LMFDB - Embedded newform 169.4.e.a.147.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
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			147.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(3.00000 - 1.73205i) q^{6} +(12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(3.00000 - 1.73205i) q^{6} +(12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-12.0000 - 6.92820i) q^{11} +10.0000 q^{12} -24.0000 q^{14} +(-3.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-58.5000 - 101.325i) q^{17} -39.8372i q^{18} +(99.0000 - 57.1577i) q^{19} +(7.50000 - 4.33013i) q^{20} +27.7128i q^{21} +(12.0000 + 20.7846i) q^{22} +(39.0000 - 67.5500i) q^{23} +(-39.0000 - 22.5167i) q^{24} +122.000 q^{25} -100.000 q^{27} +(-60.0000 - 34.6410i) q^{28} +(70.5000 - 122.110i) q^{29} +(3.00000 + 5.19615i) q^{30} -155.885i q^{31} +(157.500 - 90.9327i) q^{32} +(24.0000 - 13.8564i) q^{33} +202.650i q^{34} +(12.0000 + 20.7846i) q^{35} +(57.5000 - 99.5929i) q^{36} +(124.500 + 71.8801i) q^{37} -198.000 q^{38} -39.0000 q^{40} +(-235.500 - 135.966i) q^{41} +(24.0000 - 41.5692i) q^{42} +(-52.0000 - 90.0666i) q^{43} +69.2820i q^{44} +(-34.5000 + 19.9186i) q^{45} +(-117.000 + 67.5500i) q^{46} -301.377i q^{47} +(-1.00000 - 1.73205i) q^{48} +(-75.5000 + 130.770i) q^{49} +(-183.000 - 105.655i) q^{50} +234.000 q^{51} +93.0000 q^{53} +(150.000 + 86.6025i) q^{54} +(12.0000 - 20.7846i) q^{55} +(156.000 + 270.200i) q^{56} +228.631i q^{57} +(-211.500 + 122.110i) q^{58} +(246.000 - 142.028i) q^{59} +17.3205i q^{60} +(-72.5000 - 125.574i) q^{61} +(-135.000 + 233.827i) q^{62} +(276.000 + 159.349i) q^{63} -307.000 q^{64} -48.0000 q^{66} +(681.000 + 393.176i) q^{67} +(-292.500 + 506.625i) q^{68} +(78.0000 + 135.100i) q^{69} -41.5692i q^{70} +(-915.000 + 528.275i) q^{71} +(-448.500 + 258.942i) q^{72} -458.993i q^{73} +(-124.500 - 215.640i) q^{74} +(-122.000 + 211.310i) q^{75} +(-495.000 - 285.788i) q^{76} -192.000 q^{77} +1276.00 q^{79} +(-1.50000 - 0.866025i) q^{80} +(-210.500 + 364.597i) q^{81} +(235.500 + 407.898i) q^{82} +789.815i q^{83} +(120.000 - 69.2820i) q^{84} +(175.500 - 101.325i) q^{85} +180.133i q^{86} +(141.000 + 244.219i) q^{87} +(156.000 - 270.200i) q^{88} +(846.000 + 488.438i) q^{89} +69.0000 q^{90} -390.000 q^{92} +(270.000 + 155.885i) q^{93} +(-261.000 + 452.065i) q^{94} +(99.0000 + 171.473i) q^{95} +363.731i q^{96} +(-174.000 + 100.459i) q^{97} +(226.500 - 130.770i) q^{98} -318.697i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{6} + 24 q^{7} + 23 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 2 * q^3 - 5 * q^4 + 6 * q^6 + 24 * q^7 + 23 * q^9	$ 2 q - 3 q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{6} + 24 q^{7} + 23 q^{9} + 3 q^{10} - 24 q^{11} + 20 q^{12} - 48 q^{14} - 6 q^{15} - q^{16} - 117 q^{17} + 198 q^{19} + 15 q^{20} + 24 q^{22} + 78 q^{23} - 78 q^{24} + 244 q^{25} - 200 q^{27} - 120 q^{28} + 141 q^{29} + 6 q^{30} + 315 q^{32} + 48 q^{33} + 24 q^{35} + 115 q^{36} + 249 q^{37} - 396 q^{38} - 78 q^{40} - 471 q^{41} + 48 q^{42} - 104 q^{43} - 69 q^{45} - 234 q^{46} - 2 q^{48} - 151 q^{49} - 366 q^{50} + 468 q^{51} + 186 q^{53} + 300 q^{54} + 24 q^{55} + 312 q^{56} - 423 q^{58} + 492 q^{59} - 145 q^{61} - 270 q^{62} + 552 q^{63} - 614 q^{64} - 96 q^{66} + 1362 q^{67} - 585 q^{68} + 156 q^{69} - 1830 q^{71} - 897 q^{72} - 249 q^{74} - 244 q^{75} - 990 q^{76} - 384 q^{77} + 2552 q^{79} - 3 q^{80} - 421 q^{81} + 471 q^{82} + 240 q^{84} + 351 q^{85} + 282 q^{87} + 312 q^{88} + 1692 q^{89} + 138 q^{90} - 780 q^{92} + 540 q^{93} - 522 q^{94} + 198 q^{95} - 348 q^{97} + 453 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - 2 * q^3 - 5 * q^4 + 6 * q^6 + 24 * q^7 + 23 * q^9 + 3 * q^10 - 24 * q^11 + 20 * q^12 - 48 * q^14 - 6 * q^15 - q^16 - 117 * q^17 + 198 * q^19 + 15 * q^20 + 24 * q^22 + 78 * q^23 - 78 * q^24 + 244 * q^25 - 200 * q^27 - 120 * q^28 + 141 * q^29 + 6 * q^30 + 315 * q^32 + 48 * q^33 + 24 * q^35 + 115 * q^36 + 249 * q^37 - 396 * q^38 - 78 * q^40 - 471 * q^41 + 48 * q^42 - 104 * q^43 - 69 * q^45 - 234 * q^46 - 2 * q^48 - 151 * q^49 - 366 * q^50 + 468 * q^51 + 186 * q^53 + 300 * q^54 + 24 * q^55 + 312 * q^56 - 423 * q^58 + 492 * q^59 - 145 * q^61 - 270 * q^62 + 552 * q^63 - 614 * q^64 - 96 * q^66 + 1362 * q^67 - 585 * q^68 + 156 * q^69 - 1830 * q^71 - 897 * q^72 - 249 * q^74 - 244 * q^75 - 990 * q^76 - 384 * q^77 + 2552 * q^79 - 3 * q^80 - 421 * q^81 + 471 * q^82 + 240 * q^84 + 351 * q^85 + 282 * q^87 + 312 * q^88 + 1692 * q^89 + 138 * q^90 - 780 * q^92 + 540 * q^93 - 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−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	$0.765720\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	−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	$0.975319\pi$
$6$	3.00000	−	1.73205i	0.204124	−	0.117851i
$7$	12.0000	−	6.92820i	0.647939	−	0.374088i	−0.139727	−	0.990190i	$-0.544623\pi$
$7$	12.0000	−	6.92820i	0.647939	−	0.374088i	0.787666	+	0.616102i	$0.211289\pi$
$8$			22.5167i			0.995105i
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	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	$0.727484\pi$
$12$	10.0000			0.240563
$13$		0			0
$13$		0			0
$14$	−24.0000			−0.458162
$15$	−3.00000	−	1.73205i	−0.0516398	−	0.0298142i
$16$	−0.500000	+	0.866025i	−0.00781250	+	0.0135316i
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	−0.894349	−	0.447369i	$-0.852361\pi$
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	0.0597414	−	0.998214i	$-0.480972\pi$
$18$		−	39.8372i		−	0.521651i
$19$	99.0000	−	57.1577i	1.19538	−	0.690151i	0.235856	−	0.971788i	$-0.424211\pi$
$19$	99.0000	−	57.1577i	1.19538	−	0.690151i	0.959521	+	0.281637i	$0.0908774\pi$
$20$	7.50000	−	4.33013i	0.0838525	−	0.0484123i
$21$			27.7128i			0.287973i
$22$	12.0000	+	20.7846i	0.116291	+	0.201422i
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	−0.633304	−	0.773903i	$-0.718302\pi$
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	0.986872	+	0.161506i	$0.0516350\pi$
$24$	−39.0000	−	22.5167i	−0.331702	−	0.191508i
$25$	122.000			0.976000
$26$		0			0
$27$	−100.000			−0.712778
$28$	−60.0000	−	34.6410i	−0.404962	−	0.233805i
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	−0.547043	−	0.837104i	$-0.684247\pi$
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	0.998475	+	0.0552014i	$0.0175801\pi$
$30$	3.00000	+	5.19615i	0.0182574	+	0.0316228i
$31$		−	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
$33$	24.0000	−	13.8564i	0.126602	−	0.0730937i
$34$			202.650i			1.02218i
$35$	12.0000	+	20.7846i	0.0579534	+	0.100378i
$36$	57.5000	−	99.5929i	0.266204	−	0.461078i
$37$	124.500	+	71.8801i	0.553180	+	0.319379i	0.750404	−	0.660980i	$-0.229859\pi$
$37$	124.500	+	71.8801i	0.553180	+	0.319379i	−0.197223	+	0.980359i	$0.563192\pi$
$38$	−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	$0.839957\pi$
$42$	24.0000	−	41.5692i	0.0881733	−	0.152721i
$43$	−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
$45$	−34.5000	+	19.9186i	−0.114288	+	0.0659842i
