.983109	+	0.183020i	$0.0585873\pi$
$13$			17.1571i			0.366040i	−0.983109	+	0.183020i	$0.941413\pi$
$14$		0			0
$15$	17.6550	−	17.6958i	0.303900	−	0.304602i
$16$		0			0
$17$	−50.4770	+	87.4288i	−0.720146	+	1.24733i	0.240795	+	0.970576i	$0.422592\pi$
$17$	−50.4770	+	87.4288i	−0.720146	+	1.24733i	−0.960941	+	0.276753i	$0.910742\pi$
$18$		0			0
$19$	119.893	−	69.2205i	1.44766	−	0.835804i	0.449314	−	0.893374i	$-0.351669\pi$
$19$	119.893	−	69.2205i	1.44766	−	0.835804i	0.998341	+	0.0575700i	$0.0183352\pi$
$20$		0			0
$21$	95.9403	−	7.51333i	0.996948	−	0.0780735i
$22$		0			0
$23$	0.541507	−	0.312639i	0.00490922	−	0.00283434i	−0.497543	−	0.867439i	$-0.665764\pi$
$23$	0.541507	−	0.312639i	0.00490922	−	0.00283434i	0.502453	+	0.864605i	$0.332431\pi$
$24$		0			0
$25$	50.9289	−	88.2114i	0.407431	−	0.705691i
$26$		0			0
$27$	99.5470	+	98.8605i	0.709549	+	0.704656i
$28$		0			0
$29$			222.968i			1.42773i	0.700284	+	0.713864i	$0.253057\pi$
$29$			222.968i			1.42773i	−0.700284	+	0.713864i	$0.746943\pi$
$30$		0			0
$31$	247.848	+	143.095i	1.43596	+	0.829053i	0.997566	−	0.0697292i	$-0.0222135\pi$
$31$	247.848	+	143.095i	1.43596	+	0.829053i	0.438396	+	0.898782i	$0.355547\pi$
$32$		0			0
$33$	45.9092	−	172.129i	0.242175	−	0.907996i
$34$		0			0
$35$	−84.0296	+	29.6109i	−0.405817	+	0.143004i
$36$		0			0
$37$	9.19197	+	15.9210i	0.0408419	+	0.0707402i	0.885724	−	0.464213i	$-0.153663\pi$
$37$	9.19197	+	15.9210i	0.0408419	+	0.0707402i	−0.844882	+	0.534953i	$0.820329\pi$
$38$		0			0
$39$	86.0864	−	23.1732i	0.353458	−	0.0951459i
$40$		0			0
$41$	−219.751			−0.837056			−0.418528	−	0.908204i	$-0.637454\pi$
$41$	−219.751			−0.837056			−0.418528	+	0.908204i	$0.637454\pi$
$42$		0			0
$43$	−370.491			−1.31394			−0.656970	−	0.753917i	$-0.728162\pi$
$43$	−370.491			−1.31394			−0.656970	+	0.753917i	$0.728162\pi$
$44$		0			0
$45$	−112.635	−	64.6839i	−0.373126	−	0.214278i
$46$		0			0
$47$	143.066	+	247.797i	0.444006	+	0.769041i	0.997982	−	0.0634912i	$-0.0202235\pi$
$47$	143.066	+	247.797i	0.444006	+	0.769041i	−0.553976	+	0.832532i	$0.686890\pi$
$48$		0			0
$49$	−319.838	−	123.906i	−0.932472	−	0.361242i
$50$		0			0
$51$	506.855	+	135.185i	1.39164	+	0.371170i
$52$		0			0
$53$	29.3942	+	16.9708i	0.0761813	+	0.0439833i	0.537607	−	0.843196i	$-0.319329\pi$
$53$	29.3942	+	16.9708i	0.0761813	+	0.0439833i	−0.461425	+	0.887179i	$0.652662\pi$
$54$		0			0
$55$			164.929i			0.404347i
$56$		0			0
$57$	−509.251	−	508.078i	−1.18337	−	1.18064i
$58$		0			0
$59$	−127.350	+	220.577i	−0.281010	+	0.486723i	−0.971634	−	0.236491i	$-0.924003\pi$
$59$	−127.350	+	220.577i	−0.281010	+	0.486723i	0.690624	+	0.723214i	$0.257336\pi$
$60$		0			0
$61$	−29.2617	+	16.8943i	−0.0614193	+	0.0354605i	−0.530395	−	0.847751i	$-0.677956\pi$
$61$	−29.2617	+	16.8943i	−0.0614193	+	0.0354605i	0.468976	+	0.883211i	$0.344623\pi$
$62$		0			0
$63$	−167.280	−	471.237i	−0.334529	−	0.942385i
$64$		0			0
$65$	−71.4787	+	41.2683i	−0.136398	+	0.0787492i
$66$		0			0
$67$	87.9473	−	152.329i	0.160365	−	0.277761i	−0.774634	−	0.632409i	$-0.782066\pi$
$67$	87.9473	−	152.329i	0.160365	−	0.277761i	0.935000	+	0.354648i	$0.115399\pi$
$68$		0			0
$69$	−2.30007	−	2.29477i	−0.00401298	−	0.00400373i
$70$		0			0
$71$		−	626.114i		−	1.04656i	−0.852160	−	0.523282i	$-0.824708\pi$
$71$		−	626.114i		−	1.04656i	0.852160	−	0.523282i	$-0.175292\pi$
$72$		0			0
$73$	189.125	+	109.191i	0.303225	+	0.175067i	0.643891	−	0.765118i	$-0.277319\pi$
$73$	189.125	+	109.191i	0.303225	+	0.175067i	−0.340666	+	0.940184i	$0.610653\pi$
$74$		0			0
$75$	−511.392	−	136.395i	−0.787339	−	0.209994i
$76$		0			0
$77$	−413.113	+	482.187i	−0.611410	+	0.713641i
$78$		0			0
$79$	−263.456	−	456.319i	−0.375204	−	0.649873i	0.615153	−	0.788407i	$-0.289094\pi$
$79$	−263.456	−	456.319i	−0.375204	−	0.649873i	−0.990358	+	0.138535i	$0.955761\pi$
$80$		0			0
$81$	361.583	−	633.008i	0.495999	−	0.868323i
$82$		0			0
$83$	370.957			0.490576			0.245288	−	0.969450i	$-0.421118\pi$
$83$	370.957			0.490576			0.245288	+	0.969450i	$0.421118\pi$
$84$		0			0
$85$	−485.653			−0.619723
$86$		0			0
$87$	1118.75	−	301.152i	1.37865	−	0.371114i
$88$		0			0
$89$	−412.449	−	714.383i	−0.491231	−	0.850837i	0.508718	−	0.860933i	$-0.330120\pi$
$89$	−412.449	−	714.383i	−0.491231	−	0.850837i	−0.999949	+	0.0100964i	$0.996786\pi$
$90$		0			0
$91$	−312.343	−	58.3872i	−0.359807	−	0.0672598i
$92$		0			0
$93$	383.230	−	1436.86i	0.427302	−	1.60210i
$94$		0			0
$95$	576.764	+	332.995i	0.622892	+	0.359627i
$96$		0			0
$97$			1309.69i			1.37092i	0.728112	+	0.685458i	$0.240398\pi$
$97$			1309.69i			1.37092i	−0.728112	+	0.685458i	$0.759602\pi$
$98$		0			0
$99$	−925.674	+	2.13549i	−0.939734	+	0.00216793i
$100$		0			0
$101$	−755.381	+	1308.36i	−0.744190	+	1.28898i	0.206382	+	0.978472i	$0.433831\pi$
$101$	−755.381	+	1308.36i	−0.744190	+	1.28898i	−0.950572	+	0.310504i	$0.899502\pi$
$102$		0			0
$103$	173.735	−	100.306i	0.166200	−	0.0959555i	−0.414593	−	0.910007i	$-0.636076\pi$
$103$	173.735	−	100.306i	0.166200	−	0.0959555i	0.580793	+	0.814052i	$0.302743\pi$
$104$		0			0
$105$	262.069	+	381.628i	0.243574	+	0.354696i
$106$		0			0
$107$	−1285.76	+	742.335i	−1.16168	+	0.670694i	−0.951705	−	0.307014i	$-0.900670\pi$
$107$	−1285.76	+	742.335i	−1.16168	+	0.670694i	−0.209971	+	0.977708i	$0.567337\pi$
$108$		0			0
$109$	232.948	−	403.477i	0.204700	−	0.354552i	−0.745337	−	0.666688i	$-0.767711\pi$
$109$	232.948	−	403.477i	0.204700	−	0.354552i	0.950037	+	0.312137i	$0.101045\pi$
$110$		0			0
$111$	67.4689	−	67.6247i	0.0576925	−	0.0578257i
$112$		0			0
$113$		−	454.340i		−	0.378237i	−0.981954	−	0.189118i	$-0.939437\pi$
$113$		−	454.340i		−	0.378237i	0.981954	−	0.189118i	$-0.0605630\pi$
$114$		0			0
$115$	2.60499	+	1.50399i	0.00211232	+	0.00121955i
$116$		0			0
$117$	−232.546	−	400.643i	−0.183751	−	0.316577i
$118$		0			0
$119$	−1419.86	−	1216.46i	−1.09376	−	0.937080i
$120$		0			0
$121$	−77.7935	−	134.742i	−0.0584474	−	0.101234i
$122$		0			0
$123$	296.807	+	1102.61i	0.217578	+	0.808283i
$124$		0			0
$125$	1091.33			0.780892
$126$		0			0
$127$	80.7459			0.0564176			0.0282088	−	0.999602i	$-0.491020\pi$
$127$	80.7459			0.0564176			0.0282088	+	0.999602i	$0.491020\pi$
$128$		0			0
$129$	500.405	+	1858.96i	0.341536	+	1.26878i
$130$		0			0
