LMFDB - Embedded newform 57.3.c.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,3,Mod(37,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("57.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	57.c (of order $2$, degree $1$, 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:	$1.55313750685$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.4
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	57.37
Dual form			57.3.c.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.04547i q^{2} +1.73205i q^{3} -5.27492 q^{4} -6.27492 q^{5} -5.27492 q^{6} +12.2749 q^{7} -3.88273i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+3.04547i q^{2} +1.73205i q^{3} -5.27492 q^{4} -6.27492 q^{5} -5.27492 q^{6} +12.2749 q^{7} -3.88273i q^{8} -3.00000 q^{9} -19.1101i q^{10} +0.274917 q^{11} -9.13642i q^{12} +13.0192i q^{13} +37.3830i q^{14} -10.8685i q^{15} -9.27492 q^{16} +17.3746 q^{17} -9.13642i q^{18} +(7.54983 - 17.4356i) q^{19} +33.0997 q^{20} +21.2608i q^{21} +0.837253i q^{22} +20.5498 q^{23} +6.72508 q^{24} +14.3746 q^{25} -39.6495 q^{26} -5.19615i q^{27} -64.7492 q^{28} -26.0383i q^{29} +33.0997 q^{30} +23.5265i q^{31} -43.7774i q^{32} +0.476171i q^{33} +52.9139i q^{34} -77.0241 q^{35} +15.8248 q^{36} -66.7703i q^{37} +(53.0997 + 22.9928i) q^{38} -22.5498 q^{39} +24.3638i q^{40} -3.57919i q^{41} -64.7492 q^{42} -48.1238 q^{43} -1.45017 q^{44} +18.8248 q^{45} +62.5840i q^{46} -12.4743 q^{47} -16.0646i q^{48} +101.674 q^{49} +43.7774i q^{50} +30.0937i q^{51} -68.6750i q^{52} +25.8081i q^{53} +15.8248 q^{54} -1.72508 q^{55} -47.6602i q^{56} +(30.1993 + 13.0767i) q^{57} +79.2990 q^{58} -0.230175i q^{59} +57.3303i q^{60} -28.8248 q^{61} -71.6495 q^{62} -36.8248 q^{63} +96.2234 q^{64} -81.6941i q^{65} -1.45017 q^{66} +102.939i q^{67} -91.6495 q^{68} +35.5934i q^{69} -234.575i q^{70} -107.732i q^{71} +11.6482i q^{72} +11.1752 q^{73} +203.347 q^{74} +24.8975i q^{75} +(-39.8248 + 91.9713i) q^{76} +3.37459 q^{77} -68.6750i q^{78} +26.6454i q^{79} +58.1993 q^{80} +9.00000 q^{81} +10.9003 q^{82} -89.6977 q^{83} -112.149i q^{84} -109.024 q^{85} -146.560i q^{86} +45.0997 q^{87} -1.06743i q^{88} +139.255i q^{89} +57.3303i q^{90} +159.809i q^{91} -108.399 q^{92} -40.7492 q^{93} -37.9900i q^{94} +(-47.3746 + 109.407i) q^{95} +75.8248 q^{96} +41.3390i q^{97} +309.644i q^{98} -0.824752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} - 10 q^{5} - 6 q^{6} + 34 q^{7} - 12 q^{9}+O(q^{10}) $ 4 * q - 6 * q^4 - 10 * q^5 - 6 * q^6 + 34 * q^7 - 12 * q^9	$ 4 q - 6 q^{4} - 10 q^{5} - 6 q^{6} + 34 q^{7} - 12 q^{9} - 14 q^{11} - 22 q^{16} - 6 q^{17} + 72 q^{20} + 52 q^{23} + 42 q^{24} - 18 q^{25} - 68 q^{26} - 108 q^{28} + 72 q^{30} - 142 q^{35} + 18 q^{36} + 152 q^{38} - 60 q^{39} - 108 q^{42} + 34 q^{43} - 36 q^{44} + 30 q^{45} + 86 q^{47} + 150 q^{49} + 18 q^{54} - 22 q^{55} + 136 q^{58} - 70 q^{61} - 196 q^{62} - 102 q^{63} + 98 q^{64} - 36 q^{66} - 276 q^{68} + 90 q^{73} + 300 q^{74} - 114 q^{76} - 62 q^{77} + 112 q^{80} + 36 q^{81} + 104 q^{82} + 64 q^{83} - 270 q^{85} + 120 q^{87} - 192 q^{92} - 12 q^{93} - 114 q^{95} + 258 q^{96} + 42 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 - 10 * q^5 - 6 * q^6 + 34 * q^7 - 12 * q^9 - 14 * q^11 - 22 * q^16 - 6 * q^17 + 72 * q^20 + 52 * q^23 + 42 * q^24 - 18 * q^25 - 68 * q^26 - 108 * q^28 + 72 * q^30 - 142 * q^35 + 18 * q^36 + 152 * q^38 - 60 * q^39 - 108 * q^42 + 34 * q^43 - 36 * q^44 + 30 * q^45 + 86 * q^47 + 150 * q^49 + 18 * q^54 - 22 * q^55 + 136 * q^58 - 70 * q^61 - 196 * q^62 - 102 * q^63 + 98 * q^64 - 36 * q^66 - 276 * q^68 + 90 * q^73 + 300 * q^74 - 114 * q^76 - 62 * q^77 + 112 * q^80 + 36 * q^81 + 104 * q^82 + 64 * q^83 - 270 * q^85 + 120 * q^87 - 192 * q^92 - 12 * q^93 - 114 * q^95 + 258 * q^96 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$-1$

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 $

$2$			3.04547i			1.52274i	0.648319	+	0.761369i	$0.275472\pi$
$2$			3.04547i			1.52274i	−0.648319	+	0.761369i	$0.724528\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−5.27492			−1.31873
$5$	−6.27492			−1.25498			−0.627492	−	0.778623i	$-0.715918\pi$
$5$	−6.27492			−1.25498			−0.627492	+	0.778623i	$0.715918\pi$
$6$	−5.27492			−0.879153
$7$	12.2749			1.75356			0.876780	−	0.480892i	$-0.159687\pi$
$7$	12.2749			1.75356			0.876780	+	0.480892i	$0.159687\pi$
$8$		−	3.88273i		−	0.485341i
$9$	−3.00000			−0.333333
$10$		−	19.1101i		−	1.91101i
$11$	0.274917			0.0249925			0.0124962	−	0.999922i	$-0.496022\pi$
$11$	0.274917			0.0249925			0.0124962	+	0.999922i	$0.496022\pi$
$12$		−	9.13642i		−	0.761369i
$13$			13.0192i			1.00147i	0.865600	+	0.500737i	$0.166937\pi$
$13$			13.0192i			1.00147i	−0.865600	+	0.500737i	$0.833063\pi$
$14$			37.3830i			2.67021i
$15$		−	10.8685i		−	0.724565i
$16$	−9.27492			−0.579682
$17$	17.3746			1.02203			0.511017	−	0.859570i	$-0.329269\pi$
$17$	17.3746			1.02203			0.511017	+	0.859570i	$0.329269\pi$
$18$		−	9.13642i		−	0.507579i
$19$	7.54983	−	17.4356i	0.397360	−	0.917663i
$19$	7.54983	−	17.4356i	0.397360	−	0.917663i
$20$	33.0997			1.65498
$21$			21.2608i			1.01242i
$22$			0.837253i			0.0380570i
$23$	20.5498			0.893471			0.446736	−	0.894666i	$-0.352586\pi$
$23$	20.5498			0.893471			0.446736	+	0.894666i	$0.352586\pi$
$24$	6.72508			0.280212
$25$	14.3746			0.574983
$26$	−39.6495			−1.52498
$27$		−	5.19615i		−	0.192450i
$28$	−64.7492			−2.31247
$29$		−	26.0383i		−	0.897873i	−0.893564	−	0.448936i	$-0.851803\pi$
$29$		−	26.0383i		−	0.897873i	0.893564	−	0.448936i	$-0.148197\pi$
$30$	33.0997			1.10332
$31$			23.5265i			0.758921i	0.925208	+	0.379460i	$0.123890\pi$
$31$			23.5265i			0.758921i	−0.925208	+	0.379460i	$0.876110\pi$
$32$		−	43.7774i		−	1.36805i
$33$			0.476171i			0.0144294i
$34$			52.9139i			1.55629i
$35$	−77.0241			−2.20069
$36$	15.8248			0.439576
$37$		−	66.7703i		−	1.80460i	−0.431107	−	0.902301i	$-0.641877\pi$
$37$		−	66.7703i		−	1.80460i	0.431107	−	0.902301i	$-0.358123\pi$
$38$	53.0997	+	22.9928i	1.39736	+	0.605075i
$39$	−22.5498			−0.578201
$40$			24.3638i			0.609095i
$41$		−	3.57919i		−	0.0872973i	−0.999047	−	0.0436487i	$-0.986102\pi$
$41$		−	3.57919i		−	0.0872973i	0.999047	−	0.0436487i	$-0.0138982\pi$
$42$	−64.7492			−1.54165
$43$	−48.1238			−1.11916			−0.559579	−	0.828777i	$-0.689037\pi$
$43$	−48.1238			−1.11916			−0.559579	+	0.828777i	$0.689037\pi$
$44$	−1.45017			−0.0329583
$45$	18.8248			0.418328
$46$			62.5840i			1.36052i
$47$	−12.4743			−0.265410			−0.132705	−	0.991156i	$-0.542366\pi$
$47$	−12.4743			−0.265410			−0.132705	+	0.991156i	$0.542366\pi$
$48$		−	16.0646i		−	0.334680i
$49$	101.674			2.07497
$50$			43.7774i			0.875549i
$51$			30.0937i			0.590072i
$52$		−	68.6750i		−	1.32067i
$53$			25.8081i			0.486946i	0.969908	+	0.243473i	$0.0782867\pi$
