LMFDB - Embedded newform 117.4.g.b.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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, 2]))

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Embedding invariants

Embedding label			55.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.55
Dual form			117.4.g.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +21.0000 q^{8} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +21.0000 q^{8} +(13.5000 + 23.3827i) q^{10} +(15.0000 + 25.9808i) q^{11} +(32.5000 - 33.7750i) q^{13} -6.00000 q^{14} +(35.5000 + 61.4878i) q^{16} +(-55.5000 + 96.1288i) q^{17} +(23.0000 - 39.8372i) q^{19} +(-4.50000 + 7.79423i) q^{20} +(-45.0000 + 77.9423i) q^{22} +(-3.00000 - 5.19615i) q^{23} -44.0000 q^{25} +(136.500 + 33.7750i) q^{26} +(-1.00000 - 1.73205i) q^{28} +(-52.5000 - 90.9327i) q^{29} -100.000 q^{31} +(-22.5000 + 38.9711i) q^{32} -333.000 q^{34} +(-9.00000 + 15.5885i) q^{35} +(-8.50000 - 14.7224i) q^{37} +138.000 q^{38} +189.000 q^{40} +(-115.500 - 200.052i) q^{41} +(257.000 - 445.137i) q^{43} -30.0000 q^{44} +(9.00000 - 15.5885i) q^{46} +162.000 q^{47} +(169.500 + 293.583i) q^{49} +(-66.0000 - 114.315i) q^{50} +(13.0000 + 45.0333i) q^{52} -639.000 q^{53} +(135.000 + 233.827i) q^{55} +(-21.0000 + 36.3731i) q^{56} +(157.500 - 272.798i) q^{58} +(300.000 - 519.615i) q^{59} +(-116.500 + 201.784i) q^{61} +(-150.000 - 259.808i) q^{62} +433.000 q^{64} +(292.500 - 303.975i) q^{65} +(-463.000 - 801.940i) q^{67} +(-55.5000 - 96.1288i) q^{68} -54.0000 q^{70} +(-465.000 + 805.404i) q^{71} -253.000 q^{73} +(25.5000 - 44.1673i) q^{74} +(23.0000 + 39.8372i) q^{76} -60.0000 q^{77} -1324.00 q^{79} +(319.500 + 553.390i) q^{80} +(346.500 - 600.156i) q^{82} -810.000 q^{83} +(-499.500 + 865.159i) q^{85} +1542.00 q^{86} +(315.000 + 545.596i) q^{88} +(249.000 + 431.281i) q^{89} +(26.0000 + 90.0666i) q^{91} +6.00000 q^{92} +(243.000 + 420.888i) q^{94} +(207.000 - 358.535i) q^{95} +(-679.000 + 1176.06i) q^{97} +(-508.500 + 880.748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8}+O(q^{10}) $ 2 * q + 3 * q^2 - q^4 + 18 * q^5 - 2 * q^7 + 42 * q^8	$ 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8} + 27 q^{10} + 30 q^{11} + 65 q^{13} - 12 q^{14} + 71 q^{16} - 111 q^{17} + 46 q^{19} - 9 q^{20} - 90 q^{22} - 6 q^{23} - 88 q^{25} + 273 q^{26} - 2 q^{28} - 105 q^{29} - 200 q^{31} - 45 q^{32} - 666 q^{34} - 18 q^{35} - 17 q^{37} + 276 q^{38} + 378 q^{40} - 231 q^{41} + 514 q^{43} - 60 q^{44} + 18 q^{46} + 324 q^{47} + 339 q^{49} - 132 q^{50} + 26 q^{52} - 1278 q^{53} + 270 q^{55} - 42 q^{56} + 315 q^{58} + 600 q^{59} - 233 q^{61} - 300 q^{62} + 866 q^{64} + 585 q^{65} - 926 q^{67} - 111 q^{68} - 108 q^{70} - 930 q^{71} - 506 q^{73} + 51 q^{74} + 46 q^{76} - 120 q^{77} - 2648 q^{79} + 639 q^{80} + 693 q^{82} - 1620 q^{83} - 999 q^{85} + 3084 q^{86} + 630 q^{88} + 498 q^{89} + 52 q^{91} + 12 q^{92} + 486 q^{94} + 414 q^{95} - 1358 q^{97} - 1017 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 - q^4 + 18 * q^5 - 2 * q^7 + 42 * q^8 + 27 * q^10 + 30 * q^11 + 65 * q^13 - 12 * q^14 + 71 * q^16 - 111 * q^17 + 46 * q^19 - 9 * q^20 - 90 * q^22 - 6 * q^23 - 88 * q^25 + 273 * q^26 - 2 * q^28 - 105 * q^29 - 200 * q^31 - 45 * q^32 - 666 * q^34 - 18 * q^35 - 17 * q^37 + 276 * q^38 + 378 * q^40 - 231 * q^41 + 514 * q^43 - 60 * q^44 + 18 * q^46 + 324 * q^47 + 339 * q^49 - 132 * q^50 + 26 * q^52 - 1278 * q^53 + 270 * q^55 - 42 * q^56 + 315 * q^58 + 600 * q^59 - 233 * q^61 - 300 * q^62 + 866 * q^64 + 585 * q^65 - 926 * q^67 - 111 * q^68 - 108 * q^70 - 930 * q^71 - 506 * q^73 + 51 * q^74 + 46 * q^76 - 120 * q^77 - 2648 * q^79 + 639 * q^80 + 693 * q^82 - 1620 * q^83 - 999 * q^85 + 3084 * q^86 + 630 * q^88 + 498 * q^89 + 52 * q^91 + 12 * q^92 + 486 * q^94 + 414 * q^95 - 1358 * q^97 - 1017 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.50000	+	2.59808i	0.530330	+	0.918559i	0.999374	+	0.0353837i	$0.0112653\pi$
$2$	1.50000	+	2.59808i	0.530330	+	0.918559i	−0.469044	+	0.883175i	$0.655401\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$	9.00000			0.804984			0.402492	−	0.915423i	$-0.368144\pi$
$5$	9.00000			0.804984			0.402492	+	0.915423i	$0.368144\pi$
$6$		0			0
$7$	−1.00000	+	1.73205i	−0.0539949	+	0.0935220i	−0.891760	−	0.452510i	$-0.850529\pi$
$7$	−1.00000	+	1.73205i	−0.0539949	+	0.0935220i	0.837765	+	0.546032i	$0.183862\pi$
$8$	21.0000			0.928078
$9$		0			0
$10$	13.5000	+	23.3827i	0.426907	+	0.739425i
$11$	15.0000	+	25.9808i	0.411152	+	0.712136i	0.995016	−	0.0997155i	$-0.0317933\pi$
$11$	15.0000	+	25.9808i	0.411152	+	0.712136i	−0.583864	+	0.811851i	$0.698460\pi$
$12$		0			0
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$13$	32.5000	−	33.7750i	0.693375	−	0.720577i
$14$	−6.00000			−0.114541
$15$		0			0
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	−55.5000	+	96.1288i	−0.791807	+	1.37145i	0.133039	+	0.991111i	$0.457526\pi$
$17$	−55.5000	+	96.1288i	−0.791807	+	1.37145i	−0.924847	+	0.380340i	$0.875807\pi$
$18$		0			0
$19$	23.0000	−	39.8372i	0.277714	−	0.481014i	−0.693102	−	0.720839i	$-0.743757\pi$
$19$	23.0000	−	39.8372i	0.277714	−	0.481014i	0.970816	+	0.239825i	$0.0770900\pi$
$20$	−4.50000	+	7.79423i	−0.0503115	+	0.0871421i
$21$		0			0
$22$	−45.0000	+	77.9423i	−0.436092	+	0.755334i
$23$	−3.00000	−	5.19615i	−0.0271975	−	0.0471075i	0.852106	−	0.523369i	$-0.175325\pi$
$23$	−3.00000	−	5.19615i	−0.0271975	−	0.0471075i	−0.879304	+	0.476261i	$0.841992\pi$
$24$		0			0
$25$	−44.0000			−0.352000
$26$	136.500	+	33.7750i	1.02961	+	0.254762i
$27$		0			0
$28$	−1.00000	−	1.73205i	−0.00674937	−	0.0116902i
$29$	−52.5000	−	90.9327i	−0.336173	−	0.582268i	0.647537	−	0.762034i	$-0.275799\pi$
$29$	−52.5000	−	90.9327i	−0.336173	−	0.582268i	−0.983709	+	0.179766i	$0.942466\pi$
$30$		0			0
$31$	−100.000			−0.579372			−0.289686	−	0.957122i	$-0.593551\pi$
$31$	−100.000			−0.579372			−0.289686	+	0.957122i	$0.593551\pi$
$32$	−22.5000	+	38.9711i	−0.124296	+	0.215287i
$33$		0			0
$34$	−333.000			−1.67968
$35$	−9.00000	+	15.5885i	−0.0434651	+	0.0752837i
$36$		0			0
$37$	−8.50000	−	14.7224i	−0.0377673	−	0.0654149i	0.846524	−	0.532351i	$-0.178691\pi$
$37$	−8.50000	−	14.7224i	−0.0377673	−	0.0654149i	−0.884291	+	0.466936i	$0.845358\pi$
$38$	138.000			0.589120
$39$		0			0
$40$	189.000			0.747088
$41$	−115.500	−	200.052i	−0.439953	−	0.762021i	0.557732	−	0.830021i	$-0.311672\pi$
$41$	−115.500	−	200.052i	−0.439953	−	0.762021i	−0.997685	+	0.0680000i	$0.978338\pi$
$42$		0			0
$43$	257.000	−	445.137i	0.911445	−	1.57867i	0.0994205	−	0.995046i	$-0.468301\pi$
$43$	257.000	−	445.137i	0.911445	−	1.57867i	0.812024	−	0.583623i	$-0.198366\pi$
$44$	−30.0000			−0.102788
$45$		0			0
$46$	9.00000	−	15.5885i	0.0288473	−	0.0499651i
$47$	162.000			0.502769			0.251384	−	0.967887i	$-0.419114\pi$
$47$	162.000			0.502769			0.251384	+	0.967887i	$0.419114\pi$
$48$		0			0
$49$	169.500	+	293.583i	0.494169	+	0.855926i
$50$	−66.0000	−	114.315i	−0.186676	−	0.323333i
$51$		0			0
$52$	13.0000	+	45.0333i	0.0346688	+	0.120096i
$53$	−639.000			−1.65610			−0.828051	−	0.560653i	$-0.810550\pi$
$53$	−639.000			−1.65610			−0.828051	+	0.560653i	$0.810550\pi$
$54$		0			0
$55$	135.000	+	233.827i	0.330971	+	0.573258i
$56$	−21.0000	+	36.3731i	−0.0501115	+	0.0867956i
$57$		0			0
$58$	157.500	−	272.798i	0.356565	−	0.617588i
$59$	300.000	−	519.615i	0.661978	−	1.14658i	−0.318118	−	0.948051i	$-0.603051\pi$