$46$	−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	$-0.154904\pi$
$48$	−1.00000	−	1.73205i	−0.00300703	−	0.00520833i
$49$	−75.5000	+	130.770i	−0.220117	+	0.381253i
$50$	−183.000	−	105.655i	−0.517602	−	0.298838i
$51$	234.000			0.642481
$52$		0			0
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$	150.000	+	86.6025i	0.378008	+	0.218243i
$55$	12.0000	−	20.7846i	0.0294196	−	0.0509563i
$56$	156.000	+	270.200i	0.372257	+	0.644768i
$57$			228.631i			0.531279i
$58$	−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	$0.231866\pi$
$60$			17.3205i			0.0372678i
$61$	−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
$63$	276.000	+	159.349i	0.551948	+	0.318667i
$64$	−307.000			−0.599609
$65$		0			0
$66$	−48.0000			−0.0895211
$67$	681.000	+	393.176i	1.24175	+	0.716926i	0.969451	−	0.245286i	$-0.0788819\pi$
$67$	681.000	+	393.176i	1.24175	+	0.716926i	0.272301	+	0.962212i	$0.412215\pi$
$68$	−292.500	+	506.625i	−0.521630	+	0.903490i
$69$	78.0000	+	135.100i	0.136088	+	0.235712i
$70$		−	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	$0.988836\pi$
$72$	−448.500	+	258.942i	−0.734114	+	0.423841i
$73$		−	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
$75$	−122.000	+	211.310i	−0.187831	+	0.325333i
$76$	−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
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	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	$0.825093\pi$
$84$	120.000	−	69.2820i	0.155870	−	0.0899915i
$85$	175.500	−	101.325i	0.223949	−	0.129297i
$86$			180.133i			0.225864i
$87$	141.000	+	244.219i	0.173756	+	0.300955i
$88$	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	$0.469041\pi$
$90$	69.0000			0.0808138
$91$		0			0
$92$	−390.000			−0.441960
$93$	270.000	+	155.885i	0.301050	+	0.173812i
$94$	−261.000	+	452.065i	−0.286384	+	0.496032i
$95$	99.0000	+	171.473i	0.106918	+	0.185187i
$96$			363.731i			0.386699i
$97$	−174.000	+	100.459i	−0.182134	+	0.105155i	−0.588295	−	0.808646i	$-0.700201\pi$
$97$	−174.000	+	100.459i	−0.182134	+	0.105155i	0.406161	+	0.913802i	$0.366867\pi$
$98$	226.500	−	130.770i	0.233469	−	0.134793i
$99$		−	318.697i		−	0.323538i
$100$	−305.000	−	528.275i	−0.305000	−	0.528275i
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	−0.952129	−	0.305698i	$-0.901110\pi$
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	0.740806	+	0.671719i	$0.234444\pi$
$102$	−351.000	−	202.650i	−0.340727	−	0.196719i
$103$	182.000			0.174107			0.0870534	−	0.996204i	$-0.472255\pi$
$103$	182.000			0.174107			0.0870534	+	0.996204i	$0.472255\pi$
$104$		0			0
$105$	−48.0000			−0.0446126
$106$	−139.500	−	80.5404i	−0.127825	−	0.0737997i
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	−0.294551	−	0.955636i	$-0.595170\pi$
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	0.974880	−	0.222729i	$-0.0714967\pi$
$108$	250.000	+	433.013i	0.222743	+	0.385802i
$109$		−	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
$111$	−249.000	+	143.760i	−0.212919	+	0.122929i
$112$			13.8564i			0.0116902i
$113$	343.500	+	594.959i	0.285962	+	0.495302i	0.972842	−	0.231470i	$-0.0743534\pi$
$113$	343.500	+	594.959i	0.285962	+	0.495302i	−0.686880	+	0.726771i	$0.741020\pi$
$114$	198.000	−	342.946i	0.162670	−	0.281753i
$115$	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
$120$	39.0000	−	67.5500i	0.0296683	−	0.0513870i
$121$	−569.500	−	986.403i	−0.427874	−	0.741099i
$122$			251.147i			0.186376i
$123$	471.000	−	271.932i	0.345273	−	0.199344i
$124$	−675.000	+	389.711i	−0.488845	+	0.282235i
$125$			427.817i			0.306121i
$126$	−276.000	−	478.046i	−0.195143	−	0.337998i
$127$	−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
$129$	208.000			0.141964
$130$		0			0
$131$	−1974.00			−1.31656			−0.658279	−	0.752774i	$-0.728715\pi$
$131$	−1974.00			−1.31656			−0.658279	+	0.752774i	$0.728715\pi$
$132$	−120.000	−	69.2820i	−0.0791262	−	0.0456835i
$133$	792.000	−	1371.78i	0.516354	−	0.894352i
$134$	−681.000	−	1179.53i	−0.439026	−	0.760415i
$135$		−	173.205i		−	0.110423i
$136$	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	$0.248260\pi$
$138$		−	270.200i		−	0.166674i
$139$	−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
$141$	522.000	+	301.377i	0.311775	+	0.180004i
$142$	1830.00			1.08148
$143$		0			0
$144$	−23.0000			−0.0133102
$145$	211.500	+	122.110i	0.121132	+	0.0699355i
$146$	−397.500	+	688.490i	−0.225324	+	0.390273i
$147$	−151.000	−	261.540i	−0.0847229	−	0.146744i
$148$		−	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	$0.329241\pi$
$150$	366.000	−	211.310i	0.199225	−	0.115023i
$151$			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
$153$	1345.50	−	2330.47i	0.710962	−	1.23142i
$154$	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
$159$	−93.0000	+	161.081i	−0.0463860	+	0.0803430i
$160$	157.500	+	272.798i	0.0778217	+	0.134791i
$161$		−	1080.80i		−	0.529062i
$162$	631.500	−	364.597i	0.306267	−	0.176824i
$163$	870.000	−	502.295i	0.418059	−	0.241367i	−0.276187	−	0.961104i	$-0.589071\pi$
$163$	870.000	−	502.295i	0.418059	−	0.241367i	0.694247	+	0.719737i	$0.255738\pi$
$164$			1359.66i			0.647388i
$165$	24.0000	+	41.5692i	0.0113236	+	0.0196131i
$166$	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	$0.734625\pi$
$168$	−624.000			−0.286563
$169$		0			0
$170$	−351.000			−0.158356
$171$	2277.00	+	1314.63i	1.01828	+	0.587906i
$172$	−260.000	+	450.333i	−0.115261	+	0.199637i
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	−0.996994	−	0.0774841i	$-0.975311\pi$
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	0.431394	−	0.902164i	$-0.358022\pi$
$174$		−	488.438i		−	0.212807i
$175$	1464.00	−	845.241i	0.632389	−	0.365110i
$176$	12.0000	−	6.92820i	0.00513940	−	0.00296723i
$177$			568.113i			0.241254i
$178$	−846.000	−	1465.31i	−0.356238	−	0.617022i
$179$	−1872.00	+	3242.40i	−0.781675	+	1.35390i	0.149290	+	0.988793i	$0.452301\pi$
$179$	−1872.00	+	3242.40i	−0.781675	+	1.35390i	−0.930965	+	0.365108i	$0.881032\pi$
$180$	172.500	+	99.5929i	0.0714299	+	0.0412401i
$181$	−637.000			−0.261590			−0.130795	−	0.991409i	$-0.541753\pi$
$181$	−637.000			−0.261590			−0.130795	+	0.991409i	$0.541753\pi$
$182$		0			0
$183$	290.000			0.117144
$184$	1521.00	+	878.150i	0.609400	+	0.351837i
$185$	−124.500	+	215.640i	−0.0494780	+	0.0856983i
$186$	−270.000	−	467.654i	−0.106437	−	0.184355i
$187$			1621.20i			0.633978i
$188$	−1305.00	+	753.442i	−0.506260	+	0.292289i
$189$	−1200.00	+	692.820i	−0.461837	+	0.266642i
$190$		−	342.946i		−	0.130947i
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	0.999959	−	0.00909077i	$-0.00289372\pi$
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	−0.507852	+	0.861444i	$0.669560\pi$
$192$	307.000	−	531.740i	0.115395	−	0.199870i
$193$	−967.500	−	558.586i	−0.360840	−	0.208331i	0.308609	−	0.951189i	$-0.400137\pi$
$193$	−967.500	−	558.586i	−0.360840	−	0.208331i	−0.669449	+	0.742858i	$0.733470\pi$
$194$	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	$0.787596\pi$
$198$	−276.000	+	478.046i	−0.0990630	+	0.171582i
