LMFDB - Embedded newform 570.4.f.b.341.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.f (of order $2$, degree $1$, 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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.19
Character	$\chi$	$=$	570.341
Dual form			570.4.f.b.341.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-0.670363 - 5.15273i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-1.34073 - 10.3055i) q^{6} -23.2517 q^{7} +8.00000 q^{8} +(-26.1012 + 6.90839i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-0.670363 - 5.15273i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-1.34073 - 10.3055i) q^{6} -23.2517 q^{7} +8.00000 q^{8} +(-26.1012 + 6.90839i) q^{9} +10.0000i q^{10} -16.5969i q^{11} +(-2.68145 - 20.6109i) q^{12} -79.1872i q^{13} -46.5034 q^{14} +(25.7636 - 3.35181i) q^{15} +16.0000 q^{16} +109.031i q^{17} +(-52.2025 + 13.8168i) q^{18} +(-2.84390 + 82.7702i) q^{19} +20.0000i q^{20} +(15.5871 + 119.810i) q^{21} -33.1939i q^{22} +87.1809i q^{23} +(-5.36290 - 41.2218i) q^{24} -25.0000 q^{25} -158.374i q^{26} +(53.0944 + 129.861i) q^{27} -93.0068 q^{28} +199.094 q^{29} +(51.5273 - 6.70363i) q^{30} +32.6497i q^{31} +32.0000 q^{32} +(-85.5195 + 11.1260i) q^{33} +218.062i q^{34} -116.258i q^{35} +(-104.405 + 27.6336i) q^{36} +372.224i q^{37} +(-5.68781 + 165.540i) q^{38} +(-408.030 + 53.0841i) q^{39} +40.0000i q^{40} -481.699 q^{41} +(31.1741 + 239.619i) q^{42} -412.076 q^{43} -66.3877i q^{44} +(-34.5420 - 130.506i) q^{45} +174.362i q^{46} +242.273i q^{47} +(-10.7258 - 82.4437i) q^{48} +197.641 q^{49} -50.0000 q^{50} +(561.808 - 73.0904i) q^{51} -316.749i q^{52} -286.905 q^{53} +(106.189 + 259.723i) q^{54} +82.9847 q^{55} -186.014 q^{56} +(428.399 - 40.8322i) q^{57} +398.188 q^{58} -28.8087 q^{59} +(103.055 - 13.4073i) q^{60} -33.6974 q^{61} +65.2995i q^{62} +(606.898 - 160.632i) q^{63} +64.0000 q^{64} +395.936 q^{65} +(-171.039 + 22.2519i) q^{66} +744.150i q^{67} +436.124i q^{68} +(449.219 - 58.4428i) q^{69} -232.517i q^{70} +9.65234 q^{71} +(-208.810 + 55.2672i) q^{72} +320.060 q^{73} +744.448i q^{74} +(16.7591 + 128.818i) q^{75} +(-11.3756 + 331.081i) q^{76} +385.907i q^{77} +(-816.060 + 106.168i) q^{78} -775.625i q^{79} +80.0000i q^{80} +(633.548 - 360.635i) q^{81} -963.397 q^{82} -965.603i q^{83} +(62.3483 + 479.239i) q^{84} -545.155 q^{85} -824.153 q^{86} +(-133.465 - 1025.88i) q^{87} -132.775i q^{88} +539.531 q^{89} +(-69.0839 - 261.012i) q^{90} +1841.24i q^{91} +348.724i q^{92} +(168.235 - 21.8872i) q^{93} +484.546i q^{94} +(-413.851 - 14.2195i) q^{95} +(-21.4516 - 164.887i) q^{96} +30.1358i q^{97} +395.283 q^{98} +(114.658 + 433.200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9}+O(q^{10}) $ 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9	$ 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9} + 40 q^{12} - 40 q^{14} + 640 q^{16} + 20 q^{18} + 68 q^{19} - 78 q^{21} + 80 q^{24} - 1000 q^{25} + 292 q^{27} - 80 q^{28} - 60 q^{29} + 1280 q^{32} + 440 q^{33} + 40 q^{36} + 136 q^{38} - 634 q^{39} + 888 q^{41} - 156 q^{42} + 488 q^{43} + 160 q^{45} + 160 q^{48} + 924 q^{49} - 2000 q^{50} + 2098 q^{51} - 108 q^{53} + 584 q^{54} - 160 q^{56} + 1562 q^{57} - 120 q^{58} + 132 q^{59} - 1496 q^{61} + 762 q^{63} + 2560 q^{64} + 120 q^{65} + 880 q^{66} - 1222 q^{69} - 1128 q^{71} + 80 q^{72} - 316 q^{73} - 250 q^{75} + 272 q^{76} - 1268 q^{78} - 942 q^{81} + 1776 q^{82} - 312 q^{84} + 976 q^{86} + 1830 q^{87} + 1776 q^{89} + 320 q^{90} - 1568 q^{93} - 660 q^{95} + 320 q^{96} + 1848 q^{98} - 4016 q^{99}+O(q^{100}) $ 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9 + 40 * q^12 - 40 * q^14 + 640 * q^16 + 20 * q^18 + 68 * q^19 - 78 * q^21 + 80 * q^24 - 1000 * q^25 + 292 * q^27 - 80 * q^28 - 60 * q^29 + 1280 * q^32 + 440 * q^33 + 40 * q^36 + 136 * q^38 - 634 * q^39 + 888 * q^41 - 156 * q^42 + 488 * q^43 + 160 * q^45 + 160 * q^48 + 924 * q^49 - 2000 * q^50 + 2098 * q^51 - 108 * q^53 + 584 * q^54 - 160 * q^56 + 1562 * q^57 - 120 * q^58 + 132 * q^59 - 1496 * q^61 + 762 * q^63 + 2560 * q^64 + 120 * q^65 + 880 * q^66 - 1222 * q^69 - 1128 * q^71 + 80 * q^72 - 316 * q^73 - 250 * q^75 + 272 * q^76 - 1268 * q^78 - 942 * q^81 + 1776 * q^82 - 312 * q^84 + 976 * q^86 + 1830 * q^87 + 1776 * q^89 + 320 * q^90 - 1568 * q^93 - 660 * q^95 + 320 * q^96 + 1848 * q^98 - 4016 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	2.00000			0.707107
$2$	2.00000			0.707107
$3$	−0.670363	−	5.15273i	−0.129011	−	0.991643i
$3$	−0.670363	−	5.15273i	−0.129011	−	0.991643i
$4$	4.00000			0.500000
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−1.34073	−	10.3055i	−0.0912248	−	0.701198i
$7$	−23.2517			−1.25547			−0.627737	−	0.778426i	$-0.716019\pi$
$7$	−23.2517			−1.25547			−0.627737	+	0.778426i	$0.716019\pi$
$8$	8.00000			0.353553
$9$	−26.1012	+	6.90839i	−0.966712	+	0.255866i
$10$			10.0000i			0.316228i
$11$		−	16.5969i		−	0.454924i	−0.973787	−	0.227462i	$-0.926957\pi$
$11$		−	16.5969i		−	0.454924i	0.973787	−	0.227462i	$-0.0730428\pi$
$12$	−2.68145	−	20.6109i	−0.0645057	−	0.495822i
$13$		−	79.1872i		−	1.68943i	−0.535217	−	0.844714i	$-0.679770\pi$
$13$		−	79.1872i		−	1.68943i	0.535217	−	0.844714i	$-0.320230\pi$
$14$	−46.5034			−0.887754
$15$	25.7636	−	3.35181i	0.443476	−	0.0576956i
$16$	16.0000			0.250000
$17$			109.031i			1.55552i	0.628558	+	0.777762i	$0.283645\pi$
$17$			109.031i			1.55552i	−0.628558	+	0.777762i	$0.716355\pi$
$18$	−52.2025	+	13.8168i	−0.683569	+	0.180925i
$19$	−2.84390	+	82.7702i	−0.0343388	+	0.999410i
$19$	−2.84390	+	82.7702i	−0.0343388	+	0.999410i
$20$			20.0000i			0.223607i
$21$	15.5871	+	119.810i	0.161970	+	1.24498i
$22$		−	33.1939i		−	0.321680i
$23$			87.1809i			0.790368i	0.918602	+	0.395184i	$0.129319\pi$
$23$			87.1809i			0.790368i	−0.918602	+	0.395184i	$0.870681\pi$
$24$	−5.36290	−	41.2218i	−0.0456124	−	0.350599i
$25$	−25.0000			−0.200000
$26$		−	158.374i		−	1.19461i
$27$	53.0944	+	129.861i	0.378445	+	0.925624i
$28$	−93.0068			−0.627737
$29$	199.094			1.27486			0.637428	−	0.770510i	$-0.279998\pi$
$29$	199.094			1.27486			0.637428	+	0.770510i	$0.279998\pi$
$30$	51.5273	−	6.70363i	0.313585	−	0.0407970i
$31$			32.6497i			0.189163i	0.995517	+	0.0945817i	$0.0301514\pi$
$31$			32.6497i			0.189163i	−0.995517	+	0.0945817i	$0.969849\pi$
$32$	32.0000			0.176777
$33$	−85.5195	+	11.1260i	−0.451122	+	0.0586904i
$34$			218.062i			1.09992i
$35$		−	116.258i		−	0.561465i
$36$	−104.405	+	27.6336i	−0.483356	+	0.127933i
$37$			372.224i			1.65387i	0.562296	+	0.826936i	$0.309918\pi$
$37$			372.224i			1.65387i	−0.562296	+	0.826936i	$0.690082\pi$
$38$	−5.68781	+	165.540i	−0.0242812	+	0.706690i
$39$	−408.030	+	53.0841i	−1.67531	+	0.217956i
$40$			40.0000i			0.158114i
$41$	−481.699			−1.83485			−0.917423	−	0.397913i	$-0.869734\pi$
$41$	−481.699			−1.83485			−0.917423	+	0.397913i	$0.869734\pi$
$42$	31.1741	+	239.619i	0.114530	+	0.880335i
$43$	−412.076			−1.46142			−0.730710	−	0.682688i	$-0.760811\pi$
$43$	−412.076			−1.46142			−0.730710	+	0.682688i	$0.760811\pi$
$44$		−	66.3877i		−	0.227462i
$45$	−34.5420	−	130.506i	−0.114427	−	0.432327i
$46$			174.362i			0.558875i
$47$			242.273i			0.751896i	0.926641	+	0.375948i	$0.122683\pi$
$47$			242.273i			0.751896i	−0.926641	+	0.375948i	$0.877317\pi$
$48$	−10.7258	−	82.4437i	−0.0322528	−	0.247911i
$49$	197.641			0.576214
$50$	−50.0000			−0.141421
$51$	561.808	−	73.0904i	1.54253	−	0.200680i
$52$		−	316.749i		−	0.844714i
$53$	−286.905			−0.743573			−0.371787	−	0.928318i	$-0.621255\pi$
$53$	−286.905			−0.743573			−0.371787	+	0.928318i	$0.621255\pi$
$54$	106.189	+	259.723i	0.267601	+	0.654515i
$55$	82.9847			0.203448
$56$	−186.014			−0.443877
$57$	428.399	−	40.8322i	0.995488	−	0.0948835i
