LMFDB - Embedded newform 336.4.q.k.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$0.124036 - 0.214837i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.k.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(30.1558 + 52.2313i) q^{11} +36.4269 q^{13} -37.3038 q^{15} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +(-23.1403 - 50.5126i) q^{21} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +27.0000 q^{27} -61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(90.4673 - 156.694i) q^{33} +(133.361 - 187.748i) q^{35} +(-34.7634 + 60.2120i) q^{37} +(-54.6403 - 94.6398i) q^{39} +308.115 q^{41} -174.443 q^{43} +(55.9557 + 96.9181i) q^{45} +(194.681 - 337.197i) q^{47} +(336.954 + 64.1190i) q^{49} +(73.1192 - 126.646i) q^{51} +(-157.467 - 272.742i) q^{53} +749.950 q^{55} +151.650 q^{57} +(422.263 + 731.381i) q^{59} +(169.269 - 293.182i) q^{61} +(-96.5251 + 135.889i) q^{63} +(226.477 - 392.270i) q^{65} +(-485.775 - 841.387i) q^{67} -416.377 q^{69} +98.4698 q^{71} +(-355.117 - 615.082i) q^{73} +(-44.4291 + 76.9534i) q^{75} +(465.210 + 1015.50i) q^{77} +(-243.442 + 421.654i) q^{79} +(-40.5000 - 70.1481i) q^{81} -605.688 q^{83} +606.139 q^{85} +(91.7017 + 158.832i) q^{87} +(-109.034 + 188.853i) q^{89} +(671.656 + 63.3365i) q^{91} +(-1.75403 + 3.03807i) q^{93} +(314.284 + 544.357i) q^{95} -782.288 q^{97} -542.804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9	$ 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9} + 35 q^{11} + 124 q^{13} + 66 q^{15} - 48 q^{17} - 202 q^{19} + 3 q^{21} + 216 q^{23} - 130 q^{25} + 162 q^{27} + 106 q^{29} - 95 q^{31} + 105 q^{33} - 56 q^{35} - 262 q^{37} - 186 q^{39} + 488 q^{41} - 720 q^{43} - 99 q^{45} - 210 q^{47} - 303 q^{49} - 144 q^{51} - 393 q^{53} + 2062 q^{55} + 1212 q^{57} + 1143 q^{59} + 70 q^{61} - 126 q^{63} + 472 q^{65} - 628 q^{67} - 1296 q^{69} - 636 q^{71} - 988 q^{73} - 390 q^{75} + 1073 q^{77} + 861 q^{79} - 243 q^{81} - 1038 q^{83} + 3600 q^{85} - 159 q^{87} - 1766 q^{89} + 654 q^{91} - 285 q^{93} - 736 q^{95} + 38 q^{97} - 630 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9 + 35 * q^11 + 124 * q^13 + 66 * q^15 - 48 * q^17 - 202 * q^19 + 3 * q^21 + 216 * q^23 - 130 * q^25 + 162 * q^27 + 106 * q^29 - 95 * q^31 + 105 * q^33 - 56 * q^35 - 262 * q^37 - 186 * q^39 + 488 * q^41 - 720 * q^43 - 99 * q^45 - 210 * q^47 - 303 * q^49 - 144 * q^51 - 393 * q^53 + 2062 * q^55 + 1212 * q^57 + 1143 * q^59 + 70 * q^61 - 126 * q^63 + 472 * q^65 - 628 * q^67 - 1296 * q^69 - 636 * q^71 - 988 * q^73 - 390 * q^75 + 1073 * q^77 + 861 * q^79 - 243 * q^81 - 1038 * q^83 + 3600 * q^85 - 159 * q^87 - 1766 * q^89 + 654 * q^91 - 285 * q^93 - 736 * q^95 + 38 * q^97 - 630 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	−0.441725	−	0.897150i	$-0.645633\pi$
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	0.997818	−	0.0660299i	$-0.0210333\pi$
$6$		0			0
$7$	18.4385	+	1.73873i	0.995583	+	0.0938826i
$7$	18.4385	+	1.73873i	0.995583	+	0.0938826i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	30.1558	+	52.2313i	0.826573	+	1.43167i	0.900711	+	0.434419i	$0.143046\pi$
$11$	30.1558	+	52.2313i	0.826573	+	1.43167i	−0.0741379	+	0.997248i	$0.523621\pi$
$12$		0			0
$13$	36.4269			0.777154			0.388577	−	0.921416i	$-0.372967\pi$
$13$	36.4269			0.777154			0.388577	+	0.921416i	$0.372967\pi$
$14$		0			0
$15$	−37.3038			−0.642120
$16$		0			0
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	0.985845	−	0.167659i	$-0.0536207\pi$
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	−0.638119	+	0.769937i	$0.720287\pi$
$18$		0			0
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	−0.977302	−	0.211851i	$-0.932051\pi$
$19$	−25.2750	+	43.7776i	−0.305183	+	0.528593i	0.672119	+	0.740443i	$0.265384\pi$
$20$		0			0
$21$	−23.1403	−	50.5126i	−0.240459	−	0.524893i
$22$		0			0
$23$	69.3962	−	120.198i	0.629135	−	1.08969i	−0.358590	−	0.933495i	$-0.616743\pi$
$23$	69.3962	−	120.198i	0.629135	−	1.08969i	0.987726	−	0.156199i	$-0.0499241\pi$
$24$		0			0
$25$	−14.8097	−	25.6511i	−0.118478	−	0.205209i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−61.1345			−0.391462			−0.195731	−	0.980658i	$-0.562708\pi$
$29$	−61.1345			−0.391462			−0.195731	+	0.980658i	$0.562708\pi$
$30$		0			0
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	0.864327	−	0.502931i	$-0.167745\pi$
$31$	−0.584676	−	1.01269i	−0.00338745	−	0.00586724i	−0.867714	+	0.497064i	$0.834412\pi$
$32$		0			0
$33$	90.4673	−	156.694i	0.477222	−	0.826573i
$34$		0			0
$35$	133.361	−	187.748i	0.644062	−	0.906719i
$36$		0			0
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	−0.932863	−	0.360232i	$-0.882698\pi$
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$38$		0			0
$39$	−54.6403	−	94.6398i	−0.224345	−	0.388577i
$40$		0			0
$41$	308.115			1.17365			0.586823	−	0.809715i	$-0.300378\pi$
$41$	308.115			1.17365			0.586823	+	0.809715i	$0.300378\pi$
$42$		0			0
$43$	−174.443			−0.618657			−0.309329	−	0.950955i	$-0.600104\pi$
$43$	−174.443			−0.618657			−0.309329	+	0.950955i	$0.600104\pi$
$44$		0			0
$45$	55.9557	+	96.9181i	0.185364	+	0.321060i
$46$		0			0
$47$	194.681	−	337.197i	0.604194	−	1.04649i	−0.387984	−	0.921666i	$-0.626828\pi$
$47$	194.681	−	337.197i	0.604194	−	1.04649i	0.992178	−	0.124829i	$-0.0398382\pi$
$48$		0			0
$49$	336.954	+	64.1190i	0.982372	+	0.186936i
$50$		0			0
$51$	73.1192	−	126.646i	0.200760	−	0.347726i
$52$		0			0
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	0.586568	−	0.809900i	$-0.300479\pi$
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	−0.994678	+	0.103033i	$0.967145\pi$
$54$		0			0
$55$	749.950			1.83860
$56$		0			0
$57$	151.650			0.352395
$58$		0			0
$59$	422.263	+	731.381i	0.931762	+	1.61386i	0.780308	+	0.625396i	$0.215062\pi$
$59$	422.263	+	731.381i	0.931762	+	1.61386i	0.151455	+	0.988464i	$0.451604\pi$
$60$		0			0
$61$	169.269	−	293.182i	0.355290	−	0.615380i	−0.631878	−	0.775068i	$-0.717716\pi$
$61$	169.269	−	293.182i	0.355290	−	0.615380i	0.987167	+	0.159688i	$0.0510489\pi$
$62$		0			0
$63$	−96.5251	+	135.889i	−0.193032	+	0.271753i
$64$		0			0
$65$	226.477	−	392.270i	0.432169	−	0.748539i
$66$		0			0
$67$	−485.775	−	841.387i	−0.885774	−	1.53421i	−0.844824	−	0.535044i	$-0.820295\pi$
$67$	−485.775	−	841.387i	−0.885774	−	1.53421i	−0.0409498	−	0.999161i	$-0.513038\pi$
$68$		0			0
$69$	−416.377			−0.726463
$70$		0			0
$71$	98.4698			0.164595			0.0822973	−	0.996608i	$-0.473774\pi$
$71$	98.4698			0.164595			0.0822973	+	0.996608i	$0.473774\pi$
$72$		0			0
$73$	−355.117	−	615.082i	−0.569361	−	0.986162i	−0.996629	−	0.0820374i	$-0.973857\pi$
$73$	−355.117	−	615.082i	−0.569361	−	0.986162i	0.427268	−	0.904125i	$-0.359476\pi$
