LMFDB - Embedded newform 117.4.q.a.82.1

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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{2} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(-12.0000 + 6.92820i) q^{7} +22.5167i q^{8} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{2} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(-12.0000 + 6.92820i) q^{7} +22.5167i q^{8} +(1.50000 - 2.59808i) q^{10} +(-12.0000 - 6.92820i) q^{11} +(45.5000 + 11.2583i) q^{13} +24.0000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(58.5000 + 101.325i) q^{17} +(-99.0000 + 57.1577i) q^{19} +(7.50000 - 4.33013i) q^{20} +(12.0000 + 20.7846i) q^{22} +(-39.0000 + 67.5500i) q^{23} +122.000 q^{25} +(-58.5000 - 56.2917i) q^{26} +(60.0000 + 34.6410i) q^{28} +(-70.5000 + 122.110i) q^{29} +155.885i q^{31} +(157.500 - 90.9327i) q^{32} -202.650i q^{34} +(-12.0000 - 20.7846i) q^{35} +(-124.500 - 71.8801i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(-235.500 - 135.966i) q^{41} +(-52.0000 - 90.0666i) q^{43} +69.2820i q^{44} +(117.000 - 67.5500i) q^{46} -301.377i q^{47} +(-75.5000 + 130.770i) q^{49} +(-183.000 - 105.655i) q^{50} +(-65.0000 - 225.167i) q^{52} -93.0000 q^{53} +(12.0000 - 20.7846i) q^{55} +(-156.000 - 270.200i) q^{56} +(211.500 - 122.110i) q^{58} +(246.000 - 142.028i) q^{59} +(-72.5000 - 125.574i) q^{61} +(135.000 - 233.827i) q^{62} -307.000 q^{64} +(-19.5000 + 78.8083i) q^{65} +(-681.000 - 393.176i) q^{67} +(292.500 - 506.625i) q^{68} +41.5692i q^{70} +(-915.000 + 528.275i) q^{71} +458.993i q^{73} +(124.500 + 215.640i) q^{74} +(495.000 + 285.788i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(-1.50000 - 0.866025i) q^{80} +(235.500 + 407.898i) q^{82} +789.815i q^{83} +(-175.500 + 101.325i) q^{85} +180.133i q^{86} +(156.000 - 270.200i) q^{88} +(846.000 + 488.438i) q^{89} +(-624.000 + 180.133i) q^{91} +390.000 q^{92} +(-261.000 + 452.065i) q^{94} +(-99.0000 - 171.473i) q^{95} +(174.000 - 100.459i) q^{97} +(226.500 - 130.770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7}+O(q^{10}) $ 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7	$ 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7} + 3 q^{10} - 24 q^{11} + 91 q^{13} + 48 q^{14} - q^{16} + 117 q^{17} - 198 q^{19} + 15 q^{20} + 24 q^{22} - 78 q^{23} + 244 q^{25} - 117 q^{26} + 120 q^{28} - 141 q^{29} + 315 q^{32} - 24 q^{35} - 249 q^{37} + 396 q^{38} - 78 q^{40} - 471 q^{41} - 104 q^{43} + 234 q^{46} - 151 q^{49} - 366 q^{50} - 130 q^{52} - 186 q^{53} + 24 q^{55} - 312 q^{56} + 423 q^{58} + 492 q^{59} - 145 q^{61} + 270 q^{62} - 614 q^{64} - 39 q^{65} - 1362 q^{67} + 585 q^{68} - 1830 q^{71} + 249 q^{74} + 990 q^{76} + 384 q^{77} + 2552 q^{79} - 3 q^{80} + 471 q^{82} - 351 q^{85} + 312 q^{88} + 1692 q^{89} - 1248 q^{91} + 780 q^{92} - 522 q^{94} - 198 q^{95} + 348 q^{97} + 453 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7 + 3 * q^10 - 24 * q^11 + 91 * q^13 + 48 * q^14 - q^16 + 117 * q^17 - 198 * q^19 + 15 * q^20 + 24 * q^22 - 78 * q^23 + 244 * q^25 - 117 * q^26 + 120 * q^28 - 141 * q^29 + 315 * q^32 - 24 * q^35 - 249 * q^37 + 396 * q^38 - 78 * q^40 - 471 * q^41 - 104 * q^43 + 234 * q^46 - 151 * q^49 - 366 * q^50 - 130 * q^52 - 186 * q^53 + 24 * q^55 - 312 * q^56 + 423 * q^58 + 492 * q^59 - 145 * q^61 + 270 * q^62 - 614 * q^64 - 39 * q^65 - 1362 * q^67 + 585 * q^68 - 1830 * q^71 + 249 * q^74 + 990 * q^76 + 384 * q^77 + 2552 * q^79 - 3 * q^80 + 471 * q^82 - 351 * q^85 + 312 * q^88 + 1692 * q^89 - 1248 * q^91 + 780 * q^92 - 522 * q^94 - 198 * q^95 + 348 * q^97 + 453 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.50000	−	0.866025i	−0.530330	−	0.306186i	0.210821	−	0.977525i	$-0.432386\pi$
$2$	−1.50000	−	0.866025i	−0.530330	−	0.306186i	−0.741151	+	0.671339i	$0.765720\pi$
$3$		0			0
$3$		0			0
$4$	−2.50000	−	4.33013i	−0.312500	−	0.541266i
$5$			1.73205i			0.154919i	0.996995	+	0.0774597i	$0.0246809\pi$
$5$			1.73205i			0.154919i	−0.996995	+	0.0774597i	$0.975319\pi$
$6$		0			0
$7$	−12.0000	+	6.92820i	−0.647939	+	0.374088i	−0.787666	−	0.616102i	$-0.788711\pi$
$7$	−12.0000	+	6.92820i	−0.647939	+	0.374088i	0.139727	+	0.990190i	$0.455377\pi$
$8$			22.5167i			0.995105i
$9$		0			0
$10$	1.50000	−	2.59808i	0.0474342	−	0.0821584i
$11$	−12.0000	−	6.92820i	−0.328921	−	0.189903i	0.326441	−	0.945218i	$-0.394151\pi$
$11$	−12.0000	−	6.92820i	−0.328921	−	0.189903i	−0.655362	+	0.755315i	$0.727484\pi$
$12$		0			0
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$14$	24.0000			0.458162
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.00781250	+	0.0135316i
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	0.894349	+	0.447369i	$0.147639\pi$
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	−0.0597414	+	0.998214i	$0.519028\pi$
$18$		0			0
$19$	−99.0000	+	57.1577i	−1.19538	+	0.690151i	−0.959521	−	0.281637i	$-0.909123\pi$
$19$	−99.0000	+	57.1577i	−1.19538	+	0.690151i	−0.235856	+	0.971788i	$0.575789\pi$
$20$	7.50000	−	4.33013i	0.0838525	−	0.0484123i
$21$		0			0
$22$	12.0000	+	20.7846i	0.116291	+	0.201422i
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	−0.986872	−	0.161506i	$-0.948365\pi$
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	0.633304	+	0.773903i	$0.281698\pi$
$24$		0			0
$25$	122.000			0.976000
$26$	−58.5000	−	56.2917i	−0.441261	−	0.424604i
$27$		0			0
$28$	60.0000	+	34.6410i	0.404962	+	0.233805i
$29$	−70.5000	+	122.110i	−0.451432	+	0.781903i	−0.998475	−	0.0552014i	$-0.982420\pi$
$29$	−70.5000	+	122.110i	−0.451432	+	0.781903i	0.547043	+	0.837104i	$0.315753\pi$
$30$		0			0
$31$			155.885i			0.903151i	0.892233	+	0.451576i	$0.149138\pi$
$31$			155.885i			0.903151i	−0.892233	+	0.451576i	$0.850862\pi$
$32$	157.500	−	90.9327i	0.870073	−	0.502337i
$33$		0			0
$34$		−	202.650i		−	1.02218i
$35$	−12.0000	−	20.7846i	−0.0579534	−	0.100378i
$36$		0			0
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	0.197223	−	0.980359i	$-0.436808\pi$
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	−0.750404	+	0.660980i	$0.770141\pi$
$38$	198.000			0.845259
$39$		0			0
$40$	−39.0000			−0.154161
$41$	−235.500	−	135.966i	−0.897047	−	0.517910i	−0.0208059	−	0.999784i	$-0.506623\pi$
$41$	−235.500	−	135.966i	−0.897047	−	0.517910i	−0.876241	+	0.481873i	$0.839957\pi$
$42$		0			0
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	0.758963	−	0.651134i	$-0.225706\pi$
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	−0.943380	+	0.331714i	$0.892373\pi$
$44$			69.2820i			0.237379i
$45$		0			0
$46$	117.000	−	67.5500i	0.375015	−	0.216515i
$47$		−	301.377i		−	0.935326i	−0.883907	−	0.467663i	$-0.845096\pi$
$47$		−	301.377i		−	0.935326i	0.883907	−	0.467663i	$-0.154904\pi$
$48$		0			0
$49$	−75.5000	+	130.770i	−0.220117	+	0.381253i
$50$	−183.000	−	105.655i	−0.517602	−	0.298838i
$51$		0			0
$52$	−65.0000	−	225.167i	−0.173344	−	0.600481i
$53$	−93.0000			−0.241029			−0.120514	−	0.992712i	$-0.538454\pi$
$53$	−93.0000			−0.241029			−0.120514	+	0.992712i	$0.538454\pi$
$54$		0			0
$55$	12.0000	−	20.7846i	0.0294196	−	0.0509563i
$56$	−156.000	−	270.200i	−0.372257	−	0.644768i
$57$		0			0
$58$	211.500	−	122.110i	0.478816	−	0.276444i
$59$	246.000	−	142.028i	0.542822	−	0.313398i	−0.203400	−	0.979096i	$-0.565199\pi$
$59$	246.000	−	142.028i	0.542822	−	0.313398i	0.746222	+	0.665698i	$0.231866\pi$
$60$		0			0
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$	135.000	−	233.827i	0.276533	−	0.478968i
$63$		0			0
$64$	−307.000			−0.599609
$65$	−19.5000	+	78.8083i	−0.0372104	+	0.150384i
$66$		0			0