$58$	398.188			0.901459
$59$	−28.8087			−0.0635690			−0.0317845	−	0.999495i	$-0.510119\pi$
$59$	−28.8087			−0.0635690			−0.0317845	+	0.999495i	$0.510119\pi$
$60$	103.055	−	13.4073i	0.221738	−	0.0288478i
$61$	−33.6974			−0.0707298			−0.0353649	−	0.999374i	$-0.511259\pi$
$61$	−33.6974			−0.0707298			−0.0353649	+	0.999374i	$0.511259\pi$
$62$			65.2995i			0.133759i
$63$	606.898	−	160.632i	1.21368	−	0.321234i
$64$	64.0000			0.125000
$65$	395.936			0.755536
$66$	−171.039	+	22.2519i	−0.318992	+	0.0415004i
$67$			744.150i			1.35690i	0.734646	+	0.678451i	$0.237348\pi$
$67$			744.150i			1.35690i	−0.734646	+	0.678451i	$0.762652\pi$
$68$			436.124i			0.777762i
$69$	449.219	−	58.4428i	0.783763	−	0.101966i
$70$		−	232.517i		−	0.397016i
$71$	9.65234			0.0161341			0.00806706	−	0.999967i	$-0.497432\pi$
$71$	9.65234			0.0161341			0.00806706	+	0.999967i	$0.497432\pi$
$72$	−208.810	+	55.2672i	−0.341784	+	0.0904625i
$73$	320.060			0.513154			0.256577	−	0.966524i	$-0.417405\pi$
$73$	320.060			0.513154			0.256577	+	0.966524i	$0.417405\pi$
$74$			744.448i			1.16946i
$75$	16.7591	+	128.818i	0.0258023	+	0.198329i
$76$	−11.3756	+	331.081i	−0.0171694	+	0.499705i
$77$			385.907i			0.571145i
$78$	−816.060	+	106.168i	−1.18462	+	0.154118i
$79$		−	775.625i		−	1.10462i	−0.833640	−	0.552308i	$-0.813747\pi$
$79$		−	775.625i		−	1.10462i	0.833640	−	0.552308i	$-0.186253\pi$
$80$			80.0000i			0.111803i
$81$	633.548	−	360.635i	0.869065	−	0.494698i
$82$	−963.397			−1.29743
$83$		−	965.603i		−	1.27697i	−0.769633	−	0.638486i	$-0.779561\pi$
$83$		−	965.603i		−	1.27697i	0.769633	−	0.638486i	$-0.220439\pi$
$84$	62.3483	+	479.239i	0.0809852	+	0.622491i
$85$	−545.155			−0.695652
$86$	−824.153			−1.03338
$87$	−133.465	−	1025.88i	−0.164471	−	1.26420i
$88$		−	132.775i		−	0.160840i
$89$	539.531			0.642586			0.321293	−	0.946980i	$-0.395882\pi$
$89$	539.531			0.642586			0.321293	+	0.946980i	$0.395882\pi$
$90$	−69.0839	−	261.012i	−0.0809121	−	0.305701i
$91$			1841.24i			2.12103i
$92$			348.724i			0.395184i
$93$	168.235	−	21.8872i	0.187583	−	0.0244042i
$94$			484.546i			0.531671i
$95$	−413.851	−	14.2195i	−0.446950	−	0.0153568i
$96$	−21.4516	−	164.887i	−0.0228062	−	0.175299i
$97$			30.1358i			0.0315447i	0.999876	+	0.0157723i	$0.00502070\pi$
$97$			30.1358i			0.0315447i	−0.999876	+	0.0157723i	$0.994979\pi$
$98$	395.283			0.407445
$99$	114.658	+	433.200i	0.116400	+	0.439781i
$100$	−100.000			−0.100000
$101$			406.444i			0.400423i	0.979753	+	0.200211i	$0.0641629\pi$
$101$			406.444i			0.400423i	−0.979753	+	0.200211i	$0.935837\pi$
$102$	1123.62	−	146.181i	1.09073	−	0.141902i
$103$			1221.38i			1.16841i	0.811607	+	0.584203i	$0.198593\pi$
$103$			1221.38i			1.16841i	−0.811607	+	0.584203i	$0.801407\pi$
$104$		−	633.498i		−	0.597303i
$105$	−599.048	+	77.9353i	−0.556773	+	0.0724353i
$106$	−573.809			−0.525786
$107$	−1783.48			−1.61136			−0.805681	−	0.592349i	$-0.798201\pi$
$107$	−1783.48			−1.61136			−0.805681	+	0.592349i	$0.798201\pi$
$108$	212.377	+	519.446i	0.189223	+	0.462812i
$109$			923.031i			0.811104i	0.914072	+	0.405552i	$0.132921\pi$
$109$			923.031i			0.811104i	−0.914072	+	0.405552i	$0.867079\pi$
$110$	165.969			0.143860
$111$	1917.97	−	249.525i	1.64005	−	0.213368i
$112$	−372.027			−0.313868
$113$	132.571			0.110365			0.0551826	−	0.998476i	$-0.482426\pi$
$113$	132.571			0.110365			0.0551826	+	0.998476i	$0.482426\pi$
$114$	856.798	−	81.6644i	0.703917	−	0.0670927i
$115$	−435.904			−0.353463
$116$	796.376			0.637428
$117$	547.056	+	2066.88i	0.432268	+	1.63319i
$118$	−57.6174			−0.0449501
$119$		−	2535.16i		−	1.95292i
$120$	206.109	−	26.8145i	0.156793	−	0.0203985i
$121$	1055.54			0.793044
$122$	−67.3949			−0.0500135
$123$	322.913	+	2482.06i	0.236716	+	1.81951i
$124$			130.599i			0.0945817i
$125$		−	125.000i		−	0.0894427i
$126$	1213.80	−	321.264i	0.858202	−	0.227146i
$127$		−	1693.77i		−	1.18345i	−0.806141	−	0.591723i	$-0.798448\pi$
$127$		−	1693.77i		−	1.18345i	0.806141	−	0.591723i	$-0.201552\pi$
$128$	128.000			0.0883883
$129$	276.241	+	2123.32i	0.188540	+	1.44921i
$130$	791.872			0.534244
$131$		−	2849.12i		−	1.90022i	−0.311919	−	0.950109i	$-0.600972\pi$
$131$		−	2849.12i		−	1.90022i	0.311919	−	0.950109i	$-0.399028\pi$
$132$	−342.078	+	44.5039i	−0.225561	+	0.0293452i
$133$	66.1256	−	1924.55i	0.0431114	−	1.25473i
$134$			1488.30i			0.959475i
$135$	−649.307	+	265.472i	−0.413952	+	0.169246i
$136$			872.249i			0.549961i
$137$			1114.27i			0.694881i	0.937702	+	0.347441i	$0.112949\pi$
$137$			1114.27i			0.694881i	−0.937702	+	0.347441i	$0.887051\pi$
$138$	898.439	−	116.886i	0.554204	−	0.0721012i
$139$	−2726.40			−1.66367			−0.831836	−	0.555021i	$-0.812710\pi$
$139$	−2726.40			−1.66367			−0.831836	+	0.555021i	$0.812710\pi$
$140$		−	465.034i		−	0.280732i
$141$	1248.37	−	162.411i	0.745613	−	0.0970031i
$142$	19.3047			0.0114085
$143$	−1314.26			−0.768562
$144$	−417.620	+	110.534i	−0.241678	+	0.0639666i
$145$			995.470i			0.570133i
$146$	640.121			0.362854
$147$	−132.491	−	1018.39i	−0.0743381	−	0.571398i
$148$			1488.90i			0.826936i
$149$		−	755.459i		−	0.415367i	−0.978196	−	0.207683i	$-0.933408\pi$
$149$		−	755.459i		−	0.415367i	0.978196	−	0.207683i	$-0.0665924\pi$
$150$	33.5181	+	257.636i	0.0182450	+	0.140240i
$151$		−	1042.20i		−	0.561677i	−0.959755	−	0.280838i	$-0.909387\pi$
$151$		−	1042.20i		−	0.561677i	0.959755	−	0.280838i	$-0.0906125\pi$
$152$	−22.7512	+	662.162i	−0.0121406	+	0.353345i
$153$	−753.230	−	2845.84i	−0.398007	−	1.50374i
$154$			771.814i			0.403861i
$155$	−163.249			−0.0845965
$156$	−1632.12	+	212.337i	−0.837655	+	0.108978i
$157$	−1564.54			−0.795314			−0.397657	−	0.917534i	$-0.630177\pi$
$157$	−1564.54			−0.795314			−0.397657	+	0.917534i	$0.630177\pi$
$158$		−	1551.25i		−	0.781081i
$159$	192.330	+	1478.34i	0.0959294	+	0.737359i
$160$			160.000i			0.0790569i
$161$		−	2027.10i		−	0.992287i
$162$	1267.10	−	721.270i	0.614522	−	0.349805i
$163$	−325.538			−0.156430			−0.0782151	−	0.996937i	$-0.524922\pi$
$163$	−325.538			−0.156430			−0.0782151	+	0.996937i	$0.524922\pi$
$164$	−1926.79			−0.917423
$165$	−55.6298	−	427.598i	−0.0262471	−	0.201748i
$166$		−	1931.21i		−	0.902956i
$167$	235.623			0.109180			0.0545899	−	0.998509i	$-0.482615\pi$
$167$	235.623			0.109180			0.0545899	+	0.998509i	$0.482615\pi$
$168$	124.697	+	958.477i	0.0572652	+	0.440168i
$169$	−4073.61			−1.85417
$170$	−1090.31			−0.491900
$171$	−497.580	−	2180.05i	−0.222520	−	0.974928i
$172$	−1648.31			−0.730710
$173$	1894.58			0.832613			0.416307	−	0.909224i	$-0.363324\pi$
$173$	1894.58			0.832613			0.416307	+	0.909224i	$0.363324\pi$
$174$	−266.930	−	2051.75i	−0.116298	−	0.893926i
$175$	581.292			0.251095
$176$		−	265.551i		−	0.113731i
$177$	19.3123	+	148.443i	0.00820112	+	0.0630378i
$178$	1079.06			0.454377
$179$	−990.537			−0.413610			−0.206805	−	0.978382i	$-0.566307\pi$
$179$	−990.537			−0.413610			−0.206805	+	0.978382i	$0.566307\pi$
$180$	−138.168	−	522.025i	−0.0572135	−	0.216163i
$181$			860.031i			0.353180i	0.984284	+	0.176590i	$0.0565067\pi$
$181$			860.031i			0.353180i	−0.984284	+	0.176590i	$0.943493\pi$
$182$			3682.47i			1.49980i
$183$	22.5895	+	173.634i	0.00912494	+	0.0701387i
$184$			697.447i			0.279437i
$185$	−1861.12			−0.739634
$186$	336.471	−	43.7743i	0.132641	−	0.0172564i
$187$	1809.58			0.707646
$188$			969.091i			0.375948i
$189$	−1234.53	−	3019.50i	−0.475128	−	1.16210i
$190$	−827.702	−	28.4390i	−0.316041	−	0.0108589i
$191$		−	4401.57i		−	1.66747i	−0.552166	−	0.833734i	$-0.686199\pi$
$191$		−	4401.57i		−	1.66747i	0.552166	−	0.833734i	$-0.313801\pi$
$192$	−42.9032	−	329.775i	−0.0161264	−	0.123955i
$193$		−	1078.94i		−	0.402404i	−0.979550	−	0.201202i	$-0.935515\pi$
$193$		−	1078.94i		−	0.402404i	0.979550	−	0.201202i	$-0.0644847\pi$
