LMFDB - Embedded newform 143.4.g.a.109.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.20
Character	$\chi$	$=$	143.109
Dual form			143.4.g.a.21.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177069 - 0.177069i) q^{2} -5.26131 q^{3} -7.93729i q^{4} +(-2.40696 + 2.40696i) q^{5} +(0.931617 + 0.931617i) q^{6} +(-14.4545 + 14.4545i) q^{7} +(-2.82201 + 2.82201i) q^{8} +0.681391 q^{9} +O(q^{10})$	\(q+(-0.177069 - 0.177069i) q^{2} -5.26131 q^{3} -7.93729i q^{4} +(-2.40696 + 2.40696i) q^{5} +(0.931617 + 0.931617i) q^{6} +(-14.4545 + 14.4545i) q^{7} +(-2.82201 + 2.82201i) q^{8} +0.681391 q^{9} +0.852396 q^{10} +(36.1216 + 5.12149i) q^{11} +41.7606i q^{12} +(39.5842 - 25.1016i) q^{13} +5.11890 q^{14} +(12.6637 - 12.6637i) q^{15} -62.4990 q^{16} +72.8359 q^{17} +(-0.120654 - 0.120654i) q^{18} +(53.3396 + 53.3396i) q^{19} +(19.1047 + 19.1047i) q^{20} +(76.0497 - 76.0497i) q^{21} +(-5.48917 - 7.30289i) q^{22} +127.048i q^{23} +(14.8474 - 14.8474i) q^{24} +113.413i q^{25} +(-11.4539 - 2.56442i) q^{26} +138.470 q^{27} +(114.730 + 114.730i) q^{28} +52.5564i q^{29} -4.48472 q^{30} +(-74.2815 + 74.2815i) q^{31} +(33.6427 + 33.6427i) q^{32} +(-190.047 - 26.9457i) q^{33} +(-12.8970 - 12.8970i) q^{34} -69.5828i q^{35} -5.40840i q^{36} +(-117.423 - 117.423i) q^{37} -18.8896i q^{38} +(-208.265 + 132.067i) q^{39} -13.5849i q^{40} +(-153.677 - 153.677i) q^{41} -26.9321 q^{42} +341.728 q^{43} +(40.6507 - 286.708i) q^{44} +(-1.64008 + 1.64008i) q^{45} +(22.4964 - 22.4964i) q^{46} +(-82.1608 - 82.1608i) q^{47} +328.826 q^{48} -74.8658i q^{49} +(20.0820 - 20.0820i) q^{50} -383.212 q^{51} +(-199.239 - 314.191i) q^{52} +182.779 q^{53} +(-24.5189 - 24.5189i) q^{54} +(-99.2703 + 74.6159i) q^{55} -81.5814i q^{56} +(-280.636 - 280.636i) q^{57} +(9.30612 - 9.30612i) q^{58} +(-60.1255 - 60.1255i) q^{59} +(-100.516 - 100.516i) q^{60} +758.712i q^{61} +26.3059 q^{62} +(-9.84918 + 9.84918i) q^{63} +488.078i q^{64} +(-34.8590 + 155.696i) q^{65} +(28.8802 + 38.4228i) q^{66} +(62.3670 - 62.3670i) q^{67} -578.120i q^{68} -668.441i q^{69} +(-12.3210 + 12.3210i) q^{70} +(-225.965 + 225.965i) q^{71} +(-1.92289 + 1.92289i) q^{72} +(-187.376 + 187.376i) q^{73} +41.5840i q^{74} -596.702i q^{75} +(423.372 - 423.372i) q^{76} +(-596.149 + 448.092i) q^{77} +(60.2624 + 13.4922i) q^{78} +392.126i q^{79} +(150.432 - 150.432i) q^{80} -746.933 q^{81} +54.4231i q^{82} +(1047.65 + 1047.65i) q^{83} +(-603.629 - 603.629i) q^{84} +(-175.313 + 175.313i) q^{85} +(-60.5096 - 60.5096i) q^{86} -276.515i q^{87} +(-116.388 + 87.4825i) q^{88} +(-885.585 - 885.585i) q^{89} +0.580816 q^{90} +(-209.339 + 935.002i) q^{91} +1008.42 q^{92} +(390.818 - 390.818i) q^{93} +29.0963i q^{94} -256.772 q^{95} +(-177.005 - 177.005i) q^{96} +(523.499 - 523.499i) q^{97} +(-13.2564 + 13.2564i) q^{98} +(24.6130 + 3.48974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.177069	−	0.177069i	−0.0626035	−	0.0626035i	0.675112	−	0.737715i	$-0.264095\pi$
$2$	−0.177069	−	0.177069i	−0.0626035	−	0.0626035i	−0.737715	+	0.675112i	$0.764095\pi$
$3$	−5.26131			−1.01254			−0.506270	−	0.862375i	$-0.668976\pi$
$3$	−5.26131			−1.01254			−0.506270	+	0.862375i	$0.668976\pi$
$4$		−	7.93729i		−	0.992162i
$5$	−2.40696	+	2.40696i	−0.215285	+	0.215285i	−0.806508	−	0.591223i	$-0.798645\pi$
$5$	−2.40696	+	2.40696i	−0.215285	+	0.215285i	0.591223	+	0.806508i	$0.298645\pi$
$6$	0.931617	+	0.931617i	0.0633885	+	0.0633885i
$7$	−14.4545	+	14.4545i	−0.780470	+	0.780470i	−0.979910	−	0.199440i	$-0.936088\pi$
$7$	−14.4545	+	14.4545i	−0.780470	+	0.780470i	0.199440	+	0.979910i	$0.436088\pi$
$8$	−2.82201	+	2.82201i	−0.124716	+	0.124716i
$9$	0.681391			0.0252367
$10$	0.852396			0.0269551
$11$	36.1216	+	5.12149i	0.990098	+	0.140381i
$11$	36.1216	+	5.12149i	0.990098	+	0.140381i
$12$			41.7606i			1.00460i
$13$	39.5842	−	25.1016i	0.844514	−	0.535533i
$13$	39.5842	−	25.1016i	0.844514	−	0.535533i
$14$	5.11890			0.0977203
$15$	12.6637	−	12.6637i	0.217984	−	0.217984i
$16$	−62.4990			−0.976546
$17$	72.8359			1.03914			0.519568	−	0.854429i	$-0.326093\pi$
$17$	72.8359			1.03914			0.519568	+	0.854429i	$0.326093\pi$
$18$	−0.120654	−	0.120654i	−0.00157991	−	0.00157991i
$19$	53.3396	+	53.3396i	0.644050	+	0.644050i	0.951548	−	0.307499i	$-0.0994920\pi$
$19$	53.3396	+	53.3396i	0.644050	+	0.644050i	−0.307499	+	0.951548i	$0.599492\pi$
$20$	19.1047	+	19.1047i	0.213597	+	0.213597i
$21$	76.0497	−	76.0497i	0.790257	−	0.790257i
$22$	−5.48917	−	7.30289i	−0.0531952	−	0.0707718i
$23$			127.048i			1.15180i	0.817520	+	0.575900i	$0.195348\pi$
$23$			127.048i			1.15180i	−0.817520	+	0.575900i	$0.804652\pi$
$24$	14.8474	−	14.8474i	0.126280	−	0.126280i
$25$			113.413i			0.907305i
$26$	−11.4539	−	2.56442i	−0.0863957	−	0.0193433i
$27$	138.470			0.986987
$28$	114.730	+	114.730i	0.774353	+	0.774353i
$29$			52.5564i			0.336533i	0.985741	+	0.168267i	$0.0538170\pi$
$29$			52.5564i			0.336533i	−0.985741	+	0.168267i	$0.946183\pi$
$30$	−4.48472			−0.0272931
$31$	−74.2815	+	74.2815i	−0.430366	+	0.430366i	−0.888753	−	0.458387i	$-0.848427\pi$
$31$	−74.2815	+	74.2815i	−0.430366	+	0.430366i	0.458387	+	0.888753i	$0.348427\pi$
$32$	33.6427	+	33.6427i	0.185851	+	0.185851i
$33$	−190.047	−	26.9457i	−1.00251	−	0.142141i
$34$	−12.8970	−	12.8970i	−0.0650535	−	0.0650535i
$35$		−	69.5828i		−	0.336047i
$36$		−	5.40840i		−	0.0250389i
$37$	−117.423	−	117.423i	−0.521735	−	0.521735i	0.396360	−	0.918095i	$-0.370273\pi$
$37$	−117.423	−	117.423i	−0.521735	−	0.521735i	−0.918095	+	0.396360i	$0.870273\pi$
$38$		−	18.8896i		−	0.0806395i
$39$	−208.265	+	132.067i	−0.855104	+	0.542249i
$40$		−	13.5849i		−	0.0536990i
$41$	−153.677	−	153.677i	−0.585375	−	0.585375i	0.351000	−	0.936375i	$-0.385842\pi$
$41$	−153.677	−	153.677i	−0.585375	−	0.585375i	−0.936375	+	0.351000i	$0.885842\pi$
$42$	−26.9321			−0.0989457
$43$	341.728			1.21193			0.605966	−	0.795490i	$-0.292787\pi$
$43$	341.728			1.21193			0.605966	+	0.795490i	$0.292787\pi$
$44$	40.6507	−	286.708i	0.139280	−	0.982337i
$45$	−1.64008	+	1.64008i	−0.00543308	+	0.00543308i
$46$	22.4964	−	22.4964i	0.0721067	−	0.0721067i
$47$	−82.1608	−	82.1608i	−0.254987	−	0.254987i	0.568025	−	0.823012i	$-0.307708\pi$
$47$	−82.1608	−	82.1608i	−0.254987	−	0.254987i	−0.823012	+	0.568025i	$0.807708\pi$
$48$	328.826			0.988792
$49$		−	74.8658i		−	0.218268i
$50$	20.0820	−	20.0820i	0.0568004	−	0.0568004i
$51$	−383.212			−1.05217
$52$	−199.239	−	314.191i	−0.531336	−	0.837895i
$53$	182.779			0.473711			0.236855	−	0.971545i	$-0.423883\pi$
$53$	182.779			0.473711			0.236855	+	0.971545i	$0.423883\pi$
$54$	−24.5189	−	24.5189i	−0.0617888	−	0.0617888i
$55$	−99.2703	+	74.6159i	−0.243375	+	0.182931i
$56$		−	81.5814i		−	0.194675i
$57$	−280.636	−	280.636i	−0.652126	−	0.652126i
$58$	9.30612	−	9.30612i	0.0210682	−	0.0210682i
$59$	−60.1255	−	60.1255i	−0.132672	−	0.132672i	0.637652	−	0.770325i	$-0.279906\pi$
$59$	−60.1255	−	60.1255i	−0.132672	−	0.132672i	−0.770325	+	0.637652i	$0.779906\pi$
$60$	−100.516	−	100.516i	−0.216276	−	0.216276i
$61$			758.712i			1.59251i	0.604960	+	0.796256i	$0.293189\pi$
$61$			758.712i			1.59251i	−0.604960	+	0.796256i	$0.706811\pi$
$62$	26.3059			0.0538848
$63$	−9.84918	+	9.84918i	−0.0196965	+	0.0196965i
$64$			488.078i			0.953276i
$65$	−34.8590	+	155.696i	−0.0665189	+	0.297103i
$66$	28.8802	+	38.4228i	0.0538623	+	0.0716593i
$67$	62.3670	−	62.3670i	0.113722	−	0.113722i	−0.647956	−	0.761678i	$-0.724376\pi$
$67$	62.3670	−	62.3670i	0.113722	−	0.113722i	0.761678	+	0.647956i	$0.224376\pi$
$68$		−	578.120i		−	1.03099i
$69$		−	668.441i		−	1.16624i
$70$	−12.3210	+	12.3210i	−0.0210377	+	0.0210377i
$71$	−225.965	+	225.965i	−0.377706	+	0.377706i	−0.870274	−	0.492568i	$-0.836058\pi$
$71$	−225.965	+	225.965i	−0.377706	+	0.377706i	0.492568	+	0.870274i	$0.336058\pi$
$72$	−1.92289	+	1.92289i	−0.00314743	+	0.00314743i
$73$	−187.376	+	187.376i	−0.300421	+	0.300421i	−0.841179	−	0.540758i	$-0.818138\pi$
$73$	−187.376	+	187.376i	−0.300421	+	0.300421i	0.540758	+	0.841179i	$0.318138\pi$
$74$			41.5840i			0.0653249i
$75$		−	596.702i		−	0.918682i
$76$	423.372	−	423.372i	0.639001	−	0.639001i