$53$			25.8081i			0.486946i	−0.969908	+	0.243473i	$0.921713\pi$
$54$	15.8248			0.293051
$55$	−1.72508			−0.0313651
$56$		−	47.6602i		−	0.851074i
$57$	30.1993	+	13.0767i	0.529813	+	0.229416i
$58$	79.2990			1.36722
$59$		−	0.230175i		−	0.00390128i	−0.999998	−	0.00195064i	$-0.999379\pi$
$59$		−	0.230175i		−	0.00390128i	0.999998	−	0.00195064i	$-0.000620908\pi$
$60$			57.3303i			0.955505i
$61$	−28.8248			−0.472537			−0.236268	−	0.971688i	$-0.575924\pi$
$61$	−28.8248			−0.472537			−0.236268	+	0.971688i	$0.575924\pi$
$62$	−71.6495			−1.15564
$63$	−36.8248			−0.584520
$64$	96.2234			1.50349
$65$		−	81.6941i		−	1.25683i
$66$	−1.45017			−0.0219722
$67$			102.939i			1.53640i	0.640208	+	0.768202i	$0.278848\pi$
$67$			102.939i			1.53640i	−0.640208	+	0.768202i	$0.721152\pi$
$68$	−91.6495			−1.34779
$69$			35.5934i			0.515846i
$70$		−	234.575i		−	3.35107i
$71$		−	107.732i		−	1.51736i	−0.651465	−	0.758679i	$-0.725845\pi$
$71$		−	107.732i		−	1.51736i	0.651465	−	0.758679i	$-0.274155\pi$
$72$			11.6482i			0.161780i
$73$	11.1752			0.153086			0.0765428	−	0.997066i	$-0.475612\pi$
$73$	11.1752			0.153086			0.0765428	+	0.997066i	$0.475612\pi$
$74$	203.347			2.74793
$75$			24.8975i			0.331967i
$76$	−39.8248	+	91.9713i	−0.524010	+	1.21015i
$77$	3.37459			0.0438258
$78$		−	68.6750i		−	0.880448i
$79$			26.6454i			0.337283i	0.985677	+	0.168642i	$0.0539381\pi$
$79$			26.6454i			0.337283i	−0.985677	+	0.168642i	$0.946062\pi$
$80$	58.1993			0.727492
$81$	9.00000			0.111111
$82$	10.9003			0.132931
$83$	−89.6977			−1.08069			−0.540347	−	0.841442i	$-0.681707\pi$
$83$	−89.6977			−1.08069			−0.540347	+	0.841442i	$0.681707\pi$
$84$		−	112.149i		−	1.33511i
$85$	−109.024			−1.28264
$86$		−	146.560i		−	1.70418i
$87$	45.0997			0.518387
$88$		−	1.06743i		−	0.0121299i
$89$			139.255i			1.56466i	0.622865	+	0.782329i	$0.285968\pi$
$89$			139.255i			1.56466i	−0.622865	+	0.782329i	$0.714032\pi$
$90$			57.3303i			0.637003i
$91$			159.809i			1.75614i
$92$	−108.399			−1.17825
$93$	−40.7492			−0.438163
$94$		−	37.9900i		−	0.404149i
$95$	−47.3746	+	109.407i	−0.498680	+	1.15165i
$96$	75.8248			0.789841
$97$			41.3390i			0.426176i	0.977033	+	0.213088i	$0.0683521\pi$
$97$			41.3390i			0.426176i	−0.977033	+	0.213088i	$0.931648\pi$
$98$			309.644i			3.15964i
$99$	−0.824752			−0.00833082
$100$	−75.8248			−0.758248
$101$	150.749			1.49257			0.746283	−	0.665629i	$-0.231837\pi$
$101$	150.749			1.49257			0.746283	+	0.665629i	$0.231837\pi$
$102$	−91.6495			−0.898525
$103$		−	22.8360i		−	0.221709i	−0.993837	−	0.110854i	$-0.964641\pi$
$103$		−	22.8360i		−	0.221709i	0.993837	−	0.110854i	$-0.0353587\pi$
$104$	50.5498			0.486056
$105$		−	133.410i		−	1.27057i
$106$	−78.5980			−0.741491
$107$		−	165.063i		−	1.54264i	−0.636446	−	0.771321i	$-0.719596\pi$
$107$		−	165.063i		−	1.54264i	0.636446	−	0.771321i	$-0.280404\pi$
$108$			27.4093i			0.253790i
$109$		−	46.4460i		−	0.426110i	−0.977040	−	0.213055i	$-0.931659\pi$
$109$		−	46.4460i		−	0.426110i	0.977040	−	0.213055i	$-0.0683414\pi$
$110$		−	5.25370i		−	0.0477609i
$111$	115.650			1.04189
$112$	−113.849			−1.01651
$113$		−	4.56317i		−	0.0403820i	−0.999796	−	0.0201910i	$-0.993573\pi$
$113$		−	4.56317i		−	0.0403820i	0.999796	−	0.0201910i	$-0.00642744\pi$
$114$	−39.8248	+	91.9713i	−0.349340	+	0.806766i
$115$	−128.949			−1.12129
$116$			137.350i			1.18405i
$117$		−	39.0575i		−	0.333824i
$118$	0.700993			0.00594062
$119$	213.272			1.79220
$120$	−42.1993			−0.351661
$121$	−120.924			−0.999375
$122$		−	87.7851i		−	0.719550i
$123$	6.19934			0.0504011
$124$		−	124.101i		−	1.00081i
$125$	66.6736			0.533389
$126$		−	112.149i		−	0.890070i
$127$		−	146.790i		−	1.15583i	−0.816098	−	0.577913i	$-0.803867\pi$
$127$		−	146.790i		−	1.15583i	0.816098	−	0.577913i	$-0.196133\pi$
$128$			117.936i			0.921377i
$129$		−	83.3528i		−	0.646146i
$130$	248.797			1.91383
$131$	−188.921			−1.44215			−0.721073	−	0.692859i	$-0.756351\pi$
$131$	−188.921			−1.44215			−0.721073	+	0.692859i	$0.756351\pi$
$132$		−	2.51176i		−	0.0190285i
$133$	92.6736	−	214.020i	0.696794	−	1.60918i
$134$	−313.498			−2.33954
$135$			32.6054i			0.241522i
$136$		−	67.4608i		−	0.496035i
$137$	−71.3264			−0.520631			−0.260315	−	0.965524i	$-0.583827\pi$
$137$	−71.3264			−0.520631			−0.260315	+	0.965524i	$0.583827\pi$
$138$	−108.399			−0.785498
$139$	43.5739			0.313481			0.156741	−	0.987640i	$-0.449901\pi$
$139$	43.5739			0.313481			0.156741	+	0.987640i	$0.449901\pi$
$140$	406.296			2.90211
$141$		−	21.6060i		−	0.153234i
$142$	328.096			2.31054
$143$			3.57919i			0.0250293i
$144$	27.8248			0.193227
$145$			163.388i			1.12682i
$146$			34.0339i			0.233109i
$147$			176.104i			1.19799i
$148$			352.208i			2.37978i
$149$	−71.6769			−0.481053			−0.240527	−	0.970643i	$-0.577320\pi$
$149$	−71.6769			−0.481053			−0.240527	+	0.970643i	$0.577320\pi$
$150$	−75.8248			−0.505498
$151$		−	68.9051i		−	0.456325i	−0.973623	−	0.228163i	$-0.926728\pi$
$151$		−	68.9051i		−	0.456325i	0.973623	−	0.228163i	$-0.0732718\pi$
$152$	−67.6977	−	29.3140i	−0.445379	−	0.192855i
$153$	−52.1238			−0.340678
$154$			10.2772i			0.0667352i
$155$		−	147.627i		−	0.952433i
$156$	118.949			0.762490
$157$	157.698			1.00444			0.502222	−	0.864739i	$-0.332516\pi$
$157$	157.698			1.00444			0.502222	+	0.864739i	$0.332516\pi$
$158$	−81.1478			−0.513594
$159$	−44.7010			−0.281138
$160$			274.700i			1.71687i
$161$	252.248			1.56675
$162$			27.4093i			0.169193i
$163$	−42.3987			−0.260115			−0.130057	−	0.991506i	$-0.541516\pi$
$163$	−42.3987			−0.260115			−0.130057	+	0.991506i	$0.541516\pi$
$164$			18.8799i			0.115122i
$165$		−	2.98793i		−	0.0181087i
$166$		−	273.172i		−	1.64561i
$167$			101.558i			0.608132i	0.952651	+	0.304066i	$0.0983443\pi$
$167$			101.558i			0.608132i	−0.952651	+	0.304066i	$0.901656\pi$
$168$	82.5498			0.491368
$169$	−0.498344			−0.00294878
$170$		−	332.030i		−	1.95312i
$171$	−22.6495	+	52.3068i	−0.132453	+	0.305888i
$172$	253.849			1.47587
$173$			24.3638i			0.140831i	0.997518	+	0.0704156i	$0.0224325\pi$
$173$			24.3638i			0.140831i	−0.997518	+	0.0704156i	$0.977567\pi$
$174$			137.350i			0.789367i
$175$	176.447			1.00827
$176$	−2.54983			−0.0144877
$177$	0.398675			0.00225240
$178$	−424.096			−2.38256
$179$		−	74.7659i		−	0.417687i	−0.977949	−	0.208843i	$-0.933030\pi$
$179$		−	74.7659i		−	0.417687i	0.977949	−	0.208843i	$-0.0669699\pi$
$180$	−99.2990			−0.551661
$181$		−	28.3199i		−	0.156463i	−0.996935	−	0.0782317i	$-0.975073\pi$
$181$		−	28.3199i		−	0.156463i	0.996935	−	0.0782317i	$-0.0249274\pi$
$182$	−486.694			−2.67414
$183$		−	49.9259i		−	0.272819i
$184$		−	79.7894i		−	0.433638i
$185$			418.978i			2.26475i
$186$		−	124.101i		−	0.667207i
$187$	4.77657			0.0255432
$188$	65.8007			0.350004
$189$		−	63.7823i		−	0.337473i
$190$	−333.196	−	144.278i	−1.75366	−	0.759358i
$191$	−237.973			−1.24593			−0.622965	−	0.782250i	$-0.714072\pi$
