LMFDB - Embedded newform 98.4.g.a.65.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$7$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			65.7
Character	$\chi$	$=$	98.65
Dual form			98.4.g.a.95.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.730682 - 1.86175i) q^{2} +(0.672876 + 8.97890i) q^{3} +(-2.93221 + 2.72069i) q^{4} +(-11.3832 + 7.76096i) q^{5} +(16.2248 - 7.81345i) q^{6} +(9.97686 - 15.6033i) q^{7} +(7.20775 + 3.47107i) q^{8} +(-53.4695 + 8.05922i) q^{9} +O(q^{10})$	\(q+(-0.730682 - 1.86175i) q^{2} +(0.672876 + 8.97890i) q^{3} +(-2.93221 + 2.72069i) q^{4} +(-11.3832 + 7.76096i) q^{5} +(16.2248 - 7.81345i) q^{6} +(9.97686 - 15.6033i) q^{7} +(7.20775 + 3.47107i) q^{8} +(-53.4695 + 8.05922i) q^{9} +(22.7665 + 15.5219i) q^{10} +(-57.9216 - 8.73027i) q^{11} +(-26.4018 - 24.4973i) q^{12} +(40.2531 - 50.4757i) q^{13} +(-36.3393 - 7.17337i) q^{14} +(-77.3444 - 96.9868i) q^{15} +(1.19568 - 15.9553i) q^{16} +(-10.8783 + 3.35551i) q^{17} +(54.0734 + 93.6579i) q^{18} +(-72.7961 + 126.087i) q^{19} +(12.2628 - 53.7270i) q^{20} +(146.813 + 79.0822i) q^{21} +(26.0687 + 114.214i) q^{22} +(8.09478 + 2.49691i) q^{23} +(-26.3165 + 67.0533i) q^{24} +(23.6780 - 60.3305i) q^{25} +(-123.385 - 38.0593i) q^{26} +(-54.2442 - 237.659i) q^{27} +(13.1975 + 72.8960i) q^{28} +(-60.9392 + 266.992i) q^{29} +(-124.051 + 214.862i) q^{30} +(-10.6860 - 18.5086i) q^{31} +(-30.5783 + 9.43217i) q^{32} +(39.4142 - 525.946i) q^{33} +(14.1957 + 17.8009i) q^{34} +(7.52740 + 255.046i) q^{35} +(134.857 - 169.105i) q^{36} +(-118.869 - 110.294i) q^{37} +(287.932 + 43.3988i) q^{38} +(480.302 + 327.464i) q^{39} +(-108.986 + 16.4271i) q^{40} +(-8.69936 - 4.18939i) q^{41} +(39.9571 - 331.114i) q^{42} +(-82.0571 + 39.5166i) q^{43} +(193.590 - 131.988i) q^{44} +(546.108 - 506.714i) q^{45} +(-1.26610 - 16.8949i) q^{46} +(99.7047 + 254.043i) q^{47} +144.065 q^{48} +(-143.924 - 311.343i) q^{49} -129.621 q^{50} +(-37.4486 - 95.4174i) q^{51} +(19.2986 + 257.521i) q^{52} +(-52.4017 + 48.6216i) q^{53} +(-402.826 + 274.642i) q^{54} +(727.090 - 350.148i) q^{55} +(126.071 - 77.8341i) q^{56} +(-1181.10 - 568.788i) q^{57} +(541.599 - 81.6329i) q^{58} +(-438.370 - 298.876i) q^{59} +(490.661 + 73.9552i) q^{60} +(115.477 + 107.147i) q^{61} +(-26.6503 + 33.4185i) q^{62} +(-407.707 + 914.705i) q^{63} +(39.9033 + 50.0372i) q^{64} +(-66.4699 + 886.979i) q^{65} +(-1007.98 + 310.920i) q^{66} +(440.241 + 762.519i) q^{67} +(22.7681 - 39.4356i) q^{68} +(-16.9727 + 74.3623i) q^{69} +(469.331 - 200.372i) q^{70} +(-8.32075 - 36.4556i) q^{71} +(-413.369 - 127.507i) q^{72} +(89.8459 - 228.924i) q^{73} +(-118.485 + 301.894i) q^{74} +(557.634 + 172.007i) q^{75} +(-129.589 - 567.767i) q^{76} +(-714.096 + 816.665i) q^{77} +(258.708 - 1133.47i) q^{78} +(-313.147 + 542.386i) q^{79} +(110.217 + 190.902i) q^{80} +(702.300 - 216.631i) q^{81} +(-1.44312 + 19.2571i) q^{82} +(872.609 + 1094.22i) q^{83} +(-645.646 + 167.549i) q^{84} +(97.7884 - 122.623i) q^{85} +(133.528 + 123.896i) q^{86} +(-2438.30 - 367.514i) q^{87} +(-387.181 - 263.975i) q^{88} +(37.4322 - 5.64200i) q^{89} +(-1342.41 - 646.469i) q^{90} +(-385.988 - 1131.67i) q^{91} +(-30.5289 + 14.7019i) q^{92} +(158.997 - 108.402i) q^{93} +(400.112 - 371.250i) q^{94} +(-149.897 - 2000.24i) q^{95} +(-105.266 - 268.213i) q^{96} -525.925 q^{97} +(-474.480 + 495.444i) q^{98} +3167.39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 14 q^{2} - 8 q^{3} + 28 q^{4} + 7 q^{5} + 10 q^{6} + 20 q^{7} + 112 q^{8} + 189 q^{9}+O(q^{10}) $ 84 * q - 14 * q^2 - 8 * q^3 + 28 * q^4 + 7 * q^5 + 10 * q^6 + 20 * q^7 + 112 * q^8 + 189 * q^9	\( 84 q - 14 q^{2} - 8 q^{3} + 28 q^{4} + 7 q^{5} + 10 q^{6} + 20 q^{7} + 112 q^{8} + 189 q^{9} - 14 q^{10} - 77 q^{11} - 4 q^{12} - 62 q^{13} - 34 q^{14} - 217 q^{15} + 112 q^{16} - 165 q^{17} + 798 q^{18} + 25 q^{19} + 56 q^{20} + 394 q^{21} - 210 q^{22} + 329 q^{23} + 8 q^{24} + 126 q^{25} - 398 q^{26} - 1058 q^{27} + 132 q^{28} + 7 q^{29} - 70 q^{30} - 793 q^{31} - 224 q^{32} + 875 q^{33} + 222 q^{34} - 1260 q^{35} - 924 q^{36} + 2540 q^{38} + 1799 q^{39} + 280 q^{40} + 1220 q^{41} + 1482 q^{42} - 770 q^{43} - 112 q^{44} - 2030 q^{45} - 1834 q^{46} - 1438 q^{47} + 32 q^{48} - 2626 q^{49} - 4396 q^{50} - 2569 q^{51} - 688 q^{52} - 2744 q^{53} + 62 q^{54} + 343 q^{55} - 216 q^{56} - 2058 q^{57} + 3976 q^{58} + 396 q^{59} + 1316 q^{60} + 4930 q^{61} + 1560 q^{62} + 4717 q^{63} - 896 q^{64} + 238 q^{65} - 1624 q^{66} + 2695 q^{67} + 1076 q^{68} - 931 q^{69} - 742 q^{70} - 539 q^{71} - 336 q^{72} + 1989 q^{73} - 1176 q^{74} - 2780 q^{75} - 1096 q^{76} + 4627 q^{77} + 336 q^{78} - 1197 q^{79} + 112 q^{80} + 9674 q^{81} + 1220 q^{82} + 831 q^{83} - 404 q^{84} + 161 q^{85} - 3122 q^{86} + 9477 q^{87} + 224 q^{88} - 7537 q^{89} - 4214 q^{90} + 4351 q^{91} - 2044 q^{92} - 8176 q^{93} + 3072 q^{94} - 11753 q^{95} + 32 q^{96} + 13530 q^{97} + 862 q^{98} + 6090 q^{99}+O(q^{100}) \) 84 * q - 14 * q^2 - 8 * q^3 + 28 * q^4 + 7 * q^5 + 10 * q^6 + 20 * q^7 + 112 * q^8 + 189 * q^9 - 14 * q^10 - 77 * q^11 - 4 * q^12 - 62 * q^13 - 34 * q^14 - 217 * q^15 + 112 * q^16 - 165 * q^17 + 798 * q^18 + 25 * q^19 + 56 * q^20 + 394 * q^21 - 210 * q^22 + 329 * q^23 + 8 * q^24 + 126 * q^25 - 398 * q^26 - 1058 * q^27 + 132 * q^28 + 7 * q^29 - 70 * q^30 - 793 * q^31 - 224 * q^32 + 875 * q^33 + 222 * q^34 - 1260 * q^35 - 924 * q^36 + 2540 * q^38 + 1799 * q^39 + 280 * q^40 + 1220 * q^41 + 1482 * q^42 - 770 * q^43 - 112 * q^44 - 2030 * q^45 - 1834 * q^46 - 1438 * q^47 + 32 * q^48 - 2626 * q^49 - 4396 * q^50 - 2569 * q^51 - 688 * q^52 - 2744 * q^53 + 62 * q^54 + 343 * q^55 - 216 * q^56 - 2058 * q^57 + 3976 * q^58 + 396 * q^59 + 1316 * q^60 + 4930 * q^61 + 1560 * q^62 + 4717 * q^63 - 896 * q^64 + 238 * q^65 - 1624 * q^66 + 2695 * q^67 + 1076 * q^68 - 931 * q^69 - 742 * q^70 - 539 * q^71 - 336 * q^72 + 1989 * q^73 - 1176 * q^74 - 2780 * q^75 - 1096 * q^76 + 4627 * q^77 + 336 * q^78 - 1197 * q^79 + 112 * q^80 + 9674 * q^81 + 1220 * q^82 + 831 * q^83 - 404 * q^84 + 161 * q^85 - 3122 * q^86 + 9477 * q^87 + 224 * q^88 - 7537 * q^89 - 4214 * q^90 + 4351 * q^91 - 2044 * q^92 - 8176 * q^93 + 3072 * q^94 - 11753 * q^95 + 32 * q^96 + 13530 * q^97 + 862 * q^98 + 6090 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{10}{21}\right)$

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 $

$2$	−0.730682	−	1.86175i	−0.258335	−	0.658227i
$2$	−0.730682	−	1.86175i	−0.258335	−	0.658227i
$3$	0.672876	+	8.97890i	0.129495	+	1.72799i	0.562671	+	0.826681i	$0.309774\pi$
$3$	0.672876	+	8.97890i	0.129495	+	1.72799i	−0.433176	+	0.901309i	$0.642607\pi$
$4$	−2.93221	+	2.72069i	−0.366526	+	0.340086i
$5$	−11.3832	+	7.76096i	−1.01815	+	0.694161i	−0.952768	−	0.303699i	$-0.901778\pi$
$5$	−11.3832	+	7.76096i	−1.01815	+	0.694161i	−0.0653797	+	0.997860i	$0.520826\pi$
$6$	16.2248	−	7.81345i	1.10396	−	0.531638i
$7$	9.97686	−	15.6033i	0.538700	−	0.842498i
$7$	9.97686	−	15.6033i	0.538700	−	0.842498i
$8$	7.20775	+	3.47107i	0.318541	+	0.153401i
$9$	−53.4695	+	8.05922i	−1.98035	+	0.298490i
$10$	22.7665	+	15.5219i	0.719939	+	0.490846i
$11$	−57.9216	−	8.73027i	−1.58764	−	0.239298i	−0.704949	−	0.709258i	$-0.749030\pi$
$11$	−57.9216	−	8.73027i	−1.58764	−	0.239298i	−0.882688	+	0.469960i	$0.844268\pi$
$12$	−26.4018	−	24.4973i	−0.635129	−	0.589314i
$13$	40.2531	−	50.4757i	0.858784	−	1.07688i	−0.137479	−	0.990505i	$-0.543900\pi$
$13$	40.2531	−	50.4757i	0.858784	−	1.07688i	0.996263	−	0.0863760i	$-0.0275286\pi$
$14$	−36.3393	−	7.17337i	−0.693720	−	0.136940i
$15$	−77.3444	−	96.9868i	−1.33135	−	1.66946i
$16$	1.19568	−	15.9553i	0.0186825	−	0.249301i
$17$	−10.8783	+	3.35551i	−0.155199	+	0.0478725i	−0.371381	−	0.928481i	$-0.621116\pi$
$17$	−10.8783	+	3.35551i	−0.155199	+	0.0478725i	0.216182	+	0.976353i	$0.430639\pi$
$18$	54.0734	+	93.6579i	0.708068	+	1.22641i
$19$	−72.7961	+	126.087i	−0.878977	+	1.52243i	−0.0265124	+	0.999648i	$0.508440\pi$
$19$	−72.7961	+	126.087i	−0.878977	+	1.52243i	−0.852465	+	0.522785i	$0.824893\pi$
$20$	12.2628	−	53.7270i	0.137103	−	0.600686i
$21$	146.813	+	79.0822i	1.52559	+	0.821769i
$22$	26.0687	+	114.214i	0.252630	+	1.10684i
$23$	8.09478	+	2.49691i	0.0733860	+	0.0226366i	0.331231	−	0.943550i	$-0.392536\pi$
$23$	8.09478	+	2.49691i	0.0733860	+	0.0226366i	−0.257845	+	0.966186i	$0.583012\pi$
$24$	−26.3165	+	67.0533i	−0.223826	+	0.570300i
$25$	23.6780	−	60.3305i	0.189424	−	0.482644i
$26$	−123.385	−	38.0593i	−0.930686	−	0.287079i
$27$	−54.2442	−	237.659i	−0.386641	−	1.69398i
$28$	13.1975	+	72.8960i	0.0890745	+	0.492002i
$29$	−60.9392	+	266.992i	−0.390211	+	1.70963i	0.273700	+	0.961815i	$0.411752\pi$
$29$	−60.9392	+	266.992i	−0.390211	+	1.70963i	−0.663911	+	0.747811i	$0.731105\pi$
$30$	−124.051	+	214.862i	−0.754949	+	1.30761i
$31$	−10.6860	−	18.5086i	−0.0619114	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$31$	−10.6860	−	18.5086i	−0.0619114	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$32$	−30.5783	+	9.43217i	−0.168923	+	0.0521058i
$33$	39.4142	−	525.946i	0.207913	−	2.77441i
$34$	14.1957	+	17.8009i	0.0716042	+	0.0897889i
$35$	7.52740	+	255.046i	0.0363532	+	1.23173i
$36$	134.857	−	169.105i	0.624337	−	0.782894i
$37$	−118.869	−	110.294i	−0.528160	−	0.490061i	0.370424	−	0.928863i	$-0.379212\pi$
$37$	−118.869	−	110.294i	−0.528160	−	0.490061i	−0.898584	+	0.438802i	$0.855403\pi$
$38$	287.932	+	43.3988i	1.22918	+	0.185269i
$39$	480.302	+	327.464i	1.97205	+	1.34452i
$40$	−108.986	+	16.4271i	−0.430806	+	0.0649336i
$41$	−8.69936	−	4.18939i	−0.0331369	−	0.0159579i	0.417242	−	0.908795i	$-0.362997\pi$
$41$	−8.69936	−	4.18939i	−0.0331369	−	0.0159579i	−0.450379	+	0.892838i	$0.648711\pi$
$42$	39.9571	−	331.114i	0.146798	−	1.21647i
$43$	−82.0571	+	39.5166i	−0.291014	+	0.140145i	−0.573695	−	0.819069i	$-0.694490\pi$
$43$	−82.0571	+	39.5166i	−0.291014	+	0.140145i	0.282681	+	0.959214i	$0.408776\pi$
$44$	193.590	−	131.988i	0.663292	−	0.452225i
$45$	546.108	−	506.714i	1.80909	−	1.67859i
