LMFDB - Embedded newform 117.4.q.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +(1.50000 + 2.59808i) q^{10} +(-12.0000 + 6.92820i) q^{11} +(45.5000 - 11.2583i) q^{13} +24.0000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(58.5000 - 101.325i) q^{17} +(-99.0000 - 57.1577i) q^{19} +(7.50000 + 4.33013i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-39.0000 - 67.5500i) q^{23} +122.000 q^{25} +(-58.5000 + 56.2917i) q^{26} +(60.0000 - 34.6410i) q^{28} +(-70.5000 - 122.110i) q^{29} -155.885i q^{31} +(157.500 + 90.9327i) q^{32} +202.650i q^{34} +(-12.0000 + 20.7846i) q^{35} +(-124.500 + 71.8801i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(-235.500 + 135.966i) q^{41} +(-52.0000 + 90.0666i) q^{43} -69.2820i q^{44} +(117.000 + 67.5500i) q^{46} +301.377i q^{47} +(-75.5000 - 130.770i) q^{49} +(-183.000 + 105.655i) q^{50} +(-65.0000 + 225.167i) q^{52} -93.0000 q^{53} +(12.0000 + 20.7846i) q^{55} +(-156.000 + 270.200i) q^{56} +(211.500 + 122.110i) q^{58} +(246.000 + 142.028i) q^{59} +(-72.5000 + 125.574i) q^{61} +(135.000 + 233.827i) q^{62} -307.000 q^{64} +(-19.5000 - 78.8083i) q^{65} +(-681.000 + 393.176i) q^{67} +(292.500 + 506.625i) q^{68} -41.5692i q^{70} +(-915.000 - 528.275i) q^{71} -458.993i q^{73} +(124.500 - 215.640i) q^{74} +(495.000 - 285.788i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(-1.50000 + 0.866025i) q^{80} +(235.500 - 407.898i) q^{82} -789.815i q^{83} +(-175.500 - 101.325i) q^{85} -180.133i q^{86} +(156.000 + 270.200i) q^{88} +(846.000 - 488.438i) q^{89} +(-624.000 - 180.133i) q^{91} +390.000 q^{92} +(-261.000 - 452.065i) q^{94} +(-99.0000 + 171.473i) q^{95} +(174.000 + 100.459i) q^{97} +(226.500 + 130.770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.50000	+	0.866025i	−0.530330	+	0.306186i	−0.741151	−	0.671339i	$-0.765720\pi$
$2$	−1.50000	+	0.866025i	−0.530330	+	0.306186i	0.210821	+	0.977525i	$0.432386\pi$
$3$		0			0
$3$		0			0
$4$	−2.50000	+	4.33013i	−0.312500	+	0.541266i
$5$		−	1.73205i		−	0.154919i	−0.996995	−	0.0774597i	$-0.975319\pi$
$5$		−	1.73205i		−	0.154919i	0.996995	−	0.0774597i	$-0.0246809\pi$
$6$		0			0
$7$	−12.0000	−	6.92820i	−0.647939	−	0.374088i	0.139727	−	0.990190i	$-0.455377\pi$
$7$	−12.0000	−	6.92820i	−0.647939	−	0.374088i	−0.787666	+	0.616102i	$0.788711\pi$
$8$		−	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	−0.655362	−	0.755315i	$-0.727484\pi$
$11$	−12.0000	+	6.92820i	−0.328921	+	0.189903i	0.326441	+	0.945218i	$0.394151\pi$
$12$		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	−0.0597414	−	0.998214i	$-0.519028\pi$
$17$	58.5000	−	101.325i	0.834608	−	1.44558i	0.894349	−	0.447369i	$-0.147639\pi$
$18$		0			0
$19$	−99.0000	−	57.1577i	−1.19538	−	0.690151i	−0.235856	−	0.971788i	$-0.575789\pi$
$19$	−99.0000	−	57.1577i	−1.19538	−	0.690151i	−0.959521	+	0.281637i	$0.909123\pi$
$20$	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	0.633304	−	0.773903i	$-0.281698\pi$
$23$	−39.0000	−	67.5500i	−0.353568	−	0.612398i	−0.986872	+	0.161506i	$0.948365\pi$
$24$		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	0.547043	−	0.837104i	$-0.315753\pi$
$29$	−70.5000	−	122.110i	−0.451432	−	0.781903i	−0.998475	+	0.0552014i	$0.982420\pi$
$30$		0			0
$31$		−	155.885i		−	0.903151i	−0.892233	−	0.451576i	$-0.850862\pi$
$31$		−	155.885i		−	0.903151i	0.892233	−	0.451576i	$-0.149138\pi$
$32$	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	−0.750404	−	0.660980i	$-0.770141\pi$
$37$	−124.500	+	71.8801i	−0.553180	+	0.319379i	0.197223	+	0.980359i	$0.436808\pi$
