LMFDB - Embedded newform 43.4.c.a.6.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.9
Root			$-1.91170 + 3.31117i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.4.c.a.36.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.82341 q^{2} +(3.88258 - 6.72483i) q^{3} +6.61843 q^{4} +(-9.06615 + 15.7030i) q^{5} +(14.8447 - 25.7118i) q^{6} +(-2.59898 - 4.50156i) q^{7} -5.28231 q^{8} +(-16.6489 - 28.8368i) q^{9} +O(q^{10})$	\(q+3.82341 q^{2} +(3.88258 - 6.72483i) q^{3} +6.61843 q^{4} +(-9.06615 + 15.7030i) q^{5} +(14.8447 - 25.7118i) q^{6} +(-2.59898 - 4.50156i) q^{7} -5.28231 q^{8} +(-16.6489 - 28.8368i) q^{9} +(-34.6635 + 60.0390i) q^{10} +31.5438 q^{11} +(25.6966 - 44.5078i) q^{12} +(35.6624 + 61.7691i) q^{13} +(-9.93695 - 17.2113i) q^{14} +(70.4002 + 121.937i) q^{15} -73.1438 q^{16} +(-68.0901 - 117.936i) q^{17} +(-63.6556 - 110.255i) q^{18} +(0.699830 - 1.21214i) q^{19} +(-60.0036 + 103.929i) q^{20} -40.3630 q^{21} +120.605 q^{22} +(30.3581 - 52.5818i) q^{23} +(-20.5090 + 35.5227i) q^{24} +(-101.890 - 176.479i) q^{25} +(136.352 + 236.168i) q^{26} -48.9039 q^{27} +(-17.2012 - 29.7933i) q^{28} +(-14.8004 - 25.6351i) q^{29} +(269.168 + 466.213i) q^{30} +(-43.6330 + 75.5747i) q^{31} -237.400 q^{32} +(122.472 - 212.127i) q^{33} +(-260.336 - 450.915i) q^{34} +94.2509 q^{35} +(-110.190 - 190.854i) q^{36} +(-127.821 + 221.392i) q^{37} +(2.67573 - 4.63450i) q^{38} +553.849 q^{39} +(47.8902 - 82.9483i) q^{40} +23.1367 q^{41} -154.324 q^{42} +(275.007 - 62.2731i) q^{43} +208.771 q^{44} +603.766 q^{45} +(116.071 - 201.042i) q^{46} -1.08229 q^{47} +(-283.987 + 491.880i) q^{48} +(157.991 - 273.648i) q^{49} +(-389.567 - 674.749i) q^{50} -1057.46 q^{51} +(236.029 + 408.814i) q^{52} +(33.4462 - 57.9305i) q^{53} -186.979 q^{54} +(-285.981 + 495.333i) q^{55} +(13.7286 + 23.7787i) q^{56} +(-5.43429 - 9.41247i) q^{57} +(-56.5879 - 98.0132i) q^{58} +465.968 q^{59} +(465.938 + 807.029i) q^{60} +(290.172 + 502.593i) q^{61} +(-166.827 + 288.953i) q^{62} +(-86.5404 + 149.892i) q^{63} -322.526 q^{64} -1293.28 q^{65} +(468.258 - 811.047i) q^{66} +(-164.428 + 284.798i) q^{67} +(-450.649 - 780.548i) q^{68} +(-235.736 - 408.307i) q^{69} +360.359 q^{70} +(-416.403 - 721.231i) q^{71} +(87.9448 + 152.325i) q^{72} +(524.572 + 908.585i) q^{73} +(-488.711 + 846.473i) q^{74} -1582.39 q^{75} +(4.63177 - 8.02246i) q^{76} +(-81.9817 - 141.997i) q^{77} +2117.59 q^{78} +(-404.171 - 700.044i) q^{79} +(663.133 - 1148.58i) q^{80} +(259.648 - 449.723i) q^{81} +88.4608 q^{82} +(-519.153 + 899.199i) q^{83} -267.140 q^{84} +2469.26 q^{85} +(1051.46 - 238.095i) q^{86} -229.855 q^{87} -166.624 q^{88} +(-437.613 + 757.968i) q^{89} +2308.44 q^{90} +(185.372 - 321.073i) q^{91} +(200.923 - 348.009i) q^{92} +(338.818 + 586.850i) q^{93} -4.13803 q^{94} +(12.6895 + 21.9789i) q^{95} +(-921.726 + 1596.48i) q^{96} +88.7982 q^{97} +(604.062 - 1046.27i) q^{98} +(-525.171 - 909.622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.82341			1.35178			0.675889	−	0.737003i	$-0.263760\pi$
$2$	3.82341			1.35178			0.675889	+	0.737003i	$0.263760\pi$
$3$	3.88258	−	6.72483i	0.747204	−	1.29419i	−0.201954	−	0.979395i	$-0.564729\pi$
$3$	3.88258	−	6.72483i	0.747204	−	1.29419i	0.949158	−	0.314800i	$-0.101937\pi$
$4$	6.61843			0.827303
$5$	−9.06615	+	15.7030i	−0.810901	+	1.40452i	0.101334	+	0.994852i	$0.467689\pi$
$5$	−9.06615	+	15.7030i	−0.810901	+	1.40452i	−0.912234	+	0.409669i	$0.865644\pi$
$6$	14.8447	−	25.7118i	1.01005	−	1.74946i
$7$	−2.59898	−	4.50156i	−0.140332	−	0.243062i	0.787290	−	0.616583i	$-0.211484\pi$
$7$	−2.59898	−	4.50156i	−0.140332	−	0.243062i	−0.927622	+	0.373521i	$0.878150\pi$
$8$	−5.28231			−0.233447
$9$	−16.6489	−	28.8368i	−0.616627	−	1.06803i
$10$	−34.6635	+	60.0390i	−1.09616	+	1.89860i
$11$	31.5438			0.864620			0.432310	−	0.901725i	$-0.357699\pi$
$11$	31.5438			0.864620			0.432310	+	0.901725i	$0.357699\pi$
$12$	25.6966	−	44.5078i	0.618164	−	1.07069i
$13$	35.6624	+	61.7691i	0.760844	+	1.31782i	0.942416	+	0.334443i	$0.108548\pi$
$13$	35.6624	+	61.7691i	0.760844	+	1.31782i	−0.181572	+	0.983378i	$0.558118\pi$
$14$	−9.93695	−	17.2113i	−0.189697	−	0.328565i
$15$	70.4002	+	121.937i	1.21182	+	2.09893i
$16$	−73.1438			−1.14287
$17$	−68.0901	−	117.936i	−0.971428	−	1.68256i	−0.691251	−	0.722614i	$-0.742940\pi$
$17$	−68.0901	−	117.936i	−0.971428	−	1.68256i	−0.280177	−	0.959948i	$-0.590393\pi$
$18$	−63.6556	−	110.255i	−0.833543	−	1.44374i
$19$	0.699830	−	1.21214i	0.00845010	−	0.0146360i	−0.861769	−	0.507300i	$-0.830644\pi$
$19$	0.699830	−	1.21214i	0.00845010	−	0.0146360i	0.870220	+	0.492664i	$0.163977\pi$
$20$	−60.0036	+	103.929i	−0.670861	+	1.16197i
$21$	−40.3630			−0.419425
$22$	120.605			1.16877
$23$	30.3581	−	52.5818i	0.275222	−	0.476699i	−0.694969	−	0.719040i	$-0.744582\pi$
$23$	30.3581	−	52.5818i	0.275222	−	0.476699i	0.970191	+	0.242341i	$0.0779152\pi$
$24$	−20.5090	+	35.5227i	−0.174433	+	0.302126i
$25$	−101.890	−	176.479i	−0.815120	−	1.41183i
$26$	136.352	+	236.168i	1.02849	+	1.78140i
$27$	−48.9039			−0.348576
$28$	−17.2012	−	29.7933i	−0.116097	−	0.201086i
$29$	−14.8004	−	25.6351i	−0.0947712	−	0.164149i	0.814742	−	0.579824i	$-0.196879\pi$
$29$	−14.8004	−	25.6351i	−0.0947712	−	0.164149i	−0.909513	+	0.415675i	$0.863545\pi$
$30$	269.168	+	466.213i	1.63811	+	2.83728i
$31$	−43.6330	+	75.5747i	−0.252798	+	0.437858i	−0.964295	−	0.264830i	$-0.914684\pi$
$31$	−43.6330	+	75.5747i	−0.252798	+	0.437858i	0.711497	+	0.702689i	$0.248017\pi$
$32$	−237.400			−1.31146
$33$	122.472	−	212.127i	0.646047	−	1.11899i
$34$	−260.336	−	450.915i	−1.31316	−	2.27445i
$35$	94.2509			0.455180
$36$	−110.190	−	190.854i	−0.510138	−	0.883584i
$37$	−127.821	+	221.392i	−0.567936	+	0.983694i	0.428834	+	0.903383i	$0.358925\pi$
$37$	−127.821	+	221.392i	−0.567936	+	0.983694i	−0.996770	+	0.0803107i	$0.974409\pi$
$38$	2.67573	−	4.63450i	0.0114227	−	0.0197846i
$39$	553.849			2.27402
$40$	47.8902	−	82.9483i	0.189303	−	0.327882i
$41$	23.1367			0.0881302			0.0440651	−	0.999029i	$-0.485969\pi$
$41$	23.1367			0.0881302			0.0440651	+	0.999029i	$0.485969\pi$
$42$	−154.324			−0.566970
$43$	275.007	−	62.2731i	0.975308	−	0.220850i
$43$	275.007	−	62.2731i	0.975308	−	0.220850i
$44$	208.771			0.715303
$45$	603.766			2.00009
$46$	116.071	−	201.042i	0.372039	−	0.644391i
$47$	−1.08229			−0.00335890			−0.00167945	−	0.999999i	$-0.500535\pi$
$47$	−1.08229			−0.00335890			−0.00167945	+	0.999999i	$0.500535\pi$
$48$	−283.987	+	491.880i	−0.853959	+	1.47910i
$49$	157.991	−	273.648i	0.460614	−	0.797807i
$50$	−389.567	−	674.749i	−1.10186	−	1.90848i
$51$	−1057.46			−2.90342
$52$	236.029	+	408.814i	0.629449	+	1.09024i
$53$	33.4462	−	57.9305i	0.0866827	−	0.150139i	−0.819424	−	0.573187i	$-0.805707\pi$
$53$	33.4462	−	57.9305i	0.0866827	−	0.150139i	0.906107	+	0.423049i	$0.139040\pi$
$54$	−186.979			−0.471198
$55$	−285.981	+	495.333i	−0.701121	+	1.21438i
$56$	13.7286	+	23.7787i	0.0327601	+	0.0567421i
$57$	−5.43429	−	9.41247i	−0.0126279	−	0.0218722i
$58$	−56.5879	−	98.0132i	−0.128110	−	0.221892i
$59$	465.968			1.02820			0.514101	−	0.857730i	$-0.328126\pi$
$59$	465.968			1.02820			0.514101	+	0.857730i	$0.328126\pi$
$60$	465.938	+	807.029i	1.00254	+	1.73645i
$61$	290.172	+	502.593i	0.609062	+	1.05493i	0.991395	+	0.130902i	$0.0417872\pi$
$61$	290.172	+	502.593i	0.609062	+	1.05493i	−0.382334	+	0.924024i	$0.624879\pi$
$62$	−166.827	+	288.953i	−0.341726	+	0.591887i
$63$	−86.5404	+	149.892i	−0.173065	+	0.299757i
$64$	−322.526			−0.629933
$65$	−1293.28			−2.46788
$66$	468.258	−	811.047i	0.873313	−	1.51262i
$67$	−164.428	+	284.798i	−0.299822	+	0.519307i	−0.976095	−	0.217344i	$-0.930261\pi$
$67$	−164.428	+	284.798i	−0.299822	+	0.519307i	0.676273	+	0.736651i	$0.263594\pi$
$68$	−450.649	−	780.548i	−0.803666	−	1.39199i
$69$	−235.736	−	408.307i	−0.411294	−	0.712382i
$70$	360.359			0.615303
$71$	−416.403	−	721.231i	−0.696027	−	1.20555i	−0.969833	−	0.243769i	$-0.921616\pi$
$71$	−416.403	−	721.231i	−0.696027	−	1.20555i	0.273806	−	0.961785i	$-0.411717\pi$
$72$	87.9448	+	152.325i	0.143950	+	0.249329i
$73$	524.572	+	908.585i	0.841048	+	1.45674i	0.889010	+	0.457888i	$0.151394\pi$
$73$	524.572	+	908.585i	0.841048	+	1.45674i	−0.0479622	+	0.998849i	$0.515273\pi$
$74$	−488.711	+	846.473i	−0.767723	+	1.32974i