$74$		0			0
$75$	−44.4291	+	76.9534i	−0.0684030	+	0.118478i
$76$		0			0
$77$	465.210	+	1015.50i	0.688514	+	1.50294i
$78$		0			0
$79$	−243.442	+	421.654i	−0.346701	+	0.600504i	−0.985661	−	0.168736i	$-0.946031\pi$
$79$	−243.442	+	421.654i	−0.346701	+	0.600504i	0.638960	+	0.769240i	$0.279365\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−605.688			−0.800999			−0.400499	−	0.916297i	$-0.631163\pi$
$83$	−605.688			−0.800999			−0.400499	+	0.916297i	$0.631163\pi$
$84$		0			0
$85$	606.139			0.773470
$86$		0			0
$87$	91.7017	+	158.832i	0.113005	+	0.195731i
$88$		0			0
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	−0.923622	−	0.383303i	$-0.874786\pi$
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	0.793762	+	0.608229i	$0.208120\pi$
$90$		0			0
$91$	671.656	+	63.3365i	0.773722	+	0.0729612i
$92$		0			0
$93$	−1.75403	+	3.03807i	−0.00195575	+	0.00338745i
$94$		0			0
$95$	314.284	+	544.357i	0.339420	+	0.587893i
$96$		0			0
$97$	−782.288			−0.818859			−0.409429	−	0.912342i	$-0.634272\pi$
$97$	−782.288			−0.818859			−0.409429	+	0.912342i	$0.634272\pi$
$98$		0			0
$99$	−542.804			−0.551049
$100$		0			0
$101$	155.823	+	269.893i	0.153514	+	0.265895i	0.932517	−	0.361126i	$-0.117608\pi$
$101$	155.823	+	269.893i	0.153514	+	0.265895i	−0.779003	+	0.627021i	$0.784274\pi$
$102$		0			0
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	−0.899512	−	0.436897i	$-0.856078\pi$
$103$	−74.6289	+	129.261i	−0.0713922	+	0.123655i	0.828119	+	0.560552i	$0.189411\pi$
$104$		0			0
$105$	−687.825	−	64.8613i	−0.639284	−	0.0602839i
$106$		0			0
$107$	425.760	−	737.437i	0.384670	−	0.666269i	−0.607053	−	0.794661i	$-0.707648\pi$
$107$	425.760	−	737.437i	0.384670	−	0.666269i	0.991723	+	0.128393i	$0.0409818\pi$
$108$		0			0
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	−0.993062	−	0.117592i	$-0.962483\pi$
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	0.394694	−	0.918813i	$-0.370851\pi$
$110$		0			0
$111$	208.581			0.178357
$112$		0			0
$113$	1048.55			0.872917			0.436459	−	0.899724i	$-0.356233\pi$
$113$	1048.55			0.872917			0.436459	+	0.899724i	$0.356233\pi$
$114$		0			0
$115$	−862.914	−	1494.61i	−0.699715	−	1.21194i
$116$		0			0
$117$	−163.921	+	283.920i	−0.129526	+	0.224345i
$118$		0			0
$119$	376.001	+	820.765i	0.289646	+	0.632264i
$120$		0			0
$121$	−1153.24	+	1997.47i	−0.866446	+	1.50073i
$122$		0			0
$123$	−462.173	−	800.507i	−0.338803	−	0.586823i
$124$		0			0
$125$	1186.02			0.848647
$126$		0			0
$127$	−488.408			−0.341254			−0.170627	−	0.985336i	$-0.554579\pi$
$127$	−488.408			−0.341254			−0.170627	+	0.985336i	$0.554579\pi$
$128$		0			0
$129$	261.664	+	453.215i	0.178591	+	0.309329i
$130$		0			0
$131$	−927.114	+	1605.81i	−0.618338	+	1.07099i	0.371451	+	0.928453i	$0.378861\pi$
$131$	−927.114	+	1605.81i	−0.618338	+	1.07099i	−0.989789	+	0.142541i	$0.954473\pi$
$132$		0			0
$133$	−542.149	+	763.244i	−0.353461	+	0.497607i
$134$		0			0
$135$	167.867	−	290.754i	0.107020	−	0.185364i
$136$		0			0
$137$	255.558	+	442.639i	0.159370	+	0.276038i	0.934642	−	0.355591i	$-0.115720\pi$
$137$	255.558	+	442.639i	0.159370	+	0.276038i	−0.775271	+	0.631628i	$0.782387\pi$
$138$		0			0
$139$	−2266.10			−1.38279			−0.691397	−	0.722475i	$-0.743005\pi$
$139$	−2266.10			−1.38279			−0.691397	+	0.722475i	$0.743005\pi$
$140$		0			0
$141$	−1168.09			−0.697663
$142$		0			0
$143$	1098.48	+	1902.62i	0.642375	+	1.11263i
$144$		0			0
$145$	−380.091	+	658.338i	−0.217689	+	0.377048i
$146$		0			0
$147$	−338.844	−	971.610i	−0.190118	−	0.545150i
$148$		0			0
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	−0.995380	−	0.0960168i	$-0.969390\pi$
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	0.580843	+	0.814016i	$0.302723\pi$
$150$		0			0
$151$	795.913	+	1378.56i	0.428943	+	0.742952i	0.996780	−	0.0801897i	$-0.0255526\pi$
$151$	795.913	+	1378.56i	0.428943	+	0.742952i	−0.567836	+	0.823142i	$0.692219\pi$
$152$		0			0
$153$	−438.715			−0.231817
$154$		0			0
$155$	−14.5404			−0.00753494
$156$		0			0
$157$	−582.080	−	1008.19i	−0.295892	−	0.512500i	0.679300	−	0.733861i	$-0.262283\pi$
$157$	−582.080	−	1008.19i	−0.295892	−	0.512500i	−0.975192	+	0.221361i	$0.928950\pi$
$158$		0			0
$159$	−472.402	+	818.225i	−0.235622	+	0.408110i
$160$		0			0
$161$	1488.55	−	2095.60i	0.728660	−	1.02582i
$162$		0			0
$163$	−577.940	+	1001.02i	−0.277716	+	0.481019i	−0.970817	−	0.239822i	$-0.922911\pi$
$163$	−577.940	+	1001.02i	−0.277716	+	0.481019i	0.693101	+	0.720841i	$0.256244\pi$
$164$		0			0
$165$	−1124.92	−	1948.43i	−0.530759	−	0.919302i
$166$		0			0
$167$	2890.61			1.33941			0.669707	−	0.742626i	$-0.266420\pi$
$167$	2890.61			1.33941			0.669707	+	0.742626i	$0.266420\pi$
$168$		0			0
$169$	−870.082			−0.396032
$170$		0			0
$171$	−227.475	−	393.998i	−0.101728	−	0.176198i
$172$		0			0
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	−0.995573	−	0.0939940i	$-0.970037\pi$
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	0.579188	+	0.815194i	$0.303370\pi$
$174$		0			0
$175$	−228.467	−	498.718i	−0.0986887	−	0.215426i
$176$		0			0
$177$	1266.79	−	2194.14i	0.537953	−	0.931762i
$178$		0			0
$179$	−2144.25	−	3713.94i	−0.895355	−	1.55080i	−0.833365	−	0.552723i	$-0.813589\pi$
$179$	−2144.25	−	3713.94i	−0.895355	−	1.55080i	−0.0619893	−	0.998077i	$-0.519744\pi$
$180$		0			0
$181$	383.732			0.157583			0.0787917	−	0.996891i	$-0.474894\pi$
$181$	383.732			0.157583			0.0787917	+	0.996891i	$0.474894\pi$
$182$		0			0
$183$	−1015.61			−0.410253
$184$		0			0
$185$	432.269	+	748.712i	0.171790	+	0.297548i
$186$		0			0
$187$	−1469.98	+	2546.07i	−0.574841	+	0.995655i
$188$		0			0
$189$	497.838	+	46.9457i	0.191600	+	0.0180677i
$190$		0			0
$191$	192.655	−	333.689i	0.0729845	−	0.126413i	−0.827224	−	0.561873i	$-0.810081\pi$
$191$	192.655	−	333.689i	0.0729845	−	0.126413i	0.900208	+	0.435460i	$0.143414\pi$
$192$		0			0
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	0.801262	−	0.598314i	$-0.204163\pi$
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	−0.918786	+	0.394756i	$0.870829\pi$
$194$		0			0
$195$	−1358.86			−0.499026
$196$		0			0
$197$	−1250.23			−0.452158			−0.226079	−	0.974109i	$-0.572591\pi$
$197$	−1250.23			−0.452158			−0.226079	+	0.974109i	$0.572591\pi$
$198$		0			0
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	0.752209	−	0.658924i	$-0.228988\pi$
$199$	−546.122	−	945.912i	−0.194541	−	0.336954i	−0.946750	+	0.321970i	$0.895655\pi$
$200$		0			0
$201$	−1457.32	+	2524.16i	−0.511402	+	0.885774i
$202$		0			0
$203$	−1127.23	−	106.296i	−0.389733	−	0.0367514i
$204$		0			0
$205$	1915.65	−	3318.00i	0.652656	−	1.13043i
$206$		0			0
$207$	624.566	+	1081.78i	0.209712	+	0.363231i