$38$	198.000			0.845259
$39$		0			0
$40$	−39.0000			−0.154161
$41$	−235.500	+	135.966i	−0.897047	+	0.517910i	−0.876241	−	0.481873i	$-0.839957\pi$
$41$	−235.500	+	135.966i	−0.897047	+	0.517910i	−0.0208059	+	0.999784i	$0.506623\pi$
$42$		0			0
$43$	−52.0000	+	90.0666i	−0.184417	+	0.319419i	−0.943380	−	0.331714i	$-0.892373\pi$
$43$	−52.0000	+	90.0666i	−0.184417	+	0.319419i	0.758963	+	0.651134i	$0.225706\pi$
$44$		−	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	$0.154904\pi$
$47$			301.377i			0.935326i	−0.883907	+	0.467663i	$0.845096\pi$
$48$		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	0.746222	−	0.665698i	$-0.231866\pi$
$59$	246.000	+	142.028i	0.542822	+	0.313398i	−0.203400	+	0.979096i	$0.565199\pi$
$60$		0			0
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	−0.932027	−	0.362389i	$-0.881961\pi$
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	0.779852	+	0.625964i	$0.215294\pi$
$62$	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	−0.969451	−	0.245286i	$-0.921118\pi$
$67$	−681.000	+	393.176i	−1.24175	+	0.716926i	−0.272301	+	0.962212i	$0.587785\pi$
$68$	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	−0.999385	−	0.0350641i	$-0.988836\pi$
$71$	−915.000	−	528.275i	−1.52944	−	0.883025i	−0.530059	−	0.847961i	$-0.677830\pi$
$72$		0			0
$73$		−	458.993i		−	0.735906i	−0.929844	−	0.367953i	$-0.880059\pi$
$73$		−	458.993i		−	0.735906i	0.929844	−	0.367953i	$-0.119941\pi$
$74$	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	$-0.825093\pi$
$83$		−	789.815i		−	1.04450i	0.852793	−	0.522250i	$-0.174907\pi$
$84$		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	0.0971073	−	0.995274i	$-0.469041\pi$
$89$	846.000	−	488.438i	1.00759	−	0.581734i	0.910486	+	0.413540i	$0.135708\pi$
$90$		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	0.588295	−	0.808646i	$-0.299799\pi$
$97$	174.000	+	100.459i	0.182134	+	0.105155i	−0.406161	+	0.913802i	$0.633133\pi$
$98$	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	0.952129	−	0.305698i	$-0.0988897\pi$
$101$	214.500	+	371.525i	0.211322	+	0.366021i	−0.740806	+	0.671719i	$0.765556\pi$
$102$		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	−0.974880	−	0.222729i	$-0.928503\pi$
$107$	−753.000	−	1304.23i	−0.680330	−	1.17837i	0.294551	−	0.955636i	$-0.404830\pi$
$108$		0			0
$109$		−	1551.92i		−	1.36373i	−0.731477	−	0.681866i	$-0.761169\pi$
$109$		−	1551.92i		−	1.36373i	0.731477	−	0.681866i	$-0.238831\pi$
$110$	−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	−0.972842	−	0.231470i	$-0.925647\pi$
$113$	−343.500	+	594.959i	−0.285962	+	0.495302i	0.686880	+	0.726771i	$0.258980\pi$
$114$		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	0.811734	−	0.584027i	$-0.198524\pi$
$127$	−143.000	−	247.683i	−0.0999149	−	0.173058i	−0.911649	+	0.410969i	$0.865190\pi$
$128$	−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	0.710961	−	0.703232i	$-0.248260\pi$
$137$	733.500	+	423.486i	0.457424	+	0.264094i	−0.253536	+	0.967326i	$0.581594\pi$
$138$		0			0
$139$	−118.000	+	204.382i	−0.0720045	+	0.124716i	−0.899780	−	0.436344i	$-0.856273\pi$
$139$	−118.000	+	204.382i	−0.0720045	+	0.124716i	0.827775	+	0.561060i	$0.189606\pi$
$140$	−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	0.511093	−	0.859526i	$-0.329241\pi$
$149$	40.5000	+	23.3827i	0.0222677	+	0.0128563i	−0.488825	+	0.872382i	$0.662574\pi$
$150$		0			0
$151$			1770.16i			0.953995i	0.878905	+	0.476998i	$0.158275\pi$
$151$			1770.16i			0.953995i	−0.878905	+	0.476998i	$0.841725\pi$
