LMFDB - Embedded newform 117.4.q.b.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (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:	$6.90322347067$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 + 5.19615i) q^{7} +O(q^{10})$	\(q+(-4.00000 + 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 + 5.19615i) q^{7} +(-45.0000 + 25.9808i) q^{11} +(-32.5000 + 33.7750i) q^{13} +(-32.0000 - 55.4256i) q^{16} +(-58.5000 + 101.325i) q^{17} +(-21.0000 - 12.1244i) q^{19} +(36.0000 + 20.7846i) q^{20} +(9.00000 + 15.5885i) q^{23} +98.0000 q^{25} +(-72.0000 + 41.5692i) q^{28} +(-49.5000 - 85.7365i) q^{29} +193.990i q^{31} +(27.0000 - 46.7654i) q^{35} +(97.5000 - 56.2917i) q^{37} +(31.5000 - 18.1865i) q^{41} +(41.0000 - 71.0141i) q^{43} -415.692i q^{44} +72.7461i q^{47} +(-117.500 - 203.516i) q^{49} +(-104.000 - 360.267i) q^{52} +261.000 q^{53} +(135.000 + 233.827i) q^{55} +(684.000 + 394.908i) q^{59} +(359.500 - 622.672i) q^{61} +512.000 q^{64} +(175.500 + 168.875i) q^{65} +(-609.000 + 351.606i) q^{67} +(-468.000 - 810.600i) q^{68} +(405.000 + 233.827i) q^{71} +684.160i q^{73} +(168.000 - 96.9948i) q^{76} -540.000 q^{77} -440.000 q^{79} +(-288.000 + 166.277i) q^{80} -1195.12i q^{83} +(526.500 + 303.975i) q^{85} +(-1314.00 + 758.638i) q^{89} +(-468.000 + 135.100i) q^{91} -144.000 q^{92} +(-63.0000 + 109.119i) q^{95} +(-1002.00 - 578.505i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 18 q^{7}+O(q^{10}) $ 2 * q - 8 * q^4 + 18 * q^7	$ 2 q - 8 q^{4} + 18 q^{7} - 90 q^{11} - 65 q^{13} - 64 q^{16} - 117 q^{17} - 42 q^{19} + 72 q^{20} + 18 q^{23} + 196 q^{25} - 144 q^{28} - 99 q^{29} + 54 q^{35} + 195 q^{37} + 63 q^{41} + 82 q^{43} - 235 q^{49} - 208 q^{52} + 522 q^{53} + 270 q^{55} + 1368 q^{59} + 719 q^{61} + 1024 q^{64} + 351 q^{65} - 1218 q^{67} - 936 q^{68} + 810 q^{71} + 336 q^{76} - 1080 q^{77} - 880 q^{79} - 576 q^{80} + 1053 q^{85} - 2628 q^{89} - 936 q^{91} - 288 q^{92} - 126 q^{95} - 2004 q^{97}+O(q^{100}) $ 2 * q - 8 * q^4 + 18 * q^7 - 90 * q^11 - 65 * q^13 - 64 * q^16 - 117 * q^17 - 42 * q^19 + 72 * q^20 + 18 * q^23 + 196 * q^25 - 144 * q^28 - 99 * q^29 + 54 * q^35 + 195 * q^37 + 63 * q^41 + 82 * q^43 - 235 * q^49 - 208 * q^52 + 522 * q^53 + 270 * q^55 + 1368 * q^59 + 719 * q^61 + 1024 * q^64 + 351 * q^65 - 1218 * q^67 - 936 * q^68 + 810 * q^71 + 336 * q^76 - 1080 * q^77 - 880 * q^79 - 576 * q^80 + 1053 * q^85 - 2628 * q^89 - 936 * q^91 - 288 * q^92 - 126 * q^95 - 2004 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	$-0.666667\pi$
$2$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$3$		0			0
$3$		0			0
$4$	−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	0.722895	−	0.690958i	$-0.242811\pi$
$7$	9.00000	+	5.19615i	0.485954	+	0.280566i	−0.236940	+	0.971524i	$0.576145\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−45.0000	+	25.9808i	−1.23346	+	0.712136i	−0.967749	−	0.251918i	$-0.918939\pi$
$11$	−45.0000	+	25.9808i	−1.23346	+	0.712136i	−0.265707	+	0.964054i	$0.585605\pi$
$12$		0			0
$13$	−32.5000	+	33.7750i	−0.693375	+	0.720577i
$13$	−32.5000	+	33.7750i	−0.693375	+	0.720577i
$14$		0			0
$15$		0			0
$16$	−32.0000	−	55.4256i	−0.500000	−	0.866025i
$17$	−58.5000	+	101.325i	−0.834608	+	1.44558i	0.0597414	+	0.998214i	$0.480972\pi$
$17$	−58.5000	+	101.325i	−0.834608	+	1.44558i	−0.894349	+	0.447369i	$0.852361\pi$
$18$		0			0
$19$	−21.0000	−	12.1244i	−0.253565	−	0.146396i	0.367831	−	0.929893i	$-0.380101\pi$
$19$	−21.0000	−	12.1244i	−0.253565	−	0.146396i	−0.621395	+	0.783497i	$0.713434\pi$
$20$	36.0000	+	20.7846i	0.402492	+	0.232379i
$21$		0			0
$22$		0			0
$23$	9.00000	+	15.5885i	0.0815926	+	0.141323i	0.903934	−	0.427672i	$-0.140666\pi$
$23$	9.00000	+	15.5885i	0.0815926	+	0.141323i	−0.822342	+	0.568994i	$0.807333\pi$
$24$		0			0
$25$	98.0000			0.784000
$26$		0			0
$27$		0			0
$28$	−72.0000	+	41.5692i	−0.485954	+	0.280566i
$29$	−49.5000	−	85.7365i	−0.316963	−	0.548996i	0.662890	−	0.748717i	$-0.269330\pi$
$29$	−49.5000	−	85.7365i	−0.316963	−	0.548996i	−0.979853	+	0.199721i	$0.935996\pi$
$30$		0			0
$31$			193.990i			1.12392i	0.827164	+	0.561961i	$0.189953\pi$
$31$			193.990i			1.12392i	−0.827164	+	0.561961i	$0.810047\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	27.0000	−	46.7654i	0.130395	−	0.225851i
$36$		0			0
$37$	97.5000	−	56.2917i	0.433214	−	0.250116i	−0.267501	−	0.963558i	$-0.586198\pi$
$37$	97.5000	−	56.2917i	0.433214	−	0.250116i	0.700715	+	0.713442i	$0.252865\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	31.5000	−	18.1865i	0.119987	−	0.0692746i	−0.438805	−	0.898582i	$-0.644598\pi$
$41$	31.5000	−	18.1865i	0.119987	−	0.0692746i	0.558792	+	0.829308i	$0.311265\pi$
$42$		0			0
$43$	41.0000	−	71.0141i	0.145406	−	0.251850i	−0.784119	−	0.620611i	$-0.786885\pi$
$43$	41.0000	−	71.0141i	0.145406	−	0.251850i	0.929524	+	0.368761i	$0.120218\pi$
$44$		−	415.692i		−	1.42427i
$45$		0			0
$46$		0			0
$47$			72.7461i			0.225768i	0.993608	+	0.112884i	$0.0360089\pi$
$47$			72.7461i			0.225768i	−0.993608	+	0.112884i	$0.963991\pi$
$48$		0			0
$49$	−117.500	−	203.516i	−0.342566	−	0.593341i
$50$		0			0
$51$		0			0
$52$	−104.000	−	360.267i	−0.277350	−	0.960769i
$53$	261.000			0.676436			0.338218	−	0.941068i	$-0.390176\pi$
$53$	261.000			0.676436			0.338218	+	0.941068i	$0.390176\pi$
$54$		0			0
$55$	135.000	+	233.827i	0.330971	+	0.573258i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	684.000	+	394.908i	1.50931	+	0.871400i	0.999941	+	0.0108508i	$0.00345397\pi$
$59$	684.000	+	394.908i	1.50931	+	0.871400i	0.509368	+	0.860549i	$0.329879\pi$
$60$		0			0
