LMFDB - Embedded newform 22.4.c.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,4,Mod(3,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, 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("22.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, 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:	$1.29804202013$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	22.15
Dual form			22.4.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(-3.04508 + 9.37181i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.30902 - 0.951057i) q^{5} +(15.9443 - 11.5842i) q^{6} +(4.57295 + 14.0741i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-56.7148 - 41.2057i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(-3.04508 + 9.37181i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.30902 - 0.951057i) q^{5} +(15.9443 - 11.5842i) q^{6} +(4.57295 + 14.0741i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-56.7148 - 41.2057i) q^{9} -3.23607 q^{10} +(35.5967 - 7.99197i) q^{11} -39.4164 q^{12} +(41.1976 + 29.9318i) q^{13} +(9.14590 - 28.1482i) q^{14} +(4.92705 + 15.1639i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(48.7943 - 35.4511i) q^{17} +(43.3262 + 133.344i) q^{18} +(-8.16970 + 25.1437i) q^{19} +(5.23607 + 3.80423i) q^{20} -145.825 q^{21} +(-66.9919 - 28.9152i) q^{22} -29.1672 q^{23} +(63.7771 + 46.3368i) q^{24} +(-37.8181 + 116.392i) q^{25} +(-31.4721 - 96.8613i) q^{26} +(343.626 - 249.659i) q^{27} +(-47.8885 + 34.7931i) q^{28} +(-46.4352 - 142.913i) q^{29} +(9.85410 - 30.3278i) q^{30} +(-23.7680 - 17.2685i) q^{31} +32.0000 q^{32} +(-33.4959 + 357.942i) q^{33} -120.626 q^{34} +(19.3713 + 14.0741i) q^{35} +(86.6525 - 266.689i) q^{36} +(-69.4746 - 213.821i) q^{37} +(42.7771 - 31.0794i) q^{38} +(-405.965 + 294.951i) q^{39} +(-4.00000 - 12.3107i) q^{40} +(36.9975 - 113.867i) q^{41} +(235.949 + 171.427i) q^{42} +213.974 q^{43} +(74.4033 + 125.539i) q^{44} -113.430 q^{45} +(47.1935 + 34.2881i) q^{46} +(-54.0846 + 166.455i) q^{47} +(-48.7214 - 149.949i) q^{48} +(100.325 - 72.8902i) q^{49} +(198.018 - 143.869i) q^{50} +(183.658 + 565.243i) q^{51} +(-62.9443 + 193.723i) q^{52} +(51.1124 + 37.1353i) q^{53} -849.489 q^{54} +(38.9959 - 44.3161i) q^{55} +118.387 q^{56} +(-210.765 - 153.130i) q^{57} +(-92.8704 + 285.826i) q^{58} +(-80.9712 - 249.204i) q^{59} +(-51.5967 + 37.4872i) q^{60} +(573.568 - 416.722i) q^{61} +(18.1571 + 55.8819i) q^{62} +(320.579 - 986.641i) q^{63} +(-51.7771 - 37.6183i) q^{64} +82.3951 q^{65} +(474.984 - 539.786i) q^{66} -151.692 q^{67} +(195.177 + 141.805i) q^{68} +(88.8166 - 273.349i) q^{69} +(-14.7984 - 45.5447i) q^{70} +(-853.960 + 620.438i) q^{71} +(-453.718 + 329.646i) q^{72} +(-9.74013 - 29.9770i) q^{73} +(-138.949 + 427.642i) q^{74} +(-975.646 - 708.848i) q^{75} -105.751 q^{76} +(275.262 + 464.445i) q^{77} +1003.60 q^{78} +(-52.6797 - 38.2741i) q^{79} +(-8.00000 + 24.6215i) q^{80} +(708.479 + 2180.47i) q^{81} +(-193.721 + 140.747i) q^{82} +(186.532 - 135.523i) q^{83} +(-180.249 - 554.750i) q^{84} +(30.1565 - 92.8123i) q^{85} +(-346.217 - 251.541i) q^{86} +1480.75 q^{87} +(27.1935 - 290.593i) q^{88} -618.952 q^{89} +(183.533 + 133.344i) q^{90} +(-232.868 + 716.695i) q^{91} +(-36.0526 - 110.959i) q^{92} +(234.212 - 170.165i) q^{93} +(283.190 - 205.750i) q^{94} +(13.2188 + 40.6834i) q^{95} +(-97.4427 + 299.898i) q^{96} +(889.913 + 646.559i) q^{97} -248.016 q^{98} +(-2348.18 - 1013.53i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 + 28 * q^6 + 25 * q^7 - 8 * q^8 - 124 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9} - 4 q^{10} + 44 q^{11} - 104 q^{12} + 91 q^{13} + 50 q^{14} + 13 q^{15} - 16 q^{16} + 23 q^{17} + 142 q^{18} + 59 q^{19} + 12 q^{20} - 230 q^{21} - 22 q^{22} - 224 q^{23} + 112 q^{24} + 126 q^{25} - 108 q^{26} + 773 q^{27} - 120 q^{28} - 425 q^{29} + 26 q^{30} - 227 q^{31} + 128 q^{32} - 11 q^{33} - 724 q^{34} + 35 q^{35} + 284 q^{36} - 61 q^{37} + 28 q^{38} - 839 q^{39} - 16 q^{40} + 347 q^{41} + 510 q^{42} + 1160 q^{43} + 396 q^{44} - 248 q^{45} - 8 q^{46} + 251 q^{47} - 16 q^{48} + 48 q^{49} + 242 q^{50} - 247 q^{51} - 216 q^{52} - 245 q^{53} - 1144 q^{54} + 33 q^{55} + 80 q^{56} - 331 q^{57} - 850 q^{58} - 827 q^{59} - 108 q^{60} + 1335 q^{61} + 976 q^{62} + 370 q^{63} - 64 q^{64} + 182 q^{65} + 1408 q^{66} - 88 q^{67} + 92 q^{68} - 244 q^{69} - 10 q^{70} - 1665 q^{71} - 992 q^{72} - 153 q^{73} - 122 q^{74} - 1709 q^{75} - 584 q^{76} - 55 q^{77} + 1832 q^{78} + 677 q^{79} - 32 q^{80} + 1376 q^{81} - 596 q^{82} + 887 q^{83} - 560 q^{84} + 181 q^{85} - 240 q^{86} + 1670 q^{87} - 88 q^{88} + 1728 q^{89} + 354 q^{90} - 245 q^{91} + 464 q^{92} + 1033 q^{93} + 292 q^{94} + 73 q^{95} - 32 q^{96} + 2019 q^{97} - 1484 q^{98} - 5654 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 + 28 * q^6 + 25 * q^7 - 8 * q^8 - 124 * q^9 - 4 * q^10 + 44 * q^11 - 104 * q^12 + 91 * q^13 + 50 * q^14 + 13 * q^15 - 16 * q^16 + 23 * q^17 + 142 * q^18 + 59 * q^19 + 12 * q^20 - 230 * q^21 - 22 * q^22 - 224 * q^23 + 112 * q^24 + 126 * q^25 - 108 * q^26 + 773 * q^27 - 120 * q^28 - 425 * q^29 + 26 * q^30 - 227 * q^31 + 128 * q^32 - 11 * q^33 - 724 * q^34 + 35 * q^35 + 284 * q^36 - 61 * q^37 + 28 * q^38 - 839 * q^39 - 16 * q^40 + 347 * q^41 + 510 * q^42 + 1160 * q^43 + 396 * q^44 - 248 * q^45 - 8 * q^46 + 251 * q^47 - 16 * q^48 + 48 * q^49 + 242 * q^50 - 247 * q^51 - 216 * q^52 - 245 * q^53 - 1144 * q^54 + 33 * q^55 + 80 * q^56 - 331 * q^57 - 850 * q^58 - 827 * q^59 - 108 * q^60 + 1335 * q^61 + 976 * q^62 + 370 * q^63 - 64 * q^64 + 182 * q^65 + 1408 * q^66 - 88 * q^67 + 92 * q^68 - 244 * q^69 - 10 * q^70 - 1665 * q^71 - 992 * q^72 - 153 * q^73 - 122 * q^74 - 1709 * q^75 - 584 * q^76 - 55 * q^77 + 1832 * q^78 + 677 * q^79 - 32 * q^80 + 1376 * q^81 - 596 * q^82 + 887 * q^83 - 560 * q^84 + 181 * q^85 - 240 * q^86 + 1670 * q^87 - 88 * q^88 + 1728 * q^89 + 354 * q^90 - 245 * q^91 + 464 * q^92 + 1033 * q^93 + 292 * q^94 + 73 * q^95 - 32 * q^96 + 2019 * q^97 - 1484 * q^98 - 5654 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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
$3$	−3.04508	+	9.37181i	−0.586027	+	1.80361i	0.00908010	+	0.999959i	$0.497110\pi$
$3$	−3.04508	+	9.37181i	−0.586027	+	1.80361i	−0.595107	+	0.803646i	$0.702890\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$	1.30902	−	0.951057i	0.117082	−	0.0850651i	−0.527703	−	0.849429i	$-0.676947\pi$
$5$	1.30902	−	0.951057i	0.117082	−	0.0850651i	0.644785	+	0.764364i	$0.276947\pi$
$6$	15.9443	−	11.5842i	1.08487	−	0.788204i
$7$	4.57295	+	14.0741i	0.246916	+	0.759929i	0.995315	+	0.0966811i	$0.0308227\pi$
$7$	4.57295	+	14.0741i	0.246916	+	0.759929i	−0.748399	+	0.663248i	$0.769177\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	−56.7148	−	41.2057i	−2.10055	−	1.52614i
$10$	−3.23607			−0.102333
$11$	35.5967	−	7.99197i	0.975711	−	0.219061i
$11$	35.5967	−	7.99197i	0.975711	−	0.219061i
$12$	−39.4164			−0.948211
$13$	41.1976	+	29.9318i	0.878934	+	0.638583i	0.932969	−	0.359956i	$-0.117208\pi$
$13$	41.1976	+	29.9318i	0.878934	+	0.638583i	−0.0540349	+	0.998539i	$0.517208\pi$
$14$	9.14590	−	28.1482i	0.174596	−	0.537351i
$15$	4.92705	+	15.1639i	0.0848106	+	0.261020i
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	48.7943	−	35.4511i	0.696139	−	0.505774i	−0.182534	−	0.983200i	$-0.558430\pi$
$17$	48.7943	−	35.4511i	0.696139	−	0.505774i	0.878672	+	0.477425i	$0.158430\pi$
$18$	43.3262	+	133.344i	0.567338	+	1.74609i
$19$	−8.16970	+	25.1437i	−0.0986451	+	0.303598i	−0.988186	−	0.153256i	$-0.951024\pi$
$19$	−8.16970	+	25.1437i	−0.0986451	+	0.303598i	0.889541	+	0.456855i	$0.151024\pi$
$20$	5.23607	+	3.80423i	0.0585410	+	0.0425325i
$21$	−145.825			−1.51531
$22$	−66.9919	−	28.9152i	−0.649214	−	0.280216i
$23$	−29.1672			−0.264425			−0.132213	−	0.991221i	$-0.542208\pi$
$23$	−29.1672			−0.264425			−0.132213	+	0.991221i	$0.542208\pi$
$24$	63.7771	+	46.3368i	0.542435	+	0.394102i
$25$	−37.8181	+	116.392i	−0.302545	+	0.931137i
$26$	−31.4721	−	96.8613i	−0.237392	−	0.730618i
$27$	343.626	−	249.659i	2.44929	−	1.77951i
$28$	−47.8885	+	34.7931i	−0.323217	+	0.234831i
$29$	−46.4352	−	142.913i	−0.297338	−	0.915112i	−0.982426	−	0.186652i	$-0.940236\pi$
$29$	−46.4352	−	142.913i	−0.297338	−	0.915112i	0.685088	−	0.728460i	$-0.259764\pi$
$30$	9.85410	−	30.3278i	0.0599702	−	0.184569i
$31$	−23.7680	−	17.2685i	−0.137705	−	0.100049i	0.516800	−	0.856106i	$-0.327123\pi$
$31$	−23.7680	−	17.2685i	−0.137705	−	0.100049i	−0.654505	+	0.756057i	$0.727123\pi$
$32$	32.0000			0.176777
$33$	−33.4959	+	357.942i	−0.176694	+	1.88817i
$34$	−120.626			−0.608448
$35$	19.3713	+	14.0741i	0.0935529	+	0.0679702i
$36$	86.6525	−	266.689i	0.401169	−	1.23467i
$37$	−69.4746	−	213.821i	−0.308691	−	0.950053i	−0.978274	−	0.207316i	$-0.933527\pi$
$37$	−69.4746	−	213.821i	−0.308691	−	0.950053i	0.669583	−	0.742737i	$-0.266473\pi$
$38$	42.7771	−	31.0794i	0.182615	−	0.132677i
$39$	−405.965	+	294.951i	−1.66683	+	1.21102i
$40$	−4.00000	−	12.3107i	−0.0158114	−	0.0486624i
$41$	36.9975	−	113.867i	0.140928	−	0.433731i	−0.855537	−	0.517741i	$-0.826773\pi$
$41$	36.9975	−	113.867i	0.140928	−	0.433731i	0.996465	+	0.0840105i	$0.0267729\pi$
$42$	235.949	+	171.427i	0.866852	+	0.629805i
$43$	213.974			0.758853			0.379427	−	0.925222i	$-0.376121\pi$
$43$	213.974			0.758853			0.379427	+	0.925222i	$0.376121\pi$
$44$	74.4033	+	125.539i	0.254925	+	0.430131i
$45$	−113.430			−0.375757
$46$	47.1935	+	34.2881i	0.151267	+	0.109902i
$47$	−54.0846	+	166.455i	−0.167852	+	0.516595i	−0.999235	−	0.0391043i	$-0.987550\pi$
