LMFDB - Embedded newform 161.4.m.a.2.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(2,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.2"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.m (of order $33$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$46$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	161.2
Dual form			161.4.m.a.81.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.06577 + 2.09605i) q^{2} +(7.36412 - 5.79121i) q^{3} +(7.49662 - 10.5275i) q^{4} +(-10.5890 + 10.0966i) q^{5} +(-17.8022 + 38.9813i) q^{6} +(-11.1382 + 14.7966i) q^{7} +(-3.20542 + 22.2942i) q^{8} +(14.3267 - 59.0554i) q^{9} +(21.8896 - 63.2458i) q^{10} +(27.0547 + 13.9477i) q^{11} +(-5.76111 - 120.941i) q^{12} +(-53.1251 - 61.3096i) q^{13} +(14.2710 - 83.5060i) q^{14} +(-19.5073 + 135.676i) q^{15} +(0.118817 + 0.343300i) q^{16} +(16.5939 - 1.58452i) q^{17} +(65.5341 + 270.135i) q^{18} +(-144.313 - 13.7802i) q^{19} +(26.9106 + 187.167i) q^{20} +(3.66705 + 173.468i) q^{21} -139.233 q^{22} +(-75.6769 - 80.2496i) q^{23} +(105.505 + 182.740i) q^{24} +(4.23810 - 88.9687i) q^{25} +(344.503 + 137.918i) q^{26} +(-131.420 - 287.770i) q^{27} +(72.2728 + 228.183i) q^{28} +(-37.4221 + 81.9429i) q^{29} +(-205.072 - 592.516i) q^{30} +(-189.764 + 75.9701i) q^{31} +(-131.610 - 125.490i) q^{32} +(280.008 - 53.9672i) q^{33} +(-64.1457 + 41.2239i) q^{34} +(-31.4528 - 269.140i) q^{35} +(-514.306 - 593.541i) q^{36} +(-43.6657 + 179.993i) q^{37} +(615.627 - 246.460i) q^{38} +(-746.276 - 143.833i) q^{39} +(-191.154 - 268.438i) q^{40} +(-168.634 - 49.5155i) q^{41} +(-378.507 - 697.595i) q^{42} +(16.5209 + 114.905i) q^{43} +(349.654 - 180.259i) q^{44} +(444.555 + 769.991i) q^{45} +(475.893 + 167.654i) q^{46} +(44.0101 - 76.2277i) q^{47} +(2.86311 + 1.84001i) q^{48} +(-94.8798 - 329.616i) q^{49} +(169.252 + 370.610i) q^{50} +(113.023 - 107.767i) q^{51} +(-1043.70 + 99.6610i) q^{52} +(54.3159 + 10.4685i) q^{53} +(1137.50 + 894.543i) q^{54} +(-427.308 + 125.469i) q^{55} +(-294.176 - 295.747i) q^{56} +(-1142.54 + 734.267i) q^{57} +(-19.6069 - 411.600i) q^{58} +(-49.4696 + 142.933i) q^{59} +(1282.10 + 1222.48i) q^{60} +(-455.530 - 358.233i) q^{61} +(612.301 - 706.633i) q^{62} +(714.246 + 869.759i) q^{63} +(795.344 + 233.534i) q^{64} +(1181.56 + 112.826i) q^{65} +(-1025.33 + 806.330i) q^{66} +(30.9032 - 648.737i) q^{67} +(107.717 - 186.571i) q^{68} +(-1022.04 - 152.707i) q^{69} +(692.012 + 1028.34i) q^{70} +(646.643 + 415.572i) q^{71} +(1270.67 + 508.699i) q^{72} +(245.990 - 345.444i) q^{73} +(-199.739 - 823.335i) q^{74} +(-484.026 - 679.720i) q^{75} +(-1226.93 + 1415.95i) q^{76} +(-507.720 + 244.966i) q^{77} +(3335.67 - 979.442i) q^{78} +(-319.152 + 61.5115i) q^{79} +(-4.72433 - 2.43556i) q^{80} +(-1175.97 - 606.256i) q^{81} +(789.416 - 152.148i) q^{82} +(175.547 - 51.5453i) q^{83} +(1853.68 + 1261.82i) q^{84} +(-159.715 + 184.321i) q^{85} +(-308.017 - 432.549i) q^{86} +(198.968 + 820.157i) q^{87} +(-397.674 + 558.455i) q^{88} +(670.333 + 268.361i) q^{89} +(-3421.40 - 2198.80i) q^{90} +(1498.89 - 103.191i) q^{91} +(-1412.15 + 195.090i) q^{92} +(-957.488 + 1658.42i) q^{93} +(-19.1578 + 402.172i) q^{94} +(1667.27 - 1311.15i) q^{95} +(-1695.94 - 161.942i) q^{96} +(-371.503 - 109.083i) q^{97} +(1076.65 + 1141.27i) q^{98} +(1211.29 - 1397.90i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 7 q^{2} - 9 q^{3} + 157 q^{4} + 3 q^{5} - 52 q^{6} - 22 q^{7} - 32 q^{8} + 397 q^{9} - q^{10} - 29 q^{11} - 101 q^{12} - 36 q^{13} + 134 q^{14} - 320 q^{15} + 1157 q^{16} - q^{17} - 81 q^{18}+ \cdots + 3640 q^{99}+O(q^{100}) $ 920 * q - 7 * q^2 - 9 * q^3 + 157 * q^4 + 3 * q^5 - 52 * q^6 - 22 * q^7 - 32 * q^8 + 397 * q^9 - q^10 - 29 * q^11 - 101 * q^12 - 36 * q^13 + 134 * q^14 - 320 * q^15 + 1157 * q^16 - q^17 - 81 * q^18 + 211 * q^19 - 1956 * q^20 + 1596 * q^21 - 104 * q^22 - 654 * q^23 + 34 * q^24 + 837 * q^25 - 11 * q^26 - 252 * q^27 - 1412 * q^28 - 524 * q^29 + 1269 * q^30 - 53 * q^31 + 1191 * q^32 + 203 * q^33 + 156 * q^34 + 1462 * q^35 - 6346 * q^36 + 803 * q^37 + 649 * q^38 - 863 * q^39 - 587 * q^40 - 388 * q^41 - 2102 * q^42 + 4836 * q^43 - 3344 * q^44 - 5566 * q^45 - 329 * q^46 + 92 * q^47 + 496 * q^48 - 2464 * q^49 + 5626 * q^50 - 173 * q^51 - 1227 * q^52 + 423 * q^53 + 5347 * q^54 - 1720 * q^55 + 9137 * q^56 - 8344 * q^57 + 4116 * q^58 + 4875 * q^59 + 1549 * q^60 + 223 * q^61 + 388 * q^62 - 3556 * q^63 - 5064 * q^64 + 3881 * q^65 + 224 * q^66 - 261 * q^67 - 17618 * q^68 + 3286 * q^69 - 5226 * q^70 + 2052 * q^71 + 9111 * q^72 - 369 * q^73 + 4624 * q^74 - 4359 * q^75 - 4996 * q^76 + 864 * q^77 + 19540 * q^78 - 1805 * q^79 - 1750 * q^80 + 3759 * q^81 + 9153 * q^82 - 3932 * q^83 + 18426 * q^84 - 10396 * q^85 - 2721 * q^86 + 5109 * q^87 - 13236 * q^88 - 2629 * q^89 - 1160 * q^90 + 4752 * q^91 - 19334 * q^92 + 520 * q^93 + 5220 * q^94 - 11871 * q^95 + 961 * q^96 - 7564 * q^97 + 1336 * q^98 + 3640 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−4.06577	+	2.09605i	−1.43747	+	0.741066i	−0.988320	−	0.152391i	$-0.951303\pi$
$2$	−4.06577	+	2.09605i	−1.43747	+	0.741066i	−0.449148	+	0.893458i	$0.648272\pi$
$3$	7.36412	−	5.79121i	1.41723	−	1.11452i	0.441064	−	0.897476i	$-0.354601\pi$
$3$	7.36412	−	5.79121i	1.41723	−	1.11452i	0.976162	−	0.217043i	$-0.0696411\pi$
$4$	7.49662	−	10.5275i	0.937078	−	1.31594i
$5$	−10.5890	+	10.0966i	−0.947112	+	0.903070i	−0.995404	−	0.0957635i	$-0.969471\pi$
$5$	−10.5890	+	10.0966i	−0.947112	+	0.903070i	0.0482918	+	0.998833i	$0.484622\pi$
$6$	−17.8022	+	38.9813i	−1.21128	+	2.65234i
$7$	−11.1382	+	14.7966i	−0.601408	+	0.798942i
$7$	−11.1382	+	14.7966i	−0.601408	+	0.798942i
$8$	−3.20542	+	22.2942i	−0.141661	+	0.985273i
$9$	14.3267	−	59.0554i	0.530618	−	2.18724i
$10$	21.8896	−	63.2458i	0.692209	−	2.00001i
$11$	27.0547	+	13.9477i	0.741574	+	0.382308i	0.787238	−	0.616649i	$-0.211510\pi$
$11$	27.0547	+	13.9477i	0.741574	+	0.382308i	−0.0456646	+	0.998957i	$0.514541\pi$
$12$	−5.76111	−	120.941i	−0.138591	−	2.90938i
$13$	−53.1251	−	61.3096i	−1.13340	−	1.30802i	−0.945423	−	0.325845i	$-0.894351\pi$
$13$	−53.1251	−	61.3096i	−1.13340	−	1.30802i	−0.187981	−	0.982173i	$-0.560194\pi$
$14$	14.2710	−	83.5060i	0.272435	−	1.59414i
$15$	−19.5073	+	135.676i	−0.335784	+	2.33543i
$16$	0.118817	+	0.343300i	0.00185652	+	0.00536406i
$17$	16.5939	−	1.58452i	0.236742	−	0.0226061i	0.0239892	−	0.999712i	$-0.492363\pi$
$17$	16.5939	−	1.58452i	0.236742	−	0.0226061i	0.212752	+	0.977106i	$0.431757\pi$
$18$	65.5341	+	270.135i	0.858141	+	3.53731i
$19$	−144.313	−	13.7802i	−1.74251	−	0.166389i	−0.825272	−	0.564736i	$-0.808978\pi$
$19$	−144.313	−	13.7802i	−1.74251	−	0.166389i	−0.917235	+	0.398347i	$0.869584\pi$
$20$	26.9106	+	187.167i	0.300869	+	2.09259i
$21$	3.66705	+	173.468i	0.0381056	+	1.80256i
$22$	−139.233			−1.34930
$23$	−75.6769	−	80.2496i	−0.686075	−	0.727530i
$23$	−75.6769	−	80.2496i	−0.686075	−	0.727530i
$24$	105.505	+	182.740i	0.897339	+	1.55424i
$25$	4.23810	−	88.9687i	0.0339048	−	0.711750i
$26$	344.503	+	137.918i	2.59856	+	1.04031i
$27$	−131.420	−	287.770i	−0.936733	−	2.05116i
$28$	72.2728	+	228.183i	0.487796	+	1.54009i
$29$	−37.4221	+	81.9429i	−0.239624	+	0.524704i	−0.990790	−	0.135410i	$-0.956765\pi$
$29$	−37.4221	+	81.9429i	−0.239624	+	0.524704i	0.751165	+	0.660114i	$0.229492\pi$
$30$	−205.072	−	592.516i	−1.24803	−	3.60594i
$31$	−189.764	+	75.9701i	−1.09944	+	0.440150i	−0.849220	−	0.528039i	$-0.822927\pi$
$31$	−189.764	+	75.9701i	−1.09944	+	0.440150i	−0.250220	+	0.968189i	$0.580503\pi$
$32$	−131.610	−	125.490i	−0.727052	−	0.693243i
$33$	280.008	−	53.9672i	1.47707	−	0.284681i
$34$	−64.1457	+	41.2239i	−0.323556	+	0.207937i
$35$	−31.4528	−	269.140i	−0.151900	−	1.29980i
$36$	−514.306	−	593.541i	−2.38105	−	2.74787i
$37$	−43.6657	+	179.993i	−0.194016	+	0.799746i	0.788723	+	0.614749i	$0.210743\pi$
$37$	−43.6657	+	179.993i	−0.194016	+	0.799746i	−0.982739	+	0.184997i	$0.940772\pi$
$38$	615.627	−	246.460i	2.62810	−	1.05213i
$39$	−746.276	−	143.833i	−3.06410	−	0.590557i
$40$	−191.154	−	268.438i	−0.755601	−	1.06109i
$41$	−168.634	−	49.5155i	−0.642348	−	0.188610i	−0.0556938	−	0.998448i	$-0.517737\pi$
$41$	−168.634	−	49.5155i	−0.642348	−	0.188610i	−0.586654	+	0.809837i	$0.699555\pi$
$42$	−378.507	−	697.595i	−1.39059	−	2.56289i
$43$	16.5209	+	114.905i	0.0585908	+	0.407508i	0.997919	+	0.0644872i	$0.0205412\pi$
$43$	16.5209	+	114.905i	0.0585908	+	0.407508i	−0.939328	+	0.343021i	$0.888550\pi$
$44$	349.654	−	180.259i	1.19801	−	0.617615i
$45$	444.555	+	769.991i	1.47267	+	2.55074i
$46$	475.893	+	167.654i	1.52536	+	0.537374i
$47$	44.0101	−	76.2277i	0.136586	−	0.236573i	−0.789616	−	0.613601i	$-0.789720\pi$
$47$	44.0101	−	76.2277i	0.136586	−	0.236573i	0.926202	+	0.377027i	$0.123054\pi$
$48$	2.86311	+	1.84001i	0.00860945	+	0.00553296i
$49$	−94.8798	−	329.616i	−0.276618	−	0.960980i
$50$	169.252	+	370.610i	0.478716	+	1.04824i
$51$	113.023	−	107.767i	0.310321	−	0.295891i
$52$	−1043.70	+	99.6610i	−2.78336	+	0.265779i
$53$	54.3159	+	10.4685i	0.140771	+	0.0271314i	0.259150	−	0.965837i	$-0.416558\pi$
$53$	54.3159	+	10.4685i	0.140771	+	0.0271314i	−0.118379	+	0.992968i	$0.537770\pi$
$54$	1137.50	+	894.543i	2.86657	+	2.25429i
$55$	−427.308	+	125.469i	−1.04760	+	0.307604i
$56$	−294.176	−	295.747i	−0.701980	−	0.705729i
$57$	−1142.54	+	734.267i	−2.65497	+	1.70625i
$58$	−19.6069	−	411.600i	−0.0443882	−	0.931823i
$59$	−49.4696	+	142.933i	−0.109159	+	0.315395i	−0.986330	−	0.164784i	$-0.947307\pi$
$59$	−49.4696	+	142.933i	−0.109159	+	0.315395i	0.877170	+	0.480179i	$0.159428\pi$
$60$	1282.10	+	1222.48i	2.75863	+	2.63035i