$77$	−596.149	+	448.092i	−0.882305	+	0.663179i
$78$	60.2624	+	13.4922i	0.0874791	+	0.0195858i
$79$			392.126i			0.558450i	0.960226	+	0.279225i	$0.0900776\pi$
$79$			392.126i			0.558450i	−0.960226	+	0.279225i	$0.909922\pi$
$80$	150.432	−	150.432i	0.210236	−	0.210236i
$81$	−746.933			−1.02460
$82$			54.4231i			0.0732930i
$83$	1047.65	+	1047.65i	1.38548	+	1.38548i	0.834561	+	0.550916i	$0.185722\pi$
$83$	1047.65	+	1047.65i	1.38548	+	1.38548i	0.550916	+	0.834561i	$0.314278\pi$
$84$	−603.629	−	603.629i	−0.784063	−	0.784063i
$85$	−175.313	+	175.313i	−0.223710	+	0.223710i
$86$	−60.5096	−	60.5096i	−0.0758712	−	0.0758712i
$87$		−	276.515i		−	0.340754i
$88$	−116.388	+	87.4825i	−0.140989	+	0.105973i
$89$	−885.585	−	885.585i	−1.05474	−	1.05474i	−0.998412	−	0.0563269i	$-0.982061\pi$
$89$	−885.585	−	885.585i	−1.05474	−	1.05474i	−0.0563269	−	0.998412i	$-0.517939\pi$
$90$	0.580816			0.000680259
$91$	−209.339	+	935.002i	−0.241150	+	1.07709i
$92$	1008.42			1.14277
$93$	390.818	−	390.818i	0.435763	−	0.435763i
$94$			29.0963i			0.0319261i
$95$	−256.772			−0.277308
$96$	−177.005	−	177.005i	−0.188182	−	0.188182i
$97$	523.499	−	523.499i	0.547971	−	0.547971i	−0.377882	−	0.925854i	$-0.623348\pi$
$97$	523.499	−	523.499i	0.547971	−	0.547971i	0.925854	+	0.377882i	$0.123348\pi$
$98$	−13.2564	+	13.2564i	−0.0136643	+	0.0136643i
$99$	24.6130	+	3.48974i	0.0249868	+	0.00354274i
$100$	900.193			0.900193
$101$	−639.965			−0.630484			−0.315242	−	0.949011i	$-0.602086\pi$
$101$	−639.965			−0.630484			−0.315242	+	0.949011i	$0.602086\pi$
$102$	67.8551	+	67.8551i	0.0658692	+	0.0658692i
$103$			1313.12i			1.25617i	0.778144	+	0.628086i	$0.216161\pi$
$103$			1313.12i			1.25617i	−0.778144	+	0.628086i	$0.783839\pi$
$104$	−40.8700	+	182.544i	−0.0385349	+	0.172114i
$105$			366.097i			0.340261i
$106$	−32.3646	−	32.3646i	−0.0296559	−	0.0296559i
$107$		−	1491.01i		−	1.34712i	−0.739134	−	0.673558i	$-0.764765\pi$
$107$		−	1491.01i		−	1.34712i	0.739134	−	0.673558i	$-0.235235\pi$
$108$		−	1099.08i		−	0.979250i
$109$	342.830	+	342.830i	0.301258	+	0.301258i	0.841506	−	0.540248i	$-0.181669\pi$
$109$	342.830	+	342.830i	0.301258	+	0.301258i	−0.540248	+	0.841506i	$0.681669\pi$
$110$	30.7899	+	4.36554i	0.0266882	+	0.00378398i
$111$	617.798	+	617.798i	0.528278	+	0.528278i
$112$	903.392	−	903.392i	0.762165	−	0.762165i
$113$	−513.821			−0.427754			−0.213877	−	0.976861i	$-0.568609\pi$
$113$	−513.821			−0.427754			−0.213877	+	0.976861i	$0.568609\pi$
$114$			99.3841i			0.0816507i
$115$	−305.800	−	305.800i	−0.247965	−	0.247965i
$116$	417.155			0.333896
$117$	26.9723	−	17.1040i	0.0213128	−	0.0135151i
$118$			21.2928i			0.0166115i
$119$	−1052.81	+	1052.81i	−0.811014	+	0.811014i
$120$			71.4743i			0.0543724i
$121$	1278.54	+	369.993i	0.960587	+	0.277981i
$122$	134.345	−	134.345i	0.0996967	−	0.0996967i
$123$	808.545	+	808.545i	0.592716	+	0.592716i
$124$	589.594	+	589.594i	0.426993	+	0.426993i
$125$	−573.850	−	573.850i	−0.410614	−	0.410614i
$126$	3.48798			0.00246614
$127$	2798.39			1.95525			0.977624	−	0.210359i	$-0.0674634\pi$
$127$	2798.39			1.95525			0.977624	+	0.210359i	$0.0674634\pi$
$128$	355.565	−	355.565i	0.245530	−	0.245530i
$129$	−1797.94			−1.22713
$130$	33.7414	−	21.3965i	0.0227640	−	0.0144354i
$131$			2160.53i			1.44096i	0.693474	+	0.720482i	$0.256079\pi$
$131$			2160.53i			1.44096i	−0.693474	+	0.720482i	$0.743921\pi$
$132$	−213.876	+	1508.46i	−0.141027	+	0.994655i
$133$	−1542.00			−1.00532
$134$	−22.0866			−0.0142387
$135$	−333.292	+	333.292i	−0.212483	+	0.212483i
$136$	−205.543	+	205.543i	−0.129597	+	0.129597i
$137$	1860.48	+	1860.48i	1.16023	+	1.16023i	0.984425	+	0.175806i	$0.0562531\pi$
$137$	1860.48	+	1860.48i	1.16023	+	1.16023i	0.175806	+	0.984425i	$0.443747\pi$
$138$	−118.360	+	118.360i	−0.0730109	+	0.0730109i
$139$		−	363.440i		−	0.221774i	−0.993833	−	0.110887i	$-0.964631\pi$
$139$		−	363.440i		−	0.221774i	0.993833	−	0.110887i	$-0.0353691\pi$
$140$	−552.299			−0.333413
$141$	432.274	+	432.274i	0.258184	+	0.258184i
$142$	80.0230			0.0472914
$143$	1558.40	−	703.980i	0.911330	−	0.411677i
$144$	−42.5863			−0.0246448
$145$	−126.501	−	126.501i	−0.0724505	−	0.0724505i
$146$	66.3572			0.0376148
$147$			393.892i			0.221005i
$148$	−932.020	+	932.020i	−0.517646	+	0.517646i
$149$	322.640	+	322.640i	0.177394	+	0.177394i	0.790219	−	0.612825i	$-0.209967\pi$
$149$	322.640	+	322.640i	0.177394	+	0.177394i	−0.612825	+	0.790219i	$0.709967\pi$
$150$	−105.658	+	105.658i	−0.0575127	+	0.0575127i
$151$	1774.60	−	1774.60i	0.956388	−	0.956388i	−0.0427003	−	0.999088i	$-0.513596\pi$
$151$	1774.60	−	1774.60i	0.956388	−	0.956388i	0.999088	+	0.0427003i	$0.0135961\pi$
$152$	−301.049			−0.160647
$153$	49.6298			0.0262244
$154$	184.903	+	26.2164i	0.0967526	+	0.0137180i
$155$		−	357.585i		−	0.185302i
$156$	1048.26	+	1653.06i	0.537998	+	0.848401i
$157$	566.438			0.287940			0.143970	−	0.989582i	$-0.454013\pi$
$157$	566.438			0.287940			0.143970	+	0.989582i	$0.454013\pi$
$158$	69.4334	−	69.4334i	0.0349609	−	0.0349609i
$159$	−961.659			−0.479651
$160$	−161.953			−0.0800219
$161$	−1836.42	−	1836.42i	−0.898946	−	0.898946i
$162$	132.259	+	132.259i	0.0641435	+	0.0641435i
$163$	1581.77	+	1581.77i	0.760085	+	0.760085i	0.976337	−	0.216252i	$-0.0693834\pi$
$163$	1581.77	+	1581.77i	0.760085	+	0.760085i	−0.216252	+	0.976337i	$0.569383\pi$
$164$	−1219.78	+	1219.78i	−0.580787	+	0.580787i
$165$	522.292	−	392.578i	0.246427	−	0.185225i
$166$		−	371.013i		−	0.173471i
$167$	−1009.23	+	1009.23i	−0.467643	+	0.467643i	−0.901150	−	0.433507i	$-0.857276\pi$
$167$	−1009.23	+	1009.23i	−0.467643	+	0.467643i	0.433507	+	0.901150i	$0.357276\pi$
$168$			429.225i			0.197116i
$169$	936.819	−	1987.25i	0.426408	−	0.904531i
$170$	62.0850			0.0280100
$171$	36.3452	+	36.3452i	0.0162537	+	0.0162537i
$172$		−	2712.40i		−	1.20243i
$173$	−2250.43			−0.989001			−0.494500	−	0.869177i	$-0.664649\pi$
$173$	−2250.43			−0.989001			−0.494500	+	0.869177i	$0.664649\pi$
$174$	−48.9624	+	48.9624i	−0.0213323	+	0.0213323i
$175$	−1639.33	−	1639.33i	−0.708125	−	0.708125i
$176$	−2257.56	−	320.088i	−0.966876	−	0.137088i
$177$	316.339	+	316.339i	0.134336	+	0.134336i
$178$			313.620i			0.132061i
$179$		−	4575.49i		−	1.91055i	−0.295722	−	0.955274i	$-0.595560\pi$
$179$		−	4575.49i		−	1.91055i	0.295722	−	0.955274i	$-0.404440\pi$
$180$	13.0178	+	13.0178i	0.00539049	+	0.00539049i
$181$		−	2292.82i		−	0.941569i	−0.882248	−	0.470785i	$-0.843971\pi$
$181$		−	2292.82i		−	0.941569i	0.882248	−	0.470785i	$-0.156029\pi$
$182$	202.628	−	128.493i	0.0825262	−	0.0523325i
$183$		−	3991.82i		−	1.61248i
$184$	−358.531	−	358.531i	−0.143648	−	0.143648i
$185$	565.264			0.224643
$186$	−138.404			−0.0545605
$187$	2630.95	+	373.028i	1.02885	+	0.145874i
$188$	−652.134	+	652.134i	−0.252988	+	0.252988i
$189$	−2001.52	+	2001.52i	−0.770314	+	0.770314i
$190$	45.4665	+	45.4665i	0.0173605	+	0.0173605i
$191$	−394.909			−0.149605			−0.0748027	−	0.997198i	$-0.523833\pi$
$191$	−394.909			−0.149605			−0.0748027	+	0.997198i	$0.523833\pi$
$192$		−	2567.93i		−	0.965230i
$193$	−321.261	+	321.261i	−0.119818	+	0.119818i	−0.764473	−	0.644655i	$-0.777001\pi$
$193$	−321.261	+	321.261i	−0.119818	+	0.119818i	0.644655	+	0.764473i	$0.277001\pi$
$194$	−185.391			−0.0686098
$195$	183.404	−	819.165i	0.0673530	−	0.300829i
$196$	−594.232			−0.216557
$197$	−3447.86	−	3447.86i	−1.24695	−	1.24695i	−0.957058	−	0.289896i	$-0.906379\pi$
$197$	−3447.86	−	3447.86i	−1.24695	−	1.24695i	−0.289896	−	0.957058i	$-0.593621\pi$
$198$	−3.74027	−	4.97612i	−0.00134247	−	0.00178605i
$199$			4036.98i			1.43806i	0.694979	+	0.719030i	$0.255414\pi$
$199$			4036.98i			1.43806i	−0.694979	+	0.719030i	$0.744586\pi$
$200$	−320.052	−	320.052i	−0.113156	−	0.113156i
$201$	−328.132	+	328.132i	−0.115148	+	0.115148i
$202$	113.318	+	113.318i	0.0394705	+	0.0394705i
$203$	−759.676	−	759.676i	−0.262654	−	0.262654i
$204$			3041.67i			1.04392i
$205$	739.790			0.252045
$206$	232.513	−	232.513i	0.0786407	−	0.0786407i
$207$			86.5696i			0.0290677i
$208$	−2473.97	+	1568.82i	−0.824707	+	0.522973i
$209$	1653.53	+	2199.89i	0.547260	+	0.728084i
$210$	64.8245	−	64.8245i	0.0213015	−	0.0213015i