$46$	−1.26610	−	16.8949i	−0.00405817	−	0.0541525i
$47$	99.7047	+	254.043i	0.309435	+	0.788426i	0.997998	+	0.0632500i	$0.0201465\pi$
$47$	99.7047	+	254.043i	0.309435	+	0.788426i	−0.688563	+	0.725176i	$0.741758\pi$
$48$	144.065			0.433209
$49$	−143.924	−	311.343i	−0.419605	−	0.907707i
$50$	−129.621			−0.366624
$51$	−37.4486	−	95.4174i	−0.102821	−	0.261983i
$52$	19.2986	+	257.521i	0.0514659	+	0.686765i
$53$	−52.4017	+	48.6216i	−0.135810	+	0.126013i	−0.745153	−	0.666893i	$-0.767624\pi$
$53$	−52.4017	+	48.6216i	−0.135810	+	0.126013i	0.609343	+	0.792907i	$0.291433\pi$
$54$	−402.826	+	274.642i	−1.01514	+	0.692113i
$55$	727.090	−	350.148i	1.78256	−	0.858436i
$56$	126.071	−	77.8341i	0.300838	−	0.185733i
$57$	−1181.10	−	568.788i	−2.74457	−	1.32172i
$58$	541.599	−	81.6329i	1.22613	−	0.184809i
$59$	−438.370	−	298.876i	−0.967304	−	0.659497i	−0.0269297	−	0.999637i	$-0.508573\pi$
$59$	−438.370	−	298.876i	−0.967304	−	0.659497i	−0.940375	+	0.340140i	$0.889525\pi$
$60$	490.661	+	73.9552i	1.05573	+	0.159126i
$61$	115.477	+	107.147i	0.242383	+	0.224898i	0.792004	−	0.610515i	$-0.209038\pi$
$61$	115.477	+	107.147i	0.242383	+	0.224898i	−0.549622	+	0.835414i	$0.685228\pi$
$62$	−26.6503	+	33.4185i	−0.0545902	+	0.0684540i
$63$	−407.707	+	914.705i	−0.815338	+	1.82924i
$64$	39.9033	+	50.0372i	0.0779362	+	0.0977289i
$65$	−66.4699	+	886.979i	−0.126840	+	1.69256i
$66$	−1007.98	+	310.920i	−1.87990	+	0.579873i
$67$	440.241	+	762.519i	0.802746	+	1.39040i	0.917803	+	0.397037i	$0.129962\pi$
$67$	440.241	+	762.519i	0.802746	+	1.39040i	−0.115057	+	0.993359i	$0.536705\pi$
$68$	22.7681	−	39.4356i	0.0406036	−	0.0703275i
$69$	−16.9727	+	74.3623i	−0.0296127	+	0.129742i
$70$	469.331	−	200.372i	0.801368	−	0.342128i
$71$	−8.32075	−	36.4556i	−0.0139083	−	0.0609363i	0.967498	−	0.252880i	$-0.0813779\pi$
$71$	−8.32075	−	36.4556i	−0.0139083	−	0.0609363i	−0.981406	+	0.191944i	$0.938521\pi$
$72$	−413.369	−	127.507i	−0.676611	−	0.208707i
$73$	89.8459	−	228.924i	0.144050	−	0.367034i	−0.840580	−	0.541688i	$-0.817785\pi$
$73$	89.8459	−	228.924i	0.144050	−	0.367034i	0.984630	+	0.174654i	$0.0558807\pi$
$74$	−118.485	+	301.894i	−0.186129	+	0.474249i
$75$	557.634	+	172.007i	0.858533	+	0.264822i
$76$	−129.589	−	567.767i	−0.195591	−	0.856939i
$77$	−714.096	+	816.665i	−1.05687	+	1.20867i
$78$	258.708	−	1133.47i	0.375550	−	1.64539i
$79$	−313.147	+	542.386i	−0.445972	+	0.772446i	−0.998119	−	0.0613006i	$-0.980475\pi$
$79$	−313.147	+	542.386i	−0.445972	+	0.772446i	0.552148	+	0.833746i	$0.313808\pi$
$80$	110.217	+	190.902i	0.154034	+	0.266794i
$81$	702.300	−	216.631i	0.963375	−	0.297162i
$82$	−1.44312	+	19.2571i	−0.00194349	+	0.0259341i
$83$	872.609	+	1094.22i	1.15399	+	1.44706i	0.873248	+	0.487277i	$0.162010\pi$
$83$	872.609	+	1094.22i	1.15399	+	1.44706i	0.280744	+	0.959783i	$0.409419\pi$
$84$	−645.646	+	167.549i	−0.838640	+	0.217632i
$85$	97.7884	−	122.623i	0.124784	−	0.156474i
$86$	133.528	+	123.896i	0.167426	+	0.155349i
$87$	−2438.30	−	367.514i	−3.00475	−	0.452893i
$88$	−387.181	−	263.975i	−0.469018	−	0.319771i
$89$	37.4322	−	5.64200i	0.0445821	−	0.00671967i	−0.126713	−	0.991939i	$-0.540443\pi$
$89$	37.4322	−	5.64200i	0.0445821	−	0.00671967i	0.171295	+	0.985220i	$0.445205\pi$
$90$	−1342.41	−	646.469i	−1.57224	−	0.757153i
$91$	−385.988	−	1131.67i	−0.444643	−	1.30364i
$92$	−30.5289	+	14.7019i	−0.0345963	+	0.0166607i
$93$	158.997	−	108.402i	0.177282	−	0.120869i
$94$	400.112	−	371.250i	0.439026	−	0.407356i
$95$	−149.897	−	2000.24i	−0.161886	−	2.16021i
$96$	−105.266	−	268.213i	−0.111913	−	0.285150i
$97$	−525.925			−0.550511			−0.275255	−	0.961371i	$-0.588762\pi$
$97$	−525.925			−0.550511			−0.275255	+	0.961371i	$0.588762\pi$
$98$	−474.480	+	495.444i	−0.489079	+	0.510688i
$99$	3167.39			3.21551
$100$	94.7118	+	241.322i	0.0947118	+	0.241322i
$101$	−4.54488	−	60.6472i	−0.00447755	−	0.0597487i	0.994517	−	0.104571i	$-0.0333469\pi$
$101$	−4.54488	−	60.6472i	−0.00447755	−	0.0597487i	−0.998995	+	0.0448222i	$0.985728\pi$
$102$	−150.280	+	139.440i	−0.145882	+	0.135359i
$103$	648.127	−	441.885i	0.620018	−	0.422721i	−0.212156	−	0.977236i	$-0.568048\pi$
$103$	648.127	−	441.885i	0.620018	−	0.422721i	0.832174	+	0.554515i	$0.187096\pi$
$104$	465.339	−	224.095i	0.438752	−	0.211292i
$105$	−2284.97	+	239.202i	−2.12371	+	0.222321i
$106$	128.810	+	62.0317i	0.118030	+	0.0568401i
$107$	503.511	−	75.8920i	0.454918	−	0.0685678i	0.0824134	−	0.996598i	$-0.473737\pi$
$107$	503.511	−	75.8920i	0.454918	−	0.0685678i	0.372504	+	0.928030i	$0.378499\pi$
$108$	805.653	+	549.285i	0.717815	+	0.489398i
$109$	384.810	+	58.0008i	0.338148	+	0.0509676i	0.315921	−	0.948785i	$-0.397686\pi$
$109$	384.810	+	58.0008i	0.338148	+	0.0509676i	0.0222265	+	0.999753i	$0.492924\pi$
$110$	−1183.16	−	1097.81i	−1.02554	−	0.951565i
$111$	910.336	−	1141.53i	0.778426	−	0.976116i
$112$	−237.025	−	177.840i	−0.199971	−	0.150038i
$113$	225.838	+	283.191i	0.188009	+	0.235756i	0.866899	−	0.498485i	$-0.166110\pi$
$113$	225.838	+	283.191i	0.188009	+	0.235756i	−0.678890	+	0.734240i	$0.737539\pi$
$114$	−195.931	+	2614.52i	−0.160970	+	2.14800i
$115$	−111.523	+	34.4004i	−0.0904313	+	0.0278943i
$116$	−547.716	−	948.672i	−0.438398	−	0.759328i
$117$	−1745.51	+	3023.32i	−1.37925	+	2.38894i
$118$	−236.122	+	1034.52i	−0.184210	+	0.807077i
$119$	−56.1744	+	203.215i	−0.0432731	+	0.156543i
$120$	−220.831	−	967.524i	−0.167992	−	0.736021i
$121$	2006.82	+	619.022i	1.50775	+	0.465081i
$122$	115.104	−	293.280i	0.0854183	−	0.217642i
$123$	31.7625	−	80.9296i	0.0232840	−	0.0593267i
$124$	81.6896	+	25.1979i	0.0591609	+	0.0182487i
$125$	−184.523	−	808.449i	−0.132034	−	0.578479i
$126$	2000.85	+	90.6896i	1.41468	+	0.0641212i
$127$	274.414	−	1202.29i	0.191735	−	0.840045i	−0.783942	−	0.620833i	$-0.786794\pi$
$127$	274.414	−	1202.29i	0.191735	−	0.840045i	0.975677	−	0.219212i	$-0.0703485\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−410.030	−	710.193i	−0.279854	−	0.484721i
$130$	1699.90	−	524.350i	1.14685	−	0.353758i
$131$	−93.1866	+	1243.49i	−0.0621507	+	0.829344i	0.875822	+	0.482635i	$0.160320\pi$
$131$	−93.1866	+	1243.49i	−0.0621507	+	0.829344i	−0.937973	+	0.346709i	$0.887299\pi$
$132$	1315.37	+	1649.42i	0.867333	+	1.08760i
$133$	1241.09	+	2393.81i	0.809141	+	1.56067i
$134$	1097.94	−	1376.78i	0.707819	−	0.887577i
$135$	2461.94	+	2284.35i	1.56956	+	1.45633i
$136$	−90.0554	−	13.5737i	−0.0567808	−	0.00855832i
$137$	−2044.79	−	1394.11i	−1.27517	−	0.869394i	−0.279299	−	0.960204i	$-0.590102\pi$
$137$	−2044.79	−	1394.11i	−1.27517	−	0.869394i	−0.995868	+	0.0908103i	$0.971054\pi$
$138$	150.846	−	22.7363i	0.0930495	−	0.0140250i
$139$	1221.12	+	588.059i	0.745135	+	0.358838i	0.767617	−	0.640909i	$-0.221442\pi$
$139$	1221.12	+	588.059i	0.745135	+	0.358838i	−0.0224815	+	0.999747i	$0.507157\pi$
$140$	−715.973	−	727.368i	−0.432220	−	0.439098i
$141$	−2213.94	+	1066.18i	−1.32232	+	0.636797i
$142$	−61.7913	+	42.1286i	−0.0365169	+	0.0248968i
$143$	−2772.19	+	2572.21i	−1.62113	+	1.50419i
$144$	64.6546	+	862.755i	0.0374158	+	0.499280i
$145$	−1378.43	−	3512.18i	−0.789464	−	2.01152i
$146$	−491.847			−0.278805
$147$	2698.68	−	1501.78i	1.51417	−	0.842616i
$148$	648.624			0.360247
$149$	−1108.86	−	2825.34i	−0.609675	−	1.55343i	−0.817909	−	0.575348i	$-0.804867\pi$
$149$	−1108.86	−	2825.34i	−0.609675	−	1.55343i	0.208234	−	0.978079i	$-0.433228\pi$
$150$	−87.2189	−	1163.86i	−0.0474760	−	0.633523i
$151$	−1052.15	+	976.255i	−0.567039	+	0.526136i	−0.910760	−	0.412936i	$-0.864503\pi$
$151$	−1052.15	+	976.255i	−0.567039	+	0.526136i	0.343720	+	0.939072i	$0.388313\pi$
$152$	−962.351	+	656.120i	−0.513533	+	0.350121i
$153$	554.615	−	267.088i	0.293058	−	0.141129i
$154$	2042.20	+	732.744i	1.06861	+	0.383417i
$155$	265.285	+	127.755i	0.137472	+	0.0662032i
$156$	−2299.27	+	346.560i	−1.18006	+	0.177865i
$157$	−523.616	−	356.995i	−0.266173	−	0.181473i	0.422878	−	0.906187i	$-0.361020\pi$
$157$	−523.616	−	356.995i	−0.266173	−	0.181473i	−0.689051	+	0.724713i	$0.741972\pi$
$158$	1238.60	+	186.688i	0.623655	+	0.0940009i
$159$	−471.829	−	437.793i	−0.235336	−	0.218360i
$160$	274.878	−	344.686i	0.135819	−	0.170311i
$161$	119.720	−	101.394i	0.0586043	−	0.0496332i
$162$	−916.470	−	1149.22i	−0.444474	−	0.557352i
$163$	34.9286	−	466.090i	0.0167842	−	0.223969i	−0.982504	−	0.186242i	$-0.940369\pi$
$163$	34.9286	−	466.090i	0.0167842	−	0.223969i	0.999288	−	0.0377272i	$-0.0120118\pi$
$164$	36.9064	−	11.3841i	0.0175726	−	0.00542042i
$165$	3633.19	+	6292.86i	1.71420	+	2.96908i
$166$	1399.56	−	2424.10i	0.654377	−	1.13341i
$167$	492.475	−	2157.67i	0.228197	−	0.999795i	−0.722912	−	0.690940i	$-0.757197\pi$
$167$	492.475	−	2157.67i	0.228197	−	0.999795i	0.951109	−	0.308856i	$-0.0999460\pi$
$168$	783.695	+	1079.60i	0.359901	+	0.495793i
$169$	−438.613	−	1921.69i	−0.199642	−	0.874687i
$170$	−299.745	−	92.4590i	−0.135232	−	0.0417134i
$171$	2876.21	−	7328.46i	1.28625	−	3.27732i
$172$	133.096	−	339.123i	0.0590028	−	0.150337i
$173$	999.512	+	308.309i	0.439257	+	0.135493i	0.506493	−	0.862244i	$-0.330942\pi$
$173$	999.512	+	308.309i	0.439257	+	0.135493i	−0.0672356	+	0.997737i	$0.521418\pi$
$174$	1097.40	+	4808.03i	0.478125	+	2.09480i
$175$	−705.121	−	971.363i	−0.304584	−	0.419589i
$176$	−208.549	+	913.715i	−0.0893182	+	0.391329i
$177$	2388.61	−	4137.19i	1.01434	−	1.75689i
$178$	−37.8550	−	65.5668i	−0.0159402	−	0.0276092i
$179$	−1825.66	+	563.141i	−0.762325	+	0.235146i	−0.651454	−	0.758689i	$-0.725840\pi$
$179$	−1825.66	+	563.141i	−0.762325	+	0.235146i	−0.110872	+	0.993835i	$0.535364\pi$
$180$	−222.689	+	2971.58i	−0.0922127	+	1.23049i
$181$	522.430	+	655.107i	0.214541	+	0.269026i	0.877444	−	0.479680i	$-0.159247\pi$
$181$	522.430	+	655.107i	0.214541	+	0.269026i	−0.662903	+	0.748706i	$0.730676\pi$
$182$	−1824.85	+	1545.50i	−0.743224	+	0.629452i
$183$	−884.363	+	1108.96i	−0.357235	+	0.447958i
$184$	49.6782	+	46.0947i	0.0199040	+	0.0184682i
$185$	2209.10	+	332.968i	0.877926	+	0.132326i
$186$	−317.993	−	216.804i	−0.125357	−	0.0854670i
$187$	659.383	−	99.3860i	0.257855	−	0.0388654i
