LMFDB - Embedded newform 242.4.c.d.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	242.3
Dual form			242.4.c.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 1.17557i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.23607 - 3.80423i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-3.09017 + 9.51057i) q^{7} +(2.47214 + 7.60845i) q^{8} +(21.0344 - 15.2824i) q^{9} +O(q^{10})$	\(q+(-1.61803 + 1.17557i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.23607 - 3.80423i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-3.09017 + 9.51057i) q^{7} +(2.47214 + 7.60845i) q^{8} +(21.0344 - 15.2824i) q^{9} -6.00000 q^{10} +4.00000 q^{12} +(12.9443 - 9.40456i) q^{13} +(-6.18034 - 19.0211i) q^{14} +(-0.927051 + 2.85317i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-33.9787 - 24.6870i) q^{17} +(-16.0689 + 49.4549i) q^{18} +(35.8460 + 110.323i) q^{19} +(9.70820 - 7.05342i) q^{20} -10.0000 q^{21} +189.000 q^{23} +(-6.47214 + 4.70228i) q^{24} +(-35.8460 - 110.323i) q^{25} +(-9.88854 + 30.4338i) q^{26} +(42.8779 + 31.1526i) q^{27} +(32.3607 + 23.5114i) q^{28} +(-37.0820 + 114.127i) q^{29} +(-1.85410 - 5.70634i) q^{30} +(131.870 - 95.8090i) q^{31} +32.0000 q^{32} +84.0000 q^{34} +(-24.2705 + 17.6336i) q^{35} +(-32.1378 - 98.9099i) q^{36} +(-126.388 + 388.982i) q^{37} +(-187.692 - 136.366i) q^{38} +(12.9443 + 9.40456i) q^{39} +(-7.41641 + 22.8254i) q^{40} +(144.620 + 445.094i) q^{41} +(16.1803 - 11.7557i) q^{42} +110.000 q^{43} +78.0000 q^{45} +(-305.808 + 222.183i) q^{46} +(44.4984 + 136.952i) q^{47} +(4.94427 - 15.2169i) q^{48} +(196.591 + 142.832i) q^{49} +(187.692 + 136.366i) q^{50} +(12.9787 - 39.9444i) q^{51} +(-19.7771 - 60.8676i) q^{52} +(-72.8115 + 52.9007i) q^{53} -106.000 q^{54} -80.0000 q^{56} +(-93.8460 + 68.1831i) q^{57} +(-74.1641 - 228.254i) q^{58} +(-139.985 + 430.829i) q^{59} +(9.70820 + 7.05342i) q^{60} +(-16.1803 - 11.7557i) q^{61} +(-100.740 + 310.044i) q^{62} +(80.3444 + 247.275i) q^{63} +(-51.7771 + 37.6183i) q^{64} +48.0000 q^{65} -97.0000 q^{67} +(-135.915 + 98.7479i) q^{68} +(58.4042 + 179.750i) q^{69} +(18.5410 - 57.0634i) q^{70} +(376.193 + 273.320i) q^{71} +(168.276 + 122.259i) q^{72} +(262.046 - 806.496i) q^{73} +(-252.776 - 777.964i) q^{74} +(93.8460 - 68.1831i) q^{75} +464.000 q^{76} -32.0000 q^{78} +(600.291 - 436.137i) q^{79} +(-14.8328 - 45.6507i) q^{80} +(200.552 - 617.236i) q^{81} +(-757.240 - 550.167i) q^{82} +(-354.349 - 257.450i) q^{83} +(-12.3607 + 38.0423i) q^{84} +(-38.9361 - 119.833i) q^{85} +(-177.984 + 129.313i) q^{86} -120.000 q^{87} -273.000 q^{89} +(-126.207 + 91.6945i) q^{90} +(49.4427 + 152.169i) q^{91} +(233.617 - 718.999i) q^{92} +(131.870 + 95.8090i) q^{93} +(-232.997 - 169.282i) q^{94} +(-107.538 + 330.968i) q^{95} +(9.88854 + 30.4338i) q^{96} +(-615.662 + 447.305i) q^{97} -486.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9} - 24 q^{10} + 16 q^{12} + 16 q^{13} + 20 q^{14} + 3 q^{15} - 16 q^{16} - 42 q^{17} + 52 q^{18} - 116 q^{19} + 12 q^{20} - 40 q^{21} + 756 q^{23} - 8 q^{24} + 116 q^{25} + 32 q^{26} + 53 q^{27} + 40 q^{28} + 120 q^{29} + 6 q^{30} + 163 q^{31} + 128 q^{32} + 336 q^{34} - 30 q^{35} + 104 q^{36} + 409 q^{37} - 232 q^{38} + 16 q^{39} + 24 q^{40} - 468 q^{41} + 20 q^{42} + 440 q^{43} + 312 q^{45} - 378 q^{46} - 144 q^{47} - 16 q^{48} + 243 q^{49} + 232 q^{50} - 42 q^{51} + 64 q^{52} - 90 q^{53} - 424 q^{54} - 320 q^{56} - 116 q^{57} + 240 q^{58} + 453 q^{59} + 12 q^{60} - 20 q^{61} + 326 q^{62} - 260 q^{63} - 64 q^{64} + 192 q^{65} - 388 q^{67} - 168 q^{68} - 189 q^{69} - 60 q^{70} + 465 q^{71} + 208 q^{72} - 848 q^{73} + 818 q^{74} + 116 q^{75} + 1856 q^{76} - 128 q^{78} + 742 q^{79} + 48 q^{80} - 649 q^{81} - 936 q^{82} - 438 q^{83} + 40 q^{84} + 126 q^{85} - 220 q^{86} - 480 q^{87} - 1092 q^{89} - 156 q^{90} - 160 q^{91} - 756 q^{92} + 163 q^{93} - 288 q^{94} + 348 q^{95} - 32 q^{96} - 761 q^{97} - 1944 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9 - 24 * q^10 + 16 * q^12 + 16 * q^13 + 20 * q^14 + 3 * q^15 - 16 * q^16 - 42 * q^17 + 52 * q^18 - 116 * q^19 + 12 * q^20 - 40 * q^21 + 756 * q^23 - 8 * q^24 + 116 * q^25 + 32 * q^26 + 53 * q^27 + 40 * q^28 + 120 * q^29 + 6 * q^30 + 163 * q^31 + 128 * q^32 + 336 * q^34 - 30 * q^35 + 104 * q^36 + 409 * q^37 - 232 * q^38 + 16 * q^39 + 24 * q^40 - 468 * q^41 + 20 * q^42 + 440 * q^43 + 312 * q^45 - 378 * q^46 - 144 * q^47 - 16 * q^48 + 243 * q^49 + 232 * q^50 - 42 * q^51 + 64 * q^52 - 90 * q^53 - 424 * q^54 - 320 * q^56 - 116 * q^57 + 240 * q^58 + 453 * q^59 + 12 * q^60 - 20 * q^61 + 326 * q^62 - 260 * q^63 - 64 * q^64 + 192 * q^65 - 388 * q^67 - 168 * q^68 - 189 * q^69 - 60 * q^70 + 465 * q^71 + 208 * q^72 - 848 * q^73 + 818 * q^74 + 116 * q^75 + 1856 * q^76 - 128 * q^78 + 742 * q^79 + 48 * q^80 - 649 * q^81 - 936 * q^82 - 438 * q^83 + 40 * q^84 + 126 * q^85 - 220 * q^86 - 480 * q^87 - 1092 * q^89 - 156 * q^90 - 160 * q^91 - 756 * q^92 + 163 * q^93 - 288 * q^94 + 348 * q^95 - 32 * q^96 - 761 * q^97 - 1944 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.0594703	+	0.183031i	0.976378	−	0.216068i	$-0.0693232\pi$
$3$	0.309017	+	0.951057i	0.0594703	+	0.183031i	−0.916908	+	0.399098i	$0.869323\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	2.42705	+	1.76336i	0.217082	+	0.157719i	0.691012	−	0.722843i	$-0.257165\pi$
$5$	2.42705	+	1.76336i	0.217082	+	0.157719i	−0.473930	+	0.880562i	$0.657165\pi$
$6$	−1.61803	−	1.17557i	−0.110093	−	0.0799874i
$7$	−3.09017	+	9.51057i	−0.166853	+	0.513522i	−0.999168	−	0.0407813i	$-0.987015\pi$
$7$	−3.09017	+	9.51057i	−0.166853	+	0.513522i	0.832315	+	0.554304i	$0.187015\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	21.0344	−	15.2824i	0.779053	−	0.566015i
$10$	−6.00000			−0.189737
$11$		0			0
$11$		0			0
$12$	4.00000			0.0962250
$13$	12.9443	−	9.40456i	0.276161	−	0.200643i	−0.441080	−	0.897468i	$-0.645405\pi$
$13$	12.9443	−	9.40456i	0.276161	−	0.200643i	0.717241	+	0.696825i	$0.245405\pi$
$14$	−6.18034	−	19.0211i	−0.117983	−	0.363115i
$15$	−0.927051	+	2.85317i	−0.0159576	+	0.0491123i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	−33.9787	−	24.6870i	−0.484768	−	0.352204i	0.318401	−	0.947956i	$-0.396854\pi$
$17$	−33.9787	−	24.6870i	−0.484768	−	0.352204i	−0.803169	+	0.595752i	$0.796854\pi$
$18$	−16.0689	+	49.4549i	−0.210415	+	0.647591i
$19$	35.8460	+	110.323i	0.432823	+	1.33209i	0.895301	+	0.445461i	$0.146960\pi$
$19$	35.8460	+	110.323i	0.432823	+	1.33209i	−0.462479	+	0.886630i	$0.653040\pi$
$20$	9.70820	−	7.05342i	0.108541	−	0.0788597i
$21$	−10.0000			−0.103913
$22$		0			0
$23$	189.000			1.71344			0.856722	−	0.515778i	$-0.172497\pi$
$23$	189.000			1.71344			0.856722	+	0.515778i	$0.172497\pi$
$24$	−6.47214	+	4.70228i	−0.0550466	+	0.0399937i
$25$	−35.8460	−	110.323i	−0.286768	−	0.882580i
$26$	−9.88854	+	30.4338i	−0.0745886	+	0.229560i
$27$	42.8779	+	31.1526i	0.305624	+	0.222049i
$28$	32.3607	+	23.5114i	0.218414	+	0.158687i
$29$	−37.0820	+	114.127i	−0.237447	+	0.730787i	0.759340	+	0.650694i	$0.225522\pi$
$29$	−37.0820	+	114.127i	−0.237447	+	0.730787i	−0.996787	+	0.0800930i	$0.974478\pi$
$30$	−1.85410	−	5.70634i	−0.0112837	−	0.0347277i
$31$	131.870	−	95.8090i	0.764016	−	0.555090i	−0.136123	−	0.990692i	$-0.543464\pi$
$31$	131.870	−	95.8090i	0.764016	−	0.555090i	0.900140	+	0.435601i	$0.143464\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	84.0000			0.423702
$35$	−24.2705	+	17.6336i	−0.117213	+	0.0851604i
$36$	−32.1378	−	98.9099i	−0.148786	−	0.457916i
$37$	−126.388	+	388.982i	−0.561569	+	1.72833i	0.116363	+	0.993207i	$0.462876\pi$
$37$	−126.388	+	388.982i	−0.561569	+	1.72833i	−0.677932	+	0.735125i	$0.737124\pi$
$38$	−187.692	−	136.366i	−0.801254	−	0.582145i
$39$	12.9443	+	9.40456i	0.0531472	+	0.0386137i
$40$	−7.41641	+	22.8254i	−0.0293159	+	0.0902251i
$41$	144.620	+	445.094i	0.550874	+	1.69542i	0.706597	+	0.707616i	$0.250229\pi$
$41$	144.620	+	445.094i	0.550874	+	1.69542i	−0.155723	+	0.987801i	$0.549771\pi$
$42$	16.1803	−	11.7557i	0.0594448	−	0.0431892i
$43$	110.000			0.390113			0.195056	−	0.980792i	$-0.437511\pi$
$43$	110.000			0.390113			0.195056	+	0.980792i	$0.437511\pi$
$44$		0			0
$45$	78.0000			0.258390
$46$	−305.808	+	222.183i	−0.980195	+	0.712154i
$47$	44.4984	+	136.952i	0.138101	+	0.425032i	0.996060	−	0.0886872i	$-0.0282672\pi$
$47$	44.4984	+	136.952i	0.138101	+	0.425032i	−0.857958	+	0.513720i	$0.828267\pi$
$48$	4.94427	−	15.2169i	0.0148676	−	0.0457577i
$49$	196.591	+	142.832i	0.573152	+	0.416419i
$50$	187.692	+	136.366i	0.530873	+	0.385702i
$51$	12.9787	−	39.9444i	0.0356350	−	0.109673i
$52$	−19.7771	−	60.8676i	−0.0527421	−	0.162323i
$53$	−72.8115	+	52.9007i	−0.188706	+	0.137103i	−0.678127	−	0.734945i	$-0.737208\pi$
$53$	−72.8115	+	52.9007i	−0.188706	+	0.137103i	0.489421	+	0.872048i	$0.337208\pi$
$54$	−106.000			−0.267125
$55$		0			0
$56$	−80.0000			−0.190901
$57$	−93.8460	+	68.1831i	−0.218074	+	0.158440i
$58$	−74.1641	−	228.254i	−0.167900	−	0.516744i
$59$	−139.985	+	430.829i	−0.308889	+	0.950663i	0.669308	+	0.742985i	$0.266591\pi$