$131$	1105.17	+	1914.22i	0.737095	+	1.27669i	0.953798	+	0.300449i	$0.0971364\pi$
$131$	1105.17	+	1914.22i	0.737095	+	1.27669i	−0.216703	+	0.976238i	$0.569530\pi$
$132$		0			0
$133$	852.145	+	2418.21i	0.555567	+	1.57658i
$134$		0			0
$135$	−172.424	+	652.517i	−0.109925	+	0.415998i
$136$		0			0
$137$	1820.47	+	1051.05i	1.13528	+	0.655453i	0.945257	−	0.326327i	$-0.105811\pi$
$137$	1820.47	+	1051.05i	1.13528	+	0.655453i	0.190021	+	0.981780i	$0.439144\pi$
$138$		0			0
$139$		−	3004.00i		−	1.83306i	−0.399964	−	0.916531i	$-0.630977\pi$
$139$		−	3004.00i		−	1.83306i	0.399964	−	0.916531i	$-0.369023\pi$
$140$		0			0
$141$	1050.10	−	1052.53i	0.627195	−	0.628643i
$142$		0			0
$143$	−294.109	+	509.412i	−0.171991	+	0.297896i
$144$		0			0
$145$	−928.915	+	536.309i	−0.532015	+	0.307159i
$146$		0			0
$147$	−189.714	+	1772.15i	−0.106445	+	0.994319i
$148$		0			0
$149$	1109.66	−	640.661i	0.610112	−	0.352248i	−0.162897	−	0.986643i	$-0.552084\pi$
$149$	1109.66	−	640.661i	0.610112	−	0.352248i	0.773009	+	0.634395i	$0.218751\pi$
$150$		0			0
$151$	1652.35	−	2861.96i	0.890507	−	1.54240i	0.0512388	−	0.998686i	$-0.483683\pi$
$151$	1652.35	−	2861.96i	0.890507	−	1.54240i	0.839268	−	0.543717i	$-0.182984\pi$
$152$		0			0
$153$	−6.28820	−	2725.75i	−0.00332269	−	1.44029i
$154$		0			0
$155$			1376.76i			0.713444i
$156$		0			0
$157$	2268.13	+	1309.50i	1.15297	+	0.665667i	0.949609	−	0.313437i	$-0.101480\pi$
$157$	2268.13	+	1309.50i	1.15297	+	0.665667i	0.203361	+	0.979104i	$0.434814\pi$
$158$		0			0
$159$	45.4502	−	170.408i	0.0226694	−	0.0849954i
$160$		0			0
$161$	3.84877	+	10.9220i	0.00188401	+	0.00534643i
$162$		0			0
$163$	−674.516	−	1168.30i	−0.324124	−	0.561399i	0.657211	−	0.753707i	$-0.271736\pi$
$163$	−674.516	−	1168.30i	−0.324124	−	0.561399i	−0.981335	+	0.192308i	$0.938403\pi$
$164$		0			0
$165$	827.540	−	222.762i	0.390448	−	0.105103i
$166$		0			0
$167$	−2768.59			−1.28287			−0.641437	−	0.767175i	$-0.721662\pi$
$167$	−2768.59			−1.28287			−0.641437	+	0.767175i	$0.721662\pi$
$168$		0			0
$169$	1902.63			0.866015
$170$		0			0
$171$	−1861.48	+	3241.43i	−0.832462	+	1.44958i
$172$		0			0
$173$	−635.218	−	1100.23i	−0.279160	−	0.483520i	0.692016	−	0.721882i	$-0.256723\pi$
$173$	−635.218	−	1100.23i	−0.279160	−	0.483520i	−0.971176	+	0.238362i	$0.923389\pi$
$174$		0			0
$175$	1432.57	+	1227.35i	0.618810	+	0.530164i
$176$		0			0
$177$	1278.76	+	341.062i	0.543036	+	0.144835i
$178$		0			0
$179$	1763.39	+	1018.09i	0.736323	+	0.425116i	0.820731	−	0.571315i	$-0.193566\pi$
$179$	1763.39	+	1018.09i	0.736323	+	0.425116i	−0.0844077	+	0.996431i	$0.526900\pi$
$180$		0			0
$181$			1402.45i			0.575931i	0.957641	+	0.287965i	$0.0929788\pi$
$181$			1402.45i			0.575931i	−0.957641	+	0.287965i	$0.907021\pi$
$182$		0			0
$183$	124.290	+	124.004i	0.0502065	+	0.0500908i
$184$		0			0
$185$	−44.2192	+	76.5899i	−0.0175733	+	0.0304378i
$186$		0			0
$187$	−2997.43	+	1730.57i	−1.17216	+	0.676747i
$188$		0			0
$189$	−2138.51	+	1475.81i	−0.823037	+	0.567988i
$190$		0			0
$191$	3511.17	−	2027.17i	1.33015	−	0.767964i	0.344831	−	0.938665i	$-0.387936\pi$
$191$	3511.17	−	2027.17i	1.33015	−	0.767964i	0.985323	+	0.170701i	$0.0546031\pi$
$192$		0			0
$193$	872.281	−	1510.83i	0.325327	−	0.563483i	−0.656251	−	0.754542i	$-0.727859\pi$
$193$	872.281	−	1510.83i	0.325327	−	0.563483i	0.981579	+	0.191059i	$0.0611922\pi$
$194$		0			0
$195$	303.608	+	302.908i	0.111497	+	0.111240i
$196$		0			0
$197$		−	5061.13i		−	1.83041i	−0.402989	−	0.915205i	$-0.632029\pi$
$197$		−	5061.13i		−	1.83041i	0.402989	−	0.915205i	$-0.367971\pi$
$198$		0			0
$199$	1274.50	+	735.834i	0.454005	+	0.262120i	0.709520	−	0.704685i	$-0.248912\pi$
$199$	1274.50	+	735.834i	0.454005	+	0.262120i	−0.255515	+	0.966805i	$0.582245\pi$
$200$		0			0
$201$	−883.104	−	235.536i	−0.309897	−	0.0826538i
$202$		0			0
$203$	−4059.11	−	758.781i	−1.40342	−	0.262345i
$204$		0			0
$205$	−528.570	−	915.511i	−0.180083	−	0.311912i
$206$		0			0
$207$	−8.40750	+	14.6401i	−0.00282300	+	0.00491574i
$208$		0			0
$209$	4746.35			1.57087
$210$		0			0
$211$	−5010.62			−1.63481			−0.817406	−	0.576063i	$-0.804588\pi$
$211$	−5010.62			−1.63481			−0.817406	+	0.576063i	$0.804588\pi$
$212$		0			0
$213$	−3141.55	+	845.661i	−1.01059	+	0.272036i
$214$		0			0
$215$	−891.150	−	1543.52i	−0.282679	−	0.489614i
$216$		0			0
$217$	−3448.48	+	4025.09i	−1.07879	+	1.25917i
$218$		0			0
$219$	292.430	−	1096.42i	0.0902311	−	0.338307i
$220$		0			0
$221$	−1500.02	−	866.039i	−0.456572	−	0.263602i
$222$		0			0
$223$		−	4398.14i		−	1.32072i	−0.750948	−	0.660361i	$-0.770403\pi$
$223$		−	4398.14i		−	1.32072i	0.750948	−	0.660361i	$-0.229597\pi$
$224$		0			0
$225$	6.34449	+	2750.15i	0.00187985	+	0.814860i
$226$		0			0
$227$	2060.25	−	3568.45i	0.602393	−	1.04338i	−0.390064	−	0.920788i	$-0.627547\pi$
$227$	2060.25	−	3568.45i	0.602393	−	1.04338i	0.992458	−	0.122588i	$-0.0391195\pi$
$228$		0			0
$229$	−453.529	+	261.845i	−0.130874	+	0.0755600i	−0.564007	−	0.825770i	$-0.690741\pi$
$229$	−453.529	+	261.845i	−0.130874	+	0.0755600i	0.433134	+	0.901330i	$0.357408\pi$
$230$		0			0
$231$	2977.37	+	1421.54i	0.848036	+	0.404895i
$232$		0			0
$233$	−4090.17	+	2361.46i	−1.15003	+	0.663968i	−0.948894	−	0.315596i	$-0.897796\pi$
$233$	−4090.17	+	2361.46i	−1.15003	+	0.663968i	−0.201133	+	0.979564i	$0.564462\pi$
$234$		0			0
$235$	−688.237	+	1192.06i	−0.191045	+	0.330900i
$236$		0			0
$237$	−1933.76	+	1938.23i	−0.530006	+	0.531230i
$238$		0			0
$239$		−	7159.06i		−	1.93758i	−0.247886	−	0.968789i	$-0.579736\pi$
$239$		−	7159.06i		−	1.93758i	0.247886	−	0.968789i	$-0.420264\pi$
$240$		0			0
$241$	−2440.67	−	1409.12i	−0.652355	−	0.376637i	0.137003	−	0.990571i	$-0.456253\pi$
$241$	−2440.67	−	1409.12i	−0.652355	−	0.376637i	−0.789358	+	0.613933i	$0.789586\pi$
$242$		0			0
$243$	−3664.52	−	959.287i	−0.967402	−	0.253244i
$244$		0			0
$245$	−253.103	−	1630.52i	−0.0660006	−	0.425184i
$246$		0			0
$247$	1187.62	+	2057.02i	0.305938	+	0.529900i
$248$		0			0
$249$	−501.033	−	1861.29i	−0.127517	−	0.473713i
$250$		0			0
$251$	2431.43			0.611437			0.305719	−	0.952122i	$-0.401103\pi$
$251$	2431.43			0.611437			0.305719	+	0.952122i	$0.401103\pi$
$252$		0			0
$253$	21.4372			0.00532706
$254$		0			0
$255$	655.948	+	2436.79i	0.161087	+	0.598421i
