LMFDB - Embedded newform 177.4.e.a.133.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

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("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			133.13
Character	$\chi$	$=$	177.133
Dual form			177.4.e.a.4.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.96175 - 0.430866i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(7.69682 - 1.69420i) q^{4} +(-13.8169 + 10.5033i) q^{5} +(-8.67951 - 8.22167i) q^{6} +(-7.10268 - 17.8264i) q^{7} +(-0.449126 + 0.151328i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})$	\(q+(3.96175 - 0.430866i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(7.69682 - 1.69420i) q^{4} +(-13.8169 + 10.5033i) q^{5} +(-8.67951 - 8.22167i) q^{6} +(-7.10268 - 17.8264i) q^{7} +(-0.449126 + 0.151328i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-50.2135 + 47.5647i) q^{10} +(-26.5402 - 12.2788i) q^{11} +(-18.8222 - 14.3083i) q^{12} +(-12.9395 - 78.9277i) q^{13} +(-35.8198 - 67.5633i) q^{14} +(50.8503 + 11.1930i) q^{15} +(-58.9355 + 27.2665i) q^{16} +(-42.5864 + 106.884i) q^{17} +(-1.94174 + 35.8134i) q^{18} +(42.2050 - 62.2477i) q^{19} +(-88.5514 + 104.251i) q^{20} +(-26.9653 + 50.8619i) q^{21} +(-110.436 - 37.2102i) q^{22} +(4.46007 + 82.2612i) q^{23} +(1.21828 + 0.733018i) q^{24} +(47.1455 - 169.803i) q^{25} +(-85.2704 - 307.116i) q^{26} +(23.1351 - 13.9200i) q^{27} +(-84.8695 - 125.173i) q^{28} +(82.5447 + 8.97728i) q^{29} +(206.279 + 22.4342i) q^{30} +(82.8028 + 122.125i) q^{31} +(-218.490 + 131.461i) q^{32} +(23.4699 + 84.5311i) q^{33} +(-122.664 + 441.796i) q^{34} +(285.373 + 171.703i) q^{35} +(3.84005 + 70.8256i) q^{36} +(-7.24884 - 2.44242i) q^{37} +(140.385 - 264.794i) q^{38} +(-155.336 + 182.876i) q^{39} +(4.61608 - 6.80821i) q^{40} +(18.8950 - 348.498i) q^{41} +(-84.9149 + 213.120i) q^{42} +(-125.852 + 58.2253i) q^{43} +(-225.077 - 49.5433i) q^{44} +(-73.1667 - 138.007i) q^{45} +(53.1132 + 323.976i) q^{46} +(71.0147 + 53.9840i) q^{47} +(176.806 + 81.7994i) q^{48} +(-18.3157 + 17.3496i) q^{49} +(113.616 - 693.029i) q^{50} +(327.098 - 110.212i) q^{51} +(-233.312 - 585.570i) q^{52} +(-524.149 - 496.501i) q^{53} +(85.6579 - 65.1155i) q^{54} +(495.671 - 109.105i) q^{55} +(5.88764 + 6.93147i) q^{56} +(-224.297 + 24.3938i) q^{57} +330.889 q^{58} +(-239.474 - 384.748i) q^{59} +410.349 q^{60} +(128.252 - 13.9483i) q^{61} +(380.663 + 448.151i) q^{62} +(168.666 - 37.1261i) q^{63} +(-395.392 + 300.569i) q^{64} +(1007.79 + 954.627i) q^{65} +(129.403 + 324.778i) q^{66} +(-326.766 + 110.100i) q^{67} +(-146.698 + 894.816i) q^{68} +(179.427 - 169.962i) q^{69} +(1204.56 + 557.288i) q^{70} +(-668.507 - 508.186i) q^{71} +(-0.690068 - 4.20923i) q^{72} +(-303.590 - 572.632i) q^{73} +(-29.7704 - 6.55296i) q^{74} +(-479.816 + 221.986i) q^{75} +(219.384 - 550.613i) q^{76} +(-30.3801 + 560.328i) q^{77} +(-536.608 + 791.438i) q^{78} +(-634.560 + 747.062i) q^{79} +(527.916 - 995.756i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-75.2986 - 1388.80i) q^{82} +(1010.74 + 608.144i) q^{83} +(-121.377 + 437.159i) q^{84} +(-534.224 - 1924.10i) q^{85} +(-473.506 + 284.899i) q^{86} +(-139.788 - 206.173i) q^{87} +(13.7780 + 1.49845i) q^{88} +(-588.984 - 64.0559i) q^{89} +(-349.331 - 515.224i) q^{90} +(-1315.09 + 791.264i) q^{91} +(173.695 + 625.593i) q^{92} +(118.421 - 426.513i) q^{93} +(304.602 + 183.273i) q^{94} +(70.6662 + 1303.36i) q^{95} +(724.928 + 244.257i) q^{96} +(-150.969 + 284.758i) q^{97} +(-65.0869 + 76.6262i) q^{98} +(147.697 - 217.836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{28}{29}\right)$	$1$

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 $

$2$	3.96175	−	0.430866i	1.40069	−	0.152334i	0.623609	−	0.781736i	$-0.285666\pi$
$2$	3.96175	−	0.430866i	1.40069	−	0.152334i	0.777080	+	0.629402i	$0.216700\pi$
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$3$	−1.94216	−	2.28649i	−0.373769	−	0.440034i
$4$	7.69682	−	1.69420i	0.962102	−	0.211775i
$5$	−13.8169	+	10.5033i	−1.23582	+	0.939446i	−0.999481	−	0.0322245i	$-0.989741\pi$
$5$	−13.8169	+	10.5033i	−1.23582	+	0.939446i	−0.236339	+	0.971671i	$0.575948\pi$
$6$	−8.67951	−	8.22167i	−0.590566	−	0.559414i
$7$	−7.10268	−	17.8264i	−0.383509	−	0.962535i	−0.986348	−	0.164672i	$-0.947343\pi$
$7$	−7.10268	−	17.8264i	−0.383509	−	0.962535i	0.602839	−	0.797863i	$-0.294036\pi$
$8$	−0.449126	+	0.151328i	−0.0198488	+	0.00668783i
$9$	−1.45604	+	8.88144i	−0.0539273	+	0.328942i
$10$	−50.2135	+	47.5647i	−1.58789	+	1.50413i
$11$	−26.5402	−	12.2788i	−0.727469	−	0.336563i	0.0209578	−	0.999780i	$-0.493328\pi$
$11$	−26.5402	−	12.2788i	−0.727469	−	0.336563i	−0.748427	+	0.663217i	$0.769190\pi$
$12$	−18.8222	−	14.3083i	−0.452792	−	0.344203i
$13$	−12.9395	−	78.9277i	−0.276060	−	1.68389i	−0.652766	−	0.757560i	$-0.726391\pi$
$13$	−12.9395	−	78.9277i	−0.276060	−	1.68389i	0.376706	−	0.926333i	$-0.377057\pi$
$14$	−35.8198	−	67.5633i	−0.683803	−	1.28979i
$15$	50.8503	+	11.1930i	0.875299	+	0.192668i
$16$	−58.9355	+	27.2665i	−0.920867	+	0.426038i
$17$	−42.5864	+	106.884i	−0.607572	+	1.52489i	0.226944	+	0.973908i	$0.427126\pi$
$17$	−42.5864	+	106.884i	−0.607572	+	1.52489i	−0.834516	+	0.550983i	$0.814253\pi$
$18$	−1.94174	+	35.8134i	−0.0254263	+	0.468961i
$19$	42.2050	−	62.2477i	0.509604	−	0.751610i	−0.482653	−	0.875812i	$-0.660327\pi$
$19$	42.2050	−	62.2477i	0.509604	−	0.751610i	0.992257	+	0.124202i	$0.0396370\pi$
$20$	−88.5514	+	104.251i	−0.990034	+	1.16556i
$21$	−26.9653	+	50.8619i	−0.280205	+	0.528522i
$22$	−110.436	−	37.2102i	−1.07023	−	0.360602i
$23$	4.46007	+	82.2612i	0.0404343	+	0.745767i	0.946514	+	0.322661i	$0.104577\pi$
$23$	4.46007	+	82.2612i	0.0404343	+	0.745767i	−0.906080	+	0.423106i	$0.860940\pi$
$24$	1.21828	+	0.733018i	0.0103617	+	0.00623444i
$25$	47.1455	−	169.803i	0.377164	−	1.35842i
$26$	−85.2704	−	307.116i	−0.643189	−	2.31656i
$27$	23.1351	−	13.9200i	0.164902	−	0.0992184i
$28$	−84.8695	−	125.173i	−0.572815	−	0.844839i
$29$	82.5447	+	8.97728i	0.528557	+	0.0574841i	0.368507	−	0.929625i	$-0.379869\pi$
$29$	82.5447	+	8.97728i	0.528557	+	0.0574841i	0.160050	+	0.987109i	$0.448834\pi$
$30$	206.279	+	22.4342i	1.25537	+	0.136530i
$31$	82.8028	+	122.125i	0.479736	+	0.707558i	0.988139	−	0.153562i	$-0.0490743\pi$
$31$	82.8028	+	122.125i	0.479736	+	0.707558i	−0.508403	+	0.861119i	$0.669764\pi$
$32$	−218.490	+	131.461i	−1.20700	+	0.726228i
$33$	23.4699	+	84.5311i	0.123806	+	0.445908i
$34$	−122.664	+	441.796i	−0.618726	+	2.22845i
$35$	285.373	+	171.703i	1.37820	+	0.829234i
$36$	3.84005	+	70.8256i	0.0177780	+	0.327896i
$37$	−7.24884	−	2.44242i	−0.0322081	−	0.0108522i	0.303151	−	0.952942i	$-0.401961\pi$
$37$	−7.24884	−	2.44242i	−0.0322081	−	0.0108522i	−0.335359	+	0.942090i	$0.608858\pi$
$38$	140.385	−	264.794i	0.599301	−	1.13040i
$39$	−155.336	+	182.876i	−0.637788	+	0.750862i
$40$	4.61608	−	6.80821i	0.0182467	−	0.0269118i
$41$	18.8950	−	348.498i	0.0719733	−	1.32747i	−0.710020	−	0.704182i	$-0.751314\pi$
$41$	18.8950	−	348.498i	0.0719733	−	1.32747i	0.781993	−	0.623287i	$-0.214203\pi$
$42$	−84.9149	+	213.120i	−0.311968	+	0.782980i
$43$	−125.852	+	58.2253i	−0.446331	+	0.206495i	−0.630163	−	0.776463i	$-0.717012\pi$
$43$	−125.852	+	58.2253i	−0.446331	+	0.206495i	0.183832	+	0.982958i	$0.441150\pi$
$44$	−225.077	−	49.5433i	−0.771175	−	0.169748i
$45$	−73.1667	−	138.007i	−0.242379	−	0.457175i
$46$	53.1132	+	323.976i	0.170242	+	1.03843i
$47$	71.0147	+	53.9840i	0.220395	+	0.167540i	0.709546	−	0.704659i	$-0.248900\pi$
$47$	71.0147	+	53.9840i	0.220395	+	0.167540i	−0.489151	+	0.872199i	$0.662693\pi$
$48$	176.806	+	81.7994i	0.531663	+	0.245973i
$49$	−18.3157	+	17.3496i	−0.0533986	+	0.0505818i
$50$	113.616	−	693.029i	0.321356	−	1.96018i
$51$	327.098	−	110.212i	0.898096	−	0.302604i
$52$	−233.312	−	585.570i	−0.622204	−	1.56161i
$53$	−524.149	−	496.501i	−1.35844	−	1.28678i	−0.922072	−	0.387017i	$-0.873505\pi$
$53$	−524.149	−	496.501i	−1.35844	−	1.28678i	−0.436370	−	0.899767i	$-0.643736\pi$
$54$	85.6579	−	65.1155i	0.215862	−	0.164094i
$55$	495.671	−	109.105i	1.21520	−	0.267487i
$56$	5.88764	+	6.93147i	0.0140494	+	0.0165403i
$57$	−224.297	+	24.3938i	−0.521209	+	0.0566848i
$58$	330.889			0.749101
$59$	−239.474	−	384.748i	−0.528421	−	0.848983i
$59$	−239.474	−	384.748i	−0.528421	−	0.848983i
$60$	410.349			0.882930
$61$	128.252	−	13.9483i	0.269197	−	0.0292769i	0.0274749	−	0.999622i	$-0.491253\pi$
$61$	128.252	−	13.9483i	0.269197	−	0.0292769i	0.241722	+	0.970346i	$0.422288\pi$
$62$	380.663	+	448.151i	0.779746	+	0.917988i
$63$	168.666	−	37.1261i	0.337300	−	0.0742453i
$64$	−395.392	+	300.569i	−0.772251	+	0.587050i
$65$	1007.79	+	954.627i	1.92309	+	1.82164i
$66$	129.403	+	324.778i	0.241340	+	0.605719i
$67$	−326.766	+	110.100i	−0.595833	+	0.200759i	−0.601029	−	0.799227i	$-0.705242\pi$
$67$	−326.766	+	110.100i	−0.595833	+	0.200759i	0.00519636	+	0.999986i	$0.498346\pi$
$68$	−146.698	+	894.816i	−0.261613	+	1.59577i
$69$	179.427	−	169.962i	0.313050	−	0.296537i
$70$	1204.56	+	557.288i	2.05675	+	0.951552i
$71$	−668.507	−	508.186i	−1.11743	−	0.849445i	−0.127613	−	0.991824i	$-0.540732\pi$
$71$	−668.507	−	508.186i	−1.11743	−	0.849445i	−0.989812	+	0.142379i	$0.954525\pi$
$72$	−0.690068	−	4.20923i	−0.00112952	−	0.00688975i
$73$	−303.590	−	572.632i	−0.486747	−	0.918102i	−0.998268	−	0.0588315i	$-0.981263\pi$
$73$	−303.590	−	572.632i	−0.486747	−	0.918102i	0.511521	−	0.859271i	$-0.329082\pi$
$74$	−29.7704	−	6.55296i	−0.0467667	−	0.0102941i
$75$	−479.816	+	221.986i	−0.738725	+	0.341771i
$76$	219.384	−	550.613i	0.331119	−	0.831047i
$77$	−30.3801	+	560.328i	−0.0449628	+	0.829289i
$78$	−536.608	+	791.438i	−0.778961	+	1.14888i