$67$	−681.000	−	393.176i	−1.24175	−	0.716926i	−0.272301	−	0.962212i	$-0.587785\pi$
$67$	−681.000	−	393.176i	−1.24175	−	0.716926i	−0.969451	+	0.245286i	$0.921118\pi$
$68$	292.500	−	506.625i	0.521630	−	0.903490i
$69$		0			0
$70$			41.5692i			0.0709782i
$71$	−915.000	+	528.275i	−1.52944	+	0.883025i	−0.530059	+	0.847961i	$0.677830\pi$
$71$	−915.000	+	528.275i	−1.52944	+	0.883025i	−0.999385	+	0.0350641i	$0.988836\pi$
$72$		0			0
$73$			458.993i			0.735906i	0.929844	+	0.367953i	$0.119941\pi$
$73$			458.993i			0.735906i	−0.929844	+	0.367953i	$0.880059\pi$
$74$	124.500	+	215.640i	0.195579	+	0.338752i
$75$		0			0
$76$	495.000	+	285.788i	0.747110	+	0.431344i
$77$	192.000			0.284161
$78$		0			0
$79$	1276.00			1.81723			0.908615	−	0.417634i	$-0.137141\pi$
$79$	1276.00			1.81723			0.908615	+	0.417634i	$0.137141\pi$
$80$	−1.50000	−	0.866025i	−0.00209631	−	0.00121031i
$81$		0			0
$82$	235.500	+	407.898i	0.317154	+	0.549327i
$83$			789.815i			1.04450i	0.852793	+	0.522250i	$0.174907\pi$
$83$			789.815i			1.04450i	−0.852793	+	0.522250i	$0.825093\pi$
$84$		0			0
$85$	−175.500	+	101.325i	−0.223949	+	0.129297i
$86$			180.133i			0.225864i
$87$		0			0
$88$	156.000	−	270.200i	0.188973	−	0.327311i
$89$	846.000	+	488.438i	1.00759	+	0.581734i	0.910486	−	0.413540i	$-0.135708\pi$
$89$	846.000	+	488.438i	1.00759	+	0.581734i	0.0971073	+	0.995274i	$0.469041\pi$
$90$		0			0
$91$	−624.000	+	180.133i	−0.718824	+	0.207507i
$92$	390.000			0.441960
$93$		0			0
$94$	−261.000	+	452.065i	−0.286384	+	0.496032i
$95$	−99.0000	−	171.473i	−0.106918	−	0.185187i
$96$		0			0
$97$	174.000	−	100.459i	0.182134	−	0.105155i	−0.406161	−	0.913802i	$-0.633133\pi$
$97$	174.000	−	100.459i	0.182134	−	0.105155i	0.588295	+	0.808646i	$0.299799\pi$
$98$	226.500	−	130.770i	0.233469	−	0.134793i
$99$		0			0
$100$	−305.000	−	528.275i	−0.305000	−	0.528275i
$101$	214.500	−	371.525i	0.211322	−	0.366021i	−0.740806	−	0.671719i	$-0.765556\pi$
$101$	214.500	−	371.525i	0.211322	−	0.366021i	0.952129	+	0.305698i	$0.0988897\pi$
$102$		0			0
$103$	182.000			0.174107			0.0870534	−	0.996204i	$-0.472255\pi$
$103$	182.000			0.174107			0.0870534	+	0.996204i	$0.472255\pi$
$104$	−253.500	+	1024.51i	−0.239017	+	0.965974i
$105$		0			0
$106$	139.500	+	80.5404i	0.127825	+	0.0737997i
$107$	−753.000	+	1304.23i	−0.680330	+	1.17837i	0.294551	+	0.955636i	$0.404830\pi$
$107$	−753.000	+	1304.23i	−0.680330	+	1.17837i	−0.974880	+	0.222729i	$0.928503\pi$
$108$		0			0
$109$			1551.92i			1.36373i	0.731477	+	0.681866i	$0.238831\pi$
$109$			1551.92i			1.36373i	−0.731477	+	0.681866i	$0.761169\pi$
$110$	−36.0000	+	20.7846i	−0.0312042	+	0.0180158i
$111$		0			0
$112$		−	13.8564i		−	0.0116902i
$113$	−343.500	−	594.959i	−0.285962	−	0.495302i	0.686880	−	0.726771i	$-0.258980\pi$
$113$	−343.500	−	594.959i	−0.285962	−	0.495302i	−0.972842	+	0.231470i	$0.925647\pi$
$114$		0			0
$115$	−117.000	−	67.5500i	−0.0948722	−	0.0547745i
$116$	705.000			0.564290
$117$		0			0
$118$	−492.000			−0.383833
$119$	−1404.00	−	810.600i	−1.08155	−	0.624433i
$120$		0			0
$121$	−569.500	−	986.403i	−0.427874	−	0.741099i
$122$			251.147i			0.186376i
$123$		0			0
$124$	675.000	−	389.711i	0.488845	−	0.282235i
$125$			427.817i			0.306121i
$126$		0			0
$127$	−143.000	+	247.683i	−0.0999149	+	0.173058i	−0.911649	−	0.410969i	$-0.865190\pi$
$127$	−143.000	+	247.683i	−0.0999149	+	0.173058i	0.811734	+	0.584027i	$0.198524\pi$
$128$	−799.500	−	461.592i	−0.552082	−	0.318745i
$129$		0			0
$130$	97.5000	−	101.325i	0.0657794	−	0.0683599i
$131$	1974.00			1.31656			0.658279	−	0.752774i	$-0.271285\pi$
$131$	1974.00			1.31656			0.658279	+	0.752774i	$0.271285\pi$
$132$		0			0
$133$	792.000	−	1371.78i	0.516354	−	0.894352i
$134$	681.000	+	1179.53i	0.439026	+	0.760415i
$135$		0			0
$136$	−2281.50	+	1317.22i	−1.43851	+	0.830523i
$137$	733.500	−	423.486i	0.457424	−	0.264094i	−0.253536	−	0.967326i	$-0.581594\pi$
$137$	733.500	−	423.486i	0.457424	−	0.264094i	0.710961	+	0.703232i	$0.248260\pi$
$138$		0			0
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	0.827775	−	0.561060i	$-0.189606\pi$
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	−0.899780	+	0.436344i	$0.856273\pi$
$140$	−60.0000	+	103.923i	−0.0362209	+	0.0627364i
$141$		0			0
$142$	1830.00			1.08148
$143$	−468.000	−	450.333i	−0.273679	−	0.263348i
$144$		0			0
$145$	−211.500	−	122.110i	−0.121132	−	0.0699355i
$146$	397.500	−	688.490i	0.225324	−	0.390273i
$147$		0			0
$148$			718.801i			0.399224i
$149$	40.5000	−	23.3827i	0.0222677	−	0.0128563i	−0.488825	−	0.872382i	$-0.662574\pi$
$149$	40.5000	−	23.3827i	0.0222677	−	0.0128563i	0.511093	+	0.859526i	$0.329241\pi$
$150$		0			0
$151$		−	1770.16i		−	0.953995i	−0.878905	−	0.476998i	$-0.841725\pi$
$151$		−	1770.16i		−	0.953995i	0.878905	−	0.476998i	$-0.158275\pi$
$152$	−1287.00	−	2229.15i	−0.686773	−	1.18953i
$153$		0			0
$154$	−288.000	−	166.277i	−0.150699	−	0.0870063i
$155$	−270.000			−0.139916
$156$		0			0
$157$	1211.00			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$157$	1211.00			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$158$	−1914.00	−	1105.05i	−0.963732	−	0.556411i
$159$		0			0
$160$	157.500	+	272.798i	0.0778217	+	0.134791i
$161$		−	1080.80i		−	0.529062i
$162$		0			0
$163$	−870.000	+	502.295i	−0.418059	+	0.241367i	−0.694247	−	0.719737i	$-0.744262\pi$
$163$	−870.000	+	502.295i	−0.418059	+	0.241367i	0.276187	+	0.961104i	$0.410929\pi$
$164$			1359.66i			0.647388i
$165$		0			0
$166$	684.000	−	1184.72i	0.319811	−	0.553930i
$167$	−792.000	−	457.261i	−0.366987	−	0.211880i	0.305154	−	0.952303i	$-0.401292\pi$
$167$	−792.000	−	457.261i	−0.366987	−	0.211880i	−0.672141	+	0.740423i	$0.734625\pi$
$168$		0			0
$169$	1943.50	+	1024.51i	0.884615	+	0.466321i
$170$	351.000			0.158356
$171$		0			0
$172$	−260.000	+	450.333i	−0.115261	+	0.199637i
$173$	1287.00	+	2229.15i	0.565600	+	0.979648i	0.996994	+	0.0774841i	$0.0246887\pi$
$173$	1287.00	+	2229.15i	0.565600	+	0.979648i	−0.431394	+	0.902164i	$0.641978\pi$
$174$		0			0
$175$	−1464.00	+	845.241i	−0.632389	+	0.365110i
$176$	12.0000	−	6.92820i	0.00513940	−	0.00296723i
$177$		0			0
$178$	−846.000	−	1465.31i	−0.356238	−	0.617022i
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	−0.149290	−	0.988793i	$-0.547699\pi$
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	0.930965	−	0.365108i	$-0.118968\pi$
$180$		0			0
$181$	−637.000			−0.261590			−0.130795	−	0.991409i	$-0.541753\pi$
$181$	−637.000			−0.261590			−0.130795	+	0.991409i	$0.541753\pi$
$182$	1092.00	+	270.200i	0.444750	+	0.110047i
$183$		0			0
$184$	−1521.00	−	878.150i	−0.609400	−	0.351837i
$185$	124.500	−	215.640i	0.0494780	−	0.0856983i
$186$		0			0
$187$		−	1621.20i		−	0.633978i
$188$	−1305.00	+	753.442i	−0.506260	+	0.292289i
$189$		0			0
$190$			342.946i			0.130947i
$191$	−1299.00	−	2249.93i	−0.492106	−	0.852353i	0.507852	−	0.861444i	$-0.330440\pi$
$191$	−1299.00	−	2249.93i	−0.492106	−	0.852353i	−0.999959	+	0.00909077i	$0.997106\pi$
$192$		0			0
$193$	967.500	+	558.586i	0.360840	+	0.208331i	0.669449	−	0.742858i	$-0.266530\pi$
$193$	967.500	+	558.586i	0.360840	+	0.208331i	−0.308609	+	0.951189i	$0.599863\pi$
$194$	−348.000			−0.128788
$195$		0			0
$196$	755.000			0.275146
$197$	−1776.00	−	1025.37i	−0.642308	−	0.370837i	0.143195	−	0.989695i	$-0.454262\pi$
$197$	−1776.00	−	1025.37i	−0.642308	−	0.370837i	−0.785503	+	0.618858i	$0.787596\pi$
$198$		0			0
$199$	1261.00	+	2184.12i	0.449196	+	0.778030i	0.998334	−	0.0577019i	$-0.0183773\pi$
$199$	1261.00	+	2184.12i	0.449196	+	0.778030i	−0.549138	+	0.835732i	$0.685044\pi$
