LMFDB - Embedded newform 77.4.f.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,4,Mod(15,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("77.15");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.f (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:	$4.54314707044$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	77.15
Dual form			77.4.f.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.31524 - 2.40867i) q^{2} +(-0.224082 + 0.689654i) q^{3} +(2.71704 + 8.36218i) q^{4} +(-1.39631 + 1.01448i) q^{5} +(2.40403 - 1.74663i) q^{6} +(2.16312 + 6.65740i) q^{7} +(1.00357 - 3.08868i) q^{8} +(21.4180 + 15.5611i) q^{9} +O(q^{10})$	\(q+(-3.31524 - 2.40867i) q^{2} +(-0.224082 + 0.689654i) q^{3} +(2.71704 + 8.36218i) q^{4} +(-1.39631 + 1.01448i) q^{5} +(2.40403 - 1.74663i) q^{6} +(2.16312 + 6.65740i) q^{7} +(1.00357 - 3.08868i) q^{8} +(21.4180 + 15.5611i) q^{9} +7.07264 q^{10} +(28.8768 - 22.2965i) q^{11} -6.37585 q^{12} +(-19.4797 - 14.1528i) q^{13} +(8.86417 - 27.2811i) q^{14} +(-0.386751 - 1.19030i) q^{15} +(46.1397 - 33.5224i) q^{16} +(107.498 - 78.1017i) q^{17} +(-33.5245 - 103.178i) q^{18} +(-10.2884 + 31.6646i) q^{19} +(-12.2771 - 8.91981i) q^{20} -5.07602 q^{21} +(-149.438 + 4.36369i) q^{22} +95.8630 q^{23} +(1.90524 + 1.38424i) q^{24} +(-37.7066 + 116.049i) q^{25} +(30.4905 + 93.8400i) q^{26} +(-31.3709 + 22.7923i) q^{27} +(-49.7931 + 36.1768i) q^{28} +(15.0677 + 46.3735i) q^{29} +(-1.58485 + 4.87768i) q^{30} +(239.688 + 174.143i) q^{31} -259.690 q^{32} +(8.90607 + 24.9112i) q^{33} -544.502 q^{34} +(-9.77416 - 7.10134i) q^{35} +(-71.9313 + 221.382i) q^{36} +(59.0199 + 181.645i) q^{37} +(110.378 - 80.1944i) q^{38} +(14.1256 - 10.2628i) q^{39} +(1.73210 + 5.33085i) q^{40} +(68.8506 - 211.900i) q^{41} +(16.8282 + 12.2264i) q^{42} -302.665 q^{43} +(264.906 + 180.893i) q^{44} -45.6926 q^{45} +(-317.809 - 230.902i) q^{46} +(64.7197 - 199.187i) q^{47} +(12.7798 + 39.3322i) q^{48} +(-39.6418 + 28.8015i) q^{49} +(404.530 - 293.908i) q^{50} +(29.7748 + 91.6375i) q^{51} +(65.4214 - 201.346i) q^{52} +(103.903 + 75.4896i) q^{53} +158.901 q^{54} +(-17.7016 + 60.4276i) q^{55} +22.7334 q^{56} +(-19.5321 - 14.1909i) q^{57} +(61.7453 - 190.033i) q^{58} +(119.682 + 368.343i) q^{59} +(8.90266 - 6.46816i) q^{60} +(594.964 - 432.266i) q^{61} +(-375.170 - 1154.66i) q^{62} +(-57.2668 + 176.249i) q^{63} +(491.817 + 357.326i) q^{64} +41.5573 q^{65} +(30.4770 - 104.039i) q^{66} -1021.56 q^{67} +(945.176 + 686.711i) q^{68} +(-21.4812 + 66.1123i) q^{69} +(15.2990 + 47.0854i) q^{70} +(171.731 - 124.770i) q^{71} +(69.5579 - 50.5368i) q^{72} +(-182.865 - 562.801i) q^{73} +(241.856 - 744.356i) q^{74} +(-71.5843 - 52.0090i) q^{75} -292.739 q^{76} +(210.900 + 144.014i) q^{77} -71.5495 q^{78} +(292.491 + 212.507i) q^{79} +(-30.4175 + 93.6153i) q^{80} +(212.197 + 653.075i) q^{81} +(-738.654 + 536.663i) q^{82} +(-303.345 + 220.393i) q^{83} +(-13.7917 - 42.4466i) q^{84} +(-70.8676 + 218.108i) q^{85} +(1003.41 + 729.020i) q^{86} -35.3581 q^{87} +(-39.8867 - 111.567i) q^{88} -632.790 q^{89} +(151.482 + 110.058i) q^{90} +(52.0840 - 160.298i) q^{91} +(260.463 + 801.624i) q^{92} +(-173.808 + 126.279i) q^{93} +(-694.336 + 504.465i) q^{94} +(-17.7572 - 54.6509i) q^{95} +(58.1918 - 179.096i) q^{96} +(-1017.89 - 739.539i) q^{97} +200.796 q^{98} +(965.442 - 28.1915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9	\( 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9} - 72 q^{10} - 94 q^{11} - 544 q^{12} + 72 q^{13} + 56 q^{14} + 140 q^{15} + 296 q^{16} + 8 q^{17} + 422 q^{18} + 51 q^{19} - 149 q^{20} - 294 q^{21} - 66 q^{22} - 830 q^{23} + 868 q^{24} - 256 q^{25} + 775 q^{26} + 27 q^{27} + 14 q^{28} + 236 q^{29} + 1008 q^{30} + 554 q^{31} - 1836 q^{32} + 895 q^{33} - 234 q^{34} + 112 q^{35} - 2322 q^{36} + 1439 q^{37} - 267 q^{38} - 18 q^{39} - 1232 q^{40} - 42 q^{41} + 210 q^{42} - 404 q^{43} + 591 q^{44} - 3020 q^{45} + 2169 q^{46} - 714 q^{47} + 4500 q^{48} - 392 q^{49} - 1035 q^{50} + 745 q^{51} + 725 q^{52} + 1351 q^{53} + 648 q^{54} + 1708 q^{55} - 966 q^{56} + 1561 q^{57} - 2529 q^{58} + 543 q^{59} - 316 q^{60} - 1542 q^{61} - 4231 q^{62} - 567 q^{63} + 1172 q^{64} - 4084 q^{65} + 5058 q^{66} - 1744 q^{67} + 2522 q^{68} - 1584 q^{69} + 126 q^{70} - 561 q^{71} - 4810 q^{72} - 144 q^{73} + 575 q^{74} + 1623 q^{75} - 3278 q^{76} + 567 q^{77} - 6582 q^{78} + 5785 q^{79} + 3199 q^{80} + 2403 q^{81} + 1998 q^{82} - 4177 q^{83} + 1652 q^{84} - 4090 q^{85} - 184 q^{86} - 940 q^{87} + 5446 q^{88} - 11554 q^{89} + 11896 q^{90} - 826 q^{91} + 12958 q^{92} - 578 q^{93} - 2042 q^{94} - 1390 q^{95} - 10074 q^{96} - q^{97} - 588 q^{98} + 10027 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9 - 72 * q^10 - 94 * q^11 - 544 * q^12 + 72 * q^13 + 56 * q^14 + 140 * q^15 + 296 * q^16 + 8 * q^17 + 422 * q^18 + 51 * q^19 - 149 * q^20 - 294 * q^21 - 66 * q^22 - 830 * q^23 + 868 * q^24 - 256 * q^25 + 775 * q^26 + 27 * q^27 + 14 * q^28 + 236 * q^29 + 1008 * q^30 + 554 * q^31 - 1836 * q^32 + 895 * q^33 - 234 * q^34 + 112 * q^35 - 2322 * q^36 + 1439 * q^37 - 267 * q^38 - 18 * q^39 - 1232 * q^40 - 42 * q^41 + 210 * q^42 - 404 * q^43 + 591 * q^44 - 3020 * q^45 + 2169 * q^46 - 714 * q^47 + 4500 * q^48 - 392 * q^49 - 1035 * q^50 + 745 * q^51 + 725 * q^52 + 1351 * q^53 + 648 * q^54 + 1708 * q^55 - 966 * q^56 + 1561 * q^57 - 2529 * q^58 + 543 * q^59 - 316 * q^60 - 1542 * q^61 - 4231 * q^62 - 567 * q^63 + 1172 * q^64 - 4084 * q^65 + 5058 * q^66 - 1744 * q^67 + 2522 * q^68 - 1584 * q^69 + 126 * q^70 - 561 * q^71 - 4810 * q^72 - 144 * q^73 + 575 * q^74 + 1623 * q^75 - 3278 * q^76 + 567 * q^77 - 6582 * q^78 + 5785 * q^79 + 3199 * q^80 + 2403 * q^81 + 1998 * q^82 - 4177 * q^83 + 1652 * q^84 - 4090 * q^85 - 184 * q^86 - 940 * q^87 + 5446 * q^88 - 11554 * q^89 + 11896 * q^90 - 826 * q^91 + 12958 * q^92 - 578 * q^93 - 2042 * q^94 - 1390 * q^95 - 10074 * q^96 - q^97 - 588 * q^98 + 10027 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−3.31524	−	2.40867i	−1.17212	−	0.851592i	−0.180855	−	0.983510i	$-0.557887\pi$
$2$	−3.31524	−	2.40867i	−1.17212	−	0.851592i	−0.991261	+	0.131918i	$0.957887\pi$
$3$	−0.224082	+	0.689654i	−0.0431246	+	0.132724i	−0.970301	−	0.241902i	$-0.922229\pi$
$3$	−0.224082	+	0.689654i	−0.0431246	+	0.132724i	0.927176	+	0.374626i	$0.122229\pi$
$4$	2.71704	+	8.36218i	0.339630	+	1.04527i
$5$	−1.39631	+	1.01448i	−0.124890	+	0.0907376i	−0.648477	−	0.761235i	$-0.724594\pi$
$5$	−1.39631	+	1.01448i	−0.124890	+	0.0907376i	0.523587	+	0.851972i	$0.324594\pi$
$6$	2.40403	−	1.74663i	0.163574	−	0.118843i
$7$	2.16312	+	6.65740i	0.116797	+	0.359466i
$7$	2.16312	+	6.65740i	0.116797	+	0.359466i
$8$	1.00357	−	3.08868i	0.0443521	−	0.136502i
$9$	21.4180	+	15.5611i	0.793261	+	0.576338i
$10$	7.07264			0.223657
$11$	28.8768	−	22.2965i	0.791516	−	0.611149i
$11$	28.8768	−	22.2965i	0.791516	−	0.611149i
$12$	−6.37585			−0.153379
$13$	−19.4797	−	14.1528i	−0.415591	−	0.301945i	0.360270	−	0.932848i	$-0.382685\pi$
$13$	−19.4797	−	14.1528i	−0.415591	−	0.301945i	−0.775862	+	0.630903i	$0.782685\pi$
$14$	8.86417	−	27.2811i	0.169218	−	0.520799i
$15$	−0.386751	−	1.19030i	−0.00665724	−	0.0204889i
$16$	46.1397	−	33.5224i	0.720932	−	0.523788i
$17$	107.498	−	78.1017i	1.53365	−	1.11426i	0.579484	−	0.814984i	$-0.303254\pi$
$17$	107.498	−	78.1017i	1.53365	−	1.11426i	0.954166	−	0.299278i	$-0.0967458\pi$
$18$	−33.5245	−	103.178i	−0.438989	−	1.35107i
$19$	−10.2884	+	31.6646i	−0.124228	+	0.382334i	−0.993760	−	0.111543i	$-0.964421\pi$
$19$	−10.2884	+	31.6646i	−0.124228	+	0.382334i	0.869532	+	0.493877i	$0.164421\pi$
$20$	−12.2771	−	8.91981i	−0.137262	−	0.0997265i
$21$	−5.07602			−0.0527466
$22$	−149.438	+	4.36369i	−1.44820	+	0.0422883i
$23$	95.8630			0.869079			0.434540	−	0.900653i	$-0.356911\pi$
$23$	95.8630			0.869079			0.434540	+	0.900653i	$0.356911\pi$
$24$	1.90524	+	1.38424i	0.0162044	+	0.0117732i
$25$	−37.7066	+	116.049i	−0.301653	+	0.928392i
$26$	30.4905	+	93.8400i	0.229987	+	0.707829i
$27$	−31.3709	+	22.7923i	−0.223605	+	0.162458i
$28$	−49.7931	+	36.1768i	−0.336072	+	0.244170i
$29$	15.0677	+	46.3735i	0.0964827	+	0.296943i	0.987637	−	0.156757i	$-0.0501039\pi$
$29$	15.0677	+	46.3735i	0.0964827	+	0.296943i	−0.891155	+	0.453700i	$0.850104\pi$
$30$	−1.58485	+	4.87768i	−0.00964511	+	0.0296846i
$31$	239.688	+	174.143i	1.38868	+	1.00894i	0.996008	+	0.0892605i	$0.0284504\pi$
$31$	239.688	+	174.143i	1.38868	+	1.00894i	0.392675	+	0.919677i	$0.371550\pi$
$32$	−259.690			−1.43460
$33$	8.90607	+	24.9112i	0.0469802	+	0.131409i
$34$	−544.502			−2.74651
$35$	−9.77416	−	7.10134i	−0.0472038	−	0.0342956i
$36$	−71.9313	+	221.382i	−0.333015	+	1.02492i
$37$	59.0199	+	181.645i	0.262238	+	0.807087i	0.992317	+	0.123723i	$0.0394835\pi$
$37$	59.0199	+	181.645i	0.262238	+	0.807087i	−0.730078	+	0.683363i	$0.760516\pi$
$38$	110.378	−	80.1944i	0.471202	−	0.342349i
$39$	14.1256	−	10.2628i	0.0579976	−	0.0421377i
$40$	1.73210	+	5.33085i	0.00684672	+	0.0210721i
$41$	68.8506	−	211.900i	0.262260	−	0.807153i	−0.730052	−	0.683391i	$-0.760504\pi$
$41$	68.8506	−	211.900i	0.262260	−	0.807153i	0.992312	−	0.123761i	$-0.0394958\pi$
$42$	16.8282	+	12.2264i	0.0618251	+	0.0449185i
$43$	−302.665			−1.07340			−0.536698	−	0.843774i	$-0.680329\pi$
$43$	−302.665			−1.07340			−0.536698	+	0.843774i	$0.680329\pi$
$44$	264.906	+	180.893i	0.907639	+	0.619786i
$45$	−45.6926			−0.151366
$46$	−317.809	−	230.902i	−1.01866	−	0.740101i
$47$	64.7197	−	199.187i	0.200858	−	0.618178i	−0.799000	−	0.601331i	$-0.794637\pi$
