LMFDB - Embedded newform 77.4.f.a.36.1

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			36.1
Character	$\chi$	$=$	77.36
Dual form			77.4.f.a.15.1

$q$-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 $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−3.31524	+	2.40867i	−1.17212	+	0.851592i	−0.991261	−	0.131918i	$-0.957887\pi$
$2$	−3.31524	+	2.40867i	−1.17212	+	0.851592i	−0.180855	+	0.983510i	$0.557887\pi$
$3$	−0.224082	−	0.689654i	−0.0431246	−	0.132724i	0.927176	−	0.374626i	$-0.122229\pi$
$3$	−0.224082	−	0.689654i	−0.0431246	−	0.132724i	−0.970301	+	0.241902i	$0.922229\pi$
$4$	2.71704	−	8.36218i	0.339630	−	1.04527i
$5$	−1.39631	−	1.01448i	−0.124890	−	0.0907376i	0.523587	−	0.851972i	$-0.324594\pi$
$5$	−1.39631	−	1.01448i	−0.124890	−	0.0907376i	−0.648477	+	0.761235i	$0.724594\pi$
$6$	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	−0.775862	−	0.630903i	$-0.782685\pi$
$13$	−19.4797	+	14.1528i	−0.415591	+	0.301945i	0.360270	+	0.932848i	$0.382685\pi$
$14$	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	0.954166	+	0.299278i	$0.0967458\pi$
$17$	107.498	+	78.1017i	1.53365	+	1.11426i	0.579484	+	0.814984i	$0.303254\pi$
$18$	−33.5245	+	103.178i	−0.438989	+	1.35107i
$19$	−10.2884	−	31.6646i	−0.124228	−	0.382334i	0.869532	−	0.493877i	$-0.164421\pi$
$19$	−10.2884	−	31.6646i	−0.124228	−	0.382334i	−0.993760	+	0.111543i	$0.964421\pi$
$20$	−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	−0.891155	−	0.453700i	$-0.850104\pi$
$29$	15.0677	−	46.3735i	0.0964827	−	0.296943i	0.987637	+	0.156757i	$0.0501039\pi$
$30$	−1.58485	−	4.87768i	−0.00964511	−	0.0296846i
$31$	239.688	−	174.143i	1.38868	−	1.00894i	0.392675	−	0.919677i	$-0.371550\pi$
$31$	239.688	−	174.143i	1.38868	−	1.00894i	0.996008	−	0.0892605i	$-0.0284504\pi$
$32$	−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	−0.730078	−	0.683363i	$-0.760516\pi$
$37$	59.0199	−	181.645i	0.262238	−	0.807087i	0.992317	−	0.123723i	$-0.0394835\pi$
$38$	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	0.992312	+	0.123761i	$0.0394958\pi$
$41$	68.8506	+	211.900i	0.262260	+	0.807153i	−0.730052	+	0.683391i	$0.760504\pi$
$42$	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	0.999858	+	0.0168469i	$0.00536279\pi$
$47$	64.7197	+	199.187i	0.200858	+	0.618178i	−0.799000	+	0.601331i	$0.794637\pi$
$48$	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	−0.444945	−	0.895558i	$-0.646777\pi$
$53$	103.903	−	75.4896i	0.269285	−	0.195647i	0.714230	+	0.699911i	$0.246777\pi$
$54$	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	−0.727812	−	0.685776i	$-0.759463\pi$
$59$	119.682	−	368.343i	0.264089	−	0.812783i	0.991902	−	0.127007i	$-0.0405371\pi$
$60$	8.90266	+	6.46816i	0.0191555	+	0.0139173i
$61$	594.964	+	432.266i	1.24881	+	0.907312i	0.998152	−	0.0607644i	$-0.0193538\pi$
$61$	594.964	+	432.266i	1.24881	+	0.907312i	0.250656	+	0.968076i	$0.419354\pi$
$62$	−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	0.721988	−	0.691906i	$-0.243229\pi$
$71$	171.731	+	124.770i	0.287053	+	0.208556i	−0.434935	+	0.900462i	$0.643229\pi$
$72$	69.5579	+	50.5368i	0.113854	+	0.0827197i
$73$	−182.865	+	562.801i	−0.293188	+	0.902341i	0.690636	+	0.723203i	$0.257331\pi$