$61$	359.500	−	622.672i	0.754578	−	1.30697i	−0.191006	−	0.981589i	$-0.561175\pi$
$61$	359.500	−	622.672i	0.754578	−	1.30697i	0.945584	−	0.325379i	$-0.105492\pi$
$62$		0			0
$63$		0			0
$64$	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	−0.938950	−	0.344054i	$-0.888200\pi$
$67$	−609.000	+	351.606i	−1.11047	+	0.641128i	−0.171516	+	0.985181i	$0.554866\pi$
$68$	−468.000	−	810.600i	−0.834608	−	1.44558i
$69$		0			0
$70$		0			0
$71$	405.000	+	233.827i	0.676967	+	0.390847i	0.798711	−	0.601714i	$-0.205515\pi$
$71$	405.000	+	233.827i	0.676967	+	0.390847i	−0.121744	+	0.992561i	$0.538849\pi$
$72$		0			0
$73$			684.160i			1.09692i	0.836178	+	0.548458i	$0.184785\pi$
$73$			684.160i			1.09692i	−0.836178	+	0.548458i	$0.815215\pi$
$74$		0			0
$75$		0			0
$76$	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
$81$		0			0
$82$		0			0
$83$		−	1195.12i		−	1.58049i	−0.612789	−	0.790247i	$-0.709952\pi$
$83$		−	1195.12i		−	1.58049i	0.612789	−	0.790247i	$-0.290048\pi$
$84$		0			0
$85$	526.500	+	303.975i	0.671846	+	0.387891i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1314.00	+	758.638i	−1.56499	+	0.903545i	−0.568246	+	0.822859i	$0.692378\pi$
$89$	−1314.00	+	758.638i	−1.56499	+	0.903545i	−0.996740	+	0.0806862i	$0.974289\pi$
$90$		0			0
$91$	−468.000	+	135.100i	−0.539118	+	0.155630i
$92$	−144.000			−0.163185
$93$		0			0
$94$		0			0
$95$	−63.0000	+	109.119i	−0.0680386	+	0.117846i
$96$		0			0
$97$	−1002.00	−	578.505i	−1.04884	−	0.605549i	−0.126517	−	0.991964i	$-0.540380\pi$
$97$	−1002.00	−	578.505i	−1.04884	−	0.605549i	−0.922325	+	0.386415i	$0.873713\pi$
$98$		0			0
$99$		0			0
$100$	−392.000	+	678.964i	−0.392000	+	0.678964i
$101$	787.500	+	1363.99i	0.775833	+	1.34378i	0.934325	+	0.356423i	$0.116004\pi$
$101$	787.500	+	1363.99i	0.775833	+	1.34378i	−0.158491	+	0.987360i	$0.550663\pi$
$102$		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
$105$		0			0
$106$		0			0
$107$	225.000	+	389.711i	0.203286	+	0.352101i	0.949585	−	0.313509i	$-0.101505\pi$
$107$	225.000	+	389.711i	0.203286	+	0.352101i	−0.746299	+	0.665610i	$0.768171\pi$
$108$		0			0
$109$			595.825i			0.523576i	0.965125	+	0.261788i	$0.0843120\pi$
$109$			595.825i			0.523576i	−0.965125	+	0.261788i	$0.915688\pi$
$110$		0			0
$111$		0			0
$112$		−	665.108i		−	0.561132i
$113$	−850.500	+	1473.11i	−0.708038	+	1.22636i	0.257546	+	0.966266i	$0.417086\pi$
$113$	−850.500	+	1473.11i	−0.708038	+	1.22636i	−0.965584	+	0.260092i	$0.916247\pi$
$114$		0			0
$115$	81.0000	−	46.7654i	0.0656808	−	0.0379208i
$116$	792.000			0.633925
$117$		0			0
$118$		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
$123$		0			0
$124$	−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	0.995323	+	0.0966044i	$0.0307982\pi$
$127$	832.000	+	1441.07i	0.581323	+	1.00688i	−0.414000	+	0.910277i	$0.635868\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1476.00			0.984418			0.492209	−	0.870477i	$-0.336190\pi$
$131$	1476.00			0.984418			0.492209	+	0.870477i	$0.336190\pi$
$132$		0			0
$133$	−126.000	−	218.238i	−0.0821473	−	0.142283i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−877.500	−	506.625i	−0.547225	−	0.315941i	0.200777	−	0.979637i	$-0.435653\pi$
$137$	−877.500	−	506.625i	−0.547225	−	0.315941i	−0.748002	+	0.663696i	$0.768987\pi$
$138$		0			0
$139$	−562.000	+	973.413i	−0.342937	+	0.593984i	−0.984977	−	0.172687i	$-0.944755\pi$
$139$	−562.000	+	973.413i	−0.342937	+	0.593984i	0.642040	+	0.766671i	$0.278088\pi$
$140$	216.000	+	374.123i	0.130395	+	0.225851i
$141$		0			0
$142$		0			0
$143$	585.000	−	2364.25i	0.342099	−	1.38258i
$144$		0			0
$145$	−445.500	+	257.210i	−0.255150	+	0.147311i
$146$		0			0
$147$		0			0
$148$			900.666i			0.500232i
$149$	−2830.50	−	1634.19i	−1.55627	−	0.898510i	−0.997609	−	0.0691115i	$-0.977984\pi$
$149$	−2830.50	−	1634.19i	−1.55627	−	0.898510i	−0.558657	−	0.829399i	$-0.688683\pi$
$150$		0			0
$151$		−	1638.52i		−	0.883052i	−0.897248	−	0.441526i	$-0.854437\pi$
$151$		−	1638.52i		−	0.883052i	0.897248	−	0.441526i	$-0.145563\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1008.00			0.522352
$156$		0			0
$157$	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
$159$		0			0
$160$		0			0
$161$			187.061i			0.0915684i
$162$		0			0
$163$	2556.00	+	1475.71i	1.22823	+	0.709118i	0.966659	−	0.256066i	$-0.0824264\pi$
$163$	2556.00	+	1475.71i	1.22823	+	0.709118i	0.261570	+	0.965185i	$0.415760\pi$
$164$			290.985i			0.138549i
$165$		0			0
$166$		0			0
$167$	2718.00	−	1569.24i	1.25943	−	0.727133i	0.286468	−	0.958090i	$-0.407519\pi$
$167$	2718.00	−	1569.24i	1.25943	−	0.727133i	0.972964	+	0.230956i	$0.0741855\pi$
$168$		0			0
$169$	−84.5000	−	2195.37i	−0.0384615	−	0.999260i
$170$		0			0
$171$		0			0
$172$	328.000	+	568.113i	0.145406	+	0.251850i
$173$	2133.00	−	3694.46i	0.937393	−	1.62361i	0.167083	−	0.985943i	$-0.446565\pi$
$173$	2133.00	−	3694.46i	0.937393	−	1.62361i	0.770310	−	0.637669i	$-0.220101\pi$
$174$		0			0
$175$	882.000	+	509.223i	0.380988	+	0.219964i
$176$	2880.00	+	1662.77i	1.23346	+	0.712136i
$177$		0			0
$178$		0			0
$179$	1503.00	+	2603.27i	0.627595	+	1.08703i	0.988033	+	0.154243i	$0.0492939\pi$
$179$	1503.00	+	2603.27i	0.627595	+	1.08703i	−0.360438	+	0.932783i	$0.617373\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$		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
$189$		0			0
$190$		0			0
$191$	−1368.00	+	2369.45i	−0.518246	+	0.897629i	0.481529	+	0.876430i	$0.340082\pi$
$191$	−1368.00	+	2369.45i	−0.518246	+	0.897629i	−0.999775	+	0.0211985i	$0.993252\pi$
$192$		0			0
$193$	−2254.50	+	1301.64i	−0.840842	+	0.485460i	−0.857550	−	0.514400i	$-0.828015\pi$