$59$	300.000	−	519.615i	0.661978	−	1.14658i	0.980095	−	0.198527i	$-0.0636159\pi$
$60$		0			0
$61$	−116.500	+	201.784i	−0.244529	+	0.423537i	−0.961999	−	0.273052i	$-0.911967\pi$
$61$	−116.500	+	201.784i	−0.244529	+	0.423537i	0.717470	+	0.696590i	$0.245300\pi$
$62$	−150.000	−	259.808i	−0.307258	−	0.532187i
$63$		0			0
$64$	433.000			0.845703
$65$	292.500	−	303.975i	0.558156	−	0.580053i
$66$		0			0
$67$	−463.000	−	801.940i	−0.844246	−	1.46228i	−0.886275	−	0.463160i	$-0.846716\pi$
$67$	−463.000	−	801.940i	−0.844246	−	1.46228i	0.0420292	−	0.999116i	$-0.486618\pi$
$68$	−55.5000	−	96.1288i	−0.0989759	−	0.171431i
$69$		0			0
$70$	−54.0000			−0.0922033
$71$	−465.000	+	805.404i	−0.777258	+	1.34625i	0.156258	+	0.987716i	$0.450057\pi$
$71$	−465.000	+	805.404i	−0.777258	+	1.34625i	−0.933516	+	0.358535i	$0.883276\pi$
$72$		0			0
$73$	−253.000			−0.405636			−0.202818	−	0.979216i	$-0.565010\pi$
$73$	−253.000			−0.405636			−0.202818	+	0.979216i	$0.565010\pi$
$74$	25.5000	−	44.1673i	0.0400583	−	0.0693830i
$75$		0			0
$76$	23.0000	+	39.8372i	0.0347142	+	0.0601268i
$77$	−60.0000			−0.0888004
$78$		0			0
$79$	−1324.00			−1.88559			−0.942795	−	0.333373i	$-0.891813\pi$
$79$	−1324.00			−1.88559			−0.942795	+	0.333373i	$0.891813\pi$
$80$	319.500	+	553.390i	0.446515	+	0.773386i
$81$		0			0
$82$	346.500	−	600.156i	0.466641	−	0.808245i
$83$	−810.000			−1.07119			−0.535597	−	0.844474i	$-0.679913\pi$
$83$	−810.000			−1.07119			−0.535597	+	0.844474i	$0.679913\pi$
$84$		0			0
$85$	−499.500	+	865.159i	−0.637393	+	1.10400i
$86$	1542.00			1.93347
$87$		0			0
$88$	315.000	+	545.596i	0.381581	+	0.660917i
$89$	249.000	+	431.281i	0.296561	+	0.513659i	0.975347	−	0.220677i	$-0.0708268\pi$
$89$	249.000	+	431.281i	0.296561	+	0.513659i	−0.678786	+	0.734336i	$0.737493\pi$
$90$		0			0
$91$	26.0000	+	90.0666i	0.0299510	+	0.103753i
$92$	6.00000			0.00679938
$93$		0			0
$94$	243.000	+	420.888i	0.266633	+	0.461823i
$95$	207.000	−	358.535i	0.223555	−	0.387209i
$96$		0			0
$97$	−679.000	+	1176.06i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−679.000	+	1176.06i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	−508.500	+	880.748i	−0.524145	+	0.907847i
$99$		0			0
$100$	22.0000	−	38.1051i	0.0220000	−	0.0381051i
$101$	−178.500	−	309.171i	−0.175856	−	0.304591i	0.764601	−	0.644503i	$-0.222936\pi$
$101$	−178.500	−	309.171i	−0.175856	−	0.304591i	−0.940457	+	0.339913i	$0.889603\pi$
$102$		0			0
$103$	1118.00			1.06951			0.534756	−	0.845006i	$-0.320403\pi$
$103$	1118.00			1.06951			0.534756	+	0.845006i	$0.320403\pi$
$104$	682.500	−	709.275i	0.643506	−	0.668751i
$105$		0			0
$106$	−958.500	−	1660.17i	−0.878281	−	1.52123i
$107$	357.000	+	618.342i	0.322547	+	0.558667i	0.981013	−	0.193943i	$-0.0621277\pi$
$107$	357.000	+	618.342i	0.322547	+	0.558667i	−0.658466	+	0.752610i	$0.728794\pi$
$108$		0			0
$109$	2006.00			1.76275			0.881376	−	0.472416i	$-0.156618\pi$
$109$	2006.00			1.76275			0.881376	+	0.472416i	$0.156618\pi$
$110$	−405.000	+	701.481i	−0.351048	+	0.608032i
$111$		0			0
$112$	−142.000			−0.119801
$113$	−559.500	+	969.082i	−0.465782	+	0.806758i	−0.999236	−	0.0390710i	$-0.987560\pi$
$113$	−559.500	+	969.082i	−0.465782	+	0.806758i	0.533455	+	0.845829i	$0.320893\pi$
$114$		0			0
$115$	−27.0000	−	46.7654i	−0.0218936	−	0.0379208i
$116$	105.000			0.0840431
$117$		0			0
$118$	1800.00			1.40427
$119$	−111.000	−	192.258i	−0.0855072	−	0.148103i
$120$		0			0
$121$	215.500	−	373.257i	0.161908	−	0.280433i
$122$	−699.000			−0.518725
$123$		0			0
$124$	50.0000	−	86.6025i	0.0362107	−	0.0627189i
$125$	−1521.00			−1.08834
$126$		0			0
$127$	302.000	+	523.079i	0.211009	+	0.365479i	0.952031	−	0.306003i	$-0.0989917\pi$
$127$	302.000	+	523.079i	0.211009	+	0.365479i	−0.741021	+	0.671481i	$0.765658\pi$
$128$	829.500	+	1436.74i	0.572798	+	0.992115i
$129$		0			0
$130$	1228.50	+	303.975i	0.828820	+	0.205080i
$131$	1584.00			1.05645			0.528224	−	0.849105i	$-0.322858\pi$
$131$	1584.00			1.05645			0.528224	+	0.849105i	$0.322858\pi$
$132$		0			0
$133$	46.0000	+	79.6743i	0.0299903	+	0.0519447i
$134$	1389.00	−	2405.82i	0.895458	−	1.55098i
$135$		0			0
$136$	−1165.50	+	2018.71i	−0.734859	+	1.27281i
$137$	358.500	−	620.940i	0.223567	−	0.387230i	−0.732321	−	0.680959i	$-0.761563\pi$
$137$	358.500	−	620.940i	0.223567	−	0.387230i	0.955889	+	0.293729i	$0.0948964\pi$
$138$		0			0
$139$	410.000	−	710.141i	0.250185	−	0.433334i	−0.713391	−	0.700766i	$-0.752842\pi$
$139$	410.000	−	710.141i	0.250185	−	0.433334i	0.963577	+	0.267432i	$0.0861751\pi$
$140$	−9.00000	−	15.5885i	−0.00543313	−	0.00941046i
$141$		0			0
$142$	−2790.00			−1.64881
$143$	1365.00	+	337.750i	0.798231	+	0.197511i
$144$		0			0
$145$	−472.500	−	818.394i	−0.270614	−	0.468717i
$146$	−379.500	−	657.313i	−0.215121	−	0.372600i
$147$		0			0
$148$	17.0000			0.00944183
$149$	−874.500	+	1514.68i	−0.480818	+	0.832801i	−0.999758	−	0.0220100i	$-0.992993\pi$
$149$	−874.500	+	1514.68i	−0.480818	+	0.832801i	0.518940	+	0.854811i	$0.326327\pi$
$150$		0			0
$151$	−370.000			−0.199405			−0.0997026	−	0.995017i	$-0.531789\pi$
$151$	−370.000			−0.199405			−0.0997026	+	0.995017i	$0.531789\pi$
$152$	483.000	−	836.581i	0.257740	−	0.446419i
$153$		0			0
$154$	−90.0000	−	155.885i	−0.0470935	−	0.0815684i
$155$	−900.000			−0.466385
$156$		0			0
$157$	−2611.00			−1.32726			−0.663632	−	0.748059i	$-0.730986\pi$
$157$	−2611.00			−1.32726			−0.663632	+	0.748059i	$0.730986\pi$
$158$	−1986.00	−	3439.85i	−0.999985	−	1.73203i
$159$		0			0
$160$	−202.500	+	350.740i	−0.100056	+	0.173303i
$161$	12.0000			0.00587411
$162$		0			0
$163$	818.000	−	1416.82i	0.393072	−	0.680820i	−0.599781	−	0.800164i	$-0.704746\pi$
$163$	818.000	−	1416.82i	0.393072	−	0.680820i	0.992853	+	0.119344i	$0.0380790\pi$
$164$	231.000			0.109988
$165$		0			0
$166$	−1215.00	−	2104.44i	−0.568086	−	0.983954i
$167$	132.000	+	228.631i	0.0611645	+	0.105940i	0.894986	−	0.446094i	$-0.147185\pi$
$167$	132.000	+	228.631i	0.0611645	+	0.105940i	−0.833822	+	0.552034i	$0.813852\pi$
$168$		0			0
$169$	−84.5000	−	2195.37i	−0.0384615	−	0.999260i
$170$	−2997.00			−1.35211
$171$		0			0
$172$	257.000	+	445.137i	0.113931	+	0.197334i
$173$	705.000	−	1221.10i	0.309827	−	0.536637i	−0.668497	−	0.743715i	$-0.733062\pi$
$173$	705.000	−	1221.10i	0.309827	−	0.536637i	0.978324	+	0.207078i	$0.0663954\pi$
$174$		0			0
$175$	44.0000	−	76.2102i	0.0190062	−	0.0329197i
$176$	−1065.00	+	1844.63i	−0.456122	+	0.790026i
$177$		0			0
$178$	−747.000	+	1293.84i	−0.314551	+	0.544818i
$179$	−237.000	−	410.496i	−0.0989621	−	0.171407i	0.812293	−	0.583249i	$-0.198219\pi$
$179$	−237.000	−	410.496i	−0.0989621	−	0.171407i	−0.911255	+	0.411842i	$0.864886\pi$
$180$		0			0
$181$	2249.00			0.923574			0.461787	−	0.886991i	$-0.347208\pi$
$181$	2249.00			0.923574			0.461787	+	0.886991i	$0.347208\pi$
$182$	−195.000	+	202.650i	−0.0794196	+	0.0825352i
$183$		0			0
$184$	−63.0000	−	109.119i	−0.0252414	−	0.0437194i
$185$	−76.5000	−	132.502i	−0.0304021	−	0.0526580i
$186$		0			0
$187$	−3330.00			−1.30221
$188$	−81.0000	+	140.296i	−0.0314230	+	0.0544263i
$189$		0			0
$190$	1242.00			0.474232
$191$	1722.00	−	2982.59i	0.652354	−	1.12991i	−0.330197	−	0.943912i	$-0.607115\pi$
$191$	1722.00	−	2982.59i	0.652354	−	1.12991i	0.982550	−	0.185997i	$-0.0595516\pi$
$192$		0			0
$193$	2136.50	+	3700.53i	0.796832	+	1.38015i	0.921669	+	0.387977i	$0.126826\pi$
$193$	2136.50	+	3700.53i	0.796832	+	1.38015i	−0.124837	+	0.992177i	$0.539841\pi$
$194$	−4074.00			−1.50771
$195$		0			0
$196$	−339.000			−0.123542