$47$	−54.0846	+	166.455i	−0.167852	+	0.516595i	0.831383	+	0.555700i	$0.187550\pi$
$48$	−48.7214	−	149.949i	−0.146507	−	0.450901i
$49$	100.325	−	72.8902i	0.292492	−	0.212508i
$50$	198.018	−	143.869i	0.560080	−	0.406922i
$51$	183.658	+	565.243i	0.504261	+	1.55196i
$52$	−62.9443	+	193.723i	−0.167862	+	0.516625i
$53$	51.1124	+	37.1353i	0.132468	+	0.0962440i	0.652046	−	0.758179i	$-0.273911\pi$
$53$	51.1124	+	37.1353i	0.132468	+	0.0962440i	−0.519578	+	0.854423i	$0.673911\pi$
$54$	−849.489			−2.14076
$55$	38.9959	−	44.3161i	0.0956038	−	0.108647i
$56$	118.387			0.282502
$57$	−210.765	−	153.130i	−0.489763	−	0.355834i
$58$	−92.8704	+	285.826i	−0.210250	+	0.647082i
$59$	−80.9712	−	249.204i	−0.178670	−	0.549891i	0.821112	−	0.570767i	$-0.193354\pi$
$59$	−80.9712	−	249.204i	−0.178670	−	0.549891i	−0.999782	+	0.0208768i	$0.993354\pi$
$60$	−51.5967	+	37.4872i	−0.111019	+	0.0806597i
$61$	573.568	−	416.722i	1.20390	−	0.874684i	0.209237	−	0.977865i	$-0.432902\pi$
$61$	573.568	−	416.722i	1.20390	−	0.874684i	0.994663	+	0.103180i	$0.0329019\pi$
$62$	18.1571	+	55.8819i	0.0371929	+	0.114468i
$63$	320.579	−	986.641i	0.641098	−	1.97310i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$	82.3951			0.157229
$66$	474.984	−	539.786i	0.885855	−	1.00671i
$67$	−151.692			−0.276599			−0.138299	−	0.990390i	$-0.544164\pi$
$67$	−151.692			−0.276599			−0.138299	+	0.990390i	$0.544164\pi$
$68$	195.177	+	141.805i	0.348069	+	0.252887i
$69$	88.8166	−	273.349i	0.154960	−	0.476919i
$70$	−14.7984	−	45.5447i	−0.0252678	−	0.0777662i
$71$	−853.960	+	620.438i	−1.42741	+	1.03708i	−0.436924	+	0.899498i	$0.643932\pi$
$71$	−853.960	+	620.438i	−1.42741	+	1.03708i	−0.990491	+	0.137579i	$0.956068\pi$
$72$	−453.718	+	329.646i	−0.742656	+	0.539571i
$73$	−9.74013	−	29.9770i	−0.0156164	−	0.0480623i	0.942945	−	0.332949i	$-0.108044\pi$
$73$	−9.74013	−	29.9770i	−0.0156164	−	0.0480623i	−0.958561	+	0.284887i	$0.908044\pi$
$74$	−138.949	+	427.642i	−0.218277	+	0.671789i
$75$	−975.646	−	708.848i	−1.50210	−	1.09134i
$76$	−105.751			−0.159611
$77$	275.262	+	464.445i	0.407390	+	0.687382i
$78$	1003.60			1.45686
$79$	−52.6797	−	38.2741i	−0.0750245	−	0.0545085i	0.549641	−	0.835401i	$-0.314765\pi$
$79$	−52.6797	−	38.2741i	−0.0750245	−	0.0545085i	−0.624665	+	0.780893i	$0.714765\pi$
$80$	−8.00000	+	24.6215i	−0.0111803	+	0.0344095i
$81$	708.479	+	2180.47i	0.971851	+	2.99105i
$82$	−193.721	+	140.747i	−0.260890	+	0.189547i
$83$	186.532	−	135.523i	0.246681	−	0.179224i	−0.457573	−	0.889172i	$-0.651281\pi$
$83$	186.532	−	135.523i	0.246681	−	0.179224i	0.704255	+	0.709947i	$0.251281\pi$
$84$	−180.249	−	554.750i	−0.234129	−	0.720574i
$85$	30.1565	−	92.8123i	0.0384816	−	0.118434i
$86$	−346.217	−	251.541i	−0.434111	−	0.315400i
$87$	1480.75			1.82475
$88$	27.1935	−	290.593i	0.0329413	−	0.352015i
$89$	−618.952			−0.737177			−0.368589	−	0.929593i	$-0.620159\pi$
$89$	−618.952			−0.737177			−0.368589	+	0.929593i	$0.620159\pi$
$90$	183.533	+	133.344i	0.214956	+	0.156175i
$91$	−232.868	+	716.695i	−0.268255	+	0.825605i
$92$	−36.0526	−	110.959i	−0.0408559	−	0.125742i
$93$	234.212	−	170.165i	0.261147	−	0.189734i
$94$	283.190	−	205.750i	0.310733	−	0.225760i
$95$	13.2188	+	40.6834i	0.0142761	+	0.0439372i
$96$	−97.4427	+	299.898i	−0.103596	+	0.318835i
$97$	889.913	+	646.559i	0.931515	+	0.676785i	0.946363	−	0.323105i	$-0.104727\pi$
$97$	889.913	+	646.559i	0.931515	+	0.676785i	−0.0148484	+	0.999890i	$0.504727\pi$
$98$	−248.016			−0.255647
$99$	−2348.18	−	1013.53i	−2.38384	−	1.02892i
$100$	−489.528			−0.489528
$101$	−1091.59	−	793.084i	−1.07541	−	0.781335i	−0.0985372	−	0.995133i	$-0.531416\pi$
$101$	−1091.59	−	793.084i	−1.07541	−	0.781335i	−0.976878	+	0.213799i	$0.931416\pi$
$102$	367.317	−	1130.49i	0.356567	−	1.09740i
$103$	−458.805	−	1412.06i	−0.438907	−	1.35082i	−0.889030	−	0.457849i	$-0.848620\pi$
$103$	−458.805	−	1412.06i	−0.438907	−	1.35082i	0.450123	−	0.892966i	$-0.351380\pi$
$104$	329.580	−	239.454i	0.310750	−	0.225773i
$105$	−190.887	+	138.688i	−0.177416	+	0.128900i
$106$	−39.0464	−	120.172i	−0.0357785	−	0.110115i
$107$	−544.547	+	1675.94i	−0.491994	+	1.51420i	0.329597	+	0.944122i	$0.393087\pi$
$107$	−544.547	+	1675.94i	−0.491994	+	1.51420i	−0.821590	+	0.570079i	$0.806913\pi$
$108$	1374.50	+	998.634i	1.22464	+	0.889756i
$109$	688.087			0.604649			0.302325	−	0.953205i	$-0.402237\pi$
$109$	688.087			0.604649			0.302325	+	0.953205i	$0.402237\pi$
$110$	−115.193	+	25.8626i	−0.0998479	+	0.0224172i
$111$	2215.45			1.89442
$112$	−191.554	−	139.172i	−0.161609	−	0.117416i
$113$	93.6925	−	288.356i	0.0779987	−	0.240055i	−0.904453	−	0.426574i	$-0.859720\pi$
$113$	93.6925	−	288.356i	0.0779987	−	0.240055i	0.982451	+	0.186519i	$0.0597204\pi$
$114$	161.010	+	495.538i	0.132280	+	0.407117i
$115$	−38.1803	+	27.7396i	−0.0309594	+	0.0224933i
$116$	486.276	−	353.300i	0.389220	−	0.282785i
$117$	−1103.15	−	3395.15i	−0.871678	−	2.68275i
$118$	−161.942	+	498.407i	−0.126339	+	0.388831i
$119$	722.076	+	524.619i	0.556241	+	0.404132i
$120$	127.554			0.0970337
$121$	1203.26	−	568.976i	0.904025	−	0.427480i
$122$	−1417.94			−1.05225
$123$	954.475	+	693.467i	0.699692	+	0.508356i
$124$	36.3143	−	111.764i	0.0262993	−	0.0809410i
$125$	123.691	+	380.682i	0.0885061	+	0.272394i
$126$	−1678.57	+	1219.55i	−1.18682	+	0.862274i
$127$	−1832.93	+	1331.71i	−1.28068	+	0.930470i	−0.999573	−	0.0292057i	$-0.990702\pi$
$127$	−1832.93	+	1331.71i	−1.28068	+	0.930470i	−0.281109	+	0.959676i	$0.590702\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	−651.568	+	2005.32i	−0.444708	+	1.36867i
$130$	−133.318	−	96.8613i	−0.0899444	−	0.0653484i
$131$	1457.48			0.972068			0.486034	−	0.873940i	$-0.338443\pi$
$131$	1457.48			0.972068			0.486034	+	0.873940i	$0.338443\pi$
$132$	−1403.10	+	315.015i	−0.925180	+	0.207716i
$133$	−391.235			−0.255070
$134$	245.443	+	178.325i	0.158232	+	0.114962i
$135$	212.372	−	653.615i	0.135393	−	0.416698i
$136$	−149.102	−	458.889i	−0.0940103	−	0.289334i
$137$	159.260	−	115.709i	0.0993177	−	0.0721585i	−0.537018	−	0.843571i	$-0.680449\pi$
$137$	159.260	−	115.709i	0.0993177	−	0.0721585i	0.636336	+	0.771412i	$0.280449\pi$
$138$	−465.050	+	337.878i	−0.286867	+	0.208421i
$139$	−12.2537	−	37.7129i	−0.00747728	−	0.0230127i	0.947248	−	0.320501i	$-0.103851\pi$
$139$	−12.2537	−	37.7129i	−0.00747728	−	0.0230127i	−0.954726	+	0.297488i	$0.903851\pi$
$140$	−29.5967	+	91.0894i	−0.0178670	+	0.0549890i
$141$	−1395.29	−	1013.74i	−0.833368	−	0.605477i
$142$	2111.11			1.24761
$143$	1705.71	+	736.224i	0.997475	+	0.430533i
$144$	1121.65			0.649105
$145$	−196.703	−	142.913i	−0.112657	−	0.0818501i
$146$	−19.4803	+	59.9541i	−0.0110425	+	0.0339852i
$147$	377.615	+	1162.18i	0.211872	+	0.652075i
$148$	727.548	−	528.595i	0.404082	−	0.293582i
$149$	1983.05	−	1440.77i	1.09032	−	0.792165i	0.110868	−	0.993835i	$-0.464637\pi$
$149$	1983.05	−	1440.77i	1.09032	−	0.792165i	0.979453	+	0.201670i	$0.0646369\pi$
$150$	745.327	+	2293.88i	0.405705	+	1.24863i
$151$	853.976	−	2628.27i	0.460236	−	1.41646i	−0.404642	−	0.914475i	$-0.632604\pi$
$151$	853.976	−	2628.27i	0.460236	−	1.41646i	0.864877	−	0.501984i	$-0.167396\pi$
$152$	171.108	+	124.317i	0.0913074	+	0.0663387i
$153$	−4228.15			−2.23415
$154$	100.605	−	1075.08i	0.0526427	−	0.562547i
$155$	−47.5360			−0.0246334
$156$	−1623.86	−	1179.80i	−0.833416	−	0.605512i
$157$	−1102.59	+	3393.41i	−0.560483	+	1.72499i	0.120521	+	0.992711i	$0.461544\pi$
$157$	−1102.59	+	3393.41i	−0.560483	+	1.72499i	−0.681004	+	0.732280i	$0.738456\pi$
$158$	40.2437	+	123.858i	0.0202634	+	0.0623644i
$159$	−503.667	+	365.935i	−0.251216	+	0.182519i
$160$	41.8885	−	30.4338i	0.0206974	−	0.0150375i
$161$	−133.380	−	410.502i	−0.0652908	−	0.200944i
$162$	1416.96	−	4360.95i	0.687202	−	2.11499i
$163$	57.4193	+	41.7176i	0.0275916	+	0.0200464i	0.601496	−	0.798876i	$-0.294572\pi$
$163$	57.4193	+	41.7176i	0.0275916	+	0.0200464i	−0.573904	+	0.818923i	$0.694572\pi$
$164$	478.906			0.228026
$165$	296.576	+	500.409i	0.139930	+	0.236102i
$166$	−461.132			−0.215607
$167$	−2218.99	−	1612.19i	−1.02821	−	0.747035i	−0.0602564	−	0.998183i	$-0.519192\pi$
$167$	−2218.99	−	1612.19i	−1.02821	−	0.747035i	−0.967949	+	0.251148i	$0.919192\pi$
$168$	−360.498	+	1109.50i	−0.165554	+	0.509523i
$169$	122.417	+	376.761i	0.0557202	+	0.171489i
$170$	−157.902	+	114.722i	−0.0712383	+	0.0517576i
$171$	1499.41	−	1089.38i	0.670542	−	0.487177i
$172$	264.486	+	814.004i	0.117249	+	0.360856i
$173$	412.124	−	1268.39i	0.181117	−	0.557421i	−0.818743	−	0.574160i	$-0.805329\pi$
$173$	412.124	−	1268.39i	0.181117	−	0.557421i	0.999860	+	0.0167395i	$0.00532860\pi$
$174$	−2395.90	−	1740.73i	−1.04387	−	0.758415i
$175$	−1811.05			−0.782302
$176$	−385.613	+	438.222i	−0.165152	+	0.187683i
$177$	2582.05			1.09649
$178$	1001.49	+	727.622i	0.421711	+	0.306391i
$179$	1001.56	−	3082.48i	0.418212	−	1.28713i	−0.491134	−	0.871084i	$-0.663417\pi$
$179$	1001.56	−	3082.48i	0.418212	−	1.28713i	0.909346	−	0.416041i	$-0.136583\pi$
$180$	−140.207	−	431.512i	−0.0580577	−	0.178683i
$181$	−2152.17	+	1563.65i	−0.883811	+	0.642126i	−0.934257	−	0.356600i	$-0.883936\pi$
$181$	−2152.17	+	1563.65i	−0.883811	+	0.642126i	0.0504458	+	0.998727i	$0.483936\pi$
$182$	1219.31	−	885.883i	0.496602	−	0.360802i
$183$	2158.87	+	6644.32i	0.872068	+	2.68395i
$184$	−72.1052	+	221.917i	−0.0288895	+	0.0889128i
$185$	−294.299	−	213.821i	−0.116958	−	0.0849753i
$186$	−579.005			−0.228251
$187$	1453.59	−	1651.91i	0.568435	−	0.645986i
$188$	−700.085			−0.271590
$189$	5085.10	+	3694.54i	1.95707	+	1.42190i
$190$	26.4377	−	81.3669i	0.0100947	−	0.0310683i