$199$	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
$201$	−1362.00	+	786.351i	−0.477951	+	0.275945i
$202$	643.500	−	371.525i	0.224141	−	0.129408i
$203$		−	1953.75i		−	0.675500i
$204$	−585.000	−	1013.25i	−0.200775	−	0.347753i
$205$	235.500	−	407.898i	0.0802343	−	0.138970i
$206$	−273.000	−	157.617i	−0.0923340	−	0.0533091i
$207$	1794.00			0.602375
$208$		0			0
$209$	−1584.00			−0.524247
$210$	72.0000	+	41.5692i	0.0236594	+	0.0136598i
$211$	−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
$213$		−	2113.10i		−	0.679753i
$214$	−2259.00	+	1304.23i	−0.721598	+	0.416615i
$215$	156.000	−	90.0666i	0.0494842	−	0.0285697i
$216$		−	2251.67i		−	0.709289i
$217$	−1080.00	−	1870.61i	−0.337858	−	0.585187i
$218$	−1344.00	+	2327.88i	−0.417556	+	0.723228i
$219$	795.000	+	458.993i	0.245302	+	0.141625i
$220$	−120.000			−0.0367745
$221$		0			0
$222$	498.000			0.150557
$223$	2085.00	+	1203.78i	0.626107	+	0.361483i	0.779243	−	0.626722i	$-0.215604\pi$
$223$	2085.00	+	1203.78i	0.626107	+	0.361483i	−0.153136	+	0.988205i	$0.548937\pi$
$224$	1260.00	−	2182.38i	0.375836	−	0.650967i
$225$	1403.00	+	2430.07i	0.415704	+	0.720020i
$226$		−	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	$0.447822\pi$
$228$	990.000	−	571.577i	0.287563	−	0.166025i
$229$		−	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
$231$	192.000	−	332.554i	0.0546869	−	0.0947205i
$232$	2749.50	+	1587.42i	0.778076	+	0.449222i
$233$	−5850.00			−1.64483			−0.822417	−	0.568885i	$-0.807375\pi$
$233$	−5850.00			−1.64483			−0.822417	+	0.568885i	$0.807375\pi$
$234$		0			0
$235$	522.000			0.144900
$236$	−1230.00	−	710.141i	−0.339263	−	0.195874i
$237$	−1276.00	+	2210.10i	−0.349726	+	0.605744i
$238$	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	$0.740229\pi$
$240$	3.00000	−	1.73205i	0.000806872	−	0.000465847i
$241$	−4258.50	+	2458.65i	−1.13823	+	0.657159i	−0.945992	−	0.324189i	$-0.894909\pi$
$241$	−4258.50	+	2458.65i	−1.13823	+	0.657159i	−0.192240	+	0.981348i	$0.561575\pi$
$242$			1972.81i			0.524036i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	−362.500	+	627.868i	−0.0951094	+	0.164734i
$245$	−226.500	−	130.770i	−0.0590635	−	0.0341003i
$246$	−942.000			−0.244145
$247$		0			0
$248$	3510.00			0.898731
$249$	−1368.00	−	789.815i	−0.348167	−	0.201014i
$250$	370.500	−	641.725i	0.0937299	−	0.162345i
$251$	1989.00	+	3445.05i	0.500178	+	0.866333i	1.00000		0.000205037i	$6.52654e-5\pi$
$251$	1989.00	+	3445.05i	0.500178	+	0.866333i	−0.499822	+	0.866128i	$0.666601\pi$
$252$		−	1593.49i		−	0.398334i
$253$	−936.000	+	540.400i	−0.232592	+	0.134287i
$254$	429.000	−	247.683i	0.105976	−	0.0611852i
$255$			405.300i			0.0995328i
$256$	2027.50	+	3511.73i	0.494995	+	0.857357i
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	−0.963760	−	0.266772i	$-0.914043\pi$
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	0.712911	+	0.701254i	$0.247376\pi$
$258$	−312.000	−	180.133i	−0.0752879	−	0.0434675i
$259$	1992.00			0.477903
$260$		0			0
$261$	3243.00			0.769106
$262$	2961.00	+	1709.53i	0.698211	+	0.403112i
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	−0.720318	−	0.693644i	$-0.756004\pi$
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	0.960872	+	0.276991i	$0.0893373\pi$
$264$	312.000	+	540.400i	0.0727359	+	0.125982i
$265$			161.081i			0.0373400i
$266$	−2376.00	+	1371.78i	−0.547676	+	0.316201i
$267$	−1692.00	+	976.877i	−0.387823	+	0.223910i
$268$		−	3931.76i		−	0.896157i
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	0.613295	−	0.789854i	$-0.289844\pi$
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	−0.990681	+	0.136202i	$0.956510\pi$
$270$	−150.000	+	259.808i	−0.0338100	+	0.0585607i
$271$	−2430.00	−	1402.96i	−0.544694	−	0.314479i	0.202285	−	0.979327i	$-0.435163\pi$
$271$	−2430.00	−	1402.96i	−0.544694	−	0.314479i	−0.746979	+	0.664848i	$0.768496\pi$
$272$	117.000			0.0260815
$273$		0			0
$274$	−1467.00			−0.323448
$275$	−1464.00	−	845.241i	−0.321027	−	0.185345i
$276$	390.000	−	675.500i	0.0850552	−	0.147320i
$277$	−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
$279$	3105.00	−	1792.67i	0.666278	−	0.384676i
$280$	−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	$0.998771\pi$
$282$	−522.000	−	904.131i	−0.110229	−	0.190923i
$283$	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
$285$	−396.000			−0.0823053
$286$		0			0
$287$	−3768.00			−0.774976
$288$	3622.50	+	2091.45i	0.741173	+	0.427917i
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$	−211.500	−	366.329i	−0.0428266	−	0.0741778i
$291$		−	401.836i		−	0.0809486i
$292$	−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	$0.0218432\pi$
$294$			523.079i			0.103764i
$295$	246.000	+	426.084i	0.0485514	+	0.0840936i
$296$	−1618.50	+	2803.32i	−0.317816	+	0.550473i
$297$	1200.00	+	692.820i	0.234448	+	0.135359i
$298$	−81.0000			−0.0157457
$299$		0			0
$300$	1220.00			0.234789
$301$	−1248.00	−	720.533i	−0.238982	−	0.137976i
$302$	1533.00	−	2655.23i	0.292100	−	0.505932i
$303$	−429.000	−	743.050i	−0.0813380	−	0.140882i
$304$			114.315i			0.0215672i
$305$	217.500	−	125.574i	0.0408328	−	0.0235748i
$306$	−4036.50	+	2330.47i	−0.754089	+	0.435374i
$307$			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
$309$	−182.000	+	315.233i	−0.0335069	+	0.0580356i
$310$	−405.000	−	233.827i	−0.0742015	−	0.0428402i
$311$	4914.00			0.895972			0.447986	−	0.894041i	$-0.352141\pi$
$311$	4914.00			0.895972			0.447986	+	0.894041i	$0.352141\pi$
$312$		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
$315$	−276.000	+	478.046i	−0.0493677	+	0.0855074i
$316$	−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	$-0.112776\pi$
$318$	279.000	−	161.081i	0.0491998	−	0.0284055i
$319$	−1692.00	+	976.877i	−0.296971	+	0.171456i
$320$		−	531.740i		−	0.0928911i
$321$	1506.00	+	2608.47i	0.261859	+	0.453553i
$322$	−936.000	+	1621.20i	−0.161991	+	0.280577i
$323$	−11583.0	−	6687.45i	−1.99534	−	1.15201i
$324$	2105.00			0.360940
$325$		0			0
$326$	−1740.00			−0.295613
$327$	2688.00	+	1551.92i	0.454577	+	0.262450i
$328$	3061.50	−	5302.67i	0.515375	−	0.892656i
$329$	−2088.00	−	3616.52i	−0.349894	−	0.606034i
$330$		−	83.1384i		−	0.0138685i
$331$	6456.00	−	3727.37i	1.07207	−	0.618958i	0.143321	−	0.989676i	$-0.454222\pi$
$331$	6456.00	−	3727.37i	1.07207	−	0.618958i	0.928745	+	0.370719i	$0.120889\pi$
$332$	3420.00	−	1974.54i	0.565352	−	0.326406i
$333$			3306.48i			0.544127i
$334$	792.000	+	1371.78i	0.129749	+	0.224733i
$335$	−681.000	+	1179.53i	−0.111066	+	0.192371i
$336$	−24.0000	−	13.8564i	−0.00389675	−	0.00224979i
$337$	−3575.00			−0.577871			−0.288936	−	0.957349i	$-0.593301\pi$
$337$	−3575.00			−0.577871			−0.288936	+	0.957349i	$0.593301\pi$
$338$		0			0
$339$	−1374.00			−0.220134
$340$	−877.500	−	506.625i	−0.139968	−	0.0808106i
$341$	−1080.00	+	1870.61i	−0.171511	+	0.297066i
$342$	−2277.00	−	3943.88i	−0.360018	−	0.623569i
$343$			6845.06i			1.07755i
$344$	2028.00	−	1170.87i	0.317856	−	0.183514i
$345$	−234.000	+	135.100i	−0.0365163	+	0.0210827i