$152$	−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	0.276187	−	0.961104i	$-0.410929\pi$
$163$	−870.000	−	502.295i	−0.418059	−	0.241367i	−0.694247	+	0.719737i	$0.744262\pi$
$164$		−	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	−0.672141	−	0.740423i	$-0.734625\pi$
$167$	−792.000	+	457.261i	−0.366987	+	0.211880i	0.305154	+	0.952303i	$0.401292\pi$
$168$		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	−0.431394	−	0.902164i	$-0.641978\pi$
$173$	1287.00	−	2229.15i	0.565600	−	0.979648i	0.996994	−	0.0774841i	$-0.0246887\pi$
$174$		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	0.930965	+	0.365108i	$0.118968\pi$
$179$	1872.00	+	3242.40i	0.781675	+	1.35390i	−0.149290	+	0.988793i	$0.547699\pi$
$180$		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	−0.999959	−	0.00909077i	$-0.997106\pi$
$191$	−1299.00	+	2249.93i	−0.492106	+	0.852353i	0.507852	+	0.861444i	$0.330440\pi$
$192$		0			0
$193$	967.500	−	558.586i	0.360840	−	0.208331i	−0.308609	−	0.951189i	$-0.599863\pi$
$193$	967.500	−	558.586i	0.360840	−	0.208331i	0.669449	+	0.742858i	$0.266530\pi$
$194$	−348.000			−0.128788
$195$		0			0
$196$	755.000			0.275146
$197$	−1776.00	+	1025.37i	−0.642308	+	0.370837i	−0.785503	−	0.618858i	$-0.787596\pi$
$197$	−1776.00	+	1025.37i	−0.642308	+	0.370837i	0.143195	+	0.989695i	$0.454262\pi$
$198$		0			0
$199$	1261.00	−	2184.12i	0.449196	−	0.778030i	−0.549138	−	0.835732i	$-0.685044\pi$
$199$	1261.00	−	2184.12i	0.449196	−	0.778030i	0.998334	+	0.0577019i	$0.0183773\pi$
$200$		−	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	0.768428	−	0.639936i	$-0.221039\pi$
$211$	−521.000	−	902.398i	−0.169986	−	0.294425i	−0.938415	+	0.345511i	$0.887706\pi$
$212$	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	−0.779243	−	0.626722i	$-0.784396\pi$
$223$	−2085.00	+	1203.78i	−0.626107	+	0.361483i	0.153136	+	0.988205i	$0.451063\pi$
$224$	−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	0.163190	−	0.986595i	$-0.447822\pi$
$227$	−2085.00	−	1203.78i	−0.609631	−	0.351971i	−0.772821	+	0.634624i	$0.781155\pi$
$228$		0			0
$229$		−	2508.01i		−	0.723729i	−0.932231	−	0.361864i	$-0.882140\pi$
$229$		−	2508.01i		−	0.723729i	0.932231	−	0.361864i	$-0.117860\pi$
$230$	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	$-0.740229\pi$
$239$		−	5383.21i		−	1.45695i	0.685072	−	0.728475i	$-0.259771\pi$
$240$		0			0
$241$	4258.50	+	2458.65i	1.13823	+	0.657159i	0.945992	−	0.324189i	$-0.105091\pi$
$241$	4258.50	+	2458.65i	1.13823	+	0.657159i	0.192240	+	0.981348i	$0.438425\pi$
$242$		−	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	0.499822	+	0.866128i	$0.333399\pi$
$251$	−1989.00	+	3445.05i	−0.500178	+	0.866333i	−1.00000		0.000205037i	$0.999935\pi$
$252$		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	0.963760	−	0.266772i	$-0.0859572\pi$
$257$	1033.50	+	1790.07i	0.250848	+	0.434482i	−0.712911	+	0.701254i	$0.752624\pi$
$258$		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	0.720318	−	0.693644i	$-0.243996\pi$
$263$	−1026.00	−	1777.08i	−0.240555	−	0.416653i	−0.960872	+	0.276991i	$0.910663\pi$
$264$		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	−0.613295	−	0.789854i	$-0.710156\pi$
$269$	1665.00	−	2883.86i	0.377386	−	0.653652i	0.990681	+	0.136202i	$0.0434897\pi$
$270$		0			0
$271$	2430.00	−	1402.96i	0.544694	−	0.314479i	−0.202285	−	0.979327i	$-0.564837\pi$
$271$	2430.00	−	1402.96i	0.544694	−	0.314479i	0.746979	+	0.664848i	$0.231504\pi$