$191$	−308.593	−	949.751i	−0.116906	−	0.359799i	0.875434	−	0.483338i	$-0.160576\pi$
$191$	−308.593	−	949.751i	−0.116906	−	0.359799i	−0.992340	+	0.123539i	$0.960576\pi$
$192$	510.217	−	370.694i	0.191780	−	0.139336i
$193$	−3108.04	+	2258.12i	−1.15918	+	0.842192i	−0.989674	−	0.143337i	$-0.954217\pi$
$193$	−3108.04	+	2258.12i	−1.15918	+	0.842192i	−0.169504	+	0.985529i	$0.554217\pi$
$194$	−679.833	−	2092.31i	−0.251594	−	0.774325i
$195$	−250.900	+	772.191i	−0.0921402	+	0.283578i
$196$	401.299	+	291.561i	0.146246	+	0.106254i
$197$	−3386.25			−1.22467			−0.612335	−	0.790598i	$-0.709770\pi$
$197$	−3386.25			−1.22467			−0.612335	+	0.790598i	$0.709770\pi$
$198$	2607.96	+	4400.37i	0.936058	+	1.57940i
$199$	−4895.30			−1.74381			−0.871906	−	0.489674i	$-0.837116\pi$
$199$	−4895.30			−1.74381			−0.871906	+	0.489674i	$0.837116\pi$
$200$	792.073	+	575.475i	0.280040	+	0.203461i
$201$	461.915	−	1421.63i	0.162094	−	0.498875i
$202$	833.898	+	2566.47i	0.290460	+	0.893943i
$203$	1799.02	−	1307.07i	0.622003	−	0.451912i
$204$	−1923.30	+	1397.36i	−0.660087	+	0.479581i
$205$	−59.8632	−	184.240i	−0.0203953	−	0.0627701i
$206$	−917.609	+	2824.11i	−0.310354	+	0.955171i
$207$	1654.21	+	1201.85i	0.555438	+	0.403549i
$208$	−814.768			−0.271606
$209$	−89.8667	+	960.327i	−0.0297426	+	0.317834i
$210$	471.899			0.155067
$211$	1188.79	+	863.709i	0.387867	+	0.281802i	0.764581	−	0.644528i	$-0.222946\pi$
$211$	1188.79	+	863.709i	0.387867	+	0.281802i	−0.376714	+	0.926330i	$0.622946\pi$
$212$	−78.0928	+	240.345i	−0.0252992	+	0.0778630i
$213$	−3214.25	−	9892.44i	−1.03398	−	3.18225i
$214$	2851.28	−	2071.58i	0.910793	−	0.661730i
$215$	280.095	−	203.501i	0.0888481	−	0.0645519i
$216$	−1050.03	−	3231.65i	−0.330765	−	1.01799i
$217$	134.348	−	413.481i	0.0420283	−	0.129350i
$218$	−1113.35	−	808.894i	−0.345896	−	0.251308i
$219$	310.599			0.0958370
$220$	216.790	+	93.5716i	0.0664363	+	0.0286754i
$221$	3071.32			0.934839
$222$	−3584.67	−	2604.41i	−1.08373	−	0.787373i
$223$	539.379	−	1660.04i	0.161971	−	0.498495i	−0.836829	−	0.547464i	$-0.815593\pi$
$223$	539.379	−	1660.04i	0.161971	−	0.498495i	0.998800	+	0.0489686i	$0.0155934\pi$
$224$	146.334	+	450.371i	0.0436490	+	0.134338i
$225$	6940.87	−	5042.83i	2.05655	−	1.49417i
$226$	−490.580	+	356.428i	−0.144393	+	0.104908i
$227$	730.475	+	2248.17i	0.213583	+	0.657341i	0.999251	+	0.0386928i	$0.0123194\pi$
$227$	730.475	+	2248.17i	0.213583	+	0.657341i	−0.785668	+	0.618648i	$0.787681\pi$
$228$	322.020	−	991.076i	0.0935364	−	0.287875i
$229$	2502.89	+	1818.46i	0.722253	+	0.524748i	0.887103	−	0.461571i	$-0.152714\pi$
$229$	2502.89	+	1818.46i	0.722253	+	0.524748i	−0.164850	+	0.986319i	$0.552714\pi$
$230$	94.3870			0.0270595
$231$	−5190.88	+	1165.43i	−1.47851	+	0.331946i
$232$	−1202.14			−0.340191
$233$	−2184.39	−	1587.05i	−0.614182	−	0.446229i	0.236703	−	0.971582i	$-0.423933\pi$
$233$	−2184.39	−	1587.05i	−0.614182	−	0.446229i	−0.850884	+	0.525353i	$0.823933\pi$
$234$	−2206.30	+	6790.30i	−0.616369	+	1.89699i
$235$	87.5106	+	269.330i	0.0242918	+	0.0747624i
$236$	847.941	−	616.065i	0.233882	−	0.169926i
$237$	519.112	−	377.157i	0.142278	−	0.103371i
$238$	−551.617	−	1697.70i	−0.150235	−	0.462377i
$239$	110.604	−	340.405i	0.0299347	−	0.0921296i	−0.934973	−	0.354719i	$-0.884577\pi$
$239$	110.604	−	340.405i	0.0299347	−	0.0921296i	0.964908	+	0.262590i	$0.0845765\pi$
$240$	−206.387	−	149.949i	−0.0555093	−	0.0403298i
$241$	4290.72			1.14685			0.573423	−	0.819260i	$-0.305615\pi$
$241$	4290.72			1.14685			0.573423	+	0.819260i	$0.305615\pi$
$242$	−2615.78	−	493.891i	−0.694830	−	0.131192i
$243$	−11124.3			−2.93672
$244$	2294.27	+	1666.89i	0.601950	+	0.437342i
$245$	62.0041	−	190.829i	0.0161685	−	0.0497617i
$246$	−729.154	−	2244.11i	−0.188980	−	0.581622i
$247$	−1089.17	+	791.327i	−0.280575	+	0.203850i
$248$	−190.144	+	138.148i	−0.0486861	+	0.0353725i
$249$	702.094	+	2160.82i	0.178688	+	0.549946i
$250$	247.382	−	761.363i	0.0625832	−	0.192611i
$251$	4362.71	+	3169.69i	1.09710	+	0.797088i	0.980584	−	0.196101i	$-0.0628280\pi$
$251$	4362.71	+	3169.69i	1.09710	+	0.797088i	0.116514	+	0.993189i	$0.462828\pi$
$252$	4149.66			1.03732
$253$	−1038.26	+	233.103i	−0.258003	+	0.0579252i
$254$	4531.26			1.11936
$255$	777.990	+	565.243i	0.191057	+	0.138811i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	1259.96	+	3877.75i	0.305813	+	0.941196i	0.979373	+	0.202063i	$0.0647645\pi$
$257$	1259.96	+	3877.75i	0.305813	+	0.941196i	−0.673560	+	0.739133i	$0.735236\pi$
$258$	3411.65	−	2478.71i	0.823257	−	0.598131i
$259$	2691.63	−	1955.58i	0.645752	−	0.469167i
$260$	101.846	+	313.450i	0.0242932	+	0.0747666i
$261$	−3255.26	+	10018.7i	−0.772014	+	2.37601i
$262$	−2358.26	−	1713.37i	−0.556082	−	0.404018i
$263$	−3256.10			−0.763421			−0.381711	−	0.924282i	$-0.624665\pi$
$263$	−3256.10			−0.763421			−0.381711	+	0.924282i	$0.624665\pi$
$264$	2640.58	+	1139.73i	0.615592	+	0.265704i
$265$	102.225			0.0236967
$266$	633.031	+	459.924i	0.145916	+	0.106014i
$267$	1884.76	−	5800.70i	0.432006	−	1.32958i
$268$	−187.502	−	577.070i	−0.0427369	−	0.131531i
$269$	−1666.61	+	1210.86i	−0.377750	+	0.274452i	−0.760417	−	0.649435i	$-0.775006\pi$
$269$	−1666.61	+	1210.86i	−0.377750	+	0.274452i	0.382667	+	0.923886i	$0.375006\pi$
$270$	−1112.00	+	807.912i	−0.250644	+	0.182104i
$271$	−1652.93	−	5087.21i	−0.370511	−	1.14032i	−0.946457	−	0.322829i	$-0.895366\pi$
$271$	−1652.93	−	5087.21i	−0.370511	−	1.14032i	0.575946	−	0.817488i	$-0.304634\pi$
$272$	−298.204	+	917.778i	−0.0664753	+	0.204590i
$273$	−6007.62	−	4364.79i	−1.33186	−	0.967653i
$274$	−393.713			−0.0868068
$275$	−415.999	+	4445.42i	−0.0912207	+	0.974797i
$276$	1149.67			0.250731
$277$	6799.60	+	4940.20i	1.47490	+	1.07158i	0.979155	+	0.203116i	$0.0651067\pi$
$277$	6799.60	+	4940.20i	1.47490	+	1.07158i	0.495750	+	0.868465i	$0.334893\pi$
$278$	−24.5073	+	75.4257i	−0.00528723	+	0.0162724i
$279$	636.438	+	1958.75i	0.136568	+	0.420314i
$280$	154.971	−	112.593i	0.0330759	−	0.0240311i
$281$	−5691.91	+	4135.42i	−1.20837	+	0.877930i	−0.995081	−	0.0990600i	$-0.968416\pi$
$281$	−5691.91	+	4135.42i	−1.20837	+	0.877930i	−0.213285	+	0.976990i	$0.568416\pi$
$282$	1065.91	+	3280.53i	0.225085	+	0.692741i
$283$	2334.20	−	7183.92i	0.490295	−	1.50897i	−0.333867	−	0.942620i	$-0.608354\pi$
$283$	2334.20	−	7183.92i	0.490295	−	1.50897i	0.824162	−	0.566354i	$-0.191646\pi$
$284$	−3415.84	−	2481.75i	−0.713707	−	0.518539i
$285$	−421.530			−0.0876115
$286$	−1894.42	−	3196.42i	−0.391676	−	0.660869i
$287$	1771.76			0.364402
$288$	−1814.87	−	1318.58i	−0.371328	−	0.269785i
$289$	−394.099	+	1212.91i	−0.0802156	+	0.246878i
$290$	150.267	+	462.476i	0.0304276	+	0.0936465i
$291$	−8769.29	+	6371.26i	−1.76655	+	1.28347i
$292$	102.000	−	74.1073i	0.0204421	−	0.0148521i
$293$	1008.60	+	3104.15i	0.201103	+	0.618930i	0.999851	+	0.0172649i	$0.00549588\pi$
$293$	1008.60	+	3104.15i	0.201103	+	0.618930i	−0.798748	+	0.601665i	$0.794504\pi$
$294$	755.231	−	2324.36i	0.149816	−	0.461087i
$295$	−342.999	−	249.204i	−0.0676956	−	0.0491837i
$296$	−1798.60			−0.353180
$297$	10236.7	−	11633.3i	1.99998	−	2.27283i
$298$	−4902.37			−0.952976
$299$	−1201.62	−	873.026i	−0.232412	−	0.168857i
$300$	1490.65	−	4587.76i	0.286876	−	0.882915i
$301$	978.491	+	3011.48i	0.187373	+	0.576675i
$302$	−4471.48	+	3248.72i	−0.852002	+	0.619015i
$303$	10756.6	−	7815.13i	2.03944	−	1.48174i
$304$	−130.715	−	402.300i	−0.0246613	−	0.0758996i
$305$	354.485	−	1090.99i	0.0665500	−	0.204820i
$306$	6841.29	+	4970.49i	1.27807	+	0.928574i
$307$	−5505.74			−1.02355			−0.511774	−	0.859120i	$-0.671012\pi$
$307$	−5505.74			−1.02355			−0.511774	+	0.859120i	$0.671012\pi$
$308$	−1426.61	+	1621.24i	−0.263924	+	0.299932i
$309$	14630.6			2.69355
$310$	76.9149	+	55.8819i	0.0140918	+	0.0102383i
$311$	−373.968	+	1150.95i	−0.0681857	+	0.209854i	−0.979344	−	0.202203i	$-0.935190\pi$
$311$	−373.968	+	1150.95i	−0.0681857	+	0.209854i	0.911158	+	0.412058i	$0.135190\pi$
$312$	1240.52	+	3817.92i	0.225098	+	0.692780i
$313$	3966.86	−	2882.09i	0.716358	−	0.520464i	−0.168861	−	0.985640i	$-0.554009\pi$
$313$	3966.86	−	2882.09i	0.716358	−	0.520464i	0.885218	+	0.465176i	$0.154009\pi$
$314$	5773.21	−	4194.48i	1.03758	−	0.753848i
$315$	−518.708	−	1596.42i	−0.0927805	−	0.285549i
$316$	80.4875	−	247.715i	0.0143284	−	0.0440983i
$317$	−6220.65	−	4519.57i	−1.10217	−	0.800771i	−0.120754	−	0.992682i	$-0.538531\pi$
$317$	−6220.65	−	4519.57i	−1.10217	−	0.800771i	−0.981412	+	0.191912i	$0.938531\pi$
$318$	1245.13			0.219571
$319$	−2795.10	−	4716.12i	−0.490581	−	0.827750i
$320$	−103.554			−0.0180902
$321$	−14048.4	−	10206.8i	−2.44270	−	1.77472i
$322$	−266.760	+	821.003i	−0.0461676	+	0.142089i
$323$	492.740	+	1516.50i	0.0848816	+	0.261239i
$324$	−7419.29	+	5390.43i	−1.27217	+	0.924285i
$325$	−5041.84	+	3663.11i	−0.860526	+	0.625209i
$326$	−43.8644	−	135.001i	−0.00745223	−	0.0229356i
$327$	−2095.28	+	6448.62i	−0.354341	+	1.09055i
$328$	−774.885	−	562.987i	−0.130445	−	0.0947737i
$329$	−2590.03			−0.434021
$330$	108.395	−	1158.32i	0.0180817	−	0.193223i
$331$	3085.35			0.512344			0.256172	−	0.966631i	$-0.417539\pi$
$331$	3085.35			0.512344			0.256172	+	0.966631i	$0.417539\pi$
$332$	746.128	+	542.094i	0.123341	+	0.0896122i
$333$	−4870.40	+	14989.6i	−0.801491	+	2.46674i
$334$	1695.15	+	5217.15i	0.277709	+	0.854699i
$335$	−198.567	+	144.268i	−0.0323848	+	0.0235289i
$336$	1887.59	−	1371.42i	0.306478	−	0.222670i
$337$	−1785.06	−	5493.84i	−0.288541	−	0.888038i	−0.985315	−	0.170747i	$-0.945382\pi$
$337$	−1785.06	−	5493.84i	−0.288541	−	0.888038i	0.696774	−	0.717291i	$-0.254618\pi$
$338$	244.834	−	753.523i	0.0394001	−	0.121261i