$346$			4458.30i			0.692716i
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	0.998967	+	0.0454442i	$0.0144703\pi$
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	−0.460128	+	0.887853i	$0.652196\pi$
$348$	705.000	−	1221.10i	0.108598	−	0.188097i
$349$	5760.00	+	3325.54i	0.883455	+	0.510063i	0.871796	−	0.489869i	$-0.162955\pi$
$349$	5760.00	+	3325.54i	0.883455	+	0.510063i	0.0116588	+	0.999932i	$0.496289\pi$
$350$	−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	$0.806219\pi$
$354$	492.000	−	852.169i	0.0738687	−	0.127944i
$355$	−915.000	−	1584.83i	−0.136798	−	0.236940i
$356$		−	4884.38i		−	0.727168i
$357$	2808.00	−	1621.20i	0.416289	−	0.240344i
$358$	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	$0.824424\pi$
$360$	−448.500	−	776.825i	−0.0656612	−	0.113729i
$361$	3104.50	−	5377.15i	0.452617	−	0.783956i
$362$	955.500	+	551.658i	0.138729	+	0.0800953i
$363$	2278.00			0.329377
$364$		0			0
$365$	795.000			0.114006
$366$	−435.000	−	251.147i	−0.0621252	−	0.0358680i
$367$	−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
$369$		−	6254.44i		−	0.882366i
$370$	373.500	−	215.640i	0.0524793	−	0.0302989i
$371$	1116.00	−	644.323i	0.156172	−	0.0901660i
$372$		−	1558.85i		−	0.217264i
$373$	−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
$375$	−741.000	−	427.817i	−0.102040	−	0.0589129i
$376$	6786.00			0.930748
$377$		0			0
$378$	2400.00			0.326568
$379$	−4779.00	−	2759.16i	−0.647706	−	0.373953i	0.139871	−	0.990170i	$-0.455331\pi$
$379$	−4779.00	−	2759.16i	−0.647706	−	0.373953i	−0.787577	+	0.616216i	$0.788665\pi$
$380$	495.000	−	857.365i	0.0668236	−	0.115742i
$381$	−286.000	−	495.367i	−0.0384573	−	0.0666100i
$382$		−	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	$0.169864\pi$
$384$	1599.00	−	923.183i	0.212496	−	0.122685i
$385$		−	332.554i		−	0.0440221i
$386$	967.500	+	1675.76i	0.127576	+	0.220969i
$387$	1196.00	−	2071.53i	0.157096	−	0.272098i
$388$	870.000	+	502.295i	0.113834	+	0.0657220i
$389$	−1209.00			−0.157580			−0.0787901	−	0.996891i	$-0.525106\pi$
$389$	−1209.00			−0.157580			−0.0787901	+	0.996891i	$0.525106\pi$
$390$		0			0
$391$	−9126.00			−1.18036
$392$	−2944.50	−	1700.01i	−0.379387	−	0.219039i
$393$	1974.00	−	3419.07i	0.253372	−	0.438853i
$394$	1776.00	+	3076.12i	0.227090	+	0.393332i
$395$			2210.10i			0.281524i
$396$	−1380.00	+	796.743i	−0.175120	+	0.101106i
$397$	−10128.0	+	5847.40i	−1.28038	+	0.739226i	−0.976917	−	0.213618i	$-0.931475\pi$
$397$	−10128.0	+	5847.40i	−1.28038	+	0.739226i	−0.303460	+	0.952844i	$0.598142\pi$
$398$		−	4368.23i		−	0.550150i
$399$	1584.00	+	2743.57i	0.198745	+	0.344236i
$400$	−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	$0.607241\pi$
$402$	2724.00			0.337962
$403$		0			0
$404$	2145.00			0.264153
$405$	−631.500	−	364.597i	−0.0774802	−	0.0447332i
$406$	−1692.00	+	2930.63i	−0.206829	+	0.358238i
$407$	−996.000	−	1725.12i	−0.121302	−	0.210101i
$408$			5268.90i			0.639337i
$409$	−37.5000	+	21.6506i	−0.00453363	+	0.00261749i	−0.502265	−	0.864714i	$-0.667500\pi$
$409$	−37.5000	+	21.6506i	−0.00453363	+	0.00261749i	0.497731	+	0.867331i	$0.334167\pi$
$410$	−706.500	+	407.898i	−0.0851013	+	0.0491333i
$411$			1693.95i			0.203300i
$412$	−455.000	−	788.083i	−0.0544084	−	0.0942380i
$413$	1968.00	−	3408.68i	0.234477	−	0.406126i
$414$	−2691.00	−	1553.65i	−0.319458	−	0.184439i
$415$	−1368.00			−0.161813
$416$		0			0
$417$	472.000			0.0554291
$418$	2376.00	+	1371.78i	0.278024	+	0.160517i
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	−0.446549	−	0.894759i	$-0.647347\pi$
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	0.998159	−	0.0606569i	$-0.0193195\pi$
$420$	120.000	+	207.846i	0.0139414	+	0.0241473i
$421$		−	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
$423$	6003.00	−	3465.83i	0.690014	−	0.398380i
$424$			2094.05i			0.239849i
$425$	−7137.00	−	12361.6i	−0.814577	−	1.41089i
$426$	−1830.00	+	3169.65i	−0.208131	+	0.360493i
$427$	−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	$0.479469\pi$
$432$	50.0000	−	86.6025i	0.00556858	−	0.00964506i
$433$	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
$435$	−423.000	+	244.219i	−0.0466237	+	0.0269182i
$436$	−6720.00	+	3879.79i	−0.738141	+	0.426166i
$437$		−	8916.60i		−	0.976061i
$438$	−795.000	−	1376.98i	−0.0867273	−	0.150216i
$439$	−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
$441$	−3473.00			−0.375013
$442$		0			0
$443$	2004.00			0.214928			0.107464	−	0.994209i	$-0.465727\pi$
$443$	2004.00			0.214928			0.107464	+	0.994209i	$0.465727\pi$
$444$	1245.00	+	718.801i	0.133075	+	0.0768306i
$445$	−846.000	+	1465.31i	−0.0901219	+	0.156096i
$446$	−2085.00	−	3611.33i	−0.221362	−	0.383411i
$447$			93.5307i			0.00989676i
$448$	−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	$0.491731\pi$
$450$		−	4860.13i		−	0.509131i
$451$	1884.00	+	3263.18i	0.196705	+	0.340704i
$452$	1717.50	−	2974.80i	0.178727	−	0.309563i
$453$	−3066.00	−	1770.16i	−0.317998	−	0.183596i
$454$	4170.00			0.431074
$455$		0			0
$456$	−5148.00			−0.528678
$457$	−2185.50	−	1261.80i	−0.223705	−	0.129156i	0.383959	−	0.923350i	$-0.374560\pi$
$457$	−2185.50	−	1261.80i	−0.223705	−	0.129156i	−0.607665	+	0.794194i	$0.707894\pi$
$458$	−2172.00	+	3762.01i	−0.221596	+	0.383815i
$459$	5850.00	+	10132.5i	0.594890	+	1.03038i
$460$		−	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	$0.879563\pi$
$462$	−576.000	+	332.554i	−0.0580042	+	0.0334887i
$463$		−	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
$465$	−270.000	+	467.654i	−0.0269268	+	0.0466385i
$466$	8775.00	+	5066.25i	0.872305	+	0.503625i
$467$	5460.00			0.541025			0.270512	−	0.962716i	$-0.412807\pi$
$467$	5460.00			0.541025			0.270512	+	0.962716i	$0.412807\pi$
$468$		0			0
$469$	10896.0			1.07277
$470$	−783.000	−	452.065i	−0.0768449	−	0.0443664i
$471$	−1211.00	+	2097.51i	−0.118471	+	0.205198i
$472$	3198.00	+	5539.10i	0.311864	+	0.540165i
$473$			1441.07i			0.140085i
$474$	3828.00	−	2210.10i	0.370941	−	0.214163i
$475$	12078.0	−	6973.24i	1.16669	−	0.673587i
$476$			8106.00i			0.780542i
$477$	1069.50	+	1852.43i	0.102660	+	0.177813i
$478$	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	$0.627811\pi$
$480$	−630.000			−0.0599072
$481$		0			0
$482$	8517.00			0.804852
$483$	1872.00	+	1080.80i	0.176354	+	0.101818i
$484$	−2847.50	+	4932.01i	−0.267421	+	0.463187i
$485$	−174.000	−	301.377i	−0.0162906	−	0.0282161i
$486$			6134.92i			0.572605i
$487$	−9378.00	+	5414.39i	−0.872603	+	0.503798i	−0.868212	−	0.496193i	$-0.834731\pi$
$487$	−9378.00	+	5414.39i	−0.872603	+	0.503798i	−0.00439074	+	0.999990i	$0.501398\pi$
$488$	2827.50	−	1632.46i	0.262285	−	0.151430i
$489$			2009.18i			0.185804i
$490$	226.500	+	392.310i	0.0208821	+	0.0361689i
$491$	−5694.00	+	9862.30i	−0.523354	+	0.906475i	0.476277	+	0.879295i	$0.341986\pi$
$491$	−5694.00	+	9862.30i	−0.523354	+	0.906475i	−0.999631	+	0.0271797i	$0.991347\pi$
$492$	−2355.00	−	1359.66i	−0.215796	−	0.124590i
$493$	−16497.0			−1.50707
$494$		0			0
$495$	552.000			0.0501223
$496$	135.000	+	77.9423i	0.0122211	+	0.00705587i