$272$	−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	−0.885745	−	0.464172i	$-0.846352\pi$
$277$	−188.500	+	326.492i	−0.0408876	+	0.0708194i	0.844857	+	0.534992i	$0.179685\pi$
$278$		−	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	$-0.998771\pi$
$281$		−	36.3731i		−	0.00772183i	0.999993	−	0.00386092i	$-0.00122897\pi$
$282$		0			0
$283$	3562.00	+	6169.56i	0.748194	+	1.29591i	0.948688	+	0.316215i	$0.102412\pi$
$283$	3562.00	+	6169.56i	0.748194	+	1.29591i	−0.200493	+	0.979695i	$0.564255\pi$
$284$	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	0.997646	−	0.0685685i	$-0.0218432\pi$
$293$	7207.50	+	4161.25i	1.43709	+	0.829703i	0.439441	+	0.898271i	$0.355177\pi$
$294$		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	$0.0661750\pi$
$307$			2220.49i			0.412801i	−0.978468	+	0.206401i	$0.933825\pi$
$308$	−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	$0.112776\pi$
$317$			3916.17i			0.693861i	−0.937891	+	0.346930i	$0.887224\pi$
$318$		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	−0.143321	−	0.989676i	$-0.545778\pi$
$331$	−6456.00	−	3727.37i	−1.07207	−	0.618958i	−0.928745	+	0.370719i	$0.879111\pi$
$332$	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	0.460128	+	0.887853i	$0.347804\pi$
$347$	−3483.00	+	6032.73i	−0.538839	+	0.933297i	−0.998967	+	0.0454442i	$0.985530\pi$
$348$		0			0
$349$	−5760.00	+	3325.54i	−0.883455	+	0.510063i	−0.871796	−	0.489869i	$-0.837045\pi$
$349$	−5760.00	+	3325.54i	−0.883455	+	0.510063i	−0.0116588	+	0.999932i	$0.503711\pi$
$350$	2928.00			0.447166
$351$		0			0
$352$	−2520.00			−0.381581
$353$	−4876.50	+	2815.45i	−0.735269	+	0.424508i	−0.820347	−	0.571867i	$-0.806219\pi$
$353$	−4876.50	+	2815.45i	−0.735269	+	0.424508i	0.0850777	+	0.996374i	$0.472886\pi$
$354$		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	$-0.824424\pi$
$359$		−	7129.12i		−	1.04808i	0.851694	−	0.524040i	$-0.175576\pi$
$360$		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	0.865954	−	0.500123i	$-0.166712\pi$
$367$	−1.00000	−	1.73205i	−0.000142233	−	0.000246355i	−0.866097	+	0.499877i	$0.833379\pi$
$368$	−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	−0.961527	−	0.274711i	$-0.911418\pi$
$373$	−1749.50	+	3030.22i	−0.242857	+	0.420641i	0.718670	+	0.695351i	$0.244751\pi$
$374$	−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	−0.139871	−	0.990170i	$-0.544669\pi$
$379$	4779.00	−	2759.16i	0.647706	−	0.373953i	0.787577	+	0.616216i	$0.211335\pi$
$380$	−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	0.860960	−	0.508673i	$-0.169864\pi$
$383$	6378.00	+	3682.34i	0.850915	+	0.491276i	−0.0100443	+	0.999950i	$0.503197\pi$
$384$		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	0.976917	−	0.213618i	$-0.0685248\pi$
$397$	10128.0	+	5847.40i	1.28038	+	0.739226i	0.303460	+	0.952844i	$0.401858\pi$
$398$			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	−0.330571	−	0.943781i	$-0.607241\pi$
$401$	2581.50	−	1490.43i	0.321481	−	0.185607i	0.652053	+	0.758174i	$0.273908\pi$
$402$		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	0.502265	−	0.864714i	$-0.332500\pi$
$409$	37.5000	+	21.6506i	0.00453363	+	0.00261749i	−0.497731	+	0.867331i	$0.665833\pi$
$410$	−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	−0.998159	−	0.0606569i	$-0.980680\pi$
$419$	−4731.00	−	8194.33i	−0.551610	−	0.955416i	0.446549	−	0.894759i	$-0.352653\pi$
$420$		0			0
$421$		−	7068.50i		−	0.818284i	−0.912471	−	0.409142i	$-0.865828\pi$
$421$		−	7068.50i		−	0.818284i	0.912471	−	0.409142i	$-0.134172\pi$
