LMFDB - Embedded newform 336.4.bc.f.257.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(17,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, 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("336.17"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.23
Character	$\chi$	$=$	336.257
Dual form			336.4.bc.f.17.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.02065 + 1.33907i) q^{3} +(-2.40532 + 4.16613i) q^{5} +(3.40309 + 18.2049i) q^{7} +(23.4138 + 13.4460i) q^{9} +(29.6911 - 17.1421i) q^{11} -17.1571i q^{13} +(-17.6550 + 17.6958i) q^{15} +(50.4770 + 87.4288i) q^{17} +(-119.893 - 69.2205i) q^{19} +(-7.29198 + 95.9574i) q^{21} +(0.541507 + 0.312639i) q^{23} +(50.9289 + 88.2114i) q^{25} +(99.5470 + 98.8605i) q^{27} +222.968i q^{29} +(-247.848 + 143.095i) q^{31} +(172.023 - 46.3061i) q^{33} +(-84.0296 - 29.6109i) q^{35} +(9.19197 - 15.9210i) q^{37} +(22.9746 - 86.1397i) q^{39} +219.751 q^{41} +370.491 q^{43} +(-112.335 + 65.2029i) q^{45} +(143.066 - 247.797i) q^{47} +(-319.838 + 123.906i) q^{49} +(136.354 + 506.541i) q^{51} +(-29.3942 + 16.9708i) q^{53} +164.929i q^{55} +(-509.251 - 508.078i) q^{57} +(-127.350 - 220.577i) q^{59} +(-29.2617 - 16.8943i) q^{61} +(-165.104 + 472.004i) q^{63} +(71.4787 + 41.2683i) q^{65} +(-87.9473 - 152.329i) q^{67} +(2.30007 + 2.29477i) q^{69} +626.114i q^{71} +(189.125 - 109.191i) q^{73} +(137.574 + 511.076i) q^{75} +(413.113 + 482.187i) q^{77} +(263.456 - 456.319i) q^{79} +(367.409 + 629.644i) q^{81} +370.957 q^{83} -485.653 q^{85} +(-298.571 + 1119.44i) q^{87} +(412.449 - 714.383i) q^{89} +(312.343 - 58.3872i) q^{91} +(-1435.97 + 386.543i) q^{93} +(576.764 - 332.995i) q^{95} -1309.69i q^{97} +(925.674 - 2.13549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	5.02065	+	1.33907i	0.966224	+	0.257705i
$3$	5.02065	+	1.33907i	0.966224	+	0.257705i
$4$		0			0
$5$	−2.40532	+	4.16613i	−0.215138	+	0.372630i	−0.953315	−	0.301977i	$-0.902354\pi$
$5$	−2.40532	+	4.16613i	−0.215138	+	0.372630i	0.738177	+	0.674607i	$0.235687\pi$
$6$		0			0
$7$	3.40309	+	18.2049i	0.183750	+	0.982973i
$7$	3.40309	+	18.2049i	0.183750	+	0.982973i
$8$		0			0
$9$	23.4138	+	13.4460i	0.867177	+	0.498001i
$10$		0			0
$11$	29.6911	−	17.1421i	0.813836	−	0.469868i	−0.0344503	−	0.999406i	$-0.510968\pi$
$11$	29.6911	−	17.1421i	0.813836	−	0.469868i	0.848286	+	0.529538i	$0.177635\pi$
$12$		0			0
$13$		−	17.1571i		−	0.366040i	−0.983109	−	0.183020i	$-0.941413\pi$
$13$		−	17.1571i		−	0.366040i	0.983109	−	0.183020i	$-0.0585873\pi$
$14$		0			0
$15$	−17.6550	+	17.6958i	−0.303900	+	0.304602i
$16$		0			0
$17$	50.4770	+	87.4288i	0.720146	+	1.24733i	0.960941	+	0.276753i	$0.0892584\pi$
$17$	50.4770	+	87.4288i	0.720146	+	1.24733i	−0.240795	+	0.970576i	$0.577408\pi$
$18$		0			0
$19$	−119.893	−	69.2205i	−1.44766	−	0.835804i	−0.449314	−	0.893374i	$-0.648331\pi$
$19$	−119.893	−	69.2205i	−1.44766	−	0.835804i	−0.998341	+	0.0575700i	$0.981665\pi$
$20$		0			0
$21$	−7.29198	+	95.9574i	−0.0757734	+	0.997125i
$22$		0			0
$23$	0.541507	+	0.312639i	0.00490922	+	0.00283434i	0.502453	−	0.864605i	$-0.332431\pi$
$23$	0.541507	+	0.312639i	0.00490922	+	0.00283434i	−0.497543	+	0.867439i	$0.665764\pi$
$24$		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	$-0.977786\pi$
$31$	−247.848	+	143.095i	−1.43596	+	0.829053i	−0.438396	+	0.898782i	$0.644453\pi$
$32$		0			0
$33$	172.023	−	46.3061i	0.907435	−	0.244269i
$34$		0			0
$35$	−84.0296	−	29.6109i	−0.405817	−	0.143004i
$36$		0			0
$37$	9.19197	−	15.9210i	0.0408419	−	0.0707402i	−0.844882	−	0.534953i	$-0.820329\pi$
$37$	9.19197	−	15.9210i	0.0408419	−	0.0707402i	0.885724	+	0.464213i	$0.153663\pi$
$38$		0			0
$39$	22.9746	−	86.1397i	0.0943302	−	0.353677i
$40$		0			0
$41$	219.751			0.837056			0.418528	−	0.908204i	$-0.362546\pi$
$41$	219.751			0.837056			0.418528	+	0.908204i	$0.362546\pi$
$42$		0			0
$43$	370.491			1.31394			0.656970	−	0.753917i	$-0.271838\pi$
$43$	370.491			1.31394			0.656970	+	0.753917i	$0.271838\pi$
$44$		0			0
$45$	−112.335	+	65.2029i	−0.372133	+	0.215997i
$46$		0			0
$47$	143.066	−	247.797i	0.444006	−	0.769041i	−0.553976	−	0.832532i	$-0.686890\pi$
$47$	143.066	−	247.797i	0.444006	−	0.769041i	0.997982	+	0.0634912i	$0.0202235\pi$
$48$		0			0
$49$	−319.838	+	123.906i	−0.932472	+	0.361242i
$50$		0			0
$51$	136.354	+	506.541i	0.374379	+	1.39078i
$52$		0			0
$53$	−29.3942	+	16.9708i	−0.0761813	+	0.0439833i	−0.537607	−	0.843196i	$-0.680671\pi$
$53$	−29.3942	+	16.9708i	−0.0761813	+	0.0439833i	0.461425	+	0.887179i	$0.347338\pi$
$54$		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	0.690624	−	0.723214i	$-0.257336\pi$
$59$	−127.350	−	220.577i	−0.281010	−	0.486723i	−0.971634	+	0.236491i	$0.924003\pi$
$60$		0			0
$61$	−29.2617	−	16.8943i	−0.0614193	−	0.0354605i	0.468976	−	0.883211i	$-0.344623\pi$
$61$	−29.2617	−	16.8943i	−0.0614193	−	0.0354605i	−0.530395	+	0.847751i	$0.677956\pi$
$62$		0			0
$63$	−165.104	+	472.004i	−0.330178	+	0.943919i
$64$		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	$-0.217934\pi$
$67$	−87.9473	−	152.329i	−0.160365	−	0.277761i	−0.935000	+	0.354648i	$0.884601\pi$