$208$		0			0
$209$	−3048.75			−1.00902
$210$		0			0
$211$	3620.05			1.18111			0.590556	−	0.806997i	$-0.298909\pi$
$211$	3620.05			1.18111			0.590556	+	0.806997i	$0.298909\pi$
$212$		0			0
$213$	−147.705	−	255.832i	−0.0475143	−	0.0822973i
$214$		0			0
$215$	−1084.56	+	1878.52i	−0.344030	+	0.595878i
$216$		0			0
$217$	−9.01974	−	19.6890i	−0.00282166	−	0.00615935i
$218$		0			0
$219$	−1065.35	+	1845.24i	−0.328721	+	0.569361i
$220$		0			0
$221$	887.835	+	1537.78i	0.270236	+	0.468063i
$222$		0			0
$223$	183.844			0.0552069			0.0276034	−	0.999619i	$-0.491212\pi$
$223$	183.844			0.0552069			0.0276034	+	0.999619i	$0.491212\pi$
$224$		0			0
$225$	266.574			0.0789850
$226$		0			0
$227$	1139.76	+	1974.12i	0.333253	+	0.577211i	0.983148	−	0.182813i	$-0.0585203\pi$
$227$	1139.76	+	1974.12i	0.333253	+	0.577211i	−0.649895	+	0.760024i	$0.725187\pi$
$228$		0			0
$229$	−2706.34	+	4687.51i	−0.780960	+	1.35266i	0.150424	+	0.988622i	$0.451936\pi$
$229$	−2706.34	+	4687.51i	−0.780960	+	1.35266i	−0.931383	+	0.364040i	$0.881397\pi$
$230$		0			0
$231$	1940.53	−	2731.90i	0.552715	−	0.778120i
$232$		0			0
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	−0.934882	−	0.354960i	$-0.884494\pi$
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	0.774845	+	0.632151i	$0.217828\pi$
$234$		0			0
$235$	−2420.78	−	4192.91i	−0.671975	−	1.16390i
$236$		0			0
$237$	1460.65			0.400336
$238$		0			0
$239$	6226.36			1.68515			0.842573	−	0.538583i	$-0.181040\pi$
$239$	6226.36			1.68515			0.842573	+	0.538583i	$0.181040\pi$
$240$		0			0
$241$	1598.10	+	2767.99i	0.427147	+	0.739841i	0.996618	−	0.0821704i	$-0.0261852\pi$
$241$	1598.10	+	2767.99i	0.427147	+	0.739841i	−0.569471	+	0.822012i	$0.692852\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	2785.42	−	3229.90i	0.726343	−	0.842248i
$246$		0			0
$247$	−920.689	+	1594.68i	−0.237174	+	0.410798i
$248$		0			0
$249$	908.532	+	1573.62i	0.231228	+	0.400499i
$250$		0			0
$251$	−239.608			−0.0602546			−0.0301273	−	0.999546i	$-0.509591\pi$
$251$	−239.608			−0.0602546			−0.0301273	+	0.999546i	$0.509591\pi$
$252$		0			0
$253$	8370.78			2.08010
$254$		0			0
$255$	−909.208	−	1574.79i	−0.223282	−	0.386735i
$256$		0			0
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	−0.905325	−	0.424720i	$-0.860372\pi$
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	0.820481	+	0.571674i	$0.193706\pi$
$258$		0			0
$259$	−745.676	+	1049.77i	−0.178896	+	0.251852i
$260$		0			0
$261$	275.105	−	476.496i	0.0652436	−	0.113005i
$262$		0			0
$263$	−459.520	−	795.912i	−0.107738	−	0.186609i	0.807115	−	0.590394i	$-0.201028\pi$
$263$	−459.520	−	795.912i	−0.107738	−	0.186609i	−0.914854	+	0.403785i	$0.867694\pi$
$264$		0			0
$265$	−3916.09			−0.907787
$266$		0			0
$267$	654.206			0.149950
$268$		0			0
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	0.979429	−	0.201788i	$-0.0646751\pi$
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	−0.664468	+	0.747317i	$0.731342\pi$
$270$		0			0
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	−0.713820	−	0.700329i	$-0.753036\pi$
$271$	1113.49	−	1928.62i	0.249593	−	0.432308i	0.963413	+	0.268021i	$0.0863698\pi$
$272$		0			0
$273$	−842.931	−	1840.02i	−0.186874	−	0.407923i
$274$		0			0
$275$	893.195	−	1547.06i	0.195861	−	0.339241i
$276$		0			0
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	−0.924379	−	0.381476i	$-0.875416\pi$
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	0.131821	−	0.991273i	$-0.457917\pi$
$278$		0			0
$279$	10.5242			0.00225830
$280$		0			0
$281$	2730.61			0.579696			0.289848	−	0.957073i	$-0.406395\pi$
$281$	2730.61			0.579696			0.289848	+	0.957073i	$0.406395\pi$
$282$		0			0
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	0.757994	−	0.652261i	$-0.226179\pi$
$283$	−884.926	−	1532.74i	−0.185878	−	0.321950i	−0.943872	+	0.330312i	$0.892846\pi$
$284$		0			0
$285$	942.853	−	1633.07i	0.195964	−	0.339420i
$286$		0			0
$287$	5681.17	+	535.729i	1.16846	+	0.110185i
$288$		0			0
$289$	1268.41	−	2196.95i	0.258174	−	0.447170i
$290$		0			0
$291$	1173.43	+	2032.44i	0.236384	+	0.409429i
$292$		0			0
$293$	8228.81			1.64072			0.820362	−	0.571844i	$-0.193772\pi$
$293$	8228.81			1.64072			0.820362	+	0.571844i	$0.193772\pi$
$294$		0			0
$295$	10501.4			2.07258
$296$		0			0
$297$	814.206	+	1410.25i	0.159074	+	0.275524i
$298$		0			0
$299$	2527.89	−	4378.43i	0.488935	−	0.846860i
$300$		0			0
$301$	−3216.45	−	303.309i	−0.615925	−	0.0580811i
$302$		0			0
$303$	467.468	−	809.679i	0.0886316	−	0.153514i
$304$		0			0
$305$	−2104.79	−	3645.61i	−0.395148	−	0.684416i
$306$		0			0
$307$	−6019.62			−1.11908			−0.559541	−	0.828803i	$-0.689023\pi$
$307$	−6019.62			−1.11908			−0.559541	+	0.828803i	$0.689023\pi$
$308$		0			0
$309$	447.773			0.0824366
$310$		0			0
$311$	596.857	+	1033.79i	0.108825	+	0.188491i	0.915295	−	0.402785i	$-0.131958\pi$
$311$	596.857	+	1033.79i	0.108825	+	0.188491i	−0.806469	+	0.591276i	$0.798624\pi$
$312$		0			0
$313$	4423.02	−	7660.89i	0.798734	−	1.38345i	−0.121707	−	0.992566i	$-0.538837\pi$
$313$	4423.02	−	7660.89i	0.798734	−	1.38345i	0.920441	−	0.390882i	$-0.127830\pi$
$314$		0			0
$315$	863.223	+	1884.31i	0.154403	+	0.337045i
$316$		0			0
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	0.460222	+	0.887804i	$0.347770\pi$
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	−0.998972	+	0.0453380i	$0.985564\pi$
$318$		0			0
$319$	−1843.56	−	3193.13i	−0.323572	−	0.560442i
$320$		0			0
$321$	−2554.56			−0.444179
$322$		0			0
$323$	−2464.12			−0.424480
$324$		0			0
$325$	−539.471	−	934.391i	−0.0920753	−	0.159479i
$326$		0			0
$327$	−2042.82	+	3538.26i	−0.345468	+	0.598369i
$328$		0			0
$329$	4175.91	−	5878.90i	0.699773	−	0.985149i
$330$		0			0
$331$	1526.65	−	2644.23i	0.253511	−	0.439094i	−0.710979	−	0.703213i	$-0.751748\pi$
$331$	1526.65	−	2644.23i	0.253511	−	0.439094i	0.964490	+	0.264119i	$0.0850813\pi$
$332$		0			0
$333$	−312.871	−	541.908i	−0.0514871	−	0.0891783i
$334$		0			0
$335$	−12080.8			−1.97029
$336$		0			0
$337$	3865.80			0.624877			0.312438	−	0.949938i	$-0.398854\pi$
$337$	3865.80			0.624877			0.312438	+	0.949938i	$0.398854\pi$
$338$		0			0
$339$	−1572.83	−	2724.22i	−0.251989	−	0.436459i
$340$		0			0
$341$	35.2627	−	61.0768i	0.00559995	−	0.00969940i
$342$		0			0
$343$	6101.42	+	1768.13i	0.960483	+	0.278338i
$344$		0			0
$345$	−2588.74	+	4483.83i	−0.403980	+	0.699715i
$346$		0			0
$347$	−49.7965	−	86.2501i	−0.00770380	−	0.0133434i	0.862148	−	0.506657i	$-0.169119\pi$
$347$	−49.7965	−	86.2501i	−0.00770380	−	0.0133434i	−0.869852	+	0.493313i	$0.835786\pi$
$348$		0			0
$349$	−3607.34			−0.553285			−0.276643	−	0.960973i	$-0.589222\pi$
