LMFDB - Embedded newform 336.4.q.k.289.2

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			289.2
Root			$2.65415 - 4.59712i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.k.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(-2.78070 + 4.81631i) q^{5} +(-9.67799 - 15.7904i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(-2.78070 + 4.81631i) q^{5} +(-9.67799 - 15.7904i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-6.95869 - 12.0528i) q^{11} +38.6718 q^{13} +16.6842 q^{15} +(-21.7394 - 37.6537i) q^{17} +(-54.5139 + 94.4208i) q^{19} +(-26.5077 + 48.8297i) q^{21} +(-37.4389 + 64.8461i) q^{23} +(47.0354 + 81.4677i) q^{25} +27.0000 q^{27} -72.3589 q^{29} +(32.0215 + 55.4629i) q^{31} +(-20.8761 + 36.1584i) q^{33} +(102.963 - 2.70387i) q^{35} +(-94.3636 + 163.443i) q^{37} +(-58.0077 - 100.472i) q^{39} -24.7923 q^{41} +243.881 q^{43} +(-25.0263 - 43.3468i) q^{45} +(-310.274 + 537.411i) q^{47} +(-155.673 + 305.638i) q^{49} +(-65.2182 + 112.961i) q^{51} +(143.919 + 249.276i) q^{53} +77.4001 q^{55} +327.083 q^{57} +(262.526 + 454.708i) q^{59} +(191.718 - 332.065i) q^{61} +(166.625 - 4.37567i) q^{63} +(-107.535 + 186.255i) q^{65} +(99.0583 + 171.574i) q^{67} +224.634 q^{69} -785.432 q^{71} +(165.570 + 286.776i) q^{73} +(141.106 - 244.403i) q^{75} +(-122.972 + 226.527i) q^{77} +(218.823 - 379.013i) q^{79} +(-40.5000 - 70.1481i) q^{81} -241.241 q^{83} +241.803 q^{85} +(108.538 + 187.994i) q^{87} +(-792.772 + 1373.12i) q^{89} +(-374.265 - 610.643i) q^{91} +(96.0646 - 166.389i) q^{93} +(-303.173 - 525.112i) q^{95} +79.2754 q^{97} +125.256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.78070	+	4.81631i	−0.248713	+	0.430784i	−0.963169	−	0.268897i	$-0.913341\pi$
$5$	−2.78070	+	4.81631i	−0.248713	+	0.430784i	0.714456	+	0.699681i	$0.246674\pi$
$6$		0			0
$7$	−9.67799	−	15.7904i	−0.522562	−	0.852601i
$7$	−9.67799	−	15.7904i	−0.522562	−	0.852601i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−6.95869	−	12.0528i	−0.190738	−	0.330369i	0.754757	−	0.656005i	$-0.227755\pi$
$11$	−6.95869	−	12.0528i	−0.190738	−	0.330369i	−0.945495	+	0.325636i	$0.894422\pi$
$12$		0			0
$13$	38.6718			0.825048			0.412524	−	0.910947i	$-0.364647\pi$
$13$	38.6718			0.825048			0.412524	+	0.910947i	$0.364647\pi$
$14$		0			0
$15$	16.6842			0.287189
$16$		0			0
$17$	−21.7394	−	37.6537i	−0.310152	−	0.537198i	0.668243	−	0.743943i	$-0.267046\pi$
$17$	−21.7394	−	37.6537i	−0.310152	−	0.537198i	−0.978395	+	0.206744i	$0.933713\pi$
$18$		0			0
$19$	−54.5139	+	94.4208i	−0.658228	+	1.14009i	0.322845	+	0.946452i	$0.395361\pi$
$19$	−54.5139	+	94.4208i	−0.658228	+	1.14009i	−0.981074	+	0.193633i	$0.937973\pi$
$20$		0			0
$21$	−26.5077	+	48.8297i	−0.275450	+	0.507406i
$22$		0			0
$23$	−37.4389	+	64.8461i	−0.339415	+	0.587885i	−0.984323	−	0.176376i	$-0.943563\pi$
$23$	−37.4389	+	64.8461i	−0.339415	+	0.587885i	0.644907	+	0.764261i	$0.276896\pi$
$24$		0			0
$25$	47.0354	+	81.4677i	0.376283	+	0.651742i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−72.3589			−0.463335			−0.231667	−	0.972795i	$-0.574418\pi$
$29$	−72.3589			−0.463335			−0.231667	+	0.972795i	$0.574418\pi$
$30$		0			0
$31$	32.0215	+	55.4629i	0.185524	+	0.321337i	0.943753	−	0.330652i	$-0.107268\pi$
$31$	32.0215	+	55.4629i	0.185524	+	0.321337i	−0.758229	+	0.651988i	$0.773935\pi$
$32$		0			0
$33$	−20.8761	+	36.1584i	−0.110123	+	0.190738i
$34$		0			0
$35$	102.963	−	2.70387i	0.497255	−	0.0130582i
$36$		0			0
$37$	−94.3636	+	163.443i	−0.419278	+	0.726211i	−0.995867	−	0.0908235i	$-0.971050\pi$
$37$	−94.3636	+	163.443i	−0.419278	+	0.726211i	0.576589	+	0.817034i	$0.304383\pi$
$38$		0			0
$39$	−58.0077	−	100.472i	−0.238171	−	0.412524i
$40$		0			0
$41$	−24.7923			−0.0944367			−0.0472184	−	0.998885i	$-0.515036\pi$
$41$	−24.7923			−0.0944367			−0.0472184	+	0.998885i	$0.515036\pi$
$42$		0			0
$43$	243.881			0.864920			0.432460	−	0.901653i	$-0.357646\pi$
$43$	243.881			0.864920			0.432460	+	0.901653i	$0.357646\pi$
$44$		0			0
$45$	−25.0263	−	43.3468i	−0.0829044	−	0.143595i
$46$		0			0
$47$	−310.274	+	537.411i	−0.962940	+	1.66786i	−0.247888	+	0.968789i	$0.579736\pi$
$47$	−310.274	+	537.411i	−0.962940	+	1.66786i	−0.715052	+	0.699071i	$0.753597\pi$
$48$		0			0
$49$	−155.673	+	305.638i	−0.453857	+	0.891074i
$50$		0			0
$51$	−65.2182	+	112.961i	−0.179066	+	0.310152i
$52$		0			0
$53$	143.919	+	249.276i	0.372997	+	0.646050i	0.990025	−	0.140891i	$-0.0449967\pi$
$53$	143.919	+	249.276i	0.372997	+	0.646050i	−0.617028	+	0.786941i	$0.711663\pi$
$54$		0			0
$55$	77.4001			0.189757
$56$		0			0
$57$	327.083			0.760057
$58$		0			0
$59$	262.526	+	454.708i	0.579287	+	1.00335i	0.995561	+	0.0941152i	$0.0300022\pi$
$59$	262.526	+	454.708i	0.579287	+	1.00335i	−0.416275	+	0.909239i	$0.636664\pi$
$60$		0			0
$61$	191.718	−	332.065i	0.402409	−	0.696993i	−0.591607	−	0.806226i	$-0.701506\pi$
$61$	191.718	−	332.065i	0.402409	−	0.696993i	0.994016	+	0.109234i	$0.0348397\pi$
$62$		0			0
$63$	166.625	−	4.37567i	0.333218	−	0.00875052i
$64$		0			0
$65$	−107.535	+	186.255i	−0.205200	+	0.355417i
$66$		0			0
$67$	99.0583	+	171.574i	0.180625	+	0.312852i	0.942094	−	0.335350i	$-0.108855\pi$
$67$	99.0583	+	171.574i	0.180625	+	0.312852i	−0.761468	+	0.648202i	$0.775521\pi$
$68$		0			0
$69$	224.634			0.391923
$70$		0			0
$71$	−785.432			−1.31287			−0.656434	−	0.754384i	$-0.727936\pi$
$71$	−785.432			−1.31287			−0.656434	+	0.754384i	$0.727936\pi$
$72$		0			0
$73$	165.570	+	286.776i	0.265459	+	0.459789i	0.967684	−	0.252166i	$-0.0811430\pi$
$73$	165.570	+	286.776i	0.265459	+	0.459789i	−0.702224	+	0.711956i	$0.747810\pi$
$74$		0			0
$75$	141.106	−	244.403i	0.217247	−	0.376283i
$76$		0			0
$77$	−122.972	+	226.527i	−0.182000	+	0.335262i
$78$		0			0
$79$	218.823	−	379.013i	0.311640	−	0.539776i	−0.667078	−	0.744988i	$-0.732455\pi$
$79$	218.823	−	379.013i	0.311640	−	0.539776i	0.978718	+	0.205212i	$0.0657884\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−241.241			−0.319032			−0.159516	−	0.987195i	$-0.550993\pi$
$83$	−241.241			−0.319032			−0.159516	+	0.987195i	$0.550993\pi$
$84$		0			0
$85$	241.803			0.308555
$86$		0			0
$87$	108.538	+	187.994i	0.133753	+	0.231667i
$88$		0			0
$89$	−792.772	+	1373.12i	−0.944198	+	1.63540i	−0.186849	+	0.982389i	$0.559828\pi$
$89$	−792.772	+	1373.12i	−0.944198	+	1.63540i	−0.757349	+	0.653010i	$0.773506\pi$
$90$		0			0