$75$	−1582.39			−2.43624
$76$	4.63177	−	8.02246i	0.00699080	−	0.0121084i
$77$	−81.9817	−	141.997i	−0.121334	−	0.210156i
$78$	2117.59			3.07397
$79$	−404.171	−	700.044i	−0.575605	−	0.996976i	−0.995976	−	0.0896240i	$-0.971433\pi$
$79$	−404.171	−	700.044i	−0.575605	−	0.996976i	0.420371	−	0.907352i	$-0.361900\pi$
$80$	663.133	−	1148.58i	0.926756	−	1.60519i
$81$	259.648	−	449.723i	0.356169	−	0.616904i
$82$	88.4608			0.119132
$83$	−519.153	+	899.199i	−0.686560	+	1.18916i	0.286384	+	0.958115i	$0.407547\pi$
$83$	−519.153	+	899.199i	−0.686560	+	1.18916i	−0.972944	+	0.231041i	$0.925787\pi$
$84$	−267.140			−0.346992
$85$	2469.26			3.15093
$86$	1051.46	−	238.095i	1.31840	−	0.298540i
$87$	−229.855			−0.283254
$88$	−166.624			−0.201843
$89$	−437.613	+	757.968i	−0.521201	+	0.902746i	0.478495	+	0.878090i	$0.341182\pi$
$89$	−437.613	+	757.968i	−0.521201	+	0.902746i	−0.999696	+	0.0246562i	$0.992151\pi$
$90$	2308.44			2.70368
$91$	185.372	−	321.073i	0.213541	−	0.369864i
$92$	200.923	−	348.009i	0.227692	−	0.394375i
$93$	338.818	+	586.850i	0.377783	+	0.654339i
$94$	−4.13803			−0.00454048
$95$	12.6895	+	21.9789i	0.0137044	+	0.0237367i
$96$	−921.726	+	1596.48i	−0.979930	+	1.69729i
$97$	88.7982			0.0929494			0.0464747	−	0.998919i	$-0.485201\pi$
$97$	88.7982			0.0929494			0.0464747	+	0.998919i	$0.485201\pi$
$98$	604.062	−	1046.27i	0.622648	−	1.07846i
$99$	−525.171	−	909.622i	−0.533148	−	0.923439i
$100$	−674.352	−	1168.01i	−0.674352	−	1.16801i
$101$	−638.678	−	1106.22i	−0.629216	−	1.08983i	−0.987709	−	0.156302i	$-0.950043\pi$
$101$	−638.678	−	1106.22i	−0.629216	−	1.08983i	0.358493	−	0.933532i	$-0.383291\pi$
$102$	−4043.11			−3.92478
$103$	464.034	+	803.730i	0.443909	+	0.768872i	0.997975	−	0.0635999i	$-0.0202582\pi$
$103$	464.034	+	803.730i	0.443909	+	0.768872i	−0.554067	+	0.832472i	$0.686925\pi$
$104$	−188.380	−	326.284i	−0.177617	−	0.307642i
$105$	365.937	−	633.822i	0.340112	−	0.589092i
$106$	127.878	−	221.492i	0.117176	−	0.202954i
$107$	−1194.14			−1.07890			−0.539448	−	0.842019i	$-0.681367\pi$
$107$	−1194.14			−1.07890			−0.539448	+	0.842019i	$0.681367\pi$
$108$	−323.667			−0.288378
$109$	−335.715	+	581.476i	−0.295007	+	0.510966i	−0.974986	−	0.222264i	$-0.928655\pi$
$109$	−335.715	+	581.476i	−0.295007	+	0.510966i	0.679980	+	0.733231i	$0.261988\pi$
$110$	−1093.42	+	1893.86i	−0.947760	+	1.64157i
$111$	992.551	+	1719.15i	0.848728	+	1.47004i
$112$	190.099	+	329.262i	0.160381	+	0.277788i
$113$	−263.783			−0.219598			−0.109799	−	0.993954i	$-0.535021\pi$
$113$	−263.783			−0.219598			−0.109799	+	0.993954i	$0.535021\pi$
$114$	−20.7775	−	35.9877i	−0.0170701	−	0.0295663i
$115$	550.463	+	953.429i	0.446356	+	0.773111i
$116$	−97.9554	−	169.664i	−0.0784046	−	0.135801i
$117$	1187.48	−	2056.78i	0.938314	−	1.62521i
$118$	1781.59			1.38990
$119$	−353.930	+	613.024i	−0.272644	+	0.472234i
$120$	−371.876	−	644.107i	−0.282895	−	0.489989i
$121$	−335.987			−0.252432
$122$	1109.45	+	1921.62i	0.823316	+	1.42603i
$123$	89.8300	−	155.590i	0.0658512	−	0.114058i
$124$	−288.782	+	500.185i	−0.209140	+	0.362242i
$125$	1428.46			1.02212
$126$	−330.879	+	573.099i	−0.233945	+	0.405204i
$127$	−1082.71			−0.756499			−0.378249	−	0.925704i	$-0.623474\pi$
$127$	−1082.71			−0.756499			−0.378249	+	0.925704i	$0.623474\pi$
$128$	666.053			0.459932
$129$	648.964	−	2091.16i	0.442931	−	1.42726i
$130$	−4944.74			−3.33602
$131$	1370.38			0.913972			0.456986	−	0.889474i	$-0.348929\pi$
$131$	1370.38			0.913972			0.456986	+	0.889474i	$0.348929\pi$
$132$	810.569	−	1403.95i	0.534477	−	0.925742i
$133$	−7.27537			−0.00474327
$134$	−628.675	+	1088.90i	−0.405293	+	0.701988i
$135$	443.370	−	767.939i	0.282661	−	0.489583i
$136$	359.673	+	622.972i	0.226777	+	0.392790i
$137$	1001.07			0.624283			0.312142	−	0.950036i	$-0.398954\pi$
$137$	1001.07			0.624283			0.312142	+	0.950036i	$0.398954\pi$
$138$	−901.315	−	1561.12i	−0.555978	−	0.962983i
$139$	299.262	−	518.338i	0.182612	−	0.316294i	−0.760157	−	0.649739i	$-0.774878\pi$
$139$	299.262	−	518.338i	0.182612	−	0.316294i	0.942769	+	0.333446i	$0.108211\pi$
$140$	623.793			0.376572
$141$	−4.20208	+	7.27822i	−0.00250978	+	0.00434707i
$142$	−1592.08	−	2757.56i	−0.940874	−	1.62964i
$143$	1124.93	+	1948.43i	0.657841	+	1.13941i
$144$	1217.77	+	2109.23i	0.704726	+	1.22062i
$145$	536.730			0.307400
$146$	2005.65	+	3473.89i	1.13691	+	1.96919i
$147$	−1226.82	−	2124.92i	−0.688345	−	1.19225i
$148$	−845.974	+	1465.27i	−0.469855	+	0.813814i
$149$	355.005	−	614.887i	0.195189	−	0.338077i	−0.751773	−	0.659421i	$-0.770801\pi$
$149$	355.005	−	614.887i	0.195189	−	0.338077i	0.946962	+	0.321344i	$0.104135\pi$
$150$	−6050.10			−3.29326
$151$	1699.83			0.916093			0.458047	−	0.888928i	$-0.348549\pi$
$151$	1699.83			0.916093			0.458047	+	0.888928i	$0.348549\pi$
$152$	−3.69672	+	6.40290i	−0.00197265	+	0.00341674i
$153$	−2267.25	+	3927.00i	−1.19802	+	2.07503i
$154$	−313.449	−	542.910i	−0.164016	−	0.284084i
$155$	−791.167	−	1370.34i	−0.409988	−	0.710119i
$156$	3665.61			1.88131
$157$	−680.959	−	1179.45i	−0.346155	−	0.599559i	0.639408	−	0.768868i	$-0.279180\pi$
$157$	−680.959	−	1179.45i	−0.346155	−	0.599559i	−0.985563	+	0.169309i	$0.945846\pi$
$158$	−1545.31	−	2676.55i	−0.778089	−	1.34769i
$159$	−259.715	−	449.840i	−0.129539	−	0.224369i
$160$	2152.30	−	3727.90i	1.06347	−	1.84198i
$161$	−315.601			−0.154490
$162$	992.738	−	1719.47i	0.481462	−	0.833917i
$163$	−1440.78	−	2495.51i	−0.692336	−	1.19916i	−0.971070	−	0.238793i	$-0.923248\pi$
$163$	−1440.78	−	2495.51i	−0.692336	−	1.19916i	0.278734	−	0.960368i	$-0.410085\pi$
$164$	153.128			0.0729104
$165$	2220.69	+	3846.35i	1.04776	+	1.81477i
$166$	−1984.93	+	3438.00i	−0.928076	+	1.60747i
$167$	−493.391	+	854.578i	−0.228621	+	0.395983i	−0.957400	−	0.288766i	$-0.906755\pi$
$167$	−493.391	+	854.578i	−0.228621	+	0.395983i	0.728779	+	0.684749i	$0.240088\pi$
$168$	213.210			0.0979138
$169$	−1445.12	+	2503.01i	−0.657768	+	1.13929i
$170$	9440.98			4.25935
$171$	−46.6056			−0.0208422
$172$	1820.12	−	412.150i	0.806875	−	0.182710i
$173$	595.012			0.261491			0.130746	−	0.991416i	$-0.458263\pi$
$173$	595.012			0.261491			0.130746	+	0.991416i	$0.458263\pi$
$174$	−878.830			−0.382896
$175$	−529.620	+	917.329i	−0.228774	+	0.396249i
$176$	−2307.24			−0.988150
$177$	1809.16	−	3133.56i	0.768276	−	1.33069i
$178$	−1673.17	+	2898.02i	−0.704548	+	1.22031i
$179$	−1160.16	−	2009.45i	−0.484436	−	0.839068i	0.515404	−	0.856947i	$-0.327642\pi$
$179$	−1160.16	−	2009.45i	−0.484436	−	0.839068i	−0.999840	+	0.0178794i	$0.994309\pi$
$180$	3995.98			1.65468
$181$	−765.587	−	1326.04i	−0.314396	−	0.544550i	0.664913	−	0.746921i	$-0.268469\pi$
$181$	−765.587	−	1326.04i	−0.314396	−	0.544550i	−0.979309	+	0.202371i	$0.935135\pi$
$182$	708.751	−	1227.59i	0.288660	−	0.499974i
$183$	4506.48			1.82037
$184$	−160.361	+	277.754i	−0.0642499	+	0.111284i
$185$	−2317.69	−	4014.35i	−0.921080	−	1.59536i
$186$	1295.44	+	2243.77i	0.510678	+	0.884521i
$187$	−2147.82	−	3720.14i	−0.839916	−	1.45478i
$188$	−7.16306			−0.00277883
$189$	127.100	+	220.144i	0.0489163	+	0.0847255i
$190$	48.5172	+	84.0342i	0.0185253	+	0.0320867i
$191$	−866.754	+	1501.26i	−0.328357	+	0.568731i	−0.982186	−	0.187912i	$-0.939828\pi$
$191$	−866.754	+	1501.26i	−0.328357	+	0.568731i	0.653829	+	0.756642i	$0.273162\pi$
$192$	−1252.23	+	2168.93i	−0.470689	+	0.815256i
$193$	1109.49			0.413798			0.206899	−	0.978362i	$-0.433663\pi$
$193$	1109.49			0.413798			0.206899	+	0.978362i	$0.433663\pi$
$194$	339.512			0.125647
$195$	−5021.28	+	8697.11i	−1.84401	+	3.19391i
$196$	1045.65	−	1811.12i	0.381068	−	0.660028i
$197$	−789.890	−	1368.13i	−0.285672	−	0.494798i	0.687100	−	0.726563i	$-0.258883\pi$
$197$	−789.890	−	1368.13i	−0.285672	−	0.494798i	−0.972772	+	0.231765i	$0.925550\pi$
$198$	−2007.94	−	3477.86i	−0.720698	−	1.24828i
$199$	3596.57			1.28118			0.640588	−	0.767885i	$-0.278691\pi$
$199$	3596.57			1.28118			0.640588	+	0.767885i	$0.278691\pi$
$200$	538.215	+	932.215i	0.190288	+	0.329588i
$201$	1276.81	+	2211.50i	0.448056	+	0.776056i
$202$	−2441.92	−	4229.54i	−0.850561	−	1.47321i
$203$	−76.9319	+	133.250i	−0.0265988	+	0.0460705i
$204$	−6998.74			−2.40201
$205$	−209.760	+	363.315i	−0.0714648	+	0.123781i
$206$	1774.19	+	3072.98i	0.600066	+	1.03934i
$207$	−2021.72			−0.678838
$208$	−2608.49	−	4518.03i	−0.869548	−	1.50610i