$188$	−983.528	−	473.642i	−0.381549	−	0.183744i
$189$	−4249.45	−	1524.71i	−1.63546	−	0.586805i
$190$	−3614.41	+	1740.61i	−1.38009	+	0.664617i
$191$	−2915.69	+	1987.89i	−1.10457	+	0.753080i	−0.971266	−	0.237995i	$-0.923510\pi$
$191$	−2915.69	+	1987.89i	−1.10457	+	0.753080i	−0.133300	+	0.991076i	$0.542557\pi$
$192$	−422.429	+	391.957i	−0.158782	+	0.147328i
$193$	−128.345	−	1712.65i	−0.0478678	−	0.638751i	−0.968611	−	0.248582i	$-0.920035\pi$
$193$	−128.345	−	1712.65i	−0.0478678	−	0.638751i	0.920743	−	0.390169i	$-0.127584\pi$
$194$	384.284	+	979.139i	0.142216	+	0.362361i
$195$	−8008.83			−2.94115
$196$	1269.09	+	521.350i	0.462495	+	0.189996i
$197$	769.662			0.278356			0.139178	−	0.990267i	$-0.455554\pi$
$197$	769.662			0.278356			0.139178	+	0.990267i	$0.455554\pi$
$198$	−2314.36	−	5896.89i	−0.830678	−	2.11653i
$199$	123.848	+	1652.64i	0.0441173	+	0.588705i	0.974829	+	0.222952i	$0.0715694\pi$
$199$	123.848	+	1652.64i	0.0441173	+	0.588705i	−0.930712	+	0.365753i	$0.880812\pi$
$200$	380.076	−	352.659i	0.134377	−	0.124684i
$201$	−6550.36	+	4465.96i	−2.29864	+	1.56719i
$202$	−109.589	+	52.7752i	−0.0381715	+	0.0183824i
$203$	3557.97	+	3614.59i	1.23015	+	1.24973i
$204$	369.408	+	177.898i	0.126783	+	0.0610555i
$205$	131.541	−	19.8266i	0.0448156	−	0.00675486i
$206$	−1296.25	−	883.771i	−0.438419	−	0.298909i
$207$	−452.947	−	68.2707i	−0.152087	−	0.0229234i
$208$	−757.224	−	702.601i	−0.252423	−	0.234214i
$209$	5317.23	−	6667.60i	1.75981	−	2.20673i
$210$	2114.92	+	4079.25i	0.694967	+	1.34045i
$211$	2672.43	+	3351.12i	0.871931	+	1.09337i	0.994891	+	0.100955i	$0.0321899\pi$
$211$	2672.43	+	3351.12i	0.871931	+	1.09337i	−0.122960	+	0.992412i	$0.539239\pi$
$212$	21.3681	−	285.137i	0.00692248	−	0.0923741i
$213$	321.732	−	99.2412i	0.103496	−	0.0319244i
$214$	−509.198	−	881.957i	−0.162654	−	0.281726i
$215$	627.389	−	1086.67i	0.199012	−	0.344699i
$216$	433.954	−	1901.27i	0.136698	−	0.598914i
$217$	−395.407	−	17.9220i	−0.123696	−	0.00560657i
$218$	−173.191	−	758.799i	−0.0538072	−	0.235745i
$219$	2115.94	+	652.681i	0.652885	+	0.201388i
$220$	−1179.33	+	3004.89i	−0.361412	+	0.920863i
$221$	−268.513	+	684.160i	−0.0817292	+	0.208243i
$222$	−2790.40	−	860.724i	−0.843601	−	0.260216i
$223$	755.306	+	3309.21i	0.226812	+	0.993728i	0.952221	+	0.305410i	$0.0987935\pi$
$223$	755.306	+	3309.21i	0.226812	+	0.993728i	−0.725409	+	0.688318i	$0.758349\pi$
$224$	−157.903	+	571.226i	−0.0470998	+	0.170387i
$225$	−779.831	+	3416.66i	−0.231061	+	1.01234i
$226$	362.215	−	627.376i	0.106612	−	0.184657i
$227$	1162.40	+	2013.33i	0.339873	+	0.588677i	0.984409	−	0.175897i	$-0.0562826\pi$
$227$	1162.40	+	2013.33i	0.339873	+	0.588677i	−0.644536	+	0.764574i	$0.722949\pi$
$228$	5010.73	−	1545.61i	1.45545	−	0.448948i
$229$	221.178	−	2951.41i	0.0638247	−	0.851681i	−0.869795	−	0.493414i	$-0.835749\pi$
$229$	221.178	−	2951.41i	0.0638247	−	0.851681i	0.933619	−	0.358267i	$-0.116632\pi$
$230$	145.533	+	182.492i	0.0417224	+	0.0523182i
$231$	−7813.25	−	5862.28i	−2.22543	−	1.66974i
$232$	−1365.98	+	1712.89i	−0.386557	+	0.484727i
$233$	−2075.72	−	1925.98i	−0.583625	−	0.541525i	0.332144	−	0.943229i	$-0.392228\pi$
$233$	−2075.72	−	1925.98i	−0.583625	−	0.541525i	−0.915770	+	0.401703i	$0.868418\pi$
$234$	6904.07	+	1040.62i	1.92877	+	0.290716i
$235$	−3106.58	−	2118.03i	−0.862345	−	0.587937i
$236$	2098.54	−	316.304i	0.578828	−	0.0872443i
$237$	−5080.74	−	2446.76i	−1.39253	−	0.670607i
$238$	419.380	−	43.9029i	0.114220	−	0.0119571i
$239$	347.500	−	167.347i	0.0940498	−	0.0452920i	−0.386267	−	0.922387i	$-0.626236\pi$
$239$	347.500	−	167.347i	0.0940498	−	0.0452920i	0.480317	+	0.877095i	$0.340522\pi$
$240$	−1639.93	+	1118.08i	−0.441071	+	0.300717i
$241$	4696.58	−	4357.79i	1.25533	−	1.16477i	0.276292	−	0.961074i	$-0.410894\pi$
$241$	4696.58	−	4357.79i	1.25533	−	1.16477i	0.979034	−	0.203698i	$-0.0652961\pi$
$242$	−313.885	−	4188.50i	−0.0833772	−	1.11259i
$243$	13.0595	+	33.2750i	0.00344760	+	0.00878433i
$244$	−630.118			−0.165325
$245$	4054.65	+	2427.10i	1.05731	+	0.632906i
$246$	−173.879			−0.0450655
$247$	3434.04	+	8749.80i	0.884628	+	2.25399i
$248$	−12.7770	−	170.497i	−0.00327153	−	0.0436556i
$249$	−9237.71	+	8571.34i	−2.35107	+	2.18147i
$250$	−1370.30	+	934.255i	−0.346662	+	0.236350i
$251$	298.207	−	143.609i	0.0749906	−	0.0361136i	−0.396013	−	0.918245i	$-0.629606\pi$
$251$	298.207	−	143.609i	0.0749906	−	0.0361136i	0.471003	+	0.882132i	$0.343892\pi$
$252$	−1293.15	−	3791.35i	−0.323256	−	0.947748i
$253$	−447.064	−	215.295i	−0.111093	−	0.0534998i
$254$	−2438.86	+	367.600i	−0.602472	+	0.0908081i
$255$	1166.82	+	795.522i	0.286545	+	0.195363i
$256$	−253.141	−	38.1548i	−0.0618019	−	0.00931514i
$257$	4112.84	+	3816.16i	0.998257	+	0.926248i	0.997277	−	0.0737520i	$-0.0234973\pi$
$257$	4112.84	+	3816.16i	0.998257	+	0.926248i	0.000980835		1.00000i	$0.499688\pi$
$258$	−1022.60	+	1282.30i	−0.246760	+	0.309428i
$259$	−2906.89	+	754.354i	−0.697395	+	0.180978i
$260$	−2218.29	−	2781.65i	−0.529126	−	0.663503i
$261$	1106.64	−	14767.0i	0.262449	−	3.50213i
$262$	2383.15	−	735.105i	0.561952	−	0.173339i
$263$	3230.57	+	5595.50i	0.757434	+	1.31191i	0.944155	+	0.329502i	$0.106881\pi$
$263$	3230.57	+	5595.50i	0.757434	+	1.31191i	−0.186721	+	0.982413i	$0.559786\pi$
$264$	2109.68	−	3654.08i	0.491826	−	0.851868i
$265$	219.150	−	960.159i	0.0508010	−	0.222574i
$266$	3549.82	−	4059.70i	0.818246	−	0.935775i
$267$	75.8462	+	332.304i	0.0173847	+	0.0761673i
$268$	−3365.46	−	1038.11i	−0.767082	−	0.236613i
$269$	−1510.82	+	3849.50i	−0.342439	+	0.872521i	0.651096	+	0.758996i	$0.274310\pi$
$269$	−1510.82	+	3849.50i	−0.342439	+	0.872521i	−0.993535	+	0.113526i	$0.963786\pi$
$270$	2453.98	−	6252.64i	0.553128	−	1.40935i
$271$	3622.42	+	1117.37i	0.811980	+	0.250463i	0.672819	−	0.739807i	$-0.265083\pi$
$271$	3622.42	+	1117.37i	0.811980	+	0.250463i	0.139161	+	0.990270i	$0.455560\pi$
$272$	40.5311	+	177.578i	0.00903515	+	0.0395856i
$273$	9901.42	−	4227.22i	2.19510	−	0.937153i
$274$	−1101.40	+	4825.53i	−0.242838	+	1.06394i
$275$	−1898.17	+	3287.72i	−0.416232	+	0.720934i
$276$	−152.549	−	264.223i	−0.0332696	−	0.0576246i
$277$	−5889.66	+	1816.72i	−1.27753	+	0.394065i	−0.857987	−	0.513671i	$-0.828285\pi$
$277$	−5889.66	+	1816.72i	−1.27753	+	0.394065i	−0.419541	+	0.907736i	$0.637809\pi$
$278$	202.569	−	2703.10i	0.0437025	−	0.583169i
$279$	720.537	+	903.525i	0.154614	+	0.193880i
$280$	−831.026	+	1864.43i	−0.177369	+	0.397933i
$281$	−923.405	+	1157.91i	−0.196035	+	0.245820i	−0.870127	−	0.492827i	$-0.835963\pi$
$281$	−923.405	+	1157.91i	−0.196035	+	0.245820i	0.674093	+	0.738647i	$0.264535\pi$
$282$	3602.64	+	3342.76i	0.760760	+	0.705882i
$283$	−6966.67	−	1050.06i	−1.46334	−	0.220563i	−0.631413	−	0.775447i	$-0.717525\pi$
$283$	−6966.67	−	1050.06i	−1.46334	−	0.220563i	−0.831928	+	0.554884i	$0.812763\pi$
$284$	123.583	+	84.2571i	0.0258214	+	0.0176047i
$285$	17859.1	−	2691.83i	3.71186	−	0.559474i
$286$	6814.40	+	3281.64i	1.40889	+	0.678488i
$287$	−152.161	+	93.9415i	−0.0312953	+	0.0193212i
$288$	1558.99	−	750.770i	0.318974	−	0.153610i
$289$	−3952.23	+	2694.59i	−0.804444	+	0.548461i
$290$	−5531.60	+	5132.57i	−1.12009	+	1.03929i
$291$	−353.882	−	4722.23i	−0.0712884	−	0.951277i
$292$	359.384	+	915.695i	0.0720251	+	0.183517i
$293$	−115.784			−0.0230859			−0.0115430	−	0.999933i	$-0.503674\pi$
$293$	−115.784			−0.0230859			−0.0115430	+	0.999933i	$0.503674\pi$
$294$	−4767.81	−	3926.94i	−0.945797	−	0.778992i
$295$	7309.64			1.44266
$296$	−473.938	−	1207.57i	−0.0930645	−	0.237125i
$297$	1067.08	+	14239.2i	0.208479	+	2.78195i
$298$	−4449.84	+	4128.84i	−0.865007	+	0.802609i
$299$	451.873	−	308.082i	0.0873996	−	0.0595881i
$300$	−2103.08	+	1012.79i	−0.404737	+	0.194911i
$301$	−202.084	+	1674.61i	−0.0386974	+	0.320675i
$302$	2586.33	+	1245.51i	0.492803	+	0.237321i
$303$	541.487	−	81.6160i	0.102665	−	0.0154743i
$304$	1924.70	+	1312.24i	0.363123	+	0.247573i
$305$	−2146.07	−	323.468i	−0.402897	−	0.0607270i
$306$	−902.498	−	837.396i	−0.168603	−	0.156440i
$307$	2684.08	−	3365.73i	0.498986	−	0.625708i	−0.467014	−	0.884250i	$-0.654670\pi$
$307$	2684.08	−	3365.73i	0.498986	−	0.625708i	0.966000	+	0.258541i	$0.0832418\pi$
$308$	−128.016	−	4337.47i	−0.0236830	−	0.802435i
$309$	4403.75	+	5522.13i	0.810747	+	1.01664i
$310$	44.0077	−	587.242i	0.00806281	−	0.107591i
$311$	−845.941	+	260.938i	−0.154241	+	0.0475770i	−0.370914	−	0.928667i	$-0.620956\pi$
$311$	−845.941	+	260.938i	−0.154241	+	0.0475770i	0.216673	+	0.976244i	$0.430479\pi$
$312$	2325.24	+	4027.44i	0.421926	+	0.730798i
$313$	2868.24	−	4967.94i	0.517963	−	0.897138i	−0.481819	−	0.876271i	$-0.660024\pi$
$313$	2868.24	−	4967.94i	0.517963	−	0.897138i	0.999782	−	0.0208677i	$-0.00664288\pi$
$314$	−282.038	+	1235.69i	−0.0506890	+	0.222083i
$315$	−2457.96	−	13576.5i	−0.439651	−	2.42841i
$316$	−557.454	−	2442.36i	−0.0992381	−	0.434790i
$317$	6277.15	+	1936.25i	1.11218	+	0.343061i	0.795792	−	0.605570i	$-0.207055\pi$
$317$	6277.15	+	1936.25i	1.11218	+	0.343061i	0.316385	+	0.948631i	$0.397531\pi$
$318$	−470.303	+	1198.31i	−0.0829349	+	0.211315i
$319$	5860.60	−	14932.6i	1.02862	−	2.62089i
$320$	−842.566	−	259.897i	−0.147190	−	0.0454022i
$321$	1020.23	+	4469.91i	0.177394	+	0.777214i
$322$	−276.247	−	148.803i	−0.0478095	−	0.0257530i
$323$	368.813	−	1615.88i	0.0635335	−	0.278358i
$324$	−1469.90	+	2545.95i	−0.252041	+	0.436548i
$325$	−2092.11	−	3623.65i	−0.357076	−	0.618473i
$326$	−893.263	+	275.535i	−0.151759	+	0.0468113i
$327$	−261.854	+	3494.20i	−0.0442831	+	0.590916i
$328$	−48.1612	−	60.3922i	−0.00810749	−	0.0101665i
$329$	4958.65	+	978.836i	0.830940	+	0.164027i
$330$	9061.02	−	11362.2i	1.51149	−	1.89535i
$331$	2053.62	+	1905.48i	0.341019	+	0.316419i	0.832026	−	0.554736i	$-0.187181\pi$
$331$	2053.62	+	1905.48i	0.341019	+	0.316419i	−0.491007	+	0.871155i	$0.663371\pi$
$332$	−5535.70	−	834.372i	−0.915093	−	0.137928i
$333$	7244.74	+	4939.38i	1.19222	+	0.812842i
$334$	−4376.89	+	659.710i	−0.717044	+	0.108077i
$335$	−10929.2	−	5263.25i	−1.78247	−	0.858394i