$211$			5695.09i			1.85813i	0.369913	+	0.929066i	$0.379387\pi$
$211$			5695.09i			1.85813i	−0.369913	+	0.929066i	$0.620613\pi$
$212$		−	1450.77i		−	0.469998i
$213$	1188.87	−	1188.87i	0.382443	−	0.382443i
$214$	−264.012	+	264.012i	−0.0843341	+	0.0843341i
$215$	−822.525	+	822.525i	−0.260911	+	0.260911i
$216$	−390.764	+	390.764i	−0.123093	+	0.123093i
$217$		−	2147.40i		−	0.671776i
$218$		−	121.409i		−	0.0377196i
$219$	985.845	−	985.845i	0.304188	−	0.304188i
$220$	592.249	+	787.938i	0.181497	+	0.241467i
$221$	2883.15	−	1828.30i	0.877564	−	0.556491i
$222$		−	218.786i		−	0.0661440i
$223$	−4263.47	+	4263.47i	−1.28028	+	1.28028i	−0.339775	+	0.940507i	$0.610351\pi$
$223$	−4263.47	+	4263.47i	−1.28028	+	1.28028i	−0.940507	+	0.339775i	$0.889649\pi$
$224$	−972.577			−0.290103
$225$			77.2787i			0.0228974i
$226$	90.9819	+	90.9819i	0.0267789	+	0.0267789i
$227$	−2966.74	−	2966.74i	−0.867442	−	0.867442i	0.124746	−	0.992189i	$-0.460188\pi$
$227$	−2966.74	−	2966.74i	−0.867442	−	0.867442i	−0.992189	+	0.124746i	$0.960188\pi$
$228$	−2227.49	+	2227.49i	−0.647014	+	0.647014i
$229$	−2387.53	−	2387.53i	−0.688962	−	0.688962i	0.273041	−	0.962002i	$-0.411971\pi$
$229$	−2387.53	−	2387.53i	−0.688962	−	0.688962i	−0.962002	+	0.273041i	$0.911971\pi$
$230$			108.296i			0.0310469i
$231$	3136.52	−	2357.55i	0.893368	−	0.671495i
$232$	−148.314	−	148.314i	−0.0419712	−	0.0419712i
$233$	3968.40			1.11579			0.557894	−	0.829912i	$-0.311609\pi$
$233$	3968.40			1.11579			0.557894	+	0.829912i	$0.311609\pi$
$234$	−7.80457	−	1.74738i	−0.00218035	−	0.000488161i
$235$	395.515			0.109790
$236$	−477.234	+	477.234i	−0.131633	+	0.131633i
$237$		−	2063.10i		−	0.565453i
$238$	372.840			0.101545
$239$	−286.400	−	286.400i	−0.0775133	−	0.0775133i	0.667287	−	0.744800i	$-0.267455\pi$
$239$	−286.400	−	286.400i	−0.0775133	−	0.0775133i	−0.744800	+	0.667287i	$0.767455\pi$
$240$	−791.471	+	791.471i	−0.212872	+	0.212872i
$241$	−1063.69	+	1063.69i	−0.284308	+	0.284308i	−0.834824	−	0.550516i	$-0.814431\pi$
$241$	−1063.69	+	1063.69i	−0.284308	+	0.284308i	0.550516	+	0.834824i	$0.314431\pi$
$242$	−160.876	−	291.905i	−0.0427335	−	0.0775386i
$243$	191.148			0.0504615
$244$	6022.12			1.58003
$245$	180.199	+	180.199i	0.0469897	+	0.0469897i
$246$		−	286.337i		−	0.0742121i
$247$	3450.32	+	772.496i	0.888819	+	0.198999i
$248$		−	419.245i		−	0.107347i
$249$	−5512.01	−	5512.01i	−1.40285	−	1.40285i
$250$			203.222i			0.0514117i
$251$			1877.54i			0.472147i	0.971735	+	0.236074i	$0.0758607\pi$
$251$			1877.54i			0.472147i	−0.971735	+	0.236074i	$0.924139\pi$
$252$	78.1758	+	78.1758i	0.0195421	+	0.0195421i
$253$	−650.676	+	4589.19i	−0.161690	+	1.14039i
$254$	−495.508	−	495.508i	−0.122405	−	0.122405i
$255$	922.375	−	922.375i	0.226515	−	0.226515i
$256$	3778.70			0.922534
$257$		−	1491.33i		−	0.361970i	−0.983486	−	0.180985i	$-0.942071\pi$
$257$		−	1491.33i		−	0.361970i	0.983486	−	0.180985i	$-0.0579286\pi$
$258$	318.360	+	318.360i	0.0768226	+	0.0768226i
$259$	3394.58			0.814398
$260$	1235.80	+	276.686i	0.294774	+	0.0659975i
$261$			35.8115i			0.00849300i
$262$	382.563	−	382.563i	0.0902093	−	0.0902093i
$263$		−	5422.03i		−	1.27124i	−0.772001	−	0.635621i	$-0.780744\pi$
$263$		−	5422.03i		−	1.27124i	0.772001	−	0.635621i	$-0.219256\pi$
$264$	612.355	−	460.273i	0.142757	−	0.107302i
$265$	−439.942	+	439.942i	−0.101983	+	0.101983i
$266$	273.040	+	273.040i	0.0629367	+	0.0629367i
$267$	4659.34	+	4659.34i	1.06797	+	1.06797i
$268$	−495.025	−	495.025i	−0.112830	−	0.112830i
$269$	1301.12			0.294909			0.147455	−	0.989069i	$-0.452892\pi$
$269$	1301.12			0.294909			0.147455	+	0.989069i	$0.452892\pi$
$270$	118.032			0.0266044
$271$	−4550.29	+	4550.29i	−1.01996	+	1.01996i	−0.0201679	+	0.999797i	$0.506420\pi$
$271$	−4550.29	+	4550.29i	−1.01996	+	1.01996i	−0.999797	+	0.0201679i	$0.993580\pi$
$272$	−4552.17			−1.01476
$273$	1101.40	−	4919.33i	0.244174	−	1.09059i
$274$		−	658.868i		−	0.145269i
$275$	−580.844	+	4096.66i	−0.127368	+	0.898320i
$276$	−5305.61			−1.15710
$277$	−1207.10			−0.261833			−0.130917	−	0.991393i	$-0.541792\pi$
$277$	−1207.10			−0.261833			−0.130917	+	0.991393i	$0.541792\pi$
$278$	−64.3540	+	64.3540i	−0.0138838	+	0.0138838i
$279$	−50.6148	+	50.6148i	−0.0108610	+	0.0108610i
$280$	196.363	+	196.363i	0.0419105	+	0.0419105i
$281$	66.7436	−	66.7436i	0.0141694	−	0.0141694i	−0.699987	−	0.714156i	$-0.746811\pi$
$281$	66.7436	−	66.7436i	0.0141694	−	0.0141694i	0.714156	+	0.699987i	$0.246811\pi$
$282$		−	153.085i		−	0.0323265i
$283$	2264.55			0.475665			0.237833	−	0.971306i	$-0.423563\pi$
$283$	2264.55			0.475665			0.237833	+	0.971306i	$0.423563\pi$
$284$	1793.55	+	1793.55i	0.374746	+	0.374746i
$285$	1350.96			0.280786
$286$	−400.599	−	151.292i	−0.0828248	−	0.0312800i
$287$	4442.66			0.913736
$288$	22.9238	+	22.9238i	0.00469028	+	0.00469028i
$289$	392.067			0.0798020
$290$			44.7988i			0.00907131i
$291$	−2754.29	+	2754.29i	−0.554843	+	0.554843i
$292$	1487.26	+	1487.26i	0.298066	+	0.298066i
$293$	−249.220	+	249.220i	−0.0496914	+	0.0496914i	−0.731516	−	0.681824i	$-0.761187\pi$
$293$	−249.220	+	249.220i	−0.0496914	+	0.0496914i	0.681824	+	0.731516i	$0.261187\pi$
$294$	69.7462	−	69.7462i	0.0138357	−	0.0138357i
$295$	289.439			0.0571247
$296$	662.736			0.130138
$297$	5001.77	+	709.174i	0.977213	+	0.138554i
$298$		−	114.259i		−	0.0222110i
$299$	3189.12	+	5029.11i	0.616827	+	0.972712i
$300$	−4736.20			−0.911481
$301$	−4939.52	+	4939.52i	−0.945877	+	0.945877i
$302$	−628.453			−0.119746
$303$	3367.06			0.638390
$304$	−3333.67	−	3333.67i	−0.628944	−	0.628944i
$305$	−1826.19	−	1826.19i	−0.342843	−	0.342843i
$306$	−8.78791	−	8.78791i	−0.00164174	−	0.00164174i
$307$	3033.65	−	3033.65i	0.563973	−	0.563973i	−0.366460	−	0.930434i	$-0.619430\pi$
$307$	3033.65	−	3033.65i	0.563973	−	0.563973i	0.930434	+	0.366460i	$0.119430\pi$
$308$	3556.63	+	4731.81i	0.657981	+	0.875389i
$309$		−	6908.74i		−	1.27192i
$310$	−63.3173	+	63.3173i	−0.0116006	+	0.0116006i
$311$		−	7291.68i		−	1.32950i	−0.747067	−	0.664748i	$-0.768539\pi$
$311$		−	7291.68i		−	1.32950i	0.747067	−	0.664748i	$-0.231461\pi$
$312$	215.030	−	960.419i	0.0390181	−	0.174273i
$313$	−3893.12			−0.703043			−0.351521	−	0.936180i	$-0.614336\pi$
$313$	−3893.12			−0.703043			−0.351521	+	0.936180i	$0.614336\pi$
$314$	−100.299	−	100.299i	−0.0180261	−	0.0180261i
$315$		−	47.4131i		−	0.00848072i
$316$	3112.42			0.554073
$317$	−3850.14	+	3850.14i	−0.682162	+	0.682162i	−0.960487	−	0.278325i	$-0.910221\pi$
$317$	−3850.14	+	3850.14i	−0.682162	+	0.682162i	0.278325	+	0.960487i	$0.410221\pi$
$318$	170.280	+	170.280i	0.0300278	+	0.0300278i
$319$	−269.167	+	1898.42i	−0.0472428	+	0.333201i
$320$	−1174.78	−	1174.78i	−0.205226	−	0.205226i
$321$			7844.67i			1.36401i
$322$			650.348i			0.112554i
$323$	3885.04	+	3885.04i	0.669255	+	0.669255i
$324$			5928.63i			1.01657i
$325$	2846.85	+	4489.37i	0.485892	+	0.766232i
$326$		−	560.166i		−	0.0951679i
$327$	−1803.74	−	1803.74i	−0.305036	−	0.305036i
$328$	867.357			0.146012
$329$	2375.19			0.398019
$330$	−161.995	−	22.9684i	−0.0270229	−	0.00383143i
$331$	−3385.28	+	3385.28i	−0.562150	+	0.562150i	−0.929918	−	0.367768i	$-0.880122\pi$
$331$	−3385.28	+	3385.28i	−0.562150	+	0.562150i	0.367768	+	0.929918i	$0.380122\pi$
$332$	8315.51	−	8315.51i	1.37462	−	1.37462i
$333$	−80.0109	−	80.0109i	−0.0131669	−	0.0131669i
$334$	357.407			0.0585522
$335$			300.229i			0.0489650i
$336$	−4753.03	+	4753.03i	−0.771723	+	0.771723i
$337$	2251.11			0.363874			0.181937	−	0.983310i	$-0.441763\pi$
$337$	2251.11			0.363874			0.181937	+	0.983310i	$0.441763\pi$
$338$	−517.764	+	186.000i	−0.0833214	+	0.0299321i
$339$	2703.37			0.433118
$340$	1391.51	+	1391.51i	0.221956	+	0.221956i
$341$	−3063.60	+	2302.73i	−0.486519	+	0.365689i
$342$		−	12.8712i		−	0.00203508i
$343$	−3875.75	−	3875.75i	−0.610119	−	0.610119i
$344$	−964.360	+	964.360i	−0.151148	+	0.151148i
$345$	1608.91	+	1608.91i	0.251074	+	0.251074i
$346$	398.482	+	398.482i	0.0619149	+	0.0619149i
$347$			1101.36i			0.170387i	0.996364	+	0.0851935i	$0.0271508\pi$
$347$			1101.36i			0.170387i	−0.996364	+	0.0851935i	$0.972849\pi$
$348$	−2194.78			−0.338083
