LMFDB - Embedded newform 570.4.f.a.341.21

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			341.21
Character	$\chi$	$=$	570.341
Dual form			570.4.f.a.341.22

$q$-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} +(424.586 + 70.1399i) 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} + 114 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 + 114 * 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	$0.0730428\pi$
$11$			16.5969i			0.454924i	−0.973787	+	0.227462i	$0.926957\pi$
$12$	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	$-0.716355\pi$
$17$		−	109.031i		−	1.55552i	0.628558	−	0.777762i	$-0.283645\pi$
$18$	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	$-0.870681\pi$
$23$		−	87.1809i		−	0.790368i	0.918602	−	0.395184i	$-0.129319\pi$
$24$	−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	$-0.720002\pi$
$29$	−199.094			−1.27486			−0.637428	+	0.770510i	$0.720002\pi$
$30$	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	$-0.130266\pi$
$41$	481.699			1.83485			0.917423	+	0.397913i	$0.130266\pi$
$42$	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	$-0.877317\pi$
$47$		−	242.273i		−	0.751896i	0.926641	−	0.375948i	$-0.122683\pi$
$48$	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	$-0.378745\pi$
$53$	286.905			0.743573			0.371787	+	0.928318i	$0.378745\pi$
$54$	106.189	−	259.723i	0.267601	−	0.654515i
$55$	82.9847			0.203448
$56$	186.014			0.443877
$57$	424.586	+	70.1399i	0.986628	+	0.162987i
$58$	398.188			0.901459
$59$	28.8087			0.0635690			0.0317845	−	0.999495i	$-0.489881\pi$
$59$	28.8087			0.0635690			0.0317845	+	0.999495i	$0.489881\pi$
$60$	−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	$-0.502568\pi$
$71$	−9.65234			−0.0161341			−0.00806706	+	0.999967i	$0.502568\pi$
$72$	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	$0.220439\pi$
$83$			965.603i			1.27697i	−0.769633	+	0.638486i	$0.779561\pi$
$84$	−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	$-0.604118\pi$
$89$	−539.531			−0.642586			−0.321293	+	0.946980i	$0.604118\pi$
$90$	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	$-0.935837\pi$
$101$		−	406.444i		−	0.400423i	0.979753	−	0.200211i	$-0.0641629\pi$
$102$	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	$-0.201799\pi$
$107$	1783.48			1.61136			0.805681	+	0.592349i	$0.201799\pi$
$108$	−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	$-0.517574\pi$
$113$	−132.571			−0.110365			−0.0551826	+	0.998476i	$0.517574\pi$
$114$	−849.172	−	140.280i	−0.697651	−	0.115249i
$115$	−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	$0.399028\pi$
$131$			2849.12i			1.90022i	−0.311919	+	0.950109i	$0.600972\pi$
$132$	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	$-0.887051\pi$
$137$		−	1114.27i		−	0.694881i	0.937702	−	0.347441i	$-0.112949\pi$
$138$	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	$0.0665924\pi$
$149$			755.459i			0.415367i	−0.978196	+	0.207683i	$0.933408\pi$
$150$	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	$-0.517385\pi$
$167$	−235.623			−0.109180			−0.0545899	+	0.998509i	$0.517385\pi$
$168$	124.697	−	958.477i	0.0572652	−	0.440168i
$169$	−4073.61			−1.85417
$170$	1090.31			0.491900
$171$	646.039	−	2140.76i	0.288911	−	0.957356i
$172$	−1648.31			−0.730710
$173$	−1894.58			−0.832613			−0.416307	−	0.909224i	$-0.636676\pi$
$173$	−1894.58			−0.832613			−0.416307	+	0.909224i	$0.636676\pi$
$174$	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	$-0.433693\pi$
$179$	990.537			0.413610			0.206805	+	0.978382i	$0.433693\pi$
$180$	−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	$0.313801\pi$
$191$			4401.57i			1.66747i	−0.552166	+	0.833734i	$0.686199\pi$
$192$	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	$-0.784147\pi$
$197$		−	3469.17i		−	1.25466i	0.778753	−	0.627331i	$-0.215853\pi$
$198$	−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	$-0.322273\pi$