$194$			60.2717i			0.0223054i
$195$	−265.421	−	2040.15i	−0.0974727	−	0.749222i
$196$	790.565			0.288107
$197$			3469.17i			1.25466i	0.778753	+	0.627331i	$0.215853\pi$
$197$			3469.17i			1.25466i	−0.778753	+	0.627331i	$0.784147\pi$
$198$	229.316	+	866.401i	0.0823071	+	0.310972i
$199$	−682.454			−0.243105			−0.121552	−	0.992585i	$-0.538787\pi$
$199$	−682.454			−0.243105			−0.121552	+	0.992585i	$0.538787\pi$
$200$	−200.000			−0.0707107
$201$	3834.41	−	498.851i	1.34556	−	0.175056i
$202$			812.888i			0.283142i
$203$	−4629.27			−1.60055
$204$	2247.23	−	292.361i	0.771263	−	0.100340i
$205$		−	2408.49i		−	0.820568i
$206$			2442.75i			0.826188i
$207$	−602.280	−	2275.53i	−0.202229	−	0.764059i
$208$		−	1267.00i		−	0.422357i
$209$	1373.73	+	47.2001i	0.454656	+	0.0156215i
$210$	−1198.10	+	155.871i	−0.393698	+	0.0512195i
$211$		−	600.475i		−	0.195917i	−0.995191	−	0.0979583i	$-0.968769\pi$
$211$		−	600.475i		−	0.195917i	0.995191	−	0.0979583i	$-0.0312312\pi$
$212$	−1147.62			−0.371787
$213$	−6.47057	−	49.7359i	−0.00208148	−	0.0159993i
$214$	−3566.97			−1.13941
$215$		−	2060.38i		−	0.653567i
$216$	424.755	+	1038.89i	0.133801	+	0.327257i
$217$		−	759.162i		−	0.237490i
$218$			1846.06i			0.573537i
$219$	−214.556	−	1649.18i	−0.0662027	−	0.508865i
$220$	331.939			0.101724
$221$	8633.86			2.62795
$222$	3835.94	−	499.050i	1.15969	−	0.150874i
$223$			3120.83i			0.937158i	0.883421	+	0.468579i	$0.155234\pi$
$223$			3120.83i			0.937158i	−0.883421	+	0.468579i	$0.844766\pi$
$224$	−744.054			−0.221938
$225$	652.531	−	172.710i	0.193342	−	0.0511733i
$226$	265.143			0.0780400
$227$	−3623.82			−1.05957			−0.529783	−	0.848133i	$-0.677727\pi$
$227$	−3623.82			−1.05957			−0.529783	+	0.848133i	$0.677727\pi$
$228$	1713.60	−	163.329i	0.497744	−	0.0474417i
$229$	3344.10			0.964997			0.482498	−	0.875897i	$-0.339729\pi$
$229$	3344.10			0.964997			0.482498	+	0.875897i	$0.339729\pi$
$230$	−871.809			−0.249936
$231$	1988.47	−	258.698i	0.566372	−	0.0736842i
$232$	1592.75			0.450730
$233$			3432.63i			0.965146i	0.875856	+	0.482573i	$0.160298\pi$
$233$			3432.63i			0.965146i	−0.875856	+	0.482573i	$0.839702\pi$
$234$	1094.11	+	4133.77i	0.305660	+	1.15484i
$235$	−1211.36			−0.336258
$236$	−115.235			−0.0317845
$237$	−3996.59	+	519.950i	−1.09538	+	0.142508i
$238$		−	5070.31i		−	1.38092i
$239$			3086.93i			0.835467i	0.908570	+	0.417734i	$0.137175\pi$
$239$			3086.93i			0.835467i	−0.908570	+	0.417734i	$0.862825\pi$
$240$	412.218	−	53.6290i	0.110869	−	0.0144239i
$241$		−	3276.96i		−	0.875883i	−0.899004	−	0.437941i	$-0.855708\pi$
$241$		−	3276.96i		−	0.875883i	0.899004	−	0.437941i	$-0.144292\pi$
$242$	2111.08			0.560767
$243$	−2282.96	−	3022.75i	−0.602683	−	0.797980i
$244$	−134.790			−0.0353649
$245$			988.207i			0.257691i
$246$	645.826	+	4964.12i	0.167383	+	1.28659i
$247$	6554.34	+	225.201i	1.68843	+	0.0580129i
$248$			261.198i			0.0668794i
$249$	−4975.49	+	647.304i	−1.26630	+	0.164744i
$250$		−	250.000i		−	0.0632456i
$251$			2409.82i			0.606003i	0.952990	+	0.303002i	$0.0979888\pi$
$251$			2409.82i			0.606003i	−0.952990	+	0.303002i	$0.902011\pi$
$252$	2427.59	−	642.528i	0.606841	−	0.160617i
$253$	1446.94			0.359558
$254$		−	3387.54i		−	0.836823i
$255$	365.452	+	2809.04i	0.0897470	+	0.689838i
$256$	256.000			0.0625000
$257$	7545.05			1.83131			0.915656	−	0.401963i	$-0.131672\pi$
$257$	7545.05			1.83131			0.915656	+	0.401963i	$0.131672\pi$
$258$	552.481	+	4246.64i	0.133318	+	1.02474i
$259$		−	8654.84i		−	2.07639i
$260$	1583.74			0.377768
$261$	−5196.60	+	1375.42i	−1.23242	+	0.326193i
$262$		−	5698.23i		−	1.34366i
$263$		−	1753.11i		−	0.411031i	−0.978654	−	0.205516i	$-0.934113\pi$
$263$		−	1753.11i		−	0.411031i	0.978654	−	0.205516i	$-0.0658872\pi$
$264$	−684.156	+	89.0077i	−0.159496	+	0.0207502i
$265$		−	1434.52i		−	0.332536i
$266$	132.251	−	3849.10i	0.0304844	−	0.887230i
$267$	−361.682	−	2780.06i	−0.0829009	−	0.637216i
$268$			2976.60i			0.678451i
$269$	−668.848			−0.151600			−0.0758000	−	0.997123i	$-0.524151\pi$
$269$	−668.848			−0.151600			−0.0758000	+	0.997123i	$0.524151\pi$
$270$	−1298.61	+	530.944i	−0.292708	+	0.119675i
$271$	−8105.43			−1.81686			−0.908431	−	0.418034i	$-0.862719\pi$
$271$	−8105.43			−1.81686			−0.908431	+	0.418034i	$0.862719\pi$
$272$			1744.50i			0.388881i
$273$	9487.39	−	1234.30i	2.10331	−	0.273637i
$274$			2228.55i			0.491355i
$275$			414.923i			0.0909848i
$276$	1796.88	−	233.771i	0.391882	−	0.0509832i
$277$	−7476.12			−1.62165			−0.810825	−	0.585289i	$-0.800981\pi$
$277$	−7476.12			−1.62165			−0.810825	+	0.585289i	$0.800981\pi$
$278$	−5452.80			−1.17639
$279$	−225.557	−	852.198i	−0.0484006	−	0.182867i
$280$		−	930.068i		−	0.198508i
$281$	5536.39			1.17535			0.587675	−	0.809097i	$-0.300043\pi$
$281$	5536.39			1.17535			0.587675	+	0.809097i	$0.300043\pi$
$282$	2496.73	−	324.821i	0.527228	−	0.0685916i
$283$	−2047.64			−0.430104			−0.215052	−	0.976603i	$-0.568992\pi$
$283$	−2047.64			−0.430104			−0.215052	+	0.976603i	$0.568992\pi$
$284$	38.6094			0.00806706
$285$	204.161	+	2142.00i	0.0424332	+	0.445196i
$286$	−2628.53			−0.543455
$287$	11200.3			2.30360
$288$	−835.239	+	221.069i	−0.170892	+	0.0452312i
$289$	−6974.77			−1.41966
$290$			1990.94i			0.403145i
$291$	155.282	−	20.2019i	0.0312810	−	0.00406962i
$292$	1280.24			0.256577
$293$	−7267.47			−1.44904			−0.724522	−	0.689251i	$-0.757940\pi$
$293$	−7267.47			−1.44904			−0.724522	+	0.689251i	$0.757940\pi$
$294$	−264.983	−	2036.78i	−0.0525650	−	0.404040i
$295$		−	144.043i		−	0.0284289i
$296$			2977.79i			0.584732i
$297$	2155.30	−	881.204i	0.421088	−	0.172164i
$298$		−	1510.92i		−	0.293709i
$299$	6903.61			1.33527
$300$	67.0363	+	515.273i	0.0129011	+	0.0991643i
$301$	9581.47			1.83477
$302$		−	2084.40i		−	0.397166i
$303$	2094.30	−	272.465i	0.397076	−	0.0516591i
$304$	−45.5025	+	1324.32i	−0.00858469	+	0.249853i
$305$		−	168.487i		−	0.0316313i
$306$	−1506.46	−	5691.69i	−0.281433	−	1.06331i
$307$			6345.36i			1.17964i	0.807536	+	0.589819i	$0.200801\pi$
$307$			6345.36i			1.17964i	−0.807536	+	0.589819i	$0.799199\pi$
$308$			1543.63i			0.285573i
$309$	6293.43	−	818.766i	1.15864	−	0.150738i
$310$	−326.497			−0.0598187
$311$			8487.06i			1.54745i	0.633522	+	0.773725i	$0.281609\pi$
$311$			8487.06i			1.54745i	−0.633522	+	0.773725i	$0.718391\pi$
$312$	−3264.24	+	424.673i	−0.592312	+	0.0770589i
$313$	−2032.51			−0.367043			−0.183521	−	0.983016i	$-0.558750\pi$
$313$	−2032.51			−0.367043			−0.183521	+	0.983016i	$0.558750\pi$
$314$	−3129.09			−0.562372
$315$	803.159	+	3034.49i	0.143660	+	0.542775i
$316$		−	3102.50i		−	0.552308i
$317$	4594.70			0.814082			0.407041	−	0.913410i	$-0.366561\pi$
$317$	4594.70			0.814082			0.407041	+	0.913410i	$0.366561\pi$
$318$	384.660	+	2956.68i	0.0678323	+	0.521392i
$319$		−	3304.35i		−	0.579962i
$320$			320.000i			0.0559017i
$321$	1195.58	+	9189.80i	0.207884	+	1.59790i
$322$		−	4054.21i		−	0.701653i
$323$	−9024.53	−	310.074i	−1.55461	−	0.0534148i
$324$	2534.19	−	1442.54i	0.434532	−	0.247349i
$325$			1979.68i			0.337886i
$326$	−651.076			−0.110613
$327$	4756.13	−	618.765i	0.804325	−	0.104642i
$328$	−3853.59			−0.648716
$329$		−	5633.25i		−	0.943986i
$330$	−111.260	−	855.195i	−0.0185595	−	0.142657i
$331$		−	3938.39i		−	0.653998i	−0.945025	−	0.326999i	$-0.893963\pi$
$331$		−	3938.39i		−	0.653998i	0.945025	−	0.326999i	$-0.106037\pi$
$332$		−	3862.41i		−	0.638486i
$333$	−2571.47	−	9715.51i	−0.423170	−	1.59882i
$334$	471.246			0.0772018
$335$	−3720.75			−0.606825
$336$	249.393	+	1916.95i	0.0404926	+	0.311245i
$337$			3661.41i			0.591839i	0.955213	+	0.295920i	$0.0956261\pi$
$337$			3661.41i			0.591839i	−0.955213	+	0.295920i	$0.904374\pi$
$338$	−8147.22			−1.31110