$59$	−139.985	+	430.829i	−0.308889	+	0.950663i	−0.978197	+	0.207678i	$0.933409\pi$
$60$	9.70820	+	7.05342i	0.0208887	+	0.0151765i
$61$	−16.1803	−	11.7557i	−0.0339620	−	0.0246748i	0.570675	−	0.821176i	$-0.306682\pi$
$61$	−16.1803	−	11.7557i	−0.0339620	−	0.0246748i	−0.604637	+	0.796501i	$0.706682\pi$
$62$	−100.740	+	310.044i	−0.206354	+	0.635092i
$63$	80.3444	+	247.275i	0.160674	+	0.494503i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	48.0000			0.0915949
$66$		0			0
$67$	−97.0000			−0.176872			−0.0884361	−	0.996082i	$-0.528187\pi$
$67$	−97.0000			−0.176872			−0.0884361	+	0.996082i	$0.528187\pi$
$68$	−135.915	+	98.7479i	−0.242384	+	0.176102i
$69$	58.4042	+	179.750i	0.101899	+	0.313613i
$70$	18.5410	−	57.0634i	0.0316582	−	0.0974340i
$71$	376.193	+	273.320i	0.628815	+	0.456861i	0.855990	−	0.516993i	$-0.172949\pi$
$71$	376.193	+	273.320i	0.628815	+	0.456861i	−0.227174	+	0.973854i	$0.572949\pi$
$72$	168.276	+	122.259i	0.275437	+	0.200117i
$73$	262.046	−	806.496i	0.420140	−	1.29306i	−0.487432	−	0.873161i	$-0.662066\pi$
$73$	262.046	−	806.496i	0.420140	−	1.29306i	0.907572	−	0.419897i	$-0.137934\pi$
$74$	−252.776	−	777.964i	−0.397089	−	1.22211i
$75$	93.8460	−	68.1831i	0.144485	−	0.104975i
$76$	464.000			0.700322
$77$		0			0
$78$	−32.0000			−0.0464524
$79$	600.291	−	436.137i	0.854911	−	0.621129i	−0.0715847	−	0.997435i	$-0.522806\pi$
$79$	600.291	−	436.137i	0.854911	−	0.621129i	0.926496	+	0.376305i	$0.122806\pi$
$80$	−14.8328	−	45.6507i	−0.0207295	−	0.0637988i
$81$	200.552	−	617.236i	0.275106	−	0.846688i
$82$	−757.240	−	550.167i	−1.01979	−	0.740924i
$83$	−354.349	−	257.450i	−0.468613	−	0.340467i	0.328287	−	0.944578i	$-0.393529\pi$
$83$	−354.349	−	257.450i	−0.468613	−	0.340467i	−0.796901	+	0.604110i	$0.793529\pi$
$84$	−12.3607	+	38.0423i	−0.0160555	+	0.0494137i
$85$	−38.9361	−	119.833i	−0.0496849	−	0.152914i
$86$	−177.984	+	129.313i	−0.223168	+	0.162141i
$87$	−120.000			−0.147878
$88$		0			0
$89$	−273.000			−0.325145			−0.162573	−	0.986697i	$-0.551979\pi$
$89$	−273.000			−0.325145			−0.162573	+	0.986697i	$0.551979\pi$
$90$	−126.207	+	91.6945i	−0.147815	+	0.107394i
$91$	49.4427	+	152.169i	0.0569561	+	0.175293i
$92$	233.617	−	718.999i	0.264742	−	0.814791i
$93$	131.870	+	95.8090i	0.147035	+	0.106827i
$94$	−232.997	−	169.282i	−0.255657	−	0.185746i
$95$	−107.538	+	330.968i	−0.116138	+	0.357438i
$96$	9.88854	+	30.4338i	0.0105130	+	0.0323556i
$97$	−615.662	+	447.305i	−0.644443	+	0.468215i	−0.861374	−	0.507972i	$-0.830395\pi$
$97$	−615.662	+	447.305i	−0.644443	+	0.468215i	0.216931	+	0.976187i	$0.430395\pi$
$98$	−486.000			−0.500953
$99$		0			0
$100$	−464.000			−0.464000
$101$	1276.63	−	927.525i	1.25772	−	0.913784i	0.259073	−	0.965858i	$-0.416583\pi$
$101$	1276.63	−	927.525i	1.25772	−	0.913784i	0.998643	+	0.0520737i	$0.0165831\pi$
$102$	25.9574	+	79.8887i	0.0251977	+	0.0775506i
$103$	373.293	−	1148.88i	0.357103	−	1.09905i	−0.597677	−	0.801737i	$-0.703910\pi$
$103$	373.293	−	1148.88i	0.357103	−	1.09905i	0.954780	−	0.297313i	$-0.0960905\pi$
$104$	103.554	+	75.2365i	0.0976377	+	0.0709380i
$105$	−24.2705	−	17.6336i	−0.0225577	−	0.0163891i
$106$	55.6231	−	171.190i	0.0509678	−	0.156863i
$107$	−446.839	−	1375.23i	−0.403715	−	1.24251i	−0.921963	−	0.387277i	$-0.873416\pi$
$107$	−446.839	−	1375.23i	−0.403715	−	1.24251i	0.518248	−	0.855230i	$-0.326584\pi$
$108$	171.512	−	124.610i	0.152812	−	0.111025i
$109$	−1342.00			−1.17927			−0.589634	−	0.807670i	$-0.700728\pi$
$109$	−1342.00			−1.17927			−0.589634	+	0.807670i	$0.700728\pi$
$110$		0			0
$111$	−409.000			−0.349735
$112$	129.443	−	94.0456i	0.109207	−	0.0793436i
$113$	544.179	+	1674.81i	0.453027	+	1.39427i	0.873436	+	0.486939i	$0.161887\pi$
$113$	544.179	+	1674.81i	0.453027	+	1.39427i	−0.420409	+	0.907335i	$0.638113\pi$
$114$	71.6919	−	220.645i	0.0588997	−	0.181275i
$115$	458.713	+	333.274i	0.371958	+	0.270243i
$116$	388.328	+	282.137i	0.310822	+	0.225825i
$117$	128.551	−	395.640i	0.101577	−	0.312623i
$118$	−279.969	−	861.657i	−0.218418	−	0.672220i
$119$	339.787	−	246.870i	0.261750	−	0.190172i
$120$	−24.0000			−0.0182574
$121$		0			0
$122$	40.0000			0.0296839
$123$	−378.620	+	275.083i	−0.277553	+	0.201654i
$124$	−201.479	−	620.089i	−0.145914	−	0.449078i
$125$	223.419	−	687.614i	0.159866	−	0.492016i
$126$	−420.689	−	305.648i	−0.297444	−	0.216106i
$127$	−1724.82	−	1253.16i	−1.20514	−	0.875589i	−0.210364	−	0.977623i	$-0.567465\pi$
$127$	−1724.82	−	1253.16i	−1.20514	−	0.875589i	−0.994781	+	0.102034i	$0.967465\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	33.9919	+	104.616i	0.0232001	+	0.0714027i
$130$	−77.6656	+	56.4274i	−0.0523979	+	0.0380693i
$131$	1782.00			1.18850			0.594252	−	0.804279i	$-0.297448\pi$
$131$	1782.00			1.18850			0.594252	+	0.804279i	$0.297448\pi$
$132$		0			0
$133$	−1160.00			−0.756276
$134$	156.949	−	114.030i	0.101182	−	0.0735128i
$135$	49.1337	+	151.218i	0.0313241	+	0.0964057i
$136$	103.830	−	319.555i	0.0654656	−	0.201482i
$137$	−745.105	−	541.350i	−0.464661	−	0.337596i	0.330696	−	0.943737i	$-0.392717\pi$
$137$	−745.105	−	541.350i	−0.464661	−	0.337596i	−0.795357	+	0.606141i	$0.792717\pi$
$138$	−305.808	−	222.183i	−0.188639	−	0.137054i
$139$	445.603	−	1371.42i	0.271910	−	0.836853i	−0.718110	−	0.695929i	$-0.754993\pi$
$139$	445.603	−	1371.42i	0.271910	−	0.836853i	0.990020	−	0.140924i	$-0.0450073\pi$
$140$	37.0820	+	114.127i	0.0223857	+	0.0688962i
$141$	−116.498	+	84.6411i	−0.0695811	+	0.0505536i
$142$	−930.000			−0.549605
$143$		0			0
$144$	−416.000			−0.240741
$145$	−291.246	+	211.603i	−0.166805	+	0.121191i
$146$	524.093	+	1612.99i	0.297084	+	0.914330i
$147$	−75.0911	+	231.107i	−0.0421321	+	0.129669i
$148$	1323.55	+	961.617i	0.735103	+	0.534084i
$149$	1461.08	+	1061.54i	0.803334	+	0.583656i	0.911890	−	0.410434i	$-0.134623\pi$
$149$	1461.08	+	1061.54i	0.803334	+	0.583656i	−0.108557	+	0.994090i	$0.534623\pi$
$150$	−71.6919	+	220.645i	−0.0390242	+	0.120104i
$151$	−433.242	−	1333.38i	−0.233488	−	0.718603i	−0.997318	−	0.0731855i	$-0.976683\pi$
$151$	−433.242	−	1333.38i	−0.233488	−	0.718603i	0.763830	−	0.645417i	$-0.223317\pi$
$152$	−750.768	+	545.465i	−0.400627	+	0.291073i
$153$	−1092.00			−0.577013
$154$		0			0
$155$	489.000			0.253403
$156$	51.7771	−	37.6183i	0.0265736	−	0.0193069i
$157$	−910.673	−	2802.76i	−0.462928	−	1.42474i	−0.861570	−	0.507638i	$-0.830519\pi$
$157$	−910.673	−	2802.76i	−0.462928	−	1.42474i	0.398643	−	0.917106i	$-0.369481\pi$
$158$	−458.581	+	1411.37i	−0.230904	+	0.710648i
$159$	−72.8115	−	52.9007i	−0.0363165	−	0.0263855i
$160$	77.6656	+	56.4274i	0.0383750	+	0.0278811i
$161$	−584.042	+	1797.50i	−0.285894	+	0.879892i
$162$	401.104	+	1234.47i	0.194529	+	0.598699i
$163$	−268.594	+	195.145i	−0.129067	+	0.0937725i	−0.650446	−	0.759553i	$-0.725418\pi$
$163$	−268.594	+	195.145i	−0.129067	+	0.0937725i	0.521379	+	0.853325i	$0.325418\pi$
$164$	1872.00			0.891333
$165$		0			0
$166$	876.000			0.409583
$167$	−1553.31	+	1128.55i	−0.719754	+	0.522932i	−0.886306	−	0.463101i	$-0.846737\pi$
$167$	−1553.31	+	1128.55i	−0.719754	+	0.522932i	0.166552	+	0.986033i	$0.446737\pi$
$168$	−24.7214	−	76.0845i	−0.0113529	−	0.0349408i
$169$	−599.802	+	1846.00i	−0.273010	+	0.840237i
$170$	203.872	+	148.122i	0.0919782	+	0.0668261i
$171$	2440.00	+	1772.76i	1.09118	+	0.792786i
$172$	135.967	−	418.465i	0.0602757	−	0.185510i
$173$	613.708	+	1888.80i	0.269707	+	0.830073i	0.990571	+	0.136997i	$0.0437451\pi$
$173$	613.708	+	1888.80i	0.269707	+	0.830073i	−0.720864	+	0.693076i	$0.756255\pi$
$174$	194.164	−	141.068i	0.0845951	−	0.0614619i
$175$	1160.00			0.501073
$176$		0			0
$177$	−453.000			−0.192370
$178$	441.723	−	320.931i	0.186003	−	0.135139i
$179$	34.3009	+	105.567i	0.0143227	+	0.0440808i	0.957962	−	0.286894i	$-0.0926226\pi$
$179$	34.3009	+	105.567i	0.0143227	+	0.0440808i	−0.943640	+	0.330974i	$0.892623\pi$
$180$	96.4133	−	296.730i	0.0399235	−	0.122872i
$181$	−727.306	−	528.419i	−0.298675	−	0.217000i	0.428347	−	0.903614i	$-0.359096\pi$
$181$	−727.306	−	528.419i	−0.298675	−	0.217000i	−0.727022	+	0.686614i	$0.759096\pi$
$182$	−258.885	−	188.091i	−0.105439	−	0.0766058i
$183$	6.18034	−	19.0211i	0.00249652	−	0.00768351i
$184$	467.234	+	1438.00i	0.187201	+	0.576144i
$185$	−992.664	+	721.213i	−0.394498	+	0.286619i
$186$	−326.000			−0.128513
$187$		0			0
$188$	576.000			0.223453
$189$	−428.779	+	311.526i	−0.165022	+	0.119895i
$190$	−215.076	−	661.935i	−0.0821223	−	0.252747i
$191$	−466.307	+	1435.14i	−0.176653	+	0.543683i	−0.999705	−	0.0242835i	$-0.992270\pi$
$191$	−466.307	+	1435.14i	−0.176653	+	0.543683i	0.823052	+	0.567966i	$0.192270\pi$
$192$	−51.7771	−	37.6183i	−0.0194619	−	0.0141399i
$193$	−16.1803	−	11.7557i	−0.00603464	−	0.00438443i	0.584764	−	0.811204i	$-0.301187\pi$
$193$	−16.1803	−	11.7557i	−0.00603464	−	0.00438443i	−0.590798	+	0.806819i	$0.701187\pi$
$194$	470.324	−	1447.51i	0.174058	−	0.535696i
$195$	14.8328	+	45.6507i	0.00544718	+	0.0167647i
$196$	786.365	−	571.327i	0.286576	−	0.208210i
$197$	1254.00			0.453522			0.226761	−	0.973950i	$-0.427186\pi$
