LMFDB - Embedded newform 39.4.j.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(4,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("39.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.j (of order $6$, degree $2$, 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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(45.0000 + 25.9808i) q^{11} -24.0000 q^{12} +(-32.5000 - 33.7750i) q^{13} +(-13.5000 - 7.79423i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(58.5000 + 101.325i) q^{17} +(-21.0000 + 12.1244i) q^{19} +(-36.0000 + 20.7846i) q^{20} -31.1769i q^{21} +(-9.00000 + 15.5885i) q^{23} +98.0000 q^{25} -27.0000 q^{27} +(-72.0000 - 41.5692i) q^{28} +(49.5000 - 85.7365i) q^{29} -193.990i q^{31} +(135.000 - 77.9423i) q^{33} +(-27.0000 - 46.7654i) q^{35} +(-36.0000 + 62.3538i) q^{36} +(97.5000 + 56.2917i) q^{37} +(-136.500 + 33.7750i) q^{39} +(-31.5000 - 18.1865i) q^{41} +(41.0000 + 71.0141i) q^{43} -415.692i q^{44} +(-40.5000 + 23.3827i) q^{45} +72.7461i q^{47} +(96.0000 + 166.277i) q^{48} +(-117.500 + 203.516i) q^{49} +351.000 q^{51} +(-104.000 + 360.267i) q^{52} -261.000 q^{53} +(135.000 - 233.827i) q^{55} +72.7461i q^{57} +(-684.000 + 394.908i) q^{59} +124.708i q^{60} +(359.500 + 622.672i) q^{61} +(-81.0000 - 46.7654i) q^{63} +512.000 q^{64} +(-175.500 + 168.875i) q^{65} +(-609.000 - 351.606i) q^{67} +(468.000 - 810.600i) q^{68} +(27.0000 + 46.7654i) q^{69} +(-405.000 + 233.827i) q^{71} -684.160i q^{73} +(147.000 - 254.611i) q^{75} +(168.000 + 96.9948i) q^{76} +540.000 q^{77} -440.000 q^{79} +(288.000 + 166.277i) q^{80} +(-40.5000 + 70.1481i) q^{81} -1195.12i q^{83} +(-216.000 + 124.708i) q^{84} +(526.500 - 303.975i) q^{85} +(-148.500 - 257.210i) q^{87} +(1314.00 + 758.638i) q^{89} +(-468.000 - 135.100i) q^{91} +144.000 q^{92} +(-504.000 - 290.985i) q^{93} +(63.0000 + 109.119i) q^{95} +(-1002.00 + 578.505i) q^{97} -467.654i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 8 * q^4 + 18 * q^7 - 9 * q^9	$ 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9} + 90 q^{11} - 48 q^{12} - 65 q^{13} - 27 q^{15} - 64 q^{16} + 117 q^{17} - 42 q^{19} - 72 q^{20} - 18 q^{23} + 196 q^{25} - 54 q^{27} - 144 q^{28} + 99 q^{29} + 270 q^{33} - 54 q^{35} - 72 q^{36} + 195 q^{37} - 273 q^{39} - 63 q^{41} + 82 q^{43} - 81 q^{45} + 192 q^{48} - 235 q^{49} + 702 q^{51} - 208 q^{52} - 522 q^{53} + 270 q^{55} - 1368 q^{59} + 719 q^{61} - 162 q^{63} + 1024 q^{64} - 351 q^{65} - 1218 q^{67} + 936 q^{68} + 54 q^{69} - 810 q^{71} + 294 q^{75} + 336 q^{76} + 1080 q^{77} - 880 q^{79} + 576 q^{80} - 81 q^{81} - 432 q^{84} + 1053 q^{85} - 297 q^{87} + 2628 q^{89} - 936 q^{91} + 288 q^{92} - 1008 q^{93} + 126 q^{95} - 2004 q^{97}+O(q^{100}) $ 2 * q + 3 * q^3 - 8 * q^4 + 18 * q^7 - 9 * q^9 + 90 * q^11 - 48 * q^12 - 65 * q^13 - 27 * q^15 - 64 * q^16 + 117 * q^17 - 42 * q^19 - 72 * q^20 - 18 * q^23 + 196 * q^25 - 54 * q^27 - 144 * q^28 + 99 * q^29 + 270 * q^33 - 54 * q^35 - 72 * q^36 + 195 * q^37 - 273 * q^39 - 63 * q^41 + 82 * q^43 - 81 * q^45 + 192 * q^48 - 235 * q^49 + 702 * q^51 - 208 * q^52 - 522 * q^53 + 270 * q^55 - 1368 * q^59 + 719 * q^61 - 162 * q^63 + 1024 * q^64 - 351 * q^65 - 1218 * q^67 + 936 * q^68 + 54 * q^69 - 810 * q^71 + 294 * q^75 + 336 * q^76 + 1080 * q^77 - 880 * q^79 + 576 * q^80 - 81 * q^81 - 432 * q^84 + 1053 * q^85 - 297 * q^87 + 2628 * q^89 - 936 * q^91 + 288 * q^92 - 1008 * q^93 + 126 * q^95 - 2004 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−4.00000	−	6.92820i	−0.500000	−	0.866025i
$5$		−	5.19615i		−	0.464758i	−0.972625	−	0.232379i	$-0.925349\pi$
$5$		−	5.19615i		−	0.464758i	0.972625	−	0.232379i	$-0.0746510\pi$
$6$		0			0
$7$	9.00000	−	5.19615i	0.485954	−	0.280566i	−0.236940	−	0.971524i	$-0.576145\pi$
$7$	9.00000	−	5.19615i	0.485954	−	0.280566i	0.722895	+	0.690958i	$0.242811\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	45.0000	+	25.9808i	1.23346	+	0.712136i	0.967749	−	0.251918i	$-0.0810613\pi$
$11$	45.0000	+	25.9808i	1.23346	+	0.712136i	0.265707	+	0.964054i	$0.414395\pi$
$12$	−24.0000			−0.577350
$13$	−32.5000	−	33.7750i	−0.693375	−	0.720577i
$13$	−32.5000	−	33.7750i	−0.693375	−	0.720577i
$14$		0			0
$15$	−13.5000	−	7.79423i	−0.232379	−	0.134164i
$16$	−32.0000	+	55.4256i	−0.500000	+	0.866025i
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	0.894349	+	0.447369i	$0.147639\pi$
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	−0.0597414	+	0.998214i	$0.519028\pi$
$18$		0			0
$19$	−21.0000	+	12.1244i	−0.253565	+	0.146396i	−0.621395	−	0.783497i	$-0.713434\pi$
$19$	−21.0000	+	12.1244i	−0.253565	+	0.146396i	0.367831	+	0.929893i	$0.380101\pi$
$20$	−36.0000	+	20.7846i	−0.402492	+	0.232379i
$21$		−	31.1769i		−	0.323970i
$22$		0			0
$23$	−9.00000	+	15.5885i	−0.0815926	+	0.141323i	−0.903934	−	0.427672i	$-0.859334\pi$
$23$	−9.00000	+	15.5885i	−0.0815926	+	0.141323i	0.822342	+	0.568994i	$0.192667\pi$
$24$		0			0
$25$	98.0000			0.784000
$26$		0			0
$27$	−27.0000			−0.192450
$28$	−72.0000	−	41.5692i	−0.485954	−	0.280566i
$29$	49.5000	−	85.7365i	0.316963	−	0.548996i	−0.662890	−	0.748717i	$-0.730670\pi$
$29$	49.5000	−	85.7365i	0.316963	−	0.548996i	0.979853	+	0.199721i	$0.0640037\pi$
$30$		0			0
$31$		−	193.990i		−	1.12392i	−0.827164	−	0.561961i	$-0.810047\pi$
$31$		−	193.990i		−	1.12392i	0.827164	−	0.561961i	$-0.189953\pi$
$32$		0			0
$33$	135.000	−	77.9423i	0.712136	−	0.411152i
$34$		0			0
$35$	−27.0000	−	46.7654i	−0.130395	−	0.225851i
$36$	−36.0000	+	62.3538i	−0.166667	+	0.288675i
$37$	97.5000	+	56.2917i	0.433214	+	0.250116i	0.700715	−	0.713442i	$-0.252865\pi$
$37$	97.5000	+	56.2917i	0.433214	+	0.250116i	−0.267501	+	0.963558i	$0.586198\pi$
$38$		0			0
$39$	−136.500	+	33.7750i	−0.560449	+	0.138675i
$40$		0			0
$41$	−31.5000	−	18.1865i	−0.119987	−	0.0692746i	0.438805	−	0.898582i	$-0.355402\pi$
$41$	−31.5000	−	18.1865i	−0.119987	−	0.0692746i	−0.558792	+	0.829308i	$0.688735\pi$
$42$		0			0
$43$	41.0000	+	71.0141i	0.145406	+	0.251850i	0.929524	−	0.368761i	$-0.120218\pi$
$43$	41.0000	+	71.0141i	0.145406	+	0.251850i	−0.784119	+	0.620611i	$0.786885\pi$
$44$		−	415.692i		−	1.42427i
$45$	−40.5000	+	23.3827i	−0.134164	+	0.0774597i
$46$		0			0
$47$			72.7461i			0.225768i	0.993608	+	0.112884i	$0.0360089\pi$
$47$			72.7461i			0.225768i	−0.993608	+	0.112884i	$0.963991\pi$
$48$	96.0000	+	166.277i	0.288675	+	0.500000i
$49$	−117.500	+	203.516i	−0.342566	+	0.593341i
$50$		0			0
$51$	351.000			0.963722
$52$	−104.000	+	360.267i	−0.277350	+	0.960769i
$53$	−261.000			−0.676436			−0.338218	−	0.941068i	$-0.609824\pi$
$53$	−261.000			−0.676436			−0.338218	+	0.941068i	$0.609824\pi$
$54$		0			0
$55$	135.000	−	233.827i	0.330971	−	0.573258i
$56$		0			0
$57$			72.7461i			0.169043i
$58$		0			0
$59$	−684.000	+	394.908i	−1.50931	+	0.871400i	−0.509368	+	0.860549i	$0.670121\pi$
$59$	−684.000	+	394.908i	−1.50931	+	0.871400i	−0.999941	+	0.0108508i	$0.996546\pi$
$60$			124.708i			0.268328i
$61$	359.500	+	622.672i	0.754578	+	1.30697i	0.945584	+	0.325379i	$0.105492\pi$
$61$	359.500	+	622.672i	0.754578	+	1.30697i	−0.191006	+	0.981589i	$0.561175\pi$
$62$		0			0
$63$	−81.0000	−	46.7654i	−0.161985	−	0.0935220i
$64$	512.000			1.00000
$65$	−175.500	+	168.875i	−0.334894	+	0.322252i
$66$		0			0
$67$	−609.000	−	351.606i	−1.11047	−	0.641128i	−0.171516	−	0.985181i	$-0.554866\pi$