$73$	−182.865	+	562.801i	−0.293188	+	0.902341i	−0.983824	+	0.179138i	$0.942669\pi$
$74$	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	−0.359695	−	0.933070i	$-0.617119\pi$
$79$	292.491	−	212.507i	0.416555	−	0.302645i	0.776250	+	0.630425i	$0.217119\pi$
$80$	−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	0.368852	−	0.929488i	$-0.379751\pi$
$83$	−303.345	−	220.393i	−0.401163	−	0.291462i	−0.770014	+	0.638027i	$0.779751\pi$
$84$	−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	−0.975093	−	0.221795i	$-0.928808\pi$
$97$	−1017.89	+	739.539i	−1.06547	+	0.774112i	−0.0903804	+	0.995907i	$0.528808\pi$
$98$	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	−0.849819	−	0.527074i	$-0.823289\pi$
$101$	−620.341	+	450.704i	−0.611151	+	0.444027i	0.238669	+	0.971101i	$0.423289\pi$
$102$	122.013	+	375.518i	0.118442	+	0.364528i
$103$	6.79248	−	20.9051i	0.00649789	−	0.0199985i	−0.947755	−	0.318999i	$-0.896653\pi$
$103$	6.79248	−	20.9051i	0.00649789	−	0.0199985i	0.954253	+	0.299001i	$0.0966533\pi$
$104$	−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	0.891982	−	0.452071i	$-0.149315\pi$
$107$	−105.554	−	324.861i	−0.0953671	−	0.293510i	−0.987349	+	0.158561i	$0.949315\pi$
$108$	−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	0.992684	−	0.120742i	$-0.0385273\pi$
$113$	142.482	+	438.513i	0.118615	+	0.365061i	−0.874068	+	0.485803i	$0.838527\pi$
$114$	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	0.389260	−	0.921128i	$-0.372731\pi$
$127$	−524.537	−	381.098i	−0.366497	−	0.266276i	−0.755757	+	0.654852i	$0.772731\pi$
$128$	−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	0.992654	−	0.120992i	$-0.0386075\pi$
$137$	1899.13	+	1379.80i	1.18433	+	0.860466i	0.191677	+	0.981458i	$0.438607\pi$
$138$	230.458	+	167.438i	0.142159	+	0.103284i
$139$	459.845	−	1415.26i	0.280601	−	0.863602i	−0.707082	−	0.707132i	$-0.749989\pi$
$139$	459.845	−	1415.26i	0.280601	−	0.863602i	0.987683	−	0.156470i	$-0.0500114\pi$
$140$	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	0.0730690	−	0.997327i	$-0.476721\pi$
$149$	−1551.17	−	1126.99i	−0.852866	−	0.619643i	−0.925935	+	0.377684i	$0.876721\pi$
$150$	112.047	−	344.845i	0.0609907	−	0.187710i
$151$	−484.099	−	1489.90i	−0.260897	−	0.802958i	−0.992610	−	0.121346i	$-0.961279\pi$
$151$	−484.099	−	1489.90i	−0.260897	−	0.802958i	0.731713	−	0.681612i	$-0.238721\pi$
$152$	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	0.999978	+	0.00669019i	$0.00212957\pi$
$157$	383.430	+	1180.08i	0.194911	+	0.599875i	−0.805066	+	0.593185i	$0.797870\pi$
$158$	−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	−0.00610569	−	0.999981i	$-0.501944\pi$
$163$	1962.52	−	1425.86i	0.943046	−	0.685163i	0.949152	+	0.314818i	$0.101944\pi$
$164$	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	−0.999998	−	0.00206828i	$-0.999342\pi$
$167$	−2820.76	+	2049.40i	−1.30705	+	0.949625i	−0.307049	+	0.951694i	$0.599342\pi$
$168$	−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	0.837715	+	0.546108i	$0.183891\pi$
$173$	1094.46	+	3368.40i	0.480984	+	1.48032i	−0.356731	+	0.934207i	$0.616109\pi$
$174$	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	−0.767735	−	0.640767i	$-0.778616\pi$