$79$	−634.560	+	747.062i	−0.903716	+	1.06394i	0.0939447	+	0.995577i	$0.470052\pi$
$79$	−634.560	+	747.062i	−0.903716	+	1.06394i	−0.997661	+	0.0683594i	$0.978224\pi$
$80$	527.916	−	995.756i	0.737786	−	1.39161i
$81$	−76.7599	−	25.8634i	−0.105295	−	0.0354779i
$82$	−75.2986	−	1388.80i	−0.101407	−	1.87034i
$83$	1010.74	+	608.144i	1.33667	+	0.804247i	0.990968	−	0.134098i	$-0.0428136\pi$
$83$	1010.74	+	608.144i	1.33667	+	0.804247i	0.345701	+	0.938345i	$0.387641\pi$
$84$	−121.377	+	437.159i	−0.157658	+	0.567833i
$85$	−534.224	−	1924.10i	−0.681703	−	2.45527i
$86$	−473.506	+	284.899i	−0.593715	+	0.357226i
$87$	−139.788	−	206.173i	−0.172263	−	0.254069i
$88$	13.7780	+	1.49845i	0.0166902	+	0.00181517i
$89$	−588.984	−	64.0559i	−0.701485	−	0.0762911i	−0.249576	−	0.968355i	$-0.580291\pi$
$89$	−588.984	−	64.0559i	−0.701485	−	0.0762911i	−0.451909	+	0.892064i	$0.649257\pi$
$90$	−349.331	−	515.224i	−0.409141	−	0.603437i
$91$	−1315.09	+	791.264i	−1.51493	+	0.911505i
$92$	173.695	+	625.593i	0.196837	+	0.708942i
$93$	118.421	−	426.513i	0.132039	−	0.475563i
$94$	304.602	+	183.273i	0.334227	+	0.201097i
$95$	70.6662	+	1303.36i	0.0763179	+	1.40760i
$96$	724.928	+	244.257i	0.770704	+	0.259680i
$97$	−150.969	+	284.758i	−0.158027	+	0.298070i	−0.949865	−	0.312661i	$-0.898780\pi$
$97$	−150.969	+	284.758i	−0.158027	+	0.298070i	0.791838	+	0.610731i	$0.209124\pi$
$98$	−65.0869	+	76.6262i	−0.0670895	+	0.0789838i
$99$	147.697	−	217.836i	0.149940	−	0.221145i
$100$	75.1909	−	1386.82i	0.0751909	−	1.38682i
$101$	−346.349	+	869.269i	−0.341218	+	0.856391i	0.653798	+	0.756669i	$0.273175\pi$
$101$	−346.349	+	869.269i	−0.341218	+	0.856391i	−0.995015	+	0.0997221i	$0.968205\pi$
$102$	1248.39	−	577.568i	1.21186	−	0.560664i
$103$	887.294	+	195.308i	0.848813	+	0.186838i	0.618017	−	0.786165i	$-0.287936\pi$
$103$	887.294	+	195.308i	0.848813	+	0.186838i	0.230795	+	0.973002i	$0.425867\pi$
$104$	17.7555	+	33.4904i	0.0167410	+	0.0315770i
$105$	−161.643	−	985.978i	−0.150236	−	0.916396i
$106$	−2290.47	−	1741.17i	−2.09878	−	1.59545i
$107$	1552.58	+	718.298i	1.40274	+	0.648977i	0.967855	−	0.251509i	$-0.0809268\pi$
$107$	1552.58	+	718.298i	1.40274	+	0.648977i	0.434885	+	0.900486i	$0.356789\pi$
$108$	154.484	−	146.335i	0.137641	−	0.130380i
$109$	−38.3236	+	233.763i	−0.0336764	+	0.205417i	−0.998305	−	0.0581948i	$-0.981466\pi$
$109$	−38.3236	+	233.763i	−0.0336764	+	0.205417i	0.964629	+	0.263612i	$0.0849138\pi$
$110$	1916.71	−	645.815i	1.66137	−	0.559782i
$111$	8.49384	+	21.3179i	0.00726306	+	0.0182289i
$112$	904.663	+	856.942i	0.763237	+	0.722977i
$113$	−1231.35	+	936.048i	−1.02509	+	0.779256i	−0.975608	−	0.219519i	$-0.929551\pi$
$113$	−1231.35	+	936.048i	−1.02509	+	0.779256i	−0.0494857	+	0.998775i	$0.515758\pi$
$114$	−878.098	+	193.284i	−0.721416	+	0.158796i
$115$	−925.641	−	1089.75i	−0.750578	−	0.883649i
$116$	650.541	−	70.7506i	0.520700	−	0.0566295i
$117$	719.832			0.568791
$118$	−1114.51	−	1421.09i	−0.869482	−	1.10866i
$119$	2207.83			1.70077
$120$	−24.5320	+	2.66802i	−0.0186621	+	0.00202963i
$121$	−308.060	−	362.676i	−0.231450	−	0.272484i
$122$	502.092	−	110.519i	0.372601	−	0.0820157i
$123$	−833.533	+	633.635i	−0.611034	+	0.464496i
$124$	844.222	+	799.689i	0.611398	+	0.579147i
$125$	329.081	+	825.932i	0.235471	+	0.590989i
$126$	652.215	−	219.757i	0.461142	−	0.155377i
$127$	−217.662	+	1327.68i	−0.152082	+	0.927658i	0.794987	+	0.606627i	$0.207478\pi$
$127$	−217.662	+	1327.68i	−0.152082	+	0.927658i	−0.947069	+	0.321031i	$0.895971\pi$
$128$	44.0367	−	41.7138i	0.0304089	−	0.0288048i
$129$	377.556	+	174.676i	0.257689	+	0.119220i
$130$	4403.91	+	3347.77i	2.97114	+	2.25861i
$131$	−316.100	−	1928.12i	−0.210823	−	1.28596i	−0.854012	−	0.520254i	$-0.825837\pi$
$131$	−316.100	−	1928.12i	−0.210823	−	1.28596i	0.643189	−	0.765707i	$-0.277611\pi$
$132$	323.856	+	610.857i	0.213546	+	0.402790i
$133$	−1409.42	−	310.237i	−0.918889	−	0.202263i
$134$	−1247.12	+	576.981i	−0.803994	+	0.371967i
$135$	−173.450	+	435.326i	−0.110579	+	0.277533i
$136$	2.95213	−	54.4489i	0.00186135	−	0.0343305i
$137$	427.817	−	630.982i	0.266794	−	0.393492i	−0.670568	−	0.741848i	$-0.733950\pi$
$137$	427.817	−	630.982i	0.266794	−	0.393492i	0.937362	+	0.348356i	$0.113260\pi$
$138$	637.613	−	750.656i	0.393313	−	0.463044i
$139$	780.591	−	1472.35i	0.476323	−	0.898440i	−0.522624	−	0.852563i	$-0.675047\pi$
$139$	780.591	−	1472.35i	0.476323	−	0.898440i	0.998947	−	0.0458770i	$-0.0146082\pi$
$140$	2487.37	+	838.092i	1.50158	+	0.505940i
$141$	−14.4882	−	267.220i	−0.00865339	−	0.159602i
$142$	−2867.42	−	1725.27i	−1.69456	−	1.01959i
$143$	−625.719	+	2253.64i	−0.365911	+	1.31789i
$144$	−156.353	−	563.133i	−0.0904821	−	0.325887i
$145$	−1234.80	+	742.956i	−0.707205	+	0.425511i
$146$	−1449.47	−	2137.81i	−0.821639	−	1.21183i
$147$	75.2416	+	8.18302i	0.0422165	+	0.00459132i
$148$	−59.9309	−	6.51788i	−0.0332858	−	0.00362004i
$149$	832.019	+	1227.14i	0.457461	+	0.674704i	0.984550	−	0.175106i	$-0.0560268\pi$
$149$	832.019	+	1227.14i	0.457461	+	0.674704i	−0.527089	+	0.849810i	$0.676716\pi$
$150$	−1805.26	+	1086.19i	−0.982660	+	0.591247i
$151$	−330.220	−	1189.35i	−0.177966	−	0.640977i	−0.997672	−	0.0681924i	$-0.978277\pi$
$151$	−330.220	−	1189.35i	−0.177966	−	0.640977i	0.819706	−	0.572785i	$-0.194137\pi$
$152$	−9.53553	+	34.3439i	−0.00508838	+	0.0183267i
$153$	−887.275	−	533.856i	−0.468836	−	0.282089i
$154$	121.068	+	2232.97i	0.0633502	+	1.16843i
$155$	−2426.79	−	817.682i	−1.25758	−	0.423728i
$156$	−885.768	+	1670.74i	−0.454604	+	0.857474i
$157$	1908.29	−	2246.61i	0.970051	−	1.14203i	−0.0197832	−	0.999804i	$-0.506298\pi$
$157$	1908.29	−	2246.61i	0.970051	−	1.14203i	0.989834	−	0.142228i	$-0.0454266\pi$
$158$	−2192.08	+	3233.08i	−1.10375	+	1.62791i
$159$	−117.261	+	2162.74i	−0.0584866	+	1.07872i
$160$	1638.08	−	4111.26i	0.809383	−	2.03140i
$161$	1434.74	−	663.783i	0.702320	−	0.324928i
$162$	−315.247	−	69.3911i	−0.152890	−	0.0336536i
$163$	66.6738	+	125.760i	0.0320386	+	0.0604312i	0.899015	−	0.437919i	$-0.144284\pi$
$163$	66.6738	+	125.760i	0.0320386	+	0.0604312i	−0.866976	+	0.498350i	$0.833939\pi$
$164$	−444.993	−	2714.34i	−0.211879	−	1.29240i
$165$	−1212.14	−	921.444i	−0.571908	−	0.434753i
$166$	4266.34	+	1973.82i	1.99477	+	0.922879i
$167$	−1899.31	+	1799.12i	−0.880077	+	0.833654i	−0.987018	−	0.160612i	$-0.948653\pi$
$167$	−1899.31	+	1799.12i	−0.880077	+	0.833654i	0.106940	+	0.994265i	$0.465895\pi$
$168$	4.41397	−	26.9240i	0.00202705	−	0.0123645i
$169$	−3980.16	+	1341.07i	−1.81163	+	0.610410i
$170$	−2945.49	−	7392.62i	−1.32888	−	3.33523i
$171$	491.397	+	465.476i	0.219755	+	0.208163i
$172$	−870.014	+	661.367i	−0.385686	+	0.293191i
$173$	−340.758	+	75.0065i	−0.149753	+	0.0329632i	−0.289214	−	0.957264i	$-0.593394\pi$
$173$	−340.758	+	75.0065i	−0.149753	+	0.0329632i	0.139461	+	0.990228i	$0.455463\pi$
$174$	−642.639	−	756.573i	−0.279991	−	0.329630i
$175$	−3361.83	+	365.621i	−1.45217	+	0.157934i
$176$	1898.96			0.813291
$177$	−414.626	+	1294.80i	−0.176075	+	0.549846i
$178$	−2361.00			−0.994184
$179$	−4065.86	+	442.189i	−1.69775	+	0.184641i	−0.905146	−	0.425100i	$-0.860239\pi$
$179$	−4065.86	+	442.189i	−1.69775	+	0.184641i	−0.792601	+	0.609741i	$0.791273\pi$
$180$	−796.962	−	938.257i	−0.330011	−	0.388520i
$181$	−3117.78	+	686.276i	−1.28035	+	0.281826i	−0.802519	−	0.596627i	$-0.796507\pi$
$181$	−3117.78	+	686.276i	−1.28035	+	0.281826i	−0.477829	+	0.878453i	$0.658576\pi$
$182$	−4869.13	+	3701.41i	−1.98310	+	1.50751i
$183$	−280.978	−	266.157i	−0.113500	−	0.107513i
$184$	−14.4516	−	36.2708i	−0.00579014	−	0.0145321i
$185$	125.810	−	42.3903i	0.0499985	−	0.0168465i
$186$	285.383	−	1740.76i	0.112502	−	0.686230i
$187$	2442.65	−	2313.81i	0.955212	−	0.904825i
$188$	638.047	+	295.192i	0.247523	+	0.114516i
$189$	−412.464	−	313.547i	−0.158743	−	0.120673i
$190$	841.536	+	5133.14i	0.321323	+	1.95998i
$191$	−1364.52	−	2573.75i	−0.516926	−	0.975026i	−0.995297	−	0.0968684i	$-0.969117\pi$
$191$	−1364.52	−	2573.75i	−0.516926	−	0.975026i	0.478371	−	0.878158i	$-0.341227\pi$
$192$	1455.16	+	320.305i	0.546965	+	0.120396i
$193$	−1119.71	+	518.031i	−0.417607	+	0.193206i	−0.617429	−	0.786627i	$-0.711826\pi$
$193$	−1119.71	+	518.031i	−0.417607	+	0.193206i	0.199822	+	0.979832i	$0.435964\pi$
$194$	−475.408	+	1193.18i	−0.175940	+	0.441576i
$195$	225.458	−	4158.33i	0.0827969	−	1.52710i
$196$	−111.579	+	164.567i	−0.0406630	+	0.0599734i
$197$	3479.95	−	4096.91i	1.25856	−	1.48169i	0.450284	−	0.892886i	$-0.351323\pi$
$197$	3479.95	−	4096.91i	1.25856	−	1.48169i	0.808275	−	0.588805i	$-0.200401\pi$
$198$	491.279	−	926.650i	0.176332	−	0.332597i
$199$	−836.668	−	281.906i	−0.298039	−	0.100421i	0.166309	−	0.986074i	$-0.446815\pi$
$199$	−836.668	−	281.906i	−0.298039	−	0.100421i	−0.464349	+	0.885653i	$0.653712\pi$
$200$	4.52167	+	83.3974i	0.00159865	+	0.0294854i
$201$	886.374	+	533.313i	0.311045	+	0.187149i
$202$	−997.606	+	3593.05i	−0.347482	+	1.25152i
$203$	−426.256	−	1535.24i	−0.147376	−	0.530801i
$204$	2330.89	−	1402.45i	0.799976	−	0.481330i
$205$	3399.32	+	5013.62i	1.15814	+	1.70813i
$206$	3599.39	+	391.457i	1.21738	+	0.132398i
$207$	−737.092	−	80.1636i	−0.247495	−	0.0269167i
$208$	2914.68	+	4298.83i	0.971618	+	1.43303i
$209$	−1884.45	+	1133.84i	−0.623686	+	0.375259i
$210$	−1065.21	−	3836.55i	−0.350031	−	1.26070i
$211$	−426.157	+	1534.88i	−0.139042	+	0.500784i	−0.999968	−	0.00794570i	$-0.997471\pi$
$211$	−426.157	+	1534.88i	−0.139042	+	0.500784i	0.860927	+	0.508729i	$0.169885\pi$
$212$	−4875.45	−	2933.46i	−1.57947	−	0.950335i
$213$	136.387	+	2515.51i	0.0438736	+	0.809202i
$214$	6460.40	+	2176.76i	2.06366	+	0.695329i
$215$	1127.32	−	2126.36i	0.357594	−	0.674494i
$216$	−8.28412	+	9.75282i	−0.00260955	+	0.00307220i