$191$	−237.973			−1.24593			−0.622965	+	0.782250i	$0.714072\pi$
$192$			166.664i			0.868041i
$193$		−	249.876i		−	1.29469i	−0.762196	−	0.647346i	$-0.775879\pi$
$193$		−	249.876i		−	1.29469i	0.762196	−	0.647346i	$-0.224121\pi$
$194$	−125.897			−0.648954
$195$	141.498			0.725633
$196$	−536.320			−2.73633
$197$	253.251			1.28554			0.642769	−	0.766060i	$-0.277786\pi$
$197$	253.251			1.28554			0.642769	+	0.766060i	$0.277786\pi$
$198$		−	2.51176i		−	0.0126857i
$199$	−48.0274			−0.241344			−0.120672	−	0.992692i	$-0.538505\pi$
$199$	−48.0274			−0.241344			−0.120672	+	0.992692i	$0.538505\pi$
$200$		−	55.8126i		−	0.279063i
$201$	−178.296			−0.887043
$202$			459.103i			2.27279i
$203$		−	319.618i		−	1.57447i
$204$		−	158.742i		−	0.778145i
$205$			22.4591i			0.109557i
$206$	69.5465			0.337604
$207$	−61.6495			−0.297824
$208$		−	120.752i		−	0.580536i
$209$	2.07558	−	4.79335i	0.00993100	−	0.0229347i
$210$	406.296			1.93474
$211$			278.279i			1.31886i	0.751767	+	0.659429i	$0.229202\pi$
$211$			278.279i			1.31886i	−0.751767	+	0.659429i	$0.770798\pi$
$212$		−	136.136i		−	0.642150i
$213$	186.598			0.876047
$214$	502.694			2.34904
$215$	301.973			1.40452
$216$	−20.1752			−0.0934039
$217$			288.786i			1.33081i
$218$	141.450			0.648854
$219$			19.3561i			0.0883840i
$220$	9.09967			0.0413621
$221$			226.202i			1.02354i
$222$			352.208i			1.58652i
$223$		−	67.6910i		−	0.303547i	−0.988415	−	0.151773i	$-0.951502\pi$
$223$		−	67.6910i		−	0.303547i	0.988415	−	0.151773i	$-0.0484984\pi$
$224$		−	537.364i		−	2.39895i
$225$	−43.1238			−0.191661
$226$	13.8970			0.0614912
$227$			409.224i			1.80275i	0.433039	+	0.901375i	$0.357441\pi$
$227$			409.224i			1.80275i	−0.433039	+	0.901375i	$0.642559\pi$
$228$	−159.299	−	68.9785i	−0.698680	−	0.302537i
$229$	−246.419			−1.07607			−0.538034	−	0.842923i	$-0.680833\pi$
$229$	−246.419			−1.07607			−0.538034	+	0.842923i	$0.680833\pi$
$230$		−	392.709i		−	1.70743i
$231$			5.84495i			0.0253028i
$232$	−101.100			−0.435774
$233$	−226.323			−0.971344			−0.485672	−	0.874141i	$-0.661425\pi$
$233$	−226.323			−0.971344			−0.485672	+	0.874141i	$0.661425\pi$
$234$	118.949			0.508327
$235$	78.2749			0.333085
$236$			1.21416i			0.00514473i
$237$	−46.1512			−0.194731
$238$			649.513i			2.72905i
$239$	69.1204			0.289207			0.144603	−	0.989490i	$-0.453809\pi$
$239$	69.1204			0.289207			0.144603	+	0.989490i	$0.453809\pi$
$240$			100.804i			0.420018i
$241$			108.486i			0.450150i	0.974341	+	0.225075i	$0.0722628\pi$
$241$			108.486i			0.450150i	−0.974341	+	0.225075i	$0.927737\pi$
$242$		−	368.272i		−	1.52179i
$243$			15.5885i			0.0641500i
$244$	152.048			0.623148
$245$	−637.993			−2.60405
$246$			18.8799i			0.0767477i
$247$	226.997	+	98.2924i	0.919015	+	0.397945i
$248$	91.3472			0.368335
$249$		−	155.361i		−	0.623940i
$250$			203.053i			0.812211i
$251$	46.7766			0.186361			0.0931804	−	0.995649i	$-0.470297\pi$
$251$	46.7766			0.186361			0.0931804	+	0.995649i	$0.470297\pi$
$252$	194.248			0.770823
$253$	5.64950			0.0223301
$254$	447.045			1.76002
$255$		−	188.835i		−	0.740530i
$256$	25.7218			0.100476
$257$		−	217.139i		−	0.844900i	−0.906386	−	0.422450i	$-0.861170\pi$
$257$		−	217.139i		−	0.844900i	0.906386	−	0.422450i	$-0.138830\pi$
$258$	253.849			0.983910
$259$		−	819.600i		−	3.16448i
$260$			430.930i			1.65742i
$261$			78.1149i			0.299291i
$262$		−	575.354i		−	2.19601i
$263$	−34.8796			−0.132622			−0.0663109	−	0.997799i	$-0.521123\pi$
$263$	−34.8796			−0.132622			−0.0663109	+	0.997799i	$0.521123\pi$
$264$	1.84884			0.00700319
$265$		−	161.944i		−	0.611109i
$266$	651.794	+	282.235i	2.45035	+	1.06103i
$267$	−241.196			−0.903356
$268$		−	542.995i		−	2.02610i
$269$			90.2335i			0.335441i	0.985835	+	0.167720i	$0.0536406\pi$
$269$			90.2335i			0.335441i	−0.985835	+	0.167720i	$0.946359\pi$
$270$	−99.2990			−0.367774
$271$	−144.997			−0.535043			−0.267522	−	0.963552i	$-0.586205\pi$
$271$	−144.997			−0.535043			−0.267522	+	0.963552i	$0.586205\pi$
$272$	−161.148			−0.592455
$273$	−276.797			−1.01391
$274$		−	217.223i		−	0.792784i
$275$	3.95182			0.0143703
$276$		−	187.752i		−	0.680261i
$277$	496.371			1.79195			0.895977	−	0.444100i	$-0.146477\pi$
$277$	496.371			1.79195			0.895977	+	0.444100i	$0.146477\pi$
$278$			132.703i			0.477350i
$279$		−	70.5796i		−	0.252974i
$280$			299.064i			1.06808i
$281$			187.459i			0.667112i	0.942730	+	0.333556i	$0.108249\pi$
$281$			187.459i			0.667112i	−0.942730	+	0.333556i	$0.891751\pi$
$282$	65.8007			0.233336
$283$	51.5739			0.182240			0.0911200	−	0.995840i	$-0.470955\pi$
$283$	51.5739			0.182240			0.0911200	+	0.995840i	$0.470955\pi$
$284$			568.280i			2.00098i
$285$	−189.498	−	82.0552i	−0.664906	−	0.287913i
$286$	−10.9003			−0.0381130
$287$		−	43.9343i		−	0.153081i
$288$			131.332i			0.456015i
$289$	12.8762			0.0445545
$290$	−497.595			−1.71584
$291$	−71.6013			−0.246053
$292$	−58.9485			−0.201878
$293$		−	82.6781i		−	0.282178i	−0.989997	−	0.141089i	$-0.954940\pi$
$293$		−	82.6781i		−	0.282178i	0.989997	−	0.141089i	$-0.0450603\pi$
$294$	−536.320			−1.82422
$295$			1.44433i			0.00489604i
$296$	−259.251			−0.875847
$297$		−	1.42851i		−	0.00480980i
$298$		−	218.290i		−	0.732517i
$299$			267.541i			0.894787i
$300$		−	131.332i		−	0.437774i
$301$	−590.715			−1.96251
$302$	209.849			0.694864
$303$			261.105i			0.861733i
$304$	−70.0241	+	161.714i	−0.230342	+	0.531953i
$305$	180.873			0.593026
$306$		−	158.742i		−	0.518763i
$307$			83.3053i			0.271353i	0.990753	+	0.135676i	$0.0433208\pi$
$307$			83.3053i			0.271353i	−0.990753	+	0.135676i	$0.956679\pi$
$308$	−17.8007			−0.0577944
$309$	39.5531			0.128004
$310$	449.595			1.45031
$311$	4.22674			0.0135908			0.00679540	−	0.999977i	$-0.497837\pi$
$311$	4.22674			0.0135908			0.00679540	+	0.999977i	$0.497837\pi$
$312$			87.5549i			0.280625i
$313$	−158.894			−0.507648			−0.253824	−	0.967250i	$-0.581688\pi$
$313$	−158.894			−0.507648			−0.253824	+	0.967250i	$0.581688\pi$
$314$			480.264i			1.52950i
$315$	231.072			0.733563
$316$		−	140.552i		−	0.444785i
$317$			278.572i			0.878777i	0.898297	+	0.439389i	$0.144805\pi$
$317$			278.572i			0.878777i	−0.898297	+	0.439389i	$0.855195\pi$
$318$		−	136.136i		−	0.428100i
$319$		−	7.15838i		−	0.0224401i
$320$	−603.794			−1.88686
$321$	285.897			0.890645
$322$			768.213i			2.38576i
$323$	131.175	−	302.936i	0.406115	−	0.937883i
$324$	−47.4743			−0.146525
$325$			187.145i			0.575831i
$326$		−	129.124i		−	0.396086i
$327$	80.4469			0.246015
$328$	−13.8970			−0.0423690
$329$	−153.120			−0.465412
$330$	9.09967			0.0275748
$331$			133.080i			0.402055i	0.979586	+	0.201027i	$0.0644281\pi$
$331$			133.080i			0.402055i	−0.979586	+	0.201027i	$0.935572\pi$
$332$	473.148			1.42514
$333$			200.311i			0.601534i
$334$	−309.292			−0.926025
$335$		−	645.934i		−	1.92816i