$197$	1254.00			0.453522			0.226761	+	0.973950i	$0.427186\pi$
$198$		0			0
$199$	4688.00			1.66997			0.834984	−	0.550275i	$-0.185477\pi$
$199$	4688.00			1.66997			0.834984	+	0.550275i	$0.185477\pi$
$200$	750.768	−	545.465i	0.265436	−	0.192851i
$201$	−29.9746	−	92.2525i	−0.0105187	−	0.0323731i
$202$	−975.258	+	3001.53i	−0.339697	+	1.04548i
$203$	−970.820	−	705.342i	−0.335656	−	0.243869i
$204$	−135.915	−	98.7479i	−0.0466468	−	0.0338909i
$205$	−433.860	+	1335.28i	−0.147815	+	0.454928i
$206$	746.585	+	2297.75i	0.252510	+	0.777146i
$207$	3975.51	−	2888.38i	1.33486	−	0.969836i
$208$	−256.000			−0.0853385
$209$		0			0
$210$	60.0000			0.0197162
$211$	−3938.29	+	2861.34i	−1.28494	+	0.933567i	−0.999690	−	0.0248846i	$-0.992078\pi$
$211$	−3938.29	+	2861.34i	−1.28494	+	0.933567i	−0.285255	+	0.958452i	$0.592078\pi$
$212$	111.246	+	342.380i	0.0360397	+	0.110919i
$213$	−143.693	+	442.241i	−0.0462238	+	0.142262i
$214$	2339.68	+	1699.87i	0.747369	+	0.542996i
$215$	266.976	+	193.969i	0.0846864	+	0.0615283i
$216$	−131.023	+	403.248i	−0.0412731	+	0.127026i
$217$	503.698	+	1550.22i	0.157572	+	0.484958i
$218$	2171.40	−	1577.62i	0.674614	−	0.490136i
$219$	848.000			0.261655
$220$		0			0
$221$	−672.000			−0.204541
$222$	661.776	−	480.808i	0.200070	−	0.145359i
$223$	−1440.95	−	4434.78i	−0.432704	−	1.33172i	−0.895422	−	0.445219i	$-0.853126\pi$
$223$	−1440.95	−	4434.78i	−0.432704	−	1.33172i	0.462718	−	0.886506i	$-0.346874\pi$
$224$	−98.8854	+	304.338i	−0.0294958	+	0.0907788i
$225$	−2440.00	−	1772.76i	−0.722962	−	0.525262i
$226$	−2849.36	−	2070.18i	−0.838657	−	0.609320i
$227$	−1811.46	+	5575.09i	−0.529651	+	1.63010i	0.225282	+	0.974294i	$0.427670\pi$
$227$	−1811.46	+	5575.09i	−0.529651	+	1.63010i	−0.754932	+	0.655803i	$0.772330\pi$
$228$	143.384	+	441.290i	0.0416484	+	0.128181i
$229$	−4086.34	+	2968.90i	−1.17918	+	0.856728i	−0.992079	−	0.125612i	$-0.959911\pi$
$229$	−4086.34	+	2968.90i	−1.17918	+	0.856728i	−0.187105	+	0.982340i	$0.559911\pi$
$230$	−1134.00			−0.325103
$231$		0			0
$232$	−960.000			−0.271668
$233$	582.492	−	423.205i	0.163778	−	0.118992i	−0.502877	−	0.864358i	$-0.667725\pi$
$233$	582.492	−	423.205i	0.163778	−	0.118992i	0.666656	+	0.745366i	$0.267725\pi$
$234$	257.102	+	791.279i	0.0718260	+	0.221058i
$235$	−133.495	+	410.856i	−0.0370565	+	0.114048i
$236$	1465.94	+	1065.07i	0.404341	+	0.293771i
$237$	600.291	+	436.137i	0.164528	+	0.119536i
$238$	−259.574	+	798.887i	−0.0706962	+	0.217581i
$239$	−161.307	−	496.452i	−0.0436572	−	0.134363i	0.926852	−	0.375427i	$-0.122504\pi$
$239$	−161.307	−	496.452i	−0.0436572	−	0.134363i	−0.970509	+	0.241064i	$0.922504\pi$
$240$	38.8328	−	28.2137i	0.0104444	−	0.00758827i
$241$	−5632.00			−1.50535			−0.752674	−	0.658393i	$-0.771236\pi$
$241$	−5632.00			−1.50535			−0.752674	+	0.658393i	$0.771236\pi$
$242$		0			0
$243$	2080.00			0.549103
$244$	−64.7214	+	47.0228i	−0.0169810	+	0.0123374i
$245$	225.273	+	693.320i	0.0587436	+	0.180794i
$246$	289.240	−	890.189i	0.0749645	−	0.230717i
$247$	1501.54	+	1090.93i	0.386803	+	0.281029i
$248$	1054.96	+	766.472i	0.270121	+	0.196254i
$249$	135.349	−	416.563i	0.0344475	−	0.106018i
$250$	446.839	+	1375.23i	0.113042	+	0.347908i
$251$	5133.21	−	3729.50i	1.29086	−	0.937864i	0.291036	−	0.956712i	$-0.406000\pi$
$251$	5133.21	−	3729.50i	1.29086	−	0.937864i	0.999822	+	0.0188483i	$0.00599996\pi$
$252$	1040.00			0.259976
$253$		0			0
$254$	4264.00			1.05334
$255$	101.936	−	74.0609i	0.0250333	−	0.0181877i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	461.671	−	1420.88i	0.112056	−	0.344871i	−0.879266	−	0.476331i	$-0.841966\pi$
$257$	461.671	−	1420.88i	0.112056	−	0.344871i	0.991322	+	0.131460i	$0.0419664\pi$
$258$	−177.984	−	129.313i	−0.0429488	−	0.0312041i
$259$	−3308.88	−	2404.04i	−0.793837	−	0.576756i
$260$	59.3313	−	182.603i	0.0141522	−	0.0435560i
$261$	964.133	+	2967.30i	0.228653	+	0.703720i
$262$	−2883.34	+	2094.87i	−0.679897	+	0.493974i
$263$	1254.00			0.294011			0.147006	−	0.989136i	$-0.453036\pi$
$263$	1254.00			0.294011			0.147006	+	0.989136i	$0.453036\pi$
$264$		0			0
$265$	−270.000			−0.0625886
$266$	1876.92	−	1363.66i	0.432637	−	0.314329i
$267$	−84.3616	−	259.638i	−0.0193365	−	0.0595117i
$268$	−119.899	+	369.010i	−0.0273283	+	0.0841077i
$269$	−4402.67	−	3198.73i	−0.997902	−	0.725018i	−0.0362644	−	0.999342i	$-0.511546\pi$
$269$	−4402.67	−	3198.73i	−0.997902	−	0.725018i	−0.961637	+	0.274324i	$0.911546\pi$
$270$	−257.267	−	186.916i	−0.0579881	−	0.0421308i
$271$	751.529	−	2312.97i	0.168458	−	0.518461i	−0.830816	−	0.556547i	$-0.812126\pi$
$271$	751.529	−	2312.97i	0.168458	−	0.518461i	0.999274	+	0.0380859i	$0.0121260\pi$
$272$	207.659	+	639.110i	0.0462912	+	0.142470i
$273$	−129.443	+	94.0456i	−0.0286968	+	0.0208495i
$274$	1842.00			0.406129
$275$		0			0
$276$	756.000			0.164876
$277$	1347.82	−	979.250i	0.292357	−	0.212410i	−0.431932	−	0.901906i	$-0.642168\pi$
$277$	1347.82	−	979.250i	0.292357	−	0.212410i	0.724289	+	0.689496i	$0.242168\pi$
$278$	891.205	+	2742.85i	0.192270	+	0.591745i
$279$	1309.61	−	4030.58i	0.281020	−	0.864890i
$280$	−194.164	−	141.068i	−0.0414412	−	0.0301088i
$281$	2635.78	+	1915.00i	0.559563	+	0.406547i	0.831299	−	0.555825i	$-0.187598\pi$
$281$	2635.78	+	1915.00i	0.559563	+	0.406547i	−0.271736	+	0.962372i	$0.587598\pi$
$282$	88.9969	−	273.904i	0.0187932	−	0.0578396i
$283$	−2411.57	−	7422.05i	−0.506547	−	1.55899i	−0.798154	−	0.602454i	$-0.794190\pi$
$283$	−2411.57	−	7422.05i	−0.506547	−	1.55899i	0.291606	−	0.956538i	$-0.405810\pi$
$284$	1504.77	−	1093.28i	0.314408	−	0.228431i
$285$	−348.000			−0.0723289
$286$		0			0
$287$	−4680.00			−0.962549
$288$	673.102	−	489.037i	0.137718	−	0.100058i
$289$	−973.095	−	2994.88i	−0.198065	−	0.609582i
$290$	222.492	−	684.761i	0.0450524	−	0.138657i
$291$	−615.662	−	447.305i	−0.124023	−	0.0901081i
$292$	−2744.19	−	1993.77i	−0.549970	−	0.399577i
$293$	3.70820	−	11.4127i	0.000739371	−	0.00227555i	−0.950686	−	0.310155i	$-0.899619\pi$
$293$	3.70820	−	11.4127i	0.000739371	−	0.00227555i	0.951426	+	0.307879i	$0.0996192\pi$
$294$	−150.182	−	462.213i	−0.0297919	−	0.0916899i
$295$	−1099.45	+	798.800i	−0.216992	+	0.157654i
$296$	−3272.00			−0.642504
$297$		0			0
$298$	−3612.00			−0.702139
$299$	2446.47	−	1777.46i	0.473187	−	0.343790i
$300$	−143.384	−	441.290i	−0.0275942	−	0.0849263i
$301$	−339.919	+	1046.16i	−0.0650917	+	0.200332i
$302$	2268.48	+	1648.15i	0.432240	+	0.314041i
$303$	1276.63	+	927.525i	0.242048	+	0.175858i
$304$	573.536	−	1765.16i	0.108206	−	0.333023i
$305$	−18.5410	−	57.0634i	−0.00348084	−	0.0107129i
$306$	1766.89	−	1283.72i	0.330087	−	0.239822i
$307$	5852.00			1.08792			0.543960	−	0.839111i	$-0.316924\pi$
$307$	5852.00			1.08792			0.543960	+	0.839111i	$0.316924\pi$
$308$		0			0
$309$	1208.00			0.222397
$310$	−791.219	+	574.854i	−0.144962	+	0.105321i
$311$	819.513	+	2522.20i	0.149422	+	0.459874i	0.997553	−	0.0699123i	$-0.0222720\pi$
$311$	819.513	+	2522.20i	0.149422	+	0.459874i	−0.848131	+	0.529787i	$0.822272\pi$
$312$	−39.5542	+	121.735i	−0.00717729	+	0.0220894i
$313$	5786.90	+	4204.43i	1.04503	+	0.759260i	0.971261	−	0.238015i	$-0.0764969\pi$
$313$	5786.90	+	4204.43i	1.04503	+	0.759260i	0.0737701	+	0.997275i	$0.476497\pi$
$314$	4768.35	+	3464.41i	0.856985	+	0.622636i
$315$	−241.033	+	741.824i	−0.0431133	+	0.132689i
$316$	−917.162	−	2822.74i	−0.163273	−	0.502504i
$317$	−4958.47	+	3602.54i	−0.878534	+	0.638292i	−0.932863	−	0.360231i	$-0.882698\pi$
$317$	−4958.47	+	3602.54i	−0.878534	+	0.638292i	0.0543295	+	0.998523i	$0.482698\pi$
$318$	180.000			0.0317418
$319$		0			0
$320$	−192.000			−0.0335410
$321$	1169.84	−	849.937i	0.203408	−	0.147785i
$322$	−1168.08	−	3594.99i	−0.202158	−	0.622178i
$323$	1505.53	−	4633.55i	0.259350	−	0.798197i
$324$	−2100.21	−	1525.89i	−0.360118	−	0.261641i
$325$	−1501.54	−	1090.93i	−0.256278	−	0.186197i
$326$	205.187	−	631.502i	0.0348597	−	0.107287i
$327$	−414.701	−	1276.32i	−0.0701315	−	0.215843i
$328$	−3028.96	+	2200.67i	−0.509897	+	0.370462i
$329$	−1440.00			−0.241306
$330$		0			0
$331$	−823.000			−0.136665			−0.0683326	−	0.997663i	$-0.521768\pi$
$331$	−823.000			−0.136665			−0.0683326	+	0.997663i	$0.521768\pi$
$332$	−1417.40	+	1029.80i	−0.234307	+	0.170234i
$333$	3286.09	+	10113.5i	0.540770	+	1.66432i
$334$	1186.63	−	3652.06i	0.194399	−	0.598298i
$335$	−235.424	−	171.046i	−0.0383958	−	0.0278962i
$336$	129.443	+	94.0456i	0.0210169	+	0.0152697i
$337$	1628.52	−	5012.07i	0.263238	−	0.810162i	−0.728856	−	0.684667i	$-0.759948\pi$
$337$	1628.52	−	5012.07i	0.263238	−	0.810162i	0.992094	−	0.125496i	$-0.0400522\pi$
$338$	−1199.60	−	3692.00i	−0.193047	−	0.594137i
$339$	−1424.68	+	1035.09i	−0.228254	+	0.165836i
$340$	−504.000			−0.0803919
$341$		0			0
$342$	−6032.00			−0.953723
$343$	−4740.84	+	3444.42i	−0.746301	+	0.542219i
$344$	271.935	+	836.930i	0.0426214	+	0.131175i
$345$	−175.213	+	539.249i	−0.0273424	+	0.0841513i
$346$	−3213.42	−	2334.68i	−0.499290	−	0.362755i
$347$	−5320.10	−	3865.28i	−0.823048	−	0.597979i	0.0945358	−	0.995521i	$-0.469863\pi$