$193$	−2254.50	+	1301.64i	−0.840842	+	0.485460i	0.0167085	+	0.999860i	$0.494681\pi$
$194$		0			0
$195$		0			0
$196$	1880.00			0.685131
$197$	−3222.00	+	1860.22i	−1.16527	+	0.672768i	−0.952561	−	0.304347i	$-0.901562\pi$
$197$	−3222.00	+	1860.22i	−1.16527	+	0.672768i	−0.212708	+	0.977116i	$0.568228\pi$
$198$		0			0
$199$	−599.000	+	1037.50i	−0.213377	+	0.369579i	−0.952769	−	0.303695i	$-0.901780\pi$
$199$	−599.000	+	1037.50i	−0.213377	+	0.369579i	0.739392	+	0.673275i	$0.235113\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	1028.84i		−	0.355716i
$204$		0			0
$205$	−94.5000	−	163.679i	−0.0321959	−	0.0557650i
$206$		0			0
$207$		0			0
$208$	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	0.602260	−	0.798300i	$-0.294267\pi$
$211$	−1196.00	−	2071.53i	−0.390218	−	0.675878i	−0.992478	+	0.122422i	$0.960934\pi$
$212$	−1044.00	+	1808.26i	−0.338218	+	0.585811i
$213$		0			0
$214$		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
$219$		0			0
$220$	−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	−0.740900	−	0.671615i	$-0.765601\pi$
$223$	−1764.00	+	1018.45i	−0.529714	+	0.305830i	0.211186	+	0.977446i	$0.432267\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1863.00	−	1075.60i	−0.544721	−	0.314495i	0.202269	−	0.979330i	$-0.435168\pi$
$227$	−1863.00	−	1075.60i	−0.544721	−	0.314495i	−0.746990	+	0.664835i	$0.768502\pi$
$228$		0			0
$229$			3471.03i			1.00162i	0.865556	+	0.500812i	$0.166965\pi$
$229$			3471.03i			1.00162i	−0.865556	+	0.500812i	$0.833035\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1854.00			0.521286			0.260643	−	0.965435i	$-0.416065\pi$
$233$	1854.00			0.521286			0.260643	+	0.965435i	$0.416065\pi$
$234$		0			0
$235$	378.000			0.104928
$236$	−5472.00	+	3159.26i	−1.50931	+	0.871400i
$237$		0			0
$238$		0			0
$239$			4458.30i			1.20662i	0.797505	+	0.603312i	$0.206153\pi$
$239$			4458.30i			1.20662i	−0.797505	+	0.603312i	$0.793847\pi$
$240$		0			0
$241$	−361.500	−	208.712i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−361.500	−	208.712i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$		0			0
$244$	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
$249$		0			0
$250$		0			0
$251$	2052.00	−	3554.17i	0.516020	−	0.893773i	−0.483807	−	0.875175i	$-0.660746\pi$
$251$	2052.00	−	3554.17i	0.516020	−	0.893773i	0.999827	−	0.0185985i	$-0.00592043\pi$
$252$		0			0
$253$	−810.000	−	467.654i	−0.201282	−	0.116210i
$254$		0			0
$255$		0			0
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	994.500	+	1722.52i	0.241382	+	0.418086i	0.961108	−	0.276172i	$-0.0890660\pi$
$257$	994.500	+	1722.52i	0.241382	+	0.418086i	−0.719726	+	0.694258i	$0.755733\pi$
$258$		0			0
$259$	1170.00			0.280696
$260$	−1872.00	+	540.400i	−0.446525	+	0.128901i
$261$		0			0
$262$		0			0
$263$	369.000	+	639.127i	0.0865153	+	0.149849i	0.906036	−	0.423201i	$-0.139094\pi$
$263$	369.000	+	639.127i	0.0865153	+	0.149849i	−0.819521	+	0.573050i	$0.805760\pi$
$264$		0			0
$265$		−	1356.20i		−	0.314379i
$266$		0			0
$267$		0			0
$268$		−	5625.70i		−	1.28226i
$269$	−1053.00	+	1823.85i	−0.238671	+	0.413391i	−0.960333	−	0.278855i	$-0.910045\pi$
$269$	−1053.00	+	1823.85i	−0.238671	+	0.413391i	0.721662	+	0.692246i	$0.243378\pi$
$270$		0			0
$271$	594.000	−	342.946i	0.133147	−	0.0768727i	−0.431947	−	0.901899i	$-0.642173\pi$
$271$	594.000	−	342.946i	0.133147	−	0.0768727i	0.565094	+	0.825026i	$0.308840\pi$
$272$	7488.00			1.66922
$273$		0			0
$274$		0			0
$275$	−4410.00	+	2546.11i	−0.967029	+	0.558315i
$276$		0			0
$277$	−1832.50	+	3173.98i	−0.397488	+	0.688470i	−0.993415	−	0.114569i	$-0.963451\pi$
$277$	−1832.50	+	3173.98i	−0.397488	+	0.688470i	0.595927	+	0.803039i	$0.296785\pi$
$278$		0			0
$279$		0			0
$280$		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	0.945838	−	0.324638i	$-0.105242\pi$
$283$	913.000	+	1581.36i	0.191775	+	0.332163i	−0.754064	+	0.656801i	$0.771909\pi$
$284$	−3240.00	+	1870.61i	−0.676967	+	0.390847i
$285$		0			0
$286$		0			0
$287$	378.000			0.0777444
$288$		0			0
$289$	−4388.00	−	7600.24i	−0.893141	−	1.54696i
$290$		0			0
$291$		0			0
$292$	−4740.00	−	2736.64i	−0.949957	−	0.548458i
$293$	436.500	+	252.013i	0.0870328	+	0.0502484i	0.542885	−	0.839807i	$-0.317332\pi$
$293$	436.500	+	252.013i	0.0870328	+	0.0502484i	−0.455852	+	0.890056i	$0.650665\pi$
$294$		0			0
$295$	2052.00	−	3554.17i	0.404990	−	0.701463i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−819.000	−	202.650i	−0.158408	−	0.0391958i
$300$		0			0
$301$	738.000	−	426.084i	0.141321	−	0.0815917i
$302$		0			0
$303$		0			0
$304$			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	$0.0580256\pi$
$307$			1950.29i			0.362570i	−0.983431	+	0.181285i	$0.941974\pi$
$308$	2160.00	−	3741.23i	0.399602	−	0.692131i
$309$		0			0
$310$		0			0
$311$	3798.00			0.692491			0.346246	−	0.938144i	$-0.387456\pi$
$311$	3798.00			0.692491			0.346246	+	0.938144i	$0.387456\pi$
$312$		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
$315$		0			0
$316$	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
$321$		0			0
$322$		0			0
$323$	2457.00	−	1418.55i	0.423254	−	0.244366i
$324$		0			0
$325$	−3185.00	+	3309.95i	−0.543606	+	0.564932i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−378.000	+	654.715i	−0.0633429	+	0.109713i
$330$		0			0
$331$	8724.00	+	5036.80i	1.44868	+	0.836398i	0.998403	−	0.0564889i	$-0.0179906\pi$
$331$	8724.00	+	5036.80i	1.44868	+	0.836398i	0.450281	+	0.892887i	$0.351324\pi$
$332$	8280.00	+	4780.46i	1.36875	+	0.790247i
$333$		0			0
$334$		0			0
$335$	1827.00	+	3164.46i	0.297969	+	0.516098i
$336$		0			0
$337$	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