$217$	1588.93	−	2343.49i	0.497066	−	0.733117i
$218$	−51.1076	+	942.624i	−0.0158782	+	0.292856i
$219$	−719.694	+	1806.30i	−0.222066	+	0.557343i
$220$	3630.24	−	1679.53i	1.11250	−	0.514699i
$221$	8987.15	+	1978.22i	2.73548	+	0.602125i
$222$	42.8356	+	80.7965i	0.0129502	+	0.0244266i
$223$	287.442	+	1753.32i	0.0863164	+	0.526507i	0.994223	+	0.107334i	$0.0342315\pi$
$223$	287.442	+	1753.32i	0.0863164	+	0.526507i	−0.907907	+	0.419173i	$0.862320\pi$
$224$	3895.35	+	2961.17i	1.16192	+	0.883265i
$225$	1439.45	+	665.959i	0.426503	+	0.197321i
$226$	−4474.98	+	4238.93i	−1.31713	+	1.24765i
$227$	306.275	−	1868.19i	0.0895515	−	0.546240i	−0.903503	−	0.428582i	$-0.859013\pi$
$227$	306.275	−	1868.19i	0.0895515	−	0.546240i	0.993054	−	0.117658i	$-0.0375385\pi$
$228$	−1685.05	+	567.758i	−0.489452	+	0.164915i
$229$	−1441.59	−	3618.13i	−0.415996	−	1.04407i	−0.976423	−	0.215868i	$-0.930742\pi$
$229$	−1441.59	−	3618.13i	−0.415996	−	1.04407i	0.560426	−	0.828204i	$-0.310637\pi$
$230$	−4136.69	−	3918.48i	−1.18594	−	1.12338i
$231$	1340.18	−	1018.78i	0.381721	−	0.290177i
$232$	−38.4315	+	8.45942i	−0.0108757	+	0.00239391i
$233$	2415.65	+	2843.92i	0.679203	+	0.799620i	0.988480	−	0.151353i	$-0.0483629\pi$
$233$	2415.65	+	2843.92i	0.679203	+	0.799620i	−0.309277	+	0.950972i	$0.600087\pi$
$234$	2851.79	−	310.151i	0.796698	−	0.0866462i
$235$	−1548.21			−0.429763
$236$	−2495.03	−	2555.62i	−0.688188	−	0.704902i
$237$	2940.56			0.805950
$238$	8746.87	−	951.279i	2.38225	−	0.259085i
$239$	−2067.70	−	2434.28i	−0.559616	−	0.658831i	0.407488	−	0.913210i	$-0.366405\pi$
$239$	−2067.70	−	2434.28i	−0.559616	−	0.658831i	−0.967104	+	0.254379i	$0.918129\pi$
$240$	−3302.08	+	726.843i	−0.888118	+	0.195490i
$241$	4891.17	−	3718.17i	1.30734	−	0.993811i	0.308239	−	0.951309i	$-0.400260\pi$
$241$	4891.17	−	3718.17i	1.30734	−	0.993811i	0.999096	−	0.0425019i	$-0.0135329\pi$
$242$	−1376.72	−	1304.10i	−0.365698	−	0.346407i
$243$	89.9436	+	225.741i	0.0237444	+	0.0595939i
$244$	963.502	−	324.642i	0.252795	−	0.0851765i
$245$	70.8381	−	432.093i	0.0184722	−	0.112675i
$246$	−3029.23	+	2869.44i	−0.785109	+	0.743695i
$247$	−5459.18	−	2525.68i	−1.40631	−	0.650629i
$248$	−55.6699	−	42.3191i	−0.0142542	−	0.0108358i
$249$	−572.511	−	3492.16i	−0.145709	−	0.888783i
$250$	1659.60	+	3130.34i	0.419850	+	0.791921i
$251$	1197.19	+	263.521i	0.301059	+	0.0662681i	0.362931	−	0.931816i	$-0.381776\pi$
$251$	1197.19	+	263.521i	0.301059	+	0.0662681i	−0.0618721	+	0.998084i	$0.519707\pi$
$252$	1235.29	−	571.506i	0.308794	−	0.142863i
$253$	891.697	−	2237.99i	0.221583	−	0.556131i
$254$	−290.270	+	5353.71i	−0.0717053	+	1.32253i
$255$	−3361.88	+	4958.41i	−0.825605	+	1.21768i
$256$	2728.77	−	3212.55i	0.666203	−	0.784315i
$257$	3096.63	−	5840.86i	0.751605	−	1.41768i	−0.151589	−	0.988444i	$-0.548439\pi$
$257$	3096.63	−	5840.86i	0.751605	−	1.41768i	0.903194	−	0.429233i	$-0.141216\pi$
$258$	1571.04	+	529.345i	0.379104	+	0.127735i
$259$	7.94670	+	146.568i	0.00190650	+	0.0351634i
$260$	9374.09	+	5640.20i	2.23598	+	1.34535i
$261$	−199.919	+	720.044i	−0.0474126	+	0.170765i
$262$	−2083.07	−	7502.53i	−0.491192	−	1.76912i
$263$	−2397.21	+	1442.35i	−0.562047	+	0.338172i	−0.768061	−	0.640377i	$-0.778778\pi$
$263$	−2397.21	+	1442.35i	−0.562047	+	0.338172i	0.206014	+	0.978549i	$0.433951\pi$
$264$	−23.3329	−	34.4135i	−0.00543955	−	0.00802274i
$265$	12457.0	+	1354.78i	2.88766	+	0.314051i
$266$	−5717.43	−	621.808i	−1.31789	−	0.143329i
$267$	997.438	+	1471.11i	0.228622	+	0.337193i
$268$	−2328.53	+	1401.03i	−0.530736	+	0.319333i
$269$	1753.47	+	6315.44i	0.397439	+	1.43145i	0.843831	+	0.536609i	$0.180295\pi$
$269$	1753.47	+	6315.44i	0.397439	+	1.43145i	−0.446392	+	0.894838i	$0.647291\pi$
$270$	−499.597	+	1799.39i	−0.112609	+	0.405582i
$271$	−2246.15	−	1351.46i	−0.503483	−	0.302935i	0.241060	−	0.970510i	$-0.422505\pi$
$271$	−2246.15	−	1351.46i	−0.503483	−	0.302935i	−0.744543	+	0.667575i	$0.767332\pi$
$272$	−404.493	−	7460.43i	−0.0901691	−	1.66307i
$273$	4363.33	+	1470.18i	0.967329	+	0.325931i
$274$	1423.03	−	2684.12i	0.313754	−	0.591802i
$275$	−3336.22	+	3927.70i	−0.731570	+	0.861271i
$276$	1093.07	−	1612.15i	0.238387	−	0.351595i
$277$	−350.342	+	6461.68i	−0.0759928	+	1.40161i	0.673301	+	0.739368i	$0.264876\pi$
$277$	−350.342	+	6461.68i	−0.0759928	+	1.40161i	−0.749294	+	0.662237i	$0.769607\pi$
$278$	2458.12	−	6169.41i	0.530317	−	1.33100i
$279$	−1205.21	+	557.589i	−0.258616	+	0.119649i
$280$	−154.152	−	33.9315i	−0.0329013	−	0.00724212i
$281$	−1238.04	−	2335.20i	−0.262831	−	0.495752i	0.716612	−	0.697472i	$-0.245692\pi$
$281$	−1238.04	−	2335.20i	−0.262831	−	0.495752i	−0.979443	+	0.201720i	$0.935347\pi$
$282$	−172.534	−	1052.41i	−0.0364336	−	0.222235i
$283$	5783.51	+	4396.51i	1.21482	+	0.923482i	0.998602	−	0.0528631i	$-0.0168347\pi$
$283$	5783.51	+	4396.51i	1.21482	+	0.923482i	0.216218	+	0.976345i	$0.430628\pi$
$284$	−6006.35	−	2778.83i	−1.25497	−	0.580610i
$285$	2842.87	−	2692.91i	0.590868	−	0.559700i
$286$	−1507.92	+	9197.93i	−0.311767	+	1.90170i
$287$	−6346.67	+	2138.44i	−1.30534	+	0.439820i
$288$	−849.435	−	2131.92i	−0.173797	−	0.436197i
$289$	−6043.74	−	5724.94i	−1.23015	−	1.16526i
$290$	−4571.86	+	3475.44i	−0.925754	+	0.703740i
$291$	944.300	−	207.856i	0.190226	−	0.0418720i
$292$	−3306.83	−	3893.10i	−0.662731	−	0.780228i
$293$	3086.48	−	335.674i	0.615405	−	0.0669294i	0.204893	−	0.978784i	$-0.434315\pi$
$293$	3086.48	−	335.674i	0.615405	−	0.0669294i	0.410512	+	0.911855i	$0.365350\pi$
$294$	301.614			0.0598316
$295$	7349.92	+	2800.76i	1.45061	+	0.552767i
$296$	3.62525			0.000711870
$297$	−784.931	+	85.3663i	−0.153355	+	0.0166783i
$298$	3824.98	+	4503.11i	0.743541	+	0.875364i
$299$	6434.98	−	1416.45i	1.24463	−	0.273964i
$300$	−3316.97	+	2521.49i	−0.638351	+	0.485261i
$301$	1931.83	+	1829.93i	0.369930	+	0.350417i
$302$	−1820.70	−	4569.60i	−0.346918	−	0.870699i
$303$	2660.24	−	896.338i	0.504378	−	0.169945i
$304$	−790.096	+	4819.38i	−0.149063	+	0.909244i
$305$	−1625.54	+	1539.80i	−0.305175	+	0.289077i
$306$	−3745.18	−	1732.70i	−0.699665	−	0.323700i
$307$	4810.97	+	3657.20i	0.894386	+	0.679894i	0.947864	−	0.318675i	$-0.103238\pi$
$307$	4810.97	+	3657.20i	0.894386	+	0.679894i	−0.0534785	+	0.998569i	$0.517031\pi$
$308$	715.476	+	4364.21i	0.132364	+	0.807383i
$309$	−1276.70	−	2408.11i	−0.235044	−	0.443341i
$310$	−9966.66	−	2193.83i	−1.82603	−	0.401939i
$311$	1781.18	−	824.064i	0.324764	−	0.150252i	−0.250732	−	0.968057i	$-0.580671\pi$
$311$	1781.18	−	824.064i	0.324764	−	0.150252i	0.575496	+	0.817805i	$0.304809\pi$
$312$	42.0914	−	105.641i	0.00763767	−	0.0191691i
$313$	−261.834	+	4829.24i	−0.0472835	+	0.872092i	0.874653	+	0.484750i	$0.161089\pi$
$313$	−261.834	+	4829.24i	−0.0472835	+	0.872092i	−0.921936	+	0.387342i	$0.873393\pi$
$314$	6592.16	−	9722.72i	1.18477	−	1.74740i
$315$	−1940.49	+	2284.52i	−0.347093	+	0.408629i
$316$	−3618.42	+	6825.07i	−0.644152	+	1.21500i
$317$	2204.48	+	742.777i	0.390587	+	0.131604i	0.507741	−	0.861510i	$-0.330481\pi$
$317$	2204.48	+	742.777i	0.390587	+	0.131604i	−0.117154	+	0.993114i	$0.537377\pi$
$318$	467.296	+	8618.76i	0.0824045	+	1.51986i
$319$	−2080.52	−	1251.81i	−0.365162	−	0.219711i
$320$	2306.11	−	8305.87i	0.402861	−	1.45098i
$321$	−1372.97	−	4944.99i	−0.238728	−	0.859821i
$322$	5398.08	−	3247.92i	0.934234	−	0.562110i
$323$	4855.91	+	7161.94i	0.836502	+	1.23375i
$324$	−634.625	−	69.0196i	−0.108818	−	0.0118346i
$325$	−14012.2	−	1523.92i	−2.39156	−	0.260098i
$326$	318.330	+	469.502i	0.0540819	+	0.0797648i
$327$	608.927	−	366.379i	0.102978	−	0.0619597i
$328$	44.2514	+	159.379i	0.00744931	+	0.0268300i
$329$	457.944	−	1649.37i	0.0767395	−	0.276391i
$330$	−5199.20	−	3128.26i	−0.867293	−	0.521833i
$331$	−121.571	−	2242.24i	−0.0201877	−	0.372340i	−0.991119	−	0.132981i	$-0.957545\pi$
$331$	−121.571	−	2242.24i	−0.0201877	−	0.372340i	0.970931	−	0.239360i	$-0.0769375\pi$
$332$	8809.83	+	2968.38i	1.45633	+	0.490695i
$333$	32.2468	−	60.8238i	0.00530664	−	0.0100094i
$334$	−6749.40	+	7946.01i	−1.10572	+	1.30175i
$335$	3358.47	−	4953.37i	0.547740	−	0.807855i
$336$	202.387	−	3732.82i	0.0328605	−	0.606077i
$337$	3905.61	−	9802.34i	0.631312	−	1.58447i	−0.169482	−	0.985533i	$-0.554209\pi$
$337$	3905.61	−	9802.34i	0.631312	−	1.58447i	0.800794	−	0.598940i	$-0.204411\pi$
$338$	−15190.5	+	7027.90i	−2.44455	+	1.13097i
$339$	4531.74	+	997.511i	0.726048	+	0.159815i
$340$	−7371.64	−	13904.4i	−1.17583	−	2.21786i
$341$	−698.053	−	4257.93i	−0.110855	−	0.676188i
$342$	2147.35	+	1632.37i	0.339518	+	0.258095i
$343$	−5534.22	−	2560.40i	−0.871195	−	0.403058i
$344$	47.7123	−	45.1955i	0.00747812	−	0.00708365i
$345$	−693.954	+	4232.93i	−0.108293	+	0.660560i
$346$	−1317.68	+	443.977i	−0.204736	+	0.0689837i
$347$	931.209	+	2337.16i	0.144063	+	0.361571i	0.983247	−	0.182276i	$-0.0583464\pi$
$347$	931.209	+	2337.16i	0.144063	+	0.361571i	−0.839184	+	0.543847i	$0.816967\pi$
$348$	−1425.22	−	1350.04i	−0.219540	−	0.207960i
$349$	4543.04	−	3453.53i	0.696800	−	0.529693i	−0.195743	−	0.980655i	$-0.562712\pi$
$349$	4543.04	−	3453.53i	0.696800	−	0.529693i	0.892543	+	0.450962i	$0.148919\pi$
$350$	−13161.2	+	2897.00i	−2.00999	+	0.442431i
$351$	−1398.03	−	1645.89i	−0.212596	−	0.250287i
$352$	7412.96	−	806.207i	1.12248	−	0.122077i
$353$	5491.94			0.828064			0.414032	−	0.910262i	$-0.364120\pi$
$353$	5491.94			0.828064			0.414032	+	0.910262i	$0.364120\pi$
$354$	−1084.76	+	5308.30i	−0.162865	+	0.796986i
$355$	14574.3			2.17894
$356$	−4641.83	+	504.829i	−0.691057	+	0.0751570i
$357$	−4287.96	−	5048.18i	−0.635694	−	0.748397i
$358$	−15917.4	+	3503.68i	−2.34989	+	0.517249i
$359$	−9247.95	+	7030.11i	−1.35958	+	1.03352i	−0.364840	+	0.931070i	$0.618876\pi$