$349$	−3607.34			−0.553285			−0.276643	+	0.960973i	$0.589222\pi$
$350$		0			0
$351$	983.526			0.149563
$352$		0			0
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	−0.999034	−	0.0439501i	$-0.986006\pi$
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	0.461455	−	0.887164i	$-0.347328\pi$
$354$		0			0
$355$	612.216	−	1060.39i	0.0915298	−	0.158534i
$356$		0			0
$357$	1568.41	−	2208.03i	0.232518	−	0.327342i
$358$		0			0
$359$	−3250.14	+	5629.41i	−0.477816	+	0.827602i	−0.999677	−	0.0254289i	$-0.991905\pi$
$359$	−3250.14	+	5629.41i	−0.477816	+	0.827602i	0.521860	+	0.853031i	$0.325238\pi$
$360$		0			0
$361$	2151.85	+	3727.11i	0.313727	+	0.543390i
$362$		0			0
$363$	6919.44			1.00049
$364$		0			0
$365$	−8831.49			−1.26647
$366$		0			0
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	0.893866	−	0.448335i	$-0.147983\pi$
$367$	412.443	+	714.372i	0.0586631	+	0.101607i	−0.835202	+	0.549943i	$0.814650\pi$
$368$		0			0
$369$	−1386.52	+	2401.52i	−0.195608	+	0.338803i
$370$		0			0
$371$	−2429.23	−	5302.73i	−0.339945	−	0.742059i
$372$		0			0
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	−0.908596	−	0.417677i	$-0.862845\pi$
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	0.816016	+	0.578029i	$0.196178\pi$
$374$		0			0
$375$	−1779.03	−	3081.37i	−0.244983	−	0.424324i
$376$		0			0
$377$	−2226.94			−0.304226
$378$		0			0
$379$	1338.29			0.181380			0.0906902	−	0.995879i	$-0.471093\pi$
$379$	1338.29			0.181380			0.0906902	+	0.995879i	$0.471093\pi$
$380$		0			0
$381$	732.612	+	1268.92i	0.0985114	+	0.170627i
$382$		0			0
$383$	176.688	−	306.032i	0.0235727	−	0.0408290i	−0.853998	−	0.520276i	$-0.825829\pi$
$383$	176.688	−	306.032i	0.0235727	−	0.0408290i	0.877571	+	0.479447i	$0.159163\pi$
$384$		0			0
$385$	13827.9	+	1303.96i	1.83048	+	0.172613i
$386$		0			0
$387$	784.992	−	1359.65i	0.103110	−	0.178591i
$388$		0			0
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	−0.940295	−	0.340360i	$-0.889451\pi$
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	0.175387	−	0.984500i	$-0.443882\pi$
$390$		0			0
$391$	6765.59			0.875066
$392$		0			0
$393$	5562.68			0.713996
$394$		0			0
$395$	3027.11	+	5243.10i	0.385595	+	0.667871i
$396$		0			0
$397$	−6640.71	+	11502.1i	−0.839516	+	1.45408i	0.0507841	+	0.998710i	$0.483828\pi$
$397$	−6640.71	+	11502.1i	−0.839516	+	1.45408i	−0.890300	+	0.455374i	$0.849505\pi$
$398$		0			0
$399$	2796.19	+	263.678i	0.350839	+	0.0330838i
$400$		0			0
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	−0.533343	−	0.845899i	$-0.679064\pi$
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	0.999242	+	0.0389385i	$0.0123976\pi$
$402$		0			0
$403$	−21.2979	−	36.8891i	−0.00263257	−	0.00455975i
$404$		0			0
$405$	−1007.20			−0.123576
$406$		0			0
$407$	−4193.27			−0.510694
$408$		0			0
$409$	6898.30	+	11948.2i	0.833983	+	1.44450i	0.894856	+	0.446355i	$0.147278\pi$
$409$	6898.30	+	11948.2i	0.833983	+	1.44450i	−0.0608735	+	0.998145i	$0.519389\pi$
$410$		0			0
$411$	766.673	−	1327.92i	0.0920126	−	0.159370i
$412$		0			0
$413$	6514.21	+	14219.7i	0.776134	+	1.69421i
$414$		0			0
$415$	−3765.75	+	6522.46i	−0.445429	+	0.771506i
$416$		0			0
$417$	3399.16	+	5887.51i	0.399179	+	0.691397i
$418$		0			0
$419$	−9497.56			−1.10737			−0.553683	−	0.832728i	$-0.686778\pi$
$419$	−9497.56			−1.10737			−0.553683	+	0.832728i	$0.686778\pi$
$420$		0			0
$421$	624.367			0.0722797			0.0361399	−	0.999347i	$-0.488494\pi$
$421$	624.367			0.0722797			0.0361399	+	0.999347i	$0.488494\pi$
$422$		0			0
$423$	1752.13	+	3034.77i	0.201398	+	0.348832i
$424$		0			0
$425$	721.915	−	1250.39i	0.0823954	−	0.142713i
$426$		0			0
$427$	3630.82	−	5111.52i	0.411494	−	0.579306i
$428$		0			0
$429$	3295.44	−	5707.87i	0.370875	−	0.642375i
$430$		0			0
$431$	−6698.64	−	11602.4i	−0.748636	−	1.29668i	−0.948476	−	0.316848i	$-0.897376\pi$
$431$	−6698.64	−	11602.4i	−0.748636	−	1.29668i	0.199840	−	0.979829i	$-0.435958\pi$
$432$		0			0
$433$	−14057.3			−1.56016			−0.780079	−	0.625681i	$-0.784821\pi$
$433$	−14057.3			−1.56016			−0.780079	+	0.625681i	$0.784821\pi$
$434$		0			0
$435$	2280.55			0.251365
$436$		0			0
$437$	3507.98	+	6075.99i	0.384003	+	0.665112i
$438$		0			0
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.0496832	+	0.998765i	$0.515821\pi$
$439$	−8184.42	+	14175.8i	−0.889798	+	1.54117i	−0.840114	+	0.542409i	$0.817512\pi$
$440$		0			0
$441$	−2016.05	+	2337.76i	−0.217692	+	0.252430i
$442$		0			0
$443$	−589.354	+	1020.79i	−0.0632078	+	0.109479i	−0.895898	−	0.444261i	$-0.853466\pi$
$443$	−589.354	+	1020.79i	−0.0632078	+	0.109479i	0.832690	+	0.553740i	$0.186800\pi$
$444$		0			0
$445$	1355.80	+	2348.31i	0.144429	+	0.250159i
$446$		0			0
$447$	4523.70			0.478666
$448$		0			0
$449$	−12400.9			−1.30342			−0.651709	−	0.758469i	$-0.725948\pi$
$449$	−12400.9			−1.30342			−0.651709	+	0.758469i	$0.725948\pi$
$450$		0			0
$451$	9291.45	+	16093.3i	0.970105	+	1.68027i
$452$		0			0
$453$	2387.74	−	4135.68i	0.247651	−	0.428943i
$454$		0			0
$455$	4857.94	−	6839.07i	0.500535	−	0.704660i
$456$		0			0
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	0.491971	+	0.870611i	$0.336277\pi$
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	−0.999957	+	0.00924618i	$0.997057\pi$
$458$		0			0
$459$	658.073	+	1139.82i	0.0669198	+	0.115909i
$460$		0			0
$461$	−16010.3			−1.61751			−0.808755	−	0.588146i	$-0.799858\pi$
$461$	−16010.3			−1.61751			−0.808755	+	0.588146i	$0.799858\pi$
$462$		0			0
$463$	−17372.4			−1.74377			−0.871883	−	0.489714i	$-0.837101\pi$
$463$	−17372.4			−1.74377			−0.871883	+	0.489714i	$0.837101\pi$
$464$		0			0
$465$	21.8107	+	37.7772i	0.00217515	+	0.00376747i
$466$		0			0
$467$	1054.03	−	1825.64i	0.104443	−	0.180900i	−0.809068	−	0.587716i	$-0.800027\pi$
$467$	1054.03	−	1825.64i	0.104443	−	0.180900i	0.913510	+	0.406815i	$0.133361\pi$
$468$		0			0
$469$	−7494.00	−	16358.5i	−0.737826	−	1.61059i
$470$		0			0
$471$	−1746.24	+	3024.58i	−0.170833	+	0.295892i
$472$		0			0
$473$	−5260.45	−	9111.37i	−0.511365	−	0.885711i
$474$		0			0
$475$	1497.26			0.144629
$476$		0			0
$477$	2834.41			0.272073
$478$		0			0
$479$	−1225.02	−	2121.80i	−0.116853	−	0.202395i	0.801666	−	0.597772i	$-0.203947\pi$
$479$	−1225.02	−	2121.80i	−0.116853	−	0.202395i	−0.918519	+	0.395377i	$0.870614\pi$
$480$		0			0
$481$	−1266.32	+	2193.34i	−0.120040	+	0.207916i
$482$		0			0
$483$	−7677.35	−	723.967i	−0.723254	−	0.0682022i
$484$		0			0
$485$	−4863.72	+	8424.21i	−0.455361	+	0.788709i
$486$		0			0
$487$	322.618	+	558.791i	0.0300189	+	0.0519943i	0.880645	−	0.473778i	$-0.157110\pi$
$487$	322.618	+	558.791i	0.0300189	+	0.0519943i	−0.850626	+	0.525772i	$0.823777\pi$
$488$		0			0
$489$	3467.64			0.320679