$197$	−993.000	−	1719.93i	−0.359129	−	0.622029i	0.628687	−	0.777658i	$-0.283593\pi$
$197$	−993.000	−	1719.93i	−0.359129	−	0.622029i	−0.987815	+	0.155630i	$0.950259\pi$
$198$		0			0
$199$	1193.00	−	2066.34i	0.424973	−	0.736074i	−0.571445	−	0.820640i	$-0.693617\pi$
$199$	1193.00	−	2066.34i	0.424973	−	0.736074i	0.996418	+	0.0845661i	$0.0269504\pi$
$200$	−924.000			−0.326683
$201$		0			0
$202$	535.500	−	927.513i	0.186523	−	0.323067i
$203$	210.000			0.0726065
$204$		0			0
$205$	−1039.50	−	1800.47i	−0.354155	−	0.613415i
$206$	1677.00	+	2904.65i	0.567195	+	0.982410i
$207$		0			0
$208$	3230.50	+	799.341i	1.07690	+	0.266463i
$209$	1380.00			0.456730
$210$		0			0
$211$	800.000	+	1385.64i	0.261016	+	0.452092i	0.966512	−	0.256621i	$-0.0826093\pi$
$211$	800.000	+	1385.64i	0.261016	+	0.452092i	−0.705497	+	0.708713i	$0.749276\pi$
$212$	319.500	−	553.390i	0.103506	−	0.179278i
$213$		0			0
$214$	−1071.00	+	1855.03i	−0.342112	+	0.592556i
$215$	2313.00	−	4006.23i	0.733699	−	1.27080i
$216$		0			0
$217$	100.000	−	173.205i	0.0312831	−	0.0541840i
$218$	3009.00	+	5211.74i	0.934840	+	1.61919i
$219$		0			0
$220$	−270.000			−0.0827427
$221$	1443.00	+	4998.70i	0.439216	+	1.52149i
$222$		0			0
$223$	1916.00	+	3318.61i	0.575358	+	0.996549i	0.996003	+	0.0893239i	$0.0284706\pi$
$223$	1916.00	+	3318.61i	0.575358	+	0.996549i	−0.420645	+	0.907226i	$0.638196\pi$
$224$	−45.0000	−	77.9423i	−0.0134227	−	0.0232488i
$225$		0			0
$226$	−3357.00			−0.988072
$227$	−699.000	+	1210.70i	−0.204380	+	0.353997i	−0.949935	−	0.312448i	$-0.898851\pi$
$227$	−699.000	+	1210.70i	−0.204380	+	0.353997i	0.745555	+	0.666444i	$0.232184\pi$
$228$		0			0
$229$	4466.00			1.28874			0.644370	−	0.764714i	$-0.277120\pi$
$229$	4466.00			1.28874			0.644370	+	0.764714i	$0.277120\pi$
$230$	81.0000	−	140.296i	0.0232217	−	0.0402211i
$231$		0			0
$232$	−1102.50	−	1909.59i	−0.311994	−	0.540390i
$233$	1638.00			0.460553			0.230277	−	0.973125i	$-0.426037\pi$
$233$	1638.00			0.460553			0.230277	+	0.973125i	$0.426037\pi$
$234$		0			0
$235$	1458.00			0.404721
$236$	300.000	+	519.615i	0.0827472	+	0.143322i
$237$		0			0
$238$	333.000	−	576.773i	0.0906941	−	0.157087i
$239$	594.000			0.160764			0.0803821	−	0.996764i	$-0.474386\pi$
$239$	594.000			0.160764			0.0803821	+	0.996764i	$0.474386\pi$
$240$		0			0
$241$	−1151.50	+	1994.46i	−0.307779	+	0.533088i	−0.977876	−	0.209185i	$-0.932919\pi$
$241$	−1151.50	+	1994.46i	−0.307779	+	0.533088i	0.670098	+	0.742273i	$0.266252\pi$
$242$	1293.00			0.343459
$243$		0			0
$244$	−116.500	−	201.784i	−0.0305662	−	0.0529422i
$245$	1525.50	+	2642.24i	0.397798	+	0.689007i
$246$		0			0
$247$	−598.000	−	2071.53i	−0.154048	−	0.533638i
$248$	−2100.00			−0.537702
$249$		0			0
$250$	−2281.50	−	3951.67i	−0.577179	−	0.999703i
$251$	3162.00	−	5476.74i	0.795154	−	1.37725i	−0.127587	−	0.991827i	$-0.540723\pi$
$251$	3162.00	−	5476.74i	0.795154	−	1.37725i	0.922741	−	0.385420i	$-0.125943\pi$
$252$		0			0
$253$	90.0000	−	155.885i	0.0223646	−	0.0387367i
$254$	−906.000	+	1569.24i	−0.223809	+	0.387649i
$255$		0			0
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	3916.50	+	6783.58i	0.950601	+	1.64649i	0.744127	+	0.668038i	$0.232866\pi$
$257$	3916.50	+	6783.58i	0.950601	+	1.64649i	0.206474	+	0.978452i	$0.433801\pi$
$258$		0			0
$259$	34.0000			0.00815698
$260$	117.000	+	405.300i	0.0279078	+	0.0966755i
$261$		0			0
$262$	2376.00	+	4115.35i	0.560266	+	0.970410i
$263$	−1515.00	−	2624.06i	−0.355205	−	0.615233i	0.631948	−	0.775011i	$-0.282256\pi$
$263$	−1515.00	−	2624.06i	−0.355205	−	0.615233i	−0.987153	+	0.159778i	$0.948922\pi$
$264$		0			0
$265$	−5751.00			−1.33314
$266$	−138.000	+	239.023i	−0.0318095	+	0.0550956i
$267$		0			0
$268$	926.000			0.211061
$269$	−267.000	+	462.458i	−0.0605178	+	0.104820i	−0.894697	−	0.446674i	$-0.852609\pi$
$269$	−267.000	+	462.458i	−0.0605178	+	0.104820i	0.834179	+	0.551493i	$0.185942\pi$
$270$		0			0
$271$	1844.00	+	3193.90i	0.413340	+	0.715925i	0.995253	−	0.0973259i	$-0.0310289\pi$
$271$	1844.00	+	3193.90i	0.413340	+	0.715925i	−0.581913	+	0.813251i	$0.697696\pi$
$272$	−7881.00			−1.75682
$273$		0			0
$274$	2151.00			0.474258
$275$	−660.000	−	1143.15i	−0.144725	−	0.250672i
$276$		0			0
$277$	−932.500	+	1615.14i	−0.202269	+	0.350340i	−0.949259	−	0.314495i	$-0.898165\pi$
$277$	−932.500	+	1615.14i	−0.202269	+	0.350340i	0.746990	+	0.664835i	$0.231498\pi$
$278$	2460.00			0.530723
$279$		0			0
$280$	−189.000	+	327.358i	−0.0403390	+	0.0698691i
$281$	−2997.00			−0.636249			−0.318125	−	0.948049i	$-0.603053\pi$
$281$	−2997.00			−0.636249			−0.318125	+	0.948049i	$0.603053\pi$
$282$		0			0
$283$	2057.00	+	3562.83i	0.432071	+	0.748368i	0.997051	−	0.0767359i	$-0.0244498\pi$
$283$	2057.00	+	3562.83i	0.432071	+	0.748368i	−0.564981	+	0.825104i	$0.691116\pi$
$284$	−465.000	−	805.404i	−0.0971573	−	0.168281i
$285$		0			0
$286$	1170.00	+	4053.00i	0.241901	+	0.837968i
$287$	462.000			0.0950209
$288$		0			0
$289$	−3704.00	−	6415.52i	−0.753918	−	1.30582i
$290$	1417.50	−	2455.18i	0.287029	−	0.497149i
$291$		0			0
$292$	126.500	−	219.104i	0.0253522	−	0.0439114i
$293$	−2332.50	+	4040.01i	−0.465072	+	0.805528i	−0.999205	−	0.0398722i	$-0.987305\pi$
$293$	−2332.50	+	4040.01i	−0.465072	+	0.805528i	0.534133	+	0.845401i	$0.320638\pi$
$294$		0			0
$295$	2700.00	−	4676.54i	0.532882	−	0.922978i
$296$	−178.500	−	309.171i	−0.0350510	−	0.0607101i
$297$		0			0
$298$	−5247.00			−1.01997
$299$	−273.000	−	67.5500i	−0.0528027	−	0.0130653i
$300$		0			0
$301$	514.000	+	890.274i	0.0984268	+	0.170480i
$302$	−555.000	−	961.288i	−0.105751	−	0.183165i
$303$		0			0
$304$	3266.00			0.616177
$305$	−1048.50	+	1816.06i	−0.196842	+	0.340941i
$306$		0			0
$307$	1502.00			0.279230			0.139615	−	0.990206i	$-0.455413\pi$
$307$	1502.00			0.279230			0.139615	+	0.990206i	$0.455413\pi$
$308$	30.0000	−	51.9615i	0.00555003	−	0.00961293i
$309$		0			0
$310$	−1350.00	−	2338.27i	−0.247338	−	0.428402i
$311$	−2106.00			−0.383988			−0.191994	−	0.981396i	$-0.561495\pi$
$311$	−2106.00			−0.383988			−0.191994	+	0.981396i	$0.561495\pi$
$312$		0			0
$313$	−3898.00			−0.703923			−0.351962	−	0.936014i	$-0.614485\pi$
$313$	−3898.00			−0.703923			−0.351962	+	0.936014i	$0.614485\pi$
$314$	−3916.50	−	6783.58i	−0.703888	−	1.21917i
$315$		0			0
$316$	662.000	−	1146.62i	0.117849	−	0.204121i
$317$	−9351.00			−1.65680			−0.828398	−	0.560140i	$-0.810747\pi$
$317$	−9351.00			−1.65680			−0.828398	+	0.560140i	$0.810747\pi$
$318$		0			0
$319$	1575.00	−	2727.98i	0.276436	−	0.478801i
$320$	3897.00			0.680778
$321$		0			0
$322$	18.0000	+	31.1769i	0.00311522	+	0.00539572i
$323$	2553.00	+	4421.93i	0.439792	+	0.761742i
$324$		0			0
$325$	−1430.00	+	1486.10i	−0.244068	+	0.253643i
$326$	4908.00			0.833831
$327$		0			0
$328$	−2425.50	−	4201.09i	−0.408310	−	0.707214i
$329$	−162.000	+	280.592i	−0.0271470	+	0.0470199i
$330$		0			0
$331$	4586.00	−	7943.19i	0.761539	−	1.31902i	−0.180518	−	0.983572i	$-0.557778\pi$
$331$	4586.00	−	7943.19i	0.761539	−	1.31902i	0.942057	−	0.335452i	$-0.108889\pi$
$332$	405.000	−	701.481i	0.0669496	−	0.115960i
$333$		0			0
$334$	−396.000	+	685.892i	−0.0648747	+	0.112366i
$335$	−4167.00	−	7217.46i	−0.679605	−	1.17711i
$336$		0			0
$337$	−11089.0			−1.79245			−0.896226	−	0.443598i	$-0.853702\pi$
$337$	−11089.0			−1.79245			−0.896226	+	0.443598i	$0.853702\pi$
$338$	5577.00	−	3512.60i	0.897482	−	0.565267i
$339$		0			0
$340$	−499.500	−	865.159i	−0.0796741	−	0.138000i
$341$	−1500.00	−	2598.08i	−0.238210	−	0.412592i