$349$	5053.24	−	5053.24i	0.775054	−	0.775054i	−0.203931	−	0.978985i	$-0.565372\pi$
$349$	5053.24	−	5053.24i	0.775054	−	0.775054i	0.978985	+	0.203931i	$0.0653718\pi$
$350$			580.551i			0.0886621i
$351$	5481.24	−	3475.83i	0.833524	−	0.528564i
$352$	1042.93	+	1387.53i	0.157921	+	0.210101i
$353$	2864.71	−	2864.71i	0.431935	−	0.431935i	−0.457351	−	0.889286i	$-0.651202\pi$
$353$	2864.71	−	2864.71i	0.431935	−	0.431935i	0.889286	+	0.457351i	$0.151202\pi$
$354$		−	112.028i		−	0.0168198i
$355$		−	1087.78i		−	0.162629i
$356$	−7029.15	+	7029.15i	−1.04647	+	1.04647i
$357$	5539.15	−	5539.15i	0.821184	−	0.821184i
$358$	−810.179	+	810.179i	−0.119607	+	0.119607i
$359$	5297.61	−	5297.61i	0.778822	−	0.778822i	−0.200809	−	0.979631i	$-0.564357\pi$
$359$	5297.61	−	5297.61i	0.778822	−	0.778822i	0.979631	+	0.200809i	$0.0643569\pi$
$360$		−	9.25663i		−	0.00135519i
$361$		−	1168.77i		−	0.170400i
$362$	−405.988	+	405.988i	−0.0589455	+	0.0589455i
$363$	−6726.80	−	1946.65i	−0.972632	−	0.281467i
$364$	7421.38	+	1661.58i	1.06864	+	0.239260i
$365$		−	902.013i		−	0.129352i
$366$	−706.829	+	706.829i	−0.100947	+	0.100947i
$367$	8129.45			1.15628			0.578139	−	0.815938i	$-0.303779\pi$
$367$	8129.45			1.15628			0.578139	+	0.815938i	$0.303779\pi$
$368$		−	7940.39i		−	1.12479i
$369$	−104.714	−	104.714i	−0.0147730	−	0.0147730i
$370$	−100.091	−	100.091i	−0.0140634	−	0.0140634i
$371$	−2641.99	+	2641.99i	−0.369717	+	0.369717i
$372$	−3102.04	−	3102.04i	−0.432347	−	0.432347i
$373$		−	2979.05i		−	0.413538i	−0.978390	−	0.206769i	$-0.933705\pi$
$373$		−	2979.05i		−	0.413538i	0.978390	−	0.206769i	$-0.0662948\pi$
$374$	−399.809	−	531.912i	−0.0552770	−	0.0735415i
$375$	3019.20	+	3019.20i	0.415763	+	0.415763i
$376$	463.717			0.0636020
$377$	1319.25	+	2080.40i	0.180225	+	0.284207i
$378$	708.816			0.0964486
$379$	−5837.73	+	5837.73i	−0.791198	+	0.791198i	−0.981689	−	0.190491i	$-0.938992\pi$
$379$	−5837.73	+	5837.73i	−0.791198	+	0.791198i	0.190491	+	0.981689i	$0.438992\pi$
$380$			2038.08i			0.275135i
$381$	−14723.2			−1.97977
$382$	69.9263	+	69.9263i	0.00936581	+	0.00936581i
$383$	444.975	−	444.975i	0.0593659	−	0.0593659i	−0.676801	−	0.736166i	$-0.736634\pi$
$383$	444.975	−	444.975i	0.0593659	−	0.0593659i	0.736166	+	0.676801i	$0.236634\pi$
$384$	−1870.74	+	1870.74i	−0.248609	+	0.248609i
$385$	356.367	−	2513.44i	0.0471744	−	0.332719i
$386$	113.771			0.0150021
$387$	232.851			0.0305852
$388$	−4155.16	−	4155.16i	−0.543676	−	0.543676i
$389$			7247.94i			0.944691i	0.881413	+	0.472346i	$0.156593\pi$
$389$			7247.94i			0.944691i	−0.881413	+	0.472346i	$0.843407\pi$
$390$	−177.524	+	112.574i	−0.0230494	+	0.0146164i
$391$			9253.68i			1.19688i
$392$	211.272	+	211.272i	0.0272215	+	0.0272215i
$393$		−	11367.2i		−	1.45903i
$394$			1221.02i			0.156127i
$395$	−943.829	−	943.829i	−0.120226	−	0.120226i
$396$	27.6991	−	195.360i	0.00351498	−	0.0247910i
$397$	−4266.33	−	4266.33i	−0.539348	−	0.539348i	0.383990	−	0.923337i	$-0.374550\pi$
$397$	−4266.33	−	4266.33i	−0.539348	−	0.539348i	−0.923337	+	0.383990i	$0.874550\pi$
$398$	714.826	−	714.826i	0.0900276	−	0.0900276i
$399$	8112.92			1.01793
$400$		−	7088.20i		−	0.886025i
$401$	−3334.39	−	3334.39i	−0.415240	−	0.415240i	0.468319	−	0.883559i	$-0.344860\pi$
$401$	−3334.39	−	3334.39i	−0.415240	−	0.415240i	−0.883559	+	0.468319i	$0.844860\pi$
$402$	116.204			0.0144173
$403$	−1075.79	+	4804.96i	−0.132975	+	0.593925i
$404$			5079.59i			0.625542i
$405$	1797.84	−	1797.84i	0.220581	−	0.220581i
$406$			269.031i			0.0328861i
$407$	−3640.12	−	4842.88i	−0.443327	−	0.589810i
$408$	1081.43	−	1081.43i	0.131222	−	0.131222i
$409$	−9289.12	−	9289.12i	−1.12303	−	1.12303i	−0.991284	−	0.131741i	$-0.957943\pi$
$409$	−9289.12	−	9289.12i	−1.12303	−	1.12303i	−0.131741	−	0.991284i	$-0.542057\pi$
$410$	−130.994	−	130.994i	−0.0157789	−	0.0157789i
$411$	−9788.57	−	9788.57i	−1.17478	−	1.17478i
$412$	10422.6			1.24632
$413$	1738.17			0.207094
$414$	15.3288	−	15.3288i	0.00181974	−	0.00181974i
$415$	−5043.30			−0.596544
$416$	2176.20	+	487.234i	0.256484	+	0.0574245i
$417$			1912.17i			0.224555i
$418$	96.7429	−	682.323i	0.0113202	−	0.0798410i
$419$	−12142.9			−1.41580			−0.707900	−	0.706313i	$-0.750357\pi$
$419$	−12142.9			−1.41580			−0.707900	+	0.706313i	$0.750357\pi$
$420$	2905.82			0.337593
$421$	3791.10	−	3791.10i	0.438876	−	0.438876i	−0.452757	−	0.891634i	$-0.649560\pi$
$421$	3791.10	−	3791.10i	0.438876	−	0.438876i	0.891634	+	0.452757i	$0.149560\pi$
$422$	1008.43	−	1008.43i	0.116326	−	0.116326i
$423$	−55.9837	−	55.9837i	−0.00643503	−	0.00643503i
$424$	−515.804	+	515.804i	−0.0590794	+	0.0590794i
$425$			8260.55i			0.942813i
$426$	−421.026			−0.0478845
$427$	−10966.8	−	10966.8i	−1.24291	−	1.24291i
$428$	−11834.6			−1.33656
$429$	−8199.24	+	3703.86i	−0.922758	+	0.416839i
$430$	291.288			0.0326678
$431$	−4614.33	−	4614.33i	−0.515695	−	0.515695i	0.400571	−	0.916266i	$-0.368812\pi$
$431$	−4614.33	−	4614.33i	−0.515695	−	0.515695i	−0.916266	+	0.400571i	$0.868812\pi$
$432$	−8654.26			−0.963838
$433$		−	8774.90i		−	0.973891i	−0.873432	−	0.486945i	$-0.838111\pi$
$433$		−	8774.90i		−	0.973891i	0.873432	−	0.486945i	$-0.161889\pi$
$434$	−380.239	+	380.239i	−0.0420555	+	0.0420555i
$435$	665.560	+	665.560i	0.0733590	+	0.0733590i
$436$	2721.14	−	2721.14i	0.298897	−	0.298897i
$437$	−6776.71	+	6776.71i	−0.741817	+	0.741817i
$438$	−349.126			−0.0380865
$439$	2248.53			0.244457			0.122228	−	0.992502i	$-0.460996\pi$
$439$	2248.53			0.244457			0.122228	+	0.992502i	$0.460996\pi$
$440$	69.5748	−	490.708i	0.00753829	−	0.0531672i
$441$		−	51.0129i		−	0.00550836i
$442$	−834.253	−	186.782i	−0.0897769	−	0.0201003i
$443$	3351.20			0.359413			0.179707	−	0.983720i	$-0.442485\pi$
$443$	3351.20			0.359413			0.179707	+	0.983720i	$0.442485\pi$
$444$	4903.65	−	4903.65i	0.524137	−	0.524137i
$445$	4263.13			0.454139
$446$	1509.86			0.160300
$447$	−1697.51	−	1697.51i	−0.179619	−	0.179619i
$448$	−7054.92	−	7054.92i	−0.744004	−	0.744004i
$449$	10506.9	+	10506.9i	1.10434	+	1.10434i	0.993880	+	0.110464i	$0.0352336\pi$
$449$	10506.9	+	10506.9i	1.10434	+	1.10434i	0.110464	+	0.993880i	$0.464766\pi$
$450$	13.6837	−	13.6837i	0.00143346	−	0.00143346i
$451$	−4764.02	−	6338.13i	−0.497403	−	0.661754i
$452$			4078.34i			0.424401i
$453$	−9336.70	+	9336.70i	−0.968380	+	0.968380i
$454$			1050.64i			0.108610i
$455$	−1746.64	−	2754.38i	−0.179964	−	0.283796i
$456$	1583.91			0.162661
$457$	−1038.93	−	1038.93i	−0.106344	−	0.106344i	0.651933	−	0.758277i	$-0.273958\pi$
$457$	−1038.93	−	1038.93i	−0.106344	−	0.106344i	−0.758277	+	0.651933i	$0.773958\pi$
$458$			845.516i			0.0862628i
$459$	10085.6			1.02561
$460$	−2427.22	+	2427.22i	−0.246021	+	0.246021i
$461$	10531.6	+	10531.6i	1.06401	+	1.06401i	0.997806	+	0.0661994i	$0.0210873\pi$
$461$	10531.6	+	10531.6i	1.06401	+	1.06401i	0.0661994	+	0.997806i	$0.478913\pi$
$462$	−972.832	−	137.933i	−0.0979659	−	0.0138900i
$463$	7606.71	+	7606.71i	0.763528	+	0.763528i	0.976958	−	0.213430i	$-0.0684635\pi$
$463$	7606.71	+	7606.71i	0.763528	+	0.763528i	−0.213430	+	0.976958i	$0.568464\pi$
$464$		−	3284.72i		−	0.328641i
$465$			1881.36i			0.187626i
$466$	−702.682	−	702.682i	−0.0698522	−	0.0698522i
$467$			7569.94i			0.750097i	0.927005	+	0.375048i	$0.122374\pi$
$467$			7569.94i			0.750097i	−0.927005	+	0.375048i	$0.877626\pi$
$468$	−135.760	−	214.087i	−0.0134092	−	0.0211457i
$469$			1802.97i			0.177513i
$470$	−70.0336	−	70.0336i	−0.00687321	−	0.00687321i
$471$	−2980.20			−0.291551
$472$	339.349			0.0330928
$473$	12343.8	+	1750.16i	1.19993	+	0.170132i
$474$	−365.311	+	365.311i	−0.0353993	+	0.0353993i
$475$	−6049.41	+	6049.41i	−0.584350	+	0.584350i
$476$	8356.44	+	8356.44i	0.804657	+	0.804657i
$477$	124.544			0.0119549
$478$			101.425i			0.00970520i
$479$	10898.7	−	10898.7i	1.03962	−	1.03962i	0.0404338	−	0.999182i	$-0.487126\pi$
$479$	10898.7	−	10898.7i	1.03962	−	1.03962i	0.999182	−	0.0404338i	$-0.0128740\pi$
$480$	852.085			0.0810254
$481$	−7595.59	−	1700.59i	−0.720019	−	0.161206i
$482$	376.694			0.0355974
$483$	9661.98	+	9661.98i	0.910218	+	0.910218i
$484$	2936.74	−	10148.2i	0.275802	−	0.953057i