$179$	−1253.13	−	3856.73i	−0.523258	−	1.61042i	0.244477	−	0.969655i	$-0.421384\pi$
$180$	−124.149	+	382.090i	−0.0514083	+	0.158218i
$181$	1318.53	+	957.967i	0.541466	+	0.393398i	0.824629	−	0.565673i	$-0.191384\pi$
$181$	1318.53	+	957.967i	0.541466	+	0.393398i	−0.283163	+	0.959072i	$0.591384\pi$
$182$	−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	0.752410	+	0.658695i	$0.228891\pi$
$191$	−642.690	+	1978.00i	−0.243473	+	0.749334i	−0.995884	+	0.0906395i	$0.971109\pi$
$192$	−356.639	−	259.113i	−0.134053	−	0.0973953i
$193$	−2723.50	−	1978.74i	−1.01576	−	0.737993i	−0.0503508	−	0.998732i	$-0.516034\pi$
$193$	−2723.50	−	1978.74i	−1.01576	−	0.737993i	−0.965409	+	0.260739i	$0.916034\pi$
$194$	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	−0.910670	−	0.413135i	$-0.864434\pi$
$211$	−2449.41	+	1779.60i	−0.799167	+	0.580629i	0.111502	+	0.993764i	$0.464434\pi$
$212$	−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	−0.904278	−	0.426944i	$-0.859590\pi$
$223$	−1410.81	−	4342.02i	−0.423653	−	1.30387i	0.480625	−	0.876926i	$-0.340410\pi$
$224$	−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	−0.916964	−	0.398969i	$-0.869368\pi$
$227$	203.098	−	625.073i	0.0593838	−	0.182764i	0.976348	+	0.216205i	$0.0693680\pi$
$228$	65.5976	+	201.889i	0.0190540	+	0.0586421i
$229$	−2252.25	+	1636.35i	−0.649925	+	0.472198i	−0.863245	−	0.504784i	$-0.831572\pi$
$229$	−2252.25	+	1636.35i	−0.649925	+	0.472198i	0.213321	+	0.976982i	$0.431572\pi$
$230$	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	−0.503414	−	0.864045i	$-0.667923\pi$
$233$	578.934	−	420.620i	0.162778	−	0.118265i	0.666192	+	0.745780i	$0.267923\pi$
$234$	−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	−0.949166	−	0.314775i	$-0.898071\pi$
$239$	−1353.40	−	4165.35i	−0.366295	−	1.12734i	0.582871	−	0.812564i	$-0.301929\pi$
$240$	−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	−0.993253	−	0.115969i	$-0.963003\pi$
$251$	−4731.71	+	3437.79i	−1.18989	+	0.864507i	−0.196639	+	0.980476i	$0.563003\pi$
$252$	−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	−0.926349	−	0.376668i	$-0.877070\pi$
$257$	183.270	−	564.047i	0.0444828	−	0.136904i	0.970831	+	0.239764i	$0.0770699\pi$
$258$	−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	0.998115	+	0.0613788i	$0.0195498\pi$
$269$	6021.94	+	4375.20i	1.36492	+	0.991675i	0.366809	+	0.930296i	$0.380450\pi$
$270$	−221.875	−	161.202i	−0.0500107	−	0.0363349i
$271$	1782.11	−	5484.76i	0.399466	−	1.22943i	−0.525963	−	0.850507i	$-0.676295\pi$
$271$	1782.11	−	5484.76i	0.399466	−	1.22943i	0.925429	−	0.378922i	$-0.123705\pi$
$272$	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	−0.693097	−	0.720845i	$-0.743754\pi$
$277$	−1022.13	+	742.624i	−0.221712	+	0.161083i	0.471385	+	0.881927i	$0.343754\pi$
$278$	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	0.783051	−	0.621958i	$-0.213662\pi$
$281$	2042.01	+	1483.61i	0.433510	+	0.314963i	−0.349541	+	0.936921i	$0.613662\pi$
$282$	−192.318	+	591.893i	−0.0406112	+	0.124988i
$283$	463.178	+	1425.51i	0.0972899	+	0.299428i	0.987844	−	0.155450i	$-0.0496829\pi$
$283$	463.178	+	1425.51i	0.0972899	+	0.299428i	−0.890554	+	0.454878i	$0.849683\pi$
$284$	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	−0.976682	−	0.214693i	$-0.931125\pi$