$227$	3623.82			1.05957			0.529783	+	0.848133i	$0.322273\pi$
$228$	1698.34	+	280.560i	0.493314	+	0.0814935i
$229$	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	$-0.839702\pi$
$233$		−	3432.63i		−	0.965146i	0.875856	−	0.482573i	$-0.160298\pi$
$234$	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	$-0.862825\pi$
$239$		−	3086.93i		−	0.835467i	0.908570	−	0.417734i	$-0.137175\pi$
$240$	−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	$-0.902011\pi$
$251$		−	2409.82i		−	0.606003i	0.952990	−	0.303002i	$-0.0979888\pi$
$252$	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	$-0.868328\pi$
$257$	−7545.05			−1.83131			−0.915656	+	0.401963i	$0.868328\pi$
$258$	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	$0.0658872\pi$
$263$			1753.11i			0.411031i	−0.978654	+	0.205516i	$0.934113\pi$
$264$	−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	$-0.475849\pi$
$269$	668.848			0.151600			0.0758000	+	0.997123i	$0.475849\pi$
$270$	−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	$-0.699957\pi$
$281$	−5536.39			−1.17535			−0.587675	+	0.809097i	$0.699957\pi$
$282$	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
$285$	350.700	−	2122.93i	0.0728900	−	0.441234i
$286$	−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	$-0.242060\pi$
$293$	7267.47			1.44904			0.724522	+	0.689251i	$0.242060\pi$
$294$	−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	$-0.718391\pi$
$311$		−	8487.06i		−	1.54745i	0.633522	−	0.773725i	$-0.281609\pi$
$312$	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	$-0.633439\pi$
$317$	−4594.70			−0.814082			−0.407041	+	0.913410i	$0.633439\pi$
$318$	−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
$342$	−1292.08	+	4281.52i	−0.204291	+	0.676953i
$343$	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	$-0.873067\pi$
$347$		−	5019.67i		−	0.776571i	0.921539	−	0.388285i	$-0.126933\pi$
$348$	−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	$0.0976596\pi$
$353$			4006.10i			0.604032i	−0.953303	+	0.302016i	$0.902340\pi$
$354$	−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	$0.233289\pi$
$359$			9101.56i			1.33806i	−0.743237	+	0.669028i	$0.766711\pi$
$360$	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	$-0.433097\pi$
$383$	3127.66			0.417274			0.208637	+	0.977993i	$0.433097\pi$
$384$	−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	$-0.712642\pi$
$389$		−	12046.1i		−	1.57008i	0.619443	−	0.785042i	$-0.287358\pi$
$390$	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
$399$	−9872.35	−	1630.87i	−1.23869	−	0.204626i
$400$	−400.000			−0.0500000
$401$	−13358.1			−1.66352			−0.831760	−	0.555135i	$-0.812667\pi$
$401$	−13358.1			−1.66352			−0.831760	+	0.555135i	$0.812667\pi$
$402$	−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	$0.104735\pi$
$419$			5542.81i			0.646262i	−0.946354	+	0.323131i	$0.895265\pi$
$420$	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	$-0.386606\pi$
$431$	6241.11			0.697502			0.348751	+	0.937215i	$0.386606\pi$
$432$	−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	$-0.870285\pi$
$443$		−	7390.77i		−	0.792655i	0.918109	−	0.396327i	$-0.129715\pi$
$444$	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	$-0.716926\pi$
$449$	−11986.9			−1.25991			−0.629954	+	0.776632i	$0.716926\pi$
$450$	−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
$456$	−3396.69	−	561.120i	−0.348826	−	0.0576246i
$457$	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	$-0.881307\pi$
$461$		−	7211.83i		−	0.728608i	0.931280	−	0.364304i	$-0.118693\pi$
$462$	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	$-0.996534\pi$
$467$		−	219.774i		−	0.0217772i	0.999941	−	0.0108886i	$-0.00346601\pi$
$468$	−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	$0.0266450\pi$
$479$			1753.04i			0.167220i	−0.996499	+	0.0836100i	$0.973355\pi$