$68$		0			0
$69$	2.30007	+	2.29477i	0.00401298	+	0.00400373i
$70$		0			0
$71$			626.114i			1.04656i	0.852160	+	0.523282i	$0.175292\pi$
$71$			626.114i			1.04656i	−0.852160	+	0.523282i	$0.824708\pi$
$72$		0			0
$73$	189.125	−	109.191i	0.303225	−	0.175067i	−0.340666	−	0.940184i	$-0.610653\pi$
$73$	189.125	−	109.191i	0.303225	−	0.175067i	0.643891	+	0.765118i	$0.277319\pi$
$74$		0			0
$75$	137.574	+	511.076i	0.211810	+	0.786853i
$76$		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	$-0.710906\pi$
$79$	263.456	−	456.319i	0.375204	−	0.649873i	0.990358	+	0.138535i	$0.0442393\pi$
$80$		0			0
$81$	367.409	+	629.644i	0.503990	+	0.863709i
$82$		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
$87$	−298.571	+	1119.44i	−0.367932	+	1.37951i
$88$		0			0
$89$	412.449	−	714.383i	0.491231	−	0.850837i	−0.508718	−	0.860933i	$-0.669880\pi$
$89$	412.449	−	714.383i	0.491231	−	0.850837i	0.999949	+	0.0100964i	$0.00321383\pi$
$90$		0			0
$91$	312.343	−	58.3872i	0.359807	−	0.0672598i
$92$		0			0
$93$	−1435.97	+	386.543i	−1.60111	+	0.430996i
$94$		0			0
$95$	576.764	−	332.995i	0.622892	−	0.359627i
$96$		0			0
$97$		−	1309.69i		−	1.37092i	−0.728112	−	0.685458i	$-0.759602\pi$
$97$		−	1309.69i		−	1.37092i	0.728112	−	0.685458i	$-0.240398\pi$
$98$		0			0
$99$	925.674	−	2.13549i	0.939734	−	0.00216793i
$100$		0			0
$101$	755.381	+	1308.36i	0.744190	+	1.28898i	0.950572	+	0.310504i	$0.100498\pi$
$101$	755.381	+	1308.36i	0.744190	+	1.28898i	−0.206382	+	0.978472i	$0.566169\pi$
$102$		0			0
$103$	−173.735	−	100.306i	−0.166200	−	0.0959555i	0.414593	−	0.910007i	$-0.363924\pi$
$103$	−173.735	−	100.306i	−0.166200	−	0.0959555i	−0.580793	+	0.814052i	$0.697257\pi$
$104$		0			0
$105$	−382.232	−	261.188i	−0.355257	−	0.242755i
$106$		0			0
$107$	−1285.76	−	742.335i	−1.16168	−	0.670694i	−0.209971	−	0.977708i	$-0.567337\pi$
$107$	−1285.76	−	742.335i	−1.16168	−	0.670694i	−0.951705	+	0.307014i	$0.900670\pi$
$108$		0			0
$109$	232.948	+	403.477i	0.204700	+	0.354552i	0.950037	−	0.312137i	$-0.101045\pi$
$109$	232.948	+	403.477i	0.204700	+	0.354552i	−0.745337	+	0.666688i	$0.767711\pi$
$110$		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
$117$	230.695	−	401.712i	0.182288	−	0.317421i
$118$		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
$123$	1103.29	+	294.262i	0.808783	+	0.215713i
$124$		0			0
$125$	−1091.33			−0.780892
$126$		0			0
$127$	−80.7459			−0.0564176			−0.0282088	−	0.999602i	$-0.508980\pi$
$127$	−80.7459			−0.0564176			−0.0282088	+	0.999602i	$0.508980\pi$
$128$		0			0
$129$	1860.11	+	496.115i	1.26956	+	0.338608i
$130$		0			0
$131$	1105.17	−	1914.22i	0.737095	−	1.27669i	−0.216703	−	0.976238i	$-0.569530\pi$
$131$	1105.17	−	1914.22i	0.737095	−	1.27669i	0.953798	−	0.300449i	$-0.0971364\pi$
$132$		0			0
$133$	852.145	−	2418.21i	0.555567	−	1.57658i
$134$		0			0
$135$	−651.308	+	176.935i	−0.415227	+	0.112801i
$136$		0			0
$137$	−1820.47	+	1051.05i	−1.13528	+	0.655453i	−0.945257	−	0.326327i	$-0.894189\pi$
$137$	−1820.47	+	1051.05i	−1.13528	+	0.655453i	−0.190021	+	0.981780i	$0.560856\pi$
$138$		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
$147$	−1771.71	+	193.802i	−0.994070	+	0.108738i
$148$		0			0
$149$	−1109.66	−	640.661i	−0.610112	−	0.352248i	0.162897	−	0.986643i	$-0.447916\pi$
$149$	−1109.66	−	640.661i	−0.610112	−	0.352248i	−0.773009	+	0.634395i	$0.781249\pi$
$150$		0			0
$151$	−1652.35	−	2861.96i	−0.890507	−	1.54240i	−0.839268	−	0.543717i	$-0.817016\pi$
$151$	−1652.35	−	2861.96i	−0.890507	−	1.54240i	−0.0512388	−	0.998686i	$-0.516317\pi$
$152$		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	0.203361	−	0.979104i	$-0.434814\pi$
$157$	2268.13	−	1309.50i	1.15297	−	0.665667i	0.949609	+	0.313437i	$0.101480\pi$
$158$		0			0
$159$	−170.303	+	45.8432i	−0.0849429	+	0.0228654i
$160$		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	$-0.728264\pi$
$163$	674.516	−	1168.30i	0.324124	−	0.561399i	0.981335	+	0.192308i	$0.0615973\pi$
$164$		0			0
$165$	−220.852	+	828.052i	−0.104202	+	0.390689i
$166$		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
$171$	−1876.42	−	3232.80i	−0.839142	−	1.44572i
$172$		0			0
$173$	635.218	−	1100.23i	0.279160	−	0.483520i	−0.692016	−	0.721882i	$-0.743277\pi$
$173$	635.218	−	1100.23i	0.279160	−	0.483520i	0.971176	+	0.238362i	$0.0766106\pi$
$174$		0			0
$175$	−1432.57	+	1227.35i	−0.618810	+	0.530164i
$176$		0			0
$177$	−344.011	−	1277.97i	−0.146087	−	0.542701i
$178$		0			0
$179$	1763.39	−	1018.09i	0.736323	−	0.425116i	−0.0844077	−	0.996431i	$-0.526900\pi$
$179$	1763.39	−	1018.09i	0.736323	−	0.425116i	0.820731	+	0.571315i	$0.193566\pi$
$180$		0			0
$181$		−	1402.45i		−	0.575931i	−0.957641	−	0.287965i	$-0.907021\pi$
$181$		−	1402.45i		−	0.575931i	0.957641	−	0.287965i	$-0.0929788\pi$
$182$		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
$189$	−1460.98	+	2148.68i	−0.562278	+	0.826948i
$190$		0			0
$191$	3511.17	+	2027.17i	1.33015	+	0.767964i	0.985323	−	0.170701i	$-0.0546031\pi$
$191$	3511.17	+	2027.17i	1.33015	+	0.767964i	0.344831	+	0.938665i	$0.387936\pi$