$342$		0			0
$343$	−1364.00			−0.214720
$344$	5397.00	−	9347.88i	0.845892	−	1.46513i
$345$		0			0
$346$	4230.00			0.657243
$347$	4881.00	−	8454.14i	0.755118	−	1.30790i	−0.190198	−	0.981746i	$-0.560913\pi$
$347$	4881.00	−	8454.14i	0.755118	−	1.30790i	0.945316	−	0.326156i	$-0.105754\pi$
$348$		0			0
$349$	4145.00	+	7179.35i	0.635750	+	1.10115i	0.986356	+	0.164628i	$0.0526424\pi$
$349$	4145.00	+	7179.35i	0.635750	+	1.10115i	−0.350606	+	0.936523i	$0.614024\pi$
$350$	264.000			0.0403183
$351$		0			0
$352$	−1350.00			−0.204418
$353$	6202.50	+	10743.0i	0.935200	+	1.61981i	0.774276	+	0.632848i	$0.218114\pi$
$353$	6202.50	+	10743.0i	0.935200	+	1.61981i	0.160924	+	0.986967i	$0.448552\pi$
$354$		0			0
$355$	−4185.00	+	7248.63i	−0.625681	+	1.08371i
$356$	−498.000			−0.0741403
$357$		0			0
$358$	711.000	−	1231.49i	0.104965	−	0.181805i
$359$	1098.00			0.161421			0.0807106	−	0.996738i	$-0.474281\pi$
$359$	1098.00			0.161421			0.0807106	+	0.996738i	$0.474281\pi$
$360$		0			0
$361$	2371.50	+	4107.56i	0.345750	+	0.598857i
$362$	3373.50	+	5843.07i	0.489799	+	0.848357i
$363$		0			0
$364$	−91.0000	−	22.5167i	−0.0131036	−	0.00324229i
$365$	−2277.00			−0.326530
$366$		0			0
$367$	2867.00	+	4965.79i	0.407783	+	0.706300i	0.994641	−	0.103390i	$-0.0329688\pi$
$367$	2867.00	+	4965.79i	0.407783	+	0.706300i	−0.586858	+	0.809690i	$0.699635\pi$
$368$	213.000	−	368.927i	0.0301723	−	0.0522599i
$369$		0			0
$370$	229.500	−	397.506i	0.0322463	−	0.0558523i
$371$	639.000	−	1106.78i	0.0894211	−	0.154882i
$372$		0			0
$373$	4485.50	−	7769.11i	0.622655	−	1.07847i	−0.366334	−	0.930483i	$-0.619387\pi$
$373$	4485.50	−	7769.11i	0.622655	−	1.07847i	0.988989	−	0.147987i	$-0.0472794\pi$
$374$	−4995.00	−	8651.59i	−0.690602	−	1.19616i
$375$		0			0
$376$	3402.00			0.466608
$377$	−4777.50	−	1182.12i	−0.652663	−	0.161492i
$378$		0			0
$379$	−3622.00	−	6273.49i	−0.490896	−	0.850257i	0.509049	−	0.860738i	$-0.329997\pi$
$379$	−3622.00	−	6273.49i	−0.490896	−	0.850257i	−0.999945	+	0.0104805i	$0.996664\pi$
$380$	207.000	+	358.535i	0.0279444	+	0.0484011i
$381$		0			0
$382$	10332.0			1.38385
$383$	−3156.00	+	5466.35i	−0.421055	+	0.729289i	−0.996043	−	0.0888732i	$-0.971673\pi$
$383$	−3156.00	+	5466.35i	−0.421055	+	0.729289i	0.574988	+	0.818162i	$0.305007\pi$
$384$		0			0
$385$	−540.000			−0.0714830
$386$	−6409.50	+	11101.6i	−0.845168	+	1.46387i
$387$		0			0
$388$	−679.000	−	1176.06i	−0.0888428	−	0.153880i
$389$	−3627.00			−0.472741			−0.236370	−	0.971663i	$-0.575958\pi$
$389$	−3627.00			−0.472741			−0.236370	+	0.971663i	$0.575958\pi$
$390$		0			0
$391$	666.000			0.0861408
$392$	3559.50	+	6165.23i	0.458627	+	0.794366i
$393$		0			0
$394$	2979.00	−	5159.78i	0.380913	−	0.659761i
$395$	−11916.0			−1.51787
$396$		0			0
$397$	1949.00	−	3375.77i	0.246392	−	0.426763i	−0.716130	−	0.697967i	$-0.754088\pi$
$397$	1949.00	−	3375.77i	0.246392	−	0.426763i	0.962522	+	0.271204i	$0.0874217\pi$
$398$	7158.00			0.901503
$399$		0			0
$400$	−1562.00	−	2705.46i	−0.195250	−	0.338183i
$401$	−2851.50	−	4938.94i	−0.355105	−	0.615060i	0.632031	−	0.774943i	$-0.282222\pi$
$401$	−2851.50	−	4938.94i	−0.355105	−	0.615060i	−0.987136	+	0.159883i	$0.948888\pi$
$402$		0			0
$403$	−3250.00	+	3377.50i	−0.401722	+	0.417482i
$404$	357.000			0.0439639
$405$		0			0
$406$	315.000	+	545.596i	0.0385054	+	0.0666933i
$407$	255.000	−	441.673i	0.0310562	−	0.0537909i
$408$		0			0
$409$	−3155.50	+	5465.49i	−0.381490	+	0.660760i	−0.991275	−	0.131806i	$-0.957922\pi$
$409$	−3155.50	+	5465.49i	−0.381490	+	0.660760i	0.609785	+	0.792567i	$0.291256\pi$
$410$	3118.50	−	5401.40i	0.375638	−	0.650625i
$411$		0			0
$412$	−559.000	+	968.216i	−0.0668445	+	0.115778i
$413$	600.000	+	1039.23i	0.0714869	+	0.123819i
$414$		0			0
$415$	−7290.00			−0.862294
$416$	585.000	+	2026.50i	0.0689471	+	0.238840i
$417$		0			0
$418$	2070.00	+	3585.35i	0.242218	+	0.419533i
$419$	−1164.00	−	2016.11i	−0.135716	−	0.235067i	0.790155	−	0.612908i	$-0.210000\pi$
$419$	−1164.00	−	2016.11i	−0.135716	−	0.235067i	−0.925871	+	0.377840i	$0.876667\pi$
$420$		0			0
$421$	2045.00			0.236739			0.118370	−	0.992970i	$-0.462233\pi$
$421$	2045.00			0.236739			0.118370	+	0.992970i	$0.462233\pi$
$422$	−2400.00	+	4156.92i	−0.276849	+	0.479516i
$423$		0			0
$424$	−13419.0			−1.53699
$425$	2442.00	−	4229.67i	0.278716	−	0.482751i
$426$		0			0
$427$	−233.000	−	403.568i	−0.0264067	−	0.0457377i
$428$	−714.000			−0.0806367
$429$		0			0
$430$	13878.0			1.55641
$431$	2517.00	+	4359.57i	0.281298	+	0.487223i	0.971705	−	0.236199i	$-0.0759016\pi$
$431$	2517.00	+	4359.57i	0.281298	+	0.487223i	−0.690406	+	0.723422i	$0.742568\pi$
$432$		0			0
$433$	−2141.50	+	3709.19i	−0.237676	+	0.411668i	−0.960047	−	0.279838i	$-0.909719\pi$
$433$	−2141.50	+	3709.19i	−0.237676	+	0.411668i	0.722371	+	0.691506i	$0.243052\pi$
$434$	600.000			0.0663616
$435$		0			0
$436$	−1003.00	+	1737.25i	−0.110172	+	0.190823i
$437$	−276.000			−0.0302125
$438$		0			0
$439$	653.000	+	1131.03i	0.0709931	+	0.122964i	0.899337	−	0.437257i	$-0.144050\pi$
$439$	653.000	+	1131.03i	0.0709931	+	0.122964i	−0.828344	+	0.560220i	$0.810716\pi$
$440$	2835.00	+	4910.36i	0.307167	+	0.532028i
$441$		0			0
$442$	−10822.5	+	11247.1i	−1.16465	+	1.21034i
$443$	5796.00			0.621617			0.310808	−	0.950473i	$-0.399400\pi$
$443$	5796.00			0.621617			0.310808	+	0.950473i	$0.399400\pi$
$444$		0			0
$445$	2241.00	+	3881.53i	0.238727	+	0.413488i
$446$	−5748.00	+	9955.83i	−0.610259	+	1.05700i
$447$		0			0
$448$	−433.000	+	749.978i	−0.0456637	+	0.0790918i
$449$	1353.00	−	2343.46i	0.142209	−	0.246314i	−0.786119	−	0.618075i	$-0.787913\pi$
$449$	1353.00	−	2343.46i	0.142209	−	0.246314i	0.928328	+	0.371761i	$0.121246\pi$
$450$		0			0
$451$	3465.00	−	6001.56i	0.361775	−	0.626612i
$452$	−559.500	−	969.082i	−0.0582227	−	0.100845i
$453$		0			0
$454$	−4194.00			−0.433555
$455$	234.000	+	810.600i	0.0241101	+	0.0835198i
$456$		0			0
$457$	414.500	+	717.935i	0.0424278	+	0.0734871i	0.886459	−	0.462806i	$-0.153157\pi$
$457$	414.500	+	717.935i	0.0424278	+	0.0734871i	−0.844032	+	0.536293i	$0.819824\pi$
$458$	6699.00	+	11603.0i	0.683458	+	1.18378i
$459$		0			0
$460$	54.0000			0.00547340
$461$	−2746.50	+	4757.08i	−0.277478	+	0.480606i	−0.970757	−	0.240063i	$-0.922832\pi$
$461$	−2746.50	+	4757.08i	−0.277478	+	0.480606i	0.693279	+	0.720669i	$0.256165\pi$
$462$		0			0
$463$	−15346.0			−1.54037			−0.770183	−	0.637823i	$-0.779835\pi$
$463$	−15346.0			−1.54037			−0.770183	+	0.637823i	$0.779835\pi$
$464$	3727.50	−	6456.22i	0.372941	−	0.645954i
$465$		0			0
$466$	2457.00	+	4255.65i	0.244245	+	0.423045i
$467$	9594.00			0.950658			0.475329	−	0.879808i	$-0.342329\pi$
$467$	9594.00			0.950658			0.475329	+	0.879808i	$0.342329\pi$
$468$		0			0
$469$	1852.00			0.182340
$470$	2187.00	+	3788.00i	0.214636	+	0.371760i
$471$		0			0
$472$	6300.00	−	10911.9i	0.614367	−	1.06411i
$473$	15420.0			1.49897
$474$		0			0
$475$	−1012.00	+	1752.84i	−0.0977553	+	0.169317i
$476$	222.000			0.0213768
$477$		0			0
$478$	891.000	+	1543.26i	0.0852581	+	0.147671i
$479$	−6420.00	−	11119.8i	−0.612395	−	1.06070i	−0.990836	−	0.135074i	$-0.956873\pi$
$479$	−6420.00	−	11119.8i	−0.612395	−	1.06070i	0.378440	−	0.925626i	$-0.376461\pi$
$480$		0			0
$481$	−773.500	−	191.392i	−0.0733234	−	0.0181428i
$482$	−6909.00			−0.652897
$483$		0			0
$484$	215.500	+	373.257i	0.0202385	+	0.0350542i
$485$	−6111.00	+	10584.6i	−0.572137	+	0.990970i
$486$		0			0