$359$	−9247.95	+	7030.11i	−1.35958	+	1.03352i	−0.994738	+	0.102454i	$0.967331\pi$
$360$	53.7455	+	50.9104i	0.00786843	+	0.00745338i
$361$	445.265	+	1117.53i	0.0649168	+	0.162929i
$362$	−12056.2	+	4062.20i	−1.75044	+	0.589791i
$363$	−230.953	+	1408.75i	−0.0333936	+	0.203692i
$364$	−8781.46	+	8318.24i	−1.26449	+	1.19779i
$365$	10209.2	+	4723.28i	1.46404	+	0.677337i
$366$	−1227.84	−	933.382i	−0.175356	−	0.133302i
$367$	−408.944	−	2494.45i	−0.0581654	−	0.354794i	−0.999833	−	0.0182503i	$-0.994190\pi$
$367$	−408.944	−	2494.45i	−0.0581654	−	0.354794i	0.941668	−	0.336543i	$-0.109258\pi$
$368$	−2505.83	−	4726.49i	−0.354960	−	0.669526i
$369$	3067.65	+	675.241i	0.432779	+	0.0952619i
$370$	480.162	−	222.147i	0.0674661	−	0.0312131i
$371$	−5127.95	+	12870.2i	−0.717600	+	1.80104i
$372$	188.866	−	3483.42i	0.0263232	−	0.485503i
$373$	2341.09	−	3452.86i	0.324979	−	0.479309i	−0.629744	−	0.776802i	$-0.716840\pi$
$373$	2341.09	−	3452.86i	0.324979	−	0.479309i	0.954724	+	0.297494i	$0.0961507\pi$
$374$	8680.24	−	10219.2i	1.20012	−	1.41289i
$375$	1249.35	−	2356.53i	0.172044	−	0.324509i
$376$	−40.0639	−	13.4991i	−0.00549504	−	0.00185150i
$377$	−359.535	−	6631.23i	−0.0491166	−	0.905903i
$378$	−1769.17	−	1064.48i	−0.240732	−	0.144843i
$379$	−1563.21	+	5630.18i	−0.211865	+	0.763069i	0.778861	+	0.627196i	$0.215798\pi$
$379$	−1563.21	+	5630.18i	−0.211865	+	0.763069i	−0.990726	+	0.135873i	$0.956616\pi$
$380$	2752.06	+	9912.02i	0.371520	+	1.33809i
$381$	3458.46	−	2080.88i	0.465045	−	0.279808i
$382$	−6514.81	−	9608.62i	−0.872582	−	1.28696i
$383$	−7662.14	−	833.308i	−1.02224	−	0.111175i	−0.418384	−	0.908270i	$-0.637403\pi$
$383$	−7662.14	−	833.308i	−1.02224	−	0.111175i	−0.603854	+	0.797095i	$0.706369\pi$
$384$	−180.904	−	19.6745i	−0.0240410	−	0.00261461i
$385$	−5465.55	−	8061.08i	−0.723507	−	1.06709i
$386$	−4212.79	+	2534.75i	−0.555506	+	0.334237i
$387$	−333.879	−	1202.52i	−0.0438554	−	0.157953i
$388$	−679.545	+	2447.50i	−0.0889141	+	0.320240i
$389$	−2490.92	−	1498.74i	−0.324665	−	0.195344i	0.343885	−	0.939012i	$-0.388257\pi$
$389$	−2490.92	−	1498.74i	−0.324665	−	0.195344i	−0.668550	+	0.743668i	$0.733085\pi$
$390$	−898.475	−	16571.4i	−0.116656	−	2.15160i
$391$	−8982.34	−	3026.50i	−1.16178	−	0.391450i
$392$	5.60059	−	10.5638i	0.000721614	−	0.00136111i
$393$	−3794.71	+	4467.48i	−0.487068	+	0.573421i
$394$	12021.5	−	17730.3i	1.53714	−	2.26711i
$395$	921.012	−	16987.1i	0.117319	−	2.16383i
$396$	767.737	−	1926.87i	0.0974249	−	0.244518i
$397$	−183.741	+	85.0076i	−0.0232284	+	0.0107466i	−0.431469	−	0.902128i	$-0.642005\pi$
$397$	−183.741	+	85.0076i	−0.0232284	+	0.0107466i	0.408241	+	0.912874i	$0.366142\pi$
$398$	−3436.13	−	756.349i	−0.432758	−	0.0952572i
$399$	2027.97	+	3825.15i	0.254449	+	0.479942i
$400$	1851.38	+	11292.9i	0.231422	+	1.41161i
$401$	6654.47	+	5058.60i	0.828699	+	0.629961i	0.931092	−	0.364783i	$-0.118857\pi$
$401$	6654.47	+	5058.60i	0.828699	+	0.629961i	−0.102393	+	0.994744i	$0.532650\pi$
$402$	3741.37	+	1730.94i	0.464186	+	0.214755i
$403$	8567.61	−	8115.67i	1.05902	−	1.00315i
$404$	−1193.07	+	7277.39i	−0.146924	+	0.896197i
$405$	1332.24	−	448.882i	0.163455	−	0.0550744i
$406$	−2350.20	−	5898.56i	−0.287287	−	0.721036i
$407$	162.395	+	153.829i	0.0197780	+	0.0187347i
$408$	−130.230	+	98.9984i	−0.0158023	+	0.0120126i
$409$	−11340.6	+	2496.25i	−1.37104	+	0.301789i	−0.838632	−	0.544699i	$-0.816644\pi$
$409$	−11340.6	+	2496.25i	−1.37104	+	0.301789i	−0.532408	+	0.846488i	$0.678713\pi$
$410$	15627.4	+	18398.0i	1.88240	+	2.21613i
$411$	−2273.62	+	247.271i	−0.272870	+	0.0296764i
$412$	7160.23			0.856212
$413$	−5157.77	+	7001.70i	−0.614521	+	0.834216i
$414$	−2954.71			−0.350764
$415$	−20352.9	+	2213.51i	−2.40743	+	0.261824i
$416$	13203.1	+	15543.9i	1.55609	+	1.83198i
$417$	−4882.54	+	1074.73i	−0.573379	+	0.126210i
$418$	−6977.19	+	5303.92i	−0.816425	+	0.620630i
$419$	−2498.90	−	2367.08i	−0.291358	−	0.275989i	0.528033	−	0.849224i	$-0.322930\pi$
$419$	−2498.90	−	2367.08i	−0.291358	−	0.275989i	−0.819391	+	0.573235i	$0.805688\pi$
$420$	−2914.58	−	7315.04i	−0.338611	−	0.849851i
$421$	−7594.78	+	2558.98i	−0.879208	+	0.296240i	−0.722472	−	0.691401i	$-0.756994\pi$
$421$	−7594.78	+	2558.98i	−0.879208	+	0.296240i	−0.156737	+	0.987640i	$0.550097\pi$
$422$	−1027.00	+	6264.41i	−0.118468	+	0.722623i
$423$	−582.855	+	552.110i	−0.0669962	+	0.0634622i
$424$	310.544	+	143.673i	0.0355692	+	0.0164561i
$425$	16141.4	+	12270.4i	1.84229	+	1.40047i
$426$	1624.18	+	9907.05i	0.184722	+	1.12676i
$427$	−1159.58	−	2187.20i	−0.131419	−	0.247883i
$428$	13166.8	+	2898.24i	1.48702	+	0.327317i
$429$	6368.15	−	2946.22i	0.716684	−	0.331573i
$430$	3549.99	−	8909.81i	0.398130	−	0.999230i
$431$	106.682	−	1967.63i	0.0119227	−	0.219901i	−0.986500	−	0.163760i	$-0.947638\pi$
$431$	106.682	−	1967.63i	0.0119227	−	0.219901i	0.998423	−	0.0561408i	$-0.0178796\pi$
$432$	−983.933	+	1451.19i	−0.109582	+	0.161622i
$433$	−1999.55	+	2354.05i	−0.221922	+	0.261267i	−0.861844	−	0.507173i	$-0.830691\pi$
$433$	−1999.55	+	2354.05i	−0.221922	+	0.261267i	0.639923	+	0.768439i	$0.278966\pi$
$434$	5285.19	−	9968.92i	0.584556	−	1.10259i
$435$	4096.94	+	1380.42i	0.451571	+	0.152152i
$436$	101.072	+	1864.16i	0.0111020	+	0.204764i
$437$	5308.81	+	3194.20i	0.581132	+	0.349656i
$438$	−2072.97	+	7466.18i	−0.226143	+	0.814493i
$439$	7.83512	+	28.2196i	0.000851822	+	0.00306799i	0.963975	−	0.265994i	$-0.0857001\pi$
$439$	7.83512	+	28.2196i	0.000851822	+	0.00306799i	−0.963123	+	0.269062i	$0.913286\pi$
$440$	−206.108	+	124.011i	−0.0223314	+	0.0134364i
$441$	−127.421	−	187.932i	−0.0137589	−	0.0202928i
$442$	36457.1	+	3964.95i	3.92328	+	0.426682i
$443$	3469.27	+	377.305i	0.372076	+	0.0404657i	0.292247	−	0.956343i	$-0.405597\pi$
$443$	3469.27	+	377.305i	0.372076	+	0.0404657i	0.0798291	+	0.996809i	$0.474563\pi$
$444$	101.492	+	149.690i	0.0108482	+	0.0159999i
$445$	8810.73	−	5301.24i	0.938581	−	0.564726i
$446$	1894.22	+	6822.36i	0.201107	+	0.724323i
$447$	1189.92	−	4285.69i	0.125909	−	0.453482i
$448$	8166.42	+	4913.57i	0.861221	+	0.518179i
$449$	611.354	+	11275.8i	0.0642574	+	1.18516i	0.835820	+	0.549004i	$0.184993\pi$
$449$	611.354	+	11275.8i	0.0642574	+	1.18516i	−0.771562	+	0.636154i	$0.780524\pi$
$450$	5989.66	+	2018.15i	0.627457	+	0.211415i
$451$	−4780.61	+	9017.18i	−0.499135	+	0.941469i
$452$	−7891.62	+	9290.74i	−0.821219	+	0.966813i
$453$	−2078.08	+	3064.94i	−0.215534	+	0.317889i
$454$	408.442	−	7533.28i	0.0422228	−	0.778754i
$455$	9859.56	−	24745.6i	1.01588	−	2.54966i
$456$	97.0463	−	44.8984i	0.00996625	−	0.00461088i
$457$	97.3952	+	21.4383i	0.00996926	+	0.00219440i	0.219952	−	0.975511i	$-0.429410\pi$
$457$	97.3952	+	21.4383i	0.00996926	+	0.00219440i	−0.209983	+	0.977705i	$0.567341\pi$
$458$	−7270.15	−	13713.0i	−0.741729	−	1.39905i
$459$	502.575	+	3065.57i	0.0511072	+	0.311740i
$460$	−8970.74	−	6819.38i	−0.909267	−	0.691207i
$461$	−14907.0	−	6896.73i	−1.50605	−	0.696774i	−0.518648	−	0.854988i	$-0.673564\pi$
$461$	−14907.0	−	6896.73i	−1.50605	−	0.696774i	−0.987405	+	0.158214i	$0.949426\pi$
$462$	4870.51	−	4613.59i	0.490469	−	0.464597i
$463$	−230.113	+	1403.63i	−0.0230978	+	0.140890i	−0.995858	−	0.0909242i	$-0.971018\pi$
$463$	−230.113	+	1403.63i	−0.0230978	+	0.140890i	0.972760	+	0.231814i	$0.0744662\pi$
$464$	−5109.59	+	1721.62i	−0.511221	+	0.172251i
$465$	2843.60	+	7136.90i	0.283589	+	0.711755i
$466$	10795.5	+	10226.1i	1.07316	+	1.01655i
$467$	−675.145	+	513.232i	−0.0668994	+	0.0508556i	−0.638089	−	0.769962i	$-0.720275\pi$
$467$	−675.145	+	513.232i	−0.0668994	+	0.0508556i	0.571190	+	0.820818i	$0.306482\pi$
$468$	5540.42	−	1219.54i	0.547235	−	0.120455i
$469$	4283.60	+	5043.05i	0.421745	+	0.496517i
$470$	−6133.63	+	667.072i	−0.601964	+	0.0654675i
$471$	−8843.04			−0.865108
$472$	165.777	+	136.562i	0.0161664	+	0.0133173i
$473$	4055.07			0.394190
$474$	11649.8	−	1266.99i	1.12888	−	0.122774i
$475$	−8580.06	−	10101.2i	−0.828800	−	0.975739i
$476$	16993.3	−	3740.50i	1.63631	−	0.360180i
$477$	5172.82	−	3932.28i	0.496535	−	0.377456i
$478$	−9240.54	−	8753.10i	−0.884210	−	0.837568i
$479$	−75.7179	−	190.038i	−0.00722263	−	0.0181274i	0.925321	−	0.379184i	$-0.123795\pi$
$479$	−75.7179	−	190.038i	−0.00722263	−	0.0181274i	−0.932544	+	0.361057i	$0.882416\pi$
$480$	−12581.7	+	4239.28i	−1.19641	+	0.403117i
$481$	−98.9778	+	603.738i	−0.00938253	+	0.0572309i
$482$	17775.5	−	16837.9i	1.67978	−	1.59117i
$483$	−4304.23	−	1991.35i	−0.405485	−	0.187597i
$484$	−2985.52	−	2269.54i	−0.280384	−	0.213142i
$485$	−904.981	−	5520.14i	−0.0847280	−	0.516818i
$486$	453.598	+	855.576i	0.0423367	+	0.0798554i
$487$	128.859	+	28.3639i	0.0119900	+	0.00263920i	0.220961	−	0.975283i	$-0.429081\pi$
$487$	128.859	+	28.3639i	0.0119900	+	0.00263920i	−0.208971	+	0.977922i	$0.567012\pi$
$488$	−55.4906	+	25.6727i	−0.00514743	+	0.00238145i
$489$	158.058	−	396.695i	0.0146168	−	0.0366854i
$490$	94.4683	−	1742.36i	0.00870947	−	0.160637i
$491$	−1980.03	+	2920.33i	−0.181991	+	0.268417i	−0.907731	−	0.419552i	$-0.862187\pi$
$491$	−1980.03	+	2920.33i	−0.181991	+	0.268417i	0.725740	+	0.687969i	$0.241497\pi$
$492$	−5342.05	+	6289.15i	−0.489508	+	0.576294i
$493$	−4474.81	+	8440.39i	−0.408794	+	0.771067i
$494$	−22716.1	−	7653.95i	−2.06892	−	0.697100i
$495$	247.297	+	4561.13i	0.0224549	+	0.414157i
$496$	−8209.93	−	4939.75i	−0.743220	−	0.447180i
$497$	−4310.93	+	15526.6i	−0.389078	+	1.40133i
$498$	−3772.80	−	13588.4i	−0.339484	−	1.22271i
$499$	18610.7	−	11197.7i	1.66959	−	1.00456i	0.718566	−	0.695458i	$-0.244799\pi$
$499$	18610.7	−	11197.7i	1.66959	−	1.00456i	0.951028	−	0.309103i	$-0.100029\pi$
$500$	3932.17	+	5799.52i	0.351704	+	0.518725i
$501$	7802.42	+	848.565i	0.695782	+	0.0756708i
