LMFDB - Embedded newform 336.4.bc.e.17.1

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)

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);

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")

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 = [16,0,0] 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$2.99617 + 0.151487i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.e.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.18952 - 0.262384i) q^{3} +(-2.24534 - 3.88904i) q^{5} +(9.71288 - 15.7690i) q^{7} +(26.8623 + 2.72329i) q^{9} +(20.2835 + 11.7107i) q^{11} -5.91384i q^{13} +(10.6318 + 20.7714i) q^{15} +(-58.0418 + 100.531i) q^{17} +(-8.02533 + 4.63343i) q^{19} +(-54.5428 + 79.2849i) q^{21} +(107.721 - 62.1928i) q^{23} +(52.4169 - 90.7888i) q^{25} +(-138.688 - 21.1808i) q^{27} -207.807i q^{29} +(-122.764 - 70.8780i) q^{31} +(-102.189 - 66.0951i) q^{33} +(-83.1348 - 2.36716i) q^{35} +(-149.838 - 259.526i) q^{37} +(-1.55170 + 30.6900i) q^{39} +508.379 q^{41} -391.127 q^{43} +(-49.7240 - 110.583i) q^{45} +(-40.2575 - 69.7281i) q^{47} +(-154.320 - 306.324i) q^{49} +(327.587 - 506.481i) q^{51} +(-258.697 - 149.359i) q^{53} -105.178i q^{55} +(42.8634 - 21.9396i) q^{57} +(102.276 - 177.147i) q^{59} +(-543.757 + 313.939i) q^{61} +(303.854 - 397.139i) q^{63} +(-22.9992 + 13.2786i) q^{65} +(-51.3894 + 89.0091i) q^{67} +(-575.340 + 294.487i) q^{69} +46.9785i q^{71} +(-228.182 - 131.741i) q^{73} +(-295.840 + 457.397i) q^{75} +(381.677 - 206.105i) q^{77} +(-533.634 - 924.281i) q^{79} +(714.167 + 146.308i) q^{81} -270.436 q^{83} +521.294 q^{85} +(-54.5252 + 1078.42i) q^{87} +(-443.765 - 768.624i) q^{89} +(-93.2551 - 57.4405i) q^{91} +(618.491 + 400.034i) q^{93} +(36.0392 + 20.8072i) q^{95} -219.564i q^{97} +(512.971 + 369.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) $ 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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
$3$	−5.18952	−	0.262384i	−0.998724	−	0.0504958i
$3$	−5.18952	−	0.262384i	−0.998724	−	0.0504958i
$4$		0			0
$5$	−2.24534	−	3.88904i	−0.200829	−	0.347846i	0.747967	−	0.663736i	$-0.231030\pi$
$5$	−2.24534	−	3.88904i	−0.200829	−	0.347846i	−0.948796	+	0.315890i	$0.897697\pi$
$6$		0			0
$7$	9.71288	−	15.7690i	0.524446	−	0.851443i
$7$	9.71288	−	15.7690i	0.524446	−	0.851443i
$8$		0			0
$9$	26.8623	+	2.72329i	0.994900	+	0.100863i
$10$		0			0
$11$	20.2835	+	11.7107i	0.555974	+	0.320992i	0.751528	−	0.659701i	$-0.229317\pi$
$11$	20.2835	+	11.7107i	0.555974	+	0.320992i	−0.195554	+	0.980693i	$0.562650\pi$
$12$		0			0
$13$		−	5.91384i		−	0.126170i	−0.998008	−	0.0630848i	$-0.979906\pi$
$13$		−	5.91384i		−	0.126170i	0.998008	−	0.0630848i	$-0.0200939\pi$
$14$		0			0
$15$	10.6318	+	20.7714i	0.183008	+	0.357544i
$16$		0			0
$17$	−58.0418	+	100.531i	−0.828071	+	1.43426i	0.0714778	+	0.997442i	$0.477228\pi$
$17$	−58.0418	+	100.531i	−0.828071	+	1.43426i	−0.899549	+	0.436819i	$0.856105\pi$
$18$		0			0
$19$	−8.02533	+	4.63343i	−0.0969019	+	0.0559464i	−0.547668	−	0.836696i	$-0.684484\pi$
$19$	−8.02533	+	4.63343i	−0.0969019	+	0.0559464i	0.450766	+	0.892642i	$0.351151\pi$
$20$		0			0
$21$	−54.5428	+	79.2849i	−0.566772	+	0.823875i
$22$		0			0
$23$	107.721	−	62.1928i	0.976583	−	0.563830i	0.0753461	−	0.997157i	$-0.475994\pi$
$23$	107.721	−	62.1928i	0.976583	−	0.563830i	0.901237	+	0.433327i	$0.142661\pi$
$24$		0			0
$25$	52.4169	−	90.7888i	0.419335	−	0.726310i
$26$		0			0
$27$	−138.688	−	21.1808i	−0.988538	−	0.150972i
$28$		0			0
$29$		−	207.807i		−	1.33065i	−0.746555	−	0.665324i	$-0.768293\pi$
$29$		−	207.807i		−	1.33065i	0.746555	−	0.665324i	$-0.231707\pi$
$30$		0			0
$31$	−122.764	−	70.8780i	−0.711262	−	0.410647i	0.100266	−	0.994961i	$-0.468030\pi$
$31$	−122.764	−	70.8780i	−0.711262	−	0.410647i	−0.811528	+	0.584314i	$0.801364\pi$
$32$		0			0
$33$	−102.189	−	66.0951i	−0.539056	−	0.348657i
$34$		0			0
$35$	−83.1348	−	2.36716i	−0.401496	−	0.0114321i
$36$		0			0
$37$	−149.838	−	259.526i	−0.665761	−	1.15313i	−0.979078	−	0.203483i	$-0.934774\pi$
$37$	−149.838	−	259.526i	−0.665761	−	1.15313i	0.313317	−	0.949648i	$-0.398560\pi$
$38$		0			0
$39$	−1.55170	+	30.6900i	−0.00637103	+	0.126009i
$40$		0			0
$41$	508.379			1.93647			0.968237	−	0.250032i	$-0.0804412\pi$
$41$	508.379			1.93647			0.968237	+	0.250032i	$0.0804412\pi$
$42$		0			0
$43$	−391.127			−1.38712			−0.693562	−	0.720397i	$-0.743959\pi$
$43$	−391.127			−1.38712			−0.693562	+	0.720397i	$0.743959\pi$
$44$		0			0
$45$	−49.7240	−	110.583i	−0.164720	−	0.366329i
$46$		0			0
$47$	−40.2575	−	69.7281i	−0.124940	−	0.216402i	0.796770	−	0.604283i	$-0.206540\pi$
$47$	−40.2575	−	69.7281i	−0.124940	−	0.216402i	−0.921709	+	0.387881i	$0.873207\pi$
$48$		0			0
$49$	−154.320	−	306.324i	−0.449912	−	0.893073i
$50$		0			0
$51$	327.587	−	506.481i	0.899439	−	1.39062i
$52$		0			0
$53$	−258.697	−	149.359i	−0.670467	−	0.387094i	0.125786	−	0.992057i	$-0.459855\pi$
$53$	−258.697	−	149.359i	−0.670467	−	0.387094i	−0.796254	+	0.604963i	$0.793188\pi$
$54$		0			0
$55$		−	105.178i		−	0.257858i
$56$		0			0
$57$	42.8634	−	21.9396i	0.0996034	−	0.0509818i
$58$		0			0
$59$	102.276	−	177.147i	0.225682	−	0.390892i	−0.730842	−	0.682547i	$-0.760872\pi$
$59$	102.276	−	177.147i	0.225682	−	0.390892i	0.956524	+	0.291655i	$0.0942058\pi$
$60$		0			0
$61$	−543.757	+	313.939i	−1.14133	+	0.658946i	−0.946759	−	0.321943i	$-0.895664\pi$
$61$	−543.757	+	313.939i	−1.14133	+	0.658946i	−0.194569	+	0.980889i	$0.562331\pi$
$62$		0			0
$63$	303.854	−	397.139i	0.607651	−	0.794204i
$64$		0			0
$65$	−22.9992	+	13.2786i	−0.0438876	+	0.0253385i
$66$		0			0
$67$	−51.3894	+	89.0091i	−0.0937048	+	0.162301i	−0.909067	−	0.416649i	$-0.863204\pi$
$67$	−51.3894	+	89.0091i	−0.0937048	+	0.162301i	0.815363	+	0.578951i	$0.196538\pi$
$68$		0			0
$69$	−575.340	+	294.487i	−1.00381	+	0.513798i
$70$		0			0
$71$			46.9785i			0.0785256i	0.999229	+	0.0392628i	$0.0125010\pi$
$71$			46.9785i			0.0785256i	−0.999229	+	0.0392628i	$0.987499\pi$
$72$		0			0
$73$	−228.182	−	131.741i	−0.365845	−	0.211221i	0.305797	−	0.952097i	$-0.401077\pi$
$73$	−228.182	−	131.741i	−0.365845	−	0.211221i	−0.671642	+	0.740876i	$0.734411\pi$
$74$		0			0
$75$	−295.840	+	457.397i	−0.455476	+	0.704209i
$76$		0			0
$77$	381.677	−	206.105i	0.564885	−	0.305038i
$78$		0			0
$79$	−533.634	−	924.281i	−0.759981	−	1.31633i	−0.942860	−	0.333190i	$-0.891875\pi$
$79$	−533.634	−	924.281i	−0.759981	−	1.31633i	0.182878	−	0.983136i	$-0.441459\pi$
$80$		0			0
$81$	714.167	+	146.308i	0.979653	+	0.200697i
$82$		0			0