$200$			2747.03i			0.971223i
$201$		0			0
$202$	−643.500	+	371.525i	−0.224141	+	0.129408i
$203$		−	1953.75i		−	0.675500i
$204$		0			0
$205$	235.500	−	407.898i	0.0802343	−	0.138970i
$206$	−273.000	−	157.617i	−0.0923340	−	0.0533091i
$207$		0			0
$208$	−32.5000	+	33.7750i	−0.0108340	+	0.0112590i
$209$	1584.00			0.524247
$210$		0			0
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	−0.938415	−	0.345511i	$-0.887706\pi$
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	0.768428	+	0.639936i	$0.221039\pi$
$212$	232.500	+	402.702i	0.0753215	+	0.130461i
$213$		0			0
$214$	2259.00	−	1304.23i	0.721598	−	0.416615i
$215$	156.000	−	90.0666i	0.0494842	−	0.0285697i
$216$		0			0
$217$	−1080.00	−	1870.61i	−0.337858	−	0.585187i
$218$	1344.00	−	2327.88i	0.417556	−	0.723228i
$219$		0			0
$220$	−120.000			−0.0367745
$221$	1521.00	+	5268.90i	0.462957	+	1.60373i
$222$		0			0
$223$	−2085.00	−	1203.78i	−0.626107	−	0.361483i	0.153136	−	0.988205i	$-0.451063\pi$
$223$	−2085.00	−	1203.78i	−0.626107	−	0.361483i	−0.779243	+	0.626722i	$0.784396\pi$
$224$	−1260.00	+	2182.38i	−0.375836	+	0.650967i
$225$		0			0
$226$			1189.92i			0.350231i
$227$	−2085.00	+	1203.78i	−0.609631	+	0.351971i	−0.772821	−	0.634624i	$-0.781155\pi$
$227$	−2085.00	+	1203.78i	−0.609631	+	0.351971i	0.163190	+	0.986595i	$0.447822\pi$
$228$		0			0
$229$			2508.01i			0.723729i	0.932231	+	0.361864i	$0.117860\pi$
$229$			2508.01i			0.723729i	−0.932231	+	0.361864i	$0.882140\pi$
$230$	117.000	+	202.650i	0.0335424	+	0.0580971i
$231$		0			0
$232$	−2749.50	−	1587.42i	−0.778076	−	0.449222i
$233$	5850.00			1.64483			0.822417	−	0.568885i	$-0.192625\pi$
$233$	5850.00			1.64483			0.822417	+	0.568885i	$0.192625\pi$
$234$		0			0
$235$	522.000			0.144900
$236$	−1230.00	−	710.141i	−0.339263	−	0.195874i
$237$		0			0
$238$	1404.00	+	2431.80i	0.382386	+	0.662312i
$239$			5383.21i			1.45695i	0.685072	+	0.728475i	$0.259771\pi$
$239$			5383.21i			1.45695i	−0.685072	+	0.728475i	$0.740229\pi$
$240$		0			0
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.192240	−	0.981348i	$-0.438425\pi$
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.945992	+	0.324189i	$0.105091\pi$
$242$			1972.81i			0.524036i
$243$		0			0
$244$	−362.500	+	627.868i	−0.0951094	+	0.164734i
$245$	−226.500	−	130.770i	−0.0590635	−	0.0341003i
$246$		0			0
$247$	−5148.00	+	1486.10i	−1.32615	+	0.382827i
$248$	−3510.00			−0.898731
$249$		0			0
$250$	370.500	−	641.725i	0.0937299	−	0.162345i
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	−1.00000		0.000205037i	$-0.999935\pi$
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	0.499822	−	0.866128i	$-0.333399\pi$
$252$		0			0
$253$	936.000	−	540.400i	0.232592	−	0.134287i
$254$	429.000	−	247.683i	0.105976	−	0.0611852i
$255$		0			0
$256$	2027.50	+	3511.73i	0.494995	+	0.857357i
$257$	1033.50	−	1790.07i	0.250848	−	0.434482i	−0.712911	−	0.701254i	$-0.752624\pi$
$257$	1033.50	−	1790.07i	0.250848	−	0.434482i	0.963760	+	0.266772i	$0.0859572\pi$
$258$		0			0
$259$	1992.00			0.477903
$260$	390.000	−	112.583i	0.0930261	−	0.0268543i
$261$		0			0
$262$	−2961.00	−	1709.53i	−0.698211	−	0.403112i
$263$	−1026.00	+	1777.08i	−0.240555	+	0.416653i	−0.960872	−	0.276991i	$-0.910663\pi$
$263$	−1026.00	+	1777.08i	−0.240555	+	0.416653i	0.720318	+	0.693644i	$0.243996\pi$
$264$		0			0
$265$		−	161.081i		−	0.0373400i
$266$	−2376.00	+	1371.78i	−0.547676	+	0.316201i
$267$		0			0
$268$			3931.76i			0.896157i
$269$	1665.00	+	2883.86i	0.377386	+	0.653652i	0.990681	−	0.136202i	$-0.0434897\pi$
$269$	1665.00	+	2883.86i	0.377386	+	0.653652i	−0.613295	+	0.789854i	$0.710156\pi$
$270$		0			0
$271$	2430.00	+	1402.96i	0.544694	+	0.314479i	0.746979	−	0.664848i	$-0.231504\pi$
$271$	2430.00	+	1402.96i	0.544694	+	0.314479i	−0.202285	+	0.979327i	$0.564837\pi$
$272$	−117.000			−0.0260815
$273$		0			0
$274$	−1467.00			−0.323448
$275$	−1464.00	−	845.241i	−0.321027	−	0.185345i
$276$		0			0
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	0.844857	−	0.534992i	$-0.179685\pi$
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	−0.885745	+	0.464172i	$0.846352\pi$
$278$			408.764i			0.0881872i
$279$		0			0
$280$	468.000	−	270.200i	0.0998870	−	0.0576698i
$281$			36.3731i			0.00772183i	0.999993	+	0.00386092i	$0.00122897\pi$
$281$			36.3731i			0.00772183i	−0.999993	+	0.00386092i	$0.998771\pi$
$282$		0			0
$283$	3562.00	−	6169.56i	0.748194	−	1.29591i	−0.200493	−	0.979695i	$-0.564255\pi$
$283$	3562.00	−	6169.56i	0.748194	−	1.29591i	0.948688	−	0.316215i	$-0.102412\pi$
$284$	4575.00	+	2641.38i	0.955902	+	0.551891i
$285$		0			0
$286$	312.000	+	1080.80i	0.0645068	+	0.223458i
$287$	3768.00			0.774976
$288$		0			0
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$	211.500	+	366.329i	0.0428266	+	0.0741778i
$291$		0			0
$292$	1987.50	−	1147.48i	0.398321	−	0.229971i
$293$	7207.50	−	4161.25i	1.43709	−	0.829703i	0.439441	−	0.898271i	$-0.355177\pi$
$293$	7207.50	−	4161.25i	1.43709	−	0.829703i	0.997646	+	0.0685685i	$0.0218432\pi$
$294$		0			0
$295$	246.000	+	426.084i	0.0485514	+	0.0840936i
$296$	1618.50	−	2803.32i	0.317816	−	0.550473i
$297$		0			0
$298$	−81.0000			−0.0157457
$299$	−2535.00	+	2634.45i	−0.490310	+	0.509546i
$300$		0			0
$301$	1248.00	+	720.533i	0.238982	+	0.137976i
$302$	−1533.00	+	2655.23i	−0.292100	+	0.505932i
$303$		0			0
$304$		−	114.315i		−	0.0215672i
$305$	217.500	−	125.574i	0.0408328	−	0.0235748i
$306$		0			0
$307$		−	2220.49i		−	0.412801i	−0.978468	−	0.206401i	$-0.933825\pi$
$307$		−	2220.49i		−	0.412801i	0.978468	−	0.206401i	$-0.0661750\pi$
$308$	−480.000	−	831.384i	−0.0888004	−	0.153807i
$309$		0			0
$310$	405.000	+	233.827i	0.0742015	+	0.0428402i
$311$	−4914.00			−0.895972			−0.447986	−	0.894041i	$-0.647859\pi$
$311$	−4914.00			−0.895972			−0.447986	+	0.894041i	$0.647859\pi$
$312$		0			0
$313$	−518.000			−0.0935434			−0.0467717	−	0.998906i	$-0.514893\pi$
$313$	−518.000			−0.0935434			−0.0467717	+	0.998906i	$0.514893\pi$
$314$	−1816.50	−	1048.76i	−0.326468	−	0.188487i
$315$		0			0
$316$	−3190.00	−	5525.24i	−0.567885	−	0.983605i
$317$		−	3916.17i		−	0.693861i	−0.937891	−	0.346930i	$-0.887224\pi$
$317$		−	3916.17i		−	0.693861i	0.937891	−	0.346930i	$-0.112776\pi$
$318$		0			0
$319$	1692.00	−	976.877i	0.296971	−	0.171456i
$320$		−	531.740i		−	0.0928911i
$321$		0			0
$322$	−936.000	+	1621.20i	−0.161991	+	0.280577i
$323$	−11583.0	−	6687.45i	−1.99534	−	1.15201i
$324$		0			0
$325$	5551.00	+	1373.52i	0.947428	+	0.234428i
$326$	1740.00			0.295613
$327$		0			0
$328$	3061.50	−	5302.67i	0.515375	−	0.892656i
$329$	2088.00	+	3616.52i	0.349894	+	0.606034i
$330$		0			0
$331$	−6456.00	+	3727.37i	−1.07207	+	0.618958i	−0.928745	−	0.370719i	$-0.879111\pi$
$331$	−6456.00	+	3727.37i	−1.07207	+	0.618958i	−0.143321	+	0.989676i	$0.545778\pi$
$332$	3420.00	−	1974.54i	0.565352	−	0.326406i
$333$		0			0
$334$	792.000	+	1371.78i	0.129749	+	0.224733i
$335$	681.000	−	1179.53i	0.111066	−	0.192371i
$336$		0			0
$337$	−3575.00			−0.577871			−0.288936	−	0.957349i	$-0.593301\pi$
$337$	−3575.00			−0.577871			−0.288936	+	0.957349i	$0.593301\pi$
$338$	−2028.00	−	3219.88i	−0.326357	−	0.518161i
$339$		0			0
$340$	877.500	+	506.625i	0.139968	+	0.0808106i
$341$	1080.00	−	1870.61i	0.171511	−	0.297066i
$342$		0			0
$343$		−	6845.06i		−	1.07755i
$344$	2028.00	−	1170.87i	0.317856	−	0.183514i
$345$		0			0
$346$		−	4458.30i		−	0.692716i
$347$	−3483.00	−	6032.73i	−0.538839	−	0.933297i	−0.998967	−	0.0454442i	$-0.985530\pi$
$347$	−3483.00	−	6032.73i	−0.538839	−	0.933297i	0.460128	−	0.887853i	$-0.347804\pi$