$502$	4856.49	+	528.175i	0.431785	+	0.0469594i
$503$	1946.02	+	2870.17i	0.172503	+	0.254422i	0.904106	−	0.427308i	$-0.140538\pi$
$503$	1946.02	+	2870.17i	0.172503	+	0.254422i	−0.731603	+	0.681730i	$0.761228\pi$
$504$	−70.1340	+	42.1982i	−0.00619845	+	0.00372948i
$505$	−4344.76	−	15648.4i	−0.382850	−	1.37890i
$506$	2568.40	−	9250.55i	0.225651	−	0.812722i
$507$	10796.4	+	6496.00i	0.945733	+	0.569029i
$508$	574.047	+	10587.7i	0.0501363	+	0.924709i
$509$	−13653.9	−	4600.55i	−1.18900	−	0.400620i	−0.345844	−	0.938292i	$-0.612407\pi$
$509$	−13653.9	−	4600.55i	−1.18900	−	0.400620i	−0.843154	+	0.537672i	$0.819304\pi$
$510$	−11182.5	+	21092.5i	−0.970922	+	1.83135i
$511$	−8051.65	+	9479.14i	−0.697034	+	0.820611i
$512$	9154.18	−	13501.4i	0.790159	−	1.16540i
$513$	109.933	−	2027.60i	0.00946135	−	0.174504i
$514$	9751.43	−	24474.2i	0.836804	−	2.10022i
$515$	−14311.0	+	6620.99i	−1.22450	+	0.566516i
$516$	3201.91	+	704.794i	0.273171	+	0.0601295i
$517$	−1221.88	−	2304.72i	−0.103943	−	0.196057i
$518$	94.6341	+	577.243i	0.00802700	+	0.0489625i
$519$	833.307	+	633.463i	0.0704781	+	0.0535760i
$520$	−597.086	−	276.241i	−0.0503538	−	0.0232961i
$521$	4289.79	−	4063.51i	0.360728	−	0.341700i	−0.485775	−	0.874084i	$-0.661462\pi$
$521$	4289.79	−	4063.51i	0.360728	−	0.341700i	0.846503	+	0.532384i	$0.178704\pi$
$522$	−481.787	+	2938.77i	−0.0403970	+	0.246411i
$523$	13336.5	−	4493.60i	1.11504	−	0.375701i	0.299323	−	0.954152i	$-0.403239\pi$
$523$	13336.5	−	4493.60i	1.11504	−	0.375701i	0.815717	+	0.578451i	$0.196343\pi$
$524$	−5699.58	−	14304.9i	−0.475167	−	1.19258i
$525$	7365.20	+	6976.69i	0.612274	+	0.579976i
$526$	−8875.68	+	6747.11i	−0.735738	+	0.559293i
$527$	−16579.5	+	3649.42i	−1.37042	+	0.301653i
$528$	−3688.07	−	4341.94i	−0.303983	−	0.357876i
$529$	5348.66	−	581.702i	0.439604	−	0.0478098i
$530$	49935.3			4.09255
$531$	3765.80	−	1566.66i	0.307763	−	0.128036i
$532$	−11373.7			−0.926899
$533$	−27750.6	+	3018.06i	−2.25519	+	0.245266i
$534$	4585.45	+	5398.40i	0.371595	+	0.437475i
$535$	−28996.3	+	6382.57i	−2.34321	+	0.515780i
$536$	130.098	−	98.8978i	0.0104839	−	0.00796966i
$537$	8907.61	+	8437.73i	0.715813	+	0.678054i
$538$	9667.92	+	24264.7i	0.774747	+	1.94447i
$539$	699.134	−	235.566i	0.0558698	−	0.0188247i
$540$	−597.483	+	3644.49i	−0.0476140	+	0.290433i
$541$	−6871.72	+	6509.23i	−0.546096	+	0.517290i	−0.910256	−	0.414047i	$-0.864115\pi$
$541$	−6871.72	+	6509.23i	−0.546096	+	0.517290i	0.364159	+	0.931337i	$0.381356\pi$
$542$	−9480.97	−	4386.36i	−0.751370	−	0.347621i
$543$	7624.39	+	5795.91i	0.602567	+	0.458060i
$544$	−4746.37	−	28951.6i	−0.374079	−	2.28178i
$545$	−1925.78	−	3632.41i	−0.151360	−	0.285496i
$546$	17919.8	+	3944.46i	1.40458	+	0.309171i
$547$	7024.31	−	3249.79i	0.549063	−	0.254024i	−0.125687	−	0.992070i	$-0.540113\pi$
$547$	7024.31	−	3249.79i	0.549063	−	0.254024i	0.674750	+	0.738046i	$0.264251\pi$
$548$	2223.82	−	5581.36i	0.173352	−	0.435080i
$549$	−62.8594	+	1159.37i	−0.00488665	+	0.0901290i
$550$	−11525.0	+	16998.0i	−0.893501	+	1.31782i
$551$	4042.61	−	4759.33i	0.312561	−	0.367975i
$552$	−54.8653	+	103.487i	−0.00423047	+	0.00797952i
$553$	17824.5	+	6005.77i	1.37066	+	0.461829i
$554$	1396.15	+	25750.5i	0.107070	+	1.97479i
$555$	−341.268	−	205.334i	−0.0261009	−	0.0157044i
$556$	3513.61	−	12654.9i	0.268004	−	0.965264i
$557$	−2950.99	−	10628.5i	−0.224484	−	0.808517i	−0.986887	−	0.161414i	$-0.948394\pi$
$557$	−2950.99	−	10628.5i	−0.224484	−	0.808517i	0.762403	−	0.647102i	$-0.224019\pi$
$558$	−4534.49	+	2728.31i	−0.344015	+	0.206987i
$559$	6224.05	+	9179.79i	0.470929	+	0.694569i
$560$	−21500.4	−	2338.31i	−1.62242	−	0.176449i
$561$	−10034.5	−	1091.32i	−0.755182	−	0.0821310i
$562$	−5910.98	−	8718.04i	−0.443665	−	0.654356i
$563$	−552.326	+	332.324i	−0.0413460	+	0.0248770i	−0.536077	−	0.844169i	$-0.680094\pi$
$563$	−552.326	+	332.324i	−0.0413460	+	0.0248770i	0.494731	+	0.869046i	$0.335267\pi$
$564$	−564.236	−	2032.19i	−0.0421252	−	0.151721i
$565$	7181.81	−	25866.5i	0.534763	−	1.92604i
$566$	24807.1	+	14925.9i	1.84226	+	1.10845i
$567$	84.1498	+	1552.05i	0.00623273	+	0.114956i
$568$	377.147	+	127.076i	0.0278605	+	0.00938728i
$569$	3128.42	−	5900.82i	0.230492	−	0.434755i	−0.741107	−	0.671387i	$-0.765699\pi$
$569$	3128.42	−	5900.82i	0.230492	−	0.434755i	0.971599	+	0.236632i	$0.0760437\pi$
$570$	10102.5	−	11893.5i	0.742360	−	0.873974i
$571$	−10786.6	+	15909.0i	−0.790549	+	1.16597i	0.192260	+	0.981344i	$0.438418\pi$
$571$	−10786.6	+	15909.0i	−0.790549	+	1.16597i	−0.982808	+	0.184628i	$0.940892\pi$
$572$	−997.940	+	18405.9i	−0.0729475	+	1.34544i
$573$	−3234.74	+	8118.58i	−0.235834	+	0.591900i
$574$	−24222.5	+	11206.5i	−1.76137	+	0.814898i
$575$	14178.5	+	3120.92i	1.02832	+	0.226350i
$576$	−2093.78	−	3949.29i	−0.151460	−	0.285684i
$577$	−1764.03	−	10760.1i	−0.127275	−	0.776342i	−0.970913	−	0.239431i	$-0.923039\pi$
$577$	−1764.03	−	10760.1i	−0.127275	−	0.776342i	0.843639	−	0.536911i	$-0.180409\pi$
$578$	−26410.4	−	20076.7i	−1.90057	−	1.44478i
$579$	3359.12	+	1554.09i	0.241106	+	0.111547i
$580$	−8245.33	+	7810.39i	−0.590291	+	0.559153i
$581$	3662.03	−	22337.4i	0.261491	−	1.59503i
$582$	3651.52	−	1230.34i	0.260069	−	0.0876275i
$583$	7814.58	+	19613.1i	0.555140	+	1.39330i
$584$	223.006	+	211.242i	0.0158014	+	0.0149679i
$585$	−9945.84	+	7560.63i	−0.702923	+	0.534348i
$586$	12083.2	−	2659.71i	0.851796	−	0.187494i
$587$	−10164.4	−	11966.5i	−0.714701	−	0.841411i	0.278179	−	0.960529i	$-0.410269\pi$
$587$	−10164.4	−	11966.5i	−0.714701	−	0.841411i	−0.992880	+	0.119118i	$0.961993\pi$
$588$	592.985	−	64.4910i	0.0415889	−	0.00452307i
$589$	11096.7			0.776283
$590$	30325.3	+	7929.05i	2.11605	+	0.553278i
$591$	−16126.1			−1.12240
$592$	493.810	−	53.7050i	0.0342829	−	0.00372849i
$593$	−17216.6	−	20268.9i	−1.19224	−	1.40362i	−0.893369	−	0.449324i	$-0.851665\pi$
$593$	−17216.6	−	20268.9i	−1.19224	−	1.40362i	−0.298874	−	0.954293i	$-0.596611\pi$
$594$	−3072.91	+	676.399i	−0.212261	+	0.0467222i
$595$	−30505.4	+	23189.6i	−2.10185	+	1.59778i
$596$	8482.91	+	8035.44i	0.583009	+	0.552256i
$597$	980.367	+	2460.54i	0.0672090	+	0.168682i
$598$	24883.5	−	8384.21i	1.70161	−	0.573338i
$599$	3197.36	−	19503.0i	0.218098	−	1.33034i	−0.619907	−	0.784675i	$-0.712830\pi$
$599$	3197.36	−	19503.0i	0.218098	−	1.33034i	0.838005	−	0.545663i	$-0.183722\pi$
$600$	181.905	−	172.310i	0.0123771	−	0.0117242i
$601$	−5524.30	−	2555.81i	−0.374943	−	0.173467i	0.223362	−	0.974736i	$-0.428297\pi$
$601$	−5524.30	−	2555.81i	−0.374943	−	0.173467i	−0.598305	+	0.801268i	$0.704159\pi$
$602$	8441.89	+	6417.35i	0.571537	+	0.434471i
$603$	−502.065	−	3062.46i	−0.0339066	−	0.206821i
$604$	−4556.63	−	8594.72i	−0.306965	−	0.578997i
$605$	8065.73	+	1775.40i	0.542014	+	0.119306i
$606$	10153.0	−	4697.27i	0.680588	−	0.314874i
$607$	2806.25	−	7043.14i	0.187647	−	0.470960i	−0.804812	−	0.593529i	$-0.797734\pi$
$607$	2806.25	−	7043.14i	0.187647	−	0.470960i	0.992460	+	0.122570i	$0.0391135\pi$
$608$	−1038.22	+	19148.8i	−0.0692523	+	1.27728i
$609$	−2682.44	+	3956.30i	−0.178486	+	0.263247i
$610$	−5776.54	+	6800.67i	−0.383418	+	0.451395i
$611$	3341.93	−	6303.55i	0.221277	−	0.417372i
$612$	−7733.65	−	2605.77i	−0.510808	−	0.172111i
$613$	301.300	+	5557.14i	0.0198522	+	0.366152i	0.991533	+	0.129855i	$0.0414511\pi$
$613$	301.300	+	5557.14i	0.0198522	+	0.366152i	−0.971681	+	0.236297i	$0.924066\pi$
$614$	20635.6	+	12416.0i	1.35633	+	0.816075i
$615$	4861.55	−	17509.7i	0.318759	−	1.14807i
$616$	−71.1489	−	256.255i	−0.00465369	−	0.0167611i
$617$	808.840	−	486.663i	0.0527758	−	0.0317542i	−0.488921	−	0.872328i	$-0.662610\pi$
$617$	808.840	−	486.663i	0.0527758	−	0.0317542i	0.541697	+	0.840574i	$0.317782\pi$
$618$	−6095.52	−	8990.22i	−0.396760	−	0.585177i
$619$	12315.5	+	1339.39i	0.799677	+	0.0869701i	0.498827	−	0.866701i	$-0.333764\pi$
$619$	12315.5	+	1339.39i	0.799677	+	0.0869701i	0.300850	+	0.953672i	$0.402730\pi$
$620$	−20063.9	−	2182.08i	−1.29966	−	0.141346i
$621$	1248.26	+	1841.04i	0.0806616	+	0.118967i
$622$	6701.54	−	4032.18i	0.432005	−	0.259929i
$623$	3041.48	+	10954.4i	0.195593	+	0.704462i
$624$	4168.44	−	15013.4i	0.267422	−	0.963166i
$625$	5653.19	+	3401.41i	0.361804	+	0.217690i
$626$	1043.44	+	19245.0i	0.0666199	+	1.22873i
$627$	6252.41	+	2106.68i	0.398241	+	0.134183i
$628$	10881.5	−	20524.8i	0.691435	−	1.30418i
$629$	569.757	−	670.770i	0.0361172	−	0.0425204i
$630$	−6703.40	+	9886.78i	−0.423920	+	0.625236i
$631$	−925.943	+	17078.0i	−0.0584171	+	1.07744i	0.811535	+	0.584304i	$0.198632\pi$
$631$	−925.943	+	17078.0i	−0.0584171	+	1.07744i	−0.869952	+	0.493136i	$0.835850\pi$
$632$	171.946	−	431.552i	0.0108222	−	0.0271617i
$633$	4337.14	−	2006.57i	0.272332	−	0.125994i
$634$	9053.65	+	1992.86i	0.567139	+	0.124837i
$635$	−10937.6	−	20630.6i	−0.683539	−	1.28929i
$636$	2761.58	+	16844.9i	0.172176	+	1.05023i
$637$	1606.36	+	1221.12i	0.0999156	+	0.0759539i
$638$	−8781.85	−	4062.92i	−0.544948	−	0.252120i
$639$	5486.80	−	5197.37i	0.339678	−	0.321760i
$640$	−170.317	+	1038.89i	−0.0105193	+	0.0641650i
$641$	−4850.86	+	1634.45i	−0.298904	+	0.100712i	−0.464758	−	0.885438i	$-0.653859\pi$
$641$	−4850.86	+	1634.45i	−0.298904	+	0.100712i	0.165854	+	0.986150i	$0.446962\pi$
$642$	−7569.99	−	18999.2i	−0.465364	−	1.16798i
$643$	5290.84	+	5011.75i	0.324495	+	0.307378i	0.832554	−	0.553944i	$-0.186878\pi$
$643$	5290.84	+	5011.75i	0.324495	+	0.307378i	−0.508058	+	0.861323i	$0.669637\pi$
$644$	9918.37	−	7539.75i	0.606892	−	0.461348i
$645$	−7051.32	+	1552.11i	−0.430458	+	0.0947510i
$646$	22323.7	+	26281.5i	1.35962	+	1.60067i
$647$	−24102.9	+	2621.34i	−1.46458	+	0.159282i	−0.805412	−	0.592716i	$-0.798056\pi$
$647$	−24102.9	+	2621.34i	−1.46458	+	0.159282i	−0.659165	+	0.751998i	$0.729090\pi$