$336$		−	197.192i		−	0.586881i
$337$		−	351.831i		−	1.04401i	−0.852943	−	0.522004i	$-0.825185\pi$
$337$		−	351.831i		−	1.04401i	0.852943	−	0.522004i	$-0.174815\pi$
$338$		−	1.51770i		−	0.00449022i
$339$	7.90364			0.0233146
$340$	575.093			1.69145
$341$			6.46785i			0.0189673i
$342$	−159.299	−	68.9785i	−0.465787	−	0.201692i
$343$	646.564			1.88503
$344$			186.851i			0.543173i
$345$		−	223.345i		−	0.647378i
$346$	−74.1993			−0.214449
$347$	−348.124			−1.00324			−0.501619	−	0.865089i	$-0.667262\pi$
$347$	−348.124			−1.00324			−0.501619	+	0.865089i	$0.667262\pi$
$348$	−237.897			−0.683612
$349$	−614.323			−1.76024			−0.880119	−	0.474753i	$-0.842537\pi$
$349$	−614.323			−1.76024			−0.880119	+	0.474753i	$0.842537\pi$
$350$			537.364i			1.53533i
$351$	67.6495			0.192734
$352$		−	12.0352i		−	0.0341908i
$353$	151.292			0.428590			0.214295	−	0.976769i	$-0.431255\pi$
$353$	151.292			0.428590			0.214295	+	0.976769i	$0.431255\pi$
$354$			1.21416i			0.00342982i
$355$			676.012i			1.90426i
$356$		−	734.556i		−	2.06336i
$357$			369.397i			1.03473i
$358$	227.698			0.636027
$359$	497.519			1.38585			0.692924	−	0.721011i	$-0.256322\pi$
$359$	497.519			1.38585			0.692924	+	0.721011i	$0.256322\pi$
$360$		−	73.0914i		−	0.203032i
$361$	−247.000	−	263.272i	−0.684211	−	0.729285i
$362$	86.2475			0.238253
$363$		−	209.447i		−	0.576990i
$364$		−	842.979i		−	2.31588i
$365$	−70.1238			−0.192120
$366$	152.048			0.415432
$367$	−267.003			−0.727529			−0.363765	−	0.931491i	$-0.618509\pi$
$367$	−267.003			−0.727529			−0.363765	+	0.931491i	$0.618509\pi$
$368$	−190.598			−0.517929
$369$			10.7376i			0.0290991i
$370$	−1275.99			−3.44861
$371$			316.793i			0.853889i
$372$	214.949			0.577819
$373$		−	51.4695i		−	0.137988i	−0.997617	−	0.0689940i	$-0.978021\pi$
$373$		−	51.4695i		−	0.137988i	0.997617	−	0.0689940i	$-0.0219789\pi$
$374$			14.5469i			0.0388955i
$375$			115.482i			0.307952i
$376$			48.4341i			0.128814i
$377$	338.997			0.899195
$378$	194.248			0.513882
$379$			447.214i			1.17999i	0.807409	+	0.589993i	$0.200869\pi$
$379$			447.214i			1.17999i	−0.807409	+	0.589993i	$0.799131\pi$
$380$	249.897	−	577.112i	0.657624	−	1.51872i
$381$	254.248			0.667316
$382$		−	724.740i		−	1.89722i
$383$		−	201.839i		−	0.526994i	−0.964660	−	0.263497i	$-0.915124\pi$
$383$		−	201.839i		−	0.526994i	0.964660	−	0.263497i	$-0.0848759\pi$
$384$	−204.272			−0.531957
$385$	−21.1752			−0.0550006
$386$	760.990			1.97148
$387$	144.371			0.373052
$388$		−	218.060i		−	0.562010i
$389$	−26.7700			−0.0688174			−0.0344087	−	0.999408i	$-0.510955\pi$
$389$	−26.7700			−0.0688174			−0.0344087	+	0.999408i	$0.510955\pi$
$390$			430.930i			1.10495i
$391$	357.045			0.913158
$392$		−	394.771i		−	1.00707i
$393$		−	327.221i		−	0.832623i
$394$			771.269i			1.95754i
$395$		−	167.198i		−	0.423285i
$396$	4.35050			0.0109861
$397$	268.069			0.675237			0.337618	−	0.941283i	$-0.390379\pi$
$397$	268.069			0.675237			0.337618	+	0.941283i	$0.390379\pi$
$398$		−	146.266i		−	0.367503i
$399$	370.694	+	160.515i	0.929059	+	0.402294i
$400$	−133.323			−0.333308
$401$			445.540i			1.11107i	0.831492	+	0.555536i	$0.187487\pi$
$401$			445.540i			1.11107i	−0.831492	+	0.555536i	$0.812513\pi$
$402$		−	542.995i		−	1.35073i
$403$	−306.296			−0.760039
$404$	−795.189			−1.96829
$405$	−56.4743			−0.139443
$406$	973.389			2.39751
$407$		−	18.3563i		−	0.0451015i
$408$	116.846			0.286386
$409$		−	325.039i		−	0.794716i	−0.917664	−	0.397358i	$-0.869927\pi$
$409$		−	325.039i		−	0.794716i	0.917664	−	0.397358i	$-0.130073\pi$
$410$	−68.3987			−0.166826
$411$		−	123.541i		−	0.300586i
$412$			120.458i			0.292374i
$413$		−	2.82538i		−	0.00684112i
$414$		−	187.752i		−	0.453507i
$415$	562.846			1.35625
$416$	569.945			1.37006
$417$			75.4722i			0.180989i
$418$	14.5980	+	6.32113i	0.0349235	+	0.0151223i
$419$	−51.0033			−0.121726			−0.0608631	−	0.998146i	$-0.519385\pi$
$419$	−51.0033			−0.121726			−0.0608631	+	0.998146i	$0.519385\pi$
$420$			703.725i			1.67554i
$421$			214.794i			0.510201i	0.966915	+	0.255100i	$0.0821085\pi$
$421$			214.794i			0.510201i	−0.966915	+	0.255100i	$0.917892\pi$
$422$	−847.492			−2.00827
$423$	37.4228			0.0884699
$424$	100.206			0.236335
$425$	249.752			0.587653
$426$			568.280i			1.33399i
$427$	−353.821			−0.828622
$428$			870.692i			2.03433i
$429$	−6.19934			−0.0144507
$430$			919.650i			2.13872i
$431$		−	469.547i		−	1.08944i	−0.838619	−	0.544718i	$-0.816637\pi$
$431$		−	469.547i		−	1.08944i	0.838619	−	0.544718i	$-0.183363\pi$
$432$			48.1939i			0.111560i
$433$			175.110i			0.404411i	0.979343	+	0.202205i	$0.0648108\pi$
$433$			175.110i			0.404411i	−0.979343	+	0.202205i	$0.935189\pi$
$434$	−879.492			−2.02648
$435$	−282.997			−0.650567
$436$			244.999i			0.561924i
$437$	155.148	−	358.299i	0.355029	−	0.819905i
$438$	−58.9485			−0.134586
$439$			542.848i			1.23656i	0.785959	+	0.618278i	$0.212170\pi$
$439$			542.848i			1.23656i	−0.785959	+	0.618278i	$0.787830\pi$
$440$			6.69803i			0.0152228i
$441$	−305.021			−0.691657
$442$	−688.894			−1.55858
$443$	134.680			0.304019			0.152009	−	0.988379i	$-0.451426\pi$
$443$	134.680			0.304019			0.152009	+	0.988379i	$0.451426\pi$
$444$	−610.042			−1.37397
$445$		−	873.811i		−	1.96362i
$446$	206.151			0.462222
$447$		−	124.148i		−	0.277736i
$448$	1181.13			2.63646
$449$			722.541i			1.60922i	0.593801	+	0.804612i	$0.297627\pi$
$449$			722.541i			1.60922i	−0.593801	+	0.804612i	$0.702373\pi$
$450$		−	131.332i		−	0.291850i
$451$		−	0.983981i		−	0.00218178i
$452$			24.0703i			0.0532530i
$453$	119.347			0.263460
$454$	−1246.28			−2.74512
$455$		−	1002.79i		−	2.20393i
$456$	50.7733	−	117.256i	0.111345	−	0.257140i
$457$	−42.7218			−0.0934831			−0.0467415	−	0.998907i	$-0.514884\pi$
$457$	−42.7218			−0.0934831			−0.0467415	+	0.998907i	$0.514884\pi$
$458$		−	750.464i		−	1.63857i
$459$		−	90.2810i		−	0.196691i
$460$	680.193			1.47868
$461$	39.6221			0.0859482			0.0429741	−	0.999076i	$-0.486317\pi$
$461$	39.6221			0.0859482			0.0429741	+	0.999076i	$0.486317\pi$
$462$	−17.8007			−0.0385296
$463$	−158.625			−0.342603			−0.171302	−	0.985219i	$-0.554797\pi$
$463$	−158.625			−0.342603			−0.171302	+	0.985219i	$0.554797\pi$
$464$			241.503i			0.520481i
$465$	255.698			0.549887
$466$		−	689.261i		−	1.47910i
$467$	−672.619			−1.44030			−0.720149	−	0.693820i	$-0.755926\pi$
$467$	−672.619			−1.44030			−0.720149	+	0.693820i	$0.755926\pi$
$468$			206.025i			0.440224i
$469$			1263.57i			2.69418i
$470$			238.384i			0.507201i
$471$			273.140i			0.579916i
$472$	−0.893709			−0.00189345
$473$	−13.2300			−0.0279705
$474$		−	140.552i		−	0.296524i
$475$	108.526	−	250.629i	0.228475	−	0.527641i
$476$	−1124.99			−2.36342
$477$		−	77.4244i		−	0.162315i
$478$			210.505i			0.440386i
$479$	870.846			1.81805			0.909025	−	0.416743i	$-0.136828\pi$
$479$	870.846			1.81805			0.909025	+	0.416743i	$0.136828\pi$
