LMFDB - Embedded newform 57.3.c.b.37.2

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			37.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	57.37
Dual form			57.3.c.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31342i q^{2} +1.73205i q^{3} +2.27492 q^{4} +1.27492 q^{5} +2.27492 q^{6} +4.72508 q^{7} -8.24163i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.31342i q^{2} +1.73205i q^{3} +2.27492 q^{4} +1.27492 q^{5} +2.27492 q^{6} +4.72508 q^{7} -8.24163i q^{8} -3.00000 q^{9} -1.67451i q^{10} -7.27492 q^{11} +3.94027i q^{12} +4.30136i q^{13} -6.20604i q^{14} +2.20822i q^{15} -1.72508 q^{16} -20.3746 q^{17} +3.94027i q^{18} +(-7.54983 + 17.4356i) q^{19} +2.90033 q^{20} +8.18408i q^{21} +9.55505i q^{22} +5.45017 q^{23} +14.2749 q^{24} -23.3746 q^{25} +5.64950 q^{26} -5.19615i q^{27} +10.7492 q^{28} -8.60271i q^{29} +2.90033 q^{30} -20.0624i q^{31} -30.7007i q^{32} -12.6005i q^{33} +26.7605i q^{34} +6.02409 q^{35} -6.82475 q^{36} -40.6169i q^{37} +(22.9003 + 9.91613i) q^{38} -7.45017 q^{39} -10.5074i q^{40} +31.2920i q^{41} +10.7492 q^{42} +65.1238 q^{43} -16.5498 q^{44} -3.82475 q^{45} -7.15838i q^{46} +55.4743 q^{47} -2.98793i q^{48} -26.6736 q^{49} +30.7007i q^{50} -35.2898i q^{51} +9.78523i q^{52} +78.1149i q^{53} -6.82475 q^{54} -9.27492 q^{55} -38.9424i q^{56} +(-30.1993 - 13.0767i) q^{57} -11.2990 q^{58} +69.5122i q^{59} +5.02352i q^{60} -6.17525 q^{61} -26.3505 q^{62} -14.1752 q^{63} -47.2234 q^{64} +5.48387i q^{65} -16.5498 q^{66} -123.724i q^{67} -46.3505 q^{68} +9.43996i q^{69} -7.91218i q^{70} -3.11884i q^{71} +24.7249i q^{72} +33.8248 q^{73} -53.3472 q^{74} -40.4860i q^{75} +(-17.1752 + 39.6645i) q^{76} -34.3746 q^{77} +9.78523i q^{78} +87.6700i q^{79} -2.19934 q^{80} +9.00000 q^{81} +41.0997 q^{82} +121.698 q^{83} +18.6181i q^{84} -25.9759 q^{85} -85.5351i q^{86} +14.9003 q^{87} +59.9572i q^{88} -69.9726i q^{89} +5.02352i q^{90} +20.3243i q^{91} +12.3987 q^{92} +34.7492 q^{93} -72.8612i q^{94} +(-9.62541 + 22.2289i) q^{95} +53.1752 q^{96} +111.081i q^{97} +35.0337i q^{98} +21.8248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.31342i		−	0.656712i	−0.944554	−	0.328356i	$-0.893505\pi$
$2$		−	1.31342i		−	0.656712i	0.944554	−	0.328356i	$-0.106495\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.27492			0.568729
$5$	1.27492			0.254983			0.127492	−	0.991840i	$-0.459307\pi$
$5$	1.27492			0.254983			0.127492	+	0.991840i	$0.459307\pi$
$6$	2.27492			0.379153
$7$	4.72508			0.675012			0.337506	−	0.941323i	$-0.390417\pi$
$7$	4.72508			0.675012			0.337506	+	0.941323i	$0.390417\pi$
$8$		−	8.24163i		−	1.03020i
$9$	−3.00000			−0.333333
$10$		−	1.67451i		−	0.167451i
$11$	−7.27492			−0.661356			−0.330678	−	0.943744i	$-0.607277\pi$
$11$	−7.27492			−0.661356			−0.330678	+	0.943744i	$0.607277\pi$
$12$			3.94027i			0.328356i
$13$			4.30136i			0.330873i	0.986220	+	0.165437i	$0.0529034\pi$
$13$			4.30136i			0.330873i	−0.986220	+	0.165437i	$0.947097\pi$
$14$		−	6.20604i		−	0.443288i
$15$			2.20822i			0.147215i
$16$	−1.72508			−0.107818
$17$	−20.3746			−1.19851			−0.599253	−	0.800560i	$-0.704535\pi$
$17$	−20.3746			−1.19851			−0.599253	+	0.800560i	$0.704535\pi$
$18$			3.94027i			0.218904i
$19$	−7.54983	+	17.4356i	−0.397360	+	0.917663i
$19$	−7.54983	+	17.4356i	−0.397360	+	0.917663i
$20$	2.90033			0.145017
$21$			8.18408i			0.389718i
$22$			9.55505i			0.434321i
$23$	5.45017			0.236964			0.118482	−	0.992956i	$-0.462197\pi$
$23$	5.45017			0.236964			0.118482	+	0.992956i	$0.462197\pi$
$24$	14.2749			0.594788
$25$	−23.3746			−0.934983
$26$	5.64950			0.217289
$27$		−	5.19615i		−	0.192450i
$28$	10.7492			0.383899
$29$		−	8.60271i		−	0.296645i	−0.988939	−	0.148323i	$-0.952613\pi$
$29$		−	8.60271i		−	0.296645i	0.988939	−	0.148323i	$-0.0473874\pi$
$30$	2.90033			0.0966777
$31$		−	20.0624i		−	0.647176i	−0.946198	−	0.323588i	$-0.895111\pi$
$31$		−	20.0624i		−	0.647176i	0.946198	−	0.323588i	$-0.104889\pi$
$32$		−	30.7007i		−	0.959398i
$33$		−	12.6005i		−	0.381834i
$34$			26.7605i			0.787073i
$35$	6.02409			0.172117
$36$	−6.82475			−0.189576
$37$		−	40.6169i		−	1.09775i	−0.835903	−	0.548877i	$-0.815056\pi$
$37$		−	40.6169i		−	1.09775i	0.835903	−	0.548877i	$-0.184944\pi$
$38$	22.9003	+	9.91613i	0.602640	+	0.260951i
$39$	−7.45017			−0.191030
$40$		−	10.5074i		−	0.262685i
$41$			31.2920i			0.763220i	0.924324	+	0.381610i	$0.124630\pi$
$41$			31.2920i			0.763220i	−0.924324	+	0.381610i	$0.875370\pi$
$42$	10.7492			0.255933
$43$	65.1238			1.51451			0.757253	−	0.653122i	$-0.226541\pi$
$43$	65.1238			1.51451			0.757253	+	0.653122i	$0.226541\pi$
$44$	−16.5498			−0.376133
$45$	−3.82475			−0.0849945
$46$		−	7.15838i		−	0.155617i
$47$	55.4743			1.18030			0.590152	−	0.807292i	$-0.299068\pi$
$47$	55.4743			1.18030			0.590152	+	0.807292i	$0.299068\pi$
$48$		−	2.98793i		−	0.0622486i
$49$	−26.6736			−0.544359
$50$			30.7007i			0.614015i
$51$		−	35.2898i		−	0.691957i
$52$			9.78523i			0.188177i
$53$			78.1149i			1.47387i	0.675966	+	0.736933i	$0.263727\pi$
$53$			78.1149i			1.47387i	−0.675966	+	0.736933i	$0.736273\pi$
$54$	−6.82475			−0.126384
$55$	−9.27492			−0.168635
$56$		−	38.9424i		−	0.695399i
$57$	−30.1993	−	13.0767i	−0.529813	−	0.229416i
$58$	−11.2990			−0.194810
$59$			69.5122i			1.17817i	0.808070	+	0.589087i	$0.200512\pi$
$59$			69.5122i			1.17817i	−0.808070	+	0.589087i	$0.799488\pi$
$60$			5.02352i			0.0837253i
$61$	−6.17525			−0.101234			−0.0506168	−	0.998718i	$-0.516119\pi$
$61$	−6.17525			−0.101234			−0.0506168	+	0.998718i	$0.516119\pi$
$62$	−26.3505			−0.425008
$63$	−14.1752			−0.225004
$64$	−47.2234			−0.737866
$65$			5.48387i			0.0843673i
$66$	−16.5498			−0.250755
$67$		−	123.724i		−	1.84662i	−0.384053	−	0.923311i	$-0.625472\pi$
$67$		−	123.724i		−	1.84662i	0.384053	−	0.923311i	$-0.374528\pi$
$68$	−46.3505			−0.681625
$69$			9.43996i			0.136811i
$70$		−	7.91218i		−	0.113031i
$71$		−	3.11884i		−	0.0439273i	−0.999759	−	0.0219637i	$-0.993008\pi$
$71$		−	3.11884i		−	0.0439273i	0.999759	−	0.0219637i	$-0.00699181\pi$
$72$			24.7249i			0.343401i
$73$	33.8248			0.463353			0.231676	−	0.972793i	$-0.425579\pi$
$73$	33.8248			0.463353			0.231676	+	0.972793i	$0.425579\pi$
$74$	−53.3472			−0.720908
$75$		−	40.4860i		−	0.539813i
$76$	−17.1752	+	39.6645i	−0.225990	+	0.521902i
$77$	−34.3746			−0.446423
$78$			9.78523i			0.125452i
$79$			87.6700i			1.10975i	0.831935	+	0.554873i	$0.187233\pi$
$79$			87.6700i			1.10975i	−0.831935	+	0.554873i	$0.812767\pi$