$256$		0			0
$257$	665.134	+	1152.05i	0.161439	+	0.279621i	0.935385	−	0.353631i	$-0.115053\pi$
$257$	665.134	+	1152.05i	0.161439	+	0.279621i	−0.773946	+	0.633252i	$0.781720\pi$
$258$		0			0
$259$	−321.121	+	113.158i	−0.0770404	+	0.0271480i
$260$		0			0
$261$	−3022.09	−	5206.63i	−0.716715	−	1.23480i
$262$		0			0
$263$	3964.07	+	2288.66i	0.929411	+	0.536596i	0.886625	−	0.462489i	$-0.153043\pi$
$263$	3964.07	+	2288.66i	0.929411	+	0.536596i	0.0427856	+	0.999084i	$0.486377\pi$
$264$		0			0
$265$			163.280i			0.0378499i
$266$		0			0
$267$	−3027.37	+	3034.37i	−0.693903	+	0.695506i
$268$		0			0
$269$	−519.041	+	899.006i	−0.117645	+	0.203767i	−0.918834	−	0.394644i	$-0.870868\pi$
$269$	−519.041	+	899.006i	−0.117645	+	0.203767i	0.801189	+	0.598411i	$0.204201\pi$
$270$		0			0
$271$	3895.37	−	2249.00i	0.873163	−	0.504121i	0.00476491	−	0.999989i	$-0.498483\pi$
$271$	3895.37	−	2249.00i	0.873163	−	0.504121i	0.868398	+	0.495868i	$0.165150\pi$
$272$		0			0
$273$	128.907	+	1646.06i	0.0285780	+	0.364923i
$274$		0			0
$275$	3024.27	−	1746.06i	0.663164	−	0.382878i
$276$		0			0
$277$	−315.706	+	546.820i	−0.0684800	+	0.118611i	−0.898232	−	0.439521i	$-0.855148\pi$
$277$	−315.706	+	546.820i	−0.0684800	+	0.118611i	0.829752	+	0.558132i	$0.188482\pi$
$278$		0			0
$279$	−7727.11	+	17.8261i	−1.65810	+	0.00382517i
$280$		0			0
$281$		−	5539.62i		−	1.17604i	−0.808848	−	0.588018i	$-0.799908\pi$
$281$		−	5539.62i		−	1.17604i	0.808848	−	0.588018i	$-0.200092\pi$
$282$		0			0
$283$	3676.15	+	2122.43i	0.772171	+	0.445813i	0.833649	−	0.552295i	$-0.186248\pi$
$283$	3676.15	+	2122.43i	0.772171	+	0.445813i	−0.0614774	+	0.998108i	$0.519581\pi$
$284$		0			0
$285$	891.809	−	3343.70i	0.185355	−	0.694960i
$286$		0			0
$287$	747.832	−	4000.54i	0.153809	−	0.822803i
$288$		0			0
$289$	−2639.36	−	4571.51i	−0.537220	−	0.930492i
$290$		0			0
$291$	6571.43	−	1768.94i	1.32379	−	0.356346i
$292$		0			0
$293$	1973.35			0.393462			0.196731	−	0.980458i	$-0.436967\pi$
$293$	1973.35			0.393462			0.196731	+	0.980458i	$0.436967\pi$
$294$		0			0
$295$	−1225.27			−0.241824
$296$		0			0
$297$	1260.98	+	4641.72i	0.246361	+	0.906869i
$298$		0			0
$299$	5.36397	+	9.29068i	0.00103748	+	0.00179697i
$300$		0			0
$301$	1260.82	−	6744.77i	0.241436	−	1.29157i
$302$		0			0
$303$	7585.00	+	2023.02i	1.43811	+	0.383563i
$304$		0			0
$305$	−140.768	−	81.2722i	−0.0264273	−	0.0152578i
$306$		0			0
$307$			2596.86i			0.482771i	0.970429	+	0.241385i	$0.0776018\pi$
$307$			2596.86i			0.482771i	−0.970429	+	0.241385i	$0.922398\pi$
$308$		0			0
$309$	−737.943	−	736.242i	−0.135858	−	0.135545i
$310$		0			0
$311$	−162.730	+	281.857i	−0.0296706	+	0.0513910i	−0.880479	−	0.474084i	$-0.842779\pi$
$311$	−162.730	+	281.857i	−0.0296706	+	0.0513910i	0.850809	+	0.525475i	$0.176113\pi$
$312$		0			0
$313$	554.704	−	320.259i	0.100172	−	0.0578342i	−0.449077	−	0.893493i	$-0.648247\pi$
$313$	554.704	−	320.259i	0.100172	−	0.0578342i	0.549249	+	0.835659i	$0.314914\pi$
$314$		0			0
$315$	1560.87	−	1830.39i	0.279191	−	0.327399i
$316$		0			0
$317$	−6616.35	+	3819.95i	−1.17228	+	0.676814i	−0.954215	−	0.299122i	$-0.903306\pi$
$317$	−6616.35	+	3819.95i	−1.17228	+	0.676814i	−0.218060	+	0.975935i	$0.569973\pi$
$318$		0			0
$319$	−3822.15	+	6620.16i	−0.670845	+	1.16194i
$320$		0			0
$321$	5461.32	+	5448.73i	0.949598	+	0.947410i
$322$		0			0
$323$			13976.2i			2.40760i
$324$		0			0
$325$	1513.45	+	873.791i	0.258311	+	0.149136i
$326$		0			0
$327$	−2339.10	−	623.868i	−0.395573	−	0.105505i
$328$		0			0
$329$	−4997.99	+	1761.22i	−0.837533	+	0.295135i
$330$		0			0
$331$	2458.08	+	4257.53i	0.408183	+	0.706993i	0.994686	−	0.102953i	$-0.0328293\pi$
$331$	2458.08	+	4257.53i	0.408183	+	0.706993i	−0.586503	+	0.809947i	$0.699496\pi$
$332$		0			0
$333$	−430.437	−	247.191i	−0.0708343	−	0.0406786i
$334$		0			0
$335$	846.165			0.138003
$336$		0			0
$337$	−5086.79			−0.822240			−0.411120	−	0.911581i	$-0.634862\pi$
$337$	−5086.79			−0.822240			−0.411120	+	0.911581i	$0.634862\pi$
$338$		0			0
$339$	−2279.67	+	613.656i	−0.365235	+	0.0983162i
$340$		0			0
$341$	4905.91	+	8497.29i	0.779091	+	1.34943i
$342$		0			0
$343$	3344.14	−	5400.96i	0.526433	−	0.850217i
$344$		0			0
$345$	4.02791	−	15.1020i	0.000628567	−	0.00235671i
$346$		0			0
$347$	−5183.76	−	2992.84i	−0.801956	−	0.463009i	0.0421990	−	0.999109i	$-0.486564\pi$
$347$	−5183.76	−	2992.84i	−0.801956	−	0.463009i	−0.844154	+	0.536100i	$0.819897\pi$
$348$		0			0
$349$			4392.81i			0.673759i	0.941548	+	0.336879i	$0.109371\pi$
$349$			4392.81i			0.673759i	−0.941548	+	0.336879i	$0.890629\pi$
$350$		0			0
$351$	−1696.16	+	1707.94i	−0.257932	+	0.259723i
$352$		0			0
$353$	4415.94	−	7648.63i	0.665826	−	1.15324i	−0.313234	−	0.949676i	$-0.601413\pi$
$353$	4415.94	−	7648.63i	0.665826	−	1.15324i	0.979061	−	0.203569i	$-0.0652541\pi$
$354$		0			0
$355$	2608.47	−	1506.00i	0.389981	−	0.225156i
$356$		0			0
$357$	−4185.90	+	8767.20i	−0.620564	+	1.29975i
$358$		0			0
$359$	−5040.82	+	2910.32i	−0.741070	+	0.427857i	−0.822458	−	0.568825i	$-0.807398\pi$
$359$	−5040.82	+	2910.32i	−0.741070	+	0.427857i	0.0813881	+	0.996682i	$0.474065\pi$
$360$		0			0
$361$	6153.46	−	10658.1i	0.897137	−	1.55389i
$362$		0			0
$363$	−571.003	+	572.322i	−0.0825617	+	0.0827524i
$364$		0			0
$365$			1050.56i			0.150654i
$366$		0			0
$367$	6166.91	+	3560.47i	0.877140	+	0.506417i	0.869714	−	0.493556i	$-0.164303\pi$
$367$	6166.91	+	3560.47i	0.877140	+	0.506417i	0.00742533	+	0.999972i	$0.497636\pi$
$368$		0			0
$369$	5131.50	−	2978.48i	0.723944	−	0.420199i
$370$		0			0
$371$	−408.983	+	477.366i	−0.0572327	+	0.0668022i
$372$		0			0
$373$	3073.51	+	5323.47i	0.426649	+	0.738978i	0.996573	−	0.0827194i	$-0.0263605\pi$
$373$	3073.51	+	5323.47i	0.426649	+	0.738978i	−0.569924	+	0.821698i	$0.693027\pi$
$374$		0			0
$375$	−1474.01	−	5475.80i	−0.202980	−	0.754050i
$376$		0			0
$377$	−3825.48			−0.522606
$378$		0			0
$379$	−17.4452			−0.00236438			−0.00118219	−	0.999999i	$-0.500376\pi$
$379$	−17.4452			−0.00236438			−0.00118219	+	0.999999i	$0.500376\pi$
$380$		0			0
$381$	−109.060	−	405.146i	−0.0146648	−	0.0544784i
$382$		0			0
$383$	5669.44	+	9819.75i	0.756383	+	1.31009i	0.944684	+	0.327982i	$0.106369\pi$