$293$	−302.607	+	931.328i	−0.0603361	+	0.185695i	0.916345	+	0.400389i	$0.131125\pi$
$294$	−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	0.998587	+	0.0531322i	$0.0169205\pi$
$311$	1217.26	+	3746.34i	0.221944	+	0.683072i	−0.776644	+	0.629940i	$0.783080\pi$
$312$	−17.5226	+	53.9290i	−0.00317955	+	0.00978566i
$313$	−4565.59	−	3317.09i	−0.824480	−	0.599020i	0.0935120	−	0.995618i	$-0.470191\pi$
$313$	−4565.59	−	3317.09i	−0.824480	−	0.599020i	−0.917992	+	0.396598i	$0.870191\pi$
$314$	−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	−0.00318949	−	0.999995i	$-0.501015\pi$
$317$	5344.19	−	3882.78i	0.946877	−	0.687946i	0.950066	+	0.312049i	$0.101015\pi$
$318$	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	−0.669179	−	0.743101i	$-0.733354\pi$
$337$	1911.52	−	5883.04i	0.308982	−	0.950949i	0.978161	−	0.207848i	$-0.0666458\pi$
$338$	−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	0.442955	−	0.896544i	$-0.353930\pi$
$347$	−1763.53	−	1281.28i	−0.272828	−	0.198221i	−0.715783	+	0.698323i	$0.753930\pi$
$348$	−96.0693	+	295.671i	−0.0147984	+	0.0455449i
$349$	−2913.21	−	8965.95i	−0.446822	−	1.37518i	−0.880474	−	0.474095i	$-0.842775\pi$
$349$	−2913.21	−	8965.95i	−0.446822	−	1.37518i	0.433652	−	0.901081i	$-0.357225\pi$
$350$	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	0.723770	+	0.690041i	$0.242408\pi$
$359$	−1818.66	+	5597.26i	−0.267368	+	0.822875i	−0.991138	+	0.132834i	$0.957592\pi$
$360$	−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	0.637941	+	0.770085i	$0.279786\pi$
$367$	−2325.82	+	7158.14i	−0.330809	+	1.01812i	−0.968750	+	0.248040i	$0.920214\pi$
$368$	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	0.239757	−	0.970833i	$-0.422932\pi$
$379$	−4496.89	−	3267.18i	−0.609471	−	0.442807i	−0.849228	+	0.528026i	$0.822932\pi$
$380$	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	−0.949157	−	0.314803i	$-0.898061\pi$
$383$	−7068.72	+	5135.72i	−0.943067	+	0.685178i	0.00609020	+	0.999981i	$0.498061\pi$
$384$	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	0.682145	+	0.731217i	$0.261047\pi$
$389$	−2298.01	+	7072.53i	−0.299521	+	0.921830i	−0.981665	+	0.190613i	$0.938953\pi$
$390$	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	0.689754	−	0.724044i	$-0.257719\pi$
$401$	1720.77	+	1250.22i	0.214293	+	0.155693i	−0.475461	+	0.879737i	$0.657719\pi$
$402$	−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	−0.999998	−	0.00216100i	$-0.999312\pi$
$409$	−10810.5	+	7854.31i	−1.30696	+	0.949561i	−0.306961	+	0.951722i	$0.599312\pi$
$410$	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	0.835959	−	0.548792i	$-0.184912\pi$
$421$	−1407.32	−	4331.27i	−0.162918	−	0.501409i	−0.998877	+	0.0473826i	$0.984912\pi$
$422$	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	−0.782828	−	0.622238i	$-0.786224\pi$
$431$	−3873.96	+	2814.60i	−0.432952	+	0.314558i	0.349876	+	0.936796i	$0.386224\pi$
$432$	−683.389	−	2103.26i	−0.0761102	−	0.234243i
$433$	−524.318	+	1613.69i	−0.0581920	+	0.179096i	−0.975927	−	0.218096i	$-0.930015\pi$
$433$	−524.318	+	1613.69i	−0.0581920	+	0.179096i	0.917735	+	0.397192i	$0.130015\pi$