$480$	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	$0.121640\pi$
$491$			8114.41i			0.745821i	−0.927867	+	0.372911i	$0.878360\pi$
$492$	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	$0.112507\pi$
$503$			7809.65i			0.692276i	−0.938184	+	0.346138i	$0.887493\pi$
$504$	−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	$-0.638146\pi$
$509$	−9657.74			−0.841006			−0.420503	+	0.907291i	$0.638146\pi$
$510$	730.904	−	5618.08i	0.0634607	−	0.487789i
$511$	−7441.94			−0.644251
$512$	−512.000			−0.0441942
$513$	−10597.7	−	4763.95i	−0.912083	−	0.410007i
$514$	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	$-0.519262\pi$
$521$	−1438.40			−0.120954			−0.0604772	+	0.998170i	$0.519262\pi$
$522$	−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	$0.00704130\pi$
$557$			581.541i			0.0442382i	−0.999755	+	0.0221191i	$0.992959\pi$
$558$	−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	$-0.879070\pi$
$563$	−24812.3			−1.85740			−0.928698	+	0.370838i	$0.879070\pi$
$564$	−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	$-0.273287\pi$
$569$	17740.4			1.30706			0.653530	+	0.756900i	$0.273287\pi$
$570$	−701.399	+	4245.86i	−0.0515410	+	0.311999i
$571$	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	$0.280804\pi$
$587$			21962.0i			1.54424i	−0.635477	+	0.772120i	$0.719196\pi$
$588$	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	$-0.991749\pi$
$593$		−	748.550i		−	0.0518369i	0.999664	−	0.0259184i	$-0.00825102\pi$
$594$	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	$-0.293110\pi$
$599$	17743.5			1.21032			0.605159	+	0.796105i	$0.293110\pi$
$600$	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	$-0.812388\pi$
$617$		−	17038.3i		−	1.11173i	0.831274	−	0.555863i	$-0.187612\pi$
$618$	−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
$627$	−1164.11	+	7046.83i	−0.0741467	+	0.448841i
$628$	−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	$-0.695769\pi$
$641$	−18727.4			−1.15396			−0.576980	+	0.816758i	$0.695769\pi$
$642$	−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	$-0.860301\pi$
$647$		−	13986.1i		−	0.849847i	0.905229	−	0.424924i	$-0.139699\pi$
$648$	−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	$0.0538483\pi$
$653$			5618.86i			0.336727i	−0.985725	+	0.168364i	$0.946152\pi$
$654$	−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	$-0.876062\pi$
$659$	−31301.9			−1.85030			−0.925151	+	0.379599i	$0.876062\pi$
$660$	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	$-0.567130\pi$
$677$	−7374.83			−0.418667			−0.209334	+	0.977844i	$0.567130\pi$
$678$	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	$-0.451110\pi$
$683$	5461.62			0.305978			0.152989	+	0.988228i	$0.451110\pi$
$684$	2584.16	−	8563.03i	0.144456	−	0.478678i
$685$	−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	$-0.655254\pi$
$701$		−	32791.4i		−	1.76678i	0.468635	−	0.883392i	$-0.344746\pi$
$702$	−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	$-0.997704\pi$
$719$		−	278.138i		−	0.0144267i	0.999974	−	0.00721336i	$-0.00229610\pi$
$720$	−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
$741$	5554.19	−	33621.8i	0.275355	−	1.66684i
$742$	13342.0			0.660110
$743$	−8788.13			−0.433924			−0.216962	−	0.976180i	$-0.569615\pi$
$743$	−8788.13			−0.433924			−0.216962	+	0.976180i	$0.569615\pi$
$744$	−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	$0.387701\pi$
$761$			39400.3i			1.87682i	−0.345524	+	0.938410i	$0.612299\pi$
$762$	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	$-0.323905\pi$
$773$	22584.6			1.05085			0.525427	+	0.850839i	$0.323905\pi$
$774$	−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	$-0.356513\pi$
$797$	19605.2			0.871333			0.435666	+	0.900108i	$0.356513\pi$
$798$	19744.7	+	3261.75i	0.875883	+	0.144692i
$799$	−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	$0.151479\pi$