$348$		0			0
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.0116588	−	0.999932i	$-0.503711\pi$
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.871796	+	0.489869i	$0.837045\pi$
$350$	2928.00			0.447166
$351$		0			0
$352$	−2520.00			−0.381581
$353$	−4876.50	−	2815.45i	−0.735269	−	0.424508i	0.0850777	−	0.996374i	$-0.472886\pi$
$353$	−4876.50	−	2815.45i	−0.735269	−	0.424508i	−0.820347	+	0.571867i	$0.806219\pi$
$354$		0			0
$355$	−915.000	−	1584.83i	−0.136798	−	0.236940i
$356$		−	4884.38i		−	0.727168i
$357$		0			0
$358$	−5616.00	+	3242.40i	−0.829092	+	0.478676i
$359$			7129.12i			1.04808i	0.851694	+	0.524040i	$0.175576\pi$
$359$			7129.12i			1.04808i	−0.851694	+	0.524040i	$0.824424\pi$
$360$		0			0
$361$	3104.50	−	5377.15i	0.452617	−	0.783956i
$362$	955.500	+	551.658i	0.138729	+	0.0800953i
$363$		0			0
$364$	2340.00	+	2251.67i	0.336949	+	0.324229i
$365$	−795.000			−0.114006
$366$		0			0
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	−0.866097	−	0.499877i	$-0.833379\pi$
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	0.865954	+	0.500123i	$0.166712\pi$
$368$	−39.0000	−	67.5500i	−0.00552450	−	0.00956871i
$369$		0			0
$370$	−373.500	+	215.640i	−0.0524793	+	0.0302989i
$371$	1116.00	−	644.323i	0.156172	−	0.0901660i
$372$		0			0
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	0.718670	−	0.695351i	$-0.244751\pi$
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	−0.961527	+	0.274711i	$0.911418\pi$
$374$	−1404.00	+	2431.80i	−0.194115	+	0.336218i
$375$		0			0
$376$	6786.00			0.930748
$377$	−4582.50	+	4762.27i	−0.626023	+	0.650582i
$378$		0			0
$379$	4779.00	+	2759.16i	0.647706	+	0.373953i	0.787577	−	0.616216i	$-0.211335\pi$
$379$	4779.00	+	2759.16i	0.647706	+	0.373953i	−0.139871	+	0.990170i	$0.544669\pi$
$380$	−495.000	+	857.365i	−0.0668236	+	0.115742i
$381$		0			0
$382$			4499.87i			0.602705i
$383$	6378.00	−	3682.34i	0.850915	−	0.491276i	−0.0100443	−	0.999950i	$-0.503197\pi$
$383$	6378.00	−	3682.34i	0.850915	−	0.491276i	0.860960	+	0.508673i	$0.169864\pi$
$384$		0			0
$385$			332.554i			0.0440221i
$386$	−967.500	−	1675.76i	−0.127576	−	0.220969i
$387$		0			0
$388$	−870.000	−	502.295i	−0.113834	−	0.0657220i
$389$	1209.00			0.157580			0.0787901	−	0.996891i	$-0.474894\pi$
$389$	1209.00			0.157580			0.0787901	+	0.996891i	$0.474894\pi$
$390$		0			0
$391$	−9126.00			−1.18036
$392$	−2944.50	−	1700.01i	−0.379387	−	0.219039i
$393$		0			0
$394$	1776.00	+	3076.12i	0.227090	+	0.393332i
$395$			2210.10i			0.281524i
$396$		0			0
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.303460	−	0.952844i	$-0.401858\pi$
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.976917	+	0.213618i	$0.0685248\pi$
$398$		−	4368.23i		−	0.550150i
$399$		0			0
$400$	−61.0000	+	105.655i	−0.00762500	+	0.0132069i
$401$	2581.50	+	1490.43i	0.321481	+	0.185607i	0.652053	−	0.758174i	$-0.273908\pi$
$401$	2581.50	+	1490.43i	0.321481	+	0.185607i	−0.330571	+	0.943781i	$0.607241\pi$
$402$		0			0
$403$	−1755.00	+	7092.75i	−0.216930	+	0.876712i
$404$	−2145.00			−0.264153
$405$		0			0
$406$	−1692.00	+	2930.63i	−0.206829	+	0.358238i
$407$	996.000	+	1725.12i	0.121302	+	0.210101i
$408$		0			0
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	−0.497731	−	0.867331i	$-0.665833\pi$
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	0.502265	+	0.864714i	$0.332500\pi$
$410$	−706.500	+	407.898i	−0.0851013	+	0.0491333i
$411$		0			0
$412$	−455.000	−	788.083i	−0.0544084	−	0.0942380i
$413$	−1968.00	+	3408.68i	−0.234477	+	0.406126i
$414$		0			0
$415$	−1368.00			−0.161813
$416$	8190.00	−	2364.25i	0.965259	−	0.278646i
$417$		0			0
$418$	−2376.00	−	1371.78i	−0.278024	−	0.160517i
$419$	−4731.00	+	8194.33i	−0.551610	+	0.955416i	0.446549	+	0.894759i	$0.352653\pi$
$419$	−4731.00	+	8194.33i	−0.551610	+	0.955416i	−0.998159	+	0.0606569i	$0.980680\pi$
$420$		0			0
$421$			7068.50i			0.818284i	0.912471	+	0.409142i	$0.134172\pi$
$421$			7068.50i			0.818284i	−0.912471	+	0.409142i	$0.865828\pi$
$422$	1563.00	−	902.398i	0.180298	−	0.104095i
$423$		0			0
$424$		−	2094.05i		−	0.239849i
$425$	7137.00	+	12361.6i	0.814577	+	1.41089i
$426$		0			0
$427$	1740.00	+	1004.59i	0.197200	+	0.113854i
$428$	7530.00			0.850412
$429$		0			0
$430$	−312.000			−0.0349906
$431$	8598.00	+	4964.06i	0.960907	+	0.554780i	0.896452	−	0.443140i	$-0.146136\pi$
$431$	8598.00	+	4964.06i	0.960907	+	0.554780i	0.0644552	+	0.997921i	$0.479469\pi$
$432$		0			0
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	0.989126	−	0.147070i	$-0.0469841\pi$
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	−0.621929	+	0.783074i	$0.713651\pi$
$434$			3741.23i			0.413790i
$435$		0			0
$436$	6720.00	−	3879.79i	0.738141	−	0.426166i
$437$		−	8916.60i		−	0.976061i
$438$		0			0
$439$	−6994.00	+	12114.0i	−0.760377	+	1.31701i	0.182280	+	0.983247i	$0.441652\pi$
$439$	−6994.00	+	12114.0i	−0.760377	+	1.31701i	−0.942656	+	0.333765i	$0.891681\pi$
$440$	468.000	+	270.200i	0.0507069	+	0.0292756i
$441$		0			0
$442$	2281.50	−	9220.57i	0.245520	−	0.992258i
$443$	−2004.00			−0.214928			−0.107464	−	0.994209i	$-0.534273\pi$
$443$	−2004.00			−0.214928			−0.107464	+	0.994209i	$0.534273\pi$
$444$		0			0
$445$	−846.000	+	1465.31i	−0.0901219	+	0.156096i
$446$	2085.00	+	3611.33i	0.221362	+	0.383411i
$447$		0			0
$448$	3684.00	−	2126.96i	0.388510	−	0.224307i
$449$	−7866.00	+	4541.44i	−0.826769	+	0.477336i	−0.852745	−	0.522327i	$-0.825064\pi$
$449$	−7866.00	+	4541.44i	−0.826769	+	0.477336i	0.0259758	+	0.999663i	$0.491731\pi$
$450$		0			0
$451$	1884.00	+	3263.18i	0.196705	+	0.340704i
$452$	−1717.50	+	2974.80i	−0.178727	+	0.309563i
$453$		0			0
$454$	4170.00			0.431074
$455$	−312.000	−	1080.80i	−0.0321468	−	0.111360i
$456$		0			0
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	0.607665	−	0.794194i	$-0.292106\pi$
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	−0.383959	+	0.923350i	$0.625440\pi$
$458$	2172.00	−	3762.01i	0.221596	−	0.383815i
$459$		0			0
$460$			675.500i			0.0684681i
$461$	−16963.5	+	9793.88i	−1.71382	+	0.989472i	−0.784545	+	0.620072i	$0.787103\pi$
$461$	−16963.5	+	9793.88i	−1.71382	+	0.989472i	−0.929270	+	0.369400i	$0.879563\pi$
$462$		0			0
$463$			8632.54i			0.866497i	0.901274	+	0.433249i	$0.142633\pi$
$463$			8632.54i			0.866497i	−0.901274	+	0.433249i	$0.857367\pi$
$464$	−70.5000	−	122.110i	−0.00705362	−	0.0122172i
$465$		0			0
$466$	−8775.00	−	5066.25i	−0.872305	−	0.503625i
$467$	−5460.00			−0.541025			−0.270512	−	0.962716i	$-0.587193\pi$
$467$	−5460.00			−0.541025			−0.270512	+	0.962716i	$0.587193\pi$
$468$		0			0
$469$	10896.0			1.07277
$470$	−783.000	−	452.065i	−0.0768449	−	0.0443664i
$471$		0			0
$472$	3198.00	+	5539.10i	0.311864	+	0.540165i
$473$			1441.07i			0.140085i
$474$		0			0
$475$	−12078.0	+	6973.24i	−1.16669	+	0.673587i
$476$			8106.00i			0.780542i
$477$		0			0
$478$	4662.00	−	8074.82i	0.446098	−	0.772665i
$479$	2211.00	+	1276.52i	0.210904	+	0.121766i	0.601732	−	0.798698i	$-0.294478\pi$
$479$	2211.00	+	1276.52i	0.210904	+	0.121766i	−0.390827	+	0.920464i	$0.627811\pi$
$480$		0			0
$481$	−4855.50	−	4672.21i	−0.460274	−	0.442899i
$482$	−8517.00			−0.804852
$483$		0			0
$484$	−2847.50	+	4932.01i	−0.267421	+	0.463187i
$485$	174.000	+	301.377i	0.0162906	+	0.0282161i
$486$		0			0
$487$	9378.00	−	5414.39i	0.872603	−	0.503798i	0.00439074	−	0.999990i	$-0.498602\pi$
$487$	9378.00	−	5414.39i	0.872603	−	0.503798i	0.868212	+	0.496193i	$0.165269\pi$
$488$	2827.50	−	1632.46i	0.262285	−	0.151430i
$489$		0			0
$490$	226.500	+	392.310i	0.0208821	+	0.0361689i