$80$	−2.19934			−0.0274917
$81$	9.00000			0.111111
$82$	41.0997			0.501215
$83$	121.698			1.46624			0.733119	−	0.680101i	$-0.238064\pi$
$83$	121.698			1.46624			0.733119	+	0.680101i	$0.238064\pi$
$84$			18.6181i			0.221644i
$85$	−25.9759			−0.305599
$86$		−	85.5351i		−	0.994594i
$87$	14.9003			0.171268
$88$			59.9572i			0.681331i
$89$		−	69.9726i		−	0.786209i	−0.919494	−	0.393104i	$-0.871401\pi$
$89$		−	69.9726i		−	0.786209i	0.919494	−	0.393104i	$-0.128599\pi$
$90$			5.02352i			0.0558169i
$91$			20.3243i			0.223344i
$92$	12.3987			0.134768
$93$	34.7492			0.373647
$94$		−	72.8612i		−	0.775119i
$95$	−9.62541	+	22.2289i	−0.101320	+	0.233989i
$96$	53.1752			0.553909
$97$			111.081i			1.14517i	0.819846	+	0.572585i	$0.194059\pi$
$97$			111.081i			1.14517i	−0.819846	+	0.572585i	$0.805941\pi$
$98$			35.0337i			0.357487i
$99$	21.8248			0.220452
$100$	−53.1752			−0.531752
$101$	75.2508			0.745058			0.372529	−	0.928021i	$-0.378491\pi$
$101$	75.2508			0.745058			0.372529	+	0.928021i	$0.378491\pi$
$102$	−46.3505			−0.454417
$103$		−	188.474i		−	1.82985i	−0.403628	−	0.914923i	$-0.632251\pi$
$103$		−	188.474i		−	1.82985i	0.403628	−	0.914923i	$-0.367749\pi$
$104$	35.4502			0.340867
$105$			10.4340i			0.0993717i
$106$	102.598			0.967906
$107$		−	8.14236i		−	0.0760968i	−0.999276	−	0.0380484i	$-0.987886\pi$
$107$		−	8.14236i		−	0.0760968i	0.999276	−	0.0380484i	$-0.0121141\pi$
$108$		−	11.8208i		−	0.109452i
$109$			119.192i			1.09351i	0.837294	+	0.546753i	$0.184136\pi$
$109$			119.192i			1.09351i	−0.837294	+	0.546753i	$0.815864\pi$
$110$			12.1819i			0.110745i
$111$	70.3505			0.633788
$112$	−8.15116			−0.0727782
$113$		−	196.355i		−	1.73765i	−0.495117	−	0.868826i	$-0.664875\pi$
$113$		−	196.355i		−	1.73765i	0.495117	−	0.868826i	$-0.335125\pi$
$114$	−17.1752	+	39.6645i	−0.150660	+	0.347935i
$115$	6.94851			0.0604218
$116$		−	19.5705i		−	0.168711i
$117$		−	12.9041i		−	0.110291i
$118$	91.2990			0.773720
$119$	−96.2716			−0.809005
$120$	18.1993			0.151661
$121$	−68.0756			−0.562608
$122$			8.11072i			0.0664813i
$123$	−54.1993			−0.440645
$124$		−	45.6404i		−	0.368068i
$125$	−61.6736			−0.493389
$126$			18.6181i			0.147763i
$127$		−	16.0229i		−	0.126165i	−0.998008	−	0.0630823i	$-0.979907\pi$
$127$		−	16.0229i		−	0.126165i	0.998008	−	0.0630823i	$-0.0200931\pi$
$128$		−	60.7786i		−	0.474833i
$129$			112.798i			0.874400i
$130$	7.20265			0.0554050
$131$	165.921			1.26657			0.633287	−	0.773917i	$-0.281705\pi$
$131$	165.921			1.26657			0.633287	+	0.773917i	$0.281705\pi$
$132$		−	28.6652i		−	0.217160i
$133$	−35.6736	+	82.3846i	−0.268223	+	0.619433i
$134$	−162.502			−1.21270
$135$		−	6.62466i		−	0.0490716i
$136$			167.920i			1.23470i
$137$	−199.674			−1.45747			−0.728736	−	0.684795i	$-0.759892\pi$
$137$	−199.674			−1.45747			−0.728736	+	0.684795i	$0.759892\pi$
$138$	12.3987			0.0898455
$139$	−54.5739			−0.392618			−0.196309	−	0.980542i	$-0.562896\pi$
$139$	−54.5739			−0.392618			−0.196309	+	0.980542i	$0.562896\pi$
$140$	13.7043			0.0978879
$141$			96.0842i			0.681448i
$142$	−4.09636			−0.0288476
$143$		−	31.2920i		−	0.218825i
$144$	5.17525			0.0359392
$145$		−	10.9677i		−	0.0756396i
$146$		−	44.4262i		−	0.304289i
$147$		−	46.2000i		−	0.314286i
$148$		−	92.4000i		−	0.624325i
$149$	−245.323			−1.64646			−0.823232	−	0.567705i	$-0.807831\pi$
$149$	−245.323			−1.64646			−0.823232	+	0.567705i	$0.807831\pi$
$150$	−53.1752			−0.354502
$151$			79.2974i			0.525149i	0.964912	+	0.262574i	$0.0845715\pi$
$151$			79.2974i			0.525149i	−0.964912	+	0.262574i	$0.915429\pi$
$152$	143.698	+	62.2229i	0.945379	+	0.409361i
$153$	61.1238			0.399502
$154$			45.1484i			0.293171i
$155$		−	25.5780i		−	0.165019i
$156$	−16.9485			−0.108644
$157$	−53.6977			−0.342023			−0.171012	−	0.985269i	$-0.554704\pi$
$157$	−53.6977			−0.342023			−0.171012	+	0.985269i	$0.554704\pi$
$158$	115.148			0.728784
$159$	−135.299			−0.850937
$160$		−	39.1409i		−	0.244631i
$161$	25.7525			0.159953
$162$		−	11.8208i		−	0.0729680i
$163$	78.3987			0.480973			0.240487	−	0.970652i	$-0.422693\pi$
$163$	78.3987			0.480973			0.240487	+	0.970652i	$0.422693\pi$
$164$			71.1867i			0.434065i
$165$		−	16.0646i		−	0.0973614i
$166$		−	159.841i		−	0.962896i
$167$			293.350i			1.75658i	0.478124	+	0.878292i	$0.341317\pi$
$167$			293.350i			1.75658i	−0.478124	+	0.878292i	$0.658683\pi$
$168$	67.4502			0.401489
$169$	150.498			0.890523
$170$			34.1174i			0.200691i
$171$	22.6495	−	52.3068i	0.132453	−	0.305888i
$172$	148.151			0.861344
$173$		−	10.5074i		−	0.0607364i	−0.999539	−	0.0303682i	$-0.990332\pi$
$173$		−	10.5074i		−	0.0607364i	0.999539	−	0.0303682i	$-0.00966798\pi$
$174$		−	19.5705i		−	0.112474i
$175$	−110.447			−0.631125
$176$	12.5498			0.0713059
$177$	−120.399			−0.680219
$178$	−91.9036			−0.516313
$179$			12.4121i			0.0693412i	0.999399	+	0.0346706i	$0.0110382\pi$
$179$			12.4121i			0.0693412i	−0.999399	+	0.0346706i	$0.988962\pi$
$180$	−8.70099			−0.0483389
$181$		−	106.780i		−	0.589945i	−0.955506	−	0.294973i	$-0.904689\pi$
$181$		−	106.780i		−	0.589945i	0.955506	−	0.294973i	$-0.0953105\pi$
$182$	26.6944			0.146672
$183$		−	10.6958i		−	0.0584472i
$184$		−	44.9182i		−	0.244121i
$185$		−	51.7832i		−	0.279909i
$186$		−	45.6404i		−	0.245378i
$187$	148.223			0.792639
$188$	126.199			0.671273
$189$		−	24.5523i		−	0.129906i
$190$	29.1960	+	12.6423i	0.153663	+	0.0665382i
$191$	−19.0274			−0.0996199			−0.0498099	−	0.998759i	$-0.515862\pi$
$191$	−19.0274			−0.0996199			−0.0498099	+	0.998759i	$0.515862\pi$
$192$		−	81.7934i		−	0.426007i
$193$		−	110.391i		−	0.571974i	−0.958234	−	0.285987i	$-0.907679\pi$
$193$		−	110.391i		−	0.571974i	0.958234	−	0.285987i	$-0.0923213\pi$
$194$	145.897			0.752046
$195$	−9.49834			−0.0487095
$196$	−60.6802			−0.309593
$197$	328.749			1.66878			0.834389	−	0.551176i	$-0.185821\pi$
$197$	328.749			1.66878			0.834389	+	0.551176i	$0.185821\pi$
$198$		−	28.6652i		−	0.144774i
$199$	−266.973			−1.34157			−0.670785	−	0.741651i	$-0.734043\pi$
$199$	−266.973			−1.34157			−0.670785	+	0.741651i	$0.734043\pi$
$200$			192.645i			0.963223i
$201$	214.296			1.06615
$202$		−	98.8362i		−	0.489288i
$203$		−	40.6485i		−	0.200239i
$204$		−	80.2814i		−	0.393536i
$205$			39.8947i			0.194608i
$206$	−247.547			−1.20168
$207$	−16.3505			−0.0789879
$208$		−	7.42019i		−	0.0356740i
$209$	54.9244	−	126.843i	0.262796	−	0.606902i
$210$	13.7043			0.0652586
$211$		−	70.4329i		−	0.333805i	−0.985973	−	0.166903i	$-0.946623\pi$