$209$	22.0753	−	38.2355i	0.00730613	−	0.0126546i
$210$	1399.13	−	2423.36i	0.459756	−	0.796322i
$211$	3927.29			1.28135			0.640676	−	0.767811i	$-0.278654\pi$
$211$	3927.29			1.28135			0.640676	+	0.767811i	$0.278654\pi$
$212$	221.361	−	383.409i	0.0717129	−	0.124210i
$213$	−6466.88			−2.08030
$214$	−4565.68			−1.45843
$215$	−1515.38	+	4883.02i	−0.480689	+	1.54893i
$216$	258.326			0.0813742
$217$	453.606			0.141902
$218$	−1283.58	+	2223.22i	−0.398783	+	0.690713i
$219$	8146.78			2.51374
$220$	−1892.74	+	3278.33i	−0.580040	+	1.00466i
$221$	4856.52	−	8411.73i	1.47821	−	2.56034i
$222$	3794.93	+	6573.00i	1.14729	+	1.98717i
$223$	−249.842			−0.0750255			−0.0375127	−	0.999296i	$-0.511943\pi$
$223$	−249.842			−0.0750255			−0.0375127	+	0.999296i	$0.511943\pi$
$224$	616.998	+	1068.67i	0.184040	+	0.318766i
$225$	−3392.72	+	5876.36i	−1.00525	+	1.74114i
$226$	−1008.55			−0.296848
$227$	−2616.00	+	4531.04i	−0.764889	+	1.32483i	0.175417	+	0.984494i	$0.443873\pi$
$227$	−2616.00	+	4531.04i	−0.764889	+	1.32483i	−0.940305	+	0.340332i	$0.889461\pi$
$228$	−35.9665	−	62.2958i	−0.0104471	−	0.0180949i
$229$	474.200	+	821.339i	0.136839	+	0.237011i	0.926298	−	0.376791i	$-0.122972\pi$
$229$	474.200	+	821.339i	0.136839	+	0.237011i	−0.789460	+	0.613802i	$0.789639\pi$
$230$	2104.64	+	3645.35i	0.603374	+	1.04507i
$231$	−1273.20			−0.362644
$232$	78.1803	+	135.412i	0.0221241	+	0.0383201i
$233$	−1726.19	−	2989.85i	−0.485350	−	0.840650i	0.514509	−	0.857485i	$-0.327974\pi$
$233$	−1726.19	−	2989.85i	−0.485350	−	0.840650i	−0.999858	+	0.0168351i	$0.994641\pi$
$234$	4540.22	−	7863.90i	1.26839	−	2.19692i
$235$	9.81220	−	16.9952i	0.00272373	−	0.00471764i
$236$	3083.98			0.850635
$237$	−6276.91			−1.72038
$238$	−1353.22	+	2343.84i	−0.368555	+	0.638355i
$239$	516.979	−	895.434i	0.139919	−	0.242346i	−0.787547	−	0.616255i	$-0.788649\pi$
$239$	516.979	−	895.434i	0.139919	−	0.242346i	0.927466	+	0.373908i	$0.121983\pi$
$240$	−5149.34	−	8918.91i	−1.38495	−	2.39881i
$241$	−462.946	−	801.847i	−0.123739	−	0.214322i	0.797501	−	0.603318i	$-0.206155\pi$
$241$	−462.946	−	801.847i	−0.123739	−	0.214322i	−0.921239	+	0.388997i	$0.872822\pi$
$242$	−1284.62			−0.341232
$243$	−2676.41	−	4635.68i	−0.706550	−	1.22378i
$244$	1920.49	+	3326.38i	0.503879	+	0.872744i
$245$	2864.73	+	4961.86i	0.747024	+	1.29388i
$246$	343.457	−	594.884i	0.0890162	−	0.154181i
$247$	99.8304			0.0257168
$248$	230.483	−	399.209i	0.0590149	−	0.102217i
$249$	4031.31	+	6982.44i	1.02600	+	1.77708i
$250$	5461.59			1.38168
$251$	688.189	+	1191.98i	0.173060	+	0.299749i	0.939488	−	0.342581i	$-0.111301\pi$
$251$	688.189	+	1191.98i	0.173060	+	0.299749i	−0.766428	+	0.642330i	$0.777968\pi$
$252$	−572.762	+	992.052i	−0.143177	+	0.247990i
$253$	957.612	−	1658.63i	0.237963	−	0.412163i
$254$	−4139.65			−1.02262
$255$	9587.11	−	16605.4i	2.35438	−	4.07791i
$256$	5126.80			1.25166
$257$	−582.311			−0.141337			−0.0706685	−	0.997500i	$-0.522513\pi$
$257$	−582.311			−0.141337			−0.0706685	+	0.997500i	$0.522513\pi$
$258$	2481.25	−	7995.35i	0.598744	−	1.92934i
$259$	1328.82			0.318798
$260$	−8559.50			−2.04168
$261$	−492.822	+	853.592i	−0.116877	+	0.202437i
$262$	5239.50			1.23549
$263$	65.3309	−	113.156i	0.0153174	−	0.0265305i	−0.858265	−	0.513207i	$-0.828457\pi$
$263$	65.3309	−	113.156i	0.0153174	−	0.0265305i	0.873583	+	0.486676i	$0.161791\pi$
$264$	−646.933	+	1120.52i	−0.150818	+	0.261225i
$265$	606.456	+	1050.41i	0.140582	+	0.243495i
$266$	−27.8167			−0.00641184
$267$	3398.14	+	5885.75i	0.778887	+	1.34907i
$268$	−1088.25	+	1884.91i	−0.248044	+	0.429624i
$269$	−7250.60			−1.64341			−0.821704	−	0.569914i	$-0.806976\pi$
$269$	−7250.60			−1.64341			−0.821704	+	0.569914i	$0.806976\pi$
$270$	1695.18	−	2936.14i	0.382094	−	0.661807i
$271$	−2109.96	−	3654.55i	−0.472955	−	0.819182i	0.526566	−	0.850134i	$-0.323479\pi$
$271$	−2109.96	−	3654.55i	−0.472955	−	0.819182i	−0.999521	+	0.0309526i	$0.990146\pi$
$272$	4980.37	+	8626.26i	1.11022	+	1.92295i
$273$	−1439.44	−	2493.19i	−0.319117	−	0.552728i
$274$	3827.48			0.843892
$275$	−3214.00	−	5566.81i	−0.704769	−	1.22070i
$276$	−1560.20	−	2702.35i	−0.340265	−	0.589356i
$277$	−198.958	+	344.605i	−0.0431560	+	0.0747485i	−0.886797	−	0.462160i	$-0.847075\pi$
$277$	−198.958	+	344.605i	−0.0431560	+	0.0747485i	0.843641	+	0.536908i	$0.180408\pi$
$278$	1144.20	−	1981.82i	0.246851	−	0.427559i
$279$	2905.77			0.623527
$280$	−497.863			−0.106261
$281$	2632.09	−	4558.92i	0.558781	−	0.967838i	−0.438817	−	0.898576i	$-0.644602\pi$
$281$	2632.09	−	4558.92i	0.558781	−	0.967838i	0.997599	−	0.0692613i	$-0.0220642\pi$
$282$	−16.0663	+	27.8276i	−0.00339267	+	0.00587627i
$283$	2316.31	+	4011.96i	0.486538	+	0.842708i	0.999880	−	0.0154755i	$-0.00492621\pi$
$283$	2316.31	+	4011.96i	0.486538	+	0.842708i	−0.513342	+	0.858184i	$0.671593\pi$
$284$	−2755.93	−	4773.41i	−0.575826	−	0.997359i
$285$	197.072			0.0409599
$286$	4301.06	+	7449.65i	0.889255	+	1.54024i
$287$	−60.1317	−	104.151i	−0.0123675	−	0.0214211i
$288$	3952.46	+	6845.85i	0.808683	+	1.40068i
$289$	−6816.03	+	11805.7i	−1.38735	+	2.40295i
$290$	2052.14			0.415537
$291$	344.767	−	597.153i	0.0694522	−	0.120295i
$292$	3471.84	+	6013.40i	0.695802	+	1.20516i
$293$	−519.305			−0.103543			−0.0517716	−	0.998659i	$-0.516487\pi$
$293$	−519.305			−0.103543			−0.0517716	+	0.998659i	$0.516487\pi$
$294$	−4690.64	−	8124.43i	−0.930490	−	1.61166i
$295$	−4224.54	+	7317.11i	−0.833770	+	1.44413i
$296$	675.190	−	1169.46i	0.132583	−	0.229641i
$297$	−1542.62			−0.301386
$298$	1357.33	−	2350.96i	0.263852	−	0.457005i
$299$	4330.58			0.837605
$300$	−10472.9			−2.01551
$301$	−995.065	−	1076.12i	−0.190547	−	0.206068i
$302$	6499.13			1.23835
$303$	−9918.88			−1.88061
$304$	−51.1882	+	88.6606i	−0.00965739	+	0.0167271i
$305$	−10523.0			−1.97555
$306$	−8668.63	+	15014.5i	−1.61945	+	2.80498i
$307$	−596.862	+	1033.79i	−0.110960	+	0.192188i	−0.916158	−	0.400818i	$-0.868726\pi$
$307$	−596.862	+	1033.79i	−0.110960	+	0.192188i	0.805198	+	0.593007i	$0.202059\pi$
$308$	−542.590	−	939.794i	−0.100380	−	0.173863i
$309$	7206.60			1.32676
$310$	−3024.95	−	5239.37i	−0.554212	−	0.959924i
$311$	1294.18	−	2241.59i	0.235969	−	0.408710i	−0.723585	−	0.690235i	$-0.757507\pi$
$311$	1294.18	−	2241.59i	0.235969	−	0.408710i	0.959554	+	0.281525i	$0.0908403\pi$
$312$	−2925.60			−0.530865
$313$	−211.868	+	366.967i	−0.0382604	+	0.0662689i	−0.884521	−	0.466499i	$-0.845515\pi$
$313$	−211.868	+	366.967i	−0.0382604	+	0.0662689i	0.846261	+	0.532768i	$0.178848\pi$
$314$	−2603.58	−	4509.53i	−0.467925	−	0.810470i
$315$	−1569.18	−	2717.89i	−0.280676	−	0.486146i
$316$	−2674.97	−	4633.19i	−0.476200	−	0.824802i
$317$	1368.80			0.242522			0.121261	−	0.992621i	$-0.461306\pi$
$317$	1368.80			0.242522			0.121261	+	0.992621i	$0.461306\pi$
$318$	−992.996	−	1719.92i	−0.175108	−	0.303297i
$319$	−466.861	−	808.628i	−0.0819411	−	0.141926i
$320$	2924.07	−	5064.63i	0.510813	−	0.884755i
$321$	−4636.35	+	8030.40i	−0.806156	+	1.39630i
$322$	−1206.67			−0.208836
$323$	−190.606			−0.0328347
$324$	1718.46	−	2976.46i	0.294660	−	0.510366i
$325$	7267.29	−	12587.3i	1.24036	−	2.14836i
$326$	−5508.70	−	9541.34i	−0.935885	−	1.62100i
$327$	2606.89	+	4515.26i	0.440860	+	0.763592i
$328$	−122.215			−0.0205738
$329$	2.81285	+	4.87200i	0.000471360	+	0.000816419i
$330$	8490.60	+	14706.1i	1.41634	+	2.45317i
$331$	1227.29	+	2125.73i	0.203801	+	0.352993i	0.949750	−	0.313010i	$-0.101337\pi$
$331$	1227.29	+	2125.73i	0.203801	+	0.352993i	−0.745949	+	0.666003i	$0.768004\pi$
$332$	−3435.98	+	5951.29i	−0.567993	+	0.983793i
$333$	8512.33			1.40082
$334$	−1886.43	+	3267.40i	−0.309045	+	0.535282i
$335$	−2981.46	−	5164.03i	−0.486252	−	0.842213i
$336$	2952.31			0.479350
$337$	−3704.54	−	6416.45i	−0.598810	−	1.03717i	−0.992997	−	0.118140i	$-0.962307\pi$
$337$	−3704.54	−	6416.45i	−0.598810	−	1.03717i	0.394187	−	0.919030i	$-0.371026\pi$
$338$	−5525.26	+	9570.04i	−0.889156	+	1.54006i
$339$	−1024.16	+	1773.89i	−0.164085	+	0.284203i
$340$	16342.6			2.60677
$341$	−1376.35	+	2383.91i	−0.218574	+	0.378581i
$342$	−178.192			−0.0281741
$343$	−3425.36			−0.539218
$344$	−1452.67	+	328.946i	−0.227683	+	0.0515569i
$345$	8548.87			1.33407
$346$	2274.97			0.353478
$347$	5062.76	−	8768.96i	0.783237	−	1.35661i	−0.146809	−	0.989165i	$-0.546900\pi$