$61$	−455.530	−	358.233i	−0.956142	−	0.751919i	0.0126173	−	0.999920i	$-0.495984\pi$
$61$	−455.530	−	358.233i	−0.956142	−	0.751919i	−0.968760	+	0.248002i	$0.920226\pi$
$62$	612.301	−	706.633i	1.25423	−	1.44746i
$63$	714.246	+	869.759i	1.42836	+	1.73935i
$64$	795.344	+	233.534i	1.55341	+	0.456121i
$65$	1181.56	+	112.826i	2.25469	+	0.215297i
$66$	−1025.33	+	806.330i	−1.91227	+	1.50382i
$67$	30.9032	−	648.737i	0.0563496	−	1.18292i	−0.776753	−	0.629805i	$-0.783135\pi$
$67$	30.9032	−	648.737i	0.0563496	−	1.18292i	0.833103	−	0.553118i	$-0.186562\pi$
$68$	107.717	−	186.571i	0.192097	−	0.332722i
$69$	−1022.04	−	152.707i	−1.78317	−	0.266431i
$70$	692.012	+	1028.34i	1.18159	+	1.75585i
$71$	646.643	+	415.572i	1.08088	+	0.694639i	0.954760	−	0.297376i	$-0.0961116\pi$
$71$	646.643	+	415.572i	1.08088	+	0.694639i	0.126119	+	0.992015i	$0.459748\pi$
$72$	1270.67	+	508.699i	2.07986	+	0.832649i
$73$	245.990	−	345.444i	0.394396	−	0.553852i	−0.568860	−	0.822434i	$-0.692616\pi$
$73$	245.990	−	345.444i	0.394396	−	0.553852i	0.963257	+	0.268582i	$0.0865550\pi$
$74$	−199.739	−	823.335i	−0.313773	−	1.29339i
$75$	−484.026	−	679.720i	−0.745207	−	1.04650i
$76$	−1226.93	+	1415.95i	−1.85182	+	2.13712i
$77$	−507.720	+	244.966i	−0.751430	+	0.362552i
$78$	3335.67	−	979.442i	4.84219	−	1.42179i
$79$	−319.152	+	61.5115i	−0.454524	+	0.0876024i	−0.411375	−	0.911466i	$-0.634951\pi$
$79$	−319.152	+	61.5115i	−0.454524	+	0.0876024i	−0.0431494	+	0.999069i	$0.513739\pi$
$80$	−4.72433	−	2.43556i	−0.00660245	−	0.00340380i
$81$	−1175.97	−	606.256i	−1.61313	−	0.831627i
$82$	789.416	−	152.148i	1.06313	−	0.204901i
$83$	175.547	−	51.5453i	0.232155	−	0.0681667i	−0.163586	−	0.986529i	$-0.552306\pi$
$83$	175.547	−	51.5453i	0.232155	−	0.0681667i	0.395741	+	0.918362i	$0.370488\pi$
$84$	1853.68	+	1261.82i	2.40777	+	1.63900i
$85$	−159.715	+	184.321i	−0.203806	+	0.235205i
$86$	−308.017	−	432.549i	−0.386213	−	0.542360i
$87$	198.968	+	820.157i	0.245191	+	1.01069i
$88$	−397.674	+	558.455i	−0.481729	+	0.676494i
$89$	670.333	+	268.361i	0.798372	+	0.319620i	0.734736	−	0.678353i	$-0.237306\pi$
$89$	670.333	+	268.361i	0.798372	+	0.319620i	0.0636361	+	0.997973i	$0.479730\pi$
$90$	−3421.40	−	2198.80i	−4.00719	−	2.57526i
$91$	1498.89	−	103.191i	1.72667	−	0.118872i
$92$	−1412.15	+	195.090i	−1.60029	+	0.221082i
$93$	−957.488	+	1658.42i	−1.06760	+	1.84914i
$94$	−19.1578	+	402.172i	−0.0210210	+	0.441286i
$95$	1667.27	−	1311.15i	1.80061	−	1.41602i
$96$	−1695.94	−	161.942i	−1.80303	−	0.172168i
$97$	−371.503	−	109.083i	−0.388871	−	0.114183i	0.0814520	−	0.996677i	$-0.474044\pi$
$97$	−371.503	−	109.083i	−0.388871	−	0.114183i	−0.470323	+	0.882495i	$0.655862\pi$
$98$	1076.65	+	1141.27i	1.10978	+	1.17639i
$99$	1211.29	−	1397.90i	1.22969	−	1.41914i
$100$	−904.849	−	711.581i	−0.904849	−	0.711581i
$101$	−122.103	−	116.425i	−0.120295	−	0.114701i	0.627545	−	0.778581i	$-0.284060\pi$
$101$	−122.103	−	116.425i	−0.120295	−	0.114701i	−0.747839	+	0.663880i	$0.768909\pi$
$102$	−233.640	+	675.059i	−0.226802	+	0.655302i
$103$	45.3553	+	952.125i	0.0433883	+	0.910832i	0.910701	+	0.413067i	$0.135543\pi$
$103$	45.3553	+	952.125i	0.0433883	+	0.910832i	−0.867312	+	0.497764i	$0.834154\pi$
$104$	1537.14	−	987.857i	1.44931	−	0.931417i
$105$	−1790.27	−	1799.83i	−1.66393	−	1.67282i
$106$	−242.779	+	71.2863i	−0.222460	+	0.0653201i
$107$	−412.976	−	324.768i	−0.373121	−	0.293426i	0.413936	−	0.910306i	$-0.364154\pi$
$107$	−412.976	−	324.768i	−0.373121	−	0.293426i	−0.787057	+	0.616881i	$0.788396\pi$
$108$	−4014.71	−	773.772i	−3.57700	−	0.689409i
$109$	872.126	−	83.2779i	0.766371	−	0.0731796i	0.295454	−	0.955357i	$-0.404529\pi$
$109$	872.126	−	83.2779i	0.766371	−	0.0731796i	0.470917	+	0.882177i	$0.343923\pi$
$110$	1474.35	−	1405.79i	1.27794	−	1.21852i
$111$	720.815	+	1578.36i	0.616367	+	1.34966i
$112$	−6.40309	−	2.06566i	−0.00540210	−	0.00174274i
$113$	918.433	+	590.241i	0.764592	+	0.491373i	0.863888	−	0.503685i	$-0.168023\pi$
$113$	918.433	+	590.241i	0.764592	+	0.491373i	−0.0992957	+	0.995058i	$0.531659\pi$
$114$	3106.25	−	5380.19i	2.55199	−	4.42018i
$115$	1611.60	+	85.6843i	1.30680	+	0.0694792i
$116$	582.117	+	1008.26i	0.465933	+	0.807020i
$117$	−4381.77	+	2258.96i	−3.46235	+	1.78497i
$118$	−98.4629	−	684.824i	−0.0768156	−	0.534264i
$119$	−161.381	+	263.182i	−0.124317	+	0.202738i
$120$	−2962.26	−	869.797i	−2.25347	−	0.661677i
$121$	−234.635	−	329.499i	−0.176285	−	0.247557i
$122$	2602.96	+	501.679i	1.93165	+	0.372294i
$123$	−1528.60	+	611.959i	−1.12056	+	0.448605i
$124$	−622.812	+	2567.27i	−0.451050	+	1.85925i
$125$	−344.262	−	397.299i	−0.246334	−	0.284284i
$126$	−4727.02	−	2039.15i	−3.34220	−	1.44176i
$127$	750.091	−	482.054i	0.524093	−	0.336814i	−0.251696	−	0.967806i	$-0.580988\pi$
$127$	750.091	−	482.054i	0.524093	−	0.336814i	0.775789	+	0.630992i	$0.217352\pi$
$128$	−2294.68	+	442.264i	−1.58456	+	0.305398i
$129$	787.101	+	750.499i	0.537212	+	0.512231i
$130$	−5040.46	+	2017.90i	−3.40060	+	1.36139i
$131$	117.381	+	339.150i	0.0782872	+	0.226196i	0.977352	−	0.211619i	$-0.0678736\pi$
$131$	117.381	+	339.150i	0.0782872	+	0.226196i	−0.899065	+	0.437815i	$0.855752\pi$
$132$	1530.97	−	3352.37i	1.00950	−	2.21050i
$133$	1811.29	−	1981.85i	1.18089	−	1.29209i
$134$	1234.14	+	2702.39i	0.795623	+	1.74217i
$135$	4297.11	+	1720.30i	2.73953	+	1.09674i
$136$	−17.8647	+	375.026i	−0.0112639	+	0.236457i
$137$	697.186	+	1207.56i	0.434778	+	0.753058i	0.997277	−	0.0737401i	$-0.0234935\pi$
$137$	697.186	+	1207.56i	0.434778	+	0.753058i	−0.562500	+	0.826798i	$0.690160\pi$
$138$	4475.45	−	1521.37i	2.76069	−	0.938461i
$139$	−977.167			−0.596275			−0.298137	−	0.954523i	$-0.596365\pi$
$139$	−977.167			−0.596275			−0.298137	+	0.954523i	$0.596365\pi$
$140$	−3069.17	−	1686.52i	−1.85280	−	1.01812i
$141$	−117.355	−	816.221i	−0.0700927	−	0.487505i
$142$	−3500.16	−	334.225i	−2.06850	−	0.197518i
$143$	−582.158	−	2399.69i	−0.340437	−	1.40330i
$144$	21.9760	−	2.09845i	0.0127176	−	0.00121438i
$145$	−431.083	−	1245.53i	−0.246893	−	0.713351i
$146$	−276.070	+	1920.11i	−0.156491	+	1.08842i
$147$	−2607.58	−	1877.86i	−1.46306	−	1.05363i
$148$	1567.53	+	1809.03i	0.870611	+	1.00474i
$149$	33.6462	+	706.321i	0.0184994	+	0.388350i	0.989062	+	0.147501i	$0.0471228\pi$
$149$	33.6462	+	706.321i	0.0184994	+	0.388350i	−0.970563	+	0.240849i	$0.922574\pi$
$150$	3392.67	+	1749.04i	1.84674	+	0.952058i
$151$	7.89660	−	22.8157i	0.00425574	−	0.0122961i	−0.942853	−	0.333209i	$-0.891868\pi$
$151$	7.89660	−	22.8157i	0.00425574	−	0.0122961i	0.947109	+	0.320913i	$0.103990\pi$
$152$	769.801	−	3173.16i	0.410784	−	1.69327i
$153$	144.161	−	1002.66i	0.0761745	−	0.529805i
$154$	1550.81	−	2060.18i	0.811481	−	1.07802i
$155$	1242.38	−	2720.43i	0.643808	−	1.40974i
$156$	−7108.76	+	6778.19i	−3.64844	+	3.47878i
$157$	1366.31	−	1918.71i	0.694542	−	0.975347i	−0.305192	−	0.952291i	$-0.598721\pi$
$157$	1366.31	−	1918.71i	0.694542	−	0.975347i	0.999734	−	0.0230567i	$-0.00733983\pi$
$158$	1168.67	−	919.051i	0.588445	−	0.462758i
$159$	460.614	−	237.463i	0.229743	−	0.118441i
$160$	2660.66			1.31465
$161$	2030.33	−	225.924i	0.993866	−	0.110592i
$162$	6051.98			2.93512
$163$	622.943	−	321.150i	0.299342	−	0.154321i	−0.302012	−	0.953304i	$-0.597658\pi$
$163$	622.943	−	321.150i	0.299342	−	0.154321i	0.601354	+	0.798983i	$0.294628\pi$
$164$	−1785.46	+	1404.10i	−0.850130	+	0.668550i
$165$	−2420.13	+	3398.60i	−1.14186	+	1.60352i
$166$	−605.694	+	577.528i	−0.283199	+	0.270029i
$167$	375.039	−	821.220i	0.173781	−	0.380527i	−0.802621	−	0.596489i	$-0.796562\pi$
$167$	375.039	−	821.220i	0.173781	−	0.380527i	0.976402	+	0.215963i	$0.0692890\pi$
$168$	−3879.08	−	474.283i	−1.78141	−	0.217808i
$169$	−623.929	+	4339.52i	−0.283991	+	1.97520i
$170$	263.019	−	1084.18i	0.118662	−	0.489133i
$171$	−2881.32	+	8325.03i	−1.28854	+	3.72299i
$172$	1333.52	+	687.476i	0.591161	+	0.304765i
$173$	197.537	+	4146.82i	0.0868121	+	1.82241i	0.452602	+	0.891713i	$0.350496\pi$
$173$	197.537	+	4146.82i	0.0868121	+	1.82241i	−0.365789	+	0.930698i	$0.619201\pi$
$174$	−2528.05	−	2917.52i	−1.10144	−	1.27113i
$175$	1269.23	+	1053.66i	0.548256	+	0.455140i
$176$	−1.57367	+	10.9451i	−0.000673976	+	0.00468761i
$177$	463.455	+	1339.07i	0.196810	+	0.568646i
$178$	−3287.92	+	313.958i	−1.38449	+	0.132203i
$179$	−463.505	−	1910.59i	−0.193542	−	0.797791i	−0.982943	−	0.183912i	$-0.941124\pi$
$179$	−463.505	−	1910.59i	−0.193542	−	0.797791i	0.789401	−	0.613878i	$-0.210391\pi$
$180$	11438.8	+	1092.27i	4.73664	+	0.452294i
$181$	388.317	+	2700.80i	0.159466	+	1.10911i	0.899620	+	0.436674i	$0.143844\pi$
$181$	388.317	+	2700.80i	0.159466	+	1.10911i	−0.740154	+	0.672438i	$0.765247\pi$
$182$	−5877.87	+	3561.31i	−2.39394	+	1.45045i
$183$	−5429.18			−2.19310
$184$	2031.68	−	1429.92i	0.814006	−	0.572909i
$185$	−1354.94	−	2346.83i	−0.538471	−	0.932660i
$186$	416.799	−	8749.69i	0.164307	−	3.44924i
$187$	471.044	+	188.577i	0.184204	+	0.0737441i
$188$	−472.562	−	1034.77i	−0.183325	−	0.401426i
$189$	5721.80	+	1260.67i	2.20212	+	0.485187i
$190$	−4030.48	+	8825.53i	−1.53896	+	3.36985i
$191$	−458.905	−	1325.92i	−0.173849	−	0.502304i	0.824091	−	0.566457i	$-0.191686\pi$
$191$	−458.905	−	1325.92i	−0.173849	−	0.502304i	−0.997940	+	0.0641536i	$0.979565\pi$
$192$	7209.45	−	2886.23i	2.70988	−	1.08487i
$193$	−729.627	−	695.698i	−0.272123	−	0.259469i	0.541713	−	0.840564i	$-0.317776\pi$
$193$	−729.627	−	695.698i	−0.272123	−	0.259469i	−0.813836	+	0.581095i	$0.802625\pi$
$194$	1739.09	−	335.183i	0.643606	−	0.124045i
$195$	9354.58	−	6011.82i	3.43536	−	2.20777i
$196$	−4181.32	−	1472.16i	−1.52381	−	0.536501i
$197$	−846.075	−	976.422i	−0.305992	−	0.353133i	0.581839	−	0.813304i	$-0.302333\pi$