$192$		0			0
$193$	872.281	+	1510.83i	0.325327	+	0.563483i	0.981579	−	0.191059i	$-0.0611922\pi$
$193$	872.281	+	1510.83i	0.325327	+	0.563483i	−0.656251	+	0.754542i	$0.727859\pi$
$194$		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	$-0.751088\pi$
$199$	−1274.50	+	735.834i	−0.454005	+	0.262120i	0.255515	+	0.966805i	$0.417755\pi$
$200$		0			0
$201$	−237.572	−	882.559i	−0.0833685	−	0.309706i
$202$		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
$207$	8.47496	+	14.6012i	0.00284565	+	0.00490266i
$208$		0			0
$209$	−4746.35			−1.57087
$210$		0			0
$211$	5010.62			1.63481			0.817406	−	0.576063i	$-0.195412\pi$
$211$	5010.62			1.63481			0.817406	+	0.576063i	$0.195412\pi$
$212$		0			0
$213$	−838.412	+	3143.49i	−0.269704	+	1.01121i
$214$		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
$219$	1095.74	−	294.959i	0.338098	−	0.0910113i
$220$		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	0.992458	+	0.122588i	$0.0391195\pi$
$227$	2060.25	+	3568.45i	0.602393	+	1.04338i	−0.390064	+	0.920788i	$0.627547\pi$
$228$		0			0
$229$	−453.529	−	261.845i	−0.130874	−	0.0755600i	0.433134	−	0.901330i	$-0.357408\pi$
$229$	−453.529	−	261.845i	−0.130874	−	0.0755600i	−0.564007	+	0.825770i	$0.690741\pi$
$230$		0			0
$231$	1428.41	+	2974.08i	0.406850	+	0.847100i
$232$		0			0
$233$	4090.17	+	2361.46i	1.15003	+	0.663968i	0.948894	−	0.315596i	$-0.102204\pi$
$233$	4090.17	+	2361.46i	1.15003	+	0.663968i	0.201133	+	0.979564i	$0.435538\pi$
$234$		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	$0.420264\pi$
$239$			7159.06i			1.93758i	−0.247886	+	0.968789i	$0.579736\pi$
$240$		0			0
$241$	−2440.67	+	1409.12i	−0.652355	+	0.376637i	−0.789358	−	0.613933i	$-0.789586\pi$
$241$	−2440.67	+	1409.12i	−0.652355	+	0.376637i	0.137003	+	0.990571i	$0.456253\pi$
$242$		0			0
$243$	1001.49	+	3653.21i	0.264386	+	0.964417i
$244$		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
$249$	1862.44	+	496.738i	0.474006	+	0.126424i
$250$		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
$255$	−2438.29	−	650.325i	−0.598791	−	0.159706i
$256$		0			0
$257$	−665.134	+	1152.05i	−0.161439	+	0.279621i	−0.935385	−	0.353631i	$-0.884947\pi$
$257$	−665.134	+	1152.05i	−0.161439	+	0.279621i	0.773946	+	0.633252i	$0.218280\pi$
$258$		0			0
$259$	321.121	+	113.158i	0.0770404	+	0.0271480i
$260$		0			0
$261$	−2998.03	+	5220.52i	−0.711010	+	1.23809i
$262$		0			0
$263$	3964.07	−	2288.66i	0.929411	−	0.536596i	0.0427856	−	0.999084i	$-0.486377\pi$
$263$	3964.07	−	2288.66i	0.929411	−	0.536596i	0.886625	+	0.462489i	$0.153043\pi$
$264$		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	$-0.129132\pi$
$269$	519.041	+	899.006i	0.117645	+	0.203767i	−0.801189	+	0.598411i	$0.795799\pi$
$270$		0			0
$271$	−3895.37	−	2249.00i	−0.873163	−	0.504121i	−0.00476491	−	0.999989i	$-0.501517\pi$
$271$	−3895.37	−	2249.00i	−0.873163	−	0.504121i	−0.868398	+	0.495868i	$0.834850\pi$
$272$		0			0
$273$	1646.35	+	125.109i	0.364988	+	0.0277361i
$274$		0			0
$275$	3024.27	+	1746.06i	0.663164	+	0.382878i
$276$		0			0
$277$	−315.706	−	546.820i	−0.0684800	−	0.118611i	0.829752	−	0.558132i	$-0.188482\pi$
$277$	−315.706	−	546.820i	−0.0684800	−	0.118611i	−0.898232	+	0.439521i	$0.855148\pi$
$278$		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	$-0.813752\pi$
$283$	−3676.15	+	2122.43i	−0.772171	+	0.445813i	0.0614774	+	0.998108i	$0.480419\pi$
$284$		0			0
$285$	3341.63	−	899.520i	0.694530	−	0.186958i
$286$		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
$291$	1753.77	−	6575.49i	0.353292	−	1.32461i
$292$		0			0
$293$	−1973.35			−0.393462			−0.196731	−	0.980458i	$-0.563033\pi$
$293$	−1973.35			−0.393462			−0.196731	+	0.980458i	$0.563033\pi$
$294$		0			0
$295$	1225.27			0.241824
$296$		0			0
$297$	4650.34	+	1228.82i	0.908552	+	0.240079i
$298$		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
$303$	2040.51	+	7580.32i	0.386879	+	1.43722i
$304$		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	0.850809	−	0.525475i	$-0.176113\pi$
$311$	−162.730	−	281.857i	−0.0296706	−	0.0513910i	−0.880479	+	0.474084i	$0.842779\pi$
$312$		0			0
$313$	554.704	+	320.259i	0.100172	+	0.0578342i	0.549249	−	0.835659i	$-0.314914\pi$
$313$	554.704	+	320.259i	0.100172	+	0.0578342i	−0.449077	+	0.893493i	$0.648247\pi$
$314$		0			0
$315$	−1569.30	−	1823.17i	−0.280699	−	0.326107i
$316$		0			0
$317$	6616.35	+	3819.95i	1.17228	+	0.676814i	0.954215	−	0.299122i	$-0.0966937\pi$
$317$	6616.35	+	3819.95i	1.17228	+	0.676814i	0.218060	+	0.975935i	$0.430027\pi$
$318$		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
$327$	629.263	+	2337.65i	0.106417	+	0.395328i
$328$		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	$-0.967171\pi$
$331$	−2458.08	+	4257.53i	−0.408183	+	0.706993i	0.586503	+	0.809947i	$0.300504\pi$
$332$		0			0
$333$	429.292	−	249.174i	0.0706458	−	0.0410050i
$334$		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
$339$	608.395	−	2281.08i	0.0974734	−	0.365461i
$340$		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
$345$	−15.0927	+	4.06274i	−0.00235526	+	0.000634002i