$339$		0			0
$340$	−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
$345$		0			0
$346$		0			0
$347$	1647.00	−	2852.69i	0.254800	−	0.441327i	−0.710041	−	0.704160i	$-0.751324\pi$
$347$	1647.00	−	2852.69i	0.254800	−	0.441327i	0.964841	+	0.262834i	$0.0846570\pi$
$348$		0			0
$349$	−9132.00	+	5272.36i	−1.40064	+	0.808662i	−0.994459	−	0.105129i	$-0.966475\pi$
$349$	−9132.00	+	5272.36i	−1.40064	+	0.808662i	−0.406185	+	0.913791i	$0.633141\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2146.50	−	1239.28i	0.323645	−	0.186856i	−0.329371	−	0.944201i	$-0.606837\pi$
$353$	2146.50	−	1239.28i	0.323645	−	0.186856i	0.653016	+	0.757344i	$0.273503\pi$
$354$		0			0
$355$	1215.00	−	2104.44i	0.181649	−	0.314626i
$356$		−	12138.2i		−	1.80709i
$357$		0			0
$358$		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
$363$		0			0
$364$	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	0.965846	+	0.259118i	$0.0834318\pi$
$367$	4973.00	+	8613.49i	0.707326	+	1.22512i	−0.258520	+	0.966006i	$0.583235\pi$
$368$	576.000	−	997.661i	0.0815926	−	0.141323i
$369$		0			0
$370$		0			0
$371$	2349.00	+	1356.20i	0.328717	+	0.189785i
$372$		0			0
$373$	3650.50	−	6322.85i	0.506745	−	0.877707i	−0.493225	−	0.869902i	$-0.664182\pi$
$373$	3650.50	−	6322.85i	0.506745	−	0.877707i	0.999970	−	0.00780555i	$-0.00248461\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4504.50	+	1114.57i	0.615368	+	0.152264i
$378$		0			0
$379$	−2964.00	+	1711.27i	−0.401716	+	0.231931i	−0.687224	−	0.726445i	$-0.741171\pi$
$379$	−2964.00	+	1711.27i	−0.401716	+	0.231931i	0.285508	+	0.958376i	$0.407838\pi$
$380$	−504.000	−	872.954i	−0.0680386	−	0.117846i
$381$		0			0
$382$		0			0
$383$	5004.00	+	2889.06i	0.667604	+	0.385442i	0.795168	−	0.606389i	$-0.207382\pi$
$383$	5004.00	+	2889.06i	0.667604	+	0.385442i	−0.127564	+	0.991830i	$0.540716\pi$
$384$		0			0
$385$			2805.92i			0.371436i
$386$		0			0
$387$		0			0
$388$	8016.00	−	4628.04i	1.04884	−	0.605549i
$389$	−9153.00			−1.19300			−0.596498	−	0.802614i	$-0.703442\pi$
$389$	−9153.00			−1.19300			−0.596498	+	0.802614i	$0.703442\pi$
$390$		0			0
$391$	−2106.00			−0.272391
$392$		0			0
$393$		0			0
$394$		0			0
$395$			2286.31i			0.291232i
$396$		0			0
$397$	1752.00	+	1011.52i	0.221487	+	0.127876i	0.606639	−	0.794978i	$-0.292518\pi$
$397$	1752.00	+	1011.52i	0.221487	+	0.127876i	−0.385152	+	0.922853i	$0.625851\pi$
$398$		0			0
$399$		0			0
$400$	−3136.00	−	5431.71i	−0.392000	−	0.678964i
$401$	−7195.50	+	4154.32i	−0.896075	+	0.517349i	−0.875925	−	0.482448i	$-0.839748\pi$
$401$	−7195.50	+	4154.32i	−0.896075	+	0.517349i	−0.0201504	+	0.999797i	$0.506414\pi$
$402$		0			0
$403$	−6552.00	−	6304.66i	−0.809872	−	0.779300i
$404$	−12600.0			−1.55167
$405$		0			0
$406$		0			0
$407$	−2925.00	+	5066.25i	−0.356233	+	0.617014i
$408$		0			0
$409$	−9022.50	−	5209.14i	−1.09079	−	0.629769i	−0.157005	−	0.987598i	$-0.550184\pi$
$409$	−9022.50	−	5209.14i	−1.09079	−	0.629769i	−0.933787	+	0.357829i	$0.883517\pi$
$410$		0			0
$411$		0			0
$412$	−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
$417$		0			0
$418$		0			0
$419$	2088.00	+	3616.52i	0.243450	+	0.421667i	0.961695	−	0.274123i	$-0.0883875\pi$
$419$	2088.00	+	3616.52i	0.243450	+	0.421667i	−0.718245	+	0.695790i	$0.755054\pi$
$420$		0			0
$421$			14471.3i			1.67527i	0.546233	+	0.837633i	$0.316061\pi$
$421$			14471.3i			1.67527i	−0.546233	+	0.837633i	$0.683939\pi$
$422$		0			0
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	5697.00	−	3289.16i	0.636693	−	0.367595i	−0.146646	−	0.989189i	$-0.546848\pi$
$431$	5697.00	−	3289.16i	0.636693	−	0.367595i	0.783340	+	0.621594i	$0.213515\pi$
$432$		0			0
$433$	3302.50	−	5720.10i	0.366531	−	0.634851i	−0.622489	−	0.782628i	$-0.713879\pi$
$433$	3302.50	−	5720.10i	0.366531	−	0.634851i	0.989021	+	0.147778i	$0.0472120\pi$
$434$		0			0
$435$		0			0
$436$	−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	0.999171	−	0.0407023i	$-0.0129595\pi$
$439$	4271.00	+	7397.59i	0.464336	+	0.804254i	−0.534835	+	0.844957i	$0.679626\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14328.0			1.53667			0.768334	−	0.640049i	$-0.221086\pi$
$443$	14328.0			1.53667			0.768334	+	0.640049i	$0.221086\pi$
$444$		0			0
$445$	3942.00	+	6827.74i	0.419930	+	0.727340i
$446$		0			0
$447$		0			0
$448$	4608.00	+	2660.43i	0.485954	+	0.280566i
$449$	−2610.00	−	1506.88i	−0.274329	−	0.158384i	0.356525	−	0.934286i	$-0.383962\pi$
$449$	−2610.00	−	1506.88i	−0.274329	−	0.158384i	−0.630853	+	0.775902i	$0.717295\pi$
$450$		0			0
$451$	−945.000	+	1636.79i	−0.0986659	+	0.170894i
$452$	−6804.00	−	11784.9i	−0.708038	−	1.22636i
$453$		0			0
$454$		0			0
$455$	702.000	+	2431.80i	0.0723303	+	0.250559i
$456$		0			0
$457$	−2500.50	+	1443.66i	−0.255948	+	0.147772i	−0.622485	−	0.782632i	$-0.713877\pi$
$457$	−2500.50	+	1443.66i	−0.255948	+	0.147772i	0.366536	+	0.930404i	$0.380543\pi$
$458$		0			0
$459$		0			0
$460$			748.246i			0.0758416i
$461$	−3118.50	−	1800.47i	−0.315061	−	0.181900i	0.334128	−	0.942528i	$-0.391558\pi$
$461$	−3118.50	−	1800.47i	−0.315061	−	0.181900i	−0.649189	+	0.760627i	$0.724892\pi$
$462$		0			0
$463$			2677.75i			0.268781i	0.990928	+	0.134391i	$0.0429077\pi$
$463$			2677.75i			0.268781i	−0.990928	+	0.134391i	$0.957092\pi$
$464$	−3168.00	+	5487.14i	−0.316963	+	0.548996i
$465$		0			0
$466$		0			0
$467$	−13878.0			−1.37515			−0.687577	−	0.726111i	$-0.741326\pi$
$467$	−13878.0			−1.37515			−0.687577	+	0.726111i	$0.741326\pi$
$468$		0			0
$469$	−7308.00			−0.719514
$470$		0			0
$471$		0			0
$472$		0			0
$473$			4260.84i			0.414194i
$474$		0			0