$83$	−270.436			−0.357642			−0.178821	−	0.983882i	$-0.557228\pi$
$83$	−270.436			−0.357642			−0.178821	+	0.983882i	$0.557228\pi$
$84$		0			0
$85$	521.294			0.665203
$86$		0			0
$87$	−54.5252	+	1078.42i	−0.0671921	+	1.32895i
$88$		0			0
$89$	−443.765	−	768.624i	−0.528528	−	0.915438i	−0.999447	−	0.0332610i	$-0.989411\pi$
$89$	−443.765	−	768.624i	−0.528528	−	0.915438i	0.470918	−	0.882177i	$-0.343923\pi$
$90$		0			0
$91$	−93.2551	−	57.4405i	−0.107426	−	0.0661692i
$92$		0			0
$93$	618.491	+	400.034i	0.689618	+	0.446039i
$94$		0			0
$95$	36.0392	+	20.8072i	0.0389215	+	0.0224713i
$96$		0			0
$97$		−	219.564i		−	0.229828i	−0.993375	−	0.114914i	$-0.963341\pi$
$97$		−	219.564i		−	0.229828i	0.993375	−	0.114914i	$-0.0366593\pi$
$98$		0			0
$99$	512.971	+	369.815i	0.520763	+	0.375432i
$100$		0			0
$101$	−492.533	+	853.093i	−0.485237	+	0.840455i	−0.999856	−	0.0169642i	$-0.994600\pi$
$101$	−492.533	+	853.093i	−0.485237	+	0.840455i	0.514619	+	0.857419i	$0.327933\pi$
$102$		0			0
$103$	1112.87	−	642.516i	1.06461	−	0.614650i	0.137903	−	0.990446i	$-0.455964\pi$
$103$	1112.87	−	642.516i	1.06461	−	0.614650i	0.926703	+	0.375796i	$0.122631\pi$
$104$		0			0
$105$	430.809	+	34.0976i	0.400406	+	0.0316913i
$106$		0			0
$107$	158.409	−	91.4575i	0.143121	−	0.0826311i	−0.426729	−	0.904379i	$-0.640334\pi$
$107$	158.409	−	91.4575i	0.143121	−	0.0826311i	0.569851	+	0.821748i	$0.307001\pi$
$108$		0			0
$109$	291.471	−	504.843i	0.256127	−	0.443625i	−0.709074	−	0.705134i	$-0.750887\pi$
$109$	291.471	−	504.843i	0.256127	−	0.443625i	0.965201	+	0.261509i	$0.0842201\pi$
$110$		0			0
$111$	709.490	+	1386.13i	0.606683	+	1.18528i
$112$		0			0
$113$			2283.94i			1.90137i	0.310152	+	0.950687i	$0.399620\pi$
$113$			2283.94i			1.90137i	−0.310152	+	0.950687i	$0.600380\pi$
$114$		0			0
$115$	−483.741	−	279.288i	−0.392253	−	0.226467i
$116$		0			0
$117$	16.1051	−	158.859i	0.0127258	−	0.125526i
$118$		0			0
$119$	1021.52	+	1891.71i	0.786914	+	1.45725i
$120$		0			0
$121$	−391.219	−	677.611i	−0.293928	−	0.509099i
$122$		0			0
$123$	−2638.25	−	133.390i	−1.93400	−	0.0977838i
$124$		0			0
$125$	−1032.11			−0.738517
$126$		0			0
$127$	1554.48			1.08613			0.543064	−	0.839692i	$-0.317264\pi$
$127$	1554.48			1.08613			0.543064	+	0.839692i	$0.317264\pi$
$128$		0			0
$129$	2029.76	+	102.625i	1.38535	+	0.0700439i
$130$		0			0
$131$	−1047.46	−	1814.26i	−0.698605	−	1.21002i	−0.968950	−	0.247256i	$-0.920471\pi$
$131$	−1047.46	−	1814.26i	−0.698605	−	1.21002i	0.270345	−	0.962763i	$-0.412862\pi$
$132$		0			0
$133$	−4.88481	+	171.555i	−0.00318471	+	0.111847i
$134$		0			0
$135$	229.028	+	586.921i	0.146012	+	0.374179i
$136$		0			0
$137$	−529.002	−	305.420i	−0.329896	−	0.190465i	0.325899	−	0.945405i	$-0.394333\pi$
$137$	−529.002	−	305.420i	−0.329896	−	0.190465i	−0.655795	+	0.754939i	$0.727666\pi$
$138$		0			0
$139$			1806.61i			1.10241i	0.834370	+	0.551204i	$0.185831\pi$
$139$			1806.61i			1.10241i	−0.834370	+	0.551204i	$0.814169\pi$
$140$		0			0
$141$	190.622	+	372.419i	0.113853	+	0.222435i
$142$		0			0
$143$	69.2553	−	119.954i	0.0404994	−	0.0701470i
$144$		0			0
$145$	−808.170	+	466.597i	−0.462861	+	0.267233i
$146$		0			0
$147$	720.472	+	1630.17i	0.404242	+	0.914652i
$148$		0			0
$149$	2341.75	−	1352.01i	1.28754	−	0.743363i	0.309328	−	0.950956i	$-0.399896\pi$
$149$	2341.75	−	1352.01i	1.28754	−	0.743363i	0.978215	+	0.207592i	$0.0665627\pi$
$150$		0			0
$151$	770.352	−	1334.29i	0.415168	−	0.719092i	−0.580278	−	0.814418i	$-0.697056\pi$
$151$	770.352	−	1334.29i	0.415168	−	0.719092i	0.995446	+	0.0953266i	$0.0303895\pi$
$152$		0			0
$153$	−1832.91	+	2542.44i	−0.968512	+	1.34343i
$154$		0			0
$155$			636.580i			0.329880i
$156$		0			0
$157$	477.498	+	275.684i	0.242729	+	0.140140i	0.616430	−	0.787409i	$-0.288578\pi$
$157$	477.498	+	275.684i	0.242729	+	0.140140i	−0.373701	+	0.927549i	$0.621911\pi$
$158$		0			0
$159$	1303.32	+	842.979i	0.650065	+	0.420456i
$160$		0			0
$161$	65.5670	−	2302.72i	0.0320957	−	1.12720i
$162$		0			0
$163$	−1155.82	−	2001.94i	−0.555403	−	0.961986i	−0.997872	−	0.0652023i	$-0.979231\pi$
$163$	−1155.82	−	2001.94i	−0.555403	−	0.961986i	0.442469	−	0.896784i	$-0.354103\pi$
$164$		0			0
$165$	−27.5970	+	545.824i	−0.0130207	+	0.257529i
$166$		0			0
$167$	−2580.87			−1.19589			−0.597944	−	0.801538i	$-0.704016\pi$
$167$	−2580.87			−1.19589			−0.597944	+	0.801538i	$0.704016\pi$
$168$		0			0
$169$	2162.03			0.984081
$170$		0			0
$171$	−228.197	+	102.609i	−0.102051	+	0.0458873i
$172$		0			0
$173$	501.050	+	867.845i	0.220197	+	0.381393i	0.954868	−	0.297031i	$-0.0959965\pi$
$173$	501.050	+	867.845i	0.220197	+	0.381393i	−0.734670	+	0.678424i	$0.762663\pi$
$174$		0			0
$175$	−922.524	−	1708.38i	−0.398493	−	0.737951i
$176$		0			0
$177$	−577.245	+	892.475i	−0.245132	+	0.378997i
$178$		0			0
$179$	2598.36	+	1500.17i	1.08498	+	0.626411i	0.932234	−	0.361855i	$-0.117856\pi$
$179$	2598.36	+	1500.17i	1.08498	+	0.626411i	0.152742	+	0.988266i	$0.451190\pi$
$180$		0			0
$181$		−	967.850i		−	0.397457i	−0.980055	−	0.198729i	$-0.936319\pi$
$181$		−	967.850i		−	0.397457i	0.980055	−	0.198729i	$-0.0636812\pi$
$182$		0			0
$183$	2904.21	−	1486.52i	1.17315	−	0.600473i
$184$		0			0
$185$	−672.872	+	1165.45i	−0.267408	+	0.463165i
$186$		0			0
$187$	−2354.59	+	1359.42i	−0.920773	+	0.531608i
$188$		0			0
$189$	−1681.06	+	1981.24i	−0.646980	+	0.762507i
$190$		0			0
$191$	356.214	−	205.660i	0.134946	−	0.0779113i	−0.431007	−	0.902349i	$-0.641842\pi$
$191$	356.214	−	205.660i	0.134946	−	0.0779113i	0.565953	+	0.824437i	$0.308508\pi$
$192$		0			0
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	−0.932053	−	0.362321i	$-0.881984\pi$
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	0.779806	+	0.626021i	$0.215318\pi$
$194$		0			0
$195$	122.839	−	62.8749i	0.0451111	−	0.0230901i
$196$		0			0
$197$			633.331i			0.229051i	0.993420	+	0.114525i	$0.0365347\pi$
$197$			633.331i			0.229051i	−0.993420	+	0.114525i	$0.963465\pi$
$198$		0			0
$199$	2964.48	+	1711.54i	1.05601	+	0.609688i	0.924326	−	0.381603i	$-0.124628\pi$
$199$	2964.48	+	1711.54i	1.05601	+	0.609688i	0.131685	+	0.991292i	$0.457961\pi$
$200$		0			0
$201$	290.041	−	448.431i	0.101781	−	0.157363i
$202$		0			0
$203$	−3276.90	−	2018.41i	−1.13297	−	0.697854i
$204$		0			0
$205$	−1141.48	−	1977.11i	−0.388901	−	0.673596i
$206$		0			0
$207$	3063.01	−	1377.29i	1.02847	−	0.462454i
$208$		0			0
$209$	−217.043			−0.0718333
$210$		0			0
$211$	−1023.65			−0.333986			−0.166993	−	0.985958i	$-0.553406\pi$
$211$	−1023.65			−0.333986			−0.166993	+	0.985958i	$0.553406\pi$
$212$		0			0
$213$	12.3264	−	243.796i	0.00396521	−	0.0784254i