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	−0.476277	−	0.879295i	$-0.658014\pi$
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	0.999631	−	0.0271797i	$-0.00865264\pi$
$492$		0			0
$493$	−16497.0			−1.50707
$494$	9009.00	+	2229.15i	0.820514	+	0.203025i
$495$		0			0
$496$	−135.000	−	77.9423i	−0.0122211	−	0.00705587i
$497$	7320.00	−	12678.6i	0.660658	−	1.14429i
$498$		0			0
$499$		−	17677.3i		−	1.58586i	−0.609311	−	0.792931i	$-0.708554\pi$
$499$		−	17677.3i		−	1.58586i	0.609311	−	0.792931i	$-0.291446\pi$
$500$	1852.50	−	1069.54i	0.165693	−	0.0956627i
$501$		0			0
$502$			6890.10i			0.612590i
$503$	1938.00	+	3356.71i	0.171792	+	0.297552i	0.939046	−	0.343791i	$-0.111711\pi$
$503$	1938.00	+	3356.71i	0.171792	+	0.297552i	−0.767255	+	0.641343i	$0.778378\pi$
$504$		0			0
$505$	643.500	+	371.525i	0.0567037	+	0.0327379i
$506$	−1872.00			−0.164467
$507$		0			0
$508$	1430.00			0.124894
$509$	14779.5	+	8532.95i	1.28701	+	0.743058i	0.978120	−	0.208039i	$-0.0667082\pi$
$509$	14779.5	+	8532.95i	1.28701	+	0.743058i	0.308893	+	0.951097i	$0.400042\pi$
$510$		0			0
$511$	−3180.00	−	5507.92i	−0.275293	−	0.476822i
$512$			361.999i			0.0312465i
$513$		0			0
$514$	−3100.50	+	1790.07i	−0.266065	+	0.153612i
$515$			315.233i			0.0269725i
$516$		0			0
$517$	−2088.00	+	3616.52i	−0.177621	+	0.307649i
$518$	−2988.00	−	1725.12i	−0.253446	−	0.146327i
$519$		0			0
$520$	−1774.50	−	439.075i	−0.149648	−	0.0370283i
$521$	−2121.00			−0.178355			−0.0891773	−	0.996016i	$-0.528424\pi$
$521$	−2121.00			−0.178355			−0.0891773	+	0.996016i	$0.528424\pi$
$522$		0			0
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	−0.520476	−	0.853876i	$-0.674245\pi$
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	0.999717	+	0.0238072i	$0.00757878\pi$
$524$	−4935.00	−	8547.67i	−0.411425	−	0.712608i
$525$		0			0
$526$	3078.00	−	1777.08i	0.255147	−	0.147309i
$527$	−15795.0	+	9119.25i	−1.30558	+	0.753777i
$528$		0			0
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$	−139.500	+	241.621i	−0.0114330	+	0.0198025i
$531$		0			0
$532$	−7920.00			−0.645443
$533$	−9184.50	−	8837.79i	−0.746388	−	0.718212i
$534$		0			0
$535$	−2259.00	−	1304.23i	−0.182552	−	0.105396i
$536$	8853.00	−	15333.8i	0.713417	−	1.23567i
$537$		0			0
$538$		−	5767.73i		−	0.462202i
$539$	1812.00	−	1046.16i	0.144802	−	0.0836016i
$540$		0			0
$541$		−	4764.87i		−	0.378665i	−0.981913	−	0.189333i	$-0.939368\pi$
$541$		−	4764.87i		−	0.378665i	0.981913	−	0.189333i	$-0.0606324\pi$
$542$	−2430.00	−	4208.88i	−0.192578	−	0.333555i
$543$		0			0
$544$	18427.5	+	10639.1i	1.45234	+	0.838508i
$545$	−2688.00			−0.211268
$546$		0			0
$547$	6554.00			0.512301			0.256151	−	0.966637i	$-0.417546\pi$
$547$	6554.00			0.512301			0.256151	+	0.966637i	$0.417546\pi$
$548$	−3667.50	−	2117.43i	−0.285890	−	0.165059i
$549$		0			0
$550$	1464.00	+	2535.72i	0.113500	+	0.196588i
$551$		−	16118.5i		−	1.24622i
$552$		0			0
$553$	−15312.0	+	8840.39i	−1.17745	+	0.679804i
$554$			652.983i			0.0500769i
$555$		0			0
$556$	−590.000	+	1021.91i	−0.0450028	+	0.0779472i
$557$	15685.5	+	9056.03i	1.19321	+	0.688898i	0.959032	−	0.283297i	$-0.0914281\pi$
$557$	15685.5	+	9056.03i	1.19321	+	0.688898i	0.234174	+	0.972195i	$0.424761\pi$
$558$		0			0
$559$	−1352.00	−	4683.47i	−0.102296	−	0.354364i
$560$	24.0000			0.00181104
$561$		0			0
$562$	31.5000	−	54.5596i	0.00236432	−	0.00409512i
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	0.543278	−	0.839553i	$-0.317183\pi$
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	−0.998713	+	0.0507160i	$0.983850\pi$
$564$		0			0
$565$	1030.50	−	594.959i	0.0767318	−	0.0443011i
$566$	−10686.0	+	6169.56i	−0.793580	+	0.458173i
$567$		0			0
$568$	−11895.0	−	20602.7i	−0.878703	−	1.52196i
$569$	−3861.00	+	6687.45i	−0.284467	+	0.492711i	−0.972480	−	0.232988i	$-0.925150\pi$
$569$	−3861.00	+	6687.45i	−0.284467	+	0.492711i	0.688013	+	0.725698i	$0.258483\pi$
$570$		0			0
$571$	11440.0			0.838440			0.419220	−	0.907885i	$-0.362304\pi$
$571$	11440.0			0.838440			0.419220	+	0.907885i	$0.362304\pi$
$572$	−780.000	+	3152.33i	−0.0570165	+	0.230429i
$573$		0			0
$574$	−5652.00	−	3263.18i	−0.410993	−	0.237287i
$575$	−4758.00	+	8241.10i	−0.345082	+	0.597700i
$576$		0			0
$577$			15444.7i			1.11433i	0.830400	+	0.557167i	$0.188112\pi$
$577$			15444.7i			1.11433i	−0.830400	+	0.557167i	$0.811888\pi$
$578$	13164.0	−	7600.24i	0.947319	−	0.546935i
$579$		0			0
$580$			1221.10i			0.0874194i
$581$	−5472.00	−	9477.78i	−0.390735	−	0.676772i
$582$		0			0
$583$	1116.00	+	644.323i	0.0792796	+	0.0457721i
$584$	−10335.0			−0.732304
$585$		0			0
$586$	−14415.0			−1.01617
$587$	12186.0	+	7035.59i	0.856848	+	0.494702i	0.862956	−	0.505280i	$-0.168611\pi$
$587$	12186.0	+	7035.59i	0.856848	+	0.494702i	−0.00610719	+	0.999981i	$0.501944\pi$
$588$		0			0
$589$	−8910.00	−	15432.6i	−0.623311	−	1.07961i
$590$		−	852.169i		−	0.0594631i
$591$		0			0
$592$	124.500	−	71.8801i	0.00864344	−	0.00499029i
$593$		−	26938.6i		−	1.86549i	−0.360538	−	0.932745i	$-0.617407\pi$
$593$		−	26938.6i		−	1.86549i	0.360538	−	0.932745i	$-0.382593\pi$
$594$		0			0
$595$	1404.00	−	2431.80i	0.0967368	−	0.167553i
$596$	−202.500	−	116.913i	−0.0139173	−	0.00803517i
$597$		0			0
$598$	6084.00	−	1756.30i	0.416042	−	0.120101i
$599$	10554.0			0.719908			0.359954	−	0.932970i	$-0.382792\pi$
$599$	10554.0			0.719908			0.359954	+	0.932970i	$0.382792\pi$
$600$		0			0
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	−0.496691	−	0.867928i	$-0.665452\pi$
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	0.999993	−	0.00381713i	$-0.00121503\pi$
$602$	−1248.00	−	2161.60i	−0.0844928	−	0.146346i
$603$		0			0
$604$	−7665.00	+	4425.39i	−0.516365	+	0.298123i
$605$	1708.50	−	986.403i	0.114811	−	0.0662859i
$606$		0			0
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	0.967808	−	0.251691i	$-0.0809866\pi$
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	−0.701874	+	0.712301i	$0.747653\pi$
$608$	−10395.0	+	18004.7i	−0.693377	+	1.20096i
$609$		0			0
$610$	−435.000			−0.0288732
$611$	3393.00	−	13712.6i	0.224658	−	0.907945i
$612$		0			0
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.997787	−	0.0664859i	$-0.0211787\pi$
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.441315	+	0.897352i	$0.354512\pi$
$614$	−1923.00	+	3330.73i	−0.126394	+	0.218921i
$615$		0			0
$616$			4323.20i			0.282771i
$617$	15055.5	−	8692.30i	0.982353	−	0.567162i	0.0793731	−	0.996845i	$-0.474708\pi$
$617$	15055.5	−	8692.30i	0.982353	−	0.567162i	0.902980	+	0.429683i	$0.141375\pi$
$618$		0			0
$619$		−	8209.92i		−	0.533093i	−0.963822	−	0.266547i	$-0.914117\pi$
$619$		−	8209.92i		−	0.533093i	0.963822	−	0.266547i	$-0.0858826\pi$
$620$	675.000	+	1169.13i	0.0437236	+	0.0757316i
$621$		0			0
$622$	7371.00	+	4255.65i	0.475161	+	0.274334i
$623$	−13536.0			−0.870479
$624$		0			0
$625$	14509.0			0.928576
$626$	777.000	+	448.601i	0.0496089	+	0.0286417i
$627$		0			0
$628$	−3027.50	−	5243.78i	−0.192373	−	0.333200i
$629$		−	16819.9i		−	1.06622i
$630$		0			0
$631$	11142.0	−	6432.84i	0.702941	−	0.405843i	−0.105501	−	0.994419i	$-0.533645\pi$
$631$	11142.0	−	6432.84i	0.702941	−	0.405843i	0.808442	+	0.588576i	$0.200311\pi$
$632$			28731.3i			1.80834i
$633$		0			0
$634$	−3391.50	+	5874.25i	−0.212451	+	0.367975i
$635$	−429.000	−	247.683i	−0.0268100	−	0.0154788i
$636$		0			0
$637$	−4907.50	+	5100.02i	−0.305247	+	0.317222i
$638$	−3384.00			−0.209990
$639$		0			0
$640$	799.500	−	1384.77i	0.0493797	−	0.0855282i
$641$	3100.50	+	5370.22i	0.191049	+	0.330907i	0.945598	−	0.325337i	$-0.105478\pi$