$480$	−475.794			−0.991238
$481$	869.292			1.80726
$482$	−330.392			−0.685461
$483$			436.906i			0.904566i
$484$	637.866			1.31791
$485$		−	259.399i		−	0.534843i
$486$	−47.4743			−0.0976837
$487$		−	274.616i		−	0.563894i	−0.959430	−	0.281947i	$-0.909020\pi$
$487$		−	274.616i		−	0.563894i	0.959430	−	0.281947i	$-0.0909802\pi$
$488$			111.919i			0.229342i
$489$		−	73.4367i		−	0.150177i
$490$		−	1942.99i		−	3.96529i
$491$	−781.588			−1.59183			−0.795915	−	0.605409i	$-0.793010\pi$
$491$	−781.588			−1.59183			−0.795915	+	0.605409i	$0.793010\pi$
$492$	−32.7010			−0.0664654
$493$		−	452.405i		−	0.917657i
$494$	−299.347	+	691.313i	−0.605966	+	1.39942i
$495$	5.17525			0.0104550
$496$		−	218.207i		−	0.439933i
$497$		−	1322.41i		−	2.66078i
$498$	473.148			0.950096
$499$	−387.918			−0.777390			−0.388695	−	0.921366i	$-0.627074\pi$
$499$	−387.918			−0.777390			−0.388695	+	0.921366i	$0.627074\pi$
$500$	−351.698			−0.703395
$501$	−175.904			−0.351105
$502$			142.457i			0.283779i
$503$	−914.846			−1.81878			−0.909389	−	0.415946i	$-0.863450\pi$
$503$	−914.846			−1.81878			−0.909389	+	0.415946i	$0.863450\pi$
$504$			142.981i			0.283691i
$505$	−945.939			−1.87315
$506$			17.2054i			0.0340028i
$507$		−	0.863158i		−	0.00170248i
$508$			774.304i			1.52422i
$509$		−	185.554i		−	0.364546i	−0.983248	−	0.182273i	$-0.941655\pi$
$509$		−	185.554i		−	0.364546i	0.983248	−	0.182273i	$-0.0583455\pi$
$510$	575.093			1.12763
$511$	137.175			0.268445
$512$			550.080i			1.07438i
$513$	−90.5980	−	39.2301i	−0.176604	−	0.0764719i
$514$	661.292			1.28656
$515$			143.294i			0.278241i
$516$			439.679i			0.852091i
$517$	−3.42939			−0.00663324
$518$	2496.07			4.81867
$519$	−42.1993			−0.0813089
$520$	−317.196			−0.609992
$521$			212.283i			0.407452i	0.979028	+	0.203726i	$0.0653052\pi$
$521$			212.283i			0.407452i	−0.979028	+	0.203726i	$0.934695\pi$
$522$	−237.897			−0.455741
$523$			209.227i			0.400052i	0.979791	+	0.200026i	$0.0641026\pi$
$523$			209.227i			0.400052i	−0.979791	+	0.200026i	$0.935897\pi$
$524$	996.543			1.90180
$525$			305.615i			0.582124i
$526$		−	106.225i		−	0.201948i
$527$			408.764i			0.775643i
$528$		−	4.41644i		−	0.00836447i
$529$	−106.704			−0.201709
$530$	493.196			0.930559
$531$			0.690526i			0.00130043i
$532$	−488.846	+	1128.94i	−0.918883	+	2.12207i
$533$	46.5980			0.0874259
$534$		−	734.556i		−	1.37557i
$535$			1035.75i			1.93599i
$536$	399.684			0.745680
$537$	129.498			0.241151
$538$	−274.804			−0.510788
$539$	27.9518			0.0518587
$540$		−	171.991i		−	0.318502i
$541$	989.664			1.82932			0.914661	−	0.404221i	$-0.132457\pi$
$541$	989.664			1.82932			0.914661	+	0.404221i	$0.132457\pi$
$542$		−	441.584i		−	0.814730i
$543$	49.0515			0.0903342
$544$		−	760.615i		−	1.39819i
$545$			291.445i			0.534761i
$546$		−	842.979i		−	1.54392i
$547$		−	851.749i		−	1.55713i	−0.627565	−	0.778564i	$-0.715948\pi$
$547$		−	851.749i		−	1.55713i	0.627565	−	0.778564i	$-0.284052\pi$
$548$	376.241			0.686571
$549$	86.4743			0.157512
$550$			12.0352i			0.0218821i
$551$	−453.993	−	196.585i	−0.823944	−	0.356778i
$552$	138.199			0.250361
$553$			327.070i			0.591446i
$554$			1511.69i			2.72868i
$555$	−725.691			−1.30755
$556$	−229.849			−0.413397
$557$	125.423			0.225176			0.112588	−	0.993642i	$-0.464086\pi$
$557$	125.423			0.225176			0.112588	+	0.993642i	$0.464086\pi$
$558$	214.949			0.385212
$559$		−	626.531i		−	1.12081i
$560$	714.392			1.27570
$561$			8.27327i			0.0147474i
$562$	−570.900			−1.01584
$563$			762.666i			1.35465i	0.735685	+	0.677324i	$0.236860\pi$
$563$			762.666i			1.35465i	−0.735685	+	0.677324i	$0.763140\pi$
$564$			113.970i			0.202075i
$565$			28.6335i			0.0506788i
$566$			157.067i			0.277504i
$567$	110.474			0.194840
$568$	−418.296			−0.736436
$569$			598.818i			1.05240i	0.850360	+	0.526202i	$0.176384\pi$
$569$			598.818i			1.05240i	−0.850360	+	0.526202i	$0.823616\pi$
$570$	249.897	−	577.112i	0.438416	−	1.01248i
$571$	−165.492			−0.289828			−0.144914	−	0.989444i	$-0.546291\pi$
$571$	−165.492			−0.289828			−0.144914	+	0.989444i	$0.546291\pi$
$572$		−	18.8799i		−	0.0330069i
$573$		−	412.181i		−	0.719338i
$574$	133.801			0.233102
$575$	295.395			0.513731
$576$	−288.670			−0.501164
$577$	852.262			1.47706			0.738528	−	0.674222i	$-0.235521\pi$
$577$	852.262			1.47706			0.738528	+	0.674222i	$0.235521\pi$
$578$			39.2143i			0.0678448i
$579$	432.797			0.747491
$580$		−	861.859i		−	1.48596i
$581$	−1101.03			−1.89506
$582$		−	218.060i		−	0.374674i
$583$			7.09510i			0.0121700i
$584$		−	43.3905i		−	0.0742987i
$585$			245.082i			0.418944i
$586$	251.794			0.429683
$587$	429.375			0.731473			0.365736	−	0.930718i	$-0.380817\pi$
$587$	429.375			0.731473			0.365736	+	0.930718i	$0.380817\pi$
$588$		−	928.933i		−	1.57982i
$589$	410.199	+	177.622i	0.696434	+	0.301565i
$590$	−4.39868			−0.00745538
$591$			438.643i			0.742205i
$592$			619.289i			1.04610i
$593$	−243.100			−0.409949			−0.204974	−	0.978767i	$-0.565711\pi$
$593$	−243.100			−0.409949			−0.204974	+	0.978767i	$0.565711\pi$
$594$	4.35050			0.00732407
$595$	−1338.26			−2.24918
$596$	378.090			0.634379
$597$		−	83.1859i		−	0.139340i
$598$	−814.791			−1.36253
$599$		−	725.096i		−	1.21051i	−0.796031	−	0.605256i	$-0.793071\pi$
$599$		−	725.096i		−	1.21051i	0.796031	−	0.605256i	$-0.206929\pi$
$600$	96.6703			0.161117
$601$		−	595.929i		−	0.991563i	−0.868447	−	0.495781i	$-0.834882\pi$
$601$		−	595.929i		−	0.991563i	0.868447	−	0.495781i	$-0.165118\pi$
$602$		−	1799.01i		−	2.98839i
$603$		−	308.817i		−	0.512135i
$604$			363.469i			0.601770i
$605$	758.791			1.25420
$606$	−795.189			−1.31219
$607$		−	724.886i		−	1.19421i	−0.802163	−	0.597106i	$-0.796317\pi$
$607$		−	724.886i		−	1.19421i	0.802163	−	0.597106i	$-0.203683\pi$
$608$	−763.286	−	330.512i	−1.25540	−	0.543606i
$609$	553.595			0.909022
$610$			550.844i			0.903023i
$611$		−	162.404i		−	0.265801i
$612$	274.949			0.449262
$613$	499.368			0.814630			0.407315	−	0.913288i	$-0.366465\pi$
$613$	499.368			0.814630			0.407315	+	0.913288i	$0.366465\pi$
$614$	−253.704			−0.413199
$615$	−38.9003			−0.0632526
$616$		−	13.1026i		−	0.0212705i
$617$	−87.2300			−0.141378			−0.0706889	−	0.997498i	$-0.522520\pi$
$617$	−87.2300			−0.141378			−0.0706889	+	0.997498i	$0.522520\pi$
$618$			120.458i			0.194916i
$619$	−846.482			−1.36750			−0.683749	−	0.729717i	$-0.739652\pi$
$619$	−846.482			−1.36750			−0.683749	+	0.729717i	$0.739652\pi$
$620$			778.721i			1.25600i
$621$		−	106.780i		−	0.171949i
$622$			12.8724i			0.0206952i
$623$			1709.34i			2.74372i
$624$	209.148			0.335173
$625$	−777.736			−1.24438
$626$		−	483.907i		−	0.773014i
$627$	8.30232	+	3.59501i	0.0132413	+	0.00573367i
$628$	−831.842			−1.32459
$629$		−	1160.11i		−	1.84437i
$630$			703.725i			1.11702i
$631$	−800.509			−1.26864			−0.634318	−	0.773072i	$-0.718719\pi$