$490$		0			0
$491$	−11766.1			−1.08146			−0.540731	−	0.841196i	$-0.681852\pi$
$491$	−11766.1			−1.08146			−0.540731	+	0.841196i	$0.681852\pi$
$492$		0			0
$493$	−1490.03	−	2580.81i	−0.136121	−	0.235769i
$494$		0			0
$495$	−3374.77	+	5845.28i	−0.306434	+	0.530759i
$496$		0			0
$497$	1815.63	+	171.212i	0.163868	+	0.0154526i
$498$		0			0
$499$	−22.0104	+	38.1232i	−0.00197459	+	0.00342010i	−0.867011	−	0.498289i	$-0.833962\pi$
$499$	−22.0104	+	38.1232i	−0.00197459	+	0.00342010i	0.865036	+	0.501709i	$0.167295\pi$
$500$		0			0
$501$	−4335.91	−	7510.02i	−0.386655	−	0.669707i
$502$		0			0
$503$	−8290.27			−0.734880			−0.367440	−	0.930047i	$-0.619766\pi$
$503$	−8290.27			−0.734880			−0.367440	+	0.930047i	$0.619766\pi$
$504$		0			0
$505$	3875.19			0.341473
$506$		0			0
$507$	1305.12	+	2260.54i	0.114324	+	0.198016i
$508$		0			0
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	−0.976382	−	0.216052i	$-0.930682\pi$
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	0.675298	+	0.737545i	$0.264015\pi$
$510$		0			0
$511$	−5478.36	−	11958.6i	−0.474263	−	1.03526i
$512$		0			0
$513$	−682.425	+	1181.99i	−0.0587325	+	0.101728i
$514$		0			0
$515$	927.980	+	1607.31i	0.0794014	+	0.137527i
$516$		0			0
$517$	23483.0			1.99764
$518$		0			0
$519$	5684.81			0.480800
$520$		0			0
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	−0.997199	−	0.0747919i	$-0.976171\pi$
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	0.433828	−	0.900996i	$-0.357163\pi$
$522$		0			0
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	−0.995471	−	0.0950662i	$-0.969694\pi$
$523$	−4968.50	+	8605.69i	−0.415406	+	0.719504i	0.580065	+	0.814570i	$0.303027\pi$
$524$		0			0
$525$	−953.005	+	1341.65i	−0.0792239	+	0.111532i
$526$		0			0
$527$	28.5007	−	49.3647i	0.00235581	−	0.00408038i
$528$		0			0
$529$	−3548.17	−	6145.60i	−0.291622	−	0.505104i
$530$		0			0
$531$	−7600.74			−0.621175
$532$		0			0
$533$	11223.7			0.912104
$534$		0			0
$535$	−5294.15	−	9169.74i	−0.427825	−	0.741014i
$536$		0			0
$537$	−6432.74	+	11141.8i	−0.516933	+	0.895355i
$538$		0			0
$539$	6812.07	+	19533.1i	0.544373	+	1.56095i
$540$		0			0
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	−0.989407	−	0.145166i	$-0.953628\pi$
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	0.620421	+	0.784269i	$0.286962\pi$
$542$		0			0
$543$	−575.599	−	996.966i	−0.0454904	−	0.0787917i
$544$		0			0
$545$	−16934.4			−1.33099
$546$		0			0
$547$	16821.6			1.31488			0.657438	−	0.753508i	$-0.271640\pi$
$547$	16821.6			1.31488			0.657438	+	0.753508i	$0.271640\pi$
$548$		0			0
$549$	1523.42	+	2638.64i	0.118430	+	0.205127i
$550$		0			0
$551$	1545.17	−	2676.32i	0.119467	−	0.206924i
$552$		0			0
$553$	−5221.84	+	7351.37i	−0.401546	+	0.565302i
$554$		0			0
$555$	1296.81	−	2246.14i	0.0991828	−	0.171790i
$556$		0			0
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	0.829635	−	0.558306i	$-0.188549\pi$
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	−0.898325	+	0.439332i	$0.855215\pi$
$558$		0			0
$559$	−6354.40			−0.480792
$560$		0			0
$561$	8819.86			0.663770
$562$		0			0
$563$	6107.45	+	10578.4i	0.457190	+	0.791877i	0.998811	−	0.0487460i	$-0.0155225\pi$
$563$	6107.45	+	10578.4i	0.457190	+	0.791877i	−0.541621	+	0.840623i	$0.682189\pi$
$564$		0			0
$565$	6519.17	−	11291.5i	0.485423	−	0.840776i
$566$		0			0
$567$	−624.789	−	1363.84i	−0.0462763	−	0.101016i
$568$		0			0
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	−0.934078	−	0.357070i	$-0.883776\pi$
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	0.776270	+	0.630400i	$0.217109\pi$
$570$		0			0
$571$	3179.97	+	5507.87i	0.233060	+	0.403673i	0.958707	−	0.284395i	$-0.0917927\pi$
$571$	3179.97	+	5507.87i	0.233060	+	0.403673i	−0.725647	+	0.688067i	$0.758459\pi$
$572$		0			0
$573$	−1155.93			−0.0842753
$574$		0			0
$575$	−4110.95			−0.298153
$576$		0			0
$577$	−7234.36	−	12530.3i	−0.521959	−	0.904059i	−0.999674	−	0.0255444i	$-0.991868\pi$
$577$	−7234.36	−	12530.3i	−0.521959	−	0.904059i	0.477715	−	0.878515i	$-0.341465\pi$
$578$		0			0
$579$	−945.335	+	1637.37i	−0.0678528	+	0.117525i
$580$		0			0
$581$	−11168.0	−	1053.13i	−0.797461	−	0.0751998i
$582$		0			0
$583$	9497.10	−	16449.5i	0.674665	−	1.16855i
$584$		0			0
$585$	2038.29	+	3530.43i	0.144056	+	0.249513i
$586$		0			0
$587$	11132.6			0.782777			0.391388	−	0.920226i	$-0.371995\pi$
$587$	11132.6			0.782777			0.391388	+	0.920226i	$0.371995\pi$
$588$		0			0
$589$	59.1108			0.00413517
$590$		0			0
$591$	1875.34	+	3248.19i	0.130527	+	0.226079i
$592$		0			0
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	−0.288794	−	0.957391i	$-0.593254\pi$
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	0.973522	−	0.228592i	$-0.0734123\pi$
$594$		0			0
$595$	11176.3	+	1053.91i	0.770054	+	0.0726154i
$596$		0			0
$597$	−1638.37	+	2837.73i	−0.112318	+	0.194541i
$598$		0			0
$599$	−11945.5	−	20690.2i	−0.814825	−	1.41132i	−0.909453	−	0.415806i	$-0.863500\pi$
$599$	−11945.5	−	20690.2i	−0.814825	−	1.41132i	0.0946282	−	0.995513i	$-0.469834\pi$
$600$		0			0
$601$	19395.5			1.31641			0.658204	−	0.752840i	$-0.271317\pi$
$601$	19395.5			1.31641			0.658204	+	0.752840i	$0.271317\pi$
$602$		0			0
$603$	8743.95			0.590516
$604$		0			0
$605$	14340.1	+	24837.8i	0.963648	+	1.66909i
$606$		0			0
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	−0.511880	−	0.859057i	$-0.671051\pi$
$607$	7298.36	−	12641.1i	0.488025	−	0.845285i	0.999905	+	0.0137724i	$0.00438402\pi$
$608$		0			0
$609$	1414.67	+	3088.06i	0.0941304	+	0.205475i
$610$		0			0
$611$	7091.62	−	12283.0i	0.469552	−	0.813288i
$612$		0			0
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	0.831570	−	0.555420i	$-0.187442\pi$
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	−0.896793	+	0.442451i	$0.854109\pi$
$614$		0			0
$615$	−11493.9			−0.753622
$616$		0			0
$617$	16262.4			1.06110			0.530551	−	0.847653i	$-0.321985\pi$
$617$	16262.4			1.06110			0.530551	+	0.847653i	$0.321985\pi$
$618$		0			0
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	0.602208	−	0.798339i	$-0.294288\pi$
$619$	−6010.49	−	10410.5i	−0.390278	−	0.675981i	−0.992486	+	0.122358i	$0.960954\pi$
$620$		0			0
$621$	1873.70	−	3245.34i	0.121077	−	0.209712i
$622$		0			0
$623$	−2338.79	+	3292.58i	−0.150404	+	0.211740i
$624$		0			0
$625$	9225.06	−	15978.3i	0.590404	−	1.02261i
$626$		0			0
$627$	4573.12	+	7920.87i	0.291280	+	0.504512i
$628$		0			0
$629$	−3389.16			−0.214841
$630$		0			0
$631$	−25347.6			−1.59916			−0.799582	−	0.600557i	$-0.794945\pi$
$631$	−25347.6			−1.59916			−0.799582	+	0.600557i	$0.794945\pi$
$632$		0			0
$633$	−5430.07	−	9405.16i	−0.340957	−	0.590556i
$634$		0			0