$339$	2417.12	+	1756.14i	0.387256	+	0.281358i
$340$	390.354			0.0622645
$341$	−984.072	−	424.748i	−0.156277	−	0.0674528i
$342$	−3706.74			−0.586075
$343$	5591.08	+	4062.16i	0.880146	+	0.639464i
$344$	528.972	−	1628.01i	0.0829077	−	0.255164i
$345$	−143.708	−	442.288i	−0.0224261	−	0.0690203i
$346$	−2157.91	+	1567.81i	−0.335289	+	0.243602i
$347$	−735.627	+	534.465i	−0.113806	+	0.0826846i	−0.643232	−	0.765671i	$-0.722407\pi$
$347$	−735.627	+	534.465i	−0.113806	+	0.0826846i	0.529427	+	0.848356i	$0.322407\pi$
$348$	1830.31	+	5633.11i	0.281939	+	0.867719i
$349$	3533.36	−	10874.6i	0.541938	−	1.66791i	−0.186223	−	0.982508i	$-0.559625\pi$
$349$	3533.36	−	10874.6i	0.541938	−	1.66791i	0.728161	−	0.685406i	$-0.240375\pi$
$350$	2930.35	+	2129.02i	0.447525	+	0.325146i
$351$	21629.3			3.28913
$352$	1139.10	−	255.743i	0.172483	−	0.0387248i
$353$	2773.55			0.418190			0.209095	−	0.977895i	$-0.432948\pi$
$353$	2773.55			0.418190			0.209095	+	0.977895i	$0.432948\pi$
$354$	−4177.85	−	3035.39i	−0.627260	−	0.455731i
$355$	−527.776	+	1624.33i	−0.0789055	+	0.242846i
$356$	−765.067	−	2354.63i	−0.113900	−	0.350549i
$357$	−7115.41	+	5169.65i	−1.05487	+	0.766406i
$358$	−5244.23	+	3810.16i	−0.774207	+	0.562494i
$359$	−779.606	−	2399.38i	−0.114613	−	0.352742i	0.877253	−	0.480028i	$-0.159373\pi$
$359$	−779.606	−	2399.38i	−0.114613	−	0.352742i	−0.991866	+	0.127286i	$0.959373\pi$
$360$	−280.413	+	863.023i	−0.0410530	+	0.126348i
$361$	4983.58	+	3620.79i	0.726576	+	0.527888i
$362$	5320.47			0.772479
$363$	1668.32	+	13009.3i	0.241223	+	1.88102i
$364$	−3014.31			−0.434046
$365$	−41.2599	−	29.9770i	−0.00591682	−	0.00429882i
$366$	4317.74	−	13288.6i	0.616645	−	1.89784i
$367$	1623.66	+	4997.11i	0.230938	+	0.710754i	0.997634	+	0.0687443i	$0.0218993\pi$
$367$	1623.66	+	4997.11i	0.230938	+	0.710754i	−0.766696	+	0.642010i	$0.778101\pi$
$368$	377.548	−	274.305i	0.0534811	−	0.0388563i
$369$	−6790.26	+	4933.41i	−0.957958	+	0.695997i
$370$	224.825	+	691.939i	0.0315894	+	0.0972222i
$371$	−288.912	+	889.179i	−0.0404300	+	0.124431i
$372$	936.849	+	680.661i	0.130574	+	0.0948672i
$373$	316.370			0.0439169			0.0219585	−	0.999759i	$-0.493010\pi$
$373$	316.370			0.0439169			0.0219585	+	0.999759i	$0.493010\pi$
$374$	−4293.90	+	964.040i	−0.593669	+	0.133287i
$375$	−3944.33			−0.543158
$376$	1132.76	+	822.999i	0.155366	+	0.112880i
$377$	2364.62	−	7277.55i	0.323035	−	0.994198i
$378$	−3884.67	−	11955.8i	−0.528587	−	1.62682i
$379$	−4253.04	+	3090.01i	−0.576422	+	0.418795i	−0.837432	−	0.546541i	$-0.815944\pi$
$379$	−4253.04	+	3090.01i	−0.576422	+	0.418795i	0.261011	+	0.965336i	$0.415944\pi$
$380$	−138.430	+	100.575i	−0.0186876	+	0.0135773i
$381$	−6899.04	−	21233.1i	−0.927687	−	2.85513i
$382$	−617.186	+	1899.50i	−0.0826648	+	0.254416i
$383$	1152.22	+	837.137i	0.153722	+	0.111686i	0.661988	−	0.749515i	$-0.269713\pi$
$383$	1152.22	+	837.137i	0.153722	+	0.111686i	−0.508265	+	0.861201i	$0.669713\pi$
$384$	−1261.33			−0.167622
$385$	802.036	+	346.177i	0.106170	+	0.0458255i
$386$	7683.49			1.01316
$387$	−12135.5	−	8816.94i	−1.59401	−	1.15811i
$388$	−1359.67	+	4184.62i	−0.177904	+	0.547531i
$389$	−608.800	−	1873.69i	−0.0793506	−	0.244216i	0.903510	−	0.428567i	$-0.140982\pi$
$389$	−608.800	−	1873.69i	−0.0793506	−	0.244216i	−0.982860	+	0.184351i	$0.940982\pi$
$390$	1313.73	−	954.481i	0.170573	−	0.123928i
$391$	−1423.19	+	1034.01i	−0.184077	+	0.133739i
$392$	−306.565	−	943.510i	−0.0394997	−	0.121567i
$393$	−4438.16	+	13659.2i	−0.569658	+	1.75323i
$394$	5479.06	+	3980.77i	0.700587	+	0.509006i
$395$	−105.359			−0.0134208
$396$	953.177	−	10185.8i	0.120957	−	1.29256i
$397$	−4148.62			−0.524467			−0.262233	−	0.965004i	$-0.584459\pi$
$397$	−4148.62			−0.524467			−0.262233	+	0.965004i	$0.584459\pi$
$398$	7920.76	+	5754.77i	0.997567	+	0.724775i
$399$	1191.34	−	3666.58i	0.149478	−	0.460046i
$400$	−605.090	−	1862.27i	−0.0756362	−	0.232784i
$401$	6237.68	−	4531.94i	0.776795	−	0.564375i	−0.127220	−	0.991874i	$-0.540606\pi$
$401$	6237.68	−	4531.94i	0.776795	−	0.564375i	0.904015	+	0.427500i	$0.140606\pi$
$402$	−2418.62	+	1757.23i	−0.300074	+	0.218016i
$403$	−462.308	−	1422.84i	−0.0571444	−	0.175872i
$404$	1667.80	−	5132.95i	0.205386	−	0.632113i
$405$	3001.17	+	2180.47i	0.368220	+	0.267528i
$406$	−4447.43			−0.543650
$407$	−4181.92	−	7056.09i	−0.509312	−	0.859355i
$408$	4754.65			0.576937
$409$	2828.03	+	2054.69i	0.341900	+	0.248405i	0.745463	−	0.666547i	$-0.232228\pi$
$409$	2828.03	+	2054.69i	0.341900	+	0.248405i	−0.403563	+	0.914952i	$0.632228\pi$
$410$	−119.726	+	368.480i	−0.0144216	+	0.0443852i
$411$	599.445	+	1844.90i	0.0719426	+	0.221417i
$412$	4804.67	−	3490.79i	0.574536	−	0.417425i
$413$	3137.04	−	2279.19i	0.373762	−	0.271554i
$414$	−1263.70	−	3889.28i	−0.150019	−	0.461710i
$415$	115.283	−	354.805i	0.0136362	−	0.0419679i
$416$	1318.32	+	957.817i	0.155375	+	0.112887i
$417$	390.751			0.0458877
$418$	1274.34	−	1448.20i	0.149115	−	0.169459i
$419$	6493.78			0.757140			0.378570	−	0.925573i	$-0.376416\pi$
$419$	6493.78			0.757140			0.378570	+	0.925573i	$0.376416\pi$
$420$	−763.548	−	554.750i	−0.0887079	−	0.0644501i
$421$	−3078.30	+	9474.04i	−0.356359	+	1.09676i	0.598858	+	0.800855i	$0.295621\pi$
$421$	−3078.30	+	9474.04i	−0.356359	+	1.09676i	−0.955217	+	0.295906i	$0.904379\pi$
$422$	−908.157	−	2795.02i	−0.104759	−	0.322416i
$423$	9926.29	−	7211.87i	1.14098	−	0.828968i
$424$	408.899	−	297.083i	0.0468347	−	0.0340274i
$425$	2280.93	+	7019.97i	0.260332	+	0.801220i
$426$	−6428.50	+	19784.9i	−0.731131	+	2.25019i
$427$	8487.88	+	6166.80i	0.961961	+	0.698905i
$428$	−7048.76			−0.796062
$429$	−12093.8	+	13743.7i	−1.36106	+	1.54675i
$430$	−692.433			−0.0776561
$431$	−4447.02	−	3230.95i	−0.496996	−	0.361089i	0.310872	−	0.950452i	$-0.399379\pi$
$431$	−4447.02	−	3230.95i	−0.496996	−	0.361089i	−0.807868	+	0.589363i	$0.799379\pi$
$432$	−2100.05	+	6463.30i	−0.233886	+	0.719828i
$433$	30.3861	+	93.5189i	0.00337243	+	0.0103793i	0.952729	−	0.303823i	$-0.0982631\pi$
$433$	30.3861	+	93.5189i	0.00337243	+	0.0103793i	−0.949356	+	0.314202i	$0.898263\pi$
$434$	−703.455	+	511.090i	−0.0778040	+	0.0565279i
$435$	1938.33	−	1408.28i	0.213645	−	0.155222i
$436$	850.522	+	2617.64i	0.0934234	+	0.287528i
$437$	238.287	−	733.372i	0.0260842	−	0.0802791i
$438$	−502.559	−	365.131i	−0.0548247	−	0.0398325i
$439$	−1951.20			−0.212131			−0.106065	−	0.994359i	$-0.533825\pi$
$439$	−1951.20			−0.212131			−0.106065	+	0.994359i	$0.533825\pi$
$440$	−240.774	−	406.254i	−0.0260874	−	0.0440168i
$441$	−8693.38			−0.938709
$442$	−4969.50	−	3610.56i	−0.534785	−	0.388544i
$443$	2916.72	−	8976.73i	0.312816	−	0.962747i	−0.663829	−	0.747885i	$-0.731070\pi$
$443$	2916.72	−	8976.73i	0.312816	−	0.962747i	0.976644	−	0.214863i	$-0.0689304\pi$
$444$	2738.44	+	8428.06i	0.292704	+	0.900851i
$445$	−810.219	+	588.658i	−0.0863102	+	0.0627080i
$446$	−2824.23	+	2051.92i	−0.299845	+	0.217850i
$447$	7464.07	+	22972.0i	0.789795	+	2.43074i
$448$	292.669	−	900.742i	0.0308645	−	0.0949912i
$449$	−10419.2	−	7569.98i	−1.09513	−	0.795656i	−0.114869	−	0.993381i	$-0.536645\pi$
$449$	−10419.2	−	7569.98i	−1.09513	−	0.795656i	−0.980258	+	0.197725i	$0.936645\pi$
$450$	−17158.8			−1.79749
$451$	406.972	−	4348.96i	0.0424913	−	0.454068i
$452$	1212.78			0.126205
$453$	22031.2	+	16006.6i	2.28502	+	1.66017i
$454$	1460.95	−	4496.34i	0.151026	−	0.464810i
$455$	376.789	+	1159.64i	0.0388223	+	0.119483i
$456$	−1686.12	+	1225.04i	−0.173157	+	0.125806i
$457$	6276.04	−	4559.81i	0.642409	−	0.466738i	−0.218268	−	0.975889i	$-0.570041\pi$
$457$	6276.04	−	4559.81i	0.642409	−	0.466738i	0.860677	+	0.509151i	$0.170041\pi$
$458$	−1912.04	−	5884.66i	−0.195074	−	0.600376i
$459$	7916.29	−	24363.8i	0.805013	−	2.47757i
$460$	−152.721	−	110.959i	−0.0154797	−	0.0112467i
$461$	13529.3			1.36686			0.683432	−	0.730014i	$-0.260487\pi$
$461$	13529.3			1.36686			0.683432	+	0.730014i	$0.260487\pi$
$462$	9769.07	+	4216.55i	0.983762	+	0.424614i
$463$	−14558.3			−1.46130			−0.730651	−	0.682752i	$-0.760783\pi$
$463$	−14558.3			−1.46130			−0.730651	+	0.682752i	$0.760783\pi$
$464$	1945.10	+	1413.20i	0.194610	+	0.141393i
$465$	144.751	−	445.498i	0.0144359	−	0.0444290i
$466$	1668.73	+	5135.82i	0.165885	+	0.510541i
$467$	3748.30	−	2723.30i	0.371415	−	0.269849i	−0.386382	−	0.922339i	$-0.626275\pi$
$467$	3748.30	−	2723.30i	0.371415	−	0.269849i	0.757797	+	0.652490i	$0.226275\pi$
$468$	11552.3	−	8393.27i	1.14104	−	0.829015i
$469$	−693.680	−	2134.93i	−0.0682967	−	0.210196i
$470$	175.021	−	538.660i	0.0171769	−	0.0528650i
$471$	−28444.9	−	20666.4i	−2.78274	−	2.02178i
$472$	−2096.23			−0.204421
$473$	7616.77	−	1710.07i	0.740421	−	0.166235i
$474$	−1283.31			−0.124356
$475$	−2617.57	−	1901.78i	−0.252847	−	0.183704i
$476$	−1103.23	+	3395.41i	−0.106233	+	0.326950i
$477$	−1368.64	−	4212.25i	−0.131375	−	0.404330i
$478$	−579.132	+	420.764i	−0.0554160	+	0.0402621i
$479$	−15857.6	+	11521.2i	−1.51263	+	1.09899i	−0.547643	+	0.836712i	$0.684475\pi$
$479$	−15857.6	+	11521.2i	−1.51263	+	1.09899i	−0.964991	+	0.262281i	$0.915525\pi$
$480$	157.666	+	485.245i	0.0149925	+	0.0461423i
$481$	3537.86	−	10888.4i	0.335369	−	1.03216i
$482$	−6942.54	−	5044.05i	−0.656066	−	0.476660i
$483$	4253.30			0.400687
$484$	3651.82	+	3874.17i	0.342958	+	0.363840i
$485$	1779.83			0.166634
$486$	17999.4	+	13077.4i	1.67998	+	1.22058i
$487$	−1135.70	+	3495.33i	−0.105675	+	0.325233i	−0.989888	−	0.141850i	$-0.954695\pi$
$487$	−1135.70	+	3495.33i	−0.105675	+	0.325233i	0.884213	+	0.467083i	$0.154695\pi$
$488$	−1752.67	−	5394.16i	−0.162581	−	0.500373i
$489$	−565.816	+	411.089i	−0.0523253	+	0.0380165i