$336$	1437.32	−	2247.89i	0.233370	−	0.364977i
$337$	−8615.34	+	4148.93i	−1.39260	+	0.670642i	−0.971647	−	0.236438i	$-0.924020\pi$
$337$	−8615.34	+	4148.93i	−1.39260	+	0.670642i	−0.420957	+	0.907081i	$0.638306\pi$
$338$	−3257.21	+	2220.73i	−0.524168	+	0.357372i
$339$	−2390.79	+	2218.33i	−0.383038	+	0.355407i
$340$	46.8828	+	625.607i	0.00747816	+	0.0997892i
$341$	457.362	+	1165.34i	0.0726321	+	0.185063i
$342$	−15745.3			−2.48950
$343$	−6293.89	−	860.539i	−0.990782	−	0.135466i
$344$	−728.612			−0.114198
$345$	−383.919	−	978.209i	−0.0599116	−	0.152652i
$346$	−156.333	−	2086.11i	−0.0242904	−	0.324133i
$347$	1127.34	−	1046.02i	0.174406	−	0.161825i	−0.588140	−	0.808759i	$-0.700140\pi$
$347$	1127.34	−	1046.02i	0.174406	−	0.161825i	0.762546	+	0.646934i	$0.223949\pi$
$348$	8149.49	−	5556.23i	1.25534	−	0.855877i
$349$	−3987.22	+	1920.15i	−0.611551	+	0.294507i	−0.713907	−	0.700241i	$-0.753076\pi$
$349$	−3987.22	+	1920.15i	−0.611551	+	0.294507i	0.102356	+	0.994748i	$0.467362\pi$
$350$	−1293.21	+	2022.51i	−0.197500	+	0.308880i
$351$	−14179.5	−	6828.50i	−2.15626	−	1.03840i
$352$	1853.49	−	279.369i	0.280657	−	0.0423023i
$353$	−150.226	−	102.422i	−0.0226508	−	0.0154430i	0.551942	−	0.833883i	$-0.313887\pi$
$353$	−150.226	−	102.422i	−0.0226508	−	0.0154430i	−0.574593	+	0.818440i	$0.694839\pi$
$354$	−9447.72	−	1424.01i	−1.41848	−	0.213801i
$355$	377.647	+	350.405i	0.0564604	+	0.0523876i
$356$	−94.4089	+	118.385i	−0.0140552	+	0.0176247i
$357$	−1862.44	−	367.646i	−0.276109	−	0.0545039i
$358$	2382.40	+	2987.44i	0.351715	+	0.441037i
$359$	420.903	−	5616.56i	0.0618785	−	0.825712i	−0.876786	−	0.480880i	$-0.840317\pi$
$359$	420.903	−	5616.56i	0.0618785	−	0.825712i	0.938665	−	0.344831i	$-0.112064\pi$
$360$	5695.05	−	1756.69i	0.833766	−	0.257183i
$361$	−7169.04	−	12417.1i	−1.04520	−	1.81034i
$362$	837.913	−	1451.31i	0.121657	−	0.210716i
$363$	−4207.80	+	18435.6i	−0.608408	+	2.66561i
$364$	4210.72	+	2268.14i	0.606323	+	0.326600i
$365$	753.930	+	3303.18i	0.108116	+	0.473689i
$366$	2710.78	+	836.166i	0.387145	+	0.119418i
$367$	−1149.62	+	2929.18i	−0.163514	+	0.416627i	−0.989023	−	0.147762i	$-0.952793\pi$
$367$	−1149.62	+	2929.18i	−0.163514	+	0.416627i	0.825509	+	0.564389i	$0.190888\pi$
$368$	49.5176	−	126.169i	0.00701436	−	0.0178723i
$369$	498.913	+	153.894i	0.0703859	+	0.0217112i
$370$	−994.247	−	4356.08i	−0.139699	−	0.612059i
$371$	235.853	+	1302.73i	0.0330050	+	0.182303i
$372$	−171.283	+	750.438i	−0.0238726	+	0.104593i
$373$	−6324.68	+	10954.7i	−0.877961	+	1.52067i	−0.0243854	+	0.999703i	$0.507763\pi$
$373$	−6324.68	+	10954.7i	−0.877961	+	1.52067i	−0.853575	+	0.520970i	$0.825570\pi$
$374$	−666.831	−	1154.99i	−0.0921952	−	0.159687i
$375$	7134.83	−	2200.80i	0.982509	−	0.303064i
$376$	−163.156	+	2177.16i	−0.0223780	+	0.298613i
$377$	11023.6	+	13823.2i	1.50596	+	1.88841i
$378$	266.377	+	9025.48i	0.0362459	+	1.22810i
$379$	−5525.51	+	6928.77i	−0.748883	+	0.939069i	−0.999580	−	0.0289964i	$-0.990769\pi$
$379$	−5525.51	+	6928.77i	−0.748883	+	0.939069i	0.250697	+	0.968066i	$0.419340\pi$
$380$	5881.56	+	5457.29i	0.793994	+	0.736719i
$381$	10979.9	+	1654.95i	1.47642	+	0.222534i
$382$	5831.38	+	3975.77i	0.781046	+	0.532508i
$383$	−6203.70	+	935.058i	−0.827662	+	0.124750i	−0.549193	−	0.835695i	$-0.685065\pi$
$383$	−6203.70	+	935.058i	−0.827662	+	0.124750i	−0.278468	+	0.960445i	$0.589827\pi$
$384$	1038.39	+	500.061i	0.137995	+	0.0664547i
$385$	1790.62	−	14838.4i	0.237035	−	1.96424i
$386$	−3094.74	+	1490.35i	−0.408077	+	0.196520i
$387$	4069.08	−	2774.25i	0.534478	−	0.364401i
$388$	1542.12	−	1430.88i	0.201777	−	0.187221i
$389$	−809.583	−	10803.1i	−0.105521	−	1.40807i	−0.758981	−	0.651113i	$-0.774302\pi$
$389$	−809.583	−	10803.1i	−0.105521	−	1.40807i	0.653460	−	0.756961i	$-0.273317\pi$
$390$	5851.91	+	14910.4i	0.759802	+	1.93594i
$391$	−96.4360			−0.0124731
$392$	43.3236	−	2743.66i	0.00558207	−	0.353509i
$393$	−11227.9			−1.44115
$394$	−562.378	−	1432.92i	−0.0719092	−	0.183222i
$395$	−644.813	−	8604.43i	−0.0821369	−	1.09604i
$396$	−9287.46	+	8617.50i	−1.17857	+	1.09355i
$397$	−5096.29	+	3474.59i	−0.644271	+	0.439256i	−0.840877	−	0.541226i	$-0.817960\pi$
$397$	−5096.29	+	3474.59i	−0.644271	+	0.439256i	0.196606	+	0.980482i	$0.437008\pi$
$398$	2986.30	−	1438.13i	0.376105	−	0.181122i
$399$	−20658.6	+	12754.3i	−2.59204	+	1.60029i
$400$	−934.277	−	449.924i	−0.116785	−	0.0562405i
$401$	5822.03	−	877.530i	0.725034	−	0.109281i	0.223852	−	0.974623i	$-0.428137\pi$
$401$	5822.03	−	877.530i	0.725034	−	0.109281i	0.501182	+	0.865342i	$0.332899\pi$
$402$	13100.7	+	8931.91i	1.62538	+	1.10817i
$403$	−1364.38	−	205.647i	−0.168646	−	0.0254194i
$404$	178.329	+	165.465i	0.0219609	+	0.0203767i
$405$	−6313.19	+	7916.49i	−0.774580	+	0.971292i
$406$	4129.72	−	9265.15i	0.504814	−	1.13257i
$407$	5922.17	+	7426.17i	0.721256	+	0.904426i
$408$	61.2805	−	817.732i	0.00743588	−	0.0992249i
$409$	12253.2	−	3779.62i	1.48137	−	0.456944i	0.554458	−	0.832211i	$-0.312925\pi$
$409$	12253.2	−	3779.62i	1.48137	−	0.456944i	0.926916	+	0.375268i	$0.122449\pi$
$410$	−133.026	−	230.408i	−0.0160237	−	0.0277538i
$411$	11141.7	−	19298.0i	1.33718	−	2.31606i
$412$	−698.209	+	3059.05i	−0.0834910	+	0.365798i
$413$	−9037.00	+	3858.17i	−1.07671	+	0.459681i
$414$	203.857	+	893.157i	0.0242006	+	0.106030i
$415$	−18425.3	−	5683.45i	−2.17943	−	0.672264i
$416$	−754.776	+	1923.14i	−0.0889565	+	0.226658i
$417$	−4458.46	+	11360.0i	−0.523578	+	1.33405i
$418$	−16298.6	−	5027.45i	−1.90715	−	0.588279i
$419$	−2661.67	−	11661.6i	−0.310337	−	1.35968i	−0.853957	−	0.520344i	$-0.825804\pi$
$419$	−2661.67	−	11661.6i	−0.310337	−	1.35968i	0.543620	−	0.839332i	$-0.317053\pi$
$420$	6049.20	−	6918.08i	0.702787	−	0.803732i
$421$	−1392.11	+	6099.23i	−0.161157	+	0.706077i	0.828183	+	0.560457i	$0.189375\pi$
$421$	−1392.11	+	6099.23i	−0.161157	+	0.706077i	−0.989341	+	0.145620i	$0.953482\pi$
$422$	4286.24	−	7423.98i	0.494433	−	0.856384i
$423$	−7378.55	−	12780.0i	−0.848126	−	1.46900i
$424$	−546.467	+	168.563i	−0.0625915	+	0.0193069i
$425$	−55.1365	+	735.745i	−0.00629297	+	0.0839738i
$426$	−419.846	−	526.470i	−0.0477502	−	0.0598769i
$427$	2823.95	−	732.831i	0.320048	−	0.0830542i
$428$	−1269.92	+	1592.43i	−0.143420	+	0.179843i
$429$	−24961.0	−	23160.4i	−2.80915	−	2.60651i
$430$	−2481.53	−	374.030i	−0.278302	−	0.0419473i
$431$	698.131	+	475.978i	0.0780227	+	0.0531950i	0.601703	−	0.798720i	$-0.294489\pi$
$431$	698.131	+	475.978i	0.0780227	+	0.0531950i	−0.523680	+	0.851915i	$0.675441\pi$
$432$	−3856.78	+	581.315i	−0.429535	+	0.0647420i
$433$	−959.405	−	462.025i	−0.106481	−	0.0512783i	0.379885	−	0.925034i	$-0.375963\pi$
$433$	−959.405	−	462.025i	−0.106481	−	0.0512783i	−0.486366	+	0.873755i	$0.661678\pi$
$434$	255.551	+	749.244i	0.0282646	+	0.0828683i
$435$	30608.0	−	14740.0i	3.37366	−	1.62467i
$436$	−1286.15	+	876.879i	−0.141273	+	0.0963186i
$437$	−904.095	+	838.878i	−0.0989673	+	0.0918283i
$438$	−330.952	−	4416.24i	−0.0361039	−	0.481772i
$439$	5389.06	+	13731.1i	0.585891	+	1.49283i	0.849177	+	0.528108i	$0.177098\pi$
$439$	5389.06	+	13731.1i	0.585891	+	1.49283i	−0.263287	+	0.964718i	$0.584807\pi$
$440$	6456.07			0.699503
$441$	10204.7	+	15487.4i	1.10191	+	1.67233i
$442$	1469.93			0.158184
$443$	−950.800	−	2422.60i	−0.101973	−	0.259822i	0.870778	−	0.491677i	$-0.163616\pi$
$443$	−950.800	−	2422.60i	−0.101973	−	0.259822i	−0.972750	+	0.231855i	$0.925521\pi$
$444$	436.444	+	5823.93i	0.0466502	+	0.622504i
$445$	−382.313	+	354.734i	−0.0407266	+	0.0377888i
$446$	5609.03	−	3824.17i	0.595505	−	0.406009i
$447$	24622.3	−	11857.5i	2.60536	−	1.25467i
$448$	1178.85	−	123.409i	0.124321	−	0.0130145i
$449$	45.2905	+	21.8107i	0.00476033	+	0.00229245i	0.436262	−	0.899819i	$-0.356302\pi$
$449$	45.2905	+	21.8107i	0.00476033	+	0.00229245i	−0.431502	+	0.902112i	$0.642016\pi$
$450$	6930.77	−	1044.65i	0.726044	−	0.109434i
$451$	467.306	+	318.604i	0.0487906	+	0.0332649i
$452$	−1432.68	−	215.942i	−0.149088	−	0.0224713i
$453$	−9473.66	−	8790.27i	−0.982586	−	0.911707i
$454$	2898.98	−	3635.20i	0.299682	−	0.375789i
$455$	13176.6	+	9886.42i	1.35765	+	1.01864i
$456$	−6538.78	−	8199.37i	−0.671505	−	0.842041i
$457$	199.789	−	2666.00i	0.0204502	−	0.272889i	−0.977600	−	0.210472i	$-0.932500\pi$
$457$	199.789	−	2666.00i	0.0204502	−	0.272889i	0.998050	−	0.0624171i	$-0.0198809\pi$
$458$	−5656.40	+	1744.77i	−0.577088	+	0.178008i
$459$	1387.55	+	2403.31i	0.141101	+	0.244395i
$460$	233.416	−	404.289i	0.0236589	−	0.0409784i
$461$	4147.27	−	18170.4i	0.418997	−	1.83575i	−0.119123	−	0.992880i	$-0.538008\pi$
$461$	4147.27	−	18170.4i	0.418997	−	1.83575i	0.538120	−	0.842868i	$-0.319135\pi$
$462$	−5205.09	+	18829.8i	−0.524162	+	1.89619i
$463$	−2299.94	−	10076.7i	−0.230859	−	1.01146i	−0.948930	−	0.315488i	$-0.897832\pi$
$463$	−2299.94	−	10076.7i	−0.230859	−	1.01146i	0.718071	−	0.695970i	$-0.245025\pi$
$464$	4187.06	+	1291.54i	0.418921	+	0.129220i
$465$	−968.593	+	2467.93i	−0.0965966	+	0.246124i
$466$	−2069.01	+	5271.74i	−0.205676	+	0.524053i
$467$	15978.3	+	4928.65i	1.58327	+	0.488374i	0.956721	−	0.291007i	$-0.0939904\pi$
$467$	15978.3	+	4928.65i	1.58327	+	0.488374i	0.626550	+	0.779382i	$0.284467\pi$
$468$	−3107.31	−	13614.0i	−0.306913	−	1.34467i
$469$	16290.0	+	738.353i	1.60384	+	0.0726950i
$470$	−1673.32	+	7331.28i	−0.164222	+	0.719504i
$471$	2853.10	−	4941.71i	0.279116	−	0.483444i
$472$	−2122.25	−	3675.84i	−0.206958	−	0.358462i
$473$	5097.87	−	1572.48i	0.495561	−	0.152860i
$474$	−842.835	+	11246.9i	−0.0816724	+	1.08984i
$475$	5883.19	+	7377.29i	0.568294	+	0.712618i
$476$	−388.170	−	748.701i	−0.0373776	−	0.0720938i
$477$	2410.04	−	3022.09i	0.231337	−	0.290088i
$478$	−565.470	−	524.680i	−0.0541088	−	0.0502056i
$479$	−14477.2	−	2182.09i	−1.38096	−	0.208146i	−0.583792	−	0.811904i	$-0.698431\pi$
$479$	−14477.2	−	2182.09i	−1.38096	−	0.208146i	−0.797168	+	0.603757i	$0.793670\pi$
$480$	3279.86	+	2236.17i	0.311884	+	0.212639i
$481$	−10352.0	+	1560.31i	−0.981312	+	0.147909i
$482$	−11544.8	−	5559.69i	−1.09098	−	0.525388i