$347$	−5320.10	−	3865.28i	−0.823048	−	0.597979i	−0.917584	+	0.397542i	$0.869863\pi$
$348$	−148.328	+	456.507i	−0.0228483	+	0.0703200i
$349$	−1942.48	−	5978.34i	−0.297933	−	0.916943i	−0.982220	−	0.187731i	$-0.939887\pi$
$349$	−1942.48	−	5978.34i	−0.297933	−	0.916943i	0.684287	−	0.729212i	$-0.260113\pi$
$350$	−1876.92	+	1363.66i	−0.286644	+	0.208259i
$351$	848.000			0.128954
$352$		0			0
$353$	−10701.0			−1.61348			−0.806738	−	0.590910i	$-0.798769\pi$
$353$	−10701.0			−1.61348			−0.806738	+	0.590910i	$0.798769\pi$
$354$	732.969	−	532.533i	0.110048	−	0.0799543i
$355$	431.079	+	1326.72i	0.0644487	+	0.198353i
$356$	−337.447	+	1038.55i	−0.0502377	+	0.154616i
$357$	339.787	+	246.870i	0.0503738	+	0.0365987i
$358$	−179.602	−	130.488i	−0.0265147	−	0.0192640i
$359$	2573.49	−	7920.40i	0.378339	−	1.16441i	−0.562859	−	0.826553i	$-0.690299\pi$
$359$	2573.49	−	7920.40i	0.378339	−	1.16441i	0.941198	−	0.337855i	$-0.109701\pi$
$360$	192.827	+	593.459i	0.0282302	+	0.0868835i
$361$	−5337.09	+	3877.62i	−0.778114	+	0.565333i
$362$	1798.00			0.261052
$363$		0			0
$364$	640.000			0.0921569
$365$	2058.14	−	1495.33i	0.295145	−	0.214435i
$366$	12.3607	+	38.0423i	0.00176531	+	0.00543306i
$367$	−1125.75	+	3464.70i	−0.160119	+	0.492795i	−0.998644	−	0.0520685i	$-0.983419\pi$
$367$	−1125.75	+	3464.70i	−0.160119	+	0.492795i	0.838525	+	0.544864i	$0.183419\pi$
$368$	−2446.47	−	1777.46i	−0.346551	−	0.251784i
$369$	9844.12	+	7152.17i	1.38879	+	1.00902i
$370$	758.328	−	2333.89i	0.106550	−	0.327928i
$371$	−278.115	−	855.951i	−0.0389192	−	0.119781i
$372$	527.479	−	383.236i	0.0735175	−	0.0534136i
$373$	−7942.00			−1.10247			−0.551235	−	0.834350i	$-0.685843\pi$
$373$	−7942.00			−1.10247			−0.551235	+	0.834350i	$0.685843\pi$
$374$		0			0
$375$	723.000			0.0995615
$376$	−931.988	+	677.129i	−0.127829	+	0.0928730i
$377$	593.313	+	1826.03i	0.0810535	+	0.249457i
$378$	327.558	−	1008.12i	0.0445708	−	0.137175i
$379$	7548.94	+	5484.62i	1.02312	+	0.743341i	0.966920	−	0.255079i	$-0.0821013\pi$
$379$	7548.94	+	5484.62i	1.02312	+	0.743341i	0.0562007	+	0.998419i	$0.482101\pi$
$380$	1126.15	+	818.197i	0.152027	+	0.110454i
$381$	658.824	−	2027.65i	0.0885895	−	0.272650i
$382$	−932.613	−	2870.29i	−0.124913	−	0.384442i
$383$	6254.51	−	4544.17i	0.834440	−	0.606256i	−0.0863719	−	0.996263i	$-0.527527\pi$
$383$	6254.51	−	4544.17i	0.834440	−	0.606256i	0.920812	+	0.390007i	$0.127527\pi$
$384$	128.000			0.0170103
$385$		0			0
$386$	40.0000			0.00527447
$387$	2313.79	−	1681.07i	0.303919	−	0.220810i
$388$	940.648	+	2895.02i	0.123078	+	0.378794i
$389$	451.474	−	1389.49i	0.0588448	−	0.181106i	−0.917313	−	0.398166i	$-0.869647\pi$
$389$	451.474	−	1389.49i	0.0588448	−	0.181106i	0.976158	+	0.217060i	$0.0696468\pi$
$390$	−77.6656	−	56.4274i	−0.0100840	−	0.00732644i
$391$	−6421.98	−	4665.84i	−0.830622	−	0.603482i
$392$	−600.729	+	1848.85i	−0.0774015	+	0.238217i
$393$	550.668	+	1694.78i	0.0706808	+	0.217533i
$394$	−2029.01	+	1474.17i	−0.259442	+	0.188496i
$395$	2226.00			0.283550
$396$		0			0
$397$	−6466.00			−0.817429			−0.408714	−	0.912662i	$-0.634023\pi$
$397$	−6466.00			−0.817429			−0.408714	+	0.912662i	$0.634023\pi$
$398$	−7585.34	+	5511.07i	−0.955324	+	0.694083i
$399$	−358.460	−	1103.23i	−0.0449760	−	0.138422i
$400$	−573.536	+	1765.16i	−0.0716919	+	0.220645i
$401$	−1626.12	−	1181.45i	−0.202506	−	0.147129i	0.481911	−	0.876220i	$-0.339943\pi$
$401$	−1626.12	−	1181.45i	−0.202506	−	0.147129i	−0.684416	+	0.729091i	$0.739943\pi$
$402$	156.949	+	114.030i	0.0194724	+	0.0141476i
$403$	805.916	−	2480.36i	0.0996168	−	0.306589i
$404$	−1950.52	−	6003.07i	−0.240202	−	0.739267i
$405$	1575.16	−	1144.42i	0.193260	−	0.140411i
$406$	2400.00			0.293374
$407$		0			0
$408$	336.000			0.0407708
$409$	10211.4	−	7419.03i	1.23453	−	0.896937i	0.237307	−	0.971435i	$-0.423735\pi$
$409$	10211.4	−	7419.03i	1.23453	−	0.896937i	0.997221	+	0.0744979i	$0.0237354\pi$
$410$	−867.720	−	2670.57i	−0.104521	−	0.321683i
$411$	284.605	−	875.923i	0.0341570	−	0.105124i
$412$	−3909.17	−	2840.18i	−0.467454	−	0.339625i
$413$	−3664.85	−	2662.67i	−0.436647	−	0.317243i
$414$	−3037.02	+	9346.98i	−0.360535	+	1.10961i
$415$	−406.048	−	1249.69i	−0.0480292	−	0.147819i
$416$	414.217	−	300.946i	0.0488189	−	0.0354690i
$417$	1442.00			0.169341
$418$		0			0
$419$	10980.0			1.28021			0.640105	−	0.768287i	$-0.278891\pi$
$419$	10980.0			1.28021			0.640105	+	0.768287i	$0.278891\pi$
$420$	−97.0820	+	70.5342i	−0.0112789	+	0.00819457i
$421$	−166.251	−	511.668i	−0.0192460	−	0.0592332i	0.940972	−	0.338484i	$-0.109914\pi$
$421$	−166.251	−	511.668i	−0.0192460	−	0.0592332i	−0.960218	+	0.279251i	$0.909914\pi$
$422$	3008.59	−	9259.49i	0.347052	−	1.06812i
$423$	3028.96	+	2200.67i	0.348163	+	0.252955i
$424$	−582.492	−	423.205i	−0.0667177	−	0.0484733i
$425$	−1505.53	+	4633.55i	−0.171833	+	0.528847i
$426$	−287.386	−	884.483i	−0.0326852	−	0.100595i
$427$	161.803	−	117.557i	0.0183377	−	0.0133231i
$428$	−5784.00			−0.653225
$429$		0			0
$430$	−660.000			−0.0740187
$431$	−4062.88	+	2951.86i	−0.454065	+	0.329898i	−0.791199	−	0.611559i	$-0.790543\pi$
$431$	−4062.88	+	2951.86i	−0.454065	+	0.329898i	0.337133	+	0.941457i	$0.390543\pi$
$432$	−262.046	−	806.496i	−0.0291845	−	0.0898207i
$433$	−799.427	+	2460.38i	−0.0887252	+	0.273068i	−0.985568	−	0.169282i	$-0.945855\pi$
$433$	−799.427	+	2460.38i	−0.0887252	+	0.273068i	0.896842	+	0.442350i	$0.145855\pi$
$434$	−2637.40	−	1916.18i	−0.291703	−	0.211935i
$435$	−291.246	−	211.603i	−0.0321016	−	0.0233232i
$436$	−1658.80	+	5105.27i	−0.182207	+	0.560776i
$437$	6774.89	+	20851.0i	0.741618	+	2.28246i
$438$	−1372.09	+	996.884i	−0.149683	+	0.108751i
$439$	704.000			0.0765378			0.0382689	−	0.999267i	$-0.487816\pi$
$439$	704.000			0.0765378			0.0382689	+	0.999267i	$0.487816\pi$
$440$		0			0
$441$	6318.00			0.682216
$442$	1087.32	−	789.983i	0.117010	−	0.0850128i
$443$	1298.80	+	3997.29i	0.139295	+	0.428707i	0.996233	−	0.0867127i	$-0.0276362\pi$
$443$	1298.80	+	3997.29i	0.139295	+	0.428707i	−0.856938	+	0.515419i	$0.827636\pi$
$444$	−505.552	+	1555.93i	−0.0540370	+	0.166309i
$445$	−662.585	−	481.396i	−0.0705832	−	0.0512817i
$446$	7544.89	+	5481.69i	0.801034	+	0.581985i
$447$	−558.085	+	1717.61i	−0.0590526	+	0.181745i
$448$	−197.771	−	608.676i	−0.0208567	−	0.0641903i
$449$	754.813	−	548.404i	0.0793359	−	0.0576409i	−0.547410	−	0.836864i	$-0.684386\pi$
$449$	754.813	−	548.404i	0.0793359	−	0.0576409i	0.626746	+	0.779223i	$0.284386\pi$
$450$	6032.00			0.631892
$451$		0			0
$452$	7044.00			0.733013
$453$	1134.24	−	824.075i	0.117641	−	0.0854711i
$454$	−3622.92	−	11150.2i	−0.374519	−	1.15265i
$455$	−148.328	+	456.507i	−0.0152829	+	0.0470360i
$456$	−750.768	−	545.465i	−0.0771007	−	0.0560169i
$457$	−8345.82	−	6063.59i	−0.854269	−	0.620663i	0.0720507	−	0.997401i	$-0.477046\pi$
$457$	−8345.82	−	6063.59i	−0.854269	−	0.620663i	−0.926320	+	0.376738i	$0.877046\pi$
$458$	3121.69	−	9607.57i	0.318487	−	0.980202i
$459$	−687.872	−	2117.05i	−0.0699501	−	0.215284i
$460$	1834.85	−	1333.10i	0.185979	−	0.135122i
$461$	132.000			0.0133359			0.00666795	−	0.999978i	$-0.497878\pi$
$461$	132.000			0.0133359			0.00666795	+	0.999978i	$0.497878\pi$
$462$		0			0
$463$	7823.00			0.785239			0.392619	−	0.919701i	$-0.371569\pi$
$463$	7823.00			0.785239			0.392619	+	0.919701i	$0.371569\pi$
$464$	1553.31	−	1128.55i	0.155411	−	0.112913i
$465$	151.109	+	465.067i	0.0150699	+	0.0463805i
$466$	−444.984	+	1369.52i	−0.0442350	+	0.136141i
$467$	−584.919	−	424.969i	−0.0579590	−	0.0421097i	0.558429	−	0.829553i	$-0.311404\pi$
$467$	−584.919	−	424.969i	−0.0579590	−	0.0421097i	−0.616388	+	0.787443i	$0.711404\pi$
$468$	−1346.20	−	978.075i	−0.132966	−	0.0966058i
$469$	299.746	−	922.525i	0.0295117	−	0.0908278i
$470$	−266.991	−	821.713i	−0.0262029	−	0.0806442i
$471$	2384.17	−	1732.20i	0.233242	−	0.169460i
$472$	−3624.00			−0.353407
$473$		0			0
$474$	−1484.00			−0.143802
$475$	10886.1	−	7909.24i	1.05156	−	0.764002i
$476$	−519.149	−	1597.77i	−0.0499898	−	0.153853i
$477$	−723.100	+	2225.47i	−0.0694098	+	0.213621i
$478$	844.614	+	613.648i	0.0808195	+	0.0587188i
$479$	5999.67	+	4359.02i	0.572300	+	0.415801i	0.835940	−	0.548821i	$-0.184923\pi$
$479$	5999.67	+	4359.02i	0.572300	+	0.415801i	−0.263640	+	0.964621i	$0.584923\pi$
$480$	−29.6656	+	91.3014i	−0.00282093	+	0.00868192i
$481$	2022.21	+	6223.71i	0.191694	+	0.589973i
$482$	9112.77	−	6620.81i	0.861152	−	0.625663i
$483$	−1890.00			−0.178050
$484$		0			0
$485$	−2283.00			−0.213744
$486$	−3365.51	+	2445.19i	−0.314121	+	0.228222i
$487$	−2215.96	−	6820.03i	−0.206190	−	0.634589i	−0.999662	−	0.0259822i	$-0.991729\pi$
$487$	−2215.96	−	6820.03i	−0.206190	−	0.634589i	0.793472	−	0.608607i	$-0.208271\pi$
$488$	49.4427	−	152.169i	0.00458641	−	0.0141155i
$489$	−268.594	−	195.145i	−0.0248389	−	0.0180465i
$490$	−1179.55	−	856.991i	−0.108748	−	0.0790100i
$491$	−3789.78	+	11663.8i	−0.348331	+	1.07205i	0.611445	+	0.791287i	$0.290589\pi$
$491$	−3789.78	+	11663.8i	−0.348331	+	1.07205i	−0.959776	+	0.280766i	$0.909411\pi$
$492$	578.480	+	1780.38i	0.0530079	+	0.163142i