$346$		0			0
$347$	−5183.76	+	2992.84i	−0.801956	+	0.463009i	−0.844154	−	0.536100i	$-0.819897\pi$
$347$	−5183.76	+	2992.84i	−0.801956	+	0.463009i	0.0421990	+	0.999109i	$0.486564\pi$
$348$		0			0
$349$		−	4392.81i		−	0.673759i	−0.941548	−	0.336879i	$-0.890629\pi$
$349$		−	4392.81i		−	0.673759i	0.941548	−	0.336879i	$-0.109371\pi$
$350$		0			0
$351$	1696.16	−	1707.94i	0.257932	−	0.259723i
$352$		0			0
$353$	−4415.94	−	7648.63i	−0.665826	−	1.15324i	−0.979061	−	0.203569i	$-0.934746\pi$
$353$	−4415.94	−	7648.63i	−0.665826	−	1.15324i	0.313234	−	0.949676i	$-0.398587\pi$
$354$		0			0
$355$	−2608.47	−	1506.00i	−0.389981	−	0.225156i
$356$		0			0
$357$	−8757.52	+	4206.12i	−1.29831	+	0.623561i
$358$		0			0
$359$	−5040.82	−	2910.32i	−0.741070	−	0.427857i	0.0813881	−	0.996682i	$-0.474065\pi$
$359$	−5040.82	−	2910.32i	−0.741070	−	0.427857i	−0.822458	+	0.568825i	$0.807398\pi$
$360$		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	$-0.835697\pi$
$367$	−6166.91	+	3560.47i	−0.877140	+	0.506417i	−0.00742533	+	0.999972i	$0.502364\pi$
$368$		0			0
$369$	5145.19	+	2954.77i	0.725875	+	0.416854i
$370$		0			0
$371$	−408.983	−	477.366i	−0.0572327	−	0.0668022i
$372$		0			0
$373$	3073.51	−	5323.47i	0.426649	−	0.738978i	−0.569924	−	0.821698i	$-0.693027\pi$
$373$	3073.51	−	5323.47i	0.426649	−	0.738978i	0.996573	+	0.0827194i	$0.0263605\pi$
$374$		0			0
$375$	−5479.18	−	1461.37i	−0.754517	−	0.201240i
$376$		0			0
$377$	3825.48			0.522606
$378$		0			0
$379$	17.4452			0.00236438			0.00118219	−	0.999999i	$-0.499624\pi$
$379$	17.4452			0.00236438			0.00118219	+	0.999999i	$0.499624\pi$
$380$		0			0
$381$	−405.397	−	108.125i	−0.0545121	−	0.0145391i
$382$		0			0
$383$	5669.44	−	9819.75i	0.756383	−	1.31009i	−0.188301	−	0.982111i	$-0.560298\pi$
$383$	5669.44	−	9819.75i	0.756383	−	1.31009i	0.944684	−	0.327982i	$-0.106369\pi$
$384$		0			0
$385$	−3002.52	+	561.270i	−0.397462	+	0.0742986i
$386$		0			0
$387$	8674.60	+	4981.64i	1.13942	+	0.654343i
$388$		0			0
$389$	−8129.57	+	4693.61i	−1.05960	+	0.611762i	−0.925322	−	0.379181i	$-0.876206\pi$
$389$	−8129.57	+	4693.61i	−1.05960	+	0.611762i	−0.134281	+	0.990943i	$0.542872\pi$
$390$		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	0.691352	−	0.722518i	$-0.257016\pi$
$397$	3253.52	+	1878.42i	0.411308	+	0.237469i	−0.280044	+	0.959987i	$0.590349\pi$
$398$		0			0
$399$	7516.48	−	10999.9i	0.943095	−	1.38016i
$400$		0			0
$401$	13062.8	+	7541.80i	1.62674	+	0.939201i	0.985056	+	0.172235i	$0.0550989\pi$
$401$	13062.8	+	7541.80i	1.62674	+	0.939201i	0.641688	+	0.766966i	$0.278234\pi$
$402$		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	−0.833982	−	0.551791i	$-0.813944\pi$
$409$	−6394.77	+	3692.02i	−0.773108	+	0.446354i	0.0608743	+	0.998145i	$0.480611\pi$
$410$		0			0
$411$	−10547.4	+	2839.20i	−1.26585	+	0.340748i
$412$		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
$417$	4022.57	−	15082.0i	0.472389	−	1.77115i
$418$		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
$423$	6681.60	−	3878.20i	0.768015	−	0.445779i
$424$		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
$429$	−794.479	−	2951.41i	−0.0894121	−	0.332157i
$430$		0			0
$431$	−1705.81	+	984.849i	−0.190640	+	0.110066i	−0.592282	−	0.805731i	$-0.701773\pi$
$431$	−1705.81	+	984.849i	−0.190640	+	0.110066i	0.401642	+	0.915797i	$0.368440\pi$
$432$		0			0
$433$		−	7664.99i		−	0.850706i	−0.905027	−	0.425353i	$-0.860150\pi$
$433$		−	7664.99i		−	0.850706i	0.905027	−	0.425353i	$-0.139850\pi$
$434$		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	$-0.196730\pi$
$439$	6629.12	+	3827.33i	0.720708	+	0.416101i	−0.0943054	+	0.995543i	$0.530063\pi$
$440$		0			0
$441$	−9154.65	−	1399.44i	−0.988517	−	0.151111i
$442$		0			0
$443$	2595.85	+	1498.71i	0.278403	+	0.160736i	0.632700	−	0.774397i	$-0.281947\pi$
$443$	2595.85	+	1498.71i	0.278403	+	0.160736i	−0.354297	+	0.935133i	$0.615280\pi$
$444$		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
$453$	−4463.51	−	16581.5i	−0.462945	−	1.71979i
$454$		0			0
$455$	−508.036	+	1441.70i	−0.0523453	+	0.148545i
$456$		0			0
$457$	−4738.58	+	8207.46i	−0.485036	+	0.840107i	−0.999852	−	0.0171938i	$-0.994527\pi$
$457$	−4738.58	+	8207.46i	−0.485036	+	0.840107i	0.514816	+	0.857300i	$0.327860\pi$
$458$		0			0
$459$	−3618.41	+	13693.5i	−0.367958	+	1.39250i
$460$		0			0
$461$	−18908.7			−1.91034			−0.955171	−	0.296054i	$-0.904329\pi$
$461$	−18908.7			−1.91034			−0.955171	+	0.296054i	$0.904329\pi$
$462$		0			0
$463$	12725.2			1.27730			0.638649	−	0.769499i	$-0.279494\pi$
$463$	12725.2			1.27730			0.638649	+	0.769499i	$0.279494\pi$
$464$		0			0
$465$	1843.58	−	6912.21i	0.183858	−	0.689346i
$466$		0			0
$467$	−3585.52	+	6210.31i	−0.355285	+	0.615372i	−0.987167	−	0.159693i	$-0.948950\pi$
$467$	−3585.52	+	6210.31i	−0.355285	+	0.615372i	0.631881	+	0.775065i	$0.282283\pi$
$468$		0			0
$469$	2473.85	−	2119.46i	0.243564	−	0.208673i
$470$		0			0
$471$	13141.0	−	3537.37i	1.28557	−	0.346058i
$472$		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	0.914227	−	0.405203i	$-0.132799\pi$