$47$	64.7197	−	199.187i	0.200858	−	0.618178i	0.999858	−	0.0168469i	$-0.00536279\pi$
$48$	12.7798	+	39.3322i	0.0384293	+	0.118273i
$49$	−39.6418	+	28.8015i	−0.115574	+	0.0839693i
$50$	404.530	−	293.908i	1.14418	−	0.831298i
$51$	29.7748	+	91.6375i	0.0817512	+	0.251604i
$52$	65.4214	−	201.346i	0.174468	−	0.536956i
$53$	103.903	+	75.4896i	0.269285	+	0.195647i	0.714230	−	0.699911i	$-0.246777\pi$
$53$	103.903	+	75.4896i	0.269285	+	0.195647i	−0.444945	+	0.895558i	$0.646777\pi$
$54$	158.901			0.400439
$55$	−17.7016	+	60.4276i	−0.0433980	+	0.148146i
$56$	22.7334			0.0542479
$57$	−19.5321	−	14.1909i	−0.0453876	−	0.0329760i
$58$	61.7453	−	190.033i	0.139786	−	0.430216i
$59$	119.682	+	368.343i	0.264089	+	0.812783i	0.991902	+	0.127007i	$0.0405371\pi$
$59$	119.682	+	368.343i	0.264089	+	0.812783i	−0.727812	+	0.685776i	$0.759463\pi$
$60$	8.90266	−	6.46816i	0.0191555	−	0.0139173i
$61$	594.964	−	432.266i	1.24881	−	0.907312i	0.250656	−	0.968076i	$-0.419354\pi$
$61$	594.964	−	432.266i	1.24881	−	0.907312i	0.998152	+	0.0607644i	$0.0193538\pi$
$62$	−375.170	−	1154.66i	−0.768495	−	2.36518i
$63$	−57.2668	+	176.249i	−0.114523	+	0.352465i
$64$	491.817	+	357.326i	0.960581	+	0.697903i
$65$	41.5573			0.0793008
$66$	30.4770	−	104.039i	0.0568403	−	0.194034i
$67$	−1021.56			−1.86274			−0.931372	−	0.364068i	$-0.881387\pi$
$67$	−1021.56			−1.86274			−0.931372	+	0.364068i	$0.881387\pi$
$68$	945.176	+	686.711i	1.68558	+	1.22465i
$69$	−21.4812	+	66.1123i	−0.0374787	+	0.115348i
$70$	15.2990	+	47.0854i	0.0261225	+	0.0803968i
$71$	171.731	−	124.770i	0.287053	−	0.208556i	−0.434935	−	0.900462i	$-0.643229\pi$
$71$	171.731	−	124.770i	0.287053	−	0.208556i	0.721988	+	0.691906i	$0.243229\pi$
$72$	69.5579	−	50.5368i	0.113854	−	0.0827197i
$73$	−182.865	−	562.801i	−0.293188	−	0.902341i	−0.983824	−	0.179138i	$-0.942669\pi$
$73$	−182.865	−	562.801i	−0.293188	−	0.902341i	0.690636	−	0.723203i	$-0.257331\pi$
$74$	241.856	−	744.356i	0.379935	−	1.16932i
$75$	−71.5843	−	52.0090i	−0.110211	−	0.0800732i
$76$	−292.739			−0.441835
$77$	210.900	+	144.014i	0.312134	+	0.213142i
$78$	−71.5495			−0.103864
$79$	292.491	+	212.507i	0.416555	+	0.302645i	0.776250	−	0.630425i	$-0.217119\pi$
$79$	292.491	+	212.507i	0.416555	+	0.302645i	−0.359695	+	0.933070i	$0.617119\pi$
$80$	−30.4175	+	93.6153i	−0.0425097	+	0.130831i
$81$	212.197	+	653.075i	0.291080	+	0.895851i
$82$	−738.654	+	536.663i	−0.994764	+	0.722738i
$83$	−303.345	+	220.393i	−0.401163	+	0.291462i	−0.770014	−	0.638027i	$-0.779751\pi$
$83$	−303.345	+	220.393i	−0.401163	+	0.291462i	0.368852	+	0.929488i	$0.379751\pi$
$84$	−13.7917	−	42.4466i	−0.0179143	−	0.0551345i
$85$	−70.8676	+	218.108i	−0.0904315	+	0.278319i
$86$	1003.41	+	729.020i	1.25814	+	0.914096i
$87$	−35.3581			−0.0435722
$88$	−39.8867	−	111.567i	−0.0483174	−	0.135149i
$89$	−632.790			−0.753659			−0.376829	−	0.926283i	$-0.622986\pi$
$89$	−632.790			−0.753659			−0.376829	+	0.926283i	$0.622986\pi$
$90$	151.482	+	110.058i	0.177418	+	0.128902i
$91$	52.0840	−	160.298i	0.0599988	−	0.184657i
$92$	260.463	+	801.624i	0.295165	+	0.908425i
$93$	−173.808	+	126.279i	−0.193797	+	0.140802i
$94$	−694.336	+	504.465i	−0.761865	+	0.553527i
$95$	−17.7572	−	54.6509i	−0.0191773	−	0.0590217i
$96$	58.1918	−	179.096i	0.0618665	−	0.190405i
$97$	−1017.89	−	739.539i	−1.06547	−	0.774112i	−0.0903804	−	0.995907i	$-0.528808\pi$
$97$	−1017.89	−	739.539i	−1.06547	−	0.774112i	−0.975093	+	0.221795i	$0.928808\pi$
$98$	200.796			0.206974
$99$	965.442	−	28.1915i	0.980107	−	0.0286197i
$100$	−1072.87			−1.07287
$101$	−620.341	−	450.704i	−0.611151	−	0.444027i	0.238669	−	0.971101i	$-0.423289\pi$
$101$	−620.341	−	450.704i	−0.611151	−	0.444027i	−0.849819	+	0.527074i	$0.823289\pi$
$102$	122.013	−	375.518i	0.118442	−	0.364528i
$103$	6.79248	+	20.9051i	0.00649789	+	0.0199985i	0.954253	−	0.299001i	$-0.0966533\pi$
$103$	6.79248	+	20.9051i	0.00649789	+	0.0199985i	−0.947755	+	0.318999i	$0.896653\pi$
$104$	−63.2628	+	45.9631i	−0.0596483	+	0.0433371i
$105$	7.08768	−	5.14950i	0.00658750	−	0.00478610i
$106$	−162.633	−	500.533i	−0.149022	−	0.458642i
$107$	−105.554	+	324.861i	−0.0953671	+	0.293510i	−0.987349	−	0.158561i	$-0.949315\pi$
$107$	−105.554	+	324.861i	−0.0953671	+	0.293510i	0.891982	+	0.452071i	$0.149315\pi$
$108$	−275.829	−	200.401i	−0.245756	−	0.178552i
$109$	1030.34			0.905397			0.452699	−	0.891664i	$-0.350461\pi$
$109$	1030.34			0.905397			0.452699	+	0.891664i	$0.350461\pi$
$110$	204.235	−	157.695i	0.177028	−	0.136687i
$111$	−138.497			−0.118429
$112$	322.978	+	234.657i	0.272487	+	0.197973i
$113$	142.482	−	438.513i	0.118615	−	0.365061i	−0.874068	−	0.485803i	$-0.838527\pi$
$113$	142.482	−	438.513i	0.118615	−	0.365061i	0.992684	+	0.120742i	$0.0385273\pi$
$114$	30.5726	+	94.0928i	0.0251174	+	0.0773035i
$115$	−133.854	+	97.2509i	−0.108539	+	0.0788582i
$116$	−346.844	+	251.997i	−0.277618	+	0.201701i
$117$	−196.983	−	606.251i	−0.155650	−	0.479042i
$118$	490.441	−	1509.42i	0.382617	−	1.17757i
$119$	752.485	+	546.712i	0.579665	+	0.421151i
$120$	−4.06458			−0.00309203
$121$	336.736	−	1287.70i	0.252995	−	0.967468i
$122$	−3013.63			−2.23641
$123$	130.710	+	94.9662i	0.0958187	+	0.0696164i
$124$	−804.978	+	2477.47i	−0.582977	+	1.79422i
$125$	−131.747	−	405.475i	−0.0942704	−	0.290134i
$126$	614.378	−	446.372i	0.434390	−	0.315603i
$127$	−524.537	+	381.098i	−0.366497	+	0.266276i	−0.755757	−	0.654852i	$-0.772731\pi$
$127$	−524.537	+	381.098i	−0.366497	+	0.266276i	0.389260	+	0.921128i	$0.372731\pi$
$128$	−127.827	−	393.411i	−0.0882689	−	0.271664i
$129$	67.8219	−	208.734i	0.0462898	−	0.142465i
$130$	−137.773	−	100.098i	−0.0929497	−	0.0675319i
$131$	−1619.10			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$131$	−1619.10			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$132$	−184.114	+	142.159i	−0.121402	+	0.0937375i
$133$	−233.059			−0.151945
$134$	3386.73	+	2460.61i	2.18335	+	1.58630i
$135$	20.6812	−	63.6501i	0.0131848	−	0.0405787i
$136$	−133.349	−	410.407i	−0.0840781	−	0.258766i
$137$	1899.13	−	1379.80i	1.18433	−	0.860466i	0.191677	−	0.981458i	$-0.438607\pi$
$137$	1899.13	−	1379.80i	1.18433	−	0.860466i	0.992654	+	0.120992i	$0.0386075\pi$
$138$	230.458	−	167.438i	0.142159	−	0.103284i
$139$	459.845	+	1415.26i	0.280601	+	0.863602i	0.987683	+	0.156470i	$0.0500114\pi$
$139$	459.845	+	1415.26i	0.280601	+	0.863602i	−0.707082	+	0.707132i	$0.749989\pi$
$140$	32.8260	−	101.028i	0.0198164	−	0.0609887i
$141$	122.867	+	89.2684i	0.0733851	+	0.0533174i
$142$	−869.860			−0.514063
$143$	−878.068	+	25.6401i	−0.513480	+	0.0149940i
$144$	1509.87			0.873767
$145$	−68.0840	−	49.4659i	−0.0389936	−	0.0283305i
$146$	−749.357	+	2306.28i	−0.424776	+	1.30733i
$147$	−10.9800	−	33.7931i	−0.00616066	−	0.0189606i
$148$	−1358.59	+	987.071i	−0.754562	+	0.548221i
$149$	−1551.17	+	1126.99i	−0.852866	+	0.619643i	−0.925935	−	0.377684i	$-0.876721\pi$
$149$	−1551.17	+	1126.99i	−0.852866	+	0.619643i	0.0730690	+	0.997327i	$0.476721\pi$
$150$	112.047	+	344.845i	0.0609907	+	0.187710i
$151$	−484.099	+	1489.90i	−0.260897	+	0.802958i	0.731713	+	0.681612i	$0.238721\pi$
$151$	−484.099	+	1489.90i	−0.260897	+	0.802958i	−0.992610	+	0.121346i	$0.961279\pi$
$152$	87.4766	+	63.5554i	0.0466795	+	0.0339146i
$153$	3517.74			1.85878
$154$	−352.304	−	985.431i	−0.184347	−	0.515638i
$155$	−511.343			−0.264981
$156$	124.200	+	90.2362i	0.0637431	+	0.0463120i
$157$	383.430	−	1180.08i	0.194911	−	0.599875i	−0.805066	−	0.593185i	$-0.797870\pi$
$157$	383.430	−	1180.08i	0.194911	−	0.599875i	0.999978	−	0.00669019i	$-0.00212957\pi$
$158$	−457.821	−	1409.03i	−0.230521	−	0.709470i
$159$	−75.3445	+	54.7410i	−0.0375799	+	0.0273034i
$160$	362.607	−	263.449i	0.179166	−	0.130172i
$161$	207.363	+	638.198i	0.101506	+	0.312404i
$162$	869.555	−	2676.22i	0.421720	−	1.29792i
$163$	1962.52	+	1425.86i	0.943046	+	0.685163i	0.949152	−	0.314818i	$-0.101944\pi$
$163$	1962.52	+	1425.86i	0.943046	+	0.685163i	−0.00610569	+	0.999981i	$0.501944\pi$
$164$	1959.02			0.932766
$165$	−37.7075	−	25.7487i	−0.0177911	−	0.0121487i
$166$	1536.52			0.718415
$167$	−2820.76	−	2049.40i	−1.30705	−	0.949625i	−0.307049	−	0.951694i	$-0.599342\pi$
$167$	−2820.76	−	2049.40i	−1.30705	−	0.949625i	−0.999998	+	0.00206828i	$0.999342\pi$
$168$	−5.09416	+	15.6782i	−0.00233942	+	0.00720000i
$169$	−499.755	−	1538.09i	−0.227471	−	0.700085i
$170$	760.293	−	552.385i	0.343011	−	0.249212i
$171$	−713.095	+	518.094i	−0.318899	+	0.231694i
$172$	−822.353	−	2530.94i	−0.364557	−	1.12199i
$173$	1094.46	−	3368.40i	0.480984	−	1.48032i	−0.356731	−	0.934207i	$-0.616109\pi$
$173$	1094.46	−	3368.40i	0.480984	−	1.48032i	0.837715	−	0.546108i	$-0.183891\pi$
$174$	117.221	+	85.1658i	0.0510717	+	0.0371058i
$175$	−854.148			−0.368957
$176$	584.933	−	1996.77i	0.250517	−	0.855183i
$177$	−280.848			−0.119265
$178$	2097.85	+	1524.18i	0.883376	+	0.641810i
$179$	−1253.13	+	3856.73i	−0.523258	+	1.61042i	0.244477	+	0.969655i	$0.421384\pi$
$179$	−1253.13	+	3856.73i	−0.523258	+	1.61042i	−0.767735	+	0.640767i	$0.778616\pi$
$180$	−124.149	−	382.090i	−0.0514083	−	0.158218i
$181$	1318.53	−	957.967i	0.541466	−	0.393398i	−0.283163	−	0.959072i	$-0.591384\pi$
$181$	1318.53	−	957.967i	0.541466	−	0.393398i	0.824629	+	0.565673i	$0.191384\pi$
$182$	−558.776	+	405.974i	−0.227578	+	0.165345i
$183$	164.793	+	507.182i	0.0665677	+	0.204874i
$184$	96.2056	−	296.090i	0.0385455	−	0.118631i
$185$	−266.684	−	193.758i	−0.105984	−	0.0770019i
$186$	880.382			0.347058
$187$	1362.80	−	4652.15i	0.532929	−	1.81924i