$91$	−374.265	−	610.643i	−0.431139	−	0.703437i
$92$		0			0
$93$	96.0646	−	166.389i	0.107112	−	0.185524i
$94$		0			0
$95$	−303.173	−	525.112i	−0.327420	−	0.567109i
$96$		0			0
$97$	79.2754			0.0829814			0.0414907	−	0.999139i	$-0.486789\pi$
$97$	79.2754			0.0829814			0.0414907	+	0.999139i	$0.486789\pi$
$98$		0			0
$99$	125.256			0.127159
$100$		0			0
$101$	−577.487	−	1000.24i	−0.568931	−	0.985418i	−0.996672	−	0.0815165i	$-0.974024\pi$
$101$	−577.487	−	1000.24i	−0.568931	−	0.985418i	0.427741	−	0.903902i	$-0.359310\pi$
$102$		0			0
$103$	−722.430	+	1251.28i	−0.691098	+	1.19702i	0.280380	+	0.959889i	$0.409539\pi$
$103$	−722.430	+	1251.28i	−0.691098	+	1.19702i	−0.971478	+	0.237128i	$0.923794\pi$
$104$		0			0
$105$	−161.469	−	263.450i	−0.150074	−	0.244858i
$106$		0			0
$107$	495.480	−	858.197i	0.447662	−	0.775374i	−0.550571	−	0.834788i	$-0.685590\pi$
$107$	495.480	−	858.197i	0.447662	−	0.775374i	0.998233	+	0.0594143i	$0.0189233\pi$
$108$		0			0
$109$	−976.585	−	1691.49i	−0.858164	−	1.48638i	−0.873678	−	0.486504i	$-0.838272\pi$
$109$	−976.585	−	1691.49i	−0.858164	−	1.48638i	0.0155145	−	0.999880i	$-0.495061\pi$
$110$		0			0
$111$	566.182			0.484141
$112$		0			0
$113$	672.882			0.560172			0.280086	−	0.959975i	$-0.409637\pi$
$113$	672.882			0.560172			0.280086	+	0.959975i	$0.409637\pi$
$114$		0			0
$115$	−208.213	−	360.635i	−0.168834	−	0.292430i
$116$		0			0
$117$	−174.023	+	301.417i	−0.137508	+	0.238171i
$118$		0			0
$119$	−384.174	+	707.686i	−0.295942	+	0.545155i
$120$		0			0
$121$	568.653	−	984.936i	0.427238	−	0.739997i
$122$		0			0
$123$	37.1884	+	64.4123i	0.0272615	+	0.0472184i
$124$		0			0
$125$	−1218.34			−0.871773
$126$		0			0
$127$	−175.815			−0.122843			−0.0614216	−	0.998112i	$-0.519563\pi$
$127$	−175.815			−0.122843			−0.0614216	+	0.998112i	$0.519563\pi$
$128$		0			0
$129$	−365.822	−	633.622i	−0.249681	−	0.432460i
$130$		0			0
$131$	562.965	−	975.085i	0.375470	−	0.650332i	−0.614928	−	0.788584i	$-0.710815\pi$
$131$	562.965	−	975.085i	0.375470	−	0.650332i	0.990397	+	0.138251i	$0.0441481\pi$
$132$		0			0
$133$	2018.53	−	53.0078i	1.31600	−	0.0345591i
$134$		0			0
$135$	−75.0789	+	130.040i	−0.0478649	+	0.0829044i
$136$		0			0
$137$	−934.350	−	1618.34i	−0.582678	−	1.00923i	−0.995161	−	0.0982624i	$-0.968672\pi$
$137$	−934.350	−	1618.34i	−0.582678	−	1.00923i	0.412483	−	0.910966i	$-0.364662\pi$
$138$		0			0
$139$	2817.19			1.71907			0.859537	−	0.511074i	$-0.170752\pi$
$139$	2817.19			1.71907			0.859537	+	0.511074i	$0.170752\pi$
$140$		0			0
$141$	1861.65			1.11191
$142$		0			0
$143$	−269.105	−	466.103i	−0.157368	−	0.272570i
$144$		0			0
$145$	201.208	−	348.503i	0.115238	−	0.199597i
$146$		0			0
$147$	1027.58	−	54.0071i	0.576555	−	0.0303023i
$148$		0			0
$149$	−900.163	+	1559.13i	−0.494928	+	0.857240i	−0.999983	−	0.00584714i	$-0.998139\pi$
$149$	−900.163	+	1559.13i	−0.494928	+	0.857240i	0.505055	+	0.863087i	$0.331472\pi$
$150$		0			0
$151$	−226.492	−	392.296i	−0.122064	−	0.211421i	0.798517	−	0.601972i	$-0.205618\pi$
$151$	−226.492	−	392.296i	−0.122064	−	0.211421i	−0.920581	+	0.390551i	$0.872285\pi$
$152$		0			0
$153$	391.309			0.206768
$154$		0			0
$155$	−356.169			−0.184569
$156$		0			0
$157$	931.829	+	1613.98i	0.473682	+	0.820441i	0.999546	−	0.0301273i	$-0.00959128\pi$
$157$	931.829	+	1613.98i	0.473682	+	0.820441i	−0.525864	+	0.850569i	$0.676258\pi$
$158$		0			0
$159$	431.758	−	747.827i	0.215350	−	0.372997i
$160$		0			0
$161$	1386.28	−	36.4046i	0.678597	−	0.0178204i
$162$		0			0
$163$	1160.57	−	2010.16i	0.557686	−	0.965940i	−0.440004	−	0.897996i	$-0.645023\pi$
$163$	1160.57	−	2010.16i	0.557686	−	0.965940i	0.997689	−	0.0679437i	$-0.0216438\pi$
$164$		0			0
$165$	−116.100	−	201.091i	−0.0547781	−	0.0948784i
$166$		0			0
$167$	−3211.62			−1.48816			−0.744079	−	0.668092i	$-0.767111\pi$
$167$	−3211.62			−1.48816			−0.744079	+	0.668092i	$0.767111\pi$
$168$		0			0
$169$	−701.494			−0.319296
$170$		0			0
$171$	−490.625	−	849.787i	−0.219409	−	0.380028i
$172$		0			0
$173$	−107.139	+	185.569i	−0.0470844	+	0.0815525i	−0.888607	−	0.458669i	$-0.848326\pi$
$173$	−107.139	+	185.569i	−0.0470844	+	0.0815525i	0.841523	+	0.540222i	$0.181660\pi$
$174$		0			0
$175$	831.199	−	1531.15i	0.359044	−	0.661395i
$176$		0			0
$177$	787.577	−	1364.12i	0.334451	−	0.579287i
$178$		0			0
$179$	−1218.61	−	2110.70i	−0.508845	−	0.881345i	−0.999948	−	0.0102437i	$-0.996739\pi$
$179$	−1218.61	−	2110.70i	−0.508845	−	0.881345i	0.491102	−	0.871102i	$-0.336594\pi$
$180$		0			0
$181$	−248.631			−0.102103			−0.0510514	−	0.998696i	$-0.516257\pi$
$181$	−248.631			−0.102103			−0.0510514	+	0.998696i	$0.516257\pi$
$182$		0			0
$183$	−1150.31			−0.464662
$184$		0			0
$185$	−524.794	−	908.970i	−0.208560	−	0.361237i
$186$		0			0
$187$	−302.555	+	524.041i	−0.118316	+	0.204929i
$188$		0			0
$189$	−261.306	−	426.341i	−0.100567	−	0.164083i
$190$		0			0
$191$	−2156.54	+	3735.24i	−0.816972	+	1.41504i	0.0909306	+	0.995857i	$0.471016\pi$
$191$	−2156.54	+	3735.24i	−0.816972	+	1.41504i	−0.907903	+	0.419180i	$0.862317\pi$
$192$		0			0
$193$	−1030.43	−	1784.75i	−0.384309	−	0.665643i	0.607364	−	0.794424i	$-0.292227\pi$
$193$	−1030.43	−	1784.75i	−0.384309	−	0.665643i	−0.991673	+	0.128781i	$0.958894\pi$
$194$		0			0
$195$	645.208			0.236945
$196$		0			0
$197$	−1666.09			−0.602557			−0.301279	−	0.953536i	$-0.597413\pi$
$197$	−1666.09			−0.602557			−0.301279	+	0.953536i	$0.597413\pi$
$198$		0			0
$199$	−543.767	−	941.832i	−0.193702	−	0.335501i	0.752773	−	0.658281i	$-0.228716\pi$
$199$	−543.767	−	941.832i	−0.193702	−	0.335501i	−0.946474	+	0.322780i	$0.895383\pi$
$200$		0			0
$201$	297.175	−	514.722i	0.104284	−	0.180625i
$202$		0			0
$203$	700.288	+	1142.58i	0.242121	+	0.395040i
$204$		0			0
$205$	68.9399	−	119.407i	0.0234877	−	0.0406818i
$206$		0			0
$207$	−336.950	−	583.615i	−0.113138	−	0.195962i
$208$		0			0
$209$	1517.38			0.502198
$210$		0			0
$211$	4676.47			1.52579			0.762895	−	0.646522i	$-0.223777\pi$
$211$	4676.47			1.52579			0.762895	+	0.646522i	$0.223777\pi$
$212$		0			0
$213$	1178.15	+	2040.61i	0.378992	+	0.656434i
$214$		0			0
$215$	−678.161	+	1174.61i	−0.215117	+	0.372594i
$216$		0			0
$217$	565.878	−	1042.40i	0.177024	−	0.326096i
$218$		0			0
$219$	496.711	−	860.329i	0.153263	−	0.265459i
$220$		0			0
$221$	−840.701	−	1456.14i	−0.255890	−	0.443214i
$222$		0			0