$483$	990.962	+	1006.73i	0.0933547	+	0.0948404i
$484$	−7568.59	+	3644.84i	−0.710799	+	0.342303i
$485$	5986.73	−	4081.68i	0.560501	−	0.382143i
$486$	52.4073	−	48.6269i	0.00489145	−	0.00453860i
$487$	1358.09	+	18122.5i	0.126368	+	1.68626i	0.595677	+	0.803224i	$0.296884\pi$
$487$	1358.09	+	18122.5i	0.126368	+	1.68626i	−0.469310	+	0.883034i	$0.655497\pi$
$488$	460.416	+	1173.12i	0.0427091	+	0.108821i
$489$	4208.48			0.389190
$490$	1556.00	−	9322.18i	0.143455	−	0.859455i
$491$	−5621.19			−0.516661			−0.258331	−	0.966057i	$-0.583172\pi$
$491$	−5621.19			−0.516661			−0.258331	+	0.966057i	$0.583172\pi$
$492$	127.050	+	323.719i	0.0116420	+	0.0296633i
$493$	−232.980	−	3108.90i	−0.0212838	−	0.284012i
$494$	13780.7	−	12786.6i	1.25511	−	1.16457i
$495$	−36055.2	+	24582.0i	−3.27386	+	2.23208i
$496$	−308.087	+	148.367i	−0.0278901	+	0.0134312i
$497$	−651.841	−	233.881i	−0.0588311	−	0.0211087i
$498$	22707.5	+	10935.4i	2.04327	+	0.983986i
$499$	−10060.8	+	1516.42i	−0.902571	+	0.136041i	−0.583901	−	0.811825i	$-0.698474\pi$
$499$	−10060.8	+	1516.42i	−0.902571	+	0.136041i	−0.318670	+	0.947866i	$0.603236\pi$
$500$	2740.60	+	1868.51i	0.245127	+	0.167125i
$501$	19704.9	+	2970.04i	1.75719	+	0.264853i
$502$	−485.258	−	450.253i	−0.0431437	−	0.0400315i
$503$	−12594.6	+	15793.1i	−1.11643	+	1.39996i	−0.209951	+	0.977712i	$0.567331\pi$
$503$	−12594.6	+	15793.1i	−1.11643	+	1.39996i	−0.906480	+	0.422249i	$0.861241\pi$
$504$	−6113.66	+	5177.78i	−0.540325	+	0.457613i
$505$	522.416	+	655.088i	0.0460340	+	0.0577249i
$506$	−74.1626	+	989.631i	−0.00651567	+	0.0869456i
$507$	16959.5	−	5231.32i	1.48560	−	0.458246i
$508$	2466.41	+	4271.95i	0.215412	+	0.373105i
$509$	−1530.64	+	2651.15i	−0.133290	+	0.230864i	−0.924943	−	0.380106i	$-0.875887\pi$
$509$	−1530.64	+	2651.15i	−0.133290	+	0.230864i	0.791653	+	0.610971i	$0.209221\pi$
$510$	628.489	−	2753.59i	0.0545686	−	0.239081i
$511$	−2675.58	−	3685.83i	−0.231626	−	0.319083i
$512$	113.931	+	499.163i	0.00983413	+	0.0430861i
$513$	33914.4	+	10461.2i	2.91882	+	0.900338i
$514$	4099.55	−	10445.5i	0.351796	−	0.896362i
$515$	−3948.33	+	10060.2i	−0.337833	+	0.860785i
$516$	3134.51	+	966.868i	0.267421	+	0.0824884i
$517$	−3557.18	−	15585.0i	−0.302601	−	1.32578i
$518$	3528.43	+	4860.70i	0.299286	+	0.412291i
$519$	−2095.72	+	9181.97i	−0.177249	+	0.776578i
$520$	−3557.87	+	6162.41i	−0.300044	+	0.519691i
$521$	5160.70	+	8938.60i	0.433962	+	0.751645i	0.997210	−	0.0746430i	$-0.0237817\pi$
$521$	5160.70	+	8938.60i	0.433962	+	0.751645i	−0.563248	+	0.826288i	$0.690448\pi$
$522$	−28301.1	+	8729.73i	−2.37300	+	0.731973i
$523$	859.847	−	11473.9i	0.0718900	−	0.959306i	−0.838325	−	0.545170i	$-0.816465\pi$
$523$	859.847	−	11473.9i	0.0718900	−	0.959306i	0.910215	−	0.414135i	$-0.135916\pi$
$524$	−3109.90	−	3899.70i	−0.259269	−	0.325113i
$525$	8247.31	−	6984.82i	0.685604	−	0.580652i
$526$	8056.90	−	10103.0i	0.667866	−	0.837478i
$527$	178.351	+	165.486i	0.0147421	+	0.0136787i
$528$	−8344.48	−	1257.73i	−0.687778	−	0.103666i
$529$	−9993.56	−	6813.49i	−0.821366	−	0.559998i
$530$	−1947.70	+	293.569i	−0.159628	+	0.0240600i
$531$	25848.1	+	12447.8i	2.11245	+	1.01730i
$532$	−10151.9	−	3642.52i	−0.827334	−	0.296848i
$533$	−561.638	+	270.471i	−0.0456421	+	0.0219801i
$534$	563.246	−	384.015i	0.0456443	−	0.0311198i
$535$	−5142.59	+	4771.62i	−0.415576	+	0.385599i
$536$	526.388	+	7024.15i	0.0424188	+	0.566040i
$537$	−6284.83	−	16013.5i	−0.505048	−	1.28684i
$538$	8270.73			0.662781
$539$	5618.21	+	19290.0i	0.448968	+	1.54152i
$540$	−13433.9			−1.07056
$541$	6841.60	+	17432.1i	0.543703	+	1.38533i	0.893735	+	0.448595i	$0.148076\pi$
$541$	6841.60	+	17432.1i	0.543703	+	1.38533i	−0.350032	+	0.936738i	$0.613829\pi$
$542$	−566.579	−	7560.48i	−0.0449016	−	0.599170i
$543$	−5530.61	+	5131.66i	−0.437092	+	0.405562i
$544$	300.991	−	205.212i	0.0237222	−	0.0161735i
$545$	−4830.53	+	2326.26i	−0.379664	+	0.182837i
$546$	−15104.8	−	15345.2i	−1.18393	−	1.20277i
$547$	−10558.6	−	5084.75i	−0.825325	−	0.397455i	−0.0269650	−	0.999636i	$-0.508584\pi$
$547$	−10558.6	−	5084.75i	−0.825325	−	0.397455i	−0.798360	+	0.602181i	$0.794299\pi$
$548$	9788.68	−	1475.41i	0.763051	−	0.115011i
$549$	−7038.03	−	4798.45i	−0.547133	−	0.373029i
$550$	7507.86	+	1131.63i	0.582066	+	0.0877323i
$551$	−29227.9	−	27119.6i	−2.25980	−	2.09679i
$552$	−380.452	+	477.072i	−0.0293354	+	0.0367854i
$553$	5338.78	+	10297.4i	0.410539	+	0.791847i
$554$	7685.74	+	9637.62i	0.589415	+	0.739103i
$555$	−1503.24	+	20059.3i	−0.114971	+	1.53418i
$556$	−5180.50	+	1597.97i	−0.395147	+	0.121887i
$557$	−730.377	−	1265.05i	−0.0555603	−	0.0962332i	0.836908	−	0.547344i	$-0.184361\pi$
$557$	−730.377	−	1265.05i	−0.0555603	−	0.0962332i	−0.892468	+	0.451111i	$0.851028\pi$
$558$	1155.65	−	2001.65i	0.0876750	−	0.151858i
$559$	−1308.42	+	5732.56i	−0.0989986	+	0.433741i
$560$	4078.32	+	184.852i	0.307751	+	0.0139490i
$561$	1336.06	+	5853.66i	0.100550	+	0.440538i
$562$	2830.46	+	873.081i	0.212448	+	0.0655315i
$563$	9367.35	−	23867.6i	0.701220	−	1.78668i	0.0889398	−	0.996037i	$-0.471652\pi$
$563$	9367.35	−	23867.6i	0.701220	−	1.78668i	0.612280	−	0.790641i	$-0.290253\pi$
$564$	3590.99	−	9149.71i	0.268100	−	0.683107i
$565$	−4768.60	−	1470.92i	−0.355074	−	0.109526i
$566$	3135.48	+	13737.4i	0.232852	+	1.02019i
$567$	3626.60	−	13119.5i	0.268612	−	0.971722i
$568$	66.5660	−	291.645i	0.00491733	−	0.0215443i
$569$	−9050.23	+	15675.5i	−0.666793	+	1.15492i	0.312002	+	0.950081i	$0.399000\pi$
$569$	−9050.23	+	15675.5i	−0.666793	+	1.15492i	−0.978796	+	0.204839i	$0.934333\pi$
$570$	−18060.8	−	31282.3i	−1.32717	−	2.29872i
$571$	−18163.7	+	5602.76i	−1.33122	+	0.410628i	−0.877098	−	0.480311i	$-0.840524\pi$
$571$	−18163.7	+	5602.76i	−1.33122	+	0.410628i	−0.454124	+	0.890939i	$0.650048\pi$
$572$	1130.43	−	15084.5i	0.0826322	−	1.10265i
$573$	−19810.9	−	24842.1i	−1.44435	−	1.81116i
$574$	286.076	+	214.643i	0.0208024	+	0.0156081i
$575$	342.308	−	429.240i	0.0248265	−	0.0311314i
$576$	−2536.87	−	2353.87i	−0.183512	−	0.170274i
$577$	6124.18	+	923.071i	0.441859	+	0.0665996i	0.366204	−	0.930534i	$-0.380657\pi$
$577$	6124.18	+	923.071i	0.441859	+	0.0665996i	0.0756550	+	0.997134i	$0.475895\pi$
$578$	7904.47	+	5389.17i	0.568828	+	0.387820i
$579$	15291.3	−	2304.80i	1.09756	−	0.165430i
$580$	13597.4	+	6548.16i	0.973450	+	0.468789i
$581$	25779.3	−	2698.71i	1.84080	−	0.192704i
$582$	−8533.02	+	4109.28i	−0.607740	+	0.292672i
$583$	3459.67	−	2358.76i	0.245771	−	0.167564i
$584$	1442.20	−	1338.16i	0.102189	−	0.0948178i
$585$	−3594.26	−	47962.0i	−0.254024	−	3.38972i
$586$	84.6012	+	215.560i	0.00596390	+	0.0151958i
$587$	−24142.6			−1.69757			−0.848783	−	0.528742i	$-0.822664\pi$
$587$	−24142.6			−1.69757			−0.848783	+	0.528742i	$0.822664\pi$
$588$	−3827.21	+	11745.8i	−0.268421	+	0.823790i
$589$	3111.58			0.217675
$590$	−5341.02	−	13608.7i	−0.372689	−	0.949595i
$591$	517.887	+	6910.72i	0.0360457	+	0.480997i
$592$	−1901.90	+	1764.71i	−0.132040	+	0.122515i
$593$	−2468.21	+	1682.80i	−0.170923	+	0.116533i	−0.645760	−	0.763540i	$-0.723459\pi$
$593$	−2468.21	+	1682.80i	−0.170923	+	0.116533i	0.474837	+	0.880074i	$0.342507\pi$
$594$	25730.0	−	12390.9i	1.77730	−	0.855902i
$595$	−937.695	−	2749.21i	−0.0646080	−	0.189423i
$596$	10938.3	+	5267.60i	0.751761	+	0.362029i
$597$	−14755.5	+	2224.04i	−1.01156	+	0.152469i
$598$	−903.746	−	616.164i	−0.0618009	−	0.0421351i
$599$	14952.2	+	2253.68i	1.01992	+	0.153728i	0.637652	−	0.770325i	$-0.279906\pi$
$599$	14952.2	+	2253.68i	1.01992	+	0.153728i	0.382266	+	0.924053i	$0.375144\pi$
$600$	3422.23	+	3175.37i	0.232854	+	0.216057i
$601$	−10464.5	+	13122.1i	−0.710244	+	0.890618i	−0.997742	−	0.0671632i	$-0.978605\pi$
$601$	−10464.5	+	13122.1i	−0.710244	+	0.890618i	0.287498	+	0.957781i	$0.407177\pi$
$602$	3265.36	−	847.380i	0.221074	−	0.0573698i
$603$	−29684.7	−	37223.5i	−2.00474	−	2.51386i
$604$	429.042	−	5725.16i	0.0289031	−	0.385685i
$605$	−27648.3	+	8528.38i	−1.85796	+	0.573104i
$606$	−547.603	−	948.476i	−0.0367077	−	0.0635796i
$607$	−12567.8	+	21768.1i	−0.840382	+	1.45558i	0.0491899	+	0.998789i	$0.484336\pi$
$607$	−12567.8	+	21768.1i	−0.840382	+	1.45558i	−0.889572	+	0.456795i	$0.848997\pi$
$608$	1036.71	−	4542.14i	0.0691518	−	0.302974i
$609$	−30061.0	+	34378.8i	−2.00022	+	2.28752i
$610$	965.880	+	4231.80i	0.0641104	+	0.280886i
$611$	16836.4	+	5193.35i	1.11478	+	0.343864i
$612$	−899.580	+	2292.09i	−0.0594173	+	0.151393i
$613$	5227.71	−	13320.0i	0.344446	−	0.877633i	−0.648732	−	0.761017i	$-0.724700\pi$
$613$	5227.71	−	13320.0i	0.344446	−	0.877633i	0.993177	−	0.116616i	$-0.0372046\pi$
$614$	−8227.35	−	2537.80i	−0.540764	−	0.166804i
$615$	266.531	+	1167.75i	0.0174757	+	0.0765662i
$616$	−7981.73	+	3407.64i	−0.522067	+	0.222886i
$617$	5955.75	−	26093.9i	0.388606	−	1.70259i	−0.280860	−	0.959749i	$-0.590620\pi$
$617$	5955.75	−	26093.9i	0.388606	−	1.70259i	0.669465	−	0.742843i	$-0.266523\pi$
$618$	7063.07	−	12233.6i	0.459739	−	0.796291i
$619$	14230.6	+	24648.1i	0.924033	+	1.60047i	0.793110	+	0.609079i	$0.208461\pi$
$619$	14230.6	+	24648.1i	0.924033	+	1.60047i	0.130923	+	0.991393i	$0.458206\pi$
$620$	−1125.45	+	347.156i	−0.0729020	+	0.0224873i
$621$	154.319	−	2059.24i	0.00997199	−	0.133067i
$622$	1103.91	+	1384.27i	0.0711623	+	0.0892347i
$623$	285.422	−	640.355i	0.0183551	−	0.0411802i
$624$	5799.07	−	7271.80i	0.372033	−	0.466514i
$625$	14313.5	+	13281.0i	0.916064	+	0.849984i
$626$	−11344.8	−	1709.96i	−0.724329	−	0.109175i
$627$	63445.5	+	43256.4i	4.04110	+	2.75518i
$628$	2506.62	−	377.813i	0.159276	−	0.0240070i
$629$	1663.19	+	800.948i	0.105430	+	0.0507725i
$630$	−23480.0	+	14496.2i	−1.48487	+	0.916734i
$631$	27498.9	−	13242.8i	1.73489	−	0.835477i	0.750184	−	0.661229i	$-0.229965\pi$
$631$	27498.9	−	13242.8i	1.73489	−	0.835477i	0.984702	−	0.174249i	$-0.0557496\pi$
$632$	−4139.74	+	2822.43i	−0.260554	+	0.177643i
$633$	−28291.1	+	26250.3i	−1.77642	+	1.64827i
$634$	−981.803	−	13101.3i	−0.0615022	−	0.820690i
$635$	6207.18	+	15815.6i	0.387913	+	0.988385i