$648$	38.3888			0.00232724
$649$	1631.43	+	13151.7i	0.0986735	+	0.795455i
$650$	−56169.3			−3.38945
$651$	−8444.30	+	918.373i	−0.508385	+	0.0552901i
$652$	726.239	+	854.994i	0.0436222	+	0.0513561i
$653$	−4017.20	+	884.253i	−0.240743	+	0.0529916i	−0.333703	−	0.942678i	$-0.608298\pi$
$653$	−4017.20	+	884.253i	−0.240743	+	0.0529916i	0.0929598	+	0.995670i	$0.470367\pi$
$654$	2254.55	−	1713.87i	0.134801	−	0.102473i
$655$	24619.2	+	23320.6i	1.46863	+	1.39116i
$656$	8388.72	+	21054.1i	0.499275	+	1.25309i
$657$	5527.83	−	1862.54i	0.328252	−	0.110601i
$658$	1103.60	−	6731.68i	0.0653844	−	0.398827i
$659$	−8508.94	+	8060.09i	−0.502976	+	0.476444i	−0.896609	−	0.442824i	$-0.853977\pi$
$659$	−8508.94	+	8060.09i	−0.502976	+	0.476444i	0.393633	+	0.919268i	$0.371218\pi$
$660$	−10890.7	−	5038.58i	−0.642304	−	0.297162i
$661$	−14360.0	−	10916.2i	−0.844991	−	0.642346i	0.0904213	−	0.995904i	$-0.471179\pi$
$661$	−14360.0	−	10916.2i	−0.844991	−	0.642346i	−0.935413	+	0.353558i	$0.884972\pi$
$662$	−1447.74	−	8830.80i	−0.0849968	−	0.518458i
$663$	−12931.3	−	24391.0i	−0.757481	−	1.42876i
$664$	−545.981	−	120.180i	−0.0319099	−	0.00702390i
$665$	22732.3	−	10517.1i	1.32560	−	0.613286i
$666$	101.547	−	254.863i	0.00590818	−	0.0148284i
$667$	−370.326	+	6830.27i	−0.0214979	+	0.396505i
$668$	−11570.6	+	17065.3i	−0.670178	+	0.988438i
$669$	3450.68	−	4062.46i	0.199419	−	0.234774i
$670$	11171.2	−	21071.0i	0.644149	−	1.21499i
$671$	−3575.10	−	1204.59i	−0.205686	−	0.0693036i
$672$	−794.718	−	14657.7i	−0.0456204	−	0.841419i
$673$	−21442.7	−	12901.7i	−1.22817	−	0.738964i	−0.254530	−	0.967065i	$-0.581921\pi$
$673$	−21442.7	−	12901.7i	−1.22817	−	0.738964i	−0.973638	+	0.228101i	$0.926748\pi$
$674$	11249.5	−	40517.2i	0.642902	−	2.31552i
$675$	−1272.93	−	4584.68i	−0.0725853	−	0.261429i
$676$	−28362.5	+	17065.2i	−1.61371	+	0.970935i
$677$	−2721.22	−	4013.50i	−0.154483	−	0.227845i	0.742570	−	0.669769i	$-0.233607\pi$
$677$	−2721.22	−	4013.50i	−0.154483	−	0.227845i	−0.897053	+	0.441923i	$0.854296\pi$
$678$	18383.4	+	1999.31i	1.04131	+	0.113249i
$679$	6148.49	+	668.688i	0.347507	+	0.0377937i
$680$	531.105	+	783.322i	0.0299514	+	0.0441750i
$681$	−4866.44	+	2928.04i	−0.273836	+	0.164762i
$682$	−4600.11	−	16568.1i	−0.258280	−	0.930241i
$683$	−6195.33	+	22313.6i	−0.347083	+	1.25008i	0.559775	+	0.828644i	$0.310887\pi$
$683$	−6195.33	+	22313.6i	−0.347083	+	1.25008i	−0.906858	+	0.421436i	$0.861526\pi$
$684$	4570.80	+	2750.16i	0.255510	+	0.153735i
$685$	716.318	+	13211.7i	0.0399549	+	0.736925i
$686$	−23028.4	−	7759.16i	−1.28167	−	0.431846i
$687$	−5472.99	+	10323.2i	−0.303941	+	0.573294i
$688$	5829.54	−	6863.07i	0.323037	−	0.380308i
$689$	−32405.4	+	47794.4i	−1.79180	+	2.64270i
$690$	−925.443	+	17068.8i	−0.0510594	+	0.941736i
$691$	9432.97	−	23675.0i	0.519316	−	1.30338i	−0.402381	−	0.915472i	$-0.631817\pi$
$691$	9432.97	−	23675.0i	0.519316	−	1.30338i	0.921696	−	0.387912i	$-0.126803\pi$
$692$	−2495.67	+	1154.62i	−0.137097	+	0.0634280i
$693$	−4932.28	−	1085.68i	−0.270363	−	0.0595115i
$694$	4696.21	+	8858.00i	0.256867	+	0.484503i
$695$	4679.24	+	28542.1i	0.255387	+	1.55779i
$696$	93.9824	+	71.4436i	0.00511838	+	0.00389089i
$697$	36444.1	+	16860.9i	1.98052	+	0.916285i
$698$	16510.3	−	15639.4i	0.895309	−	0.848082i
$699$	1811.01	−	11046.7i	0.0979954	−	0.597745i
$700$	−25256.0	+	8509.73i	−1.36369	+	0.459482i
$701$	−11714.2	−	29400.5i	−0.631155	−	1.58408i	−0.801037	−	0.598615i	$-0.795718\pi$
$701$	−11714.2	−	29400.5i	−0.631155	−	1.58408i	0.169881	−	0.985465i	$-0.445662\pi$
$702$	−6247.79	−	5918.22i	−0.335908	−	0.318189i
$703$	−457.972	+	348.141i	−0.0245700	+	0.0186777i
$704$	14184.4	−	3122.22i	0.759368	−	0.167149i
$705$	3006.88	+	3539.97i	0.160632	+	0.189110i
$706$	21757.7	−	2366.29i	1.15986	−	0.126142i
$707$	17955.9			0.955166
$708$	−997.661	+	10668.3i	−0.0529582	+	0.566297i
$709$	28221.5			1.49490			0.747449	−	0.664319i	$-0.231278\pi$
$709$	28221.5			1.49490			0.747449	+	0.664319i	$0.231278\pi$
$710$	57739.8	−	6279.58i	3.05202	−	0.331928i
$711$	−5711.04	−	6723.56i	−0.301239	−	0.354646i
$712$	274.222	−	60.3608i	0.0144338	−	0.00317713i
$713$	−9676.84	+	7356.14i	−0.508276	+	0.386381i
$714$	−19162.9	−	18152.1i	−1.00442	−	0.951434i
$715$	−15025.2	−	37710.4i	−0.785888	−	1.97243i
$716$	−30545.0	+	10291.8i	−1.59430	+	0.537184i
$717$	−1550.15	+	9455.52i	−0.0807414	+	0.492501i
$718$	−33609.0	+	31836.1i	−1.74690	+	1.65476i
$719$	15873.8	+	7344.01i	0.823357	+	0.380925i	0.785885	−	0.618372i	$-0.212208\pi$
$719$	15873.8	+	7344.01i	0.823357	+	0.380925i	0.0374713	+	0.999298i	$0.488070\pi$
$720$	8075.08	+	6138.52i	0.417973	+	0.317735i
$721$	−2820.53	−	17204.5i	−0.145689	−	0.888666i
$722$	2245.53	+	4235.52i	0.115748	+	0.218324i
$723$	−18001.0	−	3962.31i	−0.925952	−	0.203817i
$724$	−22834.3	+	10564.3i	−1.17214	+	0.542291i
$725$	5415.98	−	13593.1i	0.277441	−	0.696323i
$726$	−307.994	+	5680.61i	−0.0157448	+	0.290396i
$727$	−18934.9	+	27926.9i	−0.965965	+	1.42469i	−0.0615178	+	0.998106i	$0.519594\pi$
$727$	−18934.9	+	27926.9i	−0.965965	+	1.42469i	−0.904447	+	0.426586i	$0.859716\pi$
$728$	470.901	−	554.388i	0.0239736	−	0.0282239i
$729$	341.470	−	644.080i	0.0173485	−	0.0327227i
$730$	42481.4	+	14313.6i	2.15384	+	0.725715i
$731$	−863.762	−	15931.1i	−0.0437037	−	0.806067i
$732$	−2613.56	−	1572.53i	−0.131967	−	0.0794021i
$733$	792.929	−	2855.87i	0.0399557	−	0.143907i	−0.940882	−	0.338735i	$-0.890001\pi$
$733$	792.929	−	2855.87i	0.0399557	−	0.143907i	0.980837	+	0.194828i	$0.0624148\pi$
$734$	−2694.91	−	9706.18i	−0.135519	−	0.488095i
$735$	−1125.55	+	677.223i	−0.0564853	+	0.0339861i
$736$	−11788.7	−	17387.0i	−0.590401	−	0.870777i
$737$	10024.3	+	1090.21i	0.501018	+	0.0544890i
$738$	12444.2	+	1353.39i	0.620701	+	0.0675053i
$739$	−20744.1	−	30595.3i	−1.03259	−	1.52296i	−0.840670	−	0.541548i	$-0.817838\pi$
$739$	−20744.1	−	30595.3i	−1.03259	−	1.52296i	−0.191921	−	0.981410i	$-0.561472\pi$
$740$	896.518	−	539.417i	0.0445360	−	0.0267964i
$741$	4827.65	+	17387.6i	0.239336	+	0.862011i
$742$	−14770.3	+	53197.8i	−0.730775	+	2.63201i
$743$	26472.7	+	15928.1i	1.30712	+	0.786467i	0.986971	−	0.160901i	$-0.0514400\pi$
$743$	26472.7	+	15928.1i	1.30712	+	0.786467i	0.320147	+	0.947368i	$0.396268\pi$
$744$	11.3576	+	209.479i	0.000559664	+	0.0103224i
$745$	−24384.9	−	8216.24i	−1.19919	−	0.404053i
$746$	7787.10	−	14688.0i	0.382180	−	0.720868i
$747$	−6872.88	+	8091.38i	−0.336634	+	0.396316i
$748$	14880.6	−	21947.3i	0.727392	−	1.07282i
$749$	1777.21	−	32778.7i	0.0866993	−	1.59907i
$750$	3934.27	−	9874.28i	0.191546	−	0.480743i
$751$	−3720.59	+	1721.33i	−0.180780	+	0.0836379i	−0.508192	−	0.861244i	$-0.669686\pi$
$751$	−3720.59	+	1721.33i	−0.180780	+	0.0836379i	0.327411	+	0.944882i	$0.393824\pi$
$752$	−5657.23	−	1245.25i	−0.274333	−	0.0603852i
$753$	−1722.59	−	3249.15i	−0.0833661	−	0.157245i
$754$	−4281.55	−	26116.3i	−0.206797	−	1.26141i
$755$	17054.7	+	12964.6i	0.822098	+	0.624943i
$756$	−3705.87	−	1714.52i	−0.178282	−	0.0824821i
$757$	−1103.50	+	1045.29i	−0.0529819	+	0.0501871i	−0.713732	−	0.700418i	$-0.752997\pi$
$757$	−1103.50	+	1045.29i	−0.0529819	+	0.0501871i	0.660751	+	0.750606i	$0.270238\pi$
$758$	−3767.20	+	22978.9i	−0.180516	+	1.10110i
$759$	−6848.95	+	2307.68i	−0.327538	+	0.110360i
$760$	−228.974	−	574.680i	−0.0109286	−	0.0274287i
$761$	26943.2	+	25521.9i	1.28343	+	1.21573i	0.963323	+	0.268346i	$0.0864770\pi$
$761$	26943.2	+	25521.9i	1.28343	+	1.21573i	0.320106	+	0.947382i	$0.396282\pi$
$762$	12804.9	−	9734.06i	0.608759	−	0.462766i
$763$	4439.36	−	977.177i	0.210636	−	0.0463646i
$764$	−14862.9	−	17497.9i	−0.703822	−	0.828603i
$765$	17866.6	−	1943.11i	0.844405	−	0.0918346i
$766$	−30714.5			−1.44877
$767$	−27268.6	+	23879.6i	−1.28372	+	1.12417i
$768$	−12645.2			−0.594131
$769$	3234.02	−	351.721i	0.151654	−	0.0164933i	−0.0319772	−	0.999489i	$-0.510180\pi$
$769$	3234.02	−	351.721i	0.151654	−	0.0164933i	0.183631	+	0.982995i	$0.441215\pi$
$770$	−25126.3	−	29581.0i	−1.17596	−	1.38445i
$771$	−19369.2	+	4263.48i	−0.904753	+	0.199151i
$772$	−7740.52	+	5884.19i	−0.360865	+	0.274322i
$773$	−10901.2	−	10326.2i	−0.507231	−	0.480475i	0.390758	−	0.920494i	$-0.372213\pi$
$773$	−10901.2	−	10326.2i	−0.507231	−	0.480475i	−0.897988	+	0.440019i	$0.854972\pi$
$774$	−1840.87	−	4620.24i	−0.0854893	−	0.214562i
$775$	24640.9	−	8302.50i	1.14210	−	0.384819i
$776$	24.7122	−	150.738i	0.00114319	−	0.00697317i
$777$	319.693	−	302.829i	0.0147605	−	0.0139819i
$778$	−10514.1	−	4864.36i	−0.484512	−	0.224159i
$779$	−20895.7	−	15884.5i	−0.961062	−	0.730580i
$780$	−5309.72	−	32387.9i	−0.243742	−	1.48676i
$781$	11502.4	+	21695.8i	0.527001	+	0.994029i
$782$	−36889.8	−	8120.05i	−1.68692	−	0.371320i
$783$	2034.65	−	941.328i	0.0928638	−	0.0429634i
$784$	606.384	−	1521.91i	0.0276232	−	0.0693290i
$785$	−2769.72	+	51084.5i	−0.125931	+	2.32266i
$786$	−13108.8	+	19334.0i	−0.594879	+	0.877381i
$787$	−4579.16	+	5391.00i	−0.207407	+	0.244178i	−0.856023	−	0.516937i	$-0.827072\pi$
$787$	−4579.16	+	5391.00i	−0.207407	+	0.244178i	0.648616	+	0.761115i	$0.275348\pi$
$788$	19843.6	−	37428.9i	0.897078	−	1.69207i
$789$	7953.69	+	2679.91i	0.358883	+	0.120922i
$790$	−3670.33	−	67695.2i	−0.165297	−	3.04872i
$791$	25432.2	+	15302.1i	1.14319	+	0.687837i
$792$	−33.3697	+	120.187i	−0.00149715	+	0.00539224i
$793$	−2760.43	−	9942.16i	−0.123614	−	0.445216i
$794$	−691.308	+	415.946i	−0.0308987	+	0.0185911i
$795$	−21095.8	−	31114.0i	−0.941122	−	1.38805i
$796$	−6917.28	−	752.300i	−0.308011	−	0.0334982i
$797$	22877.6	+	2488.09i	1.01677	+	0.110580i	0.601297	−	0.799025i	$-0.294651\pi$
$797$	22877.6	+	2488.09i	1.01677	+	0.110580i	0.415472	+	0.909606i	$0.363616\pi$