$339$	−88.8710	−	683.105i	−0.0142384	−	0.109443i
$340$	−2180.62			−0.347826
$341$	541.886			0.0860550
$342$	−995.160	−	4360.10i	−0.157345	−	0.689378i
$343$	3379.84			0.532052
$344$	−3296.61			−0.516690
$345$	292.214	+	2246.10i	0.0456008	+	0.350510i
$346$	3789.16			0.588747
$347$			5019.67i			0.776571i	0.921539	+	0.388285i	$0.126933\pi$
$347$			5019.67i			0.776571i	−0.921539	+	0.388285i	$0.873067\pi$
$348$	−533.861	−	4103.51i	−0.0822354	−	0.632101i
$349$	−1305.05			−0.200166			−0.100083	−	0.994979i	$-0.531911\pi$
$349$	−1305.05			−0.200166			−0.100083	+	0.994979i	$0.531911\pi$
$350$	1162.58			0.177551
$351$	10283.4	−	4204.39i	1.56378	−	0.639356i
$352$		−	531.102i		−	0.0804200i
$353$		−	4006.10i		−	0.604032i	−0.953303	−	0.302016i	$-0.902340\pi$
$353$		−	4006.10i		−	0.604032i	0.953303	−	0.302016i	$-0.0976596\pi$
$354$	38.6245	+	296.887i	0.00579907	+	0.0445744i
$355$			48.2617i			0.00721539i
$356$	2158.12			0.321293
$357$	−13063.0	+	1699.47i	−1.93660	+	0.251949i
$358$	−1981.07			−0.292466
$359$		−	9101.56i		−	1.33806i	−0.743237	−	0.669028i	$-0.766711\pi$
$359$		−	9101.56i		−	1.33806i	0.743237	−	0.669028i	$-0.233289\pi$
$360$	−276.336	−	1044.05i	−0.0404560	−	0.152851i
$361$	−6842.82	−	470.781i	−0.997642	−	0.0686370i
$362$			1720.06i			0.249736i
$363$	−707.596	−	5438.92i	−0.102312	−	0.786417i
$364$			7364.95i			1.06052i
$365$			1600.30i			0.229489i
$366$	45.1790	+	347.268i	0.00645231	+	0.0495955i
$367$	−7039.60			−1.00127			−0.500633	−	0.865660i	$-0.666899\pi$
$367$	−7039.60			−1.00127			−0.500633	+	0.865660i	$0.666899\pi$
$368$			1394.89i			0.197592i
$369$	12572.9	−	3327.76i	1.77377	−	0.469476i
$370$	−3722.24			−0.523000
$371$	6671.02			0.933537
$372$	672.941	−	87.5487i	0.0937913	−	0.0122021i
$373$		−	1565.96i		−	0.217378i	−0.994076	−	0.108689i	$-0.965335\pi$
$373$		−	1565.96i		−	0.217378i	0.994076	−	0.108689i	$-0.0346653\pi$
$374$	3619.16			0.500381
$375$	−644.091	+	83.7953i	−0.0886953	+	0.0115391i
$376$			1938.18i			0.265835i
$377$		−	15765.7i		−	2.15378i
$378$	−2469.07	−	6039.00i	−0.335966	−	0.821726i
$379$			11110.9i			1.50588i	0.658087	+	0.752942i	$0.271366\pi$
$379$			11110.9i			1.50588i	−0.658087	+	0.752942i	$0.728634\pi$
$380$	−1655.40	−	56.8781i	−0.223475	−	0.00767838i
$381$	−8727.54	+	1135.44i	−1.17356	+	0.152678i
$382$		−	8803.14i		−	1.17908i
$383$	−3127.66			−0.417274			−0.208637	−	0.977993i	$-0.566903\pi$
$383$	−3127.66			−0.417274			−0.208637	+	0.977993i	$0.566903\pi$
$384$	−85.8064	−	659.549i	−0.0114031	−	0.0876497i
$385$	−1929.53			−0.255424
$386$		−	2157.88i		−	0.284542i
$387$	10755.7	−	2846.79i	1.41277	−	0.373928i
$388$			120.543i			0.0157723i
$389$			12046.1i			1.57008i	0.619443	+	0.785042i	$0.287358\pi$
$389$			12046.1i			1.57008i	−0.619443	+	0.785042i	$0.712642\pi$
$390$	−530.841	−	4080.30i	−0.0689236	−	0.529780i
$391$	−9505.43			−1.22944
$392$	1581.13			0.203722
$393$	−14680.7	+	1909.94i	−1.88434	+	0.245150i
$394$			6938.34i			0.887180i
$395$	3878.13			0.493999
$396$	458.633	+	1732.80i	0.0581999	+	0.219890i
$397$	−15527.7			−1.96301			−0.981505	−	0.191438i	$-0.938685\pi$
$397$	−15527.7			−1.96301			−0.981505	+	0.191438i	$0.938685\pi$
$398$	−1364.91			−0.171901
$399$	−9961.00	+	949.418i	−1.24981	+	0.119124i
$400$	−400.000			−0.0500000
$401$	13358.1			1.66352			0.831760	−	0.555135i	$-0.187333\pi$
$401$	13358.1			1.66352			0.831760	+	0.555135i	$0.187333\pi$
$402$	7668.81	−	997.701i	0.951457	−	0.123783i
$403$	2585.44			0.319578
$404$			1625.78i			0.200211i
$405$	1803.18	+	3167.74i	0.221236	+	0.388658i
$406$	−9258.54			−1.13176
$407$	6177.78			0.752386
$408$	4494.46	−	584.723i	0.545365	−	0.0709512i
$409$			2526.53i			0.305450i	0.988269	+	0.152725i	$0.0488048\pi$
$409$			2526.53i			0.305450i	−0.988269	+	0.152725i	$0.951195\pi$
$410$		−	4816.99i		−	0.580229i
$411$	5741.55	−	746.967i	0.689074	−	0.0896476i
$412$			4885.51i			0.584203i
$413$	669.851			0.0798092
$414$	−1204.56	−	4551.06i	−0.142997	−	0.540271i
$415$	4828.02			0.571079
$416$		−	2533.99i		−	0.298652i
$417$	1827.68	+	14048.4i	0.214633	+	1.64977i
$418$	2747.46	+	94.4002i	0.321490	+	0.0110461i
$419$		−	5542.81i		−	0.646262i	−0.946354	−	0.323131i	$-0.895265\pi$
$419$		−	5542.81i		−	0.646262i	0.946354	−	0.323131i	$-0.104735\pi$
$420$	−2396.19	+	311.741i	−0.278386	+	0.0362177i
$421$			15209.3i			1.76071i	0.474318	+	0.880353i	$0.342695\pi$
$421$			15209.3i			1.76071i	−0.474318	+	0.880353i	$0.657305\pi$
$422$		−	1200.95i		−	0.138534i
$423$	−1673.72	−	6323.62i	−0.192385	−	0.726867i
$424$	−2295.24			−0.262893
$425$		−	2725.78i		−	0.311105i
$426$	−12.9411	−	99.4718i	−0.00147183	−	0.0113132i
$427$	783.523			0.0887993
$428$	−7133.93			−0.805681
$429$	881.034	+	6772.05i	0.0991532	+	0.762139i
$430$		−	4120.76i		−	0.462142i
$431$	−6241.11			−0.697502			−0.348751	−	0.937215i	$-0.613394\pi$
$431$	−6241.11			−0.697502			−0.348751	+	0.937215i	$0.613394\pi$
$432$	849.510	+	2077.78i	0.0946113	+	0.231406i
$433$		−	9217.00i		−	1.02296i	−0.859296	−	0.511479i	$-0.829098\pi$
$433$		−	9217.00i		−	1.02296i	0.859296	−	0.511479i	$-0.170902\pi$
$434$		−	1518.32i		−	0.167931i
$435$	5129.38	−	667.326i	0.565368	−	0.0735536i
$436$			3692.12i			0.405552i
$437$	−7215.98	−	247.934i	−0.789902	−	0.0271403i
$438$	−429.113	−	3298.37i	−0.0468123	−	0.359822i
$439$			302.650i			0.0329037i	0.999865	+	0.0164518i	$0.00523702\pi$
$439$			302.650i			0.0329037i	−0.999865	+	0.0164518i	$0.994763\pi$
$440$	663.877			0.0719298
$441$	−5158.68	+	1365.38i	−0.557033	+	0.147434i
$442$	17267.7			1.85824
$443$			7390.77i			0.792655i	0.918109	+	0.396327i	$0.129715\pi$
$443$			7390.77i			0.792655i	−0.918109	+	0.396327i	$0.870285\pi$
$444$	7671.88	−	998.101i	0.820026	−	0.106684i
$445$			2697.66i			0.287373i
$446$			6241.66i			0.662671i
$447$	−3892.68	+	506.432i	−0.411896	+	0.0535870i
$448$	−1488.11			−0.156934
$449$	11986.9			1.25991			0.629954	−	0.776632i	$-0.283074\pi$
$449$	11986.9			1.25991			0.629954	+	0.776632i	$0.283074\pi$
$450$	1305.06	−	345.420i	0.136714	−	0.0361850i
$451$			7994.72i			0.834715i
$452$	530.286			0.0551826
$453$	−5370.19	+	698.654i	−0.556983	+	0.0724627i
$454$	−7247.65			−0.749227
$455$	−9206.18			−0.948555
$456$	3427.19	−	326.658i	0.351958	−	0.0335464i
$457$	652.956			0.0668359			0.0334179	−	0.999441i	$-0.489361\pi$
$457$	652.956			0.0668359			0.0334179	+	0.999441i	$0.489361\pi$
$458$	6688.20			0.682356
$459$	−14158.9	+	5788.94i	−1.43983	+	0.588681i
$460$	−1743.62			−0.176732
$461$			7211.83i			0.728608i	0.931280	+	0.364304i	$0.118693\pi$
$461$			7211.83i			0.728608i	−0.931280	+	0.364304i	$0.881307\pi$
$462$	3976.95	−	517.395i	0.400486	−	0.0521026i
$463$	−3301.08			−0.331348			−0.165674	−	0.986181i	$-0.552980\pi$
$463$	−3301.08			−0.331348			−0.165674	+	0.986181i	$0.552980\pi$
$464$	3185.50			0.318714
$465$	109.436	+	841.176i	0.0109139	+	0.0838895i
$466$			6865.26i			0.682461i
$467$			219.774i			0.0217772i	0.999941	+	0.0108886i	$0.00346601\pi$
$467$			219.774i			0.0217772i	−0.999941	+	0.0108886i	$0.996534\pi$
$468$	2188.23	+	8267.53i	0.216134	+	0.816596i
$469$		−	17302.8i		−	1.70355i
$470$	−2422.73			−0.237770
$471$	1048.81	+	8061.67i	0.102604	+	0.788667i
$472$	−230.469			−0.0224750
$473$			6839.20i			0.664835i
$474$	−7993.17	+	1039.90i	−0.774554	+	0.100768i
$475$	71.0976	−	2069.26i	0.00686775	−	0.199882i
$476$		−	10140.6i		−	0.976460i
$477$	7488.56	−	1982.05i	0.718821	−	0.190255i
$478$			6173.85i			0.590765i
$479$		−	1753.04i		−	0.167220i	−0.996499	−	0.0836100i	$-0.973355\pi$
$479$		−	1753.04i		−	0.167220i	0.996499	−	0.0836100i	$-0.0266450\pi$
$480$	824.437	−	107.258i	0.0783963	−	0.0101992i
$481$	29475.4			2.79410
$482$		−	6553.92i		−	0.619343i
$483$	−10445.1	+	1358.89i	−0.983994	+	0.128016i
$484$	4222.17			0.396522