$67$	−609.000	−	351.606i	−1.11047	−	0.641128i	−0.938950	+	0.344054i	$0.888200\pi$
$68$	468.000	−	810.600i	0.834608	−	1.44558i
$69$	27.0000	+	46.7654i	0.0471075	+	0.0815926i
$70$		0			0
$71$	−405.000	+	233.827i	−0.676967	+	0.390847i	−0.798711	−	0.601714i	$-0.794485\pi$
$71$	−405.000	+	233.827i	−0.676967	+	0.390847i	0.121744	+	0.992561i	$0.461151\pi$
$72$		0			0
$73$		−	684.160i		−	1.09692i	−0.836178	−	0.548458i	$-0.815215\pi$
$73$		−	684.160i		−	1.09692i	0.836178	−	0.548458i	$-0.184785\pi$
$74$		0			0
$75$	147.000	−	254.611i	0.226321	−	0.392000i
$76$	168.000	+	96.9948i	0.253565	+	0.146396i
$77$	540.000			0.799204
$78$		0			0
$79$	−440.000			−0.626631			−0.313316	−	0.949649i	$-0.601440\pi$
$79$	−440.000			−0.626631			−0.313316	+	0.949649i	$0.601440\pi$
$80$	288.000	+	166.277i	0.402492	+	0.232379i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	1195.12i		−	1.58049i	−0.612789	−	0.790247i	$-0.709952\pi$
$83$		−	1195.12i		−	1.58049i	0.612789	−	0.790247i	$-0.290048\pi$
$84$	−216.000	+	124.708i	−0.280566	+	0.161985i
$85$	526.500	−	303.975i	0.671846	−	0.387891i
$86$		0			0
$87$	−148.500	−	257.210i	−0.182999	−	0.316963i
$88$		0			0
$89$	1314.00	+	758.638i	1.56499	+	0.903545i	0.996740	+	0.0806862i	$0.0257112\pi$
$89$	1314.00	+	758.638i	1.56499	+	0.903545i	0.568246	+	0.822859i	$0.307622\pi$
$90$		0			0
$91$	−468.000	−	135.100i	−0.539118	−	0.155630i
$92$	144.000			0.163185
$93$	−504.000	−	290.985i	−0.561961	−	0.324448i
$94$		0			0
$95$	63.0000	+	109.119i	0.0680386	+	0.117846i
$96$		0			0
$97$	−1002.00	+	578.505i	−1.04884	+	0.605549i	−0.922325	−	0.386415i	$-0.873713\pi$
$97$	−1002.00	+	578.505i	−1.04884	+	0.605549i	−0.126517	+	0.991964i	$0.540380\pi$
$98$		0			0
$99$		−	467.654i		−	0.474757i
$100$	−392.000	−	678.964i	−0.392000	−	0.678964i
$101$	−787.500	+	1363.99i	−0.775833	+	1.34378i	0.158491	+	0.987360i	$0.449337\pi$
$101$	−787.500	+	1363.99i	−0.775833	+	1.34378i	−0.934325	+	0.356423i	$0.883996\pi$
$102$		0			0
$103$	794.000			0.759565			0.379782	−	0.925076i	$-0.375999\pi$
$103$	794.000			0.759565			0.379782	+	0.925076i	$0.375999\pi$
$104$		0			0
$105$	−162.000			−0.150567
$106$		0			0
$107$	−225.000	+	389.711i	−0.203286	+	0.352101i	−0.949585	−	0.313509i	$-0.898495\pi$
$107$	−225.000	+	389.711i	−0.203286	+	0.352101i	0.746299	+	0.665610i	$0.231829\pi$
$108$	108.000	+	187.061i	0.0962250	+	0.166667i
$109$		−	595.825i		−	0.523576i	−0.965125	−	0.261788i	$-0.915688\pi$
$109$		−	595.825i		−	0.523576i	0.965125	−	0.261788i	$-0.0843120\pi$
$110$		0			0
$111$	292.500	−	168.875i	0.250116	−	0.144405i
$112$			665.108i			0.561132i
$113$	850.500	+	1473.11i	0.708038	+	1.22636i	0.965584	+	0.260092i	$0.0837529\pi$
$113$	850.500	+	1473.11i	0.708038	+	1.22636i	−0.257546	+	0.966266i	$0.582914\pi$
$114$		0			0
$115$	81.0000	+	46.7654i	0.0656808	+	0.0379208i
$116$	−792.000			−0.633925
$117$	−117.000	+	405.300i	−0.0924500	+	0.320256i
$118$		0			0
$119$	1053.00	+	607.950i	0.811163	+	0.468325i
$120$		0			0
$121$	684.500	+	1185.59i	0.514275	+	0.890750i
$122$		0			0
$123$	−94.5000	+	54.5596i	−0.0692746	+	0.0399957i
$124$	−1344.00	+	775.959i	−0.973345	+	0.561961i
$125$		−	1158.74i		−	0.829128i
$126$		0			0
$127$	832.000	−	1441.07i	0.581323	−	1.00688i	−0.414000	−	0.910277i	$-0.635868\pi$
$127$	832.000	−	1441.07i	0.581323	−	1.00688i	0.995323	−	0.0966044i	$-0.0307982\pi$
$128$		0			0
$129$	246.000			0.167900
$130$		0			0
$131$	−1476.00			−0.984418			−0.492209	−	0.870477i	$-0.663810\pi$
$131$	−1476.00			−0.984418			−0.492209	+	0.870477i	$0.663810\pi$
$132$	−1080.00	−	623.538i	−0.712136	−	0.411152i
$133$	−126.000	+	218.238i	−0.0821473	+	0.142283i
$134$		0			0
$135$			140.296i			0.0894427i
$136$		0			0
$137$	877.500	−	506.625i	0.547225	−	0.315941i	−0.200777	−	0.979637i	$-0.564347\pi$
$137$	877.500	−	506.625i	0.547225	−	0.315941i	0.748002	+	0.663696i	$0.231013\pi$
$138$		0			0
$139$	−562.000	−	973.413i	−0.342937	−	0.593984i	0.642040	−	0.766671i	$-0.278088\pi$
$139$	−562.000	−	973.413i	−0.342937	−	0.593984i	−0.984977	+	0.172687i	$0.944755\pi$
$140$	−216.000	+	374.123i	−0.130395	+	0.225851i
$141$	189.000	+	109.119i	0.112884	+	0.0651737i
$142$		0			0
$143$	−585.000	−	2364.25i	−0.342099	−	1.38258i
$144$	576.000			0.333333
$145$	−445.500	−	257.210i	−0.255150	−	0.147311i
$146$		0			0
$147$	352.500	+	610.548i	0.197780	+	0.342566i
$148$		−	900.666i		−	0.500232i
$149$	2830.50	−	1634.19i	1.55627	−	0.898510i	0.558657	−	0.829399i	$-0.311317\pi$
$149$	2830.50	−	1634.19i	1.55627	−	0.898510i	0.997609	−	0.0691115i	$-0.0220164\pi$
$150$		0			0
$151$			1638.52i			0.883052i	0.897248	+	0.441526i	$0.145563\pi$
$151$			1638.52i			0.883052i	−0.897248	+	0.441526i	$0.854437\pi$
$152$		0			0
$153$	526.500	−	911.925i	0.278203	−	0.481861i
$154$		0			0
$155$	−1008.00			−0.522352
$156$	780.000	+	810.600i	0.400320	+	0.416025i
$157$	1259.00			0.639995			0.319997	−	0.947418i	$-0.396318\pi$
$157$	1259.00			0.639995			0.319997	+	0.947418i	$0.396318\pi$
$158$		0			0
$159$	−391.500	+	678.098i	−0.195270	+	0.338218i
$160$		0			0
$161$			187.061i			0.0915684i
$162$		0			0
$163$	2556.00	−	1475.71i	1.22823	−	0.709118i	0.261570	−	0.965185i	$-0.415760\pi$
$163$	2556.00	−	1475.71i	1.22823	−	0.709118i	0.966659	+	0.256066i	$0.0824264\pi$
$164$			290.985i			0.138549i
$165$	−405.000	−	701.481i	−0.191086	−	0.330971i
$166$		0			0
$167$	−2718.00	−	1569.24i	−1.25943	−	0.727133i	−0.286468	−	0.958090i	$-0.592481\pi$
$167$	−2718.00	−	1569.24i	−1.25943	−	0.727133i	−0.972964	+	0.230956i	$0.925815\pi$
$168$		0			0
$169$	−84.5000	+	2195.37i	−0.0384615	+	0.999260i
$170$		0			0
$171$	189.000	+	109.119i	0.0845216	+	0.0487986i
$172$	328.000	−	568.113i	0.145406	−	0.251850i
$173$	−2133.00	−	3694.46i	−0.937393	−	1.62361i	−0.770310	−	0.637669i	$-0.779899\pi$
$173$	−2133.00	−	3694.46i	−0.937393	−	1.62361i	−0.167083	−	0.985943i	$-0.553435\pi$
$174$		0			0
$175$	882.000	−	509.223i	0.380988	−	0.219964i
$176$	−2880.00	+	1662.77i	−1.23346	+	0.712136i
$177$			2369.45i			1.00621i
$178$		0			0
$179$	−1503.00	+	2603.27i	−0.627595	+	1.08703i	0.360438	+	0.932783i	$0.382627\pi$
$179$	−1503.00	+	2603.27i	−0.627595	+	1.08703i	−0.988033	+	0.154243i	$0.950706\pi$
$180$	324.000	+	187.061i	0.134164	+	0.0774597i
$181$	−1873.00			−0.769166			−0.384583	−	0.923090i	$-0.625655\pi$
$181$	−1873.00			−0.769166			−0.384583	+	0.923090i	$0.625655\pi$
$182$		0			0
$183$	2157.00			0.871312
$184$		0			0
$185$	292.500	−	506.625i	0.116243	−	0.201339i
$186$		0			0
$187$			6079.50i			2.37742i
$188$	504.000	−	290.985i	0.195521	−	0.112884i
$189$	−243.000	+	140.296i	−0.0935220	+	0.0539949i
$190$		0			0
$191$	1368.00	+	2369.45i	0.518246	+	0.897629i	0.999775	+	0.0211985i	$0.00674821\pi$
$191$	1368.00	+	2369.45i	0.518246	+	0.897629i	−0.481529	+	0.876430i	$0.659918\pi$
$192$	768.000	−	1330.22i	0.288675	−	0.500000i
$193$	−2254.50	−	1301.64i	−0.840842	−	0.485460i	0.0167085	−	0.999860i	$-0.494681\pi$
$193$	−2254.50	−	1301.64i	−0.840842	−	0.485460i	−0.857550	+	0.514400i	$0.828015\pi$
$194$		0			0
$195$	175.500	+	709.275i	0.0644503	+	0.260473i
$196$	1880.00			0.685131
$197$	3222.00	+	1860.22i	1.16527	+	0.672768i	0.952561	−	0.304347i	$-0.0984384\pi$
$197$	3222.00	+	1860.22i	1.16527	+	0.672768i	0.212708	+	0.977116i	$0.431772\pi$
$198$		0			0
$199$	−599.000	−	1037.50i	−0.213377	−	0.369579i	0.739392	−	0.673275i	$-0.235113\pi$