$493$	4077.45	−	2962.44i	0.372493	−	0.270632i
$494$	−3712.00			−0.338078
$495$		0			0
$496$	−2608.00			−0.236094
$497$	−3761.93	+	2733.20i	−0.339528	+	0.246682i
$498$	270.699	+	833.126i	0.0243580	+	0.0749664i
$499$	−3664.94	+	11279.5i	−0.328788	+	1.01191i	0.640913	+	0.767613i	$0.278556\pi$
$499$	−3664.94	+	11279.5i	−0.328788	+	1.01191i	−0.969702	+	0.244293i	$0.921444\pi$
$500$	−2339.68	−	1699.87i	−0.209267	−	0.152041i
$501$	−1553.31	−	1128.55i	−0.138517	−	0.100638i
$502$	−3921.43	+	12068.9i	−0.348649	+	1.07303i
$503$	4774.31	+	14693.8i	0.423213	+	1.30252i	0.904695	+	0.426059i	$0.140099\pi$
$503$	4774.31	+	14693.8i	0.423213	+	1.30252i	−0.481482	+	0.876456i	$0.659901\pi$
$504$	−1682.76	+	1222.59i	−0.148722	+	0.108053i
$505$	4734.00			0.417149
$506$		0			0
$507$	−1941.00			−0.170025
$508$	−6899.30	+	5012.63i	−0.602572	+	0.437795i
$509$	−5309.22	−	16340.1i	−0.462332	−	1.42291i	−0.862307	−	0.506386i	$-0.830981\pi$
$509$	−5309.22	−	16340.1i	−0.462332	−	1.42291i	0.399975	−	0.916526i	$-0.369019\pi$
$510$	−77.8723	+	239.666i	−0.00676126	+	0.0208090i
$511$	6860.46	+	4984.42i	0.593912	+	0.431502i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	−1899.84	+	5847.10i	−0.163508	+	0.503227i
$514$	923.343	+	2841.76i	0.0792352	+	0.243861i
$515$	2931.88	−	2130.13i	0.250862	−	0.182262i
$516$	440.000			0.0375386
$517$		0			0
$518$	8180.00			0.693839
$519$	−1606.71	+	1167.34i	−0.135889	+	0.0987295i
$520$	118.663	+	365.206i	0.0100071	+	0.0307987i
$521$	−853.814	+	2627.77i	−0.0717971	+	0.220969i	−0.980516	−	0.196440i	$-0.937062\pi$
$521$	−853.814	+	2627.77i	−0.0717971	+	0.220969i	0.908719	+	0.417409i	$0.137062\pi$
$522$	−5048.27	−	3667.78i	−0.423289	−	0.307537i
$523$	624.561	+	453.770i	0.0522183	+	0.0379388i	0.613588	−	0.789626i	$-0.289726\pi$
$523$	624.561	+	453.770i	0.0522183	+	0.0379388i	−0.561370	+	0.827565i	$0.689726\pi$
$524$	2202.67	−	6779.13i	0.183634	−	0.565167i
$525$	358.460	+	1103.23i	0.0297990	+	0.0917118i
$526$	−2029.01	+	1474.17i	−0.168192	+	0.122199i
$527$	−6846.00			−0.565876
$528$		0			0
$529$	23554.0			1.93589
$530$	436.869	−	317.404i	0.0358045	−	0.0260135i
$531$	3639.60	+	11201.5i	0.297449	+	0.915453i
$532$	−1433.84	+	4412.90i	−0.116851	+	0.359631i
$533$	6057.92	+	4401.34i	0.492303	+	0.357679i
$534$	441.723	+	320.931i	0.0357963	+	0.0260076i
$535$	1340.52	−	4125.68i	0.108328	−	0.333400i
$536$	−239.797	−	738.020i	−0.0193240	−	0.0594731i
$537$	−89.8009	+	65.2442i	−0.00721638	+	0.00524300i
$538$	10884.0			0.872198
$539$		0			0
$540$	636.000			0.0506835
$541$	−15685.2	+	11396.0i	−1.24651	+	0.905640i	−0.998014	−	0.0629932i	$-0.979935\pi$
$541$	−15685.2	+	11396.0i	−1.24651	+	0.905640i	−0.248493	+	0.968634i	$0.579935\pi$
$542$	1503.06	+	4625.94i	0.119118	+	0.366607i
$543$	277.806	−	855.000i	0.0219554	−	0.0675719i
$544$	−1087.32	−	789.983i	−0.0856956	−	0.0622615i
$545$	−3257.10	−	2366.42i	−0.255998	−	0.185993i
$546$	98.8854	−	304.338i	0.00775074	−	0.0238543i
$547$	484.539	+	1491.26i	0.0378745	+	0.116566i	0.968206	−	0.250153i	$-0.0804810\pi$
$547$	484.539	+	1491.26i	0.0378745	+	0.116566i	−0.930332	+	0.366719i	$0.880481\pi$
$548$	−2980.42	+	2165.40i	−0.232331	+	0.168798i
$549$	−520.000			−0.0404245
$550$		0			0
$551$	−13920.0			−1.07625
$552$	−1223.23	+	888.731i	−0.0943194	+	0.0685270i
$553$	2292.91	+	7056.84i	0.176319	+	0.542653i
$554$	−1029.64	+	3168.92i	−0.0789628	+	0.243023i
$555$	−992.664	−	721.213i	−0.0759211	−	0.0551599i
$556$	−4666.41	−	3390.35i	−0.355935	−	0.258602i
$557$	−1485.14	+	4570.78i	−0.112975	+	0.347702i	−0.991519	−	0.129959i	$-0.958515\pi$
$557$	−1485.14	+	4570.78i	−0.112975	+	0.347702i	0.878544	+	0.477661i	$0.158515\pi$
$558$	2619.23	+	8061.16i	0.198711	+	0.611570i
$559$	1423.87	−	1034.50i	0.107734	−	0.0782733i
$560$	480.000			0.0362209
$561$		0			0
$562$	−6516.00			−0.489076
$563$	−8067.52	+	5861.39i	−0.603917	+	0.438771i	−0.847267	−	0.531167i	$-0.821754\pi$
$563$	−8067.52	+	5861.39i	−0.603917	+	0.438771i	0.243350	+	0.969939i	$0.421754\pi$
$564$	177.994	+	547.809i	0.0132888	+	0.0408988i
$565$	−1632.54	+	5024.43i	−0.121560	+	0.374123i
$566$	12627.1	+	9174.15i	0.937735	+	0.681305i
$567$	5250.52	+	3814.73i	0.388891	+	0.282546i
$568$	−1149.54	+	3537.93i	−0.0849186	+	0.261353i
$569$	−140.912	−	433.682i	−0.0103819	−	0.0319523i	0.945731	−	0.324950i	$-0.105347\pi$
$569$	−140.912	−	433.682i	−0.0103819	−	0.0319523i	−0.956113	+	0.292997i	$0.905347\pi$
$570$	563.076	−	409.099i	0.0413766	−	0.0300618i
$571$	11132.0			0.815866			0.407933	−	0.913012i	$-0.366250\pi$
$571$	11132.0			0.815866			0.407933	+	0.913012i	$0.366250\pi$
$572$		0			0
$573$	−1509.00			−0.110016
$574$	7572.40	−	5501.67i	0.550637	−	0.400061i
$575$	−6774.89	−	20851.0i	−0.491361	−	1.51225i
$576$	−514.204	+	1582.56i	−0.0371965	+	0.114479i
$577$	−9430.71	−	6851.81i	−0.680426	−	0.494358i	0.193073	−	0.981184i	$-0.438155\pi$
$577$	−9430.71	−	6851.81i	−0.680426	−	0.494358i	−0.873499	+	0.486826i	$0.838155\pi$
$578$	5095.19	+	3701.87i	0.366664	+	0.266397i
$579$	6.18034	−	19.0211i	0.000443603	−	0.00136527i
$580$	444.984	+	1369.52i	0.0318569	+	0.0980453i
$581$	3543.49	−	2574.50i	0.253027	−	0.183835i
$582$	1522.00			0.108400
$583$		0			0
$584$	6784.00			0.480692
$585$	1009.65	−	733.556i	0.0713573	−	0.0518441i
$586$	7.41641	+	22.8254i	0.000522814	+	0.00160906i
$587$	−4698.29	+	14459.9i	−0.330357	+	1.01673i	0.638608	+	0.769533i	$0.279511\pi$
$587$	−4698.29	+	14459.9i	−0.330357	+	1.01673i	−0.968964	+	0.247201i	$0.920489\pi$
$588$	786.365	+	571.327i	0.0551516	+	0.0400700i
$589$	15296.9	+	11113.8i	1.07011	+	0.777484i
$590$	839.908	−	2584.97i	0.0586076	−	0.180376i
$591$	387.507	+	1192.62i	0.0269711	+	0.0830085i
$592$	5294.21	−	3846.47i	0.367552	−	0.267042i
$593$	−4884.00			−0.338216			−0.169108	−	0.985598i	$-0.554089\pi$
$593$	−4884.00			−0.338216			−0.169108	+	0.985598i	$0.554089\pi$
$594$		0			0
$595$	1260.00			0.0868151
$596$	5844.34	−	4246.16i	0.401667	−	0.291828i
$597$	1448.67	+	4458.55i	0.0993135	+	0.305656i
$598$	−1868.93	+	5751.99i	−0.127803	+	0.393338i
$599$	−17804.8	−	12936.0i	−1.21450	−	0.882387i	−0.218870	−	0.975754i	$-0.570237\pi$
$599$	−17804.8	−	12936.0i	−1.21450	−	0.882387i	−0.995632	+	0.0933673i	$0.970237\pi$
$600$	750.768	+	545.465i	0.0510833	+	0.0371142i
$601$	6033.87	−	18570.3i	0.409528	−	1.26040i	−0.507526	−	0.861636i	$-0.669440\pi$
$601$	6033.87	−	18570.3i	0.409528	−	1.26040i	0.917054	−	0.398762i	$-0.130560\pi$
$602$	−679.837	−	2092.32i	−0.0460267	−	0.141656i
$603$	−2040.34	+	1482.39i	−0.137793	+	0.100112i
$604$	−5608.00			−0.377792
$605$		0			0
$606$	−3156.00			−0.211557
$607$	−3991.69	+	2900.13i	−0.266915	+	0.193925i	−0.713190	−	0.700971i	$-0.752750\pi$
$607$	−3991.69	+	2900.13i	−0.266915	+	0.193925i	0.446275	+	0.894896i	$0.352750\pi$
$608$	1147.07	+	3530.32i	0.0765130	+	0.235483i
$609$	370.820	−	1141.27i	0.0246739	−	0.0759384i
$610$	97.0820	+	70.5342i	0.00644383	+	0.00468172i
$611$	1863.98	+	1354.26i	0.123418	+	0.0896684i
$612$	−1349.79	+	4154.21i	−0.0891534	+	0.274386i
$613$	−6368.22	−	19599.4i	−0.419592	−	1.29137i	−0.908078	−	0.418801i	$-0.862451\pi$
$613$	−6368.22	−	19599.4i	−0.419592	−	1.29137i	0.488486	−	0.872572i	$-0.337549\pi$
$614$	−9468.73	+	6879.44i	−0.622357	+	0.452169i
$615$	−1404.00			−0.0920565
$616$		0			0
$617$	−7038.00			−0.459221			−0.229610	−	0.973283i	$-0.573745\pi$
$617$	−7038.00			−0.459221			−0.229610	+	0.973283i	$0.573745\pi$
$618$	−1954.59	+	1420.09i	−0.127225	+	0.0924342i
$619$	4514.43	+	13894.0i	0.293134	+	0.902175i	0.983842	+	0.179041i	$0.0572993\pi$
$619$	4514.43	+	13894.0i	0.293134	+	0.902175i	−0.690707	+	0.723135i	$0.742701\pi$
$620$	604.437	−	1860.27i	0.0391529	−	0.120500i
$621$	8103.92	+	5887.84i	0.523670	+	0.380469i
$622$	−4291.03	−	3117.61i	−0.276615	−	0.200972i
$623$	843.616	−	2596.38i	0.0542516	−	0.166969i
$624$	−79.1084	−	243.470i	−0.00507511	−	0.0156196i
$625$	−9975.99	+	7247.98i	−0.638463	+	0.463871i
$626$	−14306.0			−0.913391
$627$		0			0
$628$	−11788.0			−0.749032
$629$	13897.3	−	10097.0i	0.880956	−	0.640052i
$630$	−482.067	−	1483.65i	−0.0304857	−	0.0938253i
$631$	4748.05	−	14613.0i	0.299551	−	0.921923i	−0.682104	−	0.731256i	$-0.738935\pi$
$631$	4748.05	−	14613.0i	0.299551	−	0.921923i	0.981655	−	0.190668i	$-0.0610653\pi$
$632$	4802.32	+	3489.09i	0.302257	+	0.219602i
$633$	−3938.29	−	2861.34i	−0.247288	−	0.179665i
$634$	3787.93	−	11658.1i	0.237284	−	0.730284i
$635$	−1976.47	−	6082.96i	−0.123518	−	0.380149i
$636$	−291.246	+	211.603i	−0.0181583	+	0.0131928i
$637$	3888.00			0.241834
$638$		0			0
$639$	12090.0			0.748471
$640$	310.663	−	225.710i	0.0191875	−	0.0139406i
$641$	−2086.79	−	6422.48i	−0.128586	−	0.395746i	0.865952	−	0.500128i	$-0.166714\pi$
$641$	−2086.79	−	6422.48i	−0.128586	−	0.395746i	−0.994537	+	0.104382i	$0.966714\pi$
$642$	−893.677	+	2750.46i	−0.0549387	+	0.169084i
$643$	−4144.59	−	3011.22i	−0.254194	−	0.184683i	0.453389	−	0.891313i	$-0.350215\pi$
$643$	−4144.59	−	3011.22i	−0.254194	−	0.184683i	−0.707584	+	0.706630i	$0.750215\pi$
$644$	6116.17	+	4443.66i	0.374240	+	0.271902i