$485$	−150.679			−0.0141072
$486$	−4565.92	−	6045.49i	−0.426162	−	0.564257i
$487$		−	20147.3i		−	1.87466i	−0.348442	−	0.937330i	$-0.613289\pi$
$487$		−	20147.3i		−	1.87466i	0.348442	−	0.937330i	$-0.386711\pi$
$488$	−269.580			−0.0250067
$489$	218.229	+	1677.41i	0.0201813	+	0.155123i
$490$			1976.41i			0.182215i
$491$		−	8114.41i		−	0.745821i	−0.927867	−	0.372911i	$-0.878360\pi$
$491$		−	8114.41i		−	0.745821i	0.927867	−	0.372911i	$-0.121640\pi$
$492$	1291.65	+	9928.25i	0.118358	+	0.909756i
$493$			21707.4i			1.98307i
$494$	13108.7	+	450.402i	1.19390	+	0.0410213i
$495$	−2166.00	+	573.291i	−0.196676	+	0.0520556i
$496$			522.396i			0.0472909i
$497$	−224.433			−0.0202560
$498$	−9950.98	+	1294.61i	−0.895410	+	0.116492i
$499$	5899.83			0.529284			0.264642	−	0.964347i	$-0.414746\pi$
$499$	5899.83			0.529284			0.264642	+	0.964347i	$0.414746\pi$
$500$		−	500.000i		−	0.0447214i
$501$	−157.953	−	1214.10i	−0.0140854	−	0.108267i
$502$			4819.65i			0.428509i
$503$		−	7809.65i		−	0.692276i	−0.938184	−	0.346138i	$-0.887493\pi$
$503$		−	7809.65i		−	0.692276i	0.938184	−	0.346138i	$-0.112507\pi$
$504$	4855.18	−	1285.06i	0.429101	−	0.113573i
$505$	−2032.22			−0.179074
$506$	2893.87			0.254246
$507$	2730.80	+	20990.2i	0.239209	+	1.83867i
$508$		−	6775.08i		−	0.591723i
$509$	9657.74			0.841006			0.420503	−	0.907291i	$-0.361854\pi$
$509$	9657.74			0.841006			0.420503	+	0.907291i	$0.361854\pi$
$510$	730.904	+	5618.08i	0.0634607	+	0.487789i
$511$	−7441.94			−0.644251
$512$	512.000			0.0441942
$513$	−10899.7	+	4025.32i	−0.938073	+	0.346437i
$514$	15090.1			1.29493
$515$	−6106.89			−0.522527
$516$	1104.96	+	8493.27i	0.0942699	+	0.724603i
$517$	4020.99			0.342056
$518$		−	17309.7i		−	1.46823i
$519$	−1270.05	−	9762.25i	−0.107417	−	0.825655i
$520$	3167.49			0.267122
$521$	1438.40			0.120954			0.0604772	−	0.998170i	$-0.480738\pi$
$521$	1438.40			0.120954			0.0604772	+	0.998170i	$0.480738\pi$
$522$	−10393.2	+	2750.84i	−0.871451	+	0.230653i
$523$		−	7578.50i		−	0.633623i	−0.948489	−	0.316811i	$-0.897388\pi$
$523$		−	7578.50i		−	0.633623i	0.948489	−	0.316811i	$-0.102612\pi$
$524$		−	11396.5i		−	0.950109i
$525$	−389.677	−	2995.24i	−0.0323941	−	0.248996i
$526$		−	3506.21i		−	0.290643i
$527$	−3559.84			−0.294248
$528$	−1368.31	+	178.015i	−0.112781	+	0.0146726i
$529$	4566.49			0.375318
$530$		−	2869.05i		−	0.235139i
$531$	751.942	−	199.022i	0.0614529	−	0.0162652i
$532$	264.502	−	7698.19i	0.0215557	−	0.627367i
$533$			38144.4i			3.09984i
$534$	−723.363	−	5560.12i	−0.0586198	−	0.450580i
$535$		−	8917.42i		−	0.720623i
$536$			5953.20i			0.479737i
$537$	664.019	+	5103.97i	0.0533604	+	0.410154i
$538$	−1337.70			−0.107197
$539$		−	3280.24i		−	0.262134i
$540$	−2597.23	+	1061.89i	−0.206976	+	0.0846229i
$541$	7674.59			0.609901			0.304950	−	0.952368i	$-0.401360\pi$
$541$	7674.59			0.609901			0.304950	+	0.952368i	$0.401360\pi$
$542$	−16210.9			−1.28472
$543$	4431.51	−	576.533i	0.350229	−	0.0455642i
$544$			3488.99i			0.274981i
$545$	−4615.15			−0.362737
$546$	18974.8	−	2468.59i	1.48726	−	0.193491i
$547$			11852.3i			0.926452i	0.886240	+	0.463226i	$0.153308\pi$
$547$			11852.3i			0.926452i	−0.886240	+	0.463226i	$0.846692\pi$
$548$			4457.09i			0.347441i
$549$	879.545	−	232.795i	0.0683753	−	0.0180974i
$550$			829.847i			0.0643360i
$551$	−566.204	+	16479.1i	−0.0437770	+	1.27410i
$552$	3593.76	−	467.542i	0.277102	−	0.0360506i
$553$			18034.6i			1.38682i
$554$	−14952.2			−1.14668
$555$	1247.63	+	9589.85i	0.0954212	+	0.733453i
$556$	−10905.6			−0.831836
$557$		−	581.541i		−	0.0442382i	−0.999755	−	0.0221191i	$-0.992959\pi$
$557$		−	581.541i		−	0.0442382i	0.999755	−	0.0221191i	$-0.00704130\pi$
$558$	−451.115	−	1704.40i	−0.0342244	−	0.129306i
$559$			32631.2i			2.46896i
$560$		−	1860.14i		−	0.140366i
$561$	−1213.08	−	9324.28i	−0.0912943	−	0.701732i
$562$	11072.8			0.831098
$563$	24812.3			1.85740			0.928698	−	0.370838i	$-0.120930\pi$
$563$	24812.3			1.85740			0.928698	+	0.370838i	$0.120930\pi$
$564$	4993.46	−	649.643i	0.372806	−	0.0485016i
$565$			662.857i			0.0493569i
$566$	−4095.28			−0.304130
$567$	−14731.1	+	8385.38i	−1.09109	+	0.621081i
$568$	77.2187			0.00570427
$569$	−17740.4			−1.30706			−0.653530	−	0.756900i	$-0.726713\pi$
$569$	−17740.4			−1.30706			−0.653530	+	0.756900i	$0.726713\pi$
$570$	408.322	+	4283.99i	0.0300048	+	0.314801i
$571$	13610.6			0.997527			0.498763	−	0.866738i	$-0.333788\pi$
$571$	13610.6			0.997527			0.498763	+	0.866738i	$0.333788\pi$
$572$	−5257.06			−0.384281
$573$	−22680.1	+	2950.65i	−1.65353	+	0.215122i
$574$	22400.6			1.62889
$575$		−	2179.52i		−	0.158074i
$576$	−1670.48	+	442.137i	−0.120839	+	0.0319833i
$577$	−20538.8			−1.48188			−0.740938	−	0.671573i	$-0.765619\pi$
$577$	−20538.8			−1.48188			−0.740938	+	0.671573i	$0.765619\pi$
$578$	−13949.5			−1.00385
$579$	−5559.50	+	723.282i	−0.399041	+	0.0519147i
$580$			3981.88i			0.285066i
$581$			22451.9i			1.60320i
$582$	310.564	−	40.4039i	0.0221190	−	0.00287766i
$583$			4761.74i			0.338269i
$584$	2560.48			0.181427
$585$	−10334.4	+	2735.28i	−0.730385	+	0.193316i
$586$	−14534.9			−1.02463
$587$		−	21962.0i		−	1.54424i	−0.635477	−	0.772120i	$-0.719196\pi$
$587$		−	21962.0i		−	1.54424i	0.635477	−	0.772120i	$-0.280804\pi$
$588$	−529.966	−	4073.57i	−0.0371691	−	0.285699i
$589$	−2702.43	−	92.8528i	−0.189052	−	0.00649564i
$590$		−	288.087i		−	0.0201023i
$591$	17875.7	−	2325.60i	1.24418	−	0.161866i
$592$			5955.59i			0.413468i
$593$			748.550i			0.0518369i	0.999664	+	0.0259184i	$0.00825102\pi$
$593$			748.550i			0.0518369i	−0.999664	+	0.0259184i	$0.991749\pi$
$594$	4310.60	−	1762.41i	0.297755	−	0.121738i
$595$	12675.8			0.873372
$596$		−	3021.84i		−	0.207683i
$597$	457.492	+	3516.50i	0.0313633	+	0.241073i
$598$	13807.2			0.944179
$599$	−17743.5			−1.21032			−0.605159	−	0.796105i	$-0.706890\pi$
$599$	−17743.5			−1.21032			−0.605159	+	0.796105i	$0.706890\pi$
$600$	134.073	+	1030.55i	0.00912248	+	0.0701198i
$601$			4184.92i			0.284037i	0.989864	+	0.142019i	$0.0453593\pi$
$601$			4184.92i			0.284037i	−0.989864	+	0.142019i	$0.954641\pi$
$602$	19162.9			1.29738
$603$	−5140.88	−	19423.2i	−0.347186	−	1.31173i
$604$		−	4168.81i		−	0.280838i
$605$			5277.71i			0.354660i
$606$	4188.59	−	544.930i	0.280775	−	0.0365285i
$607$		−	4829.88i		−	0.322963i	−0.986876	−	0.161482i	$-0.948373\pi$
$607$		−	4829.88i		−	0.322963i	0.986876	−	0.161482i	$-0.0516273\pi$
$608$	−91.0050	+	2648.65i	−0.00607029	+	0.176672i
$609$	3103.29	+	23853.4i	0.206489	+	1.58717i
$610$		−	336.974i		−	0.0223667i
$611$	19184.9			1.27028
$612$	−3012.92	−	11383.4i	−0.199003	−	0.751872i
$613$	24016.8			1.58243			0.791214	−	0.611539i	$-0.209449\pi$
$613$	24016.8			1.58243			0.791214	+	0.611539i	$0.209449\pi$
$614$			12690.7i			0.834129i
$615$	−12410.3	+	1614.56i	−0.813711	+	0.105863i
$616$			3087.26i			0.201930i
$617$			17038.3i			1.11173i	0.831274	+	0.555863i	$0.187612\pi$
$617$			17038.3i			1.11173i	−0.831274	+	0.555863i	$0.812388\pi$
$618$	12586.9	−	1637.53i	0.819284	−	0.106588i
$619$	12696.4			0.824413			0.412206	−	0.911090i	$-0.364758\pi$
$619$	12696.4			0.824413			0.412206	+	0.911090i	$0.364758\pi$
$620$	−652.995			−0.0422982
$621$	−11321.4	+	4628.81i	−0.731584	+	0.299111i
$622$			16974.1i			1.09421i
$623$	−12545.0			−0.806750
$624$	−6528.48	+	849.346i	−0.418828	+	0.0544889i
$625$	625.000			0.0400000
$626$	−4065.03			−0.259539
$627$	−677.690	−	7110.11i	−0.0431648	−	0.452872i
$628$	−6258.18			−0.397657
$629$	−40584.0			−2.57264
$630$	1606.32	+	6068.98i	0.101583	+	0.383800i
$631$	13761.3			0.868194			0.434097	−	0.900866i	$-0.357068\pi$
$631$	13761.3			0.868194			0.434097	+	0.900866i	$0.357068\pi$
$632$		−	6205.00i		−	0.390541i
$633$	−3094.08	+	402.536i	−0.194279	+	0.0252755i