$635$	−3036.58	+	5259.51i	−0.189769	+	0.328689i
$636$		0			0
$637$	12274.2	+	2335.66i	0.763454	+	0.145278i
$638$		0			0
$639$	−443.114	+	767.496i	−0.0274324	+	0.0475143i
$640$		0			0
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	0.933961	−	0.357374i	$-0.116328\pi$
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	−0.776476	+	0.630147i	$0.782995\pi$
$642$		0			0
$643$	10931.3			0.670435			0.335217	−	0.942141i	$-0.391190\pi$
$643$	10931.3			0.670435			0.335217	+	0.942141i	$0.391190\pi$
$644$		0			0
$645$	6507.38			0.397252
$646$		0			0
$647$	−9203.06	−	15940.2i	−0.559211	−	0.968582i	−0.997563	−	0.0697783i	$-0.977771\pi$
$647$	−9203.06	−	15940.2i	−0.559211	−	0.968582i	0.438352	−	0.898804i	$-0.355563\pi$
$648$		0			0
$649$	−25467.3	+	44110.7i	−1.54034	+	2.66795i
$650$		0			0
$651$	−37.6240	+	52.9675i	−0.00226513	+	0.00318888i
$652$		0			0
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	0.396346	+	0.918101i	$0.370278\pi$
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	−0.993272	+	0.115805i	$0.963055\pi$
$654$		0			0
$655$	11528.3	+	19967.6i	0.687707	+	1.19114i
$656$		0			0
$657$	6392.11			0.379574
$658$		0			0
$659$	18858.8			1.11477			0.557385	−	0.830254i	$-0.311805\pi$
$659$	18858.8			1.11477			0.557385	+	0.830254i	$0.311805\pi$
$660$		0			0
$661$	−12916.0	−	22371.2i	−0.760023	−	1.31640i	−0.942838	−	0.333251i	$-0.891854\pi$
$661$	−12916.0	−	22371.2i	−0.760023	−	1.31640i	0.182815	−	0.983147i	$-0.441479\pi$
$662$		0			0
$663$	2663.50	−	4613.33i	0.156021	−	0.270236i
$664$		0			0
$665$	4848.43	+	10583.6i	0.282728	+	0.617162i
$666$		0			0
$667$	−4242.50	+	7348.22i	−0.246282	+	0.426573i
$668$		0			0
$669$	−275.767	−	477.642i	−0.0159369	−	0.0276034i
$670$		0			0
$671$	20417.7			1.17469
$672$		0			0
$673$	−16275.0			−0.932178			−0.466089	−	0.884738i	$-0.654337\pi$
$673$	−16275.0			−0.932178			−0.466089	+	0.884738i	$0.654337\pi$
$674$		0			0
$675$	−399.862	−	692.581i	−0.0228010	−	0.0394925i
$676$		0			0
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	−0.204137	−	0.978942i	$-0.565439\pi$
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	0.949857	−	0.312683i	$-0.101228\pi$
$678$		0			0
$679$	−14424.2	−	1360.19i	−0.815242	−	0.0768766i
$680$		0			0
$681$	3419.28	−	5922.36i	0.192404	−	0.333253i
$682$		0			0
$683$	−4036.14	−	6990.81i	−0.226118	−	0.391648i	0.730536	−	0.682874i	$-0.239270\pi$
$683$	−4036.14	−	6990.81i	−0.226118	−	0.391648i	−0.956654	+	0.291226i	$0.905937\pi$
$684$		0			0
$685$	6355.51			0.354499
$686$		0			0
$687$	16238.0			0.901774
$688$		0			0
$689$	−5736.05	−	9935.13i	−0.317164	−	0.549344i
$690$		0			0
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	0.302763	+	0.953066i	$0.402091\pi$
$691$	−12242.6	+	21204.9i	−0.673997	+	1.16740i	−0.976761	+	0.214332i	$0.931243\pi$
$692$		0			0
$693$	−10008.5	−	943.789i	−0.548615	−	0.0517339i
$694$		0			0
$695$	−14089.1	+	24403.0i	−0.768962	+	1.33188i
$696$		0			0
$697$	7509.71	+	13007.2i	0.408107	+	0.706862i
$698$		0			0
$699$	3415.10			0.184794
$700$		0			0
$701$	778.448			0.0419423			0.0209712	−	0.999780i	$-0.493324\pi$
$701$	778.448			0.0419423			0.0209712	+	0.999780i	$0.493324\pi$
$702$		0			0
$703$	−1757.29	−	3043.72i	−0.0942780	−	0.163294i
$704$		0			0
$705$	−7262.34	+	12578.7i	−0.387965	+	0.671975i
$706$		0			0
$707$	2403.86	+	5247.35i	0.127873	+	0.279133i
$708$		0			0
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	0.985389	−	0.170322i	$-0.0544806\pi$
$710$		0			0
$711$	−2190.98	−	3794.89i	−0.115567	−	0.200168i
$712$		0			0
$713$	−162.297			−0.00852466
$714$		0			0
$715$	27318.3			1.42888
$716$		0			0
$717$	−9339.54	−	16176.6i	−0.486460	−	0.842573i
$718$		0			0
$719$	−40.9418	+	70.9132i	−0.00212360	+	0.00367819i	−0.867085	−	0.498160i	$-0.834009\pi$
$719$	−40.9418	+	70.9132i	−0.00212360	+	0.00367819i	0.864962	+	0.501838i	$0.167343\pi$
$720$		0			0
$721$	−1600.79	+	2253.61i	−0.0826860	+	0.116406i
$722$		0			0
$723$	4794.29	−	8303.96i	0.246614	−	0.427147i
$724$		0			0
$725$	905.382	+	1568.17i	0.0463794	+	0.0803315i
$726$		0			0
$727$	32542.9			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$727$	32542.9			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−4251.70	−	7364.16i	−0.215123	−	0.372604i
$732$		0			0
$733$	2534.47	−	4389.83i	0.127712	−	0.221203i	−0.795078	−	0.606507i	$-0.792570\pi$
$733$	2534.47	−	4389.83i	0.127712	−	0.221203i	0.922790	+	0.385304i	$0.125903\pi$
$734$		0			0
$735$	−12569.7	−	2391.88i	−0.630801	−	0.120035i
$736$		0			0
$737$	29297.8	−	50745.3i	1.46431	−	2.53627i
$738$		0			0
$739$	−19214.2	−	33280.0i	−0.956437	−	1.65660i	−0.731045	−	0.682329i	$-0.760967\pi$
$739$	−19214.2	−	33280.0i	−0.956437	−	1.65660i	−0.225392	−	0.974268i	$-0.572366\pi$
$740$		0			0
$741$	5524.14			0.273865
$742$		0			0
$743$	−21592.9			−1.06617			−0.533086	−	0.846061i	$-0.678968\pi$
$743$	−21592.9			−1.06617			−0.533086	+	0.846061i	$0.678968\pi$
$744$		0			0
$745$	9375.07	+	16238.1i	0.461042	+	0.798548i
$746$		0			0
$747$	2725.60	−	4720.87i	0.133500	−	0.231228i
$748$		0			0
$749$	9132.55	−	12856.9i	0.445522	−	0.627212i
$750$		0			0
$751$	4056.30	−	7025.72i	0.197093	−	0.341374i	−0.750492	−	0.660880i	$-0.770183\pi$
$751$	4056.30	−	7025.72i	0.197093	−	0.341374i	0.947585	+	0.319505i	$0.103517\pi$
$752$		0			0
$753$	359.411	+	622.519i	0.0173940	+	0.0301273i
$754$		0			0
$755$	19793.7			0.954129
$756$		0			0
$757$	3108.01			0.149224			0.0746120	−	0.997213i	$-0.476228\pi$
$757$	3108.01			0.149224			0.0746120	+	0.997213i	$0.476228\pi$
$758$		0			0
$759$	−12556.2	−	21747.9i	−0.600475	−	1.04005i
$760$		0			0
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	−0.767269	−	0.641325i	$-0.778385\pi$
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	0.939038	+	0.343812i	$0.111718\pi$
$762$		0			0
$763$	−10504.8	−	22930.7i	−0.498425	−	1.08800i
$764$		0			0
$765$	−2727.62	+	4724.38i	−0.128912	+	0.223282i
$766$		0			0
$767$	15381.7	+	26641.9i	0.724123	+	1.25422i
$768$		0			0
$769$	−7533.07			−0.353250			−0.176625	−	0.984278i	$-0.556518\pi$
$769$	−7533.07			−0.353250			−0.176625	+	0.984278i	$0.556518\pi$
$770$		0			0
$771$	2097.35			0.0979693
$772$		0			0
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	0.995739	+	0.0922122i	$0.0293938\pi$
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	−0.418012	+	0.908442i	$0.637273\pi$
$774$		0			0
$775$	−17.3178	+	29.9952i	−0.000802674	+	0.00139027i
$776$		0			0
$777$	3845.90	+	362.665i	0.177569	+	0.0167446i
$778$		0			0
$779$	−7787.61	+	13488.5i	−0.358177	+	0.620381i
$780$		0			0
$781$	2969.43	+	5143.20i	0.136049	+	0.235644i
$782$		0			0
$783$	−1650.63			−0.0753368
$784$		0			0
$785$	−14475.9			−0.658173
$786$		0			0