$434$	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	0.818804	−	0.574073i	$-0.194637\pi$
$443$	−1688.16	−	5195.62i	−0.181054	−	0.557226i	−0.999858	+	0.0168465i	$0.994637\pi$
$444$	−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	−0.707042	−	0.707171i	$-0.749971\pi$
$449$	−2406.79	+	1748.64i	−0.252970	+	0.183794i	0.454072	+	0.890965i	$0.349971\pi$
$450$	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	0.372720	−	0.927944i	$-0.378425\pi$
$457$	−3855.35	−	2801.08i	−0.394630	−	0.286715i	−0.767350	+	0.641229i	$0.778425\pi$
$458$	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	0.249496	−	0.968376i	$-0.419735\pi$
$467$	−5998.51	−	4358.17i	−0.594385	−	0.431846i	−0.843882	+	0.536530i	$0.819735\pi$
$468$	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	0.740082	−	0.672516i	$-0.234787\pi$
$479$	3450.92	+	2507.24i	0.329179	+	0.239163i	−0.410903	+	0.911679i	$0.634787\pi$
$480$	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	0.707279	+	0.706935i	$0.249923\pi$
$487$	5917.43	+	18212.0i	0.550604	+	1.69459i	−0.156674	+	0.987650i	$0.550077\pi$
$488$	−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	−0.936727	−	0.350062i	$-0.886161\pi$
$491$	292.258	−	899.476i	0.0268623	−	0.0826737i	0.963589	+	0.267388i	$0.0861606\pi$
$492$	−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	−0.0578692	+	0.998324i	$0.518431\pi$
$499$	−6664.15	+	20510.1i	−0.597852	+	1.84000i	−0.539983	+	0.841676i	$0.681569\pi$
$500$	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	−0.995310	−	0.0967373i	$-0.969159\pi$
$503$	−2785.85	−	8573.96i	−0.246948	−	0.760028i	0.748362	−	0.663291i	$-0.230841\pi$
$504$	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	−0.878570	−	0.477615i	$-0.841502\pi$
$509$	−5150.68	−	15852.2i	−0.448527	−	1.38042i	0.430043	−	0.902808i	$-0.358498\pi$
$510$	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	−0.999894	−	0.0145844i	$-0.995357\pi$
$521$	−2168.99	+	6675.47i	−0.182390	+	0.561339i	0.817503	+	0.575924i	$0.195357\pi$
$522$	4279.59	+	3109.30i	0.358836	+	0.260710i
$523$	5439.12	+	3951.75i	0.454754	+	0.330398i	0.791470	−	0.611208i	$-0.209316\pi$
$523$	5439.12	+	3951.75i	0.454754	+	0.330398i	−0.336716	+	0.941606i	$0.609316\pi$
$524$	−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	−0.558866	−	0.829258i	$-0.688763\pi$
$541$	718.581	−	522.080i	0.0571058	−	0.0414898i	0.615972	+	0.787768i	$0.288763\pi$
$542$	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	0.962593	−	0.270950i	$-0.0873379\pi$
$547$	314.437	+	967.739i	0.0245784	+	0.0756445i	−0.938015	+	0.346595i	$0.887338\pi$
$548$	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	0.728636	+	0.684901i	$0.240155\pi$
$557$	−3462.80	+	10657.4i	−0.263418	+	0.810716i	−0.992054	+	0.125815i	$0.959845\pi$
$558$	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	−0.281871	−	0.959452i	$-0.590955\pi$
$563$	7260.68	−	5275.19i	0.543519	−	0.394889i	0.825390	+	0.564563i	$0.190955\pi$
$564$	−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	0.866722	−	0.498792i	$-0.166223\pi$
$569$	−1732.61	−	5332.43i	−0.127653	−	0.392877i	−0.994375	+	0.105915i	$0.966223\pi$
$570$	−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	0.389475	−	0.921037i	$-0.372656\pi$