$197$	−846.075	−	976.422i	−0.305992	−	0.353133i	−0.887830	+	0.460171i	$0.847788\pi$
$198$	−1994.75	+	8222.49i	−0.715965	+	2.95125i
$199$	−2216.43	+	887.326i	−0.789541	+	0.316085i	−0.731157	−	0.682209i	$-0.761019\pi$
$199$	−2216.43	+	887.326i	−0.789541	+	0.316085i	−0.0583846	+	0.998294i	$0.518595\pi$
$200$	1969.90	+	379.667i	0.696464	+	0.134233i
$201$	−3529.40	−	4956.34i	−1.23853	−	1.73927i
$202$	740.479	+	217.424i	0.257920	+	0.0757322i
$203$	−795.662	−	1466.42i	−0.275096	−	0.507007i
$204$	−287.232	−	1997.74i	−0.0985798	−	0.685638i
$205$	2285.62	−	1178.32i	0.778704	−	0.401450i
$206$	−2180.11	−	3776.06i	−0.737356	−	1.27714i
$207$	−5823.37	+	3319.42i	−1.95533	+	1.11457i
$208$	14.7354	−	25.5225i	0.00491210	−	0.00850801i
$209$	−3712.14	−	2385.65i	−1.22859	−	0.789564i
$210$	11051.4	+	3565.21i	3.63151	+	1.17154i
$211$	−913.899	−	2001.16i	−0.298177	−	0.652917i	0.699943	−	0.714199i	$-0.253209\pi$
$211$	−913.899	−	2001.16i	−0.298177	−	0.652917i	−0.998121	+	0.0612812i	$0.980481\pi$
$212$	517.393	−	493.334i	0.167617	−	0.159822i
$213$	7168.62	−	684.520i	2.30604	−	0.220200i
$214$	2359.80	+	454.814i	0.753797	+	0.145282i
$215$	−1335.09	−	1049.93i	−0.423500	−	0.333044i
$216$	6836.84	−	2007.48i	2.15365	−	0.632368i
$217$	989.536	−	3654.04i	0.309558	−	1.14310i
$218$	−3371.31	+	2166.61i	−1.04740	+	0.673125i
$219$	−189.042	−	3968.47i	−0.0583299	−	1.22450i
$220$	−1882.49	+	5439.09i	−0.576897	+	1.66683i
$221$	−978.698	−	933.187i	−0.297893	−	0.284040i
$222$	−6239.00	−	4906.41i	−1.88619	−	1.48332i
$223$	3363.61	−	3881.81i	1.01006	−	1.16567i	0.0239288	−	0.999714i	$-0.492382\pi$
$223$	3363.61	−	3881.81i	1.01006	−	1.16567i	0.986133	−	0.165959i	$-0.0530721\pi$
$224$	3322.74	−	549.650i	0.991115	−	0.163951i
$225$	−5193.36	−	1524.91i	−1.53877	−	0.451825i
$226$	−4971.31	−	474.703i	−1.46322	−	0.139720i
$227$	−2087.68	+	1641.77i	−0.610414	+	0.480035i	−0.874867	−	0.484364i	$-0.839051\pi$
$227$	−2087.68	+	1641.77i	−0.610414	+	0.480035i	0.264452	+	0.964399i	$0.414809\pi$
$228$	−835.183	+	17532.7i	−0.242594	+	5.09267i
$229$	−766.812	+	1328.16i	−0.221277	+	0.383262i	−0.955196	−	0.295974i	$-0.904356\pi$
$229$	−766.812	+	1328.16i	−0.221277	+	0.383262i	0.733919	+	0.679237i	$0.237689\pi$
$230$	−6731.98	+	3029.62i	−1.92997	+	0.868552i
$231$	−2320.26	+	4744.27i	−0.660875	+	1.35130i
$232$	−1706.90	−	1096.96i	−0.483031	−	0.310425i
$233$	−5811.14	−	2326.43i	−1.63391	−	0.654118i	−0.640416	−	0.768028i	$-0.721238\pi$
$233$	−5811.14	−	2326.43i	−1.63391	−	0.654118i	−0.993491	+	0.113910i	$0.963662\pi$
$234$	13080.4	−	18368.8i	3.65424	−	5.13166i
$235$	303.618	+	1251.53i	0.0842802	+	0.347408i
$236$	1133.88	+	1592.31i	0.312751	+	0.439197i
$237$	−1994.05	+	2301.25i	−0.546529	+	0.630728i
$238$	104.495	−	1408.30i	0.0284596	−	0.383557i
$239$	−4155.05	+	1220.03i	−1.12455	+	0.330198i	−0.790564	−	0.612379i	$-0.790213\pi$
$239$	−4155.05	+	1220.03i	−1.12455	+	0.330198i	−0.333988	+	0.942577i	$0.608395\pi$
$240$	−48.8954	+	9.42381i	−0.0131508	+	0.00253460i
$241$	−4062.07	−	2094.14i	−1.08573	−	0.559733i	−0.180035	−	0.983660i	$-0.557621\pi$
$241$	−4062.07	−	2094.14i	−1.08573	−	0.559733i	−0.905696	+	0.423927i	$0.860651\pi$
$242$	1644.62	+	847.860i	0.436860	+	0.225217i
$243$	−3783.65	+	729.239i	−0.998853	+	0.192513i
$244$	−7186.25	+	2110.07i	−1.88546	+	0.553621i
$245$	4332.70	+	2532.35i	1.12982	+	0.660351i
$246$	4932.24	−	5692.11i	1.27833	−	1.47527i
$247$	6821.77	+	9579.84i	1.75732	+	2.46782i
$248$	−1085.42	−	4474.15i	−0.277920	−	1.14560i
$249$	994.242	−	1396.22i	0.253042	−	0.355348i
$250$	2232.45	+	893.738i	0.564770	+	0.226100i
$251$	2692.09	+	1730.10i	0.676986	+	0.435072i	0.833438	−	0.552613i	$-0.186369\pi$
$251$	2692.09	+	1730.10i	0.676986	+	0.435072i	−0.156452	+	0.987686i	$0.550006\pi$
$252$	14510.9	−	998.998i	3.62737	−	0.249726i
$253$	−928.123	−	3226.65i	−0.230635	−	0.801809i
$254$	−2039.29	+	3532.15i	−0.503766	+	0.872547i
$255$	−108.720	+	2282.30i	−0.0266991	+	0.560484i
$256$	3190.05	−	2508.68i	0.778820	−	0.612471i
$257$	6851.36	+	654.226i	1.66294	+	0.158792i	0.883739	−	0.467980i	$-0.155018\pi$
$257$	6851.36	+	654.226i	1.66294	+	0.158792i	0.779203	+	0.626771i	$0.215624\pi$
$258$	−4773.26	−	1401.55i	−1.15182	−	0.338205i
$259$	−2176.92	−	2650.90i	−0.522268	−	0.635981i
$260$	10045.5	−	11593.1i	2.39614	−	2.76529i
$261$	4303.04	+	3383.95i	1.02050	+	0.802533i
$262$	−1188.12	−	1132.87i	−0.280162	−	0.267133i
$263$	−333.866	+	964.643i	−0.0782778	+	0.226169i	−0.977349	−	0.211633i	$-0.932122\pi$
$263$	−333.866	+	964.643i	−0.0782778	+	0.226169i	0.899071	+	0.437802i	$0.144243\pi$
$264$	305.610	+	6415.54i	0.0712462	+	1.49564i
$265$	−680.850	+	437.556i	−0.157827	+	0.101430i
$266$	−3210.22	+	11854.3i	−0.739967	+	2.73246i
$267$	6490.54	−	1905.80i	1.48770	−	0.436827i
$268$	−6597.93	−	5188.67i	−1.50385	−	1.18264i
$269$	−7365.28	−	1419.54i	−1.66940	−	0.321751i	−0.735026	−	0.678039i	$-0.762830\pi$
$269$	−7365.28	−	1419.54i	−1.66940	−	0.321751i	−0.934376	+	0.356288i	$0.884042\pi$
$270$	−21076.9	+	2012.60i	−4.75075	+	0.453641i
$271$	−3953.92	+	3770.05i	−0.886285	+	0.845071i	−0.988737	−	0.149667i	$-0.952180\pi$
$271$	−3953.92	+	3770.05i	−0.886285	+	0.845071i	0.102451	+	0.994738i	$0.467331\pi$
$272$	2.51561	+	5.50841i	0.000560776	+	0.00122793i
$273$	10440.4	−	9440.32i	2.31459	−	2.09287i
$274$	−5365.71	−	3448.33i	−1.18304	−	0.760297i
$275$	1355.57	−	2347.91i	0.297250	−	0.514853i
$276$	−9269.45	+	9614.73i	−2.02158	+	2.09688i
$277$	2801.75	+	4852.78i	0.607730	+	1.05262i	0.991614	+	0.129237i	$0.0412529\pi$
$277$	2801.75	+	4852.78i	0.607730	+	1.05262i	−0.383884	+	0.923381i	$0.625414\pi$
$278$	3972.94	−	2048.19i	0.857126	−	0.441879i
$279$	1767.75	+	12295.0i	0.379329	+	2.63829i
$280$	6101.08	+	161.493i	1.30218	+	0.0344680i
$281$	4696.04	+	1378.88i	0.996948	+	0.292730i	0.739203	−	0.673483i	$-0.235202\pi$
$281$	4696.04	+	1378.88i	0.996948	+	0.292730i	0.257745	+	0.966213i	$0.417021\pi$
$282$	2187.98	+	3072.59i	0.462029	+	0.648830i
$283$	−1395.67	−	268.994i	−0.293159	−	0.0565018i	0.0405512	−	0.999177i	$-0.487089\pi$
$283$	−1395.67	−	268.994i	−0.293159	−	0.0565018i	−0.333710	+	0.942676i	$0.608301\pi$
$284$	9222.59	−	3692.17i	1.92697	−	0.771443i
$285$	4684.79	−	19311.0i	0.973696	−	4.01363i
$286$	7396.79	+	8536.35i	1.52931	+	1.76491i
$287$	2610.95	−	1943.70i	0.537002	−	0.399767i
$288$	−9296.42	+	5974.45i	−1.90207	+	1.22239i
$289$	−4551.37	+	877.205i	−0.926393	+	0.178548i
$290$	4363.39	+	4160.48i	0.883541	+	0.842455i
$291$	−3367.52	+	1348.15i	−0.678376	+	0.271581i
$292$	−1792.58	−	5179.33i	−0.359257	−	1.03801i
$293$	−661.997	+	1449.57i	−0.131994	+	0.289027i	−0.964076	−	0.265626i	$-0.914421\pi$
$293$	−661.997	+	1449.57i	−0.131994	+	0.289027i	0.832082	+	0.554652i	$0.187149\pi$
$294$	14537.9	+	2169.34i	2.88391	+	0.430336i
$295$	−919.306	−	2013.00i	−0.181438	−	0.397293i
$296$	−3872.82	−	1550.44i	−0.760483	−	0.304452i
$297$	458.187	−	9618.53i	0.0895176	−	1.87921i
$298$	−1617.28	−	2801.22i	−0.314385	−	0.544531i
$299$	−899.729	+	8902.99i	−0.174022	+	1.72198i
$300$	−10784.3			−2.07545
$301$	−1884.22	−	1035.39i	−0.360813	−	0.198268i
$302$	15.7172	+	109.315i	0.00299477	+	0.0208291i
$303$	−1573.43	−	150.244i	−0.298320	−	0.0284862i
$304$	−12.4161	−	51.1799i	−0.00234248	−	0.00965582i
$305$	8440.57	−	805.977i	1.58461	−	0.151312i
$306$	1515.50	+	4378.75i	0.283122	+	0.818029i
$307$	−796.396	+	5539.06i	−0.148054	+	1.02974i	0.771345	+	0.636417i	$0.219584\pi$
$307$	−796.396	+	5539.06i	−0.148054	+	1.02974i	−0.919400	+	0.393324i	$0.871325\pi$
$308$	−1227.30	+	7181.46i	−0.227051	+	1.32858i
$309$	5847.96	+	6748.90i	1.07663	+	1.24250i
$310$	650.931	+	13664.7i	0.119259	+	2.50356i
$311$	6078.55	+	3133.71i	1.10830	+	0.571371i	0.912420	−	0.409256i	$-0.134212\pi$
$311$	6078.55	+	3133.71i	1.10830	+	0.571371i	0.195885	+	0.980627i	$0.437242\pi$
$312$	5598.77	−	16176.6i	1.01592	−	2.93531i
$313$	1706.09	−	7032.59i	0.308095	−	1.26999i	−0.581616	−	0.813463i	$-0.697579\pi$
$313$	1706.09	−	7032.59i	0.308095	−	1.26999i	0.889712	−	0.456523i	$-0.150905\pi$
$314$	−1533.38	+	10664.9i	−0.275584	+	1.91673i
$315$	−16344.8	−	1998.43i	−2.92357	−	0.357457i
$316$	−1745.00	+	3821.01i	−0.310645	+	0.680218i
$317$	3458.29	−	3297.47i	0.612734	−	0.584241i	−0.318833	−	0.947811i	$-0.603291\pi$
$317$	3458.29	−	3297.47i	0.612734	−	0.584241i	0.931567	+	0.363570i	$0.118442\pi$
$318$	−1375.02	+	1930.94i	−0.242475	+	0.340509i
$319$	−2155.36	+	1694.99i	−0.378297	+	0.297496i
$320$	−10779.8	+	5557.39i	−1.88316	+	0.970836i
$321$	−4922.01			−0.855825
$322$	−7781.31	+	5174.23i	−1.34669	+	0.895493i
$323$	−2416.55			−0.416285
$324$	−15198.2	+	7835.22i	−2.60600	+	1.34349i
$325$	−5679.79	+	4466.63i	−0.969409	+	0.762352i
$326$	−1859.60	+	2611.44i	−0.315932	+	0.443664i
$327$	5940.16	−	5663.93i	1.00456	−	0.957847i
$328$	1644.45	−	3600.85i	0.276828	−	0.606169i
$329$	637.718	+	1500.24i	0.106865	+	0.251401i
$330$	2716.07	−	18890.7i	0.453074	−	3.15120i
$331$	1080.08	−	4452.15i	0.179355	−	0.739311i	−0.809084	−	0.587693i	$-0.800036\pi$
$331$	1080.08	−	4452.15i	0.179355	−	0.739311i	0.988439	−	0.151618i	$-0.0484485\pi$
$332$	773.367	−	2234.50i	0.127843	−	0.369379i
$333$	10004.0	+	5157.40i	1.64629	+	0.848719i
$334$	196.498	+	4125.00i	0.0321913	+	0.675778i
$335$	6222.82	+	7181.52i	1.01489	+	1.17125i
$336$	−59.1158	+	21.8699i	−0.00959831	+	0.00355089i
$337$	1194.58	−	8308.51i	0.193095	−	1.34301i	−0.630659	−	0.776060i	$-0.717215\pi$
$337$	1194.58	−	8308.51i	0.193095	−	1.34301i	0.823754	−	0.566947i	$-0.191876\pi$
$338$	−6559.11	−	18951.3i	−1.05553	−	3.04975i
$339$	10181.7	−	972.230i	1.63124	−	0.155765i
$340$	743.121	+	3063.19i	0.118534	+	0.488602i