$188$	1841.48			0.714382
$189$	−219.596	−	159.546i	−0.0845146	−	0.0614035i
$190$	−72.7665	+	223.952i	−0.0277844	+	0.0855116i
$191$	−642.690	−	1978.00i	−0.243473	−	0.749334i	−0.995884	−	0.0906395i	$-0.971109\pi$
$191$	−642.690	−	1978.00i	−0.243473	−	0.749334i	0.752410	−	0.658695i	$-0.228891\pi$
$192$	−356.639	+	259.113i	−0.134053	+	0.0973953i
$193$	−2723.50	+	1978.74i	−1.01576	+	0.737993i	−0.965409	−	0.260739i	$-0.916034\pi$
$193$	−2723.50	+	1978.74i	−1.01576	+	0.737993i	−0.0503508	+	0.998732i	$0.516034\pi$
$194$	1593.25	+	4903.51i	0.589631	+	1.81470i
$195$	−9.31226	+	28.6602i	−0.00341982	+	0.0105251i
$196$	−348.552	−	253.237i	−0.127023	−	0.0922877i
$197$	−1616.74			−0.584711			−0.292356	−	0.956310i	$-0.594439\pi$
$197$	−1616.74			−0.584711			−0.292356	+	0.956310i	$0.594439\pi$
$198$	−3268.58	−	2231.97i	−1.17317	−	0.801106i
$199$	3640.59			1.29686			0.648428	−	0.761276i	$-0.275427\pi$
$199$	3640.59			1.29686			0.648428	+	0.761276i	$0.275427\pi$
$200$	320.597	+	232.927i	0.113348	+	0.0823523i
$201$	228.914	−	704.526i	0.0803302	−	0.247231i
$202$	970.986	+	2988.39i	0.338210	+	1.04090i
$203$	−276.134	+	200.623i	−0.0954719	+	0.0693644i
$204$	−685.390	+	497.965i	−0.235230	+	0.170905i
$205$	118.831	+	365.726i	0.0404856	+	0.124602i
$206$	27.8347	−	85.6663i	0.00941424	−	0.0289741i
$207$	2053.20	+	1491.74i	0.689407	+	0.500883i
$208$	−1373.22			−0.457768
$209$	408.911	+	1143.77i	0.135335	+	0.378545i
$210$	−35.9008			−0.0117971
$211$	−2449.41	−	1779.60i	−0.799167	−	0.580629i	0.111502	−	0.993764i	$-0.464434\pi$
$211$	−2449.41	−	1779.60i	−0.799167	−	0.580629i	−0.910670	+	0.413135i	$0.864434\pi$
$212$	−348.951	+	1073.96i	−0.113047	+	0.347924i
$213$	47.5662	+	146.394i	0.0153013	+	0.0470927i
$214$	1132.42	−	822.751i	0.361732	−	0.262813i
$215$	422.614	−	307.047i	0.134056	−	0.0973974i
$216$	38.9151	+	119.768i	0.0122585	+	0.0377278i
$217$	−640.868	+	1972.39i	−0.200484	+	0.617025i
$218$	−3415.82	−	2481.74i	−1.06123	−	0.771029i
$219$	429.115			0.132406
$220$	−553.402	+	16.1597i	−0.169593	+	0.00495221i
$221$	−3199.38			−0.973817
$222$	459.152	+	333.594i	0.138812	+	0.100853i
$223$	−1410.81	+	4342.02i	−0.423653	+	1.30387i	0.480625	+	0.876926i	$0.340410\pi$
$223$	−1410.81	+	4342.02i	−0.423653	+	1.30387i	−0.904278	+	0.426944i	$0.859590\pi$
$224$	−561.740	−	1728.86i	−0.167557	−	0.515688i
$225$	−2613.46	+	1898.79i	−0.774357	+	0.562603i
$226$	−1528.59	+	1110.59i	−0.449914	+	0.326882i
$227$	203.098	+	625.073i	0.0593838	+	0.182764i	0.976348	−	0.216205i	$-0.0693680\pi$
$227$	203.098	+	625.073i	0.0593838	+	0.182764i	−0.916964	+	0.398969i	$0.869368\pi$
$228$	65.5976	−	201.889i	0.0190540	−	0.0586421i
$229$	−2252.25	−	1636.35i	−0.649925	−	0.472198i	0.213321	−	0.976982i	$-0.431572\pi$
$229$	−2252.25	−	1636.35i	−0.649925	−	0.472198i	−0.863245	+	0.504784i	$0.831572\pi$
$230$	678.005			0.194375
$231$	−146.579	+	113.177i	−0.0417497	+	0.0322360i
$232$	158.355			0.0448124
$233$	578.934	+	420.620i	0.162778	+	0.118265i	0.666192	−	0.745780i	$-0.267923\pi$
$233$	578.934	+	420.620i	0.162778	+	0.118265i	−0.503414	+	0.864045i	$0.667923\pi$
$234$	−807.210	+	2484.34i	−0.225508	+	0.694043i
$235$	111.702	+	343.783i	0.0310069	+	0.0954294i
$236$	−2754.97	+	2001.61i	−0.759888	+	0.552091i
$237$	−212.099	+	154.099i	−0.0581320	+	0.0422354i
$238$	−1177.82	−	3624.97i	−0.320786	−	0.987276i
$239$	−1353.40	+	4165.35i	−0.366295	+	1.12734i	0.582871	+	0.812564i	$0.301929\pi$
$239$	−1353.40	+	4165.35i	−0.366295	+	1.12734i	−0.949166	+	0.314775i	$0.898071\pi$
$240$	−57.7462	−	41.9551i	−0.0155312	−	0.0112841i
$241$	4451.86			1.18991			0.594957	−	0.803757i	$-0.297169\pi$
$241$	4451.86			1.18991			0.594957	+	0.803757i	$0.297169\pi$
$242$	−4218.00	+	3457.95i	−1.12043	+	0.918536i
$243$	−1544.91			−0.407844
$244$	5231.23	+	3800.71i	1.37252	+	0.997195i
$245$	26.1338	−	80.4315i	0.00681480	−	0.0209738i
$246$	−204.593	−	629.672i	−0.0530259	−	0.163197i
$247$	648.558	−	471.205i	0.167072	−	0.121385i
$248$	778.418	−	565.553i	0.199313	−	0.144809i
$249$	−84.0209	−	258.590i	−0.0213840	−	0.0658131i
$250$	−539.881	+	1661.58i	−0.136580	+	0.420351i
$251$	−4731.71	−	3437.79i	−1.18989	−	0.864507i	−0.196639	−	0.980476i	$-0.563003\pi$
$251$	−4731.71	−	3437.79i	−1.18989	−	0.864507i	−0.993253	+	0.115969i	$0.963003\pi$
$252$	−1629.42			−0.407317
$253$	2768.22	−	2137.41i	0.687890	−	0.531137i
$254$	2656.91			0.656335
$255$	−134.539	−	97.7483i	−0.0330398	−	0.0240049i
$256$	979.042	−	3013.18i	0.239024	−	0.735640i
$257$	183.270	+	564.047i	0.0444828	+	0.136904i	0.970831	−	0.239764i	$-0.0770699\pi$
$257$	183.270	+	564.047i	0.0444828	+	0.136904i	−0.926349	+	0.376668i	$0.877070\pi$
$258$	−727.618	+	528.645i	−0.175579	+	0.127566i
$259$	−1081.61	+	785.838i	−0.259491	+	0.188531i
$260$	112.913	+	347.510i	0.0269329	+	0.0828910i
$261$	−398.904	+	1227.70i	−0.0946036	+	0.291160i
$262$	5367.72	+	3899.87i	1.26572	+	0.919600i
$263$	4087.15			0.958267			0.479133	−	0.877742i	$-0.340951\pi$
$263$	4087.15			0.958267			0.479133	+	0.877742i	$0.340951\pi$
$264$	85.8807	−	2.50777i	0.0200212	−	0.000584631i
$265$	−221.663			−0.0513835
$266$	772.646	+	561.361i	0.178098	+	0.129396i
$267$	141.797	−	436.406i	0.0325013	−	0.100029i
$268$	−2775.63	−	8542.50i	−0.632643	−	1.94708i
$269$	6021.94	−	4375.20i	1.36492	−	0.991675i	0.366809	−	0.930296i	$-0.380450\pi$
$269$	6021.94	−	4375.20i	1.36492	−	0.991675i	0.998115	−	0.0613788i	$-0.0195498\pi$
$270$	−221.875	+	161.202i	−0.0500107	+	0.0363349i
$271$	1782.11	+	5484.76i	0.399466	+	1.22943i	0.925429	+	0.378922i	$0.123705\pi$
$271$	1782.11	+	5484.76i	0.399466	+	1.22943i	−0.525963	+	0.850507i	$0.676295\pi$
$272$	2341.75	−	7207.18i	0.522021	−	1.60661i
$273$	98.8791	+	71.8399i	0.0219210	+	0.0159266i
$274$	−9619.53			−2.12094
$275$	1498.64	+	4191.85i	0.328622	+	0.919192i
$276$	−611.209			−0.133299
$277$	−1022.13	−	742.624i	−0.221712	−	0.161083i	0.471385	−	0.881927i	$-0.343754\pi$
$277$	−1022.13	−	742.624i	−0.221712	−	0.161083i	−0.693097	+	0.720845i	$0.743754\pi$
$278$	1884.39	−	5799.54i	0.406539	−	1.25120i
$279$	2423.78	+	7459.62i	0.520100	+	1.60070i
$280$	−31.7429	+	23.0625i	−0.00677500	+	0.00492232i
$281$	2042.01	−	1483.61i	0.433510	−	0.314963i	−0.349541	−	0.936921i	$-0.613662\pi$
$281$	2042.01	−	1483.61i	0.433510	−	0.314963i	0.783051	+	0.621958i	$0.213662\pi$
$282$	−192.318	−	591.893i	−0.0406112	−	0.124988i
$283$	463.178	−	1425.51i	0.0972899	−	0.299428i	−0.890554	−	0.454878i	$-0.849683\pi$
$283$	463.178	−	1425.51i	0.0972899	−	0.299428i	0.987844	+	0.155450i	$0.0496829\pi$
$284$	1509.95	+	1097.04i	0.315489	+	0.229216i
$285$	41.6693			0.00866061
$286$	2972.77	+	2029.97i	0.614627	+	0.419701i
$287$	1559.64			0.320775
$288$	−5562.05	−	4041.06i	−1.13801	−	0.826812i
$289$	3937.70	−	12119.0i	0.801485	−	2.46672i
$290$	106.568	+	327.983i	0.0215790	+	0.0664133i
$291$	738.117	−	536.273i	0.148691	−	0.108031i
$292$	4209.39	−	3058.30i	0.843617	−	0.612924i
$293$	−302.607	−	931.328i	−0.0603361	−	0.185695i	0.916345	−	0.400389i	$-0.131125\pi$
$293$	−302.607	−	931.328i	−0.0603361	−	0.185695i	−0.976682	+	0.214693i	$0.931125\pi$
$294$	−44.9947	+	138.479i	−0.00892566	+	0.0274704i
$295$	−540.789	−	392.906i	−0.106732	−	0.0775454i
$296$	620.273			0.121800
$297$	−397.703	+	1357.63i	−0.0777005	+	0.265244i
$298$	7857.06			1.52734
$299$	−1867.38	−	1356.73i	−0.361182	−	0.262414i
$300$	240.412	−	739.911i	0.0462673	−	0.142396i
$301$	−654.701	−	2014.96i	−0.125370	−	0.385849i
$302$	5193.59	−	3773.36i	0.989594	−	0.718982i
$303$	449.837	−	326.826i	0.0852887	−	0.0619659i
$304$	586.768	+	1805.89i	0.110702	+	0.340706i
$305$	−392.228	+	1207.15i	−0.0736358	+	0.226628i
$306$	−11662.2	−	8473.07i	−2.17870	−	1.58292i
$307$	4324.16			0.803885			0.401942	−	0.915665i	$-0.368335\pi$
$307$	4324.16			0.803885			0.401942	+	0.915665i	$0.368335\pi$
$308$	−631.249	+	2154.88i	−0.116782	+	0.398654i
$309$	−15.9394			−0.00293449
$310$	1695.23	+	1231.65i	0.310588	+	0.225656i
$311$	1217.26	−	3746.34i	0.221944	−	0.683072i	−0.776644	−	0.629940i	$-0.783080\pi$
$311$	1217.26	−	3746.34i	0.221944	−	0.683072i	0.998587	−	0.0531322i	$-0.0169205\pi$
$312$	−17.5226	−	53.9290i	−0.00317955	−	0.00978566i
$313$	−4565.59	+	3317.09i	−0.824480	+	0.599020i	−0.917992	−	0.396598i	$-0.870191\pi$
$313$	−4565.59	+	3317.09i	−0.824480	+	0.599020i	0.0935120	+	0.995618i	$0.470191\pi$
$314$	−4113.57	+	2988.69i	−0.739307	+	0.537138i
$315$	−98.8386	−	304.194i	−0.0176791	−	0.0544107i
$316$	−982.315	+	3023.26i	−0.174872	+	0.538201i
$317$	5344.19	+	3882.78i	0.946877	+	0.687946i	0.950066	−	0.312049i	$-0.101015\pi$
$317$	5344.19	+	3882.78i	0.946877	+	0.687946i	−0.00318949	+	0.999995i	$0.501015\pi$
$318$	381.638			0.0672994
$319$	1469.07	+	1003.16i	0.257844	+	0.176070i
$320$	−1049.23			−0.183293
$321$	−200.389	−	145.591i	−0.0348431	−	0.0253150i
$322$	849.747	−	2615.25i	0.147064	−	0.452616i
$323$	1367.07	+	4207.42i	0.235498	+	0.724789i
$324$	−4884.59	+	3548.86i	−0.837549	+	0.608515i
$325$	2376.93	−	1726.94i	0.405688	−	0.294749i
$326$	−3071.83	−	9454.12i	−0.521880	−	1.60618i
$327$	−230.880	+	710.575i	−0.0390449	+	0.120168i
$328$	−585.396	−	425.315i	−0.0985460	−	0.0715978i
$329$	1466.06			0.245674
$330$	62.9894	+	176.188i	0.0105074	+	0.0293904i
$331$	−4462.73			−0.741069			−0.370534	−	0.928819i	$-0.620825\pi$
$331$	−4462.73			−0.741069			−0.370534	+	0.928819i	$0.620825\pi$
$332$	−2667.17	−	1937.81i	−0.440904	−	0.320335i
$333$	−1562.50	+	4808.89i	−0.257131	+	0.791368i
$334$	4415.18	+	13588.5i	0.723317	+	2.22614i
$335$	1426.42	−	1036.35i	0.232637	−	0.169021i