$475$	−2058.00	−	1188.19i	−0.198795	−	0.114774i
$476$		−	9727.20i		−	0.936650i
$477$		0			0
$478$		0			0
$479$	−954.000	+	550.792i	−0.0910008	+	0.0525393i	−0.544810	−	0.838560i	$-0.683398\pi$
$479$	−954.000	+	550.792i	−0.0910008	+	0.0525393i	0.453809	+	0.891099i	$0.350065\pi$
$480$		0			0
$481$	−1267.50	+	5122.54i	−0.120152	+	0.485588i
$482$		0			0
$483$		0			0
$484$	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	−0.387671	−	0.921798i	$-0.626720\pi$
$487$	−14829.0	−	8561.53i	−1.37981	−	0.796632i	−0.992136	+	0.125166i	$0.960054\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	225.000	+	389.711i	0.0206805	+	0.0358196i	0.876180	−	0.481983i	$-0.160083\pi$
$491$	225.000	+	389.711i	0.0206805	+	0.0358196i	−0.855500	+	0.517803i	$0.826750\pi$
$492$		0			0
$493$	11583.0			1.05816
$494$		0			0
$495$		0			0
$496$	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	$0.202037\pi$
$499$			13219.0i			1.18590i	−0.805239	+	0.592950i	$0.797963\pi$
$500$	8028.00	+	4634.97i	0.718046	+	0.414564i
$501$		0			0
$502$		0			0
$503$	2673.00	−	4629.77i	0.236945	−	0.410400i	−0.722891	−	0.690962i	$-0.757187\pi$
$503$	2673.00	−	4629.77i	0.236945	−	0.410400i	0.959836	+	0.280561i	$0.0905206\pi$
$504$		0			0
$505$	7087.50	−	4091.97i	0.624534	−	0.360575i
$506$		0			0
$507$		0			0
$508$	−13312.0			−1.16265
$509$	5080.50	−	2933.23i	0.442415	−	0.255428i	−0.262207	−	0.965012i	$-0.584450\pi$
$509$	5080.50	−	2933.23i	0.442415	−	0.255428i	0.704621	+	0.709583i	$0.251117\pi$
$510$		0			0
$511$	−3555.00	+	6157.44i	−0.307757	+	0.533051i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	4125.75i		−	0.353014i
$516$		0			0
$517$	−1890.00	−	3273.58i	−0.160778	−	0.278475i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9657.00			0.812055			0.406028	−	0.913861i	$-0.366914\pi$
$521$	9657.00			0.812055			0.406028	+	0.913861i	$0.366914\pi$
$522$		0			0
$523$	−10813.0	−	18728.7i	−0.904053	−	1.56586i	−0.822184	−	0.569222i	$-0.807245\pi$
$523$	−10813.0	−	18728.7i	−0.904053	−	1.56586i	−0.0818685	−	0.996643i	$-0.526089\pi$
$524$	−5904.00	+	10226.0i	−0.492209	+	0.852531i
$525$		0			0
$526$		0			0
$527$	−19656.0	−	11348.4i	−1.62472	−	0.938034i
$528$		0			0
$529$	5921.50	−	10256.3i	0.486685	−	0.842964i
$530$		0			0
$531$		0			0
$532$	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
$537$		0			0
$538$		0			0
$539$	10575.0	+	6105.48i	0.845079	+	0.487906i
$540$		0			0
$541$		−	5371.09i		−	0.426841i	−0.976960	−	0.213421i	$-0.931540\pi$
$541$		−	5371.09i		−	0.426841i	0.976960	−	0.213421i	$-0.0684605\pi$
$542$		0			0
$543$		0			0
$544$		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
$549$		0			0
$550$		0			0
$551$			2400.62i			0.185608i
$552$		0			0
$553$	−3960.00	−	2286.31i	−0.304514	−	0.175811i
$554$		0			0
$555$		0			0
$556$	−4496.00	−	7787.30i	−0.342937	−	0.593984i
$557$	−3343.50	+	1930.37i	−0.254342	+	0.146845i	−0.621751	−	0.783215i	$-0.713578\pi$
$557$	−3343.50	+	1930.37i	−0.254342	+	0.146845i	0.367409	+	0.930060i	$0.380245\pi$
$558$		0			0
$559$	1066.00	+	3692.73i	0.0806565	+	0.279402i
$560$	−3456.00			−0.260790
$561$		0			0
$562$		0			0
$563$	10836.0	−	18768.5i	0.811160	−	1.40497i	−0.100893	−	0.994897i	$-0.532170\pi$
$563$	10836.0	−	18768.5i	0.811160	−	1.40497i	0.912053	−	0.410073i	$-0.134497\pi$
$564$		0			0
$565$	7654.50	+	4419.33i	0.569960	+	0.329066i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−693.000	−	1200.31i	−0.0510581	−	0.0884353i	0.839367	−	0.543565i	$-0.182926\pi$
$569$	−693.000	−	1200.31i	−0.0510581	−	0.0884353i	−0.890425	+	0.455130i	$0.849593\pi$
$570$		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
$573$		0			0
$574$		0			0
$575$	882.000	+	1527.67i	0.0639686	+	0.110797i
$576$		0			0
$577$		−	8045.38i		−	0.580474i	−0.956955	−	0.290237i	$-0.906266\pi$
$577$		−	8045.38i		−	0.580474i	0.956955	−	0.290237i	$-0.0937341\pi$
$578$		0			0
$579$		0			0
$580$		−	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
$585$		0			0
$586$		0			0
$587$	23922.0	−	13811.4i	1.68206	−	0.971135i	0.721763	−	0.692140i	$-0.243332\pi$
$587$	23922.0	−	13811.4i	1.68206	−	0.971135i	0.960293	−	0.278995i	$-0.0900013\pi$
$588$		0			0
$589$	2352.00	−	4073.78i	0.164537	−	0.284987i
$590$		0			0
$591$		0			0
$592$	−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
$597$		0			0
$598$		0			0
$599$	−22356.0			−1.52494			−0.762472	−	0.647021i	$-0.776014\pi$
$599$	−22356.0			−1.52494			−0.762472	+	0.647021i	$0.776014\pi$
$600$		0			0
$601$	9041.50	+	15660.3i	0.613661	+	1.06289i	0.990618	+	0.136662i	$0.0436373\pi$
$601$	9041.50	+	15660.3i	0.613661	+	1.06289i	−0.376956	+	0.926231i	$0.623029\pi$
$602$		0			0
$603$		0			0
$604$	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	−0.942975	−	0.332865i	$-0.891985\pi$
$607$	−2740.00	+	4745.82i	−0.183218	+	0.317342i	0.759757	+	0.650207i	$0.225318\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2457.00	−	2364.25i	−0.162683	−	0.156542i
$612$		0			0
$613$	15361.5	−	8868.97i	1.01215	−	0.584362i	0.100326	−	0.994955i	$-0.468011\pi$
$613$	15361.5	−	8868.97i	1.01215	−	0.584362i	0.911819	+	0.410592i	$0.134678\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8545.50	−	4933.75i	−0.557583	−	0.321921i	0.194592	−	0.980884i	$-0.437662\pi$
$617$	−8545.50	−	4933.75i	−0.557583	−	0.321921i	−0.752175	+	0.658963i	$0.770995\pi$
$618$		0			0
$619$			4115.35i			0.267221i	0.991034	+	0.133611i	$0.0426572\pi$
$619$			4115.35i			0.267221i	−0.991034	+	0.133611i	$0.957343\pi$
$620$	−4032.00	+	6983.63i	−0.261176	+	0.452370i
$621$		0			0
$622$		0			0
$623$	−15768.0			−1.01402
$624$		0			0
$625$	6229.00			0.398656
$626$		0			0