$577$	−5074.55	−	3686.88i	−0.366129	−	0.266008i	−0.755604	+	0.655029i	$0.772656\pi$
$578$	−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	0.503373	+	0.864069i	$0.332092\pi$
$587$	−5855.88	+	18022.5i	−0.411751	+	1.26724i	−0.915124	+	0.403171i	$0.867908\pi$
$588$	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	0.909692	−	0.415285i	$-0.136318\pi$
$599$	11667.2	+	8476.73i	0.795843	+	0.578214i	−0.113849	+	0.993498i	$0.536318\pi$
$600$	−232.479	−	168.906i	−0.0158182	−	0.0114926i
$601$	5654.63	−	17403.2i	0.383789	−	1.18118i	−0.553565	−	0.832806i	$-0.686733\pi$
$601$	5654.63	−	17403.2i	0.383789	−	1.18118i	0.937355	−	0.348376i	$-0.113267\pi$
$602$	−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	0.271983	−	0.962302i	$-0.412321\pi$
$607$	19011.2	−	13812.4i	1.27123	−	0.923605i	0.999251	+	0.0386967i	$0.0123206\pi$
$608$	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	−0.737248	−	0.675622i	$-0.763875\pi$
$613$	−8164.14	−	25126.6i	−0.537922	−	1.65555i	0.199326	−	0.979933i	$-0.436125\pi$
$614$	−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	0.998041	+	0.0625583i	$0.0199259\pi$
$619$	3501.77	+	10777.3i	0.227380	+	0.699803i	−0.770662	+	0.637245i	$0.780074\pi$
$620$	−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	−0.987466	−	0.157830i	$-0.949550\pi$
$631$	−1518.79	+	4674.34i	−0.0958192	+	0.294901i	0.891647	+	0.452731i	$0.149550\pi$
$632$	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	−0.972451	−	0.233106i	$-0.925111\pi$
$641$	−5237.66	−	16119.9i	−0.322738	−	0.993286i	0.649713	−	0.760179i	$-0.274889\pi$
$642$	313.658	−	965.341i	0.0192821	−	0.0593442i
$643$	−6239.11	−	4532.98i	−0.382654	−	0.278014i	0.379785	−	0.925075i	$-0.375998\pi$
$643$	−6239.11	−	4532.98i	−0.382654	−	0.278014i	−0.762439	+	0.647061i	$0.775998\pi$
$644$	−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	0.560868	−	0.827905i	$-0.310467\pi$
$647$	25040.8	−	18193.2i	1.52157	−	1.10549i	0.960702	−	0.277581i	$-0.0895326\pi$
$648$	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	−0.980824	−	0.194896i	$-0.937563\pi$
$653$	−1214.19	+	3736.89i	−0.0727639	+	0.223944i	0.908060	+	0.418840i	$0.137563\pi$
$654$	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	−0.00215246	−	0.999998i	$-0.500685\pi$
$673$	16555.4	−	12028.2i	0.948237	−	0.688934i	0.950389	+	0.311063i	$0.100685\pi$
$674$	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	0.667041	−	0.745021i	$-0.267561\pi$
$677$	2899.61	+	2106.69i	0.164610	+	0.119596i	−0.502430	+	0.864618i	$0.667561\pi$
$678$	−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	−0.963336	−	0.268299i	$-0.913539\pi$
$691$	−18270.6	+	13274.4i	−1.00586	+	0.730797i	−0.0425198	+	0.999096i	$0.513539\pi$
$692$	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	0.875256	+	0.483660i	$0.160693\pi$
$701$	8378.84	+	25787.4i	0.451447	+	1.38941i	−0.423809	+	0.905752i	$0.639307\pi$
$702$	−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	0.626023	−	0.779804i	$-0.284682\pi$
$709$	1469.45	+	1067.62i	0.0778369	+	0.0565518i	−0.548186	+	0.836356i	$0.684682\pi$
$710$	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	−0.870489	−	0.492188i	$-0.836197\pi$
$719$	2372.37	−	7301.40i	0.123052	−	0.378715i	0.993541	+	0.113472i	$0.0361973\pi$