$336$	−234.206	+	170.160i	−0.0380267	+	0.0276280i
$337$	1911.52	+	5883.04i	0.308982	+	0.950949i	0.978161	+	0.207848i	$0.0666458\pi$
$337$	1911.52	+	5883.04i	0.308982	+	0.950949i	−0.669179	+	0.743101i	$0.733354\pi$
$338$	−2047.93	+	6302.88i	−0.329564	+	1.01429i
$339$	270.495	+	196.526i	0.0433371	+	0.0314862i
$340$	−2016.41			−0.321633
$341$	10804.2	−	315.489i	1.71578	−	0.0501017i
$342$	3612.00			0.571095
$343$	−277.493	−	201.610i	−0.0436828	−	0.0317374i
$344$	−303.747	+	934.837i	−0.0476074	+	0.146520i
$345$	−37.0751	−	114.105i	−0.00578567	−	0.0178065i
$346$	−11741.7	+	8530.88i	−1.82439	+	1.32550i
$347$	−1763.53	+	1281.28i	−0.272828	+	0.198221i	−0.715783	−	0.698323i	$-0.753930\pi$
$347$	−1763.53	+	1281.28i	−0.272828	+	0.198221i	0.442955	+	0.896544i	$0.353930\pi$
$348$	−96.0693	−	295.671i	−0.0147984	−	0.0455449i
$349$	−2913.21	+	8965.95i	−0.446822	+	1.37518i	0.433652	+	0.901081i	$0.357225\pi$
$349$	−2913.21	+	8965.95i	−0.446822	+	1.37518i	−0.880474	+	0.474095i	$0.842775\pi$
$350$	2831.71	+	2057.36i	0.432461	+	0.314201i
$351$	933.669			0.141982
$352$	−7499.00	+	5790.16i	−1.13551	+	0.876752i
$353$	−11430.0			−1.72339			−0.861693	−	0.507430i	$-0.830595\pi$
$353$	−11430.0			−1.72339			−0.861693	+	0.507430i	$0.830595\pi$
$354$	931.080	+	676.469i	0.139792	+	0.101565i
$355$	−113.213	+	348.435i	−0.0169260	+	0.0520929i
$356$	−1719.32	−	5291.51i	−0.255965	−	0.787779i
$357$	−545.661	+	396.446i	−0.0808947	+	0.0587735i
$358$	13444.0	−	9767.64i	1.98474	−	1.44200i
$359$	−1818.66	−	5597.26i	−0.267368	−	0.822875i	−0.991138	−	0.132834i	$-0.957592\pi$
$359$	−1818.66	−	5597.26i	−0.267368	−	0.822875i	0.723770	−	0.690041i	$-0.242408\pi$
$360$	−45.8559	+	141.130i	−0.00671338	+	0.0206617i
$361$	4652.25	+	3380.06i	0.678270	+	0.492792i
$362$	−6678.66			−0.969676
$363$	812.611	+	520.782i	0.117496	+	0.0753002i
$364$	1481.96			0.213394
$365$	826.285	+	600.331i	0.118492	+	0.0860898i
$366$	675.302	−	2078.37i	0.0964442	−	0.296825i
$367$	−2325.82	−	7158.14i	−0.330809	−	1.01812i	−0.968750	−	0.248040i	$-0.920214\pi$
$367$	−2325.82	−	7158.14i	−0.330809	−	1.01812i	0.637941	−	0.770085i	$-0.279786\pi$
$368$	4423.09	−	3213.56i	0.626548	−	0.455213i
$369$	4772.05	−	3467.10i	0.673233	−	0.489133i
$370$	417.427	+	1284.71i	0.0586513	+	0.180510i
$371$	−277.811	+	855.014i	−0.0388766	+	0.119650i
$372$	−1528.21	−	1110.31i	−0.212995	−	0.154750i
$373$	−8639.75			−1.19933			−0.599664	−	0.800252i	$-0.704699\pi$
$373$	−8639.75			−1.19933			−0.599664	+	0.800252i	$0.704699\pi$
$374$	−15723.5	+	12140.5i	−2.17391	+	1.67853i
$375$	309.160			0.0425732
$376$	−550.273	−	399.797i	−0.0754739	−	0.0548350i
$377$	362.802	−	1116.59i	0.0495631	−	0.152539i
$378$	343.722	+	1057.87i	0.0467702	+	0.143944i
$379$	−4496.89	+	3267.18i	−0.609471	+	0.442807i	−0.849228	−	0.528026i	$-0.822932\pi$
$379$	−4496.89	+	3267.18i	−0.609471	+	0.442807i	0.239757	+	0.970833i	$0.422932\pi$
$380$	408.754	−	296.977i	0.0551806	−	0.0400911i
$381$	−145.287	−	447.147i	−0.0195361	−	0.0601260i
$382$	−2633.66	+	8105.57i	−0.352748	+	1.08565i
$383$	−7068.72	−	5135.72i	−0.943067	−	0.685178i	0.00609020	−	0.999981i	$-0.498061\pi$
$383$	−7068.72	−	5135.72i	−0.943067	−	0.685178i	−0.949157	+	0.314803i	$0.898061\pi$
$384$	299.961			0.0398629
$385$	−440.581	+	12.8652i	−0.0583223	+	0.00170305i
$386$	13795.2			1.81906
$387$	−6482.50	−	4709.81i	−0.851483	−	0.618639i
$388$	3418.52	−	10521.1i	0.447292	−	1.37662i
$389$	−2298.01	−	7072.53i	−0.299521	−	0.921830i	−0.981665	−	0.190613i	$-0.938953\pi$
$389$	−2298.01	−	7072.53i	−0.299521	−	0.921830i	0.682145	−	0.731217i	$-0.261047\pi$
$390$	99.9052	−	72.5854i	0.0129715	−	0.00942437i
$391$	10305.1	−	7487.07i	1.33286	−	0.968382i
$392$	49.1751	+	151.345i	0.00633601	+	0.0195002i
$393$	362.812	−	1116.62i	0.0465685	−	0.143323i
$394$	5359.90	+	3894.19i	0.685350	+	0.497936i
$395$	−623.992			−0.0794847
$396$	2858.88	+	7996.60i	0.362789	+	1.01476i
$397$	4778.63			0.604112			0.302056	−	0.953290i	$-0.402327\pi$
$397$	4778.63			0.604112			0.302056	+	0.953290i	$0.402327\pi$
$398$	−12069.4	−	8768.96i	−1.52007	−	1.10439i
$399$	52.2243	−	160.730i	0.00655259	−	0.0201668i
$400$	2150.48	+	6618.48i	0.268809	+	0.827310i
$401$	1720.77	−	1250.22i	0.214293	−	0.155693i	−0.475461	−	0.879737i	$-0.657719\pi$
$401$	1720.77	−	1250.22i	0.214293	−	0.155693i	0.689754	+	0.724044i	$0.257719\pi$
$402$	−2455.87	+	1784.30i	−0.304696	+	0.221375i
$403$	−2204.42	−	6784.51i	−0.272481	−	0.838612i
$404$	2083.38	−	6411.98i	0.256564	−	0.789624i
$405$	−958.822	−	696.625i	−0.117640	−	0.0854706i
$406$	1398.68			0.170974
$407$	5754.34	+	3929.38i	0.700816	+	0.478555i
$408$	312.920			0.0379703
$409$	−10810.5	−	7854.31i	−1.30696	−	0.949561i	−0.306961	−	0.951722i	$-0.599312\pi$
$409$	−10810.5	−	7854.31i	−1.30696	−	0.949561i	−0.999998	+	0.00216100i	$0.999312\pi$
$410$	486.955	−	1498.69i	0.0586561	−	0.180525i
$411$	526.021	+	1618.93i	0.0631307	+	0.194296i
$412$	−156.357	+	113.600i	−0.0186970	+	0.0135841i
$413$	−2193.32	+	1593.54i	−0.261323	+	0.189862i
$414$	−3213.76	−	9890.94i	−0.381516	−	1.17419i
$415$	199.980	−	615.474i	0.0236545	−	0.0728011i
$416$	5058.67	+	3675.34i	0.596206	+	0.433169i
$417$	−1079.08			−0.126722
$418$	1399.31	−	4776.79i	0.163738	−	0.558949i
$419$	−3656.14			−0.426287			−0.213144	−	0.977021i	$-0.568370\pi$
$419$	−3656.14			−0.426287			−0.213144	+	0.977021i	$0.568370\pi$
$420$	62.3186	+	45.2771i	0.00724009	+	0.00526023i
$421$	−1407.32	+	4331.27i	−0.162918	+	0.501409i	−0.998877	−	0.0473826i	$-0.984912\pi$
$421$	−1407.32	+	4331.27i	−0.162918	+	0.501409i	0.835959	+	0.548792i	$0.184912\pi$
$422$	3833.93	+	11799.6i	0.442258	+	1.36113i
$423$	4485.74	−	3259.08i	0.515613	−	0.374614i
$424$	337.437	−	245.163i	0.0386495	−	0.0280805i
$425$	5010.25	+	15420.0i	0.571842	+	1.75995i
$426$	194.920	−	599.902i	0.0221688	−	0.0682286i
$427$	4164.74	+	3025.86i	0.472005	+	0.342932i
$428$	−3003.34			−0.339187
$429$	179.076	−	611.308i	0.0201536	−	0.0687978i
$430$	−2140.64			−0.240072
$431$	−3873.96	−	2814.60i	−0.432952	−	0.314558i	0.349876	−	0.936796i	$-0.386224\pi$
$431$	−3873.96	−	2814.60i	−0.432952	−	0.314558i	−0.782828	+	0.622238i	$0.786224\pi$
$432$	−683.389	+	2103.26i	−0.0761102	+	0.234243i
$433$	−524.318	−	1613.69i	−0.0581920	−	0.179096i	0.917735	−	0.397192i	$-0.130015\pi$
$433$	−524.318	−	1613.69i	−0.0581920	−	0.179096i	−0.975927	+	0.218096i	$0.930015\pi$
$434$	6875.46	−	4995.31i	0.760444	−	0.552495i
$435$	49.3708	−	35.8700i	0.00544172	−	0.00395364i
$436$	2799.46	+	8615.86i	0.307500	+	0.946387i
$437$	−986.281	+	3035.46i	−0.107964	+	0.332279i
$438$	−1422.62	−	1033.59i	−0.155195	−	0.112756i
$439$	−6330.27			−0.688217			−0.344109	−	0.938930i	$-0.611819\pi$
$439$	−6330.27			−0.688217			−0.344109	+	0.938930i	$0.611819\pi$
$440$	168.877	+	115.318i	0.0182974	+	0.0124945i
$441$	−1297.23			−0.140075
$442$	10606.7	+	7706.24i	1.14143	+	0.829295i
$443$	−1688.16	+	5195.62i	−0.181054	+	0.557226i	−0.999858	−	0.0168465i	$-0.994637\pi$
$443$	−1688.16	+	5195.62i	−0.181054	+	0.557226i	0.818804	+	0.574073i	$0.194637\pi$
$444$	−376.302	−	1158.14i	−0.0402219	−	0.123790i
$445$	883.571	−	641.952i	0.0941242	−	0.0683852i
$446$	15135.6	−	10996.7i	1.60694	−	1.16751i
$447$	−429.645	−	1322.31i	−0.0454620	−	0.139918i
$448$	−1315.00	+	4047.16i	−0.138679	+	0.426809i
$449$	−2406.79	−	1748.64i	−0.252970	−	0.183794i	0.454072	−	0.890965i	$-0.349971\pi$
$449$	−2406.79	−	1748.64i	−0.252970	−	0.183794i	−0.707042	+	0.707171i	$0.749971\pi$
$450$	13237.8			1.38674
$451$	−2736.44	−	7654.12i	−0.285707	−	0.799154i
$452$	4054.06			0.421873
$453$	−919.040	−	667.722i	−0.0953207	−	0.0692546i
$454$	832.270	−	2561.46i	0.0860361	−	0.264792i
$455$	89.8935	+	276.664i	0.00926213	+	0.0285059i
$456$	−63.4332	+	46.0869i	−0.00651432	+	0.00473293i
$457$	−3855.35	+	2801.08i	−0.394630	+	0.286715i	−0.767350	−	0.641229i	$-0.778425\pi$
$457$	−3855.35	+	2801.08i	−0.394630	+	0.286715i	0.372720	+	0.927944i	$0.378425\pi$
$458$	3525.32	+	10849.8i	0.359667	+	1.10694i
$459$	−1592.18	+	4900.24i	−0.161910	+	0.498308i
$460$	−1176.92	−	855.080i	−0.119291	−	0.0866703i
$461$	−15835.9			−1.59989			−0.799946	−	0.600072i	$-0.795139\pi$
$461$	−15835.9			−1.59989			−0.799946	+	0.600072i	$0.795139\pi$
$462$	758.551	−	22.1502i	0.0763874	−	0.00223056i
$463$	−842.121			−0.0845285			−0.0422642	−	0.999106i	$-0.513457\pi$
$463$	−842.121			−0.0845285			−0.0422642	+	0.999106i	$0.513457\pi$
$464$	2249.77	+	1634.55i	0.225093	+	0.163539i
$465$	114.583	−	352.649i	0.0114272	−	0.0351693i
$466$	−906.174	−	2788.92i	−0.0900809	−	0.277241i
$467$	−5998.51	+	4358.17i	−0.594385	+	0.431846i	−0.843882	−	0.536530i	$-0.819735\pi$
$467$	−5998.51	+	4358.17i	−0.594385	+	0.431846i	0.249496	+	0.968376i	$0.419735\pi$
$468$	4534.37	−	3294.41i	0.447866	−	0.325394i
$469$	−2209.76	−	6800.95i	−0.217564	−	0.669593i
$470$	457.739	−	1408.78i	0.0449233	−	0.138260i
$471$	727.925	+	528.868i	0.0712123	+	0.0517388i
$472$	1257.80			0.122659
$473$	−8740.00	+	6748.36i	−0.849610	+	0.656004i
$474$	1074.33			0.104105
$475$	−3286.70	−	2387.93i	−0.317482	−	0.230664i
$476$	−2527.18	+	7777.85i	−0.243347	+	0.748944i
$477$	1050.69	+	3233.68i	0.100855	+	0.310399i
$478$	14519.8	−	10549.3i	1.38937	−	1.00944i
$479$	3450.92	−	2507.24i	0.329179	−	0.239163i	−0.410903	−	0.911679i	$-0.634787\pi$
$479$	3450.92	−	2507.24i	0.329179	−	0.239163i	0.740082	+	0.672516i	$0.234787\pi$
$480$	100.435	+	309.108i	0.00955045	+	0.0293933i
$481$	1421.09	−	4373.68i	0.134712	−	0.414600i
$482$	−14759.0	−	10723.0i	−1.39472	−	1.01332i