$627$		0			0
$628$	−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	0.112383	−	0.993665i	$-0.464151\pi$
$631$	−10968.0	−	6332.38i	−0.691964	−	0.399506i	−0.804347	+	0.594159i	$0.797485\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7488.00	−	4323.20i	0.467956	−	0.270175i
$636$		0			0
$637$	10692.5	+	2645.71i	0.665074	+	0.164563i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1894.50	+	3281.37i	−0.116737	+	0.202194i	−0.918473	−	0.395484i	$-0.870577\pi$
$641$	−1894.50	+	3281.37i	−0.116737	+	0.202194i	0.801736	+	0.597678i	$0.203910\pi$
$642$		0			0
$643$	14646.0	+	8455.87i	0.898261	+	0.518611i	0.876636	−	0.481155i	$-0.159783\pi$
$643$	14646.0	+	8455.87i	0.898261	+	0.518611i	0.0216255	+	0.999766i	$0.493116\pi$
$644$	−1296.00	−	748.246i	−0.0793006	−	0.0457842i
$645$		0			0
$646$		0			0
$647$	−13896.0	−	24068.6i	−0.844371	−	1.46249i	−0.886166	−	0.463368i	$-0.846641\pi$
$647$	−13896.0	−	24068.6i	−0.844371	−	1.46249i	0.0417951	−	0.999126i	$-0.486692\pi$
$648$		0			0
$649$	−41040.0			−2.48222
$650$		0			0
$651$		0			0
$652$	−20448.0	+	11805.7i	−1.22823	+	0.709118i
$653$	−297.000	−	514.419i	−0.0177986	−	0.0308281i	0.856989	−	0.515335i	$-0.172332\pi$
$653$	−297.000	−	514.419i	−0.0177986	−	0.0308281i	−0.874788	+	0.484507i	$0.838999\pi$
$654$		0			0
$655$		−	7669.52i		−	0.457516i
$656$	−2016.00	−	1163.94i	−0.119987	−	0.0692746i
$657$		0			0
$658$		0			0
$659$	8874.00	−	15370.2i	0.524555	−	0.908556i	−0.475036	−	0.879966i	$-0.657565\pi$
$659$	8874.00	−	15370.2i	0.524555	−	0.908556i	0.999591	−	0.0285901i	$-0.00910174\pi$
$660$		0			0
$661$	13675.5	−	7895.55i	0.804713	−	0.464601i	−0.0404035	−	0.999183i	$-0.512864\pi$
$661$	13675.5	−	7895.55i	0.804713	−	0.464601i	0.845117	+	0.534582i	$0.179531\pi$
$662$		0			0
$663$		0			0
$664$		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
$669$		0			0
$670$		0			0
$671$			37360.3i			2.14945i
$672$		0			0
$673$	−10466.5	−	18128.5i	−0.599486	−	1.03834i	−0.992897	−	0.118977i	$-0.962038\pi$
$673$	−10466.5	−	18128.5i	−0.599486	−	1.03834i	0.393411	−	0.919363i	$-0.371295\pi$
$674$		0			0
$675$		0			0
$676$	15548.0	+	8196.06i	0.884615	+	0.466321i
$677$	−3402.00			−0.193131			−0.0965653	−	0.995327i	$-0.530786\pi$
$677$	−3402.00			−0.193131			−0.0965653	+	0.995327i	$0.530786\pi$
$678$		0			0
$679$	−6012.00	−	10413.1i	−0.339793	−	0.588539i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21636.0	−	12491.6i	−1.21212	−	0.699818i	−0.248900	−	0.968529i	$-0.580069\pi$
$683$	−21636.0	−	12491.6i	−1.21212	−	0.699818i	−0.963221	+	0.268711i	$0.913402\pi$
$684$		0			0
$685$	−2632.50	+	4559.62i	−0.146836	+	0.254327i
$686$		0			0
$687$		0			0
$688$	−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	−0.131575	−	0.991306i	$-0.542003\pi$
$691$	12009.0	−	6933.40i	0.661134	−	0.381706i	0.792709	+	0.609600i	$0.208670\pi$
$692$	17064.0	+	29555.7i	0.937393	+	1.62361i
$693$		0			0
$694$		0			0
$695$	5058.00	+	2920.24i	0.276059	+	0.159383i
$696$		0			0
$697$			4255.65i			0.231269i
$698$		0			0
$699$		0			0
$700$	−7056.00	+	4073.78i	−0.380988	+	0.219964i
$701$	21906.0			1.18028			0.590141	−	0.807300i	$-0.299072\pi$
$701$	21906.0			1.18028			0.590141	+	0.807300i	$0.299072\pi$
$702$		0			0
$703$	−2730.00			−0.146464
$704$	−23040.0	+	13302.2i	−1.23346	+	0.712136i
$705$		0			0
$706$		0			0
$707$			16367.9i			0.870690i
$708$		0			0
$709$	−11308.5	−	6528.97i	−0.599012	−	0.345840i	0.169641	−	0.985506i	$-0.445739\pi$
$709$	−11308.5	−	6528.97i	−0.599012	−	0.345840i	−0.768653	+	0.639666i	$0.779073\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	−7110.00	+	12314.9i	−0.368788	+	0.638759i	−0.989376	−	0.145377i	$-0.953560\pi$
$719$	−7110.00	+	12314.9i	−0.368788	+	0.638759i	0.620589	+	0.784136i	$0.286894\pi$
$720$		0			0
$721$	7146.00	+	4125.75i	0.369114	+	0.213108i
$722$		0			0
$723$		0			0
$724$	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
$729$		0			0
$730$		0			0
$731$	4797.00	+	8308.65i	0.242713	+	0.420392i
$732$		0			0
$733$			11419.4i			0.575424i	0.957717	+	0.287712i	$0.0928945\pi$
$733$			11419.4i			0.575424i	−0.957717	+	0.287712i	$0.907105\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18270.0	−	31644.6i	0.913140	−	1.58160i
$738$		0			0
$739$	−17784.0	+	10267.6i	−0.885244	+	0.511096i	−0.872384	−	0.488822i	$-0.837427\pi$
$739$	−17784.0	+	10267.6i	−0.885244	+	0.511096i	−0.0128599	+	0.999917i	$0.504094\pi$
$740$	4680.00			0.232487
$741$		0			0
$742$		0			0
$743$	18036.0	−	10413.1i	0.890547	−	0.514158i	0.0164258	−	0.999865i	$-0.494771\pi$
$743$	18036.0	−	10413.1i	0.890547	−	0.514158i	0.874121	+	0.485707i	$0.161438\pi$
$744$		0			0
$745$	−8491.50	+	14707.7i	−0.417590	+	0.723287i
$746$		0			0
$747$		0			0
$748$	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	0.918753	−	0.394834i	$-0.129198\pi$
$751$	2417.00	+	4186.37i	0.117440	+	0.203412i	−0.801312	+	0.598246i	$0.795864\pi$
$752$	4032.00	−	2327.88i	0.195521	−	0.112884i
$753$		0			0
$754$		0			0
$755$	−8514.00			−0.410406
$756$		0			0
$757$	−4523.00	−	7834.07i	−0.217161	−	0.376135i	0.736778	−	0.676135i	$-0.236346\pi$
$757$	−4523.00	−	7834.07i	−0.217161	−	0.376135i	−0.953939	+	0.300001i	$0.903013\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10422.0	+	6017.14i	0.496448	+	0.286625i	0.727246	−	0.686377i	$-0.240800\pi$
$761$	10422.0	+	6017.14i	0.496448	+	0.286625i	−0.230797	+	0.973002i	$0.574133\pi$
$762$		0			0
$763$	−3096.00	+	5362.43i	−0.146897	+	0.254434i
$764$	−10944.0	−	18955.6i	−0.518246	−	0.897629i
$765$		0			0
$766$		0			0
$767$	−35568.0	+	10267.6i	−1.67443	+	0.483366i
$768$		0			0