$211$		−	70.4329i		−	0.333805i	0.985973	−	0.166903i	$-0.0533766\pi$
$212$			177.705i			0.838231i
$213$	5.40199			0.0253614
$214$	−10.6944			−0.0499737
$215$	83.0274			0.386174
$216$	−42.8248			−0.198263
$217$		−	94.7967i		−	0.436851i
$218$	156.550			0.718119
$219$			58.5862i			0.267517i
$220$	−21.0997			−0.0959076
$221$		−	87.6383i		−	0.396554i
$222$		−	92.4000i		−	0.416216i
$223$			237.432i			1.06472i	0.846519	+	0.532359i	$0.178694\pi$
$223$			237.432i			1.06472i	−0.846519	+	0.532359i	$0.821306\pi$
$224$		−	145.064i		−	0.647605i
$225$	70.1238			0.311661
$226$	−257.897			−1.14114
$227$			269.740i			1.18828i	0.804362	+	0.594140i	$0.202508\pi$
$227$			269.740i			1.18828i	−0.804362	+	0.594140i	$0.797492\pi$
$228$	−68.7010	−	29.7484i	−0.301320	−	0.130475i
$229$	259.419			1.13284			0.566418	−	0.824118i	$-0.308329\pi$
$229$	259.419			1.13284			0.566418	+	0.824118i	$0.308329\pi$
$230$		−	9.12634i		−	0.0396797i
$231$		−	59.5385i		−	0.257743i
$232$	−70.9003			−0.305605
$233$	−52.6769			−0.226081			−0.113041	−	0.993590i	$-0.536059\pi$
$233$	−52.6769			−0.226081			−0.113041	+	0.993590i	$0.536059\pi$
$234$	−16.9485			−0.0724295
$235$	70.7251			0.300958
$236$			158.135i			0.670062i
$237$	−151.849			−0.640712
$238$			126.445i			0.531283i
$239$	−346.120			−1.44820			−0.724101	−	0.689694i	$-0.757745\pi$
$239$	−346.120			−1.44820			−0.724101	+	0.689694i	$0.757745\pi$
$240$		−	3.80936i		−	0.0158724i
$241$			300.278i			1.24597i	0.782235	+	0.622983i	$0.214079\pi$
$241$			300.278i			1.24597i	−0.782235	+	0.622983i	$0.785921\pi$
$242$			89.4121i			0.369472i
$243$			15.5885i			0.0641500i
$244$	−14.0482			−0.0575745
$245$	−34.0066			−0.138803
$246$			71.1867i			0.289377i
$247$	−74.9967	−	32.4745i	−0.303630	−	0.131476i
$248$	−165.347			−0.666723
$249$			210.787i			0.846532i
$250$			81.0036i			0.324014i
$251$	190.223			0.757862			0.378931	−	0.925425i	$-0.376292\pi$
$251$	190.223			0.757862			0.378931	+	0.925425i	$0.376292\pi$
$252$	−32.2475			−0.127966
$253$	−39.6495			−0.156717
$254$	−21.0449			−0.0828538
$255$		−	44.9916i		−	0.176438i
$256$	−268.722			−1.04969
$257$		−	25.3478i		−	0.0986295i	−0.998783	−	0.0493147i	$-0.984296\pi$
$257$		−	25.3478i		−	0.0986295i	0.998783	−	0.0493147i	$-0.0157037\pi$
$258$	148.151			0.574229
$259$		−	191.918i		−	0.740997i
$260$			12.4754i			0.0479821i
$261$			25.8081i			0.0988817i
$262$		−	217.925i		−	0.831774i
$263$	−450.120			−1.71148			−0.855742	−	0.517402i	$-0.826899\pi$
$263$	−450.120			−1.71148			−0.855742	+	0.517402i	$0.826899\pi$
$264$	−103.849			−0.393367
$265$			99.5901i			0.375812i
$266$	108.206	+	46.8546i	0.406789	+	0.176145i
$267$	121.196			0.453918
$268$		−	281.461i		−	1.05023i
$269$		−	485.141i		−	1.80350i	−0.432259	−	0.901749i	$-0.642284\pi$
$269$		−	485.141i		−	1.80350i	0.432259	−	0.901749i	$-0.357716\pi$
$270$	−8.70099			−0.0322259
$271$	156.997			0.579324			0.289662	−	0.957129i	$-0.406457\pi$
$271$	156.997			0.579324			0.289662	+	0.957129i	$0.406457\pi$
$272$	35.1478			0.129220
$273$	−35.2026			−0.128947
$274$			262.256i			0.957139i
$275$	170.048			0.618357
$276$			21.4751i			0.0778085i
$277$	156.629			0.565447			0.282723	−	0.959202i	$-0.408762\pi$
$277$	156.629			0.565447			0.282723	+	0.959202i	$0.408762\pi$
$278$			71.6787i			0.257837i
$279$			60.1873i			0.215725i
$280$		−	49.6483i		−	0.177315i
$281$		−	457.658i		−	1.62868i	−0.580390	−	0.814339i	$-0.697100\pi$
$281$		−	457.658i		−	1.62868i	0.580390	−	0.814339i	$-0.302900\pi$
$282$	126.199			0.447515
$283$	−46.5739			−0.164572			−0.0822861	−	0.996609i	$-0.526222\pi$
$283$	−46.5739			−0.164572			−0.0822861	+	0.996609i	$0.526222\pi$
$284$		−	7.09510i		−	0.0249827i
$285$	−38.5017	−	16.6717i	−0.135094	−	0.0584972i
$286$	−41.0997			−0.143705
$287$			147.857i			0.515182i
$288$			92.1022i			0.319799i
$289$	126.124			0.436414
$290$	−14.4053			−0.0496734
$291$	−192.399			−0.661164
$292$	76.9485			0.263522
$293$		−	222.163i		−	0.758235i	−0.925349	−	0.379117i	$-0.876228\pi$
$293$		−	222.163i		−	0.758235i	0.925349	−	0.379117i	$-0.123772\pi$
$294$	−60.6802			−0.206395
$295$			88.6223i			0.300415i
$296$	−334.749			−1.13091
$297$			37.8016i			0.127278i
$298$			322.213i			1.08125i
$299$			23.4431i			0.0784050i
$300$		−	92.1022i		−	0.307007i
$301$	307.715			1.02231
$302$	104.151			0.344871
$303$			130.338i			0.430159i
$304$	13.0241	−	30.0778i	0.0428424	−	0.0989403i
$305$	−7.87293			−0.0258129
$306$		−	80.2814i		−	0.262358i
$307$		−	492.069i		−	1.60283i	−0.598108	−	0.801416i	$-0.704080\pi$
$307$		−	492.069i		−	1.60283i	0.598108	−	0.801416i	$-0.295920\pi$
$308$	−78.1993			−0.253894
$309$	326.447			1.05646
$310$	−33.5947			−0.108370
$311$	162.773			0.523387			0.261693	−	0.965151i	$-0.415719\pi$
$311$	162.773			0.523387			0.261693	+	0.965151i	$0.415719\pi$
$312$			61.4015i			0.196800i
$313$	414.894			1.32554			0.662770	−	0.748823i	$-0.269381\pi$
$313$	414.894			1.32554			0.662770	+	0.748823i	$0.269381\pi$
$314$			70.5278i			0.224611i
$315$	−18.0723			−0.0573723
$316$			199.442i			0.631145i
$317$			365.750i			1.15379i	0.816819	+	0.576893i	$0.195735\pi$
$317$			365.750i			1.15379i	−0.816819	+	0.576893i	$0.804265\pi$
$318$			177.705i			0.558821i
$319$			62.5840i			0.196188i
$320$	−60.2060			−0.188144
$321$	14.1030			0.0439345
$322$		−	33.8239i		−	0.105043i
$323$	153.825	−	355.243i	0.476238	−	1.09982i
$324$	20.4743			0.0631921
$325$		−	100.542i		−	0.309361i
$326$		−	102.971i		−	0.315861i
$327$	−206.447			−0.631336
$328$	257.897			0.786271
$329$	262.120			0.796719
$330$	−21.0997			−0.0639384
$331$			220.258i			0.665433i	0.943027	+	0.332716i	$0.107965\pi$
$331$			220.258i			0.665433i	−0.943027	+	0.332716i	$0.892035\pi$
$332$	276.852			0.833892
$333$			121.851i			0.365918i
$334$	385.292			1.15357
$335$		−	157.737i		−	0.470858i
$336$		−	14.1182i		−	0.0420185i
$337$			240.980i			0.715073i	0.933899	+	0.357536i	$0.116383\pi$
$337$			240.980i			0.715073i	−0.933899	+	0.357536i	$0.883617\pi$
$338$		−	197.668i		−	0.584817i
$339$	340.096			1.00323
$340$	−59.0930			−0.173803
$341$			145.953i			0.428014i
$342$	−68.7010	−	29.7484i	−0.200880	−	0.0869836i
$343$	−357.564			−1.04246
$344$		−	536.726i		−	1.56025i
$345$			12.0352i			0.0348846i
$346$	−13.8007			−0.0398863
$347$	−234.876			−0.676877			−0.338438	−	0.940989i	$-0.609899\pi$
$347$	−234.876			−0.676877			−0.338438	+	0.940989i	$0.609899\pi$
$348$	33.8970			0.0974052
$349$	−440.677			−1.26268			−0.631342	−	0.775504i	$-0.717496\pi$