$214$		0			0
$215$	878.212	+	1521.11i	0.278575	+	0.482506i
$216$		0			0
$217$	−2310.07	+	1247.43i	−0.722661	+	0.390237i
$218$		0			0
$219$	1149.59	+	743.545i	0.354713	+	0.229425i
$220$		0			0
$221$	594.527	+	343.250i	0.180960	+	0.104477i
$222$		0			0
$223$			1521.32i			0.456840i	0.973563	+	0.228420i	$0.0733559\pi$
$223$			1521.32i			0.456840i	−0.973563	+	0.228420i	$0.926644\pi$
$224$		0			0
$225$	1655.28	−	2296.05i	0.490454	−	0.680311i
$226$		0			0
$227$	729.575	−	1263.66i	0.213320	−	0.369481i	−0.739432	−	0.673232i	$-0.764906\pi$
$227$	729.575	−	1263.66i	0.213320	−	0.369481i	0.952752	+	0.303751i	$0.0982390\pi$
$228$		0			0
$229$	4152.17	−	2397.26i	1.19818	−	0.691770i	0.238031	−	0.971257i	$-0.423498\pi$
$229$	4152.17	−	2397.26i	1.19818	−	0.691770i	0.960149	+	0.279488i	$0.0901646\pi$
$230$		0			0
$231$	−2034.80	+	969.443i	−0.579568	+	0.276124i
$232$		0			0
$233$	−1445.76	+	834.708i	−0.406501	+	0.234693i	−0.689285	−	0.724490i	$-0.742075\pi$
$233$	−1445.76	+	834.708i	−0.406501	+	0.234693i	0.282784	+	0.959183i	$0.408742\pi$
$234$		0			0
$235$	−180.784	+	313.126i	−0.0501831	+	0.0869196i
$236$		0			0
$237$	2526.79	+	4936.60i	0.692543	+	1.35302i
$238$		0			0
$239$			3529.25i			0.955181i	0.878583	+	0.477590i	$0.158490\pi$
$239$			3529.25i			0.955181i	−0.878583	+	0.477590i	$0.841510\pi$
$240$		0			0
$241$	−4269.15	−	2464.80i	−1.14108	−	0.658803i	−0.194382	−	0.980926i	$-0.562270\pi$
$241$	−4269.15	−	2464.80i	−1.14108	−	0.658803i	−0.946698	+	0.322123i	$0.895603\pi$
$242$		0			0
$243$	−3667.80	−	946.654i	−0.968269	−	0.249909i
$244$		0			0
$245$	−844.806	+	1287.96i	−0.220297	+	0.335855i
$246$		0			0
$247$	27.4014	+	47.4605i	0.00705873	+	0.0122261i
$248$		0			0
$249$	1403.44	+	70.9581i	0.357185	+	0.0180594i
$250$		0			0
$251$	−1294.99			−0.325652			−0.162826	−	0.986655i	$-0.552061\pi$
$251$	−1294.99			−0.325652			−0.162826	+	0.986655i	$0.552061\pi$
$252$		0			0
$253$	2913.29			0.723940
$254$		0			0
$255$	−2705.27	−	136.779i	−0.664355	−	0.0335900i
$256$		0			0
$257$	728.040	+	1261.00i	0.176708	+	0.306067i	0.940751	−	0.339098i	$-0.110122\pi$
$257$	728.040	+	1261.00i	0.176708	+	0.306067i	−0.764043	+	0.645165i	$0.776789\pi$
$258$		0			0
$259$	−5547.82	−	157.967i	−1.33098	−	0.0378980i
$260$		0			0
$261$	565.920	−	5582.18i	0.134213	−	1.32386i
$262$		0			0
$263$	1850.30	+	1068.27i	0.433820	+	0.250466i	0.700973	−	0.713188i	$-0.252749\pi$
$263$	1850.30	+	1068.27i	0.433820	+	0.250466i	−0.267153	+	0.963654i	$0.586083\pi$
$264$		0			0
$265$			1341.44i			0.310959i
$266$		0			0
$267$	2101.26	+	4105.23i	0.481628	+	0.940958i
$268$		0			0
$269$	1443.73	−	2500.61i	0.327233	−	0.566784i	−0.654729	−	0.755864i	$-0.727217\pi$
$269$	1443.73	−	2500.61i	0.327233	−	0.566784i	0.981962	+	0.189080i	$0.0605506\pi$
$270$		0			0
$271$	5072.92	−	2928.85i	1.13711	−	0.656513i	0.191400	−	0.981512i	$-0.438697\pi$
$271$	5072.92	−	2928.85i	1.13711	−	0.656513i	0.945714	+	0.324999i	$0.105364\pi$
$272$		0			0
$273$	468.878	+	322.557i	0.103948	+	0.0715094i
$274$		0			0
$275$	2126.40	−	1227.68i	0.466279	−	0.269206i
$276$		0			0
$277$	1401.52	−	2427.50i	0.304003	−	0.526549i	−0.673036	−	0.739610i	$-0.735010\pi$
$277$	1401.52	−	2427.50i	0.304003	−	0.526549i	0.977039	+	0.213061i	$0.0683433\pi$
$278$		0			0
$279$	−3104.71	−	2238.27i	−0.666215	−	0.480293i
$280$		0			0
$281$		−	4665.53i		−	0.990469i	−0.868759	−	0.495235i	$-0.835082\pi$
$281$		−	4665.53i		−	0.990469i	0.868759	−	0.495235i	$-0.164918\pi$
$282$		0			0
$283$	−4654.53	−	2687.29i	−0.977679	−	0.564463i	−0.0761103	−	0.997099i	$-0.524250\pi$
$283$	−4654.53	−	2687.29i	−0.977679	−	0.564463i	−0.901569	+	0.432636i	$0.857583\pi$
$284$		0			0
$285$	−181.567	−	117.436i	−0.0377371	−	0.0244080i
$286$		0			0
$287$	4937.83	−	8016.61i	1.01558	−	1.64880i
$288$		0			0
$289$	−4281.21	−	7415.27i	−0.871404	−	1.50932i
$290$		0			0
$291$	−57.6101	+	1139.43i	−0.0116054	+	0.229535i
$292$		0			0
$293$	−1302.13			−0.259630			−0.129815	−	0.991538i	$-0.541438\pi$
$293$	−1302.13			−0.259630			−0.129815	+	0.991538i	$0.541438\pi$
$294$		0			0
$295$	−918.578			−0.181294
$296$		0			0
$297$	−2565.04	−	2053.76i	−0.501141	−	0.401249i
$298$		0			0
$299$	−367.799	−	637.046i	−0.0711383	−	0.123215i
$300$		0			0
$301$	−3798.97	+	6167.66i	−0.727472	+	1.18106i
$302$		0			0
$303$	2779.85	−	4297.91i	0.527057	−	0.814880i
$304$		0			0
$305$	2441.84	+	1409.80i	0.458424	+	0.264671i
$306$		0			0
$307$		−	644.894i		−	0.119889i	−0.998202	−	0.0599447i	$-0.980908\pi$
$307$		−	644.894i		−	0.119889i	0.998202	−	0.0599447i	$-0.0190924\pi$
$308$		0			0
$309$	−5943.85	+	3042.35i	−1.09428	+	0.560108i
$310$		0			0
$311$	668.420	−	1157.74i	0.121873	−	0.211091i	−0.798633	−	0.601818i	$-0.794443\pi$
$311$	668.420	−	1157.74i	0.121873	−	0.211091i	0.920506	+	0.390727i	$0.127776\pi$
$312$		0			0
$313$	−1459.67	+	842.739i	−0.263595	+	0.152187i	−0.625973	−	0.779844i	$-0.715298\pi$
$313$	−1459.67	+	842.739i	−0.263595	+	0.152187i	0.362378	+	0.932031i	$0.381965\pi$
$314$		0			0
$315$	−2226.75	−	289.988i	−0.398295	−	0.0518697i
$316$		0			0
$317$	−2609.95	+	1506.85i	−0.462427	+	0.266982i	−0.713064	−	0.701099i	$-0.752693\pi$
$317$	−2609.95	+	1506.85i	−0.462427	+	0.266982i	0.250637	+	0.968081i	$0.419360\pi$
$318$		0			0
$319$	2433.57	−	4215.06i	0.427127	−	0.739806i
$320$		0			0
$321$	−846.064	+	433.057i	−0.147111	+	0.0752987i
$322$		0			0
$323$		−	1075.73i		−	0.185310i
$324$		0			0
$325$	−536.910	−	309.985i	−0.0916382	−	0.0529074i
$326$		0			0
$327$	−1645.06	+	2543.42i	−0.278202	+	0.430126i
$328$		0			0
$329$	−1490.56	−	42.4417i	−0.249778	−	0.00711211i
$330$		0			0
$331$	−394.460	−	683.225i	−0.0655030	−	0.113454i	0.831414	−	0.555653i	$-0.187532\pi$
$331$	−394.460	−	683.225i	−0.0655030	−	0.113454i	−0.896917	+	0.442199i	$0.854199\pi$
$332$		0			0
$333$	−3318.22	−	7379.53i	−0.546058	−	1.21440i
$334$		0			0
$335$	461.547			0.0752746
$336$		0			0
$337$	1906.16			0.308116			0.154058	−	0.988062i	$-0.450766\pi$
$337$	1906.16			0.308116			0.154058	+	0.988062i	$0.450766\pi$
$338$		0			0
$339$	599.269	−	11852.6i	0.0960113	−	1.89895i
$340$		0			0
$341$	−1660.06	−	2875.31i	−0.263629	−	0.456618i
$342$		0			0
$343$	−6329.30	−	541.828i	−0.996356	−	0.0852944i
$344$		0			0
$345$	2437.10	+	1576.30i	0.380317	+	0.245985i
$346$		0			0
$347$	−4538.98	−	2620.58i	−0.702205	−	0.405418i	0.105963	−	0.994370i	$-0.466207\pi$
$347$	−4538.98	−	2620.58i	−0.702205	−	0.405418i	−0.808168	+	0.588952i	$0.799541\pi$
$348$		0			0
$349$			4502.54i			0.690588i	0.938495	+	0.345294i	$0.112221\pi$
$349$			4502.54i			0.690588i	−0.938495	+	0.345294i	$0.887779\pi$