$483$	−486.602			−0.0458409
$484$	11682.9	−	682.878i	1.09719	−	0.0641321i
$485$	2171.53			0.203308
$486$	5121.76	+	3721.18i	0.478041	+	0.347317i
$487$	5917.43	−	18212.0i	0.550604	−	1.69459i	−0.156674	−	0.987650i	$-0.550077\pi$
$487$	5917.43	−	18212.0i	0.550604	−	1.69459i	0.707279	−	0.706935i	$-0.249923\pi$
$488$	−738.043	−	2271.46i	−0.0684624	−	0.210706i
$489$	−1423.11	+	1033.95i	−0.131606	+	0.0956175i
$490$	−280.372	+	203.703i	−0.0258489	+	0.0187803i
$491$	292.258	+	899.476i	0.0268623	+	0.0826737i	0.963589	−	0.267388i	$-0.0861606\pi$
$491$	292.258	+	899.476i	0.0268623	+	0.0826737i	−0.936727	+	0.350062i	$0.886161\pi$
$492$	−438.981	+	1351.05i	−0.0402252	+	0.123800i
$493$	5241.59	+	3808.24i	0.478843	+	0.347900i
$494$	−3285.10			−0.299198
$495$	−1319.46	+	1018.78i	−0.119808	+	0.0925069i
$496$	16896.8			1.52962
$497$	1202.12	+	873.390i	0.108496	+	0.0788267i
$498$	−344.306	+	1059.67i	−0.0309814	+	0.0953510i
$499$	−6664.15	−	20510.1i	−0.597852	−	1.84000i	−0.539983	−	0.841676i	$-0.681569\pi$
$499$	−6664.15	−	20510.1i	−0.597852	−	1.84000i	−0.0578692	−	0.998324i	$-0.518431\pi$
$500$	3032.70	−	2203.38i	0.271253	−	0.197076i
$501$	2045.46	−	1486.11i	0.182404	−	0.132524i
$502$	7406.29	+	22794.2i	0.658484	+	2.02661i
$503$	−2785.85	+	8573.96i	−0.246948	+	0.760028i	0.748362	+	0.663291i	$0.230841\pi$
$503$	−2785.85	+	8573.96i	−0.246948	+	0.760028i	−0.995310	+	0.0967373i	$0.969159\pi$
$504$	486.906	+	353.758i	0.0430327	+	0.0312651i
$505$	1323.42			0.116616
$506$	−14325.6	+	418.317i	−1.25860	+	0.0367519i
$507$	1172.73			0.102728
$508$	−4612.00	−	3350.82i	−0.402804	−	0.292654i
$509$	−5150.68	+	15852.2i	−0.448527	+	1.38042i	0.430043	+	0.902808i	$0.358498\pi$
$509$	−5150.68	+	15852.2i	−0.448527	+	1.38042i	−0.878570	+	0.477615i	$0.841502\pi$
$510$	210.587	+	648.119i	0.0182842	+	0.0562729i
$511$	3351.23	−	2434.81i	0.290117	−	0.210782i
$512$	−13180.8	+	9576.38i	−1.13772	+	0.826602i
$513$	−398.950	−	1227.84i	−0.0343354	−	0.105674i
$514$	751.017	−	2311.39i	0.0644473	−	0.198348i
$515$	−30.6922	−	22.2992i	−0.00262613	−	0.00190800i
$516$	1929.75			0.164637
$517$	−2572.26	−	7194.89i	−0.218816	−	0.612052i
$518$	5478.63			0.464705
$519$	2077.78	+	1509.60i	0.175731	+	0.127676i
$520$	41.7058	−	128.357i	0.00351716	−	0.0108247i
$521$	−2168.99	−	6675.47i	−0.182390	−	0.561339i	0.817503	−	0.575924i	$-0.195357\pi$
$521$	−2168.99	−	6675.47i	−0.182390	−	0.561339i	−0.999894	+	0.0145844i	$0.995357\pi$
$522$	4279.59	−	3109.30i	0.358836	−	0.260710i
$523$	5439.12	−	3951.75i	0.454754	−	0.330398i	−0.336716	−	0.941606i	$-0.609316\pi$
$523$	5439.12	−	3951.75i	0.454754	−	0.330398i	0.791470	+	0.611208i	$0.209316\pi$
$524$	−4399.16	−	13539.2i	−0.366752	−	1.12875i
$525$	191.399	−	589.067i	0.0159112	−	0.0489695i
$526$	−13549.9	−	9844.57i	−1.12320	−	0.816052i
$527$	39366.8			3.25398
$528$	1246.01	+	850.843i	0.102700	+	0.0701291i
$529$	−2977.28			−0.244701
$530$	734.866	+	533.911i	0.0602274	+	0.0437578i
$531$	−3168.48	+	9751.58i	−0.258946	+	0.796954i
$532$	−633.229	−	1948.88i	−0.0516052	−	0.158824i
$533$	−4340.17	+	3153.32i	−0.352709	+	0.256258i
$534$	−1521.25	+	1105.25i	−0.123279	+	0.0895673i
$535$	−182.179	−	560.689i	−0.0147220	−	0.0453097i
$536$	−1025.21	+	3155.29i	−0.0826166	+	0.254268i
$537$	−2379.01	−	1728.45i	−0.191176	−	0.138898i
$538$	−30502.6			−2.44435
$539$	−502.557	+	1715.57i	−0.0401608	+	0.137096i
$540$	588.445			0.0468938
$541$	718.581	+	522.080i	0.0571058	+	0.0414898i	0.615972	−	0.787768i	$-0.288763\pi$
$541$	718.581	+	522.080i	0.0571058	+	0.0414898i	−0.558866	+	0.829258i	$0.688763\pi$
$542$	7302.83	−	22475.8i	0.578752	−	1.78122i
$543$	365.207	+	1123.99i	0.0288629	+	0.0888307i
$544$	−27916.1	+	20282.2i	−2.20017	+	1.59852i
$545$	−1438.67	+	1045.25i	−0.113075	+	0.0821536i
$546$	−154.770	−	476.334i	−0.0121310	−	0.0373355i
$547$	314.437	−	967.739i	0.0245784	−	0.0756445i	−0.938015	−	0.346595i	$-0.887338\pi$
$547$	314.437	−	967.739i	0.0245784	−	0.0756445i	0.962593	+	0.270950i	$0.0873379\pi$
$548$	16698.1	+	12131.9i	1.30166	+	0.945708i
$549$	19469.5			1.51355
$550$	5128.41	−	17506.7i	0.397593	−	1.35725i
$551$	−1623.42			−0.125517
$552$	182.642	+	132.697i	0.0140829	+	0.0102318i
$553$	−782.052	+	2406.91i	−0.0601379	+	0.185085i
$554$	1599.89	+	4923.96i	0.122695	+	0.377616i
$555$	193.385	−	140.502i	0.0147905	−	0.0107459i
$556$	−10585.2	+	7690.62i	−0.807399	+	0.586610i
$557$	−3462.80	−	10657.4i	−0.263418	−	0.810716i	−0.992054	−	0.125815i	$-0.959845\pi$
$557$	−3462.80	−	10657.4i	−0.263418	−	0.810716i	0.728636	−	0.684901i	$-0.240155\pi$
$558$	9932.32	−	30568.5i	0.753528	−	2.31912i
$559$	5895.82	+	4283.56i	0.446094	+	0.324106i
$560$	−689.031			−0.0519944
$561$	2902.99	+	1982.32i	0.218475	+	0.149187i
$562$	−10343.3			−0.776344
$563$	7260.68	+	5275.19i	0.543519	+	0.394889i	0.825390	−	0.564563i	$-0.190955\pi$
$563$	7260.68	+	5275.19i	0.543519	+	0.394889i	−0.281871	+	0.959452i	$0.590955\pi$
$564$	−412.643	+	1269.99i	−0.0308075	+	0.0948157i
$565$	245.914	+	756.844i	0.0183109	+	0.0563552i
$566$	−4969.13	+	3610.29i	−0.369025	+	0.268112i
$567$	−3888.77	+	2825.36i	−0.288030	+	0.209266i
$568$	−213.030	−	655.638i	−0.0157369	−	0.0484331i
$569$	−1732.61	+	5332.43i	−0.127653	+	0.392877i	−0.994375	−	0.105915i	$-0.966223\pi$
$569$	−1732.61	+	5332.43i	−0.127653	+	0.392877i	0.866722	+	0.498792i	$0.166223\pi$
$570$	−138.144	−	100.367i	−0.0101512	−	0.00737531i
$571$	−9599.03			−0.703515			−0.351758	−	0.936091i	$-0.614416\pi$
$571$	−9599.03			−0.703515			−0.351758	+	0.936091i	$0.614416\pi$
$572$	−2600.15	−	7272.89i	−0.190066	−	0.531635i
$573$	1508.15			0.109954
$574$	−5170.58	−	3756.64i	−0.375985	−	0.273169i
$575$	−3614.67	+	11124.8i	−0.262160	+	0.806847i
$576$	4973.37	+	15306.5i	0.359764	+	1.10724i
$577$	−5074.55	+	3686.88i	−0.366129	+	0.266008i	−0.755604	−	0.655029i	$-0.772656\pi$
$577$	−5074.55	+	3686.88i	−0.366129	+	0.266008i	0.389475	+	0.921037i	$0.372656\pi$
$578$	−42245.0	+	30692.8i	−3.04007	+	2.20874i
$579$	−754.357	−	2321.67i	−0.0541451	−	0.166641i
$580$	228.656	−	703.732i	0.0163697	−	0.0503808i
$581$	−2123.42	−	1542.75i	−0.151625	−	0.110162i
$582$	−3738.74			−0.266282
$583$	4683.52	−	136.762i	0.332713	−	0.00971543i
$584$	−1921.83			−0.136175
$585$	890.077	+	646.679i	0.0629063	+	0.0457041i
$586$	−1240.04	+	3816.46i	−0.0874158	+	0.269038i
$587$	−5855.88	−	18022.5i	−0.411751	−	1.26724i	−0.915124	−	0.403171i	$-0.867908\pi$
$587$	−5855.88	−	18022.5i	−0.411751	−	1.26724i	0.503373	−	0.864069i	$-0.332092\pi$
$588$	252.750	−	183.634i	0.0177266	−	0.0128791i
$589$	−7980.19	+	5797.95i	−0.558265	+	0.405603i
$590$	846.468	+	2605.16i	0.0590653	+	0.181784i
$591$	362.283	−	1114.99i	0.0252155	−	0.0776052i
$592$	8812.33	+	6402.54i	0.611798	+	0.444498i
$593$	23801.9			1.64827			0.824136	−	0.566392i	$-0.191661\pi$
$593$	23801.9			1.64827			0.824136	+	0.566392i	$0.191661\pi$
$594$	4588.55	−	3542.93i	0.316954	−	0.244728i
$595$	−1605.33			−0.110608
$596$	−13638.7	−	9909.10i	−0.937354	−	0.681028i
$597$	−815.791	+	2510.75i	−0.0559265	+	0.172124i
$598$	2922.91	+	8995.79i	0.199877	+	0.615159i
$599$	11667.2	−	8476.73i	0.795843	−	0.578214i	−0.113849	−	0.993498i	$-0.536318\pi$
$599$	11667.2	−	8476.73i	0.795843	−	0.578214i	0.909692	+	0.415285i	$0.136318\pi$
$600$	−232.479	+	168.906i	−0.0158182	+	0.0114926i
$601$	5654.63	+	17403.2i	0.383789	+	1.18118i	0.937355	+	0.348376i	$0.113267\pi$
$601$	5654.63	+	17403.2i	0.383789	+	1.18118i	−0.553565	+	0.832806i	$0.686733\pi$
$602$	−2682.88	+	8257.05i	−0.181638	+	0.559024i
$603$	−21879.9	−	15896.7i	−1.47764	−	1.07357i
$604$	−13774.2			−0.927918
$605$	836.154	+	2139.64i	0.0561893	+	0.143783i
$606$	−2278.53			−0.152738
$607$	19011.2	+	13812.4i	1.27123	+	0.923605i	0.999251	−	0.0386967i	$-0.0123206\pi$
$607$	19011.2	+	13812.4i	1.27123	+	0.923605i	0.271983	+	0.962302i	$0.412321\pi$
$608$	2671.80	−	8222.96i	0.178217	−	0.548495i
$609$	−76.4838	−	235.393i	−0.00508913	−	0.0156627i
$610$	4207.96	−	3057.26i	0.279304	−	0.202926i
$611$	−4079.77	+	2964.13i	−0.270131	+	0.196261i
$612$	9557.84	+	29416.0i	0.631295	+	1.94293i
$613$	−8164.14	+	25126.6i	−0.537922	+	1.65555i	0.199326	+	0.979933i	$0.436125\pi$
$613$	−8164.14	+	25126.6i	−0.537922	+	1.65555i	−0.737248	+	0.675622i	$0.763875\pi$
$614$	−14335.6	−	10415.5i	−0.942246	−	0.684582i
$615$	−278.852			−0.0182836
$616$	656.468	−	506.875i	0.0429381	−	0.0331535i
$617$	11799.5			0.769901			0.384951	−	0.922937i	$-0.374218\pi$
$617$	11799.5			0.769901			0.384951	+	0.922937i	$0.374218\pi$
$618$	52.8429	+	38.3926i	0.00343957	+	0.00249899i
$619$	3501.77	−	10777.3i	0.227380	−	0.699803i	−0.770662	−	0.637245i	$-0.780074\pi$
$619$	3501.77	−	10777.3i	0.227380	−	0.699803i	0.998041	−	0.0625583i	$-0.0199259\pi$
$620$	−1389.34	−	4275.94i	−0.0899953	−	0.276977i
$621$	−3007.31	+	2184.94i	−0.194330	+	0.141189i
$622$	−13059.2	+	9488.06i	−0.841842	+	0.611634i
$623$	−1368.80	−	4212.74i	−0.0880254	−	0.270914i
$624$	307.715	−	947.048i	0.0197411	−	0.0607569i
$625$	−11744.3	−	8532.77i	−0.751638	−	0.546097i
$626$	23125.8			1.47651
$627$	−880.433	+	25.7092i	−0.0560783	+	0.00163752i
$628$	10909.8			0.693230
$629$	20531.3	+	14916.8i	1.30149	+	0.945586i
$630$	−405.027	+	1246.55i	−0.0256138	+	0.0788311i
$631$	−1518.79	−	4674.34i	−0.0958192	−	0.294901i	0.891647	−	0.452731i	$-0.149550\pi$
$631$	−1518.79	−	4674.34i	−0.0958192	−	0.294901i	−0.987466	+	0.157830i	$0.949550\pi$
$632$	949.904	−	690.146i	0.0597866	−	0.0434375i
$633$	1776.18	−	1290.47i	0.111527	−	0.0810293i
$634$	−8364.98	−	25744.8i	−0.524000	−	1.61271i