$349$	−440.677			−1.26268			−0.631342	+	0.775504i	$0.717496\pi$
$350$			145.064i			0.414467i
$351$	22.3505			0.0636766
$352$			223.345i			0.634504i
$353$	−543.292			−1.53907			−0.769536	−	0.638603i	$-0.779512\pi$
$353$	−543.292			−1.53907			−0.769536	+	0.638603i	$0.779512\pi$
$354$			158.135i			0.446708i
$355$		−	3.97626i		−	0.0112007i
$356$		−	159.182i		−	0.447140i
$357$		−	166.747i		−	0.467079i
$358$	16.3023			0.0455372
$359$	−38.5191			−0.107296			−0.0536478	−	0.998560i	$-0.517085\pi$
$359$	−38.5191			−0.107296			−0.0536478	+	0.998560i	$0.517085\pi$
$360$			31.5222i			0.0875616i
$361$	−247.000	−	263.272i	−0.684211	−	0.729285i
$362$	−140.248			−0.387424
$363$		−	117.910i		−	0.324822i
$364$			46.2360i			0.127022i
$365$	43.1238			0.118147
$366$	−14.0482			−0.0383830
$367$	−568.997			−1.55040			−0.775200	−	0.631716i	$-0.782351\pi$
$367$	−568.997			−1.55040			−0.775200	+	0.631716i	$0.782351\pi$
$368$	−9.40199			−0.0255489
$369$		−	93.8760i		−	0.254407i
$370$	−68.0132			−0.183820
$371$			369.099i			0.994877i
$372$	79.0515			0.212504
$373$			61.8618i			0.165849i	0.996556	+	0.0829247i	$0.0264261\pi$
$373$			61.8618i			0.165849i	−0.996556	+	0.0829247i	$0.973574\pi$
$374$		−	194.680i		−	0.520535i
$375$		−	106.822i		−	0.284858i
$376$		−	457.198i		−	1.21595i
$377$	37.0033			0.0981520
$378$	−32.2475			−0.0853109
$379$			342.601i			0.903960i	0.892028	+	0.451980i	$0.149282\pi$
$379$			342.601i			0.903960i	−0.892028	+	0.451980i	$0.850718\pi$
$380$	−21.8970	+	50.5690i	−0.0576237	+	0.133076i
$381$	27.7525			0.0728412
$382$			24.9910i			0.0654216i
$383$			77.1309i			0.201386i	0.994918	+	0.100693i	$0.0321060\pi$
$383$			77.1309i			0.201386i	−0.994918	+	0.100693i	$0.967894\pi$
$384$	105.272			0.274145
$385$	−43.8248			−0.113831
$386$	−144.990			−0.375622
$387$	−195.371			−0.504835
$388$			252.701i			0.651291i
$389$	433.770			1.11509			0.557545	−	0.830147i	$-0.311743\pi$
$389$	433.770			1.11509			0.557545	+	0.830147i	$0.311743\pi$
$390$			12.4754i			0.0319881i
$391$	−111.045			−0.284002
$392$			219.834i			0.560801i
$393$			287.384i			0.731256i
$394$		−	431.787i		−	1.09591i
$395$			111.772i			0.282967i
$396$	49.6495			0.125378
$397$	−283.069			−0.713020			−0.356510	−	0.934291i	$-0.616033\pi$
$397$	−283.069			−0.713020			−0.356510	+	0.934291i	$0.616033\pi$
$398$			350.648i			0.881026i
$399$	−142.694	−	61.7885i	−0.357630	−	0.154858i
$400$	40.3231			0.100808
$401$			323.491i			0.806710i	0.915044	+	0.403355i	$0.132156\pi$
$401$			323.491i			0.806710i	−0.915044	+	0.403355i	$0.867844\pi$
$402$		−	281.461i		−	0.700152i
$403$	86.2957			0.214133
$404$	171.189			0.423736
$405$	11.4743			0.0283315
$406$	−53.3887			−0.131499
$407$			295.484i			0.726006i
$408$	−290.846			−0.712857
$409$			546.741i			1.33678i	0.743813	+	0.668388i	$0.233015\pi$
$409$			546.741i			1.33678i	−0.743813	+	0.668388i	$0.766985\pi$
$410$	52.3987			0.127802
$411$		−	345.845i		−	0.841472i
$412$		−	428.763i		−	1.04069i
$413$			328.451i			0.795281i
$414$			21.4751i			0.0518723i
$415$	155.154			0.373866
$416$	132.055			0.317439
$417$		−	94.5248i		−	0.226678i
$418$	−166.598	−	72.1391i	−0.398560	−	0.172581i
$419$	−352.997			−0.842474			−0.421237	−	0.906951i	$-0.638404\pi$
$419$	−352.997			−0.842474			−0.421237	+	0.906951i	$0.638404\pi$
$420$			23.7366i			0.0565156i
$421$		−	578.525i		−	1.37417i	−0.726578	−	0.687084i	$-0.758890\pi$
$421$		−	578.525i		−	1.37417i	0.726578	−	0.687084i	$-0.241110\pi$
$422$	−92.5083			−0.219214
$423$	−166.423			−0.393434
$424$	643.794			1.51838
$425$	476.248			1.12058
$426$		−	7.09510i		−	0.0166552i
$427$	−29.1786			−0.0683339
$428$		−	18.5232i		−	0.0432785i
$429$	54.1993			0.126339
$430$		−	109.050i		−	0.253605i
$431$			628.896i			1.45915i	0.683898	+	0.729577i	$0.260283\pi$
$431$			628.896i			1.45915i	−0.683898	+	0.729577i	$0.739717\pi$
$432$			8.96379i			0.0207495i
$433$			122.803i			0.283610i	0.989895	+	0.141805i	$0.0452905\pi$
$433$			122.803i			0.283610i	−0.989895	+	0.141805i	$0.954709\pi$
$434$	−124.508			−0.286885
$435$	18.9967			0.0436705
$436$			271.152i			0.621909i
$437$	−41.1478	+	95.0269i	−0.0941598	+	0.217453i
$438$	76.9485			0.175682
$439$			63.3694i			0.144350i	0.997392	+	0.0721748i	$0.0229939\pi$
$439$			63.3694i			0.144350i	−0.997392	+	0.0721748i	$0.977006\pi$
$440$			76.4404i			0.173728i
$441$	80.0208			0.181453
$442$	−115.106			−0.260421
$443$	610.320			1.37770			0.688849	−	0.724905i	$-0.258117\pi$
$443$	610.320			1.37770			0.688849	+	0.724905i	$0.258117\pi$
$444$	160.042			0.360454
$445$		−	89.2092i		−	0.200470i
$446$	311.849			0.699213
$447$		−	424.912i		−	0.950586i
$448$	−223.135			−0.498068
$449$		−	410.772i		−	0.914860i	−0.889246	−	0.457430i	$-0.848770\pi$
$449$		−	410.772i		−	0.914860i	0.889246	−	0.457430i	$-0.151230\pi$
$450$		−	92.1022i		−	0.204672i
$451$		−	227.647i		−	0.504760i
$452$		−	446.691i		−	0.988254i
$453$	−137.347			−0.303195
$454$	354.282			0.780358
$455$			25.9117i			0.0569489i
$456$	−107.773	+	248.892i	−0.236345	+	0.545815i
$457$	251.722			0.550814			0.275407	−	0.961328i	$-0.411187\pi$
$457$	251.722			0.550814			0.275407	+	0.961328i	$0.411187\pi$
$458$		−	340.728i		−	0.743947i
$459$			105.869i			0.230652i
$460$	15.8073			0.0343637
$461$	−224.622			−0.487250			−0.243625	−	0.969870i	$-0.578337\pi$
$461$	−224.622			−0.487250			−0.243625	+	0.969870i	$0.578337\pi$
$462$	−78.1993			−0.169263
$463$	−196.375			−0.424135			−0.212068	−	0.977255i	$-0.568020\pi$
$463$	−196.375			−0.424135			−0.212068	+	0.977255i	$0.568020\pi$
$464$			14.8404i			0.0319836i
$465$	44.3023			0.0952738
$466$			69.1871i			0.148470i
$467$	−106.381			−0.227797			−0.113899	−	0.993492i	$-0.536334\pi$
$467$	−106.381			−0.227797			−0.113899	+	0.993492i	$0.536334\pi$
$468$		−	29.3557i		−	0.0627258i
$469$		−	584.605i		−	1.24649i
$470$		−	92.8920i		−	0.197643i
$471$		−	93.0071i		−	0.197467i
$472$	572.894			1.21376
$473$	−473.770			−1.00163
$474$			199.442i			0.420764i
$475$	176.474	−	407.550i	0.371525	−	0.858000i
$476$	−219.010			−0.460105
$477$		−	234.345i		−	0.491289i
$478$			454.603i			0.951052i
$479$	463.154			0.966920			0.483460	−	0.875367i	$-0.339380\pi$
$479$	463.154			0.966920			0.483460	+	0.875367i	$0.339380\pi$
$480$	67.7940			0.141238
$481$	174.708			0.363217
$482$	394.392			0.818241
$483$			44.6046i			0.0923491i
$484$	−154.866			−0.319972
$485$			141.620i			0.291999i
$486$	20.4743			0.0421281
$487$		−	248.463i		−	0.510191i	−0.966916	−	0.255095i	$-0.917893\pi$