$223$	−3246.03			−0.974754			−0.487377	−	0.873192i	$-0.662046\pi$
$223$	−3246.03			−0.974754			−0.487377	+	0.873192i	$0.662046\pi$
$224$		0			0
$225$	−846.638			−0.250856
$226$		0			0
$227$	2569.08	+	4449.77i	0.751171	+	1.30107i	0.947256	+	0.320479i	$0.103844\pi$
$227$	2569.08	+	4449.77i	0.751171	+	1.30107i	−0.196085	+	0.980587i	$0.562823\pi$
$228$		0			0
$229$	−307.403	+	532.438i	−0.0887064	+	0.153644i	−0.906965	−	0.421207i	$-0.861607\pi$
$229$	−307.403	+	532.438i	−0.0887064	+	0.153644i	0.818258	+	0.574851i	$0.194940\pi$
$230$		0			0
$231$	772.994	−	20.2993i	0.220170	−	0.00578180i
$232$		0			0
$233$	−1413.71	+	2448.61i	−0.397490	+	0.688472i	−0.993415	−	0.114567i	$-0.963452\pi$
$233$	−1413.71	+	2448.61i	−0.397490	+	0.688472i	0.595926	+	0.803039i	$0.296785\pi$
$234$		0			0
$235$	−1725.56	−	2988.76i	−0.478992	−	0.829638i
$236$		0			0
$237$	−1312.94			−0.359851
$238$		0			0
$239$	3432.45			0.928983			0.464491	−	0.885578i	$-0.346237\pi$
$239$	3432.45			0.928983			0.464491	+	0.885578i	$0.346237\pi$
$240$		0			0
$241$	1318.06	+	2282.94i	0.352296	+	0.610195i	0.986651	−	0.162847i	$-0.0520675\pi$
$241$	1318.06	+	2282.94i	0.352296	+	0.610195i	−0.634355	+	0.773042i	$0.718734\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−1039.17	−	1599.66i	−0.270980	−	0.417137i
$246$		0			0
$247$	−2108.15	+	3651.42i	−0.543070	+	0.940625i
$248$		0			0
$249$	361.862	+	626.763i	0.0920967	+	0.159516i
$250$		0			0
$251$	−2057.57			−0.517422			−0.258711	−	0.965955i	$-0.583298\pi$
$251$	−2057.57			−0.517422			−0.258711	+	0.965955i	$0.583298\pi$
$252$		0			0
$253$	1042.10			0.258958
$254$		0			0
$255$	−362.704	−	628.222i	−0.0890722	−	0.154278i
$256$		0			0
$257$	−1075.10	+	1862.13i	−0.260946	+	0.451972i	−0.966494	−	0.256691i	$-0.917368\pi$
$257$	−1075.10	+	1862.13i	−0.260946	+	0.451972i	0.705548	+	0.708663i	$0.250701\pi$
$258$		0			0
$259$	3494.07	−	91.7566i	0.838267	−	0.0220134i
$260$		0			0
$261$	325.615	−	563.982i	0.0772225	−	0.133753i
$262$		0			0
$263$	−2295.08	−	3975.19i	−0.538100	−	0.932017i	−0.999006	−	0.0445683i	$-0.985809\pi$
$263$	−2295.08	−	3975.19i	−0.538100	−	0.932017i	0.460906	−	0.887449i	$-0.347525\pi$
$264$		0			0
$265$	−1600.79			−0.371078
$266$		0			0
$267$	4756.63			1.09027
$268$		0			0
$269$	189.689	+	328.551i	0.0429945	+	0.0744687i	0.886722	−	0.462303i	$-0.152977\pi$
$269$	189.689	+	328.551i	0.0429945	+	0.0744687i	−0.843727	+	0.536772i	$0.819644\pi$
$270$		0			0
$271$	−2684.42	+	4649.55i	−0.601723	+	1.04221i	0.390837	+	0.920460i	$0.372185\pi$
$271$	−2684.42	+	4649.55i	−0.601723	+	1.04221i	−0.992560	+	0.121755i	$0.961148\pi$
$272$		0			0
$273$	−1025.10	+	1888.33i	−0.227259	+	0.418634i
$274$		0			0
$275$	654.610	−	1133.82i	0.143543	−	0.248624i
$276$		0			0
$277$	2390.80	+	4140.99i	0.518590	+	0.898224i	0.999767	+	0.0216003i	$0.00687613\pi$
$277$	2390.80	+	4140.99i	0.518590	+	0.898224i	−0.481177	+	0.876624i	$0.659791\pi$
$278$		0			0
$279$	−576.388			−0.123683
$280$		0			0
$281$	−2076.57			−0.440845			−0.220423	−	0.975404i	$-0.570744\pi$
$281$	−2076.57			−0.440845			−0.220423	+	0.975404i	$0.570744\pi$
$282$		0			0
$283$	1278.81	+	2214.96i	0.268612	+	0.465250i	0.968504	−	0.248999i	$-0.0801017\pi$
$283$	1278.81	+	2214.96i	0.268612	+	0.465250i	−0.699892	+	0.714249i	$0.746768\pi$
$284$		0			0
$285$	−909.520	+	1575.34i	−0.189036	+	0.327420i
$286$		0			0
$287$	239.940	+	391.480i	0.0493491	+	0.0805169i
$288$		0			0
$289$	1511.30	−	2617.65i	0.307612	−	0.532800i
$290$		0			0
$291$	−118.913	−	205.963i	−0.0239547	−	0.0414907i
$292$		0			0
$293$	560.049			0.111667			0.0558335	−	0.998440i	$-0.482218\pi$
$293$	560.049			0.111667			0.0558335	+	0.998440i	$0.482218\pi$
$294$		0			0
$295$	−2920.02			−0.576305
$296$		0			0
$297$	−187.885	−	325.426i	−0.0367076	−	0.0635795i
$298$		0			0
$299$	−1447.83	+	2507.71i	−0.280034	+	0.485033i
$300$		0			0
$301$	−2360.28	−	3850.98i	−0.451975	−	0.737432i
$302$		0			0
$303$	−1732.46	+	3000.71i	−0.328473	+	0.568931i
$304$		0			0
$305$	1066.22	+	1846.75i	0.200169	+	0.346703i
$306$		0			0
$307$	−3653.02			−0.679117			−0.339558	−	0.940585i	$-0.610278\pi$
$307$	−3653.02			−0.679117			−0.339558	+	0.940585i	$0.610278\pi$
$308$		0			0
$309$	4334.58			0.798011
$310$		0			0
$311$	1746.13	+	3024.39i	0.318374	+	0.551439i	0.980149	−	0.198263i	$-0.0635300\pi$
$311$	1746.13	+	3024.39i	0.318374	+	0.551439i	−0.661775	+	0.749702i	$0.730197\pi$
$312$		0			0
$313$	−4356.05	+	7544.90i	−0.786640	+	1.36250i	0.141374	+	0.989956i	$0.454848\pi$
$313$	−4356.05	+	7544.90i	−0.786640	+	1.36250i	−0.928014	+	0.372544i	$0.878485\pi$
$314$		0			0
$315$	−442.259	+	814.685i	−0.0791063	+	0.145722i
$316$		0			0
$317$	−970.165	+	1680.37i	−0.171892	+	0.297726i	−0.939081	−	0.343695i	$-0.888321\pi$
$317$	−970.165	+	1680.37i	−0.171892	+	0.297726i	0.767189	+	0.641421i	$0.221655\pi$
$318$		0			0
$319$	503.523	+	872.127i	0.0883758	+	0.153071i
$320$		0			0
$321$	−2972.88			−0.516916
$322$		0			0
$323$	4740.39			0.816602
$324$		0			0
$325$	1818.94	+	3150.50i	0.310452	+	0.537718i
$326$		0			0
$327$	−2929.75	+	5074.48i	−0.495461	+	0.858164i
$328$		0			0
$329$	11488.8	−	301.702i	1.92522	−	0.0505574i
$330$		0			0
$331$	−2865.75	+	4963.63i	−0.475879	+	0.824247i	−0.999618	−	0.0276315i	$-0.991203\pi$
$331$	−2865.75	+	4963.63i	−0.475879	+	0.824247i	0.523739	+	0.851879i	$0.324537\pi$
$332$		0			0
$333$	−849.273	−	1470.98i	−0.139759	−	0.242070i
$334$		0			0
$335$	−1101.81			−0.179696
$336$		0			0
$337$	2403.74			0.388547			0.194273	−	0.980947i	$-0.437765\pi$
$337$	2403.74			0.388547			0.194273	+	0.980947i	$0.437765\pi$
$338$		0			0
$339$	−1009.32	−	1748.20i	−0.161708	−	0.280086i
$340$		0			0
$341$	445.656	−	771.898i	0.0707731	−	0.122583i
$342$		0			0
$343$	6332.75	−	499.826i	0.996900	−	0.0786824i
$344$		0			0
$345$	−624.638	+	1081.91i	−0.0974765	+	0.168834i
$346$		0			0
$347$	−1668.22	−	2889.45i	−0.258083	−	0.447013i	0.707645	−	0.706568i	$-0.249758\pi$
$347$	−1668.22	−	2889.45i	−0.258083	−	0.447013i	−0.965728	+	0.259555i	$0.916424\pi$
$348$		0			0
$349$	−2424.54			−0.371870			−0.185935	−	0.982562i	$-0.559531\pi$
$349$	−2424.54			−0.371870			−0.185935	+	0.982562i	$0.559531\pi$
$350$		0			0
$351$	1044.14			0.158781
$352$		0			0
$353$	6201.56	+	10741.4i	0.935059	+	1.61957i	0.774528	+	0.632540i	$0.217987\pi$
$353$	6201.56	+	10741.4i	0.935059	+	1.61957i	0.160531	+	0.987031i	$0.448679\pi$
$354$		0			0