$487$	7043.00	−	12198.8i	0.655336	−	1.13508i	−0.326473	−	0.945207i	$-0.605860\pi$
$487$	7043.00	−	12198.8i	0.655336	−	1.13508i	0.981809	−	0.189869i	$-0.0608064\pi$
$488$	−2446.50	+	4237.46i	−0.226942	+	0.393076i
$489$		0			0
$490$	−4576.50	+	7926.73i	−0.421929	+	0.730802i
$491$	5847.00	+	10127.3i	0.537416	+	0.930832i	0.999042	+	0.0437577i	$0.0139329\pi$
$491$	5847.00	+	10127.3i	0.537416	+	0.930832i	−0.461626	+	0.887075i	$0.652734\pi$
$492$		0			0
$493$	11655.0			1.06474
$494$	4485.00	−	4660.95i	0.408481	−	0.424506i
$495$		0			0
$496$	−3550.00	−	6148.78i	−0.321370	−	0.556630i
$497$	−930.000	−	1610.81i	−0.0839360	−	0.145381i
$498$		0			0
$499$	−3688.00			−0.330857			−0.165428	−	0.986222i	$-0.552901\pi$
$499$	−3688.00			−0.330857			−0.165428	+	0.986222i	$0.552901\pi$
$500$	760.500	−	1317.22i	0.0680212	−	0.117816i
$501$		0			0
$502$	18972.0			1.68678
$503$	−2373.00	+	4110.16i	−0.210352	+	0.364340i	−0.951825	−	0.306643i	$-0.900794\pi$
$503$	−2373.00	+	4110.16i	−0.210352	+	0.364340i	0.741473	+	0.670983i	$0.234128\pi$
$504$		0			0
$505$	−1606.50	−	2782.54i	−0.141561	−	0.245191i
$506$	540.000			0.0474425
$507$		0			0
$508$	−604.000			−0.0527523
$509$	−7252.50	−	12561.7i	−0.631555	−	1.09389i	−0.987234	−	0.159277i	$-0.949084\pi$
$509$	−7252.50	−	12561.7i	−0.631555	−	1.09389i	0.355679	−	0.934608i	$-0.384250\pi$
$510$		0			0
$511$	253.000	−	438.209i	0.0219023	−	0.0379358i
$512$	8733.00			0.753804
$513$		0			0
$514$	−11749.5	+	20350.7i	−1.00827	+	1.74637i
$515$	10062.0			0.860941
$516$		0			0
$517$	2430.00	+	4208.88i	0.206714	+	0.358040i
$518$	51.0000	+	88.3346i	0.00432589	+	0.00749266i
$519$		0			0
$520$	6142.50	−	6383.47i	0.518012	−	0.538334i
$521$	−5085.00			−0.427597			−0.213798	−	0.976878i	$-0.568584\pi$
$521$	−5085.00			−0.427597			−0.213798	+	0.976878i	$0.568584\pi$
$522$		0			0
$523$	5441.00	+	9424.09i	0.454911	+	0.787929i	0.998683	−	0.0513043i	$-0.0163378\pi$
$523$	5441.00	+	9424.09i	0.454911	+	0.787929i	−0.543772	+	0.839233i	$0.683004\pi$
$524$	−792.000	+	1371.78i	−0.0660280	+	0.114364i
$525$		0			0
$526$	4545.00	−	7872.17i	0.376752	−	0.652553i
$527$	5550.00	−	9612.88i	0.458751	−	0.794580i
$528$		0			0
$529$	6065.50	−	10505.8i	0.498521	−	0.863463i
$530$	−8626.50	−	14941.5i	−0.707002	−	1.22456i
$531$		0			0
$532$	−92.0000			−0.00749757
$533$	−10510.5	−	2600.67i	−0.854147	−	0.211347i
$534$		0			0
$535$	3213.00	+	5565.08i	0.259645	+	0.449718i
$536$	−9723.00	−	16840.7i	−0.783525	−	1.35711i
$537$		0			0
$538$	−1602.00			−0.128378
$539$	−5085.00	+	8807.48i	−0.406357	+	0.703831i
$540$		0			0
$541$	−4699.00			−0.373430			−0.186715	−	0.982414i	$-0.559784\pi$
$541$	−4699.00			−0.373430			−0.186715	+	0.982414i	$0.559784\pi$
$542$	−5532.00	+	9581.71i	−0.438413	+	0.759353i
$543$		0			0
$544$	−2497.50	−	4325.80i	−0.196837	−	0.340932i
$545$	18054.0			1.41899
$546$		0			0
$547$	8270.00			0.646434			0.323217	−	0.946325i	$-0.395236\pi$
$547$	8270.00			0.646434			0.323217	+	0.946325i	$0.395236\pi$
$548$	358.500	+	620.940i	0.0279459	+	0.0484037i
$549$		0			0
$550$	1980.00	−	3429.46i	0.153505	−	0.265878i
$551$	−4830.00			−0.373439
$552$		0			0
$553$	1324.00	−	2293.24i	0.101812	−	0.176344i
$554$	−5595.00			−0.429077
$555$		0			0
$556$	410.000	+	710.141i	0.0312732	+	0.0541667i
$557$	−11392.5	−	19732.4i	−0.866635	−	1.50106i	−0.865414	−	0.501057i	$-0.832945\pi$
$557$	−11392.5	−	19732.4i	−0.866635	−	1.50106i	−0.00122056	−	0.999999i	$-0.500389\pi$
$558$		0			0
$559$	−6682.00	−	23147.1i	−0.505579	−	1.75138i
$560$	−1278.00			−0.0964381
$561$		0			0
$562$	−4495.50	−	7786.43i	−0.337422	−	0.584432i
$563$	−5964.00	+	10330.0i	−0.446452	+	0.773278i	−0.998152	−	0.0607647i	$-0.980646\pi$
$563$	−5964.00	+	10330.0i	−0.446452	+	0.773278i	0.551700	+	0.834043i	$0.313979\pi$
$564$		0			0
$565$	−5035.50	+	8721.74i	−0.374947	+	0.649427i
$566$	−6171.00	+	10688.5i	−0.458280	+	0.793764i
$567$		0			0
$568$	−9765.00	+	16913.5i	−0.721356	+	1.24943i
$569$	−3981.00	−	6895.29i	−0.293308	−	0.508024i	0.681282	−	0.732021i	$-0.261423\pi$
$569$	−3981.00	−	6895.29i	−0.293308	−	0.508024i	−0.974590	+	0.223997i	$0.928089\pi$
$570$		0			0
$571$	20618.0			1.51110			0.755549	−	0.655093i	$-0.227370\pi$
$571$	20618.0			1.51110			0.755549	+	0.655093i	$0.227370\pi$
$572$	−975.000	+	1013.25i	−0.0712706	+	0.0740666i
$573$		0			0
$574$	693.000	+	1200.31i	0.0503924	+	0.0872823i
$575$	132.000	+	228.631i	0.00957353	+	0.0165818i
$576$		0			0
$577$	−3493.00			−0.252020			−0.126010	−	0.992029i	$-0.540217\pi$
$577$	−3493.00			−0.252020			−0.126010	+	0.992029i	$0.540217\pi$
$578$	11112.0	−	19246.5i	0.799651	−	1.38504i
$579$		0			0
$580$	945.000			0.0676534
$581$	810.000	−	1402.96i	0.0578390	−	0.100180i
$582$		0			0
$583$	−9585.00	−	16601.7i	−0.680909	−	1.17937i
$584$	−5313.00			−0.376461
$585$		0			0
$586$	−13995.0			−0.986567
$587$	5208.00	+	9020.52i	0.366196	+	0.634270i	0.988967	−	0.148134i	$-0.0473266\pi$
$587$	5208.00	+	9020.52i	0.366196	+	0.634270i	−0.622771	+	0.782404i	$0.713993\pi$
$588$		0			0
$589$	−2300.00	+	3983.72i	−0.160900	+	0.278686i
$590$	16200.0			1.13041
$591$		0			0
$592$	603.500	−	1045.29i	0.0418981	−	0.0725697i
$593$	−2061.00			−0.142724			−0.0713618	−	0.997450i	$-0.522734\pi$
$593$	−2061.00			−0.142724			−0.0713618	+	0.997450i	$0.522734\pi$
$594$		0			0
$595$	−999.000	−	1730.32i	−0.0688319	−	0.119220i
$596$	−874.500	−	1514.68i	−0.0601022	−	0.104100i
$597$		0			0
$598$	−234.000	−	810.600i	−0.0160016	−	0.0554313i
$599$	−12456.0			−0.849647			−0.424823	−	0.905276i	$-0.639664\pi$
$599$	−12456.0			−0.849647			−0.424823	+	0.905276i	$0.639664\pi$
$600$		0			0
$601$	390.500	+	676.366i	0.0265039	+	0.0459061i	0.878973	−	0.476871i	$-0.158229\pi$
$601$	390.500	+	676.366i	0.0265039	+	0.0459061i	−0.852469	+	0.522777i	$0.824896\pi$
$602$	−1542.00	+	2670.82i	−0.104397	+	0.180822i
$603$		0			0
$604$	185.000	−	320.429i	0.0124628	−	0.0215862i
$605$	1939.50	−	3359.31i	0.130334	−	0.225745i
$606$		0			0
$607$	−9652.00	+	16717.8i	−0.645408	+	1.11788i	0.338799	+	0.940859i	$0.389979\pi$
$607$	−9652.00	+	16717.8i	−0.645408	+	1.11788i	−0.984207	+	0.177021i	$0.943354\pi$
$608$	1035.00	+	1792.67i	0.0690375	+	0.119576i
$609$		0			0
$610$	−6291.00			−0.417566
$611$	5265.00	−	5471.55i	0.348607	−	0.362283i
$612$		0			0
$613$	−6020.50	−	10427.8i	−0.396681	−	0.687072i	0.596633	−	0.802514i	$-0.296505\pi$
$613$	−6020.50	−	10427.8i	−0.396681	−	0.687072i	−0.993314	+	0.115442i	$0.963172\pi$
$614$	2253.00	+	3902.31i	0.148084	+	0.256489i
$615$		0			0
$616$	−1260.00			−0.0824137
$617$	4858.50	−	8415.17i	0.317011	−	0.549079i	−0.662852	−	0.748751i	$-0.730654\pi$
$617$	4858.50	−	8415.17i	0.317011	−	0.549079i	0.979863	+	0.199671i	$0.0639874\pi$
$618$		0			0
$619$	−21040.0			−1.36619			−0.683093	−	0.730332i	$-0.739366\pi$
$619$	−21040.0			−1.36619			−0.683093	+	0.730332i	$0.739366\pi$
$620$	450.000	−	779.423i	0.0291491	−	0.0504877i
$621$		0			0
$622$	−3159.00	−	5471.55i	−0.203640	−	0.352716i
$623$	−996.000			−0.0640512
$624$		0			0
$625$	−8189.00			−0.524096
$626$	−5847.00	−	10127.3i	−0.373312	−	0.646595i
$627$		0			0
$628$	1305.50	−	2261.19i	0.0829540	−	0.143681i
$629$	1887.00			0.119618
$630$		0			0
$631$	2534.00	−	4389.02i	0.159868	−	0.276900i	−0.774953	−	0.632019i	$-0.782226\pi$
$631$	2534.00	−	4389.02i	0.159868	−	0.276900i	0.934821	+	0.355119i	$0.115560\pi$
$632$	−27804.0			−1.74997
$633$		0			0
$634$	−14026.5	−	24294.6i	−0.878649	−	1.52186i
$635$	2718.00	+	4707.71i	0.169859	+	0.294205i
$636$		0			0