$798$	9682.41	+	14280.5i	0.429516	+	0.633488i
$799$	−8794.28	+	5291.34i	−0.389386	+	0.234286i
$800$	12021.7	+	43298.1i	0.531287	+	1.91352i
$801$	1426.49	−	5137.76i	0.0629246	−	0.226634i
$802$	28542.9	+	17173.7i	1.25671	+	0.756140i
$803$	1026.11	+	18925.5i	0.0450941	+	0.831712i
$804$	7725.80	+	2603.12i	0.338890	+	0.114185i
$805$	−12851.8	+	24241.0i	−0.562689	+	1.06134i
$806$	30445.9	−	35843.7i	1.33054	−	1.56643i
$807$	11034.6	−	16274.9i	0.481336	−	0.709917i
$808$	24.0092	−	442.824i	0.00104535	−	0.0192803i
$809$	−8977.73	+	22532.4i	−0.390161	+	0.979230i	0.594397	+	0.804172i	$0.297391\pi$
$809$	−8977.73	+	22532.4i	−0.390161	+	0.979230i	−0.984558	+	0.175058i	$0.943989\pi$
$810$	5084.57	−	2352.37i	0.220560	−	0.102042i
$811$	4215.63	+	927.929i	0.182529	+	0.0401776i	0.305294	−	0.952258i	$-0.401245\pi$
$811$	4215.63	+	927.929i	0.182529	+	0.0401776i	−0.122765	+	0.992436i	$0.539176\pi$
$812$	−5881.81	−	11094.3i	−0.254201	−	0.479474i
$813$	1272.28	+	7760.54i	0.0548840	+	0.334777i
$814$	709.649	+	539.461i	0.0305567	+	0.0232286i
$815$	−2242.12	−	1037.32i	−0.0963659	−	0.0445836i
$816$	−16272.6	+	15414.2i	−0.698106	+	0.661281i
$817$	−1687.19	+	10291.4i	−0.0722487	+	0.440698i
$818$	−43852.9	+	14775.8i	−1.87443	+	0.631568i
$819$	−5112.74	−	12832.0i	−0.218136	−	0.547481i
$820$	34658.0	+	32829.8i	1.47599	+	1.39813i
$821$	24159.8	−	18365.8i	1.02702	−	0.780720i	0.0510656	−	0.998695i	$-0.483738\pi$
$821$	24159.8	−	18365.8i	1.02702	−	0.780720i	0.975954	+	0.217975i	$0.0699451\pi$
$822$	−8900.96	+	1959.25i	−0.377685	+	0.0831347i
$823$	−1513.16	−	1781.42i	−0.0640891	−	0.0754515i	0.729183	−	0.684318i	$-0.239900\pi$
$823$	−1513.16	−	1781.42i	−0.0640891	−	0.0754515i	−0.793272	+	0.608867i	$0.791624\pi$
$824$	−428.063	+	46.5546i	−0.0180974	+	0.00196821i
$825$	15460.1			0.652427
$826$	−17417.0	+	29961.3i	−0.733674	+	1.26209i
$827$	18008.7			0.757223			0.378612	−	0.925556i	$-0.376402\pi$
$827$	18008.7			0.757223			0.378612	+	0.925556i	$0.376402\pi$
$828$	−5809.08	+	631.775i	−0.243816	+	0.0265166i
$829$	−12558.5	−	14785.0i	−0.526146	−	0.619427i	0.433324	−	0.901238i	$-0.357341\pi$
$829$	−12558.5	−	14785.0i	−0.526146	−	0.619427i	−0.959470	+	0.281811i	$0.909065\pi$
$830$	−79679.2	+	17538.7i	−3.33217	+	0.733467i
$831$	15455.0	−	11748.6i	0.645158	−	0.490437i
$832$	28839.4	+	27318.2i	1.20172	+	1.13833i
$833$	−1074.39	−	2696.51i	−0.0446883	−	0.112159i
$834$	−18880.3	+	6361.52i	−0.783900	+	0.264127i
$835$	7345.79	−	44807.3i	0.304445	−	1.85703i
$836$	−12583.3	+	11919.6i	−0.520579	+	0.493119i
$837$	3615.63	+	1672.77i	0.149312	+	0.0690792i
$838$	−10919.9	−	8301.08i	−0.450145	−	0.342191i
$839$	−2587.31	−	15781.9i	−0.106465	−	0.649406i	−0.985109	−	0.171929i	$-0.945000\pi$
$839$	−2587.31	−	15781.9i	−0.106465	−	0.649406i	0.878645	−	0.477476i	$-0.158448\pi$
$840$	221.804	+	418.368i	0.00911069	+	0.0171846i
$841$	−17085.8	−	3760.86i	−0.700552	−	0.154203i
$842$	−28986.0	+	13410.3i	−1.18637	+	0.548873i
$843$	−2934.92	+	7366.10i	−0.119910	+	0.300951i
$844$	−679.664	+	12535.7i	−0.0277192	+	0.511251i
$845$	40907.7	−	60334.3i	1.66540	−	2.45629i
$846$	−2071.24	+	2438.45i	−0.0841734	+	0.0990965i
$847$	−4277.15	+	8067.56i	−0.173512	+	0.327278i
$848$	44428.8	+	14969.8i	1.79916	+	0.606209i
$849$	−1179.94	−	21762.6i	−0.0476976	−	0.879731i
$850$	69235.1	+	41657.4i	2.79382	+	1.68098i
$851$	168.586	−	607.192i	0.00679089	−	0.0244586i
$852$	5311.52	+	19130.4i	0.213579	+	0.769243i
$853$	−39034.2	+	23486.1i	−1.56683	+	0.942730i	−0.574583	+	0.818446i	$0.694836\pi$
$853$	−39034.2	+	23486.1i	−1.56683	+	0.942730i	−0.992247	+	0.124284i	$0.960337\pi$
$854$	−5536.36	−	8165.52i	−0.221839	−	0.327188i
$855$	−11678.6	−	1270.13i	−0.467135	−	0.0508040i
$856$	−806.002	−	87.6580i	−0.0321829	−	0.00350010i
$857$	15134.1	+	22321.1i	0.603234	+	0.889703i	0.999597	−	0.0283906i	$-0.00903823\pi$
$857$	15134.1	+	22321.1i	0.603234	+	0.889703i	−0.396363	+	0.918094i	$0.629728\pi$
$858$	23959.6	−	14416.0i	0.953341	−	0.573606i
$859$	6154.17	+	22165.3i	0.244444	+	0.880408i	0.979339	+	0.202227i	$0.0648179\pi$
$859$	6154.17	+	22165.3i	0.244444	+	0.880408i	−0.734894	+	0.678181i	$0.762768\pi$
$860$	5074.33	−	18276.1i	0.201201	−	0.724662i
$861$	17215.8	+	10358.4i	0.681430	+	0.410003i
$862$	−425.138	−	7841.21i	−0.0167984	−	0.309829i
$863$	8587.42	+	2893.44i	0.338724	+	0.114130i	0.483523	−	0.875332i	$-0.339357\pi$
$863$	8587.42	+	2893.44i	0.338724	+	0.114130i	−0.144799	+	0.989461i	$0.546253\pi$
$864$	−3224.87	+	6082.75i	−0.126982	+	0.239513i
$865$	3920.39	−	4615.45i	0.154101	−	0.181422i
$866$	−6907.42	+	10187.7i	−0.271044	+	0.399759i
$867$	−1352.08	+	24937.7i	−0.0529632	+	0.976848i
$868$	8259.34	−	20729.4i	0.322972	−	0.810600i
$869$	26014.3	−	12035.5i	1.01551	−	0.469824i
$870$	16825.8	+	3703.64i	0.655688	+	0.144328i
$871$	12918.2	+	24366.2i	0.502543	+	0.947897i
$872$	−18.1629	−	110.789i	−0.000705359	−	0.00430250i
$873$	−2309.24	−	1755.44i	−0.0895257	−	0.0680557i
$874$	22408.4	+	10367.2i	0.867249	+	0.401232i
$875$	12386.0	−	11732.7i	0.478542	−	0.453299i
$876$	−2479.13	+	15122.0i	−0.0956189	+	0.583249i
$877$	−3495.82	+	1177.88i	−0.134601	+	0.0453525i	−0.385796	−	0.922584i	$-0.626073\pi$
$877$	−3495.82	+	1177.88i	−0.134601	+	0.0453525i	0.251195	+	0.967937i	$0.419177\pi$
$878$	43.1996	+	108.423i	0.00166050	+	0.00416753i
$879$	−6761.94	−	6405.25i	−0.259471	−	0.245784i
$880$	−26237.7	+	19945.4i	−1.00508	+	0.764043i
$881$	23394.4	−	5149.50i	0.894640	−	0.196925i	0.256224	−	0.966617i	$-0.417521\pi$
$881$	23394.4	−	5149.50i	0.894640	−	0.196925i	0.638415	+	0.769692i	$0.279590\pi$
$882$	−585.782	−	689.636i	−0.0223632	−	0.0263279i
$883$	28162.5	−	3062.85i	1.07332	−	0.116731i	0.445649	−	0.895208i	$-0.352973\pi$
$883$	28162.5	−	3062.85i	1.07332	−	0.116731i	0.627673	+	0.778477i	$0.284008\pi$
$884$	72523.9			2.75933
$885$	−7870.82	−	22245.0i	−0.298955	−	0.844924i
$886$	13906.9			0.527327
$887$	−50225.7	+	5462.38i	−1.90126	+	0.206774i	−0.982265	−	0.187499i	$-0.939962\pi$
$887$	−50225.7	+	5462.38i	−1.90126	+	0.206774i	−0.918993	+	0.394274i	$0.870996\pi$
$888$	−7.04081	−	8.28909i	−0.000266075	−	0.000313247i
$889$	25213.7	−	5549.96i	0.951228	−	0.209381i
$890$	32621.7	−	24798.4i	1.22863	−	0.933982i
$891$	1719.65	+	1628.94i	0.0646581	+	0.0612474i
$892$	5182.86	+	13008.0i	0.194546	+	0.488274i
$893$	6357.55	−	2142.11i	0.238239	−	0.0802720i
$894$	2867.59	−	17491.5i	0.107278	−	0.654367i
$895$	51533.1	−	48814.7i	1.92465	−	1.82312i
$896$	−1056.39	−	488.736i	−0.0393877	−	0.0182227i
$897$	−15736.4	−	11962.5i	−0.585757	−	0.445281i
$898$	7280.37	+	44408.3i	0.270545	+	1.65025i
$899$	5738.58	+	10824.1i	0.212895	+	0.401562i
$900$	12207.4	+	2687.06i	0.452127	+	0.0995207i
$901$	75389.5	−	34878.9i	2.78756	−	1.28966i
$902$	−15054.4	+	37783.6i	−0.555715	+	1.39474i
$903$	432.182	−	7971.12i	0.0159270	−	0.293757i
$904$	411.381	−	606.742i	0.0151353	−	0.0223229i
$905$	35869.9	−	42229.3i	1.31752	−	1.55110i
$906$	−6912.25	+	13037.9i	−0.253470	+	0.478096i
$907$	−28366.8	−	9557.87i	−1.03848	−	0.349905i	−0.252136	−	0.967692i	$-0.581133\pi$
$907$	−28366.8	−	9557.87i	−1.03848	−	0.349905i	−0.786346	+	0.617787i	$0.788029\pi$
$908$	−807.749	−	14898.0i	−0.0295221	−	0.544503i
$909$	−7216.07	−	4341.76i	−0.263302	−	0.158424i
$910$	28399.0	−	102284.i	1.03453	−	3.72603i
$911$	−7092.56	−	25545.1i	−0.257944	−	0.929031i	−0.973160	−	0.230128i	$-0.926086\pi$
$911$	−7092.56	−	25545.1i	−0.257944	−	0.929031i	0.715216	−	0.698903i	$-0.246328\pi$
$912$	12553.9	−	7553.45i	0.455814	−	0.274254i
$913$	−19358.0	−	28550.9i	−0.701705	−	1.03494i
$914$	395.092	+	42.9688i	0.0142981	+	0.00155501i
$915$	6677.78	+	726.253i	0.241268	+	0.0262395i
$916$	−17225.5	−	25405.7i	−0.621339	−	0.916407i
$917$	−32126.3	+	19329.8i	−1.15693	+	0.696101i
$918$	3311.93	+	11928.5i	0.119074	+	0.428866i
$919$	−1951.90	+	7030.10i	−0.0700622	+	0.252341i	−0.990285	−	0.139054i	$-0.955594\pi$
$919$	−1951.90	+	7030.10i	−0.0700622	+	0.252341i	0.920223	+	0.391396i	$0.128008\pi$
$920$	580.640	+	349.359i	0.0208077	+	0.0125196i
$921$	−981.520	−	18103.1i	−0.0351164	−	0.647684i
$922$	−62029.5	−	20900.2i	−2.21565	−	0.746541i
$923$	−31459.8	+	59339.4i	−1.12190	+	2.11612i
$924$	8589.14	−	10111.9i	0.305803	−	0.360019i
$925$	−756.480	+	1115.72i	−0.0268896	+	0.0396592i
$926$	−306.875	+	5659.97i	−0.0108904	+	0.200862i
$927$	−3026.55	+	7596.07i	−0.107233	+	0.269135i
$928$	−19215.4	+	8889.99i	−0.679716	+	0.314470i
$929$	−14462.6	−	3183.46i	−0.510767	−	0.112428i	−0.0478933	−	0.998852i	$-0.515251\pi$
$929$	−14462.6	−	3183.46i	−0.510767	−	0.112428i	−0.462874	+	0.886424i	$0.653182\pi$
$930$	14340.7	+	27049.4i	0.505644	+	0.953746i
$931$	306.956	+	1872.35i	0.0108057	+	0.0659117i
$932$	23411.0	+	17796.5i	0.822802	+	0.625478i
$933$	−5343.55	−	2472.19i	−0.187503	−	0.0867480i
$934$	−2453.62	+	2324.19i	−0.0859581	+	0.0814239i
$935$	−9447.24	+	57625.6i	−0.330436	+	2.01557i
$936$	−323.296	+	108.931i	−0.0112898	+	0.00380397i
$937$	7960.30	+	19978.9i	0.277537	+	0.696564i	0.999987	+	0.00514141i	$0.00163657\pi$
$937$	7960.30	+	19978.9i	0.277537	+	0.696564i	−0.722450	+	0.691423i	$0.756984\pi$
$938$	19143.4	+	18133.6i	0.666370	+	0.631219i
$939$	11550.5	−	8780.47i	0.401424	−	0.305154i
$940$	−11916.3	+	2622.98i	−0.413476	+	0.0910129i
$941$	−2272.57	−	2675.48i	−0.0787287	−	0.0926866i	0.721387	−	0.692532i	$-0.243505\pi$
$941$	−2272.57	−	2675.48i	−0.0787287	−	0.0926866i	−0.800116	+	0.599845i	$0.795229\pi$
$942$	−35033.9	+	3810.16i	−1.21175	+	0.131785i
$943$	28752.1			0.992894
$944$	24604.2	+	16145.7i	0.848304	+	0.556672i
$945$	8992.26			0.309543
$946$	16065.1	−	1747.19i	0.552138	−	0.0600486i
$947$	−3562.95	−	4194.62i	−0.122260	−	0.143936i	0.697627	−	0.716461i	$-0.254239\pi$