$350$		0			0
$351$	−125.260	+	820.179i	−0.0190481	+	0.124723i
$352$		0			0
$353$	4799.70	−	8313.33i	0.723689	−	1.25347i	−0.235822	−	0.971796i	$-0.575778\pi$
$353$	4799.70	−	8313.33i	0.723689	−	1.25347i	0.959511	−	0.281671i	$-0.0908885\pi$
$354$		0			0
$355$	182.701	−	105.483i	0.0273148	−	0.0157702i
$356$		0			0
$357$	−4804.86	−	10085.1i	−0.712325	−	1.49513i
$358$		0			0
$359$	−8803.94	+	5082.96i	−1.29430	+	0.747265i	−0.979414	−	0.201863i	$-0.935300\pi$
$359$	−8803.94	+	5082.96i	−1.29430	+	0.747265i	−0.314888	+	0.949129i	$0.601967\pi$
$360$		0			0
$361$	−3386.56	+	5865.70i	−0.493740	+	0.855183i
$362$		0			0
$363$	1852.44	+	3619.13i	0.267846	+	0.523292i
$364$		0			0
$365$			1183.21i			0.169677i
$366$		0			0
$367$	−332.544	−	191.995i	−0.0472988	−	0.0273080i	0.476164	−	0.879356i	$-0.342027\pi$
$367$	−332.544	−	191.995i	−0.0472988	−	0.0273080i	−0.523463	+	0.852048i	$0.675360\pi$
$368$		0			0
$369$	13656.2	+	1384.47i	1.92660	+	0.195318i
$370$		0			0
$371$	−4867.92	+	2628.68i	−0.681213	+	0.367855i
$372$		0			0
$373$	1481.79	+	2566.54i	0.205695	+	0.356275i	0.950354	−	0.311171i	$-0.100721\pi$
$373$	1481.79	+	2566.54i	0.205695	+	0.356275i	−0.744659	+	0.667445i	$0.767388\pi$
$374$		0			0
$375$	5356.16	+	270.809i	0.737575	+	0.0372920i
$376$		0			0
$377$	−1228.94			−0.167887
$378$		0			0
$379$	13195.4			1.78839			0.894195	−	0.447677i	$-0.147749\pi$
$379$	13195.4			1.78839			0.894195	+	0.447677i	$0.147749\pi$
$380$		0			0
$381$	−8067.03	−	407.871i	−1.08474	−	0.0548448i
$382$		0			0
$383$	4475.95	+	7752.57i	0.597155	+	1.03430i	0.993239	+	0.116088i	$0.0370356\pi$
$383$	4475.95	+	7752.57i	0.597155	+	1.03430i	−0.396084	+	0.918214i	$0.629631\pi$
$384$		0			0
$385$	−1658.55	−	1021.58i	−0.219552	−	0.135233i
$386$		0			0
$387$	−10506.6	−	1065.15i	−1.38005	−	0.139909i
$388$		0			0
$389$	7594.74	+	4384.82i	0.989893	+	0.571515i	0.905242	−	0.424896i	$-0.139689\pi$
$389$	7594.74	+	4384.82i	0.989893	+	0.571515i	0.0846507	+	0.996411i	$0.473023\pi$
$390$		0			0
$391$			14439.1i			1.86757i
$392$		0			0
$393$	4959.80	+	9689.97i	0.636613	+	1.24375i
$394$		0			0
$395$	−2396.38	+	4150.65i	−0.305253	+	0.528713i
$396$		0			0
$397$	−1187.30	+	685.490i	−0.150098	+	0.0866594i	−0.573168	−	0.819438i	$-0.694286\pi$
$397$	−1187.30	+	685.490i	−0.150098	+	0.0866594i	0.423070	+	0.906097i	$0.360953\pi$
$398$		0			0
$399$	70.3631	−	889.007i	0.00882847	−	0.111544i
$400$		0			0
$401$	2392.14	−	1381.10i	0.297899	−	0.171992i	−0.343599	−	0.939116i	$-0.611646\pi$
$401$	2392.14	−	1381.10i	0.297899	−	0.171992i	0.641499	+	0.767124i	$0.278313\pi$
$402$		0			0
$403$	−419.161	+	726.008i	−0.0518112	+	0.0897396i
$404$		0			0
$405$	−1034.55	−	3105.94i	−0.126931	−	0.381075i
$406$		0			0
$407$		−	7018.82i		−	0.854815i
$408$		0			0
$409$	2310.01	+	1333.69i	0.279273	+	0.161239i	0.633094	−	0.774075i	$-0.281784\pi$
$409$	2310.01	+	1333.69i	0.279273	+	0.161239i	−0.353821	+	0.935313i	$0.615118\pi$
$410$		0			0
$411$	2665.13	+	1723.78i	0.319857	+	0.206881i
$412$		0			0
$413$	−1800.03	−	3333.40i	−0.214465	−	0.397157i
$414$		0			0
$415$	607.221	+	1051.74i	0.0718249	+	0.124404i
$416$		0			0
$417$	474.025	−	9375.45i	0.0556670	−	1.10100i
$418$		0			0
$419$	14480.6			1.68836			0.844179	−	0.536061i	$-0.180088\pi$
$419$	14480.6			1.68836			0.844179	+	0.536061i	$0.180088\pi$
$420$		0			0
$421$	14248.8			1.64951			0.824753	−	0.565494i	$-0.191314\pi$
$421$	14248.8			1.64951			0.824753	+	0.565494i	$0.191314\pi$
$422$		0			0
$423$	−891.520	−	1982.69i	−0.102476	−	0.227900i
$424$		0			0
$425$	6084.75	+	10539.1i	0.694479	+	1.20287i
$426$		0			0
$427$	−330.971	+	11623.7i	−0.0375101	+	1.31736i
$428$		0			0
$429$	−390.876	+	604.331i	−0.0439899	+	0.0680125i
$430$		0			0
$431$	−4826.49	−	2786.57i	−0.539405	−	0.311426i	0.205433	−	0.978671i	$-0.434140\pi$
$431$	−4826.49	−	2786.57i	−0.539405	−	0.311426i	−0.744838	+	0.667246i	$0.767473\pi$
$432$		0			0
$433$			2939.93i			0.326291i	0.986602	+	0.163146i	$0.0521640\pi$
$433$			2939.93i			0.326291i	−0.986602	+	0.163146i	$0.947836\pi$
$434$		0			0
$435$	4316.44	−	2209.37i	0.475765	−	0.243520i
$436$		0			0
$437$	−576.332	+	998.236i	−0.0630885	+	0.109273i
$438$		0			0
$439$	8290.73	−	4786.66i	0.901355	−	0.520398i	0.0237157	−	0.999719i	$-0.492450\pi$
$439$	8290.73	−	4786.66i	0.901355	−	0.520398i	0.877640	+	0.479321i	$0.159117\pi$
$440$		0			0
$441$	−3311.18	−	8648.83i	−0.357540	−	0.933898i
$442$		0			0
$443$	6197.42	−	3578.08i	0.664669	−	0.383747i	−0.129385	−	0.991594i	$-0.541300\pi$
$443$	6197.42	−	3578.08i	0.664669	−	0.383747i	0.794054	+	0.607848i	$0.207967\pi$
$444$		0			0
$445$	−1992.81	+	3451.64i	−0.212288	+	0.367693i
$446$		0			0
$447$	−12507.3	+	6401.86i	−1.32344	+	0.677400i
$448$		0			0
$449$			14839.2i			1.55970i	0.625964	+	0.779852i	$0.284706\pi$
$449$			14839.2i			1.55970i	−0.625964	+	0.779852i	$0.715294\pi$
$450$		0			0
$451$	10311.7	+	5953.48i	1.07663	+	0.621593i
$452$		0			0
$453$	−4347.85	+	6722.19i	−0.450949	+	0.697210i
$454$		0			0
$455$	−13.9990	+	491.646i	−0.00144238	+	0.0506565i
$456$		0			0
$457$	3787.42	+	6560.00i	0.387676	+	0.671474i	0.992136	−	0.125161i	$-0.0399447\pi$
$457$	3787.42	+	6560.00i	0.387676	+	0.671474i	−0.604461	+	0.796635i	$0.706611\pi$
$458$		0			0
$459$	10179.0	−	12713.1i	1.03511	−	1.29281i
$460$		0			0
$461$	−14850.5			−1.50034			−0.750170	−	0.661245i	$-0.770029\pi$
$461$	−14850.5			−1.50034			−0.750170	+	0.661245i	$0.770029\pi$
$462$		0			0
$463$	−3361.43			−0.337406			−0.168703	−	0.985667i	$-0.553958\pi$
$463$	−3361.43			−0.337406			−0.168703	+	0.985667i	$0.553958\pi$
$464$		0			0
$465$	167.028	−	3303.55i	0.0166575	−	0.329459i
$466$		0			0
$467$	−115.422	−	199.917i	−0.0114371	−	0.0198096i	0.860250	−	0.509872i	$-0.170307\pi$
$467$	−115.422	−	199.917i	−0.0114371	−	0.0198096i	−0.871687	+	0.490063i	$0.836974\pi$
$468$		0			0
$469$	904.441	+	1674.89i	0.0890473	+	0.164903i
$470$		0			0
$471$	−2405.65	−	1555.95i	−0.235343	−	0.152218i
$472$		0			0
$473$	−7933.44	−	4580.37i	−0.771205	−	0.445255i
$474$		0			0
$475$			971.480i			0.0938411i
$476$		0			0
$477$	−6542.45	−	4716.63i	−0.628005	−	0.452745i
$478$		0			0
$479$	−2200.43	+	3811.26i	−0.209896	+	0.363551i	−0.951682	−	0.307087i	$-0.900646\pi$
$479$	−2200.43	+	3811.26i	−0.209896	+	0.363551i	0.741786	+	0.670637i	$0.233979\pi$
$480$		0			0
$481$	−1534.80	+	886.116i	−0.145490	+	0.0839988i
$482$		0			0
$483$	−944.458	+	11932.8i	−0.0889738	+	1.12415i
$484$		0			0
$485$	−853.894	+	492.996i	−0.0799450	+	0.0461563i
$486$		0			0
$487$	−5972.31	+	10344.3i	−0.555711	+	0.962520i	0.442137	+	0.896948i	$0.354221\pi$