$355$	2184.05	−	3782.88i	0.326528	−	0.565562i
$356$		0			0
$357$	2414.88	−	63.4163i	0.358009	−	0.00940153i
$358$		0			0
$359$	676.921	−	1172.46i	0.0995168	−	0.172368i	−0.811968	−	0.583702i	$-0.801604\pi$
$359$	676.921	−	1172.46i	0.0995168	−	0.172368i	0.911485	+	0.411334i	$0.134937\pi$
$360$		0			0
$361$	−2514.03	−	4354.42i	−0.366529	−	0.634848i
$362$		0			0
$363$	−3411.92			−0.493332
$364$		0			0
$365$	−1841.61			−0.264093
$366$		0			0
$367$	−689.031	−	1193.44i	−0.0980031	−	0.169746i	0.812855	−	0.582466i	$-0.197912\pi$
$367$	−689.031	−	1193.44i	−0.0980031	−	0.169746i	−0.910858	+	0.412720i	$0.864579\pi$
$368$		0			0
$369$	111.565	−	193.237i	0.0157395	−	0.0272615i
$370$		0			0
$371$	2543.31	−	4685.03i	0.355909	−	0.655619i
$372$		0			0
$373$	−2728.46	+	4725.83i	−0.378752	+	0.656017i	−0.990881	−	0.134741i	$-0.956980\pi$
$373$	−2728.46	+	4725.83i	−0.378752	+	0.656017i	0.612129	+	0.790758i	$0.290313\pi$
$374$		0			0
$375$	1827.51	+	3165.34i	0.251659	+	0.435887i
$376$		0			0
$377$	−2798.25			−0.382273
$378$		0			0
$379$	−554.675			−0.0751761			−0.0375881	−	0.999293i	$-0.511967\pi$
$379$	−554.675			−0.0751761			−0.0375881	+	0.999293i	$0.511967\pi$
$380$		0			0
$381$	263.723	+	456.781i	0.0354618	+	0.0614216i
$382$		0			0
$383$	2930.33	−	5075.48i	0.390948	−	0.677141i	−0.601627	−	0.798777i	$-0.705481\pi$
$383$	2930.33	−	5075.48i	0.390948	−	0.677141i	0.992575	+	0.121636i	$0.0388140\pi$
$384$		0			0
$385$	−749.077	−	1222.18i	−0.0991597	−	0.161787i
$386$		0			0
$387$	−1097.47	+	1900.87i	−0.144153	+	0.249681i
$388$		0			0
$389$	−3889.43	−	6736.69i	−0.506946	−	0.878056i	−0.999968	−	0.00803932i	$-0.997441\pi$
$389$	−3889.43	−	6736.69i	−0.506946	−	0.878056i	0.493022	−	0.870017i	$-0.335892\pi$
$390$		0			0
$391$	3255.60			0.421081
$392$		0			0
$393$	−3377.79			−0.433555
$394$		0			0
$395$	1216.96	+	2107.84i	0.155018	+	0.268499i
$396$		0			0
$397$	−4013.94	+	6952.35i	−0.507440	+	0.878912i	0.492523	+	0.870300i	$0.336075\pi$
$397$	−4013.94	+	6952.35i	−0.507440	+	0.878912i	−0.999963	+	0.00861270i	$0.997258\pi$
$398$		0			0
$399$	−3165.51	−	5164.77i	−0.397177	−	0.648025i
$400$		0			0
$401$	−389.990	+	675.482i	−0.0485665	+	0.0841196i	−0.889287	−	0.457350i	$-0.848799\pi$
$401$	−389.990	+	675.482i	−0.0485665	+	0.0841196i	0.840720	+	0.541470i	$0.182132\pi$
$402$		0			0
$403$	1238.33	+	2144.85i	0.153066	+	0.265118i
$404$		0			0
$405$	450.473			0.0552696
$406$		0			0
$407$	2626.59			0.319890
$408$		0			0
$409$	−7346.25	−	12724.1i	−0.888139	−	1.53830i	−0.842073	−	0.539363i	$-0.818665\pi$
$409$	−7346.25	−	12724.1i	−0.888139	−	1.53830i	−0.0460654	−	0.998938i	$-0.514668\pi$
$410$		0			0
$411$	−2803.05	+	4855.02i	−0.336409	+	0.582678i
$412$		0			0
$413$	4639.29	−	8546.04i	0.552748	−	1.01822i
$414$		0			0
$415$	670.820	−	1161.89i	0.0793476	−	0.137434i
$416$		0			0
$417$	−4225.79	−	7319.28i	−0.496254	−	0.859537i
$418$		0			0
$419$	−3370.31			−0.392960			−0.196480	−	0.980508i	$-0.562951\pi$
$419$	−3370.31			−0.392960			−0.196480	+	0.980508i	$0.562951\pi$
$420$		0			0
$421$	15651.0			1.81184			0.905919	−	0.423450i	$-0.139181\pi$
$421$	15651.0			1.81184			0.905919	+	0.423450i	$0.139181\pi$
$422$		0			0
$423$	−2792.47	−	4836.70i	−0.320980	−	0.555953i
$424$		0			0
$425$	2045.04	−	3542.12i	0.233410	−	0.404277i
$426$		0			0
$427$	−7098.88	+	186.421i	−0.804541	+	0.0211277i
$428$		0			0
$429$	−807.314	+	1398.31i	−0.0908567	+	0.157368i
$430$		0			0
$431$	2444.06	+	4233.24i	0.273147	+	0.473104i	0.969666	−	0.244434i	$-0.0786022\pi$
$431$	2444.06	+	4233.24i	0.273147	+	0.473104i	−0.696519	+	0.717538i	$0.745269\pi$
$432$		0			0
$433$	−5255.73			−0.583313			−0.291656	−	0.956523i	$-0.594206\pi$
$433$	−5255.73			−0.583313			−0.291656	+	0.956523i	$0.594206\pi$
$434$		0			0
$435$	−1207.25			−0.133065
$436$		0			0
$437$	−4081.88	−	7070.03i	−0.446826	−	0.773925i
$438$		0			0
$439$	−412.488	+	714.451i	−0.0448451	+	0.0776740i	−0.887577	−	0.460660i	$-0.847613\pi$
$439$	−412.488	+	714.451i	−0.0448451	+	0.0776740i	0.842732	+	0.538334i	$0.180946\pi$
$440$		0			0
$441$	−1681.69	−	2588.72i	−0.181588	−	0.279530i
$442$		0			0
$443$	6513.64	−	11281.9i	0.698583	−	1.20998i	−0.270375	−	0.962755i	$-0.587148\pi$
$443$	6513.64	−	11281.9i	0.698583	−	1.20998i	0.968958	−	0.247226i	$-0.0795190\pi$
$444$		0			0
$445$	−4408.92	−	7636.47i	−0.469669	−	0.813491i
$446$		0			0
$447$	5400.98			0.571493
$448$		0			0
$449$	16526.1			1.73700			0.868500	−	0.495689i	$-0.165084\pi$
$449$	16526.1			1.73700			0.868500	+	0.495689i	$0.165084\pi$
$450$		0			0
$451$	172.522	+	298.817i	0.0180127	+	0.0311989i
$452$		0			0
$453$	−679.476	+	1176.89i	−0.0704737	+	0.122064i
$454$		0			0
$455$	3981.76	−	104.564i	0.410259	−	0.0107737i
$456$		0			0
$457$	1855.41	−	3213.67i	0.189918	−	0.328947i	−0.755305	−	0.655374i	$-0.772511\pi$
$457$	1855.41	−	3213.67i	0.189918	−	0.328947i	0.945223	+	0.326426i	$0.105844\pi$
$458$		0			0
$459$	−586.963	−	1016.65i	−0.0596887	−	0.103384i
$460$		0			0
$461$	−9714.00			−0.981401			−0.490701	−	0.871328i	$-0.663259\pi$
$461$	−9714.00			−0.981401			−0.490701	+	0.871328i	$0.663259\pi$
$462$		0			0
$463$	43.2780			0.00434406			0.00217203	−	0.999998i	$-0.499309\pi$
$463$	43.2780			0.00434406			0.00217203	+	0.999998i	$0.499309\pi$
$464$		0			0
$465$	534.254	+	925.355i	0.0532805	+	0.0922845i
$466$		0			0
$467$	−766.618	+	1327.82i	−0.0759633	+	0.131572i	−0.901505	−	0.432769i	$-0.857537\pi$
$467$	−766.618	+	1327.82i	−0.0759633	+	0.131572i	0.825541	+	0.564341i	$0.190870\pi$
$468$		0			0
$469$	1750.54	−	3224.66i	0.172350	−	0.317486i
$470$		0			0
$471$	2795.49	−	4841.93i	0.273480	−	0.473682i
$472$		0			0
$473$	−1697.09	−	2939.45i	−0.164974	−	0.285743i
$474$		0			0
$475$	−10256.3			−0.990722
$476$		0			0
$477$	−2590.55			−0.248665
$478$		0			0
$479$	−3517.69	−	6092.81i	−0.335547	−	0.581185i	0.648042	−	0.761604i	$-0.275588\pi$
$479$	−3517.69	−	6092.81i	−0.335547	−	0.581185i	−0.983590	+	0.180419i	$0.942255\pi$
$480$		0			0
$481$	−3649.21	+	6320.62i	−0.345924	+	0.599159i
$482$		0			0
$483$	−2174.00	−	3547.05i	−0.204804	−	0.334154i
$484$		0			0
$485$	−220.441	+	381.815i	−0.0206386	+	0.0357471i
$486$		0			0
$487$	−7685.64	−	13311.9i	−0.715132	−	1.23865i	−0.962908	−	0.269828i	$-0.913033\pi$
$487$	−7685.64	−	13311.9i	−0.715132	−	1.23865i	0.247776	−	0.968817i	$-0.420300\pi$
$488$		0			0
$489$	−6963.41			−0.643960
$490$		0			0