$347$	5062.76	−	8768.96i	0.783237	−	1.35661i	0.930046	−	0.367442i	$-0.119766\pi$
$348$	−1521.28			−0.234337
$349$	−33.9030	+	58.7216i	−0.00519995	+	0.00900658i	−0.868614	−	0.495490i	$-0.834989\pi$
$349$	−33.9030	+	58.7216i	−0.00519995	+	0.00900658i	0.863414	+	0.504497i	$0.168322\pi$
$350$	−2024.95	+	3507.32i	−0.309252	+	0.535640i
$351$	−1744.03	−	3020.75i	−0.265212	−	0.459361i
$352$	−7488.51			−1.13392
$353$	3362.53	+	5824.08i	0.506996	+	0.878143i	0.999967	+	0.00809740i	$0.00257751\pi$
$353$	3362.53	+	5824.08i	0.506996	+	0.878143i	−0.492971	+	0.870046i	$0.664089\pi$
$354$	6917.16	−	11980.9i	1.03854	−	1.79880i
$355$	15100.7			2.25764
$356$	−2896.31	+	5016.56i	−0.431191	+	0.746845i
$357$	2748.32	+	4760.24i	0.407442	+	0.705710i
$358$	−4435.74	−	7682.93i	−0.654850	−	1.13423i
$359$	4630.45	+	8020.17i	0.680740	+	1.17908i	0.974755	+	0.223276i	$0.0716750\pi$
$359$	4630.45	+	8020.17i	0.680740	+	1.17908i	−0.294015	+	0.955801i	$0.594992\pi$
$360$	−3189.28			−0.466916
$361$	3428.52	+	5938.37i	0.499857	+	0.865778i
$362$	−2927.15	−	5069.97i	−0.424993	−	0.736110i
$363$	−1304.50	+	2259.46i	−0.188618	+	0.326696i
$364$	1226.87	−	2125.00i	0.176663	−	0.305990i
$365$	−19023.4			−2.72802
$366$	17230.1			2.46074
$367$	−590.231	+	1022.31i	−0.0839504	+	0.145406i	−0.904943	−	0.425532i	$-0.860087\pi$
$367$	−590.231	+	1022.31i	−0.0839504	+	0.145406i	0.820993	+	0.570938i	$0.193420\pi$
$368$	−2220.51	+	3846.04i	−0.314544	+	0.544806i
$369$	−385.200	−	667.187i	−0.0543434	−	0.0941256i
$370$	−8861.46	−	15348.5i	−1.24509	−	2.15657i
$371$	−347.704			−0.0486573
$372$	2242.44	+	3884.02i	0.312541	+	0.541337i
$373$	3072.19	+	5321.19i	0.426466	+	0.738661i	0.996556	−	0.0829211i	$-0.0264249\pi$
$373$	3072.19	+	5321.19i	0.426466	+	0.738661i	−0.570090	+	0.821582i	$0.693092\pi$
$374$	−8212.00	−	14223.6i	−1.13538	−	1.96654i
$375$	5546.12	−	9606.17i	0.763735	−	1.32283i
$376$	5.71699			0.000784126
$377$	1055.64	−	1828.42i	0.144212	−	0.249783i
$378$	485.956	+	841.700i	0.0661240	+	0.114530i
$379$	−8452.78			−1.14562			−0.572810	−	0.819688i	$-0.694147\pi$
$379$	−8452.78			−1.14562			−0.572810	+	0.819688i	$0.694147\pi$
$380$	83.9846	+	145.466i	0.0113377	+	0.0196374i
$381$	−4203.73	+	7281.07i	−0.565259	+	0.979057i
$382$	−3313.95	+	5739.94i	−0.443865	+	0.768798i
$383$	3796.02			0.506443			0.253221	−	0.967408i	$-0.418510\pi$
$383$	3796.02			0.506443			0.253221	+	0.967408i	$0.418510\pi$
$384$	2586.01	−	4479.10i	0.343663	−	0.595242i
$385$	2973.03			0.393558
$386$	4242.04			0.559363
$387$	−6374.33	−	6893.55i	−0.837275	−	0.905475i
$388$	587.705			0.0768974
$389$	12372.4			1.61261			0.806303	−	0.591502i	$-0.201465\pi$
$389$	12372.4			1.61261			0.806303	+	0.591502i	$0.201465\pi$
$390$	−19198.4	+	33252.6i	−2.49269	+	4.31746i
$391$	−8268.36			−1.06943
$392$	−834.556	+	1445.49i	−0.107529	+	0.186246i
$393$	5320.60	−	9215.55i	0.682923	−	1.18286i
$394$	−3020.07	−	5230.91i	−0.386165	−	0.668857i
$395$	14657.1			1.86703
$396$	−3475.80	−	6020.27i	−0.441075	−	0.763965i
$397$	6262.73	−	10847.4i	0.791731	−	1.37132i	−0.133163	−	0.991094i	$-0.542513\pi$
$397$	6262.73	−	10847.4i	0.791731	−	1.37132i	0.924894	−	0.380225i	$-0.124153\pi$
$398$	13751.1			1.73186
$399$	−28.2472	+	48.9257i	−0.00354419	+	0.00613871i
$400$	7452.62	+	12908.3i	0.931578	+	1.61354i
$401$	−4271.21	−	7397.95i	−0.531905	−	0.921287i	−0.999306	−	0.0372416i	$-0.988143\pi$
$401$	−4271.21	−	7397.95i	−0.531905	−	0.921287i	0.467401	−	0.884045i	$-0.345190\pi$
$402$	4881.77	+	8455.47i	0.605673	+	1.04906i
$403$	−6224.24			−0.769358
$404$	−4227.04	−	7321.45i	−0.520553	−	0.901624i
$405$	4708.00	+	8154.50i	0.577636	+	1.00050i
$406$	−294.142	+	509.468i	−0.0359557	+	0.0622771i
$407$	−4031.96	+	6983.56i	−0.491049	+	0.850522i
$408$	5585.85			0.677796
$409$	−9148.33			−1.10601			−0.553003	−	0.833180i	$-0.686518\pi$
$409$	−9148.33			−1.10601			−0.553003	+	0.833180i	$0.686518\pi$
$410$	−801.998	+	1389.10i	−0.0966046	+	0.167324i
$411$	3886.72	−	6732.00i	0.466467	−	0.807944i
$412$	3071.17	+	5319.43i	0.367247	+	0.636091i
$413$	−1211.04	−	2097.59i	−0.144289	−	0.249916i
$414$	−7729.86			−0.917638
$415$	−9413.43	−	16304.5i	−1.11346	−	1.92858i
$416$	−8466.26	−	14664.0i	−0.997818	−	1.72827i
$417$	−2323.82	−	4024.98i	−0.272897	−	0.472672i
$418$	84.4028	−	146.190i	0.00987626	−	0.0171062i
$419$	8781.89			1.02392			0.511961	−	0.859009i	$-0.328919\pi$
$419$	8781.89			1.02392			0.511961	+	0.859009i	$0.328919\pi$
$420$	2421.93	−	4194.90i	0.281376	−	0.487358i
$421$	3861.97	+	6689.12i	0.447080	+	0.774365i	0.998195	−	0.0600642i	$-0.0191306\pi$
$421$	3861.97	+	6689.12i	0.447080	+	0.774365i	−0.551114	+	0.834430i	$0.685797\pi$
$422$	15015.6			1.73210
$423$	18.0190	+	31.2098i	0.00207119	+	0.00358740i
$424$	−176.673	+	306.007i	−0.0202359	+	0.0350495i
$425$	−13875.4	+	24032.9i	−1.58366	+	2.74298i
$426$	−24725.5			−2.81210
$427$	1508.30	−	2612.46i	0.170941	−	0.296079i
$428$	−7903.33			−0.892575
$429$	17470.5			1.96617
$430$	−5793.92	+	18669.8i	−0.649785	+	2.09381i
$431$	−5925.41			−0.662221			−0.331110	−	0.943592i	$-0.607423\pi$
$431$	−5925.41			−0.662221			−0.331110	+	0.943592i	$0.607423\pi$
$432$	3577.02			0.398378
$433$	1954.62	−	3385.51i	0.216936	−	0.375744i	−0.736934	−	0.675965i	$-0.763727\pi$
$433$	1954.62	−	3385.51i	0.216936	−	0.375744i	0.953870	+	0.300221i	$0.0970605\pi$
$434$	1734.32			0.191820
$435$	2083.90	−	3609.42i	0.229691	−	0.397836i
$436$	−2221.91	+	3848.46i	−0.244060	+	0.422724i
$437$	−42.4911	−	73.5967i	−0.00465131	−	0.00805631i
$438$	31148.4			3.39801
$439$	2220.63	+	3846.24i	0.241423	+	0.418157i	0.961120	−	0.276131i	$-0.0890525\pi$
$439$	2220.63	+	3846.24i	0.241423	+	0.418157i	−0.719697	+	0.694289i	$0.755719\pi$
$440$	1510.64	−	2616.51i	0.163675	−	0.283493i
$441$	−10521.5			−1.13611
$442$	18568.4	−	32161.5i	1.99821	−	3.46101i
$443$	3856.14	+	6679.02i	0.413568	+	0.716321i	0.995277	−	0.0970764i	$-0.0309491\pi$
$443$	3856.14	+	6679.02i	0.413568	+	0.716321i	−0.581709	+	0.813397i	$0.697616\pi$
$444$	6569.13	+	11378.1i	0.702156	+	1.21617i
$445$	−7934.93	−	13743.7i	−0.845284	−	1.46408i
$446$	−955.248			−0.101418
$447$	−2756.68	−	4774.70i	−0.291692	−	0.505225i
$448$	838.238	+	1451.87i	0.0883996	+	0.153113i
$449$	−646.741	+	1120.19i	−0.0679769	+	0.117739i	−0.898011	−	0.439974i	$-0.854988\pi$
$449$	−646.741	+	1120.19i	−0.0679769	+	0.117739i	0.830034	+	0.557713i	$0.188321\pi$
$450$	−12971.7	+	22467.7i	−1.35887	+	2.35364i
$451$	729.818			0.0761991
$452$	−1745.83			−0.181674
$453$	6599.73	−	11431.1i	0.684508	−	1.18560i
$454$	−10002.0	+	17324.0i	−1.03396	+	1.79087i
$455$	3361.21	+	5821.79i	0.346321	+	0.599846i
$456$	28.7056	+	49.7196i	0.00294795	+	0.00510600i
$457$	−5561.70			−0.569290			−0.284645	−	0.958633i	$-0.591876\pi$
$457$	−5561.70			−0.569290			−0.284645	+	0.958633i	$0.591876\pi$
$458$	1813.06	+	3140.31i	0.184975	+	0.320387i
$459$	3329.87	+	5767.51i	0.338617	+	0.586501i
$460$	3643.20	+	6310.20i	0.369272	+	0.639597i
$461$	7956.85	−	13781.7i	0.803878	−	1.39236i	−0.113169	−	0.993576i	$-0.536100\pi$
$461$	7956.85	−	13781.7i	0.803878	−	1.39236i	0.917046	−	0.398781i	$-0.130567\pi$
$462$	−4867.98			−0.490214
$463$	−7823.17	+	13550.1i	−0.785256	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$463$	−7823.17	+	13550.1i	−0.785256	+	1.36010i	−0.928846	+	0.370466i	$0.879198\pi$
$464$	1082.56	+	1875.05i	0.108311	+	0.187601i
$465$	−12287.1			−1.22538
$466$	−6599.92	−	11431.4i	−0.656085	−	1.13637i
$467$	−4731.93	+	8195.94i	−0.468881	+	0.812126i	−0.999367	−	0.0355676i	$-0.988676\pi$
$467$	−4731.93	+	8195.94i	−0.468881	+	0.812126i	0.530486	+	0.847694i	$0.322009\pi$
$468$	7859.26	−	13612.6i	0.776270	−	1.34454i
$469$	1709.38			0.168298
$470$	37.5160	−	64.9796i	0.00368188	−	0.00637721i
$471$	−10575.5			−1.03459
$472$	−2461.39			−0.240031
$473$	8674.78	−	1964.33i	0.843271	−	0.190951i
$474$	−23999.2			−2.32557
$475$	−285.223			−0.0275514
$476$	−2342.46	+	4057.26i	−0.225560	+	0.390681i
$477$	−2227.37			−0.213804
$478$	1976.62	−	3423.61i	0.189139	−	0.327599i
$479$	−1930.53	+	3343.77i	−0.184150	+	0.318958i	−0.943290	−	0.331970i	$-0.892287\pi$
$479$	−1930.53	+	3343.77i	−0.184150	+	0.318958i	0.759140	+	0.650928i	$0.225620\pi$
$480$	−16713.0	−	28947.8i	−1.58925	−	2.75266i
$481$	−18233.6			−1.72844
$482$	−1770.03	−	3065.79i	−0.167267	−	0.289715i