$769$	32514.0	−	18772.0i	1.52469	−	0.880279i	0.525115	−	0.851031i	$-0.324022\pi$
$769$	32514.0	−	18772.0i	1.52469	−	0.880279i	0.999572	−	0.0292479i	$-0.00931121\pi$
$770$		0			0
$771$		0			0
$772$		−	20826.2i		−	0.970920i
$773$	13608.0	+	7856.58i	0.633177	+	0.365565i	0.781981	−	0.623302i	$-0.214209\pi$
$773$	13608.0	+	7856.58i	0.633177	+	0.365565i	−0.148804	+	0.988867i	$0.547543\pi$
$774$		0			0
$775$			19011.0i			0.881155i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−882.000			−0.0405660
$780$		0			0
$781$	−24300.0			−1.11334
$782$		0			0
$783$		0			0
$784$	−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	0.424541	−	0.905409i	$-0.360435\pi$
$787$	−3252.00	−	1877.54i	−0.147295	−	0.0850409i	−0.571836	+	0.820368i	$0.693769\pi$
$788$		−	29763.6i		−	1.34554i
$789$		0			0
$790$		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
$795$		0			0
$796$	−4792.00	−	8299.99i	−0.213377	−	0.369579i
$797$	−3915.00	+	6780.98i	−0.173998	+	0.301373i	−0.939814	−	0.341686i	$-0.889002\pi$
$797$	−3915.00	+	6780.98i	−0.173998	+	0.301373i	0.765816	+	0.643060i	$0.222335\pi$
$798$		0			0
$799$	−7371.00	−	4255.65i	−0.326367	−	0.188428i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17775.0	−	30787.2i	−0.781153	−	1.35300i
$804$		0			0
$805$	972.000			0.0425571
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3082.50	−	5339.05i	−0.133962	−	0.232028i	0.791239	−	0.611507i	$-0.209437\pi$
$809$	−3082.50	−	5339.05i	−0.133962	−	0.232028i	−0.925200	+	0.379479i	$0.876103\pi$
$810$		0			0
$811$		−	29839.8i		−	1.29201i	−0.763335	−	0.646003i	$-0.776440\pi$
$811$		−	29839.8i		−	1.29201i	0.763335	−	0.646003i	$-0.223560\pi$
$812$	7128.00	+	4115.35i	0.308059	+	0.177858i
$813$		0			0
$814$		0			0
$815$	7668.00	−	13281.4i	0.329568	−	0.570829i
$816$		0			0
$817$	−1722.00	+	994.197i	−0.0737395	+	0.0425735i
$818$		0			0
$819$		0			0
$820$	1512.00			0.0643919
$821$	25776.0	−	14881.8i	1.09572	−	0.632616i	0.160629	−	0.987015i	$-0.448648\pi$
$821$	25776.0	−	14881.8i	1.09572	−	0.632616i	0.935094	+	0.354399i	$0.115315\pi$
$822$		0			0
$823$	4460.00	−	7724.95i	0.188901	−	0.327187i	−0.755983	−	0.654591i	$-0.772841\pi$
$823$	4460.00	−	7724.95i	0.188901	−	0.327187i	0.944884	+	0.327405i	$0.106174\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			18041.0i			0.758583i	0.925277	+	0.379292i	$0.123832\pi$
$827$			18041.0i			0.758583i	−0.925277	+	0.379292i	$0.876168\pi$
$828$		0			0
$829$	10511.5	+	18206.5i	0.440385	+	0.762770i	0.997718	−	0.0675195i	$-0.0215085\pi$
$829$	10511.5	+	18206.5i	0.440385	+	0.762770i	−0.557333	+	0.830289i	$0.688175\pi$
$830$		0			0
$831$		0			0
$832$	−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
$837$		0			0
$838$		0			0
$839$	19116.0	+	11036.6i	0.786600	+	0.454144i	0.838764	−	0.544495i	$-0.183279\pi$
$839$	19116.0	+	11036.6i	0.786600	+	0.454144i	−0.0521641	+	0.998639i	$0.516612\pi$
$840$		0			0
$841$	7294.00	−	12633.6i	0.299069	−	0.518003i
$842$		0			0
$843$		0			0
$844$	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
$849$		0			0
$850$		0			0
$851$	1755.00	+	1013.25i	0.0706940	+	0.0408152i
$852$		0			0
$853$		−	26609.5i		−	1.06810i	−0.845452	−	0.534051i	$-0.820669\pi$
$853$		−	26609.5i		−	1.06810i	0.845452	−	0.534051i	$-0.179331\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12771.0			0.509042			0.254521	−	0.967067i	$-0.418082\pi$
$857$	12771.0			0.509042			0.254521	+	0.967067i	$0.418082\pi$
$858$		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
$861$		0			0
$862$		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
$867$		0			0
$868$	−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
$873$		0			0
$874$		0			0
$875$	6021.00	−	10428.7i	0.232625	−	0.402918i
$876$		0			0
$877$	8542.50	+	4932.01i	0.328916	+	0.189900i	0.655360	−	0.755317i	$-0.272517\pi$
$877$	8542.50	+	4932.01i	0.328916	+	0.189900i	−0.326443	+	0.945217i	$0.605850\pi$
$878$		0			0
$879$		0			0
$880$	8640.00	−	14964.9i	0.330971	−	0.573258i
$881$	14584.5	+	25261.1i	0.557735	+	0.966025i	0.997685	+	0.0680028i	$0.0216627\pi$
$881$	14584.5	+	25261.1i	0.557735	+	0.966025i	−0.439950	+	0.898022i	$0.645004\pi$
$882$		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
$885$		0			0
$886$		0			0
$887$	−7200.00	−	12470.8i	−0.272551	−	0.472071i	0.696964	−	0.717106i	$-0.254534\pi$
$887$	−7200.00	−	12470.8i	−0.272551	−	0.472071i	−0.969514	+	0.245035i	$0.921201\pi$
$888$		0			0
$889$			17292.8i			0.652398i
$890$		0			0
$891$		0			0
$892$		−	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
$897$		0			0
$898$		0			0
$899$	16632.0	−	9602.49i	0.617028	−	0.356241i
$900$		0			0
$901$	−15268.5	+	26445.8i	−0.564559	+	0.977845i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			9732.39i			0.357476i
$906$		0			0
$907$	−9842.00	−	17046.8i	−0.360307	−	0.624070i	0.627704	−	0.778452i	$-0.283995\pi$
$907$	−9842.00	−	17046.8i	−0.360307	−	0.624070i	−0.988011	+	0.154382i	$0.950661\pi$
$908$	14904.0	−	8604.83i	0.544721	−	0.314495i
$909$		0			0
$910$		0			0
$911$	−24480.0			−0.890295			−0.445147	−	0.895457i	$-0.646849\pi$
$911$	−24480.0			−0.890295			−0.445147	+	0.895457i	$0.646849\pi$
$912$		0			0
$913$	31050.0	+	53780.2i	1.12553	+	1.94947i
$914$		0			0
$915$		0			0
$916$	−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	0.277976	+	0.960588i	$0.410336\pi$
$919$	−19304.0	+	33435.5i	−0.692906	+	1.20015i	−0.970882	+	0.239560i	$0.922997\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21060.0	+	6079.50i	−0.751027	+	0.216803i
$924$		0			0
$925$	9555.00	−	5516.58i	0.339639	−	0.196091i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8842.50	−	5105.22i	−0.312285	−	0.180298i	0.335663	−	0.941982i	$-0.391040\pi$