$341$	−6193.63	−	591.420i	−0.983588	−	0.0939213i
$342$	−5734.89	−	39887.1i	−0.906747	−	6.30657i
$343$	5934.00	+	2267.44i	0.934128	+	0.356939i
$344$	−2614.67			−0.409807
$345$	12364.2	−	8702.10i	1.92947	−	1.35799i
$346$	−9495.09	−	16446.0i	−1.47532	−	2.55532i
$347$	287.769	−	6041.02i	0.0445195	−	0.934579i	−0.860563	−	0.509343i	$-0.829888\pi$
$347$	287.769	−	6041.02i	0.0445195	−	0.934579i	0.905083	−	0.425235i	$-0.139809\pi$
$348$	10125.8	+	4053.76i	1.55977	+	0.624438i
$349$	−3787.85	−	8294.24i	−0.580971	−	1.27215i	−0.940746	−	0.339111i	$-0.889874\pi$
$349$	−3787.85	−	8294.24i	−0.580971	−	1.27215i	0.359775	−	0.933039i	$-0.382853\pi$
$350$	−7368.94	−	1623.58i	−1.12539	−	0.247955i
$351$	−10661.3	+	23345.1i	−1.62126	+	3.55005i
$352$	−1810.39	−	5230.77i	−0.274130	−	0.792048i
$353$	−4931.18	+	1974.15i	−0.743514	+	0.297658i	−0.712320	−	0.701855i	$-0.752355\pi$
$353$	−4931.18	+	1974.15i	−0.743514	+	0.297658i	−0.0311943	+	0.999513i	$0.509931\pi$
$354$	−4691.05	−	4472.91i	−0.704313	−	0.671561i
$355$	−11043.2	+	2128.40i	−1.65102	+	0.318208i
$356$	7850.41	−	5045.15i	1.16874	−	0.751102i
$357$	335.715	+	2872.70i	0.0497700	+	0.425880i
$358$	5889.21	+	6796.51i	0.869426	+	1.00337i
$359$	−1369.71	+	5646.01i	−0.201366	+	0.830041i	0.778052	+	0.628200i	$0.216208\pi$
$359$	−1369.71	+	5646.01i	−0.201366	+	0.830041i	−0.979418	+	0.201842i	$0.935307\pi$
$360$	−18591.3	+	7442.83i	−2.72180	+	1.08964i
$361$	13901.2	+	2679.25i	2.02672	+	0.390617i
$362$	−7239.84	−	10166.9i	−1.05115	−	1.47614i
$363$	−3636.08	−	1067.65i	−0.525743	−	0.154372i
$364$	10150.3	−	16553.2i	1.46159	−	2.38359i
$365$	883.028	+	6141.59i	0.126630	+	0.880728i
$366$	22073.8	−	11379.8i	3.15251	−	1.62523i
$367$	−2738.69	−	4743.55i	−0.389533	−	0.674691i	0.602854	−	0.797852i	$-0.294030\pi$
$367$	−2738.69	−	4743.55i	−0.389533	−	0.674691i	−0.992387	+	0.123161i	$0.960697\pi$
$368$	18.5580	−	35.5149i	0.00262881	−	0.00503082i
$369$	−5340.13	+	9249.38i	−0.753377	+	1.30489i
$370$	10427.9	+	6701.63i	1.46520	+	0.941625i
$371$	−759.882	+	687.091i	−0.106337	+	0.0961509i
$372$	10281.1	+	22512.5i	1.43293	+	3.13769i
$373$	−4721.05	+	4501.51i	−0.655352	+	0.624877i	−0.942974	−	0.332867i	$-0.891984\pi$
$373$	−4721.05	+	4501.51i	−0.655352	+	0.624877i	0.287621	+	0.957744i	$0.407136\pi$
$374$	−2310.42	+	220.619i	−0.319436	+	0.0305025i
$375$	−4836.03	−	932.068i	−0.665950	−	0.128351i
$376$	1558.36	+	1225.51i	0.213740	+	0.168087i
$377$	7011.94	−	2058.89i	0.957913	−	0.281269i
$378$	−25906.0	+	6867.59i	−3.52503	+	0.934472i
$379$	−8930.10	+	5739.03i	−1.21031	+	0.777820i	−0.980711	−	0.195464i	$-0.937379\pi$
$379$	−8930.10	+	5739.03i	−1.21031	+	0.777820i	−0.229601	+	0.973285i	$0.573742\pi$
$380$	−1304.34	−	27381.4i	−0.176082	−	3.69642i
$381$	2732.09	−	7893.84i	0.367373	−	1.06145i
$382$	4644.99	+	4428.99i	0.622143	+	0.593212i
$383$	−7822.65	−	6151.80i	−1.04365	−	0.820737i	−0.0595294	−	0.998227i	$-0.518960\pi$
$383$	−7822.65	−	6151.80i	−1.04365	−	0.820737i	−0.984123	+	0.177489i	$0.943202\pi$
$384$	−14337.1	+	16545.9i	−1.90530	+	2.19884i
$385$	2902.94	−	7720.22i	0.384279	−	1.02197i
$386$	4424.72	+	1299.21i	0.583451	+	0.171317i
$387$	7022.45	+	670.563i	0.922407	+	0.0880792i
$388$	−3933.40	+	3093.26i	−0.514660	+	0.404733i
$389$	65.8579	−	1382.53i	0.00858388	−	0.180198i	−0.990504	−	0.137487i	$-0.956098\pi$
$389$	65.8579	−	1382.53i	0.00858388	−	0.180198i	0.999087	−	0.0427109i	$-0.0135994\pi$
$390$	−25432.5	+	44050.4i	−3.30211	+	5.71943i
$391$	−1382.93	−	1211.74i	−0.178869	−	0.156727i
$392$	7652.65	−	1058.71i	0.986013	−	0.136410i
$393$	2828.50	+	1817.76i	0.363050	+	0.233318i
$394$	5486.58	+	2196.49i	0.701548	+	0.280857i
$395$	2758.45	−	3873.71i	0.351374	−	0.493436i
$396$	−5635.89	−	23231.5i	−0.715187	−	2.94804i
$397$	−5652.65	−	7938.04i	−0.714606	−	1.00352i	−0.998995	−	0.0448144i	$-0.985730\pi$
$397$	−5652.65	−	7938.04i	−0.714606	−	1.00352i	0.284390	−	0.958709i	$-0.408209\pi$
$398$	7151.63	−	8253.42i	0.900701	−	1.03946i
$399$	1861.22	−	25084.2i	0.233528	−	3.14732i
$400$	31.0465	−	9.11608i	0.00388081	−	0.00113951i
$401$	−14170.0	+	2731.05i	−1.76463	+	0.340105i	−0.965372	−	0.260878i	$-0.915988\pi$
$401$	−14170.0	+	2731.05i	−1.76463	+	0.340105i	−0.799262	+	0.600983i	$0.794776\pi$
$402$	24738.5	+	12753.6i	3.06926	+	1.58231i
$403$	14738.9	+	7598.45i	1.82183	+	0.939220i
$404$	−2141.04	+	412.651i	−0.263665	+	0.0508172i
$405$	18573.6	−	5453.69i	2.27883	−	0.669126i
$406$	6308.67	+	4294.38i	0.771168	+	0.524942i
$407$	−3691.84	+	4260.62i	−0.449626	+	0.518897i
$408$	2040.30	+	2865.20i	0.247573	+	0.347667i
$409$	1117.51	+	4606.46i	0.135104	+	0.556906i	0.998617	+	0.0525793i	$0.0167442\pi$
$409$	1117.51	+	4606.46i	0.135104	+	0.556906i	−0.863513	+	0.504327i	$0.831741\pi$
$410$	−6822.98	+	9581.54i	−0.821861	+	1.15414i
$411$	12127.4	+	4855.08i	1.45548	+	0.582684i
$412$	10363.5	+	6660.24i	1.23926	+	0.796424i
$413$	−1563.92	−	2324.00i	−0.186333	−	0.276893i
$414$	16718.8	−	25702.1i	1.98475	−	3.05118i
$415$	−1338.44	+	2318.25i	−0.158317	+	0.274213i
$416$	−701.947	+	14735.7i	−0.0827302	+	1.73672i
$417$	−7195.98	+	5658.98i	−0.845056	+	0.664560i
$418$	20093.2	+	1918.67i	2.35117	+	0.224510i
$419$	−999.807	−	293.570i	−0.116572	−	0.0342287i	0.222926	−	0.974835i	$-0.428439\pi$
$419$	−999.807	−	293.570i	−0.116572	−	0.0342287i	−0.339498	+	0.940607i	$0.610257\pi$
$420$	−32368.8	+	5354.47i	−3.76056	+	0.622074i
$421$	−5138.43	+	5930.07i	−0.594850	+	0.686494i	−0.970730	−	0.240175i	$-0.922795\pi$
$421$	−5138.43	+	5930.07i	−0.594850	+	0.686494i	0.375880	+	0.926669i	$0.377341\pi$
$422$	7910.24	+	6220.68i	0.912475	+	0.717579i
$423$	−3871.14	−	3691.12i	−0.444967	−	0.424275i
$424$	−407.492	+	1177.37i	−0.0466735	+	0.134854i
$425$	−70.6465	−	1483.05i	−0.00806319	−	0.169267i
$426$	−27711.2	+	17808.9i	−3.15167	+	2.02546i
$427$	10374.4	−	2750.23i	1.17577	−	0.311693i
$428$	−6514.94	+	1912.96i	−0.735774	+	0.216043i
$429$	−18184.2	−	14300.2i	−2.04648	−	1.60937i
$430$	7628.89	+	1470.35i	0.855576	+	0.164899i
$431$	−9037.20	+	862.948i	−1.00999	+	0.0964426i	−0.586913	−	0.809650i	$-0.699657\pi$
$431$	−9037.20	+	862.948i	−1.00999	+	0.0964426i	−0.423079	+	0.906093i	$0.639051\pi$
$432$	83.1763	−	79.3085i	0.00926348	−	0.00883271i
$433$	−5852.60	−	12815.4i	−0.649556	−	1.42233i	−0.891942	−	0.452150i	$-0.850657\pi$
$433$	−5852.60	−	12815.4i	−0.649556	−	1.42233i	0.242386	−	0.970180i	$-0.422070\pi$
$434$	3635.83	+	16930.6i	0.402132	+	1.87257i
$435$	−10387.7	−	6675.76i	−1.14495	−	0.735812i
$436$	5661.29	−	9805.63i	0.621849	−	1.07707i
$437$	9815.30	+	12623.9i	1.07444	+	1.38188i
$438$	9086.73	+	15738.7i	0.991280	+	1.71695i
$439$	7586.78	−	3911.26i	0.824823	−	0.425226i	0.00649626	−	0.999979i	$-0.497932\pi$
$439$	7586.78	−	3911.26i	0.824823	−	0.425226i	0.818327	+	0.574753i	$0.194902\pi$
$440$	−1427.53	−	9928.66i	−0.154670	−	1.07575i
$441$	−20824.9	+	880.858i	−2.24867	+	0.0951148i
$442$	5935.17	+	1742.72i	0.638704	+	0.187541i
$443$	7942.33	+	11153.4i	0.851809	+	1.19620i	0.978907	+	0.204308i	$0.0654944\pi$
$443$	7942.33	+	11153.4i	0.851809	+	1.19620i	−0.127098	+	0.991890i	$0.540566\pi$
$444$	22020.0	+	4244.00i	2.35365	+	0.453629i
$445$	−9807.71	+	3926.42i	−1.04479	+	0.418270i
$446$	−5539.19	+	22832.8i	−0.588090	+	2.42414i
$447$	4338.23	+	5006.58i	0.459041	+	0.529761i
$448$	−12314.2	+	9167.24i	−1.29864	+	0.966767i
$449$	2263.96	−	1454.96i	0.237958	−	0.152926i	−0.416228	−	0.909260i	$-0.636648\pi$
$449$	2263.96	−	1454.96i	0.237958	−	0.152926i	0.654185	+	0.756334i	$0.273012\pi$
$450$	24311.3	−	4685.62i	2.54677	−	0.490850i
$451$	−3871.73	−	3691.69i	−0.404241	−	0.385443i
$452$	13098.9	−	5244.02i	1.36310	−	0.545703i
$453$	−73.9791	−	213.749i	−0.00767294	−	0.0221695i
$454$	5046.79	−	11050.9i	0.521713	−	1.14239i
$455$	−14830.0	+	16226.5i	−1.52800	+	1.67189i
$456$	−12707.5	−	27825.6i	−1.30501	−	2.85758i
$457$	7652.54	+	3063.62i	0.783306	+	0.313588i	0.728623	−	0.684915i	$-0.240161\pi$
$457$	7652.54	+	3063.62i	0.783306	+	0.313588i	0.0546834	+	0.998504i	$0.482585\pi$
$458$	333.797	−	7007.26i	0.0340553	−	0.714908i
$459$	−2636.75	−	4566.98i	−0.268132	−	0.464419i
$460$	12983.6	−	16323.8i	1.31600	−	1.65457i
$461$	−11306.1			−1.14225			−0.571125	−	0.820863i	$-0.693493\pi$
$461$	−11306.1			−1.14225			−0.571125	+	0.820863i	$0.693493\pi$
$462$	−510.577	−	24152.5i	−0.0514160	−	2.43220i
$463$	−2163.44	−	15047.0i	−0.217157	−	1.51036i	−0.748462	−	0.663177i	$-0.769208\pi$
$463$	−2163.44	−	15047.0i	−0.217157	−	1.51036i	0.531306	−	0.847180i	$-0.321702\pi$
$464$	−32.5774	−	3.11076i	−0.00325941	−	0.000311236i
$465$	−6605.55	−	27228.4i	−0.658763	−	2.71546i
$466$	28503.1	−	2721.71i	2.83343	−	0.270560i
$467$	−2773.84	−	8014.47i	−0.274856	−	0.794145i	−0.994959	−	0.100278i	$-0.968027\pi$
$467$	−2773.84	−	8014.47i	−0.274856	−	0.794145i	0.720103	−	0.693867i	$-0.244094\pi$
$468$	−9067.21	+	63063.8i	−0.895581	+	6.22890i
$469$	9254.91	+	7683.04i	0.911198	+	0.756439i
$470$	−3857.71	−	4452.04i	−0.378602	−	0.436930i
$471$	−1050.00	−	22042.2i	−0.102720	−	2.15637i
$472$	−3028.00	−	1561.04i	−0.295286	−	0.152231i
$473$	−1155.69	+	3339.15i	−0.112344	+	0.324597i
$474$	3283.80	−	13536.0i	0.318207	−	1.31167i
$475$	−1837.62	+	12780.9i	−0.177507	+	1.23459i
$476$	1560.85	+	3671.92i	0.150297	+	0.353576i
$477$	1396.39	−	3057.67i	0.134038	−	0.293503i
$478$	14336.2	−	13669.6i	1.37181	−	1.30802i
$479$	5307.87	−	7453.86i	0.506311	−	0.711014i	−0.479749	−	0.877406i	$-0.659272\pi$
$479$	5307.87	−	7453.86i	0.506311	−	0.711014i	0.986060	+	0.166392i	$0.0532117\pi$
$480$	19593.4	−	15408.4i	1.86315	−	1.46520i
$481$	13355.0	−	6884.99i	1.26598	−	0.652658i
$482$	20904.9			1.97550
$483$	13643.2	−	13421.8i	1.28528	−	1.26442i