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	0.903907	+	0.427730i	$0.140686\pi$
$787$	18156.6	+	31448.1i	0.822378	+	1.42440i	−0.0815287	+	0.996671i	$0.525980\pi$
$788$		0			0
$789$	−1378.56	+	2387.74i	−0.0622028	+	0.107738i
$790$		0			0
$791$	19333.7	+	1823.15i	0.869062	+	0.0819517i
$792$		0			0
$793$	6165.94	−	10679.7i	0.276115	−	0.478245i
$794$		0			0
$795$	5874.14	+	10174.3i	0.262056	+	0.453893i
$796$		0			0
$797$	31665.7			1.40735			0.703675	−	0.710522i	$-0.251541\pi$
$797$	31665.7			1.40735			0.703675	+	0.710522i	$0.251541\pi$
$798$		0			0
$799$	18979.9			0.840375
$800$		0			0
$801$	−981.308	−	1699.68i	−0.0432869	−	0.0749752i
$802$		0			0
$803$	21417.7	−	37096.5i	0.941237	−	1.63027i
$804$		0			0
$805$	−13312.1	−	29058.7i	−0.582844	−	1.27228i
$806$		0			0
$807$	4168.76	−	7220.51i	0.181843	−	0.314961i
$808$		0			0
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	0.699523	−	0.714610i	$-0.253396\pi$
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	−0.968632	+	0.248499i	$0.920063\pi$
$810$		0			0
$811$	−16742.4			−0.724914			−0.362457	−	0.932000i	$-0.618062\pi$
$811$	−16742.4			−0.724914			−0.362457	+	0.932000i	$0.618062\pi$
$812$		0			0
$813$	−6680.94			−0.288205
$814$		0			0
$815$	7186.45	+	12447.3i	0.308872	+	0.534982i
$816$		0			0
$817$	4409.04	−	7636.67i	0.188804	−	0.327018i
$818$		0			0
$819$	−3516.11	+	4950.02i	−0.150016	+	0.211194i
$820$		0			0
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	0.434971	+	0.900444i	$0.356759\pi$
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	−0.997293	+	0.0735259i	$0.976575\pi$
$822$		0			0
$823$	11549.3	+	20003.9i	0.489164	+	0.847257i	0.999922	−	0.0124673i	$-0.00396856\pi$
$823$	11549.3	+	20003.9i	0.489164	+	0.847257i	−0.510758	+	0.859724i	$0.670635\pi$
$824$		0			0
$825$	−5359.17			−0.226160
$826$		0			0
$827$	−20647.6			−0.868183			−0.434092	−	0.900869i	$-0.642931\pi$
$827$	−20647.6			−0.868183			−0.434092	+	0.900869i	$0.642931\pi$
$828$		0			0
$829$	11684.3	+	20237.7i	0.489519	+	0.847871i	0.999927	−	0.0120609i	$-0.00383919\pi$
$829$	11684.3	+	20237.7i	0.489519	+	0.847871i	−0.510409	+	0.859932i	$0.670506\pi$
$830$		0			0
$831$	−10961.5	+	18985.9i	−0.457583	+	0.792557i
$832$		0			0
$833$	5505.78	+	15787.4i	0.229009	+	0.656664i
$834$		0			0
$835$	17971.8	−	31128.0i	0.744838	−	1.29010i
$836$		0			0
$837$	−15.7863	−	27.3426i	−0.000651915	−	0.00112915i
$838$		0			0
$839$	−16735.5			−0.688645			−0.344322	−	0.938851i	$-0.611891\pi$
$839$	−16735.5			−0.688645			−0.344322	+	0.938851i	$0.611891\pi$
$840$		0			0
$841$	−20651.6			−0.846758
$842$		0			0
$843$	−4095.92	−	7094.34i	−0.167344	−	0.289848i
$844$		0			0
$845$	−5409.56	+	9369.63i	−0.220230	+	0.381450i
$846$		0			0
$847$	−24737.0	+	34825.1i	−1.00351	+	1.41276i
$848$		0			0
$849$	−2654.78	+	4598.21i	−0.107317	+	0.185878i
$850$		0			0
$851$	4824.90	+	8356.97i	0.194354	+	0.336631i
$852$		0			0
$853$	−10294.5			−0.413219			−0.206609	−	0.978424i	$-0.566243\pi$
$853$	−10294.5			−0.413219			−0.206609	+	0.978424i	$0.566243\pi$
$854$		0			0
$855$	−5657.12			−0.226280
$856$		0			0
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	0.982277	+	0.187437i	$0.0600180\pi$
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	−0.328813	+	0.944395i	$0.606649\pi$
$858$		0			0
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	−0.910653	−	0.413173i	$-0.864421\pi$
$859$	−2454.88	+	4251.98i	−0.0975081	+	0.168889i	0.813145	+	0.582062i	$0.197754\pi$
$860$		0			0
$861$	−7129.89	−	15563.7i	−0.282214	−	0.616039i
$862$		0			0
$863$	8897.48	−	15410.9i	0.350954	−	0.607871i	−0.635463	−	0.772132i	$-0.719191\pi$
$863$	8897.48	−	15410.9i	0.350954	−	0.607871i	0.986417	+	0.164261i	$0.0525239\pi$
$864$		0			0
$865$	11781.4	+	20406.0i	0.463097	+	0.802108i
$866$		0			0
$867$	−7610.44			−0.298113
$868$		0			0
$869$	−29364.7			−1.14629
$870$		0			0
$871$	−17695.3	−	30649.1i	−0.688383	−	1.19231i
$872$		0			0
$873$	3520.30	−	6097.33i	0.136476	−	0.236384i
$874$		0			0
$875$	21868.4	+	2062.17i	0.844899	+	0.0796732i
$876$		0			0
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	0.311099	+	0.950377i	$0.399303\pi$
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	−0.978601	+	0.205769i	$0.934030\pi$
$878$		0			0
$879$	−12343.2	−	21379.1i	−0.473636	−	0.820362i
$880$		0			0
$881$	40848.2			1.56210			0.781051	−	0.624467i	$-0.214684\pi$
$881$	40848.2			1.56210			0.781051	+	0.624467i	$0.214684\pi$
$882$		0			0
$883$	−30035.1			−1.14469			−0.572345	−	0.820013i	$-0.693966\pi$
$883$	−30035.1			−1.14469			−0.572345	+	0.820013i	$0.693966\pi$
$884$		0			0
$885$	−15752.0	−	27283.3i	−0.598304	−	1.03629i
$886$		0			0
$887$	16605.4	−	28761.3i	0.628583	−	1.08874i	−0.359253	−	0.933240i	$-0.616968\pi$
$887$	16605.4	−	28761.3i	0.628583	−	1.08874i	0.987836	−	0.155498i	$-0.0496983\pi$
$888$		0			0
$889$	−9005.49	−	849.210i	−0.339746	−	0.0320378i
$890$		0			0
$891$	2442.62	−	4230.74i	0.0918415	−	0.159074i
$892$		0			0
$893$	9841.11	+	17045.3i	0.368780	+	0.638745i
$894$		0			0
$895$	−53325.7			−1.99160
$896$		0			0
$897$	−15167.3			−0.564573
$898$		0			0
$899$	35.7439	+	61.9102i	0.00132606	+	0.00229680i
$900$		0			0
$901$	7675.93	−	13295.1i	0.283820	−	0.491591i
$902$		0			0
$903$	4036.66	+	8811.55i	0.148762	+	0.324729i
$904$		0			0
$905$	2385.78	−	4132.29i	0.0876310	−	0.151781i
$906$		0			0
$907$	1248.92	+	2163.18i	0.0457217	+	0.0791923i	0.887981	−	0.459881i	$-0.152108\pi$
$907$	1248.92	+	2163.18i	0.0457217	+	0.0791923i	−0.842259	+	0.539073i	$0.818775\pi$
$908$		0			0
$909$	−2804.81			−0.102343
$910$		0			0
$911$	1895.00			0.0689180			0.0344590	−	0.999406i	$-0.489029\pi$
$911$	1895.00			0.0689180			0.0344590	+	0.999406i	$0.489029\pi$
$912$		0			0
$913$	−18265.0	−	31635.9i	−0.662084	−	1.14676i
$914$		0			0
$915$	−6314.38	+	10936.8i	−0.228139	+	0.395148i
$916$		0			0
$917$	−19886.6	+	27996.6i	−0.716155	+	1.00821i
$918$		0			0
$919$	3135.36	−	5430.59i	0.112542	−	0.194928i	−0.804253	−	0.594287i	$-0.797434\pi$
$919$	3135.36	−	5430.59i	0.112542	−	0.194928i	0.916794	+	0.399360i	$0.130767\pi$
$920$		0			0
$921$	9029.44	+	15639.4i	0.323051	+	0.559541i
$922$		0			0
$923$	3586.95			0.127915
$924$		0			0
$925$	2059.34			0.0732008
$926$		0			0
$927$	−671.660	−	1163.35i	−0.0237974	−	0.0412183i
$928$		0			0
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	−0.440570	−	0.897718i	$-0.645224\pi$
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	0.997732	−	0.0673138i	$-0.0214429\pi$
$930$		0			0
$931$	−11323.5	+	13130.4i	−0.398616	+	0.462225i
$932$		0			0
$933$	1790.57	−	3101.36i	0.0628303	−	0.108825i
$934$		0			0
$935$	18278.6	+	31659.4i	0.639330	+	1.10735i
$936$		0			0