$487$		−	248.463i		−	0.510191i	0.966916	−	0.255095i	$-0.0821069\pi$
$488$			50.8941i			0.104291i
$489$			135.790i			0.277690i
$490$			44.6651i			0.0911533i
$491$	305.588			0.622379			0.311189	−	0.950348i	$-0.399273\pi$
$491$	305.588			0.622379			0.311189	+	0.950348i	$0.399273\pi$
$492$	−123.299			−0.250608
$493$			175.277i			0.355531i
$494$	−42.6528	+	98.5025i	−0.0863417	+	0.199398i
$495$	27.8248			0.0562116
$496$			34.6094i			0.0697770i
$497$		−	14.7368i		−	0.0296514i
$498$	276.852			0.555928
$499$	268.918			0.538913			0.269457	−	0.963013i	$-0.413156\pi$
$499$	268.918			0.538913			0.269457	+	0.963013i	$0.413156\pi$
$500$	−140.302			−0.280605
$501$	−508.096			−1.01416
$502$		−	249.844i		−	0.497697i
$503$	−507.154			−1.00826			−0.504130	−	0.863628i	$-0.668187\pi$
$503$	−507.154			−1.00826			−0.504130	+	0.863628i	$0.668187\pi$
$504$			116.827i			0.231800i
$505$	95.9386			0.189977
$506$			52.0766i			0.102918i
$507$			260.671i			0.514144i
$508$		−	36.4508i		−	0.0717535i
$509$			407.256i			0.800111i	0.916491	+	0.400055i	$0.131009\pi$
$509$			407.256i			0.800111i	−0.916491	+	0.400055i	$0.868991\pi$
$510$	−59.0930			−0.115869
$511$	159.825			0.312769
$512$			109.831i			0.214514i
$513$	90.5980	+	39.2301i	0.176604	+	0.0764719i
$514$	−33.2924			−0.0647712
$515$		−	240.289i		−	0.466581i
$516$			256.605i			0.497297i
$517$	−403.571			−0.780601
$518$	−252.070			−0.486621
$519$	18.1993			0.0350662
$520$	45.1960			0.0869154
$521$		−	607.190i		−	1.16543i	−0.812676	−	0.582716i	$-0.801990\pi$
$521$		−	607.190i		−	1.16543i	0.812676	−	0.582716i	$-0.198010\pi$
$522$	33.8970			0.0649368
$523$		−	209.227i		−	0.400052i	−0.979791	−	0.200026i	$-0.935897\pi$
$523$		−	209.227i		−	0.400052i	0.979791	−	0.200026i	$-0.0641026\pi$
$524$	377.457			0.720337
$525$		−	191.300i		−	0.364380i
$526$			591.199i			1.12395i
$527$			408.764i			0.775643i
$528$			21.7370i			0.0411685i
$529$	−499.296			−0.943848
$530$	130.804			0.246800
$531$		−	208.537i		−	0.392724i
$532$	−81.1545	+	187.418i	−0.152546	+	0.352290i
$533$	−134.598			−0.252529
$534$		−	159.182i		−	0.298093i
$535$		−	10.3808i		−	0.0194034i
$536$	−1019.68			−1.90240
$537$	−21.4983			−0.0400342
$538$	−637.196			−1.18438
$539$	194.048			0.360015
$540$		−	15.0706i		−	0.0279084i
$541$	−44.6637			−0.0825576			−0.0412788	−	0.999148i	$-0.513143\pi$
$541$	−44.6637			−0.0825576			−0.0412788	+	0.999148i	$0.513143\pi$
$542$		−	206.203i		−	0.380449i
$543$	184.949			0.340605
$544$			625.515i			1.14984i
$545$			151.960i			0.278826i
$546$			46.2360i			0.0846813i
$547$			595.405i			1.08849i	0.838925	+	0.544246i	$0.183184\pi$
$547$			595.405i			1.08849i	−0.838925	+	0.544246i	$0.816816\pi$
$548$	−454.241			−0.828907
$549$	18.5257			0.0337445
$550$		−	223.345i		−	0.406082i
$551$	149.993	+	64.9490i	0.272220	+	0.117875i
$552$	77.8007			0.140943
$553$			414.248i			0.749092i
$554$		−	205.720i		−	0.371336i
$555$	89.6911			0.161606
$556$	−124.151			−0.223293
$557$	−78.4228			−0.140795			−0.0703975	−	0.997519i	$-0.522427\pi$
$557$	−78.4228			−0.140795			−0.0703975	+	0.997519i	$0.522427\pi$
$558$	79.0515			0.141669
$559$			280.120i			0.501110i
$560$	−10.3921			−0.0185572
$561$			256.731i			0.457630i
$562$	−601.100			−1.06957
$563$		−	457.825i		−	0.813189i	−0.913609	−	0.406594i	$-0.866716\pi$
$563$		−	457.825i		−	0.813189i	0.913609	−	0.406594i	$-0.133284\pi$
$564$			218.584i			0.387560i
$565$		−	250.336i		−	0.443073i
$566$			61.1713i			0.108077i
$567$	42.5257			0.0750013
$568$	−25.7043			−0.0452541
$569$		−	307.833i		−	0.541007i	−0.962719	−	0.270504i	$-0.912810\pi$
$569$		−	307.833i		−	0.541007i	0.962719	−	0.270504i	$-0.0871902\pi$
$570$	−21.8970	+	50.5690i	−0.0384158	+	0.0887175i
$571$	589.492			1.03238			0.516192	−	0.856473i	$-0.327349\pi$
$571$	589.492			1.03238			0.516192	+	0.856473i	$0.327349\pi$
$572$		−	71.1867i		−	0.124452i
$573$		−	32.9564i		−	0.0575156i
$574$	194.199			0.338326
$575$	−127.395			−0.221557
$576$	141.670			0.245955
$577$	−363.262			−0.629570			−0.314785	−	0.949163i	$-0.601932\pi$
$577$	−363.262			−0.629570			−0.314785	+	0.949163i	$0.601932\pi$
$578$		−	165.654i		−	0.286599i
$579$	191.203			0.330229
$580$		−	24.9507i		−	0.0430185i
$581$	575.032			0.989727
$582$			252.701i			0.434194i
$583$		−	568.280i		−	0.974751i
$584$		−	278.771i		−	0.477348i
$585$		−	16.4516i		−	0.0281224i
$586$	−291.794			−0.497942
$587$	391.625			0.667164			0.333582	−	0.942721i	$-0.391743\pi$
$587$	391.625			0.667164			0.333582	+	0.942721i	$0.391743\pi$
$588$		−	105.101i		−	0.178744i
$589$	349.801	+	151.468i	0.593889	+	0.257162i
$590$	116.399			0.197286
$591$			569.410i			0.963469i
$592$			70.0675i			0.118357i
$593$	−212.900			−0.359022			−0.179511	−	0.983756i	$-0.557452\pi$
$593$	−212.900			−0.359022			−0.179511	+	0.983756i	$0.557452\pi$
$594$	49.6495			0.0835850
$595$	−122.738			−0.206283
$596$	−558.090			−0.936392
$597$		−	462.410i		−	0.774556i
$598$	30.7907			0.0514895
$599$		−	916.888i		−	1.53070i	−0.643616	−	0.765349i	$-0.722566\pi$
$599$		−	916.888i		−	1.53070i	0.643616	−	0.765349i	$-0.277434\pi$
$600$	−333.670			−0.556117
$601$			485.078i			0.807118i	0.914954	+	0.403559i	$0.132227\pi$
$601$			485.078i			0.807118i	−0.914954	+	0.403559i	$0.867773\pi$
$602$		−	404.160i		−	0.671363i
$603$			371.171i			0.615541i
$604$			180.395i			0.298667i
$605$	−86.7907			−0.143456
$606$	171.189			0.282491
$607$		−	193.101i		−	0.318123i	−0.987269	−	0.159061i	$-0.949153\pi$
$607$		−	193.101i		−	0.318123i	0.987269	−	0.159061i	$-0.0508468\pi$
$608$	535.286	+	231.786i	0.880404	+	0.381226i
$609$	70.4053			0.115608
$610$			10.3405i			0.0169516i
$611$			238.614i			0.390531i
$612$	139.051			0.227208
$613$	−142.368			−0.232248			−0.116124	−	0.993235i	$-0.537047\pi$
$613$	−142.368			−0.232248			−0.116124	+	0.993235i	$0.537047\pi$
$614$	−646.296			−1.05260
$615$	−69.0997			−0.112357
$616$			283.303i			0.459907i
$617$	−547.770			−0.887796			−0.443898	−	0.896077i	$-0.646405\pi$
$617$	−547.770			−0.887796			−0.443898	+	0.896077i	$0.646405\pi$
$618$		−	428.763i		−	0.693792i
$619$	814.482			1.31580			0.657901	−	0.753104i	$-0.271444\pi$
$619$	814.482			1.31580			0.657901	+	0.753104i	$0.271444\pi$
$620$		−	58.1877i		−	0.0938512i
$621$		−	28.3199i		−	0.0456037i
$622$		−	213.790i		−	0.343714i
$623$		−	330.626i		−	0.530700i
$624$	12.8522			0.0205964
$625$	505.736			0.809177
$626$		−	544.931i		−	0.870497i
$627$	219.698	+	95.1319i	0.350395	+	0.151725i