$479$	1113.31	+	1928.31i	0.106197	+	0.183939i	−0.808029	+	0.589142i	$0.799466\pi$
$480$		0			0
$481$	−273.157	−	157.707i	−0.0258938	−	0.0149498i
$482$		0			0
$483$	−33.9487	+	49.6818i	−0.00319818	+	0.00468033i
$484$		0			0
$485$	5456.34	+	3150.22i	0.510845	+	0.294936i
$486$		0			0
$487$	7511.82	+	13010.8i	0.698959	+	1.21063i	0.968828	+	0.247735i	$0.0796862\pi$
$487$	7511.82	+	13010.8i	0.698959	+	1.21063i	−0.269869	+	0.962897i	$0.586980\pi$
$488$		0			0
$489$	4950.94	−	4962.37i	0.457851	−	0.458908i
$490$		0			0
$491$		−	8830.77i		−	0.811664i	−0.913948	−	0.405832i	$-0.866982\pi$
$491$		−	8830.77i		−	0.811664i	0.913948	−	0.405832i	$-0.133018\pi$
$492$		0			0
$493$	−19493.8	+	11254.8i	−1.78085	+	1.02817i
$494$		0			0
$495$	−2217.64	+	3861.62i	−0.201365	+	0.350640i
$496$		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	$-0.959102\pi$
$499$	−4290.57	+	7431.48i	−0.384914	+	0.666691i	0.606843	+	0.794822i	$0.292436\pi$
$500$		0			0
$501$	−13900.1	−	3707.35i	−1.23954	−	0.330603i
$502$		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
$507$	9552.45	+	2547.77i	0.836764	+	0.223176i
$508$		0			0
$509$	4853.13	−	8405.87i	0.422616	−	0.731992i	−0.573579	−	0.819150i	$-0.694445\pi$
$509$	4853.13	−	8405.87i	0.422616	−	0.731992i	0.996194	+	0.0871587i	$0.0277787\pi$
$510$		0			0
$511$	2631.43	+	3071.41i	0.227803	+	0.265893i
$512$		0			0
$513$	−5091.87	−	18743.4i	−0.438229	−	1.61314i
$514$		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	−0.893962	−	0.448143i	$-0.852086\pi$
$521$	−9930.86	−	17200.7i	−0.835084	−	1.44641i	0.0588781	−	0.998265i	$-0.481248\pi$
$522$		0			0
$523$	−3046.39	−	1758.83i	−0.254702	−	0.147052i	0.367213	−	0.930137i	$-0.380312\pi$
$523$	−3046.39	−	1758.83i	−0.254702	−	0.147052i	−0.621915	+	0.783084i	$0.713645\pi$
$524$		0			0
$525$	−8835.91	+	4243.77i	−0.734535	+	0.352787i
$526$		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
$537$	10216.7	−	2750.18i	0.821008	−	0.221004i
$538$		0			0
$539$	−7372.31	+	9161.61i	−0.589143	+	0.732131i
$540$		0			0
$541$	1477.08	−	2558.37i	0.117383	−	0.203314i	−0.801347	−	0.598200i	$-0.795883\pi$
$541$	1477.08	−	2558.37i	0.117383	−	0.203314i	0.918730	+	0.394886i	$0.129216\pi$
$542$		0			0
$543$	1877.99	−	7041.21i	0.148420	−	0.556478i
$544$		0			0
$545$	−2241.25			−0.176156
$546$		0			0
$547$	−19117.2			−1.49432			−0.747159	−	0.664645i	$-0.768583\pi$
$547$	−19117.2			−1.49432			−0.747159	+	0.664645i	$0.768583\pi$
$548$		0			0
$549$	−457.967	−	789.012i	−0.0356021	−	0.0613374i
$550$		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
$555$	119.449	+	443.744i	0.00913576	+	0.0339385i
$556$		0			0
$557$	21330.1	−	12315.0i	1.62260	−	0.936806i	0.636374	−	0.771381i	$-0.280433\pi$
$557$	21330.1	−	12315.0i	1.62260	−	0.936806i	0.986222	−	0.165426i	$-0.0528999\pi$
$558$		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	0.981197	+	0.193011i	$0.0618254\pi$
$563$	8786.67	+	15219.0i	0.657751	+	1.13926i	−0.323445	+	0.946247i	$0.604841\pi$
$564$		0			0
$565$	1892.84	+	1092.83i	0.140942	+	0.0813732i
$566$		0			0
$567$	−10212.3	+	8831.39i	−0.756395	+	0.654115i
$568$		0			0
$569$	−1590.17	−	918.088i	−0.117159	−	0.0676419i	0.440275	−	0.897863i	$-0.354881\pi$
$569$	−1590.17	−	918.088i	−0.117159	−	0.0676419i	−0.557434	+	0.830221i	$0.688214\pi$
$570$		0			0
$571$	707.209	+	1224.92i	0.0518315	+	0.0897748i	0.890777	−	0.454441i	$-0.150161\pi$
$571$	707.209	+	1224.92i	0.0518315	+	0.0897748i	−0.838946	+	0.544215i	$0.816827\pi$
$572$		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	−0.837302	−	0.546740i	$-0.815869\pi$
$577$	−10844.9	+	6261.33i	−0.782463	+	0.451755i	0.0548397	+	0.998495i	$0.482535\pi$
$578$		0			0
$579$	2356.30	+	8753.41i	0.169127	+	0.628289i
$580$		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
$585$	1118.69	+	1927.35i	0.0790636	+	0.136216i
$586$		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
$591$	6777.22	−	25410.2i	0.471705	−	1.76859i
$592$		0			0
$593$	−9283.24	+	16079.0i	−0.642861	+	1.11347i	0.341930	+	0.939726i	$0.388920\pi$
$593$	−9283.24	+	16079.0i	−0.642861	+	1.11347i	−0.984791	+	0.173743i	$0.944414\pi$
$594$		0			0
$595$	−1652.72	−	8841.28i	−0.113874	−	0.609171i
$596$		0			0
$597$	−7384.16	+	1987.71i	−0.506220	+	0.136267i
$598$		0			0
$599$	4258.02	−	2458.37i	0.290447	−	0.167690i	−0.347696	−	0.937607i	$-0.613036\pi$
$599$	4258.02	−	2458.37i	0.290447	−	0.167690i	0.638143	+	0.769917i	$0.279703\pi$
$600$		0			0
$601$			16157.9i			1.09666i	0.836262	+	0.548330i	$0.184736\pi$
$601$			16157.9i			1.09666i	−0.836262	+	0.548330i	$0.815264\pi$
$602$		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	$-0.219813\pi$
$607$	9043.22	+	5221.10i	0.604700	+	0.349124i	−0.166188	+	0.986094i	$0.553146\pi$
$608$		0			0
$609$	−21395.4	−	1625.88i	−1.42362	−	0.108184i
$610$		0			0
$611$	−4251.48	−	2454.59i	−0.281500	−	0.162524i
$612$		0			0
$613$	−5235.58	−	9068.30i	−0.344965	−	0.597496i	0.640383	−	0.768056i	$-0.278776\pi$
$613$	−5235.58	−	9068.30i	−0.344965	−	0.597496i	−0.985347	+	0.170560i	$0.945442\pi$