$641$	3100.50	+	5370.22i	0.191049	+	0.330907i	−0.754549	+	0.656244i	$0.772144\pi$
$642$		0			0
$643$	−14568.0	+	8410.84i	−0.893477	+	0.515849i	−0.875078	−	0.483981i	$-0.839190\pi$
$643$	−14568.0	+	8410.84i	−0.893477	+	0.515849i	−0.0183989	+	0.999831i	$0.505857\pi$
$644$	−4680.00	+	2702.00i	−0.286363	+	0.165332i
$645$		0			0
$646$	11583.0	+	20062.3i	0.705460	+	1.22189i
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	−0.994886	−	0.101003i	$-0.967795\pi$
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	0.584914	+	0.811095i	$0.301128\pi$
$648$		0			0
$649$	−3936.00			−0.238061
$650$	−7137.00	−	6867.58i	−0.430671	−	0.414413i
$651$		0			0
$652$	4350.00	+	2511.47i	0.261287	+	0.150854i
$653$	−5667.00	+	9815.53i	−0.339612	+	0.588226i	−0.984360	−	0.176170i	$-0.943629\pi$
$653$	−5667.00	+	9815.53i	−0.339612	+	0.588226i	0.644747	+	0.764396i	$0.276963\pi$
$654$		0			0
$655$			3419.07i			0.203960i
$656$	235.500	−	135.966i	0.0140164	−	0.00809235i
$657$		0			0
$658$		−	7233.04i		−	0.428531i
$659$	6618.00	+	11462.7i	0.391200	+	0.677578i	0.992608	−	0.121364i	$-0.0387268\pi$
$659$	6618.00	+	11462.7i	0.391200	+	0.677578i	−0.601408	+	0.798942i	$0.705393\pi$
$660$		0			0
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	0.166615	−	0.986022i	$-0.446716\pi$
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	−0.770613	+	0.637304i	$0.780050\pi$
$662$	12912.0			0.758065
$663$		0			0
$664$	−17784.0			−1.03939
$665$	2376.00	+	1371.78i	0.138552	+	0.0799932i
$666$		0			0
$667$	−5499.00	−	9524.55i	−0.319224	−	0.552911i
$668$			4572.61i			0.264850i
$669$		0			0
$670$	−2043.00	+	1179.53i	−0.117803	+	0.0680136i
$671$			2009.18i			0.115594i
$672$		0			0
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	−0.957722	−	0.287697i	$-0.907110\pi$
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	0.728014	+	0.685563i	$0.240444\pi$
$674$	5362.50	+	3096.04i	0.306463	+	0.176936i
$675$		0			0
$676$	−422.500	−	10976.9i	−0.0240385	−	0.624538i
$677$	21630.0			1.22793			0.613965	−	0.789333i	$-0.289574\pi$
$677$	21630.0			1.22793			0.613965	+	0.789333i	$0.289574\pi$
$678$		0			0
$679$	−1392.00	+	2411.01i	−0.0786746	+	0.136268i
$680$	−2281.50	−	3951.67i	−0.128664	−	0.222853i
$681$		0			0
$682$	−3240.00	+	1870.61i	−0.181915	+	0.105029i
$683$	22983.0	−	13269.2i	1.28758	−	0.743387i	0.309361	−	0.950945i	$-0.399885\pi$
$683$	22983.0	−	13269.2i	1.28758	−	0.743387i	0.978223	+	0.207557i	$0.0665514\pi$
$684$		0			0
$685$	733.500	+	1270.46i	0.0409133	+	0.0708639i
$686$	−5928.00	+	10267.6i	−0.329930	+	0.571456i
$687$		0			0
$688$	104.000			0.00576303
$689$	−4231.50	−	1047.02i	−0.233973	−	0.0578933i
$690$		0			0
$691$	−720.000	−	415.692i	−0.0396383	−	0.0228852i	0.480050	−	0.877241i	$-0.340619\pi$
$691$	−720.000	−	415.692i	−0.0396383	−	0.0228852i	−0.519688	+	0.854356i	$0.673952\pi$
$692$	6435.00	−	11145.7i	0.353500	−	0.612280i
$693$		0			0
$694$			12065.5i			0.659941i
$695$	354.000	−	204.382i	0.0193208	−	0.0111549i
$696$		0			0
$697$		−	31816.0i		−	1.72901i
$698$	5760.00	+	9976.61i	0.312348	+	0.541003i
$699$		0			0
$700$	7320.00	+	4226.20i	0.395243	+	0.228194i
$701$	−30186.0			−1.62640			−0.813202	−	0.581981i	$-0.802278\pi$
$701$	−30186.0			−1.62640			−0.813202	+	0.581981i	$0.802278\pi$
$702$		0			0
$703$	16434.0			0.881679
$704$	3684.00	+	2126.96i	0.197224	+	0.113868i
$705$		0			0
$706$	4876.50	+	8446.35i	0.259957	+	0.450258i
$707$			5944.40i			0.316212i
$708$		0			0
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	−0.747096	−	0.664716i	$-0.768552\pi$
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	0.202113	+	0.979362i	$0.435219\pi$
$710$			3169.65i			0.167542i
$711$		0			0
$712$	−10998.0	+	19049.1i	−0.578887	+	1.00266i
$713$	−10530.0	−	6079.50i	−0.553088	−	0.319325i
$714$		0			0
$715$	780.000	−	810.600i	0.0407977	−	0.0423982i
$716$	−18720.0			−0.977094
$717$		0			0
$718$	6174.00	−	10693.7i	0.320908	−	0.555828i
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	0.999665	−	0.0259014i	$-0.00824561\pi$
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	−0.522264	+	0.852784i	$0.674912\pi$
$720$		0			0
$721$	−2184.00	+	1260.93i	−0.112811	+	0.0651312i
$722$	−9313.50	+	5377.15i	−0.480073	+	0.277170i
$723$		0			0
$724$	1592.50	+	2758.29i	0.0817470	+	0.141590i
$725$	−8601.00	+	14897.4i	−0.440597	+	0.763137i
$726$		0			0
$727$	21112.0			1.07703			0.538515	−	0.842616i	$-0.318986\pi$
$727$	21112.0			1.07703			0.538515	+	0.842616i	$0.318986\pi$
$728$	−4056.00	−	14050.4i	−0.206491	−	0.715305i
$729$		0			0
$730$	1192.50	+	688.490i	0.0604608	+	0.0349071i
$731$	6084.00	−	10537.8i	0.307832	−	0.533180i
$732$		0			0
$733$		−	23959.5i		−	1.20732i	−0.797243	−	0.603658i	$-0.793709\pi$
$733$		−	23959.5i		−	1.20732i	0.797243	−	0.603658i	$-0.206291\pi$
$734$	3.00000	−	1.73205i	0.000150861	−	8.70997e-5i
$735$		0			0
$736$			14185.5i			0.710441i
$737$	5448.00	+	9436.21i	0.272293	+	0.471625i
$738$		0			0
$739$	2742.00	+	1583.09i	0.136490	+	0.0788025i	0.566690	−	0.823931i	$-0.308224\pi$
$739$	2742.00	+	1583.09i	0.136490	+	0.0788025i	−0.430200	+	0.902734i	$0.641557\pi$
$740$	−1245.00			−0.0618474
$741$		0			0
$742$	−2232.00			−0.110430
$743$	26070.0	+	15051.5i	1.28723	+	0.743185i	0.978160	−	0.207852i	$-0.0666474\pi$
$743$	26070.0	+	15051.5i	1.28723	+	0.743185i	0.309075	+	0.951038i	$0.399981\pi$
$744$		0			0
$745$	40.5000	+	70.1481i	0.00199168	+	0.00344970i
$746$			6060.45i			0.297438i
$747$		0			0
$748$	−7020.00	+	4053.00i	−0.343151	+	0.198118i
$749$		−	20867.7i		−	1.01801i
$750$		0			0
$751$	−14248.0	+	24678.3i	−0.692299	+	1.19910i	0.278783	+	0.960354i	$0.410069\pi$
$751$	−14248.0	+	24678.3i	−0.692299	+	1.19910i	−0.971083	+	0.238744i	$0.923264\pi$
$752$	261.000	+	150.688i	0.0126565	+	0.00730724i
$753$		0			0
$754$	10998.0	−	3174.85i	0.531198	−	0.153344i
$755$	3066.00			0.147792
$756$		0			0
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	−0.995762	−	0.0919633i	$-0.970686\pi$
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	0.577524	+	0.816374i	$0.304019\pi$
$758$	−4779.00	−	8277.47i	−0.228999	−	0.396638i
$759$		0			0
$760$	3861.00	−	2229.15i	0.184281	−	0.106394i
$761$	−35790.0	+	20663.4i	−1.70484	+	0.984292i	−0.764149	+	0.645040i	$0.776841\pi$
$761$	−35790.0	+	20663.4i	−1.70484	+	0.984292i	−0.940695	+	0.339252i	$0.889826\pi$
$762$		0			0
$763$	−10752.0	−	18623.0i	−0.510155	−	0.883615i
$764$	−6495.00	+	11249.7i	−0.307567	+	0.532721i
$765$		0			0
$766$	−12756.0			−0.601688
$767$	12792.0	−	3692.73i	0.602206	−	0.173842i
$768$		0			0
$769$	−12186.0	−	7035.59i	−0.571441	−	0.329922i	0.186283	−	0.982496i	$-0.440356\pi$
$769$	−12186.0	−	7035.59i	−0.571441	−	0.329922i	−0.757725	+	0.652574i	$0.773689\pi$
$770$	288.000	−	498.831i	0.0134790	−	0.0233462i
$771$		0			0
$772$		−	5585.86i		−	0.260414i
$773$	−174.000	+	100.459i	−0.00809618	+	0.00467433i	−0.504043	−	0.863679i	$-0.668155\pi$
$773$	−174.000	+	100.459i	−0.00809618	+	0.00467433i	0.495946	+	0.868353i	$0.334821\pi$
$774$		0			0
$775$			19017.9i			0.881476i
$776$	2262.00	+	3917.90i	0.104641	+	0.181243i
$777$		0			0
$778$	−1813.50	−	1047.02i	−0.0835696	−	0.0482489i
$779$	31086.0			1.42975
$780$		0			0
$781$	14640.0			0.670756
$782$	13689.0	+	7903.35i	0.625982	+	0.361411i
$783$		0			0
$784$	−75.5000	−	130.770i	−0.00343932	−	0.00595708i
$785$			2097.51i			0.0953675i
$786$		0			0
$787$	−5979.00	+	3451.98i	−0.270811	+	0.156353i	−0.629256	−	0.777198i	$-0.716640\pi$
$787$	−5979.00	+	3451.98i	−0.270811	+	0.156353i	0.358445	+	0.933551i	$0.383307\pi$