$484$	−5227.78			−0.490963
$485$	5035.23	−	2595.84i	0.471419	−	0.243033i
$486$	13854.9	−	10895.6i	1.29315	−	1.01695i
$487$	−3742.85	+	5256.10i	−0.348264	+	0.489069i	−0.951137	−	0.308768i	$-0.900083\pi$
$487$	−3742.85	+	5256.10i	−0.348264	+	0.489069i	0.602873	+	0.797837i	$0.294023\pi$
$488$	9446.67	−	9007.39i	0.876293	−	0.835543i
$489$	2727.59	−	5972.58i	0.252241	−	0.552330i
$490$	−22923.7	−	1214.41i	−2.11344	−	0.111962i
$491$	380.433	−	2645.97i	0.0349668	−	0.243200i	−0.964840	−	0.262837i	$-0.915342\pi$
$491$	380.433	−	2645.97i	0.0349668	−	0.243200i	0.999807	+	0.0196370i	$0.00625104\pi$
$492$	−5016.91	+	20680.0i	−0.459715	+	1.89497i
$493$	−491.137	+	1419.05i	−0.0448675	+	0.129636i
$494$	−47815.6	−	24650.7i	−4.35491	−	2.24511i
$495$	1287.71	+	27032.4i	0.116926	+	2.45458i
$496$	−48.6278	−	56.1195i	−0.00440212	−	0.00508032i
$497$	−13351.5	+	4939.39i	−1.20503	+	0.445799i
$498$	−1115.82	+	7760.69i	−0.100404	+	0.698323i
$499$	4631.23	+	13381.1i	0.415475	+	1.20044i	0.937645	+	0.347595i	$0.113002\pi$
$499$	4631.23	+	13381.1i	0.415475	+	1.20044i	−0.522169	+	0.852842i	$0.674877\pi$
$500$	−6763.38	+	645.824i	−0.604935	+	0.0577643i
$501$	−1994.03	−	8219.49i	−0.177818	−	0.732974i
$502$	−14571.8	−	1391.44i	−1.29556	−	0.123711i
$503$	365.947	+	2545.21i	0.0324389	+	0.225617i	0.999592	−	0.0285789i	$-0.00909820\pi$
$503$	365.947	+	2545.21i	0.0324389	+	0.225617i	−0.967153	+	0.254196i	$0.918189\pi$
$504$	−21680.0	+	13135.6i	−1.91608	+	1.16092i
$505$	2468.46			0.217515
$506$	10536.8	+	11173.4i	0.925724	+	0.981659i
$507$	20536.4	+	35570.1i	1.79892	+	3.11582i
$508$	548.307	−	11510.4i	0.0478882	−	1.00530i
$509$	12533.6	+	5017.69i	1.09144	+	0.436946i	0.846389	−	0.532565i	$-0.178772\pi$
$509$	12533.6	+	5017.69i	1.09144	+	0.436946i	0.245049	+	0.969511i	$0.421196\pi$
$510$	−4341.80	−	9507.21i	−0.376976	−	0.825463i
$511$	2371.52	+	7487.46i	0.205303	+	0.648191i
$512$	54.6357	−	119.635i	0.00471597	−	0.0103265i
$513$	15000.1	+	43339.8i	1.29097	+	3.73002i
$514$	−29227.4	+	11700.9i	−2.50810	+	1.00409i
$515$	−10093.5	−	9624.15i	−0.863638	−	0.823477i
$516$	13801.5	−	2660.02i	1.17747	−	0.226940i
$517$	2253.88	−	1448.48i	0.191732	−	0.123219i
$518$	14407.3	+	6215.03i	1.22205	+	0.527167i
$519$	25469.8	+	29393.7i	2.15414	+	2.48601i
$520$	−6302.76	+	25980.3i	−0.531528	+	2.19099i
$521$	−6323.59	+	2531.59i	−0.531750	+	0.212881i	−0.621970	−	0.783041i	$-0.713667\pi$
$521$	−6323.59	+	2531.59i	−0.531750	+	0.212881i	0.0902197	+	0.995922i	$0.471243\pi$
$522$	−24588.1	−	4738.97i	−2.06167	−	0.397354i
$523$	−2477.26	−	3478.82i	−0.207118	−	0.290857i	0.697930	−	0.716166i	$-0.254105\pi$
$523$	−2477.26	−	3478.82i	−0.207118	−	0.290857i	−0.905048	+	0.425309i	$0.860165\pi$
$524$	4450.37	+	1306.75i	0.371022	+	0.108942i
$525$	15448.8	+	408.921i	1.28426	+	0.0339939i
$526$	−664.517	−	4621.82i	−0.0550843	−	0.383120i
$527$	−3028.55	+	1561.33i	−0.250333	+	0.129056i
$528$	51.7967	+	89.7146i	0.00426925	+	0.00739456i
$529$	−713.001	+	12146.1i	−0.0586012	+	0.998281i
$530$	1851.04	−	3206.10i	0.151706	−	0.262762i
$531$	7732.24	+	4969.21i	0.631922	+	0.406111i
$532$	−7285.49	−	33925.6i	−0.593733	−	2.76478i
$533$	5922.94	+	12969.4i	0.481334	+	1.05397i
$534$	−22394.4	+	21353.0i	−1.81480	+	1.73041i
$535$	7652.09	−	730.686i	0.618371	−	0.0590473i
$536$	14364.0	+	2768.43i	1.15752	+	0.223094i
$537$	−14478.0	−	11385.6i	−1.16345	−	0.914944i
$538$	32921.0	−	9666.48i	2.63815	−	0.774631i
$539$	2030.43	−	10241.0i	0.162258	−	0.818390i
$540$	50324.4	−	32341.5i	4.01040	−	2.57733i
$541$	−265.564	−	5574.87i	−0.0211044	−	0.443036i	−0.984547	−	0.175121i	$-0.943968\pi$
$541$	−265.564	−	5574.87i	−0.0211044	−	0.443036i	0.963443	−	0.267915i	$-0.0863347\pi$
$542$	8173.50	−	23615.8i	0.647753	−	1.87156i
$543$	18500.5	+	17640.2i	1.46213	+	1.39413i
$544$	−2382.77	−	1873.83i	−0.187795	−	0.147684i
$545$	−8394.15	+	9687.36i	−0.659754	+	0.761396i
$546$	−22661.0	+	60265.9i	−1.77620	+	4.72370i
$547$	10415.9	+	3058.38i	0.814171	+	0.239062i	0.662204	−	0.749323i	$-0.269621\pi$
$547$	10415.9	+	3058.38i	0.814171	+	0.239062i	0.151967	+	0.988386i	$0.451439\pi$
$548$	17939.2	+	1712.98i	1.39840	+	0.133531i
$549$	−27681.8	+	21769.2i	−2.15197	+	1.69233i
$550$	−590.086	+	12387.4i	−0.0457479	+	0.960366i
$551$	6529.67	−	11309.7i	0.504852	−	0.874429i
$552$	6680.53	−	22296.0i	0.515113	−	1.71917i
$553$	2644.63	−	5407.50i	0.203365	−	0.415823i
$554$	−21563.0	−	13857.7i	−1.65365	−	1.06274i
$555$	−23568.9	−	9435.56i	−1.80260	−	0.721653i
$556$	−7325.45	+	10287.2i	−0.558756	+	0.784663i
$557$	−1208.43	−	4981.20i	−0.0919258	−	0.378923i	0.907201	−	0.420697i	$-0.138214\pi$
$557$	−1208.43	−	4981.20i	−0.0919258	−	0.378923i	−0.999127	+	0.0417734i	$0.986699\pi$
$558$	−32958.2	−	46283.4i	−2.50042	−	3.51135i
$559$	6167.11	−	7117.23i	0.466621	−	0.538509i
$560$	88.6588	−	42.7763i	0.00669021	−	0.00322791i
$561$	4560.91	−	1339.20i	0.343248	−	0.100787i
$562$	−21983.3	+	4236.92i	−1.65001	+	0.318014i
$563$	−12317.1	−	6349.91i	−0.922033	−	0.475341i	−0.0692456	−	0.997600i	$-0.522059\pi$
$563$	−12317.1	−	6349.91i	−0.922033	−	0.475341i	−0.852787	+	0.522259i	$0.825090\pi$
$564$	−9472.56	−	4883.44i	−0.707210	−	0.364592i
$565$	−15684.8	+	3022.99i	−1.16790	+	0.225094i
$566$	6238.31	−	1831.73i	0.463278	−	0.136031i
$567$	22068.8	−	10647.8i	1.63457	−	0.788652i
$568$	−11337.6	+	13084.3i	−0.837527	+	0.966557i
$569$	8092.56	+	11364.4i	0.596235	+	0.837295i	0.996879	−	0.0789387i	$-0.0251531\pi$
$569$	8092.56	+	11364.4i	0.596235	+	0.837295i	−0.400644	+	0.916234i	$0.631214\pi$
$570$	21429.5	+	88333.7i	1.57471	+	6.49103i
$571$	−3992.02	+	5606.00i	−0.292576	+	0.410865i	−0.934534	−	0.355875i	$-0.884183\pi$
$571$	−3992.02	+	5606.00i	−0.292576	+	0.410865i	0.641958	+	0.766740i	$0.278122\pi$
$572$	−29627.0	−	11860.9i	−2.16568	−	0.867006i
$573$	−11058.1	−	7106.61i	−0.806210	−	0.518120i
$574$	−6541.43	+	13375.3i	−0.475669	+	0.972606i
$575$	−7460.43	+	6392.77i	−0.541081	+	0.463647i
$576$	25186.1	−	43623.6i	1.82191	−	3.15564i
$577$	748.966	−	15722.7i	0.0540379	−	1.13439i	−0.795187	−	0.606364i	$-0.792628\pi$
$577$	748.966	−	15722.7i	0.0540379	−	1.13439i	0.849225	−	0.528031i	$-0.177069\pi$
$578$	16666.2	−	13106.4i	1.19934	−	0.943175i
$579$	−9402.00	−	897.782i	−0.674842	−	0.0644396i
$580$	−16344.1	−	4799.05i	−1.17009	−	0.343568i
$581$	−1192.59	+	3171.63i	−0.0851582	+	0.226474i
$582$	10865.8	−	12539.8i	0.773884	−	0.893110i
$583$	1323.49	+	1040.80i	0.0940195	+	0.0739378i
$584$	6912.90	+	6591.44i	0.489825	+	0.467047i
$585$	23590.9	−	68161.3i	1.66729	−	4.81731i
$586$	−346.846	−	7281.20i	−0.0244507	−	0.513283i
$587$	−17491.4	+	11241.0i	−1.22989	+	0.790404i	−0.983874	−	0.178861i	$-0.942759\pi$
$587$	−17491.4	+	11241.0i	−1.22989	+	0.790404i	−0.246019	+	0.969265i	$0.579122\pi$
$588$	−39317.3	+	13373.8i	−2.75752	+	0.937967i
$589$	28432.3	−	8348.47i	1.98902	−	0.584029i
$590$	7957.04	+	6257.49i	0.555231	+	0.436638i
$591$	−11885.3	−	2290.70i	−0.827232	−	0.159436i
$592$	−66.9797	+	6.39578i	−0.00465008	+	0.000444029i
$593$	16511.1	−	15743.3i	1.14339	−	1.09022i	0.148537	−	0.988907i	$-0.452544\pi$
$593$	16511.1	−	15743.3i	1.14339	−	1.09022i	0.994854	−	0.101315i	$-0.0323049\pi$
$594$	18298.1	+	40067.2i	1.26394	+	2.76764i
$595$	−948.384	−	4416.25i	−0.0653445	−	0.304283i
$596$	7688.05	+	4940.81i	0.528381	+	0.339570i
$597$	−11183.4	+	19370.2i	−0.766676	+	1.32792i
$598$	−15003.0	−	38083.4i	−1.02595	−	2.60426i
$599$	−6176.22	−	10697.5i	−0.421292	−	0.729698i	0.574775	−	0.818312i	$-0.305090\pi$
$599$	−6176.22	−	10697.5i	−0.421292	−	0.729698i	−0.996066	+	0.0886134i	$0.971756\pi$
$600$	16705.3	−	8612.18i	1.13665	−	0.585985i
$601$	−2754.84	−	19160.3i	−0.186975	−	1.30044i	−0.839784	−	0.542920i	$-0.817319\pi$
$601$	−2754.84	−	19160.3i	−0.186975	−	1.30044i	0.652809	−	0.757523i	$-0.273590\pi$
$602$	9831.03	+	260.223i	0.665586	+	0.0176178i
$603$	−37868.7	−	11119.3i	−2.55743	−	0.750930i
$604$	−180.995	−	254.173i	−0.0121930	−	0.0171227i
$605$	5811.39	+	1120.05i	0.390523	+	0.0752671i
$606$	6712.12	−	2687.13i	0.449936	−	0.180127i
$607$	−5395.56	+	22240.8i	−0.360789	+	1.48719i	0.445290	+	0.895386i	$0.353101\pi$
$607$	−5395.56	+	22240.8i	−0.360789	+	1.48719i	−0.806079	+	0.591808i	$0.798415\pi$
$608$	17263.8	+	19923.5i	1.15154	+	1.32895i
$609$	−14351.7	−	6191.04i	−0.954942	−	0.411943i
$610$	−32628.1	+	20968.8i	−2.16569	+	1.39181i
$611$	−7011.53	+	1351.36i	−0.464249	+	0.0894766i
$612$	−9474.81	−	9034.22i	−0.625811	−	0.596710i
$613$	−1584.93	+	634.512i	−0.104429	+	0.0418070i	−0.423289	−	0.905995i	$-0.639124\pi$
$613$	−1584.93	+	634.512i	−0.104429	+	0.0418070i	0.318860	+	0.947802i	$0.396700\pi$
$614$	−8372.18	−	24189.8i	−0.550283	−	1.58994i
$615$	10007.7	−	21913.7i	0.656176	−	1.43683i
$616$	−3833.86	−	12104.4i	−0.250764	−	0.791723i
$617$	−3033.21	−	6641.80i	−0.197913	−	0.433369i	0.784490	−	0.620141i	$-0.212925\pi$
$617$	−3033.21	−	6641.80i	−0.197913	−	0.433369i	−0.982403	+	0.186772i	$0.940197\pi$
$618$	−37922.5	−	15181.9i	−2.46839	−	0.988195i
$619$	−863.363	+	18124.2i	−0.0560605	+	1.17686i	0.779118	+	0.626877i	$0.215667\pi$
$619$	−863.363	+	18124.2i	−0.0560605	+	1.17686i	−0.835179	+	0.549979i	$0.814636\pi$
$620$	−19325.8	−	33473.2i	−1.25184	−	2.16825i
$621$	−13147.9	+	32323.9i	−0.849611	+	2.08875i
$622$	−31282.4			−2.01658
$623$	−11437.1	+	6929.59i	−0.735505	+	0.445631i
$624$	−39.2927	−	273.286i	−0.00252078	−	0.0175324i
$625$	18740.1	+	1789.46i	1.19936	+	0.114525i
$626$	7804.11	+	32169.0i	0.498267	+	2.05388i
$627$	−41152.5	+	3929.58i	−2.62117	+	0.250291i
$628$	−9956.58	−	28767.6i	−0.632661	−	1.82795i
$629$	−439.382	+	3055.97i	−0.0278526	+	0.193719i
$630$	70643.1	−	26134.4i	4.46744	−	1.65273i