$634$	9189.39			0.575643
$635$	8468.85			0.529254
$636$	769.321	+	5913.37i	0.0479647	+	0.368680i
$637$		−	15650.7i		−	0.973472i
$638$		−	6608.70i		−	0.410095i
$639$	−251.938	+	66.6822i	−0.0155970	+	0.00412818i
$640$			640.000i			0.0395285i
$641$	18727.4			1.15396			0.576980	−	0.816758i	$-0.304231\pi$
$641$	18727.4			1.15396			0.576980	+	0.816758i	$0.304231\pi$
$642$	2391.16	+	18379.6i	0.146996	+	1.12988i
$643$	−14064.5			−0.862597			−0.431299	−	0.902209i	$-0.641944\pi$
$643$	−14064.5			−0.862597			−0.431299	+	0.902209i	$0.641944\pi$
$644$		−	8108.41i		−	0.496143i
$645$	−10616.6	+	1381.20i	−0.648105	+	0.0843175i
$646$	−18049.1	−	620.148i	−1.09927	−	0.0377700i
$647$			13986.1i			0.849847i	0.905229	+	0.424924i	$0.139699\pi$
$647$			13986.1i			0.849847i	−0.905229	+	0.424924i	$0.860301\pi$
$648$	5068.39	−	2885.08i	0.307261	−	0.174902i
$649$			478.136i			0.0289191i
$650$			3959.36i			0.238921i
$651$	−3911.76	+	508.914i	−0.235505	+	0.0306389i
$652$	−1302.15			−0.0782151
$653$		−	5618.86i		−	0.336727i	−0.985725	−	0.168364i	$-0.946152\pi$
$653$		−	5618.86i		−	0.336727i	0.985725	−	0.168364i	$-0.0538483\pi$
$654$	9512.25	−	1237.53i	0.568744	−	0.0739928i
$655$	14245.6			0.849803
$656$	−7707.18			−0.458711
$657$	−8353.97	+	2211.10i	−0.496072	+	0.131299i
$658$		−	11266.5i		−	0.667499i
$659$	31301.9			1.85030			0.925151	−	0.379599i	$-0.123938\pi$
$659$	31301.9			1.85030			0.925151	+	0.379599i	$0.123938\pi$
$660$	−222.519	−	1710.39i	−0.0131236	−	0.100874i
$661$		−	9539.92i		−	0.561361i	−0.959801	−	0.280681i	$-0.909440\pi$
$661$		−	9539.92i		−	0.561361i	0.959801	−	0.280681i	$-0.0905602\pi$
$662$		−	7876.77i		−	0.462446i
$663$	−5787.82	−	44488.0i	−0.339035	−	2.60599i
$664$		−	7724.82i		−	0.451478i
$665$	9622.74	+	330.628i	0.561134	+	0.0192800i
$666$	−5142.94	−	19431.0i	−0.299227	−	1.13054i
$667$			17357.2i			1.00761i
$668$	942.491			0.0545899
$669$	16080.8	−	2092.09i	0.929327	−	0.120904i
$670$	−7441.50			−0.429090
$671$			559.274i			0.0321767i
$672$	498.786	+	3833.91i	0.0286326	+	0.220084i
$673$			21552.1i			1.23443i	0.786793	+	0.617217i	$0.211740\pi$
$673$			21552.1i			1.23443i	−0.786793	+	0.617217i	$0.788260\pi$
$674$			7322.83i			0.418494i
$675$	−1327.36	−	3246.54i	−0.0756890	−	0.185125i
$676$	−16294.4			−0.927085
$677$	7374.83			0.418667			0.209334	−	0.977844i	$-0.432870\pi$
$677$	7374.83			0.418667			0.209334	+	0.977844i	$0.432870\pi$
$678$	−177.742	−	1366.21i	−0.0100681	−	0.0773879i
$679$		−	700.710i		−	0.0396035i
$680$	−4361.24			−0.245950
$681$	2429.28	+	18672.6i	0.136696	+	1.05071i
$682$	1083.77			0.0608501
$683$	−5461.62			−0.305978			−0.152989	−	0.988228i	$-0.548890\pi$
$683$	−5461.62			−0.305978			−0.152989	+	0.988228i	$0.548890\pi$
$684$	−1990.32	−	8720.21i	−0.111260	−	0.487464i
$685$	−5571.36			−0.310760
$686$	6759.67			0.376218
$687$	−2241.76	−	17231.2i	−0.124496	−	0.956932i
$688$	−6593.22			−0.365355
$689$			22719.2i			1.25621i
$690$	584.428	+	4492.19i	0.0322446	+	0.247848i
$691$	10866.0			0.598210			0.299105	−	0.954220i	$-0.403312\pi$
$691$	10866.0			0.598210			0.299105	+	0.954220i	$0.403312\pi$
$692$	7578.31			0.416307
$693$	−2666.00	−	10072.6i	−0.146137	−	0.552133i
$694$			10039.3i			0.549118i
$695$		−	13632.0i		−	0.744017i
$696$	−1067.72	−	8207.02i	−0.0581492	−	0.446963i
$697$		−	52520.1i		−	2.85415i
$698$	−2610.10			−0.141539
$699$	17687.4	−	2301.11i	0.957080	−	0.124515i
$700$	2325.17			0.125547
$701$			32791.4i			1.76678i	0.468635	+	0.883392i	$0.344746\pi$
$701$			32791.4i			1.76678i	−0.468635	+	0.883392i	$0.655254\pi$
$702$	20566.7	−	8408.79i	1.10576	−	0.452093i
$703$	−30809.1	−	1058.57i	−1.65290	−	0.0567919i
$704$		−	1062.20i		−	0.0568655i
$705$	812.053	+	6241.83i	0.0433811	+	0.333448i
$706$		−	8012.20i		−	0.427115i
$707$		−	9450.51i		−	0.502720i
$708$	77.2491	+	593.773i	0.00410056	+	0.0315189i
$709$	−34760.5			−1.84127			−0.920635	−	0.390425i	$-0.872328\pi$
$709$	−34760.5			−1.84127			−0.920635	+	0.390425i	$0.872328\pi$
$710$			96.5234i			0.00510205i
$711$	5358.32	+	20244.8i	0.282634	+	1.06785i
$712$	4316.25			0.227189
$713$	−2846.43			−0.149509
$714$	−26126.0	+	3398.95i	−1.36938	+	0.178155i
$715$		−	6571.32i		−	0.343711i
$716$	−3962.15			−0.206805
$717$	15906.1	−	2069.36i	0.828485	−	0.107785i
$718$		−	18203.1i		−	0.946148i
$719$			278.138i			0.0144267i	0.999974	+	0.00721336i	$0.00229610\pi$
$719$			278.138i			0.0144267i	−0.999974	+	0.00721336i	$0.997704\pi$
$720$	−552.672	−	2088.10i	−0.0286067	−	0.108082i
$721$		−	28399.1i		−	1.46690i
$722$	−13685.6	−	941.563i	−0.705439	−	0.0485337i
$723$	−16885.3	+	2196.75i	−0.868563	+	0.112999i
$724$			3440.12i			0.176590i
$725$	−4977.35			−0.254971
$726$	−1415.19	−	10877.8i	−0.0723453	−	0.556081i
$727$	27866.1			1.42159			0.710795	−	0.703399i	$-0.248335\pi$
$727$	27866.1			1.42159			0.710795	+	0.703399i	$0.248335\pi$
$728$			14729.9i			0.749898i
$729$	−14045.0	+	13789.8i	−0.713559	+	0.700595i
$730$			3200.60i			0.162273i
$731$		−	44929.1i		−	2.27327i
$732$	90.3580	+	694.535i	0.00456247	+	0.0350693i
$733$	−36945.3			−1.86167			−0.930837	−	0.365435i	$-0.880920\pi$
$733$	−36945.3			−1.86167			−0.930837	+	0.365435i	$0.880920\pi$
$734$	−14079.2			−0.708001
$735$	5091.96	−	662.457i	0.255537	−	0.0332450i
$736$			2789.79i			0.139719i
$737$	12350.6			0.617287
$738$	25145.8	−	6655.53i	1.25424	−	0.331969i
$739$	20508.6			1.02087			0.510435	−	0.859917i	$-0.329485\pi$
$739$	20508.6			1.02087			0.510435	+	0.859917i	$0.329485\pi$
$740$	−7444.48			−0.369817
$741$	−3233.39	−	33923.7i	−0.160299	−	1.68181i
$742$	13342.0			0.660110
$743$	8788.13			0.433924			0.216962	−	0.976180i	$-0.430385\pi$
$743$	8788.13			0.433924			0.216962	+	0.976180i	$0.430385\pi$
$744$	1345.88	−	175.097i	0.0663205	−	0.00862820i
$745$	3777.30			0.185758
$746$		−	3131.91i		−	0.153710i
$747$	6670.77	+	25203.4i	0.326734	+	1.23446i
$748$	7238.33			0.353823
$749$	41469.0			2.02302
$750$	−1288.18	+	167.591i	−0.0627170	+	0.00815939i
$751$			3399.44i			0.165176i	0.996584	+	0.0825880i	$0.0263186\pi$
$751$			3399.44i			0.165176i	−0.996584	+	0.0825880i	$0.973681\pi$
$752$			3876.36i			0.187974i
$753$	12417.2	−	1615.46i	0.600939	−	0.0781813i
$754$		−	31531.4i		−	1.52295i
$755$	5211.01			0.251190
$756$	−4938.14	−	12078.0i	−0.237564	−	0.581048i
$757$	−4390.37			−0.210793			−0.105397	−	0.994430i	$-0.533611\pi$
$757$	−4390.37			−0.210793			−0.105397	+	0.994430i	$0.533611\pi$
$758$			22221.9i			1.06482i
$759$	−969.972	−	7455.67i	−0.0463870	−	0.356553i
$760$	−3310.81	−	113.756i	−0.158021	−	0.00542944i
$761$		−	39400.3i		−	1.87682i	−0.345524	−	0.938410i	$-0.612299\pi$
$761$		−	39400.3i		−	1.87682i	0.345524	−	0.938410i	$-0.387701\pi$
$762$	−17455.1	+	2270.88i	−0.829830	+	0.107960i
$763$		−	21462.0i		−	1.01832i
$764$		−	17606.3i		−	0.833734i
$765$	14229.2	−	3766.15i	0.672495	−	0.177994i
$766$	−6255.31			−0.295057
$767$			2281.28i			0.107395i
$768$	−171.613	−	1319.10i	−0.00806321	−	0.0619777i
$769$	35821.0			1.67977			0.839883	−	0.542768i	$-0.182624\pi$
$769$	35821.0			1.67977			0.839883	+	0.542768i	$0.182624\pi$
$770$	−3859.07			−0.180612
$771$	−5057.92	−	38877.6i	−0.236260	−	1.81601i
$772$		−	4315.77i		−	0.201202i
$773$	−22584.6			−1.05085			−0.525427	−	0.850839i	$-0.676095\pi$
$773$	−22584.6			−1.05085			−0.525427	+	0.850839i	$0.676095\pi$
$774$	21511.4	−	5693.57i	0.998981	−	0.264407i
$775$		−	816.244i		−	0.0378327i
$776$			241.087i			0.0111527i
$777$	−44596.1	+	5801.88i	−2.05904	+	0.267878i
$778$			24092.2i			1.11022i
$779$	1369.90	−	39870.3i	0.0630063	−	1.83376i
$780$	−1061.68	−	8160.60i	−0.0487363	−	0.374611i
$781$		−	160.199i		−	0.00733980i
$782$	−19010.9			−0.869344
$783$	10570.8	+	25854.6i	0.482463	+	1.18004i
$784$	3162.26			0.144053