$645$	−101.976	+	313.849i	−0.00622525	+	0.0191593i
$646$	3011.06	+	9267.09i	0.183388	+	0.564410i
$647$	−14623.0	+	10624.2i	−0.888545	+	0.645566i	−0.935498	−	0.353331i	$-0.885049\pi$
$647$	−14623.0	+	10624.2i	−0.888545	+	0.645566i	0.0469531	+	0.998897i	$0.485049\pi$
$648$	5192.00			0.314755
$649$		0			0
$650$	3712.00			0.223995
$651$	−1318.70	+	958.090i	−0.0793915	+	0.0576813i
$652$	410.375	+	1263.00i	0.0246496	+	0.0758635i
$653$	4754.84	−	14633.9i	0.284949	−	0.876982i	−0.701465	−	0.712703i	$-0.747471\pi$
$653$	4754.84	−	14633.9i	0.284949	−	0.876982i	0.986414	−	0.164278i	$-0.0525295\pi$
$654$	2171.40	+	1577.62i	0.129830	+	0.0943267i
$655$	4325.00	+	3142.30i	0.258003	+	0.187450i
$656$	2313.92	−	7121.51i	0.137719	−	0.423854i
$657$	−6813.21	−	20968.9i	−0.404579	−	1.24517i
$658$	2329.97	−	1692.82i	0.138042	−	0.100293i
$659$	24222.0			1.43180			0.715899	−	0.698204i	$-0.246017\pi$
$659$	24222.0			1.43180			0.715899	+	0.698204i	$0.246017\pi$
$660$		0			0
$661$	−12967.0			−0.763022			−0.381511	−	0.924364i	$-0.624596\pi$
$661$	−12967.0			−0.763022			−0.381511	+	0.924364i	$0.624596\pi$
$662$	1331.64	−	967.495i	0.0781809	−	0.0568017i
$663$	−207.659	−	639.110i	−0.0121641	−	0.0374374i
$664$	1082.80	−	3332.50i	0.0632841	−	0.194768i
$665$	−2815.38	−	2045.49i	−0.164174	−	0.119279i
$666$	−17206.2	−	12501.0i	−1.00109	−	0.727334i
$667$	−7008.51	+	21570.0i	−0.406852	+	1.25216i
$668$	2373.25	+	7304.11i	0.137461	+	0.423061i
$669$	3772.45	−	2740.84i	0.218014	−	0.158396i
$670$	582.000			0.0335591
$671$		0			0
$672$	−320.000			−0.0183694
$673$	−14457.1	+	10503.7i	−0.828056	+	0.601618i	−0.919009	−	0.394237i	$-0.871009\pi$
$673$	−14457.1	+	10503.7i	−0.828056	+	0.601618i	0.0909528	+	0.995855i	$0.471009\pi$
$674$	3257.04	+	10024.1i	0.186137	+	0.572871i
$675$	1899.84	−	5847.10i	0.108333	−	0.333415i
$676$	6281.21	+	4563.56i	0.357374	+	0.259648i
$677$	−10499.4	−	7628.28i	−0.596050	−	0.433055i	0.248425	−	0.968651i	$-0.420087\pi$
$677$	−10499.4	−	7628.28i	−0.596050	−	0.433055i	−0.844474	+	0.535596i	$0.820087\pi$
$678$	1088.36	−	3349.62i	0.0616492	−	0.189737i
$679$	−2351.62	−	7237.54i	−0.132911	−	0.409059i
$680$	815.489	−	592.488i	0.0459891	−	0.0334130i
$681$	−5862.00			−0.329857
$682$		0			0
$683$	−28488.0			−1.59599			−0.797996	−	0.602662i	$-0.794107\pi$
$683$	−28488.0			−1.59599			−0.797996	+	0.602662i	$0.794107\pi$
$684$	9759.98	−	7091.04i	0.545588	−	0.396393i
$685$	−853.814	−	2627.77i	−0.0476242	−	0.146572i
$686$	3621.68	−	11146.4i	0.201569	−	0.620366i
$687$	−4086.34	−	2968.90i	−0.226934	−	0.164877i
$688$	−1423.87	−	1034.50i	−0.0789019	−	0.0573256i
$689$	−444.984	+	1369.52i	−0.0246046	+	0.0757251i
$690$	−350.425	−	1078.50i	−0.0193340	−	0.0595039i
$691$	−14445.0	+	10494.9i	−0.795244	+	0.577779i	−0.909515	−	0.415671i	$-0.863547\pi$
$691$	−14445.0	+	10494.9i	−0.795244	+	0.577779i	0.114271	+	0.993450i	$0.463547\pi$
$692$	7944.00			0.436395
$693$		0			0
$694$	13152.0			0.719370
$695$	3499.81	−	2542.76i	0.191015	−	0.138780i
$696$	−296.656	−	913.014i	−0.0161562	−	0.0497237i
$697$	6074.04	−	18694.0i	0.330087	−	1.01590i
$698$	10171.0	+	7389.64i	0.551542	+	0.400719i
$699$	582.492	+	423.205i	0.0315191	+	0.0229000i
$700$	1433.84	−	4412.90i	0.0774200	−	0.238274i
$701$	−9787.80	−	30123.8i	−0.527361	−	1.62305i	−0.759599	−	0.650392i	$-0.774605\pi$
$701$	−9787.80	−	30123.8i	−0.527361	−	1.62305i	0.232237	−	0.972659i	$-0.425395\pi$
$702$	−1372.09	+	996.884i	−0.0737697	+	0.0535968i
$703$	−47444.0			−2.54535
$704$		0			0
$705$	−432.000			−0.0230781
$706$	17314.6	−	12579.8i	0.923007	−	0.670604i
$707$	4876.29	+	15007.7i	0.259394	+	0.798333i
$708$	−559.939	+	1723.31i	−0.0297229	+	0.0914776i
$709$	−300.145	−	218.068i	−0.0158987	−	0.0115511i	0.579808	−	0.814753i	$-0.303128\pi$
$709$	−300.145	−	218.068i	−0.0158987	−	0.0115511i	−0.595706	+	0.803202i	$0.703128\pi$
$710$	−2257.16	−	1639.92i	−0.119309	−	0.0866833i
$711$	5961.56	−	18347.8i	0.314453	−	0.967786i
$712$	−674.893	−	2077.11i	−0.0355234	−	0.109330i
$713$	24923.4	−	18107.9i	1.30910	−	0.951117i
$714$	−840.000			−0.0440283
$715$		0			0
$716$	444.000			0.0231747
$717$	422.307	−	306.824i	0.0219963	−	0.0159812i
$718$	5146.99	+	15840.8i	0.267526	+	0.823361i
$719$	8364.78	−	25744.1i	0.433872	−	1.33532i	−0.460367	−	0.887729i	$-0.652282\pi$
$719$	8364.78	−	25744.1i	0.433872	−	1.33532i	0.894238	−	0.447591i	$-0.147718\pi$
$720$	−1009.65	−	733.556i	−0.0522605	−	0.0379695i
$721$	9772.93	+	7100.45i	0.504803	+	0.366761i
$722$	4077.17	−	12548.2i	0.210161	−	0.646810i
$723$	−1740.38	−	5356.35i	−0.0895236	−	0.275525i
$724$	−2909.23	+	2113.68i	−0.149338	+	0.108500i
$725$	13920.0			0.713070
$726$		0			0
$727$	−20095.0			−1.02515			−0.512574	−	0.858643i	$-0.671308\pi$
$727$	−20095.0			−1.02515			−0.512574	+	0.858643i	$0.671308\pi$
$728$	−1035.54	+	752.365i	−0.0527194	+	0.0383029i
$729$	−4772.15	−	14687.2i	−0.242450	−	0.746185i
$730$	−1572.28	+	4838.98i	−0.0797159	+	0.245340i
$731$	−3737.66	−	2715.57i	−0.189114	−	0.137399i
$732$	−64.7214	−	47.0228i	−0.00326799	−	0.00237434i
$733$	−3776.19	+	11621.9i	−0.190282	+	0.585628i	−0.999999	−	0.00119247i	$-0.999620\pi$
$733$	−3776.19	+	11621.9i	−0.190282	+	0.585628i	0.809717	+	0.586820i	$0.199620\pi$
$734$	−2251.50	−	6929.40i	−0.113221	−	0.348459i
$735$	−589.773	+	428.495i	−0.0295974	+	0.0215038i
$736$	6048.00			0.302897
$737$		0			0
$738$	−24336.0			−1.21385
$739$	26550.3	−	19289.9i	1.32161	−	0.960205i	0.321699	−	0.946842i	$-0.395746\pi$
$739$	26550.3	−	19289.9i	1.32161	−	0.960205i	0.999911	−	0.0133633i	$-0.00425379\pi$
$740$	1516.66	+	4667.79i	0.0753424	+	0.231880i
$741$	−573.536	+	1765.16i	−0.0284337	+	0.0875099i
$742$	1456.23	+	1058.01i	0.0720484	+	0.0523462i
$743$	−19736.8	−	14339.6i	−0.974525	−	0.708034i	−0.0180468	−	0.999837i	$-0.505745\pi$
$743$	−19736.8	−	14339.6i	−0.974525	−	0.708034i	−0.956478	+	0.291803i	$0.905745\pi$
$744$	−402.958	+	1240.18i	−0.0198564	+	0.0611117i
$745$	1674.25	+	5152.82i	0.0823355	+	0.253403i
$746$	12850.4	−	9336.38i	0.630680	−	0.458216i
$747$	−11388.0			−0.557785
$748$		0			0
$749$	14460.0			0.705416
$750$	−1169.84	+	849.937i	−0.0569553	+	0.0413804i
$751$	−767.907	−	2363.38i	−0.0373120	−	0.114835i	0.930666	−	0.365871i	$-0.119229\pi$
$751$	−767.907	−	2363.38i	−0.0373120	−	0.114835i	−0.967978	+	0.251036i	$0.919229\pi$
$752$	711.975	−	2191.23i	0.0345253	−	0.106258i
$753$	5133.21	+	3729.50i	0.248426	+	0.180492i
$754$	−3106.63	−	2257.10i	−0.150049	−	0.109017i
$755$	1299.73	−	4000.14i	0.0626515	−	0.192821i
$756$	655.116	+	2016.24i	0.0315163	+	0.0969973i
$757$	11531.7	−	8378.29i	0.553669	−	0.402264i	−0.275467	−	0.961310i	$-0.588833\pi$
$757$	11531.7	−	8378.29i	0.553669	−	0.402264i	0.829137	+	0.559046i	$0.188833\pi$
$758$	−18662.0			−0.894241
$759$		0			0
$760$	−2784.00			−0.132877
$761$	−13941.0	+	10128.7i	−0.664074	+	0.482478i	−0.868036	−	0.496501i	$-0.834618\pi$
$761$	−13941.0	+	10128.7i	−0.664074	+	0.482478i	0.203962	+	0.978979i	$0.434618\pi$
$762$	1317.65	+	4055.30i	0.0626422	+	0.192793i
$763$	4147.01	−	12763.2i	0.196765	−	0.605581i
$764$	4883.23	+	3547.87i	0.231242	+	0.168007i
$765$	−2650.34	−	1925.58i	−0.125259	−	0.0910061i
$766$	−4778.02	+	14705.2i	−0.225375	+	0.693632i
$767$	2239.76	+	6893.26i	0.105441	+	0.324513i
$768$	−207.108	+	150.473i	−0.00973096	+	0.00706996i
$769$	25520.0			1.19672			0.598358	−	0.801229i	$-0.295820\pi$
$769$	25520.0			1.19672			0.598358	+	0.801229i	$0.295820\pi$
$770$		0			0
$771$	1494.00			0.0697861
$772$	−64.7214	+	47.0228i	−0.00301732	+	0.00219221i
$773$	4633.40	+	14260.1i	0.215591	+	0.663521i	0.999111	+	0.0421544i	$0.0134222\pi$
$773$	4633.40	+	14260.1i	0.215591	+	0.663521i	−0.783520	+	0.621366i	$0.786578\pi$
$774$	−1767.58	+	5440.04i	−0.0820856	+	0.252633i
$775$	−15296.9	−	11113.8i	−0.709007	−	0.515124i
$776$	−4925.30	−	3578.44i	−0.227845	−	0.165539i
$777$	1263.88	−	3889.82i	0.0583545	−	0.179597i
$778$	902.948	+	2778.99i	0.0416096	+	0.128061i
$779$	−43919.9	+	31909.7i	−2.02002	+	1.46763i
$780$	192.000			0.00881372
$781$		0			0
$782$	15876.0			0.725991
$783$	−5145.35	+	3738.31i	−0.234840	+	0.170621i
$784$	−1201.46	−	3697.71i	−0.0547311	−	0.168445i
$785$	2732.02	−	8408.29i	0.124216	−	0.382299i
$786$	−2883.34	−	2094.87i	−0.130846	−	0.0950654i
$787$	28496.8	+	20704.1i	1.29073	+	0.937768i	0.999820	−	0.0189838i	$-0.00604308\pi$
$787$	28496.8	+	20704.1i	1.29073	+	0.937768i	0.290907	+	0.956751i	$0.406043\pi$
$788$	1550.03	−	4770.50i	0.0700730	−	0.215662i
$789$	387.507	+	1192.62i	0.0174850	+	0.0538131i
$790$	−3601.74	+	2616.82i	−0.162208	+	0.117851i
$791$	−17610.0			−0.791580
$792$		0			0
$793$	−320.000			−0.0143298
$794$	10462.2	−	7601.24i	0.467619	−	0.339745i
$795$	−83.4346	−	256.785i	−0.00372216	−	0.0114556i
$796$	5794.69	−	17834.2i	0.258024	−	0.794117i
$797$	−15055.0	−	10938.1i	−0.669103	−	0.486132i	0.200622	−	0.979669i	$-0.435704\pi$
$797$	−15055.0	−	10938.1i	−0.669103	−	0.486132i	−0.869725	+	0.493537i	$0.835704\pi$
$798$	1876.92	+	1363.66i	0.0832609	+	0.0604926i
$799$	1868.93	−	5751.99i	0.0827511	−	0.254682i