$636$	2574.60			0.160518
$637$	−21508.7	−	5267.83i	−1.33784	−	0.327660i
$638$	−32082.9			−1.99087
$639$	738.710	+	1882.20i	0.0457322	+	0.116524i
$640$	131.785	+	1758.55i	0.00813946	+	0.108614i
$641$	5127.02	−	4757.18i	0.315921	−	0.293132i	−0.506233	−	0.862396i	$-0.668963\pi$
$641$	5127.02	−	4757.18i	0.315921	−	0.293132i	0.822154	+	0.569265i	$0.192772\pi$
$642$	7576.38	−	5165.49i	0.465757	−	0.317547i
$643$	6516.45	−	3138.16i	0.399664	−	0.192468i	−0.223245	−	0.974762i	$-0.571665\pi$
$643$	6516.45	−	3138.16i	0.399664	−	0.192468i	0.622909	+	0.782294i	$0.285951\pi$
$644$	−75.1842	+	623.030i	−0.00460042	+	0.0381224i
$645$	10179.3	+	4902.07i	0.621407	+	0.299254i
$646$	−3277.84	+	494.055i	−0.199636	+	0.0300903i
$647$	−48.5420	−	33.0954i	−0.00294959	−	0.00201099i	0.561844	−	0.827243i	$-0.310092\pi$
$647$	−48.5420	−	33.0954i	−0.00294959	−	0.00201099i	−0.564794	+	0.825232i	$0.691044\pi$
$648$	5813.95	+	876.312i	0.352459	+	0.0531246i
$649$	22781.8	+	21138.4i	1.37791	+	1.27852i
$650$	−5217.65	+	6542.72i	−0.314851	+	0.394810i
$651$	−105.140	−	3562.38i	−0.00632988	−	0.214471i
$652$	1165.67	+	1461.70i	0.0700170	+	0.0877986i
$653$	−167.761	+	2238.61i	−0.0100536	+	0.134156i	−0.999972	−	0.00748295i	$-0.997618\pi$
$653$	−167.761	+	2238.61i	−0.0100536	+	0.134156i	0.989918	+	0.141639i	$0.0452371\pi$
$654$	6696.65	−	2065.64i	0.400397	−	0.123506i
$655$	−8589.90	−	14878.1i	−0.512420	−	0.887537i
$656$	−77.2445	+	133.791i	−0.00459739	+	0.00796292i
$657$	−2959.07	+	12964.5i	−0.175714	+	0.769854i
$658$	−1800.85	−	9946.97i	−0.106694	−	0.589321i
$659$	−5392.28	−	23625.1i	−0.318746	−	1.39652i	−0.839755	−	0.542965i	$-0.817301\pi$
$659$	−5392.28	−	23625.1i	−0.318746	−	1.39652i	0.521009	−	0.853551i	$-0.325556\pi$
$660$	−27774.2	−	8567.20i	−1.63804	−	0.505270i
$661$	3554.80	−	9057.48i	0.209176	−	0.532973i	−0.787326	−	0.616537i	$-0.788535\pi$
$661$	3554.80	−	9057.48i	0.209176	−	0.532973i	0.996502	+	0.0835640i	$0.0266303\pi$
$662$	2046.98	−	5215.63i	0.120179	−	0.306210i
$663$	−6323.68	−	1950.60i	−0.370425	−	0.114261i
$664$	2491.44	+	10915.7i	0.145613	+	0.637971i
$665$	−32705.8	−	17617.2i	−1.90718	−	1.02732i
$666$	3902.28	−	17097.0i	0.227042	−	0.994737i
$667$	−1159.94	+	2009.08i	−0.0673361	+	0.116630i
$668$	4426.33	+	7666.62i	0.256377	+	0.444058i
$669$	−29204.9	+	9008.51i	−1.68778	+	0.520612i
$670$	−1813.03	+	24193.3i	−0.104543	+	1.39503i
$671$	−5753.20	−	7214.29i	−0.330998	−	0.415059i
$672$	−5235.23	−	1033.43i	−0.300526	−	0.0593237i
$673$	−6970.38	+	8740.58i	−0.399240	+	0.500631i	−0.940297	−	0.340355i	$-0.889453\pi$
$673$	−6970.38	+	8740.58i	−0.399240	+	0.500631i	0.541057	+	0.840986i	$0.318024\pi$
$674$	14019.3	+	13008.0i	0.801193	+	0.743399i
$675$	−15622.5	−	2354.71i	−0.890829	−	0.134271i
$676$	6514.42	+	4441.46i	0.370643	+	0.252700i
$677$	18380.9	−	2770.48i	1.04348	−	0.157280i	0.395134	−	0.918624i	$-0.370698\pi$
$677$	18380.9	−	2770.48i	1.04348	−	0.157280i	0.648348	+	0.761344i	$0.275460\pi$
$678$	5876.87	+	2830.15i	0.332891	+	0.160312i
$679$	−5247.08	+	8206.15i	−0.296560	+	0.463804i
$680$	1130.47	−	544.404i	0.0637521	−	0.0307014i
$681$	−17295.4	+	11791.8i	−0.973216	+	0.663528i
$682$	1835.38	−	1702.98i	0.103050	−	0.0956168i
$683$	918.113	+	12251.4i	0.0514357	+	0.686362i	0.962010	+	0.273016i	$0.0880211\pi$
$683$	918.113	+	12251.4i	0.0514357	+	0.686362i	−0.910574	+	0.413347i	$0.864360\pi$
$684$	11504.8	+	29313.8i	0.643126	+	1.63866i
$685$	34095.9			1.90181
$686$	2996.73	+	12346.4i	0.166787	+	0.687155i
$687$	26649.3			1.47996
$688$	532.384	+	1356.49i	0.0295014	+	0.0751683i
$689$	344.886	+	4602.18i	0.0190698	+	0.254469i
$690$	−1540.66	+	1429.52i	−0.0850025	+	0.0788708i
$691$	−10111.6	+	6894.00i	−0.556679	+	0.379537i	−0.808733	−	0.588176i	$-0.799846\pi$
$691$	−10111.6	+	6894.00i	−0.556679	+	0.379537i	0.252054	+	0.967713i	$0.418894\pi$
$692$	−3769.59	+	1815.34i	−0.207078	+	0.0997237i
$693$	31600.7	−	49421.7i	1.73219	−	2.70906i
$694$	−2771.15	−	1334.52i	−0.151573	−	0.0729936i
$695$	−18464.2	+	2783.03i	−1.00775	+	0.151894i
$696$	−16299.0	−	11112.5i	−0.887660	−	0.605196i
$697$	108.692	+	16.3827i	0.00590674	+	0.000890298i
$698$	6488.22	+	6020.19i	0.351838	+	0.326458i
$699$	15896.5	−	19933.6i	0.860174	−	1.07862i
$700$	4710.34	+	929.820i	0.254334	+	0.0502056i
$701$	4397.32	+	5514.07i	0.236925	+	0.297095i	0.886052	−	0.463585i	$-0.153437\pi$
$701$	4397.32	+	5514.07i	0.236925	+	0.297095i	−0.649127	+	0.760680i	$0.724866\pi$
$702$	−2352.22	+	31388.1i	−0.126465	+	1.68756i
$703$	22559.8	−	6958.77i	1.21033	−	0.373336i
$704$	−1874.43	−	3246.60i	−0.100348	−	0.173808i
$705$	16927.3	−	29318.9i	0.904280	−	1.56626i
$706$	−80.9171	+	354.521i	−0.00431353	+	0.0188988i
$707$	−991.638	−	534.153i	−0.0527502	−	0.0284143i
$708$	4252.12	+	18629.8i	0.225713	+	0.988912i
$709$	−9814.51	−	3027.37i	−0.519875	−	0.160360i	0.0237025	−	0.999719i	$-0.492455\pi$
$709$	−9814.51	−	3027.37i	−0.519875	−	0.160360i	−0.543578	+	0.839359i	$0.682931\pi$
$710$	376.426	−	959.119i	0.0198972	−	0.0506973i
$711$	12372.6	−	31524.8i	0.652613	−	1.66283i
$712$	289.386	+	89.2637i	0.0152320	+	0.00469845i
$713$	−40.2861	−	176.505i	−0.00211603	−	0.00927092i
$714$	676.390	+	3736.03i	0.0354527	+	0.195823i
$715$	11593.6	−	50794.9i	0.606401	−	2.65682i
$716$	3821.08	−	6618.30i	0.199442	−	0.345444i
$717$	1736.42	+	3007.56i	0.0904431	+	0.156652i
$718$	−10764.2	+	3320.30i	−0.559491	+	0.172580i
$719$	205.455	−	2741.61i	0.0106567	−	0.142204i	−0.989337	−	0.145642i	$-0.953475\pi$
$719$	205.455	−	2741.61i	0.0106567	−	0.142204i	0.999994	+	0.00343779i	$0.00109428\pi$
$720$	−7431.79	−	9319.17i	−0.384676	−	0.482368i
$721$	−428.587	−	14521.5i	−0.0221379	−	0.750083i
$722$	−17879.3	+	22419.9i	−0.921604	+	1.15566i
$723$	42288.4	+	39237.9i	2.17527	+	2.01836i
$724$	−3314.22	−	499.538i	−0.170127	−	0.0256425i
$725$	14664.8	+	9998.31i	0.751225	+	0.512177i
$726$	37397.0	−	5636.68i	1.91175	−	0.288150i
$727$	25286.6	+	12177.4i	1.28999	+	0.621229i	0.947939	−	0.318451i	$-0.103163\pi$
$727$	25286.6	+	12177.4i	1.28999	+	0.621229i	0.342056	+	0.939680i	$0.388877\pi$
$728$	1146.00	−	9496.58i	0.0583428	−	0.483471i
$729$	17588.6	−	8470.21i	0.893592	−	0.430331i
$730$	5598.81	−	3817.20i	0.283865	−	0.193536i
$731$	760.044	−	705.218i	0.0384559	−	0.0356818i
$732$	−423.991	−	5657.77i	−0.0214087	−	0.285679i
$733$	4456.13	+	11354.0i	0.224544	+	0.572129i	0.998101	−	0.0615979i	$-0.0196196\pi$
$733$	4456.13	+	11354.0i	0.224544	+	0.572129i	−0.773557	+	0.633727i	$0.781524\pi$
$734$	6293.41			0.316477
$735$	−19064.5	+	38039.4i	−0.956739	+	1.90899i
$736$	−271.076			−0.0135761
$737$	−18842.4	−	48009.7i	−0.941750	−	2.39954i
$738$	−78.0346	−	1041.30i	−0.00389226	−	0.0519387i
$739$	21601.5	−	20043.2i	1.07527	−	0.997702i	0.0752672	−	0.997163i	$-0.476019\pi$
$739$	21601.5	−	20043.2i	1.07527	−	0.997702i	1.00000		0.000538607i	$-0.000171444\pi$
$740$	−7383.45	+	5033.95i	−0.366785	+	0.250070i
$741$	−76252.9	+	36721.5i	−3.78033	+	1.82051i
$742$	2253.02	−	1390.98i	0.111470	−	0.0688200i
$743$	−9182.41	−	4422.02i	−0.453392	−	0.218342i	0.193229	−	0.981154i	$-0.438104\pi$
$743$	−9182.41	−	4422.02i	−0.453392	−	0.218342i	−0.646621	+	0.762812i	$0.723818\pi$
$744$	1522.28	−	229.447i	0.0750127	−	0.0113064i
$745$	34549.8	+	23555.6i	1.69907	+	1.15840i
$746$	25016.1	+	3770.58i	1.22776	+	0.185054i
$747$	−55476.5	−	51474.7i	−2.71724	−	2.52123i
$748$	−1663.05	+	2085.40i	−0.0812929	+	0.101938i
$749$	3839.29	−	8613.58i	0.187296	−	0.420205i
$750$	−9310.63	−	11675.2i	−0.453301	−	0.568422i
$751$	−398.045	+	5311.55i	−0.0193407	+	0.258084i	0.979149	+	0.203144i	$0.0651159\pi$
$751$	−398.045	+	5311.55i	−0.0193407	+	0.258084i	−0.998490	+	0.0549403i	$0.982503\pi$
$752$	4172.54	−	1287.06i	0.202336	−	0.0624125i
$753$	1490.11	+	2580.94i	0.0721148	+	0.124907i
$754$	17680.5	−	30623.6i	0.853961	−	1.47910i
$755$	4400.23	−	19278.7i	0.212107	−	0.929301i
$756$	16608.5	−	7090.68i	0.799003	−	0.341119i
$757$	1563.41	+	6849.73i	0.0750634	+	0.328874i	0.998492	−	0.0548958i	$-0.0174827\pi$
$757$	1563.41	+	6849.73i	0.0750634	+	0.328874i	−0.923429	+	0.383770i	$0.874626\pi$
$758$	16937.0	+	5224.38i	0.811584	+	0.250340i
$759$	1632.29	−	4159.01i	0.0780611	−	0.198896i
$760$	5862.55	−	14937.5i	0.279812	−	0.712949i
$761$	12283.4	+	3788.94i	0.585118	+	0.180485i	0.573160	−	0.819444i	$-0.305717\pi$
$761$	12283.4	+	3788.94i	0.585118	+	0.180485i	0.0119580	+	0.999929i	$0.496194\pi$
$762$	−4941.69	−	21651.0i	−0.234933	−	1.02931i
$763$	4744.20	−	5425.63i	0.225100	−	0.257433i
$764$	3140.99	−	13761.6i	0.148740	−	0.651671i
$765$	−4240.45	+	7344.67i	−0.200410	+	0.347120i
$766$	6273.78	+	10866.5i	0.295928	+	0.512562i
$767$	−32731.7	+	10096.4i	−1.54090	+	0.475306i
$768$	172.256	−	2298.60i	0.00809344	−	0.107999i
$769$	3210.30	+	4025.59i	0.150541	+	0.188773i	0.851384	−	0.524543i	$-0.175764\pi$
$769$	3210.30	+	4025.59i	0.150541	+	0.188773i	−0.700843	+	0.713316i	$0.747192\pi$
$770$	−28933.7	+	7508.45i	−1.35415	+	0.351410i
$771$	−31497.5	+	39496.6i	−1.47128	+	1.84492i
$772$	5035.92	+	4672.65i	0.234775	+	0.217840i
$773$	−33324.0	−	5022.78i	−1.55056	−	0.233709i	−0.682766	−	0.730637i	$-0.739223\pi$
$773$	−33324.0	−	5022.78i	−1.55056	−	0.233709i	−0.867792	+	0.496928i	$0.834461\pi$
$774$	−8138.15	−	5548.50i	−0.377933	−	0.257670i
$775$	−1369.65	+	206.442i	−0.0634832	+	0.00956855i
$776$	−3790.73	−	1825.52i	−0.175360	−	0.0844490i
$777$	−8729.24	−	25593.1i	−0.403037	−	1.18166i
$778$	−19521.2	+	9400.90i	−0.899573	+	0.433212i
$779$	1161.51	−	791.901i	0.0534214	−	0.0364221i
$780$	23483.5	−	21789.5i	1.07801	−	1.00024i
$781$	163.684	+	2184.21i	0.00749944	+	0.100073i
$782$	70.4640	+	179.539i	0.00322224	+	0.00821012i
$783$	66758.7			3.04695
$784$	−5139.65	+	1924.08i	−0.234131	+	0.0876496i
$785$	8731.07			0.396975
$786$	8204.00	+	20903.4i	0.372299	+	0.948602i
$787$	−730.992	−	9754.40i	−0.0331093	−	0.441813i	−0.988982	−	0.148033i	$-0.952706\pi$
$787$	−730.992	−	9754.40i	−0.0331093	−	0.441813i	0.955873	−	0.293780i	$-0.0949133\pi$
$788$	−2256.81	+	2094.01i	−0.102025	+	0.0946651i