$628$	−122.158			−0.194519
$629$			827.552i			1.31566i
$630$			23.7366i			0.0376771i
$631$	641.509			1.01665			0.508327	−	0.861164i	$-0.330264\pi$
$631$	641.509			1.01665			0.508327	+	0.861164i	$0.330264\pi$
$632$	722.543			1.14326
$633$	121.993			0.192723
$634$	480.385			0.757706
$635$		−	20.4279i		−	0.0321699i
$636$	−307.794			−0.483953
$637$		−	114.733i		−	0.180114i
$638$	82.1993			0.128839
$639$			9.35652i			0.0146424i
$640$		−	77.4877i		−	0.121074i
$641$		−	352.878i		−	0.550512i	−0.961371	−	0.275256i	$-0.911237\pi$
$641$		−	352.878i		−	0.550512i	0.961371	−	0.275256i	$-0.0887626\pi$
$642$		−	18.5232i		−	0.0288523i
$643$	−455.757			−0.708797			−0.354399	−	0.935094i	$-0.615314\pi$
$643$	−455.757			−0.708797			−0.354399	+	0.935094i	$0.615314\pi$
$644$	58.5848			0.0909701
$645$			143.808i			0.222958i
$646$	−466.585	−	202.037i	−0.722267	−	0.312751i
$647$	484.368			0.748637			0.374318	−	0.927300i	$-0.377877\pi$
$647$	484.368			0.748637			0.374318	+	0.927300i	$0.377877\pi$
$648$		−	74.1746i		−	0.114467i
$649$		−	505.696i		−	0.779192i
$650$	−132.055			−0.203161
$651$	164.193			0.252216
$652$	178.350			0.273544
$653$	280.780			0.429985			0.214992	−	0.976616i	$-0.431027\pi$
$653$	280.780			0.429985			0.214992	+	0.976616i	$0.431027\pi$
$654$			271.152i			0.414606i
$655$	211.536			0.322955
$656$		−	53.9813i		−	0.0822886i
$657$	−101.474			−0.154451
$658$		−	344.275i		−	0.523215i
$659$		−	800.259i		−	1.21435i	−0.794567	−	0.607177i	$-0.792302\pi$
$659$		−	800.259i		−	1.21435i	0.794567	−	0.607177i	$-0.207698\pi$
$660$		−	36.5457i		−	0.0553723i
$661$			812.996i			1.22995i	0.788547	+	0.614975i	$0.210834\pi$
$661$			812.996i			1.22995i	−0.788547	+	0.614975i	$0.789166\pi$
$662$	289.292			0.436998
$663$	151.794			0.228950
$664$		−	1002.99i		−	1.51052i
$665$	−45.4809	+	105.034i	−0.0683923	+	0.157945i
$666$	160.042			0.240303
$667$		−	46.8862i		−	0.0702941i
$668$			667.346i			0.999021i
$669$	−411.244			−0.614715
$670$	−207.176			−0.309218
$671$	44.9244			0.0669514
$672$	251.257			0.373895
$673$			79.8930i			0.118712i	0.998237	+	0.0593559i	$0.0189047\pi$
$673$			79.8930i			0.118712i	−0.998237	+	0.0593559i	$0.981095\pi$
$674$	316.508			0.469597
$675$			121.458i			0.179938i
$676$	342.371			0.506466
$677$			1153.64i			1.70404i	0.523506	+	0.852022i	$0.324624\pi$
$677$			1153.64i			1.70404i	−0.523506	+	0.852022i	$0.675376\pi$
$678$		−	446.691i		−	0.658836i
$679$			524.869i			0.773003i
$680$			214.084i			0.314829i
$681$	−467.203			−0.686054
$682$	191.698			0.281082
$683$		−	382.766i		−	0.560419i	−0.959939	−	0.280209i	$-0.909596\pi$
$683$		−	382.766i		−	0.560419i	0.959939	−	0.280209i	$-0.0904039\pi$
$684$	51.5257	−	118.994i	0.0753300	−	0.173967i
$685$	−254.567			−0.371631
$686$			469.633i			0.684596i
$687$			449.328i			0.654043i
$688$	−112.344			−0.163291
$689$	−336.000			−0.487663
$690$	15.8073			0.0229091
$691$	133.330			0.192952			0.0964759	−	0.995335i	$-0.469243\pi$
$691$	133.330			0.192952			0.0964759	+	0.995335i	$0.469243\pi$
$692$		−	23.9034i		−	0.0345426i
$693$	103.124			0.148808
$694$			308.492i			0.444513i
$695$	−69.5772			−0.100111
$696$		−	122.803i		−	0.176441i
$697$		−	637.562i		−	0.914723i
$698$			578.796i			0.829220i
$699$		−	91.2391i		−	0.130528i
$700$	−251.257			−0.358939
$701$	−934.042			−1.33244			−0.666221	−	0.745755i	$-0.732089\pi$
$701$	−934.042			−1.33244			−0.666221	+	0.745755i	$0.732089\pi$
$702$		−	29.3557i		−	0.0418172i
$703$	708.179	+	306.651i	1.00737	+	0.436203i
$704$	343.547			0.487992
$705$			122.499i			0.173758i
$706$			713.573i			1.01073i
$707$	355.566			0.502923
$708$	−273.897			−0.386860
$709$	287.993			0.406197			0.203098	−	0.979158i	$-0.434899\pi$
$709$	287.993			0.406197			0.203098	+	0.979158i	$0.434899\pi$
$710$	−5.22252			−0.00735566
$711$		−	263.010i		−	0.369915i
$712$	−576.688			−0.809955
$713$		−	109.344i		−	0.153357i
$714$	−219.010			−0.306737
$715$		−	39.8947i		−	0.0557968i
$716$			28.2364i			0.0394364i
$717$		−	599.498i		−	0.836120i
$718$			50.5919i			0.0704623i
$719$	78.0723			0.108585			0.0542923	−	0.998525i	$-0.482710\pi$
$719$	78.0723			0.108585			0.0542923	+	0.998525i	$0.482710\pi$
$720$	6.59801			0.00916391
$721$		−	890.556i		−	1.23517i
$722$	−345.787	+	324.416i	−0.478930	+	0.449329i
$723$	−520.096			−0.719359
$724$		−	242.916i		−	0.335519i
$725$			201.085i			0.277358i
$726$	−154.866			−0.213314
$727$	−320.169			−0.440397			−0.220199	−	0.975455i	$-0.570671\pi$
$727$	−320.169			−0.440397			−0.220199	+	0.975455i	$0.570671\pi$
$728$	167.505			0.230089
$729$	−27.0000			−0.0370370
$730$		−	56.6398i		−	0.0775887i
$731$	−1326.87			−1.81514
$732$		−	24.3322i		−	0.0332407i
$733$	−565.781			−0.771870			−0.385935	−	0.922526i	$-0.626121\pi$
$733$	−565.781			−0.771870			−0.385935	+	0.922526i	$0.626121\pi$
$734$			747.334i			1.01817i
$735$		−	58.9012i		−	0.0801377i
$736$		−	167.324i		−	0.227343i
$737$			900.080i			1.22127i
$738$	−123.299			−0.167072
$739$	−869.557			−1.17667			−0.588334	−	0.808618i	$-0.700216\pi$
$739$	−869.557			−1.17667			−0.588334	+	0.808618i	$0.700216\pi$
$740$		−	117.802i		−	0.159192i
$741$	56.2475	−	129.898i	0.0759076	−	0.175301i
$742$	484.784			0.653348
$743$			7.74529i			0.0104243i	0.999986	+	0.00521217i	$0.00165909\pi$
$743$			7.74529i			0.0104243i	−0.999986	+	0.00521217i	$0.998341\pi$
$744$		−	286.390i		−	0.384932i
$745$	−312.767			−0.419821
$746$	81.2508			0.108915
$747$	−365.093			−0.488746
$748$	337.196			0.450797
$749$		−	38.4733i		−	0.0513663i
$750$	−140.302			−0.187070
$751$		−	1281.23i		−	1.70603i	−0.521890	−	0.853013i	$-0.674773\pi$
$751$		−	1281.23i		−	1.70603i	0.521890	−	0.853013i	$-0.325227\pi$
$752$	−95.6977			−0.127258
$753$			329.477i			0.437552i
$754$		−	48.6010i		−	0.0644576i
$755$			101.098i			0.133904i
$756$		−	55.8543i		−	0.0738814i
$757$	−441.172			−0.582790			−0.291395	−	0.956603i	$-0.594119\pi$
$757$	−441.172			−0.582790			−0.291395	+	0.956603i	$0.594119\pi$
$758$	449.980			0.593641
$759$		−	68.6750i		−	0.0904808i
$760$	183.203	+	79.3291i	0.241056	+	0.104380i
$761$	476.532			0.626192			0.313096	−	0.949721i	$-0.398634\pi$
$761$	476.532			0.626192			0.313096	+	0.949721i	$0.398634\pi$
$762$		−	36.4508i		−	0.0478357i
$763$			563.193i			0.738129i
$764$	−43.2858			−0.0566568
$765$	77.9277			0.101866
$766$	101.306			0.132253
$767$	−298.997			−0.389826
$768$		−	465.440i		−	0.606041i
$769$	−624.567			−0.812181			−0.406091	−	0.913833i	$-0.633108\pi$