$485$			2520.08i			0.235940i
$486$	−33.8464	−	33.8464i	−0.00315906	−	0.00315906i
$487$	−3149.01	+	3149.01i	−0.293009	+	0.293009i	−0.838268	−	0.545259i	$-0.816431\pi$
$487$	−3149.01	+	3149.01i	−0.293009	+	0.293009i	0.545259	+	0.838268i	$0.316431\pi$
$488$	−2141.09	−	2141.09i	−0.198612	−	0.198612i
$489$	−8322.19	−	8322.19i	−0.769616	−	0.769616i
$490$		−	63.8153i		−	0.00588343i
$491$	8514.23			0.782570			0.391285	−	0.920270i	$-0.372031\pi$
$491$	8514.23			0.782570			0.391285	+	0.920270i	$0.372031\pi$
$492$	6417.66	−	6417.66i	0.588070	−	0.588070i
$493$			3827.99i			0.349704i
$494$	−474.160	−	747.731i	−0.0431851	−	0.0681012i
$495$	−67.6420	+	50.8427i	−0.00614198	+	0.00461658i
$496$	4642.51	−	4642.51i	0.420272	−	0.420272i
$497$		−	6532.43i		−	0.589577i
$498$			1952.02i			0.175647i
$499$	3839.37	−	3839.37i	0.344437	−	0.344437i	−0.513596	−	0.858032i	$-0.671687\pi$
$499$	3839.37	−	3839.37i	0.344437	−	0.344437i	0.858032	+	0.513596i	$0.171687\pi$
$500$	−4554.82	+	4554.82i	−0.407395	+	0.407395i
$501$	5309.86	−	5309.86i	0.473507	−	0.473507i
$502$	332.454	−	332.454i	0.0295581	−	0.0295581i
$503$		−	6025.96i		−	0.534163i	−0.963674	−	0.267082i	$-0.913941\pi$
$503$		−	6025.96i		−	0.534163i	0.963674	−	0.267082i	$-0.0860593\pi$
$504$		−	55.5889i		−	0.00491295i
$505$	1540.37	−	1540.37i	0.135734	−	0.135734i
$506$	927.819	−	697.390i	0.0815150	−	0.0612703i
$507$	−4928.90	+	10455.6i	−0.431755	+	0.915873i
$508$		−	22211.6i		−	1.93992i
$509$	−3343.96	+	3343.96i	−0.291196	+	0.291196i	−0.837552	−	0.546357i	$-0.816014\pi$
$509$	−3343.96	+	3343.96i	−0.291196	+	0.291196i	0.546357	+	0.837552i	$0.316014\pi$
$510$	−326.649			−0.0283613
$511$		−	5416.86i		−	0.468939i
$512$	−3513.61	−	3513.61i	−0.303284	−	0.303284i
$513$	7385.96	+	7385.96i	0.635668	+	0.635668i
$514$	−264.068	+	264.068i	−0.0226606	+	0.0226606i
$515$	−3160.62	−	3160.62i	−0.270435	−	0.270435i
$516$			14270.8i			1.21751i
$517$	−2547.00	−	3388.57i	−0.216667	−	0.288257i
$518$	−601.076	−	601.076i	−0.0509841	−	0.0509841i
$519$	11840.2			1.00140
$520$	−341.003	−	537.747i	−0.0287576	−	0.0453496i
$521$	4817.90			0.405136			0.202568	−	0.979268i	$-0.435071\pi$
$521$	4817.90			0.405136			0.202568	+	0.979268i	$0.435071\pi$
$522$	6.34111	−	6.34111i	0.000531691	−	0.000531691i
$523$			10322.1i			0.863013i	0.902110	+	0.431506i	$0.142018\pi$
$523$			10322.1i			0.863013i	−0.902110	+	0.431506i	$0.857982\pi$
$524$	17148.7			1.42967
$525$	8625.03	+	8625.03i	0.717004	+	0.717004i
$526$	−960.076	+	960.076i	−0.0795842	+	0.0795842i
$527$	−5410.36	+	5410.36i	−0.447208	+	0.447208i
$528$	11877.7	+	1684.08i	0.979001	+	0.138807i
$529$	−3974.28			−0.326644
$530$	155.800			0.0127689
$531$	−40.9690	−	40.9690i	−0.00334822	−	0.00334822i
$532$			12239.3i			0.997443i
$533$	−9940.75	−	2225.65i	−0.807846	−	0.180870i
$534$		−	1650.05i		−	0.133717i
$535$	3588.80	+	3588.80i	0.290014	+	0.290014i
$536$			352.000i			0.0283658i
$537$			24073.1i			1.93451i
$538$	−230.388	−	230.388i	−0.0184623	−	0.0184623i
$539$	383.424	−	2704.27i	0.0306405	−	0.216106i
$540$	2645.44	+	2645.44i	0.210818	+	0.210818i
$541$	−14735.7	+	14735.7i	−1.17105	+	1.17105i	−0.189088	+	0.981960i	$0.560553\pi$
$541$	−14735.7	+	14735.7i	−1.17105	+	1.17105i	−0.981960	+	0.189088i	$0.939447\pi$
$542$	1611.43			0.127707
$543$			12063.2i			0.953376i
$544$	2450.40	+	2450.40i	0.193125	+	0.193125i
$545$	−1650.35			−0.129713
$546$	−1066.09	+	676.040i	−0.0835610	+	0.0529887i
$547$			14950.4i			1.16862i	0.811531	+	0.584309i	$0.198635\pi$
$547$			14950.4i			1.16862i	−0.811531	+	0.584309i	$0.801365\pi$
$548$	14767.2	−	14767.2i	1.15114	−	1.15114i
$549$			516.980i			0.0401898i
$550$	828.243	−	622.544i	0.0642116	−	0.0482643i
$551$	−2803.34	+	2803.34i	−0.216744	+	0.216744i
$552$	1886.34	+	1886.34i	0.145449	+	0.145449i
$553$	−5667.98	−	5667.98i	−0.435854	−	0.435854i
$554$	213.741	+	213.741i	0.0163917	+	0.0163917i
$555$	−2974.03			−0.227460
$556$	−2884.73			−0.220035
$557$	3548.72	−	3548.72i	0.269954	−	0.269954i	−0.559128	−	0.829082i	$-0.688864\pi$
$557$	3548.72	−	3548.72i	0.269954	−	0.269954i	0.829082	+	0.559128i	$0.188864\pi$
$558$	17.9246			0.00135988
$559$	13527.0	−	8577.93i	1.02349	−	0.649030i
$560$			4348.85i			0.328165i
$561$	−13842.2	−	1962.62i	−1.04175	−	0.147704i
$562$	−23.6365			−0.00177410
$563$	−3831.62			−0.286827			−0.143413	−	0.989663i	$-0.545808\pi$
$563$	−3831.62			−0.286827			−0.143413	+	0.989663i	$0.545808\pi$
$564$	3431.08	−	3431.08i	0.256161	−	0.256161i
$565$	1236.74	−	1236.74i	0.0920889	−	0.0920889i
$566$	−400.982	−	400.982i	−0.0297783	−	0.0297783i
$567$	10796.6	−	10796.6i	0.799670	−	0.799670i
$568$		−	1275.35i		−	0.0942122i
$569$	−5696.87			−0.419728			−0.209864	−	0.977731i	$-0.567302\pi$
$569$	−5696.87			−0.419728			−0.209864	+	0.977731i	$0.567302\pi$
$570$	−239.213	−	239.213i	−0.0175781	−	0.0175781i
$571$	−8191.24			−0.600337			−0.300169	−	0.953886i	$-0.597043\pi$
$571$	−8191.24			−0.600337			−0.300169	+	0.953886i	$0.597043\pi$
$572$	−5587.70	−	12369.5i	−0.408450	−	0.904187i
$573$	2077.74			0.151481
$574$	−786.660	−	786.660i	−0.0572030	−	0.0572030i
$575$	−14408.9			−1.04503
$576$			332.572i			0.0240576i
$577$	9541.10	−	9541.10i	0.688391	−	0.688391i	−0.273486	−	0.961876i	$-0.588177\pi$
$577$	9541.10	−	9541.10i	0.688391	−	0.688391i	0.961876	+	0.273486i	$0.0881766\pi$
$578$	−69.4231	−	69.4231i	−0.00499588	−	0.00499588i
$579$	1690.26	−	1690.26i	0.121321	−	0.121321i
$580$	−1004.07	+	1004.07i	−0.0718826	+	0.0718826i
$581$	−30286.5			−2.16265
$582$	975.400			0.0694702
$583$	6602.28	+	936.102i	0.469020	+	0.0664998i
$584$		−	1057.55i		−	0.0749347i
$585$	−23.7526	+	106.090i	−0.00167872	+	0.00749791i
$586$	88.2584			0.00622171
$587$	−11254.8	+	11254.8i	−0.791374	+	0.791374i	−0.981717	−	0.190344i	$-0.939040\pi$
$587$	−11254.8	+	11254.8i	−0.791374	+	0.791374i	0.190344	+	0.981717i	$0.439040\pi$
$588$	3126.44			0.219272
$589$	−7924.29			−0.554354
$590$	−51.2508	−	51.2508i	−0.00357621	−	0.00357621i
$591$	18140.3	+	18140.3i	1.26259	+	1.26259i
$592$	7338.81	+	7338.81i	0.509499	+	0.509499i
$593$	−1020.17	+	1020.17i	−0.0706467	+	0.0706467i	−0.741547	−	0.670901i	$-0.765908\pi$
$593$	−1020.17	+	1020.17i	−0.0706467	+	0.0706467i	0.670901	+	0.741547i	$0.265908\pi$
$594$	−760.087	−	1011.23i	−0.0525030	−	0.0698509i
$595$		−	5068.12i		−	0.349198i
$596$	2560.89	−	2560.89i	0.176004	−	0.176004i
$597$		−	21239.8i		−	1.45609i
$598$	325.806	−	1455.20i	0.0222796	−	0.0995106i
$599$	19521.6			1.33161			0.665803	−	0.746127i	$-0.268089\pi$
$599$	19521.6			1.33161			0.665803	+	0.746127i	$0.268089\pi$
$600$	1683.90	+	1683.90i	0.114575	+	0.114575i
$601$			13811.4i			0.937405i	0.883356	+	0.468703i	$0.155278\pi$
$601$			13811.4i			0.937405i	−0.883356	+	0.468703i	$0.844722\pi$
$602$	1749.27			0.118430
$603$	42.4964	−	42.4964i	0.00286996	−	0.00286996i
$604$	−14085.5	−	14085.5i	−0.948891	−	0.948891i
$605$	−3967.95	+	2186.84i	−0.266645	+	0.146955i
$606$	−596.202	−	596.202i	−0.0399655	−	0.0399655i
$607$			3152.31i			0.210788i	0.994431	+	0.105394i	$0.0336104\pi$
$607$			3152.31i			0.210788i	−0.994431	+	0.105394i	$0.966390\pi$
$608$			3588.98i			0.239395i
$609$	3996.89	+	3996.89i	0.265948	+	0.265948i
$610$			646.724i			0.0429264i
$611$	−5314.64	−	1189.90i	−0.351894	−	0.0787861i
$612$		−	393.926i		−	0.0260188i
$613$	7095.63	+	7095.63i	0.467520	+	0.467520i	0.901110	−	0.433590i	$-0.142753\pi$
$613$	7095.63	+	7095.63i	0.467520	+	0.467520i	−0.433590	+	0.901110i	$0.642753\pi$
$614$	−1074.33			−0.0706134
$615$	−3892.26			−0.255205
$616$	417.818	−	2946.85i	0.0273285	−	0.192747i
$617$	16049.0	−	16049.0i	1.04718	−	1.04718i	0.0483496	−	0.998830i	$-0.484604\pi$
$617$	16049.0	−	16049.0i	1.04718	−	1.04718i	0.998830	−	0.0483496i	$-0.0153962\pi$
$618$	−1223.33	+	1223.33i	−0.0796268	+	0.0796268i
$619$	9734.07	+	9734.07i	0.632060	+	0.632060i	0.948584	−	0.316524i	$-0.102516\pi$
$619$	9734.07	+	9734.07i	0.632060	+	0.632060i	−0.316524	+	0.948584i	$0.602516\pi$
$620$	−2838.25			−0.183850
$621$			17592.4i			1.13681i
$622$	−1291.13	+	1291.13i	−0.0832311	+	0.0832311i
$623$	25601.4			1.64639
$624$	13016.3	−	8254.07i	0.835049	−	0.529531i