$789$	−48067.7	+	32772.0i	−2.16889	+	1.47873i
$790$	−15548.1	+	7487.58i	−0.700225	+	0.337210i
$791$	6671.86	−	698.445i	0.299904	−	0.0313955i
$792$	22829.8	+	10994.2i	1.02427	+	0.493262i
$793$	10056.7	−	1515.80i	0.450343	−	0.0678783i
$794$	10192.6	+	6949.18i	0.455568	+	0.310601i
$795$	8768.63	+	1321.66i	0.391184	+	0.0589615i
$796$	−4859.46	−	4508.92i	−0.216381	−	0.200772i
$797$	−1181.74	+	1481.85i	−0.0525210	+	0.0658592i	−0.807398	−	0.590007i	$-0.799125\pi$
$797$	−1181.74	+	1481.85i	−0.0525210	+	0.0658592i	0.754877	+	0.655866i	$0.227696\pi$
$798$	38840.2	+	29141.8i	1.72297	+	1.29274i
$799$	−1937.06	−	2429.00i	−0.0857677	−	0.107549i
$800$	−154.986	+	2068.14i	−0.00684946	+	0.0913997i
$801$	−1956.01	+	603.349i	−0.0862824	+	0.0266146i
$802$	−5887.80	−	10198.0i	−0.259234	−	0.449006i
$803$	−7202.58	+	12475.2i	−0.316530	+	0.548246i
$804$	7056.51	−	30916.6i	0.309532	−	1.35615i
$805$	−575.894	+	2083.34i	−0.0252144	+	0.0912148i
$806$	614.064	+	2690.39i	0.0268356	+	0.117574i
$807$	−35580.9	−	10975.2i	−1.55205	−	0.478745i
$808$	177.752	−	452.905i	0.00773923	−	0.0197192i
$809$	−4131.88	+	10527.9i	−0.179566	+	0.457528i	−0.992110	−	0.125373i	$-0.959987\pi$
$809$	−4131.88	+	10527.9i	−0.179566	+	0.457528i	0.812543	+	0.582901i	$0.198082\pi$
$810$	19351.4	+	5969.13i	0.839432	+	0.258931i
$811$	−5328.75	−	23346.8i	−0.230725	−	1.01087i	−0.949041	−	0.315154i	$-0.897944\pi$
$811$	−5328.75	−	23346.8i	−0.230725	−	1.01087i	0.718316	−	0.695717i	$-0.244913\pi$
$812$	−20266.9	−	918.606i	−0.875897	−	0.0397004i
$813$	−7595.31	+	33277.2i	−0.327650	+	1.43553i
$814$	9498.42	−	16451.8i	0.408992	−	0.708395i
$815$	3219.70	+	5576.69i	0.138382	+	0.239685i
$816$	−1567.19	+	483.413i	−0.0672335	+	0.0207388i
$817$	990.923	−	13223.0i	0.0424333	−	0.566233i
$818$	−15989.9	−	20050.7i	−0.683464	−	0.857037i
$819$	29758.9	+	57399.0i	1.26967	+	2.44894i
$820$	−331.762	+	416.017i	−0.0141288	+	0.0177170i
$821$	1460.05	+	1354.73i	0.0620659	+	0.0575888i	0.710596	−	0.703600i	$-0.248425\pi$
$821$	1460.05	+	1354.73i	0.0620659	+	0.0575888i	−0.648530	+	0.761189i	$0.724616\pi$
$822$	−44069.0	−	6642.34i	−1.86993	−	0.281847i
$823$	971.190	+	662.146i	0.0411343	+	0.0280449i	0.583713	−	0.811960i	$-0.301599\pi$
$823$	971.190	+	662.146i	0.0411343	+	0.0280449i	−0.542578	+	0.840005i	$0.682552\pi$
$824$	6205.35	−	935.306i	0.262347	−	0.0395424i
$825$	−30797.3	−	14831.2i	−1.29967	−	0.625887i
$826$	13786.1	+	14005.5i	0.580727	+	0.589969i
$827$	−28485.2	+	13717.8i	−1.19774	+	0.576799i	−0.923030	−	0.384729i	$-0.874295\pi$
$827$	−28485.2	+	13717.8i	−1.19774	+	0.576799i	−0.274706	+	0.961528i	$0.588581\pi$
$828$	1513.88	−	1032.14i	0.0635397	−	0.0433206i
$829$	−708.797	+	657.667i	−0.0296955	+	0.0275534i	−0.694881	−	0.719125i	$-0.744543\pi$
$829$	−708.797	+	657.667i	−0.0296955	+	0.0275534i	0.665185	+	0.746678i	$0.268352\pi$
$830$	2881.88	+	38456.0i	0.120520	+	1.60823i
$831$	−20275.2	−	51660.3i	−0.846375	−	2.15653i
$832$	4131.90			0.172173
$833$	2610.37	+	2903.95i	0.108576	+	0.120787i
$834$	24407.1			1.01337
$835$	11139.7	+	28383.4i	0.461681	+	1.17634i
$836$	2549.25	+	34017.3i	0.105464	+	1.40731i
$837$	−3819.09	+	3543.60i	−0.157715	+	0.146338i
$838$	−19766.0	+	13476.3i	−0.814804	+	0.555524i
$839$	22801.7	−	10980.7i	0.938261	−	0.451843i	0.0987055	−	0.995117i	$-0.468530\pi$
$839$	22801.7	−	10980.7i	0.938261	−	0.451843i	0.839555	+	0.543274i	$0.182816\pi$
$840$	−17299.8	−	6207.17i	−0.710593	−	0.254962i
$841$	−45597.4	−	21958.5i	−1.86959	−	0.900346i
$842$	12372.4	−	1864.84i	0.506392	−	0.0763263i
$843$	−11018.1	−	7512.03i	−0.450160	−	0.306914i
$844$	−16953.5	−	2555.32i	−0.691424	−	0.104215i
$845$	19907.0	+	18471.0i	0.810439	+	0.751977i
$846$	−18401.8	+	23075.1i	−0.747833	+	0.937753i
$847$	29680.6	−	25137.1i	1.20406	−	1.01974i
$848$	713.115	+	894.218i	0.0288779	+	0.0362118i
$849$	4740.65	−	63259.6i	0.191636	−	2.55720i
$850$	1410.06	−	434.946i	0.0568996	−	0.0175512i
$851$	−686.823	−	1189.61i	−0.0276663	−	0.0479194i
$852$	−673.381	+	1166.33i	−0.0270770	+	0.0468988i
$853$	−7263.78	+	31824.7i	−0.291568	+	1.27744i	0.590776	+	0.806835i	$0.298822\pi$
$853$	−7263.78	+	31824.7i	−0.291568	+	1.27744i	−0.882344	+	0.470605i	$0.844036\pi$
$854$	−3427.76	−	4722.02i	−0.137348	−	0.189208i
$855$	24135.3	+	105744.i	0.965392	+	4.22966i
$856$	3892.61	+	1200.71i	0.155428	+	0.0479432i
$857$	5283.64	−	13462.5i	0.210602	−	0.536604i	−0.786069	−	0.618139i	$-0.787887\pi$
$857$	5283.64	−	13462.5i	0.210602	−	0.536604i	0.996671	+	0.0815347i	$0.0259822\pi$
$858$	−24880.3	+	63393.9i	−0.989975	+	2.52242i
$859$	−5933.42	−	1830.22i	−0.235676	−	0.0726965i	0.174667	−	0.984628i	$-0.444115\pi$
$859$	−5933.42	−	1830.22i	−0.235676	−	0.0726965i	−0.410343	+	0.911931i	$0.634591\pi$
$860$	1116.86	+	4893.27i	0.0442843	+	0.194022i
$861$	−945.877	−	1303.02i	−0.0374395	−	0.0515760i
$862$	376.039	−	1647.53i	0.0148584	−	0.0650988i
$863$	14661.5	−	25394.4i	0.578311	−	1.00166i	−0.417363	−	0.908740i	$-0.637046\pi$
$863$	14661.5	−	25394.4i	0.578311	−	1.00166i	0.995673	−	0.0929233i	$-0.0296211\pi$
$864$	3900.34	+	6755.58i	0.153579	+	0.266007i
$865$	−13770.4	+	4247.62i	−0.541282	+	0.166964i
$866$	−159.154	+	2123.76i	−0.00624512	+	0.0833354i
$867$	−26853.8	−	33673.6i	−1.05191	−	1.31905i
$868$	1208.18	−	1023.23i	0.0472444	−	0.0400123i
$869$	22873.1	−	28682.0i	0.892886	−	1.11964i
$870$	−49806.9	−	46214.1i	−1.94093	−	1.80092i
$871$	56209.7	+	8472.25i	2.18668	+	0.329588i
$872$	2572.29	+	1753.76i	0.0998954	+	0.0681075i
$873$	28120.9	−	4238.55i	1.09020	−	0.164322i
$874$	2222.38	+	1070.24i	0.0860106	+	0.0414205i
$875$	−14455.4	−	5186.62i	−0.558494	−	0.200388i
$876$	−7980.11	+	3843.02i	−0.307789	+	0.148223i
$877$	9490.63	−	6470.60i	0.365423	−	0.249141i	−0.366663	−	0.930354i	$-0.619500\pi$
$877$	9490.63	−	6470.60i	0.365423	−	0.249141i	0.732085	+	0.681213i	$0.238547\pi$
$878$	21626.2	−	20066.2i	0.831262	−	0.771298i
$879$	−77.9082	−	1039.61i	−0.00298951	−	0.0398922i
$880$	−4717.34	−	12019.6i	−0.180706	−	0.460432i
$881$	−9739.15			−0.372441			−0.186220	−	0.982508i	$-0.559624\pi$
$881$	−9739.15			−0.372441			−0.186220	+	0.982508i	$0.559624\pi$
$882$	21377.3	−	30315.1i	0.816112	−	1.15733i
$883$	−33363.3			−1.27153			−0.635767	−	0.771881i	$-0.719316\pi$
$883$	−33363.3			−1.27153			−0.635767	+	0.771881i	$0.719316\pi$
$884$	−1074.05	−	2736.64i	−0.0408646	−	0.104121i
$885$	4918.48	+	65632.5i	0.186817	+	2.49290i
$886$	−3815.53	+	3540.30i	−0.144679	+	0.134242i
$887$	25058.6	−	17084.6i	0.948573	−	0.646726i	0.0130208	−	0.999915i	$-0.495855\pi$
$887$	25058.6	−	17084.6i	0.948573	−	0.646726i	0.935552	+	0.353189i	$0.114903\pi$
$888$	10523.8	−	5067.99i	0.397698	−	0.191521i
$889$	−16021.8	−	16276.8i	−0.604449	−	0.614068i
$890$	939.774	+	452.571i	0.0353947	+	0.0170452i
$891$	−42569.6	+	6416.33i	−1.60060	+	0.241252i
$892$	−11218.1	−	7648.35i	−0.421086	−	0.287091i
$893$	−39289.6	−	5921.95i	−1.47231	−	0.221915i
$894$	−40066.7	−	37176.4i	−1.49892	−	1.39079i
$895$	16411.4	−	20579.2i	0.612930	−	0.768590i
$896$	−1091.12	−	2104.56i	−0.0406829	−	0.0784691i
$897$	3070.29	+	3850.02i	0.114285	+	0.143309i
$898$	7.51316	−	100.256i	0.000279195	−	0.00372560i
$899$	5592.84	−	1725.16i	0.207488	−	0.0640016i
$900$	−7009.06	−	12140.0i	−0.259595	−	0.449631i
$901$	406.891	−	704.756i	0.0150449	−	0.0260586i
$902$	251.708	−	1102.80i	0.00929152	−	0.0407088i
$903$	−15172.2	−	687.685i	−0.559134	−	0.0253430i
$904$	644.804	+	2825.07i	0.0237233	+	0.103939i
$905$	−11031.2	−	3402.68i	−0.405182	−	0.124982i
$906$	−9443.04	+	24060.5i	−0.346274	+	0.882291i
$907$	−13248.8	+	33757.3i	−0.485026	+	1.23583i	0.453698	+	0.891156i	$0.350105\pi$
$907$	−13248.8	+	33757.3i	−0.485026	+	1.23583i	−0.938724	+	0.344670i	$0.887991\pi$
$908$	−8886.05	−	2740.98i	−0.324773	−	0.100179i
$909$	731.781	+	3206.14i	0.0267015	+	0.116987i
$910$	8778.10	−	31755.4i	0.319770	−	1.15679i
$911$	1182.11	−	5179.16i	0.0429913	−	0.188357i	−0.948873	−	0.315659i	$-0.897775\pi$
$911$	1182.11	−	5179.16i	0.0429913	−	0.188357i	0.991864	+	0.127302i	$0.0406317\pi$
$912$	−10487.4	+	18164.7i	−0.380781	+	0.659532i
$913$	−40990.1	−	70996.9i	−1.48584	−	2.57355i
$914$	−5109.40	+	1576.04i	−0.184906	+	0.0570359i
$915$	1460.35	−	19487.0i	0.0527625	−	0.704067i
$916$	7381.35	+	9255.92i	0.266252	+	0.333869i
$917$	18472.8	+	13860.1i	0.665240	+	0.499129i
$918$	3460.50	−	4339.33i	0.124416	−	0.156012i
$919$	−31836.8	−	29540.3i	−1.14276	−	1.06033i	−0.997481	−	0.0709402i	$-0.977400\pi$
$919$	−31836.8	−	29540.3i	−1.14276	−	1.06033i	−0.145284	−	0.989390i	$-0.546409\pi$
$920$	−923.238	−	139.156i	−0.0330851	−	0.00498677i
$921$	32026.6	+	21835.4i	1.14583	+	0.781217i
$922$	−36859.0	+	5555.60i	−1.31658	+	0.198443i
$923$	−2175.06	−	1047.45i	−0.0775654	−	0.0373535i
$924$	38859.5	−	4068.02i	1.38353	−	0.144835i
$925$	−9468.67	+	4559.87i	−0.336571	+	0.162084i
$926$	−17079.8	+	11644.8i	−0.606130	+	0.413252i
$927$	−31093.7	+	28850.8i	−1.10167	+	1.02220i
$928$	−654.894	−	8738.96i	−0.0231659	−	0.309127i
$929$	15924.3	+	40574.4i	0.562388	+	1.43294i	0.875496	+	0.483225i	$0.160535\pi$
$929$	15924.3	+	40574.4i	0.562388	+	1.43294i	−0.313108	+	0.949718i	$0.601370\pi$
$930$	5302.40			0.186960
$931$	49733.3	+	4517.66i	1.75075	+	0.159034i
$932$	11326.4			0.398079
$933$	−2912.15	−	7420.04i	−0.102186	−	0.260366i
$934$	−2499.15	−	33348.8i	−0.0875532	−	1.16832i
$935$	−6734.58	+	6248.78i	−0.235556	+	0.218564i
$936$	−23075.4	+	15732.5i	−0.805814	+	0.549395i
$937$	−31397.3	+	15120.1i	−1.09467	+	0.527164i	−0.891978	−	0.452079i	$-0.850683\pi$
$937$	−31397.3	+	15120.1i	−1.09467	+	0.527164i	−0.202690	+	0.979243i	$0.564968\pi$
$938$	−10528.2	−	30867.4i	−0.366480	−	1.07447i
$939$	46536.6	+	22410.8i	1.61732	+	0.778860i
$940$	14871.7	−	2241.54i	0.516021	−	0.0777777i
$941$	22662.2	+	15450.8i	0.785087	+	0.535263i	0.888228	−	0.459404i	$-0.151937\pi$
$941$	22662.2	+	15450.8i	0.785087	+	0.535263i	−0.103141	+	0.994667i	$0.532889\pi$
$942$	−11284.9	−	1700.93i	−0.390321	−	0.0588315i
$943$	−59.9589	−	55.6337i	−0.00207055	−	0.00192119i