$785$		−	7822.72i		−	0.355675i
$786$	−29361.4	+	3819.88i	−1.33243	+	0.173347i
$787$		−	5345.34i		−	0.242110i	−0.992646	−	0.121055i	$-0.961372\pi$
$787$		−	5345.34i		−	0.242110i	0.992646	−	0.121055i	$-0.0386278\pi$
$788$			13876.7i			0.627331i
$789$	−9033.29	+	1175.22i	−0.407596	+	0.0530277i
$790$	7756.25			0.349310
$791$	−3082.51			−0.138561
$792$	917.265	+	3465.60i	0.0411535	+	0.155486i
$793$			2668.41i			0.119493i
$794$	−31055.5			−1.38806
$795$	−7391.71	+	961.651i	−0.329757	+	0.0429009i
$796$	−2729.82			−0.121552
$797$	−19605.2			−0.871333			−0.435666	−	0.900108i	$-0.643487\pi$
$797$	−19605.2			−0.871333			−0.435666	+	0.900108i	$0.643487\pi$
$798$	−19922.0	+	1898.84i	−0.883749	+	0.0842332i
$799$	−26415.3			−1.16959
$800$	−800.000			−0.0353553
$801$	−14082.4	+	3727.29i	−0.621196	+	0.164416i
$802$	26716.2			1.17629
$803$		−	5312.02i		−	0.233446i
$804$	15337.6	−	1995.40i	0.672781	−	0.0875279i
$805$	10135.5			0.443764
$806$	5170.88			0.225976
$807$	448.371	+	3446.39i	0.0195581	+	0.150333i
$808$			3251.55i			0.141571i
$809$		−	21083.3i		−	0.916254i	−0.888887	−	0.458127i	$-0.848521\pi$
$809$		−	21083.3i		−	0.916254i	0.888887	−	0.458127i	$-0.151479\pi$
$810$	3606.35	+	6335.48i	0.156437	+	0.274822i
$811$		−	10475.8i		−	0.453584i	−0.973943	−	0.226792i	$-0.927176\pi$
$811$		−	10475.8i		−	0.453584i	0.973943	−	0.226792i	$-0.0728237\pi$
$812$	−18517.1			−0.800274
$813$	5433.58	+	41765.1i	0.234396	+	1.80168i
$814$	12355.6			0.532017
$815$		−	1627.69i		−	0.0699577i
$816$	8988.92	−	1169.45i	0.385631	−	0.0501701i
$817$	1171.91	−	34107.7i	0.0501833	−	1.46056i
$818$			5053.06i			0.215986i
$819$	−12720.0	−	48058.5i	−0.542701	−	2.05043i
$820$		−	9633.97i		−	0.410284i
$821$		−	3627.30i		−	0.154194i	−0.997024	−	0.0770972i	$-0.975435\pi$
$821$		−	3627.30i		−	0.154194i	0.997024	−	0.0770972i	$-0.0245652\pi$
$822$	11483.1	−	1493.93i	0.487249	−	0.0633904i
$823$	−1835.81			−0.0777548			−0.0388774	−	0.999244i	$-0.512378\pi$
$823$	−1835.81			−0.0777548			−0.0388774	+	0.999244i	$0.512378\pi$
$824$			9771.02i			0.413094i
$825$	2137.99	−	278.149i	0.0902245	−	0.0117381i
$826$	1339.70			0.0564336
$827$	32429.5			1.36358			0.681791	−	0.731547i	$-0.261201\pi$
$827$	32429.5			1.36358			0.681791	+	0.731547i	$0.261201\pi$
$828$	−2409.12	−	9102.11i	−0.101114	−	0.382029i
$829$			3888.80i			0.162924i	0.996676	+	0.0814618i	$0.0259588\pi$
$829$			3888.80i			0.162924i	−0.996676	+	0.0814618i	$0.974041\pi$
$830$	9656.03			0.403814
$831$	5011.72	+	38522.4i	0.209211	+	1.60810i
$832$		−	5067.98i		−	0.211179i
$833$			21549.0i			0.896315i
$834$	3655.36	+	28096.8i	0.151768	+	1.16656i
$835$			1178.11i			0.0488267i
$836$	5494.93	+	188.800i	0.227328	+	0.00781076i
$837$	−4239.94	+	1733.52i	−0.175094	+	0.0715880i
$838$		−	11085.6i		−	0.456976i
$839$	37517.9			1.54382			0.771908	−	0.635734i	$-0.219302\pi$
$839$	37517.9			1.54382			0.771908	+	0.635734i	$0.219302\pi$
$840$	−4792.39	+	623.483i	−0.196849	+	0.0256098i
$841$	15249.4			0.625257
$842$			30418.7i			1.24501i
$843$	−3711.39	−	28527.5i	−0.151634	−	1.16553i
$844$		−	2401.90i		−	0.0979583i
$845$		−	20368.1i		−	0.829210i
$846$	−3347.43	−	12647.2i	−0.136037	−	0.513973i
$847$	−24543.1			−0.995646
$848$	−4590.48			−0.185893
$849$	1372.66	+	10550.9i	0.0554884	+	0.426510i
$850$		−	5451.55i		−	0.219984i
$851$	−32450.8			−1.30717
$852$	−25.8823	−	198.944i	−0.00104074	−	0.00799964i
$853$	34168.0			1.37150			0.685750	−	0.727837i	$-0.259474\pi$
$853$	34168.0			1.37150			0.685750	+	0.727837i	$0.259474\pi$
$854$	1567.05			0.0627906
$855$	10900.3	−	2487.90i	0.436001	−	0.0995139i
$856$	−14267.9			−0.569703
$857$	−8395.19			−0.334626			−0.167313	−	0.985904i	$-0.553509\pi$
$857$	−8395.19			−0.334626			−0.167313	+	0.985904i	$0.553509\pi$
$858$	1762.07	+	13544.1i	0.0701119	+	0.538914i
$859$	−4524.93			−0.179730			−0.0898652	−	0.995954i	$-0.528644\pi$
$859$	−4524.93			−0.179730			−0.0898652	+	0.995954i	$0.528644\pi$
$860$		−	8241.53i		−	0.326783i
$861$	−7508.27	−	57712.2i	−0.297191	−	2.28435i
$862$	−12482.2			−0.493209
$863$	−10634.8			−0.419480			−0.209740	−	0.977757i	$-0.567262\pi$
$863$	−10634.8			−0.419480			−0.209740	+	0.977757i	$0.567262\pi$
$864$	1699.02	+	4155.57i	0.0669003	+	0.163629i
$865$			9472.89i			0.372356i
$866$		−	18434.0i		−	0.723341i
$867$	4675.63	+	35939.1i	0.183152	+	1.40779i
$868$		−	3036.65i		−	0.118745i
$869$	−12873.0			−0.502516
$870$	10258.8	−	1334.65i	0.399776	−	0.0520102i
$871$	58927.2			2.29239
$872$			7384.25i			0.286768i
$873$	−208.190	−	786.583i	−0.00807122	−	0.0304946i
$874$	−14432.0	−	495.868i	−0.558545	−	0.0191911i
$875$			2906.46i			0.112293i
$876$	−858.226	−	6596.74i	−0.0331013	−	0.254433i
$877$			7964.95i			0.306679i	0.988174	+	0.153339i	$0.0490028\pi$
$877$			7964.95i			0.306679i	−0.988174	+	0.153339i	$0.950997\pi$
$878$			605.301i			0.0232664i
$879$	4871.84	+	37447.3i	0.186943	+	1.43694i
$880$	1327.75			0.0508621
$881$			14179.4i			0.542242i	0.962545	+	0.271121i	$0.0873943\pi$
$881$			14179.4i			0.542242i	−0.962545	+	0.271121i	$0.912606\pi$
$882$	−10317.4	+	2730.77i	−0.393882	+	0.104251i
$883$	−15856.3			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$883$	−15856.3			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$884$	34535.5			1.31397
$885$	−742.217	+	96.5613i	−0.0281913	+	0.00366765i
$886$			14781.5i			0.560492i
$887$	−25444.7			−0.963188			−0.481594	−	0.876394i	$-0.659942\pi$
$887$	−25444.7			−0.963188			−0.481594	+	0.876394i	$0.659942\pi$
$888$	15343.8	−	1996.20i	0.579846	−	0.0754371i
$889$			39383.0i			1.48579i
$890$			5395.31i			0.203204i
$891$	−5985.44	−	10515.0i	−0.225050	−	0.395358i
$892$			12483.3i			0.468579i
$893$	−20053.0	−	689.001i	−0.751453	−	0.0258192i
$894$	−7785.36	+	1012.86i	−0.291254	+	0.0378918i
$895$		−	4952.68i		−	0.184972i
$896$	−2976.22			−0.110969
$897$	−4627.92	−	35572.4i	−0.172265	−	1.32411i
$898$	23973.9			0.890890
$899$			6500.37i			0.241156i
$900$	2610.12	−	690.839i	0.0966712	−	0.0255866i
$901$		−	31281.5i		−	1.15665i
$902$			15989.4i			0.590233i
$903$	−6423.06	−	49370.7i	−0.236707	−	1.81944i
$904$	1060.57			0.0390200
$905$	−4300.15			−0.157947
$906$	−10740.4	+	1397.31i	−0.393847	+	0.0512389i
$907$			12301.7i			0.450356i	0.974318	+	0.225178i	$0.0722963\pi$
$907$			12301.7i			0.450356i	−0.974318	+	0.225178i	$0.927704\pi$
$908$	−14495.3			−0.529783
$909$	−2807.88	−	10608.7i	−0.102455	−	0.387093i
$910$	−18412.4			−0.670730
$911$	−38012.4			−1.38244			−0.691222	−	0.722642i	$-0.742927\pi$
$911$	−38012.4			−1.38244			−0.691222	+	0.722642i	$0.742927\pi$
$912$	6854.38	−	653.315i	0.248872	−	0.0237209i
$913$	−16026.1			−0.580925
$914$	1305.91			0.0472601
$915$	−868.169	+	112.948i	−0.0313670	+	0.00408080i
$916$	13376.4			0.482498
$917$			66246.8i			2.38567i
$918$	−28317.9	+	11577.9i	−1.01811	+	0.416260i
$919$	31290.2			1.12314			0.561571	−	0.827429i	$-0.310197\pi$
$919$	31290.2			1.12314			0.561571	+	0.827429i	$0.310197\pi$
$920$	−3487.24			−0.124968
$921$	32695.9	−	4253.69i	1.16978	−	0.152187i
$922$			14423.7i			0.515204i
$923$		−	764.342i		−	0.0272574i
$924$	7953.89	−	1034.79i	0.283186	−	0.0368421i
$925$		−	9305.60i		−	0.330774i
$926$	−6602.16			−0.234299
$927$	−8437.75	−	31879.4i	−0.298956	−	1.12951i
$928$	6371.01			0.225365
$929$			5079.53i			0.179391i	0.995969	+	0.0896953i	$0.0285893\pi$
$929$			5079.53i			0.179391i	−0.995969	+	0.0896953i	$0.971411\pi$
$930$	218.872	+	1682.35i	0.00771730	+	0.0593188i
$931$	−562.073	+	16358.8i	−0.0197865	+	0.575874i
$932$			13730.5i			0.482573i
$933$	43731.5	−	5689.41i	1.53452	−	0.199639i
$934$			439.549i			0.0153988i
$935$			9047.91i			0.316469i
$936$	4376.45	+	16535.1i	0.152830	+	0.577420i
$937$	24825.6			0.865546			0.432773	−	0.901503i	$-0.357535\pi$