$199$	−599.000	−	1037.50i	−0.213377	−	0.369579i	−0.952769	+	0.303695i	$0.901780\pi$
$200$		0			0
$201$	−1827.00	+	1054.82i	−0.641128	+	0.370155i
$202$		0			0
$203$		−	1028.84i		−	0.355716i
$204$	−1404.00	−	2431.80i	−0.481861	−	0.834608i
$205$	−94.5000	+	163.679i	−0.0321959	+	0.0557650i
$206$		0			0
$207$	162.000			0.0543951
$208$	2912.00	−	720.533i	0.970725	−	0.240192i
$209$	−1260.00			−0.417014
$210$		0			0
$211$	−1196.00	+	2071.53i	−0.390218	+	0.675878i	−0.992478	−	0.122422i	$-0.960934\pi$
$211$	−1196.00	+	2071.53i	−0.390218	+	0.675878i	0.602260	+	0.798300i	$0.294267\pi$
$212$	1044.00	+	1808.26i	0.338218	+	0.585811i
$213$			1402.96i			0.451311i
$214$		0			0
$215$	369.000	−	213.042i	0.117049	−	0.0675784i
$216$		0			0
$217$	−1008.00	−	1745.91i	−0.315334	−	0.546175i
$218$		0			0
$219$	−1777.50	−	1026.24i	−0.548458	−	0.316652i
$220$	−2160.00			−0.661942
$221$	1521.00	−	5268.90i	0.462957	−	1.60373i
$222$		0			0
$223$	−1764.00	−	1018.45i	−0.529714	−	0.305830i	0.211186	−	0.977446i	$-0.432267\pi$
$223$	−1764.00	−	1018.45i	−0.529714	−	0.305830i	−0.740900	+	0.671615i	$0.765601\pi$
$224$		0			0
$225$	−441.000	−	763.834i	−0.130667	−	0.226321i
$226$		0			0
$227$	1863.00	−	1075.60i	0.544721	−	0.314495i	−0.202269	−	0.979330i	$-0.564832\pi$
$227$	1863.00	−	1075.60i	0.544721	−	0.314495i	0.746990	+	0.664835i	$0.231498\pi$
$228$	504.000	−	290.985i	0.146396	−	0.0845216i
$229$		−	3471.03i		−	1.00162i	−0.865556	−	0.500812i	$-0.833035\pi$
$229$		−	3471.03i		−	1.00162i	0.865556	−	0.500812i	$-0.166965\pi$
$230$		0			0
$231$	810.000	−	1402.96i	0.230710	−	0.399602i
$232$		0			0
$233$	−1854.00			−0.521286			−0.260643	−	0.965435i	$-0.583935\pi$
$233$	−1854.00			−0.521286			−0.260643	+	0.965435i	$0.583935\pi$
$234$		0			0
$235$	378.000			0.104928
$236$	5472.00	+	3159.26i	1.50931	+	0.871400i
$237$	−660.000	+	1143.15i	−0.180893	+	0.313316i
$238$		0			0
$239$			4458.30i			1.20662i	0.797505	+	0.603312i	$0.206153\pi$
$239$			4458.30i			1.20662i	−0.797505	+	0.603312i	$0.793847\pi$
$240$	864.000	−	498.831i	0.232379	−	0.134164i
$241$	−361.500	+	208.712i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−361.500	+	208.712i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	2876.00	−	4981.38i	0.754578	−	1.30697i
$245$	1057.50	+	610.548i	0.275760	+	0.159210i
$246$		0			0
$247$	1092.00	+	315.233i	0.281305	+	0.0812057i
$248$		0			0
$249$	−3105.00	−	1792.67i	−0.790247	−	0.456249i
$250$		0			0
$251$	−2052.00	−	3554.17i	−0.516020	−	0.893773i	−0.999827	−	0.0185985i	$-0.994080\pi$
$251$	−2052.00	−	3554.17i	−0.516020	−	0.893773i	0.483807	−	0.875175i	$-0.339254\pi$
$252$			748.246i			0.187044i
$253$	−810.000	+	467.654i	−0.201282	+	0.116210i
$254$		0			0
$255$		−	1823.85i		−	0.447898i
$256$	−2048.00	−	3547.24i	−0.500000	−	0.866025i
$257$	−994.500	+	1722.52i	−0.241382	+	0.418086i	−0.961108	−	0.276172i	$-0.910934\pi$
$257$	−994.500	+	1722.52i	−0.241382	+	0.418086i	0.719726	+	0.694258i	$0.244267\pi$
$258$		0			0
$259$	1170.00			0.280696
$260$	1872.00	+	540.400i	0.446525	+	0.128901i
$261$	−891.000			−0.211308
$262$		0			0
$263$	−369.000	+	639.127i	−0.0865153	+	0.149849i	−0.906036	−	0.423201i	$-0.860906\pi$
$263$	−369.000	+	639.127i	−0.0865153	+	0.149849i	0.819521	+	0.573050i	$0.194240\pi$
$264$		0			0
$265$			1356.20i			0.314379i
$266$		0			0
$267$	3942.00	−	2275.91i	0.903545	−	0.521662i
$268$			5625.70i			1.28226i
$269$	1053.00	+	1823.85i	0.238671	+	0.413391i	0.960333	−	0.278855i	$-0.0899549\pi$
$269$	1053.00	+	1823.85i	0.238671	+	0.413391i	−0.721662	+	0.692246i	$0.756622\pi$
$270$		0			0
$271$	594.000	+	342.946i	0.133147	+	0.0768727i	0.565094	−	0.825026i	$-0.308840\pi$
$271$	594.000	+	342.946i	0.133147	+	0.0768727i	−0.431947	+	0.901899i	$0.642173\pi$
$272$	−7488.00			−1.66922
$273$	−1053.00	+	1013.25i	−0.233445	+	0.224632i
$274$		0			0
$275$	4410.00	+	2546.11i	0.967029	+	0.558315i
$276$	216.000	−	374.123i	0.0471075	−	0.0815926i
$277$	−1832.50	−	3173.98i	−0.397488	−	0.688470i	0.595927	−	0.803039i	$-0.296785\pi$
$277$	−1832.50	−	3173.98i	−0.397488	−	0.688470i	−0.993415	+	0.114569i	$0.963451\pi$
$278$		0			0
$279$	−1512.00	+	872.954i	−0.324448	+	0.187320i
$280$		0			0
$281$			1719.93i			0.365132i	0.983194	+	0.182566i	$0.0584404\pi$
$281$			1719.93i			0.365132i	−0.983194	+	0.182566i	$0.941560\pi$
$282$		0			0
$283$	913.000	−	1581.36i	0.191775	−	0.332163i	−0.754064	−	0.656801i	$-0.771909\pi$
$283$	913.000	−	1581.36i	0.191775	−	0.332163i	0.945838	+	0.324638i	$0.105242\pi$
$284$	3240.00	+	1870.61i	0.676967	+	0.390847i
$285$	378.000			0.0785642
$286$		0			0
$287$	−378.000			−0.0777444
$288$		0			0
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$		0			0
$291$			3471.03i			0.699228i
$292$	−4740.00	+	2736.64i	−0.949957	+	0.548458i
$293$	−436.500	+	252.013i	−0.0870328	+	0.0502484i	−0.542885	−	0.839807i	$-0.682668\pi$
$293$	−436.500	+	252.013i	−0.0870328	+	0.0502484i	0.455852	+	0.890056i	$0.349335\pi$
$294$		0			0
$295$	2052.00	+	3554.17i	0.404990	+	0.701463i
$296$		0			0
$297$	−1215.00	−	701.481i	−0.237379	−	0.137051i
$298$		0			0
$299$	819.000	−	202.650i	0.158408	−	0.0391958i
$300$	−2352.00			−0.452643
$301$	738.000	+	426.084i	0.141321	+	0.0815917i
$302$		0			0
$303$	2362.50	+	4091.97i	0.447928	+	0.775833i
$304$		−	1551.92i		−	0.292791i
$305$	3235.50	−	1868.02i	0.607424	−	0.350696i
$306$		0			0
$307$		−	1950.29i		−	0.362570i	−0.983431	−	0.181285i	$-0.941974\pi$
$307$		−	1950.29i		−	0.362570i	0.983431	−	0.181285i	$-0.0580256\pi$
$308$	−2160.00	−	3741.23i	−0.399602	−	0.692131i
$309$	1191.00	−	2062.87i	0.219267	−	0.379782i
$310$		0			0
$311$	−3798.00			−0.692491			−0.346246	−	0.938144i	$-0.612544\pi$
$311$	−3798.00			−0.692491			−0.346246	+	0.938144i	$0.612544\pi$
$312$		0			0
$313$	1378.00			0.248847			0.124424	−	0.992229i	$-0.460292\pi$
$313$	1378.00			0.248847			0.124424	+	0.992229i	$0.460292\pi$
$314$		0			0
$315$	−243.000	+	420.888i	−0.0434651	+	0.0752837i
$316$	1760.00	+	3048.41i	0.313316	+	0.542679i
$317$		−	7103.14i		−	1.25852i	−0.777193	−	0.629262i	$-0.783357\pi$
$317$		−	7103.14i		−	1.25852i	0.777193	−	0.629262i	$-0.216643\pi$
$318$		0			0
$319$	4455.00	−	2572.10i	0.781919	−	0.451441i
$320$		−	2660.43i		−	0.464758i
$321$	675.000	+	1169.13i	0.117367	+	0.203286i
$322$		0			0
$323$	−2457.00	−	1418.55i	−0.423254	−	0.244366i
$324$	648.000			0.111111
$325$	−3185.00	−	3309.95i	−0.543606	−	0.564932i
$326$		0			0
$327$	−1548.00	−	893.738i	−0.261788	−	0.151143i
$328$		0			0
$329$	378.000	+	654.715i	0.0633429	+	0.109713i
$330$		0			0
$331$	8724.00	−	5036.80i	1.44868	−	0.836398i	0.450281	−	0.892887i	$-0.351324\pi$
$331$	8724.00	−	5036.80i	1.44868	−	0.836398i	0.998403	+	0.0564889i	$0.0179906\pi$
$332$	−8280.00	+	4780.46i	−1.36875	+	0.790247i
$333$		−	1013.25i		−	0.166744i
$334$		0			0
$335$	−1827.00	+	3164.46i	−0.297969	+	0.516098i
$336$	1728.00	+	997.661i	0.280566	+	0.161985i
$337$	9001.00			1.45494			0.727471	−	0.686138i	$-0.240695\pi$
$337$	9001.00			1.45494			0.727471	+	0.686138i	$0.240695\pi$
$338$		0			0
$339$	5103.00			0.817572
$340$	−4212.00	−	2431.80i	−0.671846	−	0.387891i
$341$	5040.00	−	8729.54i	0.800385	−	1.38631i
$342$		0			0
$343$			6006.75i			0.945581i
$344$		0			0
$345$	243.000	−	140.296i	0.0379208	−	0.0218936i
$346$		0			0
$347$	−1647.00	−	2852.69i	−0.254800	−	0.441327i	0.710041	−	0.704160i	$-0.248676\pi$