$483$	−1225.35	+	2122.36i	−0.115435	+	0.199940i
$484$	−2223.71			−0.208838
$485$	−805.058	+	1394.40i	−0.0753728	+	0.130549i
$486$	−10233.0	−	17724.1i	−0.955099	−	1.65428i
$487$	−1756.56	−	3042.45i	−0.163444	−	0.283094i	0.772658	−	0.634823i	$-0.218927\pi$
$487$	−1756.56	−	3042.45i	−0.163444	−	0.283094i	−0.936102	+	0.351730i	$0.885594\pi$
$488$	−1532.78	−	2654.85i	−0.142184	−	0.246270i
$489$	−22375.8			−2.06926
$490$	10953.0	+	18971.2i	1.00981	+	1.74904i
$491$	9638.88	+	16695.0i	0.885940	+	1.53449i	0.844632	+	0.535347i	$0.179819\pi$
$491$	9638.88	+	16695.0i	0.885940	+	1.53449i	0.0413081	+	0.999146i	$0.486847\pi$
$492$	594.533	−	1029.76i	0.0544789	−	0.0943603i
$493$	−2015.52	+	3490.99i	−0.184127	+	0.318917i
$494$	381.692			0.0347635
$495$	19045.1			1.72932
$496$	3191.49	−	5527.82i	0.288915	−	0.500416i
$497$	−2164.44	+	3748.93i	−0.195349	+	0.338355i
$498$	15413.3	+	26696.7i	1.38692	+	2.40222i
$499$	3813.16	+	6604.59i	0.342085	+	0.592509i	0.984820	−	0.173580i	$-0.0555335\pi$
$499$	3813.16	+	6604.59i	0.342085	+	0.592509i	−0.642735	+	0.766089i	$0.722200\pi$
$500$	9454.17			0.845607
$501$	3831.26	+	6635.94i	0.341653	+	0.591760i
$502$	2631.22	+	4557.41i	0.233939	+	0.405194i
$503$	−4569.92	−	7915.34i	−0.405095	−	0.701645i	0.589237	−	0.807960i	$-0.299428\pi$
$503$	−4569.92	−	7915.34i	−0.405095	−	0.701645i	−0.994333	+	0.106315i	$0.966095\pi$
$504$	457.133	−	791.778i	0.0404015	−	0.0699774i
$505$	23161.4			2.04093
$506$	3661.34	−	6341.62i	0.321673	−	0.557153i
$507$	11221.6	+	19436.3i	0.982973	+	1.70256i
$508$	−7165.86			−0.625854
$509$	6910.80	+	11969.9i	0.601799	+	1.04235i	0.992549	+	0.121850i	$0.0388826\pi$
$509$	6910.80	+	11969.9i	0.601799	+	1.04235i	−0.390749	+	0.920497i	$0.627784\pi$
$510$	36655.4	−	63489.0i	3.18260	−	5.51243i
$511$	2726.70	−	4722.79i	0.236051	−	0.408853i
$512$	14273.4			1.23203
$513$	−34.2244	+	59.2784i	−0.00294550	+	0.00510176i
$514$	−2226.41			−0.191056
$515$	−16828.0			−1.43986
$516$	4295.12	−	13840.2i	0.366438	−	1.18078i
$517$	−34.1396			−0.00290417
$518$	5080.60			0.430944
$519$	2310.19	−	4001.36i	0.195387	−	0.338420i
$520$	6831.52			0.576119
$521$	5466.94	−	9469.01i	0.459714	−	0.796247i	−0.539232	−	0.842157i	$-0.681285\pi$
$521$	5466.94	−	9469.01i	0.459714	−	0.796247i	0.998946	+	0.0459099i	$0.0146187\pi$
$522$	−1884.26	+	3263.63i	−0.157992	+	0.273650i
$523$	7675.13	+	13293.7i	0.641701	+	1.11146i	0.985053	+	0.172252i	$0.0551045\pi$
$523$	7675.13	+	13293.7i	0.641701	+	1.11146i	−0.343351	+	0.939207i	$0.611562\pi$
$524$	9069.74			0.756132
$525$	4112.59	+	7123.21i	0.341882	+	0.592157i
$526$	249.787	−	432.643i	0.0207057	−	0.0358634i
$527$	11883.9			0.982299
$528$	−8958.04	+	15515.8i	−0.738350	+	1.27886i
$529$	4240.27	+	7344.36i	0.348505	+	0.603629i
$530$	2318.73	+	4016.15i	0.190036	+	0.329152i
$531$	−7757.87	−	13437.0i	−0.634017	−	1.09815i
$532$	−48.1515			−0.00392412
$533$	825.109	+	1429.13i	0.0670533	+	0.116140i
$534$	12992.5	+	22503.6i	1.05288	+	1.82364i
$535$	10826.3	−	18751.6i	0.874878	−	1.51533i
$536$	868.560	−	1504.39i	0.0699927	−	0.121231i
$537$	−18017.6			−1.44789
$538$	−27722.0			−2.22152
$539$	4983.63	−	8631.90i	0.398256	−	0.689800i
$540$	2934.41	−	5082.55i	0.233846	−	0.405033i
$541$	−10951.0	−	18967.7i	−0.870277	−	1.50736i	−0.861710	−	0.507401i	$-0.830606\pi$
$541$	−10951.0	−	18967.7i	−0.870277	−	1.50736i	−0.00856732	−	0.999963i	$-0.502727\pi$
$542$	−8067.22	−	13972.8i	−0.639330	−	1.10735i
$543$	−11889.8			−0.939671
$544$	16164.6	+	27997.9i	1.27399	+	2.20662i
$545$	−6087.29	−	10543.5i	−0.478442	−	0.828686i
$546$	−5503.57	−	9532.47i	−0.431376	−	0.747165i
$547$	−1663.30	+	2880.92i	−0.130014	+	0.225190i	−0.923682	−	0.383161i	$-0.874835\pi$
$547$	−1663.30	+	2880.92i	−0.130014	+	0.225190i	0.793668	+	0.608351i	$0.208169\pi$
$548$	6625.48			0.516472
$549$	9662.12	−	16735.3i	0.751128	−	1.30099i
$550$	−12288.4	−	21284.2i	−0.952691	−	1.65011i
$551$	−41.4310			−0.00320331
$552$	1245.23	+	2156.80i	0.0960155	+	0.166304i
$553$	−2100.86	+	3638.80i	−0.161551	+	0.279815i
$554$	−760.697	+	1317.57i	−0.0583374	+	0.101043i
$555$	−35994.5			−2.75294
$556$	1980.65	−	3430.58i	0.151076	−	0.261671i
$557$	−16723.9			−1.27220			−0.636098	−	0.771608i	$-0.719453\pi$
$557$	−16723.9			−1.27220			−0.636098	+	0.771608i	$0.719453\pi$
$558$	11109.9			0.842870
$559$	13654.0	+	14766.2i	1.03310	+	1.11725i
$560$	−6893.87			−0.520213
$561$	−33356.4			−2.51035
$562$	10063.6	−	17430.6i	0.755348	−	1.30830i
$563$	−8139.07			−0.609273			−0.304637	−	0.952469i	$-0.598535\pi$
$563$	−8139.07			−0.609273			−0.304637	+	0.952469i	$0.598535\pi$
$564$	−27.8112	+	48.1704i	−0.00207635	+	0.00359634i
$565$	2391.49	−	4142.19i	0.178072	−	0.308430i
$566$	8856.19	+	15339.4i	0.657691	+	1.13915i
$567$	−2699.27			−0.199927
$568$	2199.57	+	3809.77i	0.162486	+	0.281433i
$569$	5264.68	−	9118.69i	0.387885	−	0.671837i	−0.604280	−	0.796772i	$-0.706539\pi$
$569$	5264.68	−	9118.69i	0.387885	−	0.671837i	0.992165	+	0.124935i	$0.0398723\pi$
$570$	753.488			0.0553686
$571$	−10530.3	+	18238.9i	−0.771765	+	1.33674i	0.164830	+	0.986322i	$0.447292\pi$
$571$	−10530.3	+	18238.9i	−0.771765	+	1.33674i	−0.936595	+	0.350414i	$0.886041\pi$
$572$	7445.26	+	12895.6i	0.544234	+	0.942641i
$573$	6730.49	+	11657.6i	0.490699	+	0.849915i
$574$	−229.908	−	398.212i	−0.0167181	−	0.0289565i
$575$	−12372.8			−0.897356
$576$	5369.71	+	9300.61i	0.388434	+	0.672787i
$577$	416.075	+	720.662i	0.0300198	+	0.0519958i	0.880645	−	0.473777i	$-0.157110\pi$
$577$	416.075	+	720.662i	0.0300198	+	0.0519958i	−0.850625	+	0.525773i	$0.823776\pi$
$578$	−26060.4	+	45138.0i	−1.87538	+	3.24826i
$579$	4307.70	−	7461.16i	0.309192	−	0.535536i
$580$	3552.31			0.254313
$581$	5397.07			0.385384
$582$	1318.18	−	2283.16i	0.0938839	−	0.162612i
$583$	1055.02	−	1827.35i	0.0749476	−	0.129813i
$584$	−2770.95	−	4799.43i	−0.196340	−	0.340071i
$585$	21531.8	+	37294.1i	1.52176	+	2.63576i
$586$	−1985.51			−0.139967
$587$	10915.6	+	18906.3i	0.767519	+	1.32938i	0.938905	+	0.344177i	$0.111842\pi$
$587$	10915.6	+	18906.3i	0.767519	+	1.32938i	−0.171386	+	0.985204i	$0.554825\pi$
$588$	−8119.64	−	14063.6i	−0.569470	−	0.986351i
$589$	61.0714	+	105.779i	0.00427233	+	0.00739989i
$590$	−16152.1	+	27976.3i	−1.12707	+	1.95215i
$591$	−12267.3			−0.853820
$592$	9349.31	−	16193.5i	0.649078	−	1.12424i
$593$	−11288.2	−	19551.7i	−0.781702	−	1.35395i	−0.930950	−	0.365147i	$-0.881019\pi$
$593$	−11288.2	−	19551.7i	−0.781702	−	1.35395i	0.149248	−	0.988800i	$-0.452315\pi$
$594$	−5898.04			−0.407407
$595$	−6417.55	−	11115.5i	−0.442175	−	0.765869i
$596$	2349.58	−	4069.59i	0.161481	−	0.279693i
$597$	13964.0	−	24186.3i	0.957299	−	1.65809i
$598$	16557.6			1.13226
$599$	1463.19	−	2534.31i	0.0998065	−	0.172870i	−0.811798	−	0.583938i	$-0.801511\pi$
$599$	1463.19	−	2534.31i	0.0998065	−	0.172870i	0.911604	+	0.411068i	$0.134844\pi$
$600$	8358.66			0.568734
$601$	26815.7			1.82003			0.910013	−	0.414579i	$-0.136071\pi$
$601$	26815.7			1.82003			0.910013	+	0.414579i	$0.136071\pi$
$602$	−3804.54	−	4114.43i	−0.257577	−	0.278558i
$603$	10950.2			0.739513
$604$	11250.2			0.757887
$605$	3046.11	−	5276.01i	0.204697	−	0.354546i
$606$	−37923.9			−2.54217
$607$	−9814.75	+	16999.6i	−0.656290	+	1.13673i	0.325278	+	0.945618i	$0.394542\pi$
$607$	−9814.75	+	16999.6i	−0.656290	+	1.13673i	−0.981569	+	0.191110i	$0.938791\pi$
$608$	−166.140	+	287.762i	−0.0110820	+	0.0191946i
$609$	597.389	+	1034.71i	0.0397495	+	0.0688481i
$610$	−40233.6			−2.67051
$611$	−38.5971	−	66.8521i	−0.00255560	−	0.00442643i
$612$	−15005.7	+	25990.6i	−0.991124	+	1.71668i
$613$	−14870.5			−0.979793			−0.489896	−	0.871781i	$-0.662965\pi$
$613$	−14870.5			−0.979793			−0.489896	+	0.871781i	$0.662965\pi$
$614$	−2282.04	+	3952.62i	−0.149993	+	0.259796i
$615$	1628.82	+	2821.21i	0.106798	+	0.184979i
$616$	433.053	+	750.070i	0.0283250	+	0.0490604i
$617$	−1619.19	−	2804.53i	−0.105650	−	0.182992i	0.808353	−	0.588698i	$-0.200359\pi$
$617$	−1619.19	−	2804.53i	−0.105650	−	0.182992i	−0.914004	+	0.405706i	$0.867026\pi$
$618$	27553.7			1.79349
$619$	−10066.8	−	17436.2i	−0.653666	−	1.13218i	−0.982226	−	0.187700i	$-0.939897\pi$
$619$	−10066.8	−	17436.2i	−0.653666	−	1.13218i	0.328560	−	0.944483i	$-0.393437\pi$
$620$	−5236.28	−	9069.51i	−0.339184	−	0.587484i