$491$	2393.35			0.219980			0.109990	−	0.993933i	$-0.464918\pi$
$491$	2393.35			0.219980			0.109990	+	0.993933i	$0.464918\pi$
$492$		0			0
$493$	1573.04	+	2724.58i	0.143704	+	0.248903i
$494$		0			0
$495$	−348.300	+	603.274i	−0.0316261	+	0.0547781i
$496$		0			0
$497$	7601.40	+	12402.3i	0.686055	+	1.11935i
$498$		0			0
$499$	346.760	−	600.606i	0.0311084	−	0.0538814i	−0.850052	−	0.526699i	$-0.823430\pi$
$499$	346.760	−	600.606i	0.0311084	−	0.0538814i	0.881160	+	0.472817i	$0.156763\pi$
$500$		0			0
$501$	4817.43	+	8344.03i	0.429594	+	0.744079i
$502$		0			0
$503$	8646.95			0.766498			0.383249	−	0.923645i	$-0.374805\pi$
$503$	8646.95			0.766498			0.383249	+	0.923645i	$0.374805\pi$
$504$		0			0
$505$	6423.27			0.566003
$506$		0			0
$507$	1052.24	+	1822.53i	0.0921729	+	0.159648i
$508$		0			0
$509$	7750.44	−	13424.1i	0.674916	−	1.16899i	−0.301578	−	0.953441i	$-0.597513\pi$
$509$	7750.44	−	13424.1i	0.674916	−	1.16899i	0.976494	−	0.215546i	$-0.0691533\pi$
$510$		0			0
$511$	2925.92	−	5389.84i	0.253298	−	0.466600i
$512$		0			0
$513$	−1471.87	+	2549.36i	−0.126676	+	0.219409i
$514$		0			0
$515$	−4017.72	−	6958.89i	−0.343771	−	0.595428i
$516$		0			0
$517$	8636.41			0.734678
$518$		0			0
$519$	642.831			0.0543683
$520$		0			0
$521$	−432.354	−	748.858i	−0.0363565	−	0.0629714i	0.847275	−	0.531155i	$-0.178242\pi$
$521$	−432.354	−	748.858i	−0.0363565	−	0.0629714i	−0.883631	+	0.468184i	$0.844909\pi$
$522$		0			0
$523$	−3127.81	+	5417.52i	−0.261509	+	0.452947i	−0.966643	−	0.256127i	$-0.917554\pi$
$523$	−3127.81	+	5417.52i	−0.261509	+	0.452947i	0.705134	+	0.709074i	$0.250887\pi$
$524$		0			0
$525$	−5224.85	+	137.208i	−0.434345	+	0.0114062i
$526$		0			0
$527$	1392.26	−	2411.46i	0.115081	−	0.199326i
$528$		0			0
$529$	3280.15	+	5681.39i	0.269594	+	0.466951i
$530$		0			0
$531$	−4725.46			−0.386191
$532$		0			0
$533$	−958.762			−0.0779148
$534$		0			0
$535$	2755.56	+	4772.78i	0.222679	+	0.385692i
$536$		0			0
$537$	−3655.83	+	6332.09i	−0.293782	+	0.508845i
$538$		0			0
$539$	4767.08	−	250.546i	0.380951	−	0.0200218i
$540$		0			0
$541$	−71.9353	+	124.596i	−0.00571671	+	0.00990164i	−0.868870	−	0.495041i	$-0.835153\pi$
$541$	−71.9353	+	124.596i	−0.00571671	+	0.00990164i	0.863153	+	0.504943i	$0.168486\pi$
$542$		0			0
$543$	372.946	+	645.962i	0.0294745	+	0.0510514i
$544$		0			0
$545$	10862.4			0.853747
$546$		0			0
$547$	−5455.65			−0.426448			−0.213224	−	0.977003i	$-0.568396\pi$
$547$	−5455.65			−0.426448			−0.213224	+	0.977003i	$0.568396\pi$
$548$		0			0
$549$	1725.46	+	2988.58i	0.134136	+	0.232331i
$550$		0			0
$551$	3944.56	−	6832.18i	0.304980	−	0.528241i
$552$		0			0
$553$	−8102.54	+	212.778i	−0.623065	+	0.0163621i
$554$		0			0
$555$	−1574.38	+	2726.91i	−0.120412	+	0.208560i
$556$		0			0
$557$	−12404.9	−	21486.0i	−0.943652	−	1.63445i	−0.758428	−	0.651756i	$-0.774032\pi$
$557$	−12404.9	−	21486.0i	−0.943652	−	1.63445i	−0.185223	−	0.982696i	$-0.559301\pi$
$558$		0			0
$559$	9431.33			0.713600
$560$		0			0
$561$	1815.33			0.136619
$562$		0			0
$563$	8184.91	+	14176.7i	0.612705	+	1.06124i	0.990782	+	0.135462i	$0.0432520\pi$
$563$	8184.91	+	14176.7i	0.612705	+	1.06124i	−0.378077	+	0.925774i	$0.623415\pi$
$564$		0			0
$565$	−1871.08	+	3240.81i	−0.139322	+	0.241313i
$566$		0			0
$567$	−715.707	+	1318.40i	−0.0530104	+	0.0976503i
$568$		0			0
$569$	9225.29	−	15978.7i	0.679691	−	1.17726i	−0.295383	−	0.955379i	$-0.595447\pi$
$569$	9225.29	−	15978.7i	0.679691	−	1.17726i	0.975074	−	0.221881i	$-0.0712195\pi$
$570$		0			0
$571$	−3554.34	−	6156.30i	−0.260499	−	0.451197i	0.705876	−	0.708335i	$-0.250554\pi$
$571$	−3554.34	−	6156.30i	−0.260499	−	0.451197i	−0.966374	+	0.257139i	$0.917220\pi$
$572$		0			0
$573$	12939.2			0.943358
$574$		0			0
$575$	−7043.82			−0.510865
$576$		0			0
$577$	−3797.09	−	6576.75i	−0.273960	−	0.474512i	0.695912	−	0.718127i	$-0.255000\pi$
$577$	−3797.09	−	6576.75i	−0.273960	−	0.474512i	−0.969872	+	0.243615i	$0.921667\pi$
$578$		0			0
$579$	−3091.28	+	5354.25i	−0.221881	+	0.384309i
$580$		0			0
$581$	2334.73	+	3809.30i	0.166714	+	0.272007i
$582$		0			0
$583$	2002.98	−	3469.26i	0.142290	−	0.246453i
$584$		0			0
$585$	−967.811	−	1676.30i	−0.0684001	−	0.118472i
$586$		0			0
$587$	1763.34			0.123988			0.0619939	−	0.998077i	$-0.480254\pi$
$587$	1763.34			0.123988			0.0619939	+	0.998077i	$0.480254\pi$
$588$		0			0
$589$	−6982.47			−0.488468
$590$		0			0
$591$	2499.13	+	4328.62i	0.173943	+	0.301279i
$592$		0			0
$593$	6158.07	−	10666.1i	0.426445	−	0.738624i	−0.570109	−	0.821569i	$-0.693099\pi$
$593$	6158.07	−	10666.1i	0.426445	−	0.738624i	0.996554	+	0.0829448i	$0.0264325\pi$
$594$		0			0
$595$	−2340.16	−	3818.16i	−0.161239	−	0.263075i
$596$		0			0
$597$	−1631.30	+	2825.49i	−0.111834	+	0.193702i
$598$		0			0
$599$	−4451.70	−	7710.57i	−0.303659	−	0.525952i	0.673303	−	0.739367i	$-0.264875\pi$
$599$	−4451.70	−	7710.57i	−0.303659	−	0.525952i	−0.976962	+	0.213414i	$0.931542\pi$
$600$		0			0
$601$	−19157.1			−1.30022			−0.650112	−	0.759838i	$-0.725278\pi$
$601$	−19157.1			−1.30022			−0.650112	+	0.759838i	$0.725278\pi$
$602$		0			0
$603$	−1783.05			−0.120417
$604$		0			0
$605$	3162.51	+	5477.62i	0.212519	+	0.368094i
$606$		0			0
$607$	−3784.96	+	6555.75i	−0.253092	+	0.438369i	−0.964376	−	0.264537i	$-0.914781\pi$
$607$	−3784.96	+	6555.75i	−0.253092	+	0.438369i	0.711283	+	0.702905i	$0.248114\pi$
$608$		0			0
$609$	1918.07	−	3533.27i	0.127625	−	0.235099i
$610$		0			0
$611$	−11998.9	+	20782.6i	−0.794471	+	1.37606i
$612$		0			0
$613$	−1453.56	−	2517.65i	−0.0957730	−	0.165884i	0.814158	−	0.580643i	$-0.197199\pi$
$613$	−1453.56	−	2517.65i	−0.0957730	−	0.165884i	−0.909931	+	0.414760i	$0.863866\pi$
$614$		0			0
$615$	−413.640			−0.0271212
$616$		0			0
$617$	−12510.9			−0.816320			−0.408160	−	0.912910i	$-0.633829\pi$
$617$	−12510.9			−0.816320			−0.408160	+	0.912910i	$0.633829\pi$
$618$		0			0
$619$	5032.78	+	8717.03i	0.326792	+	0.566021i	0.981873	−	0.189538i	$-0.0606989\pi$
$619$	5032.78	+	8717.03i	0.326792	+	0.566021i	−0.655081	+	0.755558i	$0.727366\pi$
$620$		0			0
$621$	−1010.85	+	1750.84i	−0.0653205	+	0.113138i
$622$		0			0
$623$	29354.6	−	770.869i	1.88775	−	0.0495734i
$624$		0			0
$625$	−2491.59	+	4315.56i	−0.159462	+	0.276196i
$626$		0			0
$627$	−2276.07	−	3942.27i	−0.144972	−	0.251099i
$628$		0			0
$629$	8205.63			0.520159
$630$		0			0