$631$	−6148.17	−	7095.37i	−0.387884	−	0.447642i	0.527904	−	0.849304i	$-0.322978\pi$
$631$	−6148.17	−	7095.37i	−0.387884	−	0.447642i	−0.915788	+	0.401662i	$0.868433\pi$
$632$	−348.333	−	7312.40i	−0.0219239	−	0.460240i
$633$	−18319.2	−	9444.21i	−1.15027	−	0.593007i
$634$	−7148.94	+	20655.5i	−0.447825	+	1.29390i
$635$	−3075.62	+	12677.9i	−0.192208	+	0.792294i
$636$	953.150	−	6629.30i	0.0594259	−	0.413316i
$637$	−15168.1	+	23327.9i	−0.943460	+	1.45100i
$638$	5210.40	−	11409.2i	0.323326	−	0.707985i
$639$	33806.0	−	32234.0i	2.09287	−	1.99555i
$640$	19833.1	−	27851.7i	1.22496	−	1.72021i
$641$	3551.33	−	2792.79i	0.218828	−	0.172088i	−0.502727	−	0.864445i	$-0.667670\pi$
$641$	3551.33	−	2792.79i	0.218828	−	0.172088i	0.721555	+	0.692357i	$0.243428\pi$
$642$	20011.8	−	10316.8i	1.23022	−	0.634223i
$643$	−100.701			−0.00617614			−0.00308807	−	0.999995i	$-0.500983\pi$
$643$	−100.701			−0.00617614			−0.00308807	+	0.999995i	$0.500983\pi$
$644$	12842.2	−	23068.0i	0.785797	−	1.41150i
$645$	−15912.1			−0.971380
$646$	9825.12	−	5065.20i	0.598397	−	0.308495i
$647$	10837.0	−	8522.29i	0.658493	−	0.517845i	−0.232073	−	0.972698i	$-0.574551\pi$
$647$	10837.0	−	8522.29i	0.658493	−	0.517845i	0.890566	+	0.454854i	$0.150308\pi$
$648$	17285.5	−	24274.0i	1.04790	−	1.47157i
$649$	−3331.97	+	3177.03i	−0.201528	+	0.192156i
$650$	13730.4	−	30065.4i	0.828541	−	1.81425i
$651$	−13874.2	−	32639.4i	−0.835291	−	1.96504i
$652$	1289.06	−	8965.59i	0.0774285	−	0.538527i
$653$	−299.824	+	1235.89i	−0.0179679	+	0.0740645i	−0.980090	−	0.198555i	$-0.936375\pi$
$653$	−299.824	+	1235.89i	−0.0179679	+	0.0740645i	0.962122	+	0.272620i	$0.0878902\pi$
$654$	−12279.4	+	35479.1i	−0.734196	+	2.12132i
$655$	−4667.22	−	2406.12i	−0.278418	−	0.143534i
$656$	−3.03800	−	63.7755i	−0.000180814	−	0.00379575i
$657$	−16876.1	−	19476.1i	−1.00213	−	1.15652i
$658$	−5737.40	−	4762.95i	−0.339919	−	0.282187i
$659$	−4278.15	+	29755.2i	−0.252888	+	1.75887i	0.327799	+	0.944748i	$0.393693\pi$
$659$	−4278.15	+	29755.2i	−0.252888	+	1.75887i	−0.580687	+	0.814127i	$0.697216\pi$
$660$	17636.1	+	50956.0i	1.04012	+	3.00524i
$661$	33371.8	−	3186.62i	1.96371	−	0.187512i	0.966187	−	0.257844i	$-0.0830119\pi$
$661$	33371.8	−	3186.62i	1.96371	−	0.187512i	0.997524	+	0.0703320i	$0.0224059\pi$
$662$	4940.57	+	20365.3i	0.290062	+	1.19565i
$663$	−12611.5	−	1204.26i	−0.738750	−	0.0705421i
$664$	586.458	+	4078.91i	0.0342756	+	0.238392i
$665$	830.236	+	39273.8i	0.0484138	+	2.29019i
$666$	−51484.0			−2.99544
$667$	9407.87	−	3198.08i	0.546138	−	0.185653i
$668$	−5833.90	−	10104.6i	−0.337905	−	0.585268i
$669$	2289.64	−	48065.4i	0.132321	−	2.77775i
$670$	−40353.4	−	16155.1i	−2.32685	−	0.931529i
$671$	−7327.73	−	16045.5i	−0.421586	−	0.923144i
$672$	21285.9	−	23290.4i	1.22191	−	1.33697i
$673$	505.031	−	1105.86i	0.0289265	−	0.0633401i	−0.894617	−	0.446833i	$-0.852552\pi$
$673$	505.031	−	1105.86i	0.0289265	−	0.0633401i	0.923544	+	0.383493i	$0.125279\pi$
$674$	12558.2	+	36284.4i	0.717689	+	2.07363i
$675$	−26159.5	+	10472.7i	−1.49167	+	0.597175i
$676$	41007.1	+	39100.2i	2.33313	+	2.22463i
$677$	5904.47	−	1137.99i	0.335195	−	0.0646036i	−0.0188765	−	0.999822i	$-0.506009\pi$
$677$	5904.47	−	1137.99i	0.335195	−	0.0646036i	0.354072	+	0.935218i	$0.384797\pi$
$678$	−39358.5	+	25294.1i	−2.22943	+	1.43277i
$679$	5751.95	−	4282.00i	0.325095	−	0.242015i
$680$	−3597.33	−	4151.54i	−0.202869	−	0.234124i
$681$	−5866.09	+	24180.4i	−0.330087	+	1.36064i
$682$	26421.5	−	10577.6i	1.48348	−	0.593895i
$683$	7612.77	+	1467.24i	0.426493	+	0.0821998i	0.397981	−	0.917394i	$-0.369711\pi$
$683$	7612.77	+	1467.24i	0.426493	+	0.0821998i	0.0285120	+	0.999593i	$0.490923\pi$
$684$	66041.8	+	92742.8i	3.69177	+	5.18437i
$685$	−19574.8	−	5747.68i	−1.09185	−	0.320595i
$686$	−28879.0	+	3219.07i	−1.60729	+	0.179161i
$687$	2044.74	+	14221.5i	0.113554	+	0.789786i
$688$	−37.4839	+	19.3243i	−0.00207712	+	0.00107083i
$689$	−2243.72	−	3886.23i	−0.124062	−	0.214882i
$690$	−32030.0	+	61296.8i	−1.76719	+	3.38193i
$691$	6808.62	−	11792.9i	0.374837	−	0.649236i	−0.615466	−	0.788164i	$-0.711032\pi$
$691$	6808.62	−	11792.9i	0.374837	−	0.649236i	0.990303	+	0.138927i	$0.0443654\pi$
$692$	45136.7	+	29007.6i	2.47954	+	1.59350i
$693$	7192.62	+	33493.2i	0.394264	+	1.83593i
$694$	11492.3	+	25164.6i	0.628589	+	1.37642i
$695$	10347.3	−	9866.09i	0.564739	−	0.538478i
$696$	−18922.5	+	1806.88i	−1.03054	+	0.0984045i
$697$	−2876.76	−	554.450i	−0.156334	−	0.0301310i
$698$	32785.7	+	25782.9i	1.77787	+	1.39814i
$699$	−56266.8	+	16521.4i	−3.04464	+	0.893987i
$700$	20607.4	−	5462.95i	1.11270	−	0.294972i
$701$	11377.1	−	7311.64i	0.612993	−	0.393947i	−0.196985	−	0.980406i	$-0.563115\pi$
$701$	11377.1	−	7311.64i	0.612993	−	0.393947i	0.809978	+	0.586460i	$0.199479\pi$
$702$	−5585.91	−	117263.i	−0.300323	−	6.30455i
$703$	8781.86	−	25373.5i	0.471144	−	1.36128i
$704$	18260.6	+	17411.4i	0.977586	+	0.932127i
$705$	9483.76	+	7458.11i	0.506637	+	0.398424i
$706$	15911.2	−	18362.5i	0.848193	−	0.978867i
$707$	3082.72	−	509.946i	0.163985	−	0.0271266i
$708$	17571.4	+	5159.43i	0.932731	+	0.273875i
$709$	−34976.3	−	3339.83i	−1.85270	−	0.176911i	−0.891544	−	0.452934i	$-0.850377\pi$
$709$	−34976.3	−	3339.83i	−1.85270	−	0.176911i	−0.961151	+	0.276023i	$0.910983\pi$
$710$	40437.9	−	31800.7i	2.13748	−	1.68093i
$711$	−939.804	+	19728.9i	−0.0495716	+	1.04064i
$712$	−8131.58	+	14084.3i	−0.428011	+	0.741337i
$713$	20457.3	+	9479.32i	1.07452	+	0.497901i
$714$	−7386.26	−	10976.1i	−0.387148	−	0.575306i
$715$	30393.2	+	19532.5i	1.58971	+	1.02164i
$716$	−23588.6	−	9443.44i	−1.23121	−	0.492902i
$717$	−23532.8	+	33047.3i	−1.22573	+	1.72130i
$718$	−6265.41	−	25826.4i	−0.325659	−	1.34238i
$719$	13048.7	+	18324.4i	0.676824	+	0.950466i	0.999991	+	0.00412407i	$0.00131274\pi$
$719$	13048.7	+	18324.4i	0.676824	+	0.950466i	−0.323168	+	0.946342i	$0.604748\pi$
$720$	−211.517	+	244.104i	−0.0109483	+	0.0126350i
$721$	−14593.4	−	9933.88i	−0.753796	−	0.513116i
$722$	−62135.1	+	18244.5i	−3.20281	+	0.940430i
$723$	−42041.2	+	8102.78i	−2.16256	+	0.416799i
$724$	31343.9	+	16158.9i	1.60896	+	0.829476i
$725$	7131.76	+	3676.68i	0.365333	+	0.188342i
$726$	17021.3	−	3280.59i	0.870138	−	0.167705i
$727$	−16404.5	+	4816.80i	−0.836878	+	0.245730i	−0.671969	−	0.740579i	$-0.734551\pi$
$727$	−16404.5	+	4816.80i	−0.836878	+	0.245730i	−0.164909	+	0.986309i	$0.552733\pi$
$728$	−2504.02	+	33747.4i	−0.127480	+	1.71808i
$729$	−246.933	+	284.976i	−0.0125455	+	0.0144783i
$730$	−16463.3	−	23119.4i	−0.834703	−	1.17218i
$731$	456.215	+	1880.54i	0.0230831	+	0.0951497i
$732$	−40700.5	+	57155.9i	−2.05510	+	2.88599i
$733$	3034.39	+	1214.79i	0.152903	+	0.0612131i	0.446852	−	0.894608i	$-0.352545\pi$
$733$	3034.39	+	1214.79i	0.152903	+	0.0612131i	−0.293949	+	0.955821i	$0.594969\pi$
$734$	21077.6	+	13545.8i	1.05993	+	0.681176i
$735$	46571.9	−	6443.01i	2.33718	−	0.323339i
$736$	−110.672	+	20058.4i	−0.00554272	+	1.00457i
$737$	9884.46	−	17120.4i	0.494028	−	0.855682i
$738$	2324.59	−	48799.1i	0.115947	−	2.43404i
$739$	−2187.93	+	1720.61i	−0.108910	+	0.0856476i	−0.671129	−	0.741341i	$-0.734190\pi$
$739$	−2187.93	+	1720.61i	−0.108910	+	0.0856476i	0.562219	+	0.826988i	$0.309948\pi$
$740$	−34863.7	−	3329.08i	−1.73191	−	0.165378i
$741$	105715.	+	31040.8i	5.24095	+	1.53888i
$742$	1649.33	−	4386.31i	0.0816021	−	0.217017i
$743$	13396.1	−	15459.9i	0.661445	−	0.763348i	−0.321568	−	0.946887i	$-0.604210\pi$
$743$	13396.1	−	15459.9i	0.661445	−	0.763348i	0.983013	+	0.183539i	$0.0587552\pi$
$744$	−33903.9	−	26662.3i	−1.67067	−	1.31383i
$745$	−7487.74	−	7139.55i	−0.368228	−	0.351104i
$746$	9759.31	−	28197.7i	0.478973	−	1.38390i
$747$	−529.020	−	11105.5i	−0.0259114	−	0.543948i
$748$	5516.49	−	3545.23i	0.269656	−	0.173298i
$749$	9405.30	−	2493.31i	0.458828	−	0.121634i
$750$	21615.8	−	6346.99i	1.05240	−	0.309012i
$751$	15768.3	+	12400.3i	0.766169	+	0.602522i	0.922864	−	0.385125i	$-0.125842\pi$
$751$	15768.3	+	12400.3i	0.766169	+	0.602522i	−0.156695	+	0.987647i	$0.550084\pi$
$752$	31.3981	+	6.05149i	0.00152257	+	0.000293451i
$753$	29844.3	−	2849.78i	1.44434	−	0.137918i
$754$	−24193.4	+	23068.4i	−1.16853	+	1.11419i
$755$	146.744	+	321.326i	0.00707361	+	0.0154891i
$756$	56165.9	−	50785.7i	2.70203	−	2.44320i
$757$	−29349.0	−	18861.4i	−1.40912	−	0.905588i	−0.409146	−	0.912469i	$-0.634173\pi$
$757$	−29349.0	−	18861.4i	−1.40912	−	0.905588i	−0.999976	+	0.00688052i	$0.997810\pi$
$758$	24278.5	−	42051.5i	1.16337	−	2.01501i
$759$	−25521.0	−	18386.5i	−1.22049	−	0.879298i
$760$	23886.8	+	41373.1i	1.14009	+	1.97469i
$761$	−31665.9	+	16324.9i	−1.50839	+	0.777630i	−0.996672	−	0.0815213i	$-0.974022\pi$
$761$	−31665.9	+	16324.9i	−1.50839	+	0.777630i	−0.511721	+	0.859152i	$0.670992\pi$
$762$	5437.86	+	37821.2i	0.258521	+	1.79805i
$763$	−8481.70	+	13832.1i	−0.402435	+	0.656297i
$764$	−17398.9	−	5108.77i	−0.823912	−	0.241923i
$765$	8596.96	+	12072.7i	0.406305	+	0.570576i
$766$	44699.6	+	8615.14i	2.10844	+	0.406368i
$767$	11391.3	−	4560.37i	0.536264	−	0.214688i
$768$	8963.59	−	36948.4i	0.421153	−	1.73602i
$769$	−21596.2	−	24923.4i	−1.01272	−	1.16874i	−0.985598	−	0.169107i	$-0.945912\pi$
$769$	−21596.2	−	24923.4i	−1.01272	−	1.16874i	−0.0271203	−	0.999632i	$-0.508634\pi$
$770$	4379.29	+	37473.4i	0.204959	+	1.75383i
$771$	54243.0	−	34859.9i	2.53374	−	1.62834i
$772$	−12793.7	+	2465.79i	−0.596446	+	0.114956i
$773$	−29065.8	−	27714.2i	−1.35242	−	1.28953i	−0.922149	−	0.386835i	$-0.873568\pi$
$773$	−29065.8	−	27714.2i	−1.35242	−	1.28953i	−0.430275	−	0.902698i	$-0.641583\pi$
$774$	−29957.2	+	11993.1i	−1.39120	+	0.556953i
$775$	5954.72	+	17205.0i	0.276000	+	0.797449i