$635$	345.800	−	1064.26i	0.0216105	−	0.0665102i
$636$	−662.467	−	481.311i	−0.0413027	−	0.0300082i
$637$	1179.83			0.0733856
$638$	−2454.05	−	6864.23i	−0.152283	−	0.425952i
$639$	5619.71			0.347906
$640$	577.593	+	419.646i	0.0356740	+	0.0259187i
$641$	−5237.66	+	16119.9i	−0.322738	+	0.993286i	0.649713	+	0.760179i	$0.274889\pi$
$641$	−5237.66	+	16119.9i	−0.322738	+	0.993286i	−0.972451	+	0.233106i	$0.925111\pi$
$642$	313.658	+	965.341i	0.0192821	+	0.0593442i
$643$	−6239.11	+	4532.98i	−0.382654	+	0.278014i	−0.762439	−	0.647061i	$-0.775998\pi$
$643$	−6239.11	+	4532.98i	−0.382654	+	0.278014i	0.379785	+	0.925075i	$0.375998\pi$
$644$	−4773.32	+	3468.02i	−0.292073	+	0.212203i
$645$	117.056	+	360.261i	0.00714585	+	0.0219927i
$646$	5602.08	−	17241.4i	0.341193	−	1.05009i
$647$	25040.8	+	18193.2i	1.52157	+	1.10549i	0.960702	+	0.277581i	$0.0895326\pi$
$647$	25040.8	+	18193.2i	1.52157	+	1.10549i	0.560868	+	0.827905i	$0.310467\pi$
$648$	2230.10			0.135195
$649$	11668.8	+	7968.08i	0.705762	+	0.481933i
$650$	−12039.7			−0.726519
$651$	−1216.66	−	883.955i	−0.0732483	−	0.0532180i
$652$	−6591.02	+	20285.1i	−0.395896	+	1.21844i
$653$	−1214.19	−	3736.89i	−0.0727639	−	0.223944i	0.908060	−	0.418840i	$-0.137563\pi$
$653$	−1214.19	−	3736.89i	−0.0727639	−	0.223944i	−0.980824	+	0.194896i	$0.937563\pi$
$654$	2476.96	−	1799.62i	0.148099	−	0.107600i
$655$	2260.77	−	1642.54i	0.134863	−	0.0979839i
$656$	−3926.67	−	12085.1i	−0.233705	−	0.719271i
$657$	4841.20	−	14899.7i	0.287478	−	0.884768i
$658$	−4860.35	−	3531.25i	−0.287958	−	0.209214i
$659$	6456.22			0.381637			0.190818	−	0.981625i	$-0.438886\pi$
$659$	6456.22			0.381637			0.190818	+	0.981625i	$0.438886\pi$
$660$	112.863	−	385.277i	0.00665634	−	0.0227226i
$661$	−26232.6			−1.54361			−0.771807	−	0.635856i	$-0.780647\pi$
$661$	−26232.6			−1.54361			−0.771807	+	0.635856i	$0.780647\pi$
$662$	14795.0	+	10749.2i	0.868618	+	0.631088i
$663$	716.924	−	2206.47i	0.0419955	−	0.129249i
$664$	376.296	+	1158.12i	0.0219926	+	0.0676863i
$665$	325.422	−	236.433i	0.0189764	−	0.0137872i
$666$	16763.1	−	12179.1i	0.975310	−	0.708605i
$667$	1444.43	+	4445.51i	0.0838511	+	0.258067i
$668$	9473.36	−	29156.0i	0.548705	−	1.68874i
$669$	−2678.35	−	1945.94i	−0.154785	−	0.112458i
$670$	−7225.15			−0.416615
$671$	7542.62	−	25748.0i	0.433949	−	1.48136i
$672$	1318.19			0.0756700
$673$	16555.4	+	12028.2i	0.948237	+	0.688934i	0.950389	−	0.311063i	$-0.100685\pi$
$673$	16555.4	+	12028.2i	0.948237	+	0.688934i	−0.00215246	+	0.999998i	$0.500685\pi$
$674$	7833.14	−	24107.9i	0.447658	−	1.37775i
$675$	−1462.13	−	4499.98i	−0.0833740	−	0.256599i
$676$	11503.9	−	8358.08i	0.654524	−	0.475539i
$677$	2899.61	−	2106.69i	0.164610	−	0.119596i	−0.502430	−	0.864618i	$-0.667561\pi$
$677$	2899.61	−	2106.69i	0.164610	−	0.119596i	0.667041	+	0.745021i	$0.267561\pi$
$678$	−423.391	−	1303.06i	−0.0239827	−	0.0738110i
$679$	2721.59	−	8376.20i	0.153822	−	0.473415i
$680$	602.546	+	437.775i	0.0339803	+	0.0246881i
$681$	−476.595			−0.0268181
$682$	−36578.4	−	24977.8i	−2.05375	−	1.40242i
$683$	22304.3			1.24956			0.624780	−	0.780801i	$-0.285189\pi$
$683$	22304.3			1.24956			0.624780	+	0.780801i	$0.285189\pi$
$684$	−6269.90	−	4555.35i	−0.350490	−	0.254646i
$685$	−1251.99	+	3853.24i	−0.0698339	+	0.214927i
$686$	434.345	+	1336.78i	0.0241740	+	0.0743999i
$687$	1633.21	−	1186.59i	0.0906997	−	0.0658972i
$688$	−13964.9	+	10146.1i	−0.773846	+	0.562232i
$689$	−955.598	−	2941.03i	−0.0528380	−	0.162619i
$690$	−151.929	+	467.589i	−0.00838237	+	0.0257983i
$691$	−18270.6	−	13274.4i	−1.00586	−	0.730797i	−0.0425198	−	0.999096i	$-0.513539\pi$
$691$	−18270.6	−	13274.4i	−1.00586	−	0.730797i	−0.963336	+	0.268299i	$0.913539\pi$
$692$	31140.8			1.71069
$693$	2276.05	+	6366.35i	0.124762	+	0.348972i
$694$	8932.72			0.488590
$695$	−2077.83	−	1509.63i	−0.113405	−	0.0823938i
$696$	−35.4844	+	109.210i	−0.00193252	+	0.00594769i
$697$	−9148.49	−	28156.2i	−0.497165	−	1.53012i
$698$	31254.0	−	22707.4i	1.69482	−	1.23136i
$699$	−419.811	+	305.011i	−0.0227163	+	0.0165044i
$700$	−2320.75	−	7142.54i	−0.125309	−	0.385661i
$701$	8378.84	−	25787.4i	0.451447	−	1.38941i	−0.423809	−	0.905752i	$-0.639307\pi$
$701$	8378.84	−	25787.4i	0.451447	−	1.38941i	0.875256	−	0.483660i	$-0.160693\pi$
$702$	−3095.34	−	2248.90i	−0.166419	−	0.120910i
$703$	−6358.92			−0.341154
$704$	22169.2	−	647.355i	1.18684	−	0.0346564i
$705$	−262.122			−0.0140029
$706$	37893.1	+	27530.9i	2.02001	+	1.46762i
$707$	1658.64	−	5104.78i	0.0882316	−	0.271549i
$708$	−763.075	−	2348.50i	−0.0405058	−	0.124664i
$709$	1469.45	−	1067.62i	0.0778369	−	0.0565518i	−0.548186	−	0.836356i	$-0.684682\pi$
$709$	1469.45	−	1067.62i	0.0778369	−	0.0565518i	0.626023	+	0.779804i	$0.284682\pi$
$710$	1214.59	−	882.453i	0.0642012	−	0.0466449i
$711$	2957.74	+	9102.99i	0.156011	+	0.480153i
$712$	−635.052	+	1954.49i	−0.0334264	+	0.102876i
$713$	22977.2	+	16693.9i	1.20688	+	0.876847i
$714$	2763.90			0.144869
$715$	1200.04	−	926.581i	0.0627679	−	0.0484646i
$716$	−35655.5			−1.86104
$717$	−2569.38	−	1866.76i	−0.133829	−	0.0972322i
$718$	−7452.63	+	22936.8i	−0.387367	+	1.19219i
$719$	2372.37	+	7301.40i	0.123052	+	0.378715i	0.993541	−	0.113472i	$-0.0361973\pi$
$719$	2372.37	+	7301.40i	0.123052	+	0.378715i	−0.870489	+	0.492188i	$0.836197\pi$
$720$	−2108.24	+	1531.73i	−0.109124	+	0.0792835i
$721$	−124.481	+	90.4405i	−0.00642982	+	0.00467154i
$722$	−7281.92	−	22411.5i	−0.375353	−	1.15522i
$723$	−997.582	+	3070.24i	−0.0513146	+	0.157930i
$724$	11593.2	+	8422.94i	0.595107	+	0.432370i
$725$	−5949.75			−0.304784
$726$	−1439.61	−	3683.83i	−0.0735937	−	0.188319i
$727$	−4117.85			−0.210072			−0.105036	−	0.994468i	$-0.533496\pi$
$727$	−4117.85			−0.210072			−0.105036	+	0.994468i	$0.533496\pi$
$728$	−442.840	−	321.742i	−0.0225450	−	0.0163799i
$729$	−5383.13	+	16567.6i	−0.273491	+	0.841720i
$730$	−1293.34	−	3980.49i	−0.0655735	−	0.201814i
$731$	−32535.9	+	23638.7i	−1.64621	+	1.19604i
$732$	−3793.40	+	2756.07i	−0.191541	+	0.139163i
$733$	806.921	+	2483.45i	0.0406607	+	0.125141i	0.969326	−	0.245777i	$-0.0790431\pi$
$733$	806.921	+	2483.45i	0.0406607	+	0.125141i	−0.928666	+	0.370918i	$0.879043\pi$
$734$	−9530.90	+	29333.1i	−0.479281	+	1.47507i
$735$	49.6138	+	36.0465i	0.00248984	+	0.00180897i
$736$	−24894.6			−1.24678
$737$	−29499.5	+	22777.3i	−1.47439	+	1.13841i
$738$	−24171.6			−1.20565
$739$	4963.53	+	3606.22i	0.247072	+	0.179508i	0.704428	−	0.709775i	$-0.251203\pi$
$739$	4963.53	+	3606.22i	0.247072	+	0.179508i	−0.457356	+	0.889284i	$0.651203\pi$
$740$	895.645	−	2756.51i	0.0444926	−	0.136934i
$741$	179.638	+	552.869i	0.00890577	+	0.0274091i
$742$	2980.45	−	2165.43i	0.147461	−	0.107137i
$743$	5207.46	−	3783.44i	0.257124	−	0.186812i	−0.451754	−	0.892142i	$-0.649202\pi$
$743$	5207.46	−	3783.44i	0.257124	−	0.186812i	0.708878	+	0.705331i	$0.249202\pi$
$744$	215.607	+	663.569i	0.0106244	+	0.0326984i
$745$	1022.61	−	3147.26i	0.0502891	−	0.154774i
$746$	28642.9	+	20810.3i	1.40575	+	1.02134i
$747$	−9926.64			−0.486207
$748$	42604.9	−	1244.09i	2.08260	−	0.0608134i
$749$	−2391.06			−0.116645
$750$	−1024.94	−	744.662i	−0.0499007	−	0.0362550i
$751$	1255.78	−	3864.89i	0.0610173	−	0.187792i	−0.915901	−	0.401403i	$-0.868523\pi$
$751$	1255.78	−	3864.89i	0.0610173	−	0.187792i	0.976919	+	0.213611i	$0.0685226\pi$
$752$	−3691.08	−	11360.0i	−0.178989	−	0.550872i
$753$	3431.18	−	2492.90i	0.166055	−	0.120646i
$754$	−3892.27	+	2827.90i	−0.187995	+	0.136586i
$755$	−835.522	−	2571.47i	−0.0402752	−	0.123954i
$756$	737.501	−	2269.79i	0.0354797	−	0.109195i
$757$	7206.89	+	5236.11i	0.346022	+	0.251400i	0.747198	−	0.664601i	$-0.231398\pi$
$757$	7206.89	+	5236.11i	0.346022	+	0.251400i	−0.401176	+	0.916001i	$0.631398\pi$
$758$	22777.8			1.09146
$759$	853.763	+	2388.07i	0.0408296	+	0.114205i
$760$	−186.620			−0.00890712
$761$	−15377.0	−	11172.0i	−0.732476	−	0.532175i	0.157870	−	0.987460i	$-0.449537\pi$
$761$	−15377.0	−	11172.0i	−0.732476	−	0.532175i	−0.890346	+	0.455285i	$0.849537\pi$
$762$	−595.366	+	1832.35i	−0.0283042	+	0.0871115i
$763$	2228.74	+	6859.35i	0.105748	+	0.325459i
$764$	14794.2	−	10748.6i	0.700568	−	0.508992i
$765$	−4911.86	+	3568.67i	−0.232142	+	0.168661i
$766$	11064.3	+	34052.4i	0.521891	+	1.60622i
$767$	2881.73	−	8869.04i	0.135662	−	0.417526i
$768$	1858.67	+	1350.40i	0.0873293	+	0.0634484i
$769$	−30408.6			−1.42596			−0.712978	−	0.701186i	$-0.752654\pi$
$769$	−30408.6			−1.42596			−0.712978	+	0.701186i	$0.752654\pi$
$770$	1491.62	+	1018.56i	0.0698108	+	0.0476706i
$771$	−430.065			−0.0200887
$772$	−23946.4	−	17398.1i	−1.11639	−	0.811102i
$773$	−11357.9	+	34956.2i	−0.528482	+	1.62650i	0.228842	+	0.973463i	$0.426506\pi$
$773$	−11357.9	+	34956.2i	−0.528482	+	1.62650i	−0.757325	+	0.653038i	$0.773494\pi$
$774$	10146.7	+	31228.4i	0.471209	+	1.45023i
$775$	−29247.0	+	21249.2i	−1.35559	+	0.984894i
$776$	−3305.73	+	2401.75i	−0.152924	+	0.111105i
$777$	−299.586	−	922.031i	−0.0138322	−	0.0425710i
$778$	−9416.92	+	28982.3i	−0.433950	+	1.33556i
$779$	6001.37	+	4360.25i	0.276022	+	0.200542i
$780$	−264.963			−0.0121631
$781$	2177.11	−	7431.95i	0.0997480	−	0.340507i
$782$	−52197.7			−2.38694
$783$	−1529.64	−	1111.35i	−0.0698149	−	0.0507235i
$784$	−863.566	+	2657.78i	−0.0393388	+	0.121072i
$785$	661.774	+	2036.73i	0.0300888	+	0.0926039i
$786$	−3892.37	+	2827.98i	−0.176637	+	0.128334i
$787$	8731.71	−	6343.96i	0.395492	−	0.287342i	−0.372210	−	0.928148i	$-0.621400\pi$
$787$	8731.71	−	6343.96i	0.395492	−	0.287342i	0.767702	+	0.640807i	$0.221400\pi$