$631$	25146.6			1.58648			0.793242	−	0.608907i	$-0.208392\pi$
$631$	25146.6			1.58648			0.793242	+	0.608907i	$0.208392\pi$
$632$		0			0
$633$	−7014.71	−	12149.8i	−0.440458	−	0.762895i
$634$		0			0
$635$	488.889	−	846.781i	0.0305527	−	0.0529189i
$636$		0			0
$637$	−6020.16	+	11819.6i	−0.374454	+	0.735179i
$638$		0			0
$639$	3534.44	−	6121.83i	0.218811	−	0.378992i
$640$		0			0
$641$	14479.5	+	25079.1i	0.892206	+	1.54535i	0.837225	+	0.546859i	$0.184176\pi$
$641$	14479.5	+	25079.1i	0.892206	+	1.54535i	0.0549809	+	0.998487i	$0.482490\pi$
$642$		0			0
$643$	−7341.90			−0.450290			−0.225145	−	0.974325i	$-0.572286\pi$
$643$	−7341.90			−0.450290			−0.225145	+	0.974325i	$0.572286\pi$
$644$		0			0
$645$	4068.97			0.248396
$646$		0			0
$647$	3035.99	+	5258.49i	0.184478	+	0.319525i	0.943400	−	0.331656i	$-0.107607\pi$
$647$	3035.99	+	5258.49i	0.184478	+	0.319525i	−0.758923	+	0.651181i	$0.774274\pi$
$648$		0			0
$649$	3653.67	−	6328.34i	0.220985	−	0.382756i
$650$		0			0
$651$	−3557.06	+	93.4105i	−0.214151	+	0.00562373i
$652$		0			0
$653$	−13131.1	+	22743.7i	−0.786920	+	1.36298i	0.140926	+	0.990020i	$0.454992\pi$
$653$	−13131.1	+	22743.7i	−0.786920	+	1.36298i	−0.927846	+	0.372965i	$0.878341\pi$
$654$		0			0
$655$	3130.88	+	5422.84i	0.186769	+	0.323493i
$656$		0			0
$657$	−2980.27			−0.176973
$658$		0			0
$659$	−26130.1			−1.54459			−0.772296	−	0.635263i	$-0.780892\pi$
$659$	−26130.1			−1.54459			−0.772296	+	0.635263i	$0.780892\pi$
$660$		0			0
$661$	5962.75	+	10327.8i	0.350868	+	0.607722i	0.986402	−	0.164351i	$-0.0525531\pi$
$661$	5962.75	+	10327.8i	0.350868	+	0.607722i	−0.635533	+	0.772073i	$0.719220\pi$
$662$		0			0
$663$	−2522.10	+	4368.41i	−0.147738	+	0.255890i
$664$		0			0
$665$	−5357.61	+	9869.25i	−0.312420	+	0.575509i
$666$		0			0
$667$	2709.04	−	4692.19i	0.157263	−	0.272387i
$668$		0			0
$669$	4869.04	+	8433.43i	0.281387	+	0.487377i
$670$		0			0
$671$	−5336.42			−0.307019
$672$		0			0
$673$	−6359.85			−0.364271			−0.182135	−	0.983273i	$-0.558301\pi$
$673$	−6359.85			−0.364271			−0.182135	+	0.983273i	$0.558301\pi$
$674$		0			0
$675$	1269.96	+	2199.63i	0.0724158	+	0.125428i
$676$		0			0
$677$	−4280.81	+	7414.57i	−0.243020	+	0.420924i	−0.961573	−	0.274549i	$-0.911472\pi$
$677$	−4280.81	+	7414.57i	−0.243020	+	0.420924i	0.718553	+	0.695472i	$0.244805\pi$
$678$		0			0
$679$	−767.226	−	1251.79i	−0.0433629	−	0.0707500i
$680$		0			0
$681$	7707.24	−	13349.3i	0.433689	−	0.751171i
$682$		0			0
$683$	−3352.94	−	5807.47i	−0.187843	−	0.325354i	0.756688	−	0.653776i	$-0.226816\pi$
$683$	−3352.94	−	5807.47i	−0.187843	−	0.325354i	−0.944531	+	0.328423i	$0.893483\pi$
$684$		0			0
$685$	10392.6			0.579679
$686$		0			0
$687$	1844.42			0.102429
$688$		0			0
$689$	5565.62	+	9639.94i	0.307741	+	0.533022i
$690$		0			0
$691$	−12665.3	+	21937.0i	−0.697267	+	1.20770i	0.272143	+	0.962257i	$0.412268\pi$
$691$	−12665.3	+	21937.0i	−0.697267	+	1.20770i	−0.969410	+	0.245445i	$0.921066\pi$
$692$		0			0
$693$	−1212.23	−	1977.85i	−0.0664485	−	0.108416i
$694$		0			0
$695$	−7833.77	+	13568.5i	−0.427557	+	0.740550i
$696$		0			0
$697$	538.969	+	933.522i	0.0292897	+	0.0507312i
$698$		0			0
$699$	8482.25			0.458981
$700$		0			0
$701$	−27184.1			−1.46467			−0.732333	−	0.680947i	$-0.761568\pi$
$701$	−27184.1			−1.46467			−0.732333	+	0.680947i	$0.761568\pi$
$702$		0			0
$703$	−10288.3	−	17819.8i	−0.551961	−	0.956025i
$704$		0			0
$705$	−5176.68	+	8966.27i	−0.276546	+	0.478992i
$706$		0			0
$707$	−10205.2	+	18799.0i	−0.542867	+	1.00001i
$708$		0			0
$709$	−8072.75	+	13982.4i	−0.427614	+	0.740649i	−0.996661	−	0.0816561i	$-0.973979\pi$
$709$	−8072.75	+	13982.4i	−0.427614	+	0.740649i	0.569047	+	0.822305i	$0.307312\pi$
$710$		0			0
$711$	1969.41	+	3411.12i	0.103880	+	0.179925i
$712$		0			0
$713$	−4795.41			−0.251879
$714$		0			0
$715$	2993.20			0.156558
$716$		0			0
$717$	−5148.68	−	8917.77i	−0.268174	−	0.464491i
$718$		0			0
$719$	8648.74	−	14980.0i	0.448600	−	0.776998i	−0.549695	−	0.835365i	$-0.685256\pi$
$719$	8648.74	−	14980.0i	0.448600	−	0.776998i	0.998295	+	0.0583673i	$0.0185895\pi$
$720$		0			0
$721$	26749.9	−	702.470i	1.38172	−	0.0362848i
$722$		0			0
$723$	3954.17	−	6848.82i	0.203398	−	0.352296i
$724$		0			0
$725$	−3403.43	−	5894.91i	−0.174345	−	0.301975i
$726$		0			0
$727$	−3514.71			−0.179303			−0.0896516	−	0.995973i	$-0.528575\pi$
$727$	−3514.71			−0.179303			−0.0896516	+	0.995973i	$0.528575\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−5301.83	−	9183.04i	−0.268256	−	0.464633i
$732$		0			0
$733$	13755.6	−	23825.4i	0.693144	−	1.20056i	−0.277658	−	0.960680i	$-0.589558\pi$
$733$	13755.6	−	23825.4i	0.693144	−	1.20056i	0.970802	−	0.239881i	$-0.0771083\pi$
$734$		0			0
$735$	−2597.28	+	5099.33i	−0.130343	+	0.255907i
$736$		0			0
$737$	1378.63	−	2387.86i	0.0689044	−	0.119346i
$738$		0			0
$739$	8050.80	+	13944.4i	0.400749	+	0.694117i	0.993816	−	0.111035i	$-0.0354167\pi$
$739$	8050.80	+	13944.4i	0.400749	+	0.694117i	−0.593068	+	0.805153i	$0.702083\pi$
$740$		0			0
$741$	12648.9			0.627083
$742$		0			0
$743$	−14682.4			−0.724961			−0.362480	−	0.931991i	$-0.618070\pi$
$743$	−14682.4			−0.724961			−0.362480	+	0.931991i	$0.618070\pi$
$744$		0			0
$745$	−5006.17	−	8670.93i	−0.246190	−	0.426414i
$746$		0			0
$747$	1085.59	−	1880.29i	0.0531720	−	0.0920967i
$748$		0			0
$749$	−18346.5	+	481.791i	−0.895016	+	0.0235037i
$750$		0			0
$751$	−3636.53	+	6298.66i	−0.176696	+	0.306047i	−0.940747	−	0.339109i	$-0.889874\pi$
$751$	−3636.53	+	6298.66i	−0.176696	+	0.306047i	0.764051	+	0.645156i	$0.223208\pi$
$752$		0			0
$753$	3086.36	+	5345.73i	0.149367	+	0.258711i
$754$		0			0
$755$	2519.23			0.121436
$756$		0			0
$757$	8505.93			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$757$	8505.93			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$758$		0			0
$759$	−1563.15	−	2707.46i	−0.0747548	−	0.129479i
$760$		0			0
$761$	−7108.86	+	12312.9i	−0.338628	+	0.586521i	−0.984175	−	0.177200i	$-0.943296\pi$
$761$	−7108.86	+	12312.9i	−0.338628	+	0.586521i	0.645547	+	0.763721i	$0.276630\pi$
$762$		0			0
$763$	−17258.0	+	31790.9i	−0.818848	+	1.50840i
$764$		0			0
$765$	−1088.11	+	1884.67i	−0.0514259	+	0.0890722i
$766$		0			0
$767$	10152.3	+	17584.4i	0.477939	+	0.827815i
$768$		0			0
$769$	16379.1			0.768068			0.384034	−	0.923319i	$-0.374534\pi$
$769$	16379.1			0.768068			0.384034	+	0.923319i	$0.374534\pi$
$770$		0			0