$720$	−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	−0.928666	−	0.370918i	$-0.879043\pi$
$733$	806.921	−	2483.45i	0.0406607	−	0.125141i	0.969326	+	0.245777i	$0.0790431\pi$
$734$	−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	−0.457356	−	0.889284i	$-0.651203\pi$
$739$	4963.53	−	3606.22i	0.247072	−	0.179508i	0.704428	+	0.709775i	$0.251203\pi$
$740$	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	0.708878	−	0.705331i	$-0.249202\pi$
$743$	5207.46	+	3783.44i	0.257124	+	0.186812i	−0.451754	+	0.892142i	$0.649202\pi$
$744$	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	0.976919	−	0.213611i	$-0.0685226\pi$
$751$	1255.78	+	3864.89i	0.0610173	+	0.187792i	−0.915901	+	0.401403i	$0.868523\pi$
$752$	−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	−0.401176	−	0.916001i	$-0.631398\pi$
$757$	7206.89	−	5236.11i	0.346022	−	0.251400i	0.747198	+	0.664601i	$0.231398\pi$
$758$	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	−0.890346	−	0.455285i	$-0.849537\pi$
$761$	−15377.0	+	11172.0i	−0.732476	+	0.532175i	0.157870	+	0.987460i	$0.449537\pi$
$762$	−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	−0.757325	−	0.653038i	$-0.773494\pi$
$773$	−11357.9	−	34956.2i	−0.528482	−	1.62650i	0.228842	−	0.973463i	$-0.426506\pi$
$774$	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	0.767702	−	0.640807i	$-0.221400\pi$
$787$	8731.71	+	6343.96i	0.395492	+	0.287342i	−0.372210	+	0.928148i	$0.621400\pi$
$788$	−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	0.913451	−	0.406949i	$-0.133407\pi$
$797$	18195.8	+	13220.0i	0.808691	+	0.587548i	−0.104760	+	0.994498i	$0.533407\pi$
$798$	−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	0.997872	−	0.0651961i	$-0.0207673\pi$
$809$	28630.1	+	20801.0i	1.24423	+	0.903984i	0.246354	+	0.969180i	$0.420767\pi$
$810$	1500.79	−	4618.97i	0.0651018	−	0.200363i
$811$	−3276.64	−	10084.5i	−0.141872	−	0.436638i	0.854723	−	0.519084i	$-0.173727\pi$
$811$	−3276.64	−	10084.5i	−0.141872	−	0.436638i	−0.996596	+	0.0824460i	$0.973727\pi$
$812$	−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	−0.999107	−	0.0422504i	$-0.986547\pi$
$821$	−3904.51	+	12016.8i	−0.165978	+	0.510829i	0.833129	+	0.553079i	$0.186547\pi$
$822$	2155.57	+	6634.15i	0.0914647	+	0.281499i
$823$	19827.7	−	14405.6i	0.839792	−	0.610145i	−0.0825206	−	0.996589i	$-0.526297\pi$
$823$	19827.7	−	14405.6i	0.839792	−	0.610145i	0.922313	+	0.386445i	$0.126297\pi$
$824$	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	−0.984394	−	0.175979i	$-0.943691\pi$
$827$	−26665.5	+	19373.6i	−1.12122	+	0.814616i	−0.136828	+	0.990595i	$0.543691\pi$
$828$	−6895.55	−	21222.3i	−0.289417	−	0.890733i
$829$	−2111.05	+	6497.13i	−0.0884435	+	0.272201i	−0.985490	−	0.169736i	$-0.945709\pi$
$829$	−2111.05	+	6497.13i	−0.0884435	+	0.272201i	0.897046	+	0.441937i	$0.145709\pi$
$830$	−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	0.823592	−	0.567183i	$-0.191967\pi$
$839$	−4279.34	−	13170.4i	−0.176090	−	0.541948i	−0.999682	+	0.0252348i	$0.991967\pi$
$840$	−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	0.951588	−	0.307375i	$-0.0994507\pi$
$853$	23749.8	+	17255.2i	0.953314	+	0.692623i	0.00172579	+	0.999999i	$0.499451\pi$