$614$		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	$-0.851259\pi$
$619$	−14616.4	+	8438.76i	−0.949082	+	0.547953i	−0.0562861	+	0.998415i	$0.517926\pi$
$620$		0			0
$621$	22.9977	+	84.6559i	0.00148610	+	0.00547041i
$622$		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
$627$	−23829.8	−	6355.71i	−1.51781	−	0.404821i
$628$		0			0
$629$	1855.93			0.117648
$630$		0			0
$631$	−27123.5			−1.71120			−0.855601	−	0.517635i	$-0.826812\pi$
$631$	−27123.5			−1.71120			−0.855601	+	0.517635i	$0.826812\pi$
$632$		0			0
$633$	25156.5	+	6709.58i	1.57959	+	0.421299i
$634$		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
$639$	−8418.74	+	14659.7i	−0.521190	+	0.907555i
$640$		0			0
$641$	−3189.14	+	1841.25i	−0.196511	+	0.113455i	−0.595027	−	0.803706i	$-0.702859\pi$
$641$	−3189.14	+	1841.25i	−0.196511	+	0.113455i	0.398516	+	0.917161i	$0.369525\pi$
$642$		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	0.989535	−	0.144295i	$-0.0460913\pi$
$647$	6085.96	+	10541.2i	0.369805	+	0.640520i	−0.619730	+	0.784815i	$0.712758\pi$
$648$		0			0
$649$	−7562.32	−	4366.11i	−0.457391	−	0.264075i
$650$		0			0
$651$	−11923.7	−	24826.3i	−0.717862	−	1.49465i
$652$		0			0
$653$	7276.24	+	4200.94i	0.436051	+	0.251754i	0.701921	−	0.712255i	$-0.252326\pi$
$653$	7276.24	+	4200.94i	0.436051	+	0.251754i	−0.265870	+	0.964009i	$0.585659\pi$
$654$		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	$0.0936845\pi$
$659$			9814.94i			0.580175i	−0.957000	+	0.290088i	$0.906316\pi$
$660$		0			0
$661$	−1870.41	+	1079.88i	−0.110061	+	0.0635438i	−0.554020	−	0.832503i	$-0.686907\pi$
$661$	−1870.41	+	1079.88i	−0.110061	+	0.0635438i	0.443959	+	0.896047i	$0.353574\pi$
$662$		0			0
$663$	8690.77	−	2339.43i	0.509082	−	0.137038i
$664$		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
$669$	5889.42	−	22081.5i	0.340356	−	1.27611i
$670$		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
$675$	−3650.80	+	13816.0i	−0.208177	+	0.787822i
$676$		0			0
$677$	−5190.37	+	8989.98i	−0.294656	+	0.510359i	−0.974905	−	0.222622i	$-0.928538\pi$
$677$	−5190.37	+	8989.98i	−0.294656	+	0.510359i	0.680249	+	0.732981i	$0.261872\pi$
$678$		0			0
$679$	23842.8	−	4457.00i	1.34757	−	0.251906i
$680$		0			0
$681$	5565.35	+	20674.7i	0.313164	+	1.16337i
$682$		0			0
$683$	3799.53	−	2193.66i	0.212862	−	0.122896i	−0.389779	−	0.920909i	$-0.627448\pi$
$683$	3799.53	−	2193.66i	0.212862	−	0.122896i	0.602641	+	0.798013i	$0.294115\pi$
$684$		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	$-0.500905\pi$
$691$	−15808.1	−	9126.79i	−0.870285	−	0.502459i	−0.867443	+	0.497537i	$0.834238\pi$
$692$		0			0
$693$	3189.03	+	16844.5i	0.174807	+	0.923335i
$694$		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
$705$	1859.14	+	6906.52i	0.0993180	+	0.368957i
$706$		0			0
$707$	−21247.9	+	18204.1i	−1.13028	+	0.968368i
$708$		0			0
$709$	9585.59	−	16602.7i	0.507749	−	0.879448i	−0.492210	−	0.870476i	$-0.663811\pi$
$709$	9585.59	−	16602.7i	0.507749	−	0.879448i	0.999960	−	0.00897144i	$-0.00285574\pi$
$710$		0			0
$711$	12304.2	−	7141.72i	0.649005	−	0.376702i
$712$		0			0
$713$	−178.948			−0.00939926
$714$		0			0
$715$	2829.71			0.148007
$716$		0			0
$717$	−9586.51	+	35943.1i	−0.499323	+	1.87213i
$718$		0			0
$719$	1665.92	−	2885.46i	0.0864094	−	0.149666i	−0.819582	−	0.572963i	$-0.805794\pi$
$719$	1665.92	−	2885.46i	0.0864094	−	0.149666i	0.905991	+	0.423297i	$0.139127\pi$
$720$		0			0
$721$	1234.82	−	3504.17i	0.0637825	−	0.181002i
$722$		0			0
$723$	−14140.7	+	3806.47i	−0.727382	+	0.195801i
$724$		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	0.839075	−	0.544015i	$-0.183097\pi$
$733$	15627.7	+	9022.68i	0.787482	+	0.454653i	−0.0515936	+	0.998668i	$0.516430\pi$
$734$		0			0
$735$	3454.13	−	7847.34i	0.173343	−	0.393815i
$736$		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	$-0.00738372\pi$
$739$	9638.45	+	16694.3i	0.479778	+	0.831001i	−0.519953	+	0.854195i	$0.674050\pi$
$740$		0			0
$741$	−8717.14	+	8737.27i	−0.432162	+	0.433160i
$742$		0			0
$743$			843.042i			0.0416261i	0.999783	+	0.0208131i	$0.00662549\pi$
$743$			843.042i			0.0416261i	−0.999783	+	0.0208131i	$0.993375\pi$
$744$		0			0
$745$	5338.16	−	3081.99i	0.262517	−	0.151564i
$746$		0			0
$747$	8685.49	+	4987.89i	0.425416	+	0.244307i
$748$		0			0
$749$	9138.58	−	25933.4i	0.445816	−	1.26514i
$750$		0			0
$751$	11343.3	−	19647.2i	0.551162	−	0.954640i	−0.447029	−	0.894519i	$-0.647518\pi$
$751$	11343.3	−	19647.2i	0.551162	−	0.954640i	0.998191	−	0.0601209i	$-0.0191486\pi$
$752$		0			0
$753$	12207.4	+	3255.87i	0.590785	+	0.157570i
$754$		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
$759$	107.629	+	28.7060i	0.00514713	+	0.00137281i
$760$		0			0
$761$	17635.9	−	30546.3i	0.840080	−	1.45506i	−0.0497457	−	0.998762i	$-0.515841\pi$
$761$	17635.9	−	30546.3i	0.840080	−	1.45506i	0.889826	−	0.456300i	$-0.150826\pi$
$762$		0			0
$763$	−6552.53	+	5613.87i	−0.310901	+	0.266364i
$764$		0			0
$765$	−11371.0	−	6530.10i	−0.537410	−	0.308623i
$766$		0			0
$767$	−3784.45	+	2184.96i	−0.178160	+	0.102861i
$768$		0			0