$771$	6450.62			0.301314
$772$		0			0
$773$	19948.3	+	34551.6i	0.928192	+	1.60768i	0.786346	+	0.617787i	$0.211970\pi$
$773$	19948.3	+	34551.6i	0.928192	+	1.60768i	0.141846	+	0.989889i	$0.454696\pi$
$774$		0			0
$775$	−3012.29	+	5217.45i	−0.139619	+	0.241827i
$776$		0			0
$777$	−5479.50	−	8940.23i	−0.252994	−	0.412779i
$778$		0			0
$779$	1351.52	−	2340.91i	0.0621609	−	0.107666i
$780$		0			0
$781$	5465.57	+	9466.65i	0.250414	+	0.433730i
$782$		0			0
$783$	−1953.69			−0.0891688
$784$		0			0
$785$	−10364.5			−0.471244
$786$		0			0
$787$	−16564.3	−	28690.2i	−0.750257	−	1.29948i	−0.947698	−	0.319169i	$-0.896596\pi$
$787$	−16564.3	−	28690.2i	−0.750257	−	1.29948i	0.197440	−	0.980315i	$-0.436737\pi$
$788$		0			0
$789$	−6885.23	+	11925.6i	−0.310672	+	0.538100i
$790$		0			0
$791$	−6512.15	−	10625.1i	−0.292725	−	0.477603i
$792$		0			0
$793$	7414.07	−	12841.5i	0.332007	−	0.575052i
$794$		0			0
$795$	2401.18	+	4158.97i	0.107121	+	0.185539i
$796$		0			0
$797$	−17851.5			−0.793390			−0.396695	−	0.917951i	$-0.629843\pi$
$797$	−17851.5			−0.793390			−0.396695	+	0.917951i	$0.629843\pi$
$798$		0			0
$799$	26980.7			1.19463
$800$		0			0
$801$	−7134.94	−	12358.1i	−0.314733	−	0.545133i
$802$		0			0
$803$	2304.30	−	3991.17i	0.101267	−	0.175399i
$804$		0			0
$805$	−3679.49	+	6777.98i	−0.161099	+	0.296761i
$806$		0			0
$807$	569.066	−	985.652i	0.0248229	−	0.0429945i
$808$		0			0
$809$	2528.52	+	4379.52i	0.109886	+	0.190328i	0.915724	−	0.401808i	$-0.131618\pi$
$809$	2528.52	+	4379.52i	0.109886	+	0.190328i	−0.805838	+	0.592136i	$0.798285\pi$
$810$		0			0
$811$	17535.4			0.759251			0.379626	−	0.925140i	$-0.376053\pi$
$811$	17535.4			0.759251			0.379626	+	0.925140i	$0.376053\pi$
$812$		0			0
$813$	16106.5			0.694810
$814$		0			0
$815$	6454.39	+	11179.3i	0.277408	+	0.480484i
$816$		0			0
$817$	−13294.9	+	23027.5i	−0.569315	+	0.986083i
$818$		0			0
$819$	6443.68	−	169.215i	0.274921	−	0.00721960i
$820$		0			0
$821$	9350.39	−	16195.3i	0.397480	−	0.688455i	−0.595935	−	0.803033i	$-0.703218\pi$
$821$	9350.39	−	16195.3i	0.397480	−	0.688455i	0.993414	+	0.114578i	$0.0365516\pi$
$822$		0			0
$823$	11111.3	+	19245.4i	0.470615	+	0.815129i	0.999435	−	0.0336046i	$-0.0106987\pi$
$823$	11111.3	+	19245.4i	0.470615	+	0.815129i	−0.528820	+	0.848734i	$0.677365\pi$
$824$		0			0
$825$	−3927.66			−0.165750
$826$		0			0
$827$	−25178.9			−1.05872			−0.529358	−	0.848399i	$-0.677567\pi$
$827$	−25178.9			−1.05872			−0.529358	+	0.848399i	$0.677567\pi$
$828$		0			0
$829$	−6139.45	−	10633.8i	−0.257216	−	0.445511i	0.708279	−	0.705933i	$-0.249472\pi$
$829$	−6139.45	−	10633.8i	−0.257216	−	0.445511i	−0.965495	+	0.260421i	$0.916139\pi$
$830$		0			0
$831$	7172.41	−	12423.0i	0.299408	−	0.518590i
$832$		0			0
$833$	14892.7	−	782.721i	0.619448	−	0.0325566i
$834$		0			0
$835$	8930.54	−	15468.2i	0.370125	−	0.641075i
$836$		0			0
$837$	864.582	+	1497.50i	0.0357041	+	0.0618413i
$838$		0			0
$839$	25765.0			1.06020			0.530098	−	0.847936i	$-0.322155\pi$
$839$	25765.0			1.06020			0.530098	+	0.847936i	$0.322155\pi$
$840$		0			0
$841$	−19153.2			−0.785321
$842$		0			0
$843$	3114.85	+	5395.08i	0.127261	+	0.220423i
$844$		0			0
$845$	1950.64	−	3378.61i	0.0794132	−	0.137548i
$846$		0			0
$847$	−21056.0	+	552.943i	−0.854181	+	0.0224313i
$848$		0			0
$849$	3836.42	−	6644.88i	0.155083	−	0.268612i
$850$		0			0
$851$	−7065.75	−	12238.2i	−0.284619	−	0.492974i
$852$		0			0
$853$	37864.5			1.51988			0.759939	−	0.649995i	$-0.225229\pi$
$853$	37864.5			1.51988			0.759939	+	0.649995i	$0.225229\pi$
$854$		0			0
$855$	5457.12			0.218280
$856$		0			0
$857$	14604.4	+	25295.5i	0.582118	+	1.00826i	0.995228	+	0.0975771i	$0.0311093\pi$
$857$	14604.4	+	25295.5i	0.582118	+	1.00826i	−0.413110	+	0.910681i	$0.635557\pi$
$858$		0			0
$859$	17451.5	−	30226.8i	0.693173	−	1.20061i	−0.277619	−	0.960691i	$-0.589545\pi$
$859$	17451.5	−	30226.8i	0.693173	−	1.20061i	0.970793	−	0.239920i	$-0.0771213\pi$
$860$		0			0
$861$	657.186	−	1210.60i	0.0260126	−	0.0479178i
$862$		0			0
$863$	−6794.67	+	11768.7i	−0.268011	+	0.464208i	−0.968348	−	0.249604i	$-0.919700\pi$
$863$	−6794.67	+	11768.7i	−0.268011	+	0.464208i	0.700337	+	0.713812i	$0.253033\pi$
$864$		0			0
$865$	−595.840	−	1032.03i	−0.0234210	−	0.0405664i
$866$		0			0
$867$	−9067.79			−0.355200
$868$		0			0
$869$	−6090.89			−0.237767
$870$		0			0
$871$	3830.76	+	6635.07i	0.149025	+	0.258118i
$872$		0			0
$873$	−356.739	+	617.890i	−0.0138302	+	0.0239547i
$874$		0			0
$875$	11791.1	+	19238.1i	0.455556	+	0.743275i
$876$		0			0
$877$	1189.87	−	2060.92i	0.0458144	−	0.0793528i	−0.842209	−	0.539151i	$-0.818745\pi$
$877$	1189.87	−	2060.92i	0.0458144	−	0.0793528i	0.888023	+	0.459799i	$0.152078\pi$
$878$		0			0
$879$	−840.074	−	1455.05i	−0.0322355	−	0.0558335i
$880$		0			0
$881$	−24235.5			−0.926803			−0.463401	−	0.886148i	$-0.653371\pi$
$881$	−24235.5			−0.926803			−0.463401	+	0.886148i	$0.653371\pi$
$882$		0			0
$883$	9844.13			0.375177			0.187589	−	0.982248i	$-0.439933\pi$
$883$	9844.13			0.375177			0.187589	+	0.982248i	$0.439933\pi$
$884$		0			0
$885$	4380.03	+	7586.43i	0.166365	+	0.288153i
$886$		0			0
$887$	14304.9	−	24776.9i	0.541502	−	0.937910i	−0.457316	−	0.889304i	$-0.651189\pi$
$887$	14304.9	−	24776.9i	0.541502	−	0.937910i	0.998818	−	0.0486051i	$-0.0154776\pi$
$888$		0			0
$889$	1701.54	+	2776.19i	0.0641932	+	0.104736i
$890$		0			0
$891$	−563.654	+	976.277i	−0.0211932	+	0.0367076i
$892$		0			0
$893$	−33828.5	−	58592.7i	−1.26767	−	2.19567i
$894$		0			0
$895$	13554.4			0.506226
$896$		0			0
$897$	8686.98			0.323355
$898$		0			0
$899$	−2317.04	−	4013.24i	−0.0859596	−	0.148886i
$900$		0			0
$901$	6257.44	−	10838.2i	0.231371	−	0.400747i
$902$		0			0
$903$	−6464.73	+	11908.7i	−0.238242	+	0.438866i
$904$		0			0
$905$	691.368	−	1197.48i	0.0253943	−	0.0439842i
$906$		0			0
$907$	22289.2	+	38606.0i	0.815986	+	1.41333i	0.908618	+	0.417629i	$0.137139\pi$
$907$	22289.2	+	38606.0i	0.815986	+	1.41333i	−0.0926313	+	0.995700i	$0.529528\pi$
$908$		0			0
$909$	10394.8			0.379288
$910$		0			0
$911$	−45870.6			−1.66823			−0.834116	−	0.551589i	$-0.814022\pi$
$911$	−45870.6			−1.66823			−0.834116	+	0.551589i	$0.814022\pi$
$912$		0			0
$913$	1678.72	+	2907.63i	0.0608517	+	0.105398i
$914$		0			0
$915$	3198.66	−	5540.24i	0.115568	−	0.200169i
$916$		0			0
$917$	−20845.3	+	547.412i	−0.750680	+	0.0197133i
$918$		0			0