$383$	5669.44	+	9819.75i	0.756383	+	1.31009i	−0.188301	+	0.982111i	$0.560298\pi$
$384$		0			0
$385$	−3002.52	−	561.270i	−0.397462	−	0.0742986i
$386$		0			0
$387$	8651.52	−	5021.61i	1.13639	−	0.659593i
$388$		0			0
$389$	8129.57	+	4693.61i	1.05960	+	0.611762i	0.925322	−	0.379181i	$-0.123794\pi$
$389$	8129.57	+	4693.61i	1.05960	+	0.611762i	0.134281	+	0.990943i	$0.457128\pi$
$390$		0			0
$391$			63.1244i			0.00816454i
$392$		0			0
$393$	8111.96	−	8130.70i	1.04121	−	1.04361i
$394$		0			0
$395$	1267.39	−	2195.19i	0.161441	−	0.279625i
$396$		0			0
$397$	3253.52	−	1878.42i	0.411308	−	0.237469i	−0.280044	−	0.959987i	$-0.590349\pi$
$397$	3253.52	−	1878.42i	0.411308	−	0.237469i	0.691352	+	0.722518i	$0.257016\pi$
$398$		0			0
$399$	10982.5	−	7541.84i	1.37798	−	0.946276i
$400$		0			0
$401$	−13062.8	+	7541.80i	−1.62674	+	0.939201i	−0.641688	+	0.766966i	$0.721766\pi$
$401$	−13062.8	+	7541.80i	−1.62674	+	0.939201i	−0.985056	+	0.172235i	$0.944901\pi$
$402$		0			0
$403$	−2455.09	+	4252.35i	−0.303466	+	0.525619i
$404$		0			0
$405$	3506.92	−	16.1807i	0.430272	−	0.00198525i
$406$		0			0
$407$			630.280i			0.0767613i
$408$		0			0
$409$	−6394.77	−	3692.02i	−0.773108	−	0.446354i	0.0608743	−	0.998145i	$-0.480611\pi$
$409$	−6394.77	−	3692.02i	−0.773108	−	0.446354i	−0.833982	+	0.551791i	$0.813944\pi$
$410$		0			0
$411$	2814.86	−	10553.9i	0.337827	−	1.26663i
$412$		0			0
$413$	−3582.20	−	3069.04i	−0.426800	−	0.365660i
$414$		0			0
$415$	892.269	+	1545.45i	0.105542	+	0.182803i
$416$		0			0
$417$	−15072.7	+	4057.35i	−1.77005	+	0.476473i
$418$		0			0
$419$	−8290.31			−0.966606			−0.483303	−	0.875453i	$-0.660563\pi$
$419$	−8290.31			−0.966606			−0.483303	+	0.875453i	$0.660563\pi$
$420$		0			0
$421$	16466.8			1.90628			0.953140	−	0.302530i	$-0.0978314\pi$
$421$	16466.8			1.90628			0.953140	+	0.302530i	$0.0978314\pi$
$422$		0			0
$423$	−6699.42	−	3847.33i	−0.770064	−	0.442231i
$424$		0			0
$425$	5141.48	+	8905.30i	0.586820	+	1.01640i
$426$		0			0
$427$	−207.978	−	590.200i	−0.0235709	−	0.0668894i
$428$		0			0
$429$	2953.24	+	787.668i	0.332363	+	0.0886456i
$430$		0			0
$431$	−1705.81	−	984.849i	−0.190640	−	0.110066i	0.401642	−	0.915797i	$-0.368440\pi$
$431$	−1705.81	−	984.849i	−0.190640	−	0.110066i	−0.592282	+	0.805731i	$0.701773\pi$
$432$		0			0
$433$			7664.99i			0.850706i	0.905027	+	0.425353i	$0.139850\pi$
$433$			7664.99i			0.850706i	−0.905027	+	0.425353i	$0.860150\pi$
$434$		0			0
$435$	3945.59	+	3936.50i	0.434889	+	0.433887i
$436$		0			0
$437$	43.2821	−	74.9668i	0.00473790	−	0.00820628i
$438$		0			0
$439$	−6629.12	+	3827.33i	−0.720708	+	0.416101i	−0.815013	−	0.579442i	$-0.803270\pi$
$439$	−6629.12	+	3827.33i	−0.720708	+	0.416101i	0.0943054	+	0.995543i	$0.469937\pi$
$440$		0			0
$441$	9148.10	−	1441.66i	0.987809	−	0.155670i
$442$		0			0
$443$	2595.85	−	1498.71i	0.278403	−	0.160736i	−0.354297	−	0.935133i	$-0.615280\pi$
$443$	2595.85	−	1498.71i	0.278403	−	0.160736i	0.632700	+	0.774397i	$0.281947\pi$
$444$		0			0
$445$	1984.14	−	3436.64i	0.211365	−	0.366095i
$446$		0			0
$447$	−4713.31	−	4702.45i	−0.498729	−	0.497579i
$448$		0			0
$449$			1889.58i			0.198608i	0.995057	+	0.0993039i	$0.0316616\pi$
$449$			1889.58i			0.198608i	−0.995057	+	0.0993039i	$0.968338\pi$
$450$		0			0
$451$	−6524.63	−	3767.00i	−0.681226	−	0.393306i
$452$		0			0
$453$	−16591.8	−	4425.24i	−1.72086	−	0.458976i
$454$		0			0
$455$	−508.036	−	1441.70i	−0.0523453	−	0.148545i
$456$		0			0
$457$	−4738.58	−	8207.46i	−0.485036	−	0.840107i	0.514816	−	0.857300i	$-0.327860\pi$
$457$	−4738.58	−	8207.46i	−0.485036	−	0.840107i	−0.999852	+	0.0171938i	$0.994527\pi$
$458$		0			0
$459$	−13668.1	+	3713.09i	−1.38992	+	0.377587i
$460$		0			0
$461$	18908.7			1.91034			0.955171	−	0.296054i	$-0.0956707\pi$
$461$	18908.7			1.91034			0.955171	+	0.296054i	$0.0956707\pi$
$462$		0			0
$463$	−12725.2			−1.27730			−0.638649	−	0.769499i	$-0.720506\pi$
$463$	−12725.2			−1.27730			−0.638649	+	0.769499i	$0.720506\pi$
$464$		0			0
$465$	6907.94	−	1859.52i	0.688920	−	0.185448i
$466$		0			0
$467$	−3585.52	−	6210.31i	−0.355285	−	0.615372i	0.631881	−	0.775065i	$-0.282283\pi$
$467$	−3585.52	−	6210.31i	−0.355285	−	0.615372i	−0.987167	+	0.159693i	$0.948950\pi$
$468$		0			0
$469$	2473.85	+	2119.46i	0.243564	+	0.208673i
$470$		0			0
$471$	3507.04	−	13149.1i	0.343091	−	1.28637i
$472$		0			0
$473$	−11000.3	−	6351.02i	−1.06933	−	0.617379i
$474$		0			0
$475$		−	14101.3i		−	1.36213i
$476$		0			0
$477$	−916.419	+	2.11414i	−0.0879663	+	0.000202935i
$478$		0			0
$479$	1113.31	−	1928.31i	0.106197	−	0.183939i	−0.808029	−	0.589142i	$-0.799466\pi$
$479$	1113.31	−	1928.31i	0.106197	−	0.183939i	0.914227	+	0.405203i	$0.132799\pi$
$480$		0			0
$481$	−273.157	+	157.707i	−0.0258938	+	0.0149498i
$482$		0			0
$483$	49.6034	−	34.0632i	0.00467294	−	0.00320896i
$484$		0			0
$485$	−5456.34	+	3150.22i	−0.510845	+	0.294936i
$486$		0			0
$487$	−7511.82	+	13010.8i	−0.698959	+	1.21063i	0.269869	+	0.962897i	$0.413020\pi$
$487$	−7511.82	+	13010.8i	−0.698959	+	1.21063i	−0.968828	+	0.247735i	$0.920314\pi$
$488$		0			0
$489$	−4950.94	+	4962.37i	−0.457851	+	0.458908i
$490$		0			0
$491$			8830.77i			0.811664i	0.913948	+	0.405832i	$0.133018\pi$
$491$			8830.77i			0.811664i	−0.913948	+	0.405832i	$0.866982\pi$
$492$		0			0
$493$	−19493.8	−	11254.8i	−1.78085	−	1.02817i
$494$		0			0
$495$	−2235.44	−	3851.34i	−0.202981	−	0.349707i
$496$		0			0
$497$	11398.3	+	2130.72i	1.02874	+	0.192306i
$498$		0			0
$499$	4290.57	+	7431.48i	0.384914	+	0.666691i	0.991757	−	0.128131i	$-0.0408977\pi$
$499$	4290.57	+	7431.48i	0.384914	+	0.666691i	−0.606843	+	0.794822i	$0.707564\pi$
$500$		0			0
$501$	3739.40	+	13891.5i	0.333462	+	1.23878i
$502$		0			0
$503$	−13816.4			−1.22474			−0.612369	−	0.790572i	$-0.709783\pi$
$503$	−13816.4			−1.22474			−0.612369	+	0.790572i	$0.709783\pi$
$504$		0			0
$505$	−7267.73			−0.640415
$506$		0			0
$507$	−2569.80	−	9546.55i	−0.225106	−	0.836247i
$508$		0			0
$509$	−4853.13	−	8405.87i	−0.422616	−	0.731992i	0.573579	−	0.819150i	$-0.305555\pi$
$509$	−4853.13	−	8405.87i	−0.422616	−	0.731992i	−0.996194	+	0.0871587i	$0.972221\pi$
$510$		0			0
$511$	−2631.43	+	3071.41i	−0.227803	+	0.265893i
$512$		0			0
$513$	18778.2	+	4962.02i	1.61614	+	0.427054i
$514$		0			0
$515$	835.774	+	482.534i	0.0715118	+	0.0412874i