$769$			3431.91i			0.160934i	0.996757	+	0.0804668i	$0.0256411\pi$
$769$			3431.91i			0.160934i	−0.996757	+	0.0804668i	$0.974359\pi$
$770$		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	$-0.140272\pi$
$773$	1780.10	+	3083.22i	0.0828275	+	0.143461i	−0.821636	+	0.570013i	$0.806938\pi$
$774$		0			0
$775$	−25245.2	−	14575.3i	−1.17011	−	0.675564i
$776$		0			0
$777$	1460.71	+	998.133i	0.0674421	+	0.0460847i
$778$		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	$-0.683241\pi$
$787$	−1990.24	+	1149.07i	−0.0901453	+	0.0520454i	0.454250	+	0.890874i	$0.349907\pi$
$788$		0			0
$789$	22966.9	−	6182.36i	1.03630	−	0.278958i
$790$		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
$795$	218.644	−	819.773i	0.00975411	−	0.0365715i
$796$		0			0
$797$	29634.9			1.31709			0.658546	−	0.752541i	$-0.271172\pi$
$797$	29634.9			1.31709			0.658546	+	0.752541i	$0.271172\pi$
$798$		0			0
$799$	28886.1			1.27900
$800$		0			0
$801$	19262.6	−	11180.6i	0.849701	−	0.493192i
$802$		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
$807$	1402.09	+	5208.63i	0.0611597	+	0.227202i
$808$		0			0
$809$	16234.4	−	9372.91i	0.705525	−	0.407335i	−0.103877	−	0.994590i	$-0.533125\pi$
$809$	16234.4	−	9372.91i	0.705525	−	0.407335i	0.809402	+	0.587255i	$0.199791\pi$
$810$		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
$819$	8098.21	+	2832.71i	0.345512	+	0.120858i
$820$		0			0
$821$	−31560.6	−	18221.5i	−1.34162	−	0.774586i	−0.354576	−	0.935027i	$-0.615375\pi$
$821$	−31560.6	−	18221.5i	−1.34162	−	0.774586i	−0.987045	+	0.160441i	$0.948708\pi$
$822$		0			0
$823$	−2827.83	−	4897.94i	−0.119771	−	0.207450i	0.799906	−	0.600126i	$-0.204883\pi$
$823$	−2827.83	−	4897.94i	−0.119771	−	0.207450i	−0.919677	+	0.392676i	$0.871549\pi$
$824$		0			0
$825$	12845.7	+	12816.1i	0.542095	+	0.540846i
$826$		0			0
$827$			37188.1i			1.56367i	0.623483	+	0.781837i	$0.285717\pi$
$827$			37188.1i			1.56367i	−0.623483	+	0.781837i	$0.714283\pi$
$828$		0			0
$829$	12258.2	−	7077.29i	0.513565	−	0.296507i	−0.220733	−	0.975334i	$-0.570845\pi$
$829$	12258.2	−	7077.29i	0.513565	−	0.296507i	0.734298	+	0.678827i	$0.237511\pi$
$830$		0			0
$831$	−852.819	−	3168.14i	−0.0356004	−	0.132252i
$832$		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
$837$	−38819.0	−	10257.7i	−1.60308	−	0.423605i
$838$		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
$843$	7417.96	−	27812.5i	0.303070	−	1.13631i
$844$		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
$849$	−21298.7	+	5733.32i	−0.860978	+	0.231763i
$850$		0			0
$851$	9.95502	−	5.74753i	0.000401003	−	0.000231519i
$852$		0			0
$853$		−	44235.1i		−	1.77559i	−0.460235	−	0.887797i	$-0.652235\pi$
$853$		−	44235.1i		−	1.77559i	0.460235	−	0.887797i	$-0.347765\pi$
$854$		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	$-0.303460\pi$
$857$	−10452.8	−	18104.8i	−0.416642	−	0.721645i	−0.995599	+	0.0937129i	$0.970126\pi$
$858$		0			0
$859$	977.718	+	564.486i	0.0388351	+	0.0224214i	0.519292	−	0.854597i	$-0.326196\pi$
$859$	977.718	+	564.486i	0.0388351	+	0.0224214i	−0.480457	+	0.877018i	$0.659529\pi$
$860$		0			0
$861$	−1602.42	+	21086.7i	−0.0634266	+	0.834649i
$862$		0			0
$863$	−17175.9	−	9916.54i	−0.677493	−	0.391151i	0.121417	−	0.992602i	$-0.461256\pi$
$863$	−17175.9	−	9916.54i	−0.677493	−	0.391151i	−0.798910	+	0.601451i	$0.794589\pi$
$864$		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
$873$	17610.1	−	30664.8i	0.682717	−	1.18883i
$874$		0			0
$875$	−3713.90	−	19867.6i	−0.143489	−	0.767596i
$876$		0			0
$877$	7722.35	−	13375.5i	0.297338	−	0.515004i	−0.678188	−	0.734888i	$-0.737235\pi$
$877$	7722.35	−	13375.5i	0.297338	−	0.515004i	0.975526	+	0.219884i	$0.0705680\pi$
$878$		0			0
$879$	−9907.49	−	2642.46i	−0.380172	−	0.101397i
$880$		0			0
$881$	−9043.98			−0.345856			−0.172928	−	0.984934i	$-0.555323\pi$
$881$	−9043.98			−0.345856			−0.172928	+	0.984934i	$0.555323\pi$
$882$		0			0
$883$	15055.4			0.573787			0.286894	−	0.957962i	$-0.407377\pi$
$883$	15055.4			0.573787			0.286894	+	0.957962i	$0.407377\pi$
$884$		0			0
$885$	6151.64	+	1640.72i	0.233656	+	0.0623191i
$886$		0			0
$887$	−14220.9	+	24631.3i	−0.538322	+	0.932401i	0.460673	+	0.887570i	$0.347608\pi$
$887$	−14220.9	+	24631.3i	−0.538322	+	0.932401i	−0.998995	+	0.0448306i	$0.985725\pi$
$888$		0			0
$889$	−274.786	−	1469.97i	−0.0103667	−	0.0554570i
$890$		0			0
$891$	21702.2	+	12396.6i	0.815995	+	0.466108i
$892$		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
$903$	−2701.62	+	35551.4i	−0.0995617	+	1.31016i
$904$		0			0
$905$	5842.80	+	3373.34i	0.214609	+	0.123905i
$906$		0			0
$907$	−14570.3	−	25236.4i	−0.533404	−	0.923883i	−0.999239	−	0.0390115i	$-0.987579\pi$
$907$	−14570.3	−	25236.4i	−0.533404	−	0.923883i	0.465834	−	0.884872i	$-0.345754\pi$
$908$		0			0
$909$	94.1020	+	40790.5i	0.00343363	+	1.48838i
$910$		0			0
$911$			14257.6i			0.518525i	0.965807	+	0.259263i	$0.0834795\pi$
$911$			14257.6i			0.518525i	−0.965807	+	0.259263i	$0.916520\pi$
$912$		0			0
$913$	11014.1	−	6358.99i	0.399248	−	0.230506i
$914$		0			0
$915$	815.573	−	219.541i	0.0294667	−	0.00793202i