$347$	−1647.00	−	2852.69i	−0.254800	−	0.441327i	−0.964841	+	0.262834i	$0.915343\pi$
$348$	−1188.00	+	2057.68i	−0.182999	+	0.316963i
$349$	−9132.00	−	5272.36i	−1.40064	−	0.808662i	−0.406185	−	0.913791i	$-0.633141\pi$
$349$	−9132.00	−	5272.36i	−1.40064	−	0.808662i	−0.994459	+	0.105129i	$0.966475\pi$
$350$		0			0
$351$	877.500	+	911.925i	0.133440	+	0.138675i
$352$		0			0
$353$	−2146.50	−	1239.28i	−0.323645	−	0.186856i	0.329371	−	0.944201i	$-0.393163\pi$
$353$	−2146.50	−	1239.28i	−0.323645	−	0.186856i	−0.653016	+	0.757344i	$0.726497\pi$
$354$		0			0
$355$	1215.00	+	2104.44i	0.181649	+	0.314626i
$356$		−	12138.2i		−	1.80709i
$357$	3159.00	−	1823.85i	0.468325	−	0.270388i
$358$		0			0
$359$			5414.39i			0.795991i	0.917387	+	0.397995i	$0.130294\pi$
$359$			5414.39i			0.795991i	−0.917387	+	0.397995i	$0.869706\pi$
$360$		0			0
$361$	−3135.50	+	5430.85i	−0.457137	+	0.791784i
$362$		0			0
$363$	4107.00			0.593834
$364$	936.000	+	3782.80i	0.134779	+	0.544705i
$365$	−3555.00			−0.509801
$366$		0			0
$367$	4973.00	−	8613.49i	0.707326	−	1.22512i	−0.258520	−	0.966006i	$-0.583235\pi$
$367$	4973.00	−	8613.49i	0.707326	−	1.22512i	0.965846	−	0.259118i	$-0.0834318\pi$
$368$	−576.000	−	997.661i	−0.0815926	−	0.141323i
$369$			327.358i			0.0461831i
$370$		0			0
$371$	−2349.00	+	1356.20i	−0.328717	+	0.189785i
$372$			4655.75i			0.648897i
$373$	3650.50	+	6322.85i	0.506745	+	0.877707i	0.999970	+	0.00780555i	$0.00248461\pi$
$373$	3650.50	+	6322.85i	0.506745	+	0.877707i	−0.493225	+	0.869902i	$0.664182\pi$
$374$		0			0
$375$	−3010.50	−	1738.11i	−0.414564	−	0.239349i
$376$		0			0
$377$	−4504.50	+	1114.57i	−0.615368	+	0.152264i
$378$		0			0
$379$	−2964.00	−	1711.27i	−0.401716	−	0.231931i	0.285508	−	0.958376i	$-0.407838\pi$
$379$	−2964.00	−	1711.27i	−0.401716	−	0.231931i	−0.687224	+	0.726445i	$0.741171\pi$
$380$	504.000	−	872.954i	0.0680386	−	0.117846i
$381$	−2496.00	−	4323.20i	−0.335627	−	0.581323i
$382$		0			0
$383$	−5004.00	+	2889.06i	−0.667604	+	0.385442i	−0.795168	−	0.606389i	$-0.792618\pi$
$383$	−5004.00	+	2889.06i	−0.667604	+	0.385442i	0.127564	+	0.991830i	$0.459284\pi$
$384$		0			0
$385$		−	2805.92i		−	0.371436i
$386$		0			0
$387$	369.000	−	639.127i	0.0484685	−	0.0839500i
$388$	8016.00	+	4628.04i	1.04884	+	0.605549i
$389$	9153.00			1.19300			0.596498	−	0.802614i	$-0.296558\pi$
$389$	9153.00			1.19300			0.596498	+	0.802614i	$0.296558\pi$
$390$		0			0
$391$	−2106.00			−0.272391
$392$		0			0
$393$	−2214.00	+	3834.76i	−0.284177	+	0.492209i
$394$		0			0
$395$			2286.31i			0.291232i
$396$	−3240.00	+	1870.61i	−0.411152	+	0.237379i
$397$	1752.00	−	1011.52i	0.221487	−	0.127876i	−0.385152	−	0.922853i	$-0.625851\pi$
$397$	1752.00	−	1011.52i	0.221487	−	0.127876i	0.606639	+	0.794978i	$0.292518\pi$
$398$		0			0
$399$	378.000	+	654.715i	0.0474277	+	0.0821473i
$400$	−3136.00	+	5431.71i	−0.392000	+	0.678964i
$401$	7195.50	+	4154.32i	0.896075	+	0.517349i	0.875925	−	0.482448i	$-0.160252\pi$
$401$	7195.50	+	4154.32i	0.896075	+	0.517349i	0.0201504	+	0.999797i	$0.493586\pi$
$402$		0			0
$403$	−6552.00	+	6304.66i	−0.809872	+	0.779300i
$404$	12600.0			1.55167
$405$	364.500	+	210.444i	0.0447214	+	0.0258199i
$406$		0			0
$407$	2925.00	+	5066.25i	0.356233	+	0.617014i
$408$		0			0
$409$	−9022.50	+	5209.14i	−1.09079	+	0.629769i	−0.933787	−	0.357829i	$-0.883517\pi$
$409$	−9022.50	+	5209.14i	−1.09079	+	0.629769i	−0.157005	+	0.987598i	$0.550184\pi$
$410$		0			0
$411$		−	3039.75i		−	0.364817i
$412$	−3176.00	−	5500.99i	−0.379782	−	0.657802i
$413$	−4104.00	+	7108.34i	−0.488970	+	0.846921i
$414$		0			0
$415$	−6210.00			−0.734547
$416$		0			0
$417$	−3372.00			−0.395989
$418$		0			0
$419$	−2088.00	+	3616.52i	−0.243450	+	0.421667i	−0.961695	−	0.274123i	$-0.911612\pi$
$419$	−2088.00	+	3616.52i	−0.243450	+	0.421667i	0.718245	+	0.695790i	$0.244946\pi$
$420$	648.000	+	1122.37i	0.0752837	+	0.130395i
$421$		−	14471.3i		−	1.67527i	−0.546233	−	0.837633i	$-0.683939\pi$
$421$		−	14471.3i		−	1.67527i	0.546233	−	0.837633i	$-0.316061\pi$
$422$		0			0
$423$	567.000	−	327.358i	0.0651737	−	0.0376281i
$424$		0			0
$425$	5733.00	+	9929.85i	0.654333	+	1.13334i
$426$		0			0
$427$	6471.00	+	3736.03i	0.733381	+	0.423418i
$428$	3600.00			0.406571
$429$	−7020.00	−	2026.50i	−0.790044	−	0.228066i
$430$		0			0
$431$	−5697.00	−	3289.16i	−0.636693	−	0.367595i	0.146646	−	0.989189i	$-0.453152\pi$
$431$	−5697.00	−	3289.16i	−0.636693	−	0.367595i	−0.783340	+	0.621594i	$0.786485\pi$
$432$	864.000	−	1496.49i	0.0962250	−	0.166667i
$433$	3302.50	+	5720.10i	0.366531	+	0.634851i	0.989021	−	0.147778i	$-0.0472120\pi$
$433$	3302.50	+	5720.10i	0.366531	+	0.634851i	−0.622489	+	0.782628i	$0.713879\pi$
$434$		0			0
$435$	−1336.50	+	771.629i	−0.147311	+	0.0850500i
$436$	−4128.00	+	2383.30i	−0.453430	+	0.261788i
$437$		−	436.477i		−	0.0477792i
$438$		0			0
$439$	4271.00	−	7397.59i	0.464336	−	0.804254i	−0.534835	−	0.844957i	$-0.679626\pi$
$439$	4271.00	−	7397.59i	0.464336	−	0.804254i	0.999171	+	0.0407023i	$0.0129595\pi$
$440$		0			0
$441$	2115.00			0.228377
$442$		0			0
$443$	−14328.0			−1.53667			−0.768334	−	0.640049i	$-0.778914\pi$
$443$	−14328.0			−1.53667			−0.768334	+	0.640049i	$0.778914\pi$
$444$	−2340.00	−	1351.00i	−0.250116	−	0.144405i
$445$	3942.00	−	6827.74i	0.419930	−	0.727340i
$446$		0			0
$447$		−	9805.14i		−	1.03751i
$448$	4608.00	−	2660.43i	0.485954	−	0.280566i
$449$	2610.00	−	1506.88i	0.274329	−	0.158384i	−0.356525	−	0.934286i	$-0.616038\pi$
$449$	2610.00	−	1506.88i	0.274329	−	0.158384i	0.630853	+	0.775902i	$0.282705\pi$
$450$		0			0
$451$	−945.000	−	1636.79i	−0.0986659	−	0.170894i
$452$	6804.00	−	11784.9i	0.708038	−	1.22636i
$453$	4257.00	+	2457.78i	0.441526	+	0.254915i
$454$		0			0
$455$	−702.000	+	2431.80i	−0.0723303	+	0.250559i
$456$		0			0
$457$	−2500.50	−	1443.66i	−0.255948	−	0.147772i	0.366536	−	0.930404i	$-0.380543\pi$
$457$	−2500.50	−	1443.66i	−0.255948	−	0.147772i	−0.622485	+	0.782632i	$0.713877\pi$
$458$		0			0
$459$	−1579.50	−	2735.77i	−0.160620	−	0.278203i
$460$		−	748.246i		−	0.0758416i
$461$	3118.50	−	1800.47i	0.315061	−	0.181900i	−0.334128	−	0.942528i	$-0.608442\pi$
$461$	3118.50	−	1800.47i	0.315061	−	0.181900i	0.649189	+	0.760627i	$0.275108\pi$
$462$		0			0
$463$		−	2677.75i		−	0.268781i	−0.990928	−	0.134391i	$-0.957092\pi$
$463$		−	2677.75i		−	0.268781i	0.990928	−	0.134391i	$-0.0429077\pi$
$464$	3168.00	+	5487.14i	0.316963	+	0.548996i
$465$	−1512.00	+	2618.86i	−0.150790	+	0.261176i
$466$		0			0
$467$	13878.0			1.37515			0.687577	−	0.726111i	$-0.258674\pi$
$467$	13878.0			1.37515			0.687577	+	0.726111i	$0.258674\pi$
$468$	3276.00	−	810.600i	0.323575	−	0.0800641i
$469$	−7308.00			−0.719514
$470$		0			0
$471$	1888.50	−	3270.98i	0.184751	−	0.319997i
$472$		0			0
$473$			4260.84i			0.414194i
$474$		0			0
$475$	−2058.00	+	1188.19i	−0.198795	+	0.114774i
$476$		−	9727.20i		−	0.936650i
$477$	1174.50	+	2034.29i	0.112739	+	0.195270i
$478$		0			0
$479$	954.000	+	550.792i	0.0910008	+	0.0525393i	0.544810	−	0.838560i	$-0.316602\pi$
$479$	954.000	+	550.792i	0.0910008	+	0.0525393i	−0.453809	+	0.891099i	$0.649935\pi$
$480$		0			0
$481$	−1267.50	−	5122.54i	−0.120152	−	0.485588i
$482$		0			0
$483$	486.000	+	280.592i	0.0457842	+	0.0264335i
$484$	5476.00	−	9484.71i	0.514275	−	0.890750i
$485$	3006.00	+	5206.54i	0.281434	+	0.487458i
$486$		0			0
$487$	−14829.0	+	8561.53i	−1.37981	+	0.796632i	−0.992136	−	0.125166i	$-0.960054\pi$