$947$	−3562.95	−	4194.62i	−0.122260	−	0.143936i	−0.819887	+	0.572526i	$0.805964\pi$
$948$	22633.0	−	4981.89i	0.775406	−	0.170680i
$949$	−41268.2	+	31371.3i	−1.41161	+	1.07308i
$950$	−38344.3	−	36321.6i	−1.30953	−	1.24045i
$951$	−2583.11	−	6483.12i	−0.0880789	−	0.221061i
$952$	−991.595	+	334.107i	−0.0337582	+	0.0113745i
$953$	−8379.90	+	51115.2i	−0.284839	+	1.73744i	0.325715	+	0.945468i	$0.394395\pi$
$953$	−8379.90	+	51115.2i	−0.284839	+	1.73744i	−0.610555	+	0.791974i	$0.709053\pi$
$954$	18799.1	−	17807.5i	0.637991	−	0.604338i
$955$	45886.3	+	21229.3i	1.55481	+	0.719333i
$956$	−20038.8	−	15233.1i	−0.677932	−	0.515350i
$957$	1178.46	+	7188.29i	0.0398058	+	0.242805i
$958$	−381.856	−	720.256i	−0.0128781	−	0.0242906i
$959$	−14286.8	−	3144.76i	−0.481068	−	0.105891i
$960$	−23470.1	+	10858.4i	−0.789056	+	0.365056i
$961$	2968.58	−	7450.58i	0.0996469	−	0.250095i
$962$	−131.995	+	2434.50i	−0.00442379	+	0.0815920i
$963$	−8640.13	+	12743.2i	−0.289122	+	0.426423i
$964$	31347.1	−	36904.7i	1.04733	−	1.23301i
$965$	10029.8	−	18918.2i	0.334581	−	0.631087i
$966$	−17910.3	−	6034.67i	−0.596535	−	0.200996i
$967$	−1949.15	−	35949.9i	−0.0648194	−	1.19552i	−0.832253	−	0.554396i	$-0.812949\pi$
$967$	−1949.15	−	35949.9i	−0.0648194	−	1.19552i	0.767434	−	0.641128i	$-0.221533\pi$
$968$	193.241	+	116.269i	0.00641632	+	0.00386057i
$969$	6944.71	−	25012.6i	0.230234	−	0.829226i
$970$	−5963.74	−	21479.5i	−0.197406	−	0.710994i
$971$	34896.2	−	20996.3i	1.15332	−	0.693928i	0.195330	−	0.980738i	$-0.437422\pi$
$971$	34896.2	−	20996.3i	1.15332	−	0.693928i	0.957988	+	0.286810i	$0.0925947\pi$
$972$	1074.73	+	1585.11i	0.0354650	+	0.0523070i
$973$	−31791.0	−	3457.48i	−1.04745	−	0.113917i
$974$	522.726	+	56.8499i	0.0171963	+	0.00187021i
$975$	23729.5	+	34998.4i	0.779438	+	1.14958i
$976$	−7178.28	+	4319.03i	−0.235421	+	0.141648i
$977$	−3757.10	−	13531.9i	−0.123030	−	0.443114i	0.876217	−	0.481917i	$-0.160059\pi$
$977$	−3757.10	−	13531.9i	−0.123030	−	0.443114i	−0.999247	+	0.0388030i	$0.987646\pi$
$978$	455.262	−	1639.71i	0.0148851	−	0.0536115i
$979$	14845.2	+	8932.06i	0.484632	+	0.291593i
$980$	−186.823	−	3445.76i	−0.00608965	−	0.112317i
$981$	−2020.35	−	680.737i	−0.0657543	−	0.0221552i
$982$	−6586.12	+	12422.7i	−0.214024	+	0.403692i
$983$	1363.67	−	1605.44i	0.0442465	−	0.0520910i	−0.739594	−	0.673054i	$-0.764982\pi$
$983$	1363.67	−	1605.44i	0.0442465	−	0.0520910i	0.783840	+	0.620963i	$0.213258\pi$
$984$	278.475	−	410.719i	0.00902180	−	0.0133062i
$985$	−5050.86	+	93157.6i	−0.163385	+	3.01345i
$986$	−14091.4	+	35366.7i	−0.455133	+	1.14230i
$987$	−4660.65	+	2156.25i	−0.150304	+	0.0695381i
$988$	−46297.3	−	10190.8i	−1.49080	−	0.328151i
$989$	−5350.99	−	10093.0i	−0.172044	−	0.324510i
$990$	2944.96	+	17963.5i	0.0945425	+	0.576684i
$991$	−37596.8	−	28580.4i	−1.20515	−	0.916130i	−0.207084	−	0.978323i	$-0.566397\pi$
$991$	−37596.8	−	28580.4i	−1.20515	−	0.916130i	−0.998064	+	0.0621931i	$0.980191\pi$
$992$	−34146.3	−	15797.8i	−1.09289	−	0.505625i
$993$	−4890.74	+	4632.76i	−0.156297	+	0.148052i
$994$	−10388.9	+	63369.7i	−0.331506	+	2.02210i
$995$	14521.1	−	4892.73i	0.462663	−	0.155889i
$996$	−10322.9	−	25908.6i	−0.328408	−	0.824242i
$997$	13471.9	+	12761.2i	0.427942	+	0.405368i	0.871124	−	0.491064i	$-0.163392\pi$
$997$	13471.9	+	12761.2i	0.427942	+	0.405368i	−0.443182	+	0.896432i	$0.646150\pi$
$998$	68906.0	−	52381.0i	2.18555	−	1.66141i
$999$	−201.701	+	44.3978i	−0.00638793	+	0.00140609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.a.133.13	yes	420
59.4	even	29	inner	177.4.e.a.4.13	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.a.4.13	✓	420	59.4	even	29	inner
177.4.e.a.133.13	yes	420	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(3.96175 - 0.430866i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(7.69682 - 1.69420i) q^{4} +(-13.8169 + 10.5033i) q^{5} +(-8.67951 - 8.22167i) q^{6} +(-7.10268 - 17.8264i) q^{7} +(-0.449126 + 0.151328i) q^{8} +(-1.45604 + 8.88144i) q^{9} +O(q^{10})\)	\(q+(3.96175 - 0.430866i) q^{2} +(-1.94216 - 2.28649i) q^{3} +(7.69682 - 1.69420i) q^{4} +(-13.8169 + 10.5033i) q^{5} +(-8.67951 - 8.22167i) q^{6} +(-7.10268 - 17.8264i) q^{7} +(-0.449126 + 0.151328i) q^{8} +(-1.45604 + 8.88144i) q^{9} +(-50.2135 + 47.5647i) q^{10} +(-26.5402 - 12.2788i) q^{11} +(-18.8222 - 14.3083i) q^{12} +(-12.9395 - 78.9277i) q^{13} +(-35.8198 - 67.5633i) q^{14} +(50.8503 + 11.1930i) q^{15} +(-58.9355 + 27.2665i) q^{16} +(-42.5864 + 106.884i) q^{17} +(-1.94174 + 35.8134i) q^{18} +(42.2050 - 62.2477i) q^{19} +(-88.5514 + 104.251i) q^{20} +(-26.9653 + 50.8619i) q^{21} +(-110.436 - 37.2102i) q^{22} +(4.46007 + 82.2612i) q^{23} +(1.21828 + 0.733018i) q^{24} +(47.1455 - 169.803i) q^{25} +(-85.2704 - 307.116i) q^{26} +(23.1351 - 13.9200i) q^{27} +(-84.8695 - 125.173i) q^{28} +(82.5447 + 8.97728i) q^{29} +(206.279 + 22.4342i) q^{30} +(82.8028 + 122.125i) q^{31} +(-218.490 + 131.461i) q^{32} +(23.4699 + 84.5311i) q^{33} +(-122.664 + 441.796i) q^{34} +(285.373 + 171.703i) q^{35} +(3.84005 + 70.8256i) q^{36} +(-7.24884 - 2.44242i) q^{37} +(140.385 - 264.794i) q^{38} +(-155.336 + 182.876i) q^{39} +(4.61608 - 6.80821i) q^{40} +(18.8950 - 348.498i) q^{41} +(-84.9149 + 213.120i) q^{42} +(-125.852 + 58.2253i) q^{43} +(-225.077 - 49.5433i) q^{44} +(-73.1667 - 138.007i) q^{45} +(53.1132 + 323.976i) q^{46} +(71.0147 + 53.9840i) q^{47} +(176.806 + 81.7994i) q^{48} +(-18.3157 + 17.3496i) q^{49} +(113.616 - 693.029i) q^{50} +(327.098 - 110.212i) q^{51} +(-233.312 - 585.570i) q^{52} +(-524.149 - 496.501i) q^{53} +(85.6579 - 65.1155i) q^{54} +(495.671 - 109.105i) q^{55} +(5.88764 + 6.93147i) q^{56} +(-224.297 + 24.3938i) q^{57} +330.889 q^{58} +(-239.474 - 384.748i) q^{59} +410.349 q^{60} +(128.252 - 13.9483i) q^{61} +(380.663 + 448.151i) q^{62} +(168.666 - 37.1261i) q^{63} +(-395.392 + 300.569i) q^{64} +(1007.79 + 954.627i) q^{65} +(129.403 + 324.778i) q^{66} +(-326.766 + 110.100i) q^{67} +(-146.698 + 894.816i) q^{68} +(179.427 - 169.962i) q^{69} +(1204.56 + 557.288i) q^{70} +(-668.507 - 508.186i) q^{71} +(-0.690068 - 4.20923i) q^{72} +(-303.590 - 572.632i) q^{73} +(-29.7704 - 6.55296i) q^{74} +(-479.816 + 221.986i) q^{75} +(219.384 - 550.613i) q^{76} +(-30.3801 + 560.328i) q^{77} +(-536.608 + 791.438i) q^{78} +(-634.560 + 747.062i) q^{79} +(527.916 - 995.756i) q^{80} +(-76.7599 - 25.8634i) q^{81} +(-75.2986 - 1388.80i) q^{82} +(1010.74 + 608.144i) q^{83} +(-121.377 + 437.159i) q^{84} +(-534.224 - 1924.10i) q^{85} +(-473.506 + 284.899i) q^{86} +(-139.788 - 206.173i) q^{87} +(13.7780 + 1.49845i) q^{88} +(-588.984 - 64.0559i) q^{89} +(-349.331 - 515.224i) q^{90} +(-1315.09 + 791.264i) q^{91} +(173.695 + 625.593i) q^{92} +(118.421 - 426.513i) q^{93} +(304.602 + 183.273i) q^{94} +(70.6662 + 1303.36i) q^{95} +(724.928 + 244.257i) q^{96} +(-150.969 + 284.758i) q^{97} +(-65.0869 + 76.6262i) q^{98} +(147.697 - 217.836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9	\( 420 q - 2 q^{2} + 45 q^{3} - 64 q^{4} + 14 q^{5} + 6 q^{6} + 6 q^{7} + 18 q^{8} - 135 q^{9} + 854 q^{10} + 32 q^{11} + 192 q^{12} - 22 q^{13} - 884 q^{14} - 42 q^{15} - 268 q^{16} - 56 q^{17} - 18 q^{18} - 112 q^{19} - 250 q^{20} + 243 q^{21} + 108 q^{22} + 16 q^{23} - 54 q^{24} - 197 q^{25} - 328 q^{26} + 405 q^{27} + 236 q^{28} - 54 q^{29} - 126 q^{30} + 66 q^{31} + 857 q^{32} - 96 q^{33} + 112 q^{34} + 532 q^{35} - 576 q^{36} + 110 q^{37} + 56 q^{38} + 66 q^{39} - 6044 q^{40} + 304 q^{41} - 306 q^{42} - 324 q^{43} - 568 q^{44} + 126 q^{45} + 5842 q^{46} + 4082 q^{47} + 804 q^{48} + 739 q^{49} + 576 q^{50} + 168 q^{51} - 1372 q^{52} - 1498 q^{53} + 54 q^{54} - 4422 q^{55} - 12036 q^{56} + 336 q^{57} + 6298 q^{58} - 3305 q^{59} + 750 q^{60} - 1718 q^{61} - 4333 q^{62} + 54 q^{63} - 6250 q^{64} - 5884 q^{65} - 324 q^{66} + 382 q^{67} + 734 q^{68} + 3780 q^{69} + 8082 q^{70} + 8638 q^{71} + 162 q^{72} + 8894 q^{73} + 12428 q^{74} + 243 q^{75} - 15468 q^{76} - 9916 q^{77} + 984 q^{78} - 578 q^{79} + 24570 q^{80} - 1215 q^{81} - 1382 q^{82} - 32 q^{83} + 7557 q^{84} + 708 q^{85} + 2296 q^{86} - 5928 q^{87} - 17646 q^{88} - 2284 q^{89} + 378 q^{90} + 11124 q^{91} + 762 q^{92} - 198 q^{93} - 1232 q^{94} + 24184 q^{95} - 396 q^{96} - 658 q^{97} - 4356 q^{98} + 288 q^{99}+O(q^{100}) \) 420 * q - 2 * q^2 + 45 * q^3 - 64 * q^4 + 14 * q^5 + 6 * q^6 + 6 * q^7 + 18 * q^8 - 135 * q^9 + 854 * q^10 + 32 * q^11 + 192 * q^12 - 22 * q^13 - 884 * q^14 - 42 * q^15 - 268 * q^16 - 56 * q^17 - 18 * q^18 - 112 * q^19 - 250 * q^20 + 243 * q^21 + 108 * q^22 + 16 * q^23 - 54 * q^24 - 197 * q^25 - 328 * q^26 + 405 * q^27 + 236 * q^28 - 54 * q^29 - 126 * q^30 + 66 * q^31 + 857 * q^32 - 96 * q^33 + 112 * q^34 + 532 * q^35 - 576 * q^36 + 110 * q^37 + 56 * q^38 + 66 * q^39 - 6044 * q^40 + 304 * q^41 - 306 * q^42 - 324 * q^43 - 568 * q^44 + 126 * q^45 + 5842 * q^46 + 4082 * q^47 + 804 * q^48 + 739 * q^49 + 576 * q^50 + 168 * q^51 - 1372 * q^52 - 1498 * q^53 + 54 * q^54 - 4422 * q^55 - 12036 * q^56 + 336 * q^57 + 6298 * q^58 - 3305 * q^59 + 750 * q^60 - 1718 * q^61 - 4333 * q^62 + 54 * q^63 - 6250 * q^64 - 5884 * q^65 - 324 * q^66 + 382 * q^67 + 734 * q^68 + 3780 * q^69 + 8082 * q^70 + 8638 * q^71 + 162 * q^72 + 8894 * q^73 + 12428 * q^74 + 243 * q^75 - 15468 * q^76 - 9916 * q^77 + 984 * q^78 - 578 * q^79 + 24570 * q^80 - 1215 * q^81 - 1382 * q^82 - 32 * q^83 + 7557 * q^84 + 708 * q^85 + 2296 * q^86 - 5928 * q^87 - 17646 * q^88 - 2284 * q^89 + 378 * q^90 + 11124 * q^91 + 762 * q^92 - 198 * q^93 - 1232 * q^94 + 24184 * q^95 - 396 * q^96 - 658 * q^97 - 4356 * q^98 + 288 * q^99

Introduction

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