$929$	−8842.50	−	5105.22i	−0.312285	−	0.180298i	−0.647949	+	0.761684i	$0.724373\pi$
$930$		0			0
$931$			5698.45i			0.200600i
$932$	−7416.00	+	12844.9i	−0.260643	+	0.451447i
$933$		0			0
$934$		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
$939$		0			0
$940$	−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
$945$		0			0
$946$		0			0
$947$	−29412.0	+	16981.0i	−1.00925	+	0.582692i	−0.910973	−	0.412467i	$-0.864667\pi$
$947$	−29412.0	+	16981.0i	−1.00925	+	0.582692i	−0.0982794	+	0.995159i	$0.531334\pi$
$948$		0			0
$949$	−23107.5	−	22235.2i	−0.790412	−	0.760575i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11907.0	−	20623.5i	0.404728	−	0.701009i	−0.589562	−	0.807723i	$-0.700700\pi$
$953$	11907.0	−	20623.5i	0.404728	−	0.701009i	0.994290	+	0.106714i	$0.0340330\pi$
$954$		0			0
$955$	12312.0	+	7108.34i	0.417180	+	0.240859i
$956$	−30888.0	−	17833.2i	−1.04497	−	0.603312i
$957$		0			0
$958$		0			0
$959$	−5265.00	−	9119.25i	−0.177284	−	0.307066i
$960$		0			0
$961$	−7841.00			−0.263200
$962$		0			0
$963$		0			0
$964$	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	$0.327762\pi$
$967$			51549.3i			1.71429i	−0.515079	+	0.857143i	$0.672238\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6156.00	+	10662.5i	−0.203456	+	0.352396i	−0.949640	−	0.313344i	$-0.898551\pi$
$971$	−6156.00	+	10662.5i	−0.203456	+	0.352396i	0.746184	+	0.665740i	$0.231884\pi$
$972$		0			0
$973$	−10116.0	+	5840.48i	−0.333303	+	0.192433i
$974$		0			0
$975$		0			0
$976$	−46016.0			−1.50916
$977$	−18652.5	+	10769.0i	−0.610795	+	0.352642i	−0.773276	−	0.634069i	$-0.781383\pi$
$977$	−18652.5	+	10769.0i	−0.610795	+	0.352642i	0.162482	+	0.986712i	$0.448050\pi$
$978$		0			0
$979$	39420.0	−	68277.4i	1.28689	−	2.22896i
$980$		−	9768.77i		−	0.318420i
$981$		0			0
$982$		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
$987$		0			0
$988$	−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	0.987608	−	0.156941i	$-0.0501633\pi$
$991$	11165.0	+	19338.3i	0.357889	+	0.619882i	−0.629719	+	0.776823i	$0.716830\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5391.00	+	3112.50i	0.171765	+	0.0991686i
$996$		0			0
$997$	12465.5	−	21590.9i	0.395974	−	0.685848i	−0.597251	−	0.802055i	$-0.703740\pi$
$997$	12465.5	−	21590.9i	0.395974	−	0.685848i	0.993225	+	0.116207i	$0.0370736\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.b.10.1		2
3.2	odd	2		39.4.j.a.10.1	yes	2
12.11	even	2		624.4.bv.a.49.1		2
13.2	odd	12		1521.4.a.m.1.1		2
13.4	even	6	inner	117.4.q.b.82.1		2
13.11	odd	12		1521.4.a.m.1.2		2
39.2	even	12		507.4.a.g.1.2		2
39.11	even	12		507.4.a.g.1.1		2
39.17	odd	6		39.4.j.a.4.1	✓	2
39.23	odd	6		507.4.b.a.337.1		2
39.29	odd	6		507.4.b.a.337.2		2
156.95	even	6		624.4.bv.a.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.a.4.1	✓	2	39.17	odd	6
39.4.j.a.10.1	yes	2	3.2	odd	2
117.4.q.b.10.1		2	1.1	even	1	trivial
117.4.q.b.82.1		2	13.4	even	6	inner
507.4.a.g.1.1		2	39.11	even	12
507.4.a.g.1.2		2	39.2	even	12
507.4.b.a.337.1		2	39.23	odd	6
507.4.b.a.337.2		2	39.29	odd	6
624.4.bv.a.49.1		2	12.11	even	2
624.4.bv.a.433.1		2	156.95	even	6
1521.4.a.m.1.1		2	13.2	odd	12
1521.4.a.m.1.2		2	13.11	odd	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 + 5.19615i) q^{7} +O(q^{10})\)	\(q+(-4.00000 + 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 + 5.19615i) q^{7} +(-45.0000 + 25.9808i) q^{11} +(-32.5000 + 33.7750i) q^{13} +(-32.0000 - 55.4256i) q^{16} +(-58.5000 + 101.325i) q^{17} +(-21.0000 - 12.1244i) q^{19} +(36.0000 + 20.7846i) q^{20} +(9.00000 + 15.5885i) q^{23} +98.0000 q^{25} +(-72.0000 + 41.5692i) q^{28} +(-49.5000 - 85.7365i) q^{29} +193.990i q^{31} +(27.0000 - 46.7654i) q^{35} +(97.5000 - 56.2917i) q^{37} +(31.5000 - 18.1865i) q^{41} +(41.0000 - 71.0141i) q^{43} -415.692i q^{44} +72.7461i q^{47} +(-117.500 - 203.516i) q^{49} +(-104.000 - 360.267i) q^{52} +261.000 q^{53} +(135.000 + 233.827i) q^{55} +(684.000 + 394.908i) q^{59} +(359.500 - 622.672i) q^{61} +512.000 q^{64} +(175.500 + 168.875i) q^{65} +(-609.000 + 351.606i) q^{67} +(-468.000 - 810.600i) q^{68} +(405.000 + 233.827i) q^{71} +684.160i q^{73} +(168.000 - 96.9948i) q^{76} -540.000 q^{77} -440.000 q^{79} +(-288.000 + 166.277i) q^{80} -1195.12i q^{83} +(526.500 + 303.975i) q^{85} +(-1314.00 + 758.638i) q^{89} +(-468.000 + 135.100i) q^{91} -144.000 q^{92} +(-63.0000 + 109.119i) q^{95} +(-1002.00 - 578.505i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 18 q^{7}+O(q^{10}) \) 2 * q - 8 * q^4 + 18 * q^7	\( 2 q - 8 q^{4} + 18 q^{7} - 90 q^{11} - 65 q^{13} - 64 q^{16} - 117 q^{17} - 42 q^{19} + 72 q^{20} + 18 q^{23} + 196 q^{25} - 144 q^{28} - 99 q^{29} + 54 q^{35} + 195 q^{37} + 63 q^{41} + 82 q^{43} - 235 q^{49} - 208 q^{52} + 522 q^{53} + 270 q^{55} + 1368 q^{59} + 719 q^{61} + 1024 q^{64} + 351 q^{65} - 1218 q^{67} - 936 q^{68} + 810 q^{71} + 336 q^{76} - 1080 q^{77} - 880 q^{79} - 576 q^{80} + 1053 q^{85} - 2628 q^{89} - 936 q^{91} - 288 q^{92} - 126 q^{95} - 2004 q^{97}+O(q^{100}) \) 2 * q - 8 * q^4 + 18 * q^7 - 90 * q^11 - 65 * q^13 - 64 * q^16 - 117 * q^17 - 42 * q^19 + 72 * q^20 + 18 * q^23 + 196 * q^25 - 144 * q^28 - 99 * q^29 + 54 * q^35 + 195 * q^37 + 63 * q^41 + 82 * q^43 - 235 * q^49 - 208 * q^52 + 522 * q^53 + 270 * q^55 + 1368 * q^59 + 719 * q^61 + 1024 * q^64 + 351 * q^65 - 1218 * q^67 - 936 * q^68 + 810 * q^71 + 336 * q^76 - 1080 * q^77 - 880 * q^79 - 576 * q^80 + 1053 * q^85 - 2628 * q^89 - 936 * q^91 - 288 * q^92 - 126 * q^95 - 2004 * q^97

Introduction

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