$490$	−324.658	+	235.877i	−0.0299317	+	0.0217466i
$491$	6356.81	+	19564.3i	0.584275	+	1.79821i	0.602163	+	0.798373i	$0.294306\pi$
$491$	6356.81	+	19564.3i	0.584275	+	1.79821i	−0.0178877	+	0.999840i	$0.505694\pi$
$492$	−1458.31	+	4488.21i	−0.133629	+	0.411269i
$493$	−7332.19	−	5327.15i	−0.669828	−	0.486659i
$494$	2692.57			0.245232
$495$	−4037.72	+	906.525i	−0.366631	+	0.0823137i
$496$	470.062			0.0425532
$497$	−12637.2	−	9181.48i	−1.14056	−	0.828663i
$498$	1404.19	−	4321.64i	0.126352	−	0.388870i
$499$	299.378	+	921.390i	0.0268577	+	0.0826594i	0.963587	−	0.267395i	$-0.0861630\pi$
$499$	299.378	+	921.390i	0.0268577	+	0.0826594i	−0.936729	+	0.350055i	$0.886163\pi$
$500$	−1295.31	+	941.097i	−0.115856	+	0.0841743i
$501$	21866.1	−	15886.7i	1.94991	−	1.41669i
$502$	−3332.81	−	10257.3i	−0.296316	−	0.911967i
$503$	−3990.19	+	12280.5i	−0.353705	+	1.08859i	0.603052	+	0.797702i	$0.293951\pi$
$503$	−3990.19	+	12280.5i	−0.353705	+	1.08859i	−0.956757	+	0.290890i	$0.906049\pi$
$504$	−6714.29	−	4878.22i	−0.593409	−	0.431137i
$505$	−2183.17			−0.192376
$506$	1953.96	+	843.375i	0.171669	+	0.0740961i
$507$	−3903.71			−0.341952
$508$	−7331.74	−	5326.82i	−0.640341	−	0.465235i
$509$	−741.973	+	2283.56i	−0.0646117	+	0.198855i	−0.978151	−	0.207896i	$-0.933338\pi$
$509$	−741.973	+	2283.56i	−0.0646117	+	0.198855i	0.913539	+	0.406751i	$0.133338\pi$
$510$	−594.331	−	1829.16i	−0.0516028	−	0.158817i
$511$	377.359	−	274.167i	0.0326680	−	0.0237347i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	3470.03	+	10679.7i	0.298647	+	0.919140i
$514$	2519.91	−	7755.50i	0.216242	−	0.665526i
$515$	−1943.53	−	1412.06i	−0.166295	−	0.120821i
$516$	−8434.07			−0.719553
$517$	−594.930	+	6357.50i	−0.0506093	+	0.540818i
$518$	−6654.08			−0.564408
$519$	10632.1	+	7724.70i	0.899228	+	0.653327i
$520$	203.692	−	626.899i	0.0171779	−	0.0528680i
$521$	4413.81	+	13584.3i	0.371157	+	1.14230i	0.946035	+	0.324064i	$0.105049\pi$
$521$	4413.81	+	13584.3i	0.371157	+	1.14230i	−0.574878	+	0.818239i	$0.694951\pi$
$522$	17044.8	−	12383.7i	1.42917	−	1.03836i
$523$	7496.61	−	5446.60i	0.626776	−	0.455379i	−0.228506	−	0.973543i	$-0.573384\pi$
$523$	7496.61	−	5446.60i	0.626776	−	0.455379i	0.855282	+	0.518163i	$0.173384\pi$
$524$	1801.55	+	5544.59i	0.150193	+	0.462246i
$525$	5514.81	−	16972.9i	0.458450	−	1.41096i
$526$	5268.48	+	3827.78i	0.436724	+	0.317298i
$527$	−1771.93			−0.146464
$528$	−2932.71	−	4948.31i	−0.241723	−	0.407856i
$529$	−11316.3			−0.930079
$530$	−165.403	−	120.172i	−0.0135560	−	0.00984898i
$531$	−5676.35	+	17470.0i	−0.463903	+	1.42775i
$532$	−483.593	−	1488.35i	−0.0394105	−	0.121293i
$533$	4932.44	−	3583.62i	0.400840	−	0.291227i
$534$	−9868.74	+	7170.06i	−0.799742	+	0.581046i
$535$	881.095	+	2711.73i	0.0712020	+	0.219137i
$536$	−375.003	+	1154.14i	−0.0302195	+	0.0930061i
$537$	25838.6	+	18772.8i	2.07638	+	1.50858i
$538$	4120.08			0.330166
$539$	2988.70	−	3396.44i	0.238835	−	0.271420i
$540$	2749.00			0.219071
$541$	−4262.05	−	3096.56i	−0.338706	−	0.246084i	0.405410	−	0.914135i	$-0.367129\pi$
$541$	−4262.05	−	3096.56i	−0.338706	−	0.246084i	−0.744116	+	0.668051i	$0.767129\pi$
$542$	−3305.87	+	10174.4i	−0.261991	+	0.806326i
$543$	−8100.64	−	24931.2i	−0.640205	−	1.97035i
$544$	1561.42	−	1134.44i	0.123061	−	0.0894091i
$545$	900.717	−	654.409i	0.0707935	−	0.0514345i
$546$	4589.41	+	14124.8i	0.359723	+	1.10711i
$547$	−5988.10	+	18429.5i	−0.468067	+	1.44056i	0.387018	+	0.922072i	$0.373505\pi$
$547$	−5988.10	+	18429.5i	−0.468067	+	1.44056i	−0.855084	+	0.518489i	$0.826495\pi$
$548$	637.041	+	462.837i	0.0496588	+	0.0360793i
$549$	−49701.1			−3.86374
$550$	5899.01	−	6703.81i	0.457336	−	0.519730i
$551$	3972.72			0.307157
$552$	−1860.20	−	1351.51i	−0.143433	−	0.104211i
$553$	297.771	−	916.445i	0.0228978	−	0.0704723i
$554$	−5194.44	−	15986.8i	−0.398358	−	1.22602i
$555$	2900.06	−	2107.01i	0.221803	−	0.161149i
$556$	128.322	−	93.2314i	0.00978788	−	0.00711131i
$557$	−1640.80	−	5049.86i	−0.124817	−	0.384146i	0.869051	−	0.494723i	$-0.164730\pi$
$557$	−1640.80	−	5049.86i	−0.124817	−	0.384146i	−0.993868	+	0.110576i	$0.964730\pi$
$558$	1272.88	−	3917.51i	0.0965683	−	0.297207i
$559$	8815.19	+	6404.61i	0.666982	+	0.484591i
$560$	−383.108			−0.0289094
$561$	11055.0	+	18653.0i	0.831986	+	1.40380i
$562$	14071.2			1.05615
$563$	3636.30	+	2641.93i	0.272206	+	0.197769i	0.715511	−	0.698602i	$-0.246194\pi$
$563$	3636.30	+	2641.93i	0.272206	+	0.197769i	−0.443305	+	0.896371i	$0.646194\pi$
$564$	2131.82	−	6561.06i	0.159159	−	0.489842i
$565$	−151.598	−	466.570i	−0.0112881	−	0.0347411i
$566$	−12222.0	+	8879.81i	−0.907649	+	0.659446i
$567$	−27448.4	+	19942.4i	−2.03302	+	1.47708i
$568$	2609.47	+	8031.12i	0.192766	+	0.593272i
$569$	−6870.82	+	21146.2i	−0.506221	+	1.55799i	0.292488	+	0.956269i	$0.405517\pi$
$569$	−6870.82	+	21146.2i	−0.506221	+	1.55799i	−0.798709	+	0.601718i	$0.794483\pi$
$570$	682.050	+	495.538i	0.0501191	+	0.0364137i
$571$	2370.18			0.173711			0.0868554	−	0.996221i	$-0.472318\pi$
$571$	2370.18			0.173711			0.0868554	+	0.996221i	$0.472318\pi$
$572$	−692.387	+	7398.94i	−0.0506122	+	0.540848i
$573$	9840.57			0.717445
$574$	−2866.76	−	2082.82i	−0.208460	−	0.151455i
$575$	1103.05	−	3394.83i	0.0800005	−	0.246216i
$576$	1386.44	+	4267.02i	0.100292	+	0.308668i
$577$	11203.3	−	8139.68i	0.808318	−	0.587277i	−0.105024	−	0.994470i	$-0.533492\pi$
$577$	11203.3	−	8139.68i	0.808318	−	0.587277i	0.913343	+	0.407192i	$0.133492\pi$
$578$	2063.53	−	1499.24i	0.148498	−	0.107890i
$579$	−11698.4	−	36004.1i	−0.839673	−	2.58425i
$580$	300.535	−	924.951i	0.0215156	−	0.0662181i
$581$	2760.37	+	2005.53i	0.197107	+	0.143207i
$582$	21678.9			1.54402
$583$	2116.22	+	913.409i	0.150334	+	0.0648877i
$584$	−252.158			−0.0178671
$585$	−4673.02	−	3395.15i	−0.330266	−	0.239952i
$586$	2017.20	−	6208.31i	0.142201	−	0.437650i
$587$	−6142.87	−	18905.8i	−0.431931	−	1.32935i	−0.896199	−	0.443652i	$-0.853683\pi$
$587$	−6142.87	−	18905.8i	−0.431931	−	1.32935i	0.464268	−	0.885695i	$-0.346317\pi$
$588$	−3954.44	+	2873.07i	−0.277344	+	0.201502i
$589$	628.371	−	456.538i	0.0439585	−	0.0319377i
$590$	262.028	+	806.440i	0.0182840	+	0.0562722i
$591$	10311.4	−	31735.2i	0.717690	−	2.20882i
$592$	2910.19	+	2114.38i	0.202041	+	0.146791i
$593$	23426.3			1.62226			0.811132	−	0.584863i	$-0.198852\pi$
$593$	23426.3			1.62226			0.811132	+	0.584863i	$0.198852\pi$
$594$	−30239.1	+	6789.09i	−2.08876	+	0.468956i
$595$	1444.15			0.0995034
$596$	7932.20	+	5763.08i	0.545161	+	0.396082i
$597$	14906.6	−	45877.8i	1.02192	−	3.14515i
$598$	917.954	+	2825.17i	0.0627724	+	0.193194i
$599$	715.720	−	520.001i	0.0488206	−	0.0354702i	−0.563107	−	0.826384i	$-0.690394\pi$
$599$	715.720	−	520.001i	0.0488206	−	0.0354702i	0.611928	+	0.790914i	$0.290394\pi$
$600$	−7805.17	+	5670.78i	−0.531074	+	0.385848i
$601$	−2132.95	−	6564.54i	−0.144767	−	0.445546i	0.852214	−	0.523193i	$-0.175259\pi$
$601$	−2132.95	−	6564.54i	−0.144767	−	0.445546i	−0.996981	+	0.0776468i	$0.975259\pi$
$602$	1956.98	−	6022.97i	0.132493	−	0.407771i
$603$	8603.18	+	6250.57i	0.581009	+	0.422128i
$604$	11054.1			0.744677
$605$	1033.96	−	1889.16i	0.0694814	−	0.126951i
$606$	−26591.8			−1.78254
$607$	15358.8	+	11158.8i	1.02701	+	0.746165i	0.967708	−	0.252075i	$-0.0811131\pi$
$607$	15358.8	+	11158.8i	1.02701	+	0.746165i	0.0593000	+	0.998240i	$0.481113\pi$
$608$	−261.430	+	804.600i	−0.0174382	+	0.0536691i
$609$	6771.40	+	20840.2i	0.450560	+	1.38668i
$610$	−1856.11	+	1348.54i	−0.123199	+	0.0895095i
$611$	−7210.45	+	5238.70i	−0.477420	+	0.346866i
$612$	−5226.28	−	16084.8i	−0.345196	−	1.06240i
$613$	−5602.31	+	17242.1i	−0.369127	+	1.13606i	0.578229	+	0.815875i	$0.303744\pi$
$613$	−5602.31	+	17242.1i	−0.369127	+	1.13606i	−0.947356	+	0.320182i	$0.896256\pi$
$614$	8908.48	+	6472.39i	0.585533	+	0.425414i
$615$	1908.95			0.125165
$616$	4214.19	−	946.145i	0.275641	−	0.0618852i
$617$	−15257.7			−0.995549			−0.497774	−	0.867307i	$-0.665849\pi$
$617$	−15257.7			−0.995549			−0.497774	+	0.867307i	$0.665849\pi$
$618$	−23672.8	−	17199.3i	−1.54088	−	1.11951i
$619$	−2351.71	+	7237.82i	−0.152703	+	0.469972i	−0.997921	−	0.0644500i	$-0.979471\pi$
$619$	−2351.71	+	7237.82i	−0.152703	+	0.469972i	0.845218	+	0.534422i	$0.179471\pi$
$620$	−58.7577	−	180.838i	−0.00380608	−	0.0117139i
$621$	−10022.6	+	7281.84i	−0.647653	+	0.470548i
$622$	1958.12	−	1422.66i	0.126227	−	0.0917096i
$623$	−2830.44	−	8711.19i	−0.182021	−	0.560203i
$624$	2481.04	−	7635.85i	0.159168	−	0.489869i
$625$	−11852.2	−	8611.11i	−0.758539	−	0.551111i
$626$	−9806.61			−0.626120
$627$	−8726.35	−	3766.49i	−0.555816	−	0.239903i
$628$	−14272.2			−0.906881
$629$	−10970.2	−	7970.29i	−0.695404	−	0.505241i
$630$	−1037.42	+	3192.84i	−0.0656057	+	0.201914i
$631$	−8054.72	−	24789.9i	−0.508167	−	1.56398i	−0.795381	−	0.606110i	$-0.792729\pi$
$631$	−8054.72	−	24789.9i	−0.508167	−	1.56398i	0.287214	−	0.957866i	$-0.407271\pi$
$632$	−421.438	+	306.193i	−0.0265252	+	0.0192717i
$633$	−11714.5	+	8511.07i	−0.735559	+	0.534415i
$634$	4752.16	+	14625.6i	0.297685	+	0.916180i
$635$	−1132.82	+	3486.45i	−0.0707944	+	0.217883i
$636$	−2014.67	−	1463.74i	−0.125608	−	0.0912597i
$637$	6314.86			0.392785
$638$	−1021.57	+	10916.7i	−0.0633926	+	0.677422i
$639$	73997.8			4.58107
$640$	167.554	+	121.735i	0.0103487	+	0.00751876i
$641$	−7101.22	+	21855.3i	−0.437568	+	1.34670i	0.452864	+	0.891580i	$0.350402\pi$
$641$	−7101.22	+	21855.3i	−0.437568	+	1.34670i	−0.890432	+	0.455117i	$0.849598\pi$
$642$	10732.0	+	33029.8i	0.659750	+	2.03050i
$643$	−5300.09	+	3850.74i	−0.325062	+	0.236172i	−0.738333	−	0.674437i	$-0.764386\pi$