$625$	−11414.2			−0.730507
$626$	689.353	+	689.353i	0.0440129	+	0.0440129i
$627$	−8699.76	−	11574.3i	−0.554123	−	0.737214i
$628$		−	4495.98i		−	0.285683i
$629$	−8552.60	−	8552.60i	−0.542153	−	0.542153i
$630$	−8.39541	+	8.39541i	−0.000530922	+	0.000530922i
$631$	−7495.12	−	7495.12i	−0.472862	−	0.472862i	0.429977	−	0.902840i	$-0.358522\pi$
$631$	−7495.12	−	7495.12i	−0.472862	−	0.472862i	−0.902840	+	0.429977i	$0.858522\pi$
$632$	−1106.58	−	1106.58i	−0.0696478	−	0.0696478i
$633$		−	29963.6i		−	1.88143i
$634$	1363.48			0.0854114
$635$	−6735.59	+	6735.59i	−0.420935	+	0.420935i
$636$			7632.97i			0.475891i
$637$	−1879.25	−	2963.50i	−0.116890	−	0.184330i
$638$	383.813	−	288.491i	0.0238171	−	0.0179020i
$639$	−153.971	+	153.971i	−0.00953207	+	0.00953207i
$640$			1711.66i			0.105718i
$641$			8362.09i			0.515261i	0.966243	+	0.257631i	$0.0829418\pi$
$641$			8362.09i			0.515261i	−0.966243	+	0.257631i	$0.917058\pi$
$642$	1389.05	−	1389.05i	0.0853917	−	0.0853917i
$643$	−16281.7	+	16281.7i	−0.998582	+	0.998582i	−0.999999	−	0.00141660i	$-0.999549\pi$
$643$	−16281.7	+	16281.7i	−0.998582	+	0.998582i	0.00141660	+	0.999999i	$0.499549\pi$
$644$	−14576.2	+	14576.2i	−0.891900	+	0.891900i
$645$	4327.56	−	4327.56i	0.264182	−	0.264182i
$646$		−	1375.84i		−	0.0837953i
$647$			6538.20i			0.397285i	0.980072	+	0.198642i	$0.0636532\pi$
$647$			6538.20i			0.397285i	−0.980072	+	0.198642i	$0.936347\pi$
$648$	2107.85	−	2107.85i	0.127784	−	0.127784i
$649$	−1863.90	−	2479.76i	−0.112734	−	0.149983i
$650$	290.839	−	1299.02i	0.0175502	−	0.0783873i
$651$			11298.2i			0.680200i
$652$	12555.0	−	12555.0i	0.754127	−	0.754127i
$653$	30618.5			1.83491			0.917455	−	0.397839i	$-0.130240\pi$
$653$	30618.5			1.83491			0.917455	+	0.397839i	$0.130240\pi$
$654$			638.773i			0.0381926i
$655$	−5200.30	−	5200.30i	−0.310217	−	0.310217i
$656$	9604.68	+	9604.68i	0.571646	+	0.571646i
$657$	−127.677	+	127.677i	−0.00758164	+	0.00758164i
$658$	−420.573	−	420.573i	−0.0249174	−	0.0249174i
$659$		−	26971.1i		−	1.59430i	−0.603782	−	0.797149i	$-0.706340\pi$
$659$		−	26971.1i		−	1.59430i	0.603782	−	0.797149i	$-0.293660\pi$
$660$	−3116.00	−	4145.58i	−0.183773	−	0.244495i
$661$	−20378.3	−	20378.3i	−1.19913	−	1.19913i	−0.974428	−	0.224701i	$-0.927859\pi$
$661$	−20378.3	−	20378.3i	−1.19913	−	1.19913i	−0.224701	−	0.974428i	$-0.572141\pi$
$662$	1198.86			0.0703851
$663$	−15169.2	+	9619.24i	−0.888569	+	0.563470i
$664$	−5912.95			−0.345583
$665$	3711.52	−	3711.52i	0.216431	−	0.216431i
$666$			28.3350i			0.00164859i
$667$	−6677.20			−0.387619
$668$	8010.54	+	8010.54i	0.463978	+	0.463978i
$669$	22431.4	−	22431.4i	1.29634	−	1.29634i
$670$	53.1614	−	53.1614i	0.00306538	−	0.00306538i
$671$	−3885.74	+	27405.9i	−0.223558	+	1.57674i
$672$	5117.03			0.293741
$673$	−13616.2			−0.779889			−0.389944	−	0.920838i	$-0.627506\pi$
$673$	−13616.2			−0.779889			−0.389944	+	0.920838i	$0.627506\pi$
$674$	−398.602	−	398.602i	−0.0227798	−	0.0227798i
$675$			15704.4i			0.895498i
$676$	−15773.4	−	7435.81i	−0.897441	−	0.423066i
$677$		−	25802.6i		−	1.46481i	−0.680871	−	0.732403i	$-0.738399\pi$
$677$		−	25802.6i		−	1.46481i	0.680871	−	0.732403i	$-0.261601\pi$
$678$	−478.684	−	478.684i	−0.0271147	−	0.0271147i
$679$			15133.8i			0.855351i
$680$		−	989.468i		−	0.0558005i
$681$	15608.9	+	15608.9i	0.878320	+	0.878320i
$682$	950.213	+	134.725i	0.0533512	+	0.00756438i
$683$	11929.0	+	11929.0i	0.668300	+	0.668300i	0.957322	−	0.289022i	$-0.0933302\pi$
$683$	11929.0	+	11929.0i	0.668300	+	0.668300i	−0.289022	+	0.957322i	$0.593330\pi$
$684$	288.482	−	288.482i	0.0161263	−	0.0161263i
$685$	−8956.19			−0.499560
$686$			1372.55i			0.0763911i
$687$	12561.5	+	12561.5i	0.697601	+	0.697601i
$688$	−21357.7			−1.18351
$689$	7235.17	−	4588.05i	0.400055	−	0.253688i
$690$		−	569.776i		−	0.0314363i
$691$	16812.6	−	16812.6i	0.925588	−	0.925588i	−0.0718287	−	0.997417i	$-0.522884\pi$
$691$	16812.6	−	16812.6i	0.925588	−	0.925588i	0.997417	+	0.0718287i	$0.0228835\pi$
$692$			17862.3i			0.981249i
$693$	−406.211	+	305.326i	−0.0222665	+	0.0167365i
$694$	195.018	−	195.018i	0.0106668	−	0.0106668i
$695$	874.784	+	874.784i	0.0477445	+	0.0477445i
$696$	780.328	+	780.328i	0.0424975	+	0.0424975i
$697$	−11193.2	−	11193.2i	−0.608284	−	0.608284i
$698$	−1789.55			−0.0970422
$699$	−20879.0			−1.12978
$700$	−13011.9	+	13011.9i	−0.702574	+	0.702574i
$701$	−10452.6			−0.563181			−0.281591	−	0.959535i	$-0.590862\pi$
$701$	−10452.6			−0.563181			−0.281591	+	0.959535i	$0.590862\pi$
$702$	−1586.02	−	355.097i	−0.0852714	−	0.0190916i
$703$		−	12526.6i		−	0.672047i
$704$	−2499.68	+	17630.1i	−0.133821	+	0.943837i
$705$	−2080.93			−0.111166
$706$	−1014.50			−0.0540812
$707$	9250.38	−	9250.38i	0.492074	−	0.492074i
$708$	2510.88	−	2510.88i	0.133283	−	0.133283i
$709$	−17085.4	−	17085.4i	−0.905016	−	0.905016i	0.0908486	−	0.995865i	$-0.471042\pi$
$709$	−17085.4	−	17085.4i	−0.905016	−	0.905016i	−0.995865	+	0.0908486i	$0.971042\pi$
$710$	−192.612	+	192.612i	−0.0101811	+	0.0101811i
$711$			267.191i			0.0140935i
$712$	4998.25			0.263086
$713$	−9437.34	−	9437.34i	−0.495696	−	0.495696i
$714$	−1961.63			−0.102818
$715$	−2056.56	+	5445.46i	−0.107568	+	0.284823i
$716$	−36317.0			−1.89557
$717$	1506.84	+	1506.84i	0.0784853	+	0.0784853i
$718$	−1876.09			−0.0975139
$719$		−	18134.0i		−	0.940591i	−0.882509	−	0.470296i	$-0.844147\pi$
$719$		−	18134.0i		−	0.940591i	0.882509	−	0.470296i	$-0.155853\pi$
$720$	102.503	−	102.503i	0.00530565	−	0.00530565i
$721$	−18980.5	−	18980.5i	−0.980404	−	0.980404i
$722$	−206.954	+	206.954i	−0.0106676	+	0.0106676i
$723$	5596.40	−	5596.40i	0.287873	−	0.287873i
$724$	−18198.8			−0.934189
$725$	−5960.58			−0.305338
$726$	846.419	+	1535.80i	0.0432693	+	0.0785109i
$727$		−	30588.7i		−	1.56049i	−0.625477	−	0.780243i	$-0.715096\pi$
$727$		−	30588.7i		−	1.56049i	0.625477	−	0.780243i	$-0.284904\pi$
$728$	−2047.82	−	3229.34i	−0.104255	−	0.164405i
$729$	19161.5			0.973506
$730$	−159.719	+	159.719i	−0.00809789	+	0.00809789i
$731$	24890.1			1.25936
$732$	−31684.3			−1.59984
$733$	21298.7	+	21298.7i	1.07324	+	1.07324i	0.997097	+	0.0761425i	$0.0242604\pi$
$733$	21298.7	+	21298.7i	1.07324	+	1.07324i	0.0761425	+	0.997097i	$0.475740\pi$
$734$	−1439.48	−	1439.48i	−0.0723870	−	0.0723870i
$735$	−948.081	−	948.081i	−0.0475789	−	0.0475789i
$736$	−4274.25	+	4274.25i	−0.214064	+	0.214064i
$737$	2572.21	−	1933.39i	0.128560	−	0.0966312i
$738$			37.0834i			0.00184968i
$739$	−4160.87	+	4160.87i	−0.207118	+	0.207118i	−0.803041	−	0.595924i	$-0.796786\pi$
$739$	−4160.87	+	4160.87i	−0.207118	+	0.207118i	0.595924	+	0.803041i	$0.296786\pi$
$740$		−	4486.66i		−	0.222882i
$741$	−18153.2	−	4064.34i	−0.899965	−	0.201494i
$742$	935.629			0.0462911
$743$	−13009.5	−	13009.5i	−0.642359	−	0.642359i	0.308776	−	0.951135i	$-0.400081\pi$
$743$	−13009.5	−	13009.5i	−0.642359	−	0.642359i	−0.951135	+	0.308776i	$0.900081\pi$
$744$			2205.78i			0.108693i
$745$	−1553.16			−0.0763805
$746$	−527.499	+	527.499i	−0.0258889	+	0.0258889i
$747$	713.860	+	713.860i	0.0349649	+	0.0349649i
$748$	2960.83	−	20882.6i	0.144731	−	1.02078i
$749$	21551.8	+	21551.8i	1.05138	+	1.05138i
$750$		−	1069.22i		−	0.0520564i
$751$		−	6031.00i		−	0.293042i	−0.989208	−	0.146521i	$-0.953192\pi$
$751$		−	6031.00i		−	0.293042i	0.989208	−	0.146521i	$-0.0468076\pi$
$752$	5134.97	+	5134.97i	0.249007	+	0.249007i
$753$		−	9878.30i		−	0.478068i
$754$	134.777	−	601.974i	0.00650966	−	0.0290751i
$755$			8542.75i			0.411791i
$756$	15886.7	+	15886.7i	0.764276	+	0.764276i
$757$	38206.2			1.83438			0.917191	−	0.398448i	$-0.130451\pi$
$757$	38206.2			1.83438			0.917191	+	0.398448i	$0.130451\pi$
$758$	2067.37			0.0990635
$759$	3423.41	−	24145.2i	0.163718	−	1.15469i
$760$	724.613	−	724.613i	0.0345848	−	0.0345848i
$761$	22425.6	−	22425.6i	1.06823	−	1.06823i	0.0707400	−	0.997495i	$-0.477464\pi$
$761$	22425.6	−	22425.6i	1.06823	−	1.06823i	0.997495	−	0.0707400i	$-0.0225361\pi$
$762$	2607.02	+	2607.02i	0.123940	+	0.123940i
$763$	−9910.88			−0.470247
$764$			3134.51i			0.148433i
$765$	−119.457	+	119.457i	−0.00564571	+	0.00564571i
$766$	−157.583			−0.00743302
$767$	−3889.27	−	870.774i	−0.183094	−	0.0409933i