$919$	15544.1	−	26923.3i	0.557948	−	0.966394i	−0.439720	−	0.898135i	$-0.644922\pi$
$919$	15544.1	−	26923.3i	0.557948	−	0.966394i	0.997668	−	0.0682590i	$-0.0217444\pi$
$920$		0			0
$921$	5479.53	+	9490.83i	0.196044	+	0.339558i
$922$		0			0
$923$	−30374.0			−1.08318
$924$		0			0
$925$	−17753.7			−0.631069
$926$		0			0
$927$	−6501.87	−	11261.6i	−0.230366	−	0.399006i
$928$		0			0
$929$	21047.3	−	36454.9i	0.743313	−	1.28746i	−0.207665	−	0.978200i	$-0.566586\pi$
$929$	21047.3	−	36454.9i	0.743313	−	1.28746i	0.950979	−	0.309257i	$-0.100080\pi$
$930$		0			0
$931$	−20372.3	−	31360.3i	−0.717159	−	1.10397i
$932$		0			0
$933$	5238.40	−	9073.18i	0.183813	−	0.318374i
$934$		0			0
$935$	−1682.63	−	2914.40i	−0.0588534	−	0.101937i
$936$		0			0
$937$	−44385.1			−1.54749			−0.773745	−	0.633497i	$-0.781619\pi$
$937$	−44385.1			−1.54749			−0.773745	+	0.633497i	$0.781619\pi$
$938$		0			0
$939$	26136.3			0.908334
$940$		0			0
$941$	−20495.8	−	35499.8i	−0.710036	−	1.22982i	−0.964843	−	0.262827i	$-0.915345\pi$
$941$	−20495.8	−	35499.8i	−0.710036	−	1.22982i	0.254807	−	0.966992i	$-0.417988\pi$
$942$		0			0
$943$	928.197	−	1607.68i	0.0320533	−	0.0555179i
$944$		0			0
$945$	2780.00	−	73.0046i	0.0956968	−	0.00251306i
$946$		0			0
$947$	−26311.2	+	45572.4i	−0.902851	+	1.56378i	−0.0790737	+	0.996869i	$0.525196\pi$
$947$	−26311.2	+	45572.4i	−0.902851	+	1.56378i	−0.823777	+	0.566914i	$0.808137\pi$
$948$		0			0
$949$	6402.90	+	11090.1i	0.219017	+	0.379348i
$950$		0			0
$951$	5820.99			0.198484
$952$		0			0
$953$	−10798.1			−0.367035			−0.183517	−	0.983016i	$-0.558748\pi$
$953$	−10798.1			−0.367035			−0.183517	+	0.983016i	$0.558748\pi$
$954$		0			0
$955$	−11993.4	−	20773.1i	−0.406384	−	0.703877i
$956$		0			0
$957$	1510.57	−	2616.38i	0.0510238	−	0.0883758i
$958$		0			0
$959$	−16511.6	+	30416.0i	−0.555983	+	1.02418i
$960$		0			0
$961$	12844.7	−	22247.7i	0.431162	−	0.746794i
$962$		0			0
$963$	4459.32	+	7723.77i	0.149221	+	0.258458i
$964$		0			0
$965$	11461.2			0.382331
$966$		0			0
$967$	−15648.9			−0.520408			−0.260204	−	0.965554i	$-0.583790\pi$
$967$	−15648.9			−0.520408			−0.260204	+	0.965554i	$0.583790\pi$
$968$		0			0
$969$	−7110.59	−	12315.9i	−0.235733	−	0.408301i
$970$		0			0
$971$	23629.9	−	40928.2i	0.780968	−	1.35268i	−0.150411	−	0.988624i	$-0.548060\pi$
$971$	23629.9	−	40928.2i	0.780968	−	1.35268i	0.931379	−	0.364052i	$-0.118607\pi$
$972$		0			0
$973$	−27264.8	−	44484.6i	−0.898323	−	1.46568i
$974$		0			0
$975$	5456.83	−	9451.51i	0.179239	−	0.310452i
$976$		0			0
$977$	24483.2	+	42406.2i	0.801728	+	1.38863i	0.918478	+	0.395473i	$0.129419\pi$
$977$	24483.2	+	42406.2i	0.801728	+	1.38863i	−0.116749	+	0.993161i	$0.537247\pi$
$978$		0			0
$979$	22066.6			0.720380
$980$		0			0
$981$	17578.5			0.572109
$982$		0			0
$983$	−9555.64	−	16550.9i	−0.310049	−	0.537020i	0.668324	−	0.743870i	$-0.267012\pi$
$983$	−9555.64	−	16550.9i	−0.310049	−	0.537020i	−0.978373	+	0.206850i	$0.933679\pi$
$984$		0			0
$985$	4632.89	−	8024.39i	0.149864	−	0.259572i
$986$		0			0
$987$	−18017.0	−	29396.1i	−0.581040	−	0.948013i
$988$		0			0
$989$	−9130.65	+	15814.8i	−0.293567	+	0.508473i
$990$		0			0
$991$	−27051.3	−	46854.1i	−0.867115	−	1.50189i	−0.864931	−	0.501890i	$-0.832638\pi$
$991$	−27051.3	−	46854.1i	−0.867115	−	1.50189i	−0.00218424	−	0.999998i	$-0.500695\pi$
$992$		0			0
$993$	17194.5			0.549498
$994$		0			0
$995$	6048.21			0.192705
$996$		0			0
$997$	−4596.40	−	7961.20i	−0.146008	−	0.252892i	0.783741	−	0.621088i	$-0.213309\pi$
$997$	−4596.40	−	7961.20i	−0.146008	−	0.252892i	−0.929748	+	0.368196i	$0.879976\pi$
$998$		0			0
$999$	−2547.82	+	4412.95i	−0.0806901	+	0.139759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.k.289.2		6
4.3	odd	2		21.4.e.b.16.1	yes	6
7.2	even	3		2352.4.a.ci.1.2		3
7.4	even	3	inner	336.4.q.k.193.2		6
7.5	odd	6		2352.4.a.cg.1.2		3
12.11	even	2		63.4.e.c.37.3		6
28.3	even	6		147.4.e.n.67.1		6
28.11	odd	6		21.4.e.b.4.1	✓	6
28.19	even	6		147.4.a.m.1.3		3
28.23	odd	6		147.4.a.l.1.3		3
28.27	even	2		147.4.e.n.79.1		6
84.11	even	6		63.4.e.c.46.3		6
84.23	even	6		441.4.a.s.1.1		3
84.47	odd	6		441.4.a.t.1.1		3
84.59	odd	6		441.4.e.w.361.3		6
84.83	odd	2		441.4.e.w.226.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	28.11	odd	6
21.4.e.b.16.1	yes	6	4.3	odd	2
63.4.e.c.37.3		6	12.11	even	2
63.4.e.c.46.3		6	84.11	even	6
147.4.a.l.1.3		3	28.23	odd	6
147.4.a.m.1.3		3	28.19	even	6
147.4.e.n.67.1		6	28.3	even	6
147.4.e.n.79.1		6	28.27	even	2
336.4.q.k.193.2		6	7.4	even	3	inner
336.4.q.k.289.2		6	1.1	even	1	trivial
441.4.a.s.1.1		3	84.23	even	6
441.4.a.t.1.1		3	84.47	odd	6
441.4.e.w.226.3		6	84.83	odd	2
441.4.e.w.361.3		6	84.59	odd	6
2352.4.a.cg.1.2		3	7.5	odd	6
2352.4.a.ci.1.2		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)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-2.78070 + 4.81631i) q^{5} +(-9.67799 - 15.7904i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-2.78070 + 4.81631i) q^{5} +(-9.67799 - 15.7904i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-6.95869 - 12.0528i) q^{11} +38.6718 q^{13} +16.6842 q^{15} +(-21.7394 - 37.6537i) q^{17} +(-54.5139 + 94.4208i) q^{19} +(-26.5077 + 48.8297i) q^{21} +(-37.4389 + 64.8461i) q^{23} +(47.0354 + 81.4677i) q^{25} +27.0000 q^{27} -72.3589 q^{29} +(32.0215 + 55.4629i) q^{31} +(-20.8761 + 36.1584i) q^{33} +(102.963 - 2.70387i) q^{35} +(-94.3636 + 163.443i) q^{37} +(-58.0077 - 100.472i) q^{39} -24.7923 q^{41} +243.881 q^{43} +(-25.0263 - 43.3468i) q^{45} +(-310.274 + 537.411i) q^{47} +(-155.673 + 305.638i) q^{49} +(-65.2182 + 112.961i) q^{51} +(143.919 + 249.276i) q^{53} +77.4001 q^{55} +327.083 q^{57} +(262.526 + 454.708i) q^{59} +(191.718 - 332.065i) q^{61} +(166.625 - 4.37567i) q^{63} +(-107.535 + 186.255i) q^{65} +(99.0583 + 171.574i) q^{67} +224.634 q^{69} -785.432 q^{71} +(165.570 + 286.776i) q^{73} +(141.106 - 244.403i) q^{75} +(-122.972 + 226.527i) q^{77} +(218.823 - 379.013i) q^{79} +(-40.5000 - 70.1481i) q^{81} -241.241 q^{83} +241.803 q^{85} +(108.538 + 187.994i) q^{87} +(-792.772 + 1373.12i) q^{89} +(-374.265 - 610.643i) q^{91} +(96.0646 - 166.389i) q^{93} +(-303.173 - 525.112i) q^{95} +79.2754 q^{97} +125.256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9}+O(q^{10}) \) 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

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