$788$	−4392.75	−	13519.5i	−0.198585	−	0.611183i
$789$	−915.857	+	2818.72i	−0.0413249	+	0.127185i
$790$	2068.69	+	1502.99i	0.0931653	+	0.0676885i
$791$	3227.56			0.145081
$792$	881.817	−	3010.24i	0.0395631	−	0.135056i
$793$	−17707.5			−0.792952
$794$	−15842.3	−	11510.1i	−0.708090	−	0.514457i
$795$	49.6706	−	152.871i	0.00221589	−	0.00681982i
$796$	9891.61	+	30443.3i	0.440451	+	1.35557i
$797$	18195.8	−	13220.0i	0.808691	−	0.587548i	−0.104760	−	0.994498i	$-0.533407\pi$
$797$	18195.8	−	13220.0i	0.808691	−	0.587548i	0.913451	+	0.406949i	$0.133407\pi$
$798$	−560.281	+	407.068i	−0.0248543	+	0.0180577i
$799$	−8599.60	−	26466.9i	−0.380766	−	1.17188i
$800$	9792.02	−	30136.7i	0.432750	−	1.33187i
$801$	−13553.1	−	9846.93i	−0.597848	−	0.434362i
$802$	−8716.14			−0.383763
$803$	−17829.0	−	12174.6i	−0.783528	−	0.535036i
$804$	6513.34			0.285706
$805$	−936.981	−	680.756i	−0.0410239	−	0.0298056i
$806$	−9033.43	+	27802.0i	−0.394775	+	1.21499i
$807$	1667.96	+	5133.46i	0.0727572	+	0.223924i
$808$	−2014.64	+	1463.72i	−0.0877163	+	0.0637296i
$809$	28630.1	−	20801.0i	1.24423	−	0.903984i	0.246354	−	0.969180i	$-0.420767\pi$
$809$	28630.1	−	20801.0i	1.24423	−	0.903984i	0.997872	+	0.0651961i	$0.0207673\pi$
$810$	1500.79	+	4618.97i	0.0651018	+	0.200363i
$811$	−3276.64	+	10084.5i	−0.141872	+	0.436638i	−0.996596	−	0.0824460i	$-0.973727\pi$
$811$	−3276.64	+	10084.5i	−0.141872	+	0.436638i	0.854723	+	0.519084i	$0.173727\pi$
$812$	−2427.91	−	1763.98i	−0.104930	−	0.0762359i
$813$	−4181.92			−0.180402
$814$	−9612.48	−	26887.1i	−0.413903	−	1.15773i
$815$	−4186.78			−0.179947
$816$	4445.71	+	3230.00i	0.190724	+	0.138569i
$817$	3113.95	−	9583.77i	0.133346	−	0.410396i
$818$	16921.1	+	52077.9i	0.723268	+	2.22599i
$819$	3609.96	−	2622.79i	0.154020	−	0.111902i
$820$	−2735.39	+	1987.38i	−0.116493	+	0.0846370i
$821$	−3904.51	−	12016.8i	−0.165978	−	0.510829i	0.833129	−	0.553079i	$-0.186547\pi$
$821$	−3904.51	−	12016.8i	−0.165978	−	0.510829i	−0.999107	+	0.0422504i	$0.986547\pi$
$822$	2155.57	−	6634.15i	0.0914647	−	0.281499i
$823$	19827.7	+	14405.6i	0.839792	+	0.610145i	0.922313	−	0.386445i	$-0.126297\pi$
$823$	19827.7	+	14405.6i	0.839792	+	0.610145i	−0.0825206	+	0.996589i	$0.526297\pi$
$824$	71.3860			0.00301802
$825$	−3226.74	+	94.2229i	−0.136171	+	0.00397627i
$826$	11109.7			0.467985
$827$	−26665.5	−	19373.6i	−1.12122	−	0.814616i	−0.136828	−	0.990595i	$-0.543691\pi$
$827$	−26665.5	−	19373.6i	−1.12122	−	0.814616i	−0.984394	+	0.175979i	$0.943691\pi$
$828$	−6895.55	+	21222.3i	−0.289417	+	0.890733i
$829$	−2111.05	−	6497.13i	−0.0884435	−	0.272201i	0.897046	−	0.441937i	$-0.145709\pi$
$829$	−2111.05	−	6497.13i	−0.0884435	−	0.272201i	−0.985490	+	0.169736i	$0.945709\pi$
$830$	−2145.45	+	1558.76i	−0.0897226	+	0.0651873i
$831$	741.196	−	538.511i	0.0309408	−	0.0224798i
$832$	−4523.27	−	13921.2i	−0.188481	−	0.580085i
$833$	−2011.96	+	6192.19i	−0.0836860	+	0.257559i
$834$	3577.42	+	2599.15i	0.148532	+	0.107915i
$835$	6017.72			0.249403
$836$	−8453.36	+	6527.04i	−0.349719	+	0.270027i
$837$	−11488.3			−0.474427
$838$	12121.0	+	8806.43i	0.499658	+	0.363023i
$839$	−4279.34	+	13170.4i	−0.176090	+	0.541948i	−0.999682	−	0.0252348i	$-0.991967\pi$
$839$	−4279.34	+	13170.4i	−0.176090	+	0.541948i	0.823592	+	0.567183i	$0.191967\pi$
$840$	−8.79217	−	27.0595i	−0.000361141	−	0.00111148i
$841$	17807.6	−	12938.0i	0.730151	−	0.530486i
$842$	15098.2	−	10969.5i	0.617955	−	0.448970i
$843$	565.599	+	1740.73i	0.0231082	+	0.0711199i
$844$	8226.20	−	25317.6i	0.335495	−	1.03255i
$845$	2258.17	+	1640.65i	0.0919329	+	0.0667932i
$846$	−22721.4			−0.923376
$847$	9301.12	−	543.661i	0.377320	−	0.0220548i
$848$	7324.63			0.296614
$849$	879.322	+	638.865i	0.0355456	+	0.0258254i
$850$	20531.3	−	63189.0i	0.828493	−	2.54984i
$851$	5657.83	+	17413.0i	0.227906	+	0.701422i
$852$	−1094.93	+	795.515i	−0.0440279	+	0.0319881i
$853$	23749.8	−	17255.2i	0.953314	−	0.692623i	0.00172579	−	0.999999i	$-0.499451\pi$
$853$	23749.8	−	17255.2i	0.953314	−	0.692623i	0.951588	+	0.307375i	$0.0994507\pi$
$854$	−6518.85	−	20063.0i	−0.261207	−	0.803911i
$855$	470.106	−	1446.84i	0.0188038	−	0.0578723i
$856$	897.462	+	652.044i	0.0358348	+	0.0260355i
$857$	−1221.29			−0.0486798			−0.0243399	−	0.999704i	$-0.507748\pi$
$857$	−1221.29			−0.0486798			−0.0243399	+	0.999704i	$0.507748\pi$
$858$	−2066.12	+	1595.30i	−0.0822100	+	0.0634763i
$859$	−19335.2			−0.767998			−0.383999	−	0.923334i	$-0.625453\pi$
$859$	−19335.2			−0.767998			−0.383999	+	0.923334i	$0.625453\pi$
$860$	3715.84	+	2699.72i	0.147336	+	0.107046i
$861$	−349.487	+	1075.61i	−0.0138333	+	0.0425745i
$862$	6063.71	+	18662.2i	0.239595	+	0.737397i
$863$	−36058.3	+	26197.9i	−1.42229	+	1.03336i	−0.430906	+	0.902397i	$0.641806\pi$
$863$	−36058.3	+	26197.9i	−1.42229	+	1.03336i	−0.991388	+	0.130960i	$0.958194\pi$
$864$	8146.69	−	5918.92i	0.320783	−	0.233062i
$865$	1888.96	+	5813.63i	0.0742504	+	0.228519i
$866$	−2148.59	+	6612.67i	−0.0843094	+	0.259478i
$867$	7475.54	+	5431.30i	0.292829	+	0.212753i
$868$	−18234.7			−0.713050
$869$	13184.4	−	384.992i	0.514671	−	0.0150287i
$870$	−250.075			−0.00974522
$871$	19899.7	+	14458.0i	0.774141	+	0.562446i
$872$	1034.02	−	3182.38i	0.0401563	−	0.123588i
$873$	−10293.1	−	31679.0i	−0.399049	−	1.22815i
$874$	10581.2	−	7687.68i	0.409512	−	0.297528i
$875$	2414.42	−	1754.18i	0.0932828	−	0.0677739i
$876$	1165.92	+	3588.34i	0.0449690	+	0.138400i
$877$	7489.97	−	23051.8i	0.288390	−	0.887574i	−0.696972	−	0.717099i	$-0.745470\pi$
$877$	7489.97	−	23051.8i	0.288390	−	0.887574i	0.985362	−	0.170475i	$-0.0545303\pi$
$878$	20986.4	+	15247.5i	0.806671	+	0.586080i
$879$	710.103			0.0272482
$880$	1208.93	+	3381.51i	0.0463103	+	0.129535i
$881$	40076.8			1.53260			0.766301	−	0.642482i	$-0.222095\pi$
$881$	40076.8			1.53260			0.766301	+	0.642482i	$0.222095\pi$
$882$	4300.65	+	3124.60i	0.164184	+	0.119287i
$883$	−144.127	+	443.577i	−0.00549292	+	0.0169055i	−0.953765	−	0.300552i	$-0.902829\pi$
$883$	−144.127	+	443.577i	−0.00549292	+	0.0169055i	0.948272	+	0.317458i	$0.102829\pi$
$884$	−8692.84	−	26753.8i	−0.330737	−	1.01790i
$885$	392.151	−	284.914i	0.0148949	−	0.0108218i
$886$	18111.2	−	13158.5i	0.686746	−	0.498950i
$887$	−6158.44	−	18953.7i	−0.233123	−	0.717479i	−0.997365	−	0.0725491i	$-0.976887\pi$
$887$	−6158.44	−	18953.7i	−0.233123	−	0.717479i	0.764242	−	0.644930i	$-0.223113\pi$
$888$	−138.992	+	427.774i	−0.00525256	+	0.0161657i
$889$	−3671.76	−	2667.69i	−0.138523	−	0.100643i
$890$	−4475.50			−0.168561
$891$	20688.8	+	14127.5i	0.777892	+	0.531187i
$892$	−40141.9			−1.50678
$893$	5641.30	+	4098.64i	0.211398	+	0.153590i
$894$	−1760.63	+	5418.66i	−0.0658660	+	0.202715i
$895$	−2162.81	−	6656.46i	−0.0807764	−	0.248604i
$896$	2342.59	−	1701.99i	0.0873442	−	0.0634593i
$897$	1354.12	−	983.827i	0.0504045	−	0.0366210i
$898$	3767.22	+	11594.3i	0.139993	+	0.430855i
$899$	−4464.11	+	13739.1i	−0.165613	+	0.509705i
$900$	−22978.9	−	16695.1i	−0.851069	−	0.618337i
$901$	17065.2			0.630991
$902$	−9364.24	+	31966.5i	−0.345671	+	1.18001i
$903$	1536.33			0.0566179
$904$	−1211.44	−	880.161i	−0.0445706	−	0.0323824i
$905$	−869.236	+	2675.23i	−0.0319275	+	0.0982627i
$906$	1438.52	+	4427.32i	0.0527503	+	0.162349i
$907$	−17650.1	+	12823.5i	−0.646154	+	0.469458i	−0.861959	−	0.506978i	$-0.830763\pi$
$907$	−17650.1	+	12823.5i	−0.646154	+	0.469458i	0.215805	+	0.976437i	$0.430763\pi$
$908$	−4675.14	+	3396.69i	−0.170870	+	0.124144i
$909$	−6273.03	−	19306.4i	−0.228892	−	0.704459i
$910$	368.371	−	1133.73i	0.0134191	−	0.0412998i
$911$	−17304.1	−	12572.2i	−0.629320	−	0.457228i	0.226844	−	0.973931i	$-0.427159\pi$
$911$	−17304.1	−	12572.2i	−0.629320	−	0.457228i	−0.856165	+	0.516703i	$0.827159\pi$
$912$	−1376.92			−0.0499939
$913$	−3845.65	+	13127.8i	−0.139400	+	0.475866i
$914$	19528.3			0.706716
$915$	−744.627	−	541.004i	−0.0269034	−	0.0195465i
$916$	7564.05	−	23279.7i	0.272842	−	0.839721i
$917$	−3502.31	−	10779.0i	−0.126125	−	0.388172i
$918$	17081.5	−	12410.4i	0.614133	−	0.446194i
$919$	39213.6	−	28490.3i	1.40755	−	1.02264i	0.413874	−	0.910334i	$-0.364175\pi$
$919$	39213.6	−	28490.3i	1.40755	−	1.02264i	0.993673	−	0.112309i	$-0.0358246\pi$
$920$	166.044	+	511.032i	0.00595035	+	0.0183133i
$921$	−968.967	+	2982.17i	−0.0346673	+	0.106695i
$922$	52499.8	+	38143.3i	1.87526	+	1.36246i
$923$	−5111.11			−0.182269
$924$	−1344.67	−	918.213i	−0.0478748	−	0.0326916i
$925$	−23305.1			−0.828398
$926$	2791.84	+	2028.39i	0.0990771	+	0.0719838i
$927$	−179.825	+	553.445i	−0.00637134	+	0.0196090i
$928$	−3912.92	−	12042.7i	−0.138414	−	0.425993i
$929$	27374.5	−	19888.8i	0.966770	−	0.702399i	0.0120565	−	0.999927i	$-0.496162\pi$
$929$	27374.5	−	19888.8i	0.966770	−	0.702399i	0.954713	+	0.297528i	$0.0961622\pi$
$930$	−1229.28	+	893.128i	−0.0433439	+	0.0314912i
$931$	−504.134	−	1551.56i	−0.0177468	−	0.0546192i
$932$	−1944.32	+	5983.99i	−0.0683350	+	0.210313i
$933$	2310.91	+	1678.98i	0.0810888	+	0.0589145i
$934$	30383.9			1.06445
$935$	2816.61	+	7878.36i	0.0985166	+	0.275561i
$936$	−2070.20			−0.0722935
$937$	−32203.7	−	23397.4i	−1.12279	−	0.815752i	−0.138157	−	0.990410i	$-0.544118\pi$
$937$	−32203.7	−	23397.4i	−1.12279	−	0.815752i	−0.984629	+	0.174659i	$0.944118\pi$
$938$	−9055.32	+	27869.4i	−0.315210	+	0.970116i
$939$	−1264.58	−	3891.98i	−0.0439489	−	0.135261i
$940$	−2571.28	+	1868.14i	−0.0892189	+	0.0648213i
$941$	−9486.91	+	6892.65i	−0.328655	+	0.238782i	−0.739860	−	0.672761i	$-0.765108\pi$
$941$	−9486.91	+	6892.65i	−0.328655	+	0.238782i	0.411205	+	0.911543i	$0.365108\pi$