$768$	−19880.9			−0.934103
$769$	−15337.9	−	15337.9i	−0.719246	−	0.719246i	0.249205	−	0.968451i	$-0.419831\pi$
$769$	−15337.9	−	15337.9i	−0.719246	−	0.719246i	−0.968451	+	0.249205i	$0.919831\pi$
$770$	−508.155	+	381.952i	−0.0237826	+	0.0178761i
$771$			7846.33i			0.366509i
$772$	2549.95	+	2549.95i	0.118879	+	0.118879i
$773$	−22491.0	+	22491.0i	−1.04650	+	1.04650i	−0.0476356	+	0.998865i	$0.515169\pi$
$773$	−22491.0	+	22491.0i	−1.04650	+	1.04650i	−0.998865	+	0.0476356i	$0.984831\pi$
$774$	−41.2307	−	41.2307i	−0.00191474	−	0.00191474i
$775$	−8424.49	−	8424.49i	−0.390473	−	0.390473i
$776$			2954.63i			0.136682i
$777$	−17859.9			−0.824610
$778$	1283.39	−	1283.39i	0.0591409	−	0.0591409i
$779$		−	16394.2i		−	0.754022i
$780$	−6501.95	−	1455.73i	−0.298471	−	0.0668251i
$781$	−9319.51	+	7004.95i	−0.426989	+	0.320943i
$782$	1638.54	−	1638.54i	0.0749286	−	0.0749286i
$783$			7277.50i			0.332154i
$784$			4679.03i			0.213148i
$785$	−1363.39	+	1363.39i	−0.0619892	+	0.0619892i
$786$	−2012.78	+	2012.78i	−0.0913405	+	0.0913405i
$787$	25040.8	−	25040.8i	1.13419	−	1.13419i	0.144715	−	0.989473i	$-0.453773\pi$
$787$	25040.8	−	25040.8i	1.13419	−	1.13419i	0.989473	−	0.144715i	$-0.0462266\pi$
$788$	−27366.7	+	27366.7i	−1.23718	+	1.23718i
$789$			28527.0i			1.28718i
$790$			334.246i			0.0150531i
$791$	7427.03	−	7427.03i	0.333849	−	0.333849i
$792$	−79.3060	+	59.6098i	−0.00355810	+	0.00267442i
$793$	19044.9	+	30033.0i	0.852843	+	1.34490i
$794$			1510.87i			0.0675301i
$795$	2314.67	−	2314.67i	0.103262	−	0.103262i
$796$	32042.7			1.42679
$797$		−	2596.99i		−	0.115421i	−0.998333	−	0.0577103i	$-0.981620\pi$
$797$		−	2596.99i		−	0.115421i	0.998333	−	0.0577103i	$-0.0183800\pi$
$798$	−1436.55	−	1436.55i	−0.0637259	−	0.0637259i
$799$	−5984.26	−	5984.26i	−0.264966	−	0.264966i
$800$	−3815.52	+	3815.52i	−0.168624	+	0.168624i
$801$	−603.430	−	603.430i	−0.0266182	−	0.0266182i
$802$			1180.83i			0.0519909i
$803$	−7727.98	+	5808.69i	−0.339619	+	0.255273i
$804$	2604.48	+	2604.48i	0.114245	+	0.114245i
$805$	8840.37			0.387059
$806$	1041.30	−	660.321i	0.0455065	−	0.0288571i
$807$	−6845.58			−0.298607
$808$	1805.99	−	1805.99i	0.0786316	−	0.0786316i
$809$		−	15527.0i		−	0.674783i	−0.941365	−	0.337391i	$-0.890455\pi$
$809$		−	15527.0i		−	0.674783i	0.941365	−	0.337391i	$-0.109545\pi$
$810$	−636.683			−0.0276182
$811$	3027.82	+	3027.82i	0.131099	+	0.131099i	0.769611	−	0.638513i	$-0.220450\pi$
$811$	3027.82	+	3027.82i	0.131099	+	0.131099i	−0.638513	+	0.769611i	$0.720450\pi$
$812$	−6029.77	+	6029.77i	−0.260596	+	0.260596i
$813$	23940.5	−	23940.5i	1.03275	−	1.03275i
$814$	−212.972	+	1502.08i	−0.00917034	+	0.0646780i
$815$	−7614.51			−0.327269
$816$	23950.4			1.02749
$817$	18227.7	+	18227.7i	0.780545	+	0.780545i
$818$			3289.64i			0.140611i
$819$	−142.642	+	637.102i	−0.00608585	+	0.0271821i
$820$		−	5871.93i		−	0.250069i
$821$	25255.1	+	25255.1i	1.07358	+	1.07358i	0.997069	+	0.0765134i	$0.0243788\pi$
$821$	25255.1	+	25255.1i	1.07358	+	1.07358i	0.0765134	+	0.997069i	$0.475621\pi$
$822$			3466.51i			0.147091i
$823$			38094.1i			1.61346i	0.590919	+	0.806731i	$0.298765\pi$
$823$			38094.1i			1.61346i	−0.590919	+	0.806731i	$0.701235\pi$
$824$	−3705.63	−	3705.63i	−0.156665	−	0.156665i
$825$	3056.00	−	21553.8i	0.128965	−	0.909585i
$826$	−307.777	−	307.777i	−0.0129648	−	0.0129648i
$827$	16275.7	−	16275.7i	0.684356	−	0.684356i	−0.276623	−	0.960979i	$-0.589215\pi$
$827$	16275.7	−	16275.7i	0.684356	−	0.684356i	0.960979	+	0.276623i	$0.0892152\pi$
$828$	687.129			0.0288398
$829$			25965.8i			1.08785i	0.839134	+	0.543925i	$0.183063\pi$
$829$			25965.8i			1.08785i	−0.839134	+	0.543925i	$0.816937\pi$
$830$	893.013	+	893.013i	0.0373457	+	0.0373457i
$831$	6350.95			0.265117
$832$	12251.5	+	19320.2i	0.510511	+	0.805055i
$833$		−	5452.92i		−	0.226810i
$834$	338.587	−	338.587i	0.0140579	−	0.0140579i
$835$		−	4858.34i		−	0.201353i
$836$	17461.2	−	13124.6i	0.722377	−	0.542970i
$837$	−10285.8	+	10285.8i	−0.424765	+	0.424765i
$838$	2150.14	+	2150.14i	0.0886340	+	0.0886340i
$839$	−12381.7	−	12381.7i	−0.509493	−	0.509493i	0.404878	−	0.914371i	$-0.367314\pi$
$839$	−12381.7	−	12381.7i	−0.509493	−	0.509493i	−0.914371	+	0.404878i	$0.867314\pi$
$840$	−1033.13	−	1033.13i	−0.0424360	−	0.0424360i
$841$	21626.8			0.886745
$842$	−1342.58			−0.0549504
$843$	−351.159	+	351.159i	−0.0143470	+	0.0143470i
$844$	45203.6			1.84357
$845$	2528.35	+	7038.12i	0.102932	+	0.286531i
$846$			19.8260i			0.000805711i
$847$	−23828.7	+	13132.6i	−0.966665	+	0.532753i
$848$	−11423.5			−0.462600
$849$	−11914.5			−0.481630
$850$	1462.69	−	1462.69i	0.0590233	−	0.0590233i
$851$	14918.4	−	14918.4i	0.600935	−	0.600935i
$852$	−9436.44	−	9436.44i	−0.379445	−	0.379445i
$853$	2285.54	−	2285.54i	0.0917414	−	0.0917414i	−0.659747	−	0.751488i	$-0.729336\pi$
$853$	2285.54	−	2285.54i	0.0917414	−	0.0917414i	0.751488	+	0.659747i	$0.229336\pi$
$854$			3883.77i			0.155621i
$855$	−174.962			−0.00699835
$856$	4207.64	+	4207.64i	0.168007	+	0.168007i
$857$	46269.3			1.84426			0.922130	−	0.386880i	$-0.126447\pi$
$857$	46269.3			1.84426			0.922130	+	0.386880i	$0.126447\pi$
$858$	2107.67	+	795.994i	0.0838634	+	0.0316723i
$859$	−22798.6			−0.905564			−0.452782	−	0.891621i	$-0.649568\pi$
$859$	−22798.6			−0.905564			−0.452782	+	0.891621i	$0.649568\pi$
$860$	6528.63	+	6528.63i	0.258865	+	0.258865i
$861$	−23374.2			−0.925194
$862$			1634.11i			0.0645686i
$863$	−16723.7	+	16723.7i	−0.659654	+	0.659654i	−0.955298	−	0.295644i	$-0.904466\pi$
$863$	−16723.7	+	16723.7i	−0.659654	+	0.659654i	0.295644	+	0.955298i	$0.404466\pi$
$864$	4658.52	+	4658.52i	0.183433	+	0.183433i
$865$	5416.69	−	5416.69i	0.212917	−	0.212917i
$866$	−1553.77	+	1553.77i	−0.0609689	+	0.0609689i
$867$	−2062.79			−0.0808027
$868$	−17044.6			−0.666510
$869$	−2008.27	+	14164.2i	−0.0783956	+	0.552920i
$870$		−	235.701i		−	0.00918506i
$871$	903.237	−	4034.26i	0.0351378	−	0.156941i
$872$	−1934.94			−0.0751436
$873$	356.707	−	356.707i	0.0138290	−	0.0138290i
$874$	2399.89			0.0928806
$875$	16589.4			0.640943
$876$	−7824.94	−	7824.94i	−0.301804	−	0.301804i
$877$	22320.7	+	22320.7i	0.859427	+	0.859427i	0.991271	−	0.131843i	$-0.0420896\pi$
$877$	22320.7	+	22320.7i	0.859427	+	0.859427i	−0.131843	+	0.991271i	$0.542090\pi$
$878$	−398.145	−	398.145i	−0.0153038	−	0.0153038i
$879$	1311.22	−	1311.22i	0.0503145	−	0.0503145i
$880$	6204.29	−	4663.42i	0.237667	−	0.178641i
$881$			27135.6i			1.03771i	0.854863	+	0.518855i	$0.173641\pi$
$881$			27135.6i			1.03771i	−0.854863	+	0.518855i	$0.826359\pi$
$882$	−9.03282	+	9.03282i	−0.000344842	+	0.000344842i
$883$		−	45709.7i		−	1.74208i	−0.491216	−	0.871038i	$-0.663448\pi$
$883$		−	45709.7i		−	1.74208i	0.491216	−	0.871038i	$-0.336552\pi$
$884$	−14511.7	−	22884.4i	−0.552129	−	0.870686i
$885$	−1522.83			−0.0578411
$886$	−593.394	−	593.394i	−0.0225005	−	0.0225005i
$887$			14520.5i			0.549663i	0.961492	+	0.274831i	$0.0886221\pi$
$887$			14520.5i			0.549663i	−0.961492	+	0.274831i	$0.911378\pi$
$888$	−3486.86			−0.131770
$889$	−40449.3	+	40449.3i	−1.52601	+	1.52601i
$890$	−754.869	−	754.869i	−0.0284306	−	0.0284306i
$891$	−26980.4	−	3825.41i	−1.01445	−	0.143834i
$892$	33840.4	+	33840.4i	1.27025	+	1.27025i
$893$		−	8764.85i		−	0.328449i
$894$			601.154i			0.0224895i
$895$	11013.0	+	11013.0i	0.411312	+	0.411312i
$896$			10279.0i			0.383257i
$897$	−16778.9	−	26459.7i	−0.624562	−	0.984909i
$898$		−	3720.89i		−	0.138271i
$899$	−3903.96	−	3903.96i	−0.144833	−	0.144833i
$900$	613.384			0.0227179
$901$	13312.9			0.492249
$902$	−278.727	+	1965.85i	−0.0102889	+	0.0725672i
$903$	25988.3	−	25988.3i	0.957738	−	0.957738i
$904$	1450.00	−	1450.00i	0.0533478	−	0.0533478i
$905$	5518.72	+	5518.72i	0.202705	+	0.202705i
$906$	3306.49			0.121248
$907$			19337.2i			0.707916i	0.935261	+	0.353958i	$0.115164\pi$
$907$			19337.2i			0.707916i	−0.935261	+	0.353958i	$0.884836\pi$
$908$	−23547.9	+	23547.9i	−0.860643	+	0.860643i
$909$	−436.067			−0.0159114
$910$	−178.440	+	796.992i	−0.00650024	+	0.0290330i
$911$	16029.7			0.582971			0.291485	−	0.956575i	$-0.405851\pi$
$911$	16029.7			0.582971			0.291485	+	0.956575i	$0.405851\pi$