$497$	−7320.00	+	12678.6i	−0.660658	+	1.14429i
$498$	1368.00	+	2369.45i	0.123095	+	0.213208i
$499$			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
$501$	1584.00	−	914.523i	0.141253	−	0.0815526i
$502$		−	6890.10i		−	0.612590i
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	0.767255	−	0.641343i	$-0.221622\pi$
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	−0.939046	+	0.343791i	$0.888289\pi$
$504$	−3588.00	+	6214.60i	−0.317108	+	0.549246i
$505$	−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	$0.400042\pi$
$510$	351.000	−	607.950i	0.0304756	−	0.0527852i
$511$	−3180.00	−	5507.92i	−0.275293	−	0.476822i
$512$			361.999i			0.0312465i
$513$	−9900.00	+	5715.77i	−0.852038	+	0.491925i
$514$	3100.50	−	1790.07i	0.266065	−	0.153612i
$515$			315.233i			0.0269725i
$516$	−520.000	−	900.666i	−0.0443638	−	0.0768404i
$517$	−2088.00	+	3616.52i	−0.177621	+	0.307649i
$518$	−2988.00	−	1725.12i	−0.253446	−	0.146327i
$519$	5148.00			0.435399
$520$		0			0
$521$	2121.00			0.178355			0.0891773	−	0.996016i	$-0.471576\pi$
$521$	2121.00			0.178355			0.0891773	+	0.996016i	$0.471576\pi$
$522$	−4864.50	−	2808.52i	−0.407880	−	0.235490i
$523$	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
$525$			3380.96i			0.281062i
$526$	−3078.00	+	1777.08i	−0.255147	+	0.147309i
$527$	−15795.0	+	9119.25i	−1.30558	+	0.753777i
$528$			27.7128i			0.00228418i
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$	139.500	−	241.621i	0.0114330	−	0.0198025i
$531$	5658.00	+	3266.65i	0.462404	+	0.266969i
$532$	−7920.00			−0.645443
$533$		0			0
$534$	3384.00			0.274232
$535$	2259.00	+	1304.23i	0.182552	+	0.105396i
$536$	−8853.00	+	15333.8i	−0.713417	+	1.23567i
$537$	−3744.00	−	6484.80i	−0.300867	−	0.521117i
$538$			5767.73i			0.462202i
$539$	1812.00	−	1046.16i	0.144802	−	0.0836016i
$540$	−750.000	+	433.013i	−0.0597683	+	0.0345072i
$541$			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
$543$	637.000	−	1103.32i	0.0503431	−	0.0871968i
$544$	−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
$549$	1667.50	−	2888.19i	0.129631	−	0.224527i
$550$	1464.00	+	2535.72i	0.113500	+	0.196588i
$551$		−	16118.5i		−	1.24622i
$552$	−3042.00	+	1756.30i	−0.234558	+	0.135422i
$553$	15312.0	−	8840.39i	1.17745	−	0.679804i
$554$			652.983i			0.0500769i
$555$	−249.000	−	431.281i	−0.0190441	−	0.0329853i
$556$	−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	$0.424761\pi$
$558$	−6210.00			−0.471130
$559$		0			0
$560$	−24.0000			−0.00181104
$561$	−2808.00	−	1621.20i	−0.211326	−	0.122009i
$562$	31.5000	−	54.5596i	0.00236432	−	0.00409512i
$563$	6084.00	+	10537.8i	0.455435	+	0.788837i	0.998713	−	0.0507160i	$-0.0161503\pi$
$563$	6084.00	+	10537.8i	0.455435	+	0.788837i	−0.543278	+	0.839553i	$0.682817\pi$
$564$		−	3013.77i		−	0.225005i
$565$	−1030.50	+	594.959i	−0.0767318	+	0.0443011i
$566$	−10686.0	+	6169.56i	−0.793580	+	0.458173i
$567$			5833.55i			0.432074i
$568$	−11895.0	−	20602.7i	−0.878703	−	1.52196i
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	−0.688013	−	0.725698i	$-0.741517\pi$
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	0.972480	+	0.232988i	$0.0748502\pi$
$570$	594.000	+	342.946i	0.0436490	+	0.0252008i
$571$	11440.0			0.838440			0.419220	−	0.907885i	$-0.362304\pi$
$571$	11440.0			0.838440			0.419220	+	0.907885i	$0.362304\pi$
$572$		0			0
$573$	−5196.00			−0.378824
$574$	5652.00	+	3263.18i	0.410993	+	0.237287i
$575$	4758.00	−	8241.10i	0.345082	−	0.597700i
$576$	−3530.50	−	6115.01i	−0.255389	−	0.442347i
$577$		−	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
$579$	1935.00	−	1117.17i	0.138887	−	0.0801867i
$580$		−	1221.10i		−	0.0874194i
$581$	5472.00	+	9477.78i	0.390735	+	0.676772i
$582$	−348.000	+	602.754i	−0.0247853	+	0.0429295i
$583$	−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	$0.501944\pi$
$588$	−755.000	+	1307.70i	−0.0529518	+	0.0917153i
$589$	−8910.00	−	15432.6i	−0.623311	−	1.07961i
$590$		−	852.169i		−	0.0594631i
$591$	3552.00	−	2050.75i	0.247225	−	0.142735i
$592$	−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	$-0.382593\pi$
$594$	−1200.00	−	2078.46i	−0.0828899	−	0.143570i
$595$	1404.00	−	2431.80i	0.0967368	−	0.167553i
$596$	−202.500	−	116.913i	−0.0139173	−	0.00803517i
$597$	−5044.00			−0.345791
$598$		0			0
$599$	−10554.0			−0.719908			−0.359954	−	0.932970i	$-0.617208\pi$
$599$	−10554.0			−0.719908			−0.359954	+	0.932970i	$0.617208\pi$
$600$	−4758.00	−	2747.03i	−0.323741	−	0.186912i
$601$	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
$603$			18086.1i			1.22143i
$604$	7665.00	−	4425.39i	0.516365	−	0.298123i
$605$	1708.50	−	986.403i	0.114811	−	0.0662859i
$606$			1486.10i			0.0996183i
$607$	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
$609$	3384.00	+	1953.75i	0.225167	+	0.130000i
$610$	−435.000			−0.0288732
$611$		0			0
$612$	−13455.0			−0.888703
$613$	−21841.5	−	12610.2i	−1.43910	−	0.830866i	−0.441315	−	0.897352i	$-0.645488\pi$
$613$	−21841.5	−	12610.2i	−1.43910	−	0.830866i	−0.997787	+	0.0664859i	$0.978821\pi$
$614$	1923.00	−	3330.73i	0.126394	−	0.218921i
$615$	471.000	+	815.796i	0.0308822	+	0.0534895i
$616$		−	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	$0.141375\pi$
$618$	546.000	−	315.233i	0.0355394	−	0.0205187i
$619$			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
$621$	−3900.00	+	6755.00i	−0.252015	+	0.436504i
$622$	−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
$627$	1584.00	−	2743.57i	0.100891	−	0.174749i
$628$	−3027.50	−	5243.78i	−0.192373	−	0.333200i
$629$		−	16819.9i		−	1.06622i
$630$	828.000	−	478.046i	0.0523624	−	0.0302314i
$631$	−11142.0	+	6432.84i	−0.702941	+	0.405843i	−0.808442	−	0.588576i	$-0.799689\pi$
$631$	−11142.0	+	6432.84i	−0.702941	+	0.405843i	0.105501	+	0.994419i	$0.466355\pi$
$632$			28731.3i			1.80834i
$633$	−1042.00	−	1804.80i	−0.0654278	−	0.113324i
$634$	−3391.50	+	5874.25i	−0.212451	+	0.367975i
$635$	−429.000	−	247.683i	−0.0268100	−	0.0154788i
$636$	930.000			0.0579825
$637$		0			0
$638$	3384.00			0.209990
$639$	−21045.0	−	12150.3i	−1.30286	−	0.752206i
$640$	799.500	−	1384.77i	0.0493797	−	0.0855282i
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	0.754549	−	0.656244i	$-0.227856\pi$
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	−0.945598	+	0.325337i	$0.894522\pi$
$642$		−	5216.94i		−	0.320710i
$643$	14568.0	−	8410.84i	0.893477	−	0.515849i	0.0183989	−	0.999831i	$-0.494143\pi$
$643$	14568.0	−	8410.84i	0.893477	−	0.515849i	0.875078	+	0.483981i	$0.160810\pi$
$644$	−4680.00	+	2702.00i	−0.286363	+	0.165332i
$645$			360.267i			0.0219930i
$646$	11583.0	+	20062.3i	0.705460	+	1.22189i
$647$	6747.00	−	11686.1i	0.409972	−	0.710092i	−0.584914	−	0.811095i	$-0.698872\pi$
$647$	6747.00	−	11686.1i	0.409972	−	0.710092i	0.994886	+	0.101003i	$0.0322051\pi$
$648$	−8209.50	−	4739.76i	−0.497685	−	0.287338i
$649$	−3936.00			−0.238061
$650$		0			0
$651$	4320.00			0.260083
$652$	−4350.00	−	2511.47i	−0.261287	−	0.150854i
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	−0.644747	−	0.764396i	$-0.723037\pi$