$621$	−1484.63	+	2571.46i	−0.0959359	+	0.166166i
$622$	4948.18	−	8570.51i	0.318978	−	0.552486i
$623$	4549.39			0.292564
$624$	−40510.7			−2.59892
$625$	−214.392	+	371.338i	−0.0137211	+	0.0237656i
$626$	−810.058	+	1403.06i	−0.0517195	+	0.0895809i
$627$	−171.418	−	296.905i	−0.0109183	−	0.0189111i
$628$	−4506.88	−	7806.14i	−0.286376	−	0.496017i
$629$	34813.4			2.20684
$630$	−5999.60	−	10391.6i	−0.379412	−	0.657161i
$631$	3113.67	+	5393.03i	0.196439	+	0.340243i	0.947371	−	0.320137i	$-0.103729\pi$
$631$	3113.67	+	5393.03i	0.196439	+	0.340243i	−0.750932	+	0.660379i	$0.770395\pi$
$632$	2134.96	+	3697.85i	0.134373	+	0.232741i
$633$	15248.0	−	26410.3i	0.957432	−	1.65832i
$634$	5233.47			0.327835
$635$	9816.04	−	17001.9i	0.613445	−	1.06252i
$636$	−1718.91	−	2977.23i	−0.107168	−	0.185621i
$637$	22537.3			1.40182
$638$	−1785.00	−	3091.71i	−0.110766	−	0.191853i
$639$	−13865.3	+	24015.4i	−0.858378	+	1.48675i
$640$	−6038.54	+	10459.1i	−0.372959	+	0.645985i
$641$	12495.3			0.769945			0.384973	−	0.922928i	$-0.374211\pi$
$641$	12495.3			0.769945			0.384973	+	0.922928i	$0.374211\pi$
$642$	−17726.7	+	30703.5i	−1.08974	+	1.88749i
$643$	4940.90			0.303033			0.151516	−	0.988455i	$-0.451584\pi$
$643$	4940.90			0.303033			0.151516	+	0.988455i	$0.451584\pi$
$644$	−2088.78			−0.127810
$645$	26953.9	+	29149.4i	1.64544	+	1.77947i
$646$	−728.764			−0.0443852
$647$	6624.13			0.402506			0.201253	−	0.979539i	$-0.435499\pi$
$647$	6624.13			0.402506			0.201253	+	0.979539i	$0.435499\pi$
$648$	−1371.54	+	2375.58i	−0.0831468	+	0.144015i
$649$	14698.4			0.889004
$650$	27785.8	−	48126.4i	1.67669	−	2.90411i
$651$	1761.16	−	3050.42i	0.106030	−	0.183649i
$652$	−9535.72	−	16516.3i	−0.572772	−	0.992071i
$653$	−4497.38			−0.269519			−0.134760	−	0.990878i	$-0.543026\pi$
$653$	−4497.38			−0.269519			−0.134760	+	0.990878i	$0.543026\pi$
$654$	9967.19	+	17263.7i	0.595945	+	1.03221i
$655$	−12424.0	+	21519.1i	−0.741141	+	1.28369i
$656$	−1692.30			−0.100722
$657$	17467.1	−	30253.9i	1.03723	−	1.79653i
$658$	10.7547	+	18.6276i	0.000637174	+	0.00110362i
$659$	−13154.2	−	22783.7i	−0.777562	−	1.34678i	−0.933343	−	0.358986i	$-0.883123\pi$
$659$	−13154.2	−	22783.7i	−0.777562	−	1.34678i	0.155781	−	0.987792i	$-0.450211\pi$
$660$	14697.5	+	25456.8i	0.866816	+	1.50137i
$661$	15971.0			0.939788			0.469894	−	0.882723i	$-0.344292\pi$
$661$	15971.0			0.939788			0.469894	+	0.882723i	$0.344292\pi$
$662$	4692.43	+	8127.52i	0.275493	+	0.477168i
$663$	−37711.7	−	65318.5i	−2.20905	−	3.82619i
$664$	2742.33	−	4749.85i	0.160276	−	0.277605i
$665$	65.9596	−	114.245i	0.00384632	−	0.00666202i
$666$	32546.1			1.89360
$667$	−1797.25			−0.104333
$668$	−3265.47	+	5655.96i	−0.189139	+	0.327598i
$669$	−970.034	+	1680.15i	−0.0560593	+	0.0970976i
$670$	−11399.3	−	19744.2i	−0.657304	−	1.13848i
$671$	9153.15	+	15853.7i	0.526607	+	0.912110i
$672$	9582.18			0.550061
$673$	−1639.81	−	2840.23i	−0.0939226	−	0.162679i	0.815236	−	0.579129i	$-0.196607\pi$
$673$	−1639.81	−	2840.23i	−0.0939226	−	0.162679i	−0.909158	+	0.416450i	$0.863274\pi$
$674$	−14164.0	−	24532.7i	−0.809459	−	1.40202i
$675$	4982.82	+	8630.49i	0.284131	+	0.492130i
$676$	−9564.39	+	16566.0i	−0.544174	+	0.942536i
$677$	−33062.8			−1.87697			−0.938483	−	0.345325i	$-0.887769\pi$
$677$	−33062.8			−1.87697			−0.938483	+	0.345325i	$0.887769\pi$
$678$	−3915.77	+	6782.32i	−0.221806	+	0.384179i
$679$	−230.785	−	399.731i	−0.0130438	−	0.0225924i
$680$	−13043.4			−0.735576
$681$	20313.6	+	35184.3i	1.14306	+	1.97983i
$682$	−5262.36	+	9114.67i	−0.295463	+	0.511758i
$683$	14092.9	−	24409.6i	0.789531	−	1.36751i	−0.136723	−	0.990609i	$-0.543657\pi$
$683$	14092.9	−	24409.6i	0.789531	−	1.36751i	0.926255	−	0.376899i	$-0.123009\pi$
$684$	−308.456			−0.0172429
$685$	−9075.81	+	15719.8i	−0.506232	+	0.876819i
$686$	−13096.5			−0.728903
$687$	7364.49			0.408985
$688$	−20115.1	+	4554.89i	−1.11465	+	0.252403i
$689$	4771.08			0.263808
$690$	32685.8			1.80337
$691$	10378.3	−	17975.7i	0.571359	−	0.989623i	−0.425068	−	0.905162i	$-0.639750\pi$
$691$	10378.3	−	17975.7i	0.571359	−	0.989623i	0.996427	−	0.0844613i	$-0.0269169\pi$
$692$	3938.05			0.216332
$693$	−2729.82	+	4728.18i	−0.149635	+	0.259176i
$694$	19357.0	−	33527.3i	1.05876	−	1.83383i
$695$	5426.31	+	9398.65i	0.296161	+	0.512966i
$696$	1214.17			0.0661248
$697$	−1575.38	−	2728.63i	−0.0856122	−	0.148285i
$698$	−129.625	+	224.517i	−0.00702918	+	0.0121749i
$699$	−26808.3			−1.45062
$700$	−3505.25	+	6071.27i	−0.189266	+	0.327818i
$701$	16476.6	+	28538.4i	0.887751	+	1.53763i	0.842528	+	0.538653i	$0.181067\pi$
$701$	16476.6	+	28538.4i	0.887751	+	1.53763i	0.0452237	+	0.998977i	$0.485600\pi$
$702$	−6668.14	−	11549.5i	−0.358508	−	0.620954i
$703$	178.906	+	309.874i	0.00959823	+	0.0166246i
$704$	−10173.7			−0.544653
$705$	−76.1934	−	131.971i	−0.00407037	−	0.00705008i
$706$	12856.3	+	22267.8i	0.685346	+	1.18705i
$707$	−3319.82	+	5750.10i	−0.176598	+	0.305877i
$708$	11973.8	−	20739.2i	0.635598	−	1.10089i
$709$	10596.1			0.561276			0.280638	−	0.959814i	$-0.409454\pi$
$709$	10596.1			0.561276			0.280638	+	0.959814i	$0.409454\pi$
$710$	57736.0			3.05182
$711$	−13458.0	+	23310.0i	−0.709866	+	1.22952i
$712$	2311.61	−	4003.82i	0.121673	−	0.210744i
$713$	2649.24	+	4588.61i	0.139151	+	0.241017i
$714$	10508.0	+	18200.3i	0.550771	+	0.953963i
$715$	−40795.1			−2.13378
$716$	−7678.40	−	13299.4i	−0.400776	−	0.694164i
$717$	−4014.43	−	6953.19i	−0.209096	−	0.362164i
$718$	17704.1	+	30664.4i	0.920209	+	1.59385i
$719$	13540.8	−	23453.3i	0.702344	−	1.21649i	−0.265298	−	0.964166i	$-0.585470\pi$
$719$	13540.8	−	23453.3i	0.702344	−	1.21649i	0.967642	−	0.252328i	$-0.0811963\pi$
$720$	−44161.8			−2.28585
$721$	2412.03	−	4177.75i	0.124589	−	0.215794i
$722$	13108.6	+	22704.8i	0.675696	+	1.17034i
$723$	−7189.72			−0.369832
$724$	−5066.98	−	8776.27i	−0.260101	−	0.450508i
$725$	−3016.03	+	5223.91i	−0.154500	+	0.267602i
$726$	−4987.63	+	8638.82i	−0.254970	+	0.441621i
$727$	−2011.78			−0.102631			−0.0513155	−	0.998682i	$-0.516341\pi$
$727$	−2011.78			−0.102631			−0.0513155	+	0.998682i	$0.516341\pi$
$728$	−979.191	+	1696.01i	−0.0498506	+	0.0863438i
$729$	−27544.6			−1.39941
$730$	−72734.1			−3.68768
$731$	−26069.5	−	28193.0i	−1.31904	−	1.42648i
$732$	29825.8			1.50600
$733$	9401.81			0.473757			0.236878	−	0.971539i	$-0.423876\pi$
$733$	9401.81			0.473757			0.236878	+	0.971539i	$0.423876\pi$
$734$	−2256.69	+	3908.70i	−0.113482	+	0.196557i
$735$	44490.3			2.23272
$736$	−7207.02	+	12482.9i	−0.360944	+	0.625173i
$737$	−5186.69	+	8983.61i	−0.259232	+	0.449003i
$738$	−1472.78	−	2550.93i	−0.0734603	−	0.127237i
$739$	−18781.6			−0.934900			−0.467450	−	0.884019i	$-0.654827\pi$
$739$	−18781.6			−0.934900			−0.467450	+	0.884019i	$0.654827\pi$
$740$	−15339.4	−	26568.7i	−0.762012	−	1.31984i
$741$	387.600	−	671.343i	0.0192157	−	0.0332826i
$742$	−1329.41			−0.0657739
$743$	−16049.8	+	27799.0i	−0.792474	+	1.37261i	0.131957	+	0.991255i	$0.457874\pi$
$743$	−16049.8	+	27799.0i	−0.792474	+	1.37261i	−0.924431	+	0.381350i	$0.875459\pi$
$744$	−1789.74	−	3099.92i	−0.0881924	−	0.152754i
$745$	6437.06	+	11149.3i	0.316558	+	0.548294i
$746$	11746.2	+	20345.1i	0.576488	+	0.998506i
$747$	34573.4			1.69340
$748$	−14215.2	−	24621.5i	−0.694866	−	1.20354i
$749$	3103.55	+	5375.50i	0.151403	+	0.262238i
$750$	21205.1	−	36728.3i	1.03240	−	1.78817i
$751$	11491.3	−	19903.5i	0.558353	−	0.967096i	−0.439281	−	0.898350i	$-0.644767\pi$
$751$	11491.3	−	19903.5i	0.558353	−	0.967096i	0.997634	−	0.0687463i	$-0.0218999\pi$
$752$	79.1628			0.00383879
$753$	10687.8			0.517245
$754$	4036.13	−	6990.77i	0.194943	−	0.337651i
$755$	−15410.9	+	26692.4i	−0.742860	+	1.28667i
$756$	841.203	+	1457.01i	0.0404686	+	0.0700937i
$757$	−2335.41	−	4045.05i	−0.112129	−	0.194214i	0.804499	−	0.593954i	$-0.202434\pi$
$757$	−2335.41	−	4045.05i	−0.112129	−	0.194214i	−0.916629	+	0.399740i	$0.869100\pi$
$758$	−32318.4			−1.54862
$759$	−7436.02	−	12879.6i	−0.355613	−	0.615940i
$760$	−67.0300	−	116.099i	−0.00319925	−	0.00554127i
$761$	7385.83	+	12792.6i	0.351821	+	0.609372i	0.986569	−	0.163347i	$-0.0522291\pi$
$761$	7385.83	+	12792.6i	0.351821	+	0.609372i	−0.634747	+	0.772720i	$0.718896\pi$
$762$	−16072.6	+	27838.5i	−0.764104	+	1.32347i
$763$	3490.07			0.165595
$764$	−5736.55	+	9936.00i	−0.271651	+	0.470513i