$800$	−1147.07	−	3530.32i	−0.0506939	−	0.156020i
$801$	−5742.40	+	4172.10i	−0.253306	+	0.184037i
$802$	4020.00			0.176996
$803$		0			0
$804$	−388.000			−0.0170195
$805$	−4587.13	+	3332.74i	−0.200838	+	0.145918i
$806$	1611.83	+	4960.71i	0.0704397	+	0.216791i
$807$	1681.67	−	5175.65i	0.0733551	−	0.225764i
$808$	10213.0	+	7420.20i	0.444670	+	0.323071i
$809$	−13329.4	−	9684.35i	−0.579277	−	0.420870i	0.259186	−	0.965827i	$-0.416546\pi$
$809$	−13329.4	−	9684.35i	−0.579277	−	0.420870i	−0.838464	+	0.544958i	$0.816546\pi$
$810$	−1203.31	+	3703.41i	−0.0521976	+	0.160648i
$811$	−841.144	−	2588.78i	−0.0364199	−	0.112089i	0.931194	−	0.364525i	$-0.118768\pi$
$811$	−841.144	−	2588.78i	−0.0364199	−	0.112089i	−0.967614	+	0.252435i	$0.918768\pi$
$812$	−3883.28	+	2821.37i	−0.167828	+	0.121934i
$813$	2432.00			0.104913
$814$		0			0
$815$	−996.000			−0.0428078
$816$	−543.659	+	394.992i	−0.0233234	+	0.0169454i
$817$	3943.06	+	12135.5i	0.168850	+	0.519666i
$818$	−7800.83	+	24008.5i	−0.333435	+	1.02621i
$819$	3365.51	+	2445.19i	0.143590	+	0.104324i
$820$	4543.44	+	3301.00i	0.193492	+	0.140580i
$821$	−5686.53	+	17501.3i	−0.241731	+	0.743972i	0.754426	+	0.656385i	$0.227915\pi$
$821$	−5686.53	+	17501.3i	−0.241731	+	0.743972i	−0.996157	+	0.0875866i	$0.972085\pi$
$822$	569.209	+	1751.85i	0.0241526	+	0.0743341i
$823$	32168.9	−	23372.1i	1.36250	−	0.989915i	0.364220	−	0.931313i	$-0.381336\pi$
$823$	32168.9	−	23372.1i	1.36250	−	0.989915i	0.998281	−	0.0586025i	$-0.0186645\pi$
$824$	9664.00			0.408570
$825$		0			0
$826$	9060.00			0.381644
$827$	1009.65	−	733.556i	0.0424535	−	0.0308443i	−0.566356	−	0.824161i	$-0.691647\pi$
$827$	1009.65	−	733.556i	0.0424535	−	0.0308443i	0.608810	+	0.793316i	$0.291647\pi$
$828$	−6074.04	−	18694.0i	−0.254936	−	0.784614i
$829$	−2675.78	+	8235.20i	−0.112103	+	0.345018i	−0.991332	−	0.131382i	$-0.958059\pi$
$829$	−2675.78	+	8235.20i	−0.112103	+	0.345018i	0.879229	+	0.476400i	$0.158059\pi$
$830$	2126.10	+	1544.70i	0.0889131	+	0.0645992i
$831$	1347.82	+	979.250i	0.0562641	+	0.0408782i
$832$	−316.433	+	973.882i	−0.0131855	+	0.0405809i
$833$	−3153.83	−	9706.48i	−0.131181	−	0.403733i
$834$	−2333.21	+	1695.17i	−0.0968732	+	0.0703825i
$835$	−5760.00			−0.238722
$836$		0			0
$837$	8639.00			0.356759
$838$	−17766.0	+	12907.8i	−0.732359	+	0.532090i
$839$	−12753.4	−	39251.1i	−0.524789	−	1.61513i	−0.764733	−	0.644347i	$-0.777129\pi$
$839$	−12753.4	−	39251.1i	−0.524789	−	1.61513i	0.239945	−	0.970787i	$-0.422871\pi$
$840$	74.1641	−	228.254i	0.00304631	−	0.00937559i
$841$	8081.27	+	5871.39i	0.331349	+	0.240739i
$842$	870.502	+	632.457i	0.0356288	+	0.0258859i
$843$	−1006.78	+	3098.54i	−0.0411332	+	0.126595i
$844$	6017.18	+	18519.0i	0.245403	+	0.755272i
$845$	−4710.91	+	3422.67i	−0.191787	+	0.139341i
$846$	−7488.00			−0.304306
$847$		0			0
$848$	1440.00			0.0583134
$849$	6313.57	−	4587.08i	0.255219	−	0.185428i
$850$	−3011.06	−	9267.09i	−0.121504	−	0.373951i
$851$	−23887.3	+	73517.6i	−0.962217	+	2.96140i
$852$	1504.77	+	1093.28i	0.0605078	+	0.0439615i
$853$	−1778.22	−	1291.95i	−0.0713776	−	0.0518588i	0.551524	−	0.834159i	$-0.314046\pi$
$853$	−1778.22	−	1291.95i	−0.0713776	−	0.0518588i	−0.622902	+	0.782300i	$0.714046\pi$
$854$	−123.607	+	380.423i	−0.00495285	+	0.0152433i
$855$	2795.99	+	8605.16i	0.111837	+	0.344199i
$856$	9358.71	−	6799.50i	0.373685	−	0.271498i
$857$	27192.0			1.08385			0.541926	−	0.840426i	$-0.317695\pi$
$857$	27192.0			1.08385			0.541926	+	0.840426i	$0.317695\pi$
$858$		0			0
$859$	27095.0			1.07622			0.538108	−	0.842876i	$-0.319139\pi$
$859$	27095.0			1.07622			0.538108	+	0.842876i	$0.319139\pi$
$860$	1067.90	−	775.877i	0.0423432	−	0.0307642i
$861$	−1446.20	−	4450.94i	−0.0572431	−	0.176176i
$862$	3103.77	−	9552.41i	0.122639	−	0.377444i
$863$	12950.7	+	9409.27i	0.510833	+	0.371142i	0.813139	−	0.582069i	$-0.197757\pi$
$863$	12950.7	+	9409.27i	0.510833	+	0.371142i	−0.302307	+	0.953211i	$0.597757\pi$
$864$	1372.09	+	996.884i	0.0540273	+	0.0392531i
$865$	−1841.12	+	5666.39i	−0.0723700	+	0.222732i
$866$	−1598.85	−	4920.77i	−0.0627382	−	0.193088i
$867$	2547.59	−	1850.94i	0.0997934	−	0.0725041i
$868$	6520.00			0.254958
$869$		0			0
$870$	720.000			0.0280578
$871$	−1255.59	+	912.243i	−0.0488452	+	0.0354881i
$872$	−3317.61	−	10210.5i	−0.128840	−	0.396528i
$873$	−6114.21	+	18817.6i	−0.237039	+	0.729530i
$874$	−35473.8	−	25773.2i	−1.37290	−	0.997473i
$875$	5849.19	+	4249.69i	0.225987	+	0.164189i
$876$	1048.19	−	3225.98i	0.0404280	−	0.124425i
$877$	6929.40	+	21326.5i	0.266806	+	0.821145i	0.991272	+	0.131834i	$0.0420867\pi$
$877$	6929.40	+	21326.5i	0.266806	+	0.821145i	−0.724465	+	0.689311i	$0.757913\pi$
$878$	−1139.10	+	827.602i	−0.0437843	+	0.0318112i
$879$	12.0000			0.000460466
$880$		0			0
$881$	−11427.0			−0.436987			−0.218493	−	0.975838i	$-0.570114\pi$
$881$	−11427.0			−0.436987			−0.218493	+	0.975838i	$0.570114\pi$
$882$	−10222.7	+	7427.25i	−0.390269	+	0.283547i
$883$	9276.69	+	28550.7i	0.353551	+	1.08812i	0.956845	+	0.290599i	$0.0938546\pi$
$883$	9276.69	+	28550.7i	0.353551	+	1.08812i	−0.603294	+	0.797519i	$0.706145\pi$
$884$	−830.638	+	2556.44i	−0.0316034	+	0.0972651i
$885$	−1099.45	−	798.800i	−0.0417602	−	0.0303405i
$886$	−6800.60	−	4940.92i	−0.257867	−	0.187352i
$887$	3695.23	−	11372.7i	0.139880	−	0.430506i	−0.856437	−	0.516251i	$-0.827327\pi$
$887$	3695.23	−	11372.7i	0.139880	−	0.430506i	0.996317	+	0.0857451i	$0.0273271\pi$
$888$	−1011.10	−	3111.86i	−0.0382099	−	0.117598i
$889$	17248.2	−	12531.6i	0.650717	−	0.472774i
$890$	1638.00			0.0616920
$891$		0			0
$892$	−18652.0			−0.700129
$893$	−13513.8	+	9818.36i	−0.506408	+	0.367927i
$894$	−1116.17	−	3435.22i	−0.0417565	−	0.128513i
$895$	−102.903	+	316.702i	−0.00384319	+	0.0118281i
$896$	1035.54	+	752.365i	0.0386105	+	0.0280522i
$897$	2446.47	+	1777.46i	0.0910648	+	0.0661625i
$898$	−576.626	+	1774.67i	−0.0214279	+	0.0659483i
$899$	6044.37	+	18602.7i	0.224239	+	0.690138i
$900$	−9759.98	+	7091.04i	−0.361481	+	0.262631i
$901$	3780.00			0.139767
$902$		0			0
$903$	−1100.00			−0.0405379
$904$	−11397.4	+	8280.72i	−0.419328	+	0.304660i
$905$	−833.419	−	2565.00i	−0.0306119	−	0.0942138i
$906$	−866.484	+	2666.76i	−0.0317737	+	0.0977895i
$907$	10565.8	+	7676.48i	0.386803	+	0.281029i	0.764144	−	0.645045i	$-0.223162\pi$
$907$	10565.8	+	7676.48i	0.386803	+	0.281029i	−0.377341	+	0.926074i	$0.623162\pi$
$908$	18969.8	+	13782.4i	0.693322	+	0.503728i
$909$	12678.3	−	39019.9i	0.462612	−	1.42377i
$910$	−296.656	−	913.014i	−0.0108067	−	0.0332595i
$911$	−8242.27	+	5988.36i	−0.299757	+	0.217786i	−0.727489	−	0.686120i	$-0.759313\pi$
$911$	−8242.27	+	5988.36i	−0.299757	+	0.217786i	0.427732	+	0.903906i	$0.359313\pi$
$912$	1856.00			0.0673885
$913$		0			0
$914$	20632.0			0.746659
$915$	48.5410	−	35.2671i	0.00175379	−	0.00127420i
$916$	6243.38	+	19215.1i	0.225204	+	0.693107i
$917$	−5506.68	+	16947.8i	−0.198306	+	0.610323i
$918$	3601.74	+	2616.82i	0.129494	+	0.0940827i
$919$	35384.8	+	25708.6i	1.27012	+	0.922793i	0.999207	−	0.0398120i	$-0.0126759\pi$
$919$	35384.8	+	25708.6i	1.27012	+	0.922793i	0.270909	+	0.962605i	$0.412676\pi$
$920$	−1401.70	+	4313.99i	−0.0502312	+	0.154596i
$921$	1808.37	+	5565.58i	0.0646990	+	0.199123i
$922$	−213.580	+	155.175i	−0.00762896	+	0.00554276i
$923$	7440.00			0.265320
$924$		0			0
$925$	47444.0			1.68643
$926$	−12657.9	+	9196.49i	−0.449205	+	0.326366i
$927$	−9705.61	−	29870.8i	−0.343877	−	1.05834i
$928$	−1186.63	+	3652.06i	−0.0419751	+	0.129186i
$929$	13324.5	+	9680.82i	0.470574	+	0.341892i	0.797665	−	0.603101i	$-0.206068\pi$
$929$	13324.5	+	9680.82i	0.470574	+	0.341892i	−0.327091	+	0.944993i	$0.606068\pi$
$930$	−791.219	−	574.854i	−0.0278979	−	0.0202690i
$931$	−8710.57	+	26808.4i	−0.306635	+	0.943726i
$932$	−889.969	−	2739.04i	−0.0312789	−	0.0962664i
$933$	−2145.51	+	1558.81i	−0.0752850	+	0.0546978i
$934$	1446.00			0.0506580
$935$		0			0
$936$	3328.00			0.116217
$937$	−19316.1	+	14034.0i	−0.673457	+	0.489295i	−0.871181	−	0.490963i	$-0.836645\pi$
$937$	−19316.1	+	14034.0i	−0.673457	+	0.489295i	0.197724	+	0.980258i	$0.436645\pi$
$938$	599.493	+	1845.05i	0.0208680	+	0.0642250i
$939$	−2210.40	+	6802.91i	−0.0768196	+	0.236427i
$940$	1397.98	+	1015.69i	0.0485076	+	0.0352428i
$941$	−17974.7	−	13059.4i	−0.622699	−	0.452417i	0.231164	−	0.972915i	$-0.425747\pi$
$941$	−17974.7	−	13059.4i	−0.622699	−	0.452417i	−0.853863	+	0.520497i	$0.825747\pi$
$942$	−1821.35	+	5605.53i	−0.0629965	+	0.193883i
$943$	27333.2	+	84122.9i	0.943892	+	2.90500i
$944$	5863.76	−	4260.27i	0.202171	−	0.146885i
$945$	−1590.00			−0.0547330
$946$		0			0
$947$	−9909.00			−0.340020			−0.170010	−	0.985442i	$-0.554380\pi$
$947$	−9909.00			−0.340020			−0.170010	+	0.985442i	$0.554380\pi$
$948$	2401.16	−	1744.55i	0.0822639	−	0.0597682i
$949$	−4192.74	−	12903.9i	−0.143416	−	0.441390i
$950$	−8316.27	+	25594.8i	−0.284016	+	0.874112i
$951$	−4958.47	−	3602.54i	−0.169074	−	0.122839i
$952$	2718.30	+	1974.96i	0.0925426	+	0.0672361i
$953$	−14170.9	+	43613.5i	−0.481679	+	1.48246i	0.355054	+	0.934846i	$0.384463\pi$