$422$	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	0.0644552	−	0.997921i	$-0.479469\pi$
$431$	8598.00	−	4964.06i	0.960907	−	0.554780i	0.896452	+	0.443140i	$0.146136\pi$
$432$		0			0
$433$	3308.50	−	5730.49i	0.367197	−	0.636004i	−0.621929	−	0.783074i	$-0.713651\pi$
$433$	3308.50	−	5730.49i	0.367197	−	0.636004i	0.989126	+	0.147070i	$0.0469841\pi$
$434$		−	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	−0.942656	−	0.333765i	$-0.891681\pi$
$439$	−6994.00	−	12114.0i	−0.760377	−	1.31701i	0.182280	−	0.983247i	$-0.441652\pi$
$440$	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	0.0259758	−	0.999663i	$-0.491731\pi$
$449$	−7866.00	−	4541.44i	−0.826769	−	0.477336i	−0.852745	+	0.522327i	$0.825064\pi$
$450$		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	−0.383959	−	0.923350i	$-0.625440\pi$
$457$	2185.50	−	1261.80i	0.223705	−	0.129156i	0.607665	+	0.794194i	$0.292106\pi$
$458$	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	−0.929270	−	0.369400i	$-0.879563\pi$
$461$	−16963.5	−	9793.88i	−1.71382	−	0.989472i	−0.784545	−	0.620072i	$-0.787103\pi$
$462$		0			0
$463$		−	8632.54i		−	0.866497i	−0.901274	−	0.433249i	$-0.857367\pi$
$463$		−	8632.54i		−	0.866497i	0.901274	−	0.433249i	$-0.142633\pi$
$464$	−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	−0.390827	−	0.920464i	$-0.627811\pi$
$479$	2211.00	−	1276.52i	0.210904	−	0.121766i	0.601732	+	0.798698i	$0.294478\pi$
$480$		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	0.868212	−	0.496193i	$-0.165269\pi$
$487$	9378.00	+	5414.39i	0.872603	+	0.503798i	0.00439074	+	0.999990i	$0.498602\pi$
$488$	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	0.999631	+	0.0271797i	$0.00865264\pi$
$491$	5694.00	+	9862.30i	0.523354	+	0.906475i	−0.476277	+	0.879295i	$0.658014\pi$
$492$		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	$0.291446\pi$
$499$			17677.3i			1.58586i	−0.609311	+	0.792931i	$0.708554\pi$
$500$	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	−0.767255	−	0.641343i	$-0.778378\pi$
$503$	1938.00	−	3356.71i	0.171792	−	0.297552i	0.939046	+	0.343791i	$0.111711\pi$
$504$		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	0.308893	−	0.951097i	$-0.400042\pi$
$509$	14779.5	−	8532.95i	1.28701	−	0.743058i	0.978120	+	0.208039i	$0.0667082\pi$
$510$		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	0.999717	−	0.0238072i	$-0.00757878\pi$
$523$	5732.00	+	9928.12i	0.479241	+	0.830069i	−0.520476	+	0.853876i	$0.674245\pi$
$524$	−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	$0.0606324\pi$
$541$			4764.87i			0.378665i	−0.981913	+	0.189333i	$0.939368\pi$
$542$	−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	0.234174	−	0.972195i	$-0.424761\pi$
$557$	15685.5	−	9056.03i	1.19321	−	0.688898i	0.959032	+	0.283297i	$0.0914281\pi$
$558$		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	−0.998713	−	0.0507160i	$-0.983850\pi$
$563$	−6084.00	+	10537.8i	−0.455435	+	0.788837i	0.543278	+	0.839553i	$0.317183\pi$
$564$		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	0.688013	−	0.725698i	$-0.258483\pi$
$569$	−3861.00	−	6687.45i	−0.284467	−	0.492711i	−0.972480	+	0.232988i	$0.925150\pi$
$570$		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	$-0.811888\pi$
$577$		−	15444.7i		−	1.11433i	0.830400	−	0.557167i	$-0.188112\pi$
$578$	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	−0.00610719	−	0.999981i	$-0.501944\pi$
$587$	12186.0	−	7035.59i	0.856848	−	0.494702i	0.862956	+	0.505280i	$0.168611\pi$