$487$	−14829.0	+	8561.53i	−1.37981	+	0.796632i	−0.387671	+	0.921798i	$0.626720\pi$
$488$		0			0
$489$		−	8854.24i		−	0.818820i
$490$		0			0
$491$	−225.000	+	389.711i	−0.0206805	+	0.0358196i	−0.876180	−	0.481983i	$-0.839917\pi$
$491$	−225.000	+	389.711i	−0.0206805	+	0.0358196i	0.855500	+	0.517803i	$0.173250\pi$
$492$	756.000	+	436.477i	0.0692746	+	0.0399957i
$493$	11583.0			1.05816
$494$		0			0
$495$	−2430.00			−0.220647
$496$	10752.0	+	6207.67i	0.973345	+	0.561961i
$497$	−2430.00	+	4208.88i	−0.219317	+	0.379868i
$498$		0			0
$499$		−	13219.0i		−	1.18590i	−0.805239	−	0.592950i	$-0.797963\pi$
$499$		−	13219.0i		−	1.18590i	0.805239	−	0.592950i	$-0.202037\pi$
$500$	−8028.00	+	4634.97i	−0.718046	+	0.414564i
$501$	−8154.00	+	4707.71i	−0.727133	+	0.419811i
$502$		0			0
$503$	−2673.00	−	4629.77i	−0.236945	−	0.410400i	0.722891	−	0.690962i	$-0.242813\pi$
$503$	−2673.00	−	4629.77i	−0.236945	−	0.410400i	−0.959836	+	0.280561i	$0.909479\pi$
$504$		0			0
$505$	7087.50	+	4091.97i	0.624534	+	0.360575i
$506$		0			0
$507$	5577.00	+	3512.60i	0.488527	+	0.307692i
$508$	−13312.0			−1.16265
$509$	−5080.50	−	2933.23i	−0.442415	−	0.255428i	0.262207	−	0.965012i	$-0.415550\pi$
$509$	−5080.50	−	2933.23i	−0.442415	−	0.255428i	−0.704621	+	0.709583i	$0.748883\pi$
$510$		0			0
$511$	−3555.00	−	6157.44i	−0.307757	−	0.533051i
$512$		0			0
$513$	567.000	−	327.358i	0.0487986	−	0.0281739i
$514$		0			0
$515$		−	4125.75i		−	0.353014i
$516$	−984.000	−	1704.34i	−0.0839500	−	0.145406i
$517$	−1890.00	+	3273.58i	−0.160778	+	0.278475i
$518$		0			0
$519$	−12798.0			−1.08241
$520$		0			0
$521$	−9657.00			−0.812055			−0.406028	−	0.913861i	$-0.633086\pi$
$521$	−9657.00			−0.812055			−0.406028	+	0.913861i	$0.633086\pi$
$522$		0			0
$523$	−10813.0	+	18728.7i	−0.904053	+	1.56586i	−0.0818685	+	0.996643i	$0.526089\pi$
$523$	−10813.0	+	18728.7i	−0.904053	+	1.56586i	−0.822184	+	0.569222i	$0.807245\pi$
$524$	5904.00	+	10226.0i	0.492209	+	0.852531i
$525$		−	3055.34i		−	0.253992i
$526$		0			0
$527$	19656.0	−	11348.4i	1.62472	−	0.938034i
$528$			9976.61i			0.822304i
$529$	5921.50	+	10256.3i	0.486685	+	0.842964i
$530$		0			0
$531$	6156.00	+	3554.17i	0.503103	+	0.290467i
$532$	2016.00			0.164295
$533$	409.500	+	1654.97i	0.0332785	+	0.134493i
$534$		0			0
$535$	2025.00	+	1169.13i	0.163642	+	0.0944787i
$536$		0			0
$537$	4509.00	+	7809.82i	0.362342	+	0.627595i
$538$		0			0
$539$	−10575.0	+	6105.48i	−0.845079	+	0.487906i
$540$	972.000	−	561.184i	0.0774597	−	0.0447214i
$541$			5371.09i			0.426841i	0.976960	+	0.213421i	$0.0684605\pi$
$541$			5371.09i			0.426841i	−0.976960	+	0.213421i	$0.931540\pi$
$542$		0			0
$543$	−2809.50	+	4866.20i	−0.222039	+	0.384583i
$544$		0			0
$545$	−3096.00			−0.243336
$546$		0			0
$547$	16946.0			1.32460			0.662302	−	0.749237i	$-0.269579\pi$
$547$	16946.0			1.32460			0.662302	+	0.749237i	$0.269579\pi$
$548$	−7020.00	−	4053.00i	−0.547225	−	0.315941i
$549$	3235.50	−	5604.05i	0.251526	−	0.435656i
$550$		0			0
$551$			2400.62i			0.185608i
$552$		0			0
$553$	−3960.00	+	2286.31i	−0.304514	+	0.175811i
$554$		0			0
$555$	−877.500	−	1519.87i	−0.0671132	−	0.116243i
$556$	−4496.00	+	7787.30i	−0.342937	+	0.593984i
$557$	3343.50	+	1930.37i	0.254342	+	0.146845i	0.621751	−	0.783215i	$-0.286422\pi$
$557$	3343.50	+	1930.37i	0.254342	+	0.146845i	−0.367409	+	0.930060i	$0.619755\pi$
$558$		0			0
$559$	1066.00	−	3692.73i	0.0806565	−	0.279402i
$560$	3456.00			0.260790
$561$	15795.0	+	9119.25i	1.18871	+	0.686301i
$562$		0			0
$563$	−10836.0	−	18768.5i	−0.811160	−	1.40497i	−0.912053	−	0.410073i	$-0.865503\pi$
$563$	−10836.0	−	18768.5i	−0.811160	−	1.40497i	0.100893	−	0.994897i	$-0.467830\pi$
$564$		−	1745.91i		−	0.130347i
$565$	7654.50	−	4419.33i	0.569960	−	0.329066i
$566$		0			0
$567$			841.777i			0.0623480i
$568$		0			0
$569$	693.000	−	1200.31i	0.0510581	−	0.0884353i	−0.839367	−	0.543565i	$-0.817074\pi$
$569$	693.000	−	1200.31i	0.0510581	−	0.0884353i	0.890425	+	0.455130i	$0.150407\pi$
$570$		0			0
$571$	1162.00			0.0851632			0.0425816	−	0.999093i	$-0.486442\pi$
$571$	1162.00			0.0851632			0.0425816	+	0.999093i	$0.486442\pi$
$572$	−14040.0	+	13510.0i	−1.02630	+	0.987555i
$573$	8208.00			0.598419
$574$		0			0
$575$	−882.000	+	1527.67i	−0.0639686	+	0.110797i
$576$	−2304.00	−	3990.65i	−0.166667	−	0.288675i
$577$			8045.38i			0.580474i	0.956955	+	0.290237i	$0.0937341\pi$
$577$			8045.38i			0.580474i	−0.956955	+	0.290237i	$0.906266\pi$
$578$		0			0
$579$	−6763.50	+	3904.91i	−0.485460	+	0.280281i
$580$			4115.35i			0.294622i
$581$	−6210.00	−	10756.0i	−0.443432	−	0.768047i
$582$		0			0
$583$	−11745.0	−	6780.98i	−0.834354	−	0.481714i
$584$		0			0
$585$	2106.00	+	607.950i	0.148842	+	0.0429669i
$586$		0			0
$587$	−23922.0	−	13811.4i	−1.68206	−	0.971135i	−0.960293	−	0.278995i	$-0.909999\pi$
$587$	−23922.0	−	13811.4i	−1.68206	−	0.971135i	−0.721763	−	0.692140i	$-0.756668\pi$
$588$	2820.00	−	4884.38i	0.197780	−	0.342566i
$589$	2352.00	+	4073.78i	0.164537	+	0.284987i
$590$		0			0
$591$	9666.00	−	5580.67i	0.672768	−	0.388423i
$592$	−6240.00	+	3602.67i	−0.433214	+	0.250116i
$593$			275.396i			0.0190711i	0.999955	+	0.00953555i	$0.00303531\pi$
$593$			275.396i			0.0190711i	−0.999955	+	0.00953555i	$0.996965\pi$
$594$		0			0
$595$	3159.00	−	5471.55i	0.217658	−	0.376994i
$596$	−22644.0	−	13073.5i	−1.55627	−	0.898510i
$597$	−3594.00			−0.246386
$598$		0			0
$599$	22356.0			1.52494			0.762472	−	0.647021i	$-0.223986\pi$
$599$	22356.0			1.52494			0.762472	+	0.647021i	$0.223986\pi$
$600$		0			0
$601$	9041.50	−	15660.3i	0.613661	−	1.06289i	−0.376956	−	0.926231i	$-0.623029\pi$
$601$	9041.50	−	15660.3i	0.613661	−	1.06289i	0.990618	−	0.136662i	$-0.0436373\pi$
$602$		0			0
$603$			6328.91i			0.427418i
$604$	11352.0	−	6554.08i	0.764746	−	0.441526i
$605$	6160.50	−	3556.77i	0.413983	−	0.239013i
$606$		0			0
$607$	−2740.00	−	4745.82i	−0.183218	−	0.317342i	0.759757	−	0.650207i	$-0.225318\pi$
$607$	−2740.00	−	4745.82i	−0.183218	−	0.317342i	−0.942975	+	0.332865i	$0.891985\pi$
$608$		0			0
$609$	−2673.00	−	1543.26i	−0.177858	−	0.102686i
$610$		0			0
$611$	2457.00	−	2364.25i	0.162683	−	0.156542i
$612$	−8424.00			−0.556405
$613$	15361.5	+	8868.97i	1.01215	+	0.584362i	0.911819	−	0.410592i	$-0.134678\pi$
$613$	15361.5	+	8868.97i	1.01215	+	0.584362i	0.100326	+	0.994955i	$0.468011\pi$
$614$		0			0
$615$	283.500	+	491.036i	0.0185883	+	0.0321959i
$616$		0			0
$617$	8545.50	−	4933.75i	0.557583	−	0.321921i	−0.194592	−	0.980884i	$-0.562338\pi$
$617$	8545.50	−	4933.75i	0.557583	−	0.321921i	0.752175	+	0.658963i	$0.229005\pi$
$618$		0			0
$619$		−	4115.35i		−	0.267221i	−0.991034	−	0.133611i	$-0.957343\pi$
$619$		−	4115.35i		−	0.267221i	0.991034	−	0.133611i	$-0.0426572\pi$
$620$	4032.00	+	6983.63i	0.261176	+	0.452370i
$621$	243.000	−	420.888i	0.0157025	−	0.0271975i
$622$		0			0
$623$	15768.0			1.01402
$624$	2496.00	−	8646.40i	0.160128	−	0.554700i
$625$	6229.00			0.398656
$626$		0			0
$627$	−1890.00	+	3273.58i	−0.120382	+	0.208507i
$628$	−5036.00	−	8722.61i	−0.319997	−	0.554252i
$629$			13172.2i			0.834995i
$630$		0			0
$631$	−10968.0	+	6332.38i	−0.691964	+	0.399506i	−0.804347	−	0.594159i	$-0.797485\pi$
$631$	−10968.0	+	6332.38i	−0.691964	+	0.399506i	0.112383	+	0.993665i	$0.464151\pi$
$632$		0			0
$633$	3588.00	+	6214.60i	0.225293	+	0.390218i
$634$		0			0