$916$		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	$-0.706995\pi$
$919$	10769.5	−	18653.3i	0.386563	−	0.669548i	0.991985	+	0.126358i	$0.0403287\pi$
$920$		0			0
$921$	−3477.38	+	13037.9i	−0.124412	+	0.466465i
$922$		0			0
$923$	10742.3			0.383084
$924$		0			0
$925$	1872.55			0.0665610
$926$		0			0
$927$	−2719.07	−	4684.57i	−0.0963386	−	0.165978i
$928$		0			0
$929$	−9507.93	+	16468.2i	−0.335786	+	0.581598i	−0.983636	−	0.180170i	$-0.942335\pi$
$929$	−9507.93	+	16468.2i	−0.335786	+	0.581598i	0.647849	+	0.761768i	$0.275669\pi$
$930$		0			0
$931$	46923.3	+	7283.82i	1.65183	+	0.256410i
$932$		0			0
$933$	−439.583	−	1633.01i	−0.0154248	−	0.0573015i
$934$		0			0
$935$	−14419.6	+	8325.14i	−0.504353	+	0.291188i
$936$		0			0
$937$		−	13655.6i		−	0.476105i	−0.971252	−	0.238052i	$-0.923491\pi$
$937$		−	13655.6i		−	0.476105i	0.971252	−	0.238052i	$-0.0765090\pi$
$938$		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	$-0.00737030\pi$
$941$	13850.3	+	23989.4i	0.479815	+	0.831065i	−0.519917	+	0.854217i	$0.674037\pi$
$942$		0			0
$943$	118.996	+	68.7026i	0.00410929	+	0.00237250i
$944$		0			0
$945$	−5437.56	−	11254.9i	−0.187179	−	0.387430i
$946$		0			0
$947$	15651.0	+	9036.10i	0.537052	+	0.310067i	0.743883	−	0.668309i	$-0.232982\pi$
$947$	15651.0	+	9036.10i	0.537052	+	0.310067i	−0.206831	+	0.978377i	$0.566315\pi$
$948$		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
$957$	10324.8	+	38355.6i	0.348749	+	1.29557i
$958$		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
$963$	−20123.1	−	34669.3i	−0.673372	−	1.16013i
$964$		0			0
$965$	−8392.45			−0.279961
$966$		0			0
$967$	−37827.6			−1.25796			−0.628982	−	0.777420i	$-0.716528\pi$
$967$	−37827.6			−1.25796			−0.628982	+	0.777420i	$0.716528\pi$
$968$		0			0
$969$	18715.1	−	70169.5i	0.620451	−	2.32628i
$970$		0			0
$971$	−386.167	+	668.861i	−0.0127628	+	0.0221059i	−0.872336	−	0.488906i	$-0.837396\pi$
$971$	−386.167	+	668.861i	−0.0127628	+	0.0221059i	0.859573	+	0.511012i	$0.170729\pi$
$972$		0			0
$973$	54687.5	−	10222.9i	1.80185	−	0.336825i
$974$		0			0
$975$	8768.57	−	2360.38i	0.288020	−	0.0775308i
$976$		0			0
$977$	3885.24	−	2243.15i	0.127226	−	0.0734540i	−0.435036	−	0.900413i	$-0.643264\pi$
$977$	3885.24	−	2243.15i	0.127226	−	0.0734540i	0.562262	+	0.826959i	$0.309931\pi$
$978$		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	−0.988120	−	0.153683i	$-0.950887\pi$
$983$	−19328.8	−	33478.4i	−0.627153	−	1.08626i	0.360967	−	0.932579i	$-0.382447\pi$
$984$		0			0
$985$	21085.4	+	12173.6i	0.682066	+	0.393791i
$986$		0			0
$987$	22734.7	+	15535.2i	0.733186	+	0.501003i
$988$		0			0
$989$	200.624	+	115.830i	0.00645041	+	0.00372415i
$990$		0			0
$991$	−20930.9	−	36253.4i	−0.670932	−	1.16209i	−0.977640	−	0.210284i	$-0.932561\pi$
$991$	−20930.9	−	36253.4i	−0.670932	−	1.16209i	0.306709	−	0.951803i	$-0.400772\pi$
$992$		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	−0.786193	−	0.617981i	$-0.787951\pi$
$997$	−20276.7	+	11706.8i	−0.644103	+	0.371873i	0.142090	+	0.989854i	$0.454618\pi$
$998$		0			0
$999$	2488.99	−	676.162i	0.0788268	−	0.0214142i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.2	✓	48	84.59	odd	6
168.4.u.a.17.11	yes	48	28.3	even	6
168.4.u.a.89.2	yes	48	4.3	odd	2
168.4.u.a.89.11	yes	48	12.11	even	2
336.4.bc.f.17.14		48	7.3	odd	6	inner
336.4.bc.f.17.23		48	21.17	even	6	inner
336.4.bc.f.257.14		48	3.2	odd	2	inner
336.4.bc.f.257.23		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.02065 + 1.33907i) q^{3} +(-2.40532 + 4.16613i) q^{5} +(3.40309 + 18.2049i) q^{7} +(23.4138 + 13.4460i) q^{9} +(29.6911 - 17.1421i) q^{11} -17.1571i q^{13} +(-17.6550 + 17.6958i) q^{15} +(50.4770 + 87.4288i) q^{17} +(-119.893 - 69.2205i) q^{19} +(-7.29198 + 95.9574i) q^{21} +(0.541507 + 0.312639i) q^{23} +(50.9289 + 88.2114i) q^{25} +(99.5470 + 98.8605i) q^{27} +222.968i q^{29} +(-247.848 + 143.095i) q^{31} +(172.023 - 46.3061i) q^{33} +(-84.0296 - 29.6109i) q^{35} +(9.19197 - 15.9210i) q^{37} +(22.9746 - 86.1397i) q^{39} +219.751 q^{41} +370.491 q^{43} +(-112.335 + 65.2029i) q^{45} +(143.066 - 247.797i) q^{47} +(-319.838 + 123.906i) q^{49} +(136.354 + 506.541i) q^{51} +(-29.3942 + 16.9708i) q^{53} +164.929i q^{55} +(-509.251 - 508.078i) q^{57} +(-127.350 - 220.577i) q^{59} +(-29.2617 - 16.8943i) q^{61} +(-165.104 + 472.004i) q^{63} +(71.4787 + 41.2683i) q^{65} +(-87.9473 - 152.329i) q^{67} +(2.30007 + 2.29477i) q^{69} +626.114i q^{71} +(189.125 - 109.191i) q^{73} +(137.574 + 511.076i) q^{75} +(413.113 + 482.187i) q^{77} +(263.456 - 456.319i) q^{79} +(367.409 + 629.644i) q^{81} +370.957 q^{83} -485.653 q^{85} +(-298.571 + 1119.44i) q^{87} +(412.449 - 714.383i) q^{89} +(312.343 - 58.3872i) q^{91} +(-1435.97 + 386.543i) q^{93} +(576.764 - 332.995i) q^{95} -1309.69i q^{97} +(925.674 - 2.13549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61}+ \cdots - 1988 q^{99}+O(q^{100}) \) 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

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Database

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