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	0.984360	+	0.176170i	$0.0563708\pi$
$654$	−2688.00	−	4655.75i	−0.160717	−	0.278371i
$655$		−	3419.07i		−	0.203960i
$656$	235.500	−	135.966i	0.0140164	−	0.00809235i
$657$	9142.50	−	5278.42i	0.542896	−	0.313441i
$658$			7233.04i			0.428531i
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	0.601408	−	0.798942i	$-0.294607\pi$
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	−0.992608	+	0.121364i	$0.961273\pi$
$660$	120.000	−	207.846i	0.00707726	−	0.0122582i
$661$	10264.5	+	5926.21i	0.603998	+	0.348718i	0.770613	−	0.637304i	$-0.219950\pi$
$661$	10264.5	+	5926.21i	0.603998	+	0.348718i	−0.166615	+	0.986022i	$0.553284\pi$
$662$	−12912.0			−0.758065
$663$		0			0
$664$	−17784.0			−1.03939
$665$	2376.00	+	1371.78i	0.138552	+	0.0799932i
$666$	2863.50	−	4959.73i	0.166604	−	0.288567i
$667$	−5499.00	−	9524.55i	−0.319224	−	0.552911i
$668$			4572.61i			0.264850i
$669$	−4170.00	+	2407.55i	−0.240989	+	0.139135i
$670$	2043.00	−	1179.53i	0.117803	−	0.0680136i
$671$			2009.18i			0.115594i
$672$	2520.00	+	4364.77i	0.144659	+	0.250557i
$673$	−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
$675$	−12200.0			−0.695671
$676$		0			0
$677$	−21630.0			−1.22793			−0.613965	−	0.789333i	$-0.710426\pi$
$677$	−21630.0			−1.22793			−0.613965	+	0.789333i	$0.710426\pi$
$678$	2061.00	+	1189.92i	0.116744	+	0.0674020i
$679$	−1392.00	+	2411.01i	−0.0786746	+	0.136268i
$680$	2281.50	+	3951.67i	0.128664	+	0.222853i
$681$		−	4815.10i		−	0.270947i
$682$	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	$0.0665514\pi$
$684$		−	13146.3i		−	0.734883i
$685$	733.500	+	1270.46i	0.0409133	+	0.0708639i
$686$	5928.00	−	10267.6i	0.329930	−	0.571456i
$687$	4344.00	+	2508.01i	0.241243	+	0.139282i
$688$	104.000			0.00576303
$689$		0			0
$690$	468.000			0.0258210
$691$	720.000	+	415.692i	0.0396383	+	0.0228852i	0.519688	−	0.854356i	$-0.326048\pi$
$691$	720.000	+	415.692i	0.0396383	+	0.0228852i	−0.480050	+	0.877241i	$0.659381\pi$
$692$	−6435.00	+	11145.7i	−0.353500	+	0.612280i
$693$	−2208.00	−	3824.37i	−0.121032	−	0.209633i
$694$		−	12065.5i		−	0.659941i
$695$	354.000	−	204.382i	0.0193208	−	0.0111549i
$696$	−5499.00	+	3174.85i	−0.299481	+	0.172906i
$697$			31816.0i			1.72901i
$698$	−5760.00	−	9976.61i	−0.312348	−	0.541003i
$699$	5850.00	−	10132.5i	0.316548	−	0.548278i
$700$	−7320.00	−	4226.20i	−0.395243	−	0.228194i
$701$	30186.0			1.62640			0.813202	−	0.581981i	$-0.197722\pi$
$701$	30186.0			1.62640			0.813202	+	0.581981i	$0.197722\pi$
$702$		0			0
$703$	16434.0			0.881679
$704$	3684.00	+	2126.96i	0.197224	+	0.113868i
$705$	−522.000	+	904.131i	−0.0278860	+	0.0483000i
$706$	4876.50	+	8446.35i	0.259957	+	0.450258i
$707$			5944.40i			0.316212i
$708$	2460.00	−	1420.28i	0.130583	−	0.0753919i
$709$	10288.5	−	5940.07i	0.544983	−	0.314646i	−0.202113	−	0.979362i	$-0.564781\pi$
$709$	10288.5	−	5940.07i	0.544983	−	0.314646i	0.747096	+	0.664716i	$0.231448\pi$
$710$			3169.65i			0.167542i
$711$	14674.0	+	25416.1i	0.774006	+	1.34062i
$712$	−10998.0	+	19049.1i	−0.578887	+	1.00266i
$713$	−10530.0	−	6079.50i	−0.553088	−	0.319325i
$714$	−5616.00			−0.294361
$715$		0			0
$716$	18720.0			0.977094
$717$	−9324.00	−	5383.21i	−0.485650	−	0.280390i
$718$	6174.00	−	10693.7i	0.320908	−	0.555828i
$719$	−9204.00	−	15941.8i	−0.477401	−	0.826883i	0.522264	−	0.852784i	$-0.325088\pi$
$719$	−9204.00	−	15941.8i	−0.477401	−	0.826883i	−0.999665	+	0.0259014i	$0.991754\pi$
$720$		−	39.8372i		−	0.00206201i
$721$	2184.00	−	1260.93i	0.112811	−	0.0651312i
$722$	−9313.50	+	5377.15i	−0.480073	+	0.277170i
$723$		−	9834.58i		−	0.505881i
$724$	1592.50	+	2758.29i	0.0817470	+	0.141590i
$725$	8601.00	−	14897.4i	0.440597	−	0.763137i
$726$	−3417.00	−	1972.81i	−0.174679	−	0.100851i
$727$	21112.0			1.07703			0.538515	−	0.842616i	$-0.318986\pi$
$727$	21112.0			1.07703			0.538515	+	0.842616i	$0.318986\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	−1192.50	−	688.490i	−0.0604608	−	0.0349071i
$731$	−6084.00	+	10537.8i	−0.307832	+	0.533180i
$732$	−725.000	−	1255.74i	−0.0366076	−	0.0634062i
$733$			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
$735$	453.000	−	261.540i	0.0227335	−	0.0131252i
$736$		−	14185.5i		−	0.710441i
$737$	−5448.00	−	9436.21i	−0.272293	−	0.471625i
$738$	−5416.50	+	9381.65i	−0.270168	+	0.467945i
$739$	−2742.00	−	1583.09i	−0.136490	−	0.0788025i	0.430200	−	0.902734i	$-0.358443\pi$
$739$	−2742.00	−	1583.09i	−0.136490	−	0.0788025i	−0.566690	+	0.823931i	$0.691776\pi$
$740$	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	$0.399981\pi$
$744$	−3510.00	+	6079.50i	−0.172961	+	0.299577i
$745$	40.5000	+	70.1481i	0.00199168	+	0.00344970i
$746$			6060.45i			0.297438i
$747$	−15732.0	+	9082.87i	−0.770554	+	0.444880i
$748$	7020.00	−	4053.00i	0.343151	−	0.198118i
$749$		−	20867.7i		−	1.01801i
$750$	741.000	+	1283.45i	0.0360767	+	0.0624866i
$751$	−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
$753$	−7956.00			−0.385037
$754$		0			0
$755$	−3066.00			−0.147792
$756$	6000.00	+	3464.10i	0.288648	+	0.166651i
$757$	−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
$759$		−	2161.60i		−	0.103374i
$760$	−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	$0.889826\pi$
$762$			990.733i			0.0471004i
$763$	−10752.0	−	18623.0i	−0.510155	−	0.883615i
$764$	6495.00	−	11249.7i	0.307567	−	0.532721i
$765$	4036.50	+	2330.47i	0.190771	+	0.110142i
$766$	−12756.0			−0.601688
$767$		0			0
$768$	−8110.00			−0.381047
$769$	12186.0	+	7035.59i	0.571441	+	0.329922i	0.757725	−	0.652574i	$-0.226311\pi$
$769$	12186.0	+	7035.59i	0.571441	+	0.329922i	−0.186283	+	0.982496i	$0.559644\pi$
$770$	−288.000	+	498.831i	−0.0134790	+	0.0233462i
$771$	−2067.00	−	3580.15i	−0.0965515	−	0.167232i
$772$			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	$0.334821\pi$
$774$	−3588.00	+	2071.53i	−0.166625	+	0.0962012i
$775$		−	19017.9i		−	0.881476i
$776$	−2262.00	−	3917.90i	−0.104641	−	0.181243i
$777$	−1992.00	+	3450.25i	−0.0919725	+	0.159301i
$778$	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
$783$	−7050.00	+	12211.0i	−0.321771	+	0.557323i
$784$	−75.5000	−	130.770i	−0.00343932	−	0.00595708i
$785$			2097.51i			0.0953675i
$786$	−5922.00	+	3419.07i	−0.268741	+	0.155158i
$787$	5979.00	−	3451.98i	0.270811	−	0.156353i	−0.358445	−	0.933551i	$-0.616693\pi$
$787$	5979.00	−	3451.98i	0.270811	−	0.156353i	0.629256	+	0.777198i	$0.283360\pi$
$788$			10253.7i			0.463546i
$789$	2052.00	+	3554.17i	0.0925895	+	0.160370i
$790$	1914.00	−	3315.15i	0.0861988	−	0.149301i
$791$	8244.00	+	4759.68i	0.370573	+	0.213950i
$792$	7176.00			0.321955
$793$		0			0
$794$	20256.0			0.905363
$795$	−279.000	−	161.081i	−0.0124467	−	0.00718609i
$796$	6305.00	−	10920.6i	0.280747	−	0.486268i
$797$	15639.0	+	27087.5i	0.695059	+	1.20388i	0.970161	+	0.242462i	$0.0779550\pi$
$797$	15639.0	+	27087.5i	0.695059	+	1.20388i	−0.275102	+	0.961415i	$0.588712\pi$
$798$		−	5487.14i		−	0.243412i
$799$	−30537.0	+	17630.5i	−1.35209	+	0.780631i