$944$	−5292.79	+	6636.95i	−0.182485	+	0.228829i
$945$	60205.7	−	15623.7i	2.07248	−	0.537819i
$946$	−6652.49	−	8341.96i	−0.228637	−	0.286702i
$947$	−178.773	+	2385.55i	−0.00613445	+	0.0818586i	−0.999431	−	0.0337378i	$-0.989259\pi$
$947$	−178.773	+	2385.55i	−0.00613445	+	0.0818586i	0.993296	+	0.115596i	$0.0368779\pi$
$948$	21554.7	−	6648.73i	0.738463	−	0.227786i
$949$	−7938.52	−	13749.9i	−0.271544	−	0.470328i
$950$	9435.91	−	16343.5i	0.322254	−	0.558160i
$951$	−13161.6	+	57664.8i	−0.448785	+	1.96626i
$952$	−1110.26	+	1269.74i	−0.0377982	+	0.0432273i
$953$	−190.164	−	833.162i	−0.00646381	−	0.0283198i	0.971593	−	0.236657i	$-0.0760519\pi$
$953$	−190.164	−	833.162i	−0.00646381	−	0.0283198i	−0.978057	+	0.208338i	$0.933195\pi$
$954$	−7387.34	−	2278.69i	−0.250706	−	0.0773327i
$955$	17762.1	−	45257.1i	0.601852	−	1.53349i
$956$	−563.642	+	1436.14i	−0.0190685	+	0.0485858i
$957$	138022.	+	42574.0i	4.66207	+	1.43806i
$958$	6515.73	+	28547.3i	0.219743	+	0.962757i
$959$	−42153.3	+	17996.5i	−1.41939	+	0.605983i
$960$	1766.65	−	7740.20i	0.0593941	−	0.260223i
$961$	14667.1	−	25404.2i	0.492334	−	0.852747i
$962$	10468.9	+	18132.7i	0.350865	+	0.607716i
$963$	−26310.8	+	8115.81i	−0.880430	+	0.271577i
$964$	−1915.15	+	25555.9i	−0.0639863	+	0.853838i
$965$	14752.8	+	18499.4i	0.492133	+	0.617115i
$966$	1150.20	−	2580.52i	0.0383098	−	0.0859492i
$967$	−8754.23	+	10977.5i	−0.291124	+	0.365058i	−0.905788	−	0.423731i	$-0.860720\pi$
$967$	−8754.23	+	10977.5i	−0.291124	+	0.365058i	0.614664	+	0.788789i	$0.289292\pi$
$968$	12316.0	+	11427.6i	0.408937	+	0.379438i
$969$	14757.0	+	2224.25i	0.489228	+	0.0737392i
$970$	−11973.5	−	8163.36i	−0.396334	−	0.270216i
$971$	−21259.7	+	3204.38i	−0.702632	+	0.105905i	−0.490634	−	0.871366i	$-0.663235\pi$
$971$	−21259.7	+	3204.38i	−0.702632	+	0.105905i	−0.211997	+	0.977270i	$0.567997\pi$
$972$	−128.824	−	62.0384i	−0.00425106	−	0.00204720i
$973$	21358.6	−	13186.4i	0.703725	−	0.434469i
$974$	32747.1	−	15770.2i	1.07730	−	0.518798i
$975$	31128.6	−	21223.1i	1.02248	−	0.697113i
$976$	1847.64	−	1714.36i	0.0605957	−	0.0562246i
$977$	−2453.82	−	32744.0i	−0.0803528	−	1.07223i	−0.881006	−	0.473105i	$-0.843133\pi$
$977$	−2453.82	−	32744.0i	−0.0803528	−	1.07223i	0.800653	−	0.599128i	$-0.204486\pi$
$978$	−3075.06	−	7835.12i	−0.100541	−	0.256175i
$979$	−2217.39			−0.0723882
$980$	−18492.5	+	3914.67i	−0.602776	+	0.127602i
$981$	−21043.0			−0.684865
$982$	4107.30	+	10465.2i	0.133472	+	0.340080i
$983$	2678.71	+	35744.9i	0.0869151	+	1.15980i	0.854710	+	0.519106i	$0.173735\pi$
$983$	2678.71	+	35744.9i	0.0869151	+	1.15980i	−0.767795	+	0.640696i	$0.778646\pi$
$984$	509.849	−	473.071i	0.0165177	−	0.0153262i
$985$	−8761.25	+	5973.32i	−0.283408	+	0.193224i
$986$	−5617.76	+	2705.37i	−0.181446	+	0.0873798i
$987$	−5452.32	+	45181.9i	−0.175835	+	1.45710i
$988$	−33874.8	−	16313.3i	−1.09079	−	0.525298i
$989$	−762.904	+	114.989i	−0.0245288	+	0.00369711i
$990$	72110.4	+	49164.0i	2.31497	+	1.57832i
$991$	37353.6	+	5630.16i	1.19735	+	0.180472i	0.717298	−	0.696766i	$-0.245378\pi$
$991$	37353.6	+	5630.16i	1.19735	+	0.180472i	0.480055	+	0.877238i	$0.340617\pi$
$992$	501.335	+	465.171i	0.0160458	+	0.0148883i
$993$	−15727.3	+	19721.4i	−0.502609	+	0.630252i
$994$	40.8607	+	1384.46i	0.00130385	+	0.0441774i
$995$	−14235.8	−	17851.2i	−0.453574	−	0.568764i
$996$	3766.91	−	50265.9i	0.119838	−	1.59913i
$997$	45981.3	−	14183.4i	1.46063	−	0.450543i	0.540225	−	0.841521i	$-0.318339\pi$
$997$	45981.3	−	14183.4i	1.46063	−	0.450543i	0.920400	+	0.390977i	$0.127863\pi$
$998$	10174.4	+	17622.6i	0.322711	+	0.558953i
$999$	−19764.5	+	34233.1i	−0.625947	+	1.08417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.4.g.a.65.7	✓	84
49.46	even	21	inner	98.4.g.a.95.7	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.4.g.a.65.7	✓	84	1.1	even	1	trivial
98.4.g.a.95.7	yes	84	49.46	even	21	inner

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.730682 - 1.86175i) q^{2} +(0.672876 + 8.97890i) q^{3} +(-2.93221 + 2.72069i) q^{4} +(-11.3832 + 7.76096i) q^{5} +(16.2248 - 7.81345i) q^{6} +(9.97686 - 15.6033i) q^{7} +(7.20775 + 3.47107i) q^{8} +(-53.4695 + 8.05922i) q^{9} +O(q^{10})\)	\(q+(-0.730682 - 1.86175i) q^{2} +(0.672876 + 8.97890i) q^{3} +(-2.93221 + 2.72069i) q^{4} +(-11.3832 + 7.76096i) q^{5} +(16.2248 - 7.81345i) q^{6} +(9.97686 - 15.6033i) q^{7} +(7.20775 + 3.47107i) q^{8} +(-53.4695 + 8.05922i) q^{9} +(22.7665 + 15.5219i) q^{10} +(-57.9216 - 8.73027i) q^{11} +(-26.4018 - 24.4973i) q^{12} +(40.2531 - 50.4757i) q^{13} +(-36.3393 - 7.17337i) q^{14} +(-77.3444 - 96.9868i) q^{15} +(1.19568 - 15.9553i) q^{16} +(-10.8783 + 3.35551i) q^{17} +(54.0734 + 93.6579i) q^{18} +(-72.7961 + 126.087i) q^{19} +(12.2628 - 53.7270i) q^{20} +(146.813 + 79.0822i) q^{21} +(26.0687 + 114.214i) q^{22} +(8.09478 + 2.49691i) q^{23} +(-26.3165 + 67.0533i) q^{24} +(23.6780 - 60.3305i) q^{25} +(-123.385 - 38.0593i) q^{26} +(-54.2442 - 237.659i) q^{27} +(13.1975 + 72.8960i) q^{28} +(-60.9392 + 266.992i) q^{29} +(-124.051 + 214.862i) q^{30} +(-10.6860 - 18.5086i) q^{31} +(-30.5783 + 9.43217i) q^{32} +(39.4142 - 525.946i) q^{33} +(14.1957 + 17.8009i) q^{34} +(7.52740 + 255.046i) q^{35} +(134.857 - 169.105i) q^{36} +(-118.869 - 110.294i) q^{37} +(287.932 + 43.3988i) q^{38} +(480.302 + 327.464i) q^{39} +(-108.986 + 16.4271i) q^{40} +(-8.69936 - 4.18939i) q^{41} +(39.9571 - 331.114i) q^{42} +(-82.0571 + 39.5166i) q^{43} +(193.590 - 131.988i) q^{44} +(546.108 - 506.714i) q^{45} +(-1.26610 - 16.8949i) q^{46} +(99.7047 + 254.043i) q^{47} +144.065 q^{48} +(-143.924 - 311.343i) q^{49} -129.621 q^{50} +(-37.4486 - 95.4174i) q^{51} +(19.2986 + 257.521i) q^{52} +(-52.4017 + 48.6216i) q^{53} +(-402.826 + 274.642i) q^{54} +(727.090 - 350.148i) q^{55} +(126.071 - 77.8341i) q^{56} +(-1181.10 - 568.788i) q^{57} +(541.599 - 81.6329i) q^{58} +(-438.370 - 298.876i) q^{59} +(490.661 + 73.9552i) q^{60} +(115.477 + 107.147i) q^{61} +(-26.6503 + 33.4185i) q^{62} +(-407.707 + 914.705i) q^{63} +(39.9033 + 50.0372i) q^{64} +(-66.4699 + 886.979i) q^{65} +(-1007.98 + 310.920i) q^{66} +(440.241 + 762.519i) q^{67} +(22.7681 - 39.4356i) q^{68} +(-16.9727 + 74.3623i) q^{69} +(469.331 - 200.372i) q^{70} +(-8.32075 - 36.4556i) q^{71} +(-413.369 - 127.507i) q^{72} +(89.8459 - 228.924i) q^{73} +(-118.485 + 301.894i) q^{74} +(557.634 + 172.007i) q^{75} +(-129.589 - 567.767i) q^{76} +(-714.096 + 816.665i) q^{77} +(258.708 - 1133.47i) q^{78} +(-313.147 + 542.386i) q^{79} +(110.217 + 190.902i) q^{80} +(702.300 - 216.631i) q^{81} +(-1.44312 + 19.2571i) q^{82} +(872.609 + 1094.22i) q^{83} +(-645.646 + 167.549i) q^{84} +(97.7884 - 122.623i) q^{85} +(133.528 + 123.896i) q^{86} +(-2438.30 - 367.514i) q^{87} +(-387.181 - 263.975i) q^{88} +(37.4322 - 5.64200i) q^{89} +(-1342.41 - 646.469i) q^{90} +(-385.988 - 1131.67i) q^{91} +(-30.5289 + 14.7019i) q^{92} +(158.997 - 108.402i) q^{93} +(400.112 - 371.250i) q^{94} +(-149.897 - 2000.24i) q^{95} +(-105.266 - 268.213i) q^{96} -525.925 q^{97} +(-474.480 + 495.444i) q^{98} +3167.39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 14 q^{2} - 8 q^{3} + 28 q^{4} + 7 q^{5} + 10 q^{6} + 20 q^{7} + 112 q^{8} + 189 q^{9}+O(q^{10}) \) 84 * q - 14 * q^2 - 8 * q^3 + 28 * q^4 + 7 * q^5 + 10 * q^6 + 20 * q^7 + 112 * q^8 + 189 * q^9	\( 84 q - 14 q^{2} - 8 q^{3} + 28 q^{4} + 7 q^{5} + 10 q^{6} + 20 q^{7} + 112 q^{8} + 189 q^{9} - 14 q^{10} - 77 q^{11} - 4 q^{12} - 62 q^{13} - 34 q^{14} - 217 q^{15} + 112 q^{16} - 165 q^{17} + 798 q^{18} + 25 q^{19} + 56 q^{20} + 394 q^{21} - 210 q^{22} + 329 q^{23} + 8 q^{24} + 126 q^{25} - 398 q^{26} - 1058 q^{27} + 132 q^{28} + 7 q^{29} - 70 q^{30} - 793 q^{31} - 224 q^{32} + 875 q^{33} + 222 q^{34} - 1260 q^{35} - 924 q^{36} + 2540 q^{38} + 1799 q^{39} + 280 q^{40} + 1220 q^{41} + 1482 q^{42} - 770 q^{43} - 112 q^{44} - 2030 q^{45} - 1834 q^{46} - 1438 q^{47} + 32 q^{48} - 2626 q^{49} - 4396 q^{50} - 2569 q^{51} - 688 q^{52} - 2744 q^{53} + 62 q^{54} + 343 q^{55} - 216 q^{56} - 2058 q^{57} + 3976 q^{58} + 396 q^{59} + 1316 q^{60} + 4930 q^{61} + 1560 q^{62} + 4717 q^{63} - 896 q^{64} + 238 q^{65} - 1624 q^{66} + 2695 q^{67} + 1076 q^{68} - 931 q^{69} - 742 q^{70} - 539 q^{71} - 336 q^{72} + 1989 q^{73} - 1176 q^{74} - 2780 q^{75} - 1096 q^{76} + 4627 q^{77} + 336 q^{78} - 1197 q^{79} + 112 q^{80} + 9674 q^{81} + 1220 q^{82} + 831 q^{83} - 404 q^{84} + 161 q^{85} - 3122 q^{86} + 9477 q^{87} + 224 q^{88} - 7537 q^{89} - 4214 q^{90} + 4351 q^{91} - 2044 q^{92} - 8176 q^{93} + 3072 q^{94} - 11753 q^{95} + 32 q^{96} + 13530 q^{97} + 862 q^{98} + 6090 q^{99}+O(q^{100}) \) 84 * q - 14 * q^2 - 8 * q^3 + 28 * q^4 + 7 * q^5 + 10 * q^6 + 20 * q^7 + 112 * q^8 + 189 * q^9 - 14 * q^10 - 77 * q^11 - 4 * q^12 - 62 * q^13 - 34 * q^14 - 217 * q^15 + 112 * q^16 - 165 * q^17 + 798 * q^18 + 25 * q^19 + 56 * q^20 + 394 * q^21 - 210 * q^22 + 329 * q^23 + 8 * q^24 + 126 * q^25 - 398 * q^26 - 1058 * q^27 + 132 * q^28 + 7 * q^29 - 70 * q^30 - 793 * q^31 - 224 * q^32 + 875 * q^33 + 222 * q^34 - 1260 * q^35 - 924 * q^36 + 2540 * q^38 + 1799 * q^39 + 280 * q^40 + 1220 * q^41 + 1482 * q^42 - 770 * q^43 - 112 * q^44 - 2030 * q^45 - 1834 * q^46 - 1438 * q^47 + 32 * q^48 - 2626 * q^49 - 4396 * q^50 - 2569 * q^51 - 688 * q^52 - 2744 * q^53 + 62 * q^54 + 343 * q^55 - 216 * q^56 - 2058 * q^57 + 3976 * q^58 + 396 * q^59 + 1316 * q^60 + 4930 * q^61 + 1560 * q^62 + 4717 * q^63 - 896 * q^64 + 238 * q^65 - 1624 * q^66 + 2695 * q^67 + 1076 * q^68 - 931 * q^69 - 742 * q^70 - 539 * q^71 - 336 * q^72 + 1989 * q^73 - 1176 * q^74 - 2780 * q^75 - 1096 * q^76 + 4627 * q^77 + 336 * q^78 - 1197 * q^79 + 112 * q^80 + 9674 * q^81 + 1220 * q^82 + 831 * q^83 - 404 * q^84 + 161 * q^85 - 3122 * q^86 + 9477 * q^87 + 224 * q^88 - 7537 * q^89 - 4214 * q^90 + 4351 * q^91 - 2044 * q^92 - 8176 * q^93 + 3072 * q^94 - 11753 * q^95 + 32 * q^96 + 13530 * q^97 + 862 * q^98 + 6090 * q^99

Introduction

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