$631$	−800.509			−1.26864			−0.634318	+	0.773072i	$0.718719\pi$
$632$	103.457			0.163697
$633$	−481.993			−0.761443
$634$	−848.385			−1.33815
$635$			921.094i			1.45054i
$636$	235.794			0.370745
$637$			1323.70i			2.07803i
$638$	21.8007			0.0341703
$639$			323.197i			0.505786i
$640$		−	740.040i		−	1.15631i
$641$		−	492.363i		−	0.768117i	−0.923309	−	0.384058i	$-0.874526\pi$
$641$		−	492.363i		−	0.768117i	0.923309	−	0.384058i	$-0.125474\pi$
$642$			870.692i			1.35622i
$643$	1212.76			1.88609			0.943046	−	0.332663i	$-0.107947\pi$
$643$	1212.76			1.88609			0.943046	+	0.332663i	$0.107947\pi$
$644$	−1330.58			−2.06613
$645$			523.032i			0.810902i
$646$	922.585	+	399.491i	1.42815	+	0.618407i
$647$	−157.368			−0.243227			−0.121614	−	0.992578i	$-0.538807\pi$
$647$	−157.368			−0.243227			−0.121614	+	0.992578i	$0.538807\pi$
$648$		−	34.9446i		−	0.0539268i
$649$		−	0.0632792i		−	9.75026e-5i
$650$	−569.945			−0.876839
$651$	−500.193			−0.768345
$652$	223.650			0.343021
$653$	726.220			1.11213			0.556064	−	0.831139i	$-0.312311\pi$
$653$	726.220			1.11213			0.556064	+	0.831139i	$0.312311\pi$
$654$			244.999i			0.374616i
$655$	1185.46			1.80987
$656$			33.1967i			0.0506047i
$657$	−33.5257			−0.0510285
$658$		−	466.324i		−	0.708700i
$659$		−	259.756i		−	0.394167i	−0.980387	−	0.197083i	$-0.936853\pi$
$659$		−	259.756i		−	0.394167i	0.980387	−	0.197083i	$-0.0631469\pi$
$660$			15.7611i			0.0238804i
$661$			874.021i			1.32227i	0.750267	+	0.661135i	$0.229925\pi$
$661$			874.021i			1.32227i	−0.750267	+	0.661135i	$0.770075\pi$
$662$	−405.292			−0.612224
$663$	−391.794			−0.590941
$664$			348.272i			0.524506i
$665$	−581.519	+	1342.96i	−0.874465	+	2.01949i
$666$	−610.042			−0.915978
$667$		−	535.083i		−	0.802223i
$668$		−	535.710i		−	0.801961i
$669$	117.244			0.175253
$670$	1967.18			2.93608
$671$	−7.92442			−0.0118099
$672$	930.743			1.38503
$673$		−	1035.99i		−	1.53935i	−0.638434	−	0.769677i	$-0.720417\pi$
$673$		−	1035.99i		−	1.53935i	0.638434	−	0.769677i	$-0.279583\pi$
$674$	1071.49			1.58975
$675$		−	74.6925i		−	0.110656i
$676$	2.62873			0.00388865
$677$		−	973.505i		−	1.43797i	−0.695026	−	0.718984i	$-0.744607\pi$
$677$		−	973.505i		−	1.43797i	0.695026	−	0.718984i	$-0.255393\pi$
$678$			24.0703i			0.0355020i
$679$			507.433i			0.747325i
$680$			423.311i			0.622516i
$681$	−708.797			−1.04082
$682$	−19.6977			−0.0288822
$683$			1186.44i			1.73710i	0.495604	+	0.868549i	$0.334947\pi$
$683$			1186.44i			1.73710i	−0.495604	+	0.868549i	$0.665053\pi$
$684$	119.474	−	275.914i	0.174670	−	0.403383i
$685$	447.567			0.653383
$686$			1969.09i			2.87040i
$687$		−	426.811i		−	0.621268i
$688$	446.344			0.648756
$689$	−336.000			−0.487663
$690$	680.193			0.985787
$691$	563.670			0.815731			0.407866	−	0.913042i	$-0.366273\pi$
$691$	563.670			0.815731			0.407866	+	0.913042i	$0.366273\pi$
$692$		−	128.517i		−	0.185718i
$693$	−10.1238			−0.0146086
$694$		−	1060.20i		−	1.52767i
$695$	−273.423			−0.393414
$696$		−	175.110i		−	0.251594i
$697$		−	62.1869i		−	0.0892209i
$698$		−	1870.91i		−	2.68038i
$699$		−	392.003i		−	0.560806i
$700$	−930.743			−1.32963
$701$	−163.958			−0.233892			−0.116946	−	0.993138i	$-0.537310\pi$
$701$	−163.958			−0.233892			−0.116946	+	0.993138i	$0.537310\pi$
$702$			206.025i			0.293483i
$703$	−1164.18	−	504.104i	−1.65602	−	0.717076i
$704$	26.4535			0.0375760
$705$			135.576i			0.192307i
$706$			460.757i			0.652631i
$707$	1850.43			2.61730
$708$	−2.10298			−0.00297031
$709$	−315.993			−0.445689			−0.222844	−	0.974854i	$-0.571534\pi$
$709$	−315.993			−0.445689			−0.222844	+	0.974854i	$0.571534\pi$
$710$	−2058.78			−2.89969
$711$		−	79.9362i		−	0.112428i
$712$	540.688			0.759393
$713$			483.467i			0.678074i
$714$	−1124.99			−1.57562
$715$		−	22.4591i		−	0.0314114i
$716$			394.384i			0.550816i
$717$			119.720i			0.166974i
$718$			1515.18i			2.11028i
$719$	−171.072			−0.237931			−0.118965	−	0.992898i	$-0.537958\pi$
$719$	−171.072			−0.237931			−0.118965	+	0.992898i	$0.537958\pi$
$720$	−174.598			−0.242497
$721$		−	280.310i		−	0.388780i
$722$	801.787	−	752.232i	1.11051	−	1.04187i
$723$	−187.904			−0.259894
$724$			149.385i			0.206333i
$725$		−	374.290i		−	0.516262i
$726$	637.866			0.878604
$727$	261.169			0.359242			0.179621	−	0.983736i	$-0.442513\pi$
$727$	261.169			0.359242			0.179621	+	0.983736i	$0.442513\pi$
$728$	620.495			0.852328
$729$	−27.0000			−0.0370370
$730$		−	213.560i		−	0.292548i
$731$	−836.130			−1.14382
$732$			263.355i			0.359775i
$733$	1185.78			1.61771			0.808855	−	0.588009i	$-0.200088\pi$
$733$	1185.78			1.61771			0.808855	+	0.588009i	$0.200088\pi$
$734$		−	813.152i		−	1.10784i
$735$		−	1105.04i		−	1.50345i
$736$		−	899.619i		−	1.22231i
$737$			28.2997i			0.0383985i
$738$	−32.7010			−0.0443103
$739$	738.557			0.999401			0.499701	−	0.866198i	$-0.333443\pi$
$739$	738.557			0.999401			0.499701	+	0.866198i	$0.333443\pi$
$740$		−	2210.07i		−	2.98659i
$741$	−170.248	+	393.170i	−0.229754	+	0.530594i
$742$	−964.784			−1.30025
$743$			809.783i			1.08988i	0.838474	+	0.544941i	$0.183448\pi$
$743$			809.783i			1.08988i	−0.838474	+	0.544941i	$0.816552\pi$
$744$			158.218i			0.212659i
$745$	449.767			0.603714
$746$	156.749			0.210120
$747$	269.093			0.360232
$748$	−25.1960			−0.0336845
$749$		−	2026.13i		−	2.70512i
$750$	−351.698			−0.468930
$751$		−	1167.89i		−	1.55512i	−0.628809	−	0.777559i	$-0.716457\pi$
$751$		−	1167.89i		−	1.55512i	0.628809	−	0.777559i	$-0.283543\pi$
$752$	115.698			0.153853
$753$			81.0194i			0.107595i
$754$			1032.41i			1.36924i
$755$			432.374i			0.572681i
$756$			336.447i			0.445035i
$757$	−161.828			−0.213776			−0.106888	−	0.994271i	$-0.534089\pi$
$757$	−161.828			−0.213776			−0.106888	+	0.994271i	$0.534089\pi$
$758$	−1361.98			−1.79681
$759$			9.78523i			0.0128923i
$760$	424.797	+	183.943i	0.558944	+	0.242030i
$761$	1148.47			1.50916			0.754578	−	0.656210i	$-0.227842\pi$
$761$	1148.47			1.50916			0.754578	+	0.656210i	$0.227842\pi$
$762$			774.304i			1.01615i
$763$		−	570.121i		−	0.747210i
$764$	1255.29			1.64304
$765$	327.072			0.427545
$766$	614.694			0.802473
$767$	2.99669			0.00390703
$768$			44.5514i			0.0580097i
$769$	77.5673			0.100868			0.0504339	−	0.998727i	$-0.483940\pi$
$769$	77.5673			0.100868			0.0504339	+	0.998727i	$0.483940\pi$
$770$		−	64.4887i		−	0.0837515i
$771$	376.096			0.487803
$772$			1318.07i			1.70735i
$773$		−	1165.42i		−	1.50766i	−0.657068	−	0.753831i	$-0.728204\pi$
$773$		−	1165.42i		−	1.50766i	0.657068	−	0.753831i	$-0.271796\pi$
$774$			439.679i			0.568061i
$775$			338.184i			0.436367i
$776$	160.508			0.206841
$777$	1419.59			1.82701
$778$		−	81.5272i		−	0.104791i
$779$	−62.4053	−	27.0223i	−0.0801095	−	0.0346884i
$780$	−746.392			−0.956913
$781$		−	29.6175i		−	0.0379225i
$782$			1087.37i			1.39050i
$783$	−135.299			−0.172796