$637$	15424.5	+	3816.57i	0.959405	+	0.237391i
$638$	9450.00			0.586409
$639$		0			0
$640$	7465.50	+	12930.6i	0.461093	+	0.798637i
$641$	5092.50	−	8820.47i	0.313794	−	0.543506i	−0.665387	−	0.746499i	$-0.731733\pi$
$641$	5092.50	−	8820.47i	0.313794	−	0.543506i	0.979180	+	0.202992i	$0.0650667\pi$
$642$		0			0
$643$	−12964.0	+	22454.3i	−0.795101	+	1.37716i	0.127673	+	0.991816i	$0.459249\pi$
$643$	−12964.0	+	22454.3i	−0.795101	+	1.37716i	−0.922775	+	0.385340i	$0.874084\pi$
$644$	−6.00000	+	10.3923i	−0.000367132	+	0.000635892i
$645$		0			0
$646$	−7659.00	+	13265.8i	−0.466470	+	0.807949i
$647$	11580.0	+	20057.1i	0.703643	+	1.21874i	0.967179	+	0.254095i	$0.0817777\pi$
$647$	11580.0	+	20057.1i	0.703643	+	1.21874i	−0.263537	+	0.964649i	$0.584889\pi$
$648$		0			0
$649$	18000.0			1.08869
$650$	−6006.00	−	1486.10i	−0.362423	−	0.0896763i
$651$		0			0
$652$	818.000	+	1416.82i	0.0491340	+	0.0851025i
$653$	8313.00	+	14398.5i	0.498182	+	0.862876i	0.999998	−	0.00209801i	$-0.000667816\pi$
$653$	8313.00	+	14398.5i	0.498182	+	0.862876i	−0.501816	+	0.864974i	$0.667334\pi$
$654$		0			0
$655$	14256.0			0.850424
$656$	8200.50	−	14203.7i	0.488073	−	0.845367i
$657$		0			0
$658$	−972.000			−0.0575874
$659$	−7404.00	+	12824.1i	−0.437661	+	0.758052i	−0.997509	−	0.0705440i	$-0.977526\pi$
$659$	−7404.00	+	12824.1i	−0.437661	+	0.758052i	0.559847	+	0.828596i	$0.310860\pi$
$660$		0			0
$661$	−2426.50	−	4202.82i	−0.142784	−	0.247308i	0.785760	−	0.618531i	$-0.212272\pi$
$661$	−2426.50	−	4202.82i	−0.142784	−	0.247308i	−0.928544	+	0.371223i	$0.878939\pi$
$662$	27516.0			1.61547
$663$		0			0
$664$	−17010.0			−0.994151
$665$	414.000	+	717.069i	0.0241417	+	0.0418147i
$666$		0			0
$667$	−315.000	+	545.596i	−0.0182861	+	0.0316725i
$668$	−264.000			−0.0152911
$669$		0			0
$670$	12501.0	−	21652.4i	0.720829	−	1.24851i
$671$	−6990.00			−0.402155
$672$		0			0
$673$	8082.50	+	13999.3i	0.462938	+	0.801833i	0.999106	−	0.0422789i	$-0.0134618\pi$
$673$	8082.50	+	13999.3i	0.462938	+	0.801833i	−0.536168	+	0.844112i	$0.680128\pi$
$674$	−16633.5	−	28810.1i	−0.950591	−	1.64647i
$675$		0			0
$676$	1943.50	+	1024.51i	0.110577	+	0.0582902i
$677$	25686.0			1.45819			0.729094	−	0.684414i	$-0.239942\pi$
$677$	25686.0			1.45819			0.729094	+	0.684414i	$0.239942\pi$
$678$		0			0
$679$	−1358.00	−	2352.12i	−0.0767530	−	0.132940i
$680$	−10489.5	+	18168.3i	−0.591550	+	1.02459i
$681$		0			0
$682$	4500.00	−	7794.23i	0.252660	−	0.437619i
$683$	−9528.00	+	16503.0i	−0.533790	+	0.924552i	0.465431	+	0.885084i	$0.345900\pi$
$683$	−9528.00	+	16503.0i	−0.533790	+	0.924552i	−0.999221	+	0.0394675i	$0.987434\pi$
$684$		0			0
$685$	3226.50	−	5588.46i	0.179968	−	0.311714i
$686$	−2046.00	−	3543.78i	−0.113873	−	0.197233i
$687$		0			0
$688$	36494.0			2.02227
$689$	−20767.5	+	21582.2i	−1.14830	+	1.19335i
$690$		0			0
$691$	8195.00	+	14194.2i	0.451161	+	0.781434i	0.998458	−	0.0555040i	$-0.0176766\pi$
$691$	8195.00	+	14194.2i	0.451161	+	0.781434i	−0.547297	+	0.836938i	$0.684343\pi$
$692$	705.000	+	1221.10i	0.0387284	+	0.0670796i
$693$		0			0
$694$	29286.0			1.60185
$695$	3690.00	−	6391.27i	0.201395	−	0.348827i
$696$		0			0
$697$	25641.0			1.39343
$698$	−12435.0	+	21538.1i	−0.674315	+	1.16795i
$699$		0			0
$700$	44.0000	+	76.2102i	0.00237578	+	0.00411497i
$701$	27846.0			1.50033			0.750163	−	0.661253i	$-0.229975\pi$
$701$	27846.0			1.50033			0.750163	+	0.661253i	$0.229975\pi$
$702$		0			0
$703$	−782.000			−0.0419540
$704$	6495.00	+	11249.7i	0.347712	+	0.602256i
$705$		0			0
$706$	−18607.5	+	32229.1i	−0.991930	+	1.71807i
$707$	714.000			0.0379812
$708$		0			0
$709$	6141.50	−	10637.4i	0.325316	−	0.563463i	−0.656260	−	0.754534i	$-0.727863\pi$
$709$	6141.50	−	10637.4i	0.325316	−	0.563463i	0.981576	+	0.191071i	$0.0611961\pi$
$710$	−25110.0			−1.32727
$711$		0			0
$712$	5229.00	+	9056.89i	0.275232	+	0.476716i
$713$	300.000	+	519.615i	0.0157575	+	0.0272928i
$714$		0			0
$715$	12285.0	+	3039.75i	0.642564	+	0.158993i
$716$	474.000			0.0247405
$717$		0			0
$718$	1647.00	+	2852.69i	0.0856065	+	0.148275i
$719$	12756.0	−	22094.0i	0.661639	−	1.14599i	−0.318546	−	0.947908i	$-0.603194\pi$
$719$	12756.0	−	22094.0i	0.661639	−	1.14599i	0.980185	−	0.198085i	$-0.0634722\pi$
$720$		0			0
$721$	−1118.00	+	1936.43i	−0.0577483	+	0.100023i
$722$	−7114.50	+	12322.7i	−0.366723	+	0.635184i
$723$		0			0
$724$	−1124.50	+	1947.69i	−0.0577234	+	0.0999798i
$725$	2310.00	+	4001.04i	0.118333	+	0.204958i
$726$		0			0
$727$	6110.00			0.311702			0.155851	−	0.987781i	$-0.450188\pi$
$727$	6110.00			0.311702			0.155851	+	0.987781i	$0.450188\pi$
$728$	546.000	+	1891.40i	0.0277968	+	0.0962911i
$729$		0			0
$730$	−3415.50	−	5915.82i	−0.173169	−	0.299937i
$731$	28527.0	+	49410.2i	1.44338	+	2.50000i
$732$		0			0
$733$	−27127.0			−1.36693			−0.683464	−	0.729984i	$-0.739527\pi$
$733$	−27127.0			−1.36693			−0.683464	+	0.729984i	$0.739527\pi$
$734$	−8601.00	+	14897.4i	−0.432519	+	0.749144i
$735$		0			0
$736$	270.000			0.0135222
$737$	13890.0	−	24058.2i	0.694226	−	1.20244i
$738$		0			0
$739$	440.000	+	762.102i	0.0219021	+	0.0379356i	0.876769	−	0.480912i	$-0.159694\pi$
$739$	440.000	+	762.102i	0.0219021	+	0.0379356i	−0.854867	+	0.518848i	$0.826361\pi$
$740$	153.000			0.00760053
$741$		0			0
$742$	3834.00			0.189691
$743$	−10938.0	−	18945.2i	−0.540076	−	0.935439i	−0.998899	−	0.0469111i	$-0.985062\pi$
$743$	−10938.0	−	18945.2i	−0.540076	−	0.935439i	0.458823	−	0.888528i	$-0.348271\pi$
$744$		0			0
$745$	−7870.50	+	13632.1i	−0.387051	+	0.670392i
$746$	26913.0			1.32085
$747$		0			0
$748$	1665.00	−	2883.86i	0.0813883	−	0.140969i
$749$	−1428.00			−0.0696635
$750$		0			0
$751$	−5899.00	−	10217.4i	−0.286628	−	0.496454i	0.686375	−	0.727248i	$-0.259201\pi$
$751$	−5899.00	−	10217.4i	−0.286628	−	0.496454i	−0.973003	+	0.230794i	$0.925868\pi$
$752$	5751.00	+	9961.02i	0.278880	+	0.483033i
$753$		0			0
$754$	−4095.00	−	14185.5i	−0.197787	−	0.685153i
$755$	−3330.00			−0.160518
$756$		0			0
$757$	4037.00	+	6992.29i	0.193827	+	0.335719i	0.946515	−	0.322658i	$-0.104577\pi$
$757$	4037.00	+	6992.29i	0.193827	+	0.335719i	−0.752688	+	0.658377i	$0.771243\pi$
$758$	10866.0	−	18820.5i	0.520674	−	0.901834i
$759$		0			0
$760$	4347.00	−	7529.22i	0.207477	−	0.359360i
$761$	9777.00	−	16934.3i	0.465724	−	0.806658i	−0.533510	−	0.845794i	$-0.679127\pi$
$761$	9777.00	−	16934.3i	0.465724	−	0.806658i	0.999234	+	0.0391362i	$0.0124606\pi$
$762$		0			0
$763$	−2006.00	+	3474.49i	−0.0951797	+	0.164856i
$764$	1722.00	+	2982.59i	0.0815442	+	0.141239i
$765$		0			0
$766$	−18936.0			−0.893193
$767$	−7800.00	−	27020.0i	−0.367199	−	1.27201i
$768$		0			0
$769$	−7015.00	−	12150.3i	−0.328956	−	0.569769i	0.653349	−	0.757057i	$-0.273364\pi$
$769$	−7015.00	−	12150.3i	−0.328956	−	0.569769i	−0.982305	+	0.187288i	$0.940030\pi$
$770$	−810.000	−	1402.96i	−0.0379096	−	0.0656613i
$771$		0			0
$772$	−4273.00			−0.199208
$773$	18021.0	−	31213.3i	0.838513	−	1.45235i	−0.0526253	−	0.998614i	$-0.516759\pi$
$773$	18021.0	−	31213.3i	0.838513	−	1.45235i	0.891138	−	0.453732i	$-0.149908\pi$
$774$		0			0
$775$	4400.00			0.203939
$776$	−14259.0	+	24697.3i	−0.659624	+	1.14250i
$777$		0			0
$778$	−5440.50	−	9423.22i	−0.250709	−	0.434240i
$779$	−10626.0			−0.488724
$780$		0			0
$781$	−27900.0			−1.27828
$782$	999.000	+	1730.32i	0.0456831	+	0.0791254i
$783$		0			0
$784$	−12034.5	+	20844.4i	−0.548219	+	0.949543i
$785$	−23499.0			−1.06843
$786$		0			0
$787$	−14314.0	+	24792.6i	−0.648334	+	1.12295i	0.335186	+	0.942152i	$0.391201\pi$