$776$	3622.74	−	7932.70i	0.167589	−	0.366968i
$777$	−31383.1	−	6914.56i	−1.44898	−	0.319252i
$778$	2630.09	+	5759.08i	0.121199	+	0.265390i
$779$	23653.8	+	9469.54i	1.08791	+	0.435535i
$780$	6838.08	−	143549.i	0.313901	−	6.58959i
$781$	11698.5	+	20262.4i	0.535985	+	0.928354i
$782$	8162.56	+	2027.97i	0.373264	+	0.0927365i
$783$	28498.7			1.30072
$784$	101.884	−	71.7363i	0.00464121	−	0.00326787i
$785$	4904.61	+	34112.3i	0.222998	+	1.55098i
$786$	−15310.2	−	1461.94i	−0.694777	−	0.0663432i
$787$	2738.22	+	11287.1i	0.124024	+	0.511235i	0.999603	+	0.0281601i	$0.00896483\pi$
$787$	2738.22	+	11287.1i	0.124024	+	0.511235i	−0.875579	+	0.483075i	$0.839520\pi$
$788$	−16622.0	+	1587.21i	−0.751440	+	0.0717538i
$789$	3127.82	+	9037.23i	0.141132	+	0.407774i
$790$	−3095.76	+	21531.5i	−0.139420	+	0.969691i
$791$	−18963.3	+	7015.46i	−0.852410	+	0.315349i
$792$	27282.4	+	31485.6i	1.22404	+	1.41262i
$793$	2236.96	+	46959.6i	0.100172	+	2.10288i
$794$	39620.9	+	20426.0i	1.77090	+	0.912962i
$795$	−2479.88	+	7165.16i	−0.110632	+	0.319650i
$796$	−7274.41	+	29985.5i	−0.323913	+	1.33519i
$797$	−973.836	+	6773.18i	−0.0432811	+	0.301027i	0.956670	+	0.291173i	$0.0940456\pi$
$797$	−973.836	+	6773.18i	−0.0432811	+	0.301027i	−0.999951	+	0.00985343i	$0.996864\pi$
$798$	45010.4	+	105888.i	1.99668	+	4.69723i
$799$	609.513	−	1334.65i	0.0269875	−	0.0590944i
$800$	−11722.5	+	11177.4i	−0.518066	+	0.493975i
$801$	25451.8	−	35742.0i	1.12272	−	1.57663i
$802$	51887.7	−	40805.0i	2.28456	−	1.79660i
$803$	11473.3	−	5914.92i	0.504216	−	0.259941i
$804$	−78636.6			−3.44938
$805$	−19218.2	+	22891.8i	−0.841430	+	1.00227i
$806$	−75851.9			−3.31485
$807$	−62459.7	+	32200.2i	−2.72452	+	1.40459i
$808$	2987.00	−	2349.00i	0.130052	−	0.102274i
$809$	4255.74	−	5976.35i	0.184949	−	0.259725i	−0.711683	−	0.702501i	$-0.752067\pi$
$809$	4255.74	−	5976.35i	0.184949	−	0.259725i	0.896632	+	0.442776i	$0.146006\pi$
$810$	−64084.7	+	61104.6i	−2.77988	+	2.65061i
$811$	−68.7673	+	150.579i	−0.00297749	+	0.00651980i	−0.911115	−	0.412152i	$-0.864777\pi$
$811$	−68.7673	+	150.579i	−0.00297749	+	0.00651980i	0.908137	+	0.418672i	$0.137504\pi$
$812$	−21402.5	−	2616.83i	−0.924978	−	0.113094i
$813$	−7283.96	+	50661.1i	−0.314219	+	2.18544i
$814$	6079.73	−	25061.0i	0.261787	−	1.07910i
$815$	−3353.84	+	9690.29i	−0.144147	+	0.416486i
$816$	50.4256	+	25.9962i	0.00216329	+	0.00111526i
$817$	−800.756	−	16809.9i	−0.0342900	−	0.719835i
$818$	−14198.9	−	16386.4i	−0.606912	−	0.700414i
$819$	15380.2	−	89996.2i	0.656200	−	3.83971i
$820$	4729.63	−	32895.3i	0.201422	−	1.40092i
$821$	−12227.1	−	35327.9i	−0.519768	−	1.50177i	−0.833642	−	0.552306i	$-0.813748\pi$
$821$	−12227.1	−	35327.9i	−0.519768	−	1.50177i	0.313874	−	0.949465i	$-0.398373\pi$
$822$	−59483.7	+	5680.01i	−2.52401	+	0.241013i
$823$	−2557.73	−	10543.1i	−0.108331	−	0.446548i	0.891650	−	0.452726i	$-0.149549\pi$
$823$	−2557.73	−	10543.1i	−0.108331	−	0.446548i	−0.999981	+	0.00617827i	$0.998033\pi$
$824$	−21372.2	−	2040.80i	−0.903564	−	0.0862799i
$825$	−3614.69	−	25140.7i	−0.152542	−	1.06095i
$826$	11229.8	+	6170.81i	0.473044	+	0.259939i
$827$	27841.2			1.17066			0.585329	−	0.810796i	$-0.300966\pi$
$827$	27841.2			1.17066			0.585329	+	0.810796i	$0.300966\pi$
$828$	−8710.31	+	86190.2i	−0.365585	+	3.61753i
$829$	−15377.0	−	26633.8i	−0.644230	−	1.11584i	−0.984479	−	0.175504i	$-0.943845\pi$
$829$	−15377.0	−	26633.8i	−0.644230	−	1.11584i	0.340249	−	0.940335i	$-0.389489\pi$
$830$	582.631	−	12230.9i	0.0243656	−	0.511496i
$831$	48735.9	+	19510.9i	2.03445	+	0.814472i
$832$	−27934.8	−	61168.7i	−1.16402	−	2.54885i
$833$	−2096.71	−	5319.27i	−0.0872109	−	0.221251i
$834$	17395.7	−	38091.3i	0.722259	−	1.58153i
$835$	4320.26	+	12482.6i	0.179052	+	0.517338i
$836$	−52943.5	+	21195.4i	−2.19030	+	0.876864i
$837$	46800.7	+	44624.4i	1.93270	+	1.84282i
$838$	4680.33	−	902.059i	0.192935	−	0.0371851i
$839$	37097.0	−	23840.8i	1.52650	−	0.981021i	0.535891	−	0.844287i	$-0.319976\pi$
$839$	37097.0	−	23840.8i	1.52650	−	0.981021i	0.990608	−	0.136734i	$-0.0436605\pi$
$840$	45864.4	−	34143.4i	1.88389	−	1.40245i
$841$	10657.2	+	12299.0i	0.436966	+	0.504286i
$842$	8461.97	−	34880.7i	0.346341	−	1.42764i
$843$	42567.6	−	17041.5i	1.73915	−	0.696252i
$844$	−27918.4	−	5380.84i	−1.13862	−	0.219450i
$845$	−37207.7	−	52250.9i	−1.51477	−	2.12720i
$846$	23475.9	+	6893.16i	0.954042	+	0.280132i
$847$	7488.89	+	198.227i	0.303803	+	0.00804153i
$848$	2.85982	+	19.8905i	0.000115810	+	0.000805474i
$849$	−11835.7	+	6101.72i	−0.478445	+	0.246656i
$850$	3395.79	+	5881.67i	0.137029	+	0.237341i
$851$	17748.8	−	10117.1i	0.714949	−	0.407533i
$852$	46534.1	−	80599.5i	1.87117	−	3.24095i
$853$	12791.5	+	8220.59i	0.513449	+	0.329974i	0.771576	−	0.636137i	$-0.219469\pi$
$853$	12791.5	+	8220.59i	0.513449	+	0.329974i	−0.258127	+	0.966111i	$0.583105\pi$
$854$	−36415.5	+	32927.2i	−1.45915	+	1.31937i
$855$	−53544.3	−	117246.i	−2.14173	−	4.68973i
$856$	8564.20	−	8165.95i	0.341961	−	0.326059i
$857$	−37974.9	+	3626.16i	−1.51365	+	0.144536i	−0.818574	−	0.574401i	$-0.805235\pi$
$857$	−37974.9	+	3626.16i	−1.51365	+	0.144536i	−0.695075	+	0.718937i	$0.744629\pi$
$858$	103907.	+	20026.4i	4.13440	+	0.796840i
$859$	11066.5	+	8702.77i	0.439561	+	0.345675i	0.813285	−	0.581865i	$-0.197677\pi$
$859$	11066.5	+	8702.77i	0.439561	+	0.345675i	−0.373724	+	0.927540i	$0.621919\pi$
$860$	−21061.8	+	6184.32i	−0.835120	+	0.245213i
$861$	7970.96	−	29434.2i	0.315505	−	1.16506i
$862$	34934.4	−	22451.0i	1.38036	−	0.887104i
$863$	577.105	+	12114.9i	0.0227635	+	0.477864i	0.981252	+	0.192732i	$0.0617347\pi$
$863$	577.105	+	12114.9i	0.0227635	+	0.477864i	−0.958488	+	0.285133i	$0.907962\pi$
$864$	−18816.1	+	54365.4i	−0.740897	+	2.14068i
$865$	−43960.6	−	41916.4i	−1.72798	−	1.64763i
$866$	50657.1	+	39837.2i	1.98776	+	1.56319i
$867$	−28436.8	+	32817.8i	−1.11391	+	1.28552i
$868$	−31049.9	−	37810.3i	−1.21417	−	1.47853i
$869$	−9492.52	−	2787.25i	−0.370554	−	0.108805i
$870$	56226.7	+	5369.00i	2.19111	+	0.209226i
$871$	−41415.6	+	32569.6i	−1.61115	+	1.26702i
$872$	−938.916	+	19710.3i	−0.0364630	+	0.765452i
$873$	−11764.4	+	20376.5i	−0.456086	+	0.789965i
$874$	−66367.1	−	30752.5i	−2.56854	−	1.19018i
$875$	9713.15	−	668.700i	0.375274	−	0.0258357i
$876$	−43195.4	−	27760.0i	−1.66602	−	1.07069i
$877$	−17274.3	−	6915.59i	−0.665122	−	0.266275i	0.0144367	−	0.999896i	$-0.495404\pi$
$877$	−17274.3	−	6915.59i	−0.665122	−	0.266275i	−0.679559	+	0.733621i	$0.737829\pi$
$878$	−22647.9	+	31804.6i	−0.870536	+	1.22250i
$879$	3519.74	+	14508.6i	0.135060	+	0.556726i
$880$	−93.8451	−	131.787i	−0.00359491	−	0.00504834i
$881$	17562.8	−	20268.6i	0.671632	−	0.775104i	−0.312999	−	0.949753i	$-0.601334\pi$
$881$	17562.8	−	20268.6i	0.671632	−	0.775104i	0.984631	+	0.174649i	$0.0558792\pi$
$882$	82823.1	−	47231.5i	3.16190	−	1.80314i
$883$	14092.0	−	4137.79i	0.537072	−	0.157698i	−0.00193793	−	0.999998i	$-0.500617\pi$
$883$	14092.0	−	4137.79i	0.537072	−	0.157698i	0.539010	+	0.842300i	$0.318799\pi$
$884$	−17161.1	+	3307.53i	−0.652929	+	0.125842i
$885$	−18427.6	−	9500.08i	−0.699928	−	0.360838i
$886$	−55669.9	−	28699.8i	−2.11091	−	1.08825i
$887$	−1596.87	+	307.771i	−0.0604482	+	0.0116504i	−0.219386	−	0.975638i	$-0.570405\pi$
$887$	−1596.87	+	307.771i	−0.0604482	+	0.0116504i	0.158937	+	0.987289i	$0.449193\pi$
$888$	−37498.9	+	11010.7i	−1.41709	+	0.416096i
$889$	−1221.91	+	16468.0i	−0.0460986	+	0.621283i
$890$	31646.0	−	36521.4i	1.19188	−	1.37551i
$891$	−23359.8	−	32804.2i	−0.878318	−	1.23343i
$892$	−15650.2	−	64510.9i	−0.587451	−	2.42151i
$893$	−7401.65	+	10394.2i	−0.277365	+	0.389504i
$894$	−28132.3	−	11262.5i	−1.05244	−	0.421335i
$895$	24198.6	+	15551.5i	0.903767	+	0.580816i
$896$	19014.7	−	38879.6i	0.708969	−	1.44964i
$897$	44933.4	+	70773.2i	1.67255	+	2.63439i
$898$	−6155.09	+	10660.9i	−0.228728	+	0.396169i
$899$	876.156	−	18392.8i	0.0325044	−	0.682351i
$900$	−54986.2	+	43241.6i	−2.03653	+	1.60154i
$901$	917.899	+	87.6488i	0.0339397	+	0.00324085i
$902$	23479.6	+	6894.22i	0.866722	+	0.254493i
$903$	−19871.8	+	3287.20i	−0.732326	+	0.121142i
$904$	−16102.9	+	18583.7i	−0.592450	+	0.683723i
$905$	−31380.9	−	24678.2i	−1.15264	−	0.906444i
$906$	748.810	+	713.989i	0.0274587	+	0.0261818i
$907$	−9398.39	+	27154.9i	−0.344067	+	0.994115i	0.631683	+	0.775227i	$0.282364\pi$
$907$	−9398.39	+	27154.9i	−0.344067	+	0.994115i	−0.975750	+	0.218889i	$0.929757\pi$
$908$	1633.23	+	34285.8i	0.0596925	+	1.25310i
$909$	−8624.89	+	5542.88i	−0.314708	+	0.202250i
$910$	26283.7	−	97057.5i	0.957470	−	3.53563i
$911$	−11659.2	+	3423.44i	−0.424024	+	0.124505i	−0.486781	−	0.873524i	$-0.661829\pi$
$911$	−11659.2	+	3423.44i	−0.424024	+	0.124505i	0.0627567	+	0.998029i	$0.480011\pi$
$912$	−387.827	−	304.991i	−0.0140814	−	0.0110737i
$913$	5468.32	+	1053.93i	0.198220	+	0.0382038i
$914$	−37535.0	+	3584.16i	−1.35837	+	0.129708i
$915$	57489.8	−	54816.4i	2.07711	−	1.98052i
$916$	8233.72	+	18029.3i	0.296997	+	0.650334i
$917$	−6325.69	−	2040.69i	−0.227800	−	0.0734891i
$918$	20293.0	+	13041.5i	0.729597	+	0.468883i
$919$	913.796	−	1582.74i	0.0328002	−	0.0568116i	−0.849159	−	0.528137i	$-0.822891\pi$
$919$	913.796	−	1582.74i	0.0328002	−	0.0568116i	0.881960	+	0.471325i	$0.156224\pi$
$920$	−7076.10	+	35654.6i	−0.253578	+	1.27771i
$921$	26213.1	+	45402.4i	0.937839	+	1.62439i
$922$	45968.0	−	23698.2i	1.64195	−	0.846483i
$923$	−8874.39	−	61722.7i	−0.316473	−	2.20111i
$924$	32551.4	+	59992.7i	1.15894	+	2.13595i
$925$	15828.6	+	4647.71i	0.562641	+	0.165206i
$926$	40335.4	+	56643.2i	1.43143	+	2.01016i
$927$	56877.9	+	10962.3i	2.01523	+	0.388403i
$928$	15208.2	−	6088.44i	0.537966	−	0.215369i