$588$		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	$0.382593\pi$
$593$			26938.6i			1.86549i	−0.360538	+	0.932745i	$0.617407\pi$
$594$		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	0.999993	+	0.00381713i	$0.00121503\pi$
$601$	7415.50	+	12844.0i	0.503302	+	0.871745i	−0.496691	+	0.867928i	$0.665452\pi$
$602$	−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	−0.701874	−	0.712301i	$-0.747653\pi$
$607$	3977.00	−	6888.37i	0.265933	−	0.460610i	0.967808	+	0.251691i	$0.0809866\pi$
$608$	−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	0.441315	−	0.897352i	$-0.354512\pi$
$613$	21841.5	−	12610.2i	1.43910	−	0.830866i	0.997787	+	0.0664859i	$0.0211787\pi$
$614$	−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	0.902980	−	0.429683i	$-0.141375\pi$
$617$	15055.5	+	8692.30i	0.982353	+	0.567162i	0.0793731	+	0.996845i	$0.474708\pi$
$618$		0			0
$619$			8209.92i			0.533093i	0.963822	+	0.266547i	$0.0858826\pi$
$619$			8209.92i			0.533093i	−0.963822	+	0.266547i	$0.914117\pi$
$620$	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	0.808442	−	0.588576i	$-0.200311\pi$
$631$	11142.0	+	6432.84i	0.702941	+	0.405843i	−0.105501	+	0.994419i	$0.533645\pi$
$632$		−	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	−0.754549	−	0.656244i	$-0.772144\pi$
$641$	3100.50	−	5370.22i	0.191049	−	0.330907i	0.945598	+	0.325337i	$0.105478\pi$
$642$		0			0
$643$	−14568.0	−	8410.84i	−0.893477	−	0.515849i	−0.0183989	−	0.999831i	$-0.505857\pi$
$643$	−14568.0	−	8410.84i	−0.893477	−	0.515849i	−0.875078	+	0.483981i	$0.839190\pi$
$644$	−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	0.584914	−	0.811095i	$-0.301128\pi$
$647$	−6747.00	−	11686.1i	−0.409972	−	0.710092i	−0.994886	+	0.101003i	$0.967795\pi$
$648$		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	0.644747	−	0.764396i	$-0.276963\pi$
$653$	−5667.00	−	9815.53i	−0.339612	−	0.588226i	−0.984360	+	0.176170i	$0.943629\pi$
$654$		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	−0.601408	−	0.798942i	$-0.705393\pi$
$659$	6618.00	−	11462.7i	0.391200	−	0.677578i	0.992608	+	0.121364i	$0.0387268\pi$
$660$		0			0
$661$	−10264.5	+	5926.21i	−0.603998	+	0.348718i	−0.770613	−	0.637304i	$-0.780050\pi$
$661$	−10264.5	+	5926.21i	−0.603998	+	0.348718i	0.166615	+	0.986022i	$0.446716\pi$
$662$	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	0.728014	−	0.685563i	$-0.240444\pi$
$673$	−4010.50	−	6946.39i	−0.229708	−	0.397866i	−0.957722	+	0.287697i	$0.907110\pi$
$674$	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	0.978223	−	0.207557i	$-0.0665514\pi$
$683$	22983.0	+	13269.2i	1.28758	+	0.743387i	0.309361	+	0.950945i	$0.399885\pi$
$684$		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	−0.519688	−	0.854356i	$-0.673952\pi$
$691$	−720.000	+	415.692i	−0.0396383	+	0.0228852i	0.480050	+	0.877241i	$0.340619\pi$
$692$	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	0.202113	−	0.979362i	$-0.435219\pi$
$709$	−10288.5	−	5940.07i	−0.544983	−	0.314646i	−0.747096	+	0.664716i	$0.768552\pi$
$710$		−	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	−0.522264	−	0.852784i	$-0.674912\pi$
$719$	9204.00	−	15941.8i	0.477401	−	0.826883i	0.999665	+	0.0259014i	$0.00824561\pi$
$720$		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	$0.206291\pi$
$733$			23959.5i			1.20732i	−0.797243	+	0.603658i	$0.793709\pi$
$734$	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	−0.430200	−	0.902734i	$-0.641557\pi$
$739$	2742.00	−	1583.09i	0.136490	−	0.0788025i	0.566690	+	0.823931i	$0.308224\pi$