$643$	−5300.09	+	3850.74i	−0.325062	+	0.236172i	0.413270	+	0.910608i	$0.364386\pi$
$644$	1396.77	−	1014.82i	0.0854668	−	0.0620952i
$645$	1054.26	+	3244.68i	0.0643588	+	0.198076i
$646$	985.479	−	3032.99i	0.0600204	−	0.184724i
$647$	5081.70	+	3692.07i	0.308783	+	0.224344i	0.731374	−	0.681977i	$-0.238879\pi$
$647$	5081.70	+	3692.07i	0.308783	+	0.224344i	−0.422591	+	0.906320i	$0.638879\pi$
$648$	18341.5			1.11192
$649$	−4873.94	−	8223.72i	−0.294790	−	0.497395i
$650$	12464.1			0.752127
$651$	3465.96	+	2518.17i	0.208666	+	0.151605i
$652$	−87.7289	+	270.002i	−0.00526952	+	0.0162179i
$653$	364.184	+	1120.84i	0.0218248	+	0.0671699i	0.961376	−	0.275239i	$-0.0887571\pi$
$653$	364.184	+	1120.84i	0.0218248	+	0.0671699i	−0.939551	+	0.342409i	$0.888757\pi$
$654$	10971.0	−	7970.93i	0.655966	−	0.476587i
$655$	1907.87	−	1386.15i	0.113812	−	0.0826890i
$656$	591.960	+	1821.86i	0.0352319	+	0.108433i
$657$	−682.816	+	2101.49i	−0.0405467	+	0.124790i
$658$	4190.76	+	3044.76i	0.248287	+	0.180391i
$659$	−15421.0			−0.911561			−0.455781	−	0.890092i	$-0.650640\pi$
$659$	−15421.0			−0.911561			−0.455781	+	0.890092i	$0.650640\pi$
$660$	−1537.08	+	1746.78i	−0.0906526	+	0.103020i
$661$	−9587.68			−0.564172			−0.282086	−	0.959389i	$-0.591026\pi$
$661$	−9587.68			−0.564172			−0.282086	+	0.959389i	$0.591026\pi$
$662$	−4992.20	−	3627.04i	−0.293092	−	0.212944i
$663$	−9352.44	+	28783.8i	−0.547841	+	1.68608i
$664$	−569.991	−	1754.25i	−0.0333132	−	0.102527i
$665$	−512.133	+	372.086i	−0.0298642	+	0.0216976i
$666$	25501.8	−	18528.1i	1.48374	−	1.07800i
$667$	1354.38	+	4168.36i	0.0786236	+	0.241979i
$668$	3390.31	−	10434.3i	0.196370	−	0.604364i
$669$	13915.1	+	10109.9i	0.804169	+	0.584263i
$670$	490.885			0.0283053
$671$	17086.7	−	19417.9i	0.983050	−	1.11717i
$672$	−4666.39			−0.267872
$673$	−13066.9	−	9493.66i	−0.748428	−	0.543765i	0.146911	−	0.989150i	$-0.453067\pi$
$673$	−13066.9	−	9493.66i	−0.748428	−	0.543765i	−0.895339	+	0.445385i	$0.853067\pi$
$674$	−3570.12	+	10987.7i	−0.204029	+	0.627937i
$675$	16063.0	+	49436.9i	0.915950	+	2.81901i
$676$	−1281.97	+	931.406i	−0.0729387	+	0.0529930i
$677$	6493.60	−	4717.87i	0.368640	−	0.267832i	−0.388007	−	0.921656i	$-0.626836\pi$
$677$	6493.60	−	4717.87i	0.368640	−	0.267832i	0.756647	+	0.653824i	$0.226836\pi$
$678$	−1846.51	−	5682.98i	−0.104594	−	0.321908i
$679$	−5030.21	+	15481.4i	−0.284303	+	0.874995i
$680$	−631.607	−	458.889i	−0.0356191	−	0.0258788i
$681$	−23293.8			−1.31075
$682$	1092.94	+	1844.10i	0.0613649	+	0.103540i
$683$	−17912.7			−1.00353			−0.501765	−	0.865004i	$-0.667316\pi$
$683$	−17912.7			−1.00353			−0.501765	+	0.865004i	$0.667316\pi$
$684$	5997.63	+	4357.53i	0.335271	+	0.243588i
$685$	98.4282	−	302.931i	0.00549015	−	0.0168969i
$686$	−4271.21	−	13145.4i	−0.237719	−	0.731625i
$687$	−24663.8	+	17919.3i	−1.36970	+	0.995143i
$688$	−2769.73	+	2012.33i	−0.153481	+	0.111511i
$689$	994.180	+	3059.77i	0.0549713	+	0.169184i
$690$	−287.416	+	884.577i	−0.0158576	+	0.0488047i
$691$	−22242.6	−	16160.2i	−1.22453	−	0.889672i	−0.228060	−	0.973647i	$-0.573238\pi$
$691$	−22242.6	−	16160.2i	−1.22453	−	0.889672i	−0.996468	+	0.0839750i	$0.973238\pi$
$692$	5334.65			0.293053
$693$	3526.37	−	37683.2i	0.193298	−	2.06561i
$694$	1818.57			0.0994698
$695$	−51.9073	−	37.7129i	−0.00283303	−	0.00205832i
$696$	3660.62	−	11266.2i	0.199361	−	0.613570i
$697$	−2231.43	−	6867.64i	−0.121265	−	0.373215i
$698$	−18500.9	+	13441.7i	−1.00325	+	0.728905i
$699$	21525.2	−	15639.0i	1.16475	−	0.846239i
$700$	−2238.59	−	6889.66i	−0.120872	−	0.372007i
$701$	691.682	−	2128.78i	0.0372674	−	0.114697i	−0.930692	−	0.365803i	$-0.880794\pi$
$701$	691.682	−	2128.78i	0.0372674	−	0.114697i	0.967960	+	0.251106i	$0.0807943\pi$
$702$	−34996.9	−	25426.7i	−1.88158	−	1.36705i
$703$	5943.85			0.318885
$704$	−2143.74	−	925.287i	−0.114766	−	0.0495356i
$705$	−2790.59			−0.149077
$706$	−4487.69	−	3260.50i	−0.239230	−	0.173811i
$707$	6170.17	−	18989.8i	0.328222	−	1.01016i
$708$	3191.59	+	9822.71i	0.169417	+	0.521413i
$709$	−19598.0	+	14238.8i	−1.03811	+	0.754229i	−0.969915	−	0.243443i	$-0.921723\pi$
$709$	−19598.0	+	14238.8i	−1.03811	+	0.754229i	−0.0681922	+	0.997672i	$0.521723\pi$
$710$	2763.47	−	2007.78i	0.146072	−	0.106128i
$711$	1410.61	+	4341.41i	0.0744051	+	0.228995i
$712$	−1530.13	+	4709.27i	−0.0805396	+	0.247875i
$713$	693.246	+	503.672i	0.0364127	+	0.0264554i
$714$	17590.3			0.921988
$715$	2933.00	−	658.499i	0.153410	−	0.0344426i
$716$	12964.4			0.676682
$717$	2853.41	+	2073.12i	0.148623	+	0.107981i
$718$	−1559.21	+	4798.76i	−0.0810436	+	0.249426i
$719$	3011.07	+	9267.11i	0.156181	+	0.480674i	0.998279	−	0.0586501i	$-0.0186796\pi$
$719$	3011.07	+	9267.11i	0.156181	+	0.480674i	−0.842098	+	0.539324i	$0.818680\pi$
$720$	1468.26	−	1066.76i	0.0759985	−	0.0552162i
$721$	17775.3	−	12914.5i	0.918151	−	0.667076i
$722$	−3807.12	−	11717.1i	−0.196241	−	0.603969i
$723$	−13065.6	+	40211.8i	−0.672082	+	2.06846i
$724$	−8608.70	−	6254.58i	−0.441906	−	0.321063i
$725$	18390.0			0.942053
$726$	12593.9	−	23010.7i	0.643808	−	1.17632i
$727$	14917.2			0.761002			0.380501	−	0.924781i	$-0.375752\pi$
$727$	14917.2			0.761002			0.380501	+	0.924781i	$0.375752\pi$
$728$	4877.26	+	3543.53i	0.248301	+	0.180401i
$729$	14745.4	−	45381.6i	0.749143	−	2.30563i
$730$	31.5197	+	97.0078i	0.00159808	+	0.00491838i
$731$	10440.7	−	7585.61i	0.528267	−	0.383808i
$732$	−22608.0	+	16425.7i	−1.14155	+	0.829386i
$733$	−2192.28	−	6747.15i	−0.110469	−	0.339989i	0.880506	−	0.474035i	$-0.157203\pi$
$733$	−2192.28	−	6747.15i	−0.110469	−	0.339989i	−0.990975	+	0.134046i	$0.957203\pi$
$734$	3247.32	−	9994.21i	0.163298	−	0.502579i
$735$	1599.60	+	1162.18i	0.0802752	+	0.0583234i
$736$	−933.350			−0.0467442
$737$	−5399.74	+	1212.32i	−0.269881	+	0.0605920i
$738$	16786.4			0.837286
$739$	24019.6	+	17451.3i	1.19564	+	0.868681i	0.993848	−	0.110749i	$-0.0353249\pi$
$739$	24019.6	+	17451.3i	1.19564	+	0.868681i	0.201788	+	0.979429i	$0.435325\pi$
$740$	449.649	−	1383.88i	0.0223371	−	0.0687465i
$741$	−4099.56	−	12617.1i	−0.203240	−	0.625509i
$742$	1512.76	−	1099.09i	0.0748453	−	0.0543783i
$743$	15616.2	−	11345.8i	0.771065	−	0.560212i	−0.131219	−	0.991353i	$-0.541889\pi$
$743$	15616.2	−	11345.8i	0.771065	−	0.560212i	0.902284	+	0.431142i	$0.141889\pi$
$744$	−715.689	−	2202.66i	−0.0352667	−	0.108540i
$745$	1225.59	−	3771.99i	0.0602715	−	0.185497i
$746$	−511.897	−	371.915i	−0.0251232	−	0.0182531i
$747$	−16163.5			−0.791687
$748$	8080.97	+	3487.93i	0.395013	+	0.170497i
$749$	−26077.5			−1.27217
$750$	6382.05	+	4636.83i	0.310719	+	0.225751i
$751$	3888.27	−	11966.9i	0.188928	−	0.581461i	−0.811066	−	0.584955i	$-0.801112\pi$
$751$	3888.27	−	11966.9i	0.188928	−	0.581461i	0.999994	+	0.00349415i	$0.00111222\pi$
$752$	−865.353	−	2663.28i	−0.0419630	−	0.129149i
$753$	−42990.5	+	31234.5i	−2.08056	+	1.51162i
$754$	−12381.3	+	8995.54i	−0.598011	+	0.434481i
$755$	−1381.76	−	4252.63i	−0.0666059	−	0.204992i
$756$	−7769.34	+	23911.6i	−0.373767	+	1.15034i
$757$	−2207.59	−	1603.91i	−0.105992	−	0.0770079i	0.533527	−	0.845783i	$-0.320866\pi$
$757$	−2207.59	−	1603.91i	−0.105992	−	0.0770079i	−0.639519	+	0.768775i	$0.720866\pi$
$758$	10514.1			0.503811
$759$	976.982	−	10440.2i	0.0467223	−	0.499281i
$760$	342.217			0.0163336
$761$	17098.3	+	12422.6i	0.814471	+	0.591748i	0.915123	−	0.403174i	$-0.132093\pi$
$761$	17098.3	+	12422.6i	0.814471	+	0.591748i	−0.100652	+	0.994922i	$0.532093\pi$
$762$	−13798.1	+	42466.1i	−0.655974	+	2.01888i
$763$	3146.58	+	9684.19i	0.149298	+	0.459491i
$764$	3231.63	−	2347.91i	0.153032	−	0.111184i
$765$	−5534.72	+	4021.21i	−0.261579	+	0.190048i
$766$	−880.217	−	2709.03i	−0.0415190	−	0.127782i
$767$	4123.29	−	12690.2i	0.194111	−	0.597414i
$768$	2040.87	+	1482.78i	0.0958899	+	0.0696681i
$769$	10493.4			0.492068			0.246034	−	0.969261i	$-0.420873\pi$
$769$	10493.4			0.492068			0.246034	+	0.969261i	$0.420873\pi$
$770$	−890.766	−	1502.98i	−0.0416896	−	0.0703422i
$771$	−40178.2			−1.87676
$772$	−12432.1	−	9032.48i	−0.579589	−	0.421096i
$773$	−4552.70	+	14011.8i	−0.211836	+	0.651965i	0.787527	+	0.616280i	$0.211361\pi$
$773$	−4552.70	+	14011.8i	−0.211836	+	0.651965i	−0.999363	+	0.0356844i	$0.988639\pi$
$774$	9270.67	+	28532.2i	0.430527	+	1.32502i
$775$	2908.77	−	2113.35i	0.134821	−	0.0979532i
$776$	7119.30	−	5172.48i	0.329340	−	0.239280i
$777$	10131.1	+	31180.4i	0.467763	+	1.43963i
$778$	−1217.60	+	3747.39i	−0.0561093	+	0.172687i
$779$	2560.77	+	1860.51i	0.117778	+	0.0855709i
$780$	−3247.72			−0.149086
$781$	−25439.7	+	28910.4i	−1.16556	+	1.32458i
$782$	3518.33			0.160889
$783$	−51635.7	−	37515.5i	−2.35672	−	1.71226i
$784$	−613.130	+	1887.02i	−0.0279305	+	0.0859612i
$785$	1784.02	+	5490.65i	0.0811139	+	0.249643i
$786$	23238.5	−	16883.8i	1.05457	−	0.766188i
$787$	20429.3	−	14842.8i	0.925319	−	0.672284i	−0.0195232	−	0.999809i	$-0.506215\pi$
$787$	20429.3	−	14842.8i	0.925319	−	0.672284i	0.944842	+	0.327526i	$0.106215\pi$
$788$	−4185.63	−	12882.0i	−0.189222	−	0.582365i
$789$	9915.10	−	30515.5i	0.447385	−	1.37691i
$790$	170.475	+	123.858i	0.00767752	+	0.00557804i
$791$	4486.80			0.201684
$792$	−13516.4	+	15360.4i	−0.606419	+	0.689152i
$793$	36102.8			1.61671
$794$	6712.61	+	4877.00i	0.300027	+	0.217983i
$795$	−311.283	+	958.031i	−0.0138869	+	0.0427395i
$796$	−6050.92	−	18622.8i	−0.269434	−	0.829232i
$797$	23715.1	−	17230.0i	1.05399	−	0.765770i	0.0810250	−	0.996712i	$-0.474181\pi$
$797$	23715.1	−	17230.0i	1.05399	−	0.765770i	0.972968	+	0.230942i	$0.0741806\pi$
$798$	−6237.96	+	4532.14i	−0.276718	+	0.201048i
$799$	3262.01	+	10039.4i	0.144432	+	0.444517i
$800$	−1210.18	+	3724.55i	−0.0534829	+	0.164603i