$765$	−41110.5	−	71205.5i	−1.94295	−	3.36528i
$766$	14513.7			0.684598
$767$	16617.6	+	28782.5i	0.782302	+	1.35499i
$768$	19905.2	−	34476.9i	0.935245	−	1.61989i
$769$	−7825.32	+	13553.9i	−0.366955	+	0.635585i	−0.989088	−	0.147327i	$-0.952933\pi$
$769$	−7825.32	+	13553.9i	−0.366955	+	0.635585i	0.622133	+	0.782912i	$0.286266\pi$
$770$	11367.1			0.532003
$771$	−2260.87	+	3915.95i	−0.105607	+	0.182918i
$772$	7343.10			0.342337
$773$	−31462.6			−1.46395			−0.731975	−	0.681332i	$-0.761401\pi$
$773$	−31462.6			−1.46395			−0.731975	+	0.681332i	$0.761401\pi$
$774$	−24371.7	−	26356.8i	−1.13181	−	1.22400i
$775$	17783.1			0.824242
$776$	−469.060			−0.0216988
$777$	5159.24	−	8936.07i	0.238207	−	0.412586i
$778$	47304.6			2.17989
$779$	16.1917	−	28.0449i	0.000744709	−	0.00128987i
$780$	−33233.0	+	57561.2i	−1.52555	+	2.64234i
$781$	−13134.9	−	22750.4i	−0.601799	−	1.04235i
$782$	−31613.3			−1.44564
$783$	723.797	+	1253.65i	0.0330350	+	0.0572183i
$784$	−11556.0	+	20015.6i	−0.526423	+	0.911792i
$785$	24694.7			1.12279
$786$	20342.8	−	35234.8i	0.923161	−	1.59896i
$787$	−7058.28	−	12225.3i	−0.319696	−	0.553729i	0.660729	−	0.750625i	$-0.270247\pi$
$787$	−7058.28	−	12225.3i	−0.319696	−	0.553729i	−0.980424	+	0.196896i	$0.936914\pi$
$788$	−5227.83	−	9054.86i	−0.236337	−	0.409348i
$789$	−507.306	−	878.679i	−0.0228904	−	0.0396474i
$790$	56040.0			2.52381
$791$	685.566	+	1187.43i	0.0308166	+	0.0533759i
$792$	2774.12	+	4804.91i	0.124462	+	0.215574i
$793$	−20696.5	+	35847.4i	−0.926802	+	1.60527i
$794$	23945.0	−	41473.9i	1.07024	−	1.85372i
$795$	9418.46			0.420174
$796$	23803.6			1.05992
$797$	−10765.8	+	18646.8i	−0.478473	+	0.828739i	−0.999695	−	0.0246816i	$-0.992143\pi$
$797$	−10765.8	+	18646.8i	−0.478473	+	0.828739i	0.521223	+	0.853421i	$0.325476\pi$
$798$	−108.001	+	187.063i	−0.00479095	+	0.00829818i
$799$	73.6932	+	127.640i	0.00326293	+	0.00565156i
$800$	24188.7	+	41896.0i	1.06900	+	1.85156i
$801$	29143.1			1.28555
$802$	−16330.6	−	28285.4i	−0.719018	−	1.24538i
$803$	16547.0	+	28660.2i	0.727187	+	1.25952i
$804$	8450.48	+	14636.7i	0.370678	+	0.642034i
$805$	2861.28	−	4955.89i	0.125276	−	0.216984i
$806$	−23797.8			−1.04000
$807$	−28151.1	+	48759.1i	−1.22796	+	2.12689i
$808$	3373.70	+	5843.41i	0.146889	+	0.254419i
$809$	−9241.88			−0.401641			−0.200820	−	0.979628i	$-0.564361\pi$
$809$	−9241.88			−0.401641			−0.200820	+	0.979628i	$0.564361\pi$
$810$	18000.6	+	31178.0i	0.780836	+	1.35245i
$811$	−12586.9	+	21801.2i	−0.544989	+	0.943948i	0.453619	+	0.891196i	$0.350133\pi$
$811$	−12586.9	+	21801.2i	−0.544989	+	0.943948i	−0.998608	+	0.0527525i	$0.983201\pi$
$812$	−509.168	+	881.905i	−0.0220053	+	0.0381143i
$813$	−32768.3			−1.41357
$814$	−15415.8	+	26701.0i	−0.663789	+	1.14972i
$815$	52249.4			2.24566
$816$	77346.9			3.31824
$817$	116.975	−	376.928i	0.00500909	−	0.0161408i
$818$	−34977.8			−1.49507
$819$	−12345.0			−0.526701
$820$	−1388.28	+	2404.58i	−0.0591231	+	0.102404i
$821$	−10451.1			−0.444272			−0.222136	−	0.975016i	$-0.571303\pi$
$821$	−10451.1			−0.444272			−0.222136	+	0.975016i	$0.571303\pi$
$822$	14860.5	−	25739.2i	0.630560	−	1.09216i
$823$	−2378.95	+	4120.47i	−0.100760	+	0.174521i	−0.911998	−	0.410195i	$-0.865461\pi$
$823$	−2378.95	+	4120.47i	−0.100760	+	0.174521i	0.811238	+	0.584716i	$0.198794\pi$
$824$	−2451.17	−	4245.55i	−0.103629	−	0.179491i
$825$	−49914.5			−2.10642
$826$	−4630.31	−	8019.92i	−0.195047	−	0.337832i
$827$	7952.70	−	13774.5i	0.334393	−	0.579185i	−0.648975	−	0.760809i	$-0.724802\pi$
$827$	7952.70	−	13774.5i	0.334393	−	0.579185i	0.983368	+	0.181624i	$0.0581355\pi$
$828$	−13380.6			−0.561605
$829$	1971.61	−	3414.92i	0.0826016	−	0.143070i	−0.821765	−	0.569826i	$-0.807010\pi$
$829$	1971.61	−	3414.92i	0.0826016	−	0.143070i	0.904367	+	0.426756i	$0.140344\pi$
$830$	−35991.4	−	62338.9i	−1.50516	−	2.60701i
$831$	1544.94	+	2675.92i	0.0644927	+	0.111705i
$832$	−11502.1	−	19922.1i	−0.479281	−	0.830139i
$833$	−43030.4			−1.78981
$834$	−8884.92	−	15389.1i	−0.368896	−	0.638947i
$835$	−8946.30	−	15495.5i	−0.370778	−	0.642206i
$836$	146.104	−	253.059i	0.00604438	−	0.0104692i
$837$	2133.83	−	3695.89i	0.0881192	−	0.152627i
$838$	33576.7			1.38411
$839$	−19902.5			−0.818962			−0.409481	−	0.912319i	$-0.634290\pi$
$839$	−19902.5			−0.818962			−0.409481	+	0.912319i	$0.634290\pi$
$840$	−1932.99	+	3348.04i	−0.0793983	+	0.137522i
$841$	11756.4	−	20362.7i	0.482037	−	0.834912i
$842$	14765.9	+	25575.2i	0.604353	+	1.04677i
$843$	−20438.7	−	35400.8i	−0.835047	−	1.44634i
$844$	25992.5			1.06007
$845$	−26203.3	−	45385.4i	−1.06677	−	1.84770i
$846$	68.8938	+	119.328i	0.00279978	+	0.00484937i
$847$	873.224	+	1512.47i	0.0354242	+	0.0613566i
$848$	−2446.38	+	4237.26i	−0.0990673	+	0.171590i
$849$	35973.1			1.45417
$850$	−53051.3	+	91887.5i	−2.14076	+	3.70790i
$851$	7760.81	+	13442.1i	0.312617	+	0.541469i
$852$	−42800.6			−1.72104
$853$	−22036.0	−	38167.4i	−0.884521	−	1.53204i	−0.846261	−	0.532768i	$-0.821152\pi$
$853$	−22036.0	−	38167.4i	−0.884521	−	1.53204i	−0.0382598	−	0.999268i	$-0.512181\pi$
$854$	5766.86	−	9988.49i	0.231075	−	0.400233i
$855$	422.534	−	731.850i	0.0169010	−	0.0292734i
$856$	6307.82			0.251866
$857$	8575.26	−	14852.8i	0.341803	−	0.592020i	−0.642965	−	0.765896i	$-0.722296\pi$
$857$	8575.26	−	14852.8i	0.341803	−	0.592020i	0.984768	+	0.173876i	$0.0556291\pi$
$858$	66796.9			2.65782
$859$	48887.4			1.94181			0.970907	−	0.239457i	$-0.0769695\pi$
$859$	48887.4			1.94181			0.970907	+	0.239457i	$0.0769695\pi$
$860$	−10029.4	+	32317.9i	−0.397676	+	1.28143i
$861$	−933.865			−0.0369640
$862$	−22655.3			−0.895175
$863$	19432.1	−	33657.5i	0.766486	−	1.32759i	−0.172971	−	0.984927i	$-0.555337\pi$
$863$	19432.1	−	33657.5i	0.766486	−	1.32759i	0.939457	−	0.342667i	$-0.111330\pi$
$864$	11609.8			0.457145
$865$	−5394.47	+	9343.49i	−0.212043	+	0.367270i
$866$	7473.31	−	12944.2i	0.293249	−	0.507922i
$867$	52927.6	+	91673.3i	2.07326	+	3.59099i
$868$	3002.16			0.117396
$869$	−12749.1	−	22082.1i	−0.497679	−	0.862006i
$870$	7967.60	−	13800.3i	0.310491	−	0.537786i
$871$	−23455.6			−0.912471
$872$	1773.35	−	3071.54i	0.0688685	−	0.119284i
$873$	−1478.40	−	2560.66i	−0.0573151	−	0.0992727i
$874$	−162.461	−	281.390i	−0.00628754	−	0.0108903i
$875$	−3712.54	−	6430.31i	−0.143436	−	0.248439i
$876$	53918.9			2.07962
$877$	6291.82	+	10897.8i	0.242258	+	0.419602i	0.961357	−	0.275305i	$-0.0887788\pi$
$877$	6291.82	+	10897.8i	0.242258	+	0.419602i	−0.719099	+	0.694907i	$0.755445\pi$
$878$	8490.36	+	14705.7i	0.326351	+	0.565256i
$879$	−2016.25	+	3492.24i	−0.0773678	+	0.134005i
$880$	20917.7	−	36230.6i	0.801292	−	1.38788i
$881$	−27901.3			−1.06699			−0.533495	−	0.845803i	$-0.679122\pi$
$881$	−27901.3			−1.06699			−0.533495	+	0.845803i	$0.679122\pi$
$882$	−40227.9			−1.53577
$883$	25089.8	−	43456.7i	0.956215	−	1.65621i	0.224651	−	0.974439i	$-0.427876\pi$
$883$	25089.8	−	43456.7i	0.956215	−	1.65621i	0.731564	−	0.681773i	$-0.238791\pi$
$884$	32142.5	−	55672.4i	1.22293	−	2.11818i
$885$	32804.2	+	56818.6i	1.24599	+	2.15812i
$886$	14743.6	+	25536.6i	0.559052	+	0.968306i
$887$	−9359.99			−0.354315			−0.177158	−	0.984182i	$-0.556690\pi$
$887$	−9359.99			−0.354315			−0.177158	+	0.984182i	$0.556690\pi$
$888$	−5242.96	−	9081.08i	−0.198133	−	0.343177i
$889$	2813.95	+	4873.91i	0.106161	+	0.183876i
$890$	−30338.4	−	52547.7i	−1.14264	−	1.97910i
$891$	8190.28	−	14186.0i	0.307951	−	0.533387i
$892$	−1653.56			−0.0620688
$893$	−0.757418	+	1.31189i	−2.83830e−5	+	4.91608e-5i
$894$	−10539.9	−	18255.6i	−0.394303	−	0.682952i
$895$	42072.5			1.57132
$896$	−1731.06	−	2998.28i	−0.0645431	−	0.111792i
$897$	16813.8	−	29122.4i	0.625861	−	1.08402i
$898$	−2472.75	+	4282.94i	−0.0918896	+	0.159157i
$899$	2583.15			0.0958318
$900$	−22454.5	+	38892.3i	−0.831647	+	1.44045i
$901$	−9109.41			−0.336824
$902$	2790.39			0.103004
$903$	−11100.1	+	2513.53i	−0.409069	+	0.0926301i
$904$	1393.38			0.0512646
$905$	27763.7			1.01978
$906$	25233.4	−	43705.6i	0.925303	−	1.60267i
$907$	−41146.5			−1.50633			−0.753167	−	0.657829i	$-0.771475\pi$
$907$	−41146.5			−1.50633			−0.753167	+	0.657829i	$0.771475\pi$
$908$	−17313.8	+	29988.3i	−0.632795	+	1.09603i
$909$	−21266.6	+	36834.8i	−0.775983	+	1.34404i
$910$	12851.3	+	22259.1i	0.468149	+	0.810859i
$911$	16872.6			0.613626			0.306813	−	0.951770i	$-0.400737\pi$