$788$			10253.7i			0.463546i
$789$		0			0
$790$	1914.00	−	3315.15i	0.0861988	−	0.149301i
$791$	8244.00	+	4759.68i	0.370573	+	0.213950i
$792$		0			0
$793$	−1885.00	−	6529.83i	−0.0844115	−	0.292410i
$794$	−20256.0			−0.905363
$795$		0			0
$796$	6305.00	−	10920.6i	0.280747	−	0.486268i
$797$	−15639.0	−	27087.5i	−0.695059	−	1.20388i	−0.970161	−	0.242462i	$-0.922045\pi$
$797$	−15639.0	−	27087.5i	−0.695059	−	1.20388i	0.275102	−	0.961415i	$-0.411288\pi$
$798$		0			0
$799$	30537.0	−	17630.5i	1.35209	−	0.780631i
$800$	19215.0	−	11093.8i	0.849191	−	0.490281i
$801$		0			0
$802$	−2581.50	−	4471.29i	−0.113661	−	0.196866i
$803$	3180.00	−	5507.92i	0.139751	−	0.242055i
$804$		0			0
$805$	1872.00			0.0819619
$806$	8775.00	−	9119.25i	0.383482	−	0.398526i
$807$		0			0
$808$	8365.50	+	4829.82i	0.364229	+	0.210288i
$809$	4024.50	−	6970.64i	0.174900	−	0.302935i	−0.765227	−	0.643761i	$-0.777373\pi$
$809$	4024.50	−	6970.64i	0.174900	−	0.302935i	0.940127	+	0.340826i	$0.110707\pi$
$810$		0			0
$811$			14026.1i			0.607305i	0.952783	+	0.303653i	$0.0982062\pi$
$811$			14026.1i			0.607305i	−0.952783	+	0.303653i	$0.901794\pi$
$812$	−8460.00	+	4884.38i	−0.365625	+	0.211094i
$813$		0			0
$814$		−	3450.25i		−	0.148564i
$815$	−870.000	−	1506.88i	−0.0373924	−	0.0647655i
$816$		0			0
$817$	10296.0	+	5944.40i	0.440895	+	0.254551i
$818$	−75.0000			−0.00320576
$819$		0			0
$820$	−2355.00			−0.100293
$821$	6960.00	+	4018.36i	0.295866	+	0.170818i	0.640584	−	0.767888i	$-0.278692\pi$
$821$	6960.00	+	4018.36i	0.295866	+	0.170818i	−0.344718	+	0.938706i	$0.612026\pi$
$822$		0			0
$823$	20150.0	+	34900.8i	0.853445	+	1.47821i	0.878081	+	0.478513i	$0.158824\pi$
$823$	20150.0	+	34900.8i	0.853445	+	1.47821i	−0.0246361	+	0.999696i	$0.507843\pi$
$824$			4098.03i			0.173255i
$825$		0			0
$826$	5904.00	−	3408.68i	0.248700	−	0.143587i
$827$		−	39525.4i		−	1.66195i	−0.556310	−	0.830975i	$-0.687783\pi$
$827$		−	39525.4i		−	1.66195i	0.556310	−	0.830975i	$-0.312217\pi$
$828$		0			0
$829$	6155.50	−	10661.6i	0.257888	−	0.446676i	−0.707788	−	0.706425i	$-0.750307\pi$
$829$	6155.50	−	10661.6i	0.257888	−	0.446676i	0.965676	+	0.259750i	$0.0836400\pi$
$830$	2052.00	+	1184.72i	0.0858144	+	0.0495450i
$831$		0			0
$832$	−13968.5	−	3456.31i	−0.582056	−	0.144022i
$833$	−17667.0			−0.734844
$834$		0			0
$835$	792.000	−	1371.78i	0.0328243	−	0.0568534i
$836$	−3960.00	−	6858.92i	−0.163827	−	0.283757i
$837$		0			0
$838$	14193.0	−	8194.33i	0.585070	−	0.337791i
$839$	−18591.0	+	10733.5i	−0.764997	+	0.441671i	−0.831087	−	0.556142i	$-0.812281\pi$
$839$	−18591.0	+	10733.5i	−0.764997	+	0.441671i	0.0660899	+	0.997814i	$0.478948\pi$
$840$		0			0
$841$	2254.00	+	3904.04i	0.0924187	+	0.160074i
$842$	6121.50	−	10602.7i	0.250547	−	0.433961i
$843$		0			0
$844$	5210.00			0.212483
$845$	−1774.50	+	3366.24i	−0.0722422	+	0.137044i
$846$		0			0
$847$	13668.0	+	7891.22i	0.554472	+	0.320125i
$848$	46.5000	−	80.5404i	0.00188304	−	0.00326152i
$849$		0			0
$850$		−	24723.3i		−	0.997649i
$851$	9711.00	−	5606.65i	0.391174	−	0.225844i
$852$		0			0
$853$			774.227i			0.0310774i	0.999879	+	0.0155387i	$0.00494632\pi$
$853$			774.227i			0.0310774i	−0.999879	+	0.0155387i	$0.995054\pi$
$854$	−1740.00	−	3013.77i	−0.0697208	−	0.120760i
$855$		0			0
$856$	−29367.0	−	16955.0i	−1.17260	−	0.676999i
$857$	−13923.0			−0.554960			−0.277480	−	0.960731i	$-0.589499\pi$
$857$	−13923.0			−0.554960			−0.277480	+	0.960731i	$0.589499\pi$
$858$		0			0
$859$	−22358.0			−0.888062			−0.444031	−	0.896011i	$-0.646452\pi$
$859$	−22358.0			−0.888062			−0.444031	+	0.896011i	$0.646452\pi$
$860$	−780.000	−	450.333i	−0.0309277	−	0.0178561i
$861$		0			0
$862$	−8598.00	−	14892.2i	−0.339732	−	0.588433i
$863$			2230.88i			0.0879955i	0.999032	+	0.0439977i	$0.0140094\pi$
$863$			2230.88i			0.0879955i	−0.999032	+	0.0439977i	$0.985991\pi$
$864$		0			0
$865$	−3861.00	+	2229.15i	−0.151766	+	0.0876224i
$866$		−	11461.0i		−	0.449723i
$867$		0			0
$868$	−5400.00	+	9353.07i	−0.211161	+	0.365742i
$869$	−15312.0	−	8840.39i	−0.597726	−	0.345097i
$870$		0			0
$871$	−26559.0	−	25556.4i	−1.03320	−	0.994197i
$872$	−34944.0			−1.35706
$873$		0			0
$874$	−7722.00	+	13374.9i	−0.298856	+	0.517635i
$875$	−2964.00	−	5133.80i	−0.114516	−	0.198348i
$876$		0			0
$877$	−14509.5	+	8377.06i	−0.558667	+	0.322547i	−0.752610	−	0.658466i	$-0.771206\pi$
$877$	−14509.5	+	8377.06i	−0.558667	+	0.322547i	0.193943	+	0.981013i	$0.437872\pi$
$878$	20982.0	−	12114.0i	0.806501	−	0.465634i
$879$		0			0
$880$	12.0000	+	20.7846i	0.000459682	+	0.000796192i
$881$	8677.50	−	15029.9i	0.331842	−	0.574766i	−0.651031	−	0.759051i	$-0.725663\pi$
$881$	8677.50	−	15029.9i	0.331842	−	0.574766i	0.982873	+	0.184284i	$0.0589967\pi$
$882$		0			0
$883$	−46982.0			−1.79057			−0.895283	−	0.445497i	$-0.853027\pi$
$883$	−46982.0			−1.79057			−0.895283	+	0.445497i	$0.853027\pi$
$884$	19012.5	−	19758.4i	0.723371	−	0.751749i
$885$		0			0
$886$	3006.00	+	1735.51i	0.113983	+	0.0658079i
$887$	−4458.00	+	7721.48i	−0.168754	+	0.292291i	−0.937982	−	0.346684i	$-0.887308\pi$
$887$	−4458.00	+	7721.48i	−0.168754	+	0.292291i	0.769228	+	0.638975i	$0.220641\pi$
$888$		0			0
$889$		−	3962.93i		−	0.149508i
$890$	2538.00	−	1465.31i	0.0955887	−	0.0551882i
$891$		0			0
$892$			12037.8i			0.451854i
$893$	17226.0	+	29836.3i	0.645516	+	1.11807i
$894$		0			0
$895$	5616.00	+	3242.40i	0.209745	+	0.121097i
$896$	12792.0			0.476954
$897$		0			0
$898$	15732.0			0.584614
$899$	−19035.0	−	10989.9i	−0.706177	−	0.407711i
$900$		0			0
$901$	−5440.50	−	9423.22i	−0.201165	−	0.348427i
$902$		−	6526.37i		−	0.240914i
$903$		0			0
$904$	13396.5	−	7734.47i	0.492877	−	0.284563i
$905$		−	1103.32i		−	0.0405254i
$906$		0			0
$907$	15418.0	−	26704.8i	0.564439	−	0.977637i	−0.432662	−	0.901556i	$-0.642426\pi$
$907$	15418.0	−	26704.8i	0.564439	−	0.977637i	0.997102	−	0.0760813i	$-0.0242408\pi$
$908$	10425.0	+	6018.88i	0.381020	+	0.219982i
$909$		0			0
$910$	−468.000	+	1891.40i	−0.0170484	+	0.0689003i
$911$	27480.0			0.999400			0.499700	−	0.866199i	$-0.333444\pi$
$911$	27480.0			0.999400			0.499700	+	0.866199i	$0.333444\pi$
$912$		0			0
$913$	5472.00	−	9477.78i	0.198354	−	0.343558i
$914$	−2185.50	−	3785.40i	−0.0790918	−	0.136991i
$915$		0			0
$916$	10860.0	−	6270.02i	0.391730	−	0.226165i
$917$	−23688.0	+	13676.3i	−0.853050	+	0.492509i
$918$		0			0
$919$	14221.0	+	24631.5i	0.510454	+	0.884133i	0.999927	+	0.0121140i	$0.00385609\pi$
$919$	14221.0	+	24631.5i	0.510454	+	0.884133i	−0.489472	+	0.872019i	$0.662811\pi$
$920$	1521.00	−	2634.45i	0.0545064	−	0.0944078i
$921$		0			0
$922$	33927.0			1.21185
$923$	−47580.0	+	13735.2i	−1.69677	+	0.489814i
$924$		0			0
$925$	−15189.0	−	8769.37i	−0.539904	−	0.311714i
$926$	7476.00	−	12948.8i	0.265310	−	0.459530i
$927$		0			0
$928$			25643.0i			0.907083i
$929$	−6043.50	+	3489.22i	−0.213435	+	0.123227i	−0.602907	−	0.797812i	$-0.705991\pi$
$929$	−6043.50	+	3489.22i	−0.213435	+	0.123227i	0.389472	+	0.921038i	$0.372658\pi$
$930$		0			0
$931$		−	17261.6i		−	0.607655i
$932$	−14625.0	−	25331.2i	−0.514011	−	0.890292i
$933$		0			0
$934$	8190.00	+	4728.50i	0.286922	+	0.165654i
$935$	2808.00			0.0982154
$936$		0			0
$937$	−38465.0			−1.34109			−0.670543	−	0.741871i	$-0.733939\pi$
$937$	−38465.0			−1.34109			−0.670543	+	0.741871i	$0.733939\pi$
$938$	−16344.0	−	9436.21i	−0.568924	−	0.328468i
$939$		0			0
$940$	−1305.00	−	2260.33i	−0.0452813	−	0.0784295i
$941$		−	4884.38i		−	0.169210i	−0.996415	−	0.0846049i	$-0.973037\pi$
$941$		−	4884.38i		−	0.169210i	0.996415	−	0.0846049i	$-0.0269628\pi$