$800$	19215.0	−	11093.8i	0.849191	−	0.490281i
$801$			22468.2i			0.991103i
$802$	−2581.50	−	4471.29i	−0.113661	−	0.196866i
$803$	−3180.00	+	5507.92i	−0.139751	+	0.242055i
$804$	6810.00	+	3931.76i	0.298719	+	0.172466i
$805$	1872.00			0.0819619
$806$		0			0
$807$	6660.00			0.290512
$808$	−8365.50	−	4829.82i	−0.364229	−	0.210288i
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	−0.940127	−	0.340826i	$-0.889293\pi$
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	0.765227	+	0.643761i	$0.222627\pi$
$810$	631.500	+	1093.79i	0.0273934	+	0.0474467i
$811$		−	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
$813$	4860.00	−	2805.92i	0.209653	−	0.121043i
$814$			3450.25i			0.148564i
$815$	870.000	+	1506.88i	0.0373924	+	0.0647655i
$816$	−117.000	+	202.650i	−0.00501939	+	0.00869383i
$817$	−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	$0.612026\pi$
$822$	1467.00	−	2540.92i	0.0622476	−	0.107816i
$823$	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
$825$	2928.00	−	1690.48i	0.123563	−	0.0713394i
$826$	−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	$-0.312217\pi$
$828$	−4485.00	−	7768.25i	−0.188242	−	0.326045i
$829$	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
$831$	754.000			0.0314753
$832$		0			0
$833$	17667.0			0.734844
$834$	−708.000	−	408.764i	−0.0293957	−	0.0169716i
$835$	792.000	−	1371.78i	0.0328243	−	0.0568534i
$836$	3960.00	+	6858.92i	0.163827	+	0.283757i
$837$			15588.5i			0.643747i
$838$	−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	$0.478948\pi$
$840$		−	1080.80i		−	0.0443942i
$841$	2254.00	+	3904.04i	0.0924187	+	0.160074i
$842$	−6121.50	+	10602.7i	−0.250547	+	0.433961i
$843$	−63.0000	−	36.3731i	−0.00257394	−	0.00148607i
$844$	5210.00			0.212483
$845$		0			0
$846$	−12006.0			−0.487913
$847$	−13668.0	−	7891.22i	−0.554472	−	0.320125i
$848$	−46.5000	+	80.5404i	−0.00188304	+	0.00326152i
$849$	7124.00	+	12339.1i	0.287980	+	0.498796i
$850$			24723.3i			0.997649i
$851$	9711.00	−	5606.65i	0.391174	−	0.225844i
$852$	−9150.00	+	5282.75i	−0.367927	+	0.212423i
$853$		−	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
$855$	−2277.00	+	3943.88i	−0.0910781	+	0.157752i
$856$	29367.0	+	16955.0i	1.17260	+	0.676999i
$857$	13923.0			0.554960			0.277480	−	0.960731i	$-0.410501\pi$
$857$	13923.0			0.554960			0.277480	+	0.960731i	$0.410501\pi$
$858$		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
$861$	3768.00	−	6526.37i	0.149144	−	0.258325i
$862$	−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	$0.985991\pi$
$864$	−15750.0	+	9093.27i	−0.620169	+	0.358055i
$865$	3861.00	−	2229.15i	0.151766	−	0.0876224i
$866$		−	11461.0i		−	0.449723i
$867$	−8776.00	−	15200.5i	−0.343770	−	0.595427i
$868$	−5400.00	+	9353.07i	−0.211161	+	0.365742i
$869$	−15312.0	−	8840.39i	−0.597726	−	0.345097i
$870$	846.000			0.0329679
$871$		0			0
$872$	34944.0			1.35706
$873$	−4002.00	−	2310.56i	−0.155151	−	0.0895767i
$874$	−7722.00	+	13374.9i	−0.298856	+	0.517635i
$875$	2964.00	+	5133.80i	0.114516	+	0.198348i
$876$		−	4589.93i		−	0.177031i
$877$	14509.5	−	8377.06i	0.558667	−	0.322547i	−0.193943	−	0.981013i	$-0.562128\pi$
$877$	14509.5	−	8377.06i	0.558667	−	0.322547i	0.752610	+	0.658466i	$0.228794\pi$
$878$	20982.0	−	12114.0i	0.806501	−	0.465634i
$879$			16645.0i			0.638706i
$880$	12.0000	+	20.7846i	0.000459682	+	0.000796192i
$881$	−8677.50	+	15029.9i	−0.331842	+	0.574766i	−0.982873	−	0.184284i	$-0.941003\pi$
$881$	−8677.50	+	15029.9i	−0.331842	+	0.574766i	0.651031	+	0.759051i	$0.274337\pi$
$882$	5209.50	+	3007.71i	0.198881	+	0.114824i
$883$	−46982.0			−1.79057			−0.895283	−	0.445497i	$-0.853027\pi$
$883$	−46982.0			−1.79057			−0.895283	+	0.445497i	$0.853027\pi$
$884$		0			0
$885$	−984.000			−0.0373749
$886$	−3006.00	−	1735.51i	−0.113983	−	0.0658079i
$887$	4458.00	−	7721.48i	0.168754	−	0.292291i	−0.769228	−	0.638975i	$-0.779359\pi$
$887$	4458.00	−	7721.48i	0.168754	−	0.292291i	0.937982	+	0.346684i	$0.112692\pi$
$888$	−3237.00	−	5606.65i	−0.122327	−	0.211877i
$889$			3962.93i			0.149508i
$890$	2538.00	−	1465.31i	0.0955887	−	0.0551882i
$891$	5052.00	−	2916.77i	0.189953	−	0.109670i
$892$		−	12037.8i		−	0.451854i
$893$	−17226.0	−	29836.3i	−0.645516	−	1.11807i
$894$	81.0000	−	140.296i	0.00303025	−	0.00524855i
$895$	−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
$900$	7015.00	−	12150.3i	0.259815	−	0.450012i
$901$	−5440.50	−	9423.22i	−0.201165	−	0.348427i
$902$		−	6526.37i		−	0.240914i
$903$	2496.00	−	1441.07i	0.0919841	−	0.0531071i
$904$	−13396.5	+	7734.47i	−0.492877	+	0.284563i
$905$		−	1103.32i		−	0.0405254i
$906$	3066.00	+	5310.47i	0.112429	+	0.194733i
$907$	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
$909$	−9867.00			−0.360031
$910$		0			0
$911$	−27480.0			−0.999400			−0.499700	−	0.866199i	$-0.666556\pi$
$911$	−27480.0			−0.999400			−0.499700	+	0.866199i	$0.666556\pi$
$912$	−198.000	−	114.315i	−0.00718907	−	0.00415061i
$913$	5472.00	−	9477.78i	0.198354	−	0.343558i
$914$	2185.50	+	3785.40i	0.0790918	+	0.136991i
$915$			502.295i			0.0181479i
$916$	−10860.0	+	6270.02i	−0.391730	+	0.226165i
$917$	−23688.0	+	13676.3i	−0.853050	+	0.492509i
$918$		−	20265.0i		−	0.728589i
$919$	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
$921$	−3846.00	−	2220.49i	−0.137600	−	0.0794437i
$922$	33927.0			1.21185
$923$		0			0
$924$	−1920.00			−0.0683586
$925$	15189.0	+	8769.37i	0.539904	+	0.311714i
$926$	−7476.00	+	12948.8i	−0.265310	+	0.459530i
$927$	2093.00	+	3625.18i	0.0741566	+	0.128443i
$928$		−	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	$0.372658\pi$
$930$	810.000	−	467.654i	0.0285602	−	0.0164892i
$931$			17261.6i			0.607655i
$932$	14625.0	+	25331.2i	0.514011	+	0.890292i
$933$	−4914.00	+	8511.30i	−0.172430	+	0.298657i
$934$	−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
$939$	518.000	−	897.202i	0.0180024	−	0.0311811i
$940$	−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	$-0.0269628\pi$
$942$	3633.00	−	2097.51i	0.125658	−	0.0725485i
$943$	−18369.0	+	10605.3i	−0.634334	+	0.366233i
$944$			284.056i			0.00979369i
$945$	−1200.00	−	2078.46i	−0.0413079	−	0.0715475i
$946$	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	$0.788483\pi$
$948$	12760.0			0.437158
$949$		0			0
$950$	−24156.0			−0.824973
$951$	6783.00	+	3916.17i	0.231287	+	0.133534i
$952$	18252.0	−	31613.4i	0.621377	−	1.07626i
$953$	−3237.00	−	5606.65i	−0.110028	−	0.190574i	0.805753	−	0.592251i	$-0.201761\pi$
$953$	−3237.00	−	5606.65i	−0.110028	−	0.190574i	−0.915781	+	0.401677i	$0.868427\pi$
$954$		−	3704.86i		−	0.125733i
$955$	−3897.00	+	2249.93i	−0.132046	+	0.0762368i
$956$	23310.0	−	13458.0i	0.788598	−	0.455297i
$957$		−	3907.51i		−	0.131987i
$958$	−2211.00	−	3829.56i	−0.0745659	−	0.129152i
$959$	5868.00	−	10163.7i	0.197589	−	0.342234i
$960$	921.000	+	531.740i	0.0309637	+	0.0178769i
$961$	5491.00			0.184317
$962$		0			0
$963$	34638.0			1.15908
$964$	21292.5	+	12293.2i	0.711395	+	0.410724i
$965$	967.500	−	1675.76i	0.0322745	−	0.0559011i
$966$	−1872.00	−	3242.40i	−0.0623505	−	0.107994i