$516$		0			0
$517$			9809.82i			0.834498i
$518$		0			0
$519$	−4662.49	+	4673.26i	−0.394336	+	0.395247i
$520$		0			0
$521$	9930.86	−	17200.7i	0.835084	−	1.44641i	−0.0588781	−	0.998265i	$-0.518752\pi$
$521$	9930.86	−	17200.7i	0.835084	−	1.44641i	0.893962	−	0.448143i	$-0.147914\pi$
$522$		0			0
$523$	3046.39	−	1758.83i	0.254702	−	0.147052i	−0.367213	−	0.930137i	$-0.619688\pi$
$523$	3046.39	−	1758.83i	0.254702	−	0.147052i	0.621915	+	0.783084i	$0.286355\pi$
$524$		0			0
$525$	4223.37	−	8845.68i	0.351092	−	0.735347i
$526$		0			0
$527$	−25021.3	+	14446.0i	−2.06820	+	1.19408i
$528$		0			0
$529$	−6083.30	+	10536.6i	−0.499984	+	0.865998i
$530$		0			0
$531$	−15.8647	−	6876.88i	−0.00129655	−	0.562018i
$532$		0			0
$533$		−	3770.28i		−	0.306396i
$534$		0			0
$535$	−6185.34	−	3571.11i	−0.499842	−	0.288584i
$536$		0			0
$537$	2726.60	−	10223.0i	0.219109	−	0.821515i
$538$		0			0
$539$	−7372.31	−	9161.61i	−0.589143	−	0.732131i
$540$		0			0
$541$	1477.08	+	2558.37i	0.117383	+	0.203314i	0.918730	−	0.394886i	$-0.129216\pi$
$541$	1477.08	+	2558.37i	0.117383	+	0.203314i	−0.801347	+	0.598200i	$0.795883\pi$
$542$		0			0
$543$	7036.86	−	1894.22i	0.556134	−	0.149703i
$544$		0			0
$545$	2241.25			0.176156
$546$		0			0
$547$	19117.2			1.49432			0.747159	−	0.664645i	$-0.231417\pi$
$547$	19117.2			1.49432			0.747159	+	0.664645i	$0.231417\pi$
$548$		0			0
$549$	454.321	−	791.117i	0.0353187	−	0.0615010i
$550$		0			0
$551$	15434.0	+	26732.4i	1.19330	+	2.06686i
$552$		0			0
$553$	9203.82	−	3243.30i	0.707751	−	0.249402i
$554$		0			0
$555$	444.018	+	118.425i	0.0339595	+	0.00905744i
$556$		0			0
$557$	−21330.1	−	12315.0i	−1.62260	−	0.936806i	−0.986222	−	0.165426i	$-0.947100\pi$
$557$	−21330.1	−	12315.0i	−1.62260	−	0.936806i	−0.636374	−	0.771381i	$-0.719567\pi$
$558$		0			0
$559$		−	6356.55i		−	0.480955i
$560$		0			0
$561$	12731.7	+	12702.4i	0.958169	+	0.955961i
$562$		0			0
$563$	8786.67	−	15219.0i	0.657751	−	1.13926i	−0.323445	−	0.946247i	$-0.604841\pi$
$563$	8786.67	−	15219.0i	0.657751	−	1.13926i	0.981197	−	0.193011i	$-0.0618254\pi$
$564$		0			0
$565$	1892.84	−	1092.83i	0.140942	−	0.0813732i
$566$		0			0
$567$	10293.3	+	8736.78i	0.762399	+	0.647108i
$568$		0			0
$569$	1590.17	−	918.088i	0.117159	−	0.0676419i	−0.440275	−	0.897863i	$-0.645119\pi$
$569$	1590.17	−	918.088i	0.117159	−	0.0676419i	0.557434	+	0.830221i	$0.311786\pi$
$570$		0			0
$571$	−707.209	+	1224.92i	−0.0518315	+	0.0897748i	−0.890777	−	0.454441i	$-0.849839\pi$
$571$	−707.209	+	1224.92i	−0.0518315	+	0.0897748i	0.838946	+	0.544215i	$0.183173\pi$
$572$		0			0
$573$	−14913.8	−	14879.4i	−1.08732	−	1.08481i
$574$		0			0
$575$		−	63.6894i		−	0.00461919i
$576$		0			0
$577$	−10844.9	−	6261.33i	−0.782463	−	0.451755i	0.0548397	−	0.998495i	$-0.482535\pi$
$577$	−10844.9	−	6261.33i	−0.782463	−	0.451755i	−0.837302	+	0.546740i	$0.815869\pi$
$578$		0			0
$579$	−8758.83	−	2336.10i	−0.628678	−	0.167677i
$580$		0			0
$581$	−1262.40	+	6753.23i	−0.0901432	+	0.482223i
$582$		0			0
$583$	581.831	+	1007.76i	0.0413327	+	0.0715904i
$584$		0			0
$585$	1109.79	−	1932.49i	0.0784343	−	0.136579i
$586$		0			0
$587$	18045.5			1.26885			0.634426	−	0.772983i	$-0.281236\pi$
$587$	18045.5			1.26885			0.634426	+	0.772983i	$0.281236\pi$
$588$		0			0
$589$	39620.5			2.77170
$590$		0			0
$591$	−25394.4	+	6835.83i	−1.76749	+	0.475784i
$592$		0			0
$593$	9283.24	+	16079.0i	0.642861	+	1.11347i	0.984791	+	0.173743i	$0.0555862\pi$
$593$	9283.24	+	16079.0i	0.642861	+	1.11347i	−0.341930	+	0.939726i	$0.611080\pi$
$594$		0			0
$595$	1652.72	−	8841.28i	0.113874	−	0.609171i
$596$		0			0
$597$	1970.67	−	7388.73i	0.135099	−	0.506533i
$598$		0			0
$599$	4258.02	+	2458.37i	0.290447	+	0.167690i	0.638143	−	0.769917i	$-0.279703\pi$
$599$	4258.02	+	2458.37i	0.290447	+	0.167690i	−0.347696	+	0.937607i	$0.613036\pi$
$600$		0			0
$601$		−	16157.9i		−	1.09666i	−0.836262	−	0.548330i	$-0.815264\pi$
$601$		−	16157.9i		−	1.09666i	0.836262	−	0.548330i	$-0.184736\pi$
$602$		0			0
$603$	10.9561	+	4749.14i	0.000739910	+	0.320730i
$604$		0			0
$605$	374.236	−	648.196i	0.0251485	−	0.0435585i
$606$		0			0
$607$	−9043.22	+	5221.10i	−0.604700	+	0.349124i	−0.770888	−	0.636970i	$-0.780187\pi$
$607$	−9043.22	+	5221.10i	−0.604700	+	0.349124i	0.166188	+	0.986094i	$0.446854\pi$
$608$		0			0
$609$	1675.23	+	21391.6i	0.111468	+	1.42337i
$610$		0			0
$611$	−4251.48	+	2454.59i	−0.281500	+	0.162524i
$612$		0			0
$613$	−5235.58	+	9068.30i	−0.344965	+	0.597496i	−0.985347	−	0.170560i	$-0.945442\pi$
$613$	−5235.58	+	9068.30i	−0.344965	+	0.597496i	0.640383	+	0.768056i	$0.278776\pi$
$614$		0			0
$615$	−3879.70	+	3888.66i	−0.254381	+	0.254969i
$616$		0			0
$617$			7308.93i			0.476899i	0.971155	+	0.238449i	$0.0766391\pi$
$617$			7308.93i			0.476899i	−0.971155	+	0.238449i	$0.923361\pi$
$618$		0			0
$619$	14616.4	+	8438.76i	0.949082	+	0.547953i	0.892796	−	0.450462i	$-0.148741\pi$
$619$	14616.4	+	8438.76i	0.949082	+	0.547953i	0.0562861	+	0.998415i	$0.482074\pi$
$620$		0			0
$621$	84.8130	+	22.4113i	0.00548056	+	0.00144820i
$622$		0			0
$623$	14408.9	−	5077.49i	0.926613	−	0.326526i
$624$		0			0
$625$	−3741.11	−	6479.80i	−0.239431	−	0.414707i
$626$		0			0
$627$	−6410.67	−	23815.0i	−0.408321	−	1.51688i
$628$		0			0
$629$	−1855.93			−0.117648
$630$		0			0
$631$	27123.5			1.71120			0.855601	−	0.517635i	$-0.173188\pi$
$631$	27123.5			1.71120			0.855601	+	0.517635i	$0.173188\pi$
$632$		0			0
$633$	6767.60	+	25141.0i	0.424941	+	1.57862i
$634$		0			0
$635$	194.220	+	336.398i	0.0121376	+	0.0210229i
$636$		0			0
$637$	2125.87	−	5487.49i	0.132229	−	0.341322i
$638$		0			0
$639$	8486.29	+	14620.7i	0.525371	+	0.905141i
$640$		0			0
$641$	3189.14	+	1841.25i	0.196511	+	0.113455i	0.595027	−	0.803706i	$-0.297141\pi$
$641$	3189.14	+	1841.25i	0.196511	+	0.113455i	−0.398516	+	0.917161i	$0.630475\pi$
$642$		0			0
$643$			14488.3i			0.888588i	0.895881	+	0.444294i	$0.146546\pi$
$643$			14488.3i			0.888588i	−0.895881	+	0.444294i	$0.853454\pi$
$644$		0			0
$645$	−6541.03	+	6556.14i	−0.399307	+	0.400229i
$646$		0			0
$647$	6085.96	−	10541.2i	0.369805	−	0.640520i	−0.619730	−	0.784815i	$-0.712758\pi$
$647$	6085.96	−	10541.2i	0.369805	−	0.640520i	0.989535	+	0.144295i	$0.0460913\pi$
$648$		0			0