$912$	17539.5	+	17539.5i	0.636831	+	0.636831i
$913$	32477.3	+	43208.3i	1.17726	+	1.56625i
$914$			367.925i			0.0133149i
$915$	9608.14	+	9608.14i	0.347143	+	0.347143i
$916$	−18950.5	+	18950.5i	−0.683561	+	0.683561i
$917$	−31229.4	−	31229.4i	−1.12463	−	1.12463i
$918$	−1785.85	−	1785.85i	−0.0642069	−	0.0642069i
$919$			34058.0i			1.22249i	0.791441	+	0.611245i	$0.209331\pi$
$919$			34058.0i			1.22249i	−0.791441	+	0.611245i	$0.790669\pi$
$920$	1725.94			0.0618505
$921$	−15961.0	+	15961.0i	−0.571045	+	0.571045i
$922$		−	3729.66i		−	0.133221i
$923$	−3272.57	+	14616.7i	−0.116704	+	0.521253i
$924$	−18712.6	−	24895.5i	−0.666232	−	0.886366i
$925$	13317.3	−	13317.3i	0.473373	−	0.473373i
$926$		−	2693.83i		−	0.0955990i
$927$			894.749i			0.0317016i
$928$	−1768.14	+	1768.14i	−0.0625452	+	0.0625452i
$929$	2184.76	−	2184.76i	0.0771578	−	0.0771578i	−0.667475	−	0.744633i	$-0.732625\pi$
$929$	2184.76	−	2184.76i	0.0771578	−	0.0771578i	0.744633	+	0.667475i	$0.232625\pi$
$930$	333.132	−	333.132i	0.0117460	−	0.0117460i
$931$	3993.31	−	3993.31i	0.140575	−	0.140575i
$932$		−	31498.4i		−	1.10704i
$933$			38363.8i			1.34617i
$934$	1340.40	−	1340.40i	0.0469586	−	0.0469586i
$935$	−7230.44	+	5434.72i	−0.252899	+	0.190090i
$936$	−27.8485	+	124.384i	−0.000972495	+	0.00434360i
$937$		−	15443.8i		−	0.538449i	−0.963077	−	0.269225i	$-0.913233\pi$
$937$		−	15443.8i		−	0.538449i	0.963077	−	0.269225i	$-0.0867674\pi$
$938$	319.251	−	319.251i	0.0111129	−	0.0111129i
$939$	20482.9			0.711859
$940$		−	3139.32i		−	0.108929i
$941$	−17156.9	−	17156.9i	−0.594366	−	0.594366i	0.344442	−	0.938808i	$-0.388068\pi$
$941$	−17156.9	−	17156.9i	−0.594366	−	0.594366i	−0.938808	+	0.344442i	$0.888068\pi$
$942$	527.703	+	527.703i	0.0182521	+	0.0182521i
$943$	19524.5	−	19524.5i	0.674235	−	0.674235i
$944$	3757.78	+	3757.78i	0.129561	+	0.129561i
$945$		−	9635.15i		−	0.331674i
$946$	−1875.81	−	2495.60i	−0.0644690	−	0.0857707i
$947$	−18130.7	−	18130.7i	−0.622140	−	0.622140i	0.323938	−	0.946078i	$-0.394993\pi$
$947$	−18130.7	−	18130.7i	−0.622140	−	0.622140i	−0.946078	+	0.323938i	$0.894993\pi$
$948$	−16375.4			−0.561021
$949$	−2713.70	+	12120.6i	−0.0928244	+	0.414595i
$950$	2142.33			0.0731646
$951$	20256.8	−	20256.8i	0.690716	−	0.690716i
$952$		−	5942.06i		−	0.202293i
$953$	44586.7			1.51554			0.757768	−	0.652524i	$-0.226290\pi$
$953$	44586.7			1.51554			0.757768	+	0.652524i	$0.226290\pi$
$954$	−22.0530	−	22.0530i	−0.000748418	−	0.000748418i
$955$	950.529	−	950.529i	0.0322078	−	0.0322078i
$956$	−2273.24	+	2273.24i	−0.0769057	+	0.0769057i
$957$	1416.17	−	9988.18i	0.0478352	−	0.337379i
$958$	−3859.66			−0.130167
$959$	−53784.7			−1.81105
$960$	6180.89	+	6180.89i	0.207799	+	0.207799i
$961$			18755.5i			0.629570i
$962$	1043.82	+	1646.07i	0.0349836	+	0.0551678i
$963$		−	1015.96i		−	0.0339968i
$964$	8442.82	+	8442.82i	0.282080	+	0.282080i
$965$		−	1546.52i		−	0.0515900i
$966$		−	3421.68i		−	0.113966i
$967$	−31193.6	−	31193.6i	−1.03735	−	1.03735i	−0.999275	−	0.0380748i	$-0.987877\pi$
$967$	−31193.6	−	31193.6i	−1.03735	−	1.03735i	−0.0380748	−	0.999275i	$-0.512123\pi$
$968$	−4652.17	+	2563.93i	−0.154469	+	0.0851320i
$969$	−20440.4	−	20440.4i	−0.677647	−	0.677647i
$970$	446.228	−	446.228i	0.0147706	−	0.0147706i
$971$	40149.3			1.32693			0.663467	−	0.748205i	$-0.269084\pi$
$971$	40149.3			1.32693			0.663467	+	0.748205i	$0.269084\pi$
$972$		−	1517.20i		−	0.0500660i
$973$	5253.34	+	5253.34i	0.173088	+	0.173088i
$974$	1115.19			0.0366867
$975$	−14978.2	−	23620.0i	−0.491985	−	0.775840i
$976$		−	47418.7i		−	1.55516i
$977$	42719.6	−	42719.6i	1.39890	−	1.39890i	0.595661	−	0.803236i	$-0.296890\pi$
$977$	42719.6	−	42719.6i	1.39890	−	1.39890i	0.803236	−	0.595661i	$-0.203110\pi$
$978$			2947.21i			0.0963613i
$979$	−27453.2	−	36524.3i	−0.896230	−	1.19236i
$980$	1430.29	−	1430.29i	0.0466213	−	0.0466213i
$981$	233.602	+	233.602i	0.00760278	+	0.00760278i
$982$	−1507.61	−	1507.61i	−0.0489916	−	0.0489916i
$983$	−8763.91	−	8763.91i	−0.284360	−	0.284360i	0.550485	−	0.834845i	$-0.314443\pi$
$983$	−8763.91	−	8763.91i	−0.284360	−	0.284360i	−0.834845	+	0.550485i	$0.814443\pi$
$984$	−4563.44			−0.147842
$985$	16597.7			0.536900
$986$	677.819	−	677.819i	0.0218927	−	0.0218927i
$987$	−12496.6			−0.403011
$988$	6131.53	−	27386.2i	0.197439	−	0.881852i
$989$			43416.0i			1.39590i
$990$	20.9800	+	2.97464i	0.000673523	+	9.54952e-5i
$991$	−41111.6			−1.31781			−0.658907	−	0.752224i	$-0.728981\pi$
$991$	−41111.6			−1.31781			−0.658907	+	0.752224i	$0.728981\pi$
$992$	−4998.06			−0.159968
$993$	17811.0	−	17811.0i	0.569199	−	0.569199i
$994$	−1156.69	+	1156.69i	−0.0369096	+	0.0369096i
$995$	−9716.84	−	9716.84i	−0.309592	−	0.309592i
$996$	−43750.5	+	43750.5i	−1.39185	+	1.39185i
$997$		−	890.045i		−	0.0282728i	−0.999900	−	0.0141364i	$-0.995500\pi$
$997$		−	890.045i		−	0.0282728i	0.999900	−	0.0141364i	$-0.00449991\pi$
$998$	−1359.67			−0.0431259
$999$	−16259.6	−	16259.6i	−0.514946	−	0.514946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.109.20	yes	80
11.10	odd	2	inner	143.4.g.a.109.21	yes	80
13.8	odd	4	inner	143.4.g.a.21.21	yes	80
143.21	even	4	inner	143.4.g.a.21.20	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.20	✓	80	143.21	even	4	inner
143.4.g.a.21.21	yes	80	13.8	odd	4	inner
143.4.g.a.109.20	yes	80	1.1	even	1	trivial
143.4.g.a.109.21	yes	80	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.177069 - 0.177069i) q^{2} -5.26131 q^{3} -7.93729i q^{4} +(-2.40696 + 2.40696i) q^{5} +(0.931617 + 0.931617i) q^{6} +(-14.4545 + 14.4545i) q^{7} +(-2.82201 + 2.82201i) q^{8} +0.681391 q^{9} +O(q^{10})\)	\(q+(-0.177069 - 0.177069i) q^{2} -5.26131 q^{3} -7.93729i q^{4} +(-2.40696 + 2.40696i) q^{5} +(0.931617 + 0.931617i) q^{6} +(-14.4545 + 14.4545i) q^{7} +(-2.82201 + 2.82201i) q^{8} +0.681391 q^{9} +0.852396 q^{10} +(36.1216 + 5.12149i) q^{11} +41.7606i q^{12} +(39.5842 - 25.1016i) q^{13} +5.11890 q^{14} +(12.6637 - 12.6637i) q^{15} -62.4990 q^{16} +72.8359 q^{17} +(-0.120654 - 0.120654i) q^{18} +(53.3396 + 53.3396i) q^{19} +(19.1047 + 19.1047i) q^{20} +(76.0497 - 76.0497i) q^{21} +(-5.48917 - 7.30289i) q^{22} +127.048i q^{23} +(14.8474 - 14.8474i) q^{24} +113.413i q^{25} +(-11.4539 - 2.56442i) q^{26} +138.470 q^{27} +(114.730 + 114.730i) q^{28} +52.5564i q^{29} -4.48472 q^{30} +(-74.2815 + 74.2815i) q^{31} +(33.6427 + 33.6427i) q^{32} +(-190.047 - 26.9457i) q^{33} +(-12.8970 - 12.8970i) q^{34} -69.5828i q^{35} -5.40840i q^{36} +(-117.423 - 117.423i) q^{37} -18.8896i q^{38} +(-208.265 + 132.067i) q^{39} -13.5849i q^{40} +(-153.677 - 153.677i) q^{41} -26.9321 q^{42} +341.728 q^{43} +(40.6507 - 286.708i) q^{44} +(-1.64008 + 1.64008i) q^{45} +(22.4964 - 22.4964i) q^{46} +(-82.1608 - 82.1608i) q^{47} +328.826 q^{48} -74.8658i q^{49} +(20.0820 - 20.0820i) q^{50} -383.212 q^{51} +(-199.239 - 314.191i) q^{52} +182.779 q^{53} +(-24.5189 - 24.5189i) q^{54} +(-99.2703 + 74.6159i) q^{55} -81.5814i q^{56} +(-280.636 - 280.636i) q^{57} +(9.30612 - 9.30612i) q^{58} +(-60.1255 - 60.1255i) q^{59} +(-100.516 - 100.516i) q^{60} +758.712i q^{61} +26.3059 q^{62} +(-9.84918 + 9.84918i) q^{63} +488.078i q^{64} +(-34.8590 + 155.696i) q^{65} +(28.8802 + 38.4228i) q^{66} +(62.3670 - 62.3670i) q^{67} -578.120i q^{68} -668.441i q^{69} +(-12.3210 + 12.3210i) q^{70} +(-225.965 + 225.965i) q^{71} +(-1.92289 + 1.92289i) q^{72} +(-187.376 + 187.376i) q^{73} +41.5840i q^{74} -596.702i q^{75} +(423.372 - 423.372i) q^{76} +(-596.149 + 448.092i) q^{77} +(60.2624 + 13.4922i) q^{78} +392.126i q^{79} +(150.432 - 150.432i) q^{80} -746.933 q^{81} +54.4231i q^{82} +(1047.65 + 1047.65i) q^{83} +(-603.629 - 603.629i) q^{84} +(-175.313 + 175.313i) q^{85} +(-60.5096 - 60.5096i) q^{86} -276.515i q^{87} +(-116.388 + 87.4825i) q^{88} +(-885.585 - 885.585i) q^{89} +0.580816 q^{90} +(-209.339 + 935.002i) q^{91} +1008.42 q^{92} +(390.818 - 390.818i) q^{93} +29.0963i q^{94} -256.772 q^{95} +(-177.005 - 177.005i) q^{96} +(523.499 - 523.499i) q^{97} +(-13.2564 + 13.2564i) q^{98} +(24.6130 + 3.48974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more