$487$	−5972.31	+	10344.3i	−0.555711	+	0.962520i	−0.997848	+	0.0655721i	$0.979113\pi$
$488$		0			0
$489$	5472.87	+	10692.4i	0.506118	+	0.988804i
$490$		0			0
$491$			19916.7i			1.83060i	0.402768	+	0.915302i	$0.368048\pi$
$491$			19916.7i			1.83060i	−0.402768	+	0.915302i	$0.631952\pi$
$492$		0			0
$493$	20891.1	+	12061.5i	1.90850	+	1.10187i
$494$		0			0
$495$	286.430	−	2825.32i	0.0260083	−	0.256543i
$496$		0			0
$497$	740.801	+	456.296i	0.0668601	+	0.0411825i
$498$		0			0
$499$	665.569	+	1152.80i	0.0597093	+	0.103420i	0.894335	−	0.447398i	$-0.147649\pi$
$499$	665.569	+	1152.80i	0.0597093	+	0.103420i	−0.834626	+	0.550818i	$0.814316\pi$
$500$		0			0
$501$	13393.5	+	677.177i	1.19436	+	0.0603873i
$502$		0			0
$503$	−10393.2			−0.921288			−0.460644	−	0.887585i	$-0.652382\pi$
$503$	−10393.2			−0.921288			−0.460644	+	0.887585i	$0.652382\pi$
$504$		0			0
$505$	4423.62			0.389799
$506$		0			0
$507$	−11219.9	−	567.281i	−0.982826	−	0.0496919i
$508$		0			0
$509$	−5132.02	−	8888.91i	−0.446901	−	0.774055i	0.551281	−	0.834319i	$-0.314139\pi$
$509$	−5132.02	−	8888.91i	−0.446901	−	0.774055i	−0.998182	+	0.0602640i	$0.980806\pi$
$510$		0			0
$511$	−4293.73	+	2318.61i	−0.371709	+	0.200723i
$512$		0			0
$513$	1211.16	−	472.618i	0.104238	−	0.0406756i
$514$		0			0
$515$	−4997.54	−	2885.33i	−0.427608	−	0.246879i
$516$		0			0
$517$		−	1885.78i		−	0.160418i
$518$		0			0
$519$	−2372.50	−	4635.17i	−0.200658	−	0.392026i
$520$		0			0
$521$	−1549.97	+	2684.63i	−0.130337	+	0.225750i	−0.923806	−	0.382860i	$-0.874939\pi$
$521$	−1549.97	+	2684.63i	−0.130337	+	0.225750i	0.793470	+	0.608610i	$0.208273\pi$
$522$		0			0
$523$	8265.94	−	4772.34i	0.691098	−	0.399005i	−0.112925	−	0.993603i	$-0.536022\pi$
$523$	8265.94	−	4772.34i	0.691098	−	0.399005i	0.804023	+	0.594598i	$0.202689\pi$
$524$		0			0
$525$	4339.21	+	9107.74i	0.360721	+	0.757132i
$526$		0			0
$527$	14250.9	−	8227.77i	1.17795	−	0.680090i
$528$		0			0
$529$	1652.39	−	2862.03i	0.135809	−	0.235229i
$530$		0			0
$531$	3229.80	−	4480.06i	0.263957	−	0.366136i
$532$		0			0
$533$		−	3006.47i		−	0.244324i
$534$		0			0
$535$	−711.364	−	410.706i	−0.0574859	−	0.0331895i
$536$		0			0
$537$	−13090.6	−	8466.91i	−1.05196	−	0.680399i
$538$		0			0
$539$	457.119	−	8020.53i	0.0365297	−	0.640944i
$540$		0			0
$541$	3403.83	+	5895.60i	0.270503	+	0.468524i	0.968991	−	0.247098i	$-0.0794768\pi$
$541$	3403.83	+	5895.60i	0.270503	+	0.468524i	−0.698488	+	0.715622i	$0.746143\pi$
$542$		0			0
$543$	−253.948	+	5022.68i	−0.0200699	+	0.396950i
$544$		0			0
$545$	−2617.80			−0.205751
$546$		0			0
$547$	14906.9			1.16521			0.582606	−	0.812754i	$-0.302033\pi$
$547$	14906.9			1.16521			0.582606	+	0.812754i	$0.302033\pi$
$548$		0			0
$549$	−15461.5	+	6952.30i	−1.20197	+	0.540468i
$550$		0			0
$551$	962.859	+	1667.72i	0.0744449	+	0.128942i
$552$		0			0
$553$	−19758.1	−	562.586i	−1.51935	−	0.0432615i
$554$		0			0
$555$	3797.68	−	5871.57i	0.290455	−	0.449071i
$556$		0			0
$557$	10661.9	+	6155.67i	0.811061	+	0.468266i	0.847324	−	0.531076i	$-0.178212\pi$
$557$	10661.9	+	6155.67i	0.811061	+	0.468266i	−0.0362634	+	0.999342i	$0.511546\pi$
$558$		0			0
$559$			2313.06i			0.175013i
$560$		0			0
$561$	12575.9	−	6436.95i	0.946442	−	0.484435i
$562$		0			0
$563$	−417.925	+	723.867i	−0.0312850	+	0.0541872i	−0.881244	−	0.472662i	$-0.843293\pi$
$563$	−417.925	+	723.867i	−0.0312850	+	0.0541872i	0.849959	+	0.526849i	$0.176627\pi$
$564$		0			0
$565$	8882.34	−	5128.22i	0.661386	−	0.381851i
$566$		0			0
$567$	9243.75	−	9840.60i	0.684658	−	0.728865i
$568$		0			0
$569$	5291.04	−	3054.78i	0.389828	−	0.225067i	−0.292258	−	0.956340i	$-0.594407\pi$
$569$	5291.04	−	3054.78i	0.389828	−	0.225067i	0.682086	+	0.731272i	$0.261073\pi$
$570$		0			0
$571$	−6319.69	+	10946.0i	−0.463171	+	0.802236i	−0.999117	−	0.0420166i	$-0.986622\pi$
$571$	−6319.69	+	10946.0i	−0.463171	+	0.802236i	0.535946	+	0.844252i	$0.319955\pi$
$572$		0			0
$573$	−1902.54	+	973.814i	−0.138708	+	0.0709977i
$574$		0			0
$575$		−	13039.8i		−	0.945736i
$576$		0			0
$577$	−15334.7	−	8853.51i	−1.10640	−	0.638781i	−0.168506	−	0.985701i	$-0.553894\pi$
$577$	−15334.7	−	8853.51i	−1.10640	−	0.638781i	−0.937895	+	0.346920i	$0.887228\pi$
$578$		0			0
$579$	2303.94	−	3562.11i	0.165369	−	0.255676i
$580$		0			0
$581$	−2626.72	+	4264.50i	−0.187564	+	0.304512i
$582$		0			0
$583$	−3498.19	−	6059.05i	−0.248508	−	0.430429i
$584$		0			0
$585$	−653.972	+	294.060i	−0.0462195	+	0.0207827i
$586$		0			0
$587$	−11725.2			−0.824446			−0.412223	−	0.911083i	$-0.635248\pi$
$587$	−11725.2			−0.824446			−0.412223	+	0.911083i	$0.635248\pi$
$588$		0			0
$589$	1313.63			0.0918968
$590$		0			0
$591$	166.176	−	3286.69i	0.0115661	−	0.228758i
$592$		0			0
$593$	−7523.76	−	13031.5i	−0.521018	−	0.902430i	−0.999701	−	0.0244425i	$-0.992219\pi$
$593$	−7523.76	−	13031.5i	−0.521018	−	0.902430i	0.478683	−	0.877988i	$-0.341114\pi$
$594$		0			0
$595$	5063.27	−	8220.26i	0.348864	−	0.566383i
$596$		0			0
$597$	−14935.1	−	9659.91i	−1.02388	−	0.662234i
$598$		0			0
$599$	5292.70	+	3055.74i	0.361025	+	0.208438i	0.669530	−	0.742785i	$-0.266495\pi$
$599$	5292.70	+	3055.74i	0.361025	+	0.208438i	−0.308505	+	0.951223i	$0.599829\pi$
$600$		0			0
$601$			7494.08i			0.508636i	0.967121	+	0.254318i	$0.0818509\pi$
$601$			7494.08i			0.508636i	−0.967121	+	0.254318i	$0.918149\pi$
$602$		0			0
$603$	−1622.84	+	2251.04i	−0.109597	+	0.152022i
$604$		0			0
$605$	−1756.84	+	3042.93i	−0.118059	+	0.204484i
$606$		0			0
$607$	−17917.1	+	10344.5i	−1.19808	+	0.691711i	−0.960127	−	0.279565i	$-0.909810\pi$
$607$	−17917.1	+	10344.5i	−1.19808	+	0.691711i	−0.237953	+	0.971277i	$0.576476\pi$
$608$		0			0
$609$	16476.0	+	11334.4i	1.09629	+	0.754174i
$610$		0			0
$611$	−412.361	+	238.077i	−0.0273033	+	0.0157636i
$612$		0			0
$613$	11645.5	−	20170.6i	0.767305	−	1.32901i	−0.171714	−	0.985147i	$-0.554931\pi$
$613$	11645.5	−	20170.6i	0.767305	−	1.32901i	0.939019	−	0.343865i	$-0.111736\pi$
$614$		0			0
$615$	5404.99	+	10559.7i	0.354391	+	0.692374i
$616$		0			0
$617$		−	11640.9i		−	0.759554i	−0.925078	−	0.379777i	$-0.876001\pi$
$617$		−	11640.9i		−	0.759554i	0.925078	−	0.379777i	$-0.123999\pi$
$618$		0			0
$619$	13978.4	+	8070.44i	0.907657	+	0.524036i	0.879676	−	0.475573i	$-0.157759\pi$
$619$	13978.4	+	8070.44i	0.907657	+	0.524036i	0.0279803	+	0.999608i	$0.491092\pi$
$620$		0			0
$621$	−16256.9	+	6343.78i	−1.05051	+	0.409931i
$622$		0			0
$623$	−16430.6	−	467.841i	−1.05663	−	0.0300861i
$624$		0			0
$625$	−4234.68	−	7334.68i	−0.271019	−	0.469420i
$626$		0			0