$740$	−1245.00			−0.0618474
$741$		0			0
$742$	−2232.00			−0.110430
$743$	26070.0	−	15051.5i	1.28723	−	0.743185i	0.309075	−	0.951038i	$-0.399981\pi$
$743$	26070.0	−	15051.5i	1.28723	−	0.743185i	0.978160	+	0.207852i	$0.0666474\pi$
$744$		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	−0.971083	−	0.238744i	$-0.923264\pi$
$751$	−14248.0	−	24678.3i	−0.692299	−	1.19910i	0.278783	−	0.960354i	$-0.410069\pi$
$752$	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	0.577524	−	0.816374i	$-0.304019\pi$
$757$	−8711.00	−	15087.9i	−0.418239	−	0.724411i	−0.995762	+	0.0919633i	$0.970686\pi$
$758$	−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	−0.940695	−	0.339252i	$-0.889826\pi$
$761$	−35790.0	−	20663.4i	−1.70484	−	0.984292i	−0.764149	−	0.645040i	$-0.776841\pi$
$762$		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	−0.757725	−	0.652574i	$-0.773689\pi$
$769$	−12186.0	+	7035.59i	−0.571441	+	0.329922i	0.186283	+	0.982496i	$0.440356\pi$
$770$	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	0.495946	−	0.868353i	$-0.334821\pi$
$773$	−174.000	−	100.459i	−0.00809618	−	0.00467433i	−0.504043	+	0.863679i	$0.668155\pi$
$774$		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	0.358445	−	0.933551i	$-0.383307\pi$
$787$	−5979.00	−	3451.98i	−0.270811	−	0.156353i	−0.629256	+	0.777198i	$0.716640\pi$
$788$		−	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	0.275102	+	0.961415i	$0.411288\pi$
$797$	−15639.0	+	27087.5i	−0.695059	+	1.20388i	−0.970161	+	0.242462i	$0.922045\pi$
$798$		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	0.940127	−	0.340826i	$-0.110707\pi$
$809$	4024.50	+	6970.64i	0.174900	+	0.302935i	−0.765227	+	0.643761i	$0.777373\pi$
$810$		0			0
$811$		−	14026.1i		−	0.607305i	−0.952783	−	0.303653i	$-0.901794\pi$
$811$		−	14026.1i		−	0.607305i	0.952783	−	0.303653i	$-0.0982062\pi$
$812$	−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	−0.344718	−	0.938706i	$-0.612026\pi$
$821$	6960.00	−	4018.36i	0.295866	−	0.170818i	0.640584	+	0.767888i	$0.278692\pi$
$822$		0			0
$823$	20150.0	−	34900.8i	0.853445	−	1.47821i	−0.0246361	−	0.999696i	$-0.507843\pi$
$823$	20150.0	−	34900.8i	0.853445	−	1.47821i	0.878081	−	0.478513i	$-0.158824\pi$
$824$		−	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	$0.312217\pi$
$827$			39525.4i			1.66195i	−0.556310	+	0.830975i	$0.687783\pi$
$828$		0			0
$829$	6155.50	+	10661.6i	0.257888	+	0.446676i	0.965676	−	0.259750i	$-0.0836400\pi$
$829$	6155.50	+	10661.6i	0.257888	+	0.446676i	−0.707788	+	0.706425i	$0.750307\pi$
$830$	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	0.0660899	−	0.997814i	$-0.478948\pi$
$839$	−18591.0	−	10733.5i	−0.764997	−	0.441671i	−0.831087	+	0.556142i	$0.812281\pi$
$840$		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	$-0.995054\pi$
$853$		−	774.227i		−	0.0310774i	0.999879	−	0.0155387i	$-0.00494632\pi$
$854$	−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	$-0.985991\pi$
$863$		−	2230.88i		−	0.0879955i	0.999032	−	0.0439977i	$-0.0140094\pi$
$864$		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	0.193943	−	0.981013i	$-0.437872\pi$
$877$	−14509.5	−	8377.06i	−0.558667	−	0.322547i	−0.752610	+	0.658466i	$0.771206\pi$
$878$	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	0.982873	−	0.184284i	$-0.0589967\pi$
$881$	8677.50	+	15029.9i	0.331842	+	0.574766i	−0.651031	+	0.759051i	$0.725663\pi$
$882$		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	0.769228	−	0.638975i	$-0.220641\pi$