$801$	35103.7	+	25504.3i	1.54848	+	1.12503i
$802$	−15420.4			−0.678944
$803$	−586.293	−	989.243i	−0.0257657	−	0.0434740i
$804$	5979.15			0.262274
$805$	−565.007	−	410.502i	−0.0247377	−	0.0179730i
$806$	−924.615	+	2845.67i	−0.0404072	+	0.124361i
$807$	−6273.00	−	19306.3i	−0.273631	−	0.842149i
$808$	−8732.69	+	6344.67i	−0.380217	+	0.276244i
$809$	−5853.31	+	4252.68i	−0.254378	+	0.184816i	−0.707665	−	0.706548i	$-0.750251\pi$
$809$	−5853.31	+	4252.68i	−0.254378	+	0.184816i	0.453287	+	0.891365i	$0.350251\pi$
$810$	−2292.69	−	7056.16i	−0.0994528	−	0.306084i
$811$	−5857.20	+	18026.6i	−0.253606	+	0.780518i	0.740496	+	0.672061i	$0.234591\pi$
$811$	−5857.20	+	18026.6i	−0.253606	+	0.780518i	−0.994101	+	0.108457i	$0.965409\pi$
$812$	7196.09	+	5228.26i	0.311001	+	0.225956i
$813$	52709.7			2.27381
$814$	−1528.44	+	16333.1i	−0.0658131	+	0.703288i
$815$	114.839			0.00493573
$816$	−7693.19	−	5589.43i	−0.330043	−	0.239791i
$817$	−1748.10	+	5380.10i	−0.0748571	+	0.230387i
$818$	−2160.43	−	6649.11i	−0.0923442	−	0.284206i
$819$	42739.0	−	31051.7i	1.82347	−	1.32483i
$820$	626.895	−	455.466i	0.0266977	−	0.0193970i
$821$	3984.18	+	12262.0i	0.169365	+	0.521253i	0.999331	−	0.0365611i	$-0.0116404\pi$
$821$	3984.18	+	12262.0i	0.169365	+	0.521253i	−0.829966	+	0.557814i	$0.811640\pi$
$822$	1198.89	−	3689.80i	0.0508711	−	0.156565i
$823$	14384.7	+	10451.1i	0.609257	+	0.442651i	0.849153	−	0.528148i	$-0.177113\pi$
$823$	14384.7	+	10451.1i	0.609257	+	0.442651i	−0.239896	+	0.970799i	$0.577113\pi$
$824$	−11877.8			−0.502163
$825$	−40394.9	−	17435.4i	−1.70469	−	0.735783i
$826$	−7755.18			−0.326680
$827$	−16174.7	−	11751.6i	−0.680107	−	0.494127i	0.193286	−	0.981142i	$-0.438085\pi$
$827$	−16174.7	−	11751.6i	−0.680107	−	0.494127i	−0.873393	+	0.487016i	$0.838085\pi$
$828$	−2527.41	+	7778.56i	−0.106079	+	0.326478i
$829$	−1081.28	−	3327.83i	−0.0453008	−	0.139421i	0.925848	−	0.377896i	$-0.123352\pi$
$829$	−1081.28	−	3327.83i	−0.0453008	−	0.139421i	−0.971149	+	0.238475i	$0.923352\pi$
$830$	−603.630	+	438.563i	−0.0252437	+	0.0183406i
$831$	−67004.0	+	48681.2i	−2.79704	+	2.03217i
$832$	−1007.11	−	3099.56i	−0.0419654	−	0.129156i
$833$	2311.23	−	7113.25i	0.0961339	−	0.295870i
$834$	−632.249	−	459.356i	−0.0262506	−	0.0190722i
$835$	−4437.97			−0.183931
$836$	−3764.38	+	845.157i	−0.155734	+	0.0349645i
$837$	−12478.5			−0.515317
$838$	−10507.2	−	7633.89i	−0.433131	−	0.314688i
$839$	5818.06	−	17906.1i	0.239406	−	0.736816i	−0.757100	−	0.653299i	$-0.773385\pi$
$839$	5818.06	−	17906.1i	0.239406	−	0.736816i	0.996506	−	0.0835174i	$-0.0266154\pi$
$840$	583.299	+	1795.21i	0.0239592	+	0.0737388i
$841$	1463.27	−	1063.13i	0.0599973	−	0.0435906i
$842$	16118.2	−	11710.6i	0.659703	−	0.479302i
$843$	−21424.0	−	65936.2i	−0.875304	−	2.69391i
$844$	−1816.31	+	5590.04i	−0.0740760	+	0.227982i
$845$	518.568	+	376.761i	0.0211116	+	0.0153384i
$846$	−24539.1			−0.997250
$847$	13510.3	+	14332.8i	0.548073	+	0.581443i
$848$	−1010.85			−0.0409350
$849$	60218.5	+	43751.3i	2.43427	+	1.76860i
$850$	4561.85	−	14039.9i	0.184083	−	0.566548i
$851$	2026.38	+	6236.56i	0.0816256	+	0.251218i
$852$	33660.0	−	24455.5i	1.35349	−	0.983369i
$853$	−23396.5	+	16998.6i	−0.939134	+	0.682321i	−0.948212	−	0.317638i	$-0.897110\pi$
$853$	−23396.5	+	16998.6i	−0.939134	+	0.682321i	0.00907800	+	0.999959i	$0.497110\pi$
$854$	−6484.16	−	19956.2i	−0.259817	−	0.799634i
$855$	926.685	−	2852.04i	0.0370666	−	0.114079i
$856$	11405.1	+	8286.31i	0.455397	+	0.330865i
$857$	−13906.3			−0.554294			−0.277147	−	0.960827i	$-0.589389\pi$
$857$	−13906.3			−0.554294			−0.277147	+	0.960827i	$0.589389\pi$
$858$	35724.9	−	8020.74i	1.42148	−	0.319142i
$859$	18829.8			0.747923			0.373962	−	0.927444i	$-0.377999\pi$
$859$	18829.8			0.747923			0.373962	+	0.927444i	$0.377999\pi$
$860$	1120.38	+	814.004i	0.0444240	+	0.0322759i
$861$	−5395.15	+	16604.6i	−0.213549	+	0.657238i
$862$	3397.22	+	10455.6i	0.134234	+	0.413130i
$863$	−21161.8	+	15374.9i	−0.834710	+	0.606452i	−0.920888	−	0.389828i	$-0.872535\pi$
$863$	−21161.8	+	15374.9i	−0.834710	+	0.606452i	0.0861781	+	0.996280i	$0.472535\pi$
$864$	10996.0	−	7989.07i	0.432977	−	0.314576i
$865$	−666.831	−	2052.30i	−0.0262115	−	0.0806707i
$866$	60.7722	−	187.038i	0.00238467	−	0.00733926i
$867$	−10167.1	−	7386.85i	−0.398262	−	0.289355i
$868$	1739.04			0.0680032
$869$	−2181.11	−	941.418i	−0.0851429	−	0.0367496i
$870$	−4791.81			−0.186733
$871$	−6249.34	−	4540.41i	−0.243112	−	0.176631i
$872$	1701.04	−	5235.27i	0.0660603	−	0.203313i
$873$	−23829.3	−	73339.0i	−0.923824	−	2.84324i
$874$	−1247.69	+	906.498i	−0.0482879	+	0.0350832i
$875$	−4792.12	+	3481.68i	−0.185146	+	0.134517i
$876$	383.921	+	1181.59i	0.0148076	+	0.0455732i
$877$	437.333	−	1345.97i	0.0168389	−	0.0518247i	−0.942284	−	0.334815i	$-0.891326\pi$
$877$	437.333	−	1345.97i	0.0168389	−	0.0518247i	0.959123	+	0.282990i	$0.0913263\pi$
$878$	3157.10	+	2293.77i	0.121352	+	0.0881673i
$879$	−32162.8			−1.23416
$880$	−88.0000	+	940.380i	−0.00337100	+	0.0360230i
$881$	−5355.31			−0.204796			−0.102398	−	0.994744i	$-0.532651\pi$
$881$	−5355.31			−0.204796			−0.102398	+	0.994744i	$0.532651\pi$
$882$	14066.2	+	10219.7i	0.536999	+	0.390153i
$883$	15100.2	−	46473.5i	0.575494	−	1.77119i	−0.0589988	−	0.998258i	$-0.518791\pi$
$883$	15100.2	−	46473.5i	0.575494	−	1.77119i	0.634492	−	0.772929i	$-0.281209\pi$
$884$	3796.36	+	11684.0i	0.144441	+	0.444543i
$885$	3379.95	−	2455.68i	0.128379	−	0.0932731i
$886$	−15272.1	+	11095.8i	−0.579094	+	0.420736i
$887$	3898.08	+	11997.1i	0.147559	+	0.454140i	0.997331	−	0.0730104i	$-0.0232606\pi$
$887$	3898.08	+	11997.1i	0.147559	+	0.454140i	−0.849772	+	0.527150i	$0.823261\pi$
$888$	5476.88	−	16856.1i	0.206973	−	0.636998i
$889$	−27124.5	−	19707.1i	−1.02331	−	0.743480i
$890$	2002.97			0.0754379
$891$	42645.8	+	71955.7i	1.60347	+	2.70551i
$892$	6981.87			0.262074
$893$	−3743.45	−	2719.78i	−0.140280	−	0.101919i
$894$	14928.1	−	45944.1i	0.558469	−	1.71879i
$895$	−1620.56	−	4987.56i	−0.0605243	−	0.186275i
$896$	−1532.43	+	1113.38i	−0.0571373	+	0.0415127i
$897$	11840.9	−	8602.88i	0.440752	−	0.320225i
$898$	7959.55	+	24497.0i	0.295783	+	0.910328i
$899$	−1364.21	+	4198.62i	−0.0506107	+	0.155764i
$900$	27763.5	+	20171.3i	1.02828	+	0.747087i
$901$	3810.49			0.140894
$902$	−5771.01	+	6558.34i	−0.213030	+	0.242094i
$903$	−31202.6			−1.14990
$904$	−1962.32	−	1425.71i	−0.0721967	−	0.0524540i
$905$	−1330.12	+	4093.68i	−0.0488559	+	0.150363i
$906$	−16830.3	−	51798.4i	−0.617164	−	1.89943i
$907$	−4524.62	+	3287.33i	−0.165642	+	0.120346i	−0.667518	−	0.744593i	$-0.732643\pi$
$907$	−4524.62	+	3287.33i	−0.165642	+	0.120346i	0.501876	+	0.864940i	$0.332643\pi$
$908$	−7649.64	+	5557.79i	−0.279584	+	0.203130i
$909$	29229.5	+	89959.2i	1.06654	+	3.28246i
$910$	753.577	−	2319.27i	0.0274515	−	0.0844870i
$911$	18282.3	+	13282.8i	0.664894	+	0.483074i	0.868312	−	0.496018i	$-0.165205\pi$
$911$	18282.3	+	13282.8i	0.664894	+	0.483074i	−0.203418	+	0.979092i	$0.565205\pi$
$912$	4168.32			0.151345
$913$	5556.83	−	6314.95i	0.201429	−	0.228909i
$914$	−15515.2			−0.561486
$915$	9145.13	+	6644.32i	0.330414	+	0.240060i
$916$	−3824.08	+	11769.3i	−0.137938	+	0.424530i
$917$	6665.00	+	20512.7i	0.240019	+	0.738703i
$918$	−41450.2	+	30115.4i	−1.49026	+	1.08274i
$919$	5500.45	−	3996.31i	0.197436	−	0.143445i	−0.484675	−	0.874694i	$-0.661062\pi$
$919$	5500.45	−	3996.31i	0.197436	−	0.143445i	0.682111	+	0.731249i	$0.261062\pi$
$920$	116.669	+	359.069i	0.00418093	+	0.0128676i
$921$	16765.5	−	51598.8i	0.599827	−	1.84608i
$922$	−21890.9	−	15904.7i	−0.781930	−	0.568105i
$923$	−53751.9			−1.91686
$924$	−10849.8	−	18306.8i	−0.386291	−	0.651783i
$925$	27514.5			0.978022
$926$	23555.9	+	17114.3i	0.835954	+	0.607356i
$927$	−32163.7	+	98989.8i	−1.13959	+	3.50728i
$928$	−1485.93	−	4573.21i	−0.0525624	−	0.161770i
$929$	12838.7	−	9327.85i	0.453416	−	0.329426i	−0.337527	−	0.941316i	$-0.609590\pi$
$929$	12838.7	−	9327.85i	0.453416	−	0.329426i	0.790943	+	0.611890i	$0.209590\pi$
$930$	−757.927	+	550.666i	−0.0267241	+	0.0194162i
$931$	1013.11	+	3118.03i	0.0356641	+	0.109763i
$932$	3337.46	−	10271.6i	0.117298	−	0.361007i
$933$	−9647.76	−	7009.51i	−0.338535	−	0.245960i
$934$	−9266.32			−0.324629
$935$	331.722	−	3544.83i	0.0116026	−	0.123987i
$936$	−28559.0			−0.997307
$937$	−16439.2	−	11943.8i	−0.573154	−	0.416421i	0.263096	−	0.964770i	$-0.415257\pi$
$937$	−16439.2	−	11943.8i	−0.573154	−	0.416421i	−0.836250	+	0.548349i	$0.815257\pi$
$938$	−1387.36	+	4269.85i	−0.0482930	+	0.148631i
$939$	14931.0	+	45952.8i	0.518907	+	1.59703i
$940$	−916.423	+	665.821i	−0.0317983	+	0.0231028i
$941$	−1682.78	+	1222.61i	−0.0582964	+	0.0423548i	−0.616552	−	0.787314i	$-0.711471\pi$
$941$	−1682.78	+	1222.61i	−0.0582964	+	0.0423548i	0.558255	+	0.829669i	$0.311471\pi$
$942$	21730.0	+	66878.0i	0.751593	+	2.31317i
$943$	−1079.11	+	3321.17i	−0.0372648	+	0.114689i
$944$	3391.76	+	2464.26i	0.116941	+	0.0849628i
$945$	10170.2			0.350092
$946$	−14334.5	−	6187.09i	−0.492658	−	0.212642i
$947$	−21613.7			−0.741658			−0.370829	−	0.928701i	$-0.620926\pi$
$947$	−21613.7			−0.741658			−0.370829	+	0.928701i	$0.620926\pi$
$948$	2076.45	+	1508.63i	0.0711391	+	0.0516856i
$949$	495.997	−	1526.52i	0.0169660	−	0.0522160i
$950$	1999.65	+	6154.28i	0.0682917	+	0.210180i
$951$	61298.9	−	44536.3i	2.09017	−	1.51860i
$952$	5776.61	−	4196.95i	0.196661	−	0.142882i
$953$	−4733.66	−	14568.7i	−0.160900	−	0.495201i	0.837810	−	0.545961i	$-0.183835\pi$
$953$	−4733.66	−	14568.7i	−0.160900	−	0.495201i	−0.998711	+	0.0507606i	$0.983835\pi$
$954$	−2737.28	+	8424.49i	−0.0928960	+	0.285905i