$627$	1126.35	+	56.9485i	0.0717417	+	0.00362728i
$628$		0			0
$629$	34787.4			2.20519
$630$		0			0
$631$	−9424.67			−0.594596			−0.297298	−	0.954785i	$-0.596086\pi$
$631$	−9424.67			−0.594596			−0.297298	+	0.954785i	$0.596086\pi$
$632$		0			0
$633$	5312.26	+	268.589i	0.333560	+	0.0168649i
$634$		0			0
$635$	−3490.34	−	6045.45i	−0.218126	−	0.377805i
$636$		0			0
$637$	−1811.55	+	912.623i	−0.112679	+	0.0567652i
$638$		0			0
$639$	−127.936	+	1261.95i	−0.00792031	+	0.0781252i
$640$		0			0
$641$	−1459.54	−	842.666i	−0.0899351	−	0.0519241i	0.454358	−	0.890819i	$-0.349869\pi$
$641$	−1459.54	−	842.666i	−0.0899351	−	0.0519241i	−0.544293	+	0.838895i	$0.683202\pi$
$642$		0			0
$643$		−	10186.5i		−	0.624752i	−0.949958	−	0.312376i	$-0.898875\pi$
$643$		−	10186.5i		−	0.624752i	0.949958	−	0.312376i	$-0.101125\pi$
$644$		0			0
$645$	−4158.39	−	8124.26i	−0.253855	−	0.495957i
$646$		0			0
$647$	−163.793	+	283.698i	−0.00995266	+	0.0172385i	−0.870959	−	0.491356i	$-0.836501\pi$
$647$	−163.793	+	283.698i	−0.00995266	+	0.0172385i	0.861006	+	0.508594i	$0.169835\pi$
$648$		0			0
$649$	4149.04	−	2395.45i	0.250946	−	0.144884i
$650$		0			0
$651$	12315.4	−	5867.46i	0.741445	−	0.353247i
$652$		0			0
$653$	1769.92	−	1021.87i	0.106068	−	0.0612384i	−0.446028	−	0.895019i	$-0.647162\pi$
$653$	1769.92	−	1021.87i	0.106068	−	0.0612384i	0.552096	+	0.833781i	$0.313828\pi$
$654$		0			0
$655$	−4703.82	+	8147.25i	−0.280600	+	0.486014i
$656$		0			0
$657$	−5770.73	−	4160.28i	−0.342675	−	0.247044i
$658$		0			0
$659$			27567.4i			1.62955i	0.579778	+	0.814774i	$0.303139\pi$
$659$			27567.4i			1.62955i	−0.579778	+	0.814774i	$0.696861\pi$
$660$		0			0
$661$	18417.0	+	10633.0i	1.08372	+	0.625684i	0.931897	−	0.362724i	$-0.118153\pi$
$661$	18417.0	+	10633.0i	1.08372	+	0.625684i	0.151820	+	0.988408i	$0.451487\pi$
$662$		0			0
$663$	−2995.25	−	1937.30i	−0.175454	−	0.113482i
$664$		0			0
$665$	678.152	−	366.202i	0.0395453	−	0.0213544i
$666$		0			0
$667$	−12924.1	−	22385.2i	−0.750260	−	1.29949i
$668$		0			0
$669$	399.170	−	7894.94i	0.0230685	−	0.456257i
$670$		0			0
$671$	−14705.8			−0.846065
$672$		0			0
$673$	−9377.40			−0.537106			−0.268553	−	0.963265i	$-0.586545\pi$
$673$	−9377.40			−0.537106			−0.268553	+	0.963265i	$0.586545\pi$
$674$		0			0
$675$	−9192.58	+	11481.1i	−0.524182	+	0.654677i
$676$		0			0
$677$	5342.31	+	9253.15i	0.303282	+	0.525299i	0.976877	−	0.213801i	$-0.0685844\pi$
$677$	5342.31	+	9253.15i	0.303282	+	0.525299i	−0.673596	+	0.739100i	$0.735251\pi$
$678$		0			0
$679$	−3462.30	−	2132.60i	−0.195686	−	0.120533i
$680$		0			0
$681$	−4117.71	+	6366.37i	−0.231705	+	0.358238i
$682$		0			0
$683$	24985.9	+	14425.6i	1.39979	+	0.808172i	0.994371	−	0.105957i	$-0.0337906\pi$
$683$	24985.9	+	14425.6i	1.39979	+	0.808172i	0.405424	+	0.914129i	$0.367124\pi$
$684$		0			0
$685$			2743.08i			0.153004i
$686$		0			0
$687$	−22176.8	+	11351.2i	−1.23158	+	0.630384i
$688$		0			0
$689$	−883.284	+	1529.89i	−0.0488395	+	0.0845926i
$690$		0			0
$691$	1139.99	−	658.171i	0.0627599	−	0.0362344i	−0.468292	−	0.883574i	$-0.655130\pi$
$691$	1139.99	−	658.171i	0.0627599	−	0.0362344i	0.531052	+	0.847339i	$0.321797\pi$
$692$		0			0
$693$	10814.0	−	4497.05i	0.592771	−	0.246506i
$694$		0			0
$695$	7025.98	−	4056.45i	0.383469	−	0.221396i
$696$		0			0
$697$	−29507.3	+	51108.1i	−1.60354	+	2.77741i
$698$		0			0
$699$	7721.80	−	3952.39i	0.417833	−	0.213867i
$700$		0			0
$701$			12811.2i			0.690259i	0.938555	+	0.345129i	$0.112165\pi$
$701$			12811.2i			0.690259i	−0.938555	+	0.345129i	$0.887835\pi$
$702$		0			0
$703$	2404.99	+	1388.52i	0.129027	+	0.0744938i
$704$		0			0
$705$	1020.34	−	1577.54i	0.0545081	−	0.0842747i
$706$		0			0
$707$	8668.46	+	16052.7i	0.461119	+	0.853925i
$708$		0			0
$709$	−16482.9	−	28549.2i	−0.873101	−	1.51226i	−0.858772	−	0.512358i	$-0.828772\pi$
$709$	−16482.9	−	28549.2i	−0.873101	−	1.51226i	−0.0143290	−	0.999897i	$-0.504561\pi$
$710$		0			0
$711$	−11817.6	−	26281.6i	−0.623337	−	1.38627i
$712$		0			0
$713$	−17632.4			−0.926141
$714$		0			0
$715$	−622.006			−0.0325339
$716$		0			0
$717$	926.018	−	18315.1i	0.0482326	−	0.953962i
$718$		0			0
$719$	−4307.48	−	7460.77i	−0.223424	−	0.386982i	0.732421	−	0.680851i	$-0.238390\pi$
$719$	−4307.48	−	7460.77i	−0.223424	−	0.386982i	−0.955845	+	0.293870i	$0.905057\pi$
$720$		0			0
$721$	677.375	−	23789.5i	0.0349886	−	1.22880i
$722$		0			0
$723$	21508.1	+	13911.3i	1.10636	+	0.715582i
$724$		0			0
$725$	−18866.5	−	10892.6i	−0.966463	−	0.557988i
$726$		0			0
$727$		−	26635.3i		−	1.35880i	−0.733768	−	0.679400i	$-0.762240\pi$
$727$		−	26635.3i		−	1.35880i	0.733768	−	0.679400i	$-0.237760\pi$
$728$		0			0
$729$	18785.7	+	5875.05i	0.954415	+	0.298484i
$730$		0			0
$731$	22701.7	−	39320.5i	1.14864	−	1.98950i
$732$		0			0
$733$	−5328.35	+	3076.33i	−0.268496	+	0.155016i	−0.628204	−	0.778049i	$-0.716210\pi$
$733$	−5328.35	+	3076.33i	−0.268496	+	0.155016i	0.359708	+	0.933065i	$0.382876\pi$
$734$		0			0
$735$	4722.08	−	6462.22i	0.236975	−	0.324303i
$736$		0			0
$737$	−2084.72	+	1203.61i	−0.104195	+	0.0601569i
$738$		0			0
$739$	7364.30	−	12755.3i	0.366577	−	0.634929i	−0.622451	−	0.782659i	$-0.713863\pi$
$739$	7364.30	−	12755.3i	0.366577	−	0.634929i	0.989028	+	0.147729i	$0.0471965\pi$
$740$		0			0
$741$	−129.747	−	253.487i	−0.00643236	−	0.0125669i
$742$		0			0
$743$		−	27255.1i		−	1.34575i	−0.739755	−	0.672876i	$-0.765059\pi$
$743$		−	27255.1i		−	1.34575i	0.739755	−	0.672876i	$-0.234941\pi$
$744$		0			0
$745$	−10516.1	−	6071.45i	−0.517152	−	0.298578i
$746$		0			0
$747$	−7264.55	−	736.478i	−0.355818	−	0.0360727i
$748$		0			0
$749$	96.4195	−	3386.26i	0.00470373	−	0.165195i
$750$		0			0
$751$	−3075.69	−	5327.25i	−0.149445	−	0.258847i	0.781577	−	0.623809i	$-0.214415\pi$
$751$	−3075.69	−	5327.25i	−0.149445	−	0.258847i	−0.931023	+	0.364961i	$0.881082\pi$
$752$		0			0
$753$	6720.36	+	339.783i	0.325237	+	0.0164441i
$754$		0			0
$755$	−6918.80			−0.333511
$756$		0			0
$757$	−21107.3			−1.01342			−0.506710	−	0.862117i	$-0.669139\pi$
$757$	−21107.3			−1.01342			−0.506710	+	0.862117i	$0.669139\pi$
$758$		0			0
$759$	−15118.6	−	764.399i	−0.723016	−	0.0365559i
$760$		0			0
$761$	7530.97	+	13044.0i	0.358735	+	0.621348i	0.987750	−	0.156046i	$-0.0498748\pi$
$761$	7530.97	+	13044.0i	0.358735	+	0.621348i	−0.629015	+	0.777393i	$0.716541\pi$
$762$		0			0
$763$	−5129.82	−	9499.67i	−0.243397	−	0.450736i
$764$		0			0
$765$	14003.2	+	1419.64i	0.661811	+	0.0670942i
$766$		0			0
$767$	−1047.62	−	604.845i	−0.0493187	−	0.0284742i
$768$		0			0
$769$		−	26099.2i		−	1.22387i	−0.790906	−	0.611937i	$-0.790390\pi$