$929$	−7628.49	+	31445.1i	−0.269411	+	1.11053i	0.662854	+	0.748749i	$0.269345\pi$
$929$	−7628.49	+	31445.1i	−0.269411	+	1.11053i	−0.932264	+	0.361778i	$0.882170\pi$
$930$	83928.9	+	96859.1i	2.95929	+	3.41520i
$931$	9150.19	+	48875.3i	0.322111	+	1.72054i
$932$	−68055.5	+	43736.6i	−2.39188	+	1.53717i
$933$	62911.1	−	12125.1i	2.20752	−	0.425465i
$934$	28076.5	+	26770.9i	0.983611	+	0.937871i
$935$	−6891.89	+	2759.10i	−0.241058	+	0.0965050i
$936$	−36316.2	−	104929.i	−1.26820	−	3.66422i
$937$	−8530.76	+	18679.8i	−0.297426	+	0.651272i	−0.998061	−	0.0622484i	$-0.980173\pi$
$937$	−8530.76	+	18679.8i	−0.297426	+	0.651272i	0.700635	+	0.713520i	$0.252900\pi$
$938$	−53732.4	−	11838.7i	−1.87039	−	0.412099i
$939$	−28163.4	−	61669.2i	−0.978783	−	2.14324i
$940$	15451.6	+	6185.90i	0.536146	+	0.214640i
$941$	1518.56	−	31878.6i	0.0526076	−	1.10437i	−0.806059	−	0.591835i	$-0.798404\pi$
$941$	1518.56	−	31878.6i	0.0526076	−	1.10437i	0.858667	−	0.512535i	$-0.171293\pi$
$942$	50470.5	+	87417.6i	1.74567	+	3.02359i
$943$	8788.13	+	17280.0i	0.303479	+	0.596729i
$944$	−54.9468			−0.00189445
$945$	−73316.9	+	44421.6i	−2.52381	+	1.52914i
$946$	−2300.26	−	15998.6i	−0.0790568	−	0.549852i
$947$	1409.89	+	134.628i	0.0483795	+	0.00461968i	0.119218	−	0.992868i	$-0.461961\pi$
$947$	1409.89	+	134.628i	0.0483795	+	0.00461968i	−0.0708382	+	0.997488i	$0.522567\pi$
$948$	9277.90	+	38244.0i	0.317861	+	1.31024i
$949$	−34247.3	+	3270.22i	−1.17146	+	0.111861i
$950$	−19318.1	−	55816.1i	−0.659750	−	1.90622i
$951$	6370.91	−	44310.6i	0.217235	−	1.51090i
$952$	−5350.14	−	4441.46i	−0.182142	−	0.151207i
$953$	6826.38	+	7878.06i	0.232034	+	0.267781i	0.859812	−	0.510611i	$-0.170581\pi$
$953$	6826.38	+	7878.06i	0.232034	+	0.267781i	−0.627778	+	0.778392i	$0.716035\pi$
$954$	731.625	+	15358.7i	0.0248294	+	0.521233i
$955$	18246.7	+	9406.80i	0.618270	+	0.318740i
$956$	−18304.9	+	52888.6i	−0.619271	+	1.78927i
$957$	−6056.26	+	24964.3i	−0.204568	+	0.843239i
$958$	−5956.92	+	41431.3i	−0.200897	+	1.39727i
$959$	−25633.2	−	3134.10i	−0.863128	−	0.105532i
$960$	−47200.0	+	103354.i	−1.58685	+	3.47471i
$961$	8678.22	−	8274.67i	0.291303	−	0.277757i
$962$	−39867.2	+	55985.6i	−1.33614	+	1.87635i
$963$	−25095.9	+	19735.6i	−0.839776	+	0.660407i
$964$	−52498.0	+	27064.6i	−1.75399	+	0.904245i
$965$	14750.3			0.492049
$966$	−27337.4	+	83166.9i	−0.910526	+	2.77003i
$967$	22658.8			0.753524			0.376762	−	0.926310i	$-0.377037\pi$
$967$	22658.8			0.753524			0.376762	+	0.926310i	$0.377037\pi$
$968$	8098.01	−	4174.81i	0.268884	−	0.138619i
$969$	−17795.7	+	13994.7i	−0.589970	+	0.463958i
$970$	−15031.1	+	21108.2i	−0.497546	+	0.698705i
$971$	−25233.5	+	24060.1i	−0.833966	+	0.795185i	−0.981013	−	0.193944i	$-0.937872\pi$
$971$	−25233.5	+	24060.1i	−0.833966	+	0.795185i	0.147046	+	0.989130i	$0.453023\pi$
$972$	−20687.5	+	45299.3i	−0.682667	+	1.49483i
$973$	10883.9	−	14458.8i	0.358604	−	0.476389i
$974$	4200.53	−	29215.3i	0.138186	−	0.961107i
$975$	−15959.4	+	65785.7i	−0.524216	+	2.16085i
$976$	68.8565	−	198.948i	0.00225824	−	0.00652476i
$977$	23135.3	+	11927.1i	0.757588	+	0.390564i	0.793326	−	0.608797i	$-0.208348\pi$
$977$	23135.3	+	11927.1i	0.757588	+	0.390564i	−0.0357376	+	0.999361i	$0.511378\pi$
$978$	1429.09	+	30000.3i	0.0467253	+	0.980884i
$979$	14392.7	+	16610.0i	0.469858	+	0.542246i
$980$	59140.0	−	26628.5i	1.92771	−	0.867976i
$981$	7576.66	−	52696.8i	0.246589	−	1.71507i
$982$	3999.34	+	11555.3i	0.129963	+	0.375505i
$983$	−29076.8	+	2776.49i	−0.943443	+	0.0900879i	−0.555428	−	0.831565i	$-0.687445\pi$
$983$	−29076.8	+	2776.49i	−0.943443	+	0.0900879i	−0.388016	+	0.921653i	$0.626839\pi$
$984$	−8743.32	−	36040.4i	−0.283259	−	1.16761i
$985$	18817.7	+	1796.87i	0.608712	+	0.0581250i
$986$	−977.545	−	6798.97i	−0.0315734	−	0.219598i
$987$	13384.4	+	7354.80i	0.431643	+	0.237189i
$988$	151992.			4.89425
$989$	7970.84	−	10021.5i	0.256277	−	0.322208i
$990$	−61896.9	−	107209.i	−1.98708	−	3.44173i
$991$	−829.742	+	17418.4i	−0.0265970	+	0.558340i	0.945764	+	0.324856i	$0.105316\pi$
$991$	−829.742	+	17418.4i	−0.0265970	+	0.558340i	−0.972361	+	0.233484i	$0.924987\pi$
$992$	34508.5	+	13815.1i	1.10448	+	0.442167i
$993$	−17829.5	−	39041.1i	−0.569790	−	1.24767i
$994$	43931.0	−	48067.9i	1.40182	−	1.53382i
$995$	14510.9	−	31774.4i	0.462338	−	1.01238i
$996$	−7245.27	−	20933.8i	−0.230497	−	0.665978i
$997$	27229.7	−	10901.1i	0.864967	−	0.346281i	0.103614	−	0.994618i	$-0.466959\pi$
$997$	27229.7	−	10901.1i	0.864967	−	0.346281i	0.761354	+	0.648337i	$0.224535\pi$
$998$	−46876.9	−	44697.0i	−1.48684	−	1.41770i
$999$	57535.0	−	11089.0i	1.82215	−	0.351190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.m.a.2.6	✓	920
7.4	even	3	inner	161.4.m.a.25.41	yes	920
23.12	even	11	inner	161.4.m.a.58.41	yes	920
161.81	even	33	inner	161.4.m.a.81.6	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.m.a.2.6	✓	920	1.1	even	1	trivial
161.4.m.a.25.41	yes	920	7.4	even	3	inner
161.4.m.a.58.41	yes	920	23.12	even	11	inner
161.4.m.a.81.6	yes	920	161.81	even	33	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.06577 + 2.09605i) q^{2} +(7.36412 - 5.79121i) q^{3} +(7.49662 - 10.5275i) q^{4} +(-10.5890 + 10.0966i) q^{5} +(-17.8022 + 38.9813i) q^{6} +(-11.1382 + 14.7966i) q^{7} +(-3.20542 + 22.2942i) q^{8} +(14.3267 - 59.0554i) q^{9} +(21.8896 - 63.2458i) q^{10} +(27.0547 + 13.9477i) q^{11} +(-5.76111 - 120.941i) q^{12} +(-53.1251 - 61.3096i) q^{13} +(14.2710 - 83.5060i) q^{14} +(-19.5073 + 135.676i) q^{15} +(0.118817 + 0.343300i) q^{16} +(16.5939 - 1.58452i) q^{17} +(65.5341 + 270.135i) q^{18} +(-144.313 - 13.7802i) q^{19} +(26.9106 + 187.167i) q^{20} +(3.66705 + 173.468i) q^{21} -139.233 q^{22} +(-75.6769 - 80.2496i) q^{23} +(105.505 + 182.740i) q^{24} +(4.23810 - 88.9687i) q^{25} +(344.503 + 137.918i) q^{26} +(-131.420 - 287.770i) q^{27} +(72.2728 + 228.183i) q^{28} +(-37.4221 + 81.9429i) q^{29} +(-205.072 - 592.516i) q^{30} +(-189.764 + 75.9701i) q^{31} +(-131.610 - 125.490i) q^{32} +(280.008 - 53.9672i) q^{33} +(-64.1457 + 41.2239i) q^{34} +(-31.4528 - 269.140i) q^{35} +(-514.306 - 593.541i) q^{36} +(-43.6657 + 179.993i) q^{37} +(615.627 - 246.460i) q^{38} +(-746.276 - 143.833i) q^{39} +(-191.154 - 268.438i) q^{40} +(-168.634 - 49.5155i) q^{41} +(-378.507 - 697.595i) q^{42} +(16.5209 + 114.905i) q^{43} +(349.654 - 180.259i) q^{44} +(444.555 + 769.991i) q^{45} +(475.893 + 167.654i) q^{46} +(44.0101 - 76.2277i) q^{47} +(2.86311 + 1.84001i) q^{48} +(-94.8798 - 329.616i) q^{49} +(169.252 + 370.610i) q^{50} +(113.023 - 107.767i) q^{51} +(-1043.70 + 99.6610i) q^{52} +(54.3159 + 10.4685i) q^{53} +(1137.50 + 894.543i) q^{54} +(-427.308 + 125.469i) q^{55} +(-294.176 - 295.747i) q^{56} +(-1142.54 + 734.267i) q^{57} +(-19.6069 - 411.600i) q^{58} +(-49.4696 + 142.933i) q^{59} +(1282.10 + 1222.48i) q^{60} +(-455.530 - 358.233i) q^{61} +(612.301 - 706.633i) q^{62} +(714.246 + 869.759i) q^{63} +(795.344 + 233.534i) q^{64} +(1181.56 + 112.826i) q^{65} +(-1025.33 + 806.330i) q^{66} +(30.9032 - 648.737i) q^{67} +(107.717 - 186.571i) q^{68} +(-1022.04 - 152.707i) q^{69} +(692.012 + 1028.34i) q^{70} +(646.643 + 415.572i) q^{71} +(1270.67 + 508.699i) q^{72} +(245.990 - 345.444i) q^{73} +(-199.739 - 823.335i) q^{74} +(-484.026 - 679.720i) q^{75} +(-1226.93 + 1415.95i) q^{76} +(-507.720 + 244.966i) q^{77} +(3335.67 - 979.442i) q^{78} +(-319.152 + 61.5115i) q^{79} +(-4.72433 - 2.43556i) q^{80} +(-1175.97 - 606.256i) q^{81} +(789.416 - 152.148i) q^{82} +(175.547 - 51.5453i) q^{83} +(1853.68 + 1261.82i) q^{84} +(-159.715 + 184.321i) q^{85} +(-308.017 - 432.549i) q^{86} +(198.968 + 820.157i) q^{87} +(-397.674 + 558.455i) q^{88} +(670.333 + 268.361i) q^{89} +(-3421.40 - 2198.80i) q^{90} +(1498.89 - 103.191i) q^{91} +(-1412.15 + 195.090i) q^{92} +(-957.488 + 1658.42i) q^{93} +(-19.1578 + 402.172i) q^{94} +(1667.27 - 1311.15i) q^{95} +(-1695.94 - 161.942i) q^{96} +(-371.503 - 109.083i) q^{97} +(1076.65 + 1141.27i) q^{98} +(1211.29 - 1397.90i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 7 q^{2} - 9 q^{3} + 157 q^{4} + 3 q^{5} - 52 q^{6} - 22 q^{7} - 32 q^{8} + 397 q^{9} - q^{10} - 29 q^{11} - 101 q^{12} - 36 q^{13} + 134 q^{14} - 320 q^{15} + 1157 q^{16} - q^{17} - 81 q^{18}+ \cdots + 3640 q^{99}+O(q^{100}) \) 920 * q - 7 * q^2 - 9 * q^3 + 157 * q^4 + 3 * q^5 - 52 * q^6 - 22 * q^7 - 32 * q^8 + 397 * q^9 - q^10 - 29 * q^11 - 101 * q^12 - 36 * q^13 + 134 * q^14 - 320 * q^15 + 1157 * q^16 - q^17 - 81 * q^18 + 211 * q^19 - 1956 * q^20 + 1596 * q^21 - 104 * q^22 - 654 * q^23 + 34 * q^24 + 837 * q^25 - 11 * q^26 - 252 * q^27 - 1412 * q^28 - 524 * q^29 + 1269 * q^30 - 53 * q^31 + 1191 * q^32 + 203 * q^33 + 156 * q^34 + 1462 * q^35 - 6346 * q^36 + 803 * q^37 + 649 * q^38 - 863 * q^39 - 587 * q^40 - 388 * q^41 - 2102 * q^42 + 4836 * q^43 - 3344 * q^44 - 5566 * q^45 - 329 * q^46 + 92 * q^47 + 496 * q^48 - 2464 * q^49 + 5626 * q^50 - 173 * q^51 - 1227 * q^52 + 423 * q^53 + 5347 * q^54 - 1720 * q^55 + 9137 * q^56 - 8344 * q^57 + 4116 * q^58 + 4875 * q^59 + 1549 * q^60 + 223 * q^61 + 388 * q^62 - 3556 * q^63 - 5064 * q^64 + 3881 * q^65 + 224 * q^66 - 261 * q^67 - 17618 * q^68 + 3286 * q^69 - 5226 * q^70 + 2052 * q^71 + 9111 * q^72 - 369 * q^73 + 4624 * q^74 - 4359 * q^75 - 4996 * q^76 + 864 * q^77 + 19540 * q^78 - 1805 * q^79 - 1750 * q^80 + 3759 * q^81 + 9153 * q^82 - 3932 * q^83 + 18426 * q^84 - 10396 * q^85 - 2721 * q^86 + 5109 * q^87 - 13236 * q^88 - 2629 * q^89 - 1160 * q^90 + 4752 * q^91 - 19334 * q^92 + 520 * q^93 + 5220 * q^94 - 11871 * q^95 + 961 * q^96 - 7564 * q^97 + 1336 * q^98 + 3640 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more