$784$	−943.014			−1.20282
$785$	−989.540			−1.26056
$786$	996.543			1.26787
$787$			1141.88i			1.45092i	0.688263	+	0.725461i	$0.258374\pi$
$787$			1141.88i			1.45092i	−0.688263	+	0.725461i	$0.741626\pi$
$788$	−1335.88			−1.69528
$789$		−	60.4132i		−	0.0765693i
$790$	509.196			0.644552
$791$		−	56.0125i		−	0.0708123i
$792$			3.20229i			0.00404329i
$793$		−	375.274i		−	0.473233i
$794$			816.397i			1.02821i
$795$	280.495			0.352824
$796$	253.341			0.318267
$797$		−	798.061i		−	1.00133i	−0.865641	−	0.500666i	$-0.833089\pi$
$797$		−	798.061i		−	1.00133i	0.865641	−	0.500666i	$-0.166911\pi$
$798$	−488.846	+	1128.94i	−0.612588	+	1.41471i
$799$	−216.735			−0.271258
$800$		−	629.283i		−	0.786603i
$801$		−	417.764i		−	0.521553i
$802$	−1356.88			−1.69187
$803$	3.07227			0.00382599
$804$	940.495			1.16977
$805$	−1582.83			−1.96625
$806$		−	932.816i		−	1.15734i
$807$	−156.289			−0.193667
$808$		−	585.318i		−	0.724404i
$809$	879.175			1.08674			0.543372	−	0.839492i	$-0.317147\pi$
$809$	879.175			1.08674			0.543372	+	0.839492i	$0.317147\pi$
$810$		−	171.991i		−	0.212334i
$811$			654.537i			0.807074i	0.914963	+	0.403537i	$0.132219\pi$
$811$			654.537i			0.807074i	−0.914963	+	0.403537i	$0.867781\pi$
$812$			1685.96i			2.07630i
$813$		−	251.142i		−	0.308907i
$814$	55.9036			0.0686777
$815$	266.048			0.326439
$816$		−	279.116i		−	0.342054i
$817$	−363.326	+	839.066i	−0.444708	+	1.02701i
$818$	989.897			1.21014
$819$		−	479.427i		−	0.585381i
$820$		−	118.470i		−	0.144476i
$821$	−1419.35			−1.72880			−0.864402	−	0.502801i	$-0.832303\pi$
$821$	−1419.35			−1.72880			−0.864402	+	0.502801i	$0.832303\pi$
$822$	376.241			0.457714
$823$	−671.107			−0.815440			−0.407720	−	0.913107i	$-0.633676\pi$
$823$	−671.107			−0.815440			−0.407720	+	0.913107i	$0.633676\pi$
$824$	−88.6661			−0.107604
$825$			6.84476i			0.00829667i
$826$	8.60464			0.0104172
$827$		−	186.204i		−	0.225156i	−0.993643	−	0.112578i	$-0.964089\pi$
$827$		−	186.204i		−	0.225156i	0.993643	−	0.112578i	$-0.0359108\pi$
$828$	325.196			0.392749
$829$			924.130i			1.11475i	0.830260	+	0.557376i	$0.188192\pi$
$829$			924.130i			1.11475i	−0.830260	+	0.557376i	$0.811808\pi$
$830$			1714.13i			2.06522i
$831$			859.740i			1.03459i
$832$			1252.75i			1.50571i
$833$	1766.54			2.12069
$834$	−229.849			−0.275598
$835$		−	637.268i		−	0.763195i
$836$	−10.9485	+	25.2845i	−0.0130963	+	0.0302446i
$837$	122.248			0.146054
$838$		−	155.329i		−	0.185357i
$839$			934.157i			1.11342i	0.830708	+	0.556708i	$0.187936\pi$
$839$			934.157i			1.11342i	−0.830708	+	0.556708i	$0.812064\pi$
$840$	−517.993			−0.616659
$841$	163.007			0.193825
$842$	−654.151			−0.776902
$843$	−324.688			−0.385157
$844$		−	1467.90i		−	1.73922i
$845$	3.12707			0.00370067
$846$			113.970i			0.134716i
$847$	−1484.34			−1.75246
$848$		−	239.368i		−	0.282274i
$849$			89.3287i			0.105216i
$850$			760.615i			0.894841i
$851$		−	1372.12i		−	1.61236i
$852$	−984.289			−1.15527
$853$	344.405			0.403758			0.201879	−	0.979411i	$-0.435295\pi$
$853$	344.405			0.403758			0.201879	+	0.979411i	$0.435295\pi$
$854$		−	1077.55i		−	1.26177i
$855$	142.124	−	328.221i	0.166227	−	0.383884i
$856$	−640.894			−0.748708
$857$			931.245i			1.08663i	0.839528	+	0.543317i	$0.182832\pi$
$857$			931.245i			1.08663i	−0.839528	+	0.543317i	$0.817168\pi$
$858$		−	18.8799i		−	0.0220046i
$859$	−1072.73			−1.24881			−0.624405	−	0.781100i	$-0.714659\pi$
$859$	−1072.73			−1.24881			−0.624405	+	0.781100i	$0.714659\pi$
$860$	−1592.88			−1.85219
$861$	76.0964			0.0883814
$862$	1429.99			1.65893
$863$			1240.65i			1.43760i	0.695217	+	0.718800i	$0.255308\pi$
$863$			1240.65i			1.43760i	−0.695217	+	0.718800i	$0.744692\pi$
$864$	−227.474			−0.263280
$865$		−	152.881i		−	0.176741i
$866$	−533.292			−0.615811
$867$			22.3023i			0.0257235i
$868$		−	1523.32i		−	1.75498i
$869$			7.32527i			0.00842955i
$870$		−	861.859i		−	0.990643i
$871$	−1340.18			−1.53867
$872$	−180.337			−0.206809
$873$		−	124.017i		−	0.142059i
$874$	1091.19	+	472.499i	1.24850	+	0.540617i
$875$	818.413			0.935329
$876$		−	102.102i		−	0.116555i
$877$			526.564i			0.600415i	0.953874	+	0.300207i	$0.0970559\pi$
$877$			526.564i			0.600415i	−0.953874	+	0.300207i	$0.902944\pi$
$878$	−1653.23			−1.88295
$879$	143.203			0.162915
$880$	16.0000			0.0181818
$881$	1444.25			1.63933			0.819664	−	0.572844i	$-0.194160\pi$
$881$	1444.25			1.63933			0.819664	+	0.572844i	$0.194160\pi$
$882$		−	928.933i		−	1.05321i
$883$	593.086			0.671671			0.335836	−	0.941921i	$-0.390981\pi$
$883$	593.086			0.671671			0.335836	+	0.941921i	$0.390981\pi$
$884$		−	1193.20i		−	1.34977i
$885$	−2.50166			−0.00282673
$886$			410.165i			0.462940i
$887$			589.691i			0.664816i	0.943136	+	0.332408i	$0.107861\pi$
$887$			589.691i			0.664816i	−0.943136	+	0.332408i	$0.892139\pi$
$888$		−	449.036i		−	0.505671i
$889$		−	1801.83i		−	2.02681i
$890$	2661.17			2.99008
$891$	2.47425			0.00277694
$892$			357.064i			0.400296i
$893$	−94.1786	+	217.496i	−0.105463	+	0.243557i
$894$	378.090			0.422919
$895$			469.150i			0.524190i
$896$			1447.66i			1.61569i
$897$	−463.395			−0.516606
$898$	−2200.48			−2.45043
$899$	612.591			0.681414
$900$	227.474			0.252749
$901$			448.406i			0.497675i
$902$	2.99669			0.00332227
$903$		−	1023.15i		−	1.13305i
$904$	−17.7175			−0.0195991
$905$			177.705i			0.196359i
$906$			363.469i			0.401180i
$907$			164.499i			0.181366i	0.995880	+	0.0906829i	$0.0289050\pi$
$907$			164.499i			0.181366i	−0.995880	+	0.0906829i	$0.971095\pi$
$908$		−	2158.62i		−	2.37734i
$909$	−452.248			−0.497522
$910$	3053.97			3.35601
$911$			474.507i			0.520864i	0.965492	+	0.260432i	$0.0838650\pi$
$911$			474.507i			0.520864i	−0.965492	+	0.260432i	$0.916135\pi$
$912$	−280.096	−	121.285i	−0.307123	−	0.132988i
$913$	−24.6594			−0.0270092
$914$		−	130.108i		−	0.142350i
$915$			313.281i			0.342384i
$916$	1299.84			1.41904
$917$	−2318.99			−2.52889
$918$	274.949			0.299508
$919$	708.488			0.770934			0.385467	−	0.922722i	$-0.374040\pi$
$919$	708.488			0.770934			0.385467	+	0.922722i	$0.374040\pi$
$920$			500.672i			0.544209i
$921$	−144.289			−0.156666
$922$			120.668i			0.130876i
$923$	1402.58			1.51959
$924$		−	30.8317i		−	0.0333676i
$925$		−	959.795i		−	1.03762i
$926$		−	483.090i		−	0.521695i
$927$			68.5081i			0.0739030i
$928$	−1139.89			−1.22833
$929$	154.482			0.166288			0.0831441	−	0.996538i	$-0.473504\pi$
$929$	154.482			0.166288			0.0831441	+	0.996538i	$0.473504\pi$
$930$			778.721i			0.837334i
$931$	767.619	−	1772.74i	0.824510	−	1.90412i
$932$	1193.84			1.28094
$933$			7.32093i			0.00784665i
$934$		−	2048.44i		−	2.19319i
$935$	−29.9726			−0.0320563
$936$	−151.650			−0.162019
$937$	−289.223			−0.308670			−0.154335	−	0.988019i	$-0.549323\pi$
$937$	−289.223			−0.308670			−0.154335	+	0.988019i	$0.549323\pi$
$938$	−3848.17			−4.10252