$769$		−	26099.2i		−	1.22387i	0.790906	−	0.611937i	$-0.209610\pi$
$770$		0			0
$771$	−3447.31	−	6735.03i	−0.161027	−	0.314599i
$772$		0			0
$773$	−8.84542	+	15.3207i	−0.000411575	+	0.000712869i	−0.866231	−	0.499644i	$-0.833464\pi$
$773$	−8.84542	+	15.3207i	−0.000411575	+	0.000712869i	0.865820	+	0.500356i	$0.166798\pi$
$774$		0			0
$775$	−12869.8	+	7430.41i	−0.596514	+	0.344398i
$776$		0			0
$777$	28749.1	+	2275.43i	1.32737	+	0.105059i
$778$		0			0
$779$	−4079.91	+	2355.54i	−0.187648	+	0.108339i
$780$		0			0
$781$	−550.151	+	952.889i	−0.0252061	+	0.0436582i
$782$		0			0
$783$	−4401.53	+	28820.4i	−0.200891	+	1.31540i
$784$		0			0
$785$		−	2476.01i		−	0.112577i
$786$		0			0
$787$	−2066.21	−	1192.93i	−0.0935865	−	0.0540322i	0.452476	−	0.891776i	$-0.350541\pi$
$787$	−2066.21	−	1192.93i	−0.0935865	−	0.0540322i	−0.546063	+	0.837744i	$0.683874\pi$
$788$		0			0
$789$	−9321.90	−	6029.32i	−0.420619	−	0.272053i
$790$		0			0
$791$	36015.4	+	22183.7i	1.61891	+	0.997169i
$792$		0			0
$793$	1856.58	+	3215.70i	0.0831390	+	0.144001i
$794$		0			0
$795$	351.973	−	6961.45i	0.0157021	−	0.310563i
$796$		0			0
$797$	−13183.5			−0.585927			−0.292964	−	0.956124i	$-0.594641\pi$
$797$	−13183.5			−0.585927			−0.292964	+	0.956124i	$0.594641\pi$
$798$		0			0
$799$	9346.49			0.413836
$800$		0			0
$801$	−9827.37	−	21855.5i	−0.433499	−	0.964078i
$802$		0			0
$803$	−3085.56	−	5344.35i	−0.135600	−	0.234867i
$804$		0			0
$805$	−9102.59	+	4915.39i	−0.398539	+	0.215211i
$806$		0			0
$807$	−8148.37	+	12598.2i	−0.355435	+	0.549537i
$808$		0			0
$809$	−26645.9	−	15384.0i	−1.15800	−	0.668570i	−0.207174	−	0.978304i	$-0.566426\pi$
$809$	−26645.9	−	15384.0i	−1.15800	−	0.668570i	−0.950823	+	0.309734i	$0.899760\pi$
$810$		0			0
$811$		−	42776.4i		−	1.85214i	−0.377357	−	0.926068i	$-0.623167\pi$
$811$		−	42776.4i		−	1.85214i	0.377357	−	0.926068i	$-0.376833\pi$
$812$		0			0
$813$	−27094.5	+	13868.3i	−1.16881	+	0.598256i
$814$		0			0
$815$	−5190.41	+	8990.05i	−0.223082	+	0.386390i
$816$		0			0
$817$	3138.92	−	1812.26i	0.134415	−	0.0776045i
$818$		0			0
$819$	−2348.62	−	1796.94i	−0.100204	−	0.0766671i
$820$		0			0
$821$	36141.5	−	20866.3i	1.53635	−	0.887014i	0.537305	−	0.843388i	$-0.319442\pi$
$821$	36141.5	−	20866.3i	1.53635	−	0.887014i	0.999048	−	0.0436263i	$-0.0138911\pi$
$822$		0			0
$823$	−7822.35	+	13548.7i	−0.331312	+	0.573850i	−0.982769	−	0.184836i	$-0.940825\pi$
$823$	−7822.35	+	13548.7i	−0.331312	+	0.573850i	0.651457	+	0.758685i	$0.274158\pi$
$824$		0			0
$825$	−11357.1	+	5813.13i	−0.479278	+	0.245318i
$826$		0			0
$827$		−	24395.1i		−	1.02576i	−0.858461	−	0.512879i	$-0.828579\pi$
$827$		−	24395.1i		−	1.02576i	0.858461	−	0.512879i	$-0.171421\pi$
$828$		0			0
$829$	32786.9	+	18929.5i	1.37362	+	0.793062i	0.991382	−	0.131000i	$-0.0418188\pi$
$829$	32786.9	+	18929.5i	1.37362	+	0.793062i	0.382242	+	0.924062i	$0.375152\pi$
$830$		0			0
$831$	−7910.13	+	12229.8i	−0.330204	+	0.510526i
$832$		0			0
$833$	39752.2	+	2265.62i	1.65346	+	0.0942367i
$834$		0			0
$835$	5794.92	+	10037.1i	0.240169	+	0.415986i
$836$		0			0
$837$	15524.7	+	12430.2i	0.641113	+	0.513321i
$838$		0			0
$839$	40533.9			1.66792			0.833960	−	0.551826i	$-0.186069\pi$
$839$	40533.9			1.66792			0.833960	+	0.551826i	$0.186069\pi$
$840$		0			0
$841$	−18794.8			−0.770625
$842$		0			0
$843$	−1224.16	+	24211.9i	−0.0500145	+	0.989206i
$844$		0			0
$845$	−4854.48	−	8408.21i	−0.197632	−	0.342309i
$846$		0			0
$847$	−14485.1	−	412.444i	−0.587619	−	0.0167317i
$848$		0			0
$849$	23449.7	+	15167.1i	0.947929	+	0.613112i
$850$		0			0
$851$	−32281.4	−	18637.6i	−1.30034	−	0.750752i
$852$		0			0
$853$		−	38466.5i		−	1.54404i	−0.635598	−	0.772021i	$-0.719246\pi$
$853$		−	38466.5i		−	1.54404i	0.635598	−	0.772021i	$-0.280754\pi$
$854$		0			0
$855$	911.431	+	657.075i	0.0364565	+	0.0262824i
$856$		0			0
$857$	−13054.1	+	22610.3i	−0.520326	+	0.901230i	0.479395	+	0.877599i	$0.340856\pi$
$857$	−13054.1	+	22610.3i	−0.520326	+	0.901230i	−0.999721	+	0.0236312i	$0.992477\pi$
$858$		0			0
$859$	−21033.3	+	12143.6i	−0.835445	+	0.482345i	−0.855713	−	0.517450i	$-0.826881\pi$
$859$	−21033.3	+	12143.6i	−0.835445	+	0.482345i	0.0202681	+	0.999795i	$0.493548\pi$
$860$		0			0
$861$	−27728.4	+	40306.8i	−1.09754	+	1.59541i
$862$		0			0
$863$	−32475.9	+	18750.0i	−1.28099	+	0.739579i	−0.977029	−	0.213106i	$-0.931642\pi$
$863$	−32475.9	+	18750.0i	−1.28099	+	0.739579i	−0.303960	+	0.952685i	$0.598309\pi$
$864$		0			0
$865$	2250.06	−	3897.21i	0.0884441	−	0.153190i
$866$		0			0
$867$	20271.8	+	39605.1i	0.794079	+	1.55139i
$868$		0			0
$869$		−	24996.9i		−	0.975791i
$870$		0			0
$871$	526.386	+	303.909i	0.0204775	+	0.0118227i
$872$		0			0
$873$	597.938	−	5898.00i	0.0231811	−	0.228656i
$874$		0			0
$875$	−10024.8	+	16275.3i	−0.387313	+	0.628806i
$876$		0			0
$877$	7420.70	+	12853.0i	0.285723	+	0.494887i	0.972784	−	0.231713i	$-0.0744329\pi$
$877$	7420.70	+	12853.0i	0.285723	+	0.494887i	−0.687061	+	0.726600i	$0.741100\pi$
$878$		0			0
$879$	6757.45	+	341.659i	0.259298	+	0.0131102i
$880$		0			0
$881$	30469.3			1.16520			0.582598	−	0.812760i	$-0.302036\pi$
$881$	30469.3			1.16520			0.582598	+	0.812760i	$0.302036\pi$
$882$		0			0
$883$	6758.53			0.257580			0.128790	−	0.991672i	$-0.458891\pi$
$883$	6758.53			0.257580			0.128790	+	0.991672i	$0.458891\pi$
$884$		0			0
$885$	4766.98	+	241.020i	0.181062	+	0.00915457i
$886$		0			0
$887$	−17666.5	−	30599.4i	−0.668754	−	1.15832i	−0.978253	−	0.207416i	$-0.933495\pi$
$887$	−17666.5	−	30599.4i	−0.668754	−	1.15832i	0.309499	−	0.950900i	$-0.399839\pi$
$888$		0			0
$889$	15098.5	−	24512.6i	0.569616	−	0.924776i
$890$		0			0
$891$	12772.5	+	11331.0i	0.480240	+	0.426043i
$892$		0			0
$893$	646.160	+	373.061i	0.0242138	+	0.0139798i
$894$		0			0
$895$		−	13473.5i		−	0.503207i
$896$		0			0
$897$	1741.55	+	3402.47i	0.0648257	+	0.126650i
$898$		0			0
$899$	−14728.9	+	25511.3i	−0.546427	+	0.946439i
$900$		0			0
$901$	30030.5	−	17338.1i	1.11039	−	0.641084i
$902$		0			0
$903$	21333.1	−	31010.4i	0.786182	−	1.14282i
$904$		0			0
$905$	−3764.01	+	2173.15i	−0.138254	+	0.0798210i
$906$		0			0
$907$	−10481.2	+	18153.9i	−0.383706	+	0.664598i	−0.991589	−	0.129429i	$-0.958686\pi$
$907$	−10481.2	+	18153.9i	−0.383706	+	0.664598i	0.607883	+	0.794027i	$0.292019\pi$
$908$		0			0
$909$	−15553.8	+	21574.7i	−0.567533	+	0.787226i
$910$		0			0
$911$			5419.65i			0.197103i	0.995132	+	0.0985516i	$0.0314209\pi$
$911$			5419.65i			0.197103i	−0.995132	+	0.0985516i	$0.968579\pi$
$912$		0			0
$913$	−5485.41	−	3167.00i	−0.198840	−	0.114800i
$914$		0			0