$787$	−14314.0	+	24792.6i	−0.648334	+	1.12295i	−0.983521	+	0.180796i	$0.942133\pi$
$788$	1986.00			0.0897821
$789$		0			0
$790$	−17874.0	−	30958.7i	−0.804973	−	1.39425i
$791$	−1119.00	−	1938.16i	−0.0502997	−	0.0871216i
$792$		0			0
$793$	3029.00	+	10492.8i	0.135641	+	0.469873i
$794$	11694.0			0.522676
$795$		0			0
$796$	1193.00	+	2066.34i	0.0531216	+	0.0920092i
$797$	−18717.0	+	32418.8i	−0.831857	+	1.44082i	0.0647067	+	0.997904i	$0.479389\pi$
$797$	−18717.0	+	32418.8i	−0.831857	+	1.44082i	−0.896564	+	0.442915i	$0.853945\pi$
$798$		0			0
$799$	−8991.00	+	15572.9i	−0.398096	+	0.689523i
$800$	990.000	−	1714.73i	0.0437522	−	0.0757811i
$801$		0			0
$802$	8554.50	−	14816.8i	0.376646	−	0.652370i
$803$	−3795.00	−	6573.13i	−0.166778	−	0.288868i
$804$		0			0
$805$	108.000			0.00472857
$806$	−13650.0	−	3377.50i	−0.596527	−	0.147602i
$807$		0			0
$808$	−3748.50	−	6492.59i	−0.163208	−	0.282684i
$809$	18784.5	+	32535.7i	0.816351	+	1.41396i	0.908354	+	0.418202i	$0.137340\pi$
$809$	18784.5	+	32535.7i	0.816351	+	1.41396i	−0.0920030	+	0.995759i	$0.529327\pi$
$810$		0			0
$811$	5516.00			0.238832			0.119416	−	0.992844i	$-0.461898\pi$
$811$	5516.00			0.238832			0.119416	+	0.992844i	$0.461898\pi$
$812$	−105.000	+	181.865i	−0.00453790	+	0.00785988i
$813$		0			0
$814$	1530.00			0.0658802
$815$	7362.00	−	12751.4i	0.316417	−	0.548050i
$816$		0			0
$817$	−11822.0	−	20476.3i	−0.506242	−	0.876836i
$818$	−18933.0			−0.809263
$819$		0			0
$820$	2079.00			0.0885388
$821$	4389.00	+	7601.97i	0.186574	+	0.323155i	0.944106	−	0.329643i	$-0.106928\pi$
$821$	4389.00	+	7601.97i	0.186574	+	0.323155i	−0.757532	+	0.652798i	$0.773595\pi$
$822$		0			0
$823$	1544.00	−	2674.29i	0.0653955	−	0.113268i	−0.831474	−	0.555564i	$-0.812502\pi$
$823$	1544.00	−	2674.29i	0.0653955	−	0.113268i	0.896869	+	0.442296i	$0.145836\pi$
$824$	23478.0			0.992591
$825$		0			0
$826$	−1800.00	+	3117.69i	−0.0758233	+	0.131330i
$827$	−13176.0			−0.554020			−0.277010	−	0.960867i	$-0.589343\pi$
$827$	−13176.0			−0.554020			−0.277010	+	0.960867i	$0.589343\pi$
$828$		0			0
$829$	1179.50	+	2042.95i	0.0494158	+	0.0855907i	0.889675	−	0.456594i	$-0.150931\pi$
$829$	1179.50	+	2042.95i	0.0494158	+	0.0855907i	−0.840259	+	0.542185i	$0.817597\pi$
$830$	−10935.0	−	18940.0i	−0.457300	−	0.792068i
$831$		0			0
$832$	14072.5	−	14624.6i	0.586390	−	0.609394i
$833$	−37629.0			−1.56515
$834$		0			0
$835$	1188.00	+	2057.68i	0.0492364	+	0.0852800i
$836$	−690.000	+	1195.12i	−0.0285456	+	0.0494425i
$837$		0			0
$838$	3492.00	−	6048.32i	0.143949	−	0.249327i
$839$	−1338.00	+	2317.48i	−0.0550571	+	0.0953617i	−0.892240	−	0.451561i	$-0.850867\pi$
$839$	−1338.00	+	2317.48i	−0.0550571	+	0.0953617i	0.837183	+	0.546922i	$0.184201\pi$
$840$		0			0
$841$	6682.00	−	11573.6i	0.273976	−	0.474540i
$842$	3067.50	+	5313.07i	0.125550	+	0.217459i
$843$		0			0
$844$	−1600.00			−0.0652539
$845$	−760.500	−	19758.4i	−0.0309609	−	0.804389i
$846$		0			0
$847$	431.000	+	746.514i	0.0174845	+	0.0302840i
$848$	−22684.5	−	39290.7i	−0.918619	−	1.59109i
$849$		0			0
$850$	14652.0			0.591246
$851$	−51.0000	+	88.3346i	−0.00205436	+	0.00355825i
$852$		0			0
$853$	2477.00			0.0994266			0.0497133	−	0.998764i	$-0.484169\pi$
$853$	2477.00			0.0994266			0.0497133	+	0.998764i	$0.484169\pi$
$854$	699.000	−	1210.70i	0.0280085	−	0.0485122i
$855$		0			0
$856$	7497.00	+	12985.2i	0.299348	+	0.518487i
$857$	17199.0			0.685539			0.342769	−	0.939420i	$-0.388635\pi$
$857$	17199.0			0.685539			0.342769	+	0.939420i	$0.388635\pi$
$858$		0			0
$859$	24338.0			0.966708			0.483354	−	0.875425i	$-0.339418\pi$
$859$	24338.0			0.966708			0.483354	+	0.875425i	$0.339418\pi$
$860$	2313.00	+	4006.23i	0.0917124	+	0.158850i
$861$		0			0
$862$	−7551.00	+	13078.7i	−0.298362	+	0.516778i
$863$	−25146.0			−0.991865			−0.495933	−	0.868361i	$-0.665174\pi$
$863$	−25146.0			−0.991865			−0.495933	+	0.868361i	$0.665174\pi$
$864$		0			0
$865$	6345.00	−	10989.9i	0.249406	−	0.431984i
$866$	−12849.0			−0.504188
$867$		0			0
$868$	100.000	+	173.205i	0.00391039	+	0.00677300i
$869$	−19860.0	−	34398.5i	−0.775264	−	1.34280i
$870$		0			0
$871$	−42133.0	−	10425.2i	−1.63906	−	0.405562i
$872$	42126.0			1.63597
$873$		0			0
$874$	−414.000	−	717.069i	−0.0160226	−	0.0277520i
$875$	1521.00	−	2634.45i	0.0587648	−	0.101784i
$876$		0			0
$877$	−9044.50	+	15665.5i	−0.348245	+	0.603178i	−0.985938	−	0.167113i	$-0.946556\pi$
$877$	−9044.50	+	15665.5i	−0.348245	+	0.603178i	0.637693	+	0.770291i	$0.279889\pi$
$878$	−1959.00	+	3393.09i	−0.0752996	+	0.130423i
$879$		0			0
$880$	−9585.00	+	16601.7i	−0.367171	+	0.635958i
$881$	−7549.50	−	13076.1i	−0.288705	−	0.500052i	0.684796	−	0.728735i	$-0.259891\pi$
$881$	−7549.50	−	13076.1i	−0.288705	−	0.500052i	−0.973501	+	0.228683i	$0.926558\pi$
$882$		0			0
$883$	33488.0			1.27629			0.638143	−	0.769918i	$-0.279703\pi$
$883$	33488.0			1.27629			0.638143	+	0.769918i	$0.279703\pi$
$884$	−5050.50	−	1249.67i	−0.192157	−	0.0475465i
$885$		0			0
$886$	8694.00	+	15058.4i	0.329662	+	0.570992i
$887$	−19884.0	−	34440.1i	−0.752694	−	1.30370i	−0.946513	−	0.322667i	$-0.895421\pi$
$887$	−19884.0	−	34440.1i	−0.752694	−	1.30370i	0.193819	−	0.981037i	$-0.437913\pi$
$888$		0			0
$889$	−1208.00			−0.0455737
$890$	−6723.00	+	11644.6i	−0.253208	+	0.438570i
$891$		0			0
$892$	−3832.00			−0.143840
$893$	3726.00	−	6453.62i	0.139626	−	0.241839i
$894$		0			0
$895$	−2133.00	−	3694.46i	−0.0796629	−	0.137980i
$896$	−3318.00			−0.123713
$897$		0			0
$898$	8118.00			0.301672
$899$	5250.00	+	9093.27i	0.194769	+	0.337350i
$900$		0			0
$901$	35464.5	−	61426.3i	1.31131	−	2.27126i
$902$	20790.0			0.767440
$903$		0			0
$904$	−11749.5	+	20350.7i	−0.432282	+	0.748734i
$905$	20241.0			0.743463
$906$		0			0
$907$	−16078.0	−	27847.9i	−0.588601	−	1.01949i	−0.994416	−	0.105532i	$-0.966346\pi$
$907$	−16078.0	−	27847.9i	−0.588601	−	1.01949i	0.405815	−	0.913955i	$-0.366988\pi$
$908$	−699.000	−	1210.70i	−0.0255475	−	0.0442496i
$909$		0			0
$910$	−1755.00	+	1823.85i	−0.0639315	+	0.0664396i
$911$	−11520.0			−0.418962			−0.209481	−	0.977813i	$-0.567177\pi$
$911$	−11520.0			−0.418962			−0.209481	+	0.977813i	$0.567177\pi$
$912$		0			0
$913$	−12150.0	−	21044.4i	−0.440423	−	0.762835i
$914$	−1243.50	+	2153.81i	−0.0450014	+	0.0779448i
$915$		0			0
$916$	−2233.00	+	3867.67i	−0.0805463	+	0.139510i
$917$	−1584.00	+	2743.57i	−0.0570428	+	0.0988011i
$918$		0			0
$919$	−2476.00	+	4288.56i	−0.0888745	+	0.153935i	−0.907036	−	0.421054i	$-0.861660\pi$
$919$	−2476.00	+	4288.56i	−0.0888745	+	0.153935i	0.818161	+	0.574989i	$0.194994\pi$
$920$	−567.000	−	982.073i	−0.0203190	−	0.0351935i
$921$		0			0
$922$	−16479.0			−0.588619
$923$	12090.0	+	41881.0i	0.431145	+	1.49353i
$924$		0			0
$925$	374.000	+	647.787i	0.0132941	+	0.0230261i
$926$	−23019.0	−	39870.1i	−0.816902	−	1.41492i
$927$		0			0
$928$	4725.00			0.167140
$929$	4390.50	−	7604.57i	0.155057	−	0.268566i	−0.778023	−	0.628236i	$-0.783777\pi$
$929$	4390.50	−	7604.57i	0.155057	−	0.268566i	0.933080	+	0.359670i	$0.117111\pi$
$930$		0			0
$931$	15594.0			0.548950
$932$	−819.000	+	1418.55i	−0.0287846	+	0.0498564i
$933$		0			0
$934$	14391.0	+	24925.9i	0.504163	+	0.873235i
$935$	−29970.0			−1.04826
$936$		0			0
$937$	50039.0			1.74461			0.872307	−	0.488959i	$-0.162623\pi$
$937$	50039.0			1.74461			0.872307	+	0.488959i	$0.162623\pi$
$938$	2778.00	+	4811.64i	0.0967003	+	0.167490i
$939$		0			0
$940$	−729.000	+	1262.67i	−0.0252951	+	0.0438123i