$809$			21083.3i			0.916254i	−0.888887	+	0.458127i	$0.848521\pi$
$810$	−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	$0.0245652\pi$
$821$			3627.30i			0.154194i	−0.997024	+	0.0770972i	$0.975435\pi$
$822$	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	$-0.738799\pi$
$827$	−32429.5			−1.36358			−0.681791	+	0.731547i	$0.738799\pi$
$828$	−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	$-0.780698\pi$
$839$	−37517.9			−1.54382			−0.771908	+	0.635734i	$0.780698\pi$
$840$	−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
$855$	−10703.8	−	3230.19i	−0.428143	−	0.129205i
$856$	−14267.9			−0.569703
$857$	8395.19			0.334626			0.167313	−	0.985904i	$-0.446491\pi$
$857$	8395.19			0.334626			0.167313	+	0.985904i	$0.446491\pi$
$858$	−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	$-0.432738\pi$
$863$	10634.8			0.419480			0.209740	+	0.977757i	$0.432738\pi$
$864$	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	$-0.912606\pi$
$881$		−	14179.4i		−	0.542242i	0.962545	−	0.271121i	$-0.0873943\pi$
$882$	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	$-0.340058\pi$
$887$	25444.7			0.963188			0.481594	+	0.876394i	$0.340058\pi$
$888$	−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	$-0.257073\pi$
$911$	38012.4			1.38244			0.691222	+	0.722642i	$0.257073\pi$
$912$	6793.38	+	1122.24i	0.246657	+	0.0407468i
$913$	−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	$-0.971411\pi$
$929$		−	5079.53i		−	0.179391i	0.995969	−	0.0896953i	$-0.0285893\pi$
$930$	−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	$-0.348048\pi$
$941$	26524.6			0.918891			0.459446	+	0.888206i	$0.348048\pi$
$942$	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	$0.217830\pi$
$947$			36845.1i			1.26432i	−0.774840	+	0.632158i	$0.782170\pi$
$948$	−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	$-0.528541\pi$
$953$	−5268.81			−0.179091			−0.0895453	+	0.995983i	$0.528541\pi$
$954$	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
$969$	7647.43	−	46293.1i	0.253530	−	1.53472i
$970$	−301.358			−0.00997530
$971$	−32583.5			−1.07688			−0.538441	−	0.842663i	$-0.680987\pi$
$971$	−32583.5			−1.07688			−0.538441	+	0.842663i	$0.680987\pi$
$972$	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	$-0.510283\pi$
$977$	−1972.73			−0.0645990			−0.0322995	+	0.999478i	$0.510283\pi$
$978$	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	$-0.744998\pi$
$983$	−42895.6			−1.39182			−0.695908	+	0.718131i	$0.744998\pi$
$984$	−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.a.341.21	✓	40
3.2	odd	2		570.4.f.b.341.19	yes	40
19.18	odd	2		570.4.f.b.341.20	yes	40
57.56	even	2	inner	570.4.f.a.341.22	yes	40

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

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} +(424.586 + 70.1399i) 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	\( 40 q - 80 q^{2} - 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} - 320 q^{8} + 10 q^{9} - 40 q^{12} + 40 q^{14} + 640 q^{16} - 20 q^{18} + 68 q^{19} + 78 q^{21} + 80 q^{24} - 1000 q^{25} - 292 q^{27} - 80 q^{28} + 60 q^{29} - 1280 q^{32} - 440 q^{33} + 40 q^{36} - 136 q^{38} - 634 q^{39} - 888 q^{41} - 156 q^{42} + 488 q^{43} + 160 q^{45} - 160 q^{48} + 924 q^{49} + 2000 q^{50} - 2098 q^{51} + 108 q^{53} + 584 q^{54} + 160 q^{56} + 114 q^{57} - 120 q^{58} - 132 q^{59} - 1496 q^{61} + 762 q^{63} + 2560 q^{64} - 120 q^{65} + 880 q^{66} + 1222 q^{69} + 1128 q^{71} - 80 q^{72} - 316 q^{73} + 250 q^{75} + 272 q^{76} + 1268 q^{78} - 942 q^{81} + 1776 q^{82} + 312 q^{84} - 976 q^{86} + 1830 q^{87} - 1776 q^{89} - 320 q^{90} - 1568 q^{93} + 660 q^{95} + 320 q^{96} - 1848 q^{98} - 4016 q^{99}+O(q^{100}) \) 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 + 114 * 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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