$635$	−7488.00	−	4323.20i	−0.467956	−	0.270175i
$636$	6264.00			0.390540
$637$	10692.5	−	2645.71i	0.665074	−	0.164563i
$638$		0			0
$639$	3645.00	+	2104.44i	0.225656	+	0.130282i
$640$		0			0
$641$	1894.50	+	3281.37i	0.116737	+	0.202194i	0.918473	−	0.395484i	$-0.129423\pi$
$641$	1894.50	+	3281.37i	0.116737	+	0.202194i	−0.801736	+	0.597678i	$0.796090\pi$
$642$		0			0
$643$	14646.0	−	8455.87i	0.898261	−	0.518611i	0.0216255	−	0.999766i	$-0.493116\pi$
$643$	14646.0	−	8455.87i	0.898261	−	0.518611i	0.876636	+	0.481155i	$0.159783\pi$
$644$	1296.00	−	748.246i	0.0793006	−	0.0457842i
$645$		−	1278.25i		−	0.0780328i
$646$		0			0
$647$	13896.0	−	24068.6i	0.844371	−	1.46249i	−0.0417951	−	0.999126i	$-0.513308\pi$
$647$	13896.0	−	24068.6i	0.844371	−	1.46249i	0.886166	−	0.463368i	$-0.153359\pi$
$648$		0			0
$649$	−41040.0			−2.48222
$650$		0			0
$651$	−6048.00			−0.364116
$652$	−20448.0	−	11805.7i	−1.22823	−	0.709118i
$653$	297.000	−	514.419i	0.0177986	−	0.0308281i	−0.856989	−	0.515335i	$-0.827668\pi$
$653$	297.000	−	514.419i	0.0177986	−	0.0308281i	0.874788	+	0.484507i	$0.161001\pi$
$654$		0			0
$655$			7669.52i			0.457516i
$656$	2016.00	−	1163.94i	0.119987	−	0.0692746i
$657$	−5332.50	+	3078.72i	−0.316652	+	0.182819i
$658$		0			0
$659$	−8874.00	−	15370.2i	−0.524555	−	0.908556i	−0.999591	−	0.0285901i	$-0.990898\pi$
$659$	−8874.00	−	15370.2i	−0.524555	−	0.908556i	0.475036	−	0.879966i	$-0.342435\pi$
$660$	−3240.00	+	5611.84i	−0.191086	+	0.330971i
$661$	13675.5	+	7895.55i	0.804713	+	0.464601i	0.845117	−	0.534582i	$-0.179531\pi$
$661$	13675.5	+	7895.55i	0.804713	+	0.464601i	−0.0404035	+	0.999183i	$0.512864\pi$
$662$		0			0
$663$	−11407.5	−	11855.0i	−0.668221	−	0.694436i
$664$		0			0
$665$	1134.00	+	654.715i	0.0661273	+	0.0381786i
$666$		0			0
$667$	891.000	+	1543.26i	0.0517236	+	0.0895879i
$668$			25107.8i			1.45427i
$669$	−5292.00	+	3055.34i	−0.305830	+	0.176571i
$670$		0			0
$671$			37360.3i			2.14945i
$672$		0			0
$673$	−10466.5	+	18128.5i	−0.599486	+	1.03834i	0.393411	+	0.919363i	$0.371295\pi$
$673$	−10466.5	+	18128.5i	−0.599486	+	1.03834i	−0.992897	+	0.118977i	$0.962038\pi$
$674$		0			0
$675$	−2646.00			−0.150881
$676$	15548.0	−	8196.06i	0.884615	−	0.466321i
$677$	3402.00			0.193131			0.0965653	−	0.995327i	$-0.469214\pi$
$677$	3402.00			0.193131			0.0965653	+	0.995327i	$0.469214\pi$
$678$		0			0
$679$	−6012.00	+	10413.1i	−0.339793	+	0.588539i
$680$		0			0
$681$		−	6453.62i		−	0.363147i
$682$		0			0
$683$	21636.0	−	12491.6i	1.21212	−	0.699818i	0.248900	−	0.968529i	$-0.419931\pi$
$683$	21636.0	−	12491.6i	1.21212	−	0.699818i	0.963221	+	0.268711i	$0.0865976\pi$
$684$		−	1745.91i		−	0.0975971i
$685$	−2632.50	−	4559.62i	−0.146836	−	0.254327i
$686$		0			0
$687$	−9018.00	−	5206.54i	−0.500812	−	0.289144i
$688$	−5248.00			−0.290811
$689$	8482.50	+	8815.27i	0.469024	+	0.487424i
$690$		0			0
$691$	12009.0	+	6933.40i	0.661134	+	0.381706i	0.792709	−	0.609600i	$-0.208670\pi$
$691$	12009.0	+	6933.40i	0.661134	+	0.381706i	−0.131575	+	0.991306i	$0.542003\pi$
$692$	−17064.0	+	29555.7i	−0.937393	+	1.62361i
$693$	−2430.00	−	4208.88i	−0.133201	−	0.230710i
$694$		0			0
$695$	−5058.00	+	2920.24i	−0.276059	+	0.159383i
$696$		0			0
$697$		−	4255.65i		−	0.231269i
$698$		0			0
$699$	−2781.00	+	4816.83i	−0.150482	+	0.260643i
$700$	−7056.00	−	4073.78i	−0.380988	−	0.219964i
$701$	−21906.0			−1.18028			−0.590141	−	0.807300i	$-0.700928\pi$
$701$	−21906.0			−1.18028			−0.590141	+	0.807300i	$0.700928\pi$
$702$		0			0
$703$	−2730.00			−0.146464
$704$	23040.0	+	13302.2i	1.23346	+	0.712136i
$705$	567.000	−	982.073i	0.0302900	−	0.0524638i
$706$		0			0
$707$			16367.9i			0.870690i
$708$	16416.0	−	9477.78i	0.871400	−	0.503103i
$709$	−11308.5	+	6528.97i	−0.599012	+	0.345840i	−0.768653	−	0.639666i	$-0.779073\pi$
$709$	−11308.5	+	6528.97i	−0.599012	+	0.345840i	0.169641	+	0.985506i	$0.445739\pi$
$710$		0			0
$711$	1980.00	+	3429.46i	0.104439	+	0.180893i
$712$		0			0
$713$	3024.00	+	1745.91i	0.158835	+	0.0917037i
$714$		0			0
$715$	−12285.0	+	3039.75i	−0.642564	+	0.158993i
$716$	24048.0			1.25519
$717$	11583.0	+	6687.45i	0.603312	+	0.348323i
$718$		0			0
$719$	7110.00	+	12314.9i	0.368788	+	0.638759i	0.989376	−	0.145377i	$-0.0464397\pi$
$719$	7110.00	+	12314.9i	0.368788	+	0.638759i	−0.620589	+	0.784136i	$0.713106\pi$
$720$		−	2992.98i		−	0.154919i
$721$	7146.00	−	4125.75i	0.369114	−	0.213108i
$722$		0			0
$723$			1252.27i			0.0644157i
$724$	7492.00	+	12976.5i	0.384583	+	0.666117i
$725$	4851.00	−	8402.18i	0.248499	−	0.430413i
$726$		0			0
$727$	−5282.00			−0.269462			−0.134731	−	0.990882i	$-0.543017\pi$
$727$	−5282.00			−0.269462			−0.134731	+	0.990882i	$0.543017\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−4797.00	+	8308.65i	−0.242713	+	0.420392i
$732$	−8628.00	−	14944.1i	−0.435656	−	0.754578i
$733$		−	11419.4i		−	0.575424i	−0.957717	−	0.287712i	$-0.907105\pi$
$733$		−	11419.4i		−	0.575424i	0.957717	−	0.287712i	$-0.0928945\pi$
$734$		0			0
$735$	3172.50	−	1831.64i	0.159210	−	0.0919200i
$736$		0			0
$737$	−18270.0	−	31644.6i	−0.913140	−	1.58160i
$738$		0			0
$739$	−17784.0	−	10267.6i	−0.885244	−	0.511096i	−0.0128599	−	0.999917i	$-0.504094\pi$
$739$	−17784.0	−	10267.6i	−0.885244	−	0.511096i	−0.872384	+	0.488822i	$0.837427\pi$
$740$	−4680.00			−0.232487
$741$	2457.00	−	2364.25i	0.121809	−	0.117210i
$742$		0			0
$743$	−18036.0	−	10413.1i	−0.890547	−	0.514158i	−0.0164258	−	0.999865i	$-0.505229\pi$
$743$	−18036.0	−	10413.1i	−0.890547	−	0.514158i	−0.874121	+	0.485707i	$0.838562\pi$
$744$		0			0
$745$	−8491.50	−	14707.7i	−0.417590	−	0.723287i
$746$		0			0
$747$	−9315.00	+	5378.02i	−0.456249	+	0.263416i
$748$	42120.0	−	24318.0i	2.05890	−	1.18871i
$749$			4676.54i			0.228140i
$750$		0			0
$751$	2417.00	−	4186.37i	0.117440	−	0.203412i	−0.801312	−	0.598246i	$-0.795864\pi$
$751$	2417.00	−	4186.37i	0.117440	−	0.203412i	0.918753	+	0.394834i	$0.129198\pi$
$752$	−4032.00	−	2327.88i	−0.195521	−	0.112884i
$753$	−12312.0			−0.595849
$754$		0			0
$755$	8514.00			0.410406
$756$	1944.00	+	1122.37i	0.0935220	+	0.0539949i
$757$	−4523.00	+	7834.07i	−0.217161	+	0.376135i	−0.953939	−	0.300001i	$-0.903013\pi$
$757$	−4523.00	+	7834.07i	−0.217161	+	0.376135i	0.736778	+	0.676135i	$0.236346\pi$
$758$		0			0
$759$			2805.92i			0.134188i
$760$		0			0
$761$	−10422.0	+	6017.14i	−0.496448	+	0.286625i	−0.727246	−	0.686377i	$-0.759200\pi$
$761$	−10422.0	+	6017.14i	−0.496448	+	0.286625i	0.230797	+	0.973002i	$0.425867\pi$
$762$		0			0
$763$	−3096.00	−	5362.43i	−0.146897	−	0.254434i
$764$	10944.0	−	18955.6i	0.518246	−	0.897629i
$765$	−4738.50	−	2735.77i	−0.223949	−	0.129297i
$766$		0			0
$767$	35568.0	+	10267.6i	1.67443	+	0.483366i
$768$	−12288.0			−0.577350
$769$	32514.0	+	18772.0i	1.52469	+	0.880279i	0.999572	+	0.0292479i	$0.00931121\pi$
$769$	32514.0	+	18772.0i	1.52469	+	0.880279i	0.525115	+	0.851031i	$0.324022\pi$
$770$		0			0
$771$	2983.50	+	5167.57i	0.139362	+	0.241382i
$772$			20826.2i			0.970920i
$773$	−13608.0	+	7856.58i	−0.633177	+	0.365565i	−0.781981	−	0.623302i	$-0.785791\pi$
$773$	−13608.0	+	7856.58i	−0.633177	+	0.365565i	0.148804	+	0.988867i	$0.452457\pi$
$774$		0			0
$775$		−	19011.0i		−	0.881155i
$776$		0			0
$777$	1755.00	−	3039.75i	0.0810300	−	0.140348i
$778$		0			0
$779$	882.000			0.0405660
$780$	4212.00	−	4053.00i	0.193351	−	0.186052i
$781$	−24300.0			−1.11334