$941$	50670.0			1.75536			0.877681	−	0.479246i	$-0.159090\pi$
$941$	50670.0			1.75536			0.877681	+	0.479246i	$0.159090\pi$
$942$		0			0
$943$	−693.000	+	1200.31i	−0.0239313	+	0.0414502i
$944$	42600.0			1.46876
$945$		0			0
$946$	23130.0	+	40062.3i	0.794948	+	1.37689i
$947$	21192.0	+	36705.6i	0.727188	+	1.25953i	0.958067	+	0.286545i	$0.0925067\pi$
$947$	21192.0	+	36705.6i	0.727188	+	1.25953i	−0.230878	+	0.972983i	$0.574160\pi$
$948$		0			0
$949$	−8222.50	+	8545.07i	−0.281258	+	0.292292i
$950$	−6072.00			−0.207370
$951$		0			0
$952$	−2331.00	−	4037.41i	−0.0793573	−	0.137451i
$953$	−25269.0	+	43767.2i	−0.858912	+	1.48768i	0.0140556	+	0.999901i	$0.495526\pi$
$953$	−25269.0	+	43767.2i	−0.858912	+	1.48768i	−0.872968	+	0.487778i	$0.837808\pi$
$954$		0			0
$955$	15498.0	−	26843.3i	0.525135	−	0.909560i
$956$	−297.000	+	514.419i	−0.0100478	+	0.0174032i
$957$		0			0
$958$	19260.0	−	33359.3i	0.649543	−	1.12504i
$959$	717.000	+	1241.88i	0.0241430	+	0.0418169i
$960$		0			0
$961$	−19791.0			−0.664328
$962$	−663.000	−	2296.70i	−0.0222204	−	0.0769736i
$963$		0			0
$964$	−1151.50	−	1994.46i	−0.0384723	−	0.0666360i
$965$	19228.5	+	33304.7i	0.641438	+	1.11100i
$966$		0			0
$967$	−6886.00			−0.228996			−0.114498	−	0.993423i	$-0.536526\pi$
$967$	−6886.00			−0.228996			−0.114498	+	0.993423i	$0.536526\pi$
$968$	4525.50	−	7838.40i	0.150264	−	0.260264i
$969$		0			0
$970$	−36666.0			−1.21368
$971$	4530.00	−	7846.19i	0.149716	−	0.259316i	−0.781406	−	0.624023i	$-0.785497\pi$
$971$	4530.00	−	7846.19i	0.149716	−	0.259316i	0.931123	+	0.364706i	$0.118831\pi$
$972$		0			0
$973$	820.000	+	1420.28i	0.0270175	+	0.0467956i
$974$	42258.0			1.39018
$975$		0			0
$976$	−16543.0			−0.542550
$977$	−14155.5	−	24518.0i	−0.463536	−	0.802868i	0.535598	−	0.844473i	$-0.320086\pi$
$977$	−14155.5	−	24518.0i	−0.463536	−	0.802868i	−0.999134	+	0.0416052i	$0.986753\pi$
$978$		0			0
$979$	−7470.00	+	12938.4i	−0.243863	+	0.422384i
$980$	−3051.00			−0.0994496
$981$		0			0
$982$	−17541.0	+	30381.9i	−0.570016	+	0.987297i
$983$	−4284.00			−0.139001			−0.0695007	−	0.997582i	$-0.522141\pi$
$983$	−4284.00			−0.139001			−0.0695007	+	0.997582i	$0.522141\pi$
$984$		0			0
$985$	−8937.00	−	15479.3i	−0.289093	−	0.500724i
$986$	17482.5	+	30280.6i	0.564661	+	0.978022i
$987$		0			0
$988$	2093.00	+	517.883i	0.0673960	+	0.0166762i
$989$	−3084.00			−0.0991562
$990$		0			0
$991$	1229.00	+	2128.69i	0.0393950	+	0.0682342i	0.885051	−	0.465495i	$-0.154124\pi$
$991$	1229.00	+	2128.69i	0.0393950	+	0.0682342i	−0.845656	+	0.533729i	$0.820790\pi$
$992$	2250.00	−	3897.11i	0.0720137	−	0.124731i
$993$		0			0
$994$	2790.00	−	4832.42i	0.0890276	−	0.154200i
$995$	10737.0	−	18597.0i	0.342096	−	0.592528i
$996$		0			0
$997$	−12050.5	+	20872.1i	−0.382792	+	0.663014i	−0.991460	−	0.130410i	$-0.958371\pi$
$997$	−12050.5	+	20872.1i	−0.382792	+	0.663014i	0.608669	+	0.793425i	$0.291704\pi$
$998$	−5532.00	−	9581.71i	−0.175463	−	0.303911i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.b.55.1		2
3.2	odd	2		39.4.e.a.16.1	✓	2
12.11	even	2		624.4.q.b.289.1		2
13.3	even	3		1521.4.a.c.1.1		1
13.9	even	3	inner	117.4.g.b.100.1		2
13.10	even	6		1521.4.a.j.1.1		1
39.2	even	12		507.4.b.c.337.1		2
39.11	even	12		507.4.b.c.337.2		2
39.23	odd	6		507.4.a.a.1.1		1
39.29	odd	6		507.4.a.e.1.1		1
39.35	odd	6		39.4.e.a.22.1	yes	2
156.35	even	6		624.4.q.b.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.a.16.1	✓	2	3.2	odd	2
39.4.e.a.22.1	yes	2	39.35	odd	6
117.4.g.b.55.1		2	1.1	even	1	trivial
117.4.g.b.100.1		2	13.9	even	3	inner
507.4.a.a.1.1		1	39.23	odd	6
507.4.a.e.1.1		1	39.29	odd	6
507.4.b.c.337.1		2	39.2	even	12
507.4.b.c.337.2		2	39.11	even	12
624.4.q.b.289.1		2	12.11	even	2
624.4.q.b.529.1		2	156.35	even	6
1521.4.a.c.1.1		1	13.3	even	3
1521.4.a.j.1.1		1	13.10	even	6

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.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +21.0000 q^{8} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +9.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} +21.0000 q^{8} +(13.5000 + 23.3827i) q^{10} +(15.0000 + 25.9808i) q^{11} +(32.5000 - 33.7750i) q^{13} -6.00000 q^{14} +(35.5000 + 61.4878i) q^{16} +(-55.5000 + 96.1288i) q^{17} +(23.0000 - 39.8372i) q^{19} +(-4.50000 + 7.79423i) q^{20} +(-45.0000 + 77.9423i) q^{22} +(-3.00000 - 5.19615i) q^{23} -44.0000 q^{25} +(136.500 + 33.7750i) q^{26} +(-1.00000 - 1.73205i) q^{28} +(-52.5000 - 90.9327i) q^{29} -100.000 q^{31} +(-22.5000 + 38.9711i) q^{32} -333.000 q^{34} +(-9.00000 + 15.5885i) q^{35} +(-8.50000 - 14.7224i) q^{37} +138.000 q^{38} +189.000 q^{40} +(-115.500 - 200.052i) q^{41} +(257.000 - 445.137i) q^{43} -30.0000 q^{44} +(9.00000 - 15.5885i) q^{46} +162.000 q^{47} +(169.500 + 293.583i) q^{49} +(-66.0000 - 114.315i) q^{50} +(13.0000 + 45.0333i) q^{52} -639.000 q^{53} +(135.000 + 233.827i) q^{55} +(-21.0000 + 36.3731i) q^{56} +(157.500 - 272.798i) q^{58} +(300.000 - 519.615i) q^{59} +(-116.500 + 201.784i) q^{61} +(-150.000 - 259.808i) q^{62} +433.000 q^{64} +(292.500 - 303.975i) q^{65} +(-463.000 - 801.940i) q^{67} +(-55.5000 - 96.1288i) q^{68} -54.0000 q^{70} +(-465.000 + 805.404i) q^{71} -253.000 q^{73} +(25.5000 - 44.1673i) q^{74} +(23.0000 + 39.8372i) q^{76} -60.0000 q^{77} -1324.00 q^{79} +(319.500 + 553.390i) q^{80} +(346.500 - 600.156i) q^{82} -810.000 q^{83} +(-499.500 + 865.159i) q^{85} +1542.00 q^{86} +(315.000 + 545.596i) q^{88} +(249.000 + 431.281i) q^{89} +(26.0000 + 90.0666i) q^{91} +6.00000 q^{92} +(243.000 + 420.888i) q^{94} +(207.000 - 358.535i) q^{95} +(-679.000 + 1176.06i) q^{97} +(-508.500 + 880.748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8}+O(q^{10}) \) 2 * q + 3 * q^2 - q^4 + 18 * q^5 - 2 * q^7 + 42 * q^8	\( 2 q + 3 q^{2} - q^{4} + 18 q^{5} - 2 q^{7} + 42 q^{8} + 27 q^{10} + 30 q^{11} + 65 q^{13} - 12 q^{14} + 71 q^{16} - 111 q^{17} + 46 q^{19} - 9 q^{20} - 90 q^{22} - 6 q^{23} - 88 q^{25} + 273 q^{26} - 2 q^{28} - 105 q^{29} - 200 q^{31} - 45 q^{32} - 666 q^{34} - 18 q^{35} - 17 q^{37} + 276 q^{38} + 378 q^{40} - 231 q^{41} + 514 q^{43} - 60 q^{44} + 18 q^{46} + 324 q^{47} + 339 q^{49} - 132 q^{50} + 26 q^{52} - 1278 q^{53} + 270 q^{55} - 42 q^{56} + 315 q^{58} + 600 q^{59} - 233 q^{61} - 300 q^{62} + 866 q^{64} + 585 q^{65} - 926 q^{67} - 111 q^{68} - 108 q^{70} - 930 q^{71} - 506 q^{73} + 51 q^{74} + 46 q^{76} - 120 q^{77} - 2648 q^{79} + 639 q^{80} + 693 q^{82} - 1620 q^{83} - 999 q^{85} + 3084 q^{86} + 630 q^{88} + 498 q^{89} + 52 q^{91} + 12 q^{92} + 486 q^{94} + 414 q^{95} - 1358 q^{97} - 1017 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - q^4 + 18 * q^5 - 2 * q^7 + 42 * q^8 + 27 * q^10 + 30 * q^11 + 65 * q^13 - 12 * q^14 + 71 * q^16 - 111 * q^17 + 46 * q^19 - 9 * q^20 - 90 * q^22 - 6 * q^23 - 88 * q^25 + 273 * q^26 - 2 * q^28 - 105 * q^29 - 200 * q^31 - 45 * q^32 - 666 * q^34 - 18 * q^35 - 17 * q^37 + 276 * q^38 + 378 * q^40 - 231 * q^41 + 514 * q^43 - 60 * q^44 + 18 * q^46 + 324 * q^47 + 339 * q^49 - 132 * q^50 + 26 * q^52 - 1278 * q^53 + 270 * q^55 - 42 * q^56 + 315 * q^58 + 600 * q^59 - 233 * q^61 - 300 * q^62 + 866 * q^64 + 585 * q^65 - 926 * q^67 - 111 * q^68 - 108 * q^70 - 930 * q^71 - 506 * q^73 + 51 * q^74 + 46 * q^76 - 120 * q^77 - 2648 * q^79 + 639 * q^80 + 693 * q^82 - 1620 * q^83 - 999 * q^85 + 3084 * q^86 + 630 * q^88 + 498 * q^89 + 52 * q^91 + 12 * q^92 + 486 * q^94 + 414 * q^95 - 1358 * q^97 - 1017 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more