$649$	−7562.32	+	4366.11i	−0.457391	+	0.264075i
$650$		0			0
$651$	24853.7	+	11866.4i	1.49631	+	0.714412i
$652$		0			0
$653$	−7276.24	+	4200.94i	−0.436051	+	0.251754i	−0.701921	−	0.712255i	$-0.747674\pi$
$653$	−7276.24	+	4200.94i	−0.436051	+	0.251754i	0.265870	+	0.964009i	$0.414341\pi$
$654$		0			0
$655$	−5316.59	+	9208.60i	−0.317155	+	0.549328i
$656$		0			0
$657$	−5896.32	+	13.6026i	−0.350133	+	0.000807742i
$658$		0			0
$659$		−	9814.94i		−	0.580175i	−0.957000	−	0.290088i	$-0.906316\pi$
$659$		−	9814.94i		−	0.580175i	0.957000	−	0.290088i	$-0.0936845\pi$
$660$		0			0
$661$	−1870.41	−	1079.88i	−0.110061	−	0.0635438i	0.443959	−	0.896047i	$-0.353574\pi$
$661$	−1870.41	−	1079.88i	−0.110061	−	0.0635438i	−0.554020	+	0.832503i	$0.686907\pi$
$662$		0			0
$663$	−2319.38	+	8696.15i	−0.135863	+	0.509397i
$664$		0			0
$665$	−8024.92	+	9366.73i	−0.467960	+	0.546205i
$666$		0			0
$667$	69.7085	+	120.739i	0.00404666	+	0.00700903i
$668$		0			0
$669$	−22067.8	+	5940.35i	−1.27532	+	0.343299i
$670$		0			0
$671$	−1158.42			−0.0666470
$672$		0			0
$673$	−14794.4			−0.847372			−0.423686	−	0.905809i	$-0.639264\pi$
$673$	−14794.4			−0.847372			−0.423686	+	0.905809i	$0.639264\pi$
$674$		0			0
$675$	13790.4	−	3746.33i	0.786362	−	0.213624i
$676$		0			0
$677$	5190.37	+	8989.98i	0.294656	+	0.510359i	0.974905	−	0.222622i	$-0.0714616\pi$
$677$	5190.37	+	8989.98i	0.294656	+	0.510359i	−0.680249	+	0.732981i	$0.738128\pi$
$678$		0			0
$679$	−23842.8	−	4457.00i	−1.34757	−	0.251906i
$680$		0			0
$681$	−20687.5	−	5517.64i	−1.16409	−	0.310479i
$682$		0			0
$683$	3799.53	+	2193.66i	0.212862	+	0.122896i	0.602641	−	0.798013i	$-0.294115\pi$
$683$	3799.53	+	2193.66i	0.212862	+	0.122896i	−0.389779	+	0.920909i	$0.627448\pi$
$684$		0			0
$685$			10112.4i			0.564052i
$686$		0			0
$687$	1926.38	+	1921.94i	0.106981	+	0.106735i
$688$		0			0
$689$	−291.169	+	504.319i	−0.0160996	+	0.0278854i
$690$		0			0
$691$	15808.1	−	9126.79i	0.870285	−	0.502459i	0.00284192	−	0.999996i	$-0.499095\pi$
$691$	15808.1	−	9126.79i	0.870285	−	0.502459i	0.867443	+	0.497537i	$0.165762\pi$
$692$		0			0
$693$	3111.28	−	16859.1i	0.170545	−	0.924132i
$694$		0			0
$695$	12515.0	−	7225.57i	0.683054	−	0.394362i
$696$		0			0
$697$	11092.4	−	19212.5i	0.602802	−	1.04408i
$698$		0			0
$699$	17373.1	+	17333.1i	0.940075	+	0.937909i
$700$		0			0
$701$		−	8709.47i		−	0.469261i	−0.972085	−	0.234631i	$-0.924612\pi$
$701$		−	8709.47i		−	0.469261i	0.972085	−	0.234631i	$-0.0753880\pi$
$702$		0			0
$703$	2204.11	+	1272.55i	0.118250	+	0.0682716i
$704$		0			0
$705$	6910.79	+	1843.20i	0.369185	+	0.0984666i
$706$		0			0
$707$	−21247.9	−	18204.1i	−1.13028	−	0.968368i
$708$		0			0
$709$	9585.59	+	16602.7i	0.507749	+	0.879448i	0.999960	+	0.00897144i	$0.00285574\pi$
$709$	9585.59	+	16602.7i	0.507749	+	0.879448i	−0.492210	+	0.870476i	$0.663811\pi$
$710$		0			0
$711$	12337.0	+	7084.87i	0.650736	+	0.373704i
$712$		0			0
$713$	178.948			0.00939926
$714$		0			0
$715$	−2829.71			−0.148007
$716$		0			0
$717$	−35920.9	+	9669.40i	−1.87098	+	0.503641i
$718$		0			0
$719$	1665.92	+	2885.46i	0.0864094	+	0.149666i	0.905991	−	0.423297i	$-0.139127\pi$
$719$	1665.92	+	2885.46i	0.0864094	+	0.149666i	−0.819582	+	0.572963i	$0.805794\pi$
$720$		0			0
$721$	1234.82	+	3504.17i	0.0637825	+	0.181002i
$722$		0			0
$723$	−3773.84	+	14149.4i	−0.194122	+	0.727832i
$724$		0			0
$725$	19668.3	+	11355.5i	1.00754	+	0.581701i
$726$		0			0
$727$			690.120i			0.0352065i	0.999845	+	0.0176033i	$0.00560358\pi$
$727$			690.120i			0.0352065i	−0.999845	+	0.0176033i	$0.994396\pi$
$728$		0			0
$729$	136.222	+	19682.5i	0.00692081	+	0.999976i
$730$		0			0
$731$	18701.3	−	32391.6i	0.946228	−	1.63892i
$732$		0			0
$733$	15627.7	−	9022.68i	0.787482	−	0.454653i	−0.0515936	−	0.998668i	$-0.516430\pi$
$733$	15627.7	−	9022.68i	0.787482	−	0.454653i	0.839075	+	0.544015i	$0.183097\pi$
$734$		0			0
$735$	−7839.36	+	3472.22i	−0.393414	+	0.174251i
$736$		0			0
$737$	5222.50	−	3015.21i	0.261022	−	0.150701i
$738$		0			0
$739$	−9638.45	+	16694.3i	−0.479778	+	0.831001i	−0.999731	−	0.0231946i	$-0.992616\pi$
$739$	−9638.45	+	16694.3i	−0.479778	+	0.831001i	0.519953	+	0.854195i	$0.325950\pi$
$740$		0			0
$741$	8717.14	−	8737.27i	0.432162	−	0.433160i
$742$		0			0
$743$		−	843.042i		−	0.0416261i	−0.999783	−	0.0208131i	$-0.993375\pi$
$743$		−	843.042i		−	0.0416261i	0.999783	−	0.0208131i	$-0.00662549\pi$
$744$		0			0
$745$	5338.16	+	3081.99i	0.262517	+	0.151564i
$746$		0			0
$747$	−8662.39	+	5027.91i	−0.424284	+	0.246267i
$748$		0			0
$749$	−9138.58	−	25933.4i	−0.445816	−	1.26514i
$750$		0			0
$751$	−11343.3	−	19647.2i	−0.551162	−	0.954640i	−0.998191	−	0.0601209i	$-0.980851\pi$
$751$	−11343.3	−	19647.2i	−0.551162	−	0.954640i	0.447029	−	0.894519i	$-0.352482\pi$
$752$		0			0
$753$	−3284.02	−	12199.8i	−0.158933	−	0.590420i
$754$		0			0
$755$	15897.7			0.766328
$756$		0			0
$757$	−37545.5			−1.80266			−0.901330	−	0.433133i	$-0.857408\pi$
$757$	−37545.5			−1.80266			−0.901330	+	0.433133i	$0.857408\pi$
$758$		0			0
$759$	−28.9542	−	107.562i	−0.00138468	−	0.00514395i
$760$		0			0
$761$	−17635.9	−	30546.3i	−0.840080	−	1.45506i	−0.889826	−	0.456300i	$-0.849174\pi$
$761$	−17635.9	−	30546.3i	−0.840080	−	1.45506i	0.0497457	−	0.998762i	$-0.484159\pi$
$762$		0			0
$763$	6552.53	+	5613.87i	0.310901	+	0.266364i
$764$		0			0
$765$	11340.7	−	6582.50i	0.535980	−	0.311099i
$766$		0			0
$767$	−3784.45	−	2184.96i	−0.178160	−	0.102861i
$768$		0			0
$769$		−	3431.91i		−	0.160934i	−0.996757	−	0.0804668i	$-0.974359\pi$
$769$		−	3431.91i		−	0.160934i	0.996757	−	0.0804668i	$-0.0256411\pi$
$770$		0			0
$771$	4882.07	−	4893.35i	0.228046	−	0.228573i
$772$		0			0
$773$	−1780.10	+	3083.22i	−0.0828275	+	0.143461i	−0.904463	−	0.426551i	$-0.859728\pi$
$773$	−1780.10	+	3083.22i	−0.0828275	+	0.143461i	0.821636	+	0.570013i	$0.193062\pi$
$774$		0			0
$775$	25245.2	−	14575.3i	1.17011	−	0.675564i
$776$		0			0
$777$	1001.50	+	1458.40i	0.0462402	+	0.0673356i
$778$		0			0
$779$	−26346.7	+	15211.3i	−1.21177	+	0.699615i
$780$		0			0
$781$	10732.9	−	18590.0i	0.491747	−	0.851731i
$782$		0			0
$783$	−22042.7	+	22195.8i	−1.00606	+	1.01304i
$784$		0			0
$785$			12599.1i			0.572842i
$786$		0			0
$787$	1990.24	+	1149.07i	0.0901453	+	0.0520454i	0.544395	−	0.838829i	$-0.316759\pi$