$769$	−624.567			−0.812181			−0.406091	+	0.913833i	$0.633108\pi$
$770$			57.5605i			0.0747539i
$771$	43.9036			0.0569438
$772$		−	251.130i		−	0.325298i
$773$			334.038i			0.432133i	0.976379	+	0.216066i	$0.0693227\pi$
$773$			334.038i			0.432133i	−0.976379	+	0.216066i	$0.930677\pi$
$774$			256.605i			0.331531i
$775$			468.951i			0.605098i
$776$	915.492			1.17976
$777$	332.412			0.427815
$778$		−	569.724i		−	0.732293i
$779$	−545.595	−	236.249i	−0.700378	−	0.303273i
$780$	−21.6079			−0.0277025
$781$			22.6893i			0.0290516i
$782$			145.849i			0.186508i
$783$	−44.7010			−0.0570894
$784$	46.0142			0.0586915
$785$	−68.4601			−0.0872103
$786$	377.457			0.480225
$787$			479.323i			0.609051i	0.952504	+	0.304526i	$0.0984980\pi$
$787$			479.323i			0.609051i	−0.952504	+	0.304526i	$0.901502\pi$
$788$	747.877			0.949083
$789$		−	779.631i		−	0.988126i
$790$	146.804			0.185828
$791$		−	927.792i		−	1.17294i
$792$		−	179.871i		−	0.227110i
$793$		−	26.5619i		−	0.0334955i
$794$			371.790i			0.468249i
$795$	−172.495			−0.216975
$796$	−607.341			−0.762991
$797$			126.025i			0.158125i	0.996870	+	0.0790624i	$0.0251926\pi$
$797$			126.025i			0.158125i	−0.996870	+	0.0790624i	$0.974807\pi$
$798$	−81.1545	+	187.418i	−0.101697	+	0.234860i
$799$	−1130.26			−1.41460
$800$			717.617i			0.897021i
$801$			209.918i			0.262070i
$802$	424.880			0.529776
$803$	−246.072			−0.306441
$804$	487.505			0.606349
$805$	32.8323			0.0407854
$806$		−	113.343i		−	0.140624i
$807$	840.289			1.04125
$808$		−	620.189i		−	0.767561i
$809$	901.825			1.11474			0.557370	−	0.830264i	$-0.311810\pi$
$809$	901.825			1.11474			0.557370	+	0.830264i	$0.311810\pi$
$810$		−	15.0706i		−	0.0186056i
$811$			183.776i			0.226604i	0.993561	+	0.113302i	$0.0361427\pi$
$811$			183.776i			0.226604i	−0.993561	+	0.113302i	$0.963857\pi$
$812$		−	92.4720i		−	0.113882i
$813$			271.926i			0.334473i
$814$	388.096			0.476777
$815$	99.9518			0.122640
$816$			60.8779i			0.0746052i
$817$	−491.674	+	1135.47i	−0.601804	+	1.38981i
$818$	718.103			0.877877
$819$		−	60.9728i		−	0.0744478i
$820$			90.7572i			0.110679i
$821$	1034.35			1.25986			0.629932	−	0.776650i	$-0.283083\pi$
$821$	1034.35			1.25986			0.629932	+	0.776650i	$0.283083\pi$
$822$	−454.241			−0.552604
$823$	952.107			1.15687			0.578437	−	0.815727i	$-0.303663\pi$
$823$	952.107			1.15687			0.578437	+	0.815727i	$0.303663\pi$
$824$	−1553.33			−1.88511
$825$			294.532i			0.357009i
$826$	431.395			0.522270
$827$		−	970.806i		−	1.17389i	−0.809627	−	0.586944i	$-0.800331\pi$
$827$		−	970.806i		−	1.17389i	0.809627	−	0.586944i	$-0.199669\pi$
$828$	−37.1960			−0.0449227
$829$			374.908i			0.452242i	0.974099	+	0.226121i	$0.0726044\pi$
$829$			374.908i			0.452242i	−0.974099	+	0.226121i	$0.927396\pi$
$830$		−	203.784i		−	0.245522i
$831$			271.289i			0.326461i
$832$		−	203.125i		−	0.244140i
$833$	543.463			0.652417
$834$	−124.151			−0.148862
$835$			373.996i			0.447900i
$836$	124.949	−	288.556i	0.149460	−	0.345163i
$837$	−104.248			−0.124549
$838$			463.634i			0.553263i
$839$			1282.87i			1.52904i	0.644597	+	0.764522i	$0.277025\pi$
$839$			1282.87i			1.52904i	−0.644597	+	0.764522i	$0.722975\pi$
$840$	85.9934			0.102373
$841$	766.993			0.912002
$842$	−759.849			−0.902433
$843$	792.688			0.940318
$844$		−	160.229i		−	0.189845i
$845$	191.873			0.227069
$846$			218.584i			0.258373i
$847$	−321.663			−0.379767
$848$		−	134.755i		−	0.158909i
$849$		−	80.6684i		−	0.0950158i
$850$		−	625.515i		−	0.735900i
$851$		−	221.369i		−	0.260128i
$852$	12.2891			0.0144238
$853$	827.595			0.970217			0.485108	−	0.874454i	$-0.338780\pi$
$853$	827.595			0.970217			0.485108	+	0.874454i	$0.338780\pi$
$854$			38.3238i			0.0448757i
$855$	28.8762	−	66.6868i	0.0337734	−	0.0779963i
$856$	−67.1063			−0.0783952
$857$		−	986.671i		−	1.15131i	−0.817694	−	0.575654i	$-0.804748\pi$
$857$		−	986.671i		−	1.15131i	0.817694	−	0.575654i	$-0.195252\pi$
$858$		−	71.1867i		−	0.0829682i
$859$	−1382.27			−1.60916			−0.804582	−	0.593842i	$-0.797611\pi$
$859$	−1382.27			−1.60916			−0.804582	+	0.593842i	$0.797611\pi$
$860$	188.880			0.219628
$861$	−256.096			−0.297441
$862$	826.007			0.958244
$863$		−	485.475i		−	0.562543i	−0.959628	−	0.281272i	$-0.909244\pi$
$863$		−	485.475i		−	0.562543i	0.959628	−	0.281272i	$-0.0907562\pi$
$864$	−159.526			−0.184636
$865$		−	13.3961i		−	0.0154868i
$866$	161.292			0.186250
$867$			218.453i			0.251964i
$868$		−	215.655i		−	0.248450i
$869$		−	637.792i		−	0.733938i
$870$		−	24.9507i		−	0.0286790i
$871$	532.179			0.610998
$872$	982.337			1.12653
$873$		−	333.244i		−	0.381723i
$874$	124.811	+	54.0446i	0.142804	+	0.0618359i
$875$	−291.413			−0.333043
$876$			133.279i			0.152145i
$877$		−	266.756i		−	0.304169i	−0.988368	−	0.152084i	$-0.951401\pi$
$877$		−	266.756i		−	0.304169i	0.988368	−	0.152084i	$-0.0485985\pi$
$878$	83.2310			0.0947961
$879$	384.797			0.437767
$880$	16.0000			0.0181818
$881$	−979.248			−1.11152			−0.555760	−	0.831343i	$-0.687573\pi$
$881$	−979.248			−1.11152			−0.555760	+	0.831343i	$0.687573\pi$
$882$		−	105.101i		−	0.119162i
$883$	1551.91			1.75755			0.878774	−	0.477239i	$-0.158362\pi$
$883$	1551.91			1.75755			0.878774	+	0.477239i	$0.158362\pi$
$884$		−	199.370i		−	0.225532i
$885$	−153.498			−0.173444
$886$		−	801.609i		−	0.904750i
$887$		−	700.543i		−	0.789789i	−0.918727	−	0.394894i	$-0.870781\pi$
$887$		−	700.543i		−	0.789789i	0.918727	−	0.394894i	$-0.129219\pi$
$888$		−	579.803i		−	0.652931i
$889$		−	75.7095i		−	0.0851626i
$890$	−117.170			−0.131651
$891$	−65.4743			−0.0734840
$892$			540.138i			0.605536i
$893$	−418.821	+	967.227i	−0.469005	+	1.08312i
$894$	−558.090			−0.624261
$895$			15.8244i			0.0176809i
$896$		−	287.184i		−	0.320518i
$897$	−40.6046			−0.0452672
$898$	−539.518			−0.600800
$899$	−172.591			−0.191982
$900$	159.526			0.177251
$901$		−	1591.56i		−	1.76644i
$902$	−298.997			−0.331482
$903$			532.978i			0.590231i
$904$	−1618.28			−1.79014
$905$		−	136.136i		−	0.150426i
$906$			180.395i			0.199112i
$907$			1228.07i			1.35399i	0.735987	+	0.676996i	$0.236718\pi$
$907$			1228.07i			1.35399i	−0.735987	+	0.676996i	$0.763282\pi$
$908$			613.635i			0.675810i
$909$	−225.752			−0.248353
$910$	34.0331			0.0373990
$911$		−	1077.26i		−	1.18250i	−0.806487	−	0.591252i	$-0.798634\pi$
$911$		−	1077.26i		−	1.18250i	0.806487	−	0.591252i	$-0.201366\pi$
$912$	52.0964	+	22.5584i	0.0571232	+	0.0247351i
$913$	−885.341			−0.969705
$914$		−	330.617i		−	0.361726i
$915$		−	13.6363i		−	0.0149031i