$942$	−1139.38	−	3506.65i	−0.0394087	−	0.121288i
$943$	6600.23	−	20313.4i	0.227925	−	0.701480i
$944$	17869.9	+	12983.2i	0.616117	+	0.447635i
$945$	468.480			0.0161266
$946$	45229.8	−	1320.74i	1.55449	−	0.0453921i
$947$	−30893.8			−1.06010			−0.530049	−	0.847967i	$-0.677826\pi$
$947$	−30893.8			−1.06010			−0.530049	+	0.847967i	$0.677826\pi$
$948$	−1864.88	−	1354.92i	−0.0638909	−	0.0464194i
$949$	−4403.06	+	13551.2i	−0.150611	+	0.463532i
$950$	5144.49	+	15833.1i	0.175694	+	0.540731i
$951$	−3875.32	+	2815.58i	−0.132141	+	0.0960058i
$952$	2443.79	−	1775.52i	0.0831973	−	0.0604463i
$953$	−14914.5	−	45902.1i	−0.506955	−	1.56025i	−0.797458	−	0.603374i	$-0.793823\pi$
$953$	−14914.5	−	45902.1i	−0.506955	−	1.56025i	0.290503	−	0.956874i	$-0.406177\pi$
$954$	4305.58	−	13251.2i	0.146120	−	0.449710i
$955$	2904.03	+	2109.90i	0.0984001	+	0.0714919i
$956$	−38508.7			−1.30278
$957$	−1021.03	+	788.360i	−0.0344881	+	0.0266291i
$958$	−17479.8			−0.589505
$959$	13293.9	+	9658.57i	0.447635	+	0.325226i
$960$	235.113	−	723.605i	0.00790443	−	0.0243273i
$961$	17918.4	+	55147.1i	0.601470	+	1.85113i
$962$	−15246.0	+	11076.9i	−0.510968	+	0.371240i
$963$	−7315.96	+	5315.36i	−0.244812	+	0.177866i
$964$	12095.9	+	37227.2i	0.404130	+	1.24378i
$965$	1795.46	−	5525.86i	0.0598942	−	0.184335i
$966$	1613.21	+	1172.06i	0.0537309	+	0.0390378i
$967$	35218.9			1.17121			0.585607	−	0.810595i	$-0.300856\pi$
$967$	35218.9			1.17121			0.585607	+	0.810595i	$0.300856\pi$
$968$	−3639.35	−	2332.37i	−0.120840	−	0.0774435i
$969$	−3208.00			−0.106353
$970$	−7199.16	−	5230.50i	−0.238300	−	0.173135i
$971$	8917.30	−	27444.6i	0.294717	−	0.907045i	−0.688600	−	0.725142i	$-0.741774\pi$
$971$	8917.30	−	27444.6i	0.294717	−	0.907045i	0.983316	−	0.181903i	$-0.0582257\pi$
$972$	−4197.58	−	12918.8i	−0.138516	−	0.426308i
$973$	−8427.23	+	6122.74i	−0.277662	+	0.201733i
$974$	−63484.3	+	46124.0i	−2.08847	+	1.51736i
$975$	658.365	+	2026.24i	0.0216252	+	0.0665554i
$976$	12960.8	−	39889.3i	0.425067	−	1.30822i
$977$	−7712.04	−	5603.13i	−0.252538	−	0.183480i	0.454313	−	0.890842i	$-0.349885\pi$
$977$	−7712.04	−	5603.13i	−0.252538	−	0.183480i	−0.706851	+	0.707362i	$0.749885\pi$
$978$	7208.41			0.235685
$979$	−18272.9	+	14109.0i	−0.596533	+	0.460598i
$980$	743.589			0.0242378
$981$	22067.8	+	16033.2i	0.718216	+	0.521815i
$982$	1197.63	−	3685.93i	0.0389185	−	0.119779i
$983$	9394.63	+	28913.7i	0.304824	+	0.938153i	0.979743	+	0.200260i	$0.0641788\pi$
$983$	9394.63	+	28913.7i	0.304824	+	0.938153i	−0.674918	+	0.737892i	$0.735821\pi$
$984$	424.497	−	308.415i	0.0137525	−	0.00999178i
$985$	2257.47	−	1640.15i	0.0730244	−	0.0530553i
$986$	−8204.39	−	25250.5i	−0.264991	−	0.815558i
$987$	−328.518	+	1011.08i	−0.0105946	+	0.0326068i
$988$	5702.46	+	4143.08i	0.183623	+	0.133410i
$989$	−29014.4			−0.932866
$990$	6828.23	−	199.388i	0.219207	−	0.00640099i
$991$	25888.0			0.829829			0.414914	−	0.909860i	$-0.363812\pi$
$991$	25888.0			0.829829			0.414914	+	0.909860i	$0.363812\pi$
$992$	−62244.4	−	45223.2i	−1.99220	−	1.44742i
$993$	1000.02	−	3077.74i	0.0319583	−	0.0983576i
$994$	−1881.61	−	5791.00i	−0.0600413	−	0.184788i
$995$	−5083.38	+	3693.29i	−0.161964	+	0.117674i
$996$	1934.09	−	1405.20i	0.0615300	−	0.0447041i
$997$	18551.0	+	57094.1i	0.589284	+	1.81363i	0.581339	+	0.813662i	$0.302529\pi$
$997$	18551.0	+	57094.1i	0.589284	+	1.81363i	0.00794536	+	0.999968i	$0.497471\pi$
$998$	−27308.8	+	84047.8i	−0.866177	+	2.66582i
$999$	−5991.60	−	4353.15i	−0.189756	−	0.137866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.f.a.15.1	✓	32
11.3	even	5	inner	77.4.f.a.36.1	yes	32
11.5	even	5		847.4.a.o.1.15		16
11.6	odd	10		847.4.a.p.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.f.a.15.1	✓	32	1.1	even	1	trivial
77.4.f.a.36.1	yes	32	11.3	even	5	inner
847.4.a.o.1.15		16	11.5	even	5
847.4.a.p.1.2		16	11.6	odd	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.31524 - 2.40867i) q^{2} +(-0.224082 + 0.689654i) q^{3} +(2.71704 + 8.36218i) q^{4} +(-1.39631 + 1.01448i) q^{5} +(2.40403 - 1.74663i) q^{6} +(2.16312 + 6.65740i) q^{7} +(1.00357 - 3.08868i) q^{8} +(21.4180 + 15.5611i) q^{9} +O(q^{10})\)	\(q+(-3.31524 - 2.40867i) q^{2} +(-0.224082 + 0.689654i) q^{3} +(2.71704 + 8.36218i) q^{4} +(-1.39631 + 1.01448i) q^{5} +(2.40403 - 1.74663i) q^{6} +(2.16312 + 6.65740i) q^{7} +(1.00357 - 3.08868i) q^{8} +(21.4180 + 15.5611i) q^{9} +7.07264 q^{10} +(28.8768 - 22.2965i) q^{11} -6.37585 q^{12} +(-19.4797 - 14.1528i) q^{13} +(8.86417 - 27.2811i) q^{14} +(-0.386751 - 1.19030i) q^{15} +(46.1397 - 33.5224i) q^{16} +(107.498 - 78.1017i) q^{17} +(-33.5245 - 103.178i) q^{18} +(-10.2884 + 31.6646i) q^{19} +(-12.2771 - 8.91981i) q^{20} -5.07602 q^{21} +(-149.438 + 4.36369i) q^{22} +95.8630 q^{23} +(1.90524 + 1.38424i) q^{24} +(-37.7066 + 116.049i) q^{25} +(30.4905 + 93.8400i) q^{26} +(-31.3709 + 22.7923i) q^{27} +(-49.7931 + 36.1768i) q^{28} +(15.0677 + 46.3735i) q^{29} +(-1.58485 + 4.87768i) q^{30} +(239.688 + 174.143i) q^{31} -259.690 q^{32} +(8.90607 + 24.9112i) q^{33} -544.502 q^{34} +(-9.77416 - 7.10134i) q^{35} +(-71.9313 + 221.382i) q^{36} +(59.0199 + 181.645i) q^{37} +(110.378 - 80.1944i) q^{38} +(14.1256 - 10.2628i) q^{39} +(1.73210 + 5.33085i) q^{40} +(68.8506 - 211.900i) q^{41} +(16.8282 + 12.2264i) q^{42} -302.665 q^{43} +(264.906 + 180.893i) q^{44} -45.6926 q^{45} +(-317.809 - 230.902i) q^{46} +(64.7197 - 199.187i) q^{47} +(12.7798 + 39.3322i) q^{48} +(-39.6418 + 28.8015i) q^{49} +(404.530 - 293.908i) q^{50} +(29.7748 + 91.6375i) q^{51} +(65.4214 - 201.346i) q^{52} +(103.903 + 75.4896i) q^{53} +158.901 q^{54} +(-17.7016 + 60.4276i) q^{55} +22.7334 q^{56} +(-19.5321 - 14.1909i) q^{57} +(61.7453 - 190.033i) q^{58} +(119.682 + 368.343i) q^{59} +(8.90266 - 6.46816i) q^{60} +(594.964 - 432.266i) q^{61} +(-375.170 - 1154.66i) q^{62} +(-57.2668 + 176.249i) q^{63} +(491.817 + 357.326i) q^{64} +41.5573 q^{65} +(30.4770 - 104.039i) q^{66} -1021.56 q^{67} +(945.176 + 686.711i) q^{68} +(-21.4812 + 66.1123i) q^{69} +(15.2990 + 47.0854i) q^{70} +(171.731 - 124.770i) q^{71} +(69.5579 - 50.5368i) q^{72} +(-182.865 - 562.801i) q^{73} +(241.856 - 744.356i) q^{74} +(-71.5843 - 52.0090i) q^{75} -292.739 q^{76} +(210.900 + 144.014i) q^{77} -71.5495 q^{78} +(292.491 + 212.507i) q^{79} +(-30.4175 + 93.6153i) q^{80} +(212.197 + 653.075i) q^{81} +(-738.654 + 536.663i) q^{82} +(-303.345 + 220.393i) q^{83} +(-13.7917 - 42.4466i) q^{84} +(-70.8676 + 218.108i) q^{85} +(1003.41 + 729.020i) q^{86} -35.3581 q^{87} +(-39.8867 - 111.567i) q^{88} -632.790 q^{89} +(151.482 + 110.058i) q^{90} +(52.0840 - 160.298i) q^{91} +(260.463 + 801.624i) q^{92} +(-173.808 + 126.279i) q^{93} +(-694.336 + 504.465i) q^{94} +(-17.7572 - 54.6509i) q^{95} +(58.1918 - 179.096i) q^{96} +(-1017.89 - 739.539i) q^{97} +200.796 q^{98} +(965.442 - 28.1915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9	\( 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9} - 72 q^{10} - 94 q^{11} - 544 q^{12} + 72 q^{13} + 56 q^{14} + 140 q^{15} + 296 q^{16} + 8 q^{17} + 422 q^{18} + 51 q^{19} - 149 q^{20} - 294 q^{21} - 66 q^{22} - 830 q^{23} + 868 q^{24} - 256 q^{25} + 775 q^{26} + 27 q^{27} + 14 q^{28} + 236 q^{29} + 1008 q^{30} + 554 q^{31} - 1836 q^{32} + 895 q^{33} - 234 q^{34} + 112 q^{35} - 2322 q^{36} + 1439 q^{37} - 267 q^{38} - 18 q^{39} - 1232 q^{40} - 42 q^{41} + 210 q^{42} - 404 q^{43} + 591 q^{44} - 3020 q^{45} + 2169 q^{46} - 714 q^{47} + 4500 q^{48} - 392 q^{49} - 1035 q^{50} + 745 q^{51} + 725 q^{52} + 1351 q^{53} + 648 q^{54} + 1708 q^{55} - 966 q^{56} + 1561 q^{57} - 2529 q^{58} + 543 q^{59} - 316 q^{60} - 1542 q^{61} - 4231 q^{62} - 567 q^{63} + 1172 q^{64} - 4084 q^{65} + 5058 q^{66} - 1744 q^{67} + 2522 q^{68} - 1584 q^{69} + 126 q^{70} - 561 q^{71} - 4810 q^{72} - 144 q^{73} + 575 q^{74} + 1623 q^{75} - 3278 q^{76} + 567 q^{77} - 6582 q^{78} + 5785 q^{79} + 3199 q^{80} + 2403 q^{81} + 1998 q^{82} - 4177 q^{83} + 1652 q^{84} - 4090 q^{85} - 184 q^{86} - 940 q^{87} + 5446 q^{88} - 11554 q^{89} + 11896 q^{90} - 826 q^{91} + 12958 q^{92} - 578 q^{93} - 2042 q^{94} - 1390 q^{95} - 10074 q^{96} - q^{97} - 588 q^{98} + 10027 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9 - 72 * q^10 - 94 * q^11 - 544 * q^12 + 72 * q^13 + 56 * q^14 + 140 * q^15 + 296 * q^16 + 8 * q^17 + 422 * q^18 + 51 * q^19 - 149 * q^20 - 294 * q^21 - 66 * q^22 - 830 * q^23 + 868 * q^24 - 256 * q^25 + 775 * q^26 + 27 * q^27 + 14 * q^28 + 236 * q^29 + 1008 * q^30 + 554 * q^31 - 1836 * q^32 + 895 * q^33 - 234 * q^34 + 112 * q^35 - 2322 * q^36 + 1439 * q^37 - 267 * q^38 - 18 * q^39 - 1232 * q^40 - 42 * q^41 + 210 * q^42 - 404 * q^43 + 591 * q^44 - 3020 * q^45 + 2169 * q^46 - 714 * q^47 + 4500 * q^48 - 392 * q^49 - 1035 * q^50 + 745 * q^51 + 725 * q^52 + 1351 * q^53 + 648 * q^54 + 1708 * q^55 - 966 * q^56 + 1561 * q^57 - 2529 * q^58 + 543 * q^59 - 316 * q^60 - 1542 * q^61 - 4231 * q^62 - 567 * q^63 + 1172 * q^64 - 4084 * q^65 + 5058 * q^66 - 1744 * q^67 + 2522 * q^68 - 1584 * q^69 + 126 * q^70 - 561 * q^71 - 4810 * q^72 - 144 * q^73 + 575 * q^74 + 1623 * q^75 - 3278 * q^76 + 567 * q^77 - 6582 * q^78 + 5785 * q^79 + 3199 * q^80 + 2403 * q^81 + 1998 * q^82 - 4177 * q^83 + 1652 * q^84 - 4090 * q^85 - 184 * q^86 - 940 * q^87 + 5446 * q^88 - 11554 * q^89 + 11896 * q^90 - 826 * q^91 + 12958 * q^92 - 578 * q^93 - 2042 * q^94 - 1390 * q^95 - 10074 * q^96 - q^97 - 588 * q^98 + 10027 * q^99

Introduction

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