$887$	−4458.00	−	7721.48i	−0.168754	−	0.292291i	−0.937982	+	0.346684i	$0.887308\pi$
$888$		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	0.997102	+	0.0760813i	$0.0242408\pi$
$907$	15418.0	+	26704.8i	0.564439	+	0.977637i	−0.432662	+	0.901556i	$0.642426\pi$
$908$	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	−0.489472	−	0.872019i	$-0.662811\pi$
$919$	14221.0	−	24631.5i	0.510454	−	0.884133i	0.999927	−	0.0121140i	$-0.00385609\pi$
$920$	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	0.389472	−	0.921038i	$-0.372658\pi$
$929$	−6043.50	−	3489.22i	−0.213435	−	0.123227i	−0.602907	+	0.797812i	$0.705991\pi$
$930$		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	$0.0269628\pi$
$941$			4884.38i			0.169210i	−0.996415	+	0.0846049i	$0.973037\pi$
$942$		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	−0.787225	−	0.616665i	$-0.788483\pi$
$947$	−18849.0	+	10882.5i	−0.646790	+	0.373424i	0.140435	+	0.990090i	$0.455150\pi$
$948$		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	−0.805753	−	0.592251i	$-0.798239\pi$
$953$	3237.00	−	5606.65i	0.110028	−	0.190574i	0.915781	+	0.401677i	$0.131573\pi$
$954$		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	$-0.959980\pi$
$967$		−	7541.35i		−	0.250789i	0.992107	−	0.125395i	$-0.0400197\pi$
$968$	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	−0.417328	−	0.908756i	$-0.637033\pi$
$971$	17499.0	−	30309.2i	0.578342	−	1.00172i	0.995670	−	0.0929611i	$-0.0296332\pi$
$972$		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	−0.0978318	−	0.995203i	$-0.531191\pi$
$977$	21838.5	−	12608.5i	0.715123	−	0.412877i	0.812955	+	0.582326i	$0.197857\pi$
$978$		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	$-0.631673\pi$
$983$		−	56440.6i		−	1.83131i	0.401967	−	0.915654i	$-0.368327\pi$
$984$		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	−0.745142	−	0.666906i	$-0.767618\pi$
$991$	−29641.0	−	51339.7i	−0.950129	−	1.64567i	−0.204987	−	0.978765i	$-0.565715\pi$
$992$	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	−0.394019	−	0.919102i	$-0.628916\pi$
$997$	18855.5	−	32658.7i	0.598957	−	1.03742i	0.992975	−	0.118321i	$-0.0377511\pi$
$998$	−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.10.1		2
3.2	odd	2		13.4.e.b.10.1	yes	2
12.11	even	2		208.4.w.b.49.1		2
13.2	odd	12		1521.4.a.o.1.1		2
13.4	even	6	inner	117.4.q.a.82.1		2
13.11	odd	12		1521.4.a.o.1.2		2
39.2	even	12		169.4.a.i.1.2		2
39.5	even	4		169.4.c.h.146.1		4
39.8	even	4		169.4.c.h.146.2		4
39.11	even	12		169.4.a.i.1.1		2
39.17	odd	6		13.4.e.b.4.1	✓	2
39.20	even	12		169.4.c.h.22.2		4
39.23	odd	6		169.4.b.d.168.1		2
39.29	odd	6		169.4.b.d.168.2		2
39.32	even	12		169.4.c.h.22.1		4
39.35	odd	6		169.4.e.a.147.1		2
39.38	odd	2		169.4.e.a.23.1		2
156.95	even	6		208.4.w.b.17.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.b.4.1	✓	2	39.17	odd	6
13.4.e.b.10.1	yes	2	3.2	odd	2
117.4.q.a.10.1		2	1.1	even	1	trivial
117.4.q.a.82.1		2	13.4	even	6	inner
169.4.a.i.1.1		2	39.11	even	12
169.4.a.i.1.2		2	39.2	even	12
169.4.b.d.168.1		2	39.23	odd	6
169.4.b.d.168.2		2	39.29	odd	6
169.4.c.h.22.1		4	39.32	even	12
169.4.c.h.22.2		4	39.20	even	12
169.4.c.h.146.1		4	39.5	even	4
169.4.c.h.146.2		4	39.8	even	4
169.4.e.a.23.1		2	39.38	odd	2
169.4.e.a.147.1		2	39.35	odd	6
208.4.w.b.17.1		2	156.95	even	6
208.4.w.b.49.1		2	12.11	even	2
1521.4.a.o.1.1		2	13.2	odd	12
1521.4.a.o.1.2		2	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

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