$916$	590.158			0.644277
$917$	783.991			0.854952
$918$	139.051			0.151472
$919$	−348.488			−0.379204			−0.189602	−	0.981861i	$-0.560720\pi$
$919$	−348.488			−0.379204			−0.189602	+	0.981861i	$0.560720\pi$
$920$		−	57.2670i		−	0.0622468i
$921$	852.289			0.925395
$922$			295.024i			0.319983i
$923$	13.4152			0.0145344
$924$		−	135.445i		−	0.146586i
$925$			949.403i			1.02638i
$926$			257.923i			0.278535i
$927$			565.423i			0.609949i
$928$	−264.110			−0.284601
$929$	−1506.48			−1.62162			−0.810808	−	0.585312i	$-0.800972\pi$
$929$	−1506.48			−1.62162			−0.810808	+	0.585312i	$0.800972\pi$
$930$		−	58.1877i		−	0.0625675i
$931$	201.381	−	465.070i	0.216306	−	0.499538i
$932$	−119.836			−0.128579
$933$			281.932i			0.302177i
$934$			139.724i			0.149597i
$935$	188.973			0.202110
$936$	−106.350			−0.113622
$937$	−145.777			−0.155578			−0.0777890	−	0.996970i	$-0.524786\pi$
$937$	−145.777			−0.155578			−0.0777890	+	0.996970i	$0.524786\pi$
$938$	−767.834			−0.818586
$939$			718.617i			0.765300i
$940$	160.894			0.171164
$941$			1501.75i			1.59590i	0.602721	+	0.797952i	$0.294083\pi$
$941$			1501.75i			1.59590i	−0.602721	+	0.797952i	$0.705917\pi$
$942$	−122.158			−0.129679
$943$			170.547i			0.180855i
$944$		−	119.914i		−	0.127028i
$945$		−	31.3021i		−	0.0331239i
$946$			622.261i			0.657781i
$947$	765.794			0.808653			0.404326	−	0.914615i	$-0.367506\pi$
$947$	765.794			0.808653			0.404326	+	0.914615i	$0.367506\pi$
$948$	−345.444			−0.364392
$949$			145.492i			0.153311i
$950$	−535.286	−	231.786i	−0.563459	−	0.243985i
$951$	−633.498			−0.666139
$952$			793.435i			0.833440i
$953$		−	1308.88i		−	1.37344i	−0.726924	−	0.686718i	$-0.759051\pi$
$953$		−	1308.88i		−	1.37344i	0.726924	−	0.686718i	$-0.240949\pi$
$954$	−307.794			−0.322635
$955$	−24.2584			−0.0254014
$956$	−787.395			−0.823635
$957$	−108.399			−0.113269
$958$		−	608.318i		−	0.634988i
$959$	−943.474			−0.983810
$960$		−	104.280i		−	0.108625i
$961$	558.498			0.581164
$962$		−	229.465i		−	0.238529i
$963$			24.4271i			0.0253656i
$964$			683.107i			0.708617i
$965$		−	140.739i		−	0.145844i
$966$	58.5848			0.0606468
$967$	587.704			0.607760			0.303880	−	0.952710i	$-0.401718\pi$
$967$	587.704			0.607760			0.303880	+	0.952710i	$0.401718\pi$
$968$			561.054i			0.579601i
$969$	615.299	+	266.432i	0.634983	+	0.274956i
$970$	186.007			0.191759
$971$			653.823i			0.673351i	0.941621	+	0.336675i	$0.109302\pi$
$971$			653.823i			0.673351i	−0.941621	+	0.336675i	$0.890698\pi$
$972$			35.4624i			0.0364840i
$973$	−257.866			−0.265022
$974$	−326.337			−0.335049
$975$	174.145			0.178610
$976$	10.6528			0.0109148
$977$		−	101.034i		−	0.103413i	−0.998662	−	0.0517064i	$-0.983534\pi$
$977$		−	101.034i		−	0.103413i	0.998662	−	0.0517064i	$-0.0164660\pi$
$978$	178.350			0.182362
$979$			509.045i			0.519964i
$980$	−77.3623			−0.0789411
$981$		−	357.576i		−	0.364502i
$982$		−	401.367i		−	0.408724i
$983$		−	888.065i		−	0.903423i	−0.892164	−	0.451711i	$-0.850814\pi$
$983$		−	888.065i		−	0.903423i	0.892164	−	0.451711i	$-0.149186\pi$
$984$			446.691i			0.453954i
$985$	419.128			0.425511
$986$	230.213			0.233481
$987$			454.006i			0.459986i
$988$	−170.611	−	73.8768i	−0.172683	−	0.0747741i
$989$	354.935			0.358883
$990$		−	36.5457i		−	0.0369148i
$991$			1782.19i			1.79838i	0.437562	+	0.899188i	$0.355842\pi$
$991$			1782.19i			1.79838i	−0.437562	+	0.899188i	$0.644158\pi$
$992$	−615.932			−0.620899
$993$	−381.498			−0.384188
$994$	−19.3556			−0.0194725
$995$	−340.368			−0.342078
$996$			479.522i			0.481448i
$997$	891.200			0.893882			0.446941	−	0.894563i	$-0.352513\pi$
$997$	891.200			0.893882			0.446941	+	0.894563i	$0.352513\pi$
$998$		−	353.203i		−	0.353911i
$999$	−211.051			−0.211263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.3.c.b.37.2	✓	4
3.2	odd	2		171.3.c.f.37.3		4
4.3	odd	2		912.3.o.b.721.2		4
12.11	even	2		2736.3.o.l.721.2		4
19.18	odd	2	inner	57.3.c.b.37.3	yes	4
57.56	even	2		171.3.c.f.37.2		4
76.75	even	2		912.3.o.b.721.4		4
228.227	odd	2		2736.3.o.l.721.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.c.b.37.2	✓	4	1.1	even	1	trivial
57.3.c.b.37.3	yes	4	19.18	odd	2	inner
171.3.c.f.37.2		4	57.56	even	2
171.3.c.f.37.3		4	3.2	odd	2
912.3.o.b.721.2		4	4.3	odd	2
912.3.o.b.721.4		4	76.75	even	2
2736.3.o.l.721.1		4	228.227	odd	2
2736.3.o.l.721.2		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)

\(f(q)\)	\(=\)	\(q-1.31342i q^{2} +1.73205i q^{3} +2.27492 q^{4} +1.27492 q^{5} +2.27492 q^{6} +4.72508 q^{7} -8.24163i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.31342i q^{2} +1.73205i q^{3} +2.27492 q^{4} +1.27492 q^{5} +2.27492 q^{6} +4.72508 q^{7} -8.24163i q^{8} -3.00000 q^{9} -1.67451i q^{10} -7.27492 q^{11} +3.94027i q^{12} +4.30136i q^{13} -6.20604i q^{14} +2.20822i q^{15} -1.72508 q^{16} -20.3746 q^{17} +3.94027i q^{18} +(-7.54983 + 17.4356i) q^{19} +2.90033 q^{20} +8.18408i q^{21} +9.55505i q^{22} +5.45017 q^{23} +14.2749 q^{24} -23.3746 q^{25} +5.64950 q^{26} -5.19615i q^{27} +10.7492 q^{28} -8.60271i q^{29} +2.90033 q^{30} -20.0624i q^{31} -30.7007i q^{32} -12.6005i q^{33} +26.7605i q^{34} +6.02409 q^{35} -6.82475 q^{36} -40.6169i q^{37} +(22.9003 + 9.91613i) q^{38} -7.45017 q^{39} -10.5074i q^{40} +31.2920i q^{41} +10.7492 q^{42} +65.1238 q^{43} -16.5498 q^{44} -3.82475 q^{45} -7.15838i q^{46} +55.4743 q^{47} -2.98793i q^{48} -26.6736 q^{49} +30.7007i q^{50} -35.2898i q^{51} +9.78523i q^{52} +78.1149i q^{53} -6.82475 q^{54} -9.27492 q^{55} -38.9424i q^{56} +(-30.1993 - 13.0767i) q^{57} -11.2990 q^{58} +69.5122i q^{59} +5.02352i q^{60} -6.17525 q^{61} -26.3505 q^{62} -14.1752 q^{63} -47.2234 q^{64} +5.48387i q^{65} -16.5498 q^{66} -123.724i q^{67} -46.3505 q^{68} +9.43996i q^{69} -7.91218i q^{70} -3.11884i q^{71} +24.7249i q^{72} +33.8248 q^{73} -53.3472 q^{74} -40.4860i q^{75} +(-17.1752 + 39.6645i) q^{76} -34.3746 q^{77} +9.78523i q^{78} +87.6700i q^{79} -2.19934 q^{80} +9.00000 q^{81} +41.0997 q^{82} +121.698 q^{83} +18.6181i q^{84} -25.9759 q^{85} -85.5351i q^{86} +14.9003 q^{87} +59.9572i q^{88} -69.9726i q^{89} +5.02352i q^{90} +20.3243i q^{91} +12.3987 q^{92} +34.7492 q^{93} -72.8612i q^{94} +(-9.62541 + 22.2289i) q^{95} +53.1752 q^{96} +111.081i q^{97} +35.0337i q^{98} +21.8248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 10 q^{5} - 6 q^{6} + 34 q^{7} - 12 q^{9}+O(q^{10}) \) 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

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