$782$		0			0
$783$	−1336.50	+	2314.89i	−0.0609995	+	0.105654i
$784$	−7520.00	−	13025.0i	−0.342566	−	0.593341i
$785$		−	6541.96i		−	0.297443i
$786$		0			0
$787$	−3252.00	+	1877.54i	−0.147295	+	0.0850409i	−0.571836	−	0.820368i	$-0.693769\pi$
$787$	−3252.00	+	1877.54i	−0.147295	+	0.0850409i	0.424541	+	0.905409i	$0.360435\pi$
$788$		−	29763.6i		−	1.34554i
$789$	1107.00	+	1917.38i	0.0499496	+	0.0865153i
$790$		0			0
$791$	15309.0	+	8838.66i	0.688148	+	0.397303i
$792$		0			0
$793$	9347.00	−	32379.0i	0.418565	−	1.44995i
$794$		0			0
$795$	3523.50	+	2034.29i	0.157190	+	0.0907534i
$796$	−4792.00	+	8299.99i	−0.213377	+	0.369579i
$797$	3915.00	+	6780.98i	0.173998	+	0.301373i	0.939814	−	0.341686i	$-0.110998\pi$
$797$	3915.00	+	6780.98i	0.173998	+	0.301373i	−0.765816	+	0.643060i	$0.777665\pi$
$798$		0			0
$799$	−7371.00	+	4255.65i	−0.326367	+	0.188428i
$800$		0			0
$801$		−	13655.5i		−	0.602363i
$802$		0			0
$803$	17775.0	−	30787.2i	0.781153	−	1.35300i
$804$	14616.0	+	8438.55i	0.641128	+	0.370155i
$805$	972.000			0.0425571
$806$		0			0
$807$	6318.00			0.275594
$808$		0			0
$809$	3082.50	−	5339.05i	0.133962	−	0.232028i	−0.791239	−	0.611507i	$-0.790563\pi$
$809$	3082.50	−	5339.05i	0.133962	−	0.232028i	0.925200	+	0.379479i	$0.123897\pi$
$810$		0			0
$811$			29839.8i			1.29201i	0.763335	+	0.646003i	$0.223560\pi$
$811$			29839.8i			1.29201i	−0.763335	+	0.646003i	$0.776440\pi$
$812$	−7128.00	+	4115.35i	−0.308059	+	0.177858i
$813$	1782.00	−	1028.84i	0.0768727	−	0.0443824i
$814$		0			0
$815$	−7668.00	−	13281.4i	−0.329568	−	0.570829i
$816$	−11232.0	+	19454.4i	−0.481861	+	0.834608i
$817$	−1722.00	−	994.197i	−0.0737395	−	0.0425735i
$818$		0			0
$819$	1053.00	+	4255.65i	0.0449265	+	0.181568i
$820$	1512.00			0.0643919
$821$	−25776.0	−	14881.8i	−1.09572	−	0.632616i	−0.160629	−	0.987015i	$-0.551352\pi$
$821$	−25776.0	−	14881.8i	−1.09572	−	0.632616i	−0.935094	+	0.354399i	$0.884685\pi$
$822$		0			0
$823$	4460.00	+	7724.95i	0.188901	+	0.327187i	0.944884	−	0.327405i	$-0.106174\pi$
$823$	4460.00	+	7724.95i	0.188901	+	0.327187i	−0.755983	+	0.654591i	$0.772841\pi$
$824$		0			0
$825$	13230.0	−	7638.34i	0.558315	−	0.322343i
$826$		0			0
$827$			18041.0i			0.758583i	0.925277	+	0.379292i	$0.123832\pi$
$827$			18041.0i			0.758583i	−0.925277	+	0.379292i	$0.876168\pi$
$828$	−648.000	−	1122.37i	−0.0271975	−	0.0471075i
$829$	10511.5	−	18206.5i	0.440385	−	0.762770i	−0.557333	−	0.830289i	$-0.688175\pi$
$829$	10511.5	−	18206.5i	0.440385	−	0.762770i	0.997718	+	0.0675195i	$0.0215085\pi$
$830$		0			0
$831$	−10995.0			−0.458980
$832$	−16640.0	−	17292.8i	−0.693375	−	0.720577i
$833$	−27495.0			−1.14363
$834$		0			0
$835$	−8154.00	+	14123.1i	−0.337941	+	0.585331i
$836$	5040.00	+	8729.54i	0.208507	+	0.361145i
$837$			5237.72i			0.216299i
$838$		0			0
$839$	−19116.0	+	11036.6i	−0.786600	+	0.454144i	−0.838764	−	0.544495i	$-0.816721\pi$
$839$	−19116.0	+	11036.6i	−0.786600	+	0.454144i	0.0521641	+	0.998639i	$0.483388\pi$
$840$		0			0
$841$	7294.00	+	12633.6i	0.299069	+	0.518003i
$842$		0			0
$843$	4468.50	+	2579.89i	0.182566	+	0.105405i
$844$	19136.0			0.780436
$845$	11407.5	+	439.075i	0.464414	+	0.0178753i
$846$		0			0
$847$	12321.0	+	7113.53i	0.499828	+	0.288576i
$848$	8352.00	−	14466.1i	0.338218	−	0.585811i
$849$	−2739.00	−	4744.09i	−0.110721	−	0.191775i
$850$		0			0
$851$	−1755.00	+	1013.25i	−0.0706940	+	0.0408152i
$852$	9720.00	−	5611.84i	0.390847	−	0.225656i
$853$			26609.5i			1.06810i	0.845452	+	0.534051i	$0.179331\pi$
$853$			26609.5i			1.06810i	−0.845452	+	0.534051i	$0.820669\pi$
$854$		0			0
$855$	567.000	−	982.073i	0.0226795	−	0.0392821i
$856$		0			0
$857$	−12771.0			−0.509042			−0.254521	−	0.967067i	$-0.581918\pi$
$857$	−12771.0			−0.509042			−0.254521	+	0.967067i	$0.581918\pi$
$858$		0			0
$859$	17134.0			0.680564			0.340282	−	0.940323i	$-0.389477\pi$
$859$	17134.0			0.680564			0.340282	+	0.940323i	$0.389477\pi$
$860$	−2952.00	−	1704.34i	−0.117049	−	0.0675784i
$861$	−567.000	+	982.073i	−0.0224429	+	0.0388722i
$862$		0			0
$863$			7929.33i			0.312766i	0.987696	+	0.156383i	$0.0499835\pi$
$863$			7929.33i			0.312766i	−0.987696	+	0.156383i	$0.950017\pi$
$864$		0			0
$865$	−19197.0	+	11083.4i	−0.754587	+	0.435661i
$866$		0			0
$867$	13164.0	+	22800.7i	0.515655	+	0.893141i
$868$	−8064.00	+	13967.3i	−0.315334	+	0.546175i
$869$	−19800.0	−	11431.5i	−0.772922	−	0.446247i
$870$		0			0
$871$	7917.00	+	31996.2i	0.307988	+	1.24472i
$872$		0			0
$873$	9018.00	+	5206.54i	0.349614	+	0.201850i
$874$		0			0
$875$	−6021.00	−	10428.7i	−0.232625	−	0.402918i
$876$			16419.8i			0.633305i
$877$	8542.50	−	4932.01i	0.328916	−	0.189900i	−0.326443	−	0.945217i	$-0.605850\pi$
$877$	8542.50	−	4932.01i	0.328916	−	0.189900i	0.655360	+	0.755317i	$0.272517\pi$
$878$		0			0
$879$			1512.08i			0.0580218i
$880$	8640.00	+	14964.9i	0.330971	+	0.573258i
$881$	−14584.5	+	25261.1i	−0.557735	+	0.966025i	0.439950	+	0.898022i	$0.354996\pi$
$881$	−14584.5	+	25261.1i	−0.557735	+	0.966025i	−0.997685	+	0.0680028i	$0.978337\pi$
$882$		0			0
$883$	928.000			0.0353677			0.0176839	−	0.999844i	$-0.494371\pi$
$883$	928.000			0.0353677			0.0176839	+	0.999844i	$0.494371\pi$
$884$	−42588.0	+	10537.8i	−1.62035	+	0.400933i
$885$	12312.0			0.467642
$886$		0			0
$887$	7200.00	−	12470.8i	0.272551	−	0.472071i	−0.696964	−	0.717106i	$-0.745466\pi$
$887$	7200.00	−	12470.8i	0.272551	−	0.472071i	0.969514	+	0.245035i	$0.0787995\pi$
$888$		0			0
$889$		−	17292.8i		−	0.652398i
$890$		0			0
$891$	−3645.00	+	2104.44i	−0.137051	+	0.0791262i
$892$			16295.1i			0.611661i
$893$	−882.000	−	1527.67i	−0.0330515	−	0.0572469i
$894$		0			0
$895$	13527.0	+	7809.82i	0.505204	+	0.291680i
$896$		0			0
$897$	702.000	−	2431.80i	0.0261305	−	0.0905189i
$898$		0			0
$899$	−16632.0	−	9602.49i	−0.617028	−	0.356241i
$900$	−3528.00	+	6110.68i	−0.130667	+	0.226321i
$901$	−15268.5	−	26445.8i	−0.564559	−	0.977845i
$902$		0			0
$903$	2214.00	−	1278.25i	0.0815917	−	0.0471070i
$904$		0			0
$905$			9732.39i			0.357476i
$906$		0			0
$907$	−9842.00	+	17046.8i	−0.360307	+	0.624070i	−0.988011	−	0.154382i	$-0.950661\pi$
$907$	−9842.00	+	17046.8i	−0.360307	+	0.624070i	0.627704	+	0.778452i	$0.283995\pi$
$908$	−14904.0	−	8604.83i	−0.544721	−	0.314495i
$909$	14175.0			0.517222
$910$		0			0
$911$	24480.0			0.890295			0.445147	−	0.895457i	$-0.353151\pi$
$911$	24480.0			0.890295			0.445147	+	0.895457i	$0.353151\pi$
$912$	−4032.00	−	2327.88i	−0.146396	−	0.0845216i
$913$	31050.0	−	53780.2i	1.12553	−	1.94947i
$914$		0			0
$915$		−	11208.1i		−	0.404949i
$916$	−24048.0	+	13884.1i	−0.867433	+	0.500812i
$917$	−13284.0	+	7669.52i	−0.478382	+	0.276194i
$918$		0			0
$919$	−19304.0	−	33435.5i	−0.692906	−	1.20015i	−0.970882	−	0.239560i	$-0.922997\pi$
$919$	−19304.0	−	33435.5i	−0.692906	−	1.20015i	0.277976	−	0.960588i	$-0.410336\pi$
$920$		0			0
$921$	−5067.00	−	2925.43i	−0.181285	−	0.104665i
$922$		0			0
$923$	21060.0	+	6079.50i	0.751027	+	0.216803i
$924$	−12960.0			−0.461421
$925$	9555.00	+	5516.58i	0.339639	+	0.196091i
$926$		0			0
$927$	−3573.00	−	6188.62i	−0.126594	−	0.219267i
$928$		0			0
$929$	8842.50	−	5105.22i	0.312285	−	0.180298i	−0.335663	−	0.941982i	$-0.608960\pi$
$929$	8842.50	−	5105.22i	0.312285	−	0.180298i	0.647949	+	0.761684i	$0.275627\pi$
$930$		0			0
$931$		−	5698.45i		−	0.200600i
$932$	7416.00	+	12844.9i	0.260643	+	0.451447i