$854$	−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	−0.991388	−	0.130960i	$-0.958194\pi$
$863$	−36058.3	−	26197.9i	−1.42229	−	1.03336i	−0.430906	−	0.902397i	$-0.641806\pi$
$864$	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	0.985362	+	0.170475i	$0.0545303\pi$
$877$	7489.97	+	23051.8i	0.288390	+	0.887574i	−0.696972	+	0.717099i	$0.745470\pi$
$878$	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	0.948272	−	0.317458i	$-0.102829\pi$
$883$	−144.127	−	443.577i	−0.00549292	−	0.0169055i	−0.953765	+	0.300552i	$0.902829\pi$
$884$	−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	0.764242	+	0.644930i	$0.223113\pi$
$887$	−6158.44	+	18953.7i	−0.233123	+	0.717479i	−0.997365	+	0.0725491i	$0.976887\pi$
$888$	−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	0.215805	−	0.976437i	$-0.430763\pi$
$907$	−17650.1	−	12823.5i	−0.646154	−	0.469458i	−0.861959	+	0.506978i	$0.830763\pi$
$908$	−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	−0.856165	−	0.516703i	$-0.827159\pi$
$911$	−17304.1	+	12572.2i	−0.629320	+	0.457228i	0.226844	+	0.973931i	$0.427159\pi$
$912$	−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	0.993673	+	0.112309i	$0.0358246\pi$
$919$	39213.6	+	28490.3i	1.40755	+	1.02264i	0.413874	+	0.910334i	$0.364175\pi$
$920$	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	0.954713	−	0.297528i	$-0.0961622\pi$
$929$	27374.5	+	19888.8i	0.966770	+	0.702399i	0.0120565	+	0.999927i	$0.496162\pi$
$930$	−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	−0.984629	−	0.174659i	$-0.944118\pi$
$937$	−32203.7	+	23397.4i	−1.12279	+	0.815752i	−0.138157	+	0.990410i	$0.544118\pi$
$938$	−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	0.411205	−	0.911543i	$-0.365108\pi$
$941$	−9486.91	−	6892.65i	−0.328655	−	0.238782i	−0.739860	+	0.672761i	$0.765108\pi$
$942$	−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	0.290503	+	0.956874i	$0.406177\pi$
$953$	−14914.5	+	45902.1i	−0.506955	+	1.56025i	−0.797458	+	0.603374i	$0.793823\pi$
$954$	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	0.983316	+	0.181903i	$0.0582257\pi$
$971$	8917.30	+	27444.6i	0.294717	+	0.907045i	−0.688600	+	0.725142i	$0.741774\pi$
$972$	−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	−0.706851	−	0.707362i	$-0.749885\pi$
$977$	−7712.04	+	5603.13i	−0.252538	+	0.183480i	0.454313	+	0.890842i	$0.349885\pi$
$978$	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	−0.674918	−	0.737892i	$-0.735821\pi$
$983$	9394.63	−	28913.7i	0.304824	−	0.938153i	0.979743	−	0.200260i	$-0.0641788\pi$
$984$	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	0.00794536	−	0.999968i	$-0.497471\pi$
$997$	18551.0	−	57094.1i	0.589284	−	1.81363i	0.581339	−	0.813662i	$-0.302529\pi$
$998$	−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.36.1	yes	32
11.2	odd	10		847.4.a.p.1.2		16
11.4	even	5	inner	77.4.f.a.15.1	✓	32
11.9	even	5		847.4.a.o.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.f.a.15.1	✓	32	11.4	even	5	inner
77.4.f.a.36.1	yes	32	1.1	even	1	trivial
847.4.a.o.1.15		16	11.9	even	5
847.4.a.p.1.2		16	11.2	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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