$937$	24825.6			0.865546			0.432773	+	0.901503i	$0.357535\pi$
$938$		−	34605.5i		−	1.20460i
$939$	1362.52	+	10473.0i	0.0473527	+	0.363976i
$940$	−4845.46			−0.168129
$941$	−26524.6			−0.918891			−0.459446	−	0.888206i	$-0.651952\pi$
$941$	−26524.6			−0.918891			−0.459446	+	0.888206i	$0.651952\pi$
$942$	2097.62	+	16123.3i	0.0725523	+	0.557672i
$943$		−	41994.9i		−	1.45020i
$944$	−460.939			−0.0158923
$945$	15097.5	−	6172.67i	0.519705	−	0.212484i
$946$			13678.4i			0.470109i
$947$		−	36845.1i		−	1.26432i	−0.774840	−	0.632158i	$-0.782170\pi$
$947$		−	36845.1i		−	1.26432i	0.774840	−	0.632158i	$-0.217830\pi$
$948$	−15986.3	+	2079.80i	−0.547692	+	0.0712540i
$949$		−	25344.7i		−	0.866937i
$950$	142.195	−	4138.51i	0.00485623	−	0.141338i
$951$	−3080.11	−	23675.2i	−0.105026	−	0.807278i
$952$		−	20281.3i		−	0.690462i
$953$	5268.81			0.179091			0.0895453	−	0.995983i	$-0.471459\pi$
$953$	5268.81			0.179091			0.0895453	+	0.995983i	$0.471459\pi$
$954$	14977.1	−	3964.10i	0.508284	−	0.134531i
$955$	22007.8			0.745714
$956$			12347.7i			0.417734i
$957$	−17026.4	+	2215.11i	−0.575116	+	0.0748217i
$958$		−	3506.08i		−	0.118242i
$959$		−	25908.7i		−	0.872405i
$960$	1648.87	−	214.516i	0.0554345	−	0.00721195i
$961$	28725.0			0.964217
$962$	58950.8			1.97573
$963$	46551.1	−	12321.0i	1.55772	−	0.412294i
$964$		−	13107.8i		−	0.437941i
$965$	5394.71			0.179960
$966$	−20890.2	+	2717.79i	−0.695789	+	0.0905211i
$967$	−22613.2			−0.752006			−0.376003	−	0.926618i	$-0.622702\pi$
$967$	−22613.2			−0.752006			−0.376003	+	0.926618i	$0.622702\pi$
$968$	8444.33			0.280383
$969$	4451.98	+	46708.8i	0.147594	+	1.54851i
$970$	−301.358			−0.00997530
$971$	32583.5			1.07688			0.538441	−	0.842663i	$-0.319013\pi$
$971$	32583.5			1.07688			0.538441	+	0.842663i	$0.319013\pi$
$972$	−9131.85	−	12091.0i	−0.301342	−	0.398990i
$973$	63393.5			2.08870
$974$		−	40294.5i		−	1.32559i
$975$	10200.8	−	1327.10i	0.335062	−	0.0435911i
$976$	−539.159			−0.0176824
$977$	1972.73			0.0645990			0.0322995	−	0.999478i	$-0.489717\pi$
$977$	1972.73			0.0645990			0.0322995	+	0.999478i	$0.489717\pi$
$978$	436.457	+	3354.82i	0.0142703	+	0.109688i
$979$		−	8954.56i		−	0.292328i
$980$			3952.83i			0.128845i
$981$	−6376.66	−	24092.2i	−0.207534	−	0.784104i
$982$		−	16228.8i		−	0.527375i
$983$	42895.6			1.39182			0.695908	−	0.718131i	$-0.255002\pi$
$983$	42895.6			1.39182			0.695908	+	0.718131i	$0.255002\pi$
$984$	2583.30	+	19856.5i	0.0836917	+	0.643295i
$985$	−17345.9			−0.561102
$986$			43414.8i			1.40224i
$987$	−29026.6	+	3776.32i	−0.936097	+	0.121785i
$988$	26217.4	+	900.803i	0.844216	+	0.0290064i
$989$		−	35925.2i		−	1.15506i
$990$	−4332.00	+	1146.58i	−0.139071	+	0.0368088i
$991$			33261.1i			1.06617i	0.846062	+	0.533085i	$0.178967\pi$
$991$			33261.1i			1.06617i	−0.846062	+	0.533085i	$0.821033\pi$
$992$			1044.79i			0.0334397i
$993$	−20293.4	+	2640.15i	−0.648532	+	0.0843731i
$994$	−448.867			−0.0143231
$995$		−	3412.27i		−	0.108720i
$996$	−19902.0	+	2589.22i	−0.633150	+	0.0823720i
$997$	34037.9			1.08123			0.540617	−	0.841269i	$-0.318191\pi$
$997$	34037.9			1.08123			0.540617	+	0.841269i	$0.318191\pi$
$998$	11799.7			0.374260
$999$	−48337.6	+	19763.0i	−1.53086	+	0.625900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.f.b.341.19	yes	40
3.2	odd	2		570.4.f.a.341.21	✓	40
19.18	odd	2		570.4.f.a.341.22	yes	40
57.56	even	2	inner	570.4.f.b.341.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.f.a.341.21	✓	40	3.2	odd	2
570.4.f.a.341.22	yes	40	19.18	odd	2
570.4.f.b.341.19	yes	40	1.1	even	1	trivial
570.4.f.b.341.20	yes	40	57.56	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-0.670363 - 5.15273i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-1.34073 - 10.3055i) q^{6} -23.2517 q^{7} +8.00000 q^{8} +(-26.1012 + 6.90839i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-0.670363 - 5.15273i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-1.34073 - 10.3055i) q^{6} -23.2517 q^{7} +8.00000 q^{8} +(-26.1012 + 6.90839i) q^{9} +10.0000i q^{10} -16.5969i q^{11} +(-2.68145 - 20.6109i) q^{12} -79.1872i q^{13} -46.5034 q^{14} +(25.7636 - 3.35181i) q^{15} +16.0000 q^{16} +109.031i q^{17} +(-52.2025 + 13.8168i) q^{18} +(-2.84390 + 82.7702i) q^{19} +20.0000i q^{20} +(15.5871 + 119.810i) q^{21} -33.1939i q^{22} +87.1809i q^{23} +(-5.36290 - 41.2218i) q^{24} -25.0000 q^{25} -158.374i q^{26} +(53.0944 + 129.861i) q^{27} -93.0068 q^{28} +199.094 q^{29} +(51.5273 - 6.70363i) q^{30} +32.6497i q^{31} +32.0000 q^{32} +(-85.5195 + 11.1260i) q^{33} +218.062i q^{34} -116.258i q^{35} +(-104.405 + 27.6336i) q^{36} +372.224i q^{37} +(-5.68781 + 165.540i) q^{38} +(-408.030 + 53.0841i) q^{39} +40.0000i q^{40} -481.699 q^{41} +(31.1741 + 239.619i) q^{42} -412.076 q^{43} -66.3877i q^{44} +(-34.5420 - 130.506i) q^{45} +174.362i q^{46} +242.273i q^{47} +(-10.7258 - 82.4437i) q^{48} +197.641 q^{49} -50.0000 q^{50} +(561.808 - 73.0904i) q^{51} -316.749i q^{52} -286.905 q^{53} +(106.189 + 259.723i) q^{54} +82.9847 q^{55} -186.014 q^{56} +(428.399 - 40.8322i) q^{57} +398.188 q^{58} -28.8087 q^{59} +(103.055 - 13.4073i) q^{60} -33.6974 q^{61} +65.2995i q^{62} +(606.898 - 160.632i) q^{63} +64.0000 q^{64} +395.936 q^{65} +(-171.039 + 22.2519i) q^{66} +744.150i q^{67} +436.124i q^{68} +(449.219 - 58.4428i) q^{69} -232.517i q^{70} +9.65234 q^{71} +(-208.810 + 55.2672i) q^{72} +320.060 q^{73} +744.448i q^{74} +(16.7591 + 128.818i) q^{75} +(-11.3756 + 331.081i) q^{76} +385.907i q^{77} +(-816.060 + 106.168i) q^{78} -775.625i q^{79} +80.0000i q^{80} +(633.548 - 360.635i) q^{81} -963.397 q^{82} -965.603i q^{83} +(62.3483 + 479.239i) q^{84} -545.155 q^{85} -824.153 q^{86} +(-133.465 - 1025.88i) q^{87} -132.775i q^{88} +539.531 q^{89} +(-69.0839 - 261.012i) q^{90} +1841.24i q^{91} +348.724i q^{92} +(168.235 - 21.8872i) q^{93} +484.546i q^{94} +(-413.851 - 14.2195i) q^{95} +(-21.4516 - 164.887i) q^{96} +30.1358i q^{97} +395.283 q^{98} +(114.658 + 433.200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9}+O(q^{10}) \) 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9	\( 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9} + 40 q^{12} - 40 q^{14} + 640 q^{16} + 20 q^{18} + 68 q^{19} - 78 q^{21} + 80 q^{24} - 1000 q^{25} + 292 q^{27} - 80 q^{28} - 60 q^{29} + 1280 q^{32} + 440 q^{33} + 40 q^{36} + 136 q^{38} - 634 q^{39} + 888 q^{41} - 156 q^{42} + 488 q^{43} + 160 q^{45} + 160 q^{48} + 924 q^{49} - 2000 q^{50} + 2098 q^{51} - 108 q^{53} + 584 q^{54} - 160 q^{56} + 1562 q^{57} - 120 q^{58} + 132 q^{59} - 1496 q^{61} + 762 q^{63} + 2560 q^{64} + 120 q^{65} + 880 q^{66} - 1222 q^{69} - 1128 q^{71} + 80 q^{72} - 316 q^{73} - 250 q^{75} + 272 q^{76} - 1268 q^{78} - 942 q^{81} + 1776 q^{82} - 312 q^{84} + 976 q^{86} + 1830 q^{87} + 1776 q^{89} + 320 q^{90} - 1568 q^{93} - 660 q^{95} + 320 q^{96} + 1848 q^{98} - 4016 q^{99}+O(q^{100}) \) 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9 + 40 * q^12 - 40 * q^14 + 640 * q^16 + 20 * q^18 + 68 * q^19 - 78 * q^21 + 80 * q^24 - 1000 * q^25 + 292 * q^27 - 80 * q^28 - 60 * q^29 + 1280 * q^32 + 440 * q^33 + 40 * q^36 + 136 * q^38 - 634 * q^39 + 888 * q^41 - 156 * q^42 + 488 * q^43 + 160 * q^45 + 160 * q^48 + 924 * q^49 - 2000 * q^50 + 2098 * q^51 - 108 * q^53 + 584 * q^54 - 160 * q^56 + 1562 * q^57 - 120 * q^58 + 132 * q^59 - 1496 * q^61 + 762 * q^63 + 2560 * q^64 + 120 * q^65 + 880 * q^66 - 1222 * q^69 - 1128 * q^71 + 80 * q^72 - 316 * q^73 - 250 * q^75 + 272 * q^76 - 1268 * q^78 - 942 * q^81 + 1776 * q^82 - 312 * q^84 + 976 * q^86 + 1830 * q^87 + 1776 * q^89 + 320 * q^90 - 1568 * q^93 - 660 * q^95 + 320 * q^96 + 1848 * q^98 - 4016 * q^99

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