$937$	−22030.2			−0.768084			−0.384042	−	0.923316i	$-0.625468\pi$
$937$	−22030.2			−0.768084			−0.384042	+	0.923316i	$0.625468\pi$
$938$		0			0
$939$	−26538.1			−0.922299
$940$		0			0
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	0.997177	+	0.0750892i	$0.0239242\pi$
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	−0.433559	+	0.901125i	$0.642742\pi$
$942$		0			0
$943$	21382.0	−	37034.8i	0.738383	−	1.27892i
$944$		0			0
$945$	3600.76	−	5069.19i	0.123950	−	0.174498i
$946$		0			0
$947$	−20355.5	+	35256.8i	−0.698485	+	1.20981i	0.270507	+	0.962718i	$0.412809\pi$
$947$	−20355.5	+	35256.8i	−0.698485	+	1.20981i	−0.968992	+	0.247093i	$0.920525\pi$
$948$		0			0
$949$	−12935.8	−	22405.5i	−0.442481	−	0.766400i
$950$		0			0
$951$	18244.3			0.622095
$952$		0			0
$953$	−52516.4			−1.78507			−0.892536	−	0.450976i	$-0.851076\pi$
$953$	−52516.4			−1.78507			−0.892536	+	0.450976i	$0.851076\pi$
$954$		0			0
$955$	−2395.59	−	4149.29i	−0.0811723	−	0.140595i
$956$		0			0
$957$	−5530.67	+	9579.40i	−0.186814	+	0.323572i
$958$		0			0
$959$	3942.46	+	8605.92i	0.132751	+	0.289781i
$960$		0			0
$961$	14894.8	−	25798.6i	0.499977	−	0.865986i
$962$		0			0
$963$	3831.84	+	6636.93i	0.128223	+	0.222090i
$964$		0			0
$965$	−7836.58			−0.261418
$966$		0			0
$967$	−14721.6			−0.489570			−0.244785	−	0.969577i	$-0.578717\pi$
$967$	−14721.6			−0.489570			−0.244785	+	0.969577i	$0.578717\pi$
$968$		0			0
$969$	3696.17	+	6401.96i	0.122537	+	0.212240i
$970$		0			0
$971$	6886.25	−	11927.3i	0.227590	−	0.394198i	−0.729503	−	0.683978i	$-0.760249\pi$
$971$	6886.25	−	11927.3i	0.227590	−	0.394198i	0.957093	+	0.289779i	$0.0935819\pi$
$972$		0			0
$973$	−41783.5	−	3940.14i	−1.37669	−	0.129820i
$974$		0			0
$975$	−1618.41	+	2803.17i	−0.0531597	+	0.0920753i
$976$		0			0
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	0.588653	−	0.808386i	$-0.299659\pi$
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	−0.994409	+	0.105595i	$0.966325\pi$
$978$		0			0
$979$	−13152.0			−0.429358
$980$		0			0
$981$	12256.9			0.398912
$982$		0			0
$983$	21402.4	+	37070.0i	0.694435	+	1.20280i	0.970371	+	0.241620i	$0.0776788\pi$
$983$	21402.4	+	37070.0i	0.694435	+	1.20280i	−0.275936	+	0.961176i	$0.588988\pi$
$984$		0			0
$985$	−7773.05	+	13463.3i	−0.251442	+	0.435510i
$986$		0			0
$987$	−21537.7	−	2030.98i	−0.694582	−	0.0654984i
$988$		0			0
$989$	−12105.7	+	20967.6i	−0.389219	+	0.674147i
$990$		0			0
$991$	224.931	+	389.592i	0.00721006	+	0.0124882i	0.869608	−	0.493743i	$-0.164372\pi$
$991$	224.931	+	389.592i	0.00721006	+	0.0124882i	−0.862398	+	0.506231i	$0.831038\pi$
$992$		0			0
$993$	−9159.89			−0.292729
$994$		0			0
$995$	−13581.6			−0.432730
$996$		0			0
$997$	10736.9	+	18596.8i	0.341063	+	0.590739i	0.984630	−	0.174651i	$-0.0558796\pi$
$997$	10736.9	+	18596.8i	0.341063	+	0.590739i	−0.643567	+	0.765390i	$0.722546\pi$
$998$		0			0
$999$	−938.612	+	1625.72i	−0.0297261	+	0.0514871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.k.289.3		6
4.3	odd	2		21.4.e.b.16.2	yes	6
7.2	even	3		2352.4.a.ci.1.1		3
7.4	even	3	inner	336.4.q.k.193.3		6
7.5	odd	6		2352.4.a.cg.1.3		3
12.11	even	2		63.4.e.c.37.2		6
28.3	even	6		147.4.e.n.67.2		6
28.11	odd	6		21.4.e.b.4.2	✓	6
28.19	even	6		147.4.a.m.1.2		3
28.23	odd	6		147.4.a.l.1.2		3
28.27	even	2		147.4.e.n.79.2		6
84.11	even	6		63.4.e.c.46.2		6
84.23	even	6		441.4.a.s.1.2		3
84.47	odd	6		441.4.a.t.1.2		3
84.59	odd	6		441.4.e.w.361.2		6
84.83	odd	2		441.4.e.w.226.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.2	✓	6	28.11	odd	6
21.4.e.b.16.2	yes	6	4.3	odd	2
63.4.e.c.37.2		6	12.11	even	2
63.4.e.c.46.2		6	84.11	even	6
147.4.a.l.1.2		3	28.23	odd	6
147.4.a.m.1.2		3	28.19	even	6
147.4.e.n.67.2		6	28.3	even	6
147.4.e.n.79.2		6	28.27	even	2
336.4.q.k.193.3		6	7.4	even	3	inner
336.4.q.k.289.3		6	1.1	even	1	trivial
441.4.a.s.1.2		3	84.23	even	6
441.4.a.t.1.2		3	84.47	odd	6
441.4.e.w.226.2		6	84.83	odd	2
441.4.e.w.361.2		6	84.59	odd	6
2352.4.a.cg.1.3		3	7.5	odd	6
2352.4.a.ci.1.1		3	7.2	even	3

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(30.1558 + 52.2313i) q^{11} +36.4269 q^{13} -37.3038 q^{15} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +(-23.1403 - 50.5126i) q^{21} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +27.0000 q^{27} -61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(90.4673 - 156.694i) q^{33} +(133.361 - 187.748i) q^{35} +(-34.7634 + 60.2120i) q^{37} +(-54.6403 - 94.6398i) q^{39} +308.115 q^{41} -174.443 q^{43} +(55.9557 + 96.9181i) q^{45} +(194.681 - 337.197i) q^{47} +(336.954 + 64.1190i) q^{49} +(73.1192 - 126.646i) q^{51} +(-157.467 - 272.742i) q^{53} +749.950 q^{55} +151.650 q^{57} +(422.263 + 731.381i) q^{59} +(169.269 - 293.182i) q^{61} +(-96.5251 + 135.889i) q^{63} +(226.477 - 392.270i) q^{65} +(-485.775 - 841.387i) q^{67} -416.377 q^{69} +98.4698 q^{71} +(-355.117 - 615.082i) q^{73} +(-44.4291 + 76.9534i) q^{75} +(465.210 + 1015.50i) q^{77} +(-243.442 + 421.654i) q^{79} +(-40.5000 - 70.1481i) q^{81} -605.688 q^{83} +606.139 q^{85} +(91.7017 + 158.832i) q^{87} +(-109.034 + 188.853i) q^{89} +(671.656 + 63.3365i) q^{91} +(-1.75403 + 3.03807i) q^{93} +(314.284 + 544.357i) q^{95} -782.288 q^{97} -542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9	\( 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9} + 35 q^{11} + 124 q^{13} + 66 q^{15} - 48 q^{17} - 202 q^{19} + 3 q^{21} + 216 q^{23} - 130 q^{25} + 162 q^{27} + 106 q^{29} - 95 q^{31} + 105 q^{33} - 56 q^{35} - 262 q^{37} - 186 q^{39} + 488 q^{41} - 720 q^{43} - 99 q^{45} - 210 q^{47} - 303 q^{49} - 144 q^{51} - 393 q^{53} + 2062 q^{55} + 1212 q^{57} + 1143 q^{59} + 70 q^{61} - 126 q^{63} + 472 q^{65} - 628 q^{67} - 1296 q^{69} - 636 q^{71} - 988 q^{73} - 390 q^{75} + 1073 q^{77} + 861 q^{79} - 243 q^{81} - 1038 q^{83} + 3600 q^{85} - 159 q^{87} - 1766 q^{89} + 654 q^{91} - 285 q^{93} - 736 q^{95} + 38 q^{97} - 630 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9 + 35 * q^11 + 124 * q^13 + 66 * q^15 - 48 * q^17 - 202 * q^19 + 3 * q^21 + 216 * q^23 - 130 * q^25 + 162 * q^27 + 106 * q^29 - 95 * q^31 + 105 * q^33 - 56 * q^35 - 262 * q^37 - 186 * q^39 + 488 * q^41 - 720 * q^43 - 99 * q^45 - 210 * q^47 - 303 * q^49 - 144 * q^51 - 393 * q^53 + 2062 * q^55 + 1212 * q^57 + 1143 * q^59 + 70 * q^61 - 126 * q^63 + 472 * q^65 - 628 * q^67 - 1296 * q^69 - 636 * q^71 - 988 * q^73 - 390 * q^75 + 1073 * q^77 + 861 * q^79 - 243 * q^81 - 1038 * q^83 + 3600 * q^85 - 159 * q^87 - 1766 * q^89 + 654 * q^91 - 285 * q^93 - 736 * q^95 + 38 * q^97 - 630 * q^99

Introduction

L-functions

Modular forms

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