$939$		−	275.212i		−	0.293090i
$940$	−412.894			−0.439249
$941$			1484.31i			1.57738i	0.614794	+	0.788688i	$0.289239\pi$
$941$			1484.31i			1.57738i	−0.614794	+	0.788688i	$0.710761\pi$
$942$	−831.842			−0.883060
$943$		−	73.5517i		−	0.0779976i
$944$			2.13486i			0.00226150i
$945$			400.229i			0.423523i
$946$		−	40.2918i		−	0.0425917i
$947$	222.206			0.234642			0.117321	−	0.993094i	$-0.462569\pi$
$947$	222.206			0.234642			0.117321	+	0.993094i	$0.462569\pi$
$948$	243.444			0.256797
$949$			145.492i			0.153311i
$950$	763.286	+	330.512i	0.803459	+	0.347908i
$951$	−482.502			−0.507362
$952$		−	828.076i		−	0.869827i
$953$			1149.54i			1.20623i	0.797655	+	0.603114i	$0.206074\pi$
$953$			1149.54i			1.20623i	−0.797655	+	0.603114i	$0.793926\pi$
$954$	235.794			0.247164
$955$	1493.26			1.56362
$956$	−364.605			−0.381386
$957$	12.3987			0.0129558
$958$			2652.14i			2.76841i
$959$	−875.526			−0.912957
$960$		−	1045.80i		−	1.08938i
$961$	407.502			0.424039
$962$			2647.41i			2.75198i
$963$			495.188i			0.514214i
$964$		−	572.256i		−	0.593626i
$965$			1567.95i			1.62482i
$966$	−1330.58			−1.37742
$967$	980.296			1.01375			0.506875	−	0.862020i	$-0.330801\pi$
$967$	980.296			1.01375			0.506875	+	0.862020i	$0.330801\pi$
$968$			469.517i			0.485038i
$969$	524.701	+	227.202i	0.541487	+	0.234471i
$970$	789.993			0.814426
$971$		−	1699.98i		−	1.75075i	−0.483441	−	0.875377i	$-0.660613\pi$
$971$		−	1699.98i		−	1.75075i	0.483441	−	0.875377i	$-0.339387\pi$
$972$		−	82.2278i		−	0.0845965i
$973$	534.866			0.549708
$974$	836.337			0.858662
$975$	−324.145			−0.332456
$976$	267.347			0.273921
$977$			73.3216i			0.0750477i	0.999296	+	0.0375238i	$0.0119470\pi$
$977$			73.3216i			0.0750477i	−0.999296	+	0.0375238i	$0.988053\pi$
$978$	223.650			0.228680
$979$			38.2835i			0.0391047i
$980$	3365.36			3.43404
$981$			139.338i			0.142037i
$982$		−	2380.31i		−	2.42394i
$983$			541.654i			0.551022i	0.961298	+	0.275511i	$0.0888470\pi$
$983$			541.654i			0.551022i	−0.961298	+	0.275511i	$0.911153\pi$
$984$		−	24.0703i		−	0.0244617i
$985$	−1589.13			−1.61333
$986$	1377.79			1.39735
$987$		−	265.212i		−	0.268706i
$988$	−1197.39	−	518.485i	−1.21193	−	0.524782i
$989$	−988.935			−0.999935
$990$			15.7611i			0.0159203i
$991$			1546.81i			1.56086i	0.625244	+	0.780429i	$0.284999\pi$
$991$			1546.81i			1.56086i	−0.625244	+	0.780429i	$0.715001\pi$
$992$	1029.93			1.03824
$993$	−230.502			−0.232127
$994$	4027.36			4.05167
$995$	301.368			0.302882
$996$			819.516i			0.822807i
$997$	−1366.20			−1.37031			−0.685156	−	0.728397i	$-0.740266\pi$
$997$	−1366.20			−1.37031			−0.685156	+	0.728397i	$0.740266\pi$
$998$		−	1181.39i		−	1.18376i
$999$	−346.949			−0.347296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.3.c.b.37.4	yes	4
3.2	odd	2		171.3.c.f.37.1		4
4.3	odd	2		912.3.o.b.721.1		4
12.11	even	2		2736.3.o.l.721.4		4
19.18	odd	2	inner	57.3.c.b.37.1	✓	4
57.56	even	2		171.3.c.f.37.4		4
76.75	even	2		912.3.o.b.721.3		4
228.227	odd	2		2736.3.o.l.721.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.c.b.37.1	✓	4	19.18	odd	2	inner
57.3.c.b.37.4	yes	4	1.1	even	1	trivial
171.3.c.f.37.1		4	3.2	odd	2
171.3.c.f.37.4		4	57.56	even	2
912.3.o.b.721.1		4	4.3	odd	2
912.3.o.b.721.3		4	76.75	even	2
2736.3.o.l.721.3		4	228.227	odd	2
2736.3.o.l.721.4		4	12.11	even	2

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	57.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.04547i q^{2} +1.73205i q^{3} -5.27492 q^{4} -6.27492 q^{5} -5.27492 q^{6} +12.2749 q^{7} -3.88273i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+3.04547i q^{2} +1.73205i q^{3} -5.27492 q^{4} -6.27492 q^{5} -5.27492 q^{6} +12.2749 q^{7} -3.88273i q^{8} -3.00000 q^{9} -19.1101i q^{10} +0.274917 q^{11} -9.13642i q^{12} +13.0192i q^{13} +37.3830i q^{14} -10.8685i q^{15} -9.27492 q^{16} +17.3746 q^{17} -9.13642i q^{18} +(7.54983 - 17.4356i) q^{19} +33.0997 q^{20} +21.2608i q^{21} +0.837253i q^{22} +20.5498 q^{23} +6.72508 q^{24} +14.3746 q^{25} -39.6495 q^{26} -5.19615i q^{27} -64.7492 q^{28} -26.0383i q^{29} +33.0997 q^{30} +23.5265i q^{31} -43.7774i q^{32} +0.476171i q^{33} +52.9139i q^{34} -77.0241 q^{35} +15.8248 q^{36} -66.7703i q^{37} +(53.0997 + 22.9928i) q^{38} -22.5498 q^{39} +24.3638i q^{40} -3.57919i q^{41} -64.7492 q^{42} -48.1238 q^{43} -1.45017 q^{44} +18.8248 q^{45} +62.5840i q^{46} -12.4743 q^{47} -16.0646i q^{48} +101.674 q^{49} +43.7774i q^{50} +30.0937i q^{51} -68.6750i q^{52} +25.8081i q^{53} +15.8248 q^{54} -1.72508 q^{55} -47.6602i q^{56} +(30.1993 + 13.0767i) q^{57} +79.2990 q^{58} -0.230175i q^{59} +57.3303i q^{60} -28.8248 q^{61} -71.6495 q^{62} -36.8248 q^{63} +96.2234 q^{64} -81.6941i q^{65} -1.45017 q^{66} +102.939i q^{67} -91.6495 q^{68} +35.5934i q^{69} -234.575i q^{70} -107.732i q^{71} +11.6482i q^{72} +11.1752 q^{73} +203.347 q^{74} +24.8975i q^{75} +(-39.8248 + 91.9713i) q^{76} +3.37459 q^{77} -68.6750i q^{78} +26.6454i q^{79} +58.1993 q^{80} +9.00000 q^{81} +10.9003 q^{82} -89.6977 q^{83} -112.149i q^{84} -109.024 q^{85} -146.560i q^{86} +45.0997 q^{87} -1.06743i q^{88} +139.255i q^{89} +57.3303i q^{90} +159.809i q^{91} -108.399 q^{92} -40.7492 q^{93} -37.9900i q^{94} +(-47.3746 + 109.407i) q^{95} +75.8248 q^{96} +41.3390i q^{97} +309.644i q^{98} -0.824752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 10 q^{5} - 6 q^{6} + 34 q^{7} - 12 q^{9}+O(q^{10}) \) 4 * q - 6 * q^4 - 10 * q^5 - 6 * q^6 + 34 * q^7 - 12 * q^9	\( 4 q - 6 q^{4} - 10 q^{5} - 6 q^{6} + 34 q^{7} - 12 q^{9} - 14 q^{11} - 22 q^{16} - 6 q^{17} + 72 q^{20} + 52 q^{23} + 42 q^{24} - 18 q^{25} - 68 q^{26} - 108 q^{28} + 72 q^{30} - 142 q^{35} + 18 q^{36} + 152 q^{38} - 60 q^{39} - 108 q^{42} + 34 q^{43} - 36 q^{44} + 30 q^{45} + 86 q^{47} + 150 q^{49} + 18 q^{54} - 22 q^{55} + 136 q^{58} - 70 q^{61} - 196 q^{62} - 102 q^{63} + 98 q^{64} - 36 q^{66} - 276 q^{68} + 90 q^{73} + 300 q^{74} - 114 q^{76} - 62 q^{77} + 112 q^{80} + 36 q^{81} + 104 q^{82} + 64 q^{83} - 270 q^{85} + 120 q^{87} - 192 q^{92} - 12 q^{93} - 114 q^{95} + 258 q^{96} + 42 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 - 10 * q^5 - 6 * q^6 + 34 * q^7 - 12 * q^9 - 14 * q^11 - 22 * q^16 - 6 * q^17 + 72 * q^20 + 52 * q^23 + 42 * q^24 - 18 * q^25 - 68 * q^26 - 108 * q^28 + 72 * q^30 - 142 * q^35 + 18 * q^36 + 152 * q^38 - 60 * q^39 - 108 * q^42 + 34 * q^43 - 36 * q^44 + 30 * q^45 + 86 * q^47 + 150 * q^49 + 18 * q^54 - 22 * q^55 + 136 * q^58 - 70 * q^61 - 196 * q^62 - 102 * q^63 + 98 * q^64 - 36 * q^66 - 276 * q^68 + 90 * q^73 + 300 * q^74 - 114 * q^76 - 62 * q^77 + 112 * q^80 + 36 * q^81 + 104 * q^82 + 64 * q^83 - 270 * q^85 + 120 * q^87 - 192 * q^92 - 12 * q^93 - 114 * q^95 + 258 * q^96 + 42 * q^99

Introduction

L-functions

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