$967$		−	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
$969$	23166.0	−	13374.9i	0.768007	−	0.443409i
$970$			602.754i			0.0199518i
$971$	−17499.0	−	30309.2i	−0.578342	−	1.00172i	−0.995670	−	0.0929611i	$-0.970367\pi$
$971$	−17499.0	−	30309.2i	−0.578342	−	1.00172i	0.417328	−	0.908756i	$-0.362967\pi$
$972$	−8855.00	+	15337.3i	−0.292206	+	0.506116i
$973$	−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	$0.531191\pi$
$978$	1740.00	−	3013.77i	0.0568907	−	0.0985375i
$979$	−6768.00	−	11722.5i	−0.220946	−	0.382690i
$980$			1307.70i			0.0426254i
$981$	30912.0	−	17847.1i	1.00606	−	0.580849i
$982$	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	$0.631673\pi$
$984$	6123.00	+	10605.3i	0.198368	+	0.343583i
$985$	1776.00	−	3076.12i	0.0574498	−	0.0995060i
$986$	24745.5	+	14286.8i	0.799247	+	0.461445i
$987$	8352.00			0.269349
$988$		0			0
$989$	−8112.00			−0.260816
$990$	−828.000	−	478.046i	−0.0265814	−	0.0153468i
$991$	−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
$993$			14909.5i			0.476474i
$994$	21960.0	−	12678.6i	0.700733	−	0.404569i
$995$	−3783.00	+	2184.12i	−0.120532	+	0.0695891i
$996$			7898.15i			0.251268i
$997$	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
$999$	−12450.0	−	7188.01i	−0.394295	−	0.227646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.a.147.1		2
13.2	odd	12		169.4.c.h.146.1		4
13.3	even	3		13.4.e.b.10.1	yes	2
13.4	even	6		169.4.b.d.168.1		2
13.5	odd	4		169.4.c.h.22.1		4
13.6	odd	12		169.4.a.i.1.2		2
13.7	odd	12		169.4.a.i.1.1		2
13.8	odd	4		169.4.c.h.22.2		4
13.9	even	3		169.4.b.d.168.2		2
13.10	even	6	inner	169.4.e.a.23.1		2
13.11	odd	12		169.4.c.h.146.2		4
13.12	even	2		13.4.e.b.4.1	✓	2
39.20	even	12		1521.4.a.o.1.2		2
39.29	odd	6		117.4.q.a.10.1		2
39.32	even	12		1521.4.a.o.1.1		2
39.38	odd	2		117.4.q.a.82.1		2
52.3	odd	6		208.4.w.b.49.1		2
52.51	odd	2		208.4.w.b.17.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.b.4.1	✓	2	13.12	even	2
13.4.e.b.10.1	yes	2	13.3	even	3
117.4.q.a.10.1		2	39.29	odd	6
117.4.q.a.82.1		2	39.38	odd	2
169.4.a.i.1.1		2	13.7	odd	12
169.4.a.i.1.2		2	13.6	odd	12
169.4.b.d.168.1		2	13.4	even	6
169.4.b.d.168.2		2	13.9	even	3
169.4.c.h.22.1		4	13.5	odd	4
169.4.c.h.22.2		4	13.8	odd	4
169.4.c.h.146.1		4	13.2	odd	12
169.4.c.h.146.2		4	13.11	odd	12
169.4.e.a.23.1		2	13.10	even	6	inner
169.4.e.a.147.1		2	1.1	even	1	trivial
208.4.w.b.17.1		2	52.51	odd	2
208.4.w.b.49.1		2	52.3	odd	6
1521.4.a.o.1.1		2	39.32	even	12
1521.4.a.o.1.2		2	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(3.00000 - 1.73205i) q^{6} +(12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} +1.73205i q^{5} +(3.00000 - 1.73205i) q^{6} +(12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-12.0000 - 6.92820i) q^{11} +10.0000 q^{12} -24.0000 q^{14} +(-3.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-58.5000 - 101.325i) q^{17} -39.8372i q^{18} +(99.0000 - 57.1577i) q^{19} +(7.50000 - 4.33013i) q^{20} +27.7128i q^{21} +(12.0000 + 20.7846i) q^{22} +(39.0000 - 67.5500i) q^{23} +(-39.0000 - 22.5167i) q^{24} +122.000 q^{25} -100.000 q^{27} +(-60.0000 - 34.6410i) q^{28} +(70.5000 - 122.110i) q^{29} +(3.00000 + 5.19615i) q^{30} -155.885i q^{31} +(157.500 - 90.9327i) q^{32} +(24.0000 - 13.8564i) q^{33} +202.650i q^{34} +(12.0000 + 20.7846i) q^{35} +(57.5000 - 99.5929i) q^{36} +(124.500 + 71.8801i) q^{37} -198.000 q^{38} -39.0000 q^{40} +(-235.500 - 135.966i) q^{41} +(24.0000 - 41.5692i) q^{42} +(-52.0000 - 90.0666i) q^{43} +69.2820i q^{44} +(-34.5000 + 19.9186i) q^{45} +(-117.000 + 67.5500i) q^{46} -301.377i q^{47} +(-1.00000 - 1.73205i) q^{48} +(-75.5000 + 130.770i) q^{49} +(-183.000 - 105.655i) q^{50} +234.000 q^{51} +93.0000 q^{53} +(150.000 + 86.6025i) q^{54} +(12.0000 - 20.7846i) q^{55} +(156.000 + 270.200i) q^{56} +228.631i q^{57} +(-211.500 + 122.110i) q^{58} +(246.000 - 142.028i) q^{59} +17.3205i q^{60} +(-72.5000 - 125.574i) q^{61} +(-135.000 + 233.827i) q^{62} +(276.000 + 159.349i) q^{63} -307.000 q^{64} -48.0000 q^{66} +(681.000 + 393.176i) q^{67} +(-292.500 + 506.625i) q^{68} +(78.0000 + 135.100i) q^{69} -41.5692i q^{70} +(-915.000 + 528.275i) q^{71} +(-448.500 + 258.942i) q^{72} -458.993i q^{73} +(-124.500 - 215.640i) q^{74} +(-122.000 + 211.310i) q^{75} +(-495.000 - 285.788i) q^{76} -192.000 q^{77} +1276.00 q^{79} +(-1.50000 - 0.866025i) q^{80} +(-210.500 + 364.597i) q^{81} +(235.500 + 407.898i) q^{82} +789.815i q^{83} +(120.000 - 69.2820i) q^{84} +(175.500 - 101.325i) q^{85} +180.133i q^{86} +(141.000 + 244.219i) q^{87} +(156.000 - 270.200i) q^{88} +(846.000 + 488.438i) q^{89} +69.0000 q^{90} -390.000 q^{92} +(270.000 + 155.885i) q^{93} +(-261.000 + 452.065i) q^{94} +(99.0000 + 171.473i) q^{95} +363.731i q^{96} +(-174.000 + 100.459i) q^{97} +(226.500 - 130.770i) q^{98} -318.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{6} + 24 q^{7} + 23 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 2 * q^3 - 5 * q^4 + 6 * q^6 + 24 * q^7 + 23 * q^9	\( 2 q - 3 q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{6} + 24 q^{7} + 23 q^{9} + 3 q^{10} - 24 q^{11} + 20 q^{12} - 48 q^{14} - 6 q^{15} - q^{16} - 117 q^{17} + 198 q^{19} + 15 q^{20} + 24 q^{22} + 78 q^{23} - 78 q^{24} + 244 q^{25} - 200 q^{27} - 120 q^{28} + 141 q^{29} + 6 q^{30} + 315 q^{32} + 48 q^{33} + 24 q^{35} + 115 q^{36} + 249 q^{37} - 396 q^{38} - 78 q^{40} - 471 q^{41} + 48 q^{42} - 104 q^{43} - 69 q^{45} - 234 q^{46} - 2 q^{48} - 151 q^{49} - 366 q^{50} + 468 q^{51} + 186 q^{53} + 300 q^{54} + 24 q^{55} + 312 q^{56} - 423 q^{58} + 492 q^{59} - 145 q^{61} - 270 q^{62} + 552 q^{63} - 614 q^{64} - 96 q^{66} + 1362 q^{67} - 585 q^{68} + 156 q^{69} - 1830 q^{71} - 897 q^{72} - 249 q^{74} - 244 q^{75} - 990 q^{76} - 384 q^{77} + 2552 q^{79} - 3 q^{80} - 421 q^{81} + 471 q^{82} + 240 q^{84} + 351 q^{85} + 282 q^{87} + 312 q^{88} + 1692 q^{89} + 138 q^{90} - 780 q^{92} + 540 q^{93} - 522 q^{94} + 198 q^{95} - 348 q^{97} + 453 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - 2 * q^3 - 5 * q^4 + 6 * q^6 + 24 * q^7 + 23 * q^9 + 3 * q^10 - 24 * q^11 + 20 * q^12 - 48 * q^14 - 6 * q^15 - q^16 - 117 * q^17 + 198 * q^19 + 15 * q^20 + 24 * q^22 + 78 * q^23 - 78 * q^24 + 244 * q^25 - 200 * q^27 - 120 * q^28 + 141 * q^29 + 6 * q^30 + 315 * q^32 + 48 * q^33 + 24 * q^35 + 115 * q^36 + 249 * q^37 - 396 * q^38 - 78 * q^40 - 471 * q^41 + 48 * q^42 - 104 * q^43 - 69 * q^45 - 234 * q^46 - 2 * q^48 - 151 * q^49 - 366 * q^50 + 468 * q^51 + 186 * q^53 + 300 * q^54 + 24 * q^55 + 312 * q^56 - 423 * q^58 + 492 * q^59 - 145 * q^61 - 270 * q^62 + 552 * q^63 - 614 * q^64 - 96 * q^66 + 1362 * q^67 - 585 * q^68 + 156 * q^69 - 1830 * q^71 - 897 * q^72 - 249 * q^74 - 244 * q^75 - 990 * q^76 - 384 * q^77 + 2552 * q^79 - 3 * q^80 - 421 * q^81 + 471 * q^82 + 240 * q^84 + 351 * q^85 + 282 * q^87 + 312 * q^88 + 1692 * q^89 + 138 * q^90 - 780 * q^92 + 540 * q^93 - 522 * q^94 + 198 * q^95 - 348 * q^97 + 453 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more