$911$	16872.6			0.613626			0.306813	+	0.951770i	$0.400737\pi$
$912$	397.485	+	688.465i	0.0144321	+	0.0249971i
$913$	−16376.1	+	28364.2i	−0.593613	+	1.02817i
$914$	−21264.6			−0.769554
$915$	−40856.4	+	70765.3i	−1.47614	+	2.55675i
$916$	3138.46	+	5435.98i	0.113207	+	0.196080i
$917$	−3561.58	−	6168.84i	−0.128259	−	0.222152i
$918$	12731.4	+	22051.5i	0.457735	+	0.792820i
$919$	47698.3			1.71210			0.856052	−	0.516890i	$-0.172910\pi$
$919$	47698.3			1.71210			0.856052	+	0.516890i	$0.172910\pi$
$920$	−2907.72	−	5036.31i	−0.104201	−	0.180481i
$921$	4634.73	+	8027.59i	0.165819	+	0.287207i
$922$	30422.3	−	52692.9i	1.08666	−	1.88216i
$923$	29699.9	−	51441.7i	1.05914	−	1.83448i
$924$	−8426.61			−0.300016
$925$	52094.7			1.85174
$926$	−29911.1	+	51807.6i	−1.06149	+	1.83856i
$927$	15451.3	−	26762.5i	0.547452	−	0.948215i
$928$	3513.62	+	6085.76i	0.124289	+	0.215275i
$929$	−8837.39	−	15306.8i	−0.312105	−	0.540582i	0.666713	−	0.745315i	$-0.267701\pi$
$929$	−8837.39	−	15306.8i	−0.312105	−	0.540582i	−0.978818	+	0.204733i	$0.934367\pi$
$930$	−46978.5			−1.65644
$931$	−221.133	−	383.014i	−0.00778447	−	0.0134831i
$932$	−11424.7	−	19788.1i	−0.401531	−	0.695473i
$933$	−10049.5	−	17406.3i	−0.352634	−	0.610780i
$934$	−18092.1	+	31336.4i	−0.633823	+	1.09781i
$935$	77889.9			2.72435
$936$	−6272.65	+	10864.5i	−0.219047	+	0.379400i
$937$	−8778.96	−	15205.6i	−0.306079	−	0.530145i	0.671422	−	0.741075i	$-0.265684\pi$
$937$	−8778.96	−	15205.6i	−0.306079	−	0.530145i	−0.977501	+	0.210931i	$0.932351\pi$
$938$	6535.65			0.227502
$939$	1645.19	+	2849.56i	0.0571766	+	0.0990328i
$940$	64.9413	−	112.482i	0.00225335	−	0.00390292i
$941$	−21468.1	+	37183.8i	−0.743719	+	1.28816i	0.207071	+	0.978326i	$0.433607\pi$
$941$	−21468.1	+	37183.8i	−0.743719	+	1.28816i	−0.950791	+	0.309834i	$0.899727\pi$
$942$	−40434.5			−1.39854
$943$	702.386	−	1216.57i	0.0242554	−	0.0420116i
$944$	−34082.7			−1.17510
$945$	−4609.24			−0.158665
$946$	33167.2	−	7510.43i	1.13991	−	0.258124i
$947$	−4691.32			−0.160979			−0.0804897	−	0.996755i	$-0.525648\pi$
$947$	−4691.32			−0.160979			−0.0804897	+	0.996755i	$0.525648\pi$
$948$	−41543.3			−1.42327
$949$	−37415.0	+	64804.7i	−1.27981	+	2.21670i
$950$	−1090.52			−0.0372433
$951$	5314.48	−	9204.94i	0.181213	−	0.313870i
$952$	1869.57	−	3238.18i	0.0636481	−	0.110242i
$953$	12301.4	+	21306.7i	0.418135	+	0.724232i	0.995752	−	0.0920766i	$-0.0293505\pi$
$953$	12301.4	+	21306.7i	0.418135	+	0.724232i	−0.577617	+	0.816308i	$0.696017\pi$
$954$	−8516.14			−0.289015
$955$	−15716.2	−	27221.3i	−0.532530	−	0.922368i
$956$	3421.59	−	5926.36i	0.115755	−	0.200494i
$957$	−7250.51			−0.244907
$958$	−7381.18	+	12784.6i	−0.248930	+	0.431160i
$959$	−2601.75	−	4506.36i	−0.0876067	−	0.151739i
$960$	−22705.9	−	39327.7i	−0.763363	−	1.32218i
$961$	11087.8	+	19204.7i	0.372187	+	0.644646i
$962$	−69714.5			−2.33647
$963$	19881.2	+	34435.2i	0.665277	+	1.15229i
$964$	−3063.98	−	5306.97i	−0.102369	−	0.177309i
$965$	−10058.8	+	17422.4i	−0.335549	+	0.581188i
$966$	−4685.00	+	8114.65i	−0.156043	+	0.270274i
$967$	1371.38			0.0456056			0.0228028	−	0.999740i	$-0.492741\pi$
$967$	1371.38			0.0456056			0.0228028	+	0.999740i	$0.492741\pi$
$968$	1774.79			0.0589296
$969$	−740.044	+	1281.79i	−0.0245342	+	0.0424945i
$970$	−3078.06	+	5331.36i	−0.101887	+	0.176474i
$971$	−16893.7	−	29260.7i	−0.558335	−	0.967064i	−0.997636	−	0.0687244i	$-0.978107\pi$
$971$	−16893.7	−	29260.7i	−0.558335	−	0.967064i	0.439301	−	0.898340i	$-0.355226\pi$
$972$	−17713.6	−	30680.9i	−0.584532	−	1.01244i
$973$	−3111.11			−0.102505
$974$	−6716.04	−	11632.5i	−0.220940	−	0.382680i
$975$	−56431.7	−	97742.6i	−1.85360	−	3.21053i
$976$	−21224.3	−	36761.6i	−0.696080	−	1.20565i
$977$	−4562.12	+	7901.82i	−0.149391	+	0.258753i	−0.931003	−	0.365013i	$-0.881065\pi$
$977$	−4562.12	+	7901.82i	−0.149391	+	0.258753i	0.781611	+	0.623766i	$0.214398\pi$
$978$	−85551.9			−2.79719
$979$	−13804.0	+	23909.2i	−0.450641	+	0.780533i
$980$	18960.0	+	32839.7i	0.618016	+	1.07044i
$981$	22357.2			0.727636
$982$	36853.4	+	63831.9i	1.19759	+	2.07429i
$983$	4650.33	−	8054.60i	0.150887	−	0.261345i	−0.780666	−	0.624948i	$-0.785120\pi$
$983$	4650.33	−	8054.60i	0.150887	−	0.261345i	0.931554	+	0.363603i	$0.118454\pi$
$984$	−474.510	+	821.875i	−0.0153728	+	0.0266265i
$985$	28645.0			0.926605
$986$	−7706.16	+	13347.5i	−0.248899	+	0.431105i
$987$	43.6845			0.00140881
$988$	660.721			0.0212756
$989$	5074.28	−	16350.9i	0.163147	−	0.525711i
$990$	72817.1			2.33766
$991$	17367.8			0.556717			0.278358	−	0.960477i	$-0.410210\pi$
$991$	17367.8			0.556717			0.278358	+	0.960477i	$0.410210\pi$
$992$	10358.5	−	17941.4i	0.331535	−	0.574235i
$993$	19060.2			0.609122
$994$	−8275.55	+	14333.7i	−0.264069	+	0.457381i
$995$	−32607.0	+	56477.0i	−1.03891	+	1.79944i
$996$	26680.9	+	46212.7i	0.848813	+	1.47019i
$997$	−36720.9			−1.16646			−0.583230	−	0.812307i	$-0.698211\pi$
$997$	−36720.9			−1.16646			−0.583230	+	0.812307i	$0.698211\pi$
$998$	14579.3	+	25252.0i	0.462423	+	0.800940i
$999$	6250.94	−	10826.9i	0.197969	−	0.342892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.6.9	✓	20
43.6	even	3		1849.4.a.d.1.9		10
43.36	even	3	inner	43.4.c.a.36.9	yes	20
43.37	odd	6		1849.4.a.f.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.9	✓	20	1.1	even	1	trivial
43.4.c.a.36.9	yes	20	43.36	even	3	inner
1849.4.a.d.1.9		10	43.6	even	3
1849.4.a.f.1.2		10	43.37	odd	6

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.82341 q^{2} +(3.88258 - 6.72483i) q^{3} +6.61843 q^{4} +(-9.06615 + 15.7030i) q^{5} +(14.8447 - 25.7118i) q^{6} +(-2.59898 - 4.50156i) q^{7} -5.28231 q^{8} +(-16.6489 - 28.8368i) q^{9} +O(q^{10})\)	\(q+3.82341 q^{2} +(3.88258 - 6.72483i) q^{3} +6.61843 q^{4} +(-9.06615 + 15.7030i) q^{5} +(14.8447 - 25.7118i) q^{6} +(-2.59898 - 4.50156i) q^{7} -5.28231 q^{8} +(-16.6489 - 28.8368i) q^{9} +(-34.6635 + 60.0390i) q^{10} +31.5438 q^{11} +(25.6966 - 44.5078i) q^{12} +(35.6624 + 61.7691i) q^{13} +(-9.93695 - 17.2113i) q^{14} +(70.4002 + 121.937i) q^{15} -73.1438 q^{16} +(-68.0901 - 117.936i) q^{17} +(-63.6556 - 110.255i) q^{18} +(0.699830 - 1.21214i) q^{19} +(-60.0036 + 103.929i) q^{20} -40.3630 q^{21} +120.605 q^{22} +(30.3581 - 52.5818i) q^{23} +(-20.5090 + 35.5227i) q^{24} +(-101.890 - 176.479i) q^{25} +(136.352 + 236.168i) q^{26} -48.9039 q^{27} +(-17.2012 - 29.7933i) q^{28} +(-14.8004 - 25.6351i) q^{29} +(269.168 + 466.213i) q^{30} +(-43.6330 + 75.5747i) q^{31} -237.400 q^{32} +(122.472 - 212.127i) q^{33} +(-260.336 - 450.915i) q^{34} +94.2509 q^{35} +(-110.190 - 190.854i) q^{36} +(-127.821 + 221.392i) q^{37} +(2.67573 - 4.63450i) q^{38} +553.849 q^{39} +(47.8902 - 82.9483i) q^{40} +23.1367 q^{41} -154.324 q^{42} +(275.007 - 62.2731i) q^{43} +208.771 q^{44} +603.766 q^{45} +(116.071 - 201.042i) q^{46} -1.08229 q^{47} +(-283.987 + 491.880i) q^{48} +(157.991 - 273.648i) q^{49} +(-389.567 - 674.749i) q^{50} -1057.46 q^{51} +(236.029 + 408.814i) q^{52} +(33.4462 - 57.9305i) q^{53} -186.979 q^{54} +(-285.981 + 495.333i) q^{55} +(13.7286 + 23.7787i) q^{56} +(-5.43429 - 9.41247i) q^{57} +(-56.5879 - 98.0132i) q^{58} +465.968 q^{59} +(465.938 + 807.029i) q^{60} +(290.172 + 502.593i) q^{61} +(-166.827 + 288.953i) q^{62} +(-86.5404 + 149.892i) q^{63} -322.526 q^{64} -1293.28 q^{65} +(468.258 - 811.047i) q^{66} +(-164.428 + 284.798i) q^{67} +(-450.649 - 780.548i) q^{68} +(-235.736 - 408.307i) q^{69} +360.359 q^{70} +(-416.403 - 721.231i) q^{71} +(87.9448 + 152.325i) q^{72} +(524.572 + 908.585i) q^{73} +(-488.711 + 846.473i) q^{74} -1582.39 q^{75} +(4.63177 - 8.02246i) q^{76} +(-81.9817 - 141.997i) q^{77} +2117.59 q^{78} +(-404.171 - 700.044i) q^{79} +(663.133 - 1148.58i) q^{80} +(259.648 - 449.723i) q^{81} +88.4608 q^{82} +(-519.153 + 899.199i) q^{83} -267.140 q^{84} +2469.26 q^{85} +(1051.46 - 238.095i) q^{86} -229.855 q^{87} -166.624 q^{88} +(-437.613 + 757.968i) q^{89} +2308.44 q^{90} +(185.372 - 321.073i) q^{91} +(200.923 - 348.009i) q^{92} +(338.818 + 586.850i) q^{93} -4.13803 q^{94} +(12.6895 + 21.9789i) q^{95} +(-921.726 + 1596.48i) q^{96} +88.7982 q^{97} +(604.062 - 1046.27i) q^{98} +(-525.171 - 909.622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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