$942$		0			0
$943$	18369.0	−	10605.3i	0.634334	−	0.366233i
$944$			284.056i			0.00979369i
$945$		0			0
$946$	1248.00	−	2161.60i	0.0428922	−	0.0742914i
$947$	−18849.0	−	10882.5i	−0.646790	−	0.373424i	0.140435	−	0.990090i	$-0.455150\pi$
$947$	−18849.0	−	10882.5i	−0.646790	−	0.373424i	−0.787225	+	0.616665i	$0.788483\pi$
$948$		0			0
$949$	−5167.50	+	20884.2i	−0.176759	+	0.714362i
$950$	24156.0			0.824973
$951$		0			0
$952$	18252.0	−	31613.4i	0.621377	−	1.07626i
$953$	3237.00	+	5606.65i	0.110028	+	0.190574i	0.915781	−	0.401677i	$-0.131573\pi$
$953$	3237.00	+	5606.65i	0.110028	+	0.190574i	−0.805753	+	0.592251i	$0.798239\pi$
$954$		0			0
$955$	3897.00	−	2249.93i	0.132046	−	0.0762368i
$956$	23310.0	−	13458.0i	0.788598	−	0.455297i
$957$		0			0
$958$	−2211.00	−	3829.56i	−0.0745659	−	0.129152i
$959$	−5868.00	+	10163.7i	−0.197589	+	0.342234i
$960$		0			0
$961$	5491.00			0.184317
$962$	3237.00	+	11213.3i	0.108488	+	0.375812i
$963$		0			0
$964$	−21292.5	−	12293.2i	−0.711395	−	0.410724i
$965$	−967.500	+	1675.76i	−0.0322745	+	0.0559011i
$966$		0			0
$967$			7541.35i			0.250789i	0.992107	+	0.125395i	$0.0400197\pi$
$967$			7541.35i			0.250789i	−0.992107	+	0.125395i	$0.959980\pi$
$968$	22210.5	−	12823.2i	0.737472	−	0.425779i
$969$		0			0
$970$		−	602.754i		−	0.0199518i
$971$	17499.0	+	30309.2i	0.578342	+	1.00172i	0.995670	+	0.0929611i	$0.0296332\pi$
$971$	17499.0	+	30309.2i	0.578342	+	1.00172i	−0.417328	+	0.908756i	$0.637033\pi$
$972$		0			0
$973$	2832.00	+	1635.06i	0.0933091	+	0.0538720i
$974$	−18756.0			−0.617024
$975$		0			0
$976$	145.000			0.00475547
$977$	21838.5	+	12608.5i	0.715123	+	0.412877i	0.812955	−	0.582326i	$-0.197857\pi$
$977$	21838.5	+	12608.5i	0.715123	+	0.412877i	−0.0978318	+	0.995203i	$0.531191\pi$
$978$		0			0
$979$	−6768.00	−	11722.5i	−0.220946	−	0.382690i
$980$			1307.70i			0.0426254i
$981$		0			0
$982$	−17082.0	+	9862.30i	−0.555100	+	0.320487i
$983$			56440.6i			1.83131i	0.401967	+	0.915654i	$0.368327\pi$
$983$			56440.6i			1.83131i	−0.401967	+	0.915654i	$0.631673\pi$
$984$		0			0
$985$	1776.00	−	3076.12i	0.0574498	−	0.0995060i
$986$	24745.5	+	14286.8i	0.799247	+	0.461445i
$987$		0			0
$988$	19305.0	+	18576.2i	0.621633	+	0.598167i
$989$	8112.00			0.260816
$990$		0			0
$991$	−29641.0	+	51339.7i	−0.950129	+	1.64567i	−0.204987	+	0.978765i	$0.565715\pi$
$991$	−29641.0	+	51339.7i	−0.950129	+	1.64567i	−0.745142	+	0.666906i	$0.767618\pi$
$992$	14175.0	+	24551.8i	0.453686	+	0.785808i
$993$		0			0
$994$	−21960.0	+	12678.6i	−0.700733	+	0.404569i
$995$	−3783.00	+	2184.12i	−0.120532	+	0.0695891i
$996$		0			0
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	0.992975	+	0.118321i	$0.0377511\pi$
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	−0.394019	+	0.919102i	$0.628916\pi$
$998$	−15309.0	+	26516.0i	−0.485569	+	0.841030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.a.82.1		2
3.2	odd	2		13.4.e.b.4.1	✓	2
12.11	even	2		208.4.w.b.17.1		2
13.6	odd	12		1521.4.a.o.1.2		2
13.7	odd	12		1521.4.a.o.1.1		2
13.10	even	6	inner	117.4.q.a.10.1		2
39.2	even	12		169.4.c.h.146.2		4
39.5	even	4		169.4.c.h.22.2		4
39.8	even	4		169.4.c.h.22.1		4
39.11	even	12		169.4.c.h.146.1		4
39.17	odd	6		169.4.b.d.168.2		2
39.20	even	12		169.4.a.i.1.2		2
39.23	odd	6		13.4.e.b.10.1	yes	2
39.29	odd	6		169.4.e.a.23.1		2
39.32	even	12		169.4.a.i.1.1		2
39.35	odd	6		169.4.b.d.168.1		2
39.38	odd	2		169.4.e.a.147.1		2
156.23	even	6		208.4.w.b.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.b.4.1	✓	2	3.2	odd	2
13.4.e.b.10.1	yes	2	39.23	odd	6
117.4.q.a.10.1		2	13.10	even	6	inner
117.4.q.a.82.1		2	1.1	even	1	trivial
169.4.a.i.1.1		2	39.32	even	12
169.4.a.i.1.2		2	39.20	even	12
169.4.b.d.168.1		2	39.35	odd	6
169.4.b.d.168.2		2	39.17	odd	6
169.4.c.h.22.1		4	39.8	even	4
169.4.c.h.22.2		4	39.5	even	4
169.4.c.h.146.1		4	39.11	even	12
169.4.c.h.146.2		4	39.2	even	12
169.4.e.a.23.1		2	39.29	odd	6
169.4.e.a.147.1		2	39.38	odd	2
208.4.w.b.17.1		2	12.11	even	2
208.4.w.b.49.1		2	156.23	even	6
1521.4.a.o.1.1		2	13.7	odd	12
1521.4.a.o.1.2		2	13.6	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)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(-12.0000 + 6.92820i) q^{7} +22.5167i q^{8} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(-12.0000 + 6.92820i) q^{7} +22.5167i q^{8} +(1.50000 - 2.59808i) q^{10} +(-12.0000 - 6.92820i) q^{11} +(45.5000 + 11.2583i) q^{13} +24.0000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(58.5000 + 101.325i) q^{17} +(-99.0000 + 57.1577i) q^{19} +(7.50000 - 4.33013i) q^{20} +(12.0000 + 20.7846i) q^{22} +(-39.0000 + 67.5500i) q^{23} +122.000 q^{25} +(-58.5000 - 56.2917i) q^{26} +(60.0000 + 34.6410i) q^{28} +(-70.5000 + 122.110i) q^{29} +155.885i q^{31} +(157.500 - 90.9327i) q^{32} -202.650i q^{34} +(-12.0000 - 20.7846i) q^{35} +(-124.500 - 71.8801i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(-235.500 - 135.966i) q^{41} +(-52.0000 - 90.0666i) q^{43} +69.2820i q^{44} +(117.000 - 67.5500i) q^{46} -301.377i q^{47} +(-75.5000 + 130.770i) q^{49} +(-183.000 - 105.655i) q^{50} +(-65.0000 - 225.167i) q^{52} -93.0000 q^{53} +(12.0000 - 20.7846i) q^{55} +(-156.000 - 270.200i) q^{56} +(211.500 - 122.110i) q^{58} +(246.000 - 142.028i) q^{59} +(-72.5000 - 125.574i) q^{61} +(135.000 - 233.827i) q^{62} -307.000 q^{64} +(-19.5000 + 78.8083i) q^{65} +(-681.000 - 393.176i) q^{67} +(292.500 - 506.625i) q^{68} +41.5692i q^{70} +(-915.000 + 528.275i) q^{71} +458.993i q^{73} +(124.500 + 215.640i) q^{74} +(495.000 + 285.788i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(-1.50000 - 0.866025i) q^{80} +(235.500 + 407.898i) q^{82} +789.815i q^{83} +(-175.500 + 101.325i) q^{85} +180.133i q^{86} +(156.000 - 270.200i) q^{88} +(846.000 + 488.438i) q^{89} +(-624.000 + 180.133i) q^{91} +390.000 q^{92} +(-261.000 + 452.065i) q^{94} +(-99.0000 - 171.473i) q^{95} +(174.000 - 100.459i) q^{97} +(226.500 - 130.770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7}+O(q^{10}) \) 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7	\( 2 q - 3 q^{2} - 5 q^{4} - 24 q^{7} + 3 q^{10} - 24 q^{11} + 91 q^{13} + 48 q^{14} - q^{16} + 117 q^{17} - 198 q^{19} + 15 q^{20} + 24 q^{22} - 78 q^{23} + 244 q^{25} - 117 q^{26} + 120 q^{28} - 141 q^{29} + 315 q^{32} - 24 q^{35} - 249 q^{37} + 396 q^{38} - 78 q^{40} - 471 q^{41} - 104 q^{43} + 234 q^{46} - 151 q^{49} - 366 q^{50} - 130 q^{52} - 186 q^{53} + 24 q^{55} - 312 q^{56} + 423 q^{58} + 492 q^{59} - 145 q^{61} + 270 q^{62} - 614 q^{64} - 39 q^{65} - 1362 q^{67} + 585 q^{68} - 1830 q^{71} + 249 q^{74} + 990 q^{76} + 384 q^{77} + 2552 q^{79} - 3 q^{80} + 471 q^{82} - 351 q^{85} + 312 q^{88} + 1692 q^{89} - 1248 q^{91} + 780 q^{92} - 522 q^{94} - 198 q^{95} + 348 q^{97} + 453 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7 + 3 * q^10 - 24 * q^11 + 91 * q^13 + 48 * q^14 - q^16 + 117 * q^17 - 198 * q^19 + 15 * q^20 + 24 * q^22 - 78 * q^23 + 244 * q^25 - 117 * q^26 + 120 * q^28 - 141 * q^29 + 315 * q^32 - 24 * q^35 - 249 * q^37 + 396 * q^38 - 78 * q^40 - 471 * q^41 - 104 * q^43 + 234 * q^46 - 151 * q^49 - 366 * q^50 - 130 * q^52 - 186 * q^53 + 24 * q^55 - 312 * q^56 + 423 * q^58 + 492 * q^59 - 145 * q^61 + 270 * q^62 - 614 * q^64 - 39 * q^65 - 1362 * q^67 + 585 * q^68 - 1830 * q^71 + 249 * q^74 + 990 * q^76 + 384 * q^77 + 2552 * q^79 - 3 * q^80 + 471 * q^82 - 351 * q^85 + 312 * q^88 + 1692 * q^89 - 1248 * q^91 + 780 * q^92 - 522 * q^94 - 198 * q^95 + 348 * q^97 + 453 * q^98

Introduction

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