$787$	1990.24	+	1149.07i	0.0901453	+	0.0520454i	−0.454250	+	0.890874i	$0.650093\pi$
$788$		0			0
$789$	6129.36	−	22981.1i	0.276566	−	1.03694i
$790$		0			0
$791$	8271.23	+	1546.16i	0.371796	+	0.0695009i
$792$		0			0
$793$	−289.856	−	502.046i	−0.0129800	−	0.0224819i
$794$		0			0
$795$	819.266	−	220.535i	0.0365489	−	0.00983845i
$796$		0			0
$797$	−29634.9			−1.31709			−0.658546	−	0.752541i	$-0.728828\pi$
$797$	−29634.9			−1.31709			−0.658546	+	0.752541i	$0.728828\pi$
$798$		0			0
$799$	−28886.1			−1.27900
$800$		0			0
$801$	19314.0	+	11091.6i	0.851968	+	0.489267i
$802$		0			0
$803$	3743.55	+	6484.01i	0.164517	+	0.284951i
$804$		0			0
$805$	−36.2451	+	42.3054i	−0.00158692	+	0.00185226i
$806$		0			0
$807$	5211.85	+	1390.07i	0.227343	+	0.0606354i
$808$		0			0
$809$	−16234.4	−	9372.91i	−0.705525	−	0.407335i	0.103877	−	0.994590i	$-0.466875\pi$
$809$	−16234.4	−	9372.91i	−0.705525	−	0.407335i	−0.809402	+	0.587255i	$0.800209\pi$
$810$		0			0
$811$		−	17950.4i		−	0.777218i	−0.921403	−	0.388609i	$-0.872956\pi$
$811$		−	17950.4i		−	0.777218i	0.921403	−	0.388609i	$-0.127044\pi$
$812$		0			0
$813$	−16545.7	−	16507.6i	−0.713756	−	0.712112i
$814$		0			0
$815$	3244.85	−	5620.24i	0.139463	−	0.241557i
$816$		0			0
$817$	−44419.5	+	25645.6i	−1.90213	+	1.09820i
$818$		0			0
$819$	8085.05	−	2870.05i	0.344951	−	0.122451i
$820$		0			0
$821$	31560.6	−	18221.5i	1.34162	−	0.774586i	0.354576	−	0.935027i	$-0.384625\pi$
$821$	31560.6	−	18221.5i	1.34162	−	0.774586i	0.987045	+	0.160441i	$0.0512918\pi$
$822$		0			0
$823$	2827.83	−	4897.94i	0.119771	−	0.207450i	−0.799906	−	0.600126i	$-0.795117\pi$
$823$	2827.83	−	4897.94i	0.119771	−	0.207450i	0.919677	+	0.392676i	$0.128451\pi$
$824$		0			0
$825$	−12845.7	−	12816.1i	−0.542095	−	0.540846i
$826$		0			0
$827$		−	37188.1i		−	1.56367i	−0.623483	−	0.781837i	$-0.714283\pi$
$827$		−	37188.1i		−	1.56367i	0.623483	−	0.781837i	$-0.285717\pi$
$828$		0			0
$829$	12258.2	+	7077.29i	0.513565	+	0.296507i	0.734298	−	0.678827i	$-0.237511\pi$
$829$	12258.2	+	7077.29i	0.513565	+	0.296507i	−0.220733	+	0.975334i	$0.570845\pi$
$830$		0			0
$831$	3170.10	+	845.508i	0.132334	+	0.0352952i
$832$		0			0
$833$	26977.4	−	21708.6i	1.12210	−	0.902952i
$834$		0			0
$835$	−6659.34	−	11534.3i	−0.275995	−	0.478038i
$836$		0			0
$837$	10526.1	+	38747.1i	0.434689	+	1.60011i
$838$		0			0
$839$	30349.4			1.24884			0.624421	−	0.781088i	$-0.285335\pi$
$839$	30349.4			1.24884			0.624421	+	0.781088i	$0.285335\pi$
$840$		0			0
$841$	−25325.8			−1.03841
$842$		0			0
$843$	−27795.3	+	7482.10i	−1.13561	+	0.305691i
$844$		0			0
$845$	4576.44	+	7926.63i	0.186313	+	0.322703i
$846$		0			0
$847$	2717.71	−	957.683i	0.110250	−	0.0388505i
$848$		0			0
$849$	5684.17	−	21311.9i	0.229776	−	0.861511i
$850$		0			0
$851$	9.95502	+	5.74753i	0.000401003	+	0.000231519i
$852$		0			0
$853$			44235.1i			1.77559i	0.460235	+	0.887797i	$0.347765\pi$
$853$			44235.1i			1.77559i	−0.460235	+	0.887797i	$0.652235\pi$
$854$		0			0
$855$	−17981.7	+	41.4830i	−0.719252	+	0.00165928i
$856$		0			0
$857$	10452.8	−	18104.8i	0.416642	−	0.721645i	−0.578957	−	0.815358i	$-0.696540\pi$
$857$	10452.8	−	18104.8i	0.416642	−	0.721645i	0.995599	+	0.0937129i	$0.0298736\pi$
$858$		0			0
$859$	−977.718	+	564.486i	−0.0388351	+	0.0224214i	−0.519292	−	0.854597i	$-0.673804\pi$
$859$	−977.718	+	564.486i	−0.0388351	+	0.0224214i	0.480457	+	0.877018i	$0.340471\pi$
$860$		0			0
$861$	−21083.0	+	1651.06i	−0.834501	+	0.0653519i
$862$		0			0
$863$	−17175.9	+	9916.54i	−0.677493	+	0.391151i	−0.798910	−	0.601451i	$-0.794589\pi$
$863$	−17175.9	+	9916.54i	−0.677493	+	0.391151i	0.121417	+	0.992602i	$0.461256\pi$
$864$		0			0
$865$	3055.80	−	5292.80i	0.120116	−	0.208047i
$866$		0			0
$867$	−19372.9	+	19417.6i	−0.758867	+	0.760619i
$868$		0			0
$869$		−	18064.8i		−	0.705186i
$870$		0			0
$871$	2613.53	+	1508.92i	0.101672	+	0.0587001i
$872$		0			0
$873$	−17751.4	−	30583.2i	−0.688195	−	1.18566i
$874$		0			0
$875$	−3713.90	+	19867.6i	−0.143489	+	0.767596i
$876$		0			0
$877$	7722.35	+	13375.5i	0.297338	+	0.515004i	0.975526	−	0.219884i	$-0.0705680\pi$
$877$	7722.35	+	13375.5i	0.297338	+	0.515004i	−0.678188	+	0.734888i	$0.737235\pi$
$878$		0			0
$879$	−2665.31	−	9901.37i	−0.102274	−	0.379937i
$880$		0			0
$881$	9043.98			0.345856			0.172928	−	0.984934i	$-0.444677\pi$
$881$	9043.98			0.345856			0.172928	+	0.984934i	$0.444677\pi$
$882$		0			0
$883$	−15055.4			−0.573787			−0.286894	−	0.957962i	$-0.592623\pi$
$883$	−15055.4			−0.573787			−0.286894	+	0.957962i	$0.592623\pi$
$884$		0			0
$885$	1654.91	+	6147.84i	0.0628579	+	0.233511i
$886$		0			0
$887$	−14220.9	−	24631.3i	−0.538322	−	0.932401i	−0.998995	−	0.0448306i	$-0.985725\pi$
$887$	−14220.9	−	24631.3i	−0.538322	−	0.932401i	0.460673	−	0.887570i	$-0.347608\pi$
$888$		0			0
$889$	−274.786	+	1469.97i	−0.0103667	+	0.0554570i
$890$		0			0
$891$	21586.9	−	12596.4i	0.811659	−	0.473618i
$892$		0			0
$893$	34305.3	+	19806.2i	1.28554	+	0.742204i
$894$		0			0
$895$			9795.35i			0.365835i
$896$		0			0
$897$	39.3715	−	39.4624i	0.00146553	−	0.00146891i
$898$		0			0
$899$	−31905.6	+	55262.2i	−1.18366	+	2.05016i
$900$		0			0
$901$	−2967.47	+	1713.27i	−0.109723	+	0.0633488i
$902$		0			0
$903$	−35545.1	+	2783.63i	−1.30993	+	0.102584i
$904$		0			0
$905$	−5842.80	+	3373.34i	−0.214609	+	0.123905i
$906$		0			0
$907$	14570.3	−	25236.4i	0.533404	−	0.923883i	−0.465834	−	0.884872i	$-0.654246\pi$
$907$	14570.3	−	25236.4i	0.533404	−	0.923883i	0.999239	−	0.0390115i	$-0.0124209\pi$
$908$		0			0
$909$	−94.1020	−	40790.5i	−0.00343363	−	1.48838i
$910$		0			0
$911$		−	14257.6i		−	0.518525i	−0.965807	−	0.259263i	$-0.916520\pi$
$911$		−	14257.6i		−	0.518525i	0.965807	−	0.259263i	$-0.0834795\pi$
$912$		0			0
$913$	11014.1	+	6358.99i	0.399248	+	0.230506i
$914$		0			0
$915$	−217.659	+	816.077i	−0.00786402	+	0.0294849i
$916$		0			0
$917$	−38609.2	+	13605.3i	−1.39039	+	0.489954i
$918$		0			0
$919$	−10769.5	−	18653.3i	−0.386563	−	0.669548i	0.605421	−	0.795905i	$-0.293005\pi$
$919$	−10769.5	−	18653.3i	−0.386563	−	0.669548i	−0.991985	+	0.126358i	$0.959671\pi$
$920$		0			0
$921$	13029.9	−	3507.45i	0.466176	−	0.125488i
$922$		0			0
$923$	10742.3			0.383084
$924$		0			0