$953$	−14170.9	+	43613.5i	−0.481679	+	1.48246i	−0.836733	+	0.547611i	$0.815537\pi$
$954$	−1446.20	−	4450.94i	−0.0490801	−	0.151053i
$955$	−3662.42	+	2660.90i	−0.124098	+	0.0901621i
$956$	−2088.00			−0.0706389
$957$		0			0
$958$	−14832.0			−0.500209
$959$	7451.05	−	5413.50i	0.250893	−	0.182285i
$960$	−59.3313	−	182.603i	−0.00199470	−	0.00613904i
$961$	−995.653	+	3064.30i	−0.0334213	+	0.102860i
$962$	−10588.4	−	7692.93i	−0.354869	−	0.257828i
$963$	−30415.8	−	22098.4i	−1.01779	−	0.739471i
$964$	−6961.53	+	21425.4i	−0.232589	+	0.715836i
$965$	−18.5410	−	57.0634i	−0.000618504	−	0.00190356i
$966$	3058.08	−	2221.83i	0.101855	−	0.0740022i
$967$	−33352.0			−1.10913			−0.554565	−	0.832141i	$-0.687115\pi$
$967$	−33352.0			−1.10913			−0.554565	+	0.832141i	$0.687115\pi$
$968$		0			0
$969$	4872.00			0.161518
$970$	3693.97	−	2683.83i	0.122275	−	0.0888376i
$971$	11639.1	+	35821.5i	0.384673	+	1.18390i	0.936717	+	0.350087i	$0.113848\pi$
$971$	11639.1	+	35821.5i	0.384673	+	1.18390i	−0.552045	+	0.833815i	$0.686152\pi$
$972$	2571.02	−	7912.79i	0.0848411	−	0.261114i
$973$	11666.0	+	8475.86i	0.384374	+	0.279264i
$974$	11602.9	+	8430.02i	0.381706	+	0.277326i
$975$	573.536	−	1765.16i	0.0188388	−	0.0579799i
$976$	98.8854	+	304.338i	0.00324308	+	0.00998117i
$977$	28894.0	−	20992.8i	0.946164	−	0.687428i	−0.00373243	−	0.999993i	$-0.501188\pi$
$977$	28894.0	−	20992.8i	0.946164	−	0.687428i	0.949897	+	0.312565i	$0.101188\pi$
$978$	664.000			0.0217100
$979$		0			0
$980$	2916.00			0.0950492
$981$	−28228.2	+	20509.0i	−0.918713	+	0.667484i
$982$	−7579.57	−	23327.5i	−0.246307	−	0.758056i
$983$	1838.34	−	5657.84i	0.0596480	−	0.183578i	−0.916793	−	0.399363i	$-0.869231\pi$
$983$	1838.34	−	5657.84i	0.0596480	−	0.183578i	0.976441	+	0.215786i	$0.0692312\pi$
$984$	−3028.96	−	2200.67i	−0.0981298	−	0.0712955i
$985$	3043.52	+	2211.25i	0.0984514	+	0.0715292i
$986$	−3114.89	+	9586.65i	−0.100607	+	0.309636i
$987$	−444.984	−	1369.52i	−0.0143506	−	0.0441665i
$988$	6006.14	−	4363.72i	0.193402	−	0.140515i
$989$	20790.0			0.668436
$990$		0			0
$991$	−23560.0			−0.755205			−0.377602	−	0.925968i	$-0.623251\pi$
$991$	−23560.0			−0.755205			−0.377602	+	0.925968i	$0.623251\pi$
$992$	4219.83	−	3065.89i	0.135060	−	0.0981271i
$993$	−254.321	−	782.720i	−0.00812753	−	0.0250140i
$994$	2873.86	−	8844.83i	0.0917035	−	0.282234i
$995$	11378.0	+	8266.61i	0.362520	+	0.263386i
$996$	−1417.40	−	1029.80i	−0.0450923	−	0.0327615i
$997$	8277.33	−	25475.0i	0.262934	−	0.809229i	−0.729228	−	0.684271i	$-0.760120\pi$
$997$	8277.33	−	25475.0i	0.262934	−	0.809229i	0.992162	−	0.124958i	$-0.0398796\pi$
$998$	−7329.88	−	22559.1i	−0.232488	−	0.715526i
$999$	−17537.1	+	12741.4i	−0.555403	+	0.403524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.d.3.1		4
11.2	odd	10		242.4.a.a.1.1		1
11.3	even	5	inner	242.4.c.d.27.1		4
11.4	even	5	inner	242.4.c.d.81.1		4
11.5	even	5	inner	242.4.c.d.9.1		4
11.6	odd	10		242.4.c.k.9.1		4
11.7	odd	10		242.4.c.k.81.1		4
11.8	odd	10		242.4.c.k.27.1		4
11.9	even	5		22.4.a.c.1.1	✓	1
11.10	odd	2		242.4.c.k.3.1		4
33.2	even	10		2178.4.a.r.1.1		1
33.20	odd	10		198.4.a.b.1.1		1
44.31	odd	10		176.4.a.c.1.1		1
44.35	even	10		1936.4.a.h.1.1		1
55.9	even	10		550.4.a.e.1.1		1
55.42	odd	20		550.4.b.g.199.2		2
55.53	odd	20		550.4.b.g.199.1		2
77.20	odd	10		1078.4.a.f.1.1		1
88.53	even	10		704.4.a.e.1.1		1
88.75	odd	10		704.4.a.g.1.1		1
132.119	even	10		1584.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.a.c.1.1	✓	1	11.9	even	5
176.4.a.c.1.1		1	44.31	odd	10
198.4.a.b.1.1		1	33.20	odd	10
242.4.a.a.1.1		1	11.2	odd	10
242.4.c.d.3.1		4	1.1	even	1	trivial
242.4.c.d.9.1		4	11.5	even	5	inner
242.4.c.d.27.1		4	11.3	even	5	inner
242.4.c.d.81.1		4	11.4	even	5	inner
242.4.c.k.3.1		4	11.10	odd	2
242.4.c.k.9.1		4	11.6	odd	10
242.4.c.k.27.1		4	11.8	odd	10
242.4.c.k.81.1		4	11.7	odd	10
550.4.a.e.1.1		1	55.9	even	10
550.4.b.g.199.1		2	55.53	odd	20
550.4.b.g.199.2		2	55.42	odd	20
704.4.a.e.1.1		1	88.53	even	10
704.4.a.g.1.1		1	88.75	odd	10
1078.4.a.f.1.1		1	77.20	odd	10
1584.4.a.k.1.1		1	132.119	even	10
1936.4.a.h.1.1		1	44.35	even	10
2178.4.a.r.1.1		1	33.2	even	10

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.23607 - 3.80423i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-3.09017 + 9.51057i) q^{7} +(2.47214 + 7.60845i) q^{8} +(21.0344 - 15.2824i) q^{9} +O(q^{10})\)	\(q+(-1.61803 + 1.17557i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.23607 - 3.80423i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-3.09017 + 9.51057i) q^{7} +(2.47214 + 7.60845i) q^{8} +(21.0344 - 15.2824i) q^{9} -6.00000 q^{10} +4.00000 q^{12} +(12.9443 - 9.40456i) q^{13} +(-6.18034 - 19.0211i) q^{14} +(-0.927051 + 2.85317i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-33.9787 - 24.6870i) q^{17} +(-16.0689 + 49.4549i) q^{18} +(35.8460 + 110.323i) q^{19} +(9.70820 - 7.05342i) q^{20} -10.0000 q^{21} +189.000 q^{23} +(-6.47214 + 4.70228i) q^{24} +(-35.8460 - 110.323i) q^{25} +(-9.88854 + 30.4338i) q^{26} +(42.8779 + 31.1526i) q^{27} +(32.3607 + 23.5114i) q^{28} +(-37.0820 + 114.127i) q^{29} +(-1.85410 - 5.70634i) q^{30} +(131.870 - 95.8090i) q^{31} +32.0000 q^{32} +84.0000 q^{34} +(-24.2705 + 17.6336i) q^{35} +(-32.1378 - 98.9099i) q^{36} +(-126.388 + 388.982i) q^{37} +(-187.692 - 136.366i) q^{38} +(12.9443 + 9.40456i) q^{39} +(-7.41641 + 22.8254i) q^{40} +(144.620 + 445.094i) q^{41} +(16.1803 - 11.7557i) q^{42} +110.000 q^{43} +78.0000 q^{45} +(-305.808 + 222.183i) q^{46} +(44.4984 + 136.952i) q^{47} +(4.94427 - 15.2169i) q^{48} +(196.591 + 142.832i) q^{49} +(187.692 + 136.366i) q^{50} +(12.9787 - 39.9444i) q^{51} +(-19.7771 - 60.8676i) q^{52} +(-72.8115 + 52.9007i) q^{53} -106.000 q^{54} -80.0000 q^{56} +(-93.8460 + 68.1831i) q^{57} +(-74.1641 - 228.254i) q^{58} +(-139.985 + 430.829i) q^{59} +(9.70820 + 7.05342i) q^{60} +(-16.1803 - 11.7557i) q^{61} +(-100.740 + 310.044i) q^{62} +(80.3444 + 247.275i) q^{63} +(-51.7771 + 37.6183i) q^{64} +48.0000 q^{65} -97.0000 q^{67} +(-135.915 + 98.7479i) q^{68} +(58.4042 + 179.750i) q^{69} +(18.5410 - 57.0634i) q^{70} +(376.193 + 273.320i) q^{71} +(168.276 + 122.259i) q^{72} +(262.046 - 806.496i) q^{73} +(-252.776 - 777.964i) q^{74} +(93.8460 - 68.1831i) q^{75} +464.000 q^{76} -32.0000 q^{78} +(600.291 - 436.137i) q^{79} +(-14.8328 - 45.6507i) q^{80} +(200.552 - 617.236i) q^{81} +(-757.240 - 550.167i) q^{82} +(-354.349 - 257.450i) q^{83} +(-12.3607 + 38.0423i) q^{84} +(-38.9361 - 119.833i) q^{85} +(-177.984 + 129.313i) q^{86} -120.000 q^{87} -273.000 q^{89} +(-126.207 + 91.6945i) q^{90} +(49.4427 + 152.169i) q^{91} +(233.617 - 718.999i) q^{92} +(131.870 + 95.8090i) q^{93} +(-232.997 - 169.282i) q^{94} +(-107.538 + 330.968i) q^{95} +(9.88854 + 30.4338i) q^{96} +(-615.662 + 447.305i) q^{97} -486.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9} - 24 q^{10} + 16 q^{12} + 16 q^{13} + 20 q^{14} + 3 q^{15} - 16 q^{16} - 42 q^{17} + 52 q^{18} - 116 q^{19} + 12 q^{20} - 40 q^{21} + 756 q^{23} - 8 q^{24} + 116 q^{25} + 32 q^{26} + 53 q^{27} + 40 q^{28} + 120 q^{29} + 6 q^{30} + 163 q^{31} + 128 q^{32} + 336 q^{34} - 30 q^{35} + 104 q^{36} + 409 q^{37} - 232 q^{38} + 16 q^{39} + 24 q^{40} - 468 q^{41} + 20 q^{42} + 440 q^{43} + 312 q^{45} - 378 q^{46} - 144 q^{47} - 16 q^{48} + 243 q^{49} + 232 q^{50} - 42 q^{51} + 64 q^{52} - 90 q^{53} - 424 q^{54} - 320 q^{56} - 116 q^{57} + 240 q^{58} + 453 q^{59} + 12 q^{60} - 20 q^{61} + 326 q^{62} - 260 q^{63} - 64 q^{64} + 192 q^{65} - 388 q^{67} - 168 q^{68} - 189 q^{69} - 60 q^{70} + 465 q^{71} + 208 q^{72} - 848 q^{73} + 818 q^{74} + 116 q^{75} + 1856 q^{76} - 128 q^{78} + 742 q^{79} + 48 q^{80} - 649 q^{81} - 936 q^{82} - 438 q^{83} + 40 q^{84} + 126 q^{85} - 220 q^{86} - 480 q^{87} - 1092 q^{89} - 156 q^{90} - 160 q^{91} - 756 q^{92} + 163 q^{93} - 288 q^{94} + 348 q^{95} - 32 q^{96} - 761 q^{97} - 1944 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9 - 24 * q^10 + 16 * q^12 + 16 * q^13 + 20 * q^14 + 3 * q^15 - 16 * q^16 - 42 * q^17 + 52 * q^18 - 116 * q^19 + 12 * q^20 - 40 * q^21 + 756 * q^23 - 8 * q^24 + 116 * q^25 + 32 * q^26 + 53 * q^27 + 40 * q^28 + 120 * q^29 + 6 * q^30 + 163 * q^31 + 128 * q^32 + 336 * q^34 - 30 * q^35 + 104 * q^36 + 409 * q^37 - 232 * q^38 + 16 * q^39 + 24 * q^40 - 468 * q^41 + 20 * q^42 + 440 * q^43 + 312 * q^45 - 378 * q^46 - 144 * q^47 - 16 * q^48 + 243 * q^49 + 232 * q^50 - 42 * q^51 + 64 * q^52 - 90 * q^53 - 424 * q^54 - 320 * q^56 - 116 * q^57 + 240 * q^58 + 453 * q^59 + 12 * q^60 - 20 * q^61 + 326 * q^62 - 260 * q^63 - 64 * q^64 + 192 * q^65 - 388 * q^67 - 168 * q^68 - 189 * q^69 - 60 * q^70 + 465 * q^71 + 208 * q^72 - 848 * q^73 + 818 * q^74 + 116 * q^75 + 1856 * q^76 - 128 * q^78 + 742 * q^79 + 48 * q^80 - 649 * q^81 - 936 * q^82 - 438 * q^83 + 40 * q^84 + 126 * q^85 - 220 * q^86 - 480 * q^87 - 1092 * q^89 - 156 * q^90 - 160 * q^91 - 756 * q^92 + 163 * q^93 - 288 * q^94 + 348 * q^95 - 32 * q^96 - 761 * q^97 - 1944 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more