$933$	−5697.00	+	9867.49i	−0.199905	+	0.346246i
$934$		0			0
$935$	31590.0			1.10492
$936$		0			0
$937$	28495.0			0.993480			0.496740	−	0.867899i	$-0.334530\pi$
$937$	28495.0			0.993480			0.496740	+	0.867899i	$0.334530\pi$
$938$		0			0
$939$	2067.00	−	3580.15i	0.0718360	−	0.124424i
$940$	−1512.00	−	2618.86i	−0.0524638	−	0.0908700i
$941$		−	10724.9i		−	0.371541i	−0.982593	−	0.185771i	$-0.940522\pi$
$941$		−	10724.9i		−	0.371541i	0.982593	−	0.185771i	$-0.0594782\pi$
$942$		0			0
$943$	567.000	−	327.358i	0.0195801	−	0.0113046i
$944$		−	50548.2i		−	1.74280i
$945$	729.000	+	1262.67i	0.0250946	+	0.0434651i
$946$		0			0
$947$	29412.0	+	16981.0i	1.00925	+	0.582692i	0.910973	−	0.412467i	$-0.135333\pi$
$947$	29412.0	+	16981.0i	1.00925	+	0.582692i	0.0982794	+	0.995159i	$0.468666\pi$
$948$	10560.0			0.361786
$949$	−23107.5	+	22235.2i	−0.790412	+	0.760575i
$950$		0			0
$951$	−18454.5	−	10654.7i	−0.629262	−	0.363305i
$952$		0			0
$953$	−11907.0	−	20623.5i	−0.404728	−	0.701009i	0.589562	−	0.807723i	$-0.299300\pi$
$953$	−11907.0	−	20623.5i	−0.404728	−	0.701009i	−0.994290	+	0.106714i	$0.965967\pi$
$954$		0			0
$955$	12312.0	−	7108.34i	0.417180	−	0.240859i
$956$	30888.0	−	17833.2i	1.04497	−	0.603312i
$957$		−	15432.6i		−	0.521279i
$958$		0			0
$959$	5265.00	−	9119.25i	0.177284	−	0.307066i
$960$	−6912.00	−	3990.65i	−0.232379	−	0.134164i
$961$	−7841.00			−0.263200
$962$		0			0
$963$	4050.00			0.135524
$964$	2892.00	+	1669.70i	0.0966235	+	0.0557856i
$965$	−6763.50	+	11714.7i	−0.225622	+	0.390788i
$966$		0			0
$967$		−	51549.3i		−	1.71429i	−0.515079	−	0.857143i	$-0.672238\pi$
$967$		−	51549.3i		−	1.71429i	0.515079	−	0.857143i	$-0.327762\pi$
$968$		0			0
$969$	−7371.00	+	4255.65i	−0.244366	+	0.141085i
$970$		0			0
$971$	6156.00	+	10662.5i	0.203456	+	0.352396i	0.949640	−	0.313344i	$-0.101449\pi$
$971$	6156.00	+	10662.5i	0.203456	+	0.352396i	−0.746184	+	0.665740i	$0.768116\pi$
$972$	972.000	−	1683.55i	0.0320750	−	0.0555556i
$973$	−10116.0	−	5840.48i	−0.333303	−	0.192433i
$974$		0			0
$975$	−13377.0	+	3309.95i	−0.439392	+	0.108721i
$976$	−46016.0			−1.50916
$977$	18652.5	+	10769.0i	0.610795	+	0.352642i	0.773276	−	0.634069i	$-0.218617\pi$
$977$	18652.5	+	10769.0i	0.610795	+	0.352642i	−0.162482	+	0.986712i	$0.551950\pi$
$978$		0			0
$979$	39420.0	+	68277.4i	1.28689	+	2.22896i
$980$		−	9768.77i		−	0.318420i
$981$	−4644.00	+	2681.21i	−0.151143	+	0.0872626i
$982$		0			0
$983$			32611.1i			1.05812i	0.848585	+	0.529060i	$0.177455\pi$
$983$			32611.1i			1.05812i	−0.848585	+	0.529060i	$0.822545\pi$
$984$		0			0
$985$	9666.00	−	16742.0i	0.312674	−	0.541568i
$986$		0			0
$987$	2268.00			0.0731421
$988$	−2184.00	−	8826.53i	−0.0703262	−	0.284220i
$989$	−1476.00			−0.0474561
$990$		0			0
$991$	11165.0	−	19338.3i	0.357889	−	0.619882i	−0.629719	−	0.776823i	$-0.716830\pi$
$991$	11165.0	−	19338.3i	0.357889	−	0.619882i	0.987608	+	0.156941i	$0.0501633\pi$
$992$		0			0
$993$		−	30220.8i		−	0.965789i
$994$		0			0
$995$	−5391.00	+	3112.50i	−0.171765	+	0.0991686i
$996$			28682.8i			0.912498i
$997$	12465.5	+	21590.9i	0.395974	+	0.685848i	0.993225	−	0.116207i	$-0.0370736\pi$
$997$	12465.5	+	21590.9i	0.395974	+	0.685848i	−0.597251	+	0.802055i	$0.703740\pi$
$998$		0			0
$999$	−2632.50	−	1519.87i	−0.0833720	−	0.0481348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.a.4.1	✓	2
3.2	odd	2		117.4.q.b.82.1		2
4.3	odd	2		624.4.bv.a.433.1		2
13.4	even	6		507.4.b.a.337.2		2
13.6	odd	12		507.4.a.g.1.1		2
13.7	odd	12		507.4.a.g.1.2		2
13.9	even	3		507.4.b.a.337.1		2
13.10	even	6	inner	39.4.j.a.10.1	yes	2
39.20	even	12		1521.4.a.m.1.1		2
39.23	odd	6		117.4.q.b.10.1		2
39.32	even	12		1521.4.a.m.1.2		2
52.23	odd	6		624.4.bv.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.a.4.1	✓	2	1.1	even	1	trivial
39.4.j.a.10.1	yes	2	13.10	even	6	inner
117.4.q.b.10.1		2	39.23	odd	6
117.4.q.b.82.1		2	3.2	odd	2
507.4.a.g.1.1		2	13.6	odd	12
507.4.a.g.1.2		2	13.7	odd	12
507.4.b.a.337.1		2	13.9	even	3
507.4.b.a.337.2		2	13.4	even	6
624.4.bv.a.49.1		2	52.23	odd	6
624.4.bv.a.433.1		2	4.3	odd	2
1521.4.a.m.1.1		2	39.20	even	12
1521.4.a.m.1.2		2	39.32	even	12

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(45.0000 + 25.9808i) q^{11} -24.0000 q^{12} +(-32.5000 - 33.7750i) q^{13} +(-13.5000 - 7.79423i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(58.5000 + 101.325i) q^{17} +(-21.0000 + 12.1244i) q^{19} +(-36.0000 + 20.7846i) q^{20} -31.1769i q^{21} +(-9.00000 + 15.5885i) q^{23} +98.0000 q^{25} -27.0000 q^{27} +(-72.0000 - 41.5692i) q^{28} +(49.5000 - 85.7365i) q^{29} -193.990i q^{31} +(135.000 - 77.9423i) q^{33} +(-27.0000 - 46.7654i) q^{35} +(-36.0000 + 62.3538i) q^{36} +(97.5000 + 56.2917i) q^{37} +(-136.500 + 33.7750i) q^{39} +(-31.5000 - 18.1865i) q^{41} +(41.0000 + 71.0141i) q^{43} -415.692i q^{44} +(-40.5000 + 23.3827i) q^{45} +72.7461i q^{47} +(96.0000 + 166.277i) q^{48} +(-117.500 + 203.516i) q^{49} +351.000 q^{51} +(-104.000 + 360.267i) q^{52} -261.000 q^{53} +(135.000 - 233.827i) q^{55} +72.7461i q^{57} +(-684.000 + 394.908i) q^{59} +124.708i q^{60} +(359.500 + 622.672i) q^{61} +(-81.0000 - 46.7654i) q^{63} +512.000 q^{64} +(-175.500 + 168.875i) q^{65} +(-609.000 - 351.606i) q^{67} +(468.000 - 810.600i) q^{68} +(27.0000 + 46.7654i) q^{69} +(-405.000 + 233.827i) q^{71} -684.160i q^{73} +(147.000 - 254.611i) q^{75} +(168.000 + 96.9948i) q^{76} +540.000 q^{77} -440.000 q^{79} +(288.000 + 166.277i) q^{80} +(-40.5000 + 70.1481i) q^{81} -1195.12i q^{83} +(-216.000 + 124.708i) q^{84} +(526.500 - 303.975i) q^{85} +(-148.500 - 257.210i) q^{87} +(1314.00 + 758.638i) q^{89} +(-468.000 - 135.100i) q^{91} +144.000 q^{92} +(-504.000 - 290.985i) q^{93} +(63.0000 + 109.119i) q^{95} +(-1002.00 + 578.505i) q^{97} -467.654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 8 * q^4 + 18 * q^7 - 9 * q^9	\( 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9} + 90 q^{11} - 48 q^{12} - 65 q^{13} - 27 q^{15} - 64 q^{16} + 117 q^{17} - 42 q^{19} - 72 q^{20} - 18 q^{23} + 196 q^{25} - 54 q^{27} - 144 q^{28} + 99 q^{29} + 270 q^{33} - 54 q^{35} - 72 q^{36} + 195 q^{37} - 273 q^{39} - 63 q^{41} + 82 q^{43} - 81 q^{45} + 192 q^{48} - 235 q^{49} + 702 q^{51} - 208 q^{52} - 522 q^{53} + 270 q^{55} - 1368 q^{59} + 719 q^{61} - 162 q^{63} + 1024 q^{64} - 351 q^{65} - 1218 q^{67} + 936 q^{68} + 54 q^{69} - 810 q^{71} + 294 q^{75} + 336 q^{76} + 1080 q^{77} - 880 q^{79} + 576 q^{80} - 81 q^{81} - 432 q^{84} + 1053 q^{85} - 297 q^{87} + 2628 q^{89} - 936 q^{91} + 288 q^{92} - 1008 q^{93} + 126 q^{95} - 2004 q^{97}+O(q^{100}) \) 2 * q + 3 * q^3 - 8 * q^4 + 18 * q^7 - 9 * q^9 + 90 * q^11 - 48 * q^12 - 65 * q^13 - 27 * q^15 - 64 * q^16 + 117 * q^17 - 42 * q^19 - 72 * q^20 - 18 * q^23 + 196 * q^25 - 54 * q^27 - 144 * q^28 + 99 * q^29 + 270 * q^33 - 54 * q^35 - 72 * q^36 + 195 * q^37 - 273 * q^39 - 63 * q^41 + 82 * q^43 - 81 * q^45 + 192 * q^48 - 235 * q^49 + 702 * q^51 - 208 * q^52 - 522 * q^53 + 270 * q^55 - 1368 * q^59 + 719 * q^61 - 162 * q^63 + 1024 * q^64 - 351 * q^65 - 1218 * q^67 + 936 * q^68 + 54 * q^69 - 810 * q^71 + 294 * q^75 + 336 * q^76 + 1080 * q^77 - 880 * q^79 + 576 * q^80 - 81 * q^81 - 432 * q^84 + 1053 * q^85 - 297 * q^87 + 2628 * q^89 - 936 * q^91 + 288 * q^92 - 1008 * q^93 + 126 * q^95 - 2004 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more