$925$	1872.55			0.0665610
$926$		0			0
$927$	−2697.42	+	4697.07i	−0.0955718	+	0.166421i
$928$		0			0
$929$	9507.93	+	16468.2i	0.335786	+	0.581598i	0.983636	−	0.180170i	$-0.0576648\pi$
$929$	9507.93	+	16468.2i	0.335786	+	0.581598i	−0.647849	+	0.761768i	$0.724331\pi$
$930$		0			0
$931$	−46923.3	+	7283.82i	−1.65183	+	0.256410i
$932$		0			0
$933$	1634.02	+	435.814i	0.0573369	+	0.0152925i
$934$		0			0
$935$	−14419.6	−	8325.14i	−0.504353	−	0.291188i
$936$		0			0
$937$			13655.6i			0.476105i	0.971252	+	0.238052i	$0.0765090\pi$
$937$			13655.6i			0.476105i	−0.971252	+	0.238052i	$0.923491\pi$
$938$		0			0
$939$	−2356.12	−	2350.69i	−0.0818841	−	0.0816954i
$940$		0			0
$941$	−13850.3	+	23989.4i	−0.479815	+	0.831065i	−0.999732	−	0.0231524i	$-0.992630\pi$
$941$	−13850.3	+	23989.4i	−0.479815	+	0.831065i	0.519917	+	0.854217i	$0.325963\pi$
$942$		0			0
$943$	−118.996	+	68.7026i	−0.00410929	+	0.00237250i
$944$		0			0
$945$	−11292.2	−	5359.53i	−0.388716	−	0.184493i
$946$		0			0
$947$	15651.0	−	9036.10i	0.537052	−	0.310067i	−0.206831	−	0.978377i	$-0.566315\pi$
$947$	15651.0	−	9036.10i	0.537052	−	0.310067i	0.743883	+	0.668309i	$0.232982\pi$
$948$		0			0
$949$	−1873.40	+	3244.83i	−0.0640814	+	0.110992i
$950$		0			0
$951$	28103.2	+	28038.4i	0.958262	+	0.956054i
$952$		0			0
$953$			13088.1i			0.444874i	0.974947	+	0.222437i	$0.0714012\pi$
$953$			13088.1i			0.444874i	−0.974947	+	0.222437i	$0.928599\pi$
$954$		0			0
$955$	16891.0	+	9752.00i	0.572334	+	0.330437i
$956$		0			0
$957$	38379.3	+	10236.3i	1.29637	+	0.345760i
$958$		0			0
$959$	−25329.5	+	29564.7i	−0.852900	+	0.995509i
$960$		0			0
$961$	26056.9	+	45131.9i	0.874657	+	1.51495i
$962$		0			0
$963$	19962.9	−	34761.7i	0.668012	−	1.16322i
$964$		0			0
$965$	8392.45			0.279961
$966$		0			0
$967$	37827.6			1.25796			0.628982	−	0.777420i	$-0.283472\pi$
$967$	37827.6			1.25796			0.628982	+	0.777420i	$0.283472\pi$
$968$		0			0
$969$	70126.1	−	18877.0i	2.32485	−	0.625816i
$970$		0			0
$971$	−386.167	−	668.861i	−0.0127628	−	0.0221059i	0.859573	−	0.511012i	$-0.170729\pi$
$971$	−386.167	−	668.861i	−0.0127628	−	0.0221059i	−0.872336	+	0.488906i	$0.837396\pi$
$972$		0			0
$973$	54687.5	+	10222.9i	1.80185	+	0.336825i
$974$		0			0
$975$	2340.14	−	8773.99i	0.0768661	−	0.288198i
$976$		0			0
$977$	−3885.24	−	2243.15i	−0.127226	−	0.0734540i	0.435036	−	0.900413i	$-0.356736\pi$
$977$	−3885.24	−	2243.15i	−0.127226	−	0.0734540i	−0.562262	+	0.826959i	$0.690069\pi$
$978$		0			0
$979$		−	28281.1i		−	0.923255i
$980$		0			0
$981$	29.0196	+	12579.1i	0.000944469	+	0.409400i
$982$		0			0
$983$	−19328.8	+	33478.4i	−0.627153	+	1.08626i	0.360967	+	0.932579i	$0.382447\pi$
$983$	−19328.8	+	33478.4i	−0.627153	+	1.08626i	−0.988120	+	0.153683i	$0.950887\pi$
$984$		0			0
$985$	21085.4	−	12173.6i	0.682066	−	0.393791i
$986$		0			0
$987$	15587.6	+	22698.8i	0.502693	+	0.732029i
$988$		0			0
$989$	−200.624	+	115.830i	−0.00645041	+	0.00372415i
$990$		0			0
$991$	20930.9	−	36253.4i	0.670932	−	1.16209i	−0.306709	−	0.951803i	$-0.599228\pi$
$991$	20930.9	−	36253.4i	0.670932	−	1.16209i	0.977640	−	0.210284i	$-0.0674389\pi$
$992$		0			0
$993$	18042.3	−	18084.0i	0.576591	−	0.577923i
$994$		0			0
$995$			7079.66i			0.225568i
$996$		0			0
$997$	−20276.7	−	11706.8i	−0.644103	−	0.371873i	0.142090	−	0.989854i	$-0.454618\pi$
$997$	−20276.7	−	11706.8i	−0.644103	−	0.371873i	−0.786193	+	0.617981i	$0.787951\pi$
$998$		0			0
$999$	−658.920	+	2493.61i	−0.0208682	+	0.0789732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.u.a.17.11	yes	48
3.2	odd	2	inner	168.4.u.a.17.2	✓	48
4.3	odd	2		336.4.bc.f.17.14		48
7.5	odd	6	inner	168.4.u.a.89.2	yes	48
12.11	even	2		336.4.bc.f.17.23		48
21.5	even	6	inner	168.4.u.a.89.11	yes	48
28.19	even	6		336.4.bc.f.257.23		48
84.47	odd	6		336.4.bc.f.257.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.2	✓	48	3.2	odd	2	inner
168.4.u.a.17.11	yes	48	1.1	even	1	trivial
168.4.u.a.89.2	yes	48	7.5	odd	6	inner
168.4.u.a.89.11	yes	48	21.5	even	6	inner
336.4.bc.f.17.14		48	4.3	odd	2
336.4.bc.f.17.23		48	12.11	even	2
336.4.bc.f.257.14		48	84.47	odd	6
336.4.bc.f.257.23		48	28.19	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35065 - 5.01754i) q^{3} +(2.40532 + 4.16613i) q^{5} +(-3.40309 + 18.2049i) q^{7} +(-23.3515 + 13.5539i) q^{9} +(29.6911 + 17.1421i) q^{11} +17.1571i q^{13} +(17.6550 - 17.6958i) q^{15} +(-50.4770 + 87.4288i) q^{17} +(119.893 - 69.2205i) q^{19} +(95.9403 - 7.51333i) q^{21} +(0.541507 - 0.312639i) q^{23} +(50.9289 - 88.2114i) q^{25} +(99.5470 + 98.8605i) q^{27} +222.968i q^{29} +(247.848 + 143.095i) q^{31} +(45.9092 - 172.129i) q^{33} +(-84.0296 + 29.6109i) q^{35} +(9.19197 + 15.9210i) q^{37} +(86.0864 - 23.1732i) q^{39} -219.751 q^{41} -370.491 q^{43} +(-112.635 - 64.6839i) q^{45} +(143.066 + 247.797i) q^{47} +(-319.838 - 123.906i) q^{49} +(506.855 + 135.185i) q^{51} +(29.3942 + 16.9708i) q^{53} +164.929i q^{55} +(-509.251 - 508.078i) q^{57} +(-127.350 + 220.577i) q^{59} +(-29.2617 + 16.8943i) q^{61} +(-167.280 - 471.237i) q^{63} +(-71.4787 + 41.2683i) q^{65} +(87.9473 - 152.329i) q^{67} +(-2.30007 - 2.29477i) q^{69} -626.114i q^{71} +(189.125 + 109.191i) q^{73} +(-511.392 - 136.395i) q^{75} +(-413.113 + 482.187i) q^{77} +(-263.456 - 456.319i) q^{79} +(361.583 - 633.008i) q^{81} +370.957 q^{83} -485.653 q^{85} +(1118.75 - 301.152i) q^{87} +(-412.449 - 714.383i) q^{89} +(-312.343 - 58.3872i) q^{91} +(383.230 - 1436.86i) q^{93} +(576.764 + 332.995i) q^{95} +1309.69i q^{97} +(-925.674 + 2.13549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 14 q^{9} - 88 q^{15} - 270 q^{19} + 50 q^{21} - 438 q^{25} + 216 q^{31} - 372 q^{33} + 66 q^{37} + 242 q^{39} + 900 q^{43} - 294 q^{45} + 60 q^{49} - 138 q^{51} + 1384 q^{57} + 108 q^{61}+ \cdots + 1988 q^{99}+O(q^{100}) \) 48 * q + 12 * q^7 + 14 * q^9 - 88 * q^15 - 270 * q^19 + 50 * q^21 - 438 * q^25 + 216 * q^31 - 372 * q^33 + 66 * q^37 + 242 * q^39 + 900 * q^43 - 294 * q^45 + 60 * q^49 - 138 * q^51 + 1384 * q^57 + 108 * q^61 + 1096 * q^63 + 6 * q^67 - 1206 * q^73 - 594 * q^75 - 588 * q^79 - 54 * q^81 - 240 * q^85 - 3522 * q^87 + 234 * q^91 - 608 * q^93 + 1988 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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