$915$	−12302.1	−	7956.87i	−0.444474	−	0.287482i
$916$		0			0
$917$	−38782.8	−	1104.29i	−1.39664	−	0.0397677i
$918$		0			0
$919$	12706.3	+	22007.9i	0.456084	+	0.789961i	0.998750	−	0.0499878i	$-0.0159183\pi$
$919$	12706.3	+	22007.9i	0.456084	+	0.789961i	−0.542666	+	0.839949i	$0.682585\pi$
$920$		0			0
$921$	−169.210	+	3346.69i	−0.00605390	+	0.119736i
$922$		0			0
$923$	277.823			0.00990754
$924$		0			0
$925$	−31416.1			−1.11671
$926$		0			0
$927$	31644.0	−	14228.8i	1.12117	−	0.504137i
$928$		0			0
$929$	−276.744	−	479.335i	−0.00977360	−	0.0169284i	0.861097	−	0.508440i	$-0.169778\pi$
$929$	−276.744	−	479.335i	−0.00977360	−	0.0169284i	−0.870871	+	0.491512i	$0.836444\pi$
$930$		0			0
$931$	2657.80	+	1743.32i	0.0935615	+	0.0613696i
$932$		0			0
$933$	−3772.55	+	5832.73i	−0.132377	+	0.204668i
$934$		0			0
$935$	10573.7	+	6104.72i	0.369836	+	0.213525i
$936$		0			0
$937$		−	18956.6i		−	0.660923i	−0.943819	−	0.330462i	$-0.892796\pi$
$937$		−	18956.6i		−	0.660923i	0.943819	−	0.330462i	$-0.107204\pi$
$938$		0			0
$939$	7796.09	−	3990.42i	0.270943	−	0.138682i
$940$		0			0
$941$	−16542.7	+	28652.8i	−0.573089	+	0.992619i	0.423157	+	0.906056i	$0.360922\pi$
$941$	−16542.7	+	28652.8i	−0.573089	+	0.992619i	−0.996246	+	0.0865632i	$0.972412\pi$
$942$		0			0
$943$	54763.2	−	31617.5i	1.89113	−	1.09184i
$944$		0			0
$945$	11479.7	+	2089.16i	0.395168	+	0.0719158i
$946$		0			0
$947$	−11619.3	+	6708.40i	−0.398708	+	0.230194i	−0.685926	−	0.727671i	$-0.740603\pi$
$947$	−11619.3	+	6708.40i	−0.398708	+	0.230194i	0.287219	+	0.957865i	$0.407269\pi$
$948$		0			0
$949$	−779.096	+	1349.43i	−0.0266497	+	0.0461586i
$950$		0			0
$951$	13939.8	−	7135.05i	0.475319	−	0.243291i
$952$		0			0
$953$			36353.5i			1.23568i	0.786303	+	0.617841i	$0.211993\pi$
$953$			36353.5i			1.23568i	−0.786303	+	0.617841i	$0.788007\pi$
$954$		0			0
$955$	−1599.64	−	923.554i	−0.0542023	−	0.0312937i
$956$		0			0
$957$	−13735.0	+	21235.6i	−0.463939	+	0.717294i
$958$		0			0
$959$	−9954.29	+	5375.31i	−0.335183	+	0.180999i
$960$		0			0
$961$	−4848.13	−	8397.21i	−0.162738	−	0.281871i
$962$		0			0
$963$	4504.30	−	2025.37i	0.150726	−	0.0677741i
$964$		0			0
$965$	3666.29			0.122303
$966$		0			0
$967$	−3453.28			−0.114840			−0.0574198	−	0.998350i	$-0.518287\pi$
$967$	−3453.28			−0.114840			−0.0574198	+	0.998350i	$0.518287\pi$
$968$		0			0
$969$	−282.254	+	5582.53i	−0.00935739	+	0.185074i
$970$		0			0
$971$	25320.0	+	43855.6i	0.836826	+	1.44943i	0.892535	+	0.450978i	$0.148925\pi$
$971$	25320.0	+	43855.6i	0.836826	+	1.44943i	−0.0557091	+	0.998447i	$0.517742\pi$
$972$		0			0
$973$	28488.4	+	17547.4i	0.938638	+	0.578154i
$974$		0			0
$975$	2704.97	+	1749.55i	0.0888497	+	0.0574672i
$976$		0			0
$977$	26914.6	+	15539.1i	0.881344	+	0.508844i	0.871101	−	0.491103i	$-0.163406\pi$
$977$	26914.6	+	15539.1i	0.881344	+	0.508844i	0.0102426	+	0.999948i	$0.496740\pi$
$978$		0			0
$979$		−	20787.2i		−	0.678613i
$980$		0			0
$981$	9204.42	−	12767.5i	0.299566	−	0.415529i
$982$		0			0
$983$	−20154.8	+	34909.1i	−0.653956	+	1.13268i	0.328199	+	0.944609i	$0.393558\pi$
$983$	−20154.8	+	34909.1i	−0.653956	+	1.13268i	−0.982155	+	0.188076i	$0.939775\pi$
$984$		0			0
$985$	2463.05	−	1422.04i	0.0796744	−	0.0460001i
$986$		0			0
$987$	7724.14	+	611.350i	0.249100	+	0.0197158i
$988$		0			0
$989$	−42132.6	+	24325.3i	−1.35464	+	0.782102i
$990$		0			0
$991$	2007.28	−	3476.71i	0.0643425	−	0.111444i	−0.832060	−	0.554686i	$-0.812838\pi$
$991$	2007.28	−	3476.71i	0.0643425	−	0.111444i	0.896402	+	0.443242i	$0.146172\pi$
$992$		0			0
$993$	1867.79	+	3649.11i	0.0596904	+	0.116617i
$994$		0			0
$995$		−	15372.0i		−	0.489773i
$996$		0			0
$997$	36113.8	+	20850.3i	1.14718	+	0.662323i	0.948198	−	0.317680i	$-0.102904\pi$
$997$	36113.8	+	20850.3i	1.14718	+	0.662323i	0.198980	+	0.980004i	$0.436237\pi$
$998$		0			0
$999$	15283.7	+	39166.9i	0.484039	+	1.24043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.e.17.1		16
3.2	odd	2	inner	336.4.bc.e.17.3		16
4.3	odd	2		42.4.f.a.17.8	yes	16
7.5	odd	6	inner	336.4.bc.e.257.3		16
12.11	even	2		42.4.f.a.17.3	yes	16
21.5	even	6	inner	336.4.bc.e.257.1		16
28.3	even	6		294.4.d.a.293.14		16
28.11	odd	6		294.4.d.a.293.11		16
28.19	even	6		42.4.f.a.5.3	✓	16
28.23	odd	6		294.4.f.a.215.2		16
28.27	even	2		294.4.f.a.227.5		16
84.11	even	6		294.4.d.a.293.6		16
84.23	even	6		294.4.f.a.215.5		16
84.47	odd	6		42.4.f.a.5.8	yes	16
84.59	odd	6		294.4.d.a.293.3		16
84.83	odd	2		294.4.f.a.227.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	28.19	even	6
42.4.f.a.5.8	yes	16	84.47	odd	6
42.4.f.a.17.3	yes	16	12.11	even	2
42.4.f.a.17.8	yes	16	4.3	odd	2
294.4.d.a.293.3		16	84.59	odd	6
294.4.d.a.293.6		16	84.11	even	6
294.4.d.a.293.11		16	28.11	odd	6
294.4.d.a.293.14		16	28.3	even	6
294.4.f.a.215.2		16	28.23	odd	6
294.4.f.a.215.5		16	84.23	even	6
294.4.f.a.227.2		16	84.83	odd	2
294.4.f.a.227.5		16	28.27	even	2
336.4.bc.e.17.1		16	1.1	even	1	trivial
336.4.bc.e.17.3		16	3.2	odd	2	inner
336.4.bc.e.257.1		16	21.5	even	6	inner
336.4.bc.e.257.3		16	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-5.18952 - 0.262384i) q^{3} +(-2.24534 - 3.88904i) q^{5} +(9.71288 - 15.7690i) q^{7} +(26.8623 + 2.72329i) q^{9} +(20.2835 + 11.7107i) q^{11} -5.91384i q^{13} +(10.6318 + 20.7714i) q^{15} +(-58.0418 + 100.531i) q^{17} +(-8.02533 + 4.63343i) q^{19} +(-54.5428 + 79.2849i) q^{21} +(107.721 - 62.1928i) q^{23} +(52.4169 - 90.7888i) q^{25} +(-138.688 - 21.1808i) q^{27} -207.807i q^{29} +(-122.764 - 70.8780i) q^{31} +(-102.189 - 66.0951i) q^{33} +(-83.1348 - 2.36716i) q^{35} +(-149.838 - 259.526i) q^{37} +(-1.55170 + 30.6900i) q^{39} +508.379 q^{41} -391.127 q^{43} +(-49.7240 - 110.583i) q^{45} +(-40.2575 - 69.7281i) q^{47} +(-154.320 - 306.324i) q^{49} +(327.587 - 506.481i) q^{51} +(-258.697 - 149.359i) q^{53} -105.178i q^{55} +(42.8634 - 21.9396i) q^{57} +(102.276 - 177.147i) q^{59} +(-543.757 + 313.939i) q^{61} +(303.854 - 397.139i) q^{63} +(-22.9992 + 13.2786i) q^{65} +(-51.3894 + 89.0091i) q^{67} +(-575.340 + 294.487i) q^{69} +46.9785i q^{71} +(-228.182 - 131.741i) q^{73} +(-295.840 + 457.397i) q^{75} +(381.677 - 206.105i) q^{77} +(-533.634 - 924.281i) q^{79} +(714.167 + 146.308i) q^{81} -270.436 q^{83} +521.294 q^{85} +(-54.5252 + 1078.42i) q^{87} +(-443.765 - 768.624i) q^{89} +(-93.2551 - 57.4405i) q^{91} +(618.491 + 400.034i) q^{93} +(36.0392 + 20.8072i) q^{95} -219.564i q^{97} +(512.971 + 369.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) \) 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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