$955$	−1307.22	−	949.751i	−0.0442939	−	0.0321814i
$956$	1431.69			0.0484354
$957$	52709.9	−	11834.1i	1.78043	−	0.399731i
$958$	39202.1			1.32209
$959$	2356.79	+	1712.31i	0.0793585	+	0.0576573i
$960$	315.331	−	970.490i	0.0106013	−	0.0326275i
$961$	−8939.21	−	27512.1i	−0.300064	−	0.923502i
$962$	−18524.5	+	13458.8i	−0.620845	+	0.451070i
$963$	99942.2	−	72612.3i	3.34433	−	2.42980i
$964$	5303.63	+	16322.9i	0.177197	+	0.545358i
$965$	−1920.87	+	5911.84i	−0.0640778	+	0.197211i
$966$	−6881.98	−	5000.05i	−0.229217	−	0.166536i
$967$	−33356.0			−1.10926			−0.554631	−	0.832096i	$-0.687141\pi$
$967$	−33356.0			−1.10926			−0.554631	+	0.832096i	$0.687141\pi$
$968$	−1354.41	−	10561.5i	−0.0449716	−	0.350682i
$969$	−15712.7			−0.520915
$970$	−2879.82	−	2092.31i	−0.0953251	−	0.0692578i
$971$	−7568.22	+	23292.6i	−0.250129	+	0.769819i	0.744621	+	0.667488i	$0.232630\pi$
$971$	−7568.22	+	23292.6i	−0.250129	+	0.769819i	−0.994750	+	0.102332i	$0.967370\pi$
$972$	−13750.3	−	42319.2i	−0.453747	−	1.39649i
$973$	474.739	−	344.918i	0.0156418	−	0.0113644i
$974$	5946.62	−	4320.47i	0.195628	−	0.142132i
$975$	−18977.1	−	58405.6i	−0.623338	−	1.91844i
$976$	−3505.34	+	10788.3i	−0.114962	+	0.353817i
$977$	−35570.7	−	25843.6i	−1.16480	−	0.846276i	−0.174422	−	0.984671i	$-0.555806\pi$
$977$	−35570.7	−	25843.6i	−1.16480	−	0.846276i	−0.990377	+	0.138395i	$0.955806\pi$
$978$	1398.77			0.0457340
$979$	−22032.7	+	4946.64i	−0.719272	+	0.161487i
$980$	802.597			0.0261613
$981$	−39024.7	−	28353.1i	−1.27009	−	0.922777i
$982$	12713.6	−	39128.5i	0.413145	−	1.27153i
$983$	10717.1	+	32983.8i	0.347733	+	1.07021i	0.960104	+	0.279642i	$0.0902157\pi$
$983$	10717.1	+	32983.8i	0.347733	+	1.07021i	−0.612371	+	0.790570i	$0.709784\pi$
$984$	7635.80	−	5547.73i	0.247378	−	0.179731i
$985$	−4432.65	+	3220.51i	−0.143387	+	0.104177i
$986$	5601.30	+	17239.0i	0.180914	+	0.556797i
$987$	7886.86	−	24273.3i	0.254348	−	0.782803i
$988$	−4356.67	−	3165.31i	−0.140288	−	0.101925i
$989$	−6241.01			−0.200660
$990$	7598.86	+	3279.84i	0.243947	+	0.105293i
$991$	42734.1			1.36982			0.684910	−	0.728627i	$-0.259841\pi$
$991$	42734.1			1.36982			0.684910	+	0.728627i	$0.259841\pi$
$992$	−760.576	−	552.591i	−0.0243431	−	0.0176863i
$993$	−9395.14	+	28915.3i	−0.300248	+	0.924067i
$994$	9653.98	+	29711.9i	0.308054	+	0.948093i
$995$	−6408.03	+	4655.71i	−0.204169	+	0.148337i
$996$	−7352.42	+	5341.84i	−0.233906	+	0.169943i
$997$	9922.10	+	30537.1i	0.315182	+	0.970029i	0.975680	+	0.219202i	$0.0703452\pi$
$997$	9922.10	+	30537.1i	0.315182	+	0.970029i	−0.660498	+	0.750828i	$0.729655\pi$
$998$	598.755	−	1842.78i	0.0189912	−	0.0584491i
$999$	−77255.5	−	56129.4i	−2.44670	−	1.77763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.4.c.a.15.1	yes	4
3.2	odd	2		198.4.f.b.37.1		4
4.3	odd	2		176.4.m.a.81.1		4
11.2	odd	10		242.4.c.m.27.1		4
11.3	even	5	inner	22.4.c.a.3.1	✓	4
11.4	even	5		242.4.c.f.9.1		4
11.5	even	5		242.4.a.k.1.1		2
11.6	odd	10		242.4.a.h.1.1		2
11.7	odd	10		242.4.c.m.9.1		4
11.8	odd	10		242.4.c.j.3.1		4
11.9	even	5		242.4.c.f.27.1		4
11.10	odd	2		242.4.c.j.81.1		4
33.5	odd	10		2178.4.a.z.1.2		2
33.14	odd	10		198.4.f.b.91.1		4
33.17	even	10		2178.4.a.bi.1.2		2
44.3	odd	10		176.4.m.a.113.1		4
44.27	odd	10		1936.4.a.bb.1.2		2
44.39	even	10		1936.4.a.bc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.a.3.1	✓	4	11.3	even	5	inner
22.4.c.a.15.1	yes	4	1.1	even	1	trivial
176.4.m.a.81.1		4	4.3	odd	2
176.4.m.a.113.1		4	44.3	odd	10
198.4.f.b.37.1		4	3.2	odd	2
198.4.f.b.91.1		4	33.14	odd	10
242.4.a.h.1.1		2	11.6	odd	10
242.4.a.k.1.1		2	11.5	even	5
242.4.c.f.9.1		4	11.4	even	5
242.4.c.f.27.1		4	11.9	even	5
242.4.c.j.3.1		4	11.8	odd	10
242.4.c.j.81.1		4	11.10	odd	2
242.4.c.m.9.1		4	11.7	odd	10
242.4.c.m.27.1		4	11.2	odd	10
1936.4.a.bb.1.2		2	44.27	odd	10
1936.4.a.bc.1.2		2	44.39	even	10
2178.4.a.z.1.2		2	33.5	odd	10
2178.4.a.bi.1.2		2	33.17	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-3.04508 + 9.37181i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.30902 - 0.951057i) q^{5} +(15.9443 - 11.5842i) q^{6} +(4.57295 + 14.0741i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-56.7148 - 41.2057i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-3.04508 + 9.37181i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.30902 - 0.951057i) q^{5} +(15.9443 - 11.5842i) q^{6} +(4.57295 + 14.0741i) q^{7} +(2.47214 - 7.60845i) q^{8} +(-56.7148 - 41.2057i) q^{9} -3.23607 q^{10} +(35.5967 - 7.99197i) q^{11} -39.4164 q^{12} +(41.1976 + 29.9318i) q^{13} +(9.14590 - 28.1482i) q^{14} +(4.92705 + 15.1639i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(48.7943 - 35.4511i) q^{17} +(43.3262 + 133.344i) q^{18} +(-8.16970 + 25.1437i) q^{19} +(5.23607 + 3.80423i) q^{20} -145.825 q^{21} +(-66.9919 - 28.9152i) q^{22} -29.1672 q^{23} +(63.7771 + 46.3368i) q^{24} +(-37.8181 + 116.392i) q^{25} +(-31.4721 - 96.8613i) q^{26} +(343.626 - 249.659i) q^{27} +(-47.8885 + 34.7931i) q^{28} +(-46.4352 - 142.913i) q^{29} +(9.85410 - 30.3278i) q^{30} +(-23.7680 - 17.2685i) q^{31} +32.0000 q^{32} +(-33.4959 + 357.942i) q^{33} -120.626 q^{34} +(19.3713 + 14.0741i) q^{35} +(86.6525 - 266.689i) q^{36} +(-69.4746 - 213.821i) q^{37} +(42.7771 - 31.0794i) q^{38} +(-405.965 + 294.951i) q^{39} +(-4.00000 - 12.3107i) q^{40} +(36.9975 - 113.867i) q^{41} +(235.949 + 171.427i) q^{42} +213.974 q^{43} +(74.4033 + 125.539i) q^{44} -113.430 q^{45} +(47.1935 + 34.2881i) q^{46} +(-54.0846 + 166.455i) q^{47} +(-48.7214 - 149.949i) q^{48} +(100.325 - 72.8902i) q^{49} +(198.018 - 143.869i) q^{50} +(183.658 + 565.243i) q^{51} +(-62.9443 + 193.723i) q^{52} +(51.1124 + 37.1353i) q^{53} -849.489 q^{54} +(38.9959 - 44.3161i) q^{55} +118.387 q^{56} +(-210.765 - 153.130i) q^{57} +(-92.8704 + 285.826i) q^{58} +(-80.9712 - 249.204i) q^{59} +(-51.5967 + 37.4872i) q^{60} +(573.568 - 416.722i) q^{61} +(18.1571 + 55.8819i) q^{62} +(320.579 - 986.641i) q^{63} +(-51.7771 - 37.6183i) q^{64} +82.3951 q^{65} +(474.984 - 539.786i) q^{66} -151.692 q^{67} +(195.177 + 141.805i) q^{68} +(88.8166 - 273.349i) q^{69} +(-14.7984 - 45.5447i) q^{70} +(-853.960 + 620.438i) q^{71} +(-453.718 + 329.646i) q^{72} +(-9.74013 - 29.9770i) q^{73} +(-138.949 + 427.642i) q^{74} +(-975.646 - 708.848i) q^{75} -105.751 q^{76} +(275.262 + 464.445i) q^{77} +1003.60 q^{78} +(-52.6797 - 38.2741i) q^{79} +(-8.00000 + 24.6215i) q^{80} +(708.479 + 2180.47i) q^{81} +(-193.721 + 140.747i) q^{82} +(186.532 - 135.523i) q^{83} +(-180.249 - 554.750i) q^{84} +(30.1565 - 92.8123i) q^{85} +(-346.217 - 251.541i) q^{86} +1480.75 q^{87} +(27.1935 - 290.593i) q^{88} -618.952 q^{89} +(183.533 + 133.344i) q^{90} +(-232.868 + 716.695i) q^{91} +(-36.0526 - 110.959i) q^{92} +(234.212 - 170.165i) q^{93} +(283.190 - 205.750i) q^{94} +(13.2188 + 40.6834i) q^{95} +(-97.4427 + 299.898i) q^{96} +(889.913 + 646.559i) q^{97} -248.016 q^{98} +(-2348.18 - 1013.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 + 28 * q^6 + 25 * q^7 - 8 * q^8 - 124 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9} - 4 q^{10} + 44 q^{11} - 104 q^{12} + 91 q^{13} + 50 q^{14} + 13 q^{15} - 16 q^{16} + 23 q^{17} + 142 q^{18} + 59 q^{19} + 12 q^{20} - 230 q^{21} - 22 q^{22} - 224 q^{23} + 112 q^{24} + 126 q^{25} - 108 q^{26} + 773 q^{27} - 120 q^{28} - 425 q^{29} + 26 q^{30} - 227 q^{31} + 128 q^{32} - 11 q^{33} - 724 q^{34} + 35 q^{35} + 284 q^{36} - 61 q^{37} + 28 q^{38} - 839 q^{39} - 16 q^{40} + 347 q^{41} + 510 q^{42} + 1160 q^{43} + 396 q^{44} - 248 q^{45} - 8 q^{46} + 251 q^{47} - 16 q^{48} + 48 q^{49} + 242 q^{50} - 247 q^{51} - 216 q^{52} - 245 q^{53} - 1144 q^{54} + 33 q^{55} + 80 q^{56} - 331 q^{57} - 850 q^{58} - 827 q^{59} - 108 q^{60} + 1335 q^{61} + 976 q^{62} + 370 q^{63} - 64 q^{64} + 182 q^{65} + 1408 q^{66} - 88 q^{67} + 92 q^{68} - 244 q^{69} - 10 q^{70} - 1665 q^{71} - 992 q^{72} - 153 q^{73} - 122 q^{74} - 1709 q^{75} - 584 q^{76} - 55 q^{77} + 1832 q^{78} + 677 q^{79} - 32 q^{80} + 1376 q^{81} - 596 q^{82} + 887 q^{83} - 560 q^{84} + 181 q^{85} - 240 q^{86} + 1670 q^{87} - 88 q^{88} + 1728 q^{89} + 354 q^{90} - 245 q^{91} + 464 q^{92} + 1033 q^{93} + 292 q^{94} + 73 q^{95} - 32 q^{96} + 2019 q^{97} - 1484 q^{98} - 5654 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 + 28 * q^6 + 25 * q^7 - 8 * q^8 - 124 * q^9 - 4 * q^10 + 44 * q^11 - 104 * q^12 + 91 * q^13 + 50 * q^14 + 13 * q^15 - 16 * q^16 + 23 * q^17 + 142 * q^18 + 59 * q^19 + 12 * q^20 - 230 * q^21 - 22 * q^22 - 224 * q^23 + 112 * q^24 + 126 * q^25 - 108 * q^26 + 773 * q^27 - 120 * q^28 - 425 * q^29 + 26 * q^30 - 227 * q^31 + 128 * q^32 - 11 * q^33 - 724 * q^34 + 35 * q^35 + 284 * q^36 - 61 * q^37 + 28 * q^38 - 839 * q^39 - 16 * q^40 + 347 * q^41 + 510 * q^42 + 1160 * q^43 + 396 * q^44 - 248 * q^45 - 8 * q^46 + 251 * q^47 - 16 * q^48 + 48 * q^49 + 242 * q^50 - 247 * q^51 - 216 * q^52 - 245 * q^53 - 1144 * q^54 + 33 * q^55 + 80 * q^56 - 331 * q^57 - 850 * q^58 - 827 * q^59 - 108 * q^60 + 1335 * q^61 + 976 * q^62 + 370 * q^63 - 64 * q^64 + 182 * q^65 + 1408 * q^66 - 88 * q^67 + 92 * q^68 - 244 * q^69 - 10 * q^70 - 1665 * q^71 - 992 * q^72 - 153 * q^73 - 122 * q^74 - 1709 * q^75 - 584 * q^76 - 55 * q^77 + 1832 * q^78 + 677 * q^79 - 32 * q^80 + 1376 * q^81 - 596 * q^82 + 887 * q^83 - 560 * q^84 + 181 * q^85 - 240 * q^86 + 1670 * q^87 - 88 * q^88 + 1728 * q^89 + 354 * q^90 - 245 * q^91 + 464 * q^92 + 1033 * q^93 + 292 * q^94 + 73 * q^95 - 32 * q^96 + 2019 * q^97 - 1